LMFDB - Embedded newform 1352.2.o.c.361.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1352,2,Mod(361,1352)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1352, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1352.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1352 = 2^{3} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1352.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-2,0,0,0,0,0,-6,0,0,0,0,0,0,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$10.7957743533$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.4
Root			$1.35234 + 0.780776i$ of defining polynomial
Character	$\chi$	$=$	1352.361
Dual form			1352.2.o.c.1161.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.780776 + 1.35234i) q^{3} +0.561553i q^{5} +(1.35234 + 0.780776i) q^{7} +(0.280776 - 0.486319i) q^{9} +(1.35234 - 0.780776i) q^{11} +(-0.759413 + 0.438447i) q^{15} +(-2.50000 + 4.33013i) q^{17} +(-1.35234 - 0.780776i) q^{19} +2.43845i q^{21} +(4.34233 + 7.52113i) q^{23} +4.68466 q^{25} +5.56155 q^{27} +(2.50000 + 4.33013i) q^{29} -8.00000i q^{31} +(2.11176 + 1.21922i) q^{33} +(-0.438447 + 0.759413i) q^{35} +(0.866025 - 0.500000i) q^{37} +(-6.27540 + 3.62311i) q^{41} +(-1.21922 + 2.11176i) q^{43} +(0.273094 + 0.157671i) q^{45} -4.00000i q^{47} +(-2.28078 - 3.95042i) q^{49} -7.80776 q^{51} +8.56155 q^{53} +(0.438447 + 0.759413i) q^{55} -2.43845i q^{57} +(1.35234 + 0.780776i) q^{59} +(-4.62311 + 8.00745i) q^{61} +(0.759413 - 0.438447i) q^{63} +(-11.7446 + 6.78078i) q^{67} +(-6.78078 + 11.7446i) q^{69} +(4.05703 + 2.34233i) q^{71} +13.6847i q^{73} +(3.65767 + 6.33527i) q^{75} +2.43845 q^{77} -4.00000 q^{79} +(3.50000 + 6.06218i) q^{81} -14.2462i q^{83} +(-2.43160 - 1.40388i) q^{85} +(-3.90388 + 6.76172i) q^{87} +(-2.32498 + 1.34233i) q^{89} +(10.8188 - 6.24621i) q^{93} +(0.438447 - 0.759413i) q^{95} +(15.4220 + 8.90388i) q^{97} -0.876894i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 6 q^{9} - 20 q^{17} + 10 q^{23} - 12 q^{25} + 28 q^{27} + 20 q^{29} - 20 q^{35} - 18 q^{43} - 10 q^{49} + 20 q^{51} + 52 q^{53} + 20 q^{55} - 4 q^{61} - 46 q^{69} + 54 q^{75} + 36 q^{77}+ \cdots + 20 q^{95}+O(q^{100}) $ 8 * q - 2 * q^3 - 6 * q^9 - 20 * q^17 + 10 * q^23 - 12 * q^25 + 28 * q^27 + 20 * q^29 - 20 * q^35 - 18 * q^43 - 10 * q^49 + 20 * q^51 + 52 * q^53 + 20 * q^55 - 4 * q^61 - 46 * q^69 + 54 * q^75 + 36 * q^77 - 32 * q^79 + 28 * q^81 + 10 * q^87 + 20 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1352\mathbb{Z}\right)^\times$.

$n$	$677$	$1015$	$1185$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.780776	+	1.35234i	0.450781	+	0.780776i	0.998435	−	0.0559290i	$-0.0178120\pi$
$3$	0.780776	+	1.35234i	0.450781	+	0.780776i	−0.547653	+	0.836705i	$0.684479\pi$
$4$		0			0
$5$			0.561553i			0.251134i	0.992085	+	0.125567i	$0.0400750\pi$
$5$			0.561553i			0.251134i	−0.992085	+	0.125567i	$0.959925\pi$
$6$		0			0
$7$	1.35234	+	0.780776i	0.511138	+	0.295106i	0.733301	−	0.679904i	$-0.237978\pi$
$7$	1.35234	+	0.780776i	0.511138	+	0.295106i	−0.222163	+	0.975009i	$0.571312\pi$
$8$		0			0
$9$	0.280776	−	0.486319i	0.0935921	−	0.162106i
$10$		0			0
$11$	1.35234	−	0.780776i	0.407747	−	0.235413i	−0.282074	−	0.959393i	$-0.591022\pi$
$11$	1.35234	−	0.780776i	0.407747	−	0.235413i	0.689821	+	0.723980i	$0.257689\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	−0.759413	+	0.438447i	−0.196080	+	0.113207i
$16$		0			0
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	0.385499	+	0.922708i	$0.374029\pi$
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	−0.991838	+	0.127502i	$0.959304\pi$
$18$		0			0
$19$	−1.35234	−	0.780776i	−0.310249	−	0.179122i	0.336789	−	0.941580i	$-0.390659\pi$
$19$	−1.35234	−	0.780776i	−0.310249	−	0.179122i	−0.647038	+	0.762458i	$0.723992\pi$
$20$		0			0
$21$			2.43845i			0.532113i
$22$		0			0
$23$	4.34233	+	7.52113i	0.905438	+	1.56827i	0.820328	+	0.571893i	$0.193791\pi$
$23$	4.34233	+	7.52113i	0.905438	+	1.56827i	0.0851104	+	0.996372i	$0.472876\pi$
$24$		0			0
$25$	4.68466			0.936932
$26$		0			0
$27$	5.56155			1.07032
$28$		0			0
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	0.999167	−	0.0408130i	$-0.0129948\pi$
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	−0.534928	+	0.844897i	$0.679661\pi$
$30$		0			0
$31$		−	8.00000i		−	1.43684i	−0.695608	−	0.718421i	$-0.744865\pi$
$31$		−	8.00000i		−	1.43684i	0.695608	−	0.718421i	$-0.255135\pi$
$32$		0			0
$33$	2.11176	+	1.21922i	0.367610	+	0.212240i
$34$		0			0
$35$	−0.438447	+	0.759413i	−0.0741111	+	0.128364i
$36$		0			0
$37$	0.866025	−	0.500000i	0.142374	−	0.0821995i	−0.427121	−	0.904194i	$-0.640472\pi$
$37$	0.866025	−	0.500000i	0.142374	−	0.0821995i	0.569495	+	0.821995i	$0.307139\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−6.27540	+	3.62311i	−0.980053	+	0.565834i	−0.902286	−	0.431138i	$-0.858112\pi$
$41$	−6.27540	+	3.62311i	−0.980053	+	0.565834i	−0.0777671	+	0.996972i	$0.524779\pi$
$42$		0			0
$43$	−1.21922	+	2.11176i	−0.185930	+	0.322040i	−0.943889	−	0.330262i	$-0.892863\pi$
$43$	−1.21922	+	2.11176i	−0.185930	+	0.322040i	0.757960	+	0.652301i	$0.226196\pi$
$44$		0			0
$45$	0.273094	+	0.157671i	0.0407104	+	0.0235042i
$46$		0			0
$47$		−	4.00000i		−	0.583460i	−0.956501	−	0.291730i	$-0.905769\pi$
$47$		−	4.00000i		−	0.583460i	0.956501	−	0.291730i	$-0.0942309\pi$
$48$		0			0
$49$	−2.28078	−	3.95042i	−0.325825	−	0.564346i
$50$		0			0
$51$	−7.80776			−1.09331
$52$		0			0
$53$	8.56155			1.17602			0.588010	−	0.808854i	$-0.299912\pi$
$53$	8.56155			1.17602			0.588010	+	0.808854i	$0.299912\pi$
$54$		0			0
$55$	0.438447	+	0.759413i	0.0591202	+	0.102399i
$56$		0			0
$57$		−	2.43845i		−	0.322980i
$58$		0			0
$59$	1.35234	+	0.780776i	0.176060	+	0.101648i	0.585440	−	0.810716i	$-0.300922\pi$
$59$	1.35234	+	0.780776i	0.176060	+	0.101648i	−0.409380	+	0.912364i	$0.634255\pi$
$60$		0			0
$61$	−4.62311	+	8.00745i	−0.591928	+	1.02525i	0.402045	+	0.915620i	$0.368300\pi$
$61$	−4.62311	+	8.00745i	−0.591928	+	1.02525i	−0.993973	+	0.109629i	$0.965034\pi$
$62$		0			0
$63$	0.759413	−	0.438447i	0.0956770	−	0.0552392i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−11.7446	+	6.78078i	−1.43484	+	0.828404i	−0.997484	−	0.0708863i	$-0.977417\pi$
$67$	−11.7446	+	6.78078i	−1.43484	+	0.828404i	−0.437353	+	0.899290i	$0.644084\pi$
$68$		0			0
$69$	−6.78078	+	11.7446i	−0.816310	+	1.41389i
$70$		0			0
$71$	4.05703	+	2.34233i	0.481481	+	0.277983i	0.721034	−	0.692900i	$-0.243667\pi$
