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lfunc_lfunctions • Show schema
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{'Lhash': '2460824945839944308039492522424', 'a10': -1, 'a2': 1, 'a3': 0, 'a4': 1, 'a5': -1, 'a6': 0, 'a7': 1, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.103956112958265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [7, [1, -1]], [17, [1, -1]]], 'bad_primes': [2, 3, 7, 17], 'central_character': '2142.1', 'coefficient_field': '1.1.1.1', 'conductor': 2142, 'conductor_radical': 714, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, 1, 5], [1, -1], [1, 5, 11], [1, 1, 13], [1, -1], [1, 6, 19], [1, 6, 23], [1, 6, 29], [1, -4, 31], [1, -11, 37], [1, 0, 41], [1, 9, 43], [1, 4, 47], [1, -7, 53], [1, 12, 59], [1, -6, 61], [1, -13, 67], [1, 4, 71], [1, 13, 73], [1, -15, 79], [1, 13, 83], [1, 13, 89], [1, 9, 97], [1, 4, 101], [1, 1, 103], [1, 0, 107], [1, 14, 109], [1, -13, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [1], [[[1, 1, 5], 1]], [[[1, -1], 1]], [[[1, 5, 11], 1]], [[[1, 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1.2161368532701005, 1.2901058675202557, 1.2857280780359455, 1.205596470576671, 1.0567197212049613, 0.8501290453478672, 0.6002562385923342, 0.32411627542416716], 'positive_zeros': ['1.94124859436574581607193810396218', '2.75538936400630092821215712430502', '3.92372992981631625850996692436796', '4.56902455627867224907319278116102', '5.47583971400052312613240501777059', '6.14279974211800228995769619333233', '7.17784034658125445256753156097575', '8.058182215350688246291268937666767', '8.214818534375034915463026148943986'], 'prelabel': '2-2142-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.13569294229616, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 2250887105077805786, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.94124859436574581607193810396', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.75538936400630092821215712431', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.92372992981631625850996692437', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.103956112958265, 'bad_primes': [2, 3, 7, 17], 'central_character': '1.1', 'conductor': 2142, 'conductor_radical': 714, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, -1, 0, 1, 1, 0, -1, -5, 0, -1, 1, 0, 1, 1, 0, -6, -1, 0, -5, -6, 0, -4, -1, 0, 1, -6, 0, 4, 1, 0, 1, -1, 0, 11, -6, 0, -1, 0, 0, -9, -5, 0, -6, -4, 0, 1, -4, 0, -1, 7, 0, 5, 1, 0, -6, -12, 0, 6, 4, 0, 1, 1, 0, 13, 1, 0, -1, -4, 0, -13, 11, 0, -6, -5, 0, 15, -1, 0, 0, -13, 0, -1, -9, 0, -5, -13, 0, -1, -6, 0, -4, 6, 0, -9, 1, 0, -4], 'euler11': [1, 5, 11], 'euler13': [1, 1, 13], 'euler17': [1, -1, 0], 'euler19': [1, 6, 19], 'euler2': [1, -1, 0], 'euler23': [1, 6, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -11, 37], 'euler41': [1, 0, 41], 'euler43': [1, 9, 43], 'euler47': [1, 4, 47], 'euler5': [1, 1, 5], 'euler53': [1, -7, 53], 'euler59': [1, 12, 59], 'euler61': [1, -6, 61], 'euler67': [1, -13, 67], 'euler7': [1, -1, 0], 'euler71': [1, 4, 71], 'euler73': [1, 13, 73], 'euler79': [1, -15, 79], 'euler83': [1, 13, 83], 'euler89': [1, 13, 89], 'euler97': [1, 9, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 1, 5], [1, -1, 0], [1, 5, 11], [1, 1, 13], [1, -1, 0], [1, 6, 19], [1, 6, 23], [1, 6, 29], [1, -4, 31], [1, -11, 37], [1, 0, 41], [1, 9, 43], [1, 4, 47], [1, -7, 53], [1, 12, 59], [1, -6, 61], [1, -13, 67], [1, 4, 71], [1, 13, 73], [1, -15, 79], [1, 13, 83], [1, 13, 89], [1, 9, 97]], 'index': 38, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2142/q', 'ModularForm/GL2/Q/holomorphic/2142/2/a/q/1/1', 'ModularForm/GL2/Q/holomorphic/2142/2/a/q'], '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': '2-2142-1.1-c1-0-38', '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': '2-2142-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.13569294229616, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2250887105077805786, 'z1': {'__RealLiteral__': 0, 'data': '1.94124859436574581607193810396', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20630235
{'Lhash': '2460824945839944308039492522424', 'Lhash_array': ['2460824945839944308039492522424'], 'factors': ['2-2142-1.1-c1-0-38'], 'label': '2-2142-1.1-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2142/2/a/q'}
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id: 24555984
{'Lhash': '2460824945839944308039492522424', 'Lhash_array': ['2460824945839944308039492522424'], 'factors': ['2-2142-1.1-c1-0-38'], 'label': '2-2142-1.1-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2142/2/a/q/1/1'}
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id: 32962
{'Lhash': '2250887105077805786', 'Lhash_array': ['2250887105077805786'], 'factors': ['2-2142-1.1-c1-0-38'], 'label': '2-2142-1.1-c1-0-38', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2142/q'}