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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': -4, 'A4': 1, 'A5': 0, 'A6': 4, 'A7': 0, 'A8': -1, 'A9': 6, 'Lhash': '1287195056736887883,1459918945821948014', 'a10': [0.0, 0], 'a2': [-0.7071067811865476, 0], 'a3': [-2.309401076758503, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [1.6329931618554518, 0], 'a7': [0.0, 0], 'a8': [-0.3535533905932738, 0], 'a9': [2.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.09171126037162, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [7, [1, 0, -1]], [19, [1, -2, 19]]], 'bad_primes': [2, 7, 19], 'central_character': '566048.1', 'coefficient_field': '1.1.1.1', 'conductor': 566048, 'conductor_radical': 266, 'degree': 4, 'euler_factors': [[1, 1], [1, 4, 10, 12, 9], [1, 0, 10, 0, 25], [1, 0, -1], [1, 0, 22, 0, 121], [1, 0, 10, 0, 169], [1, -12, 70, -204, 289], [1, -2, 19], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, 8, 78, 248, 961], [1, 0, 70, 0, 1369], [1, 0, 46, 0, 1681], [1, 0, 22, 0, 1849], [1, 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'z1': {'__RealLiteral__': 0, 'data': '0.905061494360852486185250338718849', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '1.53114392297898773356855355003236', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.56658671720506586948973480293986', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.09171126037162, 'bad_primes': [2, 7, 19], 'central_character': '1.1', 'conductor': 566048, 'conductor_radical': 266, 'degree': 4, 'dirichlet_coefficients': [1, -1, -4, 1, 0, 4, 0, -1, 6, 0, 0, -4, 0, 0, 0, 1, 12, -6, 2, 0, 0, 0, 0, 4, -10, 0, 4, 0, 0, 0, -8, -1, 0, -12, 0, 6, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 1, 10, -48, 0, 0, -4, 0, 0, -8, 0, -12, 0, 16, 8, 0, 1, 0, 0, -8, 12, 0, 0, 0, -6, 4, 0, 40, 2, 0, 0, 16, 0, -37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 4, 0, -1, 0, -10], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, -12, 70, -204, 289], 'euler19': [1, -2, 19, 0, 0], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 4, 10, 12, 9], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 12, 154, 708, 3481], 'euler61': [1, -16, 186, -976, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 0, -1, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, 0, 130, 0, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, 0, 94, 0, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, 4, 10, 12, 9], [1, 0, 10, 0, 25], [1, 0, -1, 0, 0], [1, 0, 22, 0, 121], [1, 0, 10, 0, 169], [1, -12, 70, -204, 289], [1, -2, 19, 0, 0], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, 8, 78, 248, 961], [1, 0, 70, 0, 1369], [1, 0, 46, 0, 1681], [1, 0, 22, 0, 1849], [1, 0, -50, 0, 2209], [1, 0, 70, 0, 2809], [1, 12, 154, 708, 3481], [1, -16, 186, -976, 3721], [1, 8, 150, 536, 4489], [1, 0, 142, 0, 5041], [1, -4, 150, -292, 5329], [1, -16, 222, -1264, 6241], [1, 0, 130, 0, 6889], [1, 0, 142, 0, 7921], [1, 0, 94, 0, 9409]], 'index': 0, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.76.1/holomorphic/2.2.76.1-98.1-a', 'EllipticCurve/2.2.76.1/98.1/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': '4-566048-1.1-c1e2-0-0', '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': '4-566048-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.451048294866942, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 441270993345141946, 'z1': {'__RealLiteral__': 0, 'data': '0.905061494360852486185250338718849', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9481080
{'Lhash': '1287195056736887883,1459918945821948014', 'Lhash_array': ['1287195056736887883', '1459918945821948014'], 'label': '4-566048-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.76.1/98.1/a'}
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id: 9481268
{'Lhash': '1287195056736887883,1459918945821948014', 'Lhash_array': ['1287195056736887883', '1459918945821948014'], 'label': '4-566048-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.76.1/holomorphic/2.2.76.1-98.1-a'}