# Stored data for newform 2166.4.a.u, downloaded from the LMFDB on 24 April 2024. {"label": "2166.4.a.u", "space_label": "2166.4.a", "level": 2166, "weight": 4, "hecke_orbit": 21, "hecke_orbit_code": 90071992614520950, "dim": 3, "is_polredabs": true, "nf_label": "3.3.14457.1", "trace_hash": 2274781656041691887, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[5, [504, -96, -10, 1]], [13, [-37685, -4629, 9, 1]]], "qexp_display": "q+2q^{2}-3q^{3}+4q^{4}+(3-\\beta _{1})q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 34656, "fricke_eigenval": -1, "atkin_lehner_string": "-++", "analytic_conductor": 127.79813707243417, "hecke_ring_index": 24, "level_radical": 114, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [2166, 1, [1445, 1807], [1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3, 19], "conrey_indexes": [1], "field_disc": 14457, "field_disc_factorization": [[3, 1], [61, 1], [79, 1]], "field_poly": [-3, -32, -1, 1], "hecke_ring_index_factorization": [[2, 3], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.928", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "23.276", "prec": 20}, {"__RealLiteral__": 0, "data": "1.573", "prec": 17}, {"__RealLiteral__": 0, "data": "284.333", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, 1], [19, 1]], "trace_display": [6, -9, 10, 7], "traces": [0, 3, 6, -9, 12, 10, -18, 7, 24, 27, 20, -44, -36, -9, 14, -30, 48, -84, 54, 0, 40, -21, -88, -2, -72, -83, -18, -81, 28, 92, -60, -109, 96, 132, -168, 282, 108, 245, 0, 27, 80, -688, -42, -103, -176, 90, -4, 322, -144, -754, -166, 252, -36, -1322, -162, -248, 56, 0, 184, 252, -120, -435, -218, 63, 192, -1582, 264, -719, -336, 6, 564, -62, 216, -581, 490, 249, 0, -204, 54, -489, 160, 243, -1376, 2496, -84, 1632, -206, -276, -352, 1584, 180, -1573, -8, 327, 644, 0, -288, 974, -1508, -396, -332, -974, 504, -2705, -72, -846, -2644, -1586, -324, -1442, -496, -735, 112, -392, 0, -2132, 368, -81, 504, 1716, -240, 7423, -870, 2064, -436, -132, 126, 52, 384, 309, -3164, 606, 528, 0, -1438, -270, -672, -1054, 12, -5657, 1128, -966, -124, 740, 432, -3472, -1162, 2262, 980, -1440, 498, -4128, 0, -756, -408, -6470, 108, -1591, -978, 3966, 320, -2130, 486, 693, -2752, 744, 4992, -3156, -168, 2748, 3264, 0, -412, -924, -552, 1201, -704, -756, 3168, -6450, 360, 6578, -3146, 1305, -16, 5518, 654, -10248, 1288, -189, 0, -4402, -576, 985, 1948, 4746, -3016, 8344, -792, -2313, -664, 2157, -1948, -3564, 1008, -7264, -5410, -18, -144, 0, -1692, -209, -5288, 186, -3172, -5978, -648, -6361, -2884, 1743, -992, -11220, -1470, 1299, 224, -747, -784, -7150, 0, -6873, -4264, 612, 736, -3114, -162, 3052, 1008, 1467, 3432, 4386, -480, -2593, 14846, -729, -1740, -1636, 4128, 0, -872, -7488, -264, 2962, 252, -20600, 104, -4896, 768, 1090, 618, 5273, -6328, 828, 1212, -1818, 1056, -9164, 0, -4752, -2876, 648, -540, -8296, -1344, 4719, -2108, -10060, 24, 8930, -11314, -981, 2256, -2470, -1932, -1124, -248, 0, 1480, -6576, 864, 12477, -6944, -2922, -2324, -19398, 4524, 