# Stored data for newform 546.6.a.a, downloaded from the LMFDB on 24 April 2024.
{"label": "546.6.a.a", "space_label": "546.6.a", "level": 546, "weight": 6, "hecke_orbit": 1, "hecke_orbit_code": 100663842, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1090538126908290184, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [-81, 1]], [11, [-191, 1]]], "qexp_display": "q-4q^{2}+9q^{3}+2^{4}q^{4}+3^{4}q^{5}-6^{2}q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 19656, "fricke_eigenval": -1, "atkin_lehner_string": "+-++", "analytic_conductor": 87.56956561788742, "hecke_ring_index": 1, "level_radical": 546, "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": 0, "analytic_rank_proved": true, "char_values": [546, 1, [365, 157, 379], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 7, 13], "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": "1.027", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.075", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.203", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, -1], [7, 1], [13, 1]], "trace_display": [-4, 9, 81, -49], "traces": [0, 1, -4, 9, 16, 81, -36, -49, -64, 81, -324, 191, 144, -169, 196, 729, 256, -871, -324, -479, 1296, -441, -764, 1387, -576, 3436, 676, 729, -784, -5295, -2916, 5940, -1024, 1719, 3484, -3969, 1296, 13543, 1916, -1521, -5184, 9464, 1764, 17387, 3056, 6561, -5548, -8112, 2304, 2401, -13744, -7839, -2704, 18038, -2916, 15471, 3136, -4311, 21180, 28784, 11664, 14773, -23760, -3969, 4096, -13689, -6876, -54354, -13936, 12483, 15876, 64608, -5184, 39461, -54172, 30924, -7664, -9359, 6084, -95554, 20736, 6561, -37856, -69634, -7056, -70551, -69548, -47655, -12224, -51906, -26244, 8281, 22192, 53460, 32448, -38799, -9216, 162654, -9604, 15471, 54976, 30000, 31356, 26549, 10816, -35721, -72152, -76686, 11664, -121099, -61884, 121887, -12544, 155186, 17244, 112347, -84720, -13689, -115136, 42679, -46656, -124570, -59092, 85176, 95040, 25191, 15876, -8354, -16384, 156483, 54756, 332217, 27504, 23471, 217416, 59049, 55744, 80385, -49932, -132656, -63504, -73008, -258432, -32279, 20736, -428895, -157844, 21609, 216688, 149576, -123696, 264571, 30656, -70551, 37436, 481140, -24336, 473873, 382216, 162342, -82944, -67963, -26244, 77866, 151424, 139239, 278536, 224669, 28224, 28561, 282204, -38799, 278192, -268826, 190620, -168364, 48896, 259056, 207624, 171112, 104976, -643850, -33124, 132957, -88768, 1096983, -213840, -166361, -129792, -35721, 155196, 390891, 36864, 507268, -650616, -123201, 38416, -767200, -61884, 476559, -219904, -489186, -120000, 259455, -125424, 766584, -106196, 112347, -43264, -91489, 142884, -95231, 288608, 581472, 306744, 1408347, -46656, -291060, 484396, 355149, 247536, 147199, -487548, -860014, 50176, 278316, -620744, -264390, -68976, -82854, -449388, -84231, 338880, -588276, 54756, -657072, 460544, -859986, -170716, 1682260, 186624, -264906, 498280, 59049, 236368, 194481, -340704, 80951, -380160, -626706, -100764, 1915509, -63504, 264917, 33416, -634959, 65536, 222734, -625932, -663607, -219024, -428895, -1328868, 1286716, -110016, 1461078, -93884, -467154, -869664, -134666, -236196, 1459170, -222976, 74529, -321540, 656276, 199728, -1118786, 530624, 481140, 254016, 2147754, 292032, -2133208, 1033728, -349191, 129116, -463736, -82944, -661216, 1715580, 1463886, 631376, -1206294, -86436, 2331504, -866752, 139239, -598304, -234403, 494784, -851963, -1058284, 270000, -122624, 1196613, 282204, -529472, -149744, 238941, -1924560, 2669698, 97344, -1393596, -1895492, -321489, -1528864, 963472, -649368, -1011345, 331776, -690174, 271852, 417209, 104976, -580684, -311464, -1089891, -605696, 397488, -556956, 2528242, -1114144, 1096983, -898676, -4402674, -112896, 487563, -114244, 1396674, -1128816, 1134540, 155196, -117649, -1112768, 1011123, 1075304, 1301488, -762480, -3034690, 673456, -123201, -195584, -3354398, -1036224, 5233248, -830496, 384111, -684448, -2156016, -419904, -2246658, 2575400, -1121130, 132496, 3196341, -531828, -2704768, 355072, 