# Stored data for newform 207.6.a.a, downloaded from the LMFDB on 25 April 2024.
{"label": "207.6.a.a", "space_label": "207.6.a", "level": 207, "weight": 6, "hecke_orbit": 1, "hecke_orbit_code": 100663503, "dim": 2, "is_polredabs": true, "nf_label": "2.2.29.1", "trace_hash": 261781477499665550, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [-116, 0, 1]]], "qexp_display": "q-2\\beta q^{2}+84q^{4}+(-47-\\beta )q^{5}+(-59+\\cdots)q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 7452, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 33.19945070128699, "hecke_ring_index": 2, "level_radical": 69, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [207, 1, [47, 28], [1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [3, 23], "conrey_indexes": [1], "field_disc": 29, "field_disc_factorization": [[29, 1]], "field_poly": [-7, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.874", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.061", "prec": 17}, {"__RealLiteral__": 0, "data": "0.395", "prec": 17}, {"__RealLiteral__": 0, "data": "62.895", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [23, 1]], "trace_display": [0, 0, -94, -118], "traces": [0, 2, 0, 0, 168, -94, 0, -118, 0, 0, 116, -320, 0, -288, 1276, 0, 6688, 1810, 0, 730, -7896, 0, 12528, -1058, 0, -1774, 8584, 0, -9912, -8208, 0, 1772, 0, 0, 1508, 6184, 0, -23112, 36076, 0, 6032, -5516, 0, 10322, -26880, 0, 0, -42952, 0, -19634, -10904, 0, -24192, 25350, 0, 21304, 66352, 0, 30856, -18344, 0, 37224, 175624, 0, 175744, 17828, 0, -7482, 152040, 0, -66816, -126848, 0, 137660, -23896, 0, 61320, 87784, 0, 62286, -314336, 0, -159152, -83120, 0, -84316, 309372, 0, 651456, -69770, 0, 64204, -88872, 0, -133632, -16272, 0, -170104, -150568, 0, -149016, -183940, 0, 20070, 446368, 0, -506804, 204392, 0, -163668, -607376, 0, -394592, 224750, 0, 49726, -689472, 0, -58928, -98496, 0, 405610, 457736, 0, 148848, 371676, 0, 62940, 0, 0, -420152, 76352, 0, 155348, -534412, 0, 78416, -168074, 0, 617760, 519456, 0, 242208, 509616, 0, 401204, -256592, 0, -1941408, -516998, 0, -270848, 1875952, 0, -943312, 4528, 0, -119128, -171564, 0, 194880, 62422, 0, 276468, -463344, 0, 1290384, 334312, 0, -383506, 34104, 0, 867048, -393840, 0, 44694, -1070080, 0, -268772, -335976, 0, -705948, -690200, 0, 0, 1074316, 0, -208168, -3607968, 0, -1653232, -610572, 0, -21256, -1191784, 0, -1649256, 254872, 0, 1055454, -567008, 0, 105328, 653980, 0, 179676, 171332, 0, -963072, 1831304, 0, -2061756, 2129400, 0, 544736, -330448, 0, 861384, -1175776, 0, 1789536, -204844, 0, 780560, 2143680, 0, -180148, 373788, 0, -323508, -61364, 0, 1604512, -1361636, 0, 1951928, -1540896, 0, 1065808, 768584, 0, -866832, -4008960, 0, 3126816, 847514, 0, 1229692, 9132448, 0, 47096, 26868, 0, 169280, 3711304, 0, 2290176, -347812, 0, 1232180, 1497552, 0, -2129296, 232652, 0, -1444852, -1662744, 0, -628488, -139976, 0, -132092, 6052640, 0, -224228, -304976, 0, 339500, 2038352, 0, -3474432, 3454614, 0, -98834, -10655232, 0, -3177472, -549892, 0, -1191862, -1926296, 0, 11563440, -1776146, 0, 832704, -1242592, 0, -2714748, 152352, 0, 1092548, -6614784, 0, 2441120, -1520660, 0, -1666948, 7373856, 0, -8151552, -2328992, 0, -319892, 6468392, 0, 5232024, -1483184, 0, 2979504, -8259968, 0, -675004, 895144, 0, -147992, -6815928, 0, -8275904, 1799192, 0, 1061108, -6982080, 