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lfunc_lfunctions • Show schema
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{'Lhash': '3686787862036577043455628473985', 'a10': [3.8284271247461903, 1.5857864376269049], 'a2': [0.0, 1.4142135623730951], 'a3': [-0.7071067811865476, 0.2928932188134525], 'a4': [-2.0, 0.0], 'a5': [1.1213203435596426, -2.7071067811865475], 'a6': [-0.41421356237309503, -1.0], 'a7': [1.0, 1.0], 'a8': [0.0, -2.8284271247461903], 'a9': [-1.7071067811865475, 1.7071067811865475], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.25552128646809735, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.4142135623730951]]]], 'bad_primes': [2], 'central_character': '32.21', 'coefficient_field': 'CDF', 'conductor': 32, 'conductor_radical': 2, 'conjugate': '6307623411859315729371192025710', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.4142135623730951]], [[1.0, 0], [0.7071067811865476, -0.2928932188134525], [2.1213203435596424, -2.1213203435596424]], [[1.0, 0], [-1.1213203435596426, 2.7071067811865475], 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'10.72033945482938012257679558429621', '11.41255396244891181359750871590001', '12.98852540977630713683271240559278', '14.06162251805866850406576441487617', '15.20225445524948300453701258012093', '17.38104086478985457897226585607555'], 'prelabel': '2-2e5-32.21-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5054911339164094, 'root_angle': -0.31250000000000006, 'root_number': '0.5555702330196021 - 0.8314696123025453*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.15625', 'prec': 27}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.90836281020401295116138215067', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.36197067505443972357916132126', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.34456963808696468241255981512', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.25552128646809735, 'bad_primes': [2], 'central_character': '32.21', 'conductor': 32, 'conductor_radical': 2, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/32/2/g/a/21/1'], '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': '2-2e5-32.21-c1-0-0', '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': '2-2e5-32.21-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5054911339164094, 'root_angle': -0.15625000000000003, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.90836281020401295116138215067', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3686787862036577043455628473985', 'Lhash_array': ['3686787862036577043455628473985'], 'label': '2-2e5-32.21-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/32/2/g/a/21/1'}