-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_3724.1399', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.8262387743159949, 0.5633200580636221], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.8262387743159949, 0.5633200580636221], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.36534102436639504, -0.9308737486442042], 'algebraic': True, 'analytic_conductor': 400.1993799351836, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]], [19, [1]]], 'bad_primes': [2, 7, 19], 'central_character': '3724.1399', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 3724, 'conductor_radical': 266, 'conjugate': 'dirichlet_L_3724.559', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^59', 0, 'a^17', 0, 0, 0, 'a^34', 0, 'a^57', 0, 'a^22', 0, 'a^34', 0, 'a^5', 0, 0, 0, 0, 0, 'a^37', 0, 'a^34', 0, 'a^51', 0, 'a^19', 0, 'a^21', 0, 'a^32', 0, 0, 0, 'a^33', 0, 'a^39', 0, 'a^38', 0, 'a^53', 0, 'a^9', 0, 'a^22', 0, 0, 0, 'a^22', 0, 'a^37', 0, 'a^32', 0, 0, 0, 'a^53', 0, 'a^19', 0, 0, 0, 'a^39', 0, 'a^28', 0, 'a^12', 0, 'a^44', 0, 'a^41', 0, 'a^51', 0, 0, 0, 'a^56', 0, 'a^26', 0, 'a^48', 0, 'a^22', 0, 'a^36', 0, 'a^34', 0, 0, 0, 'a^38', 0, 0, 0, 'a^14', 0, 'a^49', 0], 'euler_factors': [[0], [1, 'a^59'], [1, 'a^17'], [0], [1, 'a^57'], [1, 'a^22'], [1, 'a^5'], [0], [1, 'a^37'], [1, 'a^19'], [1, 'a^21'], [1, 'a^33'], [1, 'a^38'], [1, 'a^53'], [1, 'a^22'], [1, 'a^37'], [1, 'a^53'], [1, 'a^19'], [1, 'a^28'], [1, 'a^44'], [1, 'a^41'], [1, 'a^56'], [1, 'a^48'], [1, 'a^34'], [1, 'a^14'], [1, 'a^31']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-3724-3724.1399-r1-0-0', 'leading_term': '0.00299373949711801459509454232883+0.482590479918828029921016422489*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/3724/1399', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.48259976562827034, 1.0487110598330842, 0.23654635776667426, -1.9406570860646508, -3.9839498026007885, -3.900953246422315, -1.2016501236368577, 2.132069620098047, 3.2609491022359, 1.4091432276779, -1.1854031491791006, -1.7294457870314002, -0.07192011911970232, 1.2971070805721414, 0.576767904513748, -0.9783741150138016, -0.9154424993235867, 0.7817881246042342, 1.4598541059284635, -0.4132741596594736, -2.7516076741802387, -2.559605519223061, -0.2705469516233525, 0.7268680667633265, -0.8793672383630678, -2.039544959422224, 0.34705174190760846, 4.461090944217143, 5.495590365349315, 2.2159582275153342, -1.2634454250050355, -1.185885700170462, 0.9886086840706763, 1.5259150062267879, 0.21018870490324507, -0.02546491109196871, 1.4955850021125148, 1.967312531291498, 0.10614476180147166, -1.3108689101320714, -0.24243949656411815, 0.34102847155707294, -3.2882126595587557, -8.820693295866967, -9.945233948168037, -5.154967095210166, 0.039921329749791346, 1.041868373531628, -0.048965961326083274, 0.7302862901371168, 2.503186501597625, 1.9601334935025594, -0.15019516440388286, -0.1822482173501707, 1.7403163308103236, 1.6995541217097094, -0.9921442254962096, -2.2428845157070927, -0.34098853418076625, 0.7170990632765193, -1.8497677528535668, -4.288801019581079, -2.4437003218734814, 0.817551102267424, 0.05133829502098479, -3.6024898486244843, -4.27616722190331, -1.1678951717076227, 0.47703640852685103, -1.5089157523887973, -3.0403743975179633, -1.441806432604651, 0.2989257704664996, -0.22016746753119754, -0.4730627048458462, 1.3145329691565895, 1.9758221334689747, -0.31377437532593644, -1.0015696428657348, 3.58143793381375, 8.543839087586225, 7.080666238346073, 1.3204740737771015, -1.1627651587970114, 0.7464603541924626, 1.5276994602869047, -0.5422792299251391, -1.445259254783295, -0.0013232724191098155, 0.16323203333884162, -1.5876925870101957, -1.3468182070949972, 1.2621499669637581, 1.5459121684489476, -1.3394283510341143, -2.1178898140563027, 0.8883812374075706, 2.1235392351378497, -1.1440472717389758, -3.508907930834328, -1.1836227567609066, 1.100475425458453, -1.020453421458095, -3.467538946514715, -1.4651809719960864, 1.644816303540968, 0.8493411335219421, -1.5271850908596194, -0.9631178879351568, 0.8439670893557414, 0.3882482639800278, -0.3912971528519228, 