# Stored data for newform 45.8.a.e, downloaded from the LMFDB on 27 July 2026.
{"Nk2": 2880, "analytic_conductor": 14.05732614678548, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [5, -1]], "atkin_lehner_string": "--", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [45, 1, [11, 37], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[2, [-13, 1]]], "hecke_orbit": 5, "hecke_orbit_code": 18014398643699757, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "45.8.a.e", "level": 45, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3, 5], "level_radical": 15, "minimal_twist": "15.8.a.b", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+13q^{2}+41q^{4}+5^{3}q^{5}+1380q^{7}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "7.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "45.8.a", "trace_display": [13, 0, 125, 1380], "trace_hash": 1437239149458830319, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.993", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.972", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.898", "prec": 17}], "trace_zratio": 0, "traces": [0, 1, 13, 0, 41, 125, 0, 1380, -1131, 0, 1625, 3304, 0, 8506, 17940, 0, -19951, 9994, 0, 41236, 5125, 0, 42952, -84120, 0, 15625, 110578, 0, 56580, -132802, 0, -55800, -114595, 0, 129922, 172500, 0, 228170, 536068, 0, -141375, 139670, 0, -755492, 135464, 0, -1093560, -836984, 0, 1080857, 203125, 0, 348746, -1641650, 0, 413000, -1560780, 0, -1726426, 989656, 0, -1658162, -725400, 0, 1063993, 1063250, 0, -4523844, 409754, 0, 2242500, 389408, 0, 5617330, 2966210, 0, 1690676, 4559520, 0, 3901080, -2493875, 0, 1815710, 9394116, 0, 1249250, -9821396, 0, -3736824, -2803746, 0, 11738280, -3448920, 0, -10880792, 5154500, 0, 5099426, 14051141, 0, 640625, -15172266, 0, 4705268, -9620286, 0, -21341450, -2631204, 0, -4300594, 5369000, 0, -27532380, -3982334, 0, -10515000, -5444882, 0, 12865528, 13791720, 0, -8570755, -21556106, 0, -2287800, 1953125, 0, 28017676, 28500069, 0, 13822250, 8199192, 0, 56905680, -58809972, 0, -11303214, 1666458, 0, -58745596, 7072500, 0, 5062304, 28103824, 0, -16600250, 73025290, 0, 9354970, 19369742, 0, -53395208, -46637916, 0, 59273760, -6975000, 0, 20452922, 50714040, 0, -14324375, -116085600, 0, -733588, 5726470, 0, 122123508, -16892520, 0, 9603519, 16240250, 0, -30975172, -11818554, 0, 21562500, -65918104, 0, -36448698, 31374640, 0, -58355530, 152597640, 0, 95139720, 28521250, 0, 33020176, -34316344, 0, 67008500, -4061656, 0, -133220566, 66292538, 0, 44315137, -13077138, 0, -69850232, -17671875, 0, -197239458, -183266760, 0, 17458750, 61168484, 0, -169703206, 136243744, 0, 32853500, -67307650, 0, -34205652, -94436500, 0, -77004000, -55907722, 0, 16933000, 85008964, 0, 69519356, -158141100, 0, -51770342, 230778860, 0, 146157054, -136695000, 0, 150199062, -311907438, 0, -104623000, 40575896, 0, 179292360, -227310296, 0, -198482654, -111419815, 0, -67984642, 135107125, 0, 350753416, 63109800, 0, 25390625, 132535968, 0, -277932480, 364229788, 0, 234309793, 35864226, 0, 314874600, 43593250, 0, 106589496, 479640488, 0, -205206250, 739773840, 0, -185477604, 