LMFDB - Embedded newform 1.98.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,98,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, 98, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 98);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 98 $
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:	$59.5852992940$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} + \cdots - 60\!\cdots\!00 $ x^7 - x^6 - 276087571804405990752665088x^5 - 120083887007184048105302098667336699968x^4 + 19373155893793813105741918625198082602849023860244480x^3 + 17598423525325549028964286424215233146805218189713573416303513600x^2 - 58411389055962077878580852277509525104521481793026738328029906710656876544000*x - 6001611580367435872109665775701806052295874267155389813520177925124906158334928977920000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{83}\cdot 3^{30}\cdot 5^{10}\cdot 7^{8}\cdot 11^{2}\cdot 19 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.07106e13$ 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)

$f(q)$	$=$	$q-5.16494e14 q^{2} +2.18475e23 q^{3} +1.08310e29 q^{4} -1.00097e34 q^{5} -1.12841e38 q^{6} -1.23831e41 q^{7} +2.59003e43 q^{8} +2.86433e46 q^{9} +O(q^{10})$	\(q-5.16494e14 q^{2} +2.18475e23 q^{3} +1.08310e29 q^{4} -1.00097e34 q^{5} -1.12841e38 q^{6} -1.23831e41 q^{7} +2.59003e43 q^{8} +2.86433e46 q^{9} +5.16994e48 q^{10} +3.83688e50 q^{11} +2.36630e52 q^{12} -5.53419e53 q^{13} +6.39580e55 q^{14} -2.18686e57 q^{15} -3.05398e58 q^{16} +7.49593e59 q^{17} -1.47941e61 q^{18} +6.41706e61 q^{19} -1.08415e63 q^{20} -2.70540e64 q^{21} -1.98173e65 q^{22} -1.17405e65 q^{23} +5.65857e66 q^{24} +3.70847e67 q^{25} +2.85838e68 q^{26} +2.08759e69 q^{27} -1.34121e70 q^{28} -7.39014e70 q^{29} +1.12950e72 q^{30} +2.65449e72 q^{31} +1.16695e73 q^{32} +8.38263e73 q^{33} -3.87160e74 q^{34} +1.23951e75 q^{35} +3.10236e75 q^{36} -2.05897e76 q^{37} -3.31437e76 q^{38} -1.20908e77 q^{39} -2.59253e77 q^{40} +7.98428e77 q^{41} +1.39732e79 q^{42} -1.42001e79 q^{43} +4.15573e79 q^{44} -2.86710e80 q^{45} +6.06389e79 q^{46} +1.36639e81 q^{47} -6.67218e81 q^{48} +5.90413e81 q^{49} -1.91540e82 q^{50} +1.63767e83 q^{51} -5.99409e82 q^{52} -1.20661e83 q^{53} -1.07823e84 q^{54} -3.84059e84 q^{55} -3.20726e84 q^{56} +1.40197e85 q^{57} +3.81697e85 q^{58} -1.14996e86 q^{59} -2.36859e86 q^{60} +4.96803e85 q^{61} -1.37103e87 q^{62} -3.54693e87 q^{63} -1.18804e87 q^{64} +5.53955e87 q^{65} -4.32958e88 q^{66} -2.45463e88 q^{67} +8.11884e88 q^{68} -2.56500e88 q^{69} -6.40198e89 q^{70} -4.84273e89 q^{71} +7.41870e89 q^{72} +1.83823e90 q^{73} +1.06345e91 q^{74} +8.10208e90 q^{75} +6.95032e90 q^{76} -4.75125e91 q^{77} +6.24485e91 q^{78} -3.59855e91 q^{79} +3.05693e92 q^{80} -9.06594e91 q^{81} -4.12383e92 q^{82} +6.35017e92 q^{83} -2.93022e93 q^{84} -7.50318e93 q^{85} +7.33425e93 q^{86} -1.61456e94 q^{87} +9.93763e93 q^{88} -6.29848e94 q^{89} +1.48084e95 q^{90} +6.85304e94 q^{91} -1.27161e94 q^{92} +5.79940e95 q^{93} -7.05733e95 q^{94} -6.42327e95 q^{95} +2.54951e96 q^{96} -1.43393e96 q^{97} -3.04945e96 q^{98} +1.09901e97 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots + 34\!\cdots\!51 q^{9}+O(q^{10}) $ 7 * q - 16697241085008 * q^2 + 100515854497394358147996 * q^3 + 163057083940695061811962902784 * q^4 - 3658387999529088680958306590731350 * q^5 - 30592714388364079315260992082788233536 * q^6 - 184642311743115370607493500489904481438408 * q^7 + 36028528195426625427479134330455698506199040 * q^8 + 34775775472129528349857305774273773877811641051 * q^9	$ 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots - 13\!\cdots\!28 q^{99}+O(q^{100}) $ 7 * q - 16697241085008 * q^2 + 100515854497394358147996 * q^3 + 163057083940695061811962902784 * q^4 - 3658387999529088680958306590731350 * q^5 - 30592714388364079315260992082788233536 * q^6 - 184642311743115370607493500489904481438408 * q^7 + 36028528195426625427479134330455698506199040 * q^8 + 34775775472129528349857305774273773877811641051 * q^9 + 2369114123959441270700616822719459966510786272800 * q^10 - 211379321299339211995860033669883746379479318698796 * q^11 + 29500590587146562092031430274877546417191966208812032 * q^12 - 883667637845783834437332163606692334928033653755299614 * q^13 + 24884922778173528138085777326574033504771595080747613568 * q^14 - 1421739776861319561135033238174867421082029896683725376600 * q^15 - 31468671341370205538262999960370611414173356196203424841728 * q^16 + 163250436637003263661570089512096377905088225334685131721342 * q^17 - 7054606772048003028382413409749231596837718873737440667537424 * q^18 + 133084372359310898958448501523235681541051727436663191570359820 * q^19 - 1318696260534044061297364386263469065025874939722479973417331200 * q^20 - 8226961344750528298533572507576209983448935264598913374247505696 * q^21 - 193421584410477868290586506488587370358898549812529751083484246976 * q^22 + 925260914184001305416523826357059292226482310773339215111132964776 * q^23 + 1719359518493251306391725804700467921422689016189510541760687554560 * q^24 - 15111829774373494694703308579556617230149980669179989285410298974375 * q^25 + 252570839996871764139482603418038366978372757286009959646749464447904 * q^26 - 16291464003153760806194022590188439733978909915063668620863256233960 * q^27 + 2270023864280230580582797832096861251181573169347509612847861972977664 * q^28 - 119228645746988213289933973286594685848645193803889692652451844737975470 * q^29 + 350448354156350400480979435069989695492221249186335731168327070817564800 * q^30 + 1783283666881858864849681148885200501497581294973934227348751364131906784 * q^31 - 5665372498136527985720301619489703024215195383428523596691479514791804928 * q^32 + 31524650657546522511070078635079454480923539002999356172307109465073458512 * q^33 - 360491523041063125717708388027762293189396999595568175085448186659598970272 * q^34 + 1278268341035082746531666145800358760269267683649420892787253371588938750800 * q^35 - 216561481226385812264597126278375191173372906326221899147967914271513631488 * q^36 - 4532061622841943284542390241171859851726205146853788500539269747469617514358 * q^37 - 2979582210919721773595405461863152858097797783237497905501709239616681227840 * q^38 + 43268347489134056222423767530379619668087154910038087692852374564634305176712 * q^39 - 252514831298472678734291758335102132215188475493571956673272319739362987008000 * q^40 + 123663386655433999860484853403953500874113711440208020678841289201379470695974 * q^41 + 3296122851141924824443574220618174749418258893075867148421980920155200276985344 * q^42 - 6595249409358954185694714287710218939626711013706300289026511229489118746183244 * q^43 + 31427981619155317050453798326367420934595218826815326227502736274099059309390848 * q^44 - 252057107931731391251960224707597558538839631727412739243273361199825466582835550 * q^45 + 333743461536679365083903174537100831945624746347277312419032904840551699600111744 * q^46 + 1582413179705462665936960636748613012540566075462612818643843634715630112826042192 * q^47 - 5861556434117332280930374286873664455351210291383528056190272983552191849213722624 * q^48 + 4345635008055985505106601346877321132027699788278385269907095782368403364891488399 * q^49 - 26742593205970009143775889336520990050133941492259748319418427757724876722706030000 * q^50 + 7043565089506559965061572069632281800522096763383079376468682406398600422146676984 * q^51 + 45800222007571685487736059984048709986270205428489770979037497696929384027946163712 * q^52 - 653999931744204429821742741003701830521617657540517458768483866216741544701292475654 * q^53 - 1692275654206728716605786947196644220317392594111136065941704729626944069981837438080 * q^54 - 2797264930804680667438884831689324464716285797264284803651188210713133784740241832200 * q^55 - 13571511538900847480549793700693331801076437559096966169392506220987757777557857402880 * q^56 - 32156245276763940566100505959698139630384956043693169857398532690693294678041975751120 * q^57 - 110275012470967940484400158535846043036245771061355495516009955997986614502808104491360 * q^58 - 289716843512018767811919727809674339112407721830489506743846640027004030301179845118940 * q^59 - 910863091257112962110410128770927709732237428874631129572443550789630933691032398899200 * q^60 - 1779644273771380099149369471014727845406783738447834645166296866716596067825339549188046 * q^61 - 4893410323209515393605311670149478112622973098189152140516775294151722525768562137565696 * q^62 - 12773855755538157144284595252262546905649007916763284311597736303148976241726684562602024 * q^63 - 