LMFDB - Embedded newform 3.76.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,76,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 76, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 76);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 76 $
Character orbit:	$[\chi]$	$=$	3.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:	$106.868517847$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 47\!\cdots\!88 $ x^6 - 3x^5 - 372608135375699744498x^4 - 454191572761767684323659845174x^3 + 33507084001263083029833096962584395835741x^2 + 45298525388739530181210060025322623724413504677033*x - 471634272542661261485889811340098476257538154617268089659388
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{33}\cdot 5^{7}\cdot 7^{3}\cdot 11^{2}\cdot 13\cdot 19^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.04537e10$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.36324e11 q^{2} -4.50284e17 q^{3} -1.91947e22 q^{4} -1.63436e26 q^{5} +6.13845e28 q^{6} -2.89747e31 q^{7} +7.76687e33 q^{8} +2.02756e35 q^{9} +O(q^{10})$	\(q-1.36324e11 q^{2} -4.50284e17 q^{3} -1.91947e22 q^{4} -1.63436e26 q^{5} +6.13845e28 q^{6} -2.89747e31 q^{7} +7.76687e33 q^{8} +2.02756e35 q^{9} +2.22803e37 q^{10} +1.44670e39 q^{11} +8.64307e39 q^{12} +9.60913e40 q^{13} +3.94995e42 q^{14} +7.35928e43 q^{15} -3.33656e44 q^{16} -8.93423e45 q^{17} -2.76405e46 q^{18} +9.37755e46 q^{19} +3.13711e48 q^{20} +1.30469e49 q^{21} -1.97220e50 q^{22} -1.63263e51 q^{23} -3.49730e51 q^{24} +2.41661e50 q^{25} -1.30995e52 q^{26} -9.12976e52 q^{27} +5.56161e53 q^{28} -3.37547e53 q^{29} -1.00325e55 q^{30} +8.83397e54 q^{31} -2.47939e56 q^{32} -6.51427e56 q^{33} +1.21795e57 q^{34} +4.73553e57 q^{35} -3.89183e57 q^{36} -2.17790e58 q^{37} -1.27838e58 q^{38} -4.32684e58 q^{39} -1.26939e60 q^{40} -3.91894e60 q^{41} -1.77860e60 q^{42} +3.27056e61 q^{43} -2.77690e61 q^{44} -3.31376e61 q^{45} +2.22567e62 q^{46} -7.24595e61 q^{47} +1.50240e62 q^{48} -1.57233e63 q^{49} -3.29442e61 q^{50} +4.02294e63 q^{51} -1.84444e63 q^{52} -4.63445e64 q^{53} +1.24460e64 q^{54} -2.36444e65 q^{55} -2.25043e65 q^{56} -4.22256e64 q^{57} +4.60157e64 q^{58} +6.16990e65 q^{59} -1.41259e66 q^{60} -1.32520e67 q^{61} -1.20428e66 q^{62} -5.87479e66 q^{63} +4.64052e67 q^{64} -1.57048e67 q^{65} +8.88051e67 q^{66} -5.62035e68 q^{67} +1.71490e68 q^{68} +7.35148e68 q^{69} -6.45566e68 q^{70} +2.97582e69 q^{71} +1.57478e69 q^{72} +6.83700e69 q^{73} +2.96900e69 q^{74} -1.08816e68 q^{75} -1.79999e69 q^{76} -4.19178e70 q^{77} +5.89851e69 q^{78} -2.34135e71 q^{79} +5.45315e70 q^{80} +4.11098e70 q^{81} +5.34246e71 q^{82} -6.22883e71 q^{83} -2.50431e71 q^{84} +1.46018e72 q^{85} -4.45856e72 q^{86} +1.51992e71 q^{87} +1.12364e73 q^{88} -1.23732e72 q^{89} +4.51745e72 q^{90} -2.78422e72 q^{91} +3.13379e73 q^{92} -3.97779e72 q^{93} +9.87796e72 q^{94} -1.53263e73 q^{95} +1.11643e74 q^{96} -2.23276e74 q^{97} +2.14346e74 q^{98} +2.93327e74 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 311057037486 q^{2} - 27\!\cdots\!78 q^{3}+ \cdots + 12\!\cdots\!14 q^{9}+O(q^{10}) $ 6 * q + 311057037486 * q^2 - 2701703435345984178 * q^3 + 30902560640638265713092 * q^4 + 97856522050579947592055460 * q^5 - 140063977794078462972618149418 * q^6 - 30749202116633858714981933510688 * q^7 + 6939052769539518449811063778704312 * q^8 + 1216533575426715418239367985237722614 * q^9	$ 6 q + 311057037486 q^{2} - 27\!\cdots\!78 q^{3}+ \cdots - 76\!\cdots\!24 q^{99}+O(q^{100}) $ 6 * q + 311057037486 * q^2 - 2701703435345984178 * q^3 + 30902560640638265713092 * q^4 + 97856522050579947592055460 * q^5 - 140063977794078462972618149418 * q^6 - 30749202116633858714981933510688 * q^7 + 6939052769539518449811063778704312 * q^8 + 1216533575426715418239367985237722614 * q^9 - 107545734844341425270764823551622320620 * q^10 - 379379629646545786309015638730942099896 * q^11 - 13914925707300000018474960771518286576396 * q^12 + 154669229506479970266461340344668629154596 * q^13 + 31899227014014717498689751276506679791260128 * q^14 - 44063216965843649415864165430570914609751980 * q^15 - 3260958521390361922516104888150343171861643760 * q^16 - 7401535799877014405171685814768477775195111796 * q^17 + 63068554995747571049522875917506429627377984734 * q^18 - 182729763718938971567579921571009657209643443592 * q^19 - 9428757085683313672852247515255856540783373281640 * q^20 + 13845870832109617357675133577206423227304340315744 * q^21 + 471450583148622264812447113021812911318975285911848 * q^22 - 1094918718857791395763955497794548441629464114423696 * q^23 - 3124543784251997138778029973550539122748717548729256 * q^24 + 71600575748870708223111198803019790440272165366567850 * q^25 + 17144617795232739661292142542037336623136662115361812 * q^26 - 547785489990681667554695878527543069572161447199466882 * q^27 - 421056590097566772314387078351382806371109737989226944 * q^28 + 1286761243501908998723554437372128496488806548512006196 * q^29 + 48426113547627590272391092473373486391591403144360525060 * q^30 - 19590134983123701786508136226454400260130744726276043984 * q^31 - 405443732303791628255103774085578846894562577440580267808 * q^32 + 170828541452726656011508016173932290305101051393018574248 * q^33 + 799554727652091370833855066044541676465377828794014920924 * q^34 - 36738948500466973600844998839202990635858889677989007096000 * q^35 + 6265667097666093126364187347282208187479910552227134043748 * q^36 - 91545935905237059630111535534102037526425524589341335258828 * q^37 - 684421739975642826350565409193219733278360180645855295369576 * q^38 - 69645064783328899443381547781666897855273595262949955330348 * q^39 - 3191514246209809963152113018089087413561147078084072414179760 * q^40 - 316536315385886215170089302814500575828563777084996078443524 * q^41 - 14363708534774163874007330922786686877486530852538004495042464 * q^42 + 8908593056531100512689524294334311253125705720155921361637320 * q^43 - 21785863331670136277341155880608983152526085161022719211416784 * q^44 + 19840957441502540200289838059474939574735117137669088264028740 * q^45 + 203991825673001927929491823653549685659396184023570859282558896 * q^46 + 1142730760034072985500217886491003567898472938032199023875837760 * q^47 + 1468357139960183639245050701003384530889312785645463191005404880 * q^48 + 9932613847036662039777786400812307007669956514072280038886436470 * q^49 - 8883185004616479564484651092109548958973775099745125635626453950 * q^50 + 3332792449560669445942474443428042466743787229637394800726193948 * q^51 - 26987269348801105921073028535709825459131864700220460006411048296 * q^52 + 50865557114922724445413426425120290543311269685677591074207545764 * q^53 - 28398755282386390875875670973745277845897888210594763272248256442 * q^54 - 446272596484924291179313911709667686162610277785745256318167362640 * q^55 + 252098718314851221087836050947321657945518421301909982473468909440 * q^56 + 82280271729902900189321555309233649652586075259579233170711247896 * q^57 + 5708767830293773961786560342813586714128873252994207151314483829348 * q^58 + 2188427764336584360362109164219599664600305872173254932641215849992 * q^59 + 4245617568238899773663200034809151382019999528473811552385896315320 * q^60 + 22824130148103906081748322440858509039514053708066868437237654119460 * q^61 + 47586797873032763455450207051586846920428945648357768353569220285424 * q^62 - 6234572798744552291718025661168699069836980983012258120102491383072 * q^63 - 62277215504581285171320235502281031925680209278531250485362330807232 * q^64 - 139549609673753297396326760842807258047007635314506217050746073464360 * q^65 - 212286610014750055139927453688416335167525157803438234816067618456824 * q^66 - 195051098831763858659485315535620001296749632524239458769204357711816 * q^67 - 478898943613171780503683796705180273623444550119196454935625635754872 * q^68 + 493024277360453140561624845422921878992874641767680608467523400713648 * q^69 - 757997824979604988529186642170865717977143205307772715302146700408000 * q^70 - 3034169501204758984184273945180030994909311349950008497555595439759088 * q^71 + 1406931779300427048044368642832153219815056977181277826974271096951928 * q^72 + 13747249917875809714395686690179837721964032944309940620133405822381724 * q^73 - 2369634359974005306762628635878678463122778575706094238003611098139932 * q^74 - 32240586912245726020343673100989570820986809603159036289366132710579550 * q^75 - 34154148647149103788996774156065386764182788320537620321912800871149232 * q^76 + 110964225149010328333146128762358481438061822139163262844956857145745024 * q^77 - 7719945465845697643730248299122010768040873144728767928645236282901756 * q^78 - 201509609621708284923745260863351675377795113292036868882834678557374960 * q^79 - 422838509739279884709169464673498932712468741280281559903498362323065760 * q^80 + 246658990023417981949800521634464429457648733593148649210122936867832166 * q^81 + 1272064461032237978527479940408403539923817748343630409520994189497365644 * q^82 + 2802602491348140684813265973373777054770511234236863543486293197357747832 * q^83 + 189595005990277008686672008170141905974998639885514332207558449512548672 * q^84 - 60328702368357628714477758217500517309887606952299760526919048695903160 * q^85 + 5057125471275015782616585132644541629892966424745006584268526775897314984 * q^86 - 579407878673196333670683910868657327246273741522239483060404474475661148 * q^87 - 6621568649346448861468435905169718150646541969777165734050561367125413728 * q^88 - 159920271872091417315458194799657472188764331647019387730257248766388612 * q^89 - 21805499555346694304867032644871637074335060261296261526962295449755416780 * q^90 - 63049718267601813432671733846200700661982230139950125748195604362104533184 * q^91 - 108738058107400706863040151004186657363927160845612619833607429521300941408 * q^92 + 8821122497132808149261627688896990009380329017428740779405389519816014192 * q^93 + 197757998471403159993044858359064919780754639341995946156177159925776436032 * q^94 + 526939076500447210313077859524744124394283713808433538379475932881003671760 * q^95 + 182564787400775237004572719252266001366679249548445383992572338046761790304 * q^96 + 379948778797471041696674086463609005506560736626194774039181672927157115404 * q^97 + 1466852164333826517330437746602345292601007324558710499132638626830518086494 * q^98 - 76921342882995911525969194127663130948509562843249595589628904704987708024 * 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 $

$2$	−1.36324e11	−0.701370	−0.350685	−	0.936493i	$-0.614051\pi$
$2$	−1.36324e11	−0.701370	−0.350685	+	0.936493i	$0.614051\pi$
$3$	−4.50284e17	−0.577350
$3$	−4.50284e17	−0.577350
$4$	−1.91947e22	−0.508080
$5$	−1.63436e26	−1.00455	−0.502277	−	0.864707i	$-0.667504\pi$
$5$	−1.63436e26	−1.00455	−0.502277	+	0.864707i	$0.667504\pi$
$6$	6.13845e28	0.404936
$7$	−2.89747e31	−0.589988	−0.294994	−	0.955499i	$-0.595318\pi$
$7$	−2.89747e31	−0.589988	−0.294994	+	0.955499i	$0.595318\pi$
$8$	7.76687e33	1.05772
$9$	2.02756e35	0.333333
$10$	2.22803e37	0.704565
$11$	1.44670e39	1.28278	0.641392	−	0.767213i	$-0.278357\pi$
$11$	1.44670e39	1.28278	0.641392	+	0.767213i	$0.278357\pi$
$12$	8.64307e39	0.293340
$13$	9.60913e40	0.162109	0.0810547	−	0.996710i	$-0.474171\pi$
$13$	9.60913e40	0.162109	0.0810547	+	0.996710i	$0.474171\pi$
$14$	3.94995e42	0.413800
$15$	7.35928e43	0.579980
$16$	−3.33656e44	−0.233776
$17$	−8.93423e45	−0.644500	−0.322250	−	0.946655i	$-0.604439\pi$
$17$	−8.93423e45	−0.644500	−0.322250	+	0.946655i	$0.604439\pi$
$18$	−2.76405e46	−0.233790
$19$	9.37755e46	0.104431	0.0522155	−	0.998636i	$-0.483372\pi$
$19$	9.37755e46	0.104431	0.0522155	+	0.998636i	$0.483372\pi$
$20$	3.13711e48	0.510394
$21$	1.30469e49	0.340630
$22$	−1.97220e50	−0.899707
$23$	−1.63263e51	−1.40635	−0.703177	−	0.711015i	$-0.748236\pi$
$23$	−1.63263e51	−1.40635	−0.703177	+	0.711015i	$0.748236\pi$
$24$	−3.49730e51	−0.610676
$25$	2.41661e50	0.00912969
$26$	−1.30995e52	−0.113699
$27$	−9.12976e52	−0.192450
$28$	5.56161e53	0.299761
$29$	−3.37547e53	−0.0487988	−0.0243994	−	0.999702i	$-0.507767\pi$
$29$	−3.37547e53	−0.0487988	−0.0243994	+	0.999702i	$0.507767\pi$
$30$	−1.00325e55	−0.406781
$31$	8.83397e54	0.104735	0.0523676	−	0.998628i	$-0.483323\pi$
$31$	8.83397e54	0.104735	0.0523676	+	0.998628i	$0.483323\pi$
$32$	−2.47939e56	−0.893759
$33$	−6.51427e56	−0.740616
$34$	1.21795e57	0.452033
$35$	4.73553e57	0.592675
$36$	−3.89183e57	−0.169360
$37$	−2.17790e58	−0.339214	−0.169607	−	0.985512i	$-0.554250\pi$
$37$	−2.17790e58	−0.339214	−0.169607	+	0.985512i	$0.554250\pi$
$38$	−1.27838e58	−0.0732448
$39$	−4.32684e58	−0.0935939
$40$	−1.26939e60	−1.06254
$41$	−3.91894e60	−1.29949	−0.649747	−	0.760151i	$-0.725125\pi$
$41$	−3.91894e60	−1.29949	−0.649747	+	0.760151i	$0.725125\pi$
$42$	−1.77860e60	−0.238907
$43$	3.27056e61	1.81784	0.908918	−	0.416974i	$-0.136909\pi$
$43$	3.27056e61	1.81784	0.908918	+	0.416974i	$0.136909\pi$
$44$	−2.77690e61	−0.651756
$45$	−3.31376e61	−0.334851
$46$	2.22567e62	0.986375
$47$	−7.24595e61	−0.143359	−0.0716796	−	0.997428i	$-0.522836\pi$
$47$	−7.24595e61	−0.143359	−0.0716796	+	0.997428i	$0.522836\pi$
$48$	1.50240e62	0.134970
$49$	−1.57233e63	−0.651914
$50$	−3.29442e61	−0.00640330
$51$	4.02294e63	0.372102
$52$	−1.84444e63	−0.0823645
$53$	−4.63445e64	−1.01310	−0.506551	−	0.862210i	$-0.669080\pi$
$53$	−4.63445e64	−1.01310	−0.506551	+	0.862210i	$0.669080\pi$
$54$	1.24460e64	0.134979
$55$	−2.36444e65	−1.28863
$56$	−2.25043e65	−0.624043
$57$	−4.22256e64	−0.0602932
$58$	4.60157e64	0.0342260
$59$	6.16990e65	0.241728	0.120864	−	0.992669i	$-0.461433\pi$
$59$	6.16990e65	0.241728	0.120864	+	0.992669i	$0.461433\pi$
$60$	−1.41259e66	−0.294676
$61$	−1.32520e67	−1.48735	−0.743675	−	0.668541i	$-0.766919\pi$
$61$	−1.32520e67	−1.48735	−0.743675	+	0.668541i	$0.766919\pi$
$62$	−1.20428e66	−0.0734581
$63$	−5.87479e66	−0.196663
$64$	4.64052e67	0.860632
$65$	−1.57048e67	−0.162848
$66$	8.88051e67	0.519446
$67$	−5.62035e68	−1.87050	−0.935251	−	0.353985i	$-0.884827\pi$
$67$	−5.62035e68	−1.87050	−0.935251	+	0.353985i	$0.884827\pi$
$68$	1.71490e68	0.327457
$69$	7.35148e68	0.811959
$70$	−6.45566e68	−0.415685
$71$	2.97582e69	1.12569	0.562844	−	0.826563i	$-0.309707\pi$
$71$	2.97582e69	1.12569	0.562844	+	0.826563i	$0.309707\pi$
$72$	1.57478e69	0.352574
$73$	6.83700e69	0.912553	0.456277	−	0.889838i	$-0.349183\pi$
$73$	6.83700e69	0.912553	0.456277	+	0.889838i	$0.349183\pi$
$74$	2.96900e69	0.237915
$75$	−1.08816e68	−0.00527103
$76$	−1.79999e69	−0.0530592
$77$	−4.19178e70	−0.756827
$78$	5.89851e69	0.0656440
$79$	−2.34135e71	−1.61603	−0.808017	−	0.589160i	$-0.799459\pi$
$79$	−2.34135e71	−1.61603	−0.808017	+	0.589160i	$0.799459\pi$
$80$	5.45315e70	0.234840
$81$	4.11098e70	0.111111
$82$	5.34246e71	0.911426
$83$	−6.22883e71	−0.674494	−0.337247	−	0.941416i	$-0.609496\pi$
$83$	−6.22883e71	−0.674494	−0.337247	+	0.941416i	$0.609496\pi$
$84$	−2.50431e71	−0.173067
$85$	1.46018e72	0.647435
$86$	−4.45856e72	−1.27498
$87$	1.51992e71	0.0281740
$88$	1.12364e73	1.35683
$89$	−1.23732e72	−0.0978040	−0.0489020	−	0.998804i	$-0.515572\pi$
$89$	−1.23732e72	−0.0978040	−0.0489020	+	0.998804i	$0.515572\pi$
$90$	4.51745e72	0.234855
$91$	−2.78422e72	−0.0956426
$92$	3.13379e73	0.714540
$93$	−3.97779e72	−0.0604688
$94$	9.87796e72	0.100548
$95$	−1.53263e73	−0.104907
$96$	1.11643e74	0.516012
$97$	−2.23276e74	−0.699683	−0.349841	−	0.936809i	$-0.613764\pi$
$97$	−2.23276e74	−0.699683	−0.349841	+	0.936809i	$0.613764\pi$
$98$	2.14346e74	0.457234
$99$	2.93327e74	0.427595
$100$	−4.63861e72	−0.00463861
$101$	−3.32309e74	−0.228818	−0.114409	−	0.993434i	$-0.536497\pi$
$101$	−3.32309e74	−0.228818	−0.114409	+	0.993434i	$0.536497\pi$
$102$	−5.48423e74	−0.260981
$103$	1.06457e75	0.351382	0.175691	−	0.984445i	$-0.443784\pi$
$103$	1.06457e75	0.351382	0.175691	+	0.984445i	$0.443784\pi$
$104$	7.46329e74	0.171467
$105$	−2.13233e75	−0.342181
$106$	6.31786e75	0.710559
$107$	2.08398e76	1.64817	0.824083	−	0.566469i	$-0.191691\pi$
$107$	2.08398e76	1.64817	0.824083	+	0.566469i	$0.191691\pi$
$108$	1.75243e75	0.0977800
$109$	3.32868e76	1.31455	0.657276	−	0.753650i	$-0.271708\pi$
$109$	3.32868e76	1.31455	0.657276	+	0.753650i	$0.271708\pi$
$110$	3.22330e76	0.903805
$111$	9.80675e75	0.195845
$112$	9.66758e75	0.137925
