# Stored data for newform 147.6.a.k, downloaded from the LMFDB on 25 April 2024.
{"label": "147.6.a.k", "space_label": "147.6.a", "level": 147, "weight": 6, "hecke_orbit": 11, "hecke_orbit_code": 45035996374368403, "dim": 2, "is_polredabs": true, "nf_label": "2.2.249.1", "trace_hash": 1905127183956053384, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-60, 3, 1]], [5, [-2778, -33, 1]]], "qexp_display": "q+(-1-\\beta )q^{2}+9q^{3}+(31+3\\beta )q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 5292, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 23.57642151250815, "hecke_ring_index": 1, "level_radical": 21, "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": [147, 1, [50, 52], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 7], "conrey_indexes": [1], "field_disc": 249, "field_disc_factorization": [[3, 1], [83, 1]], "field_poly": [-62, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.932", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.710", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "68.017", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [7, -1]], "trace_display": [-3, 18, 33, 0], "traces": [0, 2, -3, 18, 65, 33, -27, 0, -375, 162, -921, -1137, 585, -925, 0, 297, -895, 324, -243, -2311, 3687, 0, 1581, 1596, -3375, 395, 2508, 1458, 0, -2217, -8289, -4294, 1017, -10233, 17940, 0, 5265, -19109, 6828, -8325, -10545, 12858, 0, -2771, -36579, 2673, -40740, 23160, -8055, 0, -29352, 2916, -33424, -31653, -2187, -17889, 0, -20799, -2277, -41097, 33183, -42052, 102057, 0, -30031, -23106, 14229, 30763, -44748, 14364, 0, 102096, -30375, 28577, -77784, 3555, -85192, 0, 22572, -18464, 71511, 13122, 86040, -61179, 0, -123636, 258510, -19953, 212565, -29322, -74601, 0, 166908, -38646, -109938, -61662, 9153, 9791, 0, -92097, 99116, 143868, 161460, 47933, 179040, 0, 265479, -116685, 47385, -167213, 520227, -171981, 0, -220182, 61452, 294756, -55245, -74925, -426021, 0, -94905, 324407, -253650, 115722, -426403, 104709, 0, -60404, 555945, -24939, 456216, 114585, -329211, 0, 509250, 24057, 31380, 47634, -366660, -289357, 0, 208440, -327942, 524742, -72495, 2637, 610386, 0, -301700, 25554, -264168, 517963, 450120, 26244, 0, -740163, -300816, -604846, -823137, -284877, 416799, 0, -19683, -908120, 101904, -161001, -144657, 200472, 0, -304689, 348300, -187191, -853118, 130962, -20493, 0, 521133, -369873, 27798, -718470, 298647, -503761, 0, -378468, -490980, 429834, 918513, -202620, 978294, 0, 1154976, -388506, -270279, -573344, -141303, -207954, 0, 270882, 128061, 1017596, -217860, 276867, 1316046, 0, -402732, -525132, -2230356, 129276, 303008, 1310442, 0, -1363970, -1682721, 918864, 743619, -1826196, -273375, 0, 247458, 257193, -2061573, 15984, -700056, 538703, 0, 31995, 1421640, -553065, -766728, -445645, -1770300, 0, 387675, -467838, 203148, 908526, 127347, -166176, 0, 1060950, 643599, 1491179, -345054, 118098, -416506, 0, 774360, 1099091, 1283205, -550611, 1919721, -1494549, 0, -868980, 1881165, -1112724, -728863, 1221036, 2326590, 0, -2015616, -179577, 1557303, 1613022, 1913085, -2048271, 0, -263898, -666386, 450747, -671409, -1680775, -1969164, 0, 155886, -195798, 1502172, -2389919, 1040226, -347814, 0, 103182, -989442, -2283805, 3842514, -554958, -1366536, 0, 82377, -60178, 869661, 88119, -1031002, -221115, 0, 2735565, 3050700, -828873, 2798526, -1083264, 892044, 0, -2627637, 1294812, 701384, 1523238, 1453140, 3705899, 0, 431397, 4559019, 4767234, 1611360, 3659504, -3248292, 0, 1952419, -2855325, 2389311, 1265967, -4299609, -1050165, 0, 123120, 426465, -441523, 1738668, -1504917, -1884240, 0, 4682043, 1302493, -1279041, -1547829, 1908918, -3380172, 0, -1140770, -579429, -1981638, -4506708, 2345523, 553068, 0, 1791330, 2652804, 1599594, 2066268, -497205, 2667068, 0, -674325, -521019, -4154874, -3834189, 2908170, -904410, 