data: - - Lhash: dirichlet_L_153.121 a10: - -0.7071067811865476 - -0.7071067811865476 a2: - -0.8660254037844386 - -0.5 a3: - 1.0 - -2.8163065144692913e-30 a4: - 0.5 - 0.8660254037844386 a5: - 0.9659258262890683 - 0.25881904510252074 a6: - 1.0 - -2.8163065144692913e-30 a7: - 0.9659258262890683 - -0.25881904510252074 a8: - 2.9010907910729803e-30 - -1.0 a9: - 1.0 - -2.8163065144692913e-30 algebraic: true analytic_conductor: 0.7105290128734958 analytic_normalization: 0 bad_lfactors: - - 3 - - 1 - - 17 - - 1 bad_primes: - 3 - 17 central_character: '153.121' coeff_info: - x^24 - 1 - 0.965925826289068 + 0.258819045102521*I - \\zeta_{24} conductor: 153 conductor_radical: 51 conjugate: dirichlet_L_153.43 degree: 1 dirichlet_coefficients: - a^0 - a^14 - 0 - a^4 - a^1 - 0 - a^23 - a^18 - 0 - a^15 - a^11 - 0 - a^4 - a^13 - 0 - a^8 - 0 - 0 - a^6 - a^5 - 0 - a^1 - a^19 - 0 - a^2 - a^18 - 0 - a^3 - a^17 - 0 - a^13 - a^22 - 0 - 0 - a^0 - 0 - a^21 - a^20 - 0 - a^19 - a^7 - 0 - a^2 - a^15 - 0 - a^9 - a^20 - 0 - a^22 - a^16 - 0 - a^8 - a^6 - 0 - a^12 - a^17 - 0 - a^7 - a^10 - 0 - a^23 - a^3 - 0 - a^12 - a^5 - 0 - a^16 - 0 - 0 - a^14 - a^21 - 0 - a^9 - a^11 - 0 - a^10 - a^10 - 0 - a^11 - a^9 - 0 - a^21 - a^14 - 0 - 0 - a^16 - 0 - a^5 - a^12 - 0 - a^3 - a^23 - 0 - a^10 - a^7 - 0 - a^17 - a^12 - 0 - a^6 euler_factors: - - 1 - a^14 - - 0 - - 1 - a^1 - - 1 - a^23 - - 1 - a^11 - - 1 - a^4 - - 0 - - 1 - a^6 - - 1 - a^19 - - 1 - a^17 - - 1 - a^13 - - 1 - a^21 - - 1 - a^7 - - 1 - a^2 - - 1 - a^20 - - 1 - a^6 - - 1 - a^10 - - 1 - a^23 - - 1 - a^16 - - 1 - a^21 - - 1 - a^9 - - 1 - a^11 - - 1 - a^14 - - 1 - a^12 - - 1 - a^17 - - 1 - a^8 gamma_factors: - - 0 - [] id: 4330 index: 0 label: 1-153-153.121-r0-0-0 leading_term: 0.932535698371117957557646981662-0.0624783566148714658511290900687*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/153/121 plot_delta: __RealLiteral__: 0 data: '0.3125' prec: 20 plot_values: - 0.9346263284231854 - 1.0505440043601353 - 1.167021453102521 - 1.0327852086032474 - 0.5874726035827221 - -0.028478083012897403 - -0.5284143569981166 - -0.5967221260686876 - -0.05042595182544217 - 1.020310482897369 - 2.216210524261627 - 2.9505194318125763 - 2.706921925902909 - 1.3268662579524884 - -0.8270751389833891 - -2.9522316550523913 - -4.138026481098687 - -3.811728495261355 - -2.0674280041305684 - 0.32409289926319773 - 2.2711420879956017 - 2.9193858546773486 - 2.108937245294735 - 0.4556248779858202 - -1.0136950115638748 - -1.4711280193474405 - -0.7745750576642471 - 0.4790947848181215 - 1.3768772602766362 - 1.3148193457796165 - 0.4022243958473747 - -0.6420755903321457 - -1.038567134040037 - -0.5501953169809105 - 0.3141101665561056 - 0.6767820009088215 - -0.002465172123943817 - -1.4231573101555515 - -2.5671906026722393 - -2.42285499803904 - -0.8055845790495109 - 1.363756933010801 - 2.6098146532996447 - 1.9532438390343978 - -0.2936168044337873 - -2.620580515969511 - -3.3139227600353287 - -1.6756376864247366 - 1.426977456376935 - 4.12180196025386 - 4.824574659032491 - 3.3211859169075493 - 0.8395101743984099 - -0.9240711560144736 - -1.0559588437692493 - 0.014852366906122287 - 1.0470713961557983 - 1.1177470462169277 - 0.3855989305398101 - -0.1458844309357229 - 0.3731809455721835 - 1.784817122892981 - 2.995799650531942 - 