
# q-expansion of newform 637.2.r.f, downloaded from the LMFDB on 18 April 2024.

# We generate the q-expansion using the Hecke eigenvalues a_p at the primes.
# Each a_p is given as a linear combination
# of the following basis for the coefficient ring.

def make_data():

    from sage.all import prod, floor, prime_powers, gcd, QQ, primes_first_n, next_prime, RR

    def discrete_log(elts, gens, mod):
        # algorithm 2.2, page 16 of https://arxiv.org/abs/0903.2785
        def table_gens(gens, mod):
            T = [1]
            n = len(gens)
            r = [None]*n
            s = [None]*n
            for i in range(n):
                beta = gens[i]
                r[i] = 1
                N = len(T)
                while beta not in T:
                    for Tj in T[:N]:
                        T.append((beta*Tj) % mod)
                    beta = (beta*gens[i]) % mod
                    r[i] += 1
                s[i] = T.index(beta)
            return T, r, s
        T, r, s = table_gens(gens, mod)
        n = len(gens)
        N = [ prod(r[:j]) for j in range(n) ]
        Z = lambda s: [ (floor(s/N[j]) % r[j]) for j in range(n)]
        return [Z(T.index(elt % mod)) for elt in elts]
    def extend_multiplicatively(an):
        for pp in prime_powers(len(an)-1):
            for k in range(1, (len(an) - 1)//pp + 1):
                if gcd(k, pp) == 1:
                    an[pp*k] = an[pp]*an[k]
    from sage.all import PolynomialRing, NumberField, ZZ
    R = PolynomialRing(QQ, "x")
    f = R(poly_data)
    K = NumberField(f, "a")
    betas = [K([c/ZZ(den) for c in num]) for num, den in basis_data]
    convert_elt_to_field = lambda elt: sum(c*beta for c, beta in zip(elt, betas))
    # convert aps to K elements
    primes = primes_first_n(len(aps_data))
    good_primes = [p for p in primes if not p.divides(level)]
    aps = map(convert_elt_to_field, aps_data)
    if not hecke_ring_character_values:
        # trivial character
        char_values = dict(zip(good_primes, [1]*len(good_primes)))
    else:
        gens = [elt[0] for elt in hecke_ring_character_values]
        gens_values = [convert_elt_to_field(elt[1]) for elt in hecke_ring_character_values]
        char_values = dict([(
            p,prod(g**k for g, k in zip(gens_values, elt)))
            for p, elt in zip(good_primes, discrete_log(good_primes, gens, level))
            ])
    an_list_bound = next_prime(primes[-1])
    an = [0]*an_list_bound
    an[1] = 1
    
    from sage.all import PowerSeriesRing
    PS = PowerSeriesRing(K, "q")
    for p, ap in zip(primes, aps):
        if p.divides(level):
            euler_factor = [1, -ap]
        else:
            euler_factor = [1, -ap, p**(weight - 1) * char_values[p]]
        k = RR(an_list_bound).log(p).floor() + 1
        foo = (1/PS(euler_factor)).padded_list(k)
        for i in range(1, k):
            an[p**i] = foo[i]
    extend_multiplicatively(an)
    return PS(an)
level = 637
weight = 2
poly_data = [9, 0, -93, 0, 853, 0, -1050, 0, 952, 0, -334, 0, 85, 0, -11, 0, 1]