0, -2335836, -1300266, -854145, -2191077, -4437876, 2919663, 0, -4101240, -2282850, -1887862, 3082044, 1041498, 5925612, 0, -3837627, 4410955, -10191420, 942381, -4718490, 974940, 0, -636467, -5191464, -543636, -6775440, 1003542, 5003505, 0, -3410583, -224451, 698057, -3005184, 4105944, -5416656, 0, 1031265, -14558238, 5651175, -2962899, 545465, -7411260, 0, 2670428, -1092012, 4583250, 2846519, 80166, 216513, 0, 10969914, 282420, -1811620, -3077280, 428706, 8033192, 0, -3299940, 645525, -984672, -2604213, -3732816, 7425870, 0, 2016451, -2832702, 1875960, 7024935, -4192416, -2951478, 0, -5498037, 4722678, 8143590, -346122, -652455, 1226795, 0, 23733, -5424338, -2879520, 5493474, -5693287, 5821155, 0, -8364480, -5877939, -2715300, -370518, -13632177, 229986, 0, 5298462, -2377512, -7415100, -10430016, 4661667, 5192949, 0, 4051080, 2540380, 5405568, 236196, 13564068, 9961626, 0, 1604581, 1546755, -6661467, 2757252, 1857114, -2707344, 0, -12695526, -5443614, 5267355, 1320960, -7408233, -1232929, 0, -2563893, 911772, -690162, 3751191, 7879885, -17478183, 0, 10118558, 1047867, -177147, -3889406, 6301110, -8173080, 0, 5777085, 917136, -1188324, -4498068, -1449009, -7544419, 0, -1301913, 8851069, -2827311, 1804248, -8632629, 6841278, 0, -8349114, 23003820, -2742201, -7334807, 18855231, 3134700, 0, 1804377, -1684719, 2881518, 15900090, -7678062, -13091262, 0, 1178658, 6440160, 3484422, -184437, -7187353, -1463529, 0, -3326142, 13455540, 4690197, 211490, 20462193, -3328857, 0, -4998882, 250182, -5905443, -2991090, -6466230, -14804007, 0, 2687823, -11850113, 7250793, -4533849, -8292780, -2735484, 0, 17165656, 866094, -3406212, 16618884, 2410476, -4418820, 0, 16098996, 3868506, -11222674, -4173849, 8266617, 3570769, 0, -1823580, -7740558, 19145229, 8804646, -11272572, 26824362, 0, -20016990, 937950, 10394784, 17187229, 18792384, -3496554, 0, 9173136, -2432511, -1034566, 6060291, -5160096, -2535147, 0, -1271727, 17776731, -2091930, -1871586, 8212149, 19933797, 0, 7543349, 5758173, 2437938, 19089580, -20037870, 1152549, 0, -7680066, 9158364, 20254080, 475014, -1960740, -12629170, 0, 2491803, 22385875, 4361820, 11844414, 6609806, -2718072, 0, 10813290, -11388282, -3624588, -20764658, 2402304, -4726188, 0, 3494892, -20073204, -2300431, -34401621, 1163484, -22094088, 0, 2727072, -14044168, -21378693, 11793978, -7190812, -18849888, 0, -4669907, -792165, -12275730, -1070637, -13530579, -15144489, 0, 1424079, 8269776, 15164655, -32603430, 6692571, 27863039, 0, -16435764, -20931360, -1507428, -2460375, 23851311, 14184852, 0, -30643364, -29729301, 2227122, -10213611, -16181328, 2314737, 0, -5438028, -18554157, -9480061, -12278400, 143856, 10288935, 0, -6300504, -43596, -113538, 4848327, 829290, 24223290, 0, -37220372, 42734901, 287955, -6793005, 27411591, 12794760, 0, 23995980, -4977585, -57608679, 24833691, -6900552, -805398, 0, -4010805, -23940974, 16601508, -15932700, -35897629, -1131846, 0, 40279884, -9017724, 3489075, 17671392, -29637642, -4210542, 0, -1730349, 1828332, 19206367, 16529181, 8176734, 32937312, 0, 1146123, 7204180, -51734754, -1495584, 5416950, -32876340, 0, 12714204, -13109652, 9548550, -38761350, 7795692, 5792391, 0, -4481811, 13420611, -791680, 856320, -3105486, -24227200, 0, 1062882, 4478082, 37195416, -3748554, -11832967, 25294083, 0, 18412380, -18044160, 6969240, 18112633, -5741484, 9891819, 0, -29816052, 11548845, -19436358, -27647844, -4955499, 24900900, 0, 17277489, -24049556, -2919498, -13450941, -113328, 21501237, 0, -22394012, -32446284, -7820820, 16874040, 19313160, 16930485, 0, 9448152, -10014516, 47568354, 14618364, -6559767, -4468588, 0, 10989324, -5821883, 800928, 20939310, -22935361, -2468895, 0, 25453158, -12013590, -18140544, -57866778, 16616880, -1616193, 0, 19108968, 14015727, 43861418, 51259410, 14517198, -14469819, 0, 17217765, 16598498, -34869072, -18434439, 50726468, 9405915, 