# Stored data for newform 8033.2.a.e, downloaded from the LMFDB on 25 April 2024.
{"label": "8033.2.a.e", "space_label": "8033.2.a", "level": 8033, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014398543044449, "dim": 169, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [712050240, 408045214064, 37292115930568, 724951147191891, -26205563437937652, -790052326402088524, 6211215640906495040, 265616648879155688084, -560551411911642410071, -41208100583859234186296, 9568155452998148776021, 3508612029546969453092393, 1149356184863723057965537, -186260833888888311956088729, -68143344213101711978963175, 6732321256467448272023525979, 1317865540324583559788089773, -175711265953525367415630422959, 7881698874925602821060039641, 3451947383045726695903008902555, -1015268374394349431989077478121, -52685825179845465055378837098540, 27772149844227328620167062092771, 640812098069838019611917400924053, -472087471362583784289582740141805, -6343385306425655542824908188723152, 5857528736004653168093997469976921, 52017972007507182270542398971550578, -56737398536449413001564954475597427, -358708313566716107355950674494841297, 445833878577942136139547422745658371, 2106842602220511925747847743675286588, -2915868924940178980995765609442127871, -10655375156491154297754163371411396216, 16172736175807946626538097368609230124, 46840634673495655920310700194167476458, -77176848727785687911731581732557442419, -180426352671185719184184406738785891244, 320547804545121279818927605449553068784, 613234229873576020380544304894528996217, -1169820556307379836670975946183897515536, -1850192414870813060868104972276795783163, 3781082135283325125443281760994141228835, 4981144667039341179734573198382580425621, -10897259237573574653108056037312797863641, -12020012305164109455446635441471383080726, 28167507791427748401520989894877743318232, 26097553796763468296057939226010924703154, -65630462920145150629052365540397494195081, -51144860450715707848088581969096447460953, 138456547138681350647300195839436209920666, 90706616441643934629331331345451642895768, -265504510697386710826616886126654517436278, -145871327948657987761505700584817305646831, 464397303987854022909277996143635523737814, 212989923252461988700714610562040009360324, -743213313120836344621096300504832029093445, -282500598989496140737210692200524467162378, 1091314815121000102766070191415393989237620, 340179494964472711973443505838414622215224, -1473956402145337343803817905906194846287673, -371136163297998106178884301143616920028816, 1835253096615095092923005667750900168422094, 365242980324304877886830791377529471959758, -2110904936601763629925542489836163688843243, -321477398203620258590388744311453020090985, 2247003121396743261846086947892265570951271, 248856219744461872994141513042310179385249, -2217311998614355812232828749442313484184458, -163324514120130460530655163481218607032888, 2031403210411875544463530799114188617745049, 82101517117658179865899416457123809219469, -1730246980535462935542617958421850885469316, -18198814822430491475050444037037855452056, 1371837688569514443186700920593523676168344, -22580677668903809113899373558225616881714, -1013603367237411299218129198793285640982205, 41434188100138643255845366475349094830368, 