# q-expansion of newform 1152.2.r.e, downloaded from the LMFDB on 24 June 2026.

# 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 = 1152
weight = 2
poly_data = [14641, -26620, 4356, -704, 27528, -26388, 9592, -5096, 5298, -4684, 3244, -1680, 672, -196, 48, -8, 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], [[47055550867160087747121, -26164925147230112974401, -15244081341253689782319, -32320287519502590624801, 68021624826747292165787, -26753192554640509996863, 9168711207946115797743, -10166015451929744711481, 9420796042103919530085, -7478169727907646469221, 4108396839281842001805, -1828610314207632467421, 544837829173739081899, -144569705798207667999, 24534878448868799823, -3542765331747320841], 5472292173965809716260], [[7194999162513882, -8844524677651729, -4340506041073433, -3563883675780494, 13084848716420246, -5114941575664177, 1464163253344806, -1789798761336670, 1723884698935294, -1440688308780473, 808374348634909, -370935070238998, 111213454254400, -30093617256945, 5133556971680, -763942000002], 641806760093410], [[115561991961034084519042, -159262717919621177467617, -68576283508535700585930, -31133680207361701945403, 189033940401929944667249, -77875485628221007325544, 21203509192382187565801, -23905505641415785758192, 22532157411020853560232, -19350708047654698205647, 11004017457270374454924, -5166333671914485938481, 1556069652609418637035, -427337198197798344030, 73197694197690115323, -11130591326480295602], 5472292173965809716260], [[-850183677927686712719993983, 701141455257919465355628128, 430615534826883954173995479, 471777263951946094048207636, -1119093269634643894285386605, 423809822818633076551156992, -139759507950121115100475571, 158268858938675445008328548, -151998545733187161806590267, 121945547863069262093532816, -68062559813357123822586529, 30353514257385579109440788, -9094965481906851252108405, 2411906047131857776991872, -411547132157716902983199, 59090349116137330522156], 13538450838391413238027240], [[244205147062169704580576, -198322981475705469243146, -124334589151843049893496, -138990067210407790110996, 318940110168828589603045, -120422247305938877855061, 40223719680787074416137, -45246797037611188730001, 43445610541927565715862, -34719538026397935066932, 19368469211958363402434, -8613613116335313829002, 2580790927259582584863, -683021780482278575707, 116549458437688470151, -16672966944053949767], 2113401629471029228540], [[-1218134286703300247908, 993170372900434791733, 631253437878301238363, 701282036612306368299, -1600993988048435862117, 598025696011359970233, -200606089666861008412, 225336475966123460783, -217807534629041998706, 173870633156026297485, -97127166903798011787, 43132172058070375979, -12929512163744633687, 3417621173901014885, -583435770921430222, 83254441669016195], 7602702041279092220], [[347716407785219, -279470932674714, -178433447199915, -200580115826046, 451741206168243, -169189320269868, 57025494185977, -63879192629834, 61570024345219, -49082753599874, 27396834130473, -12157033806082, 3643425366295, -962588123140, 164299773841, -23425567614], 1840970757560], [[-2804618928601018723544179005, 2205652057493108393394671820, 1425234353706996762218178131, 1614334301256205591246709736, -3579443390670116520853478381, 1335920796289486676056794864, -453336600590056638617506213, 506124012011507579128051960, -488361278600192943929997621, 388561943479684861962560932, -216891708747773392386771937, 96084888523170774893549536, -28798251025020622906512865, 7598913251343959577291528, -1297146149114261948860093, 184500663932331760880552], 13538450838391413238027240], [[288143156724360756560612761, -217234533363616704563723700, -149363263625953221265259807, -171834938966092833311884124, 363481082337770225657148841, -133661647799125012576257022, 46166377860366791323658853, -51546536574523245922707412, 50034018357660898455246681, -39589772201858054344502828, 22091831180446503803692749, -9736420296779932642088224, 2918114496837293949946861, -766973758490093350612846, 130931633988755719691549, -18487855448241233125056], 1230768258035583021638840], [[332425684600055608077812593, -272153061253147455603849924, -173559746437441196292042615, -186861605618419554101056228, 434507456516141767089620197, -162806490008746693519043574, 54409405004643403323311069, -60776192493876793464651892, 58717956653772548398968945, -46951947686744360689947596, 26257965362531128380791253, -11676823598838345238722552, 3501748320226825565836401, -926466603948397590149686, 158218142665077846574389, -22607565394009246203568], 1230768258035583021638840], [[-326982050033832535832193, 261949637284390436774470, 168506415806824291140539, 189167990616641667167636, -424100573179187504967503, 158042868009163662648568, -53423751710030692243359, 59775548196145346892556, -57781152001034842761061, 46028267326001952829694, -25706446743754811448853, 