-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '522755914562623539208206499495', 'a10': [-1.1921627343368193, 0.0], 'a2': [1.0, 0.0], 'a3': [-2.5649070187549796, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.1921627343368193, 0.0], 'a6': [-2.5649070187549796, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [3.5787480148585584, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.022031775598045, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [31, [[1.0, 0], [1.0, 0]]], [97, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 31, 97], 'central_character': '6014.1', 'coefficient_field': 'CDF', 'conductor': 6014, 'conductor_radical': 6014, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.5649070187549796, 0], [3.0, 0]], [[1.0, 0], [1.1921627343368193, 0], [5.0, 0]], [[1.0, 0], [0, 0], [7.0, 0]], [[1.0, 0], [2.085868468814902, 0], [11.0, 0]], [[1.0, 0], [6.115573129597273, 0], [13.0, 0]], [[1.0, 0], [-3.685042280380476, 0], [17.0, 0]], [[1.0, 0], [2.2726349076905716, 0], [19.0, 0]], [[1.0, 0], [7.642330786927453, 0], [23.0, 0]], [[1.0, 0], [-2.0561638080325313, 0], [29.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [37.0, 0]], [[1.0, 0], [11.084442820399728, 0], [41.0, 0]], [[1.0, 0], [-2.085868468814902, 0], [43.0, 0]], [[1.0, 0], [-12.36429958377573, 0], [47.0, 0]], [[1.0, 0], [-13.694721056264939, 0], [53.0, 0]], [[1.0, 0], [-9.018123476526892, 0], [59.0, 0]], [[1.0, 0], [-3.0351009562435203, 0], [61.0, 0]], [[1.0, 0], [9.340100248373671, 0], [67.0, 0]], [[1.0, 0], [14.115573129597273, 0], [71.0, 0]], [[1.0, 0], [13.417124104737036, 0], [73.0, 0]], [[1.0, 0], [-2.028481815825374, 0], [79.0, 0]], [[1.0, 0], [-6.958077099880156, 0], [83.0, 0]], [[1.0, 0], [-5.810573837467121, 0], [89.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [7.524932097105897, 0], [101.0, 0]], [[1.0, 0], [-7.734384144536683, 0], [103.0, 0]], [[1.0, 0], [9.150674085840793, 0], [107.0, 0]], [[1.0, 0], [10.343473875259608, 0], [109.0, 0]], [[1.0, 0], [-1.4185922614842328, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 23, 'label': '2-6014-1.1-c1-0-23', 'leading_term': '0.72365896730894526927252006213362', '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/6014/2/a/d/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [0.7236589673089453, 0.7142649913279999, 0.6860772410273619, 0.6390838545262401, 0.5732833893567161, 0.48871109758181497, 0.38547339014304877, 0.26378840957786315, 0.12403033488489024, -0.03322509302717932, -0.2071563285169622, -0.3966554397623639, -0.6002933585495993, -0.8162928675875806, -1.0425109372534151, -1.2764317149048194, -1.5151711559925332, -1.7554939707549533, -1.9938432432033135, -2.2263827586683407, -2.449051750629219, -2.6576314463116146, -2.8478224549429423, -3.0153317061070593, -3.155967314055796, -3.2657394247841394, -3.340964805423243, -3.378372670442506, -3.3752090172860614, -3.32933657648803, -3.2393273786448145, -3.1045449125159887, -2.9252129031327314, -2.702467882310213, -2.4383929602039824, -2.136030536595984, -1.7993721124922326, -1.4333238711840115, -1.0436472846633154, -0.6368746543691648, -0.22020019966119445, 0.19865195478428224, 0.6115807908060136, 1.0102795650549297, 1.386421583887238, 1.7318563865041474, 2.0388115729214378, 2.300095055591022, 2.509292185151761, 2.660952021284142, 2.750757004850483, 2.775670448912313, 2.734056610225968, 2.6257686301315015, 2.4522003389472875, 2.21629878926778, 1.9225354027295392, 1.576834757439091, 1.1864612791395337, 0.7598653930144432, 0.3064920052674636, -0.16344452832571704, -0.6392135701839746, -1.1098430219907045, -1.564408366327524, -1.9923277434426743, -2.383654357961971, -2.7293572532657846, -3.0215815190119777, -3.253879323191997, -3.4214037876128534, -3.521058647682042, -3.5515978357985554, -3.5136705736063796, -3.4098092125086255, -3.24435887528527, -3.0233498672654973, -2.754315779567159, -2.446062131185791, -2.1083922207400403, -1.7517985123417914, -1.3871292962531707, -1.0252414823375, -0.6766511497869588, -0.35119384801432013, -0.05770659171348432, 0.19625699653269116, 0.40466786849814174, 0.5632098733888442, 0.6694077638775338, 0.7226894844599909, 0.7243796632760555, 0.6776237352349044, 0.5872447257075297, 0.45953732256229707, 0.3020063583991991, 0.12305911297716964, -0.06833716937293381, -0.26301956026337986, -0.4520014157546247, -0.6268373305316517, -0.779966355441589, -0.9050193287251131, -0.9970773333365078, -1.0528700166678786, -1.070904742951092, -1.0515202176387617, -0.9968612311888762, -0.9107744030449917, -0.7986281375199802, -0.6670632950266763, -0.5236841943076239, -0.3767023558585928, -0.23454774367765824, -0.10546404598167163, 