LMFDB - Embedded newform 936.2.be.a.685.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(685,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.685"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.be (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,1,0,-1,0,0,-2,10,0,-3,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			685.9
Character	$\chi$	$=$	936.685
Dual form			936.2.be.a.757.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.782694 - 1.17788i) q^{2} +(-0.774781 - 1.84383i) q^{4} -2.59989i q^{5} +(-0.300588 - 0.520633i) q^{7} +(-2.77822 - 0.530559i) q^{8} +(-3.06235 - 2.03492i) q^{10} +(-2.40956 - 1.39116i) q^{11} +(-3.60516 - 0.0531995i) q^{13} +(-0.848509 - 0.0534414i) q^{14} +(-2.79943 + 2.85713i) q^{16} +(1.29402 + 2.24132i) q^{17} +(4.38088 - 2.52930i) q^{19} +(-4.79376 + 2.01435i) q^{20} +(-3.52456 + 1.74931i) q^{22} +(-2.94353 + 5.09835i) q^{23} -1.75942 q^{25} +(-2.88440 + 4.20479i) q^{26} +(-0.727070 + 0.957610i) q^{28} +(-1.54071 - 0.889530i) q^{29} +5.09421 q^{31} +(1.17425 + 5.53364i) q^{32} +(3.65282 + 0.230064i) q^{34} +(-1.35359 + 0.781495i) q^{35} +(-8.82719 - 5.09638i) q^{37} +(0.449684 - 7.13981i) q^{38} +(-1.37940 + 7.22306i) q^{40} +(5.26242 - 9.11477i) q^{41} +(-8.44267 + 4.87438i) q^{43} +(-0.698182 + 5.52066i) q^{44} +(3.70134 + 7.45756i) q^{46} -2.13951 q^{47} +(3.31929 - 5.74919i) q^{49} +(-1.37709 + 2.07238i) q^{50} +(2.69512 + 6.68852i) q^{52} -6.01748i q^{53} +(-3.61686 + 6.26458i) q^{55} +(0.558872 + 1.60591i) q^{56} +(-2.25366 + 1.11854i) q^{58} +(9.44349 - 5.45220i) q^{59} +(1.84865 - 1.06732i) q^{61} +(3.98720 - 6.00034i) q^{62} +(7.43701 + 2.94802i) q^{64} +(-0.138313 + 9.37301i) q^{65} +(3.39076 + 1.95766i) q^{67} +(3.13002 - 4.12249i) q^{68} +(-0.138942 + 2.20603i) q^{70} +(-0.230832 - 0.399814i) q^{71} -14.8806 q^{73} +(-12.9119 + 6.40843i) q^{74} +(-8.05784 - 6.11795i) q^{76} +1.67266i q^{77} -7.83968 q^{79} +(7.42823 + 7.27820i) q^{80} +(-6.61721 - 13.3325i) q^{82} -0.930501i q^{83} +(5.82717 - 3.36432i) q^{85} +(-0.866614 + 13.7596i) q^{86} +(5.95619 + 5.14336i) q^{88} +(-1.17791 + 2.04019i) q^{89} +(1.05597 + 1.89296i) q^{91} +(11.6811 + 1.47727i) q^{92} +(-1.67458 + 2.52008i) q^{94} +(-6.57591 - 11.3898i) q^{95} +(5.91151 + 10.2390i) q^{97} +(-4.17383 - 8.40957i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8} - 3 q^{10} - 8 q^{14} - q^{16} + 11 q^{20} - 2 q^{22} + 14 q^{23} - 12 q^{25} + 3 q^{26} - 4 q^{28} - 8 q^{31} + 21 q^{32} + 14 q^{34} - 12 q^{38} + 54 q^{40}+ \cdots + 17 q^{98}+O(q^{100}) $ 24 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8 - 3 * q^10 - 8 * q^14 - q^16 + 11 * q^20 - 2 * q^22 + 14 * q^23 - 12 * q^25 + 3 * q^26 - 4 * q^28 - 8 * q^31 + 21 * q^32 + 14 * q^34 - 12 * q^38 + 54 * q^40 + 4 * q^41 + 24 * q^46 + 8 * q^47 + 6 * q^49 - 32 * q^50 - 4 * q^52 + 8 * q^55 - 8 * q^56 + 33 * q^58 + 14 * q^62 + 26 * q^64 - 30 * q^65 - 23 * q^68 - 16 * q^70 - 30 * q^71 - 12 * q^73 + 7 * q^74 + 14 * q^76 - 48 * q^79 - 29 * q^80 - q^82 + 96 * q^86 + 4 * q^88 + 22 * q^89 + 80 * q^92 - 42 * q^94 - 60 * q^95 + 2 * q^97 + 17 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$1$

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 $

$2$	0.782694	−	1.17788i	0.553448	−	0.832884i
$2$	0.782694	−	1.17788i	0.553448	−	0.832884i
$3$		0			0
$3$		0			0
$4$	−0.774781	−	1.84383i	−0.387391	−	0.921916i
$5$		−	2.59989i		−	1.16271i	−0.813651	−	0.581353i	$-0.802524\pi$
$5$		−	2.59989i		−	1.16271i	0.813651	−	0.581353i	$-0.197476\pi$
$6$		0			0
$7$	−0.300588	−	0.520633i	−0.113611	−	0.196781i	0.803612	−	0.595153i	$-0.202909\pi$
$7$	−0.300588	−	0.520633i	−0.113611	−	0.196781i	−0.917224	+	0.398372i	$0.869575\pi$
$8$	−2.77822	−	0.530559i	−0.982249	−	0.187581i
$9$		0			0
$10$	−3.06235	−	2.03492i	−0.968399	−	0.643497i
$11$	−2.40956	−	1.39116i	−0.726509	−	0.419450i	0.0906348	−	0.995884i	$-0.471110\pi$
$11$	−2.40956	−	1.39116i	−0.726509	−	0.419450i	−0.817144	+	0.576434i	$0.804444\pi$
$12$		0			0
$13$	−3.60516	−	0.0531995i	−0.999891	−	0.0147549i
$13$	−3.60516	−	0.0531995i	−0.999891	−	0.0147549i
$14$	−0.848509	−	0.0534414i	−0.226774	−	0.0142828i
$15$		0			0
$16$	−2.79943	+	2.85713i	−0.699857	+	0.714283i
$17$	1.29402	+	2.24132i	0.313847	+	0.543599i	0.979192	−	0.202937i	$-0.0650487\pi$
$17$	1.29402	+	2.24132i	0.313847	+	0.543599i	−0.665345	+	0.746536i	$0.731715\pi$
$18$		0			0
$19$	4.38088	−	2.52930i	1.00504	−	0.580262i	0.0953071	−	0.995448i	$-0.469617\pi$
$19$	4.38088	−	2.52930i	1.00504	−	0.580262i	0.909737	+	0.415186i	$0.136283\pi$
$20$	−4.79376	+	2.01435i	−1.07192	+	0.450421i
$21$		0			0
$22$	−3.52456	+	1.74931i	−0.751438	+	0.372954i
$23$	−2.94353	+	5.09835i	−0.613769	+	1.06308i	0.376830	+	0.926282i	$0.377014\pi$
$23$	−2.94353	+	5.09835i	−0.613769	+	1.06308i	−0.990599	+	0.136797i	$0.956319\pi$
$24$		0			0
$25$	−1.75942			−0.351885
$26$	−2.88440	+	4.20479i	−0.565677	+	0.824627i
$27$		0			0
$28$	−0.727070	+	0.957610i	−0.137403	+	0.180971i
$29$	−1.54071	−	0.889530i	−0.286103	−	0.165182i	0.350080	−	0.936720i	$-0.386154\pi$
$29$	−1.54071	−	0.889530i	−0.286103	−	0.165182i	−0.636183	+	0.771538i	$0.719488\pi$
$30$		0			0
$31$	5.09421			0.914947			0.457473	−	0.889223i	$-0.348755\pi$
$31$	5.09421			0.914947			0.457473	+	0.889223i	$0.348755\pi$
$32$	1.17425	+	5.53364i	0.207580	+	0.978218i
$33$		0			0
$34$	3.65282	+	0.230064i	0.626453	+	0.0394557i
$35$	−1.35359	+	0.781495i	−0.228798	+	0.132097i
$36$		0			0
$37$	−8.82719	−	5.09638i	−1.45118	−	0.837840i	−0.452633	−	0.891697i	$-0.649515\pi$
$37$	−8.82719	−	5.09638i	−1.45118	−	0.837840i	−0.998549	+	0.0538570i	$0.982848\pi$
$38$	0.449684	−	7.13981i	0.0729484	−	1.15823i
$39$		0			0
$40$	−1.37940	+	7.22306i	−0.218102	+	1.14207i
$41$	5.26242	−	9.11477i	0.821851	−	1.42349i	−0.0824509	−	0.996595i	$-0.526275\pi$
