LMFDB - Embedded newform 1.98.a.a.1.3

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			1.3
Root			$-2.29850e12$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.12713e14 q^{2} -2.23668e23 q^{3} -1.45752e29 q^{4} -2.02292e33 q^{5} +2.52104e37 q^{6} -1.81030e41 q^{7} +3.42884e43 q^{8} +3.09393e46 q^{9} +O(q^{10})$	\(q-1.12713e14 q^{2} -2.23668e23 q^{3} -1.45752e29 q^{4} -2.02292e33 q^{5} +2.52104e37 q^{6} -1.81030e41 q^{7} +3.42884e43 q^{8} +3.09393e46 q^{9} +2.28010e47 q^{10} -4.93878e50 q^{11} +3.26000e52 q^{12} -3.60489e53 q^{13} +2.04045e55 q^{14} +4.52463e56 q^{15} +1.92306e58 q^{16} +4.80220e59 q^{17} -3.48727e60 q^{18} +5.41141e61 q^{19} +2.94845e62 q^{20} +4.04906e64 q^{21} +5.56667e64 q^{22} +1.09041e66 q^{23} -7.66921e66 q^{24} -5.90167e67 q^{25} +4.06320e67 q^{26} -2.65074e69 q^{27} +2.63855e70 q^{28} +6.44541e70 q^{29} -5.09986e70 q^{30} -1.88517e72 q^{31} -7.60075e72 q^{32} +1.10465e74 q^{33} -5.41273e73 q^{34} +3.66210e74 q^{35} -4.50946e75 q^{36} +2.51059e75 q^{37} -6.09938e75 q^{38} +8.06299e76 q^{39} -6.93627e76 q^{40} +1.64714e77 q^{41} -4.56384e78 q^{42} +3.52284e78 q^{43} +7.19838e79 q^{44} -6.25877e79 q^{45} -1.22903e80 q^{46} -9.02851e80 q^{47} -4.30126e81 q^{48} +2.33420e82 q^{49} +6.65197e81 q^{50} -1.07410e83 q^{51} +5.25421e82 q^{52} -1.94973e83 q^{53} +2.98774e83 q^{54} +9.99077e83 q^{55} -6.20723e84 q^{56} -1.21036e85 q^{57} -7.26484e84 q^{58} -6.91580e84 q^{59} -6.59473e85 q^{60} -4.83402e86 q^{61} +2.12484e86 q^{62} -5.60094e87 q^{63} -2.19050e87 q^{64} +7.29242e86 q^{65} -1.24509e88 q^{66} -1.63992e88 q^{67} -6.99931e88 q^{68} -2.43889e89 q^{69} -4.12768e88 q^{70} +6.96780e89 q^{71} +1.06086e90 q^{72} -1.03456e90 q^{73} -2.82977e89 q^{74} +1.32001e91 q^{75} -7.88723e90 q^{76} +8.94069e91 q^{77} -9.08808e90 q^{78} -7.68512e91 q^{79} -3.89019e91 q^{80} +2.31402e90 q^{81} -1.85655e91 q^{82} +1.53118e93 q^{83} -5.90159e93 q^{84} -9.71448e92 q^{85} -3.97072e92 q^{86} -1.44163e94 q^{87} -1.69343e94 q^{88} +6.75125e94 q^{89} +7.05448e93 q^{90} +6.52595e94 q^{91} -1.58929e95 q^{92} +4.21653e95 q^{93} +1.01763e95 q^{94} -1.09468e95 q^{95} +1.70004e96 q^{96} +1.44090e96 q^{97} -2.63096e96 q^{98} -1.52802e97 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.12713e14	−0.283153	−0.141576	−	0.989927i	$-0.545217\pi$
$2$	−1.12713e14	−0.283153	−0.141576	+	0.989927i	$0.545217\pi$
$3$	−2.23668e23	−1.61891	−0.809455	−	0.587182i	$-0.800237\pi$
$3$	−2.23668e23	−1.61891	−0.809455	+	0.587182i	$0.800237\pi$
$4$	−1.45752e29	−0.919824
$5$	−2.02292e33	−0.254644	−0.127322	−	0.991861i	$-0.540638\pi$
$5$	−2.02292e33	−0.254644	−0.127322	+	0.991861i	$0.540638\pi$
$6$	2.52104e37	0.458399
$7$	−1.81030e41	−1.86422	−0.932108	−	0.362181i	$-0.882032\pi$
$7$	−1.81030e41	−1.86422	−0.932108	+	0.362181i	$0.882032\pi$
$8$	3.42884e43	0.543604
$9$	3.09393e46	1.62087
$10$	2.28010e47	0.0721032
$11$	−4.93878e50	−1.53488	−0.767441	−	0.641120i	$-0.778470\pi$
$11$	−4.93878e50	−1.53488	−0.767441	+	0.641120i	$0.778470\pi$
$12$	3.26000e52	1.48911
$13$	−3.60489e53	−0.339344	−0.169672	−	0.985501i	$-0.554271\pi$
$13$	−3.60489e53	−0.339344	−0.169672	+	0.985501i	$0.554271\pi$
$14$	2.04045e55	0.527858
$15$	4.52463e56	0.412246
$16$	1.92306e58	0.765901
$17$	4.80220e59	1.01081	0.505403	−	0.862883i	$-0.331344\pi$
$17$	4.80220e59	1.01081	0.505403	+	0.862883i	$0.331344\pi$
$18$	−3.48727e60	−0.458954
$19$	5.41141e61	0.517321	0.258661	−	0.965968i	$-0.416719\pi$
$19$	5.41141e61	0.517321	0.258661	+	0.965968i	$0.416719\pi$
$20$	2.94845e62	0.234228
$21$	4.04906e64	3.01800
$22$	5.56667e64	0.434606
$23$	1.09041e66	0.985798	0.492899	−	0.870086i	$-0.335937\pi$
$23$	1.09041e66	0.985798	0.492899	+	0.870086i	$0.335937\pi$
$24$	−7.66921e66	−0.880046
$25$	−5.90167e67	−0.935156
$26$	4.06320e67	0.0960862
$27$	−2.65074e69	−1.00513
$28$	2.63855e70	1.71475
$29$	6.44541e70	0.763744	0.381872	−	0.924215i	$-0.375280\pi$
$29$	6.44541e70	0.763744	0.381872	+	0.924215i	$0.375280\pi$
$30$	−5.09986e70	−0.116729
$31$	−1.88517e72	−0.879649	−0.439824	−	0.898084i	$-0.644959\pi$
$31$	−1.88517e72	−0.879649	−0.439824	+	0.898084i	$0.644959\pi$
$32$	−7.60075e72	−0.760471
$33$	1.10465e74	2.48483
$34$	−5.41273e73	−0.286213
$35$	3.66210e74	0.474712
$36$	−4.50946e75	−1.49092
$37$	2.51059e75	0.219782	0.109891	−	0.993944i	$-0.464950\pi$
$37$	2.51059e75	0.219782	0.109891	+	0.993944i	$0.464950\pi$
$38$	−6.09938e75	−0.146481
$39$	8.06299e76	0.549367
$40$	−6.93627e76	−0.138426
$41$	1.64714e77	0.0992460	0.0496230	−	0.998768i	$-0.484198\pi$
$41$	1.64714e77	0.0992460	0.0496230	+	0.998768i	$0.484198\pi$
$42$	−4.56384e78	−0.854555
$43$	3.52284e78	0.210704	0.105352	−	0.994435i	$-0.466403\pi$
$43$	3.52284e78	0.210704	0.105352	+	0.994435i	$0.466403\pi$
$44$	7.19838e79	1.41182
$45$	−6.25877e79	−0.412745
$46$	−1.22903e80	−0.279132
$47$	−9.02851e80	−0.722553	−0.361277	−	0.932459i	$-0.617659\pi$
$47$	−9.02851e80	−0.722553	−0.361277	+	0.932459i	$0.617659\pi$
$48$	−4.30126e81	−1.23993
$49$	2.33420e82	2.47530
$50$	6.65197e81	0.264792
$51$	−1.07410e83	−1.63640
$52$	5.25421e82	0.312137
$53$	−1.94973e83	−0.459828	−0.229914	−	0.973211i	$-0.573845\pi$
$53$	−1.94973e83	−0.459828	−0.229914	+	0.973211i	$0.573845\pi$
$54$	2.98774e83	0.284607
$55$	9.99077e83	0.390849
$56$	−6.20723e84	−1.01339
$57$	−1.21036e85	−0.837497
$58$	−7.26484e84	−0.216256
$59$	−6.91580e84	−0.0898504	−0.0449252	−	0.998990i	$-0.514305\pi$
$59$	−6.91580e84	−0.0898504	−0.0449252	+	0.998990i	$0.514305\pi$
$60$	−6.59473e85	−0.379194
$61$	−4.83402e86	−1.24684	−0.623421	−	0.781886i	$-0.714258\pi$
$61$	−4.83402e86	−1.24684	−0.623421	+	0.781886i	$0.714258\pi$
$62$	2.12484e86	0.249075
$63$	−5.60094e87	−3.02165
$64$	−2.19050e87	−0.550572
$65$	7.29242e86	0.0864120
$66$	−1.24509e88	−0.703588
$67$	−1.63992e88	−0.446884	−0.223442	−	0.974717i	$-0.571729\pi$
$67$	−1.63992e88	−0.446884	−0.223442	+	0.974717i	$0.571729\pi$
$68$	−6.99931e88	−0.929764
$69$	−2.43889e89	−1.59592
$70$	−4.12768e88	−0.134416
$71$	6.96780e89	1.14042	0.570211	−	0.821498i	$-0.306861\pi$
$71$	6.96780e89	1.14042	0.570211	+	0.821498i	$0.306861\pi$
$72$	1.06086e90	0.881111
$73$	−1.03456e90	−0.440145	−0.220072	−	0.975484i	$-0.570629\pi$
$73$	−1.03456e90	−0.440145	−0.220072	+	0.975484i	$0.570629\pi$
