LMFDB - Embedded newform 1352.2.i.h.1329.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1352,2,Mod(529,1352)] 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, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1352.529"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [4,0,1,0,2,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$10.7957743533$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1329.1
Root			$-0.780776 - 1.35234i$ of defining polynomial
Character	$\chi$	$=$	1352.1329
Dual form			1352.2.i.h.529.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.780776 - 1.35234i) q^{3} -1.56155 q^{5} +(0.219224 - 0.379706i) q^{7} +(0.280776 - 0.486319i) q^{9} +(2.56155 + 4.43674i) q^{11} +(1.21922 + 2.11176i) q^{15} +(-1.78078 + 3.08440i) q^{17} +(-1.00000 + 1.73205i) q^{19} -0.684658 q^{21} +(-1.56155 - 2.70469i) q^{23} -2.56155 q^{25} -5.56155 q^{27} +(2.56155 + 4.43674i) q^{29} -5.12311 q^{31} +(4.00000 - 6.92820i) q^{33} +(-0.342329 + 0.592932i) q^{35} +(4.78078 + 8.28055i) q^{37} +(4.00000 + 6.92820i) q^{41} +(4.78078 - 8.28055i) q^{43} +(-0.438447 + 0.759413i) q^{45} +7.56155 q^{47} +(3.40388 + 5.89570i) q^{49} +5.56155 q^{51} +12.2462 q^{53} +(-4.00000 - 6.92820i) q^{55} +3.12311 q^{57} +(5.00000 - 8.66025i) q^{59} +(-1.43845 + 2.49146i) q^{61} +(-0.123106 - 0.213225i) q^{63} +(4.56155 + 7.90084i) q^{67} +(-2.43845 + 4.22351i) q^{69} +(-3.34233 + 5.78908i) q^{71} +9.36932 q^{73} +(2.00000 + 3.46410i) q^{75} +2.24621 q^{77} -11.1231 q^{79} +(3.50000 + 6.06218i) q^{81} +8.24621 q^{83} +(2.78078 - 4.81645i) q^{85} +(4.00000 - 6.92820i) q^{87} +(-1.56155 - 2.70469i) q^{89} +(4.00000 + 6.92820i) q^{93} +(1.56155 - 2.70469i) q^{95} +(-3.12311 + 5.40938i) q^{97} +2.87689 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} + 2 q^{5} + 5 q^{7} - 3 q^{9} + 2 q^{11} + 9 q^{15} - 3 q^{17} - 4 q^{19} + 22 q^{21} + 2 q^{23} - 2 q^{25} - 14 q^{27} + 2 q^{29} - 4 q^{31} + 16 q^{33} + 11 q^{35} + 15 q^{37} + 16 q^{41}+ \cdots + 28 q^{99}+O(q^{100}) $ 4 * q + q^3 + 2 * q^5 + 5 * q^7 - 3 * q^9 + 2 * q^11 + 9 * q^15 - 3 * q^17 - 4 * q^19 + 22 * q^21 + 2 * q^23 - 2 * q^25 - 14 * q^27 + 2 * q^29 - 4 * q^31 + 16 * q^33 + 11 * q^35 + 15 * q^37 + 16 * q^41 + 15 * q^43 - 10 * q^45 + 22 * q^47 - 7 * q^49 + 14 * q^51 + 16 * q^53 - 16 * q^55 - 4 * q^57 + 20 * q^59 - 14 * q^61 + 16 * q^63 + 10 * q^67 - 18 * q^69 - q^71 - 12 * q^73 + 8 * q^75 - 24 * q^77 - 28 * q^79 + 14 * q^81 + 7 * q^85 + 16 * q^87 + 2 * q^89 + 16 * q^93 - 2 * q^95 + 4 * q^97 + 28 * q^99

Character values

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

$n$	$677$	$1015$	$1185$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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	0.547653	−	0.836705i	$-0.315521\pi$
$3$	−0.780776	−	1.35234i	−0.450781	−	0.780776i	−0.998435	+	0.0559290i	$0.982188\pi$
$4$		0			0
$5$	−1.56155			−0.698348			−0.349174	−	0.937058i	$-0.613538\pi$
$5$	−1.56155			−0.698348			−0.349174	+	0.937058i	$0.613538\pi$
$6$		0			0
$7$	0.219224	−	0.379706i	0.0828587	−	0.143516i	−0.821618	−	0.570038i	$-0.806928\pi$
$7$	0.219224	−	0.379706i	0.0828587	−	0.143516i	0.904477	+	0.426523i	$0.140262\pi$
$8$		0			0
$9$	0.280776	−	0.486319i	0.0935921	−	0.162106i
$10$		0			0
$11$	2.56155	+	4.43674i	0.772337	+	1.33773i	0.936279	+	0.351257i	$0.114246\pi$
$11$	2.56155	+	4.43674i	0.772337	+	1.33773i	−0.163942	+	0.986470i	$0.552421\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	1.21922	+	2.11176i	0.314802	+	0.545253i
$16$		0			0
$17$	−1.78078	+	3.08440i	−0.431902	+	0.748076i	−0.997037	−	0.0769225i	$-0.975491\pi$
$17$	−1.78078	+	3.08440i	−0.431902	+	0.748076i	0.565135	+	0.824998i	$0.308824\pi$
$18$		0			0
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$		0			0
$21$	−0.684658			−0.149405
$22$		0			0
$23$	−1.56155	−	2.70469i	−0.325606	−	0.563967i	0.656029	−	0.754736i	$-0.272235\pi$
$23$	−1.56155	−	2.70469i	−0.325606	−	0.563967i	−0.981635	+	0.190769i	$0.938902\pi$
$24$		0			0
$25$	−2.56155			−0.512311
$26$		0			0
$27$	−5.56155			−1.07032
$28$		0			0
$29$	2.56155	+	4.43674i	0.475668	+	0.823882i	0.999612	−	0.0278714i	$-0.00887289\pi$
$29$	2.56155	+	4.43674i	0.475668	+	0.823882i	−0.523943	+	0.851753i	$0.675540\pi$
$30$		0			0
$31$	−5.12311			−0.920137			−0.460068	−	0.887883i	$-0.652175\pi$
$31$	−5.12311			−0.920137			−0.460068	+	0.887883i	$0.652175\pi$
$32$		0			0
$33$	4.00000	−	6.92820i	0.696311	−	1.20605i
$34$		0			0
$35$	−0.342329	+	0.592932i	−0.0578642	+	0.100224i
$36$		0			0
$37$	4.78078	+	8.28055i	0.785955	+	1.36131i	0.928427	+	0.371515i	$0.121162\pi$
$37$	4.78078	+	8.28055i	0.785955	+	1.36131i	−0.142472	+	0.989799i	$0.545505\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.00000	+	6.92820i	0.624695	+	1.08200i	0.988600	+	0.150567i	$0.0481100\pi$
$41$	4.00000	+	6.92820i	0.624695	+	1.08200i	−0.363905	+	0.931436i	$0.618557\pi$
$42$		0			0
$43$	4.78078	−	8.28055i	0.729062	−	1.26277i	−0.228219	−	0.973610i	$-0.573290\pi$
$43$	4.78078	−	8.28055i	0.729062	−	1.26277i	0.957280	−	0.289162i	$-0.0933766\pi$
$44$		0			0
$45$	−0.438447	+	0.759413i	−0.0653598	+	0.113207i
$46$		0			0
$47$	7.56155			1.10297			0.551483	−	0.834186i	$-0.314062\pi$
$47$	7.56155			1.10297			0.551483	+	0.834186i	$0.314062\pi$
$48$		0			0
$49$	3.40388	+	5.89570i	0.486269	+	0.842242i
$50$		0			0
$51$	5.56155			0.778773
$52$		0			0
$53$	12.2462			1.68215			0.841073	−	0.540921i	$-0.181924\pi$
$53$	12.2462			1.68215			0.841073	+	0.540921i	$0.181924\pi$
$54$		0			0
$55$	−4.00000	−	6.92820i	−0.539360	−	0.934199i
$56$		0			0
$57$	3.12311			0.413665
$58$		0			0
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	−0.331949	−	0.943297i	$-0.607706\pi$
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	0.982894	−	0.184172i	$-0.0589603\pi$
$60$		0			0
$61$	−1.43845	+	2.49146i	−0.184174	+	0.318999i	−0.943298	−	0.331947i	$-0.892294\pi$
$61$	−1.43845	+	2.49146i	−0.184174	+	0.318999i	0.759124	+	0.650946i	$0.225628\pi$
$62$		0			0
$63$	−0.123106	−	0.213225i	−0.0155099	−	0.0268638i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.56155	+	7.90084i	0.557282	+	0.965241i	0.997722	+	0.0674592i	$0.0214892\pi$
$67$	4.56155	+	7.90084i	0.557282	+	0.965241i	−0.440440	+	0.897782i	$0.645177\pi$
$68$		0			0
$69$	−2.43845	+	4.22351i	−0.293555	+	0.508451i
$70$		0			0
$71$	−3.34233	+	5.78908i	−0.396662	+	0.687038i	−0.993312	−	0.115464i	$-0.963165\pi$
$71$	−3.34233	+	5.78908i	−0.396662	+	0.687038i	0.596650	+	0.802501i	$0.296498\pi$
