LMFDB - Embedded newform 512.2.k.a.273.6

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			273.6
Character	$\chi$	$=$	512.273
Dual form			512.2.k.a.497.6

$q$-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 $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{23}{32}\right)$	$1$

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	0.268833	−	0.963187i	$-0.413362\pi$
$3$	−0.662806	−	0.354277i	−0.382671	−	0.204542i	−0.651505	+	0.758645i	$0.725862\pi$
$4$		0			0
$5$	1.65900	−	2.02149i	0.741926	−	0.904040i	−0.256112	−	0.966647i	$-0.582442\pi$
$5$	1.65900	−	2.02149i	0.741926	−	0.904040i	0.998038	+	0.0626073i	$0.0199416\pi$
$6$		0			0
$7$	−2.34874	−	1.56938i	−0.887741	−	0.593170i	0.0259119	−	0.999664i	$-0.491751\pi$
$7$	−2.34874	−	1.56938i	−0.887741	−	0.593170i	−0.913653	+	0.406494i	$0.866751\pi$
$8$		0			0
$9$	−1.35291	−	2.02477i	−0.450970	−	0.674925i
$10$		0			0
$11$	−2.03348	−	0.616848i	−0.613116	−	0.185987i	−0.0315719	−	0.999501i	$-0.510051\pi$
$11$	−2.03348	−	0.616848i	−0.613116	−	0.185987i	−0.581544	+	0.813515i	$0.697551\pi$
$12$		0			0
$13$	−4.90337	+	4.02409i	−1.35995	+	1.11608i	−0.378238	+	0.925708i	$0.623470\pi$
$13$	−4.90337	+	4.02409i	−1.35995	+	1.11608i	−0.981712	+	0.190373i	$0.939030\pi$
$14$		0			0
$15$	−1.81576	+	0.752114i	−0.468828	+	0.194195i
$16$		0			0
$17$	1.80120	+	0.746080i	0.436854	+	0.180951i	0.590262	−	0.807212i	$-0.299025\pi$
$17$	1.80120	+	0.746080i	0.436854	+	0.180951i	−0.153407	+	0.988163i	$0.549025\pi$
$18$		0			0
$19$	−0.242682	+	2.46399i	−0.0556751	+	0.565278i	0.926368	+	0.376620i	$0.122914\pi$
$19$	−0.242682	+	2.46399i	−0.0556751	+	0.565278i	−0.982043	+	0.188658i	$0.939586\pi$
$20$		0			0
$21$	1.00077	+	1.87230i	0.218385	+	0.408570i
$22$		0			0
$23$	−1.97111	−	0.392078i	−0.411005	−	0.0817539i	−0.0147426	−	0.999891i	$-0.504693\pi$
$23$	−1.97111	−	0.392078i	−0.411005	−	0.0817539i	−0.396262	+	0.918137i	$0.629693\pi$
$24$		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	−0.771016	−	0.636816i	$-0.780251\pi$
$29$	−2.60500	−	8.58752i	−0.483736	−	1.59466i	0.287280	−	0.957847i	$-0.407249\pi$
$30$		0			0
$31$	6.20175	−	6.20175i	1.11387	−	1.11387i	0.121244	−	0.992623i	$-0.461312\pi$
$31$	6.20175	−	6.20175i	1.11387	−	1.11387i	0.992623	−	0.121244i	$-0.0386883\pi$
$32$		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	−0.741579	−	0.670866i	$-0.765923\pi$
$37$	−8.13891	+	0.801613i	−1.33803	+	0.131784i	−0.596450	+	0.802650i	$0.703423\pi$
$38$		0			0
$39$	4.67563	−	0.930040i	0.748699	−	0.148926i
$40$		0			0
$41$	−0.230739	+	1.16000i	−0.0360353	+	0.181162i	−0.994611	−	0.103676i	$-0.966940\pi$
$41$	−0.230739	+	1.16000i	−0.0360353	+	0.181162i	0.958576	+	0.284837i	$0.0919396\pi$
$42$		0			0
$43$	−2.87481	+	1.53662i	−0.438405	+	0.234332i	−0.675806	−	0.737079i	$-0.736204\pi$
$43$	−2.87481	+	1.53662i	−0.438405	+	0.234332i	0.237401	+	0.971412i	$0.423704\pi$
$44$		0			0
$45$	−6.33755	−	0.624194i	−0.944746	−	0.0930493i
$46$		0			0
$47$	4.04912	−	9.77544i	0.590625	−	1.42589i	−0.292275	−	0.956334i	$-0.594412\pi$
$47$	4.04912	−	9.77544i	0.590625	−	1.42589i	0.882900	−	0.469560i	$-0.155588\pi$
$48$		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	−0.827115	−	0.562033i	$-0.810019\pi$
$53$	1.25840	−	4.14840i	0.172855	−	0.569826i	0.999970	−	0.00779304i	$-0.00248063\pi$
$54$		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	0.834105	−	0.551605i	$-0.185984\pi$
$59$	3.50126	+	2.87341i	0.455825	+	0.374086i	−0.378280	+	0.925691i	$0.623484\pi$
$60$		0			0
$61$	0.456134	−	0.853366i	0.0584019	−	0.109262i	−0.851027	−	0.525123i	$-0.824019\pi$
$61$	0.456134	−	0.853366i	0.0584019	−	0.109262i	0.909429	+	0.415860i	$0.136519\pi$
$62$		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	−0.451671	−	0.892185i	$-0.649172\pi$
$67$	4.42900	−	8.28608i	0.541089	−	1.01231i	0.992759	−	0.120121i	$-0.0383282\pi$
$68$		0			0
$69$	1.16756	+	0.958191i	0.140558	+	0.115353i
$70$		0			0
$71$	0.382894	−	0.573041i	0.0454411	−	0.0680074i	−0.808053	−	0.589109i	$-0.799479\pi$
$71$	0.382894	−	0.573041i	0.0454411	−	0.0680074i	0.853495	+	0.521102i	$0.174479\pi$
