LMFDB - Embedded newform 512.2.k.a.497.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [512,2,Mod(17,512)] 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("512.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(512, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.k (of order $32$, degree $16$, 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			497.6
Character	$\chi$	$=$	512.497
Dual form			512.2.k.a.273.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.662806 + 0.354277i) q^{3} +(1.65900 + 2.02149i) q^{5} +(-2.34874 + 1.56938i) q^{7} +(-1.35291 + 2.02477i) q^{9} +(-2.03348 + 0.616848i) q^{11} +(-4.90337 - 4.02409i) q^{13} +(-1.81576 - 0.752114i) q^{15} +(1.80120 - 0.746080i) q^{17} +(-0.242682 - 2.46399i) q^{19} +(1.00077 - 1.87230i) q^{21} +(-1.97111 + 0.392078i) q^{23} +(-0.358715 + 1.80338i) q^{25} +(0.400380 - 4.06513i) q^{27} +(-2.60500 + 8.58752i) q^{29} +(6.20175 + 6.20175i) q^{31} +(1.12927 - 1.12927i) q^{33} +(-7.06905 - 2.14437i) q^{35} +(-8.13891 - 0.801613i) q^{37} +(4.67563 + 0.930040i) q^{39} +(-0.230739 - 1.16000i) q^{41} +(-2.87481 - 1.53662i) q^{43} +(-6.33755 + 0.624194i) q^{45} +(4.04912 + 9.77544i) q^{47} +(0.374856 - 0.904982i) q^{49} +(-0.929525 + 1.13263i) q^{51} +(1.25840 + 4.14840i) q^{53} +(-4.62049 - 3.08731i) q^{55} +(1.03379 + 1.54717i) q^{57} +(3.50126 - 2.87341i) q^{59} +(0.456134 + 0.853366i) q^{61} -6.87891i q^{63} -16.5881i q^{65} +(4.42900 + 8.28608i) q^{67} +(1.16756 - 0.958191i) q^{69} +(0.382894 + 0.573041i) q^{71} +(6.49235 + 4.33805i) q^{73} +(-0.401139 - 1.32238i) q^{75} +(3.80804 - 4.64011i) q^{77} +(-6.04837 + 14.6020i) q^{79} +(-1.62090 - 3.91319i) q^{81} +(1.78064 - 0.175377i) q^{83} +(4.49638 + 2.40336i) q^{85} +(-1.31576 - 6.61475i) q^{87} +(0.612417 + 0.121817i) q^{89} +(17.8321 + 1.75631i) q^{91} +(-6.30769 - 1.91342i) q^{93} +(4.57834 - 4.57834i) q^{95} +(8.11888 + 8.11888i) q^{97} +(1.50213 - 4.95187i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{9}{32}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.662806	+	0.354277i	−0.382671	+	0.204542i	−0.651505	−	0.758645i	$-0.725862\pi$
$3$	−0.662806	+	0.354277i	−0.382671	+	0.204542i	0.268833	+	0.963187i	$0.413362\pi$
$4$		0			0
$5$	1.65900	+	2.02149i	0.741926	+	0.904040i	0.998038	−	0.0626073i	$-0.0199416\pi$
$5$	1.65900	+	2.02149i	0.741926	+	0.904040i	−0.256112	+	0.966647i	$0.582442\pi$
$6$		0			0
$7$	−2.34874	+	1.56938i	−0.887741	+	0.593170i	−0.913653	−	0.406494i	$-0.866751\pi$
$7$	−2.34874	+	1.56938i	−0.887741	+	0.593170i	0.0259119	+	0.999664i	$0.491751\pi$
$8$		0			0
$9$	−1.35291	+	2.02477i	−0.450970	+	0.674925i
$10$		0			0
$11$	−2.03348	+	0.616848i	−0.613116	+	0.185987i	−0.581544	−	0.813515i	$-0.697551\pi$
$11$	−2.03348	+	0.616848i	−0.613116	+	0.185987i	−0.0315719	+	0.999501i	$0.510051\pi$
$12$		0			0
$13$	−4.90337	−	4.02409i	−1.35995	−	1.11608i	−0.981712	−	0.190373i	$-0.939030\pi$
$13$	−4.90337	−	4.02409i	−1.35995	−	1.11608i	−0.378238	−	0.925708i	$-0.623470\pi$
$14$		0			0
$15$	−1.81576	−	0.752114i	−0.468828	−	0.194195i
$16$		0			0
$17$	1.80120	−	0.746080i	0.436854	−	0.180951i	−0.153407	−	0.988163i	$-0.549025\pi$
$17$	1.80120	−	0.746080i	0.436854	−	0.180951i	0.590262	+	0.807212i	$0.299025\pi$
$18$		0			0
$19$	−0.242682	−	2.46399i	−0.0556751	−	0.565278i	−0.982043	−	0.188658i	$-0.939586\pi$
$19$	−0.242682	−	2.46399i	−0.0556751	−	0.565278i	0.926368	−	0.376620i	$-0.122914\pi$
$20$		0			0
$21$	1.00077	−	1.87230i	0.218385	−	0.408570i
$22$		0			0
$23$	−1.97111	+	0.392078i	−0.411005	+	0.0817539i	−0.396262	−	0.918137i	$-0.629693\pi$
$23$	−1.97111	+	0.392078i	−0.411005	+	0.0817539i	−0.0147426	+	0.999891i	$0.504693\pi$
$24$		0			0
$25$	−0.358715	+	1.80338i	−0.0717431	+	0.360677i
$26$		0			0
$27$	0.400380	−	4.06513i	0.0770532	−	0.782334i
$28$		0			0
$29$	−2.60500	+	8.58752i	−0.483736	+	1.59466i	0.287280	+	0.957847i	$0.407249\pi$
$29$	−2.60500	+	8.58752i	−0.483736	+	1.59466i	−0.771016	+	0.636816i	$0.780251\pi$
$30$		0			0
$31$	6.20175	+	6.20175i	1.11387	+	1.11387i	0.992623	+	0.121244i	$0.0386883\pi$
$31$	6.20175	+	6.20175i	1.11387	+	1.11387i	0.121244	+	0.992623i	$0.461312\pi$
$32$		0			0
$33$	1.12927	−	1.12927i	0.196580	−	0.196580i
$34$		0			0
$35$	−7.06905	−	2.14437i	−1.19489	−	0.362465i
$36$		0			0
$37$	−8.13891	−	0.801613i	−1.33803	−	0.131784i	−0.596450	−	0.802650i	$-0.703423\pi$
$37$	−8.13891	−	0.801613i	−1.33803	−	0.131784i	−0.741579	+	0.670866i	$0.765923\pi$
$38$		0			0
$39$	4.67563	+	0.930040i	0.748699	+	0.148926i
$40$		0			0
$41$	−0.230739	−	1.16000i	−0.0360353	−	0.181162i	0.958576	−	0.284837i	$-0.0919396\pi$
$41$	−0.230739	−	1.16000i	−0.0360353	−	0.181162i	−0.994611	+	0.103676i	$0.966940\pi$
$42$		0			0
$43$	−2.87481	−	1.53662i	−0.438405	−	0.234332i	0.237401	−	0.971412i	$-0.423704\pi$
$43$	−2.87481	−	1.53662i	−0.438405	−	0.234332i	−0.675806	+	0.737079i	$0.736204\pi$
$44$		0			0
$45$	−6.33755	+	0.624194i	−0.944746	+	0.0930493i
$46$		0			0
$47$	4.04912	+	9.77544i	0.590625	+	1.42589i	0.882900	+	0.469560i	$0.155588\pi$
$47$	4.04912	+	9.77544i	0.590625	+	1.42589i	−0.292275	+	0.956334i	$0.594412\pi$
$48$		0			0
$49$	0.374856	−	0.904982i	0.0535508	−	0.129283i
$50$		0			0
$51$	−0.929525	+	1.13263i	−0.130160	+	0.158600i
$52$		0			0
$53$	1.25840	+	4.14840i	0.172855	+	0.569826i	0.999970	+	0.00779304i	$0.00248063\pi$
$53$	1.25840	+	4.14840i	0.172855	+	0.569826i	−0.827115	+	0.562033i	$0.810019\pi$
$54$		0			0
$55$	−4.62049	−	3.08731i	−0.623027	−	0.416293i
$56$		0			0
$57$	1.03379	+	1.54717i	0.136928	+	0.204928i
$58$		0			0
$59$	3.50126	−	2.87341i	0.455825	−	0.374086i	−0.378280	−	0.925691i	$-0.623484\pi$
$59$	3.50126	−	2.87341i	0.455825	−	0.374086i	0.834105	+	0.551605i	$0.185984\pi$
$60$		0			0
$61$	0.456134	+	0.853366i	0.0584019	+	0.109262i	0.909429	−	0.415860i	$-0.136519\pi$
$61$	0.456134	+	0.853366i	0.0584019	+	0.109262i	−0.851027	+	0.525123i	$0.824019\pi$
$62$		0			0
$63$		−	6.87891i		−	0.866661i
$64$		0			0
$65$		−	16.5881i		−	2.05750i
$66$		0			0
$67$	4.42900	+	8.28608i	0.541089	+	1.01231i	0.992759	+	0.120121i	$0.0383282\pi$
$67$	4.42900	+	8.28608i	0.541089	+	1.01231i	−0.451671	+	0.892185i	$0.649172\pi$
$68$		0			0
$69$	1.16756	−	0.958191i	0.140558	−	0.115353i
$70$		0			0
$71$	0.382894	+	0.573041i	0.0454411	+	0.0680074i	0.853495	−	0.521102i	$-0.174479\pi$
$71$	0.382894	+	0.573041i	0.0454411	+	0.0680074i	−0.808053	+	0.589109i	$0.799479\pi$
$72$		0			0
$73$	6.49235	+	4.33805i	0.759872	+	0.507730i	0.874113	−	0.485723i	$-0.161444\pi$
$73$	6.49235	+	4.33805i	0.759872	+	0.507730i	−0.114241	+	0.993453i	$0.536444\pi$
$74$		0			0
$75$	−0.401139	−	1.32238i	−0.0463196	−	0.152695i
$76$		0			0
$77$	3.80804	−	4.64011i	0.433967	−	0.528790i
$78$		0			0
$79$	−6.04837	+	14.6020i	−0.680494	+	1.64286i	0.0826092	+	0.996582i	$0.473675\pi$