3168, 1960, 1188, -2880, 12758, 996, -5875, -8256, 2922, 0, 6422, -1512, 13372, -816, 8115, -12940, 8240, 216, -642, -3182, 2538, -1956, -9414, 7932, -10600, 640, 4758, -4260, 0, 972, -8119, 1386, 4326, -5504, 2730, 1488, -16479, 9984, 2205, -6312, 606, -336, 6947, 5496, 1176, 6528, -6740, 0, -3283, -824, 6396, -1848, -12934, -1104, 8225, 2402, 243, -1408, 2394, -1512, -6236, 6336, -5148, -12900, 6588, 720, 0, 13156, -22269, -6292, 14730, 2610, -29083, -32, -6192, 11036, -7842, 1308, 17478, -20496, 396, 2576, 22396, -378, -22031, 0, -156, -8804, 1268, -1152, -15312, 1970, -927, 3896, -6414, 9492, 5808, -6032, -1818, 16688, 6434, -1584, 5997, -4626, 0, -1328, -13300, 4314, 36967, -3896, 810, -7128, -37628, 2016, 8114, -14528, 3162, -10820, 2916, -36, -744, -288, 16971, 0, 23964, -3384, 8418, -418, 2898, -10576, 23364, 372, 6857, -6344, -2220, -11956, -21738, -1296, -6999, -12722, 10416, -5768, 0, 3486, -15303, -1984, -6786, -22440, 3476, -2940, -2400, 2598, 4320, 448, -6832, -1494, -9424, -1568, 12384, -14300, -7662, 0, -23157, -13746, 2268, -8528, 2644, 1224, -7819, 1472, 19410, -6228, -8404, -324, 1325, 6104, 4773, 2016, 25180, 2934, 0, 6864, -11898, 8772, 22322, -960, -28943, -5186, 6390, 29692, 6508, -1458, 34076, -3480, -2079, -3272, 15730, 8256, -19776, 0, -2232, -1744, -6174, -14976, 4223, -528, 9468, 5924, -31044, 504, 196, -41200, -8244, 208, 12174, -9792, 15311, 1536, 0, 2180, -17958, 1236, 58888, 10546, 2772, -12656, -21224, 1656, -11517, 2424, -3603, -3636, -31356, 2112, 23887, -18328, 2268, 0, 31888, -9504, -404, -5752, 19350, 1296, -16, -1080, -3525, -16592, -19734, -2688, -4356, 9438, -36043, -4216, -3915, -20120, 0, 48, 6923, 17860, -16554, -22628, 17498, -1962, 34117, 4512, 30744, -4940, 7770, -3864, -15152, -2248, 567, -496, 6428, 0, -32769, 2960, 13206, -13152, 10058, 1728, 12210, 24954, -2955, -13888, -3240, -5844, 31984, -4648, -14238, -38796, 55176, 9048, 0, 6336, -25032, 3920, 8108, 2376, 11232, -5760, 6939, 25516, 14124, 1992, 21269, -11750, -6471, -16512, 49754, 5844, -44025, 0, 10692, 12844, -12838, -3024, -9418, 26744, 21792, -1632, -10776, 16230, 7343, -25880, 54, 16480, -3984, 432, -15953, -1284, 0, -6364, 60084, 5076, 37311, -3912, 627, -18828, -13752, 15864, -3002, -21200, -558, 1280, -37398, 9516, -4921, -8520, 17934, 0, 57748, 1944, -4608, -16238, 19083, 2772, 19050, 8652, -5988, -11008, -5229, 5460, 9580, 2976, -3922, -32958, 33660, 19968, 0, 4410, 52448, -12624, -3897, 1212, 46220, -672, 43425, 13894, 2241, 10992, 20342, 2352, 5534, 13056, 21450, -13480, 33746, 0, -51916, -6566, 20619, -1648, 32510, 12792, 700, -3696, -1836, -25868, -11718, -2208, 3984, 16450, 9342, 4804, -23078, 486, 0, -2816, -9156, 4788, 1170, -3024, 3799, -12472, -4401, 12672, 71710, -10296, 89144, -25800, -13158, 13176, -18142, 1440, -15253, 0, 7779, 26312, -12188, -44538, -25513, -12584, 2187, 29460, -60228, 5220, 17866, -58166, 4908, -64, 20100, -12384, -38415, 22072, 0, -15684, 32776, 2616, 57000, 34956, 22464, -40992, 1182, 792, -42393, 