$74$	−2.82977e89	−0.0622320
$75$	1.32001e91	1.51393
$76$	−7.88723e90	−0.475845
$77$	8.94069e91	2.86135
$78$	−9.08808e90	−0.155555
$79$	−7.68512e91	−0.709147	−0.354574	−	0.935028i	$-0.615374\pi$
$79$	−7.68512e91	−0.709147	−0.354574	+	0.935028i	$0.615374\pi$
$80$	−3.89019e91	−0.195032
$81$	2.31402e90	0.00635102
$82$	−1.85655e91	−0.0281018
$83$	1.53118e93	1.28748	0.643739	−	0.765246i	$-0.277382\pi$
$83$	1.53118e93	1.28748	0.643739	+	0.765246i	$0.277382\pi$
$84$	−5.90159e93	−2.77603
$85$	−9.71448e92	−0.257396
$86$	−3.97072e92	−0.0596615
$87$	−1.44163e94	−1.23643
$88$	−1.69343e94	−0.834367
$89$	6.75125e94	1.92295	0.961476	−	0.274887i	$-0.0886406\pi$
$89$	6.75125e94	1.92295	0.961476	+	0.274887i	$0.0886406\pi$
$90$	7.05448e93	0.116870
$91$	6.52595e94	0.632610
$92$	−1.58929e95	−0.906761
$93$	4.21653e95	1.42407
$94$	1.01763e95	0.204593
$95$	−1.09468e95	−0.131733
$96$	1.70004e96	1.23113
$97$	1.44090e96	0.631254	0.315627	−	0.948883i	$-0.397785\pi$
$97$	1.44090e96	0.631254	0.315627	+	0.948883i	$0.397785\pi$
$98$	−2.63096e96	−0.700888
$99$	−1.52802e97	−2.48784
$100$	8.60180e96	0.860180
$101$	−8.24946e96	−0.509142	−0.254571	−	0.967054i	$-0.581934\pi$
$101$	−8.24946e96	−0.509142	−0.254571	+	0.967054i	$0.581934\pi$
$102$	1.21065e97	0.463353
$103$	−4.11930e97	−0.982241	−0.491120	−	0.871092i	$-0.663412\pi$
$103$	−4.11930e97	−0.982241	−0.491120	+	0.871092i	$0.663412\pi$
$104$	−1.23606e97	−0.184469
$105$	−8.19094e97	−0.768516
$106$	2.19761e97	0.130202
$107$	2.93147e98	1.10147	0.550734	−	0.834681i	$-0.314348\pi$
$107$	2.93147e98	1.10147	0.550734	+	0.834681i	$0.314348\pi$
$108$	3.86350e98	0.924547
$109$	8.89007e98	1.36057	0.680284	−	0.732949i	$-0.261857\pi$
$109$	8.89007e98	1.36057	0.680284	+	0.732949i	$0.261857\pi$
$110$	−1.12609e98	−0.110670
$111$	−5.61539e98	−0.355808
$112$	−3.48131e99	−1.42781
$113$	4.49778e99	1.19865	0.599326	−	0.800505i	$-0.295435\pi$
$113$	4.49778e99	1.19865	0.599326	+	0.800505i	$0.295435\pi$
$114$	1.36424e99	0.237140
$115$	−2.20580e99	−0.251028
$116$	−9.39431e99	−0.702510
$117$	−1.11533e100	−0.550033
$118$	7.79504e98	0.0254414
$119$	−8.69344e100	−1.88436
$120$	1.55142e100	0.224099
$121$	1.40380e101	1.35586
$122$	5.44859e100	0.353047
$123$	−3.68412e100	−0.160670
$124$	2.74768e101	0.809122
$125$	2.47050e101	0.492776
$126$	6.31302e101	0.855590
$127$	−1.65157e102	−1.52551	−0.762757	−	0.646685i	$-0.776155\pi$
$127$	−1.65157e102	−1.52551	−0.762757	+	0.646685i	$0.776155\pi$
$128$	1.45129e102	0.916367
$129$	−7.87947e101	−0.341111
$130$	−8.21954e100	−0.0244678
$131$	4.11864e102	0.845466	0.422733	−	0.906254i	$-0.361071\pi$
$131$	4.11864e102	0.845466	0.422733	+	0.906254i	$0.361071\pi$
$132$	−1.61005e103	−2.28561
$133$	−9.79628e102	−0.964399
$134$	1.84841e102	0.126536
$135$	5.36223e102	0.255952
$136$	1.64660e103	0.549478
$137$	2.42949e103	0.568288	0.284144	−	0.958782i	$-0.408291\pi$
$137$	2.42949e103	0.568288	0.284144	+	0.958782i	$0.408291\pi$
$138$	2.74895e103	0.451889
$139$	−3.15734e103	−0.365682	−0.182841	−	0.983142i	$-0.558529\pi$
$139$	−3.15734e103	−0.365682	−0.182841	+	0.983142i	$0.558529\pi$
$140$	−5.33758e103	−0.436651
$141$	2.01939e104	1.16975
$142$	−7.85365e103	−0.322914
$143$	1.78038e104	0.520853
$144$	5.94980e104	1.24143
$145$	−1.30386e104	−0.194483
$146$	1.16608e104	0.124628
$147$	−5.22085e105	−4.00729
$148$	−3.65924e104	−0.202161
$149$	4.81442e105	1.91871	0.959357	−	0.282196i	$-0.0910627\pi$
$149$	4.81442e105	1.91871	0.959357	+	0.282196i	$0.0910627\pi$
$150$	−1.48783e105	−0.428675
$151$	−3.18494e105	−0.664843	−0.332422	−	0.943131i	$-0.607866\pi$
$151$	−3.18494e105	−0.664843	−0.332422	+	0.943131i	$0.607866\pi$
$152$	1.85548e105	0.281218
$153$	1.48577e106	1.63839
$154$	−1.00774e106	−0.810199
$155$	3.81356e105	0.223997
$156$	−1.17520e106	−0.505321
$157$	4.16274e106	1.31295	0.656473	−	0.754350i	$-0.272048\pi$
$157$	4.16274e106	1.31295	0.656473	+	0.754350i	$0.272048\pi$
$158$	8.66216e105	0.200797
$159$	4.36093e106	0.744421
$160$	1.53757e106	0.193650
$161$	−1.97396e107	−1.83774
$162$	−2.60821e104	−0.00179831
$163$	−5.63074e106	−0.288049	−0.144025	−	0.989574i	$-0.546004\pi$
$163$	−5.63074e106	−0.288049	−0.144025	+	0.989574i	$0.546004\pi$
$164$	−2.40074e106	−0.0912889
$165$	−2.23461e107	−0.632749
$166$	−1.72585e107	−0.364553
$167$	−1.09978e107	−0.173603	−0.0868013	−	0.996226i	$-0.527665\pi$
$167$	−1.09978e107	−0.173603	−0.0868013	+	0.996226i	$0.527665\pi$
$168$	1.38836e108	1.64060
$169$	−9.98557e107	−0.884846
$170$	1.09495e107	0.0728824
$171$	1.67425e108	0.838511
$172$	−5.13462e107	−0.193811
$173$	1.06059e108	0.302213	0.151107	−	0.988517i	$-0.451716\pi$
$173$	1.06059e108	0.302213	0.151107	+	0.988517i	$0.451716\pi$
$174$	1.62491e108	0.350099
$175$	1.06838e109	1.74333
$176$	−9.49756e108	−1.17557
$177$	1.54684e108	0.145460
$178$	−7.60956e108	−0.544490
$179$	−3.26184e109	−1.77865	−0.889326	−	0.457274i	$-0.848826\pi$
$179$	−3.26184e109	−1.77865	−0.889326	+	0.457274i	$0.848826\pi$
$180$	9.12228e108	0.379653
$181$	−4.33297e109	−1.37840	−0.689199	−	0.724572i	$-0.742037\pi$
$181$	−4.33297e109	−1.37840	−0.689199	+	0.724572i	$0.742037\pi$
$182$	−7.35562e108	−0.179125
$183$	1.08121e110	2.01852
$184$	3.73882e109	0.535884
$185$	−5.07873e108	−0.0559663
$186$	−4.75260e109	−0.403230
$187$	−2.37170e110	−1.55147
$188$	1.31592e110	0.664622
$189$	4.79863e110	1.87379
$190$	1.23386e109	0.0373006
$191$	−4.22760e109	−0.0990776	−0.0495388	−	0.998772i	$-0.515775\pi$
$191$	−4.22760e109	−0.0990776	−0.0495388	+	0.998772i	$0.515775\pi$
$192$	4.89944e110	0.891327
$193$	−3.46389e110	−0.489817	−0.244909	−	0.969546i	$-0.578758\pi$
$193$	−3.46389e110	−0.489817	−0.244909	+	0.969546i	$0.578758\pi$
$194$	−1.62409e110	−0.178741
$195$	−1.63108e110	−0.139893
$196$	−3.40214e111	−2.27684
$197$	−8.47806e110	−0.443286	−0.221643	−	0.975128i	$-0.571142\pi$
$197$	−8.47806e110	−0.443286	−0.221643	+	0.975128i	$0.571142\pi$
$198$	1.72229e111	0.704440
$199$	1.90688e111	0.610871	0.305435	−	0.952213i	$-0.401198\pi$
$199$	1.90688e111	0.610871	0.305435	+	0.952213i	$0.401198\pi$
$200$	−2.02359e111	−0.508355
$201$	3.66797e111	0.723465
$202$	9.29826e110	0.144165
$203$	−1.16681e112	−1.42378
$204$	1.56552e112	1.50521
$205$	−3.33203e110	−0.0252724
