# Stored data for newform 4021.2.a.c, downloaded from the LMFDB on 19 April 2024. {"label": "4021.2.a.c", "space_label": "4021.2.a", "level": 4021, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007199288299445, "dim": 182, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-450537346108, -76772151648819, -467548084593609, 605661494630484844, 45883628123246772896, 1474752452524447232426, 22392640857456497693627, 86629579117398750063988, -1981302945534809411892995, -24355560307683041751861617, 18337037032094302488112461, 1693213834559730939423698411, 4706584074164652096685156235, -65969609629210066273414360619, -318501925936122747416151952579, 1726781666283866989604431152976, 11490505733930994368069119080872, -33081306233075683680390252703549, -285609555647061177400219770941094, 489630180428650806675499069854923, 5356461841520895317013635708006905, -5841006020677906010483557076804285, -79514427002121915557704833877296801, 58443476339617948765645398710101918, 962982221716402669322543131696453534, -511068113241233162403311636543587760, -9719009218955961527177765401726269536, 4063294082061610186867535864985214352, 83059803062594544658501692284782876342, -30197482275109153279821281151402479664, -608674704830509721423975541586918253559, 211181082699407494097073093386107956630, 3864125927525827950711114022471391926637, -1373706001762647861748920860277737642046, -21433794933535656804913326140604956097147, 8165449670258926325204882225310773309796, 104636026684171353360361798127066925860832, -43728331680417454896423782620766890815030, -452390145985232203019820183931562449172070, 209356517291364285383161782737782470925227, 1741634917288555799843572392907249460439155, -893908402534816233557762566048958880466659, -5999061085322386775207311397505343884467465, 3406921240813141296930362246462349664750724, 18565817694109503647096280858787070076280615, -11620791431007557278646673585061546676189769, -51815237424195202909975586152421640104961312, 35595668528566950038916316113162928154884814, 130837260309597711113088090276599021031867478, -98273270914983000271367602073836302425769515, -299765210114403974185053899142141166299419118, 245427010333522180652795018033485974342805967, 624727832739231592201607521961614984986592780, -556356727489528890242867872086040591301917031, -1186829947016837538069660739687790604126700796, 1148475701836974896853296244924013998913232689, 2058949440478408272732916061074102097483630517, -2165267615559815849476207501991987412944473440, -3266396459903227778792747950763591801894316101, 3738504879186469467934594458226064551545170825, 4743304580175530213784417588867334293475216792, -5925880063233498570685191641858879458084650351, -6307944090768207592914508590531750550957201878, 8642742351593509764936177757976555379447317609, 7681057988712478444841992641559105723603090115, -11621967247382007184127891055684069680191203967, -8555415112867269015458545663195962959478466718, 14435755960303588589657246086016131361452545392, 8696952130634219938649183556716943941370437893, -16590381447033115426011016356420575755323934358, -8034570638883292193141039921073725553213845445, 17667823138641888794143525122140336077397662900, 6694353800653931479982696229831811574575113784, -17458392025376439898496313005374288480927086364, -4959081821435894470427297015313886349757191673, 16026534691705562259767876717846612924580611906, 