LMFDB - Embedded newform 920.2.bv.a.217.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.30
Character	$\chi$	$=$	920.217
Dual form			920.2.bv.a.513.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.32548 - 0.505878i) q^{3} +(-2.23378 - 0.101038i) q^{5} +(-2.56741 + 1.40191i) q^{7} +(2.42307 - 1.10658i) q^{9} +O(q^{10})$	\(q+(2.32548 - 0.505878i) q^{3} +(-2.23378 - 0.101038i) q^{5} +(-2.56741 + 1.40191i) q^{7} +(2.42307 - 1.10658i) q^{9} +(-4.43127 - 3.83971i) q^{11} +(-2.71471 + 4.97162i) q^{13} +(-5.24574 + 0.895061i) q^{15} +(-4.66794 - 3.49438i) q^{17} +(-0.842493 + 5.85967i) q^{19} +(-5.26128 + 4.55893i) q^{21} +(1.25159 + 4.62963i) q^{23} +(4.97958 + 0.451393i) q^{25} +(-0.640545 + 0.479506i) q^{27} +(3.20665 - 0.461046i) q^{29} +(3.85054 - 2.47459i) q^{31} +(-12.2473 - 6.68751i) q^{33} +(5.87670 - 2.87217i) q^{35} +(-3.23149 - 1.20528i) q^{37} +(-3.79798 + 12.9347i) q^{39} +(2.20002 - 4.81737i) q^{41} +(-0.300622 - 1.38194i) q^{43} +(-5.52442 + 2.22703i) q^{45} +(-8.32609 - 8.32609i) q^{47} +(0.841769 - 1.30982i) q^{49} +(-12.6230 - 5.76471i) q^{51} +(4.08600 + 7.48295i) q^{53} +(9.51053 + 9.02482i) q^{55} +(1.00507 + 14.0528i) q^{57} +(-1.62708 - 5.54134i) q^{59} +(-1.49599 - 2.32780i) q^{61} +(-4.66969 + 6.23798i) q^{63} +(6.56640 - 10.8312i) q^{65} +(9.03916 + 0.646494i) q^{67} +(5.25259 + 10.1330i) q^{69} +(-5.72890 - 6.61151i) q^{71} +(-4.01479 - 5.36313i) q^{73} +(11.8083 - 1.46935i) q^{75} +(16.7598 + 3.64588i) q^{77} +(-6.67276 + 1.95930i) q^{79} +(-6.48024 + 7.47859i) q^{81} +(1.58280 - 4.24366i) q^{83} +(10.0741 + 8.27733i) q^{85} +(7.22378 - 2.69433i) q^{87} +(2.65747 + 1.70785i) q^{89} -16.5700i q^{91} +(7.70253 - 7.70253i) q^{93} +(2.47399 - 13.0041i) q^{95} +(-1.50508 - 4.03527i) q^{97} +(-14.9862 - 4.40034i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q+O(q^{10}) $ 720 * q	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{3}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	2.32548	−	0.505878i	1.34262	−	0.292069i	0.516849	−	0.856076i	$-0.327105\pi$
$3$	2.32548	−	0.505878i	1.34262	−	0.292069i	0.825770	+	0.564008i	$0.190741\pi$
$4$		0			0
$5$	−2.23378	−	0.101038i	−0.998979	−	0.0451854i
$5$	−2.23378	−	0.101038i	−0.998979	−	0.0451854i
$6$		0			0
$7$	−2.56741	+	1.40191i	−0.970392	+	0.529874i	−0.884555	−	0.466435i	$-0.845538\pi$
$7$	−2.56741	+	1.40191i	−0.970392	+	0.529874i	−0.0858363	+	0.996309i	$0.527356\pi$
$8$		0			0
$9$	2.42307	−	1.10658i	0.807689	−	0.368859i
$10$		0			0
$11$	−4.43127	−	3.83971i	−1.33608	−	1.15772i	−0.974250	−	0.225472i	$-0.927608\pi$
$11$	−4.43127	−	3.83971i	−1.33608	−	1.15772i	−0.361827	−	0.932245i	$-0.617847\pi$
$12$		0			0
$13$	−2.71471	+	4.97162i	−0.752925	+	1.37888i	0.166671	+	0.986013i	$0.446698\pi$
$13$	−2.71471	+	4.97162i	−0.752925	+	1.37888i	−0.919596	+	0.392867i	$0.871483\pi$
$14$		0			0
$15$	−5.24574	+	0.895061i	−1.35444	+	0.231104i
$16$		0			0
$17$	−4.66794	−	3.49438i	−1.13214	−	0.847512i	−0.142321	−	0.989821i	$-0.545456\pi$
$17$	−4.66794	−	3.49438i	−1.13214	−	0.847512i	−0.989822	+	0.142309i	$0.954547\pi$
$18$		0			0
$19$	−0.842493	+	5.85967i	−0.193281	+	1.34430i	0.629969	+	0.776620i	$0.283068\pi$
$19$	−0.842493	+	5.85967i	−0.193281	+	1.34430i	−0.823250	+	0.567679i	$0.807841\pi$
$20$		0			0
$21$	−5.26128	+	4.55893i	−1.14811	+	0.994840i
$22$		0			0
$23$	1.25159	+	4.62963i	0.260975	+	0.965345i
$23$	1.25159	+	4.62963i	0.260975	+	0.965345i
$24$		0			0
$25$	4.97958	+	0.451393i	0.995917	+	0.0902786i
$26$		0			0
$27$	−0.640545	+	0.479506i	−0.123273	+	0.0922810i
$28$		0			0
$29$	3.20665	−	0.461046i	0.595460	−	0.0856142i	0.162006	−	0.986790i	$-0.448204\pi$
$29$	3.20665	−	0.461046i	0.595460	−	0.0856142i	0.433454	+	0.901176i	$0.357295\pi$
$30$		0			0
$31$	3.85054	−	2.47459i	0.691577	−	0.444450i	−0.147069	−	0.989126i	$-0.546984\pi$
$31$	3.85054	−	2.47459i	0.691577	−	0.444450i	0.838646	+	0.544676i	$0.183348\pi$
$32$		0			0
$33$	−12.2473	−	6.68751i	−2.13197	−	1.16415i
$34$		0			0
$35$	5.87670	−	2.87217i	0.993343	−	0.485485i
$36$		0			0
$37$	−3.23149	−	1.20528i	−0.531254	−	0.198148i	0.0694992	−	0.997582i	$-0.477860\pi$
$37$	−3.23149	−	1.20528i	−0.531254	−	0.198148i	−0.600753	+	0.799434i	$0.705133\pi$
$38$		0			0
$39$	−3.79798	+	12.9347i	−0.608164	+	2.07122i
$40$		0			0
$41$	2.20002	−	4.81737i	0.343585	−	0.752347i	−0.656412	−	0.754402i	$-0.727927\pi$
$41$	2.20002	−	4.81737i	0.343585	−	0.752347i	0.999998	+	0.00205509i	$0.000654157\pi$
$42$		0			0
$43$	−0.300622	−	1.38194i	−0.0458445	−	0.210744i	0.948527	−	0.316698i	$-0.102574\pi$
$43$	−0.300622	−	1.38194i	−0.0458445	−	0.210744i	−0.994371	+	0.105954i	$0.966210\pi$
$44$		0			0
$45$	−5.52442	+	2.22703i	−0.823531	+	0.331987i
$46$		0			0
$47$	−8.32609	−	8.32609i	−1.21448	−	1.21448i	−0.969536	−	0.244948i	$-0.921229\pi$
$47$	−8.32609	−	8.32609i	−1.21448	−	1.21448i	−0.244948	−	0.969536i	$-0.578771\pi$
$48$		0			0
$49$	0.841769	−	1.30982i	0.120253	−	0.187117i
$50$		0			0
$51$	−12.6230	−	5.76471i	−1.76757	−	0.807221i
$52$		0			0
$53$	4.08600	+	7.48295i	0.561255	+	1.02786i	0.992102	+	0.125437i	$0.0400333\pi$
$53$	4.08600	+	7.48295i	0.561255	+	1.02786i	−0.430846	+	0.902425i	$0.641785\pi$
$54$		0			0
$55$	9.51053	+	9.02482i	1.28240	+	1.21691i
$56$		0			0
$57$	1.00507	+	14.0528i	0.133125	+	1.86133i
$58$		0			0
$59$	−1.62708	−	5.54134i	−0.211828	−	0.721421i	−0.995023	−	0.0996447i	$-0.968229\pi$
$59$	−1.62708	−	5.54134i	−0.211828	−	0.721421i	0.783195	−	0.621777i	$-0.213589\pi$
$60$		0			0
$61$	−1.49599	−	2.32780i	−0.191542	−	0.298045i	0.732178	−	0.681113i	$-0.238504\pi$
$61$	−1.49599	−	2.32780i	−0.191542	−	0.298045i	−0.923720	+	0.383068i	$0.874867\pi$
$62$		0			0
$63$	−4.66969	+	6.23798i	−0.588326	+	0.785911i
$64$		0			0
$65$	6.56640	−	10.8312i	0.814461	−	1.34345i
$66$		0			0
$67$	9.03916	+	0.646494i	1.10431	+	0.0789818i	0.611567	−	0.791193i	$-0.290540\pi$
$67$	9.03916	+	0.646494i	1.10431	+	0.0789818i	0.492743	+	0.870175i	$0.335994\pi$
$68$		0			0
$69$	5.25259	+	10.1330i	0.632338	+	1.21987i
$70$		0			0
$71$	−5.72890	−	6.61151i	−0.679896	−	0.784642i	0.305995	−	0.952033i	$-0.401011\pi$
$71$	−5.72890	−	6.61151i	−0.679896	−	0.784642i	−0.985890	+	0.167392i	$0.946466\pi$
$72$		0			0
$73$	−4.01479	−	5.36313i	−0.469895	−	0.627707i	0.501505	−	0.865155i	$-0.332780\pi$
$73$	−4.01479	−	5.36313i	−0.469895	−	0.627707i	−0.971400	+	0.237448i	$0.923689\pi$
$74$		0			0
$75$	11.8083	−	1.46935i	1.36350	−	0.169666i
$76$		0			0
$77$	16.7598	+	3.64588i	1.90996	+	0.415487i
$78$		0			0
$79$	−6.67276	+	1.95930i	−0.750744	+	0.220438i	−0.634650	−	0.772800i	$-0.718856\pi$
$79$	−6.67276	+	1.95930i	−0.750744	+	0.220438i	−0.116094	+	0.993238i	$0.537038\pi$
$80$		0			0
$81$	−6.48024	+	7.47859i	−0.720026	+	0.830955i
$82$		0			0
$83$	1.58280	−	4.24366i	0.173735	−	0.465802i	−0.820674	−	0.571397i	$-0.806402\pi$
