LMFDB - Embedded newform 680.2.z.d.89.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(89,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.89"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.z (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [26,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			89.3
Character	$\chi$	$=$	680.89
Dual form			680.2.z.d.489.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.69850 - 1.69850i) q^{3} +(-2.23426 + 0.0897794i) q^{5} +(-2.68873 + 2.68873i) q^{7} +2.76980i q^{9} +(1.62009 + 1.62009i) q^{11} -4.79916i q^{13} +(3.94739 + 3.64241i) q^{15} +(2.73163 + 3.08839i) q^{17} -0.473120i q^{19} +9.13362 q^{21} +(-0.747433 + 0.747433i) q^{23} +(4.98388 - 0.401182i) q^{25} +(-0.390993 + 0.390993i) q^{27} +(6.84907 - 6.84907i) q^{29} +(-3.38541 + 3.38541i) q^{31} -5.50346i q^{33} +(5.76595 - 6.24873i) q^{35} +(2.83711 + 2.83711i) q^{37} +(-8.15137 + 8.15137i) q^{39} +(1.76410 + 1.76410i) q^{41} +11.0431 q^{43} +(-0.248671 - 6.18847i) q^{45} -12.1034i q^{47} -7.45856i q^{49} +(0.605956 - 9.88531i) q^{51} -2.14408 q^{53} +(-3.76517 - 3.47427i) q^{55} +(-0.803594 + 0.803594i) q^{57} +6.46475i q^{59} +(-0.354589 - 0.354589i) q^{61} +(-7.44725 - 7.44725i) q^{63} +(0.430866 + 10.7226i) q^{65} +13.9447i q^{67} +2.53903 q^{69} +(4.21624 - 4.21624i) q^{71} +(11.2518 + 11.2518i) q^{73} +(-9.14652 - 7.78371i) q^{75} -8.71200 q^{77} +(5.88159 + 5.88159i) q^{79} +9.63761 q^{81} -2.59966 q^{83} +(-6.38047 - 6.65504i) q^{85} -23.2663 q^{87} -9.11592 q^{89} +(12.9037 + 12.9037i) q^{91} +11.5002 q^{93} +(0.0424764 + 1.05708i) q^{95} +(6.39444 + 6.39444i) q^{97} +(-4.48734 + 4.48734i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 2 q^{3} - 2 q^{5} + 2 q^{7} + 2 q^{11} - 2 q^{15} + 2 q^{17} - 12 q^{21} - 2 q^{23} + 10 q^{25} + 20 q^{27} + 10 q^{29} - 10 q^{31} + 22 q^{35} - 6 q^{37} + 8 q^{39} - 10 q^{41} + 32 q^{43} + 28 q^{45}+ \cdots - 22 q^{99}+O(q^{100}) $ 26 * q + 2 * q^3 - 2 * q^5 + 2 * q^7 + 2 * q^11 - 2 * q^15 + 2 * q^17 - 12 * q^21 - 2 * q^23 + 10 * q^25 + 20 * q^27 + 10 * q^29 - 10 * q^31 + 22 * q^35 - 6 * q^37 + 8 * q^39 - 10 * q^41 + 32 * q^43 + 28 * q^45 - 6 * q^51 - 32 * q^53 - 26 * q^55 + 20 * q^57 + 6 * q^61 - 54 * q^63 + 24 * q^65 - 20 * q^69 - 30 * q^71 + 42 * q^73 - 78 * q^75 - 4 * q^77 + 14 * q^79 - 54 * q^81 - 16 * q^83 - 26 * q^85 + 8 * q^87 + 40 * q^89 + 24 * q^91 + 88 * q^93 + 44 * q^95 + 66 * q^97 - 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.69850	−	1.69850i	−0.980629	−	0.980629i	0.0191868	−	0.999816i	$-0.493892\pi$
$3$	−1.69850	−	1.69850i	−0.980629	−	0.980629i	−0.999816	+	0.0191868i	$0.993892\pi$
$4$		0			0
$5$	−2.23426	+	0.0897794i	−0.999194	+	0.0401506i
$5$	−2.23426	+	0.0897794i	−0.999194	+	0.0401506i
$6$		0			0
$7$	−2.68873	+	2.68873i	−1.01625	+	1.01625i	−0.0163793	+	0.999866i	$0.505214\pi$
$7$	−2.68873	+	2.68873i	−1.01625	+	1.01625i	−0.999866	+	0.0163793i	$0.994786\pi$
$8$		0			0
$9$			2.76980i			0.923267i
$10$		0			0
$11$	1.62009	+	1.62009i	0.488477	+	0.488477i	0.907825	−	0.419349i	$-0.137741\pi$
$11$	1.62009	+	1.62009i	0.488477	+	0.488477i	−0.419349	+	0.907825i	$0.637741\pi$
$12$		0			0
$13$		−	4.79916i		−	1.33105i	−0.746377	−	0.665524i	$-0.768208\pi$
$13$		−	4.79916i		−	1.33105i	0.746377	−	0.665524i	$-0.231792\pi$
$14$		0			0
$15$	3.94739	+	3.64241i	1.01921	+	0.940466i
$16$		0			0
$17$	2.73163	+	3.08839i	0.662519	+	0.749045i
$17$	2.73163	+	3.08839i	0.662519	+	0.749045i
$18$		0			0
$19$		−	0.473120i		−	0.108541i	−0.998526	−	0.0542706i	$-0.982717\pi$
$19$		−	0.473120i		−	0.108541i	0.998526	−	0.0542706i	$-0.0172834\pi$
$20$		0			0
$21$	9.13362			1.99312
$22$		0			0
$23$	−0.747433	+	0.747433i	−0.155850	+	0.155850i	−0.780725	−	0.624875i	$-0.785150\pi$
$23$	−0.747433	+	0.747433i	−0.155850	+	0.155850i	0.624875	+	0.780725i	$0.285150\pi$
$24$		0			0
$25$	4.98388	−	0.401182i	0.996776	−	0.0802364i
$26$		0			0
$27$	−0.390993	+	0.390993i	−0.0752467	+	0.0752467i
$28$		0			0
$29$	6.84907	−	6.84907i	1.27184	−	1.27184i	0.326719	−	0.945122i	$-0.394057\pi$
$29$	6.84907	−	6.84907i	1.27184	−	1.27184i	0.945122	−	0.326719i	$-0.105943\pi$
$30$		0			0
$31$	−3.38541	+	3.38541i	−0.608038	+	0.608038i	−0.942433	−	0.334395i	$-0.891468\pi$
$31$	−3.38541	+	3.38541i	−0.608038	+	0.608038i	0.334395	+	0.942433i	$0.391468\pi$
$32$		0			0
$33$		−	5.50346i		−	0.958029i
$34$		0			0
$35$	5.76595	−	6.24873i	0.974623	−	1.05623i
$36$		0			0
$37$	2.83711	+	2.83711i	0.466419	+	0.466419i	0.900752	−	0.434333i	$-0.143016\pi$
$37$	2.83711	+	2.83711i	0.466419	+	0.466419i	−0.434333	+	0.900752i	$0.643016\pi$
$38$		0			0
$39$	−8.15137	+	8.15137i	−1.30526	+	1.30526i
$40$		0			0
$41$	1.76410	+	1.76410i	0.275506	+	0.275506i	0.831312	−	0.555806i	$-0.187590\pi$
$41$	1.76410	+	1.76410i	0.275506	+	0.275506i	−0.555806	+	0.831312i	$0.687590\pi$
$42$		0			0
$43$	11.0431			1.68405			0.842025	−	0.539438i	$-0.181363\pi$
$43$	11.0431			1.68405			0.842025	+	0.539438i	$0.181363\pi$
$44$		0			0
$45$	−0.248671	−	6.18847i	−0.0370697	−	0.922522i
$46$		0			0
$47$		−	12.1034i		−	1.76546i	−0.469885	−	0.882728i	$-0.655705\pi$
$47$		−	12.1034i		−	1.76546i	0.469885	−	0.882728i	$-0.344295\pi$
$48$		0			0
$49$		−	7.45856i		−	1.06551i
$50$		0			0
$51$	0.605956	−	9.88531i	0.0848507	−	1.38422i
$52$		0			0
$53$	−2.14408			−0.294512			−0.147256	−	0.989098i	$-0.547044\pi$
$53$	−2.14408			−0.294512			−0.147256	+	0.989098i	$0.547044\pi$
$54$		0			0
$55$	−3.76517	−	3.47427i	−0.507695	−	0.468470i
$56$		0			0
$57$	−0.803594	+	0.803594i	−0.106439	+	0.106439i
$58$		0			0
$59$			6.46475i			0.841639i	0.907144	+	0.420820i	$0.138257\pi$
$59$			6.46475i			0.841639i	−0.907144	+	0.420820i	$0.861743\pi$
$60$		0			0
$61$	−0.354589	−	0.354589i	−0.0454005	−	0.0454005i	0.684042	−	0.729443i	$-0.260220\pi$
$61$	−0.354589	−	0.354589i	−0.0454005	−	0.0454005i	−0.729443	+	0.684042i	$0.760220\pi$
$62$		0			0
$63$	−7.44725	−	7.44725i	−0.938266	−	0.938266i
$64$		0			0
$65$	0.430866	+	10.7226i	0.0534423	+	1.32997i
$66$		0			0
$67$			13.9447i			1.70361i	0.523858	+	0.851806i	$0.324492\pi$
$67$			13.9447i			1.70361i	−0.523858	+	0.851806i	$0.675508\pi$
$68$		0			0
$69$	2.53903			0.305663
$70$		0			0
$71$	4.21624	−	4.21624i	0.500376	−	0.500376i	−0.411179	−	0.911555i	$-0.634883\pi$
$71$	4.21624	−	4.21624i	0.500376	−	0.500376i	0.911555	+	0.411179i	$0.134883\pi$
