LMFDB - Embedded newform 680.2.z.c.89.7

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			89.7
Character	$\chi$	$=$	680.89
Dual form			680.2.z.c.489.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.258828 - 0.258828i) q^{3} +(-1.17169 - 1.90450i) q^{5} +(-2.27901 + 2.27901i) q^{7} -2.86602i q^{9} +(-1.92326 - 1.92326i) q^{11} +6.34245i q^{13} +(-0.189671 + 0.796206i) q^{15} +(2.80581 + 3.02116i) q^{17} +5.72664i q^{19} +1.17974 q^{21} +(-0.702808 + 0.702808i) q^{23} +(-2.25426 + 4.46299i) q^{25} +(-1.51829 + 1.51829i) q^{27} +(3.41223 - 3.41223i) q^{29} +(-7.01003 + 7.01003i) q^{31} +0.995585i q^{33} +(7.01069 + 1.67008i) q^{35} +(-8.12179 - 8.12179i) q^{37} +(1.64160 - 1.64160i) q^{39} +(0.982537 + 0.982537i) q^{41} +4.73645 q^{43} +(-5.45834 + 3.35810i) q^{45} +6.21775i q^{47} -3.38779i q^{49} +(0.0557394 - 1.50818i) q^{51} -5.21846 q^{53} +(-1.40938 + 5.91631i) q^{55} +(1.48222 - 1.48222i) q^{57} +2.16403i q^{59} +(0.886240 + 0.886240i) q^{61} +(6.53169 + 6.53169i) q^{63} +(12.0792 - 7.43142i) q^{65} -6.93450i q^{67} +0.363813 q^{69} +(-6.21183 + 6.21183i) q^{71} +(-5.64384 - 5.64384i) q^{73} +(1.73861 - 0.571680i) q^{75} +8.76624 q^{77} +(5.28312 + 5.28312i) q^{79} -7.81210 q^{81} -15.1635 q^{83} +(2.46626 - 8.88355i) q^{85} -1.76636 q^{87} +7.17462 q^{89} +(-14.4545 - 14.4545i) q^{91} +3.62879 q^{93} +(10.9064 - 6.70987i) q^{95} +(2.90252 + 2.90252i) q^{97} +(-5.51208 + 5.51208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

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

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
$3$	−0.258828	−	0.258828i	−0.149434	−	0.149434i	0.628431	−	0.777865i	$-0.283697\pi$
$3$	−0.258828	−	0.258828i	−0.149434	−	0.149434i	−0.777865	+	0.628431i	$0.783697\pi$
$4$		0			0
$5$	−1.17169	−	1.90450i	−0.523998	−	0.851720i
$5$	−1.17169	−	1.90450i	−0.523998	−	0.851720i
$6$		0			0
$7$	−2.27901	+	2.27901i	−0.861386	+	0.861386i	−0.991499	−	0.130114i	$-0.958466\pi$
$7$	−2.27901	+	2.27901i	−0.861386	+	0.861386i	0.130114	+	0.991499i	$0.458466\pi$
$8$		0			0
$9$		−	2.86602i		−	0.955339i
$10$		0			0
$11$	−1.92326	−	1.92326i	−0.579883	−	0.579883i	0.354988	−	0.934871i	$-0.384485\pi$
$11$	−1.92326	−	1.92326i	−0.579883	−	0.579883i	−0.934871	+	0.354988i	$0.884485\pi$
$12$		0			0
$13$			6.34245i			1.75908i	0.475825	+	0.879540i	$0.342149\pi$
$13$			6.34245i			1.75908i	−0.475825	+	0.879540i	$0.657851\pi$
$14$		0			0
$15$	−0.189671	+	0.796206i	−0.0489730	+	0.205580i
$16$		0			0
$17$	2.80581	+	3.02116i	0.680509	+	0.732740i
$17$	2.80581	+	3.02116i	0.680509	+	0.732740i
$18$		0			0
$19$			5.72664i			1.31378i	0.753986	+	0.656891i	$0.228129\pi$
$19$			5.72664i			1.31378i	−0.753986	+	0.656891i	$0.771871\pi$
$20$		0			0
$21$	1.17974			0.257441
$22$		0			0
$23$	−0.702808	+	0.702808i	−0.146546	+	0.146546i	−0.776573	−	0.630027i	$-0.783044\pi$
$23$	−0.702808	+	0.702808i	−0.146546	+	0.146546i	0.630027	+	0.776573i	$0.283044\pi$
$24$		0			0
$25$	−2.25426	+	4.46299i	−0.450853	+	0.892598i
$26$		0			0
$27$	−1.51829	+	1.51829i	−0.292195	+	0.292195i
$28$		0			0
$29$	3.41223	−	3.41223i	0.633635	−	0.633635i	−0.315342	−	0.948978i	$-0.602119\pi$
$29$	3.41223	−	3.41223i	0.633635	−	0.633635i	0.948978	+	0.315342i	$0.102119\pi$
$30$		0			0
$31$	−7.01003	+	7.01003i	−1.25904	+	1.25904i	−0.307486	+	0.951552i	$0.599488\pi$
$31$	−7.01003	+	7.01003i	−1.25904	+	1.25904i	−0.951552	+	0.307486i	$0.900512\pi$
$32$		0			0
$33$			0.995585i			0.173309i
$34$		0			0
$35$	7.01069	+	1.67008i	1.18502	+	0.282295i
$36$		0			0
$37$	−8.12179	−	8.12179i	−1.33521	−	1.33521i	−0.900633	−	0.434580i	$-0.856897\pi$
$37$	−8.12179	−	8.12179i	−1.33521	−	1.33521i	−0.434580	−	0.900633i	$-0.643103\pi$
$38$		0			0
$39$	1.64160	−	1.64160i	0.262867	−	0.262867i
$40$		0			0
$41$	0.982537	+	0.982537i	0.153447	+	0.153447i	0.779655	−	0.626209i	$-0.215394\pi$
$41$	0.982537	+	0.982537i	0.153447	+	0.153447i	−0.626209	+	0.779655i	$0.715394\pi$
$42$		0			0
$43$	4.73645			0.722301			0.361151	−	0.932507i	$-0.382384\pi$
$43$	4.73645			0.722301			0.361151	+	0.932507i	$0.382384\pi$
$44$		0			0
$45$	−5.45834	+	3.35810i	−0.813681	+	0.500595i
$46$		0			0
$47$			6.21775i			0.906952i	0.891269	+	0.453476i	$0.149816\pi$
$47$			6.21775i			0.906952i	−0.891269	+	0.453476i	$0.850184\pi$
$48$		0			0
$49$		−	3.38779i		−	0.483970i
$50$		0			0
$51$	0.0557394	−	1.50818i	0.00780508	−	0.211188i
$52$		0			0
$53$	−5.21846			−0.716810			−0.358405	−	0.933566i	$-0.616679\pi$
$53$	−5.21846			−0.716810			−0.358405	+	0.933566i	$0.616679\pi$
$54$		0			0
$55$	−1.40938	+	5.91631i	−0.190041	+	0.797756i
$56$		0			0
$57$	1.48222	−	1.48222i	0.196324	−	0.196324i
$58$		0			0
$59$			2.16403i			0.281733i	0.990029	+	0.140866i	$0.0449888\pi$
$59$			2.16403i			0.281733i	−0.990029	+	0.140866i	$0.955011\pi$
$60$		0			0
$61$	0.886240	+	0.886240i	0.113471	+	0.113471i	0.761563	−	0.648091i	$-0.224432\pi$
$61$	0.886240	+	0.886240i	0.113471	+	0.113471i	−0.648091	+	0.761563i	$0.724432\pi$
$62$		0			0
$63$	6.53169	+	6.53169i	0.822915	+	0.822915i
$64$		0			0
$65$	12.0792	−	7.43142i	1.49824	−	0.921754i
$66$		0			0
$67$		−	6.93450i		−	0.847185i	−0.905853	−	0.423592i	$-0.860769\pi$
$67$		−	6.93450i		−	0.847185i	0.905853	−	0.423592i	$-0.139231\pi$
$68$		0			0
$69$	0.363813			0.0437979
$70$		0			0
$71$	−6.21183	+	6.21183i	−0.737208	+	0.737208i	−0.972037	−	0.234829i	$-0.924547\pi$
$71$	−6.21183	+	6.21183i	−0.737208	+	0.737208i	0.234829	+	0.972037i	$0.424547\pi$
$72$		0			0
$73$	−5.64384	−	5.64384i	−0.660561	−	0.660561i	0.294951	−	0.955512i	$-0.404697\pi$
$73$	−5.64384	−	5.64384i	−0.660561	−	0.660561i	−0.955512	+	0.294951i	$0.904697\pi$
$74$		0			0
$75$	1.73861	−	0.571680i	0.200758	−	0.0660120i
$76$		0			0
$77$	8.76624			0.999006
$78$		0			0
$79$	5.28312	+	5.28312i	0.594398	+	0.594398i	0.938816	−	0.344418i	$-0.111924\pi$
$79$	5.28312	+	5.28312i	0.594398	+	0.594398i	−0.344418	+	0.938816i	$0.611924\pi$
$80$		0			0
$81$	−7.81210			−0.868011
$82$		0			0
$83$	−15.1635			−1.66441			−0.832203	−	0.554471i	$-0.812921\pi$
$83$	−15.1635			−1.66441			−0.832203	+	0.554471i	$0.812921\pi$
$84$		0			0
$85$	2.46626	−	8.88355i	0.267504	−	0.963557i
$86$		0			0