$72$		0			0
$73$	9.36932			1.09660			0.548298	−	0.836283i	$-0.315276\pi$
$73$	9.36932			1.09660			0.548298	+	0.836283i	$0.315276\pi$
$74$		0			0
$75$	2.00000	+	3.46410i	0.230940	+	0.400000i
$76$		0			0
$77$	2.24621			0.255980
$78$		0			0
$79$	−11.1231			−1.25145			−0.625724	−	0.780045i	$-0.715196\pi$
$79$	−11.1231			−1.25145			−0.625724	+	0.780045i	$0.715196\pi$
$80$		0			0
$81$	3.50000	+	6.06218i	0.388889	+	0.673575i
$82$		0			0
$83$	8.24621			0.905139			0.452570	−	0.891729i	$-0.350507\pi$
$83$	8.24621			0.905139			0.452570	+	0.891729i	$0.350507\pi$
$84$		0			0
$85$	2.78078	−	4.81645i	0.301618	−	0.522417i
$86$		0			0
$87$	4.00000	−	6.92820i	0.428845	−	0.742781i
$88$		0			0
$89$	−1.56155	−	2.70469i	−0.165524	−	0.286696i	0.771317	−	0.636451i	$-0.219598\pi$
$89$	−1.56155	−	2.70469i	−0.165524	−	0.286696i	−0.936841	+	0.349755i	$0.886265\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	4.00000	+	6.92820i	0.414781	+	0.718421i
$94$		0			0
$95$	1.56155	−	2.70469i	0.160212	−	0.277495i
$96$		0			0
$97$	−3.12311	+	5.40938i	−0.317103	+	0.549239i	−0.979882	−	0.199576i	$-0.936044\pi$
$97$	−3.12311	+	5.40938i	−0.317103	+	0.549239i	0.662779	+	0.748815i	$0.269377\pi$
$98$		0			0
$99$	2.87689			0.289139
$100$		0			0
$101$	−5.68466	−	9.84612i	−0.565645	−	0.979725i	−0.996989	−	0.0775381i	$-0.975294\pi$
$101$	−5.68466	−	9.84612i	−0.565645	−	0.979725i	0.431345	−	0.902187i	$-0.358039\pi$
$102$		0			0
$103$	−3.12311			−0.307729			−0.153864	−	0.988092i	$-0.549172\pi$
$103$	−3.12311			−0.307729			−0.153864	+	0.988092i	$0.549172\pi$
$104$		0			0
$105$	1.06913			0.104336
$106$		0			0
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$		0			0
$109$	−3.31534			−0.317552			−0.158776	−	0.987315i	$-0.550755\pi$
$109$	−3.31534			−0.317552			−0.158776	+	0.987315i	$0.550755\pi$
$110$		0			0
$111$	7.46543	−	12.9305i	0.708588	−	1.22731i
$112$		0			0
$113$	−5.00000	+	8.66025i	−0.470360	+	0.814688i	−0.999425	−	0.0338931i	$-0.989209\pi$
$113$	−5.00000	+	8.66025i	−0.470360	+	0.814688i	0.529065	+	0.848581i	$0.322543\pi$
$114$		0			0
$115$	2.43845	+	4.22351i	0.227386	+	0.393845i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.780776	+	1.35234i	0.0715737	+	0.123969i
$120$		0			0
$121$	−7.62311	+	13.2036i	−0.693010	+	1.20033i
$122$		0			0
$123$	6.24621	−	10.8188i	0.563202	−	0.975494i
$124$		0			0
$125$	11.8078			1.05612
$126$		0			0
$127$	−2.43845	−	4.22351i	−0.216377	−	0.374776i	0.737321	−	0.675543i	$-0.236091\pi$
$127$	−2.43845	−	4.22351i	−0.216377	−	0.374776i	−0.953698	+	0.300767i	$0.902757\pi$
$128$		0			0
$129$	−14.9309			−1.31459
$130$		0			0
$131$	−3.31534			−0.289663			−0.144831	−	0.989456i	$-0.546264\pi$
$131$	−3.31534			−0.289663			−0.144831	+	0.989456i	$0.546264\pi$
$132$		0			0
$133$	0.438447	+	0.759413i	0.0380182	+	0.0658494i
$134$		0			0
$135$	8.68466			0.747456
$136$		0			0
$137$	−1.56155	+	2.70469i	−0.133412	+	0.231077i	−0.924990	−	0.379992i	$-0.875927\pi$
$137$	−1.56155	+	2.70469i	−0.133412	+	0.231077i	0.791577	+	0.611069i	$0.209260\pi$
$138$		0			0
$139$	3.90388	−	6.76172i	0.331123	−	0.573522i	−0.651609	−	0.758555i	$-0.725906\pi$
$139$	3.90388	−	6.76172i	0.331123	−	0.573522i	0.982732	+	0.185033i	$0.0592392\pi$
$140$		0			0
$141$	−5.90388	−	10.2258i	−0.497197	−	0.861170i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−4.00000	−	6.92820i	−0.332182	−	0.575356i
$146$		0			0
$147$	5.31534	−	9.20644i	0.438402	−	0.759335i
$148$		0			0
$149$	−3.56155	+	6.16879i	−0.291774	+	0.505367i	−0.974229	−	0.225560i	$-0.927579\pi$
$149$	−3.56155	+	6.16879i	−0.291774	+	0.505367i	0.682455	+	0.730927i	$0.260912\pi$
$150$		0			0
$151$	−11.5616			−0.940866			−0.470433	−	0.882436i	$-0.655902\pi$
$151$	−11.5616			−0.940866			−0.470433	+	0.882436i	$0.655902\pi$
$152$		0			0
$153$	1.00000	+	1.73205i	0.0808452	+	0.140028i
$154$		0			0
$155$	8.00000			0.642575
$156$		0			0
$157$	12.2462			0.977354			0.488677	−	0.872465i	$-0.337480\pi$
$157$	12.2462			0.977354			0.488677	+	0.872465i	$0.337480\pi$
$158$		0			0
$159$	−9.56155	−	16.5611i	−0.758280	−	1.31338i
$160$		0			0
$161$	−1.36932			−0.107917
$162$		0			0
$163$	−10.1231	+	17.5337i	−0.792903	+	1.37335i	0.131260	+	0.991348i	$0.458098\pi$
$163$	−10.1231	+	17.5337i	−0.792903	+	1.37335i	−0.924162	+	0.382000i	$0.875235\pi$
$164$		0			0
$165$	−6.24621	+	10.8188i	−0.486267	+	0.842239i
$166$		0			0
$167$	−3.43845	−	5.95557i	−0.266075	−	0.460855i	0.701770	−	0.712404i	$-0.252394\pi$
$167$	−3.43845	−	5.95557i	−0.266075	−	0.460855i	−0.967845	+	0.251548i	$0.919060\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	0.561553	+	0.972638i	0.0429430	+	0.0743795i
$172$		0			0
$173$	2.12311	−	3.67733i	0.161417	−	0.279582i	−0.773960	−	0.633234i	$-0.781727\pi$
$173$	2.12311	−	3.67733i	0.161417	−	0.279582i	0.935377	+	0.353652i	$0.115060\pi$
$174$		0			0
$175$	−0.561553	+	0.972638i	−0.0424494	+	0.0735245i
$176$		0			0
$177$	−15.6155			−1.17373
$178$		0			0
$179$	8.78078	+	15.2088i	0.656306	+	1.13676i	0.981565	+	0.191130i	$0.0612153\pi$
$179$	8.78078	+	15.2088i	0.656306	+	1.13676i	−0.325259	+	0.945625i	$0.605451\pi$
$180$		0			0
$181$	8.24621			0.612936			0.306468	−	0.951881i	$-0.400853\pi$
$181$	8.24621			0.612936			0.306468	+	0.951881i	$0.400853\pi$
$182$		0			0
$183$	4.49242			0.332089
$184$		0			0
$185$	−7.46543	−	12.9305i	−0.548870	−	0.950670i
$186$		0			0
$187$	−18.2462			−1.33430
$188$		0			0
$189$	−1.21922	+	2.11176i	−0.0886855	+	0.153608i
$190$		0			0
$191$	11.1231	−	19.2658i	0.804840	−	1.39402i	−0.111560	−	0.993758i	$-0.535585\pi$
$191$	11.1231	−	19.2658i	0.804840	−	1.39402i	0.916399	−	0.400265i	$-0.131082\pi$
$192$		0			0
$193$	11.8078	+	20.4516i	0.849941	+	1.47214i	0.881260	+	0.472632i	$0.156696\pi$
$193$	11.8078	+	20.4516i	0.849941	+	1.47214i	−0.0313183	+	0.999509i	$0.509971\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−4.78078	−	8.28055i	−0.340616	−	0.589965i	0.643931	−	0.765084i	$-0.277302\pi$
$197$	−4.78078	−	8.28055i	−0.340616	−	0.589965i	−0.984547	+	0.175119i	$0.943969\pi$
$198$		0			0
$199$	−7.12311	+	12.3376i	−0.504944	+	0.874588i	0.495040	+	0.868870i	$0.335153\pi$
$199$	−7.12311	+	12.3376i	−0.504944	+	0.874588i	−0.999984	+	0.00571778i	$0.998180\pi$
$200$		0			0
$201$	7.12311	−	12.3376i	0.502425	−	0.870226i
$202$		0			0
$203$	2.24621			0.157653
$204$		0			0
$205$	−6.24621	−	10.8188i	−0.436254	−	0.755615i
$206$		0			0
$207$	−1.75379			−0.121897
$208$		0			0
$209$	−10.2462			−0.708745
$210$		0			0
$211$	11.0270	+	19.0993i	0.759129	+	1.31485i	0.943295	+	0.331955i	$0.107708\pi$
