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lfunc_lfunctions • Show schema
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{'Lhash': '2203631716965818741512276781852', 'a10': [-2.488217737135709, -0.3270091875545813], 'a2': [-0.34682012733516715, 1.067402596260469], 'a3': [-0.8090169943749475, -0.5877852522924731], 'a4': [0.5989698869710867, 0.43517709587905856], 'a5': [0.40798688134603406, 2.198532852756478], 'a6': [0.9079868813460341, -0.6596910841688512], 'a7': [1.1137344694780558, 0.0], 'a8': [-2.488217737135709, 1.8077960049663566], 'a9': [0.30901699437494745, 0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5988780151596031, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]], [5, [[1.0, 0], [-0.40798688134603406, -2.198532852756478]]]], 'bad_primes': [3, 5], 'central_character': '75.46', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '3725757350614743924167815859619', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.34682012733516715, 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.73835891101938825072449857934', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.27783528232799575203852884513', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.66615835151269864645800604719', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5988780151596031, 'bad_primes': [3, 5], 'central_character': '25.21', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/2/g/b/46/1'], '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': '2-75-25.21-c1-0-1', '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': '2-75-25.21-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7738720922475517, 'root_angle': -0.19840512363599017, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.73835891101938825072449857934', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2203631716965818741512276781852', 'Lhash_array': ['2203631716965818741512276781852'], 'label': '2-75-25.21-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/2/g/b/46/1'}