-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_5200.4163', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.10452846326765347, -0.9945218953682733], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8660254037844386, 0.5], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9781476007338057, 0.20791169081775934], 'algebraic': True, 'analytic_conductor': 24.14869847674626, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 5, 13], 'central_character': '5200.4163', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 5200, 'conductor_radical': 130, 'conjugate': 'dirichlet_L_5200.2427', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^104', 0, 0, 0, 'a^25', 0, 'a^88', 0, 'a^47', 0, 0, 0, 0, 0, 'a^1', 0, 'a^91', 0, 'a^69', 0, 'a^47', 0, 0, 0, 'a^72', 0, 'a^29', 0, 'a^66', 0, 'a^31', 0, 0, 0, 'a^98', 0, 0, 0, 'a^38', 0, 'a^70', 0, 0, 0, 'a^39', 0, 'a^50', 0, 'a^45', 0, 'a^84', 0, 0, 0, 'a^75', 0, 'a^73', 0, 'a^67', 0, 'a^53', 0, 0, 0, 'a^86', 0, 'a^91', 0, 'a^4', 0, 'a^57', 0, 0, 0, 'a^72', 0, 'a^84', 0, 'a^56', 0, 'a^96', 0, 0, 0, 'a^13', 0, 'a^32', 0, 0, 0, 'a^50', 0, 0, 0, 'a^49', 0, 'a^75', 0], 'euler_factors': [[0], [1, 'a^104'], [0], [1, 'a^25'], [1, 'a^47'], [0], [1, 'a^1'], [1, 'a^91'], [1, 'a^47'], [1, 'a^29'], [1, 'a^66'], [1, 'a^98'], [1, 'a^38'], [1, 'a^70'], [1, 'a^39'], [1, 'a^84'], [1, 'a^73'], [1, 'a^67'], [1, 'a^86'], [1, 'a^4'], [1, 'a^57'], [1, 'a^84'], [1, 'a^96'], [1, 'a^32'], [1, 'a^49'], [1, 'a^65']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-5200-5200.4163-r0-0-0', 'leading_term': '0.177926750281040831837287250802+0.162092207973923840942858644318*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/5200/4163', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.24069028304323792, 0.9569495674863809, 0.8931360166154121, -0.30095111852020706, -1.5960002603794718, -1.3909095930612052, 0.38541630216609546, 1.8040702916742917, 1.196649595114895, -0.46954552510711534, -0.5516668679120865, 1.613290700845829, 3.1680880750525233, 1.071793196860469, -3.5628061795190655, -6.204467201091149, -4.386495518086932, -0.7662611693611124, 0.5505781769601893, -0.6579704552810961, -1.2611661297311418, -0.0353983925985166, 0.5718745732777302, -1.1589210838995991, -2.9158382815329693, -1.8411032415369304, 0.6542015945230518, 0.9389359656602227, -0.7784355216810419, -0.4664936667755089, 2.954356686920186, 5.017938519741258, 2.3205209755175114, -1.7706838256525494, -1.844370573650453, 1.4436060935343948, 2.7239721941064916, 0.4068469838579382, -1.467018364630439, -0.4236190417027553, 0.7843926044686244, -0.1722812818269456, -0.9105436877477012, 0.8153919997475894, 2.319604586601631, 0.6785330551730611, -1.28912301795583, 0.5968565383398705, 3.9839618332325437, 3.0366496050722005, -1.7418774746726344, -3.8438921173297564, -1.2319680876855728, 0.8544089021763184, -0.6600547787085914, -1.7619033561119004, 0.7845302845132713, 3.426732150454164, 2.3218108689367942, -0.027753412354465403, 0.06141759954588576, 0.9254250641040918, 0.022525242285310696, -0.06778674681638452, 3.195766552710093, 5.687675225418118, 2.754303300195443, -1.8093089637642148, -1.2413868151980134, 2.7674057940056755, 3.1138742066005287, -0.47724766094528565, -1.8543159456255793, 0.09568226204947972, 0.31721354093596804, -2.158006363405339, -2.675888811037161, -0.4167480430470054, 0.1429688083215747, -1.7060938946713695, -1.7383974244023936, 0.25417121885736405, -0.07822837784524891, -2.1936768116221947, -0.8334380267523328, 3.036306026427899, 2.278589496134753, -3.4611571525966056, -6.014488835162338, -2.4954802231039235, 0.396402915419818, -1.0806398494957108, -2.152462728190982, 