0, -7377384, 13401468, -2375082, 31396008, -16899276, -5997474, 0, -50897892, 4056723, -19316010, 926118, -6042681, -12444034, 0, -15126975, 45250068, -17619396, -17722476, 10069435, -86918835, 0, -5471856, 11120073, 1402974, 11434240, -19779720, -1762182, 0, -18978561, 13519548, -40629157, 21789441, -21509271, 18780320, 0, 9362034, -12159594, 47890824, -3130326, 40236120, -25539216, 0, -38312641, 41666466, 928638, -29693054, 2227869, -8904978, 0, -7417233, -20554245, 5268720, 17536848, 34582626, -276517, 0, -4994622, 24721395, 29726850, -12298824, 10284794, -75564258, 0, 51163044, 27669960, 741393, -10411386, 3337638, -541602, 0, 11347617, 7826949, -9229337, 31335630, 793071, 51310560, 0, -9279018, -6978086, 32297145, -1990035, -40840629, -4947246, 0, 36290101, 25540992, 24620085, 43005729, -36659118, 27456300, 0, 13065786, -7459857, 55980215, -28791726, 25186734, 12040032, 0, -9749376, -14139576, 457179, 8028396, 27136140, -49556160, 0, 46740960, 28042566, -23648733, -7363823, -31064667, 11653308, 0, 2421798, 6312456, 35016687, 43757643, 13709142, -28694764, 0, 13078260, 26521045, -61907580, 33353091, -44548290, -48792582, 0, 20815345, -70830204, 3882573, 1444203, -41779032, 41031171, 0, -21371220, 42905106, -60431412, 70124220, 14502240, -26743954, 0, 32935536, 63525306, -39329481, -29234628, -22180032, 66669891, 0, -146408910, -15553542, 17571771, -7337599, 35744892, -25697925, 0, -59675490, 21503799, 45097044, 26971284, 11393703, -8962854, 0, -38696481, 25394004, 26706324, -9451485, 94187561, 20434017, 0, 17795284, -60118530, 1108080, -7927401, 11966013, 3838185, 0, 98494977, -3973707, 50174342, -87195120, 15648012, 16685742, 0, -13544253, -12707271, -44307024, -16958160, 103532958, -19550340, 0, 44268752, -80552136, 42138387, 69355834, -46071243, 11722437, 0, 57984396, -11511369, -5097253, -49571466, -13930461, -9249015, 0, 17180262, -78832356, -15949485, -30421548, -105412536, 42461028, 0, -16247156, -24891318, -10266930, -93342900, -50602413, -5214861, 0, 20278545, -17834742, -18963399, -7471749, -40560372, 38075168, 0, 21109707, -25116655, -21791082, 4977612, 882103, 25544454, 0, -80351472, 15289500, 16121970, 11099362, 60945246, 23875236, 0, -53688168, 14396346, -96118444, -31394208, 18596412, 33231666, 0, -4474845, 33992364, 10598388, 24003612, -12838785, -23393244, 0, 67564171, 55143042, -6068925, -44254140, 11645094, -4689171, 0, -61517451, -37393866, -118738167, 14612895, -34507701, 42805112, 0, 26173530, -34011720, -5439567, -8139690, -84774865, 69085413, 0, -68750498, 25972464, -21022524, -59302931, 57032937, -11702394, 0, 26167458, -7687305, 41642664, 5836242, -19719693, -68814079, 0, -39940884, -19594670, 75564468, 26276967, 76910826, -18440475, 0, 20698099, -24045324, -36911160, -7794690, 10824714, -20545650, 0, -55338996, -16990758, -868248, 50325852, 27738396, 58647264, 0, 9373482, -115214720, -28378221, 53330508, -83320806, 57285390, 0, 137774481, 98657457, -34538643, 8740960, -124547100, 39698595, 0, 34320588, -91722780, 58489349, 26110770, 8481429, 8078007, 0, -42466410, 68521996, 130860720, 8774460, -144419626, -25091454, 0, -39669033, -28382958, -5728203, -8469312, 87181992, -46723176, 0, -49089858, -4892724, -101286240, -40512846, -60978960, -40724657, 0, 9031878, -44283120, 61142634, 45031545, 108402014, 178008189, 0, -19865857, 13415760, -30695247, 40039430, 3873645, -2020059, 0, -58988415, 6282513, -22107792, -148627413, -27046656, -77460106, 0, 36953496, 78036568, -30827667, -48749904, 18120573, 21944838, 0, 65766831, -129016452, 9281385, 59321301, 133164534, -131024142, 0, 39142476, 50860575, 120917652, -93838347, -26666091, -18992808, 0, 4909185, 9392910, -113957310, -66701340, -16704, -91093632, 0, -222154446, 95063952, 24033852, 47158561, 39735753, -9828108, 0, 131294355, 41249250, -9330552, -106371525, 25618671, -145567398, 0, 