# Stored data for newform 225.6.a.b, downloaded from the LMFDB on 25 April 2024.
{"label": "225.6.a.b", "space_label": "225.6.a", "level": 225, "weight": 6, "hecke_orbit": 2, "hecke_orbit_code": 4503599728034017, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2135916679044828280, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [4, 1]], [7, [225, 1]]], "qexp_display": "q-4q^{2}-2^{4}q^{4}-15^{2}q^{7}+192q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 8100, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 36.08635945792064, "hecke_ring_index": 1, "level_radical": 15, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [225, 1, [101, 127], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [3, 5], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.008", "prec": 17}, {"__RealLiteral__": 0, "data": "1.014", "prec": 17}, {"__RealLiteral__": 0, "data": "0.037", "prec": 17}, {"__RealLiteral__": 0, "data": "2.081", "prec": 17}, {"__RealLiteral__": 0, "data": "0.143", "prec": 17}, {"__RealLiteral__": 0, "data": "5.321", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, -1]], "trace_display": [-4, 0, 0, -225], "traces": [0, 1, -4, 0, -16, 0, 0, -225, 192, 0, 0, 434, 0, 613, 900, 0, -256, 878, 0, -731, 0, 0, -1736, -2850, 0, 0, -2452, 0, 3600, 7582, 0, 2175, -5120, 0, -3512, 0, 0, -9310, 2924, 0, 0, 12040, 0, -1121, -6944, 0, 11400, -29878, 0, 33818, 0, 0, -9808, -5740, 0, 0, -43200, 0, -30328, 5174, 0, -38717, -8700, 0, 28672, 0, 0, 31707, -14048, 0, 0, -64472, 0, -19790, 37240, 0, 11696, -97650, 0, -105000, 0, 0, -48160, 3318, 0, 0, 4484, 0, 83328, 65376, 0, -137925, 45600, 0, 119512, 0, 0, -89143, -135272, 0, 0, 94644, 0, -113956, 117696, 0, 22960, 19212, 0, -152791, 0, 0, 57600, -4012, 0, 0, -121312, 0, -20696, -197550, 0, 27305, 154868, 0, -34800, 0, 0, -36368, 49152, 0, 0, 43932, 0, 164475, -126828, 0, 168576, -185214, 0, 115916, 0, 0, 257888, 266042, 0, 0, 79160, 0, 148960, -33122, 0, 431317, -140352, 0, 390600, 0, 0, 40439, 420000, 0, 0, 641250, 0, -116299, -192640, 0, -13272, 632700, 0, 4476, 0, 0, 17936, -108222, 0, 0, -111104, 0, -261504, -496570, 0, 105365, 551700, 0, -547200, 0, 0, 381052, 478048, 0, 0, -427346, 0, 646427, 356572, 0, -541088, 546954, 0, -581783, 0, 0, -378576, -1705950, 0, 0, 455824, 0, -156928, -317254, 0, -441355, 91840, 0, -76848, 0, 0, -489375, 611164, 0, 0, 538214, 0, -330457, 1152000, 0, 16048, -1125080, 0, -977379, 0, 0, 1455744, -334584, 0, 0, -82784, 0, 790200, -218764, 0, 734041, -109220, 0, 619472, 0, 0, -448103, 417600, 0, 0, -1183812, 0, -1236900, 145472, 0, -1114112, 333732, 0, 2094750, 0, 0, -175728, 731104, 0, 0, -657900, 0, -507312, -734254, 0, 335056, -224768, 0, 740856, 0, 0, -1582599, -463664, 0, 0, -1087134, 0, -607407, 1031552, 0, -1064168, -2709000, 0, -648973, 0, 0, 316640, -1233006, 0, 0, -1787520, 0, 