0.020576017562170756, 1.4098567998998615, 0.2395120782193219, 0.3432386305958995, 2.2019671715551485, 1.2461872433100984, -2.3131925822574626, -2.7959101155076818, -0.02849440608590051, 0.33372474471134506, -1.4832247683679298, 0.3373472639869125, 4.426424744098247, 3.006554947404674, -3.5090654770281233, -6.156680576062973, -2.7014087920996435, -0.00303788289020597, -0.5817725762922739, -0.04715007392107374, 2.029498588297665, 1.5955828302784494, -0.23221410269734358, 0.7786924760692617, 2.419906515326957, 0.33946989603785593, -2.078612377175848, -0.019858601286140354, 2.2181842735877955, -0.8374827774476097, -4.371658944923075, -2.1623813414253608, 1.1662426397900265, -0.803804347617885, -3.8735840663242858, -1.9394382546874402, 1.3456608583887302, 0.7832445464020339, -0.5147665156604981, 0.8070189598673118, 1.1558965488672563, -1.2297453490485777, -1.8436098985716827, 0.08232983092351612, -0.2050057495293356, -1.5091364088109067, 2.296434162176597, 8.391065523019332, 7.748437852526919, 1.7004439016809998, -0.3377028686123136, 2.0832282036972356, 1.955211716379975, -0.16688939573695513, 1.180864111278587, 3.5940626393575372, 1.7582413480694956, -1.215731649202184, -0.5358765175853527, 0.6351955811757056, -0.8452315605597289, -1.2132245419806145, 0.6507836752201559, -0.20898438795670574, -2.7551504282705315, 0.29554076363971815, 6.989740684516014, 7.340948470125765, 1.5301539937409625, -0.8490266415483123, 1.1361328987049586, 0.43319529874239904, -2.411727358534579, -1.7414386015613788, 0.39993921429756946, -0.5271643172410617, -1.299248078341864, 1.179108460447562, 2.2563152367046366, -0.15912972944989603, -0.7586990194626478, 1.0193305027046042, -0.5448077152688167, -3.671367121108956, -1.2042154190711107, 3.6410172066997157, 2.22277971736969, -2.195058971465391, -0.7911969351223299, 3.5001322134740604, 2.877729314786128, -0.10995289929919225, 0.05393091931090993, 0.5911382328295701, -1.0478582466916984, -0.8555927482022989, 1.3007501364566116, 0.16961369195173995, -2.472830318480719, -0.5289241003562382, 2.6800739528815924, 0.6817419311446841, -2.228347627910885, -0.3922025048084543, 0.38187951982931106, -4.58213208586761, -7.4544925441092715, -3.0986237741903677, 0.8099386636786949, -0.5570274728511512, -1.4026179661035052, 0.523156892369201, 0.5172445034781955, -0.7816881624600931, 0.618877527134653, 1.5810065899580141, -0.9256826119092048, -1.4444349208514857, 2.0481782176873446, 2.2378850812490025, -1.7680163196778211, -1.2193531728036482, 3.8209106935371517, 3.804969130766638, -0.8406580408150197, -1.374173055188923, 1.0754501005577317, -0.12213579833059043, -2.0308137320970614, 0.16510728339919878, 1.8994340614615675, -0.15033009271860548, -0.9520974338932522, 0.7147138653067902, 0.1297955752895492, -1.0517209513632215, 1.32935206740171, 2.169514909576522, -2.594895236196703, -4.709008129432788, 0.6258480152105387, 3.789620599115026, -0.5842306159441817, -3.781772626853207, -1.3808526598176807, 0.2621799638085253, -0.06664972518631741, 2.1880595385202963, 4.015837499337778, 0.759738722870229, -2.4550743792469825, -1.1354942533259875, -0.0046725729041044665, -0.7777719846618735, 0.9124667322236304, 2.3629414880914883, -1.9325400541952975, -5.675147397832041, -1.5894840075735555, 2.7031080551179767, -0.5330736809362547, -3.9434342677905105, -1.267531465424302, 0.8895760860742237, -0.9590478466678504, -1.01237003186522, 1.0143087844485317, 0.20868605278275185, -0.8753353790083662, 1.2275622695225206, 1.482433669441535, -1.8855877346701466, -2.219344324571758, 0.3780919231500941, -0.9013180214577668, -2.9433873471416776, 1.1116911477933282, 