$71$	4.05703	+	2.34233i	0.481481	+	0.277983i	−0.239552	+	0.970883i	$0.577001\pi$
$72$		0			0
$73$			13.6847i			1.60167i	0.598886	+	0.800834i	$0.295610\pi$
$73$			13.6847i			1.60167i	−0.598886	+	0.800834i	$0.704390\pi$
$74$		0			0
$75$	3.65767	+	6.33527i	0.422351	+	0.731534i
$76$		0			0
$77$	2.43845			0.277887
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	3.50000	+	6.06218i	0.388889	+	0.673575i
$82$		0			0
$83$		−	14.2462i		−	1.56372i	−0.623451	−	0.781862i	$-0.714270\pi$
$83$		−	14.2462i		−	1.56372i	0.623451	−	0.781862i	$-0.285730\pi$
$84$		0			0
$85$	−2.43160	−	1.40388i	−0.263744	−	0.152272i
$86$		0			0
$87$	−3.90388	+	6.76172i	−0.418540	+	0.724933i
$88$		0			0
$89$	−2.32498	+	1.34233i	−0.246448	+	0.142287i	−0.618137	−	0.786071i	$-0.712112\pi$
$89$	−2.32498	+	1.34233i	−0.246448	+	0.142287i	0.371689	+	0.928357i	$0.378779\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	10.8188	−	6.24621i	1.12185	−	0.647702i
$94$		0			0
$95$	0.438447	−	0.759413i	0.0449837	−	0.0779141i
$96$		0			0
$97$	15.4220	+	8.90388i	1.56586	+	0.904052i	0.996643	+	0.0818678i	$0.0260885\pi$
$97$	15.4220	+	8.90388i	1.56586	+	0.904052i	0.569221	+	0.822184i	$0.307245\pi$
$98$		0			0
$99$		−	0.876894i		−	0.0881312i
$100$		0			0
$101$	−5.62311	−	9.73950i	−0.559520	−	0.969117i	−0.997536	−	0.0701500i	$-0.977652\pi$
$101$	−5.62311	−	9.73950i	−0.559520	−	0.969117i	0.438017	−	0.898967i	$-0.355681\pi$
$102$		0			0
$103$	2.24621			0.221326			0.110663	−	0.993858i	$-0.464703\pi$
$103$	2.24621			0.221326			0.110663	+	0.993858i	$0.464703\pi$
$104$		0			0
$105$	−1.36932			−0.133632
$106$		0			0
$107$	−4.34233	−	7.52113i	−0.419789	−	0.727096i	0.576129	−	0.817359i	$-0.304563\pi$
$107$	−4.34233	−	7.52113i	−0.419789	−	0.727096i	−0.995918	+	0.0902631i	$0.971229\pi$
$108$		0			0
$109$		−	8.24621i		−	0.789844i	−0.918715	−	0.394922i	$-0.870772\pi$
$109$		−	8.24621i		−	0.789844i	0.918715	−	0.394922i	$-0.129228\pi$
$110$		0			0
$111$	1.35234	+	0.780776i	0.128359	+	0.0741080i
$112$		0			0
$113$	3.62311	−	6.27540i	0.340833	−	0.590340i	−0.643755	−	0.765232i	$-0.722624\pi$
$113$	3.62311	−	6.27540i	0.340833	−	0.590340i	0.984588	+	0.174892i	$0.0559576\pi$
$114$		0			0
$115$	−4.22351	+	2.43845i	−0.393845	+	0.227386i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−6.76172	+	3.90388i	−0.619846	+	0.357868i
$120$		0			0
$121$	−4.28078	+	7.41452i	−0.389161	+	0.674047i
$122$		0			0
$123$	−9.79937	−	5.65767i	−0.883580	−	0.510135i
$124$		0			0
$125$			5.43845i			0.486430i
$126$		0			0
$127$	−3.90388	−	6.76172i	−0.346414	−	0.600006i	0.639196	−	0.769044i	$-0.279267\pi$
$127$	−3.90388	−	6.76172i	−0.346414	−	0.600006i	−0.985610	+	0.169038i	$0.945934\pi$
$128$		0			0
$129$	−3.80776			−0.335255
$130$		0			0
$131$	1.75379			0.153229			0.0766146	−	0.997061i	$-0.475589\pi$
$131$	1.75379			0.153229			0.0766146	+	0.997061i	$0.475589\pi$
$132$		0			0
$133$	−1.21922	−	2.11176i	−0.105720	−	0.183113i
$134$		0			0
$135$			3.12311i			0.268794i
$136$		0			0
$137$	9.95273	+	5.74621i	0.850319	+	0.490932i	0.860759	−	0.509014i	$-0.169990\pi$
$137$	9.95273	+	5.74621i	0.850319	+	0.490932i	−0.0104394	+	0.999946i	$0.503323\pi$
$138$		0			0
$139$	−3.65767	+	6.33527i	−0.310240	+	0.537351i	−0.978414	−	0.206654i	$-0.933743\pi$
$139$	−3.65767	+	6.33527i	−0.310240	+	0.537351i	0.668175	+	0.744005i	$0.267076\pi$
$140$		0			0
$141$	5.40938	−	3.12311i	0.455552	−	0.263013i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−2.43160	+	1.40388i	−0.201933	+	0.116586i
$146$		0			0
$147$	3.56155	−	6.16879i	0.293752	−	0.508793i
$148$		0			0
$149$	2.81130	+	1.62311i	0.230311	+	0.132970i	0.610715	−	0.791850i	$-0.290882\pi$
$149$	2.81130	+	1.62311i	0.230311	+	0.132970i	−0.380405	+	0.924820i	$0.624215\pi$
$150$		0			0
$151$		−	20.4924i		−	1.66765i	−0.552029	−	0.833825i	$-0.686146\pi$
$151$		−	20.4924i		−	1.66765i	0.552029	−	0.833825i	$-0.313854\pi$
$152$		0			0
$153$	1.40388	+	2.43160i	0.113497	+	0.196583i
$154$		0			0
$155$	4.49242			0.360840
$156$		0			0
$157$	2.80776			0.224084			0.112042	−	0.993703i	$-0.464261\pi$
$157$	2.80776			0.224084			0.112042	+	0.993703i	$0.464261\pi$
$158$		0			0
$159$	6.68466	+	11.5782i	0.530128	+	0.918208i
$160$		0			0
$161$			13.5616i			1.06880i
$162$		0			0
$163$	−19.8587	−	11.4654i	−1.55545	−	0.898042i	−0.997682	−	0.0680484i	$-0.978323\pi$
$163$	−19.8587	−	11.4654i	−1.55545	−	0.898042i	−0.557773	−	0.829994i	$-0.688344\pi$
$164$		0			0
$165$	−0.684658	+	1.18586i	−0.0533006	+	0.0923193i
$166$		0			0
$167$	8.28055	−	4.78078i	0.640768	−	0.369948i	−0.144142	−	0.989557i	$-0.546042\pi$
$167$	8.28055	−	4.78078i	0.640768	−	0.369948i	0.784910	+	0.619609i	$0.212709\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	−0.759413	+	0.438447i	−0.0580737	+	0.0335289i
$172$		0			0
$173$	6.46543	−	11.1985i	0.491558	−	0.851403i	−0.508395	−	0.861124i	$-0.669761\pi$
$173$	6.46543	−	11.1985i	0.491558	−	0.851403i	0.999953	+	0.00972081i	$0.00309428\pi$
$174$		0			0
$175$	6.33527	+	3.65767i	0.478902	+	0.276494i
$176$		0			0
$177$			2.43845i			0.183285i
$178$		0			0
$179$	8.34233	+	14.4493i	0.623535	+	1.07999i	0.988822	+	0.149099i	$0.0476374\pi$
$179$	8.34233	+	14.4493i	0.623535	+	1.07999i	−0.365287	+	0.930895i	$0.619029\pi$
$180$		0			0
$181$	−10.8078			−0.803335			−0.401667	−	0.915786i	$-0.631569\pi$
$181$	−10.8078			−0.803335			−0.401667	+	0.915786i	$0.631569\pi$
$182$		0			0
$183$	−14.4384			−1.06732
$184$		0			0
$185$	0.280776	+	0.486319i	0.0206431	+	0.0357549i
$186$		0			0
$187$			7.80776i			0.570960i
$188$		0			0
$189$	7.52113	+	4.34233i	0.547082	+	0.315858i
$190$		0			0
$191$	8.34233	−	14.4493i	0.603630	−	1.04552i	−0.388637	−	0.921391i	$-0.627054\pi$
$191$	8.34233	−	14.4493i	0.603630	−	1.04552i	0.992266	−	0.124126i	$-0.0396128\pi$
$192$		0			0
$193$	−2.59808	+	1.50000i	−0.187014	+	0.107972i	−0.590584	−	0.806976i	$-0.701102\pi$
$193$	−2.59808	+	1.50000i	−0.187014	+	0.107972i	0.403570	+	0.914949i	$0.367769\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	12.7173	−	7.34233i	0.906069	−	0.523119i	0.0269049	−	0.999638i	$-0.491435\pi$
$197$	12.7173	−	7.34233i	0.906069	−	0.523119i	0.879164	+	0.476519i	$0.158102\pi$
$198$		0			0
$199$	6.78078	−	11.7446i	0.480676	−	0.832556i	−0.519078	−	0.854727i	$-0.673724\pi$
$199$	6.78078	−	11.7446i	0.480676	−	0.832556i	0.999754	+	0.0221709i	$0.00705781\pi$
$200$		0			0
$201$	−18.3399	−	10.5885i	−1.29360	−	0.746858i
$202$		0			0
$203$			7.80776i			0.547998i
$204$		0			0
$205$	−2.03457	−	3.52397i	−0.142100	−	0.246125i
$206$		0			0
