LMFDB - Embedded newform 552.2.u.a.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(17,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 11, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("552.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.u (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			17.7
Character	$\chi$	$=$	552.17
Dual form			552.2.u.a.65.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07569 - 1.35753i) q^{3} +(-0.535830 + 0.344357i) q^{5} +(-2.02223 - 0.290753i) q^{7} +(-0.685767 + 2.92057i) q^{9} +O(q^{10})$	\(q+(-1.07569 - 1.35753i) q^{3} +(-0.535830 + 0.344357i) q^{5} +(-2.02223 - 0.290753i) q^{7} +(-0.685767 + 2.92057i) q^{9} +(0.0428413 + 0.0938095i) q^{11} +(0.657474 + 4.57283i) q^{13} +(1.04386 + 0.356982i) q^{15} +(1.03008 - 1.18877i) q^{17} +(-2.88216 + 2.49740i) q^{19} +(1.78060 + 3.05800i) q^{21} +(4.75668 + 0.611543i) q^{23} +(-1.90854 + 4.17913i) q^{25} +(4.70243 - 2.21069i) q^{27} +(3.84300 + 3.32998i) q^{29} +(-1.22648 + 0.360126i) q^{31} +(0.0812649 - 0.159069i) q^{33} +(1.18370 - 0.540576i) q^{35} +(-1.41013 + 2.19421i) q^{37} +(5.50051 - 5.81150i) q^{39} +(2.08672 + 3.24700i) q^{41} +(-2.23913 + 7.62577i) q^{43} +(-0.638263 - 1.80108i) q^{45} -5.18450i q^{47} +(-2.71156 - 0.796185i) q^{49} +(-2.72184 - 0.119604i) q^{51} +(0.0372918 - 0.259370i) q^{53} +(-0.0552596 - 0.0355132i) q^{55} +(6.49062 + 1.22617i) q^{57} +(-7.30521 + 1.05033i) q^{59} +(3.48865 + 11.8813i) q^{61} +(2.23595 - 5.70669i) q^{63} +(-1.92698 - 2.22385i) q^{65} +(3.71843 + 1.69815i) q^{67} +(-4.28654 - 7.11516i) q^{69} +(6.95935 + 3.17823i) q^{71} +(-2.38975 - 2.75792i) q^{73} +(7.72629 - 1.90456i) q^{75} +(-0.0593598 - 0.202161i) q^{77} +(-10.2666 + 1.47612i) q^{79} +(-8.05945 - 4.00566i) q^{81} +(-4.49498 - 2.88875i) q^{83} +(-0.142584 + 0.991693i) q^{85} +(0.386651 - 8.79903i) q^{87} +(-7.99786 - 2.34838i) q^{89} -9.43850i q^{91} +(1.80819 + 1.27759i) q^{93} +(0.684348 - 2.33067i) q^{95} +(-3.52007 - 5.47733i) q^{97} +(-0.303356 + 0.0607896i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^9	$ 240 q - 4 q^{9} - 16 q^{25} + 12 q^{27} - 8 q^{31} + 44 q^{37} + 20 q^{39} + 44 q^{43} + 124 q^{49} + 12 q^{55} + 16 q^{69} - 74 q^{75} - 144 q^{81} + 24 q^{85} - 170 q^{87} + 12 q^{93} - 198 q^{99}+O(q^{100}) $ 240 * q - 4 * q^9 - 16 * q^25 + 12 * q^27 - 8 * q^31 + 44 * q^37 + 20 * q^39 + 44 * q^43 + 124 * q^49 + 12 * q^55 + 16 * q^69 - 74 * q^75 - 144 * q^81 + 24 * q^85 - 170 * q^87 + 12 * q^93 - 198 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{7}{22}\right)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.07569	−	1.35753i	−0.621052	−	0.783769i
$3$	−1.07569	−	1.35753i	−0.621052	−	0.783769i
$4$		0			0
$5$	−0.535830	+	0.344357i	−0.239630	+	0.154001i	−0.654944	−	0.755677i	$-0.727308\pi$
$5$	−0.535830	+	0.344357i	−0.239630	+	0.154001i	0.415314	+	0.909678i	$0.363672\pi$
$6$		0			0
$7$	−2.02223	−	0.290753i	−0.764333	−	0.109894i	−0.250887	−	0.968016i	$-0.580722\pi$
$7$	−2.02223	−	0.290753i	−0.764333	−	0.109894i	−0.513446	+	0.858122i	$0.671631\pi$
$8$		0			0
$9$	−0.685767	+	2.92057i	−0.228589	+	0.973523i
$10$		0			0
$11$	0.0428413	+	0.0938095i	0.0129172	+	0.0282846i	0.915981	−	0.401222i	$-0.131415\pi$
$11$	0.0428413	+	0.0938095i	0.0129172	+	0.0282846i	−0.903063	+	0.429507i	$0.858687\pi$
$12$		0			0
$13$	0.657474	+	4.57283i	0.182350	+	1.26827i	0.851186	+	0.524864i	$0.175884\pi$
$13$	0.657474	+	4.57283i	0.182350	+	1.26827i	−0.668835	+	0.743411i	$0.733207\pi$
$14$		0			0
$15$	1.04386	+	0.356982i	0.269524	+	0.0921723i
$16$		0			0
$17$	1.03008	−	1.18877i	0.249830	−	0.288320i	−0.616958	−	0.786996i	$-0.711635\pi$
$17$	1.03008	−	1.18877i	0.249830	−	0.288320i	0.866788	+	0.498677i	$0.166181\pi$
$18$		0			0
$19$	−2.88216	+	2.49740i	−0.661212	+	0.572944i	−0.919483	−	0.393129i	$-0.871393\pi$
$19$	−2.88216	+	2.49740i	−0.661212	+	0.572944i	0.258271	+	0.966073i	$0.416847\pi$
$20$		0			0
$21$	1.78060	+	3.05800i	0.388558	+	0.667311i
$22$		0			0
$23$	4.75668	+	0.611543i	0.991837	+	0.127515i
$23$	4.75668	+	0.611543i	0.991837	+	0.127515i
$24$		0			0
$25$	−1.90854	+	4.17913i	−0.381709	+	0.835825i
$26$		0			0
$27$	4.70243	−	2.21069i	0.904983	−	0.425447i
$28$		0			0
$29$	3.84300	+	3.32998i	0.713628	+	0.618362i	0.934092	−	0.357033i	$-0.116212\pi$
$29$	3.84300	+	3.32998i	0.713628	+	0.618362i	−0.220464	+	0.975395i	$0.570757\pi$
$30$		0			0
$31$	−1.22648	+	0.360126i	−0.220281	+	0.0646805i	−0.390011	−	0.920810i	$-0.627529\pi$
$31$	−1.22648	+	0.360126i	−0.220281	+	0.0646805i	0.169729	+	0.985491i	$0.445711\pi$
$32$		0			0
$33$	0.0812649	−	0.159069i	0.0141464	−	0.0276903i
$34$		0			0
$35$	1.18370	−	0.540576i	0.200081	−	0.0913740i
$36$		0			0
$37$	−1.41013	+	2.19421i	−0.231825	+	0.360726i	−0.937604	−	0.347706i	$-0.886961\pi$
$37$	−1.41013	+	2.19421i	−0.231825	+	0.360726i	0.705779	+	0.708432i	$0.250597\pi$
$38$		0			0
$39$	5.50051	−	5.81150i	0.880786	−	0.930585i
$40$		0			0
$41$	2.08672	+	3.24700i	0.325891	+	0.507096i	0.965081	−	0.261953i	$-0.0843666\pi$
$41$	2.08672	+	3.24700i	0.325891	+	0.507096i	−0.639190	+	0.769049i	$0.720730\pi$
$42$		0			0
$43$	−2.23913	+	7.62577i	−0.341464	+	1.16292i	0.592505	+	0.805566i	$0.298139\pi$
$43$	−2.23913	+	7.62577i	−0.341464	+	1.16292i	−0.933969	+	0.357353i	$0.883679\pi$
$44$		0			0
$45$	−0.638263	−	1.80108i	−0.0951467	−	0.268489i
$46$		0			0
$47$		−	5.18450i		−	0.756237i	−0.925757	−	0.378119i	$-0.876571\pi$
$47$		−	5.18450i		−	0.756237i	0.925757	−	0.378119i	$-0.123429\pi$
$48$		0			0
$49$	−2.71156	−	0.796185i	−0.387365	−	0.113741i
$50$		0			0
$51$	−2.72184	−	0.119604i	−0.381134	−	0.0167480i
$52$		0			0
$53$	0.0372918	−	0.259370i	0.00512242	−	0.0356272i	−0.987100	−	0.160105i	$-0.948817\pi$
$53$	0.0372918	−	0.259370i	0.00512242	−	0.0356272i	0.992222	+	0.124478i	$0.0397257\pi$
$54$		0			0
$55$	−0.0552596	−	0.0355132i	−0.00745120	−	0.00478860i
$56$		0			0
$57$	6.49062	+	1.22617i	0.859703	+	0.162410i
$58$		0			0
$59$	−7.30521	+	1.05033i	−0.951057	+	0.136741i	−0.600344	−	0.799742i	$-0.704970\pi$
$59$	−7.30521	+	1.05033i	−0.951057	+	0.136741i	−0.350713	+	0.936483i	$0.614061\pi$
$60$		0			0
$61$	3.48865	+	11.8813i	0.446676	+	1.52124i	0.808219	+	0.588883i	$0.200432\pi$
$61$	3.48865	+	11.8813i	0.446676	+	1.52124i	−0.361543	+	0.932356i	$0.617750\pi$
$62$		0			0
$63$	2.23595	−	5.70669i	0.281703	−	0.718975i
$64$		0			0
$65$	−1.92698	−	2.22385i	−0.239012	−	0.275835i
$66$		0			0
$67$	3.71843	+	1.69815i	0.454279	+	0.207462i	0.629395	−	0.777086i	$-0.283303\pi$
$67$	3.71843	+	1.69815i	0.454279	+	0.207462i	−0.175116	+	0.984548i	$0.556030\pi$
$68$		0			0
$69$	−4.28654	−	7.11516i	−0.516039	−	0.856565i
$70$		0			0
$71$	6.95935	+	3.17823i	0.825923	+	0.377186i	0.783100	−	0.621896i	$-0.213638\pi$
$71$	6.95935	+	3.17823i	0.825923	+	0.377186i	0.0428232	+	0.999083i	$0.486365\pi$
$72$		0			0
$73$	−2.38975	−	2.75792i	−0.279699	−	0.322790i	0.598466	−	0.801148i	$-0.295777\pi$
