# Stored data for newform 2352.4.a.f, downloaded from the LMFDB on 18 January 2021.
{"level_primes": [2, 3, 7], "is_polredabs": true, "sato_tate_group": "3.2.3.c1", "rm_discs": [], "conrey_indexes": [1], "cm_discs": [], "trace_hash": 720063296903422647, "level_radical": 42, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 1, "is_cm": false, "hecke_orbit": 6, "analytic_conductor": 138.77249233350193, "inner_twist_count": 1, "field_disc_factorization": [], "is_rm": false, "char_order": 1, "level_is_square": false, "weight_parity": 1, "label": "2352.4.a.f", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": false, "minimal_twist": "42.4.e.a", "field_poly_is_cyclotomic": false, "dim": 1, "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "traces": [0, 1, 0, -3, 0, -6, 0, 0, 0, 9, 0, 30, 0, 53, 0, 18, 0, -84, 0, 97, 0, 0, 0, -84, 0, -89, 0, -27, 0, -180, 0, -179, 0, -90, 0, 0, 0, -145, 0, -159, 0, 126, 0, 325, 0, -54, 0, 366, 0, 0, 0, 252, 0, -768, 0, -180, 0, -291, 0, 264, 0, 818, 0, 0, 0, -318, 0, 523, 0, 252, 0, 342, 0, -43, 0, 267, 0, 0, 0, 1171, 0, 81, 0, 810, 0, 504, 0, 540, 0, -600, 0, 0, 0, 537, 0, -582, 0, 386, 0, 270, 0, 618, 0, -1475, 0, 0, 0, -1884, 0, 413, 0, 435, 0, -882, 0, 504, 0, 477, 0, 0, 0, -431, 0, -378, 0, 1284, 0, -2483, 0, -975, 0, -2118, 0, 0, 0, 162, 0, 3012, 0, 37, 0, -1098, 0, 1590, 0, 1080, 0, 0, 0, -1644, 0, -1088, 0, -756, 0, 1074, 0, 506, 0, 2304, 0, 0, 0, -1844, 0, 540, 0, -162, 0, 612, 0, 873, 0, -2724, 0, 0, 0, -792, 0, 1254, 0, -1807, 0, -2454, 0, 870, 0, -2520, 0, 0, 0, -714, 0, -3709, 0, 954, 0, -1044, 0, 136, 0, -1569, 0, 0, 0, -756, 0, -756, 0, 2910, 0, -1484, 0, -1026, 0, -1950, 0, 0, 0, 129, 0, -4452, 0, 2032, 0, -801, 0, -6198, 0, -4591, 0, 0, 0, 4530, 0, -2196, 0, -3513, 0, -1530, 0, 5534, 0, -243, 0, 0, 0, 5141, 0, -2430, 0, 468, 0, -2520, 0, -1512, 0, -2490, 0, 0, 0, -1620, 0, -1572, 0, 4608, 0, 1800, 0, 1806, 0, 6112, 0, 0, 0, -2670, 0, -4231, 0, -1611, 0, -3816, 0, 3997, 0, 1746, 0, 0, 0, 2143, 0, -1158, 0, 4608, 0, -1584, 0, -810, 0, -4452, 0, 0, 0, -1854, 0, -4908, 0, 631, 0, 4425, 0, -3894, 0, -2185, 0, 0, 0, 3504, 0, -5400, 0, 5652, 0, -8148, 0, -4717, 0, -1239, 0, 0, 0, -2945, 0, -1305, 0, -3138, 0, 4277, 0, 2646, 0, -5370, 0, 0, 0, -1512, 0, -7188, 0, -9406, 0, -1431, 0, 3390, 0, -2052, 0, 0, 0, 4812, 0, 2550, 0, 1293, 0, 258, 0, 7099, 0, 1134, 0, 0, 0, 2963, 0, -3852, 0, -9540, 0, 11899, 0, 7449, 0, -2568, 0, 0, 0, 2925, 0, -10146, 