766584, -4387932, -883862, 855360, -64248, 665444, 226719, 519168, 894855, 142884, -2623936, -620784, -75186, -1563564, -5626883, -147456, -758079, -2029072, 1408347, 2602464, -75010, 492804, -1208077, -153664, 2989953, 3068800, -7739874, 247536, -1339586, -1906236, 211239, 879616, -1665022, 1956744, -1003860, 480000, 531441, -1037820, 2586713, 501696, 1591415, -3066336, 723465, 424784, -1410416, -449388, -5640354, 173056, -1193904, 365956, -2393381, -571536, -4672438, 380924, -657072, -1154432, -2992756, -2325888, -723877, -1226976, -290511, -5633388, -3490694, 186624, 608356, 1164240, -3860055, -1937584, -664373, -1420596, 3433337, -990144, 194481, -588796, -858506, 1950192, -4204386, 3440056, 1346184, -200704, -4883443, -1113264, 1807624, 2482976, 2381139, 1057560, 670761, 275904, 2725064, 331416, -634959, 1797552, 3362987, 336924, -664525, -1355520, 4330260, 2353104, 1925805, -219024, 2663346, 2628288, 4264857, -1842176, 3320917, 3439944, -1645844, 682864, 1461078, -6729040, 2219231, -746496, -2288767, 1059624, -611667, -1993120, 13174974, -236196, -4736216, -945472, 700794, -777924, -90374, 1362816, 4611945, -323804, 1253151, 1520640, -3165792, 2506824, 10757008, 403056, 2022021, -7662036, 5324082, 254016, 2430000, -1059668, 257049, -133664, 1091475, 2539836, -1933589, -262144, -349191, -890936, 2150469, 2503728, -1549392, 2654428, -2419434, 876096, -5676349, 1715580, 2408144, 5315472, -1515276, -5146864, -5173740, 440064, -4512574, -5844312, 2331504, 375536, -1599416, 1868616, -6211566, 3478656, 1540008, 538664, 458591, 944784, 3903685, -5836680, -5794650, 891904, -9809019, -298116, 10744684, 1286160, 1196613, -2625104, 2536305, -798912, 4682146, 4475144, 9872847, -2122496, 4775664, -1924560, -2938403, -1016064, -1497249, -8591016, -2510895, -1168128, 12570066, 8532832, -321489, -4134912, 5107882, 1396764, -4532168, -516464, 3518019, 1854944, 4765732, 331776, -8728418, 2644864, 4565412, -6862320, 3412066, -5855544, 3445258, -2525504, -1108809, 4825176, 13853430, 345744, -2845260, -9326016, -6904800, 3467008, -2521170, -556956, 3456999, 2393216, 4289031, 937612, -2900675, -1979136, 2156860, 3407852, -4402674, 4233136, -10090170, -1080000, 5219233, 490496, 2335095, -4786452, 1370928, -1128816, -12458539, 2117888, 6899256, 598976, 15786243, -955764, -2202719, 7698240, 1011123, -10678792, 2543394, -389376, -8697029, 5574384, -823401, 7581968, -11795953, 1285956, -6268993, 6115456, -857079, -3853888, -676674, 2597472, -405769, 4045380, 5233248, -1327104, 1218942, 2760696, -17702721, -1087408, 12675123, -1668836, -11273340, -419904, 5497744, 2322736, -2619540, 1245856, 10851031, 4359564, 26909577, 2422784, 3196341, -1589952, 3025134, 2227824, 9793154, -10112968, 1324791, 4456576, 1901151, -4387932, -7344165, 3594704, -7740126, 17610696, 2821643, 451584, -10300025, -1950252, 2504844, 456976, 10431878, -5586696, -7970046, 4515264, -2379510, -4538160, -4916291, -620784, 6511185, 470596, -745686, 4451072, -3048422, -4044492, -9036100, -4301216, -758079, -5205952, -10745136, 3049920, -8243144, 12138760, -5294484, -2693824, 4723746, 492804, -6487097, 782336, -5913648, 13417592, -1470000, 4144896, -15717886, -20932992, -7739874, 3321984, 8238780, -1536444, -2614599, 2737792, 15140340, 8624064, -2205138, 1679616, -1300901, 8986632, -2384154, -10301600, -18193620, 4484520, 4556497, -529984, 531441, -12785364, -15144077, 2127312, -6916924, 10819072, 1750329, -1420288, -10381614, -3066336, -16932898, 17551728, 728559, 3535448, -16590418, -3421440, 12115656, 256992, -5640354, -2661776, 3757614, -906876, 15116504, -2076672, 17239581, -3579420, 21430251, -571536, 1619318, 10495744, 2384253, 2483136, 9141008, 300744, 5933851, 6254256, -5714631, 22507532, -4864496, 589824, -26323393, 3032316, 2004606, 8116288, -25904669, -5633388, 20409840, -10409856, -5972463, 300040, -4533256, -1971216, 12340128, 4832308, -3860055, 614656, 38383713, -11959812, 26472761, -12275200, 11580444, 30959496, -7604114, -990144, -2496637, 5358344, 13149702, 7624944, -18147972, -844956, 7065552, -3518464, -4204386, 