0, -4150480, 84448, 0, 2036704, -2472192, 0, -7082544, 9200176, 0, 2313508, 16087344, 0, -10876856, 444704, 0, 1430776, -488476, 0, 21047040, 2873336, 0, 6082960, -5860680, 0, 9928208, -2818660, 0, 924070, 6764656, 0, 5393136, -6598316, 0, 416942, -3537952, 0, -217384, -4283072, 0, 39320, 11096560, 0, -6948864, 2323624, 0, -823102, -1366848, 0, 5773784, -5303148, 0, -4597504, -685560, 0, -14288736, 1669622, 0, -957490, -7829536, 0, -4626312, -3013224, 0, 1304924, 12064116, 0, -5932256, -192870, 0, 6242920, -15450960, 0, -7057208, 2407536, 0, -2046472, 7160216, 0, 1685880, 758192, 0, 4551832, 14421120, 0, -1199440, 3243584, 0, -807332, 67048, 0, -26353808, -1676346, 0, 321332, 17168928, 0, -13941808, 486560, 0, 5185604, -9231280, 0, -13748112, -386170, 0, -3255920, -31583552, 0, 7551368, -5396624, 0, 3144804, -12922400, 0, -10368896, 6010404, 0, -7711648, 18879000, 0, 3451000, -3362688, 0, -3099640, -6728000, 0, 4176984, -10500688, 0, -652232, -27447552, 0, 13212864, 2285068, 0, -2497828, 3789488, 0, -3064256, 15054568, 0, -2343082, -8273664, 0, 5329040, -8945728, 0, 2443976, -3201368, 0, 34071240, 7398996, 0, -10681584, 23802272, 0, 5937924, -11019584, 0, -7227676, -2061784, 0, 5925568, 8816176, 0, -6782764, 31220784, 0, 27462536, 5971880, 0, 8697844, -6627312, 0, 5286960, 7339272, 0, -9533196, 0, 0, 8159904, -857624, 0, -343808, -13335592, 0, -21847904, -4060090, 0, 4569102, 6413568, 0, -11528312, 2745216, 0, 559682, 25290088, 0, 13049232, -5094320, 0, -9334056, -27789424, 0, 33530264, -4989232, 0, -10841368, -12764872, 0, 2533440, 7104508, 0, 18025380, -14118216, 0, -9367696, 1802188, 0, -4618476, 1438400, 0, 51891840, -5028130, 0, 9960396, 20679296, 0, -1395364, -22554228, 0, -10653324, 21890244, 0, 12594816, 9014450, 0, -10636706, 42807744, 0, 5870760, 938446, 0, 2671080, 2729480, 0, 33701136, 12001192, 0, -31423416, -13342784, 0, 20905404, -11897632, 0, 27956312, 1705664, 0, -77286528, 4163692, 0, 5162216, -43427832, 0, -4540936, 4666488, 0, -5102296, -11667512, 0, -22751232, -21068150, 0, -18151752, 60607680, 0, -19354600, 1240704, 0, 1795968, 28101464, 0, -49052224, 10083150, 0, -10085834, 380352, 0, 4100368, 2638184, 0, -11901474, 7837424, 0, -10006752, -21071684, 0, -9442018, -8921328, 0, 40013736, -1102528, 0, -2743720, -56351872, 0, 3956992, 15288050, 0, -14634270, 5243448, 0, 33199200, 19839432, 0, -247072, -6043832, 0, 23223312, -2804708, 0, -4653192, -18445504, 0, -19519088, 6843020, 0, 15745672, 33591048, 0, 67099968, -8132728, 0, 4342032, 28082208, 0, 24683408, 18761904, 0, 6170096, -2512792, 0, -32214504, -408326, 0, 3481324, 1773408, 0, -17000032, -14208584, 0, 7787364, -25088712, 0, 34516768, -22402148, 0, 823068, -33082560, 0, 28212128, -28015544, 0, -6026468, 12238232, 0, 3754296, 37669922, 0, -12151708, -28119040, 0, 65119848, 11431764, 0, 17927484, -18740960, 0, -13976144, -937388, 0, -25540688, -28221984, 0, -70345880, -9143432, 0, -241804, 26335480, 0, -59299632, 5830264, 0, -15557894, -35890400, 0, 20044104, 11352328, 0, 22248884, 47902548, 0, 0, -27661128, 0, 12768192, 90242544, 0, 46074736, 29861236, 0, 22941532, 29185832, 0, -17486112, -9063080, 0, 4688610, -143631488, 0, -39672000, 9422464, 0, 11839076, 52376668, 0, -85968064, -36294616, 0, 3189644, -51288048, 0, 13855736, 461200, 0, 31719676, 49427136, 0, -1785504, -18333302, 0, -9826092, -61972768, 