LMFDB - Embedded newform 2.88.a.b.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2,88,Mod(1,2)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2.1"); S:= CuspForms(chi, 88); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 88, names="a")

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 88 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$95.8667262922$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2 x^{3} + \cdots + 13\!\cdots\!68 $ x^4 - 2x^3 - 281103089248735483936525960163617359x^2 - 12802046688892212650602531506830185803155982810145588*x + 13431538901013885043865389957038837902382364731827315409437340098095268
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 17\cdot 29 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-4.15109e17$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-8.79609e12 q^{2} +8.97819e20 q^{3} +7.73713e25 q^{4} +3.21672e30 q^{5} -7.89730e33 q^{6} +8.51076e36 q^{7} -6.80565e38 q^{8} +4.82821e41 q^{9} -2.82946e43 q^{10} +1.44187e45 q^{11} +6.94654e46 q^{12} +1.58019e48 q^{13} -7.48615e49 q^{14} +2.88803e51 q^{15} +5.98631e51 q^{16} -6.18852e53 q^{17} -4.24694e54 q^{18} +6.29366e55 q^{19} +2.48882e56 q^{20} +7.64113e57 q^{21} -1.26828e58 q^{22} +2.79664e58 q^{23} -6.11024e59 q^{24} +3.88493e60 q^{25} -1.38995e61 q^{26} +1.43259e62 q^{27} +6.58489e62 q^{28} +3.72251e63 q^{29} -2.54034e64 q^{30} +9.26519e64 q^{31} -5.26561e64 q^{32} +1.29454e66 q^{33} +5.44348e66 q^{34} +2.73767e67 q^{35} +3.73565e67 q^{36} +5.17665e67 q^{37} -5.53596e68 q^{38} +1.41872e69 q^{39} -2.18919e69 q^{40} -6.26732e69 q^{41} -6.72121e70 q^{42} -1.26820e71 q^{43} +1.11559e71 q^{44} +1.55310e72 q^{45} -2.45995e71 q^{46} -8.18255e72 q^{47} +5.37462e72 q^{48} +3.90498e73 q^{49} -3.41722e73 q^{50} -5.55617e74 q^{51} +1.22261e74 q^{52} -1.68903e75 q^{53} -1.26012e75 q^{54} +4.63809e75 q^{55} -5.79213e75 q^{56} +5.65056e76 q^{57} -3.27436e76 q^{58} -1.48693e77 q^{59} +2.23451e77 q^{60} -3.28414e77 q^{61} -8.14974e77 q^{62} +4.10918e78 q^{63} +4.63168e77 q^{64} +5.08302e78 q^{65} -1.13869e79 q^{66} +3.12202e79 q^{67} -4.78813e79 q^{68} +2.51088e79 q^{69} -2.40808e80 q^{70} -2.96376e80 q^{71} -3.28591e80 q^{72} +9.74503e80 q^{73} -4.55343e80 q^{74} +3.48796e81 q^{75} +4.86948e81 q^{76} +1.22714e82 q^{77} -1.24792e82 q^{78} -4.07789e82 q^{79} +1.92563e82 q^{80} -2.74553e82 q^{81} +5.51279e82 q^{82} +4.93307e82 q^{83} +5.91203e83 q^{84} -1.99067e84 q^{85} +1.11552e84 q^{86} +3.34214e84 q^{87} -9.81285e83 q^{88} -4.22584e83 q^{89} -1.36612e85 q^{90} +1.34486e85 q^{91} +2.16380e84 q^{92} +8.31846e85 q^{93} +7.19744e85 q^{94} +2.02449e86 q^{95} -4.72757e85 q^{96} -3.85645e86 q^{97} -3.43486e86 q^{98} +6.96165e86 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 35184372088832 q^{2} + 40\!\cdots\!28 q^{3} + 30\!\cdots\!56 q^{4} - 40\!\cdots\!60 q^{5} - 35\!\cdots\!24 q^{6} + 85\!\cdots\!04 q^{7} - 27\!\cdots\!48 q^{8} + 82\!\cdots\!48 q^{9} + 35\!\cdots\!80 q^{10}+ \cdots + 22\!\cdots\!76 q^{99}+O(q^{100}) $ 4 * q - 35184372088832 * q^2 + 403237985254067182128 * q^3 + 309485009821345068724781056 * q^4 - 4037922390733497835169570162760 * q^5 - 3546918828382512738768149884698624 * q^6 + 8582179387397492406597229487230375904 * q^7 - 2722258935367507707706996859454145691648 * q^8 + 820135434884318664352221575507492568732948 * q^9 + 35517940965348365626859729845107910854574080 * q^10 + 2970616434026495781757184460756379040517208848 * q^11 + 31199027956673594964608194726311446315419041792 * q^12 - 1767394568818848613362028589161957028533441611112 * q^13 - 75489648224824411010546555477731971328955260076032 * q^14 + 3370976843124805373452544557684295582910726697502880 * q^15 + 23945242826029513411849172299223580994042798784118784 * q^16 - 702353032002195299447255515013113779135644499293109816 * q^17 - 7213987576051478951188874632704563580254297738585309184 * q^18 + 38051210330377980576900552965948384772060949611758270960 * q^19 - 312419112688496434410317985513745659312699567327821168640 * q^20 - 2960768946346244712423575885216855505816696171119080255872 * q^21 - 26129818486996871127304316256231512888117802859237038096384 * q^22 + 267410844513343534387094489566271409098947974355011539188128 * q^23 - 274429552109368924814832586348763817236857825346144736116736 * q^24 + 26866935732372298920001618987293695975686810093231631671755100 * q^25 + 15546167034275791140382436144471296993092547711081656715575296 * q^26 + 98351974670575379028284146601861806526822489553847883125490400 * q^27 + 664013967999314535695892002534007752932295679741402958744518656 * q^28 - 936377285291713459807588765220376016646503474372565915415382440 * q^29 - 29651425887834852403903990749669038123824799034099618745983959040 * q^30 + 119463507882721430244886842916392661099853847057206322986794525568 * q^31 - 210624583337114373395836055367340864637790190801098222508621955072 * q^32 - 975951433415384517573045287992141578476030063995050605617360966464 * q^33 + 6177962603921142192805661314942895498269819437765021241050270793728 * q^34 + 14105085028850567766840711566409137394874532315214531645239547531840 * q^35 + 63454905780001617731151046382612710619432714548573512194720658358272 * q^36 + 182087106643248709136261820106869557597167548749803025400276539121464 * q^37 - 334701985673606721323645108291715305922613643471269213861286961479680 * q^38 - 5157167650299694789254850025641525408739411563899847457339313757250784 * q^39 + 2748067577123698321827685975535901419950085077291708477942376033157120 * q^40 + 5499251594717860286021866958065054045901150247706209838765933372175208 * q^41 + 26043199069326335451693431452427559455621627547084532573326442418405376 * q^42 - 157807090931211109929865823295822094205785343123733495078770527721821552 * q^43 + 229840314065034778104010119086398472312972227124835062038272769756495872 * q^44 - 1370445036354823659067923168385609449595471872659192002945296358462825320 * q^45 - 2352170663486569504369914341681047401963148037857733129248014646193946624 * q^46 - 11700969700600051870794491472787906623524149540240126773037581150641555136 * q^47 + 2413907868396886727226140291242059049083751312718584875630451012128473088 * q^48 + 45608750768809825384693277965554885824930550141562503946687984691665533732 * q^49 - 236324065923630760668657815178197122585685320681456781276991408990637260800 * q^50 - 914883468555652107825206155517190576830844787740672822262980556765469169312 * q^51 - 136745531372273324016576733538944106078280970896210682631976284458024173568 * q^52 - 3205407327892231366350098762423033970241498041998526172742677864692608514312 * q^53 - 865113118120226050927175001395744751092084611954848335836798017458090803200 * q^54 - 10009926131406218736826424103970095109094189414661383153140158173941128709920 * q^55 - 5840728630567416793561662980979737449788739679624018831289026246209278312448 * q^56 + 24760562583447132282306921710743074800398451150699602451361304490068034752320 * q^57 + 8236461705308510473577685400040524235406303263089755599489781422351733227520 * q^58 - 81401388903576961577929700275194040780233584053778446123485310614164754536880 * q^59 + 260816700350501796503049467891128405126358446664151554703502613334842482360320 * q^60 + 908111889319782669823282318823295371554753169091641506977419705876741077882328 * q^61 - 1050812128095696376586514967647428079039044942828517372626320439677738647814144 * q^62 + 7137835102413627130280079665652016586382162073538425059614697312278117344350048 * q^63 + 1852673427797059126777135760139006525652319754650249024631321344126610074238976 * q^64 + 11407211919915638593357605065156231994296813060854399078385375214171172364857680 * q^65 + 8584559593478959280621500012652850349171438888492092327918713325137577495232512 * q^66 - 65059771693644954593974794228917141656005263924052931483321156753263176566322896 * q^67 - 54341933751812724902023253670568124974314494093364989057139191298059718491111424 * q^68 - 144323666676858272713465642347149842097884989245184653886655055101689375583845504 * q^69 - 124069639999923005500646624090308971041908232841505948959254386145464972707102720 * q^70 - 183272612160344892942190287282961718510131375557583525213035115209249713064136992 * q^71 - 558155253956338317275929527602177423655680841848067355296117578760944212116504576 * q^72 + 354182538046550765754528347144724476790476600029207619306415675742769571814637288 * q^73 - 1601655128178723932025775974507397068426901430503198065737820251919877020961472512 * q^74 + 710386439551323791969874648476083944602337020291621916942901745237698809202501200 * q^75 + 2944069800702774064027323538684509525361173924971530627370715914294143730780733440 * q^76 + 39316760279456924611775164190833990669200449799501752350802186925973327788597118848 * q^77 + 45362926383157972415756683406366951526581873158623352931657948697548800307937411072 * q^78 + 15689408650300008287770111864298279692820798574497171271867094782550105530843081920 * q^79 - 24172258039693807695503348146758763873414302432021545297363850106765398076513320960 * q^80 - 196590592451401107987710944406206415161857917104016937408869683425180184810203702876 * q^81 - 48371928579663987252349183028740936842481506637169603120359663272770590191611019264 * q^82 + 111926752599709260117886233216331177095176580206068162806299107496899925996223203568 * q^83 - 229078401609675258913891688255885614430188449105962531942162006259872232223914590208 * q^84 - 891497844731417844264766892389844899904478293183670323386186444763703698463839596560 * q^85 + 1388085851394969400976659588554077855842466084275351230019781346209556380442549026816 * q^86 + 2027498154029213080175869882525768385333184769847411190333977363043382754362186713120 * q^87 - 2021696782769547651193529032558892722193566089333659035337753899891686714980356325376 * q^88 - 1111763274969003683091618237538433748811411444468148051875571331333583253595104867160 * q^89 + 12054562021600253271129669326554918303828197627410649510778436683009490086217184706560 * q^90 + 79630263055292573954918630151432006426386375686727482380289693283976606755116980321088 * q^91 + 20689911960136575706111408504507326985128933416561732998791094227623959804415198625792 * q^92 + 121552396376548026998325328889505560359171182104366398760596365823334350324441379006976 * q^93 + 102922817936515347171258282828953462563508237397083710417081191671708730834331304460288 * q^94 + 360329377379389097240594968925389763617374668200294178024200943546627617266362721242400 * q^95 - 21232958157458842504504822471050360495135888697596704547293213652627233307394314338304 * q^96 + 84654632295309208342666811638631082612402959416215649507302559581340331556342797429384 * q^97 - 401178814389151860471251451603139889379513741986404607571754642978513123633817249120256 * q^98 + 2203878007770692926523827334498155512549713414229081953932986276578630523661724303178576 * q^99

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 $

$2$	−8.79609e12	−0.707107
$2$	−8.79609e12	−0.707107
$3$	8.97819e20	1.57912	0.789558	−	0.613676i	$-0.210310\pi$
$3$	8.97819e20	1.57912	0.789558	+	0.613676i	$0.210310\pi$
$4$	7.73713e25	0.500000
$5$	3.21672e30	1.26537	0.632685	−	0.774409i	$-0.281953\pi$
$5$	3.21672e30	1.26537	0.632685	+	0.774409i	$0.281953\pi$
$6$	−7.89730e33	−1.11660
$7$	8.51076e36	1.47300	0.736502	−	0.676436i	$-0.236476\pi$
$7$	8.51076e36	1.47300	0.736502	+	0.676436i	$0.236476\pi$
$8$	−6.80565e38	−0.353553
$9$	4.82821e41	1.49361
$10$	−2.82946e43	−0.894752
$11$	1.44187e45	0.721679	0.360839	−	0.932628i	$-0.382490\pi$
$11$	1.44187e45	0.721679	0.360839	+	0.932628i	$0.382490\pi$
$12$	6.94654e46	0.789558
$13$	1.58019e48	0.552298	0.276149	−	0.961115i	$-0.410942\pi$
$13$	1.58019e48	0.552298	0.276149	+	0.961115i	$0.410942\pi$
$14$	−7.48615e49	−1.04157
$15$	2.88803e51	1.99817
$16$	5.98631e51	0.250000
$17$	−6.18852e53	−1.84952	−0.924759	−	0.380554i	$-0.875733\pi$
$17$	−6.18852e53	−1.84952	−0.924759	+	0.380554i	$0.875733\pi$
$18$	−4.24694e54	−1.05614
$19$	6.29366e55	1.48978	0.744889	−	0.667189i	$-0.232502\pi$
$19$	6.29366e55	1.48978	0.744889	+	0.667189i	$0.232502\pi$
$20$	2.48882e56	0.632685
$21$	7.64113e57	2.32604
$22$	−1.26828e58	−0.510304
$23$	2.79664e58	0.162733	0.0813666	−	0.996684i	$-0.474072\pi$
$23$	2.79664e58	0.162733	0.0813666	+	0.996684i	$0.474072\pi$
$24$	−6.11024e59	−0.558302
$25$	3.88493e60	0.601164
$26$	−1.38995e61	−0.390534
$27$	1.43259e62	0.779466
$28$	6.58489e62	0.736502
$29$	3.72251e63	0.904739	0.452369	−	0.891831i	$-0.350579\pi$
$29$	3.72251e63	0.904739	0.452369	+	0.891831i	$0.350579\pi$
$30$	−2.54034e64	−1.41292
$31$	9.26519e64	1.23771	0.618857	−	0.785503i	$-0.287596\pi$
$31$	9.26519e64	1.23771	0.618857	+	0.785503i	$0.287596\pi$
$32$	−5.26561e64	−0.176777
$33$	1.29454e66	1.13962
$34$	5.44348e66	1.30781
$35$	2.73767e67	1.86390
$36$	3.73565e67	0.746804
$37$	5.17665e67	0.314249	0.157124	−	0.987579i	$-0.449778\pi$
$37$	5.17665e67	0.314249	0.157124	+	0.987579i	$0.449778\pi$
$38$	−5.53596e68	−1.05343
$39$	1.41872e69	0.872143
$40$	−2.18919e69	−0.447376
$41$	−6.26732e69	−0.437506	−0.218753	−	0.975780i	$-0.570199\pi$
$41$	−6.26732e69	−0.437506	−0.218753	+	0.975780i	$0.570199\pi$
$42$	−6.72121e70	−1.64476
$43$	−1.26820e71	−1.11509	−0.557546	−	0.830146i	$-0.688257\pi$
$43$	−1.26820e71	−1.11509	−0.557546	+	0.830146i	$0.688257\pi$
$44$	1.11559e71	0.360839
$45$	1.55310e72	1.88997
$46$	−2.45995e71	−0.115070
$47$	−8.18255e72	−1.50187	−0.750934	−	0.660378i	$-0.770396\pi$
$47$	−8.18255e72	−1.50187	−0.750934	+	0.660378i	$0.770396\pi$
$48$	5.37462e72	0.394779
$49$	3.90498e73	1.16974
$50$	−3.41722e73	−0.425087
$51$	−5.55617e74	−2.92060
$52$	1.22261e74	0.276149
$53$	−1.68903e75	−1.66585	−0.832925	−	0.553385i	$-0.813336\pi$
$53$	−1.68903e75	−1.66585	−0.832925	+	0.553385i	$0.813336\pi$
$54$	−1.26012e75	−0.551166
$55$	4.63809e75	0.913192
$56$	−5.79213e75	−0.520785
$57$	5.65056e76	2.35253
$58$	−3.27436e76	−0.639747
$59$	−1.48693e77	−1.38111	−0.690554	−	0.723281i	$-0.742633\pi$
$59$	−1.48693e77	−1.38111	−0.690554	+	0.723281i	$0.742633\pi$
$60$	2.23451e77	0.999084
$61$	−3.28414e77	−0.715442	−0.357721	−	0.933829i	$-0.616446\pi$
$61$	−3.28414e77	−0.715442	−0.357721	+	0.933829i	$0.616446\pi$
$62$	−8.14974e77	−0.875196
$63$	4.10918e78	2.20009
$64$	4.63168e77	0.125000
$65$	5.08302e78	0.698862
$66$	−1.13869e79	−0.805830
$67$	3.12202e79	1.14863	0.574317	−	0.818633i	$-0.305268\pi$
$67$	3.12202e79	1.14863	0.574317	+	0.818633i	$0.305268\pi$
$68$	−4.78813e79	−0.924759
$69$	2.51088e79	0.256975
$70$	−2.40808e80	−1.31797
$71$	−2.96376e80	−0.875194	−0.437597	−	0.899171i	$-0.644170\pi$
$71$	−2.96376e80	−0.875194	−0.437597	+	0.899171i	$0.644170\pi$
$72$	−3.28591e80	−0.528071
$73$	9.74503e80	0.859486	0.429743	−	0.902951i	$-0.358604\pi$
$73$	9.74503e80	0.859486	0.429743	+	0.902951i	$0.358604\pi$
$74$	−4.55343e80	−0.222208
$75$	3.48796e81	0.949307
$76$	4.86948e81	0.744889
$77$	1.22714e82	1.06304
$78$	−1.24792e82	−0.616698
$79$	−4.07789e82	−1.15786	−0.578931	−	0.815376i	$-0.696530\pi$
$79$	−4.07789e82	−1.15786	−0.578931	+	0.815376i	$0.696530\pi$
$80$	1.92563e82	0.316343
$81$	−2.74553e82	−0.262741
$82$	5.51279e82	0.309364
$83$	4.93307e82	0.163388	0.0816940	−	0.996657i	$-0.473967\pi$
$83$	4.93307e82	0.163388	0.0816940	+	0.996657i	$0.473967\pi$
$84$	5.91203e83	1.16302
$85$	−1.99067e84	−2.34033
$86$	1.11552e84	0.788490
$87$	3.34214e84	1.42869
$88$	−9.81285e83	−0.255152
$89$	−4.22584e83	−0.0672122	−0.0336061	−	0.999435i	$-0.510699\pi$
$89$	−4.22584e83	−0.0672122	−0.0336061	+	0.999435i	$0.510699\pi$
$90$	−1.36612e85	−1.33641
$91$	1.34486e85	0.813537
$92$	2.16380e84	0.0813666
$93$	8.31846e85	1.95450
$94$	7.19744e85	1.06198
$95$	2.02449e86	1.88512
$96$	−4.72757e85	−0.279151
$97$	−3.85645e86	−1.45083	−0.725415	−	0.688311i	$-0.758352\pi$
$97$	−3.85645e86	−1.45083	−0.725415	+	0.688311i	$0.758352\pi$
$98$	−3.43486e86	−0.827131
$99$	6.96165e86	1.07791
$100$	3.00582e86	0.300582
$101$	1.18103e87	0.766089	0.383045	−	0.923730i	$-0.374876\pi$
$101$	1.18103e87	0.766089	0.383045	+	0.923730i	$0.374876\pi$
$102$	4.88726e87	2.06518
$103$	2.80000e86	0.0773997	0.0386999	−	0.999251i	$-0.487678\pi$
$103$	2.80000e86	0.0773997	0.0386999	+	0.999251i	$0.487678\pi$
$104$	−1.07542e87	−0.195267
$105$	2.45793e88	2.94331
$106$	1.48568e88	1.17793
$107$	−9.61882e87	−0.506906	−0.253453	−	0.967348i	$-0.581566\pi$
$107$	−9.61882e87	−0.506906	−0.253453	+	0.967348i	$0.581566\pi$
$108$	1.10841e88	0.389733
$109$	2.67965e88	0.630995	0.315498	−	0.948926i	$-0.397829\pi$
