LMFDB - Embedded newform 1.122.a.a.1.7

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			1.7
Root			$2.68569e16$ 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)

$f(q)$	$=$	$q+1.02857e18 q^{2} -1.22395e29 q^{3} -1.60049e36 q^{4} -2.11004e42 q^{5} -1.25893e47 q^{6} -1.42065e51 q^{7} -4.38064e54 q^{8} +9.58953e57 q^{9} +O(q^{10})$	\(q+1.02857e18 q^{2} -1.22395e29 q^{3} -1.60049e36 q^{4} -2.11004e42 q^{5} -1.25893e47 q^{6} -1.42065e51 q^{7} -4.38064e54 q^{8} +9.58953e57 q^{9} -2.17033e60 q^{10} -1.31806e63 q^{11} +1.95892e65 q^{12} +4.76201e67 q^{13} -1.46124e69 q^{14} +2.58259e71 q^{15} -2.50987e71 q^{16} +1.88878e74 q^{17} +9.86355e75 q^{18} -6.84833e76 q^{19} +3.37710e78 q^{20} +1.73880e80 q^{21} -1.35572e81 q^{22} -2.52423e82 q^{23} +5.36169e83 q^{24} +6.90684e83 q^{25} +4.89809e85 q^{26} -5.13876e86 q^{27} +2.27373e87 q^{28} -9.19986e87 q^{29} +2.65638e89 q^{30} +1.76143e90 q^{31} +1.13876e91 q^{32} +1.61324e92 q^{33} +1.94275e92 q^{34} +2.99762e93 q^{35} -1.53480e94 q^{36} +1.94368e94 q^{37} -7.04402e94 q^{38} -5.82847e96 q^{39} +9.24333e96 q^{40} +4.01337e97 q^{41} +1.78849e98 q^{42} -5.59251e98 q^{43} +2.10954e99 q^{44} -2.02343e100 q^{45} -2.59636e100 q^{46} -6.96357e100 q^{47} +3.07195e100 q^{48} +2.11632e101 q^{49} +7.10421e101 q^{50} -2.31177e103 q^{51} -7.62155e103 q^{52} +1.28958e102 q^{53} -5.28560e104 q^{54} +2.78116e105 q^{55} +6.22335e105 q^{56} +8.38202e105 q^{57} -9.46274e105 q^{58} -9.94733e106 q^{59} -4.13340e107 q^{60} +1.94182e108 q^{61} +1.81176e108 q^{62} -1.36233e109 q^{63} +1.23802e109 q^{64} -1.00480e110 q^{65} +1.65934e110 q^{66} +5.84853e109 q^{67} -3.02297e110 q^{68} +3.08954e111 q^{69} +3.08328e111 q^{70} -1.26923e112 q^{71} -4.20083e112 q^{72} +5.17143e112 q^{73} +1.99922e112 q^{74} -8.45364e112 q^{75} +1.09607e113 q^{76} +1.87250e114 q^{77} -5.99502e114 q^{78} +4.13256e114 q^{79} +5.29591e113 q^{80} +1.11984e115 q^{81} +4.12805e115 q^{82} -7.91130e115 q^{83} -2.78293e116 q^{84} -3.98540e116 q^{85} -5.75232e116 q^{86} +1.12602e117 q^{87} +5.77395e117 q^{88} +1.78521e117 q^{89} -2.08125e118 q^{90} -6.76513e118 q^{91} +4.04001e118 q^{92} -2.15591e119 q^{93} -7.16256e118 q^{94} +1.44502e119 q^{95} -1.39379e120 q^{96} -6.06788e119 q^{97} +2.17679e119 q^{98} -1.26396e121 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.02857e18	0.630843	0.315421	−	0.948952i	$-0.397854\pi$
$2$	1.02857e18	0.630843	0.315421	+	0.948952i	$0.397854\pi$
$3$	−1.22395e29	−1.66697	−0.833486	−	0.552541i	$-0.813658\pi$
$3$	−1.22395e29	−1.66697	−0.833486	+	0.552541i	$0.813658\pi$
$4$	−1.60049e36	−0.602038
$5$	−2.11004e42	−1.08794	−0.543970	−	0.839104i	$-0.683080\pi$
$5$	−2.11004e42	−1.08794	−0.543970	+	0.839104i	$0.683080\pi$
$6$	−1.25893e47	−1.05160
$7$	−1.42065e51	−1.05695	−0.528475	−	0.848949i	$-0.677236\pi$
$7$	−1.42065e51	−1.05695	−0.528475	+	0.848949i	$0.677236\pi$
$8$	−4.38064e54	−1.01063
$9$	9.58953e57	1.77879
$10$	−2.17033e60	−0.686320
$11$	−1.31806e63	−1.30520	−0.652601	−	0.757702i	$-0.726322\pi$
$11$	−1.31806e63	−1.30520	−0.652601	+	0.757702i	$0.726322\pi$
$12$	1.95892e65	1.00358
$13$	4.76201e67	1.92406	0.962028	−	0.272951i	$-0.0879996\pi$
$13$	4.76201e67	1.92406	0.962028	+	0.272951i	$0.0879996\pi$
$14$	−1.46124e69	−0.666769
$15$	2.58259e71	1.81357
$16$	−2.50987e71	−0.0355133
$17$	1.88878e74	0.682372	0.341186	−	0.939996i	$-0.389171\pi$
$17$	1.88878e74	0.682372	0.341186	+	0.939996i	$0.389171\pi$
$18$	9.86355e75	1.12214
$19$	−6.84833e76	−0.295796	−0.147898	−	0.989003i	$-0.547251\pi$
$19$	−6.84833e76	−0.295796	−0.147898	+	0.989003i	$0.547251\pi$
$20$	3.37710e78	0.654981
$21$	1.73880e80	1.76191
$22$	−1.35572e81	−0.823377
$23$	−2.52423e82	−1.04135	−0.520673	−	0.853756i	$-0.674319\pi$
$23$	−2.52423e82	−1.04135	−0.520673	+	0.853756i	$0.674319\pi$
$24$	5.36169e83	1.68470
$25$	6.90684e83	0.183615
$26$	4.89809e85	1.21378
$27$	−5.13876e86	−1.29823
$28$	2.27373e87	0.636324
$29$	−9.19986e87	−0.308108	−0.154054	−	0.988062i	$-0.549233\pi$
$29$	−9.19986e87	−0.308108	−0.154054	+	0.988062i	$0.549233\pi$
$30$	2.65638e89	1.14408
$31$	1.76143e90	1.04348	0.521739	−	0.853105i	$-0.325284\pi$
$31$	1.76143e90	1.04348	0.521739	+	0.853105i	$0.325284\pi$
$32$	1.13876e91	0.988230
$33$	1.61324e92	2.17573
$34$	1.94275e92	0.430470
$35$	2.99762e93	1.14990
$36$	−1.53480e94	−1.07090
$37$	1.94368e94	0.258476	0.129238	−	0.991614i	$-0.458747\pi$
$37$	1.94368e94	0.258476	0.129238	+	0.991614i	$0.458747\pi$
$38$	−7.04402e94	−0.186600
$39$	−5.82847e96	−3.20735
$40$	9.24333e96	1.09951
$41$	4.01337e97	1.07173	0.535865	−	0.844304i	$-0.319986\pi$
$41$	4.01337e97	1.07173	0.535865	+	0.844304i	$0.319986\pi$
$42$	1.78849e98	1.11149
$43$	−5.59251e98	−0.837077	−0.418539	−	0.908199i	$-0.637458\pi$
$43$	−5.59251e98	−0.837077	−0.418539	+	0.908199i	$0.637458\pi$
$44$	2.10954e99	0.785781
$45$	−2.02343e100	−1.93522
$46$	−2.59636e100	−0.656926
$47$	−6.96357e100	−0.479636	−0.239818	−	0.970818i	$-0.577088\pi$
$47$	−6.96357e100	−0.479636	−0.239818	+	0.970818i	$0.577088\pi$
$48$	3.07195e100	0.0591997
$49$	2.11632e101	0.117144
$50$	7.10421e101	0.115832
$51$	−2.31177e103	−1.13750
$52$	−7.62155e103	−1.15835
$53$	1.28958e102	0.00619095	0.00309548	−	0.999995i	$-0.499015\pi$
$53$	1.28958e102	0.00619095	0.00309548	+	0.999995i	$0.499015\pi$
$54$	−5.28560e104	−0.818977
$55$	2.78116e105	1.41998
$56$	6.22335e105	1.06819
$57$	8.38202e105	0.493083
$58$	−9.46274e105	−0.194367
$59$	−9.94733e106	−0.726373	−0.363187	−	0.931716i	$-0.618311\pi$
$59$	−9.94733e106	−0.726373	−0.363187	+	0.931716i	$0.618311\pi$
$60$	−4.13340e107	−1.09184
$61$	1.94182e108	1.88692	0.943461	−	0.331485i	$-0.107549\pi$
$61$	1.94182e108	1.88692	0.943461	+	0.331485i	$0.107549\pi$
$62$	1.81176e108	0.658270
$63$	−1.36233e109	−1.88010
$64$	1.23802e109	0.658931
$65$	−1.00480e110	−2.09326
$66$	1.65934e110	1.37255
$67$	5.84853e109	0.194770	0.0973848	−	0.995247i	$-0.468952\pi$
$67$	5.84853e109	0.194770	0.0973848	+	0.995247i	$0.468952\pi$
$68$	−3.02297e110	−0.410814
$69$	3.08954e111	1.73589
$70$	3.08328e111	0.725406
$71$	−1.26923e112	−1.26593	−0.632964	−	0.774181i	$-0.718162\pi$
$71$	−1.26923e112	−1.26593	−0.632964	+	0.774181i	$0.718162\pi$
$72$	−4.20083e112	−1.79771
$73$	5.17143e112	0.960678	0.480339	−	0.877083i	$-0.340514\pi$
