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lfunc_lfunctions • Show schema
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{'Lhash': '636576650698671071462756802366', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [-1.6374586088176875, 1.5227374377773877], 'a6': [0.0, 0.0], 'a7': [-2.6374586088176875, 0.2093133697914896], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1179056282979258, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.6374586088176875, -1.5227374377773877]]], [7, [[1.0, 0], [2.6374586088176875, -0.2093133697914896]]]], 'bad_primes': [2, 5, 7], 'central_character': '140.9', 'coefficient_field': 'CDF', 'conductor': 140, 'conductor_radical': 70, 'conjugate': '3980408958764440226621783537407', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.5, -0.8660254037844386], [1.5, -2.598076211353316]], [[1.0, 0], [1.6374586088176875, -1.5227374377773877]], [[1.0, 0], [2.6374586088176875, 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'12.65273153729242921623148193436854'], 'prelabel': '2-140-35.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0573105637881075, 'root_angle': -0.7838315650970817, 'root_number': '-0.778130047293616 - 0.6281031997202648*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.391915782549', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50217043291271349858529460060', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34268727866169124804183668448', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.04808688066413499244962933276', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1179056282979258, 'bad_primes': [2, 5, 7], 'central_character': '35.9', 'conductor': 140, 'conductor_radical': 70, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/140/2/q/a/9/1'], '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': '2-140-35.9-c1-0-0', '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': '2-140-35.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0573105637881075, 'root_angle': -0.39191578254854087, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.50217043291271349858529460060', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '636576650698671071462756802366', 'Lhash_array': ['636576650698671071462756802366'], 'label': '2-140-35.9-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/140/2/q/a/9/1'}