1.0066736357891413, 1.2357674115303225, -2.364733972342716, -4.734474454770572, -1.2735086642400495, 2.8281397498312906, 0.8329613641002632, -3.610904881150231, -2.839158008519205, 1.650162345501048, 2.8532457318042797, 0.6083471981559847, -0.15426972448096382, 0.5673776752978931, -0.24559224697798, -0.7141491446154338, 2.0590678013604022, 4.402650033532683, 1.9988600540887678, -1.3402906923837543, -0.40028404089200004, 1.4457534630966729, -0.9812687528877053, -3.9374469870050643, -1.5867616697215379, 2.4536513208936883, 1.5560425102251871, -1.7857325200602185, -1.4118657852765513, 0.8082471347277855, -0.20905096769834786, -2.1954696041390798, -0.5701189128087022, 1.9450875090170867, 0.8877804966845618, -1.1312717376152026, -0.4303600993106142, 0.2253383929169663, -1.3255473314188329, -0.7052121938009346, 3.4613238596816807, 3.908872145676973, -2.6622508234629225, -7.817355423257914, -4.996171307612798, -0.07286533552591233, 0.18045653744502427, -1.028812358690242, 0.5981318784264418, 1.9466952218836566, 0.5122177431755837, -0.0031240742372975368, 1.7238502713302468, 1.5040758572005952, -0.6728858597743054, 0.2878707676456644, 3.243803497348849, 1.6030801798181098, -3.1516557190896517, -2.7781215567374744, 2.3713526565463248, 3.9145320872669034, 0.945046692440044, 0.0923823911249512, 1.4807356219960743, -0.3871802472050089, -3.9127612379682, -3.080232732451649, 0.29758722215565253, 0.4320621110853656, -1.0401250227139869, 0.19297463204153317, 1.5041465412138129, -0.27012566266943666, -1.1417461582863417, 1.2775177557908548, 1.6362060132666119, -1.7100264574748192, -1.5070175329249207, 4.105643476361486, 6.119408342208553, 0.8368817101271915, -3.3057541561688923, -1.3673391869623175, 0.8336848024238634, -0.14510161005386985, -0.1490094567113779, 1.6569973355169165, 1.2186496684340478, -0.49317620350227676, 0.31134800020180853, 0.7842651247894153, -2.5476446470145238, -4.250584480252998, 0.2988996588792756, 4.243443867456397, 1.2452732068992884, -2.557498334154755, -0.8033057484991382, 1.3939614148732578, -0.8610007563090374, -2.5840100981633567, -0.47878859419864284, 0.23510570637473302, -2.2463814174161443, -2.3670833512468414, 0.48918497980674913, 0.8009655447202224, -0.8644680595579078, 0.512233183623052, 2.723792795077378, 1.0454731097041627, -0.8950174873288859, 0.9828456668902109, 1.3520524236636753, -3.2015638174758947, -4.934998510982398, 0.5532331610309194, 4.63407386465182, 1.410951523736127, -2.2099116412432727, -0.922470352410107, 0.6622341474451929, 0.03640407424513371, 0.9026160273065769, 2.645307433423365, 1.2409436336825053, -0.751562886592935, 0.3596120779381308, 0.0016945081517556642, -4.887985865569939, -6.962868849919259, -2.238838428762869, 0.7810673564999989, -2.7810319794224565, -4.928940621097065, -1.1007546956656122, 1.7472353551464028, 0.1502551926297295, -0.6779844056638691, 0.04758872401525946, -1.9278134460321867, -4.040821069412848, -1.2519598727521704, 2.336250870132737, 1.23888093348978, -0.6376080655313587, 0.44386482707957736, 0.24679396678620913, -1.9081021510226497, 0.3211039276343053, 5.534448809330803, 4.596877007339508, -1.3517745490829882, -2.4438233161779097, 0.8931103913005167, 0.4264692768843856, -2.482923889337082, -1.1981479975276803, 1.6340674500079453, 0.6644039447730911, -0.9887197026097121, -0.05466923896177255, 0.2021768442475113, -0.317774079517245, 2.370324723372812, 4.654418202523615, 0.36061044618983934, -4.620830075680949, -1.5654414014782012, 3.8928715972830275, 2.522308625427146, -1.2482236593946763, -0.17939538598985388, 1.5242760823434944, -0.5861891669485908, -1.696602932280293, 0.20491276142300968, -0.07659956474537213, -2.269814305383199, -1.2473581175897468, 0.4578703552800123, -1.920779466312718, -3.7901998705397215, -0.8263351278173745, 1.2405737437027269, -0.5339357542269455, 0.39179168967204225, 4.57289604814632, 3.7842242029816444, -1.1559224136937047, -1.0444735983865356, 2.753995053900703, 1.6287804056414876, -2.2522436092948097, -1.558635012872366, 1.0542163625971124, 0.5297603172629352, -0.07680762878942186, 