721494, -147041672, -13945521, 1948617, 49373768, 76588392, 0, -92402940, 10210794, 98729226, 64836888, 32258034, 2541780, 0, 83947188, -16304580, 96558260, 27823791, -27695520, -66764125, 0, 3858354, 125085258, 38081022, 72298728, 42259436, 124968498, 0, 156024435, 101310696, -29699460, 124082100, 199764816, 5809725, 0, -8374254, -8862048, 9632588, 99579687, -23437917, 166602191, 0, -33595344, 51461109, 92630820, 66832830, -165020880, 6893766, 0, -5667886, 78986901, 18148059, 92495107, -166240620, -25494318, 0, -76737189, 16883640, 76161135, 53285010, 63224415, -20550995, 0, -37731744, 31174839, -222777981, -26563302, 37825832, -141535497, 0, 54708090, -16756107, -49482333, -12844410, -25039722, 42504102, 0, 158312832, 73292310, -133004530, 66241440, -3115098, -190675014, 0, -5872095, -45668423, 244019727, 11041155, -54917200, -19090029, 0, 12075319, 172154940, 213597, 18012081, 41665521, -48819042, 0, -6078519, -25915680, -41806800, -52752318, 49441266, 32961126, 0, -51239583, 143670312, -34792428, 52390395, -10034257, -25810518, 0, 73305004, -56609352, -75280320, -168612407, 50783727, -52901451, 0, -1451949, -24437700, 201292825, 38101140, -3334662, -26540370, 0, -122689593, -41595121, -97132686, 2069874, 146342670, -128914452, 0, 106332531, 61645953, 47686158, -160146263, -122691474, -21397608, 0, 51946875, -66735900, -134876469, -60840201, -93870144, 117405876, 0, 41955003, 39205356, -68727768, 46736541, -22288950, 238500681, 0, -98059449, 33215418, 36459720, 134901639, -15797358, 22863420, 0, -29490468, 48650112, -61603851, -118157310, 2125764, -143460624, 0, 122076612, 34144849, 77482644, 89654634, -15575190, -127032486, 0, -15382933, -62984148, 14441229, 149616042, 59084136, 13920795, 0, 109016640, -59953203, 163590830, 32549115, 24815268, 79291937, 0, 16714026, -247160565, 63994728, -24366096, 54802998, 62073084, 0, -315198795, 141764628, -114259734, -44901972, -215148408, -48992526, 0, -201473364, 47406195, 77305759, 21000990, 11888640, 236633022, 0, -66674097, 11922055, 14723910, -11096361, 207944940, -14003157, 0, -1595438, -257288112, -23075037, 117645420, 18788682, 8205948, 0, 79876602, -6211458, -236865234, -263439126, 33760719, -66870753, 0, 70918965, -47904723, -42783105, -157303647, 112046252, 68487600, 0, 29488932, -40340694, 91067022, -30477041, 45441501, 9430803, 0, -107476584, -1594323, 709508, -128268966, -35004654, -40117080, 0, 56709990, -58811733, -124749390, -73557720, -128742385, 111656478, 0, -12601136, -191345028, 51993765, -290590530, 104534304, 8254224, 0, -27842370, -10694916, -47742060, 99910272, -40482612, 8423603, 0, -13041081, -51782346, 6022290, -67899771, -183386080, 64827522, 0, 206450272, -67290237, -11717217, -148278144, -14485500, 79659621, 0, -99065760, -25445799, -1637339, 289606881, 16238232, 46292742, 0, -77693661, -27307266, 27638304, 61571502, -288490659, 60497766, 0, -7145544, -77006814, -75142026, 79517776, -212906346, 207034380, 0, -77592072, -24679809, 117204216, 163979718, -66013263, 64858898, 0, 169697079, 36053880, 163893264, 28212300, -143969335, -114605886, 0, 180593616, 5419266, 16239393, 25277373, 220003503, -15162471, 0, -146512632, 25933662, 84459104, 86149005, 143100810, 50637918, 0, -69102558, -93024416, 115033848, -117821358, 8153561, -147080496, 0, 183262020, -160504626, 10607922, -82073880, 23122200, 57961440, 0, 179817354, 31359798, -201517008, 171607875, -1659933, -65649964, 0, -64686177, 166331436, -4965114, -13171761, -148764229, -189756030, 0, -121549950, 64308846, -29935278, -64749608, 201642357, 121099860, 0, -91062000, 42211773, -9637491, 98029320, 1903410, 119880236, 0, 184159737, -190996723, -220223580, -29959713, 188126811, -2372751, 0, -219917837, 212257080, -44989938, -131466340, -364442706, 2251638, 0, -124764360, -53148987, -347803482, -238990128, -26919810, -11866375, 0, -58196070, 