
# q-expansion of newform 525.2.g.f, downloaded from the LMFDB on 23 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 = 525
weight = 2
poly_data = [25, 0, 704, 0, 4790, 0, 8496, 0, 6263, 0, 2208, 0, 386, 0, 32, 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, -5898695, 0, -3899254, 0, -2968343, 0, -4960972, 0, -2769307, 0, -615152, 0, -58390, 0, -1982], 730740], [[1240590, 0, 7508717, 0, 12974084, 0, 10451886, 0, 4045936, 0, 756456, 0, 65570, 0, 2111, 0], 365370], [[-2302010, 15258957, 17337039, 68352861, 16015631, 93937026, -1676950, 60246093, -3908927, 19628064, -1050680, 3275277, -106269, 263853, -3709, 8094], 1461480], [[4385015, 3579531, 44382761, -29287814, 81045624, -65827487, 57068335, -51200493, 19023522, -18434731, 3176075, -3258831, 254549, -271988, 7764, -8537], 1461480], [[-229922, 0, -2662080, 0, -4632502, 0, -3188560, 0, -1064513, 0, -179552, 0, -14550, 0, -448, 0], 36537], [[-1164895, -3579531, -54181403, 29287814, -140933662, 65827487, -124193435, 51200493, -48131636, 18434731, -8868475, 3258831, -758087, 271988, -24142, 8537], 1461480], [[-3943235, 16546109, -58669455, 140138538, -106993792, 259803589, -77972107, 196162879, -27115394, 70112261, -4688987, 12354197, -385689, 1029006, -11986, 32251], 1461480], [[-3396160, -5086319, -33333957, -22784287, -65990651, -31312342, -52540388, -20082031, -19379905, -6542688, -3476218, -1091759, -292549, -87951, -9227, -2698], 487160], [[0, 7214029, 0, 84713176, 0, 162815538, 0, 123681686, 0, 44273496, 0, 7806514, 0, 650497, 0, 20394], 730740], [[0, -4103552, 0, 43497930, 0, 127014752, 0, 113317871, 0, 43834216, 0, 8051137, 0, 686544, 0, 21827], 730740], [[2564660, 0, 40009446, 0, 90432082, 0, 75452983, 0, 28523978, 0, 5194823, 0, 441570, 0, 14023, 0], 365370], [[-7159970, 41055973, -93664843, 362884003, -192035267, 667354674, -147699220, 492261521, -52601101, 172446432, -9198350, 29962597, -760867, 2472421, -23717, 77004], 1461480], [[0, -15379688, 0, -162283005, 0, -312656992, 0, -236911486, 0, -84501056, 0, -14856572, 0, -1235424, 0, -38677], 730740], [[0, 27821, 0, 330615, 0, 664072, 0, 518065, 0, 188138, 0, 33437, 0, 2799, 0, 88], 1140], [[7159970, 33896911, 93664843, 421459631, 192035267, 799009648, 147699220, 594662507, 52601101, 209315894, 9198350, 36480259, 760867, 3016397, 23717, 94078], 1461480]]

hecke_ring_character_values = [[176, [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], [127, [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], [451, [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]]
aps_data = [[0, 0, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, -1, 0, 0, 1, 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, -1, 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, -1], [0, 0, 0, 1, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 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, 0], [0, 0, 0, -1, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 1, 0], [0, -2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, -4, -1, 0, 0, 0, 0, 0, 1, 0], [0, -2, 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, -1], [0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, -1, 0], [0, -4, 0, 0, 0, 0, 0, 0, 0, 7, 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, 1, 0, -3, 0, 0, 0, 0, 0, -2, 0, 0, 2], [3, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, -1, 0, -3, 0, 0, 0, 0, 0, -1, 0, 0, 1], [0, 0, 0, -4, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1], [0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [-5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 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, -3, 0, 0, 5, 0, 0], [3, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -3, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 5, 0], [-4, 0, 0, 0, 0, -6, 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, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1], [0, 0, 0, -2, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, -2, 0], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0], [0, 0, 0, 1, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, -6, 0], [0, 0, 0, 1, 0, 0, 0, -8, -3, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, -3, 0, 0, -1], [0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, -4, 3, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 2, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, -7, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, -5, 0, 0], [0, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 2, 0, 0, -2], [0, 0, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, -4, 