1.0579146908660604, -0.036839183014266974, -2.031149503963732, -0.012054542057313882, 2.071619326916405, -0.8781789361087138, -2.0430843927073745, 4.125403999599689, 8.426279950353388, 3.7624784750934746, -1.418121418935788, -0.34610831572873824, 1.0724864856944145, -0.45303287492645733, -0.16246691904113758, 1.432655313917403, -0.1904840643457032, -1.882598178216369, 0.05940135370955854, 0.5362953023486796, -2.630216238019724, -2.6964638773702516, 0.9512032068468568, 0.8211249392494279, -1.9599424391138984, -0.25363258133663824, 2.3537260686853214, -0.8767342662352379, -4.150056610705347, -1.0923283019230092, 1.5006707794529934, -1.6188373214946106, -3.590426785290198, -0.9983807554706225, 0.1421553047054364, -0.9691016103689014, 0.38219421760335276, 1.9206232309776023, 0.002132255752313575, -0.9632782137756246, 0.895747236542636, 0.0747410521316831, -1.6225484216122268, 3.7413237650979276, 11.195660128668093, 8.901264757503744, 0.6805780147962494, -1.5201191402143674, 0.7768594357436703, 0.21547097343613042, -0.8089205627805897, 0.6217907035022995, 0.18647106402894442, -1.9142147537507226, -0.3437037341419064, 2.219143120803499, 0.5057638176277727, -1.0724089440848616, 0.9975431596970932, 0.3180116238908062, -4.14438004482623, -3.484936795921142, 2.082359399090656, 2.7547771002302164, -0.6723865237902473, -0.2948401433048941, 0.8995779066528716, -2.6867779131258898, -5.092487435489596, -1.7249969331418868, 0.570826515613849, -1.215659143371039, -1.0958792000705908, 1.086236118561725, 0.45917661375933766, -0.6462761482150913, 0.3061405757212956, -1.5304657742334233, -5.203674544370758, -2.1001867693589187, 4.95794483437677, 4.525430589179155, -0.7990050667646288, -0.21339001136723168, 3.285348764161713, 1.395376096067491, -1.698374089170832, -0.35483002975481553, 0.8805937242674506, -0.3507740499489298, 0.030118530042790023, 0.5822736662356592, -1.7551041119506596, -1.527098425237672, 3.4926228882421517, 4.730997330782903, 0.3246520592144263, -0.6926934557763518, 1.7074757667072016, -0.6569368849225686, -4.6227838138988915, -2.472565359948774, 0.5470965212906596, -1.8956047156687847, -3.5885301275501913, -0.7975471244696308, -0.08838220031468122, -2.1605803625363276, -0.8536823161164661, 1.5558760956009257, -0.10341513661790568, -1.6211300363895886, 0.029584889478327558, -0.13689187059225855, -1.48928494750919, 1.2584740266804657, 2.691214936205007, -3.5790308995859603, -8.318340746262507, -3.268409811217667, 2.2073403341121263, 0.3982857154490774, -1.3232382736887485, 1.0633558907949474, 1.5105793109845556, -0.17760961465795067, 0.5172988683189694, 0.8730501529587387, -1.0030633457933107, -0.010823704085961571, 2.605714703861331, 0.12234926345072054, -3.208263459417157, -0.07865064285944492, 2.992581558027098, -0.3813574099147891, -2.0235668420571664, 2.524311479536363, 4.257125531778639, 0.7991547371665559, 0.08173079306548545, 1.6370316711031057, -0.06513466693537852, -0.90249462861381, 2.5930729579436305, 3.661607697593229, 0.3669459595454625, -0.5630887156392592, 0.4536877706955703, -1.2410890799015837, -1.712626397070431, 1.2675447689234154, 0.7711553559879084, -2.3216237114610703, 1.4628660640295361, 8.266847914071594, 6.2941521294483795, -0.2580567911851632, -0.5589529114970022, 1.7862587167773953, 0.3765198126789321, -0.377972871966334, 1.437935628237365, 0.8077079201964797, -0.7704645937440706, 0.6409854597429416, 0.8129963639334893, -1.5354117043748836, -0.13919887806855966, 2.252978165261422, -2.824300826854728, -9.126021225026012, -6.016643300220034, 0.05001355813526816, -0.20419329698359723, -1.312931753313165, 1.0535326607206192, 0.9550966959658909, -1.1849244665581955, 0.9227347168560192, 3.4764148612168775, 1.0415759473733994, -0.8185740395450436, 1.0122022415935694, 0.8491951535725011, -0.6505464925949686, 1.3878489546443298, 2.062322410695653, -2.3251045924652343, -3.6595997900999286, 0.13934357923429896, 0.11254375960143723, -2.2791911640475067, 2.265571265576713, 8.403334683494773, 5.819716439764708, 0.1463910433663279, -0.36423302856909734, 0.11372845759240717, -1.2451930633536328, -0.5659086733933305, 