# Stored data for newform 1441.4.a.a, downloaded from the LMFDB on 25 April 2024.
{"label": "1441.4.a.a", "space_label": "1441.4.a", "level": 1441, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 67110305, "dim": 77, "analytic_rank": 1, "is_twist_minimal": true, "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 23056, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 85.02175231827222, "level_radical": 1441, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [1441, 1, [1311, 133], [1, 1]], "inner_twist_count": 1, "level_primes": [11, 131], "conrey_indexes": [1], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 77, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[11, 1], [131, -1]], "trace_display": [-14, -10, -42, -59], "traces": [77, -14, -10, 296, -42, -13, -59, -150, 541, 2, -847, -88, -20, -282, -330, 936, -56, -343, -157, -450, -122, 154, -764, -346, 1413, -408, -358, -228, -557, -267, -780, -1739, 110, -1104, -1254, 375, -541, -2133, -1458, -554, -1723, -5, -688, -3256, -1588, 276, -3086, -4280, 2452, -2234, -1570, -715, -1230, -5166, 462, -3203, 1024, -3016, -5408, -8221, 566, -3642, -3035, 1084, -1794, 143, -1925, -1105, -3710, -5875, -9614, -2198, -384, -2378, -3888, -2809, 649, -1731, -1086, -4357, 2329, -3167, -3045, -5359, 2582, -6468, -4432, 1650, -2831, 512, -6002, -7134, -4428, 1697, -10434, 195, -2506, -3435, -5951, 3834, -3852, -8917, -2156, -11444, -1930, -1578, -3306, -7955, 790, -22, -9374, -5031, -7375, -6972, -1384, -5815, -3078, 795, -14604, -2347, 9317, -5824, -7536, -7315, -9024, -10211, -480, -19337, -3402, -7246, 10087, 968, 423, -11777, -12526, -11548, -6976, -2254, -2492, -10033, -14738, -610, 220, -14366, 5608, -9411, -3100, -5412, -17568, -4242, -7091, -15005, -6668, 3102, -28360, -11986, -4761, -6114, -21360, -2520, -10808, -1980, -7670, -14154, 3630, -17680, -13389, 4216, 721, -12929, -25569, -12380, 199, -11832, -17383, -10296, -25898, -3266, -11768, -1348, -15044, -13303, -16048, -309, -25960, -750, 616, -30443, -5256, -11010, -30743, -24090, 1257, -16571, -7508, -8014, -6151, 3773, -18028, -31043, -4074, -2640, -37017, -23657, -4326, -19553, -45388, -2792, 1727, -27262, 5064, -6788, -4586, -10954, -38086, -19114, 96, -27887, -33322, 4950, -26766, -11860, -20956, -28620, -9173, -429, -29041, 18303, -11274, -20868, 1342, -36917, -22549, 13723, -942, -44528, -608, 22309, -45327, -49860, 9960, -1694, -41316, -5576, -7346, -8209, -39014, -32302, -15140, 17534, -41781, -24171, 8404, -34706, -38688, -8168, -9254, 4872, -30497, -32437, 8353, -1834, -35736, 3806, -21614, -25180, -23504, -8539, -30336, -34742, -27234, 2380, -43696, 4483, -15543, -52618, 2506, 20385, -19942, -48389, -26270, -13083, 940, -88981, 8402, 4488, -61541, -37459, 6495, 1904, -33840, -5727, -5586, -24198, -34808, -21308, 3938, -11437, -19464, -30162, -18742, -31926, -38454, 18395, -26810, -84191, -11242, 2508, -55344, -25345, -42978, -29187, -23546, -58399, -46210, -43957, -57288, 20145, 6127, -69504, -22958, -24186, -8584, -20982, -2392, -6458, 2334, -460, -11064, 2937, -79694, -59327, -28153, 8614, -77152, -57194, 31, -10253, -43886, 50610, 8580, -80124, -29623, -98071, -25832, -61704, -62449, 