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lfunc_lfunctions • Show schema
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{'Lhash': '168287804288237820169918667084', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 1.7320508075688772], 'a4': [0, 0], 'a5': [-0.6213203435596426, -0.3587194676071504], 'a6': [0, 0], 'a7': [-1.0, 2.449489742783178], 'a8': [0, 0], 'a9': [-3.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.048920523745066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, -1.7320508075688772]]], [7, [[1.0, 0], [1.0, -2.449489742783178]]]], 'bad_primes': [2, 3, 7], 'central_character': '1008.367', 'coefficient_field': 'CDF', 'conductor': 1008, 'conductor_radical': 42, 'conjugate': '2897479175456267423652261436192', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.7320508075688772]], [[1.0, 0], [0.6213203435596426, 0.3587194676071504], [2.5, 4.330127018922194]], [[1.0, 0], [1.0, -2.449489742783178]], [[1.0, 0], [-1.5, 0.8660254037844386], [5.5, -9.526279441628825]], [[1.0, 0], 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False, 'root_analytic_conductor': 2.837061952750603, 'root_angle': 0.4026260866643775, 'root_number': '-0.81860499467317773701247686965888712362381735417187114022 + 0.5743569122907172332647498573579849218112169148284951853*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4026260866643775', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.13275566962847575912898837061', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.64858666262960680356715500622', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.94629856418937598033931406224', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.048920523745066, 'bad_primes': [2, 3, 7], 'central_character': '252.115', 'conductor': 1008, 'conductor_radical': 42, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1008/2/cz/e/367/1'], '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': '2-1008-252.115-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': '2-1008-252.115-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.837061952750603, 'root_angle': 0.4026260866643775, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.13275566962847575912898837061', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '168287804288237820169918667084', 'Lhash_array': ['168287804288237820169918667084'], 'factors': ['2-1008-252.115-c1-0-1'], 'label': '2-1008-252.115-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/2/cz/e/367/1'}