LMFDB - Embedded newform 800.2.be.a.209.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [800,2,Mod(209,800)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("800.209"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(800, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.be (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			209.10
Character	$\chi$	$=$	800.209
Dual form			800.2.be.a.689.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.327557 - 1.00812i) q^{3} +(1.12940 - 1.92988i) q^{5} -3.62100i q^{7} +(1.51804 - 1.10292i) q^{9} +(0.116625 - 0.160521i) q^{11} +(-1.57920 + 1.14736i) q^{13} +(-2.31550 - 0.506422i) q^{15} +(5.99191 + 1.94689i) q^{17} +(-3.31697 - 1.07775i) q^{19} +(-3.65040 + 1.18609i) q^{21} +(0.186374 - 0.256522i) q^{23} +(-2.44891 - 4.35923i) q^{25} +(-4.18179 - 3.03825i) q^{27} +(-1.98323 + 0.644390i) q^{29} +(-2.40398 + 7.39869i) q^{31} +(-0.200025 - 0.0649921i) q^{33} +(-6.98811 - 4.08956i) q^{35} +(-3.14753 + 2.28682i) q^{37} +(1.67395 + 1.21620i) q^{39} +(-2.48445 + 1.80506i) q^{41} +10.3631 q^{43} +(-0.414034 - 4.17529i) q^{45} +(7.86154 - 2.55437i) q^{47} -6.11166 q^{49} -6.67827i q^{51} +(-4.48172 - 13.7933i) q^{53} +(-0.178070 - 0.406365i) q^{55} +3.69692i q^{57} +(0.165441 + 0.227710i) q^{59} +(-1.86928 + 2.57285i) q^{61} +(-3.99368 - 5.49683i) q^{63} +(0.430715 + 4.34351i) q^{65} +(0.0384025 - 0.118191i) q^{67} +(-0.319653 - 0.103862i) q^{69} +(1.42604 + 4.38889i) q^{71} +(7.51775 - 10.3473i) q^{73} +(-3.59246 + 3.89668i) q^{75} +(-0.581246 - 0.422300i) q^{77} +(-1.42060 - 4.37215i) q^{79} +(0.0463838 - 0.142755i) q^{81} +(-4.15123 + 12.7762i) q^{83} +(10.5245 - 9.36487i) q^{85} +(1.29924 + 1.78826i) q^{87} +(-13.8793 - 10.0839i) q^{89} +(4.15459 + 5.71830i) q^{91} +8.24620 q^{93} +(-5.82612 + 5.18416i) q^{95} +(-2.24784 + 0.730369i) q^{97} -0.372306i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79}+ \cdots - 50 q^{97}+O(q^{100}) $ 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$

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
$3$	−0.327557	−	1.00812i	−0.189115	−	0.582037i	0.810880	−	0.585213i	$-0.198989\pi$
$3$	−0.327557	−	1.00812i	−0.189115	−	0.582037i	−0.999995	+	0.00317571i	$0.998989\pi$
$4$		0			0
$5$	1.12940	−	1.92988i	0.505084	−	0.863070i
$5$	1.12940	−	1.92988i	0.505084	−	0.863070i
$6$		0			0
$7$		−	3.62100i		−	1.36861i	−0.729196	−	0.684305i	$-0.760106\pi$
$7$		−	3.62100i		−	1.36861i	0.729196	−	0.684305i	$-0.239894\pi$
$8$		0			0
$9$	1.51804	−	1.10292i	0.506014	−	0.367641i
$10$		0			0
$11$	0.116625	−	0.160521i	0.0351638	−	0.0483988i	−0.791073	−	0.611722i	$-0.790477\pi$
$11$	0.116625	−	0.160521i	0.0351638	−	0.0483988i	0.826237	+	0.563323i	$0.190477\pi$
$12$		0			0
$13$	−1.57920	+	1.14736i	−0.437992	+	0.318220i	−0.784837	−	0.619703i	$-0.787253\pi$
$13$	−1.57920	+	1.14736i	−0.437992	+	0.318220i	0.346845	+	0.937923i	$0.387253\pi$
$14$		0			0
$15$	−2.31550	−	0.506422i	−0.597858	−	0.130758i
$16$		0			0
$17$	5.99191	+	1.94689i	1.45325	+	0.472190i	0.926001	−	0.377521i	$-0.123223\pi$
$17$	5.99191	+	1.94689i	1.45325	+	0.472190i	0.527249	+	0.849711i	$0.323223\pi$
$18$		0			0
$19$	−3.31697	−	1.07775i	−0.760965	−	0.247253i	−0.0972725	−	0.995258i	$-0.531012\pi$
$19$	−3.31697	−	1.07775i	−0.760965	−	0.247253i	−0.663693	+	0.748005i	$0.731012\pi$
$20$		0			0
$21$	−3.65040	+	1.18609i	−0.796582	+	0.258825i
$22$		0			0
$23$	0.186374	−	0.256522i	0.0388618	−	0.0534886i	−0.789144	−	0.614208i	$-0.789475\pi$
$23$	0.186374	−	0.256522i	0.0388618	−	0.0534886i	0.828006	+	0.560720i	$0.189475\pi$
$24$		0			0
$25$	−2.44891	−	4.35923i	−0.489781	−	0.871845i
$26$		0			0
$27$	−4.18179	−	3.03825i	−0.804786	−	0.584711i
$28$		0			0
$29$	−1.98323	+	0.644390i	−0.368277	+	0.119660i	−0.487308	−	0.873230i	$-0.662021\pi$
$29$	−1.98323	+	0.644390i	−0.368277	+	0.119660i	0.119031	+	0.992890i	$0.462021\pi$
$30$		0			0
$31$	−2.40398	+	7.39869i	−0.431768	+	1.32884i	0.464595	+	0.885523i	$0.346200\pi$
$31$	−2.40398	+	7.39869i	−0.431768	+	1.32884i	−0.896363	+	0.443321i	$0.853800\pi$
$32$		0			0
$33$	−0.200025	−	0.0649921i	−0.0348199	−	0.0113137i
$34$		0			0
$35$	−6.98811	−	4.08956i	−1.18121	−	0.691262i
$36$		0			0
$37$	−3.14753	+	2.28682i	−0.517451	+	0.375950i	−0.815643	−	0.578556i	$-0.803617\pi$
$37$	−3.14753	+	2.28682i	−0.517451	+	0.375950i	0.298192	+	0.954506i	$0.403617\pi$
$38$		0			0
$39$	1.67395	+	1.21620i	0.268047	+	0.194747i
$40$		0			0
$41$	−2.48445	+	1.80506i	−0.388007	+	0.281903i	−0.764638	−	0.644460i	$-0.777082\pi$
$41$	−2.48445	+	1.80506i	−0.388007	+	0.281903i	0.376632	+	0.926363i	$0.377082\pi$
$42$		0			0
$43$	10.3631			1.58036			0.790179	−	0.612877i	$-0.209988\pi$
$43$	10.3631			1.58036			0.790179	+	0.612877i	$0.209988\pi$
$44$		0			0
$45$	−0.414034	−	4.17529i	−0.0617205	−	0.622415i
$46$		0			0
$47$	7.86154	−	2.55437i	1.14672	−	0.372593i	0.326816	−	0.945088i	$-0.394024\pi$
$47$	7.86154	−	2.55437i	1.14672	−	0.372593i	0.819908	+	0.572495i	$0.194024\pi$
$48$		0			0
$49$	−6.11166			−0.873094
$50$		0			0
$51$		−	6.67827i		−	0.935145i
$52$		0			0
$53$	−4.48172	−	13.7933i	−0.615612	−	1.89466i	−0.391917	−	0.920001i	$-0.628188\pi$
$53$	−4.48172	−	13.7933i	−0.615612	−	1.89466i	−0.223695	−	0.974659i	$-0.571812\pi$
$54$		0			0
$55$	−0.178070	−	0.406365i	−0.0240109	−	0.0547943i
$56$		0			0
$57$			3.69692i			0.489670i
$58$		0			0
$59$	0.165441	+	0.227710i	0.0215386	+	0.0296454i	0.819651	−	0.572864i	$-0.194168\pi$
$59$	0.165441	+	0.227710i	0.0215386	+	0.0296454i	−0.798112	+	0.602509i	$0.794168\pi$
$60$		0			0
$61$	−1.86928	+	2.57285i	−0.239337	+	0.329419i	−0.911741	−	0.410765i	$-0.865262\pi$
$61$	−1.86928	+	2.57285i	−0.239337	+	0.329419i	0.672404	+	0.740184i	$0.265262\pi$
$62$		0			0
$63$	−3.99368	−	5.49683i	−0.503157	−	0.692536i
$64$		0			0
$65$	0.430715	+	4.34351i	0.0534236	+	0.538746i
$66$		0			0
$67$	0.0384025	−	0.118191i	0.00469161	−	0.0144393i	−0.948683	−	0.316228i	$-0.897584\pi$
$67$	0.0384025	−	0.118191i	0.00469161	−	0.0144393i	0.953375	+	0.301788i	$0.0975836\pi$
$68$		0			0
$69$	−0.319653	−	0.103862i	−0.0384817	−	0.0125035i
$70$		0			0
$71$	1.42604	+	4.38889i	0.169239	+	0.520866i	0.999324	−	0.0367726i	$-0.0117077\pi$
$71$	1.42604	+	4.38889i	0.169239	+	0.520866i	−0.830084	+	0.557638i	$0.811708\pi$
$72$		0			0
$73$	7.51775	−	10.3473i	0.879886	−	1.21106i	−0.0965664	−	0.995327i	$-0.530786\pi$
$73$	7.51775	−	10.3473i	0.879886	−	1.21106i	0.976452	−	0.215733i	$-0.0692140\pi$
$74$		0			0
$75$	−3.59246	+	3.89668i	−0.414821	+	0.449950i
$76$		0			0
$77$	−0.581246	−	0.422300i	−0.0662391	−	0.0481255i
$78$		0			0
$79$	−1.42060	−	4.37215i	−0.159830	−	0.491906i	0.838788	−	0.544458i	$-0.183265\pi$
$79$	−1.42060	−	4.37215i	−0.159830	−	0.491906i	−0.998618	+	0.0525519i	$0.983265\pi$
$80$		0			0