24329532034212074257236420324752039539459926287390018025638252399891746834835822530789376 * q^64 - 40979880706222898178317998710539228015340375450212825952623031288613904725454054500850100 * q^65 - 142841613731497146561089386918878946227924637814625892149907766833242924230825872606056192 * q^66 - 183094181851902905703789039636502649221241410347877100016575616698548103898875205122783908 * q^67 - 250132580738896836682574414547500843555901286243235420681429272583107380144497499057716736 * q^68 - 372244836961332226973480986215431578494847115740354696097669790201492502675456308855459168 * q^69 - 587389541033882485666068522391834191601610745639266949076956170254929472707526921059782400 * q^70 - 36618527208607574135274147674246343687098099724640001025727994874106062220116534447931656 * q^71 + 2495502705800463241319297965149724088435827677064467496346161624547668625438549984339128320 * q^72 + 5937141741627411574629383951784847225959103237898806939243808260531064318159784943464907526 * q^73 + 25603418812897773069861990064614106209712057876935905208225093500026599325689360114519970848 * q^74 + 43416229043729585532262686371625117245611844558141193068941674421259839404159894884059222500 * q^75 + 64491781461168277038374423376126180174707623388661413952117963143585395013082375272839869440 * q^76 + 122801524700573133455664123216977109508839271312008866744292206338517188364407357732160152224 * q^77 + 256518622739178273010532892375526005382856863147760611859324715551823107217212845963281985152 * q^78 + 155279975164311735091235448536513906273532801204307686975280157544842456609207922540776901680 * q^79 + 343037548751841740038666995050634479050946344382038763901789904170114217394648666813900390400 * q^80 - 799336653019442009471583631583081099983526554777301855450568718504605547656753900698628831153 * q^81 - 2054599455199243418451530458808296516745297582440826399667363552358055209069956455679452833056 * q^82 - 2745080838526935126539434486643898932954125805020264508203796620734019354440308801326974021684 * q^83 - 12055830667015300843296227009204563031159870111997209215974794552386444770918151507927520305152 * q^84 - 16156906986132970771716277890961343081101351325821342812927748903601690598916612215092853170700 * q^85 - 16073101085057033129856695763368798351047883803740227513388827997968391823543719379002604387776 * q^86 - 44931373084677669249994770736329381356923858000626008622029156778901658182110994195783000791480 * q^87 - 20900444501134905678673788524771632932447417317035512416151379720801969394444956958395302789120 * q^88 + 8652425236627243255051028260917634407304730072980172181544783646255542601500269383337979350390 * q^89 + 169914380219009102880054256907856294069041898142575788262717672760376053145875718225670932330400 * q^90 + 235279610532724372901602846332263408075886672274330172793822218199845308058643167074949650230544 * q^91 + 622950794384614085632156625042963081233986358617743991991586248417198315809579918444522808891392 * q^92 + 1619655729334717431421579797164299646702152339363664709672746834797775058100318492643375449441152 * q^93 + 1784387548746436753701888750274366538460858609156963702431495773056050960861585984793528939671808 * q^94 + 1109691419127482658877926123378178695834970817464791602098716148821958373905367930889408748989000 * q^95 + 2773817117979873680694700349927475687549477810523157816910439588411515192104026991177258420404224 * q^96 - 462826972284038426621245345324758076530452205891330025493894671876723283114629445572915788984658 * q^97 - 10100804559243313775965110405631054964918520327952856127425837778067309219959758215138751854831056 * q^98 - 13792894935722775136702660269810636953813664741795563019740674282913700184659028566406972539495228 * 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 $

$2$	−5.16494e14	−1.29751	−0.648755	−	0.760997i	$-0.724710\pi$
$2$	−5.16494e14	−1.29751	−0.648755	+	0.760997i	$0.724710\pi$
$3$	2.18475e23	1.58132	0.790662	−	0.612252i	$-0.209736\pi$
$3$	2.18475e23	1.58132	0.790662	+	0.612252i	$0.209736\pi$
$4$	1.08310e29	0.683532
$5$	−1.00097e34	−1.26001	−0.630006	−	0.776590i	$-0.716948\pi$
$5$	−1.00097e34	−1.26001	−0.630006	+	0.776590i	$0.716948\pi$
$6$	−1.12841e38	−2.05179
$7$	−1.23831e41	−1.27519	−0.637594	−	0.770373i	$-0.720070\pi$
$7$	−1.23831e41	−1.27519	−0.637594	+	0.770373i	$0.720070\pi$
$8$	2.59003e43	0.410620
$9$	2.86433e46	1.50059
$10$	5.16994e48	1.63488
$11$	3.83688e50	1.19243	0.596216	−	0.802824i	$-0.296670\pi$
$11$	3.83688e50	1.19243	0.596216	+	0.802824i	$0.296670\pi$
$12$	2.36630e52	1.08089
$13$	−5.53419e53	−0.520957	−0.260478	−	0.965480i	$-0.583880\pi$
$13$	−5.53419e53	−0.520957	−0.260478	+	0.965480i	$0.583880\pi$
$14$	6.39580e55	1.65457
$15$	−2.18686e57	−1.99249
$16$	−3.05398e58	−1.21632
$17$	7.49593e59	1.57780	0.788901	−	0.614520i	$-0.210650\pi$
$17$	7.49593e59	1.57780	0.788901	+	0.614520i	$0.210650\pi$
$18$	−1.47941e61	−1.94703
$19$	6.41706e61	0.613460	0.306730	−	0.951797i	$-0.400765\pi$
$19$	6.41706e61	0.613460	0.306730	+	0.951797i	$0.400765\pi$
$20$	−1.08415e63	−0.861259
$21$	−2.70540e64	−2.01649
$22$	−1.98173e65	−1.54719
$23$	−1.17405e65	−0.106142	−0.0530709	−	0.998591i	$-0.516901\pi$
$23$	−1.17405e65	−0.106142	−0.0530709	+	0.998591i	$0.516901\pi$
$24$	5.65857e66	0.649324
$25$	3.70847e67	0.587630
$26$	2.85838e68	0.675947
$27$	2.08759e69	0.791593
$28$	−1.34121e70	−0.871632
$29$	−7.39014e70	−0.875689	−0.437844	−	0.899051i	$-0.644258\pi$
$29$	−7.39014e70	−0.875689	−0.437844	+	0.899051i	$0.644258\pi$
$30$	1.12950e72	2.58527
$31$	2.65449e72	1.23862	0.619312	−	0.785145i	$-0.287412\pi$
$31$	2.65449e72	1.23862	0.619312	+	0.785145i	$0.287412\pi$
$32$	1.16695e73	1.16756
$33$	8.38263e73	1.88562
$34$	−3.87160e74	−2.04721
$35$	1.23951e75	1.60675
$36$	3.10236e75	1.02570
$37$	−2.05897e76	−1.80246	−0.901232	−	0.433336i	$-0.857336\pi$
$37$	−2.05897e76	−1.80246	−0.901232	+	0.433336i	$0.857336\pi$
$38$	−3.31437e76	−0.795971
$39$	−1.20908e77	−0.823802
$40$	−2.59253e77	−0.517386
$41$	7.98428e77	0.481081	0.240541	−	0.970639i	$-0.422675\pi$
$41$	7.98428e77	0.481081	0.240541	+	0.970639i	$0.422675\pi$
$42$	1.39732e79	2.61641
$43$	−1.42001e79	−0.849317	−0.424658	−	0.905354i	$-0.639606\pi$
$43$	−1.42001e79	−0.849317	−0.424658	+	0.905354i	$0.639606\pi$
$44$	4.15573e79	0.815065
$45$	−2.86710e80	−1.89076
$46$	6.06389e79	0.137720
$47$	1.36639e81	1.09352	0.546762	−	0.837288i	$-0.315860\pi$
$47$	1.36639e81	1.09352	0.546762	+	0.837288i	$0.315860\pi$
$48$	−6.67218e81	−1.92339
$49$	5.90413e81	0.626104
$50$	−1.91540e82	−0.762456
$51$	1.63767e83	2.49502
$52$	−5.99409e82	−0.356091
$53$	−1.20661e83	−0.284570	−0.142285	−	0.989826i	$-0.545445\pi$
$53$	−1.20661e83	−0.284570	−0.142285	+	0.989826i	$0.545445\pi$
$54$	−1.07823e84	−1.02710
$55$	−3.84059e84	−1.50248
$56$	−3.20726e84	−0.523618
$57$	1.40197e85	0.970080
$58$	3.81697e85	1.13622
$59$	−1.14996e86	−1.49404	−0.747019	−	0.664803i	$-0.768515\pi$
$59$	−1.14996e86	−1.49404	−0.747019	+	0.664803i	$0.768515\pi$
$60$	−2.36859e86	−1.36193
$61$	4.96803e85	0.128141	0.0640704	−	0.997945i	$-0.479592\pi$
$61$	4.96803e85	0.128141	0.0640704	+	0.997945i	$0.479592\pi$
$62$	−1.37103e87	−1.60713
$63$	−3.54693e87	−1.91353
$64$	−1.18804e87	−0.298608
$65$	5.53955e87	0.656412
$66$	−4.32958e88	−2.44661
$67$	−2.45463e88	−0.668895	−0.334447	−	0.942414i	$-0.608550\pi$
$67$	−2.45463e88	−0.668895	−0.334447	+	0.942414i	$0.608550\pi$
$68$	8.11884e88	1.07848
$69$	−2.56500e88	−0.167845
$70$	−6.40198e89	−2.08478
$71$	−4.84273e89	−0.792612	−0.396306	−	0.918119i	$-0.629708\pi$
$71$	−4.84273e89	−0.792612	−0.396306	+	0.918119i	$0.629708\pi$
$72$	7.41870e89	0.616172
$73$	1.83823e90	0.782063	0.391031	−	0.920377i	$-0.372118\pi$
$73$	1.83823e90	0.782063	0.391031	+	0.920377i	$0.372118\pi$
$74$	1.06345e91	2.33872
$75$	8.10208e90	0.929234
$76$	6.95032e90	0.419320
$77$	−4.75125e91	−1.52057
$78$	6.24485e91	1.06889
$79$	−3.59855e91	−0.332057	−0.166029	−	0.986121i	$-0.553094\pi$
$79$	−3.59855e91	−0.332057	−0.166029	+	0.986121i	$0.553094\pi$
$80$	3.05693e92	1.53257
$81$	−9.06594e91	−0.248822
$82$	−4.12383e92	−0.624208
$83$	6.35017e92	0.533947	0.266973	−	0.963704i	$-0.413976\pi$
$83$	6.35017e92	0.533947	0.266973	+	0.963704i	$0.413976\pi$
$84$	−2.93022e93	−1.37833
$85$	−7.50318e93	−1.98805
$86$	7.33425e93	1.10200
$87$	−1.61456e94	−1.38475
$88$	9.93763e93	0.489636
$89$	−6.29848e94	−1.79399	−0.896995	−	0.442040i	$-0.854255\pi$
$89$	−6.29848e94	−1.79399	−0.896995	+	0.442040i	$0.854255\pi$
$90$	1.48084e95	2.45328
$91$	6.85304e94	0.664318
$92$	−1.27161e94	−0.0725513
$93$	5.79940e95	1.95867
$94$	−7.05733e95	−1.41886
$95$	−6.42327e95	−0.772967