$41$	5.26242	−	9.11477i	0.821851	−	1.42349i	0.904302	−	0.426893i	$-0.140392\pi$
$42$		0			0
$43$	−8.44267	+	4.87438i	−1.28749	+	0.743335i	−0.978207	−	0.207633i	$-0.933424\pi$
$43$	−8.44267	+	4.87438i	−1.28749	+	0.743335i	−0.309288	+	0.950968i	$0.600091\pi$
$44$	−0.698182	+	5.52066i	−0.105255	+	0.832271i
$45$		0			0
$46$	3.70134	+	7.45756i	0.545732	+	1.09956i
$47$	−2.13951			−0.312080			−0.156040	−	0.987751i	$-0.549873\pi$
$47$	−2.13951			−0.312080			−0.156040	+	0.987751i	$0.549873\pi$
$48$		0			0
$49$	3.31929	−	5.74919i	0.474185	−	0.821312i
$50$	−1.37709	+	2.07238i	−0.194750	+	0.293079i
$51$		0			0
$52$	2.69512	+	6.68852i	0.373746	+	0.927531i
$53$		−	6.01748i		−	0.826565i	−0.910603	−	0.413282i	$-0.864382\pi$
$53$		−	6.01748i		−	0.826565i	0.910603	−	0.413282i	$-0.135618\pi$
$54$		0			0
$55$	−3.61686	+	6.26458i	−0.487697	+	0.844716i
$56$	0.558872	+	1.60591i	0.0746824	+	0.214599i
$57$		0			0
$58$	−2.25366	+	1.11854i	−0.295920	+	0.146871i
$59$	9.44349	−	5.45220i	1.22944	−	0.709816i	0.262526	−	0.964925i	$-0.415445\pi$
$59$	9.44349	−	5.45220i	1.22944	−	0.709816i	0.966912	+	0.255109i	$0.0821112\pi$
$60$		0			0
$61$	1.84865	−	1.06732i	0.236696	−	0.136656i	−0.376961	−	0.926229i	$-0.623031\pi$
$61$	1.84865	−	1.06732i	0.236696	−	0.136656i	0.613657	+	0.789573i	$0.289698\pi$
$62$	3.98720	−	6.00034i	0.506375	−	0.762044i
$63$		0			0
$64$	7.43701	+	2.94802i	0.929627	+	0.368503i
$65$	−0.138313	+	9.37301i	−0.0171556	+	1.16258i
$66$		0			0
$67$	3.39076	+	1.95766i	0.414247	+	0.239166i	0.692613	−	0.721309i	$-0.256459\pi$
$67$	3.39076	+	1.95766i	0.414247	+	0.239166i	−0.278366	+	0.960475i	$0.589793\pi$
$68$	3.13002	−	4.12249i	0.379571	−	0.499926i
$69$		0			0
$70$	−0.138942	+	2.20603i	−0.0166067	+	0.263671i
$71$	−0.230832	−	0.399814i	−0.0273948	−	0.0474491i	0.852003	−	0.523537i	$-0.175388\pi$
$71$	−0.230832	−	0.399814i	−0.0273948	−	0.0474491i	−0.879398	+	0.476088i	$0.842054\pi$
$72$		0			0
$73$	−14.8806			−1.74165			−0.870824	−	0.491595i	$-0.836414\pi$
$73$	−14.8806			−1.74165			−0.870824	+	0.491595i	$0.836414\pi$
$74$	−12.9119	+	6.40843i	−1.50098	+	0.744965i
$75$		0			0
$76$	−8.05784	−	6.11795i	−0.924297	−	0.701777i
$77$			1.67266i			0.190617i
$78$		0			0
$79$	−7.83968			−0.882033			−0.441017	−	0.897499i	$-0.645382\pi$
$79$	−7.83968			−0.882033			−0.441017	+	0.897499i	$0.645382\pi$
$80$	7.42823	+	7.27820i	0.830501	+	0.813728i
$81$		0			0
$82$	−6.61721	−	13.3325i	−0.730748	−	1.47233i
$83$		−	0.930501i		−	0.102136i	−0.998695	−	0.0510679i	$-0.983738\pi$
$83$		−	0.930501i		−	0.102136i	0.998695	−	0.0510679i	$-0.0162625\pi$
$84$		0			0
$85$	5.82717	−	3.36432i	0.632046	−	0.364912i
$86$	−0.866614	+	13.7596i	−0.0934494	+	1.48373i
$87$		0			0
$88$	5.95619	+	5.14336i	0.634932	+	0.548284i
$89$	−1.17791	+	2.04019i	−0.124858	+	0.216260i	−0.921677	−	0.387957i	$-0.873181\pi$
$89$	−1.17791	+	2.04019i	−0.124858	+	0.216260i	0.796820	+	0.604217i	$0.206514\pi$
$90$		0			0
$91$	1.05597	+	1.89296i	0.110696	+	0.198436i
$92$	11.6811	+	1.47727i	1.21784	+	0.154016i
$93$		0			0
$94$	−1.67458	+	2.52008i	−0.172720	+	0.259926i
$95$	−6.57591	−	11.3898i	−0.674674	−	1.16857i
$96$		0			0
$97$	5.91151	+	10.2390i	0.600223	+	1.03962i	0.992787	+	0.119892i	$0.0382549\pi$
$97$	5.91151	+	10.2390i	0.600223	+	1.03962i	−0.392564	+	0.919725i	$0.628412\pi$
$98$	−4.17383	−	8.40957i	−0.421621	−	0.849495i
$99$		0			0
$100$	1.36317	+	3.24408i	0.136317	+	0.324408i
$101$	−11.2176	−	6.47646i	−1.11619	−	0.644432i	−0.175763	−	0.984432i	$-0.556239\pi$
$101$	−11.2176	−	6.47646i	−1.11619	−	0.644432i	−0.940425	+	0.340001i	$0.889573\pi$
$102$		0			0
$103$	6.61141			0.651441			0.325721	−	0.945466i	$-0.394393\pi$
$103$	6.61141			0.651441			0.325721	+	0.945466i	$0.394393\pi$
$104$	9.98770	+	2.06055i	0.979374	+	0.202054i
$105$		0			0
$106$	−7.08785	−	4.70985i	−0.688432	−	0.457461i
$107$	8.87612	+	5.12463i	0.858087	+	0.495417i	0.863371	−	0.504569i	$-0.168349\pi$
$107$	8.87612	+	5.12463i	0.858087	+	0.495417i	−0.00528438	+	0.999986i	$0.501682\pi$
$108$		0			0
$109$		−	10.8192i		−	1.03630i	−0.855291	−	0.518148i	$-0.826622\pi$
$109$		−	10.8192i		−	1.03630i	0.855291	−	0.518148i	$-0.173378\pi$
$110$	4.54801	+	9.16346i	0.433635	+	0.873701i
$111$		0			0
$112$	2.32899	+	0.598656i	0.220069	+	0.0565677i
$113$	−4.75708	−	8.23951i	−0.447509	−	0.775108i	0.550714	−	0.834694i	$-0.314355\pi$
$113$	−4.75708	−	8.23951i	−0.447509	−	0.775108i	−0.998223	+	0.0595859i	$0.981022\pi$
$114$		0			0
$115$	13.2551	+	7.65286i	1.23605	+	0.713633i
$116$	−0.446429	+	3.53000i	−0.0414499	+	0.327752i
$117$		0			0
$118$	0.969346	−	15.3907i	0.0892355	−	1.41683i
$119$	0.777936	−	1.34742i	0.0713133	−	0.123518i
$120$		0			0
$121$	−1.62936	−	2.82213i	−0.148123	−	0.256557i
$122$	0.189758	−	3.01287i	0.0171799	−	0.272772i
$123$		0			0
$124$	−3.94690	−	9.39286i	−0.354442	−	0.843504i
$125$		−	8.42514i		−	0.753567i
$126$		0			0
$127$	9.21128	−	15.9544i	0.817369	−	1.41572i	−0.0902451	−	0.995920i	$-0.528765\pi$
$127$	9.21128	−	15.9544i	0.817369	−	1.41572i	0.907614	−	0.419805i	$-0.137902\pi$
$128$	9.29330	−	6.45248i	0.821420	−	0.570324i
$129$		0			0
$130$	10.9320	+	7.49911i	0.958799	+	0.657716i
$131$			0.795820i			0.0695311i	0.999395	+	0.0347655i	$0.0110684\pi$
$131$			0.795820i			0.0695311i	−0.999395	+	0.0347655i	$0.988932\pi$
$132$		0			0
$133$	−2.63368	−	1.52056i	−0.228369	−	0.131849i
$134$	4.95980	−	2.46165i	0.428461	−	0.212654i
$135$		0			0
$136$	−2.40593	−	6.91343i	−0.206307	−	0.592822i
$137$	−1.77845	−	3.08037i	−0.151943	−	0.263174i	0.779998	−	0.625781i	$-0.215220\pi$
$137$	−1.77845	−	3.08037i	−0.151943	−	0.263174i	−0.931942	+	0.362608i	$0.881886\pi$
$138$		0			0
$139$	1.86181	−	1.07491i	0.157916	−	0.0911731i	−0.418959	−	0.908005i	$-0.637605\pi$
$139$	1.86181	−	1.07491i	0.157916	−	0.0911731i	0.576876	+	0.816832i	$0.304272\pi$
$140$	2.48968	+	1.89030i	0.210416	+	0.159760i