$73$	−2.38975	−	2.75792i	−0.279699	−	0.322790i	−0.878164	+	0.478359i	$0.841232\pi$
$74$		0			0
$75$	7.72629	−	1.90456i	0.892155	−	0.219919i
$76$		0			0
$77$	−0.0593598	−	0.202161i	−0.00676468	−	0.0230384i
$78$		0			0
$79$	−10.2666	+	1.47612i	−1.15509	+	0.166076i	−0.693120	−	0.720822i	$-0.743765\pi$
$79$	−10.2666	+	1.47612i	−1.15509	+	0.166076i	−0.461965	+	0.886898i	$0.652856\pi$
$80$		0			0
$81$	−8.05945	−	4.00566i	−0.895494	−	0.445073i
$82$		0			0
$83$	−4.49498	−	2.88875i	−0.493389	−	0.317082i	0.270178	−	0.962810i	$-0.412917\pi$
$83$	−4.49498	−	2.88875i	−0.493389	−	0.317082i	−0.763567	+	0.645729i	$0.776554\pi$
$84$		0			0
$85$	−0.142584	+	0.991693i	−0.0154654	+	0.107564i
$86$		0			0
$87$	0.386651	−	8.79903i	0.0414534	−	0.943355i
$88$		0			0
$89$	−7.99786	−	2.34838i	−0.847771	−	0.248928i	−0.171137	−	0.985247i	$-0.554744\pi$
$89$	−7.99786	−	2.34838i	−0.847771	−	0.248928i	−0.676634	+	0.736319i	$0.736562\pi$
$90$		0			0
$91$		−	9.43850i		−	0.989423i
$92$		0			0
$93$	1.80819	+	1.27759i	0.187501	+	0.132480i
$94$		0			0
$95$	0.684348	−	2.33067i	0.0702126	−	0.239122i
$96$		0			0
$97$	−3.52007	−	5.47733i	−0.357409	−	0.556139i	0.615263	−	0.788322i	$-0.289050\pi$
$97$	−3.52007	−	5.47733i	−0.357409	−	0.556139i	−0.972672	+	0.232183i	$0.925413\pi$
$98$		0			0
$99$	−0.303356	+	0.0607896i	−0.0304884	+	0.00610959i
$100$		0			0
$101$	−6.50458	+	10.1213i	−0.647230	+	1.00711i	0.350284	+	0.936644i	$0.386085\pi$
$101$	−6.50458	+	10.1213i	−0.647230	+	1.00711i	−0.997514	+	0.0704663i	$0.977551\pi$
$102$		0			0
$103$	13.5741	−	6.19907i	1.33749	−	0.610812i	0.387149	−	0.922017i	$-0.373460\pi$
$103$	13.5741	−	6.19907i	1.33749	−	0.610812i	0.950343	+	0.311205i	$0.100733\pi$
$104$		0			0
$105$	−2.00714	−	1.02541i	−0.195877	−	0.100069i
$106$		0			0
$107$	−19.0201	+	5.58479i	−1.83874	+	0.539902i	−0.999989	−	0.00461618i	$-0.998531\pi$
$107$	−19.0201	+	5.58479i	−1.83874	+	0.539902i	−0.838749	+	0.544518i	$0.816712\pi$
$108$		0			0
$109$	−5.89119	−	5.10475i	−0.564274	−	0.488946i	0.325379	−	0.945584i	$-0.394508\pi$
$109$	−5.89119	−	5.10475i	−0.564274	−	0.488946i	−0.889653	+	0.456638i	$0.849054\pi$
$110$		0			0
$111$	4.49558	−	0.446002i	0.426701	−	0.0423326i
$112$		0			0
$113$	4.45999	−	9.76602i	0.419561	−	0.918710i	−0.575346	−	0.817910i	$-0.695133\pi$
$113$	4.45999	−	9.76602i	0.419561	−	0.918710i	0.994907	−	0.100800i	$-0.0321401\pi$
$114$		0			0
$115$	−2.75936	+	1.31031i	−0.257312	+	0.122187i
$116$		0			0
$117$	−13.8061	−	1.21570i	−1.27638	−	0.112392i
$118$		0			0
$119$	−2.42870	+	2.10448i	−0.222638	+	0.192917i
$120$		0			0
$121$	7.19650	−	8.30521i	0.654228	−	0.755019i
$122$		0			0
$123$	2.16322	−	6.32555i	0.195051	−	0.570356i
$124$		0			0
$125$	−0.869688	−	6.04881i	−0.0777873	−	0.541022i
$126$		0			0
$127$	1.04473	+	2.28764i	0.0927049	+	0.202995i	0.950304	−	0.311323i	$-0.100772\pi$
$127$	1.04473	+	2.28764i	0.0927049	+	0.202995i	−0.857599	+	0.514319i	$0.828045\pi$
$128$		0			0
$129$	12.7608	−	5.16331i	1.12353	−	0.454604i
$130$		0			0
$131$	−8.01824	−	1.15285i	−0.700557	−	0.100725i	−0.217173	−	0.976133i	$-0.569683\pi$
$131$	−8.01824	−	1.15285i	−0.700557	−	0.100725i	−0.483384	+	0.875408i	$0.660593\pi$
$132$		0			0
$133$	6.55453	−	4.21234i	0.568350	−	0.365256i
$134$		0			0
$135$	−1.75844	+	2.80387i	−0.151342	+	0.241318i
$136$		0			0
$137$	13.1713			1.12530			0.562651	−	0.826695i	$-0.309782\pi$
$137$	13.1713			1.12530			0.562651	+	0.826695i	$0.309782\pi$
$138$		0			0
$139$	−6.71985			−0.569971			−0.284985	−	0.958532i	$-0.591989\pi$
$139$	−6.71985			−0.569971			−0.284985	+	0.958532i	$0.591989\pi$
$140$		0			0
$141$	−7.03811	+	5.57693i	−0.592716	+	0.469662i
$142$		0			0
$143$	−0.400808	+	0.257583i	−0.0335172	+	0.0215402i
$144$		0			0
$145$	−3.20590	−	0.460938i	−0.266235	−	0.0382789i
$146$		0			0
$147$	1.83596	+	4.53747i	0.151427	+	0.374244i
$148$		0			0
$149$	−3.28266	−	7.18802i	−0.268926	−	0.588865i	0.726199	−	0.687484i	$-0.241285\pi$
$149$	−3.28266	−	7.18802i	−0.268926	−	0.588865i	−0.995125	+	0.0986186i	$0.968558\pi$
$150$		0			0
$151$	−1.25005	−	8.69428i	−0.101728	−	0.707531i	−0.975308	−	0.220850i	$-0.929117\pi$
$151$	−1.25005	−	8.69428i	−0.101728	−	0.707531i	0.873580	−	0.486680i	$-0.161792\pi$
$152$		0			0
$153$	2.76550	+	3.82363i	0.223577	+	0.309122i
$154$		0			0
$155$	0.533170	−	0.615311i	0.0428253	−	0.0494230i
$156$		0			0
$157$	6.79208	−	5.88538i	0.542067	−	0.469704i	−0.340266	−	0.940329i	$-0.610517\pi$
$157$	6.79208	−	5.88538i	0.542067	−	0.469704i	0.882333	+	0.470625i	$0.155972\pi$
$158$		0			0
$159$	−0.392216	+	0.228378i	−0.0311048	+	0.0181115i
$160$		0			0
$161$	−9.44132	−	2.61970i	−0.744080	−	0.206462i
$162$		0			0
$163$	−6.47411	+	14.1763i	−0.507091	+	1.11037i	0.467008	+	0.884253i	$0.345332\pi$
$163$	−6.47411	+	14.1763i	−0.507091	+	1.11037i	−0.974099	+	0.226121i	$0.927395\pi$
$164$		0			0
$165$	0.0112322	+	0.113218i	0.000874427	+	0.00881399i
$166$		0			0
$167$	15.3783	+	13.3254i	1.19001	+	1.03115i	0.998769	+	0.0496079i	$0.0157972\pi$
$167$	15.3783	+	13.3254i	1.19001	+	1.03115i	0.191243	+	0.981543i	$0.438748\pi$
$168$		0			0
$169$	−8.00510	+	2.35051i	−0.615777	+	0.180808i
$170$		0			0
$171$	−5.31735	−	10.1302i	−0.406628	−	0.774674i
$172$		0			0
$173$	18.6268	−	8.50657i	1.41617	−	0.646742i	0.447314	−	0.894377i	$-0.352381\pi$
$173$	18.6268	−	8.50657i	1.41617	−	0.646742i	0.968854	+	0.247635i	$0.0796532\pi$
$174$		0			0
$175$	5.07462	−	7.89626i	0.383605	−	0.596901i
$176$		0			0
$177$	9.28402	+	8.78720i	0.697830	+	0.660486i
$178$		0			0
$179$	4.38531	+	6.82368i	0.327774	+	0.510026i	0.965558	−	0.260190i	$-0.0837851\pi$
$179$	4.38531	+	6.82368i	0.327774	+	0.510026i	−0.637784	+	0.770215i	$0.720149\pi$
$180$		0			0
$181$	−4.72462	+	16.0906i	−0.351179	+	1.19600i	0.574757	+	0.818324i	$0.305096\pi$
$181$	−4.72462	+	16.0906i	−0.351179	+	1.19600i	−0.925936	+	0.377681i	$0.876722\pi$
$182$		0			0
$183$	12.3764	−	17.5165i	0.914891	−	1.29486i
$184$		0			0
$185$		−	1.66131i		−	0.122142i
$186$		0			0
$187$	0.155648	+	0.0457024i	0.0113821	+	0.00334209i
$188$		0			0
$189$	−10.1522	+	3.10328i	−0.738463	+	0.225731i
$190$		0			0
$191$	−1.08550	+	7.54981i	−0.0785439	+	0.546285i	0.912116	+	0.409931i	$0.134447\pi$
$191$	−1.08550	+	7.54981i	−0.0785439	+	0.546285i	−0.990660	+	0.136354i	$0.956462\pi$
$192$		0			0
$193$	14.3450	+	9.21897i	1.03258	+	0.663596i	0.943140	−	0.332397i	$-0.107857\pi$
$193$	14.3450	+	9.21897i	1.03258	+	0.663596i	0.0894354	+	0.995993i	$0.471494\pi$
$194$		0			0
$195$	−0.946104	+	5.00811i	−0.0677519	+	0.358638i
$196$		0			0
$197$	23.3210	−	3.35305i	1.66155	−	0.238895i	0.753409	−	0.657553i	$-0.228408\pi$
$197$	23.3210	−	3.35305i	1.66155	−	0.238895i	0.908144	+	0.418657i	$0.137499\pi$
$198$		0			0
$199$	0.0199279	+	0.0678681i	0.00141265	+	0.00481104i	0.960196	−	0.279326i	$-0.0901111\pi$
$199$	0.0199279	+	0.0678681i	0.00141265	+	0.00481104i	−0.958784	+	0.284137i	$0.908293\pi$
$200$		0			0
