# Stored data for newform 2352.4.a.cr, downloaded from the LMFDB on 24 April 2024.
{"label": "2352.4.a.cr", "space_label": "2352.4.a", "level": 2352, "weight": 4, "hecke_orbit": 70, "hecke_orbit_code": 310748374355675440, "dim": 4, "is_polredabs": true, "nf_label": "4.4.145408.2", "trace_hash": 187933004825520047, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[5, [5444, 688, -204, -8, 1]], [11, [2039184, 79968, -2920, -40, 1]]], "qexp_display": "q+3q^{3}+(2+\\beta _{2}+3\\beta _{3})q^{5}+9q^{9}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 37632, "fricke_eigenval": -1, "atkin_lehner_string": "+-+", "analytic_conductor": 138.77249233350193, "hecke_ring_index": 8, "level_radical": 42, "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": [2352, 1, [1471, 1765, 785, 2257], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 1, "level_primes": [2, 3, 7], "conrey_indexes": [1], "field_disc": 145408, "field_disc_factorization": [[2, 11], [71, 1]], "field_poly": [142, 0, -24, 0, 1], "hecke_ring_index_factorization": [[2, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.813", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "41.299", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "668.954", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, -1], [7, 1]], "trace_display": [0, 12, 8, 0], "traces": [0, 4, 0, 12, 0, 8, 0, 0, 0, 36, 0, 40, 0, 48, 0, 24, 0, -152, 0, -224, 0, 0, 0, 8, 0, -28, 0, 108, 0, -144, 0, -400, 0, 120, 0, 0, 0, -304, 0, 144, 0, -152, 0, -160, 0, 72, 0, -544, 0, 0, 0, -456, 0, -1320, 0, -16, 0, -672, 0, -1040, 0, 896, 0, 0, 0, -648, 0, 416, 0, 24, 0, -248, 0, -752, 0, -84, 0, 0, 0, -864, 0, 324, 0, -1456, 0, -1608, 0, -432, 0, 2936, 0, 0, 0, -1200, 0, 80, 0, 144, 0, 360, 0, 2600, 0, -1936, 0, 0, 0, 952, 0, 160, 0, -912, 0, -40, 0, -5040, 0, 432, 0, 0, 0, 2116, 0, -456, 0, 1344, 0, -2640, 0, -480, 0, -4144, 0, 0, 0, 216, 0, 480, 0, -1808, 0, -1632, 0, -6976, 0, 4944, 0, 0, 0, -2056, 0, -2544, 0, -1368, 0, -3312, 0, 2464, 0, -3960, 0, 0, 0, -3168, 0, -48, 0, -2656, 0, 2932, 0, -2016, 0, 4024, 0, 0, 0, -3120, 0, -2216, 0, -624, 0, 2688, 0, -4960, 0, -11920, 0, 0, 0, -2488, 0, 1896, 0, -1944, 0, -1816, 0, -4800, 0, 1248, 0, 0, 0, 4072, 0, 72, 0, -9408, 0, -13520, 0, -744, 0, -12320, 0, 0, 0, -2256, 0, 8984, 0, -6944, 0, -252, 0, -10608, 0, 7408, 0, 0, 0, 1472, 0, -9328, 0, -2592, 0, 12968, 0, -1008, 0, 972, 0, 0, 0, 4208, 0, -4368, 0, -10512, 0, 13264, 0, -4824, 0, 808, 0, 0, 0, -1296, 0, 20440, 0, -8400, 0, 8808, 0, -2184, 0, -688, 0, 0, 0, 13032, 0, -6104, 0, -3600, 0, -6656, 0, -13536, 