46637, -8143, -36290, -54098, 19129, -49289, -29026, -28618, -4846, -68706, -10292, -61164, 11628, -32202, 39635, -1210, -61210, 19962, -2038, -16347, -32983, -23985, 85444, -38554, -15063, 54112, 12144, -83186, 5782, -13718, 130427, -56514, -12936, 28596, 4859, -43346, 122964, 13794, -80998, -19116, 21830, 11639, 35078, -26288, 30851, -1310, 71146, -24168, -4125, -63440, 21274, -21304, 88046, -47432, 48549, 50438, 38001, -9838, 120225, 5951, 76007, 16017, 50442, 13408, -6713, -16560, 188568, -3778, -30018, 71004, 23463, -35470, 70643, -36704, 53079, -35532, 34202, 6870, 17948, -25094, 83225, 16038, 46410, -117242, 50882, 62690, 31445, 22804, 114935, -36248, 94496, 56599, 6094, 6382, 2006, 11019, 139593, -6500, 60498, 3114, 102026, -53820, 242242, 18953, -112269, 42898, 86856, 8826, 65440, 45017, 151432, 44456, 101350, 18331, 55, -55500, -44899, 6948, 144892, 5296, 147413, 76355, 41233, 26796, 155633, 7568, 129520, -6577, -11932, 48130, 110396, -78078, 298072, 31062, 44858, 142936, 35816, -56008, -31238, -11408, 81202, 10526, 183544, 16233, 66558, 78226, 139693, 17468, 11753, -5362, 118412, -2141, 29014, 38504, 169770, -28084, 117361, 90102, -3036, 11136, 115629, -25465, 315694, -3452, -40542, 150060, -36134, -65418, 227816, 33946, 16364, -1608, 169538, -21692, 76273, 53152, 38776, 76152, 74193, -66310, 47080, -11659, 49419, -1352, 191186, -20092, 192575, -4532, -26833, -20112, 263792, -26972, 51338, 50535, -73361, 13262, 46474, -53548, 235210, 6607, 48157, 103146, 24574, -156273, 85316, -31184, -4318, 80710, 31316, -5806, 214749, -55200, 219868, 17270, 7626, -30584, 136768, 37984, 107681, -7623, 208101, -38795, 200003, 58641, 7865, 95504, 118619, -85842, 142162, -34315, -13996, 5280, 75664, -77265, 325400, 13530, -29469, -45476, 117629, -70782, 283890, 65704, 252353, -17198, 135026, -4422, 56826, 5724, -144937, -12212, 249949, -134951, 70957, 127023, 149969, -50773, 226420, -5082, 65270, -1776, 65009, -96536, 113289, -62886, 284018, 41214, 46496, 131508, 35233, -70886, 203849, -80521, 100904, 49334, 164637, -21327, 209810, -3515, 120114, -11264, 143279, -169920, 117458, -138715, 65274, -167138, 196697, -35756, 22687, 80616, 33176, -95052, -47714, -142213, 206154, -13210, -9969, 37990, 190397, -70383, 434484, 59488, 44106, 5676, -99510, -117444, 306744, -5502, 74413, 95834, 83988, -125222, 90431, -35969, 22330, 39838, 185526, 61016, 30067, 356, 1505, -171302, 354644, -6226, 110291, -82384, -20087, -116706, 77438, -70517, 364017, 31022, -123859, 2224, 40062, -21738, -21263, -71616, -7767, -65504, 213021, -78146, 187061, -14674, 201392, 33385, 89962, -216926, -27732, 30152, 287921, -65404, 295021, -12072, 64373, 93629, -11924, 111614, 71237, -100824, 241829, 42686, -68991, -30880, 6451, -65650, 431945, 19734, -141742, -59708, 175187, -112511, 495979, 42316, 114886, 192548, -114469, 21113, -1573, -47698, 90310, -25601, 214135, -45242, 111322, 109709, 120895, -161094, 167163, 21175, 165885, -8800, -127228, -90046, 182199, -91424, 286485, 204314, -194493, 121403, 12155, -80962, -106228, -101304, 39724, 201730, 59051, 37324, 104486, -68864, 360282, 40810, -29890, -234034, 142696, 75486, 39366, 54600, 254905, -251440, 1347, 107099, 64625, 16976, 