# Stored data for newform 8045.2.a.d, downloaded from the LMFDB on 25 April 2024.
{"label": "8045.2.a.d", "space_label": "8045.2.a", "level": 8045, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13510798915673965, "dim": 141, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-1020397287, 651168882714, -9645394931180, -470034328547216, -99051366295555, 79441218174046208, 263730013533532092, -6474494566114732248, -31607638865473001940, 314574196971532446284, 1903401214610989436527, -10089659564814227781400, -72452264414604904871423, 226745072745643748820400, 1920523043124512154156250, -3705890919854557894537288, -37486840408207956008422611, 44988380803529985241243183, 559339493157565169070976763, -406948207711198909529293291, -6557567607330153159792160838, 2662039055784210278510093811, 61719298229615466881892475833, -10941452991377789334965860419, -474625543047026938026781272006, 3671123979806782213083112731, 3026696089252366106434585514713, 372832905240264426731167836271, -16210407609851510284312551296565, -3700383426093952064464780154278, 73724799878409165626233337462050, 23277035869212593439188947343628, -287480522773378970902329874629854, -112383194788166031271966904494528, 969273376691414230691393545209010, 443426686397978260049451473075651, -2846793295445458159295882345379493, -1474448754700884978758360484633612, 7331395287487147392924712420829945, 4209023717358052334647563846753245, -16651645223231432317198416177086609, -10447490246406492524867636333744619, 33527111483038483851319374417740058, 22764425143033101906631732547205102, -60113958644882320667652877387475293, -43871498280494719832029572470867124, 96368782179700569686077535030521975, 75243690690755911097141493617620934, -138615598139422203735483873066830300, -115445624743081139347605170879787050, 179449649435315979708988280221754490, 159162647152902101850692378364847256, -209645847199853297899742264823401577, -197944310828448857764920216602490514, 221526382986626590533548472061027390, 222821203866828120546995409331109311, -212112605964758819088854539341077218, -227708751293001728615992300978995033, 184302833065982859902491206406529671, 211816600191778888017601590171388633, -145460042893354622501667289829197324, -179768116260932219825195632851035947, 104325454530948329593419428218696569, 139487599168425011633309198353603548, -67978666621851147727318933199776152, -99133534616540179442178223081044276, 40198548525421412434733477199233178, 64634211973591603203135951022029113, -21521779463233478649641594959048113, -38713837026682780047116286305393921, 10387354802382657972087922520427480, 21328128614817977609665397742674927, -4485146598392115585309854258281102, -10818403538442840562149748644962075, 1708495916271744410598134635830439, 5056640664451769467040116901397802, -558126485547208193212724624699794, -2179414271802618818739782177456259, 145887324696515589212041187017446, 