Formats: - HTML - YAML - JSON - 2026-10-17T04:18:27.318064
  • lfunc_lfunctions • Show schema
    {'Lhash': '1450554369085562704088684894555', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -1.4063382026438505], 'a4': [0, 0], 'a5': [0, 0.422133023365285], 'a6': [0, 0], 'a7': [4.722048203394063, 0], 'a8': [0, 0], 'a9': [1.022212859784464, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.574213792682123, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 13], 'central_character': '3328.1665', 'coefficient_field': 'CDF', 'conductor': 3328, 'conductor_radical': 26, 'conjugate': '1200153224001469039713645287359', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.4063382026438505], [-3.0, 0]], [[1.0, 0], [0, -0.422133023365285], [-5.0, 0]], [[1.0, 0], [-4.722048203394063, 0], [7.0, 0]], [[1.0, 0], [0, -3.7156301643310337], [-11.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [-2.390543381922416, 0], [17.0, 0]], [[1.0, 0], [0, 8.159976047480782], [-19.0, 0]], [[1.0, 0], [7.875606211811816, 0], [23.0, 0]], [[1.0, 0], [0, 5.875606211811816], [-29.0, 0]], [[1.0, 0], [0.5283065696187349, 0], [31.0, 0]], [[1.0, 0], [0, 1.2095364544967628], [-37.0, 0]], [[1.0, 0], [9.031340165081247, 0], [41.0, 0]], [[1.0, 0], [0, -2.1937416337753284], [-43.0, 0]], [[1.0, 0], [-11.134804445100944, 0], [47.0, 0]], [[1.0, 0], [0, -5.031340165081247], [-53.0, 0]], [[1.0, 0], [0, -3.7156301643310337], [-59.0, 0]], [[1.0, 0], [0, -14.656692975656648], [-61.0, 0]], [[1.0, 0], [0, 6.471443954019643], [-67.0, 0]], [[1.0, 0], [-9.34063212676843, 0], [71.0, 0]], [[1.0, 0], [-16.507026213312244, 0], [73.0, 0]], [[1.0, 0], [-11.431260328662068, 0], [79.0, 0]], [[1.0, 0], [0, 6.083960686468986], [-83.0, 0]], [[1.0, 0], [8.631420001500425, 0], [89.0, 0]], [[1.0, 0], [0.755813789688609, 0], [97.0, 0]], [[1.0, 0], [0, 1.2189132361551678], [-101.0, 0]], [[1.0, 0], [-3.200159672838358, 0], [103.0, 0]], [[1.0, 0], [0, 15.50095902238722], [-107.0, 0]], [[1.0, 0], [0, -7.634729592233807], [-109.0, 0]], [[1.0, 0], [10.256772812075829, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 60, 'label': '2-3328-8.5-c1-0-60', 'leading_term': '2.561125428541561579992715663499741433185993989547336116', '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/3328/2/b/bc/1665/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [2.5611254285415614, 2.603006311635222, 2.633479922756223, 2.6520541233813604, 2.6580929259835306, 2.6508368501370114, 2.6294357349669806, 2.5929922010674935, 2.540613474788244, 2.4714690219392628, 2.3848513628496715, 2.280237511898842, 2.157348650906895, 2.0162058607216644, 1.8571799643886515, 1.681033758012063, 1.4889551143176738, 1.2825796412513781, 1.0640017718599752, 0.8357733628360731, 0.6008890978859177, 0.36275823690686937, 0.12516252821866042, -0.10779958930798074, -0.3317820260301388, -0.542272486800694, -0.7346850980292305, -0.9044625968241263, -1.0471860700885691, -1.1586898564737491, -1.235178881386673, -1.2733454000371216, -1.2704818908480142, -1.2245866857401375, -1.134458857762163, -0.9997789212329609, -0.8211720434224522, -0.6002507251810538, -0.33963428266585005, -0.042942951321380415, 0.2852349697139678, 0.6394038201884915, 1.01324923882999, 1.3997540512259834, 1.7913397751098508, 2.1800312379171713, 2.557640921619488, 2.9159688157394443, 3.2470128028538494, 3.5431839533639184, 3.797520598061139, 4.003894705673249, 4.157203941967732, 4.253542845966666, 4.290346840158099, 4.266503301020425, 4.1824246516656975, 4.04007938960301, 3.8429781106123055, 3.5961129070938322, 3.30584997050595, 2.97977676974439, 2.626506761380684, 2.255446159513933, 1.8765287953629082, 1.4999264711684788, 1.1357434019376695, 0.7937042876694999, 0.48284621907618985, 0.2112249503129693, -0.014353958426189653, -0.18856903695524724, -0.30777254665885817, -0.37012775172069257, -0.37568723726668224, -0.32640754245366105, -0.22609749233750845, -0.08029992716803673, 0.10389103600944187, 0.3180726037173475, 0.552828750306963, 0.7980692303350937, 1.0434008756088735, 1.2785182267015853, 1.4935993052749141, 1.679691583395061, 1.8290730033476033, 1.9355732813699085, 1.9948417048202196, 2.004549194854199, 1.9645145217036155, 1.876747168963879, 1.7454023655632824, 1.5766471369125057, 1.3784397497601617, 1.1602285042216673, 0.9325793179423315, 0.7067448044788548, 0.4941904262305347, 0.30609566574030533, 0.15284988684097905, 0.04356354856338663, -0.014384384414075083, -0.015742664570949284, 0.042291014640778134, 0.15984004998302823, 0.33422331893969803, 0.5599432053921288, 0.8287921630640991, 1.13007796262222, 1.4509628131397196, 1.776906596834306, 2.092199718277846, 2.3805667564554, 2.6258184218427982, 