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lfunc_lfunctions • Show schema
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{'Lhash': '2323602147549219278660251435899', 'a10': [8.269997078228803, 0.0], 'a2': [2.7832832753243144, 0.0], 'a3': [0.0, 0.0], 'a4': [5.746665790700043, 0.0], 'a5': [2.971309874042614, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.3451285940243747, 0.0], 'a8': [10.42803223348518, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.019860620202847, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 11, 19], 'central_character': '1881.1', 'coefficient_field': 'CDF', 'conductor': 1881, 'conductor_radical': 627, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.7832832753243144, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.971309874042614, 0], [5.0, 0]], [[1.0, 0], [1.3451285940243747, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.4460031289841893, 0], [13.0, 0]], [[1.0, 0], [4.3690211640141765, 0], [17.0, 0]], [[1.0, 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'3.41096969379596577259637059322969', '4.44853854768485588662607170173725', '5.10946327475377384449589243192176', '6.03173679912631214758456579772166', '6.39824443019152864628303376289666', '7.13293898248685562074901331292181', '8.195878666714421716480301860342652', '9.681251927315359466906468886321783'], 'prelabel': '2-1881-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.875546493102985, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.83299889348916415789579579287', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.42392053261770673650481379131', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41096969379596577259637059323', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.019860620202847, 'bad_primes': [3, 11, 19], 'central_character': '1.1', 'conductor': 1881, 'conductor_radical': 627, 'degree': 2, 'index': 64, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1881/2/a/p/1/7'], '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': '2-1881-1.1-c1-0-64', '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': '2-1881-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.875546493102985, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.83299889348916415789579579287', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2323602147549219278660251435899', 'Lhash_array': ['2323602147549219278660251435899'], 'factors': ['2-1881-1.1-c1-0-64'], 'label': '2-1881-1.1-c1-0-64', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1881/2/a/p/1/7'}