$72$		0			0
$73$	6.49235	−	4.33805i	0.759872	−	0.507730i	−0.114241	−	0.993453i	$-0.536444\pi$
$73$	6.49235	−	4.33805i	0.759872	−	0.507730i	0.874113	+	0.485723i	$0.161444\pi$
$74$		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	−0.763103	−	0.646276i	$-0.776325\pi$
$79$	−6.04837	−	14.6020i	−0.680494	−	1.64286i	0.0826092	−	0.996582i	$-0.473675\pi$
$80$		0			0
$81$	−1.62090	+	3.91319i	−0.180100	+	0.434799i
$82$		0			0
$83$	1.78064	+	0.175377i	0.195450	+	0.0192502i	0.195269	−	0.980750i	$-0.437442\pi$
$83$	1.78064	+	0.175377i	0.195450	+	0.0192502i	0.000181674		1.00000i	$0.499942\pi$
$84$		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	−0.162525	−	0.986704i	$-0.551964\pi$
$89$	0.612417	−	0.121817i	0.0649161	−	0.0129126i	0.227442	+	0.973792i	$0.426964\pi$
$90$		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	−0.162381	−	0.986728i	$-0.551917\pi$
$97$	8.11888	−	8.11888i	0.824347	−	0.824347i	0.986728	+	0.162381i	$0.0519173\pi$
$98$		0			0
$99$	1.50213	+	4.95187i	0.150970	+	0.497682i
$100$		0			0
$101$	0.190851	+	1.93774i	0.0189904	+	0.192813i	0.999999	−	0.00114974i	$-0.000365975\pi$
$101$	0.190851	+	1.93774i	0.0189904	+	0.192813i	−0.981009	+	0.193963i	$0.937866\pi$
$102$		0			0
$103$	2.08681	+	10.4911i	0.205619	+	1.03372i	0.936354	+	0.351057i	$0.114178\pi$
$103$	2.08681	+	10.4911i	0.205619	+	1.03372i	−0.730735	+	0.682661i	$0.760822\pi$
$104$		0			0
$105$	5.44511	+	1.08310i	0.531389	+	0.105700i
$106$		0			0
$107$	9.60487	+	17.9694i	0.928537	+	1.73717i	0.617056	+	0.786919i	$0.288325\pi$
$107$	9.60487	+	17.9694i	0.928537	+	1.73717i	0.311481	+	0.950252i	$0.399175\pi$
$108$		0			0
$109$	0.174883	−	1.77562i	0.0167507	−	0.170073i	−0.983170	−	0.182695i	$-0.941518\pi$
$109$	0.174883	−	1.77562i	0.0167507	−	0.170073i	0.999920	+	0.0126221i	$0.00401785\pi$
$110$		0			0
$111$	5.67851	+	2.35212i	0.538981	+	0.223253i
$112$		0			0
$113$	4.85955	−	2.01289i	0.457148	−	0.189357i	−0.142212	−	0.989836i	$-0.545422\pi$
$113$	4.85955	−	2.01289i	0.457148	−	0.189357i	0.599361	+	0.800479i	$0.295422\pi$
$114$		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	−0.991872	−	0.127243i	$-0.959387\pi$
$131$	−18.8705	−	10.0865i	−1.64872	−	0.881262i	−0.656853	−	0.754019i	$-0.728113\pi$
$132$		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	0.965027	−	0.262152i	$-0.0844321\pi$
$137$	4.13797	+	6.19290i	0.353530	+	0.529096i	−0.611496	+	0.791247i	$0.709432\pi$
$138$		0			0
$139$	−2.77583	−	0.842040i	−0.235443	−	0.0714209i	0.170358	−	0.985382i	$-0.445508\pi$
$139$	−2.77583	−	0.842040i	−0.235443	−	0.0714209i	−0.405801	+	0.913961i	$0.633008\pi$
$140$		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	0.981501	−	0.191459i	$-0.0613218\pi$
$149$	3.38141	+	6.32618i	0.277016	+	0.518261i	−0.704485	+	0.709719i	$0.748822\pi$
$150$		0			0
$151$	−0.113929	−	0.0226619i	−0.00927140	−	0.00184420i	0.190452	−	0.981696i	$-0.439005\pi$
$151$	−0.113929	−	0.0226619i	−0.00927140	−	0.00184420i	−0.199724	+	0.979852i	$0.564005\pi$
$152$		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	0.984079	−	0.177731i	$-0.0568756\pi$
$157$	0.840828	+	2.77184i	0.0671054	+	0.221217i	−0.916974	+	0.398947i	$0.869376\pi$
$158$		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	−0.657469	−	0.753482i	$-0.728373\pi$
$163$	−10.0289	+	3.04222i	−0.785522	+	0.238285i	−0.128053	+	0.991767i	$0.540873\pi$
$164$		0			0
$165$	4.15625	−	0.409355i	0.323564	−	0.0318683i
$166$		0			0
$167$	−19.2664	+	3.83233i	−1.49088	+	0.296554i	−0.872223	−	0.489108i	$-0.837323\pi$
$167$	−19.2664	+	3.83233i	−1.49088	+	0.296554i	−0.618656	+	0.785662i	$0.712323\pi$
$168$		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	0.0749616	−	0.997186i	$-0.476117\pi$
$173$	−0.605806	−	0.0596667i	−0.0460586	−	0.00453638i	−0.121020	+	0.992650i	$0.538617\pi$
$174$		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	0.797404	−	0.603445i	$-0.206206\pi$
$179$	0.668794	+	0.814928i	0.0499880	+	0.0609106i	−0.747416	+	0.664356i	$0.768706\pi$
$180$		0			0
$181$	1.04511	−	3.44528i	0.0776827	−	0.256086i	−0.909494	−	0.415717i	$-0.863531\pi$