6660088, 7537051, -7826976, -5505003, 4015440, -1211994, -1920000, 8588114, -2125764, -2362107, 4151280, 13132530, -10346852, 6307146, -2006784, -8328373, -6365660, 670761, 12265344, -30141544, -2893860, -28557680, -1699136, 5906484, 5641664, -12008745, 1797552, 4340773, 22561416, -10069074, -692224, -2091271, 4775616, 18198189, -1463824, 4330260, 9573524, -39907892, 2286144, 7525876, 18689752, 19329786, -1523696, 2313441, 2628288, 6103930, 4617728, -19198872, 11971024, 18784141, 9303552, -16288852, 2895508, -3142719, 4907904, -35024758, 1162044, 15648292, 22533552, -4173624, 13962776, 21725982, -746496, -21774906, -2433424, -5950944, -4656960, -18250814, 15440220, 9185826, 7750336, 13174974, 2657492, -1234359, 5682384, -25499118, -13733348, -10856646, 3960576, -2169799, -777924, 23844707, 2355184, 20983536, 3434024, 34891452, -7800768, 409346, 16817544, 1253151, -13760224, 3885648, -5384736, 13860072, 802816, -2109627, 19533772, -31452300, 4453056, -15711098, -7230496, -7667667, -9931904, -52151850, -9524556, -2418540, -4230240, 2430000, -2683044, 44019693, -1103616, -13300094, -10900256, 10769517, -1325664, -16278633, 2539836, -15694826, -7190208, -4765248, -13451948, -10918752, -1347696, 46533748, 2658100, 2150469, 5422080, -20053332, -17321040, -1150079, -9412416, 24027282, -7703220, -13475241, 876096, -29807542, -10653384, -12542364, -10513152, -34628098, -17059428, 13126568, 7368704, -2893401, -13283668, -43102117, -13759776, -6668909, 6583376, 8671248, -2731456, -9553524, -5844312, 31662171, 26916160, -9102105, -8876924, -3938865, 2985984, 6654449, 9155068, -6211566, -4238496, 41088708, 2446668, 32247409, 7972480, 3754881, -52699896, 48342480, 944784, 6500144, 18944864, -5226156, 3781888, 11317639, -2803176, -9914046, 3111696, -9809019, 361496, 9692743, -5451264, -62143200, -18447780, 3577392, 1295216, 24115769, -5012604, -47495438, -6082560, 22754178, 12663168, 38601279, -10027296, 24084126, -43028032, 9872847, -1612224, 1581671, -8088084, -25070864, 30648144, -39624066, -21296328, -8640202, -1016064, -44029390, -9720000, 4388067, 4238672, -43911132, -1028196, 21015855, 534656, 12570066, -4365900, -48090469, -10159344, 39958878, 7734356, 10210860, 1048576, 32518304, 1396764, 16148626, 3563744, -1058841, -8601876, 9068576, -10014912, -6104994, 6197568, 9100107, -10617712, -12867283, 9677736, 46780935, -3504384, 11713392, 22705396, -7329224, -6862320, -7410609, -9632576, -27312210, -21261888, 7149734, 6061104, 10732558, 20587456, -1108809, 20694960, -7713711, -1760256, -12963979, 18050296, -30189582, 23377248, 41991960, -9326016, -54640160, -1502144, 47099232, 6397664, 31066914, -7474464, 69007067, 24846264, 3456999, -13914624, -71710185, -6160032, 59741732, -2154656, -19404144, -1834364, 11768146, -3779136, -11251344, -15614740, -20219922, 23346720, -23575860, 23178600, 20830073, -3567616, -10090170, 39236076, 37964568, 1192464, 62615842, -42978736, 28767069, -5144640, 1814742, -4786452, -23219777, 10500416, -24342912, -10145220, -63110212, 3195648, 11923119, -18728584, 6899256, -17900576, 23728488, -39491388, 5730000, 8489984, -7954758, -19102656, -69661134, 7698240, -43912384, 11753612, -578232, 4064256, -13787536, 5988996, 45012529, 34364064, 2040471, 10043580, 3330187, 4672512, -64738070, -50280264, 8053695, -34131328, 5070859, 1285956, -21415590, 16539648, -23615424, -20431528, 47342334, -5587056, -3815434, 18128672, -676674, 2065856, -6711174, -14072076, 80445420, -7419776, -50641947, -19062928, 18432489, -1327104, 34658048, 34913672, -6822711, -10579456, 8772114, -18261648, -7076267, 27449280, 12675123, -13648264, 51860727, 23422176, -47650356, -13781032, -675090, 10102016, -11008781, 4435236, 20115020, -19300704, -10872693, -55413720, -27872832, -1382976, -14647026, 11381040, 26909577, 37304064, -83798523, 27619200, -1399489, -13868032, -69658866, 10084680, -28645698, 2227824, -50111880, -13827996, -12056274, -9572864, 12603213, -17156124, 136263060, -3750448, 1901151, 11602700, -23129909, 7916544, -67308948, -8627440, -14985198, -13631408, -21457386, 