0, -88001428, -26761476, 0, 33374912, -797732, 0, -65656096, 8833212, 0, 4975714, 21409248, 0, 11676096, -14251064, 0, 11575976, 103063680, 0, 88658136, -35513706, 0, -39740168, -18318720, 0, -68405548, -35881568, 0, -3271336, -17684432, 0, 5477056, -10642296, 0, 1959820, 54934320, 0, -140950208, -16401960, 0, 51874876, -11626680, 0, 15092784, -33607644, 0, -62359116, 8909264, 0, -8226720, 40382524, 0, -45904488, -65469008, 0, -25307136, -18747462, 0, -17787904, 153829536, 0, 67622896, 33798628, 0, -3232818, -89743168, 0, -173187504, 16788686, 0, -45980270, 84770400, 0, -11205716, 12226248, 0, -21909748, -3257512, 0, 28326272, 6250340, 0, 49232800, -27757632, 0, 65604960, 54552680, 0, 13072052, -10226560, 0, 72356256, -19230216, 0, -18695836, -61140352, 0, -19084204, -21669856, 0, 10098372, 51404704, 0, 71240576, 1840118, 0, 56292492, -17206896, 0, 44113872, -5002976, 0, 16698712, 8585624, 0, 65567040, -36457256, 0, 20754976, 43526912, 0, 98567984, 16085704, 0, 19647524, -9087904, 0, -9367696, 36561884, 0, -26823466, 31398192, 0, 36163232, -10474520, 0, 82979936, -139918504, 0, -27174672, -16215896, 0, -46313322, -3190928, 0, -8302584, 27227808, 0, 21623456, 36999824, 0, 51838080, 70223092, 0, -30579734, -114377424, 0, -111864136, 15332176, 0, -48169412, 26756792, 0, 163961952, 48089970, 0, 2917964, -61342336, 0, 15157488, 41048648, 0, -29316944, -35979372, 0, 55422016, 43033786, 0, 31583776, 64561056, 0, -44856736, 8683112, 0, 77259058, -95755680, 0, -72813888, 656252, 0, -29928300, -208465920, 0, 46147816, 23363668, 0, -25236904, 72194688, 0, 124477056, 2254830, 0, -3350488, 71191176, 0, -53469504, 5033048, 0, -14292140, 21735848, 0, 103294128, -5460338, 0, -5657916, 295048320, 0, -95219296, -43574280, 0, 48596056, -143018488, 0, 2448992, -47543440, 0, -16984352, 2256912, 0, 39636272, -69555272, 0, 53330168, -15618936, 0, 14219520, 32210948, 0, -34265664, 192987808, 0, -82025224, -113618924, 0, -10769116, 102966008, 0, -60872704, 12372836, 0, -15317052, -29216208, 0, -6888544, -24038348, 0, 3463688, -247670208, 0, 103503120, 36663004, 0, -23720588, 59616832, 0, -55968260, 15571768, 0, -86671008, -82580284, 0, -110723392, 13450850, 0, -35823528, 19542768, 0, 160275808, 96936056, 0, -20401280, 0, 0, -121367568, 34612292, 0, 51189678, -86462688, 0, -756784, -37139696, 0, 66338472, -13747856, 0, -25019808, 91673480, 0, -23696098, -11757984, 0, -98896496, 59713488, 0, 22721608, -23831272, 0, -11095728, -45100688, 0, 14734972, 159048320, 0, 45768728, 34994068, 0, -29899492, 36019624, 0, -11659856, 6769872, 0, 42604708, -25617984, 0, -136793464, 6696168, 0, 13403352, 49860744, 0, 28518000, 18630894, 0, 35118112, 105994304, 0, 120457532, -43147520, 0, 31588604, -247544, 0, -112250880, -15858864, 0, 33812618, 290187576, 0, 5181720, 10386386, 0, 96099388, 21502456, 0, -8302056, 6040728, 0, -15842536, -424179712, 0, 102444356, -10244888, 0, -53799216, -169587708, 0, -165228544, 11840876, 0, -38566504, -46190928, 0, 5768216, 61678736, 0, 30388372, -56715416, 0, -100116408, 102316, 0, 84764708, -100167392, 0, -129163216, -70030360, 0, 70603324, 239881040, 0, 460335040, -42552048, 0, 27427018, -149196264, 0, 30949264, 44379128, 0, -3286976, 96066096, 0, 69947136, -23011252, 0, 9029798, -40145280, 0, -244588320, -19205344, 0, 1470448, -55805744, 0, -141166896, 25884802, 0, -33458928, 12797568, 