$96$	2.54951e96	1.84630
$97$	−1.43393e96	−0.628201	−0.314101	−	0.949390i	$-0.601703\pi$
$97$	−1.43393e96	−0.628201	−0.314101	+	0.949390i	$0.601703\pi$
$98$	−3.04945e96	−0.812376
$99$	1.09901e97	1.78935
$100$	4.01664e96	0.401664
$101$	−2.51574e97	−1.55267	−0.776334	−	0.630322i	$-0.782923\pi$
$101$	−2.51574e97	−1.55267	−0.776334	+	0.630322i	$0.782923\pi$
$102$	−8.45849e97	−3.23731
$103$	−1.91835e96	−0.0457428	−0.0228714	−	0.999738i	$-0.507281\pi$
$103$	−1.91835e96	−0.0457428	−0.0228714	+	0.999738i	$0.507281\pi$
$104$	−1.43337e97	−0.213915
$105$	2.70801e98	2.54080
$106$	6.23210e97	0.369232
$107$	−2.07185e98	−0.778475	−0.389237	−	0.921137i	$-0.627261\pi$
$107$	−2.07185e98	−0.778475	−0.389237	+	0.921137i	$0.627261\pi$
$108$	2.26107e98	0.541080
$109$	3.59315e98	0.549908	0.274954	−	0.961457i	$-0.411337\pi$
$109$	3.59315e98	0.549908	0.274954	+	0.961457i	$0.411337\pi$
$110$	1.98364e99	1.94948
$111$	−4.49834e99	−2.85028
$112$	3.78177e99	1.55103
$113$	1.76628e99	0.470713	0.235356	−	0.971909i	$-0.424374\pi$
$113$	1.76628e99	0.470713	0.235356	+	0.971909i	$0.424374\pi$
$114$	−7.24108e99	−1.25869
$115$	1.17518e99	0.133740
$116$	−8.00426e99	−0.598562
$117$	−1.58518e100	−0.781742
$118$	5.93949e100	1.93853
$119$	−9.28228e100	−2.01199
$120$	−5.66404e100	−0.818155
$121$	4.36809e100	0.421892
$122$	−2.56596e100	−0.166264
$123$	1.74437e101	0.760746
$124$	2.87508e101	0.846639
$125$	2.60494e101	0.519591
$126$	1.83197e102	2.48283
$127$	−8.85885e101	−0.818270	−0.409135	−	0.912474i	$-0.634170\pi$
$127$	−8.85885e101	−0.818270	−0.409135	+	0.912474i	$0.634170\pi$
$128$	−1.23550e102	−0.780116
$129$	−3.10236e102	−1.34305
$130$	−2.86114e102	−0.851701
$131$	−2.10198e102	−0.431491	−0.215745	−	0.976450i	$-0.569218\pi$
$131$	−2.10198e102	−0.431491	−0.215745	+	0.976450i	$0.569218\pi$
$132$	9.07923e102	1.28888
$133$	−7.94630e102	−0.782277
$134$	1.26780e103	0.867898
$135$	−2.08961e103	−0.997417
$136$	1.94147e103	0.647877
$137$	−4.09913e103	−0.958835	−0.479417	−	0.877587i	$-0.659152\pi$
$137$	−4.09913e103	−0.958835	−0.479417	+	0.877587i	$0.659152\pi$
$138$	1.32481e103	0.217780
$139$	−4.92966e103	−0.570951	−0.285476	−	0.958386i	$-0.592152\pi$
$139$	−4.92966e103	−0.570951	−0.285476	+	0.958386i	$0.592152\pi$
$140$	1.34251e104	1.09827
$141$	2.98522e104	1.72922
$142$	2.50124e104	1.02842
$143$	−2.12341e104	−0.621205
$144$	−8.74760e104	−1.82519
$145$	7.39729e104	1.10338
$146$	−9.49437e104	−1.01473
$147$	1.28991e105	0.990074
$148$	−2.23007e105	−1.23204
$149$	−1.28073e105	−0.510415	−0.255208	−	0.966886i	$-0.582144\pi$
$149$	−1.28073e105	−0.510415	−0.255208	+	0.966886i	$0.582144\pi$
$150$	−4.18468e105	−1.20569
$151$	−2.75004e105	−0.574059	−0.287030	−	0.957922i	$-0.592668\pi$
$151$	−2.75004e105	−0.574059	−0.287030	+	0.957922i	$0.592668\pi$
$152$	1.66204e105	0.251899
$153$	2.14708e106	2.36763
$154$	2.45399e106	1.97296
$155$	−2.65706e106	−1.56068
$156$	−1.30956e106	−0.563095
$157$	3.04438e106	0.960210	0.480105	−	0.877211i	$-0.340599\pi$
$157$	3.04438e106	0.960210	0.480105	+	0.877211i	$0.340599\pi$
$158$	1.85863e106	0.430848
$159$	−2.63615e106	−0.449997
$160$	−1.16808e107	−1.47114
$161$	1.45384e106	0.135351
$162$	4.68250e106	0.322849
$163$	2.97345e107	1.52112	0.760558	−	0.649270i	$-0.224925\pi$
$163$	2.97345e107	1.52112	0.760558	+	0.649270i	$0.224925\pi$
$164$	8.64777e106	0.328835
$165$	−8.39074e107	−2.37590
$166$	−3.27983e107	−0.692801
$167$	1.14359e107	0.180518	0.0902589	−	0.995918i	$-0.471231\pi$
$167$	1.14359e107	0.180518	0.0902589	+	0.995918i	$0.471231\pi$
$168$	−7.00705e107	−0.828010
$169$	−8.22236e107	−0.728604
$170$	3.87535e108	2.57952
$171$	1.83806e108	0.920551
$172$	−1.53801e108	−0.580536
$173$	3.02221e108	0.861170	0.430585	−	0.902550i	$-0.358307\pi$
$173$	3.02221e108	0.861170	0.430585	+	0.902550i	$0.358307\pi$
$174$	8.33912e108	1.79673
$175$	−4.59223e108	−0.749338
$176$	−1.17177e109	−1.45037
$177$	−2.51238e109	−2.36256
$178$	3.25313e109	2.32772
$179$	−2.40570e108	−0.131181	−0.0655904	−	0.997847i	$-0.520893\pi$
$179$	−2.40570e108	−0.131181	−0.0655904	+	0.997847i	$0.520893\pi$
$180$	−3.10536e109	−1.29240
$181$	7.40763e108	0.235651	0.117825	−	0.993034i	$-0.462408\pi$
$181$	7.40763e108	0.235651	0.117825	+	0.993034i	$0.462408\pi$
$182$	−3.53956e109	−0.861959
$183$	1.08539e109	0.202632
$184$	−3.04082e108	−0.0435839
$185$	2.06096e110	2.27113
$186$	−2.99536e110	−2.54139
$187$	2.87610e110	1.88142
$188$	1.47994e110	0.747459
$189$	−2.58508e110	−1.00943
$190$	3.31758e110	1.00293
$191$	−1.84712e110	−0.432890	−0.216445	−	0.976295i	$-0.569446\pi$
$191$	−1.84712e110	−0.432890	−0.216445	+	0.976295i	$0.569446\pi$
$192$	−2.59556e110	−0.472196
$193$	−4.55164e110	−0.643633	−0.321817	−	0.946802i	$-0.604293\pi$
$193$	−4.55164e110	−0.643633	−0.321817	+	0.946802i	$0.604293\pi$
$194$	7.40617e110	0.815098
$195$	1.21025e111	1.03800
$196$	6.39477e110	0.427962
$197$	−1.09160e111	−0.570760	−0.285380	−	0.958414i	$-0.592120\pi$
$197$	−1.09160e111	−0.570760	−0.285380	+	0.958414i	$0.592120\pi$
$198$	−5.67633e111	−2.32170
$199$	−4.02709e111	−1.29008	−0.645041	−	0.764148i	$-0.723160\pi$
$199$	−4.02709e111	−1.29008	−0.645041	+	0.764148i	$0.723160\pi$
$200$	9.60503e110	0.241293
$201$	−5.36275e111	−1.05774
$202$	1.29936e112	2.01460
$203$	9.15128e111	1.11667
$204$	1.77376e112	1.70543
$205$	−7.99200e111	−0.606168
$206$	9.90818e110	0.0593517
$207$	−3.36287e111	−0.159275
$208$	1.69013e112	0.633648
$209$	2.46215e112	0.731509
$210$	−1.39867e113	−3.29671
$211$	4.37570e112	0.819121	0.409561	−	0.912283i	$-0.365682\pi$
$211$	4.37570e112	0.819121	0.409561	+	0.912283i	$0.365682\pi$
$212$	−1.30688e112	−0.194513
$213$	−1.05802e113	−1.25338
$214$	1.07010e113	1.01008
$215$	1.42138e113	1.07015
$216$	5.40691e112	0.325044
$217$	−3.28708e113	−1.57948
$218$	−1.85584e113	−0.713512
$219$	4.01608e113	1.23670
$220$	−4.15975e113	−1.02699
$221$	−4.14839e113	−0.821967
$222$	2.32337e114	3.69827
$223$	2.26359e112	0.0289742	0.0144871	−	0.999895i	$-0.495388\pi$
$223$	2.26359e112	0.0289742	0.0144871	+	0.999895i	$0.495388\pi$
$224$	−1.44505e114	−1.48886
$225$	1.06223e114	0.881791
$226$	−9.12275e113	−0.610754
$227$	1.42488e113	0.0770059	0.0385030	−	0.999258i	$-0.487741\pi$
$227$	1.42488e113	0.0770059	0.0385030	+	0.999258i	$0.487741\pi$
$228$	1.51847e114	0.663081
$229$	8.94534e113	0.315919	0.157960	−	0.987446i	$-0.449508\pi$
$229$	8.94534e113	0.315919	0.157960	+	0.987446i	$0.449508\pi$
$230$	−6.06976e113	−0.173529
$231$	−1.03803e115	−2.40452
$232$	−1.91407e114	−0.359575
$233$	3.54332e114	0.540317	0.270158	−	0.962816i	$-0.412924\pi$
$233$	3.54332e114	0.540317	0.270158	+	0.962816i	$0.412924\pi$
$234$	8.18735e114	1.01432
$235$	−1.36771e115	−1.37785
$236$	−1.24553e115	−1.02122
$237$	−7.86193e114	−0.525090
$238$	4.79424e115	2.61058
$239$	8.03323e114	0.356937	0.178469	−	0.983946i	$-0.442886\pi$
$239$	8.03323e114	0.356937	0.178469	+	0.983946i	$0.442886\pi$
$240$	6.67863e115	2.42350
$241$	−1.15771e114	−0.0343378	−0.0171689	−	0.999853i	$-0.505465\pi$
$241$	−1.15771e114	−0.0343378	−0.0171689	+	0.999853i	$0.505465\pi$
$242$	−2.25609e115	−0.547409
$243$	−5.96548e115	−1.18506
$244$	5.38088e114	0.0875884
$245$	−5.90984e115	−0.788898
$246$	−9.00955e115	−0.987076
$247$	−3.55132e115	−0.319586
$248$	6.87521e115	0.508604
$249$	1.38735e116	0.844343
$250$	−1.34544e116	−0.674175
$251$	3.84951e116	1.58939	0.794694	−	0.607011i	$-0.207632\pi$
$251$	3.84951e116	1.58939	0.794694	+	0.607011i	$0.207632\pi$
$252$	−3.84168e116	−1.30796
$253$	−4.50469e115	−0.126567
$254$	4.57555e116	1.06171
$255$	−1.63926e117	−3.14375
$256$	8.26380e116	1.31082
$257$	−7.78691e116	−1.02237	−0.511186	−	0.859470i	$-0.670794\pi$
$257$	−7.78691e116	−1.02237	−0.511186	+	0.859470i	$0.670794\pi$
$258$	1.60235e117	1.74262
$259$	2.54964e117	2.29848
$260$	5.99988e116	0.448679
$261$	−2.11678e117	−1.31405
$262$	1.08566e117	0.559864
$263$	−3.73073e117	−1.59934	−0.799668	−	0.600443i	$-0.794991\pi$
$263$	−3.73073e117	−1.59934	−0.799668	+	0.600443i	$0.794991\pi$
$264$	2.17113e117	0.774274
$265$	1.20778e117	0.358561
$266$	4.10422e117	1.01501
$267$	−1.37606e118	−2.83688
$268$	−2.65861e117	−0.457211
$269$	−1.09435e118	−1.57098	−0.785491	−	0.618874i	$-0.787589\pi$
$269$	−1.09435e118	−1.57098	−0.785491	+	0.618874i	$0.787589\pi$
$270$	1.07927e118	1.29416
$271$	1.33152e118	1.33455	0.667276	−	0.744810i	$-0.267460\pi$
$271$	1.33152e118	1.33455	0.667276	+	0.744810i	$0.267460\pi$
$272$	−2.28924e118	−1.91911
$273$	1.49722e118	1.05050
$274$	2.11717e118	1.24410
$275$	1.42289e118	0.700708
$276$	−2.77816e117	−0.114727
$277$	−4.44016e118	−1.53861	−0.769307	−	0.638880i	$-0.779398\pi$
$277$	−4.44016e118	−1.53861	−0.769307	+	0.638880i	$0.779398\pi$
