LMFDB - Embedded newform 256.2.i.a.241.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [256,2,Mod(17,256)] 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("256.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(256, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.i (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:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			241.7
Character	$\chi$	$=$	256.241
Dual form			256.2.i.a.17.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.77714 - 2.65968i) q^{3} +(-0.159018 + 0.799435i) q^{5} +(0.742008 - 1.79137i) q^{7} +(-2.76763 - 6.68165i) q^{9} +(-1.29226 + 0.863458i) q^{11} +(1.07211 + 5.38985i) q^{13} +(1.84365 + 1.84365i) q^{15} +(1.43298 - 1.43298i) q^{17} +(-0.0883441 + 0.0175727i) q^{19} +(-3.44581 - 5.15702i) q^{21} +(-3.31519 + 1.37320i) q^{23} +(4.00559 + 1.65917i) q^{25} +(-13.2776 - 2.64108i) q^{27} +(-1.04042 - 0.695186i) q^{29} -2.58743i q^{31} +4.97148i q^{33} +(1.31409 + 0.878046i) q^{35} +(1.60572 + 0.319397i) q^{37} +(16.2406 + 6.72707i) q^{39} +(0.605183 - 0.250675i) q^{41} +(5.04263 + 7.54683i) q^{43} +(5.78164 - 1.15004i) q^{45} +(3.86580 - 3.86580i) q^{47} +(2.29133 + 2.29133i) q^{49} +(-1.26466 - 6.35787i) q^{51} +(-8.70867 + 5.81895i) q^{53} +(-0.484787 - 1.17038i) q^{55} +(-0.110262 + 0.266197i) q^{57} +(-1.17041 + 5.88407i) q^{59} +(3.52821 - 5.28034i) q^{61} -14.0229 q^{63} -4.47932 q^{65} +(-3.15404 + 4.72036i) q^{67} +(-2.23930 + 11.2577i) q^{69} +(-5.01419 + 12.1053i) q^{71} +(-1.75399 - 4.23450i) q^{73} +(11.5314 - 7.70502i) q^{75} +(0.587905 + 2.95560i) q^{77} +(-7.46021 - 7.46021i) q^{79} +(-15.2789 + 15.2789i) q^{81} +(2.65306 - 0.527725i) q^{83} +(0.917704 + 1.37344i) q^{85} +(-3.69795 + 1.53174i) q^{87} +(7.09322 + 2.93811i) q^{89} +(10.4507 + 2.07877i) q^{91} +(-6.88175 - 4.59824i) q^{93} -0.0734197i q^{95} -11.4524i q^{97} +(9.34580 + 6.24466i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{9}{16}\right)$	$1$

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
$3$	1.77714	−	2.65968i	1.02603	−	1.53557i	0.193880	−	0.981025i	$-0.437893\pi$
$3$	1.77714	−	2.65968i	1.02603	−	1.53557i	0.832154	−	0.554544i	$-0.187107\pi$
$4$		0			0
$5$	−0.159018	+	0.799435i	−0.0711148	+	0.357518i	−0.999915	−	0.0130634i	$-0.995842\pi$
$5$	−0.159018	+	0.799435i	−0.0711148	+	0.357518i	0.928800	+	0.370582i	$0.120842\pi$
$6$		0			0
$7$	0.742008	−	1.79137i	0.280453	−	0.677073i	−0.719394	−	0.694603i	$-0.755580\pi$
$7$	0.742008	−	1.79137i	0.280453	−	0.677073i	0.999846	+	0.0175299i	$0.00558022\pi$
$8$		0			0
$9$	−2.76763	−	6.68165i	−0.922543	−	2.22722i
$10$		0			0
$11$	−1.29226	+	0.863458i	−0.389630	+	0.260342i	−0.734920	−	0.678154i	$-0.762780\pi$
$11$	−1.29226	+	0.863458i	−0.389630	+	0.260342i	0.345290	+	0.938496i	$0.387780\pi$
$12$		0			0
$13$	1.07211	+	5.38985i	0.297349	+	1.49487i	0.783716	+	0.621119i	$0.213322\pi$
$13$	1.07211	+	5.38985i	0.297349	+	1.49487i	−0.486367	+	0.873755i	$0.661678\pi$
$14$		0			0
$15$	1.84365	+	1.84365i	0.476028	+	0.476028i
$16$		0			0
$17$	1.43298	−	1.43298i	0.347548	−	0.347548i	−0.511648	−	0.859195i	$-0.670965\pi$
$17$	1.43298	−	1.43298i	0.347548	−	0.347548i	0.859195	+	0.511648i	$0.170965\pi$
$18$		0			0
$19$	−0.0883441	+	0.0175727i	−0.0202675	+	0.00403146i	−0.205214	−	0.978717i	$-0.565789\pi$
$19$	−0.0883441	+	0.0175727i	−0.0202675	+	0.00403146i	0.184946	+	0.982749i	$0.440789\pi$
$20$		0			0
$21$	−3.44581	−	5.15702i	−0.751938	−	1.12535i
$22$		0			0
$23$	−3.31519	+	1.37320i	−0.691266	+	0.286332i	−0.700527	−	0.713625i	$-0.747052\pi$
$23$	−3.31519	+	1.37320i	−0.691266	+	0.286332i	0.00926165	+	0.999957i	$0.497052\pi$
$24$		0			0
$25$	4.00559	+	1.65917i	0.801118	+	0.331834i
$26$		0			0
$27$	−13.2776	−	2.64108i	−2.55528	−	0.508276i
$28$		0			0
$29$	−1.04042	−	0.695186i	−0.193201	−	0.129093i	0.455207	−	0.890385i	$-0.349565\pi$
$29$	−1.04042	−	0.695186i	−0.193201	−	0.129093i	−0.648409	+	0.761293i	$0.724565\pi$
$30$		0			0
$31$		−	2.58743i		−	0.464717i	−0.972630	−	0.232358i	$-0.925356\pi$
$31$		−	2.58743i		−	0.464717i	0.972630	−	0.232358i	$-0.0746442\pi$
$32$		0			0
$33$			4.97148i			0.865424i
$34$		0			0
$35$	1.31409	+	0.878046i	0.222122	+	0.148417i
$36$		0			0
$37$	1.60572	+	0.319397i	0.263979	+	0.0525086i	0.325305	−	0.945609i	$-0.394533\pi$
$37$	1.60572	+	0.319397i	0.263979	+	0.0525086i	−0.0613263	+	0.998118i	$0.519533\pi$
$38$		0			0
$39$	16.2406	+	6.72707i	2.60057	+	1.07719i
$40$		0			0
$41$	0.605183	−	0.250675i	0.0945137	−	0.0391488i	−0.334926	−	0.942245i	$-0.608711\pi$
$41$	0.605183	−	0.250675i	0.0945137	−	0.0391488i	0.429439	+	0.903096i	$0.358711\pi$
$42$		0			0
$43$	5.04263	+	7.54683i	0.768994	+	1.15088i	0.984672	+	0.174416i	$0.0558039\pi$
$43$	5.04263	+	7.54683i	0.768994	+	1.15088i	−0.215678	+	0.976465i	$0.569196\pi$
$44$		0			0
$45$	5.78164	−	1.15004i	0.861877	−	0.171438i
$46$		0			0
$47$	3.86580	−	3.86580i	0.563885	−	0.563885i	−0.366524	−	0.930409i	$-0.619452\pi$
$47$	3.86580	−	3.86580i	0.563885	−	0.563885i	0.930409	+	0.366524i	$0.119452\pi$
$48$		0			0
$49$	2.29133	+	2.29133i	0.327333	+	0.327333i
$50$		0			0
$51$	−1.26466	−	6.35787i	−0.177088	−	0.890280i
$52$		0			0
$53$	−8.70867	+	5.81895i	−1.19623	+	0.799294i	−0.984042	−	0.177935i	$-0.943058\pi$
$53$	−8.70867	+	5.81895i	−1.19623	+	0.799294i	−0.212186	+	0.977229i	$0.568058\pi$
$54$		0			0
$55$	−0.484787	−	1.17038i	−0.0653687	−	0.157814i
$56$		0			0
$57$	−0.110262	+	0.266197i	−0.0146046	+	0.0352586i
$58$		0			0
$59$	−1.17041	+	5.88407i	−0.152375	+	0.766040i	0.826716	+	0.562619i	$0.190206\pi$
$59$	−1.17041	+	5.88407i	−0.152375	+	0.766040i	−0.979091	+	0.203421i	$0.934794\pi$
$60$		0			0
$61$	3.52821	−	5.28034i	0.451741	−	0.676078i	−0.533782	−	0.845622i	$-0.679230\pi$
$61$	3.52821	−	5.28034i	0.451741	−	0.676078i	0.985523	+	0.169544i	$0.0542296\pi$
$62$		0			0
$63$	−14.0229			−1.76672
$64$		0			0
$65$	−4.47932			−0.555591
$66$		0			0
$67$	−3.15404	+	4.72036i	−0.385328	+	0.576684i	−0.972536	−	0.232752i	$-0.925227\pi$
$67$	−3.15404	+	4.72036i	−0.385328	+	0.576684i	0.587208	+	0.809436i	$0.300227\pi$
$68$		0			0
$69$	−2.23930	+	11.2577i	−0.269581	+	1.35527i
$70$		0			0
$71$	−5.01419	+	12.1053i	−0.595075	+	1.43664i	0.283471	+	0.958981i	$0.408514\pi$
$71$	−5.01419	+	12.1053i	−0.595075	+	1.43664i	−0.878546	+	0.477657i	$0.841486\pi$
$72$		0			0
$73$	−1.75399	−	4.23450i	−0.205289	−	0.495611i	0.787381	−	0.616466i	$-0.211436\pi$
$73$	−1.75399	−	4.23450i	−0.205289	−	0.495611i	−0.992670	+	0.120855i	$0.961436\pi$
$74$		0			0
$75$	11.5314	−	7.70502i	1.33153	−	0.889699i
$76$		0			0
$77$	0.587905	+	2.95560i	0.0669979	+	0.336821i
$78$		0			0
$79$	−7.46021	−	7.46021i	−0.839340	−	0.839340i	0.149432	−	0.988772i	$-0.452255\pi$