5.070574688522876, 1.5226168810152316, -2.305633729526792, 0.0522374030665667, 1.458208650780024, -1.9925690784558432, -3.1667365445670543, -0.49746271927371905, 0.04982743948368773, -0.7583531626181247, 0.5273055098571734, 0.29757430482908137, -2.035549072363847, 0.011325509214284608, 4.619561001172766, 3.1716157222076817, -1.2755456711563034, -0.37346386166417134, 1.341004454106631, -2.423985261130655, -4.643515175570829, -0.6164985148074202, 1.2708606314256503, -2.1153373125063797, -2.8598049871624958, -0.07612932205985559, 0.009640334238135909, -0.8976755603642892, 0.9589494040822495, 1.401964323802213, -0.6414129940746405, 0.4902472500988152, 2.897725643285648, 0.7658358102439954, -0.304723328413599, 5.429039206509652, 8.944863196091925, 3.843002518278901, -0.4877285203710976, 1.2221102335085503, 1.3279571963466137, -1.5153682135199058, -0.548234765397527, 2.1404451770941604, 0.980675167484006, 0.07629760748441108, 2.3638137208133623, 2.1966568113024083, -0.5456603624901649, 0.07584304363938392, 1.5571032371323295, -0.3539833107073977, -0.05044333010085307, 3.752689355888935, 1.3498207782242224, -6.730069792875979, -7.534337045855193, -0.8290626880114171, 1.7689649751772831, -0.09979087995143195, 0.0924927582394594, -0.18533541335073425, -2.9950301554767327, -2.4866448350608716, 0.9612539159148022, 0.7902779765111317, -0.5505564365040672, 1.7092369004892332, 2.613777930874779, 0.09933924495904989, 0.8527819221075215, 3.234500555456777, -0.616296334805591, -5.121748241230672, -1.1725587486251425, 3.8807527566755122, 1.4322723622558249, -1.499033232099193, 0.4336987443710612, 0.8764559810748244, -1.2431752356523955, -0.4047121803186807, 0.9423897898816678, -0.8625144910690046, -1.053646498417398, 0.9029787139766638, -1.0317902988417809, -3.6308223307345777, -0.5124109892692185, 1.7575216568358127, -2.4138612779764643, -4.278165990181535, -0.21688565816247882, 0.39901786120834803, -2.862265263521821, -0.9758648523765907, 3.2572003871848687, 1.9192219247268338, -0.483541796558541, 1.1111154760009916, 1.603781773471867, -0.1389819004888446, 0.6357902579677169, 1.4784017595070718, -0.0925490637082715, 2.0027508513682397, 6.944124269727831, 5.017430671691896, -0.9254670683711275, -0.06138998817755549, 3.5079007545105503, 1.1973091203284167, -1.0292099882693015, 1.7885605063230183, 1.9712135944864682, -1.9178142343198377, -1.9122467858047212, 0.5810973349539443, -0.5391319806725643, -1.5996882666190548, 0.026310315557520607, -0.8163233304056778, -2.7480377220746752, -0.4342126767664221, 1.2814890845573392, -0.8982660445480318, 1.1789368986169384, 7.362449777012899, 5.8806286644429075, -1.5025142038428254, -2.410279573199394, 0.9269829698166386, -0.21751226304155669, -1.903062290399573, -0.16146368481419238, -0.5037371982104849, -2.558288102510916, -0.8237674940839748, 0.7427281027068667, -1.6622790721045195, -1.7483171122238397, 1.4097068879869104, 1.11172394125264, -0.0071362746302702255, 2.676244850043707, 1.6363497120315176, -5.363060577719306, -6.244576624875827, 0.4488268657477106, 2.0777238107816776, -1.6636574815184697, -1.2546483243802669, 1.139818215697042, 0.22889085926847044, -0.0841501229949553, 0.4460353173828203, -2.763381280620203, -5.054615526317958, -1.7144887495315542, 0.46030740240941626, -0.9896227321584978, 0.3235790213928049, 1.466668766656897, -3.577036250246204, -6.3517062061733345, -0.668061681387675, 2.9189791449127025, -0.08474109886818734, -0.09801358320779813, 3.0857723145183718, 1.392023728989357, -1.5802881935992061, -0.0246224479677072, 1.022090366829686, -0.27540580175650947, 0.7468166786180997, 1.3477748128571878, -1.1958495709761108, -0.16600682244910003, 