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lfunc_lfunctions • Show schema
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{'Lhash': '990057122719762437288234334964', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.0, 1.4142135623730951], 'a4': [0, 0], 'a5': [1.7320508075688772, 1.4142135623730951], 'a6': [0, 0], 'a7': [1.0, 2.449489742783178], 'a8': [0, 0], 'a9': [-1.0, -2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.414867539575111, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, -1.4142135623730951]]], [5, [[1.0, 0], [-1.7320508075688772, -1.4142135623730951]]], [7, [[1.0, 0], [-1.0, -2.449489742783178]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1680.209', 'coefficient_field': 'CDF', 'conductor': 1680, 'conductor_radical': 210, 'conjugate': '1994731435607002100730833982275', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, -1.4142135623730951]], [[1.0, 0], [-1.7320508075688772, -1.4142135623730951]], [[1.0, 0], [-1.0, -2.449489742783178]], [[1.0, 0], [0, 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'2.84270818125192484025098966161739', '4.18604653068758034872309553944435', '5.17124065935850563394472220570526', '5.82056735183562409944732391328046', '6.63844157156451038617884054003425', '7.36562637058268240833868520471983', '8.383335128942816973785734164374734', '8.805635858110874036752399276459170'], 'prelabel': '2-1680-105.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6626312317205936, 'root_angle': -0.7095096896236088, 'root_number': '-0.6116892074131232279815840435188910931488929296691013569 - 0.7910981693407621022306649276403305864223332626475815081*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.35475484481180436', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78101735804922216981723828745', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.46572922768665464353829004887', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.84270818125192484025098966162', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.414867539575111, 'bad_primes': [2, 3, 5, 7], 'central_character': '105.104', 'conductor': 1680, 'conductor_radical': 210, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1680/2/k/a/209/4'], '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': '2-1680-105.104-c1-0-37', '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': '2-1680-105.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6626312317205936, 'root_angle': -0.3547548448118044, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78101735804922216981723828745', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '990057122719762437288234334964', 'Lhash_array': ['990057122719762437288234334964'], 'label': '2-1680-105.104-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1680/2/k/a/209/4'}