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lfunc_lfunctions • Show schema
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{'Lhash': '1103815758125320678706637160746', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-2.732050807568877, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -4.732050807568878], 'a8': [0, 0], 'a9': [4.464101615137754, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.776064323404867, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '1600.1249', 'coefficient_field': 'CDF', 'conductor': 1600, 'conductor_radical': 10, 'conjugate': '807459210153354155105062039554', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.732050807568877, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 4.732050807568878], [-7.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-11.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [13.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-17.0, 0]], [[1.0, 0], [0, -2.0], [-19.0, 0]], [[1.0, 0], [0, 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'6.05629870827409417482628573841841', '6.74472405175734288215549941782898', '7.952299432680398701348327371362419', '8.930876048124846572319040778155564', '9.341346696471835244945763372173903'], 'prelabel': '2-40e2-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5743620862197027, 'root_angle': 0.2690830490162334, 'root_number': '0.6634699532493302035855099969795672742431392855307140400 + 0.7482029277778399565283189230653088470343056183977741512*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1345415245081167', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.870757098151957887564925037967', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.39130949933524008626340830293', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58631853016481276828094017169', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.776064323404867, 'bad_primes': [2, 5], 'central_character': '40.29', 'conductor': 1600, 'conductor_radical': 10, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1600/2/f/d/1249/1'], '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': '2-40e2-40.29-c1-0-16', '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': '2-40e2-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5743620862197027, 'root_angle': 0.1345415245081167, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.870757098151957887564925037967', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1103815758125320678706637160746', 'Lhash_array': ['1103815758125320678706637160746'], 'label': '2-40e2-40.29-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1600/2/f/d/1249/1'}