$201$	−1.69461	−	6.87457i	−0.119528	−	0.484895i
$202$		0			0
$203$	−6.80325	−	7.85137i	−0.477495	−	0.551058i
$204$		0			0
$205$	−2.23625	−	1.02126i	−0.156187	−	0.0713280i
$206$		0			0
$207$	−5.04803	+	13.4728i	−0.350862	+	0.936427i
$208$		0			0
$209$	−0.357756	−	0.163382i	−0.0247465	−	0.0113013i
$210$		0			0
$211$	12.6387	+	14.5858i	0.870084	+	1.00413i	0.999921	+	0.0125950i	$0.00400922\pi$
$211$	12.6387	+	14.5858i	0.870084	+	1.00413i	−0.129837	+	0.991535i	$0.541445\pi$
$212$		0			0
$213$	−3.17159	−	12.8663i	−0.217314	−	0.881585i
$214$		0			0
$215$	−1.42619	−	4.85717i	−0.0972657	−	0.331257i
$216$		0			0
$217$	2.58493	−	0.371657i	0.175476	−	0.0252297i
$218$		0			0
$219$	−1.17331	+	6.21082i	−0.0792852	+	0.419688i
$220$		0			0
$221$	6.11330	+	3.92878i	0.411225	+	0.264278i
$222$		0			0
$223$	−0.574581	+	3.99630i	−0.0384768	+	0.267612i	−0.999974	−	0.00720241i	$-0.997707\pi$
$223$	−0.574581	+	3.99630i	−0.0384768	+	0.267612i	0.961497	+	0.274815i	$0.0886165\pi$
$224$		0			0
$225$	−10.8966	−	8.43994i	−0.726441	−	0.562663i
$226$		0			0
$227$	−22.2143	−	6.52272i	−1.47442	−	0.432928i	−0.556885	−	0.830590i	$-0.688003\pi$
$227$	−22.2143	−	6.52272i	−1.47442	−	0.432928i	−0.917532	+	0.397662i	$0.869822\pi$
$228$		0			0
$229$		−	19.9260i		−	1.31675i	−0.752691	−	0.658374i	$-0.771244\pi$
$229$		−	19.9260i		−	1.31675i	0.752691	−	0.658374i	$-0.228756\pi$
$230$		0			0
$231$	−0.210586	+	0.298046i	−0.0138556	+	0.0196100i
$232$		0			0
$233$	−0.478602	+	1.62997i	−0.0313542	+	0.106783i	−0.973683	−	0.227905i	$-0.926813\pi$
$233$	−0.478602	+	1.62997i	−0.0313542	+	0.106783i	0.942329	+	0.334687i	$0.108631\pi$
$234$		0			0
$235$	1.78532	+	2.77801i	0.116461	+	0.181217i
$236$		0			0
$237$	13.0476	+	12.3494i	0.847534	+	0.802179i
$238$		0			0
$239$	−8.00221	+	12.4517i	−0.517620	+	0.805432i	−0.997408	−	0.0719523i	$-0.977077\pi$
$239$	−8.00221	+	12.4517i	−0.517620	+	0.805432i	0.479788	+	0.877384i	$0.340713\pi$
$240$		0			0
$241$	−13.4146	+	6.12624i	−0.864110	+	0.394626i	−0.797619	−	0.603161i	$-0.793908\pi$
$241$	−13.4146	+	6.12624i	−0.864110	+	0.394626i	−0.0664908	+	0.997787i	$0.521180\pi$
$242$		0			0
$243$	3.23169	+	15.2498i	0.207313	+	0.978275i
$244$		0			0
$245$	1.72710	−	0.507123i	0.110341	−	0.0323989i
$246$		0			0
$247$	−13.3152	−	11.5376i	−0.847223	−	0.734123i
$248$		0			0
$249$	0.913663	+	9.20948i	0.0579010	+	0.583627i
$250$		0			0
$251$	−3.53646	+	7.74377i	−0.223220	+	0.488783i	−0.987797	−	0.155750i	$-0.950221\pi$
$251$	−3.53646	+	7.74377i	−0.223220	+	0.488783i	0.764577	+	0.644532i	$0.222948\pi$
$252$		0			0
$253$	0.146414	+	0.472421i	0.00920498	+	0.0297009i
$254$		0			0
$255$	1.49963	−	0.873196i	0.0939104	−	0.0546817i
$256$		0			0
$257$	−17.8354	+	15.4544i	−1.11254	+	0.964021i	−0.999563	−	0.0295765i	$-0.990584\pi$
$257$	−17.8354	+	15.4544i	−1.11254	+	0.964021i	−0.112977	+	0.993598i	$0.536039\pi$
$258$		0			0
$259$	3.48960	−	4.02721i	0.216833	−	0.250239i
$260$		0			0
$261$	−12.3608	+	8.94017i	−0.765117	+	0.553382i
$262$		0			0
$263$	−0.165744	−	1.15277i	−0.0102202	−	0.0710831i	0.984073	−	0.177765i	$-0.0568866\pi$
$263$	−0.165744	−	1.15277i	−0.0102202	−	0.0710831i	−0.994293	+	0.106682i	$0.965977\pi$
$264$		0			0
$265$	0.0693337	+	0.151820i	0.00425914	+	0.00932621i
$266$		0			0
$267$	5.41525	+	13.3835i	0.331408	+	0.819054i
$268$		0			0
$269$	10.6408	+	1.52992i	0.648783	+	0.0932808i	0.458846	−	0.888516i	$-0.348263\pi$
$269$	10.6408	+	1.52992i	0.648783	+	0.0932808i	0.189936	+	0.981796i	$0.439172\pi$
$270$		0			0
$271$	−6.05670	+	3.89240i	−0.367918	+	0.236447i	−0.711515	−	0.702670i	$-0.751991\pi$
$271$	−6.05670	+	3.89240i	−0.367918	+	0.236447i	0.343597	+	0.939117i	$0.388354\pi$
$272$		0			0
$273$	−12.8130	+	10.1529i	−0.775480	+	0.614483i
$274$		0			0
$275$	−0.473806			−0.0285716
$276$		0			0
$277$	−15.3419			−0.921808			−0.460904	−	0.887450i	$-0.652475\pi$
$277$	−15.3419			−0.921808			−0.460904	+	0.887450i	$0.652475\pi$
$278$		0			0
$279$	−0.210695	−	3.82897i	−0.0126140	−	0.229234i
$280$		0			0
$281$	14.9645	−	9.61709i	0.892706	−	0.573707i	−0.0119127	−	0.999929i	$-0.503792\pi$
$281$	14.9645	−	9.61709i	0.892706	−	0.573707i	0.904619	+	0.426222i	$0.140156\pi$
$282$		0			0
$283$	29.3820	+	4.22449i	1.74658	+	0.251120i	0.940283	−	0.340395i	$-0.110561\pi$
$283$	29.3820	+	4.22449i	1.74658	+	0.251120i	0.806294	+	0.591515i	$0.201470\pi$
$284$		0			0
$285$	−3.90010	+	1.57807i	−0.231022	+	0.0934768i
$286$		0			0
$287$	−3.27576	−	7.17291i	−0.193362	−	0.423403i
$288$		0			0
$289$	2.06723	+	14.3779i	0.121602	+	0.845760i
$290$		0			0
$291$	−3.64912	+	10.6705i	−0.213915	+	0.625517i
$292$		0			0
$293$	21.8593	−	25.2270i	1.27703	−	1.47377i	0.470724	−	0.882281i	$-0.343993\pi$
$293$	21.8593	−	25.2270i	1.27703	−	1.47377i	0.806309	−	0.591494i	$-0.201462\pi$
$294$		0			0
$295$	3.55266	−	3.07840i	0.206844	−	0.179231i
$296$		0			0
$297$	0.408842	+	0.346424i	0.0237234	+	0.0201015i
$298$		0			0
$299$	0.330912	+	22.1536i	0.0191371	+	1.28117i
$300$		0			0
$301$	6.74526	−	14.7701i	0.388790	−	0.851332i
$302$		0			0
$303$	20.7369	−	2.05729i	1.19131	−	0.118188i
$304$		0			0
$305$	−5.96071	−	5.16499i	−0.341309	−	0.295746i
$306$		0			0
$307$	−14.9314	+	4.38425i	−0.852180	+	0.250223i	−0.678519	−	0.734583i	$-0.737378\pi$
$307$	−14.9314	+	4.38425i	−0.852180	+	0.250223i	−0.173661	+	0.984806i	$0.555560\pi$
$308$		0			0
$309$	−23.0169	−	11.7589i	−1.30939	−	0.668939i
$310$		0			0
$311$	2.96642	−	1.35472i	0.168210	−	0.0768190i	−0.329530	−	0.944145i	$-0.606890\pi$
$311$	2.96642	−	1.35472i	0.168210	−	0.0768190i	0.497741	+	0.867326i	$0.334163\pi$
$312$		0			0
$313$	12.0448	−	18.7421i	0.680815	−	1.05937i	−0.313154	−	0.949702i	$-0.601386\pi$
$313$	12.0448	−	18.7421i	0.680815	−	1.05937i	0.993968	−	0.109666i	$-0.0349781\pi$
$314$		0			0
$315$	0.767049	+	3.82778i	0.0432183	+	0.215671i
$316$		0			0
$317$	3.53877	+	5.50643i	0.198757	+	0.309272i	0.926298	−	0.376793i	$-0.122973\pi$
$317$	3.53877	+	5.50643i	0.198757	+	0.309272i	−0.727541	+	0.686065i	$0.759337\pi$
$318$		0			0
$319$	−0.147744	+	0.503171i	−0.00827210	+	0.0281722i
$320$		0			0
$321$	28.0413	+	19.8127i	1.56511	+	1.10584i
$322$		0			0
$323$			5.99875i			0.333779i
$324$		0			0
$325$	−20.3653	−	5.97978i	−1.12966	−	0.331698i
$326$		0			0
$327$	−0.592723	+	13.4886i	−0.0327777	+	0.745922i
$328$		0			0
$329$	−1.50741	+	10.4843i	−0.0831063	+	0.578017i
$330$		0			0
$331$	16.8908	+	10.8550i	0.928401	+	0.596647i	0.915084	−	0.403264i	$-0.132124\pi$
$331$	16.8908	+	10.8550i	0.928401	+	0.596647i	0.0133177	+	0.999911i	$0.495761\pi$
$332$		0			0
$333$	−5.44132	−	5.62311i	−0.298183	−	0.308145i
$334$		0			0
$335$	−2.57722	+	0.370548i	−0.140808	+	0.0202452i
$336$		0			0
$337$	0.882914	+	3.00693i	0.0480954	+	0.163798i	0.980039	−	0.198805i	$-0.0637062\pi$
$337$	0.882914	+	3.00693i	0.0480954	+	0.163798i	−0.931944	+	0.362603i	$0.881888\pi$
$338$		0			0
$339$	−18.0552	+	4.45068i	−0.980626	+	0.241728i
$340$		0			0
