# Stored data for newform 931.4.a.a, downloaded from the LMFDB on 08 May 2024.
{"label": "931.4.a.a", "space_label": "931.4.a", "level": 931, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 67109795, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1042939735927869099, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [3, 1]], [3, [-5, 1]]], "qexp_display": "q-3q^{2}+5q^{3}+q^{4}+12q^{5}-15q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 14896, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 54.93077821534451, "hecke_ring_index": 1, "level_radical": 133, "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": [931, 1, [248, 344], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [7, 19], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.987", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.981", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.005", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[7, -1], [19, 1]], "trace_display": [-3, 5, 12, 0], "traces": [0, 1, -3, 5, 1, 12, -15, 0, 21, -2, -36, -54, 5, -11, 0, 60, -71, 93, 6, -19, 12, 0, 162, 183, 105, 19, 33, -145, 0, -249, -180, -56, 45, -270, -279, 0, -2, -250, 57, -55, 252, -240, 0, -196, -54, -24, -549, 168, -355, 0, -57, 465, -11, 435, 435, -648, 0, -95, 747, -195, 60, 358, 168, 0, 433, -132, 810, -961, 93, 915, 0, -246, -42, -353, 750, 95, -19, 0, 165, -34, -852, -671, 720, -234, 0, 1116, 588, -1245, -1134, 168, 72, 0, 183, -280, -504, -228, 225, -758, 0, 108, 19, 726, -1395, -2, -231, 0, -1305, 1413, -145, 389, 1944, -1250, 0, 342, 285, 2196, -249, 22, 585, 0, 1260, 1585, -1074, -1200, -56, -1272, 0, -1150, -1659, -980, 396, 1452, -270, 0, 2883, -1740, 1953, -1689, -2745, -2144, 0, 840, 738, 594, 142, -2988, 1059, 0, -250, -3000, -285, -1006, -399, -186, 0, -672, -55, -2846, 102, 2175, 540, 0, 2013, -1600, -240, -3240, 702, 2004, 0, -2076, -3348, 38, -196, 462, 3735, 0, 3834, -975, -504, 720, -24, 2338, 0, 1790, 3843, -3000, 840, -5022, 168, 0, 684, 2871, 2165, 1658, 2274, -660, 0, -4176, -324, 241, 399, -4805, -2178, 0, 465, -2880, 6, -366, 781, 1026, 0, -745, 435, -1230, -4239, -2352, -3045, 0, -1167, -1765, -648, -1023, 3750, 1978, 0, -38, -1026, -5355, -95, 6370, -6588, 0, -5229, -2838, -66, 2016, -195, -170, 0, -369, -4260, -6608, -4755, 560, 358, 0, 3600, 209, -1176, -1170, 3816, -4674, 0, -9882, 3450, 5580, 1513, -4512, 2940, 0, -132, 498, -4356, 3768, -5670, 5220, 0, 840, -961, -4758, 5220, 2041, -6603, 0, 5067, -1026, 915, 1964, 6432, 112, 0, -5496, -2520, -3098, -246, -1140, -1782, 0, -90, 3736, 8964, -3790, -353, -117, 0, -2340, -5250, 7830, 9000, -2013, 95, 0, 3018, 3630, 1349, 4296, 558, 1420, 0, -10, 2016, 6561, -1155, 1483, 8538, 0, -34, -1239, -6525, 13446, 5196, 7065, 0, -1767, -671, -209, 4800, 1945, -5040, 0, 9720, -8899, -234, 500, -6012, -11532, 0, 5816, 6228, 1710, 1116, 3024, -114, 0, -4116, 10980, -1386, -1578, -1245, -1658, 0, 1595, -2430, 11367, 2925, -2952, 168, 0, -2160, 2553, -504, 361, -7014, 7925, 0, -4236, -5370, 196, -12993, 480, 9000, 0, -280, 9353, 15066, -6360, 