LMFDB - Embedded newform 216.2.q.a.169.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(25,216)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("216.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.q (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			169.3
Character	$\chi$	$=$	216.169
Dual form			216.2.q.a.193.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.887369 + 1.48747i) q^{3} +(0.444259 + 2.51952i) q^{5} +(-0.612199 - 0.513696i) q^{7} +(-1.42515 + 2.63988i) q^{9} +O(q^{10})$	\(q+(0.887369 + 1.48747i) q^{3} +(0.444259 + 2.51952i) q^{5} +(-0.612199 - 0.513696i) q^{7} +(-1.42515 + 2.63988i) q^{9} +(0.313806 - 1.77968i) q^{11} +(-2.44122 - 0.888533i) q^{13} +(-3.35349 + 2.89657i) q^{15} +(3.13569 + 5.43118i) q^{17} +(2.88902 - 5.00394i) q^{19} +(0.220862 - 1.36647i) q^{21} +(1.80988 - 1.51867i) q^{23} +(-1.45214 + 0.528537i) q^{25} +(-5.19138 + 0.222667i) q^{27} +(7.05690 - 2.56850i) q^{29} +(-4.55018 + 3.81806i) q^{31} +(2.92569 - 1.11246i) q^{33} +(1.02229 - 1.77066i) q^{35} +(0.0710294 + 0.123026i) q^{37} +(-0.844597 - 4.41971i) q^{39} +(7.49635 + 2.72845i) q^{41} +(2.02041 - 11.4583i) q^{43} +(-7.28435 - 2.41791i) q^{45} +(-2.93431 - 2.46218i) q^{47} +(-1.10463 - 6.26469i) q^{49} +(-5.29622 + 9.48372i) q^{51} -12.3580 q^{53} +4.62336 q^{55} +(10.0069 - 0.142992i) q^{57} +(0.688378 + 3.90399i) q^{59} +(-10.0077 - 8.39744i) q^{61} +(2.22857 - 0.884033i) q^{63} +(1.15414 - 6.54545i) q^{65} +(13.7911 + 5.01955i) q^{67} +(3.86501 + 1.34453i) q^{69} +(-3.27722 - 5.67630i) q^{71} +(-0.483460 + 0.837377i) q^{73} +(-2.07477 - 1.69102i) q^{75} +(-1.10633 + 0.928319i) q^{77} +(-0.693372 + 0.252367i) q^{79} +(-4.93788 - 7.52445i) q^{81} +(-6.18280 + 2.25036i) q^{83} +(-12.2909 + 10.3133i) q^{85} +(10.0827 + 8.21775i) q^{87} +(-2.90794 + 5.03670i) q^{89} +(1.03808 + 1.79800i) q^{91} +(-9.71695 - 3.38025i) q^{93} +(13.8910 + 5.05591i) q^{95} +(-0.957701 + 5.43139i) q^{97} +(4.25092 + 3.36473i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{7} + 6 q^{9}+O(q^{10}) $ 24 * q - 3 * q^7 + 6 * q^9	$ 24 q - 3 q^{7} + 6 q^{9} + 6 q^{11} + 12 q^{13} - 3 q^{15} + 6 q^{17} + 9 q^{19} - 18 q^{21} + 24 q^{23} - 24 q^{25} - 9 q^{29} - 27 q^{31} + 21 q^{33} - 18 q^{35} + 15 q^{37} - 15 q^{39} - 6 q^{41} + 39 q^{43} - 69 q^{45} - 36 q^{47} + 3 q^{49} - 36 q^{51} - 18 q^{53} - 54 q^{55} + 27 q^{57} - 30 q^{59} + 12 q^{61} + 18 q^{63} - 18 q^{65} + 54 q^{67} - 57 q^{69} + 36 q^{73} - 51 q^{75} - 24 q^{77} - 45 q^{79} + 18 q^{81} + 33 q^{83} - 57 q^{85} + 90 q^{87} + 9 q^{89} + 39 q^{91} + 42 q^{93} + 87 q^{95} + 57 q^{97} - 24 q^{99}+O(q^{100}) $ 24 * q - 3 * q^7 + 6 * q^9 + 6 * q^11 + 12 * q^13 - 3 * q^15 + 6 * q^17 + 9 * q^19 - 18 * q^21 + 24 * q^23 - 24 * q^25 - 9 * q^29 - 27 * q^31 + 21 * q^33 - 18 * q^35 + 15 * q^37 - 15 * q^39 - 6 * q^41 + 39 * q^43 - 69 * q^45 - 36 * q^47 + 3 * q^49 - 36 * q^51 - 18 * q^53 - 54 * q^55 + 27 * q^57 - 30 * q^59 + 12 * q^61 + 18 * q^63 - 18 * q^65 + 54 * q^67 - 57 * q^69 + 36 * q^73 - 51 * q^75 - 24 * q^77 - 45 * q^79 + 18 * q^81 + 33 * q^83 - 57 * q^85 + 90 * q^87 + 9 * q^89 + 39 * q^91 + 42 * q^93 + 87 * q^95 + 57 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{9}\right)$

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
$3$	0.887369	+	1.48747i	0.512323	+	0.858793i
$3$	0.887369	+	1.48747i	0.512323	+	0.858793i
$4$		0			0
$5$	0.444259	+	2.51952i	0.198679	+	1.12676i	0.907082	+	0.420955i	$0.138305\pi$
$5$	0.444259	+	2.51952i	0.198679	+	1.12676i	−0.708403	+	0.705808i	$0.750584\pi$
$6$		0			0
$7$	−0.612199	−	0.513696i	−0.231389	−	0.194159i	0.519720	−	0.854337i	$-0.326036\pi$
$7$	−0.612199	−	0.513696i	−0.231389	−	0.194159i	−0.751109	+	0.660178i	$0.770481\pi$
$8$		0			0
$9$	−1.42515	+	2.63988i	−0.475051	+	0.879958i
$10$		0			0
$11$	0.313806	−	1.77968i	0.0946161	−	0.536595i	−0.900248	−	0.435377i	$-0.856615\pi$
$11$	0.313806	−	1.77968i	0.0946161	−	0.536595i	0.994864	−	0.101218i	$-0.0322738\pi$
$12$		0			0
$13$	−2.44122	−	0.888533i	−0.677074	−	0.246435i	−0.0194831	−	0.999810i	$-0.506202\pi$
$13$	−2.44122	−	0.888533i	−0.677074	−	0.246435i	−0.657590	+	0.753376i	$0.728424\pi$
$14$		0			0
$15$	−3.35349	+	2.89657i	−0.865868	+	0.747890i
$16$		0			0
$17$	3.13569	+	5.43118i	0.760517	+	1.31725i	0.942584	+	0.333968i	$0.108388\pi$
$17$	3.13569	+	5.43118i	0.760517	+	1.31725i	−0.182067	+	0.983286i	$0.558279\pi$
$18$		0			0
$19$	2.88902	−	5.00394i	0.662788	−	1.14798i	−0.317092	−	0.948395i	$-0.602706\pi$
$19$	2.88902	−	5.00394i	0.662788	−	1.14798i	0.979880	−	0.199587i	$-0.0639602\pi$
$20$		0			0
$21$	0.220862	−	1.36647i	0.0481961	−	0.298187i
$22$		0			0
$23$	1.80988	−	1.51867i	0.377386	−	0.316664i	−0.434289	−	0.900774i	$-0.643000\pi$
$23$	1.80988	−	1.51867i	0.377386	−	0.316664i	0.811675	+	0.584109i	$0.198556\pi$
$24$		0			0
$25$	−1.45214	+	0.528537i	−0.290429	+	0.105707i
$26$		0			0
$27$	−5.19138	+	0.222667i	−0.999081	+	0.0428523i
$28$		0			0
$29$	7.05690	−	2.56850i	1.31043	−	0.476959i	0.410053	−	0.912062i	$-0.365510\pi$
$29$	7.05690	−	2.56850i	1.31043	−	0.476959i	0.900381	+	0.435103i	$0.143288\pi$
$30$		0			0
$31$	−4.55018	+	3.81806i	−0.817237	+	0.685743i	−0.952323	−	0.305091i	$-0.901313\pi$
$31$	−4.55018	+	3.81806i	−0.817237	+	0.685743i	0.135086	+	0.990834i	$0.456869\pi$
$32$		0			0
$33$	2.92569	−	1.11246i	0.509298	−	0.193654i
$34$		0			0
$35$	1.02229	−	1.77066i	0.172799	−	0.299296i
$36$		0			0
$37$	0.0710294	+	0.123026i	0.0116772	+	0.0202254i	0.871805	−	0.489853i	$-0.162950\pi$
$37$	0.0710294	+	0.123026i	0.0116772	+	0.0202254i	−0.860128	+	0.510079i	$0.829616\pi$
$38$		0			0
$39$	−0.844597	−	4.41971i	−0.135244	−	0.707720i
$40$		0			0
$41$	7.49635	+	2.72845i	1.17073	+	0.426112i	0.852920	−	0.522041i	$-0.174829\pi$
$41$	7.49635	+	2.72845i	1.17073	+	0.426112i	0.317813	+	0.948153i	$0.397051\pi$
$42$		0			0
$43$	2.02041	−	11.4583i	0.308109	−	1.74738i	−0.300386	−	0.953818i	$-0.597115\pi$
$43$	2.02041	−	11.4583i	0.308109	−	1.74738i	0.608495	−	0.793558i	$-0.291774\pi$
$44$		0			0
$45$	−7.28435	−	2.41791i	−1.08589	−	0.360441i
$46$		0			0
$47$	−2.93431	−	2.46218i	−0.428013	−	0.359145i	0.403188	−	0.915117i	$-0.367902\pi$
$47$	−2.93431	−	2.46218i	−0.428013	−	0.359145i	−0.831201	+	0.555972i	$0.812346\pi$
$48$		0			0
$49$	−1.10463	−	6.26469i	−0.157805	−	0.894955i
$50$		0			0
$51$	−5.29622	+	9.48372i	−0.741619	+	1.32799i
$52$		0			0
$53$	−12.3580			−1.69750			−0.848750	−	0.528795i	$-0.822644\pi$
$53$	−12.3580			−1.69750			−0.848750	+	0.528795i	$0.822644\pi$
$54$		0			0
$55$	4.62336			0.623413
$56$		0			0
$57$	10.0069	−	0.142992i	1.32544	−	0.0189398i
$58$		0			0
$59$	0.688378	+	3.90399i	0.0896192	+	0.508256i	0.996264	+	0.0863609i	$0.0275238\pi$
$59$	0.688378	+	3.90399i	0.0896192	+	0.508256i	−0.906645	+	0.421895i	$0.861365\pi$
$60$		0			0
$61$	−10.0077	−	8.39744i	−1.28135	−	1.07518i	−0.993056	−	0.117640i	$-0.962467\pi$
$61$	−10.0077	−	8.39744i	−1.28135	−	1.07518i	−0.288295	−	0.957542i	$-0.593089\pi$
$62$		0			0
$63$	2.22857	−	0.884033i	0.280773	−	0.111378i
$64$		0			0
$65$	1.15414	−	6.54545i	0.143153	−	0.811863i
