LMFDB - Embedded newform 928.2.bn.a.591.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [928,2,Mod(15,928)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(928, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([14, 14, 27]))

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

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

chi := DirichletCharacter("928.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 928 = 2^{5} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	928.bn (of order $28$, degree $12$, not 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:	$7.41011730757$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 232)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			591.8
Character	$\chi$	$=$	928.591
Dual form			928.2.bn.a.559.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.209291 - 1.85751i) q^{3} +(2.36223 + 1.13759i) q^{5} +(-2.31875 - 1.84914i) q^{7} +(-0.481741 + 0.109954i) q^{9} +O(q^{10})$	\(q+(-0.209291 - 1.85751i) q^{3} +(2.36223 + 1.13759i) q^{5} +(-2.31875 - 1.84914i) q^{7} +(-0.481741 + 0.109954i) q^{9} +(3.02984 + 4.82196i) q^{11} +(0.208139 - 0.911918i) q^{13} +(1.61868 - 4.62593i) q^{15} +(1.87453 - 1.87453i) q^{17} +(6.66614 + 0.751093i) q^{19} +(-2.94950 + 4.69411i) q^{21} +(-1.78357 - 3.70363i) q^{23} +(1.16855 + 1.46532i) q^{25} +(-1.54707 - 4.42126i) q^{27} +(0.116624 - 5.38390i) q^{29} +(2.77667 + 7.93528i) q^{31} +(8.32270 - 6.63714i) q^{33} +(-3.37386 - 7.00588i) q^{35} +(3.67558 + 2.30952i) q^{37} +(-1.73745 - 0.195764i) q^{39} +(0.507268 + 0.507268i) q^{41} +(0.761486 - 2.17620i) q^{43} +(-1.26306 - 0.288286i) q^{45} +(-5.28080 - 8.40434i) q^{47} +(0.399638 + 1.75093i) q^{49} +(-3.87428 - 3.08964i) q^{51} +(-2.91924 + 6.06187i) q^{53} +(1.67176 + 14.8373i) q^{55} -12.5396i q^{57} -11.7585 q^{59} +(-5.72525 + 0.645081i) q^{61} +(1.32036 + 0.635852i) q^{63} +(1.52906 - 1.91738i) q^{65} +(14.0788 - 3.21338i) q^{67} +(-6.50622 + 4.08813i) q^{69} +(0.537830 - 2.35639i) q^{71} +(0.802203 + 0.280703i) q^{73} +(2.47727 - 2.47727i) q^{75} +(1.89105 - 16.7836i) q^{77} +(1.07128 - 1.70493i) q^{79} +(-9.22432 + 4.44220i) q^{81} +(6.27399 + 7.86734i) q^{83} +(6.56052 - 2.29563i) q^{85} +(-10.0250 + 0.910171i) q^{87} +(4.71953 - 1.65144i) q^{89} +(-2.16889 + 1.72963i) q^{91} +(14.1587 - 6.81847i) q^{93} +(14.8925 + 9.35757i) q^{95} +(1.22559 - 10.8774i) q^{97} +(-1.98979 - 1.98979i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 24 q^{3} - 28 q^{9}+O(q^{10}) $ 336 * q + 24 * q^3 - 28 * q^9	$ 336 q + 24 q^{3} - 28 q^{9} + 32 q^{11} - 28 q^{17} + 24 q^{19} - 52 q^{25} + 60 q^{27} - 28 q^{33} + 28 q^{35} - 20 q^{41} + 16 q^{43} + 12 q^{49} + 28 q^{51} + 48 q^{59} + 20 q^{65} + 28 q^{67} - 4 q^{73} - 64 q^{75} - 28 q^{81} + 20 q^{83} - 28 q^{89} + 28 q^{91} - 32 q^{97} + 32 q^{99}+O(q^{100}) $ 336 * q + 24 * q^3 - 28 * q^9 + 32 * q^11 - 28 * q^17 + 24 * q^19 - 52 * q^25 + 60 * q^27 - 28 * q^33 + 28 * q^35 - 20 * q^41 + 16 * q^43 + 12 * q^49 + 28 * q^51 + 48 * q^59 + 20 * q^65 + 28 * q^67 - 4 * q^73 - 64 * q^75 - 28 * q^81 + 20 * q^83 - 28 * q^89 + 28 * q^91 - 32 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/928\mathbb{Z}\right)^\times$.

$n$	$321$	$581$	$639$
$\chi(n)$	$e\left(\frac{25}{28}\right)$	$-1$	$-1$

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
$3$	−0.209291	−	1.85751i	−0.120834	−	1.07243i	−0.897039	−	0.441951i	$-0.854286\pi$
$3$	−0.209291	−	1.85751i	−0.120834	−	1.07243i	0.776205	−	0.630480i	$-0.217142\pi$
$4$		0			0
$5$	2.36223	+	1.13759i	1.05642	+	0.508745i	0.879706	−	0.475518i	$-0.157739\pi$
$5$	2.36223	+	1.13759i	1.05642	+	0.508745i	0.176713	+	0.984262i	$0.443454\pi$
$6$		0			0
$7$	−2.31875	−	1.84914i	−0.876407	−	0.698911i	0.0781497	−	0.996942i	$-0.475099\pi$
$7$	−2.31875	−	1.84914i	−0.876407	−	0.698911i	−0.954556	+	0.298031i	$0.903670\pi$
$8$		0			0
$9$	−0.481741	+	0.109954i	−0.160580	+	0.0366514i
$10$		0			0
$11$	3.02984	+	4.82196i	0.913531	+	1.45388i	0.890935	+	0.454132i	$0.150050\pi$
$11$	3.02984	+	4.82196i	0.913531	+	1.45388i	0.0225963	+	0.999745i	$0.492807\pi$
$12$		0			0
$13$	0.208139	−	0.911918i	0.0577275	−	0.252921i	−0.937828	−	0.347101i	$-0.887166\pi$
$13$	0.208139	−	0.911918i	0.0577275	−	0.252921i	0.995555	+	0.0941807i	$0.0300231\pi$
$14$		0			0
$15$	1.61868	−	4.62593i	0.417942	−	1.19441i
$16$		0			0
$17$	1.87453	−	1.87453i	0.454641	−	0.454641i	−0.442250	−	0.896892i	$-0.645820\pi$
$17$	1.87453	−	1.87453i	0.454641	−	0.454641i	0.896892	+	0.442250i	$0.145820\pi$
$18$		0			0
$19$	6.66614	+	0.751093i	1.52932	+	0.172313i	0.836164	−	0.548479i	$-0.184793\pi$
$19$	6.66614	+	0.751093i	1.52932	+	0.172313i	0.693152	+	0.720791i	$0.256221\pi$
$20$		0			0
$21$	−2.94950	+	4.69411i	−0.643634	+	1.02434i
$22$		0			0
$23$	−1.78357	−	3.70363i	−0.371901	−	0.772259i	0.628082	−	0.778147i	$-0.283840\pi$
$23$	−1.78357	−	3.70363i	−0.371901	−	0.772259i	−0.999983	+	0.00588763i	$0.998126\pi$
$24$		0			0
$25$	1.16855	+	1.46532i	0.233711	+	0.293064i
$26$		0			0
$27$	−1.54707	−	4.42126i	−0.297733	−	0.850873i
$28$		0			0
$29$	0.116624	−	5.38390i	0.0216565	−	0.999765i
$29$	0.116624	−	5.38390i	0.0216565	−	0.999765i
$30$		0			0
$31$	2.77667	+	7.93528i	0.498705	+	1.42522i	0.868307	+	0.496027i	$0.165208\pi$
$31$	2.77667	+	7.93528i	0.498705	+	1.42522i	−0.369602	+	0.929190i	$0.620506\pi$
$32$		0			0
$33$	8.32270	−	6.63714i	1.44880	−	1.15538i
$34$		0			0
$35$	−3.37386	−	7.00588i	−0.570286	−	1.18421i
$36$		0			0
$37$	3.67558	+	2.30952i	0.604262	+	0.379683i	0.799140	−	0.601145i	$-0.205288\pi$
$37$	3.67558	+	2.30952i	0.604262	+	0.379683i	−0.194879	+	0.980827i	$0.562431\pi$
$38$		0			0
$39$	−1.73745	−	0.195764i	−0.278215	−	0.0313474i
$40$		0			0
$41$	0.507268	+	0.507268i	0.0792220	+	0.0792220i	0.745607	−	0.666385i	$-0.232159\pi$
$41$	0.507268	+	0.507268i	0.0792220	+	0.0792220i	−0.666385	+	0.745607i	$0.732159\pi$
$42$		0			0
$43$	0.761486	−	2.17620i	0.116126	−	0.331868i	−0.871121	−	0.491069i	$-0.836606\pi$
$43$	0.761486	−	2.17620i	0.116126	−	0.331868i	0.987246	+	0.159201i	$0.0508919\pi$
$44$		0			0
$45$	−1.26306	−	0.288286i	−0.188286	−	0.0429751i
$46$		0			0
$47$	−5.28080	−	8.40434i	−0.770284	−	1.22590i	−0.969295	−	0.245902i	$-0.920916\pi$
$47$	−5.28080	−	8.40434i	−0.770284	−	1.22590i	0.199011	−	0.979997i	$-0.436227\pi$
$48$		0			0
$49$	0.399638	+	1.75093i	0.0570911	+	0.250132i
$50$		0			0
$51$	−3.87428	−	3.08964i	−0.542508	−	0.432636i
$52$		0			0
$53$	−2.91924	+	6.06187i	−0.400989	+	0.832662i	0.598513	+	0.801113i	$0.295758\pi$
$53$	−2.91924	+	6.06187i	−0.400989	+	0.832662i	−0.999502	+	0.0315494i	$0.989956\pi$
$54$		0			0
$55$	1.67176	+	14.8373i	0.225420	+	2.00066i
$56$		0			0
$57$		−	12.5396i		−	1.66091i
$58$		0			0
$59$	−11.7585			−1.53083			−0.765415	−	0.643537i	$-0.777466\pi$
$59$	−11.7585			−1.53083			−0.765415	+	0.643537i	$0.777466\pi$
$60$		0			0
$61$	−5.72525	+	0.645081i	−0.733043	+	0.0825941i	−0.470592	−	0.882351i	$-0.655960\pi$
$61$	−5.72525	+	0.645081i	−0.733043	+	0.0825941i	−0.262451	+	0.964945i	$0.584531\pi$
$62$		0			0
