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lfunc_lfunctions • Show schema
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{'Lhash': '1400319837778054336037955056886', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.7320508075688772, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, -1.0], 'a6': [0.0, 0.0], 'a7': [0.0, 3.4641016151377544], 'a8': [0.0, 0.0], 'a9': [3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.7320508075688772, 0]]], [5, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 5], 'central_character': '240.191', 'coefficient_field': 'CDF', 'conductor': 240, 'conductor_radical': 30, 'conjugate': '1980091840447577878771137362279', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.7320508075688772, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, -3.4641016151377544], [-7.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [11.0, 0]], [[1.0, 0], [-4.0, 0], [13.0, 0]], [[1.0, 0], [0, -6.0], [-17.0, 0]], [[1.0, 0], [0, 3.4641016151377544], 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'11.63455029835239213040350207981518'], 'prelabel': '2-240-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.384344483324411, 'root_angle': -0.16666666666666669, 'root_number': '0.8660254037844386 - 0.5*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0833333333333', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10465757482853634816726199647', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.61720455341027874233140882971', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.63300665654680173785481794124', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'bad_primes': [2, 3, 5], 'central_character': '12.11', 'conductor': 240, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/240/2/h/b/191/1'], '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': '2-240-12.11-c1-0-1', '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': '2-240-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.384344483324411, 'root_angle': -0.08333333333333334, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10465757482853634816726199647', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1400319837778054336037955056886', 'Lhash_array': ['1400319837778054336037955056886'], 'label': '2-240-12.11-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/240/2/h/b/191/1'}