# Stored data for newform 1150.4.a.n, downloaded from the LMFDB on 28 July 2026.
{"Nk2": 18400, "analytic_conductor": 67.8521965066017, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [5, 1], [23, -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": [1150, 1, [277, 51], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 4, "field_disc": 18982541, "field_disc_factorization": [[547, 1], [34703, 1]], "field_poly": [108, -45, -60, -2, 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": [[3, [-904, -365, 12, 14, 1]], [7, [-9114, -4865, -592, 8, 1]]], "hecke_orbit": 14, "hecke_orbit_code": 58546795222926462, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 3, "hecke_ring_index_factorization": [[3, 1]], "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": "1150.4.a.n", "level": 1150, "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": [2, 5, 23], "level_radical": 230, "minimal_twist": "230.4.a.j", "prim_orbit_index": 1, "qexp_display": "q-2q^{2}+(-4+\\beta _{1})q^{3}+4q^{4}+(8-2\\beta _{1}+\\cdots)q^{6}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1150.4.a", "trace_display": [-8, -14, 0, -8], "trace_hash": 2198227286922800880, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.817", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "40.172", "prec": 20}, {"__RealLiteral__": 0, "data": "0.145", "prec": 17}, {"__RealLiteral__": 0, "data": "667.648", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 4, -8, -14, 16, 0, 28, -8, -32, 64, 0, 21, -56, -70, 16, 0, 64, -56, -128, 173, 0, -120, -42, 92, 112, 0, 140, -389, -32, -118, 0, 17, -128, 89, 112, 0, 256, 343, -346, -221, 0, 139, 240, 50, 84, 0, -184, -367, -224, -124, 0, 439, -280, 353, 778, 0, 64, 238, 236, -453, 0, -327, -34, 1723, 256, 0, -178, 455, -224, -322, 0, 195, -512, 633, -686, 0, 692, 2, 442, -1140, 0, 1456, -278, 1199, -480, 0, -100, 1775, -168, -2170, 0, 557, 368, 3241, 734, 0, 448, 703, 248, -2745, 0, 1095, -878, -301, 560, 0, -706, -983, -1556, -2275, 0, -1956, -128, 1049, -476, 0, -472, -544, 906, -2911, 0, 327, 654, 3548, 68, 0, -3446, -3277, -512, -6450, 0, 47, 356, 1705, -910, 0, 448, -2343, 644, -1530, 0, 3769, -390, 1620, 1024, 0, -1266, -4841, 1372, -6607, 0, 6716, -1384, -1118, -4, 0, -884, -5103, 2280, -5588, 0, -184, -2912, -1558, 556, 0, -2398, -7172, 960, -4460, 0, 6482, 200, 3159, -3550, 0, 336, -8070, 4340, 2719, 0, 4045, -1114, -4249, -736, 0, -6482, -8501, -1468, -14541, 0, 2788, -896, -5481, -1406, 0, -496, -10730, 5490, 5270, 0, -7476, -2190, -7391, 1756, 0, 602, 1472, -1120, -5188, 0, 3921, 1412, -9874, 1966, 0, 3112, -10760, 4550, 3825, 0, -3522, 3912, -5698, 256, 0, -2098, -11648, 952, -1590, 0, 1493, 944, -7607, 1088, 0, -1812, -6848, 5822, -472, 0, -1892, -654, -17702, -1308, 0, -7096, -10595, -136, -5442, 0, -1257, 6892, 483, 6554, 0, 1024, -4943, 12900, 17469, 0, -21295, -94, -1694, -712, 