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lfunc_lfunctions • Show schema
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{'Lhash': '1184608058799577228318094109630', 'a10': [-3.1321743943335205, 0.4352970979474192], 'a2': [-1.2752318231989315, -0.6113786037315414], 'a3': [1.2224037703668815, 0.0], 'a4': [1.2524324057985419, 1.559298903002781], 'a5': [1.8640585657557296, -1.2350245598500025], 'a6': [-1.5588481887702064, -0.7473515103230758], 'a7': [0.0, 2.992296765042552], 'a8': [-0.6438196741619342, -2.754177958513578], 'a9': [-1.5057290221928323, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.547732965744995, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.2752318231989315, 0.6113786037315414]]], [5, [[1.0, 0], [-1.8640585657557296, 1.2350245598500025]]], [41, [[1.0, 0], [2.832005002238424, 5.742799636701297]]]], 'bad_primes': [2, 5, 41], 'central_character': '820.647', 'coefficient_field': 'CDF', 'conductor': 820, 'conductor_radical': 410, 'conjugate': '1935416113107144086224976373697', 'degree': 2, 'euler_factors': 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'root_angle': -0.05815316945741472, 'root_number': '0.9339855018517134 - 0.3573109042987676*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0581531694574', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.934490985596740071728981020137', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.50193213195145484479976243969', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33155427235586771523554991066', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.547732965744995, 'bad_primes': [2, 5, 41], 'central_character': '820.647', 'conductor': 820, 'conductor_radical': 410, 'degree': 2, 'index': 46, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/820/2/s/c/647/19'], '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': '2-820-820.647-c1-0-46', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-820-820.647-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.558853838292644, 'root_angle': -0.05815316945741472, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.934490985596740071728981020137', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1184608058799577228318094109630', 'Lhash_array': ['1184608058799577228318094109630'], 'factors': ['2-820-820.647-c1-0-46'], 'label': '2-820-820.647-c1-0-46', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/820/2/s/c/647/19'}