$207$	4.87689			0.338968
$208$		0			0
$209$	−2.43845			−0.168671
$210$		0			0
$211$	−12.3423	−	21.3775i	−0.849681	−	1.47169i	−0.881493	−	0.472197i	$-0.843461\pi$
$211$	−12.3423	−	21.3775i	−0.849681	−	1.47169i	0.0318122	−	0.999494i	$-0.489872\pi$
$212$		0			0
$213$			7.31534i			0.501239i
$214$		0			0
$215$	−1.18586	−	0.684658i	−0.0808752	−	0.0466933i
$216$		0			0
$217$	6.24621	−	10.8188i	0.424020	−	0.734425i
$218$		0			0
$219$	−18.5064	+	10.6847i	−1.25054	+	0.722002i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	7.52113	−	4.34233i	0.503652	−	0.290784i	−0.226568	−	0.973995i	$-0.572751\pi$
$223$	7.52113	−	4.34233i	0.503652	−	0.290784i	0.730221	+	0.683211i	$0.239417\pi$
$224$		0			0
$225$	1.31534	−	2.27824i	0.0876894	−	0.151883i
$226$		0			0
$227$	−26.0275	−	15.0270i	−1.72751	−	0.997376i	−0.899950	−	0.435994i	$-0.856397\pi$
$227$	−26.0275	−	15.0270i	−1.72751	−	0.997376i	−0.827557	−	0.561382i	$-0.810270\pi$
$228$		0			0
$229$		−	12.2462i		−	0.809252i	−0.914482	−	0.404626i	$-0.867402\pi$
$229$		−	12.2462i		−	0.809252i	0.914482	−	0.404626i	$-0.132598\pi$
$230$		0			0
$231$	1.90388	+	3.29762i	0.125266	+	0.216967i
$232$		0			0
$233$	12.2462			0.802276			0.401138	−	0.916018i	$-0.368615\pi$
$233$	12.2462			0.802276			0.401138	+	0.916018i	$0.368615\pi$
$234$		0			0
$235$	2.24621			0.146527
$236$		0			0
$237$	−3.12311	−	5.40938i	−0.202868	−	0.351377i
$238$		0			0
$239$			18.2462i			1.18025i	0.807312	+	0.590125i	$0.200921\pi$
$239$			18.2462i			1.18025i	−0.807312	+	0.590125i	$0.799079\pi$
$240$		0			0
$241$	6.48863	+	3.74621i	0.417969	+	0.241315i	0.694208	−	0.719774i	$-0.255755\pi$
$241$	6.48863	+	3.74621i	0.417969	+	0.241315i	−0.276239	+	0.961089i	$0.589088\pi$
$242$		0			0
$243$	2.87689	−	4.98293i	0.184553	−	0.319655i
$244$		0			0
$245$	2.21837	−	1.28078i	0.141726	−	0.0818258i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	19.2658	−	11.1231i	1.22092	−	0.704898i
$250$		0			0
$251$	0.534565	−	0.925894i	0.0337415	−	0.0584419i	−0.848662	−	0.528936i	$-0.822591\pi$
$251$	0.534565	−	0.925894i	0.0337415	−	0.0584419i	0.882403	+	0.470494i	$0.155924\pi$
$252$		0			0
$253$	11.7446	+	6.78078i	0.738380	+	0.426304i
$254$		0			0
$255$		−	4.38447i		−	0.274566i
$256$		0			0
$257$	2.62311	+	4.54335i	0.163625	+	0.283407i	0.936166	−	0.351558i	$-0.114348\pi$
$257$	2.62311	+	4.54335i	0.163625	+	0.283407i	−0.772541	+	0.634965i	$0.781015\pi$
$258$		0			0
$259$	1.56155			0.0970302
$260$		0			0
$261$	2.80776			0.173796
$262$		0			0
$263$	5.90388	+	10.2258i	0.364049	+	0.630551i	0.988623	−	0.150414i	$-0.0480607\pi$
$263$	5.90388	+	10.2258i	0.364049	+	0.630551i	−0.624574	+	0.780966i	$0.714727\pi$
$264$		0			0
$265$			4.80776i			0.295339i
$266$		0			0
$267$	−3.63058	−	2.09612i	−0.222188	−	0.128280i
$268$		0			0
$269$	2.90388	−	5.02967i	0.177053	−	0.306664i	−0.763817	−	0.645433i	$-0.776677\pi$
$269$	2.90388	−	5.02967i	0.177053	−	0.306664i	0.940870	+	0.338768i	$0.110010\pi$
$270$		0			0
$271$	8.28055	−	4.78078i	0.503007	−	0.290411i	−0.226947	−	0.973907i	$-0.572874\pi$
$271$	8.28055	−	4.78078i	0.503007	−	0.290411i	0.729955	+	0.683496i	$0.239541\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.33527	−	3.65767i	0.382031	−	0.220566i
$276$		0			0
$277$	5.50000	−	9.52628i	0.330463	−	0.572379i	−0.652140	−	0.758099i	$-0.726128\pi$
$277$	5.50000	−	9.52628i	0.330463	−	0.572379i	0.982603	+	0.185720i	$0.0594618\pi$
$278$		0			0
$279$	−3.89055	−	2.24621i	−0.232921	−	0.134477i
$280$		0			0
$281$		−	2.31534i		−	0.138122i	−0.997612	−	0.0690608i	$-0.978000\pi$
$281$		−	2.31534i		−	0.138122i	0.997612	−	0.0690608i	$-0.0220003\pi$
$282$		0			0
$283$	−12.7808	−	22.1370i	−0.759738	−	1.31591i	−0.942984	−	0.332838i	$-0.891994\pi$
$283$	−12.7808	−	22.1370i	−0.759738	−	1.31591i	0.183246	−	0.983067i	$-0.441340\pi$
$284$		0			0
$285$	1.36932			0.0811113
$286$		0			0
$287$	−11.3153			−0.667923
$288$		0			0
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$		0			0
$291$			27.8078i			1.63012i
$292$		0			0
$293$	−18.6130	−	10.7462i	−1.08738	−	0.627800i	−0.154504	−	0.987992i	$-0.549378\pi$
$293$	−18.6130	−	10.7462i	−1.08738	−	0.627800i	−0.932878	+	0.360192i	$0.882711\pi$
$294$		0			0
$295$	−0.438447	+	0.759413i	−0.0255274	+	0.0442147i
$296$		0			0
$297$	7.52113	−	4.34233i	0.436421	−	0.251967i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−3.29762	+	1.90388i	−0.190072	+	0.109738i
$302$		0			0
$303$	8.78078	−	15.2088i	0.504442	−	0.873720i
$304$		0			0
$305$	−4.49661	−	2.59612i	−0.257475	−	0.148653i
$306$		0			0
$307$			9.75379i			0.556678i	0.960483	+	0.278339i	$0.0897839\pi$
$307$			9.75379i			0.556678i	−0.960483	+	0.278339i	$0.910216\pi$
$308$		0			0
$309$	1.75379	+	3.03765i	0.0997696	+	0.172806i
$310$		0			0
$311$	−2.24621			−0.127371			−0.0636855	−	0.997970i	$-0.520285\pi$
$311$	−2.24621			−0.127371			−0.0636855	+	0.997970i	$0.520285\pi$
$312$		0			0
$313$	−15.7538			−0.890457			−0.445228	−	0.895417i	$-0.646878\pi$
$313$	−15.7538			−0.890457			−0.445228	+	0.895417i	$0.646878\pi$
$314$		0			0
$315$	0.246211	+	0.426450i	0.0138724	+	0.0240278i
$316$		0			0
$317$			20.5616i			1.15485i	0.816443	+	0.577426i	$0.195943\pi$
$317$			20.5616i			1.15485i	−0.816443	+	0.577426i	$0.804057\pi$
$318$		0			0
$319$	6.76172	+	3.90388i	0.378584	+	0.218575i
$320$		0			0
$321$	6.78078	−	11.7446i	0.378466	−	0.655522i
$322$		0			0
$323$	6.76172	−	3.90388i	0.376232	−	0.217218i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	11.1517	−	6.43845i	0.616691	−	0.356047i
$328$		0			0
$329$	3.12311	−	5.40938i	0.172182	−	0.298229i
$330$		0			0
$331$	6.00231	+	3.46543i	0.329917	+	0.190478i	0.655804	−	0.754931i	$-0.272330\pi$
$331$	6.00231	+	3.46543i	0.329917	+	0.190478i	−0.325887	+	0.945409i	$0.605663\pi$
$332$		0			0
$333$		−	0.561553i		−	0.0307729i
$334$		0			0
$335$	−3.80776	−	6.59524i	−0.208040	−	0.360336i
$336$		0			0
$337$	−20.5616			−1.12006			−0.560030	−	0.828473i	$-0.689210\pi$
$337$	−20.5616			−1.12006			−0.560030	+	0.828473i	$0.689210\pi$
$338$		0			0
$339$	11.3153			0.614565
$340$		0			0
$341$	−6.24621	−	10.8188i	−0.338251	−	0.585868i
$342$		0			0
$343$		−	18.0540i		−	0.974823i
$344$		0			0
$345$	−6.59524	−	3.80776i	−0.355076	−	0.205003i
$346$		0			0
$347$	−1.02699	+	1.77879i	−0.0551316	+	0.0954907i	−0.892274	−	0.451494i	$-0.850891\pi$
$347$	−1.02699	+	1.77879i	−0.0551316	+	0.0954907i	0.837142	+	0.546985i	$0.184224\pi$
$348$		0			0
$349$	−14.2361	+	8.21922i	−0.762042	+	0.439965i	−0.830028	−	0.557721i	$-0.811676\pi$