0, 85925840, -37305024, 0, 101411236, 123621896, 0, 91774032, 39140420, 0, -113223088, -343968768, 0, 211946500, -36586148, 0, -55999652, 72630384, 0, 64146560, 24136154, 0, -13410150, -127735440, 0, -165106976, -74403640, 0, 24492054, 234481240, 0, -140023632, -40307498, 0, 36411476, 293549696, 0, -139106388, -58826416, 0, -73413748, 14333076, 0, -423880704, 122914452, 0, -45687992, -195635328, 0, -28655712, -1215012, 0, 60438544, 53418696, 0, -26870928, 74427728, 0, 12468472, 336356384, 0, -39052328, 45945272, 0, -19601032, -247211660, 0, 208284384, -11269816, 0, 78856540, -124587456, 0, -170780768, -125365240, 0, -85831996, -62587336, 0, 250278336, -70767520, 0, -91462806, -107638272, 0, 172321828, -109793000, 0, 20427116, -181799492, 0, -35100208, 38539668, 0, -9253652, 75192096, 0, -199454112, -64580256, 0, -26764348, -105478336, 0, -12431328, -10500436, 0, 9922354, -354428256, 0, -237564752, 143658640, 0, 73312992, 104505328, 0, -267375360, 30384496, 0, -16698800, 151132128, 0, -73405960, 2484784, 0, 58340716, -28668472, 0, 89133072, 1334338, 0, -72962536, -277953280, 0, 87159152, -229845120, 0, 243339896, -16322824, 0, -215824960, 67779560, 0, 3449204, 7093632, 0, 159933376, 55253664, 0, 23344004, 265844856, 0, 171083136, -8636176, 0, -2516476, -128553984, 0, -109867196, -174112, 0, 9703976, -38211096, 0, -281952704, -5952824, 0, 158501952, 772814784, 0, -174882528, 115288032, 0, 130855646, 790424, 0, 194334672, -42415060, 0, -56924976, 519744960, 0, 181781976, -40482164, 0, 124816848, 216688696, 0, -565596512, -15237300, 0, 10345844, 37355136, 0, -59972464, -9277216, 0, 4080852, -148191624, 0, 120185184, 190340016, 0, -127583582, -25400752, 0, 87292436, -19691496, 0, -163064540, -425616296, 0, 427355136, -29963744, 0, -66836104, 241360224, 0, -123568072, 15590320, 0, -19935520, 205690272, 0, 510968640, 60552392, 0, 81058222, -233310880, 0, -92905096, -42229768, 0, 40180600, 178898912, 0, 516266816, 44601630, 0, 28780304, -236767440, 0, -172243296, -50604880, 0, -127198304, 2696072, 0, 77621880, 57382254, 0, -55631630, 351762112, 0, 17380744, -156451440, 0, 13705976, 245982524, 0, 214698176, -139214896, 0, 5088270, -554258544, 0, 287764448, -114643856, 0, 93931564, -334134288, 0, 35023128, -39029476, 0, -199737510, -92968576, 0, 38638672, 19040744, 0, 122012368, 284370288, 0, -11303968, 51872528, 0, -99779082, -359778048, 0, 313474456, -158966440, 0, 23478848, 97607272, 0, 3302880, 185665934, 0, -9431012, 577021120, 0, 98262672, -144818048, 0, -3943812, 223385260, 0, -224501760, -57183512, 0, 14783528, 195184416, 0, 295185664, 79603584, 0, -64888868, 225713264, 0, -69140568, 80135552, 0, -131375700, -54413568, 0, 207623528, -109720972, 0, -54531280, -35049400, 0, 300236768, 11229408, 0, -54164452, -445464432, 0, -70246816, 92397288, 0, -171441332, 24862512, 0, -386190336, 3957978, 0, -41837564, -35649120, 0, 119065764, 53618320, 0, -239071432, -165439432, 0, -568827776, 83207580, 0, 111512808, 140248248, 0, -157588088, 84064104, 0, -117126240, -833329152, 0, -80429160, 18953636, 0, 243148116, -252954240, 0, -310923848, -245052448, 0, -206739360, -167782980, 0, -240568224, 170315912, 0, 156760766, -253110816, 0, 154019232, 339411144, 0, 89716516, 93851424, 0, 109613616, -3072992, 0, -151146348, 627334032, 0, 76713932, -168212624, 0, -57079572, -153322768, 0, -155884928, 