LMFDB - Embedded newform 232.2.q.a.33.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [232,2,Mod(9,232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(232, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("232.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 232 = 2^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	232.q (of order $14$, 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:	$1.85252932689$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			33.4
Character	$\chi$	$=$	232.33
Dual form			232.2.q.a.225.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.186194 - 0.386637i) q^{3} +(0.478397 - 2.09600i) q^{5} +(-1.33207 + 0.641493i) q^{7} +(1.75565 - 2.20152i) q^{9} +O(q^{10})$	\(q+(-0.186194 - 0.386637i) q^{3} +(0.478397 - 2.09600i) q^{5} +(-1.33207 + 0.641493i) q^{7} +(1.75565 - 2.20152i) q^{9} +(2.02706 - 1.61653i) q^{11} +(-1.55115 - 1.94508i) q^{13} +(-0.899464 + 0.205297i) q^{15} -2.05780i q^{17} +(0.289294 - 0.600726i) q^{19} +(0.496050 + 0.395586i) q^{21} +(1.34616 + 5.89789i) q^{23} +(0.340513 + 0.163982i) q^{25} +(-2.43320 - 0.555363i) q^{27} +(5.10649 - 1.70990i) q^{29} +(-2.83719 - 0.647569i) q^{31} +(-1.00244 - 0.482748i) q^{33} +(0.707306 + 3.09891i) q^{35} +(2.53055 + 2.01805i) q^{37} +(-0.463224 + 0.961894i) q^{39} +6.01720i q^{41} +(-2.70498 + 0.617395i) q^{43} +(-3.77447 - 4.73303i) q^{45} +(-8.30968 + 6.62675i) q^{47} +(-3.00152 + 3.76379i) q^{49} +(-0.795620 + 0.383150i) q^{51} +(-2.47903 + 10.8613i) q^{53} +(-2.41849 - 5.02206i) q^{55} -0.286128 q^{57} +12.2401 q^{59} +(0.151602 + 0.314804i) q^{61} +(-0.926399 + 4.05882i) q^{63} +(-4.81894 + 2.32068i) q^{65} +(6.06188 - 7.60135i) q^{67} +(2.02969 - 1.61863i) q^{69} +(1.57140 + 1.97047i) q^{71} +(4.10831 - 0.937696i) q^{73} -0.162187i q^{75} +(-1.66321 + 3.45368i) q^{77} +(-4.21005 - 3.35741i) q^{79} +(-1.64143 - 7.19156i) q^{81} +(7.37393 + 3.55110i) q^{83} +(-4.31313 - 0.984444i) q^{85} +(-1.61191 - 1.65598i) q^{87} +(0.477973 + 0.109094i) q^{89} +(3.31400 + 1.59594i) q^{91} +(0.277894 + 1.21753i) q^{93} +(-1.12072 - 0.893745i) q^{95} +(-1.92488 + 3.99706i) q^{97} -7.30067i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{5} - 4 q^{7} + 6 q^{9}+O(q^{10}) $ 48 * q - 2 * q^5 - 4 * q^7 + 6 * q^9	$ 48 q - 2 q^{5} - 4 q^{7} + 6 q^{9} + 10 q^{13} + 14 q^{15} + 14 q^{21} + 4 q^{23} - 48 q^{25} - 4 q^{29} + 10 q^{33} + 8 q^{35} - 38 q^{45} - 14 q^{47} - 18 q^{49} - 56 q^{51} - 48 q^{53} - 28 q^{55} - 12 q^{57} - 128 q^{59} - 28 q^{61} + 42 q^{63} - 28 q^{65} - 4 q^{67} + 28 q^{69} - 14 q^{71} - 28 q^{73} + 14 q^{77} - 32 q^{81} + 80 q^{83} - 112 q^{87} + 42 q^{89} - 28 q^{91} + 6 q^{93} + 70 q^{97}+O(q^{100}) $ 48 * q - 2 * q^5 - 4 * q^7 + 6 * q^9 + 10 * q^13 + 14 * q^15 + 14 * q^21 + 4 * q^23 - 48 * q^25 - 4 * q^29 + 10 * q^33 + 8 * q^35 - 38 * q^45 - 14 * q^47 - 18 * q^49 - 56 * q^51 - 48 * q^53 - 28 * q^55 - 12 * q^57 - 128 * q^59 - 28 * q^61 + 42 * q^63 - 28 * q^65 - 4 * q^67 + 28 * q^69 - 14 * q^71 - 28 * q^73 + 14 * q^77 - 32 * q^81 + 80 * q^83 - 112 * q^87 + 42 * q^89 - 28 * q^91 + 6 * q^93 + 70 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/232\mathbb{Z}\right)^\times$.

$n$	$89$	$117$	$175$
$\chi(n)$	$e\left(\frac{1}{14}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.186194	−	0.386637i	−0.107499	−	0.223225i	0.840279	−	0.542154i	$-0.182391\pi$
$3$	−0.186194	−	0.386637i	−0.107499	−	0.223225i	−0.947779	+	0.318929i	$0.896677\pi$
$4$		0			0
$5$	0.478397	−	2.09600i	0.213946	−	0.937357i	−0.747910	−	0.663800i	$-0.768943\pi$
$5$	0.478397	−	2.09600i	0.213946	−	0.937357i	0.961856	−	0.273557i	$-0.0882003\pi$
$6$		0			0
$7$	−1.33207	+	0.641493i	−0.503477	+	0.242462i	−0.668342	−	0.743855i	$-0.732996\pi$
$7$	−1.33207	+	0.641493i	−0.503477	+	0.242462i	0.164865	+	0.986316i	$0.447281\pi$
$8$		0			0
$9$	1.75565	−	2.20152i	0.585217	−	0.733838i
$10$		0			0
$11$	2.02706	−	1.61653i	0.611182	−	0.487402i	−0.268299	−	0.963336i	$-0.586461\pi$
$11$	2.02706	−	1.61653i	0.611182	−	0.487402i	0.879481	+	0.475934i	$0.157890\pi$
$12$		0			0
$13$	−1.55115	−	1.94508i	−0.430211	−	0.539468i	0.518723	−	0.854942i	$-0.326408\pi$
$13$	−1.55115	−	1.94508i	−0.430211	−	0.539468i	−0.948934	+	0.315475i	$0.897836\pi$
$14$		0			0
$15$	−0.899464	+	0.205297i	−0.232240	+	0.0530074i
$16$		0			0
$17$		−	2.05780i		−	0.499089i	−0.968363	−	0.249544i	$-0.919719\pi$
$17$		−	2.05780i		−	0.499089i	0.968363	−	0.249544i	$-0.0802809\pi$
$18$		0			0
$19$	0.289294	−	0.600726i	0.0663686	−	0.137816i	−0.865146	−	0.501521i	$-0.832774\pi$
$19$	0.289294	−	0.600726i	0.0663686	−	0.137816i	0.931514	+	0.363705i	$0.118488\pi$
$20$		0			0
$21$	0.496050	+	0.395586i	0.108247	+	0.0863240i
$22$		0			0
$23$	1.34616	+	5.89789i	0.280693	+	1.22980i	0.896908	+	0.442217i	$0.145808\pi$
$23$	1.34616	+	5.89789i	0.280693	+	1.22980i	−0.616215	+	0.787578i	$0.711335\pi$
$24$		0			0
$25$	0.340513	+	0.163982i	0.0681026	+	0.0327965i
$26$		0			0
$27$	−2.43320	−	0.555363i	−0.468270	−	0.106880i
$28$		0			0
$29$	5.10649	−	1.70990i	0.948252	−	0.317520i
$29$	5.10649	−	1.70990i	0.948252	−	0.317520i
$30$		0			0
$31$	−2.83719	−	0.647569i	−0.509574	−	0.116307i	−0.0399992	−	0.999200i	$-0.512736\pi$
$31$	−2.83719	−	0.647569i	−0.509574	−	0.116307i	−0.469575	+	0.882893i	$0.655593\pi$
$32$		0			0
$33$	−1.00244	−	0.482748i	−0.174502	−	0.0840357i
$34$		0			0
$35$	0.707306	+	3.09891i	0.119557	+	0.523811i
$36$		0			0
$37$	2.53055	+	2.01805i	0.416020	+	0.331765i	0.809028	−	0.587770i	$-0.199994\pi$
$37$	2.53055	+	2.01805i	0.416020	+	0.331765i	−0.393008	+	0.919535i	$0.628566\pi$
$38$		0			0
$39$	−0.463224	+	0.961894i	−0.0741751	+	0.154026i
$40$		0			0
$41$			6.01720i			0.939729i	0.882739	+	0.469864i	$0.155697\pi$
$41$			6.01720i			0.939729i	−0.882739	+	0.469864i	$0.844303\pi$
$42$		0			0
$43$	−2.70498	+	0.617395i	−0.412506	+	0.0941519i	−0.423737	−	0.905785i	$-0.639282\pi$
$43$	−2.70498	+	0.617395i	−0.412506	+	0.0941519i	0.0112311	+	0.999937i	$0.496425\pi$
$44$		0			0
$45$	−3.77447	−	4.73303i	−0.562664	−	0.705559i
$46$		0			0
$47$	−8.30968	+	6.62675i	−1.21209	+	0.966610i	−0.999944	−	0.0106272i	$-0.996617\pi$
$47$	−8.30968	+	6.62675i	−1.21209	+	0.966610i	−0.212148	+	0.977238i	$0.568046\pi$
$48$		0			0
$49$	−3.00152	+	3.76379i	−0.428789	+	0.537684i
$50$		0			0
$51$	−0.795620	+	0.383150i	−0.111409	+	0.0536518i
$52$		0			0
$53$	−2.47903	+	10.8613i	−0.340521	+	1.49192i	0.457456	+	0.889232i	$0.348761\pi$
$53$	−2.47903	+	10.8613i	−0.340521	+	1.49192i	−0.797977	+	0.602688i	$0.794096\pi$
$54$		0			0
$55$	−2.41849	−	5.02206i	−0.326110	−	0.677174i
$56$		0			0
$57$	−0.286128			−0.0378985
$58$		0			0
$59$	12.2401			1.59352			0.796760	−	0.604296i	$-0.206546\pi$
$59$	12.2401			1.59352			0.796760	+	0.604296i	$0.206546\pi$
$60$		0			0
$61$	0.151602	+	0.314804i	0.0194106	+	0.0403065i	0.910449	−	0.413622i	$-0.135736\pi$
$61$	0.151602	+	0.314804i	0.0194106	+	0.0403065i	−0.891038	+	0.453928i	$0.850022\pi$
$62$		0			0