4.12447641557131, 2.5822522669551544, -1.089591041971156, 2.253499193144195, 5.586957049411564, 1.361276780256304, -1.701513990438949, 0.6941053833531079, 0.3416231641413024, -2.1602082757346146, 0.03629774338884301, 2.135411186509222, -0.6281191224748822, -1.7823762461041155, 0.26347308006939146, 0.0844225499188564, -0.25090818266452203, 0.986562353818272, -2.2140334589053317, -6.626953574905387, -2.2739218953995652, 4.572401705399009, 2.79710258701298, -0.6339901517602128, 1.7558251670393958, 2.0610092520571324, -1.9604189668046899, -1.7674653396399957, 1.070747730136634, 0.1240998386423266, -0.21029079206030005, 2.3500804900320027, 1.547420961801201, -0.9918185628335914, 0.31806209712241373, 0.8191843883003105, -1.6376596111737043, -0.3904279053548171, 1.643890086327305, -2.915342844746315, -5.963167128885016, -0.3532724436516961, 2.8615272754710848, -1.7081656103626872, -3.224466597719385, 0.24563515086686272, 0.4598550721797808, -0.7432971446778215, 0.5945556979431297, -0.2254870859586373, -2.3437902120932654, -0.004849653954231738, 2.1525735619658763, 0.13824486538293046, 0.9397030510047486, 4.40779503483279, 2.430256560693957, -0.8865103817489727, 0.5413018341930557, -1.474467700688662, -8.847554571158042, -8.89806785015448, -1.5161614781125767, 0.7335618015898683, -1.219585083291644, -0.03308042411363625, 0.7958100251836804, -0.3166162000503308, 1.5077319763943493, 2.9869972230028212, 0.27118852053343057, -0.2144402315263094, 2.0629653218185973, -0.1367707611149874, -2.387029860775533, 1.680735939573704, 3.2199779246200655, -1.754322168057701, -2.217932260637069, 2.2122974186875695, 1.0468539580907146, -2.324220308258716, -0.38159870030738835, 0.7628467285142134, -1.8932572001353876, -1.3173579893770364, 1.1495864420806465, 0.06617901913045189, -0.43113558373906613, 0.8208966113548599, -1.4158900918019257, -2.987288130329981, 0.23155010342157092, -0.9058699617565631, -7.569839952356821, -6.707328620834751, 0.6481644228127097, 1.6860932371592847, -0.9063461118949296, 0.577505518318281, 0.7379550496329059, -2.0049329453780085, -0.3868608898914876, 2.497249367887565, 0.24634043283241774, -1.5731455542946309, -0.10249066080670816, -0.8318868949693745, -1.465347398826007, 1.4981933972865427, 1.6337419972265896, -0.10058324502363832, 5.326919497211708, 11.049643592799354, 5.705648143271767, -1.570636633003771, -0.9248520150184834, -0.22481872837899783, -2.698509499150488, -1.3123507326465909, 1.0757119894332066, -0.7474858902649187, -0.9956828430531721, 1.4925832500813212, 0.6569306772467383, -0.25502861459245024, 2.167893713934612, 1.0067737308626428, -2.984466906564926, -1.537521229505986, 0.5900153011946042, -2.130096793439401, -0.5044747042014609, 6.376420601494786, 5.478909338575486, -1.3588087256338788, -1.8227658103413609, 0.8160275883670322, -0.1771585870923438, 0.15835483124941363, 2.2730413700967054, 0.9884856352651923, 0.047076068424197884, 1.31596617350132, -1.421407701308579, -4.738648090138828, -1.5134953225901526, 1.0999899267128748, -1.312409417066003, 0.27834541243074706, 4.644317809300681, 2.049768714319544, -1.335569791322211, 2.181747625415865, 3.2247917159635637, -1.893892664403706, -3.008565425047833, -0.03101492765555139, 0.11689158587832064, 0.369574691399168, 1.785510151592896, -0.5514530593230574, -2.448908032093228, 0.09979156362006247, -0.17948350178194797, -2.942600434925814, 0.10826751061200349, 2.759999928435917, -2.5264985952368018, -5.106319197590259, 0.04710363263248509, 1.4288976583393036, -1.8593436077312024, -1.086462259199292, -0.025004986108218243, -2.6138318328306465, -1.8539380026382053, 