-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2490022168235245031740268403871', 'a10': [-1.7169572657499892, -4.717301317816645], 'a2': [1.1642134098630619, 0.8667247706520739], 'a3': [1.6842440621588926, -0.4041310914573542], 'a4': [0.030574570220906972, 0.1021261766762845], 'a5': [-2.8897242085906263, -1.9006015109707879], 'a6': [2.3110899502043667, 0.9892812124795362], 'a7': [0.4530183634175592, 2.606678799239844], 'a8': [0.9399061792634671, -2.582371003932244], 'a9': [2.673356121834975, -1.3613107822416823], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.5275177946066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.6842440621588926, 0.4041310914573542]]], [7, [[1.0, 0], [-0.4530183634175592, -2.606678799239844]]]], 'bad_primes': [3, 7], 'central_character': '567.104', 'coefficient_field': 'CDF', 'conductor': 567, 'conductor_radical': 21, 'conjugate': '1599510867303174408181594138713', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.1642134098630619, -0.8667247706520739], [0.5736064654221805, 1.9159790246309778]], [[1.0, 0], [-1.6842440621588926, 0.4041310914573542]], [[1.0, 0], [2.8897242085906263, 1.9006015109707879], [1.9803988301957842, 4.59108053440137]], [[1.0, 0], [-0.4530183634175592, -2.606678799239844]], [[1.0, 0], [-1.509908336047227, 3.0064746829206084], [-6.5687445087306475, -8.823355120305482]], [[1.0, 0], [-6.124019294305922, -2.6416440651963486], [8.921141292293537, 9.455857340449633]], [[1.0, 0], [1.2486997497689425, 1.0477834994822814], [2.952019020337816, 16.741731801207536]], [[1.0, 0], [4.778039259466971, 5.694245453025942], [-3.2993153756716764, 18.711347307231954]], [[1.0, 0], [0.13740427644995298, 0.12963424893602554], [1.337331064940944, 22.961087640239167]], [[1.0, 0], [0.561186925227024, -4.8012609916698], [-28.218301246814892, -6.687860251530765]], [[1.0, 0], [1.015210930034427, -4.2835117325027126], [-27.70261185002578, -13.912774586214327]], [[1.0, 0], [1.1311560467212467, -6.415104722920847], [-34.76862696907861, -12.654745303049744]], [[1.0, 0], [-3.2870242346349303, -4.4152397878599805], [-11.758932541154701, 39.27757000493504]], [[1.0, 0], [-0.17250461082870253, -2.9617897852078245], [-42.70924938290355, 4.9919953073849]], [[1.0, 0], [0.2142588305883683, -0.050780275683432685], [42.00073409520038, -21.093561469421722]], [[1.0, 0], [10.015153344888994, 5.782251479647042], [26.5, 45.89934640057525]], [[1.0, 0], [-3.163498924025987, 1.5887688739234946], [35.23235691046438, -47.32526837254758]], [[1.0, 0], [-3.3458762927943613, -1.0016896058761855], [50.964756496189125, 33.520047662319165]], [[1.0, 0], [8.4422278978545, -0.9867549221512087], [65.1940063288482, -15.451263339743491]], [[1.0, 0], [-4.320925215428199, -11.871644460541077], [-54.38915546144744, 45.63792028774429]], [[1.0, 0], [3.6744752322266394, -10.095537728887972], [-55.921244347685395, -46.92349550711737]], [[1.0, 0], [-1.2097773086389019, 1.6250129376201226], [-22.65745538417613, -75.68117147292362]], [[1.0, 0], [3.985625857290118, -5.353624618647], [-23.804668315020493, -79.51312952218558]], [[1.0, 0], [-15.663845929059281, -5.701173672309406], [68.17795543758905, 57.208097262102]], [[1.0, 0], [-0.6862364408354428, -1.0433718191070758], [-38.419737305798215, 89.06696236738658]], [[1.0, 0], [-4.240994751180791, 14.165908992765445], [-84.38426895270658, -55.50040678515141]], [[1.0, 0], [-0.8378817902194164, -1.6683598132649027], [-61.50733494538697, 82.61868885376951]], [[1.0, 0], [-8.417462513073877, 4.859824247816786], [53.5, -92.66471820493493]], [[1.0, 0], [-5.29485952948193, 9.170965724002944], [-54.5, -94.39676901250381]], [[1.0, 