
# q-expansion of newform 336.2.bc.f, downloaded from the LMFDB on 25 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 = 336
weight = 2
poly_data = [6561, -13122, 13851, -10206, 5265, -1296, -846, 1332, -962, 444, -94, -48, 65, -42, 19, -6, 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, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 1], [[-52488, 28431, 21627, -14985, 2160, 378, -1272, 854, -252, -266, 384, -110, 48, 71, -15, -1], 34992], [[19683, 34992, -38880, 41067, -28890, 846, 7392, -8138, 3546, -1288, -258, 662, -363, 142, -30, -11], 69984], [[131220, -147987, 126846, -70227, 23193, 5787, -14727, 11651, -5787, 1483, 429, -737, 489, -238, 75, -22], 34992], [[69984, -131949, 133893, -88047, 39366, -2826, -13818, 13268, -7812, 2656, -66, -770, 606, -295, 111, -25], 23328], [[85293, -131463, 110970, -73926, 29421, -513, -11899, 11435, -6443, 2131, 145, -653, 500, -274, 95, -19], 11664], [[599238, -888651, 857547, -587979, 239166, 3510, -97758, 92296, -53232, 16736, 1302, -5794, 4116, -2069, 669, -125], 69984], [[-75087, 105948, -95580, 60237, -24354, -42, 10040, -9482, 5482, -1912, -74, 542, -433, 226, -82, 19], 7776], [[-708588, 958635, -849285, 515565, -197316, 756, 85788, -81374, 46218, -16018, -84, 4292, -3624, 1975, -753, 193], 69984], [[-347733, 502281, -474093, 312012, -142074, 9288, 45918, -48824, 29190, -10624, 510, 2648, -2301, 1207, -429, 100], 34992], [[255879, -374220, 331290, -197181, 85716, -1116, -33490, 32084, -18728, 6358, 100, -1772, 1463, -784, 302, -61], 23328], [[321489, -438615, 402489, -271836, 111618, -3870, -43500, 42964, -24816, 8450, 234, -2470, 2043, -1037, 351, -74], 23328], [[165483, -231579, 214650, -134892, 53433, 1875, -22783, 20887, -11879, 3863, 205, -1225, 962, -482, 179, -41], 11664], [[883548, -1358127, 1259955, -799713, 321678, -5346, -124578, 123088, -70872, 24788, 6, -7066, 5466, -2921, 1101, -275], 69984], [[4617, -7452, 7371, -5247, 2499, -349, -661, 779, -497, 195, -17, -41, 38, -21, 8, -2], 432]]

hecke_ring_character_values = [[127, [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], [85, [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], [113, [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], [241, [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]]