232396208, -198758031, -133236063, 147258240, -216033882, 0, 4156800, -54668403, 24190407, -22606373, -82817634, -106651017, 0, -29736852, 65257137, -69096901, 171407388, -40804641, 428354436, 0, -74635020, 135310392, -313666980, -24619356, 210031145, -103470057, 0, -17364306, 79137360, 154490904, -36974481, 235382607, 7794846, 0, 161620680, -30655908, 192237176, -17153100, 149569956, 44051881, 0, 21694284, 219364065, 93763758, -39769380, 130190213, 44029788, 0, -47293623, -292611273, 144890964, -15392111, -264828000, 34816554, 0, -86690271, -101004066, 283321457, -32657454, -37564641, -254543640, 0, 74399553, -122220437, 87216000, 32136921, 227637468, -178397016, 0, -59941678, 69889704, -16412220, -68538770, -305988927, -69665022, 0, 231351090, 172307061, 112324797, 33444576, 79241814, -124258747, 0, -101453148, -116157321, 166477344, 241419258, 186355103, -133193808, 0, 255126480, -37432938, -180152910, 417333891, -461378010, 8441550, 0, 245132991, 93553056, 67501017, -4074021, 154685061, 139047474, 0, 169131456, 250020120, 483361890, -31468986, 369433230, 378318, 0, -52575896, -163180548, 82558224, -73317678, 348010512, -21892599, 0, -11815002, -9311094, 24337346, -27163293, 54542619, -269561580, 0, -46440864, 467826519, -156987930, -22816323, -60621895, -225790980, 0, 75160606, 223465902, -11445543, 68503066, -234558240, 159990579, 0, -311686416, -18827370, -102275842, 190736904, -16844274, -256303471, 0, 73909341, -98441702, -235564173, 179404173, -616534038, 197368302, 0, -255490428, -5501796, 67890141, -44699520, 60867402, 51823557, 0, -293599479, 21941442, 46791348, 60542298, 171806220, 139976057, 0, -180340830, -49571862, -19984692, 10372941, -7614484, -165127425, 0, 169005048, 362508825, -69120594, 266335303, 238689828, 82425276, 0, 515889732, 182286720, 263527854, 190775664, 4275126, -94647537, 0, -17646660, -53132231, -297007380, -113662530, -58954320, 18226215, 0, 139283327, -9513888, 22426227, 91756968, -145576680, 201472875, 0, -28601664, 39256380, 125516445, 247322292, 106599726, 65248572, 0, 59488254, -417502818, 207061062, -24462648, -145257139, 85691259, 0, -60142289, -286292613, 97319610, -439205444, 107243940, -102494538, 0, -188385753, -32621292, -116177958, -4455564, -186881922, -414876, 0, 21620736, -14732146, 412570398, -42535692, 211232232, -345646374, 0, 229466535, 222536244, 31454028, 257418880, -27586008, -180658836, 0, 8834451, -20703879, -199890498, 174252159, -309614589, 290882969, 0, 10471356, 97997100, 220000638, -198846792, -214300054, 233293428, 0, -190067940, -83899314, 24543648, -213504896, 422013705, -126397512, 0, 240503331, -192408237, -248477620, -227012310, 106145802, -142896597, 0, -64717308, 6642936, -129205440, -169648992, 202941099, -123771510, 0, -152961460, 476213610, -42029163, 265005480, 223305186, -7129485, 0, -275112156, -110481570, -141756688, -421306518, -9635733, -76247934, 0, -121775211, 84813858, -243813807, -136300401, 23998212, -19764360, 0, -186412140, -31120278, 12816711, -326957226, 7564026, 74427984, 0, -124879578, 136481895, 125852832, -448666110, -293430870, 140517808, 0, 60233139, 85278132, -355803135, 250767351, 148718739, 81935232, 0, 12699055, -121646337, -147921876, -159186226, 13712988, -188382240, 0, 53122479, -13566852, 320778753, -59093538, -22143375, -196203210, 0, 214661799, -404388299, -150970395, 127663668, -284862595, 123994710, 0, -109924086, -148818096, -275790276, -113664907, -14002146, -267563709, 0, 116039016, 20044098, -256214120, 199880193, -91922499, 122412828, 0, -145631952, 411863736, -506842866, 20832633, 25377948, 584102694, 0, 192895783, -220326720, -48942252, 376930680, 398166138, -166987413, 0, -261239901, -85320549, 481840397, 247356294, -110505600, 168481961, 0, 1294704, -627494340, 291581646, 92600415, 60859196, 331236942, 0, 396544330, -464439897, -56704536, 11644585, -252458943, -392364, 