$63$	−0.926399	+	4.05882i	−0.116715	+	0.511363i
$64$		0			0
$65$	−4.81894	+	2.32068i	−0.597716	+	0.287845i
$66$		0			0
$67$	6.06188	−	7.60135i	0.740576	−	0.928653i	−0.258728	−	0.965950i	$-0.583303\pi$
$67$	6.06188	−	7.60135i	0.740576	−	0.928653i	0.999304	+	0.0372970i	$0.0118748\pi$
$68$		0			0
$69$	2.02969	−	1.61863i	0.244347	−	0.194860i
$70$		0			0
$71$	1.57140	+	1.97047i	0.186491	+	0.233852i	0.866284	−	0.499552i	$-0.166502\pi$
$71$	1.57140	+	1.97047i	0.186491	+	0.233852i	−0.679793	+	0.733404i	$0.737930\pi$
$72$		0			0
$73$	4.10831	−	0.937696i	0.480842	−	0.109749i	0.0247722	−	0.999693i	$-0.492114\pi$
$73$	4.10831	−	0.937696i	0.480842	−	0.109749i	0.456070	+	0.889944i	$0.349257\pi$
$74$		0			0
$75$		−	0.162187i		−	0.0187278i
$76$		0			0
$77$	−1.66321	+	3.45368i	−0.189540	+	0.393584i
$78$		0			0
$79$	−4.21005	−	3.35741i	−0.473668	−	0.377738i	0.357361	−	0.933966i	$-0.383676\pi$
$79$	−4.21005	−	3.35741i	−0.473668	−	0.377738i	−0.831029	+	0.556229i	$0.812248\pi$
$80$		0			0
$81$	−1.64143	−	7.19156i	−0.182381	−	0.799062i
$82$		0			0
$83$	7.37393	+	3.55110i	0.809394	+	0.389784i	0.792347	−	0.610071i	$-0.208859\pi$
$83$	7.37393	+	3.55110i	0.809394	+	0.389784i	0.0170474	+	0.999855i	$0.494573\pi$
$84$		0			0
$85$	−4.31313	−	0.984444i	−0.467825	−	0.106778i
$86$		0			0
$87$	−1.61191	−	1.65598i	−0.172815	−	0.177540i
$88$		0			0
$89$	0.477973	+	0.109094i	0.0506650	+	0.0115640i	0.247778	−	0.968817i	$-0.420300\pi$
$89$	0.477973	+	0.109094i	0.0506650	+	0.0115640i	−0.197113	+	0.980381i	$0.563157\pi$
$90$		0			0
$91$	3.31400	+	1.59594i	0.347401	+	0.167300i
$92$		0			0
$93$	0.277894	+	1.21753i	0.0288163	+	0.126252i
$94$		0			0
$95$	−1.12072	−	0.893745i	−0.114983	−	0.0916963i
$96$		0			0
$97$	−1.92488	+	3.99706i	−0.195442	+	0.405840i	−0.975541	−	0.219816i	$-0.929454\pi$
$97$	−1.92488	+	3.99706i	−0.195442	+	0.405840i	0.780099	+	0.625656i	$0.215169\pi$
$98$		0			0
$99$		−	7.30067i		−	0.733745i
$100$		0			0
$101$	−10.0401	+	2.29159i	−0.999029	+	0.228022i	−0.690609	−	0.723228i	$-0.742657\pi$
$101$	−10.0401	+	2.29159i	−0.999029	+	0.228022i	−0.308420	+	0.951250i	$0.599800\pi$
$102$		0			0
$103$	−8.49204	−	10.6487i	−0.836746	−	1.04925i	−0.998055	−	0.0623423i	$-0.980143\pi$
$103$	−8.49204	−	10.6487i	−0.836746	−	1.04925i	0.161309	−	0.986904i	$-0.448428\pi$
$104$		0			0
$105$	1.06646	−	0.850470i	0.104075	−	0.0829974i
$106$		0			0
$107$	6.37013	−	7.98789i	0.615824	−	0.772219i	−0.371926	−	0.928262i	$-0.621303\pi$
$107$	6.37013	−	7.98789i	0.615824	−	0.772219i	0.987750	+	0.156043i	$0.0498740\pi$
$108$		0			0
$109$	7.33443	−	3.53207i	0.702511	−	0.338311i	−0.0482962	−	0.998833i	$-0.515379\pi$
$109$	7.33443	−	3.53207i	0.702511	−	0.338311i	0.750807	+	0.660522i	$0.229665\pi$
$110$		0			0
$111$	0.309076	−	1.35415i	0.0293362	−	0.128530i
$112$		0			0
$113$	−1.97874	−	4.10890i	−0.186144	−	0.386533i	0.786924	−	0.617050i	$-0.211672\pi$
$113$	−1.97874	−	4.10890i	−0.186144	−	0.386533i	−0.973068	+	0.230517i	$0.925958\pi$
$114$		0			0
$115$	13.0059			1.21281
$116$		0			0
$117$	−7.00539			−0.647649
$118$		0			0
$119$	1.32006	+	2.74114i	0.121010	+	0.251280i
$120$		0			0
$121$	−0.951912	+	4.17060i	−0.0865375	+	0.379145i
$122$		0			0
$123$	2.32647	−	1.12037i	0.209771	−	0.101020i
$124$		0			0
$125$	7.20880	−	9.03955i	0.644775	−	0.808522i
$126$		0			0
$127$	9.88615	−	7.88394i	0.877254	−	0.699587i	−0.0774970	−	0.996993i	$-0.524693\pi$
$127$	9.88615	−	7.88394i	0.877254	−	0.699587i	0.954751	+	0.297406i	$0.0961214\pi$
$128$		0			0
$129$	0.742361	+	0.930891i	0.0653612	+	0.0819604i
$130$		0			0
$131$	3.47615	−	0.793408i	0.303712	−	0.0693204i	−0.0679488	−	0.997689i	$-0.521645\pi$
$131$	3.47615	−	0.793408i	0.303712	−	0.0693204i	0.371661	+	0.928368i	$0.378788\pi$
$132$		0			0
$133$			0.985791i			0.0854789i
$134$		0			0
$135$	−2.32808	+	4.83430i	−0.200369	+	0.416070i
$136$		0			0
$137$	16.7506	+	13.3582i	1.43110	+	1.14127i	0.966784	+	0.255597i	$0.0822719\pi$
$137$	16.7506	+	13.3582i	1.43110	+	1.14127i	0.464318	+	0.885669i	$0.346300\pi$
$138$		0			0
$139$	−4.21504	−	18.4673i	−0.357515	−	1.56638i	−0.759361	−	0.650670i	$-0.774488\pi$
$139$	−4.21504	−	18.4673i	−0.357515	−	1.56638i	0.401845	−	0.915708i	$-0.368369\pi$
$140$		0			0
$141$	4.10936	+	1.97896i	0.346071	+	0.166659i
$142$		0			0
$143$	−6.28855	−	1.43532i	−0.525875	−	0.120027i
$144$		0			0
$145$	−1.14101	−	11.5212i	−0.0947555	−	0.956783i
$146$		0			0
$147$	2.01408	+	0.459702i	0.166119	+	0.0379156i
$148$		0			0
$149$	2.71111	+	1.30560i	0.222103	+	0.106959i	0.541627	−	0.840619i	$-0.317809\pi$
$149$	2.71111	+	1.30560i	0.222103	+	0.106959i	−0.319524	+	0.947578i	$0.603523\pi$
$150$		0			0
$151$	−1.01292	−	4.43787i	−0.0824299	−	0.361149i	0.916844	−	0.399245i	$-0.130728\pi$
$151$	−1.01292	−	4.43787i	−0.0824299	−	0.361149i	−0.999274	+	0.0380963i	$0.987871\pi$
$152$		0			0
$153$	−4.53027	−	3.61277i	−0.366251	−	0.292075i
$154$		0			0
$155$	−2.71460	+	5.63693i	−0.218042	+	0.452769i
$156$		0			0
$157$			11.1944i			0.893414i	0.894680	+	0.446707i	$0.147403\pi$
$157$			11.1944i			0.893414i	−0.894680	+	0.446707i	$0.852597\pi$
$158$		0			0
$159$	4.66098	−	1.06384i	0.369639	−	0.0843678i
$160$		0			0
$161$	−5.57663	−	6.99288i	−0.439500	−	0.551116i
$162$		0			0
$163$	−16.7702	+	13.3738i	−1.31354	+	1.04752i	−0.318517	+	0.947917i	$0.603185\pi$
$163$	−16.7702	+	13.3738i	−1.31354	+	1.04752i	−0.995028	+	0.0995995i	$0.968244\pi$
$164$		0			0
$165$	−1.49140	+	1.87016i	−0.116105	+	0.145592i
$166$		0			0
$167$	−8.91568	+	4.29357i	−0.689916	+	0.332246i	−0.745780	−	0.666192i	$-0.767923\pi$
$167$	−8.91568	+	4.29357i	−0.689916	+	0.332246i	0.0558638	+	0.998438i	$0.482209\pi$
$168$		0			0
$169$	1.51550	−	6.63985i	0.116577	−	0.510758i
$170$		0			0
$171$	−0.814607	−	1.69155i	−0.0622946	−	0.129356i
$172$		0			0
$173$	7.96283			0.605403			0.302701	−	0.953085i	$-0.402112\pi$
$173$	7.96283			0.605403			0.302701	+	0.953085i	$0.402112\pi$
$174$		0			0
$175$	−0.558782			−0.0422400
$176$		0			0
$177$	−2.27903	−	4.73246i	−0.171302	−	0.355713i
$178$		0			0
$179$	0.307000	−	1.34505i	0.0229463	−	0.100534i	−0.962158	−	0.272492i	$-0.912152\pi$
$179$	0.307000	−	1.34505i	0.0229463	−	0.100534i	0.985104	+	0.171958i	$0.0550093\pi$
$180$		0			0
$181$	−18.1823	+	8.75612i	−1.35148	+	0.650837i	−0.962719	−	0.270503i	$-0.912810\pi$
$181$	−18.1823	+	8.75612i	−1.35148	+	0.650837i	−0.388758	+	0.921340i	$0.627096\pi$
$182$		0			0
$183$	0.0934874	−	0.117230i	0.00691079	−	0.00866586i
$184$		0			0
$185$	5.44042	−	4.33859i	0.399988	−	0.318980i
$186$		0			0
$187$	−3.32649	−	4.17128i	−0.243257	−	0.305034i
$188$		0			0
$189$	3.59747	−	0.821099i	0.261677	−	0.0597262i
$190$		0			0
$191$			23.3525i			1.68973i	0.534982	+	0.844863i	$0.320318\pi$
$191$			23.3525i			1.68973i	−0.534982	+	0.844863i	$0.679682\pi$
$192$		0			0
$193$	−10.9006	+	22.6353i	−0.784642	+	1.62933i	−0.00752369	+	0.999972i	$0.502395\pi$
$193$	−10.9006	+	22.6353i	−0.784642	+	1.62933i	−0.777118	+	0.629354i	$0.783319\pi$
$194$		0			0
$195$	1.79452	+	1.43108i	0.128508	+	0.102482i