5152, -8886, 44792, 12896, -756, 20003, -44062, 61800, 0, 39000, -312, -2914, -17608, 14688, 2536, -14724, -2304, -16591, -30624, -3270, 3940, 25782, -1854, -19179, 7792, -15819, -12828, 0, 18984, 121312, 11616, -2484, -12064, 24790, -3636, 7847, 33376, 5454, 12868, -14760, -3168, -45927, 11994, 27492, -9252, 43470, 0, -58776, -2656, 14256, -26600, 44916, 8628, 11940, 73934, -1944, -7792, 25050, 1620, 85528, -14256, 24888, -75256, 36374, 4032, 0, 16228, -14157, -29056, -64236, 6324, -15096, -21640, 30180, 5832, 11824, -72, 61735, -1488, -26790, -576, 38328, 33942, 17520, 0, 2943, 47928, -28214, -6768, -4415, 16836, 7410, -836, 6600, 5796, 42331, -21152, 3372, 46728, 25594, 744, -60731, 13714, 0, -12688, 52158, -4440, 25973, -23912, 19728, -43476, 15426, -2592, -20400, -13998, -37431, -25444, -28180, 20832, -15859, -11536, 8766, 0, -26196, 6972, -31903, -30606, 58194, -3968, -15390, -13572, -67351, -44880, -9504, 6952, 31064, -5880, -13804, -4800, -3564, 5196, 0, 8640, 42012, 896, -38274, -13664, 96596, -2988, -8880, -18848, 17625, -3136, 15604, 24768, -62148, -28600, -8766, -15324, 58008, 0, -86712, -46314, -19266, -27492, -6594, 4536, -136923, -17056, -40116, 5288, 36362, 2448, 50763, -15638, -24345, 2944, -22502, 38820, 0, -12456, -24720, -16808, -155616, -648, -33075, 2650, 1926, 12208, 30392, 9546, 84224, 4032, -7614, 50360, 5118, 5868, -98257, 0, 28242, 13728, -11156, -23796, -23500, 17544, 31800, 44644, -50862, -1920, 69486, -57886, -14274, -10372, 42486, 12780, -53051, 59384, 0, 13016, -22202, -2916, -6061, 68152, 24357, -6960, -8546, -4158, -138264, -6544, -12978, 31460, -72072, 16512, 49936, -39552, -8190, 0, 3442, -4464, -56875, -3488, 49437, -12348, -64222, -29952, 11789, 8446, -6615, -1056, 88404, 18936, 10152, 11848, -1818, -62088, 0, 1008, 78782, 392, -20841, -82400, 33888, -16488, 2784, 416, -3528, 24348, 86268, -19584, -56967, 30622, 20220, 3072, 13696, 0, -46917, 4360, 9849, -35916, 67974, 2472, 9651, 117776, -19188, 21092, 27444, 5544, 84151, -25312, 38802, -42448, 58440, 3312, 0, -23034, -24675, 4848, -165510, -7206, 27249, -7272, -729, -62712, 42234, 4224, 17024, 47774, -7182, -36656, 82302, 4536, -31657, 0, 18708, 63776, -4832, -19008, -75483, -808, 15444, -11504, -28972, 38700, -48993, 2592, -19764, -32, 46896, -2160, -145244, -7050, 0, -33184, -26334, -39468, 2180, -5376, 66807, -8712, -13504, 18876, -2149, -72086, -44190, -8432, 58262, -7830, 26381, -40240, 87249, 0, -69582, 96, -49440, 13846, 18576, 35720, 44970, -33108, -105104, -45256, 23526, 34996, 66890, -3924, 20370, 68234, -52434, 9024, 0, 61488, 67193, -9880, -1188, 15540, 14756, -7728, 94782, -30304, -67188, -4496, 86100, 1134, -89908, -992, 66093, 12856, 31596, 0, 35681, -65538, 468, 5920, 1538, 26412, -87699, -26304, -3804, 20116, -24792, 3456, 62411, 24420, 45936, 49908, 41328, -5910, 0, -27776, 2781, -6480, -55052, -11688, -66276, 63968, 19242, -9296, 20676, -28476, -5467, -77592, -17424, 110352, -62626, 18096, -139616, 0, 5454, 12672, 75402, -50064, 