$109$	2.67965e88	0.630995	0.315498	+	0.948926i	$0.397829\pi$
$110$	−4.07970e88	−0.645724
$111$	4.64769e88	0.496236
$112$	5.09481e88	0.368251
$113$	3.15948e89	1.55132	0.775662	−	0.631148i	$-0.217416\pi$
$113$	3.15948e89	1.55132	0.775662	+	0.631148i	$0.217416\pi$
$114$	−4.97029e89	−1.66349
$115$	8.99601e88	0.205918
$116$	2.88015e89	0.452369
$117$	7.62949e89	0.824917
$118$	1.30792e90	0.976590
$119$	−5.26690e90	−2.72435
$120$	−1.96549e90	−0.706459
$121$	−1.91277e90	−0.479179
$122$	2.88876e90	0.505894
$123$	−5.62692e90	−0.690873
$124$	7.16859e90	0.618857
$125$	−8.29083e90	−0.504676
$126$	−3.61447e91	−1.55570
$127$	−9.29957e89	−0.0283793	−0.0141896	−	0.999899i	$-0.504517\pi$
$127$	−9.29957e89	−0.0283793	−0.0141896	+	0.999899i	$0.504517\pi$
$128$	−4.07407e90	−0.0883883
$129$	−1.13862e92	−1.76086
$130$	−4.47108e91	−0.494170
$131$	−8.88835e91	−0.703914	−0.351957	−	0.936016i	$-0.614484\pi$
$131$	−8.88835e91	−0.703914	−0.351957	+	0.936016i	$0.614484\pi$
$132$	1.00160e92	0.569808
$133$	5.35638e92	2.19445
$134$	−2.74616e92	−0.812208
$135$	4.60823e92	0.986314
$136$	4.21169e92	0.653903
$137$	5.60345e92	0.632573	0.316287	−	0.948664i	$-0.397564\pi$
$137$	5.60345e92	0.632573	0.316287	+	0.948664i	$0.397564\pi$
$138$	−2.20859e92	−0.181708
$139$	1.14040e93	0.685349	0.342675	−	0.939454i	$-0.388667\pi$
$139$	1.14040e93	0.685349	0.342675	+	0.939454i	$0.388667\pi$
$140$	2.11817e93	0.931948
$141$	−7.34644e93	−2.37162
$142$	2.60695e93	0.618856
$143$	2.27843e93	0.398582
$144$	2.89032e93	0.373402
$145$	1.19743e94	1.14483
$146$	−8.57182e93	−0.607748
$147$	3.50596e94	1.84716
$148$	4.00524e93	0.157124
$149$	2.30398e93	0.0674336	0.0337168	−	0.999431i	$-0.489266\pi$
$149$	2.30398e93	0.0674336	0.0337168	+	0.999431i	$0.489266\pi$
$150$	−3.06804e94	−0.671262
$151$	−4.73426e94	−0.775809	−0.387905	−	0.921699i	$-0.626801\pi$
$151$	−4.73426e94	−0.775809	−0.387905	+	0.921699i	$0.626801\pi$
$152$	−4.28324e94	−0.526716
$153$	−2.98795e95	−2.76246
$154$	−1.07940e95	−0.751680
$155$	2.98035e95	1.56617
$156$	1.09768e95	0.436071
$157$	−1.22210e95	−0.367682	−0.183841	−	0.982956i	$-0.558853\pi$
$157$	−1.22210e95	−0.367682	−0.183841	+	0.982956i	$0.558853\pi$
$158$	3.58695e95	0.818733
$159$	−1.51644e96	−2.63057
$160$	−1.69380e95	−0.223688
$161$	2.38016e95	0.239706
$162$	2.41500e95	0.185786
$163$	1.45175e96	0.854540	0.427270	−	0.904124i	$-0.359475\pi$
$163$	1.45175e96	0.854540	0.427270	+	0.904124i	$0.359475\pi$
$164$	−4.84911e95	−0.218753
$165$	4.16416e96	1.44204
$166$	−4.33917e95	−0.115533
$167$	4.06110e96	0.832677	0.416339	−	0.909210i	$-0.363313\pi$
$167$	4.06110e96	0.832677	0.416339	+	0.909210i	$0.363313\pi$
$168$	−5.20028e96	−0.822381
$169$	−5.68900e96	−0.694967
$170$	1.75101e97	1.65486
$171$	3.03871e97	2.22515
$172$	−9.81225e96	−0.557546
$173$	−1.43454e97	−0.633442	−0.316721	−	0.948519i	$-0.602582\pi$
$173$	−1.43454e97	−0.633442	−0.316721	+	0.948519i	$0.602582\pi$
$174$	−2.93978e97	−1.01023
$175$	3.30637e97	0.885516
$176$	8.63148e96	0.180420
$177$	−1.33499e98	−2.18093
$178$	3.71709e96	0.0475262
$179$	1.14022e98	1.14257	0.571285	−	0.820752i	$-0.306445\pi$
$179$	1.14022e98	1.14257	0.571285	+	0.820752i	$0.306445\pi$
$180$	1.20165e98	0.944985
$181$	−1.39959e97	−0.0864937	−0.0432468	−	0.999064i	$-0.513770\pi$
$181$	−1.39959e97	−0.0864937	−0.0432468	+	0.999064i	$0.513770\pi$
$182$	−1.18295e98	−0.575257
$183$	−2.94857e98	−1.12977
$184$	−1.90330e97	−0.0575348
$185$	1.66518e98	0.397642
$186$	−7.31699e98	−1.38204
$187$	−8.92303e98	−1.33476
$188$	−6.33094e98	−0.750934
$189$	1.21924e99	1.14816
$190$	−1.78076e99	−1.33298
$191$	1.55587e99	0.926878	0.463439	−	0.886129i	$-0.346615\pi$
$191$	1.55587e99	0.926878	0.463439	+	0.886129i	$0.346615\pi$
$192$	4.15841e98	0.197390
$193$	3.82299e99	1.44764	0.723820	−	0.689989i	$-0.242385\pi$
$193$	3.82299e99	1.44764	0.723820	+	0.689989i	$0.242385\pi$
$194$	3.39217e99	1.02589
$195$	4.56364e99	1.10358
$196$	3.02133e99	0.584870
$197$	3.38893e99	0.525753	0.262877	−	0.964829i	$-0.415329\pi$
$197$	3.38893e99	0.525753	0.262877	+	0.964829i	$0.415329\pi$
$198$	−6.12353e99	−0.762195
$199$	−1.68642e100	−1.68600	−0.843001	−	0.537912i	$-0.819213\pi$
$199$	−1.68642e100	−1.68600	−0.843001	+	0.537912i	$0.819213\pi$
$200$	−2.64395e99	−0.212543
$201$	2.80301e100	1.81383
$202$	−1.03884e100	−0.541707
$203$	3.16814e100	1.33268
$204$	−4.29888e100	−1.46030
$205$	−2.01602e100	−0.553608
$206$	−2.46291e99	−0.0547299
$207$	1.35028e100	0.243060
$208$	9.45950e99	0.138074
$209$	9.07463e100	1.07514
$210$	−2.16202e101	−2.08123
$211$	1.17061e101	0.916483	0.458242	−	0.888828i	$-0.348479\pi$
$211$	1.17061e101	0.916483	0.458242	+	0.888828i	$0.348479\pi$
$212$	−1.30682e101	−0.832925
$213$	−2.66092e101	−1.38203
$214$	8.46081e100	0.358437
$215$	−4.07945e101	−1.41101
$216$	−9.74968e100	−0.275583
$217$	7.88538e101	1.82316
$218$	−2.35705e101	−0.446181
$219$	8.74927e101	1.35723
$220$	3.58855e101	0.456596
$221$	−9.77903e101	−1.02148
$222$	−4.08816e101	−0.350892
$223$	1.83791e102	1.29736	0.648682	−	0.761059i	$-0.275320\pi$
$223$	1.83791e102	1.29736	0.648682	+	0.761059i	$0.275320\pi$
$224$	−4.48144e101	−0.260393
$225$	1.87572e102	0.897903
$226$	−2.77910e102	−1.09695
$227$	−5.10224e101	−0.166202	−0.0831009	−	0.996541i	$-0.526482\pi$
$227$	−5.10224e101	−0.166202	−0.0831009	+	0.996541i	$0.526482\pi$
$228$	4.37191e102	1.17627
$229$	3.57118e102	0.794270	0.397135	−	0.917760i	$-0.370005\pi$
$229$	3.57118e102	0.794270	0.397135	+	0.917760i	$0.370005\pi$
$230$	−7.91297e101	−0.145606
$231$	1.10175e103	1.67866
$232$	−2.53341e102	−0.319873
$233$	3.49149e102	0.365618	0.182809	−	0.983148i	$-0.441481\pi$
$233$	3.49149e102	0.365618	0.182809	+	0.983148i	$0.441481\pi$
$234$	−6.71097e102	−0.583304
$235$	−2.63209e103	−1.90042
$236$	−1.15045e103	−0.690554
$237$	−3.66121e103	−1.82840
$238$	4.63281e103	1.92640
$239$	−4.31374e103	−1.49467	−0.747334	−	0.664448i	$-0.768667\pi$
$239$	−4.31374e103	−1.49467	−0.747334	+	0.664448i	$0.768667\pi$
$240$	1.72886e103	0.499542
$241$	−2.40361e103	−0.579592	−0.289796	−	0.957088i	$-0.593587\pi$
$241$	−2.40361e103	−0.579592	−0.289796	+	0.957088i	$0.593587\pi$
$242$	1.68249e103	0.338831
$243$	−7.09594e103	−1.19437
$244$	−2.54098e103	−0.357721
$245$	1.25612e104	1.48015
$246$	4.94949e103	0.488521
$247$	9.94517e103	0.822801
$248$	−6.30556e103	−0.437598
$249$	4.42900e103	0.258009
$250$	7.29269e103	0.356860
$251$	3.64103e103	0.149768	0.0748838	−	0.997192i	$-0.476141\pi$
$251$	3.64103e103	0.149768	0.0748838	+	0.997192i	$0.476141\pi$
$252$	3.17932e104	1.10005
$253$	4.03239e103	0.117441
$254$	8.17999e102	0.0200672
$255$	−1.78726e105	−3.69565
$256$	3.58359e103	0.0625000
$257$	1.10285e105	1.62339	0.811697	−	0.584079i	$-0.198544\pi$
$257$	1.10285e105	1.62339	0.811697	+	0.584079i	$0.198544\pi$
$258$	1.00154e105	1.24512
$259$	4.40573e104	0.462890
$260$	3.93280e104	0.349431
$261$	1.79731e105	1.35133
$262$	7.81828e104	0.497743
$263$	−1.64613e105	−0.887952	−0.443976	−	0.896039i	$-0.646432\pi$
$263$	−1.64613e105	−0.887952	−0.443976	+	0.896039i	$0.646432\pi$
$264$	−8.81017e104	−0.402915
$265$	−5.43312e105	−2.10792
$266$	−4.71152e105	−1.55171
$267$	−3.79404e104	−0.106136
$268$	2.41555e105	0.574317
$269$	4.37506e105	0.884626	0.442313	−	0.896861i	$-0.354158\pi$
$269$	4.37506e105	0.884626	0.442313	+	0.896861i	$0.354158\pi$
$270$	−4.05344e105	−0.697429
$271$	−9.18571e105	−1.34570	−0.672850	−	0.739779i	$-0.734930\pi$
$271$	−9.18571e105	−1.34570	−0.672850	+	0.739779i	$0.734930\pi$
$272$	−3.70464e105	−0.462379
$273$	1.20744e106	1.28467
$274$	−4.92885e105	−0.447297
$275$	5.60156e105	0.433847
$276$	1.94270e105	0.128487
$277$	1.36462e106	0.771156	0.385578	−	0.922675i	$-0.374002\pi$
$277$	1.36462e106	0.771156	0.385578	+	0.922675i	$0.374002\pi$
$278$	−1.00310e106	−0.484615
$279$	4.47343e106	1.84866
$280$	−1.86316e106	−0.658987
$281$	−2.89936e106	−0.878167	−0.439084	−	0.898446i	$-0.644697\pi$
$281$	−2.89936e106	−0.878167	−0.439084	+	0.898446i	$0.644697\pi$
$282$	6.46200e106	1.67699
$283$	−6.04289e106	−1.34442	−0.672210	−	0.740361i	$-0.734655\pi$
$283$	−6.04289e106	−1.34442	−0.672210	+	0.740361i	$0.734655\pi$
$284$	−2.29310e106	−0.437597
$285$	1.81763e107	2.97683
$286$	−2.00413e106	−0.281840
$287$	−5.33397e106	−0.644448
$288$	−2.54235e106	−0.264035
$289$	2.71019e107	2.42072