1.3492517259638033, -0.09760622097021261, -1.9214152803202043, -0.3158387872346752, -0.3040322674796929, 0.19445386547332083, 4.510336956892725, 4.163530124020944, -1.1743590529097987, 0.8996102601447293, 6.900631841567409, 3.9341119381415037, -1.6489484623405355, -0.2646995827200634, 0.9967355063998564], 'positive_zeros': ['0.87494660965948780469609664427', '1.81551142140698625193103368656', '2.715161581416418917109044553542', '3.22889437924306711909158673821', '4.14050027991484254422065171255', '5.40891054413089540582058914947', '5.80076639455468837276223299252', '6.57009737371523937904203271242', '7.0208687723807813869356588540', '8.03129953821387154397434378686', '8.61002671050971662345179251073', '9.11937270094674037524598632689', '10.15920911674057167293822742133', '10.80712983178152611713648150678', '11.60690246679000298182753584638', '12.26124321496474881243542370043', '12.776862383271730952472336691892', '13.32704253427821068811399305273', '14.14058131446063468155906770407', '14.63358091525663243596852828011', '15.51415820786500226039265260210', '16.37428233541176478956587775146', '16.78441699136361572137642499075', '17.43018275899602307023730429631', '18.43122248697056589512050653670', '18.732819384503801552560226201886', '19.38057110530563689332678079249', '19.69956753275116164555787982629', '20.79128903498372050068735999377', '21.34844108735782530329668621226', '22.146110842457858986249523433243', '22.797366533381756101021515471011', '23.17630779026336647024630721596', '24.13216668761976054971335275719', '24.408655591891300074708767353595', '25.26428121501814969309603241468', '25.612600565967902356707784963817', '26.31626868886155305147117359981', '27.01004084644901144148690411526', '28.02886195417830143311660896373', '28.285564955782823662290004012374', '29.06007583660724471859777952375', '29.76349074908178675054290938119', '29.908247428991252430972278636828', '30.736213632269313403869836836550', '31.56628048978584985294520905170', '31.93181160655571760370568637827', '32.47371827500123700529745645032', '33.27486381192069488952703669676', '34.37656960206703711564263287940', '34.47939995194170551119689668960', '35.00758685032331268243460549823', '35.87245924908804440456009579426', '36.12645613984186273083604679268', '36.90567617211825742635625434423', '37.501751433234181322819460698665', '38.069650826992947231817818861282', '38.91084765092492914814901678243', '39.30852574870098081385491791448', '40.15471795456345761544101195597', '40.75272262091212723031463732849', '41.107947713472638938479190157331', '41.72874808327633153779290519177', '42.48346665484010508448032782328', '42.7754631960764433646294203174', '43.3096121302105911265694484507', '44.50656770241871983202644597424', '44.74851256810930722151863443729', '45.5808838348305635510198101221', '45.78464605206869085350209422816', '46.71563106187397706578646997409', '47.27472480497804338390919628142', '47.673070101097626819096099897923', '48.32178991856769408886288212424', '48.7260980693626595920668841220', '49.36036694920567846764515582553', '50.41697504000815658202931764895', '50.77387312966213106371174512479', '51.29541969927855243123489210924', '52.09516743277283126232992863010', '52.40964582265072981149294874278', '53.00167720843581398870739543227', '53.73038725923816922481006232561', '54.18925228323285045551395211639', '54.63773705609721829462964008701', '55.380236732929938866656848397583', '56.07504470663903292522008436912', '56.615384059716647171992327191580', '57.481010862826118780162490135631', '57.79961262755719969975569443433', '58.25862172462173294997439357665', '58.86569102534384605310022262649', '59.39199636983478708590829459905', '60.04016876739671899483950663274', '60.67772842544085085368202855265', '61.2933591784794336905934194011', '61.60326988386372062862556909453', '62.69612843378783927615002349775', '63.05174113512708699968879021667', '63.6657457645261125579242625872', '64.15969615705942001496405989673', '64.5998965056040019429252514536', '65.215191365130912929737217644691', '65.767484946214496179522848397745', '66.423344244769219685565909397942', '66.954606964942526537759433148346', '67.74887837160774290533205959385', '68.28062237658576747381318189433', '68.7364936936722396569216600997', '69.359079534733061854209010015003', '69.98115412662204254088415816881', '70.48787500602125551215532786702', '70.95836839908447496730555536686', '71.4296684489486100064794401734', '72.042507633977715036440820011635', '72.78234231204744111105358365346', '73.40556698659113178661085662144', '74.24056594711373804028047022035', '74.534325397406729837324734339543', '74.7159504944410389443437173620', '75.67633789945391840797323434881', '76.48110093122790579966907996191', '76.55881627557928819112114919339', '77.08133807739510282399097094033', '77.70865394391311925791025206777', '78.51663363163240773287117286595', '79.03120637466276328685880234378', '79.797516193641198191672316489944', '80.17948060664549734915638167519', '80.76586678391614021988359397462', '81.28194132735971203750627695049', '81.72531229691654314771880241364', '82.33437935327752272962575408836', '83.06089730967467832204383017439', '83.339774340590292010844062058188', '84.00410908311186423058628073504', '84.77256106245585115498743633611', '85.30798649283573882485262083829', '85.781041321173678617400528968151', '86.64291402794836210099262802993', '86.88962824323213893274636050889', '87.3983216428961410194163281504', '87.85286250137404344029714462835', '88.43676669764482942220296459470', '89.26040500636130762753966105973', '89.72484872971901237764669018340', '90.15342098599862921739788613261', '90.98051206878279220294583036814', '91.39060395982411021888233753100', '92.19922008705424169454160172512', '92.502037989432805816855951979598', '92.99554494817485100256912759304', '93.63874255611348938181367117549', '94.0090319505759985648794500749', '94.76268174464395085973209646466', '95.03114044163925623632897246802', '96.1646949068987820768596898572', '96.41062726206871307690822808773', '97.0136488283779261156451567288', '97.552181669373612107479145438812', '98.301370967268204186342769651582', '98.41368866322800688477822102157', '99.29603254037836522463450489935', '99.67708673131997447877604751902', '100.26476767968181254517065006119', '100.62990986185704733646326912060', '101.30523932553792852130099088804', '102.23250644453102670451143230827', '102.79080333254725082003632384962', '103.096765733683109111621680590555', '103.40754997612891307725721517974', '104.27376731947138290476994469695', '104.80493406811103207393350107903', '105.12283386519348104072823565476', '105.95512749108063780320146945510', '106.1419826109856420991447701722', '106.844433113350054230328785324787', '107.55304503388652031755705127752', '108.225775663521098149016592885520', '108.69755161637831435269642934308', '109.185574029509690714470005651041', '109.74345937268231310586116297577', '110.19291540057492551204660445768', '110.771285085344177859117892851177', '111.15855418326281983525199817098', '111.91006867549921939171137212823', '112.35366047696570137626042382895', '113.14290794207661540507602780414', '113.47811555801225914972633479248', '114.1232647216898376346682074100', '114.8783690075105987792067381326', '115.156201390056432609312643