$66$		0			0
$67$	13.7911	+	5.01955i	1.68485	+	0.613235i	0.993962	−	0.109726i	$-0.0349973\pi$
$67$	13.7911	+	5.01955i	1.68485	+	0.613235i	0.690889	+	0.722961i	$0.257220\pi$
$68$		0			0
$69$	3.86501	+	1.34453i	0.465293	+	0.161862i
$70$		0			0
$71$	−3.27722	−	5.67630i	−0.388934	−	0.673653i	0.603372	−	0.797460i	$-0.293823\pi$
$71$	−3.27722	−	5.67630i	−0.388934	−	0.673653i	−0.992306	+	0.123806i	$0.960490\pi$
$72$		0			0
$73$	−0.483460	+	0.837377i	−0.0565847	+	0.0980075i	−0.892930	−	0.450195i	$-0.851354\pi$
$73$	−0.483460	+	0.837377i	−0.0565847	+	0.0980075i	0.836346	+	0.548203i	$0.184688\pi$
$74$		0			0
$75$	−2.07477	−	1.69102i	−0.239574	−	0.195262i
$76$		0			0
$77$	−1.10633	+	0.928319i	−0.126078	+	0.105792i
$78$		0			0
$79$	−0.693372	+	0.252367i	−0.0780104	+	0.0283935i	−0.380731	−	0.924686i	$-0.624327\pi$
$79$	−0.693372	+	0.252367i	−0.0780104	+	0.0283935i	0.302720	+	0.953079i	$0.402105\pi$
$80$		0			0
$81$	−4.93788	−	7.52445i	−0.548653	−	0.836050i
$82$		0			0
$83$	−6.18280	+	2.25036i	−0.678650	+	0.247009i	−0.658268	−	0.752784i	$-0.728711\pi$
$83$	−6.18280	+	2.25036i	−0.678650	+	0.247009i	−0.0203825	+	0.999792i	$0.506488\pi$
$84$		0			0
$85$	−12.2909	+	10.3133i	−1.33313	+	1.11863i
$86$		0			0
$87$	10.0827	+	8.21775i	1.08097	+	0.881035i
$88$		0			0
$89$	−2.90794	+	5.03670i	−0.308241	+	0.533889i	−0.977978	−	0.208709i	$-0.933074\pi$
$89$	−2.90794	+	5.03670i	−0.308241	+	0.533889i	0.669737	+	0.742599i	$0.266407\pi$
$90$		0			0
$91$	1.03808	+	1.79800i	0.108820	+	0.188482i
$92$		0			0
$93$	−9.71695	−	3.38025i	−1.00760	−	0.350516i
$94$		0			0
$95$	13.8910	+	5.05591i	1.42519	+	0.518725i
$96$		0			0
$97$	−0.957701	+	5.43139i	−0.0972398	+	0.551474i	0.896798	+	0.442440i	$0.145887\pi$
$97$	−0.957701	+	5.43139i	−0.0972398	+	0.551474i	−0.994038	+	0.109034i	$0.965224\pi$
$98$		0			0
$99$	4.25092	+	3.36473i	0.427234	+	0.338168i
$100$		0			0
$101$	3.03214	+	2.54427i	0.301709	+	0.253164i	0.781055	−	0.624462i	$-0.214682\pi$
$101$	3.03214	+	2.54427i	0.301709	+	0.253164i	−0.479346	+	0.877626i	$0.659126\pi$
$102$		0			0
$103$	1.83126	+	10.3856i	0.180439	+	1.02332i	0.931676	+	0.363290i	$0.118347\pi$
$103$	1.83126	+	10.3856i	0.180439	+	1.02332i	−0.751237	+	0.660033i	$0.770542\pi$
$104$		0			0
$105$	3.54096	−	0.0505983i	0.345562	−	0.00493789i
$106$		0			0
$107$	−12.9424			−1.25119			−0.625593	−	0.780150i	$-0.715143\pi$
$107$	−12.9424			−1.25119			−0.625593	+	0.780150i	$0.715143\pi$
$108$		0			0
$109$	13.7209			1.31422			0.657110	−	0.753795i	$-0.271779\pi$
$109$	13.7209			1.31422			0.657110	+	0.753795i	$0.271779\pi$
$110$		0			0
$111$	−0.119969	+	0.214824i	−0.0113870	+	0.0203902i
$112$		0			0
$113$	−0.475492	−	2.69665i	−0.0447305	−	0.253679i	0.954240	−	0.299042i	$-0.0966669\pi$
$113$	−0.475492	−	2.69665i	−0.0447305	−	0.253679i	−0.998971	+	0.0453622i	$0.985556\pi$
$114$		0			0
$115$	4.63037	+	3.88534i	0.431784	+	0.362310i
$116$		0			0
$117$	5.82473	−	5.17823i	0.538497	−	0.478728i
$118$		0			0
$119$	0.870306	−	4.93575i	0.0797808	−	0.452460i
$120$		0			0
$121$	7.26782	+	2.64527i	0.660711	+	0.240479i
$122$		0			0
$123$	2.59354	+	13.5718i	0.233851	+	1.22372i
$124$		0			0
$125$	4.41918	+	7.65424i	0.395263	+	0.684616i
$126$		0			0
$127$	−6.90766	+	11.9644i	−0.612956	+	1.06167i	0.377784	+	0.925894i	$0.376686\pi$
$127$	−6.90766	+	11.9644i	−0.612956	+	1.06167i	−0.990740	+	0.135776i	$0.956647\pi$
$128$		0			0
$129$	18.8368	−	7.16244i	1.65849	−	0.630618i
$130$		0			0
$131$	2.12337	−	1.78172i	0.185520	−	0.155669i	−0.545298	−	0.838242i	$-0.683583\pi$
$131$	2.12337	−	1.78172i	0.185520	−	0.155669i	0.730817	+	0.682573i	$0.239139\pi$
$132$		0			0
$133$	−4.33916	+	1.57932i	−0.376253	+	0.136945i
$134$		0			0
$135$	−2.86733	−	12.9809i	−0.246781	−	1.11721i
$136$		0			0
$137$	−1.88639	+	0.686591i	−0.161165	+	0.0586594i	−0.421343	−	0.906901i	$-0.638441\pi$
$137$	−1.88639	+	0.686591i	−0.161165	+	0.0586594i	0.260178	+	0.965561i	$0.416219\pi$
$138$		0			0
$139$	−14.4637	+	12.1364i	−1.22679	+	1.02940i	−0.228350	+	0.973579i	$0.573333\pi$
$139$	−14.4637	+	12.1364i	−1.22679	+	1.02940i	−0.998441	+	0.0558207i	$0.982222\pi$
$140$		0			0
$141$	1.05861	−	6.54956i	0.0891509	−	0.551573i
$142$		0			0
$143$	−2.34738	+	4.06578i	−0.196298	+	0.339997i
$144$		0			0
$145$	9.60648	+	16.6389i	0.797775	+	1.38179i
$146$		0			0
$147$	8.33834	−	7.20220i	0.687734	−	0.594028i
$148$		0			0
$149$	−19.8617	−	7.22907i	−1.62713	−	0.592229i	−0.642412	−	0.766360i	$-0.722066\pi$
$149$	−19.8617	−	7.22907i	−1.62713	−	0.592229i	−0.984722	+	0.174131i	$0.944288\pi$
$150$		0			0
$151$	1.10004	−	6.23861i	0.0895197	−	0.507691i	−0.906770	−	0.421626i	$-0.861460\pi$
$151$	1.10004	−	6.23861i	0.0895197	−	0.507691i	0.996290	−	0.0860653i	$-0.0274294\pi$
$152$		0			0
$153$	−18.8065	+	0.537578i	−1.52041	+	0.0434606i
$154$		0			0
$155$	−11.6411	−	9.76806i	−0.935038	−	0.784590i
$156$		0			0
$157$	−0.749302	−	4.24950i	−0.0598008	−	0.339147i	0.940198	−	0.340628i	$-0.110640\pi$
$157$	−0.749302	−	4.24950i	−0.0598008	−	0.339147i	−0.999999	+	0.00148093i	$0.999529\pi$
$158$		0			0
$159$	−10.9661	−	18.3822i	−0.869667	−	1.45780i
$160$		0			0
$161$	−1.88814			−0.148806
$162$		0			0
$163$	−4.21666			−0.330275			−0.165137	−	0.986271i	$-0.552807\pi$
$163$	−4.21666			−0.330275			−0.165137	+	0.986271i	$0.552807\pi$
$164$		0			0
$165$	4.10262	+	6.87712i	0.319389	+	0.535383i
$166$		0			0
$167$	2.70637	+	15.3486i	0.209425	+	1.18771i	0.890322	+	0.455331i	$0.150479\pi$
$167$	2.70637	+	15.3486i	0.209425	+	1.18771i	−0.680897	+	0.732379i	$0.738410\pi$
$168$		0			0
$169$	−4.78850	−	4.01803i	−0.368346	−	0.309079i
$170$		0			0
$171$	9.09247	+	14.7580i	0.695319	+	1.12858i
$172$		0			0
$173$	1.52993	−	8.67664i	0.116318	−	0.659673i	−0.869771	−	0.493456i	$-0.835734\pi$
$173$	1.52993	−	8.67664i	0.116318	−	0.659673i	0.986089	−	0.166217i	$-0.0531553\pi$
$174$		0			0
$175$	1.16051	+	0.422390i	0.0877261	+	0.0319297i
$176$		0			0
$177$	−5.19623	+	4.48822i	−0.390573	+	0.337355i
$178$		0			0
$179$	−11.5141	−	19.9430i	−0.860606	−	1.49061i	−0.871345	−	0.490671i	$-0.836752\pi$
$179$	−11.5141	−	19.9430i	−0.860606	−	1.49061i	0.0107388	−	0.999942i	$-0.496582\pi$
$180$		0			0
$181$	11.1173	−	19.2557i	0.826343	−	1.43127i	−0.0745462	−	0.997218i	$-0.523751\pi$
$181$	11.1173	−	19.2557i	0.826343	−	1.43127i	0.900889	−	0.434050i	$-0.142916\pi$
$182$		0			0
$183$	3.61046	−	22.3378i	0.266893	−	1.65126i
$184$		0			0
$185$	−0.278412	+	0.233615i	−0.0204693	+	0.0171757i
$186$		0			0
$187$	10.6498	−	3.87620i	0.778789	−	0.283456i
$188$		0			0
$189$	3.29254	+	2.53047i	0.239497	+	0.184065i
$190$		0			0
$191$	0.906442	−	0.329918i	0.0655878	−	0.0238720i	−0.309018	−	0.951056i	$-0.600000\pi$
$191$	0.906442	−	0.329918i	0.0655878	−	0.0238720i	0.374606	+	0.927184i	$0.377778\pi$
$192$		0			0
$193$	−0.0971794	+	0.0815432i	−0.00699513	+	0.00586961i	−0.646278	−	0.763102i	$-0.723676\pi$
$193$	−0.0971794	+	0.0815432i	−0.00699513	+	0.00586961i	0.639283	+	0.768971i	$0.279231\pi$
$194$		0			0
$195$	10.7603	−	4.09148i	0.770563	−	0.292997i
$196$		0			0