$206$	4.64300e111	0.278124
$207$	3.37364e112	1.59785
$208$	−6.93242e111	−0.259904
$209$	−2.67258e112	−0.794027
$210$	9.23229e111	0.217607
$211$	−2.46773e112	−0.461954	−0.230977	−	0.972959i	$-0.574192\pi$
$211$	−2.46773e112	−0.461954	−0.230977	+	0.972959i	$0.574192\pi$
$212$	2.84178e112	0.422961
$213$	−1.55847e113	−1.84624
$214$	−3.30416e112	−0.311884
$215$	−7.12644e111	−0.0536546
$216$	−9.08894e112	−0.546395
$217$	3.41273e113	1.63985
$218$	−1.00203e113	−0.385249
$219$	2.31397e113	0.712555
$220$	−1.45617e113	−0.359512
$221$	−1.73114e113	−0.343011
$222$	6.32930e112	0.100748
$223$	5.71050e113	0.730951	0.365475	−	0.930821i	$-0.380906\pi$
$223$	5.71050e113	0.730951	0.365475	+	0.930821i	$0.380906\pi$
$224$	1.37597e114	1.41768
$225$	−1.82593e114	−1.51577
$226$	−5.06960e113	−0.339402
$227$	2.37441e114	1.28322	0.641612	−	0.767029i	$-0.278266\pi$
$227$	2.37441e114	1.28322	0.641612	+	0.767029i	$0.278266\pi$
$228$	1.76412e114	0.770350
$229$	−1.57063e113	−0.0554694	−0.0277347	−	0.999615i	$-0.508829\pi$
$229$	−1.57063e113	−0.0554694	−0.0277347	+	0.999615i	$0.508829\pi$
$230$	2.48624e113	0.0710792
$231$	−1.99975e115	−4.63227
$232$	2.21003e114	0.415174
$233$	6.20004e114	0.945437	0.472718	−	0.881214i	$-0.343273\pi$
$233$	6.20004e114	0.945437	0.472718	+	0.881214i	$0.343273\pi$
$234$	1.25712e114	0.155743
$235$	1.82640e114	0.183994
$236$	1.00799e114	0.0826466
$237$	1.71891e115	1.14805
$238$	9.79868e114	0.533562
$239$	−1.24517e115	−0.553263	−0.276631	−	0.960976i	$-0.589218\pi$
$239$	−1.24517e115	−0.553263	−0.276631	+	0.960976i	$0.589218\pi$
$240$	8.70111e114	0.315740
$241$	−1.70475e115	−0.505631	−0.252815	−	0.967515i	$-0.581357\pi$
$241$	−1.70475e115	−0.505631	−0.252815	+	0.967515i	$0.581357\pi$
$242$	−1.58227e115	−0.383916
$243$	5.00798e115	0.994852
$244$	7.04568e115	1.14688
$245$	−4.72190e115	−0.630321
$246$	4.15250e114	0.0454943
$247$	−1.95076e115	−0.175550
$248$	−6.46395e115	−0.478180
$249$	−3.42476e116	−2.08431
$250$	−2.78459e115	−0.139531
$251$	−1.71502e116	−0.708100	−0.354050	−	0.935226i	$-0.615196\pi$
$251$	−1.71502e116	−0.708100	−0.354050	+	0.935226i	$0.615196\pi$
$252$	8.16349e116	2.77939
$253$	−5.38528e116	−1.51308
$254$	1.86154e116	0.431954
$255$	2.17282e116	0.416701
$256$	1.83519e116	0.291100
$257$	2.75833e116	0.362151	0.181075	−	0.983469i	$-0.442042\pi$
$257$	2.75833e116	0.362151	0.181075	+	0.983469i	$0.442042\pi$
$258$	8.88122e115	0.0965866
$259$	−4.54493e116	−0.409721
$260$	−1.06288e116	−0.0794838
$261$	1.99416e117	1.23793
$262$	−4.64227e116	−0.239396
$263$	−2.18680e117	−0.937465	−0.468733	−	0.883340i	$-0.655289\pi$
$263$	−2.18680e117	−0.937465	−0.468733	+	0.883340i	$0.655289\pi$
$264$	3.78766e117	1.35077
$265$	3.94416e116	0.117093
$266$	1.10417e117	0.273072
$267$	−1.51004e118	−3.11309
$268$	2.39021e117	0.411055
$269$	−5.84841e117	−0.839562	−0.419781	−	0.907626i	$-0.637893\pi$
$269$	−5.84841e117	−0.839562	−0.419781	+	0.907626i	$0.637893\pi$
$270$	−6.04396e116	−0.0724734
$271$	7.88052e117	0.789850	0.394925	−	0.918713i	$-0.370771\pi$
$271$	7.88052e117	0.789850	0.394925	+	0.918713i	$0.370771\pi$
$272$	9.23491e117	0.774178
$273$	−1.45965e118	−1.02414
$274$	−2.73837e117	−0.160912
$275$	2.91470e118	1.43535
$276$	3.55473e118	1.46797
$277$	5.49111e117	0.190279	0.0951396	−	0.995464i	$-0.469670\pi$
$277$	5.49111e117	0.190279	0.0951396	+	0.995464i	$0.469670\pi$
$278$	3.55875e117	0.103544
$279$	−5.83259e118	−1.42580
$280$	1.25567e118	0.258055
$281$	−3.87258e118	−0.669490	−0.334745	−	0.942309i	$-0.608650\pi$
$281$	−3.87258e118	−0.669490	−0.334745	+	0.942309i	$0.608650\pi$
$282$	−2.27612e118	−0.331218
$283$	1.38783e119	1.70097	0.850483	−	0.526003i	$-0.176310\pi$
$283$	1.38783e119	1.70097	0.850483	+	0.526003i	$0.176310\pi$
$284$	−1.01557e119	−1.04899
$285$	2.44846e118	0.213264
$286$	−2.00673e118	−0.147481
$287$	−2.98182e118	−0.185016
$288$	−2.35162e119	−1.23263
$289$	4.90449e117	0.0217294
$290$	1.46962e118	0.0550684
$291$	−3.22283e119	−1.02194
$292$	1.50789e119	0.404856
$293$	4.27458e119	0.972330	0.486165	−	0.873867i	$-0.338395\pi$
$293$	4.27458e119	0.972330	0.486165	+	0.873867i	$0.338395\pi$
$294$	5.88460e119	1.13468
$295$	1.39901e118	0.0228799
$296$	8.60841e118	0.119474
$297$	1.30914e120	1.54276
$298$	−5.42650e119	−0.543289
$299$	−3.93080e119	−0.334525
$300$	−1.92395e120	−1.39255
$301$	−6.37741e119	−0.392798
$302$	3.58985e119	0.188252
$303$	1.84514e120	0.824256
$304$	1.04064e120	0.396217
$305$	9.77884e119	0.317501
$306$	−1.67466e120	−0.463914
$307$	−4.81954e120	−1.13971	−0.569855	−	0.821745i	$-0.693001\pi$
$307$	−4.81954e120	−1.13971	−0.569855	+	0.821745i	$0.693001\pi$
$308$	−1.30312e121	−2.63194
$309$	9.21355e120	1.59016
$310$	−4.29839e119	−0.0634255
$311$	1.01240e120	0.127783	0.0638914	−	0.997957i	$-0.479649\pi$
$311$	1.01240e120	0.127783	0.0638914	+	0.997957i	$0.479649\pi$
$312$	2.76467e120	0.298638
$313$	1.46458e121	1.35461	0.677304	−	0.735703i	$-0.263148\pi$
$313$	1.46458e121	1.35461	0.677304	+	0.735703i	$0.263148\pi$
$314$	−4.69197e120	−0.371764
$315$	1.13303e121	0.769446
$316$	1.12012e121	0.652291
$317$	1.55068e121	0.774726	0.387363	−	0.921927i	$-0.373386\pi$
$317$	1.55068e121	0.774726	0.387363	+	0.921927i	$0.373386\pi$
$318$	−4.91536e120	−0.210785
$319$	−3.18325e121	−1.17226
$320$	4.43120e120	0.140200
$321$	−6.55675e121	−1.78318
$322$	2.22492e121	0.520362
$323$	2.59867e121	0.522912
$324$	−3.37273e119	−0.00584182
$325$	2.12749e121	0.317340
$326$	6.34660e120	0.0815619
$327$	−1.98842e122	−2.20264
$328$	5.64777e120	0.0539505
$329$	1.63443e122	1.34700
$330$	2.51871e121	0.179165
$331$	−1.72930e121	−0.106221	−0.0531106	−	0.998589i	$-0.516914\pi$
$331$	−1.72930e121	−0.106221	−0.0531106	+	0.998589i	$0.516914\pi$
$332$	−2.23173e122	−1.18425
$333$	7.76759e121	0.356238
$334$	1.23960e121	0.0491561
$335$	3.31743e121	0.113796
$336$	7.78658e122	2.31149
$337$	2.48323e122	0.638215	0.319108	−	0.947718i	$-0.396617\pi$
$337$	2.48323e122	0.638215	0.319108	+	0.947718i	$0.396617\pi$
$338$	1.12551e122	0.250547
$339$	−1.00601e123	−1.94051
$340$	1.41591e122	0.236759
$341$	9.31046e122	1.35016
$342$	−1.88710e122	−0.237427
$343$	−2.51850e123	−2.75028
$344$	1.20793e122	0.114540
$345$	4.93368e122	0.406392
$346$	−1.19543e122	−0.0855725
