-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1043343188526830530390604898943,2038935615642931678042688375827', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 4, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 147.5070039818273, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': '1.1.1.1', 'conductor': 2313441, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, 0, -4, 0, 4], [1], [1, 0, -10, 0, 25], [1, 0, 13, 0, 49], [1, 0, -22, 0, 121], [1], [1, 0, 34, 0, 289], [1, 0, -26, 0, 361], [1, 0, 46, 0, 529], [1, 0, 58, 0, 841], [1, 0, 13, 0, 961], [1, 0, -26, 0, 1369], [1, 0, -82, 0, 1681], [1, 26, 255, 1118, 1849], [1, 0, -94, 0, 2209], [1, 0, 106, 0, 2809], [1, 0, -118, 0, 3481], [1, -26, 291, -1586, 3721], [1, 0, 13, 0, 4489], [1, 0, -142, 0, 5041], [1, 0, -143, 0, 5329], [1, -26, 327, -2054, 6241], [1, 0, -166, 0, 6889], [1, 0, -178, 0, 7921], [1, 0, 169, 0, 9409], [1, 0, 202, 0, 10201], [1, 26, 375, 2678, 10609], [1, 0, 214, 0, 11449], [1, 0, -143, 0, 11881], [1, 0, 226, 0, 12769]], 'euler_factors_factorization': [[[[1, 0, -2], 2]], [1], [[[1, 0, -5], 2]], [[[1, -1, 7], 1], [[1, 1, 7], 1]], [[[1, 0, -11], 2]], [1], [[[1, 0, 17], 2]], [[[1, -8, 19], 1], [[1, 8, 19], 1]], [[[1, 0, 23], 2]], [[[1, 0, 29], 2]], [[[1, -7, 31], 1], [[1, 7, 31], 1]], [[[1, -10, 37], 1], [[1, 10, 37], 1]], [[[1, 0, -41], 2]], [[[1, 13, 43], 2]], [[[1, 0, -47], 2]], [[[1, 0, 53], 2]], [[[1, 0, -59], 2]], [[[1, -13, 61], 2]], [[[1, -11, 67], 1], [[1, 11, 67], 1]], [[[1, 0, -71], 2]], [[[1, -17, 73], 1], [[1, 17, 73], 1]], [[[1, -13, 79], 2]], [[[1, 0, -83], 2]], [[[1, 0, -89], 2]], [[[1, -5, 97], 1], [[1, 5, 97], 1]], [[[1, 0, 101], 2]], [[[1, 13, 103], 2]], [[[1, 0, 107], 2]], [[[1, -19, 109], 1], [[1, 19, 109], 1]], [[[1, 0, 113], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 6, 'label': '4-39e4-1.1-c1e2-0-6', 'leading_term': '4.41764307087977455070967310534155007464900623549809726920063653735522937448480358307625735', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1521/2/b/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 37}, 'plot_values': [4.417643070879774, 4.4109475034468595, 4.395218336599713, 4.367386890586562, 4.327537678407311, 4.2763177261990455, 4.213464267160836, 4.1385537607189535, 4.051372453116904, 3.9517646601347227, 3.8395303087881705, 3.7145036351607112, 3.576593639085483, 3.425787804926142, 3.2621713392051612, 3.085934798896579, 2.8974128485010238, 2.6970734273572092, 2.485561499793553, 2.263675207259231, 2.0324136409299247, 1.792939011560853, 1.5466234055426435, 1.294998610141178, 1.0397977732345685, 0.7828947572523717, 0.5263367284831322, 0.27227577002791276, 0.02298918908575619, -0.21919320688877506, -0.4518832953520703, -0.6727076498214803, -0.8793171398899772, -1.0694556850564347, -1.2409847193458468, -1.391942868036762, -1.5205831692499048, -1.625418887713589, -1.7052698777108923, -1.7592901651983905, -1.787018529964373, -1.7883843382374889, -1.763756476827776, -1.713925214814303, -1.6401431896098084, -1.5440827814396425, -1.427863052612258, -1.2939841396969918, -1.1453349551760048, -0.9851082905227652, -0.8167857079348462, -0.6440392039267311, -0.47069196992911483, -0.30061435567803446, -0.13766189493248637, 0.014425318217096254, 0.15210300835248225, 0.27211019376263, 0.3715608071624037, 0.44800860488951716, 0.49954049146178753, 0.5248108177488878, 0.5231253122872689, 0.49443915480307826, 0.4394199863110488, 0.3594075153366374, 0.25644499575651103, 0.1332021795000689, -0.007033001922472866, -0.16046196166738763, -0.32282814776938357, -0.4895446761881611, -0.655791212998338, -0.8166478592691321, -0.9672306787378687, -1.1028157174836153, -1.2190022547828077, -1.311810260474409, -1.377855753516732, -1.4144064054896528, -1.4195500816313111, -1.392196786791332, -1.3322201529628406, -1.2403993366597386, -1.1185143378726845, -0.9692283654847045, -0.7961215877420453, -0.6035221992959536, -0.3964693423859792, -0.18050874826611443, 0.038416396984203995, 0.25418280034285357, 