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lfunc_lfunctions • Show schema
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{'Lhash': '1369248004351379560591374586671', 'a10': 8, 'a2': 2, 'a3': -2, 'a4': 2, 'a5': 4, 'a6': -4, 'a7': 1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.043966331139835, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[4013, [1, None]]], 'bad_primes': [4013], 'central_character': '4013.1', 'coefficient_field': '1.1.1.1', 'conductor': 4013, 'conductor_radical': 4013, 'degree': 2, 'euler_factors': [[1, -2, 2], [1, 2, 3], [1, -4, 5], [1, -1, 7], [1, -3, 11], [1, -2, 13], [1, 2, 17], [1, -1, 19], [1, 0, 23], [1, -8, 29], [1, 5, 31], [1, 4, 37], [1, -5, 41], [1, -5, 43], [1, -12, 47], [1, -1, 53], [1, -7, 59], [1, 7, 61], [1, 7, 67], [1, -4, 71], [1, 13, 73], [1, -4, 79], [1, -12, 83], [1, 10, 89], [1, 17, 97], [1, -12, 101], [1, -14, 103], [1, 8, 107], [1, -11, 109], [1, -4, 113]], 'euler_factors_factorization': [[[[1, -2, 2], 1]], [[[1, 2, 3], 1]], [[[1, -4, 5], 1]], [[[1, -1, 7], 1]], [[[1, -3, 11], 1]], [[[1, -2, 13], 1]], [[[1, 2, 17], 1]], [[[1, -1, 19], 1]], [[[1, 0, 23], 1]], [[[1, -8, 29], 1]], [[[1, 5, 31], 1]], [[[1, 4, 37], 1]], [[[1, -5, 41], 1]], [[[1, -5, 43], 1]], [[[1, -12, 47], 1]], [[[1, -1, 53], 1]], [[[1, -7, 59], 1]], [[[1, 7, 61], 1]], [[[1, 7, 67], 1]], [[[1, -4, 71], 1]], [[[1, 13, 73], 1]], [[[1, -4, 79], 1]], [[[1, -12, 83], 1]], [[[1, 10, 89], 1]], [[[1, 17, 97], 1]], [[[1, -12, 101], 1]], [[[1, -14, 103], 1]], [[[1, 8, 107], 1]], [[[1, -11, 109], 1]], [[[1, -4, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 167, 'label': '2-4013-1.1-c1-0-167', 'leading_term': '4.22426648562893000275230864804000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4013/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': 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1916120892413200307, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08014622018469319166471885891', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.10489078586203324162174094622', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.02865667935775685711300181536', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.043966331139835, 'bad_primes': [4013], 'central_character': '1.1', 'conductor': 4013, 'conductor_radical': 4013, 'degree': 2, 'dirichlet_coefficients': [1, 2, -2, 2, 4, -4, 1, 0, 1, 8, 3, -4, 2, 2, -8, -4, -2, 2, 1, 8, -2, 6, 0, 0, 11, 4, 4, 2, 8, -16, -5, -8, -6, -4, 4, 2, -4, 2, -4, 0, 5, -4, 5, 6, 4, 0, 12, 8, -6, 22, 4, 4, 1, 8, 12, 0, -2, 16, 7, -16, -7, -10, 1, -8, 8, -12, -7, -4, 0, 8, 4, 0, -13, -8, -22, 2, 3, -8, 4, -16, -11, 10, 12, -4, -8, 10, -16, 0, -10, 8, 2, 0, 10, 24, 4, 16, -17, -12, 3, 22], 'euler11': [1, -3, 11], 'euler13': [1, -2, 13], 'euler17': [1, 2, 17], 'euler19': [1, -1, 19], 'euler2': [1, -2, 2], 'euler23': [1, 0, 23], 'euler29': [1, -8, 29], 'euler3': [1, 2, 3], 'euler31': [1, 5, 31], 'euler37': [1, 4, 37], 'euler41': [1, -5, 41], 'euler43': [1, -5, 43], 'euler47': [1, -12, 47], 'euler5': [1, -4, 5], 'euler53': [1, -1, 53], 'euler59': [1, -7, 59], 'euler61': [1, 7, 61], 'euler67': [1, 7, 67], 'euler7': [1, -1, 7], 'euler71': [1, -4, 71], 'euler73': [1, 13, 73], 'euler79': [1, -4, 79], 'euler83': [1, -12, 83], 'euler89': [1, 10, 89], 'euler97': [1, 17, 97], 'euler_factors': [[1, -2, 2], [1, 2, 3], [1, -4, 5], [1, -1, 7], [1, -3, 11], [1, -2, 13], [1, 2, 17], [1, -1, 19], [1, 0, 23], [1, -8, 29], [1, 5, 31], [1, 4, 37], [1, -5, 41], [1, -5, 43], [1, -12, 47], [1, -1, 53], [1, -7, 59], [1, 7, 61], [1, 7, 67], [1, -4, 71], [1, 13, 73], [1, -4, 79], [1, -12, 83], [1, 10, 89], [1, 17, 97]], 'index': 167, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4013/a', 'ModularForm/GL2/Q/holomorphic/4013/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/4013/2/a/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-4013-1.1-c1-0-167', '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': '2-4013-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.660739026941609, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1916120892413200307, 'z1': {'__RealLiteral__': 0, 'data': '1.08014622018469319166471885891', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20195732
{'Lhash': '1369248004351379560591374586671', 'Lhash_array': ['1369248004351379560591374586671'], 'label': '2-4013-1.1-c1-0-167', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4013/2/a/a'}
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id: 24564065
{'Lhash': '1369248004351379560591374586671', 'Lhash_array': ['1369248004351379560591374586671'], 'label': '2-4013-1.1-c1-0-167', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4013/2/a/a/1/1'}
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id: 91152
{'Lhash': '1916120892413200307', 'Lhash_array': ['1916120892413200307'], 'label': '2-4013-1.1-c1-0-167', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4013/a'}