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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '837094937245205841346842325955', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.220165286034979, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1, 0, 6, -7]], [421, [1, -36, 456, -421]]], 'bad_primes': [3, 7, 421], 'central_character': '238707.1', 'coefficient_field': '1.1.1.1', 'conductor': 238707, 'conductor_radical': 8841, 'degree': 4, 'euler_factors': [[1, 0, 1, 0, 4], [1], [1, 0, 4, 0, 25], [1, 0, 6, -7], [1, 0, -2, 0, 121], [1, 8, 42, 104, 169], [1, 0, 28, 0, 289], [1, -13, 78, -247, 361], [1, 0, -2, 0, 529], [1, 0, -32, 0, 841], [1, -4, 57, -124, 961], [1, 5, 60, 185, 1369], [1, 0, -53, 0, 1681], [1, -10, 102, -430, 1849], [1, 0, 4, 0, 2209], [1, 0, -50, 0, 2809], [1, 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0.5534209610029782, 0.7945330869422458, 0.8600143862844193, 0.7291121349339136, 0.4308791253415065], 'positive_zeros': ['0.66035146995117915029773702425523', '1.89702216041433194956964154283795', '2.67414174060325907646520992580380', '3.19153538386113992435277004405475', '3.93059813538086874936449027672477', '4.65857275195778184312068288439746', '5.02072098492052040256329725979866', '5.36806401679096366777792091708050', '5.98690415376505432253866730759292', '6.72884853074259044584197403271117', '7.25479700968238562483478879687785', '7.51032126820878630828627184416903', '7.898956608454661053902671380091956', '8.516316118849784900317874457219223', '9.212709185765994872615917055211357'], 'prelabel': '4-238707-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9751716442181615, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1891060253293977926, 'z1': {'__RealLiteral__': 0, 'data': '0.66035146995117915029773702425523', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.89702216041433194956964154283795', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.67414174060325907646520992580380', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.220165286034979, 'bad_primes': [3, 7, 421], 'central_character': '1.1', 'conductor': 238707, 'conductor_radical': 8841, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -3, 0, 0, 13, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, -6, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 7, 0, 0, 7, 0, 0, 0, 0, 0, 16, 0, 0, -13, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 4], 'euler11': [1, 0, -2, 0, 121], 'euler13': [1, 8, 42, 104, 169], 'euler17': [1, 0, 28, 0, 289], 'euler19': [1, -13, 78, -247, 361], 'euler2': [1, 0, 1, 0, 4], 'euler23': [1, 0, -2, 0, 529], 'euler29': [1, 0, -32, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -4, 57, -124, 961], 'euler37': [1, 5, 60, 185, 1369], 'euler41': [1, 0, -53, 0, 1681], 'euler43': [1, -10, 102, -430, 1849], 'euler47': [1, 0, 4, 0, 2209], 'euler5': [1, 0, 4, 0, 25], 'euler53': [1, 0, -50, 0, 2809], 'euler59': [1, 0, -116, 0, 3481], 'euler61': [1, 8, 102, 488, 3721], 'euler67': [1, -7, 90, -469, 4489], 'euler7': [1, 0, 6, -7, 0], 'euler71': [1, 0, -29, 0, 5041], 'euler73': [1, -16, 210, -1168, 5329], 'euler79': [1, 5, 108, 395, 6241], 'euler83': [1, 0, -50, 0, 6889], 'euler89': [1, 0, -65, 0, 7921], 'euler97': [1, -7, 96, -679, 9409], 'euler_factors': [[1, 0, 1, 0, 4], [1, 0, 0, 0, 0], [1, 0, 4, 0, 25], [1, 0, 6, -7, 0], [1, 0, -2, 0, 121], [1, 8, 42, 104, 169], [1, 0, 28, 0, 289], [1, -13, 78, -247, 361], [1, 0, -2, 0, 529], [1, 0, -32, 0, 841], [1, -4, 57, -124, 961], [1, 5, 60, 185, 1369], [1, 0, -53, 0, 1681], [1, -10, 102, -430, 1849], [1, 0, 4, 0, 2209], [1, 0, -50, 0, 2809], [1, 0, -116, 0, 3481], [1, 8, 102, 488, 3721], [1, -7, 90, -469, 4489], [1, 0, -29, 0, 5041], [1, -16, 210, -1168, 5329], [1, 5, 108, 395, 6241], [1, 0, -50, 0, 6889], [1, 0, -65, 0, 7921], [1, -7, 96, -679, 9409]], 'index': 0, 'instance_types': ['BMF', 'ECNF', 'ECNF', 'BMF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/26523.3/a', 'EllipticCurve/2.0.3.1/26523.2/a', 'EllipticCurve/2.0.3.1/26523.3/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/26523.2/a'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-238707-1.1-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': 0, 'prelabel': '4-238707-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9751716442181615, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1891060253293977926, 'z1': {'__RealLiteral__': 0, 'data': '0.66035146995117915029773702425523', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9748471
{'Lhash': '837094937245205841346842325955', 'Lhash_array': ['837094937245205841346842325955'], 'label': '4-238707-1.1-c1e2-0-0', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/26523.2/a'}
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id: 9748181
{'Lhash': '837094937245205841346842325955', 'Lhash_array': ['837094937245205841346842325955'], 'label': '4-238707-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/26523.3/a'}
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id: 9747948
{'Lhash': '837094937245205841346842325955', 'Lhash_array': ['837094937245205841346842325955'], 'label': '4-238707-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/26523.2/a'}
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id: 9747704
{'Lhash': '837094937245205841346842325955', 'Lhash_array': ['837094937245205841346842325955'], 'label': '4-238707-1.1-c1e2-0-0', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/26523.3/a'}