$278$	2.54614e118	0.740815
$279$	7.60335e118	1.85866
$280$	3.21036e118	0.659764
$281$	−1.71860e118	−0.297111	−0.148556	−	0.988904i	$-0.547462\pi$
$281$	−1.71860e118	−0.297111	−0.148556	+	0.988904i	$0.547462\pi$
$282$	−1.54185e119	−2.24368
$283$	−3.47199e117	−0.0425536	−0.0212768	−	0.999774i	$-0.506773\pi$
$283$	−3.47199e117	−0.0425536	−0.0212768	+	0.999774i	$0.506773\pi$
$284$	−5.24516e118	−0.541776
$285$	−1.40332e119	−1.22231
$286$	1.09673e119	0.806020
$287$	−9.88700e118	−0.613469
$288$	3.34255e119	1.75203
$289$	3.36182e119	1.48946
$290$	−3.82066e119	−1.43164
$291$	−3.13278e119	−0.993390
$292$	1.99099e119	0.534565
$293$	−1.90340e119	−0.432963	−0.216481	−	0.976287i	$-0.569458\pi$
$293$	−1.90340e119	−0.432963	−0.216481	+	0.976287i	$0.569458\pi$
$294$	−6.66229e119	−1.28463
$295$	1.15108e120	1.88250
$296$	−5.33279e119	−0.740128
$297$	8.00983e119	0.943921
$298$	6.61490e119	0.662269
$299$	6.49741e118	0.0552953
$300$	8.77536e119	0.635161
$301$	1.75841e120	1.08304
$302$	1.42038e120	0.744848
$303$	−5.49626e120	−2.45527
$304$	−1.95975e120	−0.746161
$305$	−4.97284e119	−0.161459
$306$	−1.10896e121	−3.07203
$307$	6.97023e120	1.64830	0.824149	−	0.566373i	$-0.191654\pi$
$307$	6.97023e120	1.64830	0.824149	+	0.566373i	$0.191654\pi$
$308$	−5.14608e120	−1.03936
$309$	−4.19112e119	−0.0723342
$310$	1.37236e121	2.02500
$311$	1.43423e121	1.81026	0.905129	−	0.425136i	$-0.139774\pi$
$311$	1.43423e121	1.81026	0.905129	+	0.425136i	$0.139774\pi$
$312$	−3.13156e120	−0.338270
$313$	−1.08169e121	−1.00046	−0.500231	−	0.865892i	$-0.666752\pi$
$313$	−1.08169e121	−1.00046	−0.500231	+	0.865892i	$0.666752\pi$
$314$	−1.57241e121	−1.24588
$315$	3.55036e121	2.41107
$316$	−3.89759e120	−0.226972
$317$	5.99675e120	0.299600	0.149800	−	0.988716i	$-0.452137\pi$
$317$	5.99675e120	0.299600	0.149800	+	0.988716i	$0.452137\pi$
$318$	1.36156e121	0.583876
$319$	−2.83551e121	−1.04420
$320$	1.18919e121	0.376249
$321$	−4.52647e121	−1.23102
$322$	−7.50898e120	−0.175619
$323$	4.81018e121	0.967919
$324$	−9.81932e120	−0.170078
$325$	−2.05234e121	−0.306130
$326$	−1.53577e122	−1.97366
$327$	7.85014e121	0.869584
$328$	2.06795e121	0.197542
$329$	−1.69201e122	−1.39445
$330$	4.33377e122	3.08276
$331$	−2.80948e121	−0.172571	−0.0862855	−	0.996270i	$-0.527500\pi$
$331$	−2.80948e121	−0.172571	−0.0862855	+	0.996270i	$0.527500\pi$
$332$	6.87787e121	0.364970
$333$	−5.89758e122	−2.70476
$334$	−5.90656e121	−0.234224
$335$	2.45700e122	0.842816
$336$	8.26222e122	2.45268
$337$	−5.61941e122	−1.44424	−0.722122	−	0.691766i	$-0.756833\pi$
$337$	−5.61941e122	−1.44424	−0.722122	+	0.691766i	$0.756833\pi$
$338$	4.24680e122	0.945371
$339$	3.85889e122	0.744350
$340$	−8.12669e122	−1.35890
$341$	1.01850e123	1.47697
$342$	−9.49347e122	−1.19442
$343$	4.36606e122	0.476788
$344$	−3.67785e122	−0.348747
$345$	2.56749e122	0.211486
$346$	−1.56096e123	−1.11738
$347$	−1.02002e123	−0.634791	−0.317395	−	0.948293i	$-0.602808\pi$
$347$	−1.02002e123	−0.634791	−0.317395	+	0.948293i	$0.602808\pi$
$348$	−1.74873e123	−0.946521
$349$	−3.83548e123	−1.80628	−0.903142	−	0.429341i	$-0.858746\pi$
$349$	−3.83548e123	−1.80628	−0.903142	+	0.429341i	$0.858746\pi$
$350$	2.37186e123	0.972274
$351$	−1.15531e123	−0.412386
$352$	4.47747e123	1.39224
$353$	5.37154e123	1.45555	0.727773	−	0.685819i	$-0.240556\pi$
$353$	5.37154e123	1.45555	0.727773	+	0.685819i	$0.240556\pi$
$354$	1.29763e124	3.06544
$355$	4.84742e123	0.998700
$356$	−6.82188e123	−1.22625
$357$	−2.02795e124	−3.18162
$358$	1.24253e123	0.170208
$359$	1.24747e124	1.49262	0.746309	−	0.665600i	$-0.231824\pi$
$359$	1.24747e124	1.49262	0.746309	+	0.665600i	$0.231824\pi$
$360$	−7.42588e123	−0.776384
$361$	−6.82420e123	−0.623667
$362$	−3.82600e123	−0.305759
$363$	9.54319e123	0.667148
$364$	7.42253e123	0.454083
$365$	−1.84001e124	−0.985409
$366$	−5.60599e123	−0.262917
$367$	1.60601e124	0.659849	0.329924	−	0.944007i	$-0.392977\pi$
$367$	1.60601e124	0.659849	0.329924	+	0.944007i	$0.392977\pi$
$368$	3.58552e123	0.129102
$369$	2.28696e124	0.721905
$370$	−1.06448e125	−2.94681
$371$	1.49416e124	0.362880
$372$	6.28134e124	1.33881
$373$	5.57213e124	1.04266	0.521330	−	0.853355i	$-0.325436\pi$
$373$	5.57213e124	1.04266	0.521330	+	0.853355i	$0.325436\pi$
$374$	−1.48549e125	−2.44116
$375$	5.69114e124	0.821643
$376$	3.53899e124	0.449023
$377$	4.08985e124	0.456196
$378$	1.33518e125	1.30975
$379$	1.20214e125	1.03742	0.518709	−	0.854951i	$-0.326413\pi$
$379$	1.20214e125	1.03742	0.518709	+	0.854951i	$0.326413\pi$
$380$	−6.95704e124	−0.528348
$381$	−1.93544e125	−1.29395
$382$	9.54029e124	0.561679
$383$	−1.54735e125	−0.802506	−0.401253	−	0.915967i	$-0.631425\pi$
$383$	−1.54735e125	−0.802506	−0.401253	+	0.915967i	$0.631425\pi$
$384$	−2.69926e125	−1.23362
$385$	4.75584e125	1.91594
$386$	2.35090e125	0.835121
$387$	−4.06737e125	−1.27448
$388$	−1.55309e125	−0.429396
$389$	−2.24446e125	−0.547718	−0.273859	−	0.961770i	$-0.588300\pi$
$389$	−2.24446e125	−0.547718	−0.273859	+	0.961770i	$0.588300\pi$
$390$	−6.25089e125	−1.34682
$391$	−8.80058e124	−0.167471
$392$	1.52919e125	0.257091
$393$	−4.59231e125	−0.682327
$394$	5.63807e125	0.740566
$395$	3.60203e125	0.418396
$396$	1.19034e126	1.22308
$397$	1.40872e126	1.28081	0.640405	−	0.768037i	$-0.278766\pi$
$397$	1.40872e126	1.28081	0.640405	+	0.768037i	$0.278766\pi$
$398$	2.07997e126	1.67389
$399$	−1.73607e126	−1.23703
$400$	−1.13256e126	−0.714744
$401$	−2.60572e125	−0.145689	−0.0728444	−	0.997343i	$-0.523208\pi$
$401$	−2.60572e125	−0.145689	−0.0728444	+	0.997343i	$0.523208\pi$
$402$	2.76983e126	1.37243
$403$	−1.46905e126	−0.645269
$404$	−2.72479e126	−1.06130
$405$	9.07471e125	0.313519
$406$	−4.72658e126	−1.44889
$407$	−7.90003e126	−2.14931
$408$	4.24162e126	1.02450
$409$	6.85578e126	1.47054	0.735270	−	0.677775i	$-0.237056\pi$
$409$	6.85578e126	1.47054	0.735270	+	0.677775i	$0.237056\pi$
$410$	4.12782e126	0.786509
$411$	−8.95557e126	−1.51623
$412$	−2.07777e125	−0.0312667
$413$	1.42401e127	1.90518
$414$	1.73690e126	0.206661
$415$	−6.35631e126	−0.672779
$416$	−6.45815e126	−0.608250
$417$	−1.07701e127	−0.902859
$418$	−1.27169e127	−0.949140
$419$	2.19328e127	1.45786	0.728928	−	0.684590i	$-0.240019\pi$
$419$	2.19328e127	1.45786	0.728928	+	0.684590i	$0.240019\pi$
$420$	2.93305e127	1.73672
$421$	−2.12623e127	−1.12184	−0.560918	−	0.827872i	$-0.689552\pi$
$421$	−2.12623e127	−1.12184	−0.560918	+	0.827872i	$0.689552\pi$
$422$	−2.26002e127	−1.06282
$423$	3.91379e127	1.64093
$424$	−3.12517e126	−0.116850
$425$	2.77984e127	0.927164
$426$	5.46459e127	1.62627
$427$	−6.15196e126	−0.163404
$428$	−2.24402e127	−0.532113
$429$	−4.63911e127	−0.982327
$430$	−7.34134e127	−1.38853
$431$	−1.07481e128	−1.81628	−0.908141	−	0.418664i	$-0.862499\pi$
$431$	−1.07481e128	−1.81628	−0.908141	+	0.418664i	$0.862499\pi$
$432$	−6.37544e127	−0.962828
$433$	−6.11991e127	−0.826195	−0.413097	−	0.910687i	$-0.635553\pi$
$433$	−6.11991e127	−0.826195	−0.413097	+	0.910687i	$0.635553\pi$
$434$	1.69776e128	2.04939
$435$	1.61612e128	1.74480
$436$	3.89174e127	0.375880
$437$	−7.53394e126	−0.0651137
$438$	−2.07428e128	−1.60463
$439$	3.29266e127	0.228044	0.114022	−	0.993478i	$-0.463627\pi$
$439$	3.29266e127	0.228044	0.114022	+	0.993478i	$0.463627\pi$
$440$	−9.94724e127	−0.616947
$441$	1.69114e128	0.939524
$442$	2.14262e128	1.06651
$443$	3.64232e128	1.62479	0.812395	−	0.583108i	$-0.198164\pi$
$443$	3.64232e128	1.62479	0.812395	+	0.583108i	$0.198164\pi$
$444$	−4.87215e128	−1.94826
$445$	6.30457e128	2.26045
$446$	−1.16913e127	−0.0375943
$447$	−2.79808e128	−0.807132
$448$	1.47116e128	0.380781
$449$	−6.75122e128	−1.56832	−0.784160	−	0.620559i	$-0.786906\pi$
$449$	−6.75122e128	−1.56832	−0.784160	+	0.620559i	$0.786906\pi$
$450$	−5.48635e128	−1.14413
$451$	3.06347e128	0.573656
$452$	1.91306e128	0.321747
$453$	−6.00815e128	−0.907774
$454$	−7.35942e127	−0.0999160
$455$	−6.85967e128	−0.837048
$456$	3.63114e128	0.398334
$457$	3.89533e128	0.384245	0.192123	−	0.981371i	$-0.438463\pi$
$457$	3.89533e128	0.384245	0.192123	+	0.981371i	$0.438463\pi$
$458$	−4.62022e128	−0.409908
$459$	1.56484e129	1.24898
$460$	1.27284e128	0.0914155
$461$	−1.95514e129	−1.26381	−0.631906	−	0.775045i	$-0.717727\pi$
$461$	−1.95514e129	−1.26381	−0.631906	+	0.775045i	$0.717727\pi$
$462$	5.36136e129	3.11989
$463$	−1.09032e129	−0.571317	−0.285658	−	0.958332i	$-0.592212\pi$
$463$	−1.09032e129	−0.571317	−0.285658	+	0.958332i	$0.592212\pi$
$464$	2.25693e129	1.06511
$465$	−5.80501e129	−2.46794
$466$	−1.83011e129	−0.701066
$467$	−8.34652e128	−0.288162	−0.144081	−	0.989566i	$-0.546023\pi$
$467$	−8.34652e128	−0.288162	−0.144081	+	0.989566i	$0.546023\pi$