aps_data = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 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, -1, 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, 1, 0, 0, 1, 0, 1, -1], [0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 1, 0, 0], [0, 2, 0, -1, 0, -1, 0, 2, 1, -2, 0, -1, -1, 0, -2, 1], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0], [-1, -1, 1, -1, 1, 0, -1, 1, 0, -1, 0, 1, 0, -1, 0, 0], [0, -1, 0, 2, 0, -2, 0, -1, 1, 4, 0, 1, 1, 0, 2, -1], [4, 0, 0, -1, -2, -1, -1, 0, 1, -1, 1, 0, 0, 1, 0, 0], [-1, 0, 2, -2, 1, -1, -2, 0, 2, -1, 1, 0, 0, -1, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 2, 1, 0, 2, 1, 0, -1, 2, -2, 0, 0, -1, 0, 0], [-1, -1, 1, -1, -1, -2, 1, 1, 0, -1, -2, -1, -2, 1, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, -2, 0, -1, 2], [2, 0, -2, 1, -1, 3, 1, -4, -3, 3, 1, 1, 2, 1, 3, 0], [1, 0, 1, 0, 1, 0, 1, 0, 0, 0, -2, 0, 0, 1, 0, 0], [0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0], [1, 3, -1, 0, 0, -2, 0, 1, 1, 0, 1, 0, -1, 0, 0, 3], [2, 0, 1, 1, -1, 1, 1, 0, -1, 1, -2, 0, 0, -2, 0, 0], [-4, 0, 1, -2, 4, -1, -1, 0, 2, -1, 0, 0, 0, -1, 0, 0], [1, 2, -1, 2, -2, 0, 2, 0, 2, 0, -1, -3, 0, 2, 0, -2], [1, 0, -1, 2, 1, 4, -1, -2, 0, 2, 2, 2, 4, -1, 2, 0], [-2, 0, 1, 1, 4, 0, -3, 0, -1, 0, 1, 0, 0, -3, 0, 0], [-2, -4, 2, -2, 1, 2, -1, 0, -2, -2, -1, 4, 0, -1, 4, -2], [0, 0, -1, 0, 0, 2, -1, 0, 0, 2, 1, 0, 0, 0, 0, 0], [-1, 0, 1, 0, 1, -1, -1, 2, 2, -1, 0, 4, 0, -1, 1, 0], [0, 0, 1, 1, -7, -1, 3, 0, -1, -1, -2, 0, 0, 2, 0, 0], [-1, -1, 1, 0, 0, -2, 0, 1, 1, 0, -1, 0, -1, 0, 0, -1], [6, 0, -3, 2, 0, 4, 0, 0, -2, 4, 3, 0, 0, 0, 0, 0], [0, 1, 0, -1, 0, -4, 0, 1, 0, 1, 0, -1, -2, 0, -1, 2], [0, 0, 0, -2, 1, -2, -1, 0, -2, 4, 1, 0, 2, -1, 2, 0], [-2, 0, -2, 3, 4, 0, 3, 0, -3, 0, -2, 0, 0, 3, 0, 0], [3, 6, -3, -4, -3, 2, 3, 0, -4, -2, 0, -4, 0, 3, -2, 0], [0, 0, 1, 0, -8, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [10, 0, -2, -4, -5, -4, -1, 0, 4, -4, 3, 0, 0, 3, 0, 0], [4, 0, -2, -2, -4, -1, 2, 0, 2, -1, 0, 0, 0, 2, 0, 0], [-1, -3, 1, 2, 2, 0, -2, -1, 1, 0, 1, 4, -1, -2, 0, 3], [2, 3, -2, 1, 2, 1, -2, -1, 0, 2, 4, 1, 2, -2, 0, 6], [0, 0, 0, 0, 1, 0, -1, 0, 0, -1, 1, 1, -1, -1, -2, 3], [-6, 0, 0, 3, 12, 0, 1, 0, -3, 0, 0, 0, 0, 1, 0, 0], [-1, -1, 1, 3, 1, -2, -1, 1, 4, 1, 0, -3, 0, -1, -2, 0], [0, 0, -4, -2, -5, 2, -4, 0, 2, 2, 0, 0, 0, 0, 0, 0], [-1, 1, 1, 0, 0, -6, 0, 