0, 7056, 0, 6354, 0, -7026, 0, -6229, 0, 0, 0, -2472, 0, -9487, 0, -486, 0, -4350, 0, -7075, 0, -9036, 0, 0, 0, -4860, 0, -111, 0, 4158, 0, -6595, 0, 3294, 0, 7476, 0, 0, 0, -4770, 0, -1518, 0, 8567, 0, -3240, 0, -8148, 0, -10640, 0, 0, 0, -7032, 0, 3600, 0, 4932, 0, -14814, 0, 3780, 0, 3264, 0, 0, 0, -11251, 0, 2268, 0, -3852, 0, 475, 0, -3222, 0, -5934, 0, 0, 0, -1518, 0, 9750, 0, -8633, 0, -6912, 0, 13368, 0, -7685, 0, 0, 0, -2316, 0, -6653, 0, 5532, 0, -15444, 0, 15120, 0, -1620, 0, 0, 0, -683, 0, 486, 0, -9882, 0, -3708, 0, -1836, 0, 4206, 0, 0, 0, -2619, 0, 8850, 0, 10980, 0, 8172, 0, 9060, 0, 15679, 0, 0, 0, 15036, 0, -5111, 0, 2376, 0, 6678, 0, 11304, 0, -3762, 0, 0, 0, -7711, 0, 5421, 0, -2478, 0, -4292, 0, 7362, 0, -17460, 0, 0, 0, -2610, 0, -9858, 0, 17225, 0, 7560, 0, 13890, 0, 5292, 0, 0, 0, 19038, 0, 8053, 0, 2142, 0, 7476, 0, -17137, 0, 11127, 0, 0, 0, -23040, 0, -2862, 0, -18144, 0, -17363, 0, 3132, 0, -24702, 0, 0, 0, -408, 0, 2172, 0, 4175, 0, 4707, 0, 2586, 0, -2261, 0, 0, 0, 19398, 0, -16318, 0, 2268, 0, -26550, 0, -19925, 0, 2268, 0, 0, 0, 3421, 0, -8730, 0, 12180, 0, 6832, 0, 4452, 0, 14898, 0, 0, 0, 3078, 0, 10212, 0, -3779, 0, 5850, 0, -16998, 0, 7920, 0, 0, 0, -21750, 0, 12708, 0, -387, 0, 10944, 0, 10955, 0, 13356, 0, 0, 0, 15120, 0, -6096, 0, 24540, 0, 25103, 0, 2403, 0, -5604, 0, 0, 0, 18594, 0, -10968, 0, -18072, 0, 13773, 0, -40704, 0, -8405, 0, 0, 0, -222, 0, -10584, 0, -13590, 0, 468, 0, -14065, 0, 6588, 0, 0, 0, -25066, 0, 10539, 0, 15036, 0, -9540, 0, 4590, 0, -11082, 0, 0, 0, -16602, 0, 16020, 0, -13481, 0, 729, 0, -27300, 0, 24317, 0, 0, 0, 15690, 0, 18217, 0, -15423, 0, -19782, 0, 9864, 0, 7290, 0, 0, 0, 4921, 0, -1404, 0, 6528, 0, 18098, 0, 7560, 0, -24468, 0, 0, 0, 4536, 0, 13992, 0, 21719, 0, 7470, 0, -30306, 0, 15931, 0, 0, 0, 12222, 0, 10260, 0, 4860, 0, -3036, 0, -27296, 0, 4716, 0, 0, 0, 43354, 0, -13824, 0, -35100, 0, -30744, 0, -5400, 0, -1290, 0, 0, 0, -5418, 0, 44394, 0, 8584, 0, -18336, 0, 11064, 0, 31525, 0, 0, 0, -9834, 0, -43856, 0, 8010, 0, -13266, 0, 17453, 0, 12693, 0, 0, 0, 972, 0, 4833, 0, 35172, 0, 8011, 0, 11448, 0, -3672, 0, 0, 0, -11991, 0, 12180, 0, 3503, 0, -5238, 0, 22848, 0, 13456, 0, 0, 0, -40710, 0, 16344, 0, -6429, 0, 35130, 0, 27719, 0, 3474, 0, 0, 0, 2906, 0, -13824, 0, -19188, 0, 17251, 0, 4752, 0, 2094, 0, 0, 0, 2430, 0, 35502, 0, -7524, 0, 13356, 0, 32220, 0, 64512, 0, 0, 0, 10842, 0, 40267, 0, 5562, 0, -17604, 0, 24300, 