$349$	−14.2361	+	8.21922i	−0.762042	+	0.439965i	0.0679866	+	0.997686i	$0.478342\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−7.79423	+	4.50000i	−0.414845	+	0.239511i	−0.692869	−	0.721063i	$-0.743654\pi$
$353$	−7.79423	+	4.50000i	−0.414845	+	0.239511i	0.278024	+	0.960574i	$0.410320\pi$
$354$		0			0
$355$	−1.31534	+	2.27824i	−0.0698111	+	0.120916i
$356$		0			0
$357$	−10.5588	−	6.09612i	−0.558830	−	0.322641i
$358$		0			0
$359$		−	28.4924i		−	1.50377i	−0.659293	−	0.751886i	$-0.729144\pi$
$359$		−	28.4924i		−	1.50377i	0.659293	−	0.751886i	$-0.270856\pi$
$360$		0			0
$361$	−8.28078	−	14.3427i	−0.435830	−	0.754880i
$362$		0			0
$363$	−13.3693			−0.701707
$364$		0			0
$365$	−7.68466			−0.402233
$366$		0			0
$367$	−6.58854	−	11.4117i	−0.343919	−	0.595685i	0.641238	−	0.767342i	$-0.278421\pi$
$367$	−6.58854	−	11.4117i	−0.343919	−	0.595685i	−0.985157	+	0.171657i	$0.945088\pi$
$368$		0			0
$369$			4.06913i			0.211830i
$370$		0			0
$371$	11.5782	+	6.68466i	0.601109	+	0.347050i
$372$		0			0
$373$	−2.62311	+	4.54335i	−0.135819	+	0.235246i	−0.925910	−	0.377744i	$-0.876700\pi$
$373$	−2.62311	+	4.54335i	−0.135819	+	0.235246i	0.790091	+	0.612990i	$0.210033\pi$
$374$		0			0
$375$	−7.35465	+	4.24621i	−0.379793	+	0.219273i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	2.53821	−	1.46543i	0.130379	−	0.0752743i	−0.433392	−	0.901206i	$-0.642683\pi$
$379$	2.53821	−	1.46543i	0.130379	−	0.0752743i	0.563771	+	0.825931i	$0.309350\pi$
$380$		0			0
$381$	6.09612	−	10.5588i	0.312314	−	0.540943i
$382$		0			0
$383$	25.2681	+	14.5885i	1.29114	+	0.745440i	0.978856	−	0.204550i	$-0.0655729\pi$
$383$	25.2681	+	14.5885i	1.29114	+	0.745440i	0.312283	+	0.949989i	$0.398906\pi$
$384$		0			0
$385$			1.36932i			0.0697869i
$386$		0			0
$387$	0.684658	+	1.18586i	0.0348031	+	0.0602808i
$388$		0			0
$389$	29.6847			1.50507			0.752536	−	0.658551i	$-0.228830\pi$
$389$	29.6847			1.50507			0.752536	+	0.658551i	$0.228830\pi$
$390$		0			0
$391$	−43.4233			−2.19601
$392$		0			0
$393$	1.36932	+	2.37173i	0.0690729	+	0.119638i
$394$		0			0
$395$		−	2.24621i		−	0.113019i
$396$		0			0
$397$	−8.06732	−	4.65767i	−0.404887	−	0.233762i	0.283703	−	0.958912i	$-0.408437\pi$
$397$	−8.06732	−	4.65767i	−0.404887	−	0.233762i	−0.688591	+	0.725150i	$0.741770\pi$
$398$		0			0
$399$	1.90388	−	3.29762i	0.0953133	−	0.165088i
$400$		0			0
$401$	−20.3450	+	11.7462i	−1.01598	+	0.586578i	−0.912938	−	0.408099i	$-0.866192\pi$
$401$	−20.3450	+	11.7462i	−1.01598	+	0.586578i	−0.103045	+	0.994677i	$0.532859\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−3.40423	+	1.96543i	−0.169158	+	0.0976632i
$406$		0			0
$407$	0.780776	−	1.35234i	0.0387016	−	0.0670332i
$408$		0			0
$409$	13.2036	+	7.62311i	0.652876	+	0.376938i	0.789557	−	0.613677i	$-0.210310\pi$
$409$	13.2036	+	7.62311i	0.652876	+	0.376938i	−0.136681	+	0.990615i	$0.543644\pi$
$410$		0			0
$411$			17.9460i			0.885212i
$412$		0			0
$413$	1.21922	+	2.11176i	0.0599941	+	0.103913i
$414$		0			0
$415$	8.00000			0.392705
$416$		0			0
$417$	−11.4233			−0.559401
$418$		0			0
$419$	−7.46543	−	12.9305i	−0.364710	−	0.631697i	0.624019	−	0.781409i	$-0.285499\pi$
$419$	−7.46543	−	12.9305i	−0.364710	−	0.631697i	−0.988730	+	0.149712i	$0.952165\pi$
$420$		0			0
$421$		−	33.6847i		−	1.64169i	−0.571151	−	0.820845i	$-0.693503\pi$
$421$		−	33.6847i		−	1.64169i	0.571151	−	0.820845i	$-0.306497\pi$
$422$		0			0
$423$	−1.94528	−	1.12311i	−0.0945826	−	0.0546073i
$424$		0			0
$425$	−11.7116	+	20.2852i	−0.568098	+	0.983975i
$426$		0			0
$427$	−12.5041	+	7.21922i	−0.605114	+	0.349363i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	26.7869	−	15.4654i	1.29028	−	0.744944i	0.311577	−	0.950221i	$-0.399143\pi$
$431$	26.7869	−	15.4654i	1.29028	−	0.744944i	0.978704	+	0.205277i	$0.0658096\pi$
$432$		0			0
$433$	15.7462	−	27.2732i	0.756715	−	1.31067i	−0.187803	−	0.982207i	$-0.560137\pi$
$433$	15.7462	−	27.2732i	0.756715	−	1.31067i	0.944517	−	0.328461i	$-0.106530\pi$
$434$		0			0
$435$	−3.79706	−	2.19224i	−0.182055	−	0.105110i
$436$		0			0
$437$		−	13.5616i		−	0.648737i
$438$		0			0
$439$	−4.53457	−	7.85410i	−0.216423	−	0.374856i	0.737289	−	0.675578i	$-0.236106\pi$
$439$	−4.53457	−	7.85410i	−0.216423	−	0.374856i	−0.953712	+	0.300722i	$0.902772\pi$
$440$		0			0
$441$	−2.56155			−0.121979
$442$		0			0
$443$	38.2462			1.81713			0.908566	−	0.417741i	$-0.137178\pi$
$443$	38.2462			1.81713			0.908566	+	0.417741i	$0.137178\pi$
$444$		0			0
$445$	−0.753789	−	1.30560i	−0.0357330	−	0.0618914i
$446$		0			0
$447$			5.06913i			0.239762i
$448$		0			0
$449$	−20.8314	−	12.0270i	−0.983092	−	0.567589i	−0.0798900	−	0.996804i	$-0.525457\pi$
$449$	−20.8314	−	12.0270i	−0.983092	−	0.567589i	−0.903202	+	0.429215i	$0.858790\pi$
$450$		0			0
$451$	−5.65767	+	9.79937i	−0.266409	+	0.461434i
$452$		0			0
$453$	27.7128	−	16.0000i	1.30206	−	0.751746i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−7.79423	+	4.50000i	−0.364599	+	0.210501i	−0.671096	−	0.741370i	$-0.734176\pi$
$457$	−7.79423	+	4.50000i	−0.364599	+	0.210501i	0.306497	+	0.951871i	$0.400843\pi$
$458$		0			0
$459$	−13.9039	+	24.0822i	−0.648978	+	1.12406i
$460$		0			0
$461$	−20.3450	−	11.7462i	−0.947563	−	0.547076i	−0.0552398	−	0.998473i	$-0.517592\pi$
$461$	−20.3450	−	11.7462i	−0.947563	−	0.547076i	−0.892323	+	0.451398i	$0.850926\pi$
$462$		0			0
$463$			32.9848i			1.53294i	0.642283	+	0.766468i	$0.277988\pi$
$463$			32.9848i			1.53294i	−0.642283	+	0.766468i	$0.722012\pi$
$464$		0			0
$465$	3.50758	+	6.07530i	0.162660	+	0.281735i
$466$		0			0
$467$	−26.2462			−1.21453			−0.607265	−	0.794499i	$-0.707733\pi$
$467$	−26.2462			−1.21453			−0.607265	+	0.794499i	$0.707733\pi$
$468$		0			0
$469$	−21.1771			−0.977867
$470$		0			0
$471$	2.19224	+	3.79706i	0.101013	+	0.174959i
$472$		0			0
$473$			3.80776i			0.175081i
$474$		0			0
$475$	−6.33527	−	3.65767i	−0.290682	−	0.167825i
$476$		0			0
$477$	2.40388	−	4.16365i	0.110066	−	0.190640i
$478$		0			0
$479$	17.5805	−	10.1501i	0.803273	−	0.463770i	−0.0413417	−	0.999145i	$-0.513163\pi$
$479$	17.5805	−	10.1501i	0.803273	−	0.463770i	0.844614	+	0.535375i	$0.179830\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−18.3399	+	10.5885i	−0.834494	+	0.481795i
$484$		0			0
$485$	−5.00000	+	8.66025i	−0.227038	+	0.393242i
$486$		0			0
$487$	29.8246	+	17.2192i	1.35148	+	0.780278i	0.988457	−	0.151503i	$-0.0484112\pi$
$487$	29.8246	+	17.2192i	1.35148	+	0.780278i	0.363023	+	0.931780i	$0.381744\pi$
$488$		0			0
$489$		−	35.8078i		−	1.61928i
$490$		0			0
