LMFDB - Embedded newform 680.2.z.c.489.11

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			489.11
Character	$\chi$	$=$	680.489
Dual form			680.2.z.c.89.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.69850 - 1.69850i) q^{3} +(-0.0897794 - 2.23426i) q^{5} +(2.68873 + 2.68873i) q^{7} -2.76980i q^{9} +(1.62009 - 1.62009i) q^{11} -4.79916i q^{13} +(-3.94739 - 3.64241i) q^{15} +(-2.73163 + 3.08839i) q^{17} +0.473120i q^{19} +9.13362 q^{21} +(0.747433 + 0.747433i) q^{23} +(-4.98388 + 0.401182i) q^{25} +(0.390993 + 0.390993i) q^{27} +(6.84907 + 6.84907i) q^{29} +(-3.38541 - 3.38541i) q^{31} -5.50346i q^{33} +(5.76595 - 6.24873i) q^{35} +(-2.83711 + 2.83711i) q^{37} +(-8.15137 - 8.15137i) q^{39} +(1.76410 - 1.76410i) q^{41} -11.0431 q^{43} +(-6.18847 + 0.248671i) q^{45} -12.1034i q^{47} +7.45856i q^{49} +(0.605956 + 9.88531i) q^{51} +2.14408 q^{53} +(-3.76517 - 3.47427i) q^{55} +(0.803594 + 0.803594i) q^{57} -6.46475i q^{59} +(-0.354589 + 0.354589i) q^{61} +(7.44725 - 7.44725i) q^{63} +(-10.7226 + 0.430866i) q^{65} +13.9447i q^{67} +2.53903 q^{69} +(4.21624 + 4.21624i) q^{71} +(-11.2518 + 11.2518i) q^{73} +(-7.78371 + 9.14652i) q^{75} +8.71200 q^{77} +(5.88159 - 5.88159i) q^{79} +9.63761 q^{81} +2.59966 q^{83} +(7.14553 + 5.82592i) q^{85} +23.2663 q^{87} -9.11592 q^{89} +(12.9037 - 12.9037i) q^{91} -11.5002 q^{93} +(1.05708 - 0.0424764i) q^{95} +(-6.39444 + 6.39444i) q^{97} +(-4.48734 - 4.48734i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 2 q^{3} + 8 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} - 10 q^{45}+ \cdots - 22 q^{99}+O(q^{100}) $ 26 * q - 2 * q^3 + 8 * 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 - 10 * q^45 - 6 * q^51 + 32 * q^53 - 26 * q^55 - 20 * q^57 + 6 * q^61 + 54 * q^63 - 16 * q^65 - 20 * q^69 - 30 * q^71 - 42 * q^73 + 58 * q^75 + 4 * q^77 + 14 * q^79 - 54 * q^81 + 16 * q^83 + 24 * q^85 - 8 * q^87 + 40 * q^89 + 24 * q^91 - 88 * q^93 - 8 * q^95 - 66 * q^97 - 22 * q^99

Character values

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

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

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	$-0.506108\pi$
$3$	1.69850	−	1.69850i	0.980629	−	0.980629i	0.999816	+	0.0191868i	$0.00610772\pi$
$4$		0			0
$5$	−0.0897794	−	2.23426i	−0.0401506	−	0.999194i
$5$	−0.0897794	−	2.23426i	−0.0401506	−	0.999194i
$6$		0			0
$7$	2.68873	+	2.68873i	1.01625	+	1.01625i	0.999866	+	0.0163793i	$0.00521393\pi$
$7$	2.68873	+	2.68873i	1.01625	+	1.01625i	0.0163793	+	0.999866i	$0.494786\pi$
$8$		0			0
$9$		−	2.76980i		−	0.923267i
$10$		0			0
$11$	1.62009	−	1.62009i	0.488477	−	0.488477i	−0.419349	−	0.907825i	$-0.637741\pi$
$11$	1.62009	−	1.62009i	0.488477	−	0.488477i	0.907825	+	0.419349i	$0.137741\pi$
$12$		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	$0.0172834\pi$
$19$			0.473120i			0.108541i	−0.998526	+	0.0542706i	$0.982717\pi$
$20$		0			0
$21$	9.13362			1.99312
$22$		0			0
$23$	0.747433	+	0.747433i	0.155850	+	0.155850i	0.780725	−	0.624875i	$-0.214850\pi$
$23$	0.747433	+	0.747433i	0.155850	+	0.155850i	−0.624875	+	0.780725i	$0.714850\pi$
$24$		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	0.945122	+	0.326719i	$0.105943\pi$
$29$	6.84907	+	6.84907i	1.27184	+	1.27184i	0.326719	+	0.945122i	$0.394057\pi$
$30$		0			0
$31$	−3.38541	−	3.38541i	−0.608038	−	0.608038i	0.334395	−	0.942433i	$-0.391468\pi$
$31$	−3.38541	−	3.38541i	−0.608038	−	0.608038i	−0.942433	+	0.334395i	$0.891468\pi$
$32$		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	$-0.856984\pi$
$37$	−2.83711	+	2.83711i	−0.466419	+	0.466419i	0.434333	+	0.900752i	$0.356984\pi$
$38$		0			0
$39$	−8.15137	−	8.15137i	−1.30526	−	1.30526i
$40$		0			0
$41$	1.76410	−	1.76410i	0.275506	−	0.275506i	−0.555806	−	0.831312i	$-0.687590\pi$
$41$	1.76410	−	1.76410i	0.275506	−	0.275506i	0.831312	+	0.555806i	$0.187590\pi$
$42$		0			0
$43$	−11.0431			−1.68405			−0.842025	−	0.539438i	$-0.818637\pi$
$43$	−11.0431			−1.68405			−0.842025	+	0.539438i	$0.818637\pi$
$44$		0			0
