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lfunc_lfunctions • Show schema
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{'Lhash': '1415005024976340770514298856723', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.0, 1.0], 'a6': [0, 0], 'a7': [0, 4.0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.795065251406015, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '4608.3457', 'coefficient_field': 'CDF', 'conductor': 4608, 'conductor_radical': 6, 'conjugate': '108047405690000721368252608124', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, -1.0], [0, 5.0]], [[1.0, 0], [0, -4.0], [-7.0, 0]], [[1.0, 0], [4.0, 4.0], [0, 11.0]], [[1.0, 0], [3.0, -3.0], [0, -13.0]], [[1.0, 0], [6.0, 0], [17.0, 0]], [[1.0, 0], [-4.0, 4.0], [0, -19.0]], [[1.0, 0], [0, -8.0], [-23.0, 0]], [[1.0, 0], [-3.0, 3.0], [0, -29.0]], [[1.0, 0], [-4.0, 0], [31.0, 0]], [[1.0, 0], [1.0, 1.0], [0, 37.0]], 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'-0.3826834323650897717284599840303988667613445624856270415 + 0.9238795325112867561281831893967882868224166258636424861*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11624214489511659905299625634', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24008687379058077700155885649', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.08006260132763794948884773551', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.795065251406015, 'bad_primes': [2, 3], 'central_character': '16.5', 'conductor': 4608, 'conductor_radical': 6, 'degree': 2, 'index': 56, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4608/2/k/m/3457/1'], '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': '2-4608-16.5-c1-0-56', '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': '2-4608-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': 0.3125, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11624214489511659905299625634', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1415005024976340770514298856723', 'Lhash_array': ['1415005024976340770514298856723'], 'label': '2-4608-16.5-c1-0-56', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4608/2/k/m/3457/1'}