$63$	1.32036	+	0.635852i	0.166350	+	0.0801098i
$64$		0			0
$65$	1.52906	−	1.91738i	0.189656	−	0.237822i
$66$		0			0
$67$	14.0788	−	3.21338i	1.71999	−	0.392577i	0.755181	−	0.655516i	$-0.227549\pi$
$67$	14.0788	−	3.21338i	1.71999	−	0.392577i	0.964812	+	0.262939i	$0.0846918\pi$
$68$		0			0
$69$	−6.50622	+	4.08813i	−0.783257	+	0.492153i
$70$		0			0
$71$	0.537830	−	2.35639i	0.0638287	−	0.279652i	−0.932934	−	0.360046i	$-0.882761\pi$
$71$	0.537830	−	2.35639i	0.0638287	−	0.279652i	0.996763	+	0.0803946i	$0.0256181\pi$
$72$		0			0
$73$	0.802203	+	0.280703i	0.0938907	+	0.0328538i	0.376816	−	0.926288i	$-0.377019\pi$
$73$	0.802203	+	0.280703i	0.0938907	+	0.0328538i	−0.282925	+	0.959142i	$0.591305\pi$
$74$		0			0
$75$	2.47727	−	2.47727i	0.286051	−	0.286051i
$76$		0			0
$77$	1.89105	−	16.7836i	0.215505	−	1.91266i
$78$		0			0
$79$	1.07128	−	1.70493i	0.120528	−	0.191820i	−0.781011	−	0.624518i	$-0.785296\pi$
$79$	1.07128	−	1.70493i	0.120528	−	0.191820i	0.901539	+	0.432698i	$0.142438\pi$
$80$		0			0
$81$	−9.22432	+	4.44220i	−1.02492	+	0.493578i
$82$		0			0
$83$	6.27399	+	7.86734i	0.688660	+	0.863552i	0.996120	−	0.0880088i	$-0.0280504\pi$
$83$	6.27399	+	7.86734i	0.688660	+	0.863552i	−0.307460	+	0.951561i	$0.599479\pi$
$84$		0			0
$85$	6.56052	−	2.29563i	0.711589	−	0.248996i
$86$		0			0
$87$	−10.0250	+	0.910171i	−1.07480	+	0.0975805i
$88$		0			0
$89$	4.71953	−	1.65144i	0.500270	−	0.175052i	−0.0683357	−	0.997662i	$-0.521769\pi$
$89$	4.71953	−	1.65144i	0.500270	−	0.175052i	0.568605	+	0.822610i	$0.307483\pi$
$90$		0			0
$91$	−2.16889	+	1.72963i	−0.227362	+	0.181315i
$92$		0			0
$93$	14.1587	−	6.81847i	1.46819	−	0.707042i
$94$		0			0
$95$	14.8925	+	9.35757i	1.52794	+	0.960066i
$96$		0			0
$97$	1.22559	−	10.8774i	0.124439	−	1.10443i	−0.763929	−	0.645300i	$-0.776732\pi$
$97$	1.22559	−	10.8774i	0.124439	−	1.10443i	0.888369	−	0.459131i	$-0.151839\pi$
$98$		0			0
$99$	−1.98979	−	1.98979i	−0.199982	−	0.199982i
$100$		0			0
$101$	−3.75976	−	1.31560i	−0.374110	−	0.130907i	0.136674	−	0.990616i	$-0.456359\pi$
$101$	−3.75976	−	1.31560i	−0.374110	−	0.130907i	−0.510783	+	0.859709i	$0.670645\pi$
$102$		0			0
$103$	1.55646	+	0.355252i	0.153362	+	0.0350040i	0.298513	−	0.954406i	$-0.403509\pi$
$103$	1.55646	+	0.355252i	0.153362	+	0.0350040i	−0.145150	+	0.989410i	$0.546367\pi$
$104$		0			0
$105$	−12.3074	+	7.73322i	−1.20107	+	0.754685i
$106$		0			0
$107$	0.583135	+	2.55488i	0.0563738	+	0.246990i	0.995262	−	0.0972336i	$-0.0309994\pi$
$107$	0.583135	+	2.55488i	0.0563738	+	0.246990i	−0.938888	+	0.344223i	$0.888142\pi$
$108$		0			0
$109$	−0.727458	+	0.912203i	−0.0696778	+	0.0873732i	−0.815449	−	0.578829i	$-0.803510\pi$
$109$	−0.727458	+	0.912203i	−0.0696778	+	0.0873732i	0.745771	+	0.666202i	$0.232081\pi$
$110$		0			0
$111$	3.52068	−	7.31077i	0.334168	−	0.693908i
$112$		0			0
$113$	−8.91983	+	1.00502i	−0.839107	+	0.0945446i	−0.521049	−	0.853527i	$-0.674459\pi$
$113$	−8.91983	+	1.00502i	−0.839107	+	0.0945446i	−0.318058	+	0.948071i	$0.603031\pi$
$114$		0			0
$115$		−	10.7778i		−	1.00503i
$116$		0			0
$117$			0.462194i			0.0427299i
$118$		0			0
$119$	−7.81287	+	0.880299i	−0.716205	+	0.0806969i
$120$		0			0
$121$	−9.29867	+	19.3089i	−0.845333	+	1.75535i
$122$		0			0
$123$	0.836087	−	1.04842i	0.0753874	−	0.0945328i
$124$		0			0
$125$	−1.82365	−	7.98993i	−0.163112	−	0.714641i
$126$		0			0
$127$	−1.35915	+	0.854011i	−0.120605	+	0.0757812i	−0.590984	−	0.806684i	$-0.701260\pi$
$127$	−1.35915	+	0.854011i	−0.120605	+	0.0757812i	0.470379	+	0.882465i	$0.344117\pi$
$128$		0			0
$129$	−4.20168	−	0.959006i	−0.369937	−	0.0844358i
$130$		0			0
$131$	3.60185	+	1.26034i	0.314695	+	0.110116i	0.483005	−	0.875618i	$-0.339545\pi$
$131$	3.60185	+	1.26034i	0.314695	+	0.110116i	−0.168310	+	0.985734i	$0.553831\pi$
$132$		0			0
$133$	−14.0682	−	14.0682i	−1.21987	−	1.21987i
$134$		0			0
$135$	1.37505	−	12.2039i	0.118346	−	1.05035i
$136$		0			0
$137$	11.0502	+	6.94331i	0.944083	+	0.593207i	0.913725	−	0.406332i	$-0.133192\pi$
$137$	11.0502	+	6.94331i	0.944083	+	0.593207i	0.0303579	+	0.999539i	$0.490335\pi$
$138$		0			0
$139$	4.16653	−	2.00650i	0.353400	−	0.170189i	−0.248757	−	0.968566i	$-0.580022\pi$
$139$	4.16653	−	2.00650i	0.353400	−	0.170189i	0.602158	+	0.798377i	$0.294308\pi$
$140$		0			0
$141$	−14.5059	+	11.5681i	−1.22162	+	0.974207i
$142$		0			0
$143$	5.02786	−	1.75933i	0.420451	−	0.147122i
$144$		0			0
$145$	6.40015	−	12.5853i	0.531504	−	1.04515i
$146$		0			0
$147$	3.16872	−	1.10878i	0.261351	−	0.0914508i
$148$		0			0
$149$	7.02571	+	8.80996i	0.575568	+	0.721740i	0.981350	−	0.192230i	$-0.0615720\pi$
$149$	7.02571	+	8.80996i	0.575568	+	0.721740i	−0.405781	+	0.913970i	$0.633001\pi$
$150$		0			0
$151$	4.58879	−	2.20985i	0.373431	−	0.179835i	−0.237749	−	0.971327i	$-0.576410\pi$
$151$	4.58879	−	2.20985i	0.373431	−	0.179835i	0.611180	+	0.791492i	$0.290695\pi$
$152$		0			0
$153$	−0.696927	+	1.10915i	−0.0563432	+	0.0896697i
$154$		0			0
$155$	−2.46795	+	21.9036i	−0.198230	+	1.75934i
$156$		0			0
$157$	−17.1254	+	17.1254i	−1.36676	+	1.36676i	−0.501738	+	0.865020i	$0.667306\pi$
$157$	−17.1254	+	17.1254i	−1.36676	+	1.36676i	−0.865020	+	0.501738i	$0.832694\pi$
$158$		0			0
$159$	11.8709	+	4.15382i	0.941426	+	0.329419i
$160$		0			0
$161$	−2.71287	+	11.8859i	−0.213804	+	0.936739i
$162$		0			0
$163$	−12.5667	+	7.89617i	−0.984298	+	0.618476i	−0.925081	−	0.379770i	$-0.876003\pi$
$163$	−12.5667	+	7.89617i	−0.984298	+	0.618476i	−0.0592172	+	0.998245i	$0.518860\pi$
$164$		0			0
$165$	27.2104	−	6.21060i	2.11833	−	0.483495i
$166$		0			0
$167$	−11.3996	+	14.2946i	−0.882127	+	1.10615i	0.111537	+	0.993760i	$0.464423\pi$
$167$	−11.3996	+	14.2946i	−0.882127	+	1.10615i	−0.993664	+	0.112392i	$0.964149\pi$
$168$		0			0
$169$	10.9243	+	5.26088i	0.840332	+	0.404683i
$170$		0			0
$171$	−3.29394	+	0.371138i	−0.251894	+	0.0283816i
$172$		0			0
$173$	12.5204			0.951906			0.475953	−	0.879471i	$-0.342103\pi$
$173$	12.5204			0.951906			0.475953	+	0.879471i	$0.342103\pi$
$174$		0			0
$175$		−	5.55854i		−	0.420186i
$176$		0			0
$177$	2.46095	+	21.8415i	0.184976	+	1.64171i
$178$		0			0
$179$	−8.95782	+	18.6011i	−0.669539	+	1.39031i	0.238382	+	0.971171i	$0.423383\pi$
$179$	−8.95782	+	18.6011i	−0.669539	+	1.39031i	−0.907921	+	0.419141i	$0.862331\pi$
$180$		0			0
$181$	−1.22357	−	0.975762i	−0.0909470	−	0.0725278i	0.576961	−	0.816772i	$-0.304239\pi$
$181$	−1.22357	−	0.975762i	−0.0909470	−	0.0725278i	−0.667908	+	0.744244i	$0.732810\pi$
$182$		0			0
$183$	2.39648	+	10.4997i	0.177153	+	0.776158i
$184$		0			0
$185$	6.05527	+	9.63690i	0.445192	+	0.708519i
$186$		0			0
$187$	14.7185	+	3.35940i	1.07632	+	0.245663i
$188$		0			0
$189$	−4.58829	+	13.1126i	−0.333749	+	0.953799i
$190$		0			0
$191$	2.73230	+	2.73230i	0.197702	+	0.197702i	0.799014	−	0.601312i	$-0.205355\pi$
$191$	2.73230	+	2.73230i	0.197702	+	0.197702i	−0.601312	+	0.799014i	$0.705355\pi$
$192$		0			0
$193$	−12.9538	−	1.45954i	−0.932432	−	0.105060i	−0.367339	−	0.930087i	$-0.619731\pi$
$193$	−12.9538	−	1.45954i	−0.932432	−	0.105060i	−0.565093	+	0.825027i	$0.691160\pi$
$194$		0			0