17610696, -56273568, -16932544, -9034740, 40360680, 13172474, 4320000, -92927522, -20876932, 4782969, -1961984, -40173382, -9340380, 25018706, 19145808, 23280417, -5483712, 46287820, 4515264, 8249836, 49834156, 14322735, -8471552, -67368964, -27597024, 20028397, -2395904, 6511185, -63144972, 6557031, 3823056, -19647302, 8810876, -12693744, -30792960, -34370531, -4044492, 29640526, 42715168, -50763186, -10173576, -92064165, 1557504, -39574898, 34788116, -10745136, -22297536, -8384488, 3293604, 155156229, -30327872, -21540429, 47183812, -8147996, -5143824, -27488526, 25075972, -42051942, -24461824, 21458277, 3428316, 31548650, 15415552, -5913648, 2706696, 56216160, -10389888, 26035566, 1623076, -26934804, -16181520, 10048254, -20932992, 3174924, 5308416, -6514893, -4875768, 49012660, -11042784, 18041454, 70810884, -2614599, 4349632, 66927075, -50700492, -89180380, 6675344, -31416246, 45093360, -53752167, 1679616, -45140407, -21990976, 5475204, -9290944, -44295164, 10478160, -10623094, -4983424, -34740495, -43404124, -9849978, -17438256, 8151689, -107638308, -5979357, -9691136, -5070000, -12785364, 104223996, 6359808, 30900033, -12100536, 7269257, -8911296, 86114495, -39172616, 1750329, 40451872, 61978568, -5299164, -61305918, -17826304, -7726554, -7604604, -54553611, 17551728, 103278780, 29376660, -37839474, -14378816, -19153659, 30960504, -4486781, -70442784, 12115656, -11286572, 83227534, -1806336, -10907946, 41200100, -43950987, 7801008, -30947232, -10019376, -24856132, -1827904, 16268616, -41727512, 118192770, 22346784, 39923408, 31880184, 21430251, -18061056, 98803793, 9518040, 42953040, 18152640, 6036849, 19665164, 8293404, 2483136, 114068892, -26044740, 24525576, -1882384, -80485920, 2982744, 4811481, -17804288, -5714631, 12193688, 37592800, 16177968, 72123500, 36144400, 30266883, 17204864, -90621666, 3032316, -18901819, 20823808, -5980725, 42980544, 12959934, -12199680, -23351391, 32972576, 38972340, -48555040, -1595614, 21177936, -121564884, 10775296, 17332245, -18894984, 20490151, -1971216, 173968074, 25948388, 23970114, -3129344, -61881687, 23654592, 60651214, -53670368, 38383713, 5880000, -172789848, -16579584, 20465731, 62871544, 29888253, 83731968, -12713295, 30959496, -72068140, -13287936, -14812596, -32955120, 156483, 6145776, -8302326, 10458396, 13149702, -10951168, 35722397, -60561360, -37562616, -34496256, 19973079, 8820552, 84790752, -6718464, 63453447, 5203604, -20598903, -35946528, -53558496, 9536616, 112281221, 41206400, -5505003, 72774480, 63705105, -17938080, -149731926, -18225988, 118574766, 2119936, -48185280, -2125764, 72947178, 51141456, -42625944, 60576308, 4482961, -8509248, -97709814, 27667696, 6307146, -43276288, -26226434, -7001316, -135959607, 5681152, -813366, 41526456, 98901824, 12265344, 4666319, 67731592, 41507505, -70206912, 39694756, -2914236, 53358462, -14141792, 11278359, 66361672, -80169367, 13685760, 76195011, -48462624, -28492128, -1027968, 1531928, 22561416, -18986643, 10647104, 96813072, -15030456, 47957510, 3627504, 45770366, -60466016, 18198189, 8306688, -69009003, -68958324, 15353535, 14317680, 47916738, -85721004, 31406016, 2286144, 45210126, -6477272, 21870000, -41982976, 128170952, -9537012, 14261940, -9932544, 2313441, -36564032, -47959868, -1202976, 50760028, -23735404, 9823275, -25017024, -25337296, 22858524, 177238644, -90030128, -17402301, 19457984, -42887232, -2359296, -95511210, 105293572, -3142719, -12129264, -75388998, -8018424, -9539367, -32465152, 19354221, 103618676, -7212751, 22533552, 177610530, -81639360, -13944528, 41639424, 177511718, 23889852, 216245538, -1200160, -21774906, 18133024, -44745064, 7884864, 42140686, -49360512, -51087141, -19329232, -112881276, 15440220, 154995122, -2458624, 21673296, -153534852, 97407932, 47839248, 21052330, -105891044, -13637484, 49100800, 33354686, -46321776, 3357774, -123837984, -46563660, 30416456, -174985643, 3960576, 78041232, 9986548, -40613166, -21433376, 12955110, -52598808, 235472141, -30499776, 20983536, 72591888, -81918945, 3379824, 