data: - - Lhash: dirichlet_L_37.23 a10: - 1.0 - 0.0 a2: - -0.8660254037844386 - 0.5 a3: - 0.5 - -0.8660254037844386 a4: - 0.5 - -0.8660254037844386 a5: - -0.8660254037844386 - -0.5 a6: - -7.040766286173228e-31 - 1.0 a7: - -0.5 - 0.8660254037844386 a8: - -7.040766286173228e-31 - 1.0 a9: - -0.5 - -0.8660254037844386 algebraic: true analytic_conductor: 3.976202217401126 analytic_normalization: 0 bad_lfactors: - - 37 - - 1 bad_primes: - 37 central_character: '37.23' coeff_info: - x^12 - 1 - 0.866025403784439 + 0.500000000000000*I - \\zeta_{12} conductor: 37 conductor_radical: 37 conjugate: dirichlet_L_37.29 degree: 1 dirichlet_coefficients: - a^0 - a^5 - a^10 - a^10 - a^7 - a^3 - a^4 - a^3 - a^8 - a^0 - a^6 - a^8 - a^7 - a^9 - a^5 - a^8 - a^11 - a^1 - a^7 - a^5 - a^2 - a^11 - a^3 - a^1 - a^2 - a^0 - a^6 - a^2 - a^9 - a^10 - a^9 - a^1 - a^4 - a^4 - a^11 - a^6 - 0 - a^0 - a^5 - a^10 - a^10 - a^7 - a^3 - a^4 - a^3 - a^8 - a^0 - a^6 - a^8 - a^7 - a^9 - a^5 - a^8 - a^11 - a^1 - a^7 - a^5 - a^2 - a^11 - a^3 - a^1 - a^2 - a^0 - a^6 - a^2 - a^9 - a^10 - a^9 - a^1 - a^4 - a^4 - a^11 - a^6 - 0 - a^0 - a^5 - a^10 - a^10 - a^7 - a^3 - a^4 - a^3 - a^8 - a^0 - a^6 - a^8 - a^7 - a^9 - a^5 - a^8 - a^11 - a^1 - a^7 - a^5 - a^2 - a^11 - a^3 - a^1 - a^2 - a^0 euler_factors: - - 1 - a^5 - - 1 - a^10 - - 1 - a^7 - - 1 - a^4 - - 1 - a^6 - - 1 - a^7 - - 1 - a^11 - - 1 - a^7 - - 1 - a^3 - - 1 - a^9 - - 1 - a^9 - - 0 - - 1 - a^10 - - 1 - a^3 - - 1 - a^0 - - 1 - a^8 - - 1 - a^11 - - 1 - a^1 - - 1 - a^10 - - 1 - a^4 - - 1 - a^6 - - 1 - a^7 - - 1 - a^8 - - 1 - a^5 - - 1 - a^3 - - 1 - a^6 gamma_factors: - - 1 - [] id: 247 index: 0 label: 1-37-37.23-r1-0-0 leading_term: 0.0905357129197592584427649916307-0.360977788627931206767178925231*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/37/23 plot_delta: __RealLiteral__: 0 data: '0.3125' prec: 20 plot_values: - 0.37215813735104647 - -0.03536488255315987 - -0.451833662589378 - -0.8562833451092127 - -1.1944141687659076 - -1.383136782499156 - -1.3292467500269387 - -0.9564985628796623 - -0.23483805770031554 - 0.7956266165504164 - 2.014057148350352 - 3.2284752691864185 - 4.208050517437569 - 4.734098839796452 - 4.658659523771488 - 3.954225352340342 - 2.7372582615023746 - 1.2530660737876493 - -0.17987091793698562 - -1.2545140205227987 - -1.7650710061131862 - -1.672398161031042 - -1.1194364080844548 - -0.3854720398087209 - 0.21090940643112466 - 0.4295755108088458 - 0.2046666529976138 - -0.32111635152832263 - -0.8439253141847699 - -1.0175482947201193 - -0.6026128596517561 - 0.41260760430639587 - 1.7741704634171072 - 3.033454280533986 - 3.7102179668318236 - 3.4892295760537717 - 2.370445314472536 - 0.7033942897759615 - -0.9212518084064978 - -1.8908455621869547 - -1.817133181330797 - -0.706503163578058 - 1.0248934197854709 - 2.7081628954351222 - 3.692760910717462 - 3.6187395215871065 - 2.5698309256864427 - 1.0345404520415569 - -0.31317388220865783 - -0.9180015649773887 - -0.5930543340261711 - 0.40296656325403407 - 1.5004291593276808 - 2.102562813947168 - 1.880323970915273 - 0.9309170602352594 - -0.28228437696731024 - -1.1802842964690767 - -1.3805673736730886 - -0.9042392160464084 - -0.16108072500506562 - 0.28914654566391934 - 0.07728814886738013 - -0.719504729062223 - -1.5603251934429054 - -1.6939092384994692 - -0.5672054317379679 - 1.8227648159707999 - 4.832770315976155 - 7.408943885109336 - 8.55655254797045 - 7.8142776462332595 - 5.487598182003312 - 2.512011928838732 - 0.008040840109503103 - -1.2453371988451272 - -1.145853982617798 - -0.24049781607508341 - 0.6382953336946912 - 0.8618542835432108 - 0.3419470922831318 - -0.4717311837918432 - -0.9202955608282906 - -0.5845773863840323 - 0.4239838572327969 - 1.513876054634221 - 1.9801337219263138 - 1.4628989468551794 - 0.2076290918670843 - -1.05057056418996 - -1.5265766952970858 - -0.8885500456513855 - 0.4911273923903405 - 1.7132767619711307 - 1.874897330825024 - 0.6329522582100997 - -1.5397026947757988 - -3.5835458388635404 - -4.452999411299903 - -3.7394329983258636 - -1.937570946573276 - -0.17952118470842932 - 0.41969279040194163 - -0.5804140437915907 - -2.681512031018515 - -4.737952570217956 - -5.628676822917662 - -4.901143638749879 - -2.998510807708838 - -0.9438264997756767 - 0.30445577408792807 - 0.40991606715671464 - -0.21958965686493448 - -0.8003859618245874 - -0.7620838563941424 - -0.14509070438280333 - 0.46783668334090567 - 0.432935413596005 - -0.4088302536618542 - -1.5279898872735005 - -2.0228013121932946 - -1.266992863196589 - 0.5539743301030495 - 2.4190099892180434 - 3.034060685206137 - 1.6540556123044206 - -1.366774375726029 - -4.682023009444055 - -6.690059814820231 - -6.458410283878314 - -4.256074816121675 - -1.3559531197512937 - 0.7619761661302572 - 1.2897902718099203 - 0.49151190892916136 - -0.6092470344610345 - -1.0072483373519754 - -0.4086449097688612 - 0.6326364601074277 - 1.2029759920952807 - 0.7653458690306059 - -0.4031110556019653 - -1.3954732456283934 - -1.3469477612159793 - -0.09821243226395883 - 1.6467200260581116 - 2.798920990334746 - 2.6593376902843975 - 1.4200985815327807 - 0.01040601817958842 - -0.6156448473655878 - -0.22804135279636795 - 0.46510589549953946 - 0.3339617381936616 - -1.2721674028875662 - -3.897090259057206 - -6.120362111574019 - -6.431097342490485 - -4.25784423112672 - -0.43529544787599495 - 3.2441014206872905 - 5.1153974989075195 - 4.637874735071061 - 2.6369259504745166 - 0.6525921796191138 - -0.12354520984672353 - 0.42643908440675565 - 1.4363737630393207 - 1.8310882362885352 - 1.168494194897589 - -0.0838367811007662 - -1.0091285514365407 - -1.0332810279096771 - -0.39397004544773223 - 0.09658282510782916 - -0.1990241671552284 - -1.1056980643008372 - -1.6682542184265161 - -0.8878626954438906 - 1.3850645812854474 - 4.124550755133673 - 5.699446006125688 - 4.9884449163156 - 2.235658890377207 - -1.0146438400353142 - -2.9091297537139638 - -2.518106521313945 - -0.42717548490990803 - 1.7380957928175667 - 2.499537148946532 - 1.5501571674705474 - -0.12712525276291275 - -1.0986694372443553 - -0.6108995526137855 - 0.8556297994192585 - 2.012519695597809 - 1.8078724139916176 - 0.25616429627542203 - -1.5908533282268063 - -2.486178339625907 - -1.9543070430842382 - -0.6103274997894268 - 0.4047829686772178 - 0.38789170752606406 - -0.3683832191879505 - -0.885328206589664 - -0.40842504881305636 - 0.8640259224436142 - 1.8837901795513283 - 1.6481062653111016 - 0.1603595830690468 - -1.381563775273443 - -1.4174517528331436 - 0.7114702795206673 - 4.0637832587249205 - 6.581771848540312 - 6.47688233523546 - 3.514606807148081 - -0.7670291491990022 - -4.084775809740287 - -4.928208454770132 - -3.4579476615861915 - -1.171319933587304 - 0.32497227898066827 - 0.44264214821978637 - -0.20189088794019955 - -0.5783846207291952 - -0.2567895004779401 - 0.24013654640602808 - 0.015165300016028853 - -1.2496827269009274 - -2.849387818198731 - -3.5603059581001526 - -2.688894383759525 - -0.7510156561679708 - 0.8553459288539607 - 0.9711645427686223 - -0.329149643105515 - -1.736540620442073 - -1.7625535812361377 - -0.015403382851146952 - 2.3709502769330277 - 3.5626458178191545 - 2.483519289101705 - -0.2691848649300791 - -2.8189513103615678 - -3.4306071450980724 - -1.8331436895823965 - 0.6119918735578759 - 2.022912031295097 - 1.4815428945994744 - -0.30487025963551884 - -1.6679243437865423 - -1.3800076195350333 - 0.37631353220236036 - 2.242466856426371 - 2.8657832639337197 - 1.995073822528885 - 0.5766860396062301 - -0.16844766816828433 - 0.17339111867859663 - 0.9307873712418965 - 1.084688057147056 - 0.3030817746232075 - -0.7192599638766066 - -0.9706206493715311 - -0.24772697003690924 - 0.38374231323082975 - -0.6579790370595983 - -4.038015441813659 - -8.613162815442996 - -11.952434259905779 - -11.995959914902603 - -8.589574752937894 - -3.659037140015416 - 0.15182374332877724 - 1.323975012654053 - 0.3564805011563527 - -0.9254585810151805 - -0.9880142233654429 - 0.23676788237309135 - 1.5335287525438783 - 1.660520201362513 - 0.5038262397536429 - -0.8826930818593111 - -1.3200589379161243 - -0.623448841154637 - 0.24725499113829968 - 0.13752505932579792 - -1.146204530264578 - -2.5718895439244682 - -2.79061581978198 - -1.408061555667531 - 0.5608808442446948 - 1.5198030138915113 - 0.6958425076988743 - -1.1467856780920669 - -2.3714677201444214 - -1.9617689547004051 - -0.506097488237493 - 0.26101702849179387 - -0.9735540441669368 - -3.7849969509187242 - -6.152346134097339 - -6.028869821952549 - -3.0535635964636203 - 1.0521812317714065 - 3.767044905130599 - 3.678594994230868 - 1.4499863039561287 - -0.8979661067465932 - -1.697246277244941 - -0.8537306944682316 - 0.3849588317019403 - 0.7567405793003192 - 0.12321303286441676 - -0.5885868929793767 - -0.4715162301210473 - 0.3789728265511761 - 0.9692609808637574 - 0.49046466152568924 - -0.7176031875006044 - -1.3442971455340014 - -0.3566057725632582 - 1.841273020483356 - 3.5201820760221616 - 3.0650262396177856 - 0.5229151120084391 - -2.177567747929295 - -2.669877028219319 - -0.1068822025260056 - 4.041439351198364 - 7.0767231571165095 - 7.15990607679354 - 4.6515926804736445 - 1.6207433527943782 - 0.03124484921008424 - 0.2235113629294458 - 0.9601525802755381 - 0.8510936302662923 - -0.24779522404956533 - -1.160876977624301 - -0.6468417842404837 - 1.2698250090549223 - 3.1874463619337483 - 3.5530549231820046 - 2.065371718881829 - -0.07036960063533584 - -1.2646336846788255 - -0.9633699943933516 - -0.01625477971764426 - 0.32675592116456353 - -0.2304117234448657 - -0.700012186422963 - 0.11856948146010078 - 2.1995385184617495 - 3.964633583270808 - 3.5528909809306497 - 0.6200673973955682 - -3.0249347385733625 - -4.686004377458399 - -2.9703685779164 - 0.9830467356612477 - 4.349966798126583 - 4.8549800004190375 - 2.496081222420988 - -0.6667348732912389 - -2.3675743051391365 - -1.9426922696730047 - -0.5586325916877757 - 0.15692408478530995 - -0.3291473340410036 - -1.1600237354470972 - -1.1868729799250632 - -0.2405265479869465 - 0.7336927569367742 - 0.7747769532697848 - 0.05025519473409363 - -0.20730089104678262 - 1.0072464305046749 - 3.2340648152561275 - 4.699784152489498 - 3.8743936053352064 - 1.0187540552747296 - -1.8116822494912834 - -2.4537338348681152 - -0.5420777943708361 - 2.129488491969031 - 3.1803244433732654 - 1.7492055255523538 - -0.7854698107944238 - -2.1266130683772975 - -1.1898578229867578 - 0.9273201744434618 - 2.0131409022572 - 0.8176314633819765 - -1.8069681147121412 - -3.729176753844872 - -3.496170420387533 - -1.5704679746904158 - 0.2602483728514295 - 