$195$	−3.88156	−	2.43895i	−0.277964	−	0.174657i
$196$		0			0
$197$	11.6244	+	24.1383i	0.828205	+	1.71979i	0.683044	+	0.730377i	$0.260656\pi$
$197$	11.6244	+	24.1383i	0.828205	+	1.71979i	0.145161	+	0.989408i	$0.453630\pi$
$198$		0			0
$199$	−7.83836	+	6.25088i	−0.555646	+	0.443113i	−0.860620	−	0.509248i	$-0.829924\pi$
$199$	−7.83836	+	6.25088i	−0.555646	+	0.443113i	0.304974	+	0.952361i	$0.401352\pi$
$200$		0			0
$201$	−8.91543	−	25.4788i	−0.628846	−	1.79714i
$202$		0			0
$203$	−10.2260	+	12.2683i	−0.717727	+	0.861065i
$204$		0			0
$205$	0.621220	+	1.77534i	0.0433879	+	0.123995i
$206$		0			0
$207$	1.26645	+	1.58808i	0.0880243	+	0.110379i
$208$		0			0
$209$	16.5756	+	34.4195i	1.14656	+	2.38085i
$210$		0			0
$211$	−10.2746	+	16.3519i	−0.707330	+	1.12571i	0.278898	+	0.960321i	$0.410031\pi$
$211$	−10.2746	+	16.3519i	−0.707330	+	1.12571i	−0.986228	+	0.165389i	$0.947112\pi$
$212$		0			0
$213$	−4.48956	−	0.505852i	−0.307620	−	0.0346604i
$214$		0			0
$215$	4.27442	−	4.27442i	0.291513	−	0.291513i
$216$		0			0
$217$	8.23505	−	23.5344i	0.559032	−	1.59762i
$218$		0			0
$219$	0.353514	−	1.54884i	0.0238882	−	0.104661i
$220$		0			0
$221$	−1.31926	−	2.09959i	−0.0887429	−	0.141234i
$222$		0			0
$223$	8.27134	−	1.88788i	0.553890	−	0.126422i	0.0635909	−	0.997976i	$-0.479745\pi$
$223$	8.27134	−	1.88788i	0.553890	−	0.126422i	0.490299	+	0.871554i	$0.336888\pi$
$224$		0			0
$225$	−0.724059	−	0.577418i	−0.0482706	−	0.0384945i
$226$		0			0
$227$	−7.60539	−	3.66256i	−0.504787	−	0.243093i	0.164117	−	0.986441i	$-0.447522\pi$
$227$	−7.60539	−	3.66256i	−0.504787	−	0.243093i	−0.668905	+	0.743348i	$0.733237\pi$
$228$		0			0
$229$	−1.73742	−	15.4200i	−0.114812	−	1.01898i	−0.910566	−	0.413363i	$-0.864354\pi$
$229$	−1.73742	−	15.4200i	−0.114812	−	1.01898i	0.795755	−	0.605619i	$-0.207074\pi$
$230$		0			0
$231$	−31.5713			−2.07724
$232$		0			0
$233$	−22.3548			−1.46451			−0.732255	−	0.681030i	$-0.761532\pi$
$233$	−22.3548			−1.46451			−0.732255	+	0.681030i	$0.761532\pi$
$234$		0			0
$235$	−2.91376	−	25.8603i	−0.190073	−	1.68694i
$236$		0			0
$237$	−3.39113	−	1.63308i	−0.220277	−	0.106080i
$238$		0			0
$239$	−13.5159	−	10.7786i	−0.874270	−	0.697207i	0.0797938	−	0.996811i	$-0.474574\pi$
$239$	−13.5159	−	10.7786i	−0.874270	−	0.697207i	−0.954063	+	0.299605i	$0.903145\pi$
$240$		0			0
$241$	−9.73669	+	2.22234i	−0.627195	+	0.143153i	−0.524293	−	0.851538i	$-0.675670\pi$
$241$	−9.73669	+	2.22234i	−0.627195	+	0.143153i	−0.102903	+	0.994691i	$0.532813\pi$
$242$		0			0
$243$	2.70567	+	4.30605i	0.173569	+	0.276233i
$244$		0			0
$245$	−1.04780	+	4.59071i	−0.0669414	+	0.293290i
$246$		0			0
$247$	2.07242	−	5.92264i	0.131865	−	0.376849i
$248$		0			0
$249$	13.3005	−	13.3005i	0.842887	−	0.842887i
$250$		0			0
$251$	−10.7394	−	1.21004i	−0.677868	−	0.0763773i	−0.233683	−	0.972313i	$-0.575078\pi$
$251$	−10.7394	−	1.21004i	−0.677868	−	0.0763773i	−0.444184	+	0.895935i	$0.646506\pi$
$252$		0			0
$253$	12.4548	−	19.8217i	0.783027	−	1.24618i
$254$		0			0
$255$	−5.63719	−	11.7058i	−0.353015	−	0.733043i
$256$		0			0
$257$	−10.3075	−	12.9253i	−0.642967	−	0.806255i	0.348403	−	0.937345i	$-0.386724\pi$
$257$	−10.3075	−	12.9253i	−0.642967	−	0.806255i	−0.991371	+	0.131089i	$0.958153\pi$
$258$		0			0
$259$	−4.25213	−	12.1519i	−0.264215	−	0.755082i
$260$		0			0
$261$	0.535800	+	2.60647i	0.0331652	+	0.161336i
$262$		0			0
$263$	2.00006	+	5.71583i	0.123329	+	0.352453i	0.988951	−	0.148245i	$-0.0473624\pi$
$263$	2.00006	+	5.71583i	0.123329	+	0.352453i	−0.865622	+	0.500698i	$0.833077\pi$
$264$		0			0
$265$	−13.7918	+	10.9986i	−0.847225	+	0.675640i
$266$		0			0
$267$	−4.05531	−	8.42093i	−0.248181	−	0.515353i
$268$		0			0
$269$	17.2206	+	10.8204i	1.04996	+	0.659732i	0.942407	−	0.334468i	$-0.108557\pi$
$269$	17.2206	+	10.8204i	1.04996	+	0.659732i	0.107550	+	0.994200i	$0.465700\pi$
$270$		0			0
$271$	23.4692	+	2.64435i	1.42565	+	0.160633i	0.790836	−	0.612029i	$-0.209646\pi$
$271$	23.4692	+	2.64435i	1.42565	+	0.160633i	0.634819	+	0.772661i	$0.281075\pi$
$272$		0			0
$273$	3.66673	+	3.66673i	0.221921	+	0.221921i
$274$		0			0
$275$	−3.52519	+	10.0744i	−0.212577	+	0.607510i
$276$		0			0
$277$	11.0106	+	2.51310i	0.661563	+	0.150997i	0.540103	−	0.841599i	$-0.318385\pi$
$277$	11.0106	+	2.51310i	0.661563	+	0.150997i	0.121460	+	0.992596i	$0.461242\pi$
$278$		0			0
$279$	−2.21016	−	3.51744i	−0.132319	−	0.210584i
$280$		0			0
$281$	−1.90340	−	8.33936i	−0.113548	−	0.497484i	−0.999436	−	0.0335856i	$-0.989307\pi$
$281$	−1.90340	−	8.33936i	−0.113548	−	0.497484i	0.885888	−	0.463899i	$-0.153550\pi$
$282$		0			0
$283$	14.3763	+	11.4647i	0.854584	+	0.681508i	0.949428	−	0.313984i	$-0.101664\pi$
$283$	14.3763	+	11.4647i	0.854584	+	0.681508i	−0.0948446	+	0.995492i	$0.530235\pi$
$284$		0			0
$285$	14.2649	−	29.6213i	0.844978	−	1.75462i
$286$		0			0
$287$	−0.238218	−	2.11424i	−0.0140616	−	0.124800i
$288$		0			0
$289$			9.97224i			0.586602i
$290$		0			0
$291$	−20.4613			−1.19946
$292$		0			0
$293$	−17.5859	+	1.98146i	−1.02738	+	0.115758i	−0.609534	−	0.792760i	$-0.708643\pi$
$293$	−17.5859	+	1.98146i	−1.02738	+	0.115758i	−0.417846	+	0.908518i	$0.637215\pi$
$294$		0			0
$295$	−27.7763	−	13.3764i	−1.61720	−	0.778802i
$296$		0			0
$297$	16.6318	−	20.8556i	0.965075	−	1.21017i
$298$		0			0
$299$	−3.74864	+	0.855602i	−0.216789	+	0.0494807i
$300$		0			0
$301$	−5.78981	+	3.63798i	−0.333719	+	0.209690i
$302$		0			0
$303$	−1.65684	+	7.25911i	−0.0951832	+	0.417025i
$304$		0			0
$305$	−14.2582	−	4.98915i	−0.816420	−	0.285678i
$306$		0			0
$307$	−6.39423	+	6.39423i	−0.364938	+	0.364938i	−0.865627	−	0.500689i	$-0.833080\pi$
$307$	−6.39423	+	6.39423i	−0.364938	+	0.364938i	0.500689	+	0.865627i	$0.333080\pi$
$308$		0			0
$309$	0.334130	−	2.96548i	0.0190080	−	0.168700i
$310$		0			0
$311$	11.2449	−	17.8961i	0.637638	−	1.01479i	−0.359038	−	0.933323i	$-0.616895\pi$
$311$	11.2449	−	17.8961i	0.637638	−	1.01479i	0.996676	−	0.0814716i	$-0.0259620\pi$
$312$		0			0
$313$	−8.91970	+	4.29550i	−0.504171	+	0.242796i	−0.668640	−	0.743586i	$-0.733123\pi$
$313$	−8.91970	+	4.29550i	−0.504171	+	0.242796i	0.164469	+	0.986382i	$0.447409\pi$
$314$		0			0
$315$	2.39565	+	3.00405i	0.134980	+	0.169259i
$316$		0			0
$317$	−14.8444	+	5.19428i	−0.833745	+	0.291740i	−0.713194	−	0.700967i	$-0.752752\pi$
$317$	−14.8444	+	5.19428i	−0.833745	+	0.291740i	−0.120552	+	0.992707i	$0.538466\pi$
$318$		0			0
$319$	26.3143	−	15.7500i	1.47332	−	0.881831i
$320$		0			0
$321$	4.62366	−	1.61789i	0.258068	−	0.0903018i
$322$		0			0
$323$	13.9039	−	11.0880i	0.773631	−	0.616950i
$324$		0			0
$325$	1.57947	−	0.760635i	0.0876135	−	0.0421924i
$326$		0			0
$327$	1.84667	+	1.16034i	0.102121	+	0.0641670i
$328$		0			0
$329$	−3.29597	+	29.2526i	−0.181713	+	1.61275i
$330$		0			0
$331$	−24.0666	−	24.0666i	−1.32282	−	1.32282i	−0.911483	−	0.411337i	$-0.865062\pi$
$331$	−24.0666	−	24.0666i	−1.32282	−	1.32282i	−0.411337	−	0.911483i	$-0.634938\pi$
$332$		0			0
$333$	−2.02462	−	0.708445i	−0.110948	−	0.0388226i
$334$		0			0
$335$	36.9127	+	8.42508i	2.01676	+	0.460311i
$336$		0			0