98994, -137457, 93338, 46624, -169102, 105860, 154569, -115691, 306862, 105754, -28317, -192186, -4306, -265168, -1703, -65542, 206281, 76466, -32621, -171075, 24178, 97080, -43298, -106360, 68672, 10140, 151337, -40514, -201616, -264837, 329971, 4224, 116026, 60890, -43930, -79984, 188415, -119130, 586101, 11572, -297401, 193158, 26158, -61420, -198525, -28042, 115762, 35218, -38994, -76036, 98698, -55880, 54990, 42768, 97427, -178982, 150832, -93136, 136915, -206310, 281446, 40250, -30079, 77134, 30899, -139454, 129958, -131181, 260747, -55122, 106703, 35346, 291608, -208180, 377464, -7139, -137187, -148698, 60701, -180270, 335605, 98994, 270038, -216716, -34323, -92780, 19041, -36839, -166974, -191950, 115504, -85003, 86609, 34408, -197208, -73168, 331388, 11946, 124940, -166612, -53922, -188784, 239980, -262870, 210496, -42850, -144397, -9406, 47927, -123722, -156564, -52805, -187877, 135622, -29352, 54324, 70038, -170634, 35242, -25619, -276183, -192670, 227012, -46298, 54315, -80316, 513787, -179562, -127972, 222514, 34837, -29556, -16438, -312806, 9604, 23992, -152848, 189880, 36803, -429701, 141473, 33495, -228779, -123396, 62880, -7729, 321315, 28682, 69307, -218538, -206062, -38250, 58949, -57841, -222427, -31812, -35364, -11855, 72073, -15084, -124840, -101478, 245782, -28402, -326021, -88009, 170356, -259366, 185961, -160219, 506662, -77366, -523629, 189914, 71148, -109877, -159195, -116382, -116368, 26256, 143279, 5659, -15666, -137338, -216933, 48752, -64144, -293040, 128029, -116121, -2644, -134902, 207091, -163096, -320872, 62908, -18150, -92390, -93548, -71137, -304110, 190160, -180100, 434486, -69058, -239219, 254131, 31141, -263059, -237638, 183146, -330952, 472282, 72044, 14329, -184802, -293010, -142688, -5632, -68902, -215280, -76740, 20937, 81544, -83907, 92410, 61373, -499282, 386886, 66022, -121465, -73386, -18233, -43518, 182174, 6164, 331689, 50066, -314313, -18310, 78474, -73692, -36235, 20776, -569390, -87441, 154706, -304834, -107859, -205807, -140016, 48708, -90699, -346441, 183231, 8156, 288687, -41366, 148234, -375111, -232299, 248934, -18667, -84214, -201147, -274668, -52536, -8384, -152918, 89222, 151356, -254462, 178764, 114774, -534878, -126728, -19650, -386242, 732957, -107396, -98791, -188690, -198731, -51586, -2145, -46393, -220135, -356352, -145864, -105900, 1800, 171087, -422996, -67334, 35454, 27566, -23922, -91772, 55655, -745946, 157839, -303117, 224503, -24668, -639683, 100446, 37785, -650616, -466701, -197036, -217720, 431958, 54997, 289550, -153301, 52807, 219567, 65461, -125249, -112574, 83027, -314070, 209863, -108510, 485660, -147812, -108399, 23231, -42174, -55842, 177927, -213700, -384266, -138968, 137345, -26906, 155019, -311580, 286722, 42372, -104352, -201880, 89047, -90340, 304247, 185815, 452082, -287144, -686578, -4820, 98087, -86896, -442321, -16382, -22628, 11100, -139973, 191732, -152211, -322034, 119312, 23716, -394838, -111738, -286540, -379774, 581627, -182716, 674487, 167106, -352494, 56528, 125884, -13790, 81602, 27164, -536399, 264532, 122817, -176358, -554206, -297895, -301985, 21230, -75394, -11734, 199196, -458808, 364888, -117296, 592541, -263617, -636596, 