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lfunc_lfunctions • Show schema
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{'Lhash': '652949603912558818102279274939', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-11.524174696260024, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [27.04834939252005, 0.0], 'a8': [0.0, 0.0], 'a9': [-110.1933975700802, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.15352792519226, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '400.1', 'coefficient_field': 'CDF', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [11.524174696260024, 0], [243.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-27.04834939252005, 0], [16807.0, 0]], [[1.0, 0], [226.0076686214605, 0], [161051.0, 0]], [[1.0, 0], [511.2570842055212, 0], [371293.0, 0]], [[1.0, 0], [387.38679514016036, 0], [1419857.0, 0]], [[1.0, 0], [-1335.9263070793413, 0], [2476099.0, 0]], [[1.0, 0], 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['0.51508641560616226091748210156946', '2.11659886807368425994540263480814', '3.40816096822972329998766620376782', '4.95556458544384575079629690861632', '5.45226657850375047959547540479389', '6.65945158157963821284041533125361', '7.58912611084731348858165391767750', '8.610956995624248792019258833457749', '9.674978240046098165215528507630346', '10.56756038960455007365553590236620'], 'prelabel': '2-20e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.009589747620803, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.51508641560616226091748210157', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.11659886807368425994540263481', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.40816096822972329998766620377', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.15352792519226, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/400/6/a/u/1/1'], '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': '2-20e2-1.1-c5-0-5', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-20e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.009589747620803, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.51508641560616226091748210157', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '652949603912558818102279274939', 'Lhash_array': ['652949603912558818102279274939'], 'label': '2-20e2-1.1-c5-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/6/a/u/1/1'}