132447', '115.89904056092502752445739881199', '116.13032560592011326049317940282', '116.84750808876995202401239122571', '117.00156395707519515353823715200', '118.05885914957986359927347850787', '118.44195357576704469358559771839', '119.15847925324758813018507952616', '119.52336415861243514036951340942', '120.15778478309825579694119635084', '120.833170813947824569148173953124', '121.17492919293683690058908425704', '121.86827772717834638062907835462', '122.0632088031553788622312862595', '122.85202365753612478475931509939', '123.31506484659353193758907598063', '123.67725333591517829563911213374', '124.614053009545620684977873975414', '125.20156487923872081116750678664', '125.601357931085214187751353755375', '126.28306205954517742934888735741', '126.478899615364474348639118713191', '127.276764743551951036301597784502', '127.629622623370524619197354528370', '128.29112882949384649357057554894', '128.93675023702262927500110167984', '129.06456681366828615906884199322', '129.76970888826641384514254922133', '130.60246299656837267303191970549', '131.10717555772967229685765784991', '131.692759253887909871774422106428', '132.23780195829053261009599392557', '132.525116773626176330436810840467', '132.89240051375500387462876900211', '133.90401067977531402002125796571', '134.181128209902655221947849830077', '134.65130461574590773523586031672', '135.12725578475094435884752399185', '135.96835477473940833871977984583', '136.554052433740508434086764099507', '136.88486844309522044758492914361', '137.608952046652471121326904539299', '138.12803682046906752297845246230', '138.663573034192012519026245663846', '138.93365731133038866015768707905', '139.5478312547702539611424022999', '140.01238559353765983166228628097', '140.79661188051710922538596213178', '141.11369059668816137440292243931', '141.95439815043470836661176693991', '142.42009010145515411373127123321', '142.84825252676894031744813479609', '143.43451624605935977162805823405', '144.005736410225340253073984206545', '144.63929766704655185312493986238', '145.02109620650842284959067073605', '145.371407741840263444721937256826', '145.794431807469219170965012549035', '146.64714307110389718354505857255', '147.38294978971104697740483888198', '147.6438359046061782385032928322', '148.28484766015652776222971753374', '148.91541115302160600369046822248', '149.39512764915511278849775501368', '149.719556382757341250629557454281', '150.46610441326062861659487719049', '150.89413847246811805014383376285', '151.35781568907479186099000289387', '151.91038113219809885647421642890', '152.34740729549234841619075559386', '153.1410849111844069834307165648', '153.6514022607866796923876041948', '154.348846447615620488913469597593', '154.76448685664604527000200831066', '155.19202650923378970204964267493', '155.5973513485709947752470685106', '156.250399231911823543145037937118', '156.89946638380572500854439280973', '157.07943538201911057314620158639', '157.991059361935606028988223629294', '158.35328680750805376513823728834', '158.658255005570467359749722629874', '159.77787543842505638200406253026', '160.10975502406007306030663695225', '160.629819816250592967167647666952', '161.124798877347580196022198677680', '161.37735722950441554119995865998', '162.21830291687925941720049091935', '162.5295400487064167096659735821', '163.114595856272809452058035173622', '163.64903874188672578823802203722', '164.27155242746744291049460478843', '164.83537394505023214204964412242', '165.38689913822882497789328399863', '165.97610237250029690804793365082', '166.35360190213073311995240052519', '167.01025264178215396091408662829', '167.51088896136925292949380742885', '167.90153930521