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lfunc_lfunctions • Show schema
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{'Lhash': '4511783833370783065198350477735,6240177757709270566055035550805', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -1, 'a5': -6, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.053622889171894485, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[29, [1, 6, 29]]], 'bad_primes': [29], 'central_character': '29.1', 'coefficient_field': '1.1.1.1', 'conductor': 841, 'conductor_radical': 29, 'degree': 4, 'euler_factors': [[1, 0, 1, 0, 4], [1, 0, -1, 0, 9], [1, 6, 19, 30, 25], [1, -4, 18, -28, 49], [1, 0, -17, 0, 121], [1, 2, 27, 26, 169], [1, 0, -14, 0, 289], [1, 0, -38, 0, 361], [1, -12, 82, -276, 529], [1, 6, 29], [1, 0, -17, 0, 961], [1, 0, -74, 0, 1369], [1, 0, -62, 0, 1681], [1, 0, -41, 0, 1849], [1, 0, -89, 0, 2209], [1, 18, 187, 954, 2809], [1, -12, 154, -708, 3481], [1, 0, 58, 0, 3721], [1, -16, 198, -1072, 4489], [1, 0, 142, 0, 5041], [1, 0, -146, 0, 5329], [1, 0, -113, 0, 6241], [1, 12, 202, 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'c1e2-0', 'trace_hash': 274836600842853888, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.55916987895440262001177104646', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.60354096694864069732607307798', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.92263227468655885794947561274', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.053622889171894485, 'bad_primes': [29], 'central_character': '1.1', 'conductor': 841, 'conductor_radical': 29, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, -6, 0, 4, 0, 1, 0, 0, 0, -2, 0, 0, -3, 0, 0, 0, 6, 0, 0, 12, 0, 17, 0, 0, -4, -6, 0, 0, 0, 0, 0, -24, -1, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -2, 0, 0, 2, -18, 0, 0, 0, 0, 0, 12, 0, 0, 0, 4, 7, 12, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, -8, 0, -12, 0, 0, 0, 0, 0, 0, 0, -8, -12, 0, 0, 0, 0, 0, 0, 0, -17], 'euler11': [1, 0, -17, 0, 121], 'euler13': [1, 2, 27, 26, 169], 'euler17': [1, 0, -14, 0, 289], 'euler19': [1, 0, -38, 0, 361], 'euler2': [1, 0, 1, 0, 4], 'euler23': [1, -12, 82, -276, 529], 'euler29': [1, 6, 29, 0, 0], 'euler3': [1, 0, -1, 0, 9], 'euler31': [1, 0, -17, 0, 961], 'euler37': [1, 0, -74, 0, 1369], 'euler41': [1, 0, -62, 0, 1681], 'euler43': [1, 0, -41, 0, 1849], 'euler47': [1, 0, -89, 0, 2209], 'euler5': [1, 6, 19, 30, 25], 'euler53': [1, 18, 187, 954, 2809], 'euler59': [1, -12, 154, -708, 3481], 'euler61': [1, 0, 58, 0, 3721], 'euler67': [1, -16, 198, -1072, 4489], 'euler7': [1, -4, 18, -28, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, -146, 0, 5329], 'euler79': [1, 0, -113, 0, 6241], 'euler83': [1, 12, 202, 996, 6889], 'euler89': [1, 0, -158, 0, 7921], 'euler97': [1, 0, -14, 0, 9409], 'euler_factors': [[1, 0, 1, 0, 4], [1, 0, -1, 0, 9], [1, 6, 19, 30, 25], [1, -4, 18, -28, 49], [1, 0, -17, 0, 121], [1, 2, 27, 26, 169], [1, 0, -14, 0, 289], [1, 0, -38, 0, 361], [1, -12, 82, -276, 529], [1, 6, 29, 0, 0], [1, 0, -17, 0, 961], [1, 0, -74, 0, 1369], [1, 0, -62, 0, 1681], [1, 0, -41, 0, 1849], [1, 0, -89, 0, 2209], [1, 18, 187, 954, 2809], [1, -12, 154, -708, 3481], [1, 0, 58, 0, 3721], [1, -16, 198, -1072, 4489], [1, 0, 142, 0, 5041], [1, 0, -146, 0, 5329], [1, 0, -113, 0, 6241], [1, 12, 202, 996, 6889], [1, 0, -158, 0, 7921], [1, 0, -14, 0, 9409]], 'index': 1, 'instance_types': ['HMF', 'ECNF', 'CMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.29.1/holomorphic/2.2.29.1-1.1-a', 'EllipticCurve/2.2.29.1/1.1/a', 'ModularForm/GL2/Q/holomorphic/29/2/b/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-29e2-1.1-c1e2-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-29e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.4812132228666553, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 274836600842853888, 'z1': {'__RealLiteral__': 0, 'data': '3.55916987895440262001177104646', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9955614
{'Lhash': '4511783833370783065198350477735,6240177757709270566055035550805', 'Lhash_array': ['4511783833370783065198350477735', '6240177757709270566055035550805'], 'label': '4-29e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/29/2/b/a'}
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id: 9482088
{'Lhash': '_4511783833370783065198350477735', 'Lhash_array': ['_4511783833370783065198350477735'], 'label': '4-29e2-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.29.1/1.1/a'}
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id: 9481754
{'Lhash': '_4511783833370783065198350477735', 'Lhash_array': ['_4511783833370783065198350477735'], 'label': '4-29e2-1.1-c1e2-0-1', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.29.1/holomorphic/2.2.29.1-1.1-a'}