$73$	5.17143e112	0.960678	0.480339	+	0.877083i	$0.340514\pi$
$74$	1.99922e112	0.163058
$75$	−8.45364e112	−0.306082
$76$	1.09607e113	0.178080
$77$	1.87250e114	1.37953
$78$	−5.99502e114	−2.02333
$79$	4.13256e114	0.645328	0.322664	−	0.946514i	$-0.395422\pi$
$79$	4.13256e114	0.645328	0.322664	+	0.946514i	$0.395422\pi$
$80$	5.29591e113	0.0386364
$81$	1.11984e115	0.385314
$82$	4.12805e115	0.676093
$83$	−7.91130e115	−0.622334	−0.311167	−	0.950355i	$-0.600720\pi$
$83$	−7.91130e115	−0.622334	−0.311167	+	0.950355i	$0.600720\pi$
$84$	−2.78293e116	−1.06073
$85$	−3.98540e116	−0.742381
$86$	−5.75232e116	−0.528064
$87$	1.12602e117	0.513607
$88$	5.77395e117	1.31908
$89$	1.78521e117	0.205871	0.102935	−	0.994688i	$-0.467177\pi$
$89$	1.78521e117	0.205871	0.102935	+	0.994688i	$0.467177\pi$
$90$	−2.08125e118	−1.22082
$91$	−6.76513e118	−2.03363
$92$	4.04001e118	0.626929
$93$	−2.15591e119	−1.73945
$94$	−7.16256e118	−0.302575
$95$	1.44502e119	0.321808
$96$	−1.39379e120	−1.64735
$97$	−6.06788e119	−0.383131	−0.191565	−	0.981480i	$-0.561356\pi$
$97$	−6.06788e119	−0.383131	−0.191565	+	0.981480i	$0.561356\pi$
$98$	2.17679e119	0.0738992
$99$	−1.26396e121	−2.32169
$100$	−1.10543e120	−0.110543
$101$	−2.65844e121	−1.45608	−0.728038	−	0.685537i	$-0.759568\pi$
$101$	−2.65844e121	−1.45608	−0.728038	+	0.685537i	$0.759568\pi$
$102$	−2.37783e121	−0.717581
$103$	8.03084e121	1.34310	0.671551	−	0.740958i	$-0.265628\pi$
$103$	8.03084e121	1.34310	0.671551	+	0.740958i	$0.265628\pi$
$104$	−2.08607e122	−1.94452
$105$	−3.66894e122	−1.91685
$106$	1.32643e120	0.00390552
$107$	3.92304e122	0.654492	0.327246	−	0.944939i	$-0.393879\pi$
$107$	3.92304e122	0.654492	0.327246	+	0.944939i	$0.393879\pi$
$108$	8.22454e122	0.781581
$109$	7.56091e122	0.411406	0.205703	−	0.978614i	$-0.434052\pi$
$109$	7.56091e122	0.411406	0.205703	+	0.978614i	$0.434052\pi$
$110$	2.86063e123	0.895786
$111$	−2.37897e123	−0.430872
$112$	3.56563e122	0.0375358
$113$	3.35676e123	0.206383	0.103192	−	0.994661i	$-0.467094\pi$
$113$	3.35676e123	0.206383	0.103192	+	0.994661i	$0.467094\pi$
$114$	8.62153e123	0.311058
$115$	5.32623e124	1.13292
$116$	1.47243e124	0.185492
$117$	4.56655e125	3.42250
$118$	−1.02316e125	−0.458227
$119$	−2.68329e125	−0.721234
$120$	−1.13134e126	−1.83285
$121$	7.17483e125	0.703553
$122$	1.99731e126	1.19035
$123$	−4.91216e126	−1.78654
$124$	−2.81915e126	−0.628213
$125$	6.47971e126	0.888178
$126$	−1.40126e127	−1.18605
$127$	−2.90625e127	−1.52478	−0.762391	−	0.647116i	$-0.775975\pi$
$127$	−2.90625e127	−1.52478	−0.762391	+	0.647116i	$0.775975\pi$
$128$	−1.75394e127	−0.572548
$129$	6.84496e127	1.39538
$130$	−1.03352e128	−1.32052
$131$	1.82800e128	1.46914	0.734569	−	0.678534i	$-0.237384\pi$
$131$	1.82800e128	1.46914	0.734569	+	0.678534i	$0.237384\pi$
$132$	−2.58198e128	−1.30987
$133$	9.72905e127	0.312641
$134$	6.01565e127	0.122869
$135$	1.08430e129	1.41239
$136$	−8.27407e128	−0.689629
$137$	1.50424e129	0.804862	0.402431	−	0.915450i	$-0.368165\pi$
$137$	1.50424e129	0.804862	0.402431	+	0.915450i	$0.368165\pi$
$138$	3.17782e129	1.09508
$139$	7.54350e129	1.67949	0.839745	−	0.542981i	$-0.182704\pi$
$139$	7.54350e129	1.67949	0.839745	+	0.542981i	$0.182704\pi$
$140$	−4.79766e129	−0.692283
$141$	8.52308e129	0.799540
$142$	−1.30549e130	−0.798601
$143$	−6.27662e130	−2.51128
$144$	−2.40684e129	−0.0631709
$145$	1.94121e130	0.335203
$146$	5.31920e130	0.606037
$147$	−2.59027e130	−0.195275
$148$	−3.11084e130	−0.155612
$149$	−3.27334e131	−1.08949	−0.544744	−	0.838602i	$-0.683373\pi$
$149$	−3.27334e131	−1.08949	−0.544744	+	0.838602i	$0.683373\pi$
$150$	−8.69520e130	−0.193089
$151$	−9.75442e131	−1.44909	−0.724546	−	0.689227i	$-0.757950\pi$
$151$	−9.75442e131	−1.44909	−0.724546	+	0.689227i	$0.757950\pi$
$152$	3.00001e131	0.298941
$153$	1.81125e132	1.21380
$154$	1.92600e132	0.870269
$155$	−3.71669e132	−1.13524
$156$	9.32841e132	1.93094
$157$	3.10019e132	0.435973	0.217986	−	0.975952i	$-0.430051\pi$
$157$	3.10019e132	0.435973	0.217986	+	0.975952i	$0.430051\pi$
$158$	4.25065e132	0.407100
$159$	−1.57838e131	−0.0103201
$160$	−2.40283e133	−1.07514
$161$	3.58604e133	1.10065
$162$	1.15184e133	0.243072
$163$	4.69306e133	0.682506	0.341253	−	0.939972i	$-0.389149\pi$
$163$	4.69306e133	0.682506	0.341253	+	0.939972i	$0.389149\pi$
$164$	−6.42335e133	−0.645222
$165$	−3.40400e134	−2.36707
$166$	−8.13736e133	−0.392595
$167$	1.49537e133	0.0501651	0.0250826	−	0.999685i	$-0.492015\pi$
$167$	1.49537e133	0.0501651	0.0250826	+	0.999685i	$0.492015\pi$
$168$	−7.61707e134	−1.78064
$169$	1.65512e135	2.70199
$170$	−4.09928e134	−0.468326
$171$	−6.56723e134	−0.526159
$172$	8.95076e134	0.503952
$173$	−5.68540e134	−0.225409	−0.112705	−	0.993629i	$-0.535951\pi$
$173$	−5.68540e134	−0.225409	−0.112705	+	0.993629i	$0.535951\pi$
$174$	1.15819e135	0.324005
$175$	−9.81218e134	−0.194072
$176$	3.30815e134	0.0463521
$177$	1.21750e136	1.21084
$178$	1.83622e135	0.129872
$179$	1.58541e135	0.0798973	0.0399486	−	0.999202i	$-0.487281\pi$
$179$	1.58541e135	0.0798973	0.0399486	+	0.999202i	$0.487281\pi$
$180$	3.23848e136	1.16508
$181$	6.43337e136	1.65533	0.827666	−	0.561221i	$-0.189668\pi$
$181$	6.43337e136	1.65533	0.827666	+	0.561221i	$0.189668\pi$
$182$	−6.95845e136	−1.28290
$183$	−2.37669e137	−3.14544
$184$	1.10578e137	1.05242
$185$	−4.10124e136	−0.281207
$186$	−2.21751e137	−1.09732
$187$	−2.48953e137	−0.890634
$188$	1.11451e137	0.288759
$189$	7.30036e137	1.37216
$190$	1.48632e137	0.203010
$191$	9.27212e136	0.0921850	0.0460925	−	0.998937i	$-0.485323\pi$
$191$	9.27212e136	0.0921850	0.0460925	+	0.998937i	$0.485323\pi$
$192$	−1.51528e138	−1.09842
$193$	−1.18604e138	−0.627886	−0.313943	−	0.949442i	$-0.601650\pi$
$193$	−1.18604e138	−0.627886	−0.313943	+	0.949442i	$0.601650\pi$
$194$	−6.24127e137	−0.241695
$195$	1.22983e139	3.48940
$196$	−3.38715e137	−0.0705248
$197$	3.85321e138	0.589680	0.294840	−	0.955547i	$-0.404734\pi$
$197$	3.85321e138	0.589680	0.294840	+	0.955547i	$0.404734\pi$
$198$	−1.30008e139	−1.46462
$199$	1.03181e139	0.857013	0.428507	−	0.903539i	$-0.359040\pi$
$199$	1.03181e139	0.857013	0.428507	+	0.903539i	$0.359040\pi$
$200$	−3.02564e138	−0.185568
$201$	−7.15831e138	−0.324675
$202$	−2.73441e139	−0.918555
$203$	1.30697e139	0.325654
$204$	3.69997e139	0.684815
