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lfunc_lfunctions • Show schema
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{'Lhash': '2442656150122987334607857596792', 'a10': [1.420267426545041, 0.0], 'a2': [0.0, 0.5806120767764014], 'a3': [1.0, 0.0], 'a4': [1.6628896163013942, 0.0], 'a5': [0.0, -2.44615550270753], 'a6': [0.0, 0.5806120767764014], 'a7': [0.0, -1.30605281640428], 'a8': [0.0, 2.1267179471234683], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.760953935202308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [157, [[1.0, 0], [-12.361122369366868, -2.0500375044223094]]]], 'bad_primes': [3, 157], 'central_character': '471.313', 'coefficient_field': 'CDF', 'conductor': 471, 'conductor_radical': 471, 'conjugate': '1789934956224853188372245904358', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -0.5806120767764014], [-2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 2.44615550270753], [-5.0, 0]], [[1.0, 0], [0, 1.30605281640428], [-7.0, 0]], [[1.0, 0], [2.3172800417884685, 0], [11.0, 0]], [[1.0, 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'3.69170559243093634364621589800497', '5.52003515978328129791058040432339', '6.58680029152577016291526895130705', '7.30973767407896565415521912467036', '8.289474426225223311495314386232090', '9.381354824053336131499158191314229', '10.49562676402745086748817452966194', '10.82668378977981078540349519678609'], 'prelabel': '2-471-157.156-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9393179046258269, 'root_angle': 0.05231412657231579, 'root_number': '0.9865249640291035 + 0.16361080449461796*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0261570632862', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.92691594172969149582103607890', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.90574993911575778213044712159', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.69170559243093634364621589800', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.760953935202308, 'bad_primes': [3, 157], 'central_character': '157.156', 'conductor': 471, 'conductor_radical': 471, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/471/2/b/b/313/9'], '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': '2-471-157.156-c1-0-18', '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': '2-471-157.156-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9393179046258269, 'root_angle': 0.026157063286157894, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92691594172969149582103607890', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2442656150122987334607857596792', 'Lhash_array': ['2442656150122987334607857596792'], 'label': '2-471-157.156-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/471/2/b/b/313/9'}