LMFDB - Embedded newform 1.122.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,122,Mod(1,1)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 122, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 122);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 122 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$92.7173263878$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2 x^{8} + \cdots + 32\!\cdots\!74 $ x^9 - 2x^8 - 6896267302374195854288979542110036x^7 - 18182056455091876334127202245297944469939481193728x^6 + 14212629602031409229637635771022937711993825413350167099237510479606x^5 + 61258610310684835233108833192024704261087721493254347634992670795376976962606134364x^4 - 9842499772141836551134619784196809812883472316889789802022116143289674396393873883442313493192036468x^3 - 28320767833279507773472564445008628892273605282905175305275773570942014694022505516447508594331297760748650974508144x^2 + 1837990504265564297591553937106510644700471984398148609639572793490786272449115020648515508733566716122900824713245834679387771722833x + 328617579029133279802926386891335178982925368767393882742389284437302316313461583243308637651182442753765604934835620884256792770827221760481511574
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{145}\cdot 3^{53}\cdot 5^{20}\cdot 7^{8}\cdot 11^{6}\cdot 13^{2}\cdot 17^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-6.03020e16$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.15505e18 q^{2} +6.48457e28 q^{3} +7.29589e36 q^{4} -2.23954e41 q^{5} -2.04592e47 q^{6} +1.98659e51 q^{7} -1.46313e55 q^{8} -1.18606e57 q^{9} +O(q^{10})$	\(q-3.15505e18 q^{2} +6.48457e28 q^{3} +7.29589e36 q^{4} -2.23954e41 q^{5} -2.04592e47 q^{6} +1.98659e51 q^{7} -1.46313e55 q^{8} -1.18606e57 q^{9} +7.06586e59 q^{10} +1.11595e63 q^{11} +4.73107e65 q^{12} +2.72472e67 q^{13} -6.26779e69 q^{14} -1.45225e70 q^{15} +2.67668e73 q^{16} -1.03012e74 q^{17} +3.74209e75 q^{18} -2.25299e77 q^{19} -1.63394e78 q^{20} +1.28822e80 q^{21} -3.52089e81 q^{22} -1.89711e82 q^{23} -9.48780e83 q^{24} -3.71143e84 q^{25} -8.59665e85 q^{26} -4.26496e86 q^{27} +1.44939e88 q^{28} -2.78608e88 q^{29} +4.58191e88 q^{30} -1.00803e90 q^{31} -4.55539e91 q^{32} +7.23648e91 q^{33} +3.25009e92 q^{34} -4.44905e92 q^{35} -8.65339e93 q^{36} -1.04490e95 q^{37} +7.10828e95 q^{38} +1.76687e96 q^{39} +3.27675e96 q^{40} -3.09873e96 q^{41} -4.06439e98 q^{42} +3.87231e98 q^{43} +8.14187e99 q^{44} +2.65624e98 q^{45} +5.98549e100 q^{46} -1.16928e101 q^{47} +1.73571e102 q^{48} +2.13994e102 q^{49} +1.17097e103 q^{50} -6.67991e102 q^{51} +1.98793e104 q^{52} -2.20085e104 q^{53} +1.34562e105 q^{54} -2.49922e104 q^{55} -2.90665e106 q^{56} -1.46096e106 q^{57} +8.79023e106 q^{58} -1.62691e107 q^{59} -1.05954e107 q^{60} -1.71703e107 q^{61} +3.18037e108 q^{62} -2.35622e108 q^{63} +7.25665e109 q^{64} -6.10213e108 q^{65} -2.28315e110 q^{66} -1.04127e110 q^{67} -7.51567e110 q^{68} -1.23020e111 q^{69} +1.40370e111 q^{70} -1.25798e112 q^{71} +1.73537e112 q^{72} +8.19362e112 q^{73} +3.29671e113 q^{74} -2.40670e113 q^{75} -1.64375e114 q^{76} +2.21694e114 q^{77} -5.57456e114 q^{78} +4.20171e114 q^{79} -5.99454e114 q^{80} -2.12624e115 q^{81} +9.77667e114 q^{82} -6.56382e115 q^{83} +9.39870e116 q^{84} +2.30700e115 q^{85} -1.22173e117 q^{86} -1.80666e117 q^{87} -1.63279e118 q^{88} +6.88513e117 q^{89} -8.38056e116 q^{90} +5.41291e118 q^{91} -1.38411e119 q^{92} -6.53661e118 q^{93} +3.68915e119 q^{94} +5.04565e118 q^{95} -2.95398e120 q^{96} -2.55907e119 q^{97} -6.75161e120 q^{98} -1.32359e120 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 23\!\cdots\!28 q^{2}+ \cdots + 79\!\cdots\!17 q^{9}+O(q^{10}) $ 9 * q - 2345005562254519728 * q^2 - 45298662406895255983997747004 * q^3 + 8462901481545657250924227818768095488 * q^4 - 1892628936004587162449482404208025942059050 * q^5 - 169155345437237254853213475765636376857034060992 * q^6 + 2195742607988216453868262401462060909846066161833992 * q^7 - 6498505205013969366907252193209867920059782603760087040 * q^8 + 7945503363883566160952357352391639075761121301070127960917 * q^9	$ 9 q - 23\!\cdots\!28 q^{2}+ \cdots - 44\!\cdots\!96 q^{99}+O(q^{100}) $ 9 * q - 2345005562254519728 * q^2 - 45298662406895255983997747004 * q^3 + 8462901481545657250924227818768095488 * q^4 - 1892628936004587162449482404208025942059050 * q^5 - 169155345437237254853213475765636376857034060992 * q^6 + 2195742607988216453868262401462060909846066161833992 * q^7 - 6498505205013969366907252193209867920059782603760087040 * q^8 + 7945503363883566160952357352391639075761121301070127960917 * q^9 - 1722648625287605771733277740799503204814238573365164973293600 * q^10 - 946247437041242628794010189459909585820203760454440287613552692 * q^11 + 205846961050281878415699597946796712976603670706873231298938012672 * q^12 + 20596127771705642483605985955370331334854065669132980339746788779486 * q^13 - 6541972694294346334011779110963479954883365352702523229035305330483584 * q^14 + 94761650294240619608372286408346994746207880434327141095820600145938200 * q^15 + 15125444512952621416063439206177933863772762787209602627890080570611400704 * q^16 + 291951493650412549850834598805724750617640895870041885121831690800331035682 * q^17 - 2554000175718076948380008722939707666960273565314048023897922364658130426864 * q^18 + 30244684445956612332670117612595525326891015746649482369862884848315284461780 * q^19 + 4562951142663369182841621952582280345228980283169468426672463108421372089382400 * q^20 + 35146001071237823021693437259813836720201207139254364736561723878685716530560288 * q^21 - 1908843328157955617823816866863990801015534541375661383005747627202736697921398336 * q^22 - 66547277273309692585260941575189421012052896396341670760157778423156238686357058024 * q^23 - 752736756299124610400627977416074789098074869027579302337966622137134625951047925760 * q^24 - 6063954929776831553687695824368630787209822932539681432479202799269060736255468175625 * q^25 - 68842531925347949534946832128658250301897561117051749502543801676148842557574912147872 * q^26 - 599094982712902977137778651999579486037062432725587105690436473582035154107389795716440 * q^27 + 14581457392452701650088858542793969027985828891624009507886840217572255356341773965625344 * q^28 + 9039340472411915035494616975186209221844392206687458522714064361334880069082093346905070 * q^29 + 224260392412850366562482895689598093094206490242486949280006808962977358350861560270998400 * q^30 - 1034214344782654758430975917538809236085530199413694042134266190861671432181122576926086112 * q^31 - 32504525000929540761398714812123921617256100597234986820033520241386493923631009832383807488 * q^32 + 189949463814086324300823839088808170132383689196162349649439549175970470599919775108948927152 * q^33 + 939230388337351560267419962761669652735221862277825209065568487608538630630957599920217170336 * q^34 + 1343144021786280211948320998755385153610555228046229864187689603416027546078320739943060612400 * q^35 - 21747907752251375975427518389059436655823261956750397535228718126776457105689705407608776563456 * q^36 - 88515341604947210488499310221844243003334043790663530401335727647981800120006279439706998268938 * q^37 + 126431143256035943119117270678428356969446546517968603954366283120911078870917992997220500555840 * q^38 + 217837571218652472832776380975246155068206021757529611026730729062256423563336349872452629634104 * q^39 + 11699272454320878743488987607870545498317393987884112075950101149279048493373249852479799479296000 * q^40 - 36266094262194860707738000735265088509116494488735889525314316314221341311667592777599187406913222 * q^41 - 24787352510041822155108090768801766655788422577097156255869676682213614031202393800364112862967296 * q^42 - 232370696794750496427815530982465444104722554898177200564202440384179721532324359363059913691265044 * q^43 + 7755327422511594524608603055387018294701513657236683851986386901343418513803274064133364624004320256 * q^44 + 3247131420778261129864754583862668667744851710389803065112927478198766013287651133195234793708696350 * q^45 - 32066987947547067490416916557196164509339083485720964163476500441257367761070295505033101035894375552 * q^46 - 132970274906173452814801214841116212222140439777467383504750807710754558312919347426848207706456695248 * q^47 + 1792993240520940040285669530334719652675802655317197830920369780797223163120464508596735702234386661376 * q^48 + 3971615803493637002463922107037659765667323348806045910695714957649057905572825978452768033947465237313 * q^49 + 7697223557528977921454596784007095645216064886088735712319363716221302227247960859603436865144030830000 * q^50 - 12851187227364644420645646585565612980157473692407810028414511867222315540665892049707079694243262493752 * q^51 + 41491246868006007350968584983945986180424656334954442495103497331692372835472248671859508511281974820352 * q^52 + 10921805138133777254090784536986505203689729704788186882887817145907729071674310284399320645165776125446 * q^53 + 1339620561670595781535503143383501960027220441835890399944886982813214108542142442500405331111067486871680 * q^54 - 