$197$	−3.87017	+	6.70333i	−0.275738	+	0.477593i	−0.970321	−	0.241820i	$-0.922256\pi$
$197$	−3.87017	+	6.70333i	−0.275738	+	0.477593i	0.694583	+	0.719413i	$0.255589\pi$
$198$		0			0
$199$	−7.16205	−	12.4050i	−0.507704	−	0.879369i	−0.999960	−	0.00891897i	$-0.997161\pi$
$199$	−7.16205	−	12.4050i	−0.507704	−	0.879369i	0.492256	−	0.870450i	$-0.336172\pi$
$200$		0			0
$201$	4.77135	+	24.9681i	0.336545	+	1.76111i
$202$		0			0
$203$	−5.63966	−	2.05267i	−0.395826	−	0.144069i
$204$		0			0
$205$	−3.54406	+	20.0993i	−0.247528	+	1.40380i
$206$		0			0
$207$	1.42974	+	6.94219i	0.0993740	+	0.482516i
$208$		0			0
$209$	−7.99883	−	6.71182i	−0.553291	−	0.464266i
$210$		0			0
$211$	−3.57967	−	20.3013i	−0.246435	−	1.39760i	−0.817137	−	0.576444i	$-0.804440\pi$
$211$	−3.57967	−	20.3013i	−0.246435	−	1.39760i	0.570702	−	0.821157i	$-0.306671\pi$
$212$		0			0
$213$	5.53525	−	9.91175i	0.379269	−	0.679142i
$214$		0			0
$215$	29.7670			2.03009
$216$		0			0
$217$	4.74693			0.322243
$218$		0			0
$219$	−1.67458	+	0.0239289i	−0.113158	+	0.00161696i
$220$		0			0
$221$	−2.82915	−	16.0449i	−0.190309	−	1.07930i
$222$		0			0
$223$	0.930955	+	0.781164i	0.0623414	+	0.0523106i	0.673426	−	0.739255i	$-0.264822\pi$
$223$	0.930955	+	0.781164i	0.0623414	+	0.0523106i	−0.611085	+	0.791565i	$0.709266\pi$
$224$		0			0
$225$	0.674255	−	4.58672i	0.0449503	−	0.305782i
$226$		0			0
$227$	−0.820541	+	4.65352i	−0.0544612	+	0.308865i	−0.999854	−	0.0170673i	$-0.994567\pi$
$227$	−0.820541	+	4.65352i	−0.0544612	+	0.308865i	0.945393	+	0.325932i	$0.105678\pi$
$228$		0			0
$229$	11.8444	+	4.31100i	0.782698	+	0.284879i	0.702297	−	0.711884i	$-0.252158\pi$
$229$	11.8444	+	4.31100i	0.782698	+	0.284879i	0.0804007	+	0.996763i	$0.474380\pi$
$230$		0			0
$231$	−2.36257	−	0.821871i	−0.155446	−	0.0540751i
$232$		0			0
$233$	2.45436	+	4.25108i	0.160791	+	0.278498i	0.935152	−	0.354245i	$-0.115262\pi$
$233$	2.45436	+	4.25108i	0.160791	+	0.278498i	−0.774362	+	0.632743i	$0.781929\pi$
$234$		0			0
$235$	4.89991	−	8.48689i	0.319635	−	0.553624i
$236$		0			0
$237$	−0.990665	−	0.807429i	−0.0643506	−	0.0524482i
$238$		0			0
$239$	−4.92758	+	4.13473i	−0.318739	+	0.267454i	−0.788093	−	0.615557i	$-0.788931\pi$
$239$	−4.92758	+	4.13473i	−0.318739	+	0.267454i	0.469354	+	0.883010i	$0.344487\pi$
$240$		0			0
$241$	−5.26707	+	1.91706i	−0.339282	+	0.123489i	−0.506042	−	0.862509i	$-0.668892\pi$
$241$	−5.26707	+	1.91706i	−0.339282	+	0.123489i	0.166760	+	0.985998i	$0.446670\pi$
$242$		0			0
$243$	6.81069	−	14.0219i	0.436906	−	0.899507i
$244$		0			0
$245$	15.2933	−	5.56629i	0.977050	−	0.355617i
$246$		0			0
$247$	−11.4989	+	9.64874i	−0.731659	+	0.613934i
$248$		0			0
$249$	−8.83377	−	7.19985i	−0.559817	−	0.456272i
$250$		0			0
$251$	−8.34062	+	14.4464i	−0.526455	+	0.911847i	0.473069	+	0.881025i	$0.343146\pi$
$251$	−8.34062	+	14.4464i	−0.526455	+	0.911847i	−0.999525	+	0.0308224i	$0.990187\pi$
$252$		0			0
$253$	−2.13480	−	3.69758i	−0.134214	−	0.232465i
$254$		0			0
$255$	−26.2473	−	9.13069i	−1.64367	−	0.571786i
$256$		0			0
$257$	−0.310033	−	0.112843i	−0.0193393	−	0.00703893i	0.332332	−	0.943162i	$-0.392164\pi$
$257$	−0.310033	−	0.112843i	−0.0193393	−	0.00703893i	−0.351672	+	0.936123i	$0.614387\pi$
$258$		0			0
$259$	0.0197141	−	0.111804i	0.00122497	−	0.00694717i
$260$		0			0
$261$	−3.27664	+	22.2899i	−0.202819	+	1.37971i
$262$		0			0
$263$	13.0896	+	10.9835i	0.807139	+	0.677270i	0.949923	−	0.312484i	$-0.101161\pi$
$263$	13.0896	+	10.9835i	0.807139	+	0.677270i	−0.142784	+	0.989754i	$0.545605\pi$
$264$		0			0
$265$	−5.49015	−	31.1362i	−0.337257	−	1.91268i
$266$		0			0
$267$	−10.0724	+	0.143929i	−0.616419	+	0.00880829i
$268$		0			0
$269$	3.93015			0.239626			0.119813	−	0.992797i	$-0.461771\pi$
$269$	3.93015			0.239626			0.119813	+	0.992797i	$0.461771\pi$
$270$		0			0
$271$	−23.3152			−1.41630			−0.708148	−	0.706064i	$-0.750469\pi$
$271$	−23.3152			−1.41630			−0.708148	+	0.706064i	$0.750469\pi$
$272$		0			0
$273$	−1.75332	+	3.13961i	−0.106116	+	0.190018i
$274$		0			0
$275$	0.484937	+	2.75021i	0.0292428	+	0.165844i
$276$		0			0
$277$	18.2953	+	15.3516i	1.09926	+	0.922388i	0.997375	−	0.0724083i	$-0.0230685\pi$
$277$	18.2953	+	15.3516i	1.09926	+	0.922388i	0.101884	+	0.994796i	$0.467513\pi$
$278$		0			0
$279$	−3.59449	−	17.4532i	−0.215196	−	1.04490i
$280$		0			0
$281$	−1.06006	+	6.01189i	−0.0632378	+	0.358639i	0.936725	+	0.350065i	$0.113840\pi$
$281$	−1.06006	+	6.01189i	−0.0632378	+	0.358639i	−0.999963	+	0.00857452i	$0.997271\pi$
$282$		0			0
$283$	11.4192	+	4.15624i	0.678799	+	0.247063i	0.658332	−	0.752728i	$-0.271262\pi$
$283$	11.4192	+	4.15624i	0.678799	+	0.247063i	0.0204673	+	0.999791i	$0.493485\pi$
$284$		0			0
$285$	4.80591	+	25.1489i	0.284677	+	1.48969i
$286$		0			0
$287$	−3.18766	−	5.52120i	−0.188162	−	0.325906i
$288$		0			0
$289$	−11.1651	+	19.3386i	−0.656773	+	1.13756i
$290$		0			0
$291$	−8.92888	+	3.39509i	−0.523420	+	0.199024i
$292$		0			0
$293$	−2.63148	+	2.20807i	−0.153733	+	0.128997i	−0.716410	−	0.697680i	$-0.754216\pi$
$293$	−2.63148	+	2.20807i	−0.153733	+	0.128997i	0.562677	+	0.826677i	$0.309771\pi$
$294$		0			0
$295$	−9.53035	+	3.46876i	−0.554878	+	0.201959i
$296$		0			0
$297$	−1.23281	+	9.30889i	−0.0715349	+	0.540156i
$298$		0			0
$299$	−5.76771	+	2.09927i	−0.333555	+	0.121404i
$300$		0			0
$301$	−7.12297	+	5.97688i	−0.410561	+	0.344502i
$302$		0			0
$303$	−1.09390	+	6.76793i	−0.0628431	+	0.388808i
$304$		0			0
$305$	16.7115	−	28.9452i	0.956898	−	1.65740i
$306$		0			0
$307$	0.383207	+	0.663734i	0.0218708	+	0.0378813i	0.876754	−	0.480940i	$-0.159704\pi$
$307$	0.383207	+	0.663734i	0.0218708	+	0.0378813i	−0.854883	+	0.518821i	$0.826371\pi$
$308$		0			0
$309$	−13.8233	+	11.9398i	−0.786379	+	0.679231i
$310$		0			0
$311$	22.5070	+	8.19189i	1.27626	+	0.464519i	0.889192	−	0.457533i	$-0.151267\pi$
$311$	22.5070	+	8.19189i	1.27626	+	0.464519i	0.387064	+	0.922053i	$0.373489\pi$
$312$		0			0
$313$	3.46866	−	19.6718i	0.196060	−	1.11191i	−0.714840	−	0.699288i	$-0.753501\pi$
$313$	3.46866	−	19.6718i	0.196060	−	1.11191i	0.910901	−	0.412626i	$-0.135388\pi$
$314$		0			0
$315$	3.21740	+	5.22218i	0.181280	+	0.294237i
$316$		0			0
$317$	19.4962	+	16.3592i	1.09501	+	0.918826i	0.997080	−	0.0763663i	$-0.0243319\pi$
$317$	19.4962	+	16.3592i	1.09501	+	0.918826i	0.0979349	+	0.995193i	$0.468776\pi$
$318$		0			0
$319$	−2.35662	−	13.3651i	−0.131945	−	0.748300i
$320$		0			0
$321$	−11.4847	−	19.2514i	−0.641011	−	1.07451i
$322$		0			0
$323$	36.2364			2.01625
$324$		0			0
$325$	4.01463			0.222692
$326$		0			0
$327$	12.1755	+	20.4094i	0.673305	+	1.12864i
$328$		0			0
$329$	0.531570	+	3.01468i	0.0293064	+	0.166205i
$330$		0			0
$331$	−10.5483	−	8.85111i	−0.579789	−	0.486501i	0.305089	−	0.952324i	$-0.401314\pi$
$331$	−10.5483	−	8.85111i	−0.579789	−	0.486501i	−0.884878	+	0.465823i	$0.845758\pi$
$332$		0			0
$333$	−0.426002	+	0.0121772i	−0.0233448	+	0.000667304i
$334$		0			0
$335$	−6.52002	+	36.9769i	−0.356227	+	2.02026i
$336$		0			0
$337$	21.2642	+	7.73955i	1.15834	+	0.421600i	0.848503	−	0.529191i	$-0.177504\pi$
