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lfunc_lfunctions • Show schema
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{'Lhash': '1571087015997357560719883153865', 'a10': [0.585786437626905, 0.0], 'a2': [1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [0.585786437626905, 0.0], 'a6': [1.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.994841846789825, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '6762.1', 'coefficient_field': 'CDF', 'conductor': 6762, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.585786437626905, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.93089327596783, 0], [11.0, 0]], [[1.0, 0], [-6.456656431893271, 0], [13.0, 0]], [[1.0, 0], [0.37177069285291925, 0], [17.0, 0]], [[1.0, 0], [-3.2602210993005736, 0], [19.0, 0]], [[1.0, 0], 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'5.11496613284156610403570399137975', '5.99248073775134266337715682522586', '6.46163648158524132527111341047292', '7.09161220095080563302477279989416', '8.004004790914866377383081454514789'], 'prelabel': '2-6762-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.348118252096235, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23936912562065374082258074901', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.73833058124905428566825319584', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99713995526637507318493328235', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 53.994841846789825, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 6762, 'conductor_radical': 966, 'degree': 2, 'index': 103, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6762/2/a/ct/1/2'], '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': '2-6762-1.1-c1-0-103', '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': '2-6762-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.348118252096235, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23936912562065374082258074901', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1571087015997357560719883153865', 'Lhash_array': ['1571087015997357560719883153865'], 'label': '2-6762-1.1-c1-0-103', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6762/2/a/ct/1/2'}