0, -3410, -3762, 1820, -9128, 0, 5272, -896, 469, 4686, 0, -1288, 3423, 3060, -11431, 0, -20302, -7538, -11221, 780, 0, -3240, 1191, -2048, 548, 0, -769, 2532, 4881, 9682, 0, -2744, 15833, 13214, -1610, 0, -1460, -13432, -2442, 2768, 0, 2236, 3799, 8, -7099, 0, -11377, 1768, -3358, 10206, 0, -4560, 10267, 11176, 12998, 0, -19972, 368, 3162, 5824, 0, 3116, 26486, -1112, -20220, 0, 7432, 4796, 27103, 14344, 0, -1920, 1523, 8920, -584, 0, -18172, -12964, 5363, -400, 0, -6318, 12339, 7100, -1896, 0, 10918, -672, 15025, 16140, 0, -8680, 22091, -5438, -8240, 0, 6611, -8090, -1946, 2228, 0, 8498, -2871, 1472, -22898, 0, 6639, 12964, 11730, 17002, 0, 2936, 4311, 29082, 13809, 0, 12877, -5576, 11267, 1792, 0, 10962, 23648, 2812, -15959, 0, -1288, 992, 5875, 21460, 0, -10980, -12674, -10540, -26635, 0, -17634, 14952, -22424, 4380, 0, 14782, 7358, -3512, 35089, 0, 27484, -1204, 8979, -2944, 0, 2240, -13415, 10376, -29816, 0, 11129, -7842, -42526, -2824, 0, 19748, -9192, -3932, -3633, 0, 3152, -6224, -5268, 21520, 0, -9100, 3979, -7650, 28530, 0, 28646, 7044, -22564, -7824, 0, 11396, 34170, -512, -13518, 0, 36491, 4196, -28334, 23296, 0, -1904, -29363, 3180, 15379, 0, -14531, -2986, -28106, -1888, 0, 15214, -2069, -2176, 24565, 0, 53294, 3624, -20596, 13696, 0, -11644, 12761, 944, -6328, 0, -4174, 3784, -2760, 1308, 0, 35404, 17175, 2616, 39723, 0, -16542, 14192, 89, 21190, 0, 272, 2909, 10884, 26502, 0, 45068, 2514, -18070, -13784, 0, -966, 48618, -13108, -863, 0, -19792, -2048, -70187, 9886, 0, -25800, 7816, -34938, -3525, 0, -9178, 42590, 4746, 188, 0, 3388, 55413, 1424, 2116, 0, 32667, 6820, -4083, 7524, 0, -3640, -1577, 18256, -32246, 0, 3983, -10544, -32032, 1792, 0, -938, -20370, -9372, 15, 0, -32952, 2576, 21836, -6846, 0, -6120, 43753, 22862, 18842, 0, 24232, 40604, -9183, 15076, 0, 22442, 97279, -1560, -240, 0, -7413, 6480, 10256, -2382, 0, 4096, -11059, -1096, -24275, 0, -24373, 1538, 25576, -5064, 0, -9762, 37928, -19364, 35349, 0, 33278, 5488, -34224, -31666, 0, -26428, -35490, 3220, -64477, 0, 5263, 2920, 63383, 26864, 0, 4884, 48188, -5536, 70888, 0, 4731, -4472, 36898, -7598, 0, -16, -14026, 14198, -12855, 0, -8947, 22754, 4496, -3536, 0, 6716, 17053, -20412, -54931, 0, -7456, 9120, -44758, -20534, 0, -22352, 10836, -25996, 65190, 0, 584, 39944, 9311, -736, 0, -6324, -11967, -11648, -18576, 0, 73073, -6232, -8210, -52972, 0, 2224, -50418, 40440, -9618, 0, -3811, -14864, 2733, -9592, 0, -54206, -2714, -28688, -9924, 0, -12555, 3840, 843, -3046, 0, -17840, 4855, 1168, 21230, 0, 88658, 36344, -46988, 25928, 0, -10726, -36868, 800, 24522, 0, -20558, 12636, -23767, -24678, 0, -14200, -53850, 3792, -11577, 0, -19851, -21836, 55870, 1344, 0, -30050, 13287, -32280, 5997, 0, 108, 17360, 391, -44182, 0, 10876, -24279, 16480, 31688, 0, -76920, -13222, 16954, 16180, 0, 3892, -41354, -4456, 128191, 0, 25804, -16996, 70571, 5742, 