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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 0, 'A4': -1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 3, 'A9': -4, 'Lhash': '1857207520123982897030669267219', 'a10': [0.0, 0], 'a2': [-0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [1.0606601717798214, 0], 'a9': [-1.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.717283986318004, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1, 2]], [17, [1, 4, 17]]], 'bad_primes': [2, 17], 'central_character': '73984.1', 'coefficient_field': '1.1.1.1', 'conductor': 73984, 'conductor_radical': 34, 'degree': 4, 'euler_factors': [[1, 1, 2], [1, 0, 4, 0, 9], [1, 0, 4, 0, 25], [1, 0, 14, 0, 49], [1, 0, -12, 0, 121], [1, -6, 34, -78, 169], [1, 4, 17], [1, 4, 6, 76, 361], [1, 0, 2, 0, 529], [1, 0, -44, 0, 841], [1, 0, -18, 0, 961], [1, 0, -12, 0, 1369], [1, 0, -46, 0, 1681], [1, -12, 118, -516, 1849], [1, 8, 94, 376, 2209], [1, 2, 82, 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-1.2604288416737017, -1.314361396546979, -1.0548877689680753, -0.49835675982487615], 'positive_zeros': ['1.46507840550827564740297624244899', '2.46421653499910406522937777179330', '3.40460075842175198231400425194629', '4.06204669979065598143458941716282', '4.58083151074979232965665155560157', '5.41528180858206820304837242878919', '5.93973800142688428508748638828696', '6.39382338444771627597108707867212', '6.99903976181307509729847467499635', '7.83728244951620955897515038084694', '8.244299230435508944325558614123819', '8.573541937944932621204340410872967', '8.901869891792090988443503544385814', '9.489085064039932945941352684031766'], 'prelabel': '4-272e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.4737472425686935, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1568618528930753856, 'z1': {'__RealLiteral__': 0, 'data': '1.46507840550827564740297624244899', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.46421653499910406522937777179330', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.40460075842175198231400425194629', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.717283986318004, 'bad_primes': [2, 17], 'central_character': '1.1', 'conductor': 73984, 'conductor_radical': 34, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, -1, 0, 0, 0, 3, -4, 0, 0, 0, 6, 0, 0, -1, -4, 4, -4, 0, 0, 0, 0, 0, -4, -6, 0, 0, 0, 0, 0, -5, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 12, 0, 0, 0, -8, 0, -14, 4, 0, -6, -2, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 7, 0, 0, -12, 4, 0, 0, 0, -12, 0, 0, 0, 4, 0, 0, 0, 0, 7, 0, -4, 0, 0, -12, 0, 0, -4, 0, 0, 0, 0, 8, 0, 0, 0, 14, 0, 4], 'euler11': [1, 0, -12, 0, 121], 'euler13': [1, -6, 34, -78, 169], 'euler17': [1, 4, 17, 0, 0], 'euler19': [1, 4, 6, 76, 361], 'euler2': [1, 1, 2, 0, 0], 'euler23': [1, 0, 2, 0, 529], 'euler29': [1, 0, -44, 0, 841], 'euler3': [1, 0, 4, 0, 9], 'euler31': [1, 0, -18, 0, 961], 'euler37': [1, 0, -12, 0, 1369], 'euler41': [1, 0, -46, 0, 1681], 'euler43': [1, -12, 118, -516, 1849], 'euler47': [1, 8, 94, 376, 2209], 'euler5': [1, 0, 4, 0, 25], 'euler53': [1, 2, 82, 106, 2809], 'euler59': [1, -12, 150, -708, 3481], 'euler61': [1, 0, 68, 0, 3721], 'euler67': [1, 12, 166, 804, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, 0, 34, 0, 5041], 'euler73': [1, 0, 30, 0, 5329], 'euler79': [1, 0, -30, 0, 6241], 'euler83': [1, 4, 134, 332, 6889], 'euler89': [1, 4, 118, 356, 7921], 'euler97': [1, 0, -78, 0, 9409], 'euler_factors': [[1, 1, 2, 0, 0], [1, 0, 4, 0, 9], [1, 0, 4, 0, 25], [1, 0, 14, 0, 49], [1, 0, -12, 0, 121], [1, -6, 34, -78, 169], [1, 4, 17, 0, 0], [1, 4, 6, 76, 361], [1, 0, 2, 0, 529], [1, 0, -44, 0, 841], [1, 0, -18, 0, 961], [1, 0, -12, 0, 1369], [1, 0, -46, 0, 1681], [1, -12, 118, -516, 1849], [1, 8, 94, 376, 2209], [1, 2, 82, 106, 2809], [1, -12, 150, -708, 3481], [1, 0, 68, 0, 3721], [1, 12, 166, 804, 4489], [1, 0, 34, 0, 5041], [1, 0, 30, 0, 5329], [1, 0, -30, 0, 6241], [1, 4, 134, 332, 6889], [1, 4, 118, 356, 7921], [1, 0, -78, 0, 9409]], 'index': 28, 'instance_types': ['HMF', 'ECNF', 'ECNF', 'HMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-256.9-d', 'EllipticCurve/2.2.17.1/256.9/d', 'EllipticCurve/2.2.17.1/256.8/d', 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-256.8-d'], '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': '4-272e2-1.1-c1e2-0-28', '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': '4-272e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.4737472425686935, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1568618528930753856, 'z1': {'__RealLiteral__': 0, 'data': '1.46507840550827564740297624244899', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9490075
{'Lhash': '1857207520123982897030669267219', 'Lhash_array': ['1857207520123982897030669267219'], 'label': '4-272e2-1.1-c1e2-0-28', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-256.8-d'}
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id: 9489873
{'Lhash': '1857207520123982897030669267219', 'Lhash_array': ['1857207520123982897030669267219'], 'label': '4-272e2-1.1-c1e2-0-28', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.17.1/256.8/d'}
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id: 9489708
{'Lhash': '1857207520123982897030669267219', 'Lhash_array': ['1857207520123982897030669267219'], 'label': '4-272e2-1.1-c1e2-0-28', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.17.1/256.9/d'}
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id: 9489598
{'Lhash': '1857207520123982897030669267219', 'Lhash_array': ['1857207520123982897030669267219'], 'label': '4-272e2-1.1-c1e2-0-28', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-256.9-d'}