$79$	−7.46021	−	7.46021i	−0.839340	−	0.839340i	−0.988772	+	0.149432i	$0.952255\pi$
$80$		0			0
$81$	−15.2789	+	15.2789i	−1.69766	+	1.69766i
$82$		0			0
$83$	2.65306	−	0.527725i	0.291211	−	0.0579254i	−0.0473232	−	0.998880i	$-0.515069\pi$
$83$	2.65306	−	0.527725i	0.291211	−	0.0579254i	0.338534	+	0.940954i	$0.390069\pi$
$84$		0			0
$85$	0.917704	+	1.37344i	0.0995389	+	0.148971i
$86$		0			0
$87$	−3.69795	+	1.53174i	−0.396462	+	0.164220i
$88$		0			0
$89$	7.09322	+	2.93811i	0.751880	+	0.311439i	0.725508	−	0.688213i	$-0.241605\pi$
$89$	7.09322	+	2.93811i	0.751880	+	0.311439i	0.0263716	+	0.999652i	$0.491605\pi$
$90$		0			0
$91$	10.4507	+	2.07877i	1.09553	+	0.217915i
$92$		0			0
$93$	−6.88175	−	4.59824i	−0.713605	−	0.476815i
$94$		0			0
$95$		−	0.0734197i		−	0.00753271i
$96$		0			0
$97$		−	11.4524i		−	1.16281i	−0.813614	−	0.581406i	$-0.802503\pi$
$97$		−	11.4524i		−	1.16281i	0.813614	−	0.581406i	$-0.197497\pi$
$98$		0			0
$99$	9.34580	+	6.24466i	0.939288	+	0.627612i
$100$		0			0
$101$	−11.4055	−	2.26869i	−1.13489	−	0.225743i	−0.408319	−	0.912839i	$-0.633885\pi$
$101$	−11.4055	−	2.26869i	−1.13489	−	0.225743i	−0.726566	+	0.687097i	$0.758885\pi$
$102$		0			0
$103$	−12.3890	−	5.13170i	−1.22073	−	0.505641i	−0.323086	−	0.946370i	$-0.604720\pi$
$103$	−12.3890	−	5.13170i	−1.22073	−	0.505641i	−0.897640	+	0.440729i	$0.854720\pi$
$104$		0			0
$105$	4.67065	−	1.93465i	0.455809	−	0.188802i
$106$		0			0
$107$	−5.26269	−	7.87617i	−0.508764	−	0.761419i	0.484808	−	0.874620i	$-0.338889\pi$
$107$	−5.26269	−	7.87617i	−0.508764	−	0.761419i	−0.993572	+	0.113202i	$0.963889\pi$
$108$		0			0
$109$	16.8083	−	3.34339i	1.60995	−	0.320238i	0.693519	−	0.720438i	$-0.256059\pi$
$109$	16.8083	−	3.34339i	1.60995	−	0.320238i	0.916428	+	0.400200i	$0.131059\pi$
$110$		0			0
$111$	3.70309	−	3.70309i	0.351482	−	0.351482i
$112$		0			0
$113$	−9.98074	−	9.98074i	−0.938909	−	0.938909i	0.0593295	−	0.998238i	$-0.481104\pi$
$113$	−9.98074	−	9.98074i	−0.938909	−	0.938909i	−0.998238	+	0.0593295i	$0.981104\pi$
$114$		0			0
$115$	−0.570609	−	2.86865i	−0.0532096	−	0.267503i
$116$		0			0
$117$	33.0458	−	22.0805i	3.05509	−	2.04135i
$118$		0			0
$119$	−1.50371	−	3.63027i	−0.137844	−	0.332786i
$120$		0			0
$121$	−3.28515	+	7.93106i	−0.298650	+	0.721005i
$122$		0			0
$123$	0.408781	−	2.05508i	0.0368585	−	0.185300i
$124$		0			0
$125$	−4.22757	+	6.32701i	−0.378126	+	0.565905i
$126$		0			0
$127$	9.01235			0.799717			0.399858	−	0.916577i	$-0.369059\pi$
$127$	9.01235			0.799717			0.399858	+	0.916577i	$0.369059\pi$
$128$		0			0
$129$	29.0337			2.55627
$130$		0			0
$131$	−4.77693	+	7.14918i	−0.417362	+	0.624627i	−0.979267	−	0.202575i	$-0.935069\pi$
$131$	−4.77693	+	7.14918i	−0.417362	+	0.624627i	0.561904	+	0.827202i	$0.310069\pi$
$132$		0			0
$133$	−0.0340728	+	0.171296i	−0.00295449	+	0.0148532i
$134$		0			0
$135$	4.22275	−	10.1946i	0.363436	−	0.877412i
$136$		0			0
$137$	1.16308	+	2.80792i	0.0993685	+	0.239897i	0.965744	−	0.259496i	$-0.0835564\pi$
$137$	1.16308	+	2.80792i	0.0993685	+	0.239897i	−0.866376	+	0.499393i	$0.833556\pi$
$138$		0			0
$139$	−6.85100	+	4.57769i	−0.581094	+	0.388275i	−0.811094	−	0.584916i	$-0.801127\pi$
$139$	−6.85100	+	4.57769i	−0.581094	+	0.388275i	0.230000	+	0.973191i	$0.426127\pi$
$140$		0			0
$141$	−3.41173	−	17.1519i	−0.287319	−	1.44445i
$142$		0			0
$143$	−6.03934	−	6.03934i	−0.505035	−	0.505035i
$144$		0			0
$145$	0.721201	−	0.721201i	0.0598925	−	0.0598925i
$146$		0			0
$147$	10.1662	−	2.02219i	0.838497	−	0.166788i
$148$		0			0
$149$	−8.41009	−	12.5866i	−0.688982	−	1.03113i	−0.996819	−	0.0796950i	$-0.974605\pi$
$149$	−8.41009	−	12.5866i	−0.688982	−	1.03113i	0.307838	−	0.951439i	$-0.400395\pi$
$150$		0			0
$151$	15.1739	−	6.28523i	1.23483	−	0.511485i	0.332738	−	0.943019i	$-0.392028\pi$
$151$	15.1739	−	6.28523i	1.23483	−	0.511485i	0.902096	+	0.431534i	$0.142028\pi$
$152$		0			0
$153$	−13.5406	−	5.60870i	−1.09469	−	0.453436i
$154$		0			0
$155$	2.06848	+	0.411447i	0.166145	+	0.0330482i
$156$		0			0
$157$	−3.65930	−	2.44507i	−0.292044	−	0.195138i	0.400914	−	0.916116i	$-0.368693\pi$
$157$	−3.65930	−	2.44507i	−0.292044	−	0.195138i	−0.692958	+	0.720978i	$0.743693\pi$
$158$		0			0
$159$			33.5034i			2.65700i
$160$		0			0
$161$			6.95765i			0.548340i
$162$		0			0
$163$	−3.89914	−	2.60532i	−0.305404	−	0.204065i	0.393418	−	0.919360i	$-0.371292\pi$
$163$	−3.89914	−	2.60532i	−0.305404	−	0.204065i	−0.698823	+	0.715295i	$0.746292\pi$
$164$		0			0
$165$	−3.97438	−	0.790553i	−0.309405	−	0.0615444i
$166$		0			0
$167$	−9.51475	−	3.94114i	−0.736274	−	0.304975i	−0.0171464	−	0.999853i	$-0.505458\pi$
$167$	−9.51475	−	3.94114i	−0.736274	−	0.304975i	−0.719127	+	0.694878i	$0.755458\pi$
$168$		0			0
$169$	−15.8906	+	6.58210i	−1.22235	+	0.506315i
$170$		0			0
$171$	0.361918	+	0.541649i	0.0276766	+	0.0414209i
$172$		0			0
$173$	−10.2124	+	2.03137i	−0.776434	+	0.154442i	−0.567374	−	0.823460i	$-0.692040\pi$
$173$	−10.2124	+	2.03137i	−0.776434	+	0.154442i	−0.209060	+	0.977903i	$0.567040\pi$
$174$		0			0
$175$	5.94436	−	5.94436i	0.449351	−	0.449351i
$176$		0			0
$177$	13.5698	+	13.5698i	1.01997	+	1.01997i
$178$		0			0
$179$	−4.62243	−	23.2385i	−0.345497	−	1.73693i	−0.628500	−	0.777810i	$-0.716331\pi$
$179$	−4.62243	−	23.2385i	−0.345497	−	1.73693i	0.283003	−	0.959119i	$-0.408669\pi$
$180$		0			0
$181$	−6.85149	+	4.57802i	−0.509267	+	0.340282i	−0.783510	−	0.621379i	$-0.786573\pi$
$181$	−6.85149	+	4.57802i	−0.509267	+	0.340282i	0.274243	+	0.961660i	$0.411573\pi$
$182$		0			0
$183$	−7.77390	−	18.7678i	−0.574663	−	1.38736i
$184$		0			0
$185$	−0.510675	+	1.23288i	−0.0375456	+	0.0906431i
$186$		0			0
$187$	−0.614458	+	3.08909i	−0.0449336	+	0.225896i
$188$		0			0
$189$	−14.5832	+	21.8254i	−1.06077	+	1.58756i
$190$		0			0
$191$	2.15250			0.155750			0.0778748	−	0.996963i	$-0.475187\pi$
$191$	2.15250			0.155750			0.0778748	+	0.996963i	$0.475187\pi$
$192$		0			0
$193$	−5.53246			−0.398236			−0.199118	−	0.979976i	$-0.563808\pi$
$193$	−5.53246			−0.398236			−0.199118	+	0.979976i	$0.563808\pi$
$194$		0			0
$195$	−7.96039	+	11.9136i	−0.570055	+	0.853148i
$196$		0			0
$197$	2.86767	−	14.4167i	0.204313	−	1.02715i	−0.733415	−	0.679781i	$-0.762075\pi$
$197$	2.86767	−	14.4167i	0.204313	−	1.02715i	0.937728	−	0.347370i	$-0.112925\pi$
$198$		0			0
$199$	−0.633559	+	1.52955i	−0.0449118	+	0.108427i	−0.944743	−	0.327811i	$-0.893689\pi$
$199$	−0.633559	+	1.52955i	−0.0449118	+	0.108427i	0.899832	+	0.436237i	$0.143689\pi$
$200$		0			0
$201$	6.94948	+	16.7775i	0.490178	+	1.18339i
$202$		0			0
$203$	−2.01733	+	1.34794i	−0.141589	+	0.0946068i
$204$		0			0
$205$	0.104164	+	0.523666i	0.00727511	+	0.0365744i
$206$		0			0
$207$	18.3505	+	18.3505i	1.27544	+	1.27544i
$208$		0			0