698624465274385460462055041118640189161196, -44042731058710831067905224785457981660889, -449598229964776768439987947708054581804948, 37412974220795964597768598350603537261643, 270372556712766067336176608394895750389052, -27475292217939956508212126365981341990058, -152044155518070555688935818768554797134567, 18010317206456976801388722477263675880078, 80005421348480039617917220672719875993054, -10711636947905739160775233322290733843883, -39413785645592036277347027981306256894287, 5835717189256345993086302091241202309508, 18186812746664688925442117185010918596627, -2930121531502101755110346816375848834789, -7863401453691535826262826881934075324718, 1361530928634802705102633582364903245124, 3186698778543077298526497850420910828790, -587207200428710864700621693404336768553, -1210724995144587516978645016132059907966, 235559769073776035270902233262950087491, 431307592818450514774838671332373112480, -88031345036972332909330718902379743399, -144077015609242026287318086885221703352, 30683252746210849560661914490765062492, 45129700920698956332530365451805442087, -9982893016952061314503620214983168764, -13254061224405789011878348329427956067, 3033571000128786382405103151365517769, 3649020191229367698619924132700557796, -861297204118461725042999234983195195, -941517401127152027458403856755954699, 228523112195730182840815376150250189, 227588068610568670681730379333888488, -56661647623551233756935203638424811, -51515989929634253332134026862872786, 13127005881118496293491194253502566, 10913496053138368266563313328678735, -2840726712142871719462790284259382, -2162346450410379686964250282216828, 573965544495435891908096058941455, 400391737635121437707651884115810, -108211876211136925221029991430353, -69222380309287751346031160591437, 19022596661571031967195474446497, 11162247709559292193582521132991, -3115107457811026775351409236446, -1676776929455198244505926303758, 474692158867223097646205503449, 234324351749223126318687986322, -67225323308622695495513359211, -30415450084928492120835868982, 8834707846373622253110679262, 3660389431336575697065487900, -1075591010425141512507678934, -407596329630501713646827020, 121071840783842240219971295, 41897964414641985522620385, -12571816321819673280747237, -3965164355942784441516025, 1201110154258011630336639, 344439025792269461820131, -105268234288343031704168, -27366781441035911241276, 8434105785634261343740, 1980763544482569279231, -615266786304821778217, -129982352565540468904, 40675449501660069002, 7690658090451453041, -2423511564764033597, -407568676854544964, 129284368266568333, 19193094141663955, -6126269930415540, -795389496465240, 255382068510353, 28658589857430, -9253126834106, -884038152364, 286946520784, 22877593891, -7463082824, -483027112, 158324083, 7990158, -2630845, -97109, 32112, 771, -256, -3, 1]]], "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 32132, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 64.14382794369453, "level_radical": 8033, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [8033, 1, [5541, 1944], [1, 1]], "inner_twist_count": 1, "level_primes": [29, 277], "conrey_indexes": [1], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 169, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[29, 1], [277, -1]], "trace_display": [3, 8, 13, 76], "traces": [169, 3, 8, 183, 13, 17, 76, 6, 181, 30, 2, 25, 63, -3, 26, 219, 14, 31, 51, 49, 16, 53, 50, 43, 214, -2, 23, 149, -169, 26, 65, 25, 57, 60, 60, 218, 52, 35, 49, 72, 3, 78, 132, 0, 64, 32, 54, 76, 245, -6, 44, 193, 58, 54, 213, 12, 52, -3, 25, 32, 100, 78, 227, 292, 37, 59, 110, 24, -20, 47, 44, 71, 139, 35, 53, 92, 22, 83, 137, 90, 177, 91, 126, 36, 95, 21, -8, 75, 19, 130, 102, 68, 22, 82, 37, 107, 116, -13, -11, 337, 45, -97, 300, 22, -21, 17, 82, -11, 59, 16, 174, 225, -65, 46, 215, -183, 150, 118, 43, 91, 257, 84, 105, 118, 96, -4, 270, -31, 52, -92, -66, -25, 124, 3, 46, 184, -21, 39, 171, 96, -65, 93, 31, 328, -13, -109, 64, 158, 43, 78, 181, 15, 148, 107, -2, 17, 146, 87, 122, -53, 59, 155, 65, -20, 50, 1, 152, 77, 302, -8, 138, 357, 65, -17, 263, -93, 56, 330, 83, 90, 113, 15, 241, 72, -65, -302, 187, -38, 50, -145, 69, 25, 67, 39, 64, 218, 72, 175, 256, 14, 73, 103, -76, -71, 126, -10, 232, 455, 98, -45, 116, 100, 187, -38, 136, 134, 218, -187, 72, 451, -60, -84, 416, -148, 108, -77, 182, -42, 154, 75, 257, -6, 74, -115, 191, -12, 164, 25, 131, -1, 192, -37, 37, 137, 107, -208, 328, 104, -24, 78, -34, 456, 168, -38, 231, 445, 85, 55, 243, 128, -181, 50, 139, 66, 98, 42, 47, 199, 30, 27, 384, -39, -6, 105, 37, -289, 169, -56, 77, -135, -32, -169, 374, -57, 75, -106, 9, 294, 219, -30, 10, 199, -1, -19, 292, -117, 132, 68, 112, 60, 143, -181, 172, 23, -64, -168, 195, -61, -65, 225, 89, -5, 224, 94, 105, 316, -76, 93, -2, 117, -1, 124, 55, 274, 126, -111, 273, 279, 47, 148, 42, 206, -96, 61, 86, 61, 92, -128, 203, -35, 100, -86, 593, 44, -192, 21, 191, -25, 103, -137, 246, 126, -22, -130, 295, 27, 183, 125, 50, 95, 234, -125, -75, -47, 76, -220, 502, 187, -16, -45, 92, 46, 175, 59, 20, 204, -63, -13, -23, 3, -7, 231, 252, 3, 45, 8, 441, 393, -64, -275, 288, -249, -31, 14, -101, -579, 259, -60, 220, 172, -10, -37, 166, 112, 25, 3, 145, -466, 184, 61, 170, 345, 153, 59, 468, 23, 103, -68, 80, -348, 26, -171, 232, 78, -17, 284, 212, 0, -101, 28, 167, 114, 226, 130, -26, -105, -76, 161, 425, 115, 141, 136, -66, 353, 210, 131, 378, 420, -97, -388, 266, -169, -204, -85, 203, -304, 343, 163, -7, 285, -48, -172, 310, -219, -209, -279, -150, 244, -61, -208, 114, 524, 146, -12, 336, -314, 12, 51, 59, -429, 158, -118, -327, 520, -58, 78, 423, 162, 100, 293, -46, 268, -14, -80, 251, 269, -58, 111, -41, 257, -182, 318, 369, 171, 126, 115, 9, 331, -15, 209, 284, -179, 87, -65, 46, -53, 219, 247, 72, -226, 59, -31, 423, -267, 215, -128, 278, -70, 279, 72, 162, 439, 90, -136, 360, -133, -35, -47, 15, -363, -92, 223, 106, 231, 102, 101, 108, 115, -155, 178, -51, -27, -167, 3, -136, 454, -48, 74, 403, 152, -14, 321, -16, -287, -66, -299, 673, 420, -19, -543, 423, -37, -7, 98, 174, 21, -132, -7, 11, -49, -101, -344, 306, -233, 21, -21, 123, 250, 354, -24, 333, 91, 66, -172, -64, -64, 114, -127, -134, 155, 161, -115, 181, 241, 39, 72, 493, 147, -16, -92, -160, 282, 92, 14, 244, -131, -121, 222, 218, 39, -150, 257, -10, -168, 139, 89, -104, 234, 153, -466, 320, 123, 184, -319, -81, 129, 289, -53, -26, -389, 41, -2, 349, 52, 80, 69, 403, 311, 203, -484, 