$211$	11.0270	+	19.0993i	0.759129	+	1.31485i	−0.184166	+	0.982895i	$0.558958\pi$
$212$		0			0
$213$	10.4384			0.715231
$214$		0			0
$215$	−7.46543	+	12.9305i	−0.509138	+	0.881854i
$216$		0			0
$217$	−1.12311	+	1.94528i	−0.0762414	+	0.132054i
$218$		0			0
$219$	−7.31534	−	12.6705i	−0.494325	−	0.856196i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−13.5885	−	23.5360i	−0.909956	−	1.57609i	−0.814123	−	0.580693i	$-0.802782\pi$
$223$	−13.5885	−	23.5360i	−0.909956	−	1.57609i	−0.0958330	−	0.995397i	$-0.530551\pi$
$224$		0			0
$225$	−0.719224	+	1.24573i	−0.0479482	+	0.0830488i
$226$		0			0
$227$	−1.68466	+	2.91791i	−0.111815	+	0.193669i	−0.916502	−	0.400030i	$-0.869000\pi$
$227$	−1.68466	+	2.91791i	−0.111815	+	0.193669i	0.804687	+	0.593699i	$0.202333\pi$
$228$		0			0
$229$	−20.6847			−1.36688			−0.683440	−	0.730006i	$-0.739517\pi$
$229$	−20.6847			−1.36688			−0.683440	+	0.730006i	$0.739517\pi$
$230$		0			0
$231$	−1.75379	−	3.03765i	−0.115391	−	0.199863i
$232$		0			0
$233$	3.56155			0.233325			0.116663	−	0.993172i	$-0.462780\pi$
$233$	3.56155			0.233325			0.116663	+	0.993172i	$0.462780\pi$
$234$		0			0
$235$	−11.8078			−0.770254
$236$		0			0
$237$	8.68466	+	15.0423i	0.564129	+	0.977100i
$238$		0			0
$239$	−8.93087			−0.577690			−0.288845	−	0.957376i	$-0.593271\pi$
$239$	−8.93087			−0.577690			−0.288845	+	0.957376i	$0.593271\pi$
$240$		0			0
$241$	−13.5616	+	23.4893i	−0.873576	+	1.51308i	−0.0153049	+	0.999883i	$0.504872\pi$
$241$	−13.5616	+	23.4893i	−0.873576	+	1.51308i	−0.858272	+	0.513196i	$0.828461\pi$
$242$		0			0
$243$	−2.87689	+	4.98293i	−0.184553	+	0.319655i
$244$		0			0
$245$	−5.31534	−	9.20644i	−0.339585	−	0.588178i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−6.43845	−	11.1517i	−0.408020	−	0.706711i
$250$		0			0
$251$	12.2462	−	21.2111i	0.772974	−	1.33883i	−0.162952	−	0.986634i	$-0.552102\pi$
$251$	12.2462	−	21.2111i	0.772974	−	1.33883i	0.935926	−	0.352196i	$-0.114565\pi$
$252$		0			0
$253$	8.00000	−	13.8564i	0.502956	−	0.871145i
$254$		0			0
$255$	−8.68466			−0.543854
$256$		0			0
$257$	0.465435	+	0.806157i	0.0290330	+	0.0502867i	0.880177	−	0.474646i	$-0.157424\pi$
$257$	0.465435	+	0.806157i	0.0290330	+	0.0502867i	−0.851144	+	0.524933i	$0.824091\pi$
$258$		0			0
$259$	4.19224			0.260493
$260$		0			0
$261$	2.87689			0.178075
$262$		0			0
$263$	2.24621	+	3.89055i	0.138507	+	0.239902i	0.926932	−	0.375230i	$-0.122436\pi$
$263$	2.24621	+	3.89055i	0.138507	+	0.239902i	−0.788424	+	0.615132i	$0.789103\pi$
$264$		0			0
$265$	−19.1231			−1.17472
$266$		0			0
$267$	−2.43845	+	4.22351i	−0.149231	+	0.258475i
$268$		0			0
$269$	−5.43845	+	9.41967i	−0.331588	+	0.574327i	−0.982823	−	0.184549i	$-0.940918\pi$
$269$	−5.43845	+	9.41967i	−0.331588	+	0.574327i	0.651235	+	0.758876i	$0.274251\pi$
$270$		0			0
$271$	7.34233	+	12.7173i	0.446015	+	0.772520i	0.998122	−	0.0612527i	$-0.0195096\pi$
$271$	7.34233	+	12.7173i	0.446015	+	0.772520i	−0.552108	+	0.833773i	$0.686176\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−6.56155	−	11.3649i	−0.395677	−	0.685332i
$276$		0			0
$277$	3.68466	−	6.38202i	0.221390	−	0.383458i	−0.733841	−	0.679322i	$-0.762274\pi$
$277$	3.68466	−	6.38202i	0.221390	−	0.383458i	0.955230	+	0.295864i	$0.0956074\pi$
$278$		0			0
$279$	−1.43845	+	2.49146i	−0.0861176	+	0.149160i
$280$		0			0
$281$	−9.36932			−0.558927			−0.279463	−	0.960156i	$-0.590157\pi$
$281$	−9.36932			−0.558927			−0.279463	+	0.960156i	$0.590157\pi$
$282$		0			0
$283$	6.00000	+	10.3923i	0.356663	+	0.617758i	0.987401	−	0.158237i	$-0.0505811\pi$
$283$	6.00000	+	10.3923i	0.356663	+	0.617758i	−0.630738	+	0.775996i	$0.717248\pi$
$284$		0			0
$285$	−4.87689			−0.288882
$286$		0			0
$287$	3.50758			0.207046
$288$		0			0
$289$	2.15767	+	3.73720i	0.126922	+	0.219835i
$290$		0			0
$291$	9.75379			0.571777
$292$		0			0
$293$	−6.34233	+	10.9852i	−0.370523	+	0.641764i	−0.989646	−	0.143529i	$-0.954155\pi$
$293$	−6.34233	+	10.9852i	−0.370523	+	0.641764i	0.619123	+	0.785294i	$0.287488\pi$
$294$		0			0
$295$	−7.80776	+	13.5234i	−0.454586	+	0.787365i
$296$		0			0
$297$	−14.2462	−	24.6752i	−0.826649	−	1.43180i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−2.09612	−	3.63058i	−0.120818	−	0.209263i
$302$		0			0
$303$	−8.87689	+	15.3752i	−0.509964	+	0.883284i
$304$		0			0
$305$	2.24621	−	3.89055i	0.128618	−	0.222772i
$306$		0			0
$307$	−18.0000			−1.02731			−0.513657	−	0.857996i	$-0.671710\pi$
$307$	−18.0000			−1.02731			−0.513657	+	0.857996i	$0.671710\pi$
$308$		0			0
$309$	2.43845	+	4.22351i	0.138718	+	0.240267i
$310$		0			0
$311$	−19.1231			−1.08437			−0.542186	−	0.840259i	$-0.682403\pi$
$311$	−19.1231			−1.08437			−0.542186	+	0.840259i	$0.682403\pi$
$312$		0			0
$313$	4.43845			0.250876			0.125438	−	0.992101i	$-0.459966\pi$
$313$	4.43845			0.250876			0.125438	+	0.992101i	$0.459966\pi$
$314$		0			0
$315$	0.192236	+	0.332962i	0.0108313	+	0.0187603i
$316$		0			0
$317$	15.1231			0.849398			0.424699	−	0.905335i	$-0.360380\pi$
$317$	15.1231			0.849398			0.424699	+	0.905335i	$0.360380\pi$
$318$		0			0
$319$	−13.1231	+	22.7299i	−0.734753	+	1.27263i
$320$		0			0
$321$	3.12311	−	5.40938i	0.174315	−	0.301922i
$322$		0			0
$323$	−3.56155	−	6.16879i	−0.198170	−	0.343241i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	2.58854	+	4.48348i	0.143147	+	0.247937i
$328$		0			0
$329$	1.65767	−	2.87117i	0.0913903	−	0.158293i
$330$		0			0
$331$	−0.123106	+	0.213225i	−0.00676650	+	0.0117199i	−0.869389	−	0.494129i	$-0.835487\pi$
$331$	−0.123106	+	0.213225i	−0.00676650	+	0.0117199i	0.862622	+	0.505849i	$0.168821\pi$
$332$		0			0
$333$	5.36932			0.294237
$334$		0			0
$335$	−7.12311	−	12.3376i	−0.389177	−	0.674074i
$336$		0			0
$337$	−1.31534			−0.0716512			−0.0358256	−	0.999358i	$-0.511406\pi$
$337$	−1.31534			−0.0716512			−0.0358256	+	0.999358i	$0.511406\pi$
$338$		0			0
$339$	15.6155			0.848119
$340$		0			0
$341$	−13.1231	−	22.7299i	−0.710656	−	1.23089i
$342$		0			0
$343$	6.05398			0.326884
$344$		0			0
$345$	3.80776	−	6.59524i	0.205003	−	0.355076i
$346$		0			0
$347$	0.780776	−	1.35234i	0.0419143	−	0.0725977i	−0.844307	−	0.535859i	$-0.819988\pi$
$347$	0.780776	−	1.35234i	0.0419143	−	0.0725977i	0.886221	+	0.463262i	$0.153321\pi$
$348$		0			0
$349$	−5.46543	−	9.46641i	−0.292558	−	0.506725i	0.681856	−	0.731487i	$-0.261173\pi$
$349$	−5.46543	−	9.46641i	−0.292558	−	0.506725i	−0.974414	+	0.224761i	$0.927840\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.80776	−	6.59524i	−0.202667	−	0.351029i	0.746720	−	0.665138i	$-0.231628\pi$