11397162373403652154408, -3416423381946416836951, 901970243394928871736, -153983647990249267475, 21923332400030472528], 994962213448329039320], [[3433104270672875771941485, -2751195011699007423881210, -1786148388856897169147186, -1954194453852119980635120, 4448319863711578845024964, -1663369103551475665280584, 554080785650065312509897, -623814721742830332479580, 603285277433045682728331, -482436349233063036903438, 269625546113908075943672, -119796654545764154840788, 35914935804516934374562, -9495678229796327931844, 1621113229861001672099, -231361103294550671568], 5472292173965809716260], [[-424540327260797519033611580, 331518658670705150452466956, 219158010310650244986744023, 246460329399386866639028505, -546264332880225524077384851, 203309836170061821460423420, -68584704405261687216408350, 76995263560819415181199109, -74481632398451839070248890, 59340368274961885089329128, -33135447495306309200039803, 14682983946142850485802809, -4400965599302855665675549, 1161375692152327919528044, -198245679428936313175460, 28199686213166864000725], 615384129017791510819420], [[-435495401105430723494619578, 352826744361123026182515382, 227586366727265053840138045, 246249662091608119549684981, -565626895613490553306070925, 211606701857774654022055658, -70554006262405001956795374, 79193376017605177311293789, -76593234648039892166573676, 61253533440913721976915850, -34249680495542493657721609, 15222529070855267135680541, -4564598219811960637243739, 1207134713919733135762354, -206125255146324892207360, 29428109469504434946093], 615384129017791510819420], [[9193926842502155259511973, -7220492554563439100592038, -4770848664680200670586425, -5322335690997950298535582, 11819301731700019349667291, -4394902346345379746040196, 1486046183236873553379989, -1664294153299638139915368, 1611133181984210169216633, -1283032882393077537543458, 716666882055458974079591, -317494819916684207566594, 95176671253912486935035, -25111417961019082918240, 4287089407564139953697, -609571461065940385948], 10944584347931619432520]]

hecke_ring_character_values = [[127, [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], [901, [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], [641, [-1, 0, 0, 0, 0, 0, 0, -1, 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, 1, 1, 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, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [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, -1, 0, 0, 0, -1, 0], [3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 4, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 1, 1, 0], [6, 0, -1, 0, 0, 0, 0, 6, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, -4, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0], [0, 0, 0, 0, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 5, 5, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 7, 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, 1], [0, 0, 0, 0, -4, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0], [3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1], [0, 0, 0, 0, -6, -2, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 1, 1, 0], [9, 0, 6, 0, 0, 0, 0, 9, 0, 0, 0, 6, 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, -1, -9, 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, -7, -7, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 1, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0], [0, 0, 0, 0, -6, -6, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -1, -1, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3], [-4, 0, 5, 0, 0, 0, 0, -4, 0, 0, 0, 5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 2, 0], [0, -1, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -1], [0, 0, 0, 0, -11, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 2, 0], [0, 0, -2, 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, -1, 0, 0, 5], [0, 0, 0, 0, 0, 0, 0, -11, 0, 0, 0, -6, 0, 0, 0, 0], [0, 0, 0, 0, -10, -18, 10, 0, 10, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -2, 0, 0, 0, 0, -3, 0, 0, 0, -2, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -5, -5, 0], [0, 4, 0, -2, 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, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 9, 0, 0, 0, 0], [0, 0, 0, 0, -15, -15, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, -2, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -5], [0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, -9, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -5, -5, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, -1, 0, 0, 0, 0], [0, 2, 0, -2, 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, -5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, -1, 0], [0, 0, 0, 0, 17, -2, -17, 0, -17, 0, 0, 0, 0, 0, 0, 0], [0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0], [-24, 