94, -137, -138, -368, 570, -530, -47, 317, -60, -234, 75, 70, 390, 137, -64, 92, -50, 205, -540, 278, 62, 324, -9, -32, -74, 659, 142, 291, 318, 43, -47, 98, -52, 204, -130, -470, 556, 488, 61, -138, 315, 107, -92, -99, 32, -43, -32, -56, 72, 323, 164, -189, 836, -159, 122, 133, -151, 82, -259, -266, 201, 869, -144, -866, -75, 408, 109, 23, 109, -36, 244, -157, 189, 227, -214, -147, 681, -58, -446, 94, 52, 75, 402, 173, 324, 86, -105, 60, 5, -993, -136, 96, 35, -899, 366, -455, 567, -123, -124, -415, 167, 41, -87, 2, 82, -673, 381, -182, -32, -621, 172, 16, 434, -133, 428, 58, 405, -580, 112, -515, 22, -305, -216, 15, 245, -337, 264, 209, 2, 106, -95, -121, -23, 332, -366, -111, 289, -186, -126, -11, -6, 108, 74, 119, 47, 455, -160, -582, 189, -206, -444, -128, 334, -225, 138, -91, 594, -114, -158, -87, 193, -149, 6, -340, 219, -498, 132, -159, 322, 118, 109, 172, 670, -351, 102, -227, -279, -201, 328, -963, 8, 1167, -80, -391, 331, 24, -89, 217, -37, -358, 169, 152, -349, 309, -47, 490, 555, 116, -275, -14, -49, 306, 253, -79, -146, -556, -54, -16, 33, -337, -18, -174, 54, -6, 62, -189, 26, 571, -239, -26, 361, -572, 315, -227, 206, -691, 187, 148, 311, 738, -94, -288, 525, -341, -181, -750, 344, -691, -424, 68, 61, 559, 313, -284, 302, -685, -83, -29, -65, -594, -213, -114, 153, -158, -80, -432, -18, 396, 282, 180, -49, 119, 38, -302, -111, -22, -467, -724, 524, -340, -30, 417, 129, -441, 29, -253, 659, -25, -211, -947, 227, -76, -134, 44, 93, -83, 694, -123, -61, -162, 215, -518, 764, -420, 47, -730, -354, 550, -80, -418, 176, 110, 140, -475, 177, -91, -57, 206, 59, -132, -44, -333, -240, 343, 165, 15, 903, 25, 81, -115, -264, -725, 265, -97, -343, -42, -84, 185, 341, -65, -51, -156, -249, -612, 384, -60, 181, 223, 115, -250, 255, 250, 14, 190, 32, -135, 683, -310, 401, -150, -222, -246, 483, -672, -694, 28, 126, 264, 74, -390, 157, 332, -60, -405, -60, -253, -932, 513, -256, 200, -210, 10, 160, 565, -308, -12, 322, 156, -648, -555, 128, 136, 3, -974, 651, -40, -316, -305, 353, -145, -17, 160, 104, -218, -464, -146, 240, 61, -174, -306, -51, 239, 298, 308, 199, -892, 367, -313, -246, -44, 55, -448, 752, 247, -354, -290, 135, -192, 230, -323, 231, 390, -52, -738, 215, -273, -124, 264, 75, -226, -15, -167, 121, 909, -354, 172, 275, -661, -322, 335, -216, -749, 331, -830, 397, -25, -6, -494, -53, 301, -369, -35, 19, -1031, 224, -165, -25, 183, 56, -244, 581, -412, 464, -128, 122, -625, 269, -147, 419, -1440, -302, 448, 351, -647, 195, 152, 234, -96, -47, -152, -49, 542, -548, -429, 168, -635, -113, -551, -260, -128, 178, 287, 585, -323, -196, -777, 520, -286, -880, -529, 338, -106, 296, 64, -246, -581, -170, -194, 52, -72, -129, -343, -36, -717, -21, -499, 262, 514, 145, 267, 158, -257, -428, -246, -196, -944, -9, -470, -592, 314, -67, 42, 760, -534, -67, 154, -23, -127, -3, -420, 97, 3, -61, -387, 368, -133, -21, 228, -5, 489, 70, 2, -291, -281, -140, -231, 658, -1089, 267, -773, 5, 341, 3, -353, -194, -16, -32, -78, -47, -195, -126, 47, 434, -625, 440, -28, 234, 716, -16, -16, 566, -550, -187, -60, -224, -1254, -29, 366, -96, -204, 148, 138, 202, -295, -414, 246, -132, -921, -447, -22, 38, 756, -146, -429, 264, -12, -105, 