$337$	3.34338	−	2.10078i	0.182125	−	0.114437i	−0.437884	−	0.899032i	$-0.644272\pi$
$337$	3.34338	−	2.10078i	0.182125	−	0.114437i	0.620009	+	0.784595i	$0.287129\pi$
$338$		0			0
$339$	3.73367	+	16.3583i	0.202785	+	0.888460i
$340$		0			0
$341$	−29.8507	+	37.4316i	−1.61651	+	2.02704i
$342$		0			0
$343$	−6.69662	+	13.9057i	−0.361584	+	0.750836i
$344$		0			0
$345$	−20.0198	+	2.25569i	−1.07783	+	0.121442i
$346$		0			0
$347$		−	15.2521i		−	0.818778i	−0.912360	−	0.409389i	$-0.865742\pi$
$347$		−	15.2521i		−	0.818778i	0.912360	−	0.409389i	$-0.134258\pi$
$348$		0			0
$349$		−	3.00347i		−	0.160772i	−0.996764	−	0.0803860i	$-0.974385\pi$
$349$		−	3.00347i		−	0.160772i	0.996764	−	0.0803860i	$-0.0256153\pi$
$350$		0			0
$351$	−4.35384	+	0.490560i	−0.232391	+	0.0261841i
$352$		0			0
$353$	−1.76954	+	3.67450i	−0.0941834	+	0.195574i	−0.942738	−	0.333534i	$-0.891759\pi$
$353$	−1.76954	+	3.67450i	−0.0941834	+	0.195574i	0.848555	+	0.529107i	$0.177473\pi$
$354$		0			0
$355$	3.95107	−	4.95449i	0.209701	−	0.262957i
$356$		0			0
$357$	3.27032	+	14.3282i	0.173084	+	0.758329i
$358$		0			0
$359$	−14.4027	+	9.04980i	−0.760144	+	0.477630i	−0.855493	−	0.517814i	$-0.826746\pi$
$359$	−14.4027	+	9.04980i	−0.760144	+	0.477630i	0.0953495	+	0.995444i	$0.469603\pi$
$360$		0			0
$361$	25.3496	+	5.78588i	1.33419	+	0.304520i
$362$		0			0
$363$	37.8125	+	13.2312i	1.98464	+	0.694456i
$364$		0			0
$365$	1.57566	+	1.57566i	0.0824738	+	0.0824738i
$366$		0			0
$367$	3.51562	−	31.2020i	0.183514	−	1.62873i	−0.477693	−	0.878527i	$-0.658527\pi$
$367$	3.51562	−	31.2020i	0.183514	−	1.62873i	0.661207	−	0.750204i	$-0.270045\pi$
$368$		0			0
$369$	−0.300148	−	0.188596i	−0.0156251	−	0.00981789i
$370$		0			0
$371$	17.9783	−	8.65789i	0.933386	−	0.449495i
$372$		0			0
$373$	−9.82512	+	7.83527i	−0.508725	+	0.405695i	−0.843932	−	0.536450i	$-0.819765\pi$
$373$	−9.82512	+	7.83527i	−0.508725	+	0.405695i	0.335207	+	0.942145i	$0.391194\pi$
$374$		0			0
$375$	−14.4597	+	5.05966i	−0.746694	+	0.261280i
$376$		0			0
$377$	−4.88540	−	1.22695i	−0.251611	−	0.0631913i
$378$		0			0
$379$	19.1280	−	6.69319i	0.982542	−	0.343806i	0.209254	−	0.977861i	$-0.432896\pi$
$379$	19.1280	−	6.69319i	0.982542	−	0.343806i	0.773288	+	0.634055i	$0.218611\pi$
$380$		0			0
$381$	1.87079	+	2.34589i	0.0958434	+	0.120184i
$382$		0			0
$383$	4.97374	−	2.39523i	0.254146	−	0.122390i	−0.302474	−	0.953158i	$-0.597812\pi$
$383$	4.97374	−	2.39523i	0.254146	−	0.122390i	0.556620	+	0.830767i	$0.312098\pi$
$384$		0			0
$385$	23.5599	−	37.4953i	1.20072	−	1.91094i
$386$		0			0
$387$	−0.127556	+	1.13209i	−0.00648406	+	0.0575476i
$388$		0			0
$389$	24.1280	−	24.1280i	1.22334	−	1.22334i	0.256903	−	0.966437i	$-0.417298\pi$
$389$	24.1280	−	24.1280i	1.22334	−	1.22334i	0.966437	−	0.256903i	$-0.0827019\pi$
$390$		0			0
$391$	−10.2859	−	3.59921i	−0.520183	−	0.182020i
$392$		0			0
$393$	1.58726	−	6.95423i	0.0800665	−	0.350794i
$394$		0			0
$395$	4.47011	−	2.80876i	0.224916	−	0.141324i
$396$		0			0
$397$	−13.1529	+	3.00205i	−0.660123	+	0.150669i	−0.539442	−	0.842023i	$-0.681365\pi$
$397$	−13.1529	+	3.00205i	−0.660123	+	0.150669i	−0.120681	+	0.992691i	$0.538508\pi$
$398$		0			0
$399$	−23.1875	+	29.0762i	−1.16083	+	1.45563i
$400$		0			0
$401$	−19.4728	−	9.37762i	−0.972427	−	0.468296i	−0.120933	−	0.992661i	$-0.538589\pi$
$401$	−19.4728	−	9.37762i	−0.972427	−	0.468296i	−0.851494	+	0.524365i	$0.824303\pi$
$402$		0			0
$403$	7.81426	−	0.880456i	0.389256	−	0.0438586i
$404$		0			0
$405$	−26.8433			−1.33386
$406$		0			0
$407$			24.7210i			1.22537i
$408$		0			0
$409$	−0.129811	−	1.15210i	−0.00641874	−	0.0569679i	0.990095	−	0.140402i	$-0.0448396\pi$
$409$	−0.129811	−	1.15210i	−0.00641874	−	0.0569679i	−0.996513	+	0.0834345i	$0.973411\pi$
$410$		0			0
$411$	10.5845	−	21.9790i	0.522096	−	1.08414i
$412$		0			0
$413$	27.2651	+	21.7432i	1.34163	+	1.06991i
$414$		0			0
$415$	5.87080	+	25.7216i	0.288186	+	1.26263i
$416$		0			0
$417$	−4.59909	−	7.31941i	−0.225218	−	0.358433i
$418$		0			0
$419$	8.48982	+	1.93775i	0.414755	+	0.0946651i	0.424806	−	0.905284i	$-0.360342\pi$
$419$	8.48982	+	1.93775i	0.414755	+	0.0946651i	−0.0100512	+	0.999949i	$0.503199\pi$
$420$		0			0
$421$	6.82007	−	19.4906i	0.332390	−	0.949915i	−0.649483	−	0.760376i	$-0.725015\pi$
$421$	6.82007	−	19.4906i	0.332390	−	0.949915i	0.981873	−	0.189539i	$-0.0606995\pi$
$422$		0			0
$423$	3.46807	+	3.46807i	0.168623	+	0.168623i
$424$		0			0
$425$	4.93729	+	0.556299i	0.239494	+	0.0269845i
$426$		0			0
$427$	14.4683	+	9.09103i	0.700170	+	0.439946i
$428$		0			0
$429$	−4.32024	−	8.97108i	−0.208583	−	0.433128i
$430$		0			0
$431$	−19.4030	+	15.4734i	−0.934611	+	0.745327i	−0.967167	−	0.254143i	$-0.918207\pi$
$431$	−19.4030	+	15.4734i	−0.934611	+	0.745327i	0.0325561	+	0.999470i	$0.489635\pi$
$432$		0			0
$433$	7.86310	+	22.4715i	0.377877	+	1.07991i	0.963125	+	0.269055i	$0.0867113\pi$
$433$	7.86310	+	22.4715i	0.377877	+	1.07991i	−0.585248	+	0.810854i	$0.699003\pi$
$434$		0			0
$435$	−24.7168	−	9.25433i	−1.18508	−	0.443711i
$436$		0			0
$437$	−9.10777	−	26.0285i	−0.435684	−	1.24511i
$438$		0			0
$439$	22.0724	+	27.6779i	1.05346	+	1.32099i	0.945064	+	0.326886i	$0.105999\pi$
$439$	22.0724	+	27.6779i	1.05346	+	1.32099i	0.108394	+	0.994108i	$0.465429\pi$
$440$		0			0
$441$	−0.385044	−	0.799552i	−0.0183354	−	0.0380739i
$442$		0			0
$443$	−0.161274	+	0.256667i	−0.00766238	+	0.0121946i	−0.850533	−	0.525921i	$-0.823721\pi$
$443$	−0.161274	+	0.256667i	−0.00766238	+	0.0121946i	0.842871	+	0.538116i	$0.180864\pi$
$444$		0			0
$445$	13.0273	+	1.46782i	0.617551	+	0.0695813i
$446$		0			0
$447$	14.8941	−	14.8941i	0.704468	−	0.704468i
$448$		0			0
$449$	2.37111	−	6.77623i	0.111899	−	0.319790i	−0.874292	−	0.485401i	$-0.838674\pi$
$449$	2.37111	−	6.77623i	0.111899	−	0.319790i	0.986191	+	0.165611i	$0.0529595\pi$
$450$		0			0
$451$	−0.909086	+	3.98297i	−0.0428072	+	0.187551i
$452$		0			0
$453$	−5.06519	−	8.06121i	−0.237984	−	0.378749i
$454$		0			0
$455$	−7.09102	+	1.61848i	−0.332432	+	0.0758755i
$456$		0			0
$457$	10.0682	+	8.02911i	0.470970	+	0.375586i	0.830021	−	0.557732i	$-0.188328\pi$
$457$	10.0682	+	8.02911i	0.470970	+	0.375586i	−0.359051	+	0.933318i	$0.616900\pi$
$458$		0			0
$459$	−11.1878	−	5.38778i	−0.522204	−	0.251480i
$460$		0			0
$461$	0.766575	+	6.80354i	0.0357029	+	0.316872i	0.998852	+	0.0479040i	$0.0152541\pi$
$461$	0.766575	+	6.80354i	0.0357029	+	0.316872i	−0.963149	+	0.268968i	$0.913317\pi$
$462$		0			0
$463$	−0.774788			−0.0360075			−0.0180037	−	0.999838i	$-0.505731\pi$
$463$	−0.774788			−0.0360075			−0.0180037	+	0.999838i	$0.505731\pi$
$464$		0			0
$465$	41.2026			1.91073
$466$		0			0
$467$	−0.895481	−	7.94762i	−0.0414379	−	0.367772i	−0.997269	−	0.0738551i	$-0.976470\pi$
$467$	−0.895481	−	7.94762i	−0.0414379	−	0.367772i	0.955831	−	0.293917i	$-0.0949588\pi$
$468$		0			0
$469$	−38.5872	−	18.5826i	−1.78179	−	0.858065i
$470$		0			0
$471$	35.3948	+	28.2264i	1.63090	+	1.30060i
$472$		0			0
$473$	12.8007	−	2.92169i	0.588579	−	0.134339i
$474$		0			0
$475$	6.68915	+	10.6457i	0.306919	+	0.488459i
$476$		0			0
$477$	0.739791	−	3.24124i	0.0338727	−	0.148406i
