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lfunc_lfunctions • Show schema
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{'Lhash': '1777890079007731020590258835710', 'a10': [-2.251782269795138, 2.8236456553752007], 'a2': [-0.33562697043988804, -1.4704778366025975], 'a3': [-0.20106619943943405, 0.8809285784694103], 'a4': [-0.24772186884795944, 0.11929656456074467], 'a5': [-1.4929333393092936, -1.87207919426819], 'a6': [1.3628691896448195, -1.8660261890403753e-61], 'a7': [3.9516955994987204, 0.0], 'a8': [-1.6222466527362007, -2.034232960437277], 'a9': [1.9672990599001396, 0.9474012948518192], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.837064387755599, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [0.6234898018587335, -0.7818314824680298]]], [43, [[1.0, 0], [-0.07748380793387645, 6.556980727400994]]]], 'bad_primes': [17, 43], 'central_character': '731.188', 'coefficient_field': 'CDF', 'conductor': 731, 'conductor_radical': 731, 'conjugate': '1428773640382039107828901512968', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'data': '0.246583297802', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40250797710949489108450459260', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.03241317063608772552834317097', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.31490468833669825082079759745', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.837064387755599, 'bad_primes': [17, 43], 'central_character': '43.16', 'conductor': 731, 'conductor_radical': 731, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/731/2/k/b/188/8'], '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': '2-731-43.16-c1-0-31', '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': '2-731-43.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.416001735875949, 'root_angle': 0.24658329780180838, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40250797710949489108450459260', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1777890079007731020590258835710', 'Lhash_array': ['1777890079007731020590258835710'], 'label': '2-731-43.16-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/731/2/k/b/188/8'}