LMFDB - Embedded newform 512.2.k.a.273.7

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			273.7
Character	$\chi$	$=$	512.273
Dual form			512.2.k.a.497.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.205628 - 0.109910i) q^{3} +(-1.29703 + 1.58044i) q^{5} +(-1.60057 - 1.06947i) q^{7} +(-1.63651 - 2.44921i) q^{9} +(2.28487 + 0.693108i) q^{11} +(-1.01011 + 0.828973i) q^{13} +(0.440412 - 0.182425i) q^{15} +(-6.19134 - 2.56454i) q^{17} +(0.717174 - 7.28159i) q^{19} +(0.211577 + 0.395832i) q^{21} +(-6.82091 - 1.35676i) q^{23} +(0.159961 + 0.804177i) q^{25} +(0.135879 + 1.37960i) q^{27} +(-1.11935 - 3.69001i) q^{29} +(0.0726984 - 0.0726984i) q^{31} +(-0.393654 - 0.393654i) q^{33} +(3.76622 - 1.14247i) q^{35} +(2.87067 - 0.282737i) q^{37} +(0.298819 - 0.0594388i) q^{39} +(0.658149 - 3.30874i) q^{41} +(-3.06034 + 1.63579i) q^{43} +(5.99342 + 0.590300i) q^{45} +(-1.75405 + 4.23465i) q^{47} +(-1.26071 - 3.04363i) q^{49} +(0.991243 + 1.20783i) q^{51} +(-2.91014 + 9.59343i) q^{53} +(-4.05896 + 2.71211i) q^{55} +(-0.947794 + 1.41847i) q^{57} +(-4.93475 - 4.04984i) q^{59} +(-0.733515 + 1.37231i) q^{61} +5.67033i q^{63} -2.67161i q^{65} +(-2.54422 + 4.75990i) q^{67} +(1.25345 + 1.02868i) q^{69} +(-1.60349 + 2.39980i) q^{71} +(11.8626 - 7.92631i) q^{73} +(0.0554951 - 0.182943i) q^{75} +(-2.91585 - 3.55297i) q^{77} +(-3.13533 - 7.56937i) q^{79} +(-3.25805 + 7.86562i) q^{81} +(10.8406 + 1.06770i) q^{83} +(12.0834 - 6.45874i) q^{85} +(-0.175400 + 0.881798i) q^{87} +(12.0007 - 2.38709i) q^{89} +(2.50331 - 0.246555i) q^{91} +(-0.0229392 + 0.00695852i) q^{93} +(10.5779 + 10.5779i) q^{95} +(-2.03422 + 2.03422i) q^{97} +(-2.04164 - 6.73040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.205628	−	0.109910i	−0.118719	−	0.0634568i	0.410968	−	0.911650i	$-0.365191\pi$
$3$	−0.205628	−	0.109910i	−0.118719	−	0.0634568i	−0.529687	+	0.848193i	$0.677691\pi$
$4$		0			0
$5$	−1.29703	+	1.58044i	−0.580050	+	0.706793i	−0.977525	−	0.210820i	$-0.932387\pi$
$5$	−1.29703	+	1.58044i	−0.580050	+	0.706793i	0.397475	+	0.917613i	$0.369887\pi$
$6$		0			0
$7$	−1.60057	−	1.06947i	−0.604960	−	0.404221i	0.215023	−	0.976609i	$-0.431017\pi$
$7$	−1.60057	−	1.06947i	−0.604960	−	0.404221i	−0.819983	+	0.572388i	$0.806017\pi$
$8$		0			0
$9$	−1.63651	−	2.44921i	−0.545503	−	0.816403i
$10$		0			0
$11$	2.28487	+	0.693108i	0.688914	+	0.208980i	0.615284	−	0.788306i	$-0.289041\pi$
$11$	2.28487	+	0.693108i	0.688914	+	0.208980i	0.0736306	+	0.997286i	$0.476541\pi$
$12$		0			0
$13$	−1.01011	+	0.828973i	−0.280153	+	0.229916i	−0.763967	−	0.645255i	$-0.776751\pi$
$13$	−1.01011	+	0.828973i	−0.280153	+	0.229916i	0.483814	+	0.875171i	$0.339251\pi$
$14$		0			0
$15$	0.440412	−	0.182425i	0.113714	−	0.0471019i
$16$		0			0
$17$	−6.19134	−	2.56454i	−1.50162	−	0.621991i	−0.527812	−	0.849361i	$-0.676987\pi$
$17$	−6.19134	−	2.56454i	−1.50162	−	0.621991i	−0.973808	+	0.227370i	$0.926987\pi$
$18$		0			0
$19$	0.717174	−	7.28159i	0.164531	−	1.67051i	−0.458789	−	0.888545i	$-0.651717\pi$
$19$	0.717174	−	7.28159i	0.164531	−	1.67051i	0.623320	−	0.781967i	$-0.285783\pi$
$20$		0			0
$21$	0.211577	+	0.395832i	0.0461698	+	0.0863777i
$22$		0			0
$23$	−6.82091	−	1.35676i	−1.42226	−	0.282905i	−0.576773	−	0.816905i	$-0.695688\pi$
$23$	−6.82091	−	1.35676i	−1.42226	−	0.282905i	−0.845485	+	0.534000i	$0.820688\pi$
$24$		0			0
$25$	0.159961	+	0.804177i	0.0319922	+	0.160835i
$26$		0			0
$27$	0.135879	+	1.37960i	0.0261500	+	0.265505i
$28$		0			0
$29$	−1.11935	−	3.69001i	−0.207858	−	0.685217i	−0.997436	−	0.0715665i	$-0.977200\pi$
$29$	−1.11935	−	3.69001i	−0.207858	−	0.685217i	0.789577	−	0.613651i	$-0.210300\pi$
$30$		0			0
$31$	0.0726984	−	0.0726984i	0.0130570	−	0.0130570i	−0.700548	−	0.713605i	$-0.747061\pi$
$31$	0.0726984	−	0.0726984i	0.0130570	−	0.0130570i	0.713605	+	0.700548i	$0.247061\pi$
$32$		0			0
$33$	−0.393654	−	0.393654i	−0.0685263	−	0.0685263i
$34$		0			0
$35$	3.76622	−	1.14247i	0.636607	−	0.193113i
$36$		0			0
$37$	2.87067	−	0.282737i	0.471936	−	0.0464816i	0.140746	−	0.990046i	$-0.455050\pi$
$37$	2.87067	−	0.282737i	0.471936	−	0.0464816i	0.331190	+	0.943564i	$0.392550\pi$
$38$		0			0
$39$	0.298819	−	0.0594388i	0.0478493	−	0.00951783i
$40$		0			0
$41$	0.658149	−	3.30874i	0.102786	−	0.516738i	−0.894749	−	0.446569i	$-0.852646\pi$
$41$	0.658149	−	3.30874i	0.102786	−	0.516738i	0.997535	−	0.0701698i	$-0.0223541\pi$
$42$		0			0
$43$	−3.06034	+	1.63579i	−0.466698	+	0.249455i	−0.687945	−	0.725762i	$-0.741487\pi$
$43$	−3.06034	+	1.63579i	−0.466698	+	0.249455i	0.221247	+	0.975218i	$0.428987\pi$
$44$		0			0
$45$	5.99342	+	0.590300i	0.893446	+	0.0879968i
$46$		0			0
$47$	−1.75405	+	4.23465i	−0.255854	+	0.617687i	−0.998656	−	0.0518243i	$-0.983496\pi$
$47$	−1.75405	+	4.23465i	−0.255854	+	0.617687i	0.742802	+	0.669511i	$0.233496\pi$
$48$		0			0
$49$	−1.26071	−	3.04363i	−0.180102	−	0.434805i
$50$		0			0
$51$	0.991243	+	1.20783i	0.138802	+	0.169130i
$52$		0			0
$53$	−2.91014	+	9.59343i	−0.399738	+	1.31776i	0.494114	+	0.869397i	$0.335493\pi$
$53$	−2.91014	+	9.59343i	−0.399738	+	1.31776i	−0.893852	+	0.448362i	$0.852007\pi$
$54$		0			0
$55$	−4.05896	+	2.71211i	−0.547310	+	0.365701i
$56$		0			0
$57$	−0.947794	+	1.41847i	−0.125538	+	0.187882i
$58$		0			0
$59$	−4.93475	−	4.04984i	−0.642450	−	0.527245i	0.255800	−	0.966730i	$-0.417661\pi$
$59$	−4.93475	−	4.04984i	−0.642450	−	0.527245i	−0.898250	+	0.439485i	$0.855161\pi$
$60$		0			0
$61$	−0.733515	+	1.37231i	−0.0939169	+	0.175706i	−0.924493	−	0.381199i	$-0.875511\pi$
$61$	−0.733515	+	1.37231i	−0.0939169	+	0.175706i	0.830576	+	0.556905i	$0.188011\pi$
$62$		0			0
$63$			5.67033i			0.714394i
$64$		0			0
$65$		−	2.67161i		−	0.331373i
$66$		0			0
$67$	−2.54422	+	4.75990i	−0.310826	+	0.581515i	−0.988027	−	0.154284i	$-0.950693\pi$
$67$	−2.54422	+	4.75990i	−0.310826	+	0.581515i	0.677200	+	0.735799i	$0.263193\pi$
$68$		0			0
$69$	1.25345	+	1.02868i	0.150897	+	0.123838i
$70$		0			0
$71$	−1.60349	+	2.39980i	−0.190300	+	0.284804i	−0.914334	−	0.404960i	$-0.867286\pi$
$71$	−1.60349	+	2.39980i	−0.190300	+	0.284804i	0.724035	+	0.689764i	$0.242286\pi$
$72$		0			0
$73$	11.8626	−	7.92631i	1.38841	−	0.927704i	0.388427	−	0.921479i	$-0.373018\pi$
$73$	11.8626	−	7.92631i	1.38841	−	0.927704i	0.999981	−	0.00622507i	$-0.00198151\pi$
$74$		0			0
$75$	0.0554951	−	0.182943i	0.00640802	−	0.0211244i
$76$		0			0
$77$	−2.91585	−	3.55297i	−0.332291	−	0.404898i
$78$		0			0
$79$	−3.13533	−	7.56937i	−0.352753	−	0.851620i	−0.996278	−	0.0861956i	$-0.972529\pi$
$79$	−3.13533	−	7.56937i	−0.352753	−	0.851620i	0.643526	−	0.765425i	$-0.277471\pi$
$80$		0			0
$81$	−3.25805	+	7.86562i	−0.362005	+	0.873958i
$82$		0			0
$83$	10.8406	+	1.06770i	1.18991	+	0.117195i	0.673525	−	0.739164i	$-0.264779\pi$