0, 14724, 0, 0, 0, -3509, 0, -1893, 0, 18126, 0, 12905, 0, -13275, 0, -34638, 0, 0, 0, 11682, 0, 15120, 0, -17353, 0, 6555, 0, -46920, 0, -10584, 0, 0, 0, -18354, 0, -2279, 0, -10512, 0, 35568, 0, 4284, 0, 16200, 0, 0, 0, 2250, 0, -16956, 0, 22254, 0, 27343, 0, 24444, 0, -51024, 0, 0, 0, 14151, 0, -2226, 0, -18000, 0, 3717, 0, -35304, 0, 6264, 0, 0, 0, -27300, 0, 2341, 0, 8835, 0, -816, 0, 29015, 0, 3915, 0, 0, 0, -22176, 0, 9414, 0, -74496, 0, 44765, 0, -12831, 0, -40632, 0, 0, 0, -7938, 0, 51600, 0, -34522, 0, 16110, 0, -11214, 0, 62063, 0, 0, 0, 61692, 0, 41285, 0, 4536, 0, -68712, 0, -10511, 0, 21564, 0, 0, 0, -17460, 0, 28218, 0, -45576, 0, 21691, 0, 4293, 0, 8904, 0, 0, 0, -10170, 0, -58530, 0, -52208, 0, 6156, 0, 11580, 0, -41653, 0, 0, 0, 26100, 0, -28925, 0, -14436, 0, 42930, 0, -30744, 0, -7650, 0, 0, 0, 34153, 0, -3879, 0, 8424, 0, -12907, 0, -774, 0, 34392, 0, 0, 0, -21297, 0, 7986, 0, 26712, 0, -3402, 0, 64500, 0, 18540, 0, 0, 0, -12192, 0, -37810, 0, -8889, 0, 25608, 0, 52783, 0, 11556, 0, 0, 0, 11321, 0, 28620, 0, -44250, 0, 37188, 0, -35697, 0, -43932, 0, 0, 0, -22347, 0, 27546, 0, 25955, 0, 7704, 0, -37878, 0, -62791, 0, 0, 0, -31800, 0, 79346, 0, -8775, 0, 28422, 0, -27180, 0, 30438, 0, 0, 0, 26560, 0, -21168, 0, -32574, 0, -56520, 0, -19062, 0, 20928, 0, 0, 0, 21078, 0, 20208, 0, -22680, 0, 18687, 0, -71688, 0, 9180, 0, 0, 0, 12390, 0, 12035, 0, 7416, 0, -33204, 0, -28728, 0, 28461, 0, 0, 0, -10810, 0, 1458, 0, 76914, 0, 64512, 0, 13050, 0, 63168, 0, 0, 0, 21225, 0, 48174, 0, 44731, 0, 27108, 0, -30846, 0, 55790, 0, 0, 0, 3612, 0, -26460, 0, 14580, 0, -58500, 0, -52534, 0, 333, 0, 0, 0, -2808, 0, -12474, 0, -26370, 0, 20458, 0, 19785, 0, 15120, 0, 0, 0, -9882, 0, -22554, 0, 50731, 0, -22428, 0, 20994, 0, 59104, 0, 0, 0, 52638, 0, 14940, 0, 14310, 0, -16020, 0, 31492, 0, 4554, 0, 0, 0, 92735, 0, -25701, 0, -23112, 0, 40636, 0, 9720, 0, 20256, 0, 0, 0, 24444, 0, 32754, 0, 9432, 0, 31920, 0, -33576, 0, -23545, 0, 0, 0, 68352, 0, -26480, 0, 21096, 0, -52860, 0, -58175, 0, -10800, 0, 0, 0, -78175, 0, -14796, 0, -98364, 0, -10836, 0, 44442, 0, 33174, 0, 0, 0, -11340, 0, -36672, 0, -22176, 0, -9792, 0, -55524, 0, -65880, 0, 0, 0, 31128, 0, -29628, 0, 33753, 0, -26514, 0, 38520, 0, -6804, 0, 0, 0, -85879, 0, 11556, 0, 25386, 0, -4171, 0, -1425, 0, -99852, 0, 0, 0, 9666, 0, -74490, 0, 9289, 0, 17802, 0, -68712, 0, 22896, 0, 0, 0, 41646, 0, -68040, 0, 4554, 0, -23982, 0, 21889, 