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lfunc_lfunctions • Show schema
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{'Lhash': '1609416955983939422483715059462', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.5514938098341108, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.332454244549596, 0.0], 'a6': [0.0, 0.0], 'a7': [1.7138795299550225, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.6958545777146576, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.942181373576766, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]], [79, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 19, 79], 'central_character': '6004.1', 'coefficient_field': 'CDF', 'conductor': 6004, 'conductor_radical': 3002, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.5514938098341108, 0], [3.0, 0]], [[1.0, 0], [2.332454244549596, 0], [5.0, 0]], [[1.0, 0], [-1.7138795299550225, 0], [7.0, 0]], [[1.0, 0], [3.5367104986457023, 0], [11.0, 0]], [[1.0, 0], [-4.698442314704826, 0], [13.0, 0]], [[1.0, 0], [-5.329093800605736, 0], [17.0, 0]], [[1.0, 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'5.54483324590928608289375752517844', '6.19375892566273243034437756397728', '7.32326575596702770075972878191915', '7.918932718787266530937825428864385'], 'prelabel': '2-6004-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.924029273015588, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26960611677553576538793974657', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.45596973089389271541625515594', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.38207075722045803760135891281', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.942181373576766, 'bad_primes': [2, 19, 79], 'central_character': '1.1', 'conductor': 6004, 'conductor_radical': 3002, 'degree': 2, 'index': 81, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6004/2/a/g/1/17'], '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': '2-6004-1.1-c1-0-81', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-6004-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.924029273015588, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26960611677553576538793974657', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1609416955983939422483715059462', 'Lhash_array': ['1609416955983939422483715059462'], 'label': '2-6004-1.1-c1-0-81', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6004/2/a/g/1/17'}