Table lfunc_lfunctions
L-functions
{'Lhash': '3143645153939594776614465450533', 'a10': [-1.7057370639048863, 1.4312833412080066], 'a2': [-0.766044443118978, -0.6427876096865394], 'a3': [0.9396926207859084, -0.3420201433256687], 'a4': [0.17364817766693036, 0.984807753012208], 'a5': [0.38665920154716127, -2.1928533001223154], 'a6': [-0.9396926207859084, -0.3420201433256687], 'a7': [0.32635182233306964, 0.565257937423568], 'a8': [0.5, -0.8660254037844386], 'a9': [0.766044443118978, -0.6427876096865394], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0.766044443118978, 0.6427876096865394]]], [3, [[1.0, 0], [-0.9396926207859084, 0.3420201433256687]]], [19, [[1.0, 0], [2.233955556881022, -3.7429189905580915]]]], 'bad_primes': [2, 3, 19], 'central_character': '114.73', 'coefficient_field': 'CDF', 'conductor': 114, 'conductor_radical': 114, 'conjugate': '2081492717535735134972230117727', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.766044443118978, 0.6427876096865394]], [[1.0, 0], [-0.9396926207859084, 0.3420201433256687]], [[1.0, 0], [-0.38665920154716127, 2.1928533001223154], [-4.698463103929542, -1.7101007166283437]], [[1.0, 0], [-0.32635182233306964, -0.565257937423568], [-3.5, 6.06217782649107]], [[1.0, 0], [-0.766044443118978, 1.3268278963378768], [-5.5, -9.526279441628825]], [[1.0, 0], [-0.4396926207859084, -0.16003502619256754], [9.958577760546714, 8.35623892592501]], [[1.0, 0], [1.6133407984528387, 1.3537536689450353], [2.952019020337816, 16.741731801207536]], [[1.0, 0], [2.233955556881022, -3.7429189905580915]], [[1.0, 0], [-1.0248149262626116, -5.812014259786013], [-21.612930278075893, 7.866463296490381]], [[1.0, 0], [6.383255634833637, -5.3561874488992], [5.03579715234098, -28.559424837354033]], [[1.0, 0], [-4.319077862357725, -7.480862299449558], [-15.5, 26.846787517317598]], [[1.0, 0], [4.674992351140469, 0], [37.0, 0]], [[1.0, 0], [3.266044443118978, -1.1887429610858429], [31.4078221678781, -26.354291997148113]], [[1.0, 0], [-1.786988976119769, 10.134518092125312], [-40.406782693794064, -14.706866163003756]], [[1.0, 0], [3.553033419238747, -2.981349031643783], [8.161464350345726, -46.28596439157378]], [[1.0, 0], [2.075322125713077, 11.769736641406952], [-49.803708901653145, 18.127067596260442]], [[1.0, 0], [-10.904200167834428, -9.149710339113104], [10.24524248234889, 58.10365742772028]], [[1.0, 0], [1.583778132003164, 8.982052126337642], [-57.32124986794041, 20.863228742865793]], [[1.0, 0], [-0.19072231740590087, 0.16003502619256754], [11.634427903684333, -65.98211945181794]], [[1.0, 0], [0.7724410561690801, -4.3807309185780055], [-66.71817607579949, -24.28343017612248]], [[1.0, 0], [-8.543233239475121, 3.109482603562567], [55.921244347685395, -46.92349550711737]], [[1.0, 0], [11.33022221559489, -4.1238636340982024], [60.51751100639927, -50.780221165236604]], [[1.0, 0], [1.8545703153092052, 3.2122100123245763], [-41.5, 71.88010851410841]], [[1.0, 0], [15.75536691643011, 5.734484587523041], [68.17795543758905, 57.208097262102]], [[1.0, 0], [-1.8905295948089818, -1.5863426857339493], [16.843873233692243, 95.52635204218419]], [[1.0, 0], [-5.393055814597263, -1.9629117882496707], [77.37048875501678, 64.92154857834048]], [[1.0, 0], [-6.9042001678344285, 11.9584254763148], [-51.5, -89.20061658979718]], [[1.0, 0], [0.9567667605248789, 1.657168640222175], [-53.5, 92.66471820493493]], [[1.0, 0], [2.0516892457652083, -11.635707919013395], [-102.42649566566402, -37.28019562249789]], [[1.0, 0], [-5.396926207859084, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 9603034, 'index': 3, 'label': '2-114-19.16-c1-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/114/2/i/d/73/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [0.9785199348204755, 1.0242320242097938, 1.0814784819237893, 1.1499488252426948, 1.2279768624036227, 1.312706331169109, 1.4002775771135134, 1.4859924435639642, 1.5644541646642016, 1.6297030045780956, 1.6753745302054237, 1.6949028217926825, 1.6817822373898619, 1.62989199367911, 1.533878924511743, 1.3895854623375723, 1.1945021216225835, 0.9482166734672497, 0.6528261412081077, 0.31327325876584144, -0.06243323476023432, -0.4631544753771229, -0.8747494584991057, -1.2804231028222541, -1.661310409961829, -1.9972969886114396, -2.268057306406913, -2.4542710402419687, -2.538956317482005, -2.508838346798921, -2.35565505503286, -2.0772900937517695, -1.6786200555050061, -1.1719686846238224, -0.5770774081158419, 0.07947107299284613, 0.765401864951392, 1.4444496482719669, 2.0785423147080806, 2.630343855841776, 3.0659860386084974, 3.3577798488155945, 3.4866736561476785, 3.4442201018640928, 3.2338310854795305, 2.8711413163347834, 2.383364770130203, 1.807611540120292, 1.1882289018892034, 0.5733315277528376, 0.010781609209753478, -0.45604070226148746, -0.7922831833001361, -0.9750731101310307, -0.9959883062435838, -0.8622297477859352, -0.5962873178482158, -0.23403333064077128, 0.1786575262089295, 