$113$	6.55459e76	0.670044	0.335022	−	0.942210i	$-0.391256\pi$
$113$	6.55459e76	0.670044	0.335022	+	0.942210i	$0.391256\pi$
$114$	5.75636e75	0.0422879
$115$	2.66832e77	1.41276
$116$	6.47911e75	0.0247937
$117$	1.94830e76	0.0540365
$118$	−8.41106e76	−0.169541
$119$	2.58867e77	0.380247
$120$	5.71586e77	0.613458
$121$	8.21054e77	0.645536
$122$	1.80657e78	1.04318
$123$	1.76464e78	0.750263
$124$	−1.69565e77	−0.0532138
$125$	4.28663e78	0.995383
$126$	8.00875e77	0.137933
$127$	1.37949e79	1.76636	0.883182	−	0.469031i	$-0.155397\pi$
$127$	1.37949e79	1.76636	0.883182	+	0.469031i	$0.155397\pi$
$128$	3.04073e78	0.290137
$129$	−1.47268e79	−1.04953
$130$	2.14094e78	0.114217
$131$	−4.00256e79	−1.60201	−0.801004	−	0.598659i	$-0.795700\pi$
$131$	−4.00256e79	−1.60201	−0.801004	+	0.598659i	$0.795700\pi$
$132$	1.25039e79	0.376292
$133$	−2.71712e78	−0.0616130
$134$	7.66189e79	1.31192
$135$	1.49213e79	0.193327
$136$	−6.93910e79	−0.681702
$137$	−1.26017e80	−0.940607	−0.470303	−	0.882505i	$-0.655856\pi$
$137$	−1.26017e80	−0.940607	−0.470303	+	0.882505i	$0.655856\pi$
$138$	−1.00218e80	−0.569484
$139$	−3.99347e80	−1.73099	−0.865496	−	0.500915i	$-0.832997\pi$
$139$	−3.99347e80	−1.73099	−0.865496	+	0.500915i	$0.832997\pi$
$140$	−9.08970e79	−0.301126
$141$	3.26273e79	0.0827685
$142$	−4.05675e80	−0.789524
$143$	1.39016e80	0.207951
$144$	−6.76505e79	−0.0779252
$145$	5.51674e79	0.0490211
$146$	−9.32047e80	−0.640038
$147$	7.07995e80	0.376383
$148$	4.18042e80	0.172348
$149$	−3.09515e81	−0.991282	−0.495641	−	0.868527i	$-0.665067\pi$
$149$	−3.09515e81	−0.991282	−0.495641	+	0.868527i	$0.665067\pi$
$150$	1.48342e79	0.00369695
$151$	−2.63486e81	−0.511825	−0.255912	−	0.966700i	$-0.582376\pi$
$151$	−2.63486e81	−0.511825	−0.255912	+	0.966700i	$0.582376\pi$
$152$	7.28342e80	0.110459
$153$	−1.81147e81	−0.214833
$154$	5.71441e81	0.530816
$155$	−1.44379e81	−0.105212
$156$	8.30523e80	0.0475532
$157$	−2.59809e82	−1.17062	−0.585311	−	0.810809i	$-0.699028\pi$
$157$	−2.59809e82	−1.17062	−0.585311	+	0.810809i	$0.699028\pi$
$158$	3.19182e82	1.13344
$159$	2.08682e82	0.584914
$160$	4.05222e82	0.897830
$161$	4.73051e82	0.829732
$162$	−5.60426e81	−0.0779300
$163$	−1.56476e82	−0.172748	−0.0863739	−	0.996263i	$-0.527528\pi$
$163$	−1.56476e82	−0.172748	−0.0863739	+	0.996263i	$0.527528\pi$
$164$	7.52229e82	0.660246
$165$	1.06467e83	0.743989
$166$	8.49139e82	0.473070
$167$	4.05246e83	1.80240	0.901200	−	0.433404i	$-0.142688\pi$
$167$	4.05246e83	1.80240	0.901200	+	0.433404i	$0.142688\pi$
$168$	1.01333e83	0.360292
$169$	−3.42126e83	−0.973721
$170$	−1.99057e83	−0.454092
$171$	1.90135e82	0.0348103
$172$	−6.27774e83	−0.923606
$173$	−7.17523e83	−0.849390	−0.424695	−	0.905336i	$-0.639619\pi$
$173$	−7.17523e83	−0.849390	−0.424695	+	0.905336i	$0.639619\pi$
$174$	−2.07201e82	−0.0197604
$175$	−7.00206e81	−0.00538641
$176$	−4.82701e83	−0.299884
$177$	−2.77821e83	−0.139562
$178$	1.68676e83	0.0685969
$179$	−5.67455e83	−0.187044	−0.0935218	−	0.995617i	$-0.529812\pi$
$179$	−5.67455e83	−0.187044	−0.0935218	+	0.995617i	$0.529812\pi$
$180$	6.36067e83	0.170131
$181$	−6.33746e84	−1.37711	−0.688555	−	0.725184i	$-0.741755\pi$
$181$	−6.33746e84	−1.37711	−0.688555	+	0.725184i	$0.741755\pi$
$182$	3.79556e83	0.0670809
$183$	5.96717e84	0.858722
$184$	−1.26805e85	−1.48753
$185$	3.55949e84	0.340759
$186$	5.42269e83	0.0424111
$187$	−1.29252e85	−0.826754
$188$	1.39084e84	0.0728379
$189$	2.64532e84	0.113543
$190$	2.08935e84	0.0735784
$191$	−3.24072e83	−0.00937325	−0.00468663	−	0.999989i	$-0.501492\pi$
$191$	−3.24072e83	−0.00937325	−0.00468663	+	0.999989i	$0.501492\pi$
$192$	−2.08955e85	−0.496886
$193$	2.52091e85	0.493354	0.246677	−	0.969098i	$-0.420661\pi$
$193$	2.52091e85	0.493354	0.246677	+	0.969098i	$0.420661\pi$
$194$	3.04378e85	0.490737
$195$	7.07162e84	0.0940202
$196$	3.01804e85	0.331224
$197$	5.95564e85	0.540064	0.270032	−	0.962851i	$-0.412966\pi$
$197$	5.95564e85	0.540064	0.270032	+	0.962851i	$0.412966\pi$
$198$	−3.99875e85	−0.299902
$199$	1.15783e86	0.718874	0.359437	−	0.933169i	$-0.382969\pi$
$199$	1.15783e86	0.718874	0.359437	+	0.933169i	$0.382969\pi$
$200$	1.87695e84	0.00965668
$201$	2.53075e86	1.07994
$202$	4.53017e85	0.160486
$203$	9.78033e84	0.0287907
$204$	−7.72192e85	−0.189057
$205$	6.40498e86	1.30541
$206$	−1.45127e86	−0.246449
$207$	−3.31025e86	−0.468785
$208$	−3.20614e85	−0.0378972
$209$	1.35665e86	0.133962
$210$	2.90688e86	0.239996
$211$	−4.43104e85	−0.0306136	−0.0153068	−	0.999883i	$-0.504872\pi$
$211$	−4.43104e85	−0.0306136	−0.0153068	+	0.999883i	$0.504872\pi$
$212$	8.89569e86	0.514736
$213$	−1.33996e87	−0.649916
$214$	−2.84096e87	−1.15598
$215$	−5.34528e87	−1.82612
$216$	−7.09097e86	−0.203559
$217$	−2.55962e86	−0.0617924
$218$	−4.53779e87	−0.921989
$219$	−3.07859e87	−0.526863
$220$	4.53847e87	0.654725
$221$	−8.58502e86	−0.104479
$222$	−1.33689e87	−0.137360
$223$	1.19694e88	1.03906	0.519529	−	0.854453i	$-0.326107\pi$
$223$	1.19694e88	1.03906	0.519529	+	0.854453i	$0.326107\pi$
$224$	7.18396e87	0.527307
$225$	4.89981e85	0.00304323
$226$	−8.93547e87	−0.469949
$227$	1.46521e88	0.653027	0.326514	−	0.945193i	$-0.394126\pi$
$227$	1.46521e88	0.653027	0.326514	+	0.945193i	$0.394126\pi$
$228$	8.10508e86	0.0306338
$229$	8.96828e86	0.0287659	0.0143830	−	0.999897i	$-0.495422\pi$
$229$	8.96828e86	0.0287659	0.0143830	+	0.999897i	$0.495422\pi$
$230$	−3.63755e88	−0.990868
$231$	1.88749e88	0.436954
$232$	−2.62168e87	−0.0516156
$233$	6.47963e88	1.08568	0.542841	−	0.839835i	$-0.317348\pi$
$233$	6.47963e88	1.08568	0.542841	+	0.839835i	$0.317348\pi$
$234$	−2.65601e87	−0.0378996
$235$	1.18425e88	0.144012
$236$	−1.18429e88	−0.122817
$237$	1.05427e89	0.933017
$238$	−3.52898e88	−0.266694
$239$	1.69913e89	1.09725	0.548626	−	0.836068i	$-0.315151\pi$
$239$	1.69913e89	1.09725	0.548626	+	0.836068i	$0.315151\pi$
$240$	−2.45546e88	−0.135585
$241$	−7.77008e88	−0.367102	−0.183551	−	0.983010i	$-0.558759\pi$
$241$	−7.77008e88	−0.367102	−0.183551	+	0.983010i	$0.558759\pi$
$242$	−1.11929e89	−0.452760
$243$	−1.85111e88	−0.0641500
$244$	2.54369e89	0.755693
$245$	2.56976e89	0.654884
$246$	−2.40562e89	−0.526212
$247$	9.01100e87	0.0169292
$248$	6.86123e88	0.110781
$249$	2.80474e89	0.389419
$250$	−5.84370e89	−0.698132
$251$	−1.56178e89	−0.160641	−0.0803203	−	0.996769i	$-0.525594\pi$
$251$	−1.56178e89	−0.160641	−0.0803203	+	0.996769i	$0.525594\pi$
$252$	1.12765e89	0.0999202
$253$	−2.36193e90	−1.80405
$254$	−1.88058e90	−1.23888
$255$	−6.57495e89	−0.373797
$256$	−2.16766e90	−1.06413
$257$	9.67526e89	0.410365	0.205183	−	0.978724i	$-0.434221\pi$
$257$	9.67526e89	0.410365	0.205183	+	0.978724i	$0.434221\pi$
$258$	2.00762e90	0.736108
$259$	6.31042e89	0.200132
$260$	3.01449e89	0.0827396
$261$	−6.84395e88	−0.0162663
$262$	5.45645e90	1.12360
$263$	−6.00238e90	−1.07148	−0.535739	−	0.844384i	$-0.679967\pi$
$263$	−6.00238e90	−1.07148	−0.535739	+	0.844384i	$0.679967\pi$
$264$	−5.05955e90	−0.783366
$265$	7.57437e90	1.01772
$266$	3.70409e89	0.0432135
$267$	5.57145e89	0.0564672
$268$	1.07881e91	0.950364
$269$	1.86211e91	1.42658	0.713288	−	0.700871i	$-0.247205\pi$
$269$	1.86211e91	1.42658	0.713288	+	0.700871i	$0.247205\pi$
$270$	−2.03414e90	−0.135594
$271$	−7.82901e90	−0.454317	−0.227158	−	0.973858i	$-0.572943\pi$
$271$	−7.82901e90	−0.454317	−0.227158	+	0.973858i	$0.572943\pi$
$272$	2.98096e90	0.150668
$273$	1.25369e90	0.0552193
$274$	1.71791e91	0.659714
$275$	3.49612e89	0.0117114
$276$	−1.41110e91	−0.412540
$277$	1.31640e91	0.336044	0.168022	−	0.985783i	$-0.446262\pi$
$277$	1.31640e91	0.336044	0.168022	+	0.985783i	$0.446262\pi$
$278$	5.44405e91	1.21407
$279$	1.79114e90	0.0349117
$280$	3.67802e91	0.626885
$281$	−1.02015e92	−1.52117	−0.760585	−	0.649238i	$-0.775088\pi$
$281$	−1.02015e92	−1.52117	−0.760585	+	0.649238i	$0.775088\pi$
$282$	−4.44789e90	−0.0580513
$283$	−1.27556e92	−1.45784	−0.728918	−	0.684601i	$-0.759977\pi$
$283$	−1.27556e92	−1.45784	−0.728918	+	0.684601i	$0.759977\pi$
$284$	−5.71199e91	−0.571939
$285$	6.90120e90	0.0605678
$286$	−1.89511e91	−0.145851
$287$	1.13550e92	0.766685
$288$	−5.02710e91	−0.297920
$289$	−1.12342e92	−0.584620
$290$	−7.52064e90	−0.0343819
$291$	1.00537e92	0.403962
$292$	−1.31234e92	−0.463650