$181$	1.04511	−	3.44528i	0.0776827	−	0.256086i	0.987177	+	0.159632i	$0.0510306\pi$
$182$		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	$0.180287\pi$
$191$			14.8316i			1.07318i	−0.843844	+	0.536588i	$0.819713\pi$
$192$		0			0
$193$			21.5115i			1.54843i	0.632922	+	0.774216i	$0.281855\pi$
$193$			21.5115i			1.54843i	−0.632922	+	0.774216i	$0.718145\pi$
$194$		0			0
$195$	5.87678	−	10.9947i	0.420845	−	0.787346i
$196$		0			0
$197$	4.37691	+	3.59204i	0.311842	+	0.255922i	0.777275	−	0.629161i	$-0.216601\pi$
$197$	4.37691	+	3.59204i	0.311842	+	0.255922i	−0.465433	+	0.885083i	$0.654101\pi$
$198$		0			0
$199$	10.7844	−	16.1400i	0.764486	−	1.14413i	−0.221148	−	0.975240i	$-0.570981\pi$
$199$	10.7844	−	16.1400i	0.764486	−	1.14413i	0.985634	−	0.168894i	$-0.0540195\pi$
$200$		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	0.869531	−	0.493879i	$-0.164421\pi$
$211$	23.6191	+	2.32627i	1.62600	+	0.160147i	0.756472	+	0.654026i	$0.226921\pi$
$212$		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	0.664900	−	0.746933i	$-0.268474\pi$
$223$	−1.22502	−	1.22502i	−0.0820332	−	0.0820332i	−0.746933	+	0.664900i	$0.768474\pi$
$224$		0			0
$225$	−3.16614	+	3.16614i	−0.211076	+	0.211076i
$226$		0			0
$227$	−4.61807	−	15.2237i	−0.306512	−	1.01044i	−0.965961	−	0.258686i	$-0.916710\pi$
$227$	−4.61807	−	15.2237i	−0.306512	−	1.01044i	0.659449	−	0.751749i	$-0.270790\pi$
$228$		0			0
$229$	−2.74749	−	27.8958i	−0.181559	−	1.84340i	−0.466090	−	0.884737i	$-0.654338\pi$
$229$	−2.74749	−	27.8958i	−0.181559	−	1.84340i	0.284531	−	0.958667i	$-0.408162\pi$
$230$		0			0
$231$	−0.880108	−	4.42460i	−0.0579068	−	0.291117i
$232$		0			0
$233$	12.8710	+	2.56020i	0.843206	+	0.167724i	0.597749	−	0.801683i	$-0.296062\pi$
$233$	12.8710	+	2.56020i	0.843206	+	0.167724i	0.245457	+	0.969408i	$0.421062\pi$
$234$		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	0.542310	−	0.840178i	$-0.317550\pi$
$239$	5.12774	+	2.12398i	0.331686	+	0.137389i	−0.210624	+	0.977567i	$0.567550\pi$
$240$		0			0
$241$	6.38640	−	2.64533i	0.411384	−	0.170401i	−0.167386	−	0.985891i	$-0.553533\pi$
$241$	6.38640	−	2.64533i	0.411384	−	0.170401i	0.578770	+	0.815491i	$0.303533\pi$
$242$		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	−0.936283	−	0.351247i	$-0.885758\pi$
$251$	−6.48177	+	7.89806i	−0.409126	+	0.498521i	0.527157	+	0.849768i	$0.323258\pi$
$252$		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	0.999861	−	0.0166526i	$-0.00530093\pi$
$263$	22.1707	+	14.8140i	1.36711	+	0.913471i	0.367245	+	0.930124i	$0.380301\pi$
$264$		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	−0.612492	−	0.790477i	$-0.709833\pi$
$269$	0.710247	−	0.582885i	0.0433045	−	0.0355391i	0.655797	+	0.754938i	$0.272333\pi$
$270$		0			0
$271$	−27.1096	+	11.2292i	−1.64679	+	0.682124i	−0.996957	−	0.0779520i	$-0.975162\pi$
$271$	−27.1096	+	11.2292i	−1.64679	+	0.682124i	−0.649835	+	0.760076i	$0.725162\pi$
$272$		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	0.966426	−	0.256945i	$-0.0827158\pi$
$277$	3.59274	+	6.72154i	0.215867	+	0.403858i	−0.750559	+	0.660803i	$0.770216\pi$
$278$		0			0
$279$	−20.9476	−	4.16673i	−1.25410	−	0.249455i
$280$		0			0
$281$	−4.81902	−	24.2269i	−0.287479	−	1.44525i	−0.806876	−	0.590721i	$-0.798843\pi$
$281$	−4.81902	−	24.2269i	−0.287479	−	1.44525i	0.519397	−	0.854533i	$-0.326157\pi$
$282$		0			0
$283$	−1.89536	−	19.2439i	−0.112667	−	1.14393i	−0.870735	−	0.491753i	$-0.836356\pi$
$283$	−1.89536	−	19.2439i	−0.112667	−	1.14393i	0.758068	−	0.652176i	$-0.226144\pi$
$284$		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	−0.785833	−	0.618438i	$-0.787766\pi$
$293$	−24.5789	+	2.42081i	−1.43592	+	0.141425i	−0.650083	+	0.759864i	$0.725266\pi$
$294$		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	0.328706	−	0.944432i	$-0.393387\pi$
$307$	−11.5940	−	14.1274i	−0.661706	−	0.806292i	−0.990413	+	0.138141i	$0.955887\pi$
$308$		0			0
$309$	2.33361	−	7.69287i	0.132754	−	0.437632i
$310$		0			0
$311$	−4.24571	+	2.83689i	−0.240752	+	0.160865i	−0.670093	−	0.742277i	$-0.733746\pi$
