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lfunc_lfunctions • Show schema
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{'Lhash': '918998204274222049499913608321,1680585871059404628676096236224', 'a10': 8, 'a2': 2, 'a3': -1, 'a4': 3, 'a5': 4, 'a6': -2, 'a7': 3, 'a8': 4, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4021.7398968476855, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [11, [1, -2, 1]], [19, [1]]], 'bad_primes': [2, 11, 19], 'central_character': '7942.1', 'coefficient_field': '1.1.1.1', 'conductor': 63075364, 'conductor_radical': 418, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, 1, 2, 3, 9], [1, -4, 14, -20, 25], [1, -3, 12, -21, 49], [1, -2, 1], [1, -3, 24, -39, 169], [1, -3, 32, -51, 289], [1], [1, -7, 54, -161, 529], [1, 1, 20, 29, 841], [1, 4, 66, 124, 961], [1, -2, 58, -74, 1369], [1, 4, 86, 164, 1681], [1, 0, 86, 0, 1849], [1, -16, 158, -752, 2209], [1, 5, 6, 265, 2809], [1, -3, 82, -177, 3481], [1, 4, 58, 244, 3721], [1, -3, 98, -201, 4489], [1, 12, 178, 852, 5041], [1, 7, 120, 511, 5329], [1, -8, 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'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1473675384611961859, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.72496175532024712643623898876', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.32574849154556456165089571751', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.73505123945761296776573171653', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4021.7398968476855, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 63075364, 'conductor_radical': 418, 'degree': 4, 'dirichlet_coefficients': [1, 2, -1, 3, 4, -2, 3, 4, -1, 8, 2, -3, 3, 6, -4, 5, 3, -2, 0, 12, -3, 4, 7, -4, 2, 6, 0, 9, -1, -8, -4, 6, -2, 6, 12, -3, 2, 0, -3, 16, -4, -6, 0, 6, -4, 14, 16, -5, -3, 4, -3, 9, -5, 0, 8, 12, 0, -2, 3, -12, -4, -8, -3, 7, 12, -4, 3, 9, -7, 24, -12, -4, -7, 4, -2, 0, 6, -6, 8, 20, -4, -8, 12, -9, 12, 0, 1, 8, 10, -8, 9, 21, 4, 32, 0, -6, 6, -6, -2, 6], 'euler11': [1, -2, 1, 0, 0], 'euler13': [1, -3, 24, -39, 169], 'euler17': [1, -3, 32, -51, 289], 'euler19': [1, 0, 0, 0, 0], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, -7, 54, -161, 529], 'euler29': [1, 1, 20, 29, 841], 'euler3': [1, 1, 2, 3, 9], 'euler31': [1, 4, 66, 124, 961], 'euler37': [1, -2, 58, -74, 1369], 'euler41': [1, 4, 86, 164, 1681], 'euler43': [1, 0, 86, 0, 1849], 'euler47': [1, -16, 158, -752, 2209], 'euler5': [1, -4, 14, -20, 25], 'euler53': [1, 5, 6, 265, 2809], 'euler59': [1, -3, 82, -177, 3481], 'euler61': [1, 4, 58, 244, 3721], 'euler67': [1, -3, 98, -201, 4489], 'euler7': [1, -3, 12, -21, 49], 'euler71': [1, 12, 178, 852, 5041], 'euler73': [1, 7, 120, 511, 5329], 'euler79': [1, -8, 174, -632, 6241], 'euler83': [1, -12, 134, -996, 6889], 'euler89': [1, -10, 186, -890, 7921], 'euler97': [1, -6, 186, -582, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, 1, 2, 3, 9], [1, -4, 14, -20, 25], [1, -3, 12, -21, 49], [1, -2, 1, 0, 0], [1, -3, 24, -39, 169], [1, -3, 32, -51, 289], [1, 0, 0, 0, 0], [1, -7, 54, -161, 529], [1, 1, 20, 29, 841], [1, 4, 66, 124, 961], [1, -2, 58, -74, 1369], [1, 4, 86, 164, 1681], [1, 0, 86, 0, 1849], [1, -16, 158, -752, 2209], [1, 5, 6, 265, 2809], [1, -3, 82, -177, 3481], [1, 4, 58, 244, 3721], [1, -3, 98, -201, 4489], [1, 12, 178, 852, 5041], [1, 7, 120, 511, 5329], [1, -8, 174, -632, 6241], [1, -12, 134, -996, 6889], [1, -10, 186, -890, 7921], [1, -6, 186, -582, 9409]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7942/2/a/x'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '4-7942e2-1.1-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': '4-7942e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.9634910237471175, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1473675384611961859, 'z1': {'__RealLiteral__': 0, 'data': '0.72496175532024712643623898876', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '918998204274222049499913608321,1680585871059404628676096236224', 'Lhash_array': ['918998204274222049499913608321', '1680585871059404628676096236224'], 'label': '4-7942e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7942/2/a/x'}