# The entries in the following list give a basis for the
# coefficient ring in terms of a root of the defining polynomial above.
# Each line consists of the coefficients of the numerator, and a denominator.
basis_data  = [[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 1], [[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 1], [[0, -55035781, 0, -690027, 0, 6321845, 0, -17193085, 0, 6411671, 0, -1852321, 0, 246060, 0, -24498], 14163622], [[-40872159, 0, -690027, 0, 6321845, 0, -17193085, 0, 6411671, 0, -1852321, 0, 246060, 0, -24498, 0], 14163622], [[-23829231, 0, 218482087, 0, -377649654, 0, 236538400, 0, -78484018, 0, 17340370, 0, -2170865, 0, 172099, 0], 42490866], [[-20454191, 0, -2790528, 0, 25566080, 0, -66564370, 0, 25929344, 0, -7490944, 0, 1000291, 0, -99072, 0], 14163622], [[0, 61326350, 0, 3480555, 0, -31887925, 0, 83757455, 0, -32341015, 0, 9343265, 0, -1246351, 0, 123570], 14163622], [[-5618970, 0, 441286822, 0, -514968195, 0, 494434675, 0, -174659083, 0, 45125185, 0, -5861765, 0, 539569, 0], 42490866], [[0, 5618970, 0, -441286822, 0, 514968195, 0, -494434675, 0, 174659083, 0, -45125185, 0, 5861765, 0, -539569], 42490866], [[23341327, 0, 2881788, 0, -26402180, 0, 67022271, 0, -26777324, 0, 7735924, 0, -1048444, 0, 102312, 0], 7081811], [[0, 238534757, 0, 13414713, 0, -122902055, 0, 318752537, 0, -124648349, 0, 36010699, 0, -4835650, 0, 476262], 14163622], [[46491129, 0, -426433173, 0, 508646350, 0, -477241590, 0, 168247412, 0, -43272864, 0, 5615705, 0, -515071, 0], 14163622], [[366555, 0, -3361729, 0, 4460568, 0, -3722089, 0, 1287475, 0, -317920, 0, 40712, 0, -3598, 0], 95271], [[0, -187583223, 0, 1720586341, 0, -2040907245, 0, 1926159445, 0, -679401319, 0, 174943777, 0, -22708880, 0, 2084782], 42490866], [[0, -19219314, 0, 176278948, 0, -219868809, 0, 196608895, 0, -68898667, 0, 17480377, 0, -2261795, 0, 205171], 3862806], [[0, -106397226, 0, 7579585292, 0, -9751108731, 0, 9362299115, 0, -3317989973, 0, 854461673, 0, -110994637, 0, 10171607], 42490866]]