0.6390196547929892 - -0.16836802785484486 - -0.7430624818990866 - -0.0759608815854576 - 1.3903030216065193 - 2.2677157929707445 - 1.7064760502001879 - 0.2939789106741405 - -0.5756770995078168 - -0.20683072002532432 - 0.6220735966985936 - 0.5129200720993039 - -0.8605208538465255 - -1.9942274012025936 - -0.7039824247949883 - 3.7168490749803187 - 9.366239379322431 - 12.870982777421414 - 11.97338217540151 - 7.344996063867608 - 2.0235451868138052 - -1.0249861055154026 - -1.073773505345514 - 0.27639786486722934 - 0.9374990973393685 - 0.24617480156164584 - -0.787314168128448 - -0.8916625476150256 - -0.00858163342437221 - 0.6910680945417732 - 0.17499007985132248 - -1.2187251571579925 - -2.0381205750583034 - -1.2333069596287731 - 0.6495587203567237 - 1.892487408052493 - 1.289497742736695 - -0.6053267404757869 - -1.9823454661007902 - -1.5904080433454064 - -0.043109126451706004 - 0.759715291140287 - -0.4029724428599434 - -2.671350088716209 - -3.7471378135246987 - -2.069753753773634 - 1.5541879171876896 - 4.508091080725028 - 4.670001051902315 - 2.315208728286244 - -0.18725879021865094 - -0.5956078401155287 - 1.173742841410371 - 3.0981771464002157 - 3.056429723583695 - 0.8184808070080092 - -1.8496886308527765 - -2.941624275787225 - -2.027169124848454 - -0.4014202338361277 - 0.40561983447191297 - 0.11425246848912152 - -0.3254861059665335 - -0.08282226022428277 - 0.46878597797889615 - 0.18743343903311352 - -1.340851608294296 - -2.959601093722945 - -2.8714250711013847 - -0.5632197357120787 - 2.2678832746205293 - 2.960397248701113 - 0.32715613081493544 - -4.024657721264694 - -6.888555208039366 - -6.195512081823365 - -2.7922986747029004 - 0.38742925857356614 - 0.9627372922343467 - -0.9167434332498292 - -3.0188919704406776 - -3.3037001588718575 - -1.7412565536753466 - 0.0030800894919814914 - 0.4891179829973552 - -0.0464420768681368 - -0.15655616200124228 - 1.050515437622804 - 2.804534459118256 - 3.4292588490052625 - 2.1515038466944705 - 0.016106514639276474 - -1.1046690140793738 - -0.39756418653191034 - 1.0893079821688734 - 1.5861612539247423 - 0.4896666576213601 - -1.0096281005588945 - -1.2545953662706153 - -0.0016419697942680175 - 1.206924744301143 - 0.7001580466902508 - -1.3003378125705192 - -2.496458355369319 - -0.5932521777818767 - 4.280118604798935 - 9.242759992586922 - 10.925642683370832 - 8.306083742322583 - 3.4957588271557 - -0.19750237957409253 - -1.0492270915541835 - 0.024874914368558234 - 0.893409864034722 - 0.46060059174187573 - -0.5251985809539221 - -0.6951760222624132 - 0.22516880915839732 - 1.1197883740163113 - 0.837848817481168 - -0.4087818519308544 - -1.230530848025957 - -0.650434322225006 - 0.7013376945115118 - 1.2222863531065646 - 0.2201070443283653 - -1.0259745251297185 - -0.3657871834995829 - 2.9027455009802248 - 6.8868801215219975 - 8.501899894459394 - 6.246879250906911 - 1.6811686497101237 - -1.9028407955260127 - -2.385496476161347 - -0.526214133088869 - 1.1017349435798087 - 0.7702029350244105 - -0.8415484345064197 - -1.6477206379418707 - -0.5328355754119468 - 1.426174998281162 - 2.1221926960536313 - 0.668616077541908 - -1.6552011436569372 - -2.725230776504907 - -1.7244957152810272 - 0.13437624886518082 - 0.9992066306641434 - 0.31755269931968666 - -0.7509169998891576 - -0.7974974506106554 - 0.20527278866350146 - 0.953380956555529 - 0.46671102124880165 - -0.5817189197691408 - -0.500389466087467 - 1.3776281021978007 - 3.510357174232687 - 3.3600758696307653 - 0.01118843767249171 - -4.476098393325505 - -6.5794911824274065 - -4.446985669085055 - 0.33802941766576466 - 4.116499885599614 - 4.371557183905857 - 1.752993387377681 - -0.9019743978304481 - -1.3918632948101044 - 0.02106633600266626 - 1.3884032218900668 - 1.337199665523218 - 0.3329326319339158 - -0.22279829594863623 - 0.20360523481106269 - 0.7150888458185202 - 0.2587753247433608 - -0.8359467494318356 - -0.9682612430810911 - 0.9462650631694818 - 3.980322695954755 - 5.7916527910918125 - 4.868235509847696 - 2.0884814589830665 - -0.13952246270818278 - -0.34890865359158396 - 0.4998606586405968 - 0.14948423984457937 - -2.3470451048557908 - -5.326391954461889 - -6.008573868187102 - -3.3332201514978226 - 0.7975891461002573 - 3.2242837634324193 - 2.503503701268974 - 0.15579763428082471 - -1.0247303443981994 - 0.1990269538508141 - 2.4297503017768443 - 3.2910517387641223 - 1.9479571853966278 - -0.1570913834573785 - -0.9839261621415101 - -0.04980402259654219 - 1.253145789168978 - 1.3695006588252703 - 0.3001747456205204 - -0.574671651064665 - -0.24298908900135374 - 0.7363525968806836 - 1.0117057231921636 - 0.2696809141726221 - -0.13941083681151928 - 1.2623465970696672 - 3.982581143327656 - 5.406786261461521 - 3.168948279892116 - -2.19278960212 - -7.144357427125804 - -8.03878692658847 - -4.330058942199526 - 0.9874966910756731 - 4.122696637491012 - 3.7095800220428443 - 1.4630672268518965 - -0.0635056531313123 - -0.07130551537651958 - 0.1705190524285257 - -0.7134750647058313 - -2.386254029806797 - -3.173819447369334 - -2.091517539910128 - -0.1115414600853451 - 0.8232042813240255 - -0.06839728020814671 - -1.5591075270160788 - -1.8344520500801968 - -0.5791621747662208 - 0.6578575470244564 positive_zeros: - '0.28571526045412949858901243672' - '2.579042834589445045057661803713' - '5.58252641741673014664747258603' - '7.37105026768783361230159224211' - '8.259581094013353617601059207090' - '9.57824227482554863985948981713' - '11.68970330135087068399409197331' - '12.94725202815197280802513293547' - '14.91450952323888946058735694712' - '15.825254312647143323758725999466' - '17.42523841987185044704441592555' - '18.82854987735978636697766598597' - '19.41528793437835292556803549603' - '20.71377993510570818896521313163' - '23.126285210517339395797933289601' - '24.13644713481389304125848592437' - '25.13040913425457295541449611357' - '26.133635499869826101349533419327' - '27.54638552764291938485488694739' - '28.646196199413833750062426602047' - '29.78682647071996046851146011617' - '31.60795876488632470076245681358' - '32.06244533698453825966401095974' - '34.2664252735897850896988000063' - '34.9066528272182748422424713341' - '35.99938828586307145259299782521' - '36.75164285582916135106803691243' - '38.03999633230704652308911418278' - '39.24686861443641375475853869254' - '41.11222710620245400431951786036' - '42.005777268249789840846445902840' - '42.935799023439925649464605205121' - '43.96290012049395426203863964835' - '45.01820489707823843597471176743' - '46.56537272449794864426087695016' - '47.28177846164662949222094824505' - '47.9085978798626708478040331791' - '49.72094296295132798575050944527' - '51.441143036901873506043754231761' - '51.70573027846965477418377465372' - '53.1040395656579773933186741394' - '54.26962586829276207972828921105' - '54.58051710008632409956113865952' - '55.767472769279460383117370498134' - '57.39596936907852278928381669851' - '58.49252287638283681169253294377' - '59.66219500007559436059752671147' - '60.453762735190201010037754649355' - '61.6036804857967889089634519196' - '62.967887989836825