0, 240, 0, 0, 0, 11092, 0, 432, 0, -504, 0, -4272, 0, 1080, 0, -5984, 0, 0, 0, 7800, 0, 696, 0, -7904, 0, -5808, 0, -11328, 0, -8096, 0, 0, 0, 3080, 0, 3552, 0, 2856, 0, 17552, 0, -18608, 0, 480, 0, 0, 0, -16336, 0, -2736, 0, -7136, 0, 16352, 0, -120, 0, -5280, 0, 0, 0, -15120, 0, -7032, 0, -2016, 0, 1296, 0, -27816, 0, 11888, 0, 0, 0, 12632, 0, -7180, 0, 6348, 0, -13320, 0, -19680, 0, -1368, 0, 0, 0, 6344, 0, 4032, 0, -14256, 0, -17456, 0, -7920, 0, 21280, 0, 0, 0, -1440, 0, -5328, 0, -2224, 0, -12432, 0, -2400, 0, -8480, 0, 0, 0, -64, 0, -240, 0, 648, 0, 22560, 0, -29712, 0, 1440, 0, 0, 0, -26464, 0, -5424, 0, 4240, 0, 17544, 0, -4896, 0, -27896, 0, 0, 0, -20928, 0, 14248, 0, -16064, 0, 14832, 0, -18560, 0, 5024, 0, 0, 0, 32088, 0, 5528, 0, -6168, 0, 4696, 0, -6992, 0, -7632, 0, 0, 0, 15992, 0, -4104, 0, -17416, 0, -20976, 0, -9936, 0, 21392, 0, 0, 0, 7392, 0, 16448, 0, -9504, 0, -11880, 0, -1632, 0, -26944, 0, 0, 0, 27960, 0, -13456, 0, -9504, 0, 8520, 0, -23280, 0, -144, 0, 0, 0, -30592, 0, -7968, 0, -5888, 0, 52008, 0, 8796, 0, 5400, 0, 0, 0, -6048, 0, -8272, 0, -20160, 0, 12072, 0, -32040, 0, 15568, 0, 0, 0, 27728, 0, 29172, 0, -9360, 0, 2216, 0, 35376, 0, -6648, 0, 0, 0, -19272, 0, -1872, 0, 8800, 0, -63760, 0, 8064, 0, 8160, 0, 0, 0, -14880, 0, 5320, 0, -3360, 0, -35760, 0, 3696, 0, -22032, 0, 0, 0, 22784, 0, -29200, 0, -7464, 0, -3256, 0, -35680, 0, 5688, 0, 0, 0, -45584, 0, -5832, 0, -3600, 0, 21216, 0, -5448, 0, -44888, 0, 0, 0, -14400, 0, 24712, 0, -10912, 0, 3744, 0, 10056, 0, 21856, 0, 0, 0, 38192, 0, 16928, 0, 12216, 0, -26144, 0, 19152, 0, 216, 0, 0, 0, -18740, 0, -28224, 0, -7264, 0, 2640, 0, -40560, 0, 28864, 0, 0, 0, -2232, 0, -13184, 0, 16768, 0, -36960, 0, 17088, 0, -67104, 0, 0, 0, -5776, 0, 1056, 0, -6768, 0, -1816, 0, 56640, 0, 26952, 0, 0, 0, -49632, 0, -20832, 0, 22496, 0, -6800, 0, -756, 0, 8504, 0, 0, 0, -31824, 0, 29784, 0, 28880, 0, 22224, 0, 5920, 0, 6064, 0, 0, 0, 61376, 0, -10616, 0, 4416, 0, -23056, 0, -13056, 0, -27984, 0, 0, 0, 39616, 0, -7776, 0, 24992, 0, -79824, 0, 38904, 0, 7264, 0, 0, 0, -3024, 0, 41520, 0, 8400, 0, 2916, 0, 24032, 0, 76976, 0, 0, 0, 10688, 0, -31328, 0, 12624, 0, -10936, 0, -15184, 0, -13104, 0, 0, 0, -29280, 0, -31536, 0, -672, 0, 29728, 0, 39792, 0, -34280, 0, 0, 0, -14472, 0, 62544, 0, 19456, 0, 2424, 0, 31768, 0, -14544, 0, 0, 0, 18544, 0, -68784, 0, -3888, 0, -38712, 0, 20208, 0, 61320, 0, 0, 0, -6424, 0, -25200, 0, -856, 0, 46032, 0, 26424, 0, -58176, 0, 0, 0, -6552, 0, 55112, 0, -17872, 0, -2064, 0, 29504, 0, -20800, 0, 0, 0, 9544, 0, -3808, 0, 39096, 