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lfunc_lfunctions • Show schema
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{'Lhash': '330591163836331946983551498053', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [3.6742346141747673, -2.1213203435596424], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.06551863315638, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1764.557', 'coefficient_field': 'CDF', 'conductor': 1764, 'conductor_radical': 42, 'conjugate': '1868249691356057816835556059011', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.6742346141747673, 2.1213203435596424], [12.5, -21.650635094610966]], [[1.0, 0], [0, 0]], [[1.0, 0], [-18.371173070873837, -10.606601717798213], [60.5, 104.78907385791707]], [[1.0, 0], [23.0, 0], [169.0, 0]], [[1.0, 0], [14.696938456699069, 8.48528137423857], [144.5, 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'-0.5298877878159899446169159740623326777248988116559320493 - 0.8480677639926401650136803847383231169470146491903225191*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.338882981712961', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.26079044476199664155048872863', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.82932268693472603790401751696', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.61413247357182937624370124064', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.06551863315638, 'bad_primes': [2, 3, 7], 'central_character': '21.11', 'conductor': 1764, 'conductor_radical': 42, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1764/3/bk/a/557/2'], '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': '2-42e2-21.11-c2-0-5', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-42e2-21.11-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.9329300179041455, 'root_angle': -0.338882981712961, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.26079044476199664155048872863', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '330591163836331946983551498053', 'Lhash_array': ['330591163836331946983551498053'], 'label': '2-42e2-21.11-c2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1764/3/bk/a/557/2'}