2.935937680779235 - 1.548515060611916 - -0.10817493024351538 - -0.7943867869891413 - -0.24805036237181205 - 0.509372898481184 - 0.08584101623296805 - -1.895106504457333 - -4.195690595915841 - -4.809713411026652 - -2.648962392050432 - 1.3547668957650973 - 4.76083206250477 - 5.430650015668919 - 3.177741451178352 - -0.1259936198903423 - -2.08549928688793 - -1.6612973751911737 - 0.18330042348075581 - 1.5439115299386377 - 1.324448376972607 - 0.0957033484501863 - -0.6399118652447706 - 0.006550870504831947 - 1.4559054470916946 - 2.2852528264507344 - 1.6733039293725938 - 0.21979935198431783 - -0.6743824932887078 - -0.2396109491486617 - 0.8730593319615312 - 1.275175852529816 - 0.3340942945922543 - -1.0636618182263056 - -1.353216845586062 - 0.006538947308092007 - 1.6875409554398377 - 1.5100991777110422 - -1.4755032801266053 - -5.802389620803066 - -8.55844593013182 - -7.785774125087434 - -4.165364428750928 - -0.4178176822264805 - 1.0604094768301497 - 0.16516243239627157 - -1.1145395443987978 - -0.774243499333353 - 1.2894995821284223 - 3.3225975874069773 - 3.55081537254659 - 1.9143179365131413 - 0.0031142070810766674 - -0.6254771714883094 - 0.053073359995432515 - 0.7352772714719157 - 0.37805575061385394 - -0.608163885052693 - -0.8757993660563422 - 0.2100738668962593 - 1.6509601748101401 - 1.747769179648249 - -0.017376828035492127 - -2.202950626266906 - -2.734326072717231 - -1.092314862982207 - 0.9446221386626792 - 0.9576489584799406 - -1.5933698007110069 - -4.567956838545159 - -5.033419114689114 - -2.0986296081945155 - 2.104238223240024 - 4.319743254568733 - 3.126365420179552 - 0.08165842772565574 - -1.975523131553915 - -1.6610769735752522 - -0.08405894846119571 - 0.6756225076188478 - -0.14174931204375915 - -1.3598545373754096 - -1.4198530223483798 - -0.22837806939557137 - 0.7920721349768871 - 0.438093552685093 - -0.8055523960050538 - -1.2974863242972998 - -0.19259480305870844 - 1.4503275401149525 - 1.774148081987001 - 0.27416224079039464 - -1.4811599716002957 - -1.5321133270975638 - 0.15633930000709967 - 1.4097449814859364 - 0.14761766464463527 - -3.088129383140473 - -5.225790713923812 - -3.560209139652697 - 1.4139822762616818 - 6.208851095133756 - 7.49306963645639 - 5.044048289601542 - 1.5913354265697175 - -0.10046233074482416 - 0.2316694522235105 - 0.7111081175412363 - -0.1441085681029784 - -1.6983217790330583 - -2.1314667479504217 - -0.7578276399828622 - 1.059740370074612 - 1.4509065745985457 - 0.17924643431860635 - -1.1501694651419765 - -1.0372658759328972 - 0.15813297533980036 - 0.7701477314451581 - 0.019884314068022615 - -0.8688539647380371 - -0.1443527859984869 - 2.0427566939476933 - 3.2618626048976216 - 1.284133748681247 - -3.1688040376984397 - -6.631288107957976 - -6.175716745832486 - -2.4033123527075295 - 1.1140624198636715 - 1.4423611371889535 - -0.8650263594128514 - -2.6536121301510636 - -1.6901863087771498 - 1.0716044872148192 - 2.820720826144513 - 2.095831682859676 - 0.20256632376020497 - -0.5747338025891244 - 0.33203598444290494 - 1.3402412674682134 - 0.8660075000839227 - -0.6882095141881593 - -1.5134181231833708 - -0.7164605149443608 - 0.5772729882261531 - 0.7405431275618226 - -0.14700000387342296 - -0.28005294052551394 - 1.5103883140476784 - 3.9163261215495693 - 4.335505459897681 - 1.9562674515626128 - -0.9146998626768785 - -1.1495971780248373 - 1.6566553338475258 - 4.482333994114863 - 4.047801729917901 - 0.44099743087622895 - -2.885863946290046 - -2.811479914316645 - 0.1644048876604662 - 2.6455335819025025 - 2.1253217610021613 - -0.4821698220193074 - -2.2401832526423897 - -1.6079157990992954 - 0.14636124388421085 - 0.8999325494860313 - 0.3096164661985274 - -0.11925368974521275 - 0.6375118251292462 - 1.5742346424857132 - 0.9509711081523534 - -1.250914900705212 - -2.9782241537703857 - -2.48223466809311 - -0.49040931031909935 - 0.6551001674724145 - -0.06306077835349617 - -1.0335985865610666 - -0.17637757820547512 - 1.996052008465865 - 2.4030626509621076 - -1.082398396705891 - -6.626999306060533 - -9.74436030850626 - -7.8177378585209425 - -2.85821233673631 - 0.6374892540952911 - 0.330172104046342 - -1.976339145976702 - -2.953149642252676 - -1.6143135423886532 - 0.04810826201215359 - -0.009454276319198906 - -1.2900296987043807 - -1.6331323350011615 - -0.17042789129700317 - 1.5475419988213102 - 1.6316667424548525 - 0.3350156057757084 - -0.32553468358001963 - 0.7219855269113828 - 2.1650731133520495 - 2.0728552989685367 - 0.5453252589715116 - -0.34710755199813753 - 0.5865140654789096 - 1.763441791463623 - 0.6671270490126292 - -2.6072906731380137 - -4.69379067774057 - -2.528284463850279 - 2.8209141339595902 - 6.777509454383636 - 5.963766698508492 - 1.7100479479857689 - -1.6241269625866948 - -1.466914812076483 - 0.6078903616289728 - 1.4248883364461857 - 0.21170760717872364 - -0.8197235141779617 - 0.32454147432003955 - 2.733344825493252 - 3.771053499216886 - 2.406693067706673 - 0.3549868104592638 - -0.2729294461663014 - 0.43850759885761653 - 0.7460415916446504 - -0.03025403572711506 - -0.4743541757235987 - 0.7689376082028683 - 2.6387030937482288 - 2.5890286939197673 - -0.07976966716218246 - -2.879411885479792 - -2.924987709013368 - -0.6074013005516926 - 0.6290279583376395 - -1.505635772424513 - -5.041189446608843 - -5.789993666514479 - -2.3102643227116477 - 2.1945819853678583 - 3.4365265645669476 - 0.8465781916821761 - -2.0601310399556123 - -1.979432554262201 - 0.5556983037002032 - 2.388272592519026 - 1.820200935136797 - 0.31709396948575963 - 0.0572220316416986 - 0.9505961651639057 - 1.0825500142802245 - -0.31402700409346024 - -1.6265455858065463 - -1.092147805940951 - 0.6516775632881634 - 1.3298615549487214 - 0.16171030223135863 - -0.975380103200048 - -0.13149110347503695 - 1.7972358231605299 - 1.9641685398796942 - -0.5976442716304702 - -3.2953526877822212 - -3.0527675436246975 - -0.4739807322360466 - 0.42278196477609736 - -2.964759007125938 - -8.255518589054752 - -10.38452895329044 - -7.227873694580743 - -1.8698573205723776 - 1.0612943323253907 - 0.38381891683905656 - -1.1956169361190405 - -1.1013802495704863 - 0.09421691147447396 - 0.2232511058052808 - -1.0215189757291112 - -1.6181634647568437 - -0.20217474242625075 - 1.8273197032819832 - 2.088092286876079 - 0.42418831520177264 - -0.9142974533523285 - -0.369757362696122 - 0.8687190088628176 - 0.7283581034670169 - -0.6276271354399062 - -0.9868376542316319 - 0.44253383883197006 - 1.1860883900062904 - -1.6029086291867443 - -6.8801052055538054 - -9.90751318227249 - -7.381064622381442 - -1.4269071942355274 - 2.6235275265284153 - 2.1583345522352158 - -0.22923243064550322 - -0.48974555899889105 - 1.8560870247297425 - 3.6390611148503607 - 2.534128524549153 - 0.028163696507351538 - -0.7978329468791612 - 0.6456301543817279 - 1.992853942868188 - 1.3767461239570034 - -0.1406178986800927 - -0.3622166785764316 - 0.8187840889671489 - 1.3956555171569682 - 0.3366989168414866 - -0.7924107950774595 - -0.11971547489652337 - 1.6161333240502256 - 1.9218787714927874 - 0.2489740682893412 - -0.7510134271814016 - 1.3364307788322618 - 4.94083216884836 - 5.833227152709462 - 2.3723504718339203 - -2.03096318217894 - -2.754913064732939 - 0.4885206779120249 - 3.414891263581681 - 2.5492885585097893 - -0.6204602196454061 - -1.8593699126079255 - 0.34955811178550494 - 3.1620036913030494 - 3.312671988263003 - 1.153519803769032 - -0.34263324332953815 - 0.25760137177534137 - 1.3425229242613033 - 1.066708248652233 - 0.07799131108144525 - 0.25151690644323665 - 1.534708453746783 - 1.7685627004414723 - -0.0826124439710219 - -2.033215287875254 - -1.5585550172707174 - 0.8273212914695636 - 2.066158747693072 - 0.70467564207078 - -1.0808851426867434 - -0.690160742894863 - 0.7501039044313309 - -0.6354795870380068 - -6.0838615952128485 - -11.507337061871509 - -11.608570054912503 - -6.042471856947014 - 0.09473400595806455 - 2.08757858014496 - 0.4563619723192385 - -0.8568831404176964 - 0.05732905340419648 - 1.2377577089113683 - 0.406188292310701 - -1.582330768822522 - -2.1358786596184616 - -0.766241323968825 - 0.30423034352454575 - -0.4885028974768906 - -1.743654913408002 - -1.2209067879357929 - 0.7724630416917622 - 1.7544045374113246 - 0.688132086910974 - -0.5102009994296145 - 0.0848139506306969 - 1.3178165181756056 - 0.5266020550948944 - -2.161683582872956 - -3.174384012345757 - -0.13503146478314543 - 4.243159363195029 - 4.78654057179783 - 0.228647324917212 - -4.870477446837399 - -5.401239821429101 - -1.5987979054674208 - 1.7915696806989228 - 1.6093555600742238 - -0.4058678641725648 - -0.8794439469461144 - 0.43214391417546383 - 0.8793621183155058 - -0.7562402425346071 - -2.3320505042243496 - -1.4514355374956744 - 1.069611130529267 - 2.3579282747444577 - 1.4218144896704432 - 0.14118519722941153 - 0.12349837361148033 - 0.35434633632303547 - -0.7903969879341879 - -2.3713426146861414 - -1.7504867020927786 - 1.3280127113135762 - 3.5358163212568257 - 2.0898179953477425 - -1.1676754799592206 - -1.7607505162047503 - 1.5030618659239539 - 4.64944349045764 - 3.578240745231513 - -0.5027969058565552 - -2.568945529208054 - -0.29456852132693856 - 3.048210429055942 - 3.0201309495543716 - -0.3158246730121135 - -2.9075360659641767 - -2.218031131883816 - -0.06858551999158828 - 0.5528656602295144 - -0.35590973640728685 - -0.489346399546798 - 0.8659517681622491 - 1.7833914024051258 - 0.8929357217871529 - -0.2876425355981911 - 0.4071217018982263 - 2.3447138325420496 - 2.81720070269838 - 1.075301121463263 - -0.38682311382796863 - 0.4946130079890002 - 2.0255973757592116 - 1.00318219883204 - -2.323678400534327 - -3.909459139495022 - -1.33330344228419 - 2.342301799117821 - 2.0729803744915443 - -2.536897700479132 - -6.381358253998638 - -5.161034194610931 - -0.624363220146763 - 1.9943018573357691 - 0.6033754183781789 - -1.8344845624505828 - -1.962093075830813 - -0.2967804828048477 - 0.4546567365700399 - -0.2424546176170342 - -0.33229210975922835 - 1.1224256427826824 - 2.130992642261514 - 0.7478181709504792 - -1.7413496232343557 - -2.409091377890033 - -0.8129702724574448 - 0.5040374359059404 - -0.10512332364194824 - -1.0410754231677766 - -0.29519508636399616 - 0.894655961440894 - -0.4247368688584636 - -3.9342685788501033 - -5.174057483436304 - -1.0910301067074226 - 5.17607035032986 - 7.321690257159351 - 3.382229152162566 - -1.990882680392774 - -3.4341424386923665 - -1.077470701765951 - 0.8234059058570851 - 0.17294421919927905 - -0.6662589646510378 - 0.8567660921742978 - 3.40031114384634 - 3.710526959837182 - 1.3885889757750582 - -0.6482126117037309 - -0.4174477511996257 - 0.637886469479749 - 0.37574564050304743 - -0.6151317319803358 - -0.19775164760438455 - 1.554435058013162 - 2.1378411620800897 - 0.5107223429302968 - -0.9912722953973583 - -0.08826183964111736 - 1.6395521571850868 - 0.732425374315077 - -2.700114656134782 - -4.162603880452798 - -0.5952678341452776 - 4.944136584926584 - 6.63905585370268 - 3.2165320420846557 - -0.6251404639970889 - -0.5600580789900462 - 1.9599734300025031 - 2.379351160986615 - -0.40324046230051985 - -2.806121014043356 - -1.8808661449928774 - 0.7482307568844851 - 1.6362800751305702 - 0.40826459204384774 - -0.335363738088382 - 0.6508415519050524 - 1.5442641306471176 - 0.678271656560796 - -0.7124289975423306 - -0.640815704923871 - 0.11551781575198589 - -0.9947045484910091 - -4.006261612606721 - -5.61977187066343 - -3.6817945672146304 - -0.48827400054207115 - 0.3412023996634113 - -0.879304650211926 - -0.4554728752566146 - 2.7147703666414684 - 4.546977557822716 - 1.029296260704155 - -5.619366324239863 - -8.815210648228447 - -5.533079334933535 - 0.19130354866068586 - 2.6579948544846994 - 1.2468765984023715 - -0.2316522870981732 - 0.4180169473628261 - 1.303626170241068 - 0.31529208645341006 - -1.2930002458148484 - -1.034927545352162 - 0.7031270358066755 - 1.1846352408710312 - -0.38477008651131217 - -1.5844361557513147 - -0.5468861517667933 - 1.1416512012806836 - 0.9886004776645311 - -0.4109342714339377 - -0.33944161799684086 - 1.486098019572564 - 2.0958319178444813 - -0.004412601978355217 - -1.7176286129859757 - 0.6530736270017439 - 5.483237601682343 - 6.947729059048135 - 2.5484206902501163 - -3.1523446820809893 - -4.078901553217317 - -0.15543128346382779 - 3.2326146493913592 - 2.599519908638934 - 0.21482225305891858 - -0.1816956606151388 - 1.1881100483738836 - 1.3014660683315276 - -0.5015128469286839 - -1.530181095005962 - -0.13405002992933093 - 1.62152774688437 - 1.1198352258580213 positive_zeros: - '1.54804344737846902505674659889' - '2.51818630375966484109866723314' - '4.26160032579825052242964337807' - '5.89492744053203979903957318518' - '7.271402350992643488244835027426' - '8.31983973159368522802528824145' - '9.4861303734285186022237739584' - '10.5073421409702867054946634722' - '11.2493445351544522765790857315' - '12.61434315675503641205062311012' - '13.71456422612221088748916586027' - '14.86327978357153414974542894537' - '16.36991036746449477603217326926' - '17.18384784465069358609498264836' - '18.29524729521518593331755985718' - '18.61370758235773951065428027130' - '20.28779847816534255748083120883' - '21.02227932586354185525387197372' - '21.58263217197527464348450737244' - '23.02439657785070