0, 75320, 0, 78992, 0, -18312, 0, 0, 0, -49616, 0, -10800, 0, -38176, 0, -22964, 0, -19968, 0, 97448, 0, 0, 0, -40608, 0, 92832, 0, 5664, 0, 720, 0, 45976, 0, 864, 0, 0, 0, 66856, 0, -65896, 0, 33276, 0, 30400, 0, 38688, 0, 1296, 0, 0, 0, -67040, 0, -1512, 0, -18360, 0, 5600, 0, -12816, 0, -32672, 0, 0, 0, 3240, 0, 38304, 0, 59056, 0, -17952, 0, -18336, 0, 159344, 0, 0, 0, 100040, 0, 13216, 0, 23400, 0, -25016, 0, 20640, 0, 2088, 0, 0, 0, -84432, 0, -23712, 0, 47360, 0, 26448, 0, -17424, 0, -14312, 0, 0, 0, -33984, 0, -48080, 0, -30656, 0, -24288, 0, 89912, 0, -61104, 0, 0, 0, 46392, 0, 46152, 0, 9240, 0, 33224, 0, -11984, 0, 10656, 0, 0, 0, -63516, 0, 8568, 0, 95312, 0, -71280, 0, 52656, 0, -13776, 0, 0, 0, -55824, 0, 9024, 0, 1936, 0, 1440, 0, -16352, 0, -59056, 0, 0, 0, 162496, 0, -58256, 0, -49008, 0, 96032, 0, 87168, 0, -8208, 0, 0, 0, 116368, 0, -21408, 0, 99520, 0, -72, 0, 49056, 0, 198376, 0, 0, 0, -360, 0, 10200, 0, 93152, 0, -15840, 0, 17480, 0, -82016, 0, 0, 0, 21704, 0, -12816, 0, -45360, 0, -43304, 0, -13952, 0, -21096, 0, 0, 0, -4448, 0, -6048, 0, 66168, 0, -12048, 0, 3888, 0, -23424, 0, 0, 0, -83448, 0, 32816, 0, -33744, 0, 35664, 0, 52032, 0, 177792, 0, 0, 0, -23232, 0, -33056, 0, 37896, 0, -31168, 0, 52352, 0, -21540, 0, 0, 0, 16352, 0, 19044, 0, 84016, 0, -37872, 0, -39960, 0, -49384, 0, 0, 0, -59040, 0, 42568, 0, 133696, 0, -4104, 0, 126296, 0, -7056, 0, 0, 0, 36256, 0, -43448, 0, 19032, 0, 113760, 0, -28240, 0, 12096, 0, 0, 0, -18928, 0, -42768, 0, 117728, 0, 101744, 0, -52368, 0, -45280, 0, 0, 0, -23760, 0, 133992, 0, 51264, 0, 63840, 0, 1376, 0, -51024, 0, 0, 0, 110232, 0, -65104, 0, -4320, 0, 103080, 0, 133744, 0, -15984, 0, 0, 0, 38672, 0, -6672, 0, -66912, 0, -15312, 0, -37296, 0, 126824, 0, 0, 0, -7200, 0, -13992, 0, 61488, 0, -25440, 0, 21096, 0, 33680, 0, 0, 0, 111424, 0, -5264, 0, -192, 0, 168936, 0, 68336, 0, -720, 0, 0, 0, -5168, 0, 1944, 0, -90184, 0, 20272, 0, 67680, 0, -21088, 0, 0, 0, -89136, 0, 17528, 0, 88064, 0, 4320, 0, 100704, 0, 21424, 0, 0, 0, 180760, 0, 105072, 0, -79392, 0, -124992, 0, 78032, 0, -16272, 0, 0, 0, -176, 0, 12720, 0, -60880, 0, -105336, 0, 52632, 0, -141152, 0, 0, 0, -14688, 0, -13328, 0, -35776, 0, -83688, 0, 138488, 0, 14304, 0, 0, 0, 79464, 0, 36808, 0, -62784, 0, 9240, 0, 81952, 0, 42744, 0, 0, 0, -106176, 0, -48192, 0, -22696, 0, 146832, 0, 44496, 0, 148144, 0, 0, 0, -55680, 0, -20568, 0, 85456, 0, 15072, 0, 18816, 0, 5664, 0, 0, 0, -96232, 0, -39280, 0, 96264, 0, 68016, 0, 81856, 0, 16584, 0, 0, 0, -105488, 0, -18504, 0, 28448, 0, -112792, 0, 14088, 0, 92352, 