-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_225.121', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9135454576426009, -0.4067366430758002], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.6691306063588582, -0.7431448254773942], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, 0.8660254037844386], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 1.0448956071669055, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '225.121', 'coeff_info': ['x^15 - 1', '0.913545457642601 + 0.406736643075800*I', '\\\\zeta_{15}'], 'conductor': 225, 'conductor_radical': 15, 'conjugate': 'dirichlet_L_225.106', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 0, 'a^13', 0, 0, 'a^5', 'a^12', 0, 0, 'a^14', 0, 'a^1', 'a^4', 0, 'a^11', 'a^12', 0, 'a^12', 0, 0, 'a^13', 'a^4', 0, 0, 'a^0', 0, 'a^3', 'a^8', 0, 'a^7', 'a^10', 0, 'a^11', 0, 0, 'a^6', 'a^11', 0, 0, 'a^1', 0, 'a^5', 'a^12', 0, 'a^3', 'a^8', 0, 'a^10', 0, 0, 'a^14', 'a^3', 0, 0, 'a^2', 0, 'a^7', 'a^1', 0, 'a^14', 'a^6', 0, 'a^9', 0, 0, 'a^7', 'a^10', 0, 0, 'a^3', 0, 'a^9', 'a^5', 0, 'a^10', 'a^4', 0, 'a^8', 0, 0, 'a^0', 'a^2', 0, 0, 'a^4', 0, 'a^11', 'a^9', 0, 'a^6', 'a^2', 0, 'a^7', 0, 0, 'a^8', 'a^9', 0, 0], 'euler_factors': [[1, 'a^14'], [0], [0], [1, 'a^5'], [1, 'a^14'], [1, 'a^1'], [1, 'a^12'], [1, 'a^12'], [1, 'a^4'], [1, 'a^8'], [1, 'a^7'], [1, 'a^6'], [1, 'a^1'], [1, 'a^5'], [1, 'a^8'], [1, 'a^3'], [1, 'a^1'], [1, 'a^14'], [1, 'a^7'], [1, 'a^3'], [1, 'a^9'], [1, 'a^8'], [1, 'a^2'], [1, 'a^9'], [1, 'a^8'], [1, 'a^5']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-15e2-225.121-r0-0-0', 'leading_term': '1.92389161715479166464871709220-0.730817868422456726595471090226*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/225/121', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.0580217956484383, 2.1215037158247405, 2.1694157706262844, 1.7335112823185814, 0.7795632211987393, -0.3899011497572604, -1.3135103404560415, -1.6018337816418051, -1.1552593510026363, -0.25428973957423223, 0.5568751396233375, 0.7634737961735643, 0.1980331011938275, -0.8189600879897598, -1.6395188165866525, -1.690966846168512, -0.8813193406390954, 0.2794411130957058, 0.9769779820172676, 0.6625472385867854, -0.47927470285378154, -1.532007541964766, -1.4005212722374667, 0.39948994777214003, 3.261939334134714, 5.724313855225496, 6.349645044274009, 4.701946120327568, 1.7224503804576032, -0.8201963968843733, -1.4810610276973588, -0.09810811856546102, 2.1398284883541168, 3.582736789439463, 3.3142387134845954, 1.7537591182475347, 0.2185439800518172, -0.18394109848982937, 0.5731743638307556, 1.509260991184387, 1.566492567414028, 0.5766377224628533, -0.5940435172843774, -0.860591785000223, 0.03511092128016206, 1.221871639908017, 1.4688556222527809, 0.3639501962576139, -1.2037674579993716, -1.7929753414221983, -0.7953551925807314, 0.8127488267289669, 1.1585794374672207, -0.8684261478473563, -4.42345578843215, -7.135661173350822, -6.940652503947343, -3.806822804772985, 0.16157391508164926, 2.3971090830113733, 1.907471451484366, -0.0733014394036981, -1.3449683419441563, -0.7302717283524289, 1.0094718762968407, 2.091916273081097, 1.499044151121004, -0.106624498076827, -1.1636382027993575, -0.8310559403113567, 0.21688448849988629, 0.60588168302947, -0.199310875434939, -1.2762831512040675, -1.236053553504728, 0.20045682305324972, 1.7511214707101705, 1.8349510465595131, 0.3031560603477511, -1.2288192648959773, -0.9686186490495408, 1.0561734146233253, 2.7020368574887588, 1.637261494365891, -2.2650795638766037, -6.469923592112881, -7.880133052451382, -5.592525346582458, -1.6793513758955108, 0.7622066525551016, 