$87$	−1.76636			−0.189374
$88$		0			0
$89$	7.17462			0.760508			0.380254	−	0.924882i	$-0.375836\pi$
$89$	7.17462			0.760508			0.380254	+	0.924882i	$0.375836\pi$
$90$		0			0
$91$	−14.4545	−	14.4545i	−1.51525	−	1.51525i
$92$		0			0
$93$	3.62879			0.376288
$94$		0			0
$95$	10.9064	−	6.70987i	1.11897	−	0.688419i
$96$		0			0
$97$	2.90252	+	2.90252i	0.294707	+	0.294707i	0.838936	−	0.544230i	$-0.183178\pi$
$97$	2.90252	+	2.90252i	0.294707	+	0.294707i	−0.544230	+	0.838936i	$0.683178\pi$
$98$		0			0
$99$	−5.51208	+	5.51208i	−0.553985	+	0.553985i
$100$		0			0
$101$	−15.9495			−1.58704			−0.793518	−	0.608547i	$-0.791753\pi$
$101$	−15.9495			−1.58704			−0.793518	+	0.608547i	$0.791753\pi$
$102$		0			0
$103$		−	4.47989i		−	0.441416i	−0.975340	−	0.220708i	$-0.929163\pi$
$103$		−	4.47989i		−	0.441416i	0.975340	−	0.220708i	$-0.0708369\pi$
$104$		0			0
$105$	−1.38230	−	2.24683i	−0.134899	−	0.219268i
$106$		0			0
$107$	−7.10141	−	7.10141i	−0.686520	−	0.686520i	0.274941	−	0.961461i	$-0.411342\pi$
$107$	−7.10141	−	7.10141i	−0.686520	−	0.686520i	−0.961461	+	0.274941i	$0.911342\pi$
$108$		0			0
$109$	8.76599	+	8.76599i	0.839629	+	0.839629i	0.988810	−	0.149181i	$-0.0476636\pi$
$109$	8.76599	+	8.76599i	0.839629	+	0.839629i	−0.149181	+	0.988810i	$0.547664\pi$
$110$		0			0
$111$			4.20429i			0.399054i
$112$		0			0
$113$	3.28122	−	3.28122i	0.308671	−	0.308671i	−0.535723	−	0.844394i	$-0.679961\pi$
$113$	3.28122	−	3.28122i	0.308671	−	0.308671i	0.844394	+	0.535723i	$0.179961\pi$
$114$		0			0
$115$	2.16198	+	0.515024i	0.201605	+	0.0480262i
$116$		0			0
$117$	18.1776			1.68052
$118$		0			0
$119$	−13.2797	−	0.490792i	−1.21735	−	0.0449908i
$120$		0			0
$121$		−	3.60218i		−	0.327471i
$122$		0			0
$123$		−	0.508616i		−	0.0458604i
$124$		0			0
$125$	11.1411	−	0.936008i	0.996489	−	0.0837191i
$126$		0			0
$127$	2.43753			0.216296			0.108148	−	0.994135i	$-0.465508\pi$
$127$	2.43753			0.216296			0.108148	+	0.994135i	$0.465508\pi$
$128$		0			0
$129$	−1.22593	−	1.22593i	−0.107937	−	0.107937i
$130$		0			0
$131$	−0.786050	+	0.786050i	−0.0686775	+	0.0686775i	−0.740611	−	0.671934i	$-0.765464\pi$
$131$	−0.786050	+	0.786050i	−0.0686775	+	0.0686775i	0.671934	+	0.740611i	$0.265464\pi$
$132$		0			0
$133$	−13.0511	−	13.0511i	−1.13167	−	1.13167i
$134$		0			0
$135$	4.67056	+	1.11262i	0.401978	+	0.0957587i
$136$		0			0
$137$			11.2431i			0.960564i	0.877114	+	0.480282i	$0.159466\pi$
$137$			11.2431i			0.960564i	−0.877114	+	0.480282i	$0.840534\pi$
$138$		0			0
$139$	15.5391	−	15.5391i	1.31801	−	1.31801i	0.402663	−	0.915348i	$-0.368085\pi$
$139$	15.5391	−	15.5391i	1.31801	−	1.31801i	0.915348	−	0.402663i	$-0.131915\pi$
$140$		0			0
$141$	1.60933	−	1.60933i	0.135530	−	0.135530i
$142$		0			0
$143$	12.1982	−	12.1982i	1.02006	−	1.02006i
$144$		0			0
$145$	−10.4967	−	2.50051i	−0.871703	−	0.207656i
$146$		0			0
$147$	−0.876856	+	0.876856i	−0.0723218	+	0.0723218i
$148$		0			0
$149$	13.7276			1.12461			0.562305	−	0.826930i	$-0.309915\pi$
$149$	13.7276			1.12461			0.562305	+	0.826930i	$0.309915\pi$
$150$		0			0
$151$			20.8628i			1.69779i	0.528561	+	0.848896i	$0.322732\pi$
$151$			20.8628i			1.69779i	−0.528561	+	0.848896i	$0.677268\pi$
$152$		0			0
$153$	8.65870	−	8.04150i	0.700015	−	0.650117i
$154$		0			0
$155$	21.5642	+	5.13701i	1.73208	+	0.412615i
$156$		0			0
$157$			0.522998i			0.0417398i	0.999782	+	0.0208699i	$0.00664358\pi$
$157$			0.522998i			0.0417398i	−0.999782	+	0.0208699i	$0.993356\pi$
$158$		0			0
$159$	1.35068	+	1.35068i	0.107116	+	0.107116i
$160$		0			0
$161$		−	3.20341i		−	0.252464i
$162$		0			0
$163$	11.0348	−	11.0348i	0.864314	−	0.864314i	−0.127522	−	0.991836i	$-0.540702\pi$
$163$	11.0348	−	11.0348i	0.864314	−	0.864314i	0.991836	+	0.127522i	$0.0407023\pi$
$164$		0			0
$165$	1.89609	−	1.16652i	0.147611	−	0.0908136i
$166$		0			0
$167$	1.88585	+	1.88585i	0.145931	+	0.145931i	0.776298	−	0.630366i	$-0.217095\pi$
$167$	1.88585	+	1.88585i	0.145931	+	0.145931i	−0.630366	+	0.776298i	$0.717095\pi$
$168$		0			0
$169$	−27.2267			−2.09436
$170$		0			0
$171$	16.4126			1.25511
$172$		0			0
$173$	6.08455	+	6.08455i	0.462600	+	0.462600i	0.899507	−	0.436907i	$-0.143926\pi$
$173$	6.08455	+	6.08455i	0.462600	+	0.462600i	−0.436907	+	0.899507i	$0.643926\pi$
$174$		0			0
$175$	−5.03372	−	15.3087i	−0.380513	−	1.15723i
$176$		0			0
$177$	0.560111	−	0.560111i	0.0421005	−	0.0421005i
$178$		0			0
$179$		−	24.3489i		−	1.81993i	−0.414689	−	0.909963i	$-0.636110\pi$
$179$		−	24.3489i		−	1.81993i	0.414689	−	0.909963i	$-0.363890\pi$
$180$		0			0
$181$	−10.7537	−	10.7537i	−0.799319	−	0.799319i	0.183669	−	0.982988i	$-0.441202\pi$
$181$	−10.7537	−	10.7537i	−0.799319	−	0.799319i	−0.982988	+	0.183669i	$0.941202\pi$
$182$		0			0
$183$		−	0.458767i		−	0.0339131i
$184$		0			0
$185$	−5.95171	+	24.9842i	−0.437579	+	1.83688i
$186$		0			0
$187$	0.414179	−	11.2068i	0.0302878	−	0.819519i
$188$		0			0
$189$		−	6.92040i		−	0.503385i
$190$		0			0
$191$	−20.4147			−1.47716			−0.738580	−	0.674166i	$-0.764503\pi$
$191$	−20.4147			−1.47716			−0.738580	+	0.674166i	$0.764503\pi$
$192$		0			0
$193$	−9.00682	+	9.00682i	−0.648325	+	0.648325i	−0.952588	−	0.304263i	$-0.901590\pi$
$193$	−9.00682	+	9.00682i	−0.648325	+	0.648325i	0.304263	+	0.952588i	$0.401590\pi$
$194$		0			0
$195$	−5.04990	−	1.20298i	−0.361631	−	0.0861473i
$196$		0			0
$197$	2.23975	−	2.23975i	0.159576	−	0.159576i	−0.622803	−	0.782379i	$-0.714006\pi$
$197$	2.23975	−	2.23975i	0.159576	−	0.159576i	0.782379	+	0.622803i	$0.214006\pi$
$198$		0			0
$199$	−5.78576	+	5.78576i	−0.410142	+	0.410142i	−0.881788	−	0.471646i	$-0.843660\pi$
$199$	−5.78576	+	5.78576i	−0.410142	+	0.410142i	0.471646	+	0.881788i	$0.343660\pi$
$200$		0			0
$201$	−1.79484	+	1.79484i	−0.126599	+	0.126599i
$202$		0			0
$203$			15.5530i			1.09161i
$204$		0			0
$205$	0.720012	−	3.02248i	0.0502878	−	0.211099i
$206$		0			0
$207$	2.01426	+	2.01426i	0.140001	+	0.140001i
$208$		0			0
$209$	11.0138	−	11.0138i	0.761840	−	0.761840i
$210$		0			0
$211$	−13.1554	−	13.1554i	−0.905657	−	0.905657i	0.0902609	−	0.995918i	$-0.471230\pi$
$211$	−13.1554	−	13.1554i	−0.905657	−	0.905657i	−0.995918	+	0.0902609i	$0.971230\pi$
$212$		0			0
$213$	3.21559			0.220329
$214$		0			0