$290$	−1.05327e107	−0.809517
$291$	−3.46239e107	−2.29103
$292$	7.53985e106	0.429743
$293$	1.29720e107	0.637187	0.318594	−	0.947891i	$-0.396790\pi$
$293$	1.29720e107	0.637187	0.318594	+	0.947891i	$0.396790\pi$
$294$	−3.08388e107	−1.30614
$295$	−4.78303e107	−1.74761
$296$	−3.52305e106	−0.111104
$297$	2.06560e107	0.562524
$298$	−2.02660e106	−0.0476828
$299$	4.41922e106	0.0898771
$300$	2.69868e107	0.474654
$301$	−1.07934e108	−1.64254
$302$	4.16430e107	0.548580
$303$	1.06035e108	1.20974
$304$	3.76758e107	0.372444
$305$	−1.05642e108	−0.905299
$306$	2.62822e108	1.95335
$307$	−1.51511e108	−0.977066	−0.488533	−	0.872545i	$-0.662468\pi$
$307$	−1.51511e108	−0.977066	−0.488533	+	0.872545i	$0.662468\pi$
$308$	9.49454e107	0.531518
$309$	2.51390e107	0.122223
$310$	−2.62154e108	−1.10745
$311$	−1.58827e108	−0.583242	−0.291621	−	0.956534i	$-0.594195\pi$
$311$	−1.58827e108	−0.583242	−0.291621	+	0.956534i	$0.594195\pi$
$312$	−9.65534e107	−0.308349
$313$	3.50787e107	0.0974687	0.0487343	−	0.998812i	$-0.484481\pi$
$313$	3.50787e107	0.0974687	0.0487343	+	0.998812i	$0.484481\pi$
$314$	1.07497e108	0.259990
$315$	1.32181e109	2.78393
$316$	−3.15511e108	−0.578931
$317$	−2.87115e108	−0.459175	−0.229587	−	0.973288i	$-0.573738\pi$
$317$	−2.87115e108	−0.459175	−0.229587	+	0.973288i	$0.573738\pi$
$318$	1.33387e109	1.86010
$319$	5.36737e108	0.652931
$320$	1.48988e108	0.158171
$321$	−8.63596e108	−0.800464
$322$	−2.09361e108	−0.169498
$323$	−3.89484e109	−2.75537
$324$	−2.12425e108	−0.131371
$325$	6.13892e108	0.332021
$326$	−1.27698e109	−0.604251
$327$	2.40584e109	0.996415
$328$	4.26532e108	0.154682
$329$	−6.96397e109	−2.21226
$330$	−3.66284e109	−1.01967
$331$	1.66095e109	0.405358	0.202679	−	0.979245i	$-0.435035\pi$
$331$	1.66095e109	0.405358	0.202679	+	0.979245i	$0.435035\pi$
$332$	3.81678e108	0.0816940
$333$	2.49940e109	0.469365
$334$	−3.57218e109	−0.588792
$335$	1.00427e110	1.45345
$336$	4.57422e109	0.581511
$337$	−4.60181e109	−0.514077	−0.257038	−	0.966401i	$-0.582747\pi$
$337$	−4.60181e109	−0.514077	−0.257038	+	0.966401i	$0.582747\pi$
$338$	5.00410e109	0.491416
$339$	2.83664e110	2.44972
$340$	−1.54021e110	−1.17016
$341$	1.33592e110	0.893232
$342$	−2.67288e110	−1.57342
$343$	4.82261e109	0.250027
$344$	8.63094e109	0.394245
$345$	8.07679e109	0.325168
$346$	1.26183e110	0.447911
$347$	−4.71404e110	−1.47591	−0.737957	−	0.674848i	$-0.764209\pi$
$347$	−4.71404e110	−1.47591	−0.737957	+	0.674848i	$0.764209\pi$
$348$	2.58586e110	0.714344
$349$	7.55353e108	0.0184180	0.00920902	−	0.999958i	$-0.497069\pi$
$349$	7.55353e108	0.0184180	0.00920902	+	0.999958i	$0.497069\pi$
$350$	−2.90832e110	−0.626155
$351$	2.26376e110	0.430497
$352$	−7.59233e109	−0.127576
$353$	8.97229e110	1.33261	0.666306	−	0.745679i	$-0.267875\pi$
$353$	8.97229e110	1.33261	0.666306	+	0.745679i	$0.267875\pi$
$354$	1.17427e111	1.54215
$355$	−9.53357e110	−1.10745
$356$	−3.26959e109	−0.0336061
$357$	−4.72872e111	−4.30206
$358$	−1.00295e111	−0.807919
$359$	1.40978e111	1.00587	0.502935	−	0.864324i	$-0.332254\pi$
$359$	1.40978e111	1.00587	0.502935	+	0.864324i	$0.332254\pi$
$360$	−1.05698e111	−0.668205
$361$	2.17632e111	1.21944
$362$	1.23110e110	0.0611602
$363$	−1.71732e111	−0.756680
$364$	1.04054e111	0.406768
$365$	3.13470e111	1.08757
$366$	2.59359e111	0.798865
$367$	1.94715e111	0.532629	0.266315	−	0.963886i	$-0.414194\pi$
$367$	1.94715e111	0.532629	0.266315	+	0.963886i	$0.414194\pi$
$368$	1.67416e110	0.0406833
$369$	−3.02599e111	−0.653463
$370$	−1.46471e111	−0.281175
$371$	−1.43749e112	−2.45380
$372$	6.43610e111	0.977248
$373$	1.03968e112	1.40464	0.702320	−	0.711862i	$-0.252148\pi$
$373$	1.03968e112	1.40464	0.702320	+	0.711862i	$0.252148\pi$
$374$	7.84878e111	0.943816
$375$	−7.44367e111	−0.796942
$376$	5.56875e111	0.530990
$377$	5.88227e111	0.499685
$378$	−1.07246e112	−0.811869
$379$	1.66352e112	1.12259	0.561296	−	0.827615i	$-0.310303\pi$
$379$	1.66352e112	1.12259	0.561296	+	0.827615i	$0.310303\pi$
$380$	1.56638e112	0.942561
$381$	−8.34933e110	−0.0448141
$382$	−1.36856e112	−0.655401
$383$	2.10808e111	0.0901034	0.0450517	−	0.998985i	$-0.485655\pi$
$383$	2.10808e111	0.0901034	0.0450517	+	0.998985i	$0.485655\pi$
$384$	−3.65778e111	−0.139576
$385$	3.94737e112	1.34513
$386$	−3.36274e112	−1.02364
$387$	−6.12315e112	−1.66551
$388$	−2.98378e112	−0.725415
$389$	3.31733e112	0.721076	0.360538	−	0.932744i	$-0.382593\pi$
$389$	3.31733e112	0.721076	0.360538	+	0.932744i	$0.382593\pi$
$390$	−4.01422e112	−0.780352
$391$	−1.73071e112	−0.300978
$392$	−2.65759e112	−0.413565
$393$	−7.98013e112	−1.11156
$394$	−2.98094e112	−0.371764
$395$	−1.31174e113	−1.46513
$396$	5.38631e112	0.538953
$397$	6.59828e112	0.591622	0.295811	−	0.955247i	$-0.404410\pi$
$397$	6.59828e112	0.591622	0.295811	+	0.955247i	$0.404410\pi$
$398$	1.48339e113	1.19218
$399$	4.80906e113	3.46529
$400$	2.32564e112	0.150291
$401$	−2.95181e112	−0.171123	−0.0855614	−	0.996333i	$-0.527268\pi$
$401$	−2.95181e112	−0.171123	−0.0855614	+	0.996333i	$0.527268\pi$
$402$	−2.46555e113	−1.28257
$403$	1.46407e113	0.683587
$404$	9.13774e112	0.383045
$405$	−8.83160e112	−0.332465
$406$	−2.78673e113	−0.942349
$407$	7.46405e112	0.226787
$408$	3.78133e113	1.03259
$409$	−3.18283e113	−0.781357	−0.390678	−	0.920527i	$-0.627760\pi$
$409$	−3.18283e113	−0.781357	−0.390678	+	0.920527i	$0.627760\pi$
$410$	1.77331e113	0.391460
$411$	5.03088e113	0.998907
$412$	2.16640e112	0.0386999
$413$	−1.26549e114	−2.03438
$414$	−1.18772e113	−0.171869
$415$	1.58683e113	0.206746
$416$	−8.32067e112	−0.0976334
$417$	1.02387e114	1.08225
$418$	−7.98213e113	−0.760240
$419$	1.46754e114	1.25973	0.629867	−	0.776703i	$-0.283109\pi$
$419$	1.46754e114	1.25973	0.629867	+	0.776703i	$0.283109\pi$
$420$	1.90174e114	1.47165
$421$	−1.99988e114	−1.39551	−0.697754	−	0.716337i	$-0.745817\pi$
$421$	−1.99988e114	−1.39551	−0.697754	+	0.716337i	$0.745817\pi$
$422$	−1.02968e114	−0.648052
$423$	−3.95070e114	−2.24320
$424$	1.14949e114	0.588967
$425$	−2.40419e114	−1.11186
$426$	2.34057e114	0.977246
$427$	−2.79506e114	−1.05385
$428$	−7.44220e113	−0.253453
$429$	2.04561e114	0.629407
$430$	3.58832e114	0.997732
$431$	−4.46887e114	−1.12315	−0.561573	−	0.827427i	$-0.689804\pi$
$431$	−4.46887e114	−1.12315	−0.561573	+	0.827427i	$0.689804\pi$
$432$	8.57591e113	0.194867
$433$	5.90128e114	1.21261	0.606307	−	0.795231i	$-0.292650\pi$
$433$	5.90128e114	1.21261	0.606307	+	0.795231i	$0.292650\pi$
$434$	−6.93605e114	−1.28917
$435$	1.07507e115	1.80782
$436$	2.07328e114	0.315498
$437$	1.76011e114	0.242436
$438$	−7.69594e114	−0.959706
$439$	2.72880e113	0.0308153	0.0154076	−	0.999881i	$-0.495095\pi$
$439$	2.72880e113	0.0308153	0.0154076	+	0.999881i	$0.495095\pi$
$440$	−3.15652e114	−0.322862
$441$	1.88541e115	1.74713
$442$	8.60172e114	0.722299
$443$	−1.53437e113	−0.0116780	−0.00583898	−	0.999983i	$-0.501859\pi$
$443$	−1.53437e113	−0.0116780	−0.00583898	+	0.999983i	$0.501859\pi$
$444$	3.59598e114	0.248118
$445$	−1.35933e114	−0.0850483
$446$	−1.61664e115	−0.917375
$447$	2.06856e114	0.106486
$448$	3.94192e114	0.184125
$449$	−1.10481e115	−0.468350	−0.234175	−	0.972195i	$-0.575239\pi$
$449$	−1.10481e115	−0.468350	−0.234175	+	0.972195i	$0.575239\pi$
$450$	−1.64991e115	−0.634914
$451$	−9.03666e114	−0.315739
$452$	2.44453e115	0.775662
$453$	−4.25051e115	−1.22509
$454$	4.48797e114	0.117522
$455$	4.32604e115	1.02943
$456$	−3.84558e115	−0.831746
$457$	5.68270e115	1.11738	0.558689	−	0.829377i	$-0.311305\pi$
$457$	5.68270e115	1.11738	0.558689	+	0.829377i	$0.311305\pi$
$458$	−3.14124e115	−0.561633
$459$	−8.86559e115	−1.44164
$460$	6.96032e114	0.102959
$461$	−6.76860e115	−0.910980	−0.455490	−	0.890241i	$-0.650536\pi$
$461$	−6.76860e115	−0.910980	−0.455490	+	0.890241i	$0.650536\pi$
$462$	−9.69110e115	−1.18699
$463$	−1.43609e116	−1.60106	−0.800531	−	0.599291i	$-0.795449\pi$
$463$	−1.43609e116	−1.60106	−0.800531	+	0.599291i	$0.795449\pi$
$464$	2.22841e115	0.226185
$465$	2.67581e116	2.47316
$466$	−3.07114e115	−0.258531
$467$	1.23456e116	0.946735	0.473368	−	0.880865i	$-0.343038\pi$
$467$	1.23456e116	0.946735	0.473368	+	0.880865i	$0.343038\pi$
$468$	5.90303e115	0.412458
$469$	2.65708e116	1.69194
$470$	2.31521e116	1.34380
$471$	−1.09722e116	−0.580612
$472$	1.01195e116	0.488295
$473$	−1.82858e116	−0.804739
$474$	3.22043e116	1.29287