$79$	−6.04837	+	14.6020i	−0.680494	+	1.64286i	−0.763103	+	0.646276i	$0.776325\pi$
$80$		0			0
$81$	−1.62090	−	3.91319i	−0.180100	−	0.434799i
$82$		0			0
$83$	1.78064	−	0.175377i	0.195450	−	0.0192502i	0.000181674	−	1.00000i	$-0.499942\pi$
$83$	1.78064	−	0.175377i	0.195450	−	0.0192502i	0.195269	+	0.980750i	$0.437442\pi$
$84$		0			0
$85$	4.49638	+	2.40336i	0.487701	+	0.260681i
$86$		0			0
$87$	−1.31576	−	6.61475i	−0.141064	−	0.709176i
$88$		0			0
$89$	0.612417	+	0.121817i	0.0649161	+	0.0129126i	0.227442	−	0.973792i	$-0.426964\pi$
$89$	0.612417	+	0.121817i	0.0649161	+	0.0129126i	−0.162525	+	0.986704i	$0.551964\pi$
$90$		0			0
$91$	17.8321	+	1.75631i	1.86931	+	0.184111i
$92$		0			0
$93$	−6.30769	−	1.91342i	−0.654077	−	0.198412i
$94$		0			0
$95$	4.57834	−	4.57834i	0.469727	−	0.469727i
$96$		0			0
$97$	8.11888	+	8.11888i	0.824347	+	0.824347i	0.986728	−	0.162381i	$-0.0519173\pi$
$97$	8.11888	+	8.11888i	0.824347	+	0.824347i	−0.162381	+	0.986728i	$0.551917\pi$
$98$		0			0
$99$	1.50213	−	4.95187i	0.150970	−	0.497682i
$100$		0			0
$101$	0.190851	−	1.93774i	0.0189904	−	0.192813i	−0.981009	−	0.193963i	$-0.937866\pi$
$101$	0.190851	−	1.93774i	0.0189904	−	0.192813i	0.999999	+	0.00114974i	$0.000365975\pi$
$102$		0			0
$103$	2.08681	−	10.4911i	0.205619	−	1.03372i	−0.730735	−	0.682661i	$-0.760822\pi$
$103$	2.08681	−	10.4911i	0.205619	−	1.03372i	0.936354	−	0.351057i	$-0.114178\pi$
$104$		0			0
$105$	5.44511	−	1.08310i	0.531389	−	0.105700i
$106$		0			0
$107$	9.60487	−	17.9694i	0.928537	−	1.73717i	0.311481	−	0.950252i	$-0.399175\pi$
$107$	9.60487	−	17.9694i	0.928537	−	1.73717i	0.617056	−	0.786919i	$-0.288325\pi$
$108$		0			0
$109$	0.174883	+	1.77562i	0.0167507	+	0.170073i	0.999920	−	0.0126221i	$-0.00401785\pi$
$109$	0.174883	+	1.77562i	0.0167507	+	0.170073i	−0.983170	+	0.182695i	$0.941518\pi$
$110$		0			0
$111$	5.67851	−	2.35212i	0.538981	−	0.223253i
$112$		0			0
$113$	4.85955	+	2.01289i	0.457148	+	0.189357i	0.599361	−	0.800479i	$-0.295422\pi$
$113$	4.85955	+	2.01289i	0.457148	+	0.189357i	−0.142212	+	0.989836i	$0.545422\pi$
$114$		0			0
$115$	−4.06265	−	3.33413i	−0.378844	−	0.310909i
$116$		0			0
$117$	14.7817	−	4.48398i	1.36657	−	0.414544i
$118$		0			0
$119$	−3.05966	+	4.57911i	−0.280479	+	0.419766i
$120$		0			0
$121$	−5.39164	+	3.60258i	−0.490149	+	0.327507i
$122$		0			0
$123$	0.563897	+	0.687111i	0.0508449	+	0.0619547i
$124$		0			0
$125$	7.29089	−	3.89706i	0.652117	−	0.348564i
$126$		0			0
$127$	−8.50965			−0.755109			−0.377555	−	0.925987i	$-0.623235\pi$
$127$	−8.50965			−0.755109			−0.377555	+	0.925987i	$0.623235\pi$
$128$		0			0
$129$	2.44983			0.215696
$130$		0			0
$131$	−18.8705	+	10.0865i	−1.64872	+	0.881262i	−0.656853	+	0.754019i	$0.728113\pi$
$131$	−18.8705	+	10.0865i	−1.64872	+	0.881262i	−0.991872	+	0.127243i	$0.959387\pi$
$132$		0			0
$133$	4.43694	+	5.40642i	0.384731	+	0.468796i
$134$		0			0
$135$	8.88186	−	5.93467i	0.764429	−	0.510775i
$136$		0			0
$137$	4.13797	−	6.19290i	0.353530	−	0.529096i	−0.611496	−	0.791247i	$-0.709432\pi$
$137$	4.13797	−	6.19290i	0.353530	−	0.529096i	0.965027	+	0.262152i	$0.0844321\pi$
$138$		0			0
$139$	−2.77583	+	0.842040i	−0.235443	+	0.0714209i	−0.405801	−	0.913961i	$-0.633008\pi$
$139$	−2.77583	+	0.842040i	−0.235443	+	0.0714209i	0.170358	+	0.985382i	$0.445508\pi$
$140$		0			0
$141$	−6.14700	−	5.04471i	−0.517671	−	0.424841i
$142$		0			0
$143$	12.4531	+	5.15826i	1.04138	+	0.431355i
$144$		0			0
$145$	−21.6813	+	8.98069i	−1.80054	+	0.745806i
$146$		0			0
$147$	0.0721578	+	0.732630i	0.00595147	+	0.0604263i
$148$		0			0
$149$	3.38141	−	6.32618i	0.277016	−	0.518261i	−0.704485	−	0.709719i	$-0.748822\pi$
$149$	3.38141	−	6.32618i	0.277016	−	0.518261i	0.981501	+	0.191459i	$0.0613218\pi$
$150$		0			0
$151$	−0.113929	+	0.0226619i	−0.00927140	+	0.00184420i	−0.199724	−	0.979852i	$-0.564005\pi$
$151$	−0.113929	+	0.0226619i	−0.00927140	+	0.00184420i	0.190452	+	0.981696i	$0.439005\pi$
$152$		0			0
$153$	−0.926215	+	4.65640i	−0.0748800	+	0.376447i
$154$		0			0
$155$	−2.24811	+	22.8255i	−0.180573	+	1.83339i
$156$		0			0
$157$	0.840828	−	2.77184i	0.0671054	−	0.221217i	−0.916974	−	0.398947i	$-0.869376\pi$
$157$	0.840828	−	2.77184i	0.0671054	−	0.221217i	0.984079	+	0.177731i	$0.0568756\pi$
$158$		0			0
$159$	−2.30376	−	2.30376i	−0.182700	−	0.182700i
$160$		0			0
$161$	4.01431	−	4.01431i	0.316372	−	0.316372i
$162$		0			0
$163$	−10.0289	−	3.04222i	−0.785522	−	0.238285i	−0.128053	−	0.991767i	$-0.540873\pi$
$163$	−10.0289	−	3.04222i	−0.785522	−	0.238285i	−0.657469	+	0.753482i	$0.728373\pi$
$164$		0			0
$165$	4.15625	+	0.409355i	0.323564	+	0.0318683i
$166$		0			0
$167$	−19.2664	−	3.83233i	−1.49088	−	0.296554i	−0.618656	−	0.785662i	$-0.712323\pi$
$167$	−19.2664	−	3.83233i	−1.49088	−	0.296554i	−0.872223	+	0.489108i	$0.837323\pi$
$168$		0			0
$169$	5.31354	+	26.7130i	0.408734	+	2.05485i
$170$		0			0
$171$	5.31735	+	2.84218i	0.406628	+	0.217347i
$172$		0			0
$173$	−0.605806	+	0.0596667i	−0.0460586	+	0.00453638i	−0.121020	−	0.992650i	$-0.538617\pi$
$173$	−0.605806	+	0.0596667i	−0.0460586	+	0.00453638i	0.0749616	+	0.997186i	$0.476117\pi$
$174$		0			0
$175$	−1.98766	−	4.79864i	−0.150253	−	0.362743i
$176$		0			0
$177$	−1.30267	+	3.14493i	−0.0979149	+	0.236387i
$178$		0			0
$179$	0.668794	−	0.814928i	0.0499880	−	0.0609106i	−0.747416	−	0.664356i	$-0.768706\pi$
$179$	0.668794	−	0.814928i	0.0499880	−	0.0609106i	0.797404	+	0.603445i	$0.206206\pi$
$180$		0			0
$181$	1.04511	+	3.44528i	0.0776827	+	0.256086i	0.987177	−	0.159632i	$-0.0510306\pi$
$181$	1.04511	+	3.44528i	0.0776827	+	0.256086i	−0.909494	+	0.415717i	$0.863531\pi$
$182$		0			0
$183$	−0.604657	−	0.404019i	−0.0446975	−	0.0298659i
$184$		0			0
$185$	−11.8820	−	17.7826i	−0.873581	−	1.30741i
$186$		0			0
$187$	−3.20247	+	2.62820i	−0.234188	+	0.192193i
$188$		0			0
$189$	5.43934	+	10.1763i	0.395654	+	0.740216i
$190$		0			0
$191$		−	14.8316i		−	1.07318i	−0.843844	−	0.536588i	$-0.819713\pi$
$191$		−	14.8316i		−	1.07318i	0.843844	−	0.536588i	$-0.180287\pi$
$192$		0			0
$193$		−	21.5115i		−	1.54843i	−0.632922	−	0.774216i	$-0.718145\pi$
$193$		−	21.5115i		−	1.54843i	0.632922	−	0.774216i	$-0.281855\pi$
$194$		0			0
$195$	5.87678	+	10.9947i	0.420845	+	0.787346i
$196$		0			0
$197$	4.37691	−	3.59204i	0.311842	−	0.255922i	−0.465433	−	0.885083i	$-0.654101\pi$
$197$	4.37691	−	3.59204i	0.311842	−	0.255922i	0.777275	+	0.629161i	$0.216601\pi$
$198$		0			0
$199$	10.7844	+	16.1400i	0.764486	+	1.14413i	0.985634	+	0.168894i	$0.0540195\pi$
$199$	10.7844	+	16.1400i	0.764486	+	1.14413i	−0.221148	+	0.975240i	$0.570981\pi$
$200$		0			0
$201$	−5.87114	−	3.92297i	−0.414118	−	0.276705i
$202$		0			0
$203$	−7.35862	−	24.2581i	−0.516474	−	1.70259i
$204$		0			0
$205$	1.96214	−	2.39088i	0.137042	−	0.166986i
$206$		0			0