$83$	1.58280	−	4.24366i	0.173735	−	0.465802i	0.994409	+	0.105594i	$0.0336745\pi$
$84$		0			0
$85$	10.0741	+	8.27733i	1.09269	+	0.897802i
$86$		0			0
$87$	7.22378	−	2.69433i	0.774470	−	0.288862i
$88$		0			0
$89$	2.65747	+	1.70785i	0.281691	+	0.181032i	0.673855	−	0.738863i	$-0.264637\pi$
$89$	2.65747	+	1.70785i	0.281691	+	0.181032i	−0.392164	+	0.919895i	$0.628273\pi$
$90$		0			0
$91$		−	16.5700i		−	1.73701i
$92$		0			0
$93$	7.70253	−	7.70253i	0.798715	−	0.798715i
$94$		0			0
$95$	2.47399	−	13.0041i	0.253826	−	1.33419i
$96$		0			0
$97$	−1.50508	−	4.03527i	−0.152818	−	0.409720i	0.837871	−	0.545869i	$-0.183800\pi$
$97$	−1.50508	−	4.03527i	−0.152818	−	0.409720i	−0.990688	+	0.136149i	$0.956527\pi$
$98$		0			0
$99$	−14.9862	−	4.40034i	−1.50617	−	0.442251i
$100$		0			0
$101$	7.30072	+	15.9864i	0.726449	+	1.59070i	0.804640	+	0.593763i	$0.202358\pi$
$101$	7.30072	+	15.9864i	0.726449	+	1.59070i	−0.0781911	+	0.996938i	$0.524914\pi$
$102$		0			0
$103$	−9.96380	+	0.712625i	−0.981763	+	0.0702170i	−0.552983	−	0.833192i	$-0.686511\pi$
$103$	−9.96380	+	0.712625i	−0.981763	+	0.0702170i	−0.428779	+	0.903409i	$0.641056\pi$
$104$		0			0
$105$	12.2132	−	9.65207i	1.19189	−	0.941946i
$106$		0			0
$107$	−0.923960	+	4.24738i	−0.0893226	+	0.410609i	−0.999997	−	0.00251582i	$-0.999199\pi$
$107$	−0.923960	+	4.24738i	−0.0893226	+	0.410609i	0.910674	+	0.413125i	$0.135563\pi$
$108$		0			0
$109$	1.01519	+	7.06080i	0.0972375	+	0.676302i	0.978888	+	0.204398i	$0.0655238\pi$
$109$	1.01519	+	7.06080i	0.0972375	+	0.676302i	−0.881650	+	0.471903i	$0.843567\pi$
$110$		0			0
$111$	−8.12451	−	1.16813i	−0.771144	−	0.110874i
$112$		0			0
$113$	−0.989307	+	13.8323i	−0.0930661	+	1.30123i	0.709514	+	0.704691i	$0.248914\pi$
$113$	−0.989307	+	13.8323i	−0.0930661	+	1.30123i	−0.802581	+	0.596544i	$0.796540\pi$
$114$		0			0
$115$	−2.32802	−	10.4681i	−0.217089	−	0.976152i
$116$		0			0
$117$	−1.07644	+	15.0506i	−0.0995170	+	1.39143i
$118$		0			0
$119$	16.8834	+	2.42746i	1.54770	+	0.222525i
$120$		0			0
$121$	3.32725	+	23.1415i	0.302477	+	2.10378i
$122$		0			0
$123$	2.67911	−	12.3157i	0.241567	−	1.11047i
$124$		0			0
$125$	−11.0777	−	1.51144i	−0.990820	−	0.135187i
$126$		0			0
$127$	−2.57328	+	0.184045i	−0.228342	+	0.0163313i	−0.185041	−	0.982731i	$-0.559242\pi$
$127$	−2.57328	+	0.184045i	−0.228342	+	0.0163313i	−0.0433006	+	0.999062i	$0.513787\pi$
$128$		0			0
$129$	−1.39818	−	3.06160i	−0.123103	−	0.269559i
$130$		0			0
$131$	−2.38675	−	0.700812i	−0.208531	−	0.0612302i	0.175799	−	0.984426i	$-0.443749\pi$
$131$	−2.38675	−	0.700812i	−0.208531	−	0.0612302i	−0.384330	+	0.923196i	$0.625567\pi$
$132$		0			0
$133$	−6.05172	−	16.2253i	−0.524751	−	1.40691i
$134$		0			0
$135$	1.47929	−	1.00639i	0.127317	−	0.0866166i
$136$		0			0
$137$	−10.2161	+	10.2161i	−0.872824	+	0.872824i	−0.992779	−	0.119956i	$-0.961725\pi$
$137$	−10.2161	+	10.2161i	−0.872824	+	0.872824i	0.119956	+	0.992779i	$0.461725\pi$
$138$		0			0
$139$		−	15.8673i		−	1.34585i	−0.739711	−	0.672925i	$-0.765038\pi$
$139$		−	15.8673i		−	1.34585i	0.739711	−	0.672925i	$-0.234962\pi$
$140$		0			0
$141$	−23.5742	−	15.1502i	−1.98530	−	1.27588i
$142$		0			0
$143$	31.1192	−	11.6069i	2.60232	−	0.970614i
$144$		0			0
$145$	−7.20954	+	0.705886i	−0.598720	+	0.0586206i
$146$		0			0
$147$	1.29491	−	3.47179i	0.106803	−	0.286349i
$148$		0			0
$149$	3.02457	−	3.49054i	0.247782	−	0.285956i	−0.618211	−	0.786013i	$-0.712142\pi$
$149$	3.02457	−	3.49054i	0.247782	−	0.285956i	0.865993	+	0.500057i	$0.166688\pi$
$150$		0			0
$151$	−16.8478	+	4.94695i	−1.37105	+	0.402577i	−0.882646	−	0.470039i	$-0.844240\pi$
$151$	−16.8478	+	4.94695i	−1.37105	+	0.402577i	−0.488407	+	0.872616i	$0.662422\pi$
$152$		0			0
$153$	−15.1775	−	3.30167i	−1.22703	−	0.266924i
$154$		0			0
$155$	−8.85130	+	5.13865i	−0.710954	+	0.412747i
$156$		0			0
$157$	−5.61847	−	7.50539i	−0.448403	−	0.598996i	0.518205	−	0.855256i	$-0.326600\pi$
$157$	−5.61847	−	7.50539i	−0.448403	−	0.598996i	−0.966608	+	0.256261i	$0.917509\pi$
$158$		0			0
$159$	13.2874	+	15.3345i	1.05376	+	1.21610i
$160$		0			0
$161$	−9.70371	−	10.1316i	−0.764760	−	0.798479i
$162$		0			0
$163$	−2.36210	−	0.168941i	−0.185014	−	0.0132324i	−0.0214752	−	0.999769i	$-0.506836\pi$
$163$	−2.36210	−	0.168941i	−0.185014	−	0.0132324i	−0.163539	+	0.986537i	$0.552291\pi$
$164$		0			0
$165$	26.6821	+	16.1759i	2.07719	+	1.25929i
$166$		0			0
$167$	−2.63517	+	3.52017i	−0.203915	+	0.272399i	−0.890828	−	0.454341i	$-0.849875\pi$
$167$	−2.63517	+	3.52017i	−0.203915	+	0.272399i	0.686912	+	0.726740i	$0.258966\pi$
$168$		0			0
$169$	−10.3190	−	16.0567i	−0.793771	−	1.23513i
$170$		0			0
$171$	4.44276	+	15.1306i	0.339746	+	1.15707i
$172$		0			0
$173$	1.82329	+	25.4930i	0.138622	+	1.93819i	0.305452	+	0.952208i	$0.401193\pi$
$173$	1.82329	+	25.4930i	0.138622	+	1.93819i	−0.166829	+	0.985986i	$0.553353\pi$
$174$		0			0
$175$	−13.4175	+	5.82204i	−1.01427	+	0.440105i
$176$		0			0
$177$	−6.58700	−	12.0632i	−0.495110	−	0.906725i
$178$		0			0
$179$	−14.9604	−	6.83218i	−1.11819	−	0.510661i	−0.231414	−	0.972855i	$-0.574335\pi$
$179$	−14.9604	−	6.83218i	−1.11819	−	0.510661i	−0.886779	+	0.462194i	$0.847062\pi$
$180$		0			0
$181$	−1.79739	+	2.79680i	−0.133599	+	0.207884i	−0.901607	−	0.432556i	$-0.857612\pi$
$181$	−1.79739	+	2.79680i	−0.133599	+	0.207884i	0.768008	+	0.640440i	$0.221248\pi$
$182$		0			0
$183$	−4.65648	−	4.65648i	−0.344217	−	0.344217i
$184$		0			0
$185$	7.09668	+	3.01885i	0.521758	+	0.221950i
$186$		0			0
$187$	7.26749	+	33.4081i	0.531451	+	2.44304i
$188$		0			0
$189$	0.972318	−	2.12908i	0.0707258	−	0.154868i
$190$		0			0
$191$	4.01045	−	13.6583i	0.290186	−	0.988282i	−0.677374	−	0.735639i	$-0.736882\pi$
$191$	4.01045	−	13.6583i	0.290186	−	0.988282i	0.967560	−	0.252643i	$-0.0812998\pi$
$192$		0			0
$193$	14.3984	+	5.37031i	1.03642	+	0.386563i	0.809357	−	0.587317i	$-0.199816\pi$
$193$	14.3984	+	5.37031i	1.03642	+	0.386563i	0.227060	+	0.973881i	$0.427089\pi$
$194$		0			0
$195$	9.79076	−	28.5097i	0.701131	−	2.04162i
$196$		0			0
$197$	11.2598	+	6.14830i	0.802225	+	0.438048i	0.827385	−	0.561635i	$-0.189828\pi$
$197$	11.2598	+	6.14830i	0.802225	+	0.438048i	−0.0251595	+	0.999683i	$0.508009\pi$
$198$		0			0
$199$	17.7561	−	11.4112i	1.25870	−	0.808917i	0.270593	−	0.962694i	$-0.412780\pi$
$199$	17.7561	−	11.4112i	1.25870	−	0.808917i	0.988106	+	0.153777i	$0.0491437\pi$
$200$		0			0
$201$	21.3475	−	3.06930i	1.50574	−	0.216492i
$202$		0			0
$203$	−7.58645	+	5.67914i	−0.532464	+	0.398598i
$204$		0			0
$205$	−5.40111	+	10.5387i	−0.377230	+	0.736054i
$206$		0			0
$207$	8.15575	+	9.83293i	0.566864	+	0.683436i
$208$		0			0
$209$	26.2327	−	22.7308i	1.81456	−	1.57232i
$210$		0			0
$211$	−2.57449	+	17.9060i	−0.177235	+	1.23270i	0.685888	+	0.727707i	$0.259414\pi$
