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lfunc_lfunctions • Show schema
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{'A10': -4, 'A2': 1, 'A3': -1, 'A4': -1, 'A5': -4, 'A6': -1, 'A7': 0, 'A8': -3, 'A9': 1, 'Lhash': '325345116008142531,2215180138185436427', 'a10': [-1.264911064067352, 0], 'a2': [0.7071067811865476, 0], 'a3': [-0.5773502691896257, 0], 'a4': [-0.5, 0], 'a5': [-1.788854381999832, 0], 'a6': [-0.40824829046386296, 0], 'a7': [0.0, 0], 'a8': [-1.0606601717798214, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.331632165485225, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 2]], [3, [1, 1]], [11, [1, 0, -1]]], 'bad_primes': [2, 3, 11], 'central_character': '209088.1', 'coefficient_field': '1.1.1.1', 'conductor': 209088, 'conductor_radical': 66, 'degree': 4, 'euler_factors': [[1, -1, 2], [1, 1], [1, 4, 14, 20, 25], [1, 0, -2, 0, 49], [1, 0, -1], [1, 0, 22, 0, 169], [1, 0, 30, 0, 289], [1, 0, 38, 0, 361], [1, -16, 110, -368, 529], [1, 12, 94, 348, 841], [1, 0, -2, 0, 961], [1, 0, 38, 0, 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'trace_hash': 234682244979885007, 'z1': {'__RealLiteral__': 0, 'data': '1.06341230628835129193123862023277', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.57961275990012009877837343881944', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.31425171933473999322603981332143', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.331632165485225, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 209088, 'conductor_radical': 66, 'degree': 4, 'dirichlet_coefficients': [1, 1, -1, -1, -4, -1, 0, -3, 1, -4, 0, 1, 0, 0, 4, -1, 0, 1, 0, 4, 0, 0, 16, 3, 2, 0, -1, 0, -12, 4, 0, 5, 0, 0, 0, -1, 0, 0, 0, 12, 0, 0, 0, 0, -4, 16, 16, 1, 2, 2, 0, 0, 12, -1, 0, 0, 0, -12, 0, -4, 0, 0, 0, 7, 0, 0, -8, 0, -16, 0, 0, -3, -28, 0, -2, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 12, 0, 0, -4, 0, -16, 0, 16, 0, -5, 4, 2, 0, -2], 'euler11': [1, 0, -1, 0, 0], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 0, 30, 0, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, -1, 2, 0, 0], 'euler23': [1, -16, 110, -368, 529], 'euler29': [1, 12, 94, 348, 841], 'euler3': [1, 1, 0, 0, 0], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, 0, 38, 0, 1369], 'euler41': [1, 0, 78, 0, 1681], 'euler43': [1, 0, 86, 0, 1849], 'euler47': [1, -16, 158, -752, 2209], 'euler5': [1, 4, 14, 20, 25], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 0, 102, 0, 3481], 'euler61': [1, 0, 86, 0, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 28, 342, 2044, 5329], 'euler79': [1, 0, 142, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, -1, 2, 0, 0], [1, 1, 0, 0, 0], [1, 4, 14, 20, 25], [1, 0, -2, 0, 49], [1, 0, -1, 0, 0], [1, 0, 22, 0, 169], [1, 0, 30, 0, 289], [1, 0, 38, 0, 361], [1, -16, 110, -368, 529], [1, 12, 94, 348, 841], [1, 0, -2, 0, 961], [1, 0, 38, 0, 1369], [1, 0, 78, 0, 1681], [1, 0, 86, 0, 1849], [1, -16, 158, -752, 2209], [1, -12, 142, -636, 2809], [1, 0, 102, 0, 3481], [1, 0, 86, 0, 3721], [1, 8, 150, 536, 4489], [1, 0, 142, 0, 5041], [1, 28, 342, 2044, 5329], [1, 0, 142, 0, 6241], [1, 0, 22, 0, 6889], [1, 0, 142, 0, 7921], [1, -4, 198, -388, 9409]], 'index': 35, 'instance_types': ['ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.24.1/363.1/a', 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-363.1-a'], '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': '4-209088-1.1-c1e2-0-35', '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': 1, 'prelabel': '4-209088-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.9108246301713243, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 234682244979885007, 'z1': {'__RealLiteral__': 0, 'data': '1.06341230628835129193123862023277', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9511973
{'Lhash': '325345116008142531,2215180138185436427', 'Lhash_array': ['325345116008142531', '2215180138185436427'], 'label': '4-209088-1.1-c1e2-0-35', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-363.1-a'}
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id: 9512344
{'Lhash': '325345116008142531,2215180138185436427', 'Lhash_array': ['325345116008142531', '2215180138185436427'], 'label': '4-209088-1.1-c1e2-0-35', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/363.1/a'}