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lfunc_lfunctions • Show schema
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{'Lhash': '1457029901689992240412104964701', 'a10': [2.1808961494103194, 0.4936516843759806], 'a2': [0.5, -0.8660254037844386], 'a3': [0.25881904510252074, 0.9659258262890683], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.6629331754145827, 2.1355373105929893], 'a6': [0.9659258262890683, 0.25881904510252074], 'a7': [-1.1232634358166436, 0.6485164470396031], 'a8': [-1.0, 0.0], 'a9': [-0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [3, [[1.0, 0], [-0.25881904510252074, -0.9659258262890683]]], [5, [[1.0, 0], [-0.6629331754145827, -2.1355373105929893]]], [13, [[1.0, 0], [-3.0171786351420455, -1.9739891295654044]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.97', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '2470283740721983528981572884701', 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'4.42016118334997331400189400454736', '5.61334894019504208851119827727644', '6.38694474725883656414672807471004', '7.48776701108105086154792489011464', '8.363948176877556987539718713392800', '9.191592582296750835962361993890114', '10.11945621135322803674516950656831', '11.57457686971706080510764037187166'], 'prelabel': '2-390-65.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.15864567359345555, 'root_number': '0.8783484795942578 - 0.47802086606596556*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0793228367967', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14939392718124911732584926190', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.14288155315172428723389911186', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.42016118334997331400189400455', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.32', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bn/b/97/4'], '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': '2-390-65.32-c1-0-4', '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': '2-390-65.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.07932283679672777, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14939392718124911732584926190', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1457029901689992240412104964701', 'Lhash_array': ['1457029901689992240412104964701'], 'label': '2-390-65.32-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bn/b/97/4'}