$81$	0.0463838	−	0.142755i	0.00515376	−	0.0158616i
$82$		0			0
$83$	−4.15123	+	12.7762i	−0.455657	+	1.40237i	0.414705	+	0.909956i	$0.363885\pi$
$83$	−4.15123	+	12.7762i	−0.455657	+	1.40237i	−0.870362	+	0.492412i	$0.836115\pi$
$84$		0			0
$85$	10.5245	−	9.36487i	1.14155	−	1.01576i
$86$		0			0
$87$	1.29924	+	1.78826i	0.139294	+	0.191721i
$88$		0			0
$89$	−13.8793	−	10.0839i	−1.47121	−	1.06889i	−0.980262	−	0.197702i	$-0.936652\pi$
$89$	−13.8793	−	10.0839i	−1.47121	−	1.06889i	−0.490943	−	0.871192i	$-0.663348\pi$
$90$		0			0
$91$	4.15459	+	5.71830i	0.435519	+	0.599440i
$92$		0			0
$93$	8.24620			0.855091
$94$		0			0
$95$	−5.82612	+	5.18416i	−0.597748	+	0.531884i
$96$		0			0
$97$	−2.24784	+	0.730369i	−0.228234	+	0.0741577i	−0.420901	−	0.907106i	$-0.638286\pi$
$97$	−2.24784	+	0.730369i	−0.228234	+	0.0741577i	0.192667	+	0.981264i	$0.438286\pi$
$98$		0			0
$99$		−	0.372306i		−	0.0374181i
$100$		0			0
$101$			6.80661i			0.677283i	0.940916	+	0.338641i	$0.109967\pi$
$101$			6.80661i			0.677283i	−0.940916	+	0.338641i	$0.890033\pi$
$102$		0			0
$103$	13.8382	−	4.49631i	1.36352	−	0.443034i	0.466303	−	0.884625i	$-0.345586\pi$
$103$	13.8382	−	4.49631i	1.36352	−	0.443034i	0.897217	+	0.441591i	$0.145586\pi$
$104$		0			0
$105$	−1.83376	+	8.38441i	−0.178956	+	0.818235i
$106$		0			0
$107$	−10.8877			−1.05255			−0.526277	−	0.850313i	$-0.676413\pi$
$107$	−10.8877			−1.05255			−0.526277	+	0.850313i	$0.676413\pi$
$108$		0			0
$109$	8.30694	+	11.4335i	0.795661	+	1.09513i	0.993380	+	0.114874i	$0.0366466\pi$
$109$	8.30694	+	11.4335i	0.795661	+	1.09513i	−0.197719	+	0.980259i	$0.563353\pi$
$110$		0			0
$111$	3.33638	+	2.42402i	0.316675	+	0.230078i
$112$		0			0
$113$	3.47815	+	4.78726i	0.327197	+	0.450348i	0.940647	−	0.339385i	$-0.110219\pi$
$113$	3.47815	+	4.78726i	0.327197	+	0.450348i	−0.613451	+	0.789733i	$0.710219\pi$
$114$		0			0
$115$	−0.284567	−	0.649398i	−0.0265360	−	0.0605567i
$116$		0			0
$117$	−1.13185	+	3.48348i	−0.104640	+	0.322048i
$118$		0			0
$119$	7.04969	−	21.6967i	0.646244	−	1.98893i
$120$		0			0
$121$	3.38702	+	10.4242i	0.307911	+	0.947653i
$122$		0			0
$123$	2.63352	+	1.91336i	0.237456	+	0.172522i
$124$		0			0
$125$	−11.1786	−	0.197211i	−0.999844	−	0.0176391i
$126$		0			0
$127$	−5.72789	+	7.88376i	−0.508268	+	0.699571i	−0.983626	−	0.180222i	$-0.942318\pi$
$127$	−5.72789	+	7.88376i	−0.508268	+	0.699571i	0.475358	+	0.879792i	$0.342318\pi$
$128$		0			0
$129$	−3.39451	−	10.4472i	−0.298870	−	0.919827i
$130$		0			0
$131$	8.00383	+	2.60060i	0.699298	+	0.227216i	0.637025	−	0.770844i	$-0.280165\pi$
$131$	8.00383	+	2.60060i	0.699298	+	0.227216i	0.0622732	+	0.998059i	$0.480165\pi$
$132$		0			0
$133$	−3.90253	+	12.0108i	−0.338393	+	1.04147i
$134$		0			0
$135$	−10.5864	+	4.63897i	−0.911132	+	0.399259i
$136$		0			0
$137$	1.73426	+	2.38700i	0.148168	+	0.203935i	0.876649	−	0.481130i	$-0.159774\pi$
$137$	1.73426	+	2.38700i	0.148168	+	0.203935i	−0.728482	+	0.685065i	$0.759774\pi$
$138$		0			0
$139$	7.62813	−	10.4992i	0.647010	−	0.890532i	−0.351955	−	0.936017i	$-0.614483\pi$
$139$	7.62813	−	10.4992i	0.647010	−	0.890532i	0.998965	+	0.0454844i	$0.0144831\pi$
$140$		0			0
$141$	−5.15021	−	7.08866i	−0.433726	−	0.596973i
$142$		0			0
$143$			0.387305i			0.0323881i
$144$		0			0
$145$	−0.996263	+	4.55518i	−0.0827352	+	0.378287i
$146$		0			0
$147$	2.00192	+	6.16127i	0.165115	+	0.508173i
$148$		0			0
$149$		−	9.47104i		−	0.775898i	−0.921681	−	0.387949i	$-0.873184\pi$
$149$		−	9.47104i		−	0.775898i	0.921681	−	0.387949i	$-0.126816\pi$
$150$		0			0
$151$	8.83791			0.719219			0.359610	−	0.933103i	$-0.382910\pi$
$151$	8.83791			0.719219			0.359610	+	0.933103i	$0.382910\pi$
$152$		0			0
$153$	11.2432	−	3.65315i	0.908962	−	0.295340i
$154$		0			0
$155$	11.5636	+	12.9955i	0.928808	+	1.04382i
$156$		0			0
$157$	22.6986			1.81154			0.905772	−	0.423766i	$-0.139292\pi$
$157$	22.6986			1.81154			0.905772	+	0.423766i	$0.139292\pi$
$158$		0			0
$159$	−12.4373	+	9.03622i	−0.986341	+	0.716619i
$160$		0			0
$161$	−0.928868	−	0.674862i	−0.0732051	−	0.0531866i
$162$		0			0
$163$	9.27063	−	6.73551i	0.726132	−	0.527566i	−0.162206	−	0.986757i	$-0.551861\pi$
$163$	9.27063	−	6.73551i	0.726132	−	0.527566i	0.888337	+	0.459191i	$0.151861\pi$
$164$		0			0
$165$	−0.351336	+	0.312623i	−0.0273515	+	0.0243377i
$166$		0			0
$167$	18.4583	+	5.99746i	1.42835	+	0.464098i	0.918243	−	0.396016i	$-0.129608\pi$
$167$	18.4583	+	5.99746i	1.42835	+	0.464098i	0.510102	+	0.860114i	$0.329608\pi$
$168$		0			0
$169$	−2.83977	+	8.73991i	−0.218444	+	0.672301i
$170$		0			0
$171$	−6.22398	+	2.02229i	−0.475959	+	0.154649i
$172$		0			0
$173$	10.6269	+	7.72090i	0.807949	+	0.587009i	0.913235	−	0.407433i	$-0.133576\pi$
$173$	10.6269	+	7.72090i	0.807949	+	0.587009i	−0.105286	+	0.994442i	$0.533576\pi$
$174$		0			0
$175$	−15.7848	+	8.86749i	−1.19322	+	0.670320i
$176$		0			0
$177$	0.175367	−	0.241373i	0.0131814	−	0.0181427i
$178$		0			0
$179$	14.4002	−	4.67892i	1.07632	−	0.349719i	0.283376	−	0.959009i	$-0.408545\pi$
$179$	14.4002	−	4.67892i	1.07632	−	0.349719i	0.792948	+	0.609290i	$0.208545\pi$
$180$		0			0
$181$	7.53329	+	2.44771i	0.559945	+	0.181937i	0.575296	−	0.817945i	$-0.304887\pi$
$181$	7.53329	+	2.44771i	0.559945	+	0.181937i	−0.0153515	+	0.999882i	$0.504887\pi$
$182$		0			0
$183$	3.20603	+	1.04170i	0.236997	+	0.0770049i
$184$		0			0
$185$	0.858464	+	8.65711i	0.0631155	+	0.636483i
$186$		0			0
$187$	1.01132	−	0.734769i	0.0739552	−	0.0537316i
$188$		0			0
$189$	−11.0015	+	15.1423i	−0.800242	+	1.10144i
$190$		0			0
$191$	−15.4290	+	11.2098i	−1.11640	+	0.811115i	−0.983660	−	0.180035i	$-0.942379\pi$
$191$	−15.4290	+	11.2098i	−1.11640	+	0.811115i	−0.132744	+	0.991150i	$0.542379\pi$
$192$		0			0
$193$		−	21.5132i		−	1.54856i	−0.632846	−	0.774278i	$-0.718113\pi$
$193$		−	21.5132i		−	1.54856i	0.632846	−	0.774278i	$-0.281887\pi$
$194$		0			0
$195$	4.23768	−	1.85696i	0.303467	−	0.132980i
$196$		0			0
$197$	1.76320	+	5.42658i	0.125623	+	0.386628i	0.994014	−	0.109252i	$-0.0348456\pi$
$197$	1.76320	+	5.42658i	0.125623	+	0.386628i	−0.868391	+	0.495880i	$0.834846\pi$
$198$		0			0
$199$	−9.81700			−0.695909			−0.347954	−	0.937512i	$-0.613124\pi$
$199$	−9.81700			−0.695909			−0.347954	+	0.937512i	$0.613124\pi$
$200$		0			0
$201$	−0.131729			−0.00929146
$202$		0			0
$203$	2.33334	+	7.18128i	0.163768	+	0.504027i
$204$		0			0
$205$	0.677615	+	6.83335i	0.0473267	+	0.477262i
$206$		0			0
$207$		−	0.594968i		−	0.0413532i
$208$		0			0
$209$	−0.559843	+	0.406750i	−0.0387252	+	0.0281355i
$210$		0			0
$211$	−5.52862	+	7.60949i	−0.380606	+	0.523859i	−0.955745	−	0.294197i	$-0.904948\pi$
$211$	−5.52862	+	7.60949i	−0.380606	+	0.523859i	0.575139	+	0.818056i	$0.304948\pi$
$212$		0			0
$213$	3.95741	−	2.87523i	0.271157	−	0.197007i
$214$		0			0
$215$	11.7041	−	19.9996i	0.798212	−	1.36396i