$468$	−1.71691e129	−0.534346
$469$	3.03959e129	0.852967
$470$	7.06415e129	1.78778
$471$	6.65122e129	1.51840
$472$	−2.97844e129	−0.613481
$473$	−5.44839e129	−1.01275
$474$	4.06064e129	0.681310
$475$	2.37974e129	0.360488
$476$	−1.00536e130	−1.37526
$477$	−3.45615e129	−0.427022
$478$	−4.14911e129	−0.463130
$479$	−3.51237e129	−0.354265	−0.177132	−	0.984187i	$-0.556682\pi$
$479$	−3.51237e129	−0.354265	−0.177132	+	0.984187i	$0.556682\pi$
$480$	−2.55197e130	−2.32635
$481$	1.13947e130	0.939006
$482$	5.97949e128	0.0445536
$483$	3.17627e129	0.214033
$484$	4.73108e129	0.288377
$485$	1.43532e130	0.791541
$486$	3.08114e130	1.53763
$487$	−3.28077e130	−1.48191	−0.740954	−	0.671555i	$-0.765626\pi$
$487$	−3.28077e130	−1.48191	−0.740954	+	0.671555i	$0.765626\pi$
$488$	1.28673e129	0.0526172
$489$	6.49626e130	2.40538
$490$	3.05240e130	1.02360
$491$	−9.86884e129	−0.299788	−0.149894	−	0.988702i	$-0.547893\pi$
$491$	−9.86884e129	−0.299788	−0.149894	+	0.988702i	$0.547893\pi$
$492$	1.88932e130	0.519995
$493$	−5.53960e130	−1.38166
$494$	1.83424e130	0.414666
$495$	−1.10007e131	−2.25460
$496$	−8.10675e130	−1.50656
$497$	5.99680e130	1.01073
$498$	−7.16560e130	−1.09554
$499$	1.35584e131	1.88075	0.940375	−	0.340138i	$-0.110474\pi$
$499$	1.35584e131	1.88075	0.940375	+	0.340138i	$0.110474\pi$
$500$	2.82141e130	0.355157
$501$	2.49845e130	0.285457
$502$	−1.98825e131	−2.06225
$503$	3.64191e130	0.342990	0.171495	−	0.985185i	$-0.445140\pi$
$503$	3.64191e130	0.342990	0.171495	+	0.985185i	$0.445140\pi$
$504$	−9.18664e130	−0.785735
$505$	2.51817e131	1.95638
$506$	2.32665e130	0.164222
$507$	−1.79638e131	−1.15216
$508$	−9.59502e130	−0.559314
$509$	−1.84079e131	−0.975420	−0.487710	−	0.873006i	$-0.662168\pi$
$509$	−1.84079e131	−0.975420	−0.487710	+	0.873006i	$0.662168\pi$
$510$	8.46667e131	4.07905
$511$	−2.27630e131	−0.997277
$512$	−2.31048e131	−0.920681
$513$	1.33962e131	0.485611
$514$	4.02190e131	1.32654
$515$	1.92021e130	0.0576365
$516$	−3.36016e131	−0.918015
$517$	5.24268e131	1.30395
$518$	−1.31688e132	−2.98230
$519$	6.60278e131	1.36179
$520$	1.43476e131	0.269536
$521$	−1.06221e132	−1.81794	−0.908972	−	0.416857i	$-0.863131\pi$
$521$	−1.06221e132	−1.81794	−0.908972	+	0.416857i	$0.863131\pi$
$522$	1.09331e132	1.70499
$523$	−2.78275e131	−0.395496	−0.197748	−	0.980253i	$-0.563363\pi$
$523$	−2.78275e131	−0.395496	−0.197748	+	0.980253i	$0.563363\pi$
$524$	−2.27666e131	−0.294938
$525$	−1.00329e132	−1.18495
$526$	1.92690e132	2.07515
$527$	1.98979e132	1.95430
$528$	−2.56004e132	−2.29351
$529$	−1.20971e132	−0.988734
$530$	−6.23812e131	−0.465237
$531$	−3.29388e132	−2.24194
$532$	−8.60664e131	−0.534712
$533$	−4.41865e131	−0.250623
$534$	7.10727e132	3.68088
$535$	2.07385e132	0.980888
$536$	−6.35756e131	−0.274662
$537$	−5.25586e131	−0.207439
$538$	5.65226e132	2.03836
$539$	2.26535e132	0.746586
$540$	−2.26325e132	−0.681767
$541$	−2.93580e131	−0.0808460	−0.0404230	−	0.999183i	$-0.512871\pi$
$541$	−2.93580e131	−0.0808460	−0.0404230	+	0.999183i	$0.512871\pi$
$542$	−6.87720e132	−1.73159
$543$	1.61838e132	0.372640
$544$	8.74741e132	1.84218
$545$	−3.59663e132	−0.692891
$546$	−7.73305e132	−1.36304
$547$	−9.79105e132	−1.57922	−0.789612	−	0.613606i	$-0.789718\pi$
$547$	−9.79105e132	−1.57922	−0.789612	+	0.613606i	$0.789718\pi$
$548$	−4.43976e132	−0.655394
$549$	1.42301e132	0.192287
$550$	−7.34917e132	−0.909176
$551$	−4.74230e132	−0.537200
$552$	−6.64343e131	−0.0689203
$553$	4.45611e132	0.423435
$554$	2.29332e133	1.99637
$555$	4.50269e133	3.59139
$556$	−5.33931e132	−0.390264
$557$	−1.67075e133	−1.11927	−0.559635	−	0.828739i	$-0.689059\pi$
$557$	−1.67075e133	−1.11927	−0.559635	+	0.828739i	$0.689059\pi$
$558$	−3.92709e133	−2.41164
$559$	7.85858e132	0.442458
$560$	−3.78542e133	−1.95432
$561$	6.28356e133	2.97514
$562$	8.87649e132	0.385505
$563$	−2.65814e133	−1.05906	−0.529530	−	0.848291i	$-0.677632\pi$
$563$	−2.65814e133	−1.05906	−0.529530	+	0.848291i	$0.677632\pi$
$564$	3.23329e133	1.18198
$565$	−1.76799e133	−0.593104
$566$	1.79326e132	0.0552137
$567$	1.12264e133	0.317295
$568$	−1.25428e133	−0.325462
$569$	−7.63253e132	−0.181854	−0.0909272	−	0.995858i	$-0.528983\pi$
$569$	−7.63253e132	−0.181854	−0.0909272	+	0.995858i	$0.528983\pi$
$570$	7.24809e133	1.58596
$571$	−7.31612e133	−1.47038	−0.735190	−	0.677861i	$-0.762907\pi$
$571$	−7.31612e133	−1.47038	−0.735190	+	0.677861i	$0.762907\pi$
$572$	−2.29986e133	−0.424614
$573$	−4.03551e133	−0.684540
$574$	5.10658e133	0.795982
$575$	−4.35392e132	−0.0623720
$576$	−3.40293e133	−0.448087
$577$	8.98751e133	1.08796	0.543979	−	0.839099i	$-0.316917\pi$
$577$	8.98751e133	1.08796	0.543979	+	0.839099i	$0.316917\pi$
$578$	−1.73636e134	−1.93259
$579$	−9.94420e133	−1.01779
$580$	8.01201e133	0.754195
$581$	−7.86347e133	−0.680882
$582$	1.61806e134	1.28893
$583$	−4.62964e133	−0.339330
$584$	4.76107e133	0.321131
$585$	1.58671e134	0.985004
$586$	9.83095e133	0.561773
$587$	2.80671e133	0.147655	0.0738277	−	0.997271i	$-0.476479\pi$
$587$	2.80671e133	0.147655	0.0738277	+	0.997271i	$0.476479\pi$
$588$	1.39710e134	0.676747
$589$	1.70340e134	0.759846
$590$	−5.94524e134	−2.44257
$591$	−2.38488e134	−0.902557
$592$	6.28805e134	2.19237
$593$	1.84867e134	0.593889	0.296945	−	0.954895i	$-0.404032\pi$
$593$	1.84867e134	0.593889	0.296945	+	0.954895i	$0.404032\pi$
$594$	−4.13703e134	−1.22475
$595$	9.29125e134	2.53514
$596$	−1.38716e134	−0.348885
$597$	−8.79819e134	−2.04004
$598$	−3.35588e133	−0.0717462
$599$	−6.67716e134	−1.31641	−0.658205	−	0.752839i	$-0.728684\pi$
$599$	−6.67716e134	−1.31641	−0.658205	+	0.752839i	$0.728684\pi$
$600$	2.09846e134	0.381562
$601$	−1.53147e134	−0.256861	−0.128430	−	0.991719i	$-0.540994\pi$
$601$	−1.53147e134	−0.256861	−0.128430	+	0.991719i	$0.540994\pi$
$602$	−9.08206e134	−1.40525
$603$	−7.03087e134	−1.00374
$604$	−2.97857e134	−0.392388
$605$	−4.37232e134	−0.531589
$606$	2.83879e135	3.18574
$607$	−3.01154e134	−0.311988	−0.155994	−	0.987758i	$-0.549858\pi$
$607$	−3.01154e134	−0.311988	−0.155994	+	0.987758i	$0.549858\pi$
$608$	7.48842e134	0.716253
$609$	1.99933e135	1.76581
$610$	2.56844e134	0.209495
$611$	−7.56187e134	−0.569679
$612$	2.32551e135	1.61835
$613$	1.15967e135	0.745591	0.372796	−	0.927913i	$-0.378399\pi$
$613$	1.15967e135	0.745591	0.372796	+	0.927913i	$0.378399\pi$
$614$	−3.60008e135	−2.13868
$615$	−1.74605e135	−0.958549
$616$	−1.23059e135	−0.624378
$617$	−4.61031e134	−0.216222	−0.108111	−	0.994139i	$-0.534480\pi$
$617$	−4.61031e134	−0.216222	−0.108111	+	0.994139i	$0.534480\pi$
$618$	2.16469e134	0.0938544
$619$	3.93349e135	1.57682	0.788409	−	0.615151i	$-0.210905\pi$
$619$	3.93349e135	1.57682	0.788409	+	0.615151i	$0.210905\pi$
$620$	−2.87786e135	−1.06678
$621$	−2.45093e134	−0.0840211
$622$	−7.40773e135	−2.34883
$623$	7.79946e135	2.28768
$624$	3.69251e135	1.00200
$625$	−4.94783e135	−1.24232
$626$	5.58684e135	1.29811
$627$	5.37919e135	1.15675
$628$	3.29737e135	0.656335
$629$	−1.54339e136	−2.84393
$630$	−1.83374e136	−3.12839
$631$	6.69973e135	1.05836	0.529180	−	0.848510i	$-0.322500\pi$
$631$	6.69973e135	1.05836	0.529180	+	0.848510i	$0.322500\pi$
$632$	−9.32033e134	−0.136349
$633$	9.55981e135	1.29530
$634$	−3.09729e135	−0.388734
$635$	8.86742e135	1.03103
$636$	−2.85522e135	−0.307588
$637$	−3.26746e135	−0.326173
$638$	1.46453e136	1.35486
$639$	−1.38712e136	−1.18938
$640$	1.23669e136	0.982955
$641$	2.24168e135	0.165180	0.0825902	−	0.996584i	$-0.473681\pi$
$641$	2.24168e135	0.165180	0.0825902	+	0.996584i	$0.473681\pi$
$642$	2.33790e136	1.59726
$643$	−8.60749e135	−0.545311	−0.272656	−	0.962112i	$-0.587902\pi$
$643$	−8.60749e135	−0.545311	−0.272656	+	0.962112i	$0.587902\pi$
$644$	1.57465e135	0.0925165
$645$	3.10536e136	1.69225
$646$	−2.48443e136	−1.25588
$647$	−1.54235e135	−0.0723312	−0.0361656	−	0.999346i	$-0.511514\pi$
$647$	−1.54235e135	−0.0723312	−0.0361656	+	0.999346i	$0.511514\pi$
$648$	−2.34810e135	−0.102171
$649$	−4.41227e136	−1.78154
$650$	1.06002e136	0.397207
$651$	−7.18146e136	−2.49767
$652$	3.22055e136	1.03973
$653$	7.18764e135	0.215425	0.107713	−	0.994182i	$-0.465647\pi$
$653$	7.18764e135	0.215425	0.107713	+	0.994182i	$0.465647\pi$
$654$	−4.05455e136	−1.12829
$655$	2.10402e136	0.543684
$656$	−2.43838e136	−0.585147
$657$	5.26531e136	1.17355
$658$	8.73915e136	1.80931
$659$	−5.39276e136	−1.03721	−0.518607	−	0.855013i	$-0.673549\pi$
$659$	−5.39276e136	−1.03721	−0.518607	+	0.855013i	$0.673549\pi$
$660$	−9.08801e136	−1.62401
$661$	5.11339e136	0.849059	0.424530	−	0.905414i	$-0.360439\pi$
$661$	5.11339e136	0.849059	0.424530	+	0.905414i	$0.360439\pi$
$662$	1.45108e136	0.223913
$663$	−9.06320e136	−1.29980
$664$	1.64471e136	0.219249
$665$	7.95399e136	0.985678
$666$	3.04607e137	3.50945
