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lfunc_lfunctions • Show schema
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{'Lhash': '1755939154752927491552664968766', 'a10': [338.088553547813, 0.0], 'a2': [4.0, 0.0], 'a3': [26.36534782544763, 0.0], 'a4': [16.0, 0.0], 'a5': [84.52213838695324, 0.0], 'a6': [105.46139130179051, 0.0], 'a7': [15.260729860354505, 0.0], 'a8': [64.0, 0.0], 'a9': [452.1315659568359, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 115.79711790497204, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-4.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 19], 'central_character': '722.1', 'coefficient_field': 'CDF', 'conductor': 722, 'conductor_radical': 38, 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.0, 0]], [[1.0, 0], [-26.36534782544763, 0], [243.0, 0]], [[1.0, 0], [-84.52213838695324, 0], [3125.0, 0]], [[1.0, 0], [-15.260729860354505, 0], [16807.0, 0]], [[1.0, 0], [450.39719649699936, 0], [161051.0, 0]], [[1.0, 0], [-802.4485647108808, 0], [371293.0, 0]], [[1.0, 0], [1330.2775508601208, 0], 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-0.43157967886018306], 'positive_zeros': ['1.38519175113141271517070428527501', '2.28980472269412897695903782304652', '2.85069774268311497839523909227424', '3.97005799032390088207366239480459', '5.07270450564248158859353218080666', '6.08319327362038267403582419854892', '6.95823405770191628138086417266422', '8.096412785351007402345333202402212', '8.762223308045937914511505529997883', '9.531718979086245754924374271996104'], 'prelabel': '2-722-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.760906927623342, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38519175113141271517070428528', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28980472269412897695903782305', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.85069774268311497839523909227', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 115.79711790497204, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 722, 'conductor_radical': 38, 'degree': 2, 'index': 107, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/722/6/a/r/1/15'], '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': '2-722-1.1-c5-0-107', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-722-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.760906927623342, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38519175113141271517070428528', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1755939154752927491552664968766', 'Lhash_array': ['1755939154752927491552664968766'], 'label': '2-722-1.1-c5-0-107', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/722/6/a/r/1/15'}