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lfunc_lfunctions • Show schema
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{'Lhash': '797958308263273180750536448912', 'a10': [-615.451236635523, 3.315874503453894e-59], 'a2': [5.775192101468273, -5.775192101468273], 'a3': [0.0, 42.659088515143424], 'a4': [0.0, -2.7056876177230555], 'a5': [-53.28404889588451, -53.28404889588451], 'a6': [246.3644310484922, 246.3644310484922], 'a7': [-452.2669597593441, 0.0], 'a8': [353.9864287350548, 353.9864287350548], 'a9': [-1090.7978329428413, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.512001093934488, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[37, [[1.0, 0], [13204.196179572002, -48901.69334748416]]]], 'bad_primes': [37], 'central_character': '37.6', 'coefficient_field': 'CDF', 'conductor': 37, 'conductor_radical': 37, 'conjugate': '3903978662261625444469952258279', 'degree': 2, 'euler_factors': [[[1.0, 0], [-5.775192101468273, 5.775192101468273], [0, -64.0]], [[1.0, 0], [0, -42.659088515143424], [-729.0, 0]], [[1.0, 0], [53.28404889588451, 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2.9175333920855966, 'root_angle': -0.6397692043549124, 'root_number': '-0.4251231204581623 - 0.9051355326424407*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.319884602177', 'prec': 50}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62947811338519286598165141263', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.09133445971963643511911959461', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.59777645229370947185133951266', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.512001093934488, 'bad_primes': [37], 'central_character': '37.6', 'conductor': 37, 'conductor_radical': 37, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/37/7/d/a/6/14'], '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': '2-37-37.6-c6-0-1', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-37-37.6-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9175333920855966, 'root_angle': -0.3198846021774562, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62947811338519286598165141263', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '797958308263273180750536448912', 'Lhash_array': ['797958308263273180750536448912'], 'label': '2-37-37.6-c6-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/37/7/d/a/6/14'}