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lfunc_lfunctions • Show schema
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{'Lhash': '956516885542098735222313545512,2031909459818702180363121981443', 'a10': 0, 'a2': 0, 'a3': -20, 'a4': 0, 'a5': -250, 'a6': 0, 'a7': -1660, 'a8': 0, 'a9': 442, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9992.642984623664, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 250, 15625]]], 'bad_primes': [2, 5], 'central_character': '320.1', 'coefficient_field': '1.1.1.1', 'conductor': 102400, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1], [1, 20, -42, 43740, 4782969], [1, 250, 15625], [1, 1660, 1970190, 1367081380, 678223072849], [1, -3600, 5634742, -70153815600, 379749833583241], [1, 13180, 163072398, 827025454060, 3937376385699289], [1, -5460, -160982138, -2240449154580, 168377826559400929], [1, 40472, 2050920774, 36176777020808, 799006685782884121], [1, -41820, 7228954990, -142389800193540, 11592836324538749809], [1, 118668, 37435002574, 2047008321836412, 297558232675799463481], [1, 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'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c7e2-0', 'trace_hash': 1854362655300535289, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.75455877618792294764729260962', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.60289393579971851607442714322', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.70316916940780002485367871472', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 9992.642984623664, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 102400, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 0, -20, 0, -250, 0, -1660, 0, 442, 0, 3600, 0, -13180, 0, 5000, 0, 5460, 0, -40472, 0, 33200, 0, 41820, 0, 46875, 0, -53420, 0, -118668, 0, 115928, 0, -72000, 0, 415000, 0, -306940, 0, 263600, 0, -353148, 0, 1215340, 0, -110500, 0, 2068500, 0, 785410, 0, -109200, 0, -1400460, 0, -900000, 0, 809440, 0, -1992504, 0, 1678676, 0, -733720, 0, 3295000, 0, 3663940, 0, -836400, 0, -1794936, 0, 5062180, 0, -937500, 0, -5976000, 0, -10178224, 0, -2821205, 0, -7214100, 0, -1365000, 0, 2373360, 0, -15330828, 0, 21878800, 0, -2318560, 0, 10118000, 0, 14024020, 0, 1591200, 0], 'euler11': [1, -3600, 5634742, -70153815600, 379749833583241], 'euler13': [1, 13180, 163072398, 827025454060, 3937376385699289], 'euler17': [1, -5460, -160982138, -2240449154580, 168377826559400929], 'euler19': [1, 40472, 2050920774, 36176777020808, 799006685782884121], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -41820, 7228954990, -142389800193540, 11592836324538749809], 'euler29': [1, 118668, 37435002574, 2047008321836412, 297558232675799463481], 'euler3': [1, 20, -42, 43740, 4782969], 'euler31': [1, -115928, 13575043518, -3189482328660008, 756943935220796320321], 'euler37': [1, 306940, 120498758430, 29138390367203020, 9012061295995008299689], 'euler41': [1, 353148, 314020811638, 68777082312527388, 37929227194915558802161], 'euler43': [1, -1215340, 866800610214, -330352030822781380, 73885357344138503765449], 'euler47': [1, -2068500, 2082813588382, -1047949924677715500, 256666986187667409334369], 'euler5': [1, 250, 15625, 0, 0], 'euler53': [1, 1400460, 2025459025630, 1645135962896125020, 1379946262057143768386569], 'euler59': [1, 1992504, 5477605919542, 4958648038107796776, 6193386212891813387462761], 'euler61': [1, -1678676, 900787415886, -5275646973000388196, 9876832533361318095112441], 'euler67': [1, -3663940, 12525094986870, -22206083679207152620, 36732225162896895721934329], 'euler7': [1, 1660, 1970190, 1367081380, 678223072849], 'euler71': [1, 1794936, 17428289847406, 16325158596621707976, 82721210695570328927708881], 'euler73': [1, -5062180, 19516555685238, -55923919835402451460, 122045014039746588673695409], 'euler79': [1, 10178224, 57668559431262, 195461687336739201616, 368790120348678391253573281], 'euler83': [1, 7214100, 67277011758070, 195762185444268140700, 736365263311636486061599129], 'euler89': [1, 15330828, 138366637288054, 678102987493753068012, 1956410986640441413344189841], 'euler97': [1, -14024020, 210744479822310, -1133116757486746274260, 6528362774606076144776040769], 'euler_factors': [[1, 0, 0, 0, 0], [1, 20, -42, 43740, 4782969], [1, 250, 15625, 0, 0], [1, 1660, 1970190, 1367081380, 678223072849], [1, -3600, 5634742, -70153815600, 379749833583241], [1, 13180, 163072398, 827025454060, 3937376385699289], [1, -5460, -160982138, -2240449154580, 168377826559400929], [1, 40472, 2050920774, 36176777020808, 799006685782884121], [1, -41820, 7228954990, -142389800193540, 11592836324538749809], [1, 118668, 37435002574, 2047008321836412, 297558232675799463481], [1, -115928, 13575043518, -3189482328660008, 756943935220796320321], [1, 306940, 120498758430, 29138390367203020, 9012061295995008299689], [1, 353148, 314020811638, 68777082312527388, 37929227194915558802161], [1, -1215340, 866800610214, -330352030822781380, 73885357344138503765449], [1, -2068500, 2082813588382, -1047949924677715500, 256666986187667409334369], [1, 1400460, 2025459025630, 1645135962896125020, 1379946262057143768386569], [1, 1992504, 5477605919542, 4958648038107796776, 6193386212891813387462761], [1, -1678676, 900787415886, -5275646973000388196, 9876832533361318095112441], [1, -3663940, 12525094986870, -22206083679207152620, 36732225162896895721934329], [1, 1794936, 17428289847406, 16325158596621707976, 82721210695570328927708881], [1, -5062180, 19516555685238, -55923919835402451460, 122045014039746588673695409], [1, 10178224, 57668559431262, 195461687336739201616, 368790120348678391253573281], [1, 7214100, 67277011758070, 195762185444268140700, 736365263311636486061599129], [1, 15330828, 138366637288054, 678102987493753068012, 1956410986640441413344189841], [1, -14024020, 210744479822310, -1133116757486746274260, 6528362774606076144776040769]], 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/320/8/a/k'], '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': '4-320e2-1.1-c7e2-0-14', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7, 7], 'order_of_vanishing': 2, 'prelabel': '4-320e2-1.1-c7e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.998160238509833, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7e2-0', 'trace_hash': 1854362655300535289, 'z1': {'__RealLiteral__': 0, 'data': '0.75455877618792294764729260962', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '956516885542098735222313545512,2031909459818702180363121981443', 'Lhash_array': ['956516885542098735222313545512', '2031909459818702180363121981443'], 'label': '4-320e2-1.1-c7e2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/320/8/a/k'}