$196$		0			0
$197$	−4.45058	−	19.4993i	−0.317091	−	1.38926i	−0.842629	−	0.538495i	$-0.818993\pi$
$197$	−4.45058	−	19.4993i	−0.317091	−	1.38926i	0.525538	−	0.850770i	$-0.323864\pi$
$198$		0			0
$199$	18.1813	+	8.75563i	1.28883	+	0.620670i	0.947645	−	0.319324i	$-0.103456\pi$
$199$	18.1813	+	8.75563i	1.28883	+	0.620670i	0.341189	+	0.939995i	$0.389170\pi$
$200$		0			0
$201$	−4.06765	−	0.928415i	−0.286910	−	0.0654853i
$202$		0			0
$203$	−5.70534	+	5.55349i	−0.400436	+	0.389779i
$204$		0			0
$205$	12.6120	+	2.87861i	0.880862	+	0.201051i
$206$		0			0
$207$	15.3477	+	7.39105i	1.06674	+	0.513713i
$208$		0			0
$209$	−0.384673	−	1.68536i	−0.0266084	−	0.116579i
$210$		0			0
$211$	−17.2212	−	13.7335i	−1.18556	−	0.945452i	−0.186246	−	0.982503i	$-0.559632\pi$
$211$	−17.2212	−	13.7335i	−1.18556	−	0.945452i	−0.999313	+	0.0370511i	$0.988204\pi$
$212$		0			0
$213$	0.469272	−	0.974453i	0.0321540	−	0.0667684i
$214$		0			0
$215$			5.96499i			0.406809i
$216$		0			0
$217$	4.19475	−	0.957425i	0.284758	−	0.0649943i
$218$		0			0
$219$	−1.12749	−	1.41383i	−0.0761889	−	0.0955379i
$220$		0			0
$221$	−4.00257	+	3.19195i	−0.269242	+	0.214714i
$222$		0			0
$223$	−14.6839	+	18.4130i	−0.983306	+	1.23303i	−0.0108500	+	0.999941i	$0.503454\pi$
$223$	−14.6839	+	18.4130i	−0.983306	+	1.23303i	−0.972456	+	0.233086i	$0.925118\pi$
$224$		0			0
$225$	0.958831	−	0.461749i	0.0639221	−	0.0307833i
$226$		0			0
$227$	−2.17833	+	9.54387i	−0.144581	+	0.633449i	0.849756	+	0.527176i	$0.176749\pi$
$227$	−2.17833	+	9.54387i	−0.144581	+	0.633449i	−0.994337	+	0.106273i	$0.966108\pi$
$228$		0			0
$229$	−6.34366	−	13.1728i	−0.419201	−	0.870480i	−0.998467	−	0.0553418i	$-0.982375\pi$
$229$	−6.34366	−	13.1728i	−0.419201	−	0.870480i	0.579266	−	0.815138i	$-0.303339\pi$
$230$		0			0
$231$	1.64500			0.108233
$232$		0			0
$233$	16.9745			1.11204			0.556018	−	0.831170i	$-0.312329\pi$
$233$	16.9745			1.11204			0.556018	+	0.831170i	$0.312329\pi$
$234$		0			0
$235$	9.91430	+	20.5873i	0.646738	+	1.34296i
$236$		0			0
$237$	−0.514208	+	2.25289i	−0.0334014	+	0.146341i
$238$		0			0
$239$	1.57999	−	0.760881i	0.102201	−	0.0492173i	−0.382085	−	0.924127i	$-0.624794\pi$
$239$	1.57999	−	0.760881i	0.102201	−	0.0492173i	0.484286	+	0.874910i	$0.339080\pi$
$240$		0			0
$241$	−8.89245	+	11.1508i	−0.572813	+	0.718285i	−0.980868	−	0.194673i	$-0.937636\pi$
$241$	−8.89245	+	11.1508i	−0.572813	+	0.718285i	0.408055	+	0.912957i	$0.366207\pi$
$242$		0			0
$243$	−8.32873	+	6.64194i	−0.534288	+	0.426081i
$244$		0			0
$245$	6.45296	+	8.09176i	0.412265	+	0.516963i
$246$		0			0
$247$	−1.61720	+	0.369115i	−0.102900	+	0.0234862i
$248$		0			0
$249$		−	3.51223i		−	0.222578i
$250$		0			0
$251$	−2.04899	+	4.25476i	−0.129331	+	0.268558i	−0.955572	−	0.294759i	$-0.904761\pi$
$251$	−2.04899	+	4.25476i	−0.129331	+	0.268558i	0.826241	+	0.563317i	$0.190475\pi$
$252$		0			0
$253$	12.2628	+	9.77929i	0.770959	+	0.614819i
$254$		0			0
$255$	0.422459	+	1.85091i	0.0264554	+	0.115909i
$256$		0			0
$257$	−18.6551	−	8.98380i	−1.16367	−	0.560394i	−0.250558	−	0.968102i	$-0.580614\pi$
$257$	−18.6551	−	8.98380i	−1.16367	−	0.560394i	−0.913113	+	0.407708i	$0.866328\pi$
$258$		0			0
$259$	−4.66544	−	1.06486i	−0.289896	−	0.0661670i
$260$		0			0
$261$	5.20084	−	14.2440i	0.321924	−	0.881681i
$262$		0			0
$263$	−23.2715	−	5.31156i	−1.43498	−	0.327525i	−0.566834	−	0.823832i	$-0.691832\pi$
$263$	−23.2715	−	5.31156i	−1.43498	−	0.327525i	−0.868147	+	0.496307i	$0.834689\pi$
$264$		0			0
$265$	21.5794	+	10.3921i	1.32561	+	0.638380i
$266$		0			0
$267$	−0.0468161	−	0.205115i	−0.00286510	−	0.0125528i
$268$		0			0
$269$	0.885670	+	0.706298i	0.0540003	+	0.0430638i	0.650118	−	0.759833i	$-0.274719\pi$
$269$	0.885670	+	0.706298i	0.0540003	+	0.0430638i	−0.596118	+	0.802897i	$0.703291\pi$
$270$		0			0
$271$	11.3318	−	23.5308i	0.688359	−	1.42939i	−0.204414	−	0.978884i	$-0.565529\pi$
$271$	11.3318	−	23.5308i	0.688359	−	1.42939i	0.892773	−	0.450507i	$-0.148757\pi$
$272$		0			0
$273$		−	1.57847i		−	0.0955332i
$274$		0			0
$275$	0.955323	−	0.218046i	0.0576082	−	0.0131487i
$276$		0			0
$277$	−2.77705	−	3.48231i	−0.166857	−	0.209232i	0.691372	−	0.722499i	$-0.257006\pi$
$277$	−2.77705	−	3.48231i	−0.166857	−	0.209232i	−0.858229	+	0.513267i	$0.828435\pi$
$278$		0			0
$279$	−6.40674	+	5.10920i	−0.383561	+	0.305880i
$280$		0			0
$281$	4.33701	−	5.43843i	0.258724	−	0.324430i	−0.635456	−	0.772137i	$-0.719188\pi$
$281$	4.33701	−	5.43843i	0.258724	−	0.324430i	0.894180	+	0.447707i	$0.147759\pi$
$282$		0			0
$283$	−27.4270	+	13.2082i	−1.63037	+	0.785144i	−0.630407	+	0.776265i	$0.717112\pi$
$283$	−27.4270	+	13.2082i	−1.63037	+	0.785144i	−0.999961	+	0.00887909i	$0.997174\pi$
$284$		0			0
$285$	−0.136883	+	0.599722i	−0.00810823	+	0.0355245i
$286$		0			0
$287$	−3.85999	−	8.01536i	−0.227848	−	0.473131i
$288$		0			0
$289$	12.7655			0.750910
$290$		0			0
$291$	1.90381			0.111604
$292$		0			0
$293$	−6.59124	−	13.6869i	−0.385065	−	0.799595i	−0.999940	−	0.0109704i	$-0.996508\pi$
$293$	−6.59124	−	13.6869i	−0.385065	−	0.799595i	0.614875	−	0.788624i	$-0.289206\pi$
$294$		0			0
$295$	5.85561	−	25.6551i	0.340927	−	1.49370i
$296$		0			0
$297$	−5.83002	+	2.80759i	−0.338292	+	0.162913i
$298$		0			0
$299$	9.38377	−	11.7669i	0.542678	−	0.680496i
$300$		0			0
$301$	3.20719	−	2.55765i	0.184859	−	0.147420i
$302$		0			0
$303$	2.75543	+	3.45520i	0.158295	+	0.198496i
$304$		0			0
$305$	0.732354	−	0.167155i	0.0419344	−	0.00957126i
$306$		0			0
$307$			3.82094i			0.218073i	0.994038	+	0.109036i	$0.0347765\pi$
$307$			3.82094i			0.218073i	−0.994038	+	0.109036i	$0.965223\pi$
$308$		0			0
$309$	−2.53600	+	5.26606i	−0.144268	+	0.299576i
$310$		0			0
$311$	19.1179	+	15.2460i	1.08408	+	0.864522i	0.991360	−	0.131171i	$-0.0418736\pi$
$311$	19.1179	+	15.2460i	1.08408	+	0.864522i	0.0927163	+	0.995693i	$0.470445\pi$
$312$		0			0
$313$	−4.48888	−	19.6671i	−0.253727	−	1.11165i	−0.927828	−	0.373009i	$-0.878326\pi$
$313$	−4.48888	−	19.6671i	−0.253727	−	1.11165i	0.674101	−	0.738639i	$-0.264531\pi$
$314$		0			0
$315$	8.06408	+	3.88345i	0.454359	+	0.218808i
$316$		0			0
$317$	−8.66877	−	1.97859i	−0.486887	−	0.111129i	−0.0279714	−	0.999609i	$-0.508905\pi$
$317$	−8.66877	−	1.97859i	−0.486887	−	0.111129i	−0.458915	+	0.888480i	$0.651762\pi$
$318$		0			0
$319$	7.58708	−	11.7209i	0.424795	−	0.656242i
$320$		0			0
$321$	−4.27450	−	0.975626i	−0.238579	−	0.0544541i
$322$		0			0
$323$	−1.23617	−	0.595309i	−0.0687824	−	0.0331239i
$324$		0			0
$325$	−0.209227	−	0.916685i	−0.0116059	−	0.0508486i
$326$		0			0
$327$	−2.73126	−	2.17811i	−0.151039	−	0.120450i
$328$		0			0
$329$	6.81809	−	14.1579i	0.375894	−	0.780551i
$330$		0			0
$331$			18.0183i			0.990377i	0.868785	+	0.495189i	$0.164901\pi$
$331$			18.0183i			0.990377i	−0.868785	+	0.495189i	$0.835099\pi$
$332$		0			0
$333$	8.88551	−	2.02806i	0.486923	−	0.111137i
$334$		0			0
$335$	−13.0324	−	16.3421i	−0.712037	−	0.892866i
$336$		0			0
$337$	−20.9634	+	16.7178i	−1.14195	+	0.910676i	−0.996895	−	0.0787477i	$-0.974908\pi$