132488, -1747050, 0, 252225, -1725268, 0, 187136, 0, 0, 562753, 1562400, 0, 0, 2396454, 0, 1528331, -161756, 0, 1680000, -1000328, 0, 3290588, 0, 0, -2565000, -641818, 0, 0, 465196, 0, 2311680, 6722550, 0, 2290932, -53088, 0, -2530800, 0, 0, 1289041, -17904, 0, 0, 943950, 0, -3827475, -215232, 0, 432888, -19102, 0, -3246902, 0, 0, -2222080, -4288038, 0, 0, -1046016, 0, 1986280, -88656, 0, -1941738, -421460, 0, 2206800, 0, 0, -2041839, 729600, 0, 0, 1291500, 0, -806321, -1524208, 0, -5736576, 4647766, 0, -2413145, 0, 0, 1709384, 1458564, 0, 0, -2585708, 0, 1426288, -2656176, 0, -2502300, 6493056, 0, -2187816, 0, 0, 1686643, 2327132, 0, 0, 2125332, 0, 1333275, -1514304, 0, 6823800, -4040540, 0, 1971581, 0, 0, 1823296, -1164150, 0, 0, -3138560, 0, 1269016, -1757444, 0, -2839466, 1765420, 0, -1102080, 0, 0, 8711325, -307392, 0, 0, 4693350, 0, -6713429, 1957500, 0, 2444656, 2083350, 0, 3920215, 0, 0, -2152856, 6930312, 0, 0, 1321828, 0, -6451200, -4386052, 0, 5225360, 64192, 0, 4500320, 0, 0, 2419510, 3909516, 0, 0, 366228, 0, 6625344, -1940992, 0, 1338336, -3384758, 0, -7134075, 0, 0, 993408, -486514, 0, 0, 3160800, 0, 875056, -6619050, 0, -5707030, -2936164, 0, -436880, 0, 0, -287383, -7433664, 0, 0, -6513368, 0, 6656996, 1792412, 0, -556800, 14506200, 0, -1170371, 0, 0, 4735248, 1406512, 0, 0, 4947600, 0, 581888, -3656446, 0, 4452750, 2883584, 0, -1334928, 0, 0, -12967052, -8379000, 0, 0, 2708890, 0, -11401391, -702912, 0, -2924416, 1909650, 0, 1686157, 0, 0, -2631600, 7380520, 0, 0, 6087744, 0, 2937016, 14677012, 0, 6950505, -1340224, 0, -4495360, 0, 0, -8085320, 2963424, 0, 0, -5542442, 0, 23625000, 6330396, 0, -1854656, -14602482, 0, -687173, 0, 0, 4348536, -3546522, 0, 0, 2429628, 0, -12378624, 14268066, 0, -5485339, -4256672, 0, 10836000, 0, 0, -2132533, 2595892, 0, 0, -746550, 0, -2491160, -3799680, 0, 4932024, -2393028, 0, -1589925, 0, 0, 2383360, -1834784, 0, 0, 529952, 0, 6988200, 126508, 0, 10379051, -1008900, 0, -6901072, 0, 0, -366608, 3742720, 0, 0, -18315214, 0, -7492718, -2251012, 0, -18748800, -2237484, 0, 6616481, 0, 0, -9585816, -14709600, 0, 0, -6113324, 0, -647024, -8174180, 0, -6164813, -20160000, 0, 4001312, 0, 0, 20730434, -13162352, 0, 0, -4795020, 0, -1201236, -10260000, 0, 2567272, 10147988, 0, 2245516, 0, 0, 1860784, 19861414, 0, 0, -3082240, 0, -26890200, 5733080, 0, -7922438, -9163728, 0, 637056, 0, 0, -21608700, -10123200, 0, 0, -16803178, 0, -7753530, -5156164, 0, -71616, 3777774, 0, 20057175, 0, 0, -3775800, 6182904, 0, 0, 15309900, 0, 286976, -3518620, 0, -23847464, 1731552, 0, 76408, 0, 0, 10571120, 12987608, 0, 0, 5812402, 0, 6805610, 12443648, 0, 17152152, -21294900, 0, -7531331, 0, 0, 12552192, -6198750, 0, 0, 7945120, 0, 354624, 8662278, 0, 25640100, 7766952, 0, -1685840, 0, 0, 2944439, -26481600, 0, 0, -984238, 0, 19236254, 8167356, 0, 14592000, 