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lfunc_lfunctions • Show schema
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{'Lhash': '1597001149113726836723074539360', 'a10': [-1.3910558300853004, 0.254879731610216], 'a2': [-0.430955323886539, 1.3469511902121205], 'a3': [2.546367110192237, 0.25079527014536035], 'a4': [-1.6285550176276966, -1.1609515728744473], 'a5': [0.47139673682599764, 0.881921264348355], 'a6': [-1.4351794503287894, 3.321750652915726], 'a7': [0.10182972203513997, 0.5119325830594569], 'a8': [2.2655795579506623, -1.6932658582148528], 'a9': [3.478731351131789, 0.6919626885314606], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.110425729361947, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.430955323886539, -1.3469511902121205]]], [5, [[1.0, 0], [-0.47139673682599764, -0.881921264348355]]]], 'bad_primes': [2, 5], 'central_character': '640.221', 'coefficient_field': 'CDF', 'conductor': 640, 'conductor_radical': 10, 'conjugate': '2227273446679772195988845008295', 'degree': 2, 'euler_factors': [[[1.0, 0], 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-0.5131580633815112, 'root_number': '-0.041325503609072424 - 0.9991457364926583*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.256579031691', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25981177212885060755038172584', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.42014453489185420158943865717', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.47072338654195667357634583029', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.110425729361947, 'bad_primes': [2, 5], 'central_character': '128.93', 'conductor': 640, 'conductor_radical': 10, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/640/2/bm/a/221/27'], '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': '2-640-128.93-c1-0-29', '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': '2-640-128.93-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.260625074921082, 'root_angle': -0.2565790316907556, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25981177212885060755038172584', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1597001149113726836723074539360', 'Lhash_array': ['1597001149113726836723074539360'], 'label': '2-640-128.93-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/640/2/bm/a/221/27'}