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lfunc_lfunctions • Show schema
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{'Lhash': '1998914937641240915070590212363,3690564590380257623138573141583', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8728225087682089, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [13, [1, 2, 13]]], 'bad_primes': [3, 13], 'central_character': '117.1', 'coefficient_field': '1.1.1.1', 'conductor': 13689, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, 0, -1, 0, 4], [1], [1, 0, -10, 0, 25], [1, 0, -2, 0, 49], [1, 0, -10, 0, 121], [1, 2, 13], [1, -12, 70, -204, 289], [1, 0, -26, 0, 361], [1, 0, 46, 0, 529], [1, 12, 94, 348, 841], [1, 0, -50, 0, 961], [1, 0, -26, 0, 1369], [1, 0, -34, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, -82, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, -10, 0, 3481], [1, 4, 126, 244, 3721], [1, 0, -26, 0, 4489], [1, 0, -130, 0, 5041], [1, 0, -146, 0, 5329], [1, 16, 222, 1264, 6241], [1, 0, -154, 0, 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['1.57686584716747167281817741028578', '2.91134212354398266583078098641344', '3.47018727620373522194747060402127', '4.60565980587590345138887976368703', '5.34017448720661284081589497717748', '5.82159304803056284359610985675137', '6.72093424702019735750393022275841', '7.26576752323852867591516307773699', '7.71327862265261631414445850877067', '8.340846955215312984274751734418266', '9.132630457026905491932237417534412', '9.615125411710301297732032956461628', '10.10812231428556152192195977023069', '10.74876269550658365604509198493445', '11.16719593149364785823632598204590', '11.87358826855113987605804394837650', '12.12513433543839575821358493523777', '12.92870767676208291067046516078273', '12.94653876664632992175973565716730', '14.25796646071668065415399511013103'], 'prelabel': '4-117e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9665659334204683, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1798871400187607826, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57686584716747167281817741029', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.91134212354398266583078098641', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.47018727620373522194747060402', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8728225087682089, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 13689, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -3, 12, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 2, 0, 0, -2, -12, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -7, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10], 'euler11': [1, 0, -10, 0, 121], 'euler13': [1, 2, 13, 0, 0], 'euler17': [1, -12, 70, -204, 289], 'euler19': [1, 0, -26, 0, 361], 'euler2': [1, 0, -1, 0, 4], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 12, 94, 348, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -50, 0, 961], 'euler37': [1, 0, -26, 0, 1369], 'euler41': [1, 0, -34, 0, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, -82, 0, 2209], 'euler5': [1, 0, -10, 0, 25], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 0, -10, 0, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 0, -26, 0, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, 0, -130, 0, 5041], 'euler73': [1, 0, -146, 0, 5329], 'euler79': [1, 16, 222, 1264, 6241], 'euler83': [1, 0, -154, 0, 6889], 'euler89': [1, 0, -130, 0, 7921], 'euler97': [1, 0, -2, 0, 9409], 'euler_factors': [[1, 0, -1, 0, 4], [1, 0, 0, 0, 0], [1, 0, -10, 0, 25], [1, 0, -2, 0, 49], [1, 0, -10, 0, 121], [1, 2, 13, 0, 0], [1, -12, 70, -204, 289], [1, 0, -26, 0, 361], [1, 0, 46, 0, 529], [1, 12, 94, 348, 841], [1, 0, -50, 0, 961], [1, 0, -26, 0, 1369], [1, 0, -34, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, -82, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, -10, 0, 3481], [1, 4, 126, 244, 3721], [1, 0, -26, 0, 4489], [1, 0, -130, 0, 5041], [1, 0, -146, 0, 5329], [1, 16, 222, 1264, 6241], [1, 0, -154, 0, 6889], [1, 0, -130, 0, 7921], [1, 0, -2, 0, 9409]], 'index': 6, 'instance_types': ['ECNF', 'HMF', 'CMF'], 'instance_urls': ['EllipticCurve/2.2.13.1/81.1/a', 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-81.1-a', 'ModularForm/GL2/Q/holomorphic/117/2/b/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '4-117e2-1.1-c1e2-0-6', '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': '4-117e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9665659334204683, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1798871400187607826, 'z1': {'__RealLiteral__': 0, 'data': '1.57686584716747167281817741029', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9970212
{'Lhash': '1998914937641240915070590212363,3690564590380257623138573141583', 'Lhash_array': ['1998914937641240915070590212363', '3690564590380257623138573141583'], 'label': '4-117e2-1.1-c1e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/117/2/b/a'}
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id: 9530618
{'Lhash': '_1998914937641240915070590212363', 'Lhash_array': ['_1998914937641240915070590212363'], 'label': '4-117e2-1.1-c1e2-0-6', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-81.1-a'}
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id: 9530346
{'Lhash': '_1998914937641240915070590212363', 'Lhash_array': ['_1998914937641240915070590212363'], 'label': '4-117e2-1.1-c1e2-0-6', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.13.1/81.1/a'}