0, 0, 0, -20976, 0, 142192, 0, -83168, 0, -22896, 0, -184456, 0, -68256, 0, 0, 0, -31992, 0, -43316, 0, 47976, 0, 20016, 0, 136960, 0, -12312, 0, 0, 0, -34720, 0, -52248, 0, -54576, 0, 80496, 0, -62928, 0, -46368, 0, 0, 0, -29808, 0, 11616, 0, -56240, 0, 64176, 0, 40128, 0, -11152, 0, 0, 0, 106952, 0, 110112, 0, 22176, 0, -174928, 0, -236704, 0, 49344, 0, 0, 0, 163968, 0, -28512, 0, -54928, 0, -225840, 0, -35640, 0, -116648, 0, 0, 0, -4896, 0, -46216, 0, -15712, 0, -80832, 0, 145288, 0, 135344, 0, 0, 0, 133528, 0, -154368, 0, 83880, 0, 92000, 0, 57184, 0, -40368, 0, 0, 0, -11512, 0, -28512, 0, 11232, 0, 135536, 0, 25560, 0, -113232, 0, 0, 0, -69840, 0, 111992, 0, -63392, 0, -432, 0, 24864, 0, -110352, 0, 0, 0, 107736, 0, -22352, 0, -91776, 0, -111032, 0, 6592, 0, -23904, 0, 0, 0, 23872, 0, -17664, 0, -67232, 0, -145928, 0, 156024, 0, -59744, 0, 0, 0, 26388, 0, 318376, 0, 12448, 0, 16200, 0, -184608, 0, 136720, 0, 0, 0, -221328, 0, -85344, 0, -18144, 0, 79168, 0, -79872, 0, -24816, 0, 0, 0, -159368, 0, -60480, 0, -19704, 0, 65136, 0, 36216, 0, 65632, 0, 0, 0, -96120, 0, 98712, 0, 192240, 0, 46704, 0, -111600, 0, -36496, 0, 0, 0, 22656, 0, -166960, 0, 83184, 0, -128328, 0, -217456, 0, 87516, 0, 0, 0, 190336, 0, -28080, 0, 192672, 0, -28344, 0, 6648, 0, -212104, 0, 0, 0, 106128, 0, 31208, 0, 62384, 0, -19944, 0, 50376, 0, 83200, 0, 0, 0, -1160, 0, -70672, 0, -57816, 0, -114720, 0, -80352, 0, -5616, 0, 0, 0, -248816, 0, 26400, 0, -31128, 0, 31792, 0, -191280, 0, 193952, 0, 0, 0, 24192, 0, -169128, 0, -118688, 0, 24480, 0, 37088, 0, -260064, 0, 0, 0, -39008, 0, 6272, 0, -44640, 0, 94024, 0, -27280, 0, 15960, 0, 0, 0, -25568, 0, -10080, 0, 53152, 0, -201676, 0, -107280, 0, -121440, 0, 0, 0, 11088, 0, -134384, 0, 22080, 0, -66096, 0, -276312, 0, -7088, 0, 0, 0, -80704, 0, -83296, 0, 68352, 0, -69960, 0, -22560, 0, -87600, 0, 0, 0, -196408, 0, -22392, 0, 30248, 0, 169168, 0, -9768, 0, 238816, 0, 0, 0, -107040, 0, 124912, 0, -173840, 0, 17064, 0, 33024, 0, -72384, 0, 0, 0, 87592, 0, 61520, 0, -136752, 0, -221584, 0, -195216, 0, -17496, 0, 0, 0, -66752, 0, -10800, 0, -134752, 0, -147544, 0, 63648, 0, -40368, 0, 0, 0, -16344, 0, -57912, 0, -356336, 0, -134664, 0, -223248, 0, 32208, 0, 0, 0, 149688, 0, 107176, 0, -43200, 0, 205632, 0, -69008, 0, 74136, 0, 0, 0, 37448, 0, -32736, 0, -88216, 0, 73184, 0, 11232, 0, 79920, 0, 0, 0, 30168, 0, 94528, 0, -66000, 0, 65568, 0, 67648, 0, -169680, 0, 0, 0, 122336, 0, -15760, 0, 114576, 0, -43712, 0, -87232, 0, 50784, 0, 0, 0, -32784, 0, 36648, 0, -2240, 0, 48948, 0, -78432, 0, -20640, 0, 0, 