$207$	1.87287	−	4.52150i	0.130173	−	0.314266i
$208$		0			0
$209$	2.01340	+	4.86077i	0.139270	+	0.336227i
$210$		0			0
$211$	23.6191	−	2.32627i	1.62600	−	0.160147i	0.756472	−	0.654026i	$-0.226921\pi$
$211$	23.6191	−	2.32627i	1.62600	−	0.160147i	0.869531	+	0.493879i	$0.164421\pi$
$212$		0			0
$213$	−0.456800	−	0.244165i	−0.0312994	−	0.0167299i
$214$		0			0
$215$	−1.66304	−	8.36067i	−0.113418	−	0.570193i
$216$		0			0
$217$	−24.2992	−	4.83341i	−1.64954	−	0.328113i
$218$		0			0
$219$	−5.84004	−	0.575194i	−0.394633	−	0.0388680i
$220$		0			0
$221$	−11.8342	−	3.58987i	−0.796056	−	0.241481i
$222$		0			0
$223$	−1.22502	+	1.22502i	−0.0820332	+	0.0820332i	−0.746933	−	0.664900i	$-0.768474\pi$
$223$	−1.22502	+	1.22502i	−0.0820332	+	0.0820332i	0.664900	+	0.746933i	$0.268474\pi$
$224$		0			0
$225$	−3.16614	−	3.16614i	−0.211076	−	0.211076i
$226$		0			0
$227$	−4.61807	+	15.2237i	−0.306512	+	1.01044i	0.659449	+	0.751749i	$0.270790\pi$
$227$	−4.61807	+	15.2237i	−0.306512	+	1.01044i	−0.965961	+	0.258686i	$0.916710\pi$
$228$		0			0
$229$	−2.74749	+	27.8958i	−0.181559	+	1.84340i	0.284531	+	0.958667i	$0.408162\pi$
$229$	−2.74749	+	27.8958i	−0.181559	+	1.84340i	−0.466090	+	0.884737i	$0.654338\pi$
$230$		0			0
$231$	−0.880108	+	4.42460i	−0.0579068	+	0.291117i
$232$		0			0
$233$	12.8710	−	2.56020i	0.843206	−	0.167724i	0.245457	−	0.969408i	$-0.421062\pi$
$233$	12.8710	−	2.56020i	0.843206	−	0.167724i	0.597749	+	0.801683i	$0.296062\pi$
$234$		0			0
$235$	−13.0435	+	24.4027i	−0.850865	+	1.59186i
$236$		0			0
$237$	−1.16428	−	11.8211i	−0.0756281	−	0.767865i
$238$		0			0
$239$	5.12774	−	2.12398i	0.331686	−	0.137389i	−0.210624	−	0.977567i	$-0.567550\pi$
$239$	5.12774	−	2.12398i	0.331686	−	0.137389i	0.542310	+	0.840178i	$0.317550\pi$
$240$		0			0
$241$	6.38640	+	2.64533i	0.411384	+	0.170401i	0.578770	−	0.815491i	$-0.303533\pi$
$241$	6.38640	+	2.64533i	0.411384	+	0.170401i	−0.167386	+	0.985891i	$0.553533\pi$
$242$		0			0
$243$	11.9335	+	9.79354i	0.765532	+	0.628256i
$244$		0			0
$245$	2.45130	−	0.743594i	0.156608	−	0.0475065i
$246$		0			0
$247$	−8.72536	+	13.0584i	−0.555182	+	0.830888i
$248$		0			0
$249$	−1.11808	+	0.747080i	−0.0708557	+	0.0473443i
$250$		0			0
$251$	−6.48177	−	7.89806i	−0.409126	−	0.498521i	0.527157	−	0.849768i	$-0.323258\pi$
$251$	−6.48177	−	7.89806i	−0.409126	−	0.498521i	−0.936283	+	0.351247i	$0.885758\pi$
$252$		0			0
$253$	3.76635	−	2.01316i	0.236789	−	0.126566i
$254$		0			0
$255$	−3.83168			−0.239949
$256$		0			0
$257$	−12.6096			−0.786565			−0.393282	−	0.919418i	$-0.628661\pi$
$257$	−12.6096			−0.786565			−0.393282	+	0.919418i	$0.628661\pi$
$258$		0			0
$259$	20.3742	−	10.8903i	1.26599	−	0.676688i
$260$		0			0
$261$	−13.8635	−	16.8927i	−0.858127	−	1.04563i
$262$		0			0
$263$	22.1707	−	14.8140i	1.36711	−	0.913471i	0.367245	−	0.930124i	$-0.380301\pi$
$263$	22.1707	−	14.8140i	1.36711	−	0.913471i	0.999861	+	0.0166526i	$0.00530093\pi$
$264$		0			0
$265$	−6.29827	+	9.42603i	−0.386900	+	0.579037i
$266$		0			0
$267$	−0.449071	+	0.136224i	−0.0274827	+	0.00833679i
$268$		0			0
$269$	0.710247	+	0.582885i	0.0433045	+	0.0355391i	0.655797	−	0.754938i	$-0.272333\pi$
$269$	0.710247	+	0.582885i	0.0433045	+	0.0355391i	−0.612492	+	0.790477i	$0.709833\pi$
$270$		0			0
$271$	−27.1096	−	11.2292i	−1.64679	−	0.682124i	−0.649835	−	0.760076i	$-0.725162\pi$
$271$	−27.1096	−	11.2292i	−1.64679	−	0.682124i	−0.996957	+	0.0779520i	$0.975162\pi$
$272$		0			0
$273$	−12.4414	+	5.15341i	−0.752990	+	0.311899i
$274$		0			0
$275$	−0.382975	−	3.88841i	−0.0230943	−	0.234480i
$276$		0			0
$277$	3.59274	−	6.72154i	0.215867	−	0.403858i	−0.750559	−	0.660803i	$-0.770216\pi$
$277$	3.59274	−	6.72154i	0.215867	−	0.403858i	0.966426	+	0.256945i	$0.0827158\pi$
$278$		0			0
$279$	−20.9476	+	4.16673i	−1.25410	+	0.249455i
$280$		0			0
$281$	−4.81902	+	24.2269i	−0.287479	+	1.44525i	0.519397	+	0.854533i	$0.326157\pi$
$281$	−4.81902	+	24.2269i	−0.287479	+	1.44525i	−0.806876	+	0.590721i	$0.798843\pi$
$282$		0			0
$283$	−1.89536	+	19.2439i	−0.112667	+	1.14393i	0.758068	+	0.652176i	$0.226144\pi$
$283$	−1.89536	+	19.2439i	−0.112667	+	1.14393i	−0.870735	+	0.491753i	$0.836356\pi$
$284$		0			0
$285$	−1.41255	+	4.65655i	−0.0836722	+	0.275830i
$286$		0			0
$287$	2.36243	+	2.36243i	0.139450	+	0.139450i
$288$		0			0
$289$	−9.33314	+	9.33314i	−0.549008	+	0.549008i
$290$		0			0
$291$	−8.25758	−	2.50491i	−0.484068	−	0.146840i
$292$		0			0
$293$	−24.5789	−	2.42081i	−1.43592	−	0.141425i	−0.650083	−	0.759864i	$-0.725266\pi$
$293$	−24.5789	−	2.42081i	−1.43592	−	0.141425i	−0.785833	+	0.618438i	$0.787766\pi$
$294$		0			0
$295$	11.6172	+	2.31080i	0.676377	+	0.134540i
$296$		0			0
$297$	1.69340	+	8.51331i	0.0982612	+	0.493992i
$298$		0			0
$299$	11.2428	+	6.00942i	0.650190	+	0.347534i
$300$		0			0
$301$	9.16374	−	0.902550i	0.528189	−	0.0520221i
$302$		0			0
$303$	0.560002	+	1.35196i	0.0321712	+	0.0776683i
$304$		0			0
$305$	−0.968350	+	2.33780i	−0.0554476	+	0.133862i
$306$		0			0
$307$	−11.5940	+	14.1274i	−0.661706	+	0.806292i	−0.990413	−	0.138141i	$-0.955887\pi$
$307$	−11.5940	+	14.1274i	−0.661706	+	0.806292i	0.328706	+	0.944432i	$0.393387\pi$
$308$		0			0
$309$	2.33361	+	7.69287i	0.132754	+	0.437632i
$310$		0			0
$311$	−4.24571	−	2.83689i	−0.240752	−	0.160865i	0.429341	−	0.903142i	$-0.358746\pi$
$311$	−4.24571	−	2.83689i	−0.240752	−	0.160865i	−0.670093	+	0.742277i	$0.733746\pi$
$312$		0			0
$313$	−9.00582	−	13.4782i	−0.509039	−	0.761831i	0.484564	−	0.874756i	$-0.338978\pi$
$313$	−9.00582	−	13.4782i	−0.509039	−	0.761831i	−0.993604	+	0.112925i	$0.963978\pi$
$314$		0			0
$315$	13.9057	−	11.4121i	0.783496	−	0.642998i
$316$		0			0
$317$	11.1436	+	20.8482i	0.625888	+	1.17095i	0.972491	+	0.232942i	$0.0748352\pi$
$317$	11.1436	+	20.8482i	0.625888	+	1.17095i	−0.346603	+	0.938012i	$0.612665\pi$
$318$		0			0
$319$		−	19.0694i		−	1.06768i
$320$		0			0
$321$			15.3130i			0.854691i
$322$		0			0
$323$	−2.27545	−	4.25707i	−0.126610	−	0.236870i
$324$		0			0
$325$	9.01589	−	7.39915i	0.500112	−	0.410431i
$326$		0			0
$327$	−0.744974	−	1.11493i	−0.0411971	−	0.0616559i
$328$		0			0
$329$	−24.8517	−	16.6054i	−1.37012	−	0.915485i
$330$		0			0
$331$	2.67685	+	8.82439i	0.147133	+	0.485033i	0.999267	−	0.0382918i	$-0.0121916\pi$
$331$	2.67685	+	8.82439i	0.147133	+	0.485033i	−0.852134	+	0.523324i	$0.824692\pi$
$332$		0			0
$333$	12.6343	−	15.3950i	0.692356	−	0.843638i
$334$		0			0
$335$	−9.40256	+	22.6998i	−0.513717	+	1.24022i
$336$		0			0
$337$	9.37798	+	22.6404i	0.510851	+	1.23330i	0.943389	+	0.331688i	$0.107618\pi$
$337$	9.37798	+	22.6404i	0.510851	+	1.23330i	−0.432538	+	0.901616i	$0.642382\pi$
$338$		0			0
$339$	−3.93406	+	0.387472i	−0.213669	+	0.0210446i
$340$		0			0
$341$	−16.4366	−	8.78557i	−0.890094	−	0.475765i
$342$		0			0
$343$	−3.31783	−	16.6799i	−0.179146	−	0.900628i