0, -459633579, -1021842, -226324128, -339380100, 43634943, 225855675, 0, 7463610, 193959721, 507793392, 218009610, -368790744, 373364358, 0, 33741895, -347516493, -334983348, -159101238, -185717694, 384614109, 0, 271435500, 2591595, -80288229, 21885639, -61137045, 91180973, 0, 246704319, -150234551, 150181488, 115152840, -250930992, 584836665, 0, 157302771, 10635474, 215963820, 242341226, -168539754, -44798265, 0, 597562125, -518478111, -18413976, -431184375, 223503219, -131406120, 0, -62104968, -374330243, 381842652, -7248582, -205378890, 73504296, 0, -105307506, 686256936, -36097245, 20224920, 190586586, -215468766, 0, -331880055, 149413572, -549391074, -334413036, -143394300, 193123861, 0, -323078661, -358202760, 42531438, -10186614, 360494815, -132756897, 0, -205244064, 282379578, 362518956, 173688976, -2131182, -81159516, 0, -48164796, 31401675, -145312927, -651171672, 159042528, -233041048, 0, -266738778, -237097620, -222465657, -37894878, -373610268, -265601571, 0, 228223860, 314517234, -15573141, -306974670, -279566556, 16454988, 0, 509517540, 172857303, 496384446, 436404324, 148762629, -621008182, 0, 73590606, 190474073, -61073922, 296435808, 423393892, 470999745, 0, -407986995, 330216663, 10315107, 324326964, 619700712, 64837620, 0, 294195522, -465612786, -444193123, -37933536, -13460256, 79531341, 0, 48752550, 99133201, 204448038, -295887060, -372608643, -75050865, 0, 15087181, -239283090, 114427836, 132567444, 283887210, -117986868, 0, 179035500, 85936950, -155154495, -187798674, -348852150, -360218040, 0, 70161228, 35820072, 255217284, 52131519, -17743372, -566518680, 0, -349311890, -16002696, -40336299, -139844502, 338793465, 120785499, 0, -72831666, -7125120, -19069560, 161107527, 7706880, -36615660, 0, -27949374, -92115749, -307326030, -218044800, -95028435, 809616144, 0, -376451040, 118451082, 9565938, 552774340, -572618460, 40302738, 0, -43822578, 334758744, 343431726, -260239737, -33736986, 475036525, 0, -106496703, 118338060, -353444976, 227646747, 231936323, 70098072, 0, -690439098, -68216790, 165711420, -145077622, -232554240, -162397440, 0, 189822879, 62723160, -336307737, 510680400, 163013697, -121960041, 0, -51673356, 63542299, -754830162, 89026371, 69474398, -2052360, 0, 274481484, -530191215, -268344468, -594324039, 46811100, 103939605, 0, -382692678, -174927222, 473622832, -614052861, -248830596, -567486451, 0, -44599491, 442943976, 161166666, 224108100, 130767804, -841089126, 0, -57275550, -44405592, 155497401, 68299531, 511832391, -216446004, 0, 302402520, -26275482, 672588274, -391290081, -121058469, -708214176, 0, -1019952, 440342333, 545206710, 193511133, 1261735872, -5162994, 0, 70471570, 372496923, -201546108, 132148098, 26269278, -292016556, 0, 51670536, -70387380, 242620440, 489228210, 151866360, 146548082, 0, 173818440, 628511986, -291061221, 152374365, -577541248, -177459168, 0, 333121236, 58754829, 85033368, -14737163, -623933304, -90130644, 0, 90757608, 428115186, -371030263, 389697168, 131565276, -36250944, 0, -59037903, 371607786, 155905827, -40217292, -562992415, 163356621, 0, 344522872, 41133495, 98903916, -29065728, 505438914, -52396947, 0, 235241160, 7208352, -87668091, 780295602, 188453790, -357002520, 0, -206418249, 508671243, 301570506, -22220055, 41362584, 270937764, 0, 943630707, 285655857, 229078422, 434162568, -285311034, -108122310, 0, -244207647, -163264896, 108656597, 170626800, -520801002, 80861445, 0, 149551920, -106323026, 503784597, -14545737, -380803872, 506556480, 0, 186247805, -414630873, 171980712, 598263128, -67982085, 126141543, 0, -463610835, 394752762, -210935118, 42840360, 461334690, 1032788130, 0, 130654782, -177712148, 703055136, -130228371, 349981892, -923813316, 0, -289007391, -64918068, 154959885, 349418581, -124284240, 149386482, 0, 315813252, -313821648, 144155147, -292284258, -165909951, 434705898, 0, 