0, -5, 0, 0, 0, 0, -24, 0, 0, 0, -5, 0, 0, 0, 0], [1, 0, 4, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 9, 9, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0], [0, 2, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-7, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 3], [0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [15, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 11, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -3, 0, 0], [0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 3], [0, 0, 0, 0, 18, 8, -18, 0, -18, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 11, 11, -15, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 19, 19, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 1, 0], [-6, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 21, 18, -21, 0, -21, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0], [0, 0, 0, 0, -1, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 0, 0, 3, 3, 0], [0, 0, 0, 0, -11, -11, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -39, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, -11, -11, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0], [13, 0, -15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, 0, 0, 0, -21, 0, 0, 0, 0, 0, 0, 0], [9, 0, 21, 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, 3], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 13, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 7, 7, 0], [-12, 0, -7, 0, 0, 0, 0, -12, 0, 0, 0, -7, 0, 0, 0, 0], [0, 0, 0, 0, 7, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -8, 0, 0, 0, 0], [0, 0, 0, 0, -7, -7, 20, 0, 0, 0, 0, 0, 0, 0, 0, 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, -7, 0, 0, 0, -8, 0], [0, 0, 0, 0, 19, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 4, 0], [0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, -2, 0, 0], [0, 0, 0, 0, 26, 18, -26, 0, -26, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -24, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, -2, 0, 0], [0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, -3, 0], [0, 0, 0, 0, -17, -22, 17, 0, 17, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, -1], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, 0, 0, 0, 0, 0], [6, 0, -3, 0, 0, 0, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0], [-13, 0, 2, 0, 0, 0, 0, -13, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 1, 1, 0], [0, 0, 0, 0, -9, -9, -15, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 1, 0], [-9, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, -16, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 3, 0, 0], [0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, -3], [0, 0, 0, 0, -14, 0, 14, 0, 14, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 0, 0, 3, 3, 0], [0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, -5, 0, 0], [0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, -15, 0, 0, 0, 0], [0, 0, 0, 0, 23, 23, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, -1, 0], [-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 28, 8, -28, 0, -28, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3], [0, 0, 0, 0, 4, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, -5], [0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0], [11, 0, -13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -2, 0], [0, 0, 0, 0, 19, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0], [-33, 0, -7, 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, -1, 0, 0, 7], [0, 0, 0, 0, 9, 2, -9, 0, -9, 0, 0, 0, 0, 0, 0, 0], [-21, 0, -8, 0, 0, 0, 0, -21, 0, 0, 0, -8, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, -1], [0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 6, 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, 0, 0, -5, 0, 0, 0, 7, 0], [0, 0, 0, 0, 28, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 3, 0], [0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -15, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, -7], [45, 0, 6, 0, 0, 0, 0, 45, 0, 0, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, -26, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 0, 0, -5, -5, 0], [0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0], [0, 0, 0, -13, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -13], [0, 0, 0, 0, -10, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0], [-3, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, -7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, -4, -4, 0], [0, 0, 0, 0, 42, 0, 0, 0, -39, 0, 0, 0, 0, 0, 0, 0], [-37, 0, -16, 0, 0, 0, 0, -37, 0, 0, 0, -16, 0, 0, 0, 0], [0, -10, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -35, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 22, 14, -22, 0, -22, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, -32, -12, 