3171425284470996768411451627652419428447248507, -13681887053640099091410684519835081436333761633, -1625916631499383006384378344697678483009738503, 10872224586207643257131783578343334728059163898, 495291025136908352928981503126348632872269875, -8048040319984336225868787195389821455348527264, 186314103425626086362792111580476980438426488, 5553046256400749178873310081784054430011067517, -490695855057956042240031253999421097128643679, -3573104843516668061674442912769104363538646487, 539947428858995581924389021432356811877013583, 2144697782364026867716047629244651404118534349, -455558020185439874132007893830153048319703729, -1201007032774298154952831482696364946119612824, 328248356139985094463294052259862539462912004, 627402258527228793859297451836477365140086408, -210164279399354632432376819356643302276544728, -305647408603261978209104838710771808033685505, 121880610153105728403877141485074883521064191, 138767312567108712241725379671598387593931916, -64714654388492066934868077207873748528805273, -58652664515102333301766049337937995315902635, 31670016192475380739187906608704837873730298, 23042343610351382531980967674329717950129348, -14347208671791138594625987646664407208127211, -8393987551361151133464831999557078238585187, 6034693459600788880342517577908876436258158, 2825295129332697349159647856594719496772051, -2361639387333715155683260933715416044326464, -873846023479854820246500575417332425519280, 861130843083981964319614956091462338690521, 246177541455243610772379704762646912970265, -292848776278275763760954866933602702133528, -62205078782018552012605197278942467952678, 92938445187584088712647158072608765228031, 13676998766320034454966581478139298288380, -27532595331701453231198466315404097277260, -2429342015488977027698644249019581635215, 7613735057954048329940444014593492852987, 259850821851102738748448779446214399909, -1964847262138986684072061773366966599793, 32248343910781789524120623435285447757, 472935873877096281493760142524491987296, -30505291441697909387685416699362520470, -106084264644844947232508278063747509144, 11795659578359111467155894883105167495, 22149297052805322966308946318051198318, -3489864134580189874377793766658105059, -4297693872195792512588474296854198649, 880252814448022732181299824892200334, 773313730142244401747081022158774899, -196768827803194754767859487962193574, -128674128741806824037103450676166720, 39686514093135466509060298915746149, 19722996051806952309642296373351847, -7290120615484914423908953392636686, -2769878272542223906545271035113986, 1225892753848080789697658502437473, 353597426293845292151406850518911, -189219446294559556517964584713411, -40519668464337418842884949509214, 26839308546781190970823654596381, 4076896149848810590048802895211, -3498523001969175637623681618595, -343941562977968470252881210198, 418732351609940216470442608247, 21345377091750492520009653602, -45942219120357989036702584313, -372022601032633620169502359, 4609470576457444683579224011, -146535307240403652099922650, -421513691143103986101168274, 29509921762058009840918854, 34977548850347067715892616, -3774797162941585637184116, -2618613834764113199295870, 385322305029932091491173, 175500078334027676551337, -33336198731938779563502, -10415293293965393968398, 2499399731815279368328, 538471443247208520692, -163722684901238160116, -23601053888358155149, 9379301787073231506, 830675841880176702, -468195969135723340, -20176123855481398, 