$209$	0.0989898	−	0.0989898i	0.00684727	−	0.00684727i
$210$		0			0
$211$	−8.05837	+	1.60291i	−0.554761	+	0.110349i	−0.464506	−	0.885570i	$-0.653768\pi$
$211$	−8.05837	+	1.60291i	−0.554761	+	0.110349i	−0.0902547	+	0.995919i	$0.528768\pi$
$212$		0			0
$213$	23.2854	+	34.8491i	1.59549	+	2.38782i
$214$		0			0
$215$	−6.83507	+	2.83118i	−0.466148	+	0.193085i
$216$		0			0
$217$	−4.63504	−	1.91990i	−0.314647	−	0.130331i
$218$		0			0
$219$	−14.3795	−	2.86026i	−0.971678	−	0.193279i
$220$		0			0
$221$	9.25983	+	6.18722i	0.622883	+	0.416197i
$222$		0			0
$223$		−	1.76595i		−	0.118256i	−0.998250	−	0.0591282i	$-0.981168\pi$
$223$		−	1.76595i		−	0.118256i	0.998250	−	0.0591282i	$-0.0188321\pi$
$224$		0			0
$225$		−	31.3559i		−	2.09039i
$226$		0			0
$227$	6.55957	+	4.38296i	0.435374	+	0.290908i	0.753879	−	0.657014i	$-0.228181\pi$
$227$	6.55957	+	4.38296i	0.435374	+	0.290908i	−0.318505	+	0.947921i	$0.603181\pi$
$228$		0			0
$229$	22.3445	+	4.44460i	1.47657	+	0.293707i	0.866713	−	0.498807i	$-0.166228\pi$
$229$	22.3445	+	4.44460i	1.47657	+	0.293707i	0.609853	+	0.792515i	$0.291228\pi$
$230$		0			0
$231$	8.90574	+	3.68888i	0.585955	+	0.242710i
$232$		0			0
$233$	3.96025	−	1.64039i	0.259445	−	0.107466i	−0.249170	−	0.968460i	$-0.580158\pi$
$233$	3.96025	−	1.64039i	0.259445	−	0.107466i	0.508615	+	0.860994i	$0.330158\pi$
$234$		0			0
$235$	2.47573	+	3.70519i	0.161499	+	0.241700i
$236$		0			0
$237$	−33.0997	+	6.58394i	−2.15006	+	0.427673i
$238$		0			0
$239$	2.96983	−	2.96983i	0.192103	−	0.192103i	−0.604501	−	0.796604i	$-0.706628\pi$
$239$	2.96983	−	2.96983i	0.192103	−	0.192103i	0.796604	+	0.604501i	$0.206628\pi$
$240$		0			0
$241$	−16.9923	−	16.9923i	−1.09457	−	1.09457i	−0.995034	−	0.0995381i	$-0.968263\pi$
$241$	−16.9923	−	16.9923i	−1.09457	−	1.09457i	−0.0995381	−	0.995034i	$-0.531737\pi$
$242$		0			0
$243$	5.56103	+	27.9572i	0.356740	+	1.79345i
$244$		0			0
$245$	−2.19613	+	1.46741i	−0.140306	+	0.0937493i
$246$		0			0
$247$	−0.189429	−	0.457321i	−0.0120531	−	0.0290986i
$248$		0			0
$249$	3.31128	−	7.99413i	0.209844	−	0.506608i
$250$		0			0
$251$	1.88276	−	9.46528i	0.118839	−	0.597443i	−0.874767	−	0.484543i	$-0.838986\pi$
$251$	1.88276	−	9.46528i	0.118839	−	0.597443i	0.993606	−	0.112900i	$-0.0360141\pi$
$252$		0			0
$253$	3.09838	−	4.63705i	0.194793	−	0.291529i
$254$		0			0
$255$	5.28381			0.330885
$256$		0			0
$257$	−4.05808			−0.253136			−0.126568	−	0.991958i	$-0.540396\pi$
$257$	−4.05808			−0.253136			−0.126568	+	0.991958i	$0.540396\pi$
$258$		0			0
$259$	1.76361	−	2.63944i	0.109586	−	0.164007i
$260$		0			0
$261$	−1.76549	+	8.87573i	−0.109281	+	0.549394i
$262$		0			0
$263$	−8.26702	+	19.9584i	−0.509766	+	1.23068i	0.434252	+	0.900791i	$0.357013\pi$
$263$	−8.26702	+	19.9584i	−0.509766	+	1.23068i	−0.944018	+	0.329893i	$0.892987\pi$
$264$		0			0
$265$	−3.26704	−	7.88734i	−0.200693	−	0.484515i
$266$		0			0
$267$	20.4201	−	13.6443i	1.24969	−	0.835017i
$268$		0			0
$269$	4.65173	+	23.3858i	0.283621	+	1.42586i	0.815362	+	0.578952i	$0.196538\pi$
$269$	4.65173	+	23.3858i	0.283621	+	1.42586i	−0.531741	+	0.846907i	$0.678462\pi$
$270$		0			0
$271$	5.40955	+	5.40955i	0.328607	+	0.328607i	0.852057	−	0.523450i	$-0.175355\pi$
$271$	5.40955	+	5.40955i	0.328607	+	0.328607i	−0.523450	+	0.852057i	$0.675355\pi$
$272$		0			0
$273$	24.1013	−	24.1013i	1.45868	−	1.45868i
$274$		0			0
$275$	−6.60887	+	1.31458i	−0.398530	+	0.0792725i
$276$		0			0
$277$	−10.2748	−	15.3773i	−0.617351	−	0.923931i	−1.00000		3.72366e-5i	$-0.999988\pi$
$277$	−10.2748	−	15.3773i	−0.617351	−	0.923931i	0.382649	−	0.923894i	$-0.375012\pi$
$278$		0			0
$279$	−17.2883	+	7.16105i	−1.03502	+	0.428721i
$280$		0			0
$281$	22.5624	+	9.34566i	1.34596	+	0.557515i	0.935165	−	0.354212i	$-0.115251\pi$
$281$	22.5624	+	9.34566i	1.34596	+	0.557515i	0.410796	+	0.911727i	$0.365251\pi$
$282$		0			0
$283$	30.7342	+	6.11341i	1.82696	+	0.363405i	0.984504	−	0.175362i	$-0.0561095\pi$
$283$	30.7342	+	6.11341i	1.82696	+	0.363405i	0.842455	+	0.538767i	$0.181110\pi$
$284$		0			0
$285$	−0.195273	−	0.130477i	−0.0115670	−	0.00772882i
$286$		0			0
$287$		−	1.27011i		−	0.0749720i
$288$		0			0
$289$			12.8932i			0.758421i
$290$		0			0
$291$	−30.4597	−	20.3525i	−1.78558	−	1.19308i
$292$		0			0
$293$	11.5609	+	2.29960i	0.675394	+	0.134344i	0.520858	−	0.853643i	$-0.325612\pi$
$293$	11.5609	+	2.29960i	0.675394	+	0.134344i	0.154535	+	0.987987i	$0.450612\pi$
$294$		0			0
$295$	−4.51781	−	1.87134i	−0.263037	−	0.108954i
$296$		0			0
$297$	19.4385	−	8.05170i	1.12794	−	0.467207i
$298$		0			0
$299$	−10.9556	−	16.3962i	−0.633577	−	0.948215i
$300$		0			0
$301$	17.2608	−	3.43339i	0.994897	−	0.197897i
$302$		0			0
$303$	−26.3031	+	26.3031i	−1.51108	+	1.51108i
$304$		0			0
$305$	3.66024	+	3.66024i	0.209585	+	0.209585i
$306$		0			0
$307$	3.01807	+	15.1728i	0.172250	+	0.865960i	0.966164	+	0.257929i	$0.0830402\pi$
$307$	3.01807	+	15.1728i	0.172250	+	0.865960i	−0.793914	+	0.608031i	$0.791960\pi$
$308$		0			0
$309$	−35.6658	+	23.8311i	−2.02895	+	1.35570i
$310$		0			0
$311$	11.7272	+	28.3120i	0.664989	+	1.60543i	0.789884	+	0.613256i	$0.210141\pi$
$311$	11.7272	+	28.3120i	0.664989	+	1.60543i	−0.124895	+	0.992170i	$0.539859\pi$
$312$		0			0
$313$	−6.18242	+	14.9257i	−0.349451	+	0.843649i	0.647234	+	0.762291i	$0.275926\pi$
$313$	−6.18242	+	14.9257i	−0.349451	+	0.843649i	−0.996685	+	0.0813577i	$0.974074\pi$
$314$		0			0
$315$	2.22988	−	11.2104i	0.125640	−	0.631633i
$316$		0			0
$317$	15.9809	−	23.9172i	0.897579	−	1.34332i	−0.0413265	−	0.999146i	$-0.513158\pi$
$317$	15.9809	−	23.9172i	0.897579	−	1.34332i	0.938905	−	0.344176i	$-0.111842\pi$
$318$		0			0
$319$	1.94475			0.108885
$320$		0			0
$321$	−30.3007			−1.69122
$322$		0			0
$323$	−0.101414	+	0.151776i	−0.00564281	+	0.00844506i
$324$		0			0
$325$	−4.64824	+	23.3683i	−0.257838	+	1.29624i
$326$		0			0
$327$	20.9785	−	50.6466i	1.16011	−	2.80076i
$328$		0			0
$329$	−4.05661	−	9.79352i	−0.223648	−	0.539934i
$330$		0			0
$331$	−17.2884	+	11.5517i	−0.950256	+	0.634941i	−0.931057	−	0.364875i	$-0.881112\pi$
$331$	−17.2884	+	11.5517i	−0.950256	+	0.634941i	−0.0191998	+	0.999816i	$0.506112\pi$
$332$		0			0
$333$	−2.30993	−	11.6128i	−0.126584	−	0.636379i
$334$		0			0
$335$	−3.27207	−	3.27207i	−0.178772	−	0.178772i
$336$		0			0
$337$	−0.552793	+	0.552793i	−0.0301125	+	0.0301125i	−0.722003	−	0.691890i	$-0.756778\pi$
$337$	−0.552793	+	0.552793i	−0.0301125	+	0.0301125i	0.691890	+	0.722003i	$0.256778\pi$
$338$		0			0
$339$	−44.2828	+	8.80840i	−2.40511	+	0.478407i
$340$		0			0
$341$	2.23414	+	3.34362i	0.120985	+	0.181067i
$342$		0			0
$343$	18.3444	−	7.59848i	0.990502	−	0.410280i
$344$		0			0
$345$	−8.64375	−	3.58036i	−0.465364	−	0.192760i
$346$		0			0
