Formats: - HTML - YAML - JSON - 2026-09-22T01:37:30.688157
  • lfunc_lfunctions • Show schema
    {'Lhash': '1141833258146110535446119162121,1385429578154622826862633695044', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 428.3750897471616, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '2592.1', 'coefficient_field': '1.1.1.1', 'conductor': 6718464, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, -2, 11, -10, 25], [1, -2, 9, -14, 49], [1, -2, 17, -22, 121], [1, -2, 3, -26, 169], [1, 0, 10, 0, 289], [1, -8, 54, -152, 361], [1, -6, 49, -138, 529], [1, 10, 59, 290, 841], [1, -10, 81, -310, 961], [1, -8, 66, -296, 1369], [1, -14, 107, -574, 1681], [1, -10, 57, -430, 1849], [1, 2, 41, 94, 2209], [1, 8, 98, 424, 2809], [1, 14, 113, 826, 3481], [1, 6, 107, 366, 3721], [1, -10, 105, -670, 4489], [1, -4, 50, -284, 5041], [1, 0, 122, 0, 5329], [1, -22, 273, -1738, 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'5.04984282601921882511924223682406', '5.78577968604400000709266472502821', '5.85990200018754436615653833668976', '6.46165624599156787413553147634793', '6.47709954133768473051567214354154', '7.48079566639795081378120836512640', '7.54650527861848958411075158353095', '7.899487035547687580181805581580819', '8.081242119322877812522405451933370', '8.929051590057102625231748723119603', '9.241744644109786550504293156999048'], 'prelabel': '4-2592e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.549420205247685, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 941978673605929985, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.900747617632598009084088353306', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.09291123114302028547127821993', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.98753436473148648330870904532', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 428.3750897471616, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 6718464, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 8, 0, 0, 0, 6, 0, -7, 0, 0, 0, -10, 0, 10, 0, 0, 0, 4, 0, 8, 0, 0, 0, 14, 0, 10, 0, 0, 0, -2, 0, -5, 0, 0, 0, -8, 0, 4, 0, 0, 0, -14, 0, -6, 0, 0, 0, 4, 0, 10, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 22, 0, 0, 0, 6, 0, 0, 0, 0, 0, 16, 0, 4, 0, 0, 0, 16, 0, 2, 0, 0, 0], 'euler11': [1, -2, 17, -22, 121], 'euler13': [1, -2, 3, -26, 169], 'euler17': [1, 0, 10, 0, 289], 'euler19': [1, -8, 54, -152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -6, 49, -138, 529], 'euler29': [1, 10, 59, 290, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -10, 81, -310, 961], 'euler37': [1, -8, 66, -296, 1369], 'euler41': [1, -14, 107, -574, 1681], 'euler43': [1, -10, 57, -430, 1849], 'euler47': [1, 2, 41, 94, 2209], 'euler5': [1, -2, 11, -10, 25], 'euler53': [1, 8, 98, 424, 2809], 'euler59': [1, 14, 113, 826, 3481], 'euler61': [1, 6, 107, 366, 3721], 'euler67': [1, -10, 105, -670, 4489], 'euler7': [1, -2, 9, -14, 49], 'euler71': [1, -4, 50, -284, 5041], 'euler73': [1, 0, 122, 0, 5329], 'euler79': [1, -22, 273, -1738, 6241], 'euler83': [1, -6, 169, -498, 6889], 'euler89': [1, -16, 218, -1424, 7921], 'euler97': [1, -2, 171, -194, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -2, 11, -10, 25], [1, -2, 9, -14, 49], [1, -2, 17, -22, 121], [1, -2, 3, -26, 169], [1, 0, 10, 0, 289], [1, -8, 54, -152, 361], [1, -6, 49, -138, 529], [1, 10, 59, 290, 841], [1, -10, 81, -310, 961], [1, -8, 66, -296, 1369], [1, -14, 107, -574, 1681], [1, -10, 57, -430, 1849], [1, 2, 41, 94, 2209], [1, 8, 98, 424, 2809], [1, 14, 113, 826, 3481], [1, 6, 107, 366, 3721], [1, -10, 105, -670, 4489], [1, -4, 50, -284, 5041], [1, 0, 122, 0, 5329], [1, -22, 273, -1738, 6241], [1, -6, 169, -498, 6889], [1, -16, 218, -1424, 7921], [1, -2, 171, -194, 9409]], 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2592/2/a/s'], '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': '4-2592e2-1.1-c1e2-0-29', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-2592e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.549420205247685, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 941978673605929985, 'z1': {'__RealLiteral__': 0, 'data': '0.900747617632598009084088353306', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1141833258146110535446119162121,1385429578154622826862633695044', 'Lhash_array': ['1141833258146110535446119162121', '1385429578154622826862633695044'], 'factors': ['2-2592-1.1-c1-0-12', '2-2592-1.1-c1-0-19'], 'label': '4-2592e2-1.1-c1e2-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2592/2/a/s'}