131347479, -28262208, -14394744, 14073856, 76202448, 16817544, 4059846, -26640352, -55904094, -30148204, -29905108, 31307904, -145163334, 22020012, 13860072, -16061760, -53298140, 4847976, 33793929, 7680000, 4127319, -34352456, 4518689, 8503056, -51332428, 9448428, 35133165, -16605120, -4257279, -52530120, -53399404, 41387408, -52151850, -25228584, 28825524, 8027136, 89611296, 33313492, -88281171, 25462640, -127009582, -2683044, 28569016, -49061376, 96702156, 120566176, 107145720, 11575440, 32196528, 114230720, 10769517, 6796544, -141671634, -23625936, 1411826, -22566656, 22826745, 48034980, 204787602, -7190208, 46112497, -17363092, 42139314, -90245664, 50533061, 40276296, 154100336, 2768896, 88855623, 8365084, -148298480, -19102464, 127392354, -72792756, 42980976, 5855296, -82430740, -17321040, -186760344, -38294096, -26445627, 159631568, 54732407, -9144576, -26288905, -30103504, -13475241, -74759008, 39492603, -77319144, 12980394, 6094784, -22598055, -9253764, 24862974, -10513152, 10308081, -24415720, 113130594, -18470912, 186348716, 76795488, -187712338, -47884096, -2893401, -75136564, -56144673, -37214208, 91897740, 65155408, 45970938, -11582032, 62114466, 12570876, -152411280, -19631616, -40789512, 140099032, -9529569, -4648176, -26130000, -62593168, 31662171, -90134208, -153303950, 16694496, -150053764, -55851104, 42891588, -86903928, 90509743, 2985984, -3966599, 87099624, -78555762, 9733696, 107923218, 23803776, 105420528, 18627840, 41088708, 73003256, -109860816, -61760880, -172008830, -36743304, 30708594, -31001344, -245809890, -52699896, -180525962, -10629968, 31007322, 4937436, -23124179, -22729536, -186537527, 101996472, -9979281, 54933392, -93859941, 43426584, 85494652, -15842304, 124680870, 8679196, 164550568, 3111696, -271706238, -95378828, -25607340, -9420736, -78223035, -83934144, -12980933, -13736096, -62143200, -139565808, 221993088, 31203072, -108161696, -1637384, -22690530, -67270176, -13585065, -5012604, -75506392, 55040896, 31112991, -15542592, 237665657, 21538944, 63587719, -55440288, 38601279, -3211264, 14872406, 8438508, -174637296, -78135088, -26106075, 125809200, -10913966, -17812224, 152316980, 62844392, 19411740, 28921984, -181979298, 30670668, 22418864, 39727616, -39624066, 208607400, 197131364, 38098224, 32516743, 9674160, -90811530, 16920960, -132533398, -9720000, 66793506, 10732176, 46973097, -176078772, 127865440, 4414464, 135587996, 53200376, 21015855, 43601024, 170976960, -43078068, -131200187, 5302656, 12338352, 65114532, -219086208, -10159344, 42911779, 62779304, -112126851, 28760832, -63049084, 19060992, -77911266, 53807792, 62093304, 43675008, -14119264, 5390784, 155299326, -186134992, 142076187, -10632400, 105477229, -8601876, -71592822, -21688320, -19824471, 80213328, 5455151, 69284160, 122186936, 4600316, 9100107, 37649664, -5204088, -96109128, -126585515, 30812880, 22890546, 53900964, 119476828, -3504384, -12131561, 119230168, -78273261, 42613536, 286139778, 50169456, -198985884, 42052608, -7410609, 138512392, 6598634, 68237712, 72483255, -52506272, -106163577, -29474816, 146102947, 11573604, 87751620, 53134672, -56420937, 172408468, -212538816, 55039104, -71499330, 26675636, -7713711, -26333504, 90437063, -34684992, -51345766, 10925824, -6090066, 38214096, 66620043, 23377248, -96582358, -126648684, -3651921, -107664640, -269364399, 36408420, -455777523, 35507696, 47099232, 15755460, -14370000, -11943936, -135167006, -26617796, 10970478, -36620272, -32157524, 24846264, -76771968, 16953984, -159324489, -164354832, -161163836, -9786672, -71912514, -128989636, 114076107, -31889920, -25278344, -15019524, 54820514, 210799584, -101460060, -193369920, 287804430, -3779136, -6075810, -26000576, 49479696, -75779456, 54543024, 20904624, 99376848, -15127552, -23575860, -45270556, -97854237, 11212704, -12716971, 39656184, 97659279, -12446784, 244288634, 39236076, -44712499, -1445984, 242186193, -38770972, -105239946, 21805056, 32682392, 248572800, 28767069, 73791120, 25061398, -14309568, -328323544, -5180864, 27226206, -96463076, -102091401, 