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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': -1, 'Lhash': '2068404262117215796934790193417', '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': [-0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.45657802637098, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [13, [1, 3, 13]], [17, [1, 5, 17]]], 'bad_primes': [2, 13, 17], 'central_character': '195364.1', 'coefficient_field': '1.1.1.1', 'conductor': 195364, 'conductor_radical': 442, 'degree': 4, 'euler_factors': [[1, 0, -1], [1, 0, 1, 0, 9], [1, 0, 7, 0, 25], [1, 0, 3, 0, 49], [1, 0, 10, 0, 121], [1, 3, 13], [1, 5, 17], [1, -4, 38, -76, 361], [1, 0, 37, 0, 529], [1, 0, -39, 0, 841], [1, 0, -13, 0, 961], [1, 0, -1, 0, 1369], [1, 0, -17, 0, 1681], [1, 8, 86, 344, 1849], [1, 12, 126, 564, 2209], [1, 1, 76, 53, 2809], [1, 12, 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-1.3584870178980266], 'positive_zeros': ['1.63168325857678582994211492208545', '2.21484940350145742309478095087856', '3.07562043588201141617055326460754', '3.44833700322933695312312050077274', '4.43625652694183173663756275179707', '4.76507370481753523622266990779064', '5.44471179481293877004336907851045', '5.94853182652613110701521894262091', '6.53676710198420011340170421080088', '6.85497752837072961087261959684821', '7.49793203213281639607715926503768', '7.943577710210549949158302907886521', '8.200823256107863932218203065492584', '9.024297880140288752033514422157675'], 'prelabel': '4-442e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.878666486990332, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 40613424190801895, 'z1': {'__RealLiteral__': 0, 'data': '1.63168325857678582994211492208545', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.21484940350145742309478095087856', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.07562043588201141617055326460754', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.45657802637098, 'bad_primes': [2, 13, 17], 'central_character': '1.1', 'conductor': 195364, 'conductor_radical': 442, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, -3, 0, 0, 1, -5, 0, 4, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -12, 0, -3, 0, 0, -3, -1, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 1, 0, 0, -16, -5, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -8, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7], 'euler11': [1, 0, 10, 0, 121], 'euler13': [1, 3, 13, 0, 0], 'euler17': [1, 5, 17, 0, 0], 'euler19': [1, -4, 38, -76, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 0, 37, 0, 529], 'euler29': [1, 0, -39, 0, 841], 'euler3': [1, 0, 1, 0, 9], 'euler31': [1, 0, -13, 0, 961], 'euler37': [1, 0, -1, 0, 1369], 'euler41': [1, 0, -17, 0, 1681], 'euler43': [1, 8, 86, 344, 1849], 'euler47': [1, 12, 126, 564, 2209], 'euler5': [1, 0, 7, 0, 25], 'euler53': [1, 1, 76, 53, 2809], 'euler59': [1, 12, 150, 708, 3481], 'euler61': [1, 0, -23, 0, 3721], 'euler67': [1, 16, 182, 1072, 4489], 'euler7': [1, 0, 3, 0, 49], 'euler71': [1, 0, 82, 0, 5041], 'euler73': [1, 0, -41, 0, 5329], 'euler79': [1, 0, 5, 0, 6241], 'euler83': [1, -28, 358, -2324, 6889], 'euler89': [1, 0, 97, 0, 7921], 'euler97': [1, 0, -46, 0, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 0, 1, 0, 9], [1, 0, 7, 0, 25], [1, 0, 3, 0, 49], [1, 0, 10, 0, 121], [1, 3, 13, 0, 0], [1, 5, 17, 0, 0], [1, -4, 38, -76, 361], [1, 0, 37, 0, 529], [1, 0, -39, 0, 841], [1, 0, -13, 0, 961], [1, 0, -1, 0, 1369], [1, 0, -17, 0, 1681], [1, 8, 86, 344, 1849], [1, 12, 126, 564, 2209], [1, 1, 76, 53, 2809], [1, 12, 150, 708, 3481], [1, 0, -23, 0, 3721], [1, 16, 182, 1072, 4489], [1, 0, 82, 0, 5041], [1, 0, -41, 0, 5329], [1, 0, 5, 0, 6241], [1, -28, 358, -2324, 6889], [1, 0, 97, 0, 7921], [1, 0, -46, 0, 9409]], 'index': 47, 'instance_types': ['ECNF', 'HMF', 'HMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.2.17.1/676.4/h', 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-676.4-h', 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-676.5-h', 'EllipticCurve/2.2.17.1/676.5/h'], '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': '4-442e2-1.1-c1e2-0-47', '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': '4-442e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.878666486990332, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 40613424190801895, 'z1': {'__RealLiteral__': 0, 'data': '1.63168325857678582994211492208545', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9493147
{'Lhash': '2068404262117215796934790193417', 'Lhash_array': ['2068404262117215796934790193417'], 'label': '4-442e2-1.1-c1e2-0-47', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.17.1/676.5/h'}
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id: 9492471
{'Lhash': '2068404262117215796934790193417', 'Lhash_array': ['2068404262117215796934790193417'], 'label': '4-442e2-1.1-c1e2-0-47', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-676.5-h'}
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id: 9492036
{'Lhash': '2068404262117215796934790193417', 'Lhash_array': ['2068404262117215796934790193417'], 'label': '4-442e2-1.1-c1e2-0-47', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-676.4-h'}
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id: 9491444
{'Lhash': '2068404262117215796934790193417', 'Lhash_array': ['2068404262117215796934790193417'], 'label': '4-442e2-1.1-c1e2-0-47', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.17.1/676.4/h'}