0.22747499132418264, -1.7641169106586907, -1.303691353518748, 2.0114041794797464, 0.7032151793554118, -2.324915892833827, 1.3904916351032106, 5.379013909671032, 0.7595516758219713, -4.185149920420044, -1.7266183231094592, 0.30381992043905065, -2.082225979321107, -1.9550952503198042, 0.477856720473518, -0.045989181177747696, 0.0487381669874567, 2.931468034641437, 2.014744868616447, -2.148355089198717, -1.9181117541635477, 0.11846996518399155, -1.6385910913300639, -2.14723494839254, 0.5258601840347215, -0.8939828784136672, -3.9704524182666283, 0.3970756304124077, 6.260802302261081, 3.6439592787175696, -0.6388600861307364, 1.1639652856626355, 2.516816399970898, 0.2160431867149405, 0.6077339486615121, 2.751154436242998, 1.396029196464081, -0.1102090785091181, 0.32043392707560914, -1.7610707785806294, -3.6486019900436006, -0.5022824363502119, 0.004561911040147683, -6.69621055634209, -8.823891923685958, -1.7484109178616183, 2.096304504061079, -0.9053161490411016, -1.3536902695486706, 0.7008316722015155, -0.5612490259990991, -1.217045518898821, 1.3104936746722105, 1.3150877494952262, -0.13181909342935477, 2.3984749923988558, 4.000348660479096, 0.5441028204768761, -0.8508417391779879, 1.238314379816083, -0.42137898934599005, -2.948745310576659, -0.03883412207416948, 1.0723646447663764, -4.344085024051682, -6.025053188435198, -0.8726452563928095, 1.007626374190623, -0.684515145174941, 1.5403207665913832, 3.8068007390087906, 0.8804360772938167, -1.219269152155543, 0.1738453201510636, 0.10086827014308575, -0.20966533249245786, 1.1809417296386153, -1.3784685901594833, -5.969621337792999, -2.865580030566495, 3.0053232232074087, -0.09167189956279809, -5.633037086177887, -2.901243121469939, 1.293269380835908, 0.16445818980831678, 0.10324753982140708, 2.42659500061627, 1.1859058725107876, -0.8419202866924834, 0.3719042299963061, 0.07347740949393905, -1.5845070598024753, 1.1795915072466625, 3.67510527919802, 0.12639996787880495, -1.864918223721033, 1.4429285389115578, 1.447673759323274, -1.5472753419293253, 0.9183033322600914, 4.281984893361852, 1.5047484840043015, 0.2091291653450911, 4.49254354682135, 4.927534715238588, 0.2673325214810489, -0.8484789891076128, 0.4819465685221566, -0.4539624206890261, 0.19188718839871016, 2.5224649921291613, 0.8872915462155513, -1.365810362102894, -0.006392973545444744, -1.4531835119499152, -5.617837398397218, -2.3034662860946495, 4.480040403623215, 1.819575088868649, -4.795368152452361, -3.341465079934453, 0.91095128788902, 0.5014398847591538, -0.01975309633655561, 0.6413648149418427, -1.0713079753011605, -1.1340663576303722, 2.110783998444886], 'positive_zeros': ['0.6678054550099148480264593026', '1.98000974066932554945555216938', '2.968525195044188234925047517922', '3.7612528439638650418218095586', '4.48205603967067940823706495128', '5.17889865286984684293110470121', '5.88856288576702662074543038501', '6.91505491608673371348444196160', '7.36731660574935160686803527475', '8.09724965630398304440859814173', '9.233419993566818911057997440587', '9.85692316022763812763219893192', '10.684343505639628120875233552235', '10.94588607176292490251485385846', '11.889618439667559418932136746813', '12.546905282742925659975915538342', '12.87337014556883027248879679236', '14.37127448434582598665340763783', '14.97497538560428273470924857743', '15.146615553363709663768959006446', '16.2217309282844546252864403848', '16.598149943997927411059717937260', '17.39410247558879001669814888112', '18.17167462352639524416134738000', '18.56831968517356093737015126782', '19.58533371193312225684542850324', '20.00512240705168750693762588990', '21.06915178601498195104016452259', '21.37111467234660262591059442208', '22.40514204908786402012586261952', '22.74648618427608727847399281164', '23.23413016829874690043093940975', '24.02568988887095915720280934774', '24.47899575665259474412483237211', '25.71707879892530214068601986047', '26.15364355756308436304904311663', '26.802897349458778978416426153599', '27.50028731903204211420974790422', '27.84915496407424641718131245507', '28.60227796704005865227897748461', '29.240881610022310443068813898661', '29.91904