$337$	21.2642	+	7.73955i	1.15834	+	0.421600i	0.309834	+	0.950791i	$0.399727\pi$
$338$		0			0
$339$	3.58925	−	3.10020i	0.194942	−	0.168380i
$340$		0			0
$341$	5.36706	+	9.29601i	0.290642	+	0.503407i
$342$		0			0
$343$	−5.33898	+	9.24738i	−0.288278	+	0.499312i
$344$		0			0
$345$	−1.67050	+	10.3353i	−0.0899364	+	0.556433i
$346$		0			0
$347$	5.14751	−	4.31928i	0.276333	−	0.231871i	−0.494079	−	0.869417i	$-0.664495\pi$
$347$	5.14751	−	4.31928i	0.276333	−	0.231871i	0.770412	+	0.637546i	$0.220050\pi$
$348$		0			0
$349$	19.9966	−	7.27816i	1.07039	−	0.389591i	0.254069	−	0.967186i	$-0.418231\pi$
$349$	19.9966	−	7.27816i	1.07039	−	0.389591i	0.816323	+	0.577595i	$0.196009\pi$
$350$		0			0
$351$	12.8712	+	4.06913i	0.687012	+	0.217194i
$352$		0			0
$353$	−19.2591	+	7.00973i	−1.02506	+	0.373090i	−0.799197	−	0.601069i	$-0.794742\pi$
$353$	−19.2591	+	7.00973i	−1.02506	+	0.373090i	−0.225861	+	0.974160i	$0.572519\pi$
$354$		0			0
$355$	12.8456	−	10.7788i	0.681775	−	0.572077i
$356$		0			0
$357$	8.11408	−	3.08528i	0.429443	−	0.163290i
$358$		0			0
$359$	−3.53299	+	6.11933i	−0.186464	+	0.322966i	−0.944069	−	0.329748i	$-0.893036\pi$
$359$	−3.53299	+	6.11933i	−0.186464	+	0.322966i	0.757605	+	0.652714i	$0.226370\pi$
$360$		0			0
$361$	−7.19293	−	12.4585i	−0.378575	−	0.655712i
$362$		0			0
$363$	2.51447	+	13.1580i	0.131975	+	0.690617i
$364$		0			0
$365$	−2.32457	−	0.846073i	−0.121673	−	0.0442855i
$366$		0			0
$367$	−2.48007	+	14.0652i	−0.129459	+	0.734197i	0.849101	+	0.528231i	$0.177145\pi$
$367$	−2.48007	+	14.0652i	−0.129459	+	0.734197i	−0.978559	+	0.205965i	$0.933967\pi$
$368$		0			0
$369$	−17.8862	+	15.9010i	−0.931119	+	0.827772i
$370$		0			0
$371$	7.56554	+	6.34824i	0.392783	+	0.329584i
$372$		0			0
$373$	−5.29589	−	30.0345i	−0.274211	−	1.55513i	−0.741457	−	0.671000i	$-0.765865\pi$
$373$	−5.29589	−	30.0345i	−0.274211	−	1.55513i	0.467246	−	0.884127i	$-0.345246\pi$
$374$		0			0
$375$	−7.46404	+	13.3655i	−0.385441	+	0.690194i
$376$		0			0
$377$	−19.5097			−1.00480
$378$		0			0
$379$	−28.3602			−1.45676			−0.728382	−	0.685171i	$-0.759727\pi$
$379$	−28.3602			−1.45676			−0.728382	+	0.685171i	$0.759727\pi$
$380$		0			0
$381$	−23.9264	+	0.341895i	−1.22579	+	0.0175158i
$382$		0			0
$383$	−5.80487	−	32.9211i	−0.296615	−	1.68219i	−0.660565	−	0.750769i	$-0.729683\pi$
$383$	−5.80487	−	32.9211i	−0.296615	−	1.68219i	0.363950	−	0.931419i	$-0.381428\pi$
$384$		0			0
$385$	−2.83041	−	2.37500i	−0.144251	−	0.121041i
$386$		0			0
$387$	27.3691	+	21.6635i	1.39125	+	1.10122i
$388$		0			0
$389$	−1.24728	+	7.07366i	−0.0632394	+	0.358649i	0.936724	+	0.350069i	$0.113842\pi$
$389$	−1.24728	+	7.07366i	−0.0632394	+	0.358649i	−0.999963	+	0.00857925i	$0.997269\pi$
$390$		0			0
$391$	13.9234	+	5.06770i	0.704136	+	0.256285i
$392$		0			0
$393$	4.53447	+	1.57741i	0.228734	+	0.0795699i
$394$		0			0
$395$	−0.943879	−	1.63485i	−0.0474917	−	0.0822580i
$396$		0			0
$397$	−3.34112	+	5.78698i	−0.167686	+	0.290440i	−0.937606	−	0.347700i	$-0.886963\pi$
$397$	−3.34112	+	5.78698i	−0.167686	+	0.290440i	0.769920	+	0.638140i	$0.220296\pi$
$398$		0			0
$399$	−6.19964	−	5.05294i	−0.310370	−	0.252963i
$400$		0			0
$401$	4.82432	−	4.04809i	0.240915	−	0.202152i	−0.514333	−	0.857590i	$-0.671961\pi$
$401$	4.82432	−	4.04809i	0.240915	−	0.202152i	0.755249	+	0.655439i	$0.227516\pi$
$402$		0			0
$403$	14.5005	−	5.27774i	0.722320	−	0.262903i
$404$		0			0
$405$	16.7643	−	15.7839i	0.833024	−	0.784308i
$406$		0			0
$407$	0.241238	−	0.0878033i	0.0119577	−	0.00435225i
$408$		0			0
$409$	23.1252	−	19.4043i	1.14347	−	0.959482i	0.143920	−	0.989589i	$-0.454029\pi$
$409$	23.1252	−	19.4043i	1.14347	−	0.959482i	0.999547	+	0.0301074i	$0.00958492\pi$
$410$		0			0
$411$	−2.69521	−	2.19670i	−0.132945	−	0.108355i
$412$		0			0
$413$	1.58404	−	2.74363i	0.0779454	−	0.135005i
$414$		0			0
$415$	−8.41658	−	14.5779i	−0.413153	−	0.715603i
$416$		0			0
$417$	−30.8872	−	10.7448i	−1.51255	−	0.526175i
$418$		0			0
$419$	−16.3548	−	5.95267i	−0.798986	−	0.290807i	−0.0899197	−	0.995949i	$-0.528661\pi$
$419$	−16.3548	−	5.95267i	−0.798986	−	0.290807i	−0.709066	+	0.705142i	$0.750883\pi$
$420$		0			0
$421$	1.86756	−	10.5914i	0.0910192	−	0.516195i	−0.904876	−	0.425676i	$-0.860036\pi$
$421$	1.86756	−	10.5914i	0.0910192	−	0.516195i	0.995895	−	0.0905192i	$-0.0288526\pi$
$422$		0			0
$423$	10.6817	−	4.23723i	0.519361	−	0.206021i
$424$		0			0
$425$	−7.42406	−	6.22952i	−0.360120	−	0.302176i
$426$		0			0
$427$	1.81296	+	10.2818i	0.0877352	+	0.497571i
$428$		0			0
$429$	−8.13072	+	0.116184i	−0.392555	+	0.00560939i
$430$		0			0
$431$	23.2486			1.11985			0.559924	−	0.828544i	$-0.310830\pi$
$431$	23.2486			1.11985			0.559924	+	0.828544i	$0.310830\pi$
$432$		0			0
$433$	−21.7242			−1.04400			−0.521998	−	0.852947i	$-0.674813\pi$
$433$	−21.7242			−1.04400			−0.521998	+	0.852947i	$0.674813\pi$
$434$		0			0
$435$	−16.2254	+	29.0542i	−0.777951	+	1.39304i
$436$		0			0
$437$	−2.37054	−	13.4440i	−0.113398	−	0.643114i
$438$		0			0
$439$	2.58519	+	2.16923i	0.123384	+	0.103532i	0.702392	−	0.711790i	$-0.252115\pi$
$439$	2.58519	+	2.16923i	0.123384	+	0.103532i	−0.579008	+	0.815322i	$0.696560\pi$
$440$		0			0
$441$	18.1123	+	6.01204i	0.862489	+	0.286288i
$442$		0			0
$443$	−1.19211	+	6.76080i	−0.0566389	+	0.321215i	−0.999943	−	0.0107157i	$-0.996589\pi$
$443$	−1.19211	+	6.76080i	−0.0566389	+	0.321215i	0.943304	+	0.331931i	$0.107700\pi$
$444$		0			0
$445$	−13.9819	−	5.08901i	−0.662808	−	0.241242i
$446$		0			0
$447$	−6.87162	−	35.9586i	−0.325016	−	1.70078i
$448$		0			0
$449$	1.02790	+	1.78038i	0.0485097	+	0.0840212i	0.889261	−	0.457401i	$-0.151219\pi$
$449$	1.02790	+	1.78038i	0.0485097	+	0.0840212i	−0.840751	+	0.541422i	$0.817886\pi$
$450$		0			0
$451$	7.20818	−	12.4849i	0.339420	−	0.587892i
$452$		0			0
$453$	10.2559	−	3.89968i	0.481865	−	0.183223i
$454$		0			0
$455$	−4.06893	+	3.41424i	−0.190754	+	0.160062i
$456$		0			0
$457$	−29.5986	+	10.7730i	−1.38457	+	0.503941i	−0.923559	−	0.383456i	$-0.874734\pi$
$457$	−29.5986	+	10.7730i	−1.38457	+	0.503941i	−0.461007	+	0.887396i	$0.652512\pi$
$458$		0			0
$459$	−17.4879	−	27.4971i	−0.816266	−	1.28345i
$460$		0			0
$461$	23.0547	−	8.39123i	1.07376	−	0.390818i	0.256181	−	0.966629i	$-0.417536\pi$
$461$	23.0547	−	8.39123i	1.07376	−	0.390818i	0.817583	+	0.575810i	$0.195313\pi$
$462$		0			0
$463$	−12.3693	+	10.3791i	−0.574851	+	0.482357i	−0.883251	−	0.468900i	$-0.844651\pi$
$463$	−12.3693	+	10.3791i	−0.574851	+	0.482357i	0.308401	+	0.951256i	$0.400206\pi$
$464$		0			0
$465$	4.19976	−	25.9837i	0.194759	−	1.20497i
$466$		0			0
$467$	9.27038	−	16.0568i	0.428982	−	0.743019i	−0.567801	−	0.823166i	$-0.692206\pi$
$467$	9.27038	−	16.0568i	0.428982	−	0.743019i	0.996783	+	0.0801472i	$0.0255390\pi$
$468$		0			0
$469$	−5.86437	−	10.1574i	−0.270791	−	0.469025i
$470$		0			0
$471$	5.65611	−	4.88544i	0.260620	−	0.225109i
$472$		0			0
$473$	−19.7581	−	7.19138i	−0.908480	−	0.330660i
$474$		0			0
$475$	−1.55051	+	8.79340i	−0.0711424	+	0.403469i
$476$		0			0
$477$	17.6120	−	32.6235i	0.806398	−	1.49373i
$478$		0			0
$479$	11.9788	+	10.0514i	0.547325	+	0.459260i	0.874034	−	0.485865i	$-0.161495\pi$