$72$		0			0
$73$	11.2518	+	11.2518i	1.31692	+	1.31692i	0.916198	+	0.400725i	$0.131242\pi$
$73$	11.2518	+	11.2518i	1.31692	+	1.31692i	0.400725	+	0.916198i	$0.368758\pi$
$74$		0			0
$75$	−9.14652	−	7.78371i	−1.05615	−	0.898785i
$76$		0			0
$77$	−8.71200			−0.992824
$78$		0			0
$79$	5.88159	+	5.88159i	0.661731	+	0.661731i	0.955788	−	0.294057i	$-0.0950056\pi$
$79$	5.88159	+	5.88159i	0.661731	+	0.661731i	−0.294057	+	0.955788i	$0.595006\pi$
$80$		0			0
$81$	9.63761			1.07085
$82$		0			0
$83$	−2.59966			−0.285350			−0.142675	−	0.989770i	$-0.545570\pi$
$83$	−2.59966			−0.285350			−0.142675	+	0.989770i	$0.545570\pi$
$84$		0			0
$85$	−6.38047	−	6.65504i	−0.692059	−	0.721841i
$86$		0			0
$87$	−23.2663			−2.49441
$88$		0			0
$89$	−9.11592			−0.966286			−0.483143	−	0.875541i	$-0.660505\pi$
$89$	−9.11592			−0.966286			−0.483143	+	0.875541i	$0.660505\pi$
$90$		0			0
$91$	12.9037	+	12.9037i	1.35267	+	1.35267i
$92$		0			0
$93$	11.5002			1.19252
$94$		0			0
$95$	0.0424764	+	1.05708i	0.00435799	+	0.108454i
$96$		0			0
$97$	6.39444	+	6.39444i	0.649257	+	0.649257i	0.952813	−	0.303556i	$-0.0981741\pi$
$97$	6.39444	+	6.39444i	0.649257	+	0.649257i	−0.303556	+	0.952813i	$0.598174\pi$
$98$		0			0
$99$	−4.48734	+	4.48734i	−0.450994	+	0.450994i
$100$		0			0
$101$	6.01342			0.598358			0.299179	−	0.954197i	$-0.403287\pi$
$101$	6.01342			0.598358			0.299179	+	0.954197i	$0.403287\pi$
$102$		0			0
$103$			6.70413i			0.660578i	0.943880	+	0.330289i	$0.107146\pi$
$103$			6.70413i			0.660578i	−0.943880	+	0.330289i	$0.892854\pi$
$104$		0			0
$105$	−20.4069	+	0.820011i	−1.99151	+	0.0800249i
$106$		0			0
$107$	−3.08520	−	3.08520i	−0.298257	−	0.298257i	0.542074	−	0.840331i	$-0.317639\pi$
$107$	−3.08520	−	3.08520i	−0.298257	−	0.298257i	−0.840331	+	0.542074i	$0.817639\pi$
$108$		0			0
$109$	2.62204	+	2.62204i	0.251146	+	0.251146i	0.821440	−	0.570294i	$-0.193171\pi$
$109$	2.62204	+	2.62204i	0.251146	+	0.251146i	−0.570294	+	0.821440i	$0.693171\pi$
$110$		0			0
$111$		−	9.63768i		−	0.914768i
$112$		0			0
$113$	−11.4021	+	11.4021i	−1.07262	+	1.07262i	−0.0754726	+	0.997148i	$0.524047\pi$
$113$	−11.4021	+	11.4021i	−1.07262	+	1.07262i	−0.997148	+	0.0754726i	$0.975953\pi$
$114$		0			0
$115$	1.60286	−	1.73707i	0.149467	−	0.161982i
$116$		0			0
$117$	13.2927			1.22891
$118$		0			0
$119$	−15.6485	−	0.959230i	−1.43450	−	0.0879325i
$120$		0			0
$121$		−	5.75059i		−	0.522781i
$122$		0			0
$123$		−	5.99264i		−	0.540338i
$124$		0			0
$125$	−11.0993	+	1.34380i	−0.992751	+	0.120193i
$126$		0			0
$127$	0.786344			0.0697767			0.0348884	−	0.999391i	$-0.488892\pi$
$127$	0.786344			0.0697767			0.0348884	+	0.999391i	$0.488892\pi$
$128$		0			0
$129$	−18.7566	−	18.7566i	−1.65143	−	1.65143i
$130$		0			0
$131$	13.1428	−	13.1428i	1.14830	−	1.14830i	0.161407	−	0.986888i	$-0.448397\pi$
$131$	13.1428	−	13.1428i	1.14830	−	1.14830i	0.986888	−	0.161407i	$-0.0516032\pi$
$132$		0			0
$133$	1.27209	+	1.27209i	0.110304	+	0.110304i
$134$		0			0
$135$	0.838480	−	0.908686i	0.0721648	−	0.0782072i
$136$		0			0
$137$			5.81223i			0.496572i	0.968687	+	0.248286i	$0.0798673\pi$
$137$			5.81223i			0.496572i	−0.968687	+	0.248286i	$0.920133\pi$
$138$		0			0
$139$	−8.22497	+	8.22497i	−0.697633	+	0.697633i	−0.963899	−	0.266267i	$-0.914210\pi$
$139$	−8.22497	+	8.22497i	−0.697633	+	0.697633i	0.266267	+	0.963899i	$0.414210\pi$
$140$		0			0
$141$	−20.5575	+	20.5575i	−1.73126	+	1.73126i
$142$		0			0
$143$	7.77509	−	7.77509i	0.650186	−	0.650186i
$144$		0			0
$145$	−14.6877	+	15.9175i	−1.21975	+	1.32188i
$146$		0			0
$147$	−12.6684	+	12.6684i	−1.04487	+	1.04487i
$148$		0			0
$149$	21.7798			1.78427			0.892135	−	0.451768i	$-0.149207\pi$
$149$	21.7798			1.78427			0.892135	+	0.451768i	$0.149207\pi$
$150$		0			0
$151$		−	1.97928i		−	0.161071i	−0.996752	−	0.0805356i	$-0.974337\pi$
$151$		−	1.97928i		−	0.161071i	0.996752	−	0.0805356i	$-0.0256631\pi$
$152$		0			0
$153$	−8.55423	+	7.56608i	−0.691569	+	0.611682i
$154$		0			0
$155$	7.25997	−	7.86785i	0.583135	−	0.631961i
$156$		0			0
$157$			0.671587i			0.0535985i	0.999641	+	0.0267992i	$0.00853149\pi$
$157$			0.671587i			0.0535985i	−0.999641	+	0.0267992i	$0.991469\pi$
$158$		0			0
$159$	3.64171	+	3.64171i	0.288807	+	0.288807i
$160$		0			0
$161$		−	4.01929i		−	0.316765i
$162$		0			0
$163$	1.75163	−	1.75163i	0.137198	−	0.137198i	−0.635172	−	0.772370i	$-0.719071\pi$
$163$	1.75163	−	1.75163i	0.137198	−	0.137198i	0.772370	+	0.635172i	$0.219071\pi$
$164$		0			0
$165$	0.494097	+	12.2962i	0.0384654	+	0.957256i
$166$		0			0
$167$	−0.630460	−	0.630460i	−0.0487864	−	0.0487864i	0.682293	−	0.731079i	$-0.260983\pi$
$167$	−0.630460	−	0.630460i	−0.0487864	−	0.0487864i	−0.731079	+	0.682293i	$0.760983\pi$
$168$		0			0
$169$	−10.0319			−0.771687
$170$		0			0
$171$	1.31045			0.100213
$172$		0			0
$173$	−8.30526	−	8.30526i	−0.631438	−	0.631438i	0.316991	−	0.948429i	$-0.397327\pi$
$173$	−8.30526	−	8.30526i	−0.631438	−	0.631438i	−0.948429	+	0.316991i	$0.897327\pi$
$174$		0			0
$175$	−12.3216	+	14.4790i	−0.931429	+	1.09451i
$176$		0			0
$177$	10.9804	−	10.9804i	0.825336	−	0.825336i
$178$		0			0
$179$		−	8.65388i		−	0.646821i	−0.946259	−	0.323411i	$-0.895170\pi$
$179$		−	8.65388i		−	0.646821i	0.946259	−	0.323411i	$-0.104830\pi$
$180$		0			0
$181$	−12.9479	−	12.9479i	−0.962412	−	0.962412i	0.0369072	−	0.999319i	$-0.488249\pi$
$181$	−12.9479	−	12.9479i	−0.962412	−	0.962412i	−0.999319	+	0.0369072i	$0.988249\pi$
$182$		0			0
$183$			1.20454i			0.0890421i
$184$		0			0
$185$	−6.59358	−	6.08415i	−0.484770	−	0.447316i
$186$		0			0
$187$	−0.577984	+	9.42899i	−0.0422663	+	0.689516i
$188$		0			0
$189$		−	2.10255i		−	0.152938i
$190$		0			0
$191$	1.80616			0.130689			0.0653445	−	0.997863i	$-0.479185\pi$
$191$	1.80616			0.130689			0.0653445	+	0.997863i	$0.479185\pi$
$192$		0			0
$193$	−12.4874	+	12.4874i	−0.898865	+	0.898865i	−0.995336	−	0.0964710i	$-0.969245\pi$
$193$	−12.4874	+	12.4874i	−0.898865	+	0.898865i	0.0964710	+	0.995336i	$0.469245\pi$
$194$		0			0
$195$	17.4805	−	18.9441i	1.25180	−	1.35662i
$196$		0			0
$197$	15.5201	−	15.5201i	1.10576	−	1.10576i	0.112056	−	0.993702i	$-0.464256\pi$
$197$	15.5201	−	15.5201i	1.10576	−	1.10576i	0.993702	−	0.112056i	$-0.0357436\pi$
$198$		0			0
$199$	−6.53983	+	6.53983i	−0.463597	+	0.463597i	−0.899832	−	0.436236i	$-0.856311\pi$