3528, 2739, 0, 3827, -228, -5750, -8613, -5694, -8295, 0, -4974, 392, -758, 1290, 1980, 17019, 0, 7260, 12528, -408, 108, -6536, -723, 0, -1349, 2328, 14415, 616, 726, -8052, 0, 13500, 9765, 6676, 8640, -8445, -2, 0, 1098, -2808, -495, -10720, -3078, 8136, 0, -8665, 2235, -336, 9135, 1767, 3690, 0, 1413, 2970, 7056, 750, 10295, 4858, 0, -14940, 389, -3477, 5295, -6500, -13608, 0, 3069, 3486, -1250, 2016, -5934, -15000, 0, -15030, 114, 12960, 342, -5030, 16065, 0, -1995, -2959, -19110, -13485, 2196, 156, 0, 4484, 17679, -3360, 8514, -8766, 22, 0, -6048, -14230, -4095, 10584, 510, -361, 0, -870, 1107, 18996, 2700, 2750, 19824, 0, 1585, -9096, -1680, -7450, 7518, -8000, 0, 6180, -1200, -23157, -627, 1296, 3976, 0, 3510, 2576, -1272, 10020, 14022, 10545, 0, 8712, 29646, -10380, -1150, 14694, -16740, 0, 8733, 2755, 13536, -24, -980, -9072, 0, 2310, -2772, -10332, -1494, -10937, 1452, 0, -11304, -5208, 19170, 21322, -15660, 390, 0, 2640, -2520, 16956, -20181, 3600, 14274, 0, -1740, 18578, -6123, 11690, 4185, 4668, 0, 21404, -1689, -716, 3078, 4731, 19215, 0, -5892, -15000, -2144, -3948, -336, 2156, 0, -25110, 16488, -5724, 840, 4104, 9294, 0, -5166, -20592, 3420, 20684, 594, 14355, 0, 3477, -866, 19573, -11208, 8290, -2988, 0, 11370, -23490, -7413, 264, 351, -13524, 0, 1064, 7020, -20880, 17750, -8994, -23490, 0, -3000, 1205, 6039, 10128, 1995, 22696, 0, 1922, -1006, 19020, -10890, 5182, -855, 0, -12888, -1848, -186, 10082, -4260, -14400, 0, -12174, 30, -7490, -672, -26535, -19683, 0, 3905, -17639, -4449, 5130, -2846, -23250, 0, 11072, -714, -3725, 3717, -13800, 2175, 0, -40338, 492, -19908, -18894, -21195, 19834, 0, -11760, 5301, -3375, -14091, 10530, 627, 0, -1600, -24948, -5835, 17424, 17040, 706, 0, -9879, -3240, 14155, 26697, -5115, -4914, 0, -1500, -45567, 2004, 9890, 34596, -19332, 0, 8948, -17448, -2755, -2076, 11511, -5130, 0, 23436, -26775, -9072, -10476, 38, -20268, 0, 31850, 13916, -4785, -32940, -30098, 462, 0, 4734, -25728, -26145, -22320, 4974, -14190, 0, -14700, -4785, 4750, -23382, 10080, -34101, 0, -975, 31178, 8856, 68, 3528, -10248, 0, 7128, 720, -1845, -7659, 33285, 1704, 0, -1083, -33040, 2338, -4731, -23775, 34729, 0, 20917, 12708, -18228, 1790, -4196, -588, 0, 8235, 51894, -1440, -10744, -3000, 1045, 0, -2208, -5880, -36000, -28059, 468, -5022, 0, 19080, 13160, -11928, -23370, -8217, -12072, 0, 758, -11481, -49410, -4788, -4851, 17250, 0, 2871, -2232, 17082, 2145, 7565, 33091, 0, -22560, 1658, -42357, -1176, -1064, -15918, 0, -3870, 4560, -660, 13284, -51057, 36105, 0, -34152, -21780, 39877, -4176, 18840, 1224, 0, 2268, -3938, 19608, 26100, 241, 30033, 0, 15624, 855, -336, -6984, 19062, -4805, 0, -1848, -23790, 15246, 585, 24156, -28361, 0, 10205, -40500, -19200, -33015, 3724, -20028, 0, -2880, 25068, 25335, 10901, -42, -5130, 0, 12027, -366, 19339, 8424, 9820, -4763, 0, 32160, 24048, 1026, 8120, -24408, 13188, 0, 37612, 25995, -27480, -745, -24912, 1008, 0, -30885, -15490, -5301, -45750, -1230, 4678, 0, 456, 29673, -15252, -8910, 610, -2352, 0, -2250, 774, -6525, 5544, -14574, 