0.39441594718453293, -1.416673489449497, -2.2824726011769974, -1.2624887423639535, 0.39127129236755187, 0.8221196589150106, -0.35218218750508107, -1.7159575823691557, -1.7321124384610607, -0.47027355681221983, 0.5516211438588824, 0.18258527602069805, -1.0071616566425061, -1.4235422285036423, -0.4140945049457142, 0.8130903145965938, 0.5098899316341279, -1.4563039302596015, -3.140475113712582, -2.5134692933395657, 0.14524414376481254, 2.199323387115777, 1.2874803765310454, -2.0311835258903743, -4.534754204341074, -3.4483268805721643, 0.7283177231180811, 4.632892850197115, 5.296439229642802, 2.8787479911689218, 0.13652546596193257, -0.6083747216247848, 0.3378769341274015, 0.8985700427564871, -0.11244069713869458, -1.6572188241451347, -1.8767918415152587, -0.4100082258094142, 1.171720839601681, 1.2756202375302292, 0.17831102367566587, -0.41512914997276806, 0.40812159795897524, 1.5355717125035904, 1.1923373644214723, -0.7033088750283119, -2.1676808414707285, -1.4612299851474908, 0.5615339859248147, 1.0445945952729556, -1.6714173087171222, -5.807062623156051, -7.64068090384003, -5.375540604803223, -1.1682271234651176, 1.0294773665732817, -0.45088576905837835, -3.41914657188845, -4.385117183121686, -2.2991764712717737, 0.6418028282109316, 1.7512247393957698, 0.7875658448137174, -0.23999042812400898, 0.17462489415520177, 1.2409332194673066, 1.136186110396183, -0.4574161154307674, -1.8399341786795802, -1.4454764285895636, 0.12861835252871862, 0.8611399392636758, -0.09103078514173002, -1.2950990691944833, -0.9728501105624112, 0.44816764886194665, 0.5823902533660259, -1.8617418720865913, -4.947257065663698, -5.256997001416176, -1.844275684878462, 2.258519456612891, 3.057277187641427, -0.07403473115574015, -3.690534747196414, -4.063247468951704, -1.1498140464763018, 1.7039729124083527, 1.754290384740402, -0.23200090668267132, -1.3632390338512406, -0.27757392902621814, 1.4618480684984125, 1.6650870544088296, 0.32248990461163973, -0.6409091165338873, -0.11029028980097211, 0.7268366082148183, 0.1033205536236749, -1.7623181433082649, -2.7802603024590042, -1.7315285311095787, 0.012449587251664094, 0.22583210678947843, -1.141144433619231, -1.7379499732721917, 0.008401702473471105, 2.331972348554431, 1.8167828266725095, -2.3162892433477538, -6.599409536589169, -6.7676048067387615, -2.497855891137907, 2.1491438844301896, 3.190540245645156, 0.8807578467450816, -1.1738237420294342, -0.557319210340232, 1.36879644405402, 1.6942667024916853, -0.1836090778671056, -1.9851825424793934, -1.66818866760343, 0.0440973879845306, 0.9266840855123724, 0.3485861117078125, -0.06541519894639909, 1.0140768285294268, 2.5203327425795363, 2.3570277846611014, 0.4007107567105461, -1.0962713226558654, -0.476713948641726, 0.950035017599818, 0.5769923195721378, -1.7644041291694648, -3.0910330519650775, -0.9889876964027893, 2.800213514907838, 3.832488175858503, 0.1517909130035927, -5.066524237843812, -6.878134397885356, -4.051109890375947, -0.13949074892868907, 0.9340747025954212, -0.7850139472862219, -2.1340496963779434, -1.2497826287883822, 0.31017223552572726, 0.14484079824467255, -1.5631296896376825, -2.4059678655983516, -1.1501488669822675, 0.631892124009288, 0.8528791062446814, -0.22236479894495093, -0.5801482644969636, 0.41506871154968245, 0.9540608707133859, -0.5352311730500674, -2.7233896407576292, -2.768219978210009, -0.19171200161776003, 2.128902298077234, 1.648321445266766, -0.1757019917477357, 0.5903917541561395, 5.134807166877272, 9.690426533544187, 9.57395970989837, 4.7216166675292595, -0.163634263984128, -1.0525240317229019, 1.1332569461545703, 2.446129182023414, 1.1045850489318358, -0.781129227374399, -0.657632297499738, 