682898932790224607231745', '30.53766240424029007102555947443', '31.36015499566525441932128894213', '31.778469869835279699826766239349', '32.6221054158110641045287537725', '33.22221104582883349213059586884', '33.892400178420949631007712233830', '34.46625861639504952607417038788', '34.81878569354266296988658139285', '35.44862444275676887208395437492', '36.32461976123056425814117798358', '36.92809056038544741690777424941', '37.69363890930785272007422889474', '38.55037328006902438285213381797', '38.81681548345038601578040359755', '39.319841116631892688911710742952', '39.80600898733069122834263215525', '40.779496422938547640795963807058', '41.29683503413300837520729941463', '41.79489271078667772942898072382', '42.60442469628492356231361359883', '43.25671060507278018414708017450', '43.92145770253148236000977097168', '44.348472954293326137072942538398', '45.0561874445053804926311062450', '45.73403463811857620877444315195', '46.34554682682324008001671536460', '46.6309436171258576641118428769', '47.250901540145286025762462421952', '48.01858838030885166955155436794', '49.07056049520953840506397957033', '49.408148329070991461638320581348', '49.92133629007908361646782479576', '50.73446691242739230121729681112', '50.93842481902599410825191257859', '51.76236199836945002035917732207', '52.15613872600515810854924416382', '52.91362803527309992990712445207', '53.60929364465900677412847670066', '54.52487919876267541490665909698', '54.65890921159726251710378098570', '55.27951298985828974736988950577', '56.21323883118629645842475528670', '56.63775919780379856939261329528', '57.1601557584427103876849808988', '57.777165330228194795323969372282', '58.29432455756305569129189315069', '58.911934995254206362220379316791', '59.47439750279147976774840496847', '60.35368070264342886631113216720', '61.075106175579046781100225921084', '61.52944101097620777547815528311', '61.90449629170032446258864799288', '62.69049963106439324901617804755', '63.06586852467369884109227911796', '63.5424406486748892923324679472', '64.359612156407645803414155773767', '65.07566897786499292732992764656', '65.69836448681480891456544517227', '66.16747399332186147732676744813', '66.94125399063013880149014392352', '67.229765803506522763064326510160', '68.06659057272958770642854996315', '68.56854260109619793999037588319', '69.00389501924686458295524489889', '69.79970538873840213154689185087', '70.19429198290519916491379232927', '70.741290235160582410979284752140', '71.5371336360941626015843121490', '72.27580589143034692011737817222', '72.934868689694984770026297223914', '73.46897412977553357478632563761', '73.52687102043085639142907153359', '74.522148802258505368598181921432', '74.93485958589557346978781143151', '75.31267163590283915771241398768', '76.39442705160949119726709829901', '76.67729799822579890724168019524', '77.57546834901133306249809552761', '78.14730044856751591159277661504', '78.6725442110644129373652029478', '78.78542407699268378988846956187', '79.77260279515946601274994479033', '80.46331792340072729470368057308', '80.84698615118132745466616667289', '81.28598910824068715662027042180', '81.85491577124631699811125353058', '82.73512480057622486246090853827', '83.34507523263962960534127160365', '83.79221078678667108936917647069', '84.48316967847675426490437936075', '85.08785751568264332571507496343', '85.638580612778046867915324849398', '86.00564609947195950142723783535', '86.32718445749911857352365015352', '87.204391826321979431270751170499', '87.88722557465474481231430471483', '88.61470474195228561180704100530', '89.08248665483395803427740757575', '89.622652168040802827563438276299', '90.27676604114494017037231561450', '90.61357079242864363617875464356', '91.410409306671250076674939017239', '91.68064400953727848890903994751', '92.570203642469403396667113029960', '93.041008509997773096101892234733', '93.40140681709275261782239973218', '94.29105950452848182575515086261', '94.7702770270267480871818690341', '95.4293613900997435113332755904', '96.09533986192739626919722460139', '96.691327855069311676458745215812', '96.90472828277853446501782370031', '97.49546050519