0, -2944, -19654, 45796, 28138, 0, -46657, -13278, -38581, -25928, 0, -23460, 9869, -34004, 819, 0, -15074, -5872, -72234, -8622, 0, -58164, 27949, -27618, 2047, 0, -48819, -25754, 27101, 11152, 0, -22534, 43674, -3584, 610, 0, 64651, -21924, -34820, -47296, 0, -5624, -155968, 31918, 8584, 0, -73507, 2576, 152363, -1984, 0, -11750, 29829, -42920, -49533, 0, -34173, 21960, 28384, 25348, 0, 21080, 12007, 53270, 40776, 0, 21152, 35268, 50918, -29904, 0, 44848, 5543, -8760, 33678, 0, -96794, -29564, 73440, -14716, 0, 7024, -50976, -70178, -4255, 0, -25904, -54968, 48703, 2408, 0, -17958, -54981, 5888, -43561, 0, 34853, -4480, 37200, 26830, 0, -20752, 57574, 59632, 20026, 0, -12022, -22258, 67262, 15684, 0, 85052, -11091, 5648, 53616, 0, 7889, -39496, 76087, 18384, 0, 7864, -24675, 7266, -60862, 0, -5469, -6304, -135015, 12448, 0, 10536, -23302, -43040, 54980, 0, 2594, 18200, -7721, -7958, 0, 15300, -68113, -57060, -43606, 0, 34636, -57292, 90981, -14088, 0, 45128, 16489, 15648, -1990, 0, -19614, -22792, -66910, -68340, 0, 1024, -5083, 27036, 21708, 0, -62493, -72982, 10272, -8392, 0, 56668, -7611, -46592, 48003, 0, 99962, 3808, -24408, 58726, 0, -6360, -94980, -30758, 27650, 0, -44763, 29062, 2157, 5972, 0, 56212, -110239, 3776, -26226, 0, -17521, -30428, 68649, 4138, 0, 4352, -93995, -49130, 98220, 0, -69243, -106588, 3197, -7248, 0, 41192, -72024, -27392, -11341, 0, -51800, 23288, -75145, -25522, 0, -1888, -66154, 12656, 32167, 0, 97109, 8348, 118891, -7568, 0, 5520, -10077, -2616, 46803, 0, -73489, -70808, 50987, -34350, 0, -5232, -26126, -79446, -71640, 0, -47452, 33084, -10548, -28384, 0, -178, 184404, -42380, 1150, 0, -73096, -544, -29115, -5818, 0, -21768, 18086, -53004, -250116, 0, -11775, -90136, 405, -5028, 0, 36140, -51940, 27568, 26854, 0, 62094, 1932, 8662, -97236, 0, 26216, -91015, 1726, -54236, 0, -89952, 39584, 27781, 4096, 0, 140374, 97024, -19772, 18753, 0, 17956, 51600, 89874, -15632, 0, 69876, 36247, 7050, -5522, 0, -149057, 18356, -29203, -85180, 0, -9492, 99705, -376, -9732, 0, 93345, -6776, 45611, -110826, 0, -2848, 1096, -4232, -85061, 0, -56142, -65334, 147296, -13640, 0, 8166, 90607, -15048, 285, 0, -111190, 7280, -109883, 3154, 0, -36512, -141046, 64492, -24924, 0, -8441, -7966, 150419, 21088, 0, 64064, 34365, -3584, -142566, 0, -48677, 1876, -75916, 40740, 0, 18744, -27090, -30, -90395, 0, 159124, 65904, -121690, -5152, 0, -43672, 68984, 13692, -145023, 0, -22782, 12240, -51708, -87506, 0, -45724, -2315, -37684, -3748, 0, -92166, -48464, 64273, -81208, 0, 18366, -2852, -30152, 104049, 0, -633, -44884, 52147, -194558, 0, 3120, -65773, 480, -37979, 0, 6193, 14826, -153412, -12960, 0, -20512, -139889, 4764, -45902, 0, 80040, -8192, 74483, 22118, 0, 2192, 61758, 48550, -98652, 0, -23766, 48746, -49274, -3076, 0, -51152, 65077, 10128, 59112, 0, -21024, 19524, 10097, -75856, 0, 38728, -171910, -70698, -141292, 