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lfunc_lfunctions • Show schema
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{'Lhash': '2650815637450856802693415901074', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.30901699437494745, -0.9510565162951535], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.837300102699998, -0.5969749912579709], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.630445396272019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '3267.2296', 'coefficient_field': 'CDF', 'conductor': 3267, 'conductor_radical': 33, 'conjugate': '193426863523529205827188716495', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [1.837300102699998, 0.5969749912579709], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.3042600354473643, 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-0.9210885260699394, 'root_number': '-0.96942794216009096908725808871367 - 0.24537617031662084073614334696448*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.46054426303496965', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.09112482333349634024479048526', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.98738465729378153963531781143', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52747787912402605060295333950', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.630445396272019, 'bad_primes': [3, 11], 'central_character': '11.8', 'conductor': 3267, 'conductor_radical': 33, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3267/1/l/a/2296/1'], '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': '2-3267-11.8-c0-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3267-11.8-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.27688895220846, 'root_angle': -0.4605442630349697, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.09112482333349634024479048526', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2650815637450856802693415901074', 'Lhash_array': ['2650815637450856802693415901074'], 'label': '2-3267-11.8-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3267/1/l/a/2296/1'}