456538212, -399308795, -420981156, 84653235, 296257920, -277029756, 0, 58599006, 679763730, -66396456, -130275906, 426616548, 120613212, 0, 16985730, -21375738, -472824019, -139664958, 282564072, 78456069, 0, -152093484, -1098206121, 253254591, -53977266, 118141915, 926289000, 0, -48569885, 166903212, -458081028, -676778472, 558833154, 36510507, 0, 31364340, -173844090, 31182134, 56833554, 8335062, 226911131, 0, -54384129, -746400, -665504760, -111996306, -860871150, -712801275, 0, -1015403984, 919450980, -136142775, -220116390, 524929746, 407250612, 0, -513382560, -158574564, -67133514, 302066280, -159502284, -613797536, 0, 90624915, -833251988, -293428533, -782269515, 123613407, -655050300, 0, 1354834473, -379056918, -49246704, -268240812, -366482676, 100080657, 0, 129722436, 12626766, -265590691, -277398798, 102908160, -583066056, 0, -178017480, 767263153, 913438842, -15859638, -439317562, 175456686, 0, -768787381, -10205733, -170807049, 217140600, 113460234, 121675932, 0, -792858960, -365662413, -968572560, -85715094, 196104969, -498213438, 0, -193583439, -261627210, 400106676, 169022880, 310054101, -176129562, 0, -691975765, -538304196, 84258306, -56901917, -765604185, -109436346, 0, -132400632, 431017416, 226736209, 394629597, -28172934, 682069124, 0, 362125080, 778935420, -32734224, -229852944, 1061110584, 248612082, 0, 716041039, 72547368, -344813769, -367718099, -325442958, 374998194, 0, 381143403, 8357742, 986074740, 395435967, -267237486, 423994584, 0, 20050821, 508605315, -939362766, -80144802, -912001003, -607339617, 0, 308650680, -415716576, -66755097, 245875179, -559226940, -184988205, 0, -141360591, 47418480, 130920371, -220753665, 157831632, 334435269, 0, 311243634, -541891631, -1248905928, -2488653, 349908159, -252650160, 0, 263910408, -1077020310, -44951598, -1127413509, -189992484, 222492555, 0, -435034134, 267541650, 855284258, -50223471, -110689416, 508070219, 0, 92563146, -356609772, 466400976, -680078322, 33231762, 252165066, 0, -126818400, -505164294, 460467396, -523601944, 529817058, 249029640, 0, 349201584, 6672537, -268726921, 549160158, -93702474, -64222473, 0, 30038742, -511846272, 150398400, -4874418, 903520323, -48902988, 0, -211715130, 58218843, 102128553, 369111388, -364023954, 70442541, 0, -886456671, -83064033, -604186203, -117312834, 282020670, 371365865, 0, 7137639, -267745551, -101074398, 461795040, -588812258, 266683056, 0, -548749176, -826023942, -83511162, -605653272, -767275074, -62802774, 0, 177123666, 290674305, 390512220, -583275720, -17910315, 846037992, 0, -367565661, 350719157, -1507781694, -44525214, -188010154, 431891097, 0, -115685600, -295840740, 326610909, 583131156, -832493847, 229868928, 0, 169526145, 221580765, 77409783, 136623588, 387051561, 433768790, 0, -329932062, -78440433, -96495894, 247106700, 208088748, -980512170, 0, -115524108, -713008080, 117592074, 884073829, -308464194, -67138713, 0, -154389924, 503821935, -800442082, 1087533276, -259125534, 612577410, 0, 226680606, 219548077, 239224110, 108360288, -114572100, -384683466, 0, -308671766, -589021929, -87744384, -1227108275, -818517804, -127256184, 0, 419013105, 4114611, 557614152, 49274397, 72255564, -831568979, 0, 244225260, 238958115, -111954372, -446005440, 188706821, 1172153955, 0, 901696911, 295017864, 420668640, -429676127, 222686100, 252383094, 0, -621983802, -212838597, 13369223, -137615220, -66274407, 1202265300, 0, -279582003, -32248061, 51913458, 104879772, -710237535, -849142032, 0, 245094037, 989521695, 21796182, 664776246, 271311204, 56812104, 0, 1831752819, 315150183, 24840930, -424937589, 393818787, 586928212, 0, 123382278, -483591510, 667639074, -258252876, 364618538, -1094764347, 0, 1151860978, 165724416, 117704340, 20540592, 895224096, 238689405, 0, 50524254, -557168220, 860525559, 392411460, 300177819, -1237581544, 