$83$	10.8406	+	1.06770i	1.18991	+	0.117195i	0.516380	+	0.856360i	$0.327279\pi$
$84$		0			0
$85$	12.0834	−	6.45874i	1.31063	−	0.700548i
$86$		0			0
$87$	−0.175400	+	0.881798i	−0.0188049	+	0.0945386i
$88$		0			0
$89$	12.0007	−	2.38709i	1.27207	−	0.253031i	0.487531	−	0.873106i	$-0.337898\pi$
$89$	12.0007	−	2.38709i	1.27207	−	0.253031i	0.784543	+	0.620075i	$0.212898\pi$
$90$		0			0
$91$	2.50331	−	0.246555i	0.262418	−	0.0258459i
$92$		0			0
$93$	−0.0229392	+	0.00695852i	−0.00237868	+	0.000721564i
$94$		0			0
$95$	10.5779	+	10.5779i	1.08527	+	1.08527i
$96$		0			0
$97$	−2.03422	+	2.03422i	−0.206544	+	0.206544i	−0.802797	−	0.596253i	$-0.796656\pi$
$97$	−2.03422	+	2.03422i	−0.206544	+	0.206544i	0.596253	+	0.802797i	$0.296656\pi$
$98$		0			0
$99$	−2.04164	−	6.73040i	−0.205193	−	0.676431i
$100$		0			0
$101$	1.76797	+	17.9505i	0.175920	+	1.78614i	0.527067	+	0.849824i	$0.323292\pi$
$101$	1.76797	+	17.9505i	0.175920	+	1.78614i	−0.351147	+	0.936320i	$0.614208\pi$
$102$		0			0
$103$	−3.31254	−	16.6533i	−0.326395	−	1.64090i	−0.700603	−	0.713552i	$-0.747085\pi$
$103$	−3.31254	−	16.6533i	−0.326395	−	1.64090i	0.374208	−	0.927345i	$-0.377915\pi$
$104$		0			0
$105$	−0.900010	−	0.179023i	−0.0878319	−	0.0174709i
$106$		0			0
$107$	8.51371	+	15.9280i	0.823052	+	1.53982i	0.841668	+	0.539995i	$0.181574\pi$
$107$	8.51371	+	15.9280i	0.823052	+	1.53982i	−0.0186166	+	0.999827i	$0.505926\pi$
$108$		0			0
$109$	−0.331345	+	3.36420i	−0.0317371	+	0.322232i	0.966188	+	0.257840i	$0.0830108\pi$
$109$	−0.331345	+	3.36420i	−0.0317371	+	0.322232i	−0.997925	+	0.0643919i	$0.979489\pi$
$110$		0			0
$111$	−0.621367	−	0.257378i	−0.0589775	−	0.0244293i
$112$		0			0
$113$	−13.9411	+	5.77458i	−1.31146	+	0.543226i	−0.925311	−	0.379208i	$-0.876196\pi$
$113$	−13.9411	+	5.77458i	−1.31146	+	0.543226i	−0.386153	+	0.922435i	$0.626196\pi$
$114$		0			0
$115$	10.9912	−	9.02025i	1.02493	−	0.841142i
$116$		0			0
$117$	3.68338	+	1.11734i	0.340528	+	0.103298i
$118$		0			0
$119$	7.16700	+	10.7262i	0.656998	+	0.983266i
$120$		0			0
$121$	−4.40593	−	2.94395i	−0.400539	−	0.267632i
$122$		0			0
$123$	−0.498999	+	0.608032i	−0.0449932	+	0.0548244i
$124$		0			0
$125$	−10.4940	−	5.60914i	−0.938608	−	0.501697i
$126$		0			0
$127$	15.1540			1.34470			0.672349	−	0.740234i	$-0.265285\pi$
$127$	15.1540			1.34470			0.672349	+	0.740234i	$0.265285\pi$
$128$		0			0
$129$	0.809082			0.0712357
$130$		0			0
$131$	−3.90207	−	2.08570i	−0.340926	−	0.182229i	0.292045	−	0.956405i	$-0.405664\pi$
$131$	−3.90207	−	2.08570i	−0.340926	−	0.182229i	−0.632970	+	0.774176i	$0.718164\pi$
$132$		0			0
$133$	−8.93532	+	10.8877i	−0.774791	+	0.944085i
$134$		0			0
$135$	−2.35662	−	1.57464i	−0.202825	−	0.135523i
$136$		0			0
$137$	−2.46390	−	3.68749i	−0.210505	−	0.315044i	0.711159	−	0.703031i	$-0.248170\pi$
$137$	−2.46390	−	3.68749i	−0.210505	−	0.315044i	−0.921665	+	0.387987i	$0.873170\pi$
$138$		0			0
$139$	8.06008	+	2.44500i	0.683647	+	0.207382i	0.612957	−	0.790116i	$-0.289980\pi$
$139$	8.06008	+	2.44500i	0.683647	+	0.207382i	0.0706901	+	0.997498i	$0.477480\pi$
$140$		0			0
$141$	0.826114	−	0.677974i	0.0695713	−	0.0570957i
$142$		0			0
$143$	−2.88253	+	1.19398i	−0.241049	+	0.0998459i
$144$		0			0
$145$	7.28366	+	3.01699i	0.604875	+	0.250547i
$146$		0			0
$147$	−0.0752889	+	0.764421i	−0.00620973	+	0.0630484i
$148$		0			0
$149$	−0.397763	−	0.744162i	−0.0325860	−	0.0609641i	0.865101	−	0.501597i	$-0.167254\pi$
$149$	−0.397763	−	0.744162i	−0.0325860	−	0.0609641i	−0.897687	+	0.440633i	$0.854754\pi$
$150$		0			0
$151$	−5.56135	−	1.10622i	−0.452576	−	0.0900230i	−0.0364613	−	0.999335i	$-0.511609\pi$
$151$	−5.56135	−	1.10622i	−0.452576	−	0.0900230i	−0.416115	+	0.909312i	$0.636609\pi$
$152$		0			0
$153$	3.85109	+	19.3608i	0.311343	+	1.56522i
$154$		0			0
$155$	0.0206032	+	0.209187i	0.00165489	+	0.0168023i
$156$		0			0
$157$	−4.98893	−	16.4463i	−0.398160	−	1.31256i	−0.895523	−	0.445014i	$-0.853199\pi$
$157$	−4.98893	−	16.4463i	−0.398160	−	1.31256i	0.497364	−	0.867542i	$-0.334301\pi$
$158$		0			0
$159$	1.65282	−	1.65282i	0.131077	−	0.131077i
$160$		0			0
$161$	9.46634	+	9.46634i	0.746052	+	0.746052i
$162$		0			0
$163$	−8.47016	+	2.56939i	−0.663434	+	0.201250i	−0.604003	−	0.796982i	$-0.706429\pi$
$163$	−8.47016	+	2.56939i	−0.663434	+	0.201250i	−0.0594308	+	0.998232i	$0.518929\pi$
$164$		0			0
$165$	1.13273	−	0.111564i	0.0881825	−	0.00868522i
$166$		0			0
$167$	12.8178	−	2.54961i	0.991868	−	0.197295i	0.327622	−	0.944809i	$-0.393753\pi$
$167$	12.8178	−	2.54961i	0.991868	−	0.197295i	0.664246	+	0.747514i	$0.268753\pi$
$168$		0			0
$169$	−2.20305	+	11.0755i	−0.169466	+	0.851962i
$170$		0			0
$171$	−19.0078	+	10.1599i	−1.45356	+	0.776945i
$172$		0			0
$173$	8.23853	+	0.811424i	0.626364	+	0.0616914i	0.406219	−	0.913776i	$-0.366847\pi$
$173$	8.23853	+	0.811424i	0.626364	+	0.0616914i	0.220145	+	0.975467i	$0.429347\pi$
$174$		0			0
$175$	0.604013	−	1.45822i	0.0456591	−	0.110231i
$176$		0			0
$177$	0.569602	+	1.37514i	0.0428139	+	0.103362i
$178$		0			0
$179$	6.23233	+	7.59411i	0.465826	+	0.567611i	0.951940	−	0.306285i	$-0.0990860\pi$
$179$	6.23233	+	7.59411i	0.465826	+	0.567611i	−0.486114	+	0.873895i	$0.661586\pi$
$180$		0			0
$181$	5.59558	−	18.4462i	0.415916	−	1.37109i	−0.459695	−	0.888077i	$-0.652041\pi$
$181$	5.59558	−	18.4462i	0.415916	−	1.37109i	0.875612	−	0.483016i	$-0.160459\pi$
$182$		0			0
$183$	0.301662	−	0.201564i	0.0222995	−	0.0149001i
$184$		0			0
$185$	−3.27650	+	4.90364i	−0.240893	+	0.360522i
$186$		0			0
$187$	−12.3689	−	10.1509i	−0.904504	−	0.742307i
$188$		0			0
$189$	1.25796	−	2.35348i	0.0915030	−	0.171190i
$190$		0			0
$191$		−	21.9101i		−	1.58536i	−0.609636	−	0.792681i	$-0.708684\pi$
$191$		−	21.9101i		−	1.58536i	0.609636	−	0.792681i	$-0.291316\pi$
$192$		0			0
$193$		−	8.72819i		−	0.628269i	−0.949379	−	0.314134i	$-0.898286\pi$
$193$		−	8.72819i		−	0.628269i	0.949379	−	0.314134i	$-0.101714\pi$
$194$		0			0
$195$	−0.293638	+	0.549359i	−0.0210279	+	0.0393404i
$196$		0			0
$197$	−15.6420	−	12.8370i	−1.11444	−	0.914601i	−0.117528	−	0.993070i	$-0.537497\pi$
$197$	−15.6420	−	12.8370i	−1.11444	−	0.914601i	−0.996917	+	0.0784683i	$0.974997\pi$
$198$		0			0
$199$	−1.04215	+	1.55969i	−0.0738761	+	0.110563i	−0.866568	−	0.499059i	$-0.833679\pi$
$199$	−1.04215	+	1.55969i	−0.0738761	+	0.110563i	0.792692	+	0.609623i	$0.208679\pi$
$200$		0			0
$201$	1.04633	−	0.699133i	0.0738022	−	0.0493130i
$202$		0			0
$203$	−2.15474	+	7.10324i	−0.151233	+	0.498550i
$204$		0			0
$205$	4.37561	+	5.33170i	0.305606	+	0.372382i
$206$		0			0
$207$	7.83948	+	18.9262i	0.544881	+	1.31546i
$208$		0			0
$209$	6.68558	−	16.1404i	0.462451	−	1.11646i
$210$		0			0
$211$	−27.9842	−	2.75620i	−1.92651	−	0.189745i	−0.938628	−	0.344932i	$-0.887902\pi$
$211$	−27.9842	−	2.75620i	−1.92651	−	0.189745i	−0.987885	+	0.155187i	$0.950402\pi$