$199$	−6.53983	+	6.53983i	−0.463597	+	0.463597i	0.436236	+	0.899832i	$0.356311\pi$
$200$		0			0
$201$	23.6850	−	23.6850i	1.67061	−	1.67061i
$202$		0			0
$203$			36.8306i			2.58500i
$204$		0			0
$205$	−4.09984	−	3.78308i	−0.286346	−	0.264222i
$206$		0			0
$207$	−2.07024	−	2.07024i	−0.143892	−	0.143892i
$208$		0			0
$209$	0.766499	−	0.766499i	0.0530198	−	0.0530198i
$210$		0			0
$211$	10.4115	+	10.4115i	0.716755	+	0.716755i	0.967939	−	0.251184i	$-0.0808200\pi$
$211$	10.4115	+	10.4115i	0.716755	+	0.716755i	−0.251184	+	0.967939i	$0.580820\pi$
$212$		0			0
$213$	−14.3226			−0.981366
$214$		0			0
$215$	−24.6731	+	0.991439i	−1.68269	+	0.0676156i
$216$		0			0
$217$		−	18.2049i		−	1.23583i
$218$		0			0
$219$		−	38.2224i		−	2.58283i
$220$		0			0
$221$	14.8217	−	13.1095i	0.997015	−	0.881844i
$222$		0			0
$223$	11.3700			0.761394			0.380697	−	0.924700i	$-0.375684\pi$
$223$	11.3700			0.761394			0.380697	+	0.924700i	$0.375684\pi$
$224$		0			0
$225$	1.11119	+	13.8044i	0.0740796	+	0.920290i
$226$		0			0
$227$	20.5002	−	20.5002i	1.36064	−	1.36064i	0.487549	−	0.873095i	$-0.337891\pi$
$227$	20.5002	−	20.5002i	1.36064	−	1.36064i	0.873095	−	0.487549i	$-0.162109\pi$
$228$		0			0
$229$		−	2.12357i		−	0.140329i	−0.997535	−	0.0701646i	$-0.977648\pi$
$229$		−	2.12357i		−	0.140329i	0.997535	−	0.0701646i	$-0.0223525\pi$
$230$		0			0
$231$	14.7973	+	14.7973i	0.973592	+	0.973592i
$232$		0			0
$233$	−3.24570	−	3.24570i	−0.212633	−	0.212633i	0.592752	−	0.805385i	$-0.298041\pi$
$233$	−3.24570	−	3.24570i	−0.212633	−	0.212633i	−0.805385	+	0.592752i	$0.798041\pi$
$234$		0			0
$235$	1.08663	+	27.0421i	0.0708840	+	1.76403i
$236$		0			0
$237$		−	19.9798i		−	1.29782i
$238$		0			0
$239$	−4.39931			−0.284568			−0.142284	−	0.989826i	$-0.545445\pi$
$239$	−4.39931			−0.284568			−0.142284	+	0.989826i	$0.545445\pi$
$240$		0			0
$241$	2.67058	−	2.67058i	0.172027	−	0.172027i	−0.615842	−	0.787870i	$-0.711184\pi$
$241$	2.67058	−	2.67058i	0.172027	−	0.172027i	0.787870	+	0.615842i	$0.211184\pi$
$242$		0			0
$243$	−15.1965	−	15.1965i	−0.974855	−	0.974855i
$244$		0			0
$245$	0.669625	+	16.6644i	0.0427808	+	1.06465i
$246$		0			0
$247$	−2.27058			−0.144473
$248$		0			0
$249$	4.41552	+	4.41552i	0.279822	+	0.279822i
$250$		0			0
$251$	−15.6626			−0.988614			−0.494307	−	0.869288i	$-0.664578\pi$
$251$	−15.6626			−0.988614			−0.494307	+	0.869288i	$0.664578\pi$
$252$		0			0
$253$	−2.42182			−0.152259
$254$		0			0
$255$	−0.466368	+	22.1408i	−0.0292051	+	1.38651i
$256$		0			0
$257$	14.9841			0.934683			0.467342	−	0.884077i	$-0.345212\pi$
$257$	14.9841			0.934683			0.467342	+	0.884077i	$0.345212\pi$
$258$		0			0
$259$	−15.2565			−0.947992
$260$		0			0
$261$	18.9706	+	18.9706i	1.17425	+	1.17425i
$262$		0			0
$263$	15.2651			0.941286			0.470643	−	0.882324i	$-0.344022\pi$
$263$	15.2651			0.941286			0.470643	+	0.882324i	$0.344022\pi$
$264$		0			0
$265$	4.79044	−	0.192494i	0.294274	−	0.0118248i
$266$		0			0
$267$	15.4834	+	15.4834i	0.947568	+	0.947568i
$268$		0			0
$269$	−19.1451	+	19.1451i	−1.16730	+	1.16730i	−0.184456	+	0.982841i	$0.559052\pi$
$269$	−19.1451	+	19.1451i	−1.16730	+	1.16730i	−0.982841	+	0.184456i	$0.940948\pi$
$270$		0			0
$271$	21.8029			1.32443			0.662217	−	0.749312i	$-0.269616\pi$
$271$	21.8029			1.32443			0.662217	+	0.749312i	$0.269616\pi$
$272$		0			0
$273$		−	43.8337i		−	2.65294i
$274$		0			0
$275$	8.72430	+	7.42440i	0.526095	+	0.447708i
$276$		0			0
$277$	1.62425	+	1.62425i	0.0975919	+	0.0975919i	0.754217	−	0.656625i	$-0.228017\pi$
$277$	1.62425	+	1.62425i	0.0975919	+	0.0975919i	−0.656625	+	0.754217i	$0.728017\pi$
$278$		0			0
$279$	−9.37692	−	9.37692i	−0.561381	−	0.561381i
$280$		0			0
$281$		−	1.55801i		−	0.0929434i	−0.998920	−	0.0464717i	$-0.985202\pi$
$281$		−	1.55801i		−	0.0929434i	0.998920	−	0.0464717i	$-0.0147977\pi$
$282$		0			0
$283$	−2.69991	+	2.69991i	−0.160493	+	0.160493i	−0.782785	−	0.622292i	$-0.786202\pi$
$283$	−2.69991	+	2.69991i	−0.160493	+	0.160493i	0.622292	+	0.782785i	$0.286202\pi$
$284$		0			0
$285$	1.72330	−	1.86759i	0.102079	−	0.110626i
$286$		0			0
$287$	−9.48638			−0.559963
$288$		0			0
$289$	−2.07635	+	16.8727i	−0.122138	+	0.992513i
$290$		0			0
$291$		−	21.7219i		−	1.27336i
$292$		0			0
$293$			13.1831i			0.770166i	0.922882	+	0.385083i	$0.125827\pi$
$293$			13.1831i			0.770166i	−0.922882	+	0.385083i	$0.874173\pi$
$294$		0			0
$295$	−0.580402	−	14.4440i	−0.0337923	−	0.840961i
$296$		0			0
$297$	−1.26689			−0.0735125
$298$		0			0
$299$	3.58705	+	3.58705i	0.207444	+	0.207444i
$300$		0			0
$301$	−29.6918	+	29.6918i	−1.71141	+	1.71141i
$302$		0			0
$303$	−10.2138	−	10.2138i	−0.586767	−	0.586767i
$304$		0			0
$305$	0.824081	+	0.760411i	0.0471867	+	0.0435410i
$306$		0			0
$307$		−	33.8928i		−	1.93436i	−0.254086	−	0.967182i	$-0.581775\pi$
$307$		−	33.8928i		−	1.93436i	0.254086	−	0.967182i	$-0.418225\pi$
$308$		0			0
$309$	11.3870	−	11.3870i	0.647782	−	0.647782i
$310$		0			0
$311$	−13.3236	+	13.3236i	−0.755510	+	0.755510i	−0.975502	−	0.219992i	$-0.929397\pi$
$311$	−13.3236	+	13.3236i	−0.755510	+	0.755510i	0.219992	+	0.975502i	$0.429397\pi$
$312$		0			0
$313$	19.4611	−	19.4611i	1.10001	−	1.10001i	0.105597	−	0.994409i	$-0.466325\pi$
$313$	19.4611	−	19.4611i	1.10001	−	1.10001i	0.994409	−	0.105597i	$-0.0336755\pi$
$314$		0			0
$315$	17.3077	+	15.9705i	0.975181	+	0.899837i
$316$		0			0
$317$	0.210031	−	0.210031i	0.0117965	−	0.0117965i	−0.701184	−	0.712980i	$-0.747345\pi$
$317$	0.210031	−	0.210031i	0.0117965	−	0.0117965i	0.712980	+	0.701184i	$0.247345\pi$
$318$		0			0
$319$	22.1923			1.24253
$320$		0			0
$321$			10.4804i			0.584960i
$322$		0			0
$323$	1.46118	−	1.29239i	0.0813023	−	0.0719106i
$324$		0			0
$325$	−1.92534	−	23.9184i	−0.106798	−	1.32676i
$326$		0			0
$327$		−	8.90708i		−	0.492563i
$328$		0			0
$329$	32.5427	+	32.5427i	1.79414	+	1.79414i
$330$		0			0
$331$		−	0.364298i		−	0.0200236i	−0.999950	−	0.0100118i	$-0.996813\pi$
$331$		−	0.364298i		−	0.0200236i	0.999950	−	0.0100118i	$-0.00318691\pi$
$332$		0			0
$333$	−7.85824	+	7.85824i	−0.430629	+	0.430629i
$334$		0			0
$335$	−1.25194	−	31.1561i	−0.0684010	−	1.70224i
$336$		0			0
$337$	−0.532640	−	0.532640i	−0.0290148	−	0.0290148i	0.692451	−	0.721465i	$-0.256531\pi$
$337$	−0.532640	−	0.532640i	−0.0290148	−	0.0290148i	−0.721465	+	0.692451i	$0.756531\pi$
$338$		0			0
$339$	38.7330			2.10369
