LMFDB - Embedded newform 768.2.s.a.335.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [768,2,Mod(47,768)] 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("768.47"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(768, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 11, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.s (of order $16$, degree $8$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 192)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			335.5
Character	$\chi$	$=$	768.335
Dual form			768.2.s.a.431.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39786 + 1.02274i) q^{3} +(-0.0417075 - 0.0624196i) q^{5} +(0.100307 - 0.242162i) q^{7} +(0.908014 - 2.85929i) q^{9} +(2.15600 + 0.428854i) q^{11} +(0.751836 + 0.502361i) q^{13} +(0.122140 + 0.0445980i) q^{15} +(-1.66843 - 1.66843i) q^{17} +(1.06552 + 0.711956i) q^{19} +(0.107454 + 0.441097i) q^{21} +(-0.745366 - 1.79947i) q^{23} +(1.91126 - 4.61419i) q^{25} +(1.65503 + 4.92553i) q^{27} +(1.26847 + 6.37705i) q^{29} +10.1205 q^{31} +(-3.45238 + 1.60554i) q^{33} +(-0.0192992 + 0.00383886i) q^{35} +(2.54831 + 3.81381i) q^{37} +(-1.56474 + 0.0667024i) q^{39} +(4.77720 - 1.97878i) q^{41} +(9.37912 + 1.86562i) q^{43} +(-0.216346 + 0.0625756i) q^{45} +(-8.04483 + 8.04483i) q^{47} +(4.90117 + 4.90117i) q^{49} +(4.03859 + 0.625860i) q^{51} +(-1.29422 + 6.50649i) q^{53} +(-0.0631522 - 0.152463i) q^{55} +(-2.21759 + 0.0945320i) q^{57} +(-3.86117 + 2.57995i) q^{59} +(-0.853477 - 4.29072i) q^{61} +(-0.601331 - 0.506693i) q^{63} -0.0678815i q^{65} +(-1.79590 + 0.357228i) q^{67} +(2.88230 + 1.75309i) q^{69} +(-5.21738 - 2.16111i) q^{71} +(10.0231 - 4.15171i) q^{73} +(2.04744 + 8.40470i) q^{75} +(0.320114 - 0.479085i) q^{77} +(5.93698 - 5.93698i) q^{79} +(-7.35102 - 5.19254i) q^{81} +(6.79190 - 10.1648i) q^{83} +(-0.0345567 + 0.173728i) q^{85} +(-8.29520 - 7.61690i) q^{87} +(13.5709 + 5.62127i) q^{89} +(0.197067 - 0.131676i) q^{91} +(-14.1470 + 10.3506i) q^{93} -0.0962031i q^{95} +13.0044i q^{97} +(3.18389 - 5.77520i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 8 q^{3} + 16 q^{7} - 8 q^{9} - 16 q^{13} + 8 q^{15} + 16 q^{19} - 8 q^{21} - 16 q^{25} + 8 q^{27} + 32 q^{31} - 16 q^{37} + 8 q^{39} + 16 q^{43} - 8 q^{45} - 16 q^{49} + 8 q^{51} + 80 q^{55} - 8 q^{57}+ \cdots + 8 q^{99}+O(q^{100}) $ 240 * q + 8 * q^3 + 16 * q^7 - 8 * q^9 - 16 * q^13 + 8 * q^15 + 16 * q^19 - 8 * q^21 - 16 * q^25 + 8 * q^27 + 32 * q^31 - 16 * q^37 + 8 * q^39 + 16 * q^43 - 8 * q^45 - 16 * q^49 + 8 * q^51 + 80 * q^55 - 8 * q^57 - 16 * q^61 + 144 * q^67 - 8 * q^69 - 16 * q^73 + 8 * q^75 + 48 * q^79 - 8 * q^81 - 16 * q^85 + 8 * q^87 + 16 * q^91 - 32 * q^93 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{16}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.39786	+	1.02274i	−0.807054	+	0.590478i
$3$	−1.39786	+	1.02274i	−0.807054	+	0.590478i
$4$		0			0
$5$	−0.0417075	−	0.0624196i	−0.0186521	−	0.0279149i	0.822026	−	0.569449i	$-0.192844\pi$
$5$	−0.0417075	−	0.0624196i	−0.0186521	−	0.0279149i	−0.840679	+	0.541535i	$0.817844\pi$
$6$		0			0
$7$	0.100307	−	0.242162i	0.0379125	−	0.0915288i	−0.903789	−	0.427978i	$-0.859226\pi$
$7$	0.100307	−	0.242162i	0.0379125	−	0.0915288i	0.941702	+	0.336449i	$0.109226\pi$
$8$		0			0
$9$	0.908014	−	2.85929i	0.302671	−	0.953095i
$10$		0			0
$11$	2.15600	+	0.428854i	0.650058	+	0.129304i	0.509095	−	0.860710i	$-0.329980\pi$
$11$	2.15600	+	0.428854i	0.650058	+	0.129304i	0.140963	+	0.990015i	$0.454980\pi$
$12$		0			0
$13$	0.751836	+	0.502361i	0.208522	+	0.139330i	0.655446	−	0.755242i	$-0.272481\pi$
$13$	0.751836	+	0.502361i	0.208522	+	0.139330i	−0.446924	+	0.894572i	$0.647481\pi$
$14$		0			0
$15$	0.122140	+	0.0445980i	0.0315364	+	0.0115151i
$16$		0			0
$17$	−1.66843	−	1.66843i	−0.404653	−	0.404653i	0.475216	−	0.879869i	$-0.342370\pi$
$17$	−1.66843	−	1.66843i	−0.404653	−	0.404653i	−0.879869	+	0.475216i	$0.842370\pi$
$18$		0			0
$19$	1.06552	+	0.711956i	0.244446	+	0.163334i	0.671758	−	0.740770i	$-0.265539\pi$
$19$	1.06552	+	0.711956i	0.244446	+	0.163334i	−0.427312	+	0.904104i	$0.640539\pi$
$20$		0			0
$21$	0.107454	+	0.441097i	0.0234484	+	0.0962552i
$22$		0			0
$23$	−0.745366	−	1.79947i	−0.155419	−	0.375216i	0.826921	−	0.562318i	$-0.190090\pi$
$23$	−0.745366	−	1.79947i	−0.155419	−	0.375216i	−0.982340	+	0.187102i	$0.940090\pi$
$24$		0			0
$25$	1.91126	−	4.61419i	0.382252	−	0.922838i
$26$		0			0
$27$	1.65503	+	4.92553i	0.318510	+	0.947920i
$28$		0			0
$29$	1.26847	+	6.37705i	0.235550	+	1.18419i	0.899672	+	0.436566i	$0.143805\pi$
$29$	1.26847	+	6.37705i	0.235550	+	1.18419i	−0.664123	+	0.747624i	$0.731195\pi$
$30$		0			0
$31$	10.1205			1.81769			0.908844	−	0.417137i	$-0.136967\pi$
$31$	10.1205			1.81769			0.908844	+	0.417137i	$0.136967\pi$
$32$		0			0
$33$	−3.45238	+	1.60554i	−0.600983	+	0.279489i
$34$		0			0
$35$	−0.0192992	+	0.00383886i	−0.00326217	+	0.000648885i
$36$		0			0
$37$	2.54831	+	3.81381i	0.418939	+	0.626986i	0.979576	−	0.201075i	$-0.0644436\pi$
$37$	2.54831	+	3.81381i	0.418939	+	0.626986i	−0.560637	+	0.828062i	$0.689444\pi$
$38$		0			0
$39$	−1.56474	+	0.0667024i	−0.250559	+	0.0106809i
$40$		0			0
$41$	4.77720	−	1.97878i	0.746073	−	0.309033i	0.0229347	−	0.999737i	$-0.492699\pi$
$41$	4.77720	−	1.97878i	0.746073	−	0.309033i	0.723138	+	0.690704i	$0.242699\pi$
$42$		0			0
$43$	9.37912	+	1.86562i	1.43030	+	0.284505i	0.848659	−	0.528940i	$-0.177410\pi$
$43$	9.37912	+	1.86562i	1.43030	+	0.284505i	0.581643	+	0.813444i	$0.302410\pi$
$44$		0			0
$45$	−0.216346	+	0.0625756i	−0.0322510	+	0.00932823i
$46$		0			0
$47$	−8.04483	+	8.04483i	−1.17346	+	1.17346i	−0.192080	+	0.981379i	$0.561523\pi$
$47$	−8.04483	+	8.04483i	−1.17346	+	1.17346i	−0.981379	+	0.192080i	$0.938477\pi$
$48$		0			0
$49$	4.90117	+	4.90117i	0.700167	+	0.700167i
$50$		0			0
$51$	4.03859	+	0.625860i	0.565516	+	0.0876380i
$52$		0			0
$53$	−1.29422	+	6.50649i	−0.177775	+	0.893735i	0.784181	+	0.620532i	$0.213083\pi$
$53$	−1.29422	+	6.50649i	−0.177775	+	0.893735i	−0.961956	+	0.273203i	$0.911917\pi$
$54$		0			0
$55$	−0.0631522	−	0.152463i	−0.00851544	−	0.0205581i
$56$		0			0
$57$	−2.21759	+	0.0945320i	−0.293727	+	0.0125211i
$58$		0			0
$59$	−3.86117	+	2.57995i	−0.502681	+	0.335881i	−0.780920	−	0.624631i	$-0.785249\pi$
$59$	−3.86117	+	2.57995i	−0.502681	+	0.335881i	0.278239	+	0.960512i	$0.410249\pi$
$60$		0			0
$61$	−0.853477	−	4.29072i	−0.109277	−	0.549370i	−0.996173	−	0.0874022i	$-0.972143\pi$
$61$	−0.853477	−	4.29072i	−0.109277	−	0.549370i	0.886897	−	0.461968i	$-0.152857\pi$
$62$		0			0
$63$	−0.601331	−	0.506693i	−0.0757606	−	0.0638373i
$64$		0			0
$65$		−	0.0678815i		−	0.00841967i
$66$		0			0
$67$	−1.79590	+	0.357228i	−0.219405	+	0.0436423i	−0.303568	−	0.952810i	$-0.598178\pi$
$67$	−1.79590	+	0.357228i	−0.219405	+	0.0436423i	0.0841638	+	0.996452i	$0.473178\pi$
$68$		0			0
$69$	2.88230	+	1.75309i	0.346989	+	0.211048i
$70$		0			0
$71$	−5.21738	−	2.16111i	−0.619190	−	0.256477i	0.0509625	−	0.998701i	$-0.483771\pi$