$491$	−1.02699	−	1.77879i	−0.0463473	−	0.0802759i	0.841921	−	0.539601i	$-0.181425\pi$
$491$	−1.02699	−	1.77879i	−0.0463473	−	0.0802759i	−0.888268	+	0.459325i	$0.848091\pi$
$492$		0			0
$493$	−25.0000			−1.12594
$494$		0			0
$495$	0.492423			0.0221327
$496$		0			0
$497$	3.65767	+	6.33527i	0.164069	+	0.284176i
$498$		0			0
$499$		−	16.4924i		−	0.738302i	−0.929369	−	0.369151i	$-0.879648\pi$
$499$		−	16.4924i		−	0.738302i	0.929369	−	0.369151i	$-0.120352\pi$
$500$		0			0
$501$	12.9305	+	7.46543i	0.577693	+	0.333531i
$502$		0			0
$503$	16.3423	−	28.3057i	0.728668	−	1.26209i	−0.228778	−	0.973479i	$-0.573473\pi$
$503$	16.3423	−	28.3057i	0.728668	−	1.26209i	0.957446	−	0.288612i	$-0.0931938\pi$
$504$		0			0
$505$	5.46925	−	3.15767i	0.243378	−	0.140515i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−28.5788	+	16.5000i	−1.26673	+	0.731350i	−0.974369	−	0.224957i	$-0.927776\pi$
$509$	−28.5788	+	16.5000i	−1.26673	+	0.731350i	−0.292366	+	0.956306i	$0.594443\pi$
$510$		0			0
$511$	−10.6847	+	18.5064i	−0.472661	+	0.818674i
$512$		0			0
$513$	−7.52113	−	4.34233i	−0.332066	−	0.191719i
$514$		0			0
$515$			1.26137i			0.0555824i
$516$		0			0
$517$	−3.12311	−	5.40938i	−0.137354	−	0.237904i
$518$		0			0
$519$	20.1922			0.886341
$520$		0			0
$521$	9.05398			0.396662			0.198331	−	0.980135i	$-0.436448\pi$
$521$	9.05398			0.396662			0.198331	+	0.980135i	$0.436448\pi$
$522$		0			0
$523$	6.15009	+	10.6523i	0.268925	+	0.465791i	0.968584	−	0.248685i	$-0.0799984\pi$
$523$	6.15009	+	10.6523i	0.268925	+	0.465791i	−0.699660	+	0.714476i	$0.746665\pi$
$524$		0			0
$525$			11.4233i			0.498553i
$526$		0			0
$527$	34.6410	+	20.0000i	1.50899	+	0.871214i
$528$		0			0
$529$	−26.2116	+	45.3999i	−1.13964	+	1.97391i
$530$		0			0
$531$	0.759413	−	0.438447i	0.0329557	−	0.0190270i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	4.22351	−	2.43845i	0.182598	−	0.105423i
$536$		0			0
$537$	−13.0270	+	22.5634i	−0.562156	+	0.973683i
$538$		0			0
$539$	−6.16879	−	3.56155i	−0.265709	−	0.153407i
$540$		0			0
$541$			5.68466i			0.244403i	0.992505	+	0.122201i	$0.0389953\pi$
$541$			5.68466i			0.244403i	−0.992505	+	0.122201i	$0.961005\pi$
$542$		0			0
$543$	−8.43845	−	14.6158i	−0.362128	−	0.627225i
$544$		0			0
$545$	4.63068			0.198357
$546$		0			0
$547$	16.4924			0.705165			0.352583	−	0.935781i	$-0.385304\pi$
$547$	16.4924			0.705165			0.352583	+	0.935781i	$0.385304\pi$
$548$		0			0
$549$	2.59612	+	4.49661i	0.110800	+	0.191911i
$550$		0			0
$551$		−	7.80776i		−	0.332622i
$552$		0			0
$553$	−5.40938	−	3.12311i	−0.230030	−	0.132808i
$554$		0			0
$555$	−0.438447	+	0.759413i	−0.0186110	+	0.0322353i
$556$		0			0
$557$	−27.2732	+	15.7462i	−1.15560	+	0.667188i	−0.950247	−	0.311499i	$-0.899169\pi$
$557$	−27.2732	+	15.7462i	−1.15560	+	0.667188i	−0.205358	+	0.978687i	$0.565836\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−10.5588	+	6.09612i	−0.445792	+	0.257378i
$562$		0			0
$563$	3.02699	−	5.24290i	0.127572	−	0.220962i	−0.795163	−	0.606396i	$-0.792615\pi$
$563$	3.02699	−	5.24290i	0.127572	−	0.220962i	0.922736	+	0.385434i	$0.125948\pi$
$564$		0			0
$565$	3.52397	+	2.03457i	0.148255	+	0.0855948i
$566$		0			0
$567$			10.9309i			0.459053i
$568$		0			0
$569$	9.34233	+	16.1814i	0.391651	+	0.678359i	0.992667	−	0.120877i	$-0.0385708\pi$
$569$	9.34233	+	16.1814i	0.391651	+	0.678359i	−0.601017	+	0.799237i	$0.705237\pi$
$570$		0			0
$571$	8.49242			0.355397			0.177698	−	0.984085i	$-0.443135\pi$
$571$	8.49242			0.355397			0.177698	+	0.984085i	$0.443135\pi$
$572$		0			0
$573$	26.0540			1.08842
$574$		0			0
$575$	20.3423	+	35.2339i	0.848334	+	1.46936i
$576$		0			0
$577$		−	27.4384i		−	1.14228i	−0.820854	−	0.571139i	$-0.806502\pi$
$577$		−	27.4384i		−	1.14228i	0.820854	−	0.571139i	$-0.193498\pi$
$578$		0			0
$579$	−4.05703	−	2.34233i	−0.168605	−	0.0973439i
$580$		0			0
$581$	11.1231	−	19.2658i	0.461464	−	0.799279i
$582$		0			0
$583$	11.5782	−	6.68466i	0.479519	−	0.276850i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	12.9305	−	7.46543i	0.533699	−	0.308131i	−0.208822	−	0.977954i	$-0.566963\pi$
$587$	12.9305	−	7.46543i	0.533699	−	0.308131i	0.742522	+	0.669822i	$0.233630\pi$
$588$		0			0
$589$	−6.24621	+	10.8188i	−0.257371	+	0.445779i
$590$		0			0
$591$	19.8587	+	11.4654i	0.816878	+	0.471625i
$592$		0			0
$593$			19.4384i			0.798241i	0.916898	+	0.399121i	$0.130685\pi$
$593$			19.4384i			0.798241i	−0.916898	+	0.399121i	$0.869315\pi$
$594$		0			0
$595$	−2.19224	−	3.79706i	−0.0898729	−	0.155664i
$596$		0			0
$597$	21.1771			0.866720
$598$		0			0
$599$	26.7386			1.09251			0.546255	−	0.837619i	$-0.316053\pi$
$599$	26.7386			1.09251			0.546255	+	0.837619i	$0.316053\pi$
$600$		0			0
$601$	−13.9924	−	24.2356i	−0.570763	−	0.988590i	−0.996488	−	0.0837376i	$-0.973314\pi$
$601$	−13.9924	−	24.2356i	−0.570763	−	0.988590i	0.425725	−	0.904853i	$-0.360019\pi$
$602$		0			0
$603$			7.61553i			0.310128i
$604$		0			0
$605$	−4.16365	−	2.40388i	−0.169276	−	0.0977317i
$606$		0			0
$607$	−9.65767	+	16.7276i	−0.391993	+	0.678951i	−0.992712	−	0.120508i	$-0.961548\pi$
$607$	−9.65767	+	16.7276i	−0.391993	+	0.678951i	0.600720	+	0.799460i	$0.294881\pi$
$608$		0			0
$609$	−10.5588	+	6.09612i	−0.427864	+	0.247027i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−7.79423	+	4.50000i	−0.314806	+	0.181753i	−0.649075	−	0.760724i	$-0.724844\pi$
$613$	−7.79423	+	4.50000i	−0.314806	+	0.181753i	0.334269	+	0.942478i	$0.391511\pi$
$614$		0			0
$615$	3.17708	−	5.50287i	0.128112	−	0.221897i
$616$		0			0
$617$	−21.8639	−	12.6231i	−0.880206	−	0.508187i	−0.00947959	−	0.999955i	$-0.503017\pi$
$617$	−21.8639	−	12.6231i	−0.880206	−	0.508187i	−0.870726	+	0.491768i	$0.836351\pi$
$618$		0			0
$619$			28.9848i			1.16500i	0.812831	+	0.582500i	$0.197925\pi$
$619$			28.9848i			1.16500i	−0.812831	+	0.582500i	$0.802075\pi$
$620$		0			0
$621$	24.1501	+	41.8292i	0.969110	+	1.67855i
$622$		0			0
$623$	−4.19224			−0.167958
$624$		0			0
$625$	20.3693			0.814773
$626$		0			0
$627$	−1.90388	−	3.29762i	−0.0760337	−	0.131694i
$628$		0			0
$629$			5.00000i			0.199363i
$630$		0			0
$631$	8.70700	+	5.02699i	0.346620	+	0.200121i	0.663196	−	0.748446i	$-0.269200\pi$
$631$	8.70700	+	5.02699i	0.346620	+	0.200121i	−0.316576	+	0.948567i	$0.602533\pi$
$632$		0			0
$633$	19.2732	−	33.3822i	0.766041	−	1.32682i
$634$		0			0
$635$	3.79706	−	2.19224i	0.150682	−	0.0869962i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	2.27824	−	1.31534i	0.0901257	−	0.0520341i
$640$		0			0