hecke_ring_character_values = [[248, [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0]], [197, [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]]
aps_data = [[0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, 1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, -1, 0], [-1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0], [-1, 0, 0, 0, 1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, -2, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, -1, -1, -1], [0, 0, -1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 1, -2, -1], [2, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, -2, 2, 1], [-3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0], [0, -3, 2, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, -3, 1, 0], [0, 2, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 1, -1, 0, 3, 0, -1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, -1, 0, 1], [0, -5, 0, 0, 0, 0, 0, 0, -5, 0, -1, 0, 0, 3, -1, 1], [0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1], [-1, 0, 0, 0, 3, 0, 0, 1, 0, 0, 0, 2, -1, 0, 0, 0], [1, 0, 0, -2, -1, 1, 0, -5, 0, -2, 0, -2, 2, 0, 0, 0], [5, 0, 0, 2, -5, 5, 0, -3, 0, 1, 0, 2, -1, 0, 0, 0], [0, -1, 3, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [3, 0, 0, 4, 0, 5, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [-4, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0], [1, 0, 0, 6, -1, 1, 0, 5, 0, 1, 0, 6, -1, 0, 0, 0], [0, -4, 2, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0], [-4, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, -3, 0], [0, 4, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-7, 0, 0, 0, -2, 0, 0, 7, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -7, -2, 2], [0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, -1, -2], [0, 0, 0, -2, 0, 0, 0, -7, 0, 2, 0, -2, -2, 0, 0, 0], [1, 0, 0, 0, 5, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0], [9, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-7, 0, 0, 2, 7, -7, 0, -1, 0, -3, 0, 2, 3, 0, 0, 0], [0, 5, -3, 0, 0, 0, -5, 0, 0, 0, -3, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, -1, 0, 1], [-13, 0, 0, 0, 5, 0, 0, 13, 0, 0, 0, -4, 2, 0, 0, 0], [6, 0, 0, 2, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 0, -3, 0, -5, 0, 0, 0, 0, -4, -3, 1], [0, -7, 5, 0, 0, 0, -1, 0, 0, 0, -3, 0, 0, 0, 0, 0], [0, 5, 0, 0, 0, 0, 0, 0, 5, 0, 3, 0, 0, 3, -3, -3], [-4, 0, 0, -4, 4, -4, 0, 15, 0, -2, 0, -4, 2, 0, 0, 0], [0, 0, 8, 0, 0, 0, -3, 0, -1, 0, 0, 0, 0, -8, -3, -1], [0, 1, -1, 0, 0, 0, 5, 0, 0, 0, -1, 0, 0, 0, 0, 0], [8, 0, 0, -4, 0, -2, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0], [-3, 0, 0, -2, 3, -3, 0, -3, 0, -3, 0, -2, 3, 0, 0, 0], [3, 0, 0, 0, 5, 0, 0, -3, 0, 0, 0, -4, -2, 0, 0, 0], [19, 0, 0, 0, 0, 0, 0, -19, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -3, 0, -4], [7, 0, 0, 0, -4, 0, 0, -7, 0, 0, 0, -4, -2, 0, 0, 0], [0, 0, -3, 0, 0, 0, -4, 0, -3, 0, 0, 0, 0, 3, -4, -3], [1, 0, 0, 0, 3, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 5, 0, 0, 0, 2, 0, 5, 0, 0, 0, 0, -5, 2, 3], [0, 0, 6, 0, 0, 0, -1, 0, -3, 0, 0, 0, 0, -6, -1, -1], [-13, 0, 0, 0, -3, 0, 0, 13, 0, 0, 0, -2, -4, 0, 0, 0], [-5, 0, 0, -8, 5, -5, 0, -11, 0, -1, 0, -8, 1, 0, 0, 0], [0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 4, -5, -4], [0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 3, -3, -3], [5, 0, 0, -2, 0, 7, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [13, 0, 0, 0, -5, 0, 0, -13, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, -3, 0, 0, 0, -2, 0, -5, 0, 0, 0, 0, 3, -2, 5], [0, -1, 1, 0, 0, 0, -7, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, -9, 0, 0, 0, 0, 0, 0, -9, 0, 1, 0, 0, 7, 9, -1], [5, 0, 0, 0, -1, 0, 0, -5, 0, 0, 0, 2, -5, 0, 0, 0], [8, 0, 0, 4, -8, 8, 0, -11, 0, 3, 0, 4, -3, 0, 0, 0], [0, 0, 1, 0, 0, 0, -6, 0, -5, 0, 0, 0, 0, -1, -6, -3], [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 7, 3, -3], [-9, 0, 0, 0, -8, 0, 0, 9, 0, 0, 0, 2, -1, 0, 0, 0], [0, -4, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, -6, -1, -2], [0, 9, 0, 0, 0, 0, 0, 0, 9, 0, -1, 0, 0, -1, -3, 1], [0, 14, -4, 0, 0, 0, 9, 0, 0, 0, 2, 0, 0, 0, 0, 0], [2, 0, 0, 12, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, -4, 0, 0, 0, 0, 0, 8, 2], [0, 3, -3, 0, 0, 0, 5, 0, 0, 0, -3, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, -3, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [-1, 0, 0, -2, 1, -1, 0, -13, 0, 1, 0, -2, -1, 0, 0, 0], [3, 0, 0, 4, -3, 3, 0, 5, 0, 5, 0, 4, -5, 0, 0, 0], [0, 0, -8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 8, 4, -6], [0, -9, 0, 0, 0, 0, 0, 0, -9, 0, -1, 0, 