$341$	−0.0863270	−	0.0996267i	−0.00467487	−	0.00539509i
$342$		0			0
$343$	18.2607	+	8.33940i	0.985988	+	0.450285i
$344$		0			0
$345$	4.74701	+	2.33641i	0.255571	+	0.125788i
$346$		0			0
$347$	14.9892	+	6.84533i	0.804662	+	0.367477i	0.774903	−	0.632080i	$-0.217799\pi$
$347$	14.9892	+	6.84533i	0.804662	+	0.367477i	0.0297590	+	0.999557i	$0.490526\pi$
$348$		0			0
$349$	−6.54214	−	7.55003i	−0.350193	−	0.404144i	0.553137	−	0.833090i	$-0.313430\pi$
$349$	−6.54214	−	7.55003i	−0.350193	−	0.404144i	−0.903330	+	0.428946i	$0.858885\pi$
$350$		0			0
$351$	13.2008	+	20.0500i	0.704608	+	1.07019i
$352$		0			0
$353$	−9.09448	−	30.9729i	−0.484050	−	1.64852i	−0.733166	−	0.680050i	$-0.761958\pi$
$353$	−9.09448	−	30.9729i	−0.484050	−	1.64852i	0.249116	−	0.968474i	$-0.419860\pi$
$354$		0			0
$355$	−4.82347	+	0.693510i	−0.256003	+	0.0368077i
$356$		0			0
$357$	5.46942	+	1.03325i	0.289472	+	0.0546855i
$358$		0			0
$359$	10.4213	+	6.69735i	0.550014	+	0.353472i	0.785944	−	0.618298i	$-0.212177\pi$
$359$	10.4213	+	6.69735i	0.550014	+	0.353472i	−0.235930	+	0.971770i	$0.575814\pi$
$360$		0			0
$361$	−0.634174	+	4.41078i	−0.0333776	+	0.232146i
$362$		0			0
$363$	−19.0158	−	0.835601i	−0.998070	−	0.0438577i
$364$		0			0
$365$	2.23020	+	0.654847i	0.116734	+	0.0342763i
$366$		0			0
$367$		−	15.6903i		−	0.819025i	−0.912305	−	0.409512i	$-0.865699\pi$
$367$		−	15.6903i		−	0.819025i	0.912305	−	0.409512i	$-0.134301\pi$
$368$		0			0
$369$	−10.9141	+	3.86772i	−0.568164	+	0.201345i
$370$		0			0
$371$	−0.150825	+	0.513664i	−0.00783046	+	0.0266681i
$372$		0			0
$373$	3.64388	+	5.66999i	0.188673	+	0.293581i	0.922684	−	0.385556i	$-0.125990\pi$
$373$	3.64388	+	5.66999i	0.188673	+	0.293581i	−0.734011	+	0.679137i	$0.762354\pi$
$374$		0			0
$375$	−7.27592	+	7.68730i	−0.375727	+	0.396970i
$376$		0			0
$377$	−12.7008	+	19.7628i	−0.654123	+	1.01784i
$378$		0			0
$379$	1.33432	−	0.609364i	0.0685395	−	0.0313009i	−0.380850	−	0.924637i	$-0.624369\pi$
$379$	1.33432	−	0.609364i	0.0685395	−	0.0313009i	0.449390	+	0.893336i	$0.351641\pi$
$380$		0			0
$381$	1.98173	−	3.87906i	0.101527	−	0.198730i
$382$		0			0
$383$	−5.63794	+	1.65545i	−0.288085	+	0.0845894i	−0.422582	−	0.906325i	$-0.638876\pi$
$383$	−5.63794	+	1.65545i	−0.288085	+	0.0845894i	0.134497	+	0.990914i	$0.457058\pi$
$384$		0			0
$385$	0.101422	+	0.0878829i	0.00516896	+	0.00447893i
$386$		0			0
$387$	−20.7361	−	11.7690i	−1.05407	−	0.598254i
$388$		0			0
$389$	−3.64207	+	7.97502i	−0.184660	+	0.404350i	−0.979210	−	0.202850i	$-0.934980\pi$
$389$	−3.64207	+	7.97502i	−0.184660	+	0.404350i	0.794550	+	0.607199i	$0.207707\pi$
$390$		0			0
$391$	5.62673	−	5.02467i	0.284556	−	0.254109i
$392$		0			0
$393$	7.06014	+	12.1251i	0.356137	+	0.611630i
$394$		0			0
$395$	4.99285	−	4.32633i	0.251218	−	0.217681i
$396$		0			0
$397$	19.1402	−	22.0890i	0.960618	−	1.10861i	−0.0334046	−	0.999442i	$-0.510635\pi$
$397$	19.1402	−	22.0890i	0.960618	−	1.10861i	0.994023	−	0.109171i	$-0.0348195\pi$
$398$		0			0
$399$	−12.7690	−	4.36677i	−0.639251	−	0.218612i
$400$		0			0
$401$	−2.64569	−	18.4012i	−0.132119	−	0.918911i	−0.942785	−	0.333402i	$-0.891804\pi$
$401$	−2.64569	−	18.4012i	−0.132119	−	0.918911i	0.810665	−	0.585510i	$-0.199106\pi$
$402$		0			0
$403$	−2.45317	−	5.37169i	−0.122201	−	0.267583i
$404$		0			0
$405$	5.69787	−	0.628973i	0.283129	−	0.0312539i
$406$		0			0
$407$	−0.266250	−	0.0382809i	−0.0131975	−	0.00189752i
$408$		0			0
$409$	14.8692	−	9.55583i	0.735233	−	0.472505i	−0.118673	−	0.992933i	$-0.537864\pi$
$409$	14.8692	−	9.55583i	0.735233	−	0.472505i	0.853905	+	0.520428i	$0.174228\pi$
$410$		0			0
$411$	−14.1683	−	17.8804i	−0.698870	−	0.881977i
$412$		0			0
$413$	15.0782			0.741951
$414$		0			0
$415$	3.40331			0.167062
$416$		0			0
$417$	7.22850	+	9.12239i	0.353981	+	0.446726i
$418$		0			0
$419$	0.0318643	−	0.0204779i	0.00155667	−	0.00100041i	−0.539862	−	0.841753i	$-0.681524\pi$
$419$	0.0318643	−	0.0204779i	0.00155667	−	0.00100041i	0.541419	+	0.840753i	$0.317887\pi$
$420$		0			0
$421$	17.6185	+	2.53316i	0.858673	+	0.123459i	0.557567	−	0.830132i	$-0.311735\pi$
$421$	17.6185	+	2.53316i	0.858673	+	0.123459i	0.301106	+	0.953591i	$0.402644\pi$
$422$		0			0
$423$	15.1417	+	3.55536i	0.736214	+	0.172868i
$424$		0			0
$425$	3.00208	+	6.57364i	0.145622	+	0.318869i
$426$		0			0
$427$	−3.60035	−	25.0410i	−0.174233	−	1.21182i
$428$		0			0
$429$	0.780823	+	0.267027i	0.0376985	+	0.0128922i
$430$		0			0
$431$	25.8650	−	29.8498i	1.24587	−	1.43782i	0.389853	−	0.920877i	$-0.372526\pi$
$431$	25.8650	−	29.8498i	1.24587	−	1.43782i	0.856022	−	0.516939i	$-0.172929\pi$
$432$		0			0
$433$	−21.6667	+	18.7743i	−1.04124	+	0.902237i	−0.995313	−	0.0967083i	$-0.969169\pi$
$433$	−21.6667	+	18.7743i	−1.04124	+	0.902237i	−0.0459238	+	0.998945i	$0.514623\pi$
$434$		0			0
$435$	2.82283	+	4.84793i	0.135344	+	0.232440i
$436$		0			0
$437$	−15.2368	+	10.1168i	−0.728874	+	0.483952i
$438$		0			0
$439$	1.21471	−	2.65985i	0.0579752	−	0.126948i	−0.878427	−	0.477876i	$-0.841407\pi$
$439$	1.21471	−	2.65985i	0.0579752	−	0.126948i	0.936402	+	0.350928i	$0.114134\pi$
$440$		0			0
$441$	4.18481	−	7.37329i	0.199277	−	0.351109i
$442$		0			0
$443$	20.2053	+	17.5080i	0.959982	+	0.831829i	0.985815	−	0.167837i	$-0.0536784\pi$
$443$	20.2053	+	17.5080i	0.959982	+	0.831829i	−0.0258330	+	0.999666i	$0.508224\pi$
$444$		0			0
$445$	5.09417	−	1.49578i	0.241487	−	0.0709069i
$446$		0			0
$447$	−6.22681	+	12.1884i	−0.294518	+	0.576492i
$448$		0			0
$449$	−24.4965	+	11.1872i	−1.15606	+	0.527956i	−0.898789	−	0.438382i	$-0.855552\pi$
$449$	−24.4965	+	11.1872i	−1.15606	+	0.527956i	−0.257274	+	0.966338i	$0.582824\pi$
$450$		0			0
$451$	−0.215201	+	0.334860i	−0.0101334	+	0.0157679i
$452$		0			0
$453$	−10.4581	+	11.0494i	−0.491363	+	0.519144i
$454$		0			0
$455$	3.25021	+	5.05743i	0.152372	+	0.237096i
$456$		0			0
$457$	−0.423692	+	1.44296i	−0.0198195	+	0.0674989i	−0.968809	−	0.247809i	$-0.920290\pi$
$457$	−0.423692	+	1.44296i	−0.0198195	+	0.0674989i	0.948990	+	0.315308i	$0.102108\pi$
$458$		0			0
$459$	2.21586	−	7.86730i	0.103428	−	0.367214i
$460$		0			0
$461$			17.2006i			0.801112i	0.916272	+	0.400556i	$0.131183\pi$
$461$			17.2006i			0.801112i	−0.916272	+	0.400556i	$0.868817\pi$
$462$		0			0
$463$	23.2816	+	6.83609i	1.08199	+	0.317700i	0.773673	−	0.633585i	$-0.218417\pi$
$463$	23.2816	+	6.83609i	1.08199	+	0.317700i	0.308313	+	0.951285i	$0.400236\pi$
$464$		0			0
$465$	−1.40883	−	0.0619075i	−0.0653329	−	0.00287089i
$466$		0			0
$467$	5.39977	−	37.5562i	0.249872	−	1.73789i	−0.349065	−	0.937098i	$-0.613501\pi$
$467$	5.39977	−	37.5562i	0.249872	−	1.73789i	0.598937	−	0.800796i	$-0.295590\pi$
$468$		0			0
$469$	−7.02580	−	4.51521i	−0.324421	−	0.208493i
$470$		0			0
$471$	−15.2958	−	2.88959i	−0.704792	−	0.133145i
$472$		0			0
$473$	−0.811297	+	0.116647i	−0.0373035	+	0.00536343i
$474$		0			0
$475$	−4.93625	−	16.8113i	−0.226490	−	0.771356i
$476$		0			0
$477$	0.731934	+	0.286780i	0.0335130	+	0.0131308i
