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lfunc_lfunctions • Show schema
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{'Lhash': '1071147214940192187152918892082', 'a10': [4.335021185058348, 0.0], 'a2': [1.4888847792838622, 0.0], 'a3': [0.0, 0.0], 'a4': [0.21677788598315495, 0.0], 'a5': [2.911589429467771, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [-2.6550122636420723, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.888306657226465, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [127, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7, 127], 'central_character': '8001.1', 'coefficient_field': 'CDF', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4888847792838622, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.911589429467771, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.146347478218971, 0], [11.0, 0]], [[1.0, 0], [-3.3666788811409387, 0], [13.0, 0]], [[1.0, 0], [4.7957295391909796, 0], [17.0, 0]], [[1.0, 0], 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'2.17149393072623322823613206308593', '2.63800565215346419372200704551573', '3.56749936270012538000073012890740', '4.49661902068026009616723541661557', '5.13104077364198694826783739930868', '5.49872945201142467497668289047073', '6.43190587186325270531226296259692', '6.62292948183095868729963872981183', '7.916656351645875397370161080064014'], 'prelabel': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.844986161602685709467057718943', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.17149393072623322823613206309', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.63800565215346419372200704552', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.888306657226465, 'bad_primes': [3, 7, 127], 'central_character': '1.1', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'index': 120, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8001/2/a/v/1/15'], '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': '2-8001-1.1-c1-0-120', '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': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.844986161602685709467057718943', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1071147214940192187152918892082', 'Lhash_array': ['1071147214940192187152918892082'], 'label': '2-8001-1.1-c1-0-120', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8001/2/a/v/1/15'}