$667$	8.67639e135	0.0929471
$668$	1.23862e136	0.123390
$669$	4.94537e135	0.0458176
$670$	−1.26903e137	−1.09356
$671$	1.90618e136	0.152799
$672$	−3.15708e137	−2.35437
$673$	−2.56228e137	−1.77785	−0.888926	−	0.458050i	$-0.848548\pi$
$673$	−2.56228e137	−1.77785	−0.888926	+	0.458050i	$0.848548\pi$
$674$	2.90239e137	1.87392
$675$	7.74175e136	0.465164
$676$	−8.90564e136	−0.498024
$677$	8.42075e136	0.438329	0.219165	−	0.975688i	$-0.429667\pi$
$677$	8.42075e136	0.438329	0.219165	+	0.975688i	$0.429667\pi$
$678$	−1.99309e137	−0.965801
$679$	1.77565e137	0.801075
$680$	−1.94334e137	−0.816333
$681$	3.11301e136	0.121771
$682$	−5.26048e137	−1.91639
$683$	3.01344e137	1.02249	0.511245	−	0.859435i	$-0.329185\pi$
$683$	3.01344e137	1.02249	0.511245	+	0.859435i	$0.329185\pi$
$684$	1.99080e137	0.629227
$685$	4.10309e137	1.20814
$686$	−2.25505e137	−0.618637
$687$	1.95433e137	0.499571
$688$	4.33666e137	1.03304
$689$	6.67764e136	0.148249
$690$	−1.32609e137	−0.274405
$691$	−9.62487e137	−1.85656	−0.928281	−	0.371879i	$-0.878713\pi$
$691$	−9.62487e137	−1.85656	−0.928281	+	0.371879i	$0.878713\pi$
$692$	3.27336e137	0.588638
$693$	−1.36091e138	−2.28176
$694$	5.26836e137	0.823647
$695$	4.93442e137	0.719405
$696$	−4.18176e137	−0.568606
$697$	5.98496e137	0.759052
$698$	1.98100e138	2.34367
$699$	7.74128e137	0.854416
$700$	−4.97384e137	−0.512197
$701$	1.24910e138	1.20025	0.600126	−	0.799906i	$-0.295117\pi$
$701$	1.24910e138	1.20025	0.600126	+	0.799906i	$0.295117\pi$
$702$	5.96712e137	0.535075
$703$	−1.32125e138	−1.10574
$704$	−4.55836e137	−0.356069
$705$	−2.98811e138	−2.17883
$706$	−2.77437e138	−1.88858
$707$	3.11526e138	1.97994
$708$	−2.72116e138	−1.61488
$709$	1.02761e137	0.0569490	0.0284745	−	0.999595i	$-0.490935\pi$
$709$	1.02761e137	0.0569490	0.0284745	+	0.999595i	$0.490935\pi$
$710$	−2.50366e138	−1.29582
$711$	−1.03074e138	−0.498281
$712$	−1.63132e138	−0.736649
$713$	−3.11650e137	−0.131470
$714$	1.04742e139	4.12818
$715$	2.12546e138	0.782726
$716$	−2.60562e137	−0.0896663
$717$	1.75506e138	0.564434
$718$	−6.44310e138	−1.93669
$719$	−2.30460e138	−0.647506	−0.323753	−	0.946142i	$-0.604945\pi$
$719$	−2.30460e138	−0.647506	−0.323753	+	0.946142i	$0.604945\pi$
$720$	8.75606e138	2.29976
$721$	2.37551e137	0.0583307
$722$	3.52466e138	0.809214
$723$	−2.52930e137	−0.0542992
$724$	8.02321e137	0.161075
$725$	−2.74061e138	−0.514581
$726$	−4.92900e138	−0.865631
$727$	8.83184e137	0.145088	0.0725442	−	0.997365i	$-0.476888\pi$
$727$	8.83184e137	0.145088	0.0725442	+	0.997365i	$0.476888\pi$
$728$	1.77496e138	0.272782
$729$	−1.13026e139	−1.62515
$730$	9.50355e138	1.27858
$731$	−1.06443e139	−1.34005
$732$	1.17559e138	0.138506
$733$	1.54431e139	1.70291	0.851457	−	0.524424i	$-0.175719\pi$
$733$	1.54431e139	1.70291	0.851457	+	0.524424i	$0.175719\pi$
$734$	−8.29495e138	−0.856160
$735$	−1.29115e139	−1.24750
$736$	−1.37006e138	−0.123927
$737$	−9.41812e138	−0.797611
$738$	−1.18120e139	−0.936679
$739$	2.23978e139	1.66322	0.831611	−	0.555359i	$-0.187419\pi$
$739$	2.23978e139	1.66322	0.831611	+	0.555359i	$0.187419\pi$
$740$	2.23223e139	1.55239
$741$	−7.75876e138	−0.505370
$742$	−7.71726e138	−0.470840
$743$	−1.14243e139	−0.652938	−0.326469	−	0.945208i	$-0.605859\pi$
$743$	−1.14243e139	−0.652938	−0.326469	+	0.945208i	$0.605859\pi$
$744$	1.50206e139	0.804267
$745$	1.28197e139	0.643129
$746$	−2.87797e139	−1.35286
$747$	1.81890e139	0.801234
$748$	3.11510e139	1.28601
$749$	2.56559e139	0.992702
$750$	−2.93944e139	−1.06609
$751$	−2.75865e139	−0.937906	−0.468953	−	0.883223i	$-0.655369\pi$
$751$	−2.75865e139	−0.937906	−0.468953	+	0.883223i	$0.655369\pi$
$752$	−4.17292e139	−1.33007
$753$	8.41022e139	2.51334
$754$	−2.11238e139	−0.591919
$755$	2.75270e139	0.723322
$756$	−2.79990e139	−0.689978
$757$	3.59418e139	0.830711	0.415355	−	0.909659i	$-0.363657\pi$
$757$	3.59418e139	0.830711	0.415355	+	0.909659i	$0.363657\pi$
$758$	−6.20899e139	−1.34606
$759$	−9.84162e138	−0.200143
$760$	−1.66364e139	−0.317396
$761$	3.64840e139	0.653050	0.326525	−	0.945189i	$-0.394122\pi$
$761$	3.64840e139	0.653050	0.326525	+	0.945189i	$0.394122\pi$
$762$	9.99643e139	1.67892
$763$	−4.44943e139	−0.701236
$764$	−2.00062e139	−0.295894
$765$	−2.14916e140	−2.98325
$766$	7.99198e139	1.04126
$767$	6.36412e139	0.778329
$768$	1.80544e140	2.07283
$769$	−1.07508e140	−1.15881	−0.579405	−	0.815040i	$-0.696715\pi$
$769$	−1.07508e140	−1.15881	−0.579405	+	0.815040i	$0.696715\pi$
$770$	−2.45637e140	−2.48595
$771$	−1.70125e140	−1.61670
$772$	−4.92988e139	−0.439944
$773$	−1.98504e139	−0.166366	−0.0831830	−	0.996534i	$-0.526509\pi$
$773$	−1.98504e139	−0.166366	−0.0831830	+	0.996534i	$0.526509\pi$
$774$	2.10077e140	1.65364
$775$	9.84409e139	0.727852
$776$	−3.71392e139	−0.257952
$777$	5.57034e140	3.63465
$778$	1.15925e140	0.710670
$779$	5.12356e139	0.295124
$780$	1.31083e140	0.709507
$781$	−1.85810e140	−0.945135
$782$	4.54545e139	0.217295
$783$	−1.54276e140	−0.693190
$784$	−1.80311e140	−0.761540
$785$	−3.04733e140	−1.20988
$786$	2.37190e140	0.885327
$787$	3.32369e140	1.16640	0.583198	−	0.812330i	$-0.301801\pi$
$787$	3.32369e140	1.16640	0.583198	+	0.812330i	$0.301801\pi$
$788$	−1.18232e140	−0.390133
$789$	−8.15071e140	−2.52907
$790$	−1.86043e140	−0.542873
$791$	−2.18721e140	−0.600247
$792$	2.84647e140	0.734742
$793$	−2.74941e139	−0.0667559
$794$	−7.27596e140	−1.66187
$795$	2.63870e140	0.567002
$796$	−4.36174e140	−0.881813
$797$	9.63790e140	1.83339	0.916693	−	0.399592i	$-0.130848\pi$
$797$	9.63790e140	1.83339	0.916693	+	0.399592i	$0.130848\pi$
$798$	8.96670e140	1.60506
$799$	1.02424e141	1.72537
$800$	4.32761e140	0.686094
$801$	−1.80409e141	−2.69204
$802$	1.34584e140	0.189033
$803$	7.05308e140	0.932556
$804$	−5.80840e140	−0.723000
$805$	−1.45524e140	−0.170543
$806$	7.58755e140	0.837244
$807$	−2.39088e141	−2.48423
$808$	−6.51583e140	−0.637556
$809$	1.05111e141	0.968602	0.484301	−	0.874902i	$-0.339074\pi$
$809$	1.05111e141	0.968602	0.484301	+	0.874902i	$0.339074\pi$
$810$	−4.68703e140	−0.406794
$811$	1.98797e141	1.62517	0.812584	−	0.582843i	$-0.198060\pi$
$811$	1.98797e141	1.62517	0.812584	+	0.582843i	$0.198060\pi$
$812$	9.91175e140	0.763279
$813$	2.90903e141	2.11036
$814$	4.08032e141	2.78876
$815$	−2.97633e141	−1.91662
$816$	−5.00142e141	−3.03473
$817$	−9.11226e140	−0.521022
$818$	−3.54097e141	−1.90804
$819$	1.96294e141	0.996868
$820$	−8.65614e140	−0.414336
$821$	−1.15829e141	−0.522607	−0.261304	−	0.965257i	$-0.584152\pi$
$821$	−1.15829e141	−0.522607	−0.261304	+	0.965257i	$0.584152\pi$
$822$	4.62550e141	1.96732
$823$	−7.62543e140	−0.305754	−0.152877	−	0.988245i	$-0.548854\pi$
$823$	−7.62543e140	−0.305754	−0.152877	+	0.988245i	$0.548854\pi$
$824$	−4.96858e139	−0.0187829
$825$	3.10867e141	1.10805
$826$	−7.35493e141	−2.47199
$827$	1.58137e141	0.501206	0.250603	−	0.968090i	$-0.419371\pi$
$827$	1.58137e141	0.501206	0.250603	+	0.968090i	$0.419371\pi$
$828$	−3.64232e140	−0.108870
$829$	2.63387e140	0.0742506	0.0371253	−	0.999311i	$-0.488180\pi$
$829$	2.63387e140	0.0742506	0.0371253	+	0.999311i	$0.488180\pi$
$830$	3.28300e141	0.872938
$831$	−9.70064e141	−2.43305
$832$	6.57482e140	0.155562
$833$	4.42570e141	0.987868
$834$	5.56268e141	1.17147
$835$	−1.14469e141	−0.227454
$836$	2.66676e141	0.500010
$837$	5.54148e141	0.980486
$838$	−1.13282e142	−1.89158
$839$	5.43506e141	0.856542	0.428271	−	0.903650i	$-0.359123\pi$
$839$	5.43506e141	0.856542	0.428271	+	0.903650i	$0.359123\pi$
$840$	7.01383e141	1.04330
$841$	−1.66064e141	−0.233169
$842$	1.09819e142	1.45559
$843$	−3.75472e141	−0.469829
$844$	4.73932e141	0.559896
$845$	8.23032e141	0.918050
$846$	−2.02145e142	−2.12912
$847$	−5.40905e141	−0.537991
$848$	3.68497e141	0.346127
$849$	−7.58543e140	−0.0672911
$850$	−1.43577e142	−1.20300
$851$	2.41733e141	0.191317
$852$	−1.14594e142	−0.856724
$853$	−9.20634e141	−0.650218	−0.325109	−	0.945677i	$-0.605401\pi$
$853$	−9.20634e141	−0.650218	−0.325109	+	0.945677i	$0.605401\pi$
$854$	3.17745e141	0.212018
$855$	−1.83984e142	−1.15991
$856$	−5.36614e141	−0.319657
$857$	−1.19178e142	−0.670849	−0.335425	−	0.942067i	$-0.608880\pi$
$857$	−1.19178e142	−0.670849	−0.335425	+	0.942067i	$0.608880\pi$
$858$	2.39608e142	1.27458
$859$	1.50258e142	0.755388	0.377694	−	0.925930i	$-0.376717\pi$
$859$	1.50258e142	0.755388	0.377694	+	0.925930i	$0.376717\pi$
$860$	1.53950e142	0.731482
$861$	−2.16006e142	−0.970094
$862$	5.55132e142	2.35664
$863$	−4.94789e141	−0.198562	−0.0992811	−	0.995059i	$-0.531654\pi$
$863$	−4.94789e141	−0.198562	−0.0992811	+	0.995059i	$0.531654\pi$
$864$	2.43612e142	0.924234
$865$	−3.02514e142	−1.08508
$866$	3.16090e142	1.07200
$867$	7.34474e142	2.35532
$868$	−3.56024e142	−1.07962