1312854241531753321574015681587452449577731960880104498235108054018717321131599152359037095554839302748600 * q^55 - 14013489107783484379024464711764338924776495535033134010566539603721944518516633929838564532681379280158720 * q^56 - 31019370720452892632999266840260901115398140535819179494909299925851052488218537305068762474072132809464880 * q^57 + 103566512036259767730142842802003772713045020405103287191675134464175461494809359502286741327442998854097760 * q^58 - 212654227372156556243821221093344570156200984495183110384877226881440240904587127248726963633402442388397060 * q^59 - 422775085570641982781661820780199899688061805673956240019260238835680896536027096304091002230119430523545600 * q^60 + 1192163308009290988314718399559245385155131325092676542388200473202899841355909578157895873548972217626937358 * q^61 + 1941577256261942079284748865266177577315768005250991995768914948259042107075822164327427075406958896697915904 * q^62 + 451398588142208697776529182978564850520004037586377967283679997710918662905240621028803130635870486918043496 * q^63 + 58844915592066748224918413663360071934978670807229624180238002804297923325840628846335879209980431060401389568 * q^64 - 41307677239725606429137681882540847206257959638235776751518537901187469657040797622415542482923664688418764300 * q^65 - 222086041679950312339781078110357023370750120852496118683208049646663973764702391499379128192551147975013941504 * q^66 - 136956255883591433626896738276452320541908670428347212980145870863327851773988143589420054081089733226508975868 * q^67 - 141094811799092295974464545753546540483126567546619661037683966526498908594653379053568196980211372687791832576 * q^68 + 1325703171238765045361423824776857588261240408135555321965899246235283904667578177535332268855352594559670964064 * q^69 + 251934589370384384494289262861906043864096277276788575857738394556055301564200175196895771626792095349002028800 * q^70 - 21585422985838182545762327030440661631324036114582384867758341692032917773329287240302446531581657134820891213752 * q^71 - 5181834258416339630015764026055527646506354416168007949107924953264135981412995982436721696529253639785101291520 * q^72 + 91235460780032725960652165272631372912505283323159668796891496309162099636399114489032757775807008811684035374426 * q^73 + 310562981122696891225427716699672479798427405954878722327169646078571868354993002411909262537623251852286369642976 * q^74 + 43065854506087315183339457241248482679331791698024061594158993211332750535581795467446263657604087829943816477500 * q^75 - 1628928259080846394930799553567522291541981414122456953774556713740025206052658836539555750192733076653498088483840 * q^76 + 593398979324677723779464865172133117018002924612325496238799373091215617849415550444705675974821710181802828350304 * q^77 - 6873235601534959334329744558974767766222222958184019979663697300957230011165665645661869140437348638585389730736768 * q^78 + 12451904914912678516471799458709519750612136226261564829575149335945412565470277464754582893898189772426218896816720 * q^79 - 20416950898306426146345946546741629794844904073553249082791509645594723097676639519064500446972597103490830240972800 * q^80 - 40856231575215745746855879250733371261216334279125203008573307569275978049909264916389709598337529820618984078592511 * q^81 + 32147344949534769988675834932358838024355394065520493232144096322964430678203949090265848270504974541383740855029024 * q^82 - 92550876115215159531985566894207205907616571001151579100140340424113698287990359504129121116969620392280333900687084 * q^83 + 149786622283872863814961679878718479671325736759801797089969582016734283953793144464030325178406284102124769637769216 * q^84 - 457768087179221548903179340844196170221647881541175735561813412251720733334690809762523483946456540131705087221018100 * q^85 - 2597491864434159334587628292949145911098969463321219405661773952780499099399232684938429948876042525744324616394370112 * q^86 - 6860132173224607170538777320017488364980901889195600241683572931313063475309515779498812905462751134050092231747965320 * q^87 - 20006125934411614149040201757441776841868885955363484760412796241321136345672966303804893860326010500704122960860692480 * q^88 - 6037951059942933692255237205803554193360594969996068937834548367886153095083618336696729724512143193617265723073840790 * q^89 - 63101356532716899775688972110257991639639781786779198684055149646555511091876460642986977143928184313177571126402448800 * q^90 - 123641023753197596743476339553493022736411481279426005005225341366808933988856782685240985478245146307872825619974888592 * q^91 - 364595199967728361741013600374859006514622011131757842452690960184887037990775378757973866446814260984048497269830739968 * q^92 - 660210659270707805852573362768494443983824981820503945313596568722380303376948547337519220648409914639203450549706054528 * q^93 - 1077366499492799036766200119308272598652452209354508770841202268675762751723923474906601231339334467643845894468443138304 * q^94 - 1952811193153518003415269978917451688485843585663036733937657231131838392410846728976735534304153554615423725772929253000 * q^95 - 7973910491229034017269638806130805343748566540122585079441423327960922891988630774830062893111316529474837792857136300032 * q^96 - 10257092292553957046050140760321382189656293894451103156433186039799204062322028715705878067672306955149219750865890726798 * q^97 - 27691496134014026270502117819887007317432773944983420293676841151578333911041338924275151210232199410900266664836266600496 * q^98 - 44066255828766064795825662460182521807738019967004038392602001105306909448583819181101964434724044331056342593475150607396 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−3.15505e18	−1.93505	−0.967524	−	0.252780i	$-0.918655\pi$
$2$	−3.15505e18	−1.93505	−0.967524	+	0.252780i	$0.918655\pi$
$3$	6.48457e28	0.883172	0.441586	−	0.897219i	$-0.354416\pi$
$3$	6.48457e28	0.883172	0.441586	+	0.897219i	$0.354416\pi$
$4$	7.29589e36	2.74441
$5$	−2.23954e41	−0.115471	−0.0577356	−	0.998332i	$-0.518388\pi$
$5$	−2.23954e41	−0.115471	−0.0577356	+	0.998332i	$0.518388\pi$
$6$	−2.04592e47	−1.70898
$7$	1.98659e51	1.47801	0.739004	−	0.673701i	$-0.235296\pi$
$7$	1.98659e51	1.47801	0.739004	+	0.673701i	$0.235296\pi$
$8$	−1.46313e55	−3.37551
$9$	−1.18606e57	−0.220007
$10$	7.06586e59	0.223442
$11$	1.11595e63	1.10507	0.552533	−	0.833491i	$-0.313661\pi$
$11$	1.11595e63	1.10507	0.552533	+	0.833491i	$0.313661\pi$
$12$	4.73107e65	2.42379
$13$	2.72472e67	1.10091	0.550453	−	0.834866i	$-0.314455\pi$
$13$	2.72472e67	1.10091	0.550453	+	0.834866i	$0.314455\pi$
$14$	−6.26779e69	−2.86002
$15$	−1.45225e70	−0.101981
$16$	2.67668e73	3.78737
$17$	−1.03012e74	−0.372160	−0.186080	−	0.982535i	$-0.559578\pi$
$17$	−1.03012e74	−0.372160	−0.186080	+	0.982535i	$0.559578\pi$
$18$	3.74209e75	0.425724
$19$	−2.25299e77	−0.973118	−0.486559	−	0.873648i	$-0.661748\pi$
$19$	−2.25299e77	−0.973118	−0.486559	+	0.873648i	$0.661748\pi$
$20$	−1.63394e78	−0.316900
$21$	1.28822e80	1.30534
$22$	−3.52089e81	−2.13836
$23$	−1.89711e82	−0.782635	−0.391318	−	0.920256i	$-0.627981\pi$
$23$	−1.89711e82	−0.782635	−0.391318	+	0.920256i	$0.627981\pi$
$24$	−9.48780e83	−2.98116
$25$	−3.71143e84	−0.986666
$26$	−8.59665e85	−2.13030
$27$	−4.26496e86	−1.07748
$28$	1.44939e88	4.05626
$29$	−2.78608e88	−0.933072	−0.466536	−	0.884502i	$-0.654498\pi$
$29$	−2.78608e88	−0.933072	−0.466536	+	0.884502i	$0.654498\pi$
$30$	4.58191e88	0.197338
$31$	−1.00803e90	−0.597157	−0.298579	−	0.954385i	$-0.596513\pi$
$31$	−1.00803e90	−0.597157	−0.298579	+	0.954385i	$0.596513\pi$
$32$	−4.55539e91	−3.95323
$33$	7.23648e91	0.975964
$34$	3.25009e92	0.720147
$35$	−4.44905e92	−0.170667
$36$	−8.65339e93	−0.603789
$37$	−1.04490e95	−1.38953	−0.694767	−	0.719234i	$-0.744493\pi$
$37$	−1.04490e95	−1.38953	−0.694767	+	0.719234i	$0.744493\pi$
$38$	7.10828e95	1.88303
$39$	1.76687e96	0.972289
$40$	3.27675e96	0.389774
$41$	−3.09873e96	−0.0827487	−0.0413743	−	0.999144i	$-0.513174\pi$
$41$	−3.09873e96	−0.0827487	−0.0413743	+	0.999144i	$0.513174\pi$
$42$	−4.06439e98	−2.52589
$43$	3.87231e98	0.579600	0.289800	−	0.957087i	$-0.406411\pi$
$43$	3.87231e98	0.579600	0.289800	+	0.957087i	$0.406411\pi$
$44$	8.14187e99	3.03276
$45$	2.65624e98	0.0254044
$46$	5.98549e100	1.51444
$47$	−1.16928e101	−0.805377	−0.402688	−	0.915337i	$-0.631924\pi$
$47$	−1.16928e101	−0.805377	−0.402688	+	0.915337i	$0.631924\pi$
$48$	1.73571e102	3.34490
$49$	2.13994e102	1.18451
$50$	1.17097e103	1.90925
$51$	−6.67991e102	−0.328681
$52$	1.98793e104	3.02133
$53$	−2.20085e104	−1.05657	−0.528287	−	0.849066i	$-0.677165\pi$
$53$	−2.20085e104	−1.05657	−0.528287	+	0.849066i	$0.677165\pi$
$54$	1.34562e105	2.08497
$55$	−2.49922e104	−0.127603
$56$	−2.90665e106	−4.98904
$57$	−1.46096e106	−0.859431
$58$	8.79023e106	1.80554
$59$	−1.62691e107	−1.18800	−0.594000	−	0.804465i	$-0.702452\pi$
$59$	−1.62691e107	−1.18800	−0.594000	+	0.804465i	$0.702452\pi$
$60$	−1.05954e107	−0.279877
$61$	−1.71703e107	−0.166849	−0.0834243	−	0.996514i	$-0.526586\pi$
$61$	−1.71703e107	−0.166849	−0.0834243	+	0.996514i	$0.526586\pi$
$62$	3.18037e108	1.15553
$63$	−2.35622e108	−0.325172
$64$	7.25665e109	3.86231
$65$	−6.10213e108	−0.127123