$337$	−20.9634	+	16.7178i	−1.14195	+	0.910676i	−0.145057	+	0.989423i	$0.546336\pi$
$338$		0			0
$339$	−1.22022	+	1.53011i	−0.0662733	+	0.0831041i
$340$		0			0
$341$	−6.79797	+	3.27373i	−0.368131	+	0.177282i
$342$		0			0
$343$	3.88677	−	17.0291i	0.209866	−	0.919482i
$344$		0			0
$345$	−2.42163	−	5.02858i	−0.130376	−	0.270729i
$346$		0			0
$347$	14.3128			0.768349			0.384174	−	0.923261i	$-0.374486\pi$
$347$	14.3128			0.768349			0.384174	+	0.923261i	$0.374486\pi$
$348$		0			0
$349$	30.9347			1.65590			0.827949	−	0.560804i	$-0.189508\pi$
$349$	30.9347			1.65590			0.827949	+	0.560804i	$0.189508\pi$
$350$		0			0
$351$	2.69404	+	5.59422i	0.143797	+	0.298597i
$352$		0			0
$353$	2.25697	−	9.88843i	0.120126	−	0.526308i	−0.878678	−	0.477415i	$-0.841574\pi$
$353$	2.25697	−	9.88843i	0.120126	−	0.526308i	0.998804	−	0.0488924i	$-0.0155692\pi$
$354$		0			0
$355$	4.88186	−	2.35098i	0.259102	−	0.124777i
$356$		0			0
$357$	0.814036	−	1.02077i	0.0430834	−	0.0540248i
$358$		0			0
$359$	25.1718	−	20.0738i	1.32851	−	1.05946i	0.335429	−	0.942066i	$-0.391119\pi$
$359$	25.1718	−	20.0738i	1.32851	−	1.05946i	0.993086	−	0.117389i	$-0.0374526\pi$
$360$		0			0
$361$	11.5691	+	14.5072i	0.608901	+	0.763538i
$362$		0			0
$363$	1.78975	−	0.408498i	0.0939374	−	0.0214406i
$364$		0			0
$365$		−	9.05960i		−	0.474201i
$366$		0			0
$367$	2.69624	−	5.59880i	0.140743	−	0.292255i	−0.818668	−	0.574266i	$-0.805287\pi$
$367$	2.69624	−	5.59880i	0.140743	−	0.292255i	0.959411	+	0.282012i	$0.0910016\pi$
$368$		0			0
$369$	13.2470	+	10.5641i	0.689609	+	0.549945i
$370$		0			0
$371$	−3.66522	−	16.0584i	−0.190289	−	0.833710i
$372$		0			0
$373$	−3.30229	−	1.59030i	−0.170986	−	0.0823427i	0.346433	−	0.938075i	$-0.387393\pi$
$373$	−3.30229	−	1.59030i	−0.170986	−	0.0823427i	−0.517419	+	0.855732i	$0.673107\pi$
$374$		0			0
$375$	−4.83726	−	1.10407i	−0.249795	−	0.0570141i
$376$		0			0
$377$	−11.2468	−	7.28022i	−0.579240	−	0.374950i
$378$		0			0
$379$	−3.97849	−	0.908065i	−0.204361	−	0.0466442i	0.119115	−	0.992881i	$-0.461994\pi$
$379$	−3.97849	−	0.908065i	−0.204361	−	0.0466442i	−0.323476	+	0.946236i	$0.604852\pi$
$380$		0			0
$381$	−4.88897	−	2.35440i	−0.250469	−	0.120620i
$382$		0			0
$383$	−2.44734	−	10.7225i	−0.125053	−	0.547895i	−0.998175	−	0.0603920i	$-0.980765\pi$
$383$	−2.44734	−	10.7225i	−0.125053	−	0.547895i	0.873121	−	0.487503i	$-0.162092\pi$
$384$		0			0
$385$	6.44323	+	5.13830i	0.328377	+	0.261872i
$386$		0			0
$387$	−3.38980	+	7.03899i	−0.172313	+	0.357812i
$388$		0			0
$389$			6.12808i			0.310706i	0.987859	+	0.155353i	$0.0496515\pi$
$389$			6.12808i			0.310706i	−0.987859	+	0.155353i	$0.950349\pi$
$390$		0			0
$391$	12.1367	−	2.77011i	0.613777	−	0.140091i
$392$		0			0
$393$	−0.954000	−	1.19628i	−0.0481229	−	0.0603443i
$394$		0			0
$395$	−9.05118	+	7.21808i	−0.455414	+	0.363181i
$396$		0			0
$397$	2.47234	−	3.10022i	0.124083	−	0.155595i	−0.715910	−	0.698193i	$-0.753988\pi$
$397$	2.47234	−	3.10022i	0.124083	−	0.155595i	0.839993	+	0.542598i	$0.182559\pi$
$398$		0			0
$399$	0.381143	−	0.183549i	0.0190810	−	0.00918894i
$400$		0			0
$401$	−5.11780	+	22.4225i	−0.255571	+	1.11973i	0.670361	+	0.742035i	$0.266139\pi$
$401$	−5.11780	+	22.4225i	−0.255571	+	1.11973i	−0.925931	+	0.377692i	$0.876718\pi$
$402$		0			0
$403$	3.14132	+	6.52302i	0.156480	+	0.324935i
$404$		0			0
$405$	−15.8587			−0.788027
$406$		0			0
$407$	8.39181			0.415966
$408$		0			0
$409$	−10.9710	−	22.7816i	−0.542482	−	1.12648i	−0.974454	−	0.224588i	$-0.927896\pi$
$409$	−10.9710	−	22.7816i	−0.542482	−	1.12648i	0.431972	−	0.901887i	$-0.357818\pi$
$410$		0			0
$411$	2.04589	−	8.96362i	0.100916	−	0.442143i
$412$		0			0
$413$	−16.3047	+	7.85191i	−0.802300	+	0.386367i
$414$		0			0
$415$	10.9708	−	13.7569i	0.538533	−	0.675299i
$416$		0			0
$417$	−6.35532	+	5.06820i	−0.311222	+	0.248191i
$418$		0			0
$419$	−17.3185	−	21.7167i	−0.846066	−	1.06093i	−0.997372	−	0.0724458i	$-0.976920\pi$
$419$	−17.3185	−	21.7167i	−0.846066	−	1.06093i	0.151307	−	0.988487i	$-0.451652\pi$
$420$		0			0
$421$	−29.6352	+	6.76403i	−1.44433	+	0.329659i	−0.871653	−	0.490123i	$-0.836952\pi$
$421$	−29.6352	+	6.76403i	−1.44433	+	0.329659i	−0.572676	+	0.819782i	$0.694095\pi$
$422$		0			0
$423$			29.9281i			1.45516i
$424$		0			0
$425$	0.337442	−	0.700706i	0.0163684	−	0.0339892i
$426$		0			0
$427$	−0.403889	−	0.322091i	−0.0195456	−	0.0155871i
$428$		0			0
$429$	0.615945	+	2.69863i	0.0297381	+	0.130291i
$430$		0			0
$431$	11.8251	+	5.69465i	0.569593	+	0.274302i	0.696433	−	0.717622i	$-0.254769\pi$
$431$	11.8251	+	5.69465i	0.569593	+	0.274302i	−0.126840	+	0.991923i	$0.540483\pi$
$432$		0			0
$433$	27.5151	+	6.28015i	1.32229	+	0.301805i	0.824683	−	0.565596i	$-0.191354\pi$
$433$	27.5151	+	6.28015i	1.32229	+	0.301805i	0.497610	+	0.867401i	$0.334211\pi$
$434$		0			0
$435$	−4.24207	+	2.58634i	−0.203391	+	0.124005i
$436$		0			0
$437$	3.93245	+	0.897556i	0.188115	+	0.0429359i
$438$		0			0
$439$	0.788609	+	0.379774i	0.0376383	+	0.0181256i	0.452608	−	0.891709i	$-0.350494\pi$
$439$	0.788609	+	0.379774i	0.0376383	+	0.0181256i	−0.414970	+	0.909835i	$0.636208\pi$
$440$		0			0
$441$	3.01642	+	13.2158i	0.143639	+	0.629323i
$442$		0			0
$443$	−16.1609	−	12.8879i	−0.767828	−	0.612322i	0.159230	−	0.987242i	$-0.449099\pi$
$443$	−16.1609	−	12.8879i	−0.767828	−	0.612322i	−0.927057	+	0.374919i	$0.877670\pi$
$444$		0			0
$445$	0.457322	−	0.949638i	0.0216791	−	0.0450172i
$446$		0			0
$447$		−	1.29131i		−	0.0610768i
$448$		0			0
$449$	−38.6364	+	8.81850i	−1.82336	+	0.416171i	−0.990523	−	0.137344i	$-0.956143\pi$
$449$	−38.6364	+	8.81850i	−1.82336	+	0.416171i	−0.832840	+	0.553514i	$0.813286\pi$
$450$		0			0
$451$	9.72697	+	12.1972i	0.458025	+	0.574346i
$452$		0			0
$453$	−1.52725	+	1.21794i	−0.0717562	+	0.0572237i
$454$		0			0
$455$	4.93048	−	6.18263i	0.231145	−	0.289846i
$456$		0			0
$457$	8.16202	−	3.93062i	0.381803	−	0.183867i	−0.233131	−	0.972445i	$-0.574897\pi$
$457$	8.16202	−	3.93062i	0.381803	−	0.183867i	0.614934	+	0.788579i	$0.289183\pi$
$458$		0			0
$459$	−1.14282	+	5.00704i	−0.0533424	+	0.233709i
$460$		0			0
$461$	5.15447	+	10.7034i	0.240068	+	0.498506i	0.985839	−	0.167697i	$-0.0536329\pi$
$461$	5.15447	+	10.7034i	0.240068	+	0.498506i	−0.745771	+	0.666202i	$0.767919\pi$
$462$		0			0
$463$	6.11332			0.284110			0.142055	−	0.989859i	$-0.454629\pi$
$463$	6.11332			0.284110			0.142055	+	0.989859i	$0.454629\pi$
$464$		0			0
$465$	2.68489			0.124509
$466$		0			0
$467$	−7.77691	−	16.1489i	−0.359872	−	0.747283i	0.639904	−	0.768455i	$-0.278974\pi$
$467$	−7.77691	−	16.1489i	−0.359872	−	0.747283i	−0.999776	+	0.0211727i	$0.993260\pi$
$468$		0			0
$469$	−3.19865	+	14.0142i	−0.147700	+	0.647117i
$470$		0			0
$471$	4.32819	−	2.08434i	0.199432	−	0.0960415i
$472$		0			0
$473$	−4.48514	+	5.62418i	−0.206227	+	0.258600i
$474$		0			0
$475$	0.197017	−	0.157116i	0.00903975	−	0.00720896i
$476$		0			0
$477$	19.5591	+	24.5263i	0.895550	+	1.12298i
$478$		0			0