3852, 7840, -19302, 16216, 58394, 4752, 72976, 22464, -17991, -11520, 70272, 13878, 20364, 51032, 0, 28248, -54144, 3984, 17178, 42538, 39900, -23500, 4114, -12942, -160872, -33024, -110901, 99508, -19476, 11688, 5419, -88050, -2430, 0, 22216, 21384, 18508, 25688, 112884, -25676, -44958, -6048, 36322, -18836, -24342, 53488, 30168, 43584, -79192, -3264, -9486, -21552, 0, 32460, 55295, 14686, -8748, -51760, 96540, 108, 107752, 32960, 2232, -7968, 57692, 864, 2691, -31906, -50913, -2568, 48462, 0, 79660, -12728, -71892, 120168, -2174, 10152, -22490, 74622, -25254, -7824, 13912, 1254, 9026, -37656, -8694, -27504, 163808, 31728, 0, -6004, -70092, -42400, -52436, -1116, -39588, 2560, -20571, -74796, 3900, 19032, -98948, -9842, 6660, -17040, 90276, 35868, -35349, 0, 65214, 115496, 75870, 3888, -87615, -9216, 20997, -32476, 82558, 38166, -132491, 5544, -31248, 38100, -28248, 17304, -145368, -11976, 0, -22016, -17734, -10458, 64332, 10920, 45909, 19160, -3270, 5952, -22043, -7844, 20358, -65916, 194, 67320, -195656, 39936, -10428, 0, 57936, 8820, 115305, 104896, 7200, -25248, -19098, -7794, 61763, 2424, -12960, 92440, 105492, -1344, -51264, 86850, 20496, 27788, 0, 4482, 41501, 21984, 28272, 40684, -16496, 4704, -19296, 11068, -37152, 26112, 74898, 42900, -83416, -26960, 22986, 67492, 75512, 0, 50076, -103832, 69471, -13132, 87888, 41238, -95232, -3296, -6804, 65020, 41592, 25584, -76517, 1400, -7932, -7392, 2404, -3672, 0, -51736, 23457, -23436, -24538, -4416, -61909, 7968, -58230, 32900, 219312, 18684, -107571, 9608, 25212, -46156, -150238, 972, -119500, 0, -3975, -5632, 43306, -18312, -83232, 9576, -14319, 2340, 89544, -6048, 1622, 7598, -75540, -24944, -25208, -8802, 6303, 25344, 0, 143420, 29224, -20592, 78397, 178288, 35694, -51600, 12490, -26316, -65040, 26352, -66966, -36284, 90420, 2880, 47904, -30506, 86829, 0, 88822, 15558, 11664, 52624, -19170, -24376, -74508, -89076, 13891, -51026, -19524, -25168, -122798, 4374, 26361, 58920, -102228, -120456, 0, 10440, -14772, 35732, 6237, -116332, 84248, 9816, 45256, -128, -47190, 40200, 5580, -24768, 42443, -76830, 59328, 44144, 37808, 0, -83676, -31368, 6696, 65552, 13680, 5232, 31195, 114000, 18522, 69912, 38488, 44928, -95092, -81984, -12669, 2364, 87880, 1584, 0, -84786, -28404, 10304, -55890, -17772, -126544, 89584, 93132, 25792, 173526, -1512, 16920, 40006, -588, -88124, -82144, 123600, 17414, 0, 24732, 78000, 162638, -624, 11555, -5828, -36522, -35216, 337716, 29376, -121816, 5072, -45933, -29448, -42768, -4608, 18224, -33182, 0, -61248, -45654, -6540, 215435, 7880, 53874, 51564, -38220, -3708, 11301, -38358, -176664, 15584, 106560, -31638, -11800, -25656, -8316, 0, -82296, 37968, 65591, 242624, 63672, 23232, 119180, -4968, -42112, -24128, 34551, 49580, -143540, -7272, -172333, 15694, 10809, 66752, 0, 10908, -9729, 25736, 94068, -29520, -139860, -6336, 24276, -91854, -71661, 23988, -82758, 54984, -175209, -18504, -6804, 86940, 153968, 0, 38663, -117552, -95664, -5312, -153206, 28512, 8411, -53200, 