$215$	−5.54967	−	9.02058i	−0.378484	−	0.615198i
$216$		0			0
$217$		−	31.9519i		−	2.16904i
$218$		0			0
$219$			2.92157i			0.197421i
$220$		0			0
$221$	−19.1616	+	17.7957i	−1.28895	+	1.19707i
$222$		0			0
$223$	−3.07654			−0.206021			−0.103010	−	0.994680i	$-0.532847\pi$
$223$	−3.07654			−0.206021			−0.103010	+	0.994680i	$0.532847\pi$
$224$		0			0
$225$	12.7910	+	6.46076i	0.852734	+	0.430717i
$226$		0			0
$227$	−12.9209	+	12.9209i	−0.857591	+	0.857591i	−0.991054	−	0.133463i	$-0.957390\pi$
$227$	−12.9209	+	12.9209i	−0.857591	+	0.857591i	0.133463	+	0.991054i	$0.457390\pi$
$228$		0			0
$229$			11.0544i			0.730497i	0.930910	+	0.365248i	$0.119016\pi$
$229$			11.0544i			0.730497i	−0.930910	+	0.365248i	$0.880984\pi$
$230$		0			0
$231$	−2.26895	−	2.26895i	−0.149286	−	0.149286i
$232$		0			0
$233$	3.58159	+	3.58159i	0.234638	+	0.234638i	0.814625	−	0.579988i	$-0.196943\pi$
$233$	3.58159	+	3.58159i	0.234638	+	0.234638i	−0.579988	+	0.814625i	$0.696943\pi$
$234$		0			0
$235$	11.8417	−	7.28530i	0.772469	−	0.475241i
$236$		0			0
$237$		−	2.73484i		−	0.177647i
$238$		0			0
$239$	−12.0389			−0.778731			−0.389366	−	0.921083i	$-0.627306\pi$
$239$	−12.0389			−0.778731			−0.389366	+	0.921083i	$0.627306\pi$
$240$		0			0
$241$	−7.97689	+	7.97689i	−0.513836	+	0.513836i	−0.915700	−	0.401863i	$-0.868363\pi$
$241$	−7.97689	+	7.97689i	−0.513836	+	0.513836i	0.401863	+	0.915700i	$0.368363\pi$
$242$		0			0
$243$	6.57686	+	6.57686i	0.421906	+	0.421906i
$244$		0			0
$245$	−6.45206	+	3.96946i	−0.412207	+	0.253599i
$246$		0			0
$247$	−36.3210			−2.31105
$248$		0			0
$249$	3.92473	+	3.92473i	0.248720	+	0.248720i
$250$		0			0
$251$	19.9948			1.26206			0.631030	−	0.775758i	$-0.282632\pi$
$251$	19.9948			1.26206			0.631030	+	0.775758i	$0.282632\pi$
$252$		0			0
$253$	2.70336			0.169959
$254$		0			0
$255$	−2.93765	+	1.66098i	−0.183963	+	0.104014i
$256$		0			0
$257$	6.55828			0.409094			0.204547	−	0.978857i	$-0.434428\pi$
$257$	6.55828			0.409094			0.204547	+	0.978857i	$0.434428\pi$
$258$		0			0
$259$	37.0193			2.30027
$260$		0			0
$261$	−9.77951	−	9.77951i	−0.605336	−	0.605336i
$262$		0			0
$263$	21.2633			1.31115			0.655575	−	0.755130i	$-0.272427\pi$
$263$	21.2633			1.31115			0.655575	+	0.755130i	$0.272427\pi$
$264$		0			0
$265$	6.11444	+	9.93857i	0.375607	+	0.610521i
$266$		0			0
$267$	−1.85699	−	1.85699i	−0.113646	−	0.113646i
$268$		0			0
$269$	−1.03268	+	1.03268i	−0.0629638	+	0.0629638i	−0.737888	−	0.674924i	$-0.764177\pi$
$269$	−1.03268	+	1.03268i	−0.0629638	+	0.0629638i	0.674924	+	0.737888i	$0.264177\pi$
$270$		0			0
$271$	4.24432			0.257824			0.128912	−	0.991656i	$-0.458852\pi$
$271$	4.24432			0.257824			0.128912	+	0.991656i	$0.458852\pi$
$272$		0			0
$273$			7.48247i			0.452860i
$274$		0			0
$275$	12.9190	−	4.24795i	0.779045	−	0.256161i
$276$		0			0
$277$	16.8090	+	16.8090i	1.00995	+	1.00995i	0.999950	+	0.0100028i	$0.00318405\pi$
$277$	16.8090	+	16.8090i	1.00995	+	1.00995i	0.0100028	+	0.999950i	$0.496816\pi$
$278$		0			0
$279$	20.0909	+	20.0909i	1.20281	+	1.20281i
$280$		0			0
$281$			13.4960i			0.805103i	0.915397	+	0.402551i	$0.131877\pi$
$281$			13.4960i			0.805103i	−0.915397	+	0.402551i	$0.868123\pi$
$282$		0			0
$283$	−10.1398	+	10.1398i	−0.602749	+	0.602749i	−0.941041	−	0.338292i	$-0.890151\pi$
$283$	−10.1398	+	10.1398i	−0.602749	+	0.602749i	0.338292	+	0.941041i	$0.390151\pi$
$284$		0			0
$285$	−4.55959	−	1.08618i	−0.270087	−	0.0643398i
$286$		0			0
$287$	−4.47843			−0.264353
$288$		0			0
$289$	−1.25486	+	16.9536i	−0.0738151	+	0.997272i
$290$		0			0
$291$		−	1.50251i		−	0.0880787i
$292$		0			0
$293$		−	13.1804i		−	0.770005i	−0.922916	−	0.385002i	$-0.874201\pi$
$293$		−	13.1804i		−	0.770005i	0.922916	−	0.385002i	$-0.125799\pi$
$294$		0			0
$295$	4.12140	−	2.53558i	0.239957	−	0.147627i
$296$		0			0
$297$	5.84012			0.338878
$298$		0			0
$299$	−4.45752	−	4.45752i	−0.257785	−	0.257785i
$300$		0			0
$301$	−10.7944	+	10.7944i	−0.622180	+	0.622180i
$302$		0			0
$303$	4.12818	+	4.12818i	0.237158	+	0.237158i
$304$		0			0
$305$	0.649444	−	2.72625i	0.0371871	−	0.156105i
$306$		0			0
$307$			1.49316i			0.0852193i	0.999092	+	0.0426096i	$0.0135672\pi$
$307$			1.49316i			0.0852193i	−0.999092	+	0.0426096i	$0.986433\pi$
$308$		0			0
$309$	−1.15952	+	1.15952i	−0.0659628	+	0.0659628i
$310$		0			0
$311$	13.3292	−	13.3292i	0.755830	−	0.755830i	−0.219731	−	0.975561i	$-0.570518\pi$
$311$	13.3292	−	13.3292i	0.755830	−	0.755830i	0.975561	+	0.219731i	$0.0705179\pi$
$312$		0			0
$313$	−0.964982	+	0.964982i	−0.0545440	+	0.0545440i	−0.733853	−	0.679309i	$-0.762280\pi$
$313$	−0.964982	+	0.964982i	−0.0545440	+	0.0545440i	0.679309	+	0.733853i	$0.262280\pi$
$314$		0			0
$315$	4.78648	−	20.0928i	0.269687	−	1.13210i
$316$		0			0
$317$	2.67517	−	2.67517i	0.150253	−	0.150253i	−0.627978	−	0.778231i	$-0.716117\pi$
$317$	2.67517	−	2.67517i	0.150253	−	0.150253i	0.778231	+	0.627978i	$0.216117\pi$
$318$		0			0
$319$	−13.1252			−0.734869
$320$		0			0
$321$			3.67609i			0.205179i
$322$		0			0
$323$	−17.3011	+	16.0679i	−0.962660	+	0.894040i
$324$		0			0
$325$	−28.3063	−	14.2976i	−1.57015	−	0.793086i
$326$		0			0
$327$		−	4.53777i		−	0.250939i
$328$		0			0
$329$	−14.1703	−	14.1703i	−0.781235	−	0.781235i
$330$		0			0
$331$			22.8418i			1.25550i	0.778416	+	0.627748i	$0.216023\pi$
$331$			22.8418i			1.25550i	−0.778416	+	0.627748i	$0.783977\pi$
$332$		0			0
$333$	−23.2772	+	23.2772i	−1.27558	+	1.27558i
$334$		0			0
$335$	−13.2068	+	8.12512i	−0.721564	+	0.443923i
$336$		0			0
$337$	−1.75915	−	1.75915i	−0.0958269	−	0.0958269i	0.657568	−	0.753395i	$-0.271585\pi$
$337$	−1.75915	−	1.75915i	−0.0958269	−	0.0958269i	−0.753395	+	0.657568i	$0.771585\pi$
$338$		0			0
$339$	−1.69854			−0.0922522
$340$		0			0
$341$	26.9642			1.46019
$342$		0			0
$343$	−8.23227	−	8.23227i	−0.444501	−	0.444501i
$344$		0			0
$345$	−0.426277	−	0.692882i	−0.0229500	−	0.0373035i
$346$		0			0
$347$	−22.9048	+	22.9048i	−1.22959	+	1.22959i	−0.265477	+	0.964117i	$0.585529\pi$
$347$	−22.9048	+	22.9048i	−1.22959	+	1.22959i	−0.964117	+	0.265477i	$0.914471\pi$
$348$		0			0
$349$		−	1.07242i		−	0.0574056i	−0.999588	−	0.0287028i	$-0.990862\pi$