323810980377711' - '24.361872841898386572431840475549' - '25.28282275384253847420827932484' - '26.27475224815784678430939341397' - '26.873370841473353421103181047670' - '28.176056816508656757430076653368' - '28.82046995616089879161408845930' - '29.75840917320796498155246793994' - '30.62391075249082319377103889339' - '31.43893364928975392811279850729' - '33.17416298287085326874279964584' - '33.78395648008176596238388318594' - '34.512821095120859304634939120700' - '35.93818186019341636487750978848' - '36.544792284515962679178791420243' - '37.30900271340795104319794306949' - '38.08162580277622045904939653184' - '39.060180894253765910967320514930' - '40.14975722366692533433606913456' - '40.77183854742069355328433977701' - '42.02705627552921418187946565607' - '43.1336023608098685570839243866' - '44.08076417493534375680426997753' - '44.65325426290962399731066729844' - '45.67702686930168730791498153053' - '46.365954539983092597579410684207' - '47.22251440873338717449043108734' - '48.16737429098588405618348973493' - '49.037381417285982233674865144133' - '49.70476252374929060367921022492' - '50.85802821659639454893113055253' - '52.452071002166516571737633300344' - '52.7121292318041628172330122276' - '53.40621550188376955044920072903' - '54.49421893472186510717878815987' - '55.34663594924440809824113065611' - '56.209551072901060727469061612453' - '56.880373231265839881637383051211' - '57.525333251352617974901285999017' - '58.537176661822301859756220378289' - '59.87619040938677826642670472380' - '60.52325344458009615943596862013' - '61.445284828724720915155182516051' - '62.54077954811691400177723684595' - '63.04373422793599773130464321810' - '63.92865285630178772735531088456' - '64.84624616616763128571048199733' - '65.57456229867936735690908710224' - '66.0172342337592858970231636520' - '67.38209119516992674411086155753' - '67.96824663073785516929888101941' - '69.095764444365491064042062806444' - '69.98476359385421855488258701166' - '70.8823829824494209165558435891' - '71.8459046532297549725319393469' - '72.63734608443876286933759149530' - '72.911785262635379305372743004670' - '73.89923165449197496954808406250' - '75.08593575907628507495211575325' - '75.60938911739942299027787165605' - '76.278150225846781712201627828274' - '77.11815220065723168298554119437' - '78.6602231616387538038985717063' - '79.11312213646646271938106830441' - '80.29768123631018567932118931887' - '80.62196819917339466332011257405' - '81.58922445868596254835758557305' - '82.58704626330345869282209230328' - '82.96382336640781077813393764791' - '84.18490578573046914764753703133' - '84.55240952156265102686413639996' - '85.38670578649617095025960346043' - '86.40638733637281827595027199363' - '87.62778645388348764203030151152' - '88.345109224394866321435065091617' - '89.1042156967614069796999623048' - '89.63812527782434486158647746717' - '91.02163048417606353924614441227' - '91.40007470225614510839987370486' - '92.17759477921564000045260065704' - '92.67100611617492755234453753143' - '93.74250769751453098684913019644' - '94.77349866591851904449292471305' - '95.15100171984405787307795594889' - '96.39807830799351906953258791556' - '97.26343552800015665572596075807' - '98.06257836095692436817560188149' - '99.18967540746109780743953376209' - '99.33812564