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lfunc_lfunctions • Show schema
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{'Lhash': '5302763489353797909528395972289', 'a10': [12.69046614955283, 12.04610992201446], 'a2': [-1.4884121268290607, 0.4836144161186724], 'a3': [-4.163574392774883, -5.730668518752094], 'a4': [-4.490648199185577, 3.26264689501901], 'a5': [-5.333449951543674, -9.826205351730584], 'a6': [8.96854852682703, 6.516031919219666], 'a7': [0.0, -1.1826140452961023], 'a8': [12.465186433037905, -17.15685724173593], 'a9': [-7.161751099522001, 22.041603456345634], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.475047750143516, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [5.333449951543674, 9.826205351730584]]]], 'bad_primes': [5], 'central_character': '25.19', 'coefficient_field': 'CDF', 'conductor': 25, 'conductor_radical': 5, 'conjugate': '702333757077252335365577701430', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4884121268290607, -0.4836144161186724], [6.47213595499958, -4.702282018339785]], [[1.0, 0], 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.18314280638456821655115893299', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.94238037812499746843436501066', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.320779067002155009401490249261', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.475047750143516, 'bad_primes': [5], 'central_character': '25.19', 'conductor': 25, 'conductor_radical': 5, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/25/4/e/a/19/3'], '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': '2-5e2-25.19-c3-0-4', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-5e2-25.19-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2145154384129977, 'root_angle': 0.381710308436845, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '4.18314280638456821655115893299', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5302763489353797909528395972289', 'Lhash_array': ['5302763489353797909528395972289'], 'label': '2-5e2-25.19-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/25/4/e/a/19/3'}