$347$	−1.74732e123	−1.08741	−0.543705	−	0.839277i	$-0.682979\pi$
$347$	−1.74732e123	−1.08741	−0.543705	+	0.839277i	$0.682979\pi$
$348$	2.10121e123	1.13730
$349$	−1.75996e122	−0.0828836	−0.0414418	−	0.999141i	$-0.513195\pi$
$349$	−1.75996e122	−0.0828836	−0.0414418	+	0.999141i	$0.513195\pi$
$350$	−1.20421e123	−0.493630
$351$	9.55563e122	0.341086
$352$	3.75385e123	1.16723
$353$	−1.68570e123	−0.456779	−0.228390	−	0.973570i	$-0.573346\pi$
$353$	−1.68570e123	−0.456779	−0.228390	+	0.973570i	$0.573346\pi$
$354$	−1.74350e122	−0.0411873
$355$	−1.40953e123	−0.290402
$356$	−9.84008e123	−1.76878
$357$	1.94444e124	3.05061
$358$	3.67654e123	0.503630
$359$	8.93132e123	1.06865	0.534324	−	0.845280i	$-0.320566\pi$
$359$	8.93132e123	1.06865	0.534324	+	0.845280i	$0.320566\pi$
$360$	−2.14603e123	−0.224370
$361$	−8.01373e123	−0.732378
$362$	4.88384e123	0.390297
$363$	−3.13985e124	−2.19502
$364$	−9.51170e123	−0.581890
$365$	2.09283e123	0.112080
$366$	−1.21867e124	−0.571551
$367$	−5.31976e123	−0.218569	−0.109284	−	0.994011i	$-0.534856\pi$
$367$	−5.31976e123	−0.218569	−0.109284	+	0.994011i	$0.534856\pi$
$368$	2.09691e124	0.755024
$369$	5.09613e123	0.160865
$370$	5.72441e122	0.0158470
$371$	3.52961e124	0.857219
$372$	−6.14567e124	−1.30990
$373$	7.10916e124	1.33027	0.665135	−	0.746723i	$-0.268374\pi$
$373$	7.10916e124	1.33027	0.665135	+	0.746723i	$0.268374\pi$
$374$	2.67323e124	0.439302
$375$	−5.52572e124	−0.797761
$376$	−3.09573e124	−0.392783
$377$	−2.32350e124	−0.259172
$378$	−5.40871e124	−0.530568
$379$	2.11040e125	1.82122	0.910609	−	0.413268i	$-0.135613\pi$
$379$	2.11040e125	1.82122	0.910609	+	0.413268i	$0.135613\pi$
$380$	1.59553e124	0.121171
$381$	3.69403e125	2.46967
$382$	4.76507e123	0.0280541
$383$	−2.81102e125	−1.45789	−0.728943	−	0.684574i	$-0.759988\pi$
$383$	−2.81102e125	−1.45789	−0.728943	+	0.684574i	$0.759988\pi$
$384$	−3.24606e125	−1.48352
$385$	−1.80863e125	−0.728626
$386$	3.90427e124	0.138693
$387$	1.08994e125	0.341524
$388$	−2.10014e125	−0.580643
$389$	−6.39856e125	−1.56144	−0.780722	−	0.624878i	$-0.785149\pi$
$389$	−6.39856e125	−1.56144	−0.780722	+	0.624878i	$0.785149\pi$
$390$	1.83845e124	0.0396112
$391$	5.23635e125	0.996451
$392$	8.00359e125	1.34558
$393$	−9.21208e125	−1.36873
$394$	9.55591e124	0.125518
$395$	1.55464e125	0.180580
$396$	2.22712e126	2.28838
$397$	−1.17265e126	−1.06617	−0.533086	−	0.846061i	$-0.678968\pi$
$397$	−1.17265e126	−1.06617	−0.533086	+	0.846061i	$0.678968\pi$
$398$	−2.14931e125	−0.172970
$399$	2.19111e126	1.56128
$400$	−1.13492e126	−0.716238
$401$	−1.29718e126	−0.725266	−0.362633	−	0.931932i	$-0.618122\pi$
$401$	−1.29718e126	−0.725266	−0.362633	+	0.931932i	$0.618122\pi$
$402$	−4.13430e125	−0.204851
$403$	6.79585e125	0.298503
$404$	1.20238e126	0.468321
$405$	−4.68108e123	−0.00161725
$406$	1.31516e126	0.403148
$407$	−1.23993e126	−0.337339
$408$	−3.68291e126	−0.889556
$409$	−4.22786e126	−0.906860	−0.453430	−	0.891292i	$-0.649800\pi$
$409$	−4.22786e126	−0.906860	−0.453430	+	0.891292i	$0.649800\pi$
$410$	3.75565e124	0.00715596
$411$	−5.43400e126	−0.920007
$412$	6.00396e126	0.903489
$413$	1.25197e126	0.167500
$414$	−3.80254e126	−0.452436
$415$	−3.09746e126	−0.327849
$416$	2.73999e126	0.258061
$417$	7.06196e126	0.592007
$418$	3.01235e126	0.224831
$419$	2.60430e127	1.73106	0.865528	−	0.500860i	$-0.166983\pi$
$419$	2.60430e127	1.73106	0.865528	+	0.500860i	$0.166983\pi$
$420$	1.19385e127	0.706900
$421$	−1.18108e127	−0.623156	−0.311578	−	0.950221i	$-0.600858\pi$
$421$	−1.18108e127	−0.623156	−0.311578	+	0.950221i	$0.600858\pi$
$422$	2.78147e126	0.130804
$423$	−2.79335e127	−1.17117
$424$	−6.68532e126	−0.249965
$425$	−2.83410e127	−0.945262
$426$	1.75661e127	0.522769
$427$	8.75103e127	2.32438
$428$	−4.27267e127	−1.01316
$429$	−3.98214e127	−0.843214
$430$	8.03245e125	0.0151925
$431$	2.46609e127	0.416736	0.208368	−	0.978051i	$-0.433185\pi$
$431$	2.46609e127	0.416736	0.208368	+	0.978051i	$0.433185\pi$
$432$	−5.09752e127	−0.769834
$433$	−3.33591e127	−0.450351	−0.225175	−	0.974318i	$-0.572295\pi$
$433$	−3.33591e127	−0.450351	−0.225175	+	0.974318i	$0.572295\pi$
$434$	−3.84661e127	−0.464330
$435$	2.91631e127	0.314850
$436$	−1.29575e128	−1.25148
$437$	5.90063e127	0.509975
$438$	−2.60816e127	−0.201762
$439$	−9.20962e127	−0.637841	−0.318920	−	0.947781i	$-0.603320\pi$
$439$	−9.20962e127	−0.637841	−0.318920	+	0.947781i	$0.603320\pi$
$440$	3.42567e127	0.212467
$441$	7.22184e128	4.01214
$442$	1.95123e127	0.0971245
$443$	5.93667e127	0.264827	0.132414	−	0.991195i	$-0.457727\pi$
$443$	5.93667e127	0.264827	0.132414	+	0.991195i	$0.457727\pi$
$444$	8.18454e127	0.327281
$445$	−1.36572e128	−0.489669
$446$	−6.43650e127	−0.206971
$447$	−1.07683e129	−3.10623
$448$	3.96546e128	1.02638
$449$	8.64330e127	0.200785	0.100393	−	0.994948i	$-0.467990\pi$
$449$	8.64330e127	0.200785	0.100393	+	0.994948i	$0.467990\pi$
$450$	2.05807e128	0.429194
$451$	−8.13486e127	−0.152331
$452$	−6.55560e128	−1.10255
$453$	7.12369e128	1.07632
$454$	−2.67629e128	−0.363349
$455$	−1.32015e128	−0.161091
$456$	−4.15012e128	−0.455267
$457$	4.98066e128	0.491305	0.245653	−	0.969358i	$-0.420998\pi$
$457$	4.98066e128	0.491305	0.245653	+	0.969358i	$0.420998\pi$
$458$	1.77031e127	0.0157063
$459$	−1.27294e129	−1.01600
$460$	3.21500e128	0.230902
$461$	−1.94114e129	−1.25477	−0.627383	−	0.778711i	$-0.715874\pi$
$461$	−1.94114e129	−1.25477	−0.627383	+	0.778711i	$0.715874\pi$
$462$	2.25398e129	1.31164
$463$	1.80817e129	0.947460	0.473730	−	0.880670i	$-0.342907\pi$
$463$	1.80817e129	0.947460	0.473730	+	0.880670i	$0.342907\pi$
$464$	1.23949e129	0.584952
$465$	−8.52971e128	−0.362632
$466$	−6.98828e128	−0.267703
$467$	3.48140e129	1.20195	0.600974	−	0.799269i	$-0.294780\pi$
$467$	3.48140e129	1.20195	0.600974	+	0.799269i	$0.294780\pi$
$468$	1.62561e129	0.505933
$469$	2.96875e129	0.833087
$470$	−2.05859e128	−0.0520984
$471$	−9.31072e129	−2.12554
$472$	−2.37132e128	−0.0488430
$473$	−1.73986e129	−0.323406
$474$	−1.93745e129	−0.325073
$475$	−3.19363e129	−0.483776
$476$	1.26709e130	1.73328
$477$	−6.03234e129	−0.745323
$478$	1.40348e129	0.156658
$479$	−1.82246e130	−1.83816	−0.919082	−	0.394065i	$-0.871068\pi$
$479$	−1.82246e130	−1.83816	−0.919082	+	0.394065i	$0.871068\pi$
$480$	−3.43906e129	−0.313501
$481$	−9.05042e128	−0.0745817