0.4606604113861998, 0.6519158235363697, 0.822433027848936, 0.9672743376176304, 1.082324125245558, 1.1643806098598155, 1.211393151661805, 1.2224637333801534, 1.1980470292204672, 1.1398492044177957, 1.050962925855427, 0.9356623840912522, 0.7994528001265273, 0.6487730787846636, 0.4909506997393215, 0.3338355523544166, 0.1856652531594379, 0.05466376273420048, -0.051162535092912007, -0.12442150989330901, -0.15857374153139137, -0.14828326379262322, -0.08964461126330561, 0.019549154865207113, 0.17964285379832187, 0.3889605046619887, 0.6437566527346075, 0.9381786565750305, 1.2643763938171348, 1.6125789663894892, 1.9713910507840753, 2.3279584773782522, 2.668458410641759, 2.978311177426667, 3.2428468089393454, 3.4475080897758144, 3.5786508527583742, 3.6236778764323643, 3.571908190179779, 3.4145847561631566, 3.145732342233166, 2.7619943588828817, 2.26339243337142, 1.6529684888280907, 0.9373637770681144, 0.12626910377386297, -0.7672429208613949, -1.727427024287462, -2.735819969000491, -3.7720483299479732, -4.814077054325052, -5.839032560372205, -6.823715843788121, -7.7453445774885, -8.582267217923665, -9.314527209158097, -9.9246873764057, -10.398132448474808, -10.723897309578824, -10.89465016315058, -10.907416919590576, -10.763223722924945, -10.467623871928545, -10.030020626328106, -9.463931294225095, -8.78605349001774, -8.016239821757097, -7.176406895043089, -6.290237994969685, -5.3820583971345215, -4.47632602935498, -3.5966047459930377, -2.764937484195474, -2.0010389552589007, -1.321666492417904, -0.7401256743954904, -0.2657570068230572, 0.0961943328341288, 0.3448738741793474, 0.4835837214461905, 0.5197911392188886, 0.4645818252550041, 0.3323586602064878, 0.1400793416639882, -0.09332632101266544, -0.3478065183978988, -0.6029743830838455, -0.8389066314357857, -1.037019422814566, -1.1806870560116323, -1.2560707774982318, -1.2524608026719688, -1.1629229863338717, -0.9843156170063747, -0.7176418823549386, -0.36774999797116253, 0.056678569626547146, 0.5436803273497935, 1.0784012660266755, 1.643787333121761, 2.2213129832082648, 2.7916702207128417, 3.3357394812133037, 3.8351316440478262, 4.273269731006406, 4.63565855130512, 4.910930749686774, 5.0907613877675875, 5.170741719720542, 5.1499142027454345, 5.031370617362337, 4.821446927850217, 4.529993326155468, 4.1693268840701805, 3.75418074380288, 3.3005550907197905, 2.8254101856751848, 2.3455748694601515, 1.8772927336008527, 1.4353382838388573, 1.0325487611543185, 0.6792623508606238, 0.38296536085346333, 0.1481105161174825, -0.02401934367978179, -0.13512176425535868, -0.18974226537358377, -0.19478774798109014, -0.15913306326176982, -0.09296275167213625, -0.0071831242321978486, 0.08725471015809702, 0.1800250886791616, 0.2619722754639478, 0.32572835342391326, 0.366004974640487, 0.38003038358304503, 0.3675225516542128, 0.33085153295020947, 0.27469522041908095, 0.20589046403796218, 0.1328391179565597, 0.06508006570343568, 0.012565278191187147, -0.0149488958528096, -0.008609415939066254, 0.03889186450891207, 0.13276780336483873, 0.2756306546280992, 0.46720327120285243, 0.7041060389742737, 0.9798726169706351, 1.2851380886038408, 1.6079285949979616, 1.934286553316887, 2.2487333561132408, 2.5352819367203954, 2.777920609407998, 2.9618823011009288, 3.0739780230198694, 3.1039328249940707, 3.0444156716321937, 2.892228137018744, 2.647932181327645, 2.3166956971564323, 1.9075014852290935, 1.433512428680516, 0.9109380702526447, 0.35887122714704345, -0.20202624939837938, -0.7501613922734148, -1.2642851311574832, -1.7244562814198645, -2.1130398533469603, -2.4157824774678094, -2.6223266619702086, -2.727160734316839, -2.729516237310355, -2.633984195164644, -2.449769047319233, -2.1908393784163716, -1.8746294561152776, -1.521702627787454, -1.154096825292096, -0.7946006168011651, -0.46500938142792664, -0.1852215710536671, 0.028308813678499273, 0.16337941065778064, 0.2131440221918516, 0.17653473939698233, 