0.5904946275366175, 0.9501428704864708, 1.2118374678393444, 1.3406314354076885, 1.3166609240144955, 1.1378810438731088, 0.8208629920772265, 0.39944226090304197, -0.07875098278311773, -0.5575902932518205, -0.9790469133972376, -1.2903476243130478, -1.450841230220628, -1.4376923949679696, -1.2496052666840194, -0.9079719725898431, -0.4551274653464927, 0.0502566303549249, 0.5402309330997469, 0.9463191687739955, 1.2089194322677663, 1.2861491071977844, 1.1609091874243527, 0.845088892419815, 0.3801334241186046, -0.16637140799035322, -0.7079322674106524, -1.1495046106454214, -1.3998027566217608, -1.3840430984326708, -1.0554310434781247, -0.4037533800711491, 0.540281551949918, 1.705825337528836, 2.988019681461279, 4.258985180781445, 5.3824825561563685, 6.230485599118857, 6.699541667529255, 6.724708951340907, 6.289079828544707, 5.427413562071802, 4.223152541459967, 2.798988882622854, 1.302060182377082, -0.11434801707954616, -1.310153493402781, -2.176212614743925, -2.6479218874302126, -2.7126972635658078, -2.4101863350699917, -1.8251123224535395, -1.073741738676743, -0.2859437804915123, 0.41448680205895133, 0.9282604742123877, 1.1949393140166225, 1.2009555525362652, 0.9800242109305856, 0.6058661640838785, 0.17839607409642153, -0.19438861634457066, -0.4158387220714101, -0.4181557949363612, -0.17498144313481626, 0.29313985241656154, 0.921472274045723, 1.6116471443575473, 2.248383550017275, 2.719580470785373, 2.936335011807805, 2.8493668731581794, 2.4588681257799916, 1.8158765253303302, 1.0147186398644015, 0.17764241620545498, -0.5658182210645566, -1.1011914609585522, -1.3491674087760228, -1.2797850173122807, -0.9180117641511726, -0.33951357372232455, 0.34282768154924165, 0.9993773064805113, 1.5075685169681814, 1.7747335387122785, 1.7556587877588863, 1.461442302997585, 0.9577681588382729, 0.3526580040819781, -0.22423737230295468, -0.6470608246132197, -0.8191104627255947, -0.6932103172050207, -0.28294686533477886, 0.3377565621465412, 1.0470879603506968, 1.697852950292987, 2.14603514196862, 2.280059469430008, 2.0450440165296704, 1.4570591116068603, 0.6041470657991194, -0.3667027902033639, -1.2747267245155194, -1.93836249743764, -2.2099806486090605, -2.0057278100467726, -1.3245136484014042, -0.25203833136982284, 1.0515043882232358, 2.3783043841368943, 3.5097640256842393, 4.25656422840926, 4.494404612440582, 4.1884535945776395, 3.4015219602874267, 2.2839855556393753, 1.0469676546424151, -0.07642475718711372, -0.8745894023817208, -1.1973541536427734, -0.9845931768427387, -0.2778678966421641, 0.7873332512290087, 2.0074059918512575, 3.1495755559107588, 3.9964237835060894, 4.387288135733015, 4.248400831781531, 3.6058571469844893, 2.578933815535719, 1.355232956664096, 0.1527964443426661, -0.8230401215628735, -1.4192583956814142, -1.5632342661960192, -1.2737447251629368, -0.6529866766023513, 0.13829930746115734, 0.9169580017047682, 1.5168352300570078, 1.8229219741909843, 1.7929422042474359, 1.4619661154113806, 0.9294628620344442, 0.3321577086998859, -0.190756036439153, -0.5318029966512134, -0.6407509631982242, -0.5354662506431443, -0.2955508638745443, -0.040304450737354496, 0.10366534320090778, 0.03727947097517974, -0.28238434402651097, -0.8270278884961566, -1.4998932694353049, -2.156397295534466, -2.6383260589959936, -2.8137923632922814, -2.6134103396251507, -2.053607142471278, -1.2406448723131436, -0.3532245697650287, 0.39346168427963424, 0.7948246405126731, 0.704713605786497, 0.07290100902483591, -1.037000950739602, -2.4543020823518638, -3.932318416053287, -5.197816679719054, -6.008409580280871, -6.205279629815655, -5.749223979883155, -4.731409923388811, -3.355715946128592, -1.8959033410030677, -0.6366714844650999, 0.18846408104858373, 0.4485197227963057, 0.14383837129144247, -0.5945186026447674, -1.53502170698735, -2.399013303318332, -2.925185814595614, -2.9305248102924533, -2.3536819667935407, -1.2706495889672562, 0.12107882984079978, 1.5464029261232772, 2.7145644633096904, 3.384891432568236, 3.4211300589632154, 2.821778945481733, 1.719440784289887, 0.3494805691133839], 'positive_zeros': ['2.47989876183043574185938126293656', '4.36028722621144727898319685300613', '6.25259008286742400940574054806259', '7.19677649520715541997633418115832', '8.354825801656017323594847456615153', '9.487682231286897692625489882255158', '10.46278388897708711792008334841162', '11.30782229304229200177102418214089', '12.98930770664270173886092574096246', '14.04808887801591542324945659768683'], 'prelabel': '2-114-19.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.1665627857076632, 'root_number': '0.5005651511066537 + 0.8656988676771923*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.166562785708', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.47989876183043574185938126294', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.36028722621144727898319685301', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '6.25259008286742400940574054806', 'prec': 100}}