$211$	−2.57449	+	17.9060i	−0.177235	+	1.23270i	−0.863124	+	0.504992i	$0.831495\pi$
$212$		0			0
$213$	−16.6671	−	12.4768i	−1.14201	−	0.854898i
$214$		0			0
$215$	0.531897	+	3.11733i	0.0362751	+	0.212600i
$216$		0			0
$217$	−6.41677	+	11.7514i	−0.435599	+	0.797739i
$218$		0			0
$219$	−12.0494	−	10.4409i	−0.814224	−	0.705529i
$220$		0			0
$221$	30.0448	−	13.7210i	2.02103	−	0.922976i
$222$		0			0
$223$	−12.0577	+	6.58402i	−0.807446	+	0.440899i	−0.829260	−	0.558863i	$-0.811238\pi$
$223$	−12.0577	+	6.58402i	−0.807446	+	0.440899i	0.0218141	+	0.999762i	$0.493056\pi$
$224$		0			0
$225$	12.5654	−	4.41654i	0.837691	−	0.294436i
$226$		0			0
$227$	11.6336	−	2.53073i	0.772147	−	0.167970i	0.190803	−	0.981628i	$-0.438891\pi$
$227$	11.6336	−	2.53073i	0.772147	−	0.167970i	0.581344	+	0.813658i	$0.302527\pi$
$228$		0			0
$229$	5.83955			0.385889			0.192944	−	0.981210i	$-0.438196\pi$
$229$	5.83955			0.385889			0.192944	+	0.981210i	$0.438196\pi$
$230$		0			0
$231$	40.8191			2.68570
$232$		0			0
$233$	−0.0518141	+	0.0112715i	−0.00339446	+	0.000738419i	−0.214262	−	0.976776i	$-0.568735\pi$
$233$	−0.0518141	+	0.0112715i	−0.00339446	+	0.000738419i	0.210868	+	0.977515i	$0.432371\pi$
$234$		0			0
$235$	17.7574	+	19.4399i	1.15837	+	1.26812i
$236$		0			0
$237$	−14.5262	+	7.93193i	−0.943580	+	0.515234i
$238$		0			0
$239$	−15.8194	+	7.22447i	−1.02327	+	0.467312i	−0.855109	−	0.518448i	$-0.826510\pi$
$239$	−15.8194	+	7.22447i	−1.02327	+	0.467312i	−0.168161	+	0.985760i	$0.553783\pi$
$240$		0			0
$241$	0.135979	+	0.117826i	0.00875916	+	0.00758985i	0.659229	−	0.751942i	$-0.270883\pi$
$241$	0.135979	+	0.117826i	0.00875916	+	0.00758985i	−0.650470	+	0.759532i	$0.725428\pi$
$242$		0			0
$243$	−10.1360	+	18.5628i	−0.650227	+	1.19080i
$244$		0			0
$245$	−2.01267	+	2.84080i	−0.128585	+	0.181492i
$246$		0			0
$247$	−26.8449	−	20.0958i	−1.70810	−	1.27867i
$248$		0			0
$249$	1.53401	−	10.6693i	0.0972139	−	0.676137i
$250$		0			0
$251$	15.1127	−	13.0953i	0.953908	−	0.826566i	−0.0310224	−	0.999519i	$-0.509876\pi$
$251$	15.1127	−	13.0953i	0.953908	−	0.826566i	0.984930	+	0.172953i	$0.0553309\pi$
$252$		0			0
$253$	12.2303	−	25.3209i	0.768914	−	1.59191i
$254$		0			0
$255$	27.6145	+	14.1525i	1.72929	+	0.886265i
$256$		0			0
$257$	10.7061	−	8.01452i	0.667831	−	0.499932i	−0.210741	−	0.977542i	$-0.567588\pi$
$257$	10.7061	−	8.01452i	0.667831	−	0.499932i	0.878572	+	0.477610i	$0.158497\pi$
$258$		0			0
$259$	9.98629	−	1.43581i	0.620518	−	0.0892170i
$260$		0			0
$261$	7.25974	−	4.66555i	0.449367	−	0.288790i
$262$		0			0
$263$	−14.2513	−	7.78181i	−0.878774	−	0.479847i	−0.0245182	−	0.999699i	$-0.507805\pi$
$263$	−14.2513	−	7.78181i	−0.878774	−	0.479847i	−0.854256	+	0.519852i	$0.825987\pi$
$264$		0			0
$265$	−8.37118	−	17.1281i	−0.514238	−	1.05217i
$266$		0			0
$267$	7.04387	+	2.62723i	0.431078	+	0.160784i
$268$		0			0
$269$	5.60452	−	19.0872i	0.341714	−	1.16377i	−0.592057	−	0.805896i	$-0.701684\pi$
$269$	5.60452	−	19.0872i	0.341714	−	1.16377i	0.933770	−	0.357873i	$-0.116498\pi$
$270$		0			0
$271$	−1.91575	+	4.19490i	−0.116373	+	0.254822i	−0.958851	−	0.283909i	$-0.908369\pi$
$271$	−1.91575	+	4.19490i	−0.116373	+	0.254822i	0.842478	+	0.538731i	$0.181096\pi$
$272$		0			0
$273$	−8.38240	−	38.5333i	−0.507326	−	2.33214i
$274$		0			0
$275$	−20.3326	−	21.1204i	−1.22610	−	1.27361i
$276$		0			0
$277$	−3.52020	−	3.52020i	−0.211508	−	0.211508i	0.593400	−	0.804908i	$-0.297785\pi$
$277$	−3.52020	−	3.52020i	−0.211508	−	0.211508i	−0.804908	+	0.593400i	$0.797785\pi$
$278$		0			0
$279$	6.59179	−	10.2570i	0.394640	−	0.614072i
$280$		0			0
$281$	−0.260769	−	0.119089i	−0.0155562	−	0.00710427i	0.407622	−	0.913151i	$-0.366358\pi$
$281$	−0.260769	−	0.119089i	−0.0155562	−	0.00710427i	−0.423178	+	0.906047i	$0.639085\pi$
$282$		0			0
$283$	9.98369	+	18.2838i	0.593469	+	1.08686i	0.985941	+	0.167093i	$0.0534381\pi$
$283$	9.98369	+	18.2838i	0.593469	+	1.08686i	−0.392472	+	0.919764i	$0.628380\pi$
$284$		0			0
$285$	−0.825258	−	31.4924i	−0.0488840	−	1.86545i
$286$		0			0
$287$	1.10518	+	15.4524i	0.0652367	+	0.912128i
$288$		0			0
$289$	4.78956	+	16.3118i	0.281739	+	0.959515i
$290$		0			0
$291$	−5.54139	−	8.62257i	−0.324842	−	0.505464i
$292$		0			0
$293$	−13.5356	+	18.0815i	−0.790759	+	1.05633i	0.206209	+	0.978508i	$0.433887\pi$
$293$	−13.5356	+	18.0815i	−0.790759	+	1.05633i	−0.996967	+	0.0778219i	$0.975203\pi$
$294$		0			0
$295$	3.07467	+	12.5426i	0.179014	+	0.730256i
$296$		0			0
$297$	4.67959	+	0.334691i	0.271537	+	0.0194207i
$298$		0			0
$299$	−26.4145	−	6.34566i	−1.52759	−	0.366979i
$300$		0			0
$301$	2.70918	+	3.12656i	0.156155	+	0.180212i
$302$		0			0
$303$	25.0649	+	33.4827i	1.43994	+	1.92353i
$304$		0			0
$305$	3.10652	+	5.35096i	0.177879	+	0.306395i
$306$		0			0
$307$	27.8587	+	6.06029i	1.58998	+	0.345879i	0.918586	−	0.395221i	$-0.129332\pi$
$307$	27.8587	+	6.06029i	1.58998	+	0.345879i	0.671395	+	0.741100i	$0.265696\pi$
$308$		0			0
$309$	−22.8102	+	6.69767i	−1.29762	+	0.381017i
$310$		0			0
$311$	6.81172	−	7.86114i	0.386257	−	0.445765i	−0.529008	−	0.848617i	$-0.677436\pi$
$311$	6.81172	−	7.86114i	0.386257	−	0.445765i	0.915265	+	0.402852i	$0.131981\pi$
$312$		0			0
$313$	0.438124	−	1.17466i	0.0247643	−	0.0663955i	−0.923979	−	0.382443i	$-0.875083\pi$
$313$	0.438124	−	1.17466i	0.0247643	−	0.0663955i	0.948744	+	0.316047i	$0.102356\pi$
$314$		0			0
$315$	11.0614	−	13.4625i	0.623237	−	0.758525i
$316$		0			0
$317$	−8.14303	+	3.03720i	−0.457358	+	0.170586i	−0.567575	−	0.823322i	$-0.692118\pi$
$317$	−8.14303	+	3.03720i	−0.457358	+	0.170586i	0.110217	+	0.993908i	$0.464846\pi$
$318$		0			0
$319$	−15.9798	−	10.2696i	−0.894697	−	0.574987i
$320$		0			0
$321$			10.3446i			0.577380i
$322$		0			0
$323$	24.4086	−	24.4086i	1.35813	−	1.35813i
$324$		0			0
$325$	−15.7623	+	23.5312i	−0.874334	+	1.30528i
$326$		0			0
$327$	5.93271	+	15.9062i	0.328080	+	0.879615i
$328$		0			0
$329$	33.0490	+	9.70406i	1.82205	+	0.535002i
$330$		0			0
$331$	−2.16547	−	4.74171i	−0.119025	−	0.260628i	0.840737	−	0.541444i	$-0.182122\pi$
$331$	−2.16547	−	4.74171i	−0.119025	−	0.260628i	−0.959762	+	0.280816i	$0.909395\pi$
$332$		0			0
$333$	−9.16386	+	0.655413i	−0.502177	+	0.0359164i
$334$		0			0
$335$	−20.1262	−	2.35742i	−1.09961	−	0.128800i
$336$		0			0
$337$	−5.40168	+	24.8311i	−0.294248	+	1.35264i	0.558148	+	0.829742i	$0.311512\pi$
$337$	−5.40168	+	24.8311i	−0.294248	+	1.35264i	−0.852396	+	0.522897i	$0.824851\pi$
$338$		0			0
$339$	4.69685	+	32.6673i	0.255098	+	1.77424i
$340$		0			0
$341$	−26.5645	−	3.81940i	−1.43855	−	0.206832i
$342$		0			0
$343$	1.13587	−	15.8815i	0.0613311	−	0.857521i
$344$		0			0
$345$	−10.7093	−	23.1656i	−0.576572	−	1.24719i
$346$		0			0
$347$	−1.46541	+	20.4890i	−0.0786671	+	1.09991i	0.792808	+	0.609471i	$0.208618\pi$
$347$	−1.46541	+	20.4890i	−0.0786671	+	1.09991i	−0.871476	+	0.490439i	$0.836836\pi$