71840, 17358, -225332, 131646, -386419, -213334, 55704, -95947, 162550, -80474, -283562, -91228, 36366, -285982, 70871, 49845, -194836, 460182, -333643, -273874, -40616, -440433, 52674, 87505, -51153, -468458, -339276, -391526, -70580, -54850, 227248, -250957, -330579, 6073, -8690, -135219, -41438, -167584, -277516, 307066, -207784, 69549, -158758, -725718, -216350, 242, -558533, -237870, -12108, -172815, -181000, 56276, 14692, 170819, -308842, -257851, 103114, -38245, -530828, -562789, -279760, -69037, 62804, 223581, 7128, -706776, -263779, 55341, 34048, -108193, -328214, -910445, 229668, -86985, 113050, -184886, -502174, 89923, 81125, -637518, -295312, 329785, -476266, 197874, -88794, 354753, -559042, -310157, 94108, 76692, -203088, -608749, -57402, -90263, -180928, 87133, 318764, -314287, -265050, -238747, 15224, -317463, -158264, -63973, -401502, 235052, -486896, 796948, -274525, -613431, -147364, 63965, 32604, -674175, -264861, -405455, 111714, 225927, -28876, -561863, -560532, -269798, 33858, -365729, -365482, 293280, -531742, 84980, 293366, 180545, -349210, -1041407, 80350, -8745, -443516, -560186, -316339, -255322, -134752, -270890, 427148, -272382, -555888, -330230, 160644, 262, -684194, 486773, -557496, 140133, 46586, 22712, -138372, -298059, -536795, 25817, -462067, -354944, -106792, -778383, -282796, 49145, 248106, -864943, -558470, 82466, -102487, -605366, -156408, -219891, -656094, 240865, -180393, 135438, -303286, -1507337, -519770, 64064, -407944, -804345, 21118, -766671, 303534, 203098, 393388, -46352, -656671, -291524, 82896, -392398, -831508, 245320, -243860, 523140, -392543, 620704, -521110, -432921, -413476, 80465, -96758, 49178, -771650, 54482, 112472, -47302, 221520, -317330, -321796, -277671, 99264, -1013188, -196884, 366323, -813973, 425259, 227430, -72115, -661382, -725849, -162974, 112321, -378906, -442084, -148290, -744367, 146838, 452140, 117102, -524064, -810000, -323283, 5280, -186110, -665319, 181082, -459968, 80904, -218178, 93569, 88160, -805246, -84078, 212707, -808706, -812402, 9500, -371337, 112169, -241470, -448124, -908786, -395068, 25002, 37422, -328066, -296896, 51621, -742779, 398368, 121298, 535192, -236284, -1126070, -473483, 79706, -600520, 6543, 28483, -306107, 376370, -325065, 432428, -587659, -697301, 235134, -110957, -453166, -177164, -425735, -656800, 175185, 423550, 496914, -105608, -400286, -516597, -10648, -540502, -272667, -311760, -641727, 240480, 387500, 127805, -220618, -291016, 53151, -4653, -998458, 145692, 634466, -302468, 382125, 330040, 1205209, -509798, -774232, 251482, 129547, -339094, -292539, 306828, -162510, 151156, 1042400, 288870, 116922, -500126, -376660, 137786, -523076, -571868, 394808, -475408, 492901, 923682, 312846, 57014, -676811, 20318, 127028, 462792, -582679, -258926, -598698, 363844, 80825, 235293, 214687, -55866, 780140, 76736, -125256, 502780, 433987, -539654, 1062413, 225560, 273098, -127764, -789393, 553923, 24794, -651212, -584009, 108419, 465655, 81891, 309867, 846958, -553195, 119432, 165737, 27412, -278902, -57161, -116098, 22164, 92309, 130090, 1508581, 656782, -538572, 285999, 110363, -345194, 233445, 134711, -688639, 828812, 31131, 