995608530105789870', '168.301943016655644906646503168590', '169.03928244041078973217959078429', '169.31660738304999108337657333003', '170.27868236921797421514350617381', '170.79143145357955321285663730149', '171.17468039914215200379648775514', '171.64508011710629229855636428822', '172.21795490003030558102999035738', '172.83455381234105926049539447241', '173.47645907214485979273810208025', '173.57013944186829327921094003047', '174.23280109205796545104890323964', '174.89380268380834704793070447135', '175.02190258198115331583241955011', '176.14893374691691893179286147059', '176.7056606000209002368924975882', '176.827862877478895785999287220043', '177.62091967652173862967719178371', '178.03278610118556650662366706830', '178.55611762890294045774854719673', '179.16002888153872386103868944215', '179.42322640351896689805916164200', '180.07088666290448580218446375311', '180.76453317317969677812471703158', '181.03862604105508717233839578458', '181.58745774141665518272564185754', '182.42567311814612544625501349617', '182.989223783206879367975174195265', '183.40229916392657061207799080162', '183.72681128513807009313318136403', '184.55331859985766304774379972558', '184.67033486482220544717742294189', '185.21185939712585456450541399078', '186.04206853726241656582305754010', '186.411831022930880642853194768601', '186.85662277172594233538868622218', '187.62527552543202783410345146141', '187.97839884973506468189221537471', '188.63985320417493408987357532021', '189.37993952964680754084832020378', '189.73413097361627961563888794537', '189.90953092415958069118748602690', '190.577441903584641749652203671033', '191.23794050423717951313157128112', '191.54337203872939284245574133607', '192.18098190371797766287790847520', '192.69450180771863456303758240658', '193.43468625981422641260025588475', '193.88143060283307664294534406709', '194.53731696279172280087449019133', '194.68154373837447895687105881733', '195.46588051092784307393835027851', '195.92776374260892523925509157043', '196.65254886987489654212257980658', '196.76493304505622243649445363936', '197.16558426797596471604794582238', '198.04025916754845031568201072545', '198.39208324821861543909144334638', '199.245161368344480839809837897543', '199.714168957563716512199725406978'], 'prelabel': '1-5200-5200.4163-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.14869847674626, 'root_angle': 0.23518714236295002, 'root_number': '0.0929376168494208127579565092133+0.995671933607827600214184286581*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.727501459006260175462130948888-0.245351900059757504688648364235*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.874946609659', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.81551142141', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.71516158142', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 24.14869847674626, 'bad_primes': [2, 5, 13], 'central_character': '5200.4163', 'conductor': 5200, 'conductor_radical': 130, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5200/4163'], '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': '1-5200-5200.4163-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-5200-5200.4163-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.14869847674626, 'root_angle': 0.23518714236295002, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.874946609659', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_5200.4163', 'Lhash_array': ['dirichlet_L_5200.4163'], 'factors': ['1-5200-5200.4163-r0-0-0'], 'label': '1-5200-5200.4163-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5200/4163'}
Lfunction data - 1-5200-5200.4163-r0-0-0