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lfunc_lfunctions • Show schema
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{'Lhash': '1671989316885823109477832628360', 'a10': [-2.3910204122301066, 0.0], 'a2': [1.3484204855288002, 0.0], 'a3': [-1.0, 0.0], 'a4': [-0.18176219420627462, 0.0], 'a5': [-1.773200895336767, 0.0], 'a6': [-1.3484204855288002, 0.0], 'a7': [1.3140399064722386, 0.0], 'a8': [-2.9419328372200053, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.075906491948345, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [-1.0, 0]]], [103, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 13, 103], 'central_character': '4017.1', 'coefficient_field': 'CDF', 'conductor': 4017, 'conductor_radical': 4017, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3484204855288002, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.773200895336767, 0], [5.0, 0]], [[1.0, 0], [-1.3140399064722386, 0], [7.0, 0]], [[1.0, 0], [1.436811166309257, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], 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'4.95849618041190703340865727910767', '5.57469296399471639484978834086407', '6.49908240647177347467616083528590', '7.18163754639743546721855329693160', '8.117893060756582212313261364615855'], 'prelabel': '2-4017-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.66355952488789, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.31896700603841157736665563159', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.91886916540551991001846413227', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51042696328199607627057525284', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.075906491948345, 'bad_primes': [3, 13, 103], 'central_character': '1.1', 'conductor': 4017, 'conductor_radical': 4017, 'degree': 2, 'index': 133, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4017/2/a/h/1/18'], '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': '2-4017-1.1-c1-0-133', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4017-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.66355952488789, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31896700603841157736665563159', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1671989316885823109477832628360', 'Lhash_array': ['1671989316885823109477832628360'], 'label': '2-4017-1.1-c1-0-133', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4017/2/a/h/1/18'}