$212$		0			0
$213$	0.593486	−	0.317225i	0.0406650	−	0.0217359i
$214$		0			0
$215$	1.38410	−	6.95834i	0.0943949	−	0.474555i
$216$		0			0
$217$	−0.194108	+	0.0386105i	−0.0131769	+	0.00262105i
$218$		0			0
$219$	−3.31046	+	0.326052i	−0.223700	+	0.0220325i
$220$		0			0
$221$	8.37985	−	2.54200i	0.563690	−	0.170993i
$222$		0			0
$223$	8.26958	+	8.26958i	0.553772	+	0.553772i	0.927527	−	0.373755i	$-0.121930\pi$
$223$	8.26958	+	8.26958i	0.553772	+	0.553772i	−0.373755	+	0.927527i	$0.621930\pi$
$224$		0			0
$225$	1.70782	−	1.70782i	0.113855	−	0.113855i
$226$		0			0
$227$	−2.00476	−	6.60881i	−0.133061	−	0.438642i	0.864938	−	0.501879i	$-0.167358\pi$
$227$	−2.00476	−	6.60881i	−0.133061	−	0.438642i	−0.997999	+	0.0632366i	$0.979858\pi$
$228$		0			0
$229$	−1.26117	−	12.8049i	−0.0833404	−	0.846169i	−0.942443	−	0.334366i	$-0.891478\pi$
$229$	−1.26117	−	12.8049i	−0.0833404	−	0.846169i	0.859103	−	0.511803i	$-0.171022\pi$
$230$		0			0
$231$	0.209071	+	1.05107i	0.0137559	+	0.0691554i
$232$		0			0
$233$	10.3882	+	2.06634i	0.680555	+	0.135371i	0.523250	−	0.852179i	$-0.324719\pi$
$233$	10.3882	+	2.06634i	0.680555	+	0.135371i	0.157305	+	0.987550i	$0.449719\pi$
$234$		0			0
$235$	−4.41754	−	8.26463i	−0.288168	−	0.539125i
$236$		0			0
$237$	−0.187240	+	1.90108i	−0.0121625	+	0.123488i
$238$		0			0
$239$	−26.1588	−	10.8353i	−1.69207	−	0.700879i	−0.692286	−	0.721623i	$-0.743396\pi$
$239$	−26.1588	−	10.8353i	−1.69207	−	0.700879i	−0.999785	+	0.0207440i	$0.993396\pi$
$240$		0			0
$241$	−16.8342	+	6.97296i	−1.08439	+	0.449168i	−0.852046	−	0.523466i	$-0.824639\pi$
$241$	−16.8342	+	6.97296i	−1.08439	+	0.449168i	−0.232341	+	0.972634i	$0.574639\pi$
$242$		0			0
$243$	4.74929	−	3.89764i	0.304667	−	0.250034i
$244$		0			0
$245$	6.44545	+	1.95521i	0.411785	+	0.124914i
$246$		0			0
$247$	5.31182	+	7.94971i	0.337983	+	0.505828i
$248$		0			0
$249$	−2.11177	−	1.41104i	−0.133828	−	0.0894210i
$250$		0			0
$251$	3.27697	−	3.99299i	0.206840	−	0.252036i	−0.659249	−	0.751924i	$-0.729126\pi$
$251$	3.27697	−	3.99299i	0.206840	−	0.252036i	0.866090	+	0.499889i	$0.166626\pi$
$252$		0			0
$253$	−14.6445	−	7.82765i	−0.920692	−	0.492120i
$254$		0			0
$255$	−3.19458			−0.200052
$256$		0			0
$257$	−3.01190			−0.187877			−0.0939386	−	0.995578i	$-0.529946\pi$
$257$	−3.01190			−0.187877			−0.0939386	+	0.995578i	$0.529946\pi$
$258$		0			0
$259$	−4.89710	−	2.61756i	−0.304291	−	0.162647i
$260$		0			0
$261$	−7.20577	+	8.78026i	−0.446026	+	0.543484i
$262$		0			0
$263$	−13.8893	−	9.28055i	−0.856453	−	0.572263i	0.0479953	−	0.998848i	$-0.484717\pi$
$263$	−13.8893	−	9.28055i	−0.856453	−	0.572263i	−0.904448	+	0.426584i	$0.859717\pi$
$264$		0			0
$265$	−11.3873	−	17.0423i	−0.699515	−	1.04690i
$266$		0			0
$267$	−2.73005	−	0.828152i	−0.167076	−	0.0506820i
$268$		0			0
$269$	−0.976332	+	0.801255i	−0.0595280	+	0.0488534i	−0.663687	−	0.748011i	$-0.731009\pi$
$269$	−0.976332	+	0.801255i	−0.0595280	+	0.0488534i	0.604159	+	0.796864i	$0.293509\pi$
$270$		0			0
$271$	20.1334	−	8.33955i	1.22302	−	0.506591i	0.324651	−	0.945834i	$-0.394753\pi$
$271$	20.1334	−	8.33955i	1.22302	−	0.506591i	0.898369	+	0.439243i	$0.144753\pi$
$272$		0			0
$273$	−0.541850	−	0.224441i	−0.0327942	−	0.0135838i
$274$		0			0
$275$	−0.191892	+	1.94831i	−0.0115715	+	0.117488i
$276$		0			0
$277$	−12.2049	−	22.8338i	−0.733323	−	1.37195i	−0.920938	−	0.389708i	$-0.872576\pi$
$277$	−12.2049	−	22.8338i	−0.733323	−	1.37195i	0.187615	−	0.982243i	$-0.439924\pi$
$278$		0			0
$279$	−0.297025	−	0.0590820i	−0.0177824	−	0.00353715i
$280$		0			0
$281$	0.988114	+	4.96758i	0.0589459	+	0.296341i	0.999001	−	0.0446806i	$-0.0142270\pi$
$281$	0.988114	+	4.96758i	0.0589459	+	0.296341i	−0.940055	+	0.341022i	$0.889227\pi$
$282$		0			0
$283$	1.05821	+	10.7442i	0.0629042	+	0.638677i	0.974010	+	0.226504i	$0.0727298\pi$
$283$	1.05821	+	10.7442i	0.0629042	+	0.638677i	−0.911106	+	0.412172i	$0.864770\pi$
$284$		0			0
$285$	−1.01249	−	3.33773i	−0.0599747	−	0.197710i
$286$		0			0
$287$	−4.59201	+	4.59201i	−0.271058	+	0.271058i
$288$		0			0
$289$	19.7350	+	19.7350i	1.16088	+	1.16088i
$290$		0			0
$291$	0.641876	−	0.194711i	0.0376274	−	0.0114142i
$292$		0			0
$293$	−4.98960	+	0.491433i	−0.291496	+	0.0287098i	−0.242708	−	0.970099i	$-0.578036\pi$
$293$	−4.98960	+	0.491433i	−0.291496	+	0.0287098i	−0.0487875	+	0.998809i	$0.515536\pi$
$294$		0			0
$295$	12.8010	−	2.54629i	0.745306	−	0.148250i
$296$		0			0
$297$	−0.645748	+	3.24640i	−0.0374701	+	0.188375i
$298$		0			0
$299$	8.01457	−	4.28387i	0.463494	−	0.247743i
$300$		0			0
$301$	6.64773	+	0.654744i	0.383169	+	0.0377388i
$302$		0			0
$303$	1.60941	−	3.88545i	0.0924579	−	0.223213i
$304$		0			0
$305$	−1.21746	−	2.93920i	−0.0697114	−	0.168298i
$306$		0			0
$307$	6.02964	+	7.34714i	0.344130	+	0.419324i	0.916099	−	0.400951i	$-0.131320\pi$
$307$	6.02964	+	7.34714i	0.344130	+	0.419324i	−0.571969	+	0.820275i	$0.693820\pi$
$308$		0			0
$309$	−1.14922	+	3.78846i	−0.0653767	+	0.215518i
$310$		0			0
$311$	−6.79939	+	4.54321i	−0.385558	+	0.257622i	−0.733210	−	0.680002i	$-0.761979\pi$
$311$	−6.79939	+	4.54321i	−0.385558	+	0.257622i	0.347652	+	0.937624i	$0.386979\pi$
$312$		0			0
$313$	−1.49679	+	2.24010i	−0.0846034	+	0.126618i	−0.871358	−	0.490648i	$-0.836760\pi$
$313$	−1.49679	+	2.24010i	−0.0846034	+	0.126618i	0.786754	+	0.617266i	$0.211760\pi$
$314$		0			0
$315$	−8.96160	−	7.35459i	−0.504929	−	0.414384i
$316$		0			0
$317$	−9.90856	+	18.5376i	−0.556520	+	1.04118i	0.433620	+	0.901096i	$0.357236\pi$
$317$	−9.90856	+	18.5376i	−0.556520	+	1.04118i	−0.990140	+	0.140080i	$0.955264\pi$
$318$		0			0
$319$		−	9.20703i		−	0.515494i
$320$		0			0
$321$		−	4.21100i		−	0.235035i
$322$		0			0
$323$	−23.1142	+	43.2436i	−1.28611	+	2.40614i
$324$		0			0
$325$	−0.828219	−	0.679702i	−0.0459413	−	0.0377031i
$326$		0			0
$327$	0.437895	−	0.655356i	0.0242156	−	0.0362412i
$328$		0			0
$329$	7.33631	−	4.90196i	0.404464	−	0.270254i
$330$		0			0
$331$	4.72986	−	15.5923i	0.259977	−	0.857029i	−0.725646	−	0.688068i	$-0.758459\pi$
$331$	4.72986	−	15.5923i	0.259977	−	0.857029i	0.985623	−	0.168961i	$-0.0540410\pi$
$332$		0			0
$333$	−5.39036	−	6.56818i	−0.295390	−	0.359934i
$334$		0			0
$335$	−4.22279	−	10.1947i	−0.230716	−	0.556997i
$336$		0			0
$337$	2.89659	−	6.99299i	0.157787	−	0.380933i	−0.825139	−	0.564929i	$-0.808904\pi$
$337$	2.89659	−	6.99299i	0.157787	−	0.380933i	0.982927	+	0.183997i	$0.0589035\pi$
$338$		0			0
$339$	3.50136	+	0.344854i	0.190168	+	0.0187299i
$340$		0			0
$341$	0.216494	−	0.115719i	0.0117238	−	0.00626652i
$342$		0			0
$343$	−3.86604	+	19.4359i	−0.208746	+	1.04944i
$344$		0			0
$345$	−3.25152	+	0.646767i	−0.175056	+	0.0348208i
$346$		0			0
$347$	−1.59870	+	0.157459i	−0.0858230	+	0.00845283i	−0.140837	−	0.990033i	$-0.544979\pi$