$216$		0			0
$217$	26.7907	+	8.70482i	1.81867	+	0.590922i
$218$		0			0
$219$	−12.8938	−	4.18945i	−0.871282	−	0.283097i
$220$		0			0
$221$	−11.6962	+	3.80033i	−0.786772	+	0.255638i
$222$		0			0
$223$	−3.34947	+	4.61015i	−0.224297	+	0.308719i	−0.906303	−	0.422628i	$-0.861108\pi$
$223$	−3.34947	+	4.61015i	−0.224297	+	0.308719i	0.682006	+	0.731347i	$0.261108\pi$
$224$		0			0
$225$	−8.52543	−	3.91654i	−0.568362	−	0.261103i
$226$		0			0
$227$	8.52074	+	6.19068i	0.565541	+	0.410890i	0.833483	−	0.552545i	$-0.186343\pi$
$227$	8.52074	+	6.19068i	0.565541	+	0.410890i	−0.267942	+	0.963435i	$0.586343\pi$
$228$		0			0
$229$	19.9468	−	6.48109i	1.31812	−	0.428283i	0.436270	−	0.899816i	$-0.356299\pi$
$229$	19.9468	−	6.48109i	1.31812	−	0.428283i	0.881849	+	0.471533i	$0.156299\pi$
$230$		0			0
$231$	−0.235337	+	0.724292i	−0.0154840	+	0.0476549i
$232$		0			0
$233$	−9.63578	−	3.13085i	−0.631261	−	0.205109i	−0.0241273	−	0.999709i	$-0.507681\pi$
$233$	−9.63578	−	3.13085i	−0.631261	−	0.205109i	−0.607134	+	0.794600i	$0.707681\pi$
$234$		0			0
$235$	3.94920	−	18.0568i	0.257617	−	1.17789i
$236$		0			0
$237$	−3.94232	+	2.86426i	−0.256081	+	0.186054i
$238$		0			0
$239$	−17.7260	−	12.8787i	−1.14660	−	0.833054i	−0.158575	−	0.987347i	$-0.550690\pi$
$239$	−17.7260	−	12.8787i	−1.14660	−	0.833054i	−0.988025	+	0.154293i	$0.950690\pi$
$240$		0			0
$241$	−6.30258	+	4.57909i	−0.405985	+	0.294965i	−0.771974	−	0.635654i	$-0.780731\pi$
$241$	−6.30258	+	4.57909i	−0.405985	+	0.294965i	0.365989	+	0.930619i	$0.380731\pi$
$242$		0			0
$243$	−15.6660			−1.00498
$244$		0			0
$245$	−6.90251	+	11.7948i	−0.440985	+	0.753542i
$246$		0			0
$247$	6.47474	−	2.10377i	0.411978	−	0.133860i
$248$		0			0
$249$	14.2397			0.902402
$250$		0			0
$251$		−	19.5025i		−	1.23099i	−0.788142	−	0.615493i	$-0.788957\pi$
$251$		−	19.5025i		−	1.23099i	0.788142	−	0.615493i	$-0.211043\pi$
$252$		0			0
$253$	−0.0194412	−	0.0598339i	−0.00122226	−	0.00376173i
$254$		0			0
$255$	−12.8883	−	7.54244i	−0.807096	−	0.472326i
$256$		0			0
$257$		−	11.5160i		−	0.718350i	−0.933270	−	0.359175i	$-0.883058\pi$
$257$		−	11.5160i		−	0.718350i	0.933270	−	0.359175i	$-0.116942\pi$
$258$		0			0
$259$	8.28057	+	11.3972i	0.514529	+	0.708189i
$260$		0			0
$261$	−2.29991	+	3.16556i	−0.142361	+	0.195943i
$262$		0			0
$263$	−9.86176	−	13.5735i	−0.608102	−	0.836980i	0.388318	−	0.921526i	$-0.373056\pi$
$263$	−9.86176	−	13.5735i	−0.608102	−	0.836980i	−0.996420	+	0.0845451i	$0.973056\pi$
$264$		0			0
$265$	−31.6812	−	6.92899i	−1.94616	−	0.425645i
$266$		0			0
$267$	−5.61951	+	17.2951i	−0.343908	+	1.05844i
$268$		0			0
$269$	2.68291	+	0.871732i	0.163580	+	0.0531504i	0.389662	−	0.920958i	$-0.372592\pi$
$269$	2.68291	+	0.871732i	0.163580	+	0.0531504i	−0.226082	+	0.974108i	$0.572592\pi$
$270$		0			0
$271$	3.43218	+	10.5632i	0.208490	+	0.641667i	0.999552	+	0.0299305i	$0.00952860\pi$
$271$	3.43218	+	10.5632i	0.208490	+	0.641667i	−0.791062	+	0.611736i	$0.790471\pi$
$272$		0			0
$273$	4.40385	−	6.06139i	0.266533	−	0.366852i
$274$		0			0
$275$	−0.985350	−	0.115295i	−0.0594188	−	0.00695256i
$276$		0			0
$277$	0.0961570	+	0.0698621i	0.00577751	+	0.00419761i	0.590670	−	0.806913i	$-0.298863\pi$
$277$	0.0961570	+	0.0698621i	0.00577751	+	0.00419761i	−0.584893	+	0.811111i	$0.698863\pi$
$278$		0			0
$279$	4.51084	+	13.8829i	0.270057	+	0.831150i
$280$		0			0
$281$	−5.41333	+	16.6605i	−0.322932	+	0.993882i	0.649433	+	0.760418i	$0.275006\pi$
$281$	−5.41333	+	16.6605i	−0.322932	+	0.993882i	−0.972365	+	0.233464i	$0.924994\pi$
$282$		0			0
$283$	0.274023	−	0.843357i	0.0162890	−	0.0501324i	−0.942582	−	0.333976i	$-0.891610\pi$
$283$	0.274023	−	0.843357i	0.0162890	−	0.0501324i	0.958871	+	0.283843i	$0.0916096\pi$
$284$		0			0
$285$	7.13464	+	4.17531i	0.422619	+	0.247324i
$286$		0			0
$287$	6.53613	+	8.99622i	0.385816	+	0.531030i
$288$		0			0
$289$	18.3593	+	13.3388i	1.07996	+	0.784635i
$290$		0			0
$291$	1.47260	+	2.02685i	0.0863251	+	0.118816i
$292$		0			0
$293$	−14.7850			−0.863751			−0.431875	−	0.901933i	$-0.642148\pi$
$293$	−14.7850			−0.863751			−0.431875	+	0.901933i	$0.642148\pi$
$294$		0			0
$295$	0.626304	−	0.0621061i	0.0364648	−	0.00361596i
$296$		0			0
$297$	−0.975404	+	0.316928i	−0.0565987	+	0.0183900i
$298$		0			0
$299$			0.618939i			0.0357942i
$300$		0			0
$301$		−	37.5248i		−	2.16289i
$302$		0			0
$303$	6.86186	−	2.22955i	0.394204	−	0.128085i
$304$		0			0
$305$	2.85413	+	6.51328i	0.163427	+	0.372949i
$306$		0			0
$307$	9.60700			0.548300			0.274150	−	0.961687i	$-0.411603\pi$
$307$	9.60700			0.548300			0.274150	+	0.961687i	$0.411603\pi$
$308$		0			0
$309$	−9.06562	−	12.4778i	−0.515725	−	0.709835i
$310$		0			0
$311$	5.67985	+	4.12665i	0.322075	+	0.234001i	0.737060	−	0.675827i	$-0.236213\pi$
$311$	5.67985	+	4.12665i	0.322075	+	0.234001i	−0.414986	+	0.909828i	$0.636213\pi$
$312$		0			0
$313$	10.9572	+	15.0813i	0.619338	+	0.852445i	0.997305	−	0.0733737i	$-0.0233766\pi$
$313$	10.9572	+	15.0813i	0.619338	+	0.852445i	−0.377967	+	0.925819i	$0.623377\pi$
$314$		0			0
$315$	−15.1187	+	1.49922i	−0.851844	+	0.0844713i
$316$		0			0
$317$	2.03599	−	6.26613i	0.114353	−	0.351941i	−0.877459	−	0.479652i	$-0.840763\pi$
$317$	2.03599	−	6.26613i	0.114353	−	0.351941i	0.991811	+	0.127711i	$0.0407630\pi$
$318$		0			0
$319$	−0.127856	+	0.393502i	−0.00715858	+	0.0220319i
$320$		0			0
$321$	3.56635	+	10.9761i	0.199054	+	0.612626i
$322$		0			0
$323$	−17.7767	−	12.9155i	−0.989123	−	0.718640i
$324$		0			0
$325$	8.86891	+	4.07433i	0.491959	+	0.226003i
$326$		0			0
$327$	8.80535	−	12.1195i	0.486937	−	0.670211i
$328$		0			0
$329$	−9.24938	−	28.4667i	−0.509935	−	1.56942i
$330$		0			0
$331$	11.4237	+	3.71177i	0.627902	+	0.204018i	0.605645	−	0.795735i	$-0.292915\pi$
$331$	11.4237	+	3.71177i	0.627902	+	0.204018i	0.0222563	+	0.999752i	$0.492915\pi$
$332$		0			0
$333$	−2.25591	+	6.94297i	−0.123623	+	0.380472i
$334$		0			0
$335$	−0.184722	−	0.207597i	−0.0100925	−	0.0113422i
$336$		0			0
$337$	−0.639745	−	0.880533i	−0.0348491	−	0.0479657i	0.791237	−	0.611510i	$-0.209437\pi$
$337$	−0.639745	−	0.880533i	−0.0348491	−	0.0479657i	−0.826086	+	0.563544i	$0.809437\pi$
$338$		0			0
$339$	3.68683	−	5.07449i	0.200241	−	0.275608i
$340$		0			0
$341$	0.907279	+	1.24876i	0.0491319	+	0.0676243i
$342$		0			0
$343$		−	3.21669i		−	0.173685i
$344$		0			0
$345$	−0.561458	+	0.499592i	−0.0302279	+	0.0268972i
$346$		0			0
$347$	−2.73396	−	8.41426i	−0.146767	−	0.451701i	0.850467	−	0.526028i	$-0.176319\pi$
$347$	−2.73396	−	8.41426i	−0.146767	−	0.451701i	−0.997234	+	0.0743267i	$0.976319\pi$
$348$		0			0
$349$		−	25.2958i		−	1.35406i	−0.735957	−	0.677028i	$-0.763268\pi$
$349$		−	25.2958i		−	1.35406i	0.735957	−	0.677028i	$-0.236732\pi$
$350$		0			0
$351$	10.0899			0.538557
$352$		0			0