$641$	−0.746211	+	1.29248i	−0.0294736	+	0.0510497i	−0.880386	−	0.474258i	$-0.842716\pi$
$641$	−0.746211	+	1.29248i	−0.0294736	+	0.0510497i	0.850912	+	0.525308i	$0.176050\pi$
$642$		0			0
$643$	−17.5805	−	10.1501i	−0.693306	−	0.400281i	0.111543	−	0.993760i	$-0.464421\pi$
$643$	−17.5805	−	10.1501i	−0.693306	−	0.400281i	−0.804849	+	0.593479i	$0.797754\pi$
$644$		0			0
$645$		−	2.13826i		−	0.0841939i
$646$		0			0
$647$	11.4654	+	19.8587i	0.450753	+	0.780727i	0.998433	−	0.0559611i	$-0.0178223\pi$
$647$	11.4654	+	19.8587i	0.450753	+	0.780727i	−0.547680	+	0.836688i	$0.684489\pi$
$648$		0			0
$649$	2.43845			0.0957174
$650$		0			0
$651$	19.5076			0.764562
$652$		0			0
$653$	12.2732	+	21.2578i	0.480287	+	0.831882i	0.999744	−	0.0226145i	$-0.00719904\pi$
$653$	12.2732	+	21.2578i	0.480287	+	0.831882i	−0.519457	+	0.854497i	$0.673866\pi$
$654$		0			0
$655$			0.984845i			0.0384811i
$656$		0			0
$657$	6.65511	+	3.84233i	0.259641	+	0.149904i
$658$		0			0
$659$	−10.7808	+	18.6729i	−0.419959	+	0.727391i	−0.995935	−	0.0900759i	$-0.971289\pi$
$659$	−10.7808	+	18.6729i	−0.419959	+	0.727391i	0.575975	+	0.817467i	$0.304622\pi$
$660$		0			0
$661$	−4.96980	+	2.86932i	−0.193303	+	0.111603i	−0.593528	−	0.804813i	$-0.702265\pi$
$661$	−4.96980	+	2.86932i	−0.193303	+	0.111603i	0.400225	+	0.916417i	$0.368932\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.18586	−	0.684658i	0.0459858	−	0.0265499i
$666$		0			0
$667$	−21.7116	+	37.6057i	−0.840678	+	1.45610i
$668$		0			0
$669$	11.7446	+	6.78078i	0.454074	+	0.262160i
$670$		0			0
$671$			14.4384i			0.557390i
$672$		0			0
$673$	8.62311	+	14.9357i	0.332396	+	0.575727i	0.982981	−	0.183706i	$-0.0588095\pi$
$673$	8.62311	+	14.9357i	0.332396	+	0.575727i	−0.650585	+	0.759434i	$0.725476\pi$
$674$		0			0
$675$	26.0540			1.00282
$676$		0			0
$677$	−28.7386			−1.10452			−0.552258	−	0.833673i	$-0.686234\pi$
$677$	−28.7386			−1.10452			−0.552258	+	0.833673i	$0.686234\pi$
$678$		0			0
$679$	13.9039	+	24.0822i	0.533582	+	0.924191i
$680$		0			0
$681$		−	46.9309i		−	1.79839i
$682$		0			0
$683$	6.33527	+	3.65767i	0.242412	+	0.139957i	0.616285	−	0.787523i	$-0.288637\pi$
$683$	6.33527	+	3.65767i	0.242412	+	0.139957i	−0.373873	+	0.927480i	$0.621970\pi$
$684$		0			0
$685$	−3.22680	+	5.58898i	−0.123290	+	0.213544i
$686$		0			0
$687$	16.5611	−	9.56155i	0.631845	−	0.364796i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−22.1370	+	12.7808i	−0.842129	+	0.486204i	−0.857987	−	0.513671i	$-0.828285\pi$
$691$	−22.1370	+	12.7808i	−0.842129	+	0.486204i	0.0158581	+	0.999874i	$0.494952\pi$
$692$		0			0
$693$	0.684658	−	1.18586i	0.0260080	−	0.0450472i
$694$		0			0
$695$	−3.55759	−	2.05398i	−0.134947	−	0.0779117i
$696$		0			0
$697$		−	36.2311i		−	1.37235i
$698$		0			0
$699$	9.56155	+	16.5611i	0.361651	+	0.626398i
$700$		0			0
$701$	−32.7386			−1.23652			−0.618261	−	0.785973i	$-0.712162\pi$
$701$	−32.7386			−1.23652			−0.618261	+	0.785973i	$0.712162\pi$
$702$		0			0
$703$	−1.56155			−0.0588951
$704$		0			0
$705$	1.75379	+	3.03765i	0.0660515	+	0.114405i
$706$		0			0
$707$		−	17.5616i		−	0.660470i
$708$		0			0
$709$	29.2185	+	16.8693i	1.09732	+	0.633540i	0.935517	−	0.353282i	$-0.114934\pi$
$709$	29.2185	+	16.8693i	1.09732	+	0.633540i	0.161807	+	0.986822i	$0.448268\pi$
$710$		0			0
$711$	−1.12311	+	1.94528i	−0.0421198	+	0.0729535i
$712$		0			0
$713$	60.1691	−	34.7386i	2.25335	−	1.30097i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−24.6752	+	14.2462i	−0.921511	+	0.532035i
$718$		0			0
$719$	−21.4654	+	37.1792i	−0.800526	+	1.38655i	0.118745	+	0.992925i	$0.462113\pi$
$719$	−21.4654	+	37.1792i	−0.800526	+	1.38655i	−0.919271	+	0.393626i	$0.871220\pi$
$720$		0			0
$721$	3.03765	+	1.75379i	0.113128	+	0.0653145i
$722$		0			0
$723$			11.6998i			0.435121i
$724$		0			0
$725$	11.7116	+	20.2852i	0.434960	+	0.753372i
$726$		0			0
$727$	−6.73863			−0.249922			−0.124961	−	0.992162i	$-0.539881\pi$
$727$	−6.73863			−0.249922			−0.124961	+	0.992162i	$0.539881\pi$
$728$		0			0
$729$	29.9848			1.11055
$730$		0			0
$731$	−6.09612	−	10.5588i	−0.225473	−	0.390531i
$732$		0			0
$733$		−	1.19224i		−	0.0440362i	−0.999758	−	0.0220181i	$-0.992991\pi$
$733$		−	1.19224i		−	0.0440362i	0.999758	−	0.0220181i	$-0.00700915\pi$
$734$		0			0
$735$	3.46410	+	2.00000i	0.127775	+	0.0737711i
$736$		0			0
$737$	−10.5885	+	18.3399i	−0.390034	+	0.675559i
$738$		0			0
$739$	−40.6433	+	23.4654i	−1.49509	+	0.863190i	−0.999984	−	0.00564328i	$-0.998204\pi$
$739$	−40.6433	+	23.4654i	−1.49509	+	0.863190i	−0.495105	+	0.868833i	$0.664870\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−7.85410	+	4.53457i	−0.288139	+	0.166357i	−0.637102	−	0.770779i	$-0.719867\pi$
$743$	−7.85410	+	4.53457i	−0.288139	+	0.166357i	0.348963	+	0.937136i	$0.386534\pi$
$744$		0			0
$745$	−0.911460	+	1.57869i	−0.0333933	+	0.0578389i
$746$		0			0
$747$	−6.92820	−	4.00000i	−0.253490	−	0.146352i
$748$		0			0
$749$		−	13.5616i		−	0.495528i
$750$		0			0
$751$	−24.1501	−	41.8292i	−0.881249	−	1.52637i	−0.849953	−	0.526859i	$-0.823370\pi$
$751$	−24.1501	−	41.8292i	−0.881249	−	1.52637i	−0.0312965	−	0.999510i	$-0.509964\pi$
$752$		0			0
$753$	1.66950			0.0608401
$754$		0			0
$755$	11.5076			0.418804
$756$		0			0
$757$	8.27320	+	14.3296i	0.300695	+	0.520818i	0.976293	−	0.216451i	$-0.0694482\pi$
$757$	8.27320	+	14.3296i	0.300695	+	0.520818i	−0.675599	+	0.737269i	$0.736115\pi$
$758$		0			0
$759$			21.1771i			0.768679i
$760$		0			0
$761$	−19.9785	−	11.5346i	−0.724218	−	0.418128i	0.0920850	−	0.995751i	$-0.470647\pi$
$761$	−19.9785	−	11.5346i	−0.724218	−	0.418128i	−0.816303	+	0.577623i	$0.803980\pi$
$762$		0			0
$763$	6.43845	−	11.1517i	0.233087	−	0.403719i
$764$		0			0
$765$	−1.36547	+	0.788354i	−0.0493686	+	0.0285030i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	0.806157	−	0.465435i	0.0290708	−	0.0167840i	−0.485394	−	0.874295i	$-0.661324\pi$
$769$	0.806157	−	0.465435i	0.0290708	−	0.0167840i	0.514465	+	0.857511i	$0.327991\pi$
$770$		0			0
$771$	−4.09612	+	7.09468i	−0.147518	+	0.255509i
$772$		0			0
$773$	−29.6113	−	17.0961i	−1.06505	−	0.614905i	−0.138222	−	0.990401i	$-0.544139\pi$
$773$	−29.6113	−	17.0961i	−1.06505	−	0.614905i	−0.926824	+	0.375497i	$0.877472\pi$
$774$		0			0
$775$		−	37.4773i		−	1.34622i
$776$		0			0
$777$	1.21922	+	2.11176i	0.0437394	+	0.0757589i
$778$		0			0
$779$	11.3153			0.405414
$780$		0			0
$781$	7.31534			0.261764
$782$		0			0
$783$	13.9039	+	24.0822i	0.496884	+	0.860629i
$784$		0			0
$785$			1.57671i			0.0562751i
$786$		0			0