0, -209897, -66556, -7994, -10976, 0, 68448, 45974, 63332, 77130, 0, 173368, 52856, -15830, 70980, 0, -6440, 149563, 128954, -16818, 0, 26724, -10526, 59520, -5840, 0, -126766, 90154, -53728, -72988, 0, 86706, -9768, -74482, -96376, 0, 11072, 166870, -141776, 8119, 0, 464, -9462, -120935, 8944, 0, -73796, -96579, 15196, -42991, 0, 108045, 32, -68976, 28052, 0, -28396, -20266, 25710, -44214, 0, -31020, 17894, 127024, -45508, 0, -8992, -46690, 7072, -23534, 0, 77955, -13432, 112964, -34106, 0, 40824, 10426, 109862, 50676, 0, 17462, 14912, 73882, -18240, 0, 89516, -13697, 41068, 333145, 0, -47654, 44704, 60522, -21672, 0, 51992, 32567, -130380, -38096, 0, 95059, -1168, 49154, -79888, 0, -18622, -7119, 1472, 28765, 0, 187087, 12648, 220558, 23934, 0, 23296, 74723, 37152, -16038, 0, -134351, -146146, -487, 12464, 0, 16420, 117868, 105944, 90809, 0, 5474, -4448, -43902, 100836, 0, -80880, -85889, 19236, -47483, 0, -3444, 7622, -99608, 29728, 0, -5466, 823, 19184, 142253, 0, 246876, 108412, -68886, 5428, 0, 57376, 22080, 19848, 90236, 0, -188890, 25110, -133036, -7680, 0, -1686, 44416, 6092, 13760, 0, 54870, 35680, -163058, -9710, 0, -2336, -10419, -42460, 286283, 0, -103882, -177316, 166767, -72688, 0, 93976, -1936, -51856, 114965, 0, 207422, 21452, -57327, 73736, 0, -1600, -233813, -49044, 18654, 0, 194326, 41116, 160029, -25272, 0, 47534, -27208, 49356, 149594, 0, 45324, 28400, 105876, 107700, 0, -7584, 157062, 23154, 168006, 0, 287228, 39702, -7521, 43672, 0, -111740, -224544, -2688, 116045, 0, 77155, 60100, -231459, -26574, 0, 64560, -56249, -11994, 138096, 0, -91467, -216, -33412, -34720, 0, -782, -52715, 88364, 152572, 0, -23594, -21752, -63753, 48558, 0, -32960, 149018, -63376, -1157, 0, 19942, 153840, -60644, 26444, 0, -33908, 75439, -32360, 39629, 0, 208235, -7784, -64505, 82708, 0, 8912, 138071, -256382, -117245, 0, -120471, -51608, -29541, 33992, 0, -141142, -48106, -11484, 35754, 0, 14652, 5888, 95259, 39308, 0, -91592, -112587, -56276, -101962, 0, -182076, 93314, 145149, 26556, 0, 77162, 170574, 51856, 89850, 0, -54247, 46920, -97704, -19738, 0, 68008, -145775, -1638, 166346, 0, -215380, 30148, -93092, 11744, 0, 144468, 32602, 17244, -65152, 0, 159439, 116328, 106204, -55898, 0, 55236, 105111, -4094, -21700, 0, -146357, 97638, 92865, 51508, 0, -54202, 76459, -22304, -8620, 0, -174980, 45068, 147076, -87348, 0, 7168, 1899, -1220, 134840, 0, 10465, -129302, -107003, 43848, 0, 69640, 44409, 94592, -63153, 0, -72970, 11248, -183932, 311936, 0, -63836, 320445, -17168, -69910, 0, 233398, 147014, -99154, -5152, 0, -304726, -25711, 3968, 26248, 0, -108785, 23500, 137249, -59658, 0, 85840, 10612, 99066, 47509, 0, -240057, 68346, -151138, -43920, 0, -56768, -7406, -50696, 86298, 0, -108248, -42160, -64086, -24014, 0, -106540, -232892, -81552, -121386, 0, 31178, -42304, 1350, -70536, 0, -101836, -7352, 