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lfunc_lfunctions • Show schema
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{'Lhash': '629580056885547470776179580853', 'a10': [-0.5721600542664576, 0.0], 'a2': [0.3084485502428215, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.9048594918531017, 0.0], 'a5': [-1.8549610747595768, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [-1.2044482491640098, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.888306657226465, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [127, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 127], 'central_character': '8001.1', 'coefficient_field': 'CDF', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.3084485502428215, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.8549610747595768, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.1584481058838108, 0], [11.0, 0]], [[1.0, 0], [6.948414850096623, 0], [13.0, 0]], [[1.0, 0], [-5.729163916981118, 0], [17.0, 0]], [[1.0, 0], 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'3.44977841199945310394324828548922', '4.43387707664646587971576248430685', '5.08014530738664186958453168943746', '5.29479949835611797294998990186142', '6.54783807973856549944033456396367', '7.33747944686758243853587662143117', '7.78168029185382617789128861105632'], 'prelabel': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49665109358382908424045169508', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.65009083431501245999175859737', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.05591172262925007964176972484', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.888306657226465, 'bad_primes': [3, 7, 127], 'central_character': '1.1', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'index': 46, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8001/2/a/ba/1/23'], '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': '2-8001-1.1-c1-0-46', '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': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.49665109358382908424045169508', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '629580056885547470776179580853', 'Lhash_array': ['629580056885547470776179580853'], 'label': '2-8001-1.1-c1-0-46', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8001/2/a/ba/1/23'}