$479$	11.9788	+	10.0514i	0.547325	+	0.459260i	−0.326709	+	0.945125i	$0.605940\pi$
$480$		0			0
$481$	−0.0640855	−	0.363447i	−0.00292205	−	0.0165718i
$482$		0			0
$483$	−1.67548	−	2.80856i	−0.0762368	−	0.127794i
$484$		0			0
$485$	−14.1100			−0.640700
$486$		0			0
$487$	38.5757			1.74803			0.874017	−	0.485896i	$-0.161507\pi$
$487$	38.5757			1.74803			0.874017	+	0.485896i	$0.161507\pi$
$488$		0			0
$489$	−3.74174	−	6.27217i	−0.169207	−	0.283638i
$490$		0			0
$491$	2.51750	+	14.2774i	0.113613	+	0.644332i	0.987427	+	0.158073i	$0.0505280\pi$
$491$	2.51750	+	14.2774i	0.113613	+	0.644332i	−0.873814	+	0.486260i	$0.838361\pi$
$492$		0			0
$493$	36.0783	+	30.2733i	1.62488	+	1.36344i
$494$		0			0
$495$	−6.58899	+	12.2051i	−0.296153	+	0.548578i
$496$		0			0
$497$	−0.909586	+	5.15852i	−0.0408005	+	0.231391i
$498$		0			0
$499$	−11.8277	−	4.30495i	−0.529483	−	0.192716i	0.0634247	−	0.997987i	$-0.479798\pi$
$499$	−11.8277	−	4.30495i	−0.529483	−	0.192716i	−0.592907	+	0.805271i	$0.702020\pi$
$500$		0			0
$501$	−20.4291	+	17.6455i	−0.912704	+	0.788344i
$502$		0			0
$503$	−3.47691	−	6.02219i	−0.155028	−	0.268516i	0.778041	−	0.628213i	$-0.216213\pi$
$503$	−3.47691	−	6.02219i	−0.155028	−	0.268516i	−0.933069	+	0.359697i	$0.882880\pi$
$504$		0			0
$505$	−5.06327	+	8.76985i	−0.225313	+	0.390253i
$506$		0			0
$507$	1.72754	−	10.6882i	0.0767228	−	0.474681i
$508$		0			0
$509$	9.54361	−	8.00804i	0.423013	−	0.354950i	−0.406295	−	0.913742i	$-0.633179\pi$
$509$	9.54361	−	8.00804i	0.423013	−	0.354950i	0.829308	+	0.558792i	$0.188735\pi$
$510$		0			0
$511$	0.726130	−	0.264290i	0.0321221	−	0.0116915i
$512$		0			0
$513$	−13.8838	+	26.6206i	−0.612985	+	1.17533i
$514$		0			0
$515$	−25.3531	+	9.22778i	−1.11719	+	0.406625i
$516$		0			0
$517$	−5.30270	+	4.44949i	−0.233212	+	0.195688i
$518$		0			0
$519$	14.2639	−	5.42366i	0.626115	−	0.238072i
$520$		0			0
$521$	20.9298	−	36.2515i	0.916951	−	1.58821i	0.112931	−	0.993603i	$-0.463976\pi$
$521$	20.9298	−	36.2515i	0.916951	−	1.58821i	0.804020	−	0.594603i	$-0.202691\pi$
$522$		0			0
$523$	9.55868	+	16.5561i	0.417972	+	0.723949i	0.995735	−	0.0922557i	$-0.0294077\pi$
$523$	9.55868	+	16.5561i	0.417972	+	0.723949i	−0.577763	+	0.816204i	$0.696074\pi$
$524$		0			0
$525$	0.401504	+	2.10104i	0.0175231	+	0.0916969i
$526$		0			0
$527$	−35.0045	−	12.7406i	−1.52482	−	0.554989i
$528$		0			0
$529$	−3.02460	+	17.1534i	−0.131504	+	0.745798i
$530$		0			0
$531$	−11.2871	−	3.74655i	−0.489818	−	0.162586i
$532$		0			0
$533$	−15.8760	−	13.3215i	−0.687664	−	0.577019i
$534$		0			0
$535$	−5.74976	−	32.6085i	−0.248584	−	1.40979i
$536$		0			0
$537$	19.4475	−	34.8238i	0.839220	−	1.50276i
$538$		0			0
$539$	−11.4958			−0.495159
$540$		0			0
$541$	−28.6203			−1.23048			−0.615242	−	0.788338i	$-0.710942\pi$
$541$	−28.6203			−1.23048			−0.615242	+	0.788338i	$0.710942\pi$
$542$		0			0
$543$	38.5075	−	0.550251i	1.65252	−	0.0236135i
$544$		0			0
$545$	6.09562	+	34.5700i	0.261107	+	1.48081i
$546$		0			0
$547$	11.7227	+	9.83652i	0.501227	+	0.420579i	0.858029	−	0.513600i	$-0.171689\pi$
$547$	11.7227	+	9.83652i	0.501227	+	0.420579i	−0.356802	+	0.934180i	$0.616133\pi$
$548$		0			0
$549$	36.4307	−	14.4514i	1.55482	−	0.616770i
$550$		0			0
$551$	7.53494	−	42.7328i	0.320999	−	1.82048i
$552$		0			0
$553$	0.554121	+	0.201683i	0.0235636	+	0.00857645i
$554$		0			0
$555$	−0.594551	−	0.206827i	−0.0252373	−	0.00877933i
$556$		0			0
$557$	19.9031	+	34.4731i	0.843320	+	1.46067i	0.887072	+	0.461630i	$0.152735\pi$
$557$	19.9031	+	34.4731i	0.843320	+	1.46067i	−0.0437526	+	0.999042i	$0.513931\pi$
$558$		0			0
$559$	−15.1133	+	26.1771i	−0.639227	+	1.10717i
$560$		0			0
$561$	15.2160	+	12.4016i	0.642421	+	0.523598i
$562$		0			0
$563$	−4.57113	+	3.83563i	−0.192650	+	0.161653i	−0.734011	−	0.679138i	$-0.762354\pi$
$563$	−4.57113	+	3.83563i	−0.192650	+	0.161653i	0.541361	+	0.840791i	$0.317909\pi$
$564$		0			0
$565$	6.58301	−	2.39602i	0.276949	−	0.100801i
$566$		0			0
$567$	−0.842313	+	7.14303i	−0.0353738	+	0.299979i
$568$		0			0
$569$	−28.7123	+	10.4504i	−1.20368	+	0.438105i	−0.864509	−	0.502618i	$-0.832370\pi$
$569$	−28.7123	+	10.4504i	−1.20368	+	0.438105i	−0.339175	+	0.940723i	$0.610148\pi$
$570$		0			0
$571$	15.8983	−	13.3402i	0.665321	−	0.558271i	−0.246355	−	0.969180i	$-0.579233\pi$
$571$	15.8983	−	13.3402i	0.665321	−	0.558271i	0.911676	+	0.410909i	$0.134789\pi$
$572$		0			0
$573$	1.29509	+	1.05555i	0.0541033	+	0.0440962i
$574$		0			0
$575$	−1.82553	+	3.16192i	−0.0761300	+	0.131861i
$576$		0			0
$577$	4.75703	+	8.23942i	0.198038	+	0.343011i	0.947892	−	0.318591i	$-0.103210\pi$
$577$	4.75703	+	8.23942i	0.198038	+	0.343011i	−0.749854	+	0.661603i	$0.769876\pi$
$578$		0			0
$579$	−0.207527	−	0.0721929i	−0.00862454	−	0.00300023i
$580$		0			0
$581$	4.94110	+	1.79841i	0.204991	+	0.0746107i
$582$		0			0
$583$	−3.87801	+	21.9933i	−0.160611	+	0.910869i
$584$		0			0
$585$	15.6343	+	12.3750i	0.646400	+	0.511645i
$586$		0			0
$587$	−2.96025	−	2.48394i	−0.122183	−	0.102523i	0.579649	−	0.814866i	$-0.303190\pi$
$587$	−2.96025	−	2.48394i	−0.122183	−	0.102523i	−0.701832	+	0.712343i	$0.747634\pi$
$588$		0			0
$589$	5.95973	+	33.7993i	0.245566	+	1.39268i
$590$		0			0
$591$	−13.4053	+	0.191554i	−0.551420	+	0.00787949i
$592$		0			0
$593$	25.3952			1.04286			0.521429	−	0.853295i	$-0.325399\pi$
$593$	25.3952			1.04286			0.521429	+	0.853295i	$0.325399\pi$
$594$		0			0
$595$	12.8224			0.525666
$596$		0			0
$597$	12.0968	−	21.6612i	0.495088	−	0.886534i
$598$		0			0
$599$	−4.55091	−	25.8095i	−0.185945	−	1.05455i	−0.924735	−	0.380611i	$-0.875714\pi$
$599$	−4.55091	−	25.8095i	−0.185945	−	1.05455i	0.738790	−	0.673936i	$-0.235397\pi$
$600$		0			0
$601$	−4.82748	−	4.05073i	−0.196917	−	0.165233i	0.538998	−	0.842307i	$-0.318803\pi$
$601$	−4.82748	−	4.05073i	−0.196917	−	0.165233i	−0.735915	+	0.677074i	$0.763248\pi$
$602$		0			0
$603$	−32.9054	+	29.2531i	−1.34001	+	1.19128i
$604$		0			0
$605$	−3.43601	+	19.4866i	−0.139694	+	0.792243i
$606$		0			0
$607$	27.9467	+	10.1718i	1.13432	+	0.412859i	0.839859	−	0.542805i	$-0.182638\pi$
$607$	27.9467	+	10.1718i	1.13432	+	0.412859i	0.294461	+	0.955663i	$0.404860\pi$
$608$		0			0
$609$	−1.95117	−	10.2103i	−0.0790654	−	0.413743i
$610$		0			0
$611$	4.97558	+	8.61795i	0.201290	+	0.348645i
$612$		0			0
$613$	5.36046	−	9.28459i	0.216507	−	0.375001i	−0.737231	−	0.675641i	$-0.763867\pi$
$613$	5.36046	−	9.28459i	0.216507	−	0.375001i	0.953738	+	0.300640i	$0.0972003\pi$
$614$		0			0
$615$	−33.0421	+	12.5638i	−1.33239	+	0.506623i
$616$		0			0
$617$	−24.2785	+	20.3721i	−0.977417	+	0.820150i	−0.983698	−	0.179830i	$-0.942445\pi$
$617$	−24.2785	+	20.3721i	−0.977417	+	0.820150i	0.00628095	+	0.999980i	$0.498001\pi$
$618$		0			0
$619$	−4.14932	+	1.51023i	−0.166775	+	0.0607012i	−0.424058	−	0.905635i	$-0.639395\pi$
$619$	−4.14932	+	1.51023i	−0.166775	+	0.0607012i	0.257283	+	0.966336i	$0.417173\pi$
$620$		0			0
$621$	−9.05762	+	8.28699i	−0.363470	+	0.332545i
$622$		0			0
$623$	4.36757	−	1.58967i	0.174983	−	0.0636886i
$624$		0			0
$625$	−23.2407	+	19.5013i	−0.929629	+	0.780052i