0.9453119120933375, 1.4886732539097054, 0.18453917010194382, -0.9883728940470621, -0.2824457911178112, 1.2586585792635168, 1.3532518288006956, -0.1716402263616902, -1.1422086231247253, -0.27604964314146674, 0.8726228404409537, 0.27423218736963567, -1.2211491286865013, -0.6442114124952038, 2.8028361518783753, 5.895928869791495, 5.115941622827379, 1.402154829393436, -0.5891082627159947, 1.7443960787747002, 5.481503932662054, 5.673489861700565, 1.4724650108210349, -2.8991706977384015, -3.418880968249223, -0.8777311872616865, 0.8264942364304818, -0.08653000467796576, -1.5699581853441553, -1.2736900841469023, 0.09523012976775633, 0.1789250852558451, -1.3124808335294982, -2.1427376293053633, -0.91885126185166, 0.7850867990778491, 0.7179684779025447, -0.7382243047826579, -1.1868332993270914, 0.09754186723545553, 0.9597839829556363, -0.32705549079599666, -2.021250565923925, -0.9945067438423125, 2.5257599790540772, 4.398527628956978, 1.7126831778155767, -2.9704517829736945, -4.309423744825946, -0.7473266984554068, 3.534366118793299, 3.8766715621069263, 0.7651015545828704, -1.3531957506409087, -0.07833320758405189, 2.2212968714712513, 2.1556760082894315, -0.0945941242848298, -1.5390855146590354, -0.8284754134126411, 0.16965956794254894, -0.4233881048246158, -1.6121361382072352, -1.2493267459239583, 0.43098355255355564, 0.9700836303600187, -0.6090937175888245, -2.171000426573447, -1.5466961908309234, 0.19017361566142904, 0.31945638907485485, -1.212364542611842, -1.3402209319479768, 1.4850773434316478, 4.128233076709324, 2.2582133116079954, -3.62099841891481, -7.9328621190321496, -6.522657457608041, -1.6082449982077163, 1.2793290050102522, 0.21845145612488567, -1.4062840994384123, -0.16167979899164853, 2.790122209918072, 3.763580814078476, 1.8275095245339212, -0.2635885560365262, -0.3040561052124423, 0.4611364979362909, -0.23031550171403653, -1.9643961473112554, -2.351882930158751, -0.8523847092679657, 0.31524031200829306, -0.3583545378012573, -1.2231279709111416, -0.01793683859304052, 2.3331381817063703, 2.681203958070756, 0.3266492597582098, -1.615781914888102, -0.7128894196681554, 0.752453122406691, -1.434329659742428, -7.100744714583214, -10.790960115134022, -8.246896899588275, -1.8958699453333736, 2.057635967786582, 1.09722508550513, -1.3875671941636722, -1.4707919829968445, 0.2250077227717716, 0.4147164593784825, -1.5296288220943377, -2.7573054220214557, -1.3679624766033147, 0.8233632892486104, 1.1489240824332583, -0.0437655811030259, -0.35069722228085054, 0.6955819513303164, 0.9761518303420516, -0.5453786147475825, -1.7670501332852773, -0.5284182622542053, 1.8096054333577296, 2.1124124171848773, 0.2915766042121824, -0.23286220856194995, 2.2959776353031374, 4.67537891239742, 2.7902621710837363, -2.211988566781728, -4.632100634762906, -1.510297509250819, 3.3192456035284397, 4.10894081634421, 0.4522189213062253, -2.7748388800633674, -2.1765206641801185, 0.26201232935385643, 0.92813817435516, -0.19589750281741228, -0.321701851226161, 1.3131384024787323, 2.245837885552718, 0.7949447478024021, -1.2071521497880013, -1.1873968674284112, 0.3339970737785199, 0.8313238876778094, -0.07632055923319528, -0.11346568053398123, 1.6473915140640718, 2.7801644042249087, 1.134040592134177, -1.3250567469749002, -0.892666248440611, 2.1995718160434685, 3.4413493345971586, 0.33028030501900213, -3.538133494161117, -2.965799069299207, 1.6222388562983492, 4.43085909769014, 1.9257377657126913, -2.6526687209240136, -3.9227886167225736, -1.3591711120728833, 0.9123659333606486, 0.3746202269363358, -0.9373024126577297, -0.40605708896748355, 1.0252177878031257, 0.7543510897788464, -1.053729775009627, -1.6806672098124662, -0.2202374220103244, 