$348$		0			0
$349$	20.3143	+	2.92076i	1.08740	+	0.156345i	0.662623	−	0.748953i	$-0.269443\pi$
$349$	20.3143	+	2.92076i	1.08740	+	0.156345i	0.424778	+	0.905298i	$0.360352\pi$
$350$		0			0
$351$	−0.645028	−	4.48627i	−0.0344290	−	0.239459i
$352$		0			0
$353$	−2.50236	+	11.5031i	−0.133187	+	0.612251i	0.861363	+	0.507990i	$0.169611\pi$
$353$	−2.50236	+	11.5031i	−0.133187	+	0.612251i	−0.994550	+	0.104261i	$0.966752\pi$
$354$		0			0
$355$	12.1291	+	15.3475i	0.643747	+	0.814562i
$356$		0			0
$357$	40.4900	−	2.89590i	2.14296	−	0.153267i
$358$		0			0
$359$	−5.86385	−	12.8400i	−0.309482	−	0.677671i	0.689428	−	0.724354i	$-0.257862\pi$
$359$	−5.86385	−	12.8400i	−0.309482	−	0.677671i	−0.998910	+	0.0466834i	$0.985135\pi$
$360$		0			0
$361$	−15.3955	−	4.52053i	−0.810291	−	0.237923i
$362$		0			0
$363$	19.4443	+	52.1321i	1.02056	+	2.73623i
$364$		0			0
$365$	8.42629	+	12.3857i	0.441052	+	0.648298i
$366$		0			0
$367$	12.8544	−	12.8544i	0.670994	−	0.670994i	−0.286951	−	0.957945i	$-0.592642\pi$
$367$	12.8544	−	12.8544i	0.670994	−	0.670994i	0.957945	+	0.286951i	$0.0926417\pi$
$368$		0			0
$369$		−	14.1073i		−	0.734397i
$370$		0			0
$371$	−20.9809	−	13.4836i	−1.08927	−	0.700034i
$372$		0			0
$373$	−26.9512	+	10.0523i	−1.39548	+	0.520487i	−0.930975	−	0.365084i	$-0.881040\pi$
$373$	−26.9512	+	10.0523i	−1.39548	+	0.520487i	−0.464504	+	0.885571i	$0.653768\pi$
$374$		0			0
$375$	−26.5256	+	2.08914i	−1.36978	+	0.107883i
$376$		0			0
$377$	−6.41297	+	17.1938i	−0.330285	+	0.885528i
$378$		0			0
$379$	−2.59378	+	2.99339i	−0.133234	+	0.153760i	−0.818446	−	0.574584i	$-0.805164\pi$
$379$	−2.59378	+	2.99339i	−0.133234	+	0.153760i	0.685212	+	0.728344i	$0.259709\pi$
$380$		0			0
$381$	−5.89102	+	1.72976i	−0.301806	+	0.0886183i
$382$		0			0
$383$	−17.8853	−	3.89071i	−0.913896	−	0.198806i	−0.269057	−	0.963124i	$-0.586712\pi$
$383$	−17.8853	−	3.89071i	−0.913896	−	0.198806i	−0.644839	+	0.764319i	$0.723076\pi$
$384$		0			0
$385$	−37.0695	−	9.83749i	−1.88924	−	0.501365i
$386$		0			0
$387$	−2.25765	−	3.01587i	−0.114763	−	0.153305i
$388$		0			0
$389$	−0.808845	−	0.933457i	−0.0410101	−	0.0473281i	0.734874	−	0.678204i	$-0.237241\pi$
$389$	−0.808845	−	0.933457i	−0.0410101	−	0.0473281i	−0.775884	+	0.630876i	$0.782696\pi$
$390$		0			0
$391$	10.3353	−	25.9844i	0.522680	−	1.31409i
$392$		0			0
$393$	−5.90487	−	0.422324i	−0.297861	−	0.0213035i
$394$		0			0
$395$	15.1035	−	3.70245i	0.759938	−	0.186291i
$396$		0			0
$397$	1.11914	−	1.49500i	0.0561681	−	0.0750318i	−0.771578	−	0.636135i	$-0.780532\pi$
$397$	1.11914	−	1.49500i	0.0561681	−	0.0750318i	0.827746	+	0.561103i	$0.189623\pi$
$398$		0			0
$399$	−22.2812	−	34.6702i	−1.11546	−	1.73568i
$400$		0			0
$401$	−8.68799	−	29.5886i	−0.433857	−	1.47758i	−0.829149	−	0.559027i	$-0.811175\pi$
$401$	−8.68799	−	29.5886i	−0.433857	−	1.47758i	0.395292	−	0.918556i	$-0.370643\pi$
$402$		0			0
$403$	1.84963	+	25.8612i	0.0921367	+	1.28824i
$404$		0			0
$405$	15.2311	−	16.0508i	0.756838	−	0.797571i
$406$		0			0
$407$	9.69165	+	17.7489i	0.480397	+	0.879782i
$408$		0			0
$409$	−0.00798001	−	0.00364435i	−0.000394586	−	0.000180201i	0.415218	−	0.909722i	$-0.363705\pi$
$409$	−0.00798001	−	0.00364435i	−0.000394586	−	0.000180201i	−0.415612	+	0.909542i	$0.636433\pi$
$410$		0			0
$411$	−18.5893	+	28.9256i	−0.916945	+	1.42679i
$412$		0			0
$413$	11.9459	+	11.9459i	0.587819	+	0.587819i
$414$		0			0
$415$	−3.96441	+	9.31950i	−0.194605	+	0.457476i
$416$		0			0
$417$	−8.02694	−	36.8992i	−0.393081	−	1.80696i
$418$		0			0
$419$	−9.87018	+	21.6127i	−0.482190	+	1.05585i	0.499666	+	0.866218i	$0.333456\pi$
$419$	−9.87018	+	21.6127i	−0.482190	+	1.05585i	−0.981856	+	0.189630i	$0.939271\pi$
$420$		0			0
$421$	−2.62893	+	8.95332i	−0.128126	+	0.436358i	−0.998421	−	0.0561732i	$-0.982110\pi$
$421$	−2.62893	+	8.95332i	−0.128126	+	0.436358i	0.870295	+	0.492531i	$0.163928\pi$
$422$		0			0
$423$	−29.3881	−	10.9612i	−1.42890	−	0.532952i
$424$		0			0
$425$	−21.6671	−	19.5076i	−1.05101	−	0.946259i
$426$		0			0
$427$	7.10421	+	3.87919i	0.343797	+	0.187727i
$428$		0			0
$429$	66.4955	−	42.7341i	3.21043	−	2.06322i
$430$		0			0
$431$	14.2376	−	2.04706i	0.685802	−	0.0986035i	0.209399	−	0.977830i	$-0.432849\pi$
$431$	14.2376	−	2.04706i	0.685802	−	0.0986035i	0.476403	+	0.879227i	$0.341940\pi$
$432$		0			0
$433$	5.55902	−	4.16143i	0.267149	−	0.199985i	−0.457302	−	0.889311i	$-0.651184\pi$
$433$	5.55902	−	4.16143i	0.267149	−	0.199985i	0.724451	+	0.689326i	$0.242093\pi$
$434$		0			0
$435$	−16.4086	+	5.28868i	−0.786731	+	0.253573i
$436$		0			0
$437$	−28.1826	+	3.43349i	−1.34816	+	0.164246i
$438$		0			0
$439$	−22.9269	+	19.8663i	−1.09424	+	0.948167i	−0.998882	−	0.0472763i	$-0.984946\pi$
$439$	−22.9269	+	19.8663i	−1.09424	+	0.948167i	−0.0953606	+	0.995443i	$0.530400\pi$
$440$		0			0
$441$	0.590247	−	4.10526i	0.0281070	−	0.195489i
$442$		0			0
$443$	13.0401	+	9.76168i	0.619553	+	0.463792i	0.862369	−	0.506281i	$-0.168980\pi$
$443$	13.0401	+	9.76168i	0.619553	+	0.463792i	−0.242816	+	0.970072i	$0.578071\pi$
$444$		0			0
$445$	−5.76366	−	4.08348i	−0.273224	−	0.193575i
$446$		0			0
$447$	5.26779	−	9.64725i	0.249158	−	0.456299i
$448$		0			0
$449$	8.31490	+	7.20490i	0.392404	+	0.340020i	0.828610	−	0.559827i	$-0.189132\pi$
$449$	8.31490	+	7.20490i	0.392404	+	0.340020i	−0.436205	+	0.899847i	$0.643678\pi$
$450$		0			0
$451$	−28.2462	+	12.8996i	−1.33006	+	0.607419i
$452$		0			0
$453$	−36.6767	+	20.0270i	−1.72322	+	0.940950i
$454$		0			0
$455$	−1.67420	+	37.0138i	−0.0784875	+	1.73523i
$456$		0			0
$457$	−19.0656	+	4.14746i	−0.891850	+	0.194010i	−0.635065	−	0.772458i	$-0.719027\pi$
$457$	−19.0656	+	4.14746i	−0.891850	+	0.194010i	−0.256785	+	0.966469i	$0.582663\pi$
$458$		0			0
$459$	4.66560			0.217772
$460$		0			0
$461$	−15.3404			−0.714473			−0.357236	−	0.934014i	$-0.616281\pi$
$461$	−15.3404			−0.714473			−0.357236	+	0.934014i	$0.616281\pi$
$462$		0			0
$463$	−11.6770	+	2.54018i	−0.542677	+	0.118052i	−0.475544	−	0.879692i	$-0.657749\pi$
$463$	−11.6770	+	2.54018i	−0.542677	+	0.118052i	−0.0671329	+	0.997744i	$0.521385\pi$
$464$		0			0
$465$	−17.9840	+	16.4275i	−0.833989	+	0.761809i
$466$		0			0
$467$	21.9622	−	11.9922i	1.01629	−	0.554935i	0.117386	−	0.993086i	$-0.462548\pi$
$467$	21.9622	−	11.9922i	1.01629	−	0.554935i	0.898901	+	0.438151i	$0.144367\pi$
$468$		0			0
$469$	−24.1136	+	11.0123i	−1.11346	+	0.508502i
$470$		0			0
$471$	−16.8625	−	14.6114i	−0.776982	−	0.673259i
$472$		0			0
$473$	−3.97411	+	7.27804i	−0.182730	+	0.334644i
$474$		0			0
$475$	−6.84027	+	28.7984i	−0.313853	+	1.32136i
$476$		0			0
$477$	18.1811	+	13.6102i	0.832456	+	0.623169i
$478$		0			0
$479$	5.31849	−	36.9909i	0.243008	−	1.69016i	−0.393850	−	0.919175i	$-0.628857\pi$
$479$	5.31849	−	36.9909i	0.243008	−	1.69016i	0.636857	−	0.770982i	$-0.280234\pi$