$787$	−23.7493	−	13.7116i	−0.846570	−	0.488767i	0.0129221	−	0.999917i	$-0.495887\pi$
$787$	−23.7493	−	13.7116i	−0.846570	−	0.488767i	−0.859492	+	0.511149i	$0.829220\pi$
$788$		0			0
$789$	−9.21922	+	15.9682i	−0.328213	+	0.568482i
$790$		0			0
$791$	9.79937	−	5.65767i	0.348426	−	0.201164i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−6.50175	+	3.75379i	−0.230593	+	0.133133i
$796$		0			0
$797$	6.46543	−	11.1985i	0.229017	−	0.396670i	−0.728500	−	0.685046i	$-0.759782\pi$
$797$	6.46543	−	11.1985i	0.229017	−	0.396670i	0.957517	+	0.288376i	$0.0931154\pi$
$798$		0			0
$799$	17.3205	+	10.0000i	0.612756	+	0.353775i
$800$		0			0
$801$			1.50758i			0.0532676i
$802$		0			0
$803$	10.6847	+	18.5064i	0.377053	+	0.653076i
$804$		0			0
$805$	−7.61553			−0.268412
$806$		0			0
$807$	9.06913			0.319249
$808$		0			0
$809$	11.6231	+	20.1318i	0.408647	+	0.707797i	0.994738	−	0.102448i	$-0.0326675\pi$
$809$	11.6231	+	20.1318i	0.408647	+	0.707797i	−0.586092	+	0.810245i	$0.699334\pi$
$810$		0			0
$811$			8.00000i			0.280918i	0.990086	+	0.140459i	$0.0448578\pi$
$811$			8.00000i			0.280918i	−0.990086	+	0.140459i	$0.955142\pi$
$812$		0			0
$813$	12.9305	+	7.46543i	0.453493	+	0.261824i
$814$		0			0
$815$	6.43845	−	11.1517i	0.225529	−	0.390628i
$816$		0			0
$817$	3.29762	−	1.90388i	0.115369	−	0.0666084i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−11.9579	+	6.90388i	−0.417333	+	0.240947i	−0.693935	−	0.720037i	$-0.744125\pi$
$821$	−11.9579	+	6.90388i	−0.417333	+	0.240947i	0.276603	+	0.960984i	$0.410791\pi$
$822$		0			0
$823$	−0.588540	+	1.01938i	−0.0205152	+	0.0355334i	−0.876101	−	0.482128i	$-0.839864\pi$
$823$	−0.588540	+	1.01938i	−0.0205152	+	0.0355334i	0.855586	+	0.517661i	$0.173197\pi$
$824$		0			0
$825$	9.89286	+	5.71165i	0.344425	+	0.198854i
$826$		0			0
$827$			36.9848i			1.28609i	0.765829	+	0.643045i	$0.222329\pi$
$827$			36.9848i			1.28609i	−0.765829	+	0.643045i	$0.777671\pi$
$828$		0			0
$829$	3.25379	+	5.63573i	0.113009	+	0.195737i	0.916982	−	0.398929i	$-0.130618\pi$
$829$	3.25379	+	5.63573i	0.113009	+	0.195737i	−0.803973	+	0.594665i	$0.797285\pi$
$830$		0			0
$831$	17.1771			0.595866
$832$		0			0
$833$	22.8078			0.790242
$834$		0			0
$835$	2.68466	+	4.64996i	0.0929064	+	0.160919i
$836$		0			0
$837$		−	44.4924i		−	1.53788i
$838$		0			0
$839$	23.6558	+	13.6577i	0.816688	+	0.471515i	0.849273	−	0.527954i	$-0.177041\pi$
$839$	23.6558	+	13.6577i	0.816688	+	0.471515i	−0.0325849	+	0.999469i	$0.510374\pi$
$840$		0			0
$841$	2.00000	−	3.46410i	0.0689655	−	0.119452i
$842$		0			0
$843$	3.13114	−	1.80776i	0.107842	−	0.0622627i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−11.5782	+	6.68466i	−0.397831	+	0.229688i
$848$		0			0
$849$	19.9579	−	34.5680i	0.684952	−	1.18637i
$850$		0			0
$851$	7.52113	+	4.34233i	0.257821	+	0.148853i
$852$		0			0
$853$			48.4233i			1.65798i	0.559262	+	0.828991i	$0.311085\pi$
$853$			48.4233i			1.65798i	−0.559262	+	0.828991i	$0.688915\pi$
$854$		0			0
$855$	−0.246211	−	0.426450i	−0.00842025	−	0.0145843i
$856$		0			0
$857$	14.9460			0.510546			0.255273	−	0.966869i	$-0.417835\pi$
$857$	14.9460			0.510546			0.255273	+	0.966869i	$0.417835\pi$
$858$		0			0
$859$	−22.2462			−0.759031			−0.379515	−	0.925185i	$-0.623909\pi$
$859$	−22.2462			−0.759031			−0.379515	+	0.925185i	$0.623909\pi$
$860$		0			0
$861$	−8.83475	−	15.3022i	−0.301088	−	0.521499i
$862$		0			0
$863$		−	21.7538i		−	0.740508i	−0.928931	−	0.370254i	$-0.879271\pi$
$863$		−	21.7538i		−	0.740508i	0.928931	−	0.370254i	$-0.120729\pi$
$864$		0			0
$865$	6.28853	+	3.63068i	0.213816	+	0.123447i
$866$		0			0
$867$	6.24621	−	10.8188i	0.212132	−	0.367424i
$868$		0			0
$869$	−5.40938	+	3.12311i	−0.183501	+	0.105944i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	8.66025	−	5.00000i	0.293105	−	0.169224i
$874$		0			0
$875$	−4.24621	+	7.35465i	−0.143548	+	0.248633i
$876$		0			0
$877$	34.4147	+	19.8693i	1.16210	+	0.670939i	0.951807	−	0.306699i	$-0.0992245\pi$
$877$	34.4147	+	19.8693i	1.16210	+	0.670939i	0.210294	+	0.977638i	$0.432558\pi$
$878$		0			0
$879$		−	33.5616i		−	1.13200i
$880$		0			0
$881$	−7.62311	−	13.2036i	−0.256829	−	0.444841i	0.708562	−	0.705649i	$-0.249344\pi$
$881$	−7.62311	−	13.2036i	−0.256829	−	0.444841i	−0.965391	+	0.260808i	$0.916011\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$		0			0
$885$	−1.36932			−0.0460291
$886$		0			0
$887$	−10.3423	−	17.9134i	−0.347261	−	0.601474i	0.638501	−	0.769621i	$-0.279555\pi$
$887$	−10.3423	−	17.9134i	−0.347261	−	0.601474i	−0.985762	+	0.168147i	$0.946222\pi$
$888$		0			0
$889$		−	12.1922i		−	0.408914i
$890$		0			0
$891$	9.46641	+	5.46543i	0.317137	+	0.183099i
$892$		0			0
$893$	−3.12311	+	5.40938i	−0.104511	+	0.181018i
$894$		0			0
$895$	−8.11407	+	4.68466i	−0.271223	+	0.156591i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	34.6410	−	20.0000i	1.15534	−	0.667037i
$900$		0			0
$901$	−21.4039	+	37.0726i	−0.713067	+	1.23507i
$902$		0			0
$903$	−5.14941	−	2.97301i	−0.171362	−	0.0989357i
$904$		0			0
$905$		−	6.06913i		−	0.201745i
$906$		0			0
$907$	−20.1501	−	34.9010i	−0.669073	−	1.15887i	−0.978164	−	0.207836i	$-0.933358\pi$
$907$	−20.1501	−	34.9010i	−0.669073	−	1.15887i	0.309091	−	0.951033i	$-0.399975\pi$
$908$		0			0
$909$	−6.31534			−0.209467
$910$		0			0
$911$	−30.7386			−1.01842			−0.509208	−	0.860643i	$-0.670062\pi$
$911$	−30.7386			−1.01842			−0.509208	+	0.860643i	$0.670062\pi$
$912$		0			0
$913$	−11.1231	−	19.2658i	−0.368121	−	0.637604i
$914$		0			0
$915$		−	8.10795i		−	0.268041i
$916$		0			0
$917$	2.37173	+	1.36932i	0.0783213	+	0.0452188i
$918$		0			0
$919$	−29.2732	+	50.7027i	−0.965634	+	1.67253i	−0.257731	+	0.966217i	$0.582975\pi$
$919$	−29.2732	+	50.7027i	−0.965634	+	1.67253i	−0.707903	+	0.706310i	$0.750358\pi$
$920$		0			0
$921$	−13.1905	+	7.61553i	−0.434641	+	0.250940i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	4.05703	−	2.34233i	0.133394	−	0.0770153i
$926$		0			0
$927$	0.630683	−	1.09238i	0.0207144	−	0.0358783i
$928$		0			0
$929$	32.8958	+	18.9924i	1.07928	+	0.623121i	0.930701	−	0.365780i	$-0.119198\pi$
$929$	32.8958	+	18.9924i	1.07928	+	0.623121i	0.148576	+	0.988901i	$0.452531\pi$
$930$		0			0
$931$			7.12311i			0.233450i
$932$		0			0
$933$	−1.75379	−	3.03765i	−0.0574165	−	0.0994482i
$934$		0			0
$935$	−4.38447			−0.143388
$936$		0			0
$937$	−13.6847			−0.447058			−0.223529	−	0.974697i	$-0.571758\pi$
$937$	−13.6847			−0.447058			−0.223529	+	0.974697i	$0.571758\pi$
$938$		0			0
$939$	−12.3002	−	21.3045i	−0.401401	−	0.695248i
$940$		0			0