0.975259788046898, 0.07144753268049857, -1.3326082249631261, -0.8694915776608401, 0.6313506724982421, 0.4269291974464224, -1.43599281908184, -1.7055487296219165, 0.9056990328924395, 2.876924964153857, 0.5396584551564947, -4.027601052313106, -4.951424451940365, -0.41233178236367807, 4.581073524091971, 4.713060429160387, 1.199990392381831, -0.4745541448643086, 1.6565790073413456, 3.84767360657971, 2.557165134980886, -0.6044292244994061, -1.7471674338691343, -0.3720373075955747, 0.667260595341117, 0.06967816780137151, -0.18425578996609226, 1.353621884174008, 2.827300861258842, 1.9710545616386121, -0.07881941377697464, -0.3911184432706053, 1.1706126986642016, 1.7982608771227582, 0.403274262633858, -0.49467030867797046, 0.9384748120799798, 2.141152694296625, -0.3996235392104185, -5.149496161295784, -6.5139789284206575, -2.445285297910683, 2.130094790274822, 1.5763169824974068, -2.9635180339590006, -5.376476185505613, -2.972741116315423, 0.44478052243197885, 0.6015346972035012, -1.4360586136634135, -1.7786371559534677, 0.10207844877460073, 1.0216504657003511, -0.5755447873183387, -2.2827321148974247, -1.7233388376711196, -0.11411901887252276, 0.17645646750729496, -0.304486792910806, 0.7573918411559964, 3.055323067760697, 3.5569398001707215, 1.2554510872957767, -0.902341545623302, -0.41714078609827254, 0.8772740400185817, -0.016623127430425655, -1.7528091074325083, 0.022503572245625006, 5.617048354466628, 9.282291899421883, 6.356942945489582, -0.14150536897096966, -3.1781437731234328, -0.7445052217077954, 2.3146385727271053, 1.7008412962652424, -0.783401942719183, -1.003018549298536, 1.0231578835164838, 1.7252759057105145, -0.08453212547333525, -1.5575589331165778, -0.5874091033833073, 0.9898561526709342, 0.6941325096819804, -0.5508897710110031, -0.24400326630798005, 1.286984179794076, 1.4227327670788674, -0.11149935632682212, -0.4319611385471113, 1.7377343586079632, 3.510399876368036, 2.2153618912363546, 0.02894429334087247, 0.9667702118331223, 4.295145340072691, 4.889923706894775, 0.916138209722353, -2.582858896021801, -0.2897402041569541, 5.718851744070166, 8.46704093631815, 5.28304674417303, 0.6479843476242612, -0.706263965518379, 0.19911887190677707, -0.3115729115338554, -2.313428514863202, -2.6861953094908815, -0.6801153016631069, 0.757690871692883, -0.20950840897562675, -1.484448691018189, -0.7025933645636164, 0.8794211179202922, 0.679909468054144, -0.7720340846196866, -0.8593406665361625, 0.343529892848737, -0.13746395252163843, -2.9555588783745512, -4.480720063444382, -2.1358839900415734, 1.0713468251334919, 0.6527108455487933, -2.258450491037128, -2.0436888758182574, 2.921086138626649, 7.070680719796011, 5.062259037295807, -0.7667002973605148, -3.7331993803145958, -1.858274114643896, 0.46801459982308286, -0.2778483618987581, -2.0543873743957755, -1.4829256831894333, 0.6363782472151914, 1.1435410352270852, -0.09496054322997723, -0.2952918505934368, 1.2280633836437849, 1.8165262901636998, 0.04765846284199621, -1.6909659264138626, -1.058112541992676, 0.4338779715981373, 0.15078308798975398, -1.002077020843994, -0.15648674885335664, 2.0119302671633257, 1.4467839667067397, -2.6676968606384936, -5.3284268722804216, -2.402834312213397, 2.9183736259654367, 4.157957955771349, 0.7037068613990761, -1.4825438266071254, 1.2755720241189512, 5.142671093801186, 4.685611878466742, 0.6585651537413142, -1.7643771250101956, -0.7399347873274974, 0.5169183674589602, -0.3465059842695, -1.3789752181632775, -0.3590967869793199, 1.1638545196021866, 0.6216206560388321, -1.0326199633830966, -0.8783157971094989, 0.9854785531686596, 1.5979314225827717, 