$482$	1.92148e129	0.143171
$483$	4.41512e130	2.97514
$484$	−2.04607e130	−1.24715
$485$	−2.91482e129	−0.160745
$486$	−5.64467e129	−0.281695
$487$	1.25932e130	0.568828	0.284414	−	0.958702i	$-0.408201\pi$
$487$	1.25932e130	0.568828	0.284414	+	0.958702i	$0.408201\pi$
$488$	−1.65751e130	−0.677788
$489$	1.25942e130	0.466326
$490$	5.32222e129	0.178477
$491$	3.33258e130	1.01234	0.506172	−	0.862433i	$-0.331060\pi$
$491$	3.33258e130	1.01234	0.506172	+	0.862433i	$0.331060\pi$
$492$	5.36968e129	0.147789
$493$	3.09522e130	0.771997
$494$	2.19876e129	0.0497075
$495$	3.09107e130	0.633515
$496$	−3.62530e130	−0.673724
$497$	−1.26138e131	−2.12599
$498$	3.86017e130	0.590178
$499$	−1.20619e131	−1.67317	−0.836586	−	0.547835i	$-0.815452\pi$
$499$	−1.20619e131	−1.67317	−0.836586	+	0.547835i	$0.815452\pi$
$500$	−3.60081e130	−0.453268
$501$	2.45985e130	0.281047
$502$	1.93306e130	0.200501
$503$	9.91612e130	0.933887	0.466944	−	0.884287i	$-0.345355\pi$
$503$	9.91612e130	0.933887	0.466944	+	0.884287i	$0.345355\pi$
$504$	−1.92047e131	−1.64258
$505$	1.66880e130	0.129650
$506$	6.06993e130	0.428434
$507$	2.23345e131	1.43249
$508$	2.40719e131	1.40321
$509$	−1.93323e131	−1.02441	−0.512203	−	0.858864i	$-0.671170\pi$
$509$	−1.93323e131	−1.02441	−0.512203	+	0.858864i	$0.671170\pi$
$510$	−2.44906e130	−0.117990
$511$	1.87286e131	0.820525
$512$	−2.50650e131	−0.998793
$513$	−1.43442e131	−0.519977
$514$	−3.10900e130	−0.102544
$515$	8.33302e130	0.250122
$516$	1.14845e131	0.313762
$517$	4.45898e131	1.10903
$518$	5.12275e130	0.116014
$519$	−2.37221e131	−0.489256
$520$	2.50045e130	0.0469739
$521$	8.96380e131	1.53413	0.767065	−	0.641569i	$-0.221716\pi$
$521$	8.96380e131	1.53413	0.767065	+	0.641569i	$0.221716\pi$
$522$	−2.24769e131	−0.350523
$523$	−5.60728e131	−0.796931	−0.398465	−	0.917183i	$-0.630457\pi$
$523$	−5.60728e131	−0.796931	−0.398465	+	0.917183i	$0.630457\pi$
$524$	−6.00301e131	−0.777681
$525$	−2.38962e132	−2.82230
$526$	2.46482e131	0.265446
$527$	−9.05299e131	−0.889154
$528$	2.12430e132	1.90314
$529$	−3.45045e130	−0.0282018
$530$	−4.44560e130	−0.0331551
$531$	−2.13970e131	−0.145636
$532$	1.42783e132	0.887078
$533$	−5.93776e130	−0.0336785
$534$	1.70201e132	0.881480
$535$	−5.93013e131	−0.280483
$536$	−5.62302e131	−0.242928
$537$	7.29570e132	2.87948
$538$	6.59195e131	0.237724
$539$	−1.15281e133	−3.79929
$540$	−7.81556e131	−0.235430
$541$	3.84151e132	1.05787	0.528937	−	0.848661i	$-0.322591\pi$
$541$	3.84151e132	1.05787	0.528937	+	0.848661i	$0.322591\pi$
$542$	−8.88241e131	−0.223648
$543$	9.69145e132	2.23150
$544$	−3.65004e132	−0.768689
$545$	−1.79839e132	−0.346461
$546$	1.64522e132	0.289988
$547$	5.42767e130	0.00875443	0.00437721	−	0.999990i	$-0.498607\pi$
$547$	5.42767e130	0.00875443	0.00437721	+	0.999990i	$0.498607\pi$
$548$	−3.54104e132	−0.522725
$549$	−1.49561e133	−2.02097
$550$	−3.28526e132	−0.406425
$551$	3.48787e132	0.395101
$552$	−8.36255e132	−0.867548
$553$	1.39124e133	1.32200
$554$	−6.18922e131	−0.0538781
$555$	1.13595e132	0.0906043
$556$	4.60189e132	0.336363
$557$	−1.26479e133	−0.847308	−0.423654	−	0.905824i	$-0.639253\pi$
$557$	−1.26479e133	−0.847308	−0.423654	+	0.905824i	$0.639253\pi$
$558$	6.57411e132	0.403718
$559$	−1.26995e132	−0.0715012
$560$	7.04242e132	0.363582
$561$	5.30474e133	2.51169
$562$	4.36492e132	0.189568
$563$	5.35021e132	0.213164	0.106582	−	0.994304i	$-0.466009\pi$
$563$	5.35021e132	0.213164	0.106582	+	0.994304i	$0.466009\pi$
$564$	−2.94330e133	−1.07596
$565$	−9.09865e132	−0.305230
$566$	−1.56428e133	−0.481633
$567$	−4.18907e131	−0.0118397
$568$	2.38915e133	0.619938
$569$	−5.46524e133	−1.30216	−0.651080	−	0.759009i	$-0.725684\pi$
$569$	−5.46524e133	−1.30216	−0.651080	+	0.759009i	$0.725684\pi$
$570$	−2.75974e132	−0.0603863
$571$	4.37356e133	0.878990	0.439495	−	0.898245i	$-0.355157\pi$
$571$	4.37356e133	0.878990	0.439495	+	0.898245i	$0.355157\pi$
$572$	−2.59494e133	−0.479093
$573$	9.45578e132	0.160398
$574$	3.36091e132	0.0523878
$575$	−6.43521e133	−0.921875
$576$	−6.77724e133	−0.892406
$577$	8.23104e133	0.996387	0.498193	−	0.867066i	$-0.333997\pi$
$577$	8.23104e133	0.996387	0.498193	+	0.867066i	$0.333997\pi$
$578$	−5.52802e131	−0.00615276
$579$	7.74760e133	0.792970
$580$	1.90040e133	0.178890
$581$	−2.77190e134	−2.40013
$582$	3.63256e133	0.289366
$583$	9.62932e133	0.705782
$584$	−3.54733e133	−0.239264
$585$	2.25622e133	0.140063
$586$	−4.81802e133	−0.275318
$587$	3.26683e133	0.171861	0.0859307	−	0.996301i	$-0.472614\pi$
$587$	3.26683e133	0.171861	0.0859307	+	0.996301i	$0.472614\pi$
$588$	7.60950e134	3.68600
$589$	−1.02014e134	−0.455061
$590$	−1.57687e132	−0.00647850
$591$	1.89627e134	0.717641
$592$	4.82801e133	0.168331
$593$	−5.04630e134	−1.62114	−0.810571	−	0.585641i	$-0.800843\pi$
$593$	−5.04630e134	−1.62114	−0.810571	+	0.585641i	$0.800843\pi$
$594$	−1.47558e134	−0.436837
$595$	1.75861e134	0.479842
$596$	−7.01712e134	−1.76488
$597$	−4.26508e134	−0.988945
$598$	4.43054e133	0.0947216
$599$	−3.75880e134	−0.741051	−0.370526	−	0.928822i	$-0.620822\pi$
$599$	−3.75880e134	−0.741051	−0.370526	+	0.928822i	$0.620822\pi$
$600$	4.52611e134	0.822980
$601$	6.42928e134	1.07833	0.539163	−	0.842201i	$-0.318741\pi$
$601$	6.42928e134	1.07833	0.539163	+	0.842201i	$0.318741\pi$
$602$	7.18820e133	0.111222
$603$	−5.07379e134	−0.724341
$604$	4.64211e134	0.611539
$605$	−2.83978e134	−0.345262
$606$	−2.07972e134	−0.233390
$607$	−5.58240e134	−0.578321	−0.289161	−	0.957281i	$-0.593376\pi$
$607$	−5.58240e134	−0.578321	−0.289161	+	0.957281i	$0.593376\pi$
$608$	−4.11308e134	−0.393408
$609$	2.60979e135	2.30498
$610$	−1.10221e134	−0.0899013
$611$	3.25468e134	0.245194
$612$	−2.16554e135	−1.50703
$613$	−7.34401e133	−0.0472172	−0.0236086	−	0.999721i	$-0.507516\pi$
$613$	−7.34401e133	−0.0472172	−0.0236086	+	0.999721i	$0.507516\pi$
$614$	5.43227e134	0.322712
$615$	7.45269e133	0.0409138
$616$	3.06562e135	1.55544
$617$	3.33719e135	1.56513	0.782566	−	0.622568i	$-0.213911\pi$
$617$	3.33719e135	1.56513	0.782566	+	0.622568i	$0.213911\pi$
$618$	−1.03849e135	−0.450258
$619$	8.53749e134	0.342242	0.171121	−	0.985250i	$-0.445261\pi$
$619$	8.53749e134	0.342242	0.171121	+	0.985250i	$0.445261\pi$
$620$	−5.55834e134	−0.206038
$621$	−2.89038e135	−0.990859