59808, -110044, 0, 317278, -89696, 262156, -11086, 0, 17520, 162485, -67356, 198876, 0, -212837, 193588, 45851, 59128, 0, -146880, -88752, 29432, 245926, 0, 52126, -14048, 4485, 101952, 0, 140356, -123868, 8510, -24078, 0, 60243, 51808, -244777, 109936, 0, -97406, 155339, -4816, -189033, 0, 139931, 35916, 198978, 109962, 0, -11776, 165463, 87122, -77688, 0, -264349, -69706, -83126, 8960, 0, -74400, 216523, -53660, -55891, 0, -89114, 41504, -135667, -115148, 0, -119264, 188002, -40052, 14559, 0, 58889, 24044, 179500, 44516, 0, -134524, -52242, -31368, 203516, 0, -147776, -170104, 142149, 22182, 0, -11296, 180214, -107232, -72325, 0, -450837, -15778, 4059, 78992, 0, -152174, -246744, -36768, -21159, 0, -80001, -15728, 280365, 49350, 0, -14532, -5619, 121724, -90386, 0, -102136, 10938, -156233, 12608, 0, 270030, -138122, -24896, 37780, 0, -13623, -21072, 134524, 46604, 0, 86080, 244872, -109960, -335424, 0, 10352, -5188, 132152, -36400, 0, 15442, 98113, 15916, -28726, 0, 87857, -30600, -162422, 136226, 0, 114120, 327927, 87212, 48856, 0, -162156, -69272, -315538, 114584, 0, -181962, 387315, 28176, 42740, 0, 46, -90256, -138113, -32978, 0, -31296, -288971, 3980, -171768, 0, -35013, 39228, -86009, 45584, 0, 133820, 40709, 136680, -59823, 0, 326540, -2048, -108346, 10166, 0, -54072, 16087, -43416, -145630, 0, 40202, 124986, -6291, 145964, 0, -20544, 103657, 16784, -425112, 0, -181157, -113336, -55158, 15222, 0, 93184, -26220, -96006, 237201, 0, -390844, -199924, -158513, -7616, 0, 48816, -473573, -117452, -227751, 0, 95866, 12720, 26085, 189960, 0, 61516, -58900, -55300, 145630, 0, 337387, 89526, -4836, -58124, 0, -4314, -28909, -11944, 99144, 0, 145559, -112424, 11576, 220478, 0, -7552, 67710, 52452, -64242, 0, 271042, 35042, 33488, 60856, 0, -137298, -117701, -8276, 53564, 0, 236476, -8704, -141335, 187990, 0, 98260, 154968, -196440, -14373, 0, -39337, 138486, 30243, 213176, 0, -6394, 407912, 14496, -75451, 0, -41418, -82384, -242176, 144048, 0, 54784, -62956, 22682, -100101, 0, -111808, 103600, -324549, -46576, 0, 150290, 100795, 51044, 27577, 0, 147006, 3776, -252420, 132308, 0, -25312, -270682, -64334, 158184, 0, -120933, -194218, 385830, -16696, 0, -237782, 18941, 15136, -132270, 0, 64865, -11040, 195558, 20154, 0, 5232, 79065, -93606, 31702, 0, 136479, 146978, -229219, 141616, 0, -101974, 147600, 68700, -11281, 0, -25740, 10464, -458306, 52252, 0, 158892, -449500, 143280, -170373, 0, 105993, 94904, -248033, -66168, 0, 21096, 105052, 56768, -272996, 0, 315759, 356, 370870, -368808, 0, 84760, 185928, -2300, 219816, 0, 102145, 146192, -67523, 1088, 0, 58230, -81426, 11636, 29841, 0, -274758, 43536, -383432, -36172, 0, 106008, -89411, 500232, -238022, 0, 40825, 23550, -209603, 180272, 0, -810, 402362, 10056, -331663, 0, 229005, -72280, 83480, 103880, 0, -55136, 132685, -53708, -160353, 0, -542, -124188, -91584, -3864, 