$311$	−4.24571	+	2.83689i	−0.240752	+	0.160865i	0.429341	+	0.903142i	$0.358746\pi$
$312$		0			0
$313$	−9.00582	+	13.4782i	−0.509039	+	0.761831i	−0.993604	−	0.112925i	$-0.963978\pi$
$313$	−9.00582	+	13.4782i	−0.509039	+	0.761831i	0.484564	+	0.874756i	$0.338978\pi$
$314$		0			0
$315$	13.9057	+	11.4121i	0.783496	+	0.642998i
$316$		0			0
$317$	11.1436	−	20.8482i	0.625888	−	1.17095i	−0.346603	−	0.938012i	$-0.612665\pi$
$317$	11.1436	−	20.8482i	0.625888	−	1.17095i	0.972491	−	0.232942i	$-0.0748352\pi$
$318$		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	−0.852134	−	0.523324i	$-0.824692\pi$
$331$	2.67685	−	8.82439i	0.147133	−	0.485033i	0.999267	+	0.0382918i	$0.0121916\pi$
$332$		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	−0.432538	−	0.901616i	$-0.642382\pi$
$337$	9.37798	−	22.6404i	0.510851	−	1.23330i	0.943389	−	0.331688i	$-0.107618\pi$
$338$		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	−0.352736	−	0.935723i	$-0.614749\pi$
$347$	−9.61469	+	0.946965i	−0.516144	+	0.0508357i	−0.163408	+	0.986559i	$0.552249\pi$
$348$		0			0
$349$	12.6203	−	3.82833i	0.675550	−	0.204926i	0.0661751	−	0.997808i	$-0.478920\pi$
$349$	12.6203	−	3.82833i	0.675550	−	0.204926i	0.609375	+	0.792882i	$0.291420\pi$
$350$		0			0
$351$	−18.3216	−	18.3216i	−0.977937	−	0.977937i
$352$		0			0
$353$	−14.4352	+	14.4352i	−0.768308	+	0.768308i	−0.977808	−	0.209501i	$-0.932816\pi$
$353$	−14.4352	+	14.4352i	−0.768308	+	0.768308i	0.209501	+	0.977808i	$0.432816\pi$
$354$		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	0.998151	−	0.0607831i	$-0.0193598\pi$
$359$	0.998883	+	5.02172i	0.0527190	+	0.265036i	−0.945432	+	0.325820i	$0.894360\pi$
$360$		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	0.328207	−	0.944606i	$-0.393556\pi$
$367$	−2.06234	−	0.854248i	−0.107653	−	0.0445914i	−0.435860	+	0.900014i	$0.643556\pi$
$368$		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	0.256302	−	0.966597i	$-0.417496\pi$
$373$	−1.30563	−	0.396057i	−0.0676027	−	0.0205071i	−0.323905	+	0.946090i	$0.604996\pi$
$374$		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	−0.550855	−	0.834601i	$-0.685698\pi$
$379$	7.30390	−	8.89983i	0.375176	−	0.457154i	0.926031	+	0.377448i	$0.123198\pi$
$380$		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	−0.650695	−	0.759339i	$-0.725523\pi$
$389$	4.35875	−	5.31115i	0.220997	−	0.269286i	0.871693	+	0.490053i	$0.163023\pi$
$390$		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	−0.553154	−	0.833079i	$-0.686576\pi$
$397$	3.10832	−	2.55094i	0.156002	−	0.128028i	0.709157	+	0.705051i	$0.249076\pi$
$398$		0			0
$399$	−4.85620	+	2.01150i	−0.243114	+	0.100701i
$400$		0			0
$401$	20.7974	+	8.61456i	1.03857	+	0.430190i	0.835799	−	0.549035i	$-0.185005\pi$
$401$	20.7974	+	8.61456i	1.03857	+	0.430190i	0.202772	+	0.979226i	$0.435005\pi$
$402$		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	0.971293	+	0.237888i	$0.0764550\pi$
$409$	3.33633	+	16.7729i	0.164971	+	0.829365i	−0.806322	+	0.591477i	$0.798545\pi$
$410$		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	−0.206933	−	0.978355i	$-0.566348\pi$
$419$	3.36832	−	1.02177i	0.164553	−	0.0499166i	0.371486	+	0.928438i	$0.378848\pi$
$420$		0			0
$421$	−19.1790	+	1.88897i	−0.934729	+	0.0920627i	−0.553900	−	0.832583i	$-0.686861\pi$
$421$	−19.1790	+	1.88897i	−0.934729	+	0.0920627i	−0.380828	+	0.924646i	$0.624361\pi$
$422$		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	−0.988508	−	0.151165i	$-0.951697\pi$
$431$	−3.79165	+	9.15385i	−0.182637	+	0.440925i	0.805871	+	0.592091i	$0.201697\pi$
$432$		0			0
$433$	3.46071	+	8.35490i	0.166311	+	0.401511i	0.984960	−	0.172784i	$-0.0552763\pi$
$433$	3.46071	+	8.35490i	0.166311	+	0.401511i	−0.818649	+	0.574295i	$0.805276\pi$
$434$		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	−0.0102251	−	0.999948i	$-0.503255\pi$
$439$	19.0602	−	12.7356i	0.909693	−	0.607838i	0.919918	+	0.392110i	$0.128255\pi$
$440$		0			0
$441$	1.32524	−	1.98336i	0.0631065	−	0.0944456i
$442$		0			0
$443$	4.88931	+	4.01255i	0.232298	+	0.190642i	0.743340	−	0.668914i	$-0.233240\pi$