0.058768062837138306, -0.1288552352520046, -0.36907113531612457, -0.639603422891828, -0.9138040141423496, -1.1623366441908767, -1.3541111137545607, -1.4585242285187083, -1.446390538075858, -1.2924300035562013, -0.9758893278772531, -0.48288216217210883, 0.19354439256694536, 1.051622940260181, 2.081479304163691, 3.264238033574582, 4.573283745655372, 5.974461718026144, 7.4277922350642545, 8.888787437886755, 10.310290771817515, 11.644738847188155, 12.845724978103204, 13.870869618159706, 14.682713125097111, 15.251754251345224, 15.556366109019732, 15.585541614024804, 15.33768426383105, 14.822668167785809, 14.059552601632737, 13.077709779216748, 11.913710463727748, 10.61146619359334, 9.218691941695663, 7.786211781995437, 6.364489866521518, 5.002417731140889, 3.7443970641830173, 2.6290276283688234, 1.6871236292529106, 0.9407323214110538, 0.40228905214526917, 0.07431571509400633, -0.050297318965959105, 0.01228079909312021, 0.23800543504634813, 0.5963993701376216, 1.052248884055773, 1.567720408155502, 2.104095250939133, 2.6242127439852747, 3.0937858934342937, 3.4837508960174985, 3.7708166890530657, 3.939320953259742, 3.9808477296421674, 3.8952984800393606, 3.689623844824563, 3.377990329668318, 2.979868456749002, 2.5193721741983284, 2.023083300396349, 1.518817243103209, 1.033613163918302, 0.5922960886280066, 0.2160139653759877, -0.07900338689868565, -0.2821126783901254, -0.38896287709693395, -0.40130834508944563, -0.32697978743567246, -0.17897779437893713, 0.02530758231311852, 0.2654271995713078, 0.5192379468682831, 0.7642747772502748, 0.9793935728832056, 1.1458090219716768, 1.2486439384389159, 1.2773540207661578, 1.2268385861412636, 1.097136330490305, 0.8938619174763502, 0.627246135502181, 0.3118278716464827, -0.0349187667816459, -0.3935281053946838, -0.7439785347526802, -1.0670137521878935, -1.3452709011586712, -1.5646399411802936, -1.714786525012498, -1.7902165416206766, -1.790042666754983, -1.718513654960416, -1.5840576612781085, -1.3991905236879332, -1.179044262065768, -0.940745282836814, -0.701758598506676, -0.47897927782106453, -0.2872607825003623, -0.13855034398493934, -0.04091354007122598, 0.001957895143995469, -0.008950705224901313, -0.06809246147899982, -0.16572287883955386, -0.2886965183664953, -0.4213143738452164, -0.5466859157938181, -0.6477472038543816, -0.7089057242609492, -0.7168723361458493, -0.6622075104629443, -0.5396643007861579, -0.3492530085525526, -0.09593243613974158, 0.2100897339980628, 0.5542897039793926, 0.9183942331672909, 1.2817191232003857, 1.6224902461294402, 1.9192307363629904, 2.1525281478729483, 2.30606661708579, 2.3684089249486164, 2.333332236009749, 2.2011791559298453, 1.9783156030342504, 1.677707380356493, 1.317538137558479, 0.920865817968405, 0.5136615993201357, 0.12364595576022899, -0.22182373818163675, -0.4974075257157536, -0.6815560255327935, -0.7581716065952787, -0.7176154123761925, -0.5578594417877352, -0.2844811431380578, 0.08910632106736577, 0.542661703717091, 1.0500015574710813, 1.5807306023621308, 2.102156435117652, 2.581250849987721, 2.987232355100773, 3.2931697579240495, 3.478678607399661, 3.530628079551614, 3.4453409419659917, 3.228055697634156, 2.8941222577555035, 2.46716099158734, 1.9789904241067122, 1.4667431687404529, 0.9715922497165956, 0.5353499974160585, 0.19839528072369872, -0.003575753256721089, -0.04176467009943567, 0.10327783962659039, 0.4400548241953026, 0.964925549605124, 1.6618029108093868, 2.502350552054665, 3.447391963761075, 4.4482783418114344, 5.4500462220336185, 6.393410184982184, 7.219293126702553, 7.870703579234336, 8.297917562545162, 8.459489385725742, 8.327173546078699, 7.885501451468999, 7.1355477833907255, 6.0928453967827965, 4.789325314437428, 3.2697585494322663, 1.5915834873633705, -0.17954548714232435, -1.9718743165680666, -3.712047394788999, -5.32858110528961, -6.755491337425644, -7.936257943166264, -8.82581308488559, -9.39405549456355, -9.625769296818032, -9.52289405021015, -9.10239299449198, -8.396815967640523, -7.450588916581909, -6.318838509097773, -5.0629211309383475, -3.747902486028684, -2.438299278050683, -1.194919439192411, -0.07171528761829814, 