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lfunc_lfunctions • Show schema
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{'Lhash': '2209474599226892813288553902482', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [4.47213595499958, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [31.304951684997057, 0.0], 'a8': [0.0, 0.0], 'a9': [-7.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 94.40305600918502, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '1600.1', 'coefficient_field': 'CDF', 'conductor': 1600, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-4.47213595499958, 0], [27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-31.304951684997057, 0], [343.0, 0]], [[1.0, 0], [-8.94427190999916, 0], [1331.0, 0]], [[1.0, 0], [62.0, 0], [2197.0, 0]], [[1.0, 0], [-46.0, 0], [4913.0, 0]], [[1.0, 0], [107.33126291998991, 0], [6859.0, 0]], [[1.0, 0], [192.3018460649819, 0], [12167.0, 0]], [[1.0, 0], [-90.0, 0], 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'8.422777772779364027269422811469592'], 'prelabel': '2-40e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.716123507303982, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74296813240895893521529564963', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23769358432621297540510257057', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.47495529244211035028379437294', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 94.40305600918502, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 1600, 'conductor_radical': 10, 'degree': 2, 'index': 107, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1600/4/a/cg/1/2'], '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': '2-40e2-1.1-c3-0-107', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-40e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.716123507303982, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74296813240895893521529564963', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2209474599226892813288553902482', 'Lhash_array': ['2209474599226892813288553902482'], 'label': '2-40e2-1.1-c3-0-107', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1600/4/a/cg/1/2'}