$45$	−6.18847	+	0.248671i	−0.922522	+	0.0370697i
$46$		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	$-0.452956\pi$
$53$	2.14408			0.294512			0.147256	+	0.989098i	$0.452956\pi$
$54$		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	$-0.861743\pi$
$59$		−	6.46475i		−	0.841639i	0.907144	−	0.420820i	$-0.138257\pi$
$60$		0			0
$61$	−0.354589	+	0.354589i	−0.0454005	+	0.0454005i	−0.729443	−	0.684042i	$-0.760220\pi$
$61$	−0.354589	+	0.354589i	−0.0454005	+	0.0454005i	0.684042	+	0.729443i	$0.260220\pi$
$62$		0			0
$63$	7.44725	−	7.44725i	0.938266	−	0.938266i
$64$		0			0
$65$	−10.7226	+	0.430866i	−1.32997	+	0.0534423i
$66$		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	0.911555	−	0.411179i	$-0.134883\pi$
$71$	4.21624	+	4.21624i	0.500376	+	0.500376i	−0.411179	+	0.911555i	$0.634883\pi$
$72$		0			0
$73$	−11.2518	+	11.2518i	−1.31692	+	1.31692i	−0.400725	+	0.916198i	$0.631242\pi$
$73$	−11.2518	+	11.2518i	−1.31692	+	1.31692i	−0.916198	+	0.400725i	$0.868758\pi$
$74$		0			0
$75$	−7.78371	+	9.14652i	−0.898785	+	1.05615i
$76$		0			0
$77$	8.71200			0.992824
$78$		0			0
$79$	5.88159	−	5.88159i	0.661731	−	0.661731i	−0.294057	−	0.955788i	$-0.595006\pi$
$79$	5.88159	−	5.88159i	0.661731	−	0.661731i	0.955788	+	0.294057i	$0.0950056\pi$
$80$		0			0
$81$	9.63761			1.07085
$82$		0			0
$83$	2.59966			0.285350			0.142675	−	0.989770i	$-0.454430\pi$
$83$	2.59966			0.285350			0.142675	+	0.989770i	$0.454430\pi$
$84$		0			0
$85$	7.14553	+	5.82592i	0.775042	+	0.631910i
$86$		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
$95$	1.05708	−	0.0424764i	0.108454	−	0.00435799i
$96$		0			0
$97$	−6.39444	+	6.39444i	−0.649257	+	0.649257i	−0.952813	−	0.303556i	$-0.901826\pi$
$97$	−6.39444	+	6.39444i	−0.649257	+	0.649257i	0.303556	+	0.952813i	$0.401826\pi$
$98$		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
$105$	−0.820011	−	20.4069i	−0.0800249	−	1.99151i
$106$		0			0
$107$	3.08520	−	3.08520i	0.298257	−	0.298257i	−0.542074	−	0.840331i	$-0.682361\pi$
$107$	3.08520	−	3.08520i	0.298257	−	0.298257i	0.840331	+	0.542074i	$0.182361\pi$
$108$		0			0
$109$	2.62204	−	2.62204i	0.251146	−	0.251146i	−0.570294	−	0.821440i	$-0.693171\pi$
$109$	2.62204	−	2.62204i	0.251146	−	0.251146i	0.821440	+	0.570294i	$0.193171\pi$
$110$		0			0
$111$			9.63768i			0.914768i
$112$		0			0
$113$	11.4021	+	11.4021i	1.07262	+	1.07262i	0.997148	+	0.0754726i	$0.0240465\pi$
$113$	11.4021	+	11.4021i	1.07262	+	1.07262i	0.0754726	+	0.997148i	$0.475953\pi$
$114$		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
$125$	1.34380	+	11.0993i	0.120193	+	0.992751i
$126$		0			0
$127$	−0.786344			−0.0697767			−0.0348884	−	0.999391i	$-0.511108\pi$
$127$	−0.786344			−0.0697767			−0.0348884	+	0.999391i	$0.511108\pi$
$128$		0			0
$129$	−18.7566	+	18.7566i	−1.65143	+	1.65143i
$130$		0			0
$131$	13.1428	+	13.1428i	1.14830	+	1.14830i	0.986888	+	0.161407i	$0.0516032\pi$
$131$	13.1428	+	13.1428i	1.14830	+	1.14830i	0.161407	+	0.986888i	$0.448397\pi$
$132$		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	0.266267	−	0.963899i	$-0.414210\pi$
$139$	−8.22497	−	8.22497i	−0.697633	−	0.697633i	−0.963899	+	0.266267i	$0.914210\pi$
$140$		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	$0.0256631\pi$
$151$			1.97928i			0.161071i	−0.996752	+	0.0805356i	$0.974337\pi$
$152$		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	$-0.280929\pi$
$163$	−1.75163	−	1.75163i	−0.137198	−	0.137198i	−0.772370	+	0.635172i	$0.780929\pi$
$164$		0			0
$165$	−12.2962	+	0.494097i	−0.957256	+	0.0384654i
$166$		0			0
$167$	0.630460	−	0.630460i	0.0487864	−	0.0487864i	−0.682293	−	0.731079i	$-0.739017\pi$
$167$	0.630460	−	0.630460i	0.0487864	−	0.0487864i	0.731079	+	0.682293i	$0.239017\pi$
$168$		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	$-0.602673\pi$
$173$	8.30526	−	8.30526i	0.631438	−	0.631438i	0.948429	+	0.316991i	$0.102673\pi$
$174$		0			0
$175$	−14.4790	−	12.3216i	−1.09451	−	0.931429i
$176$		0			0
$177$	−10.9804	−	10.9804i	−0.825336	−	0.825336i
$178$		0			0
$179$			8.65388i			0.646821i	0.946259	+	0.323411i	$0.104830\pi$