$478$		0			0
$479$	6.82856	−	19.5149i	0.312005	−	0.891659i	−0.675954	−	0.736944i	$-0.736268\pi$
$479$	6.82856	−	19.5149i	0.312005	−	0.891659i	0.987959	−	0.154715i	$-0.0494461\pi$
$480$		0			0
$481$	2.87113	−	2.87113i	0.130912	−	0.130912i
$482$		0			0
$483$	22.6459	+	2.55158i	1.03042	+	0.116101i
$484$		0			0
$485$	15.2691	−	24.3006i	0.693333	−	1.10343i
$486$		0			0
$487$	−13.5444	−	28.1252i	−0.613755	−	1.27448i	−0.943802	−	0.330511i	$-0.892779\pi$
$487$	−13.5444	−	28.1252i	−0.613755	−	1.27448i	0.330047	−	0.943964i	$-0.392935\pi$
$488$		0			0
$489$	17.2973	+	21.6901i	0.782209	+	0.980860i
$490$		0			0
$491$	10.6274	+	30.3713i	0.479606	+	1.37064i	0.888845	+	0.458208i	$0.151509\pi$
$491$	10.6274	+	30.3713i	0.479606	+	1.37064i	−0.409239	+	0.912427i	$0.634206\pi$
$492$		0			0
$493$	−9.87370	−	10.3109i	−0.444689	−	0.464381i
$494$		0			0
$495$	−2.43678	−	6.96391i	−0.109525	−	0.313004i
$496$		0			0
$497$	−5.60439	+	4.46935i	−0.251391	+	0.200478i
$498$		0			0
$499$	−3.26553	−	6.78093i	−0.146185	−	0.303556i	0.815000	−	0.579461i	$-0.196737\pi$
$499$	−3.26553	−	6.78093i	−0.146185	−	0.303556i	−0.961185	+	0.275905i	$0.911023\pi$
$500$		0			0
$501$	28.9382	+	18.1831i	1.29286	+	0.812360i
$502$		0			0
$503$	−40.4946	−	4.56264i	−1.80556	−	0.203438i	−0.855993	−	0.516988i	$-0.827053\pi$
$503$	−40.4946	−	4.56264i	−1.80556	−	0.203438i	−0.949572	+	0.313550i	$0.898482\pi$
$504$		0			0
$505$	−7.38479	−	7.38479i	−0.328619	−	0.328619i
$506$		0			0
$507$	7.48575	−	21.3930i	0.332454	−	0.950098i
$508$		0			0
$509$	4.75036	+	1.08424i	0.210556	+	0.0480581i	0.326498	−	0.945198i	$-0.394131\pi$
$509$	4.75036	+	1.08424i	0.210556	+	0.0480581i	−0.115942	+	0.993256i	$0.536989\pi$
$510$		0			0
$511$	−1.34105	−	2.13427i	−0.0593246	−	0.0944145i
$512$		0			0
$513$	−6.99218	−	30.6347i	−0.308712	−	1.35256i
$514$		0			0
$515$	3.27258	+	2.60979i	0.144207	+	0.115001i
$516$		0			0
$517$	24.5254	−	50.9276i	1.07863	−	2.23979i
$518$		0			0
$519$	−2.62040	−	23.2567i	−0.115023	−	1.02085i
$520$		0			0
$521$		−	11.2284i		−	0.491923i	−0.969280	−	0.245962i	$-0.920896\pi$
$521$		−	11.2284i		−	0.491923i	0.969280	−	0.245962i	$-0.0791037\pi$
$522$		0			0
$523$	−15.9435			−0.697162			−0.348581	−	0.937279i	$-0.613336\pi$
$523$	−15.9435			−0.697162			−0.348581	+	0.937279i	$0.613336\pi$
$524$		0			0
$525$	−10.3250	+	1.16335i	−0.450621	+	0.0507728i
$526$		0			0
$527$	20.0799	+	9.66998i	0.874695	+	0.421231i
$528$		0			0
$529$	3.80455	−	4.77075i	0.165415	−	0.207424i
$530$		0			0
$531$	5.66457	−	1.29290i	0.245821	−	0.0561071i
$532$		0			0
$533$	0.568169	−	0.357005i	0.0246102	−	0.0154636i
$534$		0			0
$535$	−1.52891	+	6.69858i	−0.0661004	+	0.289605i
$536$		0			0
$537$	36.4264	+	12.7462i	1.57192	+	0.550038i
$538$		0			0
$539$	−7.23206	+	7.23206i	−0.311507	+	0.311507i
$540$		0			0
$541$	0.660646	−	5.86340i	0.0284034	−	0.252087i	−0.971484	−	0.237104i	$-0.923802\pi$
$541$	0.660646	−	5.86340i	0.0284034	−	0.252087i	0.999888	−	0.0149834i	$-0.00476956\pi$
$542$		0			0
$543$	−1.55640	+	2.47700i	−0.0667916	+	0.106298i
$544$		0			0
$545$	−2.75613	+	1.32728i	−0.118060	+	0.0568546i
$546$		0			0
$547$	8.67430	+	10.8772i	0.370886	+	0.465077i	0.931892	−	0.362735i	$-0.118157\pi$
$547$	8.67430	+	10.8772i	0.370886	+	0.465077i	−0.561006	+	0.827812i	$0.689586\pi$
$548$		0			0
$549$	2.68716	−	0.940277i	0.114685	−	0.0401301i
$550$		0			0
$551$	4.82124	−	35.8022i	0.205392	−	1.52523i
$552$		0			0
$553$	−5.63669	+	1.97236i	−0.239697	+	0.0838735i
$554$		0			0
$555$	16.6333	−	13.2646i	0.706044	−	0.563051i
$556$		0			0
$557$	−25.7731	+	12.4116i	−1.09204	+	0.525898i	−0.891147	−	0.453715i	$-0.850098\pi$
$557$	−25.7731	+	12.4116i	−1.09204	+	0.525898i	−0.200892	+	0.979613i	$0.564384\pi$
$558$		0			0
$559$	−1.82602	−	1.14737i	−0.0772325	−	0.0485284i
$560$		0			0
$561$	3.15966	−	28.0427i	0.133401	−	1.18397i
$562$		0			0
$563$	−18.0288	−	18.0288i	−0.759822	−	0.759822i	0.216468	−	0.976290i	$-0.430546\pi$
$563$	−18.0288	−	18.0288i	−0.759822	−	0.759822i	−0.976290	+	0.216468i	$0.930546\pi$
$564$		0			0
$565$	−22.2139	−	7.77300i	−0.934548	−	0.327012i
$566$		0			0
$567$	29.6032	+	6.75674i	1.24322	+	0.283756i
$568$		0			0
$569$	−34.8793	+	21.9161i	−1.46221	+	0.918770i	−0.462736	+	0.886496i	$0.653132\pi$
$569$	−34.8793	+	21.9161i	−1.46221	+	0.918770i	−0.999479	+	0.0322743i	$0.989725\pi$
$570$		0			0
$571$	−4.03513	−	17.6791i	−0.168865	−	0.739846i	−0.986453	−	0.164043i	$-0.947547\pi$
$571$	−4.03513	−	17.6791i	−0.168865	−	0.739846i	0.817588	−	0.575803i	$-0.195311\pi$
$572$		0			0
$573$	4.50342	−	5.64711i	0.188133	−	0.235912i
$574$		0			0
$575$	3.34280	−	6.94139i	0.139404	−	0.289476i
$576$		0			0
$577$	21.2082	−	2.38959i	0.882910	−	0.0994801i	0.341146	−	0.940010i	$-0.389185\pi$
$577$	21.2082	−	2.38959i	0.882910	−	0.0994801i	0.541765	+	0.840530i	$0.317756\pi$
$578$		0			0
$579$			24.3672i			1.01266i
$580$		0			0
$581$		−	29.8439i		−	1.23813i
$582$		0			0
$583$	−38.0750	+	4.29002i	−1.57690	+	0.177674i
$584$		0			0
$585$	−0.525787	+	1.09181i	−0.0217386	+	0.0451407i
$586$		0			0
$587$	−7.11526	+	8.92225i	−0.293678	+	0.368261i	−0.906679	−	0.421822i	$-0.861391\pi$
$587$	−7.11526	+	8.92225i	−0.293678	+	0.368261i	0.613001	+	0.790082i	$0.289962\pi$
$588$		0			0
$589$	12.5496	+	54.9832i	0.517095	+	2.26554i
$590$		0			0
$591$	42.4042	−	26.6443i	1.74428	−	1.09600i
$592$		0			0
$593$	−21.4065	−	4.88590i	−0.879061	−	0.200640i	−0.240907	−	0.970548i	$-0.577445\pi$
$593$	−21.4065	−	4.88590i	−0.879061	−	0.200640i	−0.638154	+	0.769908i	$0.720302\pi$
$594$		0			0
$595$	−19.4572	−	6.80836i	−0.797667	−	0.279116i
$596$		0			0
$597$	13.2515	+	13.2515i	0.542350	+	0.542350i
$598$		0			0
$599$	2.32951	−	20.6750i	0.0951812	−	0.844756i	−0.851887	−	0.523725i	$-0.824542\pi$
$599$	2.32951	−	20.6750i	0.0951812	−	0.844756i	0.947069	−	0.321031i	$-0.104030\pi$
$600$		0			0
$601$	−18.4009	−	11.5620i	−0.750587	−	0.471625i	0.101624	−	0.994823i	$-0.467596\pi$
$601$	−18.4009	−	11.5620i	−0.750587	−	0.471625i	−0.852211	+	0.523198i	$0.824739\pi$
$602$		0			0
$603$	−6.42899	+	3.09604i	−0.261809	+	0.126080i
$604$		0			0
$605$	−43.9311	+	35.0339i	−1.78605	+	1.42433i
$606$		0			0
$607$	0.412814	−	0.144450i	0.0167556	−	0.00586304i	−0.321888	−	0.946778i	$-0.604318\pi$
$607$	0.412814	−	0.144450i	0.0167556	−	0.00586304i	0.338644	+	0.940915i	$0.390032\pi$
$608$		0			0
$609$	24.9286	+	16.4273i	1.01016	+	0.665667i
$610$		0			0
$611$	−8.76322	+	3.06638i	−0.354522	+	0.124053i
$612$		0			0
$613$	16.5256	+	20.7224i	0.667463	+	0.836972i	0.994133	−	0.108167i	$-0.0344981\pi$
$613$	16.5256	+	20.7224i	0.667463	+	0.836972i	−0.326670	+	0.945138i	$0.605927\pi$
$614$		0			0
$615$	3.16770	−	1.52548i	0.127734	−	0.0615134i
$616$		0			0
$617$	−14.7389	+	23.4568i	−0.593365	+	0.944335i	0.406169	+	0.913798i	$0.366865\pi$
$617$	−14.7389	+	23.4568i	−0.593365	+	0.944335i	−0.999534	+	0.0305368i	$0.990278\pi$
$618$		0			0
$619$	3.27434	−	29.0606i	0.131607	−	1.16804i	−0.738176	−	0.674608i	$-0.764313\pi$
$619$	3.27434	−	29.0606i	0.131607	−	1.16804i	0.869783	−	0.493434i	$-0.164259\pi$