$622$	−1.14111e134	−0.0361821
$623$	−1.22218e136	−3.58480
$624$	1.55056e135	0.420761
$625$	3.22471e135	0.809674
$626$	−1.65078e135	−0.383561
$627$	5.97770e135	1.28546
$628$	−6.06728e135	−1.20768
$629$	1.20564e135	0.222157
$630$	−1.27707e135	−0.217871
$631$	6.63301e135	1.04782	0.523910	−	0.851774i	$-0.324473\pi$
$631$	6.63301e135	1.04782	0.523910	+	0.851774i	$0.324473\pi$
$632$	−2.63510e135	−0.385495
$633$	5.51952e135	0.747862
$634$	−1.74783e135	−0.219366
$635$	3.34099e135	0.388463
$636$	−6.35614e135	−0.684737
$637$	−8.41454e135	−0.839978
$638$	3.58795e135	0.331928
$639$	2.15579e136	1.84848
$640$	−2.93584e135	−0.233348
$641$	−3.59662e135	−0.265021	−0.132511	−	0.991182i	$-0.542304\pi$
$641$	−3.59662e135	−0.265021	−0.132511	+	0.991182i	$0.542304\pi$
$642$	7.39034e135	0.504912
$643$	−1.89570e136	−1.20098	−0.600492	−	0.799631i	$-0.705029\pi$
$643$	−1.89570e136	−1.20098	−0.600492	+	0.799631i	$0.705029\pi$
$644$	2.87709e136	1.69040
$645$	1.59395e135	0.0868620
$646$	−2.92905e135	−0.148064
$647$	2.63899e135	0.123760	0.0618801	−	0.998084i	$-0.480290\pi$
$647$	2.63899e135	0.123760	0.0618801	+	0.998084i	$0.480290\pi$
$648$	7.93440e133	0.00345244
$649$	3.41556e135	0.137910
$650$	−2.39797e135	−0.0898556
$651$	−7.63319e136	−2.65478
$652$	8.20691e135	0.264955
$653$	−2.55404e136	−0.765488	−0.382744	−	0.923855i	$-0.625021\pi$
$653$	−2.55404e136	−0.765488	−0.382744	+	0.923855i	$0.625021\pi$
$654$	2.24122e136	0.623683
$655$	−8.33169e135	−0.215293
$656$	3.16754e135	0.0760127
$657$	−3.20084e136	−0.713418
$658$	−1.84223e136	−0.381406
$659$	2.69234e136	0.517830	0.258915	−	0.965900i	$-0.416635\pi$
$659$	2.69234e136	0.517830	0.258915	+	0.965900i	$0.416635\pi$
$660$	3.25700e136	0.582018
$661$	4.30762e136	0.715265	0.357632	−	0.933862i	$-0.383584\pi$
$661$	4.30762e136	0.715265	0.357632	+	0.933862i	$0.383584\pi$
$662$	1.94915e135	0.0300769
$663$	3.87201e136	0.555304
$664$	5.25018e136	0.699877
$665$	1.98171e136	0.245579
$666$	−8.75512e135	−0.100870
$667$	7.02811e136	0.752897
$668$	1.60295e136	0.159684
$669$	−1.27726e137	−1.18334
$670$	−3.73919e135	−0.0322218
$671$	2.38742e137	1.91375
$672$	−3.07759e137	−2.29510
$673$	−2.61744e137	−1.81612	−0.908062	−	0.418835i	$-0.862438\pi$
$673$	−2.61744e137	−1.81612	−0.908062	+	0.418835i	$0.862438\pi$
$674$	−2.79894e136	−0.180713
$675$	1.56438e137	0.939957
$676$	1.45542e137	0.813903
$677$	2.86931e137	1.49357	0.746787	−	0.665064i	$-0.231596\pi$
$677$	2.86931e137	1.49357	0.746787	+	0.665064i	$0.231596\pi$
$678$	1.13391e137	0.549461
$679$	−2.60846e137	−1.17679
$680$	−3.33094e136	−0.139921
$681$	−5.31080e137	−2.07742
$682$	−1.04941e137	−0.382301
$683$	2.07909e137	0.705456	0.352728	−	0.935726i	$-0.385254\pi$
$683$	2.07909e137	0.705456	0.352728	+	0.935726i	$0.385254\pi$
$684$	−2.44025e137	−0.771283
$685$	−4.91468e136	−0.144711
$686$	2.83868e137	0.778749
$687$	3.51300e136	0.0897999
$688$	6.77463e136	0.161379
$689$	7.02859e136	0.156040
$690$	−5.56092e136	−0.115071
$691$	−6.16036e137	−1.18828	−0.594142	−	0.804360i	$-0.702508\pi$
$691$	−6.16036e137	−1.18828	−0.594142	+	0.804360i	$0.702508\pi$
$692$	−1.54584e137	−0.277983
$693$	2.76618e138	4.63788
$694$	1.96947e137	0.307903
$695$	6.38705e136	0.0931188
$696$	−4.94312e137	−0.672129
$697$	7.90990e136	0.100319
$698$	1.98371e136	0.0234687
$699$	−1.38675e138	−1.53058
$700$	−1.55719e138	−1.60356
$701$	2.99195e137	0.287495	0.143748	−	0.989614i	$-0.454085\pi$
$701$	2.99195e137	0.287495	0.143748	+	0.989614i	$0.454085\pi$
$702$	−1.07705e137	−0.0965795
$703$	1.35858e137	0.113698
$704$	1.08184e138	0.845062
$705$	−4.08506e137	−0.297870
$706$	1.90001e137	0.129338
$707$	1.49340e138	0.949151
$708$	−2.25455e137	−0.133797
$709$	−2.61734e138	−1.45050	−0.725250	−	0.688486i	$-0.758276\pi$
$709$	−2.61734e138	−1.45050	−0.725250	+	0.688486i	$0.758276\pi$
$710$	1.58873e137	0.0822282
$711$	−2.37772e138	−1.14944
$712$	2.31489e138	1.04532
$713$	−2.05560e138	−0.867156
$714$	−2.19165e138	−0.863789
$715$	−3.60157e137	−0.132632
$716$	4.75420e138	1.63605
$717$	2.78505e138	0.895683
$718$	−1.00668e138	−0.302591
$719$	−2.46641e138	−0.692970	−0.346485	−	0.938055i	$-0.612625\pi$
$719$	−2.46641e138	−0.692970	−0.346485	+	0.938055i	$0.612625\pi$
$720$	−1.20360e138	−0.316122
$721$	7.45718e138	1.83111
$722$	9.03256e137	0.207375
$723$	3.81297e138	0.818571
$724$	6.31539e138	1.26788
$725$	−3.80387e138	−0.714220
$726$	3.53903e138	0.621525
$727$	−7.91554e138	−1.30035	−0.650177	−	0.759783i	$-0.725305\pi$
$727$	−7.91554e138	−1.30035	−0.650177	+	0.759783i	$0.725305\pi$
$728$	2.23764e138	0.343889
$729$	−1.12454e139	−1.61693
$730$	−2.35890e137	−0.0317359
$731$	1.69174e138	0.212981
$732$	−1.57589e139	−1.85669
$733$	−2.05544e138	−0.226653	−0.113327	−	0.993558i	$-0.536151\pi$
$733$	−2.05544e138	−0.226653	−0.113327	+	0.993558i	$0.536151\pi$
$734$	5.99609e137	0.0618883
$735$	1.05614e139	1.02043
$736$	−8.28790e138	−0.749671
$737$	8.09920e138	0.685913
$738$	−5.74402e137	−0.0455494
$739$	7.40954e138	0.550220	0.275110	−	0.961413i	$-0.411286\pi$
$739$	7.40954e138	0.550220	0.275110	+	0.961413i	$0.411286\pi$
$740$	7.40235e137	0.0514791
$741$	4.36321e138	0.284200
$742$	−3.97834e138	−0.242724
$743$	−2.68694e139	−1.53568	−0.767841	−	0.640641i	$-0.778669\pi$
$743$	−2.68694e139	−1.53568	−0.767841	+	0.640641i	$0.778669\pi$
$744$	1.44578e139	0.774131
$745$	−9.73920e138	−0.488589
$746$	−8.01298e138	−0.376670
$747$	4.73737e139	2.08683
$748$	3.45681e139	1.42708
$749$	−5.30684e139	−2.05337
$750$	6.22823e138	0.225888
$751$	1.83639e139	0.624350	0.312175	−	0.950025i	$-0.398942\pi$
$751$	1.83639e139	0.624350	0.312175	+	0.950025i	$0.398942\pi$
$752$	−1.73623e139	−0.553405
$753$	3.83596e139	1.14635
$754$	2.61890e138	0.0733852
$755$	6.44288e138	0.169298
$756$	−6.99410e139	−1.72355
$757$	5.04230e139	1.16541	0.582705	−	0.812684i	$-0.301994\pi$
$757$	5.04230e139	1.16541	0.582705	+	0.812684i	$0.301994\pi$
$758$	−2.37870e139	−0.515683
$759$	1.20451e140	2.44955
$760$	−3.75350e138	−0.0716105
$761$	−7.69419e139	−1.37723	−0.688616	−	0.725126i	$-0.741781\pi$
$761$	−7.69419e139	−1.37723	−0.688616	+	0.725126i	$0.741781\pi$
$762$	−4.16367e139	−0.699294
$763$	−1.60937e140	−2.53639
$764$	6.16181e138	0.0911340
$765$	−3.00559e139	−0.417206
$766$	3.16840e139	0.412805