18680, 0, 1836, 44820, 10571, 8169, 1516, 10431, 0, -1765, -31039, 19500, -585, 46008, -33678, 0, -42982, -1023, -11700, -10458, -4494, -26250, 0, -6048, 36234, 1978, -3192, 45000, 8640, 0, -10065, 45090, 13944, -38, 40455, -38880, 0, 7182, 28056, 15090, -23839, -5355, -1452, 0, -10332, 6745, 12636, 8877, 21480, 6370, 0, 40455, -14371, 46116, 7100, -468, 2706, 0, -4750, -13452, 4, -11205, -26889, 10080, 0, -2838, 32805, 26298, -60264, 462, -785, 0, 7415, 2016, 18141, 42690, -43920, 13845, 0, -31752, 23100, -170, 3883, 1083, -6195, 0, 45690, 2610, 34452, -369, 67230, -56988, 0, 25980, -26655, -8250, -2826, -6608, 19896, 0, 21584, 33285, -8835, 27288, 50556, 560, 0, 22350, -1045, -25418, 8568, 24000, -9072, 0, -778, -18540, -29706, -25200, -50112, 69471, 0, 209, -35868, -3888, 30512, -2520, -44495, 0, 2892, -1170, -47756, -7728, 36250, -26712, 0, -30060, -18135, -4674, -57660, -31635, -8265, 0, 36920, -26136, 29080, -9882, 23748, 31140, 0, -24150, -684, -44082, 24237, 5580, 853, 0, 15120, -38303, -4560, -8265, 374, -4512, 0, 72, 26016, -20580, -15433, 27216, -4392, 0, 33294, -6930, -25688, 9372, -7890, 30996, 0, 498, 12312, 32811, -8290, 30492, -28830, 0, 12548, 3768, 7381, 15624, -8940, -12150, 0, -63966, 56835, 5220, -30666, -1170, 63484, 0, -14760, -7920, 40932, 840, -23024, -50868, 0, 68231, 62250, -10800, -3724, -4758, 12765, 0, 2574, -36540, 30744, -55734, 1805, 2041, 0, -35070, -4399, 40269, -3170, -14004, -54621, 0, -13138, -64212, -21180, -35469, 49116, 2148, 0, -1026, 980, -14193, -25065, -64965, -12276, 0, 34800, 1964, 52254, 45000, -39204, -45024, 0, 11844, 23736, 112, 27389, -6468, 46765, 0, 3705, 75330, 7432, -5496, 2544, 17172, 0, 17640, -29770, -12312, 13695, -3098, 108, 0, -64260, 17466, 19135, 61776, -89373, -1140, 0, -62052, 2300, 12474, 76440, -43065, 14000, 0, -28470, -10431, -30015, 3318, 37582, -58719, 0, 3736, -1848, -24870, -6802, -62748, 28420, 0, 64596, -3790, -34056, 70470, 6450, 25063, 0, -792, 55208, -117, 85095, 40572, 3192, 0, -76302, -3192, -2904, -2340, 51987, 62640, 0, -11250, -2040, 26982, -81312, 7830, 59760, 0, -32680, -63000, 18312, -3615, -4428, -2013, 0, -30384, -21006, -6745, -24847, -68088, 11640, 0, -79296, -5766, -22878, -21126, 3080, -57060, 0, 3630, -16396, -15546, 6720, -8227, -30411, 0, 79605, 4296, 67500, 5544, -26577, -3906, 0, -30246, 33380, 1420, 46938, 43200, -71444, 0, 3378, 36522, 2508, -10, -76691, 22470, 0, -14112, -32829, 79605, -18468, 6561, -14040, 0, 48804, -2475, -74324, 52917, 4288, 1483, 0, -15390, -56088, -59766, 40680, 69750, 19470, 0, 8338, -33216, -43325, 2414, -118584, 11175, 0, -1239, -24360, 41400, 13440, 45675, 18259, 0, 8835, 13446, -16176, -1476, 50749, 18156, 0, 56682, -67389, 7065, -54144, -59502, -1188, 0, 6549, 35280, -28055, -1767, 3750, 10125, 0, 47641, -48571, -31590, 24290, -209, 25620, 0, -14596, -33600, 5976, 74844, 3903, 1945, 0, -52272, -17385, -10800, -7986, -2118, 45216, 0, -32500, 29637, 59688, -68040, 48418, -42465, 0, -8899, 8265, 15345, 85907, 16614, 17430, 0, -13716, 500, 10976, 136701, 10080, 42084, 0, -29670, 