13760838, 0, -26390924, 0, 0, -5166000, 11516, 0, 0, 3225284, 0, -6096832, -4322700, 0, -24483584, 7648768, 0, -18591064, 0, 0, -10138451, 9652580, 0, 0, 13457076, 0, 34377975, 6837536, 0, -5834256, 3171662, 0, 21357347, 0, 0, -10342832, 25546824, 0, 0, -17115456, 0, 10624704, -8801240, 0, -27980848, 10009200, 0, -8657408, 0, 0, 13266793, -8751264, 0, 0, 902700, 0, -23733521, -6746572, 0, 9308528, 12491932, 0, -26232884, 0, 0, -8501328, -8588860, 0, 0, -5333100, 0, 18171648, 7835140, 0, 30475077, 27295200, 0, 16162160, 0, 0, 819451, -7886324, 0, 0, 29032986, 0, -19993453, -21879552, 0, 4656600, 196388, 0, 7050930, 0, 0, 17575936, 29692204, 0, 0, 5076064, 0, 7029776, 32611810, 0, 36975575, 11357864, 0, 7061680, 0, 0, -6143625, 1469440, 0, 0, 26533500, 0, -18468729, -34845300, 0, 3688704, 31430972, 0, 28076680, 0, 0, -18773400, 21195136, 0, 0, 26853716, 0, 7830000, -45570000, 0, 19436391, -29335872, 0, -8333400, 0, 0, 37091055, -15680860, 0, 0, 9163856, 0, 13639559, -8611424, 0, -27721248, -29040138, 0, 8182800, 0, 0, 5287312, 21840818, 0, 0, -11059200, 0, 17544208, 16490850, 0, -5039720, -20901440, 0, -770304, 0, 0, 21209988, 18001280, 0, 0, -19526722, 0, 1440012, -9678040, 0, 15638064, -9884700, 0, -28593035, 0, 0, -1464912, -39521336, 0, 0, -26501376, 0, -38819840, -23876894, 0, -24720958, 5353344, 0, 13539032, 0, 0, 34667151, 28536300, 0, 0, -46418750, 0, -34314000, -1324544, 0, 1946056, 21082926, 0, -12131270, 0, 0, -37929600, -36743848, 0, 0, 3500224, 0, 26476200, 41673150, 0, -23898526, 22828120, 0, -11744656, 0, 0, -37623448, 5242560, 0, 0, 48920490, 0, -26081100, 1149532, 0, 9911552, 28444958, 0, 28373184, 0, 0, 26053472, -45161100, 0, 0, -26627984, 0, 7169648, 3194850, 0, -28551733, -11136000, 0, -58024800, 0, 0, 32652714, 4681484, 0, 0, -59859450, 0, 4542772, 18940992, 0, -5626048, 4195940, 0, 32536925, 0, 0, 19790400, 25012918, 0, 0, -6982656, 0, 14625784, 37477746, 0, -18849857, -17811000, 0, 24117248, 0, 0, -64365000, -5339712, 0, 0, 20725686, 0, 9898581, 51868208, 0, -33516000, -33993526, 0, -3447647, 0, 0, -10835560, 7452450, 0, 0, 45605564, 0, 8434944, -31882944, 0, -4313715, -11697664, 0, -7638600, 0, 0, -97046325, -6744628, 0, 0, 63452874, 0, 35558279, 31579200, 0, -29522080, -38688062, 0, -21869825, 0, 0, -8116992, -70588420, 0, 0, 11748064, 0, -58708048, 2033934, 0, 85152300, -27802020, 0, -5360896, 0, 0, -24119365, 25174016, 0, 0, -72316136, 0, 21171397, 32341280, 0, -35561088, -22172378, 0, -9098775, 0, 0, 22169768, -7750734, 0, 0, -94500000, 0, 25321584, -50611390, 0, 41075496, 22255872, 0, 58409928, 0, 0, 80297277, 2748692, 0, 0, -3782194, 0, -30470987, 17394144, 0, 14186088, -96381300, 0, -56052427, 0, 0, 9718512, -49456904, 0, 0, 16504832, 0, -57072264, 27838746, 0, 26167275, 21941356, 0, 51080064, 0, 0, -20249250, 43344000, 0, 0, -62816134, 0, 24777169, 