$480$		0			0
$481$	14.7648	−	12.7938i	0.673216	−	0.583345i
$482$		0			0
$483$	−27.6912	−	18.6519i	−1.25999	−	0.848691i
$484$		0			0
$485$	2.95431	+	9.16599i	0.134148	+	0.416206i
$486$		0			0
$487$	−20.9391	+	15.6748i	−0.948843	+	0.710295i	−0.957126	−	0.289671i	$-0.906454\pi$
$487$	−20.9391	+	15.6748i	−0.948843	+	0.710295i	0.00828364	+	0.999966i	$0.497363\pi$
$488$		0			0
$489$	−5.57848	+	0.802065i	−0.252268	+	0.0362706i
$490$		0			0
$491$	−28.9981	+	18.6359i	−1.30866	+	0.841028i	−0.994127	−	0.108217i	$-0.965486\pi$
$491$	−28.9981	+	18.6359i	−1.30866	+	0.841028i	−0.314537	+	0.949245i	$0.601849\pi$
$492$		0			0
$493$	−16.5795	−	9.05311i	−0.746704	−	0.407731i
$494$		0			0
$495$	33.0313	+	11.3436i	1.48465	+	0.509856i
$496$		0			0
$497$	23.9772	+	8.94305i	1.07553	+	0.401151i
$498$		0			0
$499$	8.46216	−	28.8195i	0.378818	−	1.29014i	−0.520882	−	0.853629i	$-0.674397\pi$
$499$	8.46216	−	28.8195i	0.378818	−	1.29014i	0.899700	−	0.436508i	$-0.143785\pi$
$500$		0			0
$501$	−4.34726	+	9.51918i	−0.194221	+	0.425286i
$502$		0			0
$503$	−4.46216	−	20.5122i	−0.198958	−	0.914595i	−0.963015	−	0.269447i	$-0.913159\pi$
$503$	−4.46216	−	20.5122i	−0.198958	−	0.914595i	0.764057	−	0.645149i	$-0.223205\pi$
$504$		0			0
$505$	−14.6930	−	36.4477i	−0.653830	−	1.62190i
$506$		0			0
$507$	−32.1195	−	32.1195i	−1.42648	−	1.42648i
$508$		0			0
$509$	−9.78297	+	15.2226i	−0.433622	+	0.674730i	−0.987455	−	0.157898i	$-0.949528\pi$
$509$	−9.78297	+	15.2226i	−0.433622	+	0.674730i	0.553833	+	0.832628i	$0.313165\pi$
$510$		0			0
$511$	17.8263	+	8.14099i	0.788588	+	0.360136i
$512$		0			0
$513$	−2.27009	−	4.15736i	−0.100227	−	0.183552i
$514$		0			0
$515$	22.3290	−	0.585131i	0.983933	−	0.0257840i
$516$		0			0
$517$	4.92531	+	68.8649i	0.216615	+	3.02867i
$518$		0			0
$519$	17.1364	+	58.3611i	0.752203	+	2.56177i
$520$		0			0
$521$	−5.73765	−	8.92795i	−0.251371	−	0.391141i	0.692520	−	0.721399i	$-0.256501\pi$
$521$	−5.73765	−	8.92795i	−0.251371	−	0.391141i	−0.943891	+	0.330258i	$0.892864\pi$
$522$		0			0
$523$	−5.25485	+	7.01965i	−0.229778	+	0.306948i	−0.900581	−	0.434688i	$-0.856859\pi$
$523$	−5.25485	+	7.01965i	−0.229778	+	0.306948i	0.670803	+	0.741636i	$0.265950\pi$
$524$		0			0
$525$	−28.2569	+	20.3267i	−1.23323	+	0.887128i
$526$		0			0
$527$	−26.6213	−	1.90399i	−1.15964	−	0.0829391i
$528$		0			0
$529$	−19.8670	+	11.5888i	−0.863784	+	0.503863i
$530$		0			0
$531$	−10.0745	−	11.6265i	−0.437194	−	0.504549i
$532$		0			0
$533$	17.9777	+	24.0154i	0.778702	+	1.04022i
$534$		0			0
$535$	2.49307	−	9.39437i	0.107785	−	0.406154i
$536$		0			0
$537$	−38.2464	−	8.32000i	−1.65045	−	0.359034i
$538$		0			0
$539$	−8.75943	+	2.57200i	−0.377295	+	0.110784i
$540$		0			0
$541$	−7.68149	+	8.86492i	−0.330253	+	0.381133i	−0.896455	−	0.443134i	$-0.853867\pi$
$541$	−7.68149	+	8.86492i	−0.330253	+	0.381133i	0.566202	+	0.824266i	$0.308412\pi$
$542$		0			0
$543$	−2.76497	+	7.41317i	−0.118656	+	0.318130i
$544$		0			0
$545$	−1.55431	−	15.8749i	−0.0665792	−	0.680005i
$546$		0			0
$547$	−9.61125	+	3.58481i	−0.410947	+	0.153275i	−0.546431	−	0.837504i	$-0.684014\pi$
$547$	−9.61125	+	3.58481i	−0.410947	+	0.153275i	0.135484	+	0.990780i	$0.456741\pi$
$548$		0			0
$549$	−6.20078	−	3.98500i	−0.264643	−	0.170076i
$550$		0			0
$551$			19.1783i			0.817024i
$552$		0			0
$553$	14.3850	−	14.3850i	0.611712	−	0.611712i
$554$		0			0
$555$	18.0304	+	3.43023i	0.765347	+	0.145605i
$556$		0			0
$557$	−3.67471	−	9.85229i	−0.155703	−	0.417455i	0.835553	−	0.549410i	$-0.185147\pi$
$557$	−3.67471	−	9.85229i	−0.155703	−	0.417455i	−0.991256	+	0.131955i	$0.957875\pi$
$558$		0			0
$559$	7.68657	+	2.25698i	0.325107	+	0.0954601i
$560$		0			0
$561$	33.8008	+	74.0135i	1.42707	+	3.12485i
$562$		0			0
$563$	−21.7717	+	1.55715i	−0.917570	+	0.0656259i	−0.522130	−	0.852866i	$-0.674862\pi$
$563$	−21.7717	+	1.55715i	−0.917570	+	0.0656259i	−0.395440	+	0.918492i	$0.629408\pi$
$564$		0			0
$565$	3.60748	−	30.7984i	0.151768	−	1.29570i
$566$		0			0
$567$	6.15311	−	28.2854i	0.258406	−	1.18787i
$568$		0			0
$569$	−1.27065	−	8.83755i	−0.0532683	−	0.370489i	−0.998967	−	0.0454443i	$-0.985530\pi$
$569$	−1.27065	−	8.83755i	−0.0532683	−	0.370489i	0.945699	−	0.325045i	$-0.105379\pi$
$570$		0			0
$571$	8.13975	+	1.17032i	0.340638	+	0.0489763i	0.310511	−	0.950570i	$-0.399500\pi$
$571$	8.13975	+	1.17032i	0.340638	+	0.0489763i	0.0301267	+	0.999546i	$0.490409\pi$
$572$		0			0
$573$	2.41678	−	33.7910i	0.100962	−	1.41164i
$574$		0			0
$575$	4.14263	+	23.6186i	0.172760	+	0.984964i
$576$		0			0
$577$	2.76802	−	38.7020i	0.115234	−	1.61118i	−0.530543	−	0.847658i	$-0.678012\pi$
$577$	2.76802	−	38.7020i	0.115234	−	1.61118i	0.645777	−	0.763526i	$-0.276534\pi$
$578$		0			0
$579$	36.1999	+	5.20476i	1.50442	+	0.216302i
$580$		0			0
$581$	1.88554	+	13.1142i	0.0782252	+	0.544068i
$582$		0			0
$583$	10.6262	−	48.8480i	0.440094	−	2.02308i
$584$		0			0
$585$	3.92521	−	33.5110i	0.162288	−	1.38551i
$586$		0			0
$587$	−25.0511	+	1.79169i	−1.03397	+	0.0739509i	−0.577993	−	0.816041i	$-0.696164\pi$
$587$	−25.0511	+	1.79169i	−1.03397	+	0.0739509i	−0.455976	+	0.889992i	$0.650710\pi$
$588$		0			0
$589$	11.2562	+	24.6477i	0.463805	+	1.01559i
$590$		0			0
$591$	29.2947	+	8.60170i	1.20502	+	0.353827i
$592$		0			0
$593$	−12.9094	−	34.6116i	−0.530128	−	1.42133i	−0.875664	−	0.482921i	$-0.839576\pi$
$593$	−12.9094	−	34.6116i	−0.530128	−	1.42133i	0.345536	−	0.938405i	$-0.387697\pi$
$594$		0			0
$595$	−37.4685	−	7.12828i	−1.53606	−	0.292231i
$596$		0			0
$597$	35.5189	−	35.5189i	1.45369	−	1.45369i
$598$		0			0
$599$		−	0.665753i		−	0.0272019i	−0.999908	−	0.0136010i	$-0.995671\pi$
$599$		−	0.665753i		−	0.0272019i	0.999908	−	0.0136010i	$-0.00432945\pi$
$600$		0			0
$601$	−5.63494	−	3.62136i	−0.229854	−	0.147718i	0.420645	−	0.907225i	$-0.361804\pi$
$601$	−5.63494	−	3.62136i	−0.229854	−	0.147718i	−0.650499	+	0.759507i	$0.725440\pi$
$602$		0			0
$603$	22.6179	−	8.43604i	0.921072	−	0.343542i
$604$		0			0
$605$	−5.09419	−	52.0294i	−0.207108	−	2.11530i
$606$		0			0
$607$	3.88059	−	10.4043i	0.157508	−	0.422296i	−0.834094	−	0.551623i	$-0.814009\pi$
$607$	3.88059	−	10.4043i	0.157508	−	0.422296i	0.991602	+	0.129327i	$0.0412816\pi$
$608$		0			0
$609$	−14.7692	+	17.0446i	−0.598479	+	0.690681i
$610$		0			0
$611$	63.9970	−	18.7912i	2.58904	−	0.760212i
$612$		0			0
$613$	16.8656	+	3.66890i	0.681197	+	0.148185i	0.539833	−	0.841772i	$-0.318488\pi$
$613$	16.8656	+	3.66890i	0.681197	+	0.148185i	0.141364	+	0.989958i	$0.454851\pi$
$614$		0			0
$615$	−7.22890	+	27.2398i	−0.291497	+	1.09842i
$616$		0			0
$617$	29.3760	+	39.2417i	1.18263	+	1.57981i	0.721372	+	0.692548i	$0.243512\pi$
$617$	29.3760	+	39.2417i	1.18263	+	1.57981i	0.461261	+	0.887264i	$0.347397\pi$
$618$		0			0
$619$	8.65354	+	9.98671i	0.347815	+	0.401400i	0.902521	−	0.430647i	$-0.141715\pi$
