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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': -3, 'A5': 2, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '734083615354671920,1109683623272241717', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896257, 0], 'a4': [-1.5, 0], 'a5': [0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.762234739028385, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [5, [1, -2, 1]], [7, [1, -1]]], 'bad_primes': [3, 5, 7], 'central_character': '231525.1', 'coefficient_field': '1.1.1.1', 'conductor': 231525, 'conductor_radical': 105, 'degree': 4, 'euler_factors': [[1, 0, 3, 0, 4], [1, -1], [1, -2, 1], [1, -1], [1, 0, 22, 0, 121], [1, 0, -10, 0, 169], [1, -4, 38, -68, 289], [1, 0, -26, 0, 361], [1, 0, -18, 0, 529], [1, 0, 54, 0, 841], [1, 0, 46, 0, 961], [1, 4, 78, 148, 1369], [1, 12, 118, 492, 1681], [1, -8, 102, -344, 1849], [1, 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'symplectic', 'trace_hash': 1843767238626913637, 'z1': {'__RealLiteral__': 0, 'data': '0.888154170390839902230274080915430', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '1.79849192746842450415563444507533', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.63294756479994443235170715895375', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.762234739028385, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 231525, 'conductor_radical': 105, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, -3, 2, 0, 1, 0, 1, 0, 0, -3, 0, 0, 2, 5, 4, 0, 0, -6, 1, 0, 0, 0, 3, 0, 1, -3, 0, 0, 0, 0, 0, 0, 2, -3, -4, 0, 0, 0, -12, 0, 8, 0, 2, 0, 16, 5, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, -6, 0, 0, 1, -3, 0, 0, 8, -12, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 16, 10, 1, 0, -8, -3, 8, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 0, -10, 0, 169], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, 0, -26, 0, 361], 'euler2': [1, 0, 3, 0, 4], 'euler23': [1, 0, -18, 0, 529], 'euler29': [1, 0, 54, 0, 841], 'euler3': [1, -1, 0, 0, 0], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, -16, 158, -752, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, 0, 6, 0, 2809], 'euler59': [1, -8, 134, -472, 3481], 'euler61': [1, 0, 118, 0, 3721], 'euler67': [1, -8, 150, -536, 4489], 'euler7': [1, -1, 0, 0, 0], 'euler71': [1, 0, -2, 0, 5041], 'euler73': [1, 0, 142, 0, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, 8, 182, 664, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 0, -130, 0, 9409], 'euler_factors': [[1, 0, 3, 0, 4], [1, -1, 0, 0, 0], [1, -2, 1, 0, 0], [1, -1, 0, 0, 0], [1, 0, 22, 0, 121], [1, 0, -10, 0, 169], [1, -4, 38, -68, 289], [1, 0, -26, 0, 361], [1, 0, -18, 0, 529], [1, 0, 54, 0, 841], [1, 0, 46, 0, 961], [1, 4, 78, 148, 1369], [1, 12, 118, 492, 1681], [1, -8, 102, -344, 1849], [1, -16, 158, -752, 2209], [1, 0, 6, 0, 2809], [1, -8, 134, -472, 3481], [1, 0, 118, 0, 3721], [1, -8, 150, -536, 4489], [1, 0, -2, 0, 5041], [1, 0, 142, 0, 5329], [1, -16, 222, -1264, 6241], [1, 8, 182, 664, 6889], [1, 12, 214, 1068, 7921], [1, 0, -130, 0, 9409]], 'index': 8, 'instance_types': ['ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.21.1/525.1/k', 'ModularForm/GL2/TotallyReal/2.2.21.1/holomorphic/2.2.21.1-525.1-k'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, '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': '4-231525-1.1-c1e2-0-8', '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': '4-231525-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.9601442220202343, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1843767238626913637, 'z1': {'__RealLiteral__': 0, 'data': '0.888154170390839902230274080915430', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9548827
{'Lhash': '734083615354671920,1109683623272241717', 'Lhash_array': ['734083615354671920', '1109683623272241717'], 'label': '4-231525-1.1-c1e2-0-8', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.21.1/holomorphic/2.2.21.1-525.1-k'}
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id: 9548465
{'Lhash': '734083615354671920,1109683623272241717', 'Lhash_array': ['734083615354671920', '1109683623272241717'], 'label': '4-231525-1.1-c1e2-0-8', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.21.1/525.1/k'}