$349$		−	1.07242i		−	0.0574056i	0.999588	−	0.0287028i	$-0.00913763\pi$
$350$		0			0
$351$	−9.62968	−	9.62968i	−0.513994	−	0.513994i
$352$		0			0
$353$			13.4728i			0.717085i	0.933513	+	0.358542i	$0.116726\pi$
$353$			13.4728i			0.717085i	−0.933513	+	0.358542i	$0.883274\pi$
$354$		0			0
$355$	19.1088	+	4.55208i	1.01419	+	0.241599i
$356$		0			0
$357$	3.31014	+	3.56420i	0.175191	+	0.188638i
$358$		0			0
$359$		−	5.26692i		−	0.277978i	−0.990294	−	0.138989i	$-0.955615\pi$
$359$		−	5.26692i		−	0.277978i	0.990294	−	0.138989i	$-0.0443852\pi$
$360$		0			0
$361$	−13.7944			−0.726023
$362$		0			0
$363$	−0.932344	+	0.932344i	−0.0489354	+	0.0489354i
$364$		0			0
$365$	−4.13585	+	17.3616i	−0.216480	+	0.908746i
$366$		0			0
$367$	−14.7071	+	14.7071i	−0.767703	+	0.767703i	−0.977702	−	0.209999i	$-0.932654\pi$
$367$	−14.7071	+	14.7071i	−0.767703	+	0.767703i	0.209999	+	0.977702i	$0.432654\pi$
$368$		0			0
$369$	2.81597	−	2.81597i	0.146593	−	0.146593i
$370$		0			0
$371$	11.8929	−	11.8929i	0.617450	−	0.617450i
$372$		0			0
$373$			11.2190i			0.580899i	0.956890	+	0.290449i	$0.0938048\pi$
$373$			11.2190i			0.580899i	−0.956890	+	0.290449i	$0.906195\pi$
$374$		0			0
$375$	−3.12589	−	2.64136i	−0.161420	−	0.136399i
$376$		0			0
$377$	21.6419	+	21.6419i	1.11462	+	1.11462i
$378$		0			0
$379$	9.14951	−	9.14951i	0.469979	−	0.469979i	−0.431929	−	0.901908i	$-0.642167\pi$
$379$	9.14951	−	9.14951i	0.469979	−	0.469979i	0.901908	+	0.431929i	$0.142167\pi$
$380$		0			0
$381$	−0.630901	−	0.630901i	−0.0323220	−	0.0323220i
$382$		0			0
$383$	24.4086			1.24722			0.623612	−	0.781734i	$-0.285665\pi$
$383$	24.4086			1.24722			0.623612	+	0.781734i	$0.285665\pi$
$384$		0			0
$385$	−10.2714	−	16.6953i	−0.523477	−	0.850873i
$386$		0			0
$387$		−	13.5747i		−	0.690043i
$388$		0			0
$389$			14.6427i			0.742415i	0.928550	+	0.371208i	$0.121056\pi$
$389$			14.6427i			0.742415i	−0.928550	+	0.371208i	$0.878944\pi$
$390$		0			0
$391$	−4.09524	−	0.151352i	−0.207105	−	0.00765419i
$392$		0			0
$393$	0.406904			0.0205256
$394$		0			0
$395$	3.87152	−	16.2519i	0.194797	−	0.817724i
$396$		0			0
$397$	−21.5736	+	21.5736i	−1.08275	+	1.08275i	−0.0864969	+	0.996252i	$0.527567\pi$
$397$	−21.5736	+	21.5736i	−1.08275	+	1.08275i	−0.996252	+	0.0864969i	$0.972433\pi$
$398$		0			0
$399$			6.75597i			0.338222i
$400$		0			0
$401$	−0.0291011	−	0.0291011i	−0.00145324	−	0.00145324i	0.706380	−	0.707833i	$-0.250327\pi$
$401$	−0.0291011	−	0.0291011i	−0.00145324	−	0.00145324i	−0.707833	+	0.706380i	$0.750327\pi$
$402$		0			0
$403$	−44.4608	−	44.4608i	−2.21475	−	2.21475i
$404$		0			0
$405$	9.15339	+	14.8782i	0.454836	+	0.739302i
$406$		0			0
$407$			31.2405i			1.54854i
$408$		0			0
$409$	−6.48907			−0.320864			−0.160432	−	0.987047i	$-0.551289\pi$
$409$	−6.48907			−0.320864			−0.160432	+	0.987047i	$0.551289\pi$
$410$		0			0
$411$	2.91003	−	2.91003i	0.143541	−	0.143541i
$412$		0			0
$413$	−4.93185	−	4.93185i	−0.242680	−	0.242680i
$414$		0			0
$415$	17.7669	+	28.8789i	0.872145	+	1.41761i
$416$		0			0
$417$	−8.04392			−0.393913
$418$		0			0
$419$	−7.87265	−	7.87265i	−0.384604	−	0.384604i	0.488154	−	0.872758i	$-0.337671\pi$
$419$	−7.87265	−	7.87265i	−0.384604	−	0.384604i	−0.872758	+	0.488154i	$0.837671\pi$
$420$		0			0
$421$	31.6643			1.54322			0.771612	−	0.636093i	$-0.219451\pi$
$421$	31.6643			1.54322			0.771612	+	0.636093i	$0.219451\pi$
$422$		0			0
$423$	17.8202			0.866446
$424$		0			0
$425$	−19.8085	+	5.71181i	−0.960852	+	0.277063i
$426$		0			0
$427$	−4.03950			−0.195485
$428$		0			0
$429$	−6.31445			−0.304864
$430$		0			0
$431$	−24.2502	−	24.2502i	−1.16809	−	1.16809i	−0.982657	−	0.185435i	$-0.940631\pi$
$431$	−24.2502	−	24.2502i	−1.16809	−	1.16809i	−0.185435	−	0.982657i	$-0.559369\pi$
$432$		0			0
$433$	−19.3816			−0.931422			−0.465711	−	0.884937i	$-0.654201\pi$
$433$	−19.3816			−0.931422			−0.465711	+	0.884937i	$0.654201\pi$
$434$		0			0
$435$	2.06964	+	3.36404i	0.0992315	+	0.161293i
$436$		0			0
$437$	−4.02473	−	4.02473i	−0.192529	−	0.192529i
$438$		0			0
$439$	−3.83581	+	3.83581i	−0.183073	+	0.183073i	−0.792693	−	0.609620i	$-0.791322\pi$
$439$	−3.83581	+	3.83581i	−0.183073	+	0.183073i	0.609620	+	0.792693i	$0.291322\pi$
$440$		0			0
$441$	−9.70947			−0.462356
$442$		0			0
$443$		−	25.6325i		−	1.21784i	−0.793233	−	0.608919i	$-0.791604\pi$
$443$		−	25.6325i		−	1.21784i	0.793233	−	0.608919i	$-0.208396\pi$
$444$		0			0
$445$	−8.40646	−	13.6641i	−0.398505	−	0.647740i
$446$		0			0
$447$	−3.55309	−	3.55309i	−0.168056	−	0.168056i
$448$		0			0
$449$	12.4761	+	12.4761i	0.588783	+	0.588783i	0.937302	−	0.348518i	$-0.113315\pi$
$449$	12.4761	+	12.4761i	0.588783	+	0.588783i	−0.348518	+	0.937302i	$0.613315\pi$
$450$		0			0
$451$		−	3.77934i		−	0.177962i
$452$		0			0
$453$	5.39988	−	5.39988i	0.253708	−	0.253708i
$454$		0			0
$455$	−10.5924	+	44.4650i	−0.496579	+	2.08455i
$456$		0			0
$457$	32.1430			1.50359			0.751793	−	0.659400i	$-0.229189\pi$
$457$	32.1430			1.50359			0.751793	+	0.659400i	$0.229189\pi$
$458$		0			0
$459$	−8.84703	−	0.326968i	−0.412944	−	0.0152616i
$460$		0			0
$461$			16.0754i			0.748704i	0.927287	+	0.374352i	$0.122135\pi$
$461$			16.0754i			0.748704i	−0.927287	+	0.374352i	$0.877865\pi$
$462$		0			0
$463$			7.38107i			0.343027i	0.985182	+	0.171514i	$0.0548658\pi$
$463$			7.38107i			0.343027i	−0.985182	+	0.171514i	$0.945134\pi$
$464$		0			0
$465$	−4.25183	−	6.91103i	−0.197174	−	0.320492i
$466$		0			0
$467$	21.7955			1.00857			0.504287	−	0.863536i	$-0.331755\pi$
$467$	21.7955			1.00857			0.504287	+	0.863536i	$0.331755\pi$
$468$		0			0
$469$	15.8038	+	15.8038i	0.729753	+	0.729753i
$470$		0			0
$471$	0.135367	−	0.135367i	0.00623736	−	0.00623736i
$472$		0			0
$473$	−9.10940	−	9.10940i	−0.418851	−	0.418851i
$474$		0			0
$475$	−25.5580	−	12.9094i	−1.17268	−	0.592322i
$476$		0			0
$477$			14.9562i			0.684797i
$478$		0			0
$479$	21.5268	−	21.5268i	0.983586	−	0.983586i	−0.0162818	−	0.999867i	$-0.505183\pi$
$479$	21.5268	−	21.5268i	0.983586	−	0.983586i	0.999867	+	0.0162818i	$0.00518290\pi$
$480$		0			0
$481$	51.5120	−	51.5120i	2.34875	−	2.34875i
$482$		0			0
$483$	−0.829133	+	0.829133i	−0.0377269	+	0.0377269i
$484$		0			0
$485$	2.12700	−	8.92874i	0.0965819	−	0.405433i