$620$		0			0
$621$	−13.6154	+	13.6154i	−0.546367	+	0.546367i
$622$		0			0
$623$	−13.9972	−	4.89783i	−0.560785	−	0.196227i
$624$		0			0
$625$	6.86664	−	30.0847i	0.274666	−	1.20339i
$626$		0			0
$627$	60.4654	−	37.9929i	2.41475	−	1.51729i
$628$		0			0
$629$	11.2193	−	2.56073i	0.447342	−	0.102103i
$630$		0			0
$631$	−19.9637	+	25.0337i	−0.794743	+	0.996576i	0.205098	+	0.978741i	$0.434249\pi$
$631$	−19.9637	+	25.0337i	−0.794743	+	0.996576i	−0.999841	+	0.0178347i	$0.994323\pi$
$632$		0			0
$633$	32.5241	+	15.6628i	1.29272	+	0.622539i
$634$		0			0
$635$	−4.18213	+	0.471213i	−0.165963	+	0.0186995i
$636$		0			0
$637$	1.67988			0.0665594
$638$		0			0
$639$			1.19430i			0.0472460i
$640$		0			0
$641$	2.61923	+	23.2463i	0.103453	+	0.918173i	0.933035	+	0.359787i	$0.117151\pi$
$641$	2.61923	+	23.2463i	0.103453	+	0.918173i	−0.829581	+	0.558386i	$0.811421\pi$
$642$		0			0
$643$	12.2672	−	25.4731i	0.483771	−	1.00456i	−0.506085	−	0.862484i	$-0.668908\pi$
$643$	12.2672	−	25.4731i	0.483771	−	1.00456i	0.989856	−	0.142077i	$-0.0453780\pi$
$644$		0			0
$645$	−8.83436	−	7.04517i	−0.347853	−	0.277403i
$646$		0			0
$647$	−0.637275	−	2.79209i	−0.0250539	−	0.109768i	0.960855	−	0.277052i	$-0.0893575\pi$
$647$	−0.637275	−	2.79209i	−0.0250539	−	0.109768i	−0.985909	+	0.167284i	$0.946500\pi$
$648$		0			0
$649$	−35.6264	−	56.6992i	−1.39846	−	2.22564i
$650$		0			0
$651$	−45.4388	−	10.3711i	−1.78089	−	0.406476i
$652$		0			0
$653$	4.15931	−	11.8866i	0.162766	−	0.465159i	−0.833397	−	0.552675i	$-0.813607\pi$
$653$	4.15931	−	11.8866i	0.162766	−	0.465159i	0.996163	+	0.0875156i	$0.0278928\pi$
$654$		0			0
$655$	7.07462	+	7.07462i	0.276428	+	0.276428i
$656$		0			0
$657$	−0.417318	−	0.0470205i	−0.0162811	−	0.00183444i
$658$		0			0
$659$	−12.8148	−	8.05208i	−0.499194	−	0.313665i	0.258794	−	0.965932i	$-0.416675\pi$
$659$	−12.8148	−	8.05208i	−0.499194	−	0.313665i	−0.757988	+	0.652268i	$0.773818\pi$
$660$		0			0
$661$	12.2455	+	25.4280i	0.476294	+	0.989035i	0.991272	+	0.131832i	$0.0420859\pi$
$661$	12.2455	+	25.4280i	0.476294	+	0.989035i	−0.514978	+	0.857204i	$0.672200\pi$
$662$		0			0
$663$	−3.62389	+	2.88995i	−0.140740	+	0.112236i
$664$		0			0
$665$	−17.2285	−	49.2362i	−0.668093	−	1.90930i
$666$		0			0
$667$	−20.1480	+	9.17065i	−0.780132	+	0.355089i
$668$		0			0
$669$	−5.23786	−	14.9689i	−0.202507	−	0.578733i
$670$		0			0
$671$	−20.4571	−	25.6524i	−0.789739	−	0.990302i
$672$		0			0
$673$	−9.58283	−	19.8989i	−0.369391	−	0.767048i	0.630568	−	0.776134i	$-0.282822\pi$
$673$	−9.58283	−	19.8989i	−0.369391	−	0.767048i	−0.999959	+	0.00908623i	$0.997108\pi$
$674$		0			0
$675$	4.67074	−	7.43344i	0.179777	−	0.286113i
$676$		0			0
$677$	−6.10650	−	0.688037i	−0.234692	−	0.0264434i	−0.00616487	−	0.999981i	$-0.501962\pi$
$677$	−6.10650	−	0.688037i	−0.234692	−	0.0264434i	−0.228527	+	0.973538i	$0.573391\pi$
$678$		0			0
$679$	−22.9557	+	22.9557i	−0.880958	+	0.880958i
$680$		0			0
$681$	−5.21149	+	14.8936i	−0.199705	+	0.570724i
$682$		0			0
$683$	−7.10831	+	31.1435i	−0.271992	+	1.19167i	0.635666	+	0.771964i	$0.280726\pi$
$683$	−7.10831	+	31.1435i	−0.271992	+	1.19167i	−0.907658	+	0.419710i	$0.862132\pi$
$684$		0			0
$685$	18.2045	+	28.9722i	0.695557	+	1.10697i
$686$		0			0
$687$	−28.2791	+	6.45452i	−1.07891	+	0.246255i
$688$		0			0
$689$	4.92032	+	3.92383i	0.187449	+	0.149486i
$690$		0			0
$691$	−18.8471	−	9.07627i	−0.716976	−	0.345278i	0.0395708	−	0.999217i	$-0.487401\pi$
$691$	−18.8471	−	9.07627i	−0.716976	−	0.345278i	−0.756547	+	0.653939i	$0.773115\pi$
$692$		0			0
$693$	0.934426	+	8.29326i	0.0354959	+	0.315035i
$694$		0			0
$695$	12.1248			0.459922
$696$		0			0
$697$	1.90178			0.0720352
$698$		0			0
$699$	4.67865	+	41.5241i	0.176963	+	1.57059i
$700$		0			0
$701$	34.6766	+	16.6994i	1.30972	+	0.630727i	0.952854	−	0.303429i	$-0.0981315\pi$
$701$	34.6766	+	16.6994i	1.30972	+	0.630727i	0.356865	+	0.934156i	$0.383846\pi$
$702$		0			0
$703$	22.7673	+	18.1563i	0.858683	+	0.684777i
$704$		0			0
$705$	−47.4259	+	10.8246i	−1.78616	+	0.407680i
$706$		0			0
$707$	6.28522	+	10.0029i	0.236380	+	0.376197i
$708$		0			0
$709$	−1.71960	+	7.53405i	−0.0645809	+	0.282947i	−0.996899	−	0.0786919i	$-0.974926\pi$
$709$	−1.71960	+	7.53405i	−0.0645809	+	0.282947i	0.932318	+	0.361639i	$0.117783\pi$
$710$		0			0
$711$	−0.328615	+	0.939126i	−0.0123240	+	0.0352200i
$712$		0			0
$713$	24.4369	−	24.4369i	0.915169	−	0.915169i
$714$		0			0
$715$	13.8783	+	1.56371i	0.519020	+	0.0584795i
$716$		0			0
$717$	−17.1925	+	27.3617i	−0.642065	+	1.02184i
$718$		0			0
$719$	20.4772	+	42.5213i	0.763670	+	1.58578i	0.809704	+	0.586838i	$0.199627\pi$
$719$	20.4772	+	42.5213i	0.763670	+	1.58578i	−0.0460339	+	0.998940i	$0.514658\pi$
$720$		0			0
$721$	−2.95213	−	3.70186i	−0.109943	−	0.137864i
$722$		0			0
$723$	6.16580	+	17.6208i	0.229309	+	0.655326i
$724$		0			0
$725$	8.02542	−	6.12049i	0.298057	−	0.227309i
$726$		0			0
$727$	−7.50311	−	21.4427i	−0.278275	−	0.795265i	−0.995177	−	0.0980910i	$-0.968726\pi$
$727$	−7.50311	−	21.4427i	−0.278275	−	0.795265i	0.716902	−	0.697174i	$-0.245559\pi$
$728$		0			0
$729$	−16.5815	+	13.2233i	−0.614128	+	0.489751i
$730$		0			0
$731$	−2.65193	−	5.50680i	−0.0980853	−	0.203676i
$732$		0			0
$733$	37.9818	+	23.8656i	1.40289	+	0.881494i	0.999438	−	0.0335066i	$-0.0106675\pi$
$733$	37.9818	+	23.8656i	1.40289	+	0.881494i	0.403452	+	0.915001i	$0.367810\pi$
$734$		0			0
$735$	8.74656	+	0.985500i	0.322622	+	0.0363507i
$736$		0			0
$737$	58.1512	+	58.1512i	2.14203	+	2.14203i
$738$		0			0
$739$	−4.53282	+	12.9541i	−0.166743	+	0.476523i	−0.996688	−	0.0813218i	$-0.974086\pi$
$739$	−4.53282	+	12.9541i	−0.166743	+	0.476523i	0.829945	+	0.557845i	$0.188372\pi$
$740$		0			0
$741$	−11.4351	−	2.60998i	−0.420078	−	0.0958801i
$742$		0			0
$743$	2.71486	+	4.32068i	0.0995986	+	0.158510i	0.892806	−	0.450441i	$-0.148733\pi$
$743$	2.71486	+	4.32068i	0.0995986	+	0.158510i	−0.793208	+	0.608951i	$0.791590\pi$
$744$		0			0
$745$	6.57420	+	28.8035i	0.240860	+	1.05528i
$746$		0			0
$747$	−3.88749	−	3.10017i	−0.142236	−	0.113429i
$748$		0			0
$749$	3.37220	−	7.00244i	0.123217	−	0.255864i
$750$		0			0
$751$	−4.10805	−	36.4600i	−0.149905	−	1.33044i	−0.813156	−	0.582046i	$-0.802252\pi$
$751$	−4.10805	−	36.4600i	−0.149905	−	1.33044i	0.663251	−	0.748397i	$-0.269176\pi$
$752$		0			0
$753$			20.2018i			0.736195i
$754$		0			0
$755$	13.3537			0.485989
$756$		0			0
$757$	−28.3603	+	3.19544i	−1.03077	+	0.116140i	−0.611114	−	0.791542i	$-0.709278\pi$
$757$	−28.3603	+	3.19544i	−1.03077	+	0.116140i	−0.419658	+	0.907682i	$0.637850\pi$
$758$		0			0
$759$	−39.4256	−	18.9864i	−1.43106	−	0.689162i
$760$		0			0
$761$	−2.21949	+	2.78316i	−0.0804566	+	0.100889i	−0.820431	−	0.571746i	$-0.806266\pi$
$761$	−2.21949	+	2.78316i	−0.0804566	+	0.100889i	0.739974	+	0.672635i	$0.234838\pi$
$762$		0			0
$763$	3.37359	−	0.770000i	0.122132	−	0.0278759i
$764$		0			0
$765$	−2.90806	+	1.82725i	−0.105141	+	0.0660645i
$766$		0			0
$767$	−2.44741	+	10.7228i	−0.0883709	+	0.387178i
$768$		0			0
$769$	−32.0474	−	11.2139i	−1.15566	−	0.404382i	−0.316672	−	0.948535i	$-0.602565\pi$
