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lfunc_lfunctions • Show schema
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{'Lhash': '1436093719340867909212199111508,2013950676570350897402602949606', 'a10': 0, 'a2': 0, 'a3': -54, 'a4': 0, 'a5': 28, 'a6': 0, 'a7': -936, 'a8': 0, 'a9': 2187, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3597.351474464519, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 54, 729]]], 'bad_primes': [2, 3], 'central_character': '192.1', 'coefficient_field': '1.1.1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, 54, 729], [1, -28, 32030, -2187500, 6103515625], [1, 936, 1188734, 770836248, 678223072849], [1, 3384, 12585622, 65944586664, 379749833583241], [1, -17076, 174008942, -1071493676292, 3937376385699289], [1, 18668, 763976006, 7660202347564, 168377826559400929], [1, -44856, 2237619206, -40095510724584, 799006685782884121], [1, 43488, 1865158606, 148069049039136, 11592836324538749809], [1, -19484, 563275118, -336096590004556, 297558232675799463481], [1, 332856, 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7.7445416192923515, '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': 1003075157674346414, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13287819142144672799856266170', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.58872695378975618013156499611', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.64388946919992546141170401693', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 3597.351474464519, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, -54, 0, 28, 0, -936, 0, 2187, 0, -3384, 0, 17076, 0, -1512, 0, -18668, 0, 44856, 0, 50544, 0, -43488, 0, -31246, 0, -78732, 0, 19484, 0, -332856, 0, 182736, 0, -26208, 0, 9076, 0, -922104, 0, 491780, 0, 510984, 0, 61236, 0, -1781424, 0, -312638, 0, 1008072, 0, 1395692, 0, -94752, 0, -2422224, 0, 1534104, 0, -1592188, 0, -2047032, 0, 478128, 0, -1169496, 0, 2348352, 0, -5716800, 0, 1180884, 0, 1687284, 0, 3167424, 0, -6538104, 0, 2657205, 0, -16805160, 0, -522704, 0, -1052136, 0, -6118924, 0, -15983136, 0, 17974224, 0, 1255968, 0, 23720868, 0, -7400808, 0], 'euler11': [1, 3384, 12585622, 65944586664, 379749833583241], 'euler13': [1, -17076, 174008942, -1071493676292, 3937376385699289], 'euler17': [1, 18668, 763976006, 7660202347564, 168377826559400929], 'euler19': [1, -44856, 2237619206, 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-1041831063514, 7087977979578827208, 36732225162896895721934329], 'euler7': [1, 936, 1188734, 770836248, 678223072849], 'euler71': [1, 5716800, 23877712415086, 51994982921489668800, 82721210695570328927708881], 'euler73': [1, -1180884, 15089768314454, -13045696152825341748, 122045014039746588673695409], 'euler79': [1, 6538104, 48301289191022, 125557154158042102536, 368790120348678391253573281], 'euler83': [1, 16805160, 122017660191238, 456025678648840075320, 736365263311636486061599129], 'euler89': [1, 6118924, 91061417808758, 270648176644289890796, 1956410986640441413344189841], 'euler97': [1, -23720868, 287915376622982, -1916605440731767362084, 6528362774606076144776040769], 'euler_factors': [[1, 0, 0, 0, 0], [1, 54, 729, 0, 0], [1, -28, 32030, -2187500, 6103515625], [1, 936, 1188734, 770836248, 678223072849], [1, 3384, 12585622, 65944586664, 379749833583241], [1, -17076, 174008942, -1071493676292, 3937376385699289], [1, 18668, 763976006, 7660202347564, 168377826559400929], [1, -44856, 2237619206, -40095510724584, 799006685782884121], [1, 43488, 1865158606, 148069049039136, 11592836324538749809], [1, -19484, 563275118, -336096590004556, 297558232675799463481], [1, 332856, 60250867406, 9157738682531016, 756943935220796320321], [1, -9076, 83660952894, -861601716859108, 9012061295995008299689], [1, -491780, 442441281206, -95776256809198180, 37929227194915558802161], [1, -510984, 247939713878, -138894961177899288, 73885357344138503765449], [1, 1781424, 1786374389470, 902510585747679312, 256666986187667409334369], [1, -1395692, 2682288635486, -1639534940181382204, 1379946262057143768386569], [1, -1534104, 5559576794038, -3817850197466767176, 6193386212891813387462761], [1, 1592188, 6774132506478, 5003837430598603948, 9876832533361318095112441], [1, 1169496, -1041831063514, 7087977979578827208, 36732225162896895721934329], [1, 5716800, 23877712415086, 51994982921489668800, 82721210695570328927708881], [1, -1180884, 15089768314454, -13045696152825341748, 122045014039746588673695409], [1, 6538104, 48301289191022, 125557154158042102536, 368790120348678391253573281], [1, 16805160, 122017660191238, 456025678648840075320, 736365263311636486061599129], [1, 6118924, 91061417808758, 270648176644289890796, 1956410986640441413344189841], [1, -23720868, 287915376622982, -1916605440731767362084, 6528362774606076144776040769]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/8/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': '4-192e2-1.1-c7e2-0-4', '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': '4-192e2-1.1-c7e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.7445416192923515, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7e2-0', 'trace_hash': 1003075157674346414, 'z1': {'__RealLiteral__': 0, 'data': '1.13287819142144672799856266170', 'prec': 103}}
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{'Lhash': '1436093719340867909212199111508,2013950676570350897402602949606', 'Lhash_array': ['1436093719340867909212199111508', '2013950676570350897402602949606'], 'label': '4-192e2-1.1-c7e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/8/a/s'}