20209646550104653, 85877741731340, -745373091808200, 22704572524917, 23079915041867, -1459042129069, -584435737362, 56459131801, 11605589656, -1567946638, -167292476, 31854125, 1440385, -455572, -1044, 4134, -124, -18, 1]]], "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 16084, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 32.10784665275684, "level_radical": 4021, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [4021, 1, [2], [1]], "inner_twist_count": 1, "level_primes": [4021], "conrey_indexes": [1], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 182, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[4021, -1]], "trace_display": [18, 28, 22, 14], "traces": [182, 18, 28, 208, 22, 18, 14, 54, 238, 7, 138, 47, 5, 72, 41, 256, 29, 35, 48, 56, 22, 19, 91, 46, 230, 88, 103, 15, 75, 18, 43, 116, 15, 13, 185, 364, 15, 53, 80, -13, 68, 32, 82, 259, 37, 13, 121, 53, 244, 93, 144, -16, 101, 47, 49, 199, 3, 4, 254, 24, 8, 37, 19, 326, 65, 41, 91, 50, 50, 5, 212, 77, 5, 101, 127, 22, 87, -20, 86, 71, 358, -20, 139, -30, 25, 82, 36, -8, 100, -87, 74, 171, 50, -13, 217, 42, 20, 47, 389, 269, 170, -22, 41, 209, 7, 13, 209, 125, 32, 27, 101, -33, 110, 60, 102, 169, -22, -4, 224, -41, 294, 18, 133, 58, 75, 94, 31, 215, 24, -39, 366, -52, 2, 223, 82, -19, 132, -25, 86, 233, 98, 24, 59, 555, -38, 92, 160, -22, 211, -107, 54, 114, 8, -22, 481, 81, -1, 64, 114, -108, 104, -14, 79, 132, 34, -33, 49, 4, 253, 136, 199, 55, 78, 25, -28, 421, 40, -47, 648, -46, -9, 38, 63, 8, 137, 72, 31, 230, 10, -103, 451, -38, -26, 16, 90, 306, 85, -2, 30, 207, -17, -66, 295, 59, -24, 101, 139, -119, 123, -199, 220, 214, 32, 6, 86, 34, -86, 138, 334, -69, 260, -154, -2, 371, 349, -48, 108, -146, 13, -64, 83, -100, 61, 67, 182, 418, -89, -156, 304, -184, -45, 25, 267, -127, 36, 0, -19, -21, -19, -129, 568, -236, -4, 220, -113, 316, 84, -136, 196, -5, 36, -175, 286, 9, -84, -55, 138, 10, 189, -170, 52, -8, -105, -127, 584, -46, -38, -38, 108, -130, 156, -138, 39, 424, -135, -73, 147, 13, 271, 21, 289, -168, 15, -83, -19, 216, -83, -29, 363, -45, 22, 155, -24, -135, 61, -82, 1, 67, 87, -98, 395, -219, -96, -33, 334, -56, 90, -227, 39, -51, -49, -173, 242, 591, -170, 113, -105, -211, 145, -409, 233, 10, -141, -71, 102, -246, -48, 77, 259, -146, 61, -190, -41, 158, -95, -169, 406, -255, -41, -66, 121, -92, 44, -127, 28, 147, -223, -100, 357, -564, 270, -65, 86, -178, 122, 74, -84, 191, -79, -263, 321, -83, -46, -63, 3, -222, 13, -212, 241, 367, -44, -137, 43, -162, -97, 345, 309, -145, 305, -332, 20, -64, -32, -35, 202, 509, -73, -46, 29, 202, 122, -269, 97, 378, -197, -200, 219, -200, -104, 115, 230, -106, -69, -252, -30, 292, -20, -287, 525, -338, -19, 55, 202, -83, -30, -268, 68, 166, -59, -336, 213, -84, -88, 101, 103, -79, -97, -277, 11, -98, 268, -369, 806, -184, -110, 47, -103, -297, 238, -185, 45, -40, -179, -58, 79, -72, -145, -163, 379, -212, 78, -464, -15, 187, -88, -51, 423, -441, -153, -135, 175, -269, 120, -289, -20, 325, 96, -144, 214, -479, -127, -77, -68, 237, 224, -249, -6, -117, -83, -397, 1008, -11, -182, -60, -41, -194, -5, -298, 211, -82, -5, -314, 1, -3, -136, 249, 69, -247, 15, -323, 132, 124, -140, -135, 461, -351, -117, -84, 253, -347, 166, -361, -39, 479, -297, -76, 105, -495, 323, -140, 520, -313, 40, -5, -144, 574, -86, -283, 678, -451, 5, -141, 48, -397, 67, -389, -5, 194, -259, -370, 20, -429, -198, 173, 