Formats: - HTML - YAML - JSON - 2026-10-12T13:43:03.313192
  • lfunc_lfunctions • Show schema
    {'Lhash': '2232574197138276580623197439978', 'a10': [1.4210751212392276, 1.1332695927911198], 'a2': [0.4338837391175581, 0.9009688679024191], 'a3': [-2.1906431337674115, 1.746979603717467], 'a4': [-0.6234898018587335, 0.7818314824680298], 'a5': [1.637622009215464, -0.7886371948387563], 'a6': [-2.524458669761153, -1.215715221585588], 'a7': [0.8827024924549692, 1.1068739154945435], 'a8': [-0.9749279121818236, -0.2225209339563144], 'a9': [1.079416801848524, -4.729234010885294], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.46313233172342644, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [-0.4338837391175581, -0.9009688679024191]]], [29, [[1.0, 0], [-4.21464026350189, 3.3521347600102116]]]], 'bad_primes': [2, 29], 'central_character': '58.9', 'coefficient_field': 'CDF', 'conductor': 58, 'conductor_radical': 58, 'conjugate': '5369566628014941098959519837642', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.4338837391175581, -0.9009688679024191]], [[1.0, 0], [2.1906431337674115, -1.746979603717467], [0.6675628018689432, -2.924783736545471]], [[1.0, 0], [-1.637622009215464, 0.7886371948387563], [3.1174490092936677, -3.909157412340149]], [[1.0, 0], [-0.8827024924549692, -1.1068739154945435], [-1.5576465376942008, 6.8244953852727654]], [[1.0, 0], [-3.4487808662799493, 0.7871617273300068], [9.910657546926611, -4.77272113029314]], [[1.0, 0], [1.2391064372594272, 5.428880017578728], [-11.71259528273145, 5.640488608528256]], [[1.0, 0], [0, -7.463374613663354], [-17.0, 0]], [[1.0, 0], [3.9379092559370426, 3.140377839443499], [4.227897745169973, 18.523630331454648]], [[1.0, 0], [1.6121566514891525, 0.7763737248989104], [14.340265442750871, 17.982124096764686]], [[1.0, 0], [-4.21464026350189, 3.3521347600102116]], [[1.0, 0], [2.077314394548496, 4.31358778768766], [-19.32818385762074, 24.236775956508925]], [[1.0, 0], [-1.0471681972594291, -0.239009307613362], [33.335848112389506, 16.053698347349652]], [[1.0, 0], [0, -1.711641819617023], [-41.0, 0]], [[1.0, 0], [0.8814052684088612, -1.8302568989025838], [-26.81006147992554, -33.61875374612528]], [[1.0, 0], [0.37751688610642536, -0.08616576572588105], [42.3455367914137, -20.392535738525233]], [[1.0, 0], [-2.426775492465179, 1.168673482715371], [33.044959498512874, -41.43706857080558]], [[1.0, 0], [3.813020466766698, 0], [59.0, 0]], [[1.0, 0], [10.558450616873511, -8.420083394785628], [13.573776971335178, -59.47060264309124]], [[1.0, 0], [0.6590118471596893, -2.8873195561035043], [-60.36491414946208, -29.070210520876394]], [[1.0, 0], [-1.3971140905491917, -6.121156779102577], [-63.96878962107176, 30.805745477346626]], [[1.0, 0], [0.41668481775742156, -0.8652549397001306], [-45.51475553568755, -57.07369822016618]], [[1.0, 0], [-2.712295618826743, -0.6190637756141976], [71.17654056429112, 34.27681539028709]], [[1.0, 0], [5.656397169077488, -7.092897704090769], [-18.469237518374097, -80.91901671109136]], [[1.0, 0], [-2.304134896360134, -4.784585412880801], [-55.49059236542728, 69.58300193965465]], [[1.0, 0], [8.595862160842522, 6.85497132777311], [21.584530593762498, 94.56800748163688]], [[1.0, 0], [1.9789831340261679, -4.109400821261118], [-62.97246998773208, -78.96497972927101]], [[1.0, 0], [-0.33571465647170307, -1.4708620142096434], [-92.79979339394917, 44.690025129108484]], [[1.0, 0], [-2.8774828989733123, 12.607076310338066], [-96.40366886555884, -46.42556008557872]], [[1.0, 0], [-1.801798701472526, -2.2593841080987103], [-24.25478180123827, 106.26714242781877]], [[1.0, 