$293$	1.24720e92	0.387616	0.193808	−	0.981040i	$-0.437916\pi$
$293$	1.24720e92	0.387616	0.193808	+	0.981040i	$0.437916\pi$
$294$	−9.65167e91	−0.263984
$295$	−1.00839e92	−0.242829
$296$	−1.69155e92	−0.358794
$297$	−1.32080e92	−0.246872
$298$	4.21944e92	0.695256
$299$	−1.56882e92	−0.227983
$300$	2.08869e90	0.00267810
$301$	−9.47636e92	−1.07250
$302$	3.59194e92	0.358979
$303$	1.49633e92	0.132108
$304$	−3.12887e91	−0.0244134
$305$	2.16586e93	1.49412
$306$	2.46946e92	0.150678
$307$	−2.28013e93	−1.23103	−0.615517	−	0.788124i	$-0.711053\pi$
$307$	−2.28013e93	−1.23103	−0.615517	+	0.788124i	$0.711053\pi$
$308$	8.04600e92	0.384528
$309$	−4.79360e92	−0.202870
$310$	1.96823e92	0.0737927
$311$	5.91495e93	1.96533	0.982667	−	0.185377i	$-0.0593506\pi$
$311$	5.91495e93	1.96533	0.982667	+	0.185377i	$0.0593506\pi$
$312$	−3.36060e92	−0.0989964
$313$	3.24737e93	0.848435	0.424217	−	0.905560i	$-0.360549\pi$
$313$	3.24737e93	0.848435	0.424217	+	0.905560i	$0.360549\pi$
$314$	3.54182e93	0.821040
$315$	9.60154e92	0.197558
$316$	4.49415e93	0.821074
$317$	−3.51022e93	−0.569656	−0.284828	−	0.958579i	$-0.591936\pi$
$317$	−3.51022e93	−0.569656	−0.284828	+	0.958579i	$0.591936\pi$
$318$	−2.84483e93	−0.410242
$319$	−4.88330e92	−0.0625983
$320$	−7.58429e93	−0.864551
$321$	−9.38381e93	−0.951569
$322$	−6.44882e93	−0.581949
$323$	−8.37812e92	−0.0673057
$324$	−7.89091e92	−0.0564533
$325$	2.32215e91	0.00148001
$326$	2.13314e93	0.121160
$327$	−1.49885e94	−0.758957
$328$	−3.04379e94	−1.37450
$329$	2.09949e93	0.0845802
$330$	−1.45140e94	−0.521812
$331$	2.82757e94	0.907535	0.453768	−	0.891120i	$-0.350080\pi$
$331$	2.82757e94	0.907535	0.453768	+	0.891120i	$0.350080\pi$
$332$	1.19561e94	0.342697
$333$	−4.41582e93	−0.113071
$334$	−5.52448e94	−1.26415
$335$	9.18570e94	1.87902
$336$	−4.35316e93	−0.0796309
$337$	−5.46996e94	−0.895083	−0.447541	−	0.894263i	$-0.647700\pi$
$337$	−5.46996e94	−0.895083	−0.447541	+	0.894263i	$0.647700\pi$
$338$	4.66399e94	0.682939
$339$	−2.95142e94	−0.386850
$340$	−2.80277e94	−0.328949
$341$	1.27801e94	0.134353
$342$	−2.59200e93	−0.0244149
$343$	1.15441e95	0.974609
$344$	2.54020e95	1.92277
$345$	−1.20150e95	−0.815657
$346$	9.78157e94	0.595737
$347$	5.97610e94	0.326635	0.163317	−	0.986574i	$-0.447781\pi$
$347$	5.97610e94	0.326635	0.163317	+	0.986574i	$0.447781\pi$
$348$	−2.91744e93	−0.0143146
$349$	−1.08936e95	−0.479976	−0.239988	−	0.970776i	$-0.577143\pi$
$349$	−1.08936e95	−0.479976	−0.239988	+	0.970776i	$0.577143\pi$
$350$	9.54549e92	0.00377787
$351$	−8.77290e93	−0.0311980
$352$	−3.58694e95	−1.14650
$353$	6.06657e95	1.74338	0.871689	−	0.490059i	$-0.163025\pi$
$353$	6.06657e95	1.74338	0.871689	+	0.490059i	$0.163025\pi$
$354$	3.78736e94	0.0978847
$355$	−4.86357e95	−1.13082
$356$	2.37500e94	0.0496922
$357$	−1.16564e95	−0.219536
$358$	7.73577e94	0.131187
$359$	1.04798e96	1.60070	0.800351	−	0.599531i	$-0.204646\pi$
$359$	1.04798e96	1.60070	0.800351	+	0.599531i	$0.204646\pi$
$360$	−2.57376e95	−0.354180
$361$	−7.97550e95	−0.989094
$362$	8.63948e95	0.965865
$363$	−3.69707e95	−0.372700
$364$	5.34423e94	0.0485940
$365$	−1.11741e96	−0.916709
$366$	−8.13469e95	−0.602282
$367$	−2.09821e96	−1.40240	−0.701198	−	0.712967i	$-0.747351\pi$
$367$	−2.09821e96	−1.40240	−0.701198	+	0.712967i	$0.747351\pi$
$368$	5.44737e95	0.328771
$369$	−7.94587e95	−0.433165
$370$	−4.85243e95	−0.238998
$371$	1.34282e96	0.597717
$372$	7.63526e94	0.0307230
$373$	−1.11924e95	−0.0407232	−0.0203616	−	0.999793i	$-0.506482\pi$
$373$	−1.11924e95	−0.0407232	−0.0203616	+	0.999793i	$0.506482\pi$
$374$	1.76201e96	0.579861
$375$	−1.93020e96	−0.574685
$376$	−5.62783e95	−0.151634
$377$	−3.24353e94	−0.00791075
$378$	−3.60621e95	−0.0796358
$379$	4.19285e96	0.838570	0.419285	−	0.907855i	$-0.362281\pi$
$379$	4.19285e96	0.838570	0.419285	+	0.907855i	$0.362281\pi$
$380$	2.94184e95	0.0533009
$381$	−6.21164e96	−1.01981
$382$	4.41788e94	0.00657412
$383$	4.37123e96	0.589726	0.294863	−	0.955540i	$-0.404726\pi$
$383$	4.37123e96	0.589726	0.294863	+	0.955540i	$0.404726\pi$
$384$	−1.36919e96	−0.167511
$385$	6.85090e96	0.760274
$386$	−3.43661e96	−0.346024
$387$	6.63124e96	0.605946
$388$	4.28571e96	0.355494
$389$	2.04350e97	1.53909	0.769546	−	0.638592i	$-0.220483\pi$
$389$	2.04350e97	1.53909	0.769546	+	0.638592i	$0.220483\pi$
$390$	−9.64032e95	−0.0659430
$391$	1.45863e97	0.906395
$392$	−1.22121e97	−0.689545
$393$	1.80229e97	0.924920
$394$	−8.11896e96	−0.378785
$395$	3.82662e97	1.62339
$396$	−5.63033e96	−0.217252
$397$	−5.19135e97	−1.82237	−0.911185	−	0.411998i	$-0.864831\pi$
$397$	−5.19135e97	−1.82237	−0.911185	+	0.411998i	$0.864831\pi$
$398$	−1.57839e97	−0.504197
$399$	1.22348e96	0.0355723
$400$	−8.06316e94	−0.00213430
$401$	−6.90014e97	−1.66320	−0.831599	−	0.555376i	$-0.812574\pi$
$401$	−6.90014e97	−1.66320	−0.831599	+	0.555376i	$0.812574\pi$
$402$	−3.45002e97	−0.757435
$403$	8.48867e95	0.0169785
$404$	6.37857e96	0.116258
$405$	−6.71884e96	−0.111617
$406$	−1.33329e96	−0.0201929
$407$	−3.15078e97	−0.435138
$408$	3.12457e97	0.393581
$409$	−2.82660e97	−0.324818	−0.162409	−	0.986724i	$-0.551926\pi$
$409$	−2.82660e97	−0.324818	−0.162409	+	0.986724i	$0.551926\pi$
$410$	−8.73152e97	−0.915578
$411$	5.67435e97	0.543060
$412$	−2.04341e97	−0.178530
$413$	−1.78771e97	−0.142617
$414$	4.51267e97	0.328792
$415$	1.01802e98	0.677566
$416$	−2.38248e97	−0.144887
$417$	1.79819e98	0.999389
$418$	−1.84944e97	−0.0939572
$419$	−1.43283e98	−0.665529	−0.332765	−	0.943010i	$-0.607982\pi$
$419$	−1.43283e98	−0.665529	−0.332765	+	0.943010i	$0.607982\pi$
$420$	4.09295e97	0.173855
$421$	2.88040e98	1.11912	0.559558	−	0.828791i	$-0.310971\pi$
$421$	2.88040e98	1.11912	0.559558	+	0.828791i	$0.310971\pi$
$422$	6.04058e96	0.0214715
$423$	−1.46916e97	−0.0477864
$424$	−3.59952e98	−1.07158
$425$	−2.15906e96	−0.00588408
$426$	1.82669e98	0.455832
$427$	3.83974e98	0.877519
$428$	−4.00013e98	−0.837400
$429$	−6.25964e97	−0.120061
$430$	7.28690e98	1.28078
$431$	−5.28696e98	−0.851743	−0.425872	−	0.904784i	$-0.640032\pi$
$431$	−5.28696e98	−0.851743	−0.425872	+	0.904784i	$0.640032\pi$
$432$	3.04620e97	0.0449901
$433$	1.28454e99	1.73961	0.869806	−	0.493393i	$-0.164244\pi$
$433$	1.28454e99	1.73961	0.869806	+	0.493393i	$0.164244\pi$
$434$	3.48937e97	0.0433394
$435$	−2.48410e97	−0.0283023
$436$	−6.38930e98	−0.667897
$437$	−1.53101e98	−0.146867
$438$	4.19686e98	0.369526
$439$	1.03723e99	0.838411	0.419206	−	0.907891i	$-0.362309\pi$
$439$	1.03723e99	0.838411	0.419206	+	0.907891i	$0.362309\pi$
$440$	−1.83643e99	−1.36301
$441$	−3.18799e98	−0.217305
$442$	1.17034e98	0.0732788
$443$	5.12456e98	0.294793	0.147396	−	0.989077i	$-0.452911\pi$
$443$	5.12456e98	0.294793	0.147396	+	0.989077i	$0.452911\pi$
$444$	−1.88238e98	−0.0995050
$445$	2.02223e98	0.0982495
$446$	−1.63172e99	−0.728764
$447$	1.39370e99	0.572317
$448$	−1.34458e99	−0.507762
$449$	−2.33920e99	−0.812510	−0.406255	−	0.913760i	$-0.633166\pi$
$449$	−2.33920e99	−0.812510	−0.406255	+	0.913760i	$0.633166\pi$
$450$	−6.67962e96	−0.00213443
$451$	−5.66954e99	−1.66697
$452$	−1.25813e99	−0.340436
$453$	1.18643e99	0.295502
$454$	−1.99744e99	−0.458014
$455$	4.55043e98	0.0960782
$456$	−3.27961e98	−0.0637735
$457$	1.04972e100	1.88025	0.940124	−	0.340833i	$-0.110709\pi$
$457$	1.04972e100	1.88025	0.940124	+	0.340833i	$0.110709\pi$
$458$	−1.22259e98	−0.0201756
$459$	8.15674e98	0.124034
$460$	−5.12175e99	−0.717794
$461$	3.80856e99	0.492013	0.246006	−	0.969268i	$-0.420882\pi$
$461$	3.80856e99	0.492013	0.246006	+	0.969268i	$0.420882\pi$
$462$	−2.57310e99	−0.306467
$463$	−3.55590e99	−0.390537	−0.195268	−	0.980750i	$-0.562558\pi$
$463$	−3.55590e99	−0.390537	−0.195268	+	0.980750i	$0.562558\pi$
$464$	1.12624e98	0.0114080
$465$	6.50116e98	0.0607443
$466$	−8.83328e99	−0.761466
$467$	1.90689e100	1.51685	0.758424	−	0.651761i	$-0.225970\pi$
$467$	1.90689e100	1.51685	0.758424	+	0.651761i	$0.225970\pi$
$468$	−3.73971e98	−0.0274548
$469$	1.62848e100	1.10357
$470$	−1.61442e99	−0.101006
$471$	1.16988e100	0.675859
$472$	4.79208e99	0.255682
$473$	4.73153e100	2.33189
$474$	−1.43723e100	−0.654391
$475$	2.26619e97	0.000953423 0
$476$	−4.96888e99	−0.193196
$477$	−9.39660e99	−0.337701
$478$	−2.31633e100	−0.769579