$626$		0			0
$627$	2.88573	−	17.8539i	0.115245	−	0.713016i
$628$		0			0
$629$	−0.445453	+	0.771546i	−0.0177614	+	0.0307636i
$630$		0			0
$631$	3.99433	+	6.91838i	0.159012	+	0.275416i	0.934513	−	0.355930i	$-0.115836\pi$
$631$	3.99433	+	6.91838i	0.159012	+	0.275416i	−0.775501	+	0.631347i	$0.782503\pi$
$632$		0			0
$633$	27.0212	−	23.3394i	1.07400	−	0.927659i
$634$		0			0
$635$	−33.2134	−	12.0887i	−1.31803	−	0.479724i
$636$		0			0
$637$	−2.86972	+	16.2750i	−0.113703	+	0.644839i
$638$		0			0
$639$	19.6553	−	0.561840i	0.777550	−	0.0222261i
$640$		0			0
$641$	21.0232	+	17.6406i	0.830368	+	0.696761i	0.955375	−	0.295395i	$-0.0954511\pi$
$641$	21.0232	+	17.6406i	0.830368	+	0.696761i	−0.125008	+	0.992156i	$0.539896\pi$
$642$		0			0
$643$	−4.12630	−	23.4014i	−0.162725	−	0.922862i	−0.951379	−	0.308024i	$-0.900332\pi$
$643$	−4.12630	−	23.4014i	−0.162725	−	0.922862i	0.788653	−	0.614838i	$-0.210779\pi$
$644$		0			0
$645$	26.4143	+	44.2776i	1.04006	+	1.74343i
$646$		0			0
$647$	−42.8486			−1.68455			−0.842276	−	0.539047i	$-0.818785\pi$
$647$	−42.8486			−1.68455			−0.842276	+	0.539047i	$0.818785\pi$
$648$		0			0
$649$	7.16388			0.281207
$650$		0			0
$651$	4.21228	+	7.06094i	0.165092	+	0.276740i
$652$		0			0
$653$	−5.41154	−	30.6903i	−0.211770	−	1.20101i	−0.886425	−	0.462873i	$-0.846819\pi$
$653$	−5.41154	−	30.6903i	−0.211770	−	1.20101i	0.674655	−	0.738133i	$-0.264292\pi$
$654$		0			0
$655$	5.43239	+	4.55832i	0.212261	+	0.178108i
$656$		0			0
$657$	−1.52157	−	2.46966i	−0.0593619	−	0.0963507i
$658$		0			0
$659$	1.09288	−	6.19802i	0.0425725	−	0.241441i	−0.956094	−	0.293059i	$-0.905327\pi$
$659$	1.09288	−	6.19802i	0.0425725	−	0.241441i	0.998667	+	0.0516183i	$0.0164379\pi$
$660$		0			0
$661$	−9.90184	−	3.60398i	−0.385137	−	0.140178i	0.142193	−	0.989839i	$-0.454585\pi$
$661$	−9.90184	−	3.60398i	−0.385137	−	0.140178i	−0.527330	+	0.849661i	$0.676807\pi$
$662$		0			0
$663$	21.3558	−	18.4460i	0.829392	−	0.716384i
$664$		0			0
$665$	−5.90685	−	10.2310i	−0.229058	−	0.396740i
$666$		0			0
$667$	8.87144	−	15.3658i	0.343504	−	0.594966i
$668$		0			0
$669$	−0.335860	+	2.07795i	−0.0129851	+	0.0803383i
$670$		0			0
$671$	−18.0853	+	15.1753i	−0.698173	+	0.585837i
$672$		0			0
$673$	5.37459	−	1.95619i	0.207175	−	0.0754056i	−0.236348	−	0.971668i	$-0.575951\pi$
$673$	5.37459	−	1.95619i	0.207175	−	0.0754056i	0.443523	+	0.896263i	$0.353728\pi$
$674$		0			0
$675$	7.42094	−	3.06718i	0.285632	−	0.118056i
$676$		0			0
$677$	−23.4133	+	8.52175i	−0.899847	+	0.327518i	−0.750191	−	0.661221i	$-0.770039\pi$
$677$	−23.4133	+	8.52175i	−0.899847	+	0.327518i	−0.149656	+	0.988738i	$0.547816\pi$
$678$		0			0
$679$	3.37638	−	2.83312i	0.129574	−	0.108725i
$680$		0			0
$681$	−7.65011	+	2.90886i	−0.293153	+	0.111468i
$682$		0			0
$683$	−18.5061	+	32.0535i	−0.708117	+	1.22650i	0.257438	+	0.966295i	$0.417122\pi$
$683$	−18.5061	+	32.0535i	−0.708117	+	1.22650i	−0.965555	+	0.260200i	$0.916211\pi$
$684$		0			0
$685$	−2.56793	−	4.44778i	−0.0981154	−	0.169941i
$686$		0			0
$687$	4.09783	+	21.4436i	0.156342	+	0.818125i
$688$		0			0
$689$	30.1686	+	10.9805i	1.14933	+	0.418323i
$690$		0			0
$691$	−6.01978	+	34.1399i	−0.229003	+	1.29874i	0.625879	+	0.779920i	$0.284740\pi$
$691$	−6.01978	+	34.1399i	−0.229003	+	1.29874i	−0.854882	+	0.518822i	$0.826371\pi$
$692$		0			0
$693$	−0.873960	−	4.24356i	−0.0331990	−	0.161200i
$694$		0			0
$695$	−37.0036	−	31.0497i	−1.40363	−	1.17778i
$696$		0			0
$697$	8.68756	+	49.2696i	0.329065	+	1.86622i
$698$		0			0
$699$	−4.14544	+	7.42308i	−0.156795	+	0.280766i
$700$		0			0
$701$	−45.0267			−1.70063			−0.850317	−	0.526272i	$-0.823590\pi$
$701$	−45.0267			−1.70063			−0.850317	+	0.526272i	$0.823590\pi$
$702$		0			0
$703$	0.820822			0.0309579
$704$		0			0
$705$	16.9720	−	0.242521i	0.639204	−	0.00913387i
$706$		0			0
$707$	−0.549293	−	3.11519i	−0.0206583	−	0.117159i
$708$		0			0
$709$	0.672241	+	0.564077i	0.0252465	+	0.0211844i	0.655324	−	0.755348i	$-0.272532\pi$
$709$	0.672241	+	0.564077i	0.0252465	+	0.0211844i	−0.630077	+	0.776533i	$0.716977\pi$
$710$		0			0
$711$	0.321944	−	2.19008i	0.0120738	−	0.0821342i
$712$		0			0
$713$	−2.43692	+	13.8204i	−0.0912633	+	0.517580i
$714$		0			0
$715$	−11.2866	−	4.10800i	−0.422097	−	0.153631i
$716$		0			0
$717$	−10.5229	−	3.66061i	−0.392984	−	0.136708i
$718$		0			0
$719$	−3.25471	−	5.63732i	−0.121380	−	0.210237i	0.798932	−	0.601421i	$-0.205399\pi$
$719$	−3.25471	−	5.63732i	−0.121380	−	0.210237i	−0.920312	+	0.391185i	$0.872065\pi$
$720$		0			0
$721$	4.21394	−	7.29875i	0.156935	−	0.271820i
$722$		0			0
$723$	−7.52541	−	6.13349i	−0.279873	−	0.228107i
$724$		0			0
$725$	−8.89009	+	7.45967i	−0.330170	+	0.277045i
$726$		0			0
$727$	24.1627	−	8.79449i	0.896143	−	0.326169i	0.147437	−	0.989071i	$-0.452898\pi$
$727$	24.1627	−	8.79449i	0.896143	−	0.326169i	0.748706	+	0.662902i	$0.230675\pi$
$728$		0			0
$729$	26.9008	−	2.31190i	0.996327	−	0.0856258i
$730$		0			0
$731$	68.5675	−	24.9565i	2.53606	−	0.923051i
$732$		0			0
$733$	−13.4179	+	11.2589i	−0.495601	+	0.415858i	−0.856028	−	0.516929i	$-0.827075\pi$
$733$	−13.4179	+	11.2589i	−0.495601	+	0.415858i	0.360428	+	0.932787i	$0.382631\pi$
$734$		0			0
$735$	21.8505	+	17.8089i	0.805966	+	0.656893i
$736$		0			0
$737$	13.2609	−	22.9686i	0.488473	−	0.846060i
$738$		0			0
$739$	11.1750	+	19.3556i	0.411077	+	0.712007i	0.995008	−	0.0997969i	$-0.0318193\pi$
$739$	11.1750	+	19.3556i	0.411077	+	0.712007i	−0.583931	+	0.811804i	$0.698486\pi$
$740$		0			0
$741$	−24.5560	−	8.54234i	−0.902088	−	0.313811i
$742$		0			0
$743$	37.9658	+	13.8184i	1.39283	+	0.506948i	0.926042	−	0.377421i	$-0.123189\pi$
$743$	37.9658	+	13.8184i	1.39283	+	0.506948i	0.466788	+	0.884369i	$0.345411\pi$
$744$		0			0
$745$	9.39003	−	53.2535i	0.344024	−	1.95106i
$746$		0			0
$747$	2.87078	−	19.5289i	0.105036	−	0.714526i
$748$		0			0
$749$	7.92330	+	6.64844i	0.289511	+	0.242929i
$750$		0			0
$751$	2.57044	+	14.5777i	0.0937966	+	0.531947i	0.995109	+	0.0987783i	$0.0314935\pi$
$751$	2.57044	+	14.5777i	0.0937966	+	0.531947i	−0.901313	+	0.433169i	$0.857395\pi$
$752$		0			0
$753$	−28.8898	+	0.412819i	−1.05280	+	0.0150440i
$754$		0			0
$755$	16.2070			0.589833
$756$		0			0
$757$	−29.7090			−1.07979			−0.539897	−	0.841731i	$-0.681537\pi$
$757$	−29.7090			−1.07979			−0.539897	+	0.841731i	$0.681537\pi$
$758$		0			0
$759$	3.60570	−	6.45658i	0.130879	−	0.234359i
$760$		0			0
$761$	6.40101	+	36.3020i	0.232037	+	1.31594i	0.848766	+	0.528769i	$0.177346\pi$
$761$	6.40101	+	36.3020i	0.232037	+	1.31594i	−0.616729	+	0.787176i	$0.711543\pi$
$762$		0			0
$763$	−8.39989	−	7.04834i	−0.304096	−	0.255167i
$764$		0			0
$765$	−9.70938	−	47.1444i	−0.351044	−	1.70451i
$766$		0			0
$767$	1.78834	−	10.1422i	0.0645730	−	0.366212i
$768$		0			0
$769$	25.3963	+	9.24348i	0.915812	+	0.333328i	0.756571	−	0.653911i	$-0.226873\pi$
$769$	25.3963	+	9.24348i	0.915812	+	0.333328i	0.159241	+	0.987240i	$0.449095\pi$
$770$		0			0
$771$	−0.107263	−	0.561298i	−0.00386298	−	0.0202147i
$772$		0			0
$773$	14.2664	+	24.7102i	0.513128	+	0.888763i	0.999884	+	0.0152254i	$0.00484657\pi$