$66$	−2.28315e110	−1.88854
$67$	−1.04127e110	−0.346766	−0.173383	−	0.984854i	$-0.555470\pi$
$67$	−1.04127e110	−0.346766	−0.173383	+	0.984854i	$0.555470\pi$
$68$	−7.51567e110	−1.02136
$69$	−1.23020e111	−0.691202
$70$	1.40370e111	0.330249
$71$	−1.25798e112	−1.25471	−0.627354	−	0.778735i	$-0.715862\pi$
$71$	−1.25798e112	−1.25471	−0.627354	+	0.778735i	$0.715862\pi$
$72$	1.73537e112	0.742636
$73$	8.19362e112	1.52210	0.761049	−	0.648694i	$-0.224685\pi$
$73$	8.19362e112	1.52210	0.761049	+	0.648694i	$0.224685\pi$
$74$	3.29671e113	2.68882
$75$	−2.40670e113	−0.871396
$76$	−1.64375e114	−2.67063
$77$	2.21694e114	1.63330
$78$	−5.57456e114	−1.88142
$79$	4.20171e114	0.656125	0.328063	−	0.944656i	$-0.393604\pi$
$79$	4.20171e114	0.656125	0.328063	+	0.944656i	$0.393604\pi$
$80$	−5.99454e114	−0.437332
$81$	−2.12624e115	−0.731590
$82$	9.77667e114	0.160123
$83$	−6.56382e115	−0.516336	−0.258168	−	0.966100i	$-0.583119\pi$
$83$	−6.56382e115	−0.516336	−0.258168	+	0.966100i	$0.583119\pi$
$84$	9.39870e116	3.58237
$85$	2.30700e115	0.0429738
$86$	−1.22173e117	−1.12155
$87$	−1.80666e117	−0.824063
$88$	−1.63279e118	−3.73017
$89$	6.88513e117	0.793993	0.396997	−	0.917820i	$-0.370052\pi$
$89$	6.88513e117	0.793993	0.396997	+	0.917820i	$0.370052\pi$
$90$	−8.38056e116	−0.0491588
$91$	5.41291e118	1.62715
$92$	−1.38411e119	−2.14787
$93$	−6.53661e118	−0.527393
$94$	3.68915e119	1.55844
$95$	5.04565e118	0.112367
$96$	−2.95398e120	−3.49138
$97$	−2.55907e119	−0.161582	−0.0807909	−	0.996731i	$-0.525745\pi$
$97$	−2.55907e119	−0.161582	−0.0807909	+	0.996731i	$0.525745\pi$
$98$	−6.75161e120	−2.29208
$99$	−1.32359e120	−0.243122
$100$	−2.70782e121	−2.70782
$101$	1.89723e121	1.03915	0.519573	−	0.854426i	$-0.326091\pi$
$101$	1.89723e121	1.03915	0.519573	+	0.854426i	$0.326091\pi$
$102$	2.10755e121	0.636014
$103$	5.31868e121	0.889512	0.444756	−	0.895652i	$-0.353290\pi$
$103$	5.31868e121	0.889512	0.444756	+	0.895652i	$0.353290\pi$
$104$	−3.98664e122	−3.71612
$105$	−2.88502e121	−0.150729
$106$	6.94378e122	2.04452
$107$	−2.69461e122	−0.449549	−0.224774	−	0.974411i	$-0.572164\pi$
$107$	−2.69461e122	−0.449549	−0.224774	+	0.974411i	$0.572164\pi$
$108$	−3.11167e123	−2.95703
$109$	1.05976e123	0.576640	0.288320	−	0.957534i	$-0.406903\pi$
$109$	1.05976e123	0.576640	0.288320	+	0.957534i	$0.406903\pi$
$110$	7.88517e122	0.246919
$111$	−6.77571e123	−1.22720
$112$	5.31747e124	5.59776
$113$	−9.18935e122	−0.0564988	−0.0282494	−	0.999601i	$-0.508993\pi$
$113$	−9.18935e122	−0.0564988	−0.0282494	+	0.999601i	$0.508993\pi$
$114$	4.60942e124	1.66304
$115$	4.24866e123	0.0903718
$116$	−2.03270e125	−2.56073
$117$	−3.23170e124	−0.242207
$118$	5.13298e125	2.29884
$119$	−2.04643e125	−0.550056
$120$	2.12483e125	0.344238
$121$	2.25552e125	0.221173
$122$	5.41731e125	0.322860
$123$	−2.00940e125	−0.0730813
$124$	−7.35444e126	−1.63884
$125$	1.67361e126	0.229403
$126$	7.43400e126	0.629223
$127$	−3.30314e127	−1.73301	−0.866506	−	0.499166i	$-0.833640\pi$
$127$	−3.30314e127	−1.73301	−0.866506	+	0.499166i	$0.833640\pi$
$128$	−1.07848e128	−3.52053
$129$	2.51103e127	0.511887
$130$	1.92525e127	0.245989
$131$	1.04838e128	0.842568	0.421284	−	0.906929i	$-0.361580\pi$
$131$	1.04838e128	0.842568	0.421284	+	0.906929i	$0.361580\pi$
$132$	5.27966e128	2.67844
$133$	−4.47576e128	−1.43828
$134$	3.28525e128	0.671009
$135$	9.55156e127	0.124417
$136$	1.50721e129	1.25623
$137$	−2.32316e129	−1.24304	−0.621521	−	0.783398i	$-0.713485\pi$
$137$	−2.32316e129	−1.24304	−0.621521	+	0.783398i	$0.713485\pi$
$138$	3.88133e129	1.33751
$139$	−1.90079e129	−0.423193	−0.211596	−	0.977357i	$-0.567866\pi$
$139$	−1.90079e129	−0.423193	−0.211596	+	0.977357i	$0.567866\pi$
$140$	−3.24598e129	−0.468381
$141$	−7.58230e129	−0.711286
$142$	3.96898e130	2.42792
$143$	3.04067e130	1.21657
$144$	−3.17472e130	−0.833247
$145$	6.23954e129	0.107743
$146$	−2.58513e131	−2.94533
$147$	1.38766e131	1.04612
$148$	−7.62346e131	−3.81345
$149$	−2.52530e131	−0.840513	−0.420256	−	0.907405i	$-0.638060\pi$
$149$	−2.52530e131	−0.840513	−0.420256	+	0.907405i	$0.638060\pi$
$150$	7.59326e131	1.68619
$151$	1.44384e131	0.214494	0.107247	−	0.994232i	$-0.465796\pi$
$151$	1.44384e131	0.214494	0.107247	+	0.994232i	$0.465796\pi$
$152$	3.29642e132	3.28477
$153$	1.22179e131	0.0818778
$154$	−6.99456e132	−3.16051
$155$	2.25751e131	0.0689545
$156$	1.28909e133	2.66836
$157$	1.20667e133	1.69691	0.848456	−	0.529266i	$-0.177533\pi$
$157$	1.20667e133	1.69691	0.848456	+	0.529266i	$0.177533\pi$
$158$	−1.32566e133	−1.26963
$159$	−1.42716e133	−0.933136
$160$	1.02020e133	0.456484
$161$	−3.76879e133	−1.15674
$162$	6.70838e133	1.41566
$163$	2.98530e133	0.434148	0.217074	−	0.976155i	$-0.430349\pi$
$163$	2.98530e133	0.434148	0.217074	+	0.976155i	$0.430349\pi$
$164$	−2.26080e133	−0.227096
$165$	−1.62064e133	−0.112696
$166$	2.07092e134	0.999134
$167$	−1.66991e134	−0.560205	−0.280102	−	0.959970i	$-0.590368\pi$
$167$	−1.66991e134	−0.560205	−0.280102	+	0.959970i	$0.590368\pi$
$168$	−1.88484e135	−4.40618
$169$	1.29857e134	0.211992
$170$	−7.27871e133	−0.0831563
$171$	2.67218e134	0.214093
$172$	2.82519e135	1.59066
$173$	−7.43197e134	−0.294655	−0.147328	−	0.989088i	$-0.547067\pi$
$173$	−7.43197e134	−0.294655	−0.147328	+	0.989088i	$0.547067\pi$
$174$	5.70009e135	1.59460
$175$	−7.37308e135	−1.45830
$176$	2.98705e136	4.18530
$177$	−1.05498e136	−1.04921
$178$	−2.17229e136	−1.53642
$179$	2.05803e136	1.03716	0.518578	−	0.855030i	$-0.326462\pi$
$179$	2.05803e136	1.03716	0.518578	+	0.855030i	$0.326462\pi$
$180$	1.93796e135	0.0697202
$181$	−7.11612e135	−0.183100	−0.0915502	−	0.995800i	$-0.529182\pi$
$181$	−7.11612e135	−0.183100	−0.0915502	+	0.995800i	$0.529182\pi$
$182$	−1.70780e137	−3.14861
$183$	−1.11342e136	−0.147356
$184$	2.77573e137	2.64180
$185$	2.34009e136	0.160451
$186$	2.06233e137	1.02053
$187$	−1.14957e137	−0.411262
$188$	−8.53096e137	−2.21028
$189$	−8.47273e137	−1.59252
$190$	−1.59193e137	−0.217436
$191$	−8.69893e137	−0.864862	−0.432431	−	0.901667i	$-0.642344\pi$
$191$	−8.69893e137	−0.864862	−0.432431	+	0.901667i	$0.642344\pi$
$192$	4.70562e138	3.41109
$193$	−2.02209e138	−1.07049	−0.535245	−	0.844697i	$-0.679781\pi$
$193$	−2.02209e138	−1.07049	−0.535245	+	0.844697i	$0.679781\pi$
$194$	8.07400e137	0.312668
$195$	−3.95697e137	−0.112271
$196$	1.56127e139	3.25077
$197$	−8.41841e138	−1.28832	−0.644159	−	0.764891i	$-0.722793\pi$
$197$	−8.41841e138	−1.28832	−0.644159	+	0.764891i	$0.722793\pi$
$198$	4.17600e138	0.470453
$199$	−2.01570e139	−1.67423	−0.837115	−	0.547027i	$-0.815760\pi$
$199$	−2.01570e139	−1.67423	−0.837115	+	0.547027i	$0.815760\pi$
$200$	5.43031e139	3.33051
$201$	−6.75218e138	−0.306254
$202$	−5.98586e139	−2.01080
$203$	−5.53481e139	−1.37909
$204$	−4.87359e139	−0.902036
$205$	6.93974e137	0.00955509
$206$	−1.67807e140	−1.72125
$207$	2.25010e139	0.172185
$208$	7.29322e140	4.16953
$209$	−2.51423e140	−1.07536
$210$	9.10237e139	0.291667
$211$	4.97994e140	1.19711	0.598557	−	0.801080i	$-0.295741\pi$
$211$	4.97994e140	1.19711	0.598557	+	0.801080i	$0.295741\pi$
$212$	−1.60571e141	−2.89967
$213$	−8.15744e140	−1.10812
$214$	8.50162e140	0.869898
$215$	−8.67219e139	−0.0669271
$216$	6.24021e141	3.63704
$217$	−2.00253e141	−0.882603
$218$	−3.34360e141	−1.11583
$219$	5.31321e141	1.34427
$220$	−1.82340e141	−0.350196
$221$	−2.80680e141	−0.409713
$222$	2.13777e142	2.37469
$223$	8.37115e141	0.708501	0.354251	−	0.935150i	$-0.384736\pi$
$223$	8.37115e141	0.708501	0.354251	+	0.935150i	$0.384736\pi$
$224$	−9.04969e142	−5.84290
$225$	4.40199e141	0.217073
$226$	2.89929e141	0.109328
$227$	3.12339e142	0.901699	0.450850	−	0.892600i	$-0.351121\pi$
$227$	3.12339e142	0.901699	0.450850	+	0.892600i	$0.351121\pi$
$228$	−1.06590e143	−2.35863
$229$	5.42978e142	0.922010	0.461005	−	0.887398i	$-0.347489\pi$
$229$	5.42978e142	0.922010	0.461005	+	0.887398i	$0.347489\pi$
$230$	−1.34047e142	−0.174874
$231$	1.43759e143	1.44248
$232$	4.07641e143	3.14960
$233$	−1.21905e143	−0.726086	−0.363043	−	0.931772i	$-0.618262\pi$
$233$	−1.21905e143	−0.726086	−0.363043	+	0.931772i	$0.618262\pi$
$234$	1.01962e143	0.468681
$235$	2.61866e142	0.0929978
$236$	−1.18697e144	−3.26036
$237$	2.72463e143	0.579472
$238$	6.45660e143	1.06438
$239$	1.18793e144	1.51957	0.759783	−	0.650177i	$-0.225305\pi$
$239$	1.18793e144	1.51957	0.759783	+	0.650177i	$0.225305\pi$
$240$	−3.88720e143	−0.386240
$241$	−1.76523e144	−1.36386	−0.681930	−	0.731417i	$-0.738859\pi$
$241$	−1.76523e144	−1.36386	−0.681930	+	0.731417i	$0.738859\pi$
$242$	−7.11628e143	−0.427980
$243$	9.20482e143	0.431356
$244$	−1.25272e144	−0.457901
$245$	−4.79247e143	−0.136776
$246$	6.33975e143	0.141416
$247$	−6.13877e144	−1.07131
$248$	1.47488e145	2.01571
$249$	−4.25636e144	−0.456013
$250$	−5.28032e144	−0.443905
$251$	−2.47132e145	−1.63181	−0.815905	−	0.578186i	$-0.803761\pi$
$251$	−2.47132e145	−1.63181	−0.815905	+	0.578186i	$0.803761\pi$
$252$	−1.71907e145	−0.892405
$253$	−2.11709e145	−0.864864
$254$	1.04216e146	3.35346
$255$	1.49599e144	0.0379532
$256$	1.47351e146	2.95008
$257$	1.04412e146	1.65119	0.825597	−	0.564260i	$-0.190839\pi$
$257$	1.04412e146	1.65119	0.825597	+	0.564260i	$0.190839\pi$
$258$	−7.92242e145	−0.990525
$259$	−2.07578e146	−2.05374
$260$	−4.45205e145	−0.348877