$479$	36.2203	−	8.26706i	1.65495	−	0.377731i	0.709809	−	0.704394i	$-0.248781\pi$
$479$	36.2203	−	8.26706i	1.65495	−	0.377731i	0.945141	+	0.326663i	$0.105924\pi$
$480$		0			0
$481$		−	8.05240i		−	0.367158i
$482$		0			0
$483$	−1.66537	+	3.45817i	−0.0757767	+	0.157352i
$484$		0			0
$485$	7.45697	+	5.94673i	0.338603	+	0.270027i
$486$		0			0
$487$	4.75561	+	20.8357i	0.215497	+	0.944155i	0.960759	+	0.277383i	$0.0894672\pi$
$487$	4.75561	+	20.8357i	0.215497	+	0.944155i	−0.745262	+	0.666772i	$0.767676\pi$
$488$		0			0
$489$	8.29332	+	3.99385i	0.375037	+	0.180608i
$490$		0			0
$491$	−33.8424	−	7.72431i	−1.52729	−	0.348593i	−0.625309	−	0.780377i	$-0.715027\pi$
$491$	−33.8424	−	7.72431i	−1.52729	−	0.348593i	−0.901977	+	0.431784i	$0.857884\pi$
$492$		0			0
$493$	−3.51862	−	10.5081i	−0.158471	−	0.473262i
$494$		0			0
$495$	−15.3022	−	3.49262i	−0.687781	−	0.156982i
$496$		0			0
$497$	−3.35727	−	1.61678i	−0.150594	−	0.0725223i
$498$		0			0
$499$	9.63232	+	42.2019i	0.431202	+	1.88922i	0.456843	+	0.889547i	$0.348980\pi$
$499$	9.63232	+	42.2019i	0.431202	+	1.88922i	−0.0256413	+	0.999671i	$0.508163\pi$
$500$		0			0
$501$	3.32010	+	2.64769i	0.148331	+	0.118290i
$502$		0			0
$503$	−1.71333	+	3.55776i	−0.0763934	+	0.158633i	−0.935667	−	0.352883i	$-0.885201\pi$
$503$	−1.71333	+	3.55776i	−0.0763934	+	0.158633i	0.859274	+	0.511515i	$0.170916\pi$
$504$		0			0
$505$			22.1403i			0.985232i
$506$		0			0
$507$	−2.84939	+	0.650355i	−0.126546	+	0.0288833i
$508$		0			0
$509$	−20.0925	−	25.1952i	−0.890583	−	1.11676i	−0.992534	−	0.121966i	$-0.961080\pi$
$509$	−20.0925	−	25.1952i	−0.890583	−	1.11676i	0.101951	−	0.994789i	$-0.467491\pi$
$510$		0			0
$511$	−4.87105	+	3.88454i	−0.215483	+	0.171842i
$512$		0			0
$513$	−1.03753	+	1.30102i	−0.0458082	+	0.0574416i
$514$		0			0
$515$	−26.3822	+	12.7050i	−1.16254	+	0.559848i
$516$		0			0
$517$	−6.13191	+	26.8657i	−0.269681	+	1.18155i
$518$		0			0
$519$	−1.48263	−	3.07872i	−0.0650804	−	0.135141i
$520$		0			0
$521$	2.98440			0.130749			0.0653746	−	0.997861i	$-0.479176\pi$
$521$	2.98440			0.130749			0.0653746	+	0.997861i	$0.479176\pi$
$522$		0			0
$523$	−9.00557			−0.393786			−0.196893	−	0.980425i	$-0.563085\pi$
$523$	−9.00557			−0.393786			−0.196893	+	0.980425i	$0.563085\pi$
$524$		0			0
$525$	0.104042	+	0.216046i	0.00454077	+	0.00942901i
$526$		0			0
$527$	−1.33257	+	5.83835i	−0.0580475	+	0.254323i
$528$		0			0
$529$	−12.2507	+	5.89962i	−0.532639	+	0.256505i
$530$		0			0
$531$	21.4893	−	26.9467i	0.932554	−	1.16939i
$532$		0			0
$533$	11.7039	−	9.33357i	0.506953	−	0.404282i
$534$		0			0
$535$	−13.6951	−	17.1732i	−0.592092	−	0.742460i
$536$		0			0
$537$	−0.577209	+	0.131744i	−0.0249084	+	0.00568518i
$538$		0			0
$539$			12.4815i			0.537615i
$540$		0			0
$541$	−6.70668	+	13.9266i	−0.288343	+	0.598750i	−0.993948	−	0.109856i	$-0.964961\pi$
$541$	−6.70668	+	13.9266i	−0.288343	+	0.598750i	0.705605	+	0.708606i	$0.250675\pi$
$542$		0			0
$543$	6.77087	+	5.39959i	0.290566	+	0.231719i
$544$		0			0
$545$	−3.89444	−	17.0627i	−0.166819	−	0.730884i
$546$		0			0
$547$	−5.46853	−	2.63350i	−0.233817	−	0.112601i	0.313307	−	0.949652i	$-0.398563\pi$
$547$	−5.46853	−	2.63350i	−0.233817	−	0.112601i	−0.547124	+	0.837051i	$0.684277\pi$
$548$		0			0
$549$	0.959205	+	0.218932i	0.0409379	+	0.00934381i
$550$		0			0
$551$	0.450099	−	3.56226i	0.0191748	−	0.151758i
$552$		0			0
$553$	7.76186	+	1.77159i	0.330068	+	0.0753358i
$554$		0			0
$555$	−2.69043	−	1.29564i	−0.114203	−	0.0549971i
$556$		0			0
$557$	−1.46455	−	6.41661i	−0.0620549	−	0.271880i	0.934376	−	0.356287i	$-0.115958\pi$
$557$	−1.46455	−	6.41661i	−0.0620549	−	0.271880i	−0.996431	+	0.0844069i	$0.973100\pi$
$558$		0			0
$559$	5.39671	+	4.30374i	0.228257	+	0.182029i
$560$		0			0
$561$	−0.993397	+	2.06281i	−0.0419413	+	0.0870919i
$562$		0			0
$563$			18.4896i			0.779245i	0.920975	+	0.389623i	$0.127395\pi$
$563$			18.4896i			0.779245i	−0.920975	+	0.389623i	$0.872605\pi$
$564$		0			0
$565$	−9.55885	+	2.18175i	−0.402144	+	0.0917867i
$566$		0			0
$567$	6.79984	+	8.52673i	0.285566	+	0.358089i
$568$		0			0
$569$	1.87340	−	1.49399i	0.0785371	−	0.0626313i	−0.583434	−	0.812160i	$-0.698291\pi$
$569$	1.87340	−	1.49399i	0.0785371	−	0.0626313i	0.661971	+	0.749529i	$0.269720\pi$
$570$		0			0
$571$	−9.35236	+	11.7275i	−0.391384	+	0.490780i	−0.938016	−	0.346593i	$-0.887338\pi$
$571$	−9.35236	+	11.7275i	−0.391384	+	0.490780i	0.546631	+	0.837373i	$0.315910\pi$
$572$		0			0
$573$	9.02893	−	4.34810i	0.377189	−	0.181645i
$574$		0			0
$575$	−0.508767	+	2.22905i	−0.0212171	+	0.0929580i
$576$		0			0
$577$	−8.36619	−	17.3726i	−0.348289	−	0.723229i	0.651071	−	0.759017i	$-0.274320\pi$
$577$	−8.36619	−	17.3726i	−0.348289	−	0.723229i	−0.999359	+	0.0357880i	$0.988606\pi$
$578$		0			0
$579$	10.7813			0.448055
$580$		0			0
$581$	−12.1006			−0.502019
$582$		0			0
$583$	12.5325	+	26.0240i	0.519044	+	1.07781i
$584$		0			0
$585$	−3.35136	+	14.6833i	−0.138562	+	0.607078i
$586$		0			0
$587$	32.5744	−	15.6870i	1.34449	−	0.647471i	0.383366	−	0.923596i	$-0.374765\pi$
$587$	32.5744	−	15.6870i	1.34449	−	0.647471i	0.961122	+	0.276125i	$0.0890504\pi$
$588$		0			0
$589$	−1.20979	+	1.51703i	−0.0498487	+	0.0625082i
$590$		0			0
$591$	−6.71046	+	5.35141i	−0.276031	+	0.220128i
$592$		0			0
$593$	−2.45910	−	3.08361i	−0.100983	−	0.126629i	0.728772	−	0.684756i	$-0.240091\pi$
$593$	−2.45910	−	3.08361i	−0.100983	−	0.126629i	−0.829755	+	0.558128i	$0.811520\pi$
$594$		0			0
$595$	6.37692	−	1.45549i	0.261428	−	0.0596693i
$596$		0			0
$597$		−	8.65979i		−	0.354422i
$598$		0			0
$599$	5.28643	−	10.9774i	0.215998	−	0.448524i	−0.764613	−	0.644490i	$-0.777070\pi$
$599$	5.28643	−	10.9774i	0.215998	−	0.448524i	0.980611	+	0.195966i	$0.0627841\pi$
$600$		0			0
$601$	−24.1796	−	19.2825i	−0.986304	−	0.786552i	−0.00934061	−	0.999956i	$-0.502973\pi$
$601$	−24.1796	−	19.2825i	−0.986304	−	0.786552i	−0.976964	+	0.213405i	$0.931545\pi$
$602$		0			0
$603$	−6.09196	−	26.6906i	−0.248084	−	1.08693i
$604$		0			0
$605$	8.28616	+	3.99041i	0.336880	+	0.162233i
$606$		0			0
$607$	−38.5895	−	8.80781i	−1.56630	−	0.357498i	−0.650620	−	0.759404i	$-0.725491\pi$
$607$	−38.5895	−	8.80781i	−1.56630	−	0.357498i	−0.915681	+	0.401906i	$0.868348\pi$
$608$		0			0
$609$	3.20949	+	1.17186i	0.130055	+	0.0474863i
$610$		0			0
$611$	25.7791	+	5.88391i	1.04291	+	0.238037i
$612$		0			0
$613$	14.6718	+	7.06557i	0.592589	+	0.285376i	0.706045	−	0.708167i	$-0.250478\pi$
$613$	14.6718	+	7.06557i	0.592589	+	0.285376i	−0.113456	+	0.993543i	$0.536192\pi$
$614$		0			0
$615$	−1.23531	−	5.41225i	−0.0498125	−	0.218243i
$616$		0			0
$617$	28.2126	+	22.4988i	1.13580	+	0.905769i	0.996426	−	0.0844714i	$-0.0269202\pi$
$617$	28.2126	+	22.4988i	1.13580	+	0.905769i	0.139372	+	0.990240i	$0.455492\pi$
$618$		0			0
$619$	−14.4365	+	29.9776i	−0.580250	+	1.20490i	0.379798	+	0.925069i	$0.375993\pi$
$619$	−14.4365	+	29.9776i	−0.580250	+	1.20490i	−0.960049	+	0.279833i	$0.909721\pi$
$620$		0			0
$621$		−	15.0984i		−	0.605877i
$622$		0			0