8530132, 0, 10383568, 40075488, 0, 28302127, 0, 0, 2986200, 24315968, 0, 0, 9964640, 0, 5066240, -142357500, 0, -14049717, 19728096, 0, 9572112, 0, 0, 8338008, 6359700, 0, 0, 56260274, 0, -1007100, 47667200, 0, 7339136, -72160422, 0, 91287280, 0, 0, -6359424, -6120062, 0, 0, 27952800, 0, -506032, -66311294, 0, -9601514, -41516204, 0, -4035600, 0, 0, -56606416, 82812864, 0, 0, 24349950, 0, -7236858, 1466432, 0, -20959232, 63339702, 0, 16359000, 0, 0, 73260856, -41854586, 0, 0, 29970872, 0, -9004048, 100934688, 0, 54227628, 24998400, 0, 8949936, 0, 0, -23164614, -26465924, 0, 0, -17375620, 0, -1741208, -38343264, 0, 58838400, -8499422, 0, -75763766, 0, 0, -24453296, 111728250, 0, 0, 7764288, 0, 32696720, 58443228, 0, -54644659, 24659252, 0, 26880000, 0, 0, -23707125, 16005248, 0, 0, 26187000, 0, -23177817, -82921736, 0, -52649408, 98051070, 0, -76982431, 0, 0, 19180080, -61002406, 0, 0, 4804944, 0, 123120000, -32531532, 0, -5236261, 10269088, 0, -40591952, 0, 0, 80559539, -8982064, 0, 0, 96254878, 0, 33544875, -22329408, 0, -79445656, 69795428, 0, -85736700, 0, 0, -61644800, 58016772, 0, 0, -107560800, 0, -22932320, 8371914, 0, 67378598, 31689752, 0, -36654912, 0, 0, 102265399, -849408, 0, 0, -58045764, 0, -2438175, 86434800, 0, 121478400, 96152850, 0, -69855028, 0, 0, 67212712, -92190000, 0, 0, 31014120, 0, -20624656, 47129032, 0, -145446075, 859392, 0, -15111096, 0, 0, -14745900, -80228700, 0, 0, 28532022, 0, -226534996, -15103200, 0, -24731616, -79923176, 0, 17332143, 0, 0, 61239600, -105814014, 0, 0, 5739520, 0, 14074480, -123064650, 0, -51759311, 95389856, 0, -20778624, 0, 0, 14466490, 305632, 0, 0, 11776956, 0, 130901175, -42284480, 0, 51950432, -15783712, 0, 117591533, 0, 0, -23249608, 110343450, 0, 0, -27222440, 0, 21331968, 17248830, 0, 2913204, 68608608, 0, 85179600, 0, 0, -93660883, 30125324, 0, 0, 256408076, 0, 105522232, -16736256, 0, 24795000, 64273912, 0, -110312785, 0, 0, -95341440, 42781494, 0, 0, 1418496, 0, -34649112, -26002094, 0, 19066488, -102560400, 0, 31067808, 0, 0, 72133513, 20230080, 0, 0, -92936214, 0, -115514895, -11777756, 0, 35308800, -64984650, 0, 91977124, 0, 0, 3936952, 71382150, 0, 0, -76945016, 0, 32669424, -2459356, 0, 69570101, -81715200, 0, -55043352, 0, 0, 99304875, 105563696, 0, 0, -17696758, 0, -1458508, -20664000, 0, -46064, -51382632, 0, -78614622, 0, 0, 12901136, 104149324, 0, 0, 73161984, 0, 17290800, -120893214, 0, 76755000, 97934336, 0, 152975360, 0, 0, -80382876, -74364256, 0, 0, 29433612, 0, 57400128, 40553804, 0, 38610320, -112092400, 0, 73554150, 0, 0, -53828304, 27432498, 0, 0, -137511900, 0, -82050432, 50307544, 0, -140732421, -23337024, 0, -12686648, 0, 0, -43520680, -85429388, 0, 0, -90364950, 0, -135581159, 124113984, 0, -102187296, -121098150, 0, 38639307, 0, 0, 22820608, -23517606, 0, 0, 42498816, 0, 35204960, 29062814, 