$141$		0			0
$142$	−0.651602	−	0.0410396i	−0.0546812	−	0.00344397i
$143$	8.61283	+	5.14353i	0.720241	+	0.430124i
$144$		0			0
$145$	−2.31268	+	4.00568i	−0.192058	+	0.332653i
$146$	−11.6470	+	17.5275i	−0.963911	+	1.45059i
$147$		0			0
$148$	−2.55773	+	20.2244i	−0.210244	+	1.66244i
$149$	2.87752	−	1.66134i	0.235736	−	0.136102i	−0.377480	−	0.926018i	$-0.623209\pi$
$149$	2.87752	−	1.66134i	0.235736	−	0.136102i	0.613215	+	0.789916i	$0.289876\pi$
$150$		0			0
$151$	−6.66412			−0.542318			−0.271159	−	0.962535i	$-0.587407\pi$
$151$	−6.66412			−0.542318			−0.271159	+	0.962535i	$0.587407\pi$
$152$	−13.5130	+	4.70265i	−1.09605	+	0.381435i
$153$		0			0
$154$	1.97019	+	1.30918i	0.158762	+	0.105497i
$155$		−	13.2444i		−	1.06381i
$156$		0			0
$157$			1.24154i			0.0990854i	0.998772	+	0.0495427i	$0.0157764\pi$
$157$			1.24154i			0.0990854i	−0.998772	+	0.0495427i	$0.984224\pi$
$158$	−6.13607	+	9.23417i	−0.488159	+	0.734631i
$159$		0			0
$160$	14.3868	−	3.05292i	1.13738	−	0.241355i
$161$	3.53916			0.278925
$162$		0			0
$163$	9.43363	−	5.44651i	0.738899	−	0.426604i	−0.0827698	−	0.996569i	$-0.526377\pi$
$163$	9.43363	−	5.44651i	0.738899	−	0.426604i	0.821669	+	0.569965i	$0.193043\pi$
$164$	−20.8833	−	2.64105i	−1.63071	−	0.206232i
$165$		0			0
$166$	−1.09601	−	0.728297i	−0.0850672	−	0.0565268i
$167$	6.68150	−	11.5727i	0.517030	−	0.895522i	−0.482775	−	0.875745i	$-0.660371\pi$
$167$	6.68150	−	11.5727i	0.517030	−	0.895522i	0.999804	−	0.0197773i	$-0.00629571\pi$
$168$		0			0
$169$	12.9943	+	0.383585i	0.999565	+	0.0295065i
$170$	0.598142	−	9.49692i	0.0458754	−	0.728380i
$171$		0			0
$172$	15.5287	+	11.7903i	1.18406	+	0.899000i
$173$	5.66761	−	3.27220i	0.430901	−	0.248781i	−0.268830	−	0.963188i	$-0.586637\pi$
$173$	5.66761	−	3.27220i	0.430901	−	0.248781i	0.699730	+	0.714407i	$0.253304\pi$
$174$		0			0
$175$	0.528861	+	0.916015i	0.0399782	+	0.0692442i
$176$	10.7201	−	2.98997i	0.808058	−	0.225378i
$177$		0			0
$178$	1.48115	+	2.98427i	0.111017	+	0.223681i
$179$	13.5832	+	7.84225i	1.01525	+	0.586157i	0.912726	−	0.408573i	$-0.133973\pi$
$179$	13.5832	+	7.84225i	1.01525	+	0.586157i	0.102528	+	0.994730i	$0.467307\pi$
$180$		0			0
$181$		−	4.65816i		−	0.346238i	−0.984901	−	0.173119i	$-0.944615\pi$
$181$		−	4.65816i		−	0.346238i	0.984901	−	0.173119i	$-0.0553846\pi$
$182$	3.05617	+	0.237805i	0.226538	+	0.0176273i
$183$		0			0
$184$	10.8828	−	12.6026i	0.802288	−	0.929077i
$185$	−13.2500	+	22.9497i	−0.974162	+	1.68730i
$186$		0			0
$187$		−	7.20077i		−	0.526573i
$188$	1.65765	+	3.94490i	0.120897	+	0.287711i
$189$		0			0
$190$	−18.5627	−	1.16913i	−1.34668	−	0.0848176i
$191$	−4.34236	−	7.52119i	−0.314202	−	0.544214i	0.665066	−	0.746785i	$-0.268404\pi$
$191$	−4.34236	−	7.52119i	−0.314202	−	0.544214i	−0.979268	+	0.202571i	$0.935070\pi$
$192$		0			0
$193$	0.788692	−	1.36605i	0.0567713	−	0.0983308i	−0.836243	−	0.548359i	$-0.815253\pi$
$193$	0.788692	−	1.36605i	0.0567713	−	0.0983308i	0.893014	+	0.450028i	$0.148586\pi$
$194$	16.6872	+	1.05101i	1.19807	+	0.0754578i
$195$		0			0
$196$	−13.1723	−	1.66586i	−0.940875	−	0.118990i
$197$	22.1460	+	12.7860i	1.57784	+	0.910964i	0.995161	+	0.0982592i	$0.0313274\pi$
$197$	22.1460	+	12.7860i	1.57784	+	0.910964i	0.582675	+	0.812705i	$0.302006\pi$
$198$		0			0
$199$	10.3516	+	17.9295i	0.733807	+	1.27099i	0.955245	+	0.295816i	$0.0955915\pi$
$199$	10.3516	+	17.9295i	0.733807	+	1.27099i	−0.221438	+	0.975174i	$0.571075\pi$
$200$	4.88807	+	0.933479i	0.345639	+	0.0660069i
$201$		0			0
$202$	−16.4084	+	8.14380i	−1.15449	+	0.572996i
$203$			1.06953i			0.0750661i
$204$		0			0
$205$	−23.6974	−	13.6817i	−1.65510	−	0.955571i
$206$	5.17471	−	7.78741i	0.360539	−	0.542575i
$207$		0			0
$208$	10.2444	−	10.1515i	0.710320	−	0.703879i
$209$	−14.0747			−0.973564
$210$		0			0
$211$	18.3083	+	10.5703i	1.26040	+	0.727691i	0.973151	−	0.230166i	$-0.0739270\pi$
$211$	18.3083	+	10.5703i	1.26040	+	0.727691i	0.287246	+	0.957857i	$0.407260\pi$
$212$	−11.0952	+	4.66223i	−0.762023	+	0.320203i
$213$		0			0
$214$	12.9835	−	6.44395i	0.887531	−	0.440499i
$215$	12.6728	+	21.9500i	0.864281	+	1.49698i
$216$		0			0
$217$	−1.53126	−	2.65221i	−0.103948	−	0.180044i
$218$	−12.7437	−	8.46816i	−0.863114	−	0.573536i
$219$		0			0
$220$	14.3531	+	1.81520i	0.967686	+	0.122380i
$221$	−4.54593	−	8.14914i	−0.305792	−	0.548171i
$222$		0			0
$223$	4.03692	−	6.99214i	0.270332	−	0.468229i	−0.698615	−	0.715498i	$-0.746200\pi$
$223$	4.03692	−	6.99214i	0.270332	−	0.468229i	0.968947	+	0.247269i	$0.0795332\pi$
$224$	2.52803	−	2.27470i	0.168911	−	0.151985i
$225$		0			0
$226$	−13.4285	−	0.845760i	−0.893248	−	0.0562591i
$227$	−19.8519	+	11.4615i	−1.31761	+	0.760725i	−0.983344	−	0.181752i	$-0.941823\pi$
$227$	−19.8519	+	11.4615i	−1.31761	+	0.760725i	−0.334270	+	0.942477i	$0.608490\pi$
$228$		0			0
$229$		−	0.594709i		−	0.0392995i	−0.999807	−	0.0196497i	$-0.993745\pi$
$229$		−	0.594709i		−	0.0392995i	0.999807	−	0.0196497i	$-0.00625511\pi$
$230$	19.3888	−	9.62306i	1.27846	−	0.634526i
$231$		0			0
$232$	3.80849	+	3.28875i	0.250039	+	0.215917i
$233$	0.0945847			0.00619645			0.00309823	−	0.999995i	$-0.499014\pi$
$233$	0.0945847			0.00619645			0.00309823	+	0.999995i	$0.499014\pi$
$234$		0			0
$235$			5.56249i			0.362857i
$236$	−17.3696	−	13.1879i	−1.13066	−	0.858462i
$237$		0			0
$238$	−0.978213	−	1.97093i	−0.0634081	−	0.127757i
$239$	15.3694			0.994166			0.497083	−	0.867703i	$-0.334404\pi$
$239$	15.3694			0.994166			0.497083	+	0.867703i	$0.334404\pi$
$240$		0			0
$241$	5.02102	+	8.69665i	0.323432	+	0.560201i	0.981194	−	0.193025i	$-0.0618300\pi$
$241$	5.02102	+	8.69665i	0.323432	+	0.560201i	−0.657762	+	0.753226i	$0.728497\pi$
$242$	−4.59940	−	0.289683i	−0.295661	−	0.0186215i
$243$		0			0
$244$	−3.40026	−	2.58166i	−0.217679	−	0.165274i
$245$	−14.9472	−	8.62980i	−0.954945	−	0.551338i