0, -17324, 65439, 194472, 106593, 0, 344560, -52432, -94628, 182030, 0, -3452, -167339, 108472, 140912, 0, -109522, 179904, -179000, -79168, 0, -55562, -49910, -8192, 137771, 0, -187387, -280748, -377753, -194048, 0, 39544, -391762, -37506, -214996, 0, 167682, -35912, -116255, -103200, 0, -179748, 100830, 31264, 8551, 0, 218383, -139752, 163060, -72494, 0, -14100, -200037, 11044, 246824, 0, 181658, 298114, 309224, -36712, 0, 58406, -2622, 170360, -63300, 0, 210786, 18984, 12811, -199410, 0, 752, -118868, 19464, -130274, 0, 263702, -186690, -18234, 13552, 0, -91222, 348622, 221652, -243952, 0, 58731, 5696, -73957, -2192, 0, 8464, 217611, 170122, -186370, 0, -177234, 112284, -388578, 130668, 0, -294592, -166621, 27280, -1408, 0, 310683, -16332, 127444, -181214, 0, 30096, -117658, -570, 74543, 0, 70937, 222380, -2308, -14560, 0, 219766, -201784, -6308, 230940, 0, -211609, 73024, 251402, 282092, 0, -128984, -145808, 49848, -194538, 0, -220176, 16882, 689717, 15932, 0, -300838, -111235, -42176, 35362, 0, 8856, -128128, 41615, -68730, 0, 7168, -265786, 285132, 186797, 0, 254995, 97354, -38865, -3752, 0, 151832, -394556, -81480, -89030, 0, -354386, -37488, -158696, 54180, 0, 60, 58867, 180790, -560306, 0, 46424, -318248, 158530, -131808, 0, 243380, -49821, 10304, -4135, 0, 153948, 87344, -57693, -137968, 0, -27384, -165493, 290046, 273629, 0, -235826, 45564, 4351, -24480, 0, 103416, 190842, 175012, -50698, 0, 16169, 91448, 102436, 4630, 0, 75368, -74098, 7496, -6644, 0, 74268, 184332, 210206, 96928, 0, -128546, -3450, 162416, -284880, 0, 189152, -36732, -93044, 5704, 0, 60304, -262224, -208098, 368382, 0, -93729, 1266, 68237, 89768, 0, -104294, -470064, 389116, 135069, 0, -410004, -6240, 74484, 131546, 0, -960, -63135, 75958, 150652, 0, -71274, -12386, 458149, -29652, 0, 306824, -28086, 25920, -152649, 0, 61108, 41024, 26381, 279778, 0, -9528, 47269, 91804, -439662, 0, 288390, -160080, -74843, 16384, 0, -148966, 116120, -44236, 321288, 0, -144304, -4384, -371108, -123516, 0, -97100, -375355, 197304, 100238, 0, 224052, 47532, 25185, -97492, 0, 98548, -258531, 6152, -72280, 0, 859737, 102304, -250905, -130154, 0, -20256, 345497, -118224, 107603, 0, -6484, 42048, 360234, -39048, 0, -20194, 50137, 151712, -743068, 0, -167352, -77456, -132479, 343820, 0, 141396, -158279, 282584, -419321, 0, 255650, 419794, -108997, 133112, 0, 15988, 459508, 21952, -6923, 0, -413336, -136896, 288504, -91948, 0, -126664, -253575, -154260, 218117, 0, -172297, -346736, 636260, -105712, 0, 31660, 262971, -141960, -90092, 0, -357446, 12880, -106890, -299126, 0, -257908, -394554, 33636, 6636, 0, -76244, -53448, 63402, 21052, 0, -119040, 24905, 11680, -219044, 0, 73539, 253532, -412952, -180308, 0, 107456, -394873, 145976, -368217, 0, -156077, -173412, -42130, 19536, 0, 148964, 429615, 192752, 86950, 0, -54291, -22144, 563209, -333740, 0, 283552, 