$479$	−3.04388e98	−0.00935075	−0.00467537	−	0.999989i	$-0.501488\pi$
$479$	−3.04388e98	−0.00935075	−0.00467537	+	0.999989i	$0.501488\pi$
$480$	−1.82465e100	−0.518362
$481$	−2.09277e99	−0.0549898
$482$	1.05925e100	0.257474
$483$	−2.13007e100	−0.479046
$484$	−1.57599e100	−0.327983
$485$	3.64913e100	0.702869
$486$	2.52351e99	0.0449929
$487$	−6.85804e100	−1.13205	−0.566023	−	0.824389i	$-0.691519\pi$
$487$	−6.85804e100	−1.13205	−0.566023	+	0.824389i	$0.691519\pi$
$488$	−1.02927e101	−1.57320
$489$	7.04587e99	0.0997360
$490$	−3.50320e100	−0.459316
$491$	1.01875e101	1.23741	0.618703	−	0.785625i	$-0.287659\pi$
$491$	1.01875e101	1.23741	0.618703	+	0.785625i	$0.287659\pi$
$492$	−3.38717e100	−0.381193
$493$	3.01572e99	0.0314508
$494$	−1.22842e99	−0.0118737
$495$	−4.79403e100	−0.429542
$496$	−2.94750e99	−0.0244845
$497$	−8.62235e100	−0.664142
$498$	−3.82354e100	−0.273127
$499$	2.10589e101	1.39529	0.697645	−	0.716444i	$-0.254231\pi$
$499$	2.10589e101	1.39529	0.697645	+	0.716444i	$0.254231\pi$
$500$	−8.22806e100	−0.505734
$501$	−1.82476e101	−1.04062
$502$	2.12908e100	0.112669
$503$	3.15449e101	1.54928	0.774639	−	0.632403i	$-0.217931\pi$
$503$	3.15449e101	1.54928	0.774639	+	0.632403i	$0.217931\pi$
$504$	−4.56287e100	−0.208014
$505$	5.43114e100	0.229860
$506$	3.21988e101	1.26531
$507$	1.54054e101	0.562178
$508$	−2.64790e101	−0.897453
$509$	1.67930e101	0.528702	0.264351	−	0.964427i	$-0.414842\pi$
$509$	1.67930e101	0.528702	0.264351	+	0.964427i	$0.414842\pi$
$510$	8.96323e100	0.262170
$511$	−1.98100e101	−0.538395
$512$	1.80629e101	0.456209
$513$	−8.56147e99	−0.0200977
$514$	−1.31897e101	−0.287818
$515$	−1.73990e101	−0.352982
$516$	2.82677e101	0.533244
$517$	−1.04827e101	−0.183899
$518$	−8.60261e100	−0.140367
$519$	3.23089e101	0.490396
$520$	−1.21977e101	−0.172248
$521$	−8.36796e101	−1.09953	−0.549763	−	0.835321i	$-0.685282\pi$
$521$	−8.36796e101	−1.09953	−0.549763	+	0.835321i	$0.685282\pi$
$522$	9.32995e99	0.0114087
$523$	4.34684e101	0.494721	0.247361	−	0.968924i	$-0.420437\pi$
$523$	4.34684e101	0.494721	0.247361	+	0.968924i	$0.420437\pi$
$524$	7.68280e101	0.813947
$525$	3.15292e99	0.00310984
$526$	8.18268e101	0.751502
$527$	−7.89247e100	−0.0675017
$528$	2.17352e101	0.173138
$529$	1.31781e102	0.977832
$530$	−1.03257e102	−0.713796
$531$	1.25098e101	0.0805762
$532$	5.21543e100	0.0313043
$533$	−3.76576e101	−0.210660
$534$	−7.59523e100	−0.0396044
$535$	−3.40597e102	−1.65567
$536$	−4.36525e102	−1.97847
$537$	2.55516e101	0.107990
$538$	−2.53850e102	−1.00056
$539$	−2.27469e102	−0.836266
$540$	−2.86411e101	−0.0982253
$541$	3.45942e102	1.10689	0.553446	−	0.832885i	$-0.313312\pi$
$541$	3.45942e102	1.10689	0.553446	+	0.832885i	$0.313312\pi$
$542$	1.06728e102	0.318644
$543$	2.85366e102	0.795075
$544$	2.21514e102	0.576027
$545$	−5.44027e102	−1.32054
$546$	−1.70908e101	−0.0387292
$547$	1.89582e102	0.401118	0.200559	−	0.979682i	$-0.435724\pi$
$547$	1.89582e102	0.401118	0.200559	+	0.979682i	$0.435724\pi$
$548$	2.41886e102	0.477903
$549$	−2.68692e102	−0.495784
$550$	−4.76605e100	−0.00821405
$551$	−3.16536e100	−0.00509611
$552$	5.70980e102	0.858827
$553$	6.78400e102	0.953440
$554$	−1.79457e102	−0.235691
$555$	−1.60278e102	−0.196737
$556$	7.66534e102	0.879482
$557$	4.96751e102	0.532806	0.266403	−	0.963862i	$-0.414165\pi$
$557$	4.96751e102	0.532806	0.266403	+	0.963862i	$0.414165\pi$
$558$	−2.44175e101	−0.0244860
$559$	3.14272e102	0.294688
$560$	−1.58003e102	−0.138553
$561$	5.82000e102	0.477327
$562$	1.39071e103	1.06690
$563$	−1.58529e103	−1.13774	−0.568871	−	0.822426i	$-0.692620\pi$
$563$	−1.58529e103	−1.13774	−0.568871	+	0.822426i	$0.692620\pi$
$564$	−6.26272e101	−0.0420530
$565$	−1.07126e103	−0.673096
$566$	1.73889e103	1.02248
$567$	−1.19115e102	−0.0655542
$568$	2.31128e103	1.19067
$569$	−1.62497e103	−0.783676	−0.391838	−	0.920034i	$-0.628161\pi$
$569$	−1.62497e103	−0.783676	−0.391838	+	0.920034i	$0.628161\pi$
$570$	−9.40798e101	−0.0424805
$571$	−3.42032e103	−1.44615	−0.723073	−	0.690771i	$-0.757271\pi$
$571$	−3.42032e103	−1.44615	−0.723073	+	0.690771i	$0.757271\pi$
$572$	−2.66836e102	−0.105656
$573$	1.45924e101	0.00541165
$574$	−1.54796e103	−0.537730
$575$	−3.94544e101	−0.0128396
$576$	9.40891e102	0.286877
$577$	−4.48593e103	−1.28162	−0.640810	−	0.767699i	$-0.721401\pi$
$577$	−4.48593e103	−1.28162	−0.640810	+	0.767699i	$0.721401\pi$
$578$	1.53149e103	0.410035
$579$	−1.13513e103	−0.284838
$580$	−1.05892e102	−0.0249066
$581$	1.80479e103	0.397943
$582$	−1.37057e103	−0.283327
$583$	−6.70467e103	−1.29959
$584$	5.31021e103	0.965228
$585$	−3.18424e102	−0.0542826
$586$	−1.70024e103	−0.271862
$587$	−3.55089e103	−0.532608	−0.266304	−	0.963889i	$-0.585803\pi$
$587$	−3.55089e103	−0.532608	−0.266304	+	0.963889i	$0.585803\pi$
$588$	−1.35897e103	−0.191233
$589$	8.28410e101	0.0109376
$590$	1.37467e103	0.170313
$591$	−2.68173e103	−0.311806
$592$	7.26670e102	0.0793000
$593$	1.59905e104	1.63799	0.818997	−	0.573798i	$-0.194531\pi$
$593$	1.59905e104	1.63799	0.818997	+	0.573798i	$0.194531\pi$
$594$	1.80057e103	0.173149
$595$	−4.23083e103	−0.381979
$596$	5.94106e103	0.503650
$597$	−5.21350e103	−0.415042
$598$	2.13867e103	0.159901
$599$	5.48681e102	0.0385313	0.0192657	−	0.999814i	$-0.493867\pi$
$599$	5.48681e102	0.0385313	0.0192657	+	0.999814i	$0.493867\pi$
$600$	−8.45160e101	−0.00557529
$601$	1.92882e104	1.19536	0.597682	−	0.801734i	$-0.296089\pi$
$601$	1.92882e104	1.19536	0.597682	+	0.801734i	$0.296089\pi$
$602$	1.29185e104	0.752221
$603$	−1.13956e104	−0.623501
$604$	5.05753e103	0.260048
$605$	−1.34190e104	−0.648476
$606$	−2.03986e103	−0.0926568
$607$	2.00718e104	0.857060	0.428530	−	0.903528i	$-0.359032\pi$
$607$	2.00718e104	0.857060	0.428530	+	0.903528i	$0.359032\pi$
$608$	−2.32506e103	−0.0933361
$609$	−4.40393e102	−0.0166223
$610$	−2.95259e104	−1.04793
$611$	−6.96272e102	−0.0232399
$612$	3.47705e103	0.109152
$613$	1.72392e104	0.509038	0.254519	−	0.967068i	$-0.418083\pi$
$613$	1.72392e104	0.509038	0.254519	+	0.967068i	$0.418083\pi$
$614$	3.10836e104	0.863411
$615$	−2.88406e104	−0.753680
$616$	−3.25570e104	−0.800513
$617$	4.11327e104	0.951686	0.475843	−	0.879530i	$-0.342143\pi$
$617$	4.11327e104	0.951686	0.475843	+	0.879530i	$0.342143\pi$
$618$	6.53482e103	0.142287
$619$	3.92783e104	0.804921	0.402461	−	0.915437i	$-0.368155\pi$
$619$	3.92783e104	0.804921	0.402461	+	0.915437i	$0.368155\pi$
$620$	2.77132e103	0.0534561
$621$	1.49055e104	0.270653
$622$	−8.06350e104	−1.37843
$623$	3.58510e103	0.0577032
$624$	1.44367e103	0.0218800
$625$	−7.06988e104	−1.00905
$626$	−4.42694e104	−0.595067
$627$	−6.10879e103	−0.0773432
$628$	4.98695e104	0.594769
$629$	1.94579e104	0.218623
$630$	−1.30892e104	−0.138562
$631$	7.31015e104	0.729164	0.364582	−	0.931171i	$-0.381212\pi$
$631$	7.31015e104	0.729164	0.364582	+	0.931171i	$0.381212\pi$
$632$	−1.81850e105	−1.70931
$633$	1.99523e103	0.0176748
$634$	4.78528e104	0.399540
$635$	−2.25459e105	−1.77441
$636$	−4.00558e104	−0.297183
$637$	−1.51087e104	−0.105681
$638$	6.65711e103	0.0439046
$639$	6.03363e104	0.375229
$640$	−4.96966e104	−0.291459
$641$	9.90726e104	0.547996	0.273998	−	0.961730i	$-0.411654\pi$
$641$	9.90726e104	0.547996	0.273998	+	0.961730i	$0.411654\pi$
$642$	1.27924e105	0.667402
$643$	−1.31331e105	−0.646330	−0.323165	−	0.946343i	$-0.604747\pi$
$643$	−1.31331e105	−0.646330	−0.323165	+	0.946343i	$0.604747\pi$
$644$	−9.08008e104	−0.421570
$645$	2.40689e105	1.05431
$646$	1.14214e104	0.0472062
$647$	4.22887e105	1.64935	0.824677	−	0.565603i	$-0.191357\pi$
$647$	4.22887e105	1.64935	0.824677	+	0.565603i	$0.191357\pi$
$648$	3.19295e104	0.117525
$649$	8.92601e104	0.310086
$650$	−3.16565e102	−0.00103803
$651$	1.15256e104	0.0356759
$652$	3.00351e104	0.0877697
$653$	−3.93358e105	−1.08528	−0.542642	−	0.839964i	$-0.682576\pi$
$653$	−3.93358e105	−1.08528	−0.542642	+	0.839964i	$0.682576\pi$
$654$	2.04329e105	0.532310
$655$	6.54164e105	1.60930
$656$	1.30758e105	0.303790
$657$	1.38624e105	0.304184
$658$	−2.86211e104	−0.0593220
$659$	−1.56776e105	−0.306956	−0.153478	−	0.988152i	$-0.549047\pi$
$659$	−1.56776e105	−0.306956	−0.153478	+	0.988152i	$0.549047\pi$
$660$	−2.04360e105	−0.378006
$661$	1.00104e106	1.74942	0.874712	−	0.484644i	$-0.161051\pi$