1212, 89832, 50272, 17256, -310146, 23880, -58050, 147868, 119200, -3888, 0, -15584, 48, 50100, -27736, 3240, 104815, 171056, 10575, -28512, 155724, 49776, -77145, -150512, 59202, 72748, -63162, 8064, -186500, 0, 13068, 32456, -84960, -28314, -110400, -58112, 108129, -128472, 149614, 12648, -25428, -30192, 11745, -43280, -13896, 60360, 83396, 11664, 0, 23648, -79594, -144, 91673, 123470, -20769, -2976, -143056, -53580, -9553, -1152, 49662, 76656, 117840, 67884, -113933, 35040, -52494, 0, 15978, 5886, 25351, 95856, -102351, -56428, -222402, -13536, 89461, -8830, -92232, 33672, -159182, 14820, 6707, -1672, -23310, 13200, 0, 11592, -111659, 84662, 45456, -42304, -157080, 6744, 158861, 93456, -1701, 51188, 46230, 1488, 303184, -121462, -19284, 27428, -120720, 0, -26280, -25376, 98307, 104316, -153018, -8880, 170760, 51946, -39618, -47824, 103704, 39456, 18387, -86952, -30174, 30852, 193972, -5184, 0, -40800, -36630, -27996, -84660, -74862, -78820, -50888, 8865, -56360, -130898, 41664, -209219, -31718, 9720, -23072, -40610, 17532, -79696, 0, -95952, -52392, -33276, 13944, -70874, -63806, 42714, -61212, 76698, 116388, -112464, -7936, -165528, -30780, 88976, -27144, -81132, -134702, 0, -89760, -171260, -19008, 34512, 13904, 75096, 62128, -148834, -11760, 174987, -27608, -24324, -9600, 293578, -7128, -71105, 10392, -33696, 0, -62670, 17280, -132427, 84024, -20817, 1792, 94532, -76548, -43992, -27328, -42372, 193192, -100038, -5976, 28301, -17760, -63807, -37696, 0, 35250, -25861, -6272, 19413, 31208, -97890, 49536, -13438, -124296, -149262, -57200, -1546, -17532, 241464, -30648, 132075, 116016, 165282, 0, 63013, -173424, -32076, -92628, -64116, -38532, 101288, -54984, 38514, -13188, -157034, 9072, -222240, -273846, 28254, -34112, 66150, -80232, 0, 10576, -65376, 72724, 235062, 4896, -69318, 101526, 32328, -31276, 118824, -48690, -155892, 5888, -22029, -45004, -425616, 77640, 146197, 0, -162, -24912, -100516, -49440, -133240, -33616, 11952, -311232, -2184, -1296, 29383, -66150, 47859, 5300, 87270, 3852, -8143, 24416, 0, 60784, -51912, 19092, -54896, 168448, -180252, 8064, 23674, -15228, -212963, 100720, -111933, 10236, 103686, 11736, -8200, -196514, -1881, 0, 163854, 56484, 73992, 27456, 41256, -22312, 55134, -47592, 180120, -47000, 9006, 35088, 129486, 63600, 190856, 89288, 1674, -101724, 0, -3840, -187944, 138972, 112194, -115772, -116172, -28548, -240640, -20744, 14763, 84972, -113066, 25560, 131781, -106102, -53802, 118768, -366480, 0, -6526, 26032, -173244, -44404, -76644, -5832, 27612, -12122, 13824, 136304, -88940, 48714, -116232, -13920, -57249, -17092, 195456, -8316, 0, -276528, -57150, -13088, -226622, -25956, -147552, 62920, 17964, -144144, -117030, 33024, -273672, 99872, 15687, -79104, 49216, -16380, 89201, 0, -28740, 6884, 102236, -8928, 90668, -113750, 11766, -6976, 87590, 98874, 41929, -24696, -100980, -128444, 109888, -59904, -150094, 23578, 0, 16892, 80638, -13230, -135115, -2112, -157344, 176808, -222650, 37872, 32408, 20304, 