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lfunc_lfunctions • Show schema
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{'Lhash': '2028545166653990608422178625912', 'a10': [0.0, 4.247045267294318], 'a2': [-2.097636430872357, 0.0], 'a3': [0.8396902434556102, -1.5148994339709347], 'a4': [2.400078596122921, 0.0], 'a5': [0.0, -2.0246813054863244], 'a6': [-1.7613648453205666, 3.1777082418053455], 'a7': [2.0493556484201108, 1.6733623117211014], 'a8': [-0.8392194384397067, 0.0], 'a9': [-1.5898405900909165, -2.5440925490436403], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.875119614032244, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.8396902434556102, 1.5148994339709347]]], [7, [[1.0, 0], [-2.0493556484201108, -1.6733623117211014]]], [41, [[1.0, 0], [-0.4949364117954415, 6.383967257769972]]]], 'bad_primes': [3, 7, 41], 'central_character': '861.419', 'coefficient_field': 'CDF', 'conductor': 861, 'conductor_radical': 861, 'conjugate': '675494423557862609145258429031', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.097636430872357, 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0.597134885363872*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.398152851839', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60023997644837528286285471881', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.93427236846430875699903013021', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97743091959785450733711982599', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.875119614032244, 'bad_primes': [3, 7, 41], 'central_character': '861.419', 'conductor': 861, 'conductor_radical': 861, 'degree': 2, 'index': 77, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/861/2/l/a/419/16'], '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': '2-861-861.419-c1-0-77', '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': '2-861-861.419-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.622044929827146, 'root_angle': 0.3981528518389887, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60023997644837528286285471881', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2028545166653990608422178625912', 'Lhash_array': ['2028545166653990608422178625912'], 'label': '2-861-861.419-c1-0-77', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/861/2/l/a/419/16'}