$486$		0			0
$487$	22.7198	−	22.7198i	1.02953	−	1.02953i	0.0299839	−	0.999550i	$-0.490454\pi$
$487$	22.7198	−	22.7198i	1.02953	−	1.02953i	0.999550	−	0.0299839i	$-0.00954560\pi$
$488$		0			0
$489$	−5.71224			−0.258316
$490$		0			0
$491$			13.1034i			0.591349i	0.955289	+	0.295674i	$0.0955444\pi$
$491$			13.1034i			0.591349i	−0.955289	+	0.295674i	$0.904456\pi$
$492$		0			0
$493$	19.8830	+	0.734834i	0.895484	+	0.0330953i
$494$		0			0
$495$	16.9563	+	4.03930i	0.762127	+	0.181553i
$496$		0			0
$497$		−	28.3137i		−	1.27004i
$498$		0			0
$499$	−9.32184	−	9.32184i	−0.417303	−	0.417303i	0.466970	−	0.884273i	$-0.345346\pi$
$499$	−9.32184	−	9.32184i	−0.417303	−	0.417303i	−0.884273	+	0.466970i	$0.845346\pi$
$500$		0			0
$501$		−	0.976221i		−	0.0436144i
$502$		0			0
$503$	4.67930	−	4.67930i	0.208640	−	0.208640i	−0.595049	−	0.803689i	$-0.702868\pi$
$503$	4.67930	−	4.67930i	0.208640	−	0.208640i	0.803689	+	0.595049i	$0.202868\pi$
$504$		0			0
$505$	18.6879	+	30.3759i	0.831603	+	1.35171i
$506$		0			0
$507$	7.04703	+	7.04703i	0.312970	+	0.312970i
$508$		0			0
$509$	−18.9376			−0.839396			−0.419698	−	0.907664i	$-0.637864\pi$
$509$	−18.9376			−0.839396			−0.419698	+	0.907664i	$0.637864\pi$
$510$		0			0
$511$	25.7247			1.13800
$512$		0			0
$513$	−8.69470	−	8.69470i	−0.383880	−	0.383880i
$514$		0			0
$515$	−8.53196	+	5.24906i	−0.375963	+	0.231301i
$516$		0			0
$517$	11.9583	−	11.9583i	0.525926	−	0.525926i
$518$		0			0
$519$		−	3.14970i		−	0.138257i
$520$		0			0
$521$	23.1593	+	23.1593i	1.01463	+	1.01463i	0.999891	+	0.0147360i	$0.00469078\pi$
$521$	23.1593	+	23.1593i	1.01463	+	1.01463i	0.0147360	+	0.999891i	$0.495309\pi$
$522$		0			0
$523$			13.5754i			0.593611i	0.954938	+	0.296805i	$0.0959213\pi$
$523$			13.5754i			0.593611i	−0.954938	+	0.296805i	$0.904079\pi$
$524$		0			0
$525$	−2.65946	+	5.26519i	−0.116068	+	0.229792i
$526$		0			0
$527$	−40.8473	−	1.50963i	−1.77934	−	0.0657606i
$528$		0			0
$529$			22.0121i			0.957049i
$530$		0			0
$531$	6.20214			0.269150
$532$		0			0
$533$	−6.23170	+	6.23170i	−0.269925	+	0.269925i
$534$		0			0
$535$	−5.20398	+	21.8454i	−0.224988	+	0.944457i
$536$		0			0
$537$	−6.30219	+	6.30219i	−0.271960	+	0.271960i
$538$		0			0
$539$	−6.51559	+	6.51559i	−0.280646	+	0.280646i
$540$		0			0
$541$	−28.7689	+	28.7689i	−1.23687	+	1.23687i	−0.275596	+	0.961274i	$0.588875\pi$
$541$	−28.7689	+	28.7689i	−1.23687	+	1.23687i	−0.961274	+	0.275596i	$0.911125\pi$
$542$		0			0
$543$			5.56673i			0.238891i
$544$		0			0
$545$	6.42379	−	26.9659i	0.275165	−	1.15509i
$546$		0			0
$547$	−1.14183	−	1.14183i	−0.0488211	−	0.0488211i	0.682275	−	0.731096i	$-0.260991\pi$
$547$	−1.14183	−	1.14183i	−0.0488211	−	0.0488211i	−0.731096	+	0.682275i	$0.760991\pi$
$548$		0			0
$549$	2.53998	−	2.53998i	0.108404	−	0.108404i
$550$		0			0
$551$	19.5406	+	19.5406i	0.832459	+	0.832459i
$552$		0			0
$553$	−24.0806			−1.02401
$554$		0			0
$555$	8.00709	−	4.92614i	0.339882	−	0.209103i
$556$		0			0
$557$		−	43.2235i		−	1.83144i	−0.401819	−	0.915719i	$-0.631622\pi$
$557$		−	43.2235i		−	1.83144i	0.401819	−	0.915719i	$-0.368378\pi$
$558$		0			0
$559$			30.0407i			1.27059i
$560$		0			0
$561$	−3.00782	+	2.79342i	−0.126990	+	0.117938i
$562$		0			0
$563$	15.0751			0.635339			0.317670	−	0.948201i	$-0.397100\pi$
$563$	15.0751			0.635339			0.317670	+	0.948201i	$0.397100\pi$
$564$		0			0
$565$	−10.0937	−	2.40451i	−0.424645	−	0.101158i
$566$		0			0
$567$	17.8039	−	17.8039i	0.747692	−	0.747692i
$568$		0			0
$569$			4.85448i			0.203510i	0.994809	+	0.101755i	$0.0324458\pi$
$569$			4.85448i			0.203510i	−0.994809	+	0.101755i	$0.967554\pi$
$570$		0			0
$571$	17.4787	+	17.4787i	0.731460	+	0.731460i	0.970909	−	0.239449i	$-0.0769669\pi$
$571$	17.4787	+	17.4787i	0.731460	+	0.731460i	−0.239449	+	0.970909i	$0.576967\pi$
$572$		0			0
$573$	5.28391	+	5.28391i	0.220738	+	0.220738i
$574$		0			0
$575$	−1.55231	−	4.72094i	−0.0647358	−	0.196877i
$576$		0			0
$577$		−	30.6093i		−	1.27428i	−0.770748	−	0.637141i	$-0.780117\pi$
$577$		−	30.6093i		−	1.27428i	0.770748	−	0.637141i	$-0.219883\pi$
$578$		0			0
$579$	4.66243			0.193764
$580$		0			0
$581$	34.5577	−	34.5577i	1.43370	−	1.43370i
$582$		0			0
$583$	10.0364	+	10.0364i	0.415666	+	0.415666i
$584$		0			0
$585$	−21.2986	−	34.6192i	−0.880587	−	1.43133i
$586$		0			0
$587$	15.4493			0.637663			0.318831	−	0.947811i	$-0.396710\pi$
$587$	15.4493			0.637663			0.318831	+	0.947811i	$0.396710\pi$
$588$		0			0
$589$	−40.1439	−	40.1439i	−1.65410	−	1.65410i
$590$		0			0
$591$	−1.15942			−0.0476922
$592$		0			0
$593$	35.9557			1.47652			0.738261	−	0.674515i	$-0.235647\pi$
$593$	35.9557			1.47652			0.738261	+	0.674515i	$0.235647\pi$
$594$		0			0
$595$	14.6251	+	25.8664i	0.599570	+	1.06042i
$596$		0			0
$597$	2.99504			0.122579
$598$		0			0
$599$	−36.0209			−1.47178			−0.735888	−	0.677103i	$-0.763235\pi$
$599$	−36.0209			−1.47178			−0.735888	+	0.677103i	$0.763235\pi$
$600$		0			0
$601$	−11.0978	−	11.0978i	−0.452689	−	0.452689i	0.443557	−	0.896246i	$-0.353716\pi$
$601$	−11.0978	−	11.0978i	−0.452689	−	0.452689i	−0.896246	+	0.443557i	$0.853716\pi$
$602$		0			0
$603$	−19.8744			−0.809348
$604$		0			0
$605$	−6.86036	+	4.22065i	−0.278913	+	0.171594i
$606$		0			0
$607$	−15.3614	−	15.3614i	−0.623499	−	0.623499i	0.322926	−	0.946424i	$-0.395334\pi$
$607$	−15.3614	−	15.3614i	−0.623499	−	0.623499i	−0.946424	+	0.322926i	$0.895334\pi$
$608$		0			0
$609$	4.02556	−	4.02556i	0.163124	−	0.163124i
$610$		0			0
$611$	−39.4358			−1.59540
$612$		0			0
$613$		−	14.6607i		−	0.592140i	−0.955166	−	0.296070i	$-0.904324\pi$
$613$		−	14.6607i		−	0.592140i	0.955166	−	0.296070i	$-0.0956761\pi$
$614$		0			0
$615$	−0.968662	+	0.595943i	−0.0390602	+	0.0240307i
$616$		0			0
$617$	8.78776	+	8.78776i	0.353782	+	0.353782i	0.861515	−	0.507733i	$-0.169516\pi$
$617$	8.78776	+	8.78776i	0.353782	+	0.353782i	−0.507733	+	0.861515i	$0.669516\pi$
$618$		0			0
$619$	−22.1012	−	22.1012i	−0.888323	−	0.888323i	0.106039	−	0.994362i	$-0.466183\pi$
$619$	−22.1012	−	22.1012i	−0.888323	−	0.888323i	−0.994362	+	0.106039i	$0.966183\pi$
$620$		0			0
$621$		−	2.13413i		−	0.0856397i
$622$		0			0
$623$	−16.3511	+	16.3511i	−0.655091	+	0.655091i
$624$		0			0