$353$	−24.2902	+	7.89236i	−1.29284	+	0.420068i	−0.873083	−	0.487571i	$-0.837883\pi$
$353$	−24.2902	+	7.89236i	−1.29284	+	0.420068i	−0.419752	+	0.907639i	$0.637883\pi$
$354$		0			0
$355$	10.0806	+	2.20473i	0.535024	+	0.117015i
$356$		0			0
$357$	−24.1820			−1.27985
$358$		0			0
$359$	6.90798	−	5.01894i	0.364589	−	0.264890i	−0.390375	−	0.920656i	$-0.627654\pi$
$359$	6.90798	−	5.01894i	0.364589	−	0.264890i	0.754964	+	0.655767i	$0.227654\pi$
$360$		0			0
$361$	−5.53057	−	4.01819i	−0.291082	−	0.211484i
$362$		0			0
$363$	9.39936	−	6.82904i	0.493339	−	0.358431i
$364$		0			0
$365$	−11.4785	−	26.1946i	−0.600813	−	1.37109i
$366$		0			0
$367$	−6.47354	−	2.10338i	−0.337916	−	0.109796i	0.135144	−	0.990826i	$-0.456850\pi$
$367$	−6.47354	−	2.10338i	−0.337916	−	0.109796i	−0.473059	+	0.881031i	$0.656850\pi$
$368$		0			0
$369$	−1.78066	+	5.48032i	−0.0926977	+	0.285294i
$370$		0			0
$371$	−49.9457	+	16.2283i	−2.59305	+	0.842533i
$372$		0			0
$373$	13.3531	+	9.70157i	0.691395	+	0.502328i	0.877119	−	0.480274i	$-0.159463\pi$
$373$	13.3531	+	9.70157i	0.691395	+	0.502328i	−0.185723	+	0.982602i	$0.559463\pi$
$374$		0			0
$375$	3.46282	+	11.3339i	0.178819	+	0.585283i
$376$		0			0
$377$	2.39258	−	3.29310i	0.123224	−	0.169603i
$378$		0			0
$379$	−23.7494	+	7.71663i	−1.21992	+	0.396377i	−0.847054	−	0.531507i	$-0.821626\pi$
$379$	−23.7494	+	7.71663i	−1.21992	+	0.396377i	−0.372869	+	0.927884i	$0.621626\pi$
$380$		0			0
$381$	9.82397	+	3.19200i	0.503297	+	0.163531i
$382$		0			0
$383$	3.39327	+	1.10254i	0.173388	+	0.0563371i	0.394424	−	0.918928i	$-0.370944\pi$
$383$	3.39327	+	1.10254i	0.173388	+	0.0563371i	−0.221037	+	0.975266i	$0.570944\pi$
$384$		0			0
$385$	−1.47145	+	0.644791i	−0.0749920	+	0.0328616i
$386$		0			0
$387$	15.7316	−	11.4297i	0.799683	−	0.581004i
$388$		0			0
$389$	−1.01897	+	1.40249i	−0.0516638	+	0.0711092i	−0.834067	−	0.551663i	$-0.813994\pi$
$389$	−1.01897	+	1.40249i	−0.0516638	+	0.0711092i	0.782403	+	0.622772i	$0.213994\pi$
$390$		0			0
$391$	1.61616	−	1.17421i	0.0817327	−	0.0593823i
$392$		0			0
$393$		−	8.92065i		−	0.449987i
$394$		0			0
$395$	−10.0422	−	2.19632i	−0.505277	−	0.110509i
$396$		0			0
$397$	−0.607136	−	1.86857i	−0.0304713	−	0.0937809i	0.934664	−	0.355532i	$-0.115700\pi$
$397$	−0.607136	−	1.86857i	−0.0304713	−	0.0937809i	−0.965136	+	0.261751i	$0.915700\pi$
$398$		0			0
$399$	13.3866			0.670167
$400$		0			0
$401$	26.9143			1.34404			0.672019	−	0.740534i	$-0.265427\pi$
$401$	26.9143			1.34404			0.672019	+	0.740534i	$0.265427\pi$
$402$		0			0
$403$	−4.69258	−	14.4423i	−0.233754	−	0.719421i
$404$		0			0
$405$	−0.223114	−	0.250743i	−0.0110866	−	0.0124595i
$406$		0			0
$407$			0.771944i			0.0382639i
$408$		0			0
$409$	20.3675	−	14.7978i	1.00711	−	0.731705i	0.0435059	−	0.999053i	$-0.486147\pi$
$409$	20.3675	−	14.7978i	1.00711	−	0.731705i	0.963600	+	0.267348i	$0.0861473\pi$
$410$		0			0
$411$	1.83831	−	2.53022i	0.0906771	−	0.124806i
$412$		0			0
$413$	0.824540	−	0.599063i	0.0405729	−	0.0294780i
$414$		0			0
$415$	19.9681	+	22.4408i	0.980198	+	1.10158i
$416$		0			0
$417$	−13.0831	−	4.25096i	−0.640683	−	0.208170i
$418$		0			0
$419$	23.6210	+	7.67492i	1.15396	+	0.374944i	0.822634	−	0.568572i	$-0.192504\pi$
$419$	23.6210	+	7.67492i	1.15396	+	0.374944i	0.331326	+	0.943516i	$0.392504\pi$
$420$		0			0
$421$	−9.29784	+	3.02105i	−0.453149	+	0.147237i	−0.526694	−	0.850055i	$-0.676569\pi$
$421$	−9.29784	+	3.02105i	−0.453149	+	0.147237i	0.0735452	+	0.997292i	$0.476569\pi$
$422$		0			0
$423$	9.11688	−	12.5483i	0.443278	−	0.610120i
$424$		0			0
$425$	−6.18669	−	30.8878i	−0.300098	−	1.49828i
$426$		0			0
$427$	9.31629	+	6.76868i	0.450847	+	0.327559i
$428$		0			0
$429$	0.390450	−	0.126865i	0.0188511	−	0.00612509i
$430$		0			0
$431$	3.73202	−	11.4860i	0.179765	−	0.553260i	−0.820054	−	0.572286i	$-0.806057\pi$
$431$	3.73202	−	11.4860i	0.179765	−	0.553260i	0.999819	+	0.0190265i	$0.00605667\pi$
$432$		0			0
$433$	−0.593995	−	0.193001i	−0.0285456	−	0.00927502i	0.294709	−	0.955587i	$-0.404777\pi$
$433$	−0.593995	−	0.193001i	−0.0285456	−	0.00927502i	−0.323255	+	0.946312i	$0.604777\pi$
$434$		0			0
$435$	4.91849	−	0.487732i	0.235824	−	0.0233850i
$436$		0			0
$437$	−0.894666	+	0.650013i	−0.0427977	+	0.0310943i
$438$		0			0
$439$	0.528473	+	0.383958i	0.0252226	+	0.0183253i	0.600325	−	0.799756i	$-0.295038\pi$
$439$	0.528473	+	0.383958i	0.0252226	+	0.0183253i	−0.575103	+	0.818081i	$0.695038\pi$
$440$		0			0
$441$	−9.27775	+	6.74068i	−0.441798	+	0.320985i
$442$		0			0
$443$	−26.8618			−1.27624			−0.638121	−	0.769936i	$-0.720288\pi$
$443$	−26.8618			−1.27624			−0.638121	+	0.769936i	$0.720288\pi$
$444$		0			0
$445$	−35.1361	+	15.3967i	−1.66561	+	0.729873i
$446$		0			0
$447$	−9.54793	+	3.10231i	−0.451601	+	0.146734i
$448$		0			0
$449$	−27.5980			−1.30243			−0.651214	−	0.758894i	$-0.725740\pi$
$449$	−27.5980			−1.30243			−0.651214	+	0.758894i	$0.725740\pi$
$450$		0			0
$451$			0.609322i			0.0286918i
$452$		0			0
$453$	−2.89492	−	8.90966i	−0.136015	−	0.418612i
$454$		0			0
$455$	15.7278	−	1.55962i	0.737333	−	0.0731160i
$456$		0			0
$457$			9.43766i			0.441475i	0.975333	+	0.220738i	$0.0708464\pi$
$457$			9.43766i			0.441475i	−0.975333	+	0.220738i	$0.929154\pi$
$458$		0			0
$459$	−19.1418	−	26.3464i	−0.893461	−	1.22974i
$460$		0			0
$461$	0.351432	−	0.483704i	0.0163678	−	0.0225284i	−0.800755	−	0.598992i	$-0.795568\pi$
$461$	0.351432	−	0.483704i	0.0163678	−	0.0225284i	0.817122	+	0.576464i	$0.195568\pi$
$462$		0			0
$463$	−3.40130	−	4.68149i	−0.158072	−	0.217567i	0.722634	−	0.691231i	$-0.242931\pi$
$463$	−3.40130	−	4.68149i	−0.158072	−	0.217567i	−0.880706	+	0.473664i	$0.842931\pi$
$464$		0			0
$465$	9.31327	−	15.9142i	0.431893	−	0.738004i
$466$		0			0
$467$	1.50734	−	4.63913i	0.0697516	−	0.214673i	−0.910104	−	0.414379i	$-0.863999\pi$
$467$	1.50734	−	4.63913i	0.0697516	−	0.214673i	0.979856	+	0.199706i	$0.0639987\pi$
$468$		0			0
$469$	−0.427969	−	0.139055i	−0.0197618	−	0.00642098i
$470$		0			0
$471$	−7.43509	−	22.8829i	−0.342591	−	1.05439i
$472$		0			0
$473$	1.20860	−	1.66349i	0.0555713	−	0.0764874i
$474$		0			0
$475$	3.42480	+	17.0987i	0.157140	+	0.784544i
$476$		0			0
$477$	−22.0164	−	15.9959i	−1.00806	−	0.732400i
$478$		0			0
$479$	1.23698	+	3.80704i	0.0565192	+	0.173948i	0.975331	−	0.220748i	$-0.0708498\pi$
$479$	1.23698	+	3.80704i	0.0565192	+	0.173948i	−0.918812	+	0.394696i	$0.870850\pi$
$480$		0			0
$481$	2.34680	−	7.22269i	0.107005	−	0.329327i
$482$		0			0
$483$	−0.376083	+	1.15747i	−0.0171124	+	0.0526665i
$484$		0			0
$485$	−1.12919	+	5.16296i	−0.0512739	+	0.234438i
$486$		0			0
$487$	0.896846	+	1.23440i	0.0406400	+	0.0559361i	0.828853	−	0.559466i	$-0.188994\pi$
$487$	0.896846	+	1.23440i	0.0406400	+	0.0559361i	−0.788213	+	0.615402i	$0.788994\pi$
$488$		0			0
$489$	−9.82685	−	7.13963i	−0.444386	−	0.322865i