$443$	4.88931	+	4.01255i	0.232298	+	0.190642i	−0.511042	+	0.859556i	$0.670740\pi$
$444$		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	$-0.731984\pi$
$449$		−	31.6138i		−	1.49195i	0.665975	−	0.745974i	$-0.268016\pi$
$450$		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	−0.839191	−	0.543836i	$-0.816971\pi$
$457$	−14.0642	+	9.39741i	−0.657897	+	0.439592i	0.181295	+	0.983429i	$0.441971\pi$
$458$		0			0
$459$	−2.31175	+	7.62081i	−0.107903	+	0.355709i
$460$		0			0
$461$	5.17600	+	6.30698i	0.241071	+	0.293745i	0.879465	−	0.475964i	$-0.157901\pi$
$461$	5.17600	+	6.30698i	0.241071	+	0.293745i	−0.638394	+	0.769710i	$0.720401\pi$
$462$		0			0
$463$	9.87176	+	23.8325i	0.458780	+	1.10759i	0.968892	+	0.247484i	$0.0796039\pi$
$463$	9.87176	+	23.8325i	0.458780	+	1.10759i	−0.510112	+	0.860108i	$0.670396\pi$
$464$		0			0
$465$	−6.59649	+	15.9253i	−0.305905	+	0.738519i
$466$		0			0
$467$	16.7281	+	1.64758i	0.774086	+	0.0762408i	0.477344	−	0.878717i	$-0.341600\pi$
$467$	16.7281	+	1.64758i	0.774086	+	0.0762408i	0.296742	+	0.954958i	$0.404100\pi$
$468$		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	0.995794	+	0.0916184i	$0.0292040\pi$
$479$	23.7992	+	23.7992i	1.08741	+	1.08741i	0.0916184	+	0.995794i	$0.470796\pi$
$480$		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	−0.907754	−	0.419504i	$-0.862204\pi$
$487$	−5.06762	−	25.4767i	−0.229636	−	1.15446i	0.678118	−	0.734953i	$-0.262796\pi$
$488$		0			0
$489$	7.72499	+	1.53660i	0.349336	+	0.0694873i
$490$		0			0
$491$	14.1721	+	26.5142i	0.639579	+	1.19657i	0.967741	+	0.251947i	$0.0810710\pi$
$491$	14.1721	+	26.5142i	0.639579	+	1.19657i	−0.328161	+	0.944622i	$0.606429\pi$
$492$		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	−0.484490	−	0.874797i	$-0.660995\pi$
$499$	6.23192	−	5.11441i	0.278979	−	0.228952i	0.763469	+	0.645845i	$0.223495\pi$
$500$		0			0
$501$	14.1276	+	4.28556i	0.631175	+	0.191465i
$502$		0			0
$503$	−14.1261	−	21.1411i	−0.629850	−	0.942636i	−0.999907	−	0.0136277i	$-0.995662\pi$
$503$	−14.1261	−	21.1411i	−0.629850	−	0.942636i	0.370058	−	0.929009i	$-0.379338\pi$
$504$		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	0.659037	−	0.752110i	$-0.270964\pi$
$509$	9.02039	+	4.82150i	0.399822	+	0.213709i	−0.259215	+	0.965820i	$0.583464\pi$
$510$		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	0.890323	−	0.455330i	$-0.150479\pi$
$521$	2.94313	+	4.40470i	0.128941	+	0.192974i	−0.761382	+	0.648304i	$0.775479\pi$
$522$		0			0
$523$	−19.5494	−	5.93023i	−0.854834	−	0.259311i	−0.167697	−	0.985839i	$-0.553633\pi$
$523$	−19.5494	−	5.93023i	−0.854834	−	0.259311i	−0.687137	+	0.726528i	$0.741133\pi$
$524$		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	0.770301	+	0.637680i	$0.220106\pi$
$541$	11.2598	+	37.1185i	0.484095	+	1.59585i	−0.286206	+	0.958168i	$0.592394\pi$
$542$		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	−0.322281	−	0.946644i	$-0.604449\pi$
$547$	−1.50431	+	0.456328i	−0.0643197	+	0.0195112i	0.257961	+	0.966155i	$0.416949\pi$
$548$		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	−0.356788	−	0.934185i	$-0.616128\pi$
$557$	−20.9805	−	2.06640i	−0.888971	−	0.0875560i	−0.532183	+	0.846629i	$0.678628\pi$
$558$		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	0.642186	−	0.766549i	$-0.278028\pi$
$563$	−5.57406	−	6.79201i	−0.234919	−	0.286249i	−0.877104	+	0.480300i	$0.840528\pi$
$564$		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	−0.164948	−	0.986302i	$-0.552746\pi$
$569$	19.3072	−	28.8953i	0.809400	−	1.21135i	0.974347	−	0.225050i	$-0.0722544\pi$
$570$		0			0
$571$	−1.32153	−	1.08455i	−0.0553043	−	0.0453871i	0.606335	−	0.795209i	$-0.292639\pi$
$571$	−1.32153	−	1.08455i	−0.0553043	−	0.0453871i	−0.661639	+	0.749822i	$0.730139\pi$
$572$		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	$0.256142\pi$
$577$			34.6197i			1.44124i	−0.693333	+	0.720618i	$0.743858\pi$
$578$		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	−0.816548	−	0.577277i	$-0.804115\pi$