22, -11532, 6000, 57996, -3162, 0, -57096, -26844, -75150, 5816, 4674, 8265, 0, -43596, 64800, -34533, 24492, 1710, -35685, 0, 2012, -79236, 55062, 80325, -41832, 3024, 0, 31428, 54594, 798, 11847, 60804, -14795, 0, -55686, -95550, 68688, -8820, -62403, 14355, 0, 10980, 20018, 90294, 780, 9702, 23568, 0, 6707, -1578, 22420, 77184, -15543, 88395, 0, 66960, 1344, -1658, 62100, 42570, 46870, 0, -43830, 44100, 65514, 1595, -65952, -14250, 0, 89586, 40578, -30240, -21762, 11367, 5692, 0, -37176, -20475, -4279, -93534, 52920, -2952, 0, -204, -3697, -11928, -1805, 30744, 83559, 0, -34594, -21384, -63075, 15120, -101682, 5535, 0, 2553, 94980, -99855, -26814, -1080, -78408, 0, 13750, 361, 44832, 99120, 44386, 49098, 0, 14193, -8730, 7925, -58606, -104187, -45480, 0, -9408, -62751, -68447, -4236, -37250, 54684, 0, 37590, -1404, 12588, 3200, 196, -3762, 0, -46888, 79239, 30900, -155682, -3705, 480, 0, 32232, -115785, -63000, -9054, -3135, -12062, 0, 93960, 6624, 86907, 19880, -54542, 108000, 0, 9353, 76752, -1404, -24156, -105462, 12880, 0, -81534, -6360, 646, -39480, -4008, 7560, 0, 70110, 91206, 2739, 52725, 36216, -84684, 0, 15624, -2274, 43560, 3827, 60000, 148230, 0, 16188, 4152, 14553, -68700, -5750, 6802, 0, 73470, 60291, 115776, 6696, 46114, -5694, 0, -6435, 17040, 43665, -108315, -99273, 12749, 0, -175863, 67680, -25661, 34818, -120, 127071, 0, 392, -112237, 3192, -45360, 53818, -72348, 0, 78732, 1290, -924, -13680, 71460, -13860, 0, -39852, -51660, 17019, 17796, -108315, -107120, 0, -54685, 102456, -41268, 7260, -17435, -119631, 0, -87696, 4446, -56520, 59492, -408, -26040, 0, 15195, -7668, -14868, 11814, 106610, -6536, 0, -78300, 49000, 5061, 28275, -90099, 161352, 0, 20414, -46872, 13200, 8227, -82563, 1008, 0, 2328, 84780, -57186, 40131, -100905, -91802, 0, -1440, 616, -64284, 71370, -21204, -51546, 0, -1755, 37290, -8052, 11774, 85083, 92890, 0, 13992, -30615, -100316, 13500, -4676, 57600, 0, 20925, -45018, -11172, 23340, 6676, -17178, 0, 162000, -60480, 107020, -75204, -24360, -8445, 0, -32703, -51910, 142, -70494, 15390, 12650, 0, 23655, -36081, -106788, -7686, 91906, -58017, 0, -2808, 54324, -29460, 19352, 18249, 6000, 0, 8916, -10720, 98296, -72144, -19740, 21546, 0, -24360, -18259, 8136, 10780, -39564, -64599, 0, -11321, -112836, 10044, -8665, 69792, 82440, 0, -15645, -28620, 74736, -3192, -336, -49655, 0, 20520, 19575, 62142, 46470, -52283, 1767, 0, 137250, -15972, -25830, 36288, -14034, -102960, 0, 63477, -1368, 48555, -100323, 103420, 45756, 0, 2970, 67518, -1830, -5742, -49392, -34803, 0, -81367, 750, 17385, -2322, 153684, -62785, 0, -16632, 97865, 4858, -46230, -56040, -18936, 0, -3316, -5508, -42000, -14940, 52837, -31713, 0, -27619, -19896, -4548, -31291, -3477, -117450, 0, -186, -37065, 37663, 93117, 19140, -6500, 0, 1755, 51905, -29160, -67620, 101034, 47040, 0, 136404, 128946, 5320, -21483, -89142, 35100, 0, 3486, 8352, 13482, -4674, 88750, -64406, 0, -44970, 2016, 18579, -108702, 47167, 41538, 0, 9576, 59310, -15000, -83869, -25920, -482, 0, 86400, 30195, 30636, -15030, 