170498850, 0, -17917028, -16201080, 0, 903356960, 139895932, 0, -86283416, 35345664, 0, 524405280, 92106172, 0, -25472168, -615095360, 0, 456131720, -11772288, 0, -255041348, -322954440, 0, -366974816, -51778792, 0, 245993886, 202233024, 0, 336383760, 153007276, 0, 67102592, 299109016, 0, -171903648, -20875480, 0, -63876712, 372331232, 0, 111492704, -361190528, 0, -94321568, 76595960, 0, 67114080, -161690716, 0, 128254888, 63688128, 0, 164212152, -33076552, 0, -183769976, 228036280, 0, 382353888, -313862656, 0, -25184738, 292817408, 0, -151068076, -119273224, 0, -171168100, 214462656, 0, -62370880, -16036736, 0, 31753898, 272461056, 0, 388828056, -72822140, 0, -107321002, -253266048, 0, -67815888, -96981484, 0, 33535564, 3486496, 0, 93949676, -67260096, 0, 27419152, 495307820, 0, -851430720, 35971788, 0, -26600378, -140813064, 0, 12640984, -89778640, 0, -440908288, 20579328, 0, 26991888, 303848582, 0, 67446352, 683486848, 0, -276529616, -121279232, 0, -165781068, 265442800, 0, -724974016, -63276006, 0, -274201954, 40871040, 0, 126056736, 368353648, 0, -83891640, 488369512, 0, 435590736, -116711600, 0, -6795024, -480026560, 0, 417609744, 510117408, 0, 274826100, 44842584, 0, -547305792, -61127356, 0, 2512386, -32438280, 0, 234350624, 19277008, 0, 110665608, 188513456, 0, -273497280, 149458736, 0, 260374290, -1020391680, 0, 147092988, -240697268, 0, -102486868, 211907640, 0, 392671136, -91888408, 0, -46437736, -453316416, 0, 380700400, 101130400, 0, 167479660, -178811216, 0, 264163536, 15906220, 0, 10758256, -671964800, 0, -823543856, 168993216, 0, 429517116, -486112384, 0, -135120384, -412294992, 0, 97304080, 504873936, 0, -693422480, 65400380, 0, 213156188, -439543720, 0, -647778432, -30263550, 0, -13538416, 751564000, 0, -358883816, 13016520, 0, 242399008, 471630132, 0, 179452000, -32949294, 0, 188515544, -282465792, 0, -525440560, 11385264, 0, -110044596, -727125120, 0, -260369760, -60861280, 0, -477008402, -349856000, 0, 174341040, 4355000, 0, -277615840, 225070276, 0, 166283744, -77132184, 0, -247410372, -882057792, 0, -579309568, -82776348, 0, 171802518, 147202376, 0, -54787488, -155762084, 0, 224341752, -721253376, 0, 214152240, -72137408, 0, -386437392, -409115412, 0, 687068928, 12744876, 0, 352682484, 191945712, 0, -533612064, 132020816, 0, -116939760, -18924240, 0, -209817552, 103977342, 0, 37344592, 197053376, 0, 206125620, 192675036, 0, -129046328, 84191408, 0, -98999040, 183373728, 0, 379486616, 1264583712, 0, -327096336, 64874128, 0, -62413368, 627785968, 0, -196818888, -63069374, 0, -524335824, -329370624, 0, 332203700, -102866384, 0, 43970480, -306781024, 0, 277110080, -369731568, 0, 256175824, -751441152, 0, -94001760, -50759596, 0, 202227788, 311205728, 0, 205293984, -33528744, 0, 210133168, -166471136, 0, 30988472, 478968172, 0, -56324648, -642011048, 0, 1356359840, -25997964, 0, -12119300, 621515664, 0, 625965928, -40370668, 0, -122472948, 273868112, 0, -897253056, -38371022, 0, -117561750, 768996480, 0, -256011188, 44603164, 0, 33967676, -394035760, 0, 308772048, -240743788, 0, -205744896, -925645056, 0, 473033616, -211496728, 0, 589879392, 232219240, 0, -607124784, -384358340, 0, -47184174, -107212768, 0, -163657788, 360221416, 0, 126227548, 15899192, 0, 155709184, -9799588, 0, -123907656, 740558784, 0, -505797120, 478243104, 0, -180463020, -201095048, 