0.8871848878463598, 1.6488982468845568, 2.193822175289293, 2.5151402975549932, 2.619454419187815, 2.5246424512348975, 2.258999742386418, 1.8580941499624228, 1.3627165896421818, 0.8155840832455552, 0.25868870733411287, -0.2693086792756077, -0.7356178832904943, -1.1146222517122386, -1.38968318595933, -1.5528566032482465, -1.6055564212506925, -1.5569137668047888, -1.423314808412193, -1.2256944996924302, -0.9881476320320189, -0.7353700640754294, -0.49114637400977945, -0.2754545459795484, -0.10245994605624563, 0.019554025622078083], 'positive_zeros': ['0.823052652157452310745906884638063', '1.60843659544344408192544238217640', '1.99078763810558088228352808591296', '2.63157065887121620480903494218531', '3.20749209732832894567563078282558', '3.36476624665477288762519080122146', '4.01797065380307853057820167714628', '4.94242111528745808001406511267890', '5.14498838884368396271322134815200', '5.50415515788240422222198479318700', '6.32330957485005699752075428604160', '6.50618795599704138466893898083852', '6.89467014712338490590698282284488', '6.95134974112846520078597538901503', '7.63591482532445221823106186314133', '8.169273316086556433005792833823905', '8.301313944502768042012743912665270', '8.634963774147364067892326096120944', '9.562659418411670609560770303852314', '9.606834570620730067007222022531261'], 'prelabel': '4-39e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4850030340642104, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1776002362929697649, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.823052652157452310745906884638', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.60843659544344408192544238218', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.99078763810558088228352808591', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 147.5070039818273, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 2313441, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40], 'euler11': [1, 0, -22, 0, 121], 'euler13': [1, 0, 0, 0, 0], 'euler17': [1, 0, 34, 0, 289], 'euler19': [1, 0, -26, 0, 361], 'euler2': [1, 0, -4, 0, 4], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 13, 0, 961], 'euler37': [1, 0, -26, 0, 1369], 'euler41': [1, 0, -82, 0, 1681], 'euler43': [1, 26, 255, 1118, 1849], 'euler47': [1, 0, -94, 0, 2209], 'euler5': [1, 0, -10, 0, 25], 'euler53': [1, 0, 106, 0, 2809], 'euler59': [1, 0, -118, 0, 3481], 'euler61': [1, -26, 291, -1586, 3721], 'euler67': [1, 0, 13, 0, 4489], 'euler7': [1, 0, 13, 0, 49], 'euler71': [1, 0, -142, 0, 5041], 'euler73': [1, 0, -143, 0, 5329], 'euler79': [1, -26, 327, -2054, 6241], 'euler83': [1, 0, -166, 0, 6889], 'euler89': [1, 0, -178, 0, 7921], 'euler97': [1, 0, 169, 0, 9409], 'euler_factors': [[1, 0, -4, 0, 4], [1, 0, 0, 0, 0], [1, 0, -10, 0, 25], [1, 0, 13, 0, 49], [1, 0, -22, 0, 121], [1, 0, 0, 0, 0], [1, 0, 34, 0, 289], [1, 0, -26, 0, 361], [1, 0, 46, 0, 529], [1, 0, 58, 0, 841], [1, 0, 13, 0, 961], [1, 0, -26, 0, 1369], [1, 0, -82, 0, 1681], [1, 26, 255, 1118, 1849], [1, 0, -94, 0, 2209], [1, 0, 106, 0, 2809], [1, 0, -118, 0, 3481], [1, -26, 291, -1586, 3721], [1, 0, 13, 0, 4489], [1, 0, -142, 0, 5041], [1, 0, -143, 0, 5329], [1, -26, 327, -2054, 6241], [1, 0, -166, 0, 6889], [1, 0, -178, 0, 7921], [1, 0, 169, 0, 9409]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/2/b/d'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-39e4-1.1-c1e2-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-39e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4850030340642104, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1776002362929697649, 'z1': {'__RealLiteral__': 0, 'data': '0.823052652157452310745906884638', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1043343188526830530390604898943,2038935615642931678042688375827', 'Lhash_array': ['1043343188526830530390604898943', '2038935615642931678042688375827'], 'label': '4-39e4-1.1-c1e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/2/b/d'}