$347$	−20.3020	−	4.03831i	−1.08987	−	0.216788i	−0.382726	−	0.923862i	$-0.625015\pi$
$347$	−20.3020	−	4.03831i	−1.08987	−	0.216788i	−0.707140	+	0.707074i	$0.750015\pi$
$348$		0			0
$349$	−24.9728	−	16.6863i	−1.33676	−	0.893195i	−0.337913	−	0.941177i	$-0.609721\pi$
$349$	−24.9728	−	16.6863i	−1.33676	−	0.893195i	−0.998848	+	0.0479825i	$0.984721\pi$
$350$		0			0
$351$		−	74.3958i		−	3.97095i
$352$		0			0
$353$			14.1087i			0.750928i	0.926837	+	0.375464i	$0.122517\pi$
$353$			14.1087i			0.750928i	−0.926837	+	0.375464i	$0.877483\pi$
$354$		0			0
$355$	−8.88008	−	5.93348i	−0.471306	−	0.314916i
$356$		0			0
$357$	−12.3277	−	2.45212i	−0.652449	−	0.129780i
$358$		0			0
$359$	21.9299	+	9.08367i	1.15742	+	0.479418i	0.877014	−	0.480465i	$-0.159532\pi$
$359$	21.9299	+	9.08367i	1.15742	+	0.479418i	0.280403	+	0.959882i	$0.409532\pi$
$360$		0			0
$361$	−17.5462	+	7.26788i	−0.923485	+	0.382520i
$362$		0			0
$363$	15.2559	+	22.8321i	0.800728	+	1.19837i
$364$		0			0
$365$	3.66412	−	0.728839i	0.191789	−	0.0381492i
$366$		0			0
$367$	−11.6037	+	11.6037i	−0.605711	+	0.605711i	−0.941822	−	0.336111i	$-0.890888\pi$
$367$	−11.6037	+	11.6037i	−0.605711	+	0.605711i	0.336111	+	0.941822i	$0.390888\pi$
$368$		0			0
$369$	−3.34984	−	3.34984i	−0.174386	−	0.174386i
$370$		0			0
$371$	3.96196	+	19.9181i	0.205695	+	1.03410i
$372$		0			0
$373$	12.5475	−	8.38398i	0.649685	−	0.434106i	−0.186573	−	0.982441i	$-0.559738\pi$
$373$	12.5475	−	8.38398i	0.649685	−	0.434106i	0.836259	+	0.548335i	$0.184738\pi$
$374$		0			0
$375$	9.31485	+	22.4880i	0.481017	+	1.16128i
$376$		0			0
$377$	2.63150	−	6.35301i	0.135529	−	0.327197i
$378$		0			0
$379$	0.563697	−	2.83390i	0.0289552	−	0.145567i	−0.963603	−	0.267336i	$-0.913857\pi$
$379$	0.563697	−	2.83390i	0.0289552	−	0.145567i	0.992559	+	0.121769i	$0.0388566\pi$
$380$		0			0
$381$	16.0162	−	23.9700i	0.820537	−	1.22802i
$382$		0			0
$383$	34.7104			1.77362			0.886808	−	0.462137i	$-0.152917\pi$
$383$	34.7104			1.77362			0.886808	+	0.462137i	$0.152917\pi$
$384$		0			0
$385$	−2.45629			−0.125184
$386$		0			0
$387$	36.4691	−	54.5799i	1.85383	−	2.77445i
$388$		0			0
$389$	6.28614	−	31.6026i	0.318720	−	1.60231i	−0.406403	−	0.913694i	$-0.633217\pi$
$389$	6.28614	−	31.6026i	0.318720	−	1.60231i	0.725123	−	0.688619i	$-0.241783\pi$
$390$		0			0
$391$	−2.78283	+	6.71836i	−0.140734	+	0.339762i
$392$		0			0
$393$	10.5253	+	25.4103i	0.530930	+	1.28178i
$394$		0			0
$395$	7.15026	−	4.77765i	0.359769	−	0.240390i
$396$		0			0
$397$	−0.587551	−	2.95382i	−0.0294883	−	0.148248i	0.963236	−	0.268656i	$-0.0865796\pi$
$397$	−0.587551	−	2.95382i	−0.0294883	−	0.148248i	−0.992724	+	0.120408i	$0.961580\pi$
$398$		0			0
$399$	0.395040	+	0.395040i	0.0197767	+	0.0197767i
$400$		0			0
$401$	14.8685	−	14.8685i	0.742498	−	0.742498i	−0.230560	−	0.973058i	$-0.574056\pi$
$401$	14.8685	−	14.8685i	0.742498	−	0.742498i	0.973058	+	0.230560i	$0.0740558\pi$
$402$		0			0
$403$	13.9459	−	2.77400i	0.694693	−	0.138183i
$404$		0			0
$405$	−9.78490	−	14.6441i	−0.486215	−	0.727673i
$406$		0			0
$407$	−2.35079	+	0.973727i	−0.116524	+	0.0482659i
$408$		0			0
$409$	14.6721	+	6.07739i	0.725490	+	0.300508i	0.714697	−	0.699434i	$-0.246565\pi$
$409$	14.6721	+	6.07739i	0.725490	+	0.300508i	0.0107925	+	0.999942i	$0.496565\pi$
$410$		0			0
$411$	9.53514	+	1.89666i	0.470334	+	0.0935552i
$412$		0			0
$413$	9.67206	+	6.46266i	0.475931	+	0.318007i
$414$		0			0
$415$			2.20486i			0.108232i
$416$		0			0
$417$			26.3567i			1.29069i
$418$		0			0
$419$	21.4066	+	14.3034i	1.04578	+	0.698768i	0.954850	−	0.297090i	$-0.0960160\pi$
$419$	21.4066	+	14.3034i	1.04578	+	0.698768i	0.0909301	+	0.995857i	$0.471016\pi$
$420$		0			0
$421$	11.3448	+	2.25662i	0.552911	+	0.109981i	0.463635	−	0.886026i	$-0.346545\pi$
$421$	11.3448	+	2.25662i	0.552911	+	0.109981i	0.0892757	+	0.996007i	$0.471545\pi$
$422$		0			0
$423$	−36.5290	−	15.1308i	−1.77610	−	0.735686i
$424$		0			0
$425$	8.11746	−	3.36236i	0.393755	−	0.163099i
$426$		0			0
$427$	−6.84106	−	10.2384i	−0.331062	−	0.495469i
$428$		0			0
$429$	−26.7955	+	5.32996i	−1.29370	+	0.257333i
$430$		0			0
$431$	16.7738	−	16.7738i	0.807965	−	0.807965i	−0.176361	−	0.984326i	$-0.556433\pi$
$431$	16.7738	−	16.7738i	0.807965	−	0.807965i	0.984326	+	0.176361i	$0.0564326\pi$
$432$		0			0
$433$	14.5447	+	14.5447i	0.698975	+	0.698975i	0.964189	−	0.265215i	$-0.0854428\pi$
$433$	14.5447	+	14.5447i	0.698975	+	0.698975i	−0.265215	+	0.964189i	$0.585443\pi$
$434$		0			0
$435$	−0.636489	−	3.19985i	−0.0305173	−	0.153421i
$436$		0			0
$437$	0.268747	−	0.179571i	0.0128559	−	0.00859004i
$438$		0			0
$439$	−5.28898	−	12.7687i	−0.252429	−	0.609418i	0.745970	−	0.665980i	$-0.231986\pi$
$439$	−5.28898	−	12.7687i	−0.252429	−	0.609418i	−0.998399	+	0.0565614i	$0.981986\pi$
$440$		0			0
$441$	8.96831	−	21.6514i	0.427062	−	1.03102i
$442$		0			0
$443$	2.91450	−	14.6522i	0.138472	−	0.696147i	−0.847707	−	0.530465i	$-0.822017\pi$
$443$	2.91450	−	14.6522i	0.138472	−	0.696147i	0.986179	−	0.165682i	$-0.0529826\pi$
$444$		0			0
$445$	−3.47677	+	5.20336i	−0.164815	+	0.246663i
$446$		0			0
$447$	−48.4223			−2.29030
$448$		0			0
$449$	−32.7646			−1.54626			−0.773130	−	0.634248i	$-0.781310\pi$
$449$	−32.7646			−1.54626			−0.773130	+	0.634248i	$0.781310\pi$
$450$		0			0
$451$	−0.565604	+	0.846486i	−0.0266332	+	0.0398595i
$452$		0			0
$453$	10.2495	−	51.5275i	0.481562	−	2.42097i
$454$		0			0
$455$	−3.32369	+	8.02409i	−0.155817	+	0.376175i
$456$		0			0
$457$	−10.4684	−	25.2729i	−0.489691	−	1.18222i	−0.954876	−	0.297005i	$-0.904012\pi$
$457$	−10.4684	−	25.2729i	−0.489691	−	1.18222i	0.465185	−	0.885213i	$-0.345988\pi$
$458$		0			0
$459$	−22.8111	+	15.2419i	−1.06473	+	0.711431i
$460$		0			0
$461$	1.87909	+	9.44683i	0.0875181	+	0.439983i	0.999554	+	0.0298721i	$0.00951000\pi$
$461$	1.87909	+	9.44683i	0.0875181	+	0.439983i	−0.912036	+	0.410111i	$0.865490\pi$
$462$		0			0
$463$	2.57440	+	2.57440i	0.119643	+	0.119643i	0.764393	−	0.644751i	$-0.223039\pi$
$463$	2.57440	+	2.57440i	0.119643	+	0.119643i	−0.644751	+	0.764393i	$0.723039\pi$
$464$		0			0
$465$	4.77032	−	4.77032i	0.221218	−	0.221218i
$466$		0			0
$467$	29.4251	−	5.85303i	1.36163	−	0.270846i	0.540386	−	0.841417i	$-0.318278\pi$
$467$	29.4251	−	5.85303i	1.36163	−	0.270846i	0.821248	+	0.570572i	$0.193278\pi$
$468$		0			0
$469$	6.11557	+	9.15259i	0.282391	+	0.422627i
$470$		0			0
$471$	−13.0062	+	5.38735i	−0.599294	+	0.248236i
$472$		0			0
$473$	−13.0327	−	5.39834i	−0.599246	−	0.248216i
$474$		0			0
$475$	−0.383026	−	0.0761886i	−0.0175744	−	0.00349577i
$476$		0			0
$477$	62.9825	+	42.0836i	2.88377	+	1.92687i
$478$		0			0
$479$			13.1017i			0.598630i	0.954154	+	0.299315i	$0.0967582\pi$
$479$			13.1017i			0.598630i	−0.954154	+	0.299315i	$0.903242\pi$