$347$	−1.59870	+	0.157459i	−0.0858230	+	0.00845283i	0.0550145	+	0.998486i	$0.482479\pi$
$348$		0			0
$349$	4.09180	−	1.24123i	0.219029	−	0.0664417i	−0.178863	−	0.983874i	$-0.557242\pi$
$349$	4.09180	−	1.24123i	0.219029	−	0.0664417i	0.397892	+	0.917432i	$0.369742\pi$
$350$		0			0
$351$	−1.28091	−	1.28091i	−0.0683698	−	0.0683698i
$352$		0			0
$353$	1.77543	−	1.77543i	0.0944967	−	0.0944967i	−0.658278	−	0.752775i	$-0.728715\pi$
$353$	1.77543	−	1.77543i	0.0944967	−	0.0944967i	0.752775	+	0.658278i	$0.228715\pi$
$354$		0			0
$355$	−1.71295	−	5.64683i	−0.0909139	−	0.299703i
$356$		0			0
$357$	−0.294817	−	2.99333i	−0.0156034	−	0.158424i
$358$		0			0
$359$	−5.61004	−	28.2036i	−0.296087	−	1.48853i	−0.786800	−	0.617208i	$-0.788264\pi$
$359$	−5.61004	−	28.2036i	−0.296087	−	1.48853i	0.490713	−	0.871321i	$-0.336736\pi$
$360$		0			0
$361$	−33.8723	−	6.73763i	−1.78275	−	0.354612i
$362$		0			0
$363$	0.582412	+	1.08962i	0.0305687	+	0.0571900i
$364$		0			0
$365$	−2.85908	+	29.0287i	−0.149651	+	1.51943i
$366$		0			0
$367$	−21.8762	−	9.06143i	−1.14193	−	0.473003i	−0.270110	−	0.962830i	$-0.587060\pi$
$367$	−21.8762	−	9.06143i	−1.14193	−	0.473003i	−0.871820	+	0.489827i	$0.837060\pi$
$368$		0			0
$369$	−9.18086	+	3.80284i	−0.477936	+	0.197968i
$370$		0			0
$371$	14.9178	−	12.2427i	0.774492	−	0.635609i
$372$		0			0
$373$	7.84501	+	2.37976i	0.406199	+	0.123219i	0.486771	−	0.873530i	$-0.338175\pi$
$373$	7.84501	+	2.37976i	0.406199	+	0.123219i	−0.0805719	+	0.996749i	$0.525675\pi$
$374$		0			0
$375$	1.54135	+	2.30679i	0.0795949	+	0.119122i
$376$		0			0
$377$	4.18958	+	2.79939i	0.215775	+	0.144176i
$378$		0			0
$379$	20.2786	−	24.7095i	1.04164	−	1.26924i	0.0794585	−	0.996838i	$-0.474681\pi$
$379$	20.2786	−	24.7095i	1.04164	−	1.26924i	0.962183	−	0.272405i	$-0.0878191\pi$
$380$		0			0
$381$	−3.11608	−	1.66558i	−0.159642	−	0.0853303i
$382$		0			0
$383$	−7.20772			−0.368297			−0.184149	−	0.982898i	$-0.558953\pi$
$383$	−7.20772			−0.368297			−0.184149	+	0.982898i	$0.558953\pi$
$384$		0			0
$385$	9.39718			0.478925
$386$		0			0
$387$	9.01466	+	4.81844i	0.458241	+	0.244935i
$388$		0			0
$389$	6.71261	−	8.17934i	0.340343	−	0.414709i	−0.574509	−	0.818498i	$-0.694807\pi$
$389$	6.71261	−	8.17934i	0.340343	−	0.414709i	0.914852	+	0.403789i	$0.132307\pi$
$390$		0			0
$391$	38.7511	+	25.8926i	1.95973	+	1.30945i
$392$		0			0
$393$	0.573135	+	0.857757i	0.0289108	+	0.0432681i
$394$		0			0
$395$	16.0295	+	4.86250i	0.806533	+	0.244659i
$396$		0			0
$397$	14.4640	−	11.8703i	0.725929	−	0.595755i	−0.197146	−	0.980374i	$-0.563167\pi$
$397$	14.4640	−	11.8703i	0.725929	−	0.595755i	0.923075	+	0.384620i	$0.125667\pi$
$398$		0			0
$399$	3.03403	−	1.25674i	0.151891	−	0.0629155i
$400$		0			0
$401$	16.9498	+	7.02085i	0.846434	+	0.350605i	0.763387	−	0.645941i	$-0.223535\pi$
$401$	16.9498	+	7.02085i	0.846434	+	0.350605i	0.0830471	+	0.996546i	$0.473535\pi$
$402$		0			0
$403$	−0.0131681	+	0.133698i	−0.000655951	+	0.00665998i
$404$		0			0
$405$	−8.20533	−	15.3511i	−0.407726	−	0.762802i
$406$		0			0
$407$	6.75509	+	1.34367i	0.334837	+	0.0666033i
$408$		0			0
$409$	1.12295	+	5.64547i	0.0555265	+	0.279150i	0.998566	−	0.0535295i	$-0.0170471\pi$
$409$	1.12295	+	5.64547i	0.0555265	+	0.279150i	−0.943040	+	0.332680i	$0.892047\pi$
$410$		0			0
$411$	0.101354	+	1.02906i	0.00499940	+	0.0507598i
$412$		0			0
$413$	3.56724	+	11.7596i	0.175533	+	0.578654i
$414$		0			0
$415$	−15.7480	+	15.7480i	−0.773037	+	0.773037i
$416$		0			0
$417$	−1.38865	−	1.38865i	−0.0680023	−	0.0680023i
$418$		0			0
$419$	−8.49396	+	2.57661i	−0.414957	+	0.125876i	−0.490858	−	0.871240i	$-0.663317\pi$
$419$	−8.49396	+	2.57661i	−0.414957	+	0.125876i	0.0759011	+	0.997115i	$0.475817\pi$
$420$		0			0
$421$	29.4485	−	2.90043i	1.43523	−	0.141358i	0.649707	−	0.760185i	$-0.274892\pi$
$421$	29.4485	−	2.90043i	1.43523	−	0.141358i	0.785527	+	0.618827i	$0.212392\pi$
$422$		0			0
$423$	13.2420	−	2.63401i	0.643850	−	0.128070i
$424$		0			0
$425$	1.07197	−	5.38916i	0.0519982	−	0.261413i
$426$		0			0
$427$	2.64169	−	1.41201i	0.127840	−	0.0683320i
$428$		0			0
$429$	0.723960	+	0.0713039i	0.0349531	+	0.00344258i
$430$		0			0
$431$	−10.9359	+	26.4017i	−0.526765	+	1.27172i	0.406866	+	0.913488i	$0.366621\pi$
$431$	−10.9359	+	26.4017i	−0.526765	+	1.27172i	−0.933631	+	0.358235i	$0.883379\pi$
$432$		0			0
$433$	−0.211107	−	0.509658i	−0.0101452	−	0.0244926i	0.918726	−	0.394896i	$-0.129219\pi$
$433$	−0.211107	−	0.509658i	−0.0101452	−	0.0244926i	−0.928871	+	0.370404i	$0.879219\pi$
$434$		0			0
$435$	−1.16613	−	1.42093i	−0.0559114	−	0.0681283i
$436$		0			0
$437$	−14.7712	+	48.6940i	−0.706601	+	2.32935i
$438$		0			0
$439$	20.4292	−	13.6504i	0.975032	−	0.651496i	0.0374643	−	0.999298i	$-0.488072\pi$
$439$	20.4292	−	13.6504i	0.975032	−	0.651496i	0.937568	+	0.347802i	$0.113072\pi$
$440$		0			0
$441$	−5.39132	+	8.06868i	−0.256729	+	0.384223i
$442$		0			0
$443$	−4.92700	−	4.04349i	−0.234089	−	0.192112i	0.510035	−	0.860154i	$-0.329633\pi$
$443$	−4.92700	−	4.04349i	−0.234089	−	0.192112i	−0.744123	+	0.668042i	$0.767133\pi$
$444$		0			0
$445$	−11.7927	+	22.0625i	−0.559025	+	1.04586i
$446$		0			0
$447$			0.196739i			0.00930543i
$448$		0			0
$449$		−	21.0355i		−	0.992725i	−0.868115	−	0.496363i	$-0.834669\pi$
$449$		−	21.0355i		−	0.992725i	0.868115	−	0.496363i	$-0.165331\pi$
$450$		0			0
$451$	3.79710	−	7.10388i	0.178798	−	0.334508i
$452$		0			0
$453$	1.02198	+	0.838720i	0.0480170	+	0.0394065i
$454$		0			0
$455$	−2.85721	+	4.27611i	−0.133948	+	0.200467i
$456$		0			0
$457$	−0.444551	+	0.297040i	−0.0207952	+	0.0138949i	−0.565924	−	0.824457i	$-0.691481\pi$
$457$	−0.444551	+	0.297040i	−0.0207952	+	0.0138949i	0.545129	+	0.838352i	$0.316481\pi$
$458$		0			0
$459$	2.69677	−	8.89006i	0.125875	−	0.414953i
$460$		0			0
$461$	−15.0924	−	18.3901i	−0.702923	−	0.856514i	0.292077	−	0.956395i	$-0.405654\pi$
$461$	−15.0924	−	18.3901i	−0.702923	−	0.856514i	−0.994999	+	0.0998811i	$0.968154\pi$
$462$		0			0
$463$	−6.89406	−	16.6437i	−0.320394	−	0.773500i	−0.999231	−	0.0392108i	$-0.987516\pi$
$463$	−6.89406	−	16.6437i	−0.320394	−	0.773500i	0.678837	−	0.734289i	$-0.262484\pi$
$464$		0			0
$465$	0.0187553	−	0.0452793i	0.000869756	−	0.00209978i
$466$		0			0
$467$	−5.70548	−	0.561941i	−0.264018	−	0.0260035i	−0.0348580	−	0.999392i	$-0.511098\pi$
$467$	−5.70548	−	0.561941i	−0.264018	−	0.0260035i	−0.229160	+	0.973389i	$0.573598\pi$
$468$		0			0
$469$	9.16278	−	4.89761i	0.423098	−	0.226151i
$470$		0			0
$471$	−0.781756	+	3.93015i	−0.0360214	+	0.181092i
$472$		0			0
$473$	−8.12627	+	1.61641i	−0.373646	+	0.0743228i
$474$		0			0
$475$	5.97041	−	0.588034i	0.273941	−	0.0269809i
$476$		0			0
$477$	28.2588	−	8.57221i	1.29388	−	0.392494i
$478$		0			0
$479$	13.9118	+	13.9118i	0.635645	+	0.635645i	0.949478	−	0.313833i	$-0.101613\pi$
