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lfunc_lfunctions • Show schema
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{'Lhash': '2811269712045381654921950595540', 'a10': [-0.7596699498960326, -2.1030695583420345], 'a2': [0.9659258262890683, -0.25881904510252074], 'a3': [1.0418537537172567, 1.3836693087097298], 'a4': [0.8660254037844386, -0.5], 'a5': [-0.18947036918603505, -2.2280262519100864], 'a6': [1.364473417149626, 1.0668703266526924], 'a7': [0.8852379891282102, -3.3037531522165855], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [-0.8290815117305232, 2.8831621263651876], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9659258262890683, 0.25881904510252074]]], [3, [[1.0, 0], [-1.0418537537172567, -1.3836693087097298]]], [5, [[1.0, 0], [0.18947036918603505, 2.2280262519100864]]], [13, [[1.0, 0], [-2.781230755806066, 2.29450549856792]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.59', 'coefficient_field': 'CDF', 'conductor': 390, 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-0.9031442402341492], 'positive_zeros': ['2.21770076986453296793058773779456', '2.88866418017845456979528067957798', '4.34535749857252859621041762078203', '5.85457445824431834010170606879677', '6.64376030651387964453897848431381', '7.36079437295842903033015006727616', '8.627235742765001243302616534425193', '9.153562674240133084011990373825781', '10.86239717395185656645630050450863', '11.55399678319517338999020686678834'], 'prelabel': '2-390-195.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.1231148218230342, 'root_number': '0.9261297445679093 + 0.37720511161247405*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0615574109115', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.21770076986453296793058773779', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.88866418017845456979528067958', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.34535749857252859621041762078', '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': '195.59', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bj/a/59/24'], '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': '2-390-195.59-c1-0-22', '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': '2-390-195.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.0615574109115171, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.21770076986453296793058773779', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2811269712045381654921950595540', 'Lhash_array': ['2811269712045381654921950595540'], 'label': '2-390-195.59-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bj/a/59/24'}