866589659941298425228528148103398, -23411282655973240600336820992893, -318000417754044317426233984112769, -3152926909030311093775443542525, 107709335263581337231644079710081, 4772392064278616949046684914756, -33673343205655282561945305731812, -2578411883354376765546785085393, 9715026195069016596608467858890, 1040242485342106929632277137508, -2585602256051286514085417931174, -352075898496879368863950290210, 634433667116350401183666230863, 104162716030911366467084283534, -143406183111076707176258283528, -27455473351401386842054206123, 29829786263368903096939696607, 6512623965459190696031261152, -5702372134719854012698125793, -1398117023344745199588111171, 1000154564183324974201095525, 272493290292166120764064042, -160621316562289647900649109, -48291379694007846367526668, 23560411963538927097533497, 7785370935111495321252913, -3146860016167538881108901, -1141316940998180166806615, 381275600267749700195246, 151969095837249839470647, -41705448371130890104771, -18345877998840772439159, 4093207983436501454740, 2002979109621099673804, -357504032121072187571, -197142377644254803181, 27467906798245889543, 17422651406139420212, -1824243320798412673, -1375754144161788582, 101634475659363309, 96479151251308148, -4462847445599410, -5964250472968687, 127520966476594, 322020619489067, 365476577229, -15008555756359, -324246300704, 594810835306, 23963037617, -19648425499, -1127837149, 526277057, 38486623, -10978918, -962083, 167329, 16906, -1657, -188, 8, 1]]], "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 32180, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 64.23964842612007, "level_radical": 8045, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [8045, 1, [6437, 1616], [1, 1]], "inner_twist_count": 1, "level_primes": [5, 1609], "conrey_indexes": [1], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 141, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, 1], [1609, -1]], "trace_display": [-8, 11, -141, 29], "traces": [141, -8, 11, 158, -141, 23, 29, -21, 160, 8, 32, 17, 35, 18, -11, 188, -13, -16, 152, -158, 40, 14, -77, 69, 141, 27, 38, 67, 22, -23, 86, -65, 51, 79, -29, 191, 45, -9, 55, 21, 36, 6, 132, 74, -160, 72, -16, 22, 212, -8, 82, 106, -28, 86, -32, 27, 10, 23, 71, -17, 116, -36, 45, 237, -35, 69, 99, -7, 45, -18, 34, -53, 125, 50, 11, 271, -31, 2, 101, -188, 221, 67, 67, 141, 13, 48, -21, 71, 79, 16, 228, -198, -12, 114, -152, 129, 98, -31, 195, 158, 52, -2, 98, 99, -40, 105, -15, 51, 94, -14, 138, 142, -94, 85, 77, 70, 94, 93, 89, -69, 253, -28, 111, 207, -141, 78, 5, -124, 102, -27, 148, 106, 57, 55, -38, 277, -1, 7, 302, -67, 64, -4, -93, 217, -22, 73, 62, 74, 21, 23, 216, -138, 66, 153, -86, 145, 137, -35, 165, 65, 65, -103, 197, 81, -51, 135, -127, -9, 252, -79, 431, 198, -57, 111, 29, 180, -23, 88, 87, -191, 151, -71, -26, 235, -45, 105, 231, 1, 139, 9, 80, 56, 91, 88, -55, 354, -122, 58, 170, -21, 128, 87, 4, 152, -36, 135, -149, 220, 173, -6, 273, -76, 42, 100, -132, 276, 124, -60, 192, -74, 20, 135, 203, 