0, -29250, 0, 0, 0, -2360, 0, 25899, 0, 54522, 0, 74906, 0, 20736, 0, 54768, 0, 0, 0, -40104, 0, -10230, 0, -63540, 0, 23055, 0, -12858, 0, 22003, 0, 0, 0, -12738, 0, 20729, 0, 6948, 0, -65514, 0, -9164, 0, 19959, 0, 0, 0, -27648, 0, -16596, 0, -46746, 0, -18053, 0, 46332, 0, -23496, 0, 0, 0, -45360, 0, 52566, 0, -53783, 0, 4860, 0, -80610, 0, -32515, 0, 0, 0, 7590, 0, 26712, 0, 2049, 0, -34164, 0, 113587, 0, -1458, 0, 0, 0, 90360, 0, 29646, 0, 24750, 0, 50400, 0, 11124, 0, -18270, 0, 0, 0, 5508, 0, 116418, 0, -72802, 0, -12618, 0, 1110, 0, -21287, 0, 0, 0, -3786, 0, 138240, 0, 7857, 0, -43932, 0, 29329, 0, -26550, 0, 0, 0, -29386, 0, -32940, 0, 69624, 0, 23364, 0, -24516, 0, -84792, 0, 0, 0, -27180, 0, 13110, 0, 104527, 0, -47037, 0, 98310, 0, -22843, 0, 0, 0, 78570, 0, 54304, 0, -45108, 0, -21528, 0, -21024, 0, 15333, 0, 0, 0, -47125, 0, -7128, 0, 32400, 0, 40553, 0, -20034, 0, -74652, 0, 0, 0, -33912, 0, 60402, 0, 33605, 0, 11286, 0, -1704, 0, 48888, 0, 0, 0, -37776, 0, -78859, 0, 23133, 0, 68052, 0, 47791, 0, -16263, 0, 0, 0, -28728, 0, 7434, 0, -81666, 0, -49320, 0, 12876, 0, 137472, 0, 0, 0, -22086, 0, -32424, 0, -131599, 0, 52380, 0, 17670, 0, 67646, 0, 0, 0, -32640, 0, 13903, 0, 7830, 0, -50832, 0, 34577, 0, 29574, 0, 0, 0, -46547, 0, -51675, 0, 3612, 0, -53045, 0, -22680, 0, -25662, 0, 0, 0, -41670, 0, -58200, 0, 114623, 0, -15876, 0, 95910, 0, 16849, 0, 0, 0, -112254, 0, 32220, 0, -57114, 0, -14382, 0, -47520, 0, -24159, 0, 0, 0, -51912, 0, -6426, 0, 92790, 0, -61652, 0, -22428, 0, 15180, 0, 0, 0, 51411, 0, 10446, 0, 43128, 0, -33381, 0, -53070, 0, 45623, 0, 0, 0, 56436, 0, -28844, 0, 69120, 0, 123900, 0, 3077, 0, 8586, 0, 0, 0, -68165, 0, 54432, 0, 40950, 0, -20340, 0, 52089, 0, -147240, 0, 0, 0, -9396, 0, -30438, 0, 91730, 0, 74106, 0, 159636, 0, -134180, 0, 0, 0, 65526, 0, -74845, 0, 1224, 0, -55320, 0, -28872, 0, -6516, 0, 0, 0, 20915, 0, -12525, 0, -15300, 0, 1961, 0, -14121, 0, 72924, 0, 0, 0, -7758, 0, -98364, 0, 158256, 0, 6783, 0, 87816, 0, 3827, 0, 0, 0, -47256, 0, -34901, 0, -58194, 0, -42594, 0, -4860, 0, 48954, 0, 0, 0, 37442, 0, -6804, 0, -89910, 0, 26118, 0, 79650, 0, -34692, 0, 0, 0, 59775, 0, 18360, 0, -43021, 0, -6804, 0, -17778, 0, 44956, 0, 0, 0, -37290, 0, -115831, 0, -10263, 0, -74286, 0, -55727, 0, 26190, 0, 0, 0, 57240, 0, -36540, 0, 81198, 0, -146422, 0, -20496, 0, -71394, 0, 0, 0, -13356, 0, -44292, 0, -81720, 0, -44694, 0, -9060, 0, -68040, 0, 0, 0, 11226, 