$478$		0			0
$479$	−23.5632	−	27.1934i	−1.07663	−	1.24250i	−0.968672	−	0.248342i	$-0.920114\pi$
$479$	−23.5632	−	27.1934i	−1.07663	−	1.24250i	−0.107958	−	0.994155i	$-0.534431\pi$
$480$		0			0
$481$	−10.9609	−	5.00567i	−0.499773	−	0.228239i
$482$		0			0
$483$	6.59964	+	15.6349i	0.300294	+	0.711410i
$484$		0			0
$485$	3.77231	+	1.72276i	0.171292	+	0.0782264i
$486$		0			0
$487$	−10.2030	−	11.7749i	−0.462342	−	0.533571i	0.475924	−	0.879486i	$-0.342114\pi$
$487$	−10.2030	−	11.7749i	−0.462342	−	0.533571i	−0.938266	+	0.345916i	$0.887568\pi$
$488$		0			0
$489$	26.2089	−	6.46058i	1.18521	−	0.292158i
$490$		0			0
$491$	−7.99551	−	27.2302i	−0.360832	−	1.22888i	−0.917362	−	0.398054i	$-0.869686\pi$
$491$	−7.99551	−	27.2302i	−0.360832	−	1.22888i	0.556530	−	0.830828i	$-0.312132\pi$
$492$		0			0
$493$	7.91718	−	1.13832i	0.356572	−	0.0512673i
$494$		0			0
$495$	0.141614	−	0.137036i	0.00636507	−	0.00615930i
$496$		0			0
$497$	−13.1494	−	8.45058i	−0.589829	−	0.379060i
$498$		0			0
$499$	2.71046	−	18.8516i	0.121337	−	0.843915i	−0.834708	−	0.550693i	$-0.814363\pi$
$499$	2.71046	−	18.8516i	0.121337	−	0.843915i	0.956044	−	0.293222i	$-0.0947275\pi$
$500$		0			0
$501$	1.54724	−	35.2106i	0.0691256	−	1.57309i
$502$		0			0
$503$	12.4263	+	3.64870i	0.554062	+	0.162687i	0.546765	−	0.837286i	$-0.315859\pi$
$503$	12.4263	+	3.64870i	0.554062	+	0.162687i	0.00729702	+	0.999973i	$0.497677\pi$
$504$		0			0
$505$		−	7.66320i		−	0.341008i
$506$		0			0
$507$	11.8019	+	8.33872i	0.524141	+	0.370336i
$508$		0			0
$509$	−6.41159	+	21.8359i	−0.284189	+	0.967858i	0.686422	+	0.727203i	$0.259180\pi$
$509$	−6.41159	+	21.8359i	−0.284189	+	0.967858i	−0.970611	+	0.240655i	$0.922638\pi$
$510$		0			0
$511$	4.03076	+	6.27198i	0.178310	+	0.277456i
$512$		0			0
$513$	−8.03217	+	18.1154i	−0.354629	+	0.799816i
$514$		0			0
$515$	−5.13869	+	7.99597i	−0.226438	+	0.352344i
$516$		0			0
$517$	0.486355	−	0.222111i	0.0213899	−	0.00976843i
$518$		0			0
$519$	−31.5846	−	16.1359i	−1.38641	−	0.708289i
$520$		0			0
$521$	−38.8350	+	11.4030i	−1.70139	+	0.499574i	−0.981002	−	0.193997i	$-0.937855\pi$
$521$	−38.8350	+	11.4030i	−1.70139	+	0.499574i	−0.720389	+	0.693570i	$0.756037\pi$
$522$		0			0
$523$	−30.1923	−	26.1617i	−1.32022	−	1.14397i	−0.978971	−	0.203999i	$-0.934606\pi$
$523$	−30.1923	−	26.1617i	−1.32022	−	1.14397i	−0.341245	−	0.939975i	$-0.610848\pi$
$524$		0			0
$525$	−16.1781	+	1.60502i	−0.706071	+	0.0700486i
$526$		0			0
$527$	−0.835256	+	1.82896i	−0.0363843	+	0.0796706i
$528$		0			0
$529$	22.2520	+	5.81783i	0.967480	+	0.252949i
$530$		0			0
$531$	1.94211	−	22.0557i	0.0842804	−	0.957134i
$532$		0			0
$533$	−13.4760	+	11.6770i	−0.583711	+	0.505788i
$534$		0			0
$535$	8.26835	−	9.54218i	0.357472	−	0.412545i
$536$		0			0
$537$	4.54609	−	13.2934i	0.196178	−	0.573651i
$538$		0			0
$539$	−0.0414771	−	0.288479i	−0.00178654	−	0.0124257i
$540$		0			0
$541$	−0.192769	−	0.422104i	−0.00828777	−	0.0181477i	0.905443	−	0.424468i	$-0.139539\pi$
$541$	−0.192769	−	0.422104i	−0.00828777	−	0.0181477i	−0.913731	+	0.406321i	$0.866812\pi$
$542$		0			0
$543$	26.9257	−	10.8947i	1.15549	−	0.467538i
$544$		0			0
$545$	4.91453	+	0.706603i	0.210515	+	0.0302675i
$546$		0			0
$547$	−30.8167	+	19.8047i	−1.31763	+	0.846787i	−0.995013	−	0.0997433i	$-0.968198\pi$
$547$	−30.8167	+	19.8047i	−1.31763	+	0.846787i	−0.322614	+	0.946531i	$0.604561\pi$
$548$		0			0
$549$	−37.0924	+	2.04107i	−1.58307	+	0.0871107i
$550$		0			0
$551$	−19.3925			−0.826146
$552$		0			0
$553$	21.1907			0.901121
$554$		0			0
$555$	−2.25528	+	1.78706i	−0.0957313	+	0.0758566i
$556$		0			0
$557$	−22.8872	+	14.7087i	−0.969762	+	0.623228i	−0.926683	−	0.375843i	$-0.877353\pi$
$557$	−22.8872	+	14.7087i	−0.969762	+	0.623228i	−0.0430789	+	0.999072i	$0.513717\pi$
$558$		0			0
$559$	−36.3435	−	5.22541i	−1.53717	−	0.221011i
$560$		0			0
$561$	−0.105387	−	0.260458i	−0.00444945	−	0.0109966i
$562$		0			0
$563$	−7.51512	−	16.4558i	−0.316725	−	0.693530i	0.682580	−	0.730811i	$-0.260858\pi$
$563$	−7.51512	−	16.4558i	−0.316725	−	0.693530i	−0.999305	+	0.0372806i	$0.988130\pi$
$564$		0			0
$565$	0.973200	+	6.76875i	0.0409428	+	0.284764i
$566$		0			0
$567$	15.1334	+	10.4437i	0.635544	+	0.438594i
$568$		0			0
$569$	5.13183	−	5.92245i	0.215138	−	0.248282i	−0.637915	−	0.770107i	$-0.720203\pi$
$569$	5.13183	−	5.92245i	0.215138	−	0.248282i	0.853053	+	0.521825i	$0.174748\pi$
$570$		0			0
$571$	11.2944	−	9.78668i	0.472657	−	0.409560i	−0.385690	−	0.922628i	$-0.626037\pi$
$571$	11.2944	−	9.78668i	0.472657	−	0.409560i	0.858348	+	0.513068i	$0.171491\pi$
$572$		0			0
$573$	11.4167	−	6.64768i	0.476941	−	0.277711i
$574$		0			0
$575$	−11.6340	+	18.7116i	−0.485173	+	0.780328i
$576$		0			0
$577$	15.2558	−	33.4056i	0.635109	−	1.39070i	−0.268894	−	0.963170i	$-0.586658\pi$
$577$	15.2558	−	33.4056i	0.635109	−	1.39070i	0.904003	−	0.427525i	$-0.140615\pi$
$578$		0			0
$579$	−2.91580	−	29.3905i	−0.121177	−	1.22143i
$580$		0			0
$581$	8.25000	+	7.14866i	0.342267	+	0.296576i
$582$		0			0
$583$	0.0259290	−	0.00761343i	0.00107387	−	0.000315316i
$584$		0			0
$585$	7.81637	−	4.10283i	0.323167	−	0.169631i
$586$		0			0
$587$	16.7069	−	7.62980i	0.689569	−	0.314916i	−0.0396328	−	0.999214i	$-0.512619\pi$
$587$	16.7069	−	7.62980i	0.689569	−	0.314916i	0.729202	+	0.684299i	$0.239892\pi$
$588$		0			0
$589$	2.63552	−	4.10094i	0.108595	−	0.168976i
$590$		0			0
$591$	−29.6381	−	28.0521i	−1.21915	−	1.15391i
$592$		0			0
$593$	−22.1174	−	34.4153i	−0.908251	−	1.41327i	−0.910609	−	0.413269i	$-0.864387\pi$
$593$	−22.1174	−	34.4153i	−0.908251	−	1.41327i	0.00235753	−	0.999997i	$-0.499250\pi$
$594$		0			0
$595$	0.576676	−	1.96398i	0.0236414	−	0.0805153i
$596$		0			0
$597$	0.0706966	−	0.100058i	0.00289342	−	0.00409510i
$598$		0			0
$599$		−	45.1686i		−	1.84554i	−0.385355	−	0.922769i	$-0.625921\pi$
$599$		−	45.1686i		−	1.84554i	0.385355	−	0.922769i	$-0.374079\pi$
$600$		0			0
$601$	20.1974	+	5.93050i	0.823871	+	0.241910i	0.666382	−	0.745611i	$-0.267842\pi$
$601$	20.1974	+	5.93050i	0.823871	+	0.241910i	0.157489	+	0.987521i	$0.449660\pi$
$602$		0			0
$603$	−7.50955	+	9.69541i	−0.305812	+	0.394827i
$604$		0			0
$605$	−0.996145	+	6.92834i	−0.0404991	+	0.281677i
$606$		0			0
$607$	11.3581	+	7.29944i	0.461013	+	0.296275i	0.750456	−	0.660920i	$-0.229834\pi$
$607$	11.3581	+	7.29944i	0.461013	+	0.296275i	−0.289443	+	0.957195i	$0.593470\pi$
$608$		0			0
$609$	−3.34025	+	17.6813i	−0.135354	+	0.716481i
$610$		0			0
$611$	23.7078	−	3.40867i	0.959117	−	0.137900i
$612$		0			0
$613$	11.2844	+	38.4311i	0.455773	+	1.55222i	0.792050	+	0.610456i	$0.209014\pi$
$613$	11.2844	+	38.4311i	0.455773	+	1.55222i	−0.336277	+	0.941763i	$0.609168\pi$
$614$		0			0
$615$	1.01913	+	4.13434i	0.0410952	+	0.166713i
$616$		0			0
$617$	18.0484	+	20.8290i	0.726603	+	0.838545i	0.992085	−	0.125571i	$-0.0400764\pi$
$617$	18.0484	+	20.8290i	0.726603	+	0.838545i	−0.265481	+	0.964116i	$0.585531\pi$