529144, -187336, -407038, 118551, 162118, 148349, -72935, 431260, -371362, 700739, 1125607, 705483, -868360, -485475, 273044, 6710, -173474, -57376, 208376, -277132, 851742, 425857, 888832, -235283, -146922, -11528, -2420, 3499, -565537, 279598, -383109, 1360179, 221822, 640184, 405386, 109736, -544011, 158026, 660338, -839316, 550188, -173057, 386963, 112694, 685240, 107477, -243858, -24116, -61688, -476844, 767842, 344864, -947358, 777688, 462402, 740306, -286258, -1277853, 915650, 103521, -425727, -403460, 363718, -122057, 592062, 846285, 647708, 32580, -444986, 39539, 34100, 186376, -951631, 962619, 67268, 831352, -296026, 1185569, -31398, -395892, 312518, 59532, -198418, 584674, -403427, 308398, 533946, 4518, 1214496, -268166, 542896, 133215, 193248, 73466, 759608, 622141, -669222, 244692, 1161428, 322690, -375180, -12906, -45148, 46662, 46238, -768180, 784072, -405080, 475096, 78321, 930822, -73213, -670212, 890748, 78001, 731815, -237315, 290628, -50638, 443444, 553973, 1137471, 185935, -525516, -233324, 165055, 232771, -137750, 320339, -858723, 1321494, 252328, -344406, 649567, 364298, 501678, 73348, -1038742, -58976, 659466, -574044, 1005309, 420884, 776166, -777871, -869712, 603500, -34122, 334400, 295193, 339869, -263413, 333802, -149693, 1293750, 553104, -2620, 931726, 311960, -716612, -143648, -220376, -45847, 762965, 697480, 663318, 569246, -627906, -133884, 131846, 189138, -501127, -678293, 54358, 156090, 656408, 503038, -550222, 491436, -97809, 52371, 309554, 740350, 156315, -392412, 1586457, -147539, 248711, -10632, -717177, 1265531, 67254, -418802, -195124, 151964, -243628, 969452, 249667, 869162, 456214, -282694, -514540, 234960, -402368, -944960, 143664, 112832, -395678, 543830, 933466, 415731, -450390, -26904, 27720, 517658, -356733, -12228, -651580, 1532744, -201392, 1118606, 683117, -771564, 546911, 118888, 137061, 296253, 273863, -1759262, 1585663, 1265374, 715239, 299258, -1606423, 258562, 21780, -428274, 6964, 1099518, -762662, 569704, -1801, 1295307, 176241, -238520, 857476, 84370, -671025, 335634, -686879, 231922, 1126985, 111778, 1741596, 575642, -1299494, -352266, 155694, 313894, -248843, -35706, -1221453, 1267428, 189531, 262552, 652553, 7146, -302554, -39930, 352510, 465102, 583383, -681262, 1095818, 1297816, 497304, -623836, -938079, 453924, 194480, 292657, 461119, 502952, 125141, 137724, 244021, 1507748, -36942, -396766, 1092187, 147279, -1162818, -937952, 1007924, -314942, 2171126, -83204, 1120529, 860708, -965002, -68865, -46376, 567729, -1155283, 615400, -1262258, 1014158, -340444, 1022714, -488525, 399792, 309651, -7931, -18054, 10886, 146265, -612708, 655932, 107560, 894072, -204188, -1032052, 995728, 142219, -499450, 28054, 803913, -928429, 1947338, 669215, 1012752, -395995, -1027061, 879277, 281259, 617137, -835708, 503661, -10334, 738782, 652714, 1678788, 85498, -805534, 389990, 136180, 388692, 72673, -427384, -503515, 1363176, -526907, 1079804, 348196, 84402, 1184449, -2189, -465121, 581486, -903410, 156039, 1631771, 1101632, 596038, -18486, -148537, -392282, 130152, -413732, -767025, 1390472, -710105, -568346, 1373778, 935766, 289661, -815342, 499259, 191213, 322710, 333048, 241772, 361212, 