$353$	−3.80776	−	6.59524i	−0.202667	−	0.351029i	−0.949387	+	0.314109i	$0.898294\pi$
$354$		0			0
$355$	5.21922	−	9.03996i	0.277008	−	0.479791i
$356$		0			0
$357$	1.21922	−	2.11176i	0.0645282	−	0.111766i
$358$		0			0
$359$	13.1231			0.692611			0.346306	−	0.938122i	$-0.387436\pi$
$359$	13.1231			0.692611			0.346306	+	0.938122i	$0.387436\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$		0			0
$363$	23.8078			1.24958
$364$		0			0
$365$	−14.6307			−0.765805
$366$		0			0
$367$	−14.2462	−	24.6752i	−0.743646	−	1.28803i	−0.950825	−	0.309730i	$-0.899761\pi$
$367$	−14.2462	−	24.6752i	−0.743646	−	1.28803i	0.207178	−	0.978303i	$-0.433572\pi$
$368$		0			0
$369$	4.49242			0.233866
$370$		0			0
$371$	2.68466	−	4.64996i	0.139381	−	0.241414i
$372$		0			0
$373$	17.6847	−	30.6307i	0.915677	−	1.58600i	0.109770	−	0.993957i	$-0.464989\pi$
$373$	17.6847	−	30.6307i	0.915677	−	1.58600i	0.805907	−	0.592042i	$-0.201678\pi$
$374$		0			0
$375$	−9.21922	−	15.9682i	−0.476079	−	0.824592i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−13.0000	−	22.5167i	−0.667765	−	1.15660i	−0.978528	−	0.206116i	$-0.933918\pi$
$379$	−13.0000	−	22.5167i	−0.667765	−	1.15660i	0.310763	−	0.950488i	$-0.399416\pi$
$380$		0			0
$381$	−3.80776	+	6.59524i	−0.195078	+	0.337884i
$382$		0			0
$383$	14.9039	−	25.8143i	0.761553	−	1.31905i	−0.180497	−	0.983576i	$-0.557771\pi$
$383$	14.9039	−	25.8143i	0.761553	−	1.31905i	0.942050	−	0.335473i	$-0.108896\pi$
$384$		0			0
$385$	−3.50758			−0.178763
$386$		0			0
$387$	−2.68466	−	4.64996i	−0.136469	−	0.236371i
$388$		0			0
$389$	11.7538			0.595941			0.297970	−	0.954575i	$-0.403690\pi$
$389$	11.7538			0.595941			0.297970	+	0.954575i	$0.403690\pi$
$390$		0			0
$391$	11.1231			0.562520
$392$		0			0
$393$	2.58854	+	4.48348i	0.130575	+	0.226162i
$394$		0			0
$395$	17.3693			0.873945
$396$		0			0
$397$	−0.438447	+	0.759413i	−0.0220050	+	0.0381138i	−0.876818	−	0.480822i	$-0.840338\pi$
$397$	−0.438447	+	0.759413i	−0.0220050	+	0.0381138i	0.854813	+	0.518936i	$0.173672\pi$
$398$		0			0
$399$	0.684658	−	1.18586i	0.0342758	−	0.0593674i
$400$		0			0
$401$	−8.68466	−	15.0423i	−0.433691	−	0.751175i	0.563497	−	0.826118i	$-0.309456\pi$
$401$	−8.68466	−	15.0423i	−0.433691	−	0.751175i	−0.997188	+	0.0749432i	$0.976122\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−5.46543	−	9.46641i	−0.271580	−	0.470390i
$406$		0			0
$407$	−24.4924	+	42.4221i	−1.21404	+	2.10279i
$408$		0			0
$409$	−12.6847	+	21.9705i	−0.627216	+	1.08637i	0.360892	+	0.932608i	$0.382472\pi$
$409$	−12.6847	+	21.9705i	−0.627216	+	1.08637i	−0.988108	+	0.153762i	$0.950861\pi$
$410$		0			0
$411$	4.87689			0.240559
$412$		0			0
$413$	−2.19224	−	3.79706i	−0.107873	−	0.186841i
$414$		0			0
$415$	−12.8769			−0.632102
$416$		0			0
$417$	−12.1922			−0.597056
$418$		0			0
$419$	15.2192	+	26.3605i	0.743508	+	1.28779i	0.950889	+	0.309533i	$0.100173\pi$
$419$	15.2192	+	26.3605i	0.743508	+	1.28779i	−0.207381	+	0.978260i	$0.566494\pi$
$420$		0			0
$421$	−23.8078			−1.16032			−0.580160	−	0.814503i	$-0.697010\pi$
$421$	−23.8078			−1.16032			−0.580160	+	0.814503i	$0.697010\pi$
$422$		0			0
$423$	2.12311	−	3.67733i	0.103229	−	0.178798i
$424$		0			0
$425$	4.56155	−	7.90084i	0.221268	−	0.383247i
$426$		0			0
$427$	0.630683	+	1.09238i	0.0305209	+	0.0528637i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	18.7116	+	32.4095i	0.901308	+	1.56111i	0.825797	+	0.563967i	$0.190725\pi$
$431$	18.7116	+	32.4095i	0.901308	+	1.56111i	0.0755108	+	0.997145i	$0.475941\pi$
$432$		0			0
$433$	4.65767	−	8.06732i	0.223833	−	0.387691i	−0.732135	−	0.681159i	$-0.761476\pi$
$433$	4.65767	−	8.06732i	0.223833	−	0.387691i	0.955969	+	0.293468i	$0.0948095\pi$
$434$		0			0
$435$	−6.24621	+	10.8188i	−0.299483	+	0.518720i
$436$		0			0
$437$	6.24621			0.298797
$438$		0			0
$439$	−18.9309	−	32.7892i	−0.903521	−	1.56494i	−0.822890	−	0.568200i	$-0.807640\pi$
$439$	−18.9309	−	32.7892i	−0.903521	−	1.56494i	−0.0806309	−	0.996744i	$-0.525694\pi$
$440$		0			0
$441$	3.82292			0.182044
$442$		0			0
$443$	−9.17708			−0.436016			−0.218008	−	0.975947i	$-0.569956\pi$
$443$	−9.17708			−0.436016			−0.218008	+	0.975947i	$0.569956\pi$
$444$		0			0
$445$	2.43845	+	4.22351i	0.115593	+	0.200214i
$446$		0			0
$447$	11.1231			0.526105
$448$		0			0
$449$	8.00000	−	13.8564i	0.377543	−	0.653924i	−0.613161	−	0.789958i	$-0.710102\pi$
$449$	8.00000	−	13.8564i	0.377543	−	0.653924i	0.990704	+	0.136034i	$0.0434356\pi$
$450$		0			0
$451$	−20.4924	+	35.4939i	−0.964950	+	1.67134i
$452$		0			0
$453$	9.02699	+	15.6352i	0.424125	+	0.734606i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	7.80776	+	13.5234i	0.365232	+	0.632600i	0.988813	−	0.149158i	$-0.0476564\pi$
$457$	7.80776	+	13.5234i	0.365232	+	0.632600i	−0.623582	+	0.781758i	$0.714323\pi$
$458$		0			0
$459$	9.90388	−	17.1540i	0.462274	−	0.800681i
$460$		0			0
$461$	−4.58854	+	7.94759i	−0.213710	+	0.370156i	−0.952873	−	0.303371i	$-0.901888\pi$
$461$	−4.58854	+	7.94759i	−0.213710	+	0.370156i	0.739163	+	0.673527i	$0.235221\pi$
$462$		0			0
$463$	1.61553			0.0750800			0.0375400	−	0.999295i	$-0.488048\pi$
$463$	1.61553			0.0750800			0.0375400	+	0.999295i	$0.488048\pi$
$464$		0			0
$465$	−6.24621	−	10.8188i	−0.289661	−	0.501708i
$466$		0			0
$467$	−16.4924			−0.763178			−0.381589	−	0.924332i	$-0.624623\pi$
$467$	−16.4924			−0.763178			−0.381589	+	0.924332i	$0.624623\pi$
$468$		0			0
$469$	4.00000			0.184703
$470$		0			0
$471$	−9.56155	−	16.5611i	−0.440573	−	0.763095i
$472$		0			0
$473$	48.9848			2.25233
$474$		0			0
$475$	2.56155	−	4.43674i	0.117532	−	0.203572i
$476$		0			0
$477$	3.43845	−	5.95557i	0.157436	−	0.272687i
$478$		0			0
$479$	−14.9039	−	25.8143i	−0.680976	−	1.17948i	−0.974683	−	0.223589i	$-0.928223\pi$
$479$	−14.9039	−	25.8143i	−0.680976	−	1.17948i	0.293708	−	0.955895i	$-0.405111\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	1.06913	+	1.85179i	0.0486471	+	0.0842593i
$484$		0			0
$485$	4.87689	−	8.44703i	0.221448	−	0.383560i
$486$		0			0
$487$	7.93087	−	13.7367i	0.359382	−	0.622468i	−0.628476	−	0.777829i	$-0.716321\pi$
$487$	7.93087	−	13.7367i	0.359382	−	0.622468i	0.987858	+	0.155361i	$0.0496542\pi$
$488$		0			0
$489$	31.6155			1.42970
$490$		0			0
$491$	15.9039	+	27.5463i	0.717732	+	1.24315i	0.961896	+	0.273415i	$0.0881531\pi$
$491$	15.9039	+	27.5463i	0.717732	+	1.24315i	−0.244164	+	0.969734i	$0.578514\pi$
$492$		0			0
$493$	−18.2462			−0.821768
$494$		0			0