$618$		0			0
$619$	−10.1156	−	4.61963i	−0.406579	−	0.185679i	0.201618	−	0.979464i	$-0.435380\pi$
$619$	−10.1156	−	4.61963i	−0.406579	−	0.185679i	−0.608198	+	0.793786i	$0.708107\pi$
$620$		0			0
$621$	23.7199	−	7.63980i	0.951847	−	0.306575i
$622$		0			0
$623$	15.4907	+	7.07438i	0.620623	+	0.283429i
$624$		0			0
$625$	−12.4942	−	14.4191i	−0.499768	−	0.576763i
$626$		0			0
$627$	0.163040	+	0.661412i	0.00651120	+	0.0264143i
$628$		0			0
$629$	1.15587	+	3.93653i	0.0460876	+	0.156960i
$630$		0			0
$631$	−23.6718	+	3.40350i	−0.942361	+	0.135491i	−0.596337	−	0.802734i	$-0.703378\pi$
$631$	−23.6718	+	3.40350i	−0.942361	+	0.135491i	−0.346024	+	0.938226i	$0.612469\pi$
$632$		0			0
$633$	6.20532	−	32.8473i	0.246639	−	1.30556i
$634$		0			0
$635$	−1.34756	−	0.866026i	−0.0534764	−	0.0343672i
$636$		0			0
$637$	1.85804	−	12.9230i	0.0736183	−	0.512026i
$638$		0			0
$639$	−14.0547	+	18.1457i	−0.555996	+	0.717834i
$640$		0			0
$641$	−1.60949	−	0.472588i	−0.0635709	−	0.0186661i	0.249792	−	0.968299i	$-0.419638\pi$
$641$	−1.60949	−	0.472588i	−0.0635709	−	0.0186661i	−0.313363	+	0.949633i	$0.601456\pi$
$642$		0			0
$643$		−	3.01298i		−	0.118820i	−0.998234	−	0.0594101i	$-0.981078\pi$
$643$		−	3.01298i		−	0.118820i	0.998234	−	0.0594101i	$-0.0189220\pi$
$644$		0			0
$645$	−5.05960	+	7.16093i	−0.199222	+	0.281961i
$646$		0			0
$647$	−1.60800	+	5.47636i	−0.0632171	+	0.215298i	−0.985044	−	0.172305i	$-0.944879\pi$
$647$	−1.60800	+	5.47636i	−0.0632171	+	0.215298i	0.921827	+	0.387603i	$0.126697\pi$
$648$		0			0
$649$	−0.411496	−	0.640300i	−0.0161526	−	0.0251340i
$650$		0			0
$651$	−3.28512	−	3.10933i	−0.128754	−	0.121864i
$652$		0			0
$653$	−14.0872	+	21.9201i	−0.551274	+	0.857799i	−0.999345	−	0.0361994i	$-0.988475\pi$
$653$	−14.0872	+	21.9201i	−0.551274	+	0.857799i	0.448071	+	0.893998i	$0.352111\pi$
$654$		0			0
$655$	4.69340	−	2.14340i	0.183386	−	0.0837498i
$656$		0			0
$657$	9.69349	−	5.08813i	0.378179	−	0.198507i
$658$		0			0
$659$	−6.81122	+	1.99996i	−0.265328	+	0.0779072i	−0.411690	−	0.911324i	$-0.635061\pi$
$659$	−6.81122	+	1.99996i	−0.265328	+	0.0779072i	0.146363	+	0.989231i	$0.453243\pi$
$660$		0			0
$661$	24.4317	+	21.1702i	0.950284	+	0.823426i	0.984391	−	0.175993i	$-0.0563135\pi$
$661$	24.4317	+	21.1702i	0.950284	+	0.823426i	−0.0341077	+	0.999418i	$0.510859\pi$
$662$		0			0
$663$	−1.24261	−	12.5251i	−0.0482589	−	0.486436i
$664$		0			0
$665$	−2.06156	+	4.51419i	−0.0799440	+	0.175053i
$666$		0			0
$667$	16.2435	+	18.1898i	0.628952	+	0.704313i
$668$		0			0
$669$	6.04317	−	3.51879i	0.233642	−	0.136044i
$670$		0			0
$671$	−0.965115	+	0.836277i	−0.0372579	+	0.0322841i
$672$		0			0
$673$	−15.0009	+	17.3120i	−0.578243	+	0.667328i	−0.967226	−	0.253917i	$-0.918281\pi$
$673$	−15.0009	+	17.3120i	−0.578243	+	0.667328i	0.388983	+	0.921245i	$0.372827\pi$
$674$		0			0
$675$	0.263954	+	23.8712i	0.0101596	+	0.918805i
$676$		0			0
$677$	−4.88397	−	33.9688i	−0.187706	−	1.30553i	−0.837928	−	0.545781i	$-0.816233\pi$
$677$	−4.88397	−	33.9688i	−0.187706	−	1.30553i	0.650221	−	0.759745i	$-0.274676\pi$
$678$		0			0
$679$	5.52585	+	12.0999i	0.212063	+	0.464352i
$680$		0			0
$681$	15.0410	+	37.1730i	0.576374	+	1.42447i
$682$		0			0
$683$	44.7456	+	6.43345i	1.71214	+	0.246169i	0.927512	−	0.373794i	$-0.121943\pi$
$683$	44.7456	+	6.43345i	1.71214	+	0.246169i	0.784631	+	0.619963i	$0.212852\pi$
$684$		0			0
$685$	−7.05758	+	4.53563i	−0.269656	+	0.173298i
$686$		0			0
$687$	−27.0501	+	21.4343i	−1.03203	+	0.817769i
$688$		0			0
$689$	1.21057			0.0461191
$690$		0			0
$691$	13.3631			0.508355			0.254177	−	0.967158i	$-0.418195\pi$
$691$	13.3631			0.508355			0.254177	+	0.967158i	$0.418195\pi$
$692$		0			0
$693$	0.631132	−	0.0347291i	0.0239747	−	0.00131925i
$694$		0			0
$695$	3.60070	−	2.31403i	0.136582	−	0.0877761i
$696$		0			0
$697$	6.00942	+	0.864024i	0.227623	+	0.0327272i
$698$		0			0
$699$	2.72756	−	1.10363i	0.103166	−	0.0417431i
$700$		0			0
$701$	2.53732	+	5.55595i	0.0958332	+	0.209845i	0.951477	−	0.307720i	$-0.0995659\pi$
$701$	2.53732	+	5.55595i	0.0958332	+	0.209845i	−0.855644	+	0.517565i	$0.826839\pi$
$702$		0			0
$703$	−1.41560	−	9.84574i	−0.0533905	−	0.371339i
$704$		0			0
$705$	1.85077	−	5.41191i	0.0697041	−	0.203824i
$706$		0			0
$707$	16.0966	−	18.5765i	0.605375	−	0.698640i
$708$		0			0
$709$	−32.2847	+	27.9749i	−1.21248	+	1.05062i	−0.215223	+	0.976565i	$0.569048\pi$
$709$	−32.2847	+	27.9749i	−1.21248	+	1.05062i	−0.997254	+	0.0740529i	$0.976407\pi$
$710$		0			0
$711$	2.72941	−	30.9967i	0.102361	−	1.16247i
$712$		0			0
$713$	−6.05418	+	0.962961i	−0.226731	+	0.0360632i
$714$		0			0
$715$	0.126064	−	0.276042i	0.00471453	−	0.0103234i
$716$		0			0
$717$	25.5114	−	2.53096i	0.952742	−	0.0945205i
$718$		0			0
$719$	32.2772	+	27.9683i	1.20374	+	1.04304i	0.997921	+	0.0644522i	$0.0205300\pi$
$719$	32.2772	+	27.9683i	1.20374	+	1.04304i	0.205815	+	0.978591i	$0.434015\pi$
$720$		0			0
$721$	−29.2523	+	8.58926i	−1.08941	+	0.319881i
$722$		0			0
$723$	22.7465	+	11.6207i	0.845953	+	0.432180i
$724$		0			0
$725$	−21.2510	+	9.70499i	−0.789241	+	0.360434i
$726$		0			0
$727$	−23.5028	+	36.5711i	−0.871671	+	1.35635i	0.0619481	+	0.998079i	$0.480269\pi$
$727$	−23.5028	+	36.5711i	−0.871671	+	1.35635i	−0.933619	+	0.358267i	$0.883368\pi$
$728$		0			0
$729$	17.2257	−	20.7912i	0.637989	−	0.770045i
$730$		0			0
$731$	6.75883	+	10.5169i	0.249984	+	0.388983i
$732$		0			0
$733$	−5.70778	+	19.4389i	−0.210822	+	0.717992i	0.784392	+	0.620266i	$0.212975\pi$
$733$	−5.70778	+	19.4389i	−0.210822	+	0.717992i	−0.995213	+	0.0977265i	$0.968843\pi$
$734$		0			0
$735$	−2.54627	−	1.79908i	−0.0939205	−	0.0663602i
$736$		0			0
$737$			0.421575i			0.0155289i
$738$		0			0
$739$	8.38621	+	2.46241i	0.308492	+	0.0905814i	0.432314	−	0.901723i	$-0.357697\pi$
$739$	8.38621	+	2.46241i	0.308492	+	0.0905814i	−0.123822	+	0.992304i	$0.539515\pi$
$740$		0			0
$741$	−1.33966	+	30.4867i	−0.0492136	+	1.11996i
$742$		0			0
$743$	−4.58372	+	31.8805i	−0.168161	+	1.16958i	0.714522	+	0.699613i	$0.246644\pi$
$743$	−4.58372	+	31.8805i	−0.168161	+	1.16958i	−0.882683	+	0.469969i	$0.844265\pi$
$744$		0			0
$745$	4.23419	+	2.72115i	0.155129	+	0.0996951i
$746$		0			0
$747$	11.5193	−	11.1469i	0.421469	−	0.407844i
$748$		0			0
$749$	40.0868	−	5.76361i	1.46474	−	0.210598i
$750$		0			0
$751$	3.57950	+	12.1907i	0.130618	+	0.444843i	0.998666	−	0.0516367i	$-0.0164438\pi$
$751$	3.57950	+	12.1907i	0.130618	+	0.444843i	−0.868048	+	0.496480i	$0.834626\pi$
$752$		0			0
$753$	14.3165	−	3.52908i	0.521724	−	0.128607i
$754$		0			0
$755$	3.66375	+	4.22819i	0.133337	+	0.153880i
$756$		0			0
$757$	−26.7615	−	12.2216i	−0.972664	−	0.444201i	−0.135275	−	0.990808i	$-0.543192\pi$
$757$	−26.7615	−	12.2216i	−0.972664	−	0.444201i	−0.837389	+	0.546608i	$0.815919\pi$
$758$		0			0
$759$	0.483828	−	0.706942i	0.0175619	−	0.0256604i
$760$		0			0
$761$	20.8926	+	9.54134i	0.757357	+	0.345873i	0.756385	−	0.654126i	$-0.226963\pi$