70876414, 0, 407490256, -199390294, 0, 21663954, 51625000, 0, -79347702, -763692748, 0, -195097500, 87006846, 0, 277611876, 15965728, 0, 365349712, 192744600, 0, -310458637, -215803250, 0, 230310530, -246490482, 0, 123707000, -258060270, 0, 251806646, -715524720, 0, -1042578960, -694137704, 0, -822699436, -207270250, 0, 384964564, 186940320, 0, -90675000, -46443456, 0, 210558002, 265887986, 0, 159944280, 960971366, 0, -438777808, 132999125, 0, -1509112800, 412112584, 0, 132906250, -9536644, 0, -157966770, -1155037920, 0, 399922812, 385158756, 0, -219602760, -565480500, 0, 269184538, 124845747, 0, 51219250, -184363200, 0, 355093320, 854461452, 0, -153641202, 821868004, 0, 648353902, 280312500, 0, -378621880, -652666326, 0, 48676000, -114953586, 0, 407870320, 877430856, 0, 806535957, -758621890, 0, 481269480, 702166250, 0, 286988988, 1678278120, 0, 370776250, -2265477000, 0, -1770132542, 429262288, 0, 946628904, -1129613812, 0, 1463113060, 211334500, 0, -52801528, 990456408, 0, 569940000, -1731867358, 0, 209076466, 796901166, 0, -840695280, -1222449267, 0, -170002794, 487635000, 0, 795584194, -908053016, 0, -311734375, 2016318342, 0, -474634800, -622062906, 0, -2382467880, 753873680, 0, -54802966, 226963750, 0, 192915988, 1365725280, 0, 1174264500, -974745070, 0, 1771168672, -110924536, 0, -2120637986, 427095500, 0, 1856706150, 156156250, 0, -2288263560, -107879364, 0, -1227674500, 2485326480, 0, 29995642, -1001052000, 0, -176324354, -3468772320, 0, -1048734680, -467103000, 0, 1105116532, -204679116, 0, -350468250, 903751628, 0, 1468310340, -2639623418, 0, 461469680, -163275694, 0, 3000125180, 1467285000, 0, 1837383370, 1900041702, 0, -431115000, -3576778602, 0, 1280677668, 2649532702, 0, -4054796694, 4199840036, 0, -6242904720, -1360099000, 0, -1119300936, -2496145568, 0, 644312500, 565460520, 0, -2955033848, -2482019880, 0, 1940814020, -2580274502, 0, -351400955, 637428250, 0, -1080653044, 1875381222, 0, 1756392625, 947786672, 0, -1327223188, 4559794408, 0, 1113265800, 537383040, 0, -2076919244, 80078125, 0, 1722967584, -2732654896, 0, -1896533250, -3613122240, 0, 1148724716, -4524697154, 0, 7751915400, -601981523, 0, 466234938, 588158500, 0, -2765395136, 4093369800, 0, -1202535750, 279532670, 0, 1463762068, 336166872, 0, 6235326344, -557665200, 0, 3671348953, -2667681250, 0, 2333132880, 1188033020, 0, -328900500, 5116467564, 0, 921393382, 3571151528, 0, -2721936690, 5297373328, 0, -1145262430, -537574250, 0, -673048220, 68324778, 0, 671125000, -5476223272, 0, 5383490400, -1031520126, 0, -2408569436, 7199944134, 0, -6426214952, -3441547500, 0, 1131088998, -5801136324, 0, -497791750, 3608954388, 0, -440420448, 1670688894, 0, 5701386956, 1152256784, 0, 2505679800, -1314375000, 0, 2430634946, -4035962281, 0, -680610250, 12963880080, 0, -5424011600, -6353200230, 0, -3204376266, 3333782076, 0, -2300968800, 1608191000, 0, -4552219670, -3422803438, 0, 1723965000, 794159422, 0, -9301821360, 928661192, 0, -6569738374, -13553526480, 0, -2189203528, -1071344375, 0, -3507897644, -4725439420, 0, -2694513250, -7119385904, 0, 3639701194, 5004539332, 0, -5156817120, -7825585182, 