$619$	8.65354	+	9.98671i	0.347815	+	0.401400i	−0.554706	+	0.832047i	$0.687169\pi$
$620$		0			0
$621$	−3.02164	−	2.36534i	−0.121254	−	0.0949179i
$622$		0			0
$623$	−9.21710	−	0.659220i	−0.369275	−	0.0264111i
$624$		0			0
$625$	24.5925	+	4.49550i	0.983700	+	0.179820i
$626$		0			0
$627$	49.5048	−	66.1307i	1.97703	−	2.64101i
$628$		0			0
$629$	10.8727	+	16.9183i	0.433523	+	0.674575i
$630$		0			0
$631$	−5.05848	−	17.2276i	−0.201375	−	0.685820i	−0.996812	−	0.0797839i	$-0.974577\pi$
$631$	−5.05848	−	17.2276i	−0.201375	−	0.685820i	0.795437	−	0.606036i	$-0.207241\pi$
$632$		0			0
$633$	3.07131	+	42.9425i	0.122073	+	1.70681i
$634$		0			0
$635$	5.76675	−	0.151118i	0.228847	−	0.00599692i
$636$		0			0
$637$	4.22676	+	7.74073i	0.167470	+	0.306699i
$638$		0			0
$639$	−21.1977	−	9.68065i	−0.838567	−	0.382961i
$640$		0			0
$641$	10.3027	−	16.0313i	0.406931	−	0.633197i	−0.575940	−	0.817492i	$-0.695364\pi$
$641$	10.3027	−	16.0313i	0.406931	−	0.633197i	0.982871	+	0.184295i	$0.0590002\pi$
$642$		0			0
$643$	−2.97346	−	2.97346i	−0.117262	−	0.117262i	0.646041	−	0.763303i	$-0.276423\pi$
$643$	−2.97346	−	2.97346i	−0.117262	−	0.117262i	−0.763303	+	0.646041i	$0.776423\pi$
$644$		0			0
$645$	2.81390	+	6.98021i	0.110797	+	0.274846i
$646$		0			0
$647$	−4.52826	−	20.8161i	−0.178024	−	0.818364i	−0.976360	−	0.216151i	$-0.930650\pi$
$647$	−4.52826	−	20.8161i	−0.178024	−	0.818364i	0.798336	−	0.602213i	$-0.205714\pi$
$648$		0			0
$649$	−14.0671	+	30.8027i	−0.552183	+	1.20911i
$650$		0			0
$651$	−8.97730	+	30.5739i	−0.351848	+	1.19828i
$652$		0			0
$653$	−1.55480	−	0.579910i	−0.0608440	−	0.0226936i	0.318858	−	0.947803i	$-0.396701\pi$
$653$	−1.55480	−	0.579910i	−0.0608440	−	0.0226936i	−0.379702	+	0.925109i	$0.623973\pi$
$654$		0			0
$655$	5.26067	+	1.80661i	0.205551	+	0.0705903i
$656$		0			0
$657$	−15.6628	−	8.55255i	−0.611065	−	0.333667i
$658$		0			0
$659$	0.786119	−	0.505208i	0.0306228	−	0.0196801i	−0.525240	−	0.850954i	$-0.676024\pi$
$659$	0.786119	−	0.505208i	0.0306228	−	0.0196801i	0.555863	+	0.831274i	$0.312388\pi$
$660$		0			0
$661$	−2.23118	+	0.320795i	−0.0867829	+	0.0124775i	−0.185569	−	0.982631i	$-0.559413\pi$
$661$	−2.23118	+	0.320795i	−0.0867829	+	0.0124775i	0.0987866	+	0.995109i	$0.468504\pi$
$662$		0			0
$663$	62.9276	−	47.1070i	2.44391	−	1.82949i
$664$		0			0
$665$	11.8789	+	36.8553i	0.460643	+	1.42919i
$666$		0			0
$667$	6.14790	+	14.2686i	0.238048	+	0.552481i
$668$		0			0
$669$	−24.7094	+	21.4108i	−0.955319	+	0.827789i
$670$		0			0
$671$	−2.30898	+	16.0593i	−0.0891370	+	0.619962i
$672$		0			0
$673$	21.4532	+	16.0596i	0.826959	+	0.619054i	0.926633	−	0.375966i	$-0.122689\pi$
$673$	21.4532	+	16.0596i	0.826959	+	0.619054i	−0.0996744	+	0.995020i	$0.531780\pi$
$674$		0			0
$675$	−3.40609	+	2.09860i	−0.131101	+	0.0807752i
$676$		0			0
$677$	21.5333	−	39.4354i	0.827593	−	1.51562i	−0.0289688	−	0.999580i	$-0.509222\pi$
$677$	21.5333	−	39.4354i	0.827593	−	1.51562i	0.856562	−	0.516044i	$-0.172596\pi$
$678$		0			0
$679$	9.52127	+	8.25022i	0.365393	+	0.316615i
$680$		0			0
$681$	25.7734	−	11.7703i	0.987640	−	0.451040i
$682$		0			0
$683$	−33.5770	+	18.3344i	−1.28479	+	0.701547i	−0.968948	−	0.247266i	$-0.920468\pi$
$683$	−33.5770	+	18.3344i	−1.28479	+	0.701547i	−0.315840	+	0.948813i	$0.602286\pi$
$684$		0			0
$685$	23.8529	−	21.7884i	0.911371	−	0.832493i
$686$		0			0
$687$	13.5798	−	2.95410i	0.518101	−	0.112706i
$688$		0			0
$689$	−48.2947			−1.83988
$690$		0			0
$691$	−2.57647			−0.0980137			−0.0490069	−	0.998798i	$-0.515606\pi$
$691$	−2.57647			−0.0980137			−0.0490069	+	0.998798i	$0.515606\pi$
$692$		0			0
$693$	44.6447	−	9.71186i	1.69591	−	0.368923i
$694$		0			0
$695$	−1.60320	+	35.4442i	−0.0608128	+	1.34448i
$696$		0			0
$697$	−27.1033	+	14.7995i	−1.02661	+	0.560572i
$698$		0			0
$699$	−0.114791	+	0.0524233i	−0.00434179	+	0.00198283i
$700$		0			0
$701$	−5.19507	−	4.50156i	−0.196215	−	0.170021i	0.551212	−	0.834365i	$-0.314166\pi$
$701$	−5.19507	−	4.50156i	−0.196215	−	0.170021i	−0.747427	+	0.664344i	$0.768711\pi$
$702$		0			0
$703$	9.78507	−	17.9200i	0.369051	−	0.675866i
$704$		0			0
$705$	51.1289	+	36.2241i	1.92562	+	1.36428i
$706$		0			0
$707$	−41.1555	−	30.8086i	−1.54781	−	1.15868i
$708$		0			0
$709$	2.82637	−	19.6578i	0.106147	−	0.738265i	−0.865343	−	0.501181i	$-0.832899\pi$
$709$	2.82637	−	19.6578i	0.106147	−	0.738265i	0.971489	−	0.237084i	$-0.0761918\pi$
$710$		0			0
$711$	−14.0004	+	12.1314i	−0.525057	+	0.454965i
$712$		0			0
$713$	16.2758	+	14.7294i	0.609532	+	0.551621i
$714$		0			0
$715$	−70.6863	+	22.7830i	−2.64352	+	0.852036i
$716$		0			0
$717$	−33.1330	+	24.8031i	−1.23737	+	0.926287i
$718$		0			0
$719$	−25.4613	+	3.66078i	−0.949546	+	0.136524i	−0.599648	−	0.800264i	$-0.704693\pi$
$719$	−25.4613	+	3.66078i	−0.949546	+	0.136524i	−0.349898	+	0.936788i	$0.613784\pi$
$720$		0			0
$721$	24.5822	−	15.7980i	0.915488	−	0.588348i
$722$		0			0
$723$	0.375822	+	0.205214i	0.0139770	+	0.00763200i
$724$		0			0
$725$	16.1759	−	0.848361i	0.600757	−	0.0315073i
$726$		0			0
$727$	5.39747	+	2.01315i	0.200181	+	0.0746636i	0.447555	−	0.894256i	$-0.352295\pi$
$727$	5.39747	+	2.01315i	0.200181	+	0.0746636i	−0.247374	+	0.968920i	$0.579568\pi$
$728$		0			0
$729$	−5.81696	+	19.8107i	−0.215443	+	0.733731i
$730$		0			0
$731$	−3.42573	+	7.50130i	−0.126705	+	0.277446i
$732$		0			0
$733$	7.32241	+	33.6606i	0.270459	+	1.24328i	0.889138	+	0.457638i	$0.151305\pi$
$733$	7.32241	+	33.6606i	0.270459	+	1.24328i	−0.618679	+	0.785644i	$0.712332\pi$
$734$		0			0
$735$	−3.24334	+	7.62440i	−0.119632	+	0.281230i
$736$		0			0
$737$	−37.5726	−	37.5726i	−1.38400	−	1.38400i
$738$		0			0
$739$	−4.97118	+	7.73530i	−0.182868	+	0.284548i	−0.920569	−	0.390579i	$-0.872275\pi$
$739$	−4.97118	+	7.73530i	−0.182868	+	0.284548i	0.737702	+	0.675127i	$0.235911\pi$
$740$		0			0
$741$	−72.5935	−	33.1523i	−2.66679	−	1.21788i
$742$		0			0
$743$	21.3622	+	39.1219i	0.783702	+	1.43524i	0.897162	+	0.441701i	$0.145625\pi$
$743$	21.3622	+	39.1219i	0.783702	+	1.43524i	−0.113460	+	0.993543i	$0.536193\pi$
$744$		0			0
$745$	−7.10890	+	7.49151i	−0.260450	+	0.274468i
$746$		0			0
$747$	−0.860701	−	12.0342i	−0.0314914	−	0.440307i
$748$		0			0
$749$	−3.58227	−	12.2001i	−0.130893	−	0.445782i
$750$		0			0
$751$	7.47763	+	11.6354i	0.272863	+	0.424583i	0.950458	−	0.310852i	$-0.100614\pi$
$751$	7.47763	+	11.6354i	0.272863	+	0.424583i	−0.677596	+	0.735435i	$0.736978\pi$
$752$		0			0
$753$	28.5198	−	38.0980i	1.03932	−	1.38837i
$754$		0			0
$755$	38.1341	−	9.34816i	1.38784	−	0.340215i
$756$		0			0
$757$	−23.2469	−	1.66265i	−0.844923	−	0.0604301i	−0.357837	−	0.933784i	$-0.616486\pi$
$757$	−23.2469	−	1.66265i	−0.844923	−	0.0604301i	−0.487086	+	0.873354i	$0.661940\pi$
$758$		0			0
$759$	15.6321	−	65.0704i	0.567410	−	2.36191i
$760$		0			0