3, 3, 0, -1, -2, -3, 0, -4, 1], [8, 0, 2, 1, -4, 1, 2, 0, -1, 1, -4, 0, 0, -4, 0, 0], [0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 4, 0, 0], [0, 0, -1, -1, 0, 0, -1, 0, 1, 0, -1, 0, 0, -1, 0, 0], [0, 6, 0, -6, 0, 0, 0, 6, 0, -9, 0, -2, -3, 0, -5, 3], [1, 0, -2, 0, 1, 1, -2, 0, 0, 1, -1, 0, 0, 3, 0, 0], [2, 5, -2, -3, -2, 1, 2, 1, -2, -2, 0, -3, 0, 2, -2, 0], [2, -2, -2, 4, 0, 4, 0, -6, -2, 8, 2, 6, 6, 0, 12, -2], [14, 0, -1, 3, -7, 3, 0, 0, -3, 3, 1, 0, 0, 1, 0, 0], [1, 0, -1, -4, -2, 0, 2, -2, -6, 0, -1, -3, -2, 2, 0, 0], [0, 3, 0, -3, 0, 1, 0, 3, 0, -10, 0, -3, -6, 0, -6, 6], [0, 0, 0, 3, 0, 3, 0, 0, 3, -3, 0, -2, 0, 0, 2, 0], [2, 2, -2, -1, -1, 3, 1, -2, -3, 0, 1, -4, 1, 1, -3, 1], [-6, 0, 2, 0, -6, -4, 2, 0, 0, -4, -5, 0, 0, 3, 0, 0], [0, 0, -3, 3, -1, -3, -5, 0, -3, -3, 2, 0, 0, -2, 0, 0], [1, 3, -1, -4, 0, 6, 0, 1, -3, -8, 1, -2, -1, 0, -4, 3], [0, 0, -3, 2, 0, 2, 2, 0, -2, 2, 1, 0, 0, 1, 0, 0], [2, 3, -2, -2, -4, 0, 4, -1, -3, 0, -2, -1, -1, 4, 0, -3], [-10, 0, 2, -3, 20, 0, -3, 0, 3, 0, 2, 0, 0, -3, 0, 0], [4, 4, -4, -3, -2, 7, 2, -4, -7, -1, 2, -4, 2, 2, -2, 2], [1, 0, 4, 0, 1, -4, 4, 0, 0, -4, -4, 0, 0, 0, 0, 0], [-1, -5, 1, 5, 1, -1, -1, -3, 2, 4, 0, -1, 0, -1, 1, 0], [6, 0, 3, 4, -6, 2, -3, 0, -4, 2, 1, 0, 0, -2, 0, 0], [-2, 0, -7, -2, 0, -4, -2, 0, 2, -4, 7, 0, 0, 2, 0, 0], [0, 0, 0, -4, -3, -4, 3, 0, -4, -3, -3, -1, -7, 3, -6, 1], [2, 0, 0, -4, -4, 0, -2, 0, 4, 0, 0, 0, 0, -2, 0, 0], [4, 2, -4, 7, -2, -1, 2, -6, 1, 10, 2, 9, 3, 2, 12, 1], [0, -4, 0, 2, 0, 1, 0, -4, -2, 3, 0, -4, 0, 0, 0, 0], [16, 0, -2, 3, -8, 3, 1, 0, -3, 3, 1, 0, 0, 1, 0, 0], [-5, 0, 0, 6, 5, 3, 0, 0, -6, 3, 1, 0, 0, 1, 0, 0], [8, 0, 4, -3, 0, -6, 3, 0, 3, -6, -4, 0, 0, -3, 0, 0], [1, 3, -1, -1, 1, 6, -1, 1, 0, -9, 2, -1, -2, -1, -4, 6], [0, 0, 0, 1, 0, 1, 0, 0, 1, -4, 0, -5, -3, 0, 2, 3], [1, 0, 2, 0, 1, 5, 2, 0, 0, 5, 3, 0, 0, -5, 0, 0], [-2, -1, 2, -1, 2, -1, -2, 3, 2, -2, 0, -5, 0, -2, -4, 0], [6, 0, -4, 10, -3, 10, 2, 0, -10, 10, 2, 0, 0, 2, 0, 0], [-2, 0, 2, 0, 4, 0, -4, 4, 4, 0, 2, 2, 4, -4, 0, 0], [2, 0, -2, 1, 0, 2, -1, 0, -1, 2, 2, 0, 0, 1, 0, 0], [0, 0, 0, 2, 3, 2, -3, 0, 2, 1, 3, 5, 3, -3, -2, 3], [-4, 0, 2, -3, 8, 0, 1, 0, 3, 0, 2, 0, 0, 1, 0, 0], [-4, 0, 4, 0, -4, 4, 4, 0, 0, 4, 1, 0, 0, -5, 0, 0], [1, 2, -1, 6, -1, -3, 1, 0, 6, 3, 0, -6, 0, 1, -3, 0], [1, -1, -1, -4, 0, 14, 0, -3, -7, -8, 