$344$		0			0
$345$	3.87396	+	0.770578i	0.208567	+	0.0414865i
$346$		0			0
$347$	−9.61469	−	0.946965i	−0.516144	−	0.0508357i	−0.163408	−	0.986559i	$-0.552249\pi$
$347$	−9.61469	−	0.946965i	−0.516144	−	0.0508357i	−0.352736	+	0.935723i	$0.614749\pi$
$348$		0			0
$349$	12.6203	+	3.82833i	0.675550	+	0.204926i	0.609375	−	0.792882i	$-0.291420\pi$
$349$	12.6203	+	3.82833i	0.675550	+	0.204926i	0.0661751	+	0.997808i	$0.478920\pi$
$350$		0			0
$351$	−18.3216	+	18.3216i	−0.977937	+	0.977937i
$352$		0			0
$353$	−14.4352	−	14.4352i	−0.768308	−	0.768308i	0.209501	−	0.977808i	$-0.432816\pi$
$353$	−14.4352	−	14.4352i	−0.768308	−	0.768308i	−0.977808	+	0.209501i	$0.932816\pi$
$354$		0			0
$355$	−0.523179	+	1.72469i	−0.0277675	+	0.0915371i
$356$		0			0
$357$	0.405689	−	4.11903i	0.0214714	−	0.218002i
$358$		0			0
$359$	0.998883	−	5.02172i	0.0527190	−	0.265036i	−0.945432	−	0.325820i	$-0.894360\pi$
$359$	0.998883	−	5.02172i	0.0527190	−	0.265036i	0.998151	+	0.0607831i	$0.0193598\pi$
$360$		0			0
$361$	12.6226	−	2.51078i	0.664345	−	0.132147i
$362$		0			0
$363$	2.29730	−	4.29795i	0.120577	−	0.225584i
$364$		0			0
$365$	2.00145	+	20.3211i	0.104761	+	1.06365i
$366$		0			0
$367$	−2.06234	+	0.854248i	−0.107653	+	0.0445914i	−0.435860	−	0.900014i	$-0.643556\pi$
$367$	−2.06234	+	0.854248i	−0.107653	+	0.0445914i	0.328207	+	0.944606i	$0.393556\pi$
$368$		0			0
$369$	2.66091	+	1.10219i	0.138522	+	0.0573775i
$370$		0			0
$371$	−9.46607	−	7.76861i	−0.491454	−	0.403326i
$372$		0			0
$373$	−1.30563	+	0.396057i	−0.0676027	+	0.0205071i	−0.323905	−	0.946090i	$-0.604996\pi$
$373$	−1.30563	+	0.396057i	−0.0676027	+	0.0205071i	0.256302	+	0.966597i	$0.417496\pi$
$374$		0			0
$375$	−3.45181	+	5.16600i	−0.178251	+	0.266771i
$376$		0			0
$377$	47.3302	−	31.6250i	2.43763	−	1.62877i
$378$		0			0
$379$	7.30390	+	8.89983i	0.375176	+	0.457154i	0.926031	−	0.377448i	$-0.123198\pi$
$379$	7.30390	+	8.89983i	0.375176	+	0.457154i	−0.550855	+	0.834601i	$0.685698\pi$
$380$		0			0
$381$	5.64025	−	3.01478i	0.288959	−	0.154452i
$382$		0			0
$383$	23.8620			1.21929			0.609646	−	0.792673i	$-0.291311\pi$
$383$	23.8620			1.21929			0.609646	+	0.792673i	$0.291311\pi$
$384$		0			0
$385$	15.6975			0.800019
$386$		0			0
$387$	7.00068	−	3.74194i	0.355864	−	0.190213i
$388$		0			0
$389$	4.35875	+	5.31115i	0.220997	+	0.269286i	0.871693	−	0.490053i	$-0.163023\pi$
$389$	4.35875	+	5.31115i	0.220997	+	0.269286i	−0.650695	+	0.759339i	$0.725523\pi$
$390$		0			0
$391$	−3.25783	+	2.17682i	−0.164756	+	0.110086i
$392$		0			0
$393$	8.93408	−	13.3708i	0.450664	−	0.674467i
$394$		0			0
$395$	−39.5522	+	11.9980i	−1.99009	+	0.603686i
$396$		0			0
$397$	3.10832	+	2.55094i	0.156002	+	0.128028i	0.709157	−	0.705051i	$-0.249076\pi$
$397$	3.10832	+	2.55094i	0.156002	+	0.128028i	−0.553154	+	0.833079i	$0.686576\pi$
$398$		0			0
$399$	−4.85620	−	2.01150i	−0.243114	−	0.100701i
$400$		0			0
$401$	20.7974	−	8.61456i	1.03857	−	0.430190i	0.202772	−	0.979226i	$-0.435005\pi$
$401$	20.7974	−	8.61456i	1.03857	−	0.430190i	0.835799	+	0.549035i	$0.185005\pi$
$402$		0			0
$403$	−5.45306	−	55.3658i	−0.271636	−	2.75797i
$404$		0			0
$405$	5.22143	−	9.76861i	0.259455	−	0.485406i
$406$		0			0
$407$	17.0448	−	3.39041i	0.844877	−	0.168057i
$408$		0			0
$409$	3.33633	−	16.7729i	0.164971	−	0.829365i	−0.806322	−	0.591477i	$-0.798545\pi$
$409$	3.33633	−	16.7729i	0.164971	−	0.829365i	0.971293	−	0.237888i	$-0.0764550\pi$
$410$		0			0
$411$	−0.548664	+	5.57068i	−0.0270636	+	0.274782i
$412$		0			0
$413$	−3.71409	+	12.2437i	−0.182758	+	0.602473i
$414$		0			0
$415$	3.30860	+	3.30860i	0.162413	+	0.162413i
$416$		0			0
$417$	1.54152	−	1.54152i	0.0754887	−	0.0754887i
$418$		0			0
$419$	3.36832	+	1.02177i	0.164553	+	0.0499166i	0.371486	−	0.928438i	$-0.378848\pi$
$419$	3.36832	+	1.02177i	0.164553	+	0.0499166i	−0.206933	+	0.978355i	$0.566348\pi$
$420$		0			0
$421$	−19.1790	−	1.88897i	−0.934729	−	0.0920627i	−0.380828	−	0.924646i	$-0.624361\pi$
$421$	−19.1790	−	1.88897i	−0.934729	−	0.0920627i	−0.553900	+	0.832583i	$0.686861\pi$
$422$		0			0
$423$	−25.2712	−	5.02675i	−1.22873	−	0.244409i
$424$		0			0
$425$	0.699352	+	3.51588i	0.0339235	+	0.170545i
$426$		0			0
$427$	−2.41060	−	1.28849i	−0.116657	−	0.0623544i
$428$		0			0
$429$	−10.0815	+	0.992938i	−0.486738	+	0.0479395i
$430$		0			0
$431$	−3.79165	−	9.15385i	−0.182637	−	0.440925i	0.805871	−	0.592091i	$-0.201697\pi$
$431$	−3.79165	−	9.15385i	−0.182637	−	0.440925i	−0.988508	+	0.151165i	$0.951697\pi$
$432$		0			0
$433$	3.46071	−	8.35490i	0.166311	−	0.401511i	−0.818649	−	0.574295i	$-0.805276\pi$
$433$	3.46071	−	8.35490i	0.166311	−	0.401511i	0.984960	+	0.172784i	$0.0552763\pi$
$434$		0			0
$435$	11.1889	−	13.6337i	0.536464	−	0.653684i
$436$		0			0
$437$	1.44443	+	4.76165i	0.0690965	+	0.227780i
$438$		0			0
$439$	19.0602	+	12.7356i	0.909693	+	0.607838i	0.919918	−	0.392110i	$-0.128255\pi$
$439$	19.0602	+	12.7356i	0.909693	+	0.607838i	−0.0102251	+	0.999948i	$0.503255\pi$
$440$		0			0
$441$	1.32524	+	1.98336i	0.0631065	+	0.0944456i
$442$		0			0
$443$	4.88931	−	4.01255i	0.232298	−	0.190642i	−0.511042	−	0.859556i	$-0.670740\pi$
$443$	4.88931	−	4.01255i	0.232298	−	0.190642i	0.743340	+	0.668914i	$0.233240\pi$
$444$		0			0
$445$	0.769746	+	1.44009i	0.0364894	+	0.0682670i
$446$		0			0
$447$			5.39099i			0.254985i
$448$		0			0
$449$			31.6138i			1.49195i	0.665975	+	0.745974i	$0.268016\pi$
$449$			31.6138i			1.49195i	−0.665975	+	0.745974i	$0.731984\pi$
$450$		0			0
$451$	1.18475	+	2.21651i	0.0557876	+	0.104371i
$452$		0			0
$453$	0.0674842	−	0.0553828i	0.00317068	−	0.00260211i
$454$		0			0
$455$	26.0330	+	38.9612i	1.22045	+	1.82653i
$456$		0			0
$457$	−14.0642	−	9.39741i	−0.657897	−	0.439592i	0.181295	−	0.983429i	$-0.441971\pi$
$457$	−14.0642	−	9.39741i	−0.657897	−	0.439592i	−0.839191	+	0.543836i	$0.816971\pi$
$458$		0			0
$459$	−2.31175	−	7.62081i	−0.107903	−	0.355709i
$460$		0			0
$461$	5.17600	−	6.30698i	0.241071	−	0.293745i	−0.638394	−	0.769710i	$-0.720401\pi$
$461$	5.17600	−	6.30698i	0.241071	−	0.293745i	0.879465	+	0.475964i	$0.157901\pi$
$462$		0			0
$463$	9.87176	−	23.8325i	0.458780	−	1.10759i	−0.510112	−	0.860108i	$-0.670396\pi$
$463$	9.87176	−	23.8325i	0.458780	−	1.10759i	0.968892	−	0.247484i	$-0.0796039\pi$
$464$		0			0
$465$	−6.59649	−	15.9253i	−0.305905	−	0.738519i
$466$		0			0
$467$	16.7281	−	1.64758i	0.774086	−	0.0762408i	0.296742	−	0.954958i	$-0.404100\pi$
$467$	16.7281	−	1.64758i	0.774086	−	0.0762408i	0.477344	+	0.878717i	$0.341600\pi$
$468$		0			0
$469$	−23.4066	−	12.5111i	−1.08082	−	0.577708i
$470$		0			0
$471$	0.424694	+	2.13508i	0.0195688	+	0.0983792i
$472$		0			0
$473$	6.79373	+	1.35136i	0.312376	+	0.0621354i
$474$		0			0
$475$	4.53058	+	0.446223i	0.207877	+	0.0204741i
$476$		0			0
$477$	−10.1021	−	3.06443i	−0.462542	−	0.140311i