$941$			14.0000i			0.456387i	0.973616	+	0.228193i	$0.0732819\pi$
$941$			14.0000i			0.456387i	−0.973616	+	0.228193i	$0.926718\pi$
$942$		0			0
$943$	−54.4997	−	31.4654i	−1.77476	−	1.02466i
$944$		0			0
$945$	−2.43845	+	4.22351i	−0.0793227	+	0.137391i
$946$		0			0
$947$	−13.3570	+	7.71165i	−0.434043	+	0.250595i	−0.701068	−	0.713095i	$-0.747293\pi$
$947$	−13.3570	+	7.71165i	−0.434043	+	0.250595i	0.267025	+	0.963690i	$0.413960\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−27.8063	+	16.0540i	−0.901681	+	0.520586i
$952$		0			0
$953$	−12.9039	+	22.3502i	−0.417998	+	0.723993i	−0.995738	−	0.0922274i	$-0.970601\pi$
$953$	−12.9039	+	22.3502i	−0.417998	+	0.723993i	0.577740	+	0.816221i	$0.303935\pi$
$954$		0			0
$955$	8.11407	+	4.68466i	0.262565	+	0.151592i
$956$		0			0
$957$			12.1922i			0.394119i
$958$		0			0
$959$	8.97301	+	15.5417i	0.289754	+	0.501868i
$960$		0			0
$961$	−33.0000			−1.06452
$962$		0			0
$963$	−4.87689			−0.157156
$964$		0			0
$965$	−0.842329	−	1.45896i	−0.0271155	−	0.0469655i
$966$		0			0
$967$			5.75379i			0.185029i	0.995711	+	0.0925147i	$0.0294905\pi$
$967$			5.75379i			0.185029i	−0.995711	+	0.0925147i	$0.970509\pi$
$968$		0			0
$969$	10.5588	+	6.09612i	0.339197	+	0.195836i
$970$		0			0
$971$	−9.65767	+	16.7276i	−0.309929	+	0.536813i	−0.978347	−	0.206973i	$-0.933639\pi$
$971$	−9.65767	+	16.7276i	−0.309929	+	0.536813i	0.668417	+	0.743787i	$0.266972\pi$
$972$		0			0
$973$	−9.89286	+	5.71165i	−0.317151	+	0.183107i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.07925	−	0.623106i	0.0345283	−	0.0199349i	−0.482636	−	0.875821i	$-0.660321\pi$
$977$	1.07925	−	0.623106i	0.0345283	−	0.0199349i	0.517165	+	0.855886i	$0.326987\pi$
$978$		0			0
$979$	−2.09612	+	3.63058i	−0.0669922	+	0.116034i
$980$		0			0
$981$	−4.01029	−	2.31534i	−0.128039	−	0.0739232i
$982$		0			0
$983$			24.9848i			0.796893i	0.917192	+	0.398446i	$0.130451\pi$
$983$			24.9848i			0.796893i	−0.917192	+	0.398446i	$0.869549\pi$
$984$		0			0
$985$	4.12311	+	7.14143i	0.131373	+	0.227545i
$986$		0			0
$987$	9.75379			0.310467
$988$		0			0
$989$	−21.1771			−0.673392
$990$		0			0
$991$	−1.84991	−	3.20413i	−0.0587642	−	0.101783i	0.835147	−	0.550027i	$-0.185383\pi$
$991$	−1.84991	−	3.20413i	−0.0587642	−	0.101783i	−0.893911	+	0.448245i	$0.852049\pi$
$992$		0			0
$993$			10.8229i			0.343455i
$994$		0			0
$995$	6.59524	+	3.80776i	0.209083	+	0.120714i
$996$		0			0
$997$	21.6231	−	37.4523i	0.684811	−	1.18613i	−0.288686	−	0.957424i	$-0.593218\pi$
$997$	21.6231	−	37.4523i	0.684811	−	1.18613i	0.973496	−	0.228703i	$-0.0734484\pi$
$998$		0			0
$999$	4.81645	−	2.78078i	0.152386	−	0.0879799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1352.2.o.c.361.4		8
13.2	odd	12		1352.2.a.f.1.1		2
13.3	even	3		1352.2.f.d.337.2		4
13.4	even	6	inner	1352.2.o.c.1161.3		8
13.5	odd	4		104.2.i.b.81.2	yes	4
13.6	odd	12		104.2.i.b.9.2	✓	4
13.7	odd	12		1352.2.i.e.529.2		4
13.8	odd	4		1352.2.i.e.1329.2		4
13.9	even	3	inner	1352.2.o.c.1161.4		8
13.10	even	6		1352.2.f.d.337.1		4
13.11	odd	12		1352.2.a.h.1.1		2
13.12	even	2	inner	1352.2.o.c.361.3		8
39.5	even	4		936.2.t.f.289.1		4
39.32	even	12		936.2.t.f.217.1		4
52.3	odd	6		2704.2.f.l.337.4		4
52.11	even	12		2704.2.a.r.1.2		2
52.15	even	12		2704.2.a.q.1.2		2
52.19	even	12		208.2.i.e.113.1		4
52.23	odd	6		2704.2.f.l.337.3		4
52.31	even	4		208.2.i.e.81.1		4
104.5	odd	4		832.2.i.o.705.1		4
104.19	even	12		832.2.i.l.321.2		4
104.45	odd	12		832.2.i.o.321.1		4
104.83	even	4		832.2.i.l.705.2		4
156.71	odd	12		1872.2.t.s.1153.1		4
156.83	odd	4		1872.2.t.s.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.i.b.9.2	✓	4	13.6	odd	12
104.2.i.b.81.2	yes	4	13.5	odd	4
208.2.i.e.81.1		4	52.31	even	4
208.2.i.e.113.1		4	52.19	even	12
832.2.i.l.321.2		4	104.19	even	12
832.2.i.l.705.2		4	104.83	even	4
832.2.i.o.321.1		4	104.45	odd	12
832.2.i.o.705.1		4	104.5	odd	4
936.2.t.f.217.1		4	39.32	even	12
936.2.t.f.289.1		4	39.5	even	4
1352.2.a.f.1.1		2	13.2	odd	12
1352.2.a.h.1.1		2	13.11	odd	12
1352.2.f.d.337.1		4	13.10	even	6
1352.2.f.d.337.2		4	13.3	even	3
1352.2.i.e.529.2		4	13.7	odd	12
1352.2.i.e.1329.2		4	13.8	odd	4
1352.2.o.c.361.3		8	13.12	even	2	inner
1352.2.o.c.361.4		8	1.1	even	1	trivial
1352.2.o.c.1161.3		8	13.4	even	6	inner
1352.2.o.c.1161.4		8	13.9	even	3	inner
1872.2.t.s.289.1		4	156.83	odd	4
1872.2.t.s.1153.1		4	156.71	odd	12
2704.2.a.q.1.2		2	52.15	even	12
2704.2.a.r.1.2		2	52.11	even	12
2704.2.f.l.337.3		4	52.23	odd	6
2704.2.f.l.337.4		4	52.3	odd	6

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:	\( N \)	\(=\)	\( 1352 = 2^{3} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1352.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.780776 + 1.35234i) q^{3} +0.561553i q^{5} +(1.35234 + 0.780776i) q^{7} +(0.280776 - 0.486319i) q^{9} +(1.35234 - 0.780776i) q^{11} +(-0.759413 + 0.438447i) q^{15} +(-2.50000 + 4.33013i) q^{17} +(-1.35234 - 0.780776i) q^{19} +2.43845i q^{21} +(4.34233 + 7.52113i) q^{23} +4.68466 q^{25} +5.56155 q^{27} +(2.50000 + 4.33013i) q^{29} -8.00000i q^{31} +(2.11176 + 1.21922i) q^{33} +(-0.438447 + 0.759413i) q^{35} +(0.866025 - 0.500000i) q^{37} +(-6.27540 + 3.62311i) q^{41} +(-1.21922 + 2.11176i) q^{43} +(0.273094 + 0.157671i) q^{45} -4.00000i q^{47} +(-2.28078 - 3.95042i) q^{49} -7.80776 q^{51} +8.56155 q^{53} +(0.438447 + 0.759413i) q^{55} -2.43845i q^{57} +(1.35234 + 0.780776i) q^{59} +(-4.62311 + 8.00745i) q^{61} +(0.759413 - 0.438447i) q^{63} +(-11.7446 + 6.78078i) q^{67} +(-6.78078 + 11.7446i) q^{69} +(4.05703 + 2.34233i) q^{71} +13.6847i q^{73} +(3.65767 + 6.33527i) q^{75} +2.43845 q^{77} -4.00000 q^{79} +(3.50000 + 6.06218i) q^{81} -14.2462i q^{83} +(-2.43160 - 1.40388i) q^{85} +(-3.90388 + 6.76172i) q^{87} +(-2.32498 + 1.34233i) q^{89} +(10.8188 - 6.24621i) q^{93} +(0.438447 - 0.759413i) q^{95} +(15.4220 + 8.90388i) q^{97} -0.876894i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 6 q^{9} - 20 q^{17} + 10 q^{23} - 12 q^{25} + 28 q^{27} + 20 q^{29} - 20 q^{35} - 18 q^{43} - 10 q^{49} + 20 q^{51} + 52 q^{53} + 20 q^{55} - 4 q^{61} - 46 q^{69} + 54 q^{75} + 36 q^{77}+ \cdots + 20 q^{95}+O(q^{100}) \) 8 * q - 2 * q^3 - 6 * q^9 - 20 * q^17 + 10 * q^23 - 12 * q^25 + 28 * q^27 + 20 * q^29 - 20 * q^35 - 18 * q^43 - 10 * q^49 + 20 * q^51 + 52 * q^53 + 20 * q^55 - 4 * q^61 - 46 * q^69 + 54 * q^75 + 36 * q^77 - 32 * q^79 + 28 * q^81 + 10 * q^87 + 20 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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