$625$	−14.8366	−	20.1215i	−0.593463	−	0.804861i
$626$		0			0
$627$	−5.70136			−0.227690
$628$		0			0
$629$	1.74905	−	47.3254i	0.0697392	−	1.88699i
$630$		0			0
$631$		−	1.92923i		−	0.0768013i	−0.999262	−	0.0384007i	$-0.987774\pi$
$631$		−	1.92923i		−	0.0768013i	0.999262	−	0.0384007i	$-0.0122263\pi$
$632$		0			0
$633$			6.80999i			0.270673i
$634$		0			0
$635$	−2.85604	−	4.64228i	−0.113338	−	0.184223i
$636$		0			0
$637$	21.4869			0.851342
$638$		0			0
$639$	17.8032	+	17.8032i	0.704283	+	0.704283i
$640$		0			0
$641$	15.9510	−	15.9510i	0.630028	−	0.630028i	−0.318047	−	0.948075i	$-0.603027\pi$
$641$	15.9510	−	15.9510i	0.630028	−	0.630028i	0.948075	+	0.318047i	$0.103027\pi$
$642$		0			0
$643$	16.0532	+	16.0532i	0.633077	+	0.633077i	0.948839	−	0.315761i	$-0.102260\pi$
$643$	16.0532	+	16.0532i	0.633077	+	0.633077i	−0.315761	+	0.948839i	$0.602260\pi$
$644$		0			0
$645$	−0.898369	+	3.77119i	−0.0353732	+	0.148490i
$646$		0			0
$647$		−	43.9167i		−	1.72654i	−0.504741	−	0.863271i	$-0.668412\pi$
$647$		−	43.9167i		−	1.72654i	0.504741	−	0.863271i	$-0.331588\pi$
$648$		0			0
$649$	4.16198	−	4.16198i	0.163372	−	0.163372i
$650$		0			0
$651$	−8.27005	+	8.27005i	−0.324129	+	0.324129i
$652$		0			0
$653$	23.1062	−	23.1062i	0.904216	−	0.904216i	−0.0915812	−	0.995798i	$-0.529192\pi$
$653$	23.1062	−	23.1062i	0.904216	−	0.904216i	0.995798	+	0.0915812i	$0.0291921\pi$
$654$		0			0
$655$	2.41805	+	0.576025i	0.0944809	+	0.0225071i
$656$		0			0
$657$	−16.1753	+	16.1753i	−0.631060	+	0.631060i
$658$		0			0
$659$	7.61843			0.296772			0.148386	−	0.988930i	$-0.452592\pi$
$659$	7.61843			0.296772			0.148386	+	0.988930i	$0.452592\pi$
$660$		0			0
$661$		−	24.0179i		−	0.934188i	−0.884208	−	0.467094i	$-0.845301\pi$
$661$		−	24.0179i		−	0.934188i	0.884208	−	0.467094i	$-0.154699\pi$
$662$		0			0
$663$	9.56559	+	0.353524i	0.371497	+	0.0137297i
$664$		0			0
$665$	−9.56395	+	40.1477i	−0.370874	+	1.55686i
$666$		0			0
$667$			4.79628i			0.185713i
$668$		0			0
$669$	0.796295	+	0.796295i	0.0307866	+	0.0307866i
$670$		0			0
$671$		−	3.40893i		−	0.131600i
$672$		0			0
$673$	−2.30807	+	2.30807i	−0.0889697	+	0.0889697i	−0.750191	−	0.661221i	$-0.770038\pi$
$673$	−2.30807	+	2.30807i	−0.0889697	+	0.0889697i	0.661221	+	0.750191i	$0.270038\pi$
$674$		0			0
$675$	−3.35349	−	10.1987i	−0.129076	−	0.392550i
$676$		0			0
$677$	−1.00830	−	1.00830i	−0.0387522	−	0.0387522i	0.687465	−	0.726217i	$-0.258723\pi$
$677$	−1.00830	−	1.00830i	−0.0387522	−	0.0387522i	−0.726217	+	0.687465i	$0.758723\pi$
$678$		0			0
$679$	−13.2298			−0.507712
$680$		0			0
$681$	6.68859			0.256307
$682$		0			0
$683$	−0.0970845	−	0.0970845i	−0.00371483	−	0.00371483i	0.705247	−	0.708962i	$-0.250836\pi$
$683$	−0.0970845	−	0.0970845i	−0.00371483	−	0.00371483i	−0.708962	+	0.705247i	$0.750836\pi$
$684$		0			0
$685$	21.4125	−	13.1735i	0.818131	−	0.503333i
$686$		0			0
$687$	2.86119	−	2.86119i	0.109161	−	0.109161i
$688$		0			0
$689$		−	33.0978i		−	1.26093i
$690$		0			0
$691$	−1.71912	−	1.71912i	−0.0653984	−	0.0653984i	0.673651	−	0.739050i	$-0.264725\pi$
$691$	−1.71912	−	1.71912i	−0.0653984	−	0.0653984i	−0.739050	+	0.673651i	$0.764725\pi$
$692$		0			0
$693$		−	25.1242i		−	0.954389i
$694$		0			0
$695$	−47.8014	−	11.3872i	−1.81321	−	0.431941i
$696$		0			0
$697$	−0.211592	+	5.72522i	−0.00801463	+	0.216858i
$698$		0			0
$699$		−	1.85403i		−	0.0701259i
$700$		0			0
$701$	38.1019			1.43909			0.719545	−	0.694445i	$-0.244350\pi$
$701$	38.1019			1.43909			0.719545	+	0.694445i	$0.244350\pi$
$702$		0			0
$703$	46.5106	−	46.5106i	1.75418	−	1.75418i
$704$		0			0
$705$	−4.95061	−	1.17933i	−0.186451	−	0.0444161i
$706$		0			0
$707$	36.3491	−	36.3491i	1.36705	−	1.36705i
$708$		0			0
$709$	−14.4541	+	14.4541i	−0.542835	+	0.542835i	−0.924359	−	0.381524i	$-0.875399\pi$
$709$	−14.4541	+	14.4541i	−0.542835	+	0.542835i	0.381524	+	0.924359i	$0.375399\pi$
$710$		0			0
$711$	15.1415	−	15.1415i	0.567851	−	0.567851i
$712$		0			0
$713$		−	9.85341i		−	0.369013i
$714$		0			0
$715$	−37.5239	−	8.93891i	−1.40332	−	0.334296i
$716$		0			0
$717$	3.11600	+	3.11600i	0.116369	+	0.116369i
$718$		0			0
$719$	18.1680	−	18.1680i	0.677553	−	0.677553i	−0.281893	−	0.959446i	$-0.590962\pi$
$719$	18.1680	−	18.1680i	0.677553	−	0.677553i	0.959446	+	0.281893i	$0.0909624\pi$
$720$		0			0
$721$	10.2097	+	10.2097i	0.380230	+	0.380230i
$722$		0			0
$723$	4.12928			0.153570
$724$		0			0
$725$	7.53669	+	22.9208i	0.279906	+	0.851258i
$726$		0			0
$727$			38.1508i			1.41493i	0.706746	+	0.707467i	$0.250162\pi$
$727$			38.1508i			1.41493i	−0.706746	+	0.707467i	$0.749838\pi$
$728$		0			0
$729$			20.0317i			0.741916i
$730$		0			0
$731$	13.2896	+	14.3096i	0.491533	+	0.529259i
$732$		0			0
$733$	15.0872			0.557260			0.278630	−	0.960399i	$-0.410120\pi$
$733$	15.0872			0.557260			0.278630	+	0.960399i	$0.410120\pi$
$734$		0			0
$735$	2.69738	+	0.642567i	0.0994944	+	0.0237015i
$736$		0			0
$737$	−13.3368	+	13.3368i	−0.491268	+	0.491268i
$738$		0			0
$739$			29.9967i			1.10345i	0.834027	+	0.551723i	$0.186030\pi$
$739$			29.9967i			1.10345i	−0.834027	+	0.551723i	$0.813970\pi$
$740$		0			0
$741$	9.40088	+	9.40088i	0.345350	+	0.345350i
$742$		0			0
$743$	28.3721	+	28.3721i	1.04087	+	1.04087i	0.999128	+	0.0417429i	$0.0132910\pi$
$743$	28.3721	+	28.3721i	1.04087	+	1.04087i	0.0417429	+	0.999128i	$0.486709\pi$
$744$		0			0
$745$	−16.0846	−	26.1443i	−0.589293	−	0.957853i
$746$		0			0
$747$			43.4587i			1.59007i
$748$		0			0
$749$	32.3684			1.18272
$750$		0			0
$751$	0.668097	−	0.668097i	0.0243792	−	0.0243792i	−0.694812	−	0.719191i	$-0.744512\pi$
$751$	0.668097	−	0.668097i	0.0243792	−	0.0243792i	0.719191	+	0.694812i	$0.244512\pi$
$752$		0			0
$753$	−5.17521	−	5.17521i	−0.188595	−	0.188595i
$754$		0			0
$755$	39.7333	−	24.4448i	1.44604	−	0.889639i
$756$		0			0
$757$	−10.0807			−0.366390			−0.183195	−	0.983077i	$-0.558644\pi$
$757$	−10.0807			−0.366390			−0.183195	+	0.983077i	$0.558644\pi$
$758$		0			0
$759$	−0.699705	−	0.699705i	−0.0253977	−	0.0253977i
$760$		0			0
$761$	−3.99545			−0.144835			−0.0724175	−	0.997374i	$-0.523071\pi$
$761$	−3.99545			−0.144835			−0.0724175	+	0.997374i	$0.523071\pi$
$762$		0			0
$763$	−39.9556			−1.44649