$767$	2.49307e138	0.0304902
$768$	−4.10473e139	−0.471265
$769$	1.21595e140	1.31065	0.655326	−	0.755346i	$-0.272531\pi$
$769$	1.21595e140	1.31065	0.655326	+	0.755346i	$0.272531\pi$
$770$	2.03857e139	0.206313
$771$	−6.16949e139	−0.586289
$772$	5.04868e139	0.450546
$773$	2.98873e139	0.250485	0.125243	−	0.992126i	$-0.460029\pi$
$773$	2.98873e139	0.250485	0.125243	+	0.992126i	$0.460029\pi$
$774$	−1.22851e139	−0.0967036
$775$	1.11257e140	0.822609
$776$	4.94060e139	0.343152
$777$	1.01655e140	0.663302
$778$	7.21204e139	0.442128
$779$	8.91334e138	0.0513421
$780$	2.37733e139	0.128677
$781$	−3.44125e140	−1.75041
$782$	−5.90207e139	−0.282148
$783$	−1.70851e140	−0.767665
$784$	4.48879e140	1.89584
$785$	−8.42091e139	−0.334334
$786$	1.03833e140	0.387561
$787$	−1.13298e140	−0.397603	−0.198801	−	0.980040i	$-0.563705\pi$
$787$	−1.13298e140	−0.397603	−0.198801	+	0.980040i	$0.563705\pi$
$788$	1.23569e140	0.407746
$789$	4.89117e140	1.51767
$790$	−1.75229e139	−0.0511318
$791$	−8.14233e140	−2.23455
$792$	−5.23934e140	−1.35240
$793$	1.74261e140	0.423108
$794$	1.32173e140	0.301890
$795$	−8.82182e139	−0.189563
$796$	−2.77932e140	−0.561894
$797$	−7.10014e140	−1.35064	−0.675318	−	0.737527i	$-0.735994\pi$
$797$	−7.10014e140	−1.35064	−0.675318	+	0.737527i	$0.735994\pi$
$798$	−2.46968e140	−0.442080
$799$	−4.33567e140	−0.730362
$800$	4.48571e140	0.711159
$801$	2.08879e141	3.11686
$802$	1.46209e140	0.205361
$803$	5.10945e140	0.675570
$804$	−5.34614e140	−0.665460
$805$	3.99317e140	0.467970
$806$	−7.65984e139	−0.0845221
$807$	1.30810e141	1.35917
$808$	−2.82861e140	−0.276772
$809$	−1.18382e141	−1.09089	−0.545445	−	0.838147i	$-0.683639\pi$
$809$	−1.18382e141	−1.09089	−0.545445	+	0.838147i	$0.683639\pi$
$810$	5.27621e137	0.000457929 0
$811$	−5.08646e140	−0.415819	−0.207909	−	0.978148i	$-0.566666\pi$
$811$	−5.08646e140	−0.415819	−0.207909	+	0.978148i	$0.566666\pi$
$812$	1.70065e141	1.30963
$813$	−1.76262e141	−1.27870
$814$	1.39756e140	0.0955186
$815$	1.13905e140	0.0733500
$816$	−2.06555e141	−1.25332
$817$	1.90635e140	0.109002
$818$	4.76537e140	0.256780
$819$	2.01908e141	1.02538
$820$	4.85650e139	0.0232462
$821$	7.71220e140	0.347965	0.173982	−	0.984749i	$-0.444336\pi$
$821$	7.71220e140	0.347965	0.173982	+	0.984749i	$0.444336\pi$
$822$	6.12485e140	0.260503
$823$	−7.98625e139	−0.0320222	−0.0160111	−	0.999872i	$-0.505097\pi$
$823$	−7.98625e139	−0.0320222	−0.0160111	+	0.999872i	$0.505097\pi$
$824$	−1.41244e141	−0.533950
$825$	−6.51926e141	−2.32371
$826$	−1.41114e140	−0.0474282
$827$	3.54407e141	1.12327	0.561637	−	0.827384i	$-0.310172\pi$
$827$	3.54407e141	1.12327	0.561637	+	0.827384i	$0.310172\pi$
$828$	−4.91714e141	−1.46974
$829$	−9.91560e140	−0.279527	−0.139764	−	0.990185i	$-0.544634\pi$
$829$	−9.91560e140	−0.279527	−0.139764	+	0.990185i	$0.544634\pi$
$830$	3.49126e140	0.0928313
$831$	−1.22819e141	−0.308045
$832$	7.89651e140	0.186833
$833$	1.12093e142	2.50205
$834$	−7.95978e140	−0.167628
$835$	2.22476e140	0.0442069
$836$	3.89533e141	0.730365
$837$	4.99710e141	0.884165
$838$	−2.93540e141	−0.490154
$839$	1.81126e141	0.285448	0.142724	−	0.989763i	$-0.454414\pi$
$839$	1.81126e141	0.285448	0.142724	+	0.989763i	$0.454414\pi$
$840$	−2.80854e141	−0.417768
$841$	−2.96773e141	−0.416696
$842$	1.33123e141	0.176448
$843$	8.66173e141	1.08384
$844$	3.59677e141	0.424917
$845$	2.02000e141	0.225321
$846$	3.14849e141	0.331619
$847$	−2.54130e142	−2.52762
$848$	−3.74945e141	−0.352183
$849$	−3.10414e142	−2.75371
$850$	3.19441e141	0.267654
$851$	2.73756e141	0.216661
$852$	2.27151e142	1.69822
$853$	1.81782e142	1.28387	0.641937	−	0.766757i	$-0.278131\pi$
$853$	1.81782e142	1.28387	0.641937	+	0.766757i	$0.278131\pi$
$854$	−9.86359e141	−0.658155
$855$	−3.38688e141	−0.213522
$856$	1.00515e142	0.598762
$857$	−2.44014e142	−1.37355	−0.686776	−	0.726869i	$-0.740975\pi$
$857$	−2.44014e142	−1.37355	−0.686776	+	0.726869i	$0.740975\pi$
$858$	4.48840e141	0.238758
$859$	−2.45966e142	−1.23653	−0.618267	−	0.785968i	$-0.712165\pi$
$859$	−2.45966e142	−1.23653	−0.618267	+	0.785968i	$0.712165\pi$
$860$	1.03869e141	0.0493528
$861$	6.66937e141	0.299524
$862$	−2.77961e141	−0.118000
$863$	4.28714e142	1.72046	0.860230	−	0.509907i	$-0.170320\pi$
$863$	4.28714e142	1.72046	0.860230	+	0.509907i	$0.170320\pi$
$864$	2.01476e142	0.764375
$865$	−2.14550e141	−0.0769568
$866$	3.76001e141	0.127518
$867$	−1.09698e141	−0.0351780
$868$	−4.97413e142	−1.50838
$869$	3.79551e142	1.08846
$870$	−3.28707e141	−0.0891508
$871$	5.91174e141	0.151647
$872$	3.04826e142	0.739610
$873$	4.45803e142	1.02318
$874$	−6.65080e141	−0.144401
$875$	−4.47236e142	−0.918641
$876$	−3.37266e142	−0.655425
$877$	7.83172e142	1.44005	0.720024	−	0.693949i	$-0.244131\pi$
$877$	7.83172e142	1.44005	0.720024	+	0.693949i	$0.244131\pi$
$878$	1.03805e142	0.180606
$879$	−9.56085e142	−1.57411
$880$	1.92128e142	0.299351
$881$	−7.07567e142	−1.04336	−0.521682	−	0.853140i	$-0.674695\pi$
$881$	−7.07567e142	−1.04336	−0.521682	+	0.853140i	$0.674695\pi$
$882$	−8.13998e142	−1.13605
$883$	−6.58230e142	−0.869528	−0.434764	−	0.900544i	$-0.643168\pi$
$883$	−6.58230e142	−0.869528	−0.434764	+	0.900544i	$0.643168\pi$
$884$	2.52318e142	0.315510
$885$	−3.12914e141	−0.0370405
$886$	−6.69143e141	−0.0749866
$887$	−9.56399e141	−0.101471	−0.0507357	−	0.998712i	$-0.516157\pi$
$887$	−9.56399e141	−0.101471	−0.0507357	+	0.998712i	$0.516157\pi$
$888$	−1.92542e142	−0.193418
$889$	2.98984e143	2.84389
$890$	1.53935e142	0.138651
$891$	−1.14284e141	−0.00974806
$892$	−8.32317e142	−0.672346
$893$	−4.88569e142	−0.373792
$894$	1.21373e143	0.879537
$895$	6.59845e142	0.452923
$896$	−2.62727e143	−1.70831
$897$	8.79193e142	0.541565
$898$	−9.74216e141	−0.0568529
$899$	−1.21507e143	−0.671826
$900$	2.66133e143	1.39424
$901$	−9.36303e142	−0.464798
$902$	9.16908e141	0.0431329
$903$	1.42642e143	0.635905
$904$	1.54221e143	0.651592
$905$	8.76525e142	0.351001
$906$	−8.02935e142	−0.304763
$907$	4.40941e143	1.58645	0.793227	−	0.608927i	$-0.208400\pi$
$907$	4.40941e143	1.58645	0.793227	+	0.608927i	$0.208400\pi$
$908$	−3.46076e143	−1.18034
$909$	−2.55232e143	−0.825254
$910$	1.48798e142	0.0456132
$911$	3.14937e143	0.915339	0.457670	−	0.889122i	$-0.348684\pi$
$911$	3.14937e143	0.915339	0.457670	+	0.889122i	$0.348684\pi$