1, 2, 3, 0, 4, -1], [5, 0, 4, 0, -5, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0], [-2, -2, 2, -2, 4, 0, -4, 2, 0, 0, 2, 0, 2, -4, 0, 2], [-2, 0, -2, 1, 0, 2, -3, 0, -1, 2, 2, 0, 0, 3, 0, 0], [-1, -3, 1, 1, -1, -4, 1, -1, 0, 7, -2, 1, 2, 1, 0, -6], [-2, -6, 2, 12, 1, -10, -1, -2, 10, 13, -1, 9, 1, -1, 10, -3], [0, 0, 4, 3, -4, -3, -1, 0, -3, -3, 5, 0, 0, -5, 0, 0], [2, 9, -2, -4, 0, -2, 0, 5, 1, -8, 2, -3, -5, 0, -6, 9], [10, 0, 1, -4, -10, -2, -1, 0, 4, -2, 1, 0, 0, 0, 0, 0], [2, 4, -2, -4, -4, 0, 4, 0, -4, 0, -2, 2, 0, 4, 0, -4], [-2, -4, 2, 0, -2, -4, 2, 0, 0, 4, -4, 0, 0, 2, 5, -8], [2, 0, -2, 0, -1, 4, 1, -4, -4, 2, 1, -6, 2, 1, -4, 0], [0, 0, 7, 0, 0, -2, 7, 0, 0, -2, -3, 0, 0, -4, 0, 0], [-3, 0, 4, 6, 3, 3, -4, 0, -6, 3, 3, 0, 0, -1, 0, 0], [-14, 0, -4, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, -2, 0, 0], [0, 0, 0, 1, -5, 1, 5, 0, 1, -2, -5, -2, -1, 5, 1, -9], [2, -4, -2, 3, -1, 5, 1, -8, -5, 7, 1, -3, 4, 1, 1, -2], [-3, 0, 3, 2, 3, -4, -3, 6, 8, -2, 0, 2, 0, -3, -2, 0], [0, 0, -1, 2, 8, -2, 4, 0, -2, -2, -5, 0, 0, 5, 0, 0], [-6, 0, 0, 8, 3, 8, 2, 0, -8, 8, -2, 0, 0, -2, 0, 0], [-2, -7, 2, -2, 4, 0, -4, -3, -5, 0, 2, 3, -3, -4, 0, 7], [1, 2, -1, 0, 1, -4, -1, 0, 0, 4, 2, 0, 0, -1, -2, 4], [0, 0, 0, -3, -4, -3, 4, 0, -3, 5, -4, -2, 2, 4, 4, -10], [0, 0, 5, -6, 0, 0, 0, 0, 6, 0, 5, 0, 0, 0, 0, 0], [2, 0, -5, 0, 2, -9, -5, 0, 0, -9, 2, 0, 0, 3, 0, 0], [0, 0, 4, 2, -13, -2, -3, 0, -2, -2, 7, 0, 0, -7, 0, 0], [-2, -8, 2, 2, 0, 4, 0, -4, -2, 4, -2, 8, 4, 0, 16, -8], [-4, 0, 11, -2, 2, -2, -4, 0, 2, -2, -7, 0, 0, -7, 0, 0], [16, 0, 1, 1, 0, 2, 3, 0, -1, 2, -1, 0, 0, -3, 0, 0], [0, 0, 0, -3, -6, -3, 6, 0, -3, -4, -6, -11, -7, 6, 4, -5], [2, 0, -6, 1, -4, 0, 5, 0, -1, 0, -6, 0, 0, 5, 0, 0], [-8, -8, 8, 3, 4, -11, -4, 8, 11, -1, -4, 2, -4, -4, -2, -4], [1, 1, -1, 7, -1, -3, 1, -1, 6, 4, 0, 9, 0, 1, 5, 0], [3, 5, -3, -4, 0, 10, 0, -1, -5, -8, 3, 0, 1, 0, 0, 5], [-10, 0, 5, -1, 5, -1, -1, 0, 1, -1, -4, 0, 0, -4, 0, 0], [-18, 0, 7, -2, 0, -4, -2, 0, 2, -4, -7, 0, 0, 2, 0, 0], [-1, 1, 1, -3, -1, -3, 1, 3, 0, -6, -2, -3, -6, 1, -13, 2], [0, 0, 0, 7, 5, 7, -5, 0, 7, 7, 5, 3, 14, -5, 11, -4], [10, 0, 1, 0, 10, 6, 1, 0, 0, 6, -5, 0, 0, 4, 0, 0], [5, 6, -5, 2, 0, 4, 0, -4, -2, 4, 5, 3, 4, 0, 6, 6], [1, 0, -5, 0, -1, 0, 5, 0, 0, 0, -8, 0, 0, -3, 0, 0], [2, 8, -2, -4, 2, 5, -2, 