$340$		0			0
$341$	−10.9694			−0.594025
$342$		0			0
$343$	1.23294	+	1.23294i	0.0665726	+	0.0665726i
$344$		0			0
$345$	−5.67286	+	0.227952i	−0.305417	+	0.0122725i
$346$		0			0
$347$	9.48106	−	9.48106i	0.508970	−	0.508970i	−0.405240	−	0.914210i	$-0.632812\pi$
$347$	9.48106	−	9.48106i	0.508970	−	0.508970i	0.914210	+	0.405240i	$0.132812\pi$
$348$		0			0
$349$			35.1919i			1.88378i	0.335923	+	0.941889i	$0.390952\pi$
$349$			35.1919i			1.88378i	−0.335923	+	0.941889i	$0.609048\pi$
$350$		0			0
$351$	1.87644	+	1.87644i	0.100157	+	0.100157i
$352$		0			0
$353$			3.91738i			0.208501i	0.994551	+	0.104250i	$0.0332444\pi$
$353$			3.91738i			0.208501i	−0.994551	+	0.104250i	$0.966756\pi$
$354$		0			0
$355$	−9.04167	+	9.79873i	−0.479882	+	0.520063i
$356$		0			0
$357$	24.9497	+	28.2082i	1.32048	+	1.49294i
$358$		0			0
$359$			20.3757i			1.07539i	0.843141	+	0.537693i	$0.180704\pi$
$359$			20.3757i			1.07539i	−0.843141	+	0.537693i	$0.819296\pi$
$360$		0			0
$361$	18.7762			0.988219
$362$		0			0
$363$	−9.76738	+	9.76738i	−0.512654	+	0.512654i
$364$		0			0
$365$	−26.1497	−	24.1293i	−1.36874	−	1.26299i
$366$		0			0
$367$	−9.99474	+	9.99474i	−0.521721	+	0.521721i	−0.918091	−	0.396370i	$-0.870270\pi$
$367$	−9.99474	+	9.99474i	−0.521721	+	0.521721i	0.396370	+	0.918091i	$0.370270\pi$
$368$		0			0
$369$	−4.88620	+	4.88620i	−0.254366	+	0.254366i
$370$		0			0
$371$	5.76485	−	5.76485i	0.299296	−	0.299296i
$372$		0			0
$373$			14.1787i			0.734143i	0.930193	+	0.367072i	$0.119640\pi$
$373$			14.1787i			0.734143i	−0.930193	+	0.367072i	$0.880360\pi$
$374$		0			0
$375$	21.1346	+	16.5697i	1.09138	+	0.855656i
$376$		0			0
$377$	−32.8698	−	32.8698i	−1.69288	−	1.69288i
$378$		0			0
$379$	10.6162	−	10.6162i	0.545318	−	0.545318i	−0.379765	−	0.925083i	$-0.623995\pi$
$379$	10.6162	−	10.6162i	0.545318	−	0.545318i	0.925083	+	0.379765i	$0.123995\pi$
$380$		0			0
$381$	−1.33560	−	1.33560i	−0.0684251	−	0.0684251i
$382$		0			0
$383$	15.8958			0.812238			0.406119	−	0.913820i	$-0.366882\pi$
$383$	15.8958			0.812238			0.406119	+	0.913820i	$0.366882\pi$
$384$		0			0
$385$	19.4649	−	0.782158i	0.992024	−	0.0398624i
$386$		0			0
$387$			30.5871i			1.55483i
$388$		0			0
$389$		−	12.0045i		−	0.608651i	−0.952568	−	0.304326i	$-0.901569\pi$
$389$		−	12.0045i		−	0.608651i	0.952568	−	0.304326i	$-0.0984311\pi$
$390$		0			0
$391$	−4.35008	−	0.266654i	−0.219993	−	0.0134852i
$392$		0			0
$393$	−44.6462			−2.25210
$394$		0			0
$395$	−13.6691	−	12.6130i	−0.687766	−	0.634628i
$396$		0			0
$397$	−17.5677	+	17.5677i	−0.881699	+	0.881699i	−0.993707	−	0.112008i	$-0.964272\pi$
$397$	−17.5677	+	17.5677i	−0.881699	+	0.881699i	0.112008	+	0.993707i	$0.464272\pi$
$398$		0			0
$399$		−	4.32130i		−	0.216336i
$400$		0			0
$401$	−5.35680	−	5.35680i	−0.267506	−	0.267506i	0.560589	−	0.828094i	$-0.310575\pi$
$401$	−5.35680	−	5.35680i	−0.267506	−	0.267506i	−0.828094	+	0.560589i	$0.810575\pi$
$402$		0			0
$403$	16.2471	+	16.2471i	0.809327	+	0.809327i
$404$		0			0
$405$	−21.5330	+	0.865258i	−1.06998	+	0.0429950i
$406$		0			0
$407$			9.19279i			0.455669i
$408$		0			0
$409$	−24.1481			−1.19405			−0.597024	−	0.802223i	$-0.703650\pi$
$409$	−24.1481			−1.19405			−0.597024	+	0.802223i	$0.703650\pi$
$410$		0			0
$411$	9.87207	−	9.87207i	0.486953	−	0.486953i
$412$		0			0
$413$	−17.3820	−	17.3820i	−0.855312	−	0.855312i
$414$		0			0
$415$	5.80832	−	0.233396i	0.285119	−	0.0114569i
$416$		0			0
$417$	27.9402			1.36824
$418$		0			0
$419$	12.8619	+	12.8619i	0.628343	+	0.628343i	0.947651	−	0.319308i	$-0.103450\pi$
$419$	12.8619	+	12.8619i	0.628343	+	0.628343i	−0.319308	+	0.947651i	$0.603450\pi$
$420$		0			0
$421$	−21.9746			−1.07098			−0.535488	−	0.844543i	$-0.679872\pi$
$421$	−21.9746			−1.07098			−0.535488	+	0.844543i	$0.679872\pi$
$422$		0			0
$423$	33.5239			1.62999
$424$		0			0
$425$	14.8531	+	14.2963i	0.720483	+	0.693472i
$426$		0			0
$427$	1.90679			0.0922760
$428$		0			0
$429$	−26.4120			−1.27518
$430$		0			0
$431$	15.5597	+	15.5597i	0.749486	+	0.749486i	0.974383	−	0.224897i	$-0.0722044\pi$
$431$	15.5597	+	15.5597i	0.749486	+	0.749486i	−0.224897	+	0.974383i	$0.572204\pi$
$432$		0			0
$433$	38.5005			1.85021			0.925107	−	0.379706i	$-0.123975\pi$
$433$	38.5005			1.85021			0.925107	+	0.379706i	$0.123975\pi$
$434$		0			0
$435$	51.9830	−	2.08883i	2.49240	−	0.100152i
$436$		0			0
$437$	0.353625	+	0.353625i	0.0169162	+	0.0169162i
$438$		0			0
$439$	26.3114	−	26.3114i	1.25578	−	1.25578i	0.302686	−	0.953090i	$-0.402117\pi$
$439$	26.3114	−	26.3114i	1.25578	−	1.25578i	0.953090	−	0.302686i	$-0.0978832\pi$
$440$		0			0
$441$	20.6587			0.983749
$442$		0			0
$443$		−	14.1092i		−	0.670349i	−0.942156	−	0.335175i	$-0.891205\pi$
$443$		−	14.1092i		−	0.670349i	0.942156	−	0.335175i	$-0.108795\pi$
$444$		0			0
$445$	20.3674	−	0.818422i	0.965507	−	0.0387969i
$446$		0			0
$447$	−36.9930	−	36.9930i	−1.74971	−	1.74971i
$448$		0			0
$449$	−16.5479	−	16.5479i	−0.780941	−	0.780941i	0.199048	−	0.979990i	$-0.436215\pi$
$449$	−16.5479	−	16.5479i	−0.780941	−	0.780941i	−0.979990	+	0.199048i	$0.936215\pi$
$450$		0			0
$451$			5.71601i			0.269156i
$452$		0			0
$453$	−3.36180	+	3.36180i	−0.157951	+	0.157951i
$454$		0			0
$455$	−29.9887	−	27.6717i	−1.40589	−	1.29727i
$456$		0			0
$457$	26.8190			1.25454			0.627271	−	0.778801i	$-0.284172\pi$
$457$	26.8190			1.25454			0.627271	+	0.778801i	$0.284172\pi$
$458$		0			0
$459$	−2.27559	−	0.139491i	−0.106216	−	0.00651086i
$460$		0			0
$461$			5.74080i			0.267376i	0.991023	+	0.133688i	$0.0426819\pi$
$461$			5.74080i			0.267376i	−0.991023	+	0.133688i	$0.957318\pi$
$462$		0			0
$463$		−	14.5005i		−	0.673893i	−0.941524	−	0.336947i	$-0.890606\pi$
$463$		−	14.5005i		−	0.673893i	0.941524	−	0.336947i	$-0.109394\pi$
$464$		0			0
$465$	−25.6946	+	1.03248i	−1.19156	+	0.0478803i
$466$		0			0
$467$	−18.2661			−0.845254			−0.422627	−	0.906304i	$-0.638892\pi$
$467$	−18.2661			−0.845254			−0.422627	+	0.906304i	$0.638892\pi$
$468$		0			0
$469$	−37.4935	−	37.4935i	−1.73129	−	1.73129i
$470$		0			0
$471$	1.14069	−	1.14069i	0.0525602	−	0.0525602i
$472$		0			0
$473$	17.8908	+	17.8908i	0.822619	+	0.822619i
$474$		0			0
$475$	−0.189807	−	2.35797i	−0.00870895	−	0.108191i
$476$		0			0
$477$		−	5.93867i		−	0.271913i
$478$		0			0
$479$	−8.88340	+	8.88340i	−0.405893	+	0.405893i	−0.880304	−	0.474411i	$-0.842661\pi$