$71$	−5.21738	−	2.16111i	−0.619190	−	0.256477i	−0.670152	+	0.742224i	$0.733771\pi$
$72$		0			0
$73$	10.0231	−	4.15171i	1.17312	−	0.485921i	0.290895	−	0.956755i	$-0.406047\pi$
$73$	10.0231	−	4.15171i	1.17312	−	0.485921i	0.882222	+	0.470834i	$0.156047\pi$
$74$		0			0
$75$	2.04744	+	8.40470i	0.236418	+	0.970491i
$76$		0			0
$77$	0.320114	−	0.479085i	0.0364804	−	0.0545967i
$78$		0			0
$79$	5.93698	−	5.93698i	0.667963	−	0.667963i	−0.289281	−	0.957244i	$-0.593416\pi$
$79$	5.93698	−	5.93698i	0.667963	−	0.667963i	0.957244	+	0.289281i	$0.0934163\pi$
$80$		0			0
$81$	−7.35102	−	5.19254i	−0.816780	−	0.576949i
$82$		0			0
$83$	6.79190	−	10.1648i	0.745508	−	1.11573i	−0.243790	−	0.969828i	$-0.578391\pi$
$83$	6.79190	−	10.1648i	0.745508	−	1.11573i	0.989299	−	0.145904i	$-0.0466091\pi$
$84$		0			0
$85$	−0.0345567	+	0.173728i	−0.00374820	+	0.0188435i
$86$		0			0
$87$	−8.29520	−	7.61690i	−0.889339	−	0.816617i
$88$		0			0
$89$	13.5709	+	5.62127i	1.43852	+	0.595853i	0.959438	−	0.281919i	$-0.0909708\pi$
$89$	13.5709	+	5.62127i	1.43852	+	0.595853i	0.479079	+	0.877772i	$0.340971\pi$
$90$		0			0
$91$	0.197067	−	0.131676i	0.0206583	−	0.0138034i
$92$		0			0
$93$	−14.1470	+	10.3506i	−1.46697	+	1.07330i
$94$		0			0
$95$		−	0.0962031i		−	0.00987023i
$96$		0			0
$97$			13.0044i			1.32039i	0.751092	+	0.660197i	$0.229527\pi$
$97$			13.0044i			1.32039i	−0.751092	+	0.660197i	$0.770473\pi$
$98$		0			0
$99$	3.18389	−	5.77520i	0.319993	−	0.580430i
$100$		0			0
$101$	−9.68443	+	6.47093i	−0.963637	+	0.643882i	−0.934601	−	0.355697i	$-0.884244\pi$
$101$	−9.68443	+	6.47093i	−0.963637	+	0.643882i	−0.0290356	+	0.999578i	$0.509244\pi$
$102$		0			0
$103$	−12.4024	−	5.13724i	−1.22204	−	0.506187i	−0.323985	−	0.946062i	$-0.605023\pi$
$103$	−12.4024	−	5.13724i	−1.22204	−	0.506187i	−0.898059	+	0.439875i	$0.855023\pi$
$104$		0			0
$105$	0.0230514	−	0.0251042i	0.00224959	−	0.00244992i
$106$		0			0
$107$	2.77724	−	13.9621i	0.268486	−	1.34977i	−0.577424	−	0.816445i	$-0.695942\pi$
$107$	2.77724	−	13.9621i	0.268486	−	1.34977i	0.845910	−	0.533326i	$-0.179058\pi$
$108$		0			0
$109$	5.47007	−	8.18653i	0.523937	−	0.784128i	−0.471262	−	0.881993i	$-0.656201\pi$
$109$	5.47007	−	8.18653i	0.523937	−	0.784128i	0.995200	+	0.0978654i	$0.0312015\pi$
$110$		0			0
$111$	−7.46270	−	2.72491i	−0.708328	−	0.258637i
$112$		0			0
$113$	7.56860	−	7.56860i	0.711994	−	0.711994i	−0.254958	−	0.966952i	$-0.582062\pi$
$113$	7.56860	−	7.56860i	0.711994	−	0.711994i	0.966952	+	0.254958i	$0.0820617\pi$
$114$		0			0
$115$	−0.0812350	+	0.121577i	−0.00757521	+	0.0113371i
$116$		0			0
$117$	2.11907	−	1.69356i	0.195908	−	0.156570i
$118$		0			0
$119$	−0.571385	+	0.236676i	−0.0523788	+	0.0216960i
$120$		0			0
$121$	−5.69827	−	2.36030i	−0.518024	−	0.214573i
$122$		0			0
$123$	−4.65407	+	7.65187i	−0.419643	+	0.689946i
$124$		0			0
$125$	−0.735875	+	0.146375i	−0.0658186	+	0.0130921i
$126$		0			0
$127$			0.413244i			0.0366695i	0.999832	+	0.0183347i	$0.00583646\pi$
$127$			0.413244i			0.0366695i	−0.999832	+	0.0183347i	$0.994164\pi$
$128$		0			0
$129$	−15.0187	+	6.98451i	−1.32232	+	0.614951i
$130$		0			0
$131$	−1.04858	−	5.27154i	−0.0916144	−	0.460577i	−0.999173	−	0.0406521i	$-0.987056\pi$
$131$	−1.04858	−	5.27154i	−0.0916144	−	0.460577i	0.907559	−	0.419925i	$-0.137944\pi$
$132$		0			0
$133$	0.279288	−	0.186614i	0.0242173	−	0.0161815i
$134$		0			0
$135$	0.238423	−	0.308738i	0.0205202	−	0.0265719i
$136$		0			0
$137$	−5.79645	−	13.9939i	−0.495224	−	1.19558i	−0.952028	−	0.306010i	$-0.901006\pi$
$137$	−5.79645	−	13.9939i	−0.495224	−	1.19558i	0.456804	−	0.889567i	$-0.348994\pi$
$138$		0			0
$139$	−1.71904	+	8.64218i	−0.145807	+	0.733021i	0.836827	+	0.547467i	$0.184408\pi$
$139$	−1.71904	+	8.64218i	−0.145807	+	0.733021i	−0.982634	+	0.185554i	$0.940592\pi$
$140$		0			0
$141$	3.01777	−	19.4733i	0.254142	−	1.63995i
$142$		0			0
$143$	1.40552	+	1.40552i	0.117535	+	0.117535i
$144$		0			0
$145$	0.345148	−	0.345148i	0.0286630	−	0.0286630i
$146$		0			0
$147$	−11.8637	−	1.83852i	−0.978505	−	0.151639i
$148$		0			0
$149$	6.01868	+	1.19719i	0.493069	+	0.0980776i	0.435361	−	0.900256i	$-0.356621\pi$
$149$	6.01868	+	1.19719i	0.493069	+	0.0980776i	0.0577083	+	0.998333i	$0.481621\pi$
$150$		0			0
$151$	−7.84809	+	3.25079i	−0.638669	+	0.264545i	−0.678431	−	0.734664i	$-0.737340\pi$
$151$	−7.84809	+	3.25079i	−0.638669	+	0.264545i	0.0397624	+	0.999209i	$0.487340\pi$
$152$		0			0
$153$	−6.28546	+	3.25556i	−0.508150	+	0.263196i
$154$		0			0
$155$	−0.422098	−	0.631715i	−0.0339038	−	0.0507406i
$156$		0			0
$157$	−12.5487	+	2.49608i	−1.00149	+	0.199209i	−0.668493	−	0.743718i	$-0.733060\pi$
$157$	−12.5487	+	2.49608i	−1.00149	+	0.199209i	−0.332998	+	0.942927i	$0.608060\pi$
$158$		0			0
$159$	−4.84530	−	10.4188i	−0.384257	−	0.826264i
$160$		0			0
$161$	−0.510530			−0.0402354
$162$		0			0
$163$	−1.41044	−	7.09076i	−0.110474	−	0.555391i	−0.995888	−	0.0905883i	$-0.971125\pi$
$163$	−1.41044	−	7.09076i	−0.110474	−	0.555391i	0.885414	−	0.464803i	$-0.153875\pi$
$164$		0			0
$165$	0.244207	+	0.148533i	0.0190115	+	0.0115633i
$166$		0			0
$167$	−5.06460	+	12.2270i	−0.391911	+	0.946156i	0.597613	+	0.801785i	$0.296116\pi$
$167$	−5.06460	+	12.2270i	−0.391911	+	0.946156i	−0.989524	+	0.144371i	$0.953884\pi$
$168$		0			0
$169$	−4.66199	−	11.2550i	−0.358615	−	0.865773i
$170$		0			0
$171$	3.00319	−	2.40015i	0.229660	−	0.183544i
$172$		0			0
$173$	−20.0687	−	13.4095i	−1.52580	−	1.01950i	−0.983830	−	0.179104i	$-0.942680\pi$
$173$	−20.0687	−	13.4095i	−1.52580	−	1.01950i	−0.541966	−	0.840400i	$-0.682320\pi$
$174$		0			0
$175$	−0.925671	−	0.925671i	−0.0699742	−	0.0699742i
$176$		0			0
$177$	2.75875	−	7.55536i	0.207360	−	0.567896i
$178$		0			0
$179$	10.2002	+	6.81555i	0.762398	+	0.509418i	0.874941	−	0.484229i	$-0.160900\pi$
$179$	10.2002	+	6.81555i	0.762398	+	0.509418i	−0.112543	+	0.993647i	$0.535900\pi$
$180$		0			0
$181$	10.3436	+	2.05747i	0.768834	+	0.152931i	0.563897	−	0.825845i	$-0.309301\pi$
$181$	10.3436	+	2.05747i	0.768834	+	0.152931i	0.204936	+	0.978775i	$0.434301\pi$
$182$		0			0
$183$	5.58132	+	5.12493i	0.412583	+	0.378846i
$184$		0			0
$185$	0.131773	−	0.318128i	0.00968815	−	0.0233893i
$186$		0			0
$187$	−2.88161	−	4.31264i	−0.210724	−	0.315371i
$188$		0			0
$189$	1.35879	+	0.0932803i	0.0988374	+	0.00678514i
$190$		0			0
$191$	27.5926			1.99653			0.998265	−	0.0588807i	$-0.0187532\pi$
$191$	27.5926			1.99653			0.998265	+	0.0588807i	$0.0187532\pi$
$192$		0			0
$193$	−5.03806			−0.362648			−0.181324	−	0.983423i	$-0.558038\pi$
$193$	−5.03806			−0.362648			−0.181324	+	0.983423i	$0.558038\pi$
$194$		0			0
$195$	0.0694250	+	0.0948887i	0.00497163	+	0.00679512i
$196$		0			0
$197$	−7.59394	−	11.3651i	−0.541046	−	0.809732i	0.455718	−	0.890124i	$-0.349383\pi$
$197$	−7.59394	−	11.3651i	−0.541046	−	0.809732i	−0.996763	+	0.0803923i	$0.974383\pi$
$198$		0			0
$199$	−4.56453	+	11.0197i	−0.323571	+	0.781169i	0.675470	+	0.737387i	$0.263941\pi$
$199$	−4.56453	+	11.0197i	−0.323571	+	0.781169i	−0.999041	+	0.0437818i	$0.986059\pi$
