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lfunc_lfunctions • Show schema
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{'Lhash': '1737047802009702204872917959513', 'a10': [4.264139693806833, 0.0], 'a2': [1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [4.264139693806833, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.1215669064377976, 0.0], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.642188614702686, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1458.1', 'coefficient_field': 'CDF', 'conductor': 1458, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.264139693806833, 0], [5.0, 0]], [[1.0, 0], [1.1215669064377976, 0], [7.0, 0]], [[1.0, 0], [5.866626774538189, 0], [11.0, 0]], [[1.0, 0], [-0.5984269886091801, 0], [13.0, 0]], [[1.0, 0], [-3.2961276433894624, 0], [17.0, 0]], [[1.0, 0], [-4.82949935517051, 0], [19.0, 0]], [[1.0, 0], [-3.670474351831557, 0], 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'5.95522314867867893338507741269649', '6.87059595384933289545043317397587', '7.75018094730587472403293864251955', '8.846715007154415916424768755915824', '9.788616140070876534510175284895802'], 'prelabel': '2-1458-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4120651539357634, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37028910150554257092518458269', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.64985701047282270936698107438', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.08764407405529952461271954510', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.642188614702686, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 1458, 'conductor_radical': 6, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1458/2/a/h/1/6'], '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': '2-1458-1.1-c1-0-17', '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': '2-1458-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4120651539357634, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37028910150554257092518458269', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1737047802009702204872917959513', 'Lhash_array': ['1737047802009702204872917959513'], 'label': '2-1458-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1458/2/a/h/1/6'}