$761$	21.8328	+	25.1964i	0.791439	+	0.913370i	0.997879	−	0.0650894i	$-0.0207333\pi$
$761$	21.8328	+	25.1964i	0.791439	+	0.913370i	−0.206440	+	0.978459i	$0.566188\pi$
$762$		0			0
$763$	−12.5050	−	16.7048i	−0.452713	−	0.604754i
$764$		0			0
$765$	33.5698	+	8.90873i	1.21372	+	0.322096i
$766$		0			0
$767$	31.9665	+	6.95389i	1.15424	+	0.251090i
$768$		0			0
$769$	8.48528	−	2.49150i	0.305987	−	0.0898459i	−0.125134	−	0.992140i	$-0.539936\pi$
$769$	8.48528	−	2.49150i	0.305987	−	0.0898459i	0.431122	+	0.902294i	$0.358118\pi$
$770$		0			0
$771$	20.8426	−	24.0536i	0.750628	−	0.866271i
$772$		0			0
$773$	10.6902	−	28.6616i	0.384501	−	1.03089i	−0.590177	−	0.807274i	$-0.700942\pi$
$773$	10.6902	−	28.6616i	0.384501	−	1.03089i	0.974678	−	0.223613i	$-0.0717851\pi$
$774$		0			0
$775$	20.2911	−	10.5843i	0.728878	−	0.380200i
$776$		0			0
$777$	22.4966	−	8.39080i	0.807061	−	0.301018i
$778$		0			0
$779$	26.3747	+	16.9500i	0.944971	+	0.607296i
$780$		0			0
$781$			51.2947i			1.83547i
$782$		0			0
$783$	−1.83293	+	1.83293i	−0.0655035	+	0.0655035i
$784$		0			0
$785$	11.7921	+	17.3331i	0.420879	+	0.618645i
$786$		0			0
$787$	6.24284	+	16.7377i	0.222533	+	0.596635i	0.999457	−	0.0329604i	$-0.0104935\pi$
$787$	6.24284	+	16.7377i	0.222533	+	0.596635i	−0.776923	+	0.629595i	$0.783221\pi$
$788$		0			0
$789$	−37.0779	−	10.8870i	−1.32001	−	0.387589i
$790$		0			0
$791$	−16.8518	−	36.9002i	−0.599180	−	1.31202i
$792$		0			0
$793$	15.6341	−	1.11818i	0.555184	−	0.0397076i
$794$		0			0
$795$	−28.1318	−	35.5964i	−0.997732	−	1.26247i
$796$		0			0
$797$	−8.47094	+	38.9403i	−0.300056	+	1.37934i	0.542196	+	0.840252i	$0.317593\pi$
$797$	−8.47094	+	38.9403i	−0.300056	+	1.37934i	−0.842252	+	0.539084i	$0.818771\pi$
$798$		0			0
$799$	9.77120	+	67.9602i	0.345680	+	2.40426i
$800$		0			0
$801$	8.32910	+	1.19754i	0.294294	+	0.0423131i
$802$		0			0
$803$	−2.80229	+	39.1811i	−0.0988905	+	1.38267i
$804$		0			0
$805$	20.6523	+	23.6122i	0.727899	+	0.832220i
$806$		0			0
$807$	3.37740	−	47.2223i	0.118890	−	1.66230i
$808$		0			0
$809$	−43.9499	−	6.31905i	−1.54520	−	0.222166i	−0.683637	−	0.729822i	$-0.739603\pi$
$809$	−43.9499	−	6.31905i	−1.54520	−	0.222166i	−0.861560	+	0.507656i	$0.830512\pi$
$810$		0			0
$811$	−6.14511	−	42.7402i	−0.215784	−	1.50081i	−0.753367	−	0.657600i	$-0.771572\pi$
$811$	−6.14511	−	42.7402i	−0.215784	−	1.50081i	0.537583	−	0.843211i	$-0.319337\pi$
$812$		0			0
$813$	−2.33293	+	10.7243i	−0.0818194	+	0.376118i
$814$		0			0
$815$	5.25935	+	0.616038i	0.184227	+	0.0215789i
$816$		0			0
$817$	8.35097	−	0.597273i	0.292163	−	0.0208959i
$818$		0			0
$819$	−18.3360	−	40.1502i	−0.640712	−	1.40296i
$820$		0			0
$821$	−28.5262	−	8.37604i	−0.995570	−	0.292326i	−0.256933	−	0.966429i	$-0.582712\pi$
$821$	−28.5262	−	8.37604i	−0.995570	−	0.292326i	−0.738637	+	0.674103i	$0.764530\pi$
$822$		0			0
$823$	−7.81268	−	20.9466i	−0.272333	−	0.730153i	−0.999065	−	0.0432320i	$-0.986235\pi$
$823$	−7.81268	−	20.9466i	−0.272333	−	0.730153i	0.726732	−	0.686921i	$-0.241038\pi$
$824$		0			0
$825$	−57.9676	−	38.8293i	−2.01817	−	1.35186i
$826$		0			0
$827$	−12.8301	+	12.8301i	−0.446147	+	0.446147i	−0.894072	−	0.447924i	$-0.852163\pi$
$827$	−12.8301	+	12.8301i	−0.446147	+	0.446147i	0.447924	+	0.894072i	$0.352163\pi$
$828$		0			0
$829$		−	12.6212i		−	0.438352i	−0.975685	−	0.219176i	$-0.929663\pi$
$829$		−	12.6212i		−	0.438352i	0.975685	−	0.219176i	$-0.0703369\pi$
$830$		0			0
$831$	−9.96696	−	6.40537i	−0.345750	−	0.222200i
$832$		0			0
$833$	−8.50633	+	3.17270i	−0.294727	+	0.109927i
$834$		0			0
$835$	6.24207	−	7.59705i	0.216016	−	0.262907i
$836$		0			0
$837$	−1.27986	+	3.43144i	−0.0442385	+	0.118608i
$838$		0			0
$839$	−14.4886	+	16.7207i	−0.500201	+	0.577263i	−0.948563	−	0.316590i	$-0.897462\pi$
$839$	−14.4886	+	16.7207i	−0.500201	+	0.577263i	0.448362	+	0.893852i	$0.352008\pi$
$840$		0			0
$841$	−17.7553	+	5.21342i	−0.612251	+	0.179773i
$842$		0			0
$843$	−0.666659	−	0.145023i	−0.0229610	−	0.00499485i
$844$		0			0
$845$	21.4281	+	36.9098i	0.737150	+	1.26974i
$846$		0			0
$847$	−40.9849	−	54.7494i	−1.40826	−	1.88121i
$848$		0			0
$849$	32.4663	+	37.4681i	1.11424	+	1.28590i
$850$		0			0
$851$	1.53551	−	16.4692i	0.0526366	−	0.564555i
$852$		0			0
$853$	24.6455	+	1.76268i	0.843848	+	0.0603532i	0.486566	−	0.873644i	$-0.338249\pi$
$853$	24.6455	+	1.76268i	0.843848	+	0.0603532i	0.357281	+	0.933997i	$0.383704\pi$
$854$		0			0
$855$	−8.39540	−	34.2475i	−0.287117	−	1.17124i
$856$		0			0
$857$	24.7961	−	33.1237i	0.847017	−	1.13148i	−0.142886	−	0.989739i	$-0.545638\pi$
$857$	24.7961	−	33.1237i	0.847017	−	1.13148i	0.989903	−	0.141744i	$-0.0452708\pi$
$858$		0			0
$859$	0.923336	+	1.43674i	0.0315038	+	0.0490209i	0.856648	−	0.515901i	$-0.172543\pi$
$859$	0.923336	+	1.43674i	0.0315038	+	0.0490209i	−0.825144	+	0.564922i	$0.808906\pi$
$860$		0			0
$861$	10.3871	+	35.3753i	0.353992	+	1.20559i
$862$		0			0
$863$	−1.29150	−	18.0575i	−0.0439632	−	0.614686i	−0.970903	−	0.239475i	$-0.923025\pi$
$863$	−1.29150	−	18.0575i	−0.0439632	−	0.614686i	0.926939	−	0.375211i	$-0.122430\pi$
$864$		0			0
$865$	−1.49709	−	57.1300i	−0.0509026	−	1.94248i
$866$		0			0
$867$	19.3898	+	35.5098i	0.658513	+	1.20598i
$868$		0			0
$869$	37.0919	+	16.9393i	1.25826	+	0.574627i
$870$		0			0
$871$	−27.7528	+	43.1842i	−0.940369	+	1.46324i
$872$		0			0
$873$	−8.11225	−	8.11225i	−0.274558	−	0.274558i
$874$		0			0
$875$	30.5600	−	11.6495i	1.03312	−	0.393825i
$876$		0			0
$877$	3.17543	+	14.5972i	0.107227	+	0.492913i	0.999169	+	0.0407635i	$0.0129790\pi$
$877$	3.17543	+	14.5972i	0.107227	+	0.492913i	−0.891942	+	0.452150i	$0.850657\pi$
$878$		0			0
$879$	−22.3298	+	48.8955i	−0.753166	+	1.64920i
$880$		0			0
$881$	9.57615	−	32.6134i	0.322629	−	1.09877i	−0.625325	−	0.780364i	$-0.715034\pi$
$881$	9.57615	−	32.6134i	0.322629	−	1.09877i	0.947954	−	0.318408i	$-0.103148\pi$
$882$		0			0
$883$	−25.5280	−	9.52145i	−0.859086	−	0.320422i	−0.118967	−	0.992898i	$-0.537958\pi$
$883$	−25.5280	−	9.52145i	−0.859086	−	0.320422i	−0.740119	+	0.672476i	$0.765231\pi$
$884$		0			0
$885$	13.4951	+	27.6121i	0.453633	+	0.928171i
$886$		0			0
$887$	−39.3825	−	21.5045i	−1.32233	−	0.722049i	−0.345983	−	0.938241i	$-0.612455\pi$
$887$	−39.3825	−	21.5045i	−1.32233	−	0.722049i	−0.976351	+	0.216192i	$0.930636\pi$
$888$		0			0
$889$	6.34867	−	4.08004i	0.212927	−	0.136840i
$890$		0			0
$891$	57.4313	−	8.25737i	1.92402	−	0.276632i
$892$		0			0
$893$	55.8028	−	41.7734i	1.86737	−	1.39789i
$894$		0			0
$895$	32.7280	+	16.7732i	1.09398	+	0.560666i
$896$		0			0
$897$	−64.6366	−	1.39422i	−2.15815	−	0.0465518i
$898$		0			0
$899$	11.2064	−	9.71042i	0.373755	−	0.323861i
$900$		0			0
$901$	7.07505	−	49.2080i	0.235704	−	1.63936i
$902$		0			0
$903$	7.88182	+	5.90025i	0.262290	+	0.196348i
$904$		0			0
$905$	4.29757	−	6.06584i	0.142856	−	0.201635i