363, -72, -22, -423, -13, 149, -41, -216, 356, -32, -164, -49, -240, -195, 223, -484, 188, -173, -165, -288, 385, 728, -167, -109, -13, -655, 214, -400, 19, 112, -62, -163, 335, -266, -107, -58, -6, -392, 28, -274, -43, 355, -77, -454, 749, -674, -123, -329, 276, -153, -102, -254, -203, 28, -174, -466, 832, -517, -210, 195, -202, -318, 76, -439, 157, 349, -77, -230, 45, -332, 162, -315, 301, -278, -1, -575, 83, -27, -190, -154, -54, -309, -371, -3, 345, -618, 252, -364, -167, -81, -301, -300, 187, -447, -104, -265, 94, -399, 202, -572, -166, -55, -246, -359, 1031, -728, -98, -30, -214, -365, -34, -244, -17, -153, 21, -598, 127, -646, -219, 75, 251, 40, -187, -620, -59, 166, -109, -436, 530, -176, -138, 48, -130, -210, 18, -704, 205, -77, -306, -351, 99, -360, -207, -168, 100, -663, 263, -462, -241, 566, -299, -363, 416, -257, -75, -391, 111, -487, 70, -534, 8, 849, -235, -278, 440, -834, -219, -125, 114, -492, -173, -347, -102, -382, 433, -395, 967, -455, -278, -223, -290, -385, 121, -758, 113, 110, -189, -572, 48, -204, -297, 280, 39, -562, 193, -753, 93, 103, -165, -484, 232, -874, -162, -17, -220, -750, 105, -496, -124, 705, -252, -266, 182, -441, -159, -571, 566, -444, -183, -628, -291, -176, -405, -512, 1029, -834, -149, -447, -204, -37, 254, -137, -174, -206, -330, -478, 268, -690, -377, -11, 162, -453, -98, -946, -130, 155, -142, -544, 427, -617, -344, -22, 100, -719, 374, -1001, 80, -64, -397, -483, 225, -578, -351, -302, 47, -594, 172, -801, 53, -197, -193, -530, 237, -147, -229, -258, -57, -738, -110, -473, 60, -106, -256, -475, 115, -1240, 163, -100, -177, -125, -139, -662, -239, 202, -59, -816, 1127, -533, -210, -198, 0, -415, -18, -877, 155, -398, -469, -308, 168, -649, -432, -88, 88, -876, 216, -658, -232, -30, -219, -575, 578, -107, -269, -215, -117, -804, 250, -872, 187, 497, -467, -481, -69, -989, -194, -471, 667, -558, -121, -788, -251, 477, -476, -345, 643, -185, -290, -567, -488, -579, -71, -667, 2, -394, -46, -740, 415, -1012, -202, 303, -286, -363, -21, -746, 139, -701, -173, -575, -106, -1039, -306, -32, -108, -579, 79, -1046, -105, -281, -456, -512, 112, -271, -209, -346, 491, -530, -171, -721, -401, 347, -429, -399, 734, -1156, -175, -173, -181, -721, -214, -817, -83, 279, -513, -731, 167, -1247, 131, -463, 2, -758, -188, -1032, -148, -255, -364, -497, 1022, -383, -325, 129, -331, -858, 41, -918, 2, -605, -183, -348, -18, -542, -483, -422, -298, -796, 268, -1329, -128, -425, -475, -555, 891, -700, -443, -425, -25, -866, -117, -1014, -238, 429, -367, -503, -19, -1422, -255, -246, 396, -400, -131, -725, -341, 425, -151, -410, 527, -927, -251, -679, -248, 156, -89, -320, -146, 51, -403, -526, 343, -789, -134, -279, 48, 37, 105, -286, -91, -369, -120, -337, 633, -127, -211, 115, -252, -262, 179, -402, 116, 347, -374, -226, 32, -381, -361, 22, 587, -431, 410, -507, -196, -210, -246, 1, 75, -30, -263, 207, 421, -166, -75, -168, 213, 127, -372, -296, 513, -779, -241, -235, 77, 76, -139, -154, -38, -260, 385, -272, 521, -748, -115, 209, -414, -324, -206, -106, 171, 862, -146, -97, 278, -264, -499, 204, 470, -176, 253, -298, 75, -234, -272, 131, 600, 196, -182, -49, -133, -351, 247, -143, 144, 454, -524, -310, 155, 198, 4, -236, 721, -214, 84, -42, 109, 726, -93, 223, 388, -277, -184, -71, -357, 51, 141, -128, -168, 72, 106, -407, 325, -145, -140, 182, 32, 481, -169, 333, -144, 37, -285, 79, 736, 