2.8125264444636677, 2.9266941088586425, 2.956394328928472, 2.892347498364694, 2.7284128919609474, 2.4619701095753754, 2.0941708755813067, 1.6300463085586607, 1.0784603868761498, 0.4519065413312985, -0.23384914290515282, -0.9602680101805143, -1.7066656927971322, -2.450943331467029, -3.1703956265197335, -3.8425641049668426, -4.446101155470153, -4.961608967880389, -5.372417625568527, -5.665268281483574, -5.830870577451689, -5.864308144454342, -5.765271984132722, -5.538108549183067, -5.191677127524927, -4.739019362526972, -4.196852048782249, -3.5849023544971415, -2.92511196400139, -2.2407429531934966, -1.5554231896479551, -0.8921724232589866, -0.27245180540178787, 0.2847207740268955, 0.7635494436152421, 1.152097308309079, 1.442751653358803, 1.6324948846327598, 1.7229673325688628, 1.7203174958739849, 1.634845132860042, 1.4804523645059517, 1.2739271671796888, 1.0340918518536453, 0.7808559346547103, 0.5342178427761153, 0.3132628893958628, 0.1352057036868178, 0.014523734611951916, -0.03777541076519079, -0.01471603949741339, 0.08628299810209256, 0.26326453108561093, 0.5098169994147748, 0.815383795471548, 1.1657844996934146, 1.5439237758992326, 1.9306540181562497, 2.305749718235645, 2.6489453895797235, 2.940985087707646, 3.1646303442205563, 3.3055747919297187, 3.353217877060242, 3.3012566689364338, 3.148063594039057, 2.896828525915585, 2.555455539860764, 2.1362171993534496, 1.655181839837069, 1.1314412989295517, 0.5861772733966926, 0.04161337750678369, -0.48009346551207566, -0.9579648345606322, -1.3732575029987442, -1.7104089082267497, -1.9578205232772614, -2.1084362707097957, -2.1600835432051375, -2.115556712885748, -1.9824365951814709, -1.7726534745461864, -1.5018152453186546, -1.1883352133301763, -0.8524054203394439, -0.5148703479845105, -0.19606199771658345, 0.08533976006922711, 0.31335823959857306, 0.4756231284065352, 0.564073941728609, 0.5754222639970767, 0.5113441649778832, 0.37838885431890773, 0.18760534497614234, -0.04609522036502364, -0.3048087468178762, -0.5686924229130553, -0.8171463144721488, -1.0300563998516288, -1.1890284724729183, -1.2785415740360164, -1.286952877545318, -1.2072931136813965, -1.0378024047922052, -0.7821702056895677, -0.4494592326368046, -0.05371092594738733, 0.3867518310900166, 0.8502913429724238, 1.3131415366219217, 1.750750971685648, 2.1392088163477587, 2.45667375924511, 2.684723823220656, 2.809547666884686, 2.8229051573881185, 2.7227964627741374, 2.5137940850384037, 2.2070103521314293, 1.8196929411493785, 1.3744619157436035, 0.8982223555652168, 0.42080575458976716, -0.026590150761273326, -0.41308058671564735, -0.709800982498048, -0.891547772819463, -0.9382600966128468, -0.8362568152070601, -0.5791553404679497, -0.16841521361045275, 0.386530650279296, 1.0685717159940649, 1.853633614852075, 2.71177749148423, 3.6086303996242117, 4.507072952136021, 5.369095050233674, 6.157719981979009, 6.838892167607567], 'positive_zeros': ['1.14428563266913065714111824809808', '1.98738259066472749569406486464952', '3.55108743279336654173889089440229', '3.93347679378604215658125091056248', '5.16159006767093336425905060942516', '5.25051201461806897086922457190872', '6.33074527572323264144617288238052', '7.48886903518177157274799787980776', '8.286353250021058783444351219142256', '8.389553443702200149183290275819414'], 'prelabel': '2-3328-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.15501831157583, 'root_angle': 0.125, 'root_number': '0.70710678118654752440084436210484903928483593768847403659 + 0.70710678118654752440084436210484903928483593768847403659*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14428563266913065714111824810', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.98738259066472749569406486465', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.55108743279336654173889089440', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 26.574213792682123, 'bad_primes': [2, 13], 'central_character': '8.5', 'conductor': 3328, 'conductor_radical': 26, 'degree': 2, 'index': 60, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3328/2/b/bc/1665/3'], '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': '2-3328-8.5-c1-0-60', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-3328-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.15501831157583, 'root_angle': 0.125, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14428563266913065714111824810', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1450554369085562704088684894555', 'Lhash_array': ['1450554369085562704088684894555'], 'factors': ['2-3328-8.5-c1-0-60'], 'label': '2-3328-8.5-c1-0-60', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3328/2/b/bc/1665/3'}