0, -569752176, 84218766, 0, 531987418, 1242884544, 0, 512605856, -224429808, 0, -25137884, -67161216, 0, 1428051872, 157440220, 0, -166841630, 501637920, 0, 272279840, -302259456, 0, -63351880, 24631672, 0, 730618896, -399873544, 0, 85331998, -344620224, 0, -731752128, 150329984, 0, -146267908, 369619616, 0, 210471360, 159309528, 0, -183629296, 616498848, 0, 110891592, -252797420, 0, 256484936, 309398448, 0, -800788464, 90370844, 0, 36908330, 0, 0, 171241056, 219772336, 0, 379018456, 292036728, 0, 424315008, 341018810, 0, 552797856, -72040416, 0, -326804712, 52439928, 0, -39748384, -444668136, 0, -28879872, -81608906, 0, -242571988, -693450784, 0, 442317976, 13079392, 0, -411178936, 360078616, 0, -705855360, 210447510, 0, 349238944, -341047560, 0, -169674592, 328665144, 0, -408134032, 162589312, 0, 383804568, -33963916, 0, -118637000, 255321088, 0, -424192860, -348616816, 0, 409475856, 457121664, 0, -599472224, -6926980, 0, -302113502, 230598144, 0, -122733104, 136382232, 0, 478439048, 217471232, 0, 47013288, -599083376, 0, -292000728, 1315084576, 0, 294762496, -33619280, 0, 336672904, -210124140, 0, 519483712, -263972780, 0, 364236954, -427922880, 0, -874846016, -16731360, 0, -234006356, 5203528, 0, -784060704, -217440180, 0, -163279392, -897812160, 0, -258502752, 54020736, 0, 252907984, -330688508, 0, 1743573728, -323119382, 0, 9934160, -419095488, 0, -542566336, 81084176, 0, -147021968, 70691328, 0, -910674912, -248836668, 0, -290600368, -663773344, 0, 483830432, -201708688, 0, 277752244, 771227624, 0, 51440896, 159962552, 0, -297935126, 596778672, 0, -941748088, 218052848, 0, 8607888, -893269600, 0, 1514131920, 482589624, 0, 61979460, -562039456, 0, -518170376, 178730592, 0, 70686144, -457638792, 0, -487120192, 70964128, 0, -305915608, 151383792, 0, 334390416, -182770120, 0, 540719170, -366795248, 0, -387951984, -232272826, 0, 275698264, 74796800, 0, -520254084, 307583404, 0, -661258532, -1169052640, 0, 2065789440, 74518274, 0, 55258136, -422362920, 0, 652625280, 89985016, 0, -485726032, 292687488, 0, 836673264, 226781044, 0, 37126392, 543400448, 0, -352397792, 118825384, 0, -233204996, 1323371500, 0, -72558928, -345730712, 0, 612521542, -1894555152, 0, 79650472, 357903504, 0, -477307352, -189240080, 0, -894879216, 129782104, 0, -72273384, 1138292688, 0, 98305360, 141417744, 0, 86530992, -140517296, 0, 406909440, 86052422, 0, -24509548, 757213800, 0, -489284288, -544991784, 0, 329438072, 578526336, 0, -893483304, 75723828, 0, 195306350, 1704155904, 0, 297452536, -278439756, 0, 462707048, -2050682800, 0, 305279520, -537363294, 0, -475345630, 78829464, 0, 1187622384, 508386952, 0, 489381044, -321814624, 0, 224370720, 104156844, 0, 301046738, 141932960, 0, -260749672, 49154816, 0, 122145392, 838520152, 0, 1341626176, 333501552, 0, 97304260, 1008100128, 0, 936828992, 415724240, 0, -153564452, -699979496, 0, -2639566944, 205010474, 0, -163330264, -431074560, 0, 458169376, -89358144, 0, -321283520, -1188637268, 0, 1087081008, 130776312, 0, -430557588, -999401088, 0, 352705888, -414813976, 0, 351948784, 1193153728, 0, 2348330208, 603891750, 0, -133985892, 88694528, 0, -936289360, 572322088, 0, -699985952, -98817500, 0, -2030897664, -10617030, 0, 155138800, 349750128, 0, -1386055696, 142985168, 0, 484430200, 568058960, 0, 433626144, -740412152, 0, 90968598, -1728841312, 0, 1193647076, -636310560, 