$200$		0			0
$201$	2.14507	−	2.33609i	0.151301	−	0.164775i
$202$		0			0
$203$	1.67152	+	0.332486i	0.117318	+	0.0233359i
$204$		0			0
$205$	−0.322759	−	0.215661i	−0.0225425	−	0.0150624i
$206$		0			0
$207$	−5.82201	+	0.497268i	−0.404657	+	0.0345625i
$208$		0			0
$209$	1.99193	+	1.99193i	0.137784	+	0.137784i
$210$		0			0
$211$	−2.76673	−	1.84867i	−0.190470	−	0.127268i	0.456679	−	0.889631i	$-0.349039\pi$
$211$	−2.76673	−	1.84867i	−0.190470	−	0.127268i	−0.647149	+	0.762364i	$0.724039\pi$
$212$		0			0
$213$	9.50341	−	2.31509i	0.651163	−	0.158627i
$214$		0			0
$215$	−0.274728	−	0.663251i	−0.0187363	−	0.0452334i
$216$		0			0
$217$	1.01515	−	2.45079i	0.0689130	−	0.166371i
$218$		0			0
$219$	−9.76478	+	16.0545i	−0.659843	+	1.08486i
$220$		0			0
$221$	−0.416231	−	2.09254i	−0.0279988	−	0.140759i
$222$		0			0
$223$	12.6115			0.844531			0.422265	−	0.906472i	$-0.361235\pi$
$223$	12.6115			0.844531			0.422265	+	0.906472i	$0.361235\pi$
$224$		0			0
$225$	−11.4578	−	9.65459i	−0.763856	−	0.643639i
$226$		0			0
$227$	−13.6050	+	2.70621i	−0.902997	+	0.179617i	−0.624688	−	0.780874i	$-0.714774\pi$
$227$	−13.6050	+	2.70621i	−0.902997	+	0.179617i	−0.278309	+	0.960492i	$0.589774\pi$
$228$		0			0
$229$	−0.0914294	−	0.136834i	−0.00604182	−	0.00904223i	0.828436	−	0.560083i	$-0.189231\pi$
$229$	−0.0914294	−	0.136834i	−0.00604182	−	0.00904223i	−0.834478	+	0.551041i	$0.814231\pi$
$230$		0			0
$231$	0.0425040	+	0.997085i	0.00279656	+	0.0656034i
$232$		0			0
$233$	−15.0334	+	6.22705i	−0.984873	+	0.407948i	−0.816229	−	0.577729i	$-0.803939\pi$
$233$	−15.0334	+	6.22705i	−0.984873	+	0.407948i	−0.168645	+	0.985677i	$0.553939\pi$
$234$		0			0
$235$	0.837684	+	0.166626i	0.0546445	+	0.0108695i
$236$		0			0
$237$	−2.22708	+	14.3710i	−0.144664	+	0.933499i
$238$		0			0
$239$	−9.91200	+	9.91200i	−0.641154	+	0.641154i	−0.950839	−	0.309685i	$-0.899776\pi$
$239$	−9.91200	+	9.91200i	−0.641154	+	0.641154i	0.309685	+	0.950839i	$0.399776\pi$
$240$		0			0
$241$	6.54008	+	6.54008i	0.421283	+	0.421283i	0.885645	−	0.464362i	$-0.153716\pi$
$241$	6.54008	+	6.54008i	0.421283	+	0.421283i	−0.464362	+	0.885645i	$0.653716\pi$
$242$		0			0
$243$	15.5863	−	0.259739i	0.999861	−	0.0166623i
$244$		0			0
$245$	0.101514	−	0.510344i	0.00648548	−	0.0326047i
$246$		0			0
$247$	0.443436	+	1.07055i	0.0282151	+	0.0681174i
$248$		0			0
$249$	0.901814	+	21.1553i	0.0571502	+	1.34066i
$250$		0			0
$251$	−18.8565	+	12.5995i	−1.19021	+	0.795273i	−0.983105	−	0.183045i	$-0.941405\pi$
$251$	−18.8565	+	12.5995i	−1.19021	+	0.795273i	−0.207106	+	0.978318i	$0.566405\pi$
$252$		0			0
$253$	−0.835295	−	4.19931i	−0.0525145	−	0.264008i
$254$		0			0
$255$	−0.129373	−	0.278190i	−0.00810167	−	0.0174209i
$256$		0			0
$257$			0.247927i			0.0154652i	0.999970	+	0.00773262i	$0.00246139\pi$
$257$			0.247927i			0.0154652i	−0.999970	+	0.00773262i	$0.997539\pi$
$258$		0			0
$259$	1.17917	−	0.234552i	0.0732703	−	0.0145744i
$260$		0			0
$261$	19.3856	+	2.16352i	1.19994	+	0.133919i
$262$		0			0
$263$	24.7866	+	10.2669i	1.52841	+	0.633087i	0.979254	−	0.202635i	$-0.0649504\pi$
$263$	24.7866	+	10.2669i	1.52841	+	0.633087i	0.549153	+	0.835722i	$0.314950\pi$
$264$		0			0
$265$	0.460111	−	0.190584i	0.0282644	−	0.0117075i
$266$		0			0
$267$	−24.7193	+	6.02179i	−1.51280	+	0.368527i
$268$		0			0
$269$	7.89201	−	11.8112i	0.481184	−	0.720143i	−0.508868	−	0.860845i	$-0.669936\pi$
$269$	7.89201	−	11.8112i	0.481184	−	0.720143i	0.990052	+	0.140701i	$0.0449358\pi$
$270$		0			0
$271$	7.91386	−	7.91386i	0.480733	−	0.480733i	−0.424633	−	0.905366i	$-0.639597\pi$
$271$	7.91386	−	7.91386i	0.480733	−	0.480733i	0.905366	+	0.424633i	$0.139597\pi$
$272$		0			0
$273$	−0.140802	+	0.385613i	−0.00852172	+	0.0233384i
$274$		0			0
$275$	6.09949	−	9.12853i	0.367813	−	0.550471i
$276$		0			0
$277$	−4.80902	+	24.1766i	−0.288946	+	1.45263i	0.514622	+	0.857417i	$0.327932\pi$
$277$	−4.80902	+	24.1766i	−0.288946	+	1.45263i	−0.803568	+	0.595213i	$0.797068\pi$
$278$		0			0
$279$	9.18951	−	28.9373i	0.550161	−	1.73243i
$280$		0			0
$281$	21.3506	+	8.84369i	1.27367	+	0.527570i	0.914077	−	0.405540i	$-0.132916\pi$
$281$	21.3506	+	8.84369i	1.27367	+	0.527570i	0.359590	+	0.933110i	$0.382916\pi$
$282$		0			0
$283$	2.13260	−	1.42496i	0.126770	−	0.0847050i	−0.490569	−	0.871403i	$-0.663211\pi$
$283$	2.13260	−	1.42496i	0.126770	−	0.0847050i	0.617339	+	0.786698i	$0.288211\pi$
$284$		0			0
$285$	0.0983905	+	0.134478i	0.00582815	+	0.00796580i
$286$		0			0
$287$		−	1.35534i		−	0.0800034i
$288$		0			0
$289$		−	11.4327i		−	0.672512i
$290$		0			0
$291$	−13.3001	−	18.1783i	−0.779664	−	1.06563i
$292$		0			0
$293$	−15.6865	+	10.4814i	−0.916416	+	0.612329i	−0.921804	−	0.387656i	$-0.873285\pi$
$293$	−15.6865	+	10.4814i	−0.916416	+	0.612329i	0.00538828	+	0.999985i	$0.498285\pi$
$294$		0			0
$295$	0.322079	+	0.133409i	0.0187522	+	0.00776740i
$296$		0			0
$297$	1.45589	+	11.3292i	0.0844795	+	0.657387i
$298$		0			0
$299$	0.343591	−	1.72735i	0.0198704	−	0.0998953i
$300$		0			0
$301$	1.39257	−	2.08414i	0.0802667	−	0.120128i
$302$		0			0
$303$	6.91939	−	18.9501i	0.397509	−	1.08865i
$304$		0			0
$305$	−0.232229	+	0.232229i	−0.0132974	+	0.0132974i
$306$		0			0
$307$	−7.34995	+	11.0000i	−0.419484	+	0.627802i	−0.979682	−	0.200556i	$-0.935725\pi$
$307$	−7.34995	+	11.0000i	−0.419484	+	0.627802i	0.560198	+	0.828359i	$0.310725\pi$
$308$		0			0
$309$	22.5908	−	5.50327i	1.28515	−	0.313070i
$310$		0			0
$311$	−4.34991	+	1.80179i	−0.246661	+	0.102170i	−0.502589	−	0.864526i	$-0.667619\pi$
$311$	−4.34991	+	1.80179i	−0.246661	+	0.102170i	0.255928	+	0.966696i	$0.417619\pi$
$312$		0			0
$313$	−8.83610	−	3.66003i	−0.499446	−	0.206877i	0.118716	−	0.992928i	$-0.462122\pi$
$313$	−8.83610	−	3.66003i	−0.499446	−	0.206877i	−0.618162	+	0.786051i	$0.712122\pi$
$314$		0			0
$315$	−0.00654758	+	0.0586678i	−0.000368914	+	0.00330555i
$316$		0			0
$317$	1.84684	−	0.367359i	0.103729	−	0.0206329i	−0.142953	−	0.989729i	$-0.545660\pi$
$317$	1.84684	−	0.367359i	0.103729	−	0.0206329i	0.246682	+	0.969097i	$0.420660\pi$
$318$		0			0
$319$			14.2929i			0.800249i
$320$		0			0
$321$	10.3974	+	22.3575i	0.580327	+	1.24787i
$322$		0			0
$323$	−0.589892	−	2.96559i	−0.0328225	−	0.165010i
$324$		0			0
$325$	3.75494	−	2.50897i	0.208287	−	0.139173i
$326$		0			0
$327$	0.726304	+	17.0381i	0.0401647	+	0.942207i
$328$		0			0
$329$	1.14120	+	2.75511i	0.0629166	+	0.151894i
$330$		0			0
$331$	5.48542	−	27.5771i	0.301506	−	1.51577i	−0.471780	−	0.881716i	$-0.656388\pi$
$331$	5.48542	−	27.5771i	0.301506	−	1.51577i	0.773286	−	0.634057i	$-0.218612\pi$
$332$		0			0
$333$	13.2187	−	3.82334i	0.724378	−	0.209518i
$334$		0			0
$335$	0.0972006	+	0.0972006i	0.00531064	+	0.00531064i
$336$		0			0
$337$	−14.8867	+	14.8867i	−0.810928	+	0.810928i	−0.984773	−	0.173845i	$-0.944381\pi$
$337$	−14.8867	+	14.8867i	−0.810928	+	0.810928i	0.173845	+	0.984773i	$0.444381\pi$
$338$		0			0
$339$	−2.83913	+	18.3205i	−0.154200	+	0.995034i
$340$		0			0