$869$	−1.38072e142	−0.395955
$870$	−8.34719e142	−2.26390
$871$	1.35844e142	0.348465
$872$	9.30636e141	0.225803
$873$	−4.10725e142	−0.942672
$874$	3.89124e141	0.0844857
$875$	−3.22572e142	−0.662576
$876$	4.34982e142	0.845322
$877$	−5.28145e141	−0.0971120	−0.0485560	−	0.998820i	$-0.515462\pi$
$877$	−5.28145e141	−0.0971120	−0.0485560	+	0.998820i	$0.515462\pi$
$878$	−1.70064e142	−0.295889
$879$	−4.15845e142	−0.684655
$880$	1.17291e143	1.82749
$881$	2.90515e142	0.428387	0.214194	−	0.976791i	$-0.431288\pi$
$881$	2.90515e142	0.428387	0.214194	+	0.976791i	$0.431288\pi$
$882$	−8.73464e142	−1.21904
$883$	4.64058e142	0.613025	0.306512	−	0.951867i	$-0.400838\pi$
$883$	4.64058e142	0.613025	0.306512	+	0.951867i	$0.400838\pi$
$884$	−4.49312e142	−0.561841
$885$	2.51481e143	2.97685
$886$	−1.88124e143	−2.10818
$887$	−4.71342e142	−0.500081	−0.250041	−	0.968235i	$-0.580444\pi$
$887$	−4.71342e142	−0.500081	−0.250041	+	0.968235i	$0.580444\pi$
$888$	−1.16508e143	−1.17038
$889$	1.09700e143	1.04345
$890$	−3.25627e143	−2.93296
$891$	−3.47849e142	−0.296703
$892$	2.45169e141	0.0198048
$893$	8.76820e142	0.670834
$894$	1.44519e143	1.04726
$895$	2.40803e142	0.165289
$896$	1.52993e143	0.994794
$897$	1.41952e142	0.0874398
$898$	3.48697e143	2.03491
$899$	−1.96171e143	−1.08465
$900$	1.15050e143	0.602732
$901$	−9.04470e142	−0.448995
$902$	−1.58227e143	−0.744325
$903$	3.84168e143	1.71264
$904$	4.57472e142	0.193284
$905$	−7.41479e142	−0.296922
$906$	3.10317e143	1.17785
$907$	−3.97813e143	−1.43128	−0.715641	−	0.698468i	$-0.753865\pi$
$907$	−3.97813e143	−1.43128	−0.715641	+	0.698468i	$0.753865\pi$
$908$	1.54329e142	0.0526361
$909$	−7.20591e143	−2.32992
$910$	3.54298e143	1.08608
$911$	−9.72605e142	−0.282680	−0.141340	−	0.989961i	$-0.545141\pi$
$911$	−9.72605e142	−0.282680	−0.141340	+	0.989961i	$0.545141\pi$
$912$	−4.28157e143	−1.17992
$913$	2.43649e143	0.636694
$914$	−2.01192e143	−0.498562
$915$	−1.08644e143	−0.255319
$916$	9.68870e142	0.215941
$917$	2.60291e143	0.550232
$918$	−8.08231e143	−1.62056
$919$	−6.96931e143	−1.32552	−0.662762	−	0.748830i	$-0.730616\pi$
$919$	−6.96931e143	−1.32552	−0.662762	+	0.748830i	$0.730616\pi$
$920$	3.04376e142	0.0549162
$921$	1.52282e144	2.60650
$922$	1.00982e144	1.63981
$923$	2.68006e143	0.412917
$924$	−1.12429e144	−1.64357
$925$	−7.63563e143	−1.05918
$926$	5.63145e143	0.741289
$927$	−5.49480e142	−0.0686411
$928$	−8.62396e143	−1.02242
$929$	−4.11949e143	−0.463533	−0.231767	−	0.972771i	$-0.574451\pi$
$929$	−4.11949e143	−0.463533	−0.231767	+	0.972771i	$0.574451\pi$
$930$	2.99826e144	3.20218
$931$	3.78872e143	0.384090
$932$	3.83777e143	0.369324
$933$	3.13344e144	2.86261
$934$	4.31093e143	0.373893
$935$	−2.87888e144	−2.37061
$936$	−4.10565e143	−0.320999
$937$	−4.52153e143	−0.335672	−0.167836	−	0.985815i	$-0.553678\pi$
$937$	−4.52153e143	−0.335672	−0.167836	+	0.985815i	$0.553678\pi$
$938$	−1.56993e144	−1.10673
$939$	−2.36321e144	−1.58206
$940$	−1.48137e144	−0.941808
$941$	9.01086e141	0.00544088	0.00272044	−	0.999996i	$-0.499134\pi$
$941$	9.01086e141	0.00544088	0.00272044	+	0.999996i	$0.499134\pi$
$942$	−3.43532e144	−1.97015
$943$	−9.37393e142	−0.0510628
$944$	3.51196e144	1.81722
$945$	2.58758e144	1.27189
$946$	2.81406e144	1.31406
$947$	5.63838e143	0.250138	0.125069	−	0.992148i	$-0.460085\pi$
$947$	5.63838e143	0.250138	0.125069	+	0.992148i	$0.460085\pi$
$948$	−8.51525e143	−0.358916
$949$	−1.01731e144	−0.407421
$950$	−1.22912e144	−0.467736
$951$	1.31014e144	0.473765
$952$	−2.40414e144	−0.826165
$953$	−2.03153e144	−0.663463	−0.331732	−	0.943374i	$-0.607633\pi$
$953$	−2.03153e144	−0.663463	−0.331732	+	0.943374i	$0.607633\pi$
$954$	1.78508e144	0.554066
$955$	1.84891e144	0.545447
$956$	8.70079e143	0.243978
$957$	−6.19489e144	−1.65122
$958$	1.81412e144	0.459662
$959$	5.07598e144	1.22269
$960$	2.59807e144	0.594972
$961$	2.45346e144	0.534188
$962$	−5.88532e144	−1.21837
$963$	−5.93446e144	−1.16817
$964$	−1.25391e143	−0.0234710
$965$	4.55604e144	0.810986
$966$	−1.64052e144	−0.277710
$967$	9.23953e144	1.48753	0.743765	−	0.668441i	$-0.233038\pi$
$967$	9.23953e144	1.48753	0.743765	+	0.668441i	$0.233038\pi$
$968$	1.13135e144	0.173237
$969$	1.05090e145	1.53059
$970$	−7.41333e144	−1.02703
$971$	5.68295e143	0.0748930	0.0374465	−	0.999299i	$-0.488078\pi$
$971$	5.68295e143	0.0748930	0.0374465	+	0.999299i	$0.488078\pi$
$972$	−6.46121e144	−0.810028
$973$	6.10444e144	0.728070
$974$	1.69450e145	1.92279
$975$	−4.48385e144	−0.484091
$976$	−1.51723e144	−0.155860
$977$	−1.35022e145	−1.31983	−0.659917	−	0.751339i	$-0.729408\pi$
$977$	−1.35022e145	−1.31983	−0.659917	+	0.751339i	$0.729408\pi$
$978$	−3.35528e145	−3.12100
$979$	−2.41665e145	−2.13921
$980$	−6.40095e144	−0.539237
$981$	1.02920e145	0.825186
$982$	5.09720e144	0.388978
$983$	9.28883e144	0.674707	0.337354	−	0.941378i	$-0.390468\pi$
$983$	9.28883e144	0.674707	0.337354	+	0.941378i	$0.390468\pi$
$984$	4.51796e144	0.312378
$985$	1.09266e145	0.719164
$986$	2.86117e145	1.79272
$987$	−3.69663e145	−2.20508
$988$	−3.84644e144	−0.218448
$989$	1.66716e144	0.0901480
$990$	5.68182e145	2.92537
$991$	−5.86571e144	−0.287573	−0.143787	−	0.989609i	$-0.545928\pi$
$991$	−5.86571e144	−0.287573	−0.143787	+	0.989609i	$0.545928\pi$
$992$	3.09767e145	1.44617
$993$	−6.13801e144	−0.272891
$994$	−3.09731e145	−1.31143
$995$	4.03099e145	1.62552
$996$	1.50264e145	0.577136
$997$	2.69651e145	0.986476	0.493238	−	0.869894i	$-0.335813\pi$
$997$	2.69651e145	0.986476	0.493238	+	0.869894i	$0.335813\pi$
$998$	−7.00282e145	−2.44029
$999$	−4.29828e145	−1.42682

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.98.a.a.1.2	✓	7
3.2	odd	2		9.98.a.a.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.98.a.a.1.2	✓	7	1.1	even	1	trivial
9.98.a.a.1.6		7	3.2	odd	2

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:	\( k \)	\(=\)	\( 98 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-5.16494e14 q^{2} +2.18475e23 q^{3} +1.08310e29 q^{4} -1.00097e34 q^{5} -1.12841e38 q^{6} -1.23831e41 q^{7} +2.59003e43 q^{8} +2.86433e46 q^{9} +O(q^{10})\)	\(q-5.16494e14 q^{2} +2.18475e23 q^{3} +1.08310e29 q^{4} -1.00097e34 q^{5} -1.12841e38 q^{6} -1.23831e41 q^{7} +2.59003e43 q^{8} +2.86433e46 q^{9} +5.16994e48 q^{10} +3.83688e50 q^{11} +2.36630e52 q^{12} -5.53419e53 q^{13} +6.39580e55 q^{14} -2.18686e57 q^{15} -3.05398e58 q^{16} +7.49593e59 q^{17} -1.47941e61 q^{18} +6.41706e61 q^{19} -1.08415e63 q^{20} -2.70540e64 q^{21} -1.98173e65 q^{22} -1.17405e65 q^{23} +5.65857e66 q^{24} +3.70847e67 q^{25} +2.85838e68 q^{26} +2.08759e69 q^{27} -1.34121e70 q^{28} -7.39014e70 q^{29} +1.12950e72 q^{30} +2.65449e72 q^{31} +1.16695e73 q^{32} +8.38263e73 q^{33} -3.87160e74 q^{34} +1.23951e75 q^{35} +3.10236e75 q^{36} -2.05897e76 q^{37} -3.31437e76 q^{38} -1.20908e77 q^{39} -2.59253e77 q^{40} +7.98428e77 q^{41} +1.39732e79 q^{42} -1.42001e79 q^{43} +4.15573e79 q^{44} -2.86710e80 q^{45} +6.06389e79 q^{46} +1.36639e81 q^{47} -6.67218e81 q^{48} +5.90413e81 q^{49} -1.91540e82 q^{50} +1.63767e83 q^{51} -5.99409e82 q^{52} -1.20661e83 q^{53} -1.07823e84 q^{54} -3.84059e84 q^{55} -3.20726e84 q^{56} +1.40197e85 q^{57} +3.81697e85 q^{58} -1.14996e86 q^{59} -2.36859e86 q^{60} +4.96803e85 q^{61} -1.37103e87 q^{62} -3.54693e87 q^{63} -1.18804e87 q^{64} +5.53955e87 q^{65} -4.32958e88 q^{66} -2.45463e88 q^{67} +8.11884e88 q^{68} -2.56500e88 q^{69} -6.40198e89 q^{70} -4.84273e89 q^{71} +7.41870e89 q^{72} +1.83823e90 q^{73} +1.06345e91 q^{74} +8.10208e90 q^{75} +6.95032e90 q^{76} -4.75125e91 q^{77} +6.24485e91 q^{78} -3.59855e91 q^{79} +3.05693e92 q^{80} -9.06594e91 q^{81} -4.12383e92 q^{82} +6.35017e92 q^{83} -2.93022e93 q^{84} -7.50318e93 q^{85} +7.33425e93 q^{86} -1.61456e94 q^{87} +9.93763e93 q^{88} -6.29848e94 q^{89} +1.48084e95 q^{90} +6.85304e94 q^{91} -1.27161e94 q^{92} +5.79940e95 q^{93} -7.05733e95 q^{94} -6.42327e95 q^{95} +2.54951e96 q^{96} -1.43393e96 q^{97} -3.04945e96 q^{98} +1.09901e97 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots + 34\!\cdots\!51 q^{9}+O(q^{10}) \) 7 * q - 16697241085008 * q^2 + 100515854497394358147996 * q^3 + 163057083940695061811962902784 * q^4 - 3658387999529088680958306590731350 * q^5 - 30592714388364079315260992082788233536 * q^6 - 184642311743115370607493500489904481438408 * q^7 + 36028528195426625427479134330455698506199040 * q^8 + 34775775472129528349857305774273773877811641051 * q^9	\( 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots - 13\!