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  • lfunc_lfunctions • Show schema
    {'Lhash': '1340829976299259112702411655752,1865946947223148067040531119348', 'a10': 0, 'a2': 0, 'a3': 54, 'a4': 0, 'a5': -264, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 2187, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33739.222227301994, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 7}, 'bad_lfactors': [[2, [1]], [3, [1, -54, 729]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '588.1', 'coefficient_field': '1.1.1.1', 'conductor': 345744, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1], [1, -54, 729], [1, 264, 42310, 20625000, 6103515625], [1], [1, 4980, 38737606, 97046111580, 379749833583241], [1, -10148, 75576846, -636771950516, 3937376385699289], [1, 17832, 345159502, 7317159216936, 168377826559400929], [1, 6256, 1754965926, 5592061599184, 799006685782884121], [1, -14052, 6233591566, -47844607181244, 11592836324538749809], [1, -243588, 49005121054, -4201862870356692, 297558232675799463481], [1, 470824, 110401476030, 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'6.39626558153849916078332449176616', '6.76758102189906083857653811948503', '7.35972993514765062641935221386358', '7.56885668382840854627352854005874', '8.114020566985749368065014144628483', '8.646411207577870492610944207757982', '8.798662546833700358922201995876184', '8.934971898332537283404370285010869'], 'prelabel': '4-588e2-1.1-c7e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 13.552947833761616, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c7e2-0', 'trace_hash': 1585581996519158283, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05772834885090134828798593353', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.47197259788083612472288540204', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.29047745092843433565209089328', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 33739.222227301994, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 345744, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 54, 0, -264, 0, 0, 0, 2187, 0, -4980, 0, 10148, 0, -14256, 0, -17832, 0, -6256, 0, 0, 0, 14052, 0, 27386, 0, 78732, 0, 243588, 0, -470824, 0, -268920, 0, 0, 0, 311116, 0, 547992, 0, -919248, 0, -112616, 0, -577368, 0, 102456, 0, 0, 0, -962928, 0, 2720028, 0, 1314720, 0, -337824, 0, 19008, 0, 925148, 0, 0, 0, -2679072, 0, -2053424, 0, 758808, 0, -869508, 0, -3505228, 0, 1478844, 0, 0, 0, -6640856, 0, 2657205, 0, -7856760, 0, 4707648, 0, 13153752, 0, 9330384, 0, 0, 0, -25424496, 0, 1651584, 0, 2220212, 0, -10891260, 0], 'euler11': [1, 4980, 38737606, 97046111580, 379749833583241], 'euler13': [1, -10148, 75576846, -636771950516, 3937376385699289], 'euler17': [1, 17832, 345159502, 7317159216936, 168377826559400929], 'euler19': [1, 6256, 1754965926, 5592061599184, 799006685782884121], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -14052, 6233591566, -47844607181244, 11592836324538749809], 'euler29': [1, -243588, 49005121054, -4201862870356692, 297558232675799463481], 'euler3': [1, -54, 729, 0, 0], 'euler31': [1, 470824, 110401476030, 12953599026197464, 756943935220796320321], 'euler37': [1, -311116, 134140188030, -29534825886110428, 9012061295995008299689], 'euler41': [1, 919248, 579002453902, 179027476756561488, 37929227194915558802161], 'euler43': [1, 112616, 296638211478, 30611124708425912, 73885357344138503765449], 'euler47': [1, -102456, 463813338910, -51906578430157128, 256666986187667409334369], 'euler5': [1, 264, 42310, 20625000, 6103515625], 'euler53': [1, -2720028, 3726830950846, -3195247192268555436, 1379946262057143768386569], 'euler59': [1, -19008, -1663332768746, -47304287423439552, 6193386212891813387462761], 'euler61': [1, -925148, 2505443574174, -2907502249259156108, 9876832533361318095112441], 'euler67': [1, 2053424, 3053533142214, 12445210667448775952, 36732225162896895721934329], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 869508, 14567098422382, 7908279738682241628, 82721210695570328927708881], 'euler73': [1, 3505228, 11289516695814, 38723650616297339116, 122045014039746588673695409], 'euler79': [1, 6640856, 37612376152158, 127530394214187912104, 368790120348678391253573281], 'euler83': [1, 7856760, 50010766932550, 213201439973261828520, 736365263311636486061599129], 'euler89': [1, -9330384, 109971781045486, -412695339407885453136, 1956410986640441413344189841], 'euler97': [1, -2220212, 72228119801046, -179389320777720219956, 6528362774606076144776040769], 'euler_factors': [[1, 0, 0, 0, 0], [1, -54, 729, 0, 0], [1, 264, 42310, 20625000, 6103515625], [1, 0, 0, 0, 0], [1, 4980, 38737606, 97046111580, 379749833583241], [1, -10148, 75576846, -636771950516, 3937376385699289], [1, 17832, 345159502, 7317159216936, 168377826559400929], [1, 6256, 1754965926, 5592061599184, 799006685782884121], [1, -14052, 6233591566, -47844607181244, 11592836324538749809], [1, -243588, 49005121054, -4201862870356692, 297558232675799463481], [1, 470824, 110401476030, 12953599026197464, 756943935220796320321], [1, -311116, 134140188030, -29534825886110428, 9012061295995008299689], [1, 919248, 579002453902, 179027476756561488, 37929227194915558802161], [1, 112616, 296638211478, 30611124708425912, 73885357344138503765449], [1, -102456, 463813338910, -51906578430157128, 256666986187667409334369], [1, -2720028, 3726830950846, -3195247192268555436, 1379946262057143768386569], [1, -19008, -1663332768746, -47304287423439552, 6193386212891813387462761], [1, -925148, 2505443574174, -2907502249259156108, 9876832533361318095112441], [1, 2053424, 3053533142214, 12445210667448775952, 36732225162896895721934329], [1, 869508, 14567098422382, 7908279738682241628, 82721210695570328927708881], [1, 3505228, 11289516695814, 38723650616297339116, 122045014039746588673695409], [1, 6640856, 37612376152158, 127530394214187912104, 368790120348678391253573281], [1, 7856760, 50010766932550, 213201439973261828520, 736365263311636486061599129], [1, -9330384, 109971781045486, -412695339407885453136, 1956410986640441413344189841], [1, -2220212, 72228119801046, -179389320777720219956, 6528362774606076144776040769]], 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/588/8/a/f'], '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': '4-588e2-1.1-c7e2-0-10', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [7, 7], 'order_of_vanishing': 2, 'prelabel': '4-588e2-1.1-c7e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 13.552947833761616, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7e2-0', 'trace_hash': 1585581996519158283, 'z1': {'__RealLiteral__': 0, 'data': '1.05772834885090134828798593353', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1340829976299259112702411655752,1865946947223148067040531119348', 'Lhash_array': ['1340829976299259112702411655752', '1865946947223148067040531119348'], 'factors': ['2-588-1.1-c7-0-29', '2-588-1.1-c7-0-44'], 'label': '4-588e2-1.1-c7e2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/588/8/a/f'}