$495$	−4.49242			−0.201919
$496$		0			0
$497$	1.46543	+	2.53821i	0.0657337	+	0.113854i
$498$		0			0
$499$	−25.1231			−1.12466			−0.562332	−	0.826911i	$-0.690096\pi$
$499$	−25.1231			−1.12466			−0.562332	+	0.826911i	$0.690096\pi$
$500$		0			0
$501$	−5.36932	+	9.29993i	−0.239883	+	0.415490i
$502$		0			0
$503$	−4.68466	+	8.11407i	−0.208879	+	0.361788i	−0.951362	−	0.308077i	$-0.900315\pi$
$503$	−4.68466	+	8.11407i	−0.208879	+	0.361788i	0.742483	+	0.669865i	$0.233648\pi$
$504$		0			0
$505$	8.87689	+	15.3752i	0.395017	+	0.684189i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.31534	−	2.27824i	−0.0583015	−	0.100981i	0.835402	−	0.549640i	$-0.185235\pi$
$509$	−1.31534	−	2.27824i	−0.0583015	−	0.100981i	−0.893703	+	0.448659i	$0.851902\pi$
$510$		0			0
$511$	2.05398	−	3.55759i	0.0908625	−	0.157378i
$512$		0			0
$513$	5.56155	−	9.63289i	0.245549	−	0.425303i
$514$		0			0
$515$	4.87689			0.214902
$516$		0			0
$517$	19.3693	+	33.5486i	0.851862	+	1.47547i
$518$		0			0
$519$	−6.63068			−0.291055
$520$		0			0
$521$	0.930870			0.0407821			0.0203911	−	0.999792i	$-0.493509\pi$
$521$	0.930870			0.0407821			0.0203911	+	0.999792i	$0.493509\pi$
$522$		0			0
$523$	6.87689	+	11.9111i	0.300706	+	0.520837i	0.976296	−	0.216440i	$-0.0694445\pi$
$523$	6.87689	+	11.9111i	0.300706	+	0.520837i	−0.675590	+	0.737277i	$0.736111\pi$
$524$		0			0
$525$	1.75379			0.0765416
$526$		0			0
$527$	9.12311	−	15.8017i	0.397409	−	0.688332i
$528$		0			0
$529$	6.62311	−	11.4716i	0.287961	−	0.498763i
$530$		0			0
$531$	−2.80776	−	4.86319i	−0.121847	−	0.211044i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−3.12311	−	5.40938i	−0.135024	−	0.233868i
$536$		0			0
$537$	13.7116	−	23.7493i	0.591701	−	1.02486i
$538$		0			0
$539$	−17.4384	+	30.2043i	−0.751127	+	1.30099i
$540$		0			0
$541$	−25.1771			−1.08245			−0.541224	−	0.840879i	$-0.682039\pi$
$541$	−25.1771			−1.08245			−0.541224	+	0.840879i	$0.682039\pi$
$542$		0			0
$543$	−6.43845	−	11.1517i	−0.276300	−	0.478566i
$544$		0			0
$545$	5.17708			0.221762
$546$		0			0
$547$	23.8078			1.01795			0.508973	−	0.860782i	$-0.330025\pi$
$547$	23.8078			1.01795			0.508973	+	0.860782i	$0.330025\pi$
$548$		0			0
$549$	0.807764	+	1.39909i	0.0344745	+	0.0597116i
$550$		0			0
$551$	−10.2462			−0.436503
$552$		0			0
$553$	−2.43845	+	4.22351i	−0.103693	+	0.179602i
$554$		0			0
$555$	−11.6577	+	20.1917i	−0.494841	+	0.857089i
$556$		0			0
$557$	9.46543	+	16.3946i	0.401063	+	0.694662i	0.993855	−	0.110694i	$-0.0353074\pi$
$557$	9.46543	+	16.3946i	0.401063	+	0.694662i	−0.592791	+	0.805356i	$0.701974\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	14.2462	+	24.6752i	0.601476	+	1.04179i
$562$		0			0
$563$	−13.4654	+	23.3228i	−0.567500	+	0.982940i	0.429312	+	0.903156i	$0.358756\pi$
$563$	−13.4654	+	23.3228i	−0.567500	+	0.982940i	−0.996812	+	0.0797832i	$0.974577\pi$
$564$		0			0
$565$	7.80776	−	13.5234i	0.328475	−	0.568936i
$566$		0			0
$567$	3.06913			0.128891
$568$		0			0
$569$	−1.09612	−	1.89853i	−0.0459517	−	0.0795906i	0.842135	−	0.539267i	$-0.181299\pi$
$569$	−1.09612	−	1.89853i	−0.0459517	−	0.0795906i	−0.888086	+	0.459677i	$0.847965\pi$
$570$		0			0
$571$	14.0540			0.588141			0.294070	−	0.955784i	$-0.404990\pi$
$571$	14.0540			0.588141			0.294070	+	0.955784i	$0.404990\pi$
$572$		0			0
$573$	−34.7386			−1.45123
$574$		0			0
$575$	4.00000	+	6.92820i	0.166812	+	0.288926i
$576$		0			0
$577$	−29.8617			−1.24316			−0.621580	−	0.783351i	$-0.713509\pi$
$577$	−29.8617			−1.24316			−0.621580	+	0.783351i	$0.713509\pi$
$578$		0			0
$579$	18.4384	−	31.9363i	0.766276	−	1.32723i
$580$		0			0
$581$	1.80776	−	3.13114i	0.0749987	−	0.129902i
$582$		0			0
$583$	31.3693	+	54.3333i	1.29918	+	2.25025i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.75379	+	8.23380i	0.196210	+	0.339845i	0.947296	−	0.320358i	$-0.103803\pi$
$587$	4.75379	+	8.23380i	0.196210	+	0.339845i	−0.751087	+	0.660204i	$0.770470\pi$
$588$		0			0
$589$	5.12311	−	8.87348i	0.211094	−	0.365625i
$590$		0			0
$591$	−7.46543	+	12.9305i	−0.307087	+	0.531890i
$592$		0			0
$593$	25.7538			1.05758			0.528791	−	0.848752i	$-0.322646\pi$
$593$	25.7538			1.05758			0.528791	+	0.848752i	$0.322646\pi$
$594$		0			0
$595$	−1.21922	−	2.11176i	−0.0499833	−	0.0865736i
$596$		0			0
$597$	22.2462			0.910477
$598$		0			0
$599$	41.3693			1.69030			0.845152	−	0.534526i	$-0.179510\pi$
$599$	41.3693			1.69030			0.845152	+	0.534526i	$0.179510\pi$
$600$		0			0
$601$	−10.9039	−	18.8861i	−0.444779	−	0.770379i	0.553258	−	0.833010i	$-0.313384\pi$
$601$	−10.9039	−	18.8861i	−0.444779	−	0.770379i	−0.998037	+	0.0626307i	$0.980051\pi$
$602$		0			0
$603$	5.12311			0.208629
$604$		0			0
$605$	11.9039	−	20.6181i	0.483962	−	0.838246i
$606$		0			0
$607$	3.80776	−	6.59524i	0.154552	−	0.267693i	−0.778344	−	0.627839i	$-0.783940\pi$
$607$	3.80776	−	6.59524i	0.154552	−	0.267693i	0.932896	+	0.360146i	$0.117273\pi$
$608$		0			0
$609$	−1.75379	−	3.03765i	−0.0710671	−	0.123092i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	9.31534	+	16.1346i	0.376243	+	0.651672i	0.990512	−	0.137424i	$-0.0438824\pi$
$613$	9.31534	+	16.1346i	0.376243	+	0.651672i	−0.614269	+	0.789097i	$0.710549\pi$
$614$		0			0
$615$	−9.75379	+	16.8941i	−0.393311	+	0.681234i
$616$		0			0
$617$	0.876894	−	1.51883i	0.0353024	−	0.0611456i	−0.847834	−	0.530261i	$-0.822094\pi$
$617$	0.876894	−	1.51883i	0.0353024	−	0.0611456i	0.883137	+	0.469116i	$0.155427\pi$
$618$		0			0
$619$	−17.6155			−0.708028			−0.354014	−	0.935240i	$-0.615183\pi$
$619$	−17.6155			−0.708028			−0.354014	+	0.935240i	$0.615183\pi$
$620$		0			0
$621$	8.68466	+	15.0423i	0.348503	+	0.603625i
$622$		0			0
$623$	−1.36932			−0.0548605
$624$		0			0
$625$	−5.63068			−0.225227
$626$		0			0
$627$	8.00000	+	13.8564i	0.319489	+	0.553372i
$628$		0			0
$629$	−34.0540			−1.35782
$630$		0			0
$631$	5.78078	−	10.0126i	0.230129	−	0.398595i	−0.727717	−	0.685878i	$-0.759418\pi$
$631$	5.78078	−	10.0126i	0.230129	−	0.398595i	0.957846	+	0.287282i	$0.0927518\pi$
$632$		0			0
$633$	17.2192	−	29.8246i	0.684403	−	1.18542i
$634$		0			0
$635$	3.80776	+	6.59524i	0.151107	+	0.261724i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1.87689	+	3.25088i	0.0742488	+	0.128603i
$640$		0			0
$641$	1.87689	−	3.25088i	0.0741329	−	0.128402i	−0.826576	−	0.562825i	$-0.809714\pi$
$641$	1.87689	−	3.25088i	0.0741329	−	0.128402i	0.900709	+	0.434423i	$0.143048\pi$
$642$		0			0
$643$	12.5616	−	21.7572i	0.495379	−	0.858022i	−0.504607	−	0.863349i	$-0.668362\pi$
