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  • lfunc_lfunctions • Show schema
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'9.539264410826295415867260441328982', '11.34895122175493616646545967308879', '12.19035669906091329910107758904692', '13.04321206354133836289379117522410', '14.15821035961646171329220384061562', '14.21000976480262357162330942801842', '15.70441842117171651071931414554675', '15.85325839574730429144282105618189', '17.49591101229876690110058287825536', '18.41503997148447739979704080654068', '19.52897156300637550527526803720752', '20.05309366556374309499376322086466', '20.88966920745470466595519261826016', '21.90639216795998310222946270990652', '22.54060403502313847767575986943154', '22.60501002348992296283196614034708'], 'prelabel': '4-5e2-1.1-c7e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.249770029813729, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c7e2-0', 'trace_hash': 1509438177864283698, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.63715009395516665553552623709', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.56624038341865425167686208504', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '6.41028214690635329556348984161', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 2.4396101036678868, 'bad_primes': [5], 'central_character': '1.1', 'conductor': 25, 'conductor_radical': 5, 'degree': 4, 'dirichlet_coefficients': [1, 20, 20, 120, -250, 400, -100, -640, 790, -5000, 4544, 2400, 3540, -2000, -5000, -11584, -27340, 15800, 38760, -30000, -2000, 90880, -124140, -12800, 46875, 70800, 67340, -12000, -72260, -100000, 306824, -72960, 90880, -546800, 25000, 94800, -123020, 775200, 70800, 160000, 264364, -40000, 423300, 545280, -197500, -2482800, -105460, -231680, -1401250, 937500, -546800, 424800, -2391580, 1346800, -1136000, 64000, 775200, -1445200, -1120120, -600000, 2257044, 6136480, -79000, -1820160, -885000, 1817600, 4516460, -3280800, -2482800, 500000, 621784, -505600, 4569060, -2460400, 937500, 4651200, -454400, 1416000, 4333040, 2896000, -2253269, 5287280, -9793020, -240000, 6835000, 8466000, -1445200, -2908160, 6025620, -3950000, -354000, -14896800, 6136480, -2109200, -9690000, -1459200, 4609540, -28025000, 3589760, 5625000], 'euler11': [1, -4544, 31976326, -88549705024, 379749833583241], 'euler13': [1, -3540, 100535470, -222129750180, 3937376385699289], 'euler17': [1, 27340, 901005190, 11218659319820, 168377826559400929], 'euler19': [1, -38760, 2155545478, -34646468603640, 799006685782884121], 'euler2': [1, -20, 280, -2560, 16384], 'euler23': [1, 124140, 10649684530, 422675030990580, 11592836324538749809], 'euler29': [1, 72260, 6846819118, 1246476062088340, 297558232675799463481], 'euler3': [1, -20, -390, -43740, 4782969], 'euler31': [1, -306824, 77964629966, -8441530311993464, 756943935220796320321], 'euler37': [1, 123020, 144088599870, 11678519524901660, 9012061295995008299689], 'euler41': [1, -264364, 161786388886, -51486018860276684, 37929227194915558802161], 'euler43': [1, -423300, 446651231050, -115060818081593100, 73885357344138503765449], 'euler47': [1, 105460, 858715356610, 53428474284027980, 256666986187667409334369], 'euler5': [1, 250, 15625, 0, 0], 'euler53': [1, 2391580, 3562552504510, 2809415667811372460, 1379946262057143768386569], 'euler59': [1, 1120120, 1362334883638, 2787588301175458280, 6193386212891813387462761], 'euler61': [1, -2257044, 5613447576526, -7093308861584181924, 9876832533361318095112441], 'euler67': [1, -4516460, 16742087664890, -27372961536977116580, 36732225162896895721934329], 'euler7': [1, 100, 1411250, 82354300, 678223072849], 'euler71': [1, -621784, 17914494152446, -5655200192564989544, 82721210695570328927708881], 'euler73': [1, -4569060, 23424949855030, -50476226677665338820, 122045014039746588673695409], 'euler79': [1, -4333040, 26135588252318, -83211305793386393360, 368790120348678391253573281], 'euler83': [1, 9793020, 59971104320890, 265743890062437003540, 736365263311636486061599129], 'euler89': [1, -6025620, 89865866149558, -266521216173197452980, 1956410986640441413344189841], 'euler97': [1, -4609540, 142930351581510, -372442924233240998020, 6528362774606076144776040769], 'euler_factors': [[1, -20, 280, -2560, 16384], [1, -20, -390, -43740, 4782969], [1, 250, 15625, 0, 0], [1, 100, 1411250, 82354300, 678223072849], [1, -4544, 31976326, -88549705024, 379749833583241], [1, -3540, 100535470, -222129750180, 3937376385699289], [1, 27340, 901005190, 11218659319820, 168377826559400929], [1, -38760, 2155545478, -34646468603640, 799006685782884121], [1, 124140, 10649684530, 422675030990580, 11592836324538749809], [1, 72260, 6846819118, 1246476062088340, 297558232675799463481], [1, -306824, 77964629966, -8441530311993464, 756943935220796320321], [1, 123020, 144088599870, 11678519524901660, 9012061295995008299689], [1, -264364, 161786388886, -51486018860276684, 37929227194915558802161], [1, -423300, 446651231050, -115060818081593100, 73885357344138503765449], [1, 105460, 858715356610, 53428474284027980, 256666986187667409334369], [1, 2391580, 3562552504510, 2809415667811372460, 1379946262057143768386569], [1, 1120120, 1362334883638, 2787588301175458280, 6193386212891813387462761], [1, -2257044, 5613447576526, -7093308861584181924, 9876832533361318095112441], [1, -4516460, 16742087664890, -27372961536977116580, 36732225162896895721934329], [1, -621784, 17914494152446, -5655200192564989544, 82721210695570328927708881], [1, -4569060, 23424949855030, -50476226677665338820, 122045014039746588673695409], [1, -4333040, 26135588252318, -83211305793386393360, 368790120348678391253573281], [1, 9793020, 59971104320890, 265743890062437003540, 736365263311636486061599129], [1, -6025620, 89865866149558, -266521216173197452980, 1956410986640441413344189841], [1, -4609540, 142930351581510, -372442924233240998020, 6528362774606076144776040769]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5/8/a/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-5e2-1.1-c7e2-0-1', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [7, 7], 'order_of_vanishing': 0, 'prelabel': '4-5e2-1.1-c7e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.249770029813729, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7e2-0', 'trace_hash': 1509438177864283698, 'z1': {'__RealLiteral__': 0, 'data': '3.63715009395516665553552623709', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '4610635499722427973086668672513,5788397362827037423128441255260', 'Lhash_array': ['4610635499722427973086668672513', '5788397362827037423128441255260'], 'factors': ['2-5-1.1-c7-0-0', '2-5-1.1-c7-0-1'], 'label': '4-5e2-1.1-c7e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5/8/a/b'}