452738966838800' - '63.6121426686674182224407055950' - '64.4872166235234347990620965470' - '65.65302401798281318114578020224' - '66.484305864329560519985430112744' - '68.068529605838726631498797362460' - '69.58864540841816900383124806120' - '70.22153609888804125379476067333' - '71.07738363885565005077215645534' - '71.56850726975117828397163556943' - '73.24728839445643465481506549681' - '73.9985809795677788130654314301' - '75.00203771607693753071778905124' - '76.22209138316196458659709362503' - '77.41797411374604429726654219962' - '78.38718934338846875247846238733' - '79.31803566433855023742168172059' - '80.81043730770248248335853566635' - '81.16734888844335180728576023102' - '82.27320154934769540223142887247' - '83.20952737023529409555021881587' - '83.63438146279573741778667426049' - '85.919663958998666369296514844019' - '86.638011392912755238036118962551' - '87.450774516867384233118646711154' - '88.54135497298852433762583020791' - '89.57597995633373686490616517859' - '90.04892534644570466972098964168' - '91.46756392354150331081208865695' - '92.31150275706777183384939496957' - '93.56723845106377980531447468281' - '93.88363885642194435394433761106' - '95.54208166811114890923749398632' - '96.7394193027038462297224641388' - '97.702640930638590309622245806355' - '98.48171969456159426972031557275' - '99.24853454909395804010342157323' - '100.133206729646305000485366975257' - '100.99560382112393573619691764486' - '102.24103357603665996776773061504' - '103.13380991854125934184050926967' - '105.01820827489278701372813902841' - '105.19573818675225257528871266155' - '106.18899179062172454570739864256' - '106.99870753483504724813142805141' - '108.42592613785608593045337793547' - '109.3813266063441137274773123667' - '109.9020438522588785444936103228' - '110.601041720565824725423030199308' - '111.92616249235175300730695099982' - '113.05205562534494964600457057945' - '114.30282044769942317993955931681' - '115.48963926391907429987893819419' - '115.80086630967188223058269998568' - '116.93971608671694422344650187916' - '117.83451658783353885563443069786' - '118.22240277559432197572935842097' - '119.786297773392073373210046145666' - '120.68597458686126460246169893462' - '121.77500563729072649797735682789' - '122.67629778067216757271122548543' - '123.54227255377820680119557829463' - '124.940177308825265337843915800926' - '125.57044341200106016049667640201' - '126.26843212208128151307435608249' - '127.57160836203335634553737240975' - '128.19831705659685521449193783324' - '128.8905918207150537128957869910' - '129.75402405336463789495573689736' - '131.72949357515975110253978388069' - '132.43606543038201664401685962004' - '133.19238020271341326069321288360' - '134.06510152380438139117743854395' - '134.73272559440661230297518021426' - '135.83326644074749464434827743029' - '136.78099264697586990689122306308' - '137.821510488617787240550941755722' - '138.37086883552340224138155628053' - '139.56078410101290515387302998882' - '140.90510941681208510362087770810' - '141.38708855543963024904635281774' - '142.588997887310967077702732399' - '143.85239317256172778873613717823' - '144.437328385755243058935364362864' - '145.04391654242857188383821504394' - '145.67898157633357639138426402309' - '146.93270028206035312285171355811' - '147.83776091070777151822387943656' - '149.322916261247216039797000838294' - '149.87655472303752964659927242794' - '151.24922210418633887797604429584' - '151.8507061507371222917931803474' - '152.25768757969241334958990868422' - '