$490$		0			0
$491$	−19.8358	−	27.3017i	−0.895178	−	1.23211i	−0.971981	−	0.235060i	$-0.924471\pi$
$491$	−19.8358	−	27.3017i	−0.895178	−	1.23211i	0.0768029	−	0.997046i	$-0.475529\pi$
$492$		0			0
$493$	−13.1379			−0.591700
$494$		0			0
$495$	−0.718507	−	0.420482i	−0.0322945	−	0.0188993i
$496$		0			0
$497$	15.8922	−	5.16368i	0.712862	−	0.231623i
$498$		0			0
$499$			39.2516i			1.75714i	0.477611	+	0.878571i	$0.341503\pi$
$499$			39.2516i			1.75714i	−0.477611	+	0.878571i	$0.658497\pi$
$500$		0			0
$501$		−	20.5727i		−	0.919118i
$502$		0			0
$503$	25.3583	−	8.23943i	1.13067	−	0.367378i	0.316841	−	0.948479i	$-0.397378\pi$
$503$	25.3583	−	8.23943i	1.13067	−	0.367378i	0.813832	+	0.581101i	$0.197378\pi$
$504$		0			0
$505$	13.1360	+	7.68739i	0.584543	+	0.342084i
$506$		0			0
$507$	9.74105			0.432615
$508$		0			0
$509$	−11.9720	−	16.4780i	−0.530648	−	0.730374i	0.456581	−	0.889682i	$-0.349074\pi$
$509$	−11.9720	−	16.4780i	−0.530648	−	0.730374i	−0.987229	+	0.159308i	$0.949074\pi$
$510$		0			0
$511$	−37.4676	−	27.2218i	−1.65747	−	1.20422i
$512$		0			0
$513$	10.5964	+	14.5847i	0.467843	+	0.643931i
$514$		0			0
$515$	6.95154	−	31.7843i	0.306321	−	1.40058i
$516$		0			0
$517$	0.506824	−	1.55984i	0.0222901	−	0.0686019i
$518$		0			0
$519$	4.30266	−	13.2422i	0.188866	−	0.581269i
$520$		0			0
$521$	−4.34547	−	13.3740i	−0.190379	−	0.585925i	0.809621	−	0.586953i	$-0.199673\pi$
$521$	−4.34547	−	13.3740i	−0.190379	−	0.585925i	−0.999999	+	0.00102824i	$0.999673\pi$
$522$		0			0
$523$	35.4414	+	25.7497i	1.54974	+	1.12595i	0.943834	+	0.330419i	$0.107190\pi$
$523$	35.4414	+	25.7497i	1.54974	+	1.12595i	0.605908	+	0.795535i	$0.292810\pi$
$524$		0			0
$525$	14.1099	+	13.0083i	0.615807	+	0.567729i
$526$		0			0
$527$	−28.8089	+	39.6520i	−1.25493	+	1.72727i
$528$		0			0
$529$	7.07632	+	21.7787i	0.307666	+	0.946899i
$530$		0			0
$531$	0.502294	+	0.163205i	0.0217977	+	0.00708250i
$532$		0			0
$533$	1.85241	−	5.70112i	0.0802366	−	0.246943i
$534$		0			0
$535$	−12.2966	+	21.0120i	−0.531628	+	0.908428i
$536$		0			0
$537$	−9.43381	−	12.9845i	−0.407099	−	0.560324i
$538$		0			0
$539$	−0.712773	+	0.981047i	−0.0307013	+	0.0422567i
$540$		0			0
$541$	24.0222	+	33.0637i	1.03279	+	1.42152i	0.902829	+	0.430000i	$0.141486\pi$
$541$	24.0222	+	33.0637i	1.03279	+	1.42152i	0.129964	+	0.991519i	$0.458514\pi$
$542$		0			0
$543$		−	8.39621i		−	0.360316i
$544$		0			0
$545$	31.4473	−	3.11840i	1.34705	−	0.133578i
$546$		0			0
$547$	−9.64491	−	29.6840i	−0.412386	−	1.26919i	−0.914568	−	0.404433i	$-0.867469\pi$
$547$	−9.64491	−	29.6840i	−0.412386	−	1.26919i	0.502181	−	0.864762i	$-0.332531\pi$
$548$		0			0
$549$			5.96737i			0.254681i
$550$		0			0
$551$	7.27281			0.309832
$552$		0			0
$553$	−15.8316	+	5.14399i	−0.673227	+	0.218745i
$554$		0			0
$555$	8.44619	−	3.70113i	0.358521	−	0.157104i
$556$		0			0
$557$	−23.4264			−0.992610			−0.496305	−	0.868148i	$-0.665310\pi$
$557$	−23.4264			−0.992610			−0.496305	+	0.868148i	$0.665310\pi$
$558$		0			0
$559$	−16.3654	+	11.8902i	−0.692184	+	0.502901i
$560$		0			0
$561$	−1.07200	−	0.778854i	−0.0452599	−	0.0328832i
$562$		0			0
$563$	19.7424	−	14.3437i	0.832042	−	0.604514i	−0.0880945	−	0.996112i	$-0.528078\pi$
$563$	19.7424	−	14.3437i	0.832042	−	0.604514i	0.920136	+	0.391598i	$0.128078\pi$
$564$		0			0
$565$	13.1671	−	1.30569i	0.553944	−	0.0549306i
$566$		0			0
$567$	−0.516915	−	0.167956i	−0.0217084	−	0.00705348i
$568$		0			0
$569$	−7.23960	+	22.2812i	−0.303500	+	0.934076i	0.676733	+	0.736229i	$0.263395\pi$
$569$	−7.23960	+	22.2812i	−0.303500	+	0.934076i	−0.980233	+	0.197848i	$0.936605\pi$
$570$		0			0
$571$	22.0658	−	7.16961i	0.923425	−	0.300039i	0.191554	−	0.981482i	$-0.438647\pi$
$571$	22.0658	−	7.16961i	0.923425	−	0.300039i	0.731871	+	0.681443i	$0.238647\pi$
$572$		0			0
$573$	16.3547	+	11.8824i	0.683229	+	0.496395i
$574$		0			0
$575$	−1.57465	−	0.184249i	−0.0656676	−	0.00768372i
$576$		0			0
$577$	−12.6072	+	17.3523i	−0.524845	+	0.722387i	−0.986334	−	0.164759i	$-0.947315\pi$
$577$	−12.6072	+	17.3523i	−0.524845	+	0.722387i	0.461489	+	0.887146i	$0.347315\pi$
$578$		0			0
$579$	−21.6879	+	7.04682i	−0.901318	+	0.292856i
$580$		0			0
$581$	46.2626	+	15.0316i	1.91930	+	0.623617i
$582$		0			0
$583$	−2.73680	−	0.889239i	−0.113347	−	0.0368285i
$584$		0			0
$585$	5.44439	+	6.11858i	0.225098	+	0.252972i
$586$		0			0
$587$	−17.9454	+	13.0381i	−0.740687	+	0.538141i	−0.892926	−	0.450203i	$-0.851352\pi$
$587$	−17.9454	+	13.0381i	−0.740687	+	0.538141i	0.152239	+	0.988344i	$0.451352\pi$
$588$		0			0
$589$	15.9479	−	21.9504i	0.657121	−	0.904449i
$590$		0			0
$591$	4.89308	−	3.55503i	0.201275	−	0.146234i
$592$		0			0
$593$			27.6075i			1.13370i	0.823820	+	0.566852i	$0.191839\pi$
$593$			27.6075i			1.13370i	−0.823820	+	0.566852i	$0.808161\pi$
$594$		0			0
$595$	−33.9102	−	38.1094i	−1.39018	−	1.56233i
$596$		0			0
$597$	3.21563	+	9.89670i	0.131607	+	0.405045i
$598$		0			0
$599$	−13.7667			−0.562492			−0.281246	−	0.959636i	$-0.590748\pi$
$599$	−13.7667			−0.562492			−0.281246	+	0.959636i	$0.590748\pi$
$600$		0			0
$601$	11.4574			0.467356			0.233678	−	0.972314i	$-0.424924\pi$
$601$	11.4574			0.467356			0.233678	+	0.972314i	$0.424924\pi$
$602$		0			0
$603$	−0.0720585	−	0.221773i	−0.00293445	−	0.00903131i
$604$		0			0
$605$	23.9428	+	5.23652i	0.973412	+	0.212895i
$606$		0			0
$607$		−	32.7284i		−	1.32841i	−0.747552	−	0.664203i	$-0.768771\pi$
$607$		−	32.7284i		−	1.32841i	0.747552	−	0.664203i	$-0.231229\pi$
$608$		0			0
$609$	6.47528	−	4.70456i	0.262391	−	0.190639i
$610$		0			0
$611$	−9.48419	+	13.0539i	−0.383689	+	0.528103i
$612$		0			0
$613$	−5.53010	+	4.01785i	−0.223358	+	0.162279i	−0.693837	−	0.720132i	$-0.744081\pi$
$613$	−5.53010	+	4.01785i	−0.223358	+	0.162279i	0.470479	+	0.882411i	$0.344081\pi$
$614$		0			0
$615$	6.66687	−	2.92143i	0.268834	−	0.117803i
$616$		0			0
$617$	−4.31211	−	1.40109i	−0.173599	−	0.0564058i	0.220928	−	0.975290i	$-0.429091\pi$
$617$	−4.31211	−	1.40109i	−0.173599	−	0.0564058i	−0.394527	+	0.918884i	$0.629091\pi$
$618$		0			0
$619$	25.4717	+	8.27626i	1.02379	+	0.332651i	0.772334	−	0.635217i	$-0.219089\pi$
$619$	25.4717	+	8.27626i	1.02379	+	0.332651i	0.251461	+	0.967868i	$0.419089\pi$
$620$		0			0
$621$	−1.55876	+	0.506471i	−0.0625508	+	0.0203240i
$622$		0			0
$623$	−36.5139	+	50.2571i	−1.46290	+	2.01351i
$624$		0			0
$625$	−13.0057	+	21.3507i	−0.520229	+	0.854027i
$626$		0			0
$627$	0.593433	+	0.431154i	0.0236994	+	0.0172186i
$628$		0			0
$629$	−23.3119	+	7.57449i	−0.929506	+	0.302015i
$630$		0			0
$631$	−4.08094	+	12.5598i	−0.162460	+	0.499999i	−0.998840	−	0.0481500i	$-0.984667\pi$
$631$	−4.08094	+	12.5598i	−0.162460	+	0.499999i	0.836380	+	0.548149i	$0.184667\pi$
$632$		0			0
$633$	9.48220	+	3.08095i	0.376884	+	0.122457i
$634$		0			0
