Formats: - HTML - YAML - JSON - 2026-09-06T21:56:56.603138
  • lfunc_lfunctions • Show schema
    {'Lhash': '1249940682867020542815531156854', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.0774219157468, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, -1]], [23, [1, -1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '5520.1', 'coefficient_field': '1.1.1.1', 'conductor': 5520, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -1], [1, -4, 7], [1, 0, 11], [1, -2, 13], [1, -6, 17], [1, 2, 19], [1, -1], [1, -6, 29], [1, -4, 31], [1, -8, 37], [1, -6, 41], [1, 8, 43], [1, 12, 47], [1, 6, 53], [1, -6, 59], [1, 10, 61], [1, 8, 67], [1, -6, 71], [1, -2, 73], [1, -10, 79], [1, -12, 83], [1, -6, 89], [1, -8, 97], [1, 6, 101], [1, 8, 103], [1, -12, 107], [1, -2, 109], [1, 6, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, -1], 1]], [[[1, -4, 7], 1]], [[[1, 0, 11], 1]], [[[1, -2, 13], 1]], [[[1, -6, 17], 1]], [[[1, 2, 19], 1]], [[[1, -1], 1]], [[[1, -6, 29], 1]], [[[1, -4, 31], 1]], [[[1, -8, 37], 1]], [[[1, -6, 41], 1]], [[[1, 8, 43], 1]], [[[1, 12, 47], 1]], [[[1, 6, 53], 1]], [[[1, -6, 59], 1]], [[[1, 10, 61], 1]], [[[1, 8, 67], 1]], [[[1, -6, 71], 1]], [[[1, -2, 73], 1]], [[[1, -10, 79], 1]], [[[1, -12, 83], 1]], [[[1, -6, 89], 1]], [[[1, -8, 97], 1]], [[[1, 6, 101], 1]], [[[1, 8, 103], 1]], [[[1, -12, 107], 1]], [[[1, -2, 109], 1]], [[[1, 6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 36, 'label': '2-5520-1.1-c1-0-36', 'leading_term': '2.53254900379278885143402533107000000000000000000000000000000000000000000000000000000000000', '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/5520/2/a/o', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 17}, 'plot_values': [2.5325490037927887, 2.526054195235597, 2.5065403962626056, 2.4739247905842627, 2.4280866892388473, 2.3688923785185003, 2.296227699574949, 2.2100363921910433, 2.1103619708912498, 1.9973907944254627, 1.8714940215305351, 1.7332662873801281, 1.5835591531573665, 1.4235076450834547, 1.2545484848052055, 1.0784289040696124, 0.8972052244598235, 0.713230664954365, 0.5291321173520851, 0.34777590509076284, 0.17222281764991407, 0.005672992399971169, -0.1485985015786611, -0.28731423970279385, -0.4072737601296894, -0.5054379357885093, -0.5790164592241451, -0.6255562730138069, -0.6430285883132475, -0.6299119897171421, -0.5852690355370497, -0.5088137374869199, -0.4009673500616444, -0.2629000233845538, -0.0965560777352726, 0.09533905526474973, 0.30929181198257705, 0.541074538935222, 0.7857812252414416, 1.0379049779356322, 1.2914366706327818, 1.5399835422707213, 1.776905855107099, 1.9954690596772353, 2.189008280346939, 2.3511013505951506, 2.4757461145740542, 2.55753729257402, 2.5918379031466743, 2.5749400620067915, 2.5042099526564074, 2.378211897427536, 2.1968067573737384, 1.961220357197107, 1.6740782637563216, 1.3394040344878184, 0.9625789802422863, 0.5502625347694758, 0.11027346407379271, -0.3485666481490609, -0.8166249732807878, -1.2836801857847815, -1.7391713393808668, -2.1724667551669876, -2.5731458724701373, -2.93128625556531, -3.2377474027320847, -3.4844426989863337, -3.664590814314499, -3.772938091681413, -3.805944000979222, -3.7619225542767487, -3.6411336718753717, -3.4458198350730727, -3.1801849272985834, -2.8503139079173074, -2.464033831413715, -2.0307186604264458, -1.5610422602869474, -1.066685837775197, -0.560007828969832, -0.053685782737575016, 0.4396589362653606, 0.9078418457360988, 