$769$	−32.0474	−	11.2139i	−1.15566	−	0.404382i	−0.838986	+	0.544153i	$0.816851\pi$
$770$		0			0
$771$	−21.8515	+	21.8515i	−0.786961	+	0.786961i
$772$		0			0
$773$	3.81946	−	33.8986i	0.137376	−	1.21925i	−0.716055	−	0.698044i	$-0.754054\pi$
$773$	3.81946	−	33.8986i	0.137376	−	1.21925i	0.853432	−	0.521205i	$-0.174517\pi$
$774$		0			0
$775$	−8.38303	+	13.3415i	−0.301127	+	0.479241i
$776$		0			0
$777$	−21.6823	+	10.4416i	−0.777847	+	0.374591i
$778$		0			0
$779$	3.00051	+	3.76252i	0.107505	+	0.134806i
$780$		0			0
$781$	12.9919	−	4.54608i	0.464888	−	0.162671i
$782$		0			0
$783$	−23.9841	+	7.81363i	−0.857121	+	0.279236i
$784$		0			0
$785$	−59.9358	+	20.9724i	−2.13920	+	0.748538i
$786$		0			0
$787$	13.6142	−	10.8570i	0.485294	−	0.387009i	−0.350055	−	0.936729i	$-0.613837\pi$
$787$	13.6142	−	10.8570i	0.485294	−	0.387009i	0.835349	+	0.549720i	$0.185266\pi$
$788$		0			0
$789$	10.1986	−	4.91139i	0.363080	−	0.174850i
$790$		0			0
$791$	22.5413	+	14.1636i	0.801477	+	0.503601i
$792$		0			0
$793$	−0.603389	+	5.35523i	−0.0214270	+	0.190170i
$794$		0			0
$795$	23.3165	+	23.3165i	0.826951	+	0.826951i
$796$		0			0
$797$	−7.21132	−	2.52335i	−0.255438	−	0.0893817i	0.199522	−	0.979893i	$-0.436061\pi$
$797$	−7.21132	−	2.52335i	−0.255438	−	0.0893817i	−0.454961	+	0.890512i	$0.650347\pi$
$798$		0			0
$799$	−25.6533	−	5.85519i	−0.907548	−	0.207142i
$800$		0			0
$801$	−2.09201	+	1.31450i	−0.0739176	+	0.0464455i
$802$		0			0
$803$	1.07701	+	4.71868i	0.0380067	+	0.166518i
$804$		0			0
$805$	−19.9297	+	24.9910i	−0.702428	+	0.880817i
$806$		0			0
$807$	16.4949	−	34.2519i	0.580646	−	1.20572i
$808$		0			0
$809$	2.79412	−	0.314822i	0.0982360	−	0.0110685i	−0.0627096	−	0.998032i	$-0.519974\pi$
$809$	2.79412	−	0.314822i	0.0982360	−	0.0110685i	0.160946	+	0.986963i	$0.448546\pi$
$810$		0			0
$811$			32.3338i			1.13539i	0.823238	+	0.567696i	$0.192165\pi$
$811$			32.3338i			1.13539i	−0.823238	+	0.567696i	$0.807835\pi$
$812$		0			0
$813$		−	44.1477i		−	1.54833i
$814$		0			0
$815$	−38.6679	+	4.35683i	−1.35448	+	0.152613i
$816$		0			0
$817$	6.71070	−	13.9349i	0.234778	−	0.487521i
$818$		0			0
$819$	0.854664	−	1.07171i	0.0298644	−	0.0374487i
$820$		0			0
$821$	−1.68108	−	7.36529i	−0.0586700	−	0.257050i	0.937084	−	0.349104i	$-0.113514\pi$
$821$	−1.68108	−	7.36529i	−0.0586700	−	0.257050i	−0.995754	+	0.0920537i	$0.970657\pi$
$822$		0			0
$823$	−9.17550	+	5.76535i	−0.319838	+	0.200967i	−0.682376	−	0.731002i	$-0.739053\pi$
$823$	−9.17550	+	5.76535i	−0.319838	+	0.200967i	0.362538	+	0.931969i	$0.381910\pi$
$824$		0			0
$825$	19.4511	+	4.43958i	0.677199	+	0.154566i
$826$		0			0
$827$	−48.4051	−	16.9377i	−1.68321	−	0.588981i	−0.692074	−	0.721827i	$-0.743303\pi$
$827$	−48.4051	−	16.9377i	−1.68321	−	0.588981i	−0.991137	+	0.132846i	$0.957588\pi$
$828$		0			0
$829$	−8.97497	−	8.97497i	−0.311714	−	0.311714i	0.533860	−	0.845573i	$-0.320741\pi$
$829$	−8.97497	−	8.97497i	−0.311714	−	0.311714i	−0.845573	+	0.533860i	$0.820741\pi$
$830$		0			0
$831$	2.36368	−	20.9782i	0.0819950	−	0.727726i
$832$		0			0
$833$	4.03131	+	2.53304i	0.139677	+	0.0877646i
$834$		0			0
$835$	−43.1898	+	20.7991i	−1.49464	+	0.719783i
$836$		0			0
$837$	30.7882	−	24.5528i	1.06420	−	0.848669i
$838$		0			0
$839$	53.0318	−	18.5566i	1.83086	−	0.640646i	0.834949	−	0.550327i	$-0.185497\pi$
$839$	53.0318	−	18.5566i	1.83086	−	0.640646i	0.995913	−	0.0903192i	$-0.0287887\pi$
$840$		0			0
$841$	−28.9728	−	1.25578i	−0.999062	−	0.0433028i
$842$		0			0
$843$	−15.0920	+	5.28093i	−0.519797	+	0.181885i
$844$		0			0
$845$	19.8210	+	24.8548i	0.681863	+	0.855029i
$846$		0			0
$847$	57.2662	−	27.5780i	1.96769	−	0.947590i
$848$		0			0
$849$	18.2870	−	29.1036i	0.627607	−	0.998832i
$850$		0			0
$851$	1.99794	−	17.7322i	0.0684884	−	0.607851i
$852$		0			0
$853$	11.5062	−	11.5062i	0.393965	−	0.393965i	−0.482133	−	0.876098i	$-0.660138\pi$
$853$	11.5062	−	11.5062i	0.393965	−	0.393965i	0.876098	+	0.482133i	$0.160138\pi$
$854$		0			0
$855$	−8.20323	−	2.87043i	−0.280544	−	0.0981667i
$856$		0			0
$857$	3.93583	−	17.2440i	0.134445	−	0.589044i	−0.862154	−	0.506646i	$-0.830885\pi$
$857$	3.93583	−	17.2440i	0.134445	−	0.589044i	0.996600	−	0.0823978i	$-0.0262578\pi$
$858$		0			0
$859$	−13.9581	+	8.77044i	−0.476243	+	0.299243i	−0.748682	−	0.662930i	$-0.769313\pi$
$859$	−13.9581	+	8.77044i	−0.476243	+	0.299243i	0.272438	+	0.962173i	$0.412170\pi$
$860$		0			0
$861$	−3.87736	+	0.884982i	−0.132140	+	0.0301601i
$862$		0			0
$863$	−2.49261	+	3.12564i	−0.0848496	+	0.106398i	−0.822444	−	0.568846i	$-0.807390\pi$
$863$	−2.49261	+	3.12564i	−0.0848496	+	0.106398i	0.737595	+	0.675244i	$0.235962\pi$
$864$		0			0
$865$	29.5759	+	14.2430i	1.00561	+	0.484277i
$866$		0			0
$867$	18.5235	−	2.08710i	0.629091	−	0.0708815i
$868$		0			0
$869$	11.4669			0.388988
$870$		0			0
$871$		−	13.5075i		−	0.457684i
$872$		0			0
$873$	0.605599	+	5.37484i	0.0204964	+	0.181911i
$874$		0			0
$875$	−10.5459	+	21.8989i	−0.356518	+	0.740317i
$876$		0			0
$877$	27.3582	+	21.8174i	0.923819	+	0.736721i	0.964950	−	0.262432i	$-0.0845247\pi$
$877$	27.3582	+	21.8174i	0.923819	+	0.736721i	−0.0411310	+	0.999154i	$0.513096\pi$
$878$		0			0
$879$	7.36113	+	32.2512i	0.248285	+	1.08781i
$880$		0			0
$881$	−3.27156	−	5.20666i	−0.110222	−	0.175417i	0.787058	−	0.616878i	$-0.211603\pi$
$881$	−3.27156	−	5.20666i	−0.110222	−	0.175417i	−0.897280	+	0.441462i	$0.854460\pi$
$882$		0			0
$883$	3.62719	+	0.827882i	0.122065	+	0.0278604i	0.283117	−	0.959085i	$-0.408632\pi$
$883$	3.62719	+	0.827882i	0.122065	+	0.0278604i	−0.161052	+	0.986946i	$0.551489\pi$
$884$		0			0
$885$	−19.0333	+	54.3942i	−0.639799	+	1.82844i
$886$		0			0
$887$	15.4901	+	15.4901i	0.520107	+	0.520107i	0.917604	−	0.397497i	$-0.130121\pi$
$887$	15.4901	+	15.4901i	0.520107	+	0.520107i	−0.397497	+	0.917604i	$0.630121\pi$
$888$		0			0
$889$	4.73073	+	0.533025i	0.158663	+	0.0178771i
$890$		0			0
$891$	−49.3683	−	31.0202i	−1.65390	−	1.03922i
$892$		0			0
$893$	−28.8901	−	59.9909i	−0.966770	−	2.00752i
$894$		0			0
$895$	−42.3208	+	33.7497i	−1.41463	+	1.12813i
$896$		0			0
$897$	2.37384	+	6.78404i	0.0792602	+	0.226513i
$898$		0			0
$899$	43.0466	−	14.0239i	1.43568	−	0.467723i
$900$		0			0
$901$	5.89097	+	16.8354i	0.196257	+	0.560869i
$902$		0			0
$903$	7.96932	+	9.99321i	0.265202	+	0.332553i
$904$		0			0
$905$	−1.78033	−	3.69688i	−0.0591800	−	0.122889i
$906$		0			0
$907$	9.89198	−	15.7430i	0.328458	−	0.522738i	−0.641146	−	0.767419i	$-0.721541\pi$
$907$	9.89198	−	15.7430i	0.328458	−	0.522738i	0.969604	+	0.244682i	$0.0786834\pi$
$908$		0			0
$909$	1.95588	+	0.220375i	0.0648726	+	0.00730939i
$910$		0			0
$911$	13.5082	−	13.5082i	0.447547	−	0.447547i	−0.446991	−	0.894538i	$-0.647505\pi$
$911$	13.5082	−	13.5082i	0.447547	−	0.447547i	0.894538	+	0.446991i	$0.147505\pi$
$912$		0			0
$913$	−18.9268	+	54.0897i	−0.626386	+	1.79011i
$914$		0			0
$915$	−6.28327	+	27.5288i	−0.207719	+	0.910074i
$916$		0			0
$917$	−6.02124	−	9.58275i	−0.198839	−	0.316450i
$918$		0			0
$919$	57.3548	−	13.0909i	1.89196	−	0.431828i	0.892158	−	0.451724i	$-0.149191\pi$