258, -134, -10, -17, -181, -98, 257, 498, -85, -455, 180, 339, -197, -234, 188, 741, -74, 52, 47, -254, 358, -151, 225, 691, 53, -67, -623, 438, 155, 53, -143, -105, 317, -269, 191, 529, 357, -152, -212, 423, 133, 111, 446, -204, 675, -356, -105, 808, -283, -30, 232, -55, -601, -131, 399, 449, 209, -181, 58, 143, 22, 185, 782, -111, 577, 10, -70, -192, -92, 45, -354, 771, 122, -127, -30, -109, 96, 184, 185, -60, 909, -457, -24, 355, 371, -163, 76, 269, -499, -369, 634, 75, -422, -262, 370, 1207, 291, -229, -239, -64, 22, -207, 11, -193, 242, -155, 365, 550, -636, 175, 418, 108, -131, 177, 353, -66, -136, -406, 292, 674, 144, -263, 331, -305, 233, 235, 56, 391, -88, -419, -276, -258, 1335, 31, 99, 913, 87, 247, -418, 345, 533, -331, 135, 103, 201, -34, 199, -17, -340, -165, 440, -130, 93, -70, 419, 335, -204, -236, -91, 375, 606, 226, -105, -23, 192, -264, 190, 1422, -683, -477, 436, -95, 413, -153, 1099, 329, 317, 58, -152, 287, -572, -135, 126, 181, -164, 63, 764, -174, 292, -61, 1017, 207, 579, -250, 428, 185, -414, -51, -312, -31, -34, -669, 221, 107, -14, 191, -115, -107, -126, 97, 610, -56, 158, -513, 37, 1409, 445, 57, -2, -20, -365, -279, -648, 263, 764, -262, 457, 387, -146, -141, 483, 1204, 59, -200, -212, -175, -400, 185, 31, 455, 63, -207, -21, -79, 1187, 257, 423, 420, -48, 195, 322, 357, -216, -356, 243, -40, -148, -18, -146, -252, 635, -663, 56, 263, 251, 161, 260, 257, -200, -167, 1143, 250, 652, -404, 83, 608, -1006, 119, -16, 173, 823, -290, -93, -327, 391, -199, -303, 838, 342, -95, -111, -291, -91, 12, 479, 223, 574, -410, 173, -283, 1144, -143, 237, 57, -123, -118, 435, 219, 172, 231, 451, 940, -426, -258, 415, 171, 125, 210, 42, 152, 315, -213, 149, 37, -35, 59, 164, 75, 108, 101, 602, -73, -286, -246, 890, 1609, 24, -429, 71, -197, -154, 231, 371, 167, 461, -153, 246, 668, 212, 23, 157, -41, 406, -274, 694, 34, 820, 127, -76, 533, 24, -117, 47, 121, 142, 267, 763, 149, -157, -357, 822, -61, -95, -304, 101, 543, -135, 256, 70, 367, 1212, -179, -174, 497, 2043, 69, 363, 149, 453, -99, -118, 149, 572, -26, 679, 340, -183, -84, -16, 420, 170, 284, -4, -162, -238, 0, 918, 381, -16, -449, 75, -410, -121, 182, 1385, 112, 201, -84, -152, 544, 1391, -48, -51, 57, 1056, 343, 1166, -75, -6, -198, -284, 459, 524, 65, -15, 394, 597, -122, -561, 262, 764, -455, 102, 172, -564, -3, 184, 1816, 45, 190, 93, -351, 939, -376, 844, 1248, -658, -195, 300, -381, 921, 39, -68, -41, 238, -231, 133, 502, -211, 26, 161, 725, -285, 7, 1634, 330, 327, -210, 175, 307, 653, -487, 200, -249, 605, 195, 258, 441, -934, 90, 24, 3, -327, -377, 188, 310, 848, 275, 962, -90, 533, -120, 242, 689, 1217, -173, -6, -506, -660, 46, 600, 279, 537, -379, 703, 292, 842, 382, 120, 106, -72, -370, -424, -333, 459, -210, 144, 1123, 708, -393, 410, 518, 0, -272, 224, 497, -318, -202, 271, 341, -3, 258, -130, -212, 441, 474, 115, -318, -316, -37, 1068, 1038, -36, -82, -176, 685, -292, 87, -762, 275, 491, -72, -7, 49, 882, -334, 649, 396, 510, 292, 372, -406, 286, -353, 106, 400, 787, -99, -334, 372, 345, 84, 471, -74, -151, -97, 1052, 666, -849, 8, 667, -98, 71, 5, 1495, 218, -126, -281, -139, -14, 832, -36, -73, -559, 383, 23, 898, -9, 1708, -42, 455, 387, -464, -193, 224, 358, -670, -161, -299, -107, 112, -404, 895, 1044, 432, 9, -280, -308, -443, 320, 89, 260, 477, -493, 916, 77, 1238, -194, -139, 485, 94, -385, -205, -303, 329, 78, -121, 697, -6, -114, 