$479$	13.9118	+	13.9118i	0.635645	+	0.635645i	−0.313833	+	0.949478i	$0.601613\pi$
$480$		0			0
$481$	−2.66531	+	2.66531i	−0.121528	+	0.121528i
$482$		0			0
$483$	−0.906095	−	2.98700i	−0.0412288	−	0.135913i
$484$		0			0
$485$	−0.576511	−	5.85341i	−0.0261780	−	0.265790i
$486$		0			0
$487$	7.63478	+	38.3827i	0.345965	+	1.73928i	0.626483	+	0.779435i	$0.284494\pi$
$487$	7.63478	+	38.3827i	0.345965	+	1.73928i	−0.280518	+	0.959849i	$0.590506\pi$
$488$		0			0
$489$	2.02410	+	0.402619i	0.0915332	+	0.0182071i
$490$		0			0
$491$	−1.42967	−	2.67473i	−0.0645203	−	0.120709i	0.847593	−	0.530646i	$-0.178051\pi$
$491$	−1.42967	−	2.67473i	−0.0645203	−	0.120709i	−0.912114	+	0.409937i	$0.865551\pi$
$492$		0			0
$493$	−2.53288	+	25.7167i	−0.114075	+	1.15822i
$494$		0			0
$495$	13.2850	+	5.50285i	0.597118	+	0.247335i
$496$		0			0
$497$	5.13302	−	2.12617i	0.230247	−	0.0953716i
$498$		0			0
$499$	−18.4451	+	15.1375i	−0.825718	+	0.677649i	−0.949192	−	0.314699i	$-0.898096\pi$
$499$	−18.4451	+	15.1375i	−0.825718	+	0.677649i	0.123474	+	0.992348i	$0.460596\pi$
$500$		0			0
$501$	−2.91592	−	0.884534i	−0.130274	−	0.0395181i
$502$		0			0
$503$	−2.00233	−	2.99670i	−0.0892794	−	0.133616i	0.784142	−	0.620582i	$-0.213104\pi$
$503$	−2.00233	−	2.99670i	−0.0892794	−	0.133616i	−0.873421	+	0.486966i	$0.838104\pi$
$504$		0			0
$505$	−30.6628	−	20.4882i	−1.36448	−	0.911714i
$506$		0			0
$507$	1.67032	−	2.03530i	0.0741817	−	0.0903906i
$508$		0			0
$509$	35.4767	+	18.9627i	1.57248	+	0.840507i	0.999785	+	0.0207366i	$0.00660115\pi$
$509$	35.4767	+	18.9627i	1.57248	+	0.840507i	0.572693	+	0.819770i	$0.305899\pi$
$510$		0			0
$511$	−27.4638			−1.21493
$512$		0			0
$513$	10.1432			0.447832
$514$		0			0
$515$	30.6159	+	16.3646i	1.34910	+	0.721108i
$516$		0			0
$517$	−6.94284	+	8.45988i	−0.305346	+	0.372065i
$518$		0			0
$519$	−1.60489	−	1.07235i	−0.0704468	−	0.0470710i
$520$		0			0
$521$	10.8105	+	16.1790i	0.473615	+	0.708814i	0.988962	−	0.148167i	$-0.0473372\pi$
$521$	10.8105	+	16.1790i	0.473615	+	0.708814i	−0.515348	+	0.856981i	$0.672337\pi$
$522$		0			0
$523$	26.8616	+	8.14836i	1.17457	+	0.356303i	0.816475	−	0.577381i	$-0.195925\pi$
$523$	26.8616	+	8.14836i	1.17457	+	0.356303i	0.358099	+	0.933684i	$0.383425\pi$
$524$		0			0
$525$	−0.284475	+	0.233463i	−0.0124155	+	0.0101892i
$526$		0			0
$527$	−0.636538	+	0.263663i	−0.0277281	+	0.0114853i
$528$		0			0
$529$	23.4347	+	9.70699i	1.01890	+	0.422043i
$530$		0			0
$531$	−1.84315	+	18.7138i	−0.0799859	+	0.812111i
$532$		0			0
$533$	2.07806	+	3.88777i	0.0900106	+	0.168398i
$534$		0			0
$535$	−36.2158	−	7.20377i	−1.56575	−	0.311446i
$536$		0			0
$537$	−0.446868	−	2.24656i	−0.0192838	−	0.0969462i
$538$		0			0
$539$	−0.771002	−	7.82812i	−0.0332094	−	0.337181i
$540$		0			0
$541$	7.50875	+	24.7530i	0.322826	+	1.06422i	0.956772	+	0.290838i	$0.0939342\pi$
$541$	7.50875	+	24.7530i	0.322826	+	1.06422i	−0.633946	+	0.773377i	$0.718566\pi$
$542$		0			0
$543$	−3.17803	+	3.17803i	−0.136383	+	0.136383i
$544$		0			0
$545$	−4.88714	−	4.88714i	−0.209342	−	0.209342i
$546$		0			0
$547$	30.8967	−	9.37242i	1.32105	−	0.400736i	0.450482	−	0.892786i	$-0.351252\pi$
$547$	30.8967	−	9.37242i	1.32105	−	0.400736i	0.870567	+	0.492050i	$0.163752\pi$
$548$		0			0
$549$	4.56147	−	0.449266i	0.194679	−	0.0191742i
$550$		0			0
$551$	−27.6719	+	5.50429i	−1.17886	+	0.234490i
$552$		0			0
$553$	−3.07687	+	15.4685i	−0.130842	+	0.657786i
$554$		0			0
$555$	1.21270	−	0.648203i	0.0514763	−	0.0275147i
$556$		0			0
$557$	17.2510	+	1.69907i	0.730947	+	0.0719920i	0.456642	−	0.889651i	$-0.349052\pi$
$557$	17.2510	+	1.69907i	0.730947	+	0.0719920i	0.274305	+	0.961643i	$0.411552\pi$
$558$		0			0
$559$	1.73525	−	4.18926i	0.0733932	−	0.177187i
$560$		0			0
$561$	1.42770	+	3.44678i	0.0602777	+	0.145523i
$562$		0			0
$563$	24.4256	+	29.7627i	1.02942	+	1.25435i	0.966591	+	0.256323i	$0.0825112\pi$
$563$	24.4256	+	29.7627i	1.02942	+	1.25435i	0.0628257	+	0.998025i	$0.479989\pi$
$564$		0			0
$565$	8.95563	−	29.5228i	0.376766	−	1.24203i
$566$		0			0
$567$	13.6268	−	9.10512i	0.572271	−	0.382379i
$568$		0			0
$569$	9.94914	−	14.8899i	0.417090	−	0.624219i	−0.562123	−	0.827054i	$-0.690015\pi$
$569$	9.94914	−	14.8899i	0.417090	−	0.624219i	0.979213	+	0.202834i	$0.0650153\pi$
$570$		0			0
$571$	13.1970	+	10.8305i	0.552276	+	0.453241i	0.868673	−	0.495386i	$-0.164973\pi$
$571$	13.1970	+	10.8305i	0.552276	+	0.453241i	−0.316397	+	0.948627i	$0.602473\pi$
$572$		0			0
$573$	−2.40815	+	4.50534i	−0.100602	+	0.188213i
$574$		0			0
$575$		−	5.70225i		−	0.237800i
$576$		0			0
$577$		−	17.2485i		−	0.718062i	−0.933326	−	0.359031i	$-0.883107\pi$
$577$		−	17.2485i		−	0.718062i	0.933326	−	0.359031i	$-0.116893\pi$
$578$		0			0
$579$	−0.959319	+	1.79476i	−0.0398679	+	0.0745877i
$580$		0			0
$581$	−16.2092	−	13.3026i	−0.672472	−	0.551883i
$582$		0			0
$583$	−13.2986	+	19.9027i	−0.550771	+	0.824286i
$584$		0			0
$585$	−6.54334	+	4.37212i	−0.270534	+	0.180765i
$586$		0			0
$587$	4.78018	−	15.7581i	0.197299	−	0.650408i	−0.801338	−	0.598212i	$-0.795878\pi$
$587$	4.78018	−	15.7581i	0.197299	−	0.650408i	0.998637	−	0.0521958i	$-0.0166220\pi$
$588$		0			0
$589$	−0.477223	−	0.581498i	−0.0196636	−	0.0239602i
$590$		0			0
$591$	1.80550	+	4.35887i	0.0742685	+	0.179300i
$592$		0			0
$593$	14.4928	−	34.9888i	0.595149	−	1.43682i	−0.283324	−	0.959024i	$-0.591437\pi$
$593$	14.4928	−	34.9888i	0.595149	−	1.43682i	0.878473	−	0.477793i	$-0.158563\pi$
$594$		0			0
$595$	−26.2478	−	2.58519i	−1.07606	−	0.105982i
$596$		0			0
$597$	0.385721	−	0.206172i	0.0157865	−	0.00843807i
$598$		0			0
$599$	3.42013	−	17.1941i	0.139743	−	0.702533i	−0.845853	−	0.533416i	$-0.820908\pi$
$599$	3.42013	−	17.1941i	0.139743	−	0.702533i	0.985596	−	0.169118i	$-0.0540918\pi$
$600$		0			0
$601$	7.73397	−	1.53838i	0.315475	−	0.0627519i	−0.0348132	−	0.999394i	$-0.511084\pi$
$601$	7.73397	−	1.53838i	0.315475	−	0.0627519i	0.350288	+	0.936642i	$0.386084\pi$
$602$		0			0
$603$	15.8216	−	1.55829i	0.644307	−	0.0634587i
$604$		0			0
$605$	10.3673	−	3.14490i	0.421493	−	0.127858i
$606$		0			0
$607$	−23.7686	−	23.7686i	−0.964738	−	0.964738i	0.0346615	−	0.999399i	$-0.488965\pi$
$607$	−23.7686	−	23.7686i	−0.964738	−	0.964738i	−0.999399	+	0.0346615i	$0.988965\pi$
$608$		0			0
$609$	1.22380	−	1.22380i	0.0495907	−	0.0495907i
$610$		0			0
$611$	−1.73863	−	5.73151i	−0.0703376	−	0.231872i
$612$		0			0
$613$	0.524438	+	5.32471i	0.0211819	+	0.215063i	0.999949	+	0.0100883i	$0.00321125\pi$
$613$	0.524438	+	5.32471i	0.0211819	+	0.215063i	−0.978767	+	0.204975i	$0.934289\pi$
$614$		0			0
$615$	−0.313739	−	1.57727i	−0.0126512	−	0.0636018i
$616$		0			0
$617$	3.37485	+	0.671299i	0.135866	+	0.0270255i	0.262555	−	0.964917i	$-0.415435\pi$
