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lfunc_lfunctions • Show schema
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{'Lhash': '1832058691519095514723137241506', 'a10': [0.0, 0.0], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.7308837491277904, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-4.0, 1.7320508075688772]]]], 'bad_primes': [2, 3, 19], 'central_character': '342.235', 'coefficient_field': 'CDF', 'conductor': 342, 'conductor_radical': 114, 'conjugate': '1551263549890065323506419335466', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-2.5, 4.330127018922194]], [[1.0, 0], [-1.0, 0], [7.0, 0]], [[1.0, 0], [-2.0, 0], [11.0, 0]], [[1.0, 0], [-1.5, 2.598076211353316], [-6.5, -11.258330249197702]], [[1.0, 0], [-2.0, 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2.908635549465622, 3.543660454607478, 3.4450771721488214], 'positive_zeros': ['1.44523947780977611155881925702301', '3.48617559706665704132131698909006', '4.87586858957521118499595655105335', '5.84833753542444496259914943910998', '7.05318714727489721208141843971741', '7.70689965926038983256584618083340', '9.034949659383026950616417339882622', '9.418110536988220635410834132229982', '10.73515255721021597639373978246399', '11.54348307164942019598761102173232'], 'prelabel': '2-342-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6525385771980605, 'root_angle': 0.27101315224910716, 'root_number': '0.6589209822349098 + 0.7522121636683241*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.135506576125', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.44523947780977611155881925702', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.48617559706665704132131698909', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.87586858957521118499595655105', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.7308837491277904, 'bad_primes': [2, 3, 19], 'central_character': '19.7', 'conductor': 342, 'conductor_radical': 114, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/342/2/g/c/235/1'], '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': '2-342-19.7-c1-0-2', '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': '2-342-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6525385771980605, 'root_angle': 0.13550657612455358, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44523947780977611155881925702', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1832058691519095514723137241506', 'Lhash_array': ['1832058691519095514723137241506'], 'label': '2-342-19.7-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/342/2/g/c/235/1'}