$479$	−8.88340	+	8.88340i	−0.405893	+	0.405893i	0.474411	+	0.880304i	$0.342661\pi$
$480$		0			0
$481$	13.6158	−	13.6158i	0.620826	−	0.620826i
$482$		0			0
$483$	−6.82676	+	6.82676i	−0.310629	+	0.310629i
$484$		0			0
$485$	−14.8610	−	13.7128i	−0.674802	−	0.622666i
$486$		0			0
$487$	−9.77900	+	9.77900i	−0.443129	+	0.443129i	−0.893062	−	0.449933i	$-0.851448\pi$
$487$	−9.77900	+	9.77900i	−0.443129	+	0.443129i	0.449933	+	0.893062i	$0.351448\pi$
$488$		0			0
$489$	−5.95028			−0.269081
$490$		0			0
$491$		−	30.9519i		−	1.39684i	−0.715689	−	0.698419i	$-0.753887\pi$
$491$		−	30.9519i		−	1.39684i	0.715689	−	0.698419i	$-0.246113\pi$
$492$		0			0
$493$	39.8618	+	2.44347i	1.79528	+	0.110048i
$494$		0			0
$495$	9.62303	−	10.4288i	0.432523	−	0.468738i
$496$		0			0
$497$			22.6727i			1.01701i
$498$		0			0
$499$	−5.46055	−	5.46055i	−0.244448	−	0.244448i	0.574239	−	0.818687i	$-0.305298\pi$
$499$	−5.46055	−	5.46055i	−0.244448	−	0.244448i	−0.818687	+	0.574239i	$0.805298\pi$
$500$		0			0
$501$			2.14167i			0.0956828i
$502$		0			0
$503$	21.0635	−	21.0635i	0.939174	−	0.939174i	−0.0590792	−	0.998253i	$-0.518816\pi$
$503$	21.0635	−	21.0635i	0.939174	−	0.939174i	0.998253	+	0.0590792i	$0.0188165\pi$
$504$		0			0
$505$	−13.4356	+	0.539881i	−0.597875	+	0.0240244i
$506$		0			0
$507$	17.0392	+	17.0392i	0.756739	+	0.756739i
$508$		0			0
$509$	35.6036			1.57810			0.789052	−	0.614326i	$-0.210572\pi$
$509$	35.6036			1.57810			0.789052	+	0.614326i	$0.210572\pi$
$510$		0			0
$511$	−60.5062			−2.67663
$512$		0			0
$513$	0.184987	+	0.184987i	0.00816737	+	0.00816737i
$514$		0			0
$515$	−0.601893	−	14.9788i	−0.0265226	−	0.660045i
$516$		0			0
$517$	19.6086	−	19.6086i	0.862384	−	0.862384i
$518$		0			0
$519$			28.2130i			1.23841i
$520$		0			0
$521$	−6.84403	−	6.84403i	−0.299842	−	0.299842i	0.541110	−	0.840952i	$-0.318004\pi$
$521$	−6.84403	−	6.84403i	−0.299842	−	0.299842i	−0.840952	+	0.541110i	$0.818004\pi$
$522$		0			0
$523$		−	0.0431523i		−	0.00188692i	−1.00000		0.000943460i	$-0.999700\pi$
$523$		−	0.0431523i		−	0.00188692i	1.00000		0.000943460i	$-0.000300313\pi$
$524$		0			0
$525$	45.5209	−	3.66424i	1.98669	−	0.159921i
$526$		0			0
$527$	−19.7032	−	1.20778i	−0.858285	−	0.0526116i
$528$		0			0
$529$			21.8827i			0.951421i
$530$		0			0
$531$	−17.9061			−0.777058
$532$		0			0
$533$	8.46619	−	8.46619i	0.366711	−	0.366711i
$534$		0			0
$535$	7.17014	+	6.61617i	0.309992	+	0.286042i
$536$		0			0
$537$	−14.6986	+	14.6986i	−0.634292	+	0.634292i
$538$		0			0
$539$	12.0836	−	12.0836i	0.520476	−	0.520476i
$540$		0			0
$541$	−23.0154	+	23.0154i	−0.989510	+	0.989510i	−0.999946	−	0.0104358i	$-0.996678\pi$
$541$	−23.0154	+	23.0154i	−0.989510	+	0.989510i	0.0104358	+	0.999946i	$0.496678\pi$
$542$		0			0
$543$			43.9841i			1.88754i
$544$		0			0
$545$	−6.09375	−	5.62293i	−0.261027	−	0.240860i
$546$		0			0
$547$	−0.782615	−	0.782615i	−0.0334622	−	0.0334622i	0.690178	−	0.723640i	$-0.257532\pi$
$547$	−0.782615	−	0.782615i	−0.0334622	−	0.0334622i	−0.723640	+	0.690178i	$0.757532\pi$
$548$		0			0
$549$	0.982141	−	0.982141i	0.0419168	−	0.0419168i
$550$		0			0
$551$	−3.24043	−	3.24043i	−0.138047	−	0.138047i
$552$		0			0
$553$	−31.6280			−1.34496
$554$		0			0
$555$	0.865265	+	21.5331i	0.0367284	+	0.914030i
$556$		0			0
$557$			34.7140i			1.47088i	0.677591	+	0.735439i	$0.263024\pi$
$557$			34.7140i			1.47088i	−0.677591	+	0.735439i	$0.736976\pi$
$558$		0			0
$559$		−	52.9974i		−	2.24155i
$560$		0			0
$561$	16.9968	−	15.0334i	0.717607	−	0.634712i
$562$		0			0
$563$	12.9543			0.545960			0.272980	−	0.962020i	$-0.411991\pi$
$563$	12.9543			0.545960			0.272980	+	0.962020i	$0.411991\pi$
$564$		0			0
$565$	24.4517	−	26.4990i	1.02869	−	1.11482i
$566$		0			0
$567$	−25.9129	+	25.9129i	−1.08824	+	1.08824i
$568$		0			0
$569$			26.9552i			1.13002i	0.825083	+	0.565011i	$0.191128\pi$
$569$			26.9552i			1.13002i	−0.825083	+	0.565011i	$0.808872\pi$
$570$		0			0
$571$	−3.02208	−	3.02208i	−0.126470	−	0.126470i	0.641039	−	0.767509i	$-0.278504\pi$
$571$	−3.02208	−	3.02208i	−0.126470	−	0.126470i	−0.767509	+	0.641039i	$0.778504\pi$
$572$		0			0
$573$	−3.06776	−	3.06776i	−0.128157	−	0.128157i
$574$		0			0
$575$	−3.42526	+	4.02497i	−0.142843	+	0.167853i
$576$		0			0
$577$		−	20.7612i		−	0.864302i	−0.901801	−	0.432151i	$-0.857755\pi$
$577$		−	20.7612i		−	0.864302i	0.901801	−	0.432151i	$-0.142245\pi$
$578$		0			0
$579$	42.4198			1.76291
$580$		0			0
$581$	6.98978	−	6.98978i	0.289985	−	0.289985i
$582$		0			0
$583$	−3.47361	−	3.47361i	−0.143862	−	0.143862i
$584$		0			0
$585$	−29.6994	+	1.19341i	−1.22792	+	0.0493415i
$586$		0			0
$587$	−40.6389			−1.67735			−0.838674	−	0.544634i	$-0.816669\pi$
$587$	−40.6389			−1.67735			−0.838674	+	0.544634i	$0.816669\pi$
$588$		0			0
$589$	1.60171	+	1.60171i	0.0659972	+	0.0659972i
$590$		0			0
$591$	−52.7216			−2.16868
$592$		0			0
$593$	12.4818			0.512567			0.256284	−	0.966602i	$-0.417502\pi$
$593$	12.4818			0.512567			0.256284	+	0.966602i	$0.417502\pi$
$594$		0			0
$595$	35.0490	+	0.738262i	1.43687	+	0.0302658i
$596$		0			0
$597$	22.2158			0.909233
$598$		0			0
$599$	−37.9426			−1.55029			−0.775147	−	0.631781i	$-0.782324\pi$
$599$	−37.9426			−1.55029			−0.775147	+	0.631781i	$0.782324\pi$
$600$		0			0
$601$	4.36278	+	4.36278i	0.177962	+	0.177962i	0.790467	−	0.612505i	$-0.209838\pi$
$601$	4.36278	+	4.36278i	0.177962	+	0.177962i	−0.612505	+	0.790467i	$0.709838\pi$
$602$		0			0
$603$	−38.6239			−1.57289
$604$		0			0
$605$	0.516285	+	12.8483i	0.0209900	+	0.522360i
$606$		0			0
$607$	17.2199	+	17.2199i	0.698936	+	0.698936i	0.964181	−	0.265245i	$-0.0854529\pi$
$607$	17.2199	+	17.2199i	0.698936	+	0.698936i	−0.265245	+	0.964181i	$0.585453\pi$
$608$		0			0
$609$	62.5568	−	62.5568i	2.53493	−	2.53493i
$610$		0			0
$611$	−58.0859			−2.34990
$612$		0			0
$613$			39.7179i			1.60419i	0.597196	+	0.802095i	$0.296281\pi$
$613$			39.7179i			1.60419i	−0.597196	+	0.802095i	$0.703719\pi$
$614$		0			0
$615$	0.538016	+	13.3891i	0.0216949	+	0.539903i
$616$		0			0
$617$	10.2837	+	10.2837i	0.414005	+	0.414005i	0.883131	−	0.469126i	$-0.155431\pi$
$617$	10.2837	+	10.2837i	0.414005	+	0.414005i	−0.469126	+	0.883131i	$0.655431\pi$
$618$		0			0
$619$	−20.8463	−	20.8463i	−0.837884	−	0.837884i	0.150696	−	0.988580i	$-0.451849\pi$
$619$	−20.8463	−	20.8463i	−0.837884	−	0.837884i	−0.988580	+	0.150696i	$0.951849\pi$
