Processing math: 71%

import fractions
from fractions import Fraction as Q
import matplotlib as mpl
import matplotlib.pyplot as plt

Simplex with dictionaries

Using rational numbers and relatively nice output

No Phase I implemented, assuming a (primally or dually) feasible initial basis.

def raw_num(q):
    result = ''
    if q.denominator == 1:
        return str(q.numerator)
    if q.numerator < 0:
        result += '-'
        result += r'\frac{' + str(-q.numerator) + "}{" + str(q.denominator) + "}"
    else:
        result += r'\frac{' + str(q.numerator) + "}{" + str(q.denominator) + "}"
    return result


def op_and_num(q, varname):
    if q == 0:
        return "&{}&{}"
    result = '&{}' + ("-{}&" if q < 0 else "+{}&")
    qq = (q if q >= 0 else -q)
    if qq.denominator == 1:
        return result + str(qq.numerator) + " " + varname
    else:
        return result + r'\frac{' + str(qq.numerator) + '}{' + str(qq.denominator) + "} " + varname
    

class SimplexDictionary:
    def varname(self, index):
        if index < self.num_original_vars:
            return f"x_{{{index + 1}}}"
        if index < self.num_original_vars + self.num_original_constrs:
            return f"w_{{{index - self.num_original_vars + 1}}}"
        return f"g_{{{index - self.num_original_vars - self.num_original_constrs + 1}}}"
    
    def __init__(self, A, b, c):
        self.num_rows = len(A)
        self.num_cols = len(c)
        self.num_original_vars = len(c)
        self.num_original_constrs = len(A)
        self.original_A = A
        self.original_b = b
        self.original_c = c
        self.original_cut_defs = {}
        self.nonbasic = list(range(self.num_original_vars))
        self.basic = list(range(self.num_original_vars, self.num_original_vars + self.num_original_constrs))
        self.bas_obj_val = Q(0,1)
        self.bas_vals = [Q(b[i]) for i in range(len(A))]
        self.obj_coeffs = [Q(c[i]) for i in range(len(c))]
        self.coeffs = [[Q(-A[row][col]) for col in range(len(c))] for row in range(len(A))]
        
    def is_primal_feasible(self):
        return all(x >= 0 for x in self.bas_vals)
    
    def is_dual_feasible(self):
        return all(x <= 0 for x in self.obj_coeffs)
    
    def add_cut(self, a, b):
        varidx = self.num_rows + self.num_cols
        self.basic.append(varidx)
        self.original_cut_defs[varidx] = ([(a[i], self.nonbasic[i]) for i in range(self.num_cols)],b)
        self.num_rows += 1
        self.bas_vals.append(b)
        self.coeffs.append([Q(-x) for x in a])
    
    def _pivot_row(self, entering_nb_index, leaving_b_index):
        div = -self.coeffs[leaving_b_index][entering_nb_index]
        self.bas_vals[leaving_b_index] /= div
        self.coeffs[leaving_b_index][entering_nb_index] = Q(-1)
        for i in range(self.num_cols):
            self.coeffs[leaving_b_index][i] /= div
            
    def _pivot_objective(self, entering_nb_index, leaving_b_index):
        fac = self.obj_coeffs[entering_nb_index]
        constant_term = self.bas_vals[leaving_b_index]
        self.bas_obj_val += fac * constant_term
        for i in range(self.num_cols):
            if i != entering_nb_index:
                self.obj_coeffs[i] += fac * self.coeffs[leaving_b_index][i]
            else:
                self.obj_coeffs[i] = fac * self.coeffs[leaving_b_index][entering_nb_index]
    
    def _pivot_other_row(self, row_index, entering_nb_index, leaving_b_index):
        row = self.coeffs[row_index]
        fac = row[entering_nb_index]
        if fac == 0: return
        constant_term = self.bas_vals[leaving_b_index]
        self.bas_vals[row_index] += fac * constant_term
        for i in range(self.num_cols):
            if i != entering_nb_index:
                row[i] += fac * self.coeffs[leaving_b_index][i]
            else:
                row[i] = fac * self.coeffs[leaving_b_index][entering_nb_index]
    
    def pivot(self, entering_nb_index, leaving_b_index):
        # relabel variables
        entering_var = self.nonbasic[entering_nb_index]
        leaving_var = self.basic[leaving_b_index]
        self.nonbasic[entering_nb_index] = leaving_var
        self.basic[leaving_b_index] = entering_var
        
        # rearrange the pivot row
        self._pivot_row(entering_nb_index, leaving_b_index)
        
        # deal with the objective row
        self._pivot_objective(entering_nb_index, leaving_b_index)
        
        # deal with the other rows
        for i in range(self.num_rows):
            if i != leaving_b_index:
                self._pivot_other_row(i, entering_nb_index, leaving_b_index)
    
    def _largest_coefficient_rule(self):
        argmax = max(range(self.num_cols), key=lambda i: self.obj_coeffs[i])
        if self.obj_coeffs[argmax] <= 0:
            raise RuntimeError("Largest coefficient rule with dual feasible dictionary!")
        return argmax
    
    def _largest_infeasibility_rule(self):
        argmin = min(range(self.num_rows), key=lambda i: self.bas_vals[i])
        if self.bas_vals[argmin] >= 0:
            raise RuntimeError("Largest infeasibility rule with primal feasible dictionary!")
        return argmin
    
    def _identify_leaving(self, entering_nb_index):
        leaving = None
        step_length = None
        for row in range(self.num_rows):
            c = self.coeffs[row][entering_nb_index]
            if c < 0:
                this_step_length = self.bas_vals[row] / -c
                if leaving is None or this_step_length < step_length:
                    leaving = row
                    step_length = this_step_length
        return leaving

    def _identify_entering(self, leaving_b_index):
        entering = None
        step_length = None
        for col in range(self.num_cols):
            c = self.coeffs[leaving_b_index][col]
            if c > 0:
                this_step_length = -self.obj_coeffs[col] / c
                if entering is None or this_step_length < step_length:
                    entering = col
                    step_length = this_step_length
        return entering
    
    def primal_simplex_step(self, entering_rule="largest_coefficient"):
        if not self.is_primal_feasible():
            raise RuntimeError("Primal simplex steps require primal feasibility!")
        if self.is_dual_feasible():
            return 'optimal'
        entering_rules = {"largest_coefficient": self._largest_coefficient_rule}
        entering_nb_index = entering_rules[entering_rule]()
        leaving_b_index = self._identify_leaving(entering_nb_index)
        if leaving_b_index is None:
            return 'unbounded'
        self.pivot(entering_nb_index, leaving_b_index)
        return 'feasible' if not self.is_dual_feasible() else 'optimal'
    
    def dual_simplex_step(self, leaving_rule="largest_infeasibility"):
        if not self.is_dual_feasible():
            raise RuntimeError("Dual simplex steps require dual feasibility!")
        if self.is_primal_feasible():
            return 'optimal'
        leaving_rules = {"largest_infeasibility": self._largest_infeasibility_rule}
        leaving_b_index = leaving_rules[leaving_rule]()
        entering_nb_index = self._identify_entering(leaving_b_index)
        if entering_nb_index is None:
            return 'infeasible'
        self.pivot(entering_nb_index, leaving_b_index)
        return 'dual_feasible' if not self.is_primal_feasible() else 'optimal'

    def display(self, obj_symbol=r"\zeta"):
        # display
        from IPython.display import display, Math
        content = r"\begin{gather*}\begin{aligned}"
        content += obj_symbol + " &{}={}& " + raw_num(self.bas_obj_val)
        for i in range(self.num_cols):
            content += op_and_num(self.obj_coeffs[i], self.varname(self.nonbasic[i]))
        content += r"\\\hline" + "\n"
        for row in range(self.num_rows):
            content += self.varname(self.basic[row]) + "&{}={}&" + raw_num(self.bas_vals[row])
            for col in range(self.num_cols):
                content += op_and_num(self.coeffs[row][col], self.varname(self.nonbasic[col]))
            content += r"\\" + "\n"
        content += r"\end{aligned}\end{gather*}"
        display(Math(content))
        
    def _add_to(self, current_vars, var, val):
        if var not in current_vars:
            current_vars[var] = val
        else:
            current_vars[var] += val

    def to_original_vars(self, a, b):
        """
        Turn a cut (indices in `a` combining the current non-basic variables)
        into the form ax <= b, but using only the original variables.
        """
        highest = lambda cv: max(k for k in cv)
        
        current_b = b
        current_vars = {self.nonbasic[i]: a[i] for i in range(self.num_cols)}

        while highest(current_vars) >= self.num_original_vars:
            eliminate = highest(current_vars)
            value = current_vars[eliminate]
            if value == 0:
                del current_vars[eliminate]
                continue

            if eliminate >= self.num_original_vars + self.num_original_constrs:
                # this is a cut's slack; look up the cut's definition
                a_with_vars, cut_b = self.original_cut_defs[eliminate]
                current_b -= value * cut_b
                for a_i, x_i in a_with_vars:
                    self._add_to(current_vars, x_i, -value * a_i)
                del current_vars[eliminate]
                continue
            
            # this is an original constraint's slack
            constr_idx = eliminate - self.num_original_vars
            current_b -= value * self.original_b[constr_idx]
            for i in range(self.num_original_vars):
                a_i = self.original_A[constr_idx][i]
                if a_i == 0: continue
                self._add_to(current_vars, i, -value * a_i)
            del current_vars[eliminate]
        value_of = lambda i: (Q(0) if i not in current_vars else current_vars[i])
        orig_a = [value_of(i) for i in range(self.num_original_vars)]            
        return orig_a, current_b

Primal Simplex Example

A = [[1,2,3], [2,3,4], [5,0,1], [5,5,-1]]
b = [1, 2, 7, 8]
c = [2, 5, -3]

d = SimplexDictionary(A, b, c)
d.display()
d.primal_simplex_step()
d.display()

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& 0&{}+{}&2 x_{1}&{}+{}&5 x_{2}&{}-{}&3 x_{3}\\\hline w_{1}&{}={}&1&{}-{}&1 x_{1}&{}-{}&2 x_{2}&{}-{}&3 x_{3}\\ w_{2}&{}={}&2&{}-{}&2 x_{1}&{}-{}&3 x_{2}&{}-{}&4 x_{3}\\ w_{3}&{}={}&7&{}-{}&5 x_{1}&{}&{}&{}-{}&1 x_{3}\\ w_{4}&{}={}&8&{}-{}&5 x_{1}&{}-{}&5 x_{2}&{}+{}&1 x_{3}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& \frac{5}{2}&{}-{}&\frac{1}{2} x_{1}&{}-{}&\frac{5}{2} w_{1}&{}-{}&\frac{21}{2} x_{3}\\\hline x_{2}&{}={}&\frac{1}{2}&{}-{}&\frac{1}{2} x_{1}&{}-{}&\frac{1}{2} w_{1}&{}-{}&\frac{3}{2} x_{3}\\ w_{2}&{}={}&\frac{1}{2}&{}-{}&\frac{1}{2} x_{1}&{}+{}&\frac{3}{2} w_{1}&{}+{}&\frac{1}{2} x_{3}\\ w_{3}&{}={}&7&{}-{}&5 x_{1}&{}&{}&{}-{}&1 x_{3}\\ w_{4}&{}={}&\frac{11}{2}&{}-{}&\frac{5}{2} x_{1}&{}+{}&\frac{5}{2} w_{1}&{}+{}&\frac{17}{2} x_{3}\\ \end{aligned}\end{gather*}$

Dual Simplex Example

A = [[-2,-1], [-2,4], [-1, 3]]
b = [4, -8, -7]
c = [-1,-1]
d2 = SimplexDictionary(A, b, c)
d2.display()
d2.dual_simplex_step()
d2.display()
d2.dual_simplex_step()
d2.display()

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& 0&{}-{}&1 x_{1}&{}-{}&1 x_{2}\\\hline w_{1}&{}={}&4&{}+{}&2 x_{1}&{}+{}&1 x_{2}\\ w_{2}&{}={}&-8&{}+{}&2 x_{1}&{}-{}&4 x_{2}\\ w_{3}&{}={}&-7&{}+{}&1 x_{1}&{}-{}&3 x_{2}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -4&{}-{}&\frac{1}{2} w_{2}&{}-{}&3 x_{2}\\\hline w_{1}&{}={}&12&{}+{}&1 w_{2}&{}+{}&5 x_{2}\\ x_{1}&{}={}&4&{}+{}&\frac{1}{2} w_{2}&{}+{}&2 x_{2}\\ w_{3}&{}={}&-3&{}+{}&\frac{1}{2} w_{2}&{}-{}&1 x_{2}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -7&{}-{}&1 w_{3}&{}-{}&4 x_{2}\\\hline w_{1}&{}={}&18&{}+{}&2 w_{3}&{}+{}&7 x_{2}\\ x_{1}&{}={}&7&{}+{}&1 w_{3}&{}+{}&3 x_{2}\\ w_{2}&{}={}&6&{}+{}&2 w_{3}&{}+{}&2 x_{2}\\ \end{aligned}\end{gather*}$

Gomory Cut example

Initial solve (primal simplex, 3 iterations)

A = [[10, -2], [4, 10], [-2, 10]]
b = [32, 38, 29]
c = [8, 13]
# additionally, x_1, x_2 (and hence all slacks) should be integer!
dg = SimplexDictionary(A, b, c)
dg.display()
dg.primal_simplex_step()
dg.display()
dg.primal_simplex_step()
dg.display()
dg.primal_simplex_step()
dg.display()

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& 0&{}+{}&8 x_{1}&{}+{}&13 x_{2}\\\hline w_{1}&{}={}&32&{}-{}&10 x_{1}&{}+{}&2 x_{2}\\ w_{2}&{}={}&38&{}-{}&4 x_{1}&{}-{}&10 x_{2}\\ w_{3}&{}={}&29&{}+{}&2 x_{1}&{}-{}&10 x_{2}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& \frac{377}{10}&{}+{}&\frac{53}{5} x_{1}&{}-{}&\frac{13}{10} w_{3}\\\hline w_{1}&{}={}&\frac{189}{5}&{}-{}&\frac{48}{5} x_{1}&{}-{}&\frac{1}{5} w_{3}\\ w_{2}&{}={}&9&{}-{}&6 x_{1}&{}+{}&1 w_{3}\\ x_{2}&{}={}&\frac{29}{10}&{}+{}&\frac{1}{5} x_{1}&{}-{}&\frac{1}{10} w_{3}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& \frac{268}{5}&{}-{}&\frac{53}{30} w_{2}&{}+{}&\frac{7}{15} w_{3}\\\hline w_{1}&{}={}&\frac{117}{5}&{}+{}&\frac{8}{5} w_{2}&{}-{}&\frac{9}{5} w_{3}\\ x_{1}&{}={}&\frac{3}{2}&{}-{}&\frac{1}{6} w_{2}&{}+{}&\frac{1}{6} w_{3}\\ x_{2}&{}={}&\frac{16}{5}&{}-{}&\frac{1}{30} w_{2}&{}-{}&\frac{1}{15} w_{3}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& \frac{179}{3}&{}-{}&\frac{73}{54} w_{2}&{}-{}&\frac{7}{27} w_{1}\\\hline w_{3}&{}={}&13&{}+{}&\frac{8}{9} w_{2}&{}-{}&\frac{5}{9} w_{1}\\ x_{1}&{}={}&\frac{11}{3}&{}-{}&\frac{1}{54} w_{2}&{}-{}&\frac{5}{54} w_{1}\\ x_{2}&{}={}&\frac{7}{3}&{}-{}&\frac{5}{54} w_{2}&{}+{}&\frac{1}{27} w_{1}\\ \end{aligned}\end{gather*}$

def is_feasible_for_row(a, b, x, y):
    return a[0] * x + a[1] * y <= b

def is_feasible_point(A, b, x, y):
    return all(is_feasible_for_row(A[r], b[r], x, y) for r in range(len(A)))

def feasible_points(A, b, r1, r2):
    xs = []
    ys = []
    for x in range(r1[0], r1[1] + 1):
        for y in range(r2[0], r2[1] + 1):
            if is_feasible_point(A, b, x, y):
                xs.append(x)
                ys.append(y)
    return xs, ys

def row_to_line(a, b, **kwargs):
    if a[0] == 0:
        p1 = (0, float(b / a[1]))
        p2 = (1, float(b / a[1]))
    elif a[1] == 0:
        p1 = (float(b / a[0]), 0)
        p2 = (float(b / a[0]), 1)
    else:
        p1 = (0, float(b / a[1]))
        p2 = (float(b / a[0]), 0)
    plt.axline(p1, p2, **kwargs)

def plot_2d_integer_system(A, b, r1, r2, cuts=None):
    xs, ys = feasible_points(A, b, r1, r2)
    plt.scatter(xs, ys)
    row_to_line([-1, 0], 0)
    row_to_line([0, -1], 0)
    for r in range(len(A)):
        row_to_line(A[r], b[r])
    if cuts is not None:
        for cut in cuts:
            row_to_line(*cut, color="orange")

plot_2d_integer_system(A, b, (0,20), (0,20))
fig, ax = plt.gcf(), plt.gca()
fig.set_size_inches(5,5)
ax.set_xlim(-0.1,5)
ax.set_ylim(-0.1,5)

(-0.1, 5.0)

Introducing First Gomory Cut

def round_down(q: Q):
    if q.denominator == 1:
        return int(q.numerator)
    if q < 0:
        return int(q) - 1
    else:
        return int(q)

def most_nonintegral(dictionary: SimplexDictionary):
    compute_nonintegrality = lambda q: min(q - round_down(q), round_down(q) + 1 - q)
    nonintegrality_by_index = lambda i: compute_nonintegrality(dictionary.bas_vals[i])
    argmax = max(range(dictionary.num_rows), key=nonintegrality_by_index)
    if nonintegrality_by_index(argmax) == 0:
        return None
    return argmax

def compute_gomory_cut(dictionary: SimplexDictionary, basic_index=None):
    # if no index is given, we take the most non-integral (farthest from integrality)
    if basic_index is None:
        basic_index = most_nonintegral(dictionary)
        if basic_index is None:
            return 'integral'
        
    num_cols = dictionary.num_cols

    # now, the index should definitely point to a variable with non-integral basic value
    current_value = dictionary.bas_vals[basic_index]
    if int(current_value) == current_value:
        raise ValueError("The current solution value of the given index is already integral!")
    
    # compute the cut: rounding to get preliminary a and b (still have to add definition of basic var)
    b = round_down(current_value)
    a = [round_down(-dictionary.coeffs[basic_index][col]) for col in range(num_cols)]
    # add the definition of the basic variable
    b -= current_value  # means subtracting from RHS
    for col in range(num_cols):
        a[col] += dictionary.coeffs[basic_index][col]
    # a^Tx <= b is a Gomory cutting plane
    return (a,b)

def display_cut(dictionary, a, b, var_names=None):
    # display
    from IPython.display import display, Math
    content = ''
    for i in range(len(a)):
        if a[i] == 0: continue
        if content != '':
            content += ' + '
        if var_names is None:
            var = dictionary.nonbasic[i]
            varname = dictionary.varname(var)
        else:
            varname = var_names[i]
        content += raw_num(a[i])
        content += varname
    content += r' \leq '
    content += raw_num(b)
    display(Math(content))

a1,b1 = compute_gomory_cut(dg, 1)
display_cut(dg, a1, b1)

$\displaystyle -\frac{1}{54}w_{2} + -\frac{5}{54}w_{1} \leq -\frac{2}{3}$

orig_cuts = [dg.to_original_vars(a1, b1)]
display_cut(dg, *orig_cuts[0], var_names=["x_1", "x_2"])

$\displaystyle 1x_1 \leq 3$

plot_2d_integer_system(A, b, (0,20), (0,20), cuts=orig_cuts)
fig, ax = plt.gcf(), plt.gca()
fig.set_size_inches(5,5)
ax.set_xlim(-0.1,5)
ax.set_ylim(-0.1,5)

(-0.1, 5.0)

dg.add_cut(a1,b1)
dg.display()

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& \frac{179}{3}&{}-{}&\frac{73}{54} w_{2}&{}-{}&\frac{7}{27} w_{1}\\\hline w_{3}&{}={}&13&{}+{}&\frac{8}{9} w_{2}&{}-{}&\frac{5}{9} w_{1}\\ x_{1}&{}={}&\frac{11}{3}&{}-{}&\frac{1}{54} w_{2}&{}-{}&\frac{5}{54} w_{1}\\ x_{2}&{}={}&\frac{7}{3}&{}-{}&\frac{5}{54} w_{2}&{}+{}&\frac{1}{27} w_{1}\\ g_{1}&{}={}&-\frac{2}{3}&{}+{}&\frac{1}{54} w_{2}&{}+{}&\frac{5}{54} w_{1}\\ \end{aligned}\end{gather*}$

dg.is_primal_feasible(), dg.is_dual_feasible()

(False, True)

dg.dual_simplex_step()
dg.display()

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& \frac{289}{5}&{}-{}&\frac{13}{10} w_{2}&{}-{}&\frac{14}{5} g_{1}\\\hline w_{3}&{}={}&9&{}+{}&1 w_{2}&{}-{}&6 g_{1}\\ x_{1}&{}={}&3&{}&{}&{}-{}&1 g_{1}\\ x_{2}&{}={}&\frac{13}{5}&{}-{}&\frac{1}{10} w_{2}&{}+{}&\frac{2}{5} g_{1}\\ w_{1}&{}={}&\frac{36}{5}&{}-{}&\frac{1}{5} w_{2}&{}+{}&\frac{54}{5} g_{1}\\ \end{aligned}\end{gather*}$

a2,b2 = compute_gomory_cut(dg, 2)
display_cut(dg, a2, b2)
orig_a,orig_b = dg.to_original_vars(a2,b2)
orig_cuts.append((orig_a,orig_b))
display_cut(dg, orig_a, orig_b, var_names=["x_1","x_2"])

$\displaystyle -\frac{1}{10}w_{2} + -\frac{3}{5}g_{1} \leq -\frac{3}{5}$

$\displaystyle 1x_1 + 1x_2 \leq 5$

plot_2d_integer_system(A, b, (0,20), (0,20), cuts=orig_cuts)
fig, ax = plt.gcf(), plt.gca()
fig.set_size_inches(5,5)
ax.set_xlim(-0.1,5)
ax.set_ylim(-0.1,5)

(-0.1, 5.0)

dg.add_cut(a2,b2)
dg.display()
dg.dual_simplex_step()
dg.display()

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& \frac{289}{5}&{}-{}&\frac{13}{10} w_{2}&{}-{}&\frac{14}{5} g_{1}\\\hline w_{3}&{}={}&9&{}+{}&1 w_{2}&{}-{}&6 g_{1}\\ x_{1}&{}={}&3&{}&{}&{}-{}&1 g_{1}\\ x_{2}&{}={}&\frac{13}{5}&{}-{}&\frac{1}{10} w_{2}&{}+{}&\frac{2}{5} g_{1}\\ w_{1}&{}={}&\frac{36}{5}&{}-{}&\frac{1}{5} w_{2}&{}+{}&\frac{54}{5} g_{1}\\ g_{2}&{}={}&-\frac{3}{5}&{}+{}&\frac{1}{10} w_{2}&{}+{}&\frac{3}{5} g_{1}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& 55&{}-{}&\frac{5}{6} w_{2}&{}-{}&\frac{14}{3} g_{2}\\\hline w_{3}&{}={}&3&{}+{}&2 w_{2}&{}-{}&10 g_{2}\\ x_{1}&{}={}&2&{}+{}&\frac{1}{6} w_{2}&{}-{}&\frac{5}{3} g_{2}\\ x_{2}&{}={}&3&{}-{}&\frac{1}{6} w_{2}&{}+{}&\frac{2}{3} g_{2}\\ w_{1}&{}={}&18&{}-{}&2 w_{2}&{}+{}&18 g_{2}\\ g_{1}&{}={}&1&{}-{}&\frac{1}{6} w_{2}&{}+{}&\frac{5}{3} g_{2}\\ \end{aligned}\end{gather*}$

compute_gomory_cut(dg)

'integral'

Example with very bad Gomory cuts

Abug = [[-2,-3], [-4, -2], [-3, -4], [1, 0], [0,1]]
bbug = [-5, -15, -20, 9, 6]
cbug = [-20, -15]
dbug = SimplexDictionary(Abug, bbug, cbug)
dbug.display()

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& 0&{}-{}&20 x_{1}&{}-{}&15 x_{2}\\\hline w_{1}&{}={}&-5&{}+{}&2 x_{1}&{}+{}&3 x_{2}\\ w_{2}&{}={}&-15&{}+{}&4 x_{1}&{}+{}&2 x_{2}\\ w_{3}&{}={}&-20&{}+{}&3 x_{1}&{}+{}&4 x_{2}\\ w_{4}&{}={}&9&{}-{}&1 x_{1}&{}&{}\\ w_{5}&{}={}&6&{}&{}&{}-{}&1 x_{2}\\ \end{aligned}\end{gather*}$

while not dbug.is_primal_feasible():
    dbug.dual_simplex_step()
    dbug.display()
dbug.is_primal_feasible()

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -75&{}-{}&\frac{35}{4} x_{1}&{}-{}&\frac{15}{4} w_{3}\\\hline w_{1}&{}={}&10&{}-{}&\frac{1}{4} x_{1}&{}+{}&\frac{3}{4} w_{3}\\ w_{2}&{}={}&-5&{}+{}&\frac{5}{2} x_{1}&{}+{}&\frac{1}{2} w_{3}\\ x_{2}&{}={}&5&{}-{}&\frac{3}{4} x_{1}&{}+{}&\frac{1}{4} w_{3}\\ w_{4}&{}={}&9&{}-{}&1 x_{1}&{}&{}\\ w_{5}&{}={}&1&{}+{}&\frac{3}{4} x_{1}&{}-{}&\frac{1}{4} w_{3}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{185}{2}&{}-{}&\frac{7}{2} w_{2}&{}-{}&2 w_{3}\\\hline w_{1}&{}={}&\frac{19}{2}&{}-{}&\frac{1}{10} w_{2}&{}+{}&\frac{4}{5} w_{3}\\ x_{1}&{}={}&2&{}+{}&\frac{2}{5} w_{2}&{}-{}&\frac{1}{5} w_{3}\\ x_{2}&{}={}&\frac{7}{2}&{}-{}&\frac{3}{10} w_{2}&{}+{}&\frac{2}{5} w_{3}\\ w_{4}&{}={}&7&{}-{}&\frac{2}{5} w_{2}&{}+{}&\frac{1}{5} w_{3}\\ w_{5}&{}={}&\frac{5}{2}&{}+{}&\frac{3}{10} w_{2}&{}-{}&\frac{2}{5} w_{3}\\ \end{aligned}\end{gather*}$

True

bug_cuts = []
plot_2d_integer_system(Abug, bbug, (0,20), (0,20), cuts=bug_cuts)
fig, ax = plt.gcf(), plt.gca()
fig.set_size_inches(5,5)
ax.set_xlim(-5,10)
ax.set_ylim(-5,10)

(-5.0, 10.0)

cut1 = compute_gomory_cut(dbug, 2)
display_cut(dbug, *cut1)
ocut1 = dbug.to_original_vars(*cut1)
display_cut(dbug, *ocut1, var_names=["x_1", "x_2"])
bug_cuts.append(ocut1)
plot_2d_integer_system(Abug, bbug, (0,20), (0,20), cuts=bug_cuts)
fig, ax = plt.gcf(), plt.gca()
fig.set_size_inches(5,5)
ax.set_xlim(-5,10)
ax.set_ylim(-5,10)

$\displaystyle -\frac{3}{10}w_{2} + -\frac{3}{5}w_{3} \leq -\frac{1}{2}$

$\displaystyle -3x_1 + -3x_2 \leq -17$

(-5.0, 10.0)

dbug.add_cut(*cut1)
dbug.display()
dbug.is_primal_feasible(), dbug.is_dual_feasible()

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{185}{2}&{}-{}&\frac{7}{2} w_{2}&{}-{}&2 w_{3}\\\hline w_{1}&{}={}&\frac{19}{2}&{}-{}&\frac{1}{10} w_{2}&{}+{}&\frac{4}{5} w_{3}\\ x_{1}&{}={}&2&{}+{}&\frac{2}{5} w_{2}&{}-{}&\frac{1}{5} w_{3}\\ x_{2}&{}={}&\frac{7}{2}&{}-{}&\frac{3}{10} w_{2}&{}+{}&\frac{2}{5} w_{3}\\ w_{4}&{}={}&7&{}-{}&\frac{2}{5} w_{2}&{}+{}&\frac{1}{5} w_{3}\\ w_{5}&{}={}&\frac{5}{2}&{}+{}&\frac{3}{10} w_{2}&{}-{}&\frac{2}{5} w_{3}\\ g_{1}&{}={}&-\frac{1}{2}&{}+{}&\frac{3}{10} w_{2}&{}+{}&\frac{3}{5} w_{3}\\ \end{aligned}\end{gather*}$

(False, True)

while not dbug.is_primal_feasible():
    dbug.dual_simplex_step()
    dbug.display()
dbug.is_primal_feasible()

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{565}{6}&{}-{}&\frac{5}{2} w_{2}&{}-{}&\frac{10}{3} g_{1}\\\hline w_{1}&{}={}&\frac{61}{6}&{}-{}&\frac{1}{2} w_{2}&{}+{}&\frac{4}{3} g_{1}\\ x_{1}&{}={}&\frac{11}{6}&{}+{}&\frac{1}{2} w_{2}&{}-{}&\frac{1}{3} g_{1}\\ x_{2}&{}={}&\frac{23}{6}&{}-{}&\frac{1}{2} w_{2}&{}+{}&\frac{2}{3} g_{1}\\ w_{4}&{}={}&\frac{43}{6}&{}-{}&\frac{1}{2} w_{2}&{}+{}&\frac{1}{3} g_{1}\\ w_{5}&{}={}&\frac{13}{6}&{}+{}&\frac{1}{2} w_{2}&{}-{}&\frac{2}{3} g_{1}\\ w_{3}&{}={}&\frac{5}{6}&{}-{}&\frac{1}{2} w_{2}&{}+{}&\frac{5}{3} g_{1}\\ \end{aligned}\end{gather*}$

True

cut = compute_gomory_cut(dbug)
count = 0
while cut != 'integral' and count < 50:
    count += 1
    ocut = dbug.to_original_vars(*cut)
    bug_cuts.append(ocut)
    dbug.add_cut(*cut)
    while not dbug.is_primal_feasible():
        if dbug.dual_simplex_step() == 'infeasible':
            raise RuntimeError("INFEASIBLE")
    dbug.display()
    plot_2d_integer_system(Abug, bbug, (0,20), (0,20), cuts=bug_cuts)
    plt.show()
    plt.clf()