295, -89, -334, -401, -158, 65, 148, -348, -845, 583, -1053, -38, 187, 155, -301, 183, -202, 167, 0, 100, -569, 443, -39, -366, -475, -207, 72, 80, -484, 264, 373, 126, -671, -38, -148, 117, -1195, -507, 141, 438, -215, -96, -38, -159, -897, 235, -662, -64, -271, -577, 382, -320, -891, -343, 465, -262, -682, 419, 280, 404, 387, 30, -1081, -64, -617, -495, -730, 120, -1180, 978, 116, -181, -701, -144, -471, -47, -32, 38, -702, 192, -200, 330, -357, 60, -177, 354, -31, 248, -482, 17, -79, -78, -1190, 182, -1124, -502, 332, -308, -126, 28, -404, 81, -473, 66, -363, -54, -151, -1191, 40, 286, 54, -79, -425, -295, 413, -59, 79, 1294, 102, -50, -741, -9, -734, -476, -645, 396, -783, 13, -584, 332, 9, -640, -111, 283, -76, 114, -78, -294, -86, -151, -281, 661, -12, -266, 208, 139, -455, 246, -769, 476, -551, -265, -1579, -409, 0, -43, -462, -188, -483, 240, -250, -26, 455, -245, -75, 415, 243, -770, 159, 424, -633, -18, -809, 457, 445, -267, 12, -510, -718, -185, -110, -508, -1106, 475, -945, 44, 28, -131, -638, 1456, 19, -163, 6, 79, -444, 317, -794, 30, -874, 4, 189, 583, -232, 99, -122, 594, -874, 117, 27, -170, 300, -558, -154, -237, -97, -66, -397, -168, -144, -411, -441, -44, -564, -317, 133, 580, -573, -827, 150, 341, -69, 198, 100, 26, 521, -307, -587, 209, -557, -538, -782, 300, -1638, 103, 21, 258, -238, -374, -530, 569, -193, -519, -654, 32, -309, -31, -296, 102, -175, 10, 520, 682, -406, 279, -224, -304, -754, 555, -1161, -111, 690, -186, -870, 104, 546, -95, -237, -343, -250, -58, -301, -43, 424, -205, -117, 957, -495, -464, 187, -113, 1144, 31, -224, -343, -4, 137, -582, -422, -1006, 428, -854, -148, -1389, 61, -604, -431, 30, -233, -54, 673, -846, -186, -784, -240, -769, 485, 140, -114, 63, -57, -199, 15, -571, -102, -179, 128, -2406, -78, 56, -341, -500, 26, -861, -185, -667, -95, -16, -213, -870, -102, 79, -333, 292, -96, 766, 274, -521, -38, 485, 52, 508, -192, -1413, -149, 246, -210, -1164, 947, -606, -224, -235, -439, -380, -127, -445, 378, -12, -443, -590, 231, -533, -260, -609, 103, -365, 306, -341, 344, -193, 116, -811, 35, -185, -125, -908, -567, 288, -246, -882, 444, 100, -31, -156, 78, -363, -52, -260, -556, 498, 174, -371, -437, 231, -391, 17, 976, -14, -141, 112, -230, -914, -266, -497, -483, -438, 331, -1930, 416, 180, -139, 240, -12, -646, 172, 3, 299, -290, -122, -919, 256, -988, -184, -86, -58, -454, 797, -498, -154, -331, -98, -869, 541, -1461, -504, 489, -410, 54, -44, -275, 132, 309, -116, -1586, -25, -501, -229, 302, -245, -504, -413, 122, -314, -309, -313, 306, 417, 458, -997, -643, 260, -90, -777, -1608, -512, 110, -127, -412, 1050, -380, -278, -97, 46, -32, -17, -250, -35, -857, -306, -955, 392, 96, -26, 121, 427, 95, 265, -477, -1, 17, -217, -1504, 50, -26, -692, -185, 231, -985, 90, -170, 429, 581, -100, -1054, -39, -58, -410, -485, -445, 428, -27, -440, -245, 326, -294, 482, 145, -460, -877, -559, -647, -384, 295, -1459, 212, 256, -438, -1565, 444, -322, -239, -78, -142, -1308, 96, -828, 152, 86, 76, 130, 488, -863, 713, 204, 409, -892, -23, -595, -272, -608, -386, -79, -128, -433, -566, -57, 337, -457, 237, -673, -227, 453, -551, 94, -26, -198, -101, 212, -395, -555, 172, 181, 462, 404, -351, -759, 554, -338, -1395, -878, 