0.25248844701302414, -0.21375046973278794, 1.6163586926368452, 2.9614144939537237, 1.4269044182766484, -0.4866277848966516, 0.8700310962812816, 3.6432372389376093, 2.166303134920821, -4.3639863031723065, -9.413658483737812, -7.527679991148835, -1.6919455547324473, 1.162746983109479, -0.3181115854836006], 'positive_zeros': ['1.45735015779119323530797772495', '2.89740849139701802459868692236', '3.81658507897849875300923138298', '5.23419467107112037251158544732', '6.13267631886936271870615344149', '7.13602901605971951321140891565', '8.94138588898265858500773224225', '9.7020394478047239191341972021', '11.32356111876171551341326600251', '11.67886141193994778485692169576', '12.95288860570858869570777906139', '13.74123606335722126673910730410', '14.757726990856252982958579959167', '15.77276350895047685786175830325', '16.466185853903521042292223043807', '18.11055864640834906861318310822', '19.050943075108929371346325611362', '19.82524764209824566177337819017', '20.9167073849065934102352801593', '21.80684588237199921596790746948', '22.44602425596920710780613906171', '23.402391428578316388188568586943', '24.425284192111203953094525327847', '25.167691933801683765100729787256', '26.088302341722632146804133753984', '27.67227213980824184456351640354', '28.19967078560177523398171754329', '29.290437601989276742345019694075', '29.92899824384876664809758713220', '31.04637559255006093462608168818', '31.61489998887917227722051759186', '32.58913062399644713046572223155', '33.22501566823715285137429888160', '34.35935586396770275149244918969', '35.13455590379976071377485189998', '36.201618408202633582293526810592', '37.52301421354434315846993996525', '38.03315753954707589503231276580', '38.72776465105253436942413347769', '39.75605351313545728773635221919', '40.676291473774196580577923691833', '41.143529897361206159958464666623', '42.083876722359350460006439340254', '43.03471245624882436142038283960', '43.60018768721301349961443508095', '45.10960658691510464941906235185', '45.572485863396109649054876299644', '46.79683274418106561314522849612', '47.69953738178256037145210430786', '48.068652599120678178782147078239', '48.98567514617090164049368138042', '49.97349586424853006091665743794', '50.60522533945708043805931835818', '51.46096770371587530800410709768', '51.98299998831032849532565209855', '53.25216843325962043062094922000', '54.056909739389772128421272934844', '55.10422742496361814201547847309', '55.90259113253323023488973234521', '56.608480030727618730414123859931', '57.570232570428307289815939672309', '58.15792837076018061139858363996', '58.770834307867416996089455347920', '59.99690125316716854717085672998', '60.38158823574241647782496608457', '61.24898973706847828526339470911', '62.03605088150045373484810652412', '63.27507898131584309434455361742', '64.16404786869126755632051372948', '64.7775706874602426814561704399', '65.6004036080405439335513849972', '66.55408166795647770273579111936', '67.33906526120931995542831912850', '67.54792210281496738827430570620', '68.80925506351334353493086974629', '69.46977567817636006363584097522', '70.0918857530487392852321569583', '71.01853333992665182087950043892', '71.88386862154096084034463850663', '73.14051923597155030514466044802', '73.63377611361018064876835112636', '74.60613670733873460400670783249', '75.033871974981510787625462854086', '76.1212315745178786008641254443', '76.812494896126655278248767549486', '77.39257523206151953562806473261', '78.04806391656772684700145246859', '79.08206617020482210352842388831', '79.95808572175337212993530206811', '80.234315800898587566264688905387', '81.85952986864197406702959670344', '82.35748831717994709481149148918', '83.284770656780748445474284686', '83.88530722552937129896041927605', '84.72203464703157122756345053822', '85.367938273430735069747471817921', '86.218292057542049030013032711042', '86.93408134202367622340988486886', '87.55472350098099545147453174626', '88.201407894519137493833344161352', '89.518253129221970945775183362090', '89.8309321973112401893571740932', '91.02697447371524876271151503749', '91.98518080933199104539247626537', '92.484235243529371594675427183483', '93.41070578369452958929983634297', '93.80160764210080850785363321995', '94.83568960557577442476401215947', '95.47275373547164196585779285642', '96.23053620345732530861434836468', '96.82378686267314511103406905997', '97.59891310570420418094522747653', '98.54813509459896040430739885793', '99.42222812179886171017471966528', '100.38727172644712769949085610175', '100.947351686283227049848194237152', '101.86254010724528666894136024192', '102.7196908820108666647522780524', '103.00289814280246285436125339559', '103.98162492312385140187185093842', '104.594126315399261407140729929797', '105.58274066519474576623540976924', '106.01593679981416585183592423283', '106.73953675468813352254746962031', '107.63220313555294670378040090712', '108.87158731583201398861576148023', '109.406515071322767526105548384417', '110.0184443165718972977100146249', '111.19024690399406551842693788823', '111.667477876095744463086635525299', '112.1379804178719516387772436330', '113.29827986908194140416685680017', '113.65383147008659090188516640421', '114.37748096551795535890124076014', '115.34918632837405586016989923254', '116.05061870569131071300532693548', '116.43972019781237593086649327809', '117.91995462168817907903440453099', '118.56234152407354222996553641085', '119.32922952585124307338133134838', '119.77510022716575398492565244928', '120.80386001672402147963845366123', '121.55037021648744740120808940867', '122.00138559771101939221724907885', '122.72227978978629881720657860345', '123.50528724862054040128875102790', '124.4296887652609716838064774315', '124.73874682985012316881114641470', '125.80227584140416646073154522871', '126.65263656996557064903633288016', '127.53254883501207505382950114052', '128.39822978171161068270208547437', '129.009709197567113652212441790285', '129.45689599404034808922283561046', '130.42054741817980219573337493744', '131.18000471437553621700633433030', '131.84947235927801939794049083528', '132.21891194711368919883712610108', '133.25154210493760370570222301973', '133.85202253586110986105115238205', '134.710283769625388252412461065235', '135.5229469167195201102131182748', '136.37486275082897320252559728491', '137.3333782554301928504291597060', '137.88663413468322128213509212041', '138.51955264008906066972812596593', '139.20031608463902506339380118753', '140.037796145162710491155551342599', '140.63839582623104498692898711447', '141.41864030491082356040714437539', '141.95581781918160931011483877273', '142.72291592110430298264760791705', '143.47506418049521178596563859819', '144.396630822282056321440224770712', '145.44478972777224536732610999371', '145.74337721433264790191202523529', '146.80934988857785696458573823317', '147.57113160313639628981877539002', '148.15018486041559730353768394043', '148.50169261735145010788468434407', '149.6721905307901415047532670198', '150.09687818912750361999729196318', '151.015904279346960253075952461690', '151.40809060843714971351203685838', '152.1585284611980145626437178448', '153.26659961913059935865771591722', '153.869799884165448292482374530102', '154.94346479622527394794098523145', '155.41166588798602449585097357204', '156.23417833114644284459048595919', '156.79279226240225213468016