$179$			8.65388i			0.646821i	−0.946259	+	0.323411i	$0.895170\pi$
$180$		0			0
$181$	−12.9479	+	12.9479i	−0.962412	+	0.962412i	−0.999319	−	0.0369072i	$-0.988249\pi$
$181$	−12.9479	+	12.9479i	−0.962412	+	0.962412i	0.0369072	+	0.999319i	$0.488249\pi$
$182$		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	$-0.0307555\pi$
$193$	12.4874	+	12.4874i	0.898865	+	0.898865i	−0.0964710	+	0.995336i	$0.530755\pi$
$194$		0			0
$195$	−17.4805	+	18.9441i	−1.25180	+	1.35662i
$196$		0			0
$197$	−15.5201	−	15.5201i	−1.10576	−	1.10576i	−0.993702	−	0.112056i	$-0.964256\pi$
$197$	−15.5201	−	15.5201i	−1.10576	−	1.10576i	−0.112056	−	0.993702i	$-0.535744\pi$
$198$		0			0
$199$	−6.53983	−	6.53983i	−0.463597	−	0.463597i	0.436236	−	0.899832i	$-0.356311\pi$
$199$	−6.53983	−	6.53983i	−0.463597	−	0.463597i	−0.899832	+	0.436236i	$0.856311\pi$
$200$		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	−0.251184	−	0.967939i	$-0.580820\pi$
$211$	10.4115	−	10.4115i	0.716755	−	0.716755i	0.967939	+	0.251184i	$0.0808200\pi$
$212$		0			0
$213$	14.3226			0.981366
$214$		0			0
$215$	0.991439	+	24.6731i	0.0676156	+	1.68269i
$216$		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	$-0.624316\pi$
$223$	−11.3700			−0.761394			−0.380697	+	0.924700i	$0.624316\pi$
$224$		0			0
$225$	1.11119	+	13.8044i	0.0740796	+	0.920290i
$226$		0			0
$227$	−20.5002	−	20.5002i	−1.36064	−	1.36064i	−0.873095	−	0.487549i	$-0.837891\pi$
$227$	−20.5002	−	20.5002i	−1.36064	−	1.36064i	−0.487549	−	0.873095i	$-0.662109\pi$
$228$		0			0
$229$			2.12357i			0.140329i	0.997535	+	0.0701646i	$0.0223525\pi$
$229$			2.12357i			0.140329i	−0.997535	+	0.0701646i	$0.977648\pi$
$230$		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	$-0.701959\pi$
$233$	3.24570	−	3.24570i	0.212633	−	0.212633i	0.805385	+	0.592752i	$0.201959\pi$
$234$		0			0
$235$	−27.0421	+	1.08663i	−1.76403	+	0.0708840i
$236$		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	0.787870	−	0.615842i	$-0.211184\pi$
$241$	2.67058	+	2.67058i	0.172027	+	0.172027i	−0.615842	+	0.787870i	$0.711184\pi$
$242$		0			0
$243$	15.1965	−	15.1965i	0.974855	−	0.974855i
$244$		0			0
$245$	16.6644	−	0.669625i	1.06465	−	0.0427808i
$246$		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
$255$	22.0320	−	2.24136i	1.37970	−	0.140360i
$256$		0			0
$257$	−14.9841			−0.934683			−0.467342	−	0.884077i	$-0.654788\pi$
$257$	−14.9841			−0.934683			−0.467342	+	0.884077i	$0.654788\pi$
$258$		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	$-0.655978\pi$
$263$	−15.2651			−0.941286			−0.470643	+	0.882324i	$0.655978\pi$
$264$		0			0
$265$	−0.192494	−	4.79044i	−0.0118248	−	0.294274i
$266$		0			0
$267$	−15.4834	+	15.4834i	−0.947568	+	0.947568i
$268$		0			0
$269$	−19.1451	−	19.1451i	−1.16730	−	1.16730i	−0.982841	−	0.184456i	$-0.940948\pi$
$269$	−19.1451	−	19.1451i	−1.16730	−	1.16730i	−0.184456	−	0.982841i	$-0.559052\pi$
$270$		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
$275$	−7.42440	+	8.72430i	−0.447708	+	0.526095i
$276$		0			0
$277$	−1.62425	+	1.62425i	−0.0975919	+	0.0975919i	−0.754217	−	0.656625i	$-0.771983\pi$
$277$	−1.62425	+	1.62425i	−0.0975919	+	0.0975919i	0.656625	+	0.754217i	$0.271983\pi$
$278$		0			0
$279$	−9.37692	+	9.37692i	−0.561381	+	0.561381i
$280$		0			0
$281$			1.55801i			0.0929434i	0.998920	+	0.0464717i	$0.0147977\pi$
$281$			1.55801i			0.0929434i	−0.998920	+	0.0464717i	$0.985202\pi$
$282$		0			0
$283$	2.69991	+	2.69991i	0.160493	+	0.160493i	0.782785	−	0.622292i	$-0.213798\pi$
$283$	2.69991	+	2.69991i	0.160493	+	0.160493i	−0.622292	+	0.782785i	$0.713798\pi$
$284$		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
$295$	−14.4440	+	0.580402i	−0.840961	+	0.0337923i
$296$		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	0.219992	−	0.975502i	$-0.429397\pi$
$311$	−13.3236	−	13.3236i	−0.755510	−	0.755510i	−0.975502	+	0.219992i	$0.929397\pi$
$312$		0			0
$313$	−19.4611	−	19.4611i	−1.10001	−	1.10001i	−0.994409	−	0.105597i	$-0.966325\pi$
$313$	−19.4611	−	19.4611i	−1.10001	−	1.10001i	−0.105597	−	0.994409i	$-0.533675\pi$