0, 57456, 0, -198008, 0, -88064, 0, 648, 0, -64048, 0, 121104, 0, 0, 0, -309432, 0, 196712, 0, -56220, 0, -7224, 0, -78896, 0, -84672, 0, 0, 0, -137472, 0, -21792, 0, 3960, 0, -82928, 0, 7920, 0, 46816, 0, 0, 0, -121680, 0, -169416, 0, -136752, 0, 86592, 0, -209008, 0, 324128, 0, 0, 0, -85568, 0, 101216, 0, -6696, 0, -68112, 0, -236496, 0, -39552, 0, 0, 0, 2352, 0, 50304, 0, -97616, 0, 87768, 0, -110880, 0, -56736, 0, 0, 0, 51264, 0, -61632, 0, -233840, 0, -201312, 0, -193560, 0, 110080, 0, 0, 0, 383728, 0, -29920, 0, -17328, 0, 89312, 0, 51328, 0, 3168, 0, 0, 0, 20592, 0, -20304, 0, -37368, 0, 67616, 0, -5448, 0, -81104, 0, 0, 0, 169920, 0, 222392, 0, 77264, 0, 80856, 0, -228928, 0, -236864, 0, 0, 0, 158096, 0, 77648, 0, -148896, 0, 202184, 0, 42608, 0, -62496, 0, 0, 0, -47632, 0, 67488, 0, 126720, 0, -158912, 0, -20400, 0, 168640, 0, 0, 0, -2268, 0, 156392, 0, 142000, 0, 25512, 0, 1920, 0, -33728, 0, 0, 0, -145960, 0, -59432, 0, -95472, 0, -41928, 0, -69392, 0, 89352, 0, 0, 0, 138504, 0, 86640, 0, -350552, 0, 98016, 0, 66672, 0, -187392, 0, 0, 0, 17760, 0, 3248, 0, -117824, 0, 18192, 0, -61488, 0, -22208, 0, 0, 0, -257664, 0, -75136, 0, 184128, 0, -69560, 0, 19664, 0, -31848, 0, 0, 0, 72368, 0, 13248, 0, -455184, 0, -136496, 0, -69168, 0, -22064, 0, 0, 0, -39168, 0, -181912, 0, 16912, 0, -83952, 0, -188592, 0, -485248, 0, 0, 0, -141552, 0, -84832, 0, 118848, 0, 10528, 0, -180064, 0, -23328, 0, 0, 0, 102128, 0, 74976, 0, 4440, 0, -36816, 0, -239472, 0, -119232, 0, 0, 0, 116712, 0, -152792, 0, 273232, 0, 21792, 0, -96704, 0, -24240, 0, 0, 0, 139144, 0, -16496, 0, -9072, 0, 175248, 0, -73104, 0, 124560, 0, 0, 0, -3104, 0, 25200, 0, -121536, 0, 378016, 0, 8748, 0, 382976, 0, 0, 0, 72096, 0, -370304, 0, 117696, 0, 230928, 0, -28320, 0, -196960, 0, 0, 0, 66984, 0, -46108, 0, 32064, 0, 195920, 0, -271824, 0, -93984, 0, 0, 0, -113928, 0, 37872, 0, -59752, 0, 63904, 0, -32808, 0, -208608, 0, 0, 0, -45552, 0, -132176, 0, -154320, 0, -39312, 0, -107280, 0, 263792, 0, 0, 0, 445784, 0, 60000, 0, -87840, 0, 70672, 0, -1024, 0, -94608, 0, 0, 0, 173456, 0, -2016, 0, 352688, 0, 129568, 0, 89184, 0, -217096, 0, 0, 0, 119376, 0, 190272, 0, -22384, 0, -102840, 0, 92784, 0, 69392, 0, 0, 0, 9408, 0, 325304, 0, -43416, 0, -125312, 0, -210016, 0, 187632, 0, 0, 0, -126216, 0, 58368, 0, 103944, 0, 233280, 0, 7272, 0, -291104, 0, 0, 0, 95304, 0, -396704, 0, -553456, 0, -43632, 0, -78560, 0, 134416, 0, 0, 0, -445776, 0, 451536, 0, 55632, 0, 43192, 0, 31248, 0, -206352, 0, 0, 0, 40192, 0, -11664, 0, -169440, 0, 52600, 0, -116136, 0, -94792, 0, 0, 