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lfunc_lfunctions • Show schema
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{'Lhash': '7849080437124977575698556684885', 'a10': [-5.0, 5.0], 'a2': [-1.0, -1.0], 'a3': [-2.0, 2.0], 'a4': [0.0, 2.0], 'a5': [0.0, -5.0], 'a6': [4.0, 0.0], 'a7': [2.0, 2.0], 'a8': [2.0, -2.0], 'a9': [0.0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.27248026436029693, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 1.0]]], [5, [[1.0, 0], [0, 5.0]]]], 'bad_primes': [2, 5], 'central_character': '10.7', 'coefficient_field': 'CDF', 'conductor': 10, 'conductor_radical': 10, 'conjugate': '6383131026422173735721802768626', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [2.0, -2.0], [0, -9.0]], [[1.0, 0], [0, 5.0]], [[1.0, 0], [-2.0, -2.0], [0, 49.0]], [[1.0, 0], [8.0, 0], [121.0, 0]], [[1.0, 0], [-3.0, 3.0], [0, -169.0]], [[1.0, 0], [-7.0, -7.0], [0, 289.0]], [[1.0, 0], [0, 20.0], [-361.0, 0]], [[1.0, 0], [2.0, -2.0], [0, -529.0]], [[1.0, 0], [0, -40.0], [-841.0, 0]], [[1.0, 0], 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0.07379180882521663, 'root_number': '0.9732489894677302 + 0.22975292054736116*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0368959044126', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '6.19183269878294484670114036539', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '7.67558497356483516574264525363', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '10.23281628919080119416287605008', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.27248026436029693, 'bad_primes': [2, 5], 'central_character': '5.2', 'conductor': 10, 'conductor_radical': 10, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/10/3/c/a/7/1'], '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': '2-10-5.2-c2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-10-5.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5219964217887867, 'root_angle': 0.036895904412608316, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '6.19183269878294484670114036539', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '7849080437124977575698556684885', 'Lhash_array': ['7849080437124977575698556684885'], 'label': '2-10-5.2-c2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/10/3/c/a/7/1'}