$314$		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	$-0.252655\pi$
$317$	−0.210031	−	0.210031i	−0.0117965	−	0.0117965i	−0.712980	+	0.701184i	$0.752655\pi$
$318$		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	$0.00318691\pi$
$331$			0.364298i			0.0200236i	−0.999950	+	0.0100118i	$0.996813\pi$
$332$		0			0
$333$	7.85824	+	7.85824i	0.430629	+	0.430629i
$334$		0			0
$335$	31.1561	−	1.25194i	1.70224	−	0.0684010i
$336$		0			0
$337$	0.532640	−	0.532640i	0.0290148	−	0.0290148i	−0.692451	−	0.721465i	$-0.743469\pi$
$337$	0.532640	−	0.532640i	0.0290148	−	0.0290148i	0.721465	+	0.692451i	$0.243469\pi$
$338$		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
$345$	−0.227952	−	5.67286i	−0.0122725	−	0.305417i
$346$		0			0
$347$	−9.48106	−	9.48106i	−0.508970	−	0.508970i	0.405240	−	0.914210i	$-0.367188\pi$
$347$	−9.48106	−	9.48106i	−0.508970	−	0.508970i	−0.914210	+	0.405240i	$0.867188\pi$
$348$		0			0
$349$		−	35.1919i		−	1.88378i	−0.335923	−	0.941889i	$-0.609048\pi$
$349$		−	35.1919i		−	1.88378i	0.335923	−	0.941889i	$-0.390952\pi$
$350$		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	$-0.819296\pi$
$359$		−	20.3757i		−	1.07539i	0.843141	−	0.537693i	$-0.180704\pi$
$360$		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	$-0.129730\pi$
$367$	9.99474	+	9.99474i	0.521721	+	0.521721i	−0.396370	+	0.918091i	$0.629730\pi$
$368$		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	0.925083	−	0.379765i	$-0.123995\pi$
$379$	10.6162	+	10.6162i	0.545318	+	0.545318i	−0.379765	+	0.925083i	$0.623995\pi$
$380$		0			0
$381$	−1.33560	+	1.33560i	−0.0684251	+	0.0684251i
$382$		0			0
$383$	−15.8958			−0.812238			−0.406119	−	0.913820i	$-0.633118\pi$
$383$	−15.8958			−0.812238			−0.406119	+	0.913820i	$0.633118\pi$
$384$		0			0
$385$	−0.782158	−	19.4649i	−0.0398624	−	0.992024i
$386$		0			0
$387$			30.5871i			1.55483i
$388$		0			0
$389$			12.0045i			0.608651i	0.952568	+	0.304326i	$0.0984311\pi$
$389$			12.0045i			0.608651i	−0.952568	+	0.304326i	$0.901569\pi$
$390$		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	$-0.0357283\pi$
$397$	17.5677	+	17.5677i	0.881699	+	0.881699i	−0.112008	+	0.993707i	$0.535728\pi$
$398$		0			0
$399$			4.32130i			0.216336i
$400$		0			0
$401$	−5.35680	+	5.35680i	−0.267506	+	0.267506i	−0.828094	−	0.560589i	$-0.810575\pi$
$401$	−5.35680	+	5.35680i	−0.267506	+	0.267506i	0.560589	+	0.828094i	$0.310575\pi$
$402$		0			0
$403$	−16.2471	+	16.2471i	−0.809327	+	0.809327i
$404$		0			0
$405$	−0.865258	−	21.5330i	−0.0429950	−	1.06998i
$406$		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
$415$	−0.233396	−	5.80832i	−0.0114569	−	0.285119i
$416$		0			0
$417$	−27.9402			−1.36824
$418$		0			0
$419$	12.8619	−	12.8619i	0.628343	−	0.628343i	−0.319308	−	0.947651i	$-0.603450\pi$
$419$	12.8619	−	12.8619i	0.628343	−	0.628343i	0.947651	+	0.319308i	$0.103450\pi$
$420$		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
$425$	12.3751	−	16.4881i	0.600282	−	0.799789i
$426$		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	−0.224897	−	0.974383i	$-0.572204\pi$
$431$	15.5597	−	15.5597i	0.749486	−	0.749486i	0.974383	+	0.224897i	$0.0722044\pi$
$432$		0			0
$433$	−38.5005			−1.85021			−0.925107	−	0.379706i	$-0.876025\pi$
$433$	−38.5005			−1.85021			−0.925107	+	0.379706i	$0.876025\pi$
$434$		0			0
$435$	−2.08883	−	51.9830i	−0.100152	−	2.49240i
$436$		0			0
$437$	−0.353625	+	0.353625i	−0.0169162	+	0.0169162i
$438$		0			0
$439$	26.3114	+	26.3114i	1.25578	+	1.25578i	0.953090	+	0.302686i	$0.0978832\pi$
$439$	26.3114	+	26.3114i	1.25578	+	1.25578i	0.302686	+	0.953090i	$0.402117\pi$
$440$		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
$445$	0.818422	+	20.3674i	0.0387969	+	0.965507i
$446$		0			0
$447$	36.9930	−	36.9930i	1.74971	−	1.74971i
$448$		0			0
$449$	−16.5479	+	16.5479i	−0.780941	+	0.780941i	−0.979990	−	0.199048i	$-0.936215\pi$
$449$	−16.5479	+	16.5479i	−0.780941	+	0.780941i	0.199048	+	0.979990i	$0.436215\pi$
$450$		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	$-0.715828\pi$
