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lfunc_lfunctions • Show schema
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{'Lhash': '1197569877375304535364209723155', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.0744715851762199, -1.8610393768142834], 'a6': [0, 0], 'a7': [0.15317365739975833, -0.26530455699752997], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.596298938554515, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '3456.1153', 'coefficient_field': 'CDF', 'conductor': 3456, 'conductor_radical': 6, 'conjugate': '677677509834610876918729273807', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0744715851762199, 1.8610393768142834], [-2.5, 4.330127018922194]], [[1.0, 0], [-0.15317365739975833, 0.26530455699752997], [-3.5, -6.06217782649107]], [[1.0, 0], [2.5073641362888655, -4.34288207712837], [-5.5, -9.526279441628825]], [[1.0, 0], [-0.4707405190106895, 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5.253217960312947, 'root_angle': 0.3661809500948966, 'root_number': '0.408130169589311485852196960518470943666321335101281559 + 0.9129237452662735105837420633465426607441619600943452986*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1830904750474483', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.944716057531698841123433432041', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.40253459749084285899775691265', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39063237157834943195077828040', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.596298938554515, 'bad_primes': [2, 3], 'central_character': '9.7', 'conductor': 3456, 'conductor_radical': 6, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3456/2/i/f/1153/2'], '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': '2-3456-9.7-c1-0-25', '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': '2-3456-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.253217960312947, 'root_angle': 0.1830904750474483, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.944716057531698841123433432041', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1197569877375304535364209723155', 'Lhash_array': ['1197569877375304535364209723155'], 'label': '2-3456-9.7-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3456/2/i/f/1153/2'}