$480$		0			0
$481$			8.99701i			0.410228i
$482$		0			0
$483$	18.5052	+	12.3647i	0.842014	+	0.562616i
$484$		0			0
$485$	9.15542	+	1.82113i	0.415726	+	0.0826931i
$486$		0			0
$487$	−8.42271	−	3.48880i	−0.381670	−	0.158093i	0.183596	−	0.983002i	$-0.441226\pi$
$487$	−8.42271	−	3.48880i	−0.381670	−	0.158093i	−0.565265	+	0.824909i	$0.691226\pi$
$488$		0			0
$489$	−13.8587	+	5.74045i	−0.626711	+	0.259592i
$490$		0			0
$491$	6.91581	+	10.3502i	0.312106	+	0.467100i	0.954048	−	0.299654i	$-0.0968711\pi$
$491$	6.91581	+	10.3502i	0.312106	+	0.467100i	−0.641942	+	0.766753i	$0.721871\pi$
$492$		0			0
$493$	−2.48708	+	0.494711i	−0.112013	+	0.0222807i
$494$		0			0
$495$	−6.47835	+	6.47835i	−0.291180	+	0.291180i
$496$		0			0
$497$	17.9645	+	17.9645i	0.805818	+	0.805818i
$498$		0			0
$499$	0.940281	+	4.72711i	0.0420927	+	0.211615i	0.996108	−	0.0881445i	$-0.0280937\pi$
$499$	0.940281	+	4.72711i	0.0420927	+	0.211615i	−0.954015	+	0.299759i	$0.903094\pi$
$500$		0			0
$501$	−27.3913	+	18.3023i	−1.22375	+	0.817685i
$502$		0			0
$503$	−10.6536	−	25.7202i	−0.475022	−	1.14680i	−0.961916	−	0.273344i	$-0.911870\pi$
$503$	−10.6536	−	25.7202i	−0.475022	−	1.14680i	0.486894	−	0.873461i	$-0.338130\pi$
$504$		0			0
$505$	3.62734	−	8.75716i	0.161414	−	0.389689i
$506$		0			0
$507$	−10.7336	+	53.9613i	−0.476694	+	2.39650i
$508$		0			0
$509$	−13.0686	+	19.5585i	−0.579256	+	0.866917i	−0.999174	−	0.0406446i	$-0.987059\pi$
$509$	−13.0686	+	19.5585i	−0.579256	+	0.866917i	0.419918	+	0.907562i	$0.362059\pi$
$510$		0			0
$511$	−8.88701			−0.393138
$512$		0			0
$513$	1.21941			0.0538382
$514$		0			0
$515$	6.07253	−	9.08818i	0.267588	−	0.400473i
$516$		0			0
$517$	−1.65765	+	8.33356i	−0.0729033	+	0.366510i
$518$		0			0
$519$	−12.7461	+	30.7718i	−0.559491	+	1.35073i
$520$		0			0
$521$	7.67162	+	18.5209i	0.336100	+	0.811417i	0.998083	+	0.0618976i	$0.0197152\pi$
$521$	7.67162	+	18.5209i	0.336100	+	0.811417i	−0.661983	+	0.749519i	$0.730285\pi$
$522$		0			0
$523$	−23.7322	+	15.8574i	−1.03774	+	0.693394i	−0.952988	−	0.303008i	$-0.902009\pi$
$523$	−23.7322	+	15.8574i	−1.03774	+	0.693394i	−0.0847500	+	0.996402i	$0.527009\pi$
$524$		0			0
$525$	−5.24613	−	26.3741i	−0.228960	−	1.15106i
$526$		0			0
$527$	−3.70773	−	3.70773i	−0.161511	−	0.161511i
$528$		0			0
$529$	−7.15862	+	7.15862i	−0.311244	+	0.311244i
$530$		0			0
$531$	42.5545	−	8.46462i	1.84671	−	0.367333i
$532$		0			0
$533$	1.99992	+	2.99309i	0.0866261	+	0.129645i
$534$		0			0
$535$	7.13335	−	2.95473i	0.308402	−	0.127744i
$536$		0			0
$537$	−70.0219	−	29.0040i	−3.02167	−	1.25161i
$538$		0			0
$539$	−4.93945	−	0.982518i	−0.212757	−	0.0423201i
$540$		0			0
$541$	9.15217	+	6.11529i	0.393483	+	0.262917i	0.736535	−	0.676400i	$-0.236461\pi$
$541$	9.15217	+	6.11529i	0.393483	+	0.262917i	−0.343052	+	0.939316i	$0.611461\pi$
$542$		0			0
$543$			26.3586i			1.13116i
$544$		0			0
$545$			13.9688i			0.598359i
$546$		0			0
$547$	−22.1909	−	14.8275i	−0.948813	−	0.633976i	−0.0181423	−	0.999835i	$-0.505775\pi$
$547$	−22.1909	−	14.8275i	−0.948813	−	0.633976i	−0.930670	+	0.365859i	$0.880775\pi$
$548$		0			0
$549$	−45.0461	−	8.96023i	−1.92252	−	0.382413i
$550$		0			0
$551$	0.104131	+	0.0431326i	0.00443614	+	0.00183751i
$552$		0			0
$553$	−18.8995	+	7.82843i	−0.803689	+	0.332899i
$554$		0			0
$555$	2.37152	+	3.54924i	0.100666	+	0.150657i
$556$		0			0
$557$	−3.07874	+	0.612399i	−0.130450	+	0.0259482i	−0.259884	−	0.965640i	$-0.583684\pi$
$557$	−3.07874	+	0.612399i	−0.130450	+	0.0259482i	0.129433	+	0.991588i	$0.458684\pi$
$558$		0			0
$559$	−35.2700	+	35.2700i	−1.49176	+	1.49176i
$560$		0			0
$561$	7.12402	+	7.12402i	0.300776	+	0.300776i
$562$		0			0
$563$	−3.12631	−	15.7170i	−0.131758	−	0.662394i	−0.989052	−	0.147566i	$-0.952856\pi$
$563$	−3.12631	−	15.7170i	−0.131758	−	0.662394i	0.857294	−	0.514827i	$-0.172144\pi$
$564$		0			0
$565$	9.56607	−	6.39184i	0.402447	−	0.268907i
$566$		0			0
$567$	16.0331	+	38.7073i	0.673326	+	1.62555i
$568$		0			0
$569$	9.52243	−	22.9892i	0.399201	−	0.963756i	−0.588655	−	0.808384i	$-0.700342\pi$
$569$	9.52243	−	22.9892i	0.399201	−	0.963756i	0.987856	−	0.155372i	$-0.0496576\pi$
$570$		0			0
$571$	1.30200	−	6.54559i	0.0544870	−	0.273924i	−0.943932	−	0.330141i	$-0.892904\pi$
$571$	1.30200	−	6.54559i	0.0544870	−	0.273924i	0.998419	+	0.0562165i	$0.0179037\pi$
$572$		0			0
$573$	3.82531	−	5.72498i	0.159805	−	0.239164i
$574$		0			0
$575$	−15.5577			−0.648800
$576$		0			0
$577$	41.6755			1.73497			0.867487	−	0.497460i	$-0.165734\pi$
$577$	41.6755			1.73497			0.867487	+	0.497460i	$0.165734\pi$
$578$		0			0
$579$	−9.83199	+	14.7146i	−0.408603	+	0.611518i
$580$		0			0
$581$	1.02324	−	5.14417i	0.0424511	−	0.213416i
$582$		0			0
$583$	6.22942	−	15.0391i	0.257996	−	0.622858i
$584$		0			0
$585$	12.3971	+	29.9292i	0.512556	+	1.23742i
$586$		0			0
$587$	−8.51613	+	5.69029i	−0.351498	+	0.234864i	−0.718767	−	0.695251i	$-0.755293\pi$
$587$	−8.51613	+	5.69029i	−0.351498	+	0.234864i	0.367268	+	0.930115i	$0.380293\pi$
$588$		0			0
$589$	0.0454683	+	0.228584i	0.00187349	+	0.00941865i
$590$		0			0
$591$	−33.2477	−	33.2477i	−1.36763	−	1.36763i
$592$		0			0
$593$	−17.7593	+	17.7593i	−0.729285	+	0.729285i	−0.970477	−	0.241192i	$-0.922462\pi$
$593$	−17.7593	+	17.7593i	−0.729285	+	0.729285i	0.241192	+	0.970477i	$0.422462\pi$
$594$		0			0
$595$	3.14128	−	0.624839i	0.128780	−	0.0256159i
$596$		0			0
$597$	2.94219	+	4.40329i	0.120416	+	0.180215i
$598$		0			0
$599$	23.1403	−	9.58504i	0.945488	−	0.391634i	0.143955	−	0.989584i	$-0.454018\pi$
$599$	23.1403	−	9.58504i	0.945488	−	0.391634i	0.801533	+	0.597950i	$0.204018\pi$
$600$		0			0
$601$	10.7219	+	4.44117i	0.437356	+	0.181159i	0.590487	−	0.807047i	$-0.298936\pi$
$601$	10.7219	+	4.44117i	0.437356	+	0.181159i	−0.153131	+	0.988206i	$0.548936\pi$
$602$		0			0
$603$	40.2690	+	8.01000i	1.63988	+	0.326192i
$604$		0			0
$605$	−5.81797	−	3.88744i	−0.236534	−	0.158047i
$606$		0			0
$607$		−	23.5570i		−	0.956147i	−0.878320	−	0.478074i	$-0.841335\pi$
$607$		−	23.5570i		−	0.956147i	0.878320	−	0.478074i	$-0.158665\pi$
$608$		0			0
$609$			7.76095i			0.314490i
$610$		0			0
$611$	24.9806	+	16.6915i	1.01061	+	0.675267i
$612$		0			0
$613$	−7.55995	−	1.50377i	−0.305343	−	0.0607366i	0.0400405	−	0.999198i	$-0.487251\pi$
$613$	−7.55995	−	1.50377i	−0.305343	−	0.0607366i	−0.345384	+	0.938461i	$0.612251\pi$
$614$		0			0
$615$	1.57790	+	0.653588i	0.0636271	+	0.0263552i
$616$		0			0
$617$	41.1541	−	17.0466i	1.65680	−	0.686270i	0.658975	−	0.752165i	$-0.270990\pi$
$617$	41.1541	−	17.0466i	1.65680	−	0.686270i	0.997827	+	0.0658956i	$0.0209904\pi$
$618$		0			0
$619$	−25.0137	−	37.4356i	−1.00538	−	1.50466i	−0.856723	−	0.515777i	$-0.827503\pi$