0, -371264384, -205887008, 0, -236128672, 742951120, 0, 398020848, 391984992, 0, -837092192, -423321012, 0, 55503750, -563159584, 0, -428592864, -162744712, 0, 512745552, -606710624, 0, 100188040, 81134860, 0, 600080872, 123554848, 0, -905715712, 187866176, 0, 91017360, -1769724600, 0, 390464584, 329622864, 0, 206896096, -100156256, 0, -1524747168, 128929168, 0, 440548912, 1230624512, 0, -624656172, 538131792, 0, -106573584, 268099316, 0, -1006439200, 259945000, 0, -17105508, 104219136, 0, -377244528, 397854840, 0, -74688552, 240598384, 0, 150861312, -822699200, 0, 491185696, 1461276128, 0, -72679220, 310526724, 0, -108123368, -607768776, 0, -1584764160, 350568696, 0, -369590760, 846984600, 0, 168225984, 188632340, 0, -196605036, -282889664, 0, -847210056, -506620684, 0, 141506428, 15141632, 0, -128420120, 301552376, 0, -461969920, 1436657680, 0, 213219136, -303237048, 0, -252497496, 221607456, 0, -1110414872, 247280664, 0, 126547920, -647750264, 0, -999723816, -416670688, 0, 32836062, 407546048, 0, -800116960, 86580372, 0, -22304856, -1289180848, 0, -398364032, -220601400, 0, -260860224, -1770021456, 0, -282362560, -311550720, 0, -175398380, -558469472, 0, -793129512, 158204364, 0, 90325010, -288227520, 0, 321301904, 561720944, 0, -485529052, -849509528, 0, 2080714272, -173253872, 0, 37503628, -92612352, 0, -625379664, -818572016, 0, -385958396, -330020696, 0, -230472480, 95505706, 0, -789423242, -2930297344, 0, -164006136, 499543216, 0, -381934308, -521779716, 0, 6206464, -207875112, 0, 931356416, 1284196200, 0, -25516752, -288113536, 0, 238864436, -403688584, 0, -1229278680, 903176368, 0, -25854694, 208739168, 0, 542265200, 118803784, 0, 250589404, -207162312, 0, 1726358400, -107676128, 0, 294386916, 1666512288, 0, 698239264, 728803104, 0, -601534668, 245281536, 0, -20754048, 80054846, 0, -118892750, -314279264, 0, 1843276656, -96214464, 0, 162840100, -609579188, 0, 924508992, 172540902, 0, 158202196, -235595472, 0, 150177776, -256037936, 0, 505342248, -787508224, 0, -390868128, -99704586, 0, 802504020, -484701952, 0, -804637712, 1440908064, 0, 164794720, 555324480, 0, -1014992576, -538431106, 0, -48887248, 574813680, 0, 244708032, -355289816, 0, 542446136, 941874992, 0, 1322636448, -26305054, 0, 336778116, 1746734496, 0, 311326948, -34180752, 0, 336634692, 1016504752, 0, 2167845120, -33512836, 0, 425525330, -683149152, 0, 1164527712, -534316224, 0, 239054648, 1180499056, 0, 364730688, -65766292, 0, -501965812, 1117939328, 0, -730198192, -206898296, 0, -674973412, 61468632, 0, 1283537216, 389092280, 0, -382628186, 1575999936, 0, -108301776, -633018960, 0, -520648392, -1584041016, 0, 518288064, 580249088, 0, 185045656, -130665184, 0, -2199678304, -465213240, 0, -1564369984, 26886712, 0, -1282444064, 497628660, 0, -289682388, -34299384, 0, 592287648, -10091280, 0, -89680408, 31172912, 0, 292431216, -308087056, 0, 475971546, 57294720, 0, -92849880, -582515552, 0, 200434988, -114237728, 0, -884001664, -339528458, 0, -296573774, -1193521056, 0, 289759648, -829183048, 0, 52104384, 552284352, 0, 654138576, -38785980, 0, 299373640, -1304613024, 0, 1606865872, 387241988, 0, -530388756, 2320643104, 0, 907014784, -12538936, 0, -153099568, -1881780432, 0, 435560744, -265276624, 0, 1478678064, -775639800, 0, 69137712, 241998744, 0, 471660606, -1317000960, 0, -47913800, 205900008, 