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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1136396424553041291349105941832', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792515, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.3504806021792133, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 3]]], 'bad_primes': [2, 3], 'central_character': '36864.1', 'coefficient_field': '1.1.1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, 2, 3], [1, 0, 2, 0, 25], [1, 0, 2, 0, 49], [1, 4, 10, 44, 121], [1, -4, 14, -52, 169], [1, 0, 14, 0, 289], [1, 0, -14, 0, 361], [1, -8, 62, -184, 529], [1, 0, -14, 0, 841], [1, 0, -30, 0, 961], [1, -4, 62, -148, 1369], [1, 0, 30, 0, 1681], [1, 0, 66, 0, 1849], [1, 0, 30, 0, 2209], [1, 0, -30, 0, 2809], [1, -4, 58, -236, 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2.0491372098784715, 1.6118521297601378, 1.0110252081622437], 'positive_zeros': ['0.896458712162833399049925227728777', '2.38303978348464108346924679456979', '3.27626560022899986319936689496464', '4.09379989521195289492080539242067', '5.06643453152369135477258592643107', '5.24969047550422206798735288875615', '5.89833014178485861074934344891453', '6.55784348471676331264571227519646', '6.91644360728498526615914333305635', '7.75377023612537773032444559188771', '8.200959075936605180783682994475081', '8.761253126142270829593658544362066', '9.359432931956235852299822576830343', '9.980234498858972240800426785293284', '10.57117027388674033150373501160204'], 'prelabel': '4-192e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.2381953475960827, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2178750274657072582, 'z1': {'__RealLiteral__': 0, 'data': '0.896458712162833399049925227728777', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.38303978348464108346924679456979', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.27626560022899986319936689496464', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.3504806021792133, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, 0, 0, 1, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, -2, 0, 4, 0, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 20, 0, 0, 0, 0, 0, 0, 0, -16, 0, 8, 0, 4, 0, 4, 0, 0, 0, 0, 0, -11, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0], 'euler11': [1, 4, 10, 44, 121], 'euler13': [1, -4, 14, -52, 169], 'euler17': [1, 0, 14, 0, 289], 'euler19': [1, 0, -14, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -8, 62, -184, 529], 'euler29': [1, 0, -14, 0, 841], 'euler3': [1, 2, 3, 0, 0], 'euler31': [1, 0, -30, 0, 961], 'euler37': [1, -4, 62, -148, 1369], 'euler41': [1, 0, 30, 0, 1681], 'euler43': [1, 0, 66, 0, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, 0, -30, 0, 2809], 'euler59': [1, -4, 58, -236, 3481], 'euler61': [1, -20, 206, -1220, 3721], 'euler67': [1, 0, -94, 0, 4489], 'euler7': [1, 0, 2, 0, 49], 'euler71': [1, -8, 94, -568, 5041], 'euler73': [1, -4, 86, -292, 5329], 'euler79': [1, 0, -94, 0, 6241], 'euler83': [1, -20, 250, -1660, 6889], 'euler89': [1, 0, -82, 0, 7921], 'euler97': [1, 4, 198, 388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 3, 0, 0], [1, 0, 2, 0, 25], [1, 0, 2, 0, 49], [1, 4, 10, 44, 121], [1, -4, 14, -52, 169], [1, 0, 14, 0, 289], [1, 0, -14, 0, 361], [1, -8, 62, -184, 529], [1, 0, -14, 0, 841], [1, 0, -30, 0, 961], [1, -4, 62, -148, 1369], [1, 0, 30, 0, 1681], [1, 0, 66, 0, 1849], [1, 0, 30, 0, 2209], [1, 0, -30, 0, 2809], [1, -4, 58, -236, 3481], [1, -20, 206, -1220, 3721], [1, 0, -94, 0, 4489], [1, -8, 94, -568, 5041], [1, -4, 86, -292, 5329], [1, 0, -94, 0, 6241], [1, -20, 250, -1660, 6889], [1, 0, -82, 0, 7921], [1, 4, 198, 388, 9409]], 'index': 0, 'instance_types': ['HMF', 'HMF', 'ECNF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-256.1-e', 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-256.1-b', 'EllipticCurve/2.2.12.1/256.1/e', 'EllipticCurve/2.2.12.1/256.1/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': '4-192e2-1.1-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': '4-192e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.2381953475960827, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2178750274657072582, 'z1': {'__RealLiteral__': 0, 'data': '0.896458712162833399049925227728777', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9575759
{'Lhash': '1136396424553041291349105941832', 'Lhash_array': ['1136396424553041291349105941832'], 'label': '4-192e2-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.12.1/256.1/b'}
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id: 9575649
{'Lhash': '1136396424553041291349105941832', 'Lhash_array': ['1136396424553041291349105941832'], 'label': '4-192e2-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.12.1/256.1/e'}
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id: 9575280
{'Lhash': '1136396424553041291349105941832', 'Lhash_array': ['1136396424553041291349105941832'], 'label': '4-192e2-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-256.1-b'}
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id: 9575052
{'Lhash': '1136396424553041291349105941832', 'Lhash_array': ['1136396424553041291349105941832'], 'label': '4-192e2-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-256.1-e'}