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lfunc_lfunctions • Show schema
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{'A10': -2, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': 2, 'A6': 0, 'A7': 0, 'A8': -1, 'A9': -3, 'Lhash': '1624734421304482546365027347223', 'a10': [-0.632455532033676, 0], 'a2': [-0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [-0.3535533905932738, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.22777793843102, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 0, 3]], [17, [1, -2, 17]]], 'bad_primes': [2, 3, 17], 'central_character': '332928.1', 'coefficient_field': '1.1.1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'euler_factors': [[1, 1], [1, 0, 3], [1, -2, 10, -10, 25], [1, 0, -6, 0, 49], [1, 4, 26, 44, 121], [1, 0, 14, 0, 169], [1, -2, 17], [1, 0, 2, 0, 361], [1, 0, -30, 0, 529], [1, -10, 74, -290, 841], [1, 0, 26, 0, 961], [1, 10, 90, 370, 1369], [1, 0, -34, 0, 1681], [1, 0, 38, 0, 1849], [1, -4, 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3.1552680939004953, 1.6212867261365795, 0.16646761221550255, -1.0304315112072258, -1.8417944919918168, -2.2086508878510114, -2.146697971700181], 'positive_zeros': ['1.28168946633399086984930364789247', '2.25694907809682576965960697336011', '2.58739387145482707976838456612260', '3.25182166272888509607356036237647', '3.94261860012810658825455622411873', '4.88544323044523213778601090586674', '5.26787315094652639960258356084138', '5.79905073177474180187832103865852', '6.05940964516922099697910222065689', '6.68155059850002947589758457201587', '7.21711250154337967288393541384615', '7.73559972440307903163711231802130', '8.169314958115618812595298428597685', '8.532816213622114096654551281017394'], 'prelabel': '4-332928-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.1464764795303726, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 551173732136281800, 'z1': {'__RealLiteral__': 0, 'data': '1.28168946633399086984930364789247', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.25694907809682576965960697336011', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.58739387145482707976838456612260', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.22777793843102, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, 1, 2, 0, 0, -1, -3, -2, -4, 0, 0, 0, 0, 1, 2, 3, 0, 2, 0, 4, 0, 0, -6, 0, 0, 0, 10, 0, 0, -1, 0, -2, 0, -3, -10, 0, 0, -2, 0, 0, 0, -4, -6, 0, 4, 0, 6, 6, 0, 0, 0, 0, -8, 0, 0, -10, 0, 0, -2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 10, 0, 0, 0, 0, 0, 2, 9, 0, 0, 0, 4, 0, 0, 4, -12, 6, 0, 0, 0, -4, 0, 0, 0, -6, 12, -6], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, 0, 14, 0, 169], 'euler17': [1, -2, 17, 0, 0], 'euler19': [1, 0, 2, 0, 361], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, 0, -30, 0, 529], 'euler29': [1, -10, 74, -290, 841], 'euler3': [1, 0, 3, 0, 0], 'euler31': [1, 0, 26, 0, 961], 'euler37': [1, 10, 90, 370, 1369], 'euler41': [1, 0, -34, 0, 1681], 'euler43': [1, 0, 38, 0, 1849], 'euler47': [1, -4, 94, -188, 2209], 'euler5': [1, -2, 10, -10, 25], 'euler53': [1, 0, 86, 0, 2809], 'euler59': [1, 0, -110, 0, 3481], 'euler61': [1, 2, 42, 122, 3721], 'euler67': [1, 0, -46, 0, 4489], 'euler7': [1, 0, -6, 0, 49], 'euler71': [1, 0, 82, 0, 5041], 'euler73': [1, 0, 94, 0, 5329], 'euler79': [1, 0, 10, 0, 6241], 'euler83': [1, 0, 66, 0, 6889], 'euler89': [1, 12, 198, 1068, 7921], 'euler97': [1, 0, 34, 0, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, 0, 3, 0, 0], [1, -2, 10, -10, 25], [1, 0, -6, 0, 49], [1, 4, 26, 44, 121], [1, 0, 14, 0, 169], [1, -2, 17, 0, 0], [1, 0, 2, 0, 361], [1, 0, -30, 0, 529], [1, -10, 74, -290, 841], [1, 0, 26, 0, 961], [1, 10, 90, 370, 1369], [1, 0, -34, 0, 1681], [1, 0, 38, 0, 1849], [1, -4, 94, -188, 2209], [1, 0, 86, 0, 2809], [1, 0, -110, 0, 3481], [1, 2, 42, 122, 3721], [1, 0, -46, 0, 4489], [1, 0, 82, 0, 5041], [1, 0, 94, 0, 5329], [1, 0, 10, 0, 6241], [1, 0, 66, 0, 6889], [1, 12, 198, 1068, 7921], [1, 0, 34, 0, 9409]], 'index': 24, 'instance_types': ['HMF', 'ECNF', 'HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.136.1/holomorphic/2.2.136.1-18.3-b', 'EllipticCurve/2.2.136.1/18.2/b', 'ModularForm/GL2/TotallyReal/2.2.136.1/holomorphic/2.2.136.1-18.2-b', 'EllipticCurve/2.2.136.1/18.3/b'], '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': '4-332928-1.1-c1e2-0-24', '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': '4-332928-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.1464764795303726, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 551173732136281800, 'z1': {'__RealLiteral__': 0, 'data': '1.28168946633399086984930364789247', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9463088
{'Lhash': '1624734421304482546365027347223', 'Lhash_array': ['1624734421304482546365027347223'], 'label': '4-332928-1.1-c1e2-0-24', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.136.1/18.3/b'}
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id: 9463086
{'Lhash': '1624734421304482546365027347223', 'Lhash_array': ['1624734421304482546365027347223'], 'label': '4-332928-1.1-c1e2-0-24', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.136.1/holomorphic/2.2.136.1-18.2-b'}
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id: 9463073
{'Lhash': '1624734421304482546365027347223', 'Lhash_array': ['1624734421304482546365027347223'], 'label': '4-332928-1.1-c1e2-0-24', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.136.1/18.2/b'}
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id: 9463032
{'Lhash': '1624734421304482546365027347223', 'Lhash_array': ['1624734421304482546365027347223'], 'label': '4-332928-1.1-c1e2-0-24', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.136.1/holomorphic/2.2.136.1-18.3-b'}