$617$	3.37485	+	0.671299i	0.135866	+	0.0270255i	−0.126689	+	0.991943i	$0.540435\pi$
$618$		0			0
$619$	−9.28258	−	17.3665i	−0.373098	−	0.698018i	0.623375	−	0.781923i	$-0.285761\pi$
$619$	−9.28258	−	17.3665i	−0.373098	−	0.698018i	−0.996474	+	0.0839048i	$0.973261\pi$
$620$		0			0
$621$	0.944976	−	9.59451i	0.0379206	−	0.385014i
$622$		0			0
$623$	−21.7609	−	9.01368i	−0.871834	−	0.361125i
$624$		0			0
$625$	18.6883	−	7.74094i	0.747531	−	0.309638i
$626$		0			0
$627$	−3.14874	+	2.58411i	−0.125749	+	0.103199i
$628$		0			0
$629$	−18.4984	−	5.61143i	−0.737580	−	0.223742i
$630$		0			0
$631$	20.3134	+	30.4011i	0.808663	+	1.21025i	0.974564	+	0.224108i	$0.0719468\pi$
$631$	20.3134	+	30.4011i	0.808663	+	1.21025i	−0.165901	+	0.986142i	$0.553053\pi$
$632$		0			0
$633$	5.45140	+	3.64251i	0.216674	+	0.144777i
$634$		0			0
$635$	−19.6552	+	23.9499i	−0.779992	+	0.950423i
$636$		0			0
$637$	3.79654	+	2.02930i	0.150425	+	0.0804036i
$638$		0			0
$639$	8.50174			0.336324
$640$		0			0
$641$	−16.5782			−0.654801			−0.327401	−	0.944886i	$-0.606173\pi$
$641$	−16.5782			−0.654801			−0.327401	+	0.944886i	$0.606173\pi$
$642$		0			0
$643$	−26.9995	−	14.4315i	−1.06476	−	0.569124i	−0.156560	−	0.987668i	$-0.550040\pi$
$643$	−26.9995	−	14.4315i	−1.06476	−	0.569124i	−0.908196	+	0.418545i	$0.862540\pi$
$644$		0			0
$645$	−1.04940	+	1.27870i	−0.0413203	+	0.0503489i
$646$		0			0
$647$	−26.3694	−	17.6195i	−1.03669	−	0.692694i	−0.0839461	−	0.996470i	$-0.526752\pi$
$647$	−26.3694	−	17.6195i	−1.03669	−	0.692694i	−0.952743	+	0.303777i	$0.901752\pi$
$648$		0			0
$649$	−8.46829	−	12.6737i	−0.332409	−	0.497486i
$650$		0			0
$651$	0.0441577	+	0.0133951i	0.00173068	+	0.000524995i
$652$		0			0
$653$	−39.3709	+	32.3108i	−1.54070	+	1.26442i	−0.717772	+	0.696279i	$0.754838\pi$
$653$	−39.3709	+	32.3108i	−1.54070	+	1.26442i	−0.822930	+	0.568143i	$0.807662\pi$
$654$		0			0
$655$	8.35743	−	3.46176i	0.326552	−	0.135262i
$656$		0			0
$657$	−38.8264	−	16.0824i	−1.51476	−	0.627434i
$658$		0			0
$659$	3.92839	−	39.8856i	0.153028	−	1.55372i	−0.545481	−	0.838123i	$-0.683653\pi$
$659$	3.92839	−	39.8856i	0.153028	−	1.55372i	0.698510	−	0.715601i	$-0.253847\pi$
$660$		0			0
$661$	1.91420	+	3.58121i	0.0744537	+	0.139293i	0.916394	−	0.400278i	$-0.131086\pi$
$661$	1.91420	+	3.58121i	0.0744537	+	0.139293i	−0.841940	+	0.539571i	$0.818586\pi$
$662$		0			0
$663$	−2.00252	−	0.398327i	−0.0777716	−	0.0154697i
$664$		0			0
$665$	−5.61797	−	28.2434i	−0.217855	−	1.09523i
$666$		0			0
$667$	2.62853	+	26.6879i	0.101777	+	1.03336i
$668$		0			0
$669$	−0.791544	−	2.60937i	−0.0306029	−	0.100884i
$670$		0			0
$671$	−2.62714	+	2.62714i	−0.101420	+	0.101420i
$672$		0			0
$673$	12.5943	+	12.5943i	0.485475	+	0.485475i	0.906875	−	0.421400i	$-0.138461\pi$
$673$	12.5943	+	12.5943i	0.485475	+	0.485475i	−0.421400	+	0.906875i	$0.638461\pi$
$674$		0			0
$675$	−1.08771	+	0.329953i	−0.0418660	+	0.0126999i
$676$		0			0
$677$	18.4896	−	1.82106i	0.710612	−	0.0699891i	0.263749	−	0.964591i	$-0.415041\pi$
$677$	18.4896	−	1.82106i	0.710612	−	0.0699891i	0.446863	+	0.894602i	$0.352541\pi$
$678$		0			0
$679$	5.43146	−	1.08038i	0.208440	−	0.0414614i
$680$		0			0
$681$	−0.314143	+	1.57930i	−0.0120380	+	0.0605190i
$682$		0			0
$683$	−25.6460	+	13.7080i	−0.981315	+	0.524524i	−0.882364	−	0.470568i	$-0.844049\pi$
$683$	−25.6460	+	13.7080i	−0.981315	+	0.524524i	−0.0989517	+	0.995092i	$0.531549\pi$
$684$		0			0
$685$	9.02360	+	0.888747i	0.344774	+	0.0339573i
$686$		0			0
$687$	−1.14806	+	2.77165i	−0.0438011	+	0.105745i
$688$		0			0
$689$	−5.01315	−	12.1028i	−0.190986	−	0.461081i
$690$		0			0
$691$	−16.6203	−	20.2519i	−0.632266	−	0.770419i	0.354060	−	0.935223i	$-0.384801\pi$
$691$	−16.6203	−	20.2519i	−0.632266	−	0.770419i	−0.986326	+	0.164804i	$0.947301\pi$
$692$		0			0
$693$	−3.93015	+	12.9560i	−0.149294	+	0.492157i
$694$		0			0
$695$	−14.3183	+	9.56721i	−0.543125	+	0.362905i
$696$		0			0
$697$	−12.5602	+	18.7977i	−0.475752	+	0.712013i
$698$		0			0
$699$	−1.90899	−	1.56667i	−0.0722048	−	0.0592570i
$700$		0			0
$701$	5.72277	−	10.7066i	0.216146	−	0.404381i	−0.750358	−	0.661032i	$-0.770119\pi$
$701$	5.72277	−	10.7066i	0.216146	−	0.404381i	0.966504	+	0.256651i	$0.0826190\pi$
$702$		0			0
$703$		−	21.1058i		−	0.796022i
$704$		0			0
$705$			2.18497i			0.0822909i
$706$		0			0
$707$	16.3678	−	30.6219i	0.615573	−	1.15166i
$708$		0			0
$709$	4.66958	+	3.83223i	0.175370	+	0.143922i	0.717984	−	0.696060i	$-0.245065\pi$
$709$	4.66958	+	3.83223i	0.175370	+	0.143922i	−0.542614	+	0.839982i	$0.682565\pi$
$710$		0			0
$711$	−13.4079	+	20.0664i	−0.502837	+	0.752549i
$712$		0			0
$713$	−0.594504	+	0.397235i	−0.0222643	+	0.0148766i
$714$		0			0
$715$	1.85172	−	6.10429i	0.0692503	−	0.228288i
$716$		0			0
$717$	4.18806	+	5.10317i	0.156406	+	0.190581i
$718$		0			0
$719$	11.5925	+	27.9868i	0.432328	+	1.04373i	0.978535	+	0.206081i	$0.0660711\pi$
$719$	11.5925	+	27.9868i	0.432328	+	1.04373i	−0.546207	+	0.837650i	$0.683929\pi$
$720$		0			0
$721$	−12.5082	+	30.1975i	−0.465829	+	1.12461i
$722$		0			0
$723$	4.22799	+	0.416421i	0.157241	+	0.0154868i
$724$		0			0
$725$	2.78837	−	1.49041i	0.103557	−	0.0553526i
$726$		0			0
$727$	5.95669	−	29.9463i	0.220921	−	1.11065i	−0.697968	−	0.716129i	$-0.745912\pi$
$727$	5.95669	−	29.9463i	0.220921	−	1.11065i	0.918889	−	0.394517i	$-0.129088\pi$
$728$		0			0
$729$	23.6453	−	4.70335i	0.875753	−	0.174198i
$730$		0			0
$731$	23.1427	−	2.27935i	0.855962	−	0.0843049i
$732$		0			0
$733$	−41.9906	+	12.7377i	−1.55096	+	0.470479i	−0.945561	−	0.325444i	$-0.894486\pi$
$733$	−41.9906	+	12.7377i	−1.55096	+	0.470479i	−0.605398	+	0.795923i	$0.706986\pi$
$734$		0			0
$735$	−1.11047	−	1.11047i	−0.0409602	−	0.0409602i
$736$		0			0
$737$	−9.11235	+	9.11235i	−0.335658	+	0.335658i
$738$		0			0
$739$	1.59295	+	5.25124i	0.0585975	+	0.193170i	0.981352	−	0.192217i	$-0.0615679\pi$
$739$	1.59295	+	5.25124i	0.0585975	+	0.193170i	−0.922755	+	0.385387i	$0.874068\pi$
$740$		0			0
$741$	−0.218504	−	2.21851i	−0.00802694	−	0.0814989i
$742$		0			0
$743$	−0.480046	−	2.41335i	−0.0176112	−	0.0885374i	0.970980	−	0.239160i	$-0.0768721\pi$
$743$	−0.480046	−	2.41335i	−0.0176112	−	0.0885374i	−0.988591	+	0.150623i	$0.951872\pi$
$744$		0			0
$745$	1.69201	+	0.336562i	0.0619905	+	0.0123307i
$746$		0			0
$747$	−15.1256	−	28.2981i	−0.553418	−	1.03537i
$748$		0			0
$749$	3.40772	−	34.5991i	0.124515	−	1.26422i
$750$		0			0
$751$	34.9680	+	14.4842i	1.27600	+	0.528537i	0.914784	−	0.403944i	$-0.132361\pi$
$751$	34.9680	+	14.4842i	1.27600	+	0.528537i	0.361218	+	0.932481i	$0.382361\pi$
$752$		0			0
$753$	−1.11271	+	0.460899i	−0.0405493	+	0.0167961i
$754$		0			0
$755$	8.96155	−	7.35456i	0.326144	−	0.267660i
$756$		0			0
$757$	5.25056	+	1.59274i	0.190835	+	0.0578891i	0.384255	−	0.923227i	$-0.374458\pi$