$457$	−26.8190			−1.25454			−0.627271	+	0.778801i	$0.715828\pi$
$458$		0			0
$459$	−2.27559	+	0.139491i	−0.106216	+	0.00651086i
$460$		0			0
$461$		−	5.74080i		−	0.267376i	−0.991023	−	0.133688i	$-0.957318\pi$
$461$		−	5.74080i		−	0.267376i	0.991023	−	0.133688i	$-0.0426819\pi$
$462$		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
$465$	1.03248	+	25.6946i	0.0478803	+	1.19156i
$466$		0			0
$467$	18.2661			0.845254			0.422627	−	0.906304i	$-0.361108\pi$
$467$	18.2661			0.845254			0.422627	+	0.906304i	$0.361108\pi$
$468$		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	0.474411	−	0.880304i	$-0.342661\pi$
$479$	−8.88340	−	8.88340i	−0.405893	−	0.405893i	−0.880304	+	0.474411i	$0.842661\pi$
$480$		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	$-0.148552\pi$
$487$	9.77900	+	9.77900i	0.443129	+	0.443129i	−0.449933	+	0.893062i	$0.648552\pi$
$488$		0			0
$489$	−5.95028			−0.269081
$490$		0			0
$491$			30.9519i			1.39684i	0.715689	+	0.698419i	$0.246113\pi$
$491$			30.9519i			1.39684i	−0.715689	+	0.698419i	$0.753887\pi$
$492$		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	−0.818687	−	0.574239i	$-0.805298\pi$
$499$	−5.46055	+	5.46055i	−0.244448	+	0.244448i	0.574239	+	0.818687i	$0.305298\pi$
$500$		0			0
$501$		−	2.14167i		−	0.0956828i
$502$		0			0
$503$	−21.0635	−	21.0635i	−0.939174	−	0.939174i	0.0590792	−	0.998253i	$-0.481184\pi$
$503$	−21.0635	−	21.0635i	−0.939174	−	0.939174i	−0.998253	+	0.0590792i	$0.981184\pi$
$504$		0			0
$505$	−0.539881	−	13.4356i	−0.0240244	−	0.597875i
$506$		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
$515$	14.9788	−	0.601893i	0.660045	−	0.0265226i
$516$		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	−0.840952	−	0.541110i	$-0.818004\pi$
$521$	−6.84403	+	6.84403i	−0.299842	+	0.299842i	0.541110	+	0.840952i	$0.318004\pi$
$522$		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	0.0104358	−	0.999946i	$-0.496678\pi$
$541$	−23.0154	−	23.0154i	−0.989510	−	0.989510i	−0.999946	+	0.0104358i	$0.996678\pi$
$542$		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	$-0.742468\pi$
$547$	0.782615	−	0.782615i	0.0334622	−	0.0334622i	0.723640	+	0.690178i	$0.242468\pi$
$548$		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
$555$	21.5331	−	0.865265i	0.914030	−	0.0367284i
$556$		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	$-0.588009\pi$
$563$	−12.9543			−0.545960			−0.272980	+	0.962020i	$0.588009\pi$
$564$		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	$-0.808872\pi$
$569$		−	26.9552i		−	1.13002i	0.825083	−	0.565011i	$-0.191128\pi$
$570$		0			0
$571$	−3.02208	+	3.02208i	−0.126470	+	0.126470i	−0.767509	−	0.641039i	$-0.778504\pi$
$571$	−3.02208	+	3.02208i	−0.126470	+	0.126470i	0.641039	+	0.767509i	$0.278504\pi$
$572$		0			0
$573$	3.06776	−	3.06776i	0.128157	−	0.128157i
$574$		0			0
$575$	−4.02497	−	3.42526i	−0.167853	−	0.142843i
$576$		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
$585$	1.19341	+	29.6994i	0.0493415	+	1.22792i
$586$		0			0
$587$	40.6389			1.67735			0.838674	−	0.544634i	$-0.183331\pi$
$587$	40.6389			1.67735			0.838674	+	0.544634i	$0.183331\pi$
$588$		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	$-0.582498\pi$
$593$	−12.4818			−0.512567			−0.256284	+	0.966602i	$0.582498\pi$
$594$		0			0
$595$	3.54809	+	34.8768i	0.145457	+	1.42981i
$596$		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	−0.612505	−	0.790467i	$-0.709838\pi$
$601$	4.36278	−	4.36278i	0.177962	−	0.177962i	0.790467	+	0.612505i	$0.209838\pi$
$602$		0			0
$603$	38.6239			1.57289
$604$		0			0
$605$	12.8483	−	0.516285i	0.522360	−	0.0209900i
$606$		0			0
$607$	−17.2199	+	17.2199i	−0.698936	+	0.698936i	−0.964181	−	0.265245i	$-0.914547\pi$
$607$	−17.2199	+	17.2199i	−0.698936	+	0.698936i	0.265245	+	0.964181i	$0.414547\pi$
$608$		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
$615$	−13.3891	+	0.538016i	−0.539903	+	0.0216949i
$616$		0			0
$617$	−10.2837	+	10.2837i	−0.414005	+	0.414005i	−0.883131	−	0.469126i	$-0.844569\pi$
$617$	−10.2837	+	10.2837i	−0.414005	+	0.414005i	0.469126	+	0.883131i	$0.344569\pi$