$261$	3.30447e145	0.205282
$262$	−3.30769e146	−1.63041
$263$	1.30358e146	0.510289	0.255144	−	0.966903i	$-0.417877\pi$
$263$	1.30358e146	0.510289	0.255144	+	0.966903i	$0.417877\pi$
$264$	−1.05879e147	−3.29438
$265$	4.92888e145	0.122004
$266$	1.41212e147	2.78313
$267$	4.46471e146	0.701233
$268$	−7.59697e146	−0.951668
$269$	−2.27147e145	−0.0227140	−0.0113570	−	0.999936i	$-0.503615\pi$
$269$	−2.27147e145	−0.0227140	−0.0113570	+	0.999936i	$0.503615\pi$
$270$	−3.01356e146	−0.240754
$271$	1.42516e147	0.910380	0.455190	−	0.890394i	$-0.349571\pi$
$271$	1.42516e147	0.910380	0.455190	+	0.890394i	$0.349571\pi$
$272$	−2.75731e147	−1.40951
$273$	3.51004e147	1.43705
$274$	7.32970e147	2.40534
$275$	−4.14178e147	−1.09033
$276$	−8.97538e147	−1.89694
$277$	−2.95189e147	−0.501272	−0.250636	−	0.968081i	$-0.580640\pi$
$277$	−2.95189e147	−0.501272	−0.250636	+	0.968081i	$0.580640\pi$
$278$	5.99708e147	0.818898
$279$	1.19558e147	0.131379
$280$	6.50955e147	0.576090
$281$	4.26967e147	0.304552	0.152276	−	0.988338i	$-0.451340\pi$
$281$	4.26967e147	0.304552	0.152276	+	0.988338i	$0.451340\pi$
$282$	2.39225e148	1.37637
$283$	3.27763e148	1.52223	0.761115	−	0.648616i	$-0.224652\pi$
$283$	3.27763e148	1.52223	0.761115	+	0.648616i	$0.224652\pi$
$284$	−9.17806e148	−3.44343
$285$	3.27189e147	0.0992395
$286$	−9.59345e148	−2.35413
$287$	−6.15592e147	−0.122303
$288$	5.40298e148	0.869737
$289$	−6.60044e148	−0.861497
$290$	−1.96861e148	−0.208488
$291$	−1.65945e148	−0.142705
$292$	5.97797e149	4.17726
$293$	−2.79666e149	−1.58909	−0.794546	−	0.607204i	$-0.792291\pi$
$293$	−2.79666e149	−1.58909	−0.794546	+	0.607204i	$0.792291\pi$
$294$	−4.37813e149	−2.02430
$295$	3.64353e148	0.137180
$296$	1.52883e150	4.69039
$297$	−4.75950e149	−1.19068
$298$	7.96746e149	1.62643
$299$	−5.16911e149	−0.861607
$300$	−1.75590e150	−2.39147
$301$	7.69269e149	0.856654
$302$	−4.55540e149	−0.415056
$303$	1.23027e150	0.917746
$304$	−6.03053e150	−3.68556
$305$	3.84535e148	0.0192662
$306$	−3.85482e149	−0.158437
$307$	−4.70281e150	−1.58667	−0.793333	−	0.608788i	$-0.791656\pi$
$307$	−4.70281e150	−1.58667	−0.793333	+	0.608788i	$0.791656\pi$
$308$	1.61746e151	4.48244
$309$	3.44893e150	0.785592
$310$	−7.12257e149	−0.133430
$311$	9.84619e150	1.51798	0.758988	−	0.651105i	$-0.225694\pi$
$311$	9.84619e150	1.51798	0.758988	+	0.651105i	$0.225694\pi$
$312$	−2.58516e151	−3.28197
$313$	6.04908e150	0.632786	0.316393	−	0.948628i	$-0.397528\pi$
$313$	6.04908e150	0.632786	0.316393	+	0.948628i	$0.397528\pi$
$314$	−3.80710e151	−3.28361
$315$	5.27685e149	0.0375480
$316$	3.06552e151	1.80068
$317$	3.73586e151	1.81261	0.906307	−	0.422621i	$-0.138890\pi$
$317$	3.73586e151	1.81261	0.906307	+	0.422621i	$0.138890\pi$
$318$	4.50275e151	1.80566
$319$	−3.10914e151	−1.03111
$320$	−1.62515e151	−0.445986
$321$	−1.74734e151	−0.397029
$322$	1.18907e152	2.23835
$323$	2.32085e151	0.362156
$324$	−1.55128e152	−2.00778
$325$	−1.01126e152	−1.08623
$326$	−9.41877e151	−0.840097
$327$	6.87210e151	0.509273
$328$	4.53386e151	0.279319
$329$	−2.32289e152	−1.19035
$330$	5.11320e151	0.218072
$331$	−1.40951e152	−0.500581	−0.250290	−	0.968171i	$-0.580526\pi$
$331$	−1.40951e152	−0.500581	−0.250290	+	0.968171i	$0.580526\pi$
$332$	−4.78889e152	−1.41704
$333$	1.23932e152	0.305707
$334$	5.26865e152	1.08402
$335$	2.33196e151	0.0400415
$336$	3.44815e153	4.94379
$337$	−1.04271e153	−1.24897	−0.624487	−	0.781035i	$-0.714692\pi$
$337$	−1.04271e153	−1.24897	−0.624487	+	0.781035i	$0.714692\pi$
$338$	−4.09705e152	−0.410214
$339$	−5.95890e151	−0.0498981
$340$	1.68316e152	0.117938
$341$	−1.12491e153	−0.659899
$342$	−8.43088e152	−0.414279
$343$	6.62195e152	0.272704
$344$	−5.66571e153	−1.95645
$345$	2.75508e152	0.0798139
$346$	2.34482e153	0.570172
$347$	3.29335e153	0.672520	0.336260	−	0.941769i	$-0.390838\pi$
$347$	3.29335e153	0.672520	0.336260	+	0.941769i	$0.390838\pi$
$348$	−1.31812e154	−2.26157
$349$	1.13526e154	1.63741	0.818703	−	0.574217i	$-0.194694\pi$
$349$	1.13526e154	1.63741	0.818703	+	0.574217i	$0.194694\pi$
$350$	2.32624e154	2.82188
$351$	−1.16209e154	−1.18620
$352$	−5.08360e154	−4.36858
$353$	4.79809e153	0.347295	0.173648	−	0.984808i	$-0.444445\pi$
$353$	4.79809e153	0.347295	0.173648	+	0.984808i	$0.444445\pi$
$354$	3.32852e154	2.03027
$355$	2.81729e153	0.144882
$356$	5.02332e154	2.17904
$357$	−1.32702e154	−0.485794
$358$	−6.49320e154	−2.00695
$359$	−1.17791e154	−0.307537	−0.153768	−	0.988107i	$-0.549141\pi$
$359$	−1.17791e154	−0.307537	−0.153768	+	0.988107i	$0.549141\pi$
$360$	−3.88643e153	−0.0857531
$361$	−2.84314e153	−0.0530410
$362$	2.24517e154	0.354308
$363$	1.46261e154	0.195334
$364$	3.94920e155	4.46555
$365$	−1.83499e154	−0.175758
$366$	3.51289e154	0.285141
$367$	−1.03504e155	−0.712293	−0.356147	−	0.934430i	$-0.615910\pi$
$367$	−1.03504e155	−0.712293	−0.356147	+	0.934430i	$0.615910\pi$
$368$	−5.07797e155	−2.96413
$369$	3.67530e153	0.0182053
$370$	−7.38310e154	−0.310481
$371$	−4.37218e155	−1.56162
$372$	−4.76904e155	−1.44738
$373$	−1.83287e155	−0.472876	−0.236438	−	0.971647i	$-0.575980\pi$
$373$	−1.83287e155	−0.472876	−0.236438	+	0.971647i	$0.575980\pi$
$374$	3.62695e155	0.795811
$375$	1.08526e155	0.202602
$376$	1.71082e156	2.71856
$377$	−7.59131e155	−1.02722
$378$	2.67319e156	3.08160
$379$	−1.39674e156	−1.37228	−0.686142	−	0.727467i	$-0.740697\pi$
$379$	−1.39674e156	−1.37228	−0.686142	+	0.727467i	$0.740697\pi$
$380$	3.68125e155	0.308381
$381$	−2.14194e156	−1.53055
$382$	2.74456e156	1.67355
$383$	2.61421e156	1.36086	0.680431	−	0.732812i	$-0.261793\pi$
$383$	2.61421e156	1.36086	0.680431	+	0.732812i	$0.261793\pi$
$384$	−6.99347e156	−3.10924
$385$	−4.96493e155	−0.188599
$386$	6.37979e156	2.07145
$387$	−4.59281e155	−0.127516
$388$	−1.86707e156	−0.443446
$389$	−1.75164e156	−0.356037	−0.178019	−	0.984027i	$-0.556969\pi$
$389$	−1.75164e156	−0.356037	−0.178019	+	0.984027i	$0.556969\pi$
$390$	1.24844e156	0.217250
$391$	1.95426e156	0.291266
$392$	−3.13101e157	−3.99832
$393$	6.79829e156	0.744132
$394$	2.65605e157	2.49296
$395$	−9.40989e155	−0.0757635
$396$	−9.65678e156	−0.667227
$397$	3.10985e156	0.184465	0.0922325	−	0.995737i	$-0.470600\pi$
$397$	3.10985e156	0.184465	0.0922325	+	0.995737i	$0.470600\pi$
$398$	6.35964e157	3.23971
$399$	−2.90234e157	−1.27025
$400$	−9.93431e157	−3.73687
$401$	−2.57919e157	−0.834158	−0.417079	−	0.908870i	$-0.636946\pi$
$401$	−2.57919e157	−0.834158	−0.417079	+	0.908870i	$0.636946\pi$
$402$	2.13035e157	0.592617
$403$	−2.74659e157	−0.657414
$404$	1.38420e158	2.85184
$405$	4.76179e156	0.0844776
$406$	1.74626e158	2.66860
$407$	−1.16606e158	−1.53553
$408$	9.77361e157	1.10947
$409$	−4.37869e157	−0.428632	−0.214316	−	0.976764i	$-0.568752\pi$
$409$	−4.37869e157	−0.428632	−0.214316	+	0.976764i	$0.568752\pi$
$410$	−2.18952e156	−0.0184895
$411$	−1.50647e158	−1.09782
$412$	3.88045e158	2.44118
$413$	−3.23200e158	−1.75587
$414$	−7.09917e157	−0.333186
$415$	1.46999e157	0.0596219
$416$	−1.24122e159	−4.35213
$417$	−1.23258e158	−0.373752
$418$	7.93251e158	2.08087
$419$	6.07929e158	1.38008	0.690040	−	0.723771i	$-0.257593\pi$
$419$	6.07929e158	1.38008	0.690040	+	0.723771i	$0.257593\pi$
$420$	−2.10488e158	−0.413661
$421$	−2.90200e158	−0.493890	−0.246945	−	0.969030i	$-0.579427\pi$
$421$	−2.90200e158	−0.493890	−0.246945	+	0.969030i	$0.579427\pi$
$422$	−1.57120e159	−2.31647
$423$	1.38684e158	0.177188
$424$	3.22013e159	3.56648
$425$	3.82323e158	0.367198
$426$	2.57371e159	2.14427
$427$	−3.41103e158	−0.246604
$428$	−1.96595e159	−1.23375
$429$	1.97174e159	1.07444
$430$	2.73612e158	0.129507
$431$	−8.47725e158	−0.348642	−0.174321	−	0.984689i	$-0.555773\pi$
$431$	−8.47725e158	−0.348642	−0.174321	+	0.984689i	$0.555773\pi$
$432$	−1.14160e160	−4.08080
$433$	−2.59134e159	−0.805389	−0.402695	−	0.915334i	$-0.631926\pi$
$433$	−2.59134e159	−0.805389	−0.402695	+	0.915334i	$0.631926\pi$
$434$	6.31809e159	1.70788
$435$	4.04608e158	0.0951556
$436$	7.73190e159	1.58254
$437$	4.27417e159	0.761597
$438$	−1.67634e160	−2.60124
$439$	1.45946e160	1.97282	0.986412	−	0.164289i	$-0.0525329\pi$
$439$	1.45946e160	1.97282	0.986412	+	0.164289i	$0.0525329\pi$
$440$	3.65670e159	0.430727
$441$	−2.53810e159	−0.260600
$442$	8.85561e159	0.792814
$443$	−1.10632e160	−0.863886	−0.431943	−	0.901901i	$-0.642172\pi$
$443$	−1.10632e160	−0.863886	−0.431943	+	0.901901i	$0.642172\pi$
$444$	−4.94349e160	−3.36793
$445$	−1.54195e159	−0.0916833
$446$	−2.64114e160	−1.37098
$447$	−1.63755e160	−0.742318
$448$	1.44160e161	5.70853
$449$	9.83261e159	0.340224	0.170112	−	0.985425i	$-0.445587\pi$
$449$	9.83261e159	0.340224	0.170112	+	0.985425i	$0.445587\pi$
$450$	−1.38885e160	−0.420047
$451$	−3.45804e159	−0.0914428
$452$	−6.70445e159	−0.155056
$453$	9.36271e159	0.189435
$454$	−9.85445e160	−1.74483
$455$	−1.21224e160	−0.187888
$456$	2.13759e161	2.90102
$457$	1.27516e161	1.51578	0.757889	−	0.652383i	$-0.226231\pi$
$457$	1.27516e161	1.51578	0.757889	+	0.652383i	$0.226231\pi$
$458$	−1.71312e161	−1.78413
$459$	4.39344e160	0.400994
$460$	3.09978e160	0.248017
$461$	−9.46766e160	−0.664258	−0.332129	−	0.943234i	$-0.607767\pi$
$461$	−9.46766e160	−0.664258	−0.332129	+	0.943234i	$0.607767\pi$
$462$	−4.53567e161	−2.79127
$463$	3.40920e161	1.84078	0.920390	−	0.391001i	$-0.127871\pi$