$620$		0			0
$621$		−	0.584482i		−	0.0234545i
$622$		0			0
$623$	24.5103	−	24.5103i	0.981983	−	0.981983i
$624$		0			0
$625$	24.6781	−	3.99888i	0.987124	−	0.159955i
$626$		0			0
$627$	−2.60380			−0.103986
$628$		0			0
$629$	−1.01217	+	16.5121i	−0.0403577	+	0.658380i
$630$		0			0
$631$			38.0577i			1.51505i	0.652805	+	0.757526i	$0.273592\pi$
$631$			38.0577i			1.51505i	−0.652805	+	0.757526i	$0.726408\pi$
$632$		0			0
$633$		−	35.3677i		−	1.40574i
$634$		0			0
$635$	−1.75690	+	0.0705974i	−0.0697204	+	0.00280157i
$636$		0			0
$637$	−35.7948			−1.41824
$638$		0			0
$639$	11.6782	+	11.6782i	0.461981	+	0.461981i
$640$		0			0
$641$	15.0374	−	15.0374i	0.593940	−	0.593940i	−0.344753	−	0.938693i	$-0.612037\pi$
$641$	15.0374	−	15.0374i	0.593940	−	0.593940i	0.938693	+	0.344753i	$0.112037\pi$
$642$		0			0
$643$	−19.0963	−	19.0963i	−0.753083	−	0.753083i	0.221970	−	0.975053i	$-0.428751\pi$
$643$	−19.0963	−	19.0963i	−0.753083	−	0.753083i	−0.975053	+	0.221970i	$0.928751\pi$
$644$		0			0
$645$	43.5912	+	40.2233i	1.71640	+	1.58379i
$646$		0			0
$647$			11.0358i			0.433862i	0.976187	+	0.216931i	$0.0696047\pi$
$647$			11.0358i			0.433862i	−0.976187	+	0.216931i	$0.930395\pi$
$648$		0			0
$649$	−10.4735	+	10.4735i	−0.411121	+	0.411121i
$650$		0			0
$651$	−30.9211	+	30.9211i	−1.21189	+	1.21189i
$652$		0			0
$653$	−20.3581	+	20.3581i	−0.796673	+	0.796673i	−0.982569	−	0.185897i	$-0.940481\pi$
$653$	−20.3581	+	20.3581i	−0.796673	+	0.796673i	0.185897	+	0.982569i	$0.440481\pi$
$654$		0			0
$655$	−28.1846	+	30.5445i	−1.10126	+	1.19347i
$656$		0			0
$657$	−31.1652	+	31.1652i	−1.21587	+	1.21587i
$658$		0			0
$659$	−20.5022			−0.798653			−0.399327	−	0.916809i	$-0.630756\pi$
$659$	−20.5022			−0.798653			−0.399327	+	0.916809i	$0.630756\pi$
$660$		0			0
$661$			8.50686i			0.330879i	0.986220	+	0.165439i	$0.0529042\pi$
$661$			8.50686i			0.330879i	−0.986220	+	0.165439i	$0.947096\pi$
$662$		0			0
$663$	−47.4412	−	2.90808i	−1.84246	−	0.112940i
$664$		0			0
$665$	−2.95640	−	2.72799i	−0.114644	−	0.105787i
$666$		0			0
$667$			10.2384i			0.396434i
$668$		0			0
$669$	−19.3120	−	19.3120i	−0.746645	−	0.746645i
$670$		0			0
$671$		−	1.14894i		−	0.0443542i
$672$		0			0
$673$	−14.9441	+	14.9441i	−0.576054	+	0.576054i	−0.933814	−	0.357760i	$-0.883541\pi$
$673$	−14.9441	+	14.9441i	−0.576054	+	0.576054i	0.357760	+	0.933814i	$0.383541\pi$
$674$		0			0
$675$	−1.79180	+	2.10552i	−0.0689666	+	0.0810416i
$676$		0			0
$677$	−31.1078	−	31.1078i	−1.19557	−	1.19557i	−0.975479	−	0.220092i	$-0.929364\pi$
$677$	−31.1078	−	31.1078i	−1.19557	−	1.19557i	−0.220092	−	0.975479i	$-0.570636\pi$
$678$		0			0
$679$	−34.3859			−1.31961
$680$		0			0
$681$	−69.6391			−2.66858
$682$		0			0
$683$	−6.45703	−	6.45703i	−0.247071	−	0.247071i	0.572696	−	0.819768i	$-0.305897\pi$
$683$	−6.45703	−	6.45703i	−0.247071	−	0.247071i	−0.819768	+	0.572696i	$0.805897\pi$
$684$		0			0
$685$	−0.521818	−	12.9861i	−0.0199377	−	0.496172i
$686$		0			0
$687$	−3.60688	+	3.60688i	−0.137611	+	0.137611i
$688$		0			0
$689$			10.2898i			0.392009i
$690$		0			0
$691$	22.7756	+	22.7756i	0.866424	+	0.866424i	0.992075	−	0.125650i	$-0.0401017\pi$
$691$	22.7756	+	22.7756i	0.866424	+	0.866424i	−0.125650	+	0.992075i	$0.540102\pi$
$692$		0			0
$693$		−	24.1305i		−	0.916642i
$694$		0			0
$695$	17.6383	−	19.1152i	0.669060	−	0.725081i
$696$		0			0
$697$	−0.629359	+	10.2671i	−0.0238387	+	0.388894i
$698$		0			0
$699$			11.0256i			0.417028i
$700$		0			0
$701$	−8.81649			−0.332994			−0.166497	−	0.986042i	$-0.553246\pi$
$701$	−8.81649			−0.332994			−0.166497	+	0.986042i	$0.553246\pi$
$702$		0			0
$703$	1.34230	−	1.34230i	0.0506257	−	0.0506257i
$704$		0			0
$705$	44.0853	−	47.7766i	1.66035	−	1.79937i
$706$		0			0
$707$	−16.1685	+	16.1685i	−0.608078	+	0.608078i
$708$		0			0
$709$	0.882611	−	0.882611i	0.0331472	−	0.0331472i	−0.690339	−	0.723486i	$-0.742539\pi$
$709$	0.882611	−	0.882611i	0.0331472	−	0.0331472i	0.723486	+	0.690339i	$0.242539\pi$
$710$		0			0
$711$	−16.2908	+	16.2908i	−0.610954	+	0.610954i
$712$		0			0
$713$		−	5.06073i		−	0.189526i
$714$		0			0
$715$	−16.6736	+	18.0697i	−0.623556	+	0.675767i
$716$		0			0
$717$	7.47222	+	7.47222i	0.279055	+	0.279055i
$718$		0			0
$719$	18.3862	−	18.3862i	0.685690	−	0.685690i	−0.275586	−	0.961276i	$-0.588872\pi$
$719$	18.3862	−	18.3862i	0.685690	−	0.685690i	0.961276	+	0.275586i	$0.0888720\pi$
$720$		0			0
$721$	−18.0256	−	18.0256i	−0.671309	−	0.671309i
$722$		0			0
$723$	−9.07197			−0.337390
$724$		0			0
$725$	31.3872	−	36.8827i	1.16569	−	1.36979i
$726$		0			0
$727$			41.1201i			1.52506i	0.646953	+	0.762530i	$0.276043\pi$
$727$			41.1201i			1.52506i	−0.646953	+	0.762530i	$0.723957\pi$
$728$		0			0
$729$			22.7096i			0.841098i
$730$		0			0
$731$	30.1656	+	34.1053i	1.11571	+	1.26143i
$732$		0			0
$733$	−28.3930			−1.04872			−0.524360	−	0.851497i	$-0.675695\pi$
$733$	−28.3930			−1.04872			−0.524360	+	0.851497i	$0.675695\pi$
$734$		0			0
$735$	27.1671	−	29.4418i	1.00207	−	1.08598i
$736$		0			0
$737$	−22.5917	+	22.5917i	−0.832174	+	0.832174i
$738$		0			0
$739$			40.0186i			1.47211i	0.676923	+	0.736053i	$0.263313\pi$
$739$			40.0186i			1.47211i	−0.676923	+	0.736053i	$0.736687\pi$
$740$		0			0
$741$	3.85658	+	3.85658i	0.141675	+	0.141675i
$742$		0			0
$743$	−25.2900	−	25.2900i	−0.927800	−	0.927800i	0.0697638	−	0.997564i	$-0.477775\pi$
$743$	−25.2900	−	25.2900i	−0.927800	−	0.927800i	−0.997564	+	0.0697638i	$0.977775\pi$
$744$		0			0
$745$	−48.6618	+	1.95538i	−1.78283	+	0.0716395i
$746$		0			0
$747$		−	7.20053i		−	0.263454i
$748$		0			0
$749$	16.5905			0.606205
$750$		0			0
$751$	−4.74161	+	4.74161i	−0.173024	+	0.173024i	−0.788306	−	0.615283i	$-0.789042\pi$
$751$	−4.74161	+	4.74161i	−0.173024	+	0.173024i	0.615283	+	0.788306i	$0.289042\pi$
$752$		0			0
$753$	26.6029	+	26.6029i	0.969463	+	0.969463i
$754$		0			0
$755$	0.177698	+	4.42223i	0.00646710	+	0.160941i
$756$		0			0
$757$	−7.39432			−0.268751			−0.134376	−	0.990930i	$-0.542903\pi$
$757$	−7.39432			−0.268751			−0.134376	+	0.990930i	$0.542903\pi$
$758$		0			0
$759$	4.11346	+	4.11346i	0.149309	+	0.149309i
$760$		0			0
$761$	−20.5436			−0.744704			−0.372352	−	0.928092i	$-0.621449\pi$
$761$	−20.5436			−0.744704			−0.372352	+	0.928092i	$0.621449\pi$
$762$		0			0
$763$	−14.0999			−0.510452
$764$		0			0