$475$	2.44504e116	0.895600
$476$	−4.07507e116	−1.36217
$477$	−8.15497e116	−2.48813
$478$	3.79440e116	1.05689
$479$	−3.03388e116	−0.771621	−0.385810	−	0.922578i	$-0.626078\pi$
$479$	−3.03388e116	−0.771621	−0.385810	+	0.922578i	$0.626078\pi$
$480$	−1.52073e116	−0.353230
$481$	8.18009e115	0.173559
$482$	2.11424e116	0.409833
$483$	2.13695e116	0.378524
$484$	−1.47993e116	−0.239590
$485$	−1.24051e117	−1.83584
$486$	6.24166e116	0.844544
$487$	1.06153e117	1.31348	0.656739	−	0.754118i	$-0.271935\pi$
$487$	1.06153e117	1.31348	0.656739	+	0.754118i	$0.271935\pi$
$488$	2.23507e116	0.252947
$489$	1.30341e117	1.34942
$490$	−1.10490e117	−1.04663
$491$	−5.80317e116	−0.503061	−0.251530	−	0.967849i	$-0.580934\pi$
$491$	−5.80317e116	−0.503061	−0.251530	+	0.967849i	$0.580934\pi$
$492$	−4.35362e116	−0.345437
$493$	−2.30368e117	−1.67333
$494$	−8.74786e116	−0.581808
$495$	2.23937e117	1.36395
$496$	5.54643e116	0.309429
$497$	−2.52238e117	−1.28916
$498$	−3.89579e116	−0.182440
$499$	−1.49861e117	−0.643154	−0.321577	−	0.946883i	$-0.604213\pi$
$499$	−1.49861e117	−0.643154	−0.321577	+	0.946883i	$0.604213\pi$
$500$	−6.41472e116	−0.252338
$501$	3.64613e117	1.31489
$502$	−3.20269e116	−0.105902
$503$	3.43905e117	1.04287	0.521436	−	0.853290i	$-0.325396\pi$
$503$	3.43905e117	1.04287	0.521436	+	0.853290i	$0.325396\pi$
$504$	−2.79656e117	−0.777850
$505$	3.79902e117	0.969387
$506$	−3.54693e116	−0.0830434
$507$	−5.10769e117	−1.09743
$508$	−7.19519e115	−0.0141896
$509$	2.54328e117	0.460438	0.230219	−	0.973139i	$-0.426056\pi$
$509$	2.54328e117	0.460438	0.230219	+	0.973139i	$0.426056\pi$
$510$	1.57209e118	2.61322
$511$	8.29377e117	1.26603
$512$	−3.15216e116	−0.0441942
$513$	9.01621e117	1.16123
$514$	−9.70073e117	−1.14791
$515$	9.00683e116	0.0979394
$516$	−8.80962e117	−0.880431
$517$	−1.17982e118	−1.08387
$518$	−3.87532e117	−0.327313
$519$	−1.28796e118	−1.00028
$520$	−3.45933e117	−0.247085
$521$	−6.00755e116	−0.0394691	−0.0197345	−	0.999805i	$-0.506282\pi$
$521$	−6.00755e116	−0.0394691	−0.0197345	+	0.999805i	$0.506282\pi$
$522$	−1.58093e118	−0.955531
$523$	1.87265e118	1.04144	0.520720	−	0.853728i	$-0.325664\pi$
$523$	1.87265e118	1.04144	0.520720	+	0.853728i	$0.325664\pi$
$524$	−6.87703e117	−0.351957
$525$	2.96852e118	1.39833
$526$	1.44795e118	0.627877
$527$	−5.73378e118	−2.28917
$528$	7.74950e117	0.284904
$529$	−2.87518e118	−0.973518
$530$	4.77902e118	1.49052
$531$	−7.17920e118	−2.06283
$532$	4.14430e118	1.09722
$533$	−9.90356e117	−0.241634
$534$	3.33727e117	0.0750494
$535$	−3.09410e118	−0.641424
$536$	−2.12474e118	−0.406104
$537$	1.02371e119	1.80425
$538$	−3.84834e118	−0.625525
$539$	5.63047e118	0.844177
$540$	3.56544e118	0.493157
$541$	−3.21989e118	−0.410923	−0.205462	−	0.978665i	$-0.565870\pi$
$541$	−3.21989e118	−0.410923	−0.205462	+	0.978665i	$0.565870\pi$
$542$	8.07983e118	0.951554
$543$	−1.25658e118	−0.136584
$544$	3.25863e118	0.326952
$545$	8.61969e118	0.798443
$546$	−1.06208e119	−0.908398
$547$	1.71992e119	1.35850	0.679251	−	0.733906i	$-0.262305\pi$
$547$	1.71992e119	1.35850	0.679251	+	0.733906i	$0.262305\pi$
$548$	4.33546e118	0.316287
$549$	−1.58565e119	−1.06859
$550$	−4.92718e118	−0.306776
$551$	2.34282e119	1.34786
$552$	−1.70881e118	−0.0908542
$553$	−3.47060e119	−1.70554
$554$	−1.20033e119	−0.545289
$555$	1.49503e119	0.627922
$556$	8.82339e118	0.342675
$557$	2.60860e117	0.00936930	0.00468465	−	0.999989i	$-0.498509\pi$
$557$	2.60860e117	0.00936930	0.00468465	+	0.999989i	$0.498509\pi$
$558$	−3.93487e119	−1.30720
$559$	−2.00400e119	−0.615863
$560$	1.63886e119	0.465974
$561$	−8.01127e119	−2.10774
$562$	2.55030e119	0.620958
$563$	4.80695e119	1.08331	0.541657	−	0.840599i	$-0.317797\pi$
$563$	4.80695e119	1.08331	0.541657	+	0.840599i	$0.317797\pi$
$564$	−5.68404e119	−1.18581
$565$	1.01631e120	1.96300
$566$	5.31538e119	0.950648
$567$	−2.33666e119	−0.387019
$568$	2.01703e119	0.309428
$569$	1.04059e118	0.0147876	0.00739381	−	0.999973i	$-0.497646\pi$
$569$	1.04059e118	0.0147876	0.00739381	+	0.999973i	$0.497646\pi$
$570$	−1.59880e120	−2.10493
$571$	−8.21661e119	−1.00236	−0.501178	−	0.865344i	$-0.667100\pi$
$571$	−8.21661e119	−1.00236	−0.501178	+	0.865344i	$0.667100\pi$
$572$	1.76285e119	0.199291
$573$	1.39689e120	1.46365
$574$	4.69181e119	0.455694
$575$	1.08648e119	0.0978292
$576$	2.23627e119	0.186701
$577$	−2.15475e120	−1.66820	−0.834100	−	0.551613i	$-0.814012\pi$
$577$	−2.15475e120	−1.66820	−0.834100	+	0.551613i	$0.814012\pi$
$578$	−2.38391e120	−1.71170
$579$	3.43235e120	2.28599
$580$	9.26464e119	0.572415
$581$	4.19842e119	0.240671
$582$	3.04555e120	1.62000
$583$	−2.43535e120	−1.20221
$584$	−6.63212e119	−0.303874
$585$	2.45419e120	1.04383
$586$	−1.14103e120	−0.450559
$587$	−6.39895e119	−0.234613	−0.117306	−	0.993096i	$-0.537426\pi$
$587$	−6.39895e119	−0.234613	−0.117306	+	0.993096i	$0.537426\pi$
$588$	2.71261e120	0.923578
$589$	5.83119e120	1.84392
$590$	4.20720e120	1.23575
$591$	3.04265e120	0.830226
$592$	3.09890e119	0.0785622
$593$	−7.21074e120	−1.69864	−0.849319	−	0.527880i	$-0.822987\pi$
$593$	−7.21074e120	−1.69864	−0.849319	+	0.527880i	$0.822987\pi$
$594$	−1.81692e120	−0.397765
$595$	−1.69421e121	−3.44731
$596$	1.78262e119	0.0337168
$597$	−1.51410e121	−2.66239
$598$	−3.88719e119	−0.0635527
$599$	−3.97745e120	−0.604696	−0.302348	−	0.953198i	$-0.597771\pi$
$599$	−3.97745e120	−0.604696	−0.302348	+	0.953198i	$0.597771\pi$
$600$	−2.37378e120	−0.335631
$601$	7.35051e120	0.966669	0.483335	−	0.875436i	$-0.339425\pi$
$601$	7.35051e120	0.966669	0.483335	+	0.875436i	$0.339425\pi$
$602$	9.49396e120	1.16145
$603$	1.50738e121	1.71561
$604$	−3.66296e120	−0.387905
$605$	−6.15283e120	−0.606340
$606$	−9.32691e120	−0.855418
$607$	6.72390e120	0.574002	0.287001	−	0.957930i	$-0.407342\pi$
$607$	6.72390e120	0.574002	0.287001	+	0.957930i	$0.407342\pi$
$608$	−3.31400e120	−0.263358
$609$	2.84442e121	2.10446
$610$	9.29234e120	0.640143
$611$	−1.29300e121	−0.829478
$612$	−2.31181e121	−1.38123
$613$	1.67656e121	0.933015	0.466507	−	0.884517i	$-0.345512\pi$
$613$	1.67656e121	0.933015	0.466507	+	0.884517i	$0.345512\pi$
$614$	1.33270e121	0.690890
$615$	−1.81002e121	−0.874211
$616$	−8.35149e120	−0.375840
$617$	1.03203e121	0.432800	0.216400	−	0.976305i	$-0.430568\pi$
$617$	1.03203e121	0.432800	0.216400	+	0.976305i	$0.430568\pi$
$618$	−2.21125e120	−0.0864249
$619$	2.31175e121	0.842167	0.421083	−	0.907022i	$-0.361650\pi$
$619$	2.31175e121	0.842167	0.421083	+	0.907022i	$0.361650\pi$
$620$	2.30593e121	0.783084
$621$	4.00643e120	0.126845
$622$	1.39706e121	0.412414
$623$	−3.59651e120	−0.0990038
$624$	8.49292e120	0.218036
$625$	−5.17750e121	−1.23977
$626$	−3.08556e120	−0.0689207
$627$	8.14737e121	1.69777
$628$	−9.45554e120	−0.183841
$629$	−3.20358e121	−0.581209
$630$	−1.16267e122	−1.96854
$631$	−2.45238e121	−0.387535	−0.193768	−	0.981047i	$-0.562071\pi$
$631$	−2.45238e121	−0.387535	−0.193768	+	0.981047i	$0.562071\pi$
$632$	2.77527e121	0.409366
$633$	1.05099e122	1.44723
$634$	2.52549e121	0.324686
$635$	−2.99141e120	−0.0359103
$636$	−1.17329e122	−1.31529
$637$	6.17061e121	0.646045
$638$	−4.72119e121	−0.461692
$639$	−1.43096e122	−1.30720
$640$	−1.31051e121	−0.111844
$641$	−2.05207e122	−1.63632	−0.818160	−	0.574991i	$-0.805006\pi$
$641$	−2.05207e122	−1.63632	−0.818160	+	0.574991i	$0.805006\pi$
$642$	7.59627e121	0.566014
$643$	2.00713e122	1.39765	0.698826	−	0.715292i	$-0.253706\pi$
$643$	2.00713e122	1.39765	0.698826	+	0.715292i	$0.253706\pi$
$644$	1.84156e121	0.119853
$645$	−3.66261e122	−2.22814
$646$	3.42594e122	1.94834
$647$	5.77265e121	0.306930	0.153465	−	0.988154i	$-0.450957\pi$
$647$	5.77265e121	0.306930	0.153465	+	0.988154i	$0.450957\pi$
$648$	1.86851e121	0.0928930
$649$	−2.14396e122	−0.996716
$650$	−5.39985e121	−0.234775
$651$	7.07964e122	2.87898
$652$	1.12324e122	0.427270
$653$	−1.84671e122	−0.657168	−0.328584	−	0.944475i	$-0.606571\pi$
$653$	−1.84671e122	−0.657168	−0.328584	+	0.944475i	$0.606571\pi$
$654$	−2.11620e122	−0.704572
$655$	−2.85913e122	−0.890713
$656$	−3.75181e121	−0.109377
$657$	4.70511e122	1.28374
$658$	6.12557e122	1.56430
$659$	−4.00419e122	−0.957193	−0.478596	−	0.878035i	$-0.658854\pi$
$659$	−4.00419e122	−0.957193	−0.478596	+	0.878035i	$0.658854\pi$
$660$	3.22186e122	0.721018
$661$	−4.91223e122	−1.02924	−0.514618	−	0.857420i	$-0.672066\pi$