70, -415, 206, 47, 210, 195, 286, 78, 366, 31, 856, -463, 3, 313, 485, 346, 1055, 9, -720, -46, 591, 1175, -363, -333, 487, 94, 46, -6, 321, 13, 383, -492, -59, -183, 306, 664, 181, 181, -250, -59, -148, -240, 299, -388, 1052, 1621, 272, -667, -244, 290, 612, -496, 215, 41, 584, 405, 1434, 1327, -854, -275, 30, 481, 590, -289, 742, 178, -489, -452, 73, 304, 476, -199, 261, -150, 35, 475, 169, 285, -536, -66, 454, 79, -1001, -368, 271, 851, 1138, 577, 200, -48, 360, -22, -410, 668, 1280, -181, 385, -78, 379, 180, 872, 153, 220, -331, 648, 613, -164, -127, -468, -168, 617, -98, 727, -356, 895, -172, 794, 528, -93, -197, 1005, 253, 225, -375, 443, 339, 693, 56, 99, -277, 512, -159, -262, 382, 1159, -13, -420, -22, -321, -722, 779, 955, -775, -33, -382, 168, -349, 634, -124, 256, 1677, -804, 651, -21, 1805, 75, 312, 1034, -381, 5, 1343, 112, -494, -168, 167, 556, 1, -136, -211, -329, 681, 96, 516, -31, 485, -41, -145, 462, -994, -163, 27, -196, 165, -97, 721, 360, -131, -554, 1700, 1122, -46, -180, 345, -180, 94, -114, 447, 462, 31, -138, 86, -92, -318, -318, 27, 764, 224, 2, -182, 3, 986, 568, -441, 926, 577, -189, -497, 361, -623, -33, 328, -529, 226, -509, 1273, 935, 1467, -373, -195, -115, 21, 65, 42, -116, 189, -426, -733, 1382, -36, -113, 311, -55, 605, -621, 2228, 690, 127, -180, -146, -234, 579, 36, -209, -544, 793, 375, -759, -135, -38, 537, 401, 401, 111, -455, 429, 63, 616, 74, -29, 312, 210, -211, -576, 199, -72, -103, 242, 184, -210, -423, 313, -109, 602, -471, 935, 1336, 255, 3, 205, -213, 245, 60, 450, -177, 514, -200, 2566, 57, -1217, -240, -44, 1092, 271, -127, 368, 28, -365, -648, -180, 291, 2669, -650, -129, -267, 382, 425, -398, 89, -408, -493, 150, 419, 828, -231, 425, 460, 92, -124, 148, 54, 1444, -566, 441, 444, 903, -441, 402, 175, -640, -161, -194, 483, 976, 139, 58, 280, -1474, -255, -320, -275, 1065, -321, -351, -327, -50, -39, 511, 2015, 735, 238, 734, 12, -713, -369, 1345, 300, -260, -172, 116, -5, -857, -162, 322, 549, 248, -117, 1096, 35, 112, 66, 296, 343, -1252, -551, 230, 525, 18, 301, -688, -433, -772, -834, -123, 206, 2440, 275, -106, 771, 16, 221, 232, -193, 495, -1044, 1683, 648, 1416, -481, -849, -100, 344, -332, 395, 529, 19, -383, 86, 46, -1145, 1, 745, -88, 72, 278, 1128, -349, 679, -441, -529, 821, -410, -347, -325, -144, -235, 163, 144, 97, 68, -155, 1427, 58, -331, -651, -71, 1079, 680, -204, 130, -123, 26, -421, -266, 739, -908, 98, -267, -291, 275, -241, 775, -261, 334, -468, 311, 608, -583, -452, -702, 42, 239, -77, 246, -292, 25, 51, 512, 1750, 891, -270, -302, -849, -814, 31, 1152, 413, 481, -436, -96, 282, 1407, -426, 343, 84, -45, -40, 109, 260, -501, 288, -136, 1015, -562, -220, 942, 456, -837, 57, -1020, -155, 1135, -284, 312, -363, 300, -82, -225, 1163, -7, -46, -2, 89, -92, -433, 328, 1678, 1013, -339, -202, -369, 849, -324, -232, 43, 650, -317, -379, 66, -1101, 282, 495, -402, -710, -158, 727, -211, 42, -19, 1006, 1272, 769, -687, -17, 124, -671, 12, 1832, -66, -506, -575, 1102, 619, 1334, -344, 104, 448, 922, 552, -576, -359, 615, -1088, -13, -335, 1436, -180, -554, -95, -815, -116, 456, 218, 1786, -693, 808, 278, -491, -230, -83, 354, -64, -317, 281, -402, 427, 485, -61, 551, -717, -436, 797, -627, 1390, -235, 1310, 306, -333, -252, -121, 732, -407, -9, -475, -58, 319, -173, 1010, -41, 356, 230, -382, 63, 330, -805, 253, 80, -799, -5, -578, 648, 1592, -221, 664, 