\cdots\!28 q^{99}+O(q^{100}) \) 7 * q - 16697241085008 * q^2 + 100515854497394358147996 * q^3 + 163057083940695061811962902784 * q^4 - 3658387999529088680958306590731350 * q^5 - 30592714388364079315260992082788233536 * q^6 - 184642311743115370607493500489904481438408 * q^7 + 36028528195426625427479134330455698506199040 * q^8 + 34775775472129528349857305774273773877811641051 * q^9 + 2369114123959441270700616822719459966510786272800 * q^10 - 211379321299339211995860033669883746379479318698796 * q^11 + 29500590587146562092031430274877546417191966208812032 * q^12 - 883667637845783834437332163606692334928033653755299614 * q^13 + 24884922778173528138085777326574033504771595080747613568 * q^14 - 1421739776861319561135033238174867421082029896683725376600 * q^15 - 31468671341370205538262999960370611414173356196203424841728 * q^16 + 163250436637003263661570089512096377905088225334685131721342 * q^17 - 7054606772048003028382413409749231596837718873737440667537424 * q^18 + 133084372359310898958448501523235681541051727436663191570359820 * q^19 - 1318696260534044061297364386263469065025874939722479973417331200 * q^20 - 8226961344750528298533572507576209983448935264598913374247505696 * q^21 - 193421584410477868290586506488587370358898549812529751083484246976 * q^22 + 925260914184001305416523826357059292226482310773339215111132964776 * q^23 + 1719359518493251306391725804700467921422689016189510541760687554560 * q^24 - 15111829774373494694703308579556617230149980669179989285410298974375 * q^25 + 252570839996871764139482603418038366978372757286009959646749464447904 * q^26 - 16291464003153760806194022590188439733978909915063668620863256233960 * q^27 + 2270023864280230580582797832096861251181573169347509612847861972977664 * q^28 - 119228645746988213289933973286594685848645193803889692652451844737975470 * q^29 + 350448354156350400480979435069989695492221249186335731168327070817564800 * q^30 + 1783283666881858864849681148885200501497581294973934227348751364131906784 * q^31 - 5665372498136527985720301619489703024215195383428523596691479514791804928 * q^32 + 31524650657546522511070078635079454480923539002999356172307109465073458512 * q^33 - 360491523041063125717708388027762293189396999595568175085448186659598970272 * q^34 + 1278268341035082746531666145800358760269267683649420892787253371588938750800 * q^35 - 216561481226385812264597126278375191173372906326221899147967914271513631488 * q^36 - 4532061622841943284542390241171859851726205146853788500539269747469617514358 * q^37 - 2979582210919721773595405461863152858097797783237497905501709239616681227840 * q^38 + 43268347489134056222423767530379619668087154910038087692852374564634305176712 * q^39 - 252514831298472678734291758335102132215188475493571956673272319739362987008000 * q^40 + 123663386655433999860484853403953500874113711440208020678841289201379470695974 * q^41 + 3296122851141924824443574220618174749418258893075867148421980920155200276985344 * q^42 - 6595249409358954185694714287710218939626711013706300289026511229489118746183244 * q^43 + 31427981619155317050453798326367420934595218826815326227502736274099059309390848 * q^44 - 252057107931731391251960224707597558538839631727412739243273361199825466582835550 * q^45 + 333743461536679365083903174537100831945624746347277312419032904840551699600111744 * q^46 + 1582413179705462665936960636748613012540566075462612818643843634715630112826042192 * q^47 - 5861556434117332280930374286873664455351210291383528056190272983552191849213722624 * q^48 + 4345635008055985505106601346877321132027699788278385269907095782368403364891488399 * q^49 - 26742593205970009143775889336520990050133941492259748319418427757724876722706030000 * q^50 + 7043565089506559965061572069632281800522096763383079376468682406398600422146676984 * q^51 + 45800222007571685487736059984048709986270205428489770979037497696929384027946163712 * q^52 - 653999931744204429821742741003701830521617657540517458768483866216741544701292475654 * q^53 - 1692275654206728716605786947196644220317392594111136065941704729626944069981837438080 * q^54 - 2797264930804680667438884831689324464716285797264284803651188210713133784740241832200 * q^55 - 13571511538900847480549793700693331801076437559096966169392506220987757777557857402880 * q^56 - 32156245276763940566100505959698139630384956043693169857398532690693294678041975751120 * q^57 - 110275012470967940484400158535846043036245771061355495516009955997986614502808104491360 * q^58 - 289716843512018767811919727809674339112407721830489506743846640027004030301179845118940 * q^59 - 910863091257112962110410128770927709732237428874631129572443550789630933691032398899200 * q^60 - 1779644273771380099149369471014727845406783738447834645166296866716596067825339549188046 * q^61 - 4893410323209515393605311670149478112622973098189152140516775294151722525768562137565696 * q^62 - 12773855755538157144284595252262546905649007916763284311597736303148976241726684562602024 * q^63 - 24329532034212074257236420324752039539459926287390018025638252399891746834835822530789376 * q^64 - 40979880706222898178317998710539228015340375450212825952623031288613904725454054500850100 * q^65 - 142841613731497146561089386918878946227924637814625892149907766833242924230825872606056192 * q^66 - 183094181851902905703789039636502649221241410347877100016575616698548103898875205122783908 * q^67 - 250132580738896836682574414547500843555901286243235420681429272583107380144497499057716736 * q^68 - 372244836961332226973480986215431578494847115740354696097669790201492502675456308855459168 * q^69 - 587389541033882485666068522391834191601610745639266949076956170254929472707526921059782400 * q^70 - 36618527208607574135274147674246343687098099724640001025727994874106062220116534447931656 * q^71 + 2495502705800463241319297965149724088435827677064467496346161624547668625438549984339128320 * q^72 + 5937141741627411574629383951784847225959103237898806939243808260531064318159784943464907526 * q^73 + 25603418812897773069861990064614106209712057876935905208225093500026599325689360114519970848 * q^74 + 43416229043729585532262686371625117245611844558141193068941674421259839404159894884059222500 * q^75 + 64491781461168277038374423376126180174707623388661413952117963143585395013082375272839869440 * q^76 + 122801524700573133455664123216977109508839271312008866744292206338517188364407357732160152224 * q^77 + 256518622739178273010532892375526005382856863147760611859324715551823107217212845963281985152 * q^78 + 155279975164311735091235448536513906273532801204307686975280157544842456609207922540776901680 * q^79 + 343037548751841740038666995050634479050946344382038763901789904170114217394648666813900390400 * q^80 - 799336653019442009471583631583081099983526554777301855450568718504605547656753900698628831153 * q^81 - 2054599455199243418451530458808296516745297582440826399667363552358055209069956455679452833056 * q^82 - 2745080838526935126539434486643898932954125805020264508203796620734019354440308801326974021684 * q^83 - 12055830667015300843296227009204563031159870111997209215974794552386444770918151507927520305152 * q^84 - 16156906986132970771716277890961343081101351325821342812927748903601690598916612215092853170700 * q^85 - 16073101085057033129856695763368798351047883803740227513388827997968391823543719379002604387776 * q^86 - 44931373084677669249994770736329381356923858000626008622029156778901658182110994195783000791480 * q^87 - 20900444501134905678673788524771632932447417317035512416151379720801969394444956958395302789120 * q^88 + 8652425236627243255051028260917634407304730072980172181544783646255542601500269383337979350390 * q^89 + 169914380219009102880054256907856294069041898142575788262717672760376053145875718225670932330400 * q^90 + 235279610532724372901602846332263408075886672274330172793822218199845308058643167074949650230544 * q^91 + 622950794384614085632156625042963081233986358617743991991586248417198315809579918444522808891392 * q^92 + 1619655729334717431421579797164299646702152339363664709672746834797775058100318492643375449441152 * q^93 + 1784387548746436753701888750274366538460858609156963702431495773056050960861585984793528939671808 * q^94 + 1109691419127482658877926123378178695834970817464791602098716148821958373905367930889408748989000 * q^95 + 2773817117979873680694700349927475687549477810523157816910439588411515192104026991177258420404224 * q^96 - 462826972284038426621245345324758076530452205891330025493894671876723283114629445572915788984658 * q^97 - 10100804559243313775965110405631054964918520327952856127425837778067309219959758215138751854831056 * q^98 - 13792894935722775136702660269810636953813664741795563019740674282913700184659028566406972539495228 * q^99

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