$661$	−4.91223e122	−1.02924	−0.514618	+	0.857420i	$0.672066\pi$
$662$	−1.46099e122	−0.286632
$663$	−8.77980e122	−1.61304
$664$	−3.35727e121	−0.0577664
$665$	1.72300e123	2.77679
$666$	−2.19849e122	−0.331891
$667$	1.04105e122	0.147231
$668$	3.14212e122	0.416339
$669$	1.65011e123	2.04869
$670$	−8.83362e122	−1.02774
$671$	−4.73531e122	−0.516319
$672$	−4.02352e122	−0.411190
$673$	−9.36043e122	−0.896686	−0.448343	−	0.893862i	$-0.647986\pi$
$673$	−9.36043e122	−0.896686	−0.448343	+	0.893862i	$0.647986\pi$
$674$	4.04779e122	0.363507
$675$	5.56550e122	0.468587
$676$	−4.40165e122	−0.347484
$677$	−1.31829e123	−0.975895	−0.487947	−	0.872873i	$-0.662254\pi$
$677$	−1.31829e123	−0.975895	−0.487947	+	0.872873i	$0.662254\pi$
$678$	−2.49513e123	−1.73222
$679$	−3.28213e123	−2.13708
$680$	1.35478e123	0.827430
$681$	−4.58088e122	−0.262452
$682$	−1.17509e123	−0.631611
$683$	3.59072e122	0.181085	0.0905423	−	0.995893i	$-0.471140\pi$
$683$	3.59072e122	0.181085	0.0905423	+	0.995893i	$0.471140\pi$
$684$	2.35109e123	1.11257
$685$	1.80247e123	0.800440
$686$	−4.24201e122	−0.176796
$687$	3.20627e123	1.25424
$688$	−7.59186e122	−0.278773
$689$	−2.66898e123	−0.920046
$690$	−7.10442e122	−0.229929
$691$	1.59983e123	0.486161	0.243081	−	0.970006i	$-0.421842\pi$
$691$	1.59983e123	0.486161	0.243081	+	0.970006i	$0.421842\pi$
$692$	−1.10992e123	−0.316721
$693$	5.92489e123	1.58776
$694$	4.14651e123	1.04363
$695$	3.66833e123	0.867221
$696$	−2.27454e123	−0.505117
$697$	3.87854e123	0.809175
$698$	−6.64415e121	−0.0130235
$699$	3.13472e123	0.577354
$700$	2.55818e123	0.442758
$701$	−4.73824e123	−0.770697	−0.385348	−	0.922771i	$-0.625919\pi$
$701$	−4.73824e123	−0.770697	−0.385348	+	0.922771i	$0.625919\pi$
$702$	−1.99122e123	−0.304408
$703$	3.25801e123	0.468161
$704$	6.67828e122	0.0902099
$705$	−2.36314e124	−3.00098
$706$	−7.89211e123	−0.942299
$707$	1.00514e124	1.12845
$708$	−1.03290e124	−1.09046
$709$	5.80124e123	0.575983	0.287992	−	0.957633i	$-0.407012\pi$
$709$	5.80124e123	0.575983	0.287992	+	0.957633i	$0.407012\pi$
$710$	8.38582e123	0.783082
$711$	−1.96889e124	−1.72939
$712$	2.87596e122	0.0237631
$713$	2.59114e123	0.201417
$714$	4.15943e124	3.04202
$715$	7.32906e123	0.504354
$716$	8.82205e123	0.571285
$717$	−3.87295e124	−2.36026
$718$	−1.24005e124	−0.711257
$719$	−7.63623e122	−0.0412261	−0.0206131	−	0.999788i	$-0.506562\pi$
$719$	−7.63623e122	−0.0412261	−0.0206131	+	0.999788i	$0.506562\pi$
$720$	9.29733e123	0.472492
$721$	2.38302e123	0.114010
$722$	−1.91431e124	−0.862272
$723$	−2.15800e124	−0.915243
$724$	−1.08288e123	−0.0432468
$725$	1.44617e124	0.543896
$726$	1.51057e124	0.535054
$727$	−4.58002e123	−0.152799	−0.0763995	−	0.997077i	$-0.524342\pi$
$727$	−4.58002e123	−0.152799	−0.0763995	+	0.997077i	$0.524342\pi$
$728$	−9.15266e123	−0.287629
$729$	−5.48336e124	−1.62330
$730$	−2.75731e124	−0.769027
$731$	7.84830e124	2.06238
$732$	−2.28134e124	−0.564883
$733$	9.12974e123	0.213027	0.106514	−	0.994311i	$-0.466031\pi$
$733$	9.12974e123	0.213027	0.106514	+	0.994311i	$0.466031\pi$
$734$	−1.71273e124	−0.376626
$735$	1.12777e125	2.33734
$736$	−1.47260e123	−0.0287674
$737$	4.50155e124	0.828946
$738$	2.66169e124	0.462068
$739$	−4.63834e124	−0.759154	−0.379577	−	0.925160i	$-0.623930\pi$
$739$	−4.63834e124	−0.759154	−0.379577	+	0.925160i	$0.623930\pi$
$740$	1.28837e124	0.198821
$741$	8.92896e124	1.29930
$742$	1.26443e125	1.73510
$743$	−1.05547e125	−1.36595	−0.682974	−	0.730442i	$-0.739314\pi$
$743$	−1.05547e125	−1.36595	−0.682974	+	0.730442i	$0.739314\pi$
$744$	−5.66125e124	−0.691018
$745$	7.41126e123	0.0853285
$746$	−9.14511e124	−0.993230
$747$	2.38179e124	0.244038
$748$	−6.90386e124	−0.667379
$749$	−8.18635e124	−0.746675
$750$	6.54752e124	0.563523
$751$	1.50180e124	0.121976	0.0609880	−	0.998138i	$-0.480575\pi$
$751$	1.50180e124	0.121976	0.0609880	+	0.998138i	$0.480575\pi$
$752$	−4.89833e124	−0.375467
$753$	3.26899e124	0.236500
$754$	−5.17410e124	−0.353331
$755$	−1.52288e125	−0.981687
$756$	9.43342e124	0.574078
$757$	2.22005e125	1.27553	0.637766	−	0.770230i	$-0.279859\pi$
$757$	2.22005e125	1.27553	0.637766	+	0.770230i	$0.279859\pi$
$758$	−1.46325e125	−0.793793
$759$	3.62036e124	0.185453
$760$	−1.37780e125	−0.666491
$761$	1.86018e124	0.0849811	0.0424905	−	0.999097i	$-0.486471\pi$
$761$	1.86018e124	0.0849811	0.0424905	+	0.999097i	$0.486471\pi$
$762$	7.34415e123	0.0316884
$763$	2.28059e125	0.929458
$764$	1.20380e125	0.463439
$765$	−9.61138e125	−3.49553
$766$	−1.85429e124	−0.0637127
$767$	−2.34963e125	−0.762783
$768$	3.21742e124	0.0986948
$769$	−2.32072e125	−0.672707	−0.336354	−	0.941736i	$-0.609194\pi$
$769$	−2.32072e125	−0.672707	−0.336354	+	0.941736i	$0.609194\pi$
$770$	−3.47214e125	−0.951154
$771$	9.90156e125	2.56353
$772$	2.95790e125	0.723820
$773$	5.23576e124	0.121108	0.0605538	−	0.998165i	$-0.480713\pi$
$773$	5.23576e124	0.121108	0.0605538	+	0.998165i	$0.480713\pi$
$774$	5.38598e125	1.17770
$775$	3.59946e125	0.744069
$776$	2.62456e125	0.512946
$777$	3.95554e125	0.730957
$778$	−2.91796e125	−0.509878
$779$	−3.94444e125	−0.651787
$780$	3.53094e125	0.551792
$781$	−4.27335e125	−0.631609
$782$	1.52235e125	0.212823
$783$	5.33282e125	0.705213
$784$	2.33764e125	0.292435
$785$	−3.93115e125	−0.465253
$786$	7.01940e125	0.785994
$787$	−5.66853e125	−0.600578	−0.300289	−	0.953848i	$-0.597083\pi$
$787$	−5.66853e125	−0.600578	−0.300289	+	0.953848i	$0.597083\pi$
$788$	2.62206e125	0.262877
$789$	−1.47793e126	−1.40218
$790$	1.15382e126	1.03600
$791$	2.68896e126	2.28511
$792$	−4.73785e125	−0.381097
$793$	−5.18957e125	−0.395137
$794$	−5.80391e125	−0.418340
$795$	−4.87796e126	−3.32865
$796$	−1.30481e126	−0.843001
$797$	−1.32779e126	−0.812254	−0.406127	−	0.913817i	$-0.633121\pi$
$797$	−1.32779e126	−0.812254	−0.406127	+	0.913817i	$0.633121\pi$
$798$	−4.23010e126	−2.45033
$799$	5.06378e126	2.77773
$800$	−2.04565e125	−0.106272
$801$	−2.04032e125	−0.100389
$802$	2.59644e125	0.121002
$803$	1.40511e126	0.620273
$804$	2.16872e126	0.906914
$805$	7.65629e125	0.303318
$806$	−1.28781e126	−0.483369
$807$	3.92801e126	1.39693
$808$	−8.03764e125	−0.270853
$809$	−1.95970e126	−0.625789	−0.312894	−	0.949788i	$-0.601299\pi$
$809$	−1.95970e126	−0.625789	−0.312894	+	0.949788i	$0.601299\pi$
$810$	7.76836e125	0.235088
$811$	3.24597e126	0.930974	0.465487	−	0.885055i	$-0.345879\pi$
$811$	3.24597e126	0.930974	0.465487	+	0.885055i	$0.345879\pi$
$812$	2.45123e126	0.666342
$813$	−8.24710e126	−2.12502
$814$	−6.56545e125	−0.160363
$815$	4.66988e126	1.08131
$816$	−3.32609e126	−0.730151
$817$	−7.98164e126	−1.66124
$818$	2.79965e126	0.552503
$819$	6.49328e126	1.21511
$820$	−1.55982e126	−0.276804
$821$	5.75776e126	0.969006	0.484503	−	0.874790i	$-0.339001\pi$
$821$	5.75776e126	0.969006	0.484503	+	0.874790i	$0.339001\pi$
$822$	−4.42521e126	−0.706334
$823$	−8.10145e126	−1.22651	−0.613253	−	0.789886i	$-0.710140\pi$
$823$	−8.10145e126	−1.22651	−0.613253	+	0.789886i	$0.710140\pi$
$824$	−1.90558e125	−0.0273649
$825$	5.02919e126	0.685095
$826$	1.11314e127	1.43852
$827$	−5.55803e125	−0.0681446	−0.0340723	−	0.999419i	$-0.510848\pi$
$827$	−5.55803e125	−0.0681446	−0.0340723	+	0.999419i	$0.510848\pi$
$828$	1.04473e126	0.121530
$829$	1.76276e127	1.94567	0.972837	−	0.231493i	$-0.0743610\pi$
$829$	1.76276e127	1.94567	0.972837	+	0.231493i	$0.0743610\pi$
$830$	−1.39579e126	−0.146192
$831$	1.22518e127	1.21774
$832$	7.31894e125	0.0690372
$833$	−2.41660e127	−2.16345
$834$	−9.00605e126	−0.765264
$835$	1.30634e127	1.05365
$836$	7.02116e126	0.537571
$837$	1.32732e127	0.964756
$838$	−1.29086e127	−0.890767
$839$	−2.97966e127	−1.95219	−0.976094	−	0.217347i	$-0.930260\pi$
$839$	−2.97966e127	−1.95219	−0.976094	+	0.217347i	$0.930260\pi$
$840$	−1.67278e127	−1.04062
$841$	−3.07170e126	−0.181448
$842$	1.75911e127	0.986773
$843$	−2.60310e127	−1.38673
$844$	9.05714e126	0.458242
$845$	−1.82999e127	−0.879391
$846$	3.47508e127	1.58618
$847$	−1.62791e127	−0.705833
$848$	−1.01110e127	−0.416463
$849$	−5.42542e127	−2.12300
$850$	2.11475e127	0.786206
$851$	1.44772e126	0.0511387
$852$	−2.05879e127	−0.691017
$853$	−4.88236e127	−1.55721	−0.778605	−	0.627514i	$-0.784072\pi$
$853$	−4.88236e127	−1.55721	−0.778605	+	0.627514i	$0.784072\pi$
$854$	2.45856e127	0.745183
$855$	9.77467e127	2.81563
$856$	6.54623e126	0.179218
$857$	6.19965e127	1.61325	0.806625	−	0.591064i	$-0.201292\pi$
