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lfunc_lfunctions • Show schema
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{'Lhash': '2454407755493812591046406508675', 'a10': [-1.3107063138084283, -0.5310828174048956], 'a2': [-0.551277061079304, -1.3023415841966213], 'a3': [-1.1627860031848505, -1.1627860031848505], 'a4': [-1.3921872038555307, 1.4359020821145567], 'a5': [0.7071067811865476, -0.7071067811865476], 'a6': [-0.8733273149695211, 2.15536181596931], 'a7': [0.0, -1.0], 'a8': [2.63751586258599, 1.0215234087417102], 'a9': [0.0, -0.2958574215948022], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.471622513191703, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.551277061079304, 1.3023415841966213]]], [5, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [7, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 5, 7], 'central_character': '560.141', 'coefficient_field': 'CDF', 'conductor': 560, 'conductor_radical': 70, 'conjugate': '678818366242452567497758407882', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.551277061079304, 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'sign_arg': {'__RealLiteral__': 0, 'data': '-0.442419848153', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93618632378032081173149910630', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.10101002045737889682284251348', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.93793373884701930039831101334', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.471622513191703, 'bad_primes': [2, 5, 7], 'central_character': '16.13', 'conductor': 560, 'conductor_radical': 70, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/560/2/bd/a/141/11'], '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': '2-560-16.13-c1-0-36', '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': '2-560-16.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.114621127576215, 'root_angle': -0.44241984815317537, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93618632378032081173149910630', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2454407755493812591046406508675', 'Lhash_array': ['2454407755493812591046406508675'], 'label': '2-560-16.13-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/560/2/bd/a/141/11'}