32, 0, 32, 0, 0, 0, 0, 0, 0, 0], [15, 0, -28, 0, 0, 0, 0, 15, 0, 0, 0, -28, 0, 0, 0, 0], [-16, 0, -7, 0, 0, 0, 0, -16, 0, 0, 0, -7, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 39, 0, 0, 0, 10, 0, 0, 0, 0], [0, 4, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, -4, 0], [0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 6, 0], [0, 0, 0, 0, 0, 0, 0, -11, 0, 0, 0, -8, 0, 0, 0, 0], [0, 0, 0, 0, -36, -4, 36, 0, 36, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 1, 1, 0], [0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 13, 13, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 14, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 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, 3, 0, 0, 0, -3, 0], [0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -3], [0, 0, 0, 0, -11, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0], [0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -10, 0, 0, 0, 0], [0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 9], [0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 23, 0, 0, 0, 0], [0, 4, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13, 0, 0, 0, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 13, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 1], [-6, 0, 29, 0, 0, 0, 0, -6, 0, 0, 0, 29, 0, 0, 0, 0], [0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -41, -41, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, -33, 0, 0, 0, 12, 0, 0, 0, 0], [0, -2, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 3], [0, 0, 0, 0, -1, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0], [0, 0, 0, 0, 18, 18, -18, 0, -18, 0, 0, 0, 0, 0, 0, 0], [0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, -7], [-15, 0, 28, 0, 0, 0, 0, -15, 0, 0, 0, 28, 0, 0, 0, 0], [0, 0, 0, 0, -21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15], [-32, 0, 3, 0, 0, 0, 0, -32, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -18, -18, 0, 0, -3, -3, 0], [0, 0, 0, 0, 31, 31, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -14, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 24, 36, -24, 0, -24, 0, 0, 0, 0, 0, 0, 0], [0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, -1, -1, 0], [24, 0, 11, 0, 0, 0, 0, 24, 0, 0, 0, 11, 0, 0, 0, 0], [0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, -9], [0, 6, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 23, 23, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 21, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 7, 0, 0, 0, 7, 0], [33, 0, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 9], [0, 0, 0, 0, 0, 0, 0, -25, 0, 0, 0, -4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, -6, 0, 0], [0, 0, 0, 0, 3, -2, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, -1, -1, 0], [0, 0, 0, 0, -3, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 10, 0, 0, 0, 0, 0], [-1, 0, -1, 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, 1, 0, 0, 5], [0, 0, 0, 0, 28, 0, 0, 0, -27, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 0, 0, 5, 5, 0], [12, 0, -39, 0, 0, 0, 0, 12, 0, 0, 0, -39, 0, 0, 0, 0], [0, 0, 0, 0, 35, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 0, 0, -7, -7, 0], [0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 26, 0, 0, 0, 0], [0, 0, 0, 0, 13, 13, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 3, 0], [0, 0, 0, 0, -6, 12, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -49, 0, 0, 0, -4, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 11], [34, 0, 7, 0, 0, 0, 0, 34, 0, 0, 0, 7, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 37, 37, -33, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0], [-5, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -19, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0], [0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 7], [0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, -11], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 17, 17, -37, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [13, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 2, 0], [0, 0, 0, 19, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 19], [60, 0, -2, 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, -7, 0, 0], [0, 0, 0, 0, -39, -26, 39, 0, 39, 0, 0, 0, 0, 0, 0, 0], [33, 0, -8, 0, 0, 0, 0, 33, 0, 0, 0, -8, 0, 0, 0, 0], [0, 0, 0, 0, -37, -37, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0, 4, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, -3, 0, 0], [0, 0, 0, 0, 12, 2, -12, 0, -12, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 12, 0, 0, 0, -21, 0, 0, 0, 0, 0, 0, 0], [-37, 0, -12, 0, 0, 0, 0, -37, 0, 0, 0, -12, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 9, 9, 0], [0, -10, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]