$765$	18.4331	−	17.6726i	0.666452	−	0.638955i
$766$		0			0
$767$	31.0254			1.12026
$768$		0			0
$769$	10.4379			0.376399			0.188200	−	0.982131i	$-0.439735\pi$
$769$	10.4379			0.376399			0.188200	+	0.982131i	$0.439735\pi$
$770$		0			0
$771$	−25.4505	−	25.4505i	−0.916577	−	0.916577i
$772$		0			0
$773$	38.8806			1.39844			0.699220	−	0.714907i	$-0.253531\pi$
$773$	38.8806			1.39844			0.699220	+	0.714907i	$0.253531\pi$
$774$		0			0
$775$	−15.5143	+	18.2307i	−0.557291	+	0.654864i
$776$		0			0
$777$	25.9131	+	25.9131i	0.929628	+	0.929628i
$778$		0			0
$779$	0.834631	−	0.834631i	0.0299038	−	0.0299038i
$780$		0			0
$781$	13.6614			0.488844
$782$		0			0
$783$			5.35588i			0.191404i
$784$		0			0
$785$	−0.0602947	−	1.50050i	−0.00215201	−	0.0535553i
$786$		0			0
$787$	−33.6600	−	33.6600i	−1.19985	−	1.19985i	−0.974211	−	0.225637i	$-0.927554\pi$
$787$	−33.6600	−	33.6600i	−1.19985	−	1.19985i	−0.225637	−	0.974211i	$-0.572446\pi$
$788$		0			0
$789$	−25.9277	−	25.9277i	−0.923052	−	0.923052i
$790$		0			0
$791$		−	61.3144i		−	2.18009i
$792$		0			0
$793$	−1.70173	+	1.70173i	−0.0604302	+	0.0604302i
$794$		0			0
$795$	−8.46350	−	7.80960i	−0.300170	−	0.276978i
$796$		0			0
$797$	23.0211			0.815448			0.407724	−	0.913105i	$-0.366323\pi$
$797$	23.0211			0.815448			0.407724	+	0.913105i	$0.366323\pi$
$798$		0			0
$799$	37.3799	−	33.0619i	1.32241	−	1.16965i
$800$		0			0
$801$		−	25.2493i		−	0.892140i
$802$		0			0
$803$			36.4579i			1.28657i
$804$		0			0
$805$	0.360850	+	8.98016i	0.0127183	+	0.316509i
$806$		0			0
$807$	65.0358			2.28937
$808$		0			0
$809$	−6.65071	−	6.65071i	−0.233826	−	0.233826i	0.580461	−	0.814288i	$-0.302872\pi$
$809$	−6.65071	−	6.65071i	−0.233826	−	0.233826i	−0.814288	+	0.580461i	$0.802872\pi$
$810$		0			0
$811$	−6.08751	+	6.08751i	−0.213761	+	0.213761i	−0.805863	−	0.592102i	$-0.798298\pi$
$811$	−6.08751	+	6.08751i	−0.213761	+	0.213761i	0.592102	+	0.805863i	$0.298298\pi$
$812$		0			0
$813$	−37.0323	−	37.0323i	−1.29878	−	1.29878i
$814$		0			0
$815$	−3.75634	+	4.07086i	−0.131579	+	0.142596i
$816$		0			0
$817$		−	5.22469i		−	0.182789i
$818$		0			0
$819$	−35.7406	+	35.7406i	−1.24888	+	1.24888i
$820$		0			0
$821$	−14.4519	+	14.4519i	−0.504374	+	0.504374i	−0.912794	−	0.408420i	$-0.866080\pi$
$821$	−14.4519	+	14.4519i	−0.504374	+	0.504374i	0.408420	+	0.912794i	$0.366080\pi$
$822$		0			0
$823$	−10.0576	+	10.0576i	−0.350587	+	0.350587i	−0.860328	−	0.509741i	$-0.829741\pi$
$823$	−10.0576	+	10.0576i	−0.350587	+	0.350587i	0.509741	+	0.860328i	$0.329741\pi$
$824$		0			0
$825$	−2.20789	−	27.4286i	−0.0768688	−	0.954940i
$826$		0			0
$827$	20.4402	−	20.4402i	0.710776	−	0.710776i	−0.255922	−	0.966698i	$-0.582379\pi$
$827$	20.4402	−	20.4402i	0.710776	−	0.710776i	0.966698	+	0.255922i	$0.0823789\pi$
$828$		0			0
$829$	34.0549			1.18277			0.591387	−	0.806388i	$-0.298581\pi$
$829$	34.0549			1.18277			0.591387	+	0.806388i	$0.298581\pi$
$830$		0			0
$831$		−	5.51758i		−	0.191403i
$832$		0			0
$833$	23.0350	−	20.3741i	0.798114	−	0.705919i
$834$		0			0
$835$	1.46522	+	1.35201i	0.0507059	+	0.0467883i
$836$		0			0
$837$		−	2.64735i		−	0.0915057i
$838$		0			0
$839$	34.4736	+	34.4736i	1.19016	+	1.19016i	0.977022	+	0.213140i	$0.0683691\pi$
$839$	34.4736	+	34.4736i	1.19016	+	1.19016i	0.213140	+	0.977022i	$0.431631\pi$
$840$		0			0
$841$		−	64.8195i		−	2.23516i
$842$		0			0
$843$	−2.64629	+	2.64629i	−0.0911430	+	0.0911430i
$844$		0			0
$845$	22.4140	−	0.900661i	0.771065	−	0.0309837i
$846$		0			0
$847$	15.4618	+	15.4618i	0.531274	+	0.531274i
$848$		0			0
$849$	9.17158			0.314768
$850$		0			0
$851$	−4.24110			−0.145383
$852$		0			0
$853$	34.2445	+	34.2445i	1.17251	+	1.17251i	0.981610	+	0.190898i	$0.0611400\pi$
$853$	34.2445	+	34.2445i	1.17251	+	1.17251i	0.190898	+	0.981610i	$0.438860\pi$
$854$		0			0
$855$	−2.92789	+	0.117651i	−0.100132	+	0.00402359i
$856$		0			0
$857$	34.3909	−	34.3909i	1.17477	−	1.17477i	0.193712	−	0.981059i	$-0.437947\pi$
$857$	34.3909	−	34.3909i	1.17477	−	1.17477i	0.981059	−	0.193712i	$-0.0620526\pi$
$858$		0			0
$859$		−	38.8535i		−	1.32566i	−0.748768	−	0.662832i	$-0.769354\pi$
$859$		−	38.8535i		−	1.32566i	0.748768	−	0.662832i	$-0.230646\pi$
$860$		0			0
$861$	16.1126	+	16.1126i	0.549116	+	0.549116i
$862$		0			0
$863$		−	18.6253i		−	0.634013i	−0.948423	−	0.317006i	$-0.897322\pi$
$863$		−	18.6253i		−	0.634013i	0.948423	−	0.317006i	$-0.102678\pi$
$864$		0			0
$865$	19.3018	+	17.8105i	0.656281	+	0.605576i
$866$		0			0
$867$	32.1850	−	25.1316i	1.09306	−	0.853515i
$868$		0			0
$869$			19.0575i			0.646480i
$870$		0			0
$871$	66.9226			2.26759
$872$		0			0
$873$	−17.7113	+	17.7113i	−0.599438	+	0.599438i
$874$		0			0
$875$	26.2299	−	33.4561i	0.886733	−	1.13102i
$876$		0			0
$877$	24.8828	−	24.8828i	0.840232	−	0.840232i	−0.148657	−	0.988889i	$-0.547495\pi$
$877$	24.8828	−	24.8828i	0.840232	−	0.840232i	0.988889	+	0.148657i	$0.0474950\pi$
$878$		0			0
$879$	22.3915	−	22.3915i	0.755247	−	0.755247i
$880$		0			0
$881$	−11.8409	+	11.8409i	−0.398928	+	0.398928i	−0.877855	−	0.478927i	$-0.841026\pi$
$881$	−11.8409	+	11.8409i	−0.398928	+	0.398928i	0.478927	+	0.877855i	$0.341026\pi$
$882$		0			0
$883$		−	40.6118i		−	1.36670i	−0.730092	−	0.683349i	$-0.760523\pi$
$883$		−	40.6118i		−	1.36670i	0.730092	−	0.683349i	$-0.239477\pi$
$884$		0			0
$885$	−23.5473	+	25.5189i	−0.791533	+	0.857808i
$886$		0			0
$887$	−18.2255	−	18.2255i	−0.611952	−	0.611952i	0.331502	−	0.943454i	$-0.392445\pi$
$887$	−18.2255	−	18.2255i	−0.611952	−	0.611952i	−0.943454	+	0.331502i	$0.892445\pi$
$888$		0			0
$889$	−2.11427	+	2.11427i	−0.0709102	+	0.0709102i
$890$		0			0
$891$	15.6138	+	15.6138i	0.523083	+	0.523083i
$892$		0			0
$893$	−5.72634			−0.191625
$894$		0			0
$895$	0.776940	+	19.3351i	0.0259702	+	0.646300i
$896$		0			0
$897$		−	12.1852i		−	0.406852i
$898$		0			0
$899$			46.3739i			1.54665i
$900$		0			0
$901$	−5.85683	−	6.62175i	−0.195119	−	0.220603i
$902$		0			0
$903$	100.863			3.35651
$904$		0			0
$905$	30.0915	+	27.7666i	1.00028	+	0.922994i
$906$		0			0
$907$	8.72237	−	8.72237i	0.289621	−	0.289621i	−0.547309	−	0.836931i	$-0.684348\pi$
$907$	8.72237	−	8.72237i	0.289621	−	0.289621i	0.836931	+	0.547309i	$0.184348\pi$
$908$		0			0
$909$			16.6560i			0.552444i
$910$		0			0
$911$	2.80241	+	2.80241i	0.0928479	+	0.0928479i	0.752005	−	0.659157i	$-0.229087\pi$