0, 8351725844, -285975000, 0, -603764928, -3869169480, 0, 244140625, 2737254026, 0, 838569802, 2280330980, 0, -21681968, -4412121480, 0, 12492627758, 3502209500, 0, 9193769642, -5704111504, 0, 3562508625, 7853610750, 0, -8818195092, -4759509600, 0, 5357463592, 8719969024, 0, 3269823424, 1727781250, 0, -30077108, 665755238, 0, 1024899000, -2786556170, 0, -15015492960, 9995126680, 0, -2891603978, 5198996556, 0, -10624745196, 7113210000, 0, 11171304240, -692593320, 0, -7351246500, -5478567248, 0, -5832356070, 3499398994, 0, 393744279, 12252424782, 0, 7037207880, -1412901750, 0, -2396721600, 9692933868, 0, 208307250, 4616213160, 0, 15072820892, -13963874900, 0, 3332853076, -484560714, 0, 10684284052, -7343199500, 0, 1395861980, 8428600726, 0, 884062500, 2731988702, 0, 9408818120, 3515432872, 0, -8484662238, -20937727080, 0, 344619886, 632788000, 0, 3171036726, 4693896000, 0, 3512978000, 1286360240, 0, 11406601128, -3357493728, 0, 6493269840, 10484967441, 0, -2392576730, -2075031250, 0, -13201695988, -13275994680, 0, 9128161250, -7550387048, 0, 4301789378, 3730856844, 0, 9639731400, -14946780576, 0, -18241424636, 1169371250, 0, -29451201000, 236847232, 0, 2421217750, -23011723046, 0, 1353827216, -3631061520, 0, -14432560904, 16698667784, 0, -14684979556, -6674401000, 0, 16493357962, 19020469780, 0, -5829739500, 2968454046, 0, -5934819720, -166527896, 0, 12875933304, 8418013936, 0, 8154002498, 7409220000, 0, -5462043206, 2780590398, 0, -871875000, -5767450806, 0, 10359715158, 5759432120, 0, 1286604032, -10929038640, 0, -21564178007, 2556615250, 0, -8209818596, -536162658, 0, 6339255000, -5495620920, 0, -14104325972, 10342594522, 0, -2863859512, 54791606, 0, -8364818096, -1790546875, 0, 26212138446, 18559658320, 0, -14510700000, -6170252400, 0, 17159832846, -2049730330, 0, -15947121708, -7513937160, 0, 9800357840, -91698500, 0, -31153468112, -712438558, 0, 715808750, -9659231274, 0, 3903976844, -5321658108, 0, 17754428640, 13222440964, 0, 12048232350, 15265438500, 0, 9050324458, 10802084858, 0, -2111565000, 5585993504, 0, -1442018968, -31060309000, 0, 386494895, -27568293818, 0, 1346993500, 1200439875, 0, -11827641900, 32752559150, 0, 2030031250, -19193660400, 0, 25215704442, -29747426280, 0, 2975891724, -22531444814, 0, 4078626820, -3871896500, 0, 32309244240, 11064318272, 0, -1477319250, 389943346, 0, -3157164000, 12889168320, 0, -38479817064, 4863971814, 0, -45094040160, 2695312500, 0, 36059458650, -13633550840, 0, -8239763000, 26295355606, 0, 2788729388, 3485367524, 0, -2660828508, 18296966616, 0, 38664392880, -4556087250, 0, 2850293596, -34513872224, 0, 3921830000, 39330095220, 0, -34315104434, 7410351600, 0, -16406650100, 5999105840, 0, 4504019754, -7294441250, 0, -1212451716, 9461933260, 0, 19074705000, 20918089408, 0, 31038159264, 23885983810, 0, 5992439214, 11314884960, 0, -18154477040, 11892465000, 0, -46498121826, 3312304448, 0, 3565156250, 16648809684, 0, 15218445190, 33922505414, 0, 44570219252, -12788204958, 0, 54597920468, 4127522000, 0, 36402256938, -81157761360, 0, -4289543000, -50711742490, 0, -11749040400, -19744626856, 