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lfunc_lfunctions • Show schema
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{'Lhash': '3200751005903084886799530112348,4608386772293848630934601103137', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.14690503763620083, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 3]]], 'bad_primes': [2, 3], 'central_character': '48.1', 'coefficient_field': '1.1.1.1', 'conductor': 2304, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, 0, 3], [1, 0, -10, 0, 25], [1, 0, -2, 0, 49], [1, 0, 22, 0, 121], [1, 4, 30, 52, 169], [1, 0, -34, 0, 289], [1, 0, -26, 0, 361], [1, 0, 46, 0, 529], [1, 0, -58, 0, 841], [1, 0, 46, 0, 961], [1, 20, 174, 740, 1369], [1, 0, -82, 0, 1681], [1, 0, 22, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, -106, 0, 2809], [1, 0, 118, 0, 3481], [1, -28, 318, -1708, 3721], [1, 0, -122, 0, 4489], [1, 0, 142, 0, 5041], [1, -20, 246, -1460, 5329], [1, 0, 142, 0, 6241], [1, 0, 166, 0, 6889], [1, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.14690503763620083, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 2304, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 4, 30, 52, 169], 'euler17': [1, 0, -34, 0, 289], 'euler19': [1, 0, -26, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, -58, 0, 841], 'euler3': [1, 0, 3, 0, 0], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, 20, 174, 740, 1369], 'euler41': [1, 0, -82, 0, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, -10, 0, 25], 'euler53': [1, 0, -106, 0, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, -28, 318, -1708, 3721], 'euler67': [1, 0, -122, 0, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -20, 246, -1460, 5329], 'euler79': [1, 0, 142, 0, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 0, -178, 0, 7921], 'euler97': [1, 28, 390, 2716, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 3, 0, 0], [1, 0, -10, 0, 25], [1, 0, -2, 0, 49], [1, 0, 22, 0, 121], [1, 4, 30, 52, 169], [1, 0, -34, 0, 289], [1, 0, -26, 0, 361], [1, 0, 46, 0, 529], [1, 0, -58, 0, 841], [1, 0, 46, 0, 961], [1, 20, 174, 740, 1369], [1, 0, -82, 0, 1681], [1, 0, 22, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, -106, 0, 2809], [1, 0, 118, 0, 3481], [1, -28, 318, -1708, 3721], [1, 0, -122, 0, 4489], [1, 0, 142, 0, 5041], [1, -20, 246, -1460, 5329], [1, 0, 142, 0, 6241], [1, 0, 166, 0, 6889], [1, 0, -178, 0, 7921], [1, 28, 390, 2716, 9409]], 'index': 2, 'instance_types': ['ECNF', 'HMF', 'ECNF', 'ECNF', 'CMF'], 'instance_urls': ['EllipticCurve/2.2.12.1/16.1/a', 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-16.1-a', 'EllipticCurve/2.0.3.1/256.1/CMb', 'EllipticCurve/2.0.3.1/256.1/CMa', 'ModularForm/GL2/Q/holomorphic/48/2/c/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '4-48e2-1.1-c1e2-0-2', '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': '4-48e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.6190976737980414, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1687343896078013792, 'z1': {'__RealLiteral__': 0, 'data': '2.52494733590377164458054694339', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9956388
{'Lhash': '3200751005903084886799530112348,4608386772293848630934601103137', 'Lhash_array': ['3200751005903084886799530112348', '4608386772293848630934601103137'], 'label': '4-48e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/48/2/c/a'}
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id: 9747103
{'Lhash': '_3200751005903084886799530112348', 'Lhash_array': ['_3200751005903084886799530112348'], 'label': '4-48e2-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/256.1/CMa'}
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id: 9746406
{'Lhash': '_3200751005903084886799530112348', 'Lhash_array': ['_3200751005903084886799530112348'], 'label': '4-48e2-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/256.1/CMb'}
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id: 9570493
{'Lhash': '_3200751005903084886799530112348', 'Lhash_array': ['_3200751005903084886799530112348'], 'label': '4-48e2-1.1-c1e2-0-2', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-16.1-a'}
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id: 9570079
{'Lhash': '_3200751005903084886799530112348', 'Lhash_array': ['_3200751005903084886799530112348'], 'label': '4-48e2-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.12.1/16.1/a'}