$757$	5.25056	+	1.59274i	0.190835	+	0.0578891i	−0.193421	+	0.981116i	$0.561958\pi$
$758$		0			0
$759$	2.15098	+	3.21917i	0.0780756	+	0.116848i
$760$		0			0
$761$	−22.3639	−	14.9431i	−0.810690	−	0.541686i	0.0797347	−	0.996816i	$-0.474593\pi$
$761$	−22.3639	−	14.9431i	−0.810690	−	0.541686i	−0.890425	+	0.455130i	$0.849593\pi$
$762$		0			0
$763$	4.12825	−	5.03029i	0.149453	−	0.182109i
$764$		0			0
$765$	−35.5934	−	19.0251i	−1.28688	−	0.687854i
$766$		0			0
$767$	8.34184			0.301206
$768$		0			0
$769$	−44.1010			−1.59032			−0.795161	−	0.606398i	$-0.792614\pi$
$769$	−44.1010			−1.59032			−0.795161	+	0.606398i	$0.792614\pi$
$770$		0			0
$771$	0.619331	+	0.331039i	0.0223047	+	0.0119221i
$772$		0			0
$773$	0.528053	−	0.643434i	0.0189927	−	0.0231427i	−0.763427	−	0.645894i	$-0.776485\pi$
$773$	0.528053	−	0.643434i	0.0189927	−	0.0231427i	0.782420	+	0.622751i	$0.213985\pi$
$774$		0			0
$775$	0.0700913	+	0.0468335i	0.00251775	+	0.00168231i
$776$		0			0
$777$	0.719284	+	1.07649i	0.0258042	+	0.0386187i
$778$		0			0
$779$	−23.6209	−	7.16532i	−0.846306	−	0.256724i
$780$		0			0
$781$	−5.32710	+	4.37184i	−0.190619	+	0.156437i
$782$		0			0
$783$	4.93866	−	2.04566i	0.176493	−	0.0731058i
$784$		0			0
$785$	32.4631	+	13.4467i	1.15866	+	0.479932i
$786$		0			0
$787$	−3.42690	+	34.7939i	−0.122156	+	1.24027i	0.717270	+	0.696795i	$0.245391\pi$
$787$	−3.42690	+	34.7939i	−0.122156	+	1.24027i	−0.839426	+	0.543474i	$0.817109\pi$
$788$		0			0
$789$	1.83600	+	3.43492i	0.0653635	+	0.122286i
$790$		0			0
$791$	28.4894	+	5.66690i	1.01297	+	0.201492i
$792$		0			0
$793$	−0.396680	−	1.99424i	−0.0140865	−	0.0708177i
$794$		0			0
$795$	0.468420	+	4.75595i	0.0166131	+	0.168676i
$796$		0			0
$797$	−8.23070	−	27.1330i	−0.291547	−	0.961100i	−0.973304	−	0.229521i	$-0.926284\pi$
$797$	−8.23070	−	27.1330i	−0.291547	−	0.961100i	0.681757	−	0.731579i	$-0.261216\pi$
$798$		0			0
$799$	21.7198	−	21.7198i	0.768392	−	0.768392i
$800$		0			0
$801$	−25.4858	−	25.4858i	−0.900495	−	0.900495i
$802$		0			0
$803$	32.5982	−	9.88856i	1.15037	−	0.348960i
$804$		0			0
$805$	−27.2391	+	2.68282i	−0.960052	+	0.0945569i
$806$		0			0
$807$	0.288827	−	0.0574514i	0.0101672	−	0.00202238i
$808$		0			0
$809$	−8.48642	+	42.6641i	−0.298367	+	1.49999i	0.482835	+	0.875712i	$0.339607\pi$
$809$	−8.48642	+	42.6641i	−0.298367	+	1.49999i	−0.781201	+	0.624279i	$0.785393\pi$
$810$		0			0
$811$	−10.4751	+	5.59905i	−0.367830	+	0.196609i	−0.644948	−	0.764227i	$-0.723121\pi$
$811$	−10.4751	+	5.59905i	−0.367830	+	0.196609i	0.277118	+	0.960836i	$0.410621\pi$
$812$		0			0
$813$	−5.05660	−	0.498032i	−0.177343	−	0.0174667i
$814$		0			0
$815$	6.92529	−	16.7191i	0.242582	−	0.585646i
$816$		0			0
$817$	9.71634	+	23.4573i	0.339932	+	0.820668i
$818$		0			0
$819$	−4.70055	−	5.72764i	−0.164251	−	0.200140i
$820$		0			0
$821$	−5.56307	+	18.3390i	−0.194152	+	0.640035i	0.804768	+	0.593589i	$0.202289\pi$
$821$	−5.56307	+	18.3390i	−0.194152	+	0.640035i	−0.998921	+	0.0464458i	$0.985211\pi$
$822$		0			0
$823$	11.1704	−	7.46381i	0.389375	−	0.260172i	−0.345438	−	0.938441i	$-0.612270\pi$
$823$	11.1704	−	7.46381i	0.389375	−	0.260172i	0.734813	+	0.678269i	$0.237270\pi$
$824$		0			0
$825$	0.253598	−	0.379536i	0.00882915	−	0.0132138i
$826$		0			0
$827$	−13.3254	−	10.9359i	−0.463369	−	0.380277i	0.373544	−	0.927612i	$-0.378142\pi$
$827$	−13.3254	−	10.9359i	−0.463369	−	0.380277i	−0.836914	+	0.547335i	$0.815642\pi$
$828$		0			0
$829$	11.2497	−	21.0468i	0.390720	−	0.730985i	−0.607261	−	0.794503i	$-0.707732\pi$
$829$	11.2497	−	21.0468i	0.390720	−	0.730985i	0.997981	+	0.0635170i	$0.0202317\pi$
$830$		0			0
$831$			6.03672i			0.209412i
$832$		0			0
$833$			22.0773i			0.764933i
$834$		0			0
$835$	−12.5955	+	23.5646i	−0.435886	+	0.815486i
$836$		0			0
$837$	0.110173	+	0.0904169i	0.00380815	+	0.00312526i
$838$		0			0
$839$	8.99731	−	13.4654i	0.310622	−	0.464878i	−0.643008	−	0.765859i	$-0.722314\pi$
$839$	8.99731	−	13.4654i	0.310622	−	0.464878i	0.953630	+	0.300981i	$0.0973140\pi$
$840$		0			0
$841$	11.7494	−	7.85070i	0.405152	−	0.270714i
$842$		0			0
$843$	0.342806	−	1.13008i	0.0118068	−	0.0389220i
$844$		0			0
$845$	−14.6467	−	17.8471i	−0.503862	−	0.613957i
$846$		0			0
$847$	3.90355	+	9.42401i	0.134128	+	0.323813i
$848$		0			0
$849$	0.963302	−	2.32562i	0.0330604	−	0.0798150i
$850$		0			0
$851$	−19.9642	−	1.96630i	−0.684364	−	0.0674040i
$852$		0			0
$853$	−32.2549	+	17.2406i	−1.10439	+	0.590307i	−0.919752	−	0.392500i	$-0.871610\pi$
$853$	−32.2549	+	17.2406i	−1.10439	+	0.590307i	−0.184635	+	0.982807i	$0.559110\pi$
$854$		0			0
$855$	8.59665	−	43.2183i	0.293999	−	1.47803i
$856$		0			0
$857$	11.9080	−	2.36865i	0.406771	−	0.0809117i	0.0125358	−	0.999921i	$-0.496010\pi$
$857$	11.9080	−	2.36865i	0.406771	−	0.0809117i	0.394235	+	0.919010i	$0.371010\pi$
$858$		0			0
$859$	−1.29758	+	0.127801i	−0.0442730	+	0.00436051i	−0.120129	−	0.992758i	$-0.538331\pi$
$859$	−1.29758	+	0.127801i	−0.0442730	+	0.00436051i	0.0758564	+	0.997119i	$0.475831\pi$
$860$		0			0
$861$	1.44896	−	0.439536i	0.0493803	−	0.0149793i
$862$		0			0
$863$	−19.1934	−	19.1934i	−0.653353	−	0.653353i	0.300446	−	0.953799i	$-0.402864\pi$
$863$	−19.1934	−	19.1934i	−0.653353	−	0.653353i	−0.953799	+	0.300446i	$0.902864\pi$
$864$		0			0
$865$	−11.9680	+	11.9680i	−0.406925	+	0.406925i
$866$		0			0
$867$	−1.88899	−	6.22716i	−0.0641534	−	0.211485i
$868$		0			0
$869$	−1.91745	−	19.4681i	−0.0650449	−	0.660412i
$870$		0			0
$871$	−1.37590	−	6.91710i	−0.0466205	−	0.234377i
$872$		0			0
$873$	8.31126	+	1.65321i	0.281293	+	0.0559527i
$874$		0			0
$875$	10.7976	+	20.2008i	0.365024	+	0.682912i
$876$		0			0
$877$	2.36549	−	24.0172i	0.0798768	−	0.811003i	−0.868886	−	0.495013i	$-0.835163\pi$
$877$	2.36549	−	24.0172i	0.0798768	−	0.811003i	0.948762	−	0.315990i	$-0.102337\pi$
$878$		0			0
$879$	1.08001	+	0.447357i	0.0364280	+	0.0150890i
$880$		0			0
$881$	16.5898	−	6.87174i	0.558926	−	0.231515i	−0.0852928	−	0.996356i	$-0.527183\pi$
$881$	16.5898	−	6.87174i	0.558926	−	0.231515i	0.644219	+	0.764841i	$0.277183\pi$
$882$		0			0
$883$	−37.5467	+	30.8138i	−1.26355	+	1.03697i	−0.266220	+	0.963912i	$0.585775\pi$
$883$	−37.5467	+	30.8138i	−1.26355	+	1.03697i	−0.997328	+	0.0730551i	$0.976725\pi$
$884$		0			0
$885$	−2.91212	−	0.883381i	−0.0978897	−	0.0296945i
$886$		0			0
$887$	−18.2427	−	27.3021i	−0.612529	−	0.916714i	0.387458	−	0.921887i	$-0.373353\pi$
$887$	−18.2427	−	27.3021i	−0.612529	−	0.916714i	−0.999987	+	0.00517318i	$0.998353\pi$
$888$		0			0
$889$	−24.2551	−	16.2067i	−0.813488	−	0.543556i
$890$		0			0
$891$	−12.8959	+	15.7137i	−0.432030	+	0.526430i
$892$		0			0
$893$	29.5770	+	15.8093i	0.989758	+	0.529036i
$894$		0			0
$895$	−20.0855			−0.671385
$896$		0			0
$897$	−2.11886			−0.0707467
$898$		0			0
$899$	−0.349633	−	0.186883i	−0.0116609	−	0.00623289i
$900$		0			0