104447, -16238, -408107, 0, -233470, -928, -328319, 18924, 0, 241870, 15317, -17888, -632632, 0, -514548, 147592, -327568, 193158, 0, -30392, 40273, 85982, -541849, 0, -22609, -216090, 84924, -64, 0, 137952, 282332, -56104, 274855, 0, -277690, 56792, 73151, 40532, 0, -51420, -165434, 88428, 366949, 0, 406394, 62040, -26238, -35788, 0, -254048, -49608, 91016, -258886, 0, -98246, 17984, 106098, 93380, 0, -14144, -133888, 47068, -131433, 0, -286289, -155910, -7377, 26864, 0, -225928, -52325, 68212, 111467, 0, -1025110, -81648, 120390, -20852, 0, -219724, -567086, -101352, -208218, 0, -134340, -34924, -369403, -29824, 0, -147764, 69832, 36480, -87154, 0, 295524, -179032, 185830, 27394, 0, -82136, 522168, -666290, 25171, 0, 214253, 95308, -477799, -89408, 0, -121044, -350125, 43344, 2931, 0, 84316, -103984, -44988, -65134, 0, 260760, -345500, 76192, -513452, 0, 181341, -190118, 218562, 2336, 0, -98308, 316665, 159776, -439221, 0, -320061, 37244, 217009, 14238, 0, -2944, 73813, -57530, -185912, 0, -90418, -374174, -231090, -25296, 0, -441116, -98714, -47868, 422589, 0, 544112, -46592, -376368, -149446, 0, -74304, 37294, 32076, 24127, 0, -292477, 268702, 166489, 292292, 0, 974, -122764, -24928, 357086, 0, -430706, -32840, 52168, -235736, 0, -211888, 9541, -181618, -73813, 0, -259325, -10948, 409180, 8896, 0, 87804, -84127, -201672, 180798, 0, 200429, 161760, 176927, 171778, 0, -38472, 50643, 94966, 22800, 0, -148846, 6888, -149588, -15244, 0, 199216, -189770, -59456, -314784, 0, -327760, 10932, -125868, -1646, 0, -38368, 504973, -284506, -290878, 0, 559937, -493752, 42927, -216824, 0, 137772, 253468, -10856, 509083, 0, -32725, -114752, -37777, -44160, 0, -39696, -369657, -180472, 425602, 0, 188271, 377780, -263727, -50220, 0, 266072, 62270, 15360, -168238, 0, -12512, 3372, 309183, -88832, 0, -12184, -565821, -27520, 313326, 0, -145954, -109740, 222222, -71360, 0, 326116, 88160, 19420, 336340, 0, -161288, 4672, -74096, 20838, 0, 84920, 14937, -572566, 390460, 0, 238848, 207764, 173402, 354632, 0, -333534, -419412, 145376, 182622, 0, -143727, -187952, -31292, 3872, 0, 103712, -66953, -229930, 141410, 0, -487617, -414844, 206716, -42904, 0, 114654, -168277, -147472, 8552, 0, 780678, 3200, -437343, 467626, 0, 98088, -357078, -37308, -58694, 0, 374796, -388652, 127255, -82232, 0, -320058, -61505, 50544, 226824, 0, 207976, -95068, -98316, 54416, 0, -98712, -239310, -299188, -13568, 0, 1291361, -90648, 7521, -56800, 0, -211752, -32481, -215400, 280790, 0, -159443, 15168, -488993, -314124, 0, -46308, 284587, -336012, -321010, 0, -151418, -574456, -105584, -79404, 0, 15042, -198930, -87344, -246655, 0, 541160, 223480, 55500, 449088, 0, 5376, -630037, -232090, 311572, 0, 189166, -154310, 57991, -120200, 0, 462918, -43778, 53148, 81604, 0, -298691, -129120, 72729, 112498, 0, 23988, 65972, -276192, 56508, 0, -307687, 182934, 153004, 432, 0, 