$341$	21.8197	+	4.34020i	1.18160	+	0.235035i
$342$		0			0
$343$	3.37364	−	1.39741i	0.182159	−	0.0754528i
$344$		0			0
$345$	−0.0107862	−	0.253029i	−0.000580710	−	0.0136226i
$346$		0			0
$347$	−10.7084	−	16.0262i	−0.574855	−	0.860332i	0.424119	−	0.905606i	$-0.360584\pi$
$347$	−10.7084	−	16.0262i	−0.574855	−	0.860332i	−0.998975	+	0.0452745i	$0.985584\pi$
$348$		0			0
$349$	18.0984	−	3.59999i	0.968783	−	0.192703i	0.314755	−	0.949173i	$-0.398078\pi$
$349$	18.0984	−	3.59999i	0.968783	−	0.192703i	0.654028	+	0.756470i	$0.273078\pi$
$350$		0			0
$351$	−1.23009	+	4.53461i	−0.0656572	+	0.242040i
$352$		0			0
$353$	−10.1922			−0.542474			−0.271237	−	0.962513i	$-0.587433\pi$
$353$	−10.1922			−0.542474			−0.271237	+	0.962513i	$0.587433\pi$
$354$		0			0
$355$	0.0827081	+	0.415802i	0.00438969	+	0.0220685i
$356$		0			0
$357$	0.556659	−	0.915217i	0.0294615	−	0.0484384i
$358$		0			0
$359$	6.12003	−	14.7751i	0.323003	−	0.779798i	−0.676074	−	0.736834i	$-0.736320\pi$
$359$	6.12003	−	14.7751i	0.323003	−	0.779798i	0.999077	−	0.0429641i	$-0.0136801\pi$
$360$		0			0
$361$	−6.64254	−	16.0365i	−0.349607	−	0.844027i
$362$		0			0
$363$	10.3793	−	2.52847i	0.544774	−	0.132710i
$364$		0			0
$365$	−0.677187	−	0.452482i	−0.0354456	−	0.0236840i
$366$		0			0
$367$	9.95497	+	9.95497i	0.519645	+	0.519645i	0.917464	−	0.397819i	$-0.130233\pi$
$367$	9.95497	+	9.95497i	0.519645	+	0.519645i	−0.397819	+	0.917464i	$0.630233\pi$
$368$		0			0
$369$	−1.32014	−	15.4561i	−0.0687235	−	0.804614i
$370$		0			0
$371$	1.44581	+	0.966058i	0.0750626	+	0.0501552i
$372$		0			0
$373$	−19.3566	−	3.85026i	−1.00224	−	0.199359i	−0.333420	−	0.942779i	$-0.608203\pi$
$373$	−19.3566	−	3.85026i	−1.00224	−	0.199359i	−0.668825	+	0.743420i	$0.733203\pi$
$374$		0			0
$375$	0.878945	−	0.957218i	0.0453885	−	0.0494305i
$376$		0			0
$377$	−2.24990	+	5.43173i	−0.115876	+	0.279748i
$378$		0			0
$379$	−0.800844	−	1.19855i	−0.0411366	−	0.0615653i	0.810331	−	0.585972i	$-0.199287\pi$
$379$	−0.800844	−	1.19855i	−0.0411366	−	0.0615653i	−0.851468	+	0.524407i	$0.824287\pi$
$380$		0			0
$381$	−0.422641	−	0.577657i	−0.0216525	−	0.0295942i
$382$		0			0
$383$	21.7067			1.10916			0.554580	−	0.832130i	$-0.312879\pi$
$383$	21.7067			1.10916			0.554580	+	0.832130i	$0.312879\pi$
$384$		0			0
$385$	−0.0432554			−0.00220450
$386$		0			0
$387$	13.8507	−	25.1236i	0.704071	−	1.27710i
$388$		0			0
$389$	−17.4324	−	26.0894i	−0.883858	−	1.32279i	−0.945814	−	0.324708i	$-0.894734\pi$
$389$	−17.4324	−	26.0894i	−0.883858	−	1.32279i	0.0619565	−	0.998079i	$-0.480266\pi$
$390$		0			0
$391$	−1.75870	+	4.24588i	−0.0889413	+	0.214723i
$392$		0			0
$393$	6.85717	+	6.29645i	0.345898	+	0.317614i
$394$		0			0
$395$	−0.618201	−	0.122968i	−0.0311050	−	0.00618718i
$396$		0			0
$397$	10.9547	+	7.31968i	0.549799	+	0.367364i	0.799227	−	0.601029i	$-0.205242\pi$
$397$	10.9547	+	7.31968i	0.549799	+	0.367364i	−0.249428	+	0.968393i	$0.580242\pi$
$398$		0			0
$399$	−0.199547	+	0.546499i	−0.00998986	+	0.0273591i
$400$		0			0
$401$	20.2825	+	20.2825i	1.01286	+	1.01286i	0.999916	+	0.0129431i	$0.00412004\pi$
$401$	20.2825	+	20.2825i	1.01286	+	1.01286i	0.0129431	+	0.999916i	$0.495880\pi$
$402$		0			0
$403$	7.60892	+	5.08412i	0.379027	+	0.253258i
$404$		0			0
$405$	−0.0175239	+	0.675416i	−0.000870767	+	0.0335617i
$406$		0			0
$407$	3.85857	+	9.31541i	0.191262	+	0.461748i
$408$		0			0
$409$	−6.31288	+	15.2406i	−0.312152	+	0.753601i	0.687473	+	0.726210i	$0.258720\pi$
$409$	−6.31288	+	15.2406i	−0.312152	+	0.753601i	−0.999625	+	0.0273914i	$0.991280\pi$
$410$		0			0
$411$	22.4147	+	13.6332i	1.10563	+	0.672476i
$412$		0			0
$413$	0.237465	+	1.19382i	0.0116849	+	0.0587439i
$414$		0			0
$415$	−0.917756			−0.0450509
$416$		0			0
$417$	−6.43572	−	13.8387i	−0.315159	−	0.677683i
$418$		0			0
$419$	−31.4491	+	6.25562i	−1.53639	+	0.305607i	−0.889485	−	0.456964i	$-0.848937\pi$
$419$	−31.4491	+	6.25562i	−1.53639	+	0.305607i	−0.646904	+	0.762571i	$0.723937\pi$
$420$		0			0
$421$	−9.69566	−	14.5106i	−0.472537	−	0.707202i	0.516266	−	0.856428i	$-0.327322\pi$
$421$	−9.69566	−	14.5106i	−0.472537	−	0.707202i	−0.988803	+	0.149226i	$0.952322\pi$
$422$		0			0
$423$	15.6976	+	30.3073i	0.763246	+	1.47359i
$424$		0			0
$425$	−10.8872	+	4.50964i	−0.528109	+	0.218750i
$426$		0			0
$427$	−1.12466	−	0.223709i	−0.0544262	−	0.0108260i
$428$		0			0
$429$	−3.40219	−	0.527237i	−0.164259	−	0.0254553i
$430$		0			0
$431$	−13.1610	+	13.1610i	−0.633944	+	0.633944i	−0.949055	−	0.315111i	$-0.897958\pi$
$431$	−13.1610	+	13.1610i	−0.633944	+	0.633944i	0.315111	+	0.949055i	$0.397958\pi$
$432$		0			0
$433$	18.5364	+	18.5364i	0.890803	+	0.890803i	0.994599	−	0.103795i	$-0.0330987\pi$
$433$	18.5364	+	18.5364i	0.890803	+	0.890803i	−0.103795	+	0.994599i	$0.533099\pi$
$434$		0			0
$435$	−0.129472	+	0.835465i	−0.00620771	+	0.0400575i
$436$		0			0
$437$	0.486945	−	2.44804i	0.0232937	−	0.117105i
$438$		0			0
$439$	−8.76979	−	21.1722i	−0.418559	−	1.01049i	−0.982765	−	0.184858i	$-0.940818\pi$
$439$	−8.76979	−	21.1722i	−0.418559	−	1.01049i	0.564206	−	0.825634i	$-0.309182\pi$
$440$		0			0
$441$	18.4642	−	9.56351i	0.879246	−	0.455405i
$442$		0			0
$443$	5.76224	−	3.85021i	0.273773	−	0.182929i	−0.411103	−	0.911589i	$-0.634856\pi$
$443$	5.76224	−	3.85021i	0.273773	−	0.182929i	0.684876	+	0.728660i	$0.259856\pi$
$444$		0			0
$445$	−0.215132	−	1.08154i	−0.0101982	−	0.0512700i
$446$		0			0
$447$	−9.63767	+	4.48203i	−0.455846	+	0.211993i
$448$		0			0
$449$			6.65138i			0.313898i	0.987607	+	0.156949i	$0.0501659\pi$
$449$			6.65138i			0.313898i	−0.987607	+	0.156949i	$0.949834\pi$
$450$		0			0
$451$	11.1482	−	2.21752i	0.524950	−	0.104419i
$452$		0			0
$453$	7.64582	−	12.5707i	0.359232	−	0.590622i
$454$		0			0
$455$	−0.0164384	−	0.00680899i	−0.000770642	−	0.000319210i
$456$		0			0
$457$	−15.3039	+	6.33908i	−0.715886	+	0.296530i	−0.710738	−	0.703457i	$-0.751639\pi$
$457$	−15.3039	+	6.33908i	−0.715886	+	0.296530i	−0.00514839	+	0.999987i	$0.501639\pi$
$458$		0			0
$459$	5.45661	−	10.9792i	0.254693	−	0.512465i
$460$		0			0
$461$	−14.2247	+	21.2887i	−0.662509	+	0.991515i	0.336253	+	0.941772i	$0.390840\pi$
$461$	−14.2247	+	21.2887i	−0.662509	+	0.991515i	−0.998762	+	0.0497436i	$0.984160\pi$
$462$		0			0
$463$	−9.91878	+	9.91878i	−0.460965	+	0.460965i	−0.898972	−	0.438007i	$-0.855685\pi$
$463$	−9.91878	+	9.91878i	−0.460965	+	0.460965i	0.438007	+	0.898972i	$0.355685\pi$
$464$		0			0
$465$	1.23611	+	0.451352i	0.0573233	+	0.0209309i
$466$		0			0
$467$	2.12128	−	3.17472i	0.0981612	−	0.146909i	−0.779138	−	0.626852i	$-0.784343\pi$
$467$	2.12128	−	3.17472i	0.0981612	−	0.146909i	0.877299	+	0.479944i	$0.159343\pi$
$468$		0			0
$469$	−0.0936346	+	0.470733i	−0.00432365	+	0.0217364i
$470$		0			0
$471$	14.9884	−	16.3232i	0.690629	−	0.752131i
$472$		0			0
$473$	19.4213	+	8.04455i	0.892991	+	0.369889i
$474$		0			0
$475$	5.32158	−	3.55577i	0.244171	−	0.163150i
$476$		0			0
$477$	17.4287	+	9.60853i	0.798007	+	0.439944i
$478$		0			0
$479$			4.64745i			0.212347i	0.994348	+	0.106174i	$0.0338599\pi$