$623$	−0.706678	+	0.161295i	−0.0283125	+	0.00646214i
$624$		0			0
$625$	−14.3200	−	17.9567i	−0.572799	−	0.718267i
$626$		0			0
$627$	−0.579998	+	0.462533i	−0.0231629	+	0.0184718i
$628$		0			0
$629$	4.15273	−	5.20735i	0.165580	−	0.207631i
$630$		0			0
$631$	15.7728	−	7.59577i	0.627904	−	0.302383i	−0.0927373	−	0.995691i	$-0.529562\pi$
$631$	15.7728	−	7.59577i	0.627904	−	0.302383i	0.720642	+	0.693308i	$0.243847\pi$
$632$		0			0
$633$	−2.10337	+	9.21546i	−0.0836014	+	0.366282i
$634$		0			0
$635$	−11.7952	−	24.4930i	−0.468078	−	0.971974i
$636$		0			0
$637$	11.9767			0.474533
$638$		0			0
$639$	7.09686			0.280747
$640$		0			0
$641$	−1.59436	−	3.31073i	−0.0629736	−	0.130766i	0.867107	−	0.498123i	$-0.165977\pi$
$641$	−1.59436	−	3.31073i	−0.0629736	−	0.130766i	−0.930080	+	0.367357i	$0.880263\pi$
$642$		0			0
$643$	−2.17847	+	9.54450i	−0.0859105	+	0.376398i	−0.999546	−	0.0301364i	$-0.990406\pi$
$643$	−2.17847	+	9.54450i	−0.0859105	+	0.376398i	0.913635	+	0.406535i	$0.133263\pi$
$644$		0			0
$645$	2.30629	−	1.11065i	0.0908099	−	0.0437318i
$646$		0			0
$647$	−5.51644	+	6.91740i	−0.216874	+	0.271951i	−0.878353	−	0.478012i	$-0.841357\pi$
$647$	−5.51644	+	6.91740i	−0.216874	+	0.271951i	0.661480	+	0.749963i	$0.269929\pi$
$648$		0			0
$649$	24.8114	−	19.7864i	0.973931	−	0.776684i
$650$		0			0
$651$	−1.15122	−	1.44358i	−0.0451197	−	0.0565783i
$652$		0			0
$653$	16.2726	−	3.71410i	0.636794	−	0.145344i	0.108078	−	0.994142i	$-0.465531\pi$
$653$	16.2726	−	3.71410i	0.636794	−	0.145344i	0.528717	+	0.848798i	$0.322673\pi$
$654$		0			0
$655$		−	7.66555i		−	0.299518i
$656$		0			0
$657$	5.14841	−	10.6908i	0.200859	−	0.417087i
$658$		0			0
$659$	−33.7576	−	26.9208i	−1.31501	−	1.04869i	−0.994854	−	0.101320i	$-0.967693\pi$
$659$	−33.7576	−	26.9208i	−1.31501	−	1.04869i	−0.320156	−	0.947365i	$-0.603735\pi$
$660$		0			0
$661$	−3.61406	−	15.8342i	−0.140570	−	0.615879i	−0.995303	−	0.0968105i	$-0.969136\pi$
$661$	−3.61406	−	15.8342i	−0.140570	−	0.615879i	0.854732	−	0.519069i	$-0.173721\pi$
$662$		0			0
$663$	1.97938	+	0.953220i	0.0768728	+	0.0370200i
$664$		0			0
$665$	2.06621	+	0.471600i	0.0801243	+	0.0182879i
$666$		0			0
$667$	16.9589	+	27.8157i	0.656652	+	1.07703i
$668$		0			0
$669$	9.85321	+	2.24893i	0.380947	+	0.0869487i
$670$		0			0
$671$	0.816196	+	0.393059i	0.0315089	+	0.0151739i
$672$		0			0
$673$	−4.61343	−	20.2128i	−0.177835	−	0.779145i	−0.982627	−	0.185589i	$-0.940581\pi$
$673$	−4.61343	−	20.2128i	−0.177835	−	0.779145i	0.804793	−	0.593556i	$-0.202276\pi$
$674$		0			0
$675$	−0.737468	−	0.588111i	−0.0283852	−	0.0226364i
$676$		0			0
$677$	6.43411	−	13.3606i	0.247283	−	0.513488i	−0.739972	−	0.672638i	$-0.765161\pi$
$677$	6.43411	−	13.3606i	0.247283	−	0.513488i	0.987254	+	0.159150i	$0.0508754\pi$
$678$		0			0
$679$		−	6.55919i		−	0.251718i
$680$		0			0
$681$	4.09560	−	0.934794i	0.156944	−	0.0358214i
$682$		0			0
$683$	−0.156193	−	0.195860i	−0.00597656	−	0.00749437i	0.778834	−	0.627230i	$-0.215811\pi$
$683$	−0.156193	−	0.195860i	−0.00597656	−	0.00749437i	−0.784811	+	0.619735i	$0.787240\pi$
$684$		0			0
$685$	36.0121	−	28.7187i	1.37595	−	1.09728i
$686$		0			0
$687$	−3.91192	+	4.90539i	−0.149249	+	0.187152i
$688$		0			0
$689$	24.9715	−	12.0256i	0.951339	−	0.458140i
$690$		0			0
$691$	6.83734	−	29.9563i	0.260105	−	1.13959i	−0.661033	−	0.750357i	$-0.729882\pi$
$691$	6.83734	−	29.9563i	0.260105	−	1.13959i	0.921138	−	0.389236i	$-0.127261\pi$
$692$		0			0
$693$	4.68333	+	9.72503i	0.177905	+	0.369423i
$694$		0			0
$695$	−40.7239			−1.54474
$696$		0			0
$697$	12.3822			0.469008
$698$		0			0
$699$	−3.16056	−	6.56296i	−0.119543	−	0.248234i
$700$		0			0
$701$	−2.23950	+	9.81189i	−0.0845848	+	0.370590i	−0.999450	−	0.0331699i	$-0.989440\pi$
$701$	−2.23950	+	9.81189i	−0.0845848	+	0.370590i	0.914865	+	0.403760i	$0.132297\pi$
$702$		0			0
$703$	1.94436	−	0.936357i	0.0733331	−	0.0353154i
$704$		0			0
$705$	6.11380	−	7.66647i	0.230259	−	0.288736i
$706$		0			0
$707$	11.9041	−	9.49324i	0.447701	−	0.357030i
$708$		0			0
$709$	−5.93403	−	7.44104i	−0.222857	−	0.279454i	0.657816	−	0.753179i	$-0.271481\pi$
$709$	−5.93403	−	7.44104i	−0.222857	−	0.279454i	−0.880673	+	0.473725i	$0.842909\pi$
$710$		0			0
$711$	−14.7828	+	3.37407i	−0.554397	+	0.126537i
$712$		0			0
$713$		−	17.6051i		−	0.659318i
$714$		0			0
$715$	−6.01685	+	12.4941i	−0.225017	+	0.467253i
$716$		0			0
$717$	−0.588369	−	0.469209i	−0.0219730	−	0.0175229i
$718$		0			0
$719$	10.3629	+	45.4029i	0.386471	+	1.69324i	0.676680	+	0.736277i	$0.263418\pi$
$719$	10.3629	+	45.4029i	0.386471	+	1.69324i	−0.290209	+	0.956963i	$0.593725\pi$
$720$		0			0
$721$	18.1431	+	8.73725i	0.675684	+	0.325392i
$722$		0			0
$723$	5.96702	+	1.36193i	0.221916	+	0.0506509i
$724$		0			0
$725$	2.01922	+	0.255132i	0.0749919	+	0.00947537i
$726$		0			0
$727$	−21.3739	−	4.87846i	−0.792715	−	0.180932i	−0.193056	−	0.981188i	$-0.561840\pi$
$727$	−21.3739	−	4.87846i	−0.792715	−	0.180932i	−0.599659	+	0.800256i	$0.704697\pi$
$728$		0			0
$729$	−15.8192	−	7.61814i	−0.585897	−	0.282153i
$730$		0			0
$731$	1.27047	+	5.56631i	0.0469902	+	0.205877i
$732$		0			0
$733$	−22.3512	−	17.8245i	−0.825562	−	0.658364i	0.116727	−	0.993164i	$-0.462760\pi$
$733$	−22.3512	−	17.8245i	−0.825562	−	0.658364i	−0.942289	+	0.334800i	$0.891331\pi$
$734$		0			0
$735$	1.92707	−	4.00159i	0.0710809	−	0.147601i
$736$		0			0
$737$		−	25.2076i		−	0.928534i
$738$		0			0
$739$	−4.73316	+	1.08031i	−0.174112	+	0.0397399i	−0.308688	−	0.951163i	$-0.599890\pi$
$739$	−4.73316	+	1.08031i	−0.174112	+	0.0397399i	0.134576	+	0.990903i	$0.457033\pi$
$740$		0			0
$741$	0.443826	+	0.556540i	0.0163044	+	0.0204450i
$742$		0			0
$743$	−11.4229	+	9.10945i	−0.419065	+	0.334193i	−0.810214	−	0.586134i	$-0.800649\pi$
$743$	−11.4229	+	9.10945i	−0.419065	+	0.334193i	0.391149	+	0.920327i	$0.372078\pi$
$744$		0			0
$745$	4.03352	−	5.05787i	0.147777	−	0.185306i
$746$		0			0
$747$	20.7638	−	9.99934i	0.759709	−	0.365857i
$748$		0			0
$749$	−3.36131	+	14.7269i	−0.122820	+	0.538108i
$750$		0			0
$751$	−6.82843	−	14.1794i	−0.249173	−	0.517413i	0.738441	−	0.674319i	$-0.235563\pi$
$751$	−6.82843	−	14.1794i	−0.249173	−	0.517413i	−0.987614	+	0.156905i	$0.949848\pi$
$752$		0			0
$753$	2.02656			0.0738519
$754$		0			0
$755$	−9.78633			−0.356161
$756$		0			0
$757$	−4.34166	−	9.01555i	−0.157800	−	0.327676i	0.807047	−	0.590487i	$-0.201064\pi$
$757$	−4.34166	−	9.01555i	−0.157800	−	0.327676i	−0.964847	+	0.262812i	$0.915350\pi$
$758$		0			0
$759$	1.49776	−	6.56212i	0.0543653	−	0.238190i
$760$		0			0
$761$	−19.0469	+	9.17252i	−0.690451	+	0.332503i	−0.745994	−	0.665953i	$-0.768025\pi$
$761$	−19.0469	+	9.17252i	−0.690451	+	0.332503i	0.0555433	+	0.998456i	$0.482311\pi$
$762$		0			0
$763$	−7.50420	+	9.40997i	−0.271670	+	0.340664i
$764$		0			0
$765$	−9.73961	+	7.76708i	−0.352137	+	0.280820i
$766$		0			0
$767$	−18.9861	−	23.8079i	−0.685550	−	0.859652i
$768$		0			0
$769$	−49.2081	+	11.2314i	−1.77449	+	0.405016i	−0.979474	−	0.201572i	$-0.935395\pi$