$643$	12.5616	−	21.7572i	0.495379	−	0.858022i	0.999986	+	0.00532735i	$0.00169576\pi$
$644$		0			0
$645$	23.3153			0.918041
$646$		0			0
$647$	1.56155	+	2.70469i	0.0613910	+	0.106332i	0.895087	−	0.445891i	$-0.147113\pi$
$647$	1.56155	+	2.70469i	0.0613910	+	0.106332i	−0.833696	+	0.552223i	$0.813780\pi$
$648$		0			0
$649$	51.2311			2.01099
$650$		0			0
$651$	3.50758			0.137473
$652$		0			0
$653$	−6.80776	−	11.7914i	−0.266408	−	0.461433i	0.701523	−	0.712647i	$-0.252504\pi$
$653$	−6.80776	−	11.7914i	−0.266408	−	0.461433i	−0.967932	+	0.251214i	$0.919170\pi$
$654$		0			0
$655$	5.17708			0.202285
$656$		0			0
$657$	2.63068	−	4.55648i	0.102633	−	0.177765i
$658$		0			0
$659$	−3.36932	+	5.83583i	−0.131250	+	0.227332i	−0.924159	−	0.382009i	$-0.875232\pi$
$659$	−3.36932	+	5.83583i	−0.131250	+	0.227332i	0.792909	+	0.609340i	$0.208566\pi$
$660$		0			0
$661$	16.4384	+	28.4722i	0.639381	+	1.10744i	0.985569	+	0.169276i	$0.0541429\pi$
$661$	16.4384	+	28.4722i	0.639381	+	1.10744i	−0.346187	+	0.938165i	$0.612524\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.684658	−	1.18586i	−0.0265499	−	0.0459858i
$666$		0			0
$667$	8.00000	−	13.8564i	0.309761	−	0.536522i
$668$		0			0
$669$	−21.2192	+	36.7528i	−0.820383	+	1.42094i
$670$		0			0
$671$	−14.7386			−0.568979
$672$		0			0
$673$	−11.1501	−	19.3125i	−0.429805	−	0.744443i	0.567051	−	0.823683i	$-0.308084\pi$
$673$	−11.1501	−	19.3125i	−0.429805	−	0.744443i	−0.996856	+	0.0792394i	$0.974751\pi$
$674$		0			0
$675$	14.2462			0.548337
$676$		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
$679$	1.36932	+	2.37173i	0.0525496	+	0.0910185i
$680$		0			0
$681$	5.26137			0.201616
$682$		0			0
$683$	−6.12311	+	10.6055i	−0.234294	+	0.405809i	−0.959067	−	0.283178i	$-0.908611\pi$
$683$	−6.12311	+	10.6055i	−0.234294	+	0.405809i	0.724773	+	0.688988i	$0.241945\pi$
$684$		0			0
$685$	2.43845	−	4.22351i	0.0931683	−	0.161372i
$686$		0			0
$687$	16.1501	+	27.9728i	0.616164	+	1.06723i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	13.9309	+	24.1290i	0.529955	+	0.917909i	0.999389	+	0.0349419i	$0.0111246\pi$
$691$	13.9309	+	24.1290i	0.529955	+	0.917909i	−0.469434	+	0.882968i	$0.655542\pi$
$692$		0			0
$693$	0.630683	−	1.09238i	0.0239577	−	0.0414959i
$694$		0			0
$695$	−6.09612	+	10.5588i	−0.231239	+	0.400518i
$696$		0			0
$697$	−28.4924			−1.07923
$698$		0			0
$699$	−2.78078	−	4.81645i	−0.105179	−	0.182175i
$700$		0			0
$701$	−37.2311			−1.40620			−0.703099	−	0.711092i	$-0.748201\pi$
$701$	−37.2311			−1.40620			−0.703099	+	0.711092i	$0.748201\pi$
$702$		0			0
$703$	−19.1231			−0.721242
$704$		0			0
$705$	9.21922	+	15.9682i	0.347216	+	0.601396i
$706$		0			0
$707$	−4.98485			−0.187474
$708$		0			0
$709$	3.56155	−	6.16879i	0.133757	−	0.231674i	−0.791365	−	0.611344i	$-0.790629\pi$
$709$	3.56155	−	6.16879i	0.133757	−	0.231674i	0.925122	+	0.379670i	$0.123963\pi$
$710$		0			0
$711$	−3.12311	+	5.40938i	−0.117126	+	0.202868i
$712$		0			0
$713$	8.00000	+	13.8564i	0.299602	+	0.518927i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	6.97301	+	12.0776i	0.260412	+	0.451047i
$718$		0			0
$719$	−8.00000	+	13.8564i	−0.298350	+	0.516757i	−0.975759	−	0.218850i	$-0.929769\pi$
$719$	−8.00000	+	13.8564i	−0.298350	+	0.516757i	0.677409	+	0.735607i	$0.263103\pi$
$720$		0			0
$721$	−0.684658	+	1.18586i	−0.0254980	+	0.0441639i
$722$		0			0
$723$	42.3542			1.57517
$724$		0			0
$725$	−6.56155	−	11.3649i	−0.243690	−	0.422083i
$726$		0			0
$727$	−39.2311			−1.45500			−0.727500	−	0.686108i	$-0.759318\pi$
$727$	−39.2311			−1.45500			−0.727500	+	0.686108i	$0.759318\pi$
$728$		0			0
$729$	29.9848			1.11055
$730$		0			0
$731$	17.0270	+	29.4916i	0.629766	+	1.09079i
$732$		0			0
$733$	4.30019			0.158831			0.0794155	−	0.996842i	$-0.474695\pi$
$733$	4.30019			0.158831			0.0794155	+	0.996842i	$0.474695\pi$
$734$		0			0
$735$	−8.30019	+	14.3763i	−0.306157	+	0.530279i
$736$		0			0
$737$	−23.3693	+	40.4768i	−0.860820	+	1.49098i
$738$		0			0
$739$	7.93087	+	13.7367i	0.291742	+	0.505312i	0.974222	−	0.225593i	$-0.0724319\pi$
$739$	7.93087	+	13.7367i	0.291742	+	0.505312i	−0.682480	+	0.730904i	$0.739099\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	3.97301	+	6.88146i	0.145756	+	0.252456i	0.929655	−	0.368432i	$-0.120105\pi$
$743$	3.97301	+	6.88146i	0.145756	+	0.252456i	−0.783899	+	0.620888i	$0.786772\pi$
$744$		0			0
$745$	5.56155	−	9.63289i	0.203760	−	0.352922i
$746$		0			0
$747$	2.31534	−	4.01029i	0.0847139	−	0.146729i
$748$		0			0
$749$	1.75379			0.0640820
$750$		0			0
$751$	−1.75379	−	3.03765i	−0.0639967	−	0.110845i	0.832252	−	0.554398i	$-0.187051\pi$
$751$	−1.75379	−	3.03765i	−0.0639967	−	0.110845i	−0.896248	+	0.443552i	$0.853718\pi$
$752$		0			0
$753$	−38.2462			−1.39377
$754$		0			0
$755$	18.0540			0.657051
$756$		0			0
$757$	−11.0000	−	19.0526i	−0.399802	−	0.692477i	0.593899	−	0.804539i	$-0.297588\pi$
$757$	−11.0000	−	19.0526i	−0.399802	−	0.692477i	−0.993701	+	0.112062i	$0.964254\pi$
$758$		0			0
$759$	−24.9848			−0.906892
$760$		0			0
$761$	22.4384	−	38.8645i	0.813393	−	1.40884i	−0.0970830	−	0.995276i	$-0.530951\pi$
$761$	22.4384	−	38.8645i	0.813393	−	1.40884i	0.910476	−	0.413562i	$-0.135715\pi$
$762$		0			0
$763$	−0.726801	+	1.25886i	−0.0263120	+	0.0455737i
$764$		0			0
$765$	−1.56155	−	2.70469i	−0.0564581	−	0.0977882i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−14.2462	−	24.6752i	−0.513732	−	0.889809i	−0.999873	−	0.0159290i	$-0.994929\pi$
$769$	−14.2462	−	24.6752i	−0.513732	−	0.889809i	0.486142	−	0.873880i	$-0.338404\pi$
$770$		0			0
$771$	0.726801	−	1.25886i	0.0261751	−	0.0453366i
$772$		0			0
$773$	7.02699	−	12.1711i	0.252743	−	0.437764i	−0.711537	−	0.702649i	$-0.752001\pi$
$773$	7.02699	−	12.1711i	0.252743	−	0.437764i	0.964280	+	0.264885i	$0.0853339\pi$
$774$		0			0
$775$	13.1231			0.471396
$776$		0			0
$777$	−3.27320	−	5.66935i	−0.117425	−	0.203387i
$778$		0			0
$779$	−16.0000			−0.573259
$780$		0			0
$781$	−34.2462			−1.22543
$782$		0			0
$783$	−14.2462	−	24.6752i	−0.509118	−	0.881818i
$784$		0			0
$785$	−19.1231			−0.682533
$786$		0			0
$787$	1.68466	−	2.91791i	0.0600516	−	0.104012i	−0.834437	−	0.551104i	$-0.814207\pi$
$787$	1.68466	−	2.91791i	0.0600516	−	0.104012i	0.894488	+	0.447091i	$0.147540\pi$
$788$		0			0
$789$	3.50758	−	6.07530i	0.124873	−	0.216286i
$790$		0			0
$791$	2.19224	+	3.79706i	0.0779469	+	0.135008i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	14.9309	+	25.8610i	0.529543	+	0.917196i
$796$		0			0
$797$	6.12311	−	10.6055i	0.216892	−	0.375667i	−0.736965	−	0.675931i	$-0.763742\pi$