$479$			4.64745i			0.212347i	−0.994348	+	0.106174i	$0.966140\pi$
$480$		0			0
$481$			4.14753i			0.189111i
$482$		0			0
$483$	0.713648	−	0.522138i	0.0324721	−	0.0237581i
$484$		0			0
$485$	0.811728	−	0.542380i	0.0368587	−	0.0246282i
$486$		0			0
$487$	−18.0003	−	7.45596i	−0.815670	−	0.337862i	−0.0644565	−	0.997921i	$-0.520531\pi$
$487$	−18.0003	−	7.45596i	−0.815670	−	0.337862i	−0.751214	+	0.660059i	$0.770531\pi$
$488$		0			0
$489$	9.22358	+	8.46936i	0.417105	+	0.382998i
$490$		0			0
$491$	2.10722	−	10.5937i	0.0950974	−	0.478087i	−0.903660	−	0.428251i	$-0.859130\pi$
$491$	2.10722	−	10.5937i	0.0950974	−	0.478087i	0.998757	−	0.0498362i	$-0.0158699\pi$
$492$		0			0
$493$	8.52329	−	12.7560i	0.383870	−	0.574502i
$494$		0			0
$495$	−0.493278	+	0.0421318i	−0.0221712	+	0.00189368i
$496$		0			0
$497$	−1.04668	+	1.04668i	−0.0469500	+	0.0469500i
$498$		0			0
$499$	−19.8260	+	29.6718i	−0.887535	+	1.32829i	0.0564854	+	0.998403i	$0.482011\pi$
$499$	−19.8260	+	29.6718i	−0.887535	+	1.32829i	−0.944021	+	0.329887i	$0.892989\pi$
$500$		0			0
$501$	−5.42546	−	22.2714i	−0.242391	−	0.995013i
$502$		0			0
$503$	−0.0322396	+	0.0133541i	−0.00143749	+	0.000595428i	−0.383402	−	0.923582i	$-0.625248\pi$
$503$	−0.0322396	+	0.0133541i	−0.00143749	+	0.000595428i	0.381965	+	0.924177i	$0.375248\pi$
$504$		0			0
$505$	0.807826	+	0.334612i	0.0359478	+	0.0148901i
$506$		0			0
$507$	18.0278	+	10.9650i	0.800641	+	0.486971i
$508$		0			0
$509$	3.75595	−	0.747106i	0.166480	−	0.0331149i	−0.111147	−	0.993804i	$-0.535452\pi$
$509$	3.75595	−	0.747106i	0.166480	−	0.0331149i	0.277626	+	0.960689i	$0.410452\pi$
$510$		0			0
$511$		−	2.84367i		−	0.125796i
$512$		0			0
$513$	−1.74330	+	6.42655i	−0.0769688	+	0.283739i
$514$		0			0
$515$	0.196608	+	0.988414i	0.00866357	+	0.0435547i
$516$		0			0
$517$	−20.7947	+	13.8946i	−0.914549	+	0.611082i
$518$		0			0
$519$	41.7676	−	1.78048i	1.83339	−	0.0781545i
$520$		0			0
$521$	−5.37144	−	12.9678i	−0.235327	−	0.568130i	0.761461	−	0.648210i	$-0.224482\pi$
$521$	−5.37144	−	12.9678i	−0.235327	−	0.568130i	−0.996788	+	0.0800804i	$0.974482\pi$
$522$		0			0
$523$	2.63083	−	13.2261i	0.115038	−	0.578337i	−0.879669	−	0.475587i	$-0.842236\pi$
$523$	2.63083	−	13.2261i	0.115038	−	0.578337i	0.994707	−	0.102750i	$-0.0327642\pi$
$524$		0			0
$525$	2.24068	+	0.347238i	0.0977911	+	0.0151547i
$526$		0			0
$527$	−16.8852	−	16.8852i	−0.735533	−	0.735533i
$528$		0			0
$529$	13.5809	−	13.5809i	0.590475	−	0.590475i
$530$		0			0
$531$	3.87082	+	13.3828i	0.167979	+	0.580764i
$532$		0			0
$533$	4.58573	+	0.912158i	0.198630	+	0.0395100i
$534$		0			0
$535$	−0.987343	+	0.408971i	−0.0426866	+	0.0176814i
$536$		0			0
$537$	−21.2289	+	0.904954i	−0.916096	+	0.0390516i
$538$		0			0
$539$	8.46501	+	12.6688i	0.364614	+	0.545683i
$540$		0			0
$541$	26.2221	−	5.21590i	1.12738	−	0.224249i	0.404037	−	0.914743i	$-0.367607\pi$
$541$	26.2221	−	5.21590i	1.12738	−	0.224249i	0.723339	+	0.690494i	$0.242607\pi$
$542$		0			0
$543$	−16.5631	+	7.70274i	−0.710792	+	0.330556i
$544$		0			0
$545$	−0.739143			−0.0316614
$546$		0			0
$547$	6.71870	+	33.7772i	0.287271	+	1.44421i	0.807341	+	0.590085i	$0.200906\pi$
$547$	6.71870	+	33.7772i	0.287271	+	1.44421i	−0.520070	+	0.854124i	$0.674094\pi$
$548$		0			0
$549$	−13.0434	−	1.45570i	−0.556677	−	0.0621276i
$550$		0			0
$551$	−3.18860	+	7.69796i	−0.135839	+	0.327944i
$552$		0			0
$553$	−0.842194	−	2.03324i	−0.0358137	−	0.0864620i
$554$		0			0
$555$	0.141162	+	0.579468i	0.00599199	+	0.0245970i
$556$		0			0
$557$	11.7060	+	7.82170i	0.495999	+	0.331416i	0.778282	−	0.627915i	$-0.216092\pi$
$557$	11.7060	+	7.82170i	0.495999	+	0.331416i	−0.282282	+	0.959331i	$0.591092\pi$
$558$		0			0
$559$	6.11434	+	6.11434i	0.258609	+	0.258609i
$560$		0			0
$561$	8.43878	+	3.08132i	0.356286	+	0.130093i
$562$		0			0
$563$	1.45663	+	0.973290i	0.0613897	+	0.0410193i	0.585886	−	0.810393i	$-0.300746\pi$
$563$	1.45663	+	0.973290i	0.0613897	+	0.0410193i	−0.524497	+	0.851412i	$0.675746\pi$
$564$		0			0
$565$	−0.788096	−	0.156762i	−0.0331554	−	0.00659503i
$566$		0			0
$567$	−1.99480	+	1.25929i	−0.0837736	+	0.0528854i
$568$		0			0
$569$	3.39021	−	8.18469i	0.142125	−	0.343120i	−0.836748	−	0.547588i	$-0.815546\pi$
$569$	3.39021	−	8.18469i	0.142125	−	0.343120i	0.978873	+	0.204468i	$0.0655463\pi$
$570$		0			0
$571$	−18.1245	−	27.1252i	−0.758486	−	1.13515i	−0.986859	−	0.161581i	$-0.948341\pi$
$571$	−18.1245	−	27.1252i	−0.758486	−	1.13515i	0.228373	−	0.973574i	$-0.426659\pi$
$572$		0			0
$573$	−38.5705	+	28.2200i	−1.61131	+	1.17891i
$574$		0			0
$575$	−9.72770			−0.405673
$576$		0			0
$577$	18.8087			0.783017			0.391509	−	0.920174i	$-0.371953\pi$
$577$	18.8087			0.783017			0.391509	+	0.920174i	$0.371953\pi$
$578$		0			0
$579$	7.04250	−	5.15262i	0.292676	−	0.214136i
$580$		0			0
$581$	−1.78026	−	2.66435i	−0.0738576	−	0.110536i
$582$		0			0
$583$	−5.58067	+	13.4729i	−0.231128	+	0.557992i
$584$		0			0
$585$	−0.194093	−	0.0616373i	−0.00802474	−	0.00254839i
$586$		0			0
$587$	34.1088	+	6.78466i	1.40782	+	0.280033i	0.839762	−	0.542955i	$-0.182694\pi$
$587$	34.1088	+	6.78466i	1.40782	+	0.280033i	0.568059	+	0.822988i	$0.307694\pi$
$588$		0			0
$589$	10.7835	+	7.20532i	0.444327	+	0.296890i
$590$		0			0
$591$	22.2388	+	8.12023i	0.914782	+	0.334022i
$592$		0			0
$593$	1.14918	+	1.14918i	0.0471910	+	0.0471910i	0.730308	−	0.683118i	$-0.239376\pi$
$593$	1.14918	+	1.14918i	0.0471910	+	0.0471910i	−0.683118	+	0.730308i	$0.739376\pi$
$594$		0			0
$595$	0.0386042	+	0.0257945i	0.00158262	+	0.00105747i
$596$		0			0
$597$	−4.88975	−	20.0724i	−0.200124	−	0.821507i
$598$		0			0
$599$	1.00985	+	2.43798i	0.0412612	+	0.0996132i	0.943167	−	0.332320i	$-0.107831\pi$
$599$	1.00985	+	2.43798i	0.0412612	+	0.0996132i	−0.901905	+	0.431934i	$0.857831\pi$
$600$		0			0
$601$	−1.00588	+	2.42841i	−0.0410307	+	0.0990568i	−0.943066	−	0.332605i	$-0.892073\pi$
$601$	−1.00588	+	2.42841i	−0.0410307	+	0.0990568i	0.902036	+	0.431662i	$0.142073\pi$
$602$		0			0
$603$	−0.609290	+	5.45937i	−0.0248122	+	0.222323i
$604$		0			0
$605$	0.0903312	+	0.454126i	0.00367249	+	0.0184628i
$606$		0			0
$607$	−42.0620			−1.70725			−0.853623	−	0.520892i	$-0.825600\pi$
$607$	−42.0620			−1.70725			−0.853623	+	0.520892i	$0.825600\pi$
$608$		0			0
$609$	−2.67659	+	1.24476i	−0.108461	+	0.0504402i
$610$		0			0
$611$	−10.0898	+	2.00699i	−0.408190	+	0.0811940i
$612$		0			0
$613$	−16.8711	−	25.2494i	−0.681417	−	1.01981i	−0.997471	−	0.0710711i	$-0.977358\pi$
$613$	−16.8711	−	25.2494i	−0.681417	−	1.01981i	0.316055	−	0.948741i	$-0.397642\pi$
$614$		0			0
$615$	0.671736	−	0.0286350i	0.0270870	−	0.00115467i
$616$		0			0
$617$	−15.9796	+	6.61898i	−0.643316	+	0.266470i	−0.680399	−	0.732842i	$-0.738193\pi$
$617$	−15.9796	+	6.61898i	−0.643316	+	0.266470i	0.0370828	+	0.999312i	$0.488193\pi$
$618$		0			0
$619$	−34.6693	−	6.89615i	−1.39348	−	0.277180i	−0.559432	−	0.828876i	$-0.688981\pi$
$619$	−34.6693	−	6.89615i	−1.39348	−	0.277180i	−0.834045	+	0.551696i	$0.813981\pi$