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -95&{}-{}&5 g_{2}&{}&{}\\\hline w_{1}&{}={}&10&{}-{}&1 g_{2}&{}+{}&2 g_{1}\\ x_{1}&{}={}&2&{}+{}&1 g_{2}&{}-{}&1 g_{1}\\ x_{2}&{}={}&\frac{11}{3}&{}-{}&1 g_{2}&{}+{}&\frac{4}{3} g_{1}\\ w_{4}&{}={}&7&{}-{}&1 g_{2}&{}+{}&1 g_{1}\\ w_{5}&{}={}&\frac{7}{3}&{}+{}&1 g_{2}&{}-{}&\frac{4}{3} g_{1}\\ w_{3}&{}={}&\frac{2}{3}&{}-{}&1 g_{2}&{}+{}&\frac{7}{3} g_{1}\\ w_{2}&{}={}&\frac{1}{3}&{}+{}&2 g_{2}&{}-{}&\frac{4}{3} g_{1}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -95&{}-{}&5 g_{2}&{}&{}\\\hline w_{1}&{}={}&\frac{21}{2}&{}-{}&\frac{5}{2} g_{2}&{}+{}&3 g_{3}\\ x_{1}&{}={}&\frac{7}{4}&{}+{}&\frac{7}{4} g_{2}&{}-{}&\frac{3}{2} g_{3}\\ x_{2}&{}={}&4&{}-{}&2 g_{2}&{}+{}&2 g_{3}\\ w_{4}&{}={}&\frac{29}{4}&{}-{}&\frac{7}{4} g_{2}&{}+{}&\frac{3}{2} g_{3}\\ w_{5}&{}={}&2&{}+{}&2 g_{2}&{}-{}&2 g_{3}\\ w_{3}&{}={}&\frac{5}{4}&{}-{}&\frac{11}{4} g_{2}&{}+{}&\frac{7}{2} g_{3}\\ w_{2}&{}={}&0&{}+{}&3 g_{2}&{}-{}&2 g_{3}\\ g_{1}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{2}&{}+{}&\frac{3}{2} g_{3}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{860}{9}&{}-{}&\frac{10}{9} w_{2}&{}-{}&\frac{10}{3} g_{4}\\\hline w_{1}&{}={}&\frac{193}{18}&{}-{}&\frac{19}{18} w_{2}&{}+{}&\frac{4}{3} g_{4}\\ x_{1}&{}={}&\frac{61}{36}&{}+{}&\frac{23}{36} w_{2}&{}-{}&\frac{1}{3} g_{4}\\ x_{2}&{}={}&\frac{37}{9}&{}-{}&\frac{7}{9} w_{2}&{}+{}&\frac{2}{3} g_{4}\\ w_{4}&{}={}&\frac{263}{36}&{}-{}&\frac{23}{36} w_{2}&{}+{}&\frac{1}{3} g_{4}\\ w_{5}&{}={}&\frac{17}{9}&{}+{}&\frac{7}{9} w_{2}&{}-{}&\frac{2}{3} g_{4}\\ w_{3}&{}={}&\frac{55}{36}&{}-{}&\frac{43}{36} w_{2}&{}+{}&\frac{5}{3} g_{4}\\ g_{2}&{}={}&\frac{1}{9}&{}+{}&\frac{2}{9} w_{2}&{}+{}&\frac{2}{3} g_{4}\\ g_{1}&{}={}&\frac{5}{12}&{}-{}&\frac{5}{12} w_{2}&{}+{}&1 g_{4}\\ g_{3}&{}={}&\frac{1}{6}&{}-{}&\frac{1}{6} w_{2}&{}+{}&1 g_{4}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{2590}{27}&{}-{}&\frac{20}{9} g_{5}&{}-{}&\frac{50}{27} g_{4}\\\hline w_{1}&{}={}&\frac{280}{27}&{}-{}&\frac{19}{9} g_{5}&{}+{}&\frac{74}{27} g_{4}\\ x_{1}&{}={}&\frac{103}{54}&{}+{}&\frac{23}{18} g_{5}&{}-{}&\frac{32}{27} g_{4}\\ x_{2}&{}={}&\frac{104}{27}&{}-{}&\frac{14}{9} g_{5}&{}+{}&\frac{46}{27} g_{4}\\ w_{4}&{}={}&\frac{383}{54}&{}-{}&\frac{23}{18} g_{5}&{}+{}&\frac{32}{27} g_{4}\\ w_{5}&{}={}&\frac{58}{27}&{}+{}&\frac{14}{9} g_{5}&{}-{}&\frac{46}{27} g_{4}\\ w_{3}&{}={}&\frac{61}{54}&{}-{}&\frac{43}{18} g_{5}&{}+{}&\frac{88}{27} g_{4}\\ g_{2}&{}={}&\frac{5}{27}&{}+{}&\frac{4}{9} g_{5}&{}+{}&\frac{10}{27} g_{4}\\ g_{1}&{}={}&\frac{5}{18}&{}-{}&\frac{5}{6} g_{5}&{}+{}&\frac{14}{9} g_{4}\\ g_{3}&{}={}&\frac{1}{9}&{}-{}&\frac{1}{3} g_{5}&{}+{}&\frac{11}{9} g_{4}\\ w_{2}&{}={}&\frac{1}{3}&{}+{}&2 g_{5}&{}-{}&\frac{4}{3} g_{4}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{1735}{18}&{}-{}&\frac{5}{6} g_{5}&{}-{}&\frac{25}{9} g_{6}\\\hline w_{1}&{}={}&\frac{199}{18}&{}-{}&\frac{25}{6} g_{5}&{}+{}&\frac{37}{9} g_{6}\\ x_{1}&{}={}&\frac{29}{18}&{}+{}&\frac{13}{6} g_{5}&{}-{}&\frac{16}{9} g_{6}\\ x_{2}&{}={}&\frac{77}{18}&{}-{}&\frac{17}{6} g_{5}&{}+{}&\frac{23}{9} g_{6}\\ w_{4}&{}={}&\frac{133}{18}&{}-{}&\frac{13}{6} g_{5}&{}+{}&\frac{16}{9} g_{6}\\ w_{5}&{}={}&\frac{31}{18}&{}+{}&\frac{17}{6} g_{5}&{}-{}&\frac{23}{9} g_{6}\\ w_{3}&{}={}&\frac{35}{18}&{}-{}&\frac{29}{6} g_{5}&{}+{}&\frac{44}{9} g_{6}\\ g_{2}&{}={}&\frac{5}{18}&{}+{}&\frac{1}{6} g_{5}&{}+{}&\frac{5}{9} g_{6}\\ g_{1}&{}={}&\frac{2}{3}&{}-{}&2 g_{5}&{}+{}&\frac{7}{3} g_{6}\\ g_{3}&{}={}&\frac{5}{12}&{}-{}&\frac{5}{4} g_{5}&{}+{}&\frac{11}{6} g_{6}\\ w_{2}&{}={}&0&{}+{}&3 g_{5}&{}-{}&2 g_{6}\\ g_{4}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{5}&{}+{}&\frac{3}{2} g_{6}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{290}{3}&{}-{}&\frac{5}{3} g_{7}&{}-{}&\frac{5}{3} g_{6}\\\hline w_{1}&{}={}&\frac{29}{3}&{}-{}&\frac{25}{3} g_{7}&{}+{}&\frac{29}{3} g_{6}\\ x_{1}&{}={}&\frac{7}{3}&{}+{}&\frac{13}{3} g_{7}&{}-{}&\frac{14}{3} g_{6}\\ x_{2}&{}={}&\frac{10}{3}&{}-{}&\frac{17}{3} g_{7}&{}+{}&\frac{19}{3} g_{6}\\ w_{4}&{}={}&\frac{20}{3}&{}-{}&\frac{13}{3} g_{7}&{}+{}&\frac{14}{3} g_{6}\\ w_{5}&{}={}&\frac{8}{3}&{}+{}&\frac{17}{3} g_{7}&{}-{}&\frac{19}{3} g_{6}\\ w_{3}&{}={}&\frac{1}{3}&{}-{}&\frac{29}{3} g_{7}&{}+{}&\frac{34}{3} g_{6}\\ g_{2}&{}={}&\frac{1}{3}&{}+{}&\frac{1}{3} g_{7}&{}+{}&\frac{1}{3} g_{6}\\ g_{1}&{}={}&0&{}-{}&4 g_{7}&{}+{}&5 g_{6}\\ g_{3}&{}={}&0&{}-{}&\frac{5}{2} g_{7}&{}+{}&\frac{7}{2} g_{6}\\ w_{2}&{}={}&1&{}+{}&6 g_{7}&{}-{}&6 g_{6}\\ g_{4}&{}={}&0&{}-{}&\frac{3}{2} g_{7}&{}+{}&\frac{5}{2} g_{6}\\ g_{5}&{}={}&\frac{1}{3}&{}+{}&2 g_{7}&{}-{}&\frac{4}{3} g_{6}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{12235}{126}&{}-{}&\frac{5}{126} w_{2}&{}-{}&\frac{20}{7} g_{8}\\\hline w_{1}&{}={}&\frac{1429}{126}&{}-{}&\frac{187}{126} w_{2}&{}+{}&\frac{8}{7} g_{8}\\ x_{1}&{}={}&\frac{97}{63}&{}+{}&\frac{47}{63} w_{2}&{}-{}&\frac{2}{7} g_{8}\\ x_{2}&{}={}&\frac{557}{126}&{}-{}&\frac{125}{126} w_{2}&{}+{}&\frac{4}{7} g_{8}\\ w_{4}&{}={}&\frac{470}{63}&{}-{}&\frac{47}{63} w_{2}&{}+{}&\frac{2}{7} g_{8}\\ w_{5}&{}={}&\frac{199}{126}&{}+{}&\frac{125}{126} w_{2}&{}-{}&\frac{4}{7} g_{8}\\ w_{3}&{}={}&\frac{145}{63}&{}-{}&\frac{109}{63} w_{2}&{}+{}&\frac{10}{7} g_{8}\\ g_{2}&{}={}&\frac{53}{126}&{}+{}&\frac{1}{126} w_{2}&{}+{}&\frac{4}{7} g_{8}\\ g_{1}&{}={}&\frac{37}{42}&{}-{}&\frac{31}{42} w_{2}&{}+{}&\frac{6}{7} g_{8}\\ g_{3}&{}={}&\frac{53}{84}&{}-{}&\frac{41}{84} w_{2}&{}+{}&\frac{6}{7} g_{8}\\ g_{7}&{}={}&\frac{1}{21}&{}+{}&\frac{2}{21} w_{2}&{}+{}&\frac{6}{7} g_{8}\\ g_{4}&{}={}&\frac{13}{28}&{}-{}&\frac{9}{28} w_{2}&{}+{}&\frac{6}{7} g_{8}\\ g_{5}&{}={}&\frac{1}{7}&{}+{}&\frac{2}{7} w_{2}&{}+{}&\frac{4}{7} g_{8}\\ g_{6}&{}={}&\frac{3}{14}&{}-{}&\frac{1}{14} w_{2}&{}+{}&\frac{6}{7} g_{8}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{18355}{189}&{}-{}&\frac{5}{63} g_{9}&{}-{}&\frac{530}{189} g_{8}\\\hline w_{1}&{}={}&\frac{2050}{189}&{}-{}&\frac{187}{63} g_{9}&{}+{}&\frac{590}{189} g_{8}\\ x_{1}&{}={}&\frac{338}{189}&{}+{}&\frac{94}{63} g_{9}&{}-{}&\frac{242}{189} g_{8}\\ x_{2}&{}={}&\frac{773}{189}&{}-{}&\frac{125}{63} g_{9}&{}+{}&\frac{358}{189} g_{8}\\ w_{4}&{}={}&\frac{1363}{189}&{}-{}&\frac{94}{63} g_{9}&{}+{}&\frac{242}{189} g_{8}\\ w_{5}&{}={}&\frac{361}{189}&{}+{}&\frac{125}{63} g_{9}&{}-{}&\frac{358}{189} g_{8}\\ w_{3}&{}={}&\frac{326}{189}&{}-{}&\frac{218}{63} g_{9}&{}+{}&\frac{706}{189} g_{8}\\ g_{2}&{}={}&\frac{80}{189}&{}+{}&\frac{1}{63} g_{9}&{}+{}&\frac{106}{189} g_{8}\\ g_{1}&{}={}&\frac{40}{63}&{}-{}&\frac{31}{21} g_{9}&{}+{}&\frac{116}{63} g_{8}\\ g_{3}&{}={}&\frac{59}{126}&{}-{}&\frac{41}{42} g_{9}&{}+{}&\frac{95}{63} g_{8}\\ g_{7}&{}={}&\frac{5}{63}&{}+{}&\frac{4}{21} g_{9}&{}+{}&\frac{46}{63} g_{8}\\ g_{4}&{}={}&\frac{5}{14}&{}-{}&\frac{9}{14} g_{9}&{}+{}&\frac{9}{7} g_{8}\\ g_{5}&{}={}&\frac{5}{21}&{}+{}&\frac{4}{7} g_{9}&{}+{}&\frac{4}{21} g_{8}\\ g_{6}&{}={}&\frac{4}{21}&{}-{}&\frac{1}{7} g_{9}&{}+{}&\frac{20}{21} g_{8}\\ w_{2}&{}={}&\frac{1}{3}&{}+{}&2 g_{9}&{}-{}&\frac{4}{3} g_{8}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{680}{7}&{}-{}&\frac{10}{63} g_{10}&{}-{}&\frac{170}{63} g_{8}\\\hline w_{1}&{}={}&\frac{69}{7}&{}-{}&\frac{374}{63} g_{10}&{}+{}&\frac{446}{63} g_{8}\\ x_{1}&{}={}&\frac{16}{7}&{}+{}&\frac{188}{63} g_{10}&{}-{}&\frac{206}{63} g_{8}\\ x_{2}&{}={}&\frac{24}{7}&{}-{}&\frac{250}{63} g_{10}&{}+{}&\frac{286}{63} g_{8}\\ w_{4}&{}={}&\frac{47}{7}&{}-{}&\frac{188}{63} g_{10}&{}+{}&\frac{206}{63} g_{8}\\ w_{5}&{}={}&\frac{18}{7}&{}+{}&\frac{250}{63} g_{10}&{}-{}&\frac{286}{63} g_{8}\\ w_{3}&{}={}&\frac{4}{7}&{}-{}&\frac{436}{63} g_{10}&{}+{}&\frac{526}{63} g_{8}\\ g_{2}&{}={}&\frac{3}{7}&{}+{}&\frac{2}{63} g_{10}&{}+{}&\frac{34}{63} g_{8}\\ g_{1}&{}={}&\frac{1}{7}&{}-{}&\frac{62}{21} g_{10}&{}+{}&\frac{80}{21} g_{8}\\ g_{3}&{}={}&\frac{1}{7}&{}-{}&\frac{41}{21} g_{10}&{}+{}&\frac{59}{21} g_{8}\\ g_{7}&{}={}&\frac{1}{7}&{}+{}&\frac{8}{21} g_{10}&{}+{}&\frac{10}{21} g_{8}\\ g_{4}&{}={}&\frac{1}{7}&{}-{}&\frac{9}{7} g_{10}&{}+{}&\frac{15}{7} g_{8}\\ g_{5}&{}={}&\frac{3}{7}&{}+{}&\frac{8}{7} g_{10}&{}-{}&\frac{4}{7} g_{8}\\ g_{6}&{}={}&\frac{1}{7}&{}-{}&\frac{2}{7} g_{10}&{}+{}&\frac{8}{7} g_{8}\\ w_{2}&{}={}&1&{}+{}&4 g_{10}&{}-{}&4 g_{8}\\ g_{9}&{}={}&\frac{1}{3}&{}+{}&2 g_{10}&{}-{}&\frac{4}{3} g_{8}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{71345}{732}&{}-{}&\frac{135}{61} g_{11}&{}-{}&\frac{235}{732} g_{1}\\\hline w_{1}&{}={}&\frac{6959}{732}&{}-{}&\frac{27}{61} g_{11}&{}+{}&\frac{1417}{732} g_{1}\\ x_{1}&{}={}&\frac{1825}{732}&{}+{}&\frac{27}{61} g_{11}&{}-{}&\frac{685}{732} g_{1}\\ x_{2}&{}={}&\frac{2323}{732}&{}-{}&\frac{27}{61} g_{11}&{}+{}&\frac{929}{732} g_{1}\\ w_{4}&{}={}&\frac{4763}{732}&{}-{}&\frac{27}{61} g_{11}&{}+{}&\frac{685}{732} g_{1}\\ w_{5}&{}={}&\frac{2069}{732}&{}+{}&\frac{27}{61} g_{11}&{}-{}&\frac{929}{732} g_{1}\\ g_{8}&{}={}&\frac{53}{488}&{}+{}&\frac{93}{122} g_{11}&{}+{}&\frac{63}{488} g_{1}\\ g_{2}&{}={}&\frac{361}{732}&{}+{}&\frac{27}{61} g_{11}&{}+{}&\frac{47}{732} g_{1}\\ w_{3}&{}={}&\frac{127}{732}&{}-{}&\frac{27}{61} g_{11}&{}+{}&\frac{1661}{732} g_{1}\\ g_{3}&{}={}&\frac{39}{488}&{}+{}&\frac{27}{122} g_{11}&{}+{}&\frac{341}{488} g_{1}\\ g_{7}&{}={}&\frac{65}{244}&{}+{}&\frac{45}{61} g_{11}&{}-{}&\frac{1}{244} g_{1}\\ g_{4}&{}={}&\frac{65}{488}&{}+{}&\frac{45}{122} g_{11}&{}+{}&\frac{243}{488} g_{1}\\ g_{5}&{}={}&\frac{71}{122}&{}+{}&\frac{42}{61} g_{11}&{}-{}&\frac{33}{122} g_{1}\\ g_{6}&{}={}&\frac{13}{61}&{}+{}&\frac{36}{61} g_{11}&{}+{}&\frac{12}{61} g_{1}\\ w_{2}&{}={}&\frac{161}{122}&{}+{}&\frac{54}{61} g_{11}&{}-{}&\frac{147}{122} g_{1}\\ g_{9}&{}={}&\frac{69}{122}&{}+{}&\frac{58}{61} g_{11}&{}-{}&\frac{63}{122} g_{1}\\ g_{10}&{}={}&\frac{23}{122}&{}+{}&\frac{60}{61} g_{11}&{}-{}&\frac{21}{122} g_{1}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{95205}{976}&{}-{}&\frac{1925}{976} g_{11}&{}-{}&\frac{235}{488} g_{12}\\\hline w_{1}&{}={}&\frac{9751}{976}&{}-{}&\frac{1849}{976} g_{11}&{}+{}&\frac{1417}{488} g_{12}\\ x_{1}&{}={}&\frac{2205}{976}&{}+{}&\frac{1117}{976} g_{11}&{}-{}&\frac{685}{488} g_{12}\\ x_{2}&{}={}&\frac{3407}{976}&{}-{}&\frac{1361}{976} g_{11}&{}+{}&\frac{929}{488} g_{12}\\ w_{4}&{}={}&\frac{6579}{976}&{}-{}&\frac{1117}{976} g_{11}&{}+{}&\frac{685}{488} g_{12}\\ w_{5}&{}={}&\frac{2449}{976}&{}+{}&\frac{1361}{976} g_{11}&{}-{}&\frac{929}{488} g_{12}\\ g_{8}&{}={}&\frac{275}{1952}&{}+{}&\frac{1299}{1952} g_{11}&{}+{}&\frac{189}{976} g_{12}\\ g_{2}&{}={}&\frac{497}{976}&{}+{}&\frac{385}{976} g_{11}&{}+{}&\frac{47}{488} g_{12}\\ w_{3}&{}={}&\frac{723}{976}&{}-{}&\frac{2093}{976} g_{11}&{}+{}&\frac{1661}{488} g_{12}\\ g_{3}&{}={}&\frac{497}{1952}&{}-{}&\frac{591}{1952} g_{11}&{}+{}&\frac{1023}{976} g_{12}\\ g_{7}&{}={}&\frac{259}{976}&{}+{}&\frac{723}{976} g_{11}&{}-{}&\frac{3}{488} g_{12}\\ g_{4}&{}={}&\frac{503}{1952}&{}-{}&\frac{9}{1952} g_{11}&{}+{}&\frac{729}{976} g_{12}\\ g_{5}&{}={}&\frac{251}{488}&{}+{}&\frac{435}{488} g_{11}&{}-{}&\frac{99}{244} g_{12}\\ g_{6}&{}={}&\frac{16}{61}&{}+{}&\frac{27}{61} g_{11}&{}+{}&\frac{18}{61} g_{12}\\ w_{2}&{}={}&\frac{497}{488}&{}+{}&\frac{873}{488} g_{11}&{}-{}&\frac{441}{244} g_{12}\\ g_{9}&{}={}&\frac{213}{488}&{}+{}&\frac{653}{488} g_{11}&{}-{}&\frac{189}{244} g_{12}\\ g_{10}&{}={}&\frac{71}{488}&{}+{}&\frac{543}{488} g_{11}&{}-{}&\frac{63}{244} g_{12}\\ g_{1}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{11}&{}+{}&\frac{3}{2} g_{12}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{190645}{1952}&{}-{}&\frac{3145}{1952} g_{11}&{}-{}&\frac{705}{976} g_{13}\\\hline w_{1}&{}={}&\frac{20919}{1952}&{}-{}&\frac{7949}{1952} g_{11}&{}+{}&\frac{4251}{976} g_{13}\\ x_{1}&{}={}&\frac{3725}{1952}&{}+{}&\frac{4289}{1952} g_{11}&{}-{}&\frac{2055}{976} g_{13}\\ x_{2}&{}={}&\frac{7743}{1952}&{}-{}&\frac{5509}{1952} g_{11}&{}+{}&\frac{2787}{976} g_{13}\\ w_{4}&{}={}&\frac{13843}{1952}&{}-{}&\frac{4289}{1952} g_{11}&{}+{}&\frac{2055}{976} g_{13}\\ w_{5}&{}={}&\frac{3969}{1952}&{}+{}&\frac{5509}{1952} g_{11}&{}-{}&\frac{2787}{976} g_{13}\\ g_{8}&{}={}&\frac{739}{3904}&{}+{}&\frac{2031}{3904} g_{11}&{}+{}&\frac{567}{1952} g_{13}\\ g_{2}&{}={}&\frac{1041}{1952}&{}+{}&\frac{629}{1952} g_{11}&{}+{}&\frac{141}{976} g_{13}\\ w_{3}&{}={}&\frac{3107}{1952}&{}-{}&\frac{9169}{1952} g_{11}&{}+{}&\frac{4983}{976} g_{13}\\ g_{3}&{}={}&\frac{2017}{3904}&{}-{}&\frac{4251}{3904} g_{11}&{}+{}&\frac{3069}{1952} g_{13}\\ g_{7}&{}={}&\frac{515}{1952}&{}+{}&\frac{1455}{1952} g_{11}&{}-{}&\frac{9}{976} g_{13}\\ g_{4}&{}={}&\frac{1735}{3904}&{}-{}&\frac{2205}{3904} g_{11}&{}+{}&\frac{2187}{1952} g_{13}\\ g_{5}&{}={}&\frac{403}{976}&{}+{}&\frac{1167}{976} g_{11}&{}-{}&\frac{297}{488} g_{13}\\ g_{6}&{}={}&\frac{41}{122}&{}+{}&\frac{27}{122} g_{11}&{}+{}&\frac{27}{61} g_{13}\\ w_{2}&{}={}&\frac{553}{976}&{}+{}&\frac{3069}{976} g_{11}&{}-{}&\frac{1323}{488} g_{13}\\ g_{9}&{}={}&\frac{237}{976}&{}+{}&\frac{1873}{976} g_{11}&{}-{}&\frac{567}{488} g_{13}\\ g_{10}&{}={}&\frac{79}{976}&{}+{}&\frac{1275}{976} g_{11}&{}-{}&\frac{189}{488} g_{13}\\ g_{1}&{}={}&\frac{5}{8}&{}-{}&\frac{15}{8} g_{11}&{}+{}&\frac{9}{4} g_{13}\\ g_{12}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{11}&{}+{}&\frac{3}{2} g_{13}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{1978345}{20214}&{}-{}&\frac{4175}{20214} w_{2}&{}-{}&\frac{2160}{1123} g_{14}\\\hline w_{1}&{}={}&\frac{235453}{20214}&{}-{}&\frac{28651}{20214} w_{2}&{}+{}&\frac{864}{1123} g_{14}\\ x_{1}&{}={}&\frac{29573}{20214}&{}+{}&\frac{14743}{20214} w_{2}&{}-{}&\frac{216}{1123} g_{14}\\ x_{2}&{}={}&\frac{92459}{20214}&{}-{}&\frac{19379}{20214} w_{2}&{}+{}&\frac{432}{1123} g_{14}\\ w_{4}&{}={}&\frac{152353}{20214}&{}-{}&\frac{14743}{20214} w_{2}&{}+{}&\frac{216}{1123} g_{14}\\ w_{5}&{}={}&\frac{28825}{20214}&{}+{}&\frac{19379}{20214} w_{2}&{}-{}&\frac{432}{1123} g_{14}\\ g_{8}&{}={}&\frac{3617}{13476}&{}+{}&\frac{787}{13476} w_{2}&{}+{}&\frac{756}{1123} g_{14}\\ g_{2}&{}={}&\frac{11603}{20214}&{}+{}&\frac{835}{20214} w_{2}&{}+{}&\frac{432}{1123} g_{14}\\ w_{3}&{}={}&\frac{54275}{20214}&{}-{}&\frac{33287}{20214} w_{2}&{}+{}&\frac{1080}{1123} g_{14}\\ g_{3}&{}={}&\frac{11603}{13476}&{}-{}&\frac{5903}{13476} w_{2}&{}+{}&\frac{648}{1123} g_{14}\\ g_{7}&{}={}&\frac{1871}{6738}&{}+{}&\frac{979}{6738} w_{2}&{}+{}&\frac{648}{1123} g_{14}\\ g_{4}&{}={}&\frac{3119}{4492}&{}-{}&\frac{1219}{4492} w_{2}&{}+{}&\frac{648}{1123} g_{14}\\ g_{5}&{}={}&\frac{998}{3369}&{}+{}&\frac{1075}{3369} w_{2}&{}+{}&\frac{432}{1123} g_{14}\\ g_{6}&{}={}&\frac{499}{1123}&{}-{}&\frac{24}{1123} w_{2}&{}+{}&\frac{648}{1123} g_{14}\\ g_{11}&{}={}&\frac{217}{10107}&{}+{}&\frac{1952}{10107} w_{2}&{}+{}&\frac{882}{1123} g_{14}\\ g_{9}&{}={}&\frac{124}{10107}&{}+{}&\frac{5447}{10107} w_{2}&{}+{}&\frac{504}{1123} g_{14}\\ g_{10}&{}={}&\frac{62}{3369}&{}+{}&\frac{1039}{3369} w_{2}&{}+{}&\frac{756}{1123} g_{14}\\ g_{1}&{}={}&\frac{3743}{3369}&{}-{}&\frac{2318}{3369} w_{2}&{}+{}&\frac{648}{1123} g_{14}\\ g_{12}&{}={}&\frac{1970}{3369}&{}-{}&\frac{1220}{3369} w_{2}&{}+{}&\frac{873}{1123} g_{14}\\ g_{13}&{}={}&\frac{788}{3369}&{}-{}&\frac{488}{3369} w_{2}&{}+{}&\frac{1023}{1123} g_{14}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{2969605}{30321}&{}-{}&\frac{4175}{10107} g_{15}&{}-{}&\frac{49970}{30321} g_{14}\\\hline w_{1}&{}={}&\frac{338854}{30321}&{}-{}&\frac{28651}{10107} g_{15}&{}+{}&\frac{80630}{30321} g_{14}\\ x_{1}&{}={}&\frac{51731}{30321}&{}+{}&\frac{14743}{10107} g_{15}&{}-{}&\frac{35318}{30321} g_{14}\\ x_{2}&{}={}&\frac{128999}{30321}&{}-{}&\frac{19379}{10107} g_{15}&{}+{}&\frac{50422}{30321} g_{14}\\ w_{4}&{}={}&\frac{221158}{30321}&{}-{}&\frac{14743}{10107} g_{15}&{}+{}&\frac{35318}{30321} g_{14}\\ w_{5}&{}={}&\frac{52927}{30321}&{}+{}&\frac{19379}{10107} g_{15}&{}-{}&\frac{50422}{30321} g_{14}\\ g_{8}&{}={}&\frac{5819}{20214}&{}+{}&\frac{787}{6738} g_{15}&{}+{}&\frac{6017}{10107} g_{14}\\ g_{2}&{}={}&\frac{17822}{30321}&{}+{}&\frac{835}{10107} g_{15}&{}+{}&\frac{9994}{30321} g_{14}\\ w_{3}&{}={}&\frac{64769}{30321}&{}-{}&\frac{33287}{10107} g_{15}&{}+{}&\frac{95734}{30321} g_{14}\\ g_{3}&{}={}&\frac{14453}{20214}&{}-{}&\frac{5903}{6738} g_{15}&{}+{}&\frac{11735}{10107} g_{14}\\ g_{7}&{}={}&\frac{3296}{10107}&{}+{}&\frac{979}{3369} g_{15}&{}+{}&\frac{3874}{10107} g_{14}\\ g_{4}&{}={}&\frac{4069}{6738}&{}-{}&\frac{1219}{2246} g_{15}&{}+{}&\frac{3163}{3369} g_{14}\\ g_{5}&{}={}&\frac{4069}{10107}&{}+{}&\frac{2150}{3369} g_{15}&{}-{}&\frac{412}{10107} g_{14}\\ g_{6}&{}={}&\frac{491}{1123}&{}-{}&\frac{48}{1123} g_{15}&{}+{}&\frac{680}{1123} g_{14}\\ g_{11}&{}={}&\frac{2603}{30321}&{}+{}&\frac{3904}{10107} g_{15}&{}+{}&\frac{16006}{30321} g_{14}\\ g_{9}&{}={}&\frac{5819}{30321}&{}+{}&\frac{10894}{10107} g_{15}&{}-{}&\frac{8180}{30321} g_{14}\\ g_{10}&{}={}&\frac{1225}{10107}&{}+{}&\frac{2078}{3369} g_{15}&{}+{}&\frac{2648}{10107} g_{14}\\ g_{1}&{}={}&\frac{8911}{10107}&{}-{}&\frac{4636}{3369} g_{15}&{}+{}&\frac{15104}{10107} g_{14}\\ g_{12}&{}={}&\frac{4690}{10107}&{}-{}&\frac{2440}{3369} g_{15}&{}+{}&\frac{12737}{10107} g_{14}\\ g_{13}&{}={}&\frac{1876}{10107}&{}-{}&\frac{976}{3369} g_{15}&{}+{}&\frac{11159}{10107} g_{14}\\ w_{2}&{}={}&\frac{1}{3}&{}+{}&2 g_{15}&{}-{}&\frac{4}{3} g_{14}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{110140}{1123}&{}-{}&\frac{8350}{10107} g_{16}&{}-{}&\frac{11090}{10107} g_{14}\\\hline w_{1}&{}={}&\frac{11489}{1123}&{}-{}&\frac{57302}{10107} g_{16}&{}+{}&\frac{65078}{10107} g_{14}\\ x_{1}&{}={}&\frac{2462}{1123}&{}+{}&\frac{29486}{10107} g_{16}&{}-{}&\frac{31430}{10107} g_{14}\\ x_{2}&{}={}&\frac{4060}{1123}&{}-{}&\frac{38758}{10107} g_{16}&{}+{}&\frac{42646}{10107} g_{14}\\ w_{4}&{}={}&\frac{7645}{1123}&{}-{}&\frac{29486}{10107} g_{16}&{}+{}&\frac{31430}{10107} g_{14}\\ w_{5}&{}={}&\frac{2678}{1123}&{}+{}&\frac{38758}{10107} g_{16}&{}-{}&\frac{42646}{10107} g_{14}\\ g_{8}&{}={}&\frac{367}{1123}&{}+{}&\frac{787}{3369} g_{16}&{}+{}&\frac{1481}{3369} g_{14}\\ g_{2}&{}={}&\frac{691}{1123}&{}+{}&\frac{1670}{10107} g_{16}&{}+{}&\frac{2218}{10107} g_{14}\\ w_{3}&{}={}&\frac{1166}{1123}&{}-{}&\frac{66574}{10107} g_{16}&{}+{}&\frac{76294}{10107} g_{14}\\ g_{3}&{}={}&\frac{475}{1123}&{}-{}&\frac{5903}{3369} g_{16}&{}+{}&\frac{7847}{3369} g_{14}\\ g_{7}&{}={}&\frac{475}{1123}&{}+{}&\frac{1958}{3369} g_{16}&{}-{}&\frac{14}{3369} g_{14}\\ g_{4}&{}={}&\frac{475}{1123}&{}-{}&\frac{1219}{1123} g_{16}&{}+{}&\frac{1867}{1123} g_{14}\\ g_{5}&{}={}&\frac{691}{1123}&{}+{}&\frac{4300}{3369} g_{16}&{}-{}&\frac{3004}{3369} g_{14}\\ g_{6}&{}={}&\frac{475}{1123}&{}-{}&\frac{96}{1123} g_{16}&{}+{}&\frac{744}{1123} g_{14}\\ g_{11}&{}={}&\frac{241}{1123}&{}+{}&\frac{7808}{10107} g_{16}&{}+{}&\frac{130}{10107} g_{14}\\ g_{9}&{}={}&\frac{619}{1123}&{}+{}&\frac{21788}{10107} g_{16}&{}-{}&\frac{17252}{10107} g_{14}\\ g_{10}&{}={}&\frac{367}{1123}&{}+{}&\frac{4156}{3369} g_{16}&{}-{}&\frac{1888}{3369} g_{14}\\ g_{1}&{}={}&\frac{475}{1123}&{}-{}&\frac{9272}{3369} g_{16}&{}+{}&\frac{11216}{3369} g_{14}\\ g_{12}&{}={}&\frac{250}{1123}&{}-{}&\frac{4880}{3369} g_{16}&{}+{}&\frac{7499}{3369} g_{14}\\ g_{13}&{}={}&\frac{100}{1123}&{}-{}&\frac{1952}{3369} g_{16}&{}+{}&\frac{5021}{3369} g_{14}\\ w_{2}&{}={}&1&{}+{}&4 g_{16}&{}-{}&4 g_{14}\\ g_{15}&{}={}&\frac{1}{3}&{}+{}&2 g_{16}&{}-{}&\frac{4}{3} g_{14}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{1988065}{20214}&{}-{}&\frac{65}{20214} g_{16}&{}-{}&\frac{5545}{3369} g_{17}\\\hline w_{1}&{}={}&\frac{239341}{20214}&{}-{}&\frac{212221}{20214} g_{16}&{}+{}&\frac{32539}{3369} g_{17}\\ x_{1}&{}={}&\frac{28601}{20214}&{}+{}&\frac{106117}{20214} g_{16}&{}-{}&\frac{15715}{3369} g_{17}\\ x_{2}&{}={}&\frac{94403}{20214}&{}-{}&\frac{141485}{20214} g_{16}&{}+{}&\frac{21323}{3369} g_{17}\\ w_{4}&{}={}&\frac{153325}{20214}&{}-{}&\frac{106117}{20214} g_{16}&{}+{}&\frac{15715}{3369} g_{17}\\ w_{5}&{}={}&\frac{26881}{20214}&{}+{}&\frac{141485}{20214} g_{16}&{}-{}&\frac{21323}{3369} g_{17}\\ g_{8}&{}={}&\frac{5885}{13476}&{}-{}&\frac{1295}{13476} g_{16}&{}+{}&\frac{1481}{2246} g_{17}\\ g_{2}&{}={}&\frac{13547}{20214}&{}+{}&\frac{13}{20214} g_{16}&{}+{}&\frac{1109}{3369} g_{17}\\ w_{3}&{}={}&\frac{59135}{20214}&{}-{}&\frac{247589}{20214} g_{16}&{}+{}&\frac{38147}{3369} g_{17}\\ g_{3}&{}={}&\frac{13547}{13476}&{}-{}&\frac{47153}{13476} g_{16}&{}+{}&\frac{7847}{2246} g_{17}\\ g_{7}&{}={}&\frac{2843}{6738}&{}+{}&\frac{3937}{6738} g_{16}&{}-{}&\frac{7}{1123} g_{17}\\ g_{4}&{}={}&\frac{3767}{4492}&{}-{}&\frac{10477}{4492} g_{16}&{}+{}&\frac{5601}{2246} g_{17}\\ g_{5}&{}={}&\frac{1322}{3369}&{}+{}&\frac{6553}{3369} g_{16}&{}-{}&\frac{1502}{1123} g_{17}\\ g_{6}&{}={}&\frac{661}{1123}&{}-{}&\frac{654}{1123} g_{16}&{}+{}&\frac{1116}{1123} g_{17}\\ g_{11}&{}={}&\frac{4403}{20214}&{}+{}&\frac{15421}{20214} g_{16}&{}+{}&\frac{65}{3369} g_{17}\\ g_{9}&{}={}&\frac{1258}{10107}&{}+{}&\frac{34727}{10107} g_{16}&{}-{}&\frac{8626}{3369} g_{17}\\ g_{10}&{}={}&\frac{629}{3369}&{}+{}&\frac{5572}{3369} g_{16}&{}-{}&\frac{944}{1123} g_{17}\\ g_{1}&{}={}&\frac{4229}{3369}&{}-{}&\frac{17684}{3369} g_{16}&{}+{}&\frac{5608}{1123} g_{17}\\ g_{12}&{}={}&\frac{10499}{13476}&{}-{}&\frac{42017}{13476} g_{16}&{}+{}&\frac{7499}{2246} g_{17}\\ g_{13}&{}={}&\frac{6221}{13476}&{}-{}&\frac{22871}{13476} g_{16}&{}+{}&\frac{5021}{2246} g_{17}\\ w_{2}&{}={}&0&{}+{}&7 g_{16}&{}-{}&6 g_{17}\\ g_{15}&{}={}&0&{}+{}&3 g_{16}&{}-{}&2 g_{17}\\ g_{14}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{16}&{}+{}&\frac{3}{2} g_{17}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{82525830}{838501}&{}-{}&\frac{1224720}{838501} g_{18}&{}-{}&\frac{49775}{838501} w_{3}\\\hline w_{1}&{}={}&\frac{7823917}{838501}&{}-{}&\frac{34992}{838501} g_{18}&{}+{}&\frac{717293}{838501} w_{3}\\ x_{1}&{}={}&\frac{2244372}{838501}&{}+{}&\frac{139968}{838501} g_{18}&{}-{}&\frac{353669}{838501} w_{3}\\ x_{2}&{}={}&\frac{2509226}{838501}&{}-{}&\frac{104976}{838501} g_{18}&{}+{}&\frac{474877}{838501} w_{3}\\ w_{4}&{}={}&\frac{5302137}{838501}&{}-{}&\frac{139968}{838501} g_{18}&{}+{}&\frac{353669}{838501} w_{3}\\ w_{5}&{}={}&\frac{2521780}{838501}&{}+{}&\frac{104976}{838501} g_{18}&{}-{}&\frac{474877}{838501} w_{3}\\ g_{8}&{}={}&\frac{366952}{838501}&{}+{}&\frac{423792}{838501} g_{18}&{}+{}&\frac{47757}{1677002} w_{3}\\ g_{2}&{}={}&\frac{573647}{838501}&{}+{}&\frac{244944}{838501} g_{18}&{}+{}&\frac{9955}{838501} w_{3}\\ g_{17}&{}={}&\frac{35092}{838501}&{}+{}&\frac{742767}{838501} g_{18}&{}+{}&\frac{30321}{838501} w_{3}\\ g_{3}&{}={}&\frac{151258}{838501}&{}+{}&\frac{192456}{838501} g_{18}&{}+{}&\frac{494787}{1677002} w_{3}\\ g_{7}&{}={}&\frac{489547}{838501}&{}+{}&\frac{396576}{838501} g_{18}&{}-{}&\frac{23811}{838501} w_{3}\\ g_{4}&{}={}&\frac{247912}{838501}&{}+{}&\frac{250776}{838501} g_{18}&{}+{}&\frac{339813}{1677002} w_{3}\\ g_{5}&{}={}&\frac{734737}{838501}&{}+{}&\frac{342144}{838501} g_{18}&{}-{}&\frac{119190}{838501} w_{3}\\ g_{6}&{}={}&\frac{392893}{838501}&{}+{}&\frac{338256}{838501} g_{18}&{}+{}&\frac{53676}{838501} w_{3}\\ g_{11}&{}={}&\frac{360851}{838501}&{}+{}&\frac{538164}{838501} g_{18}&{}-{}&\frac{30257}{838501} w_{3}\\ g_{9}&{}={}&\frac{814097}{838501}&{}+{}&\frac{457488}{838501} g_{18}&{}-{}&\frac{216542}{838501} w_{3}\\ g_{10}&{}={}&\frac{511933}{838501}&{}+{}&\frac{511272}{838501} g_{18}&{}-{}&\frac{92352}{838501} w_{3}\\ g_{1}&{}={}&\frac{6277}{838501}&{}+{}&\frac{104976}{838501} g_{18}&{}+{}&\frac{363624}{838501} w_{3}\\ g_{12}&{}={}&\frac{44860}{838501}&{}+{}&\frac{339066}{838501} g_{18}&{}+{}&\frac{454575}{1677002} w_{3}\\ g_{13}&{}={}&\frac{70582}{838501}&{}+{}&\frac{495126}{838501} g_{18}&{}+{}&\frac{272793}{1677002} w_{3}\\ w_{2}&{}={}&\frac{1418425}{838501}&{}+{}&\frac{349920}{838501} g_{18}&{}-{}&\frac{464922}{838501} w_{3}\\ g_{15}&{}={}&\frac{627949}{838501}&{}+{}&\frac{574404}{838501} g_{18}&{}-{}&\frac{181926}{838501} w_{3}\\ g_{14}&{}={}&\frac{87730}{838501}&{}+{}&\frac{599166}{838501} g_{18}&{}+{}&\frac{151605}{1677002} w_{3}\\ g_{16}&{}={}&\frac{232711}{838501}&{}+{}&\frac{686646}{838501} g_{18}&{}-{}&\frac{40428}{838501} w_{3}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{330153095}{3354004}&{}-{}&\frac{4749555}{3354004} g_{18}&{}-{}&\frac{149325}{1677002} g_{19}\\\hline w_{1}&{}={}&\frac{32012961}{3354004}&{}-{}&\frac{2291847}{3354004} g_{18}&{}+{}&\frac{2151879}{1677002} g_{19}\\ x_{1}&{}={}&\frac{8623819}{3354004}&{}+{}&\frac{1620879}{3354004} g_{18}&{}-{}&\frac{1061007}{1677002} g_{19}\\ x_{2}&{}={}&\frac{10511781}{3354004}&{}-{}&\frac{1844535}{3354004} g_{18}&{}+{}&\frac{1424631}{1677002} g_{19}\\ w_{4}&{}={}&\frac{21562217}{3354004}&{}-{}&\frac{1620879}{3354004} g_{18}&{}+{}&\frac{1061007}{1677002} g_{19}\\ w_{5}&{}={}&\frac{9612243}{3354004}&{}+{}&\frac{1844535}{3354004} g_{18}&{}-{}&\frac{1424631}{1677002} g_{19}\\ g_{8}&{}={}&\frac{2983373}{6708008}&{}+{}&\frac{3247065}{6708008} g_{18}&{}+{}&\frac{143271}{3354004} g_{19}\\ g_{2}&{}={}&\frac{2304543}{3354004}&{}+{}&\frac{949911}{3354004} g_{18}&{}+{}&\frac{29865}{1677002} g_{19}\\ g_{17}&{}={}&\frac{170689}{3354004}&{}+{}&\frac{2880105}{3354004} g_{18}&{}+{}&\frac{90963}{1677002} g_{19}\\ g_{3}&{}={}&\frac{1704851}{6708008}&{}+{}&\frac{55287}{6708008} g_{18}&{}+{}&\frac{1484361}{3354004} g_{19}\\ g_{7}&{}={}&\frac{1934377}{3354004}&{}+{}&\frac{1657737}{3354004} g_{18}&{}-{}&\frac{71433}{1677002} g_{19}\\ g_{4}&{}={}&\frac{2323109}{6708008}&{}+{}&\frac{986769}{6708008} g_{18}&{}+{}&\frac{1019439}{3354004} g_{19}\\ g_{5}&{}={}&\frac{1409879}{1677002}&{}+{}&\frac{863073}{1677002} g_{18}&{}-{}&\frac{178785}{838501} g_{19}\\ g_{6}&{}={}&\frac{406312}{838501}&{}+{}&\frac{297999}{838501} g_{18}&{}+{}&\frac{80514}{838501} g_{19}\\ g_{11}&{}={}&\frac{1413147}{3354004}&{}+{}&\frac{2243427}{3354004} g_{18}&{}-{}&\frac{90771}{1677002} g_{19}\\ g_{9}&{}={}&\frac{1519923}{1677002}&{}+{}&\frac{1239789}{1677002} g_{18}&{}-{}&\frac{324813}{838501} g_{19}\\ g_{10}&{}={}&\frac{488845}{838501}&{}+{}&\frac{580536}{838501} g_{18}&{}-{}&\frac{138528}{838501} g_{19}\\ g_{1}&{}={}&\frac{97183}{838501}&{}-{}&\frac{167742}{838501} g_{18}&{}+{}&\frac{545436}{838501} g_{19}\\ g_{12}&{}={}&\frac{813455}{6708008}&{}+{}&\frac{1348803}{6708008} g_{18}&{}+{}&\frac{1363725}{3354004} g_{19}\\ g_{13}&{}={}&\frac{837449}{6708008}&{}+{}&\frac{3142629}{6708008} g_{18}&{}+{}&\frac{818379}{3354004} g_{19}\\ w_{2}&{}={}&\frac{2604389}{1677002}&{}+{}&\frac{1397223}{1677002} g_{18}&{}-{}&\frac{697383}{838501} g_{19}\\ g_{15}&{}={}&\frac{1164935}{1677002}&{}+{}&\frac{1421697}{1677002} g_{18}&{}-{}&\frac{272889}{838501} g_{19}\\ g_{14}&{}={}&\frac{853445}{6708008}&{}+{}&\frac{4338513}{6708008} g_{18}&{}+{}&\frac{454815}{3354004} g_{19}\\ g_{16}&{}={}&\frac{222604}{838501}&{}+{}&\frac{716967}{838501} g_{18}&{}-{}&\frac{60642}{838501} g_{19}\\ w_{3}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{18}&{}+{}&\frac{3}{2} g_{19}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{660455515}{6708008}&{}-{}&\frac{9051135}{6708008} g_{18}&{}-{}&\frac{447975}{3354004} g_{20}\\\hline w_{1}&{}={}&\frac{66177801}{6708008}&{}-{}&\frac{11039331}{6708008} g_{18}&{}+{}&\frac{6455637}{3354004} g_{20}\\ x_{1}&{}={}&\frac{16186631}{6708008}&{}+{}&\frac{6424779}{6708008} g_{18}&{}-{}&\frac{3183021}{3354004} g_{20}\\ x_{2}&{}={}&\frac{22448193}{6708008}&{}-{}&\frac{7962963}{6708008} g_{18}&{}+{}&\frac{4273893}{3354004} g_{20}\\ w_{4}&{}={}&\frac{44185441}{6708008}&{}-{}&\frac{6424779}{6708008} g_{18}&{}+{}&\frac{3183021}{3354004} g_{20}\\ w_{5}&{}={}&\frac{17799855}{6708008}&{}+{}&\frac{7962963}{6708008} g_{18}&{}-{}&\frac{4273893}{3354004} g_{20}\\ g_{8}&{}={}&\frac{6110017}{13416016}&{}+{}&\frac{6064317}{13416016} g_{18}&{}+{}&\frac{429813}{6708008} g_{20}\\ g_{2}&{}={}&\frac{4638951}{6708008}&{}+{}&\frac{1810227}{6708008} g_{18}&{}+{}&\frac{89595}{3354004} g_{20}\\ g_{17}&{}={}&\frac{432341}{6708008}&{}+{}&\frac{5487321}{6708008} g_{18}&{}+{}&\frac{272889}{3354004} g_{20}\\ g_{3}&{}={}&\frac{4894063}{13416016}&{}-{}&\frac{4342509}{13416016} g_{18}&{}+{}&\frac{4453083}{6708008} g_{20}\\ g_{7}&{}={}&\frac{3797321}{6708008}&{}+{}&\frac{3529773}{6708008} g_{18}&{}-{}&\frac{214299}{3354004} g_{20}\\ g_{4}&{}={}&\frac{5665657}{13416016}&{}-{}&\frac{1084779}{13416016} g_{18}&{}+{}&\frac{3058317}{6708008} g_{20}\\ g_{5}&{}={}&\frac{2640973}{3354004}&{}+{}&\frac{2262501}{3354004} g_{18}&{}-{}&\frac{536355}{1677002} g_{20}\\ g_{6}&{}={}&\frac{852881}{1677002}&{}+{}&\frac{475227}{1677002} g_{18}&{}+{}&\frac{120771}{838501} g_{20}\\ g_{11}&{}={}&\frac{2735523}{6708008}&{}+{}&\frac{4759167}{6708008} g_{18}&{}-{}&\frac{272313}{3354004} g_{20}\\ g_{9}&{}={}&\frac{2715033}{3354004}&{}+{}&\frac{3454017}{3354004} g_{18}&{}-{}&\frac{974439}{1677002} g_{20}\\ g_{10}&{}={}&\frac{454213}{838501}&{}+{}&\frac{684432}{838501} g_{18}&{}-{}&\frac{207792}{838501} g_{20}\\ g_{1}&{}={}&\frac{233542}{838501}&{}-{}&\frac{576819}{838501} g_{18}&{}+{}&\frac{818154}{838501} g_{20}\\ g_{12}&{}={}&\frac{2990635}{13416016}&{}-{}&\frac{1393569}{13416016} g_{18}&{}+{}&\frac{4091175}{6708008} g_{20}\\ g_{13}&{}={}&\frac{2493277}{13416016}&{}+{}&\frac{3830121}{13416016} g_{18}&{}+{}&\frac{2455137}{6708008} g_{20}\\ w_{2}&{}={}&\frac{4511395}{3354004}&{}+{}&\frac{4886595}{3354004} g_{18}&{}-{}&\frac{2092149}{1677002} g_{20}\\ g_{15}&{}={}&\frac{2056981}{3354004}&{}+{}&\frac{3662061}{3354004} g_{18}&{}-{}&\frac{818667}{1677002} g_{20}\\ g_{14}&{}={}&\frac{2161705}{13416016}&{}+{}&\frac{7312581}{13416016} g_{18}&{}+{}&\frac{1364445}{6708008} g_{20}\\ g_{16}&{}={}&\frac{414887}{1677002}&{}+{}&\frac{1524897}{1677002} g_{18}&{}-{}&\frac{90963}{838501} g_{20}\\ w_{3}&{}={}&\frac{5}{8}&{}-{}&\frac{15}{8} g_{18}&{}+{}&\frac{9}{4} g_{20}\\ g_{19}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{18}&{}+{}&\frac{3}{2} g_{20}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{1321359005}{13416016}&{}-{}&\frac{16758345}{13416016} g_{18}&{}-{}&\frac{1343925}{6708008} g_{21}\\\hline w_{1}&{}={}&\frac{138811239}{13416016}&{}-{}&\frac{41445573}{13416016} g_{18}&{}+{}&\frac{19366911}{6708008} g_{21}\\ x_{1}&{}={}&\frac{29190241}{13416016}&{}+{}&\frac{22398621}{13416016} g_{18}&{}-{}&\frac{9549063}{6708008} g_{21}\\ x_{2}&{}={}&\frac{49170279}{13416016}&{}-{}&\frac{28747605}{13416016} g_{18}&{}+{}&\frac{12821679}{6708008} g_{21}\\ w_{4}&{}={}&\frac{91553903}{13416016}&{}-{}&\frac{22398621}{13416016} g_{18}&{}+{}&\frac{9549063}{6708008} g_{21}\\ w_{5}&{}={}&\frac{31325817}{13416016}&{}+{}&\frac{28747605}{13416016} g_{18}&{}-{}&\frac{12821679}{6708008} g_{21}\\ g_{8}&{}={}&\frac{12649847}{26832032}&{}+{}&\frac{10839195}{26832032} g_{18}&{}+{}&\frac{1289439}{13416016} g_{21}\\ g_{2}&{}={}&\frac{9367497}{13416016}&{}+{}&\frac{3351669}{13416016} g_{18}&{}+{}&\frac{268785}{6708008} g_{21}\\ g_{17}&{}={}&\frac{1137571}{13416016}&{}+{}&\frac{10155975}{13416016} g_{18}&{}+{}&\frac{818667}{6708008} g_{21}\\ g_{3}&{}={}&\frac{14241209}{26832032}&{}-{}&\frac{22044267}{26832032} g_{18}&{}+{}&\frac{13359249}{13416016} g_{21}\\ g_{7}&{}={}&\frac{7380343}{13416016}&{}+{}&\frac{7702443}{13416016} g_{18}&{}-{}&\frac{642897}{6708008} g_{21}\\ g_{4}&{}={}&\frac{14389631}{26832032}&{}-{}&\frac{11344509}{26832032} g_{18}&{}+{}&\frac{9174951}{13416016} g_{21}\\ g_{5}&{}={}&\frac{4745591}{6708008}&{}+{}&\frac{6134067}{6708008} g_{18}&{}-{}&\frac{1609065}{3354004} g_{21}\\ g_{6}&{}={}&\frac{1826533}{3354004}&{}+{}&\frac{588141}{3354004} g_{18}&{}+{}&\frac{362313}{1677002} g_{21}\\ g_{11}&{}={}&\frac{5198733}{13416016}&{}+{}&\frac{10335273}{13416016} g_{18}&{}-{}&\frac{816939}{6708008} g_{21}\\ g_{9}&{}={}&\frac{4455627}{6708008}&{}+{}&\frac{9831351}{6708008} g_{18}&{}-{}&\frac{2923317}{3354004} g_{21}\\ g_{10}&{}={}&\frac{402265}{838501}&{}+{}&\frac{840276}{838501} g_{18}&{}-{}&\frac{311688}{838501} g_{21}\\ g_{1}&{}={}&\frac{876161}{1677002}&{}-{}&\frac{2380869}{1677002} g_{18}&{}+{}&\frac{1227231}{838501} g_{21}\\ g_{12}&{}={}&\frac{10072445}{26832032}&{}-{}&\frac{15060663}{26832032} g_{18}&{}+{}&\frac{12273525}{13416016} g_{21}\\ g_{13}&{}={}&\frac{7441691}{26832032}&{}+{}&\frac{294831}{26832032} g_{18}&{}+{}&\frac{7365411}{13416016} g_{21}\\ w_{2}&{}={}&\frac{6930641}{6708008}&{}+{}&\frac{16049637}{6708008} g_{18}&{}-{}&\frac{6276447}{3354004} g_{21}\\ g_{15}&{}={}&\frac{3295295}{6708008}&{}+{}&\frac{9780123}{6708008} g_{18}&{}-{}&\frac{2456001}{3354004} g_{21}\\ g_{14}&{}={}&\frac{5687855}{26832032}&{}+{}&\frac{10531827}{26832032} g_{18}&{}+{}&\frac{4093335}{13416016} g_{21}\\ g_{16}&{}={}&\frac{738811}{3354004}&{}+{}&\frac{3322683}{3354004} g_{18}&{}-{}&\frac{272889}{1677002} g_{21}\\ w_{3}&{}={}&\frac{19}{16}&{}-{}&\frac{57}{16} g_{18}&{}+{}&\frac{27}{8} g_{21}\\ g_{19}&{}={}&\frac{5}{8}&{}-{}&\frac{15}{8} g_{18}&{}+{}&\frac{9}{4} g_{21}\\ g_{20}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{18}&{}+{}&\frac{3}{2} g_{21}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{2644061935}{26832032}&{}-{}&\frac{29484915}{26832032} g_{18}&{}-{}&\frac{4031775}{13416016} g_{22}\\\hline w_{1}&{}={}&\frac{296989389}{26832032}&{}-{}&\frac{140991879}{26832032} g_{18}&{}+{}&\frac{58100733}{13416016} g_{22}\\ x_{1}&{}={}&\frac{48831419}{26832032}&{}+{}&\frac{73444431}{26832032} g_{18}&{}-{}&\frac{28647189}{13416016} g_{22}\\ x_{2}&{}={}&\frac{111162237}{26832032}&{}-{}&\frac{95960247}{26832032} g_{18}&{}+{}&\frac{38465037}{13416016} g_{22}\\ w_{4}&{}={}&\frac{192656869}{26832032}&{}-{}&\frac{73444431}{26832032} g_{18}&{}+{}&\frac{28647189}{13416016} g_{22}\\ w_{5}&{}={}&\frac{49829955}{26832032}&{}+{}&\frac{95960247}{26832032} g_{18}&{}-{}&\frac{38465037}{13416016} g_{22}\\ g_{8}&{}={}&\frac{26589133}{53664064}&{}+{}&\frac{17810073}{53664064} g_{18}&{}+{}&\frac{3868317}{26832032} g_{22}\\ g_{2}&{}={}&\frac{19003779}{26832032}&{}+{}&\frac{5896983}{26832032} g_{18}&{}+{}&\frac{806355}{13416016} g_{22}\\ g_{17}&{}={}&\frac{3093809}{26832032}&{}+{}&\frac{17855949}{26832032} g_{18}&{}+{}&\frac{2456001}{13416016} g_{22}\\ g_{3}&{}={}&\frac{41841667}{53664064}&{}-{}&\frac{84166281}{53664064} g_{18}&{}+{}&\frac{40077747}{26832032} g_{22}\\ g_{7}&{}={}&\frac{14117789}{26832032}&{}+{}&\frac{17333577}{26832032} g_{18}&{}-{}&\frac{1928691}{13416016} g_{22}\\ g_{4}&{}={}&\frac{37954213}{53664064}&{}-{}&\frac{50213871}{53664064} g_{18}&{}+{}&\frac{27524853}{26832032} g_{22}\\ g_{5}&{}={}&\frac{7882117}{13416016}&{}+{}&\frac{17095329}{13416016} g_{18}&{}-{}&\frac{4827195}{6708008} g_{22}\\ g_{6}&{}={}&\frac{4015379}{6708008}&{}+{}&\frac{89343}{6708008} g_{18}&{}+{}&\frac{1086939}{3354004} g_{22}\\ g_{11}&{}={}&\frac{9580527}{26832032}&{}+{}&\frac{23121363}{26832032} g_{18}&{}-{}&\frac{2450817}{13416016} g_{22}\\ g_{9}&{}={}&\frac{5987937}{13416016}&{}+{}&\frac{28432653}{13416016} g_{18}&{}-{}&\frac{8769951}{6708008} g_{22}\\ g_{10}&{}={}&\frac{324343}{838501}&{}+{}&\frac{1074042}{838501} g_{18}&{}-{}&\frac{467532}{838501} g_{22}\\ g_{1}&{}={}&\frac{2979553}{3354004}&{}-{}&\frac{8443431}{3354004} g_{18}&{}+{}&\frac{3681693}{1677002} g_{22}\\ g_{12}&{}={}&\frac{32418415}{53664064}&{}-{}&\frac{66941901}{53664064} g_{18}&{}+{}&\frac{36820575}{26832032} g_{22}\\ g_{13}&{}={}&\frac{22248793}{53664064}&{}-{}&\frac{21506571}{53664064} g_{18}&{}+{}&\frac{22096233}{26832032} g_{22}\\ w_{2}&{}={}&\frac{7584835}{13416016}&{}+{}&\frac{50928615}{13416016} g_{18}&{}-{}&\frac{18829341}{6708008} g_{22}\\ g_{15}&{}={}&\frac{4134589}{13416016}&{}+{}&\frac{26928249}{13416016} g_{18}&{}-{}&\frac{7368003}{6708008} g_{22}\\ g_{14}&{}={}&\frac{15469045}{53664064}&{}+{}&\frac{8783649}{53664064} g_{18}&{}+{}&\frac{12280005}{26832032} g_{22}\\ g_{16}&{}={}&\frac{1204733}{6708008}&{}+{}&\frac{7464033}{6708008} g_{18}&{}-{}&\frac{818667}{3354004} g_{22}\\ w_{3}&{}={}&\frac{65}{32}&{}-{}&\frac{195}{32} g_{18}&{}+{}&\frac{81}{16} g_{22}\\ g_{19}&{}={}&\frac{19}{16}&{}-{}&\frac{57}{16} g_{18}&{}+{}&\frac{27}{8} g_{22}\\ g_{20}&{}={}&\frac{5}{8}&{}-{}&\frac{15}{8} g_{18}&{}+{}&\frac{9}{4} g_{22}\\ g_{21}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{18}&{}+{}&\frac{3}{2} g_{22}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{10412421365}{105563502}&{}-{}&\frac{15624835}{105563502} w_{2}&{}-{}&\frac{6298560}{5864639} g_{23}\\\hline w_{1}&{}={}&\frac{1261972241}{105563502}&{}-{}&\frac{152095319}{105563502} w_{2}&{}+{}&\frac{2519424}{5864639} g_{23}\\ x_{1}&{}={}&\frac{146347261}{105563502}&{}+{}&\frac{77610143}{105563502} w_{2}&{}-{}&\frac{629856}{5864639} g_{23}\\ x_{2}&{}={}&\frac{499031743}{105563502}&{}-{}&\frac{102438535}{105563502} w_{2}&{}+{}&\frac{1259712}{5864639} g_{23}\\ w_{4}&{}={}&\frac{803724257}{105563502}&{}-{}&\frac{77610143}{105563502} w_{2}&{}+{}&\frac{629856}{5864639} g_{23}\\ w_{5}&{}={}&\frac{134349269}{105563502}&{}+{}&\frac{102438535}{105563502} w_{2}&{}-{}&\frac{1259712}{5864639} g_{23}\\ g_{8}&{}={}&\frac{37769713}{70375668}&{}+{}&\frac{2668355}{70375668} w_{2}&{}+{}&\frac{2204496}{5864639} g_{23}\\ g_{2}&{}={}&\frac{76777735}{105563502}&{}+{}&\frac{3124967}{105563502} w_{2}&{}+{}&\frac{1259712}{5864639} g_{23}\\ g_{17}&{}={}&\frac{18291637}{105563502}&{}+{}&\frac{9447965}{105563502} w_{2}&{}+{}&\frac{3820446}{5864639} g_{23}\\ g_{3}&{}={}&\frac{76777735}{70375668}&{}-{}&\frac{32062867}{70375668} w_{2}&{}+{}&\frac{1889568}{5864639} g_{23}\\ g_{7}&{}={}&\frac{17862631}{35187834}&{}+{}&\frac{4494803}{35187834} w_{2}&{}+{}&\frac{1889568}{5864639} g_{23}\\ g_{4}&{}={}&\frac{21682819}{23458556}&{}-{}&\frac{6777863}{23458556} w_{2}&{}+{}&\frac{1889568}{5864639} g_{23}\\ g_{5}&{}={}&\frac{7909090}{17593917}&{}+{}&\frac{5408027}{17593917} w_{2}&{}+{}&\frac{1259712}{5864639} g_{23}\\ g_{6}&{}={}&\frac{3954545}{5864639}&{}-{}&\frac{228306}{5864639} w_{2}&{}+{}&\frac{1889568}{5864639} g_{23}\\ g_{11}&{}={}&\frac{35307643}{105563502}&{}+{}&\frac{17865059}{105563502} w_{2}&{}+{}&\frac{2571912}{5864639} g_{23}\\ g_{9}&{}={}&\frac{10087898}{52781751}&{}+{}&\frac{27725053}{52781751} w_{2}&{}+{}&\frac{1469664}{5864639} g_{23}\\ g_{10}&{}={}&\frac{5043949}{17593917}&{}+{}&\frac{5065568}{17593917} w_{2}&{}+{}&\frac{2204496}{5864639} g_{23}\\ g_{1}&{}={}&\frac{23592913}{17593917}&{}-{}&\frac{12414196}{17593917} w_{2}&{}+{}&\frac{1889568}{5864639} g_{23}\\ g_{12}&{}={}&\frac{62954371}{70375668}&{}-{}&\frac{27149503}{70375668} w_{2}&{}+{}&\frac{2545668}{5864639} g_{23}\\ g_{13}&{}={}&\frac{3819047}{6397788}&{}-{}&\frac{1104059}{6397788} w_{2}&{}+{}&\frac{271188}{533149} g_{23}\\ g_{18}&{}={}&\frac{3659671}{158345253}&{}+{}&\frac{26832032}{158345253} w_{2}&{}+{}&\frac{4184298}{5864639} g_{23}\\ g_{15}&{}={}&\frac{5226182}{52781751}&{}+{}&\frac{25320169}{52781751} w_{2}&{}+{}&\frac{2183112}{5864639} g_{23}\\ g_{14}&{}={}&\frac{28046281}{70375668}&{}-{}&\frac{2141413}{70375668} w_{2}&{}+{}&\frac{3274668}{5864639} g_{23}\\ g_{16}&{}={}&\frac{2613091}{17593917}&{}+{}&\frac{3863126}{17593917} w_{2}&{}+{}&\frac{3274668}{5864639} g_{23}\\ w_{3}&{}={}&\frac{323898715}{105563502}&{}-{}&\frac{176923711}{105563502} w_{2}&{}+{}&\frac{3149280}{5864639} g_{23}\\ g_{19}&{}={}&\frac{99779225}{52781751}&{}-{}&\frac{54502565}{52781751} w_{2}&{}+{}&\frac{4191669}{5864639} g_{23}\\ g_{20}&{}={}&\frac{58332470}{52781751}&{}-{}&\frac{31863038}{52781751} w_{2}&{}+{}&\frac{4886595}{5864639} g_{23}\\ g_{21}&{}={}&\frac{30701300}{52781751}&{}-{}&\frac{16770020}{52781751} w_{2}&{}+{}&\frac{5349879}{5864639} g_{23}\\ g_{22}&{}={}&\frac{12280520}{52781751}&{}-{}&\frac{6708008}{52781751} w_{2}&{}+{}&\frac{5658735}{5864639} g_{23}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{15626444465}{158345253}&{}-{}&\frac{15624835}{52781751} g_{24}&{}-{}&\frac{138811450}{158345253} g_{23}\\\hline w_{1}&{}={}&\frac{1816910702}{158345253}&{}-{}&\frac{152095319}{52781751} g_{24}&{}+{}&\frac{372215086}{158345253} g_{23}\\ x_{1}&{}={}&\frac{258325963}{158345253}&{}+{}&\frac{77610143}{52781751} g_{24}&{}-{}&\frac{172226398}{158345253} g_{23}\\ x_{2}&{}={}&\frac{697328347}{158345253}&{}-{}&\frac{102438535}{52781751} g_{24}&{}+{}&\frac{238889294}{158345253} g_{23}\\ w_{4}&{}={}&\frac{1166781314}{158345253}&{}-{}&\frac{77610143}{52781751} g_{24}&{}+{}&\frac{172226398}{158345253} g_{23}\\ w_{5}&{}={}&\frac{252743171}{158345253}&{}+{}&\frac{102438535}{52781751} g_{24}&{}-{}&\frac{238889294}{158345253} g_{23}\\ g_{8}&{}={}&\frac{57988747}{105563502}&{}+{}&\frac{2668355}{35187834} g_{24}&{}+{}&\frac{17172109}{52781751} g_{23}\\ g_{2}&{}={}&\frac{116729086}{158345253}&{}+{}&\frac{3124967}{52781751} g_{24}&{}+{}&\frac{27762290}{158345253} g_{23}\\ g_{17}&{}={}&\frac{32161438}{158345253}&{}+{}&\frac{9447965}{52781751} g_{24}&{}+{}&\frac{84256112}{158345253} g_{23}\\ g_{3}&{}={}&\frac{99135169}{105563502}&{}-{}&\frac{32062867}{35187834} g_{24}&{}+{}&\frac{49068979}{52781751} g_{23}\\ g_{7}&{}={}&\frac{29041348}{52781751}&{}+{}&\frac{4494803}{17593917} g_{24}&{}+{}&\frac{8016506}{52781751} g_{23}\\ g_{4}&{}={}&\frac{29135297}{35187834}&{}-{}&\frac{6777863}{11729278} g_{24}&{}+{}&\frac{12446567}{17593917} g_{23}\\ g_{5}&{}={}&\frac{29135297}{52781751}&{}+{}&\frac{10816054}{17593917} g_{24}&{}-{}&\frac{10294700}{52781751} g_{23}\\ g_{6}&{}={}&\frac{3878443}{5864639}&{}-{}&\frac{456612}{5864639} g_{24}&{}+{}&\frac{2193976}{5864639} g_{23}\\ g_{11}&{}={}&\frac{61893994}{158345253}&{}+{}&\frac{17865059}{52781751} g_{24}&{}+{}&\frac{33711506}{158345253} g_{23}\\ g_{9}&{}={}&\frac{57988747}{158345253}&{}+{}&\frac{55450106}{52781751} g_{24}&{}-{}&\frac{71219284}{158345253} g_{23}\\ g_{10}&{}={}&\frac{20197415}{52781751}&{}+{}&\frac{10131136}{17593917} g_{24}&{}-{}&\frac{421808}{52781751} g_{23}\\ g_{1}&{}={}&\frac{58364543}{52781751}&{}-{}&\frac{24828392}{17593917} g_{24}&{}+{}&\frac{66662896}{52781751} g_{23}\\ g_{12}&{}={}&\frac{80856805}{105563502}&{}-{}&\frac{27149503}{35187834} g_{24}&{}+{}&\frac{50060515}{52781751} g_{23}\\ g_{13}&{}={}&\frac{5176541}{9596682}&{}-{}&\frac{1104059}{3198894} g_{24}&{}+{}&\frac{3544751}{4798341} g_{23}\\ g_{18}&{}={}&\frac{37811045}{475035759}&{}+{}&\frac{53664064}{158345253} g_{24}&{}+{}&\frac{231600010}{475035759} g_{23}\\ g_{15}&{}={}&\frac{40998715}{158345253}&{}+{}&\frac{50640338}{52781751} g_{24}&{}-{}&\frac{42336652}{158345253} g_{23}\\ g_{14}&{}={}&\frac{40998715}{105563502}&{}-{}&\frac{2141413}{35187834} g_{24}&{}+{}&\frac{31613425}{52781751} g_{23}\\ g_{16}&{}={}&\frac{11702399}{52781751}&{}+{}&\frac{7726252}{17593917} g_{24}&{}+{}&\frac{14019508}{52781751} g_{23}\\ w_{3}&{}={}&\frac{397386217}{158345253}&{}-{}&\frac{176923711}{52781751} g_{24}&{}+{}&\frac{438877982}{158345253} g_{23}\\ g_{19}&{}={}&\frac{244835110}{158345253}&{}-{}&\frac{109005130}{52781751} g_{24}&{}+{}&\frac{331185323}{158345253} g_{23}\\ g_{20}&{}={}&\frac{143134372}{158345253}&{}-{}&\frac{63726076}{52781751} g_{24}&{}+{}&\frac{259390217}{158345253} g_{23}\\ g_{21}&{}={}&\frac{75333880}{158345253}&{}-{}&\frac{33540040}{52781751} g_{24}&{}+{}&\frac{211526813}{158345253} g_{23}\\ g_{22}&{}={}&\frac{30133552}{158345253}&{}-{}&\frac{13416016}{52781751} g_{24}&{}+{}&\frac{179617877}{158345253} g_{23}\\ w_{2}&{}={}&\frac{1}{3}&{}+{}&2 g_{24}&{}-{}&\frac{4}{3} g_{23}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{52666900}{533149}&{}-{}&\frac{31249670}{52781751} g_{25}&{}-{}&\frac{25437370}{52781751} g_{23}\\\hline w_{1}&{}={}&\frac{5605439}{533149}&{}-{}&\frac{304190638}{52781751} g_{25}&{}+{}&\frac{326865454}{52781751} g_{23}\\ x_{1}&{}={}&\frac{1131098}{533149}&{}+{}&\frac{155220286}{52781751} g_{25}&{}-{}&\frac{160888990}{52781751} g_{23}\\ x_{2}&{}={}&\frac{2002996}{533149}&{}-{}&\frac{204877070}{52781751} g_{25}&{}+{}&\frac{216214478}{52781751} g_{23}\\ w_{4}&{}={}&\frac{3667243}{533149}&{}-{}&\frac{155220286}{52781751} g_{25}&{}+{}&\frac{160888990}{52781751} g_{23}\\ w_{5}&{}={}&\frac{1195898}{533149}&{}+{}&\frac{204877070}{52781751} g_{25}&{}-{}&\frac{216214478}{52781751} g_{23}\\ g_{8}&{}={}&\frac{306349}{533149}&{}+{}&\frac{2668355}{17593917} g_{25}&{}+{}&\frac{3945133}{17593917} g_{23}\\ g_{2}&{}={}&\frac{403549}{533149}&{}+{}&\frac{6249934}{52781751} g_{25}&{}+{}&\frac{5087474}{52781751} g_{23}\\ g_{17}&{}={}&\frac{140099}{533149}&{}+{}&\frac{18895930}{52781751} g_{25}&{}+{}&\frac{15488084}{52781751} g_{23}\\ g_{3}&{}={}&\frac{338749}{533149}&{}-{}&\frac{32062867}{17593917} g_{25}&{}+{}&\frac{37731571}{17593917} g_{23}\\ g_{7}&{}={}&\frac{338749}{533149}&{}+{}&\frac{8989606}{17593917} g_{25}&{}-{}&\frac{3320902}{17593917} g_{23}\\ g_{4}&{}={}&\frac{338749}{533149}&{}-{}&\frac{6777863}{5864639} g_{25}&{}+{}&\frac{8667431}{5864639} g_{23}\\ g_{5}&{}={}&\frac{403549}{533149}&{}+{}&\frac{21632108}{17593917} g_{25}&{}-{}&\frac{17852972}{17593917} g_{23}\\ g_{6}&{}={}&\frac{338749}{533149}&{}-{}&\frac{913224}{5864639} g_{25}&{}+{}&\frac{2802792}{5864639} g_{23}\\ g_{11}&{}={}&\frac{268549}{533149}&{}+{}&\frac{35730118}{52781751} g_{25}&{}-{}&\frac{12582910}{52781751} g_{23}\\ g_{9}&{}={}&\frac{381949}{533149}&{}+{}&\frac{110900212}{52781751} g_{25}&{}-{}&\frac{97673236}{52781751} g_{23}\\ g_{10}&{}={}&\frac{306349}{533149}&{}+{}&\frac{20262272}{17593917} g_{25}&{}-{}&\frac{13648784}{17593917} g_{23}\\ g_{1}&{}={}&\frac{338749}{533149}&{}-{}&\frac{49656784}{17593917} g_{25}&{}+{}&\frac{55325488}{17593917} g_{23}\\ g_{12}&{}={}&\frac{271249}{533149}&{}-{}&\frac{27149503}{17593917} g_{25}&{}+{}&\frac{34786507}{17593917} g_{23}\\ g_{13}&{}={}&\frac{226249}{533149}&{}-{}&\frac{1104059}{1599447} g_{25}&{}+{}&\frac{1917623}{1599447} g_{23}\\ g_{18}&{}={}&\frac{307997}{1599447}&{}+{}&\frac{107328128}{158345253} g_{25}&{}+{}&\frac{5647918}{158345253} g_{23}\\ g_{15}&{}={}&\frac{308549}{533149}&{}+{}&\frac{101280676}{52781751} g_{25}&{}-{}&\frac{81632668}{52781751} g_{23}\\ g_{14}&{}={}&\frac{196249}{533149}&{}-{}&\frac{2141413}{17593917} g_{25}&{}+{}&\frac{11965417}{17593917} g_{23}\\ g_{16}&{}={}&\frac{196249}{533149}&{}+{}&\frac{15452504}{17593917} g_{25}&{}-{}&\frac{5628500}{17593917} g_{23}\\ w_{3}&{}={}&\frac{742298}{533149}&{}-{}&\frac{353847422}{52781751} g_{25}&{}+{}&\frac{382190942}{52781751} g_{23}\\ g_{19}&{}={}&\frac{457340}{533149}&{}-{}&\frac{218010260}{52781751} g_{25}&{}+{}&\frac{255735281}{52781751} g_{23}\\ g_{20}&{}={}&\frac{267368}{533149}&{}-{}&\frac{127452152}{52781751} g_{25}&{}+{}&\frac{171431507}{52781751} g_{23}\\ g_{21}&{}={}&\frac{140720}{533149}&{}-{}&\frac{67080080}{52781751} g_{25}&{}+{}&\frac{115228991}{52781751} g_{23}\\ g_{22}&{}={}&\frac{56288}{533149}&{}-{}&\frac{26832032}{52781751} g_{25}&{}+{}&\frac{77760647}{52781751} g_{23}\\ w_{2}&{}={}&1&{}+{}&4 g_{25}&{}-{}&4 g_{23}\\ g_{24}&{}={}&\frac{1}{3}&{}+{}&2 g_{25}&{}-{}&\frac{4}{3} g_{23}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{10440764885}{105563502}&{}-{}&\frac{24343285}{105563502} g_{25}&{}-{}&\frac{12718685}{17593917} g_{26}\\\hline w_{1}&{}={}&\frac{1273309649}{105563502}&{}-{}&\frac{1098679457}{105563502} g_{25}&{}+{}&\frac{163432727}{17593917} g_{26}\\ x_{1}&{}={}&\frac{143512909}{105563502}&{}+{}&\frac{551774057}{105563502} g_{25}&{}-{}&\frac{80444495}{17593917} g_{26}\\ x_{2}&{}={}&\frac{504700447}{105563502}&{}-{}&\frac{734075857}{105563502} g_{25}&{}+{}&\frac{108107239}{17593917} g_{26}\\ w_{4}&{}={}&\frac{806558609}{105563502}&{}-{}&\frac{551774057}{105563502} g_{25}&{}+{}&\frac{80444495}{17593917} g_{26}\\ w_{5}&{}={}&\frac{128680565}{105563502}&{}+{}&\frac{734075857}{105563502} g_{25}&{}-{}&\frac{108107239}{17593917} g_{26}\\ g_{8}&{}={}&\frac{44383201}{70375668}&{}-{}&\frac{1161979}{70375668} g_{25}&{}+{}&\frac{3945133}{11729278} g_{26}\\ g_{2}&{}={}&\frac{82446439}{105563502}&{}+{}&\frac{4868657}{105563502} g_{25}&{}+{}&\frac{2543737}{17593917} g_{26}\\ g_{17}&{}={}&\frac{17741822}{52781751}&{}+{}&\frac{7279867}{52781751} g_{25}&{}+{}&\frac{7744042}{17593917} g_{26}\\ g_{3}&{}={}&\frac{82446439}{70375668}&{}-{}&\frac{241446181}{70375668} g_{25}&{}+{}&\frac{37731571}{11729278} g_{26}\\ g_{7}&{}={}&\frac{20696983}{35187834}&{}+{}&\frac{22960565}{35187834} g_{25}&{}-{}&\frac{1660451}{5864639} g_{26}\\ g_{4}&{}={}&\frac{23572387}{23458556}&{}-{}&\frac{53113745}{23458556} g_{25}&{}+{}&\frac{26002293}{11729278} g_{26}\\ g_{5}&{}={}&\frac{8853874}{17593917}&{}+{}&\frac{35021837}{17593917} g_{25}&{}-{}&\frac{8926486}{5864639} g_{26}\\ g_{6}&{}={}&\frac{4426937}{5864639}&{}-{}&\frac{3015318}{5864639} g_{25}&{}+{}&\frac{4204188}{5864639} g_{26}\\ g_{11}&{}={}&\frac{46881247}{105563502}&{}+{}&\frac{90334601}{105563502} g_{25}&{}-{}&\frac{6291455}{17593917} g_{26}\\ g_{9}&{}={}&\frac{13394642}{52781751}&{}+{}&\frac{184155139}{52781751} g_{25}&{}-{}&\frac{48836618}{17593917} g_{26}\\ g_{10}&{}={}&\frac{6697321}{17593917}&{}+{}&\frac{30498860}{17593917} g_{25}&{}-{}&\frac{6824392}{5864639} g_{26}\\ g_{1}&{}={}&\frac{25010089}{17593917}&{}-{}&\frac{91150900}{17593917} g_{25}&{}+{}&\frac{27662744}{5864639} g_{26}\\ g_{12}&{}={}&\frac{70591375}{70375668}&{}-{}&\frac{212957533}{70375668} g_{25}&{}+{}&\frac{34786507}{11729278} g_{26}\\ g_{13}&{}={}&\frac{4632611}{6397788}&{}-{}&\frac{10169105}{6397788} g_{25}&{}+{}&\frac{1917623}{1066298} g_{26}\\ g_{18}&{}={}&\frac{63807365}{316690506}&{}+{}&\frac{206184379}{316690506} g_{25}&{}+{}&\frac{2823959}{52781751} g_{26}\\ g_{15}&{}={}&\frac{10138184}{52781751}&{}+{}&\frac{162505177}{52781751} g_{25}&{}-{}&\frac{40816334}{17593917} g_{26}\\ g_{14}&{}={}&\frac{37870285}{70375668}&{}-{}&\frac{44461903}{70375668} g_{25}&{}+{}&\frac{11965417}{11729278} g_{26}\\ g_{16}&{}={}&\frac{5069092}{17593917}&{}+{}&\frac{19673879}{17593917} g_{25}&{}-{}&\frac{2814250}{5864639} g_{26}\\ w_{3}&{}={}&\frac{338070475}{105563502}&{}-{}&\frac{1280981257}{105563502} g_{25}&{}+{}&\frac{191095471}{17593917} g_{26}\\ g_{19}&{}={}&\frac{436841921}{211127004}&{}-{}&\frac{1639246883}{211127004} g_{25}&{}+{}&\frac{255735281}{35187834} g_{26}\\ g_{20}&{}={}&\frac{277309235}{211127004}&{}-{}&\frac{1024103129}{211127004} g_{25}&{}+{}&\frac{171431507}{35187834} g_{26}\\ g_{21}&{}={}&\frac{170954111}{211127004}&{}-{}&\frac{614007293}{211127004} g_{25}&{}+{}&\frac{115228991}{35187834} g_{26}\\ g_{22}&{}={}&\frac{100050695}{211127004}&{}-{}&\frac{340610069}{211127004} g_{25}&{}+{}&\frac{77760647}{35187834} g_{26}\\ w_{2}&{}={}&0&{}+{}&7 g_{25}&{}-{}&6 g_{26}\\ g_{24}&{}={}&0&{}+{}&3 g_{25}&{}-{}&2 g_{26}\\ g_{23}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{25}&{}+{}&\frac{3}{2} g_{26}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{423878399310}{4281821753}&{}-{}&\frac{3571283520}{4281821753} g_{27}&{}-{}&\frac{5980145}{389256523} w_{3}\\\hline w_{1}&{}={}&\frac{39882738449}{4281821753}&{}-{}&\frac{102036672}{4281821753} g_{27}&{}+{}&\frac{333477587}{389256523} w_{3}\\ x_{1}&{}={}&\frac{11741916324}{4281821753}&{}+{}&\frac{408146688}{4281821753} g_{27}&{}-{}&\frac{166140779}{389256523} w_{3}\\ x_{2}&{}={}&\frac{12602671522}{4281821753}&{}-{}&\frac{306110016}{4281821753} g_{27}&{}+{}&\frac{221919715}{389256523} w_{3}\\ w_{4}&{}={}&\frac{26794479453}{4281821753}&{}-{}&\frac{408146688}{4281821753} g_{27}&{}+{}&\frac{166140779}{389256523} w_{3}\\ w_{5}&{}={}&\frac{13088258996}{4281821753}&{}+{}&\frac{306110016}{4281821753} g_{27}&{}-{}&\frac{221919715}{389256523} w_{3}\\ g_{8}&{}={}&\frac{2724613208}{4281821753}&{}+{}&\frac{1235777472}{4281821753} g_{27}&{}+{}&\frac{10317315}{778513046} w_{3}\\ g_{2}&{}={}&\frac{3421066555}{4281821753}&{}+{}&\frac{714256704}{4281821753} g_{27}&{}+{}&\frac{1196029}{389256523} w_{3}\\ g_{17}&{}={}&\frac{1670308353}{4281821753}&{}+{}&\frac{2165908572}{4281821753} g_{27}&{}+{}&\frac{3688810}{389256523} w_{3}\\ g_{3}&{}={}&\frac{105341710}{389256523}&{}+{}&\frac{51018336}{389256523} g_{27}&{}+{}&\frac{224311773}{778513046} w_{3}\\ g_{7}&{}={}&\frac{3296010647}{4281821753}&{}+{}&\frac{1156415616}{4281821753} g_{27}&{}-{}&\frac{16599597}{389256523} w_{3}\\ g_{4}&{}={}&\frac{1769402192}{4281821753}&{}+{}&\frac{731262816}{4281821753} g_{27}&{}+{}&\frac{150737211}{778513046} w_{3}\\ g_{5}&{}={}&\frac{403527775}{389256523}&{}+{}&\frac{90699264}{389256523} g_{27}&{}-{}&\frac{60116106}{389256523} w_{3}\\ g_{6}&{}={}&\frac{2685367265}{4281821753}&{}+{}&\frac{986354496}{4281821753} g_{27}&{}+{}&\frac{20187684}{389256523} w_{3}\\ g_{11}&{}={}&\frac{265732817}{389256523}&{}+{}&\frac{142662384}{389256523} g_{27}&{}-{}&\frac{21572027}{389256523} w_{3}\\ g_{9}&{}={}&\frac{5075612869}{4281821753}&{}+{}&\frac{1334035008}{4281821753} g_{27}&{}-{}&\frac{106922738}{389256523} w_{3}\\ g_{10}&{}={}&\frac{3640578281}{4281821753}&{}+{}&\frac{1490869152}{4281821753} g_{27}&{}-{}&\frac{50022264}{389256523} w_{3}\\ g_{1}&{}={}&\frac{242793737}{4281821753}&{}+{}&\frac{306110016}{4281821753} g_{27}&{}+{}&\frac{167336808}{389256523} w_{3}\\ g_{12}&{}={}&\frac{909756026}{4281821753}&{}+{}&\frac{988716456}{4281821753} g_{27}&{}+{}&\frac{201543717}{778513046} w_{3}\\ g_{13}&{}={}&\frac{1354397552}{4281821753}&{}+{}&\frac{1443787416}{4281821753} g_{27}&{}+{}&\frac{112790451}{778513046} w_{3}\\ g_{18}&{}={}&\frac{5049891293}{12845465259}&{}+{}&\frac{2445068916}{4281821753} g_{27}&{}-{}&\frac{35177557}{1167769569} w_{3}\\ g_{15}&{}={}&\frac{4359754221}{4281821753}&{}+{}&\frac{1674962064}{4281821753} g_{27}&{}-{}&\frac{92487974}{389256523} w_{3}\\ g_{14}&{}={}&\frac{1650825236}{4281821753}&{}+{}&\frac{1747168056}{4281821753} g_{27}&{}+{}&\frac{53621607}{778513046} w_{3}\\ g_{16}&{}={}&\frac{2566790309}{4281821753}&{}+{}&\frac{2002259736}{4281821753} g_{27}&{}-{}&\frac{28370118}{389256523} w_{3}\\ g_{26}&{}={}&\frac{133384916}{4281821753}&{}+{}&\frac{3842943771}{4281821753} g_{27}&{}+{}&\frac{14395023}{389256523} w_{3}\\ g_{19}&{}={}&\frac{128011590}{4281821753}&{}+{}&\frac{1222534458}{4281821753} g_{27}&{}+{}&\frac{507282845}{778513046} w_{3}\\ g_{20}&{}={}&\frac{213352650}{4281821753}&{}+{}&\frac{2037557430}{4281821753} g_{27}&{}+{}&\frac{326462711}{778513046} w_{3}\\ g_{21}&{}={}&\frac{270246690}{4281821753}&{}+{}&\frac{2580906078}{4281821753} g_{27}&{}+{}&\frac{205915955}{778513046} w_{3}\\ g_{22}&{}={}&\frac{308176050}{4281821753}&{}+{}&\frac{2943138510}{4281821753} g_{27}&{}+{}&\frac{125551451}{778513046} w_{3}\\ w_{2}&{}={}&\frac{7945682045}{4281821753}&{}+{}&\frac{1020366720}{4281821753} g_{27}&{}-{}&\frac{220723686}{389256523} w_{3}\\ g_{24}&{}={}&\frac{3481512257}{4281821753}&{}+{}&\frac{2633267892}{4281821753} g_{27}&{}-{}&\frac{86370138}{389256523} w_{3}\\ g_{23}&{}={}&\frac{333462290}{4281821753}&{}+{}&\frac{3184626798}{4281821753} g_{27}&{}+{}&\frac{71975115}{778513046} w_{3}\\ g_{25}&{}={}&\frac{1249427363}{4281821753}&{}+{}&\frac{3439718478}{4281821753} g_{27}&{}-{}&\frac{19193364}{389256523} w_{3}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{1695579378835}{17127287012}&{}-{}&\frac{14087789295}{17127287012} g_{27}&{}-{}&\frac{17940435}{778513046} g_{28}\\\hline w_{1}&{}={}&\frac{163199207253}{17127287012}&{}-{}&\frac{11412907059}{17127287012} g_{27}&{}+{}&\frac{1000432761}{778513046} g_{28}\\ x_{1}&{}={}&\frac{45140116727}{17127287012}&{}+{}&\frac{7115232459}{17127287012} g_{27}&{}-{}&\frac{498422337}{778513046} g_{28}\\ x_{2}&{}={}&\frac{52851802953}{17127287012}&{}-{}&\frac{8547790659}{17127287012} g_{27}&{}+{}&\frac{665759145}{778513046} g_{28}\\ w_{4}&{}={}&\frac{109005466381}{17127287012}&{}-{}&\frac{7115232459}{17127287012} g_{27}&{}+{}&\frac{498422337}{778513046} g_{28}\\ w_{5}&{}={}&\frac{49911919119}{17127287012}&{}+{}&\frac{8547790659}{17127287012} g_{27}&{}-{}&\frac{665759145}{778513046} g_{28}\\ g_{8}&{}={}&\frac{21910396129}{34254574024}&{}+{}&\frac{9545748381}{34254574024} g_{27}&{}+{}&\frac{30951945}{1557026092} g_{28}\\ g_{2}&{}={}&\frac{13697422539}{17127287012}&{}+{}&\frac{2817557859}{17127287012} g_{27}&{}+{}&\frac{3588087}{778513046} g_{28}\\ g_{17}&{}={}&\frac{3360905161}{8563643506}&{}+{}&\frac{4270951779}{8563643506} g_{27}&{}+{}&\frac{5533215}{389256523} g_{28}\\ g_{3}&{}={}&\frac{1067045453}{3114052184}&{}-{}&\frac{264788631}{3114052184} g_{27}&{}+{}&\frac{672935319}{1557026092} g_{28}\\ g_{7}&{}={}&\frac{13001447021}{17127287012}&{}+{}&\frac{5173449165}{17127287012} g_{27}&{}-{}&\frac{49798791}{778513046} g_{28}\\ g_{4}&{}={}&\frac{15813326857}{34254574024}&{}+{}&\frac{875774565}{34254574024} g_{27}&{}+{}&\frac{452211633}{1557026092} g_{28}\\ g_{5}&{}={}&\frac{776997497}{778513046}&{}+{}&\frac{271572687}{778513046} g_{27}&{}-{}&\frac{90174159}{389256523} g_{28}\\ g_{6}&{}={}&\frac{2740883396}{4281821753}&{}+{}&\frac{819806103}{4281821753} g_{27}&{}+{}&\frac{30281526}{389256523} g_{28}\\ g_{11}&{}={}&\frac{1041359241}{1557026092}&{}+{}&\frac{635365617}{1557026092} g_{27}&{}-{}&\frac{64716081}{778513046} g_{28}\\ g_{9}&{}={}&\frac{9563150679}{8563643506}&{}+{}&\frac{4432295193}{8563643506} g_{27}&{}-{}&\frac{160384107}{389256523} g_{28}\\ g_{10}&{}={}&\frac{3503017055}{4281821753}&{}+{}&\frac{1903552830}{4281821753} g_{27}&{}-{}&\frac{75033396}{389256523} g_{28}\\ g_{1}&{}={}&\frac{702969959}{4281821753}&{}-{}&\frac{1074418650}{4281821753} g_{27}&{}+{}&\frac{251005212}{389256523} g_{28}\\ g_{12}&{}={}&\frac{9495029095}{34254574024}&{}+{}&\frac{1258788987}{34254574024} g_{27}&{}+{}&\frac{604631151}{1557026092} g_{28}\\ g_{13}&{}={}&\frac{12075875377}{34254574024}&{}+{}&\frac{7828214445}{34254574024} g_{27}&{}+{}&\frac{338371353}{1557026092} g_{28}\\ g_{18}&{}={}&\frac{6604204015}{17127287012}&{}+{}&\frac{10167228791}{17127287012} g_{27}&{}-{}&\frac{35177557}{778513046} g_{28}\\ g_{15}&{}={}&\frac{8210824585}{8563643506}&{}+{}&\frac{4875975699}{8563643506} g_{27}&{}-{}&\frac{138731961}{389256523} g_{28}\\ g_{14}&{}={}&\frac{13796439565}{34254574024}&{}+{}&\frac{12207831417}{34254574024} g_{27}&{}+{}&\frac{160864821}{1557026092} g_{28}\\ g_{16}&{}={}&\frac{4977544969}{8563643506}&{}+{}&\frac{4472626419}{8563643506} g_{27}&{}-{}&\frac{42555177}{389256523} g_{28}\\ g_{26}&{}={}&\frac{691884917}{17127287012}&{}+{}&\frac{14896739325}{17127287012} g_{27}&{}+{}&\frac{43185069}{778513046} g_{28}\\ g_{19}&{}={}&\frac{6604204015}{34254574024}&{}-{}&\frac{6960058221}{34254574024} g_{27}&{}+{}&\frac{1521848535}{1557026092} g_{28}\\ g_{20}&{}={}&\frac{5297911021}{34254574024}&{}+{}&\frac{5527189977}{34254574024} g_{27}&{}+{}&\frac{979388133}{1557026092} g_{28}\\ g_{21}&{}={}&\frac{4427049025}{34254574024}&{}+{}&\frac{13852022109}{34254574024} g_{27}&{}+{}&\frac{617747865}{1557026092} g_{28}\\ g_{22}&{}={}&\frac{3846474361}{34254574024}&{}+{}&\frac{19401910197}{34254574024} g_{27}&{}+{}&\frac{376654353}{1557026092} g_{28}\\ w_{2}&{}={}&\frac{14677383817}{8563643506}&{}+{}&\frac{5682674259}{8563643506} g_{27}&{}-{}&\frac{331085529}{389256523} g_{28}\\ g_{24}&{}={}&\frac{6487988755}{8563643506}&{}+{}&\frac{6691643061}{8563643506} g_{27}&{}-{}&\frac{129555207}{389256523} g_{28}\\ g_{23}&{}={}&\frac{3459424585}{34254574024}&{}+{}&\frac{23101835589}{34254574024} g_{27}&{}+{}&\frac{215925345}{1557026092} g_{28}\\ g_{25}&{}={}&\frac{1196645612}{4281821753}&{}+{}&\frac{3598063731}{4281821753} g_{27}&{}-{}&\frac{28790046}{389256523} g_{28}\\ w_{3}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{27}&{}+{}&\frac{3}{2} g_{28}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{3391356102455}{34254574024}&{}-{}&\frac{27583544235}{34254574024} g_{27}&{}-{}&\frac{53821305}{1557026092} g_{29}\\\hline w_{1}&{}={}&\frac{337403174877}{34254574024}&{}-{}&\frac{55840095231}{34254574024} g_{27}&{}+{}&\frac{3001298283}{1557026092} g_{29}\\ x_{1}&{}={}&\frac{84797587747}{34254574024}&{}+{}&\frac{30678402039}{34254574024} g_{27}&{}-{}&\frac{1495267011}{1557026092} g_{29}\\ x_{2}&{}={}&\frac{113026956501}{34254574024}&{}-{}&\frac{39065633103}{34254574024} g_{27}&{}+{}&\frac{1997277435}{1557026092} g_{29}\\ w_{4}&{}={}&\frac{223493578469}{34254574024}&{}-{}&\frac{30678402039}{34254574024} g_{27}&{}+{}&\frac{1495267011}{1557026092} g_{29}\\ w_{5}&{}={}&\frac{92500487643}{34254574024}&{}+{}&\frac{39065633103}{34254574024} g_{27}&{}-{}&\frac{1997277435}{1557026092} g_{29}\\ g_{8}&{}={}&\frac{44161263653}{68509148048}&{}+{}&\frac{18070082577}{68509148048} g_{27}&{}+{}&\frac{92855835}{3114052184} g_{29}\\ g_{2}&{}={}&\frac{27434314035}{34254574024}&{}+{}&\frac{5516708847}{34254574024} g_{27}&{}+{}&\frac{10764261}{1557026092} g_{29}\\ g_{17}&{}={}&\frac{6782675687}{17127287012}&{}+{}&\frac{8359307463}{17127287012} g_{27}&{}+{}&\frac{16599645}{778513046} g_{29}\\ g_{3}&{}={}&\frac{2807026225}{6228104368}&{}-{}&\frac{2548383219}{6228104368} g_{27}&{}+{}&\frac{2018805957}{3114052184} g_{29}\\ g_{7}&{}={}&\frac{25455107341}{34254574024}&{}+{}&\frac{11990258433}{34254574024} g_{27}&{}-{}&\frac{149396373}{1557026092} g_{29}\\ g_{4}&{}={}&\frac{36600981677}{68509148048}&{}-{}&\frac{13171434759}{68509148048} g_{27}&{}+{}&\frac{1356634899}{3114052184} g_{29}\\ g_{5}&{}={}&\frac{1463820835}{1557026092}&{}+{}&\frac{813667851}{1557026092} g_{27}&{}-{}&\frac{270522477}{778513046} g_{29}\\ g_{6}&{}={}&\frac{5648315185}{8563643506}&{}+{}&\frac{1139967027}{8563643506} g_{27}&{}+{}&\frac{45422289}{389256523} g_{29}\\ g_{11}&{}={}&\frac{2018002401}{3114052184}&{}+{}&\frac{1464879477}{3114052184} g_{27}&{}-{}&\frac{194148243}{1557026092} g_{29}\\ g_{9}&{}={}&\frac{17362076181}{17127287012}&{}+{}&\frac{14157265917}{17127287012} g_{27}&{}-{}&\frac{481152321}{778513046} g_{29}\\ g_{10}&{}={}&\frac{3296675216}{4281821753}&{}+{}&\frac{2522578347}{4281821753} g_{27}&{}-{}&\frac{112550094}{389256523} g_{29}\\ g_{1}&{}={}&\frac{1393234292}{4281821753}&{}-{}&\frac{3145211649}{4281821753} g_{27}&{}+{}&\frac{376507818}{389256523} g_{29}\\ g_{12}&{}={}&\frac{25641000851}{68509148048}&{}-{}&\frac{17435250009}{68509148048} g_{27}&{}+{}&\frac{1813893453}{3114052184} g_{29}\\ g_{13}&{}={}&\frac{27873835637}{68509148048}&{}+{}&\frac{4490174241}{68509148048} g_{27}&{}+{}&\frac{1015114059}{3114052184} g_{29}\\ g_{18}&{}={}&\frac{12821454903}{34254574024}&{}+{}&\frac{21495316963}{34254574024} g_{27}&{}-{}&\frac{105532671}{1557026092} g_{29}\\ g_{15}&{}={}&\frac{14895597599}{17127287012}&{}+{}&\frac{14330106111}{17127287012} g_{27}&{}-{}&\frac{416195883}{778513046} g_{29}\\ g_{14}&{}={}&\frac{29362392161}{68509148048}&{}+{}&\frac{19107123741}{68509148048} g_{27}&{}+{}&\frac{482594463}{3114052184} g_{29}\\ g_{16}&{}={}&\frac{9486982991}{17127287012}&{}+{}&\frac{10349573679}{17127287012} g_{27}&{}-{}&\frac{127665531}{778513046} g_{29}\\ g_{26}&{}={}&\frac{1858805593}{34254574024}&{}+{}&\frac{28368371373}{34254574024} g_{27}&{}+{}&\frac{129555207}{1557026092} g_{29}\\ g_{19}&{}={}&\frac{29948741915}{68509148048}&{}-{}&\frac{64141118097}{68509148048} g_{27}&{}+{}&\frac{4565545605}{3114052184} g_{29}\\ g_{20}&{}={}&\frac{21369091505}{68509148048}&{}-{}&\frac{21265428435}{68509148048} g_{27}&{}+{}&\frac{2938164399}{3114052184} g_{29}\\ g_{21}&{}={}&\frac{15649324565}{68509148048}&{}+{}&\frac{7318364673}{68509148048} g_{27}&{}+{}&\frac{1853243595}{3114052184} g_{29}\\ g_{22}&{}={}&\frac{11836146605}{68509148048}&{}+{}&\frac{26374226745}{68509148048} g_{27}&{}+{}&\frac{1129963059}{3114052184} g_{29}\\ w_{2}&{}={}&\frac{25712826815}{17127287012}&{}+{}&\frac{22291170975}{17127287012} g_{27}&{}-{}&\frac{993256587}{778513046} g_{29}\\ g_{24}&{}={}&\frac{11550870233}{17127287012}&{}+{}&\frac{17658607953}{17127287012} g_{27}&{}-{}&\frac{388665621}{778513046} g_{29}\\ g_{23}&{}={}&\frac{9294027965}{68509148048}&{}+{}&\frac{39078134793}{68509148048} g_{27}&{}+{}&\frac{647776035}{3114052184} g_{29}\\ g_{25}&{}={}&\frac{2234945971}{8563643506}&{}+{}&\frac{7671163221}{8563643506} g_{27}&{}-{}&\frac{43185069}{389256523} g_{29}\\ w_{3}&{}={}&\frac{5}{8}&{}-{}&\frac{15}{8} g_{27}&{}+{}&\frac{9}{4} g_{29}\\ g_{28}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{27}&{}+{}&\frac{3}{2} g_{29}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{6783304239265}{68509148048}&{}-{}&\frac{53390985405}{68509148048} g_{27}&{}-{}&\frac{161463915}{3114052184} g_{30}\\\hline w_{1}&{}={}&\frac{707820630867}{68509148048}&{}-{}&\frac{210723033801}{68509148048} g_{27}&{}+{}&\frac{9003894849}{3114052184} g_{30}\\ x_{1}&{}={}&\frac{153147238373}{68509148048}&{}+{}&\frac{110700615441}{68509148048} g_{27}&{}-{}&\frac{4485801033}{3114052184} g_{30}\\ x_{2}&{}={}&\frac{248023964787}{68509148048}&{}-{}&\frac{144041421561}{68509148048} g_{27}&{}+{}&\frac{5991832305}{3114052184} g_{30}\\ w_{4}&{}={}&\frac{463435094059}{68509148048}&{}-{}&\frac{110700615441}{68509148048} g_{27}&{}+{}&\frac{4485801033}{3114052184} g_{30}\\ w_{5}&{}={}&\frac{163030923501}{68509148048}&{}+{}&\frac{144041421561}{68509148048} g_{27}&{}-{}&\frac{5991832305}{3114052184} g_{30}\\ g_{8}&{}={}&\frac{89343941491}{137018296096}&{}+{}&\frac{33075922599}{137018296096} g_{27}&{}+{}&\frac{278567505}{6228104368} g_{30}\\ g_{2}&{}={}&\frac{54987034941}{68509148048}&{}+{}&\frac{10678197081}{68509148048} g_{27}&{}+{}&\frac{32292783}{3114052184} g_{30}\\ g_{17}&{}={}&\frac{13747947469}{34254574024}&{}+{}&\frac{16170826641}{34254574024} g_{27}&{}+{}&\frac{49798935}{1557026092} g_{30}\\ g_{3}&{}={}&\frac{7632858407}{12456208736}&{}-{}&\frac{11153184309}{12456208736} g_{27}&{}+{}&\frac{6056417871}{6228104368} g_{30}\\ g_{7}&{}={}&\frac{49266854579}{68509148048}&{}+{}&\frac{28910597175}{68509148048} g_{27}&{}-{}&\frac{448189119}{3114052184} g_{30}\\ g_{4}&{}={}&\frac{88124947243}{137018296096}&{}-{}&\frac{71111821185}{137018296096} g_{27}&{}+{}&\frac{4069904697}{6228104368} g_{30}\\ g_{5}&{}={}&\frac{2657119193}{3114052184}&{}+{}&\frac{2438903133}{3114052184} g_{27}&{}-{}&\frac{811567431}{1557026092} g_{30}\\ g_{6}&{}={}&\frac{11796275549}{17127287012}&{}+{}&\frac{780998517}{17127287012} g_{27}&{}+{}&\frac{136266867}{778513046} g_{30}\\ g_{11}&{}={}&\frac{3841856559}{6228104368}&{}+{}&\frac{3512203683}{6228104368} g_{27}&{}-{}&\frac{582444729}{3114052184} g_{30}\\ g_{9}&{}={}&\frac{29431476831}{34254574024}&{}+{}&\frac{44192558427}{34254574024} g_{27}&{}-{}&\frac{1443456963}{1557026092} g_{30}\\ g_{10}&{}={}&\frac{5974324915}{8563643506}&{}+{}&\frac{6902233245}{8563643506} g_{27}&{}-{}&\frac{168825141}{389256523} g_{30}\\ g_{1}&{}={}&\frac{4857261583}{8563643506}&{}-{}&\frac{12502802295}{8563643506} g_{27}&{}+{}&\frac{564761727}{389256523} g_{30}\\ g_{12}&{}={}&\frac{71234829685}{137018296096}&{}-{}&\frac{94728983967}{137018296096} g_{27}&{}+{}&\frac{5441680359}{6228104368} g_{30}\\ g_{13}&{}={}&\frac{66913925923}{137018296096}&{}-{}&\frac{24518415465}{137018296096} g_{27}&{}+{}&\frac{3045342177}{6228104368} g_{30}\\ g_{18}&{}={}&\frac{24482050425}{68509148048}&{}+{}&\frac{46473212069}{68509148048} g_{27}&{}-{}&\frac{316598013}{3114052184} g_{30}\\ g_{15}&{}={}&\frac{25213040485}{34254574024}&{}+{}&\frac{42394676361}{34254574024} g_{27}&{}-{}&\frac{1248587649}{1557026092} g_{30}\\ g_{14}&{}={}&\frac{64033323415}{137018296096}&{}+{}&\frac{22288630203}{137018296096} g_{27}&{}+{}&\frac{1447783389}{6228104368} g_{30}\\ g_{16}&{}={}&\frac{17569645141}{34254574024}&{}+{}&\frac{24912109881}{34254574024} g_{27}&{}-{}&\frac{382996593}{1557026092} g_{30}\\ g_{26}&{}={}&\frac{5142718463}{68509148048}&{}+{}&\frac{52461420915}{68509148048} g_{27}&{}+{}&\frac{388665621}{3114052184} g_{30}\\ g_{19}&{}={}&\frac{110118485485}{137018296096}&{}-{}&\frac{278945241159}{137018296096} g_{27}&{}+{}&\frac{13696636815}{6228104368} g_{30}\\ g_{20}&{}={}&\frac{75057991399}{137018296096}&{}-{}&\frac{139490282037}{137018296096} g_{27}&{}+{}&\frac{8814493197}{6228104368} g_{30}\\ g_{21}&{}={}&\frac{51684328675}{137018296096}&{}-{}&\frac{46520309289}{137018296096} g_{27}&{}+{}&\frac{5559730785}{6228104368} g_{30}\\ g_{22}&{}={}&\frac{36101886859}{137018296096}&{}+{}&\frac{15459672543}{137018296096} g_{27}&{}+{}&\frac{3389889177}{6228104368} g_{30}\\ w_{2}&{}={}&\frac{40499831173}{34254574024}&{}+{}&\frac{77359809321}{34254574024} g_{27}&{}-{}&\frac{2979769761}{1557026092} g_{30}\\ g_{24}&{}={}&\frac{18826418635}{34254574024}&{}+{}&\frac{48143181399}{34254574024} g_{27}&{}-{}&\frac{1165996863}{1557026092} g_{30}\\ g_{23}&{}={}&\frac{25713592315}{137018296096}&{}+{}&\frac{56779660431}{137018296096} g_{27}&{}+{}&\frac{1943328105}{6228104368} g_{30}\\ g_{25}&{}={}&\frac{3994856183}{17127287012}&{}+{}&\frac{16767433719}{17127287012} g_{27}&{}-{}&\frac{129555207}{778513046} g_{30}\\ w_{3}&{}={}&\frac{19}{16}&{}-{}&\frac{57}{16} g_{27}&{}+{}&\frac{27}{8} g_{30}\\ g_{28}&{}={}&\frac{5}{8}&{}-{}&\frac{15}{8} g_{27}&{}+{}&\frac{9}{4} g_{30}\\ g_{29}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{27}&{}+{}&\frac{3}{2} g_{30}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{13568384581595}{137018296096}&{}-{}&\frac{101453661615}{137018296096} g_{27}&{}-{}&\frac{484391745}{6228104368} g_{31}\\\hline w_{1}&{}={}&\frac{1514684105073}{137018296096}&{}-{}&\frac{718574597619}{137018296096} g_{27}&{}+{}&\frac{27011684547}{6228104368} g_{31}\\ x_{1}&{}={}&\frac{256950665383}{137018296096}&{}+{}&\frac{369432664971}{137018296096} g_{27}&{}-{}&\frac{13457403099}{6228104368} g_{31}\\ x_{2}&{}={}&\frac{561958084929}{137018296096}&{}-{}&\frac{485813309187}{137018296096} g_{27}&{}+{}&\frac{17975496915}{6228104368} g_{31}\\ w_{4}&{}={}&\frac{976213999481}{137018296096}&{}-{}&\frac{369432664971}{137018296096} g_{27}&{}+{}&\frac{13457403099}{6228104368} g_{31}\\ w_{5}&{}={}&\frac{260151691647}{137018296096}&{}+{}&\frac{485813309187}{137018296096} g_{27}&{}-{}&\frac{17975496915}{6228104368} g_{31}\\ g_{8}&{}={}&\frac{181752125537}{274036592192}&{}+{}&\frac{56959117533}{274036592192} g_{27}&{}+{}&\frac{835702515}{12456208736} g_{31}\\ g_{2}&{}={}&\frac{110329290495}{137018296096}&{}+{}&\frac{20290732323}{137018296096} g_{27}&{}+{}&\frac{96878349}{6228104368} g_{31}\\ g_{17}&{}={}&\frac{28043683223}{68509148048}&{}+{}&\frac{30698288427}{68509148048} g_{27}&{}+{}&\frac{149396805}{3114052184} g_{31}\\ g_{3}&{}={}&\frac{21322134685}{24912417472}&{}-{}&\frac{40475622231}{24912417472} g_{27}&{}+{}&\frac{18169253613}{12456208736} g_{31}\\ g_{7}&{}={}&\frac{93603628849}{137018296096}&{}+{}&\frac{72611435277}{137018296096} g_{27}&{}-{}&\frac{1344567357}{6228104368} g_{31}\\ g_{4}&{}={}&\frac{221018846153}{274036592192}&{}-{}&\frac{276530497371}{274036592192} g_{27}&{}+{}&\frac{12209714091}{12456208736} g_{31}\\ g_{5}&{}={}&\frac{4502670955}{6228104368}&{}+{}&\frac{7312508559}{6228104368} g_{27}&{}-{}&\frac{2434702293}{3114052184} g_{31}\\ g_{6}&{}={}&\frac{25091486635}{34254574024}&{}-{}&\frac{2934809577}{34254574024} g_{27}&{}+{}&\frac{408800601}{1557026092} g_{31}\\ g_{11}&{}={}&\frac{7101268389}{12456208736}&{}+{}&\frac{8771741553}{12456208736} g_{27}&{}-{}&\frac{1747334187}{6228104368} g_{31}\\ g_{9}&{}={}&\frac{42984927069}{68509148048}&{}+{}&\frac{136019196633}{68509148048} g_{27}&{}-{}&\frac{4330370889}{3114052184} g_{31}\\ g_{10}&{}={}&\frac{10091573279}{17127287012}&{}+{}&\frac{19375696143}{17127287012} g_{27}&{}-{}&\frac{506475423}{778513046} g_{31}\\ g_{1}&{}={}&\frac{15926902163}{17127287012}&{}-{}&\frac{43642741581}{17127287012} g_{27}&{}+{}&\frac{1694285181}{778513046} g_{31}\\ g_{12}&{}={}&\frac{202328143319}{274036592192}&{}-{}&\frac{369033419781}{274036592192} g_{27}&{}+{}&\frac{16325041077}{12456208736} g_{31}\\ g_{13}&{}={}&\frac{167326615793}{274036592192}&{}-{}&\frac{149533122771}{274036592192} g_{27}&{}+{}&\frac{9136026531}{12456208736} g_{31}\\ g_{18}&{}={}&\frac{45481522707}{137018296096}&{}+{}&\frac{103394158567}{137018296096} g_{27}&{}-{}&\frac{949794039}{6228104368} g_{31}\\ g_{15}&{}={}&\frac{36691616831}{68509148048}&{}+{}&\frac{125992745139}{68509148048} g_{27}&{}-{}&\frac{3745762947}{3114052184} g_{31}\\ g_{14}&{}={}&\frac{143992264109}{274036592192}&{}-{}&\frac{3199591431}{274036592192} g_{27}&{}+{}&\frac{4343350167}{12456208736} g_{31}\\ g_{16}&{}={}&\frac{30926327759}{68509148048}&{}+{}&\frac{62463107331}{68509148048} g_{27}&{}-{}&\frac{1148989779}{3114052184} g_{31}\\ g_{26}&{}={}&\frac{14560758757}{137018296096}&{}+{}&\frac{92096876337}{137018296096} g_{27}&{}+{}&\frac{1165996863}{6228104368} g_{31}\\ g_{19}&{}={}&\frac{370899975935}{274036592192}&{}-{}&\frac{1009879497213}{274036592192} g_{27}&{}+{}&\frac{41089910445}{12456208736} g_{31}\\ g_{20}&{}={}&\frac{247075407965}{274036592192}&{}-{}&\frac{569858839575}{274036592192} g_{27}&{}+{}&\frac{26443479591}{12456208736} g_{31}\\ g_{21}&{}={}&\frac{164525695985}{274036592192}&{}-{}&\frac{276511734483}{274036592192} g_{27}&{}+{}&\frac{16679192355}{12456208736} g_{31}\\ g_{22}&{}={}&\frac{109492554665}{274036592192}&{}-{}&\frac{80946997755}{274036592192} g_{27}&{}+{}&\frac{10169667531}{12456208736} g_{31}\\ w_{2}&{}={}&\frac{48222194975}{68509148048}&{}+{}&\frac{253052020755}{68509148048} g_{27}&{}-{}&\frac{8939309283}{3114052184} g_{31}\\ g_{24}&{}={}&\frac{24826871777}{68509148048}&{}+{}&\frac{134764259277}{68509148048} g_{27}&{}-{}&\frac{3497990589}{3114052184} g_{31}\\ g_{23}&{}={}&\frac{72803793785}{274036592192}&{}+{}&\frac{49429493397}{274036592192} g_{27}&{}+{}&\frac{5829984315}{12456208736} g_{31}\\ g_{25}&{}={}&\frac{6564605089}{34254574024}&{}+{}&\frac{37810189269}{34254574024} g_{27}&{}-{}&\frac{388665621}{1557026092} g_{31}\\ w_{3}&{}={}&\frac{65}{32}&{}-{}&\frac{195}{32} g_{27}&{}+{}&\frac{81}{16} g_{31}\\ g_{28}&{}={}&\frac{19}{16}&{}-{}&\frac{57}{16} g_{27}&{}+{}&\frac{27}{8} g_{31}\\ g_{29}&{}={}&\frac{5}{8}&{}-{}&\frac{15}{8} g_{27}&{}+{}&\frac{9}{4} g_{31}\\ g_{30}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{27}&{}+{}&\frac{3}{2} g_{31}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{52897853025625}{534067498566}&{}-{}&\frac{62307465215}{534067498566} w_{2}&{}-{}&\frac{18366600960}{29670416587} g_{32}\\\hline w_{1}&{}={}&\frac{6472284999685}{534067498566}&{}-{}&\frac{776178261763}{534067498566} w_{2}&{}+{}&\frac{7346640384}{29670416587} g_{32}\\ x_{1}&{}={}&\frac{718474056305}{534067498566}&{}+{}&\frac{394319877403}{534067498566} w_{2}&{}-{}&\frac{1836660096}{29670416587} g_{32}\\ x_{2}&{}={}&\frac{2568558126635}{534067498566}&{}-{}&\frac{521606005523}{534067498566} w_{2}&{}+{}&\frac{3673320192}{29670416587} g_{32}\\ w_{4}&{}={}&\frac{4088133430789}{534067498566}&{}-{}&\frac{394319877403}{534067498566} w_{2}&{}+{}&\frac{1836660096}{29670416587} g_{32}\\ w_{5}&{}={}&\frac{635846864761}{534067498566}&{}+{}&\frac{521606005523}{534067498566} w_{2}&{}-{}&\frac{3673320192}{29670416587} g_{32}\\ g_{8}&{}={}&\frac{34606782083}{50863571292}&{}+{}&\frac{1370477017}{50863571292} w_{2}&{}+{}&\frac{918330048}{4238630941} g_{32}\\ g_{2}&{}={}&\frac{432288132371}{534067498566}&{}+{}&\frac{12461493043}{534067498566} w_{2}&{}+{}&\frac{3673320192}{29670416587} g_{32}\\ g_{17}&{}={}&\frac{16110038416}{38147678469}&{}+{}&\frac{2688880109}{38147678469} w_{2}&{}+{}&\frac{1591488648}{4238630941} g_{32}\\ g_{3}&{}={}&\frac{432288132371}{356044999044}&{}-{}&\frac{165561006479}{356044999044} w_{2}&{}+{}&\frac{5509980288}{29670416587} g_{32}\\ g_{7}&{}={}&\frac{112297608131}{178022499522}&{}+{}&\frac{21065954815}{178022499522} w_{2}&{}+{}&\frac{5509980288}{29670416587} g_{32}\\ g_{4}&{}={}&\frac{124315766399}{118681666348}&{}-{}&\frac{35406724435}{118681666348} w_{2}&{}+{}&\frac{5509980288}{29670416587} g_{32}\\ g_{5}&{}={}&\frac{47322674906}{89011249761}&{}+{}&\frac{26802262663}{89011249761} w_{2}&{}+{}&\frac{3673320192}{29670416587} g_{32}\\ g_{6}&{}={}&\frac{23661337453}{29670416587}&{}-{}&\frac{1434076962}{29670416587} w_{2}&{}+{}&\frac{5509980288}{29670416587} g_{32}\\ g_{11}&{}={}&\frac{38309056205}{76295356938}&{}+{}&\frac{11935254397}{76295356938} w_{2}&{}+{}&\frac{1071385056}{4238630941} g_{32}\\ g_{9}&{}={}&\frac{10945444630}{38147678469}&{}+{}&\frac{19759077743}{38147678469} w_{2}&{}+{}&\frac{612220032}{4238630941} g_{32}\\ g_{10}&{}={}&\frac{5472722315}{12715892823}&{}+{}&\frac{3521592460}{12715892823} w_{2}&{}+{}&\frac{918330048}{4238630941} g_{32}\\ g_{1}&{}={}&\frac{130324845533}{89011249761}&{}-{}&\frac{63643064060}{89011249761} w_{2}&{}+{}&\frac{5509980288}{29670416587} g_{32}\\ g_{12}&{}={}&\frac{377579886059}{356044999044}&{}-{}&\frac{141865910567}{356044999044} w_{2}&{}+{}&\frac{7423167888}{29670416587} g_{32}\\ g_{13}&{}={}&\frac{281766888677}{356044999044}&{}-{}&\frac{66728346785}{356044999044} w_{2}&{}+{}&\frac{8698626288}{29670416587} g_{32}\\ g_{18}&{}={}&\frac{474028017853}{1602202495698}&{}+{}&\frac{238131520421}{1602202495698} w_{2}&{}+{}&\frac{12201412968}{29670416587} g_{32}\\ g_{15}&{}={}&\frac{64440153664}{267033749283}&{}+{}&\frac{125198555843}{267033749283} w_{2}&{}+{}&\frac{6365954592}{29670416587} g_{32}\\ g_{14}&{}={}&\frac{217891557089}{356044999044}&{}-{}&\frac{16636637597}{356044999044} w_{2}&{}+{}&\frac{9548931888}{29670416587} g_{32}\\ g_{16}&{}={}&\frac{32220076832}{89011249761}&{}+{}&\frac{18093653041}{89011249761} w_{2}&{}+{}&\frac{9548931888}{29670416587} g_{32}\\ g_{26}&{}={}&\frac{11774337983}{76295356938}&{}+{}&\frac{6938850295}{76295356938} w_{2}&{}+{}&\frac{2850214554}{4238630941} g_{32}\\ g_{19}&{}={}&\frac{2311059778609}{1068134997132}&{}-{}&\frac{1125242013037}{1068134997132} w_{2}&{}+{}&\frac{12222906804}{29670416587} g_{32}\\ g_{20}&{}={}&\frac{217241908405}{152590713876}&{}-{}&\frac{95826309793}{152590713876} w_{2}&{}+{}&\frac{2035615860}{4238630941} g_{32}\\ g_{21}&{}={}&\frac{993782412319}{1068134997132}&{}-{}&\frac{367812272227}{1068134997132} w_{2}&{}+{}&\frac{15600247164}{29670416587} g_{32}\\ g_{22}&{}={}&\frac{642508447975}{1068134997132}&{}-{}&\frac{165831008011}{1068134997132} w_{2}&{}+{}&\frac{16500871260}{29670416587} g_{32}\\ g_{27}&{}={}&\frac{1888012163}{801101247849}&{}+{}&\frac{137018296096}{801101247849} w_{2}&{}+{}&\frac{21851644914}{29670416587} g_{32}\\ g_{24}&{}={}&\frac{23548675966}{267033749283}&{}+{}&\frac{128320735997}{267033749283} w_{2}&{}+{}&\frac{11400858216}{29670416587} g_{32}\\ g_{23}&{}={}&\frac{136108601693}{356044999044}&{}-{}&\frac{10392277289}{356044999044} w_{2}&{}+{}&\frac{17101287324}{29670416587} g_{32}\\ g_{25}&{}={}&\frac{11774337983}{89011249761}&{}+{}&\frac{19654743118}{89011249761} w_{2}&{}+{}&\frac{17101287324}{29670416587} g_{32}\\ w_{3}&{}={}&\frac{1748304704135}{534067498566}&{}-{}&\frac{903464389883}{534067498566} w_{2}&{}+{}&\frac{9183300480}{29670416587} g_{32}\\ g_{28}&{}={}&\frac{538577278525}{267033749283}&{}-{}&\frac{278318413945}{267033749283} w_{2}&{}+{}&\frac{17048022777}{29670416587} g_{32}\\ g_{29}&{}={}&\frac{16571608570}{14054407857}&{}-{}&\frac{8563643506}{14054407857} w_{2}&{}+{}&\frac{1173219525}{1561600873} g_{32}\\ g_{30}&{}={}&\frac{165716085700}{267033749283}&{}-{}&\frac{85636435060}{267033749283} w_{2}&{}+{}&\frac{25786603107}{29670416587} g_{32}\\ g_{31}&{}={}&\frac{66286434280}{267033749283}&{}-{}&\frac{34254574024}{267033749283} w_{2}&{}+{}&\frac{28116891195}{29670416587} g_{32}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{79377933271045}{801101247849}&{}-{}&\frac{62307465215}{267033749283} g_{33}&{}-{}&\frac{371283295490}{801101247849} g_{32}\\\hline w_{1}&{}={}&\frac{9320338368646}{801101247849}&{}-{}&\frac{776178261763}{267033749283} g_{33}&{}+{}&\frac{1750715813894}{801101247849} g_{32}\\ x_{1}&{}={}&\frac{1274871023159}{801101247849}&{}+{}&\frac{394319877403}{267033749283} g_{33}&{}-{}&\frac{838229577398}{801101247849} g_{32}\\ x_{2}&{}={}&\frac{3592034187191}{801101247849}&{}-{}&\frac{521606005523}{267033749283} g_{33}&{}+{}&\frac{1142391656230}{801101247849} g_{32}\\ w_{4}&{}={}&\frac{5935040207482}{801101247849}&{}-{}&\frac{394319877403}{267033749283} g_{33}&{}+{}&\frac{838229577398}{801101247849} g_{32}\\ w_{5}&{}={}&\frac{1214573299903}{801101247849}&{}+{}&\frac{521606005523}{267033749283} g_{33}&{}-{}&\frac{1142391656230}{801101247849} g_{32}\\ g_{8}&{}={}&\frac{52595411633}{76295356938}&{}+{}&\frac{1370477017}{25431785646} g_{33}&{}+{}&\frac{6894493415}{38147678469} g_{32}\\ g_{2}&{}={}&\frac{654662945078}{801101247849}&{}+{}&\frac{12461493043}{267033749283} g_{33}&{}+{}&\frac{74256659098}{801101247849} g_{32}\\ g_{17}&{}={}&\frac{51018995357}{114443035407}&{}+{}&\frac{5377760218}{38147678469} g_{33}&{}+{}&\frac{32214673060}{114443035407} g_{32}\\ g_{3}&{}={}&\frac{565651695317}{534067498566}&{}-{}&\frac{165561006479}{178022499522} g_{33}&{}+{}&\frac{215150829071}{267033749283} g_{32}\\ g_{7}&{}={}&\frac{178979389604}{267033749283}&{}+{}&\frac{21065954815}{89011249761} g_{33}&{}+{}&\frac{7457912962}{267033749283} g_{32}\\ g_{4}&{}={}&\frac{168770287381}{178022499522}&{}-{}&\frac{35406724435}{59340833174} g_{33}&{}+{}&\frac{51936665299}{89011249761} g_{32}\\ g_{5}&{}={}&\frac{168770287381}{267033749283}&{}+{}&\frac{53604525326}{89011249761} g_{33}&{}-{}&\frac{74149168924}{267033749283} g_{32}\\ g_{6}&{}={}&\frac{23183311799}{29670416587}&{}-{}&\frac{2868153924}{29670416587} g_{33}&{}+{}&\frac{7422082904}{29670416587} g_{32}\\ g_{11}&{}={}&\frac{63431211506}{114443035407}&{}+{}&\frac{11935254397}{38147678469} g_{33}&{}+{}&\frac{5056887718}{114443035407} g_{32}\\ g_{9}&{}={}&\frac{52595411633}{114443035407}&{}+{}&\frac{39518155486}{38147678469} g_{33}&{}-{}&\frac{62506370108}{114443035407} g_{32}\\ g_{10}&{}={}&\frac{19939759405}{38147678469}&{}+{}&\frac{7043184920}{12715892823} g_{33}&{}-{}&\frac{5821399408}{38147678469} g_{32}\\ g_{1}&{}={}&\frac{327331472539}{267033749283}&{}-{}&\frac{127286128120}{89011249761} g_{33}&{}+{}&\frac{304162078832}{267033749283} g_{32}\\ g_{12}&{}={}&\frac{495436873805}{534067498566}&{}-{}&\frac{141865910567}{178022499522} g_{33}&{}+{}&\frac{208674421559}{267033749283} g_{32}\\ g_{13}&{}={}&\frac{389286159623}{534067498566}&{}-{}&\frac{66728346785}{178022499522} g_{33}&{}+{}&\frac{145015983377}{267033749283} g_{32}\\ g_{18}&{}={}&\frac{830107786990}{2403303743547}&{}+{}&\frac{238131520421}{801101247849} g_{33}&{}+{}&\frac{512051409566}{2403303743547} g_{32}\\ g_{15}&{}={}&\frac{318519016835}{801101247849}&{}+{}&\frac{250397111686}{267033749283} g_{33}&{}-{}&\frac{328913449388}{801101247849} g_{32}\\ g_{14}&{}={}&\frac{318519016835}{534067498566}&{}-{}&\frac{16636637597}{178022499522} g_{33}&{}+{}&\frac{102577024589}{267033749283} g_{32}\\ g_{16}&{}={}&\frac{114753883537}{267033749283}&{}+{}&\frac{36187306082}{89011249761} g_{33}&{}+{}&\frac{13565774828}{267033749283} g_{32}\\ g_{26}&{}={}&\frac{21130932122}{114443035407}&{}+{}&\frac{6938850295}{38147678469} g_{33}&{}+{}&\frac{63078092368}{114443035407} g_{32}\\ g_{19}&{}={}&\frac{2903968661395}{1602202495698}&{}-{}&\frac{1125242013037}{534067498566} g_{33}&{}+{}&\frac{1455260496745}{801101247849} g_{32}\\ g_{20}&{}={}&\frac{277949707711}{228886070814}&{}-{}&\frac{95826309793}{76295356938} g_{33}&{}+{}&\frac{150787938013}{114443035407} g_{32}\\ g_{21}&{}={}&\frac{1306767482365}{1602202495698}&{}-{}&\frac{367812272227}{534067498566} g_{33}&{}+{}&\frac{789018945655}{801101247849} g_{32}\\ g_{22}&{}={}&\frac{880847167957}{1602202495698}&{}-{}&\frac{165831008011}{534067498566} g_{33}&{}+{}&\frac{611354532031}{801101247849} g_{32}\\ g_{27}&{}={}&\frac{142682332585}{2403303743547}&{}+{}&\frac{274036592192}{801101247849} g_{33}&{}+{}&\frac{1221910053650}{2403303743547} g_{32}\\ g_{24}&{}={}&\frac{198966763895}{801101247849}&{}+{}&\frac{256641471994}{267033749283} g_{33}&{}-{}&\frac{205459772156}{801101247849} g_{32}\\ g_{23}&{}={}&\frac{198966763895}{534067498566}&{}-{}&\frac{10392277289}{178022499522} g_{33}&{}+{}&\frac{164303863205}{267033749283} g_{32}\\ g_{25}&{}={}&\frac{54977757067}{267033749283}&{}+{}&\frac{39309486236}{89011249761} g_{33}&{}+{}&\frac{75292613444}{267033749283} g_{32}\\ w_{3}&{}={}&\frac{2170724861261}{801101247849}&{}-{}&\frac{903464389883}{267033749283} g_{33}&{}+{}&\frac{2054877892726}{801101247849} g_{32}\\ g_{28}&{}={}&\frac{1337413421630}{801101247849}&{}-{}&\frac{556636827890}{267033749283} g_{33}&{}+{}&\frac{1573570270759}{801101247849} g_{32}\\ g_{29}&{}={}&\frac{41151182204}{42163223571}&{}-{}&\frac{17127287012}{14054407857} g_{33}&{}+{}&\frac{65931501199}{42163223571} g_{32}\\ g_{30}&{}={}&\frac{411511822040}{801101247849}&{}-{}&\frac{171272870120}{267033749283} g_{33}&{}+{}&\frac{1038784024129}{801101247849} g_{32}\\ g_{31}&{}={}&\frac{164604728816}{801101247849}&{}-{}&\frac{68509148048}{267033749283} g_{33}&{}+{}&\frac{896174358361}{801101247849} g_{32}\\ w_{2}&{}={}&\frac{1}{3}&{}+{}&2 g_{33}&{}-{}&\frac{4}{3} g_{32}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{2942231138380}{29670416587}&{}-{}&\frac{124614930430}{267033749283} g_{34}&{}-{}&\frac{40684478210}{267033749283} g_{32}\\\hline w_{1}&{}={}&\frac{316450374329}{29670416587}&{}-{}&\frac{1552356523526}{267033749283} g_{34}&{}+{}&\frac{1618476286982}{267033749283} g_{32}\\ x_{1}&{}={}&\frac{61821885206}{29670416587}&{}+{}&\frac{788639754806}{267033749283} g_{34}&{}-{}&\frac{805169695670}{267033749283} g_{32}\\ x_{2}&{}={}&\frac{113719562284}{29670416587}&{}-{}&\frac{1043212011046}{267033749283} g_{34}&{}+{}&\frac{1076271892774}{267033749283} g_{32}\\ w_{4}&{}={}&\frac{205211864077}{29670416587}&{}-{}&\frac{788639754806}{267033749283} g_{34}&{}+{}&\frac{805169695670}{267033749283} g_{32}\\ w_{5}&{}={}&\frac{64302937238}{29670416587}&{}+{}&\frac{1043212011046}{267033749283} g_{34}&{}-{}&\frac{1076271892774}{267033749283} g_{32}\\ g_{8}&{}={}&\frac{2998104925}{4238630941}&{}+{}&\frac{1370477017}{12715892823} g_{34}&{}+{}&\frac{1384513127}{12715892823} g_{32}\\ g_{2}&{}={}&\frac{24708312523}{29670416587}&{}+{}&\frac{24922986086}{267033749283} g_{34}&{}+{}&\frac{8136895642}{267033749283} g_{32}\\ g_{17}&{}={}&\frac{2088768725}{4238630941}&{}+{}&\frac{10755520436}{38147678469} g_{34}&{}+{}&\frac{3567877396}{38147678469} g_{32}\\ g_{3}&{}={}&\frac{22227260491}{29670416587}&{}-{}&\frac{165561006479}{89011249761} g_{34}&{}+{}&\frac{182090947343}{89011249761} g_{32}\\ g_{7}&{}={}&\frac{22227260491}{29670416587}&{}+{}&\frac{42131909630}{89011249761} g_{34}&{}-{}&\frac{25601968766}{89011249761} g_{32}\\ g_{4}&{}={}&\frac{22227260491}{29670416587}&{}-{}&\frac{35406724435}{29670416587} g_{34}&{}+{}&\frac{40916704723}{29670416587} g_{32}\\ g_{5}&{}={}&\frac{24708312523}{29670416587}&{}+{}&\frac{107209050652}{89011249761} g_{34}&{}-{}&\frac{96189090076}{89011249761} g_{32}\\ g_{6}&{}={}&\frac{22227260491}{29670416587}&{}-{}&\frac{5736307848}{29670416587} g_{34}&{}+{}&\frac{11246288136}{29670416587} g_{32}\\ g_{11}&{}={}&\frac{2791350589}{4238630941}&{}+{}&\frac{23870508794}{38147678469} g_{34}&{}-{}&\frac{14228043290}{38147678469} g_{32}\\ g_{9}&{}={}&\frac{3411613597}{4238630941}&{}+{}&\frac{79036310972}{38147678469} g_{34}&{}-{}&\frac{73526330684}{38147678469} g_{32}\\ g_{10}&{}={}&\frac{2998104925}{4238630941}&{}+{}&\frac{14086369840}{12715892823} g_{34}&{}-{}&\frac{11331379696}{12715892823} g_{32}\\ g_{1}&{}={}&\frac{22227260491}{29670416587}&{}-{}&\frac{254572256240}{89011249761} g_{34}&{}+{}&\frac{271102197104}{89011249761} g_{32}\\ g_{12}&{}={}&\frac{19642831291}{29670416587}&{}-{}&\frac{141865910567}{89011249761} g_{34}&{}+{}&\frac{164135414231}{89011249761} g_{32}\\ g_{13}&{}={}&\frac{17919878491}{29670416587}&{}-{}&\frac{66728346785}{89011249761} g_{34}&{}+{}&\frac{92824225649}{89011249761} g_{32}\\ g_{18}&{}={}&\frac{39564418793}{89011249761}&{}+{}&\frac{476263040842}{801101247849} g_{34}&{}-{}&\frac{146824890706}{801101247849} g_{32}\\ g_{15}&{}={}&\frac{21070967723}{29670416587}&{}+{}&\frac{500794223372}{267033749283} g_{34}&{}-{}&\frac{443500632044}{267033749283} g_{32}\\ g_{14}&{}={}&\frac{16771243291}{29670416587}&{}-{}&\frac{16636637597}{89011249761} g_{34}&{}+{}&\frac{45283433261}{89011249761} g_{32}\\ g_{16}&{}={}&\frac{16771243291}{29670416587}&{}+{}&\frac{72374612164}{89011249761} g_{34}&{}-{}&\frac{43727816500}{89011249761} g_{32}\\ g_{26}&{}={}&\frac{1039621571}{4238630941}&{}+{}&\frac{13877700590}{38147678469} g_{34}&{}+{}&\frac{11774230396}{38147678469} g_{32}\\ g_{19}&{}={}&\frac{32939382377}{29670416587}&{}-{}&\frac{1125242013037}{267033749283} g_{34}&{}+{}&\frac{1235248174273}{267033749283} g_{32}\\ g_{20}&{}={}&\frac{3372655517}{4238630941}&{}-{}&\frac{95826309793}{38147678469} g_{34}&{}+{}&\frac{114146852533}{38147678469} g_{32}\\ g_{21}&{}={}&\frac{17388059447}{29670416587}&{}-{}&\frac{367812272227}{267033749283} g_{34}&{}+{}&\frac{508214496703}{267033749283} g_{32}\\ g_{22}&{}={}&\frac{13241039999}{29670416587}&{}-{}&\frac{165831008011}{267033749283} g_{34}&{}+{}&\frac{314338849351}{267033749283} g_{32}\\ g_{27}&{}={}&\frac{15434034251}{89011249761}&{}+{}&\frac{548073184384}{801101247849} g_{34}&{}+{}&\frac{41921228294}{801101247849} g_{32}\\ g_{24}&{}={}&\frac{16874379107}{29670416587}&{}+{}&\frac{513282943988}{267033749283} g_{34}&{}-{}&\frac{410675220044}{267033749283} g_{32}\\ g_{23}&{}={}&\frac{10476360367}{29670416587}&{}-{}&\frac{10392277289}{89011249761} g_{34}&{}+{}&\frac{61696139261}{89011249761} g_{32}\\ g_{25}&{}={}&\frac{10476360367}{29670416587}&{}+{}&\frac{78618972472}{89011249761} g_{34}&{}-{}&\frac{27315110500}{89011249761} g_{32}\\ w_{3}&{}={}&\frac{46935573014}{29670416587}&{}-{}&\frac{1806928779766}{267033749283} g_{34}&{}+{}&\frac{1889578484086}{267033749283} g_{32}\\ g_{28}&{}={}&\frac{28917651620}{29670416587}&{}-{}&\frac{1113273655780}{267033749283} g_{34}&{}+{}&\frac{1266705860773}{267033749283} g_{32}\\ g_{29}&{}={}&\frac{889773896}{1561600873}&{}-{}&\frac{34254574024}{14054407857} g_{34}&{}+{}&\frac{44813549749}{14054407857} g_{32}\\ g_{30}&{}={}&\frac{8897738960}{29670416587}&{}-{}&\frac{342545740240}{267033749283} g_{34}&{}+{}&\frac{574625168203}{267033749283} g_{32}\\ g_{31}&{}={}&\frac{3559095584}{29670416587}&{}-{}&\frac{137018296096}{267033749283} g_{34}&{}+{}&\frac{390070316851}{267033749283} g_{32}\\ w_{2}&{}={}&1&{}+{}&4 g_{34}&{}-{}&4 g_{32}\\ g_{33}&{}={}&\frac{1}{3}&{}+{}&2 g_{34}&{}-{}&\frac{4}{3} g_{32}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{7568643247135}{76295356938}&{}-{}&\frac{188203143545}{534067498566} g_{34}&{}-{}&\frac{20342239105}{89011249761} g_{35}\\\hline w_{1}&{}={}&\frac{929334983059}{76295356938}&{}-{}&\frac{5532427477525}{534067498566} g_{34}&{}+{}&\frac{809238143491}{89011249761} g_{35}\\ x_{1}&{}={}&\frac{101458440839}{76295356938}&{}+{}&\frac{2785034053117}{534067498566} g_{34}&{}-{}&\frac{402584847835}{89011249761} g_{35}\\ x_{2}&{}={}&\frac{369298295357}{76295356938}&{}-{}&\frac{3700831861253}{534067498566} g_{34}&{}+{}&\frac{538135946387}{89011249761} g_{35}\\ w_{4}&{}={}&\frac{585199771603}{76295356938}&{}-{}&\frac{2785034053117}{534067498566} g_{34}&{}+{}&\frac{402584847835}{89011249761} g_{35}\\ w_{5}&{}={}&\frac{88473846271}{76295356938}&{}+{}&\frac{3700831861253}{534067498566} g_{34}&{}-{}&\frac{538135946387}{89011249761} g_{35}\\ g_{8}&{}={}&\frac{37361772227}{50863571292}&{}+{}&\frac{1328368687}{50863571292} g_{34}&{}+{}&\frac{1384513127}{8477261882} g_{35}\\ g_{2}&{}={}&\frac{64116867605}{76295356938}&{}+{}&\frac{37640628709}{534067498566} g_{34}&{}+{}&\frac{4068447821}{89011249761} g_{35}\\ g_{17}&{}={}&\frac{19690887874}{38147678469}&{}+{}&\frac{8079612389}{38147678469} g_{34}&{}+{}&\frac{1783938698}{12715892823} g_{35}\\ g_{3}&{}={}&\frac{64116867605}{50863571292}&{}-{}&\frac{1208516867945}{356044999044} g_{34}&{}+{}&\frac{182090947343}{59340833174} g_{35}\\ g_{7}&{}={}&\frac{17223225509}{25431785646}&{}+{}&\frac{122666772409}{178022499522} g_{34}&{}-{}&\frac{12800984383}{29670416587} g_{35}\\ g_{4}&{}={}&\frac{18546535241}{16954523764}&{}-{}&\frac{264377011909}{118681666348} g_{34}&{}+{}&\frac{122750114169}{59340833174} g_{35}\\ g_{5}&{}={}&\frac{7153952150}{12715892823}&{}+{}&\frac{179350868209}{89011249761} g_{34}&{}-{}&\frac{48094545038}{29670416587} g_{35}\\ g_{6}&{}={}&\frac{3576976075}{4238630941}&{}-{}&\frac{14171023950}{29670416587} g_{34}&{}+{}&\frac{16869432204}{29670416587} g_{35}\\ g_{11}&{}={}&\frac{43130288957}{76295356938}&{}+{}&\frac{69083082523}{76295356938} g_{34}&{}-{}&\frac{7114021645}{12715892823} g_{35}\\ g_{9}&{}={}&\frac{12322939702}{38147678469}&{}+{}&\frac{134181058985}{38147678469} g_{34}&{}-{}&\frac{36763165342}{12715892823} g_{35}\\ g_{10}&{}={}&\frac{6161469851}{12715892823}&{}+{}&\frac{22584904612}{12715892823} g_{34}&{}-{}&\frac{5665689848}{4238630941} g_{35}\\ g_{1}&{}={}&\frac{19208190107}{12715892823}&{}-{}&\frac{457898904068}{89011249761} g_{34}&{}+{}&\frac{135551098552}{29670416587} g_{35}\\ g_{12}&{}={}&\frac{57121341389}{50863571292}&{}-{}&\frac{1059869884961}{356044999044} g_{34}&{}+{}&\frac{164135414231}{59340833174} g_{35}\\ g_{13}&{}={}&\frac{43980395363}{50863571292}&{}-{}&\frac{545386064087}{356044999044} g_{34}&{}+{}&\frac{92824225649}{59340833174} g_{35}\\ g_{18}&{}={}&\frac{91249584703}{228886070814}&{}+{}&\frac{1172763417743}{1602202495698} g_{34}&{}-{}&\frac{73412445353}{267033749283} g_{35}\\ g_{15}&{}={}&\frac{11251935928}{38147678469}&{}+{}&\frac{833419697405}{267033749283} g_{34}&{}-{}&\frac{221750316022}{89011249761} g_{35}\\ g_{14}&{}={}&\frac{35219764679}{50863571292}&{}-{}&\frac{202396850171}{356044999044} g_{34}&{}+{}&\frac{45283433261}{59340833174} g_{35}\\ g_{16}&{}={}&\frac{5625967964}{12715892823}&{}+{}&\frac{105170474539}{89011249761} g_{34}&{}-{}&\frac{21863908250}{29670416587} g_{35}\\ g_{26}&{}={}&\frac{12300151738}{38147678469}&{}+{}&\frac{5047027793}{38147678469} g_{34}&{}+{}&\frac{5887115198}{12715892823} g_{35}\\ g_{19}&{}={}&\frac{345866562835}{152590713876}&{}-{}&\frac{8206712574967}{1068134997132} g_{34}&{}+{}&\frac{1235248174273}{178022499522} g_{35}\\ g_{20}&{}={}&\frac{235562451145}{152590713876}&{}-{}&\frac{725745796771}{152590713876} g_{34}&{}+{}&\frac{114146852533}{25431785646} g_{35}\\ g_{21}&{}={}&\frac{162026376685}{152590713876}&{}-{}&\frac{2995892579017}{1068134997132} g_{34}&{}+{}&\frac{508214496703}{178022499522} g_{35}\\ g_{22}&{}={}&\frac{113002327045}{152590713876}&{}-{}&\frac{1606340580097}{1068134997132} g_{34}&{}+{}&\frac{314338849351}{178022499522} g_{35}\\ g_{27}&{}={}&\frac{42681890095}{228886070814}&{}+{}&\frac{1033264526327}{1602202495698} g_{34}&{}+{}&\frac{20960614147}{267033749283} g_{35}\\ g_{24}&{}={}&\frac{7028658136}{38147678469}&{}+{}&\frac{821289359021}{267033749283} g_{34}&{}-{}&\frac{205337610022}{89011249761} g_{35}\\ g_{23}&{}={}&\frac{26773209095}{50863571292}&{}-{}&\frac{226657526939}{356044999044} g_{34}&{}+{}&\frac{61696139261}{59340833174} g_{35}\\ g_{25}&{}={}&\frac{3514329068}{12715892823}&{}+{}&\frac{99105305347}{89011249761} g_{34}&{}-{}&\frac{13657555250}{29670416587} g_{35}\\ w_{3}&{}={}&\frac{255661365185}{76295356938}&{}-{}&\frac{6448225285661}{534067498566} g_{34}&{}+{}&\frac{944789242043}{89011249761} g_{35}\\ g_{28}&{}={}&\frac{329677331299}{152590713876}&{}-{}&\frac{8253212205439}{1068134997132} g_{34}&{}+{}&\frac{1266705860773}{178022499522} g_{35}\\ g_{29}&{}={}&\frac{10977915715}{8031090204}&{}-{}&\frac{271458945343}{56217631428} g_{34}&{}+{}&\frac{44813549749}{9369605238} g_{35}\\ g_{30}&{}={}&\frac{127849110109}{152590713876}&{}-{}&\frac{3094058465569}{1068134997132} g_{34}&{}+{}&\frac{574625168203}{178022499522} g_{35}\\ g_{31}&{}={}&\frac{74028251125}{152590713876}&{}-{}&\frac{1718284134937}{1068134997132} g_{34}&{}+{}&\frac{390070316851}{178022499522} g_{35}\\ w_{2}&{}={}&0&{}+{}&7 g_{34}&{}-{}&6 g_{35}\\ g_{33}&{}={}&0&{}+{}&3 g_{34}&{}-{}&2 g_{35}\\ g_{32}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{34}&{}+{}&\frac{3}{2} g_{35}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{1219543359240575}{12283552467018}&{}-{}&\frac{193326135145}{12283552467018} w_{2}&{}-{}&\frac{330598817280}{682419581501} g_{36}\\\hline w_{1}&{}={}&\frac{150019650853235}{12283552467018}&{}-{}&\frac{18347998246469}{12283552467018} w_{2}&{}+{}&\frac{132239526912}{682419581501} g_{36}\\ x_{1}&{}={}&\frac{16235629329895}{12283552467018}&{}+{}&\frac{9193331736749}{12283552467018} w_{2}&{}-{}&\frac{33059881728}{682419581501} g_{36}\\ x_{2}&{}={}&\frac{59655384842845}{12283552467018}&{}-{}&\frac{12244887239989}{12283552467018} w_{2}&{}+{}&\frac{66119763456}{682419581501} g_{36}\\ w_{4}&{}={}&\frac{94316342873267}{12283552467018}&{}-{}&\frac{9193331736749}{12283552467018} w_{2}&{}+{}&\frac{33059881728}{682419581501} g_{36}\\ w_{5}&{}={}&\frac{14045929959263}{12283552467018}&{}+{}&\frac{12244887239989}{12283552467018} w_{2}&{}-{}&\frac{66119763456}{682419581501} g_{36}\\ g_{8}&{}={}&\frac{892380642949}{1169862139716}&{}-{}&\frac{9803880769}{1169862139716} w_{2}&{}+{}&\frac{16529940864}{97488511643} g_{36}\\ g_{2}&{}={}&\frac{10521174974773}{12283552467018}&{}+{}&\frac{38665227029}{12283552467018} w_{2}&{}+{}&\frac{66119763456}{682419581501} g_{36}\\ g_{17}&{}={}&\frac{495860614598}{877396604787}&{}+{}&\frac{8131500637}{877396604787} w_{2}&{}+{}&\frac{28646795664}{97488511643} g_{36}\\ g_{3}&{}={}&\frac{10521174974773}{8189034978012}&{}-{}&\frac{4055852261977}{8189034978012} w_{2}&{}+{}&\frac{99179645184}{682419581501} g_{36}\\ g_{7}&{}={}&\frac{2872118952133}{4094517489006}&{}+{}&\frac{360542404265}{4094517489006} w_{2}&{}+{}&\frac{99179645184}{682419581501} g_{36}\\ g_{4}&{}={}&\frac{3052111937257}{2729678326004}&{}-{}&\frac{897004366325}{2729678326004} w_{2}&{}+{}&\frac{99179645184}{682419581501} g_{36}\\ g_{5}&{}={}&\frac{1184846177878}{2047258744503}&{}+{}&\frac{575127189089}{2047258744503} w_{2}&{}+{}&\frac{66119763456}{682419581501} g_{36}\\ g_{6}&{}={}&\frac{592423088939}{682419581501}&{}-{}&\frac{53646196206}{682419581501} w_{2}&{}+{}&\frac{99179645184}{682419581501} g_{36}\\ g_{11}&{}={}&\frac{1049851439035}{1754793209574}&{}+{}&\frac{202192359851}{1754793209574} w_{2}&{}+{}&\frac{19284931008}{97488511643} g_{36}\\ g_{9}&{}={}&\frac{299957554010}{877396604787}&{}+{}&\frac{433796362009}{877396604787} w_{2}&{}+{}&\frac{11019960576}{97488511643} g_{36}\\ g_{10}&{}={}&\frac{149978777005}{292465534929}&{}+{}&\frac{70665413540}{292465534929} w_{2}&{}+{}&\frac{16529940864}{97488511643} g_{36}\\ g_{1}&{}={}&\frac{3142108429819}{2047258744503}&{}-{}&\frac{1525777751620}{2047258744503} w_{2}&{}+{}&\frac{99179645184}{682419581501} g_{36}\\ g_{12}&{}={}&\frac{9463770007597}{8189034978012}&{}-{}&\frac{3596958498001}{8189034978012} w_{2}&{}+{}&\frac{133617021984}{682419581501} g_{36}\\ g_{13}&{}={}&\frac{7393994199811}{8189034978012}&{}-{}&\frac{1926190159015}{8189034978012} w_{2}&{}+{}&\frac{156575273184}{682419581501} g_{36}\\ g_{18}&{}={}&\frac{724687479913}{1602202495698}&{}+{}&\frac{130706036681}{1602202495698} w_{2}&{}+{}&\frac{9548931888}{29670416587} g_{36}\\ g_{15}&{}={}&\frac{1983442458392}{6141776233509}&{}+{}&\frac{2664715816909}{6141776233509} w_{2}&{}+{}&\frac{114587182656}{682419581501} g_{36}\\ g_{14}&{}={}&\frac{6014143661287}{8189034978012}&{}-{}&\frac{812344599691}{8189034978012} w_{2}&{}+{}&\frac{171880773984}{682419581501} g_{36}\\ g_{16}&{}={}&\frac{991721229196}{2047258744503}&{}+{}&\frac{308728536203}{2047258744503} w_{2}&{}+{}&\frac{171880773984}{682419581501} g_{36}\\ g_{26}&{}={}&\frac{359859282932}{877396604787}&{}-{}&\frac{16397962805}{877396604787} w_{2}&{}+{}&\frac{51303861972}{97488511643} g_{36}\\ g_{19}&{}={}&\frac{57004590551267}{24567104934036}&{}-{}&\frac{27530658718391}{24567104934036} w_{2}&{}+{}&\frac{220012322472}{682419581501} g_{36}\\ g_{20}&{}={}&\frac{5637782889215}{3509586419148}&{}-{}&\frac{2478813266339}{3509586419148} w_{2}&{}+{}&\frac{36641085480}{97488511643} g_{36}\\ g_{21}&{}={}&\frac{27771073339997}{24567104934036}&{}-{}&\frac{10565715628361}{24567104934036} w_{2}&{}+{}&\frac{280804448952}{682419581501} g_{36}\\ g_{22}&{}={}&\frac{19975468750325}{24567104934036}&{}-{}&\frac{6041730804353}{24567104934036} w_{2}&{}+{}&\frac{297015682680}{682419581501} g_{36}\\ g_{27}&{}={}&\frac{452684816581}{1602202495698}&{}+{}&\frac{81647109797}{1602202495698} w_{2}&{}+{}&\frac{17101287324}{29670416587} g_{36}\\ g_{24}&{}={}&\frac{1439437131728}{6141776233509}&{}+{}&\frac{2566597963141}{6141776233509} w_{2}&{}+{}&\frac{205215447888}{682419581501} g_{36}\\ g_{23}&{}={}&\frac{4926133007959}{8189034978012}&{}-{}&\frac{1008580307227}{8189034978012} w_{2}&{}+{}&\frac{307823171832}{682419581501} g_{36}\\ g_{25}&{}={}&\frac{719718565864}{2047258744503}&{}+{}&\frac{259669609319}{2047258744503} w_{2}&{}+{}&\frac{307823171832}{682419581501} g_{36}\\ w_{3}&{}={}&\frac{41657378020705}{12283552467018}&{}-{}&\frac{21399553749709}{12283552467018} w_{2}&{}+{}&\frac{165299408640}{682419581501} g_{36}\\ g_{28}&{}={}&\frac{54919236799055}{24567104934036}&{}-{}&\frac{27906777157835}{24567104934036} w_{2}&{}+{}&\frac{306864409986}{682419581501} g_{36}\\ g_{29}&{}={}&\frac{1894152138815}{1293005522844}&{}-{}&\frac{946239838427}{1293005522844} w_{2}&{}+{}&\frac{21117951450}{35916820079} g_{36}\\ g_{30}&{}={}&\frac{23368659863105}{24567104934036}&{}-{}&\frac{11359743444965}{24567104934036} w_{2}&{}+{}&\frac{464158855926}{682419581501} g_{36}\\ g_{31}&{}={}&\frac{14955172680185}{24567104934036}&{}-{}&\frac{6947201121533}{24567104934036} w_{2}&{}+{}&\frac{506104041510}{682419581501} g_{36}\\ g_{34}&{}={}&\frac{3}{23}&{}+{}&\frac{2}{23} w_{2}&{}+{}&\frac{18}{23} g_{36}\\ g_{33}&{}={}&\frac{2}{23}&{}+{}&\frac{9}{23} w_{2}&{}+{}&\frac{12}{23} g_{36}\\ g_{32}&{}={}&\frac{35}{92}&{}-{}&\frac{15}{92} w_{2}&{}+{}&\frac{18}{23} g_{36}\\ g_{35}&{}={}&\frac{7}{46}&{}-{}&\frac{3}{46} w_{2}&{}+{}&\frac{21}{23} g_{36}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{1829411701928435}{18425328700527}&{}-{}&\frac{193326135145}{6141776233509} g_{37}&{}-{}&\frac{371283295490}{801101247849} g_{36}\\\hline w_{1}&{}={}&\frac{215855477156618}{18425328700527}&{}-{}&\frac{18347998246469}{6141776233509} g_{37}&{}+{}&\frac{1750715813894}{801101247849} g_{36}\\ x_{1}&{}={}&\frac{28950109863217}{18425328700527}&{}+{}&\frac{9193331736749}{6141776233509} g_{37}&{}-{}&\frac{838229577398}{801101247849} g_{36}\\ x_{2}&{}={}&\frac{83360633644273}{18425328700527}&{}-{}&\frac{12244887239989}{6141776233509} g_{37}&{}+{}&\frac{1142391656230}{801101247849} g_{36}\\ w_{4}&{}={}&\frac{136877848441526}{18425328700527}&{}-{}&\frac{9193331736749}{6141776233509} g_{37}&{}+{}&\frac{838229577398}{801101247849} g_{36}\\ w_{5}&{}={}&\frac{27191338558889}{18425328700527}&{}+{}&\frac{12244887239989}{6141776233509} g_{37}&{}-{}&\frac{1142391656230}{801101247849} g_{36}\\ g_{8}&{}={}&\frac{1333669024039}{1754793209574}&{}-{}&\frac{9803880769}{584931069858} g_{37}&{}+{}&\frac{6894493415}{38147678469} g_{36}\\ g_{2}&{}={}&\frac{15801095075674}{18425328700527}&{}+{}&\frac{38665227029}{6141776233509} g_{37}&{}+{}&\frac{74256659098}{801101247849} g_{36}\\ g_{17}&{}={}&\frac{1495713344431}{2632189814361}&{}+{}&\frac{16263001274}{877396604787} g_{37}&{}+{}&\frac{32214673060}{114443035407} g_{36}\\ g_{3}&{}={}&\frac{13753836331171}{12283552467018}&{}-{}&\frac{4055852261977}{4094517489006} g_{37}&{}+{}&\frac{215150829071}{267033749283} g_{36}\\ g_{7}&{}={}&\frac{4488449630332}{6141776233509}&{}+{}&\frac{360542404265}{2047258744503} g_{37}&{}+{}&\frac{7457912962}{267033749283} g_{36}\\ g_{4}&{}={}&\frac{4129665722723}{4094517489006}&{}-{}&\frac{897004366325}{1364839163002} g_{37}&{}+{}&\frac{51936665299}{89011249761} g_{36}\\ g_{5}&{}={}&\frac{4129665722723}{6141776233509}&{}+{}&\frac{1150254378178}{2047258744503} g_{37}&{}-{}&\frac{74149168924}{267033749283} g_{36}\\ g_{6}&{}={}&\frac{574541023537}{682419581501}&{}-{}&\frac{107292392412}{682419581501} g_{37}&{}+{}&\frac{7422082904}{29670416587} g_{36}\\ g_{11}&{}={}&\frac{1675873338478}{2632189814361}&{}+{}&\frac{202192359851}{877396604787} g_{37}&{}+{}&\frac{5056887718}{114443035407} g_{36}\\ g_{9}&{}={}&\frac{1333669024039}{2632189814361}&{}+{}&\frac{867592724018}{877396604787} g_{37}&{}-{}&\frac{62506370108}{114443035407} g_{36}\\ g_{10}&{}={}&\frac{520601744555}{877396604787}&{}+{}&\frac{141330827080}{292465534929} g_{37}&{}-{}&\frac{5821399408}{38147678469} g_{36}\\ g_{1}&{}={}&\frac{7900547537837}{6141776233509}&{}-{}&\frac{3051555503240}{2047258744503} g_{37}&{}+{}&\frac{304162078832}{267033749283} g_{36}\\ g_{12}&{}={}&\frac{12397175762395}{12283552467018}&{}-{}&\frac{3596958498001}{4094517489006} g_{37}&{}+{}&\frac{208674421559}{267033749283} g_{36}\\ g_{13}&{}={}&\frac{10127896220209}{12283552467018}&{}-{}&\frac{1926190159015}{4094517489006} g_{37}&{}+{}&\frac{145015983377}{267033749283} g_{36}\\ g_{18}&{}={}&\frac{1152384238210}{2403303743547}&{}+{}&\frac{130706036681}{801101247849} g_{37}&{}+{}&\frac{512051409566}{2403303743547} g_{36}\\ g_{15}&{}={}&\frac{8615043192085}{18425328700527}&{}+{}&\frac{5329431633818}{6141776233509} g_{37}&{}-{}&\frac{328913449388}{801101247849} g_{36}\\ g_{14}&{}={}&\frac{8615043192085}{12283552467018}&{}-{}&\frac{812344599691}{4094517489006} g_{37}&{}+{}&\frac{102577024589}{267033749283} g_{36}\\ g_{16}&{}={}&\frac{3283892223791}{6141776233509}&{}+{}&\frac{617457072406}{2047258744503} g_{37}&{}+{}&\frac{13565774828}{267033749283} g_{36}\\ g_{26}&{}={}&\frac{1063179885991}{2632189814361}&{}-{}&\frac{32795925610}{877396604787} g_{37}&{}+{}&\frac{63078092368}{114443035407} g_{36}\\ g_{19}&{}={}&\frac{71741556467705}{36850657401054}&{}-{}&\frac{27530658718391}{12283552467018} g_{37}&{}+{}&\frac{1455260496745}{801101247849} g_{36}\\ g_{20}&{}={}&\frac{7217267700653}{5264379628722}&{}-{}&\frac{2478813266339}{1754793209574} g_{37}&{}+{}&\frac{150787938013}{114443035407} g_{36}\\ g_{21}&{}={}&\frac{36373752195815}{36850657401054}&{}-{}&\frac{10565715628361}{12283552467018} g_{37}&{}+{}&\frac{789018945655}{801101247849} g_{36}\\ g_{22}&{}={}&\frac{26942337723311}{36850657401054}&{}-{}&\frac{6041730804353}{12283552467018} g_{37}&{}+{}&\frac{611354532031}{801101247849} g_{36}\\ g_{27}&{}={}&\frac{719850779770}{2403303743547}&{}+{}&\frac{81647109797}{801101247849} g_{37}&{}+{}&\frac{1221910053650}{2403303743547} g_{36}\\ g_{24}&{}={}&\frac{6884909358325}{18425328700527}&{}+{}&\frac{5133195926282}{6141776233509} g_{37}&{}-{}&\frac{205459772156}{801101247849} g_{36}\\ g_{23}&{}={}&\frac{6884909358325}{12283552467018}&{}-{}&\frac{1008580307227}{4094517489006} g_{37}&{}+{}&\frac{164303863205}{267033749283} g_{36}\\ g_{25}&{}={}&\frac{2418825306911}{6141776233509}&{}+{}&\frac{519339218638}{2047258744503} g_{37}&{}+{}&\frac{75292613444}{267033749283} g_{36}\\ w_{3}&{}={}&\frac{51786290156203}{18425328700527}&{}-{}&\frac{21399553749709}{6141776233509} g_{37}&{}+{}&\frac{2054877892726}{801101247849} g_{36}\\ g_{28}&{}={}&\frac{68425466619665}{36850657401054}&{}-{}&\frac{27906777157835}{12283552467018} g_{37}&{}+{}&\frac{1573570270759}{801101247849} g_{36}\\ g_{29}&{}={}&\frac{2368108289009}{1939508284266}&{}-{}&\frac{946239838427}{646502761422} g_{37}&{}+{}&\frac{65931501199}{42163223571} g_{36}\\ g_{30}&{}={}&\frac{29373118072175}{36850657401054}&{}-{}&\frac{11359743444965}{12283552467018} g_{37}&{}+{}&\frac{1038784024129}{801101247849} g_{36}\\ g_{31}&{}={}&\frac{18959158459511}{36850657401054}&{}-{}&\frac{6947201121533}{12283552467018} g_{37}&{}+{}&\frac{896174358361}{801101247849} g_{36}\\ g_{34}&{}={}&\frac{11}{69}&{}+{}&\frac{4}{23} g_{37}&{}+{}&\frac{2}{3} g_{36}\\ g_{33}&{}={}&\frac{5}{23}&{}+{}&\frac{18}{23} g_{37}&{}&{}\\ g_{32}&{}={}&\frac{15}{46}&{}-{}&\frac{15}{46} g_{37}&{}+{}&1 g_{36}\\ g_{35}&{}={}&\frac{3}{23}&{}-{}&\frac{3}{23} g_{37}&{}+{}&1 g_{36}\\ w_{2}&{}={}&\frac{1}{3}&{}+{}&2 g_{37}&{}-{}&\frac{4}{3} g_{36}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{67763149187540}{682419581501}&{}-{}&\frac{386652270290}{6141776233509} g_{38}&{}-{}&\frac{2588737085230}{6141776233509} g_{36}\\\hline