$635$	8.74566	+	19.9581i	0.347061	+	0.792012i
$636$		0			0
$637$	9.65155	−	7.01226i	0.382408	−	0.277836i
$638$		0			0
$639$	7.00539	+	5.08971i	0.277129	+	0.201346i
$640$		0			0
$641$	23.3026	−	16.9304i	0.920399	−	0.668709i	−0.0232242	−	0.999730i	$-0.507393\pi$
$641$	23.3026	−	16.9304i	0.920399	−	0.668709i	0.943623	+	0.331021i	$0.107393\pi$
$642$		0			0
$643$	−43.3080			−1.70790			−0.853951	−	0.520353i	$-0.825800\pi$
$643$	−43.3080			−1.70790			−0.853951	+	0.520353i	$0.825800\pi$
$644$		0			0
$645$	−23.9957	−	5.24810i	−0.944830	−	0.206644i
$646$		0			0
$647$	−37.6363	+	12.2288i	−1.47964	+	0.480763i	−0.934004	−	0.357263i	$-0.883710\pi$
$647$	−37.6363	+	12.2288i	−1.47964	+	0.480763i	−0.545631	+	0.838025i	$0.683710\pi$
$648$		0			0
$649$	0.0558468			0.00219218
$650$		0			0
$651$		−	29.8595i		−	1.17029i
$652$		0			0
$653$	−8.47955	−	26.0974i	−0.331830	−	1.02127i	−0.968262	−	0.249936i	$-0.919590\pi$
$653$	−8.47955	−	26.0974i	−0.331830	−	1.02127i	0.636432	−	0.771333i	$-0.280410\pi$
$654$		0			0
$655$	14.0584	−	12.5093i	0.549307	−	0.488780i
$656$		0			0
$657$		−	23.9991i		−	0.936295i
$658$		0			0
$659$	−0.823638	−	1.13364i	−0.0320844	−	0.0441604i	0.792673	−	0.609646i	$-0.208689\pi$
$659$	−0.823638	−	1.13364i	−0.0320844	−	0.0441604i	−0.824758	+	0.565486i	$0.808689\pi$
$660$		0			0
$661$	−13.3496	+	18.3742i	−0.519240	+	0.714673i	−0.985443	−	0.170005i	$-0.945622\pi$
$661$	−13.3496	+	18.3742i	−0.519240	+	0.714673i	0.466203	+	0.884678i	$0.345622\pi$
$662$		0			0
$663$	7.66236	+	10.5463i	0.297582	+	0.409586i
$664$		0			0
$665$	18.7719	+	21.0964i	0.727941	+	0.818083i
$666$		0			0
$667$	−0.204323	+	0.628841i	−0.00791141	+	0.0243488i
$668$		0			0
$669$	5.74473	+	1.86657i	0.222104	+	0.0721659i
$670$		0			0
$671$	0.194990	+	0.600117i	0.00752750	+	0.0231673i
$672$		0			0
$673$	−9.83764	+	13.5404i	−0.379213	+	0.521942i	−0.955376	−	0.295393i	$-0.904549\pi$
$673$	−9.83764	+	13.5404i	−0.379213	+	0.521942i	0.576163	+	0.817335i	$0.304549\pi$
$674$		0			0
$675$	−3.00360	+	25.6698i	−0.115609	+	0.988030i
$676$		0			0
$677$	5.14888	+	3.74088i	0.197888	+	0.143774i	0.682317	−	0.731057i	$-0.260973\pi$
$677$	5.14888	+	3.74088i	0.197888	+	0.143774i	−0.484429	+	0.874831i	$0.660973\pi$
$678$		0			0
$679$	2.64467	+	8.13945i	0.101493	+	0.312363i
$680$		0			0
$681$	3.44990	−	10.6177i	0.132201	−	0.406872i
$682$		0			0
$683$	−3.13870	+	9.65993i	−0.120099	+	0.369627i	−0.992976	−	0.118313i	$-0.962251\pi$
$683$	−3.13870	+	9.65993i	−0.120099	+	0.369627i	0.872877	+	0.487940i	$0.162251\pi$
$684$		0			0
$685$	6.56531	−	0.651035i	0.250847	−	0.0248748i
$686$		0			0
$687$	−13.0674	−	17.9858i	−0.498553	−	0.686200i
$688$		0			0
$689$	22.9034	+	16.6403i	0.872552	+	0.633946i
$690$		0			0
$691$	27.3168	+	37.5984i	1.03918	+	1.43031i	0.897826	+	0.440351i	$0.145146\pi$
$691$	27.3168	+	37.5984i	1.03918	+	1.43031i	0.141355	+	0.989959i	$0.454854\pi$
$692$		0			0
$693$	−1.34812			−0.0512108
$694$		0			0
$695$	−11.6471	−	26.5792i	−0.441798	−	1.00821i
$696$		0			0
$697$	−18.4009	+	5.97881i	−0.696983	+	0.226463i
$698$		0			0
$699$			10.7395i			0.406207i
$700$		0			0
$701$			7.10253i			0.268259i	0.990964	+	0.134130i	$0.0428238\pi$
$701$			7.10253i			0.268259i	−0.990964	+	0.134130i	$0.957176\pi$
$702$		0			0
$703$	12.9049	−	4.19305i	0.486717	−	0.158144i
$704$		0			0
$705$	−19.4970	+	1.93337i	−0.734298	+	0.0728151i
$706$		0			0
$707$	24.6467			0.926936
$708$		0			0
$709$	12.5939	+	17.3341i	0.472975	+	0.650994i	0.977136	−	0.212615i	$-0.0681982\pi$
$709$	12.5939	+	17.3341i	0.472975	+	0.650994i	−0.504161	+	0.863610i	$0.668198\pi$
$710$		0			0
$711$	−6.97868	−	5.07031i	−0.261721	−	0.190151i
$712$		0			0
$713$	1.44989	+	1.99560i	0.0542988	+	0.0747359i
$714$		0			0
$715$	0.747455	+	0.437423i	0.0279532	+	0.0163587i
$716$		0			0
$717$	−7.17696	+	22.0884i	−0.268029	+	0.824907i
$718$		0			0
$719$	−5.11431	+	15.7402i	−0.190732	+	0.587012i	−1.00000		0.000427596i	$-0.999864\pi$
$719$	−5.11431	+	15.7402i	−0.190732	+	0.587012i	0.809268	+	0.587439i	$0.199864\pi$
$720$		0			0
$721$	−16.2811	−	50.1082i	−0.606341	−	1.86613i
$722$		0			0
$723$	6.68073	+	4.85383i	0.248459	+	0.180516i
$724$		0			0
$725$	7.66579	+	7.06730i	0.284700	+	0.262473i
$726$		0			0
$727$	11.4199	−	15.7182i	0.423542	−	0.582955i	−0.542914	−	0.839788i	$-0.682679\pi$
$727$	11.4199	−	15.7182i	0.423542	−	0.582955i	0.966456	+	0.256833i	$0.0826791\pi$
$728$		0			0
$729$	4.99238	+	15.3650i	0.184903	+	0.569073i
$730$		0			0
$731$	62.0947	+	20.1758i	2.29665	+	0.746228i
$732$		0			0
$733$	1.75635	−	5.40548i	0.0648722	−	0.199656i	−0.913367	−	0.407138i	$-0.866527\pi$
$733$	1.75635	−	5.40548i	0.0648722	−	0.199656i	0.978239	+	0.207482i	$0.0665268\pi$
$734$		0			0
$735$	14.1515	+	3.09508i	0.521986	+	0.114164i
$736$		0			0
$737$	−0.0144934	−	0.0199484i	−0.000533869	−	0.000734808i
$738$		0			0
$739$	−14.0693	+	19.3647i	−0.517546	+	0.712341i	−0.985169	−	0.171587i	$-0.945110\pi$
$739$	−14.0693	+	19.3647i	−0.517546	+	0.712341i	0.467623	+	0.883928i	$0.345110\pi$
$740$		0			0
$741$	−4.24170	−	5.83819i	−0.155823	−	0.214471i
$742$		0			0
$743$			23.3975i			0.858370i	0.903217	+	0.429185i	$0.141199\pi$
$743$			23.3975i			0.858370i	−0.903217	+	0.429185i	$0.858801\pi$
$744$		0			0
$745$	−18.2780	−	10.6966i	−0.669654	−	0.391893i
$746$		0			0
$747$	7.78939	+	23.9733i	0.284999	+	0.877136i
$748$		0			0
$749$			39.4244i			1.44054i
$750$		0			0
$751$	−10.2670			−0.374648			−0.187324	−	0.982298i	$-0.559981\pi$
$751$	−10.2670			−0.374648			−0.187324	+	0.982298i	$0.559981\pi$
$752$		0			0
$753$	−19.6608	+	6.38819i	−0.716480	+	0.232798i
$754$		0			0
$755$	9.98155	−	17.0562i	0.363266	−	0.620737i
$756$		0			0
$757$	15.7129			0.571096			0.285548	−	0.958364i	$-0.407824\pi$
$757$	15.7129			0.571096			0.285548	+	0.958364i	$0.407824\pi$
$758$		0			0
$759$	−0.0539515	+	0.0391981i	−0.00195832	+	0.00142280i
$760$		0			0
$761$	14.8631	+	10.7986i	0.538786	+	0.391451i	0.823634	−	0.567122i	$-0.191943\pi$
$761$	14.8631	+	10.7986i	0.538786	+	0.391451i	−0.284848	+	0.958573i	$0.591943\pi$
$762$		0			0
$763$	41.4008	−	30.0795i	1.49881	−	1.08895i
$764$		0			0
$765$	5.64797	−	25.8240i	0.204203	−	0.933669i
$766$		0			0
$767$	−0.522531	−	0.169780i	−0.0188675	−	0.00613042i
$768$		0			0
$769$	3.93043	−	12.0966i	0.141735	−	0.436215i	−0.854842	−	0.518889i	$-0.826346\pi$
$769$	3.93043	−	12.0966i	0.141735	−	0.436215i	0.996577	+	0.0826738i	$0.0263460\pi$
$770$		0			0
$771$	−11.6095	+	3.77216i	−0.418106	+	0.135851i
$772$		0			0
$773$	35.6762	+	25.9203i	1.28318	+	0.932288i	0.999644	−	0.0266727i	$-0.00849118\pi$
$773$	35.6762	+	25.9203i	1.28318	+	0.932288i	0.283540	+	0.958960i	$0.408491\pi$
$774$		0			0
$775$	38.1397	−	7.63921i	1.37002	−	0.274408i
$776$		0			0
$777$	8.77739	−	12.0810i	0.314887	−	0.433405i
$778$		0			0