078446634477833595211' - '100.25619044530620652114273745273' - '101.13290408403603945423635081321' - '101.90666312461365216534296816949' - '102.52220933375311971452162126238' - '103.37963528219823574900578636888' - '104.44065379451324798699027267622' - '104.76227275416429115366169159892' - '106.39706252276104101634976546795' - '106.94180608109037658756083726986' - '107.78354458574515608142865672822' - '108.199143947543932498029111806984' - '109.09140169504183745033051397455' - '110.070779417683328416175991982832' - '110.71006231990266279959385775295' - '111.42279274320117853385010631305' - '112.10775567301055258136560416464' - '112.68605834655876999397248224902' - '114.14336796981425400436430473381' - '114.9633394350658551399179712628' - '115.39963338460802185496412569696' - '116.566765408773478471597783425483' - '117.078399151251617912875353106890' - '118.08905175273285238895097959507' - '118.55363359834699658958533842277' - '119.445304247590409695146727857629' - '120.02302020791363763045823254891' - '120.979075902888702870323357483698' - '121.42080954010156274292977419356' - '122.65295271899114100907297308539' - '123.39896219441578836491148631145' - '124.31126412325651172370189453294' - '124.965460551673505327599087068069' - '126.12696728724872026577792939191' - '126.494911459875842101033331040001' - '127.545178461195924296474525140112' - '127.70435529168509046049872192022' - '128.7393253055059168411919032184' - '129.58367783209839200294729553636' - '130.41454438956121551194684923558' - '131.06877587920278956971467876080' - '131.5007815080063348460317885516' - '133.118459627026445540416934588870' - '133.82018231669848310625868014759' - '134.36354974908813039221540425230' - '135.06520869383417833934024408350' - '136.10303101867052883840401343119' - '136.444524310146484221343110006622' - '137.382699417338200157503263694538' - '138.2655668181520405762921925938' - '138.73030235483891325373610916877' - '139.444597594303692580077186923402' - '140.32168577695129877609406431698' - '141.26210876259096184840679137699' - '142.30550125772278797399101128593' - '143.05583215499837640706929799546' - '143.657337650624672799661166521047' - '144.26108838407497564380955218803' - '145.18170473736978788836334135854' - '146.34279345188719654042551138749' - '146.45520644820819457338110253680' - '147.02375963418331446238156347252' - '148.00334329764974498919407608261' - '148.94266803704447682599787294939' - '149.57022049288264993697515750817' - '150.58605867899359925156443438182' - '151.27467944893864720832547764932' - '152.16112075511424345721095300566' - '153.13779671653789028944771232648' - '153.63968037448246838204136572899' - '154.19995840826365383293830024595' - '155.19973120840771572047069882379' - '155.538979885331410162296223071035' - '156.74183169948256103903137708553' - '157.09118161616852961606832279934' - '157.91587107815449023167221734101' - '158.85054390509840110170589540085' - '159.53558711169472336986479009077' - '160.67146947383313388977790635305' - '161.31895375746905024862607721815' - '162.25101735714646237409697063017' - '162.723450942299201514283959204157' - '163.22198191706391865670979042815' - '164.15353199830077863712032917360' - '165.14392334242567895279986254587' - '165.5980162051229858325762381351