$797$	6.12311	−	10.6055i	0.216892	−	0.375667i	0.953856	+	0.300264i	$0.0970749\pi$
$798$		0			0
$799$	−13.4654	+	23.3228i	−0.476373	+	0.825102i
$800$		0			0
$801$	−1.75379			−0.0619671
$802$		0			0
$803$	24.0000	+	41.5692i	0.846942	+	1.46695i
$804$		0			0
$805$	2.13826			0.0753638
$806$		0			0
$807$	16.9848			0.597895
$808$		0			0
$809$	−21.3423	−	36.9660i	−0.750356	−	1.29966i	−0.947650	−	0.319311i	$-0.896549\pi$
$809$	−21.3423	−	36.9660i	−0.750356	−	1.29966i	0.197294	−	0.980344i	$-0.436785\pi$
$810$		0			0
$811$	−23.3693			−0.820608			−0.410304	−	0.911949i	$-0.634577\pi$
$811$	−23.3693			−0.820608			−0.410304	+	0.911949i	$0.634577\pi$
$812$		0			0
$813$	11.4654	−	19.8587i	0.402110	−	0.696476i
$814$		0			0
$815$	15.8078	−	27.3799i	0.553722	−	0.959074i
$816$		0			0
$817$	9.56155	+	16.5611i	0.334516	+	0.579399i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	21.2732	+	36.8463i	0.742440	+	1.28594i	0.951381	+	0.308015i	$0.0996648\pi$
$821$	21.2732	+	36.8463i	0.742440	+	1.28594i	−0.208942	+	0.977928i	$0.567002\pi$
$822$		0			0
$823$	−25.1771	+	43.6080i	−0.877618	+	1.52008i	−0.0236702	+	0.999720i	$0.507535\pi$
$823$	−25.1771	+	43.6080i	−0.877618	+	1.52008i	−0.853948	+	0.520359i	$0.825798\pi$
$824$		0			0
$825$	−10.2462	+	17.7470i	−0.356727	+	0.617870i
$826$		0			0
$827$	22.0000			0.765015			0.382507	−	0.923952i	$-0.375061\pi$
$827$	22.0000			0.765015			0.382507	+	0.923952i	$0.375061\pi$
$828$		0			0
$829$	−3.43845	−	5.95557i	−0.119422	−	0.206845i	0.800117	−	0.599844i	$-0.204771\pi$
$829$	−3.43845	−	5.95557i	−0.119422	−	0.206845i	−0.919539	+	0.392999i	$0.871438\pi$
$830$		0			0
$831$	−11.5076			−0.399193
$832$		0			0
$833$	−24.2462			−0.840081
$834$		0			0
$835$	5.36932	+	9.29993i	0.185813	+	0.321837i
$836$		0			0
$837$	28.4924			0.984842
$838$		0			0
$839$	21.9309	−	37.9854i	0.757138	−	1.31140i	−0.187167	−	0.982328i	$-0.559931\pi$
$839$	21.9309	−	37.9854i	0.757138	−	1.31140i	0.944305	−	0.329073i	$-0.106736\pi$
$840$		0			0
$841$	1.37689	−	2.38485i	0.0474791	−	0.0822362i
$842$		0			0
$843$	7.31534	+	12.6705i	0.251954	+	0.436397i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	3.34233	+	5.78908i	0.114844	+	0.198915i
$848$		0			0
$849$	9.36932	−	16.2281i	0.321554	−	0.556948i
$850$		0			0
$851$	14.9309	−	25.8610i	0.511824	−	0.886505i
$852$		0			0
$853$	−4.68466			−0.160400			−0.0801998	−	0.996779i	$-0.525556\pi$
$853$	−4.68466			−0.160400			−0.0801998	+	0.996779i	$0.525556\pi$
$854$		0			0
$855$	−0.876894	−	1.51883i	−0.0299892	−	0.0519427i
$856$		0			0
$857$	50.4924			1.72479			0.862394	−	0.506237i	$-0.168964\pi$
$857$	50.4924			1.72479			0.862394	+	0.506237i	$0.168964\pi$
$858$		0			0
$859$	−10.2462			−0.349596			−0.174798	−	0.984604i	$-0.555927\pi$
$859$	−10.2462			−0.349596			−0.174798	+	0.984604i	$0.555927\pi$
$860$		0			0
$861$	−2.73863	−	4.74345i	−0.0933324	−	0.161656i
$862$		0			0
$863$	48.0540			1.63578			0.817888	−	0.575377i	$-0.195145\pi$
$863$	48.0540			1.63578			0.817888	+	0.575377i	$0.195145\pi$
$864$		0			0
$865$	−3.31534	+	5.74234i	−0.112725	+	0.195245i
$866$		0			0
$867$	3.36932	−	5.83583i	0.114428	−	0.198195i
$868$		0			0
$869$	−28.4924	−	49.3503i	−0.966539	−	1.67410i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.75379	+	3.03765i	0.0593568	+	0.102809i
$874$		0			0
$875$	2.58854	−	4.48348i	0.0875086	−	0.151569i
$876$		0			0
$877$	3.71165	−	6.42876i	0.125333	−	0.217084i	−0.796530	−	0.604599i	$-0.793333\pi$
$877$	3.71165	−	6.42876i	0.125333	−	0.217084i	0.921863	+	0.387515i	$0.126667\pi$
$878$		0			0
$879$	19.8078			0.668099
$880$		0			0
$881$	−21.3963	−	37.0595i	−0.720860	−	1.24857i	−0.960656	−	0.277742i	$-0.910414\pi$
$881$	−21.3963	−	37.0595i	−0.720860	−	1.24857i	0.239796	−	0.970823i	$-0.422920\pi$
$882$		0			0
$883$	31.8078			1.07042			0.535208	−	0.844720i	$-0.320233\pi$
$883$	31.8078			1.07042			0.535208	+	0.844720i	$0.320233\pi$
$884$		0			0
$885$	24.3845			0.819675
$886$		0			0
$887$	2.63068	+	4.55648i	0.0883297	+	0.152992i	0.906805	−	0.421550i	$-0.138514\pi$
$887$	2.63068	+	4.55648i	0.0883297	+	0.152992i	−0.818476	+	0.574541i	$0.805180\pi$
$888$		0			0
$889$	−2.13826			−0.0717150
$890$		0			0
$891$	−17.9309	+	31.0572i	−0.600707	+	1.04045i
$892$		0			0
$893$	−7.56155	+	13.0970i	−0.253038	+	0.438274i
$894$		0			0
$895$	−13.7116	−	23.7493i	−0.458330	−	0.793850i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−13.1231	−	22.7299i	−0.437680	−	0.758084i
$900$		0			0
$901$	−21.8078	+	37.7722i	−0.726522	+	1.25837i
$902$		0			0
$903$	−3.27320	+	5.66935i	−0.108925	+	0.188664i
$904$		0			0
$905$	−12.8769			−0.428042
$906$		0			0
$907$	−11.2192	−	19.4323i	−0.372528	−	0.645238i	0.617426	−	0.786629i	$-0.288176\pi$
$907$	−11.2192	−	19.4323i	−0.372528	−	0.645238i	−0.989954	+	0.141392i	$0.954842\pi$
$908$		0			0
$909$	−6.38447			−0.211760
$910$		0			0
$911$	25.7538			0.853261			0.426631	−	0.904426i	$-0.359700\pi$
$911$	25.7538			0.853261			0.426631	+	0.904426i	$0.359700\pi$
$912$		0			0
$913$	21.1231	+	36.5863i	0.699073	+	1.21083i
$914$		0			0
$915$	−7.01515			−0.231914
$916$		0			0
$917$	−0.726801	+	1.25886i	−0.0240011	+	0.0415711i
$918$		0			0
$919$	−0.876894	+	1.51883i	−0.0289261	+	0.0501014i	−0.880126	−	0.474740i	$-0.842542\pi$
$919$	−0.876894	+	1.51883i	−0.0289261	+	0.0501014i	0.851200	+	0.524841i	$0.175875\pi$
$920$		0			0
$921$	14.0540	+	24.3422i	0.463094	+	0.802103i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−12.2462	−	21.2111i	−0.402653	−	0.697415i
$926$		0			0
$927$	−0.876894	+	1.51883i	−0.0288010	+	0.0498848i
$928$		0			0
$929$	9.36932	−	16.2281i	0.307397	−	0.532428i	−0.670395	−	0.742005i	$-0.733875\pi$
$929$	9.36932	−	16.2281i	0.307397	−	0.532428i	0.977792	+	0.209577i	$0.0672086\pi$
$930$		0			0
$931$	−13.6155			−0.446231
$932$		0			0
$933$	14.9309	+	25.8610i	0.488815	+	0.846652i
$934$		0			0
$935$	28.4924			0.931802
$936$		0			0
$937$	19.7538			0.645328			0.322664	−	0.946514i	$-0.395422\pi$
$937$	19.7538			0.645328			0.322664	+	0.946514i	$0.395422\pi$
$938$		0			0
$939$	−3.46543	−	6.00231i	−0.113090	−	0.195878i
$940$		0			0
$941$	42.5464			1.38697			0.693486	−	0.720470i	$-0.256074\pi$
$941$	42.5464			1.38697			0.693486	+	0.720470i	$0.256074\pi$
$942$		0			0
$943$	12.4924	−	21.6375i	0.406809	−	0.704614i
$944$		0			0
$945$	1.90388	−	3.29762i	0.0619333	−	0.107272i
$946$		0			0
$947$	−7.68466	−	13.3102i	−0.249718	−	0.432524i	0.713730	−	0.700421i	$-0.247005\pi$