$620$		0			0
$621$	7.62976	−	6.64950i	0.306172	−	0.266835i
$622$		0			0
$623$	2.72252	−	2.72252i	0.109075	−	0.109075i
$624$		0			0
$625$	−17.6179	−	17.6179i	−0.704717	−	0.704717i
$626$		0			0
$627$	−4.82165	−	0.747211i	−0.192558	−	0.0298407i
$628$		0			0
$629$	2.11140	−	10.6147i	0.0841870	−	0.423237i
$630$		0			0
$631$	−1.74700	−	4.21763i	−0.0695470	−	0.167901i	0.885284	−	0.465051i	$-0.153964\pi$
$631$	−1.74700	−	4.21763i	−0.0695470	−	0.167901i	−0.954831	+	0.297150i	$0.903964\pi$
$632$		0			0
$633$	5.75820	−	0.245462i	0.228868	−	0.00975626i
$634$		0			0
$635$	0.0257945	−	0.0172354i	0.00102363	−	0.000683964i
$636$		0			0
$637$	1.22272	+	6.14703i	0.0484459	+	0.243554i
$638$		0			0
$639$	−10.9167	+	12.9557i	−0.431858	+	0.512518i
$640$		0			0
$641$		−	31.5734i		−	1.24708i	−0.781793	−	0.623538i	$-0.785695\pi$
$641$		−	31.5734i		−	1.24708i	0.781793	−	0.623538i	$-0.214305\pi$
$642$		0			0
$643$	−24.3933	+	4.85212i	−0.961976	+	0.191349i	−0.651008	−	0.759071i	$-0.725653\pi$
$643$	−24.3933	+	4.85212i	−0.961976	+	0.191349i	−0.310969	+	0.950420i	$0.600653\pi$
$644$		0			0
$645$	1.06236	+	0.646157i	0.0418305	+	0.0254424i
$646$		0			0
$647$	−17.3176	−	7.17319i	−0.680826	−	0.282007i	0.0153463	−	0.999882i	$-0.495115\pi$
$647$	−17.3176	−	7.17319i	−0.680826	−	0.282007i	−0.696172	+	0.717875i	$0.745115\pi$
$648$		0			0
$649$	−9.43108	+	3.90648i	−0.370202	+	0.153343i
$650$		0			0
$651$	1.08748	+	4.46410i	0.0426218	+	0.174962i
$652$		0			0
$653$	−18.8122	+	28.1544i	−0.736178	+	1.10177i	0.254702	+	0.967020i	$0.418023\pi$
$653$	−18.8122	+	28.1544i	−0.736178	+	1.10177i	−0.990880	+	0.134748i	$0.956977\pi$
$654$		0			0
$655$	−0.285314	+	0.285314i	−0.0111482	+	0.0111482i
$656$		0			0
$657$	−2.76980	−	32.4288i	−0.108060	−	1.26517i
$658$		0			0
$659$	2.59960	−	3.89057i	0.101266	−	0.151555i	−0.777376	−	0.629036i	$-0.783450\pi$
$659$	2.59960	−	3.89057i	0.101266	−	0.151555i	0.878642	+	0.477481i	$0.158450\pi$
$660$		0			0
$661$	−5.49642	+	27.6324i	−0.213786	+	1.07477i	0.713567	+	0.700587i	$0.247078\pi$
$661$	−5.49642	+	27.6324i	−0.213786	+	1.07477i	−0.927353	+	0.374187i	$0.877922\pi$
$662$		0			0
$663$	2.72195	+	2.49937i	0.105712	+	0.0970676i
$664$		0			0
$665$	−0.0232968	−	0.00964984i	−0.000903410	−	0.000374205i
$666$		0			0
$667$	10.5299	−	7.03582i	0.407718	−	0.272428i
$668$		0			0
$669$	−17.6291	+	12.8983i	−0.681581	+	0.498677i
$670$		0			0
$671$		−	9.61679i		−	0.371252i
$672$		0			0
$673$		−	11.0254i		−	0.424996i	−0.977161	−	0.212498i	$-0.931840\pi$
$673$		−	11.0254i		−	0.424996i	0.977161	−	0.212498i	$-0.0681599\pi$
$674$		0			0
$675$	25.8905	+	1.77737i	0.996527	+	0.0684111i
$676$		0			0
$677$	10.9422	−	7.31133i	0.420542	−	0.280997i	−0.327240	−	0.944941i	$-0.606119\pi$
$677$	10.9422	−	7.31133i	0.420542	−	0.280997i	0.747782	+	0.663944i	$0.231119\pi$
$678$		0			0
$679$	3.14917	+	1.30443i	0.120854	+	0.0500594i
$680$		0			0
$681$	16.2501	−	17.6973i	0.622707	−	0.678161i
$682$		0			0
$683$	−6.11205	+	30.7273i	−0.233871	+	1.17575i	0.668140	+	0.744036i	$0.267091\pi$
$683$	−6.11205	+	30.7273i	−0.233871	+	1.17575i	−0.902011	+	0.431713i	$0.857909\pi$
$684$		0			0
$685$	−0.631737	+	0.945461i	−0.0241374	+	0.0361242i
$686$		0			0
$687$	0.267750	+	0.0977658i	0.0102153	+	0.00373000i
$688$		0			0
$689$	−4.24165	+	4.24165i	−0.161594	+	0.161594i
$690$		0			0
$691$	−3.78957	+	5.67149i	−0.144162	+	0.215754i	−0.896523	−	0.442998i	$-0.853915\pi$
$691$	−3.78957	+	5.67149i	−0.144162	+	0.215754i	0.752361	+	0.658751i	$0.228915\pi$
$692$		0			0
$693$	−1.07917	−	1.35031i	−0.0409943	−	0.0512941i
$694$		0			0
$695$	0.611138	−	0.253142i	0.0231818	−	0.00960222i
$696$		0			0
$697$	−11.2719	−	4.66896i	−0.426952	−	0.176849i
$698$		0			0
$699$	14.6460	−	24.0798i	0.553961	−	0.910782i
$700$		0			0
$701$	45.6378	−	9.07793i	1.72372	−	0.342869i	0.768743	−	0.639558i	$-0.220882\pi$
$701$	45.6378	−	9.07793i	1.72372	−	0.342869i	0.954974	+	0.296689i	$0.0958824\pi$
$702$		0			0
$703$			5.87796i			0.221692i
$704$		0			0
$705$	−1.34138	+	0.623813i	−0.0505192	+	0.0234941i
$706$		0			0
$707$	0.595600	+	2.99429i	0.0223999	+	0.112612i
$708$		0			0
$709$	−32.9914	+	22.0441i	−1.23902	+	0.827885i	−0.990062	−	0.140630i	$-0.955087\pi$
$709$	−32.9914	+	22.0441i	−1.23902	+	0.827885i	−0.248955	+	0.968515i	$0.580087\pi$
$710$		0			0
$711$	−11.5847	−	22.3664i	−0.434459	−	0.838805i
$712$		0			0
$713$	−7.54344	−	18.2115i	−0.282504	−	0.682025i
$714$		0			0
$715$	0.0291113	−	0.146352i	0.00108870	−	0.00547327i
$716$		0			0
$717$	3.71819	−	23.9929i	0.138858	−	0.896033i
$718$		0			0
$719$	−27.3837	−	27.3837i	−1.02124	−	1.02124i	−0.999770	−	0.0214686i	$-0.993166\pi$
$719$	−27.3837	−	27.3837i	−1.02124	−	1.02124i	−0.0214686	−	0.999770i	$-0.506834\pi$
$720$		0			0
$721$	−2.48809	+	2.48809i	−0.0926614	+	0.0926614i
$722$		0			0
$723$	−15.8309	−	2.45331i	−0.588757	−	0.0912397i
$724$		0			0
$725$	31.8493	+	6.33523i	1.18285	+	0.235284i
$726$		0			0
$727$	−0.372141	+	0.154146i	−0.0138019	+	0.00571695i	−0.389574	−	0.920995i	$-0.627378\pi$
$727$	−0.372141	+	0.154146i	−0.0138019	+	0.00571695i	0.375772	+	0.926712i	$0.377378\pi$
$728$		0			0
$729$	−21.5218	+	16.3038i	−0.797103	+	0.603843i
$730$		0			0
$731$	−12.5357	−	18.7610i	−0.463650	−	0.693902i
$732$		0			0
$733$	−20.6905	+	4.11560i	−0.764223	+	0.152013i	−0.561787	−	0.827282i	$-0.689886\pi$
$733$	−20.6905	+	4.11560i	−0.764223	+	0.152013i	−0.202436	+	0.979295i	$0.564886\pi$
$734$		0			0
$735$	0.380047	+	0.817211i	0.0140182	+	0.0301433i
$736$		0			0
$737$	−4.02516			−0.148269
$738$		0			0
$739$	1.24476	+	6.25783i	0.0457892	+	0.230198i	0.996903	−	0.0786433i	$-0.0250588\pi$
$739$	1.24476	+	6.25783i	0.0457892	+	0.230198i	−0.951114	+	0.308841i	$0.900059\pi$
$740$		0			0
$741$	−1.71475	−	1.04296i	−0.0629929	−	0.0383139i
$742$		0			0
$743$	14.4970	−	34.9988i	0.531843	−	1.28398i	−0.398459	−	0.917186i	$-0.630455\pi$
$743$	14.4970	−	34.9988i	0.531843	−	1.28398i	0.930302	−	0.366795i	$-0.119545\pi$
$744$		0			0
$745$	−0.176296	−	0.425615i	−0.00645897	−	0.0155933i
$746$		0			0
$747$	−22.8969	−	28.6498i	−0.837755	−	1.04824i
$748$		0			0
$749$	−3.10253	−	2.07304i	−0.113364	−	0.0757474i
$750$		0			0
$751$	−16.0660	−	16.0660i	−0.586258	−	0.586258i	0.350358	−	0.936616i	$-0.386060\pi$
$751$	−16.0660	−	16.0660i	−0.586258	−	0.586258i	−0.936616	+	0.350358i	$0.886060\pi$
$752$		0			0
$753$	13.4727	−	36.8976i	0.490972	−	1.34462i
$754$		0			0
$755$	0.530237	+	0.354293i	0.0192973	+	0.0128940i
$756$		0			0
$757$	−46.1515	−	9.18010i	−1.67740	−	0.333656i	−0.737566	−	0.675276i	$-0.764025\pi$
$757$	−46.1515	−	9.18010i	−1.67740	−	0.333656i	−0.939838	+	0.341619i	$0.889025\pi$
$758$		0			0
$759$	5.46242	+	5.01575i	0.198273	+	0.182060i
$760$		0			0
$761$	13.3019	−	32.1135i	0.482192	−	1.16412i	−0.476373	−	0.879243i	$-0.658049\pi$
$761$	13.3019	−	32.1135i	0.482192	−	1.16412i	0.958566	−	0.284872i	$-0.0919511\pi$
$762$		0			0
$763$	−1.43379	−	2.14581i	−0.0519065	−	0.0776836i
$764$		0			0
$765$	0.465361	+	0.256555i	0.0168252	+	0.00927578i