0, 15408, 0, -9234, 0, 59946, 0, 74088, 0, -30636, 0, 0, 0, 46116, 0, 11337, 0, 110988, 0, -107209, 0, -17550, 0, -87132, 0, 0, 0, 50994, 0, -94140, 0, 60876, 0, -23760, 0, -31674, 0, -61307, 0, 0, 0, -42336, 0, -143075, 0, 65250, 0, 111360, 0, -57664, 0, -38124, 0, 0, 0, 37620, 0, 1161, 0, -150696, 0, -104219, 0, -32832, 0, 1626, 0, 0, 0, -32865, 0, 37374, 0, 19351, 0, -40068, 0, -54210, 0, 110870, 0, 0, 0, -37806, 0, -29036, 0, -45360, 0, 18900, 0, 14832, 0, 18288, 0, 0, 0, 133381, 0, -73620, 0, 56922, 0, -5347, 0, -75309, 0, 118950, 0, 0, 0, -7209, 0, -53034, 0, 79445, 0, 16812, 0, -182748, 0, 26100, 0, 0, 0, 129768, 0, 26818, 0, -55782, 0, 42450, 0, 50400, 0, 32904, 0, 0, 0, -96649, 0, 54216, 0, 36204, 0, -61560, 0, -41319, 0, -152112, 0, 0, 0, 122112, 0, 46446, 0, 40061, 0, 25215, 0, -72090, 0, -93617, 0, 0, 0, -88206, 0, -122264, 0, 666, 0, 69336, 0, 59201, 0, 31752, 0, 0, 0, -24948, 0, 40770, 0, -114786, 0, -21420, 0, -1404, 0, 39570, 0, 0, 0, 42195, 0, -112668, 0, -133543, 0, -19764, 0, 7740, 0, -97732, 0, 0, 0, -111270, 0, -107856, 0, 75198, 0, 68562, 0, 53917, 0, -31617, 0, 0, 0, 27047, 0, -45108, 0, 83358, 0, -32597, 0, 28620, 0, -85554, 0, 0, 0, -13770, 0, -48234, 0, 9108, 0, 33246, 0, 208572, 0, 104129, 0, 0, 0, -51402, 0, -31320, 0, 49806, 0, -8586, 0, -96768, 0, -48060, 0, 0, 0, 32671, 0, 40443, 0, -38280, 0, 48888, 0, -2187, 0, 4080, 0, 0, 0, 81900, 0, 63840, 0, -84005, 0, -72951, 0, -61218, 0, -145763, 0, 0, 0, -42204, 0, 30133, 0, -47070, 0, -121158, 0, 42192, 0, -54651, 0, 0, 0, 72629, 0, 46269, 0, 53400, 0, 177912, 0, 59346, 0, -32424, 0, 0, 0, -29592, 0, -7086, 0, 47149, 0, -21870, 0, 134346, 0, 88884, 0, 0, 0, -144372, 0, -130517, 0, -14763, 0, -22680, 0, -118610, 0, 4212, 0, 0, 0, 7697, 0, -19584, 0, 2214, 0, -89902, 0, -54294, 0, -24468, 0, 0, 0, -22680, 0, -249600, 0, 79829, 0, 73404, 0, 67506, 0, 138457, 0, 0, 0, -210780, 0, 168659, 0, -13608, 0, 7776, 0, -41807, 0, -41976, 0, 0, 0, 23112, 0, -65157, 0, 56556, 0, 115297, 0, -22410, 0, -2850, 0, 0, 0, 90918, 0, -44520, 0, -51912, 0, -47793, 0, 66462, 0, -253008, 0, 0, 0, -142278, 0, 35604, 0, -36666, 0, -56394, 0, -27379, 0, -30780, 0, 0, 0, -93260, 0, -14580, 0, 175806, 0, -95771, 0, 9108, 0, -12318, 0, 0, 0, 81888, 0, -3108, 0, -58500, 0, -14148, 0, 123900, 0, -125756, 0, 0, 0, 124548, 0, -147502, 0, -130062, 0, 55818, 0, -152120, 0, 41472, 0, 0, 0, 88523, 0, 105300, 0, -27090, 0, -80208, 0, 92232, 0, 6450, 0, 0, 0, 