$761$	20.8926	+	9.54134i	0.757357	+	0.345873i	0.000971515		1.00000i	$0.499691\pi$
$762$		0			0
$763$	10.4292	+	12.0359i	0.377561	+	0.435728i
$764$		0			0
$765$	−2.79853	−	1.09650i	−0.101181	−	0.0396439i
$766$		0			0
$767$	−9.60597	−	32.7149i	−0.346851	−	1.18127i
$768$		0			0
$769$	21.4432	−	3.08306i	0.773261	−	0.111178i	0.255621	−	0.966777i	$-0.417720\pi$
$769$	21.4432	−	3.08306i	0.773261	−	0.111178i	0.517639	+	0.855599i	$0.326811\pi$
$770$		0			0
$771$	40.1652	+	7.58779i	1.44652	+	0.273267i
$772$		0			0
$773$	−37.7994	−	24.2922i	−1.35955	−	0.873729i	−0.361276	−	0.932459i	$-0.617659\pi$
$773$	−37.7994	−	24.2922i	−1.35955	−	0.873729i	−0.998274	+	0.0587296i	$0.981295\pi$
$774$		0			0
$775$	0.835770	−	5.81291i	0.0300218	−	0.208806i
$776$		0			0
$777$	−9.22079	−	0.405184i	−0.330794	−	0.0145359i
$778$		0			0
$779$	−14.1233	−	4.14698i	−0.506020	−	0.148581i
$780$		0			0
$781$			0.789012i			0.0282331i
$782$		0			0
$783$	25.4330	+	7.16333i	0.908902	+	0.255996i
$784$		0			0
$785$	−1.61273	+	5.49246i	−0.0575609	+	0.196034i
$786$		0			0
$787$	7.16576	+	11.1501i	0.255432	+	0.397460i	0.945159	−	0.326609i	$-0.105906\pi$
$787$	7.16576	+	11.1501i	0.255432	+	0.397460i	−0.689728	+	0.724069i	$0.742270\pi$
$788$		0			0
$789$	−1.38663	+	1.46503i	−0.0493655	+	0.0521566i
$790$		0			0
$791$	−11.8587	+	18.4524i	−0.421645	+	0.656093i
$792$		0			0
$793$	−52.0372	+	23.7646i	−1.84790	+	0.843906i
$794$		0			0
$795$	0.131518	−	0.257434i	0.00466445	−	0.00913024i
$796$		0			0
$797$	40.8373	−	11.9909i	1.44653	−	0.424740i	0.538139	−	0.842856i	$-0.319128\pi$
$797$	40.8373	−	11.9909i	1.44653	−	0.424740i	0.908394	+	0.418116i	$0.137309\pi$
$798$		0			0
$799$	−6.16319	−	5.34043i	−0.218038	−	0.188931i
$800$		0			0
$801$	12.3433	−	21.7478i	0.436128	−	0.768422i
$802$		0			0
$803$	0.156339	−	0.342334i	0.00551707	−	0.0120807i
$804$		0			0
$805$	5.96105	−	1.84747i	0.210099	−	0.0651146i
$806$		0			0
$807$	−9.36936	−	16.0909i	−0.329817	−	0.566428i
$808$		0			0
$809$	−37.9129	+	32.8517i	−1.33295	+	1.15501i	−0.357713	+	0.933832i	$0.616443\pi$
$809$	−37.9129	+	32.8517i	−1.33295	+	1.15501i	−0.975234	+	0.221174i	$0.929011\pi$
$810$		0			0
$811$	−22.6744	+	26.1676i	−0.796206	+	0.918870i	−0.998167	−	0.0605233i	$-0.980723\pi$
$811$	−22.6744	+	26.1676i	−0.796206	+	0.918870i	0.201961	+	0.979394i	$0.435269\pi$
$812$		0			0
$813$	11.7992	+	4.03511i	0.413816	+	0.141517i
$814$		0			0
$815$	−1.41269	−	9.82549i	−0.0494845	−	0.344172i
$816$		0			0
$817$	−12.5911	−	27.5707i	−0.440507	−	0.964576i
$818$		0			0
$819$	27.5658	+	6.47261i	0.963226	+	0.226171i
$820$		0			0
$821$	33.7191	+	4.84808i	1.17681	+	0.169199i	0.702842	−	0.711346i	$-0.251914\pi$
$821$	33.7191	+	4.84808i	1.17681	+	0.169199i	0.473963	+	0.880545i	$0.342823\pi$
$822$		0			0
$823$	−8.31892	+	5.34625i	−0.289979	+	0.186358i	−0.677540	−	0.735486i	$-0.736954\pi$
$823$	−8.31892	+	5.34625i	−0.289979	+	0.186358i	0.387561	+	0.921844i	$0.373318\pi$
$824$		0			0
$825$	0.509670	+	0.643205i	0.0177444	+	0.0223935i
$826$		0			0
$827$	35.6621			1.24009			0.620046	−	0.784565i	$-0.287114\pi$
$827$	35.6621			1.24009			0.620046	+	0.784565i	$0.287114\pi$
$828$		0			0
$829$	−22.8738			−0.794439			−0.397220	−	0.917724i	$-0.630025\pi$
$829$	−22.8738			−0.794439			−0.397220	+	0.917724i	$0.630025\pi$
$830$		0			0
$831$	16.5032	+	20.8271i	0.572491	+	0.722485i
$832$		0			0
$833$	−3.73959	+	2.40329i	−0.129569	+	0.0832691i
$834$		0			0
$835$	−12.8289	−	1.84451i	−0.443961	−	0.0638320i
$836$		0			0
$837$	−4.97129	+	4.40482i	−0.171833	+	0.152253i
$838$		0			0
$839$	−8.20754	−	17.9720i	−0.283356	−	0.620463i	0.713417	−	0.700740i	$-0.247147\pi$
$839$	−8.20754	−	17.9720i	−0.283356	−	0.620463i	−0.996773	+	0.0802772i	$0.974419\pi$
$840$		0			0
$841$	−0.447230	−	3.11055i	−0.0154217	−	0.107260i
$842$		0			0
$843$	−29.1527	−	9.96967i	−1.00407	−	0.343374i
$844$		0			0
$845$	3.47996	−	4.01608i	0.119714	−	0.138157i
$846$		0			0
$847$	−16.9678	+	14.7027i	−0.583020	+	0.505190i
$848$		0			0
$849$	−25.8711	−	44.4311i	−0.887895	−	1.52487i
$850$		0			0
$851$	−8.04941	+	9.57481i	−0.275930	+	0.328220i
$852$		0			0
$853$	−14.3247	+	31.3667i	−0.490469	+	1.07398i	0.488982	+	0.872294i	$0.337368\pi$
$853$	−14.3247	+	31.3667i	−0.490469	+	1.07398i	−0.979451	+	0.201683i	$0.935359\pi$
$854$		0			0
$855$	6.33759	+	3.59698i	0.216741	+	0.123014i
$856$		0			0
$857$	6.61888	+	5.73529i	0.226097	+	0.195914i	0.760541	−	0.649290i	$-0.224934\pi$
$857$	6.61888	+	5.73529i	0.226097	+	0.195914i	−0.534445	+	0.845204i	$0.679479\pi$
$858$		0			0
$859$	30.8330	−	9.05337i	1.05201	−	0.308897i	0.290379	−	0.956912i	$-0.406219\pi$
$859$	30.8330	−	9.05337i	1.05201	−	0.308897i	0.761628	+	0.648015i	$0.224400\pi$
$860$		0			0
$861$	−6.21372	+	12.1628i	−0.211763	+	0.414507i
$862$		0			0
$863$	38.7548	−	17.6987i	1.31923	−	0.602471i	0.373560	−	0.927606i	$-0.378137\pi$
$863$	38.7548	−	17.6987i	1.31923	−	0.602471i	0.945668	+	0.325135i	$0.105410\pi$
$864$		0			0
$865$	−7.05149	+	10.9723i	−0.239758	+	0.373070i
$866$		0			0
$867$	17.2947	−	18.2726i	0.587359	−	0.620568i
$868$		0			0
$869$	−0.578310	−	0.899868i	−0.0196178	−	0.0305259i
$870$		0			0
$871$	−5.32059	+	18.1203i	−0.180281	+	0.613981i
$872$		0			0
$873$	18.4109	−	6.52443i	0.623114	−	0.220818i
$874$		0			0
$875$			12.4850i			0.422069i
$876$		0			0
$877$	29.8035	+	8.75111i	1.00639	+	0.295504i	0.743077	−	0.669206i	$-0.233365\pi$
$877$	29.8035	+	8.75111i	1.00639	+	0.295504i	0.263317	+	0.964709i	$0.415184\pi$
$878$		0			0
$879$	−57.7602	−	2.53813i	−1.94820	−	0.0856089i
$880$		0			0
$881$	5.02807	−	34.9710i	0.169400	−	1.17820i	−0.710729	−	0.703466i	$-0.751635\pi$
$881$	5.02807	−	34.9710i	0.169400	−	1.17820i	0.880128	−	0.474736i	$-0.157456\pi$
$882$		0			0
$883$	39.0268	+	25.0810i	1.31336	+	0.844042i	0.994599	−	0.103795i	$-0.0330984\pi$
$883$	39.0268	+	25.0810i	1.31336	+	0.844042i	0.318756	+	0.947837i	$0.396735\pi$
$884$		0			0
$885$	−8.00058	−	1.51143i	−0.268937	−	0.0508060i
$886$		0			0
$887$	−31.6407	+	4.54925i	−1.06239	+	0.152749i	−0.651281	−	0.758837i	$-0.725768\pi$
$887$	−31.6407	+	4.54925i	−1.06239	+	0.152749i	−0.411111	+	0.911585i	$0.634859\pi$
$888$		0			0
$889$	−1.44755	−	4.92991i	−0.0485493	−	0.165344i
$890$		0			0
$891$	0.0304914	−	0.927660i	0.00102150	−	0.0310778i
$892$		0			0
$893$	12.9478	+	14.9426i	0.433281	+	0.500033i
$894$		0			0
$895$	−4.69956	−	2.14622i	−0.157089	−	0.0717401i
$896$		0			0
$897$	29.7181	−	24.2797i	0.992260	−	0.810675i
$898$		0			0
$899$	−5.91256	−	2.70018i	−0.197195	−	0.0900559i
$900$		0			0
$901$	−0.269918	−	0.311502i	−0.00899228	−	0.0103776i
$902$		0			0
$903$	−27.3066	+	6.73118i	−0.908707	+	0.223999i
$904$		0			0
$905$	−3.00931	−	10.2488i	−0.100033	−	0.340681i
$906$		0			0
$907$	−49.5014	+	7.11722i	−1.64367	+	0.236323i	−0.901151	−	0.433506i	$-0.857276\pi$
$907$	−49.5014	+	7.11722i	−1.64367	+	0.236323i	−0.742515	+	0.669829i	$0.766367\pi$
$908$		0			0