$661$	1.00104e106	1.74942	0.874712	+	0.484644i	$0.161051\pi$
$662$	−3.85466e105	−0.636518
$663$	3.86570e104	0.0603212
$664$	−4.83785e105	−0.713427
$665$	4.44076e104	0.0618936
$666$	6.01982e104	0.0793049
$667$	5.51090e104	0.0686284
$668$	−7.77858e105	−0.915762
$669$	−5.38962e105	−0.599900
$670$	−1.25223e106	−1.31789
$671$	−1.91717e106	−1.90795
$672$	−3.23482e105	−0.304441
$673$	−1.92039e105	−0.170932	−0.0854662	−	0.996341i	$-0.527238\pi$
$673$	−1.92039e105	−0.170932	−0.0854662	+	0.996341i	$0.527238\pi$
$674$	7.45687e105	0.627784
$675$	−2.20631e103	−0.00175701
$676$	6.56700e105	0.494728
$677$	5.57940e104	0.0397660	0.0198830	−	0.999802i	$-0.493671\pi$
$677$	5.57940e104	0.0397660	0.0198830	+	0.999802i	$0.493671\pi$
$678$	4.02350e105	0.271325
$679$	6.46935e105	0.412804
$680$	1.13410e106	0.684806
$681$	−6.59762e105	−0.377025
$682$	−1.74224e105	−0.0942309
$683$	2.64233e105	0.135273	0.0676364	−	0.997710i	$-0.478454\pi$
$683$	2.64233e105	0.135273	0.0676364	+	0.997710i	$0.478454\pi$
$684$	−3.64959e104	−0.0176864
$685$	2.05958e106	0.944891
$686$	−1.57374e106	−0.683562
$687$	−4.03827e104	−0.0166080
$688$	−1.09124e106	−0.424966
$689$	−4.45330e105	−0.164233
$690$	1.63793e106	0.572078
$691$	−5.53570e106	−1.83124	−0.915621	−	0.402041i	$-0.868301\pi$
$691$	−5.53570e106	−1.83124	−0.915621	+	0.402041i	$0.868301\pi$
$692$	1.37727e106	0.431558
$693$	−8.49907e105	−0.252276
$694$	−8.14686e105	−0.229092
$695$	6.52678e106	1.73888
$696$	1.18050e105	0.0298003
$697$	3.50127e106	0.837523
$698$	1.48506e106	0.336641
$699$	−2.91767e106	−0.626819
$700$	1.34403e104	0.00273672
$701$	4.45243e106	0.859352	0.429676	−	0.902983i	$-0.358628\pi$
$701$	4.45243e106	0.859352	0.429676	+	0.902983i	$0.358628\pi$
$702$	1.19596e105	0.0218813
$703$	−2.04234e105	−0.0354244
$704$	6.71345e106	1.10400
$705$	−5.33249e105	−0.0831454
$706$	−8.27019e106	−1.22275
$707$	9.62856e105	0.135000
$708$	5.33269e105	0.0709086
$709$	5.77962e106	0.728896	0.364448	−	0.931224i	$-0.381258\pi$
$709$	5.77962e106	0.728896	0.364448	+	0.931224i	$0.381258\pi$
$710$	6.63021e106	0.793120
$711$	−4.74722e106	−0.538678
$712$	−9.61011e105	−0.103450
$713$	−1.44226e106	−0.147295
$714$	1.58904e106	0.153976
$715$	−2.27202e106	−0.208899
$716$	1.08921e106	0.0950330
$717$	−7.65092e106	−0.633498
$718$	−1.42865e107	−1.12269
$719$	−1.09286e107	−0.815137	−0.407569	−	0.913175i	$-0.633623\pi$
$719$	−1.09286e107	−0.815137	−0.407569	+	0.913175i	$0.633623\pi$
$720$	1.10566e106	0.0782801
$721$	−3.08457e106	−0.207311
$722$	1.08725e107	0.693721
$723$	3.49874e106	0.211946
$724$	1.21646e107	0.699682
$725$	−8.15719e103	−0.000445518 0
$726$	5.04000e106	0.261401
$727$	−1.10843e107	−0.545971	−0.272985	−	0.962018i	$-0.588011\pi$
$727$	−1.10843e107	−0.545971	−0.272985	+	0.962018i	$0.588011\pi$
$728$	−2.16247e106	−0.101163
$729$	8.33525e105	0.0370370
$730$	1.52330e107	0.642953
$731$	−2.92199e107	−1.17160
$732$	−1.14538e107	−0.436299
$733$	−5.32174e107	−1.92599	−0.962996	−	0.269516i	$-0.913136\pi$
$733$	−5.32174e107	−1.92599	−0.962996	+	0.269516i	$0.913136\pi$
$734$	2.86036e107	0.983599
$735$	−1.15712e107	−0.378097
$736$	4.04793e107	1.25694
$737$	−8.13098e107	−2.39945
$738$	1.08321e107	0.303809
$739$	2.84651e107	0.758832	0.379416	−	0.925226i	$-0.376125\pi$
$739$	2.84651e107	0.758832	0.379416	+	0.925226i	$0.376125\pi$
$740$	−6.83233e106	−0.173133
$741$	−4.05751e105	−0.00977410
$742$	−1.83058e107	−0.419221
$743$	7.42301e107	1.61622	0.808108	−	0.589034i	$-0.200492\pi$
$743$	7.42301e107	1.61622	0.808108	+	0.589034i	$0.200492\pi$
$744$	−3.08950e106	−0.0639593
$745$	5.05861e107	0.995797
$746$	1.52579e106	0.0285620
$747$	−1.26293e107	−0.224831
$748$	2.48095e107	0.420057
$749$	−6.03827e107	−0.972398
$750$	2.63132e107	0.403067
$751$	9.92000e107	1.44549	0.722743	−	0.691116i	$-0.242881\pi$
$751$	9.92000e107	1.44549	0.722743	+	0.691116i	$0.242881\pi$
$752$	2.41765e106	0.0335139
$753$	7.03244e106	0.0927459
$754$	4.42171e105	0.00554836
$755$	4.30631e107	0.514156
$756$	−5.07762e106	−0.0576890
$757$	5.32178e107	0.575389	0.287694	−	0.957722i	$-0.407111\pi$
$757$	5.32178e107	0.575389	0.287694	+	0.957722i	$0.407111\pi$
$758$	−5.71586e107	−0.588148
$759$	1.06354e108	1.04157
$760$	−1.19038e107	−0.110962
$761$	−2.10172e107	−0.186488	−0.0932441	−	0.995643i	$-0.529724\pi$
$761$	−2.10172e107	−0.186488	−0.0932441	+	0.995643i	$0.529724\pi$
$762$	8.46795e107	0.715265
$763$	−9.64476e107	−0.775570
$764$	6.22047e105	0.00476236
$765$	2.96059e107	0.215812
$766$	−5.95904e107	−0.413616
$767$	5.92874e106	0.0391865
$768$	9.76063e107	0.614373
$769$	−1.50210e108	−0.900456	−0.450228	−	0.892914i	$-0.648657\pi$
$769$	−1.50210e108	−0.900456	−0.450228	+	0.892914i	$0.648657\pi$
$770$	−9.33942e107	−0.533234
$771$	−4.35661e107	−0.236925
$772$	−4.83882e107	−0.250663
$773$	−2.63923e108	−1.30240	−0.651202	−	0.758905i	$-0.725735\pi$
$773$	−2.63923e108	−1.30240	−0.651202	+	0.758905i	$0.725735\pi$
$774$	−9.03997e107	−0.424992
$775$	2.13483e105	0.000956200 0
$776$	−1.73415e108	−0.740070
$777$	−2.84148e107	−0.115546
$778$	−2.78578e108	−1.07947
$779$	−3.67501e107	−0.135707
$780$	−1.35738e107	−0.0477697
$781$	4.30512e108	1.44402
$782$	−1.98847e108	−0.635719
$783$	3.08172e106	0.00939133
$784$	5.24617e107	0.152402
$785$	4.24622e108	1.17595
$786$	−2.45695e108	−0.648711
$787$	5.76669e108	1.45169	0.725845	−	0.687858i	$-0.241449\pi$
$787$	5.76669e108	1.45169	0.725845	+	0.687858i	$0.241449\pi$
$788$	−1.14317e108	−0.274395
$789$	2.70278e108	0.618618
$790$	−5.21660e108	−1.13860
$791$	−1.89917e108	−0.395318
$792$	2.27823e108	0.452277
$793$	−1.27340e108	−0.241114
$794$	7.07706e108	1.27816
$795$	−3.41062e108	−0.587578
$796$	−2.22241e108	−0.365245
$797$	6.02176e108	0.944140	0.472070	−	0.881561i	$-0.343507\pi$
$797$	6.02176e108	0.944140	0.472070	+	0.881561i	$0.343507\pi$
$798$	−1.66789e107	−0.0249493
$799$	6.47370e107	0.0923949
$800$	−5.99172e106	−0.00815975
$801$	−2.50874e107	−0.0326013
$802$	9.40655e108	1.16652
$803$	9.89110e108	1.17061
$804$	−4.85771e108	−0.548693
$805$	−7.73137e108	−0.833511
$806$	−1.15721e107	−0.0119083
$807$	−8.38479e108	−0.823635
$808$	−2.58100e108	−0.242026
$809$	−2.25621e108	−0.201980	−0.100990	−	0.994887i	$-0.532201\pi$
$809$	−2.25621e108	−0.201980	−0.100990	+	0.994887i	$0.532201\pi$
$810$	9.15939e107	0.0782850
$811$	1.11620e109	0.910874	0.455437	−	0.890268i	$-0.349483\pi$
$811$	1.11620e109	0.910874	0.455437	+	0.890268i	$0.349483\pi$
$812$	−1.87731e107	−0.0146280
$813$	3.52528e108	0.262300
$814$	4.29527e108	0.305193
$815$	2.55739e108	0.173535
$816$	−1.34228e108	−0.0869884
$817$	3.06698e108	0.189838
$818$	3.85333e108	0.227818
$819$	−5.64516e107	−0.0318809
$820$	−1.22942e109	−0.663253
$821$	2.52146e108	0.129952	0.0649762	−	0.997887i	$-0.479303\pi$
$821$	2.52146e108	0.129952	0.0649762	+	0.997887i	$0.479303\pi$
$822$	−7.73549e108	−0.380886
$823$	−2.93864e109	−1.38246	−0.691230	−	0.722635i	$-0.742931\pi$
$823$	−2.93864e109	−1.38246	−0.691230	+	0.722635i	$0.742931\pi$
$824$	8.26840e108	0.371664
$825$	−1.57424e107	−0.00676160
$826$	2.43708e108	0.100027
$827$	1.57221e109	0.616671	0.308335	−	0.951278i	$-0.400228\pi$
$827$	1.57221e109	0.616671	0.308335	+	0.951278i	$0.400228\pi$
$828$	6.35394e108	0.238180
$829$	2.15143e108	0.0770783	0.0385392	−	0.999257i	$-0.487730\pi$
$829$	2.15143e108	0.0770783	0.0385392	+	0.999257i	$0.487730\pi$
$830$	−1.38780e109	−0.475225
$831$	−5.92753e108	−0.194015
$832$	4.45913e108	0.139516
$833$	1.40476e109	0.420159
$834$	−2.45137e109	−0.700942
$835$	−6.62319e109	−1.81061
$836$	−2.60405e108	−0.0680635
$837$	−8.06520e107	−0.0201563
$838$	1.95328e109	0.466783
$839$	−6.15484e108	−0.140651	−0.0703256	−	0.997524i	$-0.522404\pi$
$839$	−6.15484e108	−0.140651	−0.0703256	+	0.997524i	$0.522404\pi$
$840$	−1.65615e109	−0.361932
$841$	−4.77325e109	−0.997619
$842$	−3.92668e109	−0.784914
$843$	4.59358e109	0.878248
$844$	8.50526e107	0.0155541
$845$	5.59158e109	0.978155
$846$	2.00281e108	0.0335160
$847$	−2.37898e109	−0.380858
$848$	1.54631e109	0.236838
$849$	5.74363e109	0.841682
$850$	2.94331e107	0.00412692
$851$	3.55572e109	0.477055
$852$	2.57202e109	0.330209
$853$	6.64173e109	0.816004	0.408002	−	0.912981i	$-0.366226\pi$