0, -32449892384, -23099415492, 0, 47781008980, 8376062500, 0, -15598435320, 4163677114, 0, -507707000, -9319722136, 0, -32266258440, 2299712040, 0, -24398974111, 25230582260, 0, -8137788814, -16652570750, 0, -52046779324, 9693523905, 0, 8286567250, 364572720, 0, -81068922480, -14048489572, 0, 33081990062, 18178540474, 0, -9263576784, 5539392125, 0, 12321226736, 18577791360, 0, -1634642250, -17253901444, 0, 14380890056, 63551987040, 0, 18252005552, 6394401000, 0, 6985979520, -8731279000, 0, -1245342558, -26999950172, 0, -2208984375], "weight": 8, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, 13, 0, 41, 125, 0, 1380, -1131, 0, 1625, 3304, 0, 8506, 17940, 0, -19951, 9994, 0, 41236, 5125, 0, 42952, -84120, 0, 15625, 110578, 0, 56580, -132802, 0, -55800, -114595, 0, 129922, 172500, 0, 228170, 536068, 0, -141375, 139670, 0, -755492, 135464, 0, -1093560, -836984, 0, 1080857, 203125, 0, 348746, -1641650, 0, 413000, -1560780, 0, -1726426, 989656, 0, -1658162, -725400, 0, 1063993, 1063250, 0, -4523844, 409754, 0, 2242500, 389408, 0, 5617330, 2966210, 0, 1690676, 4559520, 0, 3901080, -2493875, 0, 1815710, 9394116, 0, 1249250, -9821396, 0, -3736824, -2803746, 0, 11738280, -3448920, 0, -10880792, 5154500, 0, 5099426, 14051141, 0, 640625, -15172266, 0, 4705268, -9620286, 0, -21341450, -2631204, 0, -4300594, 5369000, 0, -27532380, -3982334, 0, -10515000, -5444882, 0, 12865528, 13791720, 0, -8570755, -21556106, 0, -2287800, 1953125, 0, 28017676, 28500069, 0, 13822250, 8199192, 0, 56905680, -58809972, 0, -11303214, 1666458, 0, -58745596, 7072500, 0, 5062304, 28103824, 0, -16600250, 73025290, 0, 9354970, 19369742, 0, -53395208, -46637916, 0, 59273760, -6975000, 0, 20452922, 50714040, 0, -14324375, -116085600, 0, -733588, 5726470, 0, 122123508, -16892520, 0, 9603519, 16240250, 0, -30975172, -11818554, 0, 21562500, -65918104, 0, -36448698, 31374640, 0, -58355530, 152597640, 0, 95139720, 28521250, 0, 33020176, -34316344, 0, 67008500, -4061656, 0, -133220566, 66292538, 0, 44315137, -13077138, 0, -69850232, -17671875, 0, -197239458, -183266760, 0, 17458750, 61168484, 0, -169703206, 136243744, 0, 32853500, -67307650, 0, -34205652, -94436500, 0, -77004000, -55907722, 0, 16933000, 85008964, 0, 69519356, -158141100, 0, -51770342, 230778860, 0, 146157054, -136695000, 0, 150199062, -311907438, 0, -104623000, 40575896, 0, 179292360, -227310296, 0, -198482654, -111419815, 0, -67984642, 135107125, 0, 350753416, 63109800, 0, 25390625, 132535968, 0, -277932480, 364229788, 0, 234309793, 35864226, 0, 314874600, 43593250, 0, 106589496, 479640488, 0, -205206250, 739773840, 0, -185477604, 70876414, 0, 407490256, -199390294, 0, 21663954, 51625000, 0, -79347702, -763692748, 0, -195097500, 87006846, 0, 277611876, 15965728, 0, 365349712, 192744600, 0, -310458637, -215803250, 0, 230310530, -246490482, 0, 123707000, -258060270, 0, 251806646, -715524720, 0, -1042578960, -694137704, 0, -822699436, -207270250, 0, 384964564, 186940320, 0, -90675000, -46443456, 0, 210558002, 265887986, 0, 159944280, 960971366, 0, -438777808, 132999125, 0, -1509112800, 412112584, 0, 132906250, -9536644, 0, -157966770, -1155037920, 