$764$		0			0
$765$	−25.4604	−	7.06835i	−0.920523	−	0.255557i
$766$		0			0
$767$	−13.7252			−0.495590
$768$		0			0
$769$	24.0023			0.865544			0.432772	−	0.901503i	$-0.357536\pi$
$769$	24.0023			0.865544			0.432772	+	0.901503i	$0.357536\pi$
$770$		0			0
$771$	−1.69747	−	1.69747i	−0.0611328	−	0.0611328i
$772$		0			0
$773$	−14.7233			−0.529561			−0.264780	−	0.964309i	$-0.585299\pi$
$773$	−14.7233			−0.529561			−0.264780	+	0.964309i	$0.585299\pi$
$774$		0			0
$775$	−15.4832	−	47.0882i	−0.556175	−	1.69146i
$776$		0			0
$777$	−9.58163	−	9.58163i	−0.343739	−	0.343739i
$778$		0			0
$779$	−5.62664	+	5.62664i	−0.201595	+	0.201595i
$780$		0			0
$781$	23.8939			0.854989
$782$		0			0
$783$			10.3615i			0.370290i
$784$		0			0
$785$	0.996052	−	0.612794i	0.0355506	−	0.0218716i
$786$		0			0
$787$	0.551240	+	0.551240i	0.0196496	+	0.0196496i	0.716863	−	0.697214i	$-0.245577\pi$
$787$	0.551240	+	0.551240i	0.0196496	+	0.0196496i	−0.697214	+	0.716863i	$0.745577\pi$
$788$		0			0
$789$	−5.50353	−	5.50353i	−0.195931	−	0.195931i
$790$		0			0
$791$			14.9559i			0.531770i
$792$		0			0
$793$	−5.62093	+	5.62093i	−0.199605	+	0.199605i
$794$		0			0
$795$	0.989792	−	4.15497i	0.0351043	−	0.147362i
$796$		0			0
$797$	−6.58323			−0.233190			−0.116595	−	0.993180i	$-0.537198\pi$
$797$	−6.58323			−0.233190			−0.116595	+	0.993180i	$0.537198\pi$
$798$		0			0
$799$	−18.7848	+	17.4458i	−0.664559	+	0.617189i
$800$		0			0
$801$		−	20.5626i		−	0.726543i
$802$		0			0
$803$			21.7091i			0.766097i
$804$		0			0
$805$	−6.10091	+	3.75342i	−0.215029	+	0.132291i
$806$		0			0
$807$	0.534575			0.0188179
$808$		0			0
$809$	10.8247	+	10.8247i	0.380576	+	0.380576i	0.871310	−	0.490733i	$-0.163271\pi$
$809$	10.8247	+	10.8247i	0.380576	+	0.380576i	−0.490733	+	0.871310i	$0.663271\pi$
$810$		0			0
$811$	16.4872	−	16.4872i	0.578945	−	0.578945i	−0.355668	−	0.934613i	$-0.615746\pi$
$811$	16.4872	−	16.4872i	0.578945	−	0.578945i	0.934613	+	0.355668i	$0.115746\pi$
$812$		0			0
$813$	−1.09855	−	1.09855i	−0.0385278	−	0.0385278i
$814$		0			0
$815$	−33.9453	−	8.08641i	−1.18905	−	0.283255i
$816$		0			0
$817$			27.1239i			0.948947i
$818$		0			0
$819$	−41.4269	+	41.4269i	−1.44757	+	1.44757i
$820$		0			0
$821$	−5.76006	+	5.76006i	−0.201028	+	0.201028i	−0.800440	−	0.599413i	$-0.795401\pi$
$821$	−5.76006	+	5.76006i	−0.201028	+	0.201028i	0.599413	+	0.800440i	$0.295401\pi$
$822$		0			0
$823$	12.6076	−	12.6076i	0.439475	−	0.439475i	−0.452360	−	0.891835i	$-0.649418\pi$
$823$	12.6076	−	12.6076i	0.439475	−	0.439475i	0.891835	+	0.452360i	$0.149418\pi$
$824$		0			0
$825$	−4.44329	−	2.24431i	−0.154695	−	0.0781369i
$826$		0			0
$827$	19.9447	−	19.9447i	0.693544	−	0.693544i	−0.269466	−	0.963010i	$-0.586847\pi$
$827$	19.9447	−	19.9447i	0.693544	−	0.693544i	0.963010	+	0.269466i	$0.0868470\pi$
$828$		0			0
$829$	−46.3143			−1.60856			−0.804282	−	0.594248i	$-0.797450\pi$
$829$	−46.3143			−1.60856			−0.804282	+	0.594248i	$0.797450\pi$
$830$		0			0
$831$		−	8.70126i		−	0.301843i
$832$		0			0
$833$	10.2351	−	9.50550i	0.354624	−	0.329346i
$834$		0			0
$835$	1.38197	−	5.80125i	0.0478249	−	0.200760i
$836$		0			0
$837$		−	21.2865i		−	0.735770i
$838$		0			0
$839$	−22.3210	−	22.3210i	−0.770605	−	0.770605i	0.207607	−	0.978212i	$-0.433432\pi$
$839$	−22.3210	−	22.3210i	−0.770605	−	0.770605i	−0.978212	+	0.207607i	$0.933432\pi$
$840$		0			0
$841$			5.71336i			0.197012i
$842$		0			0
$843$	3.49314	−	3.49314i	0.120310	−	0.120310i
$844$		0			0
$845$	31.9014	+	51.8533i	1.09744	+	1.78381i
$846$		0			0
$847$	8.20941	+	8.20941i	0.282079	+	0.282079i
$848$		0			0
$849$	5.24893			0.180143
$850$		0			0
$851$	11.4161			0.391339
$852$		0			0
$853$	0.947318	+	0.947318i	0.0324355	+	0.0324355i	0.723139	−	0.690703i	$-0.242699\pi$
$853$	0.947318	+	0.947318i	0.0324355	+	0.0324355i	−0.690703	+	0.723139i	$0.742699\pi$
$854$		0			0
$855$	−19.2306	−	31.2579i	−0.657673	−	1.06900i
$856$		0			0
$857$	−20.1011	+	20.1011i	−0.686640	+	0.686640i	−0.961488	−	0.274848i	$-0.911373\pi$
$857$	−20.1011	+	20.1011i	−0.686640	+	0.686640i	0.274848	+	0.961488i	$0.411373\pi$
$858$		0			0
$859$			39.2008i			1.33751i	0.743481	+	0.668757i	$0.233173\pi$
$859$			39.2008i			1.33751i	−0.743481	+	0.668757i	$0.766827\pi$
$860$		0			0
$861$	1.15914	+	1.15914i	0.0395035	+	0.0395035i
$862$		0			0
$863$			5.52428i			0.188049i	0.995570	+	0.0940243i	$0.0299731\pi$
$863$			5.52428i			0.188049i	−0.995570	+	0.0940243i	$0.970027\pi$
$864$		0			0
$865$	4.45881	−	18.7173i	0.151604	−	0.636407i
$866$		0			0
$867$	4.71286	−	4.06328i	0.160057	−	0.137996i
$868$		0			0
$869$		−	20.3216i		−	0.689363i
$870$		0			0
$871$	43.9818			1.49027
$872$		0			0
$873$	8.31868	−	8.31868i	0.281545	−	0.281545i
$874$		0			0
$875$	−23.2575	+	27.5239i	−0.786247	+	0.930476i
$876$		0			0
$877$	−1.37709	+	1.37709i	−0.0465009	+	0.0465009i	−0.729975	−	0.683474i	$-0.760468\pi$
$877$	−1.37709	+	1.37709i	−0.0465009	+	0.0465009i	0.683474	+	0.729975i	$0.260468\pi$
$878$		0			0
$879$	−3.41145	+	3.41145i	−0.115065	+	0.115065i
$880$		0			0
$881$	−12.7010	+	12.7010i	−0.427906	+	0.427906i	−0.887915	−	0.460008i	$-0.847846\pi$
$881$	−12.7010	+	12.7010i	−0.427906	+	0.427906i	0.460008	+	0.887915i	$0.347846\pi$
$882$		0			0
$883$			14.8270i			0.498968i	0.968379	+	0.249484i	$0.0802610\pi$
$883$			14.8270i			0.498968i	−0.968379	+	0.249484i	$0.919739\pi$
$884$		0			0
$885$	−1.72301	−	0.410454i	−0.0579184	−	0.0137973i
$886$		0			0
$887$	17.4009	+	17.4009i	0.584266	+	0.584266i	0.936073	−	0.351807i	$-0.114433\pi$
$887$	17.4009	+	17.4009i	0.584266	+	0.584266i	−0.351807	+	0.936073i	$0.614433\pi$
$888$		0			0
$889$	−5.55516	+	5.55516i	−0.186314	+	0.186314i
$890$		0			0
$891$	15.0247	+	15.0247i	0.503345	+	0.503345i
$892$		0			0
$893$	−35.6068			−1.19154
$894$		0			0
$895$	−46.3727	+	28.5295i	−1.55007	+	0.953637i
$896$		0			0
$897$			2.30746i			0.0770440i
$898$		0			0
$899$			47.8397i			1.59554i
$900$		0			0
$901$	−14.6420	−	15.7658i	−0.487796	−	0.525235i
$902$		0			0
$903$	5.58780			0.185950
$904$		0			0
$905$	−7.88043	+	33.0806i	−0.261954	+	1.09964i
$906$		0			0
$907$	−23.0135	+	23.0135i	−0.764150	+	0.764150i	−0.977070	−	0.212920i	$-0.931703\pi$