$463$	3.40920e161	1.84078	0.920390	+	0.391001i	$0.127871\pi$
$464$	−7.45746e161	−3.53389
$465$	1.46390e160	0.0608987
$466$	3.84617e161	1.40501
$467$	−6.74035e160	−0.216277	−0.108139	−	0.994136i	$-0.534489\pi$
$467$	−6.74035e160	−0.216277	−0.108139	+	0.994136i	$0.534489\pi$
$468$	−2.35781e161	−0.664714
$469$	−2.06857e161	−0.512523
$470$	−8.26199e160	−0.179955
$471$	7.82473e161	1.49867
$472$	2.38039e162	4.01011
$473$	4.32132e161	0.640497
$474$	−8.59634e161	−1.12131
$475$	8.36179e161	0.960143
$476$	−1.49306e162	−1.50958
$477$	2.61034e161	0.232453
$478$	−3.74799e162	−2.94043
$479$	1.27792e162	0.883496	0.441748	−	0.897139i	$-0.354359\pi$
$479$	1.27792e162	0.883496	0.441748	+	0.897139i	$0.354359\pi$
$480$	6.61554e161	0.403154
$481$	−2.84706e162	−1.52975
$482$	5.56939e162	2.63913
$483$	−2.44390e162	−1.02160
$484$	1.64560e162	0.606988
$485$	5.73114e160	0.0186580
$486$	−2.90417e162	−0.834695
$487$	−2.98443e162	−0.757459	−0.378729	−	0.925507i	$-0.623639\pi$
$487$	−2.98443e162	−0.757459	−0.378729	+	0.925507i	$0.623639\pi$
$488$	2.51224e162	0.563200
$489$	1.93584e162	0.383427
$490$	1.51205e162	0.264669
$491$	−9.03045e162	−1.39727	−0.698633	−	0.715480i	$-0.746208\pi$
$491$	−9.03045e162	−1.39727	−0.698633	+	0.715480i	$0.746208\pi$
$492$	−1.46603e162	−0.200565
$493$	2.87001e162	0.347252
$494$	1.93681e163	2.07304
$495$	2.96424e161	0.0280736
$496$	−2.69816e163	−2.26166
$497$	−2.49908e163	−1.85447
$498$	1.34290e163	0.882408
$499$	2.96139e162	0.172350	0.0861751	−	0.996280i	$-0.472536\pi$
$499$	2.96139e162	0.172350	0.0861751	+	0.996280i	$0.472536\pi$
$500$	1.22105e163	0.629575
$501$	−1.08287e163	−0.494757
$502$	7.79715e163	3.15763
$503$	1.25964e163	0.452254	0.226127	−	0.974098i	$-0.427394\pi$
$503$	1.25964e163	0.452254	0.226127	+	0.974098i	$0.427394\pi$
$504$	3.44747e163	1.09762
$505$	−4.24892e162	−0.119991
$506$	6.67953e163	1.67355
$507$	8.42066e162	0.187225
$508$	−2.40993e164	−4.75609
$509$	−7.45036e163	−1.30542	−0.652712	−	0.757606i	$-0.726369\pi$
$509$	−7.45036e163	−1.30542	−0.652712	+	0.757606i	$0.726369\pi$
$510$	−4.71993e162	−0.0734413
$511$	1.62774e164	2.24967
$512$	−1.78190e164	−2.18802
$513$	9.60890e163	1.04851
$514$	−3.29426e164	−3.19514
$515$	−1.19114e163	−0.102713
$516$	1.83202e164	1.40483
$517$	−1.30486e164	−0.889995
$518$	6.54920e164	3.97409
$519$	−4.81931e163	−0.260231
$520$	8.92823e163	0.429105
$521$	−2.37273e164	−1.01523	−0.507617	−	0.861583i	$-0.669473\pi$
$521$	−2.37273e164	−1.01523	−0.507617	+	0.861583i	$0.669473\pi$
$522$	−1.04258e164	−0.397231
$523$	−1.04340e164	−0.354078	−0.177039	−	0.984204i	$-0.556652\pi$
$523$	−1.04340e164	−0.354078	−0.177039	+	0.984204i	$0.556652\pi$
$524$	7.64885e164	2.31235
$525$	−4.78113e164	−1.28793
$526$	−4.11287e164	−0.987433
$527$	1.03839e164	0.222238
$528$	1.93698e165	3.69634
$529$	−2.27677e164	−0.387482
$530$	−1.55509e164	−0.236083
$531$	1.92962e164	0.261368
$532$	−3.26546e165	−3.94722
$533$	−8.44320e163	−0.0910984
$534$	−1.40864e165	−1.35692
$535$	6.03468e163	0.0519099
$536$	1.52351e165	1.17051
$537$	1.33455e165	0.915987
$538$	7.16661e163	0.0439527
$539$	2.38807e165	1.30896
$540$	6.96871e164	0.341452
$541$	−2.20936e164	−0.0967902	−0.0483951	−	0.998828i	$-0.515411\pi$
$541$	−2.20936e164	−0.0967902	−0.0483951	+	0.998828i	$0.515411\pi$
$542$	−4.49647e165	−1.76163
$543$	−4.61450e164	−0.161709
$544$	4.69262e165	1.47123
$545$	−2.37338e164	−0.0665853
$546$	−1.10744e166	−2.78076
$547$	6.97902e165	1.56878	0.784388	−	0.620270i	$-0.212977\pi$
$547$	6.97902e165	1.56878	0.784388	+	0.620270i	$0.212977\pi$
$548$	−1.69496e166	−3.41141
$549$	2.03651e164	0.0367078
$550$	1.30675e166	2.10984
$551$	6.27701e165	0.907989
$552$	1.79994e166	2.33316
$553$	8.34707e165	0.969758
$554$	9.31335e165	0.969985
$555$	1.51745e165	0.141706
$556$	−1.38679e166	−1.16141
$557$	−1.85300e166	−1.39199	−0.695996	−	0.718046i	$-0.745037\pi$
$557$	−1.85300e166	−1.39199	−0.695996	+	0.718046i	$0.745037\pi$
$558$	−3.77212e165	−0.254224
$559$	1.05510e166	0.638085
$560$	−1.19087e166	−0.646380
$561$	−7.45447e165	−0.363215
$562$	−1.34710e166	−0.589324
$563$	2.74224e166	1.07733	0.538663	−	0.842521i	$-0.318930\pi$
$563$	2.74224e166	1.07733	0.538663	+	0.842521i	$0.318930\pi$
$564$	−5.53196e166	−1.95206
$565$	2.05799e164	0.00652398
$566$	−1.03411e167	−2.94559
$567$	−4.22396e166	−1.08130
$568$	1.84059e167	4.23528
$569$	−8.57394e165	−0.177373	−0.0886866	−	0.996060i	$-0.528267\pi$
$569$	−8.57394e165	−0.177373	−0.0886866	+	0.996060i	$0.528267\pi$
$570$	−1.03230e166	−0.192033
$571$	−5.75847e166	−0.963436	−0.481718	−	0.876326i	$-0.659987\pi$
$571$	−5.75847e166	−0.963436	−0.481718	+	0.876326i	$0.659987\pi$
$572$	2.21844e167	3.33878
$573$	−5.64088e166	−0.763822
$574$	1.94222e166	0.236663
$575$	7.04100e166	0.772200
$576$	−8.60684e166	−0.849735
$577$	7.82380e166	0.695474	0.347737	−	0.937592i	$-0.386950\pi$
$577$	7.82380e166	0.695474	0.347737	+	0.937592i	$0.386950\pi$
$578$	2.08247e167	1.66704
$579$	−1.31124e167	−0.945428
$580$	4.55230e166	0.295691
$581$	−1.30396e167	−0.763148
$582$	5.23564e166	0.276140
$583$	−2.45604e167	−1.16758
$584$	−1.19884e168	−5.13786
$585$	7.23752e165	0.0279679
$586$	8.82361e167	3.07497
$587$	3.02780e167	0.951749	0.475874	−	0.879513i	$-0.342132\pi$
$587$	3.02780e167	0.951749	0.475874	+	0.879513i	$0.342132\pi$
$588$	1.01242e168	2.87099
$589$	2.27107e167	0.581105
$590$	−1.14955e167	−0.265449
$591$	−5.45898e167	−1.13781
$592$	−2.79686e168	−5.26268
$593$	1.09740e168	1.86447	0.932236	−	0.361852i	$-0.117855\pi$
$593$	1.09740e168	1.86447	0.932236	+	0.361852i	$0.117855\pi$
$594$	1.50165e168	2.30403
$595$	4.58307e166	0.0635156
$596$	−1.84243e168	−2.30671
$597$	−1.30710e168	−1.47863
$598$	1.63088e168	1.66725
$599$	−2.60355e167	−0.240571	−0.120286	−	0.992739i	$-0.538381\pi$
$599$	−2.60355e167	−0.240571	−0.120286	+	0.992739i	$0.538381\pi$
$600$	3.52133e168	2.94141
$601$	5.97035e167	0.450915	0.225457	−	0.974253i	$-0.427612\pi$
$601$	5.97035e167	0.450915	0.225457	+	0.974253i	$0.427612\pi$
$602$	−2.42708e168	−1.65767
$603$	1.23501e167	0.0762910
$604$	1.05341e168	0.588659
$605$	−5.05132e166	−0.0255391
$606$	−3.88157e168	−1.77588
$607$	6.06985e167	0.251340	0.125670	−	0.992072i	$-0.459892\pi$
$607$	6.06985e167	0.251340	0.125670	+	0.992072i	$0.459892\pi$
$608$	1.02632e169	3.84696
$609$	−3.58908e168	−1.21797
$610$	−1.21323e167	−0.0372810
$611$	−3.18597e168	−0.886643
$612$	8.91407e167	0.224706
$613$	−2.95596e167	−0.0675055	−0.0337528	−	0.999430i	$-0.510746\pi$
$613$	−2.95596e167	−0.0675055	−0.0337528	+	0.999430i	$0.510746\pi$
$614$	1.48376e169	3.07027
$615$	4.50012e166	0.00843879
$616$	−3.24368e169	−5.51322
$617$	7.36632e168	1.13501	0.567503	−	0.823372i	$-0.307910\pi$
$617$	7.36632e168	1.13501	0.567503	+	0.823372i	$0.307910\pi$
$618$	−1.08816e169	−1.52016
$619$	−1.07520e169	−1.36209	−0.681045	−	0.732242i	$-0.738474\pi$
$619$	−1.07520e169	−1.36209	−0.681045	+	0.732242i	$0.738474\pi$
$620$	1.64706e168	0.189239
$621$	8.09112e168	0.843271
$622$	−3.10652e169	−2.93736
$623$	1.36779e169	1.17353
$624$	4.72934e169	3.68242
$625$	1.35860e169	0.960177
$626$	−1.90852e169	−1.22447
$627$	−1.63037e169	−0.949729
$628$	8.80373e169	4.65702
$629$	1.07637e169	0.517129
$630$	−1.66487e168	−0.0726571
$631$	9.17817e168	0.363898	0.181949	−	0.983308i	$-0.441759\pi$
$631$	9.17817e168	0.363898	0.181949	+	0.983308i	$0.441759\pi$
$632$	−6.14766e169	−2.21476
$633$	3.22928e169	1.05726
$634$	−1.17868e170	−3.50749
$635$	7.39751e168	0.200113
$636$	−1.04124e170	−2.56091
$637$	5.83074e169	1.30403
$638$	9.80949e169	1.99524
$639$	1.49204e169	0.276044
$640$	2.41529e169	0.406520
$641$	−6.57131e169	−1.00633	−0.503166	−	0.864190i	$-0.667831\pi$
$641$	−6.57131e169	−1.00633	−0.503166	+	0.864190i	$0.667831\pi$
$642$	5.51293e169	0.768270
$643$	1.14526e170	1.45257	0.726287	−	0.687391i	$-0.241244\pi$
$643$	1.14526e170	1.45257	0.726287	+	0.687391i	$0.241244\pi$
$644$	−2.74967e170	−3.17457
$645$	−5.62355e168	−0.0591082
$646$	−7.32241e169	−0.700789
$647$	−4.71075e169	−0.410565	−0.205282	−	0.978703i	$-0.565811\pi$
$647$	−4.71075e169	−0.410565	−0.205282	+	0.978703i	$0.565811\pi$
$648$	3.11097e170	2.46949
$649$	−1.81555e170	−1.31282
$650$	3.19058e170	2.10190
$651$	−1.29856e170	−0.779491
$652$	2.17804e170	1.19148
$653$	−3.12900e170	−1.56012	−0.780061	−	0.625703i	$-0.784812\pi$
$653$	−3.12900e170	−1.56012	−0.780061	+	0.625703i	$0.784812\pi$
$654$	−2.16818e170	−0.985467
$655$	−2.34789e169	−0.0972923
$656$	−8.29433e169	−0.313400
$657$	−9.71815e169	−0.334872
$658$	7.32882e170	2.30339
$659$	−1.50634e169	−0.0431871	−0.0215935	−	0.999767i	$-0.506874\pi$
$659$	−1.50634e169	−0.0431871	−0.0215935	+	0.999767i	$0.506874\pi$
$660$	−1.18240e170	−0.309283
$661$	2.71665e167	0.000648405 0	0.000324202	−	1.00000i	$-0.499897\pi$
$661$	2.71665e167	0.000648405 0	0.000324202		1.00000i	$0.499897\pi$
$662$	4.44707e170	0.968647
$663$	−1.82009e170	−0.361847
$664$	9.60375e170	1.74290
$665$	1.00236e170	0.166079
$666$	−3.91010e170	−0.591558
$667$	5.28552e170	0.730255
$668$	−1.21835e171	−1.53743
$669$	5.42833e170	0.625729
$670$	−7.35745e169	−0.0774822
$671$	−1.91612e170	−0.184379
$672$	−5.86834e171	−5.16029
$673$	−2.31625e171	−1.86155	−0.930773	−	0.365598i	$-0.880864\pi$