$906$		0			0
$907$	−5.20693	+	9.53578i	−0.172893	+	0.316630i	−0.949729	−	0.313073i	$-0.898642\pi$
$907$	−5.20693	+	9.53578i	−0.172893	+	0.316630i	0.776836	+	0.629703i	$0.216823\pi$
$908$		0			0
$909$	35.3803	+	30.6572i	1.17349	+	1.01683i
$910$		0			0
$911$	7.85868	−	3.58894i	0.260370	−	0.118907i	−0.280954	−	0.959721i	$-0.590651\pi$
$911$	7.85868	−	3.58894i	0.260370	−	0.118907i	0.541323	+	0.840814i	$0.317923\pi$
$912$		0			0
$913$	−23.3083	+	12.7273i	−0.771391	+	0.421211i
$914$		0			0
$915$	9.93110	+	10.8721i	0.328312	+	0.359419i
$916$		0			0
$917$	7.11025	−	1.54674i	0.234801	−	0.0510779i
$918$		0			0
$919$	−1.52208			−0.0502089			−0.0251044	−	0.999685i	$-0.507992\pi$
$919$	−1.52208			−0.0502089			−0.0251044	+	0.999685i	$0.507992\pi$
$920$		0			0
$921$	67.8508			2.23576
$922$		0			0
$923$	48.4222	−	10.5336i	1.59384	−	0.346718i
$924$		0			0
$925$	−15.5474	−	7.46049i	−0.511196	−	0.245299i
$926$		0			0
$927$	−23.3544	+	12.7525i	−0.767059	+	0.418846i
$928$		0			0
$929$	−17.5400	+	8.01026i	−0.575470	+	0.262808i	−0.681819	−	0.731521i	$-0.738811\pi$
$929$	−17.5400	+	8.01026i	−0.575470	+	0.262808i	0.106350	+	0.994329i	$0.466084\pi$
$930$		0			0
$931$	6.96591	+	6.03600i	0.228299	+	0.197822i
$932$		0			0
$933$	11.8638	−	21.7269i	0.388402	−	0.711306i
$934$		0			0
$935$	−12.8585	−	75.3608i	−0.420518	−	2.46456i
$936$		0			0
$937$	17.8916	+	13.3935i	0.584495	+	0.437547i	0.850165	−	0.526517i	$-0.176502\pi$
$937$	17.8916	+	13.3935i	0.584495	+	0.437547i	−0.265670	+	0.964064i	$0.585593\pi$
$938$		0			0
$939$	0.424618	−	2.95328i	0.0138569	−	0.0963768i
$940$		0			0
$941$	−31.4711	+	27.2699i	−1.02593	+	0.888972i	−0.993875	−	0.110514i	$-0.964750\pi$
$941$	−31.4711	+	27.2699i	−1.02593	+	0.888972i	−0.0320538	+	0.999486i	$0.510205\pi$
$942$		0			0
$943$	25.0562	+	4.15589i	0.815942	+	0.135335i
$944$		0			0
$945$	−2.38707	+	4.65766i	−0.0776513	+	0.151514i
$946$		0			0
$947$	35.7832	−	26.7870i	1.16280	−	0.870460i	0.169442	−	0.985540i	$-0.445803\pi$
$947$	35.7832	−	26.7870i	1.16280	−	0.870460i	0.993356	+	0.115080i	$0.0367126\pi$
$948$		0			0
$949$	37.5624	−	5.40066i	1.21933	−	0.175313i
$950$		0			0
$951$	−17.4000	+	11.1823i	−0.564235	+	0.362612i
$952$		0			0
$953$	46.0479	+	25.1441i	1.49164	+	0.814496i	0.998462	−	0.0554334i	$-0.0176540\pi$
$953$	46.0479	+	25.1441i	1.49164	+	0.814496i	0.493176	+	0.869930i	$0.335836\pi$
$954$		0			0
$955$	−10.3385	+	30.1045i	−0.334545	+	0.974160i
$956$		0			0
$957$	−42.3559	−	15.7979i	−1.36917	−	0.510675i
$958$		0			0
$959$	11.9069	−	40.5512i	0.384494	−	1.30947i
$960$		0			0
$961$	−4.17481	+	9.14157i	−0.134671	+	0.294889i
$962$		0			0
$963$	2.46123	+	11.3141i	0.0793122	+	0.364592i
$964$		0			0
$965$	−31.6202	−	13.4509i	−1.01789	−	0.433000i
$966$		0			0
$967$	−21.3257	−	21.3257i	−0.685787	−	0.685787i	0.275511	−	0.961298i	$-0.411153\pi$
$967$	−21.3257	−	21.3257i	−0.685787	−	0.685787i	−0.961298	+	0.275511i	$0.911153\pi$
$968$		0			0
$969$	44.4140	−	69.1096i	1.42678	−	2.22012i
$970$		0			0
$971$	3.99847	+	1.82604i	0.128317	+	0.0586004i	0.478539	−	0.878066i	$-0.341167\pi$
$971$	3.99847	+	1.82604i	0.128317	+	0.0586004i	−0.350222	+	0.936667i	$0.613894\pi$
$972$		0			0
$973$	22.2447	+	40.7380i	0.713131	+	1.30600i
$974$		0			0
$975$	−24.7510	+	62.6952i	−0.792667	+	2.00785i
$976$		0			0
$977$	−3.39854	−	47.5177i	−0.108729	−	1.52023i	−0.700227	−	0.713921i	$-0.746918\pi$
$977$	−3.39854	−	47.5177i	−0.108729	−	1.52023i	0.591498	−	0.806307i	$-0.298537\pi$
$978$		0			0
$979$	−5.21829	−	17.7719i	−0.166777	−	0.567992i
$980$		0			0
$981$	10.2732	+	15.9854i	0.327998	+	0.510375i
$982$		0			0
$983$	6.81011	−	9.09725i	0.217209	−	0.290157i	−0.678681	−	0.734433i	$-0.737448\pi$
$983$	6.81011	−	9.09725i	0.217209	−	0.290157i	0.895890	+	0.444276i	$0.146539\pi$
$984$		0			0
$985$	−24.5307	−	14.8716i	−0.781613	−	0.473850i
$986$		0			0
$987$	81.7639	+	5.84787i	2.60257	+	0.186140i
$988$		0			0
$989$	6.02161	−	3.12140i	0.191476	−	0.0992546i
$990$		0			0
$991$	24.8292	+	28.6544i	0.788725	+	0.910238i	0.997707	−	0.0676820i	$-0.0215603\pi$
$991$	24.8292	+	28.6544i	0.788725	+	0.910238i	−0.208982	+	0.977920i	$0.567015\pi$
$992$		0			0
$993$	−7.43449	−	9.93131i	−0.235926	−	0.315161i
$994$		0			0
$995$	−40.8163	+	23.6961i	−1.29396	+	0.751216i
$996$		0			0
$997$	38.4077	+	8.35509i	1.21638	+	0.264608i	0.774564	−	0.632495i	$-0.217969\pi$
$997$	38.4077	+	8.35509i	1.21638	+	0.264608i	0.441820	+	0.897103i	$0.354333\pi$
$998$		0			0
$999$	2.64786	−	0.777481i	0.0837745	−	0.0245984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.217.30	yes	720
5.3	odd	4	inner	920.2.bv.a.33.30	✓	720
23.7	odd	22	inner	920.2.bv.a.697.30	yes	720
115.53	even	44	inner	920.2.bv.a.513.30	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.33.30	✓	720	5.3	odd	4	inner
920.2.bv.a.217.30	yes	720	1.1	even	1	trivial
920.2.bv.a.513.30	yes	720	115.53	even	44	inner
920.2.bv.a.697.30	yes	720	23.7	odd	22	inner

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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(2.32548 - 0.505878i) q^{3} +(-2.23378 - 0.101038i) q^{5} +(-2.56741 + 1.40191i) q^{7} +(2.42307 - 1.10658i) q^{9} +O(q^{10})\)	\(q+(2.32548 - 0.505878i) q^{3} +(-2.23378 - 0.101038i) q^{5} +(-2.56741 + 1.40191i) q^{7} +(2.42307 - 1.10658i) q^{9} +(-4.43127 - 3.83971i) q^{11} +(-2.71471 + 4.97162i) q^{13} +(-5.24574 + 0.895061i) q^{15} +(-4.66794 - 3.49438i) q^{17} +(-0.842493 + 5.85967i) q^{19} +(-5.26128 + 4.55893i) q^{21} +(1.25159 + 4.62963i) q^{23} +(4.97958 + 0.451393i) q^{25} +(-0.640545 + 0.479506i) q^{27} +(3.20665 - 0.461046i) q^{29} +(3.85054 - 2.47459i) q^{31} +(-12.2473 - 6.68751i) q^{33} +(5.87670 - 2.87217i) q^{35} +(-3.23149 - 1.20528i) q^{37} +(-3.79798 + 12.9347i) q^{39} +(2.20002 - 4.81737i) q^{41} +(-0.300622 - 1.38194i) q^{43} +(-5.52442 + 2.22703i) q^{45} +(-8.32609 - 8.32609i) q^{47} +(0.841769 - 1.30982i) q^{49} +(-12.6230 - 5.76471i) q^{51} +(4.08600 + 7.48295i) q^{53} +(9.51053 + 9.02482i) q^{55} +(1.00507 + 14.0528i) q^{57} +(-1.62708 - 5.54134i) q^{59} +(-1.49599 - 2.32780i) q^{61} +(-4.66969 + 6.23798i) q^{63} +(6.56640 - 10.8312i) q^{65} +(9.03916 + 0.646494i) q^{67} +(5.25259 + 10.1330i) q^{69} +(-5.72890 - 6.61151i) q^{71} +(-4.01479 - 5.36313i) q^{73} +(11.8083 - 1.46935i) q^{75} +(16.7598 + 3.64588i) q^{77} +(-6.67276 + 1.95930i) q^{79} +(-6.48024 + 7.47859i) q^{81} +(1.58280 - 4.24366i) q^{83} +(10.0741 + 8.27733i) q^{85} +(7.22378 - 2.69433i) q^{87} +(2.65747 + 1.70785i) q^{89} -16.5700i q^{91} +(7.70253 - 7.70253i) q^{93} +(2.47399 - 13.0041i) q^{95} +(-1.50508 - 4.03527i) q^{97} +(-14.9862 - 4.40034i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 720 * q	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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