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lfunc_lfunctions • Show schema
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{'Lhash': '753515923952813372716883613517', 'a10': [-2.6139204458899292, -5.4678300645157084e-61], 'a2': [-2.2637215096122256, 1.3069602229449646], 'a3': [-0.5383213382600506, -1.6462715865779585], 'a4': [2.416290048720703, -4.185137130207336], 'a5': [0.8660254037844386, 0.5], 'a6': [3.370221072324404, 3.0231358249315825], 'a7': [3.148271423846704, -1.8176553540399012], 'a8': [0.0, 7.404139031322979], 'a9': [-2.4204202735478164, 1.7724462472522864], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5383213382600506, 1.6462715865779585]]], [5, [[1.0, 0], [-0.8660254037844386, -0.5]]], [13, [[1.0, 0], [-0.23339163521841866, -3.5979894864507416]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.571', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '1693732719198823620194181394589', 'degree': 2, 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'5.68639903864830141761105740418500', '7.51393144028645827166071445728389', '8.352978202741212196843590895404517', '8.811772842172796447567301462097184', '9.732555599667646189000334121635302', '10.59897058049184925189686772738959'], 'prelabel': '2-585-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.44403507265106906, 'root_number': '0.17491457469322136 - 0.984583613290354*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.222017536326', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59441925386786344925684116476', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39705365065392320062422505513', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.21574266448070249921229337991', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '117.103', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/3'], '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': '2-585-117.103-c1-0-14', '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': '2-585-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.22201753632553453, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.59441925386786344925684116476', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '753515923952813372716883613517', 'Lhash_array': ['753515923952813372716883613517'], 'label': '2-585-117.103-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/3'}