0, 0, -2], [0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 3], [0, 0, 0, 1, 0, 0, 0, 8, 5, 0, 0, 0, 0, 0, -2, 0], [0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, -3, 0, 0, 3], [0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, -9, 0, 3, 0, 0, 0, 0, 0, -3, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 5, 0, 0], [0, 0, 0, 0, 11, 0, 5, 0, 0, 0, 0, 0, -3, 0, 0, 3], [0, 10, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 9, 0, -3, 0, 0, 0, 0, 0, 4, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, -7, 0, 0], [0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 7, 0, 0], [0, 0, 0, 5, 0, 0, 0, 10, -5, 0, 0, 0, 0, 0, -4, 0], [0, 0, 0, 5, 0, 0, 0, -4, 3, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 16, 0, 0], [0, 0, 0, 0, -8, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0], [0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, -1, 0, 0], [0, -4, 0, 0, 0, 0, 0, 0, 0, -23, 0, 0, 0, 0, 0, 0], [0, 0, 0, -4, 0, 0, 0, 12, 2, 0, 0, 0, 0, 0, -3, 0], [0, -6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -6], [0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 1, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, -33, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, -5, 0, 0], [-14, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 12, 6, 0, 0, 0, 0, 0, -3, 0], [0, 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -6, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -8, 0, 0, 0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 0], [0, 0, -17, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0], [0, 0, 0, 0, -6, 0, 2, 0, 0, 0, 0, 0, -6, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 11, 0, 0], [-19, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -6, 0, -8, 0, 0, 0, 0, 0, -1, 0, 0, 1], [0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 0, 0, 6, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, -1, 0, 0], [0, 0, 0, -4, 0, 0, 0, -8, 4, 0, 0, 0, 0, 0, -6, 0], [0, 0, 0, 0, 1, 0, 5, 0, 0, 0, 0, 0, 2, 0, 0, -2], [0, -2, 0, 0, 0, 0, 0, 0, 0, -31, 0, 0, 0, 0, 0, 0], [0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 9, 0], [23, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 13, 0, 0], [0, 0, 0, 0, 16, 0, 12, 0, 0, 0, 0, 0, -2, 0, 0, 2], [0, 0, 0, 0, -12, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 4], [0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0], [0, 0, 0, -1, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 16, 0], [0, 12, 0, 0, 0, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4], [0, 0, -13, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -8, 0, 0], [-2, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 4, 7, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 16, 0, 10, 0, 0, 0, 0, 0, -3, 0, 0, 3], [0, 0, 0, 0, -10, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, -4], [-15, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0], [-22, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0], [0, 0, 0, -4, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 3, 0, 0, 0, 6, -3, 0, 0, 0, 0, 0, -7, 0], [0, 0, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 3], [0, 0, 0, 0, 5, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 2], [0, 0, 0, 0, 6, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, -7, 0, 0], [0, 0, 0, 2, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -8, 0, 0], [0, -6, 0, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0, 0, 0, 0], [0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, -8, 0], [0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4], [0, 0, 0, 0, -9, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 9], [0, 0, 0, 2, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, -16, 0], [0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, -12, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 20, 11, 0, 0, 0, 0, 0, -5, 0], [0, 2, 0, 0, 0, 0, 0, 0, 0, -21, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 15, 0, -5, 0, 0, 0, 0, 0, 9, 0, 0, -1], [0, -12, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, -17, 0, 0], [-1, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, -11, 0, -13, 0, 0, 0, 0, 0, -1, 0, 0, 1], [0, 0, 0, 1, 0, 0, 0, -12, -5, 0, 0, 0, 0, 0, 3, 0], [0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, -6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 16, 9, 0, 0, 0, 0, 0, -4, 0], [0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 3], [-17, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 14, 0, 12, 0, 0, 0, 0, 0, -1, 0, 0, 1]]