$205$	−8.46836e139	−1.16598
$206$	8.26032e139	0.847286
$207$	−2.42062e140	−1.85234
$208$	−1.19520e139	−0.0683296
$209$	9.02651e139	0.386073
$210$	−3.77378e140	−1.20923
$211$	1.80431e139	0.0433733	0.0216866	−	0.999765i	$-0.493096\pi$
$211$	1.80431e139	0.0433733	0.0216866	+	0.999765i	$0.493096\pi$
$212$	−2.06396e138	−0.00372719
$213$	1.55347e141	2.11027
$214$	4.03514e140	0.412881
$215$	1.18004e141	0.910691
$216$	2.25111e141	1.31203
$217$	−2.50237e141	−1.10290
$218$	7.77696e140	0.259533
$219$	−6.32958e141	−1.60142
$220$	−4.45122e141	−0.854883
$221$	8.99439e141	1.31292
$222$	−2.44695e141	−0.271813
$223$	3.59160e141	0.303979	0.151990	−	0.988382i	$-0.451432\pi$
$223$	3.59160e141	0.303979	0.151990	+	0.988382i	$0.451432\pi$
$224$	−1.61777e142	−1.04451
$225$	6.62334e141	0.326614
$226$	3.45268e141	0.130195
$227$	−5.26010e142	−1.51855	−0.759275	−	0.650769i	$-0.774446\pi$
$227$	−5.26010e142	−1.51855	−0.759275	+	0.650769i	$0.774446\pi$
$228$	−1.34153e142	−0.296854
$229$	6.28765e142	1.06768	0.533841	−	0.845585i	$-0.320748\pi$
$229$	6.28765e142	1.06768	0.533841	+	0.845585i	$0.320748\pi$
$230$	5.47842e142	0.714696
$231$	−2.29185e143	−2.29964
$232$	4.03013e142	0.311384
$233$	1.39720e143	0.832198	0.416099	−	0.909319i	$-0.363397\pi$
$233$	1.39720e143	0.832198	0.416099	+	0.909319i	$0.363397\pi$
$234$	4.69703e143	2.15906
$235$	1.46934e143	0.521816
$236$	1.59206e143	0.437304
$237$	−5.05805e143	−1.07574
$238$	−2.75996e143	−0.454985
$239$	4.79186e143	0.612959	0.306479	−	0.951877i	$-0.400849\pi$
$239$	4.79186e143	0.612959	0.306479	+	0.951877i	$0.400849\pi$
$240$	−6.48194e142	−0.0644058
$241$	−1.21257e144	−0.936863	−0.468431	−	0.883500i	$-0.655181\pi$
$241$	−1.21257e144	−0.936863	−0.468431	+	0.883500i	$0.655181\pi$
$242$	7.37985e143	0.443831
$243$	1.39969e144	0.655920
$244$	−3.10786e144	−1.13600
$245$	−4.46552e143	−0.127445
$246$	−5.05253e144	−1.12703
$247$	−3.26118e144	−0.569127
$248$	−7.71620e144	−1.05457
$249$	9.68304e144	1.03741
$250$	6.66487e144	0.560301
$251$	5.43543e144	0.358901	0.179450	−	0.983767i	$-0.442568\pi$
$251$	5.43543e144	0.358901	0.179450	+	0.983767i	$0.442568\pi$
$252$	2.18040e145	1.13189
$253$	3.32709e145	1.35917
$254$	−2.98929e145	−0.961898
$255$	4.87793e145	1.23753
$256$	−5.09529e145	−1.02012
$257$	−1.00297e146	−1.58612	−0.793058	−	0.609146i	$-0.791512\pi$
$257$	−1.00297e146	−1.58612	−0.793058	+	0.609146i	$0.791512\pi$
$258$	7.04056e145	0.880268
$259$	−2.76128e145	−0.273196
$260$	1.60818e146	1.26022
$261$	−8.82224e145	−0.548060
$262$	1.88023e146	0.926795
$263$	7.79816e144	0.0305260	0.0152630	−	0.999884i	$-0.495141\pi$
$263$	7.79816e144	0.0305260	0.0152630	+	0.999884i	$0.495141\pi$
$264$	−7.06704e146	−2.19887
$265$	−2.72106e144	−0.00673539
$266$	1.00071e146	0.197227
$267$	−2.18501e146	−0.343181
$268$	−9.36051e145	−0.117259
$269$	−1.91666e147	−1.91660	−0.958300	−	0.285763i	$-0.907753\pi$
$269$	−1.91666e147	−1.91660	−0.958300	+	0.285763i	$0.907753\pi$
$270$	1.11528e147	0.890999
$271$	9.28602e145	0.0593181	0.0296591	−	0.999560i	$-0.490558\pi$
$271$	9.28602e145	0.0593181	0.0296591	+	0.999560i	$0.490558\pi$
$272$	−4.74058e145	−0.0242333
$273$	8.28019e147	3.39001
$274$	1.54722e147	0.507741
$275$	−9.10364e146	−0.239655
$276$	−4.94477e147	−1.04507
$277$	−7.00876e147	−1.19019	−0.595093	−	0.803657i	$-0.702885\pi$
$277$	−7.00876e147	−1.19019	−0.595093	+	0.803657i	$0.702885\pi$
$278$	7.75905e147	1.05949
$279$	1.68913e148	1.85613
$280$	−1.31315e148	−1.16213
$281$	−2.08036e148	−1.48390	−0.741952	−	0.670453i	$-0.766100\pi$
$281$	−2.08036e148	−1.48390	−0.741952	+	0.670453i	$0.766100\pi$
$282$	8.76662e147	0.504384
$283$	−7.02179e147	−0.326113	−0.163057	−	0.986617i	$-0.552135\pi$
$283$	−7.02179e147	−0.326113	−0.163057	+	0.986617i	$0.552135\pi$
$284$	2.03138e148	0.762136
$285$	−1.76864e148	−0.536445
$286$	−6.45597e148	−1.58422
$287$	−5.70157e148	−1.13277
$288$	1.09202e149	1.75786
$289$	−4.09411e148	−0.534368
$290$	1.99668e148	0.211460
$291$	7.42679e148	0.638668
$292$	−8.27683e148	−0.578364
$293$	1.89492e149	1.07671	0.538357	−	0.842717i	$-0.319045\pi$
$293$	1.89492e149	1.07671	0.538357	+	0.842717i	$0.319045\pi$
$294$	−2.66429e148	−0.123188
$295$	2.09893e149	0.790251
$296$	−8.51457e148	−0.261225
$297$	6.77320e149	1.69445
$298$	−3.36688e149	−0.687295
$299$	−1.20204e150	−2.00361
$300$	1.35300e149	0.184273
$301$	7.94498e149	0.884749
$302$	−1.00331e150	−0.914149
$303$	3.25380e150	2.42724
$304$	1.71884e148	0.0105047
$305$	−4.09732e150	−2.05286
$306$	1.86301e150	0.765717
$307$	−2.92052e150	−0.985344	−0.492672	−	0.870215i	$-0.663980\pi$
$307$	−2.92052e150	−0.985344	−0.492672	+	0.870215i	$0.663980\pi$
$308$	−2.99691e150	−0.830531
$309$	−9.82936e150	−2.23891
$310$	−3.82289e150	−0.716159
$311$	9.41624e150	1.45169	0.725845	−	0.687858i	$-0.241449\pi$
$311$	9.41624e150	1.45169	0.725845	+	0.687858i	$0.241449\pi$
$312$	2.55325e151	3.24145
$313$	−1.31702e151	−1.37771	−0.688856	−	0.724898i	$-0.741887\pi$
$313$	−1.31702e151	−1.37771	−0.688856	+	0.724898i	$0.741887\pi$
$314$	3.18878e150	0.275030
$315$	2.87458e151	2.04543
$316$	−6.61413e150	−0.388512
$317$	−2.02177e150	−0.0980950	−0.0490475	−	0.998796i	$-0.515619\pi$
$317$	−2.02177e150	−0.0980950	−0.0490475	+	0.998796i	$0.515619\pi$
$318$	−1.62348e149	−0.00651038
$319$	1.21260e151	0.402143
$320$	−2.61228e151	−0.716878
$321$	−4.80161e151	−1.09102
$322$	3.68851e151	0.694338
$323$	−1.29350e151	−0.201843
$324$	−1.79230e151	−0.231973
$325$	3.28905e151	0.353286
$326$	4.82717e151	0.430554
$327$	−9.25419e151	−0.685803
$328$	−1.75811e152	−1.08313
$329$	9.89278e151	0.506951
$330$	−3.50127e152	−1.49325
$331$	1.43355e152	0.509118	0.254559	−	0.967057i	$-0.418070\pi$
$331$	1.43355e152	0.509118	0.254559	+	0.967057i	$0.418070\pi$
$332$	1.26620e152	0.374668
$333$	1.86390e152	0.459776
$334$	1.53810e151	0.0316463
$335$	−1.23406e152	−0.211898
$336$	−4.36416e151	−0.0625711
$337$	6.69028e152	0.801375	0.400687	−	0.916215i	$-0.368771\pi$
$337$	6.69028e152	0.801375	0.400687	+	0.916215i	$0.368771\pi$
$338$	1.70242e153	1.70453
$339$	−4.10851e152	−0.344035
$340$	6.37859e152	0.446941
$341$	−2.32167e153	−1.36195
$342$	−6.75488e152	−0.331924
$343$	2.26589e153	0.933135
$344$	2.44988e153	0.845978
$345$	−6.51904e153	−1.88855
$346$	−5.84786e152	−0.142198