$587$	4.43628	−	14.6244i	0.183105	−	0.603615i	0.999653	−	0.0263383i	$-0.00838472\pi$
$588$		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	0.568606	+	0.822610i	$0.307483\pi$
$593$	−10.1091	+	24.4056i	−0.415133	+	1.00222i	−0.983738	+	0.179608i	$0.942517\pi$
$594$		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	−0.981118	−	0.193409i	$-0.938046\pi$
$599$	−0.0163657	+	0.0822762i	−0.000668686	+	0.00336171i	0.980449	+	0.196771i	$0.0630455\pi$
$600$		0			0
$601$	−12.0730	+	2.40147i	−0.492468	+	0.0979579i	−0.435076	−	0.900394i	$-0.643278\pi$
$601$	−12.0730	+	2.40147i	−0.492468	+	0.0979579i	−0.0573919	+	0.998352i	$0.518278\pi$
$602$		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	0.271873	−	0.962333i	$-0.412357\pi$
$607$	−17.0111	−	17.0111i	−0.690460	−	0.690460i	−0.962333	+	0.271873i	$0.912357\pi$
$608$		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	0.872462	+	0.488682i	$0.162522\pi$
$613$	2.77550	+	28.1801i	0.112101	+	1.13818i	−0.760361	+	0.649501i	$0.774978\pi$
$614$		0			0
$615$	−0.453487	−	2.27983i	−0.0182863	−	0.0919317i
$616$		0			0
$617$	−7.90077	−	1.57156i	−0.318073	−	0.0632687i	0.0334719	−	0.999440i	$-0.489344\pi$
$617$	−7.90077	−	1.57156i	−0.318073	−	0.0632687i	−0.351545	+	0.936171i	$0.614344\pi$
$618$		0			0
$619$	3.26475	+	6.10792i	0.131221	+	0.245498i	0.938948	−	0.344059i	$-0.111802\pi$
$619$	3.26475	+	6.10792i	0.131221	+	0.245498i	−0.807726	+	0.589557i	$0.799302\pi$
$620$		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	0.795174	−	0.606381i	$-0.207379\pi$
$631$	−1.74202	−	2.60712i	−0.0693489	−	0.103788i	−0.864523	+	0.502593i	$0.832379\pi$
$632$		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	0.128400	−	0.991723i	$-0.459016\pi$
$643$	−15.8447	−	8.46915i	−0.624853	−	0.333991i	−0.753252	+	0.657732i	$0.771516\pi$
$644$		0			0
$645$	4.06427	−	4.95233i	0.160030	−	0.194998i
$646$		0			0
$647$	−12.7810	−	8.53998i	−0.502472	−	0.335741i	0.278365	−	0.960475i	$-0.410207\pi$
$647$	−12.7810	−	8.53998i	−0.502472	−	0.335741i	−0.780838	+	0.624734i	$0.785207\pi$
$648$		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	−0.881913	−	0.471413i	$-0.843744\pi$
$653$	−15.1179	+	12.4070i	−0.591611	+	0.485522i	0.290302	+	0.956935i	$0.406244\pi$
$654$		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	−0.773907	−	0.633299i	$-0.781700\pi$
$659$	2.78992	−	28.3266i	0.108680	−	1.10345i	0.882587	−	0.470148i	$-0.155800\pi$
$660$		0			0
$661$	−12.9991	−	24.3195i	−0.505605	−	0.945921i	−0.997177	−	0.0750839i	$-0.976078\pi$
$661$	−12.9991	−	24.3195i	−0.505605	−	0.945921i	0.491572	−	0.870837i	$-0.336422\pi$
$662$		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	0.478956	−	0.877839i	$-0.341015\pi$
$673$	−10.3479	−	10.3479i	−0.398882	−	0.398882i	−0.877839	+	0.478956i	$0.841015\pi$
$674$		0			0
$675$	7.18736	−	2.18026i	0.276642	−	0.0839183i
$676$		0			0
$677$	31.1921	−	3.07215i	1.19881	−	0.118072i	0.521161	−	0.853459i	$-0.325499\pi$
$677$	31.1921	−	3.07215i	1.19881	−	0.118072i	0.677648	+	0.735386i	$0.262999\pi$
$678$		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	−0.696751	−	0.717313i	$-0.745372\pi$
$683$	−12.7384	+	6.80882i	−0.487422	+	0.260532i	0.209330	+	0.977845i	$0.432872\pi$
$684$		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	0.469047	−	0.883173i	$-0.344597\pi$
$691$	−12.8454	−	15.6522i	−0.488662	−	0.595437i	−0.957710	+	0.287736i	$0.907097\pi$
$692$		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	0.358790	+	0.933418i	$0.383190\pi$
$701$	−16.3267	+	30.5452i	−0.616652	+	1.15368i	−0.975442	+	0.220257i	$0.929310\pi$
$702$		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	0.531570	−	0.847014i	$-0.321602\pi$
$709$	−5.20466	−	4.27136i	−0.195465	−	0.160414i	−0.727035	+	0.686600i	$0.759102\pi$
$710$		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	−0.990325	−	0.138768i	$-0.955686\pi$
$719$	−10.4088	−	25.1291i	−0.388183	−	0.937158i	0.602142	−	0.798389i	$-0.294314\pi$
$720$		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	−0.884224	−	0.467064i	$-0.845312\pi$
$727$	3.00448	−	15.1046i	0.111430	−	0.560197i	0.995654	−	0.0931330i	$-0.0296882\pi$