$246$		0			0
$247$	−15.9283	+	8.88548i	−1.01350	+	0.565370i
$248$	−14.1528	−	2.70278i	−0.898705	−	0.171627i
$249$		0			0
$250$	−9.92376	−	6.59430i	−0.627634	−	0.417060i
$251$	−14.8114	+	8.55135i	−0.934886	+	0.539757i	−0.888353	−	0.459160i	$-0.848150\pi$
$251$	−14.8114	+	8.55135i	−0.934886	+	0.539757i	−0.0465324	+	0.998917i	$0.514817\pi$
$252$		0			0
$253$	14.1852	−	8.18984i	0.891818	−	0.514891i
$254$	−11.5827	−	23.3372i	−0.726763	−	1.46430i
$255$		0			0
$256$	−0.326406	−	15.9967i	−0.0204003	−	0.999792i
$257$	10.3500	−	17.9267i	0.645616	−	1.11824i	−0.338543	−	0.940951i	$-0.609934\pi$
$257$	10.3500	−	17.9267i	0.645616	−	1.11824i	0.984159	−	0.177288i	$-0.0567325\pi$
$258$		0			0
$259$			6.12764i			0.380753i
$260$	17.3894	−	7.00701i	1.07845	−	0.434556i
$261$		0			0
$262$	0.937376	+	0.622883i	0.0579113	+	0.0384818i
$263$	0.515631	−	0.893099i	0.0317952	−	0.0550708i	−0.849690	−	0.527283i	$-0.823211\pi$
$263$	0.515631	−	0.893099i	0.0317952	−	0.0550708i	0.881485	+	0.472212i	$0.156544\pi$
$264$		0			0
$265$	−15.6448			−0.961052
$266$	−3.85239	+	1.91202i	−0.236205	+	0.117233i
$267$		0			0
$268$	0.982490	−	7.76874i	0.0600151	−	0.474551i
$269$	−5.34569	+	3.08633i	−0.325932	+	0.188177i	−0.654034	−	0.756465i	$-0.726925\pi$
$269$	−5.34569	+	3.08633i	−0.325932	+	0.188177i	0.328101	+	0.944642i	$0.393591\pi$
$270$		0			0
$271$	6.85287	−	11.8695i	0.416282	−	0.721022i	−0.579280	−	0.815129i	$-0.696666\pi$
$271$	6.85287	−	11.8695i	0.416282	−	0.721022i	0.995562	+	0.0941065i	$0.0299994\pi$
$272$	−10.0263	−	2.57720i	−0.607932	−	0.156266i
$273$		0			0
$274$	−5.02027	−	0.316191i	−0.303286	−	0.0191018i
$275$	4.23944	+	2.44764i	0.255648	+	0.147598i
$276$		0			0
$277$	−24.4764	+	14.1314i	−1.47064	+	0.849076i	−0.999457	−	0.0329570i	$-0.989508\pi$
$277$	−24.4764	+	14.1314i	−1.47064	+	0.849076i	−0.471187	+	0.882033i	$0.656174\pi$
$278$	0.191109	−	3.03430i	0.0114619	−	0.181986i
$279$		0			0
$280$	4.17520	−	1.45301i	0.249516	−	0.0868337i
$281$	12.3330			0.735724			0.367862	−	0.929880i	$-0.380090\pi$
$281$	12.3330			0.735724			0.367862	+	0.929880i	$0.380090\pi$
$282$		0			0
$283$	17.0408	+	9.83851i	1.01297	+	0.584838i	0.912060	−	0.410057i	$-0.134491\pi$
$283$	17.0408	+	9.83851i	1.01297	+	0.584838i	0.100910	+	0.994896i	$0.467825\pi$
$284$	−0.558344	+	0.735384i	−0.0331316	+	0.0436370i
$285$		0			0
$286$	12.7996	−	6.11903i	0.756859	−	0.361826i
$287$	−6.32727			−0.373487
$288$		0			0
$289$	5.15100	−	8.92179i	0.303000	−	0.524811i
$290$	2.90807	+	5.85927i	0.170768	+	0.344068i
$291$		0			0
$292$	11.5292	+	27.4374i	0.674698	+	1.60565i
$293$	−10.1639	+	5.86812i	−0.593780	+	0.342819i	−0.766591	−	0.642136i	$-0.778048\pi$
$293$	−10.1639	+	5.86812i	−0.593780	+	0.342819i	0.172811	+	0.984955i	$0.444715\pi$
$294$		0			0
$295$	−14.1751	−	24.5520i	−0.825308	−	1.42947i
$296$	21.8200	+	18.8422i	1.26826	+	1.09518i
$297$		0			0
$298$	0.295369	−	4.68968i	0.0171103	−	0.271666i
$299$	10.8831	−	18.2238i	0.629388	−	1.05391i
$300$		0			0
$301$	5.07552	+	2.93036i	0.292548	+	0.168903i
$302$	−5.21596	+	7.84950i	−0.300145	+	0.451688i
$303$		0			0
$304$	−5.03741	+	19.5974i	−0.288915	+	1.12399i
$305$	−2.77491	−	4.80629i	−0.158891	−	0.275207i
$306$		0			0
$307$		−	5.08990i		−	0.290496i	−0.989395	−	0.145248i	$-0.953602\pi$
$307$		−	5.08990i		−	0.290496i	0.989395	−	0.145248i	$-0.0463980\pi$
$308$	3.08410	−	1.29595i	0.175733	−	0.0738434i
$309$		0			0
$310$	−15.6002	−	10.3663i	−0.886033	−	0.588766i
$311$	−25.1578			−1.42657			−0.713284	−	0.700875i	$-0.752793\pi$
$311$	−25.1578			−1.42657			−0.713284	+	0.700875i	$0.752793\pi$
$312$		0			0
$313$	12.4651			0.704569			0.352285	−	0.935893i	$-0.385405\pi$
$313$	12.4651			0.704569			0.352285	+	0.935893i	$0.385405\pi$
$314$	1.46237	+	0.971742i	0.0825266	+	0.0548386i
$315$		0			0
$316$	6.07404	+	14.4550i	0.341691	+	0.813160i
$317$		−	11.0238i		−	0.619160i	−0.950873	−	0.309580i	$-0.899811\pi$
$317$		−	11.0238i		−	0.619160i	0.950873	−	0.309580i	$-0.100189\pi$
$318$		0			0
$319$	2.47495	+	4.28675i	0.138571	+	0.240012i
$320$	7.66453	−	19.3354i	0.428460	−	1.08088i
$321$		0			0
$322$	2.77008	−	4.16869i	0.154370	−	0.232312i
$323$	11.3379	+	6.54597i	0.630860	+	0.364227i
$324$		0			0
$325$	6.34301	+	0.0936005i	0.351847	+	0.00519202i
$326$	0.968334	−	15.3746i	0.0536310	−	0.851520i
$327$		0			0
$328$	−19.4561	+	22.5308i	−1.07428	+	1.24406i
$329$	0.643110	+	1.11390i	0.0354558	+	0.0614113i
$330$		0			0
$331$	−14.3890	+	8.30750i	−0.790891	+	0.456621i	−0.840276	−	0.542158i	$-0.817607\pi$
$331$	−14.3890	+	8.30750i	−0.790891	+	0.456621i	0.0493848	+	0.998780i	$0.484274\pi$
$332$	−1.71569	+	0.720935i	−0.0941606	+	0.0395664i
$333$		0			0
$334$	−8.40163	−	16.9278i	−0.459717	−	0.926251i
$335$	5.08969	−	8.81560i	0.278079	−	0.481647i
$336$		0			0
$337$	−11.0591			−0.602427			−0.301214	−	0.953557i	$-0.597392\pi$
$337$	−11.0591			−0.602427			−0.301214	+	0.953557i	$0.597392\pi$
$338$	10.6224	−	15.0055i	0.577783	−	0.816191i
$339$		0			0
$340$	−10.7180	−	8.13771i	−0.581267	−	0.441330i
$341$	−12.2748	−	7.08685i	−0.664717	−	0.383774i
$342$		0			0
$343$	−8.19918			−0.442714
$344$	26.0417	−	9.06276i	1.40408	−	0.488631i
$345$		0			0
$346$	0.581763	−	9.23687i	0.0312758	−	0.496577i
$347$	1.92350	−	1.11054i	0.103259	−	0.0596167i	−0.447481	−	0.894293i	$-0.647679\pi$
$347$	1.92350	−	1.11054i	0.103259	−	0.0596167i	0.550740	+	0.834677i	$0.314345\pi$
$348$		0			0
$349$	11.6899	+	6.74919i	0.625748	+	0.361276i	0.779104	−	0.626895i	$-0.215675\pi$
$349$	11.6899	+	6.74919i	0.625748	+	0.361276i	−0.153355	+	0.988171i	$0.549008\pi$
$350$	1.49289	+	0.0940261i	0.0797982	+	0.00502591i
$351$		0			0
$352$	4.86874	−	14.9672i	0.259505	−	0.797754i
$353$	1.75509	−	3.03991i	0.0934143	−	0.161798i	−0.815531	−	0.578713i	$-0.803555\pi$
$353$	1.75509	−	3.03991i	0.0934143	−	0.161798i	0.908946	+	0.416915i	$0.136889\pi$
