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lfunc_lfunctions • Show schema
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{'Lhash': '1573000076660613217887787103142', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.0, 1.0], 'a4': [0, 0], 'a5': [2.0, -1.0], 'a6': [0, 0], 'a7': [2.0, 0], 'a8': [0, 0], 'a9': [0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.304441810213165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.0, 1.0]]], [13, [[1.0, 0], [-2.0, 3.0]]]], 'bad_primes': [2, 5, 13], 'central_character': '1040.177', 'coefficient_field': 'CDF', 'conductor': 1040, 'conductor_radical': 130, 'conjugate': '1393032691766393671444892104915', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, -1.0], [0, -3.0]], [[1.0, 0], [-2.0, 1.0]], [[1.0, 0], [-2.0, 0], [7.0, 0]], [[1.0, 0], [-1.0, 1.0], [0, -11.0]], [[1.0, 0], [-2.0, 3.0]], [[1.0, 0], [1.0, -1.0], [0, -17.0]], [[1.0, 0], [-3.0, 3.0], [0, -19.0]], [[1.0, 0], [1.0, 1.0], [0, 23.0]], [[1.0, 0], [0, -8.0], [-29.0, 0]], [[1.0, 0], [1.0, 1.0], 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2.881742842484937, 'root_angle': -0.043041246108718414, 'root_number': '0.99087195853547352101588987194876242877527148948770498107 - 0.13480638630300436645901392659965655055833662479289217066*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.021520623054359207', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24087826438721230777347148708', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.15518095014858741026724343543', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64844216811107268698501303834', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.304441810213165, 'bad_primes': [2, 5, 13], 'central_character': '65.47', 'conductor': 1040, 'conductor_radical': 130, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1040/2/cd/c/177/1'], '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': '2-1040-65.47-c1-0-23', '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': '2-1040-65.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.881742842484937, 'root_angle': -0.021520623054359207, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24087826438721230777347148708', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1573000076660613217887787103142', 'Lhash_array': ['1573000076660613217887787103142'], 'label': '2-1040-65.47-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1040/2/cd/c/177/1'}