$618$		0			0
$619$	−20.8463	+	20.8463i	−0.837884	+	0.837884i	−0.988580	−	0.150696i	$-0.951849\pi$
$619$	−20.8463	+	20.8463i	−0.837884	+	0.837884i	0.150696	+	0.988580i	$0.451849\pi$
$620$		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	$-0.726408\pi$
$631$		−	38.0577i		−	1.51505i	0.652805	−	0.757526i	$-0.273592\pi$
$632$		0			0
$633$		−	35.3677i		−	1.40574i
$634$		0			0
$635$	0.0705974	+	1.75690i	0.00280157	+	0.0697204i
$636$		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	0.938693	−	0.344753i	$-0.112037\pi$
$641$	15.0374	+	15.0374i	0.593940	+	0.593940i	−0.344753	+	0.938693i	$0.612037\pi$
$642$		0			0
$643$	19.0963	−	19.0963i	0.753083	−	0.753083i	−0.221970	−	0.975053i	$-0.571249\pi$
$643$	19.0963	−	19.0963i	0.753083	−	0.753083i	0.975053	+	0.221970i	$0.0712487\pi$
$644$		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	$-0.0595189\pi$
$653$	20.3581	+	20.3581i	0.796673	+	0.796673i	−0.185897	+	0.982569i	$0.559519\pi$
$654$		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	$-0.947096\pi$
$661$		−	8.50686i		−	0.330879i	0.986220	−	0.165439i	$-0.0529042\pi$
$662$		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	$-0.116459\pi$
$673$	14.9441	+	14.9441i	0.576054	+	0.576054i	−0.357760	+	0.933814i	$0.616459\pi$
$674$		0			0
$675$	−2.10552	−	1.79180i	−0.0810416	−	0.0689666i
$676$		0			0
$677$	31.1078	−	31.1078i	1.19557	−	1.19557i	0.220092	−	0.975479i	$-0.429364\pi$
$677$	31.1078	−	31.1078i	1.19557	−	1.19557i	0.975479	−	0.220092i	$-0.0706357\pi$
$678$		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	$-0.694103\pi$
$683$	6.45703	−	6.45703i	0.247071	−	0.247071i	0.819768	+	0.572696i	$0.194103\pi$
$684$		0			0
$685$	12.9861	−	0.521818i	0.496172	−	0.0199377i
$686$		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	−0.125650	−	0.992075i	$-0.540102\pi$
$691$	22.7756	−	22.7756i	0.866424	−	0.866424i	0.992075	+	0.125650i	$0.0401017\pi$
$692$		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	0.723486	−	0.690339i	$-0.242539\pi$
$709$	0.882611	+	0.882611i	0.0331472	+	0.0331472i	−0.690339	+	0.723486i	$0.742539\pi$
$710$		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	0.961276	−	0.275586i	$-0.0888720\pi$
$719$	18.3862	+	18.3862i	0.685690	+	0.685690i	−0.275586	+	0.961276i	$0.588872\pi$
$720$		0			0
$721$	−18.0256	+	18.0256i	−0.671309	+	0.671309i
$722$		0			0
$723$	9.07197			0.337390
$724$		0			0
$725$	−36.8827	−	31.3872i	−1.36979	−	1.16569i
$726$		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	$-0.324305\pi$
$733$	28.3930			1.04872			0.524360	+	0.851497i	$0.324305\pi$
$734$		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	$-0.736687\pi$
$739$		−	40.0186i		−	1.47211i	0.676923	−	0.736053i	$-0.263313\pi$
$740$		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	$-0.522225\pi$
$743$	25.2900	−	25.2900i	0.927800	−	0.927800i	0.997564	+	0.0697638i	$0.0222246\pi$
$744$		0			0
$745$	−1.95538	−	48.6618i	−0.0716395	−	1.78283i
$746$		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	0.615283	−	0.788306i	$-0.289042\pi$
$751$	−4.74161	−	4.74161i	−0.173024	−	0.173024i	−0.788306	+	0.615283i	$0.789042\pi$
$752$		0			0
$753$	−26.6029	+	26.6029i	−0.969463	+	0.969463i
$754$		0			0
$755$	4.42223	−	0.177698i	0.160941	−	0.00646710i
$756$		0			0
$757$	7.39432			0.268751			0.134376	−	0.990930i	$-0.457097\pi$
$757$	7.39432			0.268751			0.134376	+	0.990930i	$0.457097\pi$
$758$		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
$765$	16.1366	−	19.7917i	0.583421	−	0.715571i
$766$		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	$-0.746469\pi$
$773$	−38.8806			−1.39844			−0.699220	+	0.714907i	$0.746469\pi$
$774$		0			0
$775$	18.2307	+	15.5143i	0.654864	+	0.557291i
$776$		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
$785$	1.50050	−	0.0602947i	0.0535553	−	0.00215201i
$786$		0			0
$787$	33.6600	−	33.6600i	1.19985	−	1.19985i	0.225637	−	0.974211i	$-0.427554\pi$
$787$	33.6600	−	33.6600i	1.19985	−	1.19985i	0.974211	−	0.225637i	$-0.0724464\pi$
