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lfunc_lfunctions • Show schema
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{'Lhash': '1437606178865519617699908187815', 'a10': [-1.0491864326203733, -0.6057480693034756], 'a2': [0.6671553851112985, 1.15554702355595], 'a3': [-0.8660254037844386, -0.5], 'a4': [0.10980738423399002, -0.19019196853950843], 'a5': [-0.7863133956756881, 0.4539782506607673], 'a6': [2.117836075965323e-61, -1.334310770222597], 'a7': [-1.3593576308473616, 2.26983409778271], 'a8': [2.9616558913119615, 0.0], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.850659352159711, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8660254037844386, 0.5]]], [7, [[1.0, 0], [1.3593576308473616, -2.26983409778271]]], [17, [[1.0, 0], [0.772922866111336, -4.050011141101002]]]], 'bad_primes': [3, 7, 17], 'central_character': '357.67', 'coefficient_field': 'CDF', 'conductor': 357, 'conductor_radical': 357, 'conjugate': '2248336553666532578975680259956', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'6.50145719684151696318789133196343', '7.26930707520717791529518418745584', '8.624812321966620638991607164442999', '9.678995127558155344636305447213835', '10.70336966769949016504059141863523', '11.39160451690550244460120165374351'], 'prelabel': '2-357-119.67-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.688389573575871, 'root_angle': -0.4147092450975553, 'root_number': '0.2647539987856402 - 0.9643159856224583*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.207354622549', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13407131161117361597612846389', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.27167994487892869635824206213', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.91327300170946386970882096788', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.850659352159711, 'bad_primes': [3, 7, 17], 'central_character': '119.67', 'conductor': 357, 'conductor_radical': 357, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/357/2/p/a/67/17'], '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': '2-357-119.67-c1-0-6', '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': '2-357-119.67-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.688389573575871, 'root_angle': -0.20735462254877765, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13407131161117361597612846389', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1437606178865519617699908187815', 'Lhash_array': ['1437606178865519617699908187815'], 'label': '2-357-119.67-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/357/2/p/a/67/17'}