545181', '157.84524055821285983831110678748', '158.21935038914986791476988677432', '158.606338559483698278191279411701', '159.83278794664973807569905911542', '160.394561568467262708648243185011', '160.93488632695658098659105408066', '161.5608412187693123268707751418', '162.80491151296897145051870949833', '163.49819711462011079983945985305', '164.26555660836404050213699226795', '164.852718363145310304106268585840', '165.61334514951170165464858613349', '166.34811822066739068297796307699', '167.03351368191231167099156121428', '167.55389749143145044357825244621', '168.41449926569225827590661576841', '168.8399564476454264797607953159', '170.00894287918861909227432326936', '170.15840199593470371745135901163', '171.30891989021140764602513034743', '171.89208113316829352841115053456', '173.19452367292736400206146385886', '173.675632813886698593304076325263', '173.99567514304671494708876560092', '175.099028043926889679727481767902', '175.58556469583415212638308520655', '176.373513747686050681941956914572', '177.01896753796368195901024639289', '177.71485922762800050533045742038', '178.10201261214247838107819832133', '179.24615709966717981552499703343', '179.76140004000630500446924428780', '180.464449142959041947500151715', '181.51960917074705120470686929445', '182.40066425957306883905386121639', '182.76589451275240037056034169158', '183.64974288015242160179231682019', '184.35068603290479707688861956493', '184.76703832194658690456391179055', '185.63133871550704761879314631168', '186.448282736886628518158556315636', '186.911983886935992811078329775356', '187.52300807200272729720233094588', '188.25298421700735285585853591892', '189.1964965287563095097903358636', '190.05806183183341717249186398527', '190.52817429102732291128921803229', '191.61599493066862350096782390431', '192.320641847281275880744242622541', '192.7380437114679144537997517692', '193.49822851125347921095681200915', '194.17304106636269451492783421551', '194.841743244101483198758390190954', '195.68340626563677164924896136148', '195.99838581903460265361326650666', '197.06593383448278256570430439377', '197.39216483161752322620486598528', '198.24543565068414574353817909915', '199.49309599554833362184124479172', '199.95489663472836901993430825084'], 'prelabel': '1-15e2-225.121-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0448956071669055, 'root_angle': -0.23111111111111113, 'root_number': '0.747798090498531878105720508059-0.663926212652241594900990021760*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.115555555556', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(15)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.69208665512365992865447647267-0.442508356814033437171285277687*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.45735015779', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.8974084914', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.81658507898', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.0448956071669055, 'bad_primes': [3, 5], 'central_character': '225.121', 'conductor': 225, 'conductor_radical': 15, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/225/121'], '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': '1-15e2-225.121-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': '1-15e2-225.121-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0448956071669055, 'root_angle': -0.11555555555555556, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45735015779', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_225.121', 'Lhash_array': ['dirichlet_L_225.121'], 'label': '1-15e2-225.121-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/225/121'}