$354$		0			0
$355$	−1.03947	+	0.600139i	−0.0551694	+	0.0318521i
$356$	4.67439	+	0.591157i	0.247742	+	0.0313312i
$357$		0			0
$358$	19.8687	−	9.86121i	1.05009	−	0.521181i
$359$	−25.0138			−1.32018			−0.660090	−	0.751187i	$-0.729482\pi$
$359$	−25.0138			−1.32018			−0.660090	+	0.751187i	$0.729482\pi$
$360$		0			0
$361$	3.29476	−	5.70670i	0.173409	−	0.300353i
$362$	−5.48673	−	3.64591i	−0.288376	−	0.191625i
$363$		0			0
$364$	2.67215	−	3.41366i	0.140059	−	0.178924i
$365$			38.6880i			2.02502i
$366$		0			0
$367$	−10.2910	+	17.8245i	−0.537186	+	0.930434i	0.461868	+	0.886949i	$0.347179\pi$
$367$	−10.2910	+	17.8245i	−0.537186	+	0.930434i	−0.999054	+	0.0434851i	$0.986154\pi$
$368$	−6.32645	−	22.6825i	−0.329789	−	1.18241i
$369$		0			0
$370$	16.6612	+	33.5695i	0.866175	+	1.74519i
$371$	−3.13290	+	1.80878i	−0.162652	+	0.0939072i
$372$		0			0
$373$	12.3015	−	7.10225i	0.636946	−	0.367741i	−0.146491	−	0.989212i	$-0.546798\pi$
$373$	12.3015	−	7.10225i	0.636946	−	0.367741i	0.783437	+	0.621471i	$0.213465\pi$
$374$	−8.48162	−	5.63600i	−0.438574	−	0.291431i
$375$		0			0
$376$	5.94403	+	1.13514i	0.306540	+	0.0585402i
$377$	5.50718	+	3.28886i	0.283634	+	0.169385i
$378$		0			0
$379$	−6.23669	−	3.60075i	−0.320357	−	0.184958i	0.331195	−	0.943562i	$-0.392548\pi$
$379$	−6.23669	−	3.60075i	−0.320357	−	0.184958i	−0.651552	+	0.758604i	$0.725882\pi$
$380$	−15.9060	+	20.9495i	−0.815961	+	1.07469i
$381$		0			0
$382$	−12.2578	−	0.772027i	−0.627161	−	0.0395003i
$383$	11.8763	+	20.5704i	0.606852	+	1.05110i	0.991756	+	0.128142i	$0.0409014\pi$
$383$	11.8763	+	20.5704i	0.606852	+	1.05110i	−0.384903	+	0.922957i	$0.625765\pi$
$384$		0			0
$385$	4.34873			0.221632
$386$	−0.991738	−	1.99818i	−0.0504781	−	0.101705i
$387$		0			0
$388$	14.2989	−	18.8328i	0.725918	−	0.956093i
$389$			20.6264i			1.04580i	0.852394	+	0.522900i	$0.175150\pi$
$389$			20.6264i			1.04580i	−0.852394	+	0.522900i	$0.824850\pi$
$390$		0			0
$391$	−15.2360			−0.770519
$392$	−12.2720	+	14.2114i	−0.619830	+	0.717785i
$393$		0			0
$394$	32.3938	−	16.0777i	1.63198	−	0.809983i
$395$			20.3823i			1.02554i
$396$		0			0
$397$	−25.6669	+	14.8188i	−1.28819	+	0.743734i	−0.978330	−	0.207050i	$-0.933614\pi$
$397$	−25.6669	+	14.8188i	−1.28819	+	0.743734i	−0.309855	+	0.950784i	$0.600280\pi$
$398$	29.2209	+	1.84041i	1.46471	+	0.0922515i
$399$		0			0
$400$	4.92538	−	5.02691i	0.246269	−	0.251345i
$401$	−5.32482	+	9.22286i	−0.265909	+	0.460568i	−0.967801	−	0.251715i	$-0.919005\pi$
$401$	−5.32482	+	9.22286i	−0.265909	+	0.460568i	0.701892	+	0.712283i	$0.252339\pi$
$402$		0			0
$403$	−18.3654	−	0.271009i	−0.914847	−	0.0134999i
$404$	−3.25035	+	25.7011i	−0.161711	+	1.27868i
$405$		0			0
$406$	1.25977	+	0.837112i	0.0625213	+	0.0415452i
$407$	14.1798	+	24.5600i	0.702864	+	1.21740i
$408$		0			0
$409$	−0.271387	−	0.470056i	−0.0134192	−	0.0232428i	0.859238	−	0.511576i	$-0.170938\pi$
$409$	−0.271387	−	0.470056i	−0.0134192	−	0.0232428i	−0.872657	+	0.488334i	$0.837605\pi$
$410$	−34.6631	+	17.2040i	−1.71189	+	0.849645i
$411$		0			0
$412$	−5.12239	−	12.1903i	−0.252362	−	0.600574i
$413$	−5.67720	−	3.27773i	−0.279357	−	0.161287i
$414$		0			0
$415$	−2.41920			−0.118754
$416$	−3.93897	−	20.0121i	−0.193124	−	0.981174i
$417$		0			0
$418$	−11.0161	+	16.5782i	−0.538817	+	0.810866i
$419$	17.8473	+	10.3042i	0.871900	+	0.503392i	0.867979	−	0.496601i	$-0.165419\pi$
$419$	17.8473	+	10.3042i	0.871900	+	0.503392i	0.00392074	+	0.999992i	$0.498752\pi$
$420$		0			0
$421$			2.14198i			0.104394i	0.998637	+	0.0521968i	$0.0166223\pi$
$421$			2.14198i			0.104394i	−0.998637	+	0.0521968i	$0.983378\pi$
$422$	26.7803	−	13.2916i	1.30365	−	0.647025i
$423$		0			0
$424$	−3.19263	+	16.7179i	−0.155048	+	0.811893i
$425$	−2.27674	−	3.94343i	−0.110438	−	0.191284i
$426$		0			0
$427$	−1.11136	−	0.641646i	−0.0537827	−	0.0310514i
$428$	2.57190	−	20.3365i	0.124318	−	0.983003i
$429$		0			0
$430$	35.7733	+	2.25310i	1.72514	+	0.108654i
$431$	5.72822	−	9.92157i	0.275919	−	0.477905i	−0.694448	−	0.719543i	$-0.744351\pi$
$431$	5.72822	−	9.92157i	0.275919	−	0.477905i	0.970366	+	0.241638i	$0.0776846\pi$
$432$		0			0
$433$	−8.14866	−	14.1139i	−0.391600	−	0.678270i	0.601061	−	0.799203i	$-0.294745\pi$
$433$	−8.14866	−	14.1139i	−0.391600	−	0.678270i	−0.992661	+	0.120933i	$0.961411\pi$
$434$	−4.32248	−	0.272242i	−0.207486	−	0.0130680i
$435$		0			0
$436$	−19.9489	+	8.38255i	−0.955378	+	0.401451i
$437$			29.7804i			1.42459i
$438$		0			0
$439$	−1.34252	+	2.32532i	−0.0640751	+	0.110981i	−0.896283	−	0.443482i	$-0.853743\pi$
$439$	−1.34252	+	2.32532i	−0.0640751	+	0.110981i	0.832208	+	0.554463i	$0.187076\pi$
$440$	13.3722	−	15.4854i	0.637493	−	0.738239i
$441$		0			0
$442$	−13.1567	−	1.02375i	−0.625803	−	0.0486946i
$443$			14.6679i			0.696891i	0.937329	+	0.348446i	$0.113290\pi$
$443$			14.6679i			0.696891i	−0.937329	+	0.348446i	$0.886710\pi$
$444$		0			0
$445$	5.30428	+	3.06242i	0.251447	+	0.145173i
$446$	−5.07621	−	10.2277i	−0.240365	−	0.484295i
$447$		0			0
$448$	−0.700637	−	4.75809i	−0.0331020	−	0.224799i
$449$	−0.656457	−	1.13702i	−0.0309801	−	0.0536591i	0.850120	−	0.526590i	$-0.176530\pi$
$449$	−0.656457	−	1.13702i	−0.0309801	−	0.0536591i	−0.881100	+	0.472930i	$0.843196\pi$
$450$		0			0
$451$	−25.3602	+	14.6417i	−1.19416	+	0.689451i
$452$	−11.5066	+	15.1551i	−0.541223	+	0.712835i
$453$		0			0
$454$	−2.03773	+	32.3539i	−0.0956356	+	1.51844i
$455$	4.92148	−	2.74540i	0.230722	−	0.128706i
$456$		0			0
$457$	9.83743	−	17.0389i	0.460176	−	0.797048i	−0.538794	−	0.842438i	$-0.681120\pi$
$457$	9.83743	−	17.0389i	0.460176	−	0.797048i	0.998969	+	0.0453901i	$0.0144531\pi$
$458$	−0.700493	−	0.465475i	−0.0327319	−	0.0217502i
$459$		0			0
$460$	3.84075	−	30.3695i	0.179076	−	1.41599i
$461$	10.1402	−	5.85445i	0.472277	−	0.272669i	−0.244916	−	0.969544i	$-0.578760\pi$