$347$	3.70203e153	0.755974	0.377987	−	0.925811i	$-0.376616\pi$
$347$	3.70203e153	0.755974	0.377987	+	0.925811i	$0.376616\pi$
$348$	−1.80218e153	−0.309210
$349$	3.64076e153	0.525115	0.262557	−	0.964916i	$-0.415434\pi$
$349$	3.64076e153	0.525115	0.262557	+	0.964916i	$0.415434\pi$
$350$	−1.00926e153	−0.122429
$351$	−2.44708e154	−2.49786
$352$	−1.50095e154	−1.28984
$353$	5.25382e153	0.380282	0.190141	−	0.981757i	$-0.439105\pi$
$353$	5.25382e153	0.380282	0.190141	+	0.981757i	$0.439105\pi$
$354$	1.25229e154	0.763852
$355$	2.67812e154	1.37725
$356$	−2.85721e153	−0.123942
$357$	3.28421e154	1.20228
$358$	1.63071e153	0.0504026
$359$	−1.92692e154	−0.503094	−0.251547	−	0.967845i	$-0.580939\pi$
$359$	−1.92692e154	−0.503094	−0.251547	+	0.967845i	$0.580939\pi$
$360$	8.86392e154	1.95580
$361$	−4.89126e154	−0.912505
$362$	6.61721e154	1.04425
$363$	−8.78164e154	−1.17280
$364$	1.08275e155	1.22432
$365$	−1.09119e155	−1.04516
$366$	−2.44460e155	−1.98428
$367$	−9.99179e154	−0.687617	−0.343808	−	0.939040i	$-0.611717\pi$
$367$	−9.99179e154	−0.687617	−0.343808	+	0.939040i	$0.611717\pi$
$368$	6.33548e153	0.0369817
$369$	3.84863e155	1.90639
$370$	−4.21843e154	−0.177397
$371$	−1.83203e153	−0.00654353
$372$	3.45051e155	1.04721
$373$	−4.24212e155	−1.09446	−0.547228	−	0.836984i	$-0.684317\pi$
$373$	−4.24212e155	−1.09446	−0.547228	+	0.836984i	$0.684317\pi$
$374$	−2.56066e155	−0.561850
$375$	−7.93085e155	−1.48057
$376$	3.05049e155	0.484736
$377$	−4.38099e155	−0.592816
$378$	7.50897e155	0.865618
$379$	−4.50800e155	−0.442906	−0.221453	−	0.975171i	$-0.571080\pi$
$379$	−4.50800e155	−0.442906	−0.221453	+	0.975171i	$0.571080\pi$
$380$	−2.31275e155	−0.193741
$381$	3.55711e156	2.54177
$382$	9.53707e154	0.0581542
$383$	2.50772e156	1.30543	0.652715	−	0.757604i	$-0.273630\pi$
$383$	2.50772e156	1.30543	0.652715	+	0.757604i	$0.273630\pi$
$384$	2.14674e156	0.954422
$385$	−3.95104e156	−1.50085
$386$	−1.21993e156	−0.396098
$387$	−5.36296e156	−1.48899
$388$	9.71158e155	0.230659
$389$	−1.89148e156	−0.384460	−0.192230	−	0.981350i	$-0.561572\pi$
$389$	−1.89148e156	−0.384460	−0.192230	+	0.981350i	$0.561572\pi$
$390$	1.26497e157	2.20126
$391$	−4.76772e156	−0.710586
$392$	−9.27084e155	−0.118389
$393$	−2.23738e157	−2.44901
$394$	3.96332e156	0.371995
$395$	−8.71987e156	−0.702079
$396$	2.02295e157	1.39774
$397$	−1.37403e157	−0.815022	−0.407511	−	0.913200i	$-0.633603\pi$
$397$	−1.37403e157	−0.815022	−0.407511	+	0.913200i	$0.633603\pi$
$398$	1.06129e157	0.540640
$399$	−1.19079e157	−0.521164
$400$	−1.73352e155	−0.00652080
$401$	1.66880e156	0.0539723	0.0269862	−	0.999636i	$-0.491409\pi$
$401$	1.66880e156	0.0539723	0.0269862	+	0.999636i	$0.491409\pi$
$402$	−7.36286e156	−0.204819
$403$	8.38796e157	2.00771
$404$	4.25481e157	0.876613
$405$	−2.36292e157	−0.419198
$406$	1.34432e157	0.205437
$407$	−2.56189e157	−0.337364
$408$	1.01271e158	1.14959
$409$	−4.21949e156	−0.0413047	−0.0206524	−	0.999787i	$-0.506574\pi$
$409$	−4.21949e156	−0.0413047	−0.0206524	+	0.999787i	$0.506574\pi$
$410$	−8.71034e157	−0.735549
$411$	−1.84111e158	−1.34168
$412$	−1.28533e158	−0.808598
$413$	1.41316e158	0.767740
$414$	−2.48979e158	−1.16854
$415$	1.66932e158	0.677062
$416$	5.42279e158	1.90141
$417$	−9.23287e158	−2.79966
$418$	9.28444e157	0.243551
$419$	4.01162e158	0.910691	0.455346	−	0.890315i	$-0.349516\pi$
$419$	4.01162e158	0.910691	0.455346	+	0.890315i	$0.349516\pi$
$420$	5.87210e158	1.15402
$421$	−7.87606e158	−1.34042	−0.670212	−	0.742170i	$-0.733797\pi$
$421$	−7.87606e158	−1.34042	−0.670212	+	0.742170i	$0.733797\pi$
$422$	1.85587e157	0.0273617
$423$	−6.67774e158	−0.853174
$424$	−5.64918e156	−0.00625678
$425$	1.30455e158	0.125294
$426$	1.59786e159	1.33125
$427$	−2.75864e159	−1.99438
$428$	−6.27879e158	−0.394029
$429$	7.68228e159	4.18624
$430$	1.21376e159	0.574502
$431$	3.58975e158	0.147635	0.0738176	−	0.997272i	$-0.476482\pi$
$431$	3.58975e158	0.147635	0.0738176	+	0.997272i	$0.476482\pi$
$432$	1.28976e158	0.0461044
$433$	−2.89849e159	−0.900853	−0.450426	−	0.892814i	$-0.648728\pi$
$433$	−2.89849e159	−0.900853	−0.450426	+	0.892814i	$0.648728\pi$
$434$	−2.57387e159	−0.695759
$435$	−2.37594e159	−0.558774
$436$	−1.21012e159	−0.247682
$437$	1.72868e159	0.308026
$438$	−6.51045e159	−1.01025
$439$	−2.97213e159	−0.401758	−0.200879	−	0.979616i	$-0.564380\pi$
$439$	−2.97213e159	−0.401758	−0.200879	+	0.979616i	$0.564380\pi$
$440$	−1.21833e160	−1.43508
$441$	2.02945e159	0.208374
$442$	9.25140e159	0.828248
$443$	2.42432e159	0.189306	0.0946532	−	0.995510i	$-0.469826\pi$
$443$	2.42432e159	0.189306	0.0946532	+	0.995510i	$0.469826\pi$
$444$	3.80752e159	0.259401
$445$	−3.76687e159	−0.223975
$446$	3.69423e159	0.191763
$447$	4.00641e160	1.81614
$448$	−1.75879e160	−0.696457
$449$	−6.23639e159	−0.215789	−0.107895	−	0.994162i	$-0.534411\pi$
$449$	−6.23639e159	−0.215789	−0.107895	+	0.994162i	$0.534411\pi$
$450$	6.81260e159	0.206042
$451$	−5.28986e160	−1.39882
$452$	−5.37246e159	−0.124251
$453$	1.19389e161	2.41559
$454$	−5.41040e160	−0.957967
$455$	1.42747e161	2.21247
$456$	−3.67186e160	−0.498326
$457$	−3.94108e160	−0.468474	−0.234237	−	0.972180i	$-0.575259\pi$
$457$	−3.94108e160	−0.468474	−0.234237	+	0.972180i	$0.575259\pi$
$458$	6.46732e160	0.673539
$459$	−9.70598e160	−0.885874
$460$	−8.52458e160	−0.682062
$461$	−1.92796e161	−1.35267	−0.676335	−	0.736594i	$-0.736433\pi$
$461$	−1.92796e161	−1.35267	−0.676335	+	0.736594i	$0.736433\pi$
$462$	−2.35733e161	−1.45071
$463$	2.82505e160	0.152537	0.0762686	−	0.997087i	$-0.475699\pi$
$463$	2.82505e160	0.152537	0.0762686	+	0.997087i	$0.475699\pi$
$464$	2.30904e159	0.0109419
$465$	4.54905e161	1.89242
$466$	1.43713e161	0.524986
$467$	2.49471e161	0.800477	0.400239	−	0.916411i	$-0.368927\pi$
$467$	2.49471e161	0.800477	0.400239	+	0.916411i	$0.368927\pi$
$468$	−7.30871e161	−2.06047
$469$	−8.30869e160	−0.205862
$470$	1.51133e161	0.329184
$471$	−3.79448e161	−0.726754
$472$	4.35757e161	0.734097
$473$	7.37127e161	1.09256
$474$	−5.20259e161	−0.678625
$475$	−4.73003e160	−0.0543126
$476$	4.29457e161	0.434210
$477$	1.23664e160	0.0110124
$478$	4.92879e161	0.386681
$479$	2.82905e161	0.195588	0.0977941	−	0.995207i	$-0.468821\pi$
$479$	2.82905e161	0.195588	0.0977941	+	0.995207i	$0.468821\pi$
$480$	2.94094e162	1.79222