153.752641801432718755616403343497' - '154.45852373594066929891702110384' - '155.40567558100302543674432333014' - '156.25032522352238858323798065200' - '156.997348687007836853820995083533' - '157.85984466271449772272942751995' - '159.66234348477309847296555047752' - '160.30655298880252736637635722838' - '161.07675715554612076113468480903' - '161.81379386455935604003988836326' - '162.71702101190556475879736411176' - '163.58788895117661308618278671412' - '164.42090480407677614924834855084' - '165.04988206319572758070855175394' - '166.68390810059357013059378789675' - '167.5774167084963221453511018632' - '168.28118606617375218359544295915' - '169.14673693463746501341891675022' - '170.088861430025387225394919419699' - '171.22465082185591142780110164647' - '171.958348448510560447009449187924' - '172.75668145335924947151089258198' - '173.56878369517145432750545289241' - '174.17446534685131269584292660939' - '175.31328015589955794854008052370' - '176.54112176890734238976375601019' - '177.684711034612803659563577997858' - '178.433723570950955861457288958706' - '179.49626414701555923993383653515' - '179.90304244901540425422186744575' - '180.70148324877631211606753822246' - '181.445441361751990823221602424137' - '183.09346265347364841517794412683' - '183.56639657654999018243895086650' - '184.09173841407881445547358144191' - '185.5614350247310245826925550206' - '186.58533025863624213356225841420' - '187.157539510754225427917216485511' - '188.41007091320453857443853834970' - '189.07326122637388227429152478705' - '190.078779243119282046440456605406' - '190.70487800410851242136607802790' - '191.66788140785539543248065240629' - '191.94752762786052585670920874633' - '193.32039430684336421636942247737' - '194.62522267563943709301797830989' - '195.91142312991095251697982404307' - '196.301361762524521319422695211349' - '196.67884692424482923170320545244' - '198.14536865896053828453390564399' - '198.73581223438441070122683705002' - '199.80520383971412268768956498452' prelabel: 1-37-37.23-r1-0 primitive: true rational: false root_analytic_conductor: 3.976202217401126 root_angle: -0.8435583715590922 root_number: -0.881637314992347705789702834257-0.471927584289246511980311342444*I self_dual: false sign_arg: __RealLiteral__: 0 data: '-0.42177918578' prec: 47 spectral_label: r1-0 st_group: mu(12) symmetry_type: unitary types: - DIR values: - - 1 - 0.511763512393347267124436117761-0.154905384261690313389329572823*I z1: __RealLiteral__: 0 data: '0.285715260454' prec: 47 z2: __RealLiteral__: 0 data: '2.57904283459' prec: 44 z3: __RealLiteral__: 0 data: '5.58252641742' prec: 44 - - algebraic: true analytic_conductor: 3.976202217401126 bad_primes: - 37 central_character: '37.23' conductor: 37 conductor_radical: 37 degree: 1 id: 247 index: 0 instance_types: - DIR instance_urls: - Character/Dirichlet/37/23 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: 1-37-37.23-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: 1-37-37.23-r1-0 primitive: true rational: false root_analytic_conductor: 3.976202217401126 root_angle: -0.4217791857795461 self_dual: false spectral_label: r1-0 z1: __RealLiteral__: 0 data: '0.285715260454' prec: 47 - - Lhash: dirichlet_L_37.23 Lhash_array: - dirichlet_L_37.23 id: 1781669 label: 1-37-37.23-r1-0-0 type: DIR url: Character/Dirichlet/37/23 label_cols: - label - label - label labels: - 1-37-37.23-r1-0-0 - 1-37-37.23-r1-0-0 - 1-37-37.23-r1-0-0 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-04-18T01:51:01.911465'