' - '166.31089502388891157968312828450' - '166.8257417856807391362201660045' - '167.86589039986473121236811007121' - '168.932041882554184404688256809075' - '169.817516265657555138869948477003' - '170.35217092586304569215754389144' - '170.81990528448694787298843627932' - '172.05141054349895016929936099392' - '172.609423984916343277045947045394' - '173.2331312817542933841817821556' - '173.79146635136018652360288085093' - '174.76432069666048074101752449149' - '175.32674865268199898674093104374' - '176.01390250449359988426536463444' - '176.90792708198737994446403906957' - '178.05238196982736561299203034833' - '178.51341735888830942237815981169' - '179.33767615777027041688981061093' - '180.21735246660259893544345694852' - '181.03488919187639806653135939317' - '181.40481688147557724321828685583' - '182.32100733055937625036201854280' - '183.04062974368200572154331683830' - '183.2473263803182698649226644115' - '184.76170713773739135396165692787' - '185.104303375049353935855087095600' - '185.684300326597513817603342383014' - '186.61349054742288379143282951575' - '187.800125319206138556033629662217' - '188.65643531973783626396621495680' - '188.951288260504685479527619091772' - '189.74162148803585110834943234045' - '190.49986549225098617832181147662' - '191.187715944919424643555312557859' - '191.96355708576145404882300172793' - '192.71242743829804206029282221973' - '193.19639338740858636189399737058' - '194.06199172481517944014771644048' - '194.63859267999170060217878834999' - '195.75087768461639173995005963045' - '196.57295424182952555009676612245' - '197.54162945717245435953135139766' - '197.86503620320574198924947718596' - '198.6727772760139269013498361041' - '199.394422024883532061777473267129' prelabel: 1-153-153.121-r0-0 primitive: true rational: false root_analytic_conductor: 0.7105290128734958 root_angle: -0.04258882886735081 root_number: 0.991062559385825456274337676859-0.133397913715384585117865391756*I self_dual: false sign_arg: __RealLiteral__: 0 data: '-0.0212944144337' prec: 54 spectral_label: r0-0 st_group: mu(24) symmetry_type: unitary types: - DIR values: - - 1 - 0.890572938719947621187292880725-0.0872089638775276377524143114056*I z1: __RealLiteral__: 0 data: '1.54804344738' prec: 44 z2: __RealLiteral__: 0 data: '2.51818630376' prec: 44 z3: __RealLiteral__: 0 data: '4.2616003258' prec: 40 - - algebraic: true analytic_conductor: 0.7105290128734958 bad_primes: - 3 - 17 central_character: '153.121' conductor: 153 conductor_radical: 51 degree: 1 id: 4330 index: 0 instance_types: - DIR instance_urls: - Character/Dirichlet/153/121 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: 1-153-153.121-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: 1-153-153.121-r0-0 primitive: true rational: false root_analytic_conductor: 0.7105290128734958 root_angle: -0.021294414433675406 self_dual: false spectral_label: r0-0 z1: __RealLiteral__: 0 data: '1.54804344738' prec: 44 - - Lhash: dirichlet_L_153.121 Lhash_array: - dirichlet_L_153.121 id: 1785783 label: 1-153-153.121-r0-0-0 type: DIR url: Character/Dirichlet/153/121 label_cols: - label - label - label labels: - 1-153-153.121-r0-0-0 - 1-153-153.121-r0-0-0 - 1-153-153.121-r0-0-0 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-05-20T20:13:32.535222'