$773$	14.2664	+	24.7102i	0.513128	+	0.888763i	−0.486756	+	0.873538i	$0.661820\pi$
$774$		0			0
$775$	4.58954	−	7.94931i	0.164861	−	0.285548i
$776$		0			0
$777$	0.183799	−	0.0698873i	0.00659376	−	0.00250719i
$778$		0			0
$779$	35.3101	−	29.6287i	1.26512	−	1.06156i
$780$		0			0
$781$	−11.1304	+	4.05115i	−0.398278	+	0.144961i
$782$		0			0
$783$	−36.0631	+	14.9054i	−1.28879	+	0.532676i
$784$		0			0
$785$	10.3738	−	3.77576i	0.370257	−	0.134763i
$786$		0			0
$787$	1.88569	−	1.58228i	0.0672176	−	0.0564023i	−0.608560	−	0.793508i	$-0.708252\pi$
$787$	1.88569	−	1.58228i	0.0672176	−	0.0564023i	0.675777	+	0.737106i	$0.263808\pi$
$788$		0			0
$789$	−4.72232	+	29.2168i	−0.168119	+	1.04015i
$790$		0			0
$791$	−1.09416	+	1.89514i	−0.0389039	+	0.0673835i
$792$		0			0
$793$	16.9696	+	29.3922i	0.602607	+	1.04375i
$794$		0			0
$795$	41.4424	−	35.7957i	1.46981	−	1.26954i
$796$		0			0
$797$	16.4608	+	5.99124i	0.583072	+	0.212221i	0.616679	−	0.787214i	$-0.288477\pi$
$797$	16.4608	+	5.99124i	0.583072	+	0.212221i	−0.0336077	+	0.999435i	$0.510700\pi$
$798$		0			0
$799$	4.17143	−	23.6574i	0.147575	−	0.836938i
$800$		0			0
$801$	−9.15200	−	14.8547i	−0.323370	−	0.524864i
$802$		0			0
$803$	1.33855	+	1.12318i	0.0472365	+	0.0396361i
$804$		0			0
$805$	−0.838823	−	4.75720i	−0.0295646	−	0.167669i
$806$		0			0
$807$	3.48749	+	5.84600i	0.122766	+	0.205789i
$808$		0			0
$809$	−6.84388			−0.240618			−0.120309	−	0.992736i	$-0.538389\pi$
$809$	−6.84388			−0.240618			−0.120309	+	0.992736i	$0.538389\pi$
$810$		0			0
$811$	11.2665			0.395622			0.197811	−	0.980240i	$-0.436617\pi$
$811$	11.2665			0.395622			0.197811	+	0.980240i	$0.436617\pi$
$812$		0			0
$813$	−20.6892	−	34.6807i	−0.725600	−	1.21630i
$814$		0			0
$815$	−1.87329	−	10.6240i	−0.0656185	−	0.372141i
$816$		0			0
$817$	−51.4996	−	43.2133i	−1.80174	−	1.51184i
$818$		0			0
$819$	−6.22593	+	0.177966i	−0.217551	+	0.00621865i
$820$		0			0
$821$	−0.588262	+	3.33620i	−0.0205305	+	0.116434i	−0.993351	−	0.115127i	$-0.963272\pi$
$821$	−0.588262	+	3.33620i	−0.0205305	+	0.116434i	0.972820	+	0.231562i	$0.0743835\pi$
$822$		0			0
$823$	−44.7817	−	16.2992i	−1.56099	−	0.568154i	−0.590027	−	0.807383i	$-0.700883\pi$
$823$	−44.7817	−	16.2992i	−1.56099	−	0.568154i	−0.970963	+	0.239229i	$0.923105\pi$
$824$		0			0
$825$	−3.66055	+	3.16179i	−0.127444	+	0.110079i
$826$		0			0
$827$	−22.5176	−	39.0016i	−0.783013	−	1.35622i	−0.930179	−	0.367106i	$-0.880349\pi$
$827$	−22.5176	−	39.0016i	−0.783013	−	1.35622i	0.147166	−	0.989112i	$-0.452985\pi$
$828$		0			0
$829$	−1.00794	+	1.74581i	−0.0350073	+	0.0606344i	−0.882998	−	0.469376i	$-0.844479\pi$
$829$	−1.00794	+	1.74581i	−0.0350073	+	0.0606344i	0.847991	+	0.530011i	$0.177812\pi$
$830$		0			0
$831$	−6.60039	+	40.8363i	−0.228965	+	1.41660i
$832$		0			0
$833$	30.5608	−	25.6436i	1.05887	−	0.888498i
$834$		0			0
$835$	−37.4688	+	13.6375i	−1.29666	+	0.471946i
$836$		0			0
$837$	22.7716	−	20.8342i	0.787101	−	0.720134i
$838$		0			0
$839$	−9.45200	+	3.44024i	−0.326319	+	0.118770i	−0.499985	−	0.866034i	$-0.666661\pi$
$839$	−9.45200	+	3.44024i	−0.326319	+	0.118770i	0.173666	+	0.984805i	$0.444439\pi$
$840$		0			0
$841$	20.9874	−	17.6105i	0.723703	−	0.607259i
$842$		0			0
$843$	−9.88319	+	3.75796i	−0.340395	+	0.129431i
$844$		0			0
$845$	7.99616	−	13.8497i	0.275076	−	0.476446i
$846$		0			0
$847$	−3.09049	−	5.35288i	−0.106190	−	0.183927i
$848$		0			0
$849$	3.95072	+	20.6738i	0.135589	+	0.709524i
$850$		0			0
$851$	0.315391	+	0.114793i	0.0108115	+	0.00393505i
$852$		0			0
$853$	5.14614	−	29.1852i	0.176200	−	0.999283i	−0.760549	−	0.649281i	$-0.775070\pi$
$853$	5.14614	−	29.1852i	0.176200	−	0.999283i	0.936749	−	0.350002i	$-0.113819\pi$
$854$		0			0
$855$	−33.1437	+	29.4650i	−1.13349	+	1.00768i
$856$		0			0
$857$	−31.2591	−	26.2295i	−1.06779	−	0.895983i	−0.0729406	−	0.997336i	$-0.523238\pi$
$857$	−31.2591	−	26.2295i	−1.06779	−	0.895983i	−0.994851	+	0.101353i	$0.967683\pi$
$858$		0			0
$859$	7.22311	+	40.9643i	0.246449	+	1.39768i	0.817102	+	0.576493i	$0.195579\pi$
$859$	7.22311	+	40.9643i	0.246449	+	1.39768i	−0.570653	+	0.821191i	$0.693310\pi$
$860$		0			0
$861$	5.38400	−	9.64090i	0.183486	−	0.328561i
$862$		0			0
$863$	−8.42541			−0.286804			−0.143402	−	0.989664i	$-0.545804\pi$
$863$	−8.42541			−0.286804			−0.143402	+	0.989664i	$0.545804\pi$
$864$		0			0
$865$	22.5406			0.766405
$866$		0			0
$867$	−38.6732	+	0.552619i	−1.31341	+	0.0187679i
$868$		0			0
$869$	0.231548	+	1.31318i	0.00785474	+	0.0445464i
$870$		0			0
$871$	−29.2071	−	24.5077i	−0.989645	−	0.830411i
$872$		0			0
$873$	−12.9733	−	10.2688i	−0.439080	−	0.347545i
$874$		0			0
$875$	1.22654	−	6.95603i	0.0414645	−	0.235157i
$876$		0			0
$877$	−18.3194	−	6.66772i	−0.618602	−	0.225153i	0.0136606	−	0.999907i	$-0.495652\pi$
$877$	−18.3194	−	6.66772i	−0.618602	−	0.225153i	−0.632263	+	0.774754i	$0.717874\pi$
$878$		0			0
$879$	−5.61954	−	1.95488i	−0.189542	−	0.0659364i
$880$		0			0
$881$	−9.09407	−	15.7514i	−0.306387	−	0.530678i	0.671182	−	0.741292i	$-0.265787\pi$
$881$	−9.09407	−	15.7514i	−0.306387	−	0.530678i	−0.977569	+	0.210615i	$0.932454\pi$
$882$		0			0
$883$	−11.7231	+	20.3049i	−0.394512	+	0.683315i	−0.993039	−	0.117788i	$-0.962420\pi$
$883$	−11.7231	+	20.3049i	−0.394512	+	0.683315i	0.598527	+	0.801103i	$0.295753\pi$
$884$		0			0
$885$	−13.6166	−	11.0981i	−0.457718	−	0.373057i
$886$		0			0
$887$	−22.9867	+	19.2881i	−0.771819	+	0.647633i	−0.941174	−	0.337922i	$-0.890276\pi$
$887$	−22.9867	+	19.2881i	−0.771819	+	0.647633i	0.169355	+	0.985555i	$0.445831\pi$
$888$		0			0
$889$	10.3749	−	3.77616i	0.347964	−	0.126648i
$890$		0			0
$891$	−14.9407	+	6.42664i	−0.500531	+	0.215301i
$892$		0			0
$893$	−20.7979	+	7.56981i	−0.695974	+	0.253314i
$894$		0			0
$895$	45.1316	−	37.8699i	1.50858	−	1.26585i
$896$		0			0
$897$	−8.24070	−	6.71648i	−0.275149	−	0.224257i
$898$		0			0
$899$	−22.3035	+	38.6308i	−0.743864	+	1.28841i
$900$		0			0
$901$	−38.7508	−	67.1184i	−1.29098	−	2.23604i
$902$		0			0
$903$	−15.2112	−	5.29153i	−0.506196	−	0.176091i
$904$		0			0
$905$	53.4541	+	19.4557i	1.77688	+	0.646730i
$906$		0			0
$907$	4.88265	−	27.6909i	0.162126	−	0.919461i	−0.789853	−	0.613297i	$-0.789843\pi$
$907$	4.88265	−	27.6909i	0.162126	−	0.919461i	0.951979	−	0.306165i	$-0.0990458\pi$
$908$		0			0
$909$	−11.0378	+	4.37850i	−0.366101	+	0.145226i
$910$		0			0
$911$	15.0993	+	12.6698i	0.500261	+	0.419768i	0.857686	−	0.514173i	$-0.171901\pi$
$911$	15.0993	+	12.6698i	0.500261	+	0.419768i	−0.357426	+	0.933942i	$0.616346\pi$
$912$		0			0
$913$	2.06472	+	11.7096i	0.0683322	+	0.387531i
$914$		0			0
$915$	57.8844	−	0.827136i	1.91360	−	0.0273443i
$916$		0			0
$917$	−2.21518			−0.0731518
$918$		0			0
$919$	52.1671			1.72083			0.860417	−	0.509590i	$-0.170203\pi$
$919$	52.1671			1.72083			0.860417	+	0.509590i	$0.170203\pi$
$920$		0			0
$921$	−0.647240	+	1.15899i	−0.0213273	+	0.0381899i
$922$		0			0
$923$	2.95683	+	16.7690i	0.0973254	+	0.551960i
$924$		0			0
$925$	−0.168169	−	0.141110i	−0.00552936	−	0.00463968i
$926$		0			0