$788$		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	$-0.633677\pi$
$797$	−23.0211			−0.815448			−0.407724	+	0.913105i	$0.633677\pi$
$798$		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
$805$	8.98016	−	0.360850i	0.316509	−	0.0127183i
$806$		0			0
$807$	−65.0358			−2.28937
$808$		0			0
$809$	−6.65071	+	6.65071i	−0.233826	+	0.233826i	−0.814288	−	0.580461i	$-0.802872\pi$
$809$	−6.65071	+	6.65071i	−0.233826	+	0.233826i	0.580461	+	0.814288i	$0.302872\pi$
$810$		0			0
$811$	−6.08751	−	6.08751i	−0.213761	−	0.213761i	0.592102	−	0.805863i	$-0.298298\pi$
$811$	−6.08751	−	6.08751i	−0.213761	−	0.213761i	−0.805863	+	0.592102i	$0.798298\pi$
$812$		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	0.408420	−	0.912794i	$-0.366080\pi$
$821$	−14.4519	−	14.4519i	−0.504374	−	0.504374i	−0.912794	+	0.408420i	$0.866080\pi$
$822$		0			0
$823$	10.0576	+	10.0576i	0.350587	+	0.350587i	0.860328	−	0.509741i	$-0.170259\pi$
$823$	10.0576	+	10.0576i	0.350587	+	0.350587i	−0.509741	+	0.860328i	$0.670259\pi$
$824$		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	$-0.417621\pi$
$827$	−20.4402	−	20.4402i	−0.710776	−	0.710776i	−0.966698	+	0.255922i	$0.917621\pi$
$828$		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	0.213140	−	0.977022i	$-0.431631\pi$
$839$	34.4736	−	34.4736i	1.19016	−	1.19016i	0.977022	−	0.213140i	$-0.0683691\pi$
$840$		0			0
$841$			64.8195i			2.23516i
$842$		0			0
$843$	2.64629	+	2.64629i	0.0911430	+	0.0911430i
$844$		0			0
$845$	0.900661	+	22.4140i	0.0309837	+	0.771065i
$846$		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	−0.190898	+	0.981610i	$0.561140\pi$
$853$	−34.2445	+	34.2445i	−1.17251	+	1.17251i	−0.981610	+	0.190898i	$0.938860\pi$
$854$		0			0
$855$	−0.117651	−	2.92789i	−0.00402359	−	0.100132i
$856$		0			0
$857$	−34.3909	−	34.3909i	−1.17477	−	1.17477i	−0.981059	−	0.193712i	$-0.937947\pi$
$857$	−34.3909	−	34.3909i	−1.17477	−	1.17477i	−0.193712	−	0.981059i	$-0.562053\pi$
$858$		0			0
$859$			38.8535i			1.32566i	0.748768	+	0.662832i	$0.230646\pi$
$859$			38.8535i			1.32566i	−0.748768	+	0.662832i	$0.769354\pi$
$860$		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	$-0.452505\pi$
$877$	−24.8828	−	24.8828i	−0.840232	−	0.840232i	−0.988889	+	0.148657i	$0.952505\pi$
$878$		0			0
$879$	22.3915	+	22.3915i	0.755247	+	0.755247i
$880$		0			0
$881$	−11.8409	−	11.8409i	−0.398928	−	0.398928i	0.478927	−	0.877855i	$-0.341026\pi$
$881$	−11.8409	−	11.8409i	−0.398928	−	0.398928i	−0.877855	+	0.478927i	$0.841026\pi$
$882$		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	$-0.607555\pi$
$887$	18.2255	−	18.2255i	0.611952	−	0.611952i	0.943454	+	0.331502i	$0.107555\pi$
$888$		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
$895$	19.3351	−	0.776940i	0.646300	−	0.0259702i
$896$		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	$-0.315652\pi$
$907$	−8.72237	−	8.72237i	−0.289621	−	0.289621i	−0.836931	+	0.547309i	$0.815652\pi$
$908$		0			0
$909$		−	16.6560i		−	0.552444i
$910$		0			0
$911$	2.80241	−	2.80241i	0.0928479	−	0.0928479i	−0.659157	−	0.752005i	$-0.729087\pi$
$911$	2.80241	−	2.80241i	0.0928479	−	0.0928479i	0.752005	+	0.659157i	$0.229087\pi$
$912$		0			0
$913$	4.21169	−	4.21169i	0.139387	−	0.139387i
$914$		0			0
$915$	2.69126	−	0.108143i	0.0889703	−	0.00357509i
$916$		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
$925$	13.0016	−	15.2780i	0.427491	−	0.502339i
$926$		0			0
$927$	18.5691			0.609890
$928$		0			0
$929$	36.9557	−	36.9557i	1.21248	−	1.21248i	0.242268	−	0.970209i	$-0.422109\pi$
$929$	36.9557	−	36.9557i	1.21248	−	1.21248i	0.970209	−	0.242268i	$-0.0778915\pi$
$930$		0			0
$931$	−3.52879			−0.115652
$932$		0			0
$933$	−45.2601			−1.48175
$934$		0			0
$935$	21.0150	−	2.13790i	0.687263	−	0.0699167i
$936$		0			0
$937$	−23.6381			−0.772224			−0.386112	−	0.922452i	$-0.626182\pi$
$937$	−23.6381			−0.772224			−0.386112	+	0.922452i	$0.626182\pi$
$938$		0			0
$939$	−66.1093			−2.15740
$940$		0			0
$941$	−32.4847	+	32.4847i	−1.05897	+	1.05897i	−0.0608209	+	0.998149i	$0.519372\pi$