1795489, 329152, 2354700, 438386, -1692334, 878592, 113256, 216478, -1127949, -42068, -896987, 734960, 380950, 365309, 124947, 565532, -79795, 284878, -124958, 347351, 840733, -722113, 1409591, 935386, 618440, -519002, -1135719, 562366, 35926, 73306, 286971, 186812, -1447876, 1001184, -457783, -43230, 412172, 614576, 701550, 129448, -943831, -1075116, 1080473, -378761, 1195500, 1044122, 762848, 982256, -1214322, -721366, 14828, 1202670, -319983, -559088, -908817, 691060, 755514, 1218521, -448177, -62916, 203502, 165484, 746228, 270489, -67661, -387996, 508511, 449787, 1588393, -380015, -1134638, 1176934, 146333, -364190, -598791, 1435990, -670275, 1361654, 942590, 163160, 391622, -379510, 505517, 176528, -759268, -457556, -208648, 816749, 507532, 849498, 1211338, 103266, -1178465, -112645, 3399, 609961, 522772, -171824, 72287, 967278, 80008, 579992, 852844, 81090, 140892, 285560, -1171360, 913770, 546776, -1173913, 2923416, 1294488, 279187, -382527, -1123765, 1033248, 8250, 456052, -1771400, 1014222, -951078, 1030476, 931459, 1268122, -623711, 67392, -383209, -6776, -1420341, -393334, 272581, 720280, 1450672, 254702, 998358, 622730, -1085507, 137542, 334873, -640001, -1508783, 379896, -971892, 786622, -20510, 300455, -337470, 360472, 420922, 57816, 1042730, 351106, 252780, -657965, 747233, 917666, 429692, -361208, -1184199, 1436318, 121110, 948892, -88772, -84190, -1006746, 907512, 122616, 1971403, 877696, -705864, 820372, 338173, 446746, 284368, 643305, -891258, 1924919, 810788, -230652, 365544, -957817, -899146, 264990, 291544, -1457331, 761978, -1470318, 1176234, -1669636, 532012, -186635, 1009874, -92346, -13827, -554660, 869182, -1151191, -1129376, 1790129, 92727, 1848387, 24452, -1121844, 1037062, 182281, -157782, 388252, 536990, -714869, 1044004, -255741, 803048, 1941840, -752454, -661751, 82588, -29351, -1255527, -414752, 371376, 817461, -215647, 2520807, -596910, -837703, -510632, 88154, 1388342, -921384, -273296, -848841, 1591811, -319730, 1897072, 414118, -354624, 518338, 67661, -1479662, 358160, 1639843, -1101738, 1764869, 1589546, -64019, -665854, -1404550, 1259440, -41503, -738796, -1044469, 93304, -199820, 690512, 936906, 1605316, 33016, -27966, 449455, 198308, -945978, -480114, -521293, 282146, 1226328, 2564, 767631, 1643990, -1866232, -94450, 341473, -236510, -1059108, -114982, -1222595, 1732468, 886377, -356144, 178582, -49011, 962358, 44814, 492479, 210808, -954434, -284676, 304667, 1228182, -126752, -751050, -45667, 932946, 29040, -709662, 95567, 295693, -434225, -7336, -1080385, 2484408, -210939, -1110808, 899963, 407187, -1245224, 242818, 136818, 140890, 1463178, -228851, 2088330, 469328, -685378, -325538, 260227, -275774, -1562985, -116674, -266282, -261214, -469977, 520151, -375704, 789054, 217012, 47586, 271589, 568240, -591170, -320471, 735246, 413818, 1057290, -673426, -691696, 753780, 215083, 322507, -1690231, 733913, -912426, 523086, 1274386, 1475940, -603479, -817522, -850919, 499268, -806968, -2017720, 266052, -57540, 1378082, -64694, -449345, 591916, -2682833, 578452, 30712, -29308, -80204, -35658, 979657, 407483, -597361, 2005890, 211555, 339942, -676424, -18997, -1073102, 104274, -102031, -1356430, 