0, 74352825, 111923392, 0, 40036800, 0, 0, 101069141, -173148160, 0, 0, -166966270, 0, 16737965, -53067172, 0, 105015168, -2425458, 0, 91653011, 0, 0, -3610800, -121523866, 0, 0, 94934084, 0, -26986288, 253143000, 0, 10436510, -111702336, 0, -49967728, 0, 0, -107203850, 104931536, 0, 0, -164897602, 0, 219910275, -34005312, 0, 34355440, -56976900, 0, 147182301, 0, 0, -21332400, -69278426, 0, 0, -24228864, 0, -31340560, 65622132, 0, -122178623, -121900308, 0, -327542400, 0, 0, 68183612, 64648640, 0, 0, 75281400, 0, 183745200, -3277804, 0, -31545296, 50016564, 0, -14374948, 0, 0, -116131944, -12484500, 0, 0, 79973812, 0, 29172736, -78267554, 0, -22293584, 18626400, 0, -785552, 0, 0, -150294274, -28203720, 0, 0, 187191578, 0, -147148061, 30130176, 0, -118768816, 48225670, 0, -117255082, 0, 0, -60912768, 49221900, 0, 0, 28119104, 0, -130447240, 56401500, 0, 29105399, -147902300, 0, 45431456, 0, 0, -165159225, -84740160, 0, 0, -47789856, 0, -88347993, 24574500, 0, 29388800, 47899398, 0, -23701448, 0, 0, -106134000, 26930316, 0, 0, 73874916, 0, -139381200, 196497566, 0, 39229268, -4918272, 0, -125723888, 0, 0, 83097432, -112306720, 0, 0, -110500328, 0, 31552820, -75093600, 0, -84780544, 17550526, 0, 100823175, 0, 0, 107414864, 156638, 0, 0, -93960000, 0, 182280000, 278164180, 0, -239642641, -77745564, 0, 39114496, 0, 0, 181955848, -33333600, 0, 0, -100053368, 0, 47797466, -148364220, 0, -62723440, 266357700, 0, 75369963, 0, 0, -36655424, -13496840, 0, 0, -54558236, 0, 103337088, -293552294, 0, 278302500, -110884992, 0, 116160552, 0, 0, -55421847, -32731200, 0, 0, -113536182, 0, -128445829, -63447744, 0, -87363272, -87481266, 0, 71951655, 0, 0, 250675200, -50473766, 0, 0, 70176832, 0, -65963400, -75089700, 0, -65518329, 20158880, 0, -83605760, 0, 0, 71056508, 1027072, 0, 0, -100602240, 0, -314845580, -84839952, 0, -216015360, 299250000, 0, 16868136, 0, 0, 78106888, 234286960, 0, 0, -5760048, 0, -38712160, 11253450, 0, 197717584, -187656768, 0, 39538800, 0, 0, 274591800, 114372140, 0, 0, -164498400, 0, 65163533, -5859648, 0, 158085344, -4495070, 0, -145751802, 0, 0, -106005504, -134150498, 0, 0, 217391104, 0, 95507576, 1942584, 0, 107317251, 98883832, 0, -64240128, 0, 0, -7079007, 54156128, 0, 0, 5585850, 0, 271880881, -138668604, 0, 114145200, -169542384, 0, 100828928, 0, 0, 185675000, 165207150, 0, 0, 137256000, 0, -26490880, -11856720, 0, -84209475, 7784224, 0, -84331704, 0, 0, -75387600, 48525080, 0, 0, 50285254, 0, -46968348, 50572800, 0, 146975392, 79253572, 0, -9456300, 0, 0, -42002688, 148859124, 0, 0, 105904800, 0, -166692600, -69184764, 0, -3522536, 95594104, 0, 91312480, 0, 0, -359731120, 140935872, 0, 0, 284634696, 0, 120448451, 150493792, 0, -6990080, -20303786, 0, 356084775, 0, 0, -195681960, 240402474, 0, 0, 104324400, 0, 4598128, -245959680, 0, -171575593, 198231040, 