604, -2480, 77, -370, -107, -336, -338, -331, 796, -292, -451, -295, -270, -1022, -196, -281, 415, -1063, 25, -121, 890, -696, -334, -456, 135, 216, 374, -1664, -460, -410, -261, -734, 610, -1239, -174, -88, -363, -837, -37, -470, -140, 1142, -439, -758, -128, 236, -486, -673, -88, -413, 643, 122, -782, -374, -288, -308, 509, -2124, -128, -886, 252, -1279, -455, -580, -392, 206, -366, -59, -77, -467, 773, -535, -266, -1651, 478, 21, -226, 20, -71, -935, 690, -602, -506, -753, -124, -2638, 131, 60, -696, 193, 306, -800, 76, -1168, -942, -295, -110, -596, -602, -278, -470, 258, -182, -434, 184, -81, 524, 589, -245, 203, -48, -1350, 128, -534, -551, -1554, 786, -1317, -409, -1044, -338, -1410, -802, -433, -81, -24, 362, -641, 520, -669, -452, -725, 77, -144, 477, -869, 766, -188, -67, -996, 454, -648, -505, -1292, -376, 79, 78, -861, -373, -752, -217, -250, 413, -521, 20, -654, -829, -812, -730, -349, 677, 479, -461, -1064, 213, 889, 170, 7, -537, -930, 91, -543, -535, -868, 130, -920, 1164, -551, -993, -979, -451, -33, -2, -47, -158, 103, 129, -993, 9, -84, 297, 259, -326, 566, 388, 142, 563, -132, -62, -1607, 552, -1004, -830, 276, -645, -810, 272, -1099, -277, 95, -212, -375, -44, -556, -362, 280, 338, -651, -163, -27, -421, 297, -100, 148, 582, 772, -3, -423, 629, -138, -411, -923, 658, -1742, -159, 19, 220, -518, -718, 339, 232, -71, -124, -442, -646, 105, -86, -41, 535, 202, 376, 499, 19, 215, 335, -61, 379, -774, -173, -1362, 827, 572, -153, -759, -39, -608, 80, -1318, 76, 123, -139, -358, 526, 656, -702, 145, -151, 561, -558, -577, 569, 578, -201, 133, -200, -268, -313, 801, -373, -949, 419, -1079, -27, 309, -181, -1618, 599, -187, -1213, -35, 219, -357, 212, -460, 360, 202, -40, 266, 410, 231, 49, 804, 233, -893, -195, 447, 118, -1399, -560, 715, 770, -55, 278, -540, -367, 339, -190, 257, -53, -141, -352, -221, -159, -225, -965, 254, -85, 195, 350, 500, 462, 489, -112, -677, -27, -456, -1117, 105, 544, -1658, 564, -320, -350, -928, -353, -543, 420, -92, -747, -153, -4, 41, -343, 913, 180, 2, 277, 217, 523, 6, 256, -93, -300, -1086, 149, -1060, 585, 1030, -1, -322, 523, -968, 142, 574, 188, 244, -22, 39, -91, 964, -347, 52, 300, 297, -873, -218, 208, 319, 591, 316, -314, -131, -385, 1039, -228, -804, 893, -1066, 277, -1005, -250, 37, 53, 297, -130, -83, 755, -889, 95, -280, 260, 1251, 368, 260, 124, 832, -42, 476, 261, -442, 368, -221, 2, -2768, -238, 856, -632, 894, -26, 174, 1331, -340, -396, 116, -137, -93, -720, 604, -6, -313, 140, -226, 82, -223, -55, 475, 313, 777, -246, -487, 445, 0, -475, -895, 539, -952, 230, -56, -148, -1785, 227, 48, 28, -90, -219, -166, 576, -1025, -395, -93, 1124, 167, 74, 433, 335, 1018, 9, -368, 92, 91, 123, -280, -564, 774, -294, 127, 527, -134, -470, 17, -156, -17, -177, 274, -10, 1496, -37, -306, -516, 537, -255, 128, 735, 1223, 331, 1120, -317, -56, -48, 119, 144, -675, 378, -133, 418, 18, -197, -207, -52, -615, 3, -91, 700, -868, -147, -138, 1646, 397, 614, 115, -97, 359, 196, 0, 64, 255, 248, -1095, 96, -794, -215, 628, -455, -240, 469, 9, -307, 600, -39, 49, -126, -415, -637, -288, -181, 389, 157, 318, -743, 340, -40, -392, 290, 1149, -635, -485, 59, 689, -314, -244, 1156, -261, 