0], [11.945748220141054, 0.6957606032895757], [112.23593442483956, 13.118499296151017]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 55, 'label': '2-567-567.104-c1-0-55', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/567/2/bm/a/104/52', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.6334510939289544, 2.7286836669724863, 2.8236642042595164, 2.913628931623906, 2.989297145204231, 3.038361562389709, 3.0472156665301906, 3.0026687170809496, 2.893533748566783, 2.7120434462048624, 2.4550521560263223, 2.1249540870440686, 1.7302198002105886, 1.2854433896660125, 0.8108083733178966, 0.33092172455809626, -0.12697080514828374, -0.5352955160816071, -0.868809516580655, -1.1073490447252834, -1.2383476308921864, -1.2587749790019034, -1.1761612245543533, -1.0084352647778887, -0.7824210647359453, -0.5309954520912727, -0.28909984722055826, -0.08899386170296936, 0.04468771735838521, 0.09939208893856115, 0.07789744970378154, -0.00030600229196532425, -0.09998936612870095, -0.17372154272691218, -0.16782201244748418, -0.03019135855299866, 0.2808902131738124, 0.7881943116082485, 1.4885490606993794, 2.348716440938619, 3.3051855876342517, 4.268465799540988, 5.131843866157418, 5.783869073577966, 6.123149034331306, 6.07349536410525, 5.597159100151722, 4.703924507850766, 3.4542250972049215, 1.9551882796089006, 0.3495237799823159, -1.201692333851331, -2.540199208400329, -3.532713748509953, -4.090657115228583, -4.184128826728852, -3.8474849923531704, -3.1750638311074377, -2.307145106186407, -1.4078925400729723, -0.6385254469881152, -0.13001478224842752, 0.04002926798462535, -0.13795769136758407, -0.6022488037812874, -1.2291755964010753, -1.8540308982112712, -2.300326989432962, -2.4125020472361958, -2.086260721747026, -1.2908579162001146, -0.07883629864624968, 1.4191502290538982, 3.0141022437638743, 4.489927708461841, 5.640755404020923, 6.307493158632696, 6.406689374635918, 5.945988073332754, 5.0228820020887355, 3.8066389554474096, 2.506597283974183, 1.3328265735681326, 0.4568294362062716, -0.01987621823613971, -0.08290548372419748, 0.19567942270362884, 0.6758010113415132, 1.1817230598077484, 1.5414974646170172, 1.625052332754781, 1.3726563964394658, 0.807496955479082, 0.029543048188328563, -0.8079907837764525, -1.534324795932407, -2.0008494875145098, -2.115784178076608, -1.865670559208736, -1.3185653811977203, -0.6080235828463141, 0.09849472348043437, 0.6393754803326597, 0.8972484198579386, 0.8266785088704082, 0.4642466053126174, -0.08166996194485565, -0.6591039848068679, -1.1118071198441868, -1.3197965638348557, -1.230703819896588, -0.8735692326857083, -0.3510376644646948, 0.18855558719951132, 0.5923389809284082, 0.7466094942527683, 0.6112179249853504, 0.23467540781285162, -0.25530579283389976, -0.6847623684491949, -0.8823757886575572, -0.7318978221104794, -0.21381389314943472, 0.576230966205852, 1.4394389784035195, 2.115907871473148, 2.348275650688635, 1.9520833880619157, 0.8749649277892494, -0.7717937381718206, -2.7199710500763987, -4.591072690365932, -5.974585093111154, -6.520903445938761, -6.027208320113271, -4.494954201740206, -2.143407788176038, 0.6263560089856748, 3.310754162287184, 5.409254166790396, 6.53218157414475, 6.48551708066499, 5.312400247382783, 3.28118002528134, 0.8226857411869921, -1.5682640396977712, -3.4433915983870214, -4.497006545147358, -4.6249232014500965, -3.9331932972918304, -2.6964276623257373, -1.2782010659619056, -0.03530874247454112, 0.7689552952278907, 1.0206482877477987, 0.7673757659880711, 0.18632989499484506, -0.4802686802301207, -1.0022445271357179, -1.2283357750668022, -1.124030433355758, -0.7707599609234793, -0.3286377048585002, 