$853$	6.64173e109	0.816004	0.408002	+	0.912981i	$0.366226\pi$
$854$	−5.23448e109	−0.615466
$855$	−3.10750e108	−0.0349689
$856$	1.61860e110	1.74330
$857$	−1.32102e110	−1.36185	−0.680925	−	0.732353i	$-0.738422\pi$
$857$	−1.32102e110	−1.36185	−0.680925	+	0.732353i	$0.738422\pi$
$858$	8.53340e108	0.0842071
$859$	5.82761e109	0.550487	0.275243	−	0.961375i	$-0.411242\pi$
$859$	5.82761e109	0.550487	0.275243	+	0.961375i	$0.411242\pi$
$860$	1.02601e110	0.927812
$861$	−5.11299e109	−0.442646
$862$	7.20740e109	0.597387
$863$	2.50382e109	0.198700	0.0993500	−	0.995053i	$-0.468324\pi$
$863$	2.50382e109	0.198700	0.0993500	+	0.995053i	$0.468324\pi$
$864$	2.26362e109	0.172004
$865$	1.17269e110	0.853259
$866$	−1.75114e110	−1.22011
$867$	5.05859e109	0.337531
$868$	4.91311e108	0.0313955
$869$	−3.38724e110	−2.07302
$870$	3.38643e108	0.0198504
$871$	−5.40067e109	−0.303226
$872$	2.58534e110	1.39043
$873$	−4.52704e109	−0.233228
$874$	2.08713e109	0.103008
$875$	−1.24204e110	−0.587264
$876$	5.90926e109	0.267688
$877$	1.51377e110	0.657013	0.328507	−	0.944502i	$-0.393455\pi$
$877$	1.51377e110	0.657013	0.328507	+	0.944502i	$0.393455\pi$
$878$	−1.41400e110	−0.588037
$879$	−5.61595e109	−0.223790
$880$	7.88908e109	0.301249
$881$	−1.19861e110	−0.438612	−0.219306	−	0.975656i	$-0.570379\pi$
$881$	−1.19861e110	−0.438612	−0.219306	+	0.975656i	$0.570379\pi$
$882$	4.34599e109	0.152411
$883$	−4.40352e110	−1.48004	−0.740021	−	0.672584i	$-0.765184\pi$
$883$	−4.40352e110	−1.48004	−0.740021	+	0.672584i	$0.765184\pi$
$884$	1.64787e109	0.0530839
$885$	4.54060e109	0.140198
$886$	−6.98601e109	−0.206759
$887$	−3.20291e110	−0.908676	−0.454338	−	0.890829i	$-0.650124\pi$
$887$	−3.20291e110	−0.908676	−0.454338	+	0.890829i	$0.650124\pi$
$888$	7.61678e109	0.207150
$889$	−3.99705e110	−1.04213
$890$	−2.75679e109	−0.0689093
$891$	5.94737e109	0.142532
$892$	−2.29749e110	−0.527924
$893$	−6.79492e108	−0.0149711
$894$	−1.89994e110	−0.401406
$895$	9.27428e109	0.187895
$896$	−8.81043e109	−0.171178
$897$	7.06413e109	0.131626
$898$	3.18888e110	0.569871
$899$	−2.98188e108	−0.00511095
$900$	−9.40504e107	−0.00154620
$901$	4.14052e110	0.652944
$902$	7.72895e110	1.16916
$903$	4.26705e110	0.619209
$904$	5.09086e110	0.708721
$905$	1.03577e111	1.38338
$906$	−1.61739e110	−0.207256
$907$	4.11974e110	0.506520	0.253260	−	0.967398i	$-0.418497\pi$
$907$	4.11974e110	0.506520	0.253260	+	0.967398i	$0.418497\pi$
$908$	−2.81243e110	−0.331790
$909$	−6.73775e109	−0.0762727
$910$	−6.20332e109	−0.0673864
$911$	7.95032e110	0.828792	0.414396	−	0.910097i	$-0.363993\pi$
$911$	7.95032e110	0.828792	0.414396	+	0.910097i	$0.363993\pi$
$912$	1.40888e109	0.0140951
$913$	−9.01127e110	−0.865230
$914$	−1.43102e111	−1.31875
$915$	−9.75253e110	−0.862633
$916$	−1.72143e109	−0.0146154
$917$	1.15973e111	0.945165
$918$	−1.11196e110	−0.0869938
$919$	−1.72959e111	−1.29901	−0.649505	−	0.760358i	$-0.725024\pi$
$919$	−1.72959e111	−1.29901	−0.649505	+	0.760358i	$0.725024\pi$
$920$	2.07245e111	1.49431
$921$	1.02670e111	0.710738
$922$	−5.19198e110	−0.345083
$923$	2.85950e110	0.182485
$924$	−3.62299e110	−0.222008
$925$	−5.26314e108	−0.00309692
$926$	4.84754e110	0.273911
$927$	2.15848e110	0.117127
$928$	8.36910e109	0.0436144
$929$	3.05536e110	0.152923	0.0764616	−	0.997073i	$-0.475638\pi$
$929$	3.05536e110	0.152923	0.0764616	+	0.997073i	$0.475638\pi$
$930$	−8.86264e109	−0.0426042
$931$	−1.47446e110	−0.0680800
$932$	−1.24375e111	−0.551613
$933$	−2.66341e111	−1.13469
$934$	−2.59955e111	−1.06387
$935$	2.11244e111	0.830519
$936$	1.51322e110	0.0571556
$937$	2.08558e111	0.756821	0.378410	−	0.925638i	$-0.376471\pi$
$937$	2.08558e111	0.756821	0.378410	+	0.925638i	$0.376471\pi$
$938$	−2.22001e111	−0.774014
$939$	−1.46224e111	−0.489844
$940$	−2.27313e110	−0.0731696
$941$	2.46424e111	0.762204	0.381102	−	0.924533i	$-0.375545\pi$
$941$	2.46424e111	0.762204	0.381102	+	0.924533i	$0.375545\pi$
$942$	−1.59482e111	−0.474028
$943$	6.39819e111	1.82755
$944$	−2.05862e110	−0.0565102
$945$	−4.32342e110	−0.114060
$946$	−6.45021e111	−1.63552
$947$	−3.18895e111	−0.777183	−0.388592	−	0.921410i	$-0.627038\pi$
$947$	−3.18895e111	−0.777183	−0.388592	+	0.921410i	$0.627038\pi$
$948$	−2.02364e111	−0.474047
$949$	6.56976e110	0.147933
$950$	−3.08936e108	−0.000668702 0
$951$	1.58060e111	0.328891
$952$	2.01059e111	0.402196
$953$	−3.06097e111	−0.588675	−0.294338	−	0.955702i	$-0.595099\pi$
$953$	−3.06097e111	−0.588675	−0.294338	+	0.955702i	$0.595099\pi$
$954$	1.28098e111	0.236853
$955$	5.29652e109	0.00941594
$956$	−3.26143e111	−0.557491
$957$	2.19887e110	0.0361412
$958$	4.14954e109	0.00655834
$959$	3.65131e111	0.554946
$960$	3.41508e111	0.499149
$961$	−7.03618e111	−0.989031
$962$	2.85295e110	0.0385682
$963$	4.22538e111	0.549389
$964$	1.49144e111	0.186517
$965$	−4.12009e111	−0.495601
$966$	2.90380e111	0.335989
$967$	1.45168e112	1.61576	0.807880	−	0.589346i	$-0.200615\pi$
$967$	1.45168e112	1.61576	0.807880	+	0.589346i	$0.200615\pi$
$968$	6.37702e111	0.682797
$969$	3.77253e110	0.0388590
$970$	−4.97464e111	−0.492972
$971$	−7.21500e111	−0.687884	−0.343942	−	0.938991i	$-0.611762\pi$
$971$	−7.21500e111	−0.687884	−0.343942	+	0.938991i	$0.611762\pi$
$972$	3.55315e110	0.0325933
$973$	1.15710e112	1.02126
$974$	9.34916e111	0.793984
$975$	−1.04563e109	−0.000854484 0
$976$	4.42161e111	0.347706
$977$	1.70539e112	1.29055	0.645277	−	0.763948i	$-0.276742\pi$
$977$	1.70539e112	1.29055	0.645277	+	0.763948i	$0.276742\pi$
$978$	−9.60520e110	−0.0699519
$979$	−1.79003e111	−0.125461
$980$	−4.93257e111	−0.332733
$981$	6.74908e111	0.438184
$982$	−1.38880e112	−0.867880
$983$	−6.53585e111	−0.393138	−0.196569	−	0.980490i	$-0.562980\pi$
$983$	−6.53585e111	−0.393138	−0.196569	+	0.980490i	$0.562980\pi$
$984$	1.37057e112	0.793570
$985$	−9.73368e111	−0.542523
$986$	−4.11115e110	−0.0220587
$987$	−9.45368e110	−0.0488324
$988$	−1.72964e110	−0.00860140
$989$	−5.33962e112	−2.55652
$990$	6.53541e111	0.301268
$991$	−1.45638e112	−0.646417	−0.323209	−	0.946328i	$-0.604762\pi$
$991$	−1.45638e112	−0.646417	−0.323209	+	0.946328i	$0.604762\pi$
$992$	−2.19028e111	−0.0936080
$993$	−1.27321e112	−0.523966
$994$	1.17543e112	0.465810
$995$	−1.89231e112	−0.722148
$996$	−5.38362e111	−0.197856
$997$	1.99299e112	0.705400	0.352700	−	0.935736i	$-0.385264\pi$
$997$	1.99299e112	0.705400	0.352700	+	0.935736i	$0.385264\pi$
$998$	−2.87083e112	−0.978615
$999$	1.98837e111	0.0652818

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.76.a.b.1.2	✓	6
3.2	odd	2		9.76.a.b.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.76.a.b.1.2	✓	6	1.1	even	1	trivial
9.76.a.b.1.5		6	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 76 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-1.36324e11 q^{2} -4.50284e17 q^{3} -1.91947e22 q^{4} -1.63436e26 q^{5} +6.13845e28 q^{6} -2.89747e31 q^{7} +7.76687e33 q^{8} +2.02756e35 q^{9} +O(q^{10})\)	\(q-1.36324e11 q^{2} -4.50284e17 q^{3} -1.91947e22 q^{4} -1.63436e26 q^{5} +6.13845e28 q^{6} -2.89747e31 q^{7} +7.76687e33 q^{8} +2.02756e35 q^{9} +2.22803e37 q^{10} +1.44670e39 q^{11} +8.64307e39 q^{12} +9.60913e40 q^{13} +3.94995e42 q^{14} +7.35928e43 q^{15} -3.33656e44 q^{16} -8.93423e45 q^{17} -2.76405e46 q^{18} +9.37755e46 q^{19} +3.13711e48 q^{20} +1.30469e49 q^{21} -1.97220e50 q^{22} -1.63263e51 q^{23} -3.49730e51 q^{24} +2.41661e50 q^{25} -1.30995e52 q^{26} -9.12976e52 q^{27} +5.56161e53 q^{28} -3.37547e53 q^{29} -1.00325e55 q^{30} +8.83397e54 q^{31} -2.47939e56 q^{32} -6.51427e56 q^{33} +1.21795e57 q^{34} +4.73553e57 q^{35} -3.89183e57 q^{36} -2.17790e58 q^{37} -1.27838e58 q^{38} -4.32684e58 q^{39} -1.26939e60 q^{40} -3.91894e60 q^{41} -1.77860e60 q^{42} +3.27056e61 q^{43} -2.77690e61 q^{44} -3.31376e61 q^{45} +2.22567e62 q^{46} -7.24595e61 q^{47} +1.50240e62 q^{48} -1.57233e63 q^{49} -3.29442e61 q^{50} +4.02294e63 q^{51} -1.84444e63 q^{52} -4.63445e64 q^{53} +1.24460e64 q^{54} -2.36444e65 q^{55} -2.25043e65 q^{56} -4.22256e64 q^{57} +4.60157e64 q^{58} +6.16990e65 q^{59} -1.41259e66 q^{60} -1.32520e67 q^{61} -1.20428e66 q^{62} -5.87479e66 q^{63} +4.64052e67 q^{64} -1.57048e67 q^{65} +8.88051e67 q^{66} -5.62035e68 q^{67} +1.71490e68 q^{68} +7.35148e68 q^{69} -6.45566e68 q^{70} +2.97582e69 q^{71} +1.57478e69 q^{72} +6.83700e69 q^{73} +2.96900e69 q^{74} -1.08816e68 q^{75} -1.79999e69 q^{76} -4.19178e70 q^{77} +5.89851e69 q^{78} -2.34135e71 q^{79} +5.45315e70 q^{80} +4.11098e70 q^{81} +5.34246e71 q^{82} -6.22883e71 q^{83} -2.50431e71 q^{84} +1.46018e72 q^{85} -4.45856e72 q^{86} +1.51992e71 q^{87} +1.12364e73 q^{88} -1.23732e72 q^{89} +4.51745e72 q^{90} -2.78422e72 q^{91} +3.13379e73 q^{92} -3.97779e72 q^{93} +9.87796e72 q^{94} -1.53263e73 q^{95} +1.11643e74 q^{96} -2.23276e74 q^{97} +2.14346e74 q^{98} +2.93327e74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 311057037486 q^{2} - 27\!