0, -113779832, 0, 0, 83301836, -113492736, 0, 0, 53439400, 0, 264397321, 104213888, 0, 180644400, 244605150, 0, -215511380, 0, 0, -106511936, -158137368, 0, 0, -86035776, 0, -12779400, -234020910, 0, 136666575, 114206932, 0, 62361600, 0, 0, 96825164, -232099200, 0, 0, 45728410, 0, 135188742, -130610856, 0, 18725936, 54037676, 0, -253760957, 0, 0, 239437800, -41906742, 0, 0, -18171088, 0, -227291904, 407168720, 0, 30857788, -22504192, 0, -16783760, 0, 0, 167140997, -130147700, 0, 0, 33493238, 0, 146018925, -237484800, 0, -100051672, -132783348, 0, 16872449, 0, 0, 9310208, -14043972, 0, 0, 58503136, 0, -149910984, 1891596, 0, 24789107, 75399428, 0, -71244000, 0, 0, -186321600, -188743680, 0, 0, 277426350, 0, 102337014, 257460000, 0, 64076544, 23973790, 0, -488826704, 0, 0, -82902744, -163990494, 0, 0, -39594324, 0, 207472832, 75127956, 0, 111690221, 402192000, 0, 135974104, 0, 0, 68962725, 13790588, 0, 0, -170482620, 0, -15940669, -43342240, 0, -29809800, -96562658, 0, 146262169, 0, 0, 182422256, 393086250, 0, 0, -11246592, 0, 127531776, 36148962, 0, -185468164, 17254860, 0, 140371968, 0, 0, -37909978, -30554400, 0, 0, -171218292, 0, -166314255, 388185300, 0, -26978512, -150047780, 0, -71291287, 0, 0, -253811496, 280549318, 0, 0, -142233116, 0, -42105600, -148733838, 0, -357959680, -118088320, 0, 154752248, 0, 0, -40968445, 87479300, 0, 0, -26103796, 0, -32898881, -162339840, 0, 282353680, 2932772, 0, -126619425, 0, 0, -140976768, -309321954, 0, 0, -234832192, 0, -8135736, -31931104, 0, 245204506, -340609200, 0, -111208080, 0, 0, 237378036, 64330752, 0, 0, 387845100, 0, -69109600, 96477460, 0, 43155456, -539202150, 0, -152903755, 0, 0, 289264544, -48169940, 0, 0, -84685588, 0, 129365120, -252493822, 0, -343874475, 47414784, 0, 88689512, 0, 0, -224858821, 36395100, 0, 0, -140226600, 0, -25183379, 88679072, 0, 31002936, 378917226, 0, 663349877, 0, 0, -378000000, 88533848, 0, 0, -303859008, 0, 202445560, 225073800, 0, -334539663, -164301984, 0, -29674496, 0, 0, 38572296, 233639712, 0, 0, 254057550, 0, -740382300, -321189108, 0, 10994768, -210828022, 0, -78281245, 0, 0, 15128776, 20985022, 0, 0, 121883948, 0, -208729728, -66340086, 0, 167419973, 56744352, 0, 385525200, 0, 0, 360455270, 224209708, 0, 0, 144409050, 0, -43043250, -116622144, 0, 197827616, 290369956, 0, 266731307, 0, 0, 330096640, -401061572, 0, 0, -228289056, 0, -111354984, 6434540, 0, -320612467, -104669100, 0, 87765424, 0, 0, 76041432, -68106752, 0, 0, -796110000, 0, -42205301, 80997000, 0, -520128000, -106184360, 0, -19959955, 0, 0, 251264536, -1010414204, 0, 0, -99108676, 0, 34120528, 147770214, 0, 108310737, -124602816, 0, -160301952, 0, 0, -515459700, -113208508, 0, 0, -191548070, 0, -269735400, 11944800, 0, -97263872, -304397410, 0, -162617892, 0, 0, 39858560, 507159218, 0, 0, 101324800, 0, 569430000, 225400110, 