$857$	6.19965e127	1.61325	0.806625	+	0.591064i	$0.201292\pi$
$858$	−1.79934e127	−0.445058
$859$	4.88783e127	1.14925	0.574624	−	0.818418i	$-0.305148\pi$
$859$	4.88783e127	1.14925	0.574624	+	0.818418i	$0.305148\pi$
$860$	−3.15632e127	−0.705503
$861$	−4.78894e127	−1.01766
$862$	3.93086e127	0.794184
$863$	3.27692e126	0.0629500	0.0314750	−	0.999505i	$-0.489980\pi$
$863$	3.27692e126	0.0629500	0.0314750	+	0.999505i	$0.489980\pi$
$864$	−7.54345e126	−0.137791
$865$	−4.61450e127	−0.801539
$866$	−5.19082e127	−0.857447
$867$	2.43326e128	3.82259
$868$	6.10102e127	0.911579
$869$	−5.87978e127	−0.835605
$870$	−9.45644e127	−1.27832
$871$	4.93339e127	0.634389
$872$	−1.82368e127	−0.223090
$873$	−1.86197e128	−2.16697
$874$	−1.54821e127	−0.171428
$875$	−7.05613e127	−0.743390
$876$	6.76942e127	0.678614
$877$	1.60850e128	1.53440	0.767200	−	0.641408i	$-0.221649\pi$
$877$	1.60850e128	1.53440	0.767200	+	0.641408i	$0.221649\pi$
$878$	−2.40028e126	−0.0217897
$879$	1.16465e128	1.00619
$880$	2.77650e127	0.228298
$881$	1.71862e128	1.34502	0.672509	−	0.740089i	$-0.265217\pi$
$881$	1.71862e128	1.34502	0.672509	+	0.740089i	$0.265217\pi$
$882$	−1.65842e128	−1.23541
$883$	1.46950e128	1.04202	0.521012	−	0.853549i	$-0.325555\pi$
$883$	1.46950e128	1.04202	0.521012	+	0.853549i	$0.325555\pi$
$884$	−7.56616e127	−0.510742
$885$	−4.29429e128	−2.75968
$886$	1.34964e126	0.00825756
$887$	−3.18960e128	−1.85806	−0.929028	−	0.370009i	$-0.879355\pi$
$887$	−3.18960e128	−1.85806	−0.929028	+	0.370009i	$0.879355\pi$
$888$	−3.16306e127	−0.175446
$889$	−7.91464e126	−0.0418027
$890$	1.19568e127	0.0601382
$891$	−3.95870e127	−0.189615
$892$	1.42201e128	0.648682
$893$	−5.14981e128	−2.23745
$894$	−1.81952e127	−0.0752966
$895$	3.66778e128	1.44577
$896$	−3.46735e127	−0.130196
$897$	3.96766e127	0.141926
$898$	9.71798e127	0.331173
$899$	3.44898e128	1.11981
$900$	1.45127e128	0.448952
$901$	1.04526e129	3.08102
$902$	7.94873e127	0.223261
$903$	−9.69050e128	−2.59376
$904$	−2.15023e128	−0.548476
$905$	−4.50210e127	−0.109447
$906$	3.73879e128	0.866272
$907$	−1.17471e128	−0.259426	−0.129713	−	0.991552i	$-0.541406\pi$
$907$	−1.17471e128	−0.259426	−0.129713	+	0.991552i	$0.541406\pi$
$908$	−3.94766e127	−0.0831009
$909$	5.70224e128	1.14424
$910$	−3.80523e128	−0.727914
$911$	4.24958e128	0.774990	0.387495	−	0.921872i	$-0.373340\pi$
$911$	4.24958e128	0.774990	0.387495	+	0.921872i	$0.373340\pi$
$912$	3.38260e128	0.588133
$913$	7.11284e127	0.117914
$914$	−4.99856e128	−0.790105
$915$	−9.48471e128	−1.42957
$916$	2.76306e128	0.397135
$917$	−7.56467e128	−1.03687
$918$	7.79825e128	1.01939
$919$	7.60961e128	0.948719	0.474360	−	0.880331i	$-0.342680\pi$
$919$	7.60961e128	0.948719	0.474360	+	0.880331i	$0.342680\pi$
$920$	−6.12237e127	−0.0728029
$921$	−1.36029e129	−1.54290
$922$	5.95373e128	0.644160
$923$	−4.68330e128	−0.483368
$924$	8.52438e128	0.839329
$925$	2.01109e128	0.188915
$926$	1.26320e129	1.13212
$927$	1.35190e128	0.115605
$928$	−1.96013e128	−0.159937
$929$	4.43080e128	0.344984	0.172492	−	0.985011i	$-0.444818\pi$
$929$	4.43080e128	0.344984	0.172492	+	0.985011i	$0.444818\pi$
$930$	−2.35367e129	−1.74879
$931$	2.45766e129	1.74265
$932$	2.70141e128	0.182809
$933$	−1.42598e129	−0.921007
$934$	−1.08593e129	−0.669443
$935$	−2.87029e129	−1.68896
$936$	−5.19236e128	−0.291652
$937$	8.57093e128	0.459574	0.229787	−	0.973241i	$-0.426197\pi$
$937$	8.57093e128	0.459574	0.229787	+	0.973241i	$0.426197\pi$
$938$	−2.33719e129	−1.19638
$939$	3.14943e128	0.153914
$940$	−2.03648e129	−0.950210
$941$	−3.09635e128	−0.137943	−0.0689717	−	0.997619i	$-0.521972\pi$
$941$	−3.09635e128	−0.137943	−0.0689717	+	0.997619i	$0.521972\pi$
$942$	9.65129e128	0.410555
$943$	−1.75275e128	−0.0711967
$944$	−8.90121e128	−0.345277
$945$	3.92195e129	1.45284
$946$	1.60844e129	0.569036
$947$	1.66144e129	0.561383	0.280692	−	0.959798i	$-0.409436\pi$
$947$	1.66144e129	0.561383	0.280692	+	0.959798i	$0.409436\pi$
$948$	−2.83272e129	−0.914200
$949$	1.53990e129	0.474692
$950$	−2.15068e129	−0.633285
$951$	−2.57777e129	−0.725091
$952$	3.58447e129	0.963202
$953$	−2.81155e129	−0.721779	−0.360890	−	0.932608i	$-0.617527\pi$
$953$	−2.81155e129	−0.721779	−0.360890	+	0.932608i	$0.617527\pi$
$954$	7.17319e129	1.75937
$955$	5.00480e129	1.17284
$956$	−3.33759e129	−0.747334
$957$	4.81893e129	1.03105
$958$	2.66863e129	0.545618
$959$	4.76896e129	0.931782
$960$	1.33764e129	0.249771
$961$	2.98076e129	0.531937
$962$	−7.19528e128	−0.122725
$963$	−4.64417e129	−0.757120
$964$	−1.85970e129	−0.289796
$965$	1.22975e130	1.83180
$966$	−1.87968e129	−0.267657
$967$	−6.12643e129	−0.833980	−0.416990	−	0.908911i	$-0.636915\pi$
$967$	−6.12643e129	−0.833980	−0.416990	+	0.908911i	$0.636915\pi$
$968$	1.30176e129	0.169416
$969$	−3.49686e130	−4.35105
$970$	1.09116e130	1.29813
$971$	−1.30319e130	−1.48241	−0.741207	−	0.671276i	$-0.765746\pi$
$971$	−1.30319e130	−1.48241	−0.741207	+	0.671276i	$0.765746\pi$
$972$	−5.49022e129	−0.597183
$973$	9.70564e129	1.00952
$974$	−9.33733e129	−0.928769
$975$	5.51164e129	0.524300
$976$	−1.96599e129	−0.178860
$977$	2.62874e129	0.228736	0.114368	−	0.993438i	$-0.463516\pi$
$977$	2.62874e129	0.228736	0.114368	+	0.993438i	$0.463516\pi$
$978$	−1.14649e130	−0.954182
$979$	−6.09311e128	−0.0485056
$980$	9.71877e129	0.740077
$981$	1.29379e130	0.942460
$982$	5.10452e129	0.355718
$983$	5.46064e129	0.364054	0.182027	−	0.983294i	$-0.441734\pi$
$983$	5.46064e129	0.364054	0.182027	+	0.983294i	$0.441734\pi$
$984$	3.82948e129	0.244261
$985$	1.09012e130	0.665273
$986$	2.02634e130	1.18322
$987$	−6.25239e130	−3.49341
$988$	7.69470e129	0.411400
$989$	−3.54671e129	−0.181463
$990$	−1.96977e130	−0.964459
$991$	3.33654e129	0.156348	0.0781741	−	0.996940i	$-0.475091\pi$
$991$	3.33654e129	0.156348	0.0781741	+	0.996940i	$0.475091\pi$
$992$	−4.87869e129	−0.218799
$993$	1.49123e130	0.640108
$994$	2.21871e130	0.911577
$995$	−5.42475e130	−2.13342
$996$	3.42677e129	0.129004
$997$	3.85557e130	1.38947	0.694736	−	0.719265i	$-0.255521\pi$
$997$	3.85557e130	1.38947	0.694736	+	0.719265i	$0.255521\pi$
$998$	1.31819e130	0.454778
$999$	7.41600e129	0.244946

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.88.a.b.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.88.a.b.1.4	✓	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 88 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q-8.79609e12 q^{2} +8.97819e20 q^{3} +7.73713e25 q^{4} +3.21672e30 q^{5} -7.89730e33 q^{6} +8.51076e36 q^{7} -6.80565e38 q^{8} +4.82821e41 q^{9} -2.82946e43 q^{10} +1.44187e45 q^{11} +6.94654e46 q^{12} +1.58019e48 q^{13} -7.48615e49 q^{14} +2.88803e51 q^{15} +5.98631e51 q^{16} -6.18852e53 q^{17} -4.24694e54 q^{18} +6.29366e55 q^{19} +2.48882e56 q^{20} +7.64113e57 q^{21} -1.26828e58 q^{22} +2.79664e58 q^{23} -6.11024e59 q^{24} +3.88493e60 q^{25} -1.38995e61 q^{26} +1.43259e62 q^{27} +6.58489e62 q^{28} +3.72251e63 q^{29} -2.54034e64 q^{30} +9.26519e64 q^{31} -5.26561e64 q^{32} +1.29454e66 q^{33} +5.44348e66 q^{34} +2.73767e67 q^{35} +3.73565e67 q^{36} +5.17665e67 q^{37} -5.53596e68 q^{38} +1.41872e69 q^{39} -2.18919e69 q^{40} -6.26732e69 q^{41} -6.72121e70 q^{42} -1.26820e71 q^{43} +1.11559e71 q^{44} +1.55310e72 q^{45} -2.45995e71 q^{46} -8.18255e72 q^{47} +5.37462e72 q^{48} +3.90498e73 q^{49} -3.41722e73 q^{50} -5.55617e74 q^{51} +1.22261e74 q^{52} -1.68903e75 q^{53} -1.26012e75 q^{54} +4.63809e75 q^{55} -5.79213e75 q^{56} +5.65056e76 q^{57} -3.27436e76 q^{58} -1.48693e77 q^{59} +2.23451e77 q^{60} -3.28414e77 q^{61} -8.14974e77 q^{62} +4.10918e78 q^{63} +4.63168e77 q^{64} +5.08302e78 q^{65} -1.13869e79 q^{66} +3.12202e79 q^{67} -4.78813e79 q^{68} +2.51088e79 q^{69} -2.40808e80 q^{70} -2.96376e80 q^{71} -3.28591e80 q^{72} +9.74503e80 q^{73} -4.55343e80 q^{74} +3.48796e81 q^{75} +4.86948e81 q^{76} +1.22714e82 q^{77} -1.24792e82 q^{78} -4.07789e82 q^{79} +1.92563e82 q^{80} -2.74553e82 q^{81} +5.51279e82 q^{82} +4.93307e82 q^{83} +5.91203e83 q^{84} -1.99067e84 q^{85} +1.11552e84 q^{86} +3.34214e84 q^{87} -9.81285e83 q^{88} -4.22584e83 q^{89} -1.36612e85 q^{90} +1.34486e85 q^{91} +2.16380e84 q^{92} +8.31846e85 q^{93} +7.19744e85 q^{94} +2.02449e86 q^{95} -4.72757e85 q^{96} -3.85645e86 q^{97} -3.43486e86 q^{98} +6.96165e86 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 35184372088832 q^{2} + 40\!