$766$		0			0
$767$	−4.19903			−0.151618
$768$		0			0
$769$	−29.4345			−1.06144			−0.530718	−	0.847549i	$-0.678078\pi$
$769$	−29.4345			−1.06144			−0.530718	+	0.847549i	$0.678078\pi$
$770$		0			0
$771$	−0.253564	−	0.346566i	−0.00913189	−	0.0124813i
$772$		0			0
$773$	3.03986	+	4.54947i	0.109336	+	0.163633i	0.882103	−	0.471057i	$-0.156128\pi$
$773$	3.03986	+	4.54947i	0.109336	+	0.163633i	−0.772766	+	0.634691i	$0.781128\pi$
$774$		0			0
$775$	19.3428	−	46.6977i	0.694815	−	1.67743i
$776$		0			0
$777$	−1.40843	+	1.53386i	−0.0505272	+	0.0550268i
$778$		0			0
$779$	6.49899	+	1.29273i	0.232851	+	0.0463168i
$780$		0			0
$781$	−10.3219	−	6.89685i	−0.369345	−	0.246789i
$782$		0			0
$783$	−29.3110	+	16.8021i	−1.04749	+	0.600458i
$784$		0			0
$785$	0.679177	+	0.679177i	0.0242409	+	0.0242409i
$786$		0			0
$787$	4.45487	+	2.97665i	0.158799	+	0.106106i	0.632431	−	0.774617i	$-0.282057\pi$
$787$	4.45487	+	2.97665i	0.158799	+	0.106106i	−0.473632	+	0.880723i	$0.657057\pi$
$788$		0			0
$789$	−45.1485	+	10.9985i	−1.60733	+	0.391556i
$790$		0			0
$791$	−1.07365	−	2.59201i	−0.0381745	−	0.0921614i
$792$		0			0
$793$	1.51381	−	3.65467i	0.0537571	−	0.129781i
$794$		0			0
$795$	−0.448252	+	0.736983i	−0.0158979	+	0.0261381i
$796$		0			0
$797$	1.68618	+	8.47701i	0.0597276	+	0.300271i	0.999090	−	0.0426555i	$-0.0135818\pi$
$797$	1.68618	+	8.47701i	0.0597276	+	0.300271i	−0.939362	+	0.342927i	$0.888582\pi$
$798$		0			0
$799$	26.8444			0.949688
$800$		0			0
$801$	28.3954	−	33.6990i	1.00330	−	1.19070i
$802$		0			0
$803$	23.3903	−	4.65262i	0.825425	−	0.164187i
$804$		0			0
$805$	0.0212929	+	0.0318671i	0.000750476	+	0.00112317i
$806$		0			0
$807$	1.04788	+	24.5819i	0.0368873	+	0.865323i
$808$		0			0
$809$	−13.8531	+	5.73816i	−0.487050	+	0.201743i	−0.612675	−	0.790335i	$-0.709906\pi$
$809$	−13.8531	+	5.73816i	−0.487050	+	0.201743i	0.125625	+	0.992078i	$0.459906\pi$
$810$		0			0
$811$	20.2295	+	4.02389i	0.710352	+	0.141298i	0.537025	−	0.843566i	$-0.319548\pi$
$811$	20.2295	+	4.02389i	0.710352	+	0.141298i	0.173327	+	0.984864i	$0.444548\pi$
$812$		0			0
$813$	−2.96865	+	19.1563i	−0.104115	+	0.671840i
$814$		0			0
$815$	−0.383776	+	0.383776i	−0.0134431	+	0.0134431i
$816$		0			0
$817$	8.66537	+	8.66537i	0.303163	+	0.303163i
$818$		0			0
$819$	−0.197560	−	0.683036i	−0.00690330	−	0.0238672i
$820$		0			0
$821$	−9.97627	+	50.1541i	−0.348174	+	1.75039i	0.268602	+	0.963251i	$0.413438\pi$
$821$	−9.97627	+	50.1541i	−0.348174	+	1.75039i	−0.616776	+	0.787138i	$0.711562\pi$
$822$		0			0
$823$	6.20664	+	14.9842i	0.216350	+	0.522315i	0.994375	−	0.105919i	$-0.0337783\pi$
$823$	6.20664	+	14.9842i	0.216350	+	0.522315i	−0.778025	+	0.628233i	$0.783778\pi$
$824$		0			0
$825$	0.809877	+	18.9986i	0.0281963	+	0.661445i
$826$		0			0
$827$	20.0660	−	13.4077i	0.697763	−	0.466230i	−0.155416	−	0.987849i	$-0.549672\pi$
$827$	20.0660	−	13.4077i	0.697763	−	0.466230i	0.853178	+	0.521619i	$0.174672\pi$
$828$		0			0
$829$	0.773289	+	3.88759i	0.0268575	+	0.135022i	0.991888	−	0.127117i	$-0.0405723\pi$
$829$	0.773289	+	3.88759i	0.0268575	+	0.135022i	−0.965030	+	0.262138i	$0.915572\pi$
$830$		0			0
$831$	−18.0040	−	38.7138i	−0.624551	−	1.34297i
$832$		0			0
$833$		−	16.3545i		−	0.566649i
$834$		0			0
$835$	0.974438	−	0.193828i	0.0337218	−	0.00670769i
$836$		0			0
$837$	16.7496	+	49.8486i	0.578951	+	1.72302i
$838$		0			0
$839$	−38.8599	−	16.0963i	−1.34159	−	0.555705i	−0.407652	−	0.913137i	$-0.633652\pi$
$839$	−38.8599	−	16.0963i	−1.34159	−	0.555705i	−0.933939	+	0.357432i	$0.883652\pi$
$840$		0			0
$841$	−12.2653	+	5.08045i	−0.422941	+	0.175188i
$842$		0			0
$843$	−38.8898	+	9.47381i	−1.33944	+	0.326295i
$844$		0			0
$845$	−0.508096	+	0.760419i	−0.0174790	+	0.0261592i
$846$		0			0
$847$	−1.14315	+	1.14315i	−0.0392792	+	0.0392792i
$848$		0			0
$849$	−1.52371	+	4.17298i	−0.0522937	+	0.143216i
$850$		0			0
$851$	4.96342	−	7.42829i	0.170144	−	0.254638i
$852$		0			0
$853$	10.2912	−	51.7372i	0.352363	−	1.77145i	−0.245046	−	0.969511i	$-0.578803\pi$
$853$	10.2912	−	51.7372i	0.352363	−	1.77145i	0.597409	−	0.801937i	$-0.296197\pi$
$854$		0			0
$855$	−0.275072	−	0.0873537i	−0.00940726	−	0.00298743i
$856$		0			0
$857$	−35.5270	−	14.7158i	−1.21358	−	0.502681i	−0.318216	−	0.948018i	$-0.603084\pi$
$857$	−35.5270	−	14.7158i	−1.21358	−	0.502681i	−0.895363	+	0.445338i	$0.853084\pi$
$858$		0			0
$859$	−31.9131	+	21.3237i	−1.08886	+	0.727554i	−0.964341	−	0.264663i	$-0.914739\pi$
$859$	−31.9131	+	21.3237i	−1.08886	+	0.727554i	−0.124520	+	0.992217i	$0.539739\pi$
$860$		0			0
$861$	1.38616	+	1.89458i	0.0472402	+	0.0645670i
$862$		0			0
$863$		−	56.5922i		−	1.92642i	−0.268751	−	0.963210i	$-0.586611\pi$
$863$		−	56.5922i		−	1.92642i	0.268751	−	0.963210i	$-0.413389\pi$
$864$		0			0
$865$			1.81196i			0.0616084i
$866$		0			0
$867$	11.6927	+	15.9813i	0.397103	+	0.542753i
$868$		0			0
$869$	15.3462	−	10.2540i	0.520585	−	0.347844i
$870$		0			0
$871$	−1.52968	−	0.633615i	−0.0518313	−	0.0214692i
$872$		0			0
$873$	37.1832	+	11.8082i	1.25846	+	0.399645i
$874$		0			0
$875$	−0.0383669	+	0.192884i	−0.00129704	+	0.00652066i
$876$		0			0
$877$	−18.4579	+	27.6242i	−0.623279	+	0.932802i	0.376700	+	0.926335i	$0.377059\pi$
$877$	−18.4579	+	27.6242i	−0.623279	+	0.932802i	−0.999979	+	0.00646722i	$0.997941\pi$
$878$		0			0
$879$	11.2078	−	30.6947i	0.378030	−	1.03531i
$880$		0			0
$881$	−28.1610	+	28.1610i	−0.948767	+	0.948767i	−0.998750	−	0.0499827i	$-0.984083\pi$
$881$	−28.1610	+	28.1610i	−0.948767	+	0.948767i	0.0499827	+	0.998750i	$0.484083\pi$
$882$		0			0
$883$	7.45192	−	11.1526i	0.250777	−	0.375314i	−0.684628	−	0.728893i	$-0.740035\pi$
$883$	7.45192	−	11.1526i	0.250777	−	0.375314i	0.935405	+	0.353578i	$0.115035\pi$
$884$		0			0
$885$	−0.586663	+	0.142915i	−0.0197205	+	0.00480403i
$886$		0			0
$887$	−23.8945	+	9.89741i	−0.802298	+	0.332323i	−0.745876	−	0.666085i	$-0.767969\pi$
$887$	−23.8945	+	9.89741i	−0.802298	+	0.332323i	−0.0564213	+	0.998407i	$0.517969\pi$
$888$		0			0
$889$	0.100072	+	0.0414513i	0.00335631	+	0.00139023i
$890$		0			0
$891$	−13.6219	−	14.3476i	−0.456352	−	0.480663i
$892$		0			0
$893$	−14.2995	+	2.84434i	−0.478514	+	0.0951823i
$894$		0			0
$895$		−	0.920951i		−	0.0307840i
$896$		0			0
$897$	1.28634	+	2.76599i	0.0429495	+	0.0923539i
$898$		0			0
$899$	12.8375	+	64.5387i	0.428156	+	2.15249i
$900$		0			0
$901$	13.0149	−	8.69629i	0.433590	−	0.289715i
$902$		0			0
$903$	0.184903	+	4.33756i	0.00615319	+	0.144345i
$904$		0			0
$905$	−0.302979	−	0.731455i	−0.0100714	−	0.0243144i
$906$		0			0
$907$	0.344578	−	1.73231i	0.0114415	−	0.0575205i	−0.974643	−	0.223767i	$-0.928165\pi$
$907$	0.344578	−	1.73231i	0.0114415	−	0.0575205i	0.986084	+	0.166246i	$0.0531646\pi$
$908$		0			0
$909$	9.70864	+	33.5662i	0.322015	+	1.11332i
$910$		0			0
$911$	16.1986	+	16.1986i	0.536684	+	0.536684i	0.922554	−	0.385869i	$-0.126098\pi$
$911$	16.1986	+	16.1986i	0.536684	+	0.536684i	−0.385869	+	0.922554i	$0.626098\pi$
$912$		0			0
$913$	19.0025	−	19.0025i	0.628893	−	0.628893i