$619$	−25.0137	−	37.4356i	−1.00538	−	1.50466i	−0.148662	−	0.988888i	$-0.547497\pi$
$620$		0			0
$621$	47.6446	−	9.47710i	1.91191	−	0.380303i
$622$		0			0
$623$	10.5265	−	10.5265i	0.421734	−	0.421734i
$624$		0			0
$625$	10.9429	+	10.9429i	0.437718	+	0.437718i
$626$		0			0
$627$	−0.0873625	−	0.439201i	−0.00348892	−	0.0175400i
$628$		0			0
$629$	2.75865	−	1.84327i	0.109994	−	0.0734960i
$630$		0			0
$631$	14.4914	+	34.9853i	0.576893	+	1.39274i	0.895587	+	0.444886i	$0.146756\pi$
$631$	14.4914	+	34.9853i	0.576893	+	1.39274i	−0.318694	+	0.947858i	$0.603244\pi$
$632$		0			0
$633$	−10.0576	+	24.2813i	−0.399756	+	0.965095i
$634$		0			0
$635$	−1.43312	+	7.20479i	−0.0568717	+	0.285913i
$636$		0			0
$637$	−9.89337	+	14.8065i	−0.391989	+	0.586654i
$638$		0			0
$639$	94.7609			3.74868
$640$		0			0
$641$	−7.36049			−0.290722			−0.145361	−	0.989379i	$-0.546434\pi$
$641$	−7.36049			−0.290722			−0.145361	+	0.989379i	$0.546434\pi$
$642$		0			0
$643$	−5.65643	+	8.46545i	−0.223068	+	0.333845i	−0.926076	−	0.377337i	$-0.876840\pi$
$643$	−5.65643	+	8.46545i	−0.223068	+	0.333845i	0.703008	+	0.711182i	$0.251840\pi$
$644$		0			0
$645$	−4.61686	+	23.2105i	−0.181789	+	0.913914i
$646$		0			0
$647$	15.0418	−	36.3142i	0.591356	−	1.42766i	−0.290838	−	0.956772i	$-0.593934\pi$
$647$	15.0418	−	36.3142i	0.591356	−	1.42766i	0.882194	−	0.470886i	$-0.156066\pi$
$648$		0			0
$649$	−3.56817	−	8.61432i	−0.140063	−	0.338142i
$650$		0			0
$651$	−13.3435	+	8.91581i	−0.522971	+	0.349438i
$652$		0			0
$653$	0.411603	+	2.06927i	0.0161073	+	0.0809767i	0.988003	−	0.154436i	$-0.0493559\pi$
$653$	0.411603	+	2.06927i	0.0161073	+	0.0809767i	−0.971896	+	0.235412i	$0.924356\pi$
$654$		0			0
$655$	−4.95569	−	4.95569i	−0.193635	−	0.193635i
$656$		0			0
$657$	−23.4390	+	23.4390i	−0.914444	+	0.914444i
$658$		0			0
$659$	13.9933	−	2.78344i	0.545101	−	0.108427i	0.0851445	−	0.996369i	$-0.472865\pi$
$659$	13.9933	−	2.78344i	0.545101	−	0.108427i	0.459957	+	0.887941i	$0.347865\pi$
$660$		0			0
$661$	−2.17698	−	3.25808i	−0.0846746	−	0.126724i	0.786715	−	0.617317i	$-0.211780\pi$
$661$	−2.17698	−	3.25808i	−0.0846746	−	0.126724i	−0.871389	+	0.490593i	$0.836780\pi$
$662$		0			0
$663$	32.9121	−	13.6326i	1.27820	−	0.529448i
$664$		0			0
$665$	−0.131522	−	0.0544780i	−0.00510019	−	0.00211257i
$666$		0			0
$667$	4.40382	+	0.875975i	0.170517	+	0.0339179i
$668$		0			0
$669$	−4.69686	−	3.13834i	−0.181591	−	0.121335i
$670$		0			0
$671$			9.87001i			0.381027i
$672$		0			0
$673$		−	36.5991i		−	1.41079i	−0.708813	−	0.705397i	$-0.750769\pi$
$673$		−	36.5991i		−	1.41079i	0.708813	−	0.705397i	$-0.249231\pi$
$674$		0			0
$675$	−48.8026	−	32.6089i	−1.87841	−	1.25512i
$676$		0			0
$677$	−16.1895	−	3.22028i	−0.622211	−	0.123766i	−0.126090	−	0.992019i	$-0.540243\pi$
$677$	−16.1895	−	3.22028i	−0.622211	−	0.123766i	−0.496121	+	0.868253i	$0.665243\pi$
$678$		0			0
$679$	−20.5154	−	8.49775i	−0.787308	−	0.326114i
$680$		0			0
$681$	23.3146	−	9.65722i	0.893417	−	0.370066i
$682$		0			0
$683$	−13.9637	−	20.8982i	−0.534307	−	0.799647i	0.461875	−	0.886945i	$-0.347177\pi$
$683$	−13.9637	−	20.8982i	−0.534307	−	0.799647i	−0.996182	+	0.0872981i	$0.972177\pi$
$684$		0			0
$685$	−2.42970	+	0.483297i	−0.0928341	+	0.0184658i
$686$		0			0
$687$	51.5306	−	51.5306i	1.96602	−	1.96602i
$688$		0			0
$689$	−40.6999	−	40.6999i	−1.55054	−	1.55054i
$690$		0			0
$691$	0.174353	+	0.876532i	0.00663270	+	0.0333449i	0.983960	−	0.178390i	$-0.0570888\pi$
$691$	0.174353	+	0.876532i	0.00663270	+	0.0333449i	−0.977327	+	0.211735i	$0.932089\pi$
$692$		0			0
$693$	18.1211	−	12.1082i	0.688365	−	0.459951i
$694$		0			0
$695$	−2.57014	−	6.20486i	−0.0974909	−	0.235364i
$696$		0			0
$697$	0.508002	−	1.22642i	0.0192419	−	0.0464541i
$698$		0			0
$699$	2.67502	−	13.4482i	0.101179	−	0.508659i
$700$		0			0
$701$	−2.15514	+	3.22540i	−0.0813986	+	0.121822i	−0.869935	−	0.493167i	$-0.835839\pi$
$701$	−2.15514	+	3.22540i	−0.0813986	+	0.121822i	0.788536	+	0.614988i	$0.210839\pi$
$702$		0			0
$703$	−0.147468			−0.00556188
$704$		0			0
$705$	14.2544			0.536850
$706$		0			0
$707$	−12.5270	+	18.7480i	−0.471126	+	0.705090i
$708$		0			0
$709$	−2.60789	+	13.1108i	−0.0979414	+	0.492385i	0.900413	+	0.435036i	$0.143265\pi$
$709$	−2.60789	+	13.1108i	−0.0979414	+	0.492385i	−0.998354	+	0.0573482i	$0.981735\pi$
$710$		0			0
$711$	−29.1994	+	70.4936i	−1.09506	+	2.64372i
$712$		0			0
$713$	3.55306	+	8.57784i	0.133063	+	0.321243i
$714$		0			0
$715$	5.78842	−	3.86770i	0.216475	−	0.144644i
$716$		0			0
$717$	−2.62100	−	13.1766i	−0.0978830	−	0.492091i
$718$		0			0
$719$	−5.54087	−	5.54087i	−0.206640	−	0.206640i	0.596198	−	0.802838i	$-0.296677\pi$
$719$	−5.54087	−	5.54087i	−0.206640	−	0.206640i	−0.802838	+	0.596198i	$0.796677\pi$
$720$		0			0
$721$	−18.3855	+	18.3855i	−0.684712	+	0.684712i
$722$		0			0
$723$	−75.3920	+	14.9964i	−2.80386	+	0.557722i
$724$		0			0
$725$	−3.01406	−	4.51086i	−0.111939	−	0.167529i
$726$		0			0
$727$	1.51607	−	0.627975i	0.0562278	−	0.0232903i	−0.354392	−	0.935097i	$-0.615312\pi$
$727$	1.51607	−	0.627975i	0.0562278	−	0.0232903i	0.410620	+	0.911807i	$0.365312\pi$
$728$		0			0
$729$	24.3513	+	10.0867i	0.901901	+	0.373580i
$730$		0			0
$731$	18.0404	+	3.58846i	0.667248	+	0.132724i
$732$		0			0
$733$	−35.6822	−	23.8421i	−1.31795	−	0.880628i	−0.320182	−	0.947356i	$-0.603744\pi$
$733$	−35.6822	−	23.8421i	−1.31795	−	0.880628i	−0.997771	+	0.0667277i	$0.978744\pi$
$734$		0			0
$735$			8.44882i			0.311639i
$736$		0			0
$737$		−	8.82329i		−	0.325010i
$738$		0			0
$739$	−2.79111	−	1.86496i	−0.102673	−	0.0686036i	0.503174	−	0.864185i	$-0.332165\pi$
$739$	−2.79111	−	1.86496i	−0.102673	−	0.0686036i	−0.605847	+	0.795581i	$0.707165\pi$
$740$		0			0
$741$	−1.55297	−	0.308905i	−0.0570498	−	0.0113479i
$742$		0			0
$743$	5.81769	+	2.40977i	0.213430	+	0.0884058i	0.486837	−	0.873493i	$-0.338151\pi$
$743$	5.81769	+	2.40977i	0.213430	+	0.0884058i	−0.273407	+	0.961899i	$0.588151\pi$
$744$		0			0
$745$	11.3995	−	4.72184i	0.417646	−	0.172995i
$746$		0			0
$747$	−10.8687	−	16.2662i	−0.397667	−	0.595150i
$748$		0			0
$749$	−18.0141	+	3.58322i	−0.658220	+	0.130928i
$750$		0			0
$751$	−24.4261	+	24.4261i	−0.891321	+	0.891321i	−0.994648	−	0.103326i	$-0.967051\pi$
$751$	−24.4261	+	24.4261i	−0.891321	+	0.891321i	0.103326	+	0.994648i	$0.467051\pi$
$752$		0			0
$753$	−21.8287	−	21.8287i	−0.795483	−	0.795483i
$754$		0			0
$755$	2.61172	+	13.1300i	0.0950503	+	0.477850i
$756$		0			0
$757$	−14.3344	+	9.57795i	−0.520993	+	0.348116i	−0.788097	−	0.615551i	$-0.788933\pi$
$757$	−14.3344	+	9.57795i	−0.520993	+	0.348116i	0.267104	+	0.963668i	$0.413933\pi$
$758$		0			0
$759$	−6.82683	−	16.4814i	−0.247798	−	0.598238i
$760$		0			0
$761$	14.8711	−	35.9019i	0.539076	−	1.30144i	−0.386293	−	0.922376i	$-0.626245\pi$