$728$		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	−0.215015	−	0.976611i	$-0.568980\pi$
$733$	4.02812	−	1.22192i	0.148782	−	0.0451325i	0.363797	+	0.931478i	$0.381480\pi$
$734$		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	0.959620	−	0.281301i	$-0.0907660\pi$
$739$	0.147951	+	0.487728i	0.00544246	+	0.0179414i	−0.954177	+	0.299243i	$0.903266\pi$
$740$		0			0
$741$	1.15692	+	11.7464i	0.0425005	+	0.431515i
$742$		0			0
$743$	−1.19981	−	6.03186i	−0.0440168	−	0.221287i	0.952516	−	0.304489i	$-0.0984856\pi$
$743$	−1.19981	−	6.03186i	−0.0440168	−	0.221287i	−0.996533	+	0.0832012i	$0.973486\pi$
$744$		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	0.863774	−	0.503879i	$-0.168094\pi$
$751$	30.6452	+	12.6937i	1.11826	+	0.463198i	0.254485	+	0.967077i	$0.418094\pi$
$752$		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	−0.352639	−	0.935759i	$-0.614716\pi$
$757$	−32.0734	−	9.72937i	−1.16573	−	0.353620i	−0.813089	+	0.582139i	$0.802216\pi$
$758$		0			0
$759$	−1.78315	−	2.66867i	−0.0647241	−	0.0968665i
$760$		0			0
$761$	−6.62118	−	4.42413i	−0.240018	−	0.160375i	0.429744	−	0.902951i	$-0.358604\pi$
$761$	−6.62118	−	4.42413i	−0.240018	−	0.160375i	−0.669762	+	0.742576i	$0.733604\pi$
$762$		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	−0.0244989	−	0.999700i	$-0.507799\pi$
$773$	26.7122	−	32.5489i	0.960771	−	1.17070i	0.985270	−	0.171004i	$-0.0547010\pi$
$774$		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	−0.841427	−	0.540371i	$-0.818284\pi$
$787$	2.50387	−	25.4222i	0.0892533	−	0.906204i	0.930680	−	0.365833i	$-0.119216\pi$
$788$		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	−0.996946	−	0.0780990i	$-0.975115\pi$
$797$	−5.96822	−	19.6746i	−0.211405	−	0.696909i	0.785541	−	0.618810i	$-0.212385\pi$
$798$		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	−0.836180	−	0.548455i	$-0.815216\pi$
$809$	4.15933	−	20.9103i	0.146234	−	0.735169i	0.982414	−	0.186714i	$-0.0597837\pi$
$810$		0			0
$811$	25.0352	−	13.3816i	0.879105	−	0.469891i	0.0308774	−	0.999523i	$-0.490170\pi$
$811$	25.0352	−	13.3816i	0.879105	−	0.469891i	0.848228	+	0.529632i	$0.177670\pi$
$812$		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	−0.870345	−	0.492443i	$-0.836104\pi$
$821$	3.63629	−	11.9872i	0.126907	−	0.418357i	0.997252	+	0.0740860i	$0.0236039\pi$
$822$		0			0
$823$	10.8193	−	7.22924i	0.377138	−	0.251995i	−0.352525	−	0.935802i	$-0.614677\pi$
$823$	10.8193	−	7.22924i	0.377138	−	0.251995i	0.729663	+	0.683807i	$0.239677\pi$
$824$		0			0
$825$	1.63141	−	2.44158i	0.0567986	−	0.0850050i
$826$		0			0
$827$	−12.8275	−	10.5273i	−0.446057	−	0.366070i	0.384386	−	0.923172i	$-0.374413\pi$
$827$	−12.8275	−	10.5273i	−0.446057	−	0.366070i	−0.830444	+	0.557102i	$0.811913\pi$
$828$		0			0
$829$	−14.2605	+	26.6795i	−0.495288	+	0.926619i	0.502775	+	0.864417i	$0.332312\pi$
$829$	−14.2605	+	26.6795i	−0.495288	+	0.926619i	−0.998064	+	0.0622019i	$0.980188\pi$
$830$		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	−0.959801	−	0.280682i	$-0.909440\pi$
$839$	−9.65087	+	14.4435i	−0.333185	+	0.498647i	0.626616	+	0.779328i	$0.284440\pi$
$840$		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	0.156327	−	0.987705i	$-0.450035\pi$
$853$	31.0878	−	16.6168i	1.06442	−	0.568947i	0.908098	+	0.418759i	$0.137535\pi$
$854$		0			0
$855$	3.07602	−	15.4642i	0.105198	−	0.528864i
$856$		0			0
$857$	25.6961	−	5.11127i	0.877761	−	0.174598i	0.264412	−	0.964410i	$-0.414822\pi$
$857$	25.6961	−	5.11127i	0.877761	−	0.174598i	0.613349	+	0.789812i	$0.289822\pi$
$858$		0			0
$859$	7.59275	−	0.747820i	0.259061	−	0.0255153i	0.0323472	−	0.999477i	$-0.489702\pi$
$859$	7.59275	−	0.747820i	0.259061	−	0.0255153i	0.226714	+	0.973961i	$0.427202\pi$
$860$		0			0
$861$	−2.40279	+	0.728878i	−0.0818868	+	0.0248401i
$862$		0			0
$863$	7.80163	+	7.80163i	0.265571	+	0.265571i	0.827313	−	0.561742i	$-0.189869\pi$
$863$	7.80163	+	7.80163i	0.265571	+	0.265571i	−0.561742	+	0.827313i	$0.689869\pi$
$864$		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	0.728406	+	0.685146i	$0.240261\pi$