$947$	−7.68466	−	13.3102i	−0.249718	−	0.432524i	−0.963447	+	0.267897i	$0.913671\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−11.8078	−	20.4516i	−0.382893	−	0.663190i
$952$		0			0
$953$	10.0270	−	17.3673i	0.324806	−	0.562580i	−0.656667	−	0.754181i	$-0.728034\pi$
$953$	10.0270	−	17.3673i	0.324806	−	0.562580i	0.981473	+	0.191600i	$0.0613677\pi$
$954$		0			0
$955$	−17.3693	+	30.0845i	−0.562058	+	0.973513i
$956$		0			0
$957$	40.9848			1.32485
$958$		0			0
$959$	0.684658	+	1.18586i	0.0221088	+	0.0382935i
$960$		0			0
$961$	−4.75379			−0.153348
$962$		0			0
$963$	2.24621			0.0723831
$964$		0			0
$965$	−18.4384	−	31.9363i	−0.593555	−	1.02807i
$966$		0			0
$967$	−15.5616			−0.500426			−0.250213	−	0.968191i	$-0.580501\pi$
$967$	−15.5616			−0.500426			−0.250213	+	0.968191i	$0.580501\pi$
$968$		0			0
$969$	−5.56155	+	9.63289i	−0.178663	+	0.309453i
$970$		0			0
$971$	28.5885	−	49.5168i	0.917450	−	1.58907i	0.114176	−	0.993461i	$-0.463577\pi$
$971$	28.5885	−	49.5168i	0.917450	−	1.58907i	0.803274	−	0.595609i	$-0.203089\pi$
$972$		0			0
$973$	−1.71165	−	2.96466i	−0.0548729	−	0.0950426i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	23.6155	+	40.9033i	0.755528	+	1.30861i	0.945112	+	0.326748i	$0.105953\pi$
$977$	23.6155	+	40.9033i	0.755528	+	1.30861i	−0.189584	+	0.981865i	$0.560714\pi$
$978$		0			0
$979$	8.00000	−	13.8564i	0.255681	−	0.442853i
$980$		0			0
$981$	−0.930870	+	1.61231i	−0.0297204	+	0.0514772i
$982$		0			0
$983$	−10.1922			−0.325082			−0.162541	−	0.986702i	$-0.551969\pi$
$983$	−10.1922			−0.325082			−0.162541	+	0.986702i	$0.551969\pi$
$984$		0			0
$985$	7.46543	+	12.9305i	0.237869	+	0.412000i
$986$		0			0
$987$	−5.17708			−0.164788
$988$		0			0
$989$	−29.8617			−0.949548
$990$		0			0
$991$	3.80776	+	6.59524i	0.120958	+	0.209505i	0.920146	−	0.391576i	$-0.128070\pi$
$991$	3.80776	+	6.59524i	0.120958	+	0.209505i	−0.799188	+	0.601081i	$0.794737\pi$
$992$		0			0
$993$	0.384472			0.0122008
$994$		0			0
$995$	11.1231	−	19.2658i	0.352626	−	0.610766i
$996$		0			0
$997$	0.807764	−	1.39909i	0.0255821	−	0.0443096i	−0.852951	−	0.521991i	$-0.825189\pi$
$997$	0.807764	−	1.39909i	0.0255821	−	0.0443096i	0.878533	+	0.477682i	$0.158523\pi$
$998$		0			0
$999$	−26.5885	−	46.0527i	−0.841224	−	1.45704i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1352.2.i.h.1329.1		4
13.2	odd	12		104.2.f.a.25.4	yes	4
13.3	even	3		1352.2.a.e.1.2		2
13.4	even	6		1352.2.i.g.529.1		4
13.5	odd	4		1352.2.o.e.361.2		8
13.6	odd	12		1352.2.o.e.1161.2		8
13.7	odd	12		1352.2.o.e.1161.1		8
13.8	odd	4		1352.2.o.e.361.1		8
13.9	even	3	inner	1352.2.i.h.529.1		4
13.10	even	6		1352.2.a.d.1.2		2
13.11	odd	12		104.2.f.a.25.3	✓	4
13.12	even	2		1352.2.i.g.1329.1		4
39.2	even	12		936.2.c.d.649.2		4
39.11	even	12		936.2.c.d.649.3		4
52.3	odd	6		2704.2.a.t.1.1		2
52.11	even	12		208.2.f.b.129.1		4
52.15	even	12		208.2.f.b.129.2		4
52.23	odd	6		2704.2.a.s.1.1		2
65.2	even	12		2600.2.f.b.649.2		4
65.24	odd	12		2600.2.k.a.2001.1		4
65.28	even	12		2600.2.f.a.649.3		4
65.37	even	12		2600.2.f.a.649.2		4
65.54	odd	12		2600.2.k.a.2001.2		4
65.63	even	12		2600.2.f.b.649.3		4
104.11	even	12		832.2.f.f.129.4		4
104.37	odd	12		832.2.f.i.129.2		4
104.67	even	12		832.2.f.f.129.3		4
104.93	odd	12		832.2.f.i.129.1		4
156.11	odd	12		1872.2.c.j.1585.3		4
156.119	odd	12		1872.2.c.j.1585.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.f.a.25.3	✓	4	13.11	odd	12
104.2.f.a.25.4	yes	4	13.2	odd	12
208.2.f.b.129.1		4	52.11	even	12
208.2.f.b.129.2		4	52.15	even	12
832.2.f.f.129.3		4	104.67	even	12
832.2.f.f.129.4		4	104.11	even	12
832.2.f.i.129.1		4	104.93	odd	12
832.2.f.i.129.2		4	104.37	odd	12
936.2.c.d.649.2		4	39.2	even	12
936.2.c.d.649.3		4	39.11	even	12
1352.2.a.d.1.2		2	13.10	even	6
1352.2.a.e.1.2		2	13.3	even	3
1352.2.i.g.529.1		4	13.4	even	6
1352.2.i.g.1329.1		4	13.12	even	2
1352.2.i.h.529.1		4	13.9	even	3	inner
1352.2.i.h.1329.1		4	1.1	even	1	trivial
1352.2.o.e.361.1		8	13.8	odd	4
1352.2.o.e.361.2		8	13.5	odd	4
1352.2.o.e.1161.1		8	13.7	odd	12
1352.2.o.e.1161.2		8	13.6	odd	12
1872.2.c.j.1585.2		4	156.119	odd	12
1872.2.c.j.1585.3		4	156.11	odd	12
2600.2.f.a.649.2		4	65.37	even	12
2600.2.f.a.649.3		4	65.28	even	12
2600.2.f.b.649.2		4	65.2	even	12
2600.2.f.b.649.3		4	65.63	even	12
2600.2.k.a.2001.1		4	65.24	odd	12
2600.2.k.a.2001.2		4	65.54	odd	12
2704.2.a.s.1.1		2	52.23	odd	6
2704.2.a.t.1.1		2	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.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.780776 - 1.35234i) q^{3} -1.56155 q^{5} +(0.219224 - 0.379706i) q^{7} +(0.280776 - 0.486319i) q^{9} +(2.56155 + 4.43674i) q^{11} +(1.21922 + 2.11176i) q^{15} +(-1.78078 + 3.08440i) q^{17} +(-1.00000 + 1.73205i) q^{19} -0.684658 q^{21} +(-1.56155 - 2.70469i) q^{23} -2.56155 q^{25} -5.56155 q^{27} +(2.56155 + 4.43674i) q^{29} -5.12311 q^{31} +(4.00000 - 6.92820i) q^{33} +(-0.342329 + 0.592932i) q^{35} +(4.78078 + 8.28055i) q^{37} +(4.00000 + 6.92820i) q^{41} +(4.78078 - 8.28055i) q^{43} +(-0.438447 + 0.759413i) q^{45} +7.56155 q^{47} +(3.40388 + 5.89570i) q^{49} +5.56155 q^{51} +12.2462 q^{53} +(-4.00000 - 6.92820i) q^{55} +3.12311 q^{57} +(5.00000 - 8.66025i) q^{59} +(-1.43845 + 2.49146i) q^{61} +(-0.123106 - 0.213225i) q^{63} +(4.56155 + 7.90084i) q^{67} +(-2.43845 + 4.22351i) q^{69} +(-3.34233 + 5.78908i) q^{71} +9.36932 q^{73} +(2.00000 + 3.46410i) q^{75} +2.24621 q^{77} -11.1231 q^{79} +(3.50000 + 6.06218i) q^{81} +8.24621 q^{83} +(2.78078 - 4.81645i) q^{85} +(4.00000 - 6.92820i) q^{87} +(-1.56155 - 2.70469i) q^{89} +(4.00000 + 6.92820i) q^{93} +(1.56155 - 2.70469i) q^{95} +(-3.12311 + 5.40938i) q^{97} +2.87689 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} + 2 q^{5} + 5 q^{7} - 3 q^{9} + 2 q^{11} + 9 q^{15} - 3 q^{17} - 4 q^{19} + 22 q^{21} + 2 q^{23} - 2 q^{25} - 14 q^{27} + 2 q^{29} - 4 q^{31} + 16 q^{33} + 11 q^{35} + 15 q^{37} + 16 q^{41}+ \cdots + 28 q^{99}+O(q^{100}) \) 4 * q + q^3 + 2 * q^5 + 5 * q^7 - 3 * q^9 + 2 * q^11 + 9 * q^15 - 3 * q^17 - 4 * q^19 + 22 * q^21 + 2 * q^23 - 2 * q^25 - 14 * q^27 + 2 * q^29 - 4 * q^31 + 16 * q^33 + 11 * q^35 + 15 * q^37 + 16 * q^41 + 15 * q^43 - 10 * q^45 + 22 * q^47 - 7 * q^49 + 14 * q^51 + 16 * q^53 - 16 * q^55 - 4 * q^57 + 20 * q^59 - 14 * q^61 + 16 * q^63 + 10 * q^67 - 18 * q^69 - q^71 - 12 * q^73 + 8 * q^75 - 24 * q^77 - 28 * q^79 + 14 * q^81 + 7 * q^85 + 16 * q^87 + 2 * q^89 + 16 * q^93 - 2 * q^95 + 4 * q^97 + 28 * q^99

Introduction

L-functions

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