1.3394890807609627, 1.7243916247547224, 2.0538277512478817, 2.3208420898637883, 2.5204708646249956, 2.6499044014190307, 2.708579925093604, 2.698199910504202, 2.6226737466658308, 2.487983137151395, 2.3019744011570595, 2.074083559326281, 1.8150026840518663, 1.5362983633726768, 1.2499951727908976, 0.9681386806413315, 0.7023536524608085, 0.46341370627838124, 0.2608386609018815, 0.10253519157197873, -0.005504836502621058, -0.05943582030274447, -0.05770949456157757, -0.001138309139169246, 0.1071330010195309, 0.26174829191846755, 0.45535037028029135, 0.6788742820695299, 0.9219135334450203, 1.1731461005254666, 1.4208043673138608, 1.6531709682507607, 1.8590810091796428, 2.028410381065078, 2.152529920335249, 2.224706033223122, 2.2404300809597997, 2.1976612761622234, 2.096970992727579, 1.9415801347526518, 1.7372854087352885, 1.492274838030453, 1.2168374716214692, 0.9229767818913841, 0.6239415257428474, 0.33369167199596567, 0.06632019991923961, -0.1645460060445571, -0.346341428967461, -0.4681281134743084, -0.5211080801793959, -0.49905886925034165, -0.39867176047882397, -0.21977580381550435, 0.03456479578274408, 0.3580873264552083, 0.7415031081224421, 1.1728020137634263, 1.63767930599393, 2.1200696185572796, 2.6027679121624767, 3.0681129694383817, 3.4987056723296717, 3.8781320998527673, 4.191660523839258, 4.426881743279866, 4.5742639062142745, 4.627595984940695, 4.584298299588846, 4.445583773924695, 4.216459750936233, 3.9055669453100754, 3.5248591818893367, 3.0891346573541814, 2.6154362507678632, 2.1223445856913834, 1.6291928192902032, 1.1552362417126498, 0.7188124968102549, 0.33652942429953714, 0.02251708048724548, -0.21222160188355815, -0.3603307510722783, -0.41846649712916756, -0.3874877659515726, -0.2724612323887527, -0.082476890471538, 0.16972080830067668, 0.46827284506618194, 0.7948951249064286, 1.1296889262797918, 1.4520376083302966, 1.7415502832436338, 1.979010278234856, 2.1472852108816065, 2.2321564704422445, 2.223028834619074, 2.1134857618267766, 1.9016623991571349, 1.590416267945513, 1.187284591094361, 0.7042269093246987, 0.1571615563919298, -0.4346857360307965, -1.04959381625403, -1.6642834917907074, -2.254938752427747, -2.798265752505277, -3.2725410387745093, -3.6586003334002863, -3.940721306032718, -4.107358133661086, -4.1516920822492835, -4.0719705766709975, -3.8716168896894843, -3.559103234737541, -3.1475911927184064, -2.654354508470475, -2.1000098186654417, -1.5075902991121044, -0.9015050697651917, -0.30643306333672926, 0.253796367953809, 0.7572827714019363, 1.1850420356219122, 1.5218542401960136, 1.7569306738520944, 1.8843673559015635, 1.903362669509355, 1.8181881988663255, 1.6379139968987235, 1.3759016956992738, 1.0490904964777392, 0.6771115465945836, 0.2812749847710002, -0.11651945340903727, -0.4948932910625164, -0.8340653243083144, -1.1168380324293625, -1.3294439783024188, -1.462208777512747, -1.5099964957854075, -1.472414459533061, -1.353766877891696, -1.1627597459136454, -0.9119725534345815, -0.6171246793656266, -0.296175350288262, 0.0316949096426806, 0.34716681427693147, 0.6318705479613859, 0.8694207066972754, 1.0463414015090806, 1.1528304709008221, 1.1833200403608948, 1.136801348820892, 1.016894293830912, 0.8316558805980931, 0.5931359719932218, 0.3167026671432021, 0.02017252842342399, -0.2772079823644703, -0.555874737812119, -0.7970908598410634, -0.9840607133686708, -1.1029502092161156, -1.1437549337387396, -1.100965183443599, -0.9739874557354343, -0.7672948051437894, -0.49029305190359046, -0.1569053551579581, 