0, 60624, 0, 54464, 0, -361664, 0, 183960, 0, 238752, 0, -74688, 0, 0, 0, -225728, 0, 329960, 0, -19272, 0, -147240, 0, -220896, 0, -75600, 0, 0, 0, 206648, 0, -2568, 0, -200, 0, -117296, 0, 138096, 0, 86848, 0, 0, 0, 79272, 0, -157216, 0, -221760, 0, -174528, 0, -128624, 0, 143040, 0, 0, 0, -239976, 0, 90800, 0, -19656, 0, 114792, 0, 255408, 0, 165336, 0, 0, 0, 402160, 0, -53616, 0, -74848, 0, 258824, 0, -6192, 0, 69736, 0, 0, 0, 88512, 0, -127768, 0, 107456, 0, -62400, 0, 227136, 0, -405744, 0, 0, 0, 201352, 0, -384016, 0, 28632, 0, -421152, 0, -83440, 0, -11424, 0, 0, 0, 190384, 0, 117288, 0, -149944, 0, 5248, 0, 225960, 0, -151360, 0, 0, 0, 236976, 0, 215936, 0, 169280, 0, -54936, 0, -295552, 0, 190624, 0, 0, 0, -70104, 0, 270080, 0, -148848, 0, 172480, 0, -156064, 0, -32400, 0, 0, 0, -394048, 0, -114528, 0, -420608, 0, 75976, 0, -68892, 0, 182280, 0, 0, 0, -59904, 0, 386088, 0, 26608, 0, 292344, 0, -50752, 0, -17984, 0, 0, 0, -384936, 0, 41288, 0, -121824, 0, -85032, 0, -238640, 0, 278496, 0, 0, 0, 385432, 0, 16992, 0, 253152, 0, -282880, 0, 2160, 0, -27040, 0, 0, 0, 137928, 0, 284864, 0, 280240, 0, 2592, 0, -76016, 0, -63792, 0, 0, 0, -569824, 0, -679712, 0, 200568, 0, -457384, 0, 4064, 0, -197688, 0, 0, 0, 357040, 0, 99828, 0, -29408, 0, -26392, 0, 91200, 0, 368840, 0, 0, 0, 116064, 0, -20416, 0, 40240, 0, 3888, 0, 184280, 0, 33760, 0, 0, 0, -326496, 0, 322064, 0, -201120, 0, 193576, 0, 378848, 0, -4536, 0, 0, 0, 332352, 0, -55080, 0, -315608, 0, -4544, 0, 16800, 0, -218752, 0, 0, 0, -38448, 0, -513832, 0, -361008, 0, -98016, 0, 58560, 0, 48032, 0, 0, 0, -387928, 0, -17328, 0, 9720, 0, 126072, 0, 104048, 0, 114912, 0, 0, 0, -181584, 0, 177168, 0, 386400, 0, 293296, 0, -53856, 0, 322328, 0, 0, 0, -55008, 0, -346232, 0, 30144, 0, 478032, 0, -31504, 0, -114816, 0, 0, 0, -67864, 0, -225760, 0, 300120, 0, 227936, 0, 7392, 0, 39648, 0, 0, 0, 224288, 0, 70200, 0, 445016, 0, -448240, 0, -75048, 0, -115776, 0, 0, 0, 61920, 0, -47120, 0, 163744, 0, 6264, 0, 1376, 0, 457056, 0, 0, 0, -157064, 0, -408960, 0, -253296, 0, -324592, 0, -93600, 0, -71136, 0, 0, 0, -355952, 0, 142080, 0, -141376, 0, 390880, 0, 79344, 0, 9128, 0, 0, 0, -52272, 0, 73864, 0, 264592, 0, -42936, 0, 189288, 0, -418016, 0, 0, 0, 100608, 0, 176680, 0, -101952, 0, -312392, 0, 86928, 0, -144240, 0, 0, 0, 419676, 0, -91968, 0, 360144, 0, 70480, 0, -72864, 0, 199376, 0, 0, 0, 269736, 0, 115224, 0, 754736, 0, -183312, 0, 52288, 0, 100576, 0, 0, 0, -645712, 0, 232176, 0, 139176, 0, 555336, 0, 346896, 0, 138456, 0, 0, 0, -229568, 0, 27720, 0, 303872, 0, -214096, 