0, -400934610, -571927220, -236413158, -439133238, 1438438872, -91395216, 0, -181352694, -683726916, 187338105, -170528820, -356039040, -637471836, 0, -701344398, 34943157, -416972544, 215277384, 12997827, -989464461, 0, -376011288, 167749056, 1291201551, 369280539, -113523316, -628260450, 0, -1062996315, 893254314, -192340980, -410911412, 657374748, 386145954, 0, 69004446, -543882708, -339966577, 693031923, 631117980, 457521960, 0, 130520160, 46282343, -252331506, -240695586, 351559024, -5155581, 0, 58325325, 395857293, 296419824, -993230070, 89219595, 571727754, 0, -534590100, -353965329, 912563880, -295591722, -263111652, -698872038, 0, -199620288, 1683455874, 47067492, 600029019, 304516823, -208085028, 0, 138714070, -154101099, -1317680190, 359501112, -782144370, -139981878, 0, 109458207, 158145939, 64912884, -630909753, -66038391, -7481322, 0, 321704028, -169850390, -1544372340, -231281325, -888461415, 446752380, 0, -955907525, 1306106112, -537079410, 1127862048, -218429793, 193534191, 0, 659455884, 405873396, -1309287774, -295658448, 242741556, -648474944, 0, 102543327, 40241130, -202756068, -80665686, -556091844, 928875078, 0, 309814188, 733810770, -348268329, 1092048827, -889865901, 228546036, 0, -1252264719, 240356916, 784444901, 371984805, -85063365, 188902617, 0, 847688049, -916096398, 917618181, 183906153, 739591280, -1248650280, 0, -364567240, -64489836, 160157556, 588092988, 134996262, -541066770, 0, 679268298, 9972720, -814686103, -305742855, -71346609, 508496076, 0, 107694117, 1429898262, 1147052277, 34543665, 399148103, -359323968, 0, 760613610, -599694564, 886454793, 903876503, 1161822888, -35763363, 0, -204786102, 451569078, -228410838, 314596323, -784756080, 42925094, 0, 140832108, -7241229, 466285575, 150171678, -795598920, 1181351913, 0, 287029320, 1677562167, -121898277, 707272860, 948375258, -114365439, 0, 366535110, -398763216, 337848996, 295062726, -152623440, -1111870192, 0, 931796622, 590680834, -839647668, -175953060, -242121783, -842816652, 0, 659586282, -84503271, 398418768, -966650784, 1479266646, -724969224, 0, -799434468, 379245483, 340475942, -679502418, 624202506, -2487869520, 0, -414641187, 248744717, 756621465, 105501933, -738700590, 950790957, 0, 586699406, -932211120, 521859564, 663138885, 43996812, -103602321, 0, 1001831040, -45875277, 1129712100, 736372302, -446143194, 1557931206, 0, -125374149, 1070142660, -378925620, -83241135], "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": "21.6.e.b", "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, 0], [1, 0], [-1, -1], [9, 0], [31, 3], [13, 7], [-9, -9], [0, 0], [-185, -5], [81, 0], [-447, -27], [-569, 1], [279, 27], [-458, -9], [0, 0], [117, 63], [-497, 99], [236, -148], [-81, -81], [-1142, -27], [1705, 277], [0, 0], [507, 567], [644, 308], [-1665, -45], [82, 231], [1016, 476], [729, 0], [0, 0], [-1131, 45], [-4023, -243], [-1763, -768], [279, 459], [-5121, 9], [8940, 60], [0, 0], [2511, 243], [-9982, 855], [2816, 1196], [-4122, -81], [-4575, -1395], [6852, -846], [0, 0], [-364, -2043], [-17453, -1673], [1053, 567], [-19740, -1260], [11278, 604], [-4473, 891], [0, 0], [-14404, -544], [2124, -1332], [-15872, -1680], [-14951, -1751], [-729, -729], [-6963, -3963], [0, 0], [-10278, -243], [-1659, 1041], [-22507, 3917], [15345, 2493], [-22298, 2544], [49379, 3299], [0, 0], [-12833, -4365], [-9860, -3386], [4563, 5103], [17612, -4461], [-20212, -4324], [5796, 2772], [0, 0], [50346, 1404], [-14985, -405], [16912, -5247], [-43028, 8272], [738, 2079], [-40424, -4344], [0, 0], [9144, 4284], [-12649, 6834], [36505, -1499], [6561, 0], [45600, -5160], [-31539, 1899], [0, 0], [-61164, -1308], [127030, 4450], [-10179, 405], [104955, 2655], [-14726, 130], [-36207, -2187], [0, 0], [77252, 12404], [-15867, -6912], [-48726, -12486], [-26564, -8534], [2511, 4131], [4387, 1017], [0, 0], [-46089, 81], [45508, 8100]]}