77, 160, 187, 53, 35, 275, -72, 81, 60, -105, 166, 16, 143, 75, 32, 68, -22, 251, -99, 130, 412, -212, 102, 157, -56, 114, 8, 179, 192, 33, 136, -82, 378, -11, 153, 293, -106, 122, 125, -232, 243, 28, 84, 136, 174, 78, -86, 366, -48, 79, 154, 32, 177, 57, -79, 231, -27, 42, -26, 292, 79, -10, 198, -87, -94, 260, -23, 240, 375, 17, 119, -71, 55, 239, 70, 187, 17, 158, -161, -108, 521, -116, 270, 494, -118, 88, 36, 107, 24, 185, 120, -45, 243, -139, 83, 207, -237, 192, 167, -12, 401, 35, 89, 164, 187, 144, -69, 340, 126, -50, 246, -99, 353, 92, -85, 313, 7, 84, 101, 154, 50, -45, 190, -168, 104, 300, 18, 228, 90, 22, 44, -34, 246, 37, 177, 97, 53, 353, 46, 177, 467, -125, 71, 165, -319, 215, -50, 194, -33, 77, 11, -11, 254, -58, 95, 309, -271, 100, 77, -107, 318, 31, 88, 265, 277, 74, -2, 362, -81, -63, 92, -101, 347, 91, 58, 129, 188, 33, 27, 159, 118, -221, 185, -141, -7, 342, -67, 278, 306, -101, -27, -67, 200, 13, 12, 183, -141, 270, -23, -61, 203, -13, -100, 404, -133, 46, -48, 55, 97, 275, -4, 21, 57, -48, -122, 178, -71, 241, 141, -207, 92, -79, 163, -3, 166, 64, -16, 507, -168, 5, -125, -228, 142, 206, -64, 209, 198, 198, 174, 59, 60, 12, 51, 152, -12, 217, -114, 71, 369, -83, 9, 152, 129, -137, -128, 140, -129, 282, -89, 27, 220, -98, 151, 4, -234, 41, 31, 154, 251, 186, 45, -195, 353, 9, -148, 282, -158, 65, 133, -270, -139, -52, 64, 180, -190, 49, 2, 345, -181, -119, 176, -98, -111, 210, -84, 225, -99, 149, 55, 361, 61, 40, -59, -210, -35, 256, -105, 246, 307, -249, -132, 15, 63, -5, -122, 250, -51, 172, -8, -238, 206, -94, 101, 276, -191, 414, 14, 148, -5, 139, -130, -138, 394, -54, -679, 334, -142, 145, 1, -59, -208, 94, 17, 168, -167, 112, -85, 473, 25, -76, 69, -77, 22, 268, -432, 520, -70, 102, -66, -36, 57, -94, 0, 298, -383, 113, -93, 223, 123, -81, -280, -89, 165, 70, -346, 13, 69, 181, -42, 102, 336, -253, -111, 157, -573, -51, 28, 206, 89, 142, -166, -111, -236, -150, -468, 550, -207, 229, 333, -573, -245, 141, 154, 72, 233, 6, -78, 304, -69, -120, -187, -5, 136, 290, -271, -22, 124, 75, 171, 246, -101, -102, 328, -95, -512, 197, 27, 142, 357, -193, -360, -148, 176, 296, -286, 357, -106, 188, -178, -161, 61, -57, -143, 338, -474, 33, -55, 178, 30, -68, -93, 38, 339, -79, -214, 270, -277, 97, 223, -200, 323, 1, -25, -17, -337, 179, -7, 536, 15, -171, 1, -302, 188, 168, -415, 179, 67, 125, -52, -104, 66, -64, -45, 119, -697, 26, 4, 205, 173, -150, -444, 93, 54, 157, -363, 137, -217, 245, -63, -93, -170, 22, -50, 251, -584, 160, -73, 332, -64, 178, -47, -62, 423, -276, -420, 755, -74, 154, 52, -328, 28, -21, 276, 553, 145, -61, -23, 70, 20, -234, -70, -216, 22, 176, -652, 109, 138, 176, 85, 196, -36, -66, 222, -309, -539, 318, -153, 241, 138, -69, -239, 86, 50, -49, -404, 92, -145, 190, -12, -234, 225, -137, -75, 640, -737, -16, 35, 245, 8, 10, -49, -165, 239, -33, -758, 399, -65, 238, 104, 31, -76, -65, -52, 70, -45, -44, 103, 679, -71, -50, -205, -197, -30, 152, -533, 