$478$		0			0
$479$	23.7992	−	23.7992i	1.08741	−	1.08741i	0.0916184	−	0.995794i	$-0.470796\pi$
$479$	23.7992	−	23.7992i	1.08741	−	1.08741i	0.995794	−	0.0916184i	$-0.0292040\pi$
$480$		0			0
$481$	36.6823	+	36.6823i	1.67257	+	1.67257i
$482$		0			0
$483$	−1.23853	+	4.08289i	−0.0563551	+	0.185778i
$484$		0			0
$485$	−2.94307	+	29.8815i	−0.133638	+	1.35685i
$486$		0			0
$487$	−5.06762	+	25.4767i	−0.229636	+	1.15446i	0.678118	+	0.734953i	$0.262796\pi$
$487$	−5.06762	+	25.4767i	−0.229636	+	1.15446i	−0.907754	+	0.419504i	$0.862204\pi$
$488$		0			0
$489$	7.72499	−	1.53660i	0.349336	−	0.0694873i
$490$		0			0
$491$	14.1721	−	26.5142i	0.639579	−	1.19657i	−0.328161	−	0.944622i	$-0.606429\pi$
$491$	14.1721	−	26.5142i	0.639579	−	1.19657i	0.967741	−	0.251947i	$-0.0810710\pi$
$492$		0			0
$493$	1.71487	+	17.4114i	0.0772338	+	0.784168i
$494$		0			0
$495$	12.5022	−	5.17859i	0.561933	−	0.232760i
$496$		0			0
$497$	−1.79864	−	0.745020i	−0.0806799	−	0.0334187i
$498$		0			0
$499$	6.23192	+	5.11441i	0.278979	+	0.228952i	0.763469	−	0.645845i	$-0.223495\pi$
$499$	6.23192	+	5.11441i	0.278979	+	0.228952i	−0.484490	+	0.874797i	$0.660995\pi$
$500$		0			0
$501$	14.1276	−	4.28556i	0.631175	−	0.191465i
$502$		0			0
$503$	−14.1261	+	21.1411i	−0.629850	+	0.942636i	0.370058	+	0.929009i	$0.379338\pi$
$503$	−14.1261	+	21.1411i	−0.629850	+	0.942636i	−0.999907	+	0.0136277i	$0.995662\pi$
$504$		0			0
$505$	4.23376	−	2.82891i	0.188400	−	0.125885i
$506$		0			0
$507$	−12.9857	−	15.8231i	−0.576713	−	0.702727i
$508$		0			0
$509$	9.02039	−	4.82150i	0.399822	−	0.213709i	−0.259215	−	0.965820i	$-0.583464\pi$
$509$	9.02039	−	4.82150i	0.399822	−	0.213709i	0.659037	+	0.752110i	$0.270964\pi$
$510$		0			0
$511$	−22.0569			−0.975740
$512$		0			0
$513$	−10.1136			−0.446526
$514$		0			0
$515$	24.6697	−	13.1862i	1.08708	−	0.581055i
$516$		0			0
$517$	−14.2638	−	17.3804i	−0.627319	−	0.764391i
$518$		0			0
$519$	0.380394	−	0.254171i	0.0166974	−	0.0111569i
$520$		0			0
$521$	2.94313	−	4.40470i	0.128941	−	0.192974i	−0.761382	−	0.648304i	$-0.775479\pi$
$521$	2.94313	−	4.40470i	0.128941	−	0.192974i	0.890323	+	0.455330i	$0.150479\pi$
$522$		0			0
$523$	−19.5494	+	5.93023i	−0.854834	+	0.259311i	−0.687137	−	0.726528i	$-0.741133\pi$
$523$	−19.5494	+	5.93023i	−0.854834	+	0.259311i	−0.167697	+	0.985839i	$0.553633\pi$
$524$		0			0
$525$	3.01749	+	2.47639i	0.131694	+	0.108078i
$526$		0			0
$527$	15.7976	+	6.54357i	0.688153	+	0.285042i
$528$		0			0
$529$	−17.5177	+	7.25606i	−0.761638	+	0.315481i
$530$		0			0
$531$	1.08111	+	10.9767i	0.0469163	+	0.476349i
$532$		0			0
$533$	−3.53656	+	6.61643i	−0.153185	+	0.286589i
$534$		0			0
$535$	52.2596	−	10.3951i	2.25938	−	0.449418i
$536$		0			0
$537$	−0.154570	+	0.777078i	−0.00667021	+	0.0335334i
$538$		0			0
$539$	−0.204024	+	2.07149i	−0.00878793	+	0.0892253i
$540$		0			0
$541$	11.2598	−	37.1185i	0.484095	−	1.59585i	−0.286206	−	0.958168i	$-0.592394\pi$
$541$	11.2598	−	37.1185i	0.484095	−	1.59585i	0.770301	−	0.637680i	$-0.220106\pi$
$542$		0			0
$543$	−1.91329	−	1.91329i	−0.0821072	−	0.0821072i
$544$		0			0
$545$	−3.29927	+	3.29927i	−0.141325	+	0.141325i
$546$		0			0
$547$	−1.50431	−	0.456328i	−0.0643197	−	0.0195112i	0.257961	−	0.966155i	$-0.416949\pi$
$547$	−1.50431	−	0.456328i	−0.0643197	−	0.0195112i	−0.322281	+	0.946644i	$0.604449\pi$
$548$		0			0
$549$	−2.34498	−	0.230961i	−0.100081	−	0.00985716i
$550$		0			0
$551$	21.7918	+	4.33465i	0.928360	+	0.184662i
$552$		0			0
$553$	−8.71010	−	43.7886i	−0.370391	−	1.86208i
$554$		0			0
$555$	14.1754	+	7.57693i	0.601714	+	0.321623i
$556$		0			0
$557$	−20.9805	+	2.06640i	−0.888971	+	0.0875560i	−0.532183	−	0.846629i	$-0.678628\pi$
$557$	−20.9805	+	2.06640i	−0.888971	+	0.0875560i	−0.356788	+	0.934185i	$0.616128\pi$
$558$		0			0
$559$	7.91277	+	19.1031i	0.334675	+	0.807976i
$560$		0			0
$561$	1.19151	−	2.87655i	0.0503054	−	0.121448i
$562$		0			0
$563$	−5.57406	+	6.79201i	−0.234919	+	0.286249i	−0.877104	−	0.480300i	$-0.840528\pi$
$563$	−5.57406	+	6.79201i	−0.234919	+	0.286249i	0.642186	+	0.766549i	$0.278028\pi$
$564$		0			0
$565$	3.99294	+	13.1629i	0.167984	+	0.553769i
$566$		0			0
$567$	9.94835	+	6.64728i	0.417791	+	0.279159i
$568$		0			0
$569$	19.3072	+	28.8953i	0.809400	+	1.21135i	0.974347	+	0.225050i	$0.0722544\pi$
$569$	19.3072	+	28.8953i	0.809400	+	1.21135i	−0.164948	+	0.986302i	$0.552746\pi$
$570$		0			0
$571$	−1.32153	+	1.08455i	−0.0553043	+	0.0453871i	−0.661639	−	0.749822i	$-0.730139\pi$
$571$	−1.32153	+	1.08455i	−0.0553043	+	0.0453871i	0.606335	+	0.795209i	$0.292639\pi$
$572$		0			0
$573$	5.25450	+	9.83048i	0.219510	+	0.410674i
$574$		0			0
$575$		−	3.69531i		−	0.154105i
$576$		0			0
$577$		−	34.6197i		−	1.44124i	−0.693333	−	0.720618i	$-0.743858\pi$
$577$		−	34.6197i		−	1.44124i	0.693333	−	0.720618i	$-0.256142\pi$
$578$		0			0
$579$	7.62103	+	14.2580i	0.316719	+	0.592540i
$580$		0			0
$581$	−3.90702	+	3.20641i	−0.162091	+	0.133024i
$582$		0			0
$583$	−5.11786	−	7.65942i	−0.211960	−	0.317221i
$584$		0			0
$585$	33.5871	+	22.4422i	1.38866	+	0.927871i
$586$		0			0
$587$	4.43628	+	14.6244i	0.183105	+	0.603615i	0.999653	+	0.0263383i	$0.00838472\pi$
$587$	4.43628	+	14.6244i	0.183105	+	0.603615i	−0.816548	+	0.577277i	$0.804115\pi$
$588$		0			0
$589$	13.7760	−	16.7861i	0.567630	−	0.691659i
$590$		0			0
$591$	−1.62847	+	3.93147i	−0.0669862	+	0.161719i
$592$		0			0
$593$	−10.1091	−	24.4056i	−0.415133	−	1.00222i	−0.983738	−	0.179608i	$-0.942517\pi$
$593$	−10.1091	−	24.4056i	−0.415133	−	1.00222i	0.568606	−	0.822610i	$-0.307483\pi$
$594$		0			0
$595$	−14.3326	+	1.41164i	−0.587580	+	0.0578716i
$596$		0			0
$597$	−12.8660	−	6.87702i	−0.526570	−	0.281458i
$598$		0			0
$599$	−0.0163657	−	0.0822762i	−0.000668686	−	0.00336171i	0.980449	−	0.196771i	$-0.0630455\pi$
$599$	−0.0163657	−	0.0822762i	−0.000668686	−	0.00336171i	−0.981118	+	0.193409i	$0.938046\pi$
$600$		0			0
$601$	−12.0730	−	2.40147i	−0.492468	−	0.0979579i	−0.0573919	−	0.998352i	$-0.518278\pi$
$601$	−12.0730	−	2.40147i	−0.492468	−	0.0979579i	−0.435076	+	0.900394i	$0.643278\pi$
$602$		0			0
$603$	−22.7695	−	2.24260i	−0.927245	−	0.0913257i
$604$		0			0
$605$	−16.2273	−	4.92250i	−0.659734	−	0.200128i
$606$		0			0
$607$	−17.0111	+	17.0111i	−0.690460	+	0.690460i	−0.962333	−	0.271873i	$-0.912357\pi$
$607$	−17.0111	+	17.0111i	−0.690460	+	0.690460i	0.271873	+	0.962333i	$0.412357\pi$
$608$		0			0
$609$	13.4714	+	13.4714i	0.545890	+	0.545890i
$610$		0			0
$611$	19.4829	−	64.2266i	0.788195	−	2.59833i
$612$		0			0
$613$	2.77550	−	28.1801i	0.112101	−	1.13818i	−0.760361	−	0.649501i	$-0.774978\pi$
$613$	2.77550	−	28.1801i	0.112101	−	1.13818i	0.872462	−	0.488682i	$-0.162522\pi$
$614$		0			0
$615$	−0.453487	+	2.27983i	−0.0182863	+	0.0919317i
$616$		0			0