w_{1}&{}={}&\frac{7315091811487}{682419581501}&{}-{}&\frac{36695996492938}{6141776233509} g_{38}&{}+{}&\frac{37886152235146}{6141776233509} g_{36}\\ x_{1}&{}={}&\frac{1412720059258}{682419581501}&{}+{}&\frac{18386663473498}{6141776233509} g_{38}&{}-{}&\frac{18684202409050}{6141776233509} g_{36}\\ x_{2}&{}={}&\frac{2633916533492}{682419581501}&{}-{}&\frac{24489774479978}{6141776233509} g_{38}&{}+{}&\frac{25084852351082}{6141776233509} g_{36}\\ w_{4}&{}={}&\frac{4729056174251}{682419581501}&{}-{}&\frac{18386663473498}{6141776233509} g_{38}&{}+{}&\frac{18684202409050}{6141776233509} g_{36}\\ w_{5}&{}={}&\frac{1460600955514}{682419581501}&{}+{}&\frac{24489774479978}{6141776233509} g_{38}&{}-{}&\frac{25084852351082}{6141776233509} g_{36}\\ g_{8}&{}={}&\frac{73548063515}{97488511643}&{}-{}&\frac{9803880769}{292465534929} g_{38}&{}+{}&\frac{59393703361}{292465534929} g_{36}\\ g_{2}&{}={}&\frac{586657788989}{682419581501}&{}+{}&\frac{77330454058}{6141776233509} g_{38}&{}+{}&\frac{517747417046}{6141776233509} g_{36}\\ g_{17}&{}={}&\frac{55999123915}{97488511643}&{}+{}&\frac{32526002548}{877396604787} g_{38}&{}+{}&\frac{225295158428}{877396604787} g_{36}\\ g_{3}&{}={}&\frac{538776892733}{682419581501}&{}-{}&\frac{4055852261977}{2047258744503} g_{38}&{}+{}&\frac{4353391197529}{2047258744503} g_{36}\\ g_{7}&{}={}&\frac{538776892733}{682419581501}&{}+{}&\frac{721084808530}{2047258744503} g_{38}&{}-{}&\frac{423545872978}{2047258744503} g_{36}\\ g_{4}&{}={}&\frac{538776892733}{682419581501}&{}-{}&\frac{897004366325}{682419581501} g_{38}&{}+{}&\frac{996184011509}{682419581501} g_{36}\\ g_{5}&{}={}&\frac{586657788989}{682419581501}&{}+{}&\frac{2300508756356}{2047258744503} g_{38}&{}-{}&\frac{2102149465988}{2047258744503} g_{36}\\ g_{6}&{}={}&\frac{538776892733}{682419581501}&{}-{}&\frac{214584784824}{682419581501} g_{38}&{}+{}&\frac{313764430008}{682419581501} g_{36}\\ g_{11}&{}={}&\frac{69557988827}{97488511643}&{}+{}&\frac{404384719702}{877396604787} g_{38}&{}-{}&\frac{230820340630}{877396604787} g_{36}\\ g_{9}&{}={}&\frac{81528212891}{97488511643}&{}+{}&\frac{1735185448036}{877396604787} g_{38}&{}-{}&\frac{1636005802852}{877396604787} g_{36}\\ g_{10}&{}={}&\frac{73548063515}{97488511643}&{}+{}&\frac{282661654160}{292465534929} g_{38}&{}-{}&\frac{233071831568}{292465534929} g_{36}\\ g_{1}&{}={}&\frac{538776892733}{682419581501}&{}-{}&\frac{6103111006480}{2047258744503} g_{38}&{}+{}&\frac{6400649942032}{2047258744503} g_{36}\\ g_{12}&{}={}&\frac{488900959133}{682419581501}&{}-{}&\frac{3596958498001}{2047258744503} g_{38}&{}+{}&\frac{3997809563953}{2047258744503} g_{36}\\ g_{13}&{}={}&\frac{455650336733}{682419581501}&{}-{}&\frac{1926190159015}{2047258744503} g_{38}&{}+{}&\frac{2395915978567}{2047258744503} g_{36}\\ g_{18}&{}={}&\frac{47521862033}{89011249761}&{}+{}&\frac{261412073362}{801101247849} g_{38}&{}-{}&\frac{3590912386}{801101247849} g_{36}\\ g_{15}&{}={}&\frac{516462030589}{682419581501}&{}+{}&\frac{10658863267636}{6141776233509} g_{38}&{}-{}&\frac{9627578623732}{6141776233509} g_{36}\\ g_{14}&{}={}&\frac{433483255133}{682419581501}&{}-{}&\frac{812344599691}{2047258744503} g_{38}&{}+{}&\frac{1327986921643}{2047258744503} g_{36}\\ g_{16}&{}={}&\frac{433483255133}{682419581501}&{}+{}&\frac{1234914144812}{2047258744503} g_{38}&{}-{}&\frac{719271822860}{2047258744503} g_{36}\\ g_{26}&{}={}&\frac{38162368903}{97488511643}&{}-{}&\frac{65591851220}{877396604787} g_{38}&{}+{}&\frac{527326608968}{877396604787} g_{36}\\ g_{19}&{}={}&\frac{818720328691}{682419581501}&{}-{}&\frac{27530658718391}{6141776233509} g_{38}&{}+{}&\frac{29510769620639}{6141776233509} g_{36}\\ g_{20}&{}={}&\frac{87749156191}{97488511643}&{}-{}&\frac{2478813266339}{877396604787} g_{38}&{}+{}&\frac{2808583035659}{877396604787} g_{36}\\ g_{21}&{}={}&\frac{477926603101}{682419581501}&{}-{}&\frac{10565715628361}{6141776233509} g_{38}&{}+{}&\frac{13092955668929}{6141776233509} g_{36}\\ g_{22}&{}={}&\frac{387048276277}{682419581501}&{}-{}&\frac{6041730804353}{6141776233509} g_{38}&{}+{}&\frac{8714871948473}{6141776233509} g_{36}\\ g_{27}&{}={}&\frac{29685107021}{89011249761}&{}+{}&\frac{163294219594}{801101247849} g_{38}&{}+{}&\frac{298440538154}{801101247849} g_{36}\\ g_{24}&{}={}&\frac{445115010541}{682419581501}&{}+{}&\frac{10266391852564}{6141776233509} g_{38}&{}-{}&\frac{8419452821572}{6141776233509} g_{36}\\ g_{23}&{}={}&\frac{326462725061}{682419581501}&{}-{}&\frac{1008580307227}{2047258744503} g_{38}&{}+{}&\frac{1932049822723}{2047258744503} g_{36}\\ g_{25}&{}={}&\frac{326462725061}{682419581501}&{}+{}&\frac{1038678437276}{2047258744503} g_{38}&{}-{}&\frac{115208921780}{2047258744503} g_{36}\\ w_{3}&{}={}&\frac{1125434681722}{682419581501}&{}-{}&\frac{42799107499418}{6141776233509} g_{38}&{}+{}&\frac{44286802177178}{6141776233509} g_{36}\\ g_{28}&{}={}&\frac{750346101145}{682419581501}&{}-{}&\frac{27906777157835}{6141776233509} g_{38}&{}+{}&\frac{30668556847709}{6141776233509} g_{36}\\ g_{29}&{}={}&\frac{26330897233}{35916820079}&{}-{}&\frac{946239838427}{323251380711} g_{38}&{}+{}&\frac{1136301401477}{323251380711} g_{36}\\ g_{30}&{}={}&\frac{333581011615}{682419581501}&{}-{}&\frac{11359743444965}{6141776233509} g_{38}&{}+{}&\frac{15537173148299}{6141776233509} g_{36}\\ g_{31}&{}={}&\frac{222443654407}{682419581501}&{}-{}&\frac{6947201121533}{6141776233509} g_{38}&{}+{}&\frac{11502137495123}{6141776233509} g_{36}\\ g_{34}&{}={}&\frac{5}{23}&{}+{}&\frac{8}{23} g_{38}&{}+{}&\frac{10}{23} g_{36}\\ g_{33}&{}={}&\frac{11}{23}&{}+{}&\frac{36}{23} g_{38}&{}-{}&\frac{24}{23} g_{36}\\ g_{32}&{}={}&\frac{5}{23}&{}-{}&\frac{15}{23} g_{38}&{}+{}&\frac{33}{23} g_{36}\\ g_{35}&{}={}&\frac{2}{23}&{}-{}&\frac{6}{23} g_{38}&{}+{}&\frac{27}{23} g_{36}\\ w_{2}&{}={}&1&{}+{}&4 g_{38}&{}-{}&4 g_{36}\\ g_{37}&{}={}&\frac{1}{3}&{}+{}&2 g_{38}&{}-{}&\frac{4}{3} g_{36}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{15101458710785610}{152028418264603}&{}-{}&\frac{62483176465920}{152028418264603} g_{39}&{}-{}&\frac{163673741435}{8001495698137} w_{3}\\\hline w_{1}&{}={}&\frac{1414589115762019}{152028418264603}&{}-{}&\frac{1785233613312}{152028418264603} g_{39}&{}+{}&\frac{6853748491505}{8001495698137} w_{3}\\ x_{1}&{}={}&\frac{422780267536044}{152028418264603}&{}+{}&\frac{7140934453248}{152028418264603} g_{39}&{}-{}&\frac{3410506871609}{8001495698137} w_{3}\\ x_{2}&{}={}&\frac{443056890670982}{152028418264603}&{}-{}&\frac{5355700839936}{152028418264603} g_{39}&{}+{}&\frac{4558254078241}{8001495698137} w_{3}\\ w_{4}&{}={}&\frac{945475496845383}{152028418264603}&{}-{}&\frac{7140934453248}{152028418264603} g_{39}&{}+{}&\frac{3410506871609}{8001495698137} w_{3}\\ w_{5}&{}={}&\frac{469113618916636}{152028418264603}&{}+{}&\frac{5355700839936}{152028418264603} g_{39}&{}-{}&\frac{4558254078241}{8001495698137} w_{3}\\ g_{8}&{}={}&\frac{114533492233288}{152028418264603}&{}+{}&\frac{21621162650112}{152028418264603} g_{39}&{}+{}&\frac{240280489281}{16002991396274} w_{3}\\ g_{2}&{}={}&\frac{131751795129665}{152028418264603}&{}+{}&\frac{12496635293184}{152028418264603} g_{39}&{}+{}&\frac{32734748287}{8001495698137} w_{3}\\ g_{17}&{}={}&\frac{4762803813957}{8001495698137}&{}+{}&\frac{1994459809248}{8001495698137} g_{39}&{}+{}&\frac{100538690938}{8001495698137} w_{3}\\ g_{3}&{}={}&\frac{49223403935950}{152028418264603}&{}+{}&\frac{9818784873216}{152028418264603} g_{39}&{}+{}&\frac{4623723574815}{16002991396274} w_{3}\\ g_{7}&{}={}&\frac{133678496833237}{152028418264603}&{}+{}&\frac{20232647617536}{152028418264603} g_{39}&{}-{}&\frac{328024488399}{8001495698137} w_{3}\\ g_{4}&{}={}&\frac{73353430478032}{152028418264603}&{}+{}&\frac{12794174228736}{152028418264603} g_{39}&{}+{}&\frac{3115217131497}{16002991396274} w_{3}\\ g_{5}&{}={}&\frac{171968506033135}{152028418264603}&{}+{}&\frac{17455617552384}{152028418264603} g_{39}&{}-{}&\frac{1224353954478}{8001495698137} w_{3}\\ g_{6}&{}={}&\frac{109548470291155}{152028418264603}&{}+{}&\frac{17257258262016}{152028418264603} g_{39}&{}+{}&\frac{426228733260}{8001495698137} w_{3}\\ g_{11}&{}={}&\frac{126381857801297}{152028418264603}&{}+{}&\frac{27456231775104}{152028418264603} g_{39}&{}-{}&\frac{425526297497}{8001495698137} w_{3}\\ g_{9}&{}={}&\frac{199421880536639}{152028418264603}&{}+{}&\frac{23340276499968}{152028418264603} g_{39}&{}-{}&\frac{2182666168550}{8001495698137} w_{3}\\ g_{10}&{}={}&\frac{150728532046411}{152028418264603}&{}+{}&\frac{26084246683392}{152028418264603} g_{39}&{}-{}&\frac{1011239587848}{8001495698137} w_{3}\\ g_{1}&{}={}&\frac{13028364122827}{152028418264603}&{}+{}&\frac{5355700839936}{152028418264603} g_{39}&{}+{}&\frac{3443241619896}{8001495698137} w_{3}\\ g_{12}&{}={}&\frac{46538435271766}{152028418264603}&{}+{}&\frac{17298583114176}{152028418264603} g_{39}&{}+{}&\frac{4165462529031}{16002991396274} w_{3}\\ g_{13}&{}={}&\frac{68878482704392}{152028418264603}&{}+{}&\frac{25260504630336}{152028418264603} g_{39}&{}+{}&\frac{2351448721857}{16002991396274} w_{3}\\ g_{18}&{}={}&\frac{284922667006963}{456085254793809}&{}+{}&\frac{42778925754336}{152028418264603} g_{39}&{}-{}&\frac{639412729051}{24004487094411} w_{3}\\ g_{15}&{}={}&\frac{178914117487431}{152028418264603}&{}+{}&\frac{29305136271744}{152028418264603} g_{39}&{}-{}&\frac{1882057603730}{8001495698137} w_{3}\\ g_{14}&{}={}&\frac{83771847659476}{152028418264603}&{}+{}&\frac{30568452307776}{152028418264603} g_{39}&{}+{}&\frac{1142106183741}{16002991396274} w_{3}\\ g_{16}&{}={}&\frac{119966887472599}{152028418264603}&{}+{}&\frac{35031536341056}{152028418264603} g_{39}&{}-{}&\frac{560326740618}{8001495698137} w_{3}\\ g_{26}&{}={}&\frac{60072483595131}{152028418264603}&{}+{}&\frac{67236144217416}{152028418264603} g_{39}&{}+{}&\frac{339748174276}{8001495698137} w_{3}\\ g_{19}&{}={}&\frac{22149041457060}{152028418264603}&{}+{}&\frac{21389462877168}{152028418264603} g_{39}&{}+{}&\frac{10455523354499}{16002991396274} w_{3}\\ g_{20}&{}={}&\frac{36915069095100}{152028418264603}&{}+{}&\frac{35649104795280}{152028418264603} g_{39}&{}+{}&\frac{6757211326649}{16002991396274} w_{3}\\ g_{21}&{}={}&\frac{2461004606340}{8001495698137}&{}+{}&\frac{2376606986352}{8001495698137} g_{39}&{}+{}&\frac{4291669974749}{16002991396274} w_{3}\\ g_{22}&{}={}&\frac{53321766470700}{152028418264603}&{}+{}&\frac{51493151370960}{152028418264603} g_{39}&{}+{}&\frac{2647975740149}{16002991396274} w_{3}\\ g_{27}&{}={}&\frac{184968646433935}{456085254793809}&{}+{}&\frac{74914753390488}{152028418264603} g_{39}&{}+{}&\frac{146561287631}{24004487094411} w_{3}\\ g_{24}&{}={}&\frac{161530809561687}{152028418264603}&{}+{}&\frac{46071655038432}{152028418264603} g_{39}&{}-{}&\frac{1745366470394}{8001495698137} w_{3}\\ g_{23}&{}={}&\frac{57696885770860}{152028418264603}&{}+{}&\frac{55718230457808}{152028418264603} g_{39}&{}+{}&\frac{1552179583749}{16002991396274} w_{3}\\ g_{25}&{}={}&\frac{93891925583983}{152028418264603}&{}+{}&\frac{60181314491088}{152028418264603} g_{39}&{}-{}&\frac{355290040614}{8001495698137} w_{3}\\ g_{36}&{}={}&\frac{6206185546462}{152028418264603}&{}+{}&\frac{128397322498254}{152028418264603} g_{39}&{}+{}&\frac{969754142133}{16002991396274} w_{3}\\ g_{28}&{}={}&\frac{5490038028222}{152028418264603}&{}+{}&\frac{37457376695244}{152028418264603} g_{39}&{}+{}&\frac{10717514693393}{16002991396274} w_{3}\\ g_{29}&{}={}&\frac{9150063380370}{152028418264603}&{}+{}&\frac{62428961158740}{152028418264603} g_{39}&{}+{}&\frac{7193863558139}{16002991396274} w_{3}\\ g_{30}&{}={}&\frac{610004225358}{8001495698137}&{}+{}&\frac{4161930743916}{8001495698137} g_{39}&{}+{}&\frac{4844762801303}{16002991396274} w_{3}\\ g_{31}&{}={}&\frac{13216758216090}{152028418264603}&{}+{}&\frac{90175166118180}{152028418264603} g_{39}&{}+{}&\frac{3278695630079}{16002991396274} w_{3}\\ g_{34}&{}={}&\frac{50496249985405}{152028418264603}&{}+{}&\frac{102037238140644}{152028418264603} g_{39}&{}-{}&\frac{14054407857}{8001495698137} w_{3}\\ g_{33}&{}={}&\frac{132600359162635}{152028418264603}&{}+{}&\frac{73975604138136}{152028418264603} g_{39}&{}-{}&\frac{1517876048556}{8001495698137} w_{3}\\ g_{32}&{}={}&\frac{14301210172282}{152028418264603}&{}+{}&\frac{97574154107364}{152028418264603} g_{39}&{}+{}&\frac{2234650849263}{16002991396274} w_{3}\\ g_{35}&{}={}&\frac{9444195396790}{152028418264603}&{}+{}&\frac{116068055141898}{152028418264603} g_{39}&{}+{}&\frac{1475712824985}{16002991396274} w_{3}\\ w_{2}&{}={}&\frac{296808577517095}{152028418264603}&{}+{}&\frac{17852336133120}{152028418264603} g_{39}&{}-{}&\frac{4525519329954}{8001495698137} w_{3}\\ g_{37}&{}={}&\frac{127203676078755}{152028418264603}&{}+{}&\frac{94524383065396}{152028418264603} g_{39}&{}-{}&\frac{1939508284266}{8001495698137} w_{3}\\ g_{38}&{}={}&\frac{42401225359585}{152028418264603}&{}+{}&\frac{132860406531534}{152028418264603} g_{39}&{}-{}&\frac{646502761422}{8001495698137} w_{3}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{60408944644229705}{608113673058412}&{}-{}&\frac{240603302601885}{608113673058412} g_{39}&{}-{}&\frac{491021224305}{16002991396274} g_{40}\\\hline w_{1}&{}={}&\frac{5788577684386671}{608113673058412}&{}-{}&\frac{397804598469033}{608113673058412} g_{39}&{}+{}&\frac{20561245474515}{16002991396274} g_{40}\\ x_{1}&{}={}&\frac{1626321439583605}{608113673058412}&{}+{}&\frac{222962629494705}{608113673058412} g_{39}&{}-{}&\frac{10231520614827}{16002991396274} g_{40}\\ x_{2}&{}={}&\frac{1858834390170507}{608113673058412}&{}-{}&\frac{281243285819481}{608113673058412} g_{39}&{}+{}&\frac{13674762234723}{16002991396274} g_{40}\\ w_{4}&{}={}&\frac{3846701617942103}{608113673058412}&{}-{}&\frac{222962629494705}{608113673058412} g_{39}&{}+{}&\frac{10231520614827}{16002991396274} g_{40}\\ w_{5}&{}={}&\frac{1789847648179965}{608113673058412}&{}+{}&\frac{281243285819481}{608113673058412} g_{39}&{}-{}&\frac{13674762234723}{16002991396274} g_{40}\\ g_{8}&{}={}&\frac{920833267162643}{1216227346116824}&{}+{}&\frac{159273313311879}{1216227346116824} g_{39}&{}+{}&\frac{720841467843}{32005982792548} g_{40}\\ g_{2}&{}={}&\frac{527629140736113}{608113673058412}&{}+{}&\frac{48120660520377}{608113673058412} g_{39}&{}+{}&\frac{98204244861}{16002991396274} g_{40}\\ g_{17}&{}={}&\frac{9575876973383}{16002991396274}&{}+{}&\frac{3838111582089}{16002991396274} g_{39}&{}+{}&\frac{150808036407}{8001495698137} g_{40}\\ g_{3}&{}={}&\frac{481637979409085}{1216227346116824}&{}-{}&\frac{185001964778727}{1216227346116824} g_{39}&{}+{}&\frac{13871170724445}{32005982792548} g_{40}\\ g_{7}&{}={}&\frac{528481522053367}{608113673058412}&{}+{}&\frac{99627986308887}{608113673058412} g_{39}&{}-{}&\frac{984073465197}{16002991396274} g_{40}\\ g_{4}&{}={}&\frac{646016569322699}{1216227346116824}&{}-{}&\frac{75213982665441}{1216227346116824} g_{39}&{}+{}&\frac{9345651394491}{32005982792548} g_{40}\\ g_{5}&{}={}&\frac{332305649498729}{304056836529206}&{}+{}&\frac{69805322807391}{304056836529206} g_{39}&{}-{}&\frac{1836530931717}{8001495698137} g_{40}\\ g_{6}&{}={}&\frac{111573056774140}{152028418264603}&{}+{}&\frac{11183498813061}{152028418264603} g_{39}&{}+{}&\frac{639343099890}{8001495698137} g_{40}\\ g_{11}&{}={}&\frac{497442431552745}{608113673058412}&{}+{}&\frac{134079926057745}{608113673058412} g_{39}&{}-{}&\frac{1276578892491}{16002991396274} g_{40}\\ g_{9}&{}={}&\frac{378108432472053}{304056836529206}&{}+{}&\frac{108886538803611}{304056836529206} g_{39}&{}-{}&\frac{3273999252825}{8001495698137} g_{40}\\ g_{10}&{}={}&\frac{145925144004133}{152028418264603}&{}+{}&\frac{40494410810226}{152028418264603} g_{39}&{}-{}&\frac{1516859381772}{8001495698137} g_{40}\\ g_{1}&{}={}&\frac{29383761817333}{152028418264603}&{}-{}&\frac{43710492243582}{152028418264603} g_{39}&{}+{}&\frac{5164862429844}{8001495698137} g_{40}\\ g_{12}&{}={}&\frac{451451270225717}{1216227346116824}&{}-{}&\frac{99042699241359}{1216227346116824} g_{39}&{}+{}&\frac{12496387587093}{32005982792548} g_{40}\\ g_{13}&{}={}&\frac{595705387350419}{1216227346116824}&{}+{}&\frac{68051459896839}{1216227346116824} g_{39}&{}+{}&\frac{7054346165571}{32005982792548} g_{40}\\ g_{18}&{}={}&\frac{375847275391961}{608113673058412}&{}+{}&\frac{183264544869313}{608113673058412} g_{39}&{}-{}&\frac{639412729051}{16002991396274} g_{40}\\ g_{15}&{}={}&\frac{339948687739427}{304056836529206}&{}+{}&\frac{112248914249793}{304056836529206} g_{39}&{}-{}&\frac{2823086405595}{8001495698137} g_{40}\\ g_{14}&{}={}&\frac{691874798766887}{1216227346116824}&{}+{}&\frac{179447565988971}{1216227346116824} g_{39}&{}+{}&\frac{3426318551223}{32005982792548} g_{40}\\ g_{16}&{}={}&\frac{234610670909327}{304056836529206}&{}+{}&\frac{86032384789725}{304056836529206} g_{39}&{}-{}&\frac{840490110927}{8001495698137} g_{40}\\ g_{26}&{}={}&\frac{61686287422942}{152028418264603}&{}+{}&\frac{62394732733983}{152028418264603} g_{39}&{}+{}&\frac{509622261414}{8001495698137} g_{40}\\ g_{19}&{}={}&\frac{375847275391961}{1216227346116824}&{}-{}&\frac{424849128189099}{1216227346116824} g_{39}&{}+{}&\frac{31366570063497}{32005982792548} g_{40}\\ g_{20}&{}={}&\frac{423707567967131}{1216227346116824}&{}-{}&\frac{99968207256753}{1216227346116824} g_{39}&{}+{}&\frac{20271633979947}{32005982792548} g_{40}\\ g_{21}&{}={}&\frac{23979706825469}{64011965585096}&{}+{}&\frac{6137845966569}{64011965585096} g_{39}&{}+{}&\frac{12875009924247}{32005982792548} g_{40}\\ g_{22}&{}={}&\frac{476885670828431}{1216227346116824}&{}+{}&\frac{261010593779187}{1216227346116824} g_{39}&{}+{}&\frac{7943927220447}{32005982792548} g_{40}\\ g_{27}&{}={}&\frac{247553083400243}{608113673058412}&{}+{}&\frac{296874349096963}{608113673058412} g_{39}&{}+{}&\frac{146561287631}{16002991396274} g_{40}\\ g_{24}&{}={}&\frac{306480637654631}{304056836529206}&{}+{}&\frac{141886254483093}{304056836529206} g_{39}&{}-{}&\frac{2618049705591}{8001495698137} g_{40}\\ g_{23}&{}={}&\frac{491066498258111}{1216227346116824}&{}+{}&\frac{357271607388771}{1216227346116824} g_{39}&{}+{}&\frac{4656538751247}{32005982792548} g_{40}\\ g_{25}&{}={}&\frac{184408595782133}{304056836529206}&{}+{}&\frac{130488395139675}{304056836529206} g_{39}&{}-{}&\frac{532935060921}{8001495698137} g_{40}\\ g_{36}&{}={}&\frac{68074813072223}{1216227346116824}&{}+{}&\frac{971902593884451}{1216227346116824} g_{39}&{}+{}&\frac{2909262426399}{32005982792548} g_{40}\\ g_{28}&{}={}&\frac{247553083400243}{1216227346116824}&{}-{}&\frac{311239323961449}{1216227346116824} g_{39}&{}+{}&\frac{32152544080179}{32005982792548} g_{40}\\ g_{29}&{}={}&\frac{209883914647601}{1216227346116824}&{}+{}&\frac{89381466455997}{1216227346116824} g_{39}&{}+{}&\frac{21581590674417}{32005982792548} g_{40}\\ g_{30}&{}={}&\frac{9724796604167}{64011965585096}&{}+{}&\frac{18761157547419}{64011965585096} g_{39}&{}+{}&\frac{14534288403909}{32005982792548} g_{40}\\ g_{31}&{}={}&\frac{168029282700221}{1216227346116824}&{}+{}&\frac{534515678030937}{1216227346116824} g_{39}&{}+{}&\frac{9836086890237}{32005982792548} g_{40}\\ g_{34}&{}={}&\frac{201717966192337}{608113673058412}&{}+{}&\frac{408950053810425}{608113673058412} g_{39}&{}-{}&\frac{42163223571}{16002991396274} g_{40}\\ g_{33}&{}={}&\frac{125390447931994}{152028418264603}&{}+{}&\frac{95605337830059}{152028418264603} g_{39}&{}-{}&\frac{2276814072834}{8001495698137} g_{40}\\ g_{32}&{}={}&\frac{156868047514253}{1216227346116824}&{}+{}&\frac{653218134450921}{1216227346116824} g_{39}&{}+{}&\frac{6703952547789}{32005982792548} g_{40}\\ g_{35}&{}={}&\frac{103592106849035}{1216227346116824}&{}+{}&\frac{844428810111039}{1216227346116824} g_{39}&{}+{}&\frac{4427138474955}{32005982792548} g_{40}\\ w_{2}&{}={}&\frac{550624721399627}{304056836529206}&{}+{}&\frac{164681973169929}{304056836529206} g_{39}&{}-{}&\frac{6788278994931}{8001495698137} g_{40}\\ g_{37}&{}={}&\frac{235982023456983}{304056836529206}&{}+{}&\frac{244324752232373}{304056836529206} g_{39}&{}-{}&\frac{2909262426399}{8001495698137} g_{40}\\ g_{38}&{}={}&\frac{78660674485661}{304056836529206}&{}+{}&\frac{284146141763595}{304056836529206} g_{39}&{}-{}&\frac{969754142133}{8001495698137} g_{40}\\ w_{3}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{39}&{}+{}&\frac{3}{2} g_{40}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{120827218691721205}{1216227346116824}&{}-{}&\frac{453218395418385}{1216227346116824} g_{39}&{}-{}&\frac{1473063672915}{32005982792548} g_{41}\\\hline w_{1}&{}={}&\frac{11967819032789127}{1216227346116824}&{}-{}&\frac{1967600188985421}{1216227346116824} g_{39}&{}+{}&\frac{61683736423545}{32005982792548} g_{41}\\ x_{1}&{}={}&\frac{3058243987485497}{1216227346116824}&{}+{}&\frac{1029121934034549}{1216227346116824} g_{39}&{}-{}&\frac{30694561844481}{32005982792548} g_{41}\\ x_{2}&{}={}&\frac{3977489262800751}{1216227346116824}&{}-{}&\frac{1341948019018173}{1216227346116824} g_{39}&{}+{}&\frac{41024286704169}{32005982792548} g_{41}\\ w_{4}&{}={}&\frac{7887802127565919}{1216227346116824}&{}-{}&\frac{1029121934034549}{1216227346116824} g_{39}&{}+{}&\frac{30694561844481}{32005982792548} g_{41}\\ w_{5}&{}={}&\frac{3319874813900193}{1216227346116824}&{}+{}&\frac{1341948019018173}{1216227346116824} g_{39}&{}-{}&\frac{41024286704169}{32005982792548} g_{41}\\ g_{8}&{}={}&\frac{1855362522214303}{2432454692233648}&{}+{}&\frac{277458662956707}{2432454692233648} g_{39}&{}+{}&\frac{2162524403529}{64011965585096} g_{41}\\ g_{2}&{}={}&\frac{1057124162124585}{1216227346116824}&{}+{}&\frac{90643679083677}{1216227346116824} g_{39}&{}+{}&\frac{294612734583}{32005982792548} g_{41}\\ g_{17}&{}={}&\frac{19302561983173}{32005982792548}&{}+{}&\frac{7223799054957}{32005982792548} g_{39}&{}+{}&\frac{452424109221}{16002991396274} g_{41}\\ g_{3}&{}={}&\frac{1226828202582625}{2432454692233648}&{}-{}&\frac{1160660660850819}{2432454692233648} g_{39}&{}+{}&\frac{41613512173335}{64011965585096} g_{41}\\ g_{7}&{}={}&\frac{1038265648267991}{1216227346116824}&{}+{}&\frac{255348160134003}{1216227346116824} g_{39}&{}-{}&\frac{2952220395591}{32005982792548} g_{41}\\ g_{4}&{}={}&\frac{1469600515140727}{2432454692233648}&{}-{}&\frac{683130094816869}{2432454692233648} g_{39}&{}+{}&\frac{28036954183473}{64011965585096} g_{41}\\ g_{5}&{}={}&\frac{629717211294835}{608113673058412}&{}+{}&\frac{244292908722651}{608113673058412} g_{39}&{}-{}&\frac{5509592795151}{16002991396274} g_{41}\\ g_{6}&{}={}&\frac{229219872997235}{304056836529206}&{}+{}&\frac{4145719279257}{304056836529206} g_{39}&{}+{}&\frac{959014649835}{8001495698137} g_{41}\\ g_{11}&{}={}&\frac{970629864148161}{1216227346116824}&{}+{}&\frac{340924848987477}{1216227346116824} g_{39}&{}-{}&\frac{3829736677473}{32005982792548} g_{41}\\ g_{9}&{}={}&\frac{694010879140431}{608113673058412}&{}+{}&\frac{404391035018247}{608113673058412} g_{39}&{}-{}&\frac{9821997758475}{16002991396274} g_{41}\\ g_{10}&{}={}&\frac{138720061940716}{152028418264603}&{}+{}&\frac{62109657000477}{152028418264603} g_{39}&{}-{}&\frac{2275289072658}{8001495698137} g_{41}\\ g_{1}&{}={}&\frac{53916858359092}{152028418264603}&{}-{}&\frac{117309781868859}{152028418264603} g_{39}&{}+{}&\frac{7747293644766}{8001495698137} g_{41}\\ g_{12}&{}={}&\frac{1140333904606201}{2432454692233648}&{}-{}&\frac{910379490947019}{2432454692233648} g_{39}&{}+{}&\frac{37489162761279}{64011965585096} g_{41}\\ g_{13}&{}={}&\frac{1325443351846687}{2432454692233648}&{}-{}&\frac{265994811643869}{2432454692233648} g_{39}&{}+{}&\frac{21163038496713}{64011965585096} g_{41}\\ g_{18}&{}={}&\frac{739545708931953}{1216227346116824}&{}+{}&\frac{402975615294533}{1216227346116824} g_{39}&{}-{}&\frac{1918238187153}{32005982792548} g_{41}\\ g_{15}&{}={}&\frac{626258733772549}{608113673058412}&{}+{}&\frac{385413753618501}{608113673058412} g_{39}&{}-{}&\frac{8469259216785}{16002991396274} g_{41}\\ g_{14}&{}={}&\frac{1448849650007011}{2432454692233648}&{}+{}&\frac{163594974558231}{2432454692233648} g_{39}&{}+{}&\frac{10278955653669}{64011965585096} g_{41}\\ g_{16}&{}={}&\frac{453252029711041}{608113673058412}&{}+{}&\frac{219972705902289}{608113673058412} g_{39}&{}-{}&\frac{2521470332781}{16002991396274} g_{41}\\ g_{26}&{}={}&\frac{128213986329317}{304056836529206}&{}+{}&\frac{110265231017667}{304056836529206} g_{39}&{}+{}&\frac{764433392121}{8001495698137} g_{41}\\ g_{19}&{}={}&\frac{1347659381990365}{2432454692233648}&{}-{}&\frac{2637592749997527}{2432454692233648} g_{39}&{}+{}&\frac{94099710190491}{64011965585096} g_{41}\\ g_{20}&{}={}&\frac{1232576181553255}{2432454692233648}&{}-{}&\frac{1355419551370485}{2432454692233648} g_{39}&{}+{}&\frac{60814901939841}{64011965585096} g_{41}\\ g_{21}&{}={}&\frac{60834423575185}{128023931170192}&{}-{}&\frac{26349337839603}{128023931170192} g_{39}&{}+{}&\frac{38625029772741}{64011965585096} g_{41}\\ g_{22}&{}={}&\frac{1104705958845355}{2432454692233648}&{}+{}&\frac{69217335992895}{2432454692233648} g_{39}&{}+{}&\frac{23831781661341}{64011965585096} g_{41}\\ g_{27}&{}={}&\frac{497890831265475}{1216227346116824}&{}+{}&\frac{585394704798959}{1216227346116824} g_{39}&{}+{}&\frac{439683862893}{32005982792548} g_{41}\\ g_{24}&{}={}&\frac{563218330903033}{608113673058412}&{}+{}&\frac{433001342184873}{608113673058412} g_{39}&{}-{}&\frac{7854149116773}{16002991396274} g_{41}\\ g_{23}&{}={}&\frac{1070607232789915}{2432454692233648}&{}+{}&\frac{449120505956463}{2432454692233648} g_{39}&{}+{}&\frac{13969616253741}{64011965585096} g_{41}\\ g_{25}&{}={}&\frac{358691425406767}{608113673058412}&{}+{}&\frac{291354088751847}{608113673058412} g_{39}&{}-{}&\frac{1598805182763}{16002991396274} g_{41}\\ g_{36}&{}={}&\frac{191425612246027}{2432454692233648}&{}+{}&\frac{1777977229464159}{2432454692233648} g_{39}&{}+{}&\frac{8727787279197}{64011965585096} g_{41}\\ g_{28}&{}={}&\frac{1106004504323887}{2432454692233648}&{}-{}&\frac{2455173660493101}{2432454692233648} g_{39}&{}+{}&\frac{96457632240537}{64011965585096} g_{41}\\ g_{29}&{}={}&\frac{829818052109125}{2432454692233648}&{}-{}&\frac{1051387735529775}{2432454692233648} g_{39}&{}+{}&\frac{64744772023251}{64011965585096} g_{41}\\ g_{30}&{}={}&\frac{33983881612243}{128023931170192}&{}-{}&\frac{6080550116889}{128023931170192} g_{39}&{}+{}&\frac{43602865211727}{64011965585096} g_{41}\\ g_{31}&{}={}&\frac{522944216314945}{2432454692233648}&{}+{}&\frac{508374403318365}{2432454692233648} g_{39}&{}+{}&\frac{29508260670711}{64011965585096} g_{41}\\ g_{34}&{}={}&\frac{402634831136825}{1216227346116824}&{}+{}&\frac{820303411364397}{1216227346116824} g_{39}&{}-{}&\frac{126489670713}{32005982792548} g_{41}\\ g_{33}&{}={}&\frac{229151162172065}{304056836529206}&{}+{}&\frac{256099876735887}{304056836529206} g_{39}&{}-{}&\frac{3415221109251}{8001495698137} g_{41}\\ g_{32}&{}={}&\frac{441111193436497}{2432454692233648}&{}+{}&\frac{924310973677869}{2432454692233648} g_{39}&{}+{}&\frac{20111857643367}{64011965585096} g_{41}\\ g_{35}&{}={}&\frac{291299844722215}{2432454692233648}&{}+{}&\frac{1436510727149643}{2432454692233648} g_{39}&{}+{}&\frac{13281415424865}{64011965585096} g_{41}\\ w_{2}&{}={}&\frac{972272141895565}{608113673058412}&{}+{}&\frac{716295849050925}{608113673058412} g_{39}&{}-{}&\frac{20364836984793}{16002991396274} g_{41}\\ g_{37}&{}={}&\frac{416688060812385}{608113673058412}&{}+{}&\frac{654477462769489}{608113673058412} g_{39}&{}-{}&\frac{8727787279197}{16002991396274} g_{41}\\ g_{38}&{}={}&\frac{138896020270795}{608113673058412}&{}+{}&\frac{623568269628771}{608113673058412} g_{39}&{}-{}&\frac{2909262426399}{16002991396274} g_{41}\\ w_{3}&{}={}&\frac{5}{8}&{}-{}&\frac{15}{8} g_{39}&{}+{}&\frac{9}{4} g_{41}\\ g_{40}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{39}&{}+{}&\frac{3}{2} g_{41}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{241682425593227795}{2432454692233648}&{}-{}&\frac{822472161480615}{2432454692233648} g_{39}&{}-{}&\frac{4419191018745}{64011965585096} g_{42}\\\hline w_{1}&{}={}&\frac{25107629057625609}{2432454692233648}&{}-{}&\frac{7451173354112907}{2432454692233648} g_{39}&{}+{}&\frac{185051209270635}{64011965585096} g_{42}\\ x_{1}&{}={}&\frac{5533291299925855}{2432454692233648}&{}+{}&\frac{3807833893204515}{2432454692233648} g_{39}&{}-{}&\frac{92083685533443}{64011965585096} g_{42}\\ x_{2}&{}={}&\frac{8734439972980713}{2432454692233648}&{}-{}&\frac{5022280380173979}{2432454692233648} g_{39}&{}+{}&\frac{123072860112507}{64011965585096} g_{42}\\ w_{4}&{}={}&\frac{16358800930176977}{2432454692233648}&{}-{}&\frac{3807833893204515}{2432454692233648} g_{39}&{}+{}&\frac{92083685533443}{64011965585096} g_{42}\\ w_{5}&{}={}&\frac{5860288180421175}{2432454692233648}&{}+{}&\frac{5022280380173979}{2432454692233648} g_{39}&{}-{}&\frac{123072860112507}{64011965585096} g_{42}\\ g_{8}&{}={}&\frac{3751813008095657}{4864909384467296}&{}+{}&\frac{431653434912261}{4864909384467296} g_{39}&{}+{}&\frac{6487573210587}{128023931170192} g_{42}\\ g_{2}&{}={}&\frac{2119845966206247}{2432454692233648}&{}+{}&\frac{164494432296123}{2432454692233648} g_{39}&{}+{}&\frac{883838203749}{64011965585096} g_{42}\\ g_{17}&{}={}&\frac{39057548075567}{64011965585096}&{}+{}&\frac{13090325782251}{64011965585096} g_{39}&{}+{}&\frac{1357272327663}{32005982792548} g_{42}\\ g_{3}&{}={}&\frac{3244313136458615}{4864909384467296}&{}-{}&\frac{4693291515581733}{4864909384467296} g_{39}&{}+{}&\frac{124840536520005}{128023931170192} g_{42}\\ g_{7}&{}={}&\frac{2020439109019753}{2432454692233648}&{}+{}&\frac{678972882816693}{2432454692233648} g_{39}&{}-{}&\frac{8856661186773}{64011965585096} g_{42}\\ g_{4}&{}={}&\frac{3471903159767441}{4864909384467296}&{}-{}&\frac{2964366578091699}{4864909384467296} g_{39}&{}+{}&\frac{84110862550419}{128023931170192} g_{42}\\ g_{5}&{}={}&\frac{1154752159481801}{1216227346116824}&{}+{}&\frac{802632606768909}{1216227346116824} g_{39}&{}-{}&\frac{16528778385453}{32005982792548} g_{42}\\ g_{6}&{}={}&\frac{476661024341335}{608113673058412}&{}-{}&\frac{46372396482081}{608113673058412} g_{39}&{}+{}&\frac{2877043949505}{16002991396274} g_{42}\\ g_{11}&{}={}&\frac{1868494731424335}{2432454692233648}&{}+{}&\frac{900144688590915}{2432454692233648} g_{39}&{}-{}&\frac{11489210032419}{64011965585096} g_{42}\\ g_{9}&{}={}&\frac{1201403800869837}{1216227346116824}&{}+{}&\frac{1368635942269569}{1216227346116824} g_{39}&{}-{}&\frac{29465993275425}{32005982792548} g_{42}\\ g_{10}&{}={}&\frac{255824877691181}{304056836529206}&{}+{}&\frac{189065052571707}{304056836529206} g_{39}&{}-{}&\frac{3412933608987}{8001495698137} g_{42}\\ g_{1}&{}={}&\frac{181433006343461}{304056836529206}&{}-{}&\frac{455417432613549}{304056836529206} g_{39}&{}+{}&\frac{11620940467149}{8001495698137} g_{42}\\ g_{12}&{}={}&\frac{2992961901676703}{4864909384467296}&{}-{}&\frac{3957641259286941}{4864909384467296} g_{39}&{}+{}&\frac{112467488283837}{128023931170192} g_{42}\\ g_{13}&{}={}&\frac{3052984435130921}{4864909384467296}&{}-{}&\frac{1738282817600379}{4864909384467296} g_{39}&{}+{}&\frac{63489115490139}{128023931170192} g_{42}\\ g_{18}&{}={}&\frac{1442644892307999}{2432454692233648}&{}+{}&\frac{915290807256787}{2432454692233648} g_{39}&{}-{}&\frac{5754714561459}{64011965585096} g_{42}\\ g_{15}&{}={}&\frac{1091601542426183}{1216227346116824}&{}+{}&\frac{1253575282593747}{1216227346116824} g_{39}&{}-{}&\frac{25407777650355}{32005982792548} g_{42}\\ g_{14}&{}={}&\frac{3092999457433733}{4864909384467296}&{}-{}&\frac{258710523142671}{4864909384467296} g_{39}&{}+{}&\frac{30836866961007}{128023931170192} g_{42}\\ g_{16}&{}={}&\frac{858596123099243}{1216227346116824}&{}+{}&\frac{583669220773095}{1216227346116824} g_{39}&{}-{}&\frac{7564410998343}{32005982792548} g_{42}\\ g_{26}&{}={}&\frac{270952207108933}{608113673058412}&{}+{}&\frac{176957758684437}{608113673058412} g_{39}&{}+{}&\frac{2293300176363}{16002991396274} g_{42}\\ g_{19}&{}={}&\frac{4483213257600059}{4864909384467296}&{}-{}&\frac{10638868980853041}{4864909384467296} g_{39}&{}+{}&\frac{282299130571473}{128023931170192} g_{42}\\ g_{20}&{}={}&\frac{3620635499963489}{4864909384467296}&{}-{}&\frac{6177288513311907}{4864909384467296} g_{39}&{}+{}&\frac{182444705819523}{128023931170192} g_{42}\\ g_{21}&{}={}&\frac{160293876923111}{256047862340384}&{}-{}&\frac{168573764997429}{256047862340384} g_{39}&{}+{}&\frac{115875089318223}{128023931170192} g_{42}\\ g_{22}&{}={}&\frac{2662215769256189}{4864909384467296}&{}-{}&\frac{1219976882710647}{4864909384467296} g_{39}&{}+{}&\frac{71495344984023}{128023931170192} g_{42}\\ g_{27}&{}={}&\frac{1004135655925917}{2432454692233648}&{}+{}&\frac{1145727429413017}{2432454692233648} g_{39}&{}+{}&\frac{1319051588679}{64011965585096} g_{42}\\ g_{24}&{}={}&\frac{977207828587379}{1216227346116824}&{}+{}&\frac{1313689184025807}{1216227346116824} g_{39}&{}-{}&\frac{23562447350319}{32005982792548} g_{42}\\ g_{23}&{}={}&\frac{2406637174400909}{4864909384467296}&{}+{}&\frac{101972885449689}{4864909384467296} g_{39}&{}+{}&\frac{41908848761223}{128023931170192} g_{42}\\ g_{25}&{}={}&\frac{687005552341037}{1216227346116824}&{}+{}&\frac{673840072921185}{1216227346116824} g_{39}&{}-{}&\frac{4796415548289}{32005982792548} g_{42}\\ g_{36}&{}={}&\frac{548679182796797}{4864909384467296}&{}+{}&\frac{3058470584014089}{4864909384467296} g_{39}&{}+{}&\frac{26183361837591}{128023931170192} g_{42}\\ g_{28}&{}={}&\frac{4044704021217977}{4864909384467296}&{}-{}&\frac{10408432358696811}{4864909384467296} g_{39}&{}+{}&\frac{289372896721611}{128023931170192} g_{42}\\ g_{29}&{}={}&\frac{2889786772660019}{4864909384467296}&{}-{}&\frac{5793227476384857}{4864909384467296} g_{39}&{}+{}&\frac{194234316069753}{128023931170192} g_{42}\\ g_{30}&{}={}&\frac{111570628436213}{256047862340384}&{}-{}&\frac{142969695868959}{256047862340384} g_{39}&{}+{}&\frac{130808595635181}{128023931170192} g_{42}\\ g_{31}&{}={}&\frac{1606545385373399}{4864909384467296}&{}-{}&\frac{665222051593797}{4864909384467296} g_{39}&{}+{}&\frac{88524782012133}{128023931170192} g_{42}\\ g_{34}&{}={}&\frac{802866358530103}{2432454692233648}&{}+{}&\frac{1647816733959435}{2432454692233648} g_{39}&{}-{}&\frac{379469012139}{64011965585096} g_{42}\\ g_{33}&{}={}&\frac{393413123268361}{608113673058412}&{}+{}&\frac{706867356699081}{608113673058412} g_{39}&{}-{}&\frac{10245663327753}{16002991396274} g_{42}\\ g_{32}&{}={}&\frac{1264347682096967}{4864909384467296}&{}+{}&\frac{702246061683819}{4864909384467296} g_{39}&{}+{}&\frac{60335572930101}{128023931170192} g_{42}\\ g_{35}&{}={}&\frac{834946582516865}{4864909384467296}&{}+{}&\frac{2115980775081981}{4864909384467296} g_{39}&{}+{}&\frac{39844246274595}{128023931170192} g_{42}\\ w_{2}&{}={}&\frac{1557612381080063}{1216227346116824}&{}+{}&\frac{2593387406235051}{1216227346116824} g_{39}&{}-{}&\frac{61094510954379}{32005982792548} g_{42}\\ g_{37}&{}={}&\frac{667548163320027}{1216227346116824}&{}+{}&\frac{1806438800453207}{1216227346116824} g_{39}&{}-{}&\frac{26183361837591}{32005982792548} g_{42}\\ g_{38}&{}={}&\frac{222516054440009}{1216227346116824}&{}+{}&\frac{1412964497562285}{1216227346116824} g_{39}&{}-{}&\frac{8727787279197}{32005982792548} g_{42}\\ w_{3}&{}={}&\frac{19}{16}&{}-{}&\frac{57}{16} g_{39}&{}+{}&\frac{27}{8} g_{42}\\ g_{40}&{}={}&\frac{5}{8}&{}-{}&\frac{15}{8} g_{39}&{}+{}&\frac{9}{4} g_{42}\\ g_{41}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{39}&{}+{}&\frac{3}{2} g_{42}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{483448815815811745}{4864909384467296}&{}-{}&\frac{1393050434892765}{4864909384467296} g_{39}&{}-{}&\frac{13257573056235}{128023931170192} g_{43}\\\hline w_{1}&{}={}&\frac{53731231091393283}{4864909384467296}&{}-{}&\frac{25450265636652009}{4864909384467296} g_{39}&{}+{}&\frac{555153627811905}{128023931170192} g_{43}\\ x_{1}&{}={}&\frac{9316992574716293}{4864909384467296}&{}+{}&\frac{12864437861815281}{4864909384467296} g_{39}&{}-{}&\frac{276251056600329}{128023931170192} g_{43}\\ x_{2}&{}={}&\frac{19807264288099059}{4864909384467296}&{}-{}&\frac{17059713786760857}{4864909384467296} g_{39}&{}+{}&\frac{369218580337521}{128023931170192} g_{43}\\ w_{4}&{}={}&\frac{34467191885489371}{4864909384467296}&{}-{}&\frac{12864437861815281}{4864909384467296} g_{39}&{}+{}&\frac{276251056600329}{128023931170192} g_{43}\\ w_{5}&{}={}&\frac{9382192018704717}{4864909384467296}&{}+{}&\frac{17059713786760857}{4864909384467296} g_{39}&{}-{}&\frac{369218580337521}{128023931170192} g_{43}\\ g_{8}&{}={}&\frac{7626889907192467}{9729818768934592}&{}+{}&\frac{493515196821063}{9729818768934592} g_{39}&{}+{}&\frac{19462719631761}{256047862340384} g_{43}\\ g_{2}&{}={}&\frac{4256484858283725}{4864909384467296}&{}+{}&\frac{278610086978553}{4864909384467296} g_{39}&{}+{}&\frac{2651514611247}{128023931170192} g_{43}\\ g_{17}&{}={}&\frac{79472368478797}{128023931170192}&{}+{}&\frac{22108834581513}{128023931170192} g_{39}&{}+{}&\frac{4071816982989}{64011965585096} g_{43}\\ g_{3}&{}={}&\frac{8860596466797325}{9729818768934592}&{}-{}&\frac{16502493612803751}{9729818768934592} g_{39}&{}+{}&\frac{374521609560015}{256047862340384} g_{43}\\ g_{7}&{}={}&\frac{3872601655490819}{4864909384467296}&{}+{}&\frac{1862775453279447}{4864909384467296} g_{39}&{}-{}&\frac{26569983560319}{128023931170192} g_{43}\\ g_{4}&{}={}&\frac{8541912707992843}{9729818768934592}&{}-{}&\frac{10723052321557281}{9729818768934592} g_{39}&{}+{}&\frac{252332587651257}{256047862340384} g_{43}\\ g_{5}&{}={}&\frac{1995457529639995}{2432454692233648}&{}+{}&\frac{2547405581508639}{2432454692233648} g_{39}&{}-{}&\frac{49586335156359}{64011965585096} g_{43}\\ g_{6}&{}={}&\frac{1007985883723265}{1216227346116824}&{}-{}&\frac{256736298085947}{1216227346116824} g_{39}&{}+{}&\frac{8631131848515}{32005982792548} g_{43}\\ g_{11}&{}={}&\frac{3518694472232709}{4864909384467296}&{}+{}&\frac{2455174349029713}{4864909384467296} g_{39}&{}-{}&\frac{34467630097257}{128023931170192} g_{43}\\ g_{9}&{}={}&\frac{1842953729506599}{2432454692233648}&{}+{}&\frac{4416833501238363}{2432454692233648} g_{39}&{}-{}&\frac{88397979826275}{64011965585096} g_{43}\\ g_{10}&{}={}&\frac{446804016811609}{608113673058412}&{}+{}&\frac{572667320855673}{608113673058412} g_{39}&{}-{}&\frac{10238800826961}{16002991396274} g_{43}\\ g_{1}&{}={}&\frac{583663881562753}{608113673058412}&{}-{}&\frac{1573228471854591}{608113673058412} g_{39}&{}+{}&\frac{34862821401447}{16002991396274} g_{43}\\ g_{12}&{}={}&\frac{8122806080746309}{9729818768934592}&{}-{}&\frac{14325929350752591}{9729818768934592} g_{39}&{}+{}&\frac{337402464851511}{256047862340384} g_{43}\\ g_{13}&{}={}&\frac{7312262064574483}{9729818768934592}&{}-{}&\frac{7095445218138681}{9729818768934592} g_{39}&{}+{}&\frac{190467346470417}{256047862340384} g_{43}\\ g_{18}&{}={}&\frac{2775950207948277}{4864909384467296}&{}+{}&\frac{2158600344516737}{4864909384467296} g_{39}&{}-{}&\frac{17264143684377}{128023931170192} g_{43}\\ g_{15}&{}={}&\frac{1700455309495621}{2432454692233648}&{}+{}&\frac{3955393891257729}{2432454692233648} g_{39}&{}-{}&\frac{76223332951065}{64011965585096} g_{43}\\ g_{14}&{}={}&\frac{6771899387126599}{9729818768934592}&{}-{}&\frac{2275122463062741}{9729818768934592} g_{39}&{}+{}&\frac{92510600883021}{256047862340384} g_{43}\\ g_{16}&{}={}&\frac{1573468437229969}{2432454692233648}&{}+{}&\frac{1598509868451741}{2432454692233648} g_{39}&{}-{}&\frac{22693232995029}{64011965585096} g_{43}\\ g_{26}&{}={}&\frac{585477117568763}{1216227346116824}&{}+{}&\frac{223197407316183}{1216227346116824} g_{39}&{}+{}&\frac{6879900529089}{32005982792548} g_{43}\\ g_{19}&{}={}&\frac{14330109996058105}{9729818768934592}&{}-{}&\frac{37368788404280043}{9729818768934592} g_{39}&{}+{}&\frac{846897391714419}{256047862340384} g_{43}\\ g_{20}&{}={}&\frac{10707720410497915}{9729818768934592}&{}-{}&\frac{22753925258336625}{9729818768934592} g_{39}&{}+{}&\frac{547334117458569}{256047862340384} g_{43}\\ g_{21}&{}={}&\frac{436462843164445}{512095724680768}&{}-{}&\frac{684772797949527}{512095724680768} g_{39}&{}+{}&\frac{347625267954669}{256047862340384} g_{43}\\ g_{22}&{}={}&\frac{6682843093208815}{9729818768934592}&{}-{}&\frac{6515188429510605}{9729818768934592} g_{39}&{}+{}&\frac{214486034952069}{256047862340384} g_{43}\\ g_{27}&{}={}&\frac{2033333292036735}{4864909384467296}&{}+{}&\frac{2216268918271331}{4864909384467296} g_{39}&{}+{}&\frac{3957154766037}{128023931170192} g_{43}\\ g_{24}&{}={}&\frac{1506729157518697}{2432454692233648}&{}+{}&\frac{3970437867019797}{2432454692233648} g_{39}&{}-{}&\frac{70687342050957}{64011965585096} g_{43}\\ g_{23}&{}={}&\frac{5609542475265055}{9729818768934592}&{}-{}&\frac{2184858608490333}{9729818768934592} g_{39}&{}+{}&\frac{125726546283669}{256047862340384} g_{43}\\ g_{25}&{}={}&\frac{1282879209264583}{2432454692233648}&{}+{}&\frac{1621075832094843}{2432454692233648} g_{39}&{}-{}&\frac{14389246644867}{64011965585096} g_{43}\\ g_{36}&{}={}&\frac{1594842240507823}{9729818768934592}&{}+{}&\frac{4624489543285491}{9729818768934592} g_{39}&{}+{}&\frac{78550085512773}{256047862340384} g_{43}\\ g_{28}&{}={}&\frac{13587493080146563}{9729818768934592}&{}-{}&\frac{37311119830525449}{9729818768934592} g_{39}&{}+{}&\frac{868118690164833}{256047862340384} g_{43}\\ g_{29}&{}={}&\frac{9470025550645345}{9729818768934592}&{}-{}&\frac{22657810968745635}{9729818768934592} g_{39}&{}+{}&\frac{582702948209259}{256047862340384} g_{43}\\ g_{30}&{}={}&\frac{353949852507607}{512095724680768}&{}-{}&\frac{678365178643461}{512095724680768} g_{39}&{}+{}&\frac{392425786905543}{256047862340384} g_{43}\\ g_{31}&{}={}&\frac{4895061628977325}{9729818768934592}&{}-{}&\frac{6376356677879175}{9729818768934592} g_{39}&{}+{}&\frac{265574346036399}{256047862340384} g_{43}\\ g_{34}&{}={}&\frac{1598522805829565}{4864909384467296}&{}+{}&\frac{3317263201610793}{4864909384467296} g_{39}&{}-{}&\frac{1138407036417}{128023931170192} g_{43}\\ g_{33}&{}={}&\frac{592158643309415}{1216227346116824}&{}+{}&\frac{1997737523080083}{1216227346116824} g_{39}&{}-{}&\frac{30736989983259}{32005982792548} g_{43}\\ g_{32}&{}={}&\frac{3675071249865853}{9729818768934592}&{}-{}&\frac{2034635533648119}{9729818768934592} g_{39}&{}+{}&\frac{181006718790303}{256047862340384} g_{43}\\ g_{35}&{}={}&\frac{2426933844251035}{9729818768934592}&{}+{}&\frac{1960839512512047}{9729818768934592} g_{39}&{}+{}&\frac{119532738823785}{256047862340384} g_{43}\\ w_{2}&{}={}&\frac{1954429054026925}{2432454692233648}&{}+{}&\frac{8669161936869705}{2432454692233648} g_{39}&{}-{}&\frac{183283532863137}{64011965585096} g_{43}\\ g_{37}&{}={}&\frac{837612451725825}{2432454692233648}&{}+{}&\frac{5105329225649101}{2432454692233648} g_{39}&{}-{}&\frac{78550085512773}{64011965585096} g_{43}\\ g_{38}&{}={}&\frac{279204150575275}{2432454692233648}&{}+{}&\frac{3323412870038799}{2432454692233648} g_{39}&{}-{}&\frac{26183361837591}{64011965585096} g_{43}\\ w_{3}&{}={}&\frac{65}{32}&{}-{}&\frac{195}{32} g_{39}&{}+{}&\frac{81}{16} g_{43}\\ g_{40}&{}={}&\frac{19}{16}&{}-{}&\frac{57}{16} g_{39}&{}+{}&\frac{27}{8} g_{43}\\ g_{41}&{}={}&\frac{5}{8}&{}-{}&\frac{15}{8} g_{39}&{}+{}&\frac{9}{4} g_{43}\\ g_{42}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{39}&{}+{}&\frac{3}{2} g_{43}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{967149525519691955}{9729818768934592}&{}-{}&\frac{2030419205580135}{9729818768934592} g_{39}&{}-{}&\frac{39772719168705}{256047862340384} g_{44}\\\hline w_{1}&{}={}&\frac{118010381111212761}{9729818768934592}&{}-{}&\frac{82544288058582603}{9729818768934592} g_{39}&{}+{}&\frac{1665460883435715}{256047862340384} g_{44}\\ x_{1}&{}={}&\frac{13385215074026335}{9729818768934592}&{}+{}&\frac{41475185949849315}{9729818768934592} g_{39}&{}-{}&\frac{828753169800987}{256047862340384} g_{44}\\ x_{2}&{}={}&\frac{46629681602611017}{9729818768934592}&{}-{}&\frac{55164886652760411}{9729818768934592} g_{39}&{}+{}&\frac{1107655741012563}{256047862340384} g_{44}\\ w_{4}&{}={}&\frac{74183153846384993}{9729818768934592}&{}-{}&\frac{41475185949849315}{9729818768934592} g_{39}&{}+{}&\frac{828753169800987}{256047862340384} g_{44}\\ w_{5}&{}={}&\frac{11749231010996535}{9729818768934592}&{}+{}&\frac{55164886652760411}{9729818768934592} g_{39}&{}-{}&\frac{1107655741012563}{256047862340384} g_{44}\\ g_{8}&{}={}&\frac{15623571487388393}{19459637537869184}&{}-{}&\frac{122344625368251}{19459637537869184} g_{39}&{}+{}&\frac{58388158895283}{512095724680768} g_{44}\\ g_{2}&{}={}&\frac{8563348494181143}{9729818768934592}&{}+{}&\frac{406083841116027}{9729818768934592} g_{39}&{}+{}&\frac{7954543833741}{256047862340384} g_{44}\\ g_{17}&{}={}&\frac{163016553940583}{256047862340384}&{}+{}&\frac{32002218214059}{256047862340384} g_{39}&{}+{}&\frac{12215450948967}{128023931170192} g_{44}\\ g_{3}&{}={}&\frac{24837103515234935}{19459637537869184}&{}-{}&\frac{54352718970528357}{19459637537869184} g_{39}&{}+{}&\frac{1123564828680045}{512095724680768} g_{44}\\ g_{7}&{}={}&\frac{7240373623335577}{9729818768934592}&{}+{}&\frac{5240039969497077}{9729818768934592} g_{39}&{}-{}&\frac{79709950680957}{256047862340384} g_{44}\\ g_{4}&{}={}&\frac{21878144581359569}{19459637537869184}&{}-{}&\frac{35829062139236211}{19459637537869184} g_{39}&{}+{}&\frac{756997762953771}{512095724680768} g_{44}\\ g_{5}&{}={}&\frac{3048774691309169}{4864909384467296}&{}+{}&\frac{7921232266929741}{4864909384467296} g_{39}&{}-{}&\frac{148759005469077}{128023931170192} g_{44}\\ g_{6}&{}={}&\frac{2179963272568315}{2432454692233648}&{}-{}&\frac{1005447111537249}{2432454692233648} g_{39}&{}+{}&\frac{25893395545545}{64011965585096} g_{44}\\ g_{11}&{}={}&\frac{6382503972617535}{9729818768934592}&{}+{}&\frac{6875003613603075}{9729818768934592} g_{39}&{}-{}&\frac{103402890291771}{256047862340384} g_{44}\\ g_{9}&{}={}&\frac{2006345842313973}{4864909384467296}&{}+{}&\frac{13872351852574401}{4864909384467296} g_{39}&{}-{}&\frac{265193939478825}{128023931170192} g_{44}\\ g_{10}&{}={}&\frac{699070817910959}{1216227346116824}&{}+{}&\frac{1728946288848123}{1216227346116824} g_{39}&{}-{}&\frac{30716402480883}{32005982792548} g_{44}\\ g_{1}&{}={}&\frac{1829721369752999}{1216227346116824}&{}-{}&\frac{5133637763591661}{1216227346116824} g_{39}&{}+{}&\frac{104588464204341}{32005982792548} g_{44}\\ g_{12}&{}={}&\frac{22656258993671327}{19459637537869184}&{}-{}&\frac{47883799198041309}{19459637537869184} g_{39}&{}+{}&\frac{1012207394554533}{512095724680768} g_{44}\\ g_{13}&{}={}&\frac{18243403712086889}{19459637537869184}&{}-{}&\frac{25047529185091131}{19459637537869184} g_{39}&{}+{}&\frac{571402039411251}{512095724680768} g_{44}\\ g_{18}&{}={}&\frac{5223881685893391}{9729818768934592}&{}+{}&\frac{5301256879042963}{9729818768934592} g_{39}&{}-{}&\frac{51792431053131}{256047862340384} g_{44}\\ g_{15}&{}={}&\frac{1952667292921007}{4864909384467296}&{}+{}&\frac{12255517760726163}{4864909384467296} g_{39}&{}-{}&\frac{228669998853195}{128023931170192} g_{44}\\ g_{14}&{}={}&\frac{15301500191030597}{19459637537869184}&{}-{}&\frac{9823349176457679}{19459637537869184} g_{39}&{}+{}&\frac{277531802649063}{512095724680768} g_{44}\\ g_{16}&{}={}&\frac{2715765447554387}{4864909384467296}&{}+{}&\frac{4490534017620135}{4864909384467296} g_{39}&{}-{}&\frac{68079698985087}{128023931170192} g_{44}\\ g_{26}&{}={}&\frac{1301672345190217}{2432454692233648}&{}+{}&\frac{54240484474293}{2432454692233648} g_{39}&{}+{}&\frac{20639701587267}{64011965585096} g_{44}\\ g_{19}&{}={}&\frac{44751270434690171}{19459637537869184}&{}-{}&\frac{123010728136281969}{19459637537869184} g_{39}&{}+{}&\frac{2540692175143257}{512095724680768} g_{44}\\ g_{20}&{}={}&\frac{31814789052708641}{19459637537869184}&{}-{}&\frac{76705895211811683}{19459637537869184} g_{39}&{}+{}&\frac{1642002352375707}{512095724680768} g_{44}\\ g_{21}&{}={}&\frac{1220550954283559}{1024191449361536}&{}-{}&\frac{2412421399763061}{1024191449361536} g_{39}&{}+{}&\frac{1042875803864007}{512095724680768} g_{44}\\ g_{22}&{}={}&\frac{17440920850506941}{19459637537869184}&{}-{}&\frac{25256080851289143}{19459637537869184} g_{39}&{}+{}&\frac{643458104856207}{512095724680768} g_{44}\\ g_{27}&{}={}&\frac{4141852524628173}{9729818768934592}&{}+{}&\frac{4206980014878553}{9729818768934592} g_{39}&{}+{}&\frac{11871464298111}{256047862340384} g_{44}\\ g_{24}&{}={}&\frac{1670398816069211}{4864909384467296}&{}+{}&\frac{11970054230944143}{4864909384467296} g_{39}&{}-{}&\frac{212062026152871}{128023931170192} g_{44}\\ g_{23}&{}={}&\frac{13607889329919821}{19459637537869184}&{}-{}&\frac{11536130355149799}{19459637537869184} g_{39}&{}+{}&\frac{377179638851007}{512095724680768} g_{44}\\ g_{25}&{}={}&\frac{2292362732276693}{4864909384467296}&{}+{}&\frac{4062338722947105}{4864909384467296} g_{39}&{}-{}&\frac{43167739934601}{128023931170192} g_{44}\\ g_{36}&{}={}&\frac{4682136105758333}{19459637537869184}&{}+{}&\frac{4771624212342921}{19459637537869184} g_{39}&{}+{}&\frac{235650256538319}{512095724680768} g_{44}\\ g_{28}&{}={}&\frac{43669241273424953}{19459637537869184}&{}-{}&\frac{124105005000446379}{19459637537869184} g_{39}&{}+{}&\frac{2604356070494499}{512095724680768} g_{44}\\ g_{29}&{}={}&\frac{30011407117266611}{19459637537869184}&{}-{}&\frac{78529689985419033}{19459637537869184} g_{39}&{}+{}&\frac{1748108844627777}{512095724680768} g_{44}\\ g_{30}&{}={}&\frac{1100325491920757}{1024191449361536}&{}-{}&\frac{2534007718003551}{1024191449361536} g_{39}&{}+{}&\frac{1177277360716629}{512095724680768} g_{44}\\ g_{31}&{}={}&\frac{14836035832646231}{19459637537869184}&{}-{}&\frac{27890451079833093}{19459637537869184} g_{39}&{}+{}&\frac{796723038109197}{512095724680768} g_{44}\\ g_{34}&{}={}&\frac{3175415877967207}{9729818768934592}&{}+{}&\frac{6699415604297355}{9729818768934592} g_{39}&{}-{}&\frac{3415221109251}{256047862340384} g_{44}\\ g_{33}&{}={}&\frac{600314476936909}{2432454692233648}&{}+{}&\frac{5747483475205929}{2432454692233648} g_{39}&{}-{}&\frac{92210969949777}{64011965585096} g_{44}\\ g_{32}&{}={}&\frac{10789270156747463}{19459637537869184}&{}-{}&\frac{14386654038343509}{19459637537869184} g_{39}&{}+{}&\frac{543020156370909}{512095724680768} g_{44}\\ g_{35}&{}={}&\frac{7124989726153985}{19459637537869184}&{}-{}&\frac{2891687087931651}{19459637537869184} g_{39}&{}+{}&\frac{358598216471355}{512095724680768} g_{44}\\ w_{2}&{}={}&\frac{426470983654247}{4864909384467296}&{}+{}&\frac{27785485246938219}{4864909384467296} g_{39}&{}-{}&\frac{549850598589411}{128023931170192} g_{44}\\ g_{37}&{}={}&\frac{182773278708963}{4864909384467296}&{}+{}&\frac{14688013325526263}{4864909384467296} g_{39}&{}-{}&\frac{235650256538319}{128023931170192} g_{44}\\ g_{38}&{}={}&\frac{60924426236321}{4864909384467296}&{}+{}&\frac{8139277364820285}{4864909384467296} g_{39}&{}-{}&\frac{78550085512773}{128023931170192} g_{44}\\ w_{3}&{}={}&\frac{211}{64}&{}-{}&\frac{633}{64} g_{39}&{}+{}&\frac{243}{32} g_{44}\\ g_{40}&{}={}&\frac{65}{32}&{}-{}&\frac{195}{32} g_{39}&{}+{}&\frac{81}{16} g_{44}\\ g_{41}&{}={}&\frac{19}{16}&{}-{}&\frac{57}{16} g_{39}&{}+{}&\frac{27}{8} g_{44}\\ g_{42}&{}={}&\frac{5}{8}&{}-{}&\frac{15}{8} g_{39}&{}+{}&\frac{9}{4} g_{44}\\ g_{43}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{39}&{}+{}&\frac{3}{2} g_{44}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{1152454262322849245}{11588327281796382}&{}-{}&\frac{119586227902939}{11588327281796382} w_{2}&{}-{}&\frac{192805230237696}{643795960099799} g_{45}\\\hline w_{1}&{}={}&\frac{142302704679739193}{11588327281796382}&{}-{}&\frac{86673282157666987}{57941636408981910} w_{2}&{}+{}&\frac{385610460475392}{3218979800498995} g_{45}\\ x_{1}&{}={}&\frac{15123255687924373}{11588327281796382}&{}+{}&\frac{43396434192784963}{57941636408981910} w_{2}&{}-{}&\frac{96402615118848}{3218979800498995} g_{45}\\ x_{2}&{}={}&\frac{56665943237624119}{11588327281796382}&{}-{}&\frac{57822050181078971}{57941636408981910} w_{2}&{}+{}&\frac{192805230237696}{3218979800498995} g_{45}\\ w_{4}&{}={}&\frac{89171689848243065}{11588327281796382}&{}-{}&\frac{43396434192784963}{57941636408981910} w_{2}&{}+{}&\frac{96402615118848}{3218979800498995} g_{45}\\ w_{5}&{}={}&\frac{12864020453154173}{11588327281796382}&{}+{}&\frac{57822050181078971}{57941636408981910} w_{2}&{}-{}&\frac{192805230237696}{3218979800498995} g_{45}\\ g_{8}&{}={}&\frac{6344542147963465}{7725551521197588}&{}-{}&\frac{396979367529737}{38627757605987940} w_{2}&{}+{}&\frac{337409152915968}{3218979800498995} g_{45}\\ g_{2}&{}={}&\frac{10312634110438591}{11588327281796382}&{}+{}&\frac{119586227902939}{57941636408981910} w_{2}&{}+{}&\frac{192805230237696}{3218979800498995} g_{45}\\ g_{17}&{}={}&\frac{3861321304369970}{5794163640898191}&{}+{}&\frac{173267862681041}{28970818204490955} w_{2}&{}+{}&\frac{584738393093568}{3218979800498995} g_{45}\\ g_{3}&{}={}&\frac{10312634110438591}{7725551521197588}&{}-{}&\frac{19194292575091031}{38627757605987940} w_{2}&{}+{}&\frac{289207845356544}{3218979800498995} g_{45}\\ g_{7}&{}={}&\frac{2903031194869999}{3862775760598794}&{}+{}&\frac{1669283014200967}{19313878802993970} w_{2}&{}+{}&\frac{289207845356544}{3218979800498995} g_{45}\\ g_{4}&{}={}&\frac{3008347396746331}{2575183840399196}&{}-{}&\frac{4252110991364347}{12875919201995980} w_{2}&{}+{}&\frac{289207845356544}{3218979800498995} g_{45}\\ g_{5}&{}={}&\frac{1182275718323266}{1931387880299397}&{}+{}&\frac{2702414205066319}{9656939401496985} w_{2}&{}+{}&\frac{192805230237696}{3218979800498995} g_{45}\\ g_{6}&{}={}&\frac{591137859161633}{643795960099799}&{}-{}&\frac{258282797716338}{3218979800498995} w_{2}&{}+{}&\frac{289207845356544}{3218979800498995} g_{45}\\ g_{11}&{}={}&\frac{7723019968412119}{11588327281796382}&{}+{}&\frac{6547990657945699}{57941636408981910} w_{2}&{}+{}&\frac{393644011735296}{3218979800498995} g_{45}\\ g_{9}&{}={}&\frac{2206577133832034}{5794163640898191}&{}+{}&\frac{14286919418480609}{28970818204490955} w_{2}&{}+{}&\frac{224939435277312}{3218979800498995} g_{45}\\ g_{10}&{}={}&\frac{1103288566916017}{1931387880299397}&{}+{}&\frac{2314990008491812}{9656939401496985} w_{2}&{}+{}&\frac{337409152915968}{3218979800498995} g_{45}\\ g_{1}&{}={}&\frac{3061005497684497}{1931387880299397}&{}-{}&\frac{7212807994147004}{9656939401496985} w_{2}&{}+{}&\frac{289207845356544}{3218979800498995} g_{45}\\ g_{12}&{}={}&\frac{9449429396429767}{7725551521197588}&{}-{}&\frac{17051491098410111}{38627757605987940} w_{2}&{}+{}&\frac{389627236105344}{3218979800498995} g_{45}\\ g_{13}&{}={}&\frac{7586367666890953}{7725551521197588}&{}-{}&\frac{9184997179624841}{38627757605987940} w_{2}&{}+{}&\frac{456573496604544}{3218979800498995} g_{45}\\ g_{18}&{}={}&\frac{19580233502104469}{34764981845389146}&{}+{}&\frac{13554682328114393}{173824909226945730} w_{2}&{}+{}&\frac{640427763864384}{3218979800498995} g_{45}\\ g_{15}&{}={}&\frac{2206469316782840}{5794163640898191}&{}+{}&\frac{12515075152028147}{28970818204490955} w_{2}&{}+{}&\frac{334136224624896}{3218979800498995} g_{45}\\ g_{14}&{}={}&\frac{6344326513865077}{7725551521197588}&{}-{}&\frac{3940667900434661}{38627757605987940} w_{2}&{}+{}&\frac{501204336937344}{3218979800498995} g_{45}\\ g_{16}&{}={}&\frac{1103234658391420}{1931387880299397}&{}+{}&\frac{1429067875265581}{9656939401496985} w_{2}&{}+{}&\frac{501204336937344}{3218979800498995} g_{45}\\ g_{26}&{}={}&\frac{3427261079513789}{5794163640898191}&{}-{}&\frac{711988014350422}{28970818204490955} w_{2}&{}+{}&\frac{1047214430572464}{3218979800498995} g_{45}\\ g_{19}&{}={}&\frac{56353294577891969}{23176654563592764}&{}-{}&\frac{130280303418576529}{115883272817963820} w_{2}&{}+{}&\frac{641555932328352}{3218979800498995} g_{45}\\ g_{20}&{}={}&\frac{40232831792030675}{23176654563592764}&{}-{}&\frac{16467061633935911}{23176654563592764} w_{2}&{}+{}&\frac{149583567363552}{643795960099799} g_{45}\\ g_{21}&{}={}&\frac{29485856601456479}{23176654563592764}&{}-{}&\frac{50371978003748239}{115883272817963820} w_{2}&{}+{}&\frac{818825773144032}{3218979800498995} g_{45}\\ g_{22}&{}={}&\frac{22321206474407015}{23176654563592764}&{}-{}&\frac{5812618245292139}{23176654563592764} w_{2}&{}+{}&\frac{173219546138976}{643795960099799} g_{45}\\ g_{27}&{}={}&\frac{16727837738763851}{34764981845389146}&{}+{}&\frac{7737286564764779}{173824909226945730} w_{2}&{}+{}&\frac{1146949138246032}{3218979800498995} g_{45}\\ g_{24}&{}={}&\frac{1958434902579308}{5794163640898191}&{}+{}&\frac{12009214650867311}{28970818204490955} w_{2}&{}+{}&\frac{598408246041408}{3218979800498995} g_{45}\\ g_{23}&{}={}&\frac{5848257685458013}{7725551521197588}&{}-{}&\frac{4952388902756333}{38627757605987940} w_{2}&{}+{}&\frac{897612369062112}{3218979800498995} g_{45}\\ g_{25}&{}={}&\frac{979217451289654}{1931387880299397}&{}+{}&\frac{1176137624685163}{9656939401496985} w_{2}&{}+{}&\frac{897612369062112}{3218979800498995} g_{45}\\ g_{36}&{}={}&\frac{7987128076530263}{23176654563592764}&{}-{}&\frac{1296272065999447}{115883272817963820} w_{2}&{}+{}&\frac{1989935499656916}{3218979800498995} g_{45}\\ g_{28}&{}={}&\frac{55402495990111763}{23176654563592764}&{}-{}&\frac{132219435339693067}{115883272817963820} w_{2}&{}+{}&\frac{894816619519176}{3218979800498995} g_{45}\\ g_{29}&{}={}&\frac{38648167479063665}{23176654563592764}&{}-{}&\frac{17113438940974757}{23176654563592764} w_{2}&{}+{}&\frac{234003796427160}{643795960099799} g_{45}\\ g_{30}&{}={}&\frac{27478615138364933}{23176654563592764}&{}-{}&\frac{54465700948327597}{115883272817963820} w_{2}&{}+{}&\frac{1353487223880216}{3218979800498995} g_{45}\\ g_{31}&{}={}&\frac{20032246911232445}{23176654563592764}&{}-{}&\frac{6746274355459361}{23176654563592764} w_{2}&{}+{}&\frac{295159877008632}{643795960099799} g_{45}\\ g_{34}&{}={}&\frac{515213210309959}{1287591920199598}&{}+{}&\frac{503462918956371}{6437959600997990} w_{2}&{}+{}&\frac{1557340825818456}{3218979800498995} g_{45}\\ g_{33}&{}={}&\frac{515213210309959}{1931387880299397}&{}+{}&\frac{3722442719455366}{9656939401496985} w_{2}&{}+{}&\frac{1038227217212304}{3218979800498995} g_{45}\\ g_{32}&{}={}&\frac{1674222380719717}{2575183840399196}&{}-{}&\frac{2212053962586253}{12875919201995980} w_{2}&{}+{}&\frac{1557340825818456}{3218979800498995} g_{45}\\ g_{35}&{}={}&\frac{3606492472169713}{7725551521197588}&{}-{}&\frac{2913719168303393}{38627757605987940} w_{2}&{}+{}&\frac{1816897630121532}{3218979800498995} g_{45}\\ g_{39}&{}={}&\frac{1918843881178063}{17382490922694573}&{}+{}&\frac{9729818768934592}{86912454613472865} w_{2}&{}+{}&\frac{2321591416266402}{3218979800498995} g_{45}\\ g_{37}&{}={}&\frac{1096482217816036}{17382490922694573}&{}+{}&\frac{42808091273736709}{86912454613472865} w_{2}&{}+{}&\frac{1326623666437944}{3218979800498995} g_{45}\\ g_{38}&{}={}&\frac{548241108908018}{5794163640898191}&{}+{}&\frac{6918636534622877}{28970818204490955} w_{2}&{}+{}&\frac{1989935499656916}{3218979800498995} g_{45}\\ w_{3}&{}={}&\frac{40266994378341955}{11588327281796382}&{}-{}&\frac{20219779629192199}{11588327281796382} w_{2}&{}+{}&\frac{96402615118848}{643795960099799} g_{45}\\ g_{40}&{}={}&\frac{12776444832827297}{5794163640898191}&{}-{}&\frac{32077996253831233}{28970818204490955} w_{2}&{}+{}&\frac{1482137758529361}{3218979800498995} g_{45}\\ g_{41}&{}={}&\frac{605518712456270}{445704895453707}&{}-{}&\frac{304056836529206}{445704895453707} w_{2}&{}+{}&\frac{33059808417735}{49522766161523} g_{45}\\ g_{42}&{}={}&\frac{4601942214667652}{5794163640898191}&{}-{}&\frac{11554159788109828}{28970818204490955} w_{2}&{}+{}&\frac{2593387406235051}{3218979800498995} g_{45}\\ g_{43}&{}={}&\frac{2422074849825080}{5794163640898191}&{}-{}&\frac{1216227346116824}{5794163640898191} w_{2}&{}+{}&\frac{577944129124647}{643795960099799} g_{45}\\ g_{44}&{}={}&\frac{968829939930032}{5794163640898191}&{}-{}&\frac{2432454692233648}{28970818204490955} w_{2}&{}+{}&\frac{3087276138548691}{3218979800498995} g_{45}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{1728741186598225337}{17382490922694573}&{}-{}&\frac{119586227902939}{5794163640898191} g_{46}&{}-{}&\frac{4966568760611914}{17382490922694573} g_{45}\\\hline w_{1}&{}={}&\frac{1023933644019210454}{86912454613472865}&{}-{}&\frac{86673282157666987}{28970818204490955} g_{46}&{}+{}&\frac{183758046748169558}{86912454613472865} g_{45}\\ x_{1}&{}={}&\frac{135122634755825279}{86912454613472865}&{}+{}&\frac{43396434192784963}{28970818204490955} g_{46}&{}-{}&\frac{89395738993778822}{86912454613472865} g_{45}\\ x_{2}&{}={}&\frac{396083549191641407}{86912454613472865}&{}-{}&\frac{57822050181078971}{28970818204490955} g_{46}&{}+{}&\frac{120849841578575734}{86912454613472865} g_{45}\\ w_{4}&{}={}&\frac{647089456765430506}{86912454613472865}&{}-{}&\frac{43396434192784963}{28970818204490955} g_{46}&{}+{}&\frac{89395738993778822}{86912454613472865} g_{45}\\ w_{5}&{}={}&\frac{125391178489195783}{86912454613472865}&{}+{}&\frac{57822050181078971}{28970818204490955} g_{46}&{}-{}&\frac{120849841578575734}{86912454613472865} g_{45}\\ g_{8}&{}={}&\frac{47385576425961119}{57941636408981910}&{}-{}&\frac{396979367529737}{19313878802993970} g_{46}&{}+{}&\frac{3433661743773449}{28970818204490955} g_{45}\\ g_{2}&{}={}&\frac{77404548942240902}{86912454613472865}&{}+{}&\frac{119586227902939}{28970818204490955} g_{46}&{}+{}&\frac{4966568760611914}{86912454613472865} g_{45}\\ g_{17}&{}={}&\frac{58093087428230591}{86912454613472865}&{}+{}&\frac{346535725362082}{28970818204490955} g_{46}&{}+{}&\frac{15094865162802172}{86912454613472865} g_{45}\\ g_{3}&{}={}&\frac{67747609540743917}{57941636408981910}&{}-{}&\frac{19194292575091031}{19313878802993970} g_{46}&{}+{}&\frac{21797163183299927}{28970818204490955} g_{45}\\ g_{7}&{}={}&\frac{22607375468625476}{28970818204490955}&{}+{}&\frac{1669283014200967}{9656939401496985} g_{46}&{}-{}&\frac{735695420193038}{28970818204490955} g_{45}\\ g_{4}&{}={}&\frac{20436549979915309}{19313878802993970}&{}-{}&\frac{4252110991364347}{6437959600997990} g_{46}&{}+{}&\frac{5119734527433979}{9656939401496985} g_{45}\\ g_{5}&{}={}&\frac{20436549979915309}{28970818204490955}&{}+{}&\frac{5404828410132638}{9656939401496985} g_{46}&{}-{}&\frac{9074409748126012}{28970818204490955} g_{45}\\ g_{6}&{}={}&\frac{2869595029902719}{3218979800498995}&{}-{}&\frac{516565595432676}{3218979800498995} g_{46}&{}+{}&\frac{633584908978328}{3218979800498995} g_{45}\\ g_{11}&{}={}&\frac{61196645092063742}{86912454613472865}&{}+{}&\frac{6547990657945699}{28970818204490955} g_{46}&{}-{}&\frac{2467592999038406}{86912454613472865} g_{45}\\ g_{9}&{}={}&\frac{47385576425961119}{86912454613472865}&{}+{}&\frac{28573838836961218}{28970818204490955} g_{46}&{}-{}&\frac{51074312921435012}{86912454613472865} g_{45}\\ g_{10}&{}={}&\frac{18864318512232067}{28970818204490955}&{}+{}&\frac{4629980016983624}{9656939401496985} g_{46}&{}-{}&\frac{6223277657723536}{28970818204490955} g_{45}\\ g_{1}&{}={}&\frac{38702274471120451}{28970818204490955}&{}-{}&\frac{14425615988294008}{9656939401496985} g_{46}&{}+{}&\frac{31454102584796912}{28970818204490955} g_{45}\\ g_{12}&{}={}&\frac{62344974924018197}{57941636408981910}&{}-{}&\frac{17051491098410111}{19313878802993970} g_{46}&{}+{}&\frac{20558136223358207}{28970818204490955} g_{45}\\ g_{13}&{}={}&\frac{52305258911869727}{57941636408981910}&{}-{}&\frac{9184997179624841}{19313878802993970} g_{46}&{}+{}&\frac{13294158649065737}{28970818204490955} g_{45}\\ g_{18}&{}={}&\frac{153629092429840714}{260737363840418595}&{}+{}&\frac{13554682328114393}{86912454613472865} g_{46}&{}+{}&\frac{24765284216786318}{260737363840418595} g_{45}\\ g_{15}&{}={}&\frac{45612114903770747}{86912454613472865}&{}+{}&\frac{25030150304056294}{28970818204490955} g_{46}&{}-{}&\frac{41038622543240396}{86912454613472865} g_{45}\\ g_{14}&{}={}&\frac{45612114903770747}{57941636408981910}&{}-{}&\frac{3940667900434661}{19313878802993970} g_{46}&{}+{}&\frac{8451506932870757}{28970818204490955} g_{45}\\ g_{16}&{}={}&\frac{17977587751136881}{28970818204490955}&{}+{}&\frac{2858135750531162}{9656939401496985} g_{46}&{}-{}&\frac{1205432468626228}{28970818204490955} g_{45}\\ g_{26}&{}={}&\frac{50696928178356413}{86912454613472865}&{}-{}&\frac{1423976028700844}{28970818204490955} g_{46}&{}+{}&\frac{31122741682858216}{86912454613472865} g_{45}\\ g_{19}&{}={}&\frac{357509557624901503}{173824909226945730}&{}-{}&\frac{130280303418576529}{57941636408981910} g_{46}&{}+{}&\frac{147602313591442033}{86912454613472865} g_{45}\\ g_{20}&{}={}&\frac{52115716871078057}{34764981845389146}&{}-{}&\frac{16467061633935911}{11588327281796382} g_{46}&{}+{}&\frac{20505817952751815}{17382490922694573} g_{45}\\ g_{21}&{}={}&\frac{195957935509049473}{173824909226945730}&{}-{}&\frac{50371978003748239}{57941636408981910} g_{46}&{}+{}&\frac{72480273878637103}{86912454613472865} g_{45}\\ g_{22}&{}={}&\frac{30575500588964453}{34764981845389146}&{}-{}&\frac{5812618245292139}{11588327281796382} g_{46}&{}+{}&\frac{10489545991044491}{17382490922694573} g_{45}\\ g_{27}&{}={}&\frac{129327426323111272}{260737363840418595}&{}+{}&\frac{7737286564764779}{86912454613472865} g_{46}&{}+{}&\frac{77428307068399034}{260737363840418595} g_{45}\\ g_{24}&{}={}&\frac{41385738189556931}{86912454613472865}&{}+{}&\frac{24018429301734622}{28970818204490955} g_{46}&{}-{}&\frac{31879835960351228}{86912454613472865} g_{45}\\ g_{23}&{}={}&\frac{41385738189556931}{57941636408981910}&{}-{}&\frac{4952388902756333}{19313878802993970} g_{46}&{}+{}&\frac{13030900224315341}{28970818204490955} g_{45}\\ g_{25}&{}={}&\frac{15864399394029973}{28970818204490955}&{}+{}&\frac{2352275249370326}{9656939401496985} g_{46}&{}+{}&\frac{3373960822818356}{28970818204490955} g_{45}\\ g_{36}&{}={}&\frac{59255324540977249}{173824909226945730}&{}-{}&\frac{1296272065999447}{57941636408981910} g_{46}&{}+{}&\frac{55024530556736179}{86912454613472865} g_{45}\\ g_{28}&{}={}&\frac{349409002255991689}{173824909226945730}&{}-{}&\frac{132219435339693067}{57941636408981910} g_{46}&{}+{}&\frac{156379484066710819}{86912454613472865} g_{45}\\ g_{29}&{}={}&\frac{49415531748108119}{34764981845389146}&{}-{}&\frac{17113438940974757}{11588327281796382} g_{46}&{}+{}&\frac{23431541444508077}{17382490922694573} g_{45}\\ g_{30}&{}={}&\frac{178856763063573199}{173824909226945730}&{}-{}&\frac{54465700948327597}{57941636408981910} g_{46}&{}+{}&\frac{91009855993093429}{86912454613472865} g_{45}\\ g_{31}&{}={}&\frac{26675233189118987}{34764981845389146}&{}-{}&\frac{6746274355459361}{11588327281796382} g_{46}&{}+{}&\frac{14715591034692425}{17382490922694573} g_{45}\\ g_{34}&{}={}&\frac{1371943512267626}{3218979800498995}&{}+{}&\frac{503462918956371}{3218979800498995} g_{46}&{}+{}&\frac{1221698879847542}{3218979800498995} g_{45}\\ g_{33}&{}={}&\frac{11450640874104751}{28970818204490955}&{}+{}&\frac{7444885438910732}{9656939401496985} g_{46}&{}-{}&\frac{5545725922910728}{28970818204490955} g_{45}\\ g_{32}&{}={}&\frac{11450640874104751}{19313878802993970}&{}-{}&\frac{2212053962586253}{6437959600997990} g_{46}&{}+{}&\frac{6884076440041621}{9656939401496985} g_{45}\\ g_{35}&{}={}&\frac{25591833957121151}{57941636408981910}&{}-{}&\frac{2913719168303393}{19313878802993970} g_{46}&{}+{}&\frac{19265797839397181}{28970818204490955} g_{45}\\ g_{39}&{}={}&\frac{38512476986605537}{260737363840418595}&{}+{}&\frac{19459637537869184}{86912454613472865} g_{46}&{}+{}&\frac{149129629641840194}{260737363840418595} g_{45}\\ g_{37}&{}={}&\frac{59255324540977249}{260737363840418595}&{}+{}&\frac{85616182547473418}{86912454613472865} g_{46}&{}-{}&\frac{63775848113473372}{260737363840418595} g_{45}\\ g_{38}&{}={}&\frac{15142253168243147}{86912454613472865}&{}+{}&\frac{13837273069245754}{28970818204490955} g_{46}&{}+{}&\frac{26053712352245224}{86912454613472865} g_{45}\\ w_{3}&{}={}&\frac{50290601752916833}{17382490922694573}&{}-{}&\frac{20219779629192199}{5794163640898191} g_{46}&{}+{}&\frac{43042429866593294}{17382490922694573} g_{45}\\ g_{40}&{}={}&\frac{159568676238578222}{86912454613472865}&{}-{}&\frac{64155992507662466}{28970818204490955} g_{46}&{}+{}&\frac{168329704495617679}{86912454613472865} g_{45}\\ g_{41}&{}={}&\frac{1512499300839604}{1337114686361121}&{}-{}&\frac{608113673058412}{445704895453707} g_{46}&{}+{}&\frac{2108842173395669}{1337114686361121} g_{45}\\ g_{42}&{}={}&\frac{57474973431904952}{86912454613472865}&{}-{}&\frac{23108319576219656}{28970818204490955} g_{46}&{}+{}&\frac{116238099120785689}{86912454613472865} g_{45}\\ g_{43}&{}={}&\frac{6049997203358416}{17382490922694573}&{}-{}&\frac{2432454692233648}{5794163640898191} g_{46}&{}+{}&\frac{20469400870832765}{17382490922694573} g_{45}\\ g_{44}&{}={}&\frac{12099994406716832}{86912454613472865}&{}-{}&\frac{4864909384467296}{28970818204490955} g_{46}&{}+{}&\frac{93086274509749249}{86912454613472865} g_{45}\\ w_{2}&{}={}&\frac{1}{3}&{}+{}&2 g_{46}&{}-{}&\frac{4}{3} g_{45}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{64031880475041788}{643795960099799}&{}-{}&\frac{239172455805878}{5794163640898191} g_{47}&{}-{}&\frac{1496074616333386}{5794163640898191} g_{45}\\\hline w_{1}&{}={}&\frac{34713346735612721}{3218979800498995}&{}-{}&\frac{173346564315333974}{28970818204490955} g_{47}&{}+{}&\frac{176817058459612502}{28970818204490955} g_{45}\\ x_{1}&{}={}&\frac{6611817368467046}{3218979800498995}&{}+{}&\frac{86792868385569926}{28970818204490955} g_{47}&{}-{}&\frac{87660491921639558}{28970818204490955} g_{45}\\ x_{2}&{}={}&\frac{12528203667057868}{3218979800498995}&{}-{}&\frac{115644100362157942}{28970818204490955} g_{47}&{}+{}&\frac{117379347434297206}{28970818204490955} g_{45}\\ w_{4}&{}={}&\frac{22359000836023909}{3218979800498995}&{}-{}&\frac{86792868385569926}{28970818204490955} g_{47}&{}+{}&\frac{87660491921639558}{28970818204490955} g_{45}\\ w_{5}&{}={}&\frac{6785675135936102}{3218979800498995}&{}+{}&\frac{115644100362157942}{28970818204490955} g_{47}&{}-{}&\frac{117379347434297206}{28970818204490955} g_{45}\\ g_{8}&{}={}&\frac{2610477614357299}{3218979800498995}&{}-{}&\frac{396979367529737}{9656939401496985} g_{47}&{}+{}&\frac{1409206826277641}{9656939401496985} g_{45}\\ g_{2}&{}={}&\frac{2871264265560883}{3218979800498995}&{}+{}&\frac{239172455805878}{28970818204490955} g_{47}&{}+{}&\frac{1496074616333386}{28970818204490955} g_{45}\\ g_{17}&{}={}&\frac{2164430487170099}{3218979800498995}&{}+{}&\frac{693071450724164}{28970818204490955} g_{47}&{}+{}&\frac{4569574087117948}{28970818204490955} g_{45}\\ g_{3}&{}={}&\frac{2697406498091827}{3218979800498995}&{}-{}&\frac{19194292575091031}{9656939401496985} g_{47}&{}+{}&\frac{20061916111160663}{9656939401496985} g_{45}\\ g_{7}&{}={}&\frac{2697406498091827}{3218979800498995}&{}+{}&\frac{3338566028401934}{9656939401496985} g_{47}&{}-{}&\frac{2470942492332302}{9656939401496985} g_{45}\\ g_{4}&{}={}&\frac{2697406498091827}{3218979800498995}&{}-{}&\frac{4252110991364347}{3218979800498995} g_{47}&{}+{}&\frac{4541318836720891}{3218979800498995} g_{45}\\ g_{5}&{}={}&\frac{2871264265560883}{3218979800498995}&{}+{}&\frac{10809656820265276}{9656939401496985} g_{47}&{}-{}&\frac{10231241129552188}{9656939401496985} g_{45}\\ g_{6}&{}={}&\frac{2697406498091827}{3218979800498995}&{}-{}&\frac{1033131190865352}{3218979800498995} g_{47}&{}+{}&\frac{1322339036221896}{3218979800498995} g_{45}\\ g_{11}&{}={}&\frac{2509060583333683}{3218979800498995}&{}+{}&\frac{13095981315891398}{28970818204490955} g_{47}&{}-{}&\frac{9553185210273734}{28970818204490955} g_{45}\\ g_{9}&{}={}&\frac{2813311676404531}{3218979800498995}&{}+{}&\frac{57147677673922436}{28970818204490955} g_{47}&{}-{}&\frac{55123222756426628}{28970818204490955} g_{45}\\ g_{10}&{}={}&\frac{2610477614357299}{3218979800498995}&{}+{}&\frac{9259960033967248}{9656939401496985} g_{47}&{}-{}&\frac{8247732575219344}{9656939401496985} g_{45}\\ g_{1}&{}={}&\frac{2697406498091827}{3218979800498995}&{}-{}&\frac{28851231976588016}{9656939401496985} g_{47}&{}+{}&\frac{29718855512657648}{9656939401496985} g_{45}\\ g_{12}&{}={}&\frac{2516304656978227}{3218979800498995}&{}-{}&\frac{17051491098410111}{9656939401496985} g_{47}&{}+{}&\frac{18220372806726143}{9656939401496985} g_{45}\\ g_{13}&{}={}&\frac{2395570096235827}{3218979800498995}&{}-{}&\frac{9184997179624841}{9656939401496985} g_{47}&{}+{}&\frac{10554717669438473}{9656939401496985} g_{45}\\ g_{18}&{}={}&\frac{6191991657702041}{9656939401496985}&{}+{}&\frac{27109364656228786}{86912454613472865} g_{47}&{}-{}&\frac{9817815031890418}{86912454613472865} g_{45}\\ g_{15}&{}={}&\frac{2616380192882483}{3218979800498995}&{}+{}&\frac{50060300608112588}{28970818204490955} g_{47}&{}-{}&\frac{47053074586488524}{28970818204490955} g_{45}\\ g_{14}&{}={}&\frac{2315080389074227}{3218979800498995}&{}-{}&\frac{3940667900434661}{9656939401496985} g_{47}&{}+{}&\frac{5444280911246693}{9656939401496985} g_{45}\\ g_{16}&{}={}&\frac{2315080389074227}{3218979800498995}&{}+{}&\frac{5716271501062324}{9656939401496985} g_{47}&{}-{}&\frac{4212658490250292}{9656939401496985} g_{45}\\ g_{26}&{}={}&\frac{1824924153690947}{3218979800498995}&{}-{}&\frac{2847952057401688}{28970818204490955} g_{47}&{}+{}&\frac{12272881932553864}{28970818204490955} g_{45}\\ g_{19}&{}={}&\frac{4207949151968981}{3218979800498995}&{}-{}&\frac{130280303418576529}{28970818204490955} g_{47}&{}+{}&\frac{136054306809531697}{28970818204490955} g_{45}\\ g_{20}&{}={}&\frac{660160282169299}{643795960099799}&{}-{}&\frac{16467061633935911}{5794163640898191} g_{47}&{}+{}&\frac{17813313740207879}{5794163640898191} g_{45}\\ g_{21}&{}={}&\frac{2696036250098171}{3218979800498995}&{}-{}&\frac{50371978003748239}{28970818204490955} g_{47}&{}+{}&\frac{57741409962044527}{28970818204490955} g_{45}\\ g_{22}&{}={}&\frac{458571895253191}{643795960099799}&{}-{}&\frac{5812618245292139}{5794163640898191} g_{47}&{}+{}&\frac{7371594160542923}{5794163640898191} g_{45}\\ g_{27}&{}={}&\frac{5076470847699113}{9656939401496985}&{}+{}&\frac{15474573129529558}{86912454613472865} g_{47}&{}+{}&\frac{15493053603113306}{86912454613472865} g_{45}\\ g_{24}&{}={}&\frac{2422376573751539}{3218979800498995}&{}+{}&\frac{48036858603469244}{28970818204490955} g_{47}&{}-{}&\frac{42651184389096572}{28970818204490955} g_{45}\\ g_{23}&{}={}&\frac{2024074960377811}{3218979800498995}&{}-{}&\frac{4952388902756333}{9656939401496985} g_{47}&{}+{}&\frac{7645226009942669}{9656939401496985} g_{45}\\ g_{25}&{}={}&\frac{2024074960377811}{3218979800498995}&{}+{}&\frac{4704550498740652}{9656939401496985} g_{47}&{}-{}&\frac{2011713391554316}{9656939401496985} g_{45}\\ g_{36}&{}={}&\frac{1073315786573663}{3218979800498995}&{}-{}&\frac{1296272065999447}{28970818204490955} g_{47}&{}+{}&\frac{19205691562911691}{28970818204490955} g_{45}\\ g_{28}&{}={}&\frac{4022029016968493}{3218979800498995}&{}-{}&\frac{132219435339693067}{28970818204490955} g_{47}&{}+{}&\frac{140272784915365651}{28970818204490955} g_{45}\\ g_{29}&{}={}&\frac{598186903835803}{643795960099799}&{}-{}&\frac{17113438940974757}{5794163640898191} g_{47}&{}+{}&\frac{19219473108819197}{5794163640898191} g_{45}\\ g_{30}&{}={}&\frac{2303538187319363}{3218979800498995}&{}-{}&\frac{54465700948327597}{28970818204490955} g_{47}&{}+{}&\frac{66647085963249541}{28970818204490955} g_{45}\\ g_{31}&{}={}&\frac{369054793215919}{643795960099799}&{}-{}&\frac{6746274355459361}{5794163640898191} g_{47}&{}+{}&\frac{9402713248537049}{5794163640898191} g_{45}\\ g_{34}&{}={}&\frac{1539764485253083}{3218979800498995}&{}+{}&\frac{1006925837912742}{3218979800498995} g_{47}&{}+{}&\frac{550414987905714}{3218979800498995} g_{45}\\ g_{33}&{}={}&\frac{2099502923668387}{3218979800498995}&{}+{}&\frac{14889770877821464}{9656939401496985} g_{47}&{}-{}&\frac{11775089226184552}{9656939401496985} g_{45}\\ g_{32}&{}={}&\frac{1539764485253083}{3218979800498995}&{}-{}&\frac{2212053962586253}{3218979800498995} g_{47}&{}+{}&\frac{3769394788404709}{3218979800498995} g_{45}\\ g_{35}&{}={}&\frac{1259895266045431}{3218979800498995}&{}-{}&\frac{2913719168303393}{9656939401496985} g_{47}&{}+{}&\frac{8364412058667989}{9656939401496985} g_{45}\\ g_{39}&{}={}&\frac{2147115352758323}{9656939401496985}&{}+{}&\frac{38919275075738368}{86912454613472865} g_{47}&{}+{}&\frac{23763693163454486}{86912454613472865} g_{45}\\ g_{37}&{}={}&\frac{5365611373646321}{9656939401496985}&{}+{}&\frac{171232365094946836}{86912454613472865} g_{47}&{}-{}&\frac{135413526101122348}{86912454613472865} g_{45}\\ g_{38}&{}={}&\frac{1073315786573663}{3218979800498995}&{}+{}&\frac{27674546138491508}{28970818204490955} g_{47}&{}-{}&\frac{9765126641579264}{28970818204490955} g_{45}\\ w_{3}&{}={}&\frac{1113734152730542}{643795960099799}&{}-{}&\frac{40439559258384398}{5794163640898191} g_{47}&{}+{}&\frac{41307182794454030}{5794163640898191} g_{45}\\ g_{40}&{}={}&\frac{3533803101145028}{3218979800498995}&{}-{}&\frac{128311985015324932}{28970818204490955} g_{47}&{}+{}&\frac{141651224842089181}{28970818204490955} g_{45}\\ g_{41}&{}={}&\frac{33495763991896}{49522766161523}&{}-{}&\frac{1216227346116824}{445704895453707} g_{47}&{}+{}&\frac{1513765621876439}{445704895453707} g_{45}\\ g_{42}&{}={}&\frac{1272839031692048}{3218979800498995}&{}-{}&\frac{46216639152439312}{28970818204490955} g_{47}&{}+{}&\frac{69557125808554771}{28970818204490955} g_{45}\\ g_{43}&{}={}&\frac{133983055967584}{643795960099799}&{}-{}&\frac{4864909384467296}{5794163640898191} g_{47}&{}+{}&\frac{10066406546589119}{5794163640898191} g_{45}\\ g_{44}&{}={}&\frac{267966111935168}{3218979800498995}&{}-{}&\frac{9729818768934592}{28970818204490955} g_{47}&{}+{}&\frac{37515304015872811}{28970818204490955} g_{45}\\ w_{2}&{}={}&1&{}+{}&4 g_{47}&{}-{}&4 g_{45}\\ g_{46}&{}={}&\frac{1}{3}&{}+{}&2 g_{47}&{}-{}&\frac{4}{3} g_{45}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{14209859826117841182}{142839892708449841}&{}-{}&\frac{36440188514924544}{142839892708449841} g_{48}&{}-{}&\frac{1765767012888323}{142839892708449841} w_{3}\\\hline w_{1}&{}={}&\frac{6642442082139048749}{714199463542249205}&{}-{}&\frac{5205741216417792}{714199463542249205} g_{48}&{}+{}&\frac{611918716320086701}{714199463542249205} w_{3}\\ x_{1}&{}={}&\frac{1998210213133773204}{714199463542249205}&{}+{}&\frac{20822964865671168}{714199463542249205} g_{48}&{}-{}&\frac{305076474653599189}{714199463542249205} w_{3}\\ x_{2}&{}={}&\frac{2072339657860916122}{714199463542249205}&{}-{}&\frac{15617223649253376}{714199463542249205} g_{48}&{}+{}&\frac{407357221875761693}{714199463542249205} w_{3}\\ w_{4}&{}={}&\frac{4429584958746469641}{714199463542249205}&{}-{}&\frac{20822964865671168}{714199463542249205} g_{48}&{}+{}&\frac{305076474653599189}{714199463542249205} w_{3}\\ w_{5}&{}={}&\frac{2212857123392579108}{714199463542249205}&{}+{}&\frac{15617223649253376}{714199463542249205} g_{48}&{}-{}&\frac{407357221875761693}{714199463542249205} w_{3}\\ g_{8}&{}={}&\frac{574607258164458296}{714199463542249205}&{}+{}&\frac{63047310287726592}{714199463542249205} g_{48}&{}+{}&\frac{17446613846855613}{1428398927084498410} w_{3}\\ g_{2}&{}={}&\frac{640070018815106287}{714199463542249205}&{}+{}&\frac{36440188514924544}{714199463542249205} g_{48}&{}+{}&\frac{1765767012888323}{714199463542249205} w_{3}\\ g_{17}&{}={}&\frac{489182264387331921}{714199463542249205}&{}+{}&\frac{110501051271576192}{714199463542249205} g_{48}&{}+{}&\frac{5468218229228594}{714199463542249205} w_{3}\\ g_{3}&{}={}&\frac{247840920661065938}{714199463542249205}&{}+{}&\frac{28631576690297856}{714199463542249205} g_{48}&{}+{}&\frac{410888755901538339}{1428398927084498410} w_{3}\\ g_{7}&{}={}&\frac{662199359083279643}{714199463542249205}&{}+{}&\frac{58998400452734976}{714199463542249205} g_{48}&{}-{}&\frac{31150637385906963}{714199463542249205} w_{3}\\ g_{4}&{}={}&\frac{366229045924555568}{714199463542249205}&{}+{}&\frac{37307812050994176}{714199463542249205} g_{48}&{}+{}&\frac{275691604280580549}{1428398927084498410} w_{3}\\ g_{5}&{}={}&\frac{837383560920922337}{714199463542249205}&{}+{}&\frac{50900580782751744}{714199463542249205} g_{48}&{}-{}&\frac{110898526004576502}{714199463542249205} w_{3}\\ g_{6}&{}={}&\frac{543811233819790013}{714199463542249205}&{}+{}&\frac{50322165092038656}{714199463542249205} g_{48}&{}+{}&\frac{36447938424571932}{714199463542249205} w_{3}\\ g_{11}&{}={}&\frac{640132984549110367}{714199463542249205}&{}+{}&\frac{80062371856203264}{714199463542249205} g_{48}&{}-{}&\frac{40521740447193397}{714199463542249205} w_{3}\\ g_{9}&{}={}&\frac{976302369080857489}{714199463542249205}&{}+{}&\frac{68060246273906688}{714199463542249205} g_{48}&{}-{}&\frac{196980189482484814}{714199463542249205} w_{3}\\ g_{10}&{}={}&\frac{752189446059692741}{714199463542249205}&{}+{}&\frac{76061663328771072}{714199463542249205} g_{48}&{}-{}&\frac{92674556792290536}{714199463542249205} w_{3}\\ g_{1}&{}={}&\frac{70258732765831493}{714199463542249205}&{}+{}&\frac{15617223649253376}{714199463542249205} g_{48}&{}+{}&\frac{306842241666487512}{714199463542249205} w_{3}\\ g_{12}&{}={}&\frac{247872403528067978}{714199463542249205}&{}+{}&\frac{50442668360937216}{714199463542249205} g_{48}&{}+{}&\frac{368601248441456619}{1428398927084498410} w_{3}\\ g_{13}&{}={}&\frac{366281517369558968}{714199463542249205}&{}+{}&\frac{73659631502059776}{714199463542249205} g_{48}&{}+{}&\frac{205212425180444349}{1428398927084498410} w_{3}\\ g_{18}&{}={}&\frac{1555469468742220349}{2142598390626747615}&{}+{}&\frac{124743347499643776}{714199463542249205} g_{48}&{}-{}&\frac{68945451860293199}{2142598390626747615} w_{3}\\ g_{15}&{}={}&\frac{890044814702698377}{714199463542249205}&{}+{}&\frac{85453777368405504}{714199463542249205} g_{48}&{}-{}&\frac{170700213095957962}{714199463542249205} w_{3}\\ g_{14}&{}={}&\frac{445220926597219628}{714199463542249205}&{}+{}&\frac{89137606929474816}{714199463542249205} g_{48}&{}+{}&\frac{96286543006436169}{1428398927084498410} w_{3}\\ g_{16}&{}={}&\frac{622803114492454073}{714199463542249205}&{}+{}&\frac{102151959970519296}{714199463542249205} g_{48}&{}-{}&\frac{53254592212500258}{714199463542249205} w_{3}\\ g_{26}&{}={}&\frac{395874378720876573}{714199463542249205}&{}+{}&\frac{196060596537985056}{714199463542249205} g_{48}&{}+{}&\frac{24105227013634172}{714199463542249205} w_{3}\\ g_{19}&{}={}&\frac{140211667533328524}{714199463542249205}&{}+{}&\frac{62371673749821888}{714199463542249205} g_{48}&{}+{}&\frac{929284134102901207}{1428398927084498410} w_{3}\\ g_{20}&{}={}&\frac{46737222511109508}{142839892708449841}&{}+{}&\frac{20790557916607296}{142839892708449841} g_{48}&{}+{}&\frac{119308187756367281}{285679785416899682} w_{3}\\ g_{21}&{}={}&\frac{296002409237026884}{714199463542249205}&{}+{}&\frac{131673533471846208}{714199463542249205} g_{48}&{}+{}&\frac{374712141901126537}{1428398927084498410} w_{3}\\ g_{22}&{}={}&\frac{67509321404935956}{142839892708449841}&{}+{}&\frac{30030805879543872}{142839892708449841} g_{48}&{}+{}&\frac{45365255462797325}{285679785416899682} w_{3}\\ g_{27}&{}={}&\frac{1248886415838152777}{2142598390626747615}&{}+{}&\frac{218451420886663008}{714199463542249205} g_{48}&{}-{}&\frac{7709565854389157}{2142598390626747615} w_{3}\\ g_{24}&{}={}&\frac{836726022893295321}{714199463542249205}&{}+{}&\frac{134344946092067712}{714199463542249205} g_{48}&{}-{}&\frac{160050493790583346}{714199463542249205} w_{3}\\ g_{23}&{}={}&\frac{365242738883115044}{714199463542249205}&{}+{}&\frac{162474360014968128}{714199463542249205} g_{48}&{}+{}&\frac{128235700922560017}{1428398927084498410} w_{3}\\ g_{25}&{}={}&\frac{542824926778349489}{714199463542249205}&{}+{}&\frac{175488713056012608}{714199463542249205} g_{48}&{}-{}&\frac{37280013254438334}{714199463542249205} w_{3}\\ g_{36}&{}={}&\frac{246216876182054592}{714199463542249205}&{}+{}&\frac{374406592404908664}{714199463542249205} g_{48}&{}+{}&\frac{62802162952732861}{1428398927084498410} w_{3}\\ g_{28}&{}={}&\frac{89114492049317262}{714199463542249205}&{}+{}&\frac{109225710443331504}{714199463542249205} g_{48}&{}+{}&\frac{949696096104869221}{1428398927084498410} w_{3}\\ g_{29}&{}={}&\frac{29704830683105754}{142839892708449841}&{}+{}&\frac{36408570147777168}{142839892708449841} g_{48}&{}+{}&\frac{126112175090356619}{285679785416899682} w_{3}\\ g_{30}&{}={}&\frac{188130594326336442}{714199463542249205}&{}+{}&\frac{230587610935922064}{714199463542249205} g_{48}&{}+{}&\frac{417804061683059011}{1428398927084498410} w_{3}\\ g_{31}&{}={}&\frac{42906977653374978}{142839892708449841}&{}+{}&\frac{52590156880122576}{142839892708449841} g_{48}&{}+{}&\frac{55193237167448591}{285679785416899682} w_{3}\\ g_{34}&{}={}&\frac{409719938789134967}{714199463542249205}&{}+{}&\frac{297540586418117904}{714199463542249205} g_{48}&{}-{}&\frac{10694062745702217}{714199463542249205} w_{3}\\ g_{33}&{}={}&\frac{747989364233818973}{714199463542249205}&{}+{}&\frac{215712861666804576}{714199463542249205} g_{48}&{}-{}&\frac{142326526784759268}{714199463542249205} w_{3}\\ g_{32}&{}={}&\frac{232137750893900522}{714199463542249205}&{}+{}&\frac{284526233377073424}{714199463542249205} g_{48}&{}+{}&\frac{181407601940032251}{1428398927084498410} w_{3}\\ g_{35}&{}={}&\frac{240585226066792964}{714199463542249205}&{}+{}&\frac{338454448793774568}{714199463542249205} g_{48}&{}+{}&\frac{110244338547652617}{1428398927084498410} w_{3}\\ g_{39}&{}={}&\frac{771032616708918137}{2142598390626747615}&{}+{}&\frac{443314867659582348}{714199463542249205} g_{48}&{}-{}&\frac{42193010406295007}{2142598390626747615} w_{3}\\ g_{37}&{}={}&\frac{2272126343277765059}{2142598390626747615}&{}+{}&\frac{275633101018694736}{714199463542249205} g_{48}&{}-{}&\frac{545585019341577194}{2142598390626747615} w_{3}\\ g_{38}&{}={}&\frac{423799064077289037}{714199463542249205}&{}+{}&\frac{387420945445953144}{714199463542249205} g_{48}&{}-{}&\frac{69996782239351912}{714199463542249205} w_{3}\\ g_{45}&{}={}&\frac{5184368567329882}{142839892708449841}&{}+{}&\frac{121318677775153194}{142839892708449841} g_{48}&{}+{}&\frac{17382490922694573}{285679785416899682} w_{3}\\ g_{40}&{}={}&\frac{9472192194444822}{714199463542249205}&{}+{}&\frac{221657433829791174}{714199463542249205} g_{48}&{}+{}&\frac{938201614587567271}{1428398927084498410} w_{3}\\ g_{41}&{}={}&\frac{3157397398148274}{142839892708449841}&{}+{}&\frac{73885811276597058}{142839892708449841} g_{48}&{}+{}&\frac{122280681251255969}{285679785416899682} w_{3}\\ g_{42}&{}={}&\frac{19996850188272402}{714199463542249205}&{}+{}&\frac{467943471418448034}{714199463542249205} g_{48}&{}+{}&\frac{393537934035421561}{1428398927084498410} w_{3}\\ g_{43}&{}={}&\frac{4560685130658618}{142839892708449841}&{}+{}&\frac{106723949621751306}{142839892708449841} g_{48}&{}+{}&\frac{49658857177636541}{285679785416899682} w_{3}\\ g_{44}&{}={}&\frac{24674475963306882}{714199463542249205}&{}+{}&\frac{577403932568962194}{714199463542249205} g_{48}&{}+{}&\frac{151465187123356801}{1428398927084498410} w_{3}\\ w_{2}&{}={}&\frac{284905643024637397}{142839892708449841}&{}+{}&\frac{10411482432835584}{142839892708449841} g_{48}&{}-{}&\frac{81118290972574674}{142839892708449841} w_{3}\\ g_{46}&{}={}&\frac{122102418439130313}{142839892708449841}&{}+{}&\frac{86084859733186588}{142839892708449841} g_{48}&{}-{}&\frac{34764981845389146}{142839892708449841} w_{3}\\ g_{47}&{}={}&\frac{40700806146376771}{142839892708449841}&{}+{}&\frac{123921548383362090}{142839892708449841} g_{48}&{}-{}&\frac{11588327281796382}{142839892708449841} w_{3}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{56841205071484253051}{571359570833799364}&{}-{}&\frac{140463453021033207}{571359570833799364} g_{48}&{}-{}&\frac{5297301038664969}{285679785416899682} g_{49}\\\hline w_{1}&{}={}&\frac{27181687044876281697}{2856797854168996820}&{}-{}&\frac{1856579113825931271}{2856797854168996820} g_{48}&{}+{}&\frac{1835756148960260103}{1428398927084498410} g_{49}\\ x_{1}&{}={}&\frac{7687764377881493627}{2856797854168996820}&{}+{}&\frac{998521283423482239}{2856797854168996820} g_{48}&{}-{}&\frac{915229423960797567}{1428398927084498410} g_{49}\\ x_{2}&{}={}&\frac{8696715853319426181}{2856797854168996820}&{}-{}&\frac{1284540560224298583}{2856797854168996820} g_{48}&{}+{}&\frac{1222071665627285079}{1428398927084498410} g_{49}\\ w_{4}&{}={}&\frac{18023416309639477753}{2856797854168996820}&{}-{}&\frac{998521283423482239}{2856797854168996820} g_{48}&{}+{}&\frac{915229423960797567}{1428398927084498410} g_{49}\\ w_{5}&{}={}&\frac{8444071271694554739}{2856797854168996820}&{}+{}&\frac{1284540560224298583}{2856797854168996820} g_{48}&{}-{}&\frac{1222071665627285079}{1428398927084498410} g_{49}\\ g_{8}&{}={}&\frac{4614304679162521981}{5713595708337993640}&{}+{}&\frac{452038640761245897}{5713595708337993640} g_{48}&{}+{}&\frac{52339841540566839}{2856797854168996820} g_{49}\\ g_{2}&{}={}&\frac{2562045842273313471}{2856797854168996820}&{}+{}&\frac{140463453021033207}{2856797854168996820} g_{48}&{}+{}&\frac{5297301038664969}{1428398927084498410} g_{49}\\ g_{17}&{}={}&\frac{981098637889278139}{1428398927084498410}&{}+{}&\frac{212799775199309493}{1428398927084498410} g_{48}&{}+{}&\frac{8202327343842891}{714199463542249205} g_{49}\\ g_{3}&{}={}&\frac{2393616121190065843}{5713595708337993640}&{}-{}&\frac{1003613654182232169}{5713595708337993640} g_{48}&{}+{}&\frac{1232666267704615017}{2856797854168996820} g_{49}\\ g_{7}&{}={}&\frac{2617646798947211609}{2856797854168996820}&{}+{}&\frac{329445513968660793}{2856797854168996820} g_{48}&{}-{}&\frac{93451912157720889}{1428398927084498410} g_{49}\\ g_{4}&{}={}&\frac{3205523971677025093}{5713595708337993640}&{}-{}&\frac{528612316433788239}{5713595708337993640} g_{48}&{}+{}&\frac{827074812841741647}{2856797854168996820} g_{49}\\ g_{5}&{}={}&\frac{1619317858839556423}{1428398927084498410}&{}+{}&\frac{268148950572368241}{1428398927084498410} g_{48}&{}-{}&\frac{166347789006864753}{714199463542249205} g_{49}\\ g_{6}&{}={}&\frac{552923218425932996}{714199463542249205}&{}+{}&\frac{22986211273609707}{714199463542249205} g_{48}&{}+{}&\frac{54671907636857898}{714199463542249205} g_{49}\\ g_{11}&{}={}&\frac{2520010197749248071}{2856797854168996820}&{}+{}&\frac{441814708766393247}{2856797854168996820} g_{48}&{}-{}&\frac{121565221341580191}{1428398927084498410} g_{49}\\ g_{9}&{}={}&\frac{1854114643420472571}{1428398927084498410}&{}+{}&\frac{431590776771540597}{1428398927084498410} g_{48}&{}-{}&\frac{295470284223727221}{714199463542249205} g_{49}\\ g_{10}&{}={}&\frac{729020806861620107}{714199463542249205}&{}+{}&\frac{145567580922988974}{714199463542249205} g_{48}&{}-{}&\frac{139011835188435804}{714199463542249205} g_{49}\\ g_{1}&{}={}&\frac{146969293182453371}{714199463542249205}&{}-{}&\frac{214514457600612258}{714199463542249205} g_{48}&{}+{}&\frac{460263362499731268}{714199463542249205} g_{49}\\ g_{12}&{}={}&\frac{2351580476666000443}{5713595708337993640}&{}-{}&\frac{702262398436872129}{5713595708337993640} g_{48}&{}+{}&\frac{1105803745324369857}{2856797854168996820} g_{49}\\ g_{13}&{}={}&\frac{3135464564136916093}{5713595708337993640}&{}-{}&\frac{26360223524854839}{5713595708337993640} g_{48}&{}+{}&\frac{615637275541333047}{2856797854168996820} g_{49}\\ g_{18}&{}={}&\frac{2050977474369529399}{2856797854168996820}&{}+{}&\frac{567918841858868303}{2856797854168996820} g_{48}&{}-{}&\frac{68945451860293199}{1428398927084498410} g_{49}\\ g_{15}&{}={}&\frac{1694739522857417773}{1428398927084498410}&{}+{}&\frac{426957874380747951}{1428398927084498410} g_{48}&{}-{}&\frac{256050319643936943}{714199463542249205} g_{49}\\ g_{14}&{}={}&\frac{3658053955784193193}{5713595708337993640}&{}+{}&\frac{424241226416490021}{5713595708337993640} g_{48}&{}+{}&\frac{288859629019308507}{2856797854168996820} g_{49}\\ g_{16}&{}={}&\frac{1218978932878658017}{1428398927084498410}&{}+{}&\frac{284185808259788979}{1428398927084498410} g_{48}&{}-{}&\frac{79881888318750387}{714199463542249205} g_{49}\\ g_{26}&{}={}&\frac{401900685474285116}{714199463542249205}&{}+{}&\frac{177981676277759427}{714199463542249205} g_{48}&{}+{}&\frac{36157840520451258}{714199463542249205} g_{49}\\ g_{19}&{}={}&\frac{2050977474369529399}{5713595708337993640}&{}-{}&\frac{2288879012310128517}{5713595708337993640} g_{48}&{}+{}&\frac{2787852402308703621}{2856797854168996820} g_{49}\\ g_{20}&{}={}&\frac{493205967845243345}{1142719141667598728}&{}-{}&\frac{191600099936243475}{1142719141667598728} g_{48}&{}+{}&\frac{357924563269101843}{571359570833799364} g_{49}\\ g_{21}&{}={}&\frac{2742731415797341609}{5713595708337993640}&{}-{}&\frac{70748157928609947}{5713595708337993640} g_{48}&{}+{}&\frac{1124136425703379611}{2856797854168996820} g_{49}\\ g_{22}&{}={}&\frac{585439826702284973}{1142719141667598728}&{}+{}&\frac{104150680647959001}{1142719141667598728} g_{48}&{}+{}&\frac{136095766388391975}{571359570833799364} g_{49}\\ g_{27}&{}={}&\frac{1662612032499407317}{2856797854168996820}&{}+{}&\frac{881515249401041189}{2856797854168996820} g_{48}&{}-{}&\frac{7709565854389157}{1428398927084498410} g_{49}\\ g_{24}&{}={}&\frac{1593426798891298969}{1428398927084498410}&{}+{}&\frac{508765632870010443}{1428398927084498410} g_{48}&{}-{}&\frac{240075740685875019}{714199463542249205} g_{49}\\ g_{23}&{}={}&\frac{3050177611987480369}{5713595708337993640}&{}+{}&\frac{915087777352064973}{5713595708337993640} g_{48}&{}+{}&\frac{384707102767680051}{2856797854168996820} g_{49}\\ g_{25}&{}={}&\frac{1067009846929479811}{1428398927084498410}&{}+{}&\frac{406897445993682717}{1428398927084498410} g_{48}&{}-{}&\frac{55920019881657501}{714199463542249205} g_{49}\\ g_{36}&{}={}&\frac{2032537172409169597}{5713595708337993640}&{}+{}&\frac{2806846250381070729}{5713595708337993640} g_{48}&{}+{}&\frac{188406488858198583}{2856797854168996820} g_{49}\\ g_{28}&{}={}&\frac{1662612032499407317}{5713595708337993640}&{}-{}&\frac{1975282604767955631}{5713595708337993640} g_{48}&{}+{}&\frac{2849088288314607663}{2856797854168996820} g_{49}\\ g_{29}&{}={}&\frac{363750820555202651}{1142719141667598728}&{}-{}&\frac{87067964088852513}{1142719141667598728} g_{48}&{}+{}&\frac{378336525271069857}{571359570833799364} g_{49}\\ g_{30}&{}={}&\frac{1922848816293750547}{5713595708337993640}&{}+{}&\frac{591288702438199479}{5713595708337993640} g_{48}&{}+{}&\frac{1253412185049177033}{2856797854168996820} g_{49}\\ g_{31}&{}={}&\frac{398449058394448415}{1142719141667598728}&{}+{}&\frac{255141543538634835}{1142719141667598728} g_{48}&{}+{}&\frac{165579711502345773}{571359570833799364} g_{49}\\ g_{34}&{}={}&\frac{1628185692410837651}{2856797854168996820}&{}+{}&\frac{1222244533909578267}{2856797854168996820} g_{48}&{}-{}&\frac{32082188237106651}{1428398927084498410} g_{49}\\ g_{33}&{}={}&\frac{712407732537629156}{714199463542249205}&{}+{}&\frac{322457756755374027}{714199463542249205} g_{48}&{}-{}&\frac{213489790177138902}{714199463542249205} g_{49}\\ g_{32}&{}={}&\frac{2038509609091236427}{5713595708337993640}&{}+{}&\frac{1731987061196490639}{5713595708337993640} g_{48}&{}+{}&\frac{544222805820096753}{2856797854168996820} g_{49}\\ g_{35}&{}={}&\frac{2034926147081996329}{5713595708337993640}&{}+{}&\frac{2376902574707238693}{5713595708337993640} g_{48}&{}+{}&\frac{330733015642957851}{2856797854168996820} g_{49}\\ g_{39}&{}={}&\frac{1013979152143125847}{2856797854168996820}&{}+{}&\frac{1815452481044624399}{2856797854168996820} g_{48}&{}-{}&\frac{42193010406295007}{1428398927084498410} g_{49}\\ g_{37}&{}={}&\frac{1423820058961580507}{1428398927084498410}&{}+{}&\frac{824058711708178069}{1428398927084498410} g_{48}&{}-{}&\frac{272792509670788597}{714199463542249205} g_{49}\\ g_{38}&{}={}&\frac{406299868517451059}{714199463542249205}&{}+{}&\frac{439918532125467078}{714199463542249205} g_{48}&{}-{}&\frac{104995173359027868}{714199463542249205} g_{49}\\ g_{45}&{}={}&\frac{58857439461333629}{1142719141667598728}&{}+{}&\frac{918401949433141833}{1142719141667598728} g_{48}&{}+{}&\frac{52147472768083719}{571359570833799364} g_{49}\\ g_{40}&{}={}&\frac{1013979152143125847}{5713595708337993640}&{}-{}&\frac{1041345373124372421}{5713595708337993640} g_{48}&{}+{}&\frac{2814604843762701813}{2856797854168996820} g_{49}\\ g_{41}&{}={}&\frac{147539860436442161}{1142719141667598728}&{}+{}&\frac{224244446459008557}{1142719141667598728} g_{48}&{}+{}&\frac{366842043753767907}{571359570833799364} g_{49}\\ g_{42}&{}={}&\frac{553512735541600777}{5713595708337993640}&{}+{}&\frac{2562933969241319589}{5713595708337993640} g_{48}&{}+{}&\frac{1180613802106264683}{2856797854168996820} g_{49}\\ g_{43}&{}={}&\frac{86144338222905485}{1142719141667598728}&{}+{}&\frac{704815025441100825}{1142719141667598728} g_{48}&{}+{}&\frac{148976571532909623}{571359570833799364} g_{49}\\ g_{44}&{}={}&\frac{348860994829811857}{5713595708337993640}&{}+{}&\frac{4164835899181627149}{5713595708337993640} g_{48}&{}+{}&\frac{454395561370070403}{2856797854168996820} g_{49}\\ w_{2}&{}={}&\frac{529252140562987457}{285679785416899682}&{}+{}&\frac{142500401324533179}{285679785416899682} g_{48}&{}-{}&\frac{121677436458862011}{142839892708449841} g_{49}\\ g_{46}&{}={}&\frac{226822345955566053}{285679785416899682}&{}+{}&\frac{224317192234456895}{285679785416899682} g_{48}&{}-{}&\frac{52147472768083719}{142839892708449841} g_{49}\\ g_{47}&{}={}&\frac{75607448651855351}{285679785416899682}&{}+{}&\frac{265225587689418753}{285679785416899682} g_{48}&{}-{}&\frac{17382490922694573}{142839892708449841} g_{49}\\ w_{3}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{48}&{}+{}&\frac{3}{2} g_{49}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{113687707444007171071}{1142719141667598728}&{}-{}&\frac{265035002926071507}{1142719141667598728} g_{48}&{}-{}&\frac{15891903115994907}{571359570833799364} g_{50}\\\hline w_{1}&{}={}&\frac{56199130238712823497}{5713595708337993640}&{}-{}&\frac{9220426674532642851}{5713595708337993640} g_{48}&{}+{}&\frac{5507268446880780309}{2856797854168996820} g_{50}\\ x_{1}&{}={}&\frac{14460299331802189687}{5713595708337993640}&{}+{}&\frac{4742730838729357179}{5713595708337993640} g_{48}&{}-{}&\frac{2745688271882392701}{2856797854168996820} g_{50}\\ x_{2}&{}={}&\frac{18615503372266137441}{5713595708337993640}&{}-{}&\frac{6235296117330452403}{5713595708337993640} g_{48}&{}+{}&\frac{3666214996881855237}{2856797854168996820} g_{50}\\ w_{4}&{}={}&\frac{36962062043239753073}{5713595708337993640}&{}-{}&\frac{4742730838729357179}{5713595708337993640} g_{48}&{}+{}&\frac{2745688271882392701}{2856797854168996820} g_{50}\\ w_{5}&{}={}&\frac{15666070877761824399}{5713595708337993640}&{}+{}&\frac{6235296117330452403}{5713595708337993640} g_{48}&{}-{}&\frac{3666214996881855237}{2856797854168996820} g_{50}\\ g_{8}&{}={}&\frac{9280949199865610801}{11427191416675987280}&{}+{}&\frac{747057756900791277}{11427191416675987280} g_{48}&{}+{}&\frac{157019524621700517}{5713595708337993640} g_{50}\\ g_{2}&{}={}&\frac{5129388985585291911}{5713595708337993640}&{}+{}&\frac{265035002926071507}{5713595708337993640} g_{48}&{}+{}&\frac{15891903115994907}{2856797854168996820} g_{50}\\ g_{17}&{}={}&\frac{1970399603122399169}{2856797854168996820}&{}+{}&\frac{400992568367090313}{2856797854168996820} g_{48}&{}+{}&\frac{24606982031528673}{1428398927084498410} g_{50}\\ g_{3}&{}={}&\frac{6019898510084746703}{11427191416675987280}&{}-{}&\frac{5705226111478309389}{11427191416675987280} g_{48}&{}+{}&\frac{3697998803113845051}{5713595708337993640} g_{50}\\ g_{7}&{}={}&\frac{5141841685736702329}{5713595708337993640}&{}+{}&\frac{939246764410484253}{5713595708337993640} g_{48}&{}-{}&\frac{280355736473162667}{2856797854168996820} g_{50}\\ g_{4}&{}={}&\frac{7238122756195791833}{11427191416675987280}&{}-{}&\frac{3538449071392801419}{11427191416675987280} g_{48}&{}+{}&\frac{2481224438525224941}{5713595708337993640} g_{50}\\ g_{5}&{}={}&\frac{3072287928672248093}{2856797854168996820}&{}+{}&\frac{1035341268165330741}{2856797854168996820} g_{48}&{}-{}&\frac{499043367020594259}{1428398927084498410} g_{50}\\ g_{6}&{}={}&\frac{1133182390670294941}{1428398927084498410}&{}-{}&\frac{36035438908067433}{1428398927084498410} g_{48}&{}+{}&\frac{82007861455286847}{714199463542249205} g_{50}\\ g_{11}&{}={}&\frac{4918455174156915951}{5713595708337993640}&{}+{}&\frac{1248325081557527067}{5713595708337993640} g_{48}&{}-{}&\frac{364695664024740573}{2856797854168996820} g_{50}\\ g_{9}&{}={}&\frac{3412759002617217921}{2856797854168996820}&{}+{}&\frac{1749592406214262857}{2856797854168996820} g_{48}&{}-{}&\frac{886410852671181663}{1428398927084498410} g_{50}\\ g_{10}&{}={}&\frac{694267848064511156}{714199463542249205}&{}+{}&\frac{249826457314315827}{714199463542249205} g_{48}&{}-{}&\frac{208517752782653706}{714199463542249205} g_{50}\\ g_{1}&{}={}&\frac{262035133807386188}{714199463542249205}&{}-{}&\frac{559711979475410709}{714199463542249205} g_{48}&{}+{}&\frac{690395043749596902}{714199463542249205} g_{50}\\ g_{12}&{}={}&\frac{5808964698656370743}{11427191416675987280}&{}-{}&\frac{4721936032846853829}{11427191416675987280} g_{48}&{}+{}&\frac{3317411235973109571}{5713595708337993640} g_{50}\\ g_{13}&{}={}&\frac{6886566403815165233}{11427191416675987280}&{}-{}&\frac{1899632273673708819}{11427191416675987280} g_{48}&{}+{}&\frac{1846911826623999141}{5713595708337993640} g_{50}\\ g_{18}&{}={}&\frac{4033009496878765599}{5713595708337993640}&{}+{}&\frac{1342674039298616203}{5713595708337993640} g_{48}&{}-{}&\frac{206836355580879597}{2856797854168996820} g_{50}\\ g_{15}&{}={}&\frac{3133428726070898603}{2856797854168996820}&{}+{}&\frac{1622066707693306731}{2856797854168996820} g_{48}&{}-{}&\frac{768150958931810829}{1428398927084498410} g_{50}\\ g_{14}&{}={}&\frac{7604967540587694893}{11427191416675987280}&{}-{}&\frac{18096434224945479}{11427191416675987280} g_{48}&{}+{}&\frac{866578887057925521}{5713595708337993640} g_{50}\\ g_{16}&{}={}&\frac{2358075977438565647}{2856797854168996820}&{}+{}&\frac{808017281475829119}{2856797854168996820} g_{48}&{}-{}&\frac{239645664956251161}{1428398927084498410} g_{50}\\ g_{26}&{}={}&\frac{821880291208795861}{1428398927084498410}&{}+{}&\frac{301726591774841967}{1428398927084498410} g_{48}&{}+{}&\frac{54236760780676887}{714199463542249205} g_{50}\\ g_{19}&{}={}&\frac{6889807351047762419}{11427191416675987280}&{}-{}&\frac{12941315231546367897}{11427191416675987280} g_{48}&{}+{}&\frac{8363557206926110863}{5713595708337993640} g_{50}\\ g_{20}&{}={}&\frac{1344336498959588533}{2285438283335197456}&{}-{}&\frac{1456973889679792479}{2285438283335197456} g_{48}&{}+{}&\frac{1073773689807305529}{1142719141667598728} g_{50}\\ g_{21}&{}={}&\frac{6609599257298062829}{11427191416675987280}&{}-{}&\frac{3513905592967358727}{11427191416675987280} g_{48}&{}+{}&\frac{3372409277110138833}{5713595708337993640} g_{50}\\ g_{22}&{}={}&\frac{1306975419792961921}{2285438283335197456}&{}-{}&\frac{199985937869257923}{2285438283335197456} g_{48}&{}+{}&\frac{408287299165175925}{1142719141667598728} g_{50}\\ g_{27}&{}={}&\frac{3317514499144425477}{5713595708337993640}&{}+{}&\frac{1786159196365249849}{5713595708337993640} g_{48}&{}-{}&\frac{23128697563167471}{2856797854168996820} g_{50}\\ g_{24}&{}={}&\frac{2946777857096722919}{2856797854168996820}&{}+{}&\frac{1737758487797645943}{2856797854168996820} g_{48}&{}-{}&\frac{720227222057625057}{1428398927084498410} g_{50}\\ g_{23}&{}={}&\frac{6485062326742640789}{11427191416675987280}&{}+{}&\frac{676054246401089793}{11427191416675987280} g_{48}&{}+{}&\frac{1154121308303040153}{5713595708337993640} g_{50}\\ g_{25}&{}={}&\frac{2078099673977302121}{2856797854168996820}&{}+{}&\frac{981554951632337937}{2856797854168996820} g_{48}&{}-{}&\frac{167760059644972503}{1428398927084498410} g_{50}\\ g_{36}&{}={}&\frac{4253480833676537777}{11427191416675987280}&{}+{}&\frac{5048473034187545709}{11427191416675987280} g_{48}&{}+{}&\frac{565219466574595749}{5713595708337993640} g_{50}\\ g_{28}&{}={}&\frac{6174312353313422297}{11427191416675987280}&{}-{}&\frac{12497830074479734251}{11427191416675987280} g_{48}&{}+{}&\frac{8547264864943822989}{5713595708337993640} g_{50}\\ g_{29}&{}={}&\frac{1105838166381475159}{2285438283335197456}&{}-{}&\frac{1309145503990914597}{2285438283335197456} g_{48}&{}+{}&\frac{1135009575813209571}{1142719141667598728} g_{50}\\ g_{30}&{}={}&\frac{5099109817636678127}{11427191416675987280}&{}-{}&\frac{2577659150271132141}{11427191416675987280} g_{48}&{}+{}&\frac{3760236555147531099}{5713595708337993640} g_{50}\\ g_{31}&{}={}&\frac{962477828291242603}{2285438283335197456}&{}+{}&\frac{13543952570232351}{2285438283335197456} g_{48}&{}+{}&\frac{496739134507037319}{1142719141667598728} g_{50}\\ g_{34}&{}={}&\frac{3224289196584568651}{5713595708337993640}&{}+{}&\frac{2540735632530476487}{5713595708337993640} g_{48}&{}-{}&\frac{96246564711319953}{2856797854168996820} g_{50}\\ g_{33}&{}={}&\frac{1318070569986688861}{1428398927084498410}&{}+{}&\frac{965150198776456407}{1428398927084498410} g_{48}&{}-{}&\frac{320234685265708353}{714199463542249205} g_{50}\\ g_{32}&{}={}&\frac{4621242024002569607}{11427191416675987280}&{}+{}&\frac{1831305704932691019}{11427191416675987280} g_{48}&{}+{}&\frac{1632668417460290259}{5713595708337993640} g_{50}\\ g_{35}&{}={}&\frac{4400585309806950509}{11427191416675987280}&{}+{}&\frac{3761606102485603833}{11427191416675987280} g_{48}&{}+{}&\frac{992199046928873553}{5713595708337993640} g_{50}\\ g_{39}&{}={}&\frac{1985765293879956687}{5713595708337993640}&{}+{}&\frac{3757483993308133819}{5713595708337993640} g_{48}&{}-{}&\frac{126579031218885021}{2856797854168996820} g_{50}\\ g_{37}&{}={}&\frac{2574847608252372417}{2856797854168996820}&{}+{}&\frac{2466494952428721929}{2856797854168996820} g_{48}&{}-{}&\frac{818377529012365791}{1428398927084498410} g_{50}\\ g_{38}&{}={}&\frac{380051075177694092}{714199463542249205}&{}+{}&\frac{518664912144737979}{714199463542249205} g_{48}&{}-{}&\frac{157492760038541802}{714199463542249205} g_{50}\\ g_{45}&{}={}&\frac{169862351690750977}{2285438283335197456}&{}+{}&\frac{1680361480562032509}{2285438283335197456} g_{48}&{}+{}&\frac{156442418304251157}{1142719141667598728} g_{50}\\ g_{40}&{}={}&\frac{4842563148048953507}{11427191416675987280}&{}-{}&\frac{10526505277536850281}{11427191416675987280} g_{48}&{}+{}&\frac{8443814531288105439}{5713595708337993640} g_{50}\\ g_{41}&{}={}&\frac{661921764626652229}{2285438283335197456}&{}-{}&\frac{652037238343286607}{2285438283335197456} g_{48}&{}+{}&\frac{1100526131261303721}{1142719141667598728} g_{50}\\ g_{42}&{}={}&\frac{2287639273189466237}{11427191416675987280}&{}+{}&\frac{1584026532163845129}{11427191416675987280} g_{48}&{}+{}&\frac{3541841406318794049}{5713595708337993640} g_{50}\\ g_{43}&{}={}&\frac{321265247978720593}{2285438283335197456}&{}+{}&\frac{962700336283472781}{2285438283335197456} g_{48}&{}+{}&\frac{446929714598728869}{1142719141667598728} g_{50}\\ g_{44}&{}={}&\frac{1152117551029694117}{11427191416675987280}&{}+{}&\frac{6966485114253043089}{11427191416675987280} g_{48}&{}+{}&\frac{1363186684110211209}{5713595708337993640} g_{50}\\ w_{2}&{}={}&\frac{936826844667112903}{571359570833799364}&{}+{}&\frac{650033112025652391}{571359570833799364} g_{48}&{}-{}&\frac{365032309376586033}{285679785416899682} g_{50}\\ g_{46}&{}={}&\frac{401497219143048387}{571359570833799364}&{}+{}&\frac{605076802773164947}{571359570833799364} g_{48}&{}-{}&\frac{156442418304251157}{285679785416899682} g_{50}\\ g_{47}&{}={}&\frac{133832406381016129}{571359570833799364}&{}+{}&\frac{582598648146921225}{571359570833799364} g_{48}&{}-{}&\frac{52147472768083719}{285679785416899682} g_{50}\\ w_{3}&{}={}&\frac{5}{8}&{}-{}&\frac{15}{8} g_{48}&{}+{}&\frac{9}{4} g_{50}\\ g_{49}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{48}&{}+{}&\frac{3}{2} g_{50}\\ \end{aligned}\end{gather*}$