50640, -41832, 0, -798, -24784, -121365, 113480, 12960, 4332, 0, 23584, -24282, 139345, -84168, -13692, -5030, 0, 71517, 95100, -112455, -6222, 4356, 131409, 0, 25910, 30996, -2718, -4275, -6707, -37908, 0, -2959, 10920, -64440, -87685, 133770, -9240, 0, 2352, -13485, -108216, 43113, 50410, -155916, 0, -21300, 14402, 156, 5760, -8118, -100695, 0, -41091, 14250, -60870, 4484, 36177, -12, 0, -107817, -37450, 80667, 112104, -3360, -137279, 0, -122793, -59598, 112236, -98415, 63808, -8766, 0, 180792, -86928, -1562, -93319, 2355, -88195, 0, -1842, -22245, 122047, 42336, -2052, -54423, 0, -14230, 32868, 131760, -116250, -8775, 69318, 0, -20048, 10584, 55360, -69300, 45924, -3570, 0, -11649, 1490, -361, -130482, 18585, -24948, 0, -69000, -137070, 70812, -870, -42822, -103356, 0, -7749, 17238, -201690, -68328, 18996, 35670, 0, -13794, -99540, 31806, 79965, -94470, 2750, 0, 8478, -40320, -138768, 99170, -59688, 56268, 0, -93130, -64752, 4704, -112535, 33000, 26505, 0, -9096, -16875, -151668, 239289, 11760, 15480, 0, 52650, -7450, -4032, 3135, 27862, 16110, 0, -25704, 204228, -8000, 38, 27216, -124740, 0, -108750, 2334, 11066, 6180, 87120, 89118, 0, 85200, -38880, 150336, 51185, -23157, -78450, 0, -646, 4389, -49395, 107604, -60297, 1296, 0, -91536, 70775, -24248, -78432, 133485, -25094, 0, 2046, -8676, -126252, -24570, -27830, 143268, 0, 2576, 35385, -108750, 60779, 90312, -227835, 0, 83223, 10020, 27936, 54405, -3956, -98154, 0, 172980, -64276, 10545, -96660, 24795, 7392, 0, 142670, -110760, 44740, 8712, -32928, -87240, 0, -207522, -12749, -71244, 150123, -10380, 85255, 0, 57555, 81650, -26847, 2052, 162000, 14694, 0, -72711, -96, 117180, 31306, -2559, 10710, 0, 80112, -45360, 30744, 45045, -52380, 13680, 0, 2755, 69464, -1122, -101340, -94752, 147405, 0, 61254, -24, -12740, -78048, 154656, 69580, 0, 46299, -23925, -9072, -152454, 13176, -7391, 0, -150490, -99882, -4446, 2310, 53816, 77064, 0, -5940, 155298, 23670, 34076, -10332, -128640, 0, -128568, 10458, -181712, -36936, -111600, -10937, 0, 24870, 97632, -103092, 5676, 86490, 135546, 0, -155034, -37644, -73500, 79128, -103980, -22143, 0, -5208, 23750, 26820, -140070, -116910, -26291, 0, -4032, 21322, 87897, -170505, 17600, 109620, 0, 91998, -89532, 390, -118296, -190452, 155890, 0, 129294, 44280, 16423, 2640, 4930, -122796, 0, 17640, -100321, 69072, -51240, 16956, -83127, 0, -26674, -43245, 35640, -186750, -6498, 3600, 0, 11172, 738, -99918, 66207, -38295, 9000, 0, 166425, -7722, -106950, 123540, -152066, -92232, 0, 18578, 58296, -5415, 225504, 42861, 13216, 0, -22044, 11690, -104400, 13197, -23655, -154287, 0, 9510, -171205, 4668, 173645, 163863, 48750, 0, -41724, 39414, 89465, 21404, -13014, 63540, 0, 119919, -91140, -147348, -78000, -716, 47003, 0, -20980, -21546, 13776, -2940, -13997, 4731, 0, 75195, -98184, 41175, -75599, 36828, 259470, 0, -21588, -104400, 41832, 41244, -53720, -156762, 0, -15000, 134156, 117612, -418, 152224, 3192, 0, 135036, -3948, -11040, -71208, -138714, 2352, 0, -82167, -180000, 2156, -155127, -140295, 151117, 0, 