$617$	−7.90077	+	1.57156i	−0.318073	+	0.0632687i	−0.351545	−	0.936171i	$-0.614344\pi$
$617$	−7.90077	+	1.57156i	−0.318073	+	0.0632687i	0.0334719	+	0.999440i	$0.489344\pi$
$618$		0			0
$619$	3.26475	−	6.10792i	0.131221	−	0.245498i	−0.807726	−	0.589557i	$-0.799302\pi$
$619$	3.26475	−	6.10792i	0.131221	−	0.245498i	0.938948	+	0.344059i	$0.111802\pi$
$620$		0			0
$621$	0.804654	+	8.16979i	0.0322897	+	0.327842i
$622$		0			0
$623$	−1.62959	+	0.674998i	−0.0652881	+	0.0270432i
$624$		0			0
$625$	28.4672	+	11.7915i	1.13869	+	0.471660i
$626$		0			0
$627$	−3.05655	−	2.50845i	−0.122067	−	0.100178i
$628$		0			0
$629$	−15.2578	+	4.62842i	−0.608370	+	0.184547i
$630$		0			0
$631$	−1.74202	+	2.60712i	−0.0693489	+	0.103788i	−0.864523	−	0.502593i	$-0.832379\pi$
$631$	−1.74202	+	2.60712i	−0.0693489	+	0.103788i	0.795174	+	0.606381i	$0.207379\pi$
$632$		0			0
$633$	−14.8307	+	9.90957i	−0.589468	+	0.393870i
$634$		0			0
$635$	−14.1175	−	17.2022i	−0.560235	−	0.682649i
$636$		0			0
$637$	−5.47978	+	2.92901i	−0.217117	+	0.116051i
$638$		0			0
$639$	−1.67830			−0.0663925
$640$		0			0
$641$	−4.89846			−0.193477			−0.0967387	−	0.995310i	$-0.530841\pi$
$641$	−4.89846			−0.193477			−0.0967387	+	0.995310i	$0.530841\pi$
$642$		0			0
$643$	−15.8447	+	8.46915i	−0.624853	+	0.333991i	−0.753252	−	0.657732i	$-0.771516\pi$
$643$	−15.8447	+	8.46915i	−0.624853	+	0.333991i	0.128400	+	0.991723i	$0.459016\pi$
$644$		0			0
$645$	4.06427	+	4.95233i	0.160030	+	0.194998i
$646$		0			0
$647$	−12.7810	+	8.53998i	−0.502472	+	0.335741i	−0.780838	−	0.624734i	$-0.785207\pi$
$647$	−12.7810	+	8.53998i	−0.502472	+	0.335741i	0.278365	+	0.960475i	$0.410207\pi$
$648$		0			0
$649$	−5.34727	+	8.00276i	−0.209899	+	0.314136i
$650$		0			0
$651$	17.8180	−	5.40504i	0.698344	−	0.211840i
$652$		0			0
$653$	−15.1179	−	12.4070i	−0.591611	−	0.485522i	0.290302	−	0.956935i	$-0.406244\pi$
$653$	−15.1179	−	12.4070i	−0.591611	−	0.485522i	−0.881913	+	0.471413i	$0.843744\pi$
$654$		0			0
$655$	−51.6959	−	21.4132i	−2.01993	−	0.836681i
$656$		0			0
$657$	−17.5671	+	7.27655i	−0.685360	+	0.283885i
$658$		0			0
$659$	2.78992	+	28.3266i	0.108680	+	1.10345i	0.882587	+	0.470148i	$0.155800\pi$
$659$	2.78992	+	28.3266i	0.108680	+	1.10345i	−0.773907	+	0.633299i	$0.781700\pi$
$660$		0			0
$661$	−12.9991	+	24.3195i	−0.505605	+	0.945921i	0.491572	+	0.870837i	$0.336422\pi$
$661$	−12.9991	+	24.3195i	−0.505605	+	0.945921i	−0.997177	+	0.0750839i	$0.976078\pi$
$662$		0			0
$663$	9.11561	−	1.81321i	0.354021	−	0.0704191i
$664$		0			0
$665$	−3.56819	+	17.9385i	−0.138368	+	0.695625i
$666$		0			0
$667$	1.76775	−	17.9483i	0.0684477	−	0.694961i
$668$		0			0
$669$	0.377953	−	1.24595i	0.0146125	−	0.0481710i
$670$		0			0
$671$	−1.45393	−	1.45393i	−0.0561285	−	0.0561285i
$672$		0			0
$673$	−10.3479	+	10.3479i	−0.398882	+	0.398882i	−0.877839	−	0.478956i	$-0.841015\pi$
$673$	−10.3479	+	10.3479i	−0.398882	+	0.398882i	0.478956	+	0.877839i	$0.341015\pi$
$674$		0			0
$675$	7.18736	+	2.18026i	0.276642	+	0.0839183i
$676$		0			0
$677$	31.1921	+	3.07215i	1.19881	+	0.118072i	0.677648	−	0.735386i	$-0.262999\pi$
$677$	31.1921	+	3.07215i	1.19881	+	0.118072i	0.521161	+	0.853459i	$0.325499\pi$
$678$		0			0
$679$	−31.8108	−	6.32756i	−1.22079	−	0.242829i
$680$		0			0
$681$	−2.33254	−	11.7265i	−0.0893831	−	0.449359i
$682$		0			0
$683$	−12.7384	−	6.80882i	−0.487422	−	0.260532i	0.209330	−	0.977845i	$-0.432872\pi$
$683$	−12.7384	−	6.80882i	−0.487422	−	0.260532i	−0.696751	+	0.717313i	$0.745372\pi$
$684$		0			0
$685$	19.3838	−	1.90914i	0.740617	−	0.0729444i
$686$		0			0
$687$	−8.06178	−	19.4629i	−0.307576	−	0.742555i
$688$		0			0
$689$	10.5231	−	25.4050i	0.400899	−	0.967855i
$690$		0			0
$691$	−12.8454	+	15.6522i	−0.488662	+	0.595437i	−0.957710	−	0.287736i	$-0.907097\pi$
$691$	−12.8454	+	15.6522i	−0.488662	+	0.595437i	0.469047	+	0.883173i	$0.344597\pi$
$692$		0			0
$693$	4.24324	+	13.9881i	0.161187	+	0.531364i
$694$		0			0
$695$	−6.30728	−	4.21439i	−0.239249	−	0.159861i
$696$		0			0
$697$	−1.28106	−	1.91724i	−0.0485236	−	0.0726207i
$698$		0			0
$699$	−7.62394	+	6.25681i	−0.288364	+	0.236654i
$700$		0			0
$701$	−16.3267	−	30.5452i	−0.616652	−	1.15368i	−0.975442	−	0.220257i	$-0.929310\pi$
$701$	−16.3267	−	30.5452i	−0.616652	−	1.15368i	0.358790	−	0.933418i	$-0.383190\pi$
$702$		0			0
$703$			20.2487i			0.763696i
$704$		0			0
$705$		−	20.7953i		−	0.783196i
$706$		0			0
$707$	2.59280	+	4.85078i	0.0975122	+	0.182432i
$708$		0			0
$709$	−5.20466	+	4.27136i	−0.195465	+	0.160414i	−0.727035	−	0.686600i	$-0.759102\pi$
$709$	−5.20466	+	4.27136i	−0.195465	+	0.160414i	0.531570	+	0.847014i	$0.321602\pi$
$710$		0			0
$711$	−21.3829	−	32.0018i	−0.801923	−	1.20016i
$712$		0			0
$713$	−14.6559	−	9.79276i	−0.548868	−	0.366742i
$714$		0			0
$715$	10.2323	+	33.7315i	0.382668	+	1.26149i
$716$		0			0
$717$	−2.64622	+	3.22443i	−0.0988249	+	0.120418i
$718$		0			0
$719$	−10.4088	+	25.1291i	−0.388183	+	0.937158i	0.602142	+	0.798389i	$0.294314\pi$
$719$	−10.4088	+	25.1291i	−0.388183	+	0.937158i	−0.990325	+	0.138768i	$0.955686\pi$
$720$		0			0
$721$	11.5631	+	27.9159i	0.430634	+	1.03964i
$722$		0			0
$723$	−5.17012	+	0.509213i	−0.192279	+	0.0189378i
$724$		0			0
$725$	−14.5521	−	7.77828i	−0.540453	−	0.288878i
$726$		0			0
$727$	3.00448	+	15.1046i	0.111430	+	0.560197i	0.995654	+	0.0931330i	$0.0296882\pi$
$727$	3.00448	+	15.1046i	0.111430	+	0.560197i	−0.884224	+	0.467064i	$0.845312\pi$
$728$		0			0
$729$	1.08346	+	0.215513i	0.0401281	+	0.00798198i
$730$		0			0
$731$	−6.32455	−	0.622913i	−0.233922	−	0.0230393i
$732$		0			0
$733$	4.02812	+	1.22192i	0.148782	+	0.0451325i	0.363797	−	0.931478i	$-0.381480\pi$
$733$	4.02812	+	1.22192i	0.148782	+	0.0451325i	−0.215015	+	0.976611i	$0.568980\pi$
$734$		0			0
$735$	−1.36130	+	1.36130i	−0.0502123	+	0.0502123i
$736$		0			0
$737$	−14.1175	−	14.1175i	−0.520026	−	0.520026i
$738$		0			0
$739$	0.147951	−	0.487728i	0.00544246	−	0.0179414i	−0.954177	−	0.299243i	$-0.903266\pi$
$739$	0.147951	−	0.487728i	0.00544246	−	0.0179414i	0.959620	+	0.281301i	$0.0907660\pi$
$740$		0			0
$741$	1.15692	−	11.7464i	0.0425005	−	0.431515i
$742$		0			0
$743$	−1.19981	+	6.03186i	−0.0440168	+	0.221287i	−0.996533	−	0.0832012i	$-0.973486\pi$
$743$	−1.19981	+	6.03186i	−0.0440168	+	0.221287i	0.952516	+	0.304489i	$0.0984856\pi$
$744$		0			0
$745$	18.3981	−	3.65961i	0.674054	−	0.134078i
$746$		0			0
$747$	−2.05394	+	3.84266i	−0.0751498	+	0.140595i
$748$		0			0
$749$	5.64152	+	57.2793i	0.206137	+	2.09294i
$750$		0			0
$751$	30.6452	−	12.6937i	1.11826	−	0.463198i	0.254485	−	0.967077i	$-0.418094\pi$
$751$	30.6452	−	12.6937i	1.11826	−	0.463198i	0.863774	+	0.503879i	$0.168094\pi$
$752$		0			0
$753$	7.09426	+	2.93854i	0.258529	+	0.107086i
$754$		0			0
$755$	−0.234819	−	0.192711i	−0.00854592	−	0.00701346i
$756$		0			0