540, -222, -134, 532, 295, -879, -272, 712, -493, 355, -1028, 1095, 517, 913, -168, -418, -121, -494, -239, -999, 208, 221, -24, 402, -4, -72, -539, 1212, 1029, -519, -346, 1529, 365, 804, -313, -844, -232, 391, -594, 774, -357, 2246, 366, 299, 6, -454, 35, -61, 189, -999, -725, 1002, 537, 346, 64, -14, -465, -1066, -296, 504, 378, 1645, 63, -522, -154, -425, 281, 1547, 23, 76, -762, 380, 650, 690, -491, -811, -194, 2016, -156, -117, -227, 41, -401, 584, 2416, -705, -259, 424, 391, -363, -236, 921, 333, 150, -773, 1092, -177, -268, -195, 333, -332, -745, 454, -508, -165, -57, 102, 5, 142, 1577, -497, 645, -264, -168, 129, 149, -43, 606, -846, 338, -520, 986, -233, 199, 622, -140, -127, 836, -58, 67, -307, 647, 1021, -751, -609, -263, -570, 193, -135, 336, -561, 321, -477, -320, 997, -1043, -135, 69, -342, 566, -296, 2035, -269, -495, 21, -596, 328, 1372, 89, -340, -591, 60, 131, 1173, 80, 780, -466, 657, -209, -1261, -403, 205, 846, -252, -469, -764, 38, 426, -784, 2, 1074, 1241, -162, 210, -109, 262, 280, 1114, -549, 1601, -607, -96, 445, -1021, -119, -608, 86, -461, -422, -777, -280, 802, 613, 2376, 1129, -80, -558, 1093, -1233, -209, -563, 280, 56, -324, -234, -280, -122, -298, -843, -133, -318, 996, 304, 2795, -24, -954, -214, 563, 699, 45, -577, 286, -526, -616, -332, 1070, -205, -369, -423, 63, -30, 1334, 24, -1018, 544, -369, -115, -29, -13, 290, -737, 438, 2403, 135, -768, -99, 254, 382, 26, -58, -140, -317, -559, 644, 413, -1380, -290, -3, -668, -312, -182, 803, -190, 510, -811, 229, -264, 1310, -973, 535, -680, -29, 253, -14, 722, -205, -135, -2, -251, 225, -747, 248, 200, 2360, 147, -898, -449, 430, -196, -163, 634, 678, -372, -282, -578, -373, 166, 275, -305, -420, -1055, 2555, 861, -377, -83, -927, -214, -181, -321, 726, -128, 435, 68, -438, 448, -1498, 45, -391, -477, -995, -446, 513, -311, 85, -198, 164, -5, 1061, -150, -269, 631, 494, -567, -392, -443, -739, -365, 1892, 654, -719, -740, -547, 1013, -625, 255, -616, -276, 310, -1110, 29, -95, 916, -45, 888, 311, 265, 18, -615, -313, 632, -1096, 740, 910, -494, -263, -124, -808, 349, -133, -936, -622, 642, -668, 228, 753, -799, -902, -304, 768, 524, -219, 1698, 556, -1249, -742, -1168, 648, -281, -706, 52, -803, -590, -62, 896, -24, -277, -149, 300, -230, -221, 5, 267, 331, 92, 122, 34, -670, 1771, -771, 151, -22, -62, -534, -132, -241, -468, -312, 551, -249, 578, -877, 843, 508, -1071, -746, -639, 192, 428, -117, 130, -31, -330, -473, -177, 1261, 1044, -388, 551, -763, -849, -272, 1090, 110, -801, -363, -648, 55, 1422, -781, 271, -647, -154, 611, 229, -124, -1083, -154, -256, 593, 1656, -913, 62, -774, 2040, -117, 1048, 265, 1597, -1293, -518, 66, -718, 190, 122, -274, -712, -123, 431, -675, -498, -1229, 1081, 1360, 424, -597, -272, -35, -601, -927, -105, -205, 1547, 408, -5, 411, -1384, -229, -108, 823, 899, -546, -737, -412, 295, -819, -24, 600, 1074, -817, -543, -659, 54, 352, -1475, -276, -860, 168, 2148, -123, -325, -1129, 1158, 693, -1413, -361, 443, -382, 845, -1071, -34, -304, 627, -635, 505, 148, -217, 174, 88, -411, -162, -899, -138, 140, -1199], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": true, "level_is_prime_power": true, "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": "4021.2.a.c", "char_is_minimal": true, "conrey_index": 1, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": 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}