0, 399922812, 385158756, 0, -219602760, -565480500, 0, 269184538, 124845747, 0, 51219250, -184363200, 0, 355093320, 854461452, 0, -153641202, 821868004, 0, 648353902, 280312500, 0, -378621880, -652666326, 0, 48676000, -114953586, 0, 407870320, 877430856, 0, 806535957, -758621890, 0, 481269480, 702166250, 0, 286988988, 1678278120, 0, 370776250, -2265477000, 0, -1770132542, 429262288, 0, 946628904, -1129613812, 0, 1463113060, 211334500, 0, -52801528, 990456408, 0, 569940000, -1731867358, 0, 209076466, 796901166, 0, -840695280, -1222449267, 0, -170002794, 487635000, 0, 795584194, -908053016, 0, -311734375, 2016318342, 0, -474634800, -622062906, 0, -2382467880, 753873680, 0, -54802966, 226963750, 0, 192915988, 1365725280, 0, 1174264500, -974745070, 0, 1771168672, -110924536, 0, -2120637986, 427095500, 0, 1856706150, 156156250, 0, -2288263560, -107879364, 0, -1227674500, 2485326480, 0, 29995642, -1001052000, 0, -176324354, -3468772320, 0, -1048734680, -467103000, 0, 1105116532, -204679116, 0, -350468250, 903751628, 0, 1468310340, -2639623418, 0, 461469680, -163275694, 0, 3000125180, 1467285000, 0, 1837383370, 1900041702, 0, -431115000, -3576778602, 0, 1280677668, 2649532702, 0, -4054796694, 4199840036, 0, -6242904720, -1360099000, 0, -1119300936, -2496145568, 0, 644312500, 565460520, 0, -2955033848, -2482019880, 0, 1940814020, -2580274502, 0, -351400955, 637428250, 0, -1080653044, 1875381222, 0, 1756392625, 947786672, 0, -1327223188, 4559794408, 0, 1113265800, 537383040, 0, -2076919244, 80078125, 0, 1722967584, -2732654896, 0, -1896533250, -3613122240, 0, 1148724716, -4524697154, 0, 7751915400, -601981523, 0, 466234938, 588158500, 0, -2765395136, 4093369800, 0, -1202535750, 279532670, 0, 1463762068, 336166872, 0, 6235326344, -557665200, 0, 3671348953, -2667681250, 0, 2333132880, 1188033020, 0, -328900500, 5116467564, 0, 921393382, 3571151528, 0, -2721936690, 5297373328, 0, -1145262430, -537574250, 0, -673048220, 68324778, 0, 671125000, -5476223272, 0, 5383490400, -1031520126, 0, -2408569436, 7199944134, 0, -6426214952, -3441547500, 0, 1131088998, -5801136324, 0, -497791750, 3608954388, 0, -440420448, 1670688894, 0, 5701386956, 1152256784, 0, 2505679800, -1314375000, 0, 2430634946, -4035962281, 0, -680610250, 12963880080, 0, -5424011600, -6353200230, 0, -3204376266, 3333782076, 0, -2300968800, 1608191000, 0, -4552219670, -3422803438, 0, 1723965000, 794159422, 0, -9301821360, 928661192, 0, -6569738374, -13553526480, 0, -2189203528, -1071344375, 0, -3507897644, -4725439420, 0, -2694513250, -7119385904, 0, 3639701194, 5004539332, 0, -5156817120, -7825585182, 0, 8351725844, -285975000, 0, -603764928, -3869169480, 0, 244140625, 2737254026, 0, 838569802, 2280330980, 0, -21681968, -4412121480, 0, 12492627758, 3502209500, 0, 9193769642, -5704111504, 0, 3562508625, 7853610750, 0, -8818195092, -4759509600, 0, 5357463592, 8719969024, 0, 3269823424, 1727781250, 0, -30077108, 665755238, 0, 1024899000, -2786556170, 0, -15015492960, 9995126680, 0, -2891603978, 5198996556, 0, -10624745196, 7113210000, 0, 11171304240, -692593320, 0, -7351246500, -5478567248, 0, -5832356070, 