$757$	−32.0734	+	9.72937i	−1.16573	+	0.353620i	−0.813089	−	0.582139i	$-0.802216\pi$
$757$	−32.0734	+	9.72937i	−1.16573	+	0.353620i	−0.352639	+	0.935759i	$0.614716\pi$
$758$		0			0
$759$	−1.78315	+	2.66867i	−0.0647241	+	0.0968665i
$760$		0			0
$761$	−6.62118	+	4.42413i	−0.240018	+	0.160375i	−0.669762	−	0.742576i	$-0.733604\pi$
$761$	−6.62118	+	4.42413i	−0.240018	+	0.160375i	0.429744	+	0.902951i	$0.358604\pi$
$762$		0			0
$763$	−3.19737	−	3.89601i	−0.115753	−	0.141045i
$764$		0			0
$765$	−10.9495	+	5.85261i	−0.395879	+	0.211602i
$766$		0			0
$767$	−28.7308			−1.03741
$768$		0			0
$769$	−7.44025			−0.268302			−0.134151	−	0.990961i	$-0.542831\pi$
$769$	−7.44025			−0.268302			−0.134151	+	0.990961i	$0.542831\pi$
$770$		0			0
$771$	8.35772	−	4.46729i	0.300996	−	0.160886i
$772$		0			0
$773$	26.7122	+	32.5489i	0.960771	+	1.17070i	0.985270	+	0.171004i	$0.0547010\pi$
$773$	26.7122	+	32.5489i	0.960771	+	1.17070i	−0.0244989	+	0.999700i	$0.507799\pi$
$774$		0			0
$775$	−13.4088	+	8.95947i	−0.481658	+	0.321834i
$776$		0			0
$777$	−9.64600	+	14.4363i	−0.346048	+	0.517898i
$778$		0			0
$779$	−2.80224	+	0.850050i	−0.100401	+	0.0304562i
$780$		0			0
$781$	−1.13208	−	0.929078i	−0.0405092	−	0.0332450i
$782$		0			0
$783$	33.8664	+	14.0279i	1.21029	+	0.501317i
$784$		0			0
$785$	6.99819	−	2.89875i	0.249776	−	0.103461i
$786$		0			0
$787$	2.50387	+	25.4222i	0.0892533	+	0.906204i	0.930680	+	0.365833i	$0.119216\pi$
$787$	2.50387	+	25.4222i	0.0892533	+	0.906204i	−0.841427	+	0.540371i	$0.818284\pi$
$788$		0			0
$789$	−9.44664	+	17.6734i	−0.336309	+	0.629190i
$790$		0			0
$791$	−14.5728	+	2.89872i	−0.518150	+	0.103067i
$792$		0			0
$793$	1.19743	−	6.01989i	0.0425220	−	0.213773i
$794$		0			0
$795$	0.835106	−	8.47897i	0.0296181	−	0.300718i
$796$		0			0
$797$	−5.96822	+	19.6746i	−0.211405	+	0.696909i	0.785541	+	0.618810i	$0.212385\pi$
$797$	−5.96822	+	19.6746i	−0.211405	+	0.696909i	−0.996946	+	0.0780990i	$0.975115\pi$
$798$		0			0
$799$	14.5865	+	14.5865i	0.516034	+	0.516034i
$800$		0			0
$801$	−1.07520	+	1.07520i	−0.0379903	+	0.0379903i
$802$		0			0
$803$	−15.8780	−	4.81653i	−0.560321	−	0.169972i
$804$		0			0
$805$	14.7746	+	1.45517i	0.520738	+	0.0512882i
$806$		0			0
$807$	−0.677259	−	0.134715i	−0.0238406	−	0.00474220i
$808$		0			0
$809$	4.15933	+	20.9103i	0.146234	+	0.735169i	0.982414	+	0.186714i	$0.0597837\pi$
$809$	4.15933	+	20.9103i	0.146234	+	0.735169i	−0.836180	+	0.548455i	$0.815216\pi$
$810$		0			0
$811$	25.0352	+	13.3816i	0.879105	+	0.469891i	0.848228	−	0.529632i	$-0.177670\pi$
$811$	25.0352	+	13.3816i	0.879105	+	0.469891i	0.0308774	+	0.999523i	$0.490170\pi$
$812$		0			0
$813$	21.9467	−	2.16156i	0.769703	−	0.0758091i
$814$		0			0
$815$	−10.4880	−	25.3204i	−0.367380	−	0.886933i
$816$		0			0
$817$	−3.08855	+	7.45643i	−0.108055	+	0.260867i
$818$		0			0
$819$	−27.6813	+	33.7298i	−0.967264	+	1.17861i
$820$		0			0
$821$	3.63629	+	11.9872i	0.126907	+	0.418357i	0.997252	−	0.0740860i	$-0.0236039\pi$
$821$	3.63629	+	11.9872i	0.126907	+	0.418357i	−0.870345	+	0.492443i	$0.836104\pi$
$822$		0			0
$823$	10.8193	+	7.22924i	0.377138	+	0.251995i	0.729663	−	0.683807i	$-0.239677\pi$
$823$	10.8193	+	7.22924i	0.377138	+	0.251995i	−0.352525	+	0.935802i	$0.614677\pi$
$824$		0			0
$825$	1.63141	+	2.44158i	0.0567986	+	0.0850050i
$826$		0			0
$827$	−12.8275	+	10.5273i	−0.446057	+	0.366070i	−0.830444	−	0.557102i	$-0.811913\pi$
$827$	−12.8275	+	10.5273i	−0.446057	+	0.366070i	0.384386	+	0.923172i	$0.374413\pi$
$828$		0			0
$829$	−14.2605	−	26.6795i	−0.495288	−	0.926619i	−0.998064	−	0.0622019i	$-0.980188\pi$
$829$	−14.2605	−	26.6795i	−0.495288	−	0.926619i	0.502775	−	0.864417i	$-0.332312\pi$
$830$		0			0
$831$			5.72791i			0.198699i
$832$		0			0
$833$		−	1.90972i		−	0.0661679i
$834$		0			0
$835$	−24.2159	−	45.3048i	−0.838026	−	1.56784i
$836$		0			0
$837$	27.6939	−	22.7278i	0.957243	−	0.785589i
$838$		0			0
$839$	−9.65087	−	14.4435i	−0.333185	−	0.498647i	0.626616	−	0.779328i	$-0.284440\pi$
$839$	−9.65087	−	14.4435i	−0.333185	−	0.498647i	−0.959801	+	0.280682i	$0.909440\pi$
$840$		0			0
$841$	−42.8469	−	28.6294i	−1.47748	−	0.987221i
$842$		0			0
$843$	−5.38895	−	17.7650i	−0.185605	−	0.611859i
$844$		0			0
$845$	−45.1850	+	55.0581i	−1.55441	+	1.89406i
$846$		0			0
$847$	7.00976	−	16.9231i	0.240858	−	0.581483i
$848$		0			0
$849$	−5.56141	−	13.4264i	−0.190867	−	0.460794i
$850$		0			0
$851$	16.3570	−	1.61102i	0.560710	−	0.0552251i
$852$		0			0
$853$	31.0878	+	16.6168i	1.06442	+	0.568947i	0.908098	−	0.418759i	$-0.137535\pi$
$853$	31.0878	+	16.6168i	1.06442	+	0.568947i	0.156327	+	0.987705i	$0.450035\pi$
$854$		0			0
$855$	3.07602	+	15.4642i	0.105198	+	0.528864i
$856$		0			0
$857$	25.6961	+	5.11127i	0.877761	+	0.174598i	0.613349	−	0.789812i	$-0.289822\pi$
$857$	25.6961	+	5.11127i	0.877761	+	0.174598i	0.264412	+	0.964410i	$0.414822\pi$
$858$		0			0
$859$	7.59275	+	0.747820i	0.259061	+	0.0255153i	0.226714	−	0.973961i	$-0.427202\pi$
$859$	7.59275	+	0.747820i	0.259061	+	0.0255153i	0.0323472	+	0.999477i	$0.489702\pi$
$860$		0			0
$861$	−2.40279	−	0.728878i	−0.0818868	−	0.0248401i
$862$		0			0
$863$	7.80163	−	7.80163i	0.265571	−	0.265571i	−0.561742	−	0.827313i	$-0.689869\pi$
$863$	7.80163	−	7.80163i	0.265571	−	0.265571i	0.827313	+	0.561742i	$0.189869\pi$
$864$		0			0
$865$	−1.12565	−	1.12565i	−0.0382732	−	0.0382732i
$866$		0			0
$867$	2.87954	−	9.49258i	0.0977944	−	0.322385i
$868$		0			0
$869$	3.29196	−	33.4238i	0.111672	−	1.13383i
$870$		0			0
$871$	11.6269	−	58.4524i	0.393963	−	1.98058i
$872$		0			0
$873$	−27.4230	+	5.45478i	−0.928129	+	0.184616i
$874$		0			0
$875$	−11.0085	+	20.5954i	−0.372154	+	0.696251i
$876$		0			0
$877$	−3.54391	−	35.9819i	−0.119669	−	1.21502i	−0.848075	−	0.529876i	$-0.822239\pi$
$877$	−3.54391	−	35.9819i	−0.119669	−	1.21502i	0.728406	−	0.685146i	$-0.240261\pi$
$878$		0			0
$879$	17.1487	−	7.10322i	0.578411	−	0.239586i
$880$		0			0
$881$	−31.0850	−	12.8758i	−1.04728	−	0.433798i	−0.208360	−	0.978052i	$-0.566813\pi$
$881$	−31.0850	−	12.8758i	−1.04728	−	0.433798i	−0.838920	+	0.544255i	$0.816813\pi$
$882$		0			0
$883$	−6.29864	−	5.16916i	−0.211966	−	0.173956i	0.522419	−	0.852689i	$-0.325030\pi$
$883$	−6.29864	−	5.16916i	−0.211966	−	0.173956i	−0.734385	+	0.678733i	$0.762530\pi$
$884$		0			0
$885$	−8.51859	+	2.58409i	−0.286349	+	0.0868631i
$886$		0			0
$887$	13.4820	−	20.1773i	0.452683	−	0.677488i	−0.532997	−	0.846117i	$-0.678934\pi$
$887$	13.4820	−	20.1773i	0.452683	−	0.677488i	0.985679	+	0.168630i	$0.0539342\pi$
$888$		0			0
$889$	19.9870	−	13.3549i	0.670342	−	0.447908i
$890$		0			0
$891$	5.70990	+	6.95753i	0.191289	+	0.233086i
$892$		0			0
$893$	23.1040	−	12.3493i	0.773144	−	0.413254i
$894$		0			0
$895$	2.75690			0.0921530
$896$		0			0
$897$	−9.58082			−0.319894
$898$		0			0
$899$	−69.4132	+	37.1021i	−2.31506	+	1.23742i