0], [2.3612598059417236, -1.8830418594761538], [25.144865537063527, -110.16685407654607]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-58-29.9-c1-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/58/2/e/a/9/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [0.7824769547884476, 0.7453968501435743, 0.7184640700788703, 0.698539551678981, 0.682222128901679, 0.6660262668925185, 0.6465065735944381, 0.6203293988227575, 0.5843129308861408, 0.5354606338997502, 0.4710063740818411, 0.38848094337880484, 0.28580261774609134, 0.16138953560553781, 0.014288491827879684, -0.15568746978434642, -0.3478219659874368, -0.5603693323372276, -0.7904514951919416, -1.0339899151426095, -1.2856848786069193, -1.53905370010273, -1.7865378070556595, -2.019686108062283, -2.2294184495782265, -2.4063683766282105, -2.541298952328122, -2.6255792804917073, -2.6517029397364436, -2.613823198034184, -2.508274137743298, -2.33404224399899, -2.0931501761438382, -1.7909139102890923, -1.436036691049294, -1.040508606909396, -0.6192892593969856, -0.1897628405754663, 0.2290304075453965, 0.6173655832616433, 0.9559686485120015, 1.2272595232163979, 1.4166299145186774, 1.5136699321306546, 1.513249180160373, 1.4163558558357896, 1.2306025787372716, 0.9703209213464821, 0.6561880225063529, 0.3143576500257527, -0.024896712243925066, -0.32897985119682716, -0.5651263303136989, -0.7027793010291361, -0.7160373657064879, -0.5859864490291514, -0.30272239756806935, 0.13312604884631274, 0.7095436168151731, 1.403076278143396, 2.1796592731834186, 2.9963382378933563, 3.803822131543954, 4.549730143466794, 5.182322654244822, 5.654445795296328, 5.92737706997028, 5.974241751241893, 5.7826805302991575, 5.356489998465329, 4.716028050324864, 3.897272228260308, 2.9495334640339994, 1.9319511201342667, 0.9090163384549359, -0.054522762933262435, -0.8989404528842474, -1.574520444528623, -2.045774702973759, -2.2944666291645874, -2.321106184336601, -2.144719492867186, -1.800859287730042, -1.3379999868245638, -0.8126341952392475, -0.2835370044593648, 0.1942273563635414, 0.5749299460465883, 0.826819816289937, 0.9352546680768176, 0.9039355720375963, 0.7540598129224441, 0.5214359790942908, 0.25184297521053134, -0.004867655604831358, -0.20125588000908048, -0.2985930341429263, -0.2721930722021835, -0.11507165009009734, 0.1605990300180208, 0.5245245318417061, 0.9317992280152032, 1.3285677107223506, 1.6592177953123068, 1.8742536499467897, 1.9378580415135995, 1.8341303342468194, 1.5710925595506435, 1.1817848395125332, 0.7221027591079903, 0.2654273137313213, -0.10548399065423393, -0.30849113612837087, -0.27279668172328386, 0.05092274089831007, 0.6823135171824446, 1.6062438405894335, 2.771653319820611, 4.094748530024244, 5.466407111968401, 6.7631071530076285, 7.8602104574709974, 8.646065726884185, 9.035215733908428, 8.979025421336424, 8.472302672497557, 7.554937866671774, 6.308191516565227, 4.845937527503046, 3.3018349923359382, 1.8139632347333927, 0.5088320315375019, -0.5131878532671396, -1.1891078565633162, -1.499735718701533, -1.4703790277188715, -1.1657176051538722, -0.6795227043076545, -0.120625722138134, 0.40291557316664905, 0.7992234544560977, 1.0053802653747668, 0.9957321044422233, 0.784492642632621, 0.4222440790420699, -0.013168370051928894, -0.4300050888874732, -0.7382542111387175, -0.865118101346491, -0.767948286948679, -0.44255428914291367, 0.07451950557103128, 0.7102511609133516, 1.365428401373975, 1.9295048032459288, 2.2978078702238594, 2.3884507921049636, 2.1562717393026354, 1.6015171015646268, 0.7717495710459376, -0.24351095160907618, -1.3247710355815157, -2.3394649114216, -3.161244326795906, -3.688688519560465, -3.860490463462594, -3.6646743420482886, -3.140304868485488, -2.3713255868088954, -1.473425744866564, -0.5759786706633543, 