3499398994, 0, 393744279, 12252424782, 0, 7037207880, -1412901750, 0, -2396721600, 9692933868, 0, 208307250, 4616213160, 0, 15072820892, -13963874900, 0, 3332853076, -484560714, 0, 10684284052, -7343199500, 0, 1395861980, 8428600726, 0, 884062500, 2731988702, 0, 9408818120, 3515432872, 0, -8484662238, -20937727080, 0, 344619886, 632788000, 0, 3171036726, 4693896000, 0, 3512978000, 1286360240, 0, 11406601128, -3357493728, 0, 6493269840, 10484967441, 0, -2392576730, -2075031250, 0, -13201695988, -13275994680, 0, 9128161250, -7550387048, 0, 4301789378, 3730856844, 0, 9639731400, -14946780576, 0, -18241424636, 1169371250, 0, -29451201000, 236847232, 0, 2421217750, -23011723046, 0, 1353827216, -3631061520, 0, -14432560904, 16698667784, 0, -14684979556, -6674401000, 0, 16493357962, 19020469780, 0, -5829739500, 2968454046, 0, -5934819720, -166527896, 0, 12875933304, 8418013936, 0, 8154002498, 7409220000, 0, -5462043206, 2780590398, 0, -871875000, -5767450806, 0, 10359715158, 5759432120, 0, 1286604032, -10929038640, 0, -21564178007, 2556615250, 0, -8209818596, -536162658, 0, 6339255000, -5495620920, 0, -14104325972, 10342594522, 0, -2863859512, 54791606, 0, -8364818096, -1790546875, 0, 26212138446, 18559658320, 0, -14510700000, -6170252400, 0, 17159832846, -2049730330, 0, -15947121708, -7513937160, 0, 9800357840, -91698500, 0, -31153468112, -712438558, 0, 715808750, -9659231274, 0, 3903976844, -5321658108, 0, 17754428640, 13222440964, 0, 12048232350, 15265438500, 0, 9050324458, 10802084858, 0, -2111565000, 5585993504, 0, -1442018968, -31060309000, 0, 386494895, -27568293818, 0, 1346993500, 1200439875, 0, -11827641900, 32752559150, 0, 2030031250, -19193660400, 0, 25215704442, -29747426280, 0, 2975891724, -22531444814, 0, 4078626820, -3871896500, 0, 32309244240, 11064318272, 0, -1477319250, 389943346, 0, -3157164000, 12889168320, 0, -38479817064, 4863971814, 0, -45094040160, 2695312500, 0, 36059458650, -13633550840, 0, -8239763000, 26295355606, 0, 2788729388, 3485367524, 0, -2660828508, 18296966616, 0, 38664392880, -4556087250, 0, 2850293596, -34513872224, 0, 3921830000, 39330095220, 0, -34315104434, 7410351600, 0, -16406650100, 5999105840, 0, 4504019754, -7294441250, 0, -1212451716, 9461933260, 0, 19074705000, 20918089408, 0, 31038159264, 23885983810, 0, 5992439214, 11314884960, 0, -18154477040, 11892465000, 0, -46498121826, 3312304448, 0, 3565156250, 16648809684, 0, 15218445190, 33922505414, 0, 44570219252, -12788204958, 0, 54597920468, 4127522000, 0, 36402256938, -81157761360, 0, -4289543000, -50711742490, 0, -11749040400, -19744626856, 0, -32449892384, -23099415492, 0, 47781008980, 8376062500, 0, -15598435320, 4163677114, 0, -507707000, -9319722136, 0, -32266258440, 2299712040, 0, -24398974111, 25230582260, 0, -8137788814, -16652570750, 0, -52046779324, 9693523905, 0, 8286567250, 364572720, 0, -81068922480, -14048489572, 0, 33081990062, 18178540474, 0, -9263576784, 5539392125, 0, 12321226736, 18577791360, 0, -1634642250, -17253901444, 0, 14380890056, 63551987040, 0, 18252005552, 6394401000, 0, 6985979520, -8731279000, 0, -1245342558, -26999950172, 0, -2208984375]}