$900$		0			0
$901$	5.36167	+	6.53321i	0.178623	+	0.217653i
$902$		0			0
$903$	−5.75403	+	3.84472i	−0.191482	+	0.127944i
$904$		0			0
$905$	−5.23077	+	7.82840i	−0.173877	+	0.260225i
$906$		0			0
$907$	43.6608	−	13.2444i	1.44973	−	0.439772i	0.535353	−	0.844628i	$-0.320179\pi$
$907$	43.6608	−	13.2444i	1.44973	−	0.439772i	0.914380	+	0.404857i	$0.132679\pi$
$908$		0			0
$909$	3.66529	+	3.00803i	0.121570	+	0.0997699i
$910$		0			0
$911$	−23.5278	−	9.74555i	−0.779512	−	0.322884i	−0.0427934	−	0.999084i	$-0.513626\pi$
$911$	−23.5278	−	9.74555i	−0.779512	−	0.322884i	−0.736719	+	0.676200i	$0.763626\pi$
$912$		0			0
$913$	−3.51270	+	1.45501i	−0.116253	+	0.0481537i
$914$		0			0
$915$	−0.186402	−	1.89258i	−0.00616227	−	0.0625666i
$916$		0			0
$917$	28.4924	−	53.3056i	0.940903	−	1.76031i
$918$		0			0
$919$	−9.42163	+	1.87408i	−0.310791	+	0.0618202i	−0.348022	−	0.937487i	$-0.613146\pi$
$919$	−9.42163	+	1.87408i	−0.310791	+	0.0618202i	0.0372305	+	0.999307i	$0.488146\pi$
$920$		0			0
$921$	2.67959	−	13.4712i	0.0882955	−	0.443892i
$922$		0			0
$923$	0.428500	−	4.35063i	0.0141042	−	0.143203i
$924$		0			0
$925$	4.36517	−	14.3900i	0.143526	−	0.473141i
$926$		0			0
$927$	18.4188	+	18.4188i	0.604954	+	0.604954i
$928$		0			0
$929$	−22.9707	+	22.9707i	−0.753643	+	0.753643i	−0.975157	−	0.221514i	$-0.928900\pi$
$929$	−22.9707	+	22.9707i	−0.753643	+	0.753643i	0.221514	+	0.975157i	$0.428900\pi$
$930$		0			0
$931$	−2.32084	−	0.704018i	−0.0760624	−	0.0230733i
$932$		0			0
$933$	3.81913	+	0.376151i	0.125033	+	0.0123146i
$934$		0			0
$935$	−10.6258	−	2.11360i	−0.347500	−	0.0691221i
$936$		0			0
$937$	4.04164	+	20.3187i	0.132035	+	0.663783i	0.988941	+	0.148310i	$0.0473835\pi$
$937$	4.04164	+	20.3187i	0.132035	+	0.663783i	−0.856906	+	0.515472i	$0.827617\pi$
$938$		0			0
$939$	10.7441	+	5.74285i	0.350621	+	0.187411i
$940$		0			0
$941$	12.8088	−	1.26155i	0.417554	−	0.0411254i	0.112941	−	0.993602i	$-0.463973\pi$
$941$	12.8088	−	1.26155i	0.417554	−	0.0411254i	0.304613	+	0.952476i	$0.401473\pi$
$942$		0			0
$943$	0.909623	+	2.19602i	0.0296214	+	0.0715124i
$944$		0			0
$945$	−11.5475	+	27.8780i	−0.375639	+	0.906872i
$946$		0			0
$947$	−4.25737	+	5.18762i	−0.138346	+	0.168575i	−0.837574	−	0.546323i	$-0.816027\pi$
$947$	−4.25737	+	5.18762i	−0.138346	+	0.168575i	0.699229	+	0.714898i	$0.253527\pi$
$948$		0			0
$949$	−14.3777	−	47.3969i	−0.466719	−	1.53857i
$950$		0			0
$951$	−14.7721	−	9.87041i	−0.479019	−	0.320070i
$952$		0			0
$953$	8.56586	+	12.8197i	0.277476	+	0.415271i	0.943865	−	0.330333i	$-0.107161\pi$
$953$	8.56586	+	12.8197i	0.277476	+	0.415271i	−0.666389	+	0.745604i	$0.732161\pi$
$954$		0			0
$955$	29.9820	−	24.6056i	0.970195	−	0.796218i
$956$		0			0
$957$	6.75586	+	12.6393i	0.218386	+	0.408571i
$958$		0			0
$959$			21.0396i			0.679403i
$960$		0			0
$961$			45.9233i			1.48140i
$962$		0			0
$963$	23.3895	+	43.7587i	0.753717	+	1.41011i
$964$		0			0
$965$	43.4854	−	35.6875i	1.39984	−	1.14882i
$966$		0			0
$967$	−30.9314	−	46.2921i	−0.994686	−	1.48865i	−0.867910	−	0.496721i	$-0.834537\pi$
$967$	−30.9314	−	46.2921i	−0.994686	−	1.48865i	−0.126775	−	0.991931i	$-0.540463\pi$
$968$		0			0
$969$	3.01637	+	2.01547i	0.0968997	+	0.0647463i
$970$		0			0
$971$	8.09273	+	26.6782i	0.259708	+	0.856143i	0.985710	+	0.168450i	$0.0538763\pi$
$971$	8.09273	+	26.6782i	0.259708	+	0.856143i	−0.726002	+	0.687693i	$0.758624\pi$
$972$		0			0
$973$	5.19824	−	6.33407i	0.166648	−	0.203061i
$974$		0			0
$975$	−3.35444	+	8.09833i	−0.107428	+	0.259354i
$976$		0			0
$977$	−15.2633	−	36.8488i	−0.488316	−	1.17890i	−0.955567	−	0.294774i	$-0.904756\pi$
$977$	−15.2633	−	36.8488i	−0.488316	−	1.17890i	0.467251	−	0.884125i	$-0.345244\pi$
$978$		0			0
$979$	−1.32048	+	0.130056i	−0.0422027	+	0.00415660i
$980$		0			0
$981$	−3.83182	−	2.04815i	−0.122341	−	0.0653924i
$982$		0			0
$983$	−3.46822	−	17.4359i	−0.110619	−	0.556119i	−0.995853	−	0.0909737i	$-0.971002\pi$
$983$	−3.46822	−	17.4359i	−0.110619	−	0.556119i	0.885234	−	0.465145i	$-0.153998\pi$
$984$		0			0
$985$	14.5226	+	2.88872i	0.462728	+	0.0920423i
$986$		0			0
$987$	22.3548	+	2.20175i	0.711561	+	0.0700826i
$988$		0			0
$989$	6.26905	+	1.90170i	0.199344	+	0.0604704i
$990$		0			0
$991$	−33.1594	+	33.1594i	−1.05334	+	1.05334i	−0.0548477	+	0.998495i	$0.517467\pi$
$991$	−33.1594	+	33.1594i	−1.05334	+	1.05334i	−0.998495	+	0.0548477i	$0.982533\pi$
$992$		0			0
$993$	−4.90052	−	4.90052i	−0.155513	−	0.155513i
$994$		0			0
$995$	−14.7356	+	48.5768i	−0.467151	+	1.53999i
$996$		0			0
$997$	0.863302	−	8.76525i	0.0273410	−	0.277598i	−0.971787	−	0.235858i	$-0.924210\pi$
$997$	0.863302	−	8.76525i	0.0273410	−	0.277598i	0.999129	−	0.0417400i	$-0.0132901\pi$
$998$		0			0
$999$	−6.51731	+	32.7648i	−0.206199	+	1.03663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.497.6		240
4.3	odd	2		128.2.k.a.101.5	✓	240
128.19	odd	32		128.2.k.a.109.5	yes	240
128.109	even	32	inner	512.2.k.a.273.6		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.101.5	✓	240	4.3	odd	2
128.2.k.a.109.5	yes	240	128.19	odd	32
512.2.k.a.273.6		240	128.109	even	32	inner
512.2.k.a.497.6		240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.k (of order \(32\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.662806 + 0.354277i) q^{3} +(1.65900 + 2.02149i) q^{5} +(-2.34874 + 1.56938i) q^{7} +(-1.35291 + 2.02477i) q^{9} +(-2.03348 + 0.616848i) q^{11} +(-4.90337 - 4.02409i) q^{13} +(-1.81576 - 0.752114i) q^{15} +(1.80120 - 0.746080i) q^{17} +(-0.242682 - 2.46399i) q^{19} +(1.00077 - 1.87230i) q^{21} +(-1.97111 + 0.392078i) q^{23} +(-0.358715 + 1.80338i) q^{25} +(0.400380 - 4.06513i) q^{27} +(-2.60500 + 8.58752i) q^{29} +(6.20175 + 6.20175i) q^{31} +(1.12927 - 1.12927i) q^{33} +(-7.06905 - 2.14437i) q^{35} +(-8.13891 - 0.801613i) q^{37} +(4.67563 + 0.930040i) q^{39} +(-0.230739 - 1.16000i) q^{41} +(-2.87481 - 1.53662i) q^{43} +(-6.33755 + 0.624194i) q^{45} +(4.04912 + 9.77544i) q^{47} +(0.374856 - 0.904982i) q^{49} +(-0.929525 + 1.13263i) q^{51} +(1.25840 + 4.14840i) q^{53} +(-4.62049 - 3.08731i) q^{55} +(1.03379 + 1.54717i) q^{57} +(3.50126 - 2.87341i) q^{59} +(0.456134 + 0.853366i) q^{61} -6.87891i q^{63} -16.5881i q^{65} +(4.42900 + 8.28608i) q^{67} +(1.16756 - 0.958191i) q^{69} +(0.382894 + 0.573041i) q^{71} +(6.49235 + 4.33805i) q^{73} +(-0.401139 - 1.32238i) q^{75} +(3.80804 - 4.64011i) q^{77} +(-6.04837 + 14.6020i) q^{79} +(-1.62090 - 3.91319i) q^{81} +(1.78064 - 0.175377i) q^{83} +(4.49638 + 2.40336i) q^{85} +(-1.31576 - 6.61475i) q^{87} +(0.612417 + 0.121817i) q^{89} +(17.8321 + 1.75631i) q^{91} +(-6.30769 - 1.91342i) q^{93} +(4.57834 - 4.57834i) q^{95} +(8.11888 + 8.11888i) q^{97} +(1.50213 - 4.95187i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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