11691, 23696, 177520, -3636, -57317, -124176, -138660, 0, 86834, 2016, -281277, 157564, -130275, 784, 74614, -41682, 76345, -164800, -6723, 67776, 141270, -32976, -92085, 5568, -61026, 832, 0, -7056, -449000, 48696, -16602, 172536, -343902, -39168, -175787, -113934, -64350, 61244, 167908, 40440, 298128, 6144, -101238, 27392, 4626, 0, 27945, -93834, 155748, 8720, -141012, 19698, -31864, -71832, -61857, 135948, 141362, 4944, 33912, 19302, -97530, 235552, -287796, -38376, 0, 42184, -2100, 54888, -64272, 11088, -55495, 168302, 5508, -50624, 209210, 77604, -98993, -84896, 35154, 116880, -208062, 6624, 23698, 0, -11952, -46068, -107850, -49350, 187848, 9696, -28026, -331020, -95664, -14412, -92944, 54498, 69234, -14544, 99188, -1458, -14686, -125424, 0, 84468, -16402, 8448, 10635, 34048, 27468, 95548, -304212, -14364, -206463, -73312, -3510, 164604, 174084, 9072, -80352, -63314, -11397, 0, 124652, 37416, 36035, 127552, 13203, -9664, -49242, -38016, -149303, -150966, -215130, -1616, -218880, 30888, -99645, -23008, -267432, -57944, 0, 77400, -56140, -97986, 39474, 5184, -249738, -39528, 51252, -64, 54426, 93792, -319008, -4320, 358483, -290488, 45759, -14100, -147706, 0, -227624, -66368, -23337, -52668, -158772, -78936, 373136, 4360, 36564, -10752, -20040, 133614, 150611, -17424, 76539, -27008, 62892, 37752, 0, -4298, -6561, -144172, -40516, -88380, 119822, -16864, 180684, 116524, 108134, -15660, 26889, 52762, -53598, -80480, 26554, 174498, 399743, 0, -14724, -139164, -296644, 192, 124543, -98880, -60300, 27692, 150316, 37152, -21328, 71440, 115245, 89940, 33690, -66216, -138901, -210208, 0, -90512, 32808, 47052, -129816, 69992, -98328, 133780, -48908, -7848, 164568, 40740, -171000, 136468, 171468, -104868, -56196, 18048, -67392, 0, -243370, 122976, 111704, 134386, -3546, -19760, 106692, -2376, -173204, 31080, 127179, 29512, 232688, -15456, -21221, 189564, 26658, -60608, 0, -134376, -415285, -8992, -38688, 172200, -120518, 2268, 109921, -179816, -60009, -1984, 216498, 132186, -33907, 25712, -185400, 63192, 170482, 0, 188091, 71362, -117000, -131076, -263614, 936, -207841, 11840, 8742, 3076, -100604, 52824, -297538, -175398, -44064, -52608, 8238, -7608, 0, 40232, 44172, -49584, -138604, 6912, -20456, 124822, 49773, 48840, -7020, 91872, -282900, 99816, 9810, 82656, -93026, -11820, -63115, 0, -77346, -55552, -314220, 5562, 208444, -12960, 57537, -110104, -361722, -23376, -167304, -132552, 47457, 127936, -163688, 38484, 135464, -18592, 0, 41352, 388910, -56952, -130406, -10934, -363936, -155184, -65130, -34848, -143372, 220704, 7452, -125252, 25642, 36192, 18202, -279232, -74370, 0, 172050, 10908, -166129, 25344, -23541, 150804, -46380, -100128, 436768, 7704, -16362, 15680, -10578, -38604, 395051, 32432, 44280, 116788, 0, 9504, 141867, 145952, 137781, 44928, 290104, -35982, -220784, -23040, -82476, 140544, 309924, 27756, 262062, 40728, -130410, 102064, -371662, 0, -46012, 56496, 176328, -108288, -338000, 7968, 108887, 34356, -42768, 85076, -394522, 79800, 