0.21510670022547662], 'positive_zeros': ['0.986029338559047467037060225636708', '1.61806562620190443301969498989190', '2.73015648721643364351441045002462', '3.80189606860667529215445769859987', '4.87189977067826181898334026335157', '5.01626410668179427795341023016992', '6.10637523571841171749990073884685', '6.46308529675286474850330381553279', '7.69137159697916677212527046147359', '7.985258276404753820262702007380825'], 'prelabel': '2-5520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.639082912251269, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 82299248456024166, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.986029338559047467037060225637', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.61806562620190443301969498989', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.73015648721643364351441045002', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 44.0774219157468, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 5520, 'conductor_radical': 690, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, 4, 0, 1, 0, 0, 0, 2, 0, -1, 0, 6, 0, -2, 0, -4, 0, 1, 0, 1, 0, -1, 0, 6, 0, 4, 0, 0, 0, 4, 0, 8, 0, -2, 0, 6, 0, -8, 0, 1, 0, -12, 0, 9, 0, -6, 0, -6, 0, 0, 0, 2, 0, 6, 0, -10, 0, 4, 0, 2, 0, -8, 0, -1, 0, 6, 0, 2, 0, -1, 0, 0, 0, 10, 0, 1, 0, 12, 0, 6, 0, -6, 0, 6, 0, 8, 0, -4, 0, -2, 0, 8, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -4, 31], 'euler37': [1, -8, 37], 'euler41': [1, -6, 41], 'euler43': [1, 8, 43], 'euler47': [1, 12, 47], 'euler5': [1, -1, 0], 'euler53': [1, 6, 53], 'euler59': [1, -6, 59], 'euler61': [1, 10, 61], 'euler67': [1, 8, 67], 'euler7': [1, -4, 7], 'euler71': [1, -6, 71], 'euler73': [1, -2, 73], 'euler79': [1, -10, 79], 'euler83': [1, -12, 83], 'euler89': [1, -6, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -1, 0], [1, -4, 7], [1, 0, 11], [1, -2, 13], [1, -6, 17], [1, 2, 19], [1, -1, 0], [1, -6, 29], [1, -4, 31], [1, -8, 37], [1, -6, 41], [1, 8, 43], [1, 12, 47], [1, 6, 53], [1, -6, 59], [1, 10, 61], [1, 8, 67], [1, -6, 71], [1, -2, 73], [1, -10, 79], [1, -12, 83], [1, -6, 89], [1, -8, 97]], 'index': 36, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5520/o', 'ModularForm/GL2/Q/holomorphic/5520/2/a/o/1/1', 'ModularForm/GL2/Q/holomorphic/5520/2/a/o'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-5520-1.1-c1-0-36', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-5520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.639082912251269, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 82299248456024166, 'z1': {'__RealLiteral__': 0, 'data': '0.986029338559047467037060225637', 'prec': 100}}
  • lfunc_instances • Show schema
    • id: 22635
      {'Lhash': '82299248456024166', 'Lhash_array': ['82299248456024166'], 'factors': ['2-5520-1.1-c1-0-36'], 'label': '2-5520-1.1-c1-0-36', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5520/o'}
    • id: 21317732
      {'Lhash': '1249940682867020542815531156854', 'Lhash_array': ['1249940682867020542815531156854'], 'factors': ['2-5520-1.1-c1-0-36'], 'label': '2-5520-1.1-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5520/2/a/o'}
    • id: 24570671
      {'Lhash': '1249940682867020542815531156854', 'Lhash_array': ['1249940682867020542815531156854'], 'factors': ['2-5520-1.1-c1-0-36'], 'label': '2-5520-1.1-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5520/2/a/o/1/1'}