0, 99672, 0, -188392, 0, 0, 0, -35952, 0, -169616, 0, 164992, 0, 31968, 0, -250232, 0, 513920, 0, 0, 0, -493208, 0, 138880, 0, -190548, 0, -310680, 0, -68336, 0, 25704, 0, 0, 0, 260208, 0, 285936, 0, -102104, 0, -678368, 0, -213840, 0, -336640, 0, 0, 0, 157968, 0, -577712, 0, 175024, 0, -41328, 0, -4448, 0, -455392, 0, 0, 0, -318368, 0, 275072, 0, -167472, 0, -594856, 0, 422448, 0, 27072, 0, 0, 0, -201424, 0, 5808, 0, 308624, 0, 233720, 0, 4320, 0, 181376, 0, 0, 0, -49056, 0, -762768, 0, 218496, 0, -177168, 0, 12264, 0, 600208, 0, 0, 0, 349832, 0, 43960, 0, 487488, 0, 45024, 0, -24944, 0, -174768, 0, 0, 0, 269464, 0, -147024, 0, 34976, 0, -390704, 0, 288096, 0, 228384, 0, 0, 0, 261504, 0, -131416, 0, -81744, 0, -24624, 0, 335136, 0], "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": "1176.4.a.bb", "char_is_minimal": false, "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, 0], [1, 0, 0, 0], [0, 0, 0, 0], [3, 0, 0, 0], [0, 0, 0, 0], [2, 0, 1, 3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [9, 0, 0, 0], [0, 0, 0, 0], [10, 3, -1, 4], [0, 0, 0, 0], [12, -3, 0, -23], [0, 0, 0, 0], [6, 0, 3, 9], [0, 0, 0, 0], [-38, -5, -3, 7], [0, 0, 0, 0], [-56, -3, 2, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [2, 5, -13, -16], [0, 0, 0, 0], [-7, 6, 4, 20], [0, 0, 0, 0], [27, 0, 0, 0], [0, 0, 0, 0], [-36, 3, 12, 18], [0, 0, 0, 0], [-100, -1, -6, -6], [0, 0, 0, 0], [30, 9, -3, 12], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-76, 10, -14, 16], [0, 0, 0, 0], [36, -9, 0, -69], [0, 0, 0, 0], [-38, -1, 13, -23], [0, 0, 0, 0], [-40, 6, -30, -36], [0, 0, 0, 0], [18, 0, 9, 27], [0, 0, 0, 0], [-136, -5, -10, -170], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-114, -15, -9, 21], [0, 0, 0, 0], [-330, -18, -20, 128], [0, 0, 0, 0], [-4, 7, 26, 318], [0, 0, 0, 0], [-168, -9, 6, -6], [0, 0, 0, 0], [-260, -23, 6, -126], [0, 0, 0, 0], [224, 5, -6, 37], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-162, -29, -6, -298], [0, 0, 0, 0], [104, 6, -6, -252], [0, 0, 0, 0], [6, 15, -39, -48], [0, 0, 0, 0], [-62, -27, 35, 28], [0, 0, 0, 0], [-188, -26, -30, 57], [0, 0, 0, 0], [-21, 18, 12, 60], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-216, 12, -20, 260], [0, 0, 0, 0], [81, 0, 0, 0], [0, 0, 0, 0], [-364, 10, -64, 16], [0, 0, 0, 0], [-402, -12, -74, -604], [0, 0, 0, 0], [-108, 9, 36, 54], [0, 0, 0, 0], [734, -5, 23, -369], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-300, -3, -18, -18], [0, 0, 0, 0], [20, -2, -70, -444], [0, 0, 0, 0], [36, 24, 54, 225], [0, 0, 0, 0], [90, 27, -9, 36], [0, 0, 0, 0]]}