$911$	2.80241	+	2.80241i	0.0928479	+	0.0928479i	−0.659157	+	0.752005i	$0.729087\pi$
$912$		0			0
$913$	−4.21169	−	4.21169i	−0.139387	−	0.139387i
$914$		0			0
$915$	−0.108143	−	2.69126i	−0.00357509	−	0.0889703i
$916$		0			0
$917$			70.6751i			2.33390i
$918$		0			0
$919$	2.63743			0.0870007			0.0435004	−	0.999053i	$-0.486149\pi$
$919$	2.63743			0.0870007			0.0435004	+	0.999053i	$0.486149\pi$
$920$		0			0
$921$	−57.5669	+	57.5669i	−1.89689	+	1.89689i
$922$		0			0
$923$	−20.2344	−	20.2344i	−0.666024	−	0.666024i
$924$		0			0
$925$	15.2780	+	13.0016i	0.502339	+	0.427491i
$926$		0			0
$927$	−18.5691			−0.609890
$928$		0			0
$929$	36.9557	+	36.9557i	1.21248	+	1.21248i	0.970209	+	0.242268i	$0.0778915\pi$
$929$	36.9557	+	36.9557i	1.21248	+	1.21248i	0.242268	+	0.970209i	$0.422109\pi$
$930$		0			0
$931$	−3.52879			−0.115652
$932$		0			0
$933$	45.2601			1.48175
$934$		0			0
$935$	0.444839	−	21.1188i	0.0145478	−	0.690657i
$936$		0			0
$937$	23.6381			0.772224			0.386112	−	0.922452i	$-0.373818\pi$
$937$	23.6381			0.772224			0.386112	+	0.922452i	$0.373818\pi$
$938$		0			0
$939$	−66.1093			−2.15740
$940$		0			0
$941$	−32.4847	−	32.4847i	−1.05897	−	1.05897i	−0.998149	−	0.0608209i	$-0.980628\pi$
$941$	−32.4847	−	32.4847i	−1.05897	−	1.05897i	−0.0608209	−	0.998149i	$-0.519372\pi$
$942$		0			0
$943$	−2.63709			−0.0858755
$944$		0			0
$945$	0.188766	+	4.69766i	0.00614055	+	0.152815i
$946$		0			0
$947$	7.83973	+	7.83973i	0.254757	+	0.254757i	0.822918	−	0.568161i	$-0.192345\pi$
$947$	7.83973	+	7.83973i	0.254757	+	0.254757i	−0.568161	+	0.822918i	$0.692345\pi$
$948$		0			0
$949$	53.9992	−	53.9992i	1.75289	−	1.75289i
$950$		0			0
$951$	−0.713475			−0.0231360
$952$		0			0
$953$			46.1104i			1.49366i	0.665013	+	0.746832i	$0.268426\pi$
$953$			46.1104i			1.49366i	−0.665013	+	0.746832i	$0.731574\pi$
$954$		0			0
$955$	−4.03543	+	0.162156i	−0.130584	+	0.00524723i
$956$		0			0
$957$	−37.6936	−	37.6936i	−1.21846	−	1.21846i
$958$		0			0
$959$	−15.6275	−	15.6275i	−0.504639	−	0.504639i
$960$		0			0
$961$			8.07796i			0.260580i
$962$		0			0
$963$	8.54539	−	8.54539i	0.275371	−	0.275371i
$964$		0			0
$965$	26.7791	−	29.0213i	0.862050	−	0.934230i
$966$		0			0
$967$	−45.1573			−1.45216			−0.726080	−	0.687610i	$-0.758660\pi$
$967$	−45.1573			−1.45216			−0.726080	+	0.687610i	$0.758660\pi$
$968$		0			0
$969$	−4.67694	−	0.286690i	−0.150245	−	0.00920980i
$970$		0			0
$971$			1.04631i			0.0335776i	0.999859	+	0.0167888i	$0.00534429\pi$
$971$			1.04631i			0.0335776i	−0.999859	+	0.0167888i	$0.994656\pi$
$972$		0			0
$973$		−	44.2295i		−	1.41793i
$974$		0			0
$975$	−37.3553	+	43.8956i	−1.19633	+	1.40579i
$976$		0			0
$977$	−38.9405			−1.24582			−0.622909	−	0.782294i	$-0.714049\pi$
$977$	−38.9405			−1.24582			−0.622909	+	0.782294i	$0.714049\pi$
$978$		0			0
$979$	−14.7686	−	14.7686i	−0.472008	−	0.472008i
$980$		0			0
$981$	−7.26254	+	7.26254i	−0.231875	+	0.231875i
$982$		0			0
$983$	26.4018	+	26.4018i	0.842087	+	0.842087i	0.989130	−	0.147043i	$-0.0469756\pi$
$983$	26.4018	+	26.4018i	0.842087	+	0.842087i	−0.147043	+	0.989130i	$0.546976\pi$
$984$		0			0
$985$	−33.2825	+	36.0693i	−1.06047	+	1.14926i
$986$		0			0
$987$		−	110.547i		−	3.51876i
$988$		0			0
$989$	−8.25394	+	8.25394i	−0.262460	+	0.262460i
$990$		0			0
$991$	10.1211	−	10.1211i	0.321509	−	0.321509i	−0.527837	−	0.849346i	$-0.676997\pi$
$991$	10.1211	−	10.1211i	0.321509	−	0.321509i	0.849346	+	0.527837i	$0.176997\pi$
$992$		0			0
$993$	−0.618760	+	0.618760i	−0.0196358	+	0.0196358i
$994$		0			0
$995$	14.0246	−	15.1989i	0.444609	−	0.481836i
$996$		0			0
$997$	23.2456	−	23.2456i	0.736196	−	0.736196i	−0.235644	−	0.971840i	$-0.575720\pi$
$997$	23.2456	−	23.2456i	0.736196	−	0.736196i	0.971840	+	0.235644i	$0.0757198\pi$
$998$		0			0
$999$	−2.21859			−0.0701930

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.z.d.89.3	yes	26
5.4	even	2		680.2.z.c.89.11	✓	26
17.13	even	4		680.2.z.c.489.11	yes	26
85.64	even	4	inner	680.2.z.d.489.3	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.z.c.89.11	✓	26	5.4	even	2
680.2.z.c.489.11	yes	26	17.13	even	4
680.2.z.d.89.3	yes	26	1.1	even	1	trivial
680.2.z.d.489.3	yes	26	85.64	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.z (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69850 - 1.69850i) q^{3} +(-2.23426 + 0.0897794i) q^{5} +(-2.68873 + 2.68873i) q^{7} +2.76980i q^{9} +(1.62009 + 1.62009i) q^{11} -4.79916i q^{13} +(3.94739 + 3.64241i) q^{15} +(2.73163 + 3.08839i) q^{17} -0.473120i q^{19} +9.13362 q^{21} +(-0.747433 + 0.747433i) q^{23} +(4.98388 - 0.401182i) q^{25} +(-0.390993 + 0.390993i) q^{27} +(6.84907 - 6.84907i) q^{29} +(-3.38541 + 3.38541i) q^{31} -5.50346i q^{33} +(5.76595 - 6.24873i) q^{35} +(2.83711 + 2.83711i) q^{37} +(-8.15137 + 8.15137i) q^{39} +(1.76410 + 1.76410i) q^{41} +11.0431 q^{43} +(-0.248671 - 6.18847i) q^{45} -12.1034i q^{47} -7.45856i q^{49} +(0.605956 - 9.88531i) q^{51} -2.14408 q^{53} +(-3.76517 - 3.47427i) q^{55} +(-0.803594 + 0.803594i) q^{57} +6.46475i q^{59} +(-0.354589 - 0.354589i) q^{61} +(-7.44725 - 7.44725i) q^{63} +(0.430866 + 10.7226i) q^{65} +13.9447i q^{67} +2.53903 q^{69} +(4.21624 - 4.21624i) q^{71} +(11.2518 + 11.2518i) q^{73} +(-9.14652 - 7.78371i) q^{75} -8.71200 q^{77} +(5.88159 + 5.88159i) q^{79} +9.63761 q^{81} -2.59966 q^{83} +(-6.38047 - 6.65504i) q^{85} -23.2663 q^{87} -9.11592 q^{89} +(12.9037 + 12.9037i) q^{91} +11.5002 q^{93} +(0.0424764 + 1.05708i) q^{95} +(6.39444 + 6.39444i) q^{97} +(-4.48734 + 4.48734i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 2 q^{3} - 2 q^{5} + 2 q^{7} + 2 q^{11} - 2 q^{15} + 2 q^{17} - 12 q^{21} - 2 q^{23} + 10 q^{25} + 20 q^{27} + 10 q^{29} - 10 q^{31} + 22 q^{35} - 6 q^{37} + 8 q^{39} - 10 q^{41} + 32 q^{43} + 28 q^{45}+ \cdots - 22 q^{99}+O(q^{100}) \) 26 * q + 2 * q^3 - 2 * q^5 + 2 * q^7 + 2 * q^11 - 2 * q^15 + 2 * q^17 - 12 * q^21 - 2 * q^23 + 10 * q^25 + 20 * q^27 + 10 * q^29 - 10 * q^31 + 22 * q^35 - 6 * q^37 + 8 * q^39 - 10 * q^41 + 32 * q^43 + 28 * q^45 - 6 * q^51 - 32 * q^53 - 26 * q^55 + 20 * q^57 + 6 * q^61 - 54 * q^63 + 24 * q^65 - 20 * q^69 - 30 * q^71 + 42 * q^73 - 78 * q^75 - 4 * q^77 + 14 * q^79 - 54 * q^81 - 16 * q^83 - 26 * q^85 + 8 * q^87 + 40 * q^89 + 24 * q^91 + 88 * q^93 + 44 * q^95 + 66 * q^97 - 22 * q^99

Introduction

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