670302836121928063', '98.12608018608901877538645805648', '98.68196575470043514881945130637', '99.1983778550082627899325333316', '100.18512764360727918099212070488', '100.66587031111317704635990075299', '101.16472988753311424708139425090', '101.5890226703239873385942263179', '102.16624695233455453677354251698', '102.804937605704650175234523312727', '103.19252513701272574604575223833', '103.97386773412147303751460824531', '104.45723931902460142317938849751', '105.02075909957864591540463037978', '105.57048377544462260453246134183', '106.32691643159355704526363634524', '106.75262990828337348133161926457', '107.63880435672540978466049745643', '107.85825409155069319339811112013', '108.38843804848833997714895236301', '109.062762487690037981258046512552', '109.54195413357402461809105816379', '110.00861409962844919447998351485', '110.46557013455079405120655871699', '111.59796789618237620279375241768', '112.06997349407351702220269359044', '112.53594598228357404572411998003', '113.00556314732739795967429988800', '113.46325124993874610492171338004', '114.09412845023039321940799454106', '114.74147207894176346799406721106', '115.18407434769379502747691235361', '115.65066621573905869058428936752', '116.44095714362908183798296042064', '117.11264852633539156215968537932', '117.53968918521684024566204010631', '117.93240553926869548198479199611', '118.89977695667967912257753220244', '119.19861872796224750490444401268', '119.82937135181127381625336220113', '120.39070568040641784920583090355', '120.8329775221143802899912996245', '121.093524024641880449993987076322', '121.96177307574715524428102013894', '122.75169302585503496202353813298', '123.14188713266828524464048223895', '123.85637567454857963157512412744', '124.42134491921599317161323945203', '124.91181736223463769242056422055', '125.30567467691998811639213141325', '125.7309919624494587439025851291', '126.359283601064265943073379953870', '127.21343863389570059099439286249', '127.58530787055684793451116039358', '128.08137390286785412620714865809', '128.94752051761643996577120291105', '129.20046054921272800946017444787', '130.10801190420054575970147565218', '130.29476970489473175424573545402', '131.02052254761503133059654364979', '131.5511065649877048271520842361', '132.18183580346536319974051138908', '132.47547901311560397727505064375', '133.024211683920718697857472392150', '133.60650903543166143948068775670', '134.51661181486807094385647062100', '135.035879957800852014292699030091', '135.50486858466506963517664626649', '136.197193160204626609935291782198', '136.447822747642492521406442416141', '137.02309854887641272993332751626', '137.50110922781111979954274338871', '138.1331154280596233189042283034', '138.754797851874730464668401398151', '139.34892374620712456208581645046', '139.85002605770979242752818895346', '140.72562730632320387854143953204', '140.92066482441603899260061097727', '141.55479341434193824443790681337', '141.98092162147131959779771027420', '142.85262742520370256551686865295', '143.254249298173942941619113376637', '143.57680468728156280212768725662', '144.24581711079176287498174526394', '144.75384671202320860124575457675', '145.24720671967754548304948454835', '146.232036905853493832128378093502', '146.621996153334107629573816224606', '147.24291403171163603560822435949', '147.576263453485561402175004578172', '148.239689819569782415469078303698', '148.64958387250800460822807814604', '149.16960597815663547967418853186', '149.699503226120687146645741339476', '150.193097973718302756980595345522', '151.245214297945282208579107271917', '151.535073438887754048310483754369', '152.06223101486301690503928465066', '152.61439893894938842709988550001', '153.0463261499790989628317545149', '153.849306660186799230622662501622', '154.227196019047758554577212333785', '154.8157514290121358548747278631', '155.15752764780382766708640620744', '155.791051941532492109717496257108', '156.549291819046349035301206432848', '156.8867029170545237661072819729', '157.39945754774857447565016438671', '158.45176334975767833799057457349', '158.8425336343186607318144499325', '159.096866494117308002