580, -81, 174, -96, -145, -4, 51, 14, -42, -902, 142, -135, 74, 321, -191, -467, 127, 305, -57, -155, 202, 9, 285, 80, 323, 89, -252, 388, 197, -411, -145, 79, 13, 211, 109, -273, -431, 72, -130, -494, 612, -198, 122, -42, -483, -228, 57, 119, 326, -630, -98, -111, 506, -113, -15, -215, -29, 115, 150, -422, 44, -180, 176, -53, 26, -321, 23, -353, -266, -365, 136, -88, 402, 522, -332, -369, -87, 238, 37, -387, 339, 191, 202, 203, -184, 142, -151, -128, 194, -327, -17, 71, 92, 318, 29, -123, 26, 153, -138, -622, 220, -235, 219, 187, -117, -485, 45, -40, 227, -326, 75, -105, 904, -270, -258, 139, -231, -2, 307, -486, 180, -1, 176, -14, 181, -161, -139, 62, -276, -742, -42, -9, 243, -95, -102, -862, -80, 121, 33, -438, 59, -56, 355, 23, -121, 376, -91, -463, 249, -837, 142, -88, 271, 55, 110, -463, 55, 548, -111, -507, 402, -354, 200, 173, -387, -282, 122, -89, 210, 4, -163, -58, 244, -125, -28, -672, -170, 176, 314, -694, 358, 21, 120, -69, 493, 80, -128, 93, -166, -477, 150, -87, 597, -107, -191, -447, -4, 217, -51, -112, 371, -152, 400, -92, -354, 27, 36, -14, 872, -359, -44, -135, 265, 143, 104, -278, 149, 321, -228, -1145, 83, -220, 155, 338, -236, -87, -173, 250, -220, -297, 18, 6, 308, -510, 99, 3, -273, -54, 294, -715, 54, 76, 79, 168, 137, -300, -42, -232, 165, -431, 355, -100, 160, 291, -215, -339, 132, -181, 174, -657, 12, -276, 310, -250, -84, -10, -124, -29, 119, -743, 251, 60, 225, 375, -116, -273, -192, 555, -30, -1070, 741, 74, 32, 236, -322, -751, -20, 92, 621, -766, 15, -135, 461, -141, -119, -134, -203, 218, -81, -678, -7, -77, 243, -72, 603, -154, -160, -28, -419, -811, -48, -187, 61, 457, -155, -725, -53, -165, 352, -403, 240, -35, 411, -60, -593, 255, -275, 256, 467, -832, -174, 72, 348, -319, 125, -90, -81, 47, -194, -806, 391, -60, 149, 270, -255, -659, 105, -100, -21, -21, 69, -166, 473, -6, -208, -413, -16, -369, 213, -785, 652, -143, 177, 123, -41, -50, -75, -124, -329, -445, 164, -32, 86, 337, -200, -338, -68, 149, 137, -179, 49, 22, 340, -184, -77, -135, -251, -351, 425, -941, 8, 99, 304, -114, -173, -440, -130, 880, 135, -1062, 364, -412, 501, 238, -516, -127, 212, -303, 29, 131, 73, -102, 569, -237, 24, -245, -157, 6, 277, -910, 94, 56, 84, 65, 171, -322, -114, 64, -446, -1559, 247, -8, 530, 737, -274, -1054, -179, 73, 79, -773, 379, -192, 512, -155, -7, 5, -33, -104, 814, -958, -188, -136, 156, 90, 133, -311, 82, 67, -36, -854, 864, -378, -1, 56, -502, -534, 11, -73, 37, -72, 79, -153, 581, -154, -202, 242, -293, 338, 118, -690, 100, 106, -68, 211, -19, -490, -122, -73, 281, -736, 133, -125, 84, 482, -325, -446, 232, 117, -6, -888, 323, -243, 476, -11, -50, 462, -28, -543, 223, -626, -11, -84, 291, -138, 368, -233, -136, -43, -85, -1118, 276, -174, 242, 66, -488, -224, -78, 94, 623, -189, 232, 86, 370, -396, -315, -174, -366, -16, 287, -668, 408, 48, 159, 369, 515, -860, -79, -54, -69, -927, 306, -154, 510, 477, -463, -1011, -32, 79, 75, -409, 258, -177, 