$877$	−3.54391	+	35.9819i	−0.119669	+	1.21502i	−0.848075	+	0.529876i	$0.822239\pi$
$878$		0			0
$879$	17.1487	+	7.10322i	0.578411	+	0.239586i
$880$		0			0
$881$	−31.0850	+	12.8758i	−1.04728	+	0.433798i	−0.838920	−	0.544255i	$-0.816813\pi$
$881$	−31.0850	+	12.8758i	−1.04728	+	0.433798i	−0.208360	+	0.978052i	$0.566813\pi$
$882$		0			0
$883$	−6.29864	+	5.16916i	−0.211966	+	0.173956i	−0.734385	−	0.678733i	$-0.762530\pi$
$883$	−6.29864	+	5.16916i	−0.211966	+	0.173956i	0.522419	+	0.852689i	$0.325030\pi$
$884$		0			0
$885$	−8.51859	−	2.58409i	−0.286349	−	0.0868631i
$886$		0			0
$887$	13.4820	+	20.1773i	0.452683	+	0.677488i	0.985679	−	0.168630i	$-0.0539342\pi$
$887$	13.4820	+	20.1773i	0.452683	+	0.677488i	−0.532997	+	0.846117i	$0.678934\pi$
$888$		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	0.914380	−	0.404857i	$-0.132679\pi$
$907$	43.6608	+	13.2444i	1.44973	+	0.439772i	0.535353	+	0.844628i	$0.320179\pi$
$908$		0			0
$909$	3.66529	−	3.00803i	0.121570	−	0.0997699i
$910$		0			0
$911$	−23.5278	+	9.74555i	−0.779512	+	0.322884i	−0.736719	−	0.676200i	$-0.763626\pi$
$911$	−23.5278	+	9.74555i	−0.779512	+	0.322884i	−0.0427934	+	0.999084i	$0.513626\pi$
$912$		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	0.0372305	−	0.999307i	$-0.488146\pi$
$919$	−9.42163	−	1.87408i	−0.310791	−	0.0618202i	−0.348022	+	0.937487i	$0.613146\pi$
$920$		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	0.221514	−	0.975157i	$-0.428900\pi$
$929$	−22.9707	−	22.9707i	−0.753643	−	0.753643i	−0.975157	+	0.221514i	$0.928900\pi$
$930$		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	−0.856906	−	0.515472i	$-0.827617\pi$
$937$	4.04164	−	20.3187i	0.132035	−	0.663783i	0.988941	−	0.148310i	$-0.0473835\pi$
$938$		0			0
$939$	10.7441	−	5.74285i	0.350621	−	0.187411i
$940$		0			0
$941$	12.8088	+	1.26155i	0.417554	+	0.0411254i	0.304613	−	0.952476i	$-0.401473\pi$
$941$	12.8088	+	1.26155i	0.417554	+	0.0411254i	0.112941	+	0.993602i	$0.463973\pi$
$942$		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	0.699229	−	0.714898i	$-0.253527\pi$
$947$	−4.25737	−	5.18762i	−0.138346	−	0.168575i	−0.837574	+	0.546323i	$0.816027\pi$
$948$		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	−0.666389	−	0.745604i	$-0.732161\pi$
$953$	8.56586	−	12.8197i	0.277476	−	0.415271i	0.943865	+	0.330333i	$0.107161\pi$
$954$		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	−0.126775	+	0.991931i	$0.540463\pi$
$967$	−30.9314	+	46.2921i	−0.994686	+	1.48865i	−0.867910	+	0.496721i	$0.834537\pi$
$968$		0			0
$969$	3.01637	−	2.01547i	0.0968997	−	0.0647463i
$970$		0			0
$971$	8.09273	−	26.6782i	0.259708	−	0.856143i	−0.726002	−	0.687693i	$-0.758624\pi$
$971$	8.09273	−	26.6782i	0.259708	−	0.856143i	0.985710	−	0.168450i	$-0.0538763\pi$
$972$		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	0.467251	+	0.884125i	$0.345244\pi$
$977$	−15.2633	+	36.8488i	−0.488316	+	1.17890i	−0.955567	+	0.294774i	$0.904756\pi$
$978$		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	0.885234	+	0.465145i	$0.153998\pi$
$983$	−3.46822	+	17.4359i	−0.110619	+	0.556119i	−0.995853	+	0.0909737i	$0.971002\pi$
$984$		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	−0.998495	−	0.0548477i	$-0.982533\pi$
$991$	−33.1594	−	33.1594i	−1.05334	−	1.05334i	−0.0548477	−	0.998495i	$-0.517467\pi$
$992$		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	0.999129	+	0.0417400i	$0.0132901\pi$
$997$	0.863302	+	8.76525i	0.0273410	+	0.277598i	−0.971787	+	0.235858i	$0.924210\pi$
$998$		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.273.6		240
4.3	odd	2		128.2.k.a.109.5	yes	240
128.27	odd	32		128.2.k.a.101.5	✓	240
128.101	even	32	inner	512.2.k.a.497.6		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.101.5	✓	240	128.27	odd	32
128.2.k.a.109.5	yes	240	4.3	odd	2
512.2.k.a.273.6		240	1.1	even	1	trivial
512.2.k.a.497.6		240	128.101	even	32	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 $\F_{q}$
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

Related objects

Downloads

Learn more