0, -3, 3, 1], [0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, -1], [0, 0, 3, 0, 0, 0, -2, 0, 7, 0, 0, 0, 0, -3, -2, 1], [7, 0, 0, 10, -7, 7, 0, -1, 0, 1, 0, 10, -1, 0, 0, 0], [0, -3, -4, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0], [0, -1, -6, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [-6, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, -17, 0, 0, 0, 0, 0, 0, -17, 0, -3, 0, 0, 3, 7, 3], [-16, 0, 0, -6, 0, -8, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0], [0, -5, 0, 0, 0, 0, 0, 0, -5, 0, -1, 0, 0, 7, 9, 1], [3, 0, 0, 0, 1, 0, 0, -3, 0, 0, 0, -10, -1, 0, 0, 0], [-3, 0, 0, 2, 3, -3, 0, 5, 0, 6, 0, 2, -6, 0, 0, 0], [0, 14, 0, 0, 0, 0, 0, 0, 14, 0, 4, 0, 0, -2, -3, -4], [-12, 0, 0, -4, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, -4, 8, 0, 0, 0, -3, 0, 0, 0, 6, 0, 0, 0, 0, 0], [-17, 0, 0, 0, -5, 0, 0, 17, 0, 0, 0, 10, 3, 0, 0, 0], [14, 0, 0, 6, -14, 14, 0, -19, 0, 0, 0, 6, 0, 0, 0, 0], [1, 0, 0, 0, -7, 0, 0, -1, 0, 0, 0, 8, -6, 0, 0, 0], [0, -11, 5, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, -7, 0, 0, 0, -3, 0, -2, 0, 0, 0, 0, 7, -3, 6], [0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 1, 0], [-3, 0, 0, 0, 7, 0, 0, 3, 0, 0, 0, -8, -1, 0, 0, 0], [1, 0, 0, 2, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [7, 0, 0, 2, -7, 7, 0, 5, 0, 5, 0, 2, -5, 0, 0, 0], [0, 2, 10, 0, 0, 0, -1, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 8, 0, -13, 0, 0, 0, 0, 1, 8, 5], [0, 5, -1, 0, 0, 0, -9, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, -6, 0, 3, 0, 0, 0, 0, 1, -6, 5], [7, 0, 0, 0, 1, 0, 0, -7, 0, 0, 0, 8, 3, 0, 0, 0], [0, 0, 5, 0, 0, 0, 7, 0, 6, 0, 0, 0, 0, -5, 7, -4], [-13, 0, 0, 0, -5, 0, 0, 13, 0, 0, 0, 8, 1, 0, 0, 0], [-1, 0, 0, -10, 1, -1, 0, 1, 0, -1, 0, -10, 1, 0, 0, 0], [28, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -13, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0], [-20, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-8, 0, 0, 12, 8, -8, 0, 1, 0, 0, 0, 12, 0, 0, 0, 0], [0, -7, 3, 0, 0, 0, -9, 0, 0, 0, -3, 0, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0, 0, 0, -3, 0, 3, 0, 0, 8, -14, -3], [10, 0, 0, 10, 0, 2, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0], [0, -14, 0, 0, 0, 0, 0, 0, -14, 0, 4, 0, 0, 4, 9, -4], [1, 0, 0, -6, -1, 1, 0, -19, 0, -2, 0, -6, 2, 0, 0, 0], [20, 0, 0, 6, 0, 16, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 3, 0, 0, 5, 3, -3], [0, -3, -3, 0, 0, 0, -3, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, -6, 0, 0, 0, -5, 0, -5, 0, 0, 0, 0, 6, -5, -3], [3, 0, 0, 12, -3, 3, 0, 11, 0, -2, 0, 12, 2, 0, 0, 0], [31, 0, 0, 6, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -12, -5, 4], [0, 0, -8, 0, 0, 0, -2, 0, -16, 0, 0, 0, 0, 8, -2, 2], [0, -1, 1, 0, 0, 0, -5, 0, 0, 0, 7, 0, 0, 0, 0, 0], [0, 0, -9, 0, 0, 0, -14, 0, 0, 0, -2, 0, 0, 0, 0, 0], [12, 0, 0, -4, 0, -6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [-25, 0, 0, 0, -2, 0, 0, 25, 0, 0, 0, 8, 1, 0, 0, 0], [0, 0, 5, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -5, 0, -3], [0, 4, 0, 0, 0, 0, 0, 0, 4, 0, -6, 0, 0, -10, -11, 6], [-15, 0, 0, 0, 15, 0, 0, 15, 0, 0, 0, -12, 8, 0, 0, 0], [0, 0, -5, 0, 0, 0, 7, 0, -12, 0, 0, 0, 0, 5, 7, -2], [-1, 0, 0, 0, -4, 0, 0, 1, 0, 0, 0, -2, -10, 0, 0, 0], [0, 0, 4, 0, 0, 0, 7, 0, 1, 0, 0, 0, 0, -4, 7, -5], [0, 0, 8, 0, 0, 0, -12, 0, 6, 0, 0, 0, 0, -8, -12, -2], [3, 0, 0, 0, -12, 0, 0, -3, 0, 0, 0, 8, -6, 0, 0, 0], [1, 0, 0, -2, -1, 1, 0, -7, 0, 9, 0, -2, -9, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 9, 0, -3, 0, 0, -3, 1, 3], [0, -9, 0, 0, 0, 0, 0, 0, -9, 0, -7, 0, 0, 3, 7, 7], [8, 0, 0, 2, 0, 16, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [6, 0, 0, -2, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [-5, 0, 0, -6, 5, -5, 0, 31, 0, -6, 0, -6, 6, 0, 0, 0], [-3, 0, 0, 0, -1, 0, 0, 3, 0, 0, 0, -2, -1, 0, 0, 0], [-10, 0, 0, 2, 0, -4, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0], [-5, 0, 0, -2, 5, -5, 0, 11, 0, 8, 0, -2, -8, 0, 0, 0], [0, -17, 0, 0, 0, 0, 0, 0, -17, 0, 3, 0, 0, -1, 1, -3], [-3, 0, 0, -14, 0, -7, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 7, 3, 0, 0, 0, 1, 0, 0, 0, -3, 0, 0, 0, 0, 0], [0, 5, 0, 0, 0, 0, 0, 0, 5, 0, 3, 0, 0, -12, 12, -3], [-3, 0, 0, -8, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 13, 0, 0, 0, -7, 0, 8, 0, 0, 0, 0, -13, -7, 0], [-9, 0, 0, 6, 9, -9, 0, 25, 0, 1, 0, 6, -1, 0, 0, 0], [0, 16, 4, 0, 0, 0, -7, 0, 0, 0, -4, 0, 0, 0, 0, 0], [0, -6, -3, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0], [5, 0, 0, 0, 3, 0, 0, -5, 0, 0, 0, 4, -2, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0]]