16200, 0, 46110, 0, -145800, 0, 3870, 0, 61896, 0, -240851, 0, 0, 0, 139548, 0, 33264, 0, 16254, 0, -26802, 0, -34354, 0, -133182, 0, 0, 0, -133560, 0, -25752, 0, 39918, 0, -72622, 0, 55008, 0, -21678, 0, 0, 0, -33192, 0, 200838, 0, -209609, 0, -94575, 0, 60960, 0, 92664, 0, 0, 0, 226986, 0, 158256, 0, 29502, 0, -90720, 0, 53137, 0, 131568, 0, 0, 0, -78274, 0, -24030, 0, -40320, 0, -75835, 0, 39798, 0, -37842, 0, 0, 0, -52359, 0, -205446, 0, -281088, 0, -38079, 0, 4098, 0, -185940, 0, 0, 0, 103068, 0, 229285, 0, -2916, 0, -34692, 0, -196577, 0, -14499, 0, 0, 0, 59292, 0, -105516, 0, -137730, 0, -76258, 0, -24033, 0, -55002, 0, 0, 0, -34344, 0, 41952, 0, 138096, 0, 11016, 0, 85800, 0, -71675, 0, 0, 0, 70566, 0, -25236, 0, 35973, 0, 122670, 0, 188683, 0, -36540, 0, 0, 0, -111619, 0, -10509, 0, -55332, 0, 135900, 0, 15714, 0, 91392, 0, 0, 0, -68544, 0, -144990, 0, 131275, 0, -40368, 0, 21180, 0, 108000, 0, 0, 0, -65880, 0, 7208, 0, 122130, 0, -82836, 0, 180710, 0, -49032, 0, 0, 0, 74088, 0, 19287, 0, 292164, 0, -54360, 0, -105390, 0, 28092, 0, 0, 0, -83157, 0, -94074, 0, 187265, 0, -10422, 0, -92460, 0, 265850, 0, 0, 0, -49590, 0, -45900, 0, -8718, 0, 1332, 0, -90216, 0, 41472, 0, 0, 0, 3589, 0, 57564, 0, 30666, 0, 91072, 0, -51753, 0, 166020, 0, 0, 0, -14256, 0, 159936, 0, 235684, 0, -6282, 0, -115332, 0, -40068, 0, 0, 0, -42504, 0, -58445, 0, -7290, 0, 167676, 0, 192446, 0, -106506, 0, 0, 0, -126965, 0, 22572, 0, -124542, 0, -178471, 0, -40068, 0, 47262, 0, 0, 0, -96660, 0, -27348, 0, 6235, 0, -193536, 0, 46266, 0, -51713, 0, 0, 0, 221730, 0, 189890, 0, -32526, 0, 154230, 0, -20420, 0, -120801, 0, 0, 0, -36757, 0, -16686, 0, -34398, 0, 23671, 0, 52812, 0, 25752, 0, 0, 0, -72900, 0, -44022, 0, -78652, 0, -44172, 0, 65898, 0, 61094, 0, 0, 0, -185712, 0, 104760, 0, 10527, 0, 107400, 0, 14040, 0, 5679, 0, 0, 0, -129296, 0, -54378, 0, 154896, 0, 96624, 0, -38715, 0, 202746, 0, 0, 0, 39825, 0, 36204, 0, 59148, 0, 103914, 0, -20622, 0, 65053, 0, 0, 0, -103350, 0, -113194, 0, -35046, 0, 234828, 0, -212507, 0, -45360, 0, 0, 0, 440947, 0, 52059, 0, -69480, 0, -83340, 0, -19665, 0, 203244, 0, 0, 0, 140760, 0, 78498, 0, -74700, 0, 31752, 0, -159468, 0, 257042, 0, 0, 0, 175980, 0, 13608, 0, 55062, 0, -9648, 0, -114228, 0, 6837, 0, 0, 0, -201428, 0, 31536, 0, -48318, 0, 245609, 0, -106704, 0, 271218, 0, 0, 0, -12852, 0, 299388, 0, -105536, 0, -48600, 0, -51408, 0, -107856, 0, 0, 0, 12642, 0, 169975, 0, -6750, 