$769$	−49.2081	+	11.2314i	−1.77449	+	0.405016i	−0.795016	+	0.606588i	$0.792538\pi$
$770$		0			0
$771$			8.88546i			0.320002i
$772$		0			0
$773$	8.41458	−	17.4731i	0.302651	−	0.628462i	−0.693070	−	0.720871i	$-0.743742\pi$
$773$	8.41458	−	17.4731i	0.302651	−	0.628462i	0.995721	+	0.0924084i	$0.0294565\pi$
$774$		0			0
$775$	−0.859909	−	0.685754i	−0.0308888	−	0.0246330i
$776$		0			0
$777$	0.456967	+	2.00210i	0.0163936	+	0.0718250i
$778$		0			0
$779$	3.61469	+	1.74074i	0.129510	+	0.0623685i
$780$		0			0
$781$	6.37066	+	1.45406i	0.227960	+	0.0520304i
$782$		0			0
$783$	−13.3747	+	1.32458i	−0.477975	+	0.0473365i
$784$		0			0
$785$	23.4635	+	5.35539i	0.837449	+	0.191142i
$786$		0			0
$787$	36.3357	+	17.4983i	1.29523	+	0.623749i	0.949258	−	0.314497i	$-0.101836\pi$
$787$	36.3357	+	17.4983i	1.29523	+	0.623749i	0.345969	+	0.938246i	$0.387550\pi$
$788$		0			0
$789$	2.27937	+	9.98659i	0.0811479	+	0.355532i
$790$		0			0
$791$	5.27166	+	4.20401i	0.187439	+	0.149477i
$792$		0			0
$793$	0.377162	−	0.783185i	0.0133934	−	0.0278117i
$794$		0			0
$795$		−	10.2783i		−	0.364534i
$796$		0			0
$797$	0.256916	−	0.0586395i	0.00910044	−	0.00207712i	−0.217968	−	0.975956i	$-0.569943\pi$
$797$	0.256916	−	0.0586395i	0.00910044	−	0.00207712i	0.227069	+	0.973879i	$0.427086\pi$
$798$		0			0
$799$	13.6365	+	17.0996i	0.482425	+	0.604941i
$800$		0			0
$801$	1.07933	−	0.860733i	0.0381361	−	0.0304125i
$802$		0			0
$803$	6.81200	−	8.54197i	0.240390	−	0.301440i
$804$		0			0
$805$	−17.3249	+	8.34322i	−0.610622	+	0.294060i
$806$		0			0
$807$	0.108174	−	0.473942i	0.00380791	−	0.0166835i
$808$		0			0
$809$	20.8249	+	43.2435i	0.732166	+	1.52036i	0.849686	+	0.527288i	$0.176791\pi$
$809$	20.8249	+	43.2435i	0.732166	+	1.52036i	−0.117520	+	0.993070i	$0.537494\pi$
$810$		0			0
$811$	37.7735			1.32641			0.663203	−	0.748439i	$-0.269197\pi$
$811$	37.7735			1.32641			0.663203	+	0.748439i	$0.269197\pi$
$812$		0			0
$813$	−11.2078			−0.393074
$814$		0			0
$815$	20.0086	+	41.5483i	0.700870	+	1.45537i
$816$		0			0
$817$	−0.411651	+	1.80356i	−0.0144019	+	0.0630987i
$818$		0			0
$819$	9.33170	−	4.49391i	0.326076	−	0.157030i
$820$		0			0
$821$	−9.93205	+	12.4544i	−0.346631	+	0.434662i	−0.924333	−	0.381586i	$-0.875378\pi$
$821$	−9.93205	+	12.4544i	−0.346631	+	0.434662i	0.577702	+	0.816248i	$0.303949\pi$
$822$		0			0
$823$	12.0291	−	9.59285i	0.419306	−	0.334386i	−0.391002	−	0.920390i	$-0.627871\pi$
$823$	12.0291	−	9.59285i	0.419306	−	0.334386i	0.810308	+	0.586004i	$0.199300\pi$
$824$		0			0
$825$	−0.262181	−	0.328764i	−0.00912796	−	0.0114461i
$826$		0			0
$827$	27.0718	−	6.17896i	0.941379	−	0.214864i	0.275820	−	0.961209i	$-0.411051\pi$
$827$	27.0718	−	6.17896i	0.941379	−	0.214864i	0.665559	+	0.746346i	$0.268193\pi$
$828$		0			0
$829$		−	41.3098i		−	1.43475i	−0.696687	−	0.717375i	$-0.745344\pi$
$829$		−	41.3098i		−	1.43475i	0.696687	−	0.717375i	$-0.254656\pi$
$830$		0			0
$831$	−0.829317	+	1.72209i	−0.0287687	+	0.0597388i
$832$		0			0
$833$	7.74511	+	6.17652i	0.268352	+	0.214004i
$834$		0			0
$835$	4.73406	+	20.7413i	0.163829	+	0.717781i
$836$		0			0
$837$	6.54382	+	3.15134i	0.226187	+	0.108926i
$838$		0			0
$839$	−18.7473	−	4.27895i	−0.647228	−	0.147726i	−0.113710	−	0.993514i	$-0.536273\pi$
$839$	−18.7473	−	4.27895i	−0.647228	−	0.147726i	−0.533519	+	0.845788i	$0.679131\pi$
$840$		0			0
$841$	23.1525	−	17.4632i	0.798362	−	0.602178i
$842$		0			0
$843$	−2.91022	−	0.664240i	−0.100233	−	0.0228776i
$844$		0			0
$845$	−13.1921	−	6.35298i	−0.453822	−	0.218549i
$846$		0			0
$847$	−1.40739	−	6.16619i	−0.0483586	−	0.211873i
$848$		0			0
$849$	10.2135	+	8.14501i	0.350527	+	0.279536i
$850$		0			0
$851$	−8.49570	+	17.6415i	−0.291229	+	0.604743i
$852$		0			0
$853$			4.55306i			0.155894i	0.996958	+	0.0779469i	$0.0248364\pi$
$853$			4.55306i			0.155894i	−0.996958	+	0.0779469i	$0.975164\pi$
$854$		0			0
$855$	−3.93519	+	0.898180i	−0.134580	+	0.0307171i
$856$		0			0
$857$	−1.62830	−	2.04182i	−0.0556215	−	0.0697472i	0.753243	−	0.657743i	$-0.228489\pi$
$857$	−1.62830	−	2.04182i	−0.0556215	−	0.0697472i	−0.808864	+	0.587996i	$0.799917\pi$
$858$		0			0
$859$	−9.57308	+	7.63427i	−0.326629	+	0.260478i	−0.773050	−	0.634345i	$-0.781270\pi$
$859$	−9.57308	+	7.63427i	−0.326629	+	0.260478i	0.446421	+	0.894823i	$0.352698\pi$
$860$		0			0
$861$	−2.38032	+	2.98483i	−0.0811211	+	0.101723i
$862$		0			0
$863$	9.03684	−	4.35191i	0.307617	−	0.148141i	−0.273706	−	0.961813i	$-0.588249\pi$
$863$	9.03684	−	4.35191i	0.307617	−	0.148141i	0.581323	+	0.813673i	$0.302535\pi$
$864$		0			0
$865$	3.80939	−	16.6900i	0.129523	−	0.567479i
$866$		0			0
$867$	−2.37686	−	4.93560i	−0.0807224	−	0.167622i
$868$		0			0
$869$	−13.9614			−0.473607
$870$		0			0
$871$	−24.1881			−0.819582
$872$		0			0
$873$	5.42017	+	11.2551i	0.183445	+	0.380928i
$874$		0			0
$875$	−3.80385	+	16.6658i	−0.128594	+	0.563405i
$876$		0			0
$877$	−38.4206	+	18.5024i	−1.29737	+	0.624782i	−0.949796	−	0.312870i	$-0.898710\pi$
$877$	−38.4206	+	18.5024i	−1.29737	+	0.624782i	−0.347577	+	0.937652i	$0.612995\pi$
$878$		0			0
$879$	−4.06459	+	5.09683i	−0.137095	+	0.171912i
$880$		0			0
$881$	−30.9284	+	24.6646i	−1.04200	+	0.830971i	−0.985880	−	0.167453i	$-0.946446\pi$
$881$	−30.9284	+	24.6646i	−1.04200	+	0.830971i	−0.0561245	+	0.998424i	$0.517874\pi$
$882$		0			0
$883$	−0.919704	−	1.15327i	−0.0309505	−	0.0388107i	0.766115	−	0.642703i	$-0.222187\pi$
$883$	−0.919704	−	1.15327i	−0.0309505	−	0.0388107i	−0.797066	+	0.603892i	$0.793616\pi$
$884$		0			0
$885$	−11.0095	+	2.51284i	−0.370080	+	0.0844683i
$886$		0			0
$887$			22.6679i			0.761114i	0.924757	+	0.380557i	$0.124268\pi$
$887$			22.6679i			0.761114i	−0.924757	+	0.380557i	$0.875732\pi$
$888$		0			0
$889$	−8.11159	+	16.8439i	−0.272054	+	0.564926i
$890$		0			0
$891$	−14.9526	−	11.9243i	−0.500932	−	0.399480i
$892$		0			0
$893$	1.57692	+	6.90892i	0.0527695	+	0.231198i
$894$		0			0
$895$	−2.67236	−	1.28694i	−0.0893271	−	0.0430177i
$896$		0			0
$897$	−6.29671	−	1.43718i	−0.210241	−	0.0479862i
$898$		0			0
$899$	−15.5953	+	1.54449i	−0.520134	+	0.0515117i
$900$		0			0
$901$	22.3504	+	5.10134i	0.744601	+	0.169950i
$902$		0			0
$903$	−1.58604	−	0.763796i	−0.0527801	−	0.0254176i
$904$		0			0
$905$	9.65444	+	42.2988i	0.320924	+	1.40606i
$906$		0			0
$907$	−3.72683	−	2.97205i	−0.123747	−	0.0986853i	0.559661	−	0.828722i	$-0.310932\pi$
$907$	−3.72683	−	2.97205i	−0.123747	−	0.0986853i	−0.683408	+	0.730037i	$0.739503\pi$
$908$		0			0
$909$	−12.5820	+	26.1267i	−0.417317	+	0.866568i
$910$		0			0
$911$		−	34.8991i		−	1.15626i	−0.815945	−	0.578130i	$-0.803783\pi$
$911$		−	34.8991i		−	1.15626i	0.815945	−	0.578130i	$-0.196217\pi$
$912$		0			0
$913$	20.6879	−	4.72187i	0.684669	−	0.156271i
$914$		0			0
$915$	−0.200988	−	0.252031i	−0.00664447	−	0.00833190i
$916$		0			0
$917$	−4.12152	+	3.28680i	−0.136105	+	0.108540i
$918$		0			0
$919$	−11.9067	+	14.9306i	−0.392767	+	0.492514i	−0.938420	−	0.345497i	$-0.887710\pi$