0.02417028123086563, 0.15556434919356205, 0.02655878022744575, -0.29369963105304653, -0.6497117918180394, -0.8513054072343079, -0.7387412318824471, -0.24028150385576014, 0.5966973028192063, 1.6119117175728577, 2.5749102983468335, 3.251885331433968, 3.4760816064437945, 3.199589449331971, 2.5095787956102966, 1.6028518241563123, 0.7257103016003836, 0.09746052790791077, -0.15825496729271343, -0.05177901633545396, 0.2781359475983036, 0.6136456668450008, 0.7364524747979143, 0.5110529583860294, -0.05495543685462676, -0.7951799851340647, -1.4218657081142778, -1.6083557619971662, -1.0934997783209226, 0.2235886368068037, 2.229065032770846, 4.6002003078374525, 6.874129963463376, 8.562956485690453, 9.283675573466855, 8.865400387917795, 7.401568432419405, 5.230060850631008, 2.845112361415567, 0.7652893338018631, -0.6046227514575081, -1.0776094008911736, -0.7239046682548829, 0.1651813418299883, 1.1773133836876886, 1.911771809143358, 2.1034085678385854, 1.699458473872234, 0.8656590320878322, -0.07939831485677644, -0.77976256986052, -0.9693349492758611, -0.5685509943813378, 0.28222600829940064, 1.2650840657228821, 1.9904808896841875, 2.133214089055075, 1.5541109306762027, 0.36640054048077186, -1.077591668549246, -2.2788191189237708, -2.736952340070571, -2.1051904789199827, -0.30658859424427864, 2.425060603019801, 5.594057934792523, 8.568201253520893, 10.744151322103917, 11.704056952881427, 11.317828398098511, 9.762660692930575, 7.457145851726505, 4.933276874400691, 2.687559191945008, 1.0567605783538303, 0.1535361527995074, -0.1239338268973675, -0.018765659346089193, 0.19103943157422568, 0.29333777686503965, 0.2031289111088257, -0.03288724915483775, -0.2840512992859035, -0.41235792101573454, -0.3449924846983306, -0.11302216760451703, 0.1590755706967839, 0.30821524466643924, 0.20883730411385934, -0.16183746572923413, -0.6982263462594489, -1.194265250911506, -1.417426434678267, -1.2022952772327058], 'positive_zeros': ['1.96428114165444194355228028195261', '3.44969885993031422295789568833890', '3.87460137823059332395598972639190', '4.39138812421290963516269624126320', '6.27733208034363688139460931516738', '7.68778880066863020979295296436228', '7.80694657983995418277544513266511', '8.882086122340386965268792532626371', '10.49111761197079827930206908819319', '10.67782346201034144488090870061574'], 'prelabel': '2-567-567.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.10217501834513458, 'root_number': '0.9489228104962255 + 0.3155083195732634*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0510875091726', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.96428114165444194355228028195', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.44969885993031422295789568834', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.87460137823059332395598972639', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.5275177946066, 'bad_primes': [3, 7], 'central_character': '567.104', 'conductor': 567, 'conductor_radical': 21, 'degree': 2, 'index': 55, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/567/2/bm/a/104/52'], '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': '2-567-567.104-c1-0-55', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-567-567.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.05108750917256729, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.96428114165444194355228028195', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2490022168235245031740268403871', 'Lhash_array': ['2490022168235245031740268403871'], 'label': '2-567-567.104-c1-0-55', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/567/2/bm/a/104/52'}