$901$	42.6204	−	51.9331i	1.41989	−	1.73014i
$902$		0			0
$903$	−1.29500	−	0.865288i	−0.0430947	−	0.0287950i
$904$		0			0
$905$	21.8953	+	32.7687i	0.727826	+	1.08927i
$906$		0			0
$907$	−44.2175	−	13.4132i	−1.46822	−	0.445379i	−0.547898	−	0.836545i	$-0.684572\pi$
$907$	−44.2175	−	13.4132i	−1.46822	−	0.445379i	−0.920320	+	0.391166i	$0.872072\pi$
$908$		0			0
$909$	41.0713	−	33.7063i	1.36225	−	1.11797i
$910$		0			0
$911$	−10.4401	+	4.32444i	−0.345897	+	0.143275i	−0.548867	−	0.835910i	$-0.684941\pi$
$911$	−10.4401	+	4.32444i	−0.345897	+	0.143275i	0.202970	+	0.979185i	$0.434941\pi$
$912$		0			0
$913$	24.0292	+	9.95323i	0.795251	+	0.329404i
$914$		0			0
$915$	−0.0727057	+	0.738193i	−0.00240358	+	0.0244039i
$916$		0			0
$917$	4.01496	+	7.51146i	0.132586	+	0.248050i
$918$		0			0
$919$	−7.79488	−	1.55050i	−0.257129	−	0.0511462i	0.0648423	−	0.997896i	$-0.479346\pi$
$919$	−7.79488	−	1.55050i	−0.257129	−	0.0511462i	−0.321972	+	0.946749i	$0.604346\pi$
$920$		0			0
$921$	−0.432336	−	2.17350i	−0.0142459	−	0.0716192i
$922$		0			0
$923$	−0.369669	−	3.75331i	−0.0121678	−	0.123542i
$924$		0			0
$925$	0.686566	+	2.26330i	0.0225741	+	0.0744170i
$926$		0			0
$927$	−35.3663	+	35.3663i	−1.16158	+	1.16158i
$928$		0			0
$929$	−20.6076	−	20.6076i	−0.676113	−	0.676113i	0.283005	−	0.959118i	$-0.408669\pi$
$929$	−20.6076	−	20.6076i	−0.676113	−	0.676113i	−0.959118	+	0.283005i	$0.908669\pi$
$930$		0			0
$931$	−23.0666	+	6.99719i	−0.755978	+	0.229324i
$932$		0			0
$933$	1.89749	−	0.186887i	0.0621211	−	0.00611839i
$934$		0			0
$935$	32.0857	−	6.38224i	1.04931	−	0.208722i
$936$		0			0
$937$	−3.46724	+	17.4310i	−0.113270	+	0.569446i	0.881913	+	0.471412i	$0.156255\pi$
$937$	−3.46724	+	17.4310i	−0.113270	+	0.569446i	−0.995183	+	0.0980340i	$0.968745\pi$
$938$		0			0
$939$	0.553992	−	0.296115i	0.0180788	−	0.00966334i
$940$		0			0
$941$	−48.5174	−	4.77854i	−1.58162	−	0.155776i	−0.731306	−	0.682050i	$-0.761089\pi$
$941$	−48.5174	−	4.77854i	−1.58162	−	0.155776i	−0.850315	+	0.526274i	$0.823589\pi$
$942$		0			0
$943$	−8.97835	+	21.6757i	−0.292375	+	0.705856i
$944$		0			0
$945$	2.08791	+	5.04065i	0.0679196	+	0.163972i
$946$		0			0
$947$	−10.4049	−	12.6784i	−0.338115	−	0.411994i	0.576000	−	0.817450i	$-0.304613\pi$
$947$	−10.4049	−	12.6784i	−0.338115	−	0.411994i	−0.914115	+	0.405456i	$0.867113\pi$
$948$		0			0
$949$	−5.41176	+	17.8402i	−0.175673	+	0.579116i
$950$		0			0
$951$	4.07495	−	2.72280i	0.132139	−	0.0882927i
$952$		0			0
$953$	27.4128	−	41.0262i	0.887989	−	1.32897i	−0.0558076	−	0.998442i	$-0.517773\pi$
$953$	27.4128	−	41.0262i	0.887989	−	1.32897i	0.943796	−	0.330528i	$-0.107227\pi$
$954$		0			0
$955$	34.6276	+	28.4181i	1.12052	+	0.919589i
$956$		0			0
$957$	−1.01195	+	1.89322i	−0.0327116	+	0.0611992i
$958$		0			0
$959$			8.53716i			0.275679i
$960$		0			0
$961$			30.9894i			0.999659i
$962$		0			0
$963$	25.0783	−	46.9182i	0.808137	−	1.51192i
$964$		0			0
$965$	13.7943	+	11.3207i	0.444056	+	0.364427i
$966$		0			0
$967$	−16.2004	+	24.2456i	−0.520970	+	0.779686i	−0.994899	−	0.100877i	$-0.967835\pi$
$967$	−16.2004	+	24.2456i	−0.520970	+	0.779686i	0.473929	+	0.880563i	$0.342835\pi$
$968$		0			0
$969$	9.50584	−	6.35160i	0.305372	−	0.204043i
$970$		0			0
$971$	4.46677	−	14.7250i	0.143345	−	0.472547i	−0.855640	−	0.517571i	$-0.826836\pi$
$971$	4.46677	−	14.7250i	0.143345	−	0.472547i	0.998986	+	0.0450240i	$0.0143364\pi$
$972$		0			0
$973$	−10.2859	−	12.5334i	−0.329751	−	0.401802i
$974$		0			0
$975$	0.0955987	+	0.230796i	0.00306161	+	0.00739137i
$976$		0			0
$977$	0.456414	−	1.10188i	0.0146020	−	0.0352523i	−0.916410	−	0.400240i	$-0.868927\pi$
$977$	0.456414	−	1.10188i	0.0146020	−	0.0352523i	0.931012	+	0.364988i	$0.118927\pi$
$978$		0			0
$979$	29.0746	+	2.86360i	0.929228	+	0.0915210i
$980$		0			0
$981$	8.78187	−	4.69401i	0.280384	−	0.149868i
$982$		0			0
$983$	−1.67855	+	8.43866i	−0.0535375	+	0.269151i	−0.998277	−	0.0586694i	$-0.981314\pi$
$983$	−1.67855	+	8.43866i	−0.0535375	+	0.269151i	0.944740	+	0.327821i	$0.106314\pi$
$984$		0			0
$985$	40.5763	−	8.07112i	1.29287	−	0.257167i
$986$		0			0
$987$	−2.04733	+	0.201644i	−0.0651671	+	0.00641840i
$988$		0			0
$989$	23.0937	−	7.00539i	0.734337	−	0.222759i
$990$		0			0
$991$	19.9640	+	19.9640i	0.634177	+	0.634177i	0.949113	−	0.314936i	$-0.101983\pi$
$991$	19.9640	+	19.9640i	0.634177	+	0.634177i	−0.314936	+	0.949113i	$0.601983\pi$
$992$		0			0
$993$	−2.68635	+	2.68635i	−0.0852486	+	0.0852486i
$994$		0			0
$995$	−1.11329	−	3.67001i	−0.0352936	−	0.116347i
$996$		0			0
$997$	2.18909	+	22.2262i	0.0693291	+	0.703911i	0.965535	+	0.260273i	$0.0838124\pi$
$997$	2.18909	+	22.2262i	0.0693291	+	0.703911i	−0.896206	+	0.443638i	$0.853688\pi$
$998$		0			0
$999$	0.780129	+	3.92198i	0.0246822	+	0.124086i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.273.7		240
4.3	odd	2		128.2.k.a.109.15	yes	240
128.27	odd	32		128.2.k.a.101.15	✓	240
128.101	even	32	inner	512.2.k.a.497.7		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.101.15	✓	240	128.27	odd	32
128.2.k.a.109.15	yes	240	4.3	odd	2
512.2.k.a.273.7		240	1.1	even	1	trivial
512.2.k.a.497.7		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)

\(f(q)\)	\(=\)	\(q+(-0.205628 - 0.109910i) q^{3} +(-1.29703 + 1.58044i) q^{5} +(-1.60057 - 1.06947i) q^{7} +(-1.63651 - 2.44921i) q^{9} +(2.28487 + 0.693108i) q^{11} +(-1.01011 + 0.828973i) q^{13} +(0.440412 - 0.182425i) q^{15} +(-6.19134 - 2.56454i) q^{17} +(0.717174 - 7.28159i) q^{19} +(0.211577 + 0.395832i) q^{21} +(-6.82091 - 1.35676i) q^{23} +(0.159961 + 0.804177i) q^{25} +(0.135879 + 1.37960i) q^{27} +(-1.11935 - 3.69001i) q^{29} +(0.0726984 - 0.0726984i) q^{31} +(-0.393654 - 0.393654i) q^{33} +(3.76622 - 1.14247i) q^{35} +(2.87067 - 0.282737i) q^{37} +(0.298819 - 0.0594388i) q^{39} +(0.658149 - 3.30874i) q^{41} +(-3.06034 + 1.63579i) q^{43} +(5.99342 + 0.590300i) q^{45} +(-1.75405 + 4.23465i) q^{47} +(-1.26071 - 3.04363i) q^{49} +(0.991243 + 1.20783i) q^{51} +(-2.91014 + 9.59343i) q^{53} +(-4.05896 + 2.71211i) q^{55} +(-0.947794 + 1.41847i) q^{57} +(-4.93475 - 4.04984i) q^{59} +(-0.733515 + 1.37231i) q^{61} +5.67033i q^{63} -2.67161i q^{65} +(-2.54422 + 4.75990i) q^{67} +(1.25345 + 1.02868i) q^{69} +(-1.60349 + 2.39980i) q^{71} +(11.8626 - 7.92631i) q^{73} +(0.0554951 - 0.182943i) q^{75} +(-2.91585 - 3.55297i) q^{77} +(-3.13533 - 7.56937i) q^{79} +(-3.25805 + 7.86562i) q^{81} +(10.8406 + 1.06770i) q^{83} +(12.0834 - 6.45874i) q^{85} +(-0.175400 + 0.881798i) q^{87} +(12.0007 - 2.38709i) q^{89} +(2.50331 - 0.246555i) q^{91} +(-0.0229392 + 0.00695852i) q^{93} +(10.5779 + 10.5779i) q^{95} +(-2.03422 + 2.03422i) q^{97} +(-2.04164 - 6.73040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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