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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -2, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1574094202014471791801211761678', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-1.0, 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': 22.95391213065638, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 2]], [3, [1, 0, -1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '360000.1', 'coefficient_field': '1.1.1.1', 'conductor': 360000, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 0, 2], [1, 0, -1], [1], [1, 0, 2, 0, 49], [1, 0, -10, 0, 121], [1, 0, 22, 0, 169], [1, 0, 22, 0, 289], [1, 0, 10, 0, 361], [1, 0, 34, 0, 529], [1, 0, -10, 0, 841], [1, 4, 66, 124, 961], [1, 0, 70, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, 22, 0, 1849], [1, 0, -14, 0, 2209], [1, 0, -38, 0, 2809], [1, 0, -106, 0, 3481], [1, 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-0.7468960616572369, -1.0477494305634547], 'positive_zeros': ['1.24174137710428244225262808465689', '2.00682666441558622563445980096357', '3.00194017979805245569288086992105', '3.52093714862999742208675072165756', '4.03692737540833527234822179494440', '4.68582914817178728463656973297907', '4.97363524286420755586596678673946', '5.63401665125598587390415662684874', '5.99032722863745092835858749406380', '6.69996816528396882333362272570548', '7.10939010094640721565819959301543', '7.62737050745987647003109275481045', '8.136073050603030780287194942212527', '8.471735651756358886191812992807242'], 'prelabel': '4-600e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.188840816797061, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1914501415190828903, 'z1': {'__RealLiteral__': 0, 'data': '1.24174137710428244225262808465689', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.00682666441558622563445980096357', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.00194017979805245569288086992105', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.95391213065638, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 360000, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 20, 0, 1, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -10, 0, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 0, 22, 0, 289], 'euler19': [1, 0, 10, 0, 361], 'euler2': [1, 0, 2, 0, 0], 'euler23': [1, 0, 34, 0, 529], 'euler29': [1, 0, -10, 0, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 4, 66, 124, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 0, -14, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -38, 0, 2809], 'euler59': [1, 0, -106, 0, 3481], 'euler61': [1, 0, -122, 0, 3721], 'euler67': [1, 0, 70, 0, 4489], 'euler7': [1, 0, 2, 0, 49], 'euler71': [1, 24, 286, 1704, 5041], 'euler73': [1, 0, 146, 0, 5329], 'euler79': [1, -20, 258, -1580, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 0, 146, 0, 9409], 'euler_factors': [[1, 0, 2, 0, 0], [1, 0, -1, 0, 0], [1, 0, 0, 0, 0], [1, 0, 2, 0, 49], [1, 0, -10, 0, 121], [1, 0, 22, 0, 169], [1, 0, 22, 0, 289], [1, 0, 10, 0, 361], [1, 0, 34, 0, 529], [1, 0, -10, 0, 841], [1, 4, 66, 124, 961], [1, 0, 70, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, 22, 0, 1849], [1, 0, -14, 0, 2209], [1, 0, -38, 0, 2809], [1, 0, -106, 0, 3481], [1, 0, -122, 0, 3721], [1, 0, 70, 0, 4489], [1, 24, 286, 1704, 5041], [1, 0, 146, 0, 5329], [1, -20, 258, -1580, 6241], [1, 0, 22, 0, 6889], [1, 12, 214, 1068, 7921], [1, 0, 146, 0, 9409]], 'index': 26, 'instance_types': ['HMF', 'HMF', 'ECNF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-225.1-l', 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-225.1-e', 'EllipticCurve/2.2.40.1/225.1/l', 'EllipticCurve/2.2.40.1/225.1/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': '4-600e2-1.1-c1e2-0-26', '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': '4-600e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.188840816797061, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1914501415190828903, 'z1': {'__RealLiteral__': 0, 'data': '1.24174137710428244225262808465689', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9495058
{'Lhash': '1574094202014471791801211761678', 'Lhash_array': ['1574094202014471791801211761678'], 'label': '4-600e2-1.1-c1e2-0-26', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.40.1/225.1/e'}
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id: 9495017
{'Lhash': '1574094202014471791801211761678', 'Lhash_array': ['1574094202014471791801211761678'], 'label': '4-600e2-1.1-c1e2-0-26', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.40.1/225.1/l'}
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id: 9494916
{'Lhash': '1574094202014471791801211761678', 'Lhash_array': ['1574094202014471791801211761678'], 'label': '4-600e2-1.1-c1e2-0-26', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-225.1-e'}
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id: 9494202
{'Lhash': '1574094202014471791801211761678', 'Lhash_array': ['1574094202014471791801211761678'], 'label': '4-600e2-1.1-c1e2-0-26', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-225.1-l'}