$481$	9.25583e161	0.497323
$482$	−1.24722e162	−0.591013
$483$	−4.38914e162	−1.83475
$484$	−1.14832e162	−0.423565
$485$	1.28035e162	0.416824
$486$	1.43968e162	0.413783
$487$	−8.27990e161	−0.210147	−0.105073	−	0.994464i	$-0.533508\pi$
$487$	−8.27990e161	−0.210147	−0.105073	+	0.994464i	$0.533508\pi$
$488$	−8.50642e162	−1.90699
$489$	−5.74408e162	−1.13772
$490$	−4.59312e161	−0.0803979
$491$	−1.33947e162	−0.207253	−0.103627	−	0.994616i	$-0.533045\pi$
$491$	−1.33947e162	−0.207253	−0.103627	+	0.994616i	$0.533045\pi$
$492$	7.86187e162	1.07557
$493$	−1.73765e162	−0.210244
$494$	−3.35437e162	−0.359030
$495$	2.66700e163	2.52586
$496$	−4.42095e161	−0.0370574
$497$	1.80312e163	1.33802
$498$	9.95973e162	0.654444
$499$	−2.76377e163	−1.60849	−0.804245	−	0.594297i	$-0.797430\pi$
$499$	−2.76377e163	−1.60849	−0.804245	+	0.594297i	$0.797430\pi$
$500$	−1.03707e163	−0.534717
$501$	−1.83026e162	−0.0836239
$502$	5.59075e162	0.226410
$503$	−4.62505e163	−1.66056	−0.830278	−	0.557349i	$-0.811818\pi$
$503$	−4.62505e163	−1.66056	−0.830278	+	0.557349i	$0.811818\pi$
$504$	5.96790e163	1.90009
$505$	5.60942e163	1.58413
$506$	3.42216e163	0.857421
$507$	−2.02579e164	−4.50414
$508$	4.65142e163	0.917976
$509$	6.80867e163	1.19299	0.596494	−	0.802617i	$-0.296560\pi$
$509$	6.80867e163	1.19299	0.596494	+	0.802617i	$0.296560\pi$
$510$	5.01732e163	0.780685
$511$	−7.34678e163	−1.01539
$512$	−5.78106e162	−0.0709863
$513$	3.51919e163	0.384010
$514$	−1.03163e164	−1.00059
$515$	−1.69454e164	−1.46122
$516$	−1.09553e164	−0.840073
$517$	9.17841e163	0.626022
$518$	−2.84018e163	−0.172344
$519$	6.95866e163	0.375751
$520$	4.40169e164	2.11552
$521$	−8.96646e163	−0.383653	−0.191826	−	0.981429i	$-0.561441\pi$
$521$	−8.96646e163	−0.383653	−0.191826	+	0.981429i	$0.561441\pi$
$522$	−9.07433e163	−0.345740
$523$	4.03298e164	1.36859	0.684296	−	0.729204i	$-0.260109\pi$
$523$	4.03298e164	1.36859	0.684296	+	0.729204i	$0.260109\pi$
$524$	−2.92570e164	−0.884477
$525$	1.20096e164	0.323513
$526$	8.02099e162	0.0192571
$527$	3.32695e164	0.712040
$528$	−4.04902e163	−0.0772676
$529$	4.95930e163	0.0844018
$530$	−2.79881e162	−0.00424897
$531$	−9.53902e164	−1.29207
$532$	−1.55712e164	−0.188222
$533$	1.91117e165	2.06207
$534$	−2.24745e164	−0.216493
$535$	−8.27777e164	−0.712048
$536$	−2.56203e164	−0.196841
$537$	−1.94046e164	−0.133186
$538$	−1.97143e165	−1.20907
$539$	−2.78944e164	−0.152896
$540$	−1.73541e165	−0.850314
$541$	2.32734e165	1.01959	0.509796	−	0.860296i	$-0.329721\pi$
$541$	2.32734e165	1.01959	0.509796	+	0.860296i	$0.329721\pi$
$542$	9.55136e163	0.0374204
$543$	−7.87414e165	−2.75939
$544$	2.15086e165	0.674341
$545$	−1.59538e165	−0.447586
$546$	8.51680e165	2.13856
$547$	5.62083e165	1.26348	0.631738	−	0.775182i	$-0.282342\pi$
$547$	5.62083e165	1.26348	0.631738	+	0.775182i	$0.282342\pi$
$548$	−2.40751e165	−0.484557
$549$	1.86211e166	3.35644
$550$	−9.36377e164	−0.151185
$551$	6.30037e164	0.0911369
$552$	−1.35342e166	−1.75435
$553$	−5.87091e165	−0.682079
$554$	−7.20903e165	−0.750820
$555$	5.01972e165	0.468764
$556$	−1.20733e166	−1.01112
$557$	1.14058e166	0.856816	0.428408	−	0.903585i	$-0.359075\pi$
$557$	1.14058e166	0.856816	0.428408	+	0.903585i	$0.359075\pi$
$558$	1.73740e166	1.17093
$559$	−2.66316e166	−1.61058
$560$	−7.52362e164	−0.0408368
$561$	3.04706e166	1.48466
$562$	−2.13980e166	−0.936110
$563$	−4.04172e165	−0.158785	−0.0793923	−	0.996843i	$-0.525298\pi$
$563$	−4.04172e165	−0.158785	−0.0793923	+	0.996843i	$0.525298\pi$
$564$	−1.36411e166	−0.481353
$565$	−7.08290e165	−0.224533
$566$	−7.22244e165	−0.205726
$567$	−1.59090e166	−0.407257
$568$	5.56003e166	1.27939
$569$	−1.96984e166	−0.407511	−0.203755	−	0.979022i	$-0.565315\pi$
$569$	−1.96984e166	−0.407511	−0.203755	+	0.979022i	$0.565315\pi$
$570$	−1.81918e166	−0.338412
$571$	−8.12954e166	−1.36013	−0.680067	−	0.733150i	$-0.738049\pi$
$571$	−8.12954e166	−1.36013	−0.680067	+	0.733150i	$0.738049\pi$
$572$	1.00457e167	1.51189
$573$	−1.13486e166	−0.153670
$574$	−5.86449e166	−0.714597
$575$	−1.74345e166	−0.191207
$576$	1.18721e167	1.17210
$577$	1.87435e167	1.66615	0.833075	−	0.553160i	$-0.186578\pi$
$577$	1.87435e167	1.66615	0.833075	+	0.553160i	$0.186578\pi$
$578$	−4.21110e166	−0.337102
$579$	1.45165e167	1.04667
$580$	−3.10688e166	−0.201805
$581$	1.12392e167	0.657776
$582$	7.63901e166	0.402899
$583$	−1.69974e165	−0.00808044
$584$	−2.26542e167	−0.970893
$585$	−9.63559e167	−3.72348
$586$	1.94907e167	0.679237
$587$	3.04431e167	0.956939	0.478469	−	0.878104i	$-0.341192\pi$
$587$	3.04431e167	0.956939	0.478469	+	0.878104i	$0.341192\pi$
$588$	4.14571e166	0.117563
$589$	−1.20629e167	−0.308656
$590$	2.15890e167	0.498524
$591$	−4.71614e167	−0.982980
$592$	−4.87837e165	−0.00917935
$593$	−6.40905e167	−1.08889	−0.544446	−	0.838796i	$-0.683260\pi$
$593$	−6.40905e167	−1.08889	−0.544446	+	0.838796i	$0.683260\pi$
$594$	6.96674e167	1.06893
$595$	5.66184e167	0.784660
$596$	5.23895e167	0.655912
$597$	−1.26288e168	−1.42862
$598$	−1.23639e168	−1.26396
$599$	1.21770e168	1.12517	0.562586	−	0.826739i	$-0.309807\pi$
$599$	1.21770e168	1.12517	0.562586	+	0.826739i	$0.309807\pi$
$600$	3.70324e167	0.309336
$601$	5.83345e167	0.440575	0.220287	−	0.975435i	$-0.429300\pi$
$601$	5.83345e167	0.440575	0.220287	+	0.975435i	$0.429300\pi$
$602$	8.17201e167	0.558137
$603$	5.60847e167	0.346455
$604$	1.56118e168	0.872408
$605$	−1.51392e168	−0.765424
$606$	3.34678e168	1.53121
$607$	1.48904e168	0.616581	0.308290	−	0.951292i	$-0.400243\pi$
$607$	1.48904e168	0.616581	0.308290	+	0.951292i	$0.400243\pi$
$608$	−7.79859e167	−0.292314
$609$	−1.59967e168	−0.542857
$610$	−4.21439e168	−1.29503
$611$	−3.31606e168	−0.922847
$612$	−2.89889e168	−0.730753
$613$	3.09937e168	0.707807	0.353903	−	0.935282i	$-0.384854\pi$
$613$	3.09937e168	0.707807	0.353903	+	0.935282i	$0.384854\pi$
$614$	−3.00397e168	−0.621597
$615$	1.03649e169	1.94365
$616$	−8.20274e168	−1.39420
$617$	−7.25672e168	−1.11812	−0.559059	−	0.829128i	$-0.688838\pi$
$617$	−7.25672e168	−1.11812	−0.559059	+	0.829128i	$0.688838\pi$
$618$	−1.01102e169	−1.41240
$619$	8.29824e168	1.05124	0.525620	−	0.850720i	$-0.323833\pi$
$619$	8.29824e168	1.05124	0.525620	+	0.850720i	$0.323833\pi$
$620$	5.94852e168	0.683458
$621$	1.29714e169	1.35190
$622$	9.68530e168	0.915788