$919$	57.3548	−	13.0909i	1.89196	−	0.431828i	0.999802	+	0.0198960i	$0.00633353\pi$
$920$		0			0
$921$	13.2156	+	10.5391i	0.435468	+	0.347274i
$922$		0			0
$923$	−2.03689	−	0.980914i	−0.0670450	−	0.0322872i
$924$		0			0
$925$	0.910927	+	8.08470i	0.0299511	+	0.265823i
$926$		0			0
$927$	−0.788872			−0.0259099
$928$		0			0
$929$	42.7181			1.40153			0.700767	−	0.713390i	$-0.252841\pi$
$929$	42.7181			1.40153			0.700767	+	0.713390i	$0.252841\pi$
$930$		0			0
$931$	1.34893	+	11.9721i	0.0442094	+	0.392369i
$932$		0			0
$933$	−35.5955	−	17.1419i	−1.16535	−	0.561201i
$934$		0			0
$935$	30.9467	+	24.6792i	1.01207	+	0.807096i
$936$		0			0
$937$	43.5879	−	9.94865i	1.42395	−	0.325008i	0.559964	−	0.828517i	$-0.310815\pi$
$937$	43.5879	−	9.94865i	1.42395	−	0.325008i	0.863990	+	0.503509i	$0.167958\pi$
$938$		0			0
$939$	9.84573	+	15.6694i	0.321303	+	0.511351i
$940$		0			0
$941$	5.45696	−	23.9085i	0.177892	−	0.779395i	−0.804710	−	0.593669i	$-0.797679\pi$
$941$	5.45696	−	23.9085i	0.177892	−	0.779395i	0.982601	−	0.185727i	$-0.0594639\pi$
$942$		0			0
$943$	0.973982	−	2.78348i	0.0317172	−	0.0906426i
$944$		0			0
$945$	−25.7553	+	25.7553i	−0.837819	+	0.837819i
$946$		0			0
$947$	−30.6734	−	3.45607i	−0.996753	−	0.112307i	−0.401512	−	0.915854i	$-0.631515\pi$
$947$	−30.6734	−	3.45607i	−0.996753	−	0.112307i	−0.595242	+	0.803547i	$0.702944\pi$
$948$		0			0
$949$	0.422948	−	0.673118i	0.0137295	−	0.0218503i
$950$		0			0
$951$	12.7552	+	26.4865i	0.413616	+	0.858882i
$952$		0			0
$953$	12.0259	+	15.0800i	0.389557	+	0.488490i	0.937480	−	0.348040i	$-0.113153\pi$
$953$	12.0259	+	15.0800i	0.389557	+	0.488490i	−0.547922	+	0.836529i	$0.684581\pi$
$954$		0			0
$955$	3.34608	+	9.56255i	0.108277	+	0.309437i
$956$		0			0
$957$	−34.7631	−	45.5827i	−1.12373	−	1.47348i
$958$		0			0
$959$	−12.7835	−	36.5333i	−0.412802	−	1.17972i
$960$		0			0
$961$	−31.0219	+	24.7392i	−1.00071	+	0.798038i
$962$		0			0
$963$	−0.561840	−	1.16667i	−0.0181051	−	0.0375955i
$964$		0			0
$965$	−28.9394	−	18.1838i	−0.931591	−	0.585357i
$966$		0			0
$967$	19.8071	+	2.23172i	0.636952	+	0.0717673i	0.424535	−	0.905412i	$-0.360438\pi$
$967$	19.8071	+	2.23172i	0.636952	+	0.0717673i	0.212417	+	0.977179i	$0.431866\pi$
$968$		0			0
$969$	−23.5059	−	23.5059i	−0.755118	−	0.755118i
$970$		0			0
$971$	−14.0961	+	40.2843i	−0.452365	+	1.29278i	0.461636	+	0.887070i	$0.347263\pi$
$971$	−14.0961	+	40.2843i	−0.452365	+	1.29278i	−0.914000	+	0.405714i	$0.867023\pi$
$972$		0			0
$973$	−13.3715	−	3.05195i	−0.428669	−	0.0978410i
$974$		0			0
$975$	−1.74345	−	2.77469i	−0.0558352	−	0.0888612i
$976$		0			0
$977$	−3.98087	−	17.4413i	−0.127359	−	0.557998i	−0.997834	−	0.0657844i	$-0.979045\pi$
$977$	−3.98087	−	17.4413i	−0.127359	−	0.557998i	0.870474	−	0.492214i	$-0.163812\pi$
$978$		0			0
$979$	22.2626	+	17.7538i	0.711516	+	0.567415i
$980$		0			0
$981$	0.250146	−	0.519433i	0.00798654	−	0.0165842i
$982$		0			0
$983$	4.83367	+	42.9000i	0.154170	+	1.36830i	0.797782	+	0.602946i	$0.206007\pi$
$983$	4.83367	+	42.9000i	0.154170	+	1.36830i	−0.643612	+	0.765352i	$0.722565\pi$
$984$		0			0
$985$			70.2440i			2.23816i
$986$		0			0
$987$	55.0266			1.75152
$988$		0			0
$989$	−9.41800	+	1.06115i	−0.299475	+	0.0337427i
$990$		0			0
$991$	−45.7510	−	22.0325i	−1.45333	−	0.699886i	−0.470159	−	0.882582i	$-0.655803\pi$
$991$	−45.7510	−	22.0325i	−1.45333	−	0.699886i	−0.983169	+	0.182696i	$0.941518\pi$
$992$		0			0
$993$	−39.6669	+	49.7408i	−1.25879	+	1.57848i
$994$		0			0
$995$	−25.6269	+	5.84917i	−0.812427	+	0.185431i
$996$		0			0
$997$	−4.33204	+	2.72200i	−0.137197	+	0.0862066i	−0.598882	−	0.800838i	$-0.704388\pi$
$997$	−4.33204	+	2.72200i	−0.137197	+	0.0862066i	0.461685	+	0.887044i	$0.347245\pi$
$998$		0			0
$999$	4.52463	−	19.8237i	0.143153	−	0.627194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	928.2.bn.a.591.8		336
4.3	odd	2		232.2.v.a.11.16	yes	336
8.3	odd	2	inner	928.2.bn.a.591.7		336
8.5	even	2		232.2.v.a.11.10	✓	336
29.8	odd	28	inner	928.2.bn.a.559.7		336
116.95	even	28		232.2.v.a.211.10	yes	336
232.37	odd	28		232.2.v.a.211.16	yes	336
232.211	even	28	inner	928.2.bn.a.559.8		336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.2.v.a.11.10	✓	336	8.5	even	2
232.2.v.a.11.16	yes	336	4.3	odd	2
232.2.v.a.211.10	yes	336	116.95	even	28
232.2.v.a.211.16	yes	336	232.37	odd	28
928.2.bn.a.559.7		336	29.8	odd	28	inner
928.2.bn.a.559.8		336	232.211	even	28	inner
928.2.bn.a.591.7		336	8.3	odd	2	inner
928.2.bn.a.591.8		336	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 928 = 2^{5} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	928.bn (of order \(28\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.209291 - 1.85751i) q^{3} +(2.36223 + 1.13759i) q^{5} +(-2.31875 - 1.84914i) q^{7} +(-0.481741 + 0.109954i) q^{9} +O(q^{10})\)	\(q+(-0.209291 - 1.85751i) q^{3} +(2.36223 + 1.13759i) q^{5} +(-2.31875 - 1.84914i) q^{7} +(-0.481741 + 0.109954i) q^{9} +(3.02984 + 4.82196i) q^{11} +(0.208139 - 0.911918i) q^{13} +(1.61868 - 4.62593i) q^{15} +(1.87453 - 1.87453i) q^{17} +(6.66614 + 0.751093i) q^{19} +(-2.94950 + 4.69411i) q^{21} +(-1.78357 - 3.70363i) q^{23} +(1.16855 + 1.46532i) q^{25} +(-1.54707 - 4.42126i) q^{27} +(0.116624 - 5.38390i) q^{29} +(2.77667 + 7.93528i) q^{31} +(8.32270 - 6.63714i) q^{33} +(-3.37386 - 7.00588i) q^{35} +(3.67558 + 2.30952i) q^{37} +(-1.73745 - 0.195764i) q^{39} +(0.507268 + 0.507268i) q^{41} +(0.761486 - 2.17620i) q^{43} +(-1.26306 - 0.288286i) q^{45} +(-5.28080 - 8.40434i) q^{47} +(0.399638 + 1.75093i) q^{49} +(-3.87428 - 3.08964i) q^{51} +(-2.91924 + 6.06187i) q^{53} +(1.67176 + 14.8373i) q^{55} -12.5396i q^{57} -11.7585 q^{59} +(-5.72525 + 0.645081i) q^{61} +(1.32036 + 0.635852i) q^{63} +(1.52906 - 1.91738i) q^{65} +(14.0788 - 3.21338i) q^{67} +(-6.50622 + 4.08813i) q^{69} +(0.537830 - 2.35639i) q^{71} +(0.802203 + 0.280703i) q^{73} +(2.47727 - 2.47727i) q^{75} +(1.89105 - 16.7836i) q^{77} +(1.07128 - 1.70493i) q^{79} +(-9.22432 + 4.44220i) q^{81} +(6.27399 + 7.86734i) q^{83} +(6.56052 - 2.29563i) q^{85} +(-10.0250 + 0.910171i) q^{87} +(4.71953 - 1.65144i) q^{89} +(-2.16889 + 1.72963i) q^{91} +(14.1587 - 6.81847i) q^{93} +(14.8925 + 9.35757i) q^{95} +(1.22559 - 10.8774i) q^{97} +(-1.98979 - 1.98979i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 24 q^{3} - 28 q^{9}+O(q^{10}) \) 336 * q + 24 * q^3 - 28 * q^9	\( 336 q + 24 q^{3} - 28 q^{9} + 32 q^{11} - 28 q^{17} + 24 q^{19} - 52 q^{25} + 60 q^{27} - 28 q^{33} + 28 q^{35} - 20 q^{41} + 16 q^{43} + 12 q^{49} + 28 q^{51} + 48 q^{59} + 20 q^{65} + 28 q^{67} - 4 q^{73} - 64 q^{75} - 28 q^{81} + 20 q^{83} - 28 q^{89} + 28 q^{91} - 32 q^{97} + 32 q^{99}+O(q^{100}) \) 336 * q + 24 * q^3 - 28 * q^9 + 32 * q^11 - 28 * q^17 + 24 * q^19 - 52 * q^25 + 60 * q^27 - 28 * q^33 + 28 * q^35 - 20 * q^41 + 16 * q^43 + 12 * q^49 + 28 * q^51 + 48 * q^59 + 20 * q^65 + 28 * q^67 - 4 * q^73 - 64 * q^75 - 28 * q^81 + 20 * q^83 - 28 * q^89 + 28 * q^91 - 32 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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