20050416, 104527192, 189981752, 88138386, 24330240, -108506466, -91016712, -245865617, -50652672, 11923119, -154405116, -122975350, 40109184, -33825800, -96336504, 17110359, 172112128, 236525556, -39491388, -12825790, 6448896, -66097485, -6326684, 100369448, 32352336, -134866782, 100283456, -69661134, -122592576, 22723064, 158496264, -74780947, 85185312, 25394787, 34560808, -81312660, 4064256, -286188032, 176117560, -92700225, 38880000, -141043344, -17552268, 32399584, -16954688, 22543596, 175644528, -122367996, 4112784, -30426929, -84063420, 93886902, -2138624, 36732594, -50280264, 209523753, 17463600, -71730414, 192361876, -9181050, 40637376, -80084537, -159835512, -21415590, -30937424, 128904615, -40843440, -71993622, -4194304, -44246619, -130073216, 59108406, -5587056, -97045798, -64594504, 58600665, -14254976, 108500470, 4235364, -342099360, 34407504, -6711174, -36274304, 198837928, 40059648, -114243696, 24419976, -27435798, -24790272, 198638624, -36400428, 58006421, 42470848, -81324900, 51469132, -239262424, -38710944, -322862760, -187123740, -6822711, 14017536, 209360836, -46853568, -332031237, -90821584, -96706224, 29316896, 29069682, 27449280, -51074272, 29642436, -74188296, 38530304, 11485747, 109248840, -193863861, 85047552, -47650356, -28598936, -34191100, -24244416, 74660181, -42930232, 42513714, -82349824, -378467478, 4435236, 41746187, -82779840, -58383873, 30854844, 58578512, 7041024, -262101109, 51855916, -53222832, -72201184, -208945995, 120758328, -13159354, -93508992, -13230000, -167967840, 96888188, 37304064, -21941361, 218560640, -141460974, 6008576, -36172386, -188396928, -173357954, -25590656, -69658866, -124267656, -58634037, 29897856, -21332652, -276028268, 74149020, -99385056, -347602116, -13827996, -294267437, 55658496, -23531391, 286840740, -74334094, 24640128, 25944128, -238966928, 136263060, 8618624, -256218579, 77616576, -282746214, 7337456, -19846242, -47072584, 7276334, 15116544, -137137202, 45005376, -11708109, 62458960, 49276836, 80879688, -146535200, -93386880, -21457386, 94303440, -37969061, -92714400, 170711632, -83320292, -163742580, 14270464, -130815202, 40360680, 110702720, -156944304, 41008473, -151858272, 389821712, -4769856, -53814213, -250463368, 4782969, 171914944, 91022769, -115068276, 68286204, 20578560, -136296693, -7258968, 278100297, 19145808, -4826809, 92879108, -62252316, -42001664, 383771520, 97371648, -292614923, 40580880, 15752961, 252440848, -274722253, -12782592, -163540463, -47692476, -93434526, 74914336, 37547127, -27597024, -69538986, 71602304, -152396082, -94913952, -47210128, 157965552, -48794857, -22920000, 6557031, -33959936, -178349016, 31819032, -289361007, 76410624, -149313762, 278644536, 225601098, -30792960, 49555905, 175649536, 109040904, -47014448, -7535925, 2312928, 203296496, -16257024, -50763186, 55150144, 286438950, -23955984, -395558883, -180050116, 33818526, -137456256, 45431594, -8161884, 127726908, -40174320, 136048536, -13320748, 146417544, -18690048, 200070739, 258952280, 155156229, 201121056, -20443241, -32214780, 234398340, 136525312, 192872259, -20283436, -359140866, -5143824, 477096343, 85662360, 14573862, -66158592, 104109124, 94461696, 28453516, 81726112, 21458277, -189369336, 313626706, 22348224, 89885742, 15261736, 82269072, -72514688, 220730184, 2706696, 122765909, -8263424, 53404659, 26844696, 505958430, 56288304, 34212990, -321781680, -51431679, 29679104, -430480884, 202567788, 59669030, 76251712, -43780464, -73729956, -19476912, 5308416, 272401947, -138632192, -236910537, -139654688, -41748859, 27290844, 105831102, 42317824, 18041454, -35088456, -53826525, 73046592, -123883858, 28305068, -233142021, -109797120, -18189121, -50700492, 41610000, 54593056, 183688560, -207442908, -28917928, -93688704, -70015335, 190601424, -53752167, 55124128, -220642082, 2700360, 155990205, -40408064, -40799304, 44035124, -38510166, -17740944, 276463775, -80460080, 111061152, 77202816, 215731026, 43490772, 378762922, 221654880, -34740495, 111491328, 82127120, 5531904, 108810650, 58588104, 