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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': -1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': -3, 'A9': 1, 'Lhash': '1987289888788844114855851804750', 'a10': [0.0, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [-1.0606601717798214, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.61388896921551, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 2]], [3, [1, 0, -1]], [17, [1, 2, 17]]], 'bad_primes': [2, 3, 17], 'central_character': '166464.1', 'coefficient_field': '1.1.1.1', 'conductor': 166464, 'conductor_radical': 102, 'degree': 4, 'euler_factors': [[1, -1, 2], [1, 0, -1], [1, 0, 10, 0, 25], [1, 0, 2, 0, 49], [1, 0, 6, 0, 121], [1, 0, 22, 0, 169], [1, 2, 17], [1, 0, 22, 0, 361], [1, 0, -30, 0, 529], [1, 0, 58, 0, 841], [1, 0, -46, 0, 961], [1, 0, 10, 0, 1369], [1, 0, -18, 0, 1681], [1, 0, 70, 0, 1849], [1, 16, 158, 752, 2209], [1, 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-0.22651292653126817, 0.04916787008807459, 0.24417807398621022], 'positive_zeros': ['1.56769530060653144854680691564091', '2.45336032252096177013300497759965', '3.28532150713041810310982697520381', '3.79884678729776031688190779910596', '4.36159397767822262013932326899977', '4.81099171488550293269767138311666', '5.45184408676781858561883617451905', '5.87647456361852564136261392179976', '6.45990116372875969103688741620166', '6.85505714070999859977992001648727', '7.61015041301891599610023453537019', '8.040243271667994896507365067816602', '8.466527665107842666653023212385882', '8.990627621060578483098017594856390'], 'prelabel': '4-408e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.8049643770635035, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2253514669316047724, 'z1': {'__RealLiteral__': 0, 'data': '1.56769530060653144854680691564091', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.45336032252096177013300497759965', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.28532150713041810310982697520381', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.61388896921551, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 166464, 'conductor_radical': 102, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, -1, 0, 0, 0, -3, 1, 0, 0, 0, 0, 0, 0, -1, -2, 1, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 5, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, -2, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 2, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, -16, 0, 0, 0, -2, 0, 10], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 2, 17, 0, 0], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, -1, 2, 0, 0], 'euler23': [1, 0, -30, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 0, -46, 0, 961], 'euler37': [1, 0, 10, 0, 1369], 'euler41': [1, 0, -18, 0, 1681], 'euler43': [1, 0, 70, 0, 1849], 'euler47': [1, 16, 158, 752, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, 0, 58, 0, 3721], 'euler67': [1, 0, -10, 0, 4489], 'euler7': [1, 0, 2, 0, 49], 'euler71': [1, 0, 2, 0, 5041], 'euler73': [1, 0, -146, 0, 5329], 'euler79': [1, 0, -142, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 20, 278, 1780, 7921], 'euler97': [1, 0, 62, 0, 9409], 'euler_factors': [[1, -1, 2, 0, 0], [1, 0, -1, 0, 0], [1, 0, 10, 0, 25], [1, 0, 2, 0, 49], [1, 0, 6, 0, 121], [1, 0, 22, 0, 169], [1, 2, 17, 0, 0], [1, 0, 22, 0, 361], [1, 0, -30, 0, 529], [1, 0, 58, 0, 841], [1, 0, -46, 0, 961], [1, 0, 10, 0, 1369], [1, 0, -18, 0, 1681], [1, 0, 70, 0, 1849], [1, 16, 158, 752, 2209], [1, 0, 70, 0, 2809], [1, 0, -26, 0, 3481], [1, 0, 58, 0, 3721], [1, 0, -10, 0, 4489], [1, 0, 2, 0, 5041], [1, 0, -146, 0, 5329], [1, 0, -142, 0, 6241], [1, 0, 22, 0, 6889], [1, 20, 278, 1780, 7921], [1, 0, 62, 0, 9409]], 'index': 45, 'instance_types': ['HMF', 'ECNF', 'ECNF', 'HMF', 'ECNF', 'HMF', 'HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.136.1/holomorphic/2.2.136.1-9.1-c', 'EllipticCurve/2.2.136.1/9.1/c', 'EllipticCurve/2.2.136.1/9.1/d', 'ModularForm/GL2/TotallyReal/2.2.136.1/holomorphic/2.2.136.1-9.1-d', 'EllipticCurve/2.2.17.1/576.6/e', 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-576.7-e', 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-576.6-e', 'EllipticCurve/2.2.17.1/576.7/e'], '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': '4-408e2-1.1-c1e2-0-45', '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': '4-408e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.8049643770635035, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2253514669316047724, 'z1': {'__RealLiteral__': 0, 'data': '1.56769530060653144854680691564091', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9492076
{'Lhash': '1987289888788844114855851804750', 'Lhash_array': ['1987289888788844114855851804750'], 'label': '4-408e2-1.1-c1e2-0-45', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.17.1/576.7/e'}
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id: 9491482
{'Lhash': '1987289888788844114855851804750', 'Lhash_array': ['1987289888788844114855851804750'], 'label': '4-408e2-1.1-c1e2-0-45', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-576.6-e'}
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id: 9491360
{'Lhash': '1987289888788844114855851804750', 'Lhash_array': ['1987289888788844114855851804750'], 'label': '4-408e2-1.1-c1e2-0-45', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-576.7-e'}
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id: 9491254
{'Lhash': '1987289888788844114855851804750', 'Lhash_array': ['1987289888788844114855851804750'], 'label': '4-408e2-1.1-c1e2-0-45', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.17.1/576.6/e'}
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id: 9463106
{'Lhash': '1987289888788844114855851804750', 'Lhash_array': ['1987289888788844114855851804750'], 'label': '4-408e2-1.1-c1e2-0-45', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.136.1/holomorphic/2.2.136.1-9.1-d'}
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id: 9463105
{'Lhash': '1987289888788844114855851804750', 'Lhash_array': ['1987289888788844114855851804750'], 'label': '4-408e2-1.1-c1e2-0-45', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.136.1/9.1/d'}
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id: 9463058
{'Lhash': '1987289888788844114855851804750', 'Lhash_array': ['1987289888788844114855851804750'], 'label': '4-408e2-1.1-c1e2-0-45', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.136.1/9.1/c'}
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id: 9463054
{'Lhash': '1987289888788844114855851804750', 'Lhash_array': ['1987289888788844114855851804750'], 'label': '4-408e2-1.1-c1e2-0-45', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.136.1/holomorphic/2.2.136.1-9.1-c'}