0, 102822, 0, 87829, 0, 50868, 0, 0, 0, -47160, 0, -66762, 0, -252324, 0, 107696, 0, -82029, 0, 274164, 0, 0, 0, -73332, 0, 28932, 0, 43092, 0, 153072, 0, 138240, 0, -267013, 0, 0, 0, 208572, 0, -169795, 0, -42453, 0, -146376, 0, -111240, 0, 6678, 0, 0, 0, 108864, 0, 54000, 0, -3330, 0, 228816, 0, -11151, 0, 104178, 0, 0, 0, 105912, 0, -328494, 0, -145474, 0, -18792, 0, 58614, 0, 54180, 0, 0, 0, -92514, 0, 148212, 0, 81900, 0, 21888, 0, 92356, 0, -7023, 0, 0, 0, -243323, 0, -26505, 0, 183360, 0, 49082, 0, 2448, 0, 265500, 0, 0, 0, -87045, 0, -5418, 0, -13032, 0, -11745, 0, 277824, 0], "hecke_ring_index_factorization": [], "nf_label": "1.1.1.1", "field_poly": [0, 1], "atkin_lehner_string": "-++", "has_non_self_twist": 0, "atkin_lehner_eigenvals": [[2, -1], [3, 1], [7, 1]], "char_values": [2352, 1, [1471, 1765, 785, 2257], [1, 1, 1, 1]], "Nk2": 37632, "field_poly_root_of_unity": 0, "analytic_rank": 1, "char_orbit_label": "a", "weight": 4, "trace_display": [0, -3, -6, 0], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": false, "qexp_display": "q-3q^{3}-6q^{5}+9q^{9}+30q^{11}+53q^{13}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 1, "level_is_prime_power": false, "relative_dim": 1, "hecke_cutters": [[5, [6, 1]], [11, [-30, 1]]], "space_label": "2352.4.a", "level": 2352, "is_self_dual": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_degree": 1, "char_conductor": 1, "char_orbit_index": 1, "hecke_ring_generator_nbound": 1, "hecke_orbit_code": 22517998203963696, "fricke_eigenval": -1, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.962", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.873", "prec": 17}, {"__RealLiteral__": 0, "data": "0.003", "prec": 17}, {"__RealLiteral__": 0, "data": "4.599", "prec": 17}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "artin_degree": null, "qexp": [[0], [1], [0], [-3], [0], [-6], [0], [0], [0], [9], [0], [30], [0], [53], [0], [18], [0], [-84], [0], [97], [0], [0], [0], [-84], [0], [-89], [0], [-27], [0], [-180], [0], [-179], [0], [-90], [0], [0], [0], [-145], [0], [-159], [0], [126], [0], [325], [0], [-54], [0], [366], [0], [0], [0], [252], [0], [-768], [0], [-180], [0], [-291], [0], [264], [0], [818], [0], [0], [0], [-318], [0], [523], [0], [252], [0], [342], [0], [-43], [0], [267], [0], [0], [0], [1171], [0], [81], [0], [810], [0], [504], [0], [540], [0], [-600], [0], [0], [0], [537], [0], [-582], [0], [386], [0], [270], [0]]}