262608, -47000, -134748, 8228, 105858, -25884, 0, -321744, -35820, -66048, -197596, -221802, -102528, 199016, 5832, -38952, -42276, 23376, -20094, 10838, -75150, -176100, -65886, -4860, 759480, 0, -256584, 44432, 281080, 42768, -7414, 37016, -74664, 51376, -225890, 225768, -48835, -51352, -109122, -89916, 246660, -12096, -140417, 72644, 0, -37672, 289100, -48684, -155564, 106976, 42471, 60336, 143548, 87168, 282868, -158384, 192708, -6528, 70368, -18972, -102204, -43104, 45288, 0, -83526, 64920, -156426, 110590, -90540, 29372, 26148, -17496, -36337, -103520, -35472, 193080, 66166, 216, -150348, 215504, -185205, 65920, 0, 4464, -113900, -15936, 80370, 115384, 57346, 1728, 334640, 5382, -114984, -63812, -137360, -101826, -357401, -5136, -52560, 96924, 147492, 0, -238171, 159320, -8829, -25456, -50580, -143784, 62736, 240336, 84642, -4348, 241460, 20304, -429979, -44980, 13245, 149244, 163550, -50508, 0, -15648, -22230, 27824, -53766, 2508, 604440, 18052, -19800, -75312, -59364, -17388, -404765, -55008, -126993, 327616, -237008, 63456, 229332, 0, -10116, -12008, -270166, -140184, 650433, -84800, -76782, -104872, -24342, -2232, 95907, -79176, 182193, 5120, -157768, -41142, 207072, -149592, 0, 7800, 505776, 38064, -127951, -197896, -156474, -19684, 176952, 13320, -16295, -34080, -77919, 180552, -163490, 71736, 278808, -70698, -59184, 0, 182608, 130428, 346011, 230992, -46278, 151740, -289232, 7776, 144978, -175230, 61200, -18432, 305396, 41994, -79136, -64952, 112293, 165116, 0, 76332, 43864, -264982, 84540, 11088, 327966, -62496, -117994, 76200, 47577, -56496, -340630, 34608, -71525, -290736, -26298, -23952, -104622, 0, -70697, -44032, 78588, -35468, -468770, -20916, 201696, 128664, 95709, 21840, 263374, 91818, -105792, 38320, -174582, -6540, -77292, 11904, 0, -44086, 46170, -15688, -237766, 40716, 82448, -131832, 202053, 388, -331820, 134640, 125717, -391312, 28512, 79872, -18582, -20856, 289177, 0, -93192, 115872, 51586, 17640, 310336, 230610, 41412, 209792, 84564, 14400, 43445, -50496, 10692, -38196, 231170, -15588, -39574, 123526, 0, 4848, 189588, -25920, -198484, 184880, -126036, 210984, 48062, -2688, -56577, -102528, 114822, 173700, -439754, 40992, -41296, 55576, -289788, 0, -80502, 8964, 126701, 83002, 26640, 43968, -260110, 56544, 206651, 81368, -52875, -32992, -13614, 9408, 173718, -38592, -46812, 22136, 0, -74304, -198517, 52224, 186444, 149796, 34026, 85800, 117442, -166832, 26298, -53920, -29270, 45972, -348961, 134984, -174024, 151024, -44690, 0, 189648, 100152, 260136, -207664, -75300, 138942, -256957, -26264, 57798, 175776, 85728, 82476, -12459, -190464, 19782, -6592, -386170, -13608, 0, 130040, 410769, 83184, 241800, 51168, 701848, -153034, 120348, 2800, 21642, -15864, -128480, -14784, -109086, 4808, 114348, -7344, 44856, 0, -152289, -103472, -136894, 46914, 81593, -46872, 73035, -49076, -446530, -8832, 509876, -123818, 67506, 15936, -348966, -116460, 392277, 65800, 0, 438624, 269582, 37368, -314341, -215142, 74160, 19216, -215006, 