\cdots\!28 q^{3} + 30\!\cdots\!56 q^{4} - 40\!\cdots\!60 q^{5} - 35\!\cdots\!24 q^{6} + 85\!\cdots\!04 q^{7} - 27\!\cdots\!48 q^{8} + 82\!\cdots\!48 q^{9} + 35\!\cdots\!80 q^{10}+ \cdots + 22\!\cdots\!76 q^{99}+O(q^{100}) \) 4 * q - 35184372088832 * q^2 + 403237985254067182128 * q^3 + 309485009821345068724781056 * q^4 - 4037922390733497835169570162760 * q^5 - 3546918828382512738768149884698624 * q^6 + 8582179387397492406597229487230375904 * q^7 - 2722258935367507707706996859454145691648 * q^8 + 820135434884318664352221575507492568732948 * q^9 + 35517940965348365626859729845107910854574080 * q^10 + 2970616434026495781757184460756379040517208848 * q^11 + 31199027956673594964608194726311446315419041792 * q^12 - 1767394568818848613362028589161957028533441611112 * q^13 - 75489648224824411010546555477731971328955260076032 * q^14 + 3370976843124805373452544557684295582910726697502880 * q^15 + 23945242826029513411849172299223580994042798784118784 * q^16 - 702353032002195299447255515013113779135644499293109816 * q^17 - 7213987576051478951188874632704563580254297738585309184 * q^18 + 38051210330377980576900552965948384772060949611758270960 * q^19 - 312419112688496434410317985513745659312699567327821168640 * q^20 - 2960768946346244712423575885216855505816696171119080255872 * q^21 - 26129818486996871127304316256231512888117802859237038096384 * q^22 + 267410844513343534387094489566271409098947974355011539188128 * q^23 - 274429552109368924814832586348763817236857825346144736116736 * q^24 + 26866935732372298920001618987293695975686810093231631671755100 * q^25 + 15546167034275791140382436144471296993092547711081656715575296 * q^26 + 98351974670575379028284146601861806526822489553847883125490400 * q^27 + 664013967999314535695892002534007752932295679741402958744518656 * q^28 - 936377285291713459807588765220376016646503474372565915415382440 * q^29 - 29651425887834852403903990749669038123824799034099618745983959040 * q^30 + 119463507882721430244886842916392661099853847057206322986794525568 * q^31 - 210624583337114373395836055367340864637790190801098222508621955072 * q^32 - 975951433415384517573045287992141578476030063995050605617360966464 * q^33 + 6177962603921142192805661314942895498269819437765021241050270793728 * q^34 + 14105085028850567766840711566409137394874532315214531645239547531840 * q^35 + 63454905780001617731151046382612710619432714548573512194720658358272 * q^36 + 182087106643248709136261820106869557597167548749803025400276539121464 * q^37 - 334701985673606721323645108291715305922613643471269213861286961479680 * q^38 - 5157167650299694789254850025641525408739411563899847457339313757250784 * q^39 + 2748067577123698321827685975535901419950085077291708477942376033157120 * q^40 + 5499251594717860286021866958065054045901150247706209838765933372175208 * q^41 + 26043199069326335451693431452427559455621627547084532573326442418405376 * q^42 - 157807090931211109929865823295822094205785343123733495078770527721821552 * q^43 + 229840314065034778104010119086398472312972227124835062038272769756495872 * q^44 - 1370445036354823659067923168385609449595471872659192002945296358462825320 * q^45 - 2352170663486569504369914341681047401963148037857733129248014646193946624 * q^46 - 11700969700600051870794491472787906623524149540240126773037581150641555136 * q^47 + 2413907868396886727226140291242059049083751312718584875630451012128473088 * q^48 + 45608750768809825384693277965554885824930550141562503946687984691665533732 * q^49 - 236324065923630760668657815178197122585685320681456781276991408990637260800 * q^50 - 914883468555652107825206155517190576830844787740672822262980556765469169312 * q^51 - 136745531372273324016576733538944106078280970896210682631976284458024173568 * q^52 - 3205407327892231366350098762423033970241498041998526172742677864692608514312 * q^53 - 865113118120226050927175001395744751092084611954848335836798017458090803200 * q^54 - 10009926131406218736826424103970095109094189414661383153140158173941128709920 * q^55 - 5840728630567416793561662980979737449788739679624018831289026246209278312448 * q^56 + 24760562583447132282306921710743074800398451150699602451361304490068034752320 * q^57 + 8236461705308510473577685400040524235406303263089755599489781422351733227520 * q^58 - 81401388903576961577929700275194040780233584053778446123485310614164754536880 * q^59 + 260816700350501796503049467891128405126358446664151554703502613334842482360320 * q^60 + 908111889319782669823282318823295371554753169091641506977419705876741077882328 * q^61 - 1050812128095696376586514967647428079039044942828517372626320439677738647814144 * q^62 + 7137835102413627130280079665652016586382162073538425059614697312278117344350048 * q^63 + 1852673427797059126777135760139006525652319754650249024631321344126610074238976 * q^64 + 11407211919915638593357605065156231994296813060854399078385375214171172364857680 * q^65 + 8584559593478959280621500012652850349171438888492092327918713325137577495232512 * q^66 - 65059771693644954593974794228917141656005263924052931483321156753263176566322896 * q^67 - 54341933751812724902023253670568124974314494093364989057139191298059718491111424 * q^68 - 144323666676858272713465642347149842097884989245184653886655055101689375583845504 * q^69 - 124069639999923005500646624090308971041908232841505948959254386145464972707102720 * q^70 - 183272612160344892942190287282961718510131375557583525213035115209249713064136992 * q^71 - 558155253956338317275929527602177423655680841848067355296117578760944212116504576 * q^72 + 354182538046550765754528347144724476790476600029207619306415675742769571814637288 * q^73 - 1601655128178723932025775974507397068426901430503198065737820251919877020961472512 * q^74 + 710386439551323791969874648476083944602337020291621916942901745237698809202501200 * q^75 + 2944069800702774064027323538684509525361173924971530627370715914294143730780733440 * q^76 + 39316760279456924611775164190833990669200449799501752350802186925973327788597118848 * q^77 + 45362926383157972415756683406366951526581873158623352931657948697548800307937411072 * q^78 + 15689408650300008287770111864298279692820798574497171271867094782550105530843081920 * q^79 - 24172258039693807695503348146758763873414302432021545297363850106765398076513320960 * q^80 - 196590592451401107987710944406206415161857917104016937408869683425180184810203702876 * q^81 - 48371928579663987252349183028740936842481506637169603120359663272770590191611019264 * q^82 + 111926752599709260117886233216331177095176580206068162806299107496899925996223203568 * q^83 - 229078401609675258913891688255885614430188449105962531942162006259872232223914590208 * q^84 - 891497844731417844264766892389844899904478293183670323386186444763703698463839596560 * q^85 + 1388085851394969400976659588554077855842466084275351230019781346209556380442549026816 * q^86 + 2027498154029213080175869882525768385333184769847411190333977363043382754362186713120 * q^87 - 2021696782769547651193529032558892722193566089333659035337753899891686714980356325376 * q^88 - 1111763274969003683091618237538433748811411444468148051875571331333583253595104867160 * q^89 + 12054562021600253271129669326554918303828197627410649510778436683009490086217184706560 * q^90 + 79630263055292573954918630151432006426386375686727482380289693283976606755116980321088 * q^91 + 20689911960136575706111408504507326985128933416561732998791094227623959804415198625792 * q^92 + 121552396376548026998325328889505560359171182104366398760596365823334350324441379006976 * q^93 + 102922817936515347171258282828953462563508237397083710417081191671708730834331304460288 * q^94 + 360329377379389097240594968925389763617374668200294178024200943546627617266362721242400 * q^95 - 21232958157458842504504822471050360495135888697596704547293213652627233307394314338304 * q^96 + 84654632295309208342666811638631082612402959416215649507302559581340331556342797429384 * q^97 - 401178814389151860471251451603139889379513741986404607571754642978513123633817249120256 * q^98 + 2203878007770692926523827334498155512549713414229081953932986276578630523661724303178576 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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