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lfunc_lfunctions • Show schema
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{'Lhash': '787951886411481527269733855740', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-2.449489742783178, 1.0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.19568209498026, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.449489742783178, -1.0]]]], 'bad_primes': [2, 3, 7], 'central_character': '4032.1567', 'coefficient_field': 'CDF', 'conductor': 4032, 'conductor_radical': 42, 'conjugate': '550928855297722965153309002567', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [5.0, 0]], [[1.0, 0], [2.449489742783178, -1.0]], [[1.0, 0], [4.898979485566356, 0], [11.0, 0]], [[1.0, 0], [4.0, 0], [13.0, 0]], [[1.0, 0], [0, 4.898979485566356], [-17.0, 0]], [[1.0, 0], [0, -4.0], [-19.0, 0]], [[1.0, 0], [0, -6.0], [-23.0, 0]], [[1.0, 0], [0, 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'7.24036903728949152994384936670050', '7.54341716478062967220788771353738', '8.511554073594217532220355981219314'], 'prelabel': '2-4032-56.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.674123905501206, 'root_angle': 0.12662414278557507, 'root_number': '0.92191491262040152848284593712661187712320949723676219654 + 0.3873924287955527591137389753671048340152066675540869185*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.06331207139278754', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62158443838516518898616323332', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.36297227043972424734483420676', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.78347872471047428140613843628', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.19568209498026, 'bad_primes': [2, 3, 7], 'central_character': '56.27', 'conductor': 4032, 'conductor_radical': 42, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4032/2/p/a/1567/2'], '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': '2-4032-56.27-c1-0-31', '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': '2-4032-56.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.674123905501206, 'root_angle': 0.06331207139278754, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62158443838516518898616323332', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '787951886411481527269733855740', 'Lhash_array': ['787951886411481527269733855740'], 'label': '2-4032-56.27-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4032/2/p/a/1567/2'}