1087284, 1935804, 149586, -385980, -868258, 80170, 299882, -399583, -1857282, 291660, -461057, 406438, -777647, 2603556, -875837, -1236896, 366199, -55704, 313266, 618632, -561456, 1459856, -621557, 557770, 2307614, -843510, -1657526, 368173, 74668, -183661, -2016054, -552880, -1374963, 2242686, -335566, -80188, -1336253, 956954, 782620, 50446, -269321, -757094, 312534, -858735, 149527, 268559, 1163086, -1105578, 548655, 1197392, 120494, 291890, -773211, -383139, -44933, 84005, 1042494, 1576792, 66490, -1926886, 662652, 418946, -333076, -710754, 860799, 282240, 763644, 26090, 148536, 212388, -989350, 319244, 210254, 416544, -2024903, 10540, -409122, -36123, -76140, 738104, -1319283, 1108080, 116492, -1056, -1854029, -204637, -101273, -717118, 2440805, 55915, 893813, 930220, -2178696, 3031088, 306757, -1036171, -928734, 1309393, -730318, 471070, 2156497, 615790, -958511, -133247, 1233914, 366542, -1598678, -624766, -419372, -112308, 1088942, -449796, 2635230, -506116, -1269058, -102842, -54450, -56474, -64943, -356451, -1201156, 1514132, -737495, 1845768, -387187, -623693, -1563626, 294426, 592611, -836604, 729376, -782488, 1522740, 1107863, 259971, -724066, -177805, 518006, 130460, -930377, -1229353, -239744, 248055, -758149, 888312, 915958, -989704, -268862, -311079, 230516, -714648, -1023122, 113793, 1105158, 459091, 429284, 2046237, 548892, -917741, 61052, 314820, -1046770, -995658, 642878, -1715323, 129946, -379615, -144395, 1707991, -116028, 772852, 100903, -526188, -538217, -533301, -570655, 535084, 1514778, 1064561, -1373266, -1819259, 1921188, 4719, 413472, 1277864, -20567, -800244, 1063986, -906973, 1520732, -1320264, -844186, 1203262, 319451, -2049020, 274354, 501112, -1492776, 2058270, -666406, 503531, 420856, -1168524, 137530, -201333, -527638, -1526745, -1479276, 677896, 1177242, -1377253, 289616, -104707, 1045734, 260884, 124014, -1301154, 1267768, -812691, 829142, 495070, 441520, 2297833, -395864, -623135, 21412, 229548, -548058, -1561746, -28046, -956391, 2171096, 248026, 867256, -1358416, 239471, -907683, -14762, 968226, -1667134, 1023755, 13012, 614834, 1438530, 621273, -45494, -1918437, -275793, 406087, 329286, 126662, -867768, -1009619, 1268489, -542668, 848496, -681068, -178846, 1520286, 248039, -2169170, 934638, -586335, -1130234, -69312, 18317, 1385801, -1097900, -952731, 696104, -150953, 470670, -1055470, 1845900, -1069703, 595283, -1358432, 1073561, 93972, -1467067, 1472240, 10362, -726274, 144052, -1148100, 152418, 1765489, -1445513, 1540483, 504034, -2208204, 1563008, 489808, -194904, -1660221, -839196, -743951, 1487017, 62388, 619226, -160917, 926660, -175907, 6688, -1707007, -1430062, 291434, -512990, 219836, 1022208, 1267769, -1608608, 42468, 1275704, -245399, 181402, -58950, -643390, 873607, 276362, -1086050, 1561906, 518575, 84348, 1252137, 498597, -229892, -399144, -84416, -325499, -1290023, 722134, 135748, 657420, -1854087, -1277144, 548460, 263026, -568966, -369540, -975126, -36468, -1797006, 1138506, -496422, 912234, -1375610, -109560, 184208, 117318, -437468, -946596, 1395958, 711508, 1281778, 111014, -1777579, 1622284, 18634, -1133268, -2243167, 460616, 310520, 575366, -743175, -93652, 