0, 427898272, 2389455000, 0, 1467030656, 1019397026, 0, 489859724, -2353305696, 0, 798808480, -214567690, 0, 296550876, -38403192, 0, -506223312, -655352404, 0, -502616736, 636388064, 0, -199552480, -468262384, 0, -824703940, 976310636, 0, 149456736, -68378400, 0, -134424026, 3164273448, 0, -242142344, -364851184, 0, 592033602, 265949720, 0, -1020743472, 539599544, 0, 1062639576, -366428160, 0, -340669960, -171775048, 0, -465596656, 1105125040, 0, 3386232096, -190886294, 0, 496284736, 960268176, 0, -1034573840, -610847584, 0, -396574096, -533151312, 0, 1505908656, -88292380, 0, 275574240, -974529920, 0, 315017720, 280021128, 0, -372456972, -710732, 0, -451536960, -917270768, 0, 247876054, -78740592, 0, 58347072, 415131328, 0, -1133513112, 984245848, 0, -2145417792, -390557536, 0, 56795108, -1123503744, 0, -1090088308, -1063078560, 0, -1127458432, -307819456, 0, -3657985760, -363142178, 0, -196616604, -768048288, 0, -1220154352, -904639256, 0, -751253004, 818956288, 0, -20311536, -153898468, 0, 590002196, 1369444960, 0, -197413556, 218327320, 0, -659753168, 1959801324, 0, -2360690112, 127267254, 0, -590529440, 489742176, 0, 439627472, -1056904692, 0, -628637632, 1455236472, 0, -1306863096, 361982470, 0, 183692096, -1159536000, 0, -3890098976, 1596841072, 0, -10695320, 243673892, 0, 1042293408, -33295260, 0, -702105924, 953595552, 0, 1239138912, 687238744, 0, 768898384, -1085570456, 0, 1868906256, 180554472, 0, 574663336, 2490932496, 0, 990568312, -129928680, 0, -427124764, -226568068, 0, 0, -1265913616, 0, -445954836, -2323534752, 0, 152280624, 73861528, 0, 301263828, -1319356160, 0, 1072528128, -77889572, 0, 1833030416, 3592512704, 0, 753667544, 861059780, 0, -317987684, 1404540180, 0, 2395886272, -543130964, 0, 1235224820, 2508343824, 0, 1739624624, 37272976, 0, -202350848, -2915133592, 0, 1927088688, -668168368, 0, 962353236, 1517663264, 0, 516188284, -59580124, 0, -662498672, 222260408, 0, -696113792, -203644168, 0, -176362016, -761298720, 0, -978060496, 638067272, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "69.6.a.a", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [0, -2], [0, 0], [84, 0], [-47, -1], [0, 0], [-59, -11], [0, -104], [0, 0], [58, 94], [-160, -108], [0, 0], [-144, -74], [638, 118], [0, 0], [3344, 0], [905, -13], [0, 0], [365, -311], [-3948, -84], [0, 0], [6264, 320], [-529, 0], [0, 0], [-887, 94], [4292, 288], [0, 0], [-4956, -924], [-4104, -266], [0, 0], [886, -1514], [0, -3360], [0, 0], [754, -1810], [3092, 576], [0, 0], [-11556, 206], [18038, -730], [0, 0], [3016, 4888], [-2758, 1372], [0, 0], [5161, -2667], [-13440, -9072], [0, 0], [0, 1058], [-21476, 1152], [0, 0], [-9817, 1298], [-5452, 1774], [0, 0], [-12096, -6216], [12675, 4369], [0, 0], [10652, 5236], [33176, 6136], [0, 0], [15428, 8208], [-9172, 508], [0, 0], [18612, -3946], [87812, -1772], [0, 0], [87872, 0], [8914, 3622], [0, 0], [-3741, 4607], [76020, -1092], [0, 0], [-33408, -6184], [-63424, -2088], [0, 0], [68830, 2212], [-11948, 23112], [0, 0], [30660, -26124], [43892, 8132], [0, 0], [31143, 1479], [-157168, -3344], [0, 0], [-79576, 5516], [-41560, -11124], [0, 0], [-42158, -294], [154686, -10322], [0, 0], [325728, 16640], [-34885, 2317], [0, 0], [32102, 5950], [-44436, 0], [0, 0], [-66816, 42952], [-8136, 14252], [0, 0], [-85052, 10274], [-75284, 19634], [0, 0], [-74508, 7896]]}