0.0028943405127036365, 0.08384556520103521, 0.13202614026944284, 0.14368280776839573, 0.11689587210317405, 0.05172204418061769, -0.04975191086149436, -0.18344969081033627, -0.3434410203861154, -0.5221688788050302, -0.7107607462713178, -0.8994121571660405, -1.0778271625604823, -1.2356971812688242, -1.3631973183474828, -1.4514776882784388, -1.4931266995627457, -1.4825837016147145, -1.4164798836934298, -1.293888822890124, -1.116471530634386, -0.8885051258069824, -0.616789206107265, -0.3104293998248925, 0.019496769709682445, 0.36038093253581327, 0.6986156820349075, 1.0201961396268582, 1.311366175898757, 1.5592810804896136, 1.752656527942803, 1.8823730424964555, 1.9420059042565956, 1.9282525854535868, 1.8412333182664145, 1.684645170664978, 1.4657558775684632, 1.1952304181789566, 0.8867906745002493, 0.5567161402145812, 0.22320123693984664, -0.09440801123068474, -0.37646873755953403, -0.60395282382593, -0.7593766723317088, -0.8277080461318871, -0.7972081617854321, -0.6601683748789708, -0.4135038323875632, -0.059171311295713985, 0.39561503175681056, 0.9383883427227913, 1.5516634746154905, 2.2134006005871534, 2.897687383107016, 3.575619019157605, 4.216346021789819, 4.788251153082593, 5.260209907488883, 5.602883721079658, 5.789991944581148, 5.7995077736285205, 5.614724887283983, 5.225145508037957, 4.627146855737967, 3.8243913083593752, 2.827955686870345, 1.6561665424592247, 0.33414066141211385, -1.1069573179170187, -2.6309158239788615, -4.1976997865724215, -5.764850234185718, -7.289005201651219, -8.727480854079815, -10.03984808002889, -11.189438960603313, -12.144719574673982, -12.880470514122305, -13.378724083850413, -13.629417147721345, -13.630730535235017, -13.389099326773492, -12.918892592968247, -12.241775631395258, -11.38578175637481, -10.384133601287017, -9.2738650763479, -8.094304049846553, -6.885482048972546, -5.686540491827948, -4.534202989203592, -3.4613800679605515, -2.4959663961595475, -1.6598815120937664, -0.9683935920933517, -0.42975247205136324, -0.04514359652565672, 0.19104049677410215, 0.29062941301660455, 0.2708370515164897, 0.15320119911615923, -0.0376447883942272, -0.2753061648850987, -0.5330004548064349, -0.7849031877737574, -1.0074006119060663, -1.1801898303467038, -1.287175287123097, -1.317121518318327, -1.2640350182271944, -1.1272622817389815, -0.9113058395601839, -0.6253746376317038, -0.2826986711240763, 0.10035033935451633, 0.5052808657562086, 0.9125879462065429, 1.3028822539537126, 1.6579798183413617, 1.9618934173078812, 2.2016728969860777, 2.3680507389313505, 2.4558605905683577, 2.4642095723676594, 2.3963992535263716, 2.259604467507711, 2.0643328264602916, 1.8237001254003937, 1.552567110996584, 1.266590744504589, 0.9812476765862898, 0.7108889059093209, 0.46788243240674193, 0.26189525144079845, 0.09935756680542648, -0.01685889811701197, -0.08752951879400514, -0.11692742410303988, -0.11244573301905228, -0.0840148796915345, -0.04335119303692979], 'positive_zeros': ['0.41238170397150911278123351925036', '1.89961695232508445556965562686474', '2.84319259689133707543710568907999', '3.99437184105129699067730598370703', '4.53034583623858744489602534577488', '5.38921296658026584608781823834604', '5.65086640417123901609867159869097', '6.51291536793494643247879343980146', '7.29814279468966500154352342983070', '7.69420953713518885812763232759013'], 'prelabel': '2-6014-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.92979305431252, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41238170397150911278123351925', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.89961695232508445556965562686', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.84319259689133707543710568908', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 48.022031775598045, 'bad_primes': [2, 31, 97], 'central_character': '1.1', 'conductor': 6014, 'conductor_radical': 6014, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6014/2/a/d/1/1'], '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': '2-6014-1.1-c1-0-23', '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': '2-6014-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.92979305431252, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.41238170397150911278123351925', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '522755914562623539208206499495', 'Lhash_array': ['522755914562623539208206499495'], 'label': '2-6014-1.1-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6014/2/a/d/1/1'}