0, 145658753, 56198868, 0, -236737152, 0, 0, -40712579, 38288448, 0, 0, -79894500, 0, 64588745, -33352032, 0, 25438800, -414274076, 0, -290034225, 0, 0, -225041096, 101774248, 0, 0, 4028400, 0, -266936320, 324774600, 0, 35834901, 29356544, 0, 288641688, 0, 0, -492619734, -365149120, 0, 0, 27549250, 0, -95670707, 8479232, 0, 24480248, -212388750, 0, -199391241, 0, 0, -335433600, 261629658, 0, 0, -2024128, 0, 265245176, -288693464, 0, 292802749, 38406056, 0, -166064816, 0, 0, 25157076, 48427200, 0, 0, 153462306, 0, 26585008, 226425664, 0, -110417152, 9592374, 0, 62294960, 0, 0, -97399800, 13004678, 0, 0, 28947432, 0, 5865728, 4297950, 0, 233584876, -35930112, 0, -253358808, 0, 0, 122914207, -65436000, 0, 0, 435271706, 0, 730552950, 293043424, 0, 167418344, 543904434, 0, -228375000, 0, 0, 119883488, -143418338, 0, 0, 108048576, 0, -403738752, 419731424, 0, -54754200, -216910512, 0, 499968000, 0, 0, 293869028, 35799744, 0, 0, 964808550, 0, 86176435, 92658456, 0, -105863696, -522409272, 0, -295192170, 0, 0, 69502480, -261963098, 0, 0, 6964832, 0, 460119168, -32114292, 0, 171499720, 235353600, 0, 33997688, 0, 0, -488284720, 303055064, 0, 0, -466152680, 0, 459965532, 293439552, 0, -446913000, 435454350, 0, 396259751, 0, 0, -10352384, 19947600, 0, 0, 130786880, 0, -233772912, -424182486, 0, 353359991, 218578636, 0, 98637008, 0, 0, 436891050, 537600000, 0, 0, -556788324, 0, -29081116, 94828500, 0, -192062976, -5800054, 0, 269259819, 0, 0, -104748000, -408164110, 0, 0, 92711268, 0, -331686944, -494415804, 0, -254502576, 631792896, 0, -392204280, 0, 0, -298608875, 307929724, 0, 0, 335282802, 0, -145209456, 76720320, 0, 244009624, 378696326, 0, 459413775, 0, 0, 19219776, 7216650, 0, 0, -164160000, 0, 130126128, -150501184, 0, 495680832, 20945044, 0, -123229056, 0, 0, -356632979, -162367808, 0, 0, 35822562, 0, -673841377, -322238156, 0, -35928256, -194115320, 0, 11434200, 0, 0, -385019512, 135391434, 0, 0, -134179500, 0, 29772544, -259982532, 0, 181422225, -317782624, 0, -279181712, 0, 0, 530713813, 342946800, 0, 0, -402871982, 0, 43401757, 345210880, 0, -232067088, 600234320, 0, -94943576, 0, 0, 1290729600, -348750534, 0, 0, -91729280, 0, -33487656, -1045747350, 0, -84734596, -269514392, 0, 126759008, 0, 0, -198232544, 439858944, 0, 0, 318573794, 0, 542957625, -409061596, 0, -16988160, -324827432, 0, -118820172, 0, 0, 232183056, -424054, 0, 0, 9752700, 0, 345739200, 35505442, 0, 131750519, -161971200, 0, -384611400, 0, 0, 597545798, 279420112, 0, 0, -328176900, 0, -568808676, 268850848, 0, 368760000, 9877482, 0, 9816861, 0, 0, 124056480, -215152192, 0, 0, 247495872, 0, -188516128, 144437252, 0, 184244900, 581784300, 0, -1145856, 0, 0, -215657725, -60444384, 0, 0, 703775882, 0, -42687319, 58983600, 0, -320914800, -194476702, 0, -346327345, 0, 0, -114128088, 597639600, 0, 0, 906139984, 0, 