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lfunc_lfunctions • Show schema
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{'Lhash': '9497204262492536187434059676', 'a10': [0.9787437697432335, 4.288156637811294], 'a2': [-0.6270901763578389, -1.3021661687873727], 'a3': [-1.7170622028598495, -0.3919082429247365], 'a4': [-0.05541503813241147, 0.0694882599281103], 'a5': [-2.966975892911518, -0.6771928862299423], 'a6': [0.5664231844032674, 2.48166211943938], 'a7': [-2.6285939328212935, -0.30082210080890986], 'a8': [-2.6928821846936883, -0.6146327859578249], 'a9': [0.09180393391030742, 0.04421044447788785], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.303936668947014, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [2.6285939328212935, 0.30082210080890986]]], [11, [[1.0, 0], [2.4897806175901533, 2.191116718997962]]]], 'bad_primes': [7, 11], 'central_character': '539.76', 'coefficient_field': 'CDF', 'conductor': 539, 'conductor_radical': 77, 'conjugate': '1174388688215941170165440028233', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'z1': {'__RealLiteral__': 0, 'data': '0.00749197315157871391298192145', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.01904394092017715593119365667', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.11310121398088226958227252234', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.303936668947014, 'bad_primes': [7, 11], 'central_character': '539.76', 'conductor': 539, 'conductor_radical': 77, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/539/2/p/a/76/16'], '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': '2-539-539.76-c1-0-0', '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': '2-539-539.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0745931333509744, 'root_angle': -0.0886667349428493, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.00749197315157871391298192145', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '9497204262492536187434059676', 'Lhash_array': ['9497204262492536187434059676'], 'label': '2-539-539.76-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/539/2/p/a/76/16'}