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lfunc_lfunctions • Show schema
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{'Lhash': '708446462107391970663003543957', 'a10': [-1.48356391649411, 1.6730326074756159], 'a2': [0.8660254037844386, -0.5], 'a3': [-0.25881904510252074, 0.9659258262890683], 'a4': [0.5, -0.8660254037844386], 'a5': [-2.1213203435596424, 0.7071067811865476], 'a6': [0.25881904510252074, 0.9659258262890683], 'a7': [-1.88366349398948, 3.2626008759524923], 'a8': [0.0, -1.0], '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], [-0.8660254037844386, 0.5]]], [3, [[1.0, 0], [0.25881904510252074, -0.9659258262890683]]], [5, [[1.0, 0], [2.1213203435596424, -0.7071067811865476]]], [13, [[1.0, 0], [3.5355339059327378, 0.7071067811865476]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.223', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '3196343623912682381567726980253', 'degree': 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'3.05059978159542802998633991508609', '3.97701724763419902481156047236985', '5.17739428814890195762831522637690', '6.36285350221058473465652555351663', '7.29489192170143673126528275971181', '7.88018819673516563545146091354483', '8.946308869374130309348735418639430', '10.44795730075208321172679620676809', '11.14515959723353320254239924726431'], 'prelabel': '2-390-65.28-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.6051659968061829, 'root_number': '-0.3244107522963286 - 0.9459163090858145*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.302582998403', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55886571739866046879485687441', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.05059978159542802998633991509', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97701724763419902481156047237', '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': '65.28', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bd/a/223/1'], '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': '2-390-65.28-c1-0-3', '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': '2-390-65.28-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.30258299840309144, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55886571739866046879485687441', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '708446462107391970663003543957', 'Lhash_array': ['708446462107391970663003543957'], 'label': '2-390-65.28-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bd/a/223/1'}