345453417, -45524160, -92713274, -107638308, -23890587, -149216256, 238254849, 335194092, 115543376, -110476800, 268994277, 5597956, 104223996, 55472128, 36823463, 278635464, -229686160, -40338720, -68437026, 114582792, -12066489, -8911296, -474813160, 200447520, -22469733, 55311984, -314440644, 48225096, 310289636, 38291456, 118347318, -50412852, -55592460, 68624496, 191634010, -545052240, -163331748, 15001792, -222028987, -7604604, 179757711, -46410800, 63589968, 92519636, 209469099, -31666176, 5764801, 269235792, -37839474, 34509760, -185390127, 59940792, 368712030, 54525632, 67833459, 85829544, 254543810, -70442784, 4001566, 225094272, -49545027, 67730176, -333409422, 36138960, 272411776, -161442720, -10907946, -52689896, 195413712, -17280000, 558879144, 371710088, 77293026, 83507728, -63772912, -19131876, 28115009, 7847936, -21258963, 160693528, -383633496, 37361520, 309263513, -100074824, 118192770, -76583232, -36918667, -93121668, 148699810, 21934848, 56764314, -185151280, 395343171, -18061056, -567590760, -32999344, -74955357, -199336624, -164262674, -57290940, -7320294, 33886208, 6036849, 269475856, 382512340, 110388096, -106363482, -80113588, -271273896, 9583616, 373567545, -26044740, -348888670, 252579888, -257019120, -26228124, 164365502, -15292224, 513001262, 78589208, 53158356, -35243504, 227295687, 50774976, -736116222, 123171840, -108078705, 137482124, -66060579, 16177968, -256429152, -118562104, 39066957, -170860672, -159131943, 203052744, -146324256, 40694304, -90621666, 368256660, 871317648, -6230016, -50498490, 158299592, -18821439, -139152464, 139811672, 42980544, -315024835, 89190144, 163783701, 33537952, -167964313, -13174416, -85728292, -620624916, 38972340, 121311488, 105644784, 86161716, 431250642, -188735248, -359171028, 32591984, -15825114, 20575296, -146678419, 109954104, 67732884, -100303888, 103080000, 168207768, 110086242, 97847296, 173968074, -85833108, -120153078, -13713264, -130280696, -126194600, 20820969, -61662208, 500467408, 23654592, 231001400, -10826784, 54935370, -224864640, 358646508, 41559552, 88409475, -104142264, -172789848, -6492304, 347902053, 107739216, -236273677, 64726080, 169057269, -40193016, -156620709, 83731968, 293209596, -12699696, -146599668, -21233664, 129656800, 26059572, -112360716, 19503072, -28284471, -196050640, -230441341, 44171136, 132533632, -72165816, -315222822, -283243536, -413625960, 10458396, 91222364, -17398528, 140834628, -267708300, -303449760, 202801968, 274842270, 356721520, -37562616, -26701376, -125500752, 125664984, -80538471, -180373440, 195533838, 215008668, 339397781, -6718464, -128392689, 180561628, -195974154, 87963904, 43309238, -21900816, 215242982, 37163776, -53558496, 177180656, -38504415, -41912640, -459784269, 42492376, -164257326, 19933696, -218955783, 138961980, 3148152, 173616496, 82672434, 39399912, 195059664, 69753024, -111217210, -32606756, 118574766, 430553232, -360427578, 23917428, 256858151, 38764544, -11109231, 20280000, 874986144, 51141456, 321311660, -416895984, -229492062, -25439232, 488986191, -123600132, -419072940, 48402144, -97709814, -29077028, -43847895, 35645184, 63542224, -344457980, -19528191, 156690464, -365518494, -7001316, -645453063, -161807488, 214602363, -247914272, -50597046, 21196656, 128572864, 245223672, 188851824, 71305216, -508330370, 30906216, -54444884, 30418416, 314023068, 218214444, 303745849, -70206912, -129552696, -413115120, 3684114, -117506640, -412743383, 151357896, 207006937, 57515264, 11278359, 76614636, -263493096, -123842016, 381756253, 17947124, 34970832, 281771136, 275717267, -48462624, 566168204, 45146288, 124740648, -332910136, -347328802, 7225344, -515705418, 43631784, -18986643, -164800400, -540595734, 175803948, 37145871, -31204032, -283070700, 123788928, -476597408, 40077504, 534420323, 99424528, -141399882, 7311616, 316198485, -65074464, 2280352, 166910048, -69009003, -472771080, 317769064, -89387136, -290118214, -159693632, -469366650, -127520736, 15461641, -85721004, -161628914, 72244224, -21766860, -395215172, 