$461$	10.1402	−	5.85445i	0.472277	−	0.272669i	0.717192	+	0.696875i	$0.245427\pi$
$462$		0			0
$463$	20.0915			0.933731			0.466866	−	0.884328i	$-0.345383\pi$
$463$	20.0915			0.933731			0.466866	+	0.884328i	$0.345383\pi$
$464$	6.85461	−	1.91184i	0.318217	−	0.0887549i
$465$		0			0
$466$	0.0740309	−	0.111409i	0.00342941	−	0.00516092i
$467$			38.0472i			1.76061i	0.474405	+	0.880307i	$0.342663\pi$
$467$			38.0472i			1.76061i	−0.474405	+	0.880307i	$0.657337\pi$
$468$		0			0
$469$		−	2.35379i		−	0.108688i
$470$	6.55192	+	4.35373i	0.302218	+	0.200822i
$471$		0			0
$472$	−29.1288	+	10.1371i	−1.34076	+	0.466597i
$473$	27.1241			1.24717
$474$		0			0
$475$	−7.70784	+	4.45012i	−0.353660	+	0.204186i
$476$	−3.08715	−	0.390423i	−0.141499	−	0.0178950i
$477$		0			0
$478$	12.0296	−	18.1033i	0.550219	−	0.828025i
$479$	−4.96607	+	8.60149i	−0.226906	+	0.393012i	−0.956889	−	0.290452i	$-0.906194\pi$
$479$	−4.96607	+	8.60149i	−0.226906	+	0.393012i	0.729984	+	0.683465i	$0.239528\pi$
$480$		0			0
$481$	31.5523	+	18.8429i	1.43866	+	0.859161i
$482$	14.1735	+	0.892685i	0.645585	+	0.0406607i
$483$		0			0
$484$	−3.94113	+	5.19079i	−0.179142	+	0.235945i
$485$	26.6204	−	15.3693i	1.20877	−	0.697883i
$486$		0			0
$487$	11.7461	+	20.3448i	0.532265	+	0.921910i	0.999290	+	0.0376664i	$0.0119924\pi$
$487$	11.7461	+	20.3448i	0.532265	+	0.921910i	−0.467025	+	0.884244i	$0.654674\pi$
$488$	−5.70224	+	1.98443i	−0.258128	+	0.0898309i
$489$		0			0
$490$	−21.8639	+	10.8515i	−0.987712	+	0.490221i
$491$	−26.6538	−	15.3886i	−1.20287	−	0.694478i	−0.241679	−	0.970356i	$-0.577698\pi$
$491$	−26.6538	−	15.3886i	−1.20287	−	0.694478i	−0.961193	+	0.275878i	$0.911031\pi$
$492$		0			0
$493$		−	4.60429i		−	0.207367i
$494$	−2.00102	+	25.7162i	−0.0900300	+	1.15703i
$495$		0			0
$496$	−14.2609	+	14.5548i	−0.640332	+	0.653531i
$497$	−0.138771	+	0.240358i	−0.00622472	+	0.0107815i
$498$		0			0
$499$			4.61772i			0.206718i	0.994644	+	0.103359i	$0.0329590\pi$
$499$			4.61772i			0.206718i	−0.994644	+	0.103359i	$0.967041\pi$
$500$	−15.5345	+	6.52764i	−0.694725	+	0.291925i
$501$		0			0
$502$	−1.52034	+	24.1390i	−0.0678562	+	1.07738i
$503$	−14.8441	−	25.7107i	−0.661865	−	1.14638i	−0.980125	−	0.198381i	$-0.936432\pi$
$503$	−14.8441	−	25.7107i	−0.661865	−	1.14638i	0.318260	−	0.948004i	$-0.396902\pi$
$504$		0			0
$505$	−16.8381	+	29.1644i	−0.749285	+	1.29780i
$506$	1.45607	−	23.1186i	0.0647302	−	1.02775i
$507$		0			0
$508$	−36.5540	−	4.62287i	−1.62182	−	0.205107i
$509$	−20.3599	−	11.7548i	−0.902438	−	0.521023i	−0.0244475	−	0.999701i	$-0.507783\pi$
$509$	−20.3599	−	11.7548i	−0.902438	−	0.521023i	−0.877990	+	0.478678i	$0.841116\pi$
$510$		0			0
$511$	4.47294	+	7.74736i	0.197871	+	0.342723i
$512$	−19.0976	−	12.1360i	−0.844001	−	0.536342i
$513$		0			0
$514$	−13.0146	−	26.2222i	−0.574049	−	1.15661i
$515$		−	17.1889i		−	0.757435i
$516$		0			0
$517$	5.15527	+	2.97640i	0.226729	+	0.130902i
$518$	7.21759	+	4.79606i	0.317123	+	0.210727i
$519$		0			0
$520$	5.35720	−	25.9669i	0.234929	−	1.13872i
$521$	11.7037			0.512747			0.256374	−	0.966578i	$-0.417472\pi$
$521$	11.7037			0.512747			0.256374	+	0.966578i	$0.417472\pi$
$522$		0			0
$523$	−10.9235	−	6.30668i	−0.477651	−	0.275772i	0.241786	−	0.970330i	$-0.422267\pi$
$523$	−10.9235	−	6.30668i	−0.477651	−	0.275772i	−0.719437	+	0.694558i	$0.755600\pi$
$524$	1.46736	−	0.616586i	0.0641018	−	0.0269357i
$525$		0			0
$526$	−0.648378	−	1.30637i	−0.0282706	−	0.0569605i
$527$	6.59203	+	11.4177i	0.287153	+	0.497364i
$528$		0			0
$529$	−5.82878	−	10.0957i	−0.253425	−	0.438945i
$530$	−12.2451	+	18.4276i	−0.531892	+	0.800444i
$531$		0			0
$532$	−0.763123	+	6.03416i	−0.0330856	+	0.261614i
$533$	−19.4567	+	32.5802i	−0.842765	+	1.41121i
$534$		0			0
$535$	13.3235	−	23.0769i	0.576024	−	0.997703i
$536$	−8.38162	−	7.23780i	−0.362031	−	0.312625i
$537$		0			0
$538$	−0.548718	+	8.71221i	−0.0236569	+	0.375610i
$539$	−15.9961	+	9.23533i	−0.688999	+	0.397794i
$540$		0			0
$541$			40.4799i			1.74037i	0.492728	+	0.870183i	$0.336000\pi$
$541$			40.4799i			1.74037i	−0.492728	+	0.870183i	$0.664000\pi$
$542$	−8.61712	−	17.3620i	−0.370137	−	0.745763i
$543$		0			0
$544$	−10.8831	+	9.79253i	−0.466610	+	0.419851i
$545$	−28.1288			−1.20491
$546$		0			0
$547$			27.1567i			1.16114i	0.814212	+	0.580568i	$0.197169\pi$
$547$			27.1567i			1.16114i	−0.814212	+	0.580568i	$0.802831\pi$
$548$	−4.30177	+	5.66578i	−0.183763	+	0.242030i
$549$		0			0
$550$	6.20119	−	3.07778i	0.264420	−	0.131237i
$551$	−8.99957			−0.383394
$552$		0			0
$553$	2.35651	+	4.08160i	0.100209	+	0.173567i
$554$	−2.51243	+	39.8907i	−0.106743	+	1.69479i
$555$		0			0
$556$	−3.42445	−	2.60003i	−0.145229	−	0.110266i
$557$	26.2789	+	15.1721i	1.11347	+	0.642863i	0.939726	−	0.341927i	$-0.111080\pi$
$557$	26.2789	+	15.1721i	1.11347	+	0.642863i	0.173746	+	0.984791i	$0.444413\pi$
$558$		0			0
$559$	30.6965	−	17.1238i	1.29832	−	0.724258i
$560$	1.55644	−	6.05512i	0.0657716	−	0.255875i
$561$		0			0
$562$	9.65294	−	14.5267i	0.407185	−	0.612772i
$563$	7.83182	−	4.52170i	0.330072	−	0.190567i	−0.325801	−	0.945438i	$-0.605634\pi$
$563$	7.83182	−	4.52170i	0.330072	−	0.190567i	0.655873	+	0.754871i	$0.272301\pi$
$564$		0			0
$565$	−21.4218	+	12.3679i	−0.901222	+	0.520321i
$566$	24.9263	−	12.3714i	1.04773	−	0.520008i
$567$		0			0
$568$	0.429179	+	1.23324i	0.0180079	+	0.0517456i
$569$	18.1496	−	31.4361i	0.760872	−	1.31787i	−0.181529	−	0.983386i	$-0.558105\pi$
$569$	18.1496	−	31.4361i	0.760872	−	1.31787i	0.942401	−	0.334484i	$-0.108562\pi$
$570$		0			0
$571$		−	24.9740i		−	1.04513i	−0.852599	−	0.522566i	$-0.824975\pi$
$571$		−	24.9740i		−	1.04513i	0.852599	−	0.522566i	$-0.175025\pi$
$572$	2.81075	−	19.8657i	0.117523	−	0.830627i
$573$		0			0
$574$	−4.95231	+	7.45273i	−0.206706	+	0.311071i
$575$	5.17893	−	8.97016i	0.215976	−	0.374082i
$576$		0			0