885617220752', '159.79647367719286000163231091043', '160.05776480151799741664512178959', '160.74131497600238465263760154523', '161.30352296170490437873484634978', '161.80231934757116209831242631736', '162.53305414715707587608868796350', '163.28598132761348004939504322588', '163.502967846987941207464669185617', '164.289897257253384765223661450564', '164.67722081324451572364434634057', '164.99275468335619915955467133255', '165.76695522633406269033727029380', '166.50558197887293792323812888462', '166.64161648399532189039367235466', '167.425676505675038582054525725797', '167.734798382972084207436037957331', '168.42081315412893215387941188043', '169.28726129255285675505080381885', '169.57099633012933476967371751116', '170.35402160100590735346409442684', '170.52681908631639802023414880033', '171.48038832328034925823530280741', '171.6584996960477039912833109496', '171.98304942003108339409000407979', '172.85612816115569832447837684840', '173.12535941171543297788521250413', '174.139807023263498979978485979726', '174.60608949416331693699400365493', '175.17361738119067915512076072091', '175.54598780035343671739828630679', '176.097966994909358488047427156976', '176.78022253515482115284409662570', '176.92759647826092819166480681421', '177.85934757011716188619267933137', '178.25141750460857297844700128657', '178.71356487625501793853429280547', '179.37802974101354400722098529400', '179.7718263900055832432313066728', '180.684438127339330682949982934201', '181.09702376255164870174819470684', '181.42273661056283316647884928388', '182.2623363610837803268305416321', '182.774423468849418134569844139143', '183.15423482891311917595128636849', '183.48988936141694643021199419608', '183.9692814329065283299508060503', '184.811816134383026876652944220', '185.30836356668609470033936261625', '186.10835962710481398288343556524', '186.58992600123334027659544313918', '186.85896663490403601183735569263', '187.63051875500298095272630539424', '188.05340758897458547228533061051', '188.44853056897808460134255654266', '188.97510255947983670506780858748', '189.696065865317092737078893922527', '190.189949080734636630600746235096', '190.75348215844809996543876334031', '191.18855457970516323001422873989', '192.031796473095376169581784381', '192.15432188325396100525175131152', '193.147211416193872593082650030128', '193.59705365624762813906710835379', '193.95326794141216287910215327712', '194.34938956445646019288083435358', '195.08332251495566419363905943769', '195.62653667962256173834315495912', '195.78774285889560686304465155257', '196.653179629419792113389014995399', '197.261616143911412747540194362905', '198.02752831281839394935335576720', '198.55497928697869461777629876952', '198.75767070377469991321278722915', '199.221235767571223953517843303849', '199.80241604865874099623233690529'], 'prelabel': '1-3724-3724.1399-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 400.1993799351836, 'root_angle': 0.9960507938116285, 'root_number': '-0.999923036679498740812641704594+0.0124064788578313305073071002725*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.577687639277553495723198012817+0.201413866808037560496267926385*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.66780545501', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.98000974067', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.96852519504', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 400.1993799351836, 'bad_primes': [2, 7, 19], 'central_character': '3724.1399', 'conductor': 3724, 'conductor_radical': 266, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3724/1399'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-3724-3724.1399-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-3724-3724.1399-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 400.1993799351836, 'root_angle': 0.49802539690581427, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.66780545501', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_3724.1399', 'Lhash_array': ['dirichlet_L_3724.1399'], 'label': '1-3724-3724.1399-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3724/1399'}