$927$	−30.0265	−	9.96675i	−0.986199	−	0.327351i
$928$		0			0
$929$	2.27063	−	12.8774i	0.0744971	−	0.422494i	−0.924636	−	0.380853i	$-0.875630\pi$
$929$	2.27063	−	12.8774i	0.0744971	−	0.422494i	0.999133	−	0.0416409i	$-0.0132585\pi$
$930$		0			0
$931$	−34.5394	−	12.5713i	−1.13198	−	0.412008i
$932$		0			0
$933$	7.78683	+	40.7478i	0.254929	+	1.33402i
$934$		0			0
$935$	14.4974	+	25.1103i	0.474116	+	0.821194i
$936$		0			0
$937$	−5.96030	+	10.3236i	−0.194715	+	0.337256i	−0.946807	−	0.321802i	$-0.895711\pi$
$937$	−5.96030	+	10.3236i	−0.194715	+	0.337256i	0.752092	+	0.659058i	$0.229045\pi$
$938$		0			0
$939$	32.3392	−	12.2966i	1.05535	−	0.401283i
$940$		0			0
$941$	26.5825	−	22.3053i	0.866564	−	0.727133i	−0.0968078	−	0.995303i	$-0.530863\pi$
$941$	26.5825	−	22.3053i	0.866564	−	0.727133i	0.963372	+	0.268170i	$0.0864188\pi$
$942$		0			0
$943$	17.7111	−	6.44632i	0.576753	−	0.209921i
$944$		0			0
$945$	−4.91283	+	9.41980i	−0.159814	+	0.306426i
$946$		0			0
$947$	9.02878	−	3.28621i	0.293396	−	0.106787i	−0.191129	−	0.981565i	$-0.561215\pi$
$947$	9.02878	−	3.28621i	0.293396	−	0.106787i	0.484525	+	0.874778i	$0.338993\pi$
$948$		0			0
$949$	1.92427	−	1.61465i	0.0624644	−	0.0524139i
$950$		0			0
$951$	−7.03362	+	43.5167i	−0.228081	+	1.41113i
$952$		0			0
$953$	6.27268	−	10.8646i	0.203192	−	0.351939i	−0.746363	−	0.665539i	$-0.768202\pi$
$953$	6.27268	−	10.8646i	0.203192	−	0.351939i	0.949555	+	0.313600i	$0.101535\pi$
$954$		0			0
$955$	1.23393	+	2.13723i	0.0399290	+	0.0691591i
$956$		0			0
$957$	17.7890	−	15.3652i	0.575036	−	0.496685i
$958$		0			0
$959$	1.50755	+	0.548702i	0.0486812	+	0.0177185i
$960$		0			0
$961$	0.743513	−	4.21667i	0.0239843	−	0.136022i
$962$		0			0
$963$	18.4448	−	34.1662i	0.594377	−	1.10099i
$964$		0			0
$965$	−0.248623	−	0.208619i	−0.00800344	−	0.00671569i
$966$		0			0
$967$	1.04079	+	5.90259i	0.0334694	+	0.189814i	0.996959	−	0.0779327i	$-0.0248319\pi$
$967$	1.04079	+	5.90259i	0.0334694	+	0.189814i	−0.963489	+	0.267747i	$0.913721\pi$
$968$		0			0
$969$	32.1550	+	53.9006i	1.03297	+	1.73154i
$970$		0			0
$971$	36.0825			1.15794			0.578972	−	0.815348i	$-0.303454\pi$
$971$	36.0825			1.15794			0.578972	+	0.815348i	$0.303454\pi$
$972$		0			0
$973$	15.0891			0.483733
$974$		0			0
$975$	3.56246	+	5.97165i	0.114090	+	0.191246i
$976$		0			0
$977$	6.48450	+	36.7754i	0.207458	+	1.17655i	0.893525	+	0.449013i	$0.148224\pi$
$977$	6.48450	+	36.7754i	0.207458	+	1.17655i	−0.686068	+	0.727537i	$0.740665\pi$
$978$		0			0
$979$	8.05121	+	6.75576i	0.257318	+	0.215915i
$980$		0			0
$981$	−19.5543	+	36.2213i	−0.624321	+	1.15646i
$982$		0			0
$983$	−3.27601	+	18.5792i	−0.104488	+	0.592584i	0.886935	+	0.461894i	$0.152830\pi$
$983$	−3.27601	+	18.5792i	−0.104488	+	0.592584i	−0.991423	+	0.130689i	$0.958281\pi$
$984$		0			0
$985$	−18.6085	−	6.77295i	−0.592917	−	0.215804i
$986$		0			0
$987$	−4.01256	+	3.46583i	−0.127721	+	0.110319i
$988$		0			0
$989$	−13.7447	−	23.8065i	−0.437056	−	0.757002i
$990$		0			0
$991$	30.3982	−	52.6513i	0.965631	−	1.67252i	0.257721	−	0.966219i	$-0.417028\pi$
$991$	30.3982	−	52.6513i	0.965631	−	1.67252i	0.707910	−	0.706303i	$-0.249638\pi$
$992$		0			0
$993$	3.80551	−	23.5446i	0.120764	−	0.747164i
$994$		0			0
$995$	28.0729	−	23.5560i	0.889971	−	0.746774i
$996$		0			0
$997$	28.1844	−	10.2583i	0.892608	−	0.324883i	0.145322	−	0.989384i	$-0.453578\pi$
$997$	28.1844	−	10.2583i	0.892608	−	0.324883i	0.747287	+	0.664502i	$0.231356\pi$
$998$		0			0
$999$	−0.396134	−	0.622861i	−0.0125331	−	0.0197065i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.q.a.169.3	✓	24
3.2	odd	2		648.2.q.a.505.1		24
4.3	odd	2		432.2.u.e.385.2		24
27.2	odd	18		5832.2.a.i.1.2		12
27.4	even	9	inner	216.2.q.a.193.3	yes	24
27.23	odd	18		648.2.q.a.145.1		24
27.25	even	9		5832.2.a.h.1.11		12
108.31	odd	18		432.2.u.e.193.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.a.169.3	✓	24	1.1	even	1	trivial
216.2.q.a.193.3	yes	24	27.4	even	9	inner
432.2.u.e.193.2		24	108.31	odd	18
432.2.u.e.385.2		24	4.3	odd	2
648.2.q.a.145.1		24	27.23	odd	18
648.2.q.a.505.1		24	3.2	odd	2
5832.2.a.h.1.11		12	27.25	even	9
5832.2.a.i.1.2		12	27.2	odd	18

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.887369 + 1.48747i) q^{3} +(0.444259 + 2.51952i) q^{5} +(-0.612199 - 0.513696i) q^{7} +(-1.42515 + 2.63988i) q^{9} +O(q^{10})\)	\(q+(0.887369 + 1.48747i) q^{3} +(0.444259 + 2.51952i) q^{5} +(-0.612199 - 0.513696i) q^{7} +(-1.42515 + 2.63988i) q^{9} +(0.313806 - 1.77968i) q^{11} +(-2.44122 - 0.888533i) q^{13} +(-3.35349 + 2.89657i) q^{15} +(3.13569 + 5.43118i) q^{17} +(2.88902 - 5.00394i) q^{19} +(0.220862 - 1.36647i) q^{21} +(1.80988 - 1.51867i) q^{23} +(-1.45214 + 0.528537i) q^{25} +(-5.19138 + 0.222667i) q^{27} +(7.05690 - 2.56850i) q^{29} +(-4.55018 + 3.81806i) q^{31} +(2.92569 - 1.11246i) q^{33} +(1.02229 - 1.77066i) q^{35} +(0.0710294 + 0.123026i) q^{37} +(-0.844597 - 4.41971i) q^{39} +(7.49635 + 2.72845i) q^{41} +(2.02041 - 11.4583i) q^{43} +(-7.28435 - 2.41791i) q^{45} +(-2.93431 - 2.46218i) q^{47} +(-1.10463 - 6.26469i) q^{49} +(-5.29622 + 9.48372i) q^{51} -12.3580 q^{53} +4.62336 q^{55} +(10.0069 - 0.142992i) q^{57} +(0.688378 + 3.90399i) q^{59} +(-10.0077 - 8.39744i) q^{61} +(2.22857 - 0.884033i) q^{63} +(1.15414 - 6.54545i) q^{65} +(13.7911 + 5.01955i) q^{67} +(3.86501 + 1.34453i) q^{69} +(-3.27722 - 5.67630i) q^{71} +(-0.483460 + 0.837377i) q^{73} +(-2.07477 - 1.69102i) q^{75} +(-1.10633 + 0.928319i) q^{77} +(-0.693372 + 0.252367i) q^{79} +(-4.93788 - 7.52445i) q^{81} +(-6.18280 + 2.25036i) q^{83} +(-12.2909 + 10.3133i) q^{85} +(10.0827 + 8.21775i) q^{87} +(-2.90794 + 5.03670i) q^{89} +(1.03808 + 1.79800i) q^{91} +(-9.71695 - 3.38025i) q^{93} +(13.8910 + 5.05591i) q^{95} +(-0.957701 + 5.43139i) q^{97} +(4.25092 + 3.36473i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{7} + 6 q^{9}+O(q^{10}) \) 24 * q - 3 * q^7 + 6 * q^9	\( 24 q - 3 q^{7} + 6 q^{9} + 6 q^{11} + 12 q^{13} - 3 q^{15} + 6 q^{17} + 9 q^{19} - 18 q^{21} + 24 q^{23} - 24 q^{25} - 9 q^{29} - 27 q^{31} + 21 q^{33} - 18 q^{35} + 15 q^{37} - 15 q^{39} - 6 q^{41} + 39 q^{43} - 69 q^{45} - 36 q^{47} + 3 q^{49} - 36 q^{51} - 18 q^{53} - 54 q^{55} + 27 q^{57} - 30 q^{59} + 12 q^{61} + 18 q^{63} - 18 q^{65} + 54 q^{67} - 57 q^{69} + 36 q^{73} - 51 q^{75} - 24 q^{77} - 45 q^{79} + 18 q^{81} + 33 q^{83} - 57 q^{85} + 90 q^{87} + 9 q^{89} + 39 q^{91} + 42 q^{93} + 87 q^{95} + 57 q^{97} - 24 q^{99}+O(q^{100}) \) 24 * q - 3 * q^7 + 6 * q^9 + 6 * q^11 + 12 * q^13 - 3 * q^15 + 6 * q^17 + 9 * q^19 - 18 * q^21 + 24 * q^23 - 24 * q^25 - 9 * q^29 - 27 * q^31 + 21 * q^33 - 18 * q^35 + 15 * q^37 - 15 * q^39 - 6 * q^41 + 39 * q^43 - 69 * q^45 - 36 * q^47 + 3 * q^49 - 36 * q^51 - 18 * q^53 - 54 * q^55 + 27 * q^57 - 30 * q^59 + 12 * q^61 + 18 * q^63 - 18 * q^65 + 54 * q^67 - 57 * q^69 + 36 * q^73 - 51 * q^75 - 24 * q^77 - 45 * q^79 + 18 * q^81 + 33 * q^83 - 57 * q^85 + 90 * q^87 + 9 * q^89 + 39 * q^91 + 42 * q^93 + 87 * q^95 + 57 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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