$914$		0			0
$915$	0.0871136	−	0.562132i	0.00287989	−	0.0185835i
$916$		0			0
$917$	−1.38175	−	0.274847i	−0.0456294	−	0.00907625i
$918$		0			0
$919$	25.4121	−	10.5260i	0.838266	−	0.347221i	0.0780965	−	0.996946i	$-0.475116\pi$
$919$	25.4121	−	10.5260i	0.838266	−	0.347221i	0.760170	+	0.649725i	$0.225116\pi$
$920$		0			0
$921$	−0.975911	−	22.8935i	−0.0321574	−	0.754366i
$922$		0			0
$923$	−2.83696	−	4.24581i	−0.0933797	−	0.139753i
$924$		0			0
$925$	22.4681	−	4.46919i	0.738747	−	0.146946i
$926$		0			0
$927$	−25.9504	+	30.7973i	−0.852322	+	1.01152i
$928$		0			0
$929$	45.2667			1.48515			0.742576	−	0.669762i	$-0.233604\pi$
$929$	45.2667			1.48515			0.742576	+	0.669762i	$0.233604\pi$
$930$		0			0
$931$	1.73286	+	8.71169i	0.0567923	+	0.285514i
$932$		0			0
$933$	4.23780	−	6.96747i	0.138739	−	0.228105i
$934$		0			0
$935$	−0.149008	+	0.359738i	−0.00487310	+	0.0117647i
$936$		0			0
$937$	16.4387	+	39.6866i	0.537030	+	1.29650i	0.926787	+	0.375587i	$0.122559\pi$
$937$	16.4387	+	39.6866i	0.537030	+	1.29650i	−0.389758	+	0.920917i	$0.627441\pi$
$938$		0			0
$939$	16.0949	−	3.92081i	0.525236	−	0.127951i
$940$		0			0
$941$	13.4371	+	8.97839i	0.438037	+	0.292687i	0.754968	−	0.655762i	$-0.227652\pi$
$941$	13.4371	+	8.97839i	0.438037	+	0.292687i	−0.316931	+	0.948449i	$0.602652\pi$
$942$		0			0
$943$	−7.12152	−	7.12152i	−0.231908	−	0.231908i
$944$		0			0
$945$	−0.0508492	−	0.0887057i	−0.00165412	−	0.00288560i
$946$		0			0
$947$	−11.2306	−	7.50405i	−0.364946	−	0.243849i	0.359554	−	0.933124i	$-0.382929\pi$
$947$	−11.2306	−	7.50405i	−0.364946	−	0.243849i	−0.724499	+	0.689276i	$0.757929\pi$
$948$		0			0
$949$	9.62140	+	1.91381i	0.312324	+	0.0621250i
$950$		0			0
$951$	−2.20591	+	2.40235i	−0.0715314	+	0.0779015i
$952$		0			0
$953$	−16.3000	+	39.3517i	−0.528009	+	1.27473i	0.404817	+	0.914398i	$0.367335\pi$
$953$	−16.3000	+	39.3517i	−0.528009	+	1.27473i	−0.932826	+	0.360328i	$0.882665\pi$
$954$		0			0
$955$	−1.15082	−	1.72232i	−0.0372396	−	0.0557329i
$956$		0			0
$957$	−14.6179	−	19.9794i	−0.472529	−	0.645844i
$958$		0			0
$959$	−3.97022			−0.128205
$960$		0			0
$961$	71.4236			2.30399
$962$		0			0
$963$	−37.4000	−	20.6187i	−1.20520	−	0.664429i
$964$		0			0
$965$	0.210125	+	0.314474i	0.00676416	+	0.0101233i
$966$		0			0
$967$	−1.80085	+	4.34765i	−0.0579116	+	0.139811i	−0.950187	−	0.311681i	$-0.899108\pi$
$967$	−1.80085	+	4.34765i	−0.0579116	+	0.139811i	0.892275	+	0.451492i	$0.149108\pi$
$968$		0			0
$969$	3.85760	+	3.54216i	0.123924	+	0.113791i
$970$		0			0
$971$	49.1172	+	9.77002i	1.57625	+	0.313535i	0.904245	−	0.427015i	$-0.140435\pi$
$971$	49.1172	+	9.77002i	1.57625	+	0.313535i	0.672002	+	0.740550i	$0.265435\pi$
$972$		0			0
$973$	1.92038	+	1.28316i	0.0615646	+	0.0411361i
$974$		0			0
$975$	−2.68286	+	7.34751i	−0.0859201	+	0.235309i
$976$		0			0
$977$	−14.3409	−	14.3409i	−0.458806	−	0.458806i	0.439457	−	0.898263i	$-0.355171\pi$
$977$	−14.3409	−	14.3409i	−0.458806	−	0.458806i	−0.898263	+	0.439457i	$0.855171\pi$
$978$		0			0
$979$	26.8482	+	17.9394i	0.858073	+	0.573346i
$980$		0			0
$981$	−18.4407	−	23.0740i	−0.588768	−	0.736695i
$982$		0			0
$983$	20.8007	+	50.2173i	0.663439	+	1.60168i	0.792378	+	0.610030i	$0.208843\pi$
$983$	20.8007	+	50.2173i	0.663439	+	1.60168i	−0.128939	+	0.991652i	$0.541157\pi$
$984$		0			0
$985$	−0.392683	+	0.948021i	−0.0125119	+	0.0302065i
$986$		0			0
$987$	−4.41299	−	2.68410i	−0.140467	−	0.0854358i
$988$		0			0
$989$	−3.63374	−	18.2680i	−0.115546	−	0.580890i
$990$		0			0
$991$	21.0842			0.669761			0.334880	−	0.942261i	$-0.391304\pi$
$991$	21.0842			0.669761			0.334880	+	0.942261i	$0.391304\pi$
$992$		0			0
$993$	20.5363	+	44.1590i	0.651700	+	1.40134i
$994$		0			0
$995$	0.878223	−	0.174689i	0.0278415	−	0.00553803i
$996$		0			0
$997$	34.7772	+	52.0478i	1.10141	+	1.64837i	0.660525	+	0.750804i	$0.270334\pi$
$997$	34.7772	+	52.0478i	1.10141	+	1.64837i	0.440881	+	0.897566i	$0.354666\pi$
$998$		0			0
$999$	−14.5675	+	18.8637i	−0.460896	+	0.596822i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.s.a.335.5		240
3.2	odd	2	inner	768.2.s.a.335.2		240
4.3	odd	2		192.2.s.a.107.24	yes	240
12.11	even	2		192.2.s.a.107.7	✓	240
64.3	odd	16	inner	768.2.s.a.431.2		240
64.61	even	16		192.2.s.a.131.7	yes	240
192.125	odd	16		192.2.s.a.131.24	yes	240
192.131	even	16	inner	768.2.s.a.431.5		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.107.7	✓	240	12.11	even	2
192.2.s.a.107.24	yes	240	4.3	odd	2
192.2.s.a.131.7	yes	240	64.61	even	16
192.2.s.a.131.24	yes	240	192.125	odd	16
768.2.s.a.335.2		240	3.2	odd	2	inner
768.2.s.a.335.5		240	1.1	even	1	trivial
768.2.s.a.431.2		240	64.3	odd	16	inner
768.2.s.a.431.5		240	192.131	even	16	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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.s (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.39786 + 1.02274i) q^{3} +(-0.0417075 - 0.0624196i) q^{5} +(0.100307 - 0.242162i) q^{7} +(0.908014 - 2.85929i) q^{9} +(2.15600 + 0.428854i) q^{11} +(0.751836 + 0.502361i) q^{13} +(0.122140 + 0.0445980i) q^{15} +(-1.66843 - 1.66843i) q^{17} +(1.06552 + 0.711956i) q^{19} +(0.107454 + 0.441097i) q^{21} +(-0.745366 - 1.79947i) q^{23} +(1.91126 - 4.61419i) q^{25} +(1.65503 + 4.92553i) q^{27} +(1.26847 + 6.37705i) q^{29} +10.1205 q^{31} +(-3.45238 + 1.60554i) q^{33} +(-0.0192992 + 0.00383886i) q^{35} +(2.54831 + 3.81381i) q^{37} +(-1.56474 + 0.0667024i) q^{39} +(4.77720 - 1.97878i) q^{41} +(9.37912 + 1.86562i) q^{43} +(-0.216346 + 0.0625756i) q^{45} +(-8.04483 + 8.04483i) q^{47} +(4.90117 + 4.90117i) q^{49} +(4.03859 + 0.625860i) q^{51} +(-1.29422 + 6.50649i) q^{53} +(-0.0631522 - 0.152463i) q^{55} +(-2.21759 + 0.0945320i) q^{57} +(-3.86117 + 2.57995i) q^{59} +(-0.853477 - 4.29072i) q^{61} +(-0.601331 - 0.506693i) q^{63} -0.0678815i q^{65} +(-1.79590 + 0.357228i) q^{67} +(2.88230 + 1.75309i) q^{69} +(-5.21738 - 2.16111i) q^{71} +(10.0231 - 4.15171i) q^{73} +(2.04744 + 8.40470i) q^{75} +(0.320114 - 0.479085i) q^{77} +(5.93698 - 5.93698i) q^{79} +(-7.35102 - 5.19254i) q^{81} +(6.79190 - 10.1648i) q^{83} +(-0.0345567 + 0.173728i) q^{85} +(-8.29520 - 7.61690i) q^{87} +(13.5709 + 5.62127i) q^{89} +(0.197067 - 0.131676i) q^{91} +(-14.1470 + 10.3506i) q^{93} -0.0962031i q^{95} +13.0044i q^{97} +(3.18389 - 5.77520i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 8 q^{3} + 16 q^{7} - 8 q^{9} - 16 q^{13} + 8 q^{15} + 16 q^{19} - 8 q^{21} - 16 q^{25} + 8 q^{27} + 32 q^{31} - 16 q^{37} + 8 q^{39} + 16 q^{43} - 8 q^{45} - 16 q^{49} + 8 q^{51} + 80 q^{55} - 8 q^{57}+ \cdots + 8 q^{99}+O(q^{100}) \) 240 * q + 8 * q^3 + 16 * q^7 - 8 * q^9 - 16 * q^13 + 8 * q^15 + 16 * q^19 - 8 * q^21 - 16 * q^25 + 8 * q^27 + 32 * q^31 - 16 * q^37 + 8 * q^39 + 16 * q^43 - 8 * q^45 - 16 * q^49 + 8 * q^51 + 80 * q^55 - 8 * q^57 - 16 * q^61 + 144 * q^67 - 8 * q^69 - 16 * q^73 + 8 * q^75 + 48 * q^79 - 8 * q^81 - 16 * q^85 + 8 * q^87 + 16 * q^91 - 32 * q^93 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more