$941$	−32.4847	+	32.4847i	−1.05897	+	1.05897i	−0.998149	+	0.0608209i	$0.980628\pi$
$942$		0			0
$943$	2.63709			0.0858755
$944$		0			0
$945$	4.69766	−	0.188766i	0.152815	−	0.00614055i
$946$		0			0
$947$	−7.83973	+	7.83973i	−0.254757	+	0.254757i	−0.822918	−	0.568161i	$-0.807655\pi$
$947$	−7.83973	+	7.83973i	−0.254757	+	0.254757i	0.568161	+	0.822918i	$0.307655\pi$
$948$		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
$955$	−0.162156	−	4.03543i	−0.00524723	−	0.130584i
$956$		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	$-0.241340\pi$
$967$	45.1573			1.45216			0.726080	+	0.687610i	$0.241340\pi$
$968$		0			0
$969$	−4.67694	+	0.286690i	−0.150245	+	0.00920980i
$970$		0			0
$971$		−	1.04631i		−	0.0335776i	−0.999859	−	0.0167888i	$-0.994656\pi$
$971$		−	1.04631i		−	0.0335776i	0.999859	−	0.0167888i	$-0.00534429\pi$
$972$		0			0
$973$		−	44.2295i		−	1.41793i
$974$		0			0
$975$	43.8956	+	37.3553i	1.40579	+	1.19633i
$976$		0			0
$977$	38.9405			1.24582			0.622909	−	0.782294i	$-0.285951\pi$
$977$	38.9405			1.24582			0.622909	+	0.782294i	$0.285951\pi$
$978$		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	$-0.953024\pi$
$983$	−26.4018	+	26.4018i	−0.842087	+	0.842087i	0.147043	+	0.989130i	$0.453024\pi$
$984$		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	0.849346	−	0.527837i	$-0.176997\pi$
$991$	10.1211	+	10.1211i	0.321509	+	0.321509i	−0.527837	+	0.849346i	$0.676997\pi$
$992$		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	$-0.424280\pi$
$997$	−23.2456	−	23.2456i	−0.736196	−	0.736196i	−0.971840	+	0.235644i	$0.924280\pi$
$998$		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.c.489.11	yes	26
5.4	even	2		680.2.z.d.489.3	yes	26
17.4	even	4		680.2.z.d.89.3	yes	26
85.4	even	4	inner	680.2.z.c.89.11	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.z.c.89.11	✓	26	85.4	even	4	inner
680.2.z.c.489.11	yes	26	1.1	even	1	trivial
680.2.z.d.89.3	yes	26	17.4	even	4
680.2.z.d.489.3	yes	26	5.4	even	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 $\F_{q}$
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)

\(f(q)\)	\(=\)	\(q+(1.69850 - 1.69850i) q^{3} +(-0.0897794 - 2.23426i) q^{5} +(2.68873 + 2.68873i) q^{7} -2.76980i q^{9} +(1.62009 - 1.62009i) q^{11} -4.79916i q^{13} +(-3.94739 - 3.64241i) q^{15} +(-2.73163 + 3.08839i) q^{17} +0.473120i q^{19} +9.13362 q^{21} +(0.747433 + 0.747433i) q^{23} +(-4.98388 + 0.401182i) q^{25} +(0.390993 + 0.390993i) q^{27} +(6.84907 + 6.84907i) q^{29} +(-3.38541 - 3.38541i) q^{31} -5.50346i q^{33} +(5.76595 - 6.24873i) q^{35} +(-2.83711 + 2.83711i) q^{37} +(-8.15137 - 8.15137i) q^{39} +(1.76410 - 1.76410i) q^{41} -11.0431 q^{43} +(-6.18847 + 0.248671i) q^{45} -12.1034i q^{47} +7.45856i q^{49} +(0.605956 + 9.88531i) q^{51} +2.14408 q^{53} +(-3.76517 - 3.47427i) q^{55} +(0.803594 + 0.803594i) q^{57} -6.46475i q^{59} +(-0.354589 + 0.354589i) q^{61} +(7.44725 - 7.44725i) q^{63} +(-10.7226 + 0.430866i) q^{65} +13.9447i q^{67} +2.53903 q^{69} +(4.21624 + 4.21624i) q^{71} +(-11.2518 + 11.2518i) q^{73} +(-7.78371 + 9.14652i) q^{75} +8.71200 q^{77} +(5.88159 - 5.88159i) q^{79} +9.63761 q^{81} +2.59966 q^{83} +(7.14553 + 5.82592i) q^{85} +23.2663 q^{87} -9.11592 q^{89} +(12.9037 - 12.9037i) q^{91} -11.5002 q^{93} +(1.05708 - 0.0424764i) q^{95} +(-6.39444 + 6.39444i) q^{97} +(-4.48734 - 4.48734i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 2 q^{3} + 8 q^{5} - 2 q^{7} + 2 q^{11} + 2 q^{15} - 2 q^{17} - 12 q^{21} + 2 q^{23} - 10 q^{25} - 20 q^{27} + 10 q^{29} - 10 q^{31} + 22 q^{35} + 6 q^{37} + 8 q^{39} - 10 q^{41} - 32 q^{43} - 10 q^{45}+ \cdots - 22 q^{99}+O(q^{100}) \) 26 * q - 2 * q^3 + 8 * 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 - 10 * q^45 - 6 * q^51 + 32 * q^53 - 26 * q^55 - 20 * q^57 + 6 * q^61 + 54 * q^63 - 16 * q^65 - 20 * q^69 - 30 * q^71 - 42 * q^73 + 58 * q^75 + 4 * q^77 + 14 * q^79 - 54 * q^81 + 16 * q^83 + 24 * q^85 - 8 * q^87 + 40 * q^89 + 24 * q^91 - 88 * q^93 - 8 * q^95 - 66 * q^97 - 22 * q^99

Introduction

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