66824, -130469, 69440, -398462, 0, -436711, 1564, 503404, 105430, 0, -176728, -184488, -305144, 28299, 0, -49893, 47188, 61088, 43504, 0, 127506, 199508, -97116, 725538, 0, 158564, 65920, 202997, -298036, 0, 126752, -167723, 2314, 273907, 0, 187216, -39884, -40294, -307680, 0, 121288, 211678, -52888, -338206, 0, 453366, 67816, 102459, -150878, 0, 64720, 17678, -79258, 37256, 0, 317329, -416470, -145603, 15568, 0, 129010, -397725, -165416, -571345, 0, -674707, -17824, 228353, -276142, 0, 512764, 93322, 234490, -316944, 0, -75371, 240942, 112328, 103216, 0, 59082, 161004, -67984, -200013, 0, -224500, 282284, 291938, 96212, 0, 22968, 279032, -71508, 393862, 0, 267585, -29304, -201127, -11776, 0, -190518, -400043, -78616, 561003, 0, -75756, 183184, 213667, 225174, 0, 112552, -206441, 203924, 120926, 0, -1128354, 364152, 344256, -186628, 0, -290298, -148350, -53112, 227432, 0, -886247, -154324, -147597, -341148, 0, -103712, 129904, -179700, -335315, 0, 468052, 108494, 71116, -93840, 0, 195408, 625672, 39476, 303074, 0, 142916, -136016, 384535, 291550, 0, 3276, 1444687, -332692, -77159, 0], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [-2, 0, 0, 0], [-4, 1, 0, 0], [4, 0, 0, 0], [0, 0, 0, 0], [8, -2, 0, 0], [-1, -1, -2, 0], [-8, 0, 0, 0], [18, -4, -2, 1], [0, 0, 0, 0], [6, 1, -1, -2], [-16, 4, 0, 0], [-15, -4, 0, -1], [2, 2, 4, 0], [0, 0, 0, 0], [16, 0, 0, 0], [-18, 2, 6, 3], [-36, 8, 4, -2], [39, 8, -5, 3], [0, 0, 0, 0], [-37, 7, 16, -1], [-12, -2, 2, 4], [23, 0, 0, 0], [32, -8, 0, 0], [0, 0, 0, 0], [30, 8, 0, 2], [-105, 11, 23, -7], [-4, -4, -8, 0], [-34, 9, 10, -5], [0, 0, 0, 0], [-17, 27, 15, 8], [-32, 0, 0, 0], [25, -14, 3, 7], [36, -4, -12, -6], [0, 0, 0, 0], [72, -16, -8, 4], [96, -3, -33, -1], [-78, -16, 10, -6], [-43, -27, 7, -1], [0, 0, 0, 0], [28, 32, -15, -11], [74, -14, -32, 2], [32, -52, 18, 4], [24, 4, -4, -8], [0, 0, 0, 0], [-46, 0, 0, 0], [-106, 16, 33, -4], [-64, 16, 0, 0], [-17, -42, 10, 9], [0, 0, 0, 0], [127, -6, -43, -7], [-60, -16, 0, -4], [114, -37, -7, -11], [210, -22, -46, 14], [0, 0, 0, 0], [8, 8, 16, 0], [7, 95, 22, -1], [68, -18, -20, 10], [-76, -79, 7, 1], [0, 0, 0, 0], [-66, -47, 31, 0], [34, -54, -30, -16], [487, -86, -73, 10], [64, 0, 0, 0], [0, 0, 0, 0], [-50, 28, -6, -14], [140, -43, -33, 7], [-72, 8, 24, 12], [-92, 23, 0, 0], [0, 0, 0, 0], [68, -72, 21, 23], [-144, 32, 16, -8], [140, 44, 17, -16], [-192, 6, 66, 2], [0, 0, 0, 0], [156, 32, -20, 12], [-19, 9, 46, 7], [86, 54, -14, 2], [-220, -92, -20, -28], [0, 0, 0, 0], [482, -173, -136, 5], [-56, -64, 30, 22], [290, -13, 47, 9], [-148, 28, 64, -4], [0, 0, 0, 0], [-64, 104, -36, -8], [522, -134, -93, 24], [-48, -8, 8, 16], [-512, -92, 30, 16], [0, 0, 0, 0], [122, 19, 19, 6], [92, 0, 0, 0], [837, 19, -151, 3], [212, -32, -66, 8], [0, 0, 0, 0], [128, -32, 0, 0], [198, 13, -55, -30], [34, 84, -20, -18], [-741, 70, 41, 19], [0, 0, 0, 0]]}