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lfunc_lfunctions • Show schema
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{'Lhash': '3245697415166988920707253707935', 'a10': [-1.2007681335206093, 0.7470983131565968], 'a2': [-1.377349573291197, -0.32079300639907604], 'a3': [-0.7206730443444755, -0.7206730443444755], 'a4': [1.7941836940908846, 0.8836882209571353], 'a5': [0.7071067811865476, -0.7071067811865476], 'a6': [0.7614318375842923, 1.2238055826363703], 'a7': [0.0, -4.028399707479458], 'a8': [-2.187737144341813, -1.7927091753173823], 'a9': [0.0, -1.961260726310531], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6388032161702434, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.377349573291197, 0.32079300639907604]]], [5, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 5], 'central_character': '80.61', 'coefficient_field': 'CDF', 'conductor': 80, 'conductor_radical': 10, 'conjugate': '1619989155313315280551110761910', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.377349573291197, 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0.9656687899432321*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.208175566425', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.56040380100212905166033433798', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.45035496836055385583681898823', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.22957795488557128833993290771', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6388032161702434, 'bad_primes': [2, 5], 'central_character': '16.13', 'conductor': 80, 'conductor_radical': 10, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/80/2/l/a/61/1'], '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': '2-80-16.13-c1-0-3', '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': '2-80-16.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.799251660098522, 'root_angle': 0.2081755664246875, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.56040380100212905166033433798', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3245697415166988920707253707935', 'Lhash_array': ['3245697415166988920707253707935'], 'factors': ['2-80-16.13-c1-0-3'], 'label': '2-80-16.13-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/80/2/l/a/61/1'}