181238400, 131797164, 0, 5478355, -98926464, 0, 319692704, 0, 0, 563017500, -69328572, 0, 0, -228300924, 0, -270550615, -734875200, 0, 423256056, 381752280, 0, 771523402, 0, 0, -32141312, -194655588, 0, 0, 56297920, 0, 492258600, 142192800, 0, -513774408, 207037244, 0, 381559424, 0, 0, -257719535, 27704832, 0, 0, -102110522, 0, -154588772, -57865960, 0, -3667584, 407348740, 0, -379494675, 0, 0, -47107824, -77819250, 0, 0, -523604700, 0, -169137920, -37833404, 0, 305943040, -623405184, 0, 63134848, 0, 0, 238215317, -470366132, 0, 0, 558019864, 0, -15115419, -92998432, 0, -441373800, -478199700, 0, -385247893, 0, 0, -108889760, -675882226, 0, 0, -483524608, 0, -68995320, -718907796, 0, -299986875, -11652816, 0, -823303296, 0, 0, 144839688, 340718400, 0, 0, 24212182, 0, -20116977, 374643532, 0, 120501296, 744576852, 0, 555510600, 0, 0, -1025632304, 109217930, 0, 0, -422088928, 0, -334725120, 909121500, 0, -97065339, 99180000, 0, -257095648, 0, 0, -39578347, 441251140, 0, 0, -104903644, 0, -443605725, 127121920, 0, -171125976, 1156786526, 0, -315292727, 0, 0, -17021952, 3929928, 0, 0, -138596448, 0, 104008376, 579099826, 0, -35543547, -76265952, 0, -410241600, 0, 0, 197288233, -372813696, 0, 0, 174974332, 0, 317299136, -288534052, 0, -26973440, 352804680, 0, -202570141, 0, 0, 371744856, -280159388, 0, 0, 462059580, 0, -47111024, 26698888, 0, -776242880, 706176000, 0, 259938600, 0, 0, -665136389, -367908496, 0, 0, 103648800, 0, 977550000, 15747808, 0, -285528600, -808613946, 0, 717590808, 0, 0, -307780064, 395424900, 0, 0, -392033088, 0, 9837424, 555088634, 0, -95018916, -278280404, 0, -140083200, 0, 0, 638879850, -220173408, 0, 0, -689674040, 0, 173159198, -397219500, 0, 422254784, -611668768, 0, -318666236, 0, 0, 70787032, 521313520, 0, 0, 5834032, 0, 247968000, 781553460, 0, -52916989, -184256, 0, 205530528, 0, 0, -599133327, 314458488, 0, 0, 145414304, 0, -29560909, -154813632, 0, -416597296, -864014392, 0, -1309331506, 0, 0, -97549312, -238271600, 0, 0, 69163200, 0, 483572856, 423767594, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "75.6.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [-4], [0], [-16], [0], [0], [-225], [192], [0], [0], [434], [0], [613], [900], [0], [-256], [878], [0], [-731], [0], [0], [-1736], [-2850], [0], [0], [-2452], [0], [3600], [7582], [0], [2175], [-5120], [0], [-3512], [0], [0], [-9310], [2924], [0], [0], [12040], [0], [-1121], [-6944], [0], [11400], [-29878], [0], [33818], [0], [0], [-9808], [-5740], [0], [0], [-43200], [0], [-30328], [5174], [0], [-38717], [-8700], [0], [28672], [0], [0], [31707], [-14048], [0], [0], [-64472], [0], [-19790], [37240], [0], [11696], [-97650], [0], [-105000], [0], [0], [-48160], [3318], [0], [0], [4484], [0], [83328], [65376], [0], [-137925], [45600], [0], [119512], [0], [0], [-89143], [-135272], [0], [0]]}