33930, -11115, -138546, -25110, -180360, -22296, 0, -115416, -5082, -7632, -3742, -5724, 65800, 0, 155520, -59640, -89500, 89310, 9348, 4104, 0, -41085, 19768, -65058, -60360, -324, -13764, 0, -61567, 192780, 3790, -11070, -68580, -57405, 0, -20592, 19764, 268119, -85260, -23940, 141073, 0, -24255, 20684, -35508, -6900, -108857, -42174, 0, -229320, 8466, 14355, -176767, -42000, -161820, 0, 143583, 85410, -30115, 3477, 10725, 90045, 0, -3026, 1872, -112746, 165455, 19573, 133377, 0, -217114, 78456, 9024, 5544, 53808, 8290, 0, 20406, -211785, 212148, 40230, -85260, 132858, 0, -5320, -193788, -7920, -79590, -157077, 102168, 0, -23490, -191877, -19350, -105192, -15885, 22800, 0, 183372, 264, -102422, -165624, 66420, -2457, 0, -255285, -162079, -13524, 167079, -9576, -179610, 0, -25718, 228906, -170760, 1064, -67176, 8712, 0, -49140, 199385, -155961, -199392, -20880, 127008, 0, -7536, -108250, -366, 6120, 208888, -8994, 0, 243936, 24168, 164430, 68798, -179280, -19690, 0, -159504, 98040, 165868, 213000, -10440, -54936, 0, 1205, -99826, 13284, 150165, -42273, 21168, 0, 227952, 10128, 78120, 63018, 78717, 4275, 0, 74541, -24360, 22696, 33000, -34920, 58266, 0, 95310, 237888, 143220, 1922, 21850, 68634, 0, 71426, 40143, -9240, 46800, 19020, 9516, 0, 186726, 76230, -14402, 49188, 2925, 5182, 0, -20160, 55242, 31521, -141805, 91233, -89400, 0, -4264, -238815, -4082, 90216, -78294, -202500, 0, -1848, -96000, 79731, -135186, 13206, 1904, 0, 18620, 10082, -106812, -100140, 74160, 29820, 0, -140814, 126819, -14400, 258579, 214332, 125340, 0, -277884, -10134, -136118, -12174, 54505, -7524, 0, -210, -28348, 230073, 2052, -7490, -44298, 0, 240250, 47712, 60135, 98487, -31581, -26535, 0, 55404, 96695, 137781, -27588, 42120, 73080, 0, -3928, -146412, 30912, -23815, 289170, 222972, 0, -17639, -85920, -12864, 109082, 31143, 120240, 0, 71187, 5130, -18238, 168264, 37576, 202066, 0, -122040, 126540, -23250, 65940, -58410, -343980, 0, -24190, -25014, 188060, 11072, 13794, 129975, 0, -1530, 10992, 355752, -11598, -3725, -279000, 0, -124560, -26019, 38220, 73080, 58327, -13800, 0, -40320, 3291, -154425, 176328, -54777, 6196, 0, -236289, -26505, -170084, 282366, -228750, 48528, 0, 492, 193448, -152247, 23390, 104796, 45936, 0, 153252, -18894, 33060, 202167, -93558, 148365, 0, 162432, -76260, 19834, 13104, 3564, -38, 0, 3050, -19647, -253113, -11760, -41832, 84165, 0, -37107, -108864, -11250, -2651, -3375, 3870, 0, -158832, -30195, -42158, 145713, 27720, 10530, 0, -72870, 62586, -4389, -7472, -76860, 32091, 0, -123984, 43788, 9180, 113600, -126165, -17928, 0, -24948, 52855, -11709, -131244, 40845, -112772, 0, 109910, 17424, 64602, 52155, -70168, -103920, 0, 23958, 61500, 706, 19926, -135648, -155195, 0, -43974, 97500, -62496, -9879, 234, -179064, 0, 230040, 40736, -145254, -168390, 14155, 255864, 0, -220795, -186879, -214910, -24795, 356832, -5115, 0, -257721, 4680, -10530, -53634, -52290, 208033, 0, -22470, 41148, -97530, 10500, 31680, -32928, 0, -45567, -264678, -30240, 221357, -142284, -30240, 0, 26847, 9890, 237256, -66, -15960, -242172, 