973082, -1159614, 53131, 454476, -369256, -994066, -2380878, 77883, 1795366, -448930, 1769758, -316866, -609846, 319434, 61336, -63518, -294330, -685922, 855696, 522102, -1864444, 2147588, 361885, 4127, 1111220, 80806, -846972, -790404, 1053311, -1888247, 154225, 1950312, 335695, -956222, -2952235, 1605976, 90299, -182163, -462641, -244072, 604448, -1414355, 561120, 1306394, -775345, 907474, 300071, 429154, -809772, -713210, -2117215, 1321850, 886841, -382023, 583906, -1302516, -808415, 141072, 355322, -317800, -3259177, -26471, -2092234, 1324264, -1024709, 488888, -332567, 1275916, -44698, 166540, -702235, -1210052, -1794416, -2126820, 1090234, 748446, -48721, -127365, -2675273, 732326, -192874, -15982, 1510535, -475834, -835832, -608622, -2888092, 2240700, -480394, -748548, 216826, 459591, -893566, -2246988, 715759, -460726, 548999, 365, 1627764, -1310652, -3102347, -1177164, 265881, -710024, -1790031, -671604, -1316592, -129358, -563515, 551274, -474321, -103286, 475018, -92444, -2115439, 2027812, -1146452, -689174, -1866047, -299660, 839483, 75294, 510203, 304506, 381766, -1507672, -2394262, -157272, 395518, -1309694, -1017584, 1156692, -2229006, -786384, 334159, 425568, -378840, -2242312, -1093011, 910561, 498751, 560886, 646576, -380522, -1860679, -116990, 89848, 668238, -805889, -554351, -675773, 655250, -1743780, -346910, 510584, 88285, -429655, 101794, -2984979, -974644, -813145, -922924, 4201293, 216572, -1041131, -980518, -1887806, 744899, -53592, -846510, -2317774, 618476, -1088613, -289431, -2575586, 1940434, -652635, 451876, -1618265, 335467, -1053219, -585422, 397841, -381344, -555629, -1764754, 1168233, 1076250, -3051219, -21994, 356807, -1345854, -2399565, -386279, -1679256, 1945514, 11719, 1265686, -865407, -109603, 1396167, -91883, 91370, 291810, 486892, -946986, 296154, 2601824, -1520517, -2801510, -1462301, 1750866, 20174, -513506, 1060118, -1191946, -3580125, -228864, -412161, 345664, 275893, -2232974, 2310968, 393096, -2236616, -1276938, -1828213, 294290, -33509, 1068608, -1174440, 273586, -2654845, -406355, -41866, -507026, -1018135, 768240, -176111, -730030, -2115186, 728698, -464835, 1126034, -1443621, 237754, -269623, 789532, 642800, 134888, 416821, -275762, 912219, -950404, -1736768, 2312576, 276980, -1042781, -103689, 565710, -1544271, 530770, -855366, 29726, 248609, -1450866, 841465, 258544, -3149690, -1589021, -515295, 806910, 90459, 1157492, 675262, -87474, -2468048, 1698300, 93929, 212254, -652814, -1869590, 325971, -178174, -3530387, 1279974, -167892, 72, 582658, 333696, -2201118, -1122152, 934424, -250516, -691745, 171692, -551921, -93736, -3228157, -91096, 382162, -18088, -1433657, -143962, -1191686, -152910, -1866228, 1490746, 290263, -2563430, 1071408, 299574, -2744925, -423883, -3462004, 1578056, -1029218, -1044678, 121557, 177338, -2376157, 164884, -26180, -762050, -1516707, 342434, -665522, 596869, -2019271, 921021, -1142800], "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": "1441.4.a.a", "char_is_minimal": true, "conrey_index": 1, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "hecke_cutters": null, "qexp_display": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}