50424, -139372, -92312, 466848, -300476, 45708, 1944, 234157, -239000, 99225, 0, -28504, -7950, -168060, -11264, -5778, 86612, -428576, -36624, 49867, -166464, -91176, 19152, -160384, -28638, 313936, 4680, -252672, 179088, 0, -12096, -105499, 3244, 22842, 15196, 155898, -151080, 553176, -49888, -15354, -50416, 175718, -17604, -136696, 12606, 294771, 50688, -411372, 0, 192201, 286840, -84726, 58448, 226274, -41184, -80338, 156794, 33468, 356576, -99732, 71388, 159794, -103200, 70500, 24980, 271070, -52632, 0, -130080, -95400, 52704, 290448, -133932, 427416, -72568, 152586, 180840, 63306, 5760, -19261, 95808, -208458, -61012, 200756, 173658, 352044, 0, 42822, 177644, -55440, 31116, 954144, 23328, -127458, 105248, 338556, -38340, -379257, -48752, 159153, -149016, 10526, -178152, 248472, 27782, 0, -102052, 597018, -39048, -106000, -50336, 66606, -245596, 433912, 8748, 435897, 52722, 18183, 117840, -314856, -204456, 203209, -240912, -73071, 0, 226264, 20880, 37880, -29544, 25638, 71464, 163884, 12474, 121704, -232664, 414792, 168496, 64556, 19632, -155808, 90512, 38934, -256, 0, -94380, 90770, 80400, 216216, 11160, 417898, -49536, 39473, 84886, -149808, -153660, 477972, 118656, -686088, 88288, 24570, 75616, -43088, 0, 480920, -167352, -10326, -62736, 16154, 13392, 163587, 131104, 170625, 27360, 100284, 10464, -126069, 62390, -148311, 228000, 31456, 37044, 0, 139824, 192666, 76976, 4740, 89856, 93106, -190184, -35367, -163968, -272880, -25338, 211848, 4728, 19845, 175760, -32354, 3168], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "114.4.e.d", "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, 0, 0], [1, 0, 0], [2, 0, 0], [-3, 0, 0], [4, 0, 0], [3, -1, 0], [-6, 0, 0], [2, -1, 0], [8, 0, 0], [9, 0, 0], [6, -2, 0], [-15, 0, -1], [-12, 0, 0], [-1, 6, 0], [4, -2, 0], [-9, 3, 0], [16, 0, 0], [-30, -7, 1], [18, 0, 0], [0, 0, 0], [12, -4, 0], [-6, 3, 0], [-30, 0, -2], [3, 9, 2], [-24, 0, 0], [-29, -5, 1], [-2, 12, 0], [-27, 0, 0], [8, -4, 0], [36, 15, 1], [-18, 6, 0], [-28, 24, 1], [32, 0, 0], [45, 0, 3], [-60, -14, 2], [93, -4, 1], [36, 0, 0], [77, -17, 3], [0, 0, 0], [3, -18, 0], [24, -8, 0], [-222, 20, 2], [-12, 6, 0], [-28, 21, -2], [-60, 0, -4], [27, -9, 0], [6, 18, 4], [102, -10, -6], [-48, 0, 0], [-252, -3, 1], [-58, -10, 2], [90, 21, -3], [-4, 24, 0], [-435, 18, -1], [-54, 0, 0], [-66, 55, -5], [16, -8, 0], [0, 0, 0], [72, 30, 2], [81, -9, 0], [-36, 12, 0], [-157, -32, -4], [-56, 48, 2], [18, -9, 0], [64, 0, 0], [-525, 13, -6], [90, 0, 6], [-244, -12, -1], [-120, -28, 4], [-9, -27, -6], [186, -8, 2], [-18, 19, -11], [72, 0, 0], [-217, -66, -4], [154, -34, 6], [87, 15, -3], [0, 0, 0], [-51, 55, -4], [6, -36, 0], [-172, -30, 3], [48, -16, 0], [81, 0, 0], [-444, 40, 4], [846, 37, 5], [-24, 12, 0], [540, -24, 12], [-56, 42, -4], [-108, -45, -3], [-120, 0, -8], [543, 34, 11], [54, -18, 0], [-524, 7, -6], [12, 36, 8], [84, -72, -3], [204, -20, -12], [0, 0, 0], [-96, 0, 0], [320, -13, -1], [-504, -6, 2], [-135, 0, -9], [-116, -20, 4]]}