$673$	−2.31625e171	−1.86155	−0.930773	+	0.365598i	$0.880864\pi$
$674$	3.28979e171	2.41682
$675$	1.58291e171	1.06311
$676$	9.47421e170	0.581792
$677$	4.96619e170	0.278874	0.139437	−	0.990231i	$-0.455471\pi$
$677$	4.96619e170	0.278874	0.139437	+	0.990231i	$0.455471\pi$
$678$	1.88006e170	0.0965552
$679$	−5.08382e170	−0.238819
$680$	−3.37546e170	−0.145058
$681$	2.02538e171	0.796356
$682$	3.54914e171	1.27694
$683$	−1.27981e171	−0.421400	−0.210700	−	0.977551i	$-0.567574\pi$
$683$	−1.27981e171	−0.421400	−0.210700	+	0.977551i	$0.567574\pi$
$684$	1.94960e171	0.587558
$685$	5.20282e170	0.143535
$686$	−2.08926e171	−0.527695
$687$	3.52098e171	0.814293
$688$	1.03649e172	2.19516
$689$	−5.99670e171	−1.16319
$690$	−8.69240e170	−0.154444
$691$	−3.53473e171	−0.575354	−0.287677	−	0.957728i	$-0.592883\pi$
$691$	−3.53473e171	−0.575354	−0.287677	+	0.957728i	$0.592883\pi$
$692$	−5.42228e171	−0.808655
$693$	−2.62943e171	−0.359337
$694$	−1.03907e172	−1.30136
$695$	4.25689e170	0.0488665
$696$	2.64338e172	2.78164
$697$	3.19208e170	0.0307958
$698$	−3.58180e172	−3.16846
$699$	−7.90502e171	−0.641259
$700$	−5.37932e172	−4.00217
$701$	1.27727e172	0.871650	0.435825	−	0.900031i	$-0.356457\pi$
$701$	1.27727e172	0.871650	0.435825	+	0.900031i	$0.356457\pi$
$702$	3.66644e172	2.29535
$703$	2.35414e172	1.35218
$704$	8.09808e172	4.26811
$705$	1.69809e171	0.0821331
$706$	−1.51382e172	−0.672033
$707$	3.76902e172	1.53587
$708$	−7.69702e172	−2.87946
$709$	−4.13547e172	−1.42046	−0.710229	−	0.703971i	$-0.751408\pi$
$709$	−4.13547e172	−1.42046	−0.710229	+	0.703971i	$0.751408\pi$
$710$	−8.88869e171	−0.280354
$711$	−4.98349e171	−0.144352
$712$	−1.00739e173	−2.68014
$713$	1.91234e172	0.467356
$714$	4.18683e172	0.940034
$715$	−6.80969e171	−0.140479
$716$	1.50152e173	2.84638
$717$	7.70325e172	1.34204
$718$	3.71636e172	0.595099
$719$	−9.14867e172	−1.34667	−0.673334	−	0.739339i	$-0.735138\pi$
$719$	−9.14867e172	−1.34667	−0.673334	+	0.739339i	$0.735138\pi$
$720$	7.10990e171	0.0962161
$721$	1.05660e173	1.31471
$722$	8.97024e171	0.102637
$723$	−1.14468e173	−1.20452
$724$	−5.19184e172	−0.502503
$725$	1.03403e173	0.920631
$726$	−4.61460e172	−0.377980
$727$	1.34806e173	1.01596	0.507979	−	0.861369i	$-0.330393\pi$
$727$	1.34806e173	1.01596	0.507979	+	0.861369i	$0.330393\pi$
$728$	−7.91981e173	−5.49245
$729$	1.74315e173	1.11255
$730$	5.78950e172	0.340101
$731$	−3.98896e172	−0.215704
$732$	−8.12338e172	−0.404405
$733$	−3.32608e173	−1.52455	−0.762276	−	0.647252i	$-0.775918\pi$
$733$	−3.32608e173	−1.52455	−0.762276	+	0.647252i	$0.775918\pi$
$734$	3.26559e173	1.37832
$735$	−3.10771e172	−0.120797
$736$	8.64209e173	3.09394
$737$	−1.16201e173	−0.383200
$738$	−1.15957e172	−0.0352281
$739$	−6.46611e173	−1.80990	−0.904949	−	0.425519i	$-0.860091\pi$
$739$	−6.46611e173	−1.80990	−0.904949	+	0.425519i	$0.860091\pi$
$740$	1.70730e173	0.440344
$741$	−3.98073e173	−0.946152
$742$	1.37945e174	3.02182
$743$	−2.14787e173	−0.433695	−0.216848	−	0.976205i	$-0.569577\pi$
$743$	−2.14787e173	−0.433695	−0.216848	+	0.976205i	$0.569577\pi$
$744$	9.56394e173	1.78022
$745$	5.65552e172	0.0970550
$746$	5.78280e173	0.915037
$747$	7.78511e172	0.113597
$748$	−8.38714e173	−1.12867
$749$	−5.35308e173	−0.664436
$750$	−3.42406e173	−0.392045
$751$	9.34102e173	0.986684	0.493342	−	0.869835i	$-0.335775\pi$
$751$	9.34102e173	0.986684	0.493342	+	0.869835i	$0.335775\pi$
$752$	−3.12980e174	−3.05026
$753$	−1.60255e174	−1.44117
$754$	2.39510e174	1.98773
$755$	−3.23355e172	−0.0247679
$756$	−6.18161e174	−4.37052
$757$	2.02626e174	1.32250	0.661249	−	0.750166i	$-0.270026\pi$
$757$	2.02626e174	1.32250	0.661249	+	0.750166i	$0.270026\pi$
$758$	4.40680e174	2.65544
$759$	−1.37284e174	−0.763824
$760$	−7.38246e173	−0.379297
$761$	2.29415e174	1.08855	0.544277	−	0.838906i	$-0.316804\pi$
$761$	2.29415e174	1.08855	0.544277	+	0.838906i	$0.316804\pi$
$762$	6.75794e174	2.96168
$763$	2.10531e174	0.852279
$764$	−6.34664e174	−2.37354
$765$	−2.73625e172	−0.00945452
$766$	−8.24795e174	−2.63333
$767$	−4.43288e174	−1.30788
$768$	9.55506e174	2.60543
$769$	2.16599e174	0.545900	0.272950	−	0.962028i	$-0.412001\pi$
$769$	2.16599e174	0.545900	0.272950	+	0.962028i	$0.412001\pi$
$770$	1.56646e174	0.364948
$771$	6.77070e174	1.45829
$772$	−1.47529e175	−2.93786
$773$	8.23925e174	1.51715	0.758574	−	0.651587i	$-0.225896\pi$
$773$	8.23925e174	1.51715	0.758574	+	0.651587i	$0.225896\pi$
$774$	1.44905e174	0.246750
$775$	3.74121e174	0.589195
$776$	3.74426e174	0.545421
$777$	−1.34606e175	−1.81381
$778$	5.52653e174	0.688949
$779$	6.98141e173	0.0805242
$780$	−2.88696e174	−0.308118
$781$	−1.40384e175	−1.38654
$782$	−6.16580e174	−0.563613
$783$	1.18825e175	1.00536
$784$	5.72793e175	4.48617
$785$	−2.70238e174	−0.195944
$786$	−2.14489e175	−1.43993
$787$	−8.97856e174	−0.558130	−0.279065	−	0.960272i	$-0.590025\pi$
$787$	−8.97856e174	−0.558130	−0.279065	+	0.960272i	$0.590025\pi$
$788$	−6.14198e175	−3.53567
$789$	8.45318e174	0.450673
$790$	2.96887e174	0.146606
$791$	−1.82555e174	−0.0835056
$792$	1.93659e175	0.820663
$793$	−4.67843e174	−0.183684
$794$	−9.81174e174	−0.356948
$795$	3.19617e174	0.107750
$796$	−1.47063e176	−4.59477
$797$	−3.07497e174	−0.0890456	−0.0445228	−	0.999008i	$-0.514177\pi$
$797$	−3.07497e174	−0.0890456	−0.0445228	+	0.999008i	$0.514177\pi$
$798$	9.15702e175	2.45799
$799$	1.20451e175	0.299729
$800$	1.69070e176	3.90052
$801$	−8.16621e174	−0.174684
$802$	8.13747e175	1.61414
$803$	9.14369e175	1.68202
$804$	−4.92631e175	−0.840487
$805$	8.44035e174	0.133570
$806$	8.66563e175	1.27213
$807$	−1.47295e174	−0.0200604
$808$	−2.77590e176	−3.50765
$809$	−2.37724e175	−0.278732	−0.139366	−	0.990241i	$-0.544506\pi$
$809$	−2.37724e175	−0.278732	−0.139366	+	0.990241i	$0.544506\pi$
$810$	−1.50237e175	−0.163468
$811$	−8.31494e175	−0.839648	−0.419824	−	0.907605i	$-0.637908\pi$
$811$	−8.31494e175	−0.839648	−0.419824	+	0.907605i	$0.637908\pi$
$812$	−4.03813e176	−3.78478
$813$	9.24158e175	0.804023
$814$	3.67897e176	2.97132
$815$	−6.68570e174	−0.0501316
$816$	−1.78800e176	−1.24484
$817$	−8.72426e175	−0.564020
$818$	1.38150e176	0.829422
$819$	−6.42006e175	−0.357983
$820$	5.06316e174	0.0262231
$821$	2.69914e176	1.29857	0.649283	−	0.760547i	$-0.275069\pi$
$821$	2.69914e176	1.29857	0.649283	+	0.760547i	$0.275069\pi$
$822$	4.75300e176	2.12433
$823$	−1.32791e176	−0.551415	−0.275708	−	0.961242i	$-0.588912\pi$
$823$	−1.32791e176	−0.551415	−0.275708	+	0.961242i	$0.588912\pi$
$824$	−7.78194e176	−3.00256
$825$	−2.68577e176	−0.962951
$826$	1.01971e177	3.39770
$827$	−6.25929e176	−1.93839	−0.969196	−	0.246291i	$-0.920788\pi$
$827$	−6.25929e176	−1.93839	−0.969196	+	0.246291i	$0.920788\pi$
$828$	1.64165e176	0.472546
$829$	−7.84895e175	−0.210021	−0.105011	−	0.994471i	$-0.533488\pi$
$829$	−7.84895e175	−0.210021	−0.105011	+	0.994471i	$0.533488\pi$
$830$	−4.63791e175	−0.115371
$831$	−1.91417e176	−0.442710
$832$	1.97724e177	4.25204
$833$	−2.20440e176	−0.440827
$834$	3.88885e176	0.723228
$835$	3.73983e175	0.0646875
$836$	−1.83435e177	−2.95123
$837$	4.29919e176	0.643423
$838$	−1.91805e177	−2.67052
$839$	−1.68246e176	−0.217944	−0.108972	−	0.994045i	$-0.534756\pi$
$839$	−1.68246e176	−0.217944	−0.108972	+	0.994045i	$0.534756\pi$
$840$	4.22117e176	0.508787
$841$	−1.15349e176	−0.129376
$842$	9.15595e176	0.955700
$843$	2.76870e176	0.268972
$844$	3.63331e177	3.28537
$845$	−2.90820e175	−0.0244789
$846$	−4.37556e176	−0.342868
$847$	4.48079e176	0.326895
$848$	−5.89097e177	−4.00164
$849$	2.12540e177	1.34439
$850$	−1.20625e177	−0.710545
$851$	1.98229e177	1.08750
$852$	−5.95158e177	−3.04114
$853$	9.49378e175	0.0451880	0.0225940	−	0.999745i	$-0.492807\pi$
$853$	9.49378e175	0.0451880	0.0225940	+	0.999745i	$0.492807\pi$
$854$	1.07620e177	0.477189
$855$	−5.98446e175	−0.0247215
$856$	3.94257e177	1.51746
$857$	−3.08724e176	−0.110721	−0.0553606	−	0.998466i	$-0.517631\pi$
$857$	−3.08724e176	−0.110721	−0.0553606	+	0.998466i	$0.517631\pi$
$858$	−6.22094e177	−2.07910
$859$	1.58647e177	0.494135	0.247068	−	0.968998i	$-0.420533\pi$
$859$	1.58647e177	0.494135	0.247068	+	0.968998i	$0.420533\pi$
$860$	−6.32714e176	−0.183675
$861$	−3.99185e176	−0.108015
$862$	2.67462e177	0.674640
$863$	2.88631e177	0.678720	0.339360	−	0.940657i	$-0.389790\pi$
$863$	2.88631e177	0.678720	0.339360	+	0.940657i	$0.389790\pi$
$864$	1.94286e178	4.25951
$865$	1.66442e176	0.0340242
$866$	8.17580e177	1.55847
$867$	−4.28011e177	−0.760850
$868$	−1.46103e178	−2.42222
$869$	4.68891e177	0.725062
$870$	−1.27656e177	−0.184131
$871$	−2.83717e177	−0.381757
$872$	−1.55057e178	−1.94646
$873$	3.03522e176	0.0355491
$874$	−1.34852e178	−1.47373
$875$	3.32478e177	0.339059
$876$	3.87646e178	3.68924
$877$	1.27690e178	1.13418	0.567091	−	0.823655i	$-0.308069\pi$
$877$	1.27690e178	1.13418	0.567091	+	0.823655i	$0.308069\pi$
$878$	−4.60467e178	−3.81751
$879$	−1.81352e178	−1.40344
$880$	−6.68962e177	−0.483281
$881$	−2.39332e178	−1.61420	−0.807102	−	0.590412i	$-0.798965\pi$
$881$	−2.39332e178	−1.61420	−0.807102	+	0.590412i	$0.798965\pi$
$882$	8.00784e177	0.504273
$883$	1.05344e178	0.619420	0.309710	−	0.950831i	$-0.399768\pi$
$883$	1.05344e178	0.619420	0.309710	+	0.950831i	$0.399768\pi$
$884$	−2.04781e178	−1.12442
$885$	2.36267e177	0.121153
$886$	3.49051e178	1.67166