4, 0, -17, 4, -4, -8, -2, -8, 16], [10, 0, -1, 8, -20, 0, 2, 0, -8, 0, -1, 0, 0, 2, 0, 0], [7, 0, -2, 0, 7, -3, -2, 0, 0, -3, 1, 0, 0, 1, 0, 0], [0, 0, -7, 0, -4, 0, -6, 0, 0, 0, -1, 0, 0, 1, 0, 0], [-6, -12, 6, -2, 0, 4, 0, 0, -2, -4, -6, 2, 0, 0, 4, -12], [-14, 0, -5, 6, 14, 3, 5, 0, -6, 3, 2, 0, 0, 7, 0, 0], [20, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0], [-4, -5, 4, -3, -4, -11, 4, 3, 0, 2, -8, -3, -6, 4, 2, -10], [8, 0, -3, 0, -16, 0, -2, 0, 0, 0, -3, 0, 0, -2, 0, 0], [6, 4, -6, -6, -3, 14, 3, -8, -14, -2, 3, 0, 4, 3, 4, 2], [-32, 0, 0, -1, 16, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0], [3, 0, -3, -8, -6, 0, 6, -6, -14, 0, -3, -3, -6, 6, 0, 0], [0, 0, 0, -7, -2, -7, 2, 0, -7, 0, -2, -3, -7, 2, -4, 3], [-16, 0, 2, 2, 32, 0, -4, 0, -2, 0, 2, 0, 0, -4, 0, 0], [0, 10, 0, 2, 0, -6, 0, 10, 12, -4, 0, -8, 0, 0, -9, 0], [0, 0, -2, 3, 2, -3, -6, 0, -3, -3, 4, 0, 0, -4, 0, 0], [3, 4, -3, 4, 0, -4, 0, -2, 2, 8, 3, 7, 2, 0, 14, 4], [-6, 0, -7, 5, 3, 5, 7, 0, -5, 5, 0, 0, 0, 0, 0, 0], [0, 2, 0, -4, 0, 0, 0, 2, -2, 0, 0, -6, 2, 0, 0, -2], [8, 0, -8, 5, -16, 0, 5, 0, -5, 0, -8, 0, 0, 5, 0, 0], [2, 0, -2, 0, -1, 4, 1, -4, -4, 2, 1, -6, 2, 1, -4, 0], [2, 0, 2, 0, 2, -5, 2, 0, 0, -5, 0, 0, 0, -2, 0, 0], [4, 2, -4, 4, -4, 1, 4, -6, -2, 5, 0, -6, 0, 4, 0, 0], [11, 0, 5, -8, -11, -4, -5, 0, 8, -4, -2, 0, 0, -7, 0, 0], [-5, -3, 5, 8, 10, 0, -10, 7, 15, 0, 5, 4, 7, -10, 0, 3], [18, 0, 2, -1, 0, -2, -1, 0, 1, -2, -2, 0, 0, 1, 0, 0], [2, -2, -2, 6, 2, -3, -2, -6, 0, 21, 4, 6, 12, -2, 4, -4], [0, 0, 5, -6, 2, 6, 0, 0, 6, 6, 5, 0, 0, -5, 0, 0], [-3, -9, 3, 12, 0, -18, 0, -3, 9, 24, -3, 4, 3, 0, 8, -9], [-14, 0, 3, -20, 14, -10, -3, 0, 20, -10, 1, 0, 0, -2, 0, 0], [0, -5, 0, 5, 0, 7, 0, -5, 0, 8, 0, 5, 10, 0, 8, -10], [-14, 0, -3, 2, 28, 0, -2, 0, -2, 0, -3, 0, 0, -2, 0, 0], [-8, -20, 8, 8, 4, -4, -4, -4, 4, 10, -4, 7, 2, -4, 9, -10], [0, 2, 0, -16, 0, 7, 0, 2, -14, -9, 0, -10, 0, 0, -6, 0], [-1, -1, 1, 4, 0, -10, 0, 1, 5, 8, -1, 4, -1, 0, 8, -1], [-2, 0, 3, -2, 0, -4, 4, 0, 2, -4, -3, 0, 0, -4, 0, 0], [-1, 2, 1, -4, -1, 5, 1, 4, 0, -17, -2, -4, -8, 1, -17, 4], [0, 0, 0, 6, 7, 6, -7, 0, 6, 12, 7, 10, 18, -7, 8, -4], [-2, 6, 2, -12, 1, 2, -1, 10, -2, -17, -1, 7, -5, -1, 2, 3], [0, 0, 2, 1, -4, -1, 15, 0, -1, -1, -13, 0, 0, 13, 0, 0], [-2, 0, -11, -1, 1, -1, 9, 0, 1, -1, 2, 0, 0, 2, 0, 0]]