$\displaystyle \begin{gather*}\begin{aligned}\zeta &{}={}& -\frac{227391306791130337049}{2285438283335197456}&{}-{}&\frac{482394296504158293}{2285438283335197456} g_{48}&{}-{}&\frac{47675709347984721}{1142719141667598728} g_{51}\\\hline w_{1}&{}={}&\frac{117905528924306427303}{11427191416675987280}&{}-{}&\frac{34962658689707626629}{11427191416675987280} g_{48}&{}+{}&\frac{16521805340642340927}{5713595708337993640} g_{51}\\ x_{1}&{}={}&\frac{26174910391721986673}{11427191416675987280}&{}+{}&\frac{17722526493105892461}{11427191416675987280} g_{48}&{}-{}&\frac{8237064815647178103}{5713595708337993640} g_{51}\\ x_{2}&{}={}&\frac{40897221741414130119}{11427191416675987280}&{}-{}&\frac{23469237225306470517}{11427191416675987280} g_{48}&{}+{}&\frac{10998644990645565711}{5713595708337993640} g_{51}\\ w_{4}&{}={}&\frac{76669812358361898847}{11427191416675987280}&{}-{}&\frac{17722526493105892461}{11427191416675987280} g_{48}&{}+{}&\frac{8237064815647178103}{5713595708337993640} g_{51}\\ w_{5}&{}={}&\frac{27665926758641793561}{11427191416675987280}&{}+{}&\frac{23469237225306470517}{11427191416675987280} g_{48}&{}-{}&\frac{10998644990645565711}{5713595708337993640} g_{51}\\ g_{8}&{}={}&\frac{18718917924352922119}{22854382833351974560}&{}+{}&\frac{1023056939936481003}{22854382833351974560} g_{48}&{}+{}&\frac{471058573865101551}{11427191416675987280} g_{51}\\ g_{2}&{}={}&\frac{10274669874286578729}{11427191416675987280}&{}+{}&\frac{482394296504158293}{11427191416675987280} g_{48}&{}+{}&\frac{47675709347984721}{5713595708337993640} g_{51}\\ g_{17}&{}={}&\frac{3965406188276327011}{5713595708337993640}&{}+{}&\frac{728164190639594607}{5713595708337993640} g_{48}&{}+{}&\frac{73820946094586019}{2856797854168996820} g_{51}\\ g_{3}&{}={}&\frac{15737795823283338457}{22854382833351974560}&{}-{}&\frac{22504448632298153931}{22854382833351974560} g_{48}&{}+{}&\frac{11093996409341535153}{11427191416675987280} g_{51}\\ g_{7}&{}={}&\frac{10003327635000241991}{11427191416675987280}&{}+{}&\frac{2719560738240456507}{11427191416675987280} g_{48}&{}-{}&\frac{841067209419488001}{5713595708337993640} g_{51}\\ g_{4}&{}={}&\frac{16957469950916808607}{22854382833351974560}&{}-{}&\frac{14520571458361277661}{22854382833351974560} g_{48}&{}+{}&\frac{7443673315575674823}{11427191416675987280} g_{51}\\ g_{5}&{}={}&\frac{5645532490323901927}{5713595708337993640}&{}+{}&\frac{3567812637392444259}{5713595708337993640} g_{48}&{}-{}&\frac{1497130101061782777}{2856797854168996820} g_{51}\\ g_{6}&{}={}&\frac{2348372642795876729}{2856797854168996820}&{}-{}&\frac{318094462181995407}{2856797854168996820} g_{48}&{}+{}&\frac{246023584365860541}{1428398927084498410} g_{51}\\ g_{11}&{}={}&\frac{9472214684289091329}{11427191416675987280}&{}+{}&\frac{3590737155189275853}{11427191416675987280} g_{48}&{}-{}&\frac{1094086992074221719}{5713595708337993640} g_{51}\\ g_{9}&{}={}&\frac{5939107152563254179}{5713595708337993640}&{}+{}&\frac{6158417370442070703}{5713595708337993640} g_{48}&{}-{}&\frac{2659232558013544989}{2856797854168996820} g_{51}\\ g_{10}&{}={}&\frac{1284276819737695459}{1428398927084498410}&{}+{}&\frac{812429543802612213}{1428398927084498410} g_{48}&{}-{}&\frac{312776629173980559}{714199463542249205} g_{51}\\ g_{1}&{}={}&\frac{869267789489570827}{1428398927084498410}&{}-{}&\frac{2155016524575216771}{1428398927084498410} g_{48}&{}+{}&\frac{1035592565624395353}{714199463542249205} g_{51}\\ g_{12}&{}={}&\frac{14935340633285851057}{22854382833351974560}&{}-{}&\frac{19396105773613036371}{22854382833351974560} g_{48}&{}+{}&\frac{9952233707919328713}{11427191416675987280} g_{51}\\ g_{13}&{}={}&\frac{15620044634254329607}{22854382833351974560}&{}-{}&\frac{9340000027219415061}{22854382833351974560} g_{48}&{}+{}&\frac{5540735479871997423}{11427191416675987280} g_{51}\\ g_{18}&{}={}&\frac{7859182638176651601}{11427191416675987280}&{}+{}&\frac{3305857145339871197}{11427191416675987280} g_{48}&{}-{}&\frac{620509066742638791}{5713595708337993640} g_{51}\\ g_{15}&{}={}&\frac{5498706493209986377}{5713595708337993640}&{}+{}&\frac{5548586292182045949}{5713595708337993640} g_{48}&{}-{}&\frac{2304452876795432487}{2856797854168996820} g_{51}\\ g_{14}&{}={}&\frac{16076513968233315307}{22854382833351974560}&{}-{}&\frac{2635929529623667521}{22854382833351974560} g_{48}&{}+{}&\frac{2599736661173776563}{11427191416675987280} g_{51}\\ g_{16}&{}={}&\frac{4476506289920880133}{5713595708337993640}&{}+{}&\frac{2334971557820411721}{5713595708337993640} g_{48}&{}-{}&\frac{718936994868753483}{2856797854168996820} g_{51}\\ g_{26}&{}={}&\frac{1697997343198268609}{2856797854168996820}&{}+{}&\frac{440742901207653273}{2856797854168996820} g_{48}&{}+{}&\frac{162710282342030661}{1428398927084498410} g_{51}\\ g_{19}&{}={}&\frac{22143171909021635701}{22854382833351974560}&{}-{}&\frac{50973302083871068383}{22854382833351974560} g_{48}&{}+{}&\frac{25090671620778332589}{11427191416675987280} g_{51}\\ g_{20}&{}={}&\frac{3762446687726482595}{4570876566670394912}&{}-{}&\frac{6135268848781501545}{4570876566670394912} g_{48}&{}+{}&\frac{3221321069421916587}{2285438283335197456} g_{51}\\ g_{21}&{}={}&\frac{16591607791706264491}{22854382833351974560}&{}-{}&\frac{17145039017265133953}{22854382833351974560} g_{48}&{}+{}&\frac{10117227831330416499}{11427191416675987280} g_{51}\\ g_{22}&{}={}&\frac{3022238138751099767}{4570876566670394912}&{}-{}&\frac{1624833773234043621}{4570876566670394912} g_{48}&{}+{}&\frac{1224861897495527775}{2285438283335197456} g_{51}\\ g_{27}&{}={}&\frac{6611900300725683483}{11427191416675987280}&{}+{}&\frac{3641704485420002111}{11427191416675987280} g_{48}&{}-{}&\frac{69386092689502413}{5713595708337993640} g_{51}\\ g_{24}&{}={}&\frac{5173328492135820781}{5713595708337993640}&{}+{}&\frac{5636198641768167057}{5713595708337993640} g_{48}&{}-{}&\frac{2160681666172875171}{2856797854168996820} g_{51}\\ g_{23}&{}={}&\frac{14124245961788321731}{22854382833351974560}&{}-{}&\frac{2110255432106940873}{22854382833351974560} g_{48}&{}+{}&\frac{3462363924909120459}{11427191416675987280} g_{51}\\ g_{25}&{}={}&\frac{3988439288309631739}{5713595708337993640}&{}+{}&\frac{2466390082199593383}{5713595708337993640} g_{48}&{}-{}&\frac{503280178934917509}{2856797854168996820} g_{51}\\ g_{36}&{}={}&\frac{9072181133927671303}{22854382833351974560}&{}+{}&\frac{8401287668651304171}{22854382833351974560} g_{48}&{}+{}&\frac{1695658399723787247}{11427191416675987280} g_{51}\\ g_{28}&{}={}&\frac{20895889571570667583}{22854382833351974560}&{}-{}&\frac{50637454743790937469}{22854382833351974560} g_{48}&{}+{}&\frac{25641794594831468967}{11427191416675987280} g_{51}\\ g_{29}&{}={}&\frac{3346685908576159889}{4570876566670394912}&{}-{}&\frac{6023319735421457907}{4570876566670394912} g_{48}&{}+{}&\frac{3405028727439628713}{2285438283335197456} g_{51}\\ g_{30}&{}={}&\frac{13958456190420887353}{22854382833351974560}&{}-{}&\frac{16436027965984857579}{22854382833351974560} g_{48}&{}+{}&\frac{11280709665442593297}{11427191416675987280} g_{51}\\ g_{31}&{}={}&\frac{2421694791089522525}{4570876566670394912}&{}-{}&\frac{1463129498380647255}{4570876566670394912} g_{48}&{}+{}&\frac{1490217403521111957}{2285438283335197456} g_{51}\\ g_{34}&{}={}&\frac{6352331828457817349}{11427191416675987280}&{}+{}&\frac{5370210959194912833}{11427191416675987280} g_{48}&{}-{}&\frac{288739694133959859}{5713595708337993640} g_{51}\\ g_{33}&{}={}&\frac{2315906454707669369}{2856797854168996820}&{}+{}&\frac{2891004453350037873}{2856797854168996820} g_{48}&{}-{}&\frac{960704055797125059}{1428398927084498410} g_{51}\\ g_{32}&{}={}&\frac{10875152465465429473}{22854382833351974560}&{}-{}&\frac{1235393842515488739}{22854382833351974560} g_{48}&{}+{}&\frac{4898005252380870777}{11427191416675987280} g_{51}\\ g_{35}&{}={}&\frac{9793369666542774571}{22854382833351974560}&{}+{}&\frac{4546615064184587007}{22854382833351974560} g_{48}&{}+{}&\frac{2976597140786620659}{11427191416675987280} g_{51}\\ g_{39}&{}={}&\frac{3844951556541028353}{11427191416675987280}&{}+{}&\frac{7894705080272922701}{11427191416675987280} g_{48}&{}-{}&\frac{379737093656655063}{5713595708337993640} g_{51}\\ g_{37}&{}={}&\frac{4331317687492379043}{5713595708337993640}&{}+{}&\frac{7388122491894541231}{5713595708337993640} g_{48}&{}-{}&\frac{2455132587037097373}{2856797854168996820} g_{51}\\ g_{38}&{}={}&\frac{681355770336117283}{1428398927084498410}&{}+{}&\frac{1273568964347288661}{1428398927084498410} g_{48}&{}-{}&\frac{236239140057812703}{714199463542249205} g_{51}\\ g_{45}&{}={}&\frac{496167121685753111}{4570876566670394912}&{}+{}&\frac{2891395706211311547}{4570876566670394912} g_{48}&{}+{}&\frac{469327254912753471}{2285438283335197456} g_{51}\\ g_{40}&{}={}&\frac{18128940827386012453}{22854382833351974560}&{}-{}&\frac{46384454148938016879}{22854382833351974560} g_{48}&{}+{}&\frac{25331443593864316317}{11427191416675987280} g_{51}\\ g_{41}&{}={}&\frac{2424369660514608179}{4570876566670394912}&{}-{}&\frac{4605652870470484377}{4570876566670394912} g_{48}&{}+{}&\frac{3301578393783911163}{2285438283335197456} g_{51}\\ g_{42}&{}={}&\frac{8117119952697726523}{22854382833351974560}&{}-{}&\frac{7457471154628691889}{22854382833351974560} g_{48}&{}+{}&\frac{10625524218956382147}{11427191416675987280} g_{51}\\ g_{43}&{}={}&\frac{1089460210556170055}{4570876566670394912}&{}+{}&\frac{584611528770758955}{4570876566670394912} g_{48}&{}+{}&\frac{1340789143796186607}{2285438283335197456} g_{51}\\ g_{44}&{}={}&\frac{3667421786169599443}{22854382833351974560}&{}+{}&\frac{9843410176175452551}{22854382833351974560} g_{48}&{}+{}&\frac{4089560052330633627}{11427191416675987280} g_{51}\\ w_{2}&{}={}&\frac{1508621379957639773}{1142719141667598728}&{}+{}&\frac{2395163152181062881}{1142719141667598728} g_{48}&{}-{}&\frac{1095096928129758099}{571359570833799364} g_{51}\\ g_{46}&{}={}&\frac{646552019981845617}{1142719141667598728}&{}+{}&\frac{1679480860459083365}{1142719141667598728} g_{48}&{}-{}&\frac{469327254912753471}{571359570833799364} g_{51}\\ g_{47}&{}={}&\frac{215517339993948539}{1142719141667598728}&{}+{}&\frac{1321639714598093607}{1142719141667598728} g_{48}&{}-{}&\frac{156442418304251157}{571359570833799364} g_{51}\\ w_{3}&{}={}&\frac{19}{16}&{}-{}&\frac{57}{16} g_{48}&{}+{}&\frac{27}{8} g_{51}\\ g_{49}&{}={}&\frac{5}{8}&{}-{}&\frac{15}{8} g_{48}&{}+{}&\frac{9}{4} g_{51}\\ g_{50}&{}={}&\frac{1}{4}&{}-{}&\frac{3}{4} g_{48}&{}+{}&\frac{3}{2} g_{51}\\ \end{aligned}\end{gather*}$

<Figure size 640x480 with 0 Axes>

print("x_1 ~", float(dbug.bas_vals[1]))

x_1 ~ 2.2905812493456863

print("x_2 ~", float(dbug.bas_vals[2]))

x_2 ~ 3.5789390629907354