163, -82, -567, -5, -57, -200, 384, -1066, -63, 79, -37, 348, 161, -280, -231, 851, -257, -938, 223, 27, 22, 524, -123, -186, -42, -19, 186, -781, -15, 26, 400, -98, -56, -376, -292, -566, 276, -733, 357, -79, 181, -65, -353, -127, 10, -202, 127, -921, 164, -198, 449, 768, -300, -735, 87, -122, -14, -749, 101, 94, 472, -177, 11, 27, -260, 110, 511, -537, -272, 23, 338, 237, -15, -222, -240, 190, -188, -1694, 491, -375, 167, 391, -474, -667, -17, -57, 737, -899, 41, -119, 776, -639, 107, -256, 71, -243, 344, -1059, -295, -55, -3, 153, 824, 77, -239, -252, -2, -735, 83, -70, 14, 315, -361, -642, -187, 256, 242, -969, 329, -17, 382, -301, -372, -208, -158, -223, 515, -864, -44, 161, 75, 390, 219, -620, 108, -187, 114, -1469, 199, -521, 460, 243, -127, -643, 116, -294, -142, -749, 124, -270, 754, -105, -530, -641, -494, 150, 121, -853, 859, 118, 20, 124, -86, -402, -88, 381, 97, -944, 0, -36, 85, 581, -365, -991, -107, -64, -121, -120, 10, -24, 74, -91, 70, 91, -185, -725, 313, -1088, -90, -120, 155, 53, 77, -417, 45, -309, 40, -1305, 653, -243, 250, 387, -765, -139, 139, 222, 415, -711, -159, -83, 329, 154, -333, -156, -207, 261, 354, -1151, -150, 237, 171, 24, 413, -551, -192, 157, -278, -1250, 141, -167, 124, 377, -238, -481, 12, -92, 17, -612, 371, -401, 350, -197, -295, -474, -35, -359, 806, -1084, -125, -89, 268, -44, -42, -723, -164, 558, -208, -1207, 105, -187, -184, 353, -23, -961, -144, 280, -116, 248, 237, 69, 550, -241, -482, -765, -340, -251, 328, -452, -390, -126, -253, -76, -247, -146, 50, 69, 35, -1476, -54, -246, 163, 372, -360, -880, 99, -28, -261, -812, -34, -353, -19, -193, 90, 270, -92, -1015, 78, -954, -444, 85, 292, 139, -4, -693, -313, 262, -58, -894, 671, -7, -260, -312, -693, -1164, -84, 41, 147, -685, -81, -101, 437, -367, -364, -348, -154, -138, -85, -527, -207, -50, 4, -64, 481, -472, 45, -4, -281, -780, 106, -190, -102, 581, -461, -841, 168, -103, -269, -1064, 44, -104, 122, 277, -541, -648, -300, 37, 559, -907, -293, -18, -102, -212, 277, -481, -228, -30, -316, -1200, 374, -90, -469, 357, -24, -1349, -22, -207, 50, -455, -6, -44, 225, -325, -859, -383, 34, -415, 533, -882, 32, -246, -15, -58, 412, -71, -37, -797, -424, -860, -2, -177, 85, 656, -385, -1199, -97, -233, -292, -974, 182, -53, 41, -162, 107, -1007, -353, -647, -104, -1396, -3, -46, 264, 98, 111, -382, -177, -53, -426, -1062, 315, -467, -247, 85, -558, -744, 125, -169, 194, -155, -317, -71, 313, 34, -346, -594, -165, -349, -71, -592, -188, 319, -342, -210, -251, 16, -215, 334, -575, -1394, -79, 50, 0, -75, -258, -1319, -194, -400, -606, -1035, 365, 33, 204, -608, -738, -709, -77, -427, 671, -513, -225, -11, 279, -126, 106, -208, 11, -216, -257, -1603, 287, -254, -392, 361, 254, -808, 58, -339, -380, -62, -313, -95, 839, -561, -393, -837, -309, 114, -375, -1082, 360, 271, 74, 207, 168, -554, -100, -169, 44, -1681, 367, -77, -81, 22, -405, -1292, 107, -85, -281, -891, 197, -318, 107, -243, 