$577$	14.7654			0.614692			0.307346	−	0.951598i	$-0.400559\pi$
$577$	14.7654			0.614692			0.307346	+	0.951598i	$0.400559\pi$
$578$	−6.47711	−	13.0503i	−0.269412	−	0.542820i
$579$		0			0
$580$	9.17761	+	1.16067i	0.381080	+	0.0481940i
$581$	−0.484450	+	0.279697i	−0.0200984	+	0.0116038i
$582$		0			0
$583$	−8.37127	+	14.4995i	−0.346703	+	0.600507i
$584$	41.3417	+	7.89506i	1.71073	+	0.326700i
$585$		0			0
$586$	−1.04329	+	16.5647i	−0.0430979	+	0.684282i
$587$	−33.7254	−	19.4714i	−1.39200	−	0.803669i	−0.398460	−	0.917186i	$-0.630455\pi$
$587$	−33.7254	−	19.4714i	−1.39200	−	0.803669i	−0.993536	+	0.113517i	$0.963788\pi$
$588$		0			0
$589$	22.3171	−	12.8848i	0.919561	−	0.530909i
$590$	−40.0140	−	2.52019i	−1.64735	−	0.103755i
$591$		0			0
$592$	39.2721	−	10.9535i	1.61407	−	0.450186i
$593$	−19.6722			−0.807842			−0.403921	−	0.914794i	$-0.632353\pi$
$593$	−19.6722			−0.807842			−0.403921	+	0.914794i	$0.632353\pi$
$594$		0			0
$595$	−3.50315	−	2.02255i	−0.143615	−	0.0829163i
$596$	−5.29268	−	4.01849i	−0.216796	−	0.164604i
$597$		0			0
$598$	−12.9472	−	27.0826i	−0.529449	−	1.10749i
$599$	0.289136			0.0118138			0.00590689	−	0.999983i	$-0.498120\pi$
$599$	0.289136			0.0118138			0.00590689	+	0.999983i	$0.498120\pi$
$600$		0			0
$601$	−13.3071	+	23.0486i	−0.542808	+	0.940171i	0.455933	+	0.890014i	$0.349305\pi$
$601$	−13.3071	+	23.0486i	−0.542808	+	0.940171i	−0.998741	+	0.0501569i	$0.984028\pi$
$602$	7.42417	−	3.68476i	0.302587	−	0.150180i
$603$		0			0
$604$	5.16324	+	12.2875i	0.210089	+	0.499972i
$605$	−7.33722	+	4.23614i	−0.298300	+	0.172224i
$606$		0			0
$607$	−4.23231	−	7.33058i	−0.171784	−	0.297539i	0.767259	−	0.641337i	$-0.221620\pi$
$607$	−4.23231	−	7.33058i	−0.171784	−	0.297539i	−0.939044	+	0.343798i	$0.888287\pi$
$608$	19.1405	+	21.2722i	0.776250	+	0.862701i
$609$		0			0
$610$	−7.83312	−	0.493351i	−0.317154	−	0.0199752i
$611$	7.71327	+	0.113821i	0.312046	+	0.00460470i
$612$		0			0
$613$	−11.1194	−	6.41977i	−0.449107	−	0.259292i	0.258346	−	0.966053i	$-0.416823\pi$
$613$	−11.1194	−	6.41977i	−0.449107	−	0.259292i	−0.707453	+	0.706760i	$0.750156\pi$
$614$	−5.99527	−	3.98383i	−0.241949	−	0.160774i
$615$		0			0
$616$	0.887446	−	4.64702i	0.0357562	−	0.187234i
$617$	2.51106	+	4.34928i	0.101091	+	0.175095i	0.912135	−	0.409891i	$-0.134433\pi$
$617$	2.51106	+	4.34928i	0.101091	+	0.175095i	−0.811043	+	0.584986i	$0.801100\pi$
$618$		0			0
$619$		−	25.2782i		−	1.01602i	−0.861353	−	0.508008i	$-0.830382\pi$
$619$		−	25.2782i		−	1.01602i	0.861353	−	0.508008i	$-0.169618\pi$
$620$	−24.4204	+	10.2615i	−0.980747	+	0.412111i
$621$		0			0
$622$	−19.6909	+	29.6328i	−0.789531	+	1.18817i
$623$	1.41626			0.0567411
$624$		0			0
$625$	−30.7015			−1.22806
$626$	9.75636	−	14.6823i	0.389943	−	0.586824i
$627$		0			0
$628$	2.28918	−	0.961919i	0.0913483	−	0.0383847i
$629$		−	26.3794i		−	1.05181i
$630$		0			0
$631$	16.7070	+	28.9374i	0.665097	+	1.15198i	0.979259	+	0.202612i	$0.0649430\pi$
$631$	16.7070	+	28.9374i	0.665097	+	1.15198i	−0.314163	+	0.949369i	$0.601724\pi$
$632$	21.7804	+	4.15942i	0.866376	+	0.165453i
$633$		0			0
$634$	−12.9847	−	8.62829i	−0.515689	−	0.342673i
$635$	−41.4797	−	23.9483i	−1.64607	−	0.950360i
$636$		0			0
$637$	−12.2724	+	20.5501i	−0.486252	+	0.814226i
$638$	6.98638	+	0.440021i	0.276594	+	0.0174206i
$639$		0			0
$640$	−16.7757	−	24.1616i	−0.663119	−	0.955070i
$641$	5.95235	+	10.3098i	0.235104	+	0.407212i	0.959303	−	0.282379i	$-0.0911236\pi$
$641$	5.95235	+	10.3098i	0.235104	+	0.407212i	−0.724199	+	0.689591i	$0.757790\pi$
$642$		0			0
$643$	29.4994	−	17.0315i	1.16334	−	0.671656i	0.211239	−	0.977434i	$-0.432250\pi$
$643$	29.4994	−	17.0315i	1.16334	−	0.671656i	0.952103	+	0.305778i	$0.0989167\pi$
$644$	−2.74207	−	6.52561i	−0.108053	−	0.257145i
$645$		0			0
$646$	16.5845	−	8.23120i	0.652507	−	0.323852i
$647$	19.9224	−	34.5065i	0.783229	−	1.35659i	−0.146823	−	0.989163i	$-0.546905\pi$
$647$	19.9224	−	34.5065i	0.783229	−	1.35659i	0.930052	−	0.367429i	$-0.119762\pi$
$648$		0			0
$649$	−30.3395			−1.19093
$650$	5.07488	−	7.39801i	0.199053	−	0.290174i
$651$		0			0
$652$	−17.3514	−	13.1742i	−0.679535	−	0.515940i
$653$	17.1513	+	9.90232i	0.671183	+	0.387508i	0.796525	−	0.604606i	$-0.206669\pi$
$653$	17.1513	+	9.90232i	0.671183	+	0.387508i	−0.125342	+	0.992114i	$0.540003\pi$
$654$		0			0
$655$	2.06904			0.0808442
$656$	11.3103	+	40.5516i	0.441595	+	1.58327i
$657$		0			0
$658$	1.81539	+	0.114338i	0.0707714	+	0.00445738i
$659$	24.1533	−	13.9449i	0.940880	−	0.543218i	0.0506442	−	0.998717i	$-0.483873\pi$
$659$	24.1533	−	13.9449i	0.940880	−	0.543218i	0.890236	+	0.455499i	$0.150539\pi$
$660$		0			0
$661$	17.0661	+	9.85313i	0.663795	+	0.383242i	0.793722	−	0.608281i	$-0.208141\pi$
$661$	17.0661	+	9.85313i	0.663795	+	0.383242i	−0.129926	+	0.991524i	$0.541474\pi$
$662$	−1.47699	+	23.4507i	−0.0574048	+	0.911437i
$663$		0			0
$664$	−0.493686	+	2.58514i	−0.0191587	+	0.100323i
$665$	−3.95328	+	6.84728i	−0.153301	+	0.265526i
$666$		0			0
$667$	9.07027	−	5.23672i	0.351202	−	0.202767i
$668$	−26.5148	−	3.35325i	−1.02589	−	0.129741i
$669$		0			0
$670$	−6.40001	−	12.8949i	−0.247254	−	0.498175i
$671$	−5.93924			−0.229282
$672$		0			0
$673$	18.0814	−	31.3179i	0.696986	−	1.20722i	−0.272521	−	0.962150i	$-0.587857\pi$
$673$	18.0814	−	31.3179i	0.696986	−	1.20722i	0.969507	−	0.245065i	$-0.0788094\pi$
$674$	−8.65589	+	13.0262i	−0.333412	+	0.501752i
$675$		0			0
$676$	−9.36050	−	24.2566i	−0.360019	−	0.932945i
$677$		−	43.5560i		−	1.67399i	−0.547209	−	0.836996i	$-0.684310\pi$
$677$		−	43.5560i		−	1.67399i	0.547209	−	0.836996i	$-0.315690\pi$
$678$		0			0
$679$	3.55386	−	6.15546i	0.136384	−	0.236225i
$680$	−17.9741	+	6.25516i	−0.689277	+	0.239875i
$681$		0			0
$682$	−17.9548	+	8.91133i	−0.687526	+	0.341233i
$683$	−6.89615	+	3.98149i	−0.263874	+	0.152348i	−0.626100	−	0.779742i	$-0.715350\pi$