0, -18000, -34090, -19332, 43200, 9486, -34704, 0, -201022, 171288, 4026, 8948, 187671, 225450, 0, 122136, 69720, -14022, 78678, -2755, 88250, 0, 202275, 147396, 222936, -194400, -95330, 11511, 0, -73476, -103164, 35910, 23186, 107055, 140280, 0, -11286, -6036, 33586, 50220, -119195, -165186, 0, -26775, 7391, 125496, -105270, 63504, -230868, 0, 140924, -10476, -51660, -163782, 256848, -2698, 0, -35541, 63180, -20268, -77664, 44385, 8195, 0, -8592, 167058, 230640, 31850, -28874, -206064, 0, -84868, 200058, 187209, 56772, -4785, -71855, 0, -9408, 230580, 252396, -60054, -2840, -30098, 0, -2340, 152210, -32802, 13530, -70704, -148800, 0, -32760, -20121, -23750, -33138, 58944, -67260, 0, -25728, 290, 46629, 290055, -56025, -47376, 0, -134445, -22320, -123906, -4032, 153169, -34818, 0, -186300, 25872, -14190, -222730, -140610, -13122, 0, -54540, 131490, -121277, -14700, -301320, -196542, 0, 33495, 40348, 197856, -3925, 4750, 188742, 0, -68688, -81702, -2966, -121734, 88380, 10080, 0, 65286, 90705, 238707, 6498, -17076, 243648, 0, -219600, 111528, 57000, 69225, 60460, 12837, 0, 31178, 109866, -158760, 186372, -61992, 115500, 0, 277191, 68, -247104, 11091, 19415, 7560, 0, 5415, -175030, -10248, 2478, -250677, 248208, 0, -71323, 103782, 228450, 7128, 19368, 189225, 0, -51120, 172260, 305046, 60144, -1845, 19114, 0, -26892, 53613, -193068, -284940, -232776, 33285, 0, 80442, 25554, -10392, 188356, 235224, -133275, 0, 234876, -41250, 22120, 7581, -204885, -134496, 0, -33040, -203472, -133158, 99480, -165998, -42051, 0, -21758, -4731, 107920, 26190, -168528, 166425, 0, 175818, 3534, 34729, -176178, 136440, 59040, 0, 252780, 28224, -281880, 20917, -132869, 205341, 0, -88956, -210450, 111750, 8500, -18228, 418, 0, -98595, -127090, -180774, 4212, 42840, -4196, 0, -9600, -162288, 4116, -45360, 11286, -100425, 0, 42966, 140664, -56405, -303597, 12768, -92700, 0, 51894, -148530, 11115, 58905, 10080, 126718, 0, -250560, -10744, -13473, 347355, 256932, 213000, 0, 27162, -166257, 1045, -107928, 36186, -179340, 0, -174909, -281880, -247232, -2208, 152560, -260721, 0, -12600, -70070, 163626, 17798, -36000, -110214, 0, 54074, 196413, 14460, -230256, 498, 468, 0, 72468, -238780, 356562, 84720, -38640, 121536, 0, 167750, 244602, 206049, -133560], "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": "19.4.a.a", "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], [-3], [5], [1], [12], [-15], [0], [21], [-2], [-36], [-54], [5], [-11], [0], [60], [-71], [93], [6], [-19], [12], [0], [162], [183], [105], [19], [33], [-145], [0], [-249], [-180], [-56], [45], [-270], [-279], [0], [-2], [-250], [57], [-55], [252], [-240], [0], [-196], [-54], [-24], [-549], [168], [-355], [0], [-57], [465], [-11], [435], [435], [-648], [0], [-95], [747], [-195], [60], [358], [168], [0], [433], [-132], [810], [-961], [93], [915], [0], [-246], [-42], [-353], [750], [95], [-19], [0], [165], [-34], [-852], [-671], [720], [-234], [0], [1116], [588], [-1245], [-1134], [168], [72], [0], [183], [-280], [-504], [-228], [225], [-758], [0], [108], [19]]}