0.19807306340823444, 0.7511352789701697, 1.0255888046287882, 1.0117071397387827, 0.747542192470381, 0.3107947609057001, -0.19595064520018812, -0.6640931907045496, -0.9987109277196763, -1.1356206436549365, -1.0527505810221895, -0.773731247062391, -0.3629602764193286, 0.08708421027792716, 0.47408455042113395, 0.706410516988707, 0.7221477001779953, 0.5029930443920079, 0.0801979398406698, -0.46890300310245653, -1.0335617252787133, -1.4895612259323794, -1.7230794239620726, -1.6542318605786115, -1.2558971620269046, -0.5640628993978728, 0.32272713785346874, 1.2554007533891665, 2.0564042848019173, 2.548446520617977, 2.585258670391731, 2.079102222457264, 1.0200772018997593, -0.5165089686925222, -2.376537615478036, -4.346758500295727, -6.184966674573693, -7.655995548639795, -8.56770904573235, -8.801021072038886, -8.32885136615631, -7.220712933835503, -5.632021772376049, -3.779811904584464, -1.9088708013305788, -0.2539627434349462, 0.9955234827969076, 1.7226114520902045, 1.8970563070918103, 1.5748142089969763, 0.8831723975625735, -0.005416734895322681, -0.9057962080457408, -1.6528373552272264, -2.128527201846217, -2.278699252607045, -2.116773087398749, -1.714414163464719, -1.181548407326399, -0.6401765098408982, -0.19753826718647208, 0.07583803876168212, 0.1587972294041007, 0.08054444757144139, -0.08992945458216339, -0.2634041609105382, -0.35445933442774996, -0.30448554952953183, -0.09836392554775189, 0.22917662010138204, 0.5993083189615206, 0.906098251468095, 1.041352106644582, 0.9220332206129883, 0.5141747209937011, -0.1523250442556337, -0.981936607434307, -1.8260682093361342, -2.508272287377596, -2.8576126237488437, -2.743750311803452, -2.1066010346938646, -0.9741673421782897, 0.535740870066462, 2.231101215191758, 3.876336133398855], 'positive_zeros': ['1.76119050212757452755589190924260', '4.68089385682342042289823770543141', '6.24052614508980513058539960310903', '7.09101510986522851716412729654512', '9.367566073741005633597594899184181', '10.69670163050143776264746367694414', '11.74740596264248395767267801751729', '12.30820932630870544481691694358342', '13.83455176956665692981565562508052', '14.23615872316310021455507670337987'], 'prelabel': '2-58-29.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6805382661712907, 'root_angle': -0.25109757468316607, 'root_number': '-0.006896210460291839 - 0.9999762208579199*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.251097574683', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.76119050212757452755589190924', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.68089385682342042289823770543', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '6.24052614508980513058539960311', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.46313233172342644, 'bad_primes': [2, 29], 'central_character': '29.9', 'conductor': 58, 'conductor_radical': 58, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/58/2/e/a/9/2'], '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': '2-58-29.9-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-58-29.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6805382661712907, 'root_angle': -0.25109757468316607, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.76119050212757452755589190924', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2232574197138276580623197439978', 'Lhash_array': ['2232574197138276580623197439978'], 'factors': ['2-58-29.9-c1-0-0'], 'label': '2-58-29.9-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/58/2/e/a/9/2'}