$623$	−2.53615e168	−0.217595
$624$	1.46287e168	0.113904
$625$	−1.62705e169	−1.14990
$626$	−1.35465e169	−0.869120
$627$	−1.10480e169	−0.643573
$628$	−4.96183e168	−0.262472
$629$	3.67118e168	0.176377
$630$	2.95672e169	1.29035
$631$	4.49103e169	1.78061	0.890306	−	0.455363i	$-0.150490\pi$
$631$	4.49103e169	1.78061	0.890306	+	0.455363i	$0.150490\pi$
$632$	−1.81033e169	−0.652190
$633$	−2.20839e168	−0.0723020
$634$	−2.07954e168	−0.0618825
$635$	6.13230e169	1.65887
$636$	2.52618e167	0.00621311
$637$	1.00779e169	0.225391
$638$	1.24725e169	0.253689
$639$	−1.21713e170	−2.25182
$640$	3.70089e169	0.622899
$641$	5.44195e168	0.0833382	0.0416691	−	0.999131i	$-0.486732\pi$
$641$	5.44195e168	0.0833382	0.0416691	+	0.999131i	$0.486732\pi$
$642$	−4.93881e169	−0.688262
$643$	−1.03856e170	−1.31724	−0.658622	−	0.752474i	$-0.728860\pi$
$643$	−1.03856e170	−1.31724	−0.658622	+	0.752474i	$0.728860\pi$
$644$	−5.73942e169	−0.662633
$645$	−1.44431e170	−1.51810
$646$	−1.33046e169	−0.127331
$647$	1.59198e170	1.38749	0.693745	−	0.720221i	$-0.255959\pi$
$647$	1.59198e170	1.38749	0.693745	+	0.720221i	$0.255959\pi$
$648$	−4.90564e169	−0.389411
$649$	1.31112e170	0.948064
$650$	3.38303e169	0.222868
$651$	3.06278e170	1.83851
$652$	−7.51120e169	−0.410894
$653$	9.03638e169	0.450554	0.225277	−	0.974295i	$-0.427671\pi$
$653$	9.03638e169	0.450554	0.225277	+	0.974295i	$0.427671\pi$
$654$	−9.51862e169	−0.432634
$655$	−3.85715e170	−1.59834
$656$	−1.00730e169	−0.0380607
$657$	4.95916e170	1.70885
$658$	1.01755e170	0.319807
$659$	−9.15797e168	−0.0262562	−0.0131281	−	0.999914i	$-0.504179\pi$
$659$	−9.15797e168	−0.0262562	−0.0131281	+	0.999914i	$0.504179\pi$
$660$	5.44807e170	1.42507
$661$	−1.94150e170	−0.463394	−0.231697	−	0.972788i	$-0.574428\pi$
$661$	−1.94150e170	−0.463394	−0.231697	+	0.972788i	$0.574428\pi$
$662$	1.47451e170	0.321174
$663$	−1.10087e171	−2.18860
$664$	3.46566e170	0.628951
$665$	−2.05287e170	−0.340135
$666$	1.91716e170	0.290046
$667$	2.32226e170	0.320847
$668$	−2.39332e169	−0.0302013
$669$	−4.39595e170	−0.506725
$670$	−1.26933e170	−0.133674
$671$	−2.55943e171	−2.46281
$672$	1.98008e171	1.74117
$673$	4.85720e170	0.390368	0.195184	−	0.980767i	$-0.437470\pi$
$673$	4.85720e170	0.390368	0.195184	+	0.980767i	$0.437470\pi$
$674$	6.88146e170	0.505541
$675$	−3.54926e170	−0.238375
$676$	−2.64900e171	−1.62670
$677$	−1.76338e171	−0.990222	−0.495111	−	0.868830i	$-0.664873\pi$
$677$	−1.76338e171	−0.990222	−0.495111	+	0.868830i	$0.664873\pi$
$678$	−4.22591e170	−0.217032
$679$	8.62031e170	0.404950
$680$	1.74586e171	0.750275
$681$	6.43810e171	2.53138
$682$	−2.38801e171	−0.859176
$683$	5.19477e171	1.71046	0.855232	−	0.518246i	$-0.173415\pi$
$683$	5.19477e171	1.71046	0.855232	+	0.518246i	$0.173415\pi$
$684$	1.05108e171	0.316768
$685$	−3.17400e171	−0.875642
$686$	2.33064e171	0.588662
$687$	−7.69577e171	−1.77979
$688$	1.40365e170	0.0297274
$689$	6.14099e169	0.0119117
$690$	−6.70532e171	−1.19138
$691$	4.71550e171	0.767549	0.383775	−	0.923427i	$-0.374624\pi$
$691$	4.71550e171	0.767549	0.383775	+	0.923427i	$0.374624\pi$
$692$	9.09943e170	0.135705
$693$	1.79564e172	2.45391
$694$	3.80782e171	0.476901
$695$	−1.59171e172	−1.82719
$696$	−4.93268e171	−0.519068
$697$	7.58036e171	0.731319
$698$	3.74480e171	0.331265
$699$	−1.71011e172	−1.38725
$700$	1.57043e171	0.116839
$701$	−5.36187e170	−0.0365912	−0.0182956	−	0.999833i	$-0.505824\pi$
$701$	−5.36187e170	−0.0365912	−0.0182956	+	0.999833i	$0.505824\pi$
$702$	−2.51701e172	−1.57576
$703$	−1.33110e171	−0.0764561
$704$	−1.63179e172	−0.860038
$705$	−1.79840e172	−0.869852
$706$	5.40395e171	0.239898
$707$	3.77671e172	1.53900
$708$	−1.94860e172	−0.728973
$709$	3.93606e172	1.35196	0.675980	−	0.736920i	$-0.263720\pi$
$709$	3.93606e172	1.35196	0.675980	+	0.736920i	$0.263720\pi$
$710$	2.75464e172	0.868831
$711$	3.96293e172	1.14791
$712$	−7.82038e171	−0.208060
$713$	−4.44626e172	−1.08662
$714$	3.37806e172	0.758447
$715$	1.32439e173	2.73213
$716$	−2.53743e171	−0.0481012
$717$	−5.86500e172	−1.02178
$718$	−1.98198e172	−0.317373
$719$	−7.92384e172	−1.16637	−0.583187	−	0.812338i	$-0.698195\pi$
$719$	−7.92384e172	−1.16637	−0.583187	+	0.812338i	$0.698195\pi$
$720$	5.07853e171	0.0687262
$721$	−1.14090e173	−1.41959
$722$	−5.03103e172	−0.575647
$723$	1.48413e173	1.56172
$724$	−1.02966e173	−0.996572
$725$	−6.35420e171	−0.0565733
$726$	−9.03257e172	−0.739854
$727$	9.90901e172	0.746790	0.373395	−	0.927672i	$-0.378194\pi$
$727$	9.90901e172	0.746790	0.373395	+	0.927672i	$0.378194\pi$
$728$	2.96356e173	2.05526
$729$	−2.31686e173	−1.47871
$730$	−1.12237e173	−0.659332
$731$	−1.05630e173	−0.571198
$732$	3.80387e173	1.89368
$733$	−2.26086e173	−1.03630	−0.518148	−	0.855291i	$-0.673378\pi$
$733$	−2.26086e173	−1.03630	−0.518148	+	0.855291i	$0.673378\pi$
$734$	−1.02773e173	−0.433778
$735$	5.46558e172	0.212448
$736$	−2.87449e173	−1.02909
$737$	−7.70871e172	−0.254214
$738$	3.95860e173	1.20263
$739$	−1.67516e173	−0.468887	−0.234443	−	0.972130i	$-0.575327\pi$
$739$	−1.67516e173	−0.468887	−0.234443	+	0.972130i	$0.575327\pi$
$740$	6.56400e172	0.169297
$741$	3.99153e173	0.948719
$742$	−1.88438e171	−0.00412794
$743$	2.76872e172	0.0559057	0.0279528	−	0.999609i	$-0.491101\pi$
$743$	2.76872e172	0.0559057	0.0279528	+	0.999609i	$0.491101\pi$
$744$	9.44426e173	1.75794
$745$	6.90688e173	1.18530
$746$	−4.36333e173	−0.690430
$747$	−7.58657e173	−1.10700
$748$	3.98446e173	0.536195
$749$	−5.57325e173	−0.691765
$750$	−8.15748e173	−0.934005
$751$	4.60332e173	0.486245	0.243122	−	0.969996i	$-0.421828\pi$
$751$	4.60332e173	0.486245	0.243122	+	0.969996i	$0.421828\pi$
$752$	1.74776e172	0.0170335
$753$	−6.65271e173	−0.598277
$754$	−4.50617e173	−0.373974
$755$	2.05822e174	1.57653
$756$	−1.16842e174	−0.826092
$757$	−1.09542e173	−0.0714959	−0.0357479	−	0.999361i	$-0.511381\pi$
$757$	−1.09542e173	−0.0714959	−0.0357479	+	0.999361i	$0.511381\pi$
$758$	−4.63682e173	−0.279404
$759$	−4.07219e174	−2.26569
$760$	−6.33014e173	−0.325230
$761$	2.60256e174	1.23489	0.617446	−	0.786613i	$-0.288167\pi$
$761$	2.60256e174	1.23489	0.617446	+	0.786613i	$0.288167\pi$
$762$	3.65875e174	1.60346
$763$	−1.07414e174	−0.434836
$764$	−1.48399e173	−0.0554988
$765$	−3.82181e174	−1.32054
$766$	2.57938e174	0.823520
$767$	−4.73693e174	−1.39758