31, -376, -31, -673, -283, -871, -475, -88, 326, -113, -132, -1152, -265, -6, -163, -1069, 327, -277, -529, 497, -680, -857, -74, 29, -258, -605, -317, 2, 285, -745, -548, -160, -362, -741, 92, -1126, -173, 81, -218, -226, 511, -136, 63, -712, -528, -716, -84, -92, 424, 293, -232, -1457, 101, -545, -781, -558, 237, -347, -122, -439, -510, -595, -91, -651, 1093, -974, -1060, -58, 127, -442, 286, -243, -129, 269, -119, -978, 294, -188, -878, -135, -414, -832, -33, -469, 300, -826, 56, -27, 208, -739, -526, -730, -159, -685, -216, -1197, 378, -118, 306, -70, 50, -377, 221, 414, -325, -1180, -141, -185, -86, -2, -405, 232, 141, -254, -364, -434, 272, 7, 52, -38, 516, -159, -342, -25, 219, -700, -116, 67, 152, -453, -264, -161, -278, 235, -435, -1028, 489, -306, -75, 314, -538, -1475, 101, -447, 176, -92, -37, 27, 438, 260, -156, -855, 67, -80, 132, -296, -541, -200, 136, 59, 153, 142, -13, -275, -618, -1559, 244, -12, -110, 668, -357, -856, -183, 349, -562, 3, 643, 141, -151, 23, -187, -349, -270, -574, 1000, -596, -93, 23, -97, 206, 129, -434, 61, 20, -504, -1338, 244, -203, -649, -250, -130, -377, 13, 93, 116, -630, -171, 100, 564, -345, -85, -118, -404, -168, 270, -685, 81, 133, 287, 184, 45, -130, -46, 497, 62, -964, -343, 48, 224, 133, -51, -1235, -55, 251, -409, -184, 389, -97, 38, -44, 197, -979, -275, 351, -217, -555, -121, 4, 199, 184, 363, 91, -21, 553, -292, -303, 425, -57, -341, 493, -717, -123, 48, 133, -26, 460, -57, 122, 43, 188, -339, -567, -178, 1546, 232, -252, -168, 71, 103, 157, 304, -180, -241, -93, -1015, -385, 351, -141, 486, 601, -122, -903, 207, 286, -641, -412, 313, -92, 255, 308, -77, 594, 79, -312, 319, -813, -421, -163, 315, -608, -106, 384, 3, 250, -488, -1053, 210, -166, -238, 295, 279, 133, -64, 352, -77, -963, -131, 16, 875, -73, 207, -936, -507, -415, -221, -560, 608, 168, 226, 164, -319, 256, -5, -103, -24, 80, -50, 125, 155, -53, -129, -2122, 228, 121, -802, 35, 294, -142, 28, 158, -163, 460, -206, 190, 575, 122, -424, 64, 265, 212, 200, -499, -209, 913, -498, -1551, 1102, -198, -304, 354, -226, -584, -198, 808, 402, -529, 107, -174, 96, -560, 88, -391, -59, 771, -138, -710, -111, -60, -123, 1375, 217, 161, -12, -810, -86, -12, 132, -51, 740, 222, -113, 476, -152, 14, -368, 784, 4, 12, 34, 404, -315, -627, -217, 107, 403, 249, -399, 114, 41, -193, 100, -161, -71, 361, -350, -1427, 55, -369, -313, 377, 165, -439, 83, 112, -908, -73, 145, -9, 1370, 442, -192, -344, -152, -403, -212, 139, 431, -129, -264, 168, 435, 17, 137, 68, -97, -545, -183, 128, 47, 5, -165, -749, -140, 1440, -377, -840, 269, 129, 309, 170, 321, -368, -282, -98, 347, -523, -348, 89, 48, 977, 320, -433, -27, 836, -532, -424, 736, -220, -179, 522, -356, -1460, 98, -115, 332, -248, 165, -151, -43, -112, -366, 53, -4, -16, -755, -866, 155, 234, -161, 422, 187, -302, -41, 236, -613, -1124, 422, -31, 548, 978, 69, -337, -154, -330, -92, -205, 637, -251, 78, 487, -32, -1082, -186, 296, 