$887$	2.99575e178	1.34007	0.670034	−	0.742330i	$-0.266279\pi$
$887$	2.99575e178	1.34007	0.670034	+	0.742330i	$0.266279\pi$
$888$	9.91378e178	4.14243
$889$	−6.56198e178	−2.56141
$890$	4.86494e177	0.177412
$891$	−2.37278e178	−0.808456
$892$	6.10750e178	1.94442
$893$	2.63438e178	0.783727
$894$	5.16656e178	1.43642
$895$	−4.60905e177	−0.119762
$896$	−2.14249e179	−5.20337
$897$	−3.35195e178	−0.760947
$898$	−3.10224e178	−0.658350
$899$	2.80844e178	0.557191
$900$	3.21164e178	0.595738
$901$	2.26715e178	0.393215
$902$	1.09103e178	0.176946
$903$	4.98838e178	0.756573
$904$	1.34452e178	0.190712
$905$	1.59368e177	0.0211428
$906$	−2.95398e178	−0.366566
$907$	1.76411e178	0.204778	0.102389	−	0.994744i	$-0.467351\pi$
$907$	1.76411e178	0.204778	0.102389	+	0.994744i	$0.467351\pi$
$908$	2.27879e179	2.47463
$909$	−2.25024e178	−0.228619
$910$	3.82469e178	0.363573
$911$	−1.69392e177	−0.0150672	−0.00753359	−	0.999972i	$-0.502398\pi$
$911$	−1.69392e177	−0.0150672	−0.00753359	+	0.999972i	$0.502398\pi$
$912$	−3.91054e179	−3.25498
$913$	−7.32492e178	−0.570586
$914$	−4.02321e179	−2.93310
$915$	2.49355e177	0.0170154
$916$	3.96151e179	2.53037
$917$	2.08270e179	1.24532
$918$	−1.38615e179	−0.775942
$919$	−2.31755e178	−0.121462	−0.0607310	−	0.998154i	$-0.519343\pi$
$919$	−2.31755e178	−0.121462	−0.0607310	+	0.998154i	$0.519343\pi$
$920$	−6.21636e178	−0.305051
$921$	−3.04957e179	−1.40130
$922$	2.98709e179	1.28537
$923$	−3.42764e179	−1.38131
$924$	1.04885e180	3.95876
$925$	3.87806e179	1.37101
$926$	−1.07562e180	−3.56200
$927$	−6.30829e178	−0.195699
$928$	1.26917e180	3.68865
$929$	6.75880e178	0.184043	0.0920214	−	0.995757i	$-0.470667\pi$
$929$	6.75880e178	0.184043	0.0920214	+	0.995757i	$0.470667\pi$
$930$	−4.61868e178	−0.117842
$931$	−4.82125e179	−1.15267
$932$	−8.89406e179	−1.99268
$933$	6.38484e179	1.34063
$934$	2.12662e179	0.418507
$935$	2.57451e178	0.0474889
$936$	4.72841e179	0.817572
$937$	−6.80626e179	−1.10322	−0.551612	−	0.834101i	$-0.685987\pi$
$937$	−6.80626e179	−1.10322	−0.551612	+	0.834101i	$0.685987\pi$
$938$	6.52645e179	0.991757
$939$	3.92257e179	0.558859
$940$	1.91054e179	0.255224
$941$	6.46566e178	0.0809917	0.0404958	−	0.999180i	$-0.487106\pi$
$941$	6.46566e178	0.0809917	0.0404958	+	0.999180i	$0.487106\pi$
$942$	−2.46874e180	−2.89999
$943$	5.87865e178	0.0647620
$944$	−4.35472e180	−4.49940
$945$	1.89750e179	0.183890
$946$	−1.36340e180	−1.23939
$947$	1.28224e180	1.09344	0.546722	−	0.837314i	$-0.315875\pi$
$947$	1.28224e180	1.09344	0.546722	+	0.837314i	$0.315875\pi$
$948$	1.98786e180	1.59031
$949$	2.23254e180	1.67569
$950$	−2.63819e180	−1.85792
$951$	2.42255e180	1.60085
$952$	2.99421e180	1.85672
$953$	1.28155e180	0.745787	0.372893	−	0.927874i	$-0.378366\pi$
$953$	1.28155e180	0.745787	0.372893	+	0.927874i	$0.378366\pi$
$954$	−8.23577e179	−0.449808
$955$	1.94816e179	0.0998667
$956$	8.66704e180	4.17031
$957$	−2.01614e180	−0.910645
$958$	−4.03190e180	−1.70961
$959$	−4.61518e180	−1.83723
$960$	−1.05384e180	−0.393882
$961$	−1.83336e180	−0.643403
$962$	8.98261e180	2.96013
$963$	3.19597e179	0.0989038
$964$	−1.28789e181	−3.74299
$965$	4.52855e179	0.123611
$966$	7.71062e180	1.97685
$967$	−3.78275e180	−0.910975	−0.455488	−	0.890242i	$-0.650535\pi$
$967$	−3.78275e180	−0.910975	−0.455488	+	0.890242i	$0.650535\pi$
$968$	−3.30013e180	−0.746572
$969$	1.50497e180	0.319846
$970$	−1.80820e179	−0.0361042
$971$	3.18096e179	0.0596753	0.0298376	−	0.999555i	$-0.490501\pi$
$971$	3.18096e179	0.0596753	0.0298376	+	0.999555i	$0.490501\pi$
$972$	6.71574e180	1.18382
$973$	−3.77608e180	−0.625482
$974$	9.41603e180	1.46572
$975$	−6.55760e180	−0.959325
$976$	−4.59594e180	−0.631917
$977$	−9.00151e180	−1.16331	−0.581654	−	0.813437i	$-0.697594\pi$
$977$	−9.00151e180	−1.16331	−0.581654	+	0.813437i	$0.697594\pi$
$978$	−6.10767e180	−0.741950
$979$	7.68349e180	0.877416
$980$	−3.49653e180	−0.375371
$981$	−1.25694e180	−0.126865
$982$	2.84915e181	2.70378
$983$	−1.92949e179	−0.0172169	−0.00860845	−	0.999963i	$-0.502740\pi$
$983$	−1.92949e179	−0.0172169	−0.00860845	+	0.999963i	$0.502740\pi$
$984$	2.94002e180	0.246687
$985$	1.88534e180	0.148764
$986$	−9.05503e180	−0.671950
$987$	−1.50629e181	−1.05129
$988$	−4.47878e181	−2.94011
$989$	−7.34621e180	−0.453616
$990$	−9.35232e179	−0.0543238
$991$	1.34655e181	0.735809	0.367905	−	0.929864i	$-0.380075\pi$
$991$	1.34655e181	0.735809	0.367905	+	0.929864i	$0.380075\pi$
$992$	4.59195e181	2.36070
$993$	−9.14006e180	−0.442099
$994$	7.88473e181	3.58848
$995$	4.51424e180	0.193325
$996$	−3.10539e181	−1.25149
$997$	−8.65562e180	−0.328278	−0.164139	−	0.986437i	$-0.552484\pi$
$997$	−8.65562e180	−0.328278	−0.164139	+	0.986437i	$0.552484\pi$
$998$	−9.34332e180	−0.333506
$999$	4.45645e181	1.49719

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.122.a.a.1.1	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.122.a.a.1.1	✓	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 122 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-3.15505e18 q^{2} +6.48457e28 q^{3} +7.29589e36 q^{4} -2.23954e41 q^{5} -2.04592e47 q^{6} +1.98659e51 q^{7} -1.46313e55 q^{8} -1.18606e57 q^{9} +O(q^{10})\)	\(q-3.15505e18 q^{2} +6.48457e28 q^{3} +7.29589e36 q^{4} -2.23954e41 q^{5} -2.04592e47 q^{6} +1.98659e51 q^{7} -1.46313e55 q^{8} -1.18606e57 q^{9} +7.06586e59 q^{10} +1.11595e63 q^{11} +4.73107e65 q^{12} +2.72472e67 q^{13} -6.26779e69 q^{14} -1.45225e70 q^{15} +2.67668e73 q^{16} -1.03012e74 q^{17} +3.74209e75 q^{18} -2.25299e77 q^{19} -1.63394e78 q^{20} +1.28822e80 q^{21} -3.52089e81 q^{22} -1.89711e82 q^{23} -9.48780e83 q^{24} -3.71143e84 q^{25} -8.59665e85 q^{26} -4.26496e86 q^{27} +1.44939e88 q^{28} -2.78608e88 q^{29} +4.58191e88 q^{30} -1.00803e90 q^{31} -4.55539e91 q^{32} +7.23648e91 q^{33} +3.25009e92 q^{34} -4.44905e92 q^{35} -8.65339e93 q^{36} -1.04490e95 q^{37} +7.10828e95 q^{38} +1.76687e96 q^{39} +3.27675e96 q^{40} -3.09873e96 q^{41} -4.06439e98 q^{42} +3.87231e98 q^{43} +8.14187e99 q^{44} +2.65624e98 q^{45} +5.98549e100 q^{46} -1.16928e101 q^{47} +1.73571e102 q^{48} +2.13994e102 q^{49} +1.17097e103 q^{50} -6.67991e102 q^{51} +1.98793e104 q^{52} -2.20085e104 q^{53} +1.34562e105 q^{54} -2.49922e104 q^{55} -2.90665e106 q^{56} -1.46096e106 q^{57} +8.79023e106 q^{58} -1.62691e107 q^{59} -1.05954e107 q^{60} -1.71703e107 q^{61} +3.18037e108 q^{62} -2.35622e108 q^{63} +7.25665e109 q^{64} -6.10213e108 q^{65} -2.28315e110 q^{66} -1.04127e110 q^{67} -7.51567e110 q^{68} -1.23020e111 q^{69} +1.40370e111 q^{70} -1.25798e112 q^{71} +1.73537e112 q^{72} +8.19362e112 q^{73} +3.29671e113 q^{74} -2.40670e113 q^{75} -1.64375e114 q^{76} +2.21694e114 q^{77} -5.57456e114 q^{78} +4.20171e114 q^{79} -5.99454e114 q^{80} -2.12624e115 q^{81} +9.77667e114 q^{82} -6.56382e115 q^{83} +9.39870e116 q^{84} +2.30700e115 q^{85} -1.22173e117 q^{86} -1.80666e117 q^{87} -1.63279e118 q^{88} +6.88513e117 q^{89} -8.38056e116 q^{90} +5.41291e118 q^{91} -1.38411e119 q^{92} -6.53661e118 q^{93} +3.68915e119 q^{94} +5.04565e118 q^{95} -2.95398e120 q^{96} -2.55907e119 q^{97} -6.75161e120 q^{98} -1.32359e120 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 23\!\cdots\!28 q^{2}+ \cdots + 79\!\cdots\!17 q^{9}+O(q^{10}) \) 9 * q - 2345005562254519728 * q^2 - 45298662406895255983997747004 * q^3 + 8462901481545657250924227818768095488 * q^4 - 1892628936004587162449482404208025942059050 * q^5 - 169155345437237254853213475765636376857034060992 * q^6 + 2195742607988216453868262401462060909846066161833992 * q^7 - 6498505205013969366907252193209867920059782603760087040 * q^8 + 7945503363883566160952357352391639075761121301070127960917 * q^9	\( 9 q - 23\!\cdots\!28 q^{2}+ \cdots - 44\!\cdots\!96 q^{99}+O(q^{100}) \) 9 * q - 2345005562254519728 * q^2 - 45298662406895255983997747004 * q^3 + 8462901481545657250924227818768095488 * q^4 - 1892628936004587162449482404208025942059050 * q^5 - 169155345437237254853213475765636376857034060992 * q^6 + 2195742607988216453868262401462060909846066161833992 * q^7 - 6498505205013969366907252193209867920059782603760087040 * q^8 + 7945503363883566160952357352391639075761121301070127960917 * q^9 - 1722648625287605771733277740799503204814238573365164973293600 * q^10 - 946247437041242628794010189459909585820203760454440287613552692 * q^11 + 205846961050281878415699597946796712976603670706873231298938012672 * q^12 + 20596127771705642483605985955370331334854065669132980339746788779486 * q^13 - 6541972694294346334011779110963479954883365352702523229035305330483584 * q^14 + 94761650294240619608372286408346994746207880434327141095820600145938200 * q^15 + 15125444512952621416063439206177933863772762787209602627890080570611400704 * q^16 + 291951493650412549850834598805724750617640895870041885121831690800331035682 * q^17 - 2554000175718076948380008722939707666960273565314048023897922364658130426864 * q^18 + 30244684445956612332670117612595525326891015746649482369862884848315284461780 * q^19 + 4562951142663369182841621952582280345228980283169468426672463108421372089382400 * q^20 + 35146001071237823021693437259813836720201207139254364736561723878685716530560288 * q^21 - 1908843328157955617823816866863990801015534541375661383005747627202736697921398336 * q^22 - 66547277273309692585260941575189421012052896396341670760157778423156238686357058024 * q^23 - 752736756299124610400627977416074789098074869027579302337966622137134625951047925760 * q^24 - 6063954929776831553687695824368630787209822932539681432479202799269060736255468175625 * q^25 - 68842531925347949534946832128658250301897561117051749502543801676148842557574912147872 * q^26 - 599094982712902977137778651999579486037062432725587105690436473582035154107389795716440 * q^27 + 14581457392452701650088858542793969027985828891624009507886840217572255356341773965625344 * q^28 + 9039340472411915035494616975186209221844392206687458522714064361334880069082093346905070 * q^29 + 224260392412850366562482895689598093094206490242486949280006808962977358350861560270998400 * q^30 - 1034214344782654758430975917538809236085530199413694042134266190861671432181122576926086112 * q^31 - 32504525000929540761398714812123921617256100597234986820033520241386493923631009832383807488 * q^32 + 189949463814086324300823839088808170132383689196162349649439549175970470599919775108948927152 * q^33 + 939230388337351560267419962761669652735221862277825209065568487608538630630957599920217170336 * q^34 + 1343144021786280211948320998755385153610555228046229864187689603416027546078320739943060612400 * q^35 - 21747907752251375975427518389059436655823261956750397535228718126776457105689705407608776563456 * q^36 - 88515341604947210488499310221844243003334043790663530401335727647981800120006279439706998268938 * q^37 + 126431143256035943119117270678428356969446546517968603954366283120911078870917992997220500555840 * q^38 + 217837571218652472832776380975246155068206021757529611026730729062256423563336349872452629634104 * q^39 + 11699272454320878743488987607870545498317393987884112075950101149279048493373249852479799479296000 * q^40 - 36266094262194860707738000735265088509116494488735889525314316314221341311667592777599187406913222 * q^41 - 24787352510041822155108090768801766655788422577097156255869676682213614031202393800364112862967296 * q^42 - 232370696794750496427815530982465444104722554898177200564202440384179721532324359363059913691265044 * q^43 + 7755327422511594524608603055387018294701513657236683851986386901343418513803274064133364624004320256 * q^44 + 3247131420778261129864754583862668667744851710389803065112927478198766013287651133195234793708696350 * q^45 - 32066987947547067490416916557196164509339083485720964163476500441257367761070295505033101035894375552 * q^46 - 132970274906173452814801214841116212222140439777467383504750807710754558312919347426848207706456695248 * q^47 + 1792993240520940040285669530334719652675802655317197830920369780797223163120464508596735702234386661376 * q^48 + 3971615803493637002463922107037659765667323348806045910695714957649057905572825978452768033947465237313 * q^49 + 7697223557528977921454596784007095645216064886088735712319363716221302227247960859603436865144030830000 * q^50 - 12851187227364644420645646585565612980157473692407810028414511867222315540665892049707079694243262493752 * q^51 + 41491246868006007350968584983945986180424656334954442495103497331692372835472248671859508511281974820352 * q^52 + 10921805138133777254090784536986505203689729704788186882887817145907729071674310284399320645165776125446 * q^53 + 1339620561670595781535503143383501960027220441835890399944886982813214108542142442500405331111067486871680 * q^54 - 1312854241531753321574015681587452449577731960880104498235108054018717321131599152359037095554839302748600 * q^55 - 14013489107783484379024464711764338924776495535033134010566539603721944518516633929838564532681379280158720 * q^56 - 31019370720452892632999266840260901115398140535819179494909299925851052488218537305068762474072132809464880 * q^57 + 103566512036259767730142842802003772713045020405103287191675134464175461494809359502286741327442998854097760 * q^58 - 212654227372156556243821221093344570156200984495183110384877226881440240904587127248726963633402442388397060 * q^59 - 422775085570641982781661820780199899688061805673956240019260238835680896536027096304091002230119430523545600 * q^60 + 1192163308009290988314718399559245385155131325092676542388200473202899841355909578157895873548972217626937358 * q^61 + 1941577256261942079284748865266177577315768005250991995768914948259042107075822164327427075406958896697915904 * q^62 + 451398588142208697776529182978564850520004037586377967283679997710918662905240621028803130635870486918043496 * q^63 + 58844915592066748224918413663360071934978670807229624180238002804297923325840628846335879209980431060401389568 * q^64 - 41307677239725606429137681882540847206257959638235776751518537901187469657040797622415542482923664688418764300 * q^65 - 222086041679950312339781078110357023370750120852496118683208049646663973764702391499379128192551147975013941504 * q^66 - 136956255883591433626896738276452320541908670428347212980145870863327851773988143589420054081089733226508975868 * q^67 - 141094811799092295974464545753546540483126567546619661037683966526498908594653379053568196980211372687791832576 * q^68 + 1325703171238765045361423824776857588261240408135555321965899246235283904667578177535332268855352594559670964064 * q^69 + 251934589370384384494289262861906043864096277276788575857738394556055301564200175196895771626792095349002028800 * q^70 - 21585422985838182545762327030440661631324036114582384867758341692032917773329287240302446531581657134820891213752 * q^71 - 5181834258416339630015764026055527646506354416168007949107924953264135981412995982436721696529253639785101291520 * q^72 + 91235460780032725960652165272631372912505283323159668796891496309162099636399114489032757775807008811684035374426 * q^73 + 310562981122696891225427716699672479798427405954878722327169646078571868354993002411909262537623251852286369642976 * q^74 + 43065854506087315183339457241248482679331791698024061594158993211332750535581795467446263657604087829943816477500 * q^75 - 1628928259080846394930799553567522291541981414122456953774556713740025206052658836539555750192733076653498088483840 * q^76 + 593398979324677723779464865172133117018002924612325496238799373091215617849415550444705675974821710181802828350304 * q^77 - 6873235601534959334329744558974767766222222958184019979663697300957230011165665645661869140437348638585389730736768 * q^78 + 12451904914912678516471799458709519750612136226261564829575149335945412565470277464754582893898189772426218896816720 * q^79 - 20416950898306426146345946546741629794844904073553249082791509645594723097676639519064500446972597103490830240972800 * q^80 - 40856231575215745746855879250733371261216334279125203008573307569275978049909264916389709598337529820618984078592511 * q^81 + 32147344949534769988675834932358838024355394065520493232144096322964430678203949090265848270504974541383740855029024 * q^82 - 92550876115215159531985566894207205907616571001151579100140340424113698287990359504129121116969620392280333900687084 * q^83 + 149786622283872863814961679878718479671325736759801797089969582016734283953793144464030325178406284102124769637769216 * q^84 - 457768087179221548903179340844196170221647881541175735561813412251720733334690809762523483946456540131705087221018100 * q^85 - 2597491864434159334587628292949145911098969463321219405661773952780499099399232684938429948876042525744324616394370112 * q^86 - 6860132173224607170538777320017488364980901889195600241683572931313063475309515779498812905462751134050092231747965320 * q^87 - 20006125934411614149040201757441776841868885955363484760412796241321136345672966303804893860326010500704122960860692480 * q^88 - 6037951059942933692255237205803554193360594969996068937834548367886153095083618336696729724512143193617265723073840790 * q^89 - 63101356532716899775688972110257991639639781786779198684055149646555511091876460642986977143928184313177571126402448800 * q^90 - 123641023753197596743476339553493022736411481279426005005225341366808933988856782685240985478245146307872825619974888592 * q^91 - 364595199967728361741013600374859006514622011131757842452690960184887037990775378757973866446814260984048497269830739968 * q^92 - 660210659270707805852573362768494443983824981820503945313596568722380303376948547337519220648409914639203450549706054528 * q^93 - 1077366499492799036766200119308272598652452209354508770841202268675762751723923474906601231339334467643845894468443138304 * q^94 - 1952811193153518003415269978917451688485843585663036733937657231131838392410846728976735534304153554615423725772929253000 * q^95 - 7973910491229034017269638806130805343748566540122585079441423327960922891988630774830062893111316529474837792857136300032 * q^96 - 10257092292553957046050140760321382189656293894451103156433186039799204062322028715705878067672306955149219750865890726798 * q^97 - 27691496134014026270502117819887007317432773944983420293676841151578333911041338924275151210232199410900266664836266600496 * q^98 - 44066255828766064795825662460182521807738019967004038392602001105306909448583819181101964434724044331056342593475150607396 * q^99

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