3675490, -38072160, -416096164, -171812160, 21870000, -72610560, 456477885, -24147396, -51186097, -78660656, 396177237, -33173616, 870319404, -9932544, 59195773, -456275568, -119700846, 104178960, 290743998, -98102304, 16094039, 7529536, 96925653, 321943680, -514406256, -11930976, 132339636, -19245924, -146507697, 71217152, 102388830, 22858524, 205440705, -48774752, -141253434, -150371200, -308321640, -64711872, 365862219, -288494000, -42887232, -144577600, 379253826, -121067532, -380734557, -68819456, -98268768, 362486664, -67821286, -12129264, -233495808, 75607276, 418803732, -83295232, 558970772, 23922900, 65639714, -171922176, 19354221, -51839736, -172778590, 48798720, 386828784, 93405564, -180479988, -131890304, 582416330, -155889360, 224696881, 194220160, -10350711, 6382456, -238010643, -84711744, 612137350, 486259536, 216245538, -43101184, -121168703, -69328980, -216870851, 75579936, -121277169, -81960604, 81586078, 7884864, -92826049, -695872296, -268267878, -103793552, -861252930, -95880456, -203382495, 12517376, -112881276, 247526748, 113787300, -94618368, 49189140, -242604856, -311652882, 214681472, 533219096, -153534852, 42542194, -23520000, 118139112, 691159392, -71646904, 66318336, -115615598, -81862924, -26040609, -251486176, -777641319, -119553012, -195686699, -334927872, -387919053, 50853180, 305513320, -123837984, 413738442, 288272560, -60020181, 53151744, -126748937, 59250384, -454628795, 131820480, 78041232, -625932, -367105608, -24583104, -529034359, 33209304, -85981716, -41833584, 849550992, -52598808, -77979335, 43804672, 284959539, -142889588, -119838576, 242245440, -126729509, 150250464, -81918945, 137985024, -24876631, -79892316, 34939917, -35282208, -35449785, -339163008, 112168238, 26873856, -945052998, -253813788, 59890041, -20814416, -707001858, 82395612, 868664975, 143786112, -55904094, 214233984, 69110384, -38146464, 245762756, -449124884, 369798372, -164825600, 220489806, 22020012, 145342366, -291097920, 290226681, -254820420, -683916024, 71752320, 276377346, 598927704, 33793929, 72903952, 580328015, -474299064, 611450112, -8479744, 435082320, 192741120, 279065898, 8503056, -574681366, -291788712, 58501296, -204565824, -11586998, 170503776, -1294087822, -242305232, -47035404, -17931844, 325876824, 34036992, -158850000, 390839256, 101858751, -110670784, 117275669, -25228584, 1122127830, 173105152, -89226414, 104905736, 419299452, 28005264, 234147446, 543838428, -88281171, -22724608, -230466060, 3253464, 228949462, -166105824, 87234687, -395607296, 44681910, -49061376, 708664305, -18665276, -559288800, -270926368, -514654782, -166030020, -25721206, 280827648, 32196528, -158779024, -717407806, 11656944, -204214770, -213433848, 217041921, 56567168, -199295022, -45113436, -251686135, -265446688, -427458942, 320677468, 146645044, -54743040, 14002326, -304780044, 204787602, 193850496, 278701470, 113968512, -226985167, 4111872, 347411511, -6127712, -140576955, -90245664, 35469973, 75946572, 216757134, -42588416, 373458904, -387252288, -234954675, 60121824, 88855623, -191830040, 570143784, -14510016], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "546.6.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], [-4], [9], [16], [81], [-36], [-49], [-64], [81], [-324], [191], [144], [-169], [196], [729], [256], [-871], [-324], [-479], [1296], [-441], [-764], [1387], [-576], [3436], [676], [729], [-784], [-5295], [-2916], [5940], [-1024], [1719], [3484], [-3969], [1296], [13543], [1916], [-1521], [-5184], [9464], [1764], [17387], [3056], [6561], [-5548], [-8112], [2304], [2401], [-13744], [-7839], [-2704], [18038], [-2916], [15471], [3136], [-4311], [21180], [28784], [11664], [14773], [-23760], [-3969], [4096], [-13689], [-6876], [-54354], [-13936], [12483], [15876], [64608], [-5184], [39461], [-54172], [30924], [-7664], [-9359], [6084], [-95554], [20736], [6561], [-37856], [-69634], [-7056], [-70551], [-69548], [-47655], [-12224], [-51906], [-26244], [8281], [22192], [53460], [32448], [-38799], [-9216], [162654], [-9604], [15471], [54976]]}