$761$	14.8711	−	35.9019i	0.539076	−	1.30144i	0.925369	−	0.379068i	$-0.123755\pi$
$762$		0			0
$763$	6.48269	−	32.5907i	0.234689	−	1.17986i
$764$		0			0
$765$	6.63698	−	9.93294i	0.239961	−	0.359126i
$766$		0			0
$767$	−32.9690			−1.19044
$768$		0			0
$769$	13.8807			0.500550			0.250275	−	0.968175i	$-0.419479\pi$
$769$	13.8807			0.500550			0.250275	+	0.968175i	$0.419479\pi$
$770$		0			0
$771$	−7.21180	+	10.7932i	−0.259727	+	0.388708i
$772$		0			0
$773$	0.0884866	−	0.444852i	0.00318264	−	0.0160002i	−0.979161	−	0.203084i	$-0.934904\pi$
$773$	0.0884866	−	0.444852i	0.00318264	−	0.0160002i	0.982344	+	0.187084i	$0.0599036\pi$
$774$		0			0
$775$	4.29299	−	10.3642i	0.154209	−	0.372293i
$776$		0			0
$777$	−3.88587	−	9.38132i	−0.139405	−	0.336553i
$778$		0			0
$779$	−0.0490593	+	0.0327804i	−0.00175773	+	0.00117448i
$780$		0			0
$781$	−3.97282	−	19.9727i	−0.142159	−	0.714680i
$782$		0			0
$783$	11.9782	+	11.9782i	0.428067	+	0.428067i
$784$		0			0
$785$	2.53656	−	2.53656i	0.0905339	−	0.0905339i
$786$		0			0
$787$	9.18877	−	1.82776i	0.327544	−	0.0651526i	−0.0285792	−	0.999592i	$-0.509098\pi$
$787$	9.18877	−	1.82776i	0.327544	−	0.0651526i	0.356123	+	0.934439i	$0.384098\pi$
$788$		0			0
$789$	38.3912	+	57.4565i	1.36676	+	2.04551i
$790$		0			0
$791$	−25.2849	+	10.4734i	−0.899029	+	0.372390i
$792$		0			0
$793$	32.2428	+	13.3554i	1.14498	+	0.474265i
$794$		0			0
$795$	−26.7838	−	5.32763i	−0.949924	−	0.188952i
$796$		0			0
$797$	14.6345	+	9.77843i	0.518379	+	0.346370i	0.787077	−	0.616855i	$-0.211593\pi$
$797$	14.6345	+	9.77843i	0.518379	+	0.346370i	−0.268698	+	0.963224i	$0.586593\pi$
$798$		0			0
$799$		−	11.0792i		−	0.391954i
$800$		0			0
$801$		−	55.5260i		−	1.96191i
$802$		0			0
$803$	5.92291	+	3.95756i	0.209015	+	0.139659i
$804$		0			0
$805$	−5.56219	−	1.10639i	−0.196041	−	0.0389951i
$806$		0			0
$807$	70.4657	+	29.1879i	2.48051	+	1.02746i
$808$		0			0
$809$	4.53116	−	1.87687i	0.159307	−	0.0659871i	−0.301605	−	0.953433i	$-0.597522\pi$
$809$	4.53116	−	1.87687i	0.159307	−	0.0659871i	0.460912	+	0.887446i	$0.347522\pi$
$810$		0			0
$811$	21.6476	+	32.3980i	0.760151	+	1.13765i	0.986526	+	0.163606i	$0.0523126\pi$
$811$	21.6476	+	32.3980i	0.760151	+	1.13765i	−0.226375	+	0.974040i	$0.572687\pi$
$812$		0			0
$813$	24.0013	−	4.77415i	0.841761	−	0.167437i
$814$		0			0
$815$	2.70282	−	2.70282i	0.0946756	−	0.0946756i
$816$		0			0
$817$	−0.578105	−	0.578105i	−0.0202253	−	0.0202253i
$818$		0			0
$819$	−15.0340	−	75.5811i	−0.525331	−	2.64102i
$820$		0			0
$821$	15.4667	−	10.3345i	0.539792	−	0.360678i	−0.255590	−	0.966785i	$-0.582270\pi$
$821$	15.4667	−	10.3345i	0.539792	−	0.360678i	0.795383	+	0.606107i	$0.207270\pi$
$822$		0			0
$823$	1.39014	+	3.35609i	0.0484571	+	0.116986i	0.946255	−	0.323423i	$-0.104834\pi$
$823$	1.39014	+	3.35609i	0.0484571	+	0.116986i	−0.897797	+	0.440409i	$0.854834\pi$
$824$		0			0
$825$	−8.24852	+	19.9137i	−0.287177	+	0.693306i
$826$		0			0
$827$	−7.68456	+	38.6329i	−0.267218	+	1.34340i	0.581066	+	0.813857i	$0.302636\pi$
$827$	−7.68456	+	38.6329i	−0.267218	+	1.34340i	−0.848284	+	0.529541i	$0.822364\pi$
$828$		0			0
$829$	−6.04482	+	9.04671i	−0.209945	+	0.314205i	−0.921465	−	0.388460i	$-0.873007\pi$
$829$	−6.04482	+	9.04671i	−0.209945	+	0.314205i	0.711520	+	0.702666i	$0.248007\pi$
$830$		0			0
$831$	−59.1584			−2.05218
$832$		0			0
$833$	6.56685			0.227528
$834$		0			0
$835$	4.66370	−	6.97972i	0.161394	−	0.241543i
$836$		0			0
$837$	−6.83362	+	34.3549i	−0.236204	+	1.18748i
$838$		0			0
$839$	−4.57390	+	11.0424i	−0.157909	+	0.381225i	−0.982957	−	0.183837i	$-0.941148\pi$
$839$	−4.57390	+	11.0424i	−0.157909	+	0.381225i	0.825048	+	0.565063i	$0.191148\pi$
$840$		0			0
$841$	−10.4986	−	25.3459i	−0.362022	−	0.873998i
$842$		0			0
$843$	64.9532	−	43.4003i	2.23711	−	1.49479i
$844$		0			0
$845$	−2.73508	−	13.7502i	−0.0940895	−	0.473020i
$846$		0			0
$847$	11.7698	+	11.7698i	0.404416	+	0.404416i
$848$		0			0
$849$	70.8789	−	70.8789i	2.43256	−	2.43256i
$850$		0			0
$851$	−5.76187	+	1.14611i	−0.197514	+	0.0392880i
$852$		0			0
$853$	−15.0788	−	22.5670i	−0.516287	−	0.772678i	0.478120	−	0.878294i	$-0.341318\pi$
$853$	−15.0788	−	22.5670i	−0.516287	−	0.772678i	−0.994407	+	0.105617i	$0.966318\pi$
$854$		0			0
$855$	−0.490565	+	0.203199i	−0.0167770	+	0.00694924i
$856$		0			0
$857$	−36.9477	−	15.3043i	−1.26211	−	0.522783i	−0.351554	−	0.936168i	$-0.614347\pi$
$857$	−36.9477	−	15.3043i	−1.26211	−	0.522783i	−0.910557	+	0.413384i	$0.864347\pi$
$858$		0			0
$859$	4.65397	+	0.925733i	0.158792	+	0.0315856i	0.273846	−	0.961774i	$-0.411704\pi$
$859$	4.65397	+	0.925733i	0.158792	+	0.0315856i	−0.115054	+	0.993359i	$0.536704\pi$
$860$		0			0
$861$	−3.37808	−	2.25716i	−0.115125	−	0.0769239i
$862$		0			0
$863$		−	10.4034i		−	0.354136i	−0.984199	−	0.177068i	$-0.943339\pi$
$863$		−	10.4034i		−	0.354136i	0.984199	−	0.177068i	$-0.0566612\pi$
$864$		0			0
$865$		−	8.48717i		−	0.288572i
$866$		0			0
$867$	34.2917	+	22.9130i	1.16461	+	0.778166i
$868$		0			0
$869$	16.0821	+	3.19892i	0.545547	+	0.108516i
$870$		0			0
$871$	−28.8235	−	11.9391i	−0.976646	−	0.404540i
$872$		0			0
$873$	−76.5206	+	31.6959i	−2.58983	+	1.07274i
$874$		0			0
$875$	8.19710	+	12.2678i	0.277113	+	0.414728i
$876$		0			0
$877$	−40.0008	+	7.95665i	−1.35073	+	0.268677i	−0.816834	−	0.576873i	$-0.804273\pi$
$877$	−40.0008	+	7.95665i	−1.35073	+	0.268677i	−0.533896	+	0.845550i	$0.679273\pi$
$878$		0			0
$879$	26.6616	−	26.6616i	0.899272	−	0.899272i
$880$		0			0
$881$	26.7291	+	26.7291i	0.900526	+	0.900526i	0.995482	−	0.0949554i	$-0.0302708\pi$
$881$	26.7291	+	26.7291i	0.900526	+	0.900526i	−0.0949554	+	0.995482i	$0.530271\pi$
$882$		0			0
$883$	1.51668	+	7.62487i	0.0510404	+	0.256597i	0.997878	−	0.0651152i	$-0.0207415\pi$
$883$	1.51668	+	7.62487i	0.0510404	+	0.256597i	−0.946837	+	0.321713i	$0.895741\pi$
$884$		0			0
$885$	−13.0060	+	8.69032i	−0.437191	+	0.292122i
$886$		0			0
$887$	−7.40725	−	17.8827i	−0.248711	−	0.600442i	0.749384	−	0.662136i	$-0.230350\pi$
$887$	−7.40725	−	17.8827i	−0.248711	−	0.600442i	−0.998095	+	0.0616939i	$0.980350\pi$
$888$		0			0
$889$	6.68724	−	16.1444i	0.224283	−	0.541466i
$890$		0			0
$891$	6.55158	−	32.9370i	0.219486	−	1.10343i
$892$		0			0
$893$	−0.273588	+	0.409453i	−0.00915527	+	0.0137018i
$894$		0			0
$895$	19.3127			0.645554
$896$		0			0
$897$	−63.0783			−2.10612
$898$		0			0
$899$	−1.79875	+	2.69202i	−0.0599916	+	0.0897838i
$900$		0			0
$901$	−4.14091	+	20.8177i	−0.137954	+	0.693540i
$902$		0			0
$903$	21.5432	−	52.0099i	0.716913	−	1.73078i
$904$		0			0
$905$	−2.57032	−	6.20531i	−0.0854404	−	0.206271i
$906$		0			0
$907$	22.2411	−	14.8611i	0.738505	−	0.493453i	−0.128527	−	0.991706i	$-0.541025\pi$