$919$	−11.9067	+	14.9306i	−0.392767	+	0.492514i	0.545653	+	0.838011i	$0.316282\pi$
$920$		0			0
$921$	1.47732	−	0.711439i	0.0486793	−	0.0234427i
$922$		0			0
$923$	1.39525	−	6.11300i	0.0459253	−	0.201212i
$924$		0			0
$925$	0.530761	+	1.10214i	0.0174513	+	0.0362380i
$926$		0			0
$927$	−38.3523			−1.25965
$928$		0			0
$929$	−15.7084			−0.515376			−0.257688	−	0.966228i	$-0.582961\pi$
$929$	−15.7084			−0.515376			−0.257688	+	0.966228i	$0.582961\pi$
$930$		0			0
$931$	1.39268	+	2.89193i	0.0456433	+	0.0947793i
$932$		0			0
$933$	2.33502	−	10.2304i	0.0764452	−	0.334928i
$934$		0			0
$935$	−10.3344	+	4.97677i	−0.337970	+	0.162758i
$936$		0			0
$937$	−18.1862	+	22.8047i	−0.594116	+	0.744998i	−0.984448	−	0.175676i	$-0.943789\pi$
$937$	−18.1862	+	22.8047i	−0.594116	+	0.744998i	0.390332	+	0.920674i	$0.372360\pi$
$938$		0			0
$939$	−6.76821	+	5.39746i	−0.220872	+	0.176140i
$940$		0			0
$941$	22.7109	+	28.4786i	0.740355	+	0.928376i	0.999296	−	0.0375170i	$-0.0119448\pi$
$941$	22.7109	+	28.4786i	0.740355	+	0.928376i	−0.258941	+	0.965893i	$0.583373\pi$
$942$		0			0
$943$	−35.4888	+	8.10008i	−1.15567	+	0.263775i
$944$		0			0
$945$		−	7.93309i		−	0.258063i
$946$		0			0
$947$	9.10570	−	18.9082i	0.295896	−	0.614434i	−0.699025	−	0.715097i	$-0.746382\pi$
$947$	9.10570	−	18.9082i	0.295896	−	0.614434i	0.994921	+	0.100664i	$0.0320966\pi$
$948$		0			0
$949$	−8.19650	−	6.53649i	−0.266070	−	0.212183i
$950$		0			0
$951$	0.849081	+	3.72007i	0.0275333	+	0.120631i
$952$		0			0
$953$	−29.4508	−	14.1828i	−0.954006	−	0.459425i	−0.108917	−	0.994051i	$-0.534738\pi$
$953$	−29.4508	−	14.1828i	−0.954006	−	0.459425i	−0.845089	+	0.534626i	$0.820453\pi$
$954$		0			0
$955$	48.9467	+	11.1718i	1.58388	+	0.361510i
$956$		0			0
$957$	−5.94439	−	0.751084i	−0.192155	−	0.0242791i
$958$		0			0
$959$	−30.8822	−	7.04867i	−0.997239	−	0.227613i
$960$		0			0
$961$	−20.2998	−	9.77585i	−0.654831	−	0.315350i
$962$		0			0
$963$	−6.40175	−	28.0479i	−0.206293	−	0.903831i
$964$		0			0
$965$	42.2287	+	33.6763i	1.35939	+	1.08408i
$966$		0			0
$967$	11.2982	−	23.4609i	0.363325	−	0.754452i	−0.636534	−	0.771249i	$-0.719632\pi$
$967$	11.2982	−	23.4609i	0.363325	−	0.754452i	0.999859	+	0.0167964i	$0.00534671\pi$
$968$		0			0
$969$			0.588792i			0.0189147i
$970$		0			0
$971$	45.7716	−	10.4471i	1.46888	−	0.335262i	0.588100	−	0.808788i	$-0.299876\pi$
$971$	45.7716	−	10.4471i	1.46888	−	0.335262i	0.880780	+	0.473526i	$0.157019\pi$
$972$		0			0
$973$	17.4614	+	21.8959i	0.559787	+	0.701951i
$974$		0			0
$975$	−0.315467	+	0.251577i	−0.0101030	+	0.00805690i
$976$		0			0
$977$	−10.5332	+	13.2082i	−0.336986	+	0.422568i	−0.921235	−	0.389007i	$-0.872818\pi$
$977$	−10.5332	+	13.2082i	−0.336986	+	0.422568i	0.584248	+	0.811575i	$0.301389\pi$
$978$		0			0
$979$	1.14523	−	0.551516i	0.0366019	−	0.0176265i
$980$		0			0
$981$	5.10077	−	22.3479i	0.162855	−	0.713515i
$982$		0			0
$983$	20.0322	+	41.5972i	0.638927	+	1.32675i	0.929120	+	0.369777i	$0.120566\pi$
$983$	20.0322	+	41.5972i	0.638927	+	1.32675i	−0.290194	+	0.956968i	$0.593720\pi$
$984$		0			0
$985$	−42.9995			−1.37008
$986$		0			0
$987$	−6.74346			−0.214647
$988$		0			0
$989$	−7.28266	−	15.1226i	−0.231575	−	0.480871i
$990$		0			0
$991$	7.41703	−	32.4961i	0.235610	−	1.03227i	−0.709291	−	0.704916i	$-0.750985\pi$
$991$	7.41703	−	32.4961i	0.235610	−	1.03227i	0.944901	−	0.327357i	$-0.106158\pi$
$992$		0			0
$993$	6.96655	−	3.35491i	0.221077	−	0.106465i
$994$		0			0
$995$	27.0496	−	33.9191i	0.857531	−	1.07531i
$996$		0			0
$997$	−11.9131	+	9.50041i	−0.377293	+	0.300881i	−0.793714	−	0.608291i	$-0.791856\pi$
$997$	−11.9131	+	9.50041i	−0.377293	+	0.300881i	0.416421	+	0.909172i	$0.363284\pi$
$998$		0			0
$999$	−5.03659	−	6.31569i	−0.159351	−	0.199820i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	232.2.q.a.33.4	✓	48
4.3	odd	2		464.2.y.e.33.5		48
29.14	odd	28		6728.2.a.be.1.15		24
29.15	odd	28		6728.2.a.bf.1.10		24
29.22	even	14	inner	232.2.q.a.225.4	yes	48
116.51	odd	14		464.2.y.e.225.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.2.q.a.33.4	✓	48	1.1	even	1	trivial
232.2.q.a.225.4	yes	48	29.22	even	14	inner
464.2.y.e.33.5		48	4.3	odd	2
464.2.y.e.225.5		48	116.51	odd	14
6728.2.a.be.1.15		24	29.14	odd	28
6728.2.a.bf.1.10		24	29.15	odd	28

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:	\( N \)	\(=\)	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	232.q (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.186194 - 0.386637i) q^{3} +(0.478397 - 2.09600i) q^{5} +(-1.33207 + 0.641493i) q^{7} +(1.75565 - 2.20152i) q^{9} +O(q^{10})\)	\(q+(-0.186194 - 0.386637i) q^{3} +(0.478397 - 2.09600i) q^{5} +(-1.33207 + 0.641493i) q^{7} +(1.75565 - 2.20152i) q^{9} +(2.02706 - 1.61653i) q^{11} +(-1.55115 - 1.94508i) q^{13} +(-0.899464 + 0.205297i) q^{15} -2.05780i q^{17} +(0.289294 - 0.600726i) q^{19} +(0.496050 + 0.395586i) q^{21} +(1.34616 + 5.89789i) q^{23} +(0.340513 + 0.163982i) q^{25} +(-2.43320 - 0.555363i) q^{27} +(5.10649 - 1.70990i) q^{29} +(-2.83719 - 0.647569i) q^{31} +(-1.00244 - 0.482748i) q^{33} +(0.707306 + 3.09891i) q^{35} +(2.53055 + 2.01805i) q^{37} +(-0.463224 + 0.961894i) q^{39} +6.01720i q^{41} +(-2.70498 + 0.617395i) q^{43} +(-3.77447 - 4.73303i) q^{45} +(-8.30968 + 6.62675i) q^{47} +(-3.00152 + 3.76379i) q^{49} +(-0.795620 + 0.383150i) q^{51} +(-2.47903 + 10.8613i) q^{53} +(-2.41849 - 5.02206i) q^{55} -0.286128 q^{57} +12.2401 q^{59} +(0.151602 + 0.314804i) q^{61} +(-0.926399 + 4.05882i) q^{63} +(-4.81894 + 2.32068i) q^{65} +(6.06188 - 7.60135i) q^{67} +(2.02969 - 1.61863i) q^{69} +(1.57140 + 1.97047i) q^{71} +(4.10831 - 0.937696i) q^{73} -0.162187i q^{75} +(-1.66321 + 3.45368i) q^{77} +(-4.21005 - 3.35741i) q^{79} +(-1.64143 - 7.19156i) q^{81} +(7.37393 + 3.55110i) q^{83} +(-4.31313 - 0.984444i) q^{85} +(-1.61191 - 1.65598i) q^{87} +(0.477973 + 0.109094i) q^{89} +(3.31400 + 1.59594i) q^{91} +(0.277894 + 1.21753i) q^{93} +(-1.12072 - 0.893745i) q^{95} +(-1.92488 + 3.99706i) q^{97} -7.30067i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{5} - 4 q^{7} + 6 q^{9}+O(q^{10}) \) 48 * q - 2 * q^5 - 4 * q^7 + 6 * q^9	\( 48 q - 2 q^{5} - 4 q^{7} + 6 q^{9} + 10 q^{13} + 14 q^{15} + 14 q^{21} + 4 q^{23} - 48 q^{25} - 4 q^{29} + 10 q^{33} + 8 q^{35} - 38 q^{45} - 14 q^{47} - 18 q^{49} - 56 q^{51} - 48 q^{53} - 28 q^{55} - 12 q^{57} - 128 q^{59} - 28 q^{61} + 42 q^{63} - 28 q^{65} - 4 q^{67} + 28 q^{69} - 14 q^{71} - 28 q^{73} + 14 q^{77} - 32 q^{81} + 80 q^{83} - 112 q^{87} + 42 q^{89} - 28 q^{91} + 6 q^{93} + 70 q^{97}+O(q^{100}) \) 48 * q - 2 * q^5 - 4 * q^7 + 6 * q^9 + 10 * q^13 + 14 * q^15 + 14 * q^21 + 4 * q^23 - 48 * q^25 - 4 * q^29 + 10 * q^33 + 8 * q^35 - 38 * q^45 - 14 * q^47 - 18 * q^49 - 56 * q^51 - 48 * q^53 - 28 * q^55 - 12 * q^57 - 128 * q^59 - 28 * q^61 + 42 * q^63 - 28 * q^65 - 4 * q^67 + 28 * q^69 - 14 * q^71 - 28 * q^73 + 14 * q^77 - 32 * q^81 + 80 * q^83 - 112 * q^87 + 42 * q^89 - 28 * q^91 + 6 * q^93 + 70 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more