$912$	−2.32759e143	−0.641440
$913$	−7.56218e143	−1.97612
$914$	−5.61388e142	−0.139114
$915$	−2.18721e143	−0.514006
$916$	2.28923e142	0.0510221
$917$	−7.45599e143	−1.57613
$918$	1.43477e143	0.287682
$919$	−4.01749e143	−0.764103	−0.382052	−	0.924141i	$-0.624782\pi$
$919$	−4.01749e143	−0.764103	−0.382052	+	0.924141i	$0.624782\pi$
$920$	−7.56335e142	−0.136460
$921$	1.07798e144	1.84509
$922$	2.18793e143	0.355291
$923$	−2.51182e143	−0.386995
$924$	2.91467e144	4.26087
$925$	−1.48167e143	−0.205531
$926$	−2.03805e143	−0.268276
$927$	−1.27448e144	−1.59208
$928$	−4.89900e143	−0.580805
$929$	2.87597e143	0.323610	0.161805	−	0.986823i	$-0.448268\pi$
$929$	2.87597e143	0.323610	0.161805	+	0.986823i	$0.448268\pi$
$930$	9.61413e142	0.102680
$931$	1.26313e144	1.28053
$932$	−9.03669e143	−0.869636
$933$	−2.26441e143	−0.206869
$934$	−3.92401e143	−0.340335
$935$	4.79777e143	0.395072
$936$	−3.82428e143	−0.299000
$937$	2.28970e144	1.69984	0.849921	−	0.526910i	$-0.176650\pi$
$937$	2.28970e144	1.69984	0.849921	+	0.526910i	$0.176650\pi$
$938$	−3.34618e143	−0.235891
$939$	−3.27580e144	−2.19299
$940$	−2.66201e143	−0.169242
$941$	1.00318e144	0.605734	0.302867	−	0.953033i	$-0.402056\pi$
$941$	1.00318e144	0.605734	0.302867	+	0.953033i	$0.402056\pi$
$942$	1.04944e144	0.601853
$943$	1.79605e143	0.0978366
$944$	−1.32995e143	−0.0688165
$945$	−9.70726e143	−0.477149
$946$	1.96105e143	0.0915733
$947$	−7.02646e143	−0.311718	−0.155859	−	0.987779i	$-0.549815\pi$
$947$	−7.02646e143	−0.311718	−0.155859	+	0.987779i	$0.549815\pi$
$948$	−2.50535e144	−1.05600
$949$	3.72947e143	0.149360
$950$	3.59965e143	0.136983
$951$	−3.46837e144	−1.25421
$952$	−2.98084e144	−1.02435
$953$	3.95465e144	1.29152	0.645762	−	0.763539i	$-0.276540\pi$
$953$	3.95465e144	1.29152	0.645762	+	0.763539i	$0.276540\pi$
$954$	6.79926e143	0.211040
$955$	8.55210e142	0.0252295
$956$	1.81487e144	0.508905
$957$	7.11990e144	1.89778
$958$	2.05415e144	0.520482
$959$	−4.39812e144	−1.05941
$960$	−9.91118e143	−0.226971
$961$	−1.03899e144	−0.226218
$962$	1.02010e143	0.0211180
$963$	9.06975e144	1.78534
$964$	2.48470e144	0.465092
$965$	7.00717e143	0.124729
$966$	−4.97644e144	−0.842419
$967$	−3.61685e144	−0.582299	−0.291149	−	0.956678i	$-0.594038\pi$
$967$	−3.61685e144	−0.582299	−0.291149	+	0.956678i	$0.594038\pi$
$968$	4.81340e144	0.737051
$969$	−5.81239e144	−0.846547
$970$	3.28540e143	0.0455154
$971$	3.52227e142	0.00464183	0.00232092	−	0.999997i	$-0.499261\pi$
$971$	3.52227e142	0.00464183	0.00232092	+	0.999997i	$0.499261\pi$
$972$	−7.29924e144	−0.915089
$973$	5.71574e144	0.681710
$974$	−1.41942e144	−0.161065
$975$	−4.75851e144	−0.513744
$976$	−9.29609e144	−0.954958
$977$	1.48341e145	1.45003	0.725013	−	0.688735i	$-0.241834\pi$
$977$	1.48341e145	1.45003	0.725013	+	0.688735i	$0.241834\pi$
$978$	−1.41953e144	−0.132041
$979$	−3.33429e145	−2.95150
$980$	6.88226e144	0.579784
$981$	2.75052e145	2.20530
$982$	−3.75626e144	−0.286648
$983$	3.00019e144	0.217923	0.108962	−	0.994046i	$-0.465247\pi$
$983$	3.00019e144	0.217923	0.108962	+	0.994046i	$0.465247\pi$
$984$	−1.26323e144	−0.0873411
$985$	1.71504e144	0.112880
$986$	−3.48873e144	−0.218593
$987$	−3.65570e145	−2.18066
$988$	2.84326e144	0.161475
$989$	3.84133e144	0.207712
$990$	−3.48405e144	−0.179382
$991$	3.64914e145	1.78903	0.894517	−	0.447034i	$-0.147520\pi$
$991$	3.64914e145	1.78903	0.894517	+	0.447034i	$0.147520\pi$
$992$	1.43287e145	0.668947
$993$	3.86788e144	0.171963
$994$	1.42175e145	0.601981
$995$	−3.85747e144	−0.155555
$996$	4.99166e145	1.91720
$997$	−3.29611e145	−1.20583	−0.602916	−	0.797804i	$-0.705995\pi$
$997$	−3.29611e145	−1.20583	−0.602916	+	0.797804i	$0.705995\pi$
$998$	1.35954e145	0.473764
$999$	−6.65492e144	−0.220910

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.98.a.a.1.3	✓	7
3.2	odd	2		9.98.a.a.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.98.a.a.1.3	✓	7	1.1	even	1	trivial
9.98.a.a.1.5		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)

\(f(q)\)	\(=\)	\(q-1.12713e14 q^{2} -2.23668e23 q^{3} -1.45752e29 q^{4} -2.02292e33 q^{5} +2.52104e37 q^{6} -1.81030e41 q^{7} +3.42884e43 q^{8} +3.09393e46 q^{9} +O(q^{10})\)	\(q-1.12713e14 q^{2} -2.23668e23 q^{3} -1.45752e29 q^{4} -2.02292e33 q^{5} +2.52104e37 q^{6} -1.81030e41 q^{7} +3.42884e43 q^{8} +3.09393e46 q^{9} +2.28010e47 q^{10} -4.93878e50 q^{11} +3.26000e52 q^{12} -3.60489e53 q^{13} +2.04045e55 q^{14} +4.52463e56 q^{15} +1.92306e58 q^{16} +4.80220e59 q^{17} -3.48727e60 q^{18} +5.41141e61 q^{19} +2.94845e62 q^{20} +4.04906e64 q^{21} +5.56667e64 q^{22} +1.09041e66 q^{23} -7.66921e66 q^{24} -5.90167e67 q^{25} +4.06320e67 q^{26} -2.65074e69 q^{27} +2.63855e70 q^{28} +6.44541e70 q^{29} -5.09986e70 q^{30} -1.88517e72 q^{31} -7.60075e72 q^{32} +1.10465e74 q^{33} -5.41273e73 q^{34} +3.66210e74 q^{35} -4.50946e75 q^{36} +2.51059e75 q^{37} -6.09938e75 q^{38} +8.06299e76 q^{39} -6.93627e76 q^{40} +1.64714e77 q^{41} -4.56384e78 q^{42} +3.52284e78 q^{43} +7.19838e79 q^{44} -6.25877e79 q^{45} -1.22903e80 q^{46} -9.02851e80 q^{47} -4.30126e81 q^{48} +2.33420e82 q^{49} +6.65197e81 q^{50} -1.07410e83 q^{51} +5.25421e82 q^{52} -1.94973e83 q^{53} +2.98774e83 q^{54} +9.99077e83 q^{55} -6.20723e84 q^{56} -1.21036e85 q^{57} -7.26484e84 q^{58} -6.91580e84 q^{59} -6.59473e85 q^{60} -4.83402e86 q^{61} +2.12484e86 q^{62} -5.60094e87 q^{63} -2.19050e87 q^{64} +7.29242e86 q^{65} -1.24509e88 q^{66} -1.63992e88 q^{67} -6.99931e88 q^{68} -2.43889e89 q^{69} -4.12768e88 q^{70} +6.96780e89 q^{71} +1.06086e90 q^{72} -1.03456e90 q^{73} -2.82977e89 q^{74} +1.32001e91 q^{75} -7.88723e90 q^{76} +8.94069e91 q^{77} -9.08808e90 q^{78} -7.68512e91 q^{79} -3.89019e91 q^{80} +2.31402e90 q^{81} -1.85655e91 q^{82} +1.53118e93 q^{83} -5.90159e93 q^{84} -9.71448e92 q^{85} -3.97072e92 q^{86} -1.44163e94 q^{87} -1.69343e94 q^{88} +6.75125e94 q^{89} +7.05448e93 q^{90} +6.52595e94 q^{91} -1.58929e95 q^{92} +4.21653e95 q^{93} +1.01763e95 q^{94} -1.09468e95 q^{95} +1.70004e96 q^{96} +1.44090e96 q^{97} -2.63096e96 q^{98} -1.52802e97 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots + 34\!\cdots\!51 q^{9}+O(q^{10}) \) 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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