$768$	6.23638e174	1.70051
$769$	−2.79564e174	−0.704592	−0.352296	−	0.935889i	$-0.614599\pi$
$769$	−2.79564e174	−0.704592	−0.352296	+	0.935889i	$0.614599\pi$
$770$	−4.06394e174	−0.946801
$771$	1.22759e175	2.64401
$772$	1.89824e174	0.378011
$773$	6.86026e174	1.26323	0.631613	−	0.775284i	$-0.282393\pi$
$773$	6.86026e174	1.26323	0.631613	+	0.775284i	$0.282393\pi$
$774$	−5.51620e174	−0.939317
$775$	1.21659e174	0.191599
$776$	2.65812e174	0.387205
$777$	3.37967e174	0.455411
$778$	−1.94553e174	−0.242534
$779$	−2.74848e174	−0.317013
$780$	−1.96833e175	−2.10075
$781$	1.67292e175	1.65229
$782$	−4.90395e174	−0.448268
$783$	4.72759e174	0.399994
$784$	−5.31168e172	−0.00416016
$785$	−6.54153e174	−0.474313
$786$	−2.30131e175	−1.54494
$787$	−3.01196e175	−1.87231	−0.936156	−	0.351584i	$-0.885643\pi$
$787$	−3.01196e175	−1.87231	−0.936156	+	0.351584i	$0.885643\pi$
$788$	−6.16703e174	−0.355009
$789$	−9.54457e173	−0.0508859
$790$	−8.96904e174	−0.442901
$791$	−4.76877e174	−0.218137
$792$	5.53695e175	2.34637
$793$	9.24697e175	3.63054
$794$	−1.41329e175	−0.514151
$795$	3.33044e173	0.0112277
$796$	−1.65140e175	−0.515954
$797$	−3.25233e175	−0.941817	−0.470909	−	0.882182i	$-0.656074\pi$
$797$	−3.25233e175	−0.941817	−0.470909	+	0.882182i	$0.656074\pi$
$798$	−1.22481e175	−0.328772
$799$	−1.31527e175	−0.327290
$800$	7.86523e174	0.181454
$801$	1.71194e175	0.366201
$802$	1.71649e174	0.0340480
$803$	−6.81626e175	−1.25388
$804$	1.14568e175	0.195467
$805$	−7.56669e175	−1.19744
$806$	8.62764e175	1.26655
$807$	2.34590e176	3.19492
$808$	1.16457e176	1.47156
$809$	−1.57367e176	−1.84514	−0.922569	−	0.385832i	$-0.873914\pi$
$809$	−1.57367e176	−1.84514	−0.922569	+	0.385832i	$0.873914\pi$
$810$	−2.43044e175	−0.264448
$811$	−4.89262e175	−0.494060	−0.247030	−	0.969008i	$-0.579455\pi$
$811$	−4.89262e175	−0.494060	−0.247030	+	0.969008i	$0.579455\pi$
$812$	−2.09180e175	−0.196056
$813$	−1.13656e175	−0.0988816
$814$	−2.63509e175	−0.212823
$815$	−9.90255e175	−0.742526
$816$	5.80224e174	0.0403963
$817$	3.82994e175	0.247604
$818$	−4.34006e174	−0.0260568
$819$	−6.48745e176	−3.61741
$820$	1.35535e176	0.701963
$821$	3.28799e176	1.58187	0.790933	−	0.611902i	$-0.209595\pi$
$821$	3.28799e176	1.58187	0.790933	+	0.611902i	$0.209595\pi$
$822$	−1.89372e176	−0.846390
$823$	2.75974e176	1.14598	0.572991	−	0.819562i	$-0.305783\pi$
$823$	2.75974e176	1.14598	0.572991	+	0.819562i	$0.305783\pi$
$824$	−3.51803e176	−1.35738
$825$	1.11424e176	0.399499
$826$	1.45354e176	0.484323
$827$	1.97669e176	0.612147	0.306074	−	0.952008i	$-0.400985\pi$
$827$	1.97669e176	0.612147	0.306074	+	0.952008i	$0.400985\pi$
$828$	3.87418e176	1.11518
$829$	−5.68537e176	−1.52128	−0.760641	−	0.649173i	$-0.775115\pi$
$829$	−5.68537e176	−1.52128	−0.760641	+	0.649173i	$0.775115\pi$
$830$	1.71702e176	0.427120
$831$	8.57838e176	1.98401
$832$	5.89548e176	1.26782
$833$	3.99726e175	0.0799355
$834$	−9.49670e176	−1.76615
$835$	−3.15529e175	−0.0545767
$836$	−1.44468e176	−0.232430
$837$	−9.05157e176	−1.35467
$838$	4.12625e176	0.574503
$839$	1.81898e176	0.235630	0.117815	−	0.993036i	$-0.462411\pi$
$839$	1.81898e176	0.235630	0.117815	+	0.993036i	$0.462411\pi$
$840$	1.60723e177	1.93723
$841$	−8.06937e176	−0.905070
$842$	−8.10111e176	−0.845596
$843$	2.54626e177	2.47363
$844$	−2.88778e175	−0.0261123
$845$	−3.49237e177	−2.93961
$846$	−6.86856e176	−0.538218
$847$	−1.01929e177	−0.743620
$848$	−3.23667e173	−0.000219861 0
$849$	8.59433e176	0.543622
$850$	1.34183e176	0.0790409
$851$	−4.90630e176	−0.269163
$852$	−2.48632e177	−1.27046
$853$	2.63318e177	1.25333	0.626664	−	0.779289i	$-0.284420\pi$
$853$	2.63318e177	1.25333	0.626664	+	0.779289i	$0.284420\pi$
$854$	−2.83747e177	−1.25814
$855$	1.38571e177	0.572430
$856$	−1.71854e177	−0.661451
$857$	1.79310e177	0.643081	0.321540	−	0.946896i	$-0.395799\pi$
$857$	1.79310e177	0.643081	0.321540	+	0.946896i	$0.395799\pi$
$858$	7.90179e177	2.64086
$859$	3.08005e175	0.00959337	0.00479668	−	0.999988i	$-0.498473\pi$
$859$	3.08005e175	0.00959337	0.00479668	+	0.999988i	$0.498473\pi$
$860$	−1.88865e177	−0.548270
$861$	6.97845e177	1.88829
$862$	3.69233e176	0.0931346
$863$	−2.74394e177	−0.645240	−0.322620	−	0.946529i	$-0.604564\pi$
$863$	−2.74394e177	−0.645240	−0.322620	+	0.946529i	$0.604564\pi$
$864$	−5.85181e177	−1.28295
$865$	1.19964e177	0.245232
$866$	−2.98131e177	−0.568296
$867$	5.01099e177	0.890776
$868$	4.00502e177	0.663990
$869$	−5.44697e177	−0.842283
$870$	−2.44383e177	−0.352498
$871$	2.78508e177	0.374748
$872$	−3.31217e177	−0.415781
$873$	−5.81881e177	−0.681511
$874$	1.77807e177	0.194316
$875$	−9.20538e177	−0.938760
$876$	1.01304e178	0.964116
$877$	2.07872e178	1.84638	0.923189	−	0.384346i	$-0.125573\pi$
$877$	2.07872e178	1.84638	0.923189	+	0.384346i	$0.125573\pi$
$878$	−3.05706e177	−0.253446
$879$	−2.31929e178	−1.79485
$880$	−6.98033e176	−0.0504283
$881$	−7.66170e177	−0.516753	−0.258376	−	0.966044i	$-0.583187\pi$
$881$	−7.66170e177	−0.516753	−0.258376	+	0.966044i	$0.583187\pi$
$882$	2.08744e177	0.131451
$883$	2.40851e178	1.41620	0.708102	−	0.706111i	$-0.249552\pi$
$883$	2.40851e178	1.41620	0.708102	+	0.706111i	$0.249552\pi$
$884$	−1.43954e178	−0.790429
$885$	−2.56898e178	−1.31733
$886$	2.49360e177	0.119423
$887$	−3.02695e178	−1.35402	−0.677012	−	0.735972i	$-0.736726\pi$
$887$	−3.02695e178	−1.35402	−0.677012	+	0.735972i	$0.736726\pi$
$888$	1.04214e178	0.435454
$889$	4.12875e178	1.61162
$890$	−3.87451e177	−0.141293
$891$	−1.47602e178	−0.502912
$892$	−5.74832e177	−0.183007
$893$	4.76888e177	0.141874
$894$	4.12089e178	1.14570
$895$	−3.34527e177	−0.0869235
$896$	2.49173e178	0.605155
$897$	1.47124e179	3.33996
$898$	−6.41459e177	−0.136129
$899$	−1.62049e178	−0.321503
$900$	−1.06006e178	−0.196634
$901$	2.43573e176	0.00422453
$902$	−5.44101e178	−0.882438
$903$	−9.72427e178	−1.47485
$904$	−1.47048e178	−0.208578
$905$	−1.35747e179	−1.80090
$906$	1.22801e179	1.52386
$907$	−7.66413e178	−0.889656	−0.444828	−	0.895616i	$-0.646735\pi$
$907$	−7.66413e178	−0.889656	−0.444828	+	0.895616i	$0.646735\pi$
$908$	8.41873e178	0.914225
$909$	−2.54932e179	−2.59006
$910$	1.46826e179	1.39572
$911$	−1.43624e179	−1.27751	−0.638757	−	0.769408i	$-0.720551\pi$
$911$	−1.43624e179	−1.27751	−0.638757	+	0.769408i	$0.720551\pi$