$907$	22.2411	−	14.8611i	0.738505	−	0.493453i	0.867032	+	0.498253i	$0.166025\pi$
$908$		0			0
$909$	16.4075	+	82.4861i	0.544203	+	2.73589i
$910$		0			0
$911$	0.418109	+	0.418109i	0.0138526	+	0.0138526i	0.713999	−	0.700147i	$-0.246882\pi$
$911$	0.418109	+	0.418109i	0.0138526	+	0.0138526i	−0.700147	+	0.713999i	$0.746882\pi$
$912$		0			0
$913$	−2.97276	+	2.97276i	−0.0983839	+	0.0983839i
$914$		0			0
$915$	16.2399	−	3.23031i	0.536873	−	0.106791i
$916$		0			0
$917$	9.26228	+	13.8620i	0.305868	+	0.457763i
$918$		0			0
$919$	12.8012	−	5.30244i	0.422274	−	0.174911i	−0.161419	−	0.986886i	$-0.551607\pi$
$919$	12.8012	−	5.30244i	0.422274	−	0.174911i	0.583693	+	0.811974i	$0.301607\pi$
$920$		0			0
$921$	45.7185	+	18.9372i	1.50648	+	0.624003i
$922$		0			0
$923$	−70.6216	−	14.0475i	−2.32454	−	0.462379i
$924$		0			0
$925$	5.90192	+	3.94353i	0.194054	+	0.129663i
$926$		0			0
$927$			96.9816i			3.18530i
$928$		0			0
$929$			26.2072i			0.859830i	0.902869	+	0.429915i	$0.141456\pi$
$929$			26.2072i			0.859830i	−0.902869	+	0.429915i	$0.858544\pi$
$930$		0			0
$931$	−0.242690	−	0.162161i	−0.00795386	−	0.00531460i
$932$		0			0
$933$	96.1419	+	19.1238i	3.14755	+	0.626086i
$934$		0			0
$935$	−2.37182	−	0.982438i	−0.0775666	−	0.0321292i
$936$		0			0
$937$	15.5675	−	6.44825i	0.508567	−	0.210655i	−0.113620	−	0.993524i	$-0.536245\pi$
$937$	15.5675	−	6.44825i	0.508567	−	0.210655i	0.622186	+	0.782869i	$0.286245\pi$
$938$		0			0
$939$	28.7105	+	42.9683i	0.936933	+	1.40222i
$940$		0			0
$941$	1.05016	−	0.208890i	0.0342342	−	0.00680961i	−0.177944	−	0.984041i	$-0.556944\pi$
$941$	1.05016	−	0.208890i	0.0342342	−	0.00680961i	0.212178	+	0.977231i	$0.431944\pi$
$942$		0			0
$943$	−1.66207	+	1.66207i	−0.0541245	+	0.0541245i
$944$		0			0
$945$	−15.1290	−	15.1290i	−0.492145	−	0.492145i
$946$		0			0
$947$	5.64778	+	28.3933i	0.183528	+	0.922658i	0.957278	+	0.289168i	$0.0933785\pi$
$947$	5.64778	+	28.3933i	0.183528	+	0.922658i	−0.773750	+	0.633491i	$0.781622\pi$
$948$		0			0
$949$	20.9428	−	13.9936i	0.679833	−	0.454250i
$950$		0			0
$951$	−35.2117	−	85.0085i	−1.14182	−	2.75659i
$952$		0			0
$953$	−17.8099	+	42.9968i	−0.576918	+	1.39280i	0.318647	+	0.947873i	$0.396771\pi$
$953$	−17.8099	+	42.9968i	−0.576918	+	1.39280i	−0.895565	+	0.444930i	$0.853229\pi$
$954$		0			0
$955$	−0.342286	+	1.72079i	−0.0110761	+	0.0556834i
$956$		0			0
$957$	3.45610	−	5.17243i	0.111720	−	0.167201i
$958$		0			0
$959$	5.89303			0.190296
$960$		0			0
$961$	24.3052			0.784038
$962$		0			0
$963$	−38.0606	+	56.9618i	−1.22649	+	1.83557i
$964$		0			0
$965$	0.879759	−	4.42285i	0.0283204	−	0.142376i
$966$		0			0
$967$	−4.72582	+	11.4091i	−0.151972	+	0.366893i	−0.981470	−	0.191617i	$-0.938627\pi$
$967$	−4.72582	+	11.4091i	−0.151972	+	0.366893i	0.829498	+	0.558510i	$0.188627\pi$
$968$		0			0
$969$	0.223450	+	0.539457i	0.00717826	+	0.0173298i
$970$		0			0
$971$	11.8130	−	7.89320i	0.379097	−	0.253305i	−0.351393	−	0.936228i	$-0.614292\pi$
$971$	11.8130	−	7.89320i	0.379097	−	0.253305i	0.730490	+	0.682923i	$0.239292\pi$
$972$		0			0
$973$	3.11682	+	15.6693i	0.0999208	+	0.502336i
$974$		0			0
$975$	53.8917	+	53.8917i	1.72592	+	1.72592i
$976$		0			0
$977$	11.6219	−	11.6219i	0.371817	−	0.371817i	−0.496322	−	0.868139i	$-0.665316\pi$
$977$	11.6219	−	11.6219i	0.371817	−	0.371817i	0.868139	+	0.496322i	$0.165316\pi$
$978$		0			0
$979$	−11.7032	+	2.32791i	−0.374035	+	0.0744003i
$980$		0			0
$981$	−68.8586	−	103.054i	−2.19848	−	3.29026i
$982$		0			0
$983$	−52.2673	+	21.6498i	−1.66707	+	0.690522i	−0.998584	−	0.0532035i	$-0.983057\pi$
$983$	−52.2673	+	21.6498i	−1.66707	+	0.690522i	−0.668485	+	0.743726i	$0.733057\pi$
$984$		0			0
$985$	11.0692	+	4.58503i	0.352695	+	0.146091i
$986$		0			0
$987$	−33.2569	−	6.61520i	−1.05858	−	0.210564i
$988$		0			0
$989$	−27.0806	−	18.0947i	−0.861113	−	0.575377i
$990$		0			0
$991$		−	15.7589i		−	0.500597i	−0.968169	−	0.250299i	$-0.919471\pi$
$991$		−	15.7589i		−	0.500597i	0.968169	−	0.250299i	$-0.0805288\pi$
$992$		0			0
$993$			66.5108i			2.11066i
$994$		0			0
$995$	−1.12203	−	0.749715i	−0.0355707	−	0.0237676i
$996$		0			0
$997$	−28.9525	−	5.75900i	−0.916934	−	0.182390i	−0.286003	−	0.958229i	$-0.592327\pi$
$997$	−28.9525	−	5.75900i	−0.916934	−	0.182390i	−0.630931	+	0.775839i	$0.717327\pi$
$998$		0			0
$999$	−20.4766	−	8.48167i	−0.647850	−	0.268348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.i.a.241.7		56
4.3	odd	2		64.2.i.a.37.3	✓	56
8.3	odd	2		512.2.i.b.225.7		56
8.5	even	2		512.2.i.a.225.1		56
12.11	even	2		576.2.bd.a.37.5		56
64.13	even	16		512.2.i.a.289.1		56
64.19	odd	16		64.2.i.a.45.3	yes	56
64.45	even	16	inner	256.2.i.a.17.7		56
64.51	odd	16		512.2.i.b.289.7		56
192.83	even	16		576.2.bd.a.109.5		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.37.3	✓	56	4.3	odd	2
64.2.i.a.45.3	yes	56	64.19	odd	16
256.2.i.a.17.7		56	64.45	even	16	inner
256.2.i.a.241.7		56	1.1	even	1	trivial
512.2.i.a.225.1		56	8.5	even	2
512.2.i.a.289.1		56	64.13	even	16
512.2.i.b.225.7		56	8.3	odd	2
512.2.i.b.289.7		56	64.51	odd	16
576.2.bd.a.37.5		56	12.11	even	2
576.2.bd.a.109.5		56	192.83	even	16

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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.77714 - 2.65968i) q^{3} +(-0.159018 + 0.799435i) q^{5} +(0.742008 - 1.79137i) q^{7} +(-2.76763 - 6.68165i) q^{9} +(-1.29226 + 0.863458i) q^{11} +(1.07211 + 5.38985i) q^{13} +(1.84365 + 1.84365i) q^{15} +(1.43298 - 1.43298i) q^{17} +(-0.0883441 + 0.0175727i) q^{19} +(-3.44581 - 5.15702i) q^{21} +(-3.31519 + 1.37320i) q^{23} +(4.00559 + 1.65917i) q^{25} +(-13.2776 - 2.64108i) q^{27} +(-1.04042 - 0.695186i) q^{29} -2.58743i q^{31} +4.97148i q^{33} +(1.31409 + 0.878046i) q^{35} +(1.60572 + 0.319397i) q^{37} +(16.2406 + 6.72707i) q^{39} +(0.605183 - 0.250675i) q^{41} +(5.04263 + 7.54683i) q^{43} +(5.78164 - 1.15004i) q^{45} +(3.86580 - 3.86580i) q^{47} +(2.29133 + 2.29133i) q^{49} +(-1.26466 - 6.35787i) q^{51} +(-8.70867 + 5.81895i) q^{53} +(-0.484787 - 1.17038i) q^{55} +(-0.110262 + 0.266197i) q^{57} +(-1.17041 + 5.88407i) q^{59} +(3.52821 - 5.28034i) q^{61} -14.0229 q^{63} -4.47932 q^{65} +(-3.15404 + 4.72036i) q^{67} +(-2.23930 + 11.2577i) q^{69} +(-5.01419 + 12.1053i) q^{71} +(-1.75399 - 4.23450i) q^{73} +(11.5314 - 7.70502i) q^{75} +(0.587905 + 2.95560i) q^{77} +(-7.46021 - 7.46021i) q^{79} +(-15.2789 + 15.2789i) q^{81} +(2.65306 - 0.527725i) q^{83} +(0.917704 + 1.37344i) q^{85} +(-3.69795 + 1.53174i) q^{87} +(7.09322 + 2.93811i) q^{89} +(10.4507 + 2.07877i) q^{91} +(-6.88175 - 4.59824i) q^{93} -0.0734197i q^{95} -11.4524i q^{97} +(9.34580 + 6.24466i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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