$909$	−25.0994	−	25.9380i	−0.832495	−	0.860308i
$910$		0			0
$911$	−20.3195	−	13.0586i	−0.673216	−	0.432650i	0.158867	−	0.987300i	$-0.449216\pi$
$911$	−20.3195	−	13.0586i	−0.673216	−	0.432650i	−0.832084	+	0.554650i	$0.812852\pi$
$912$		0			0
$913$	0.0784210	−	0.545430i	0.00259536	−	0.0180511i
$914$		0			0
$915$	−0.599717	+	13.6478i	−0.0198260	+	0.451182i
$916$		0			0
$917$	15.8796	+	4.66266i	0.524389	+	0.153975i
$918$		0			0
$919$			57.5731i			1.89916i	0.313524	+	0.949580i	$0.398490\pi$
$919$			57.5731i			1.89916i	−0.313524	+	0.949580i	$0.601510\pi$
$920$		0			0
$921$	22.0134	+	15.5537i	0.725365	+	0.512511i
$922$		0			0
$923$	−9.95791	+	33.9135i	−0.327769	+	1.11628i
$924$		0			0
$925$	−6.47859	−	10.0809i	−0.213015	−	0.331457i
$926$		0			0
$927$	8.79615	+	43.8951i	0.288904	+	1.44170i
$928$		0			0
$929$	−24.6215	+	38.3117i	−0.807804	+	1.25697i	0.155308	+	0.987866i	$0.450363\pi$
$929$	−24.6215	+	38.3117i	−0.807804	+	1.25697i	−0.963112	+	0.269101i	$0.913273\pi$
$930$		0			0
$931$	9.80353	−	4.47712i	0.321298	−	0.146732i
$932$		0			0
$933$	−5.03002	−	2.56974i	−0.164676	−	0.0841294i
$934$		0			0
$935$	−0.0991387	+	0.0291097i	−0.00324218	+	0.000951991i
$936$		0			0
$937$	27.8898	+	24.1667i	0.911121	+	0.789491i	0.978072	−	0.208265i	$-0.0667817\pi$
$937$	27.8898	+	24.1667i	0.911121	+	0.789491i	−0.0669512	+	0.997756i	$0.521327\pi$
$938$		0			0
$939$	−38.3996	+	3.80958i	−1.25312	+	0.124321i
$940$		0			0
$941$	10.1644	−	22.2569i	0.331350	−	0.725555i	−0.668485	−	0.743725i	$-0.733057\pi$
$941$	10.1644	−	22.2569i	0.331350	−	0.725555i	0.999835	+	0.0181708i	$0.00578426\pi$
$942$		0			0
$943$	7.94018	+	16.7210i	0.258568	+	0.544512i
$944$		0			0
$945$	4.37120	−	5.15880i	0.142195	−	0.167816i
$946$		0			0
$947$	3.37175	−	2.92164i	0.109567	−	0.0949405i	−0.598354	−	0.801232i	$-0.704178\pi$
$947$	3.37175	−	2.92164i	0.109567	−	0.0949405i	0.707922	+	0.706291i	$0.249633\pi$
$948$		0			0
$949$	11.0403	−	12.7412i	0.358383	−	0.413596i
$950$		0			0
$951$	3.66851	−	10.7272i	0.118960	−	0.347854i
$952$		0			0
$953$	−3.90979	−	27.1932i	−0.126650	−	0.880873i	−0.949758	−	0.312987i	$-0.898671\pi$
$953$	−3.90979	−	27.1932i	−0.126650	−	0.880873i	0.823107	−	0.567886i	$-0.192239\pi$
$954$		0			0
$955$	−2.01819	−	4.41921i	−0.0653070	−	0.143002i
$956$		0			0
$957$	0.841997	−	0.340691i	0.0272179	−	0.0110130i
$958$		0			0
$959$	−26.6355	−	3.82960i	−0.860105	−	0.123664i
$960$		0			0
$961$	−24.7043	+	15.8765i	−0.796913	+	0.512145i
$962$		0			0
$963$	−3.26744	−	59.3793i	−0.105292	−	1.91347i
$964$		0			0
$965$	−10.8611			−0.349631
$966$		0			0
$967$	31.9290			1.02677			0.513384	−	0.858159i	$-0.328392\pi$
$967$	31.9290			1.02677			0.513384	+	0.858159i	$0.328392\pi$
$968$		0			0
$969$	8.14347	−	6.45281i	0.261606	−	0.207294i
$970$		0			0
$971$	43.9483	−	28.2438i	1.41037	−	0.906388i	0.410382	−	0.911914i	$-0.365395\pi$
$971$	43.9483	−	28.2438i	1.41037	−	0.906388i	0.999985	+	0.00552624i	$0.00175906\pi$
$972$		0			0
$973$	13.5891	+	1.95382i	0.435647	+	0.0626366i
$974$		0			0
$975$	13.7891	+	34.0788i	0.441603	+	1.09140i
$976$		0			0
$977$	−7.86500	−	17.2219i	−0.251624	−	0.550979i	0.741100	−	0.671395i	$-0.234304\pi$
$977$	−7.86500	−	17.2219i	−0.251624	−	0.550979i	−0.992724	+	0.120416i	$0.961577\pi$
$978$		0			0
$979$	−0.122338	−	0.850883i	−0.00390995	−	0.0271943i
$980$		0			0
$981$	18.9488	−	13.7050i	0.604987	−	0.437566i
$982$		0			0
$983$	−34.4214	+	39.7244i	−1.09787	+	1.26701i	−0.136836	+	0.990594i	$0.543693\pi$
$983$	−34.4214	+	39.7244i	−1.09787	+	1.26701i	−0.961037	+	0.276419i	$0.910852\pi$
$984$		0			0
$985$	−11.3414	+	9.82741i	−0.361368	+	0.313127i
$986$		0			0
$987$	15.8542	−	9.23151i	0.504645	−	0.293842i
$988$		0			0
$989$	−15.3143	+	34.9040i	−0.486967	+	1.10988i
$990$		0			0
$991$	1.61549	−	3.53743i	0.0513177	−	0.112370i	−0.882236	−	0.470807i	$-0.843963\pi$
$991$	1.61549	−	3.53743i	0.0513177	−	0.112370i	0.933554	+	0.358437i	$0.116690\pi$
$992$		0			0
$993$	−3.43327	−	34.6064i	−0.108951	−	1.09820i
$994$		0			0
$995$	−0.0340488	−	0.0295034i	−0.00107942	−	0.000935322i
$996$		0			0
$997$	−26.7271	+	7.84778i	−0.846455	+	0.248542i	−0.676071	−	0.736836i	$-0.736319\pi$
$997$	−26.7271	+	7.84778i	−0.846455	+	0.248542i	−0.170384	+	0.985378i	$0.554501\pi$
$998$		0			0
$999$	−1.78034	+	13.4355i	−0.0563275	+	0.425080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.u.a.17.7	yes	240
3.2	odd	2	inner	552.2.u.a.17.2	✓	240
23.19	odd	22	inner	552.2.u.a.65.2	yes	240
69.65	even	22	inner	552.2.u.a.65.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.u.a.17.2	✓	240	3.2	odd	2	inner
552.2.u.a.17.7	yes	240	1.1	even	1	trivial
552.2.u.a.65.2	yes	240	23.19	odd	22	inner
552.2.u.a.65.7	yes	240	69.65	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07569 - 1.35753i) q^{3} +(-0.535830 + 0.344357i) q^{5} +(-2.02223 - 0.290753i) q^{7} +(-0.685767 + 2.92057i) q^{9} +O(q^{10})\)	\(q+(-1.07569 - 1.35753i) q^{3} +(-0.535830 + 0.344357i) q^{5} +(-2.02223 - 0.290753i) q^{7} +(-0.685767 + 2.92057i) q^{9} +(0.0428413 + 0.0938095i) q^{11} +(0.657474 + 4.57283i) q^{13} +(1.04386 + 0.356982i) q^{15} +(1.03008 - 1.18877i) q^{17} +(-2.88216 + 2.49740i) q^{19} +(1.78060 + 3.05800i) q^{21} +(4.75668 + 0.611543i) q^{23} +(-1.90854 + 4.17913i) q^{25} +(4.70243 - 2.21069i) q^{27} +(3.84300 + 3.32998i) q^{29} +(-1.22648 + 0.360126i) q^{31} +(0.0812649 - 0.159069i) q^{33} +(1.18370 - 0.540576i) q^{35} +(-1.41013 + 2.19421i) q^{37} +(5.50051 - 5.81150i) q^{39} +(2.08672 + 3.24700i) q^{41} +(-2.23913 + 7.62577i) q^{43} +(-0.638263 - 1.80108i) q^{45} -5.18450i q^{47} +(-2.71156 - 0.796185i) q^{49} +(-2.72184 - 0.119604i) q^{51} +(0.0372918 - 0.259370i) q^{53} +(-0.0552596 - 0.0355132i) q^{55} +(6.49062 + 1.22617i) q^{57} +(-7.30521 + 1.05033i) q^{59} +(3.48865 + 11.8813i) q^{61} +(2.23595 - 5.70669i) q^{63} +(-1.92698 - 2.22385i) q^{65} +(3.71843 + 1.69815i) q^{67} +(-4.28654 - 7.11516i) q^{69} +(6.95935 + 3.17823i) q^{71} +(-2.38975 - 2.75792i) q^{73} +(7.72629 - 1.90456i) q^{75} +(-0.0593598 - 0.202161i) q^{77} +(-10.2666 + 1.47612i) q^{79} +(-8.05945 - 4.00566i) q^{81} +(-4.49498 - 2.88875i) q^{83} +(-0.142584 + 0.991693i) q^{85} +(0.386651 - 8.79903i) q^{87} +(-7.99786 - 2.34838i) q^{89} -9.43850i q^{91} +(1.80819 + 1.27759i) q^{93} +(0.684348 - 2.33067i) q^{95} +(-3.52007 - 5.47733i) q^{97} +(-0.303356 + 0.0607896i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^9	\( 240 q - 4 q^{9} - 16 q^{25} + 12 q^{27} - 8 q^{31} + 44 q^{37} + 20 q^{39} + 44 q^{43} + 124 q^{49} + 12 q^{55} + 16 q^{69} - 74 q^{75} - 144 q^{81} + 24 q^{85} - 170 q^{87} + 12 q^{93} - 198 q^{99}+O(q^{100}) \) 240 * q - 4 * q^9 - 16 * q^25 + 12 * q^27 - 8 * q^31 + 44 * q^37 + 20 * q^39 + 44 * q^43 + 124 * q^49 + 12 * q^55 + 16 * q^69 - 74 * q^75 - 144 * q^81 + 24 * q^85 - 170 * q^87 + 12 * q^93 - 198 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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