879, -384, -569, -45, 158, -333, 15, 179, 195, 981, -127, -1195, -66, -353, -229, 709, 359, -232, -9, 459, -502, 288, 363, 148, 666, -549, -126, -22, -282, -221, 209, -87, 507, 158, 45, 163, -24, 302, -65, -298, -397, -833, 281, -133, 419, 593, 334, -1026, 270, 134, -13, -524, 163, 139, 59, 682, 136, -282, 52, -285, 313, -513, -413, -64, 22, 480, -160, -2, -180, 124, -183, 82, 408, 190, -544, 467, -695, 181, -49, 405, 139, 585, 20, -2, 562, 140, -139, -401, -345, -762, -508, 139, 263, 181, -339, 198, 775, 498, 119, 505, 212, -548, 262, -176, 334, 1055, -266, -572, 98, 503, -932, -1170, 459, 111, -39, 184, -197, 57, -210, 969, 425, -373, -655, 84, 259, -162, 706, 434, -225, 1026, -601, -361, 37, 99, -597, 966, 186, -365, -149, 457, 181, 264, 139, -55, 388, 210, -294, -499, -361, -131, -285, -311, 430, -61, -47, -100, 77, 148, -40, -555, 167, 891, -249, 59, 476, 178, -287, -134, 210, 879, 96, -260, 375, 35, -22, -4, 375, -269, -256, 1048, -248, -709, -77, 105, 448, 446, 358, -62, -246, 412, -242, -548, 1034, -307, -1112, 626, 232, -600, 249, 487, 144, -864, 442, 132, 205, -69, 150, -706, -15, -42, 47, 281, 127, -63, -42, 582, 332, 974, 5, 738, -269, -1209, -157, 122, 748, 163, -13, -607, -250, 488, -1189, 270, 583, 51, 238, 1339, -620, -414, -172, 241, 795, -213, 161, 8, 229, 1586, 156, 81, 238, 548, -716, -174, 840, -206, 33, 457, 80, -452, 94, -59, -601, 876, -91, -101, 342, -77, -577, 80, -276, 699, -480, -182, 363, 191, -64, 783, 23, -302, -414, 973, 652, -513, -350, -14, 179, -405, -427, 385, -148, 1290, -362, -767, 434, 5, -1026, 433, 1276, 826, -139, -489, 245, 599, -84, 130, 781, 636, 234, 382, 138, -44, -284, -694, 543, -394, 145, 737, -746, 238, 54, 538, 110, -812, 130, 679, 197, 300, -152, -839, -334, 1347, 274, -473, 271, 142, 319, 467, 1325, 496, -145, 626, -545, -472, 91, -1, 84, 781, 276, -744, 59, 864, -611, -204, 758, 208, -98, 226, -240, -157, -94, 548, 687, 1000, -903, -17, 318, -71, 529, 35, -168, -279, -101, 1351, 2, 167, -841, 1013, -197, -112, -112, 890, -6, 0, 321, 85, 484, 720, -195, -343, -473, 282, -171, -398, 564, -25, 334, 203, 48, 709, 76, 456, -60, -33, -93, -69, 165, 222, -76, 145, 77, 758, -659, 68, 232, -22, -227, 1465, 218, 304, -268, -162, -240, -35, 232, 432, 445, -469, -30, 389, -520, 421, -195, -735, 997, 70, -181, 199, -186, -1011, -102, 232, -137, 490, 177, 66, 829, 355, -26, -246, 36, 856, -118, 246, -213, -57, -184, 1019, 880, 765, 94, -55, -1036, -613, 135, 0, 352, 737, 215, -64, -298, 1364, -987, -1025, 549, 383, -752, 774, 310, 1013, -113, 723, 124, -661, -201, 93, -123, 89, 337, 65, -223, 1351, -183, 223, 715, -123, -651, 254, -424, -189, 81, 964, -8, 570, -62, 280, 1548, 536, -313, -1406, 89, 203, -463, 444, 1008, -165, -238, 397, 203, 630, -70, 125, -54, 372, 309, 346, -10, 1199, -97, -467, -13, 368, -1458, -458, 423, -69], "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": "8045.2.a.d", "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}