\cdots\!78 q^{3}+ \cdots + 12\!\cdots\!14 q^{9}+O(q^{10}) \) 6 * q + 311057037486 * q^2 - 2701703435345984178 * q^3 + 30902560640638265713092 * q^4 + 97856522050579947592055460 * q^5 - 140063977794078462972618149418 * q^6 - 30749202116633858714981933510688 * q^7 + 6939052769539518449811063778704312 * q^8 + 1216533575426715418239367985237722614 * q^9	\( 6 q + 311057037486 q^{2} - 27\!\cdots\!78 q^{3}+ \cdots - 76\!\cdots\!24 q^{99}+O(q^{100}) \) 6 * q + 311057037486 * q^2 - 2701703435345984178 * q^3 + 30902560640638265713092 * q^4 + 97856522050579947592055460 * q^5 - 140063977794078462972618149418 * q^6 - 30749202116633858714981933510688 * q^7 + 6939052769539518449811063778704312 * q^8 + 1216533575426715418239367985237722614 * q^9 - 107545734844341425270764823551622320620 * q^10 - 379379629646545786309015638730942099896 * q^11 - 13914925707300000018474960771518286576396 * q^12 + 154669229506479970266461340344668629154596 * q^13 + 31899227014014717498689751276506679791260128 * q^14 - 44063216965843649415864165430570914609751980 * q^15 - 3260958521390361922516104888150343171861643760 * q^16 - 7401535799877014405171685814768477775195111796 * q^17 + 63068554995747571049522875917506429627377984734 * q^18 - 182729763718938971567579921571009657209643443592 * q^19 - 9428757085683313672852247515255856540783373281640 * q^20 + 13845870832109617357675133577206423227304340315744 * q^21 + 471450583148622264812447113021812911318975285911848 * q^22 - 1094918718857791395763955497794548441629464114423696 * q^23 - 3124543784251997138778029973550539122748717548729256 * q^24 + 71600575748870708223111198803019790440272165366567850 * q^25 + 17144617795232739661292142542037336623136662115361812 * q^26 - 547785489990681667554695878527543069572161447199466882 * q^27 - 421056590097566772314387078351382806371109737989226944 * q^28 + 1286761243501908998723554437372128496488806548512006196 * q^29 + 48426113547627590272391092473373486391591403144360525060 * q^30 - 19590134983123701786508136226454400260130744726276043984 * q^31 - 405443732303791628255103774085578846894562577440580267808 * q^32 + 170828541452726656011508016173932290305101051393018574248 * q^33 + 799554727652091370833855066044541676465377828794014920924 * q^34 - 36738948500466973600844998839202990635858889677989007096000 * q^35 + 6265667097666093126364187347282208187479910552227134043748 * q^36 - 91545935905237059630111535534102037526425524589341335258828 * q^37 - 684421739975642826350565409193219733278360180645855295369576 * q^38 - 69645064783328899443381547781666897855273595262949955330348 * q^39 - 3191514246209809963152113018089087413561147078084072414179760 * q^40 - 316536315385886215170089302814500575828563777084996078443524 * q^41 - 14363708534774163874007330922786686877486530852538004495042464 * q^42 + 8908593056531100512689524294334311253125705720155921361637320 * q^43 - 21785863331670136277341155880608983152526085161022719211416784 * q^44 + 19840957441502540200289838059474939574735117137669088264028740 * q^45 + 203991825673001927929491823653549685659396184023570859282558896 * q^46 + 1142730760034072985500217886491003567898472938032199023875837760 * q^47 + 1468357139960183639245050701003384530889312785645463191005404880 * q^48 + 9932613847036662039777786400812307007669956514072280038886436470 * q^49 - 8883185004616479564484651092109548958973775099745125635626453950 * q^50 + 3332792449560669445942474443428042466743787229637394800726193948 * q^51 - 26987269348801105921073028535709825459131864700220460006411048296 * q^52 + 50865557114922724445413426425120290543311269685677591074207545764 * q^53 - 28398755282386390875875670973745277845897888210594763272248256442 * q^54 - 446272596484924291179313911709667686162610277785745256318167362640 * q^55 + 252098718314851221087836050947321657945518421301909982473468909440 * q^56 + 82280271729902900189321555309233649652586075259579233170711247896 * q^57 + 5708767830293773961786560342813586714128873252994207151314483829348 * q^58 + 2188427764336584360362109164219599664600305872173254932641215849992 * q^59 + 4245617568238899773663200034809151382019999528473811552385896315320 * q^60 + 22824130148103906081748322440858509039514053708066868437237654119460 * q^61 + 47586797873032763455450207051586846920428945648357768353569220285424 * q^62 - 6234572798744552291718025661168699069836980983012258120102491383072 * q^63 - 62277215504581285171320235502281031925680209278531250485362330807232 * q^64 - 139549609673753297396326760842807258047007635314506217050746073464360 * q^65 - 212286610014750055139927453688416335167525157803438234816067618456824 * q^66 - 195051098831763858659485315535620001296749632524239458769204357711816 * q^67 - 478898943613171780503683796705180273623444550119196454935625635754872 * q^68 + 493024277360453140561624845422921878992874641767680608467523400713648 * q^69 - 757997824979604988529186642170865717977143205307772715302146700408000 * q^70 - 3034169501204758984184273945180030994909311349950008497555595439759088 * q^71 + 1406931779300427048044368642832153219815056977181277826974271096951928 * q^72 + 13747249917875809714395686690179837721964032944309940620133405822381724 * q^73 - 2369634359974005306762628635878678463122778575706094238003611098139932 * q^74 - 32240586912245726020343673100989570820986809603159036289366132710579550 * q^75 - 34154148647149103788996774156065386764182788320537620321912800871149232 * q^76 + 110964225149010328333146128762358481438061822139163262844956857145745024 * q^77 - 7719945465845697643730248299122010768040873144728767928645236282901756 * q^78 - 201509609621708284923745260863351675377795113292036868882834678557374960 * q^79 - 422838509739279884709169464673498932712468741280281559903498362323065760 * q^80 + 246658990023417981949800521634464429457648733593148649210122936867832166 * q^81 + 1272064461032237978527479940408403539923817748343630409520994189497365644 * q^82 + 2802602491348140684813265973373777054770511234236863543486293197357747832 * q^83 + 189595005990277008686672008170141905974998639885514332207558449512548672 * q^84 - 60328702368357628714477758217500517309887606952299760526919048695903160 * q^85 + 5057125471275015782616585132644541629892966424745006584268526775897314984 * q^86 - 579407878673196333670683910868657327246273741522239483060404474475661148 * q^87 - 6621568649346448861468435905169718150646541969777165734050561367125413728 * q^88 - 159920271872091417315458194799657472188764331647019387730257248766388612 * q^89 - 21805499555346694304867032644871637074335060261296261526962295449755416780 * q^90 - 63049718267601813432671733846200700661982230139950125748195604362104533184 * q^91 - 108738058107400706863040151004186657363927160845612619833607429521300941408 * q^92 + 8821122497132808149261627688896990009380329017428740779405389519816014192 * q^93 + 197757998471403159993044858359064919780754639341995946156177159925776436032 * q^94 + 526939076500447210313077859524744124394283713808433538379475932881003671760 * q^95 + 182564787400775237004572719252266001366679249548445383992572338046761790304 * q^96 + 379948778797471041696674086463609005506560736626194774039181672927157115404 * q^97 + 1466852164333826517330437746602345292601007324558710499132638626830518086494 * q^98 - 76921342882995911525969194127663130948509562843249595589628904704987708024 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more