348, -708, -255, -215, -73, -158, 373, -36, -59, -243, 615, -610, -140, 743, 817, 454, 331, 796, 591, 649, 339, -464, -526, -94, -307, -609, 251, 1036, -213, -60, 260, -523, -197, -429, -147, -639, -95, -381, 212, 117, 70, -54, 377, 914, -131, -69, 1130, 617, 58, 498, 123, -1034, -468, 206, -292, -763, 630, -1673, 915, 37, -542, -963, 200, 48, 181, -21, 381, -492, 626, 148, -473, -162, 110, 1217, 355, 258, 793, -485, 423, 150, 6, 610, -301, 263, -360, 889, -11, -261, -82, -165, -331, -673, -193, -783, 8, 15, -275, 615, 971, 547, -1058, 280, -311, 644, 569, 838, 1019, -141, 398, -1187, -27, -125, -1827, -64, 220, -500, 222, 164, 745, -870, -259, -196, 988, -75, 34, 420, 472, -794, 18, -95, 501, 13, 134, 102, 654, 568, -220, -159, 204, -313, 477, -878, -108, 1292, -86, 553, 684, -542, -509, -325, -545, 1128, -19, 632, 300, 642, -683, 61, 735, 247, -326, 535, 464, 478, 570, 1344, -683, -397, -182, -37, -260, -762, 107, -151, 772, 422, -267, -909, 931, -391, -128, -130, 219, 45, 48, -276, 695, -1015, 778, 752, 629, 599, -350, 438, 1100, -542, -228, -163, 323, -642, -265, 508, -324, 184, 222, -657, 209, 414, -566, 915, -102, 766, -275, 190, -258, -255, 114, 344, 480, 528, 214, 839, -119, 2275, -128, -894, 112, 1180, -677, -1005, 935, -1197, 240, 82, 340, -1031, -13, 347, -218, -68, 37, -244, 113, 111, 150, 236, 261, -164, 500, 95, 804, 771, 209, 1240, 209, 699, -212, -1027, -56, 1584, 65, -19, -71, -40, -299, 669, 496, -1006, -22, 30, -72, 341, 348, 480, 734, 922, -160, 1143, 169, 1401, 776, 1033, -466, 748, -363, -71, -1139, 306, 45, -1908, 1166, 571, -502, -235, 150, 892, -933, -82, 397, 259, 72, -1160, 89, 742, 886, 1025, -432, 796, 841, -49, 16, -429, 36, 214, 1025, -742, -377, 326, -557, 1075, 290, 249, -1247, 1514, -306, -210, -37, -377, -835, 521, -6, 392, -510, 822, -494, 1555, -486, -23, 1033, 864, -1158, 30, -67, 194, -710, -877, 1048, -1486, 74, 14, 364, 340, -254, -338, 685, -107, 390, -503, 204, -222, 220, 1018, 1239, 507, 150, 540, -576, -585, -81, 35, 935, -387, -130, -75, 292, 1927, -447, -996, 750, -1617, 85, -53, 24, 1952, -116, 434, 525, -24, -130, -714, 143, 1313, -374, 819, 853, 975, 84, 689, 14, -1373, -414, 90, -753, 663, 259, -182, 643, -654, -471, -949, 80, 702, -218, 13, 557, 743, 247, -13, 444, 1511, 245, 957, 276, -661, 281, 418, 694, -1361, 869, -560, 376, -525, -266, 2034, 209, 172, -392, -332, -67, 163, -34, -748, 11, 25, -538, 1659, 467, 761, -355, 95, 326, 444, 3, 566, -205, 1429, -1048, -59, 445, 655, -993, 221, -17, -179, 486, 59, -504, -121, -15, -200, 472, -337, -960, -191, 935, 275, 201, 828, 500, 1803, 58, -43, 1368, 807, 446, 173, 58, -1621, 364, -319, -49, 891, -90, 177, 531, -82, -45, -461, 191, 332, -45, 222, -423, 2142, 103, -86, 8, 220, -130, 637, 244, 1631, 323, 1580, 346, -358, -843, 348, -190, -1605, 369, 174, 675, 1276, -47, -416, -117, -793, -361, 97, 838, -692, 79, -470, 230, 684, 293, -31, 1040, 580, 357, 1059, 136, -140, -19, 127, -233, -1614, -689, 1052, 133, 836, 424, -984, 65, -1108, -648, -373, -300, 476, 140, 264, -178, -397, -226, 1179, -361, 142, -251, 467, 775, 1806], "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": "8033.2.a.e", "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}