$779$	10.1863	−	3.30972i	0.364961	−	0.118583i
$780$		0			0
$781$	0.870819	+	0.282946i	0.0311604	+	0.0101246i
$782$		0			0
$783$	10.2513	+	3.33084i	0.366351	+	0.119035i
$784$		0			0
$785$	25.6358	−	43.8056i	0.914981	−	1.56349i
$786$		0			0
$787$	−3.65925	+	2.65860i	−0.130438	+	0.0947689i	−0.651091	−	0.758999i	$-0.725689\pi$
$787$	−3.65925	+	2.65860i	−0.130438	+	0.0947689i	0.520653	+	0.853768i	$0.325689\pi$
$788$		0			0
$789$	−10.4534	+	14.3879i	−0.372152	+	0.512224i
$790$		0			0
$791$	17.3347	−	12.5944i	0.616351	−	0.447805i
$792$		0			0
$793$		−	6.20779i		−	0.220445i
$794$		0			0
$795$	3.39217	+	34.2080i	0.120308	+	1.21323i
$796$		0			0
$797$	−3.75727	−	11.5637i	−0.133089	−	0.409606i	0.862199	−	0.506570i	$-0.169087\pi$
$797$	−3.75727	−	11.5637i	−0.133089	−	0.409606i	−0.995288	+	0.0969638i	$0.969087\pi$
$798$		0			0
$799$	52.0787			1.84241
$800$		0			0
$801$	−32.1912			−1.13742
$802$		0			0
$803$	−0.784196	−	2.41351i	−0.0276737	−	0.0851709i
$804$		0			0
$805$	−2.35147	+	1.03042i	−0.0828785	+	0.0363175i
$806$		0			0
$807$		−	2.99024i		−	0.105261i
$808$		0			0
$809$	5.08569	−	3.69497i	0.178803	−	0.129908i	−0.494784	−	0.869016i	$-0.664753\pi$
$809$	5.08569	−	3.69497i	0.178803	−	0.129908i	0.673587	+	0.739108i	$0.264753\pi$
$810$		0			0
$811$	−8.25457	+	11.3614i	−0.289857	+	0.398954i	−0.928968	−	0.370161i	$-0.879303\pi$
$811$	−8.25457	+	11.3614i	−0.289857	+	0.398954i	0.639111	+	0.769115i	$0.279303\pi$
$812$		0			0
$813$	9.52469	−	6.92009i	0.334045	−	0.242698i
$814$		0			0
$815$	−2.52849	−	25.4983i	−0.0885691	−	0.893168i
$816$		0			0
$817$	−34.3741	−	11.1688i	−1.20260	−	0.390748i
$818$		0			0
$819$	12.6137	+	4.09843i	0.440758	+	0.143211i
$820$		0			0
$821$	−31.6198	+	10.2739i	−1.10354	+	0.358562i	−0.803464	−	0.595354i	$-0.797012\pi$
$821$	−31.6198	+	10.2739i	−1.10354	+	0.358562i	−0.300075	+	0.953915i	$0.597012\pi$
$822$		0			0
$823$	−27.9854	+	38.5186i	−0.975510	+	1.34267i	−0.0362964	+	0.999341i	$0.511556\pi$
$823$	−27.9854	+	38.5186i	−0.975510	+	1.34267i	−0.939214	+	0.343333i	$0.888444\pi$
$824$		0			0
$825$	0.206528	+	1.03112i	0.00719037	+	0.0358988i
$826$		0			0
$827$	−35.3159	−	25.6585i	−1.22805	−	0.892233i	−0.231311	−	0.972880i	$-0.574302\pi$
$827$	−35.3159	−	25.6585i	−1.22805	−	0.892233i	−0.996743	+	0.0806464i	$0.974302\pi$
$828$		0			0
$829$	−14.9283	+	4.85051i	−0.518483	+	0.168465i	−0.556557	−	0.830810i	$-0.687878\pi$
$829$	−14.9283	+	4.85051i	−0.518483	+	0.168465i	0.0380738	+	0.999275i	$0.487878\pi$
$830$		0			0
$831$	0.0389324	−	0.119821i	0.00135055	−	0.00415656i
$832$		0			0
$833$	−36.6205	−	11.8987i	−1.26882	−	0.412266i
$834$		0			0
$835$	32.4212	−	28.8488i	1.12198	−	0.998355i
$836$		0			0
$837$	32.5320	−	23.6359i	1.12447	−	0.816976i
$838$		0			0
$839$	17.6519	+	12.8248i	0.609410	+	0.442762i	0.849207	−	0.528061i	$-0.177081\pi$
$839$	17.6519	+	12.8248i	0.609410	+	0.442762i	−0.239796	+	0.970823i	$0.577081\pi$
$840$		0			0
$841$	−19.9435	+	14.4898i	−0.687708	+	0.499649i
$842$		0			0
$843$	18.5689			0.639548
$844$		0			0
$845$	13.6598	+	15.3513i	0.469911	+	0.528101i
$846$		0			0
$847$	37.7460	−	12.2644i	1.29697	−	0.421410i
$848$		0			0
$849$	−0.939962			−0.0322594
$850$		0			0
$851$			1.23362i			0.0422878i
$852$		0			0
$853$	2.13725	+	6.57778i	0.0731781	+	0.225219i	0.980955	−	0.194234i	$-0.0622220\pi$
$853$	2.13725	+	6.57778i	0.0731781	+	0.225219i	−0.907777	+	0.419453i	$0.862222\pi$
$854$		0			0
$855$	−3.12658	+	14.2955i	−0.106927	+	0.488897i
$856$		0			0
$857$			36.4862i			1.24634i	0.782085	+	0.623172i	$0.214156\pi$
$857$			36.4862i			1.24634i	−0.782085	+	0.623172i	$0.785844\pi$
$858$		0			0
$859$	−15.3190	−	21.0848i	−0.522678	−	0.719405i	0.463315	−	0.886194i	$-0.346660\pi$
$859$	−15.3190	−	21.0848i	−0.522678	−	0.719405i	−0.985993	+	0.166789i	$0.946660\pi$
$860$		0			0
$861$	6.92829	−	9.53597i	0.236116	−	0.324985i
$862$		0			0
$863$	−10.3548	−	14.2522i	−0.352482	−	0.485150i	0.595553	−	0.803316i	$-0.296933\pi$
$863$	−10.3548	−	14.2522i	−0.352482	−	0.485150i	−0.948035	+	0.318166i	$0.896933\pi$
$864$		0			0
$865$	26.9025	−	11.7887i	0.914712	−	0.400828i
$866$		0			0
$867$	7.43336	−	22.8775i	0.252450	−	0.776962i
$868$		0			0
$869$	−0.867499	−	0.281867i	−0.0294279	−	0.00956170i
$870$		0			0
$871$	0.0749617	+	0.230708i	0.00253998	+	0.00781726i
$872$		0			0
$873$	−2.60678	+	3.58793i	−0.0882262	+	0.121433i
$874$		0			0
$875$	−0.714101	+	40.4777i	−0.0241410	+	1.36840i
$876$		0			0
$877$	40.1802	+	29.1927i	1.35679	+	0.985766i	0.998642	+	0.0521012i	$0.0165918\pi$
$877$	40.1802	+	29.1927i	1.35679	+	0.985766i	0.358148	+	0.933665i	$0.383408\pi$
$878$		0			0
$879$	4.84295	+	14.9051i	0.163349	+	0.502735i
$880$		0			0
$881$	−2.73149	+	8.40666i	−0.0920262	+	0.283228i	−0.986467	−	0.163958i	$-0.947574\pi$
$881$	−2.73149	+	8.40666i	−0.0920262	+	0.283228i	0.894441	+	0.447186i	$0.147574\pi$
$882$		0			0
$883$	−7.32413	+	22.5414i	−0.246477	+	0.758577i	0.748913	+	0.662668i	$0.230576\pi$
$883$	−7.32413	+	22.5414i	−0.246477	+	0.758577i	−0.995390	+	0.0959094i	$0.969424\pi$
$884$		0			0
$885$	−0.267761	−	0.611045i	−0.00900069	−	0.0205401i
$886$		0			0
$887$	−2.51532	−	3.46203i	−0.0844560	−	0.116244i	0.764698	−	0.644388i	$-0.222888\pi$
$887$	−2.51532	−	3.46203i	−0.0844560	−	0.116244i	−0.849154	+	0.528145i	$0.822888\pi$
$888$		0			0
$889$	28.5471	+	20.7407i	0.957439	+	0.695620i
$890$		0			0
$891$	−0.0175056	−	0.0240943i	−0.000586458	−	0.000807191i
$892$		0			0
$893$	−28.8295			−0.964742
$894$		0			0
$895$	7.23387	−	33.0752i	0.241802	−	1.10558i
$896$		0			0
$897$	0.623964	−	0.202738i	0.0208336	−	0.00676923i
$898$		0			0
$899$		−	16.2224i		−	0.541048i
$900$		0			0
$901$		−	91.3738i		−	3.04410i
$902$		0			0
$903$	−37.8294	+	12.2915i	−1.25888	+	0.409036i
$904$		0			0
$905$	13.2319	−	11.7739i	0.439843	−	0.391378i
$906$		0			0
$907$	−41.2693			−1.37032			−0.685162	−	0.728391i	$-0.740269\pi$
$907$	−41.2693			−1.37032			−0.685162	+	0.728391i	$0.740269\pi$
$908$		0			0
$909$	7.50716	+	10.3327i	0.248997	+	0.342715i
$910$		0			0
$911$	28.3265	+	20.5804i	0.938498	+	0.681859i	0.948059	−	0.318096i	$-0.103043\pi$
$911$	28.3265	+	20.5804i	0.938498	+	0.681859i	−0.00956063	+	0.999954i	$0.503043\pi$
$912$		0			0
$913$	1.56670	+	2.15638i	0.0518503	+	0.0713658i
$914$		0			0
$915$	5.63126	−	5.01077i	0.186164	−	0.165651i
$916$		0			0
$917$	9.41678	−	28.9819i	0.310970	−	0.957066i
$918$		0			0
$919$	−14.7119	+	45.2785i	−0.485300	+	1.49360i	0.346246	+	0.938144i	$0.387456\pi$
$919$	−14.7119	+	45.2785i	−0.485300	+	1.49360i	−0.831546	+	0.555456i	$0.812544\pi$
$920$		0			0
$921$	−3.14684	−	9.68499i	−0.103692	−	0.319131i
$922$		0			0
$923$	−7.28763	−	5.29477i	−0.239875	−	0.174280i
$924$		0			0
$925$	17.6768	+	8.12061i	0.581208	+	0.267004i
$926$		0			0
$927$	16.0479	−	22.0881i	0.527083	−	0.725467i
