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lfunc_lfunctions • Show schema
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{'Lhash': '2419246796154911500111376345797', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.9238795325112867, -0.3826834323650898], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.7071067811865476, -0.7071067811865476], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8144741006170599, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.9238795325112867, 0.3826834323650898]]], [17, [[1.0, 0], [-0.9238795325112867, 0.3826834323650898]]]], 'bad_primes': [2, 3, 17], 'central_character': '1632.1391', 'coefficient_field': 'CDF', 'conductor': 1632, 'conductor_radical': 102, 'conjugate': '1471576626824945954510712198727', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.9238795325112867, 0.3826834323650898]], [[1.0, 0], [0, 0], [0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [0, 0], [-0.3826834323650898, 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'8.903785706994202587859978115014526', '9.788248893289337474316043754369775'], 'prelabel': '2-1632-408.371-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9024821885317516, 'root_angle': 0.2944701135472792, 'root_number': '0.60175061773838583773434701803586 + 0.79868403893621853420392934562195*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1472350567736396', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.90844921756779610832750500764', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.58710326822879219428261949851', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.93803556562174473399307573636', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8144741006170599, 'bad_primes': [2, 3, 17], 'central_character': '408.371', 'conductor': 1632, 'conductor_radical': 102, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1632/1/ds/a/1391/1'], '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': '2-1632-408.371-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1632-408.371-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9024821885317516, 'root_angle': 0.1472350567736396, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.90844921756779610832750500764', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2419246796154911500111376345797', 'Lhash_array': ['2419246796154911500111376345797'], 'label': '2-1632-408.371-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1632/1/ds/a/1391/1'}