$907$	−23.0135	+	23.0135i	−0.764150	+	0.764150i	0.212920	+	0.977070i	$0.431703\pi$
$908$		0			0
$909$			45.7115i			1.51616i
$910$		0			0
$911$	11.6712	+	11.6712i	0.386685	+	0.386685i	0.873503	−	0.486818i	$-0.161843\pi$
$911$	11.6712	+	11.6712i	0.386685	+	0.386685i	−0.486818	+	0.873503i	$0.661843\pi$
$912$		0			0
$913$	29.1632	+	29.1632i	0.965161	+	0.965161i
$914$		0			0
$915$	−0.873724	+	0.537535i	−0.0288844	+	0.0177704i
$916$		0			0
$917$		−	3.58284i		−	0.118316i
$918$		0			0
$919$	51.4106			1.69588			0.847940	−	0.530092i	$-0.177843\pi$
$919$	51.4106			1.69588			0.847940	+	0.530092i	$0.177843\pi$
$920$		0			0
$921$	0.386472	−	0.386472i	0.0127347	−	0.0127347i
$922$		0			0
$923$	−39.3982	−	39.3982i	−1.29681	−	1.29681i
$924$		0			0
$925$	54.5561	−	17.9388i	1.79379	−	0.589824i
$926$		0			0
$927$	−12.8394			−0.421702
$928$		0			0
$929$	−4.17792	−	4.17792i	−0.137073	−	0.137073i	0.635241	−	0.772314i	$-0.280901\pi$
$929$	−4.17792	−	4.17792i	−0.137073	−	0.137073i	−0.772314	+	0.635241i	$0.780901\pi$
$930$		0			0
$931$	19.4007			0.635831
$932$		0			0
$933$	−6.89994			−0.225894
$934$		0			0
$935$	−21.8286	+	12.3421i	−0.713872	+	0.403630i
$936$		0			0
$937$	11.1986			0.365842			0.182921	−	0.983128i	$-0.441445\pi$
$937$	11.1986			0.365842			0.182921	+	0.983128i	$0.441445\pi$
$938$		0			0
$939$	0.499529			0.0163015
$940$		0			0
$941$	0.460269	+	0.460269i	0.0150043	+	0.0150043i	0.714569	−	0.699565i	$-0.246623\pi$
$941$	0.460269	+	0.460269i	0.0150043	+	0.0150043i	−0.699565	+	0.714569i	$0.746623\pi$
$942$		0			0
$943$	−1.38107			−0.0449738
$944$		0			0
$945$	−13.1799	+	8.10859i	−0.428743	+	0.263773i
$946$		0			0
$947$	−8.16599	−	8.16599i	−0.265359	−	0.265359i	0.561868	−	0.827227i	$-0.310083\pi$
$947$	−8.16599	−	8.16599i	−0.265359	−	0.265359i	−0.827227	+	0.561868i	$0.810083\pi$
$948$		0			0
$949$	35.7958	−	35.7958i	1.16198	−	1.16198i
$950$		0			0
$951$	−1.38482			−0.0449058
$952$		0			0
$953$			8.89276i			0.288065i	0.989573	+	0.144032i	$0.0460069\pi$
$953$			8.89276i			0.288065i	−0.989573	+	0.144032i	$0.953993\pi$
$954$		0			0
$955$	23.9198	+	38.8799i	0.774028	+	1.25813i
$956$		0			0
$957$	3.39717	+	3.39717i	0.109815	+	0.109815i
$958$		0			0
$959$	−25.6232	−	25.6232i	−0.827416	−	0.827416i
$960$		0			0
$961$		−	67.2811i		−	2.17036i
$962$		0			0
$963$	−20.3528	+	20.3528i	−0.655859	+	0.655859i
$964$		0			0
$965$	27.7068	+	6.60028i	0.891912	+	0.212470i
$966$		0			0
$967$	−3.44609			−0.110819			−0.0554094	−	0.998464i	$-0.517646\pi$
$967$	−3.44609			−0.110819			−0.0554094	+	0.998464i	$0.517646\pi$
$968$		0			0
$969$	8.63683	+	0.319200i	0.277455	+	0.0102542i
$970$		0			0
$971$		−	21.7224i		−	0.697104i	−0.937289	−	0.348552i	$-0.886673\pi$
$971$		−	21.7224i		−	0.697104i	0.937289	−	0.348552i	$-0.113327\pi$
$972$		0			0
$973$			70.8277i			2.27063i
$974$		0			0
$975$	3.62586	+	11.0271i	0.116120	+	0.353149i
$976$		0			0
$977$	4.68811			0.149986			0.0749929	−	0.997184i	$-0.476107\pi$
$977$	4.68811			0.149986			0.0749929	+	0.997184i	$0.476107\pi$
$978$		0			0
$979$	−13.7986	−	13.7986i	−0.441006	−	0.441006i
$980$		0			0
$981$	25.1235	−	25.1235i	0.802130	−	0.802130i
$982$		0			0
$983$	−13.5040	−	13.5040i	−0.430710	−	0.430710i	0.458160	−	0.888870i	$-0.348509\pi$
$983$	−13.5040	−	13.5040i	−0.430710	−	0.430710i	−0.888870	+	0.458160i	$0.848509\pi$
$984$		0			0
$985$	−6.88992	−	1.64131i	−0.219531	−	0.0522965i
$986$		0			0
$987$			7.33535i			0.233487i
$988$		0			0
$989$	−3.32881	+	3.32881i	−0.105850	+	0.105850i
$990$		0			0
$991$	30.3189	−	30.3189i	0.963113	−	0.963113i	−0.0362306	−	0.999343i	$-0.511535\pi$
$991$	30.3189	−	30.3189i	0.963113	−	0.963113i	0.999343	+	0.0362306i	$0.0115351\pi$
$992$		0			0
$993$	5.91209	−	5.91209i	0.187614	−	0.187614i
$994$		0			0
$995$	17.7982	+	4.23986i	0.564239	+	0.134413i
$996$		0			0
$997$	−19.1494	+	19.1494i	−0.606467	+	0.606467i	−0.942021	−	0.335554i	$-0.891076\pi$
$997$	−19.1494	+	19.1494i	−0.606467	+	0.606467i	0.335554	+	0.942021i	$0.391076\pi$
$998$		0			0
$999$	24.6624			0.780285

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.z.c.89.7	✓	26
5.4	even	2		680.2.z.d.89.7	yes	26
17.13	even	4		680.2.z.d.489.7	yes	26
85.64	even	4	inner	680.2.z.c.489.7	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.z.c.89.7	✓	26	1.1	even	1	trivial
680.2.z.c.489.7	yes	26	85.64	even	4	inner
680.2.z.d.89.7	yes	26	5.4	even	2
680.2.z.d.489.7	yes	26	17.13	even	4

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)

\(f(q)\)	\(=\)	\(q+(-0.258828 - 0.258828i) q^{3} +(-1.17169 - 1.90450i) q^{5} +(-2.27901 + 2.27901i) q^{7} -2.86602i q^{9} +(-1.92326 - 1.92326i) q^{11} +6.34245i q^{13} +(-0.189671 + 0.796206i) q^{15} +(2.80581 + 3.02116i) q^{17} +5.72664i q^{19} +1.17974 q^{21} +(-0.702808 + 0.702808i) q^{23} +(-2.25426 + 4.46299i) q^{25} +(-1.51829 + 1.51829i) q^{27} +(3.41223 - 3.41223i) q^{29} +(-7.01003 + 7.01003i) q^{31} +0.995585i q^{33} +(7.01069 + 1.67008i) q^{35} +(-8.12179 - 8.12179i) q^{37} +(1.64160 - 1.64160i) q^{39} +(0.982537 + 0.982537i) q^{41} +4.73645 q^{43} +(-5.45834 + 3.35810i) q^{45} +6.21775i q^{47} -3.38779i q^{49} +(0.0557394 - 1.50818i) q^{51} -5.21846 q^{53} +(-1.40938 + 5.91631i) q^{55} +(1.48222 - 1.48222i) q^{57} +2.16403i q^{59} +(0.886240 + 0.886240i) q^{61} +(6.53169 + 6.53169i) q^{63} +(12.0792 - 7.43142i) q^{65} -6.93450i q^{67} +0.363813 q^{69} +(-6.21183 + 6.21183i) q^{71} +(-5.64384 - 5.64384i) q^{73} +(1.73861 - 0.571680i) q^{75} +8.76624 q^{77} +(5.28312 + 5.28312i) q^{79} -7.81210 q^{81} -15.1635 q^{83} +(2.46626 - 8.88355i) q^{85} -1.76636 q^{87} +7.17462 q^{89} +(-14.4545 - 14.4545i) q^{91} +3.62879 q^{93} +(10.9064 - 6.70987i) q^{95} +(2.90252 + 2.90252i) q^{97} +(-5.51208 + 5.51208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 2 q^{3} + 8 q^{5} - 2 q^{7} + 2 q^{11} + 2 q^{15} - 2 q^{17} - 12 q^{21} + 2 q^{23} - 10 q^{25} - 20 q^{27} + 10 q^{29} - 10 q^{31} + 22 q^{35} + 6 q^{37} + 8 q^{39} - 10 q^{41} - 32 q^{43} - 10 q^{45}+ \cdots - 22 q^{99}+O(q^{100}) \) 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

L-functions

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Database

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