$928$		0			0
$929$	5.64100	+	17.3612i	0.185075	+	0.569603i	0.999950	−	0.0100347i	$-0.00319421\pi$
$929$	5.64100	+	17.3612i	0.185075	+	0.569603i	−0.814875	+	0.579637i	$0.803194\pi$
$930$		0			0
$931$	20.2722	+	6.58683i	0.664394	+	0.215875i
$932$		0			0
$933$	2.29968	−	7.07767i	0.0752880	−	0.231713i
$934$		0			0
$935$	−0.275830	−	2.78158i	−0.00902060	−	0.0909675i
$936$		0			0
$937$	−21.0733	−	29.0049i	−0.688435	−	0.947550i	0.311561	−	0.950226i	$-0.399148\pi$
$937$	−21.0733	−	29.0049i	−0.688435	−	0.947550i	−0.999996	+	0.00267611i	$0.999148\pi$
$938$		0			0
$939$	11.6146	−	15.9862i	0.379029	−	0.521688i
$940$		0			0
$941$	21.7339	+	29.9141i	0.708504	+	0.975172i	0.999828	+	0.0185478i	$0.00590428\pi$
$941$	21.7339	+	29.9141i	0.708504	+	0.975172i	−0.291324	+	0.956624i	$0.594096\pi$
$942$		0			0
$943$			0.973736i			0.0317092i
$944$		0			0
$945$	16.7977	+	38.3333i	0.546430	+	1.24698i
$946$		0			0
$947$	7.56047	+	23.2687i	0.245682	+	0.756132i	0.995523	+	0.0945146i	$0.0301299\pi$
$947$	7.56047	+	23.2687i	0.245682	+	0.756132i	−0.749841	+	0.661618i	$0.769870\pi$
$948$		0			0
$949$			24.9660i			0.810432i
$950$		0			0
$951$	−6.98390			−0.226469
$952$		0			0
$953$	−12.5944	+	4.09216i	−0.407972	+	0.132558i	−0.505811	−	0.862644i	$-0.668807\pi$
$953$	−12.5944	+	4.09216i	−0.407972	+	0.132558i	0.0978395	+	0.995202i	$0.468807\pi$
$954$		0			0
$955$	4.20814	+	42.4366i	0.136172	+	1.37322i
$956$		0			0
$957$	0.438576			0.0141772
$958$		0			0
$959$	8.64333	−	6.27975i	0.279108	−	0.202784i
$960$		0			0
$961$	−23.8820	−	17.3513i	−0.770388	−	0.559720i
$962$		0			0
$963$	−16.5280	+	12.0083i	−0.532607	+	0.386962i
$964$		0			0
$965$	−41.5180	−	24.2971i	−1.33651	−	0.782150i
$966$		0			0
$967$	−37.4471	−	12.1673i	−1.20422	−	0.391274i	−0.362908	−	0.931825i	$-0.618216\pi$
$967$	−37.4471	−	12.1673i	−1.20422	−	0.391274i	−0.841311	+	0.540551i	$0.818216\pi$
$968$		0			0
$969$	−7.19750	+	22.1516i	−0.231217	+	0.711613i
$970$		0			0
$971$	−10.1646	+	3.30267i	−0.326197	+	0.105988i	−0.467537	−	0.883973i	$-0.654859\pi$
$971$	−10.1646	+	3.30267i	−0.326197	+	0.105988i	0.141341	+	0.989961i	$0.454859\pi$
$972$		0			0
$973$	−38.0177	−	27.6215i	−1.21879	−	0.885504i
$974$		0			0
$975$	1.20233	−	10.2755i	0.0385054	−	0.329079i
$976$		0			0
$977$	−15.2242	+	20.9543i	−0.487064	+	0.670387i	−0.979843	−	0.199768i	$-0.935981\pi$
$977$	−15.2242	+	20.9543i	−0.487064	+	0.670387i	0.492779	+	0.870155i	$0.335981\pi$
$978$		0			0
$979$	−3.23735	+	1.05188i	−0.103466	+	0.0336182i
$980$		0			0
$981$	25.2206	+	8.19466i	0.805231	+	0.261635i
$982$		0			0
$983$	−57.4643	−	18.6713i	−1.83283	−	0.595521i	−0.999057	−	0.0434073i	$-0.986179\pi$
$983$	−57.4643	−	18.6713i	−1.83283	−	0.595521i	−0.833769	−	0.552114i	$-0.813821\pi$
$984$		0			0
$985$	12.4640	+	2.72601i	0.397137	+	0.0868578i
$986$		0			0
$987$	−25.6681	+	18.6489i	−0.817023	+	0.593602i
$988$		0			0
$989$	1.93142	−	2.65837i	0.0614155	−	0.0845311i
$990$		0			0
$991$	2.63278	−	1.91282i	0.0836329	−	0.0607629i	−0.545183	−	0.838317i	$-0.683540\pi$
$991$	2.63278	−	1.91282i	0.0836329	−	0.0607629i	0.628816	+	0.777554i	$0.283540\pi$
$992$		0			0
$993$		−	12.7322i		−	0.404045i
$994$		0			0
$995$	−11.0873	+	18.9457i	−0.351492	+	0.600618i
$996$		0			0
$997$	−9.81828	−	30.2175i	−0.310948	−	0.956999i	−0.977390	−	0.211443i	$-0.932184\pi$
$997$	−9.81828	−	30.2175i	−0.310948	−	0.956999i	0.666442	−	0.745556i	$-0.267816\pi$
$998$		0			0
$999$	20.1102			0.636260

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.be.a.209.10		112
4.3	odd	2		200.2.o.a.109.4	✓	112
8.3	odd	2		200.2.o.a.109.20	yes	112
8.5	even	2	inner	800.2.be.a.209.19		112
20.3	even	4		1000.2.t.b.701.23		224
20.7	even	4		1000.2.t.b.701.34		224
20.19	odd	2		1000.2.o.a.549.25		112
25.14	even	10	inner	800.2.be.a.689.19		112
40.3	even	4		1000.2.t.b.701.46		224
40.19	odd	2		1000.2.o.a.549.9		112
40.27	even	4		1000.2.t.b.701.11		224
100.11	odd	10		1000.2.o.a.949.9		112
100.23	even	20		1000.2.t.b.301.46		224
100.27	even	20		1000.2.t.b.301.11		224
100.39	odd	10		200.2.o.a.189.20	yes	112
200.11	odd	10		1000.2.o.a.949.25		112
200.27	even	20		1000.2.t.b.301.34		224
200.123	even	20		1000.2.t.b.301.23		224
200.139	odd	10		200.2.o.a.189.4	yes	112
200.189	even	10	inner	800.2.be.a.689.10		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.4	✓	112	4.3	odd	2
200.2.o.a.109.20	yes	112	8.3	odd	2
200.2.o.a.189.4	yes	112	200.139	odd	10
200.2.o.a.189.20	yes	112	100.39	odd	10
800.2.be.a.209.10		112	1.1	even	1	trivial
800.2.be.a.209.19		112	8.5	even	2	inner
800.2.be.a.689.10		112	200.189	even	10	inner
800.2.be.a.689.19		112	25.14	even	10	inner
1000.2.o.a.549.9		112	40.19	odd	2
1000.2.o.a.549.25		112	20.19	odd	2
1000.2.o.a.949.9		112	100.11	odd	10
1000.2.o.a.949.25		112	200.11	odd	10
1000.2.t.b.301.11		224	100.27	even	20
1000.2.t.b.301.23		224	200.123	even	20
1000.2.t.b.301.34		224	200.27	even	20
1000.2.t.b.301.46		224	100.23	even	20
1000.2.t.b.701.11		224	40.27	even	4
1000.2.t.b.701.23		224	20.3	even	4
1000.2.t.b.701.34		224	20.7	even	4
1000.2.t.b.701.46		224	40.3	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:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.be (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.327557 - 1.00812i) q^{3} +(1.12940 - 1.92988i) q^{5} -3.62100i q^{7} +(1.51804 - 1.10292i) q^{9} +(0.116625 - 0.160521i) q^{11} +(-1.57920 + 1.14736i) q^{13} +(-2.31550 - 0.506422i) q^{15} +(5.99191 + 1.94689i) q^{17} +(-3.31697 - 1.07775i) q^{19} +(-3.65040 + 1.18609i) q^{21} +(0.186374 - 0.256522i) q^{23} +(-2.44891 - 4.35923i) q^{25} +(-4.18179 - 3.03825i) q^{27} +(-1.98323 + 0.644390i) q^{29} +(-2.40398 + 7.39869i) q^{31} +(-0.200025 - 0.0649921i) q^{33} +(-6.98811 - 4.08956i) q^{35} +(-3.14753 + 2.28682i) q^{37} +(1.67395 + 1.21620i) q^{39} +(-2.48445 + 1.80506i) q^{41} +10.3631 q^{43} +(-0.414034 - 4.17529i) q^{45} +(7.86154 - 2.55437i) q^{47} -6.11166 q^{49} -6.67827i q^{51} +(-4.48172 - 13.7933i) q^{53} +(-0.178070 - 0.406365i) q^{55} +3.69692i q^{57} +(0.165441 + 0.227710i) q^{59} +(-1.86928 + 2.57285i) q^{61} +(-3.99368 - 5.49683i) q^{63} +(0.430715 + 4.34351i) q^{65} +(0.0384025 - 0.118191i) q^{67} +(-0.319653 - 0.103862i) q^{69} +(1.42604 + 4.38889i) q^{71} +(7.51775 - 10.3473i) q^{73} +(-3.59246 + 3.89668i) q^{75} +(-0.581246 - 0.422300i) q^{77} +(-1.42060 - 4.37215i) q^{79} +(0.0463838 - 0.142755i) q^{81} +(-4.15123 + 12.7762i) q^{83} +(10.5245 - 9.36487i) q^{85} +(1.29924 + 1.78826i) q^{87} +(-13.8793 - 10.0839i) q^{89} +(4.15459 + 5.71830i) q^{91} +8.24620 q^{93} +(-5.82612 + 5.18416i) q^{95} +(-2.24784 + 0.730369i) q^{97} -0.372306i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79}+ \cdots - 50 q^{97}+O(q^{100}) \) 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more