$912$	−2.10377e177	−0.0175110
$913$	1.04276e179	0.812271
$914$	−4.05369e178	−0.295533
$915$	5.01491e179	3.42206
$916$	−1.00633e179	−0.642784
$917$	−2.59694e179	−1.55281
$918$	−9.98333e178	−0.558847
$919$	2.32873e179	1.22048	0.610241	−	0.792216i	$-0.291073\pi$
$919$	2.32873e179	1.22048	0.610241	+	0.792216i	$0.291073\pi$
$920$	−2.33323e179	−1.14497
$921$	3.57457e179	1.64254
$922$	−1.98305e179	−0.853322
$923$	−6.04407e179	−2.43572
$924$	3.66808e179	1.38447
$925$	1.34247e178	0.0474602
$926$	2.90577e178	0.0962269
$927$	7.70120e179	2.38910
$928$	−1.04764e179	−0.304481
$929$	4.77182e179	1.29937	0.649686	−	0.760203i	$-0.274900\pi$
$929$	4.77182e179	1.29937	0.649686	+	0.760203i	$0.274900\pi$
$930$	4.67903e179	1.19382
$931$	−1.44933e178	−0.0346505
$932$	−2.23621e179	−0.501015
$933$	−1.15250e180	−2.41993
$934$	2.56600e179	0.504975
$935$	5.25300e179	0.968957
$936$	−2.00044e180	−3.45889
$937$	2.46566e178	0.0399658	0.0199829	−	0.999800i	$-0.493639\pi$
$937$	2.46566e178	0.0399658	0.0199829	+	0.999800i	$0.493639\pi$
$938$	−8.54611e178	−0.129866
$939$	1.61196e180	2.29661
$940$	−2.35167e179	−0.314153
$941$	4.59176e179	0.575184	0.287592	−	0.957753i	$-0.407145\pi$
$941$	4.59176e179	0.575184	0.287592	+	0.957753i	$0.407145\pi$
$942$	−3.90291e179	−0.458468
$943$	−1.01307e180	−1.11604
$944$	2.49665e178	0.0257959
$945$	−1.54040e180	−1.49283
$946$	7.58190e179	0.689230
$947$	−1.60712e180	−1.37048	−0.685242	−	0.728316i	$-0.740303\pi$
$947$	−1.60712e180	−1.37048	−0.685242	+	0.728316i	$0.740303\pi$
$948$	8.09537e179	0.647638
$949$	2.46264e180	1.84840
$950$	−4.86519e178	−0.0342627
$951$	2.47455e179	0.163521
$952$	1.17545e180	0.728903
$953$	−4.73208e179	−0.275380	−0.137690	−	0.990475i	$-0.543968\pi$
$953$	−4.73208e179	−0.275380	−0.137690	+	0.990475i	$0.543968\pi$
$954$	1.27198e178	0.00694711
$955$	−1.95645e179	−0.100292
$956$	−7.66933e179	−0.369024
$957$	−1.48416e180	−0.670360
$958$	2.90989e179	0.123385
$959$	−2.13699e180	−0.850699
$960$	3.19730e180	1.19502
$961$	2.53164e179	0.0888459
$962$	9.52031e179	0.313732
$963$	3.76201e180	1.16421
$964$	1.94071e180	0.564026
$965$	2.50259e180	0.683103
$966$	−4.51456e180	−1.15744
$967$	5.60438e180	1.34966	0.674832	−	0.737972i	$-0.264216\pi$
$967$	5.60438e180	1.34966	0.674832	+	0.737972i	$0.264216\pi$
$968$	−3.14304e180	−0.711034
$969$	1.58318e180	0.336466
$970$	1.31693e180	0.262950
$971$	−5.92591e180	−1.11171	−0.555855	−	0.831279i	$-0.687609\pi$
$971$	−5.92591e180	−1.11171	−0.555855	+	0.831279i	$0.687609\pi$
$972$	−2.24018e180	−0.394889
$973$	−1.07166e181	−1.77514
$974$	−8.51650e179	−0.132570
$975$	−4.02563e180	−0.588918
$976$	−4.87370e179	−0.0670109
$977$	−2.85430e180	−0.368875	−0.184437	−	0.982844i	$-0.559046\pi$
$977$	−2.85430e180	−0.368875	−0.184437	+	0.982844i	$0.559046\pi$
$978$	−5.90822e180	−0.717721
$979$	−2.35302e180	−0.268703
$980$	7.14702e179	0.0767268
$981$	7.25056e180	0.731807
$982$	−1.37774e180	−0.130744
$983$	1.31682e181	1.17500	0.587502	−	0.809223i	$-0.300111\pi$
$983$	1.31682e181	1.17500	0.587502	+	0.809223i	$0.300111\pi$
$984$	2.15184e181	1.80554
$985$	−8.13043e180	−0.641537
$986$	−1.78730e180	−0.132631
$987$	−1.21083e181	−0.845074
$988$	5.21949e180	0.342636
$989$	1.41168e181	0.871687
$990$	2.74321e181	1.59342
$991$	−1.20857e181	−0.660413	−0.330206	−	0.943909i	$-0.607118\pi$
$991$	−1.20857e181	−0.660413	−0.330206	+	0.943909i	$0.607118\pi$
$992$	2.00585e181	1.03120
$993$	−1.75459e181	−0.848686
$994$	1.85465e181	0.844082
$995$	−2.17715e181	−0.932380
$996$	−1.54976e181	−0.624561
$997$	−2.36748e180	−0.0897902	−0.0448951	−	0.998992i	$-0.514295\pi$
$997$	−2.36748e180	−0.0897902	−0.0448951	+	0.998992i	$0.514295\pi$
$998$	−2.84274e181	−1.01470
$999$	−9.98810e180	−0.335561

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.122.a.a.1.7	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.122.a.a.1.7	✓	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)

\(f(q)\)	\(=\)	\(q+1.02857e18 q^{2} -1.22395e29 q^{3} -1.60049e36 q^{4} -2.11004e42 q^{5} -1.25893e47 q^{6} -1.42065e51 q^{7} -4.38064e54 q^{8} +9.58953e57 q^{9} +O(q^{10})\)	\(q+1.02857e18 q^{2} -1.22395e29 q^{3} -1.60049e36 q^{4} -2.11004e42 q^{5} -1.25893e47 q^{6} -1.42065e51 q^{7} -4.38064e54 q^{8} +9.58953e57 q^{9} -2.17033e60 q^{10} -1.31806e63 q^{11} +1.95892e65 q^{12} +4.76201e67 q^{13} -1.46124e69 q^{14} +2.58259e71 q^{15} -2.50987e71 q^{16} +1.88878e74 q^{17} +9.86355e75 q^{18} -6.84833e76 q^{19} +3.37710e78 q^{20} +1.73880e80 q^{21} -1.35572e81 q^{22} -2.52423e82 q^{23} +5.36169e83 q^{24} +6.90684e83 q^{25} +4.89809e85 q^{26} -5.13876e86 q^{27} +2.27373e87 q^{28} -9.19986e87 q^{29} +2.65638e89 q^{30} +1.76143e90 q^{31} +1.13876e91 q^{32} +1.61324e92 q^{33} +1.94275e92 q^{34} +2.99762e93 q^{35} -1.53480e94 q^{36} +1.94368e94 q^{37} -7.04402e94 q^{38} -5.82847e96 q^{39} +9.24333e96 q^{40} +4.01337e97 q^{41} +1.78849e98 q^{42} -5.59251e98 q^{43} +2.10954e99 q^{44} -2.02343e100 q^{45} -2.59636e100 q^{46} -6.96357e100 q^{47} +3.07195e100 q^{48} +2.11632e101 q^{49} +7.10421e101 q^{50} -2.31177e103 q^{51} -7.62155e103 q^{52} +1.28958e102 q^{53} -5.28560e104 q^{54} +2.78116e105 q^{55} +6.22335e105 q^{56} +8.38202e105 q^{57} -9.46274e105 q^{58} -9.94733e106 q^{59} -4.13340e107 q^{60} +1.94182e108 q^{61} +1.81176e108 q^{62} -1.36233e109 q^{63} +1.23802e109 q^{64} -1.00480e110 q^{65} +1.65934e110 q^{66} +5.84853e109 q^{67} -3.02297e110 q^{68} +3.08954e111 q^{69} +3.08328e111 q^{70} -1.26923e112 q^{71} -4.20083e112 q^{72} +5.17143e112 q^{73} +1.99922e112 q^{74} -8.45364e112 q^{75} +1.09607e113 q^{76} +1.87250e114 q^{77} -5.99502e114 q^{78} +4.13256e114 q^{79} +5.29591e113 q^{80} +1.11984e115 q^{81} +4.12805e115 q^{82} -7.91130e115 q^{83} -2.78293e116 q^{84} -3.98540e116 q^{85} -5.75232e116 q^{86} +1.12602e117 q^{87} +5.77395e117 q^{88} +1.78521e117 q^{89} -2.08125e118 q^{90} -6.76513e118 q^{91} +4.04001e118 q^{92} -2.15591e119 q^{93} -7.16256e118 q^{94} +1.44502e119 q^{95} -1.39379e120 q^{96} -6.06788e119 q^{97} +2.17679e119 q^{98} -1.26396e121 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 23\!\cdots\!28 q^{2}+ \cdots + 79\!\cdots\!17 q^{9}+O(q^{10}) \) 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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