$683$	−6.89615	+	3.98149i	−0.263874	+	0.152348i	0.362227	+	0.932090i	$0.382017\pi$
$684$		0			0
$685$	−8.00862	+	4.62378i	−0.305994	+	0.176666i
$686$	−6.41745	+	9.65762i	−0.245019	+	0.368730i
$687$		0			0
$688$	9.70790	−	37.7673i	0.370110	−	1.43986i
$689$	−0.320127	+	21.6940i	−0.0121959	+	0.826475i
$690$		0			0
$691$	−30.2709	−	17.4769i	−1.15156	−	0.664854i	−0.202294	−	0.979325i	$-0.564840\pi$
$691$	−30.2709	−	17.4769i	−1.15156	−	0.664854i	−0.949267	+	0.314471i	$0.898173\pi$
$692$	−10.4245	−	7.91488i	−0.396282	−	0.300879i
$693$		0			0
$694$	0.197442	−	3.13486i	0.00749479	−	0.118998i
$695$	−2.79466	−	4.84049i	−0.106007	−	0.183610i
$696$		0			0
$697$	27.2388			1.03174
$698$	17.0993	−	8.48675i	0.647220	−	0.321228i
$699$		0			0
$700$	1.27922	−	1.68484i	0.0483502	−	0.0636811i
$701$			10.8831i			0.411050i	0.978652	+	0.205525i	$0.0658901\pi$
$701$			10.8831i			0.411050i	−0.978652	+	0.205525i	$0.934110\pi$
$702$		0			0
$703$	−51.5612			−1.94467
$704$	−13.8187	−	17.4495i	−0.520814	−	0.657652i
$705$		0			0
$706$	−2.20694	−	4.44660i	−0.0830592	−	0.167350i
$707$			7.78698i			0.292859i
$708$		0			0
$709$	31.1767	−	17.9999i	1.17087	−	0.676000i	0.216982	−	0.976176i	$-0.430379\pi$
$709$	31.1767	−	17.9999i	1.17087	−	0.676000i	0.953884	+	0.300176i	$0.0970454\pi$
$710$	−0.106699	+	1.69409i	−0.00400432	+	0.0635781i
$711$		0			0
$712$	4.35492	−	5.04316i	0.163208	−	0.189000i
$713$	−14.9950	+	25.9720i	−0.561566	+	0.972661i
$714$		0			0
$715$	13.3726	−	22.3924i	0.500108	−	0.837428i
$716$	3.93580	−	31.1211i	0.147088	−	1.16305i
$717$		0			0
$718$	−19.5782	+	29.4632i	−0.730651	+	1.09956i
$719$	2.97642	+	5.15531i	0.111002	+	0.192261i	0.916174	−	0.400780i	$-0.131261\pi$
$719$	2.97642	+	5.15531i	0.111002	+	0.192261i	−0.805173	+	0.593040i	$0.797927\pi$
$720$		0			0
$721$	−1.98731	−	3.44212i	−0.0740112	−	0.128191i
$722$	−4.14299	−	8.34742i	−0.154186	−	0.310659i
$723$		0			0
$724$	−8.58887	+	3.60906i	−0.319203	+	0.134130i
$725$	2.71076	+	1.56506i	0.100675	+	0.0581249i
$726$		0			0
$727$	34.3229			1.27297			0.636484	−	0.771290i	$-0.280388\pi$
$727$	34.3229			1.27297			0.636484	+	0.771290i	$0.280388\pi$
$728$	−1.92939	−	5.81930i	−0.0715079	−	0.215678i
$729$		0			0
$730$	45.5697	+	30.2809i	1.68661	+	1.12075i
$731$	−21.8500	−	12.6151i	−0.808153	−	0.466587i
$732$		0			0
$733$		−	6.24499i		−	0.230664i	−0.993327	−	0.115332i	$-0.963207\pi$
$733$		−	6.24499i		−	0.230664i	0.993327	−	0.115332i	$-0.0367932\pi$
$734$	12.9404	+	26.0727i	0.477639	+	0.962360i
$735$		0			0
$736$	−31.6689	−	10.3017i	−1.16733	−	0.379726i
$737$	−5.44682	−	9.43417i	−0.200636	−	0.347512i
$738$		0			0
$739$	−5.26210	−	3.03807i	−0.193569	−	0.111757i	0.400083	−	0.916479i	$-0.368981\pi$
$739$	−5.26210	−	3.03807i	−0.193569	−	0.111757i	−0.593652	+	0.804722i	$0.702315\pi$
$740$	52.5813	+	6.64980i	1.93293	+	0.244452i
$741$		0			0
$742$	−0.321583	+	5.10589i	−0.0118057	+	0.187443i
$743$	4.10832	−	7.11582i	0.150720	−	0.261054i	−0.780773	−	0.624815i	$-0.785174\pi$
$743$	4.10832	−	7.11582i	0.150720	−	0.261054i	0.931492	+	0.363761i	$0.118508\pi$
$744$		0			0
$745$	−4.31929	−	7.48124i	−0.158247	−	0.274091i
$746$	1.26271	−	20.0485i	0.0462310	−	0.734027i
$747$		0			0
$748$	−13.2770	+	5.57902i	−0.485456	+	0.203989i
$749$		−	6.16160i		−	0.225140i
$750$		0			0
$751$	−10.9266	+	18.9254i	−0.398717	+	0.690599i	−0.993568	−	0.113238i	$-0.963878\pi$
$751$	−10.9266	+	18.9254i	−0.398717	+	0.690599i	0.594851	+	0.803836i	$0.297211\pi$
$752$	5.98941	−	6.11286i	0.218411	−	0.222913i
$753$		0			0
$754$	8.18431	−	3.91261i	0.298055	−	0.142489i
$755$			17.3260i			0.630557i
$756$		0			0
$757$	18.5854	+	10.7303i	0.675498	+	0.389999i	0.798157	−	0.602450i	$-0.205809\pi$
$757$	18.5854	+	10.7303i	0.675498	+	0.389999i	−0.122659	+	0.992449i	$0.539142\pi$
$758$	−9.12266	+	4.52776i	−0.331350	+	0.164456i
$759$		0			0
$760$	12.2264	+	35.1323i	0.443497	+	1.27438i
$761$	11.7372	+	20.3294i	0.425472	+	0.736939i	0.996464	−	0.0840166i	$-0.0267749\pi$
$761$	11.7372	+	20.3294i	0.425472	+	0.736939i	−0.570993	+	0.820955i	$0.693442\pi$
$762$		0			0
$763$	−5.63286	+	3.25213i	−0.203923	+	0.117735i
$764$	−10.5034	+	13.8338i	−0.380000	+	0.500491i
$765$		0			0
$766$	33.5249	+	2.11149i	1.21130	+	0.0762912i
$767$	−34.3353	+	19.1537i	−1.23978	+	0.691599i
$768$		0			0
$769$	−5.94997	+	10.3056i	−0.214561	+	0.371631i	−0.953137	−	0.302540i	$-0.902165\pi$
$769$	−5.94997	+	10.3056i	−0.214561	+	0.371631i	0.738575	+	0.674171i	$0.235499\pi$
$770$	3.40373	−	5.12227i	0.122662	−	0.184594i
$771$		0			0
$772$	−3.12984	−	0.395822i	−0.112645	−	0.0142459i
$773$	12.2803	−	7.09004i	0.441692	−	0.255011i	−0.262623	−	0.964898i	$-0.584588\pi$
$773$	12.2803	−	7.09004i	0.441692	−	0.255011i	0.704315	+	0.709888i	$0.251254\pi$
$774$		0			0
$775$	−8.96287			−0.321956
$776$	−10.9911	−	31.5827i	−0.394556	−	1.13375i
$777$		0			0
$778$	24.2953	+	16.1442i	0.871030	+	0.578796i
$779$		−	53.2410i		−	1.90756i
$780$		0			0
$781$			1.28450i			0.0459630i
$782$	−11.9251	+	17.9461i	−0.426442	+	0.641752i
$783$		0			0
$784$	7.13406	+	25.5781i	0.254788	+	0.913503i
$785$	3.22786			0.115207
$786$		0			0
$787$	−7.12142	+	4.11155i	−0.253851	+	0.146561i	−0.621526	−	0.783393i	$-0.713487\pi$
$787$	−7.12142	+	4.11155i	−0.253851	+	0.146561i	0.367675	+	0.929954i	$0.380154\pi$
$788$	6.41692	−	50.7398i	0.228593	−	1.80753i
$789$		0			0
$790$	24.0078	+	15.9531i	0.854160	+	0.567586i
$791$	−2.85984	+	4.95339i	−0.101684	+	0.176122i
$792$		0			0
$793$	−6.72146	+	3.74951i	−0.238686	+	0.133149i
$794$	−2.63463	+	41.8310i	−0.0934995	+	1.48453i
$795$		0			0
$796$	25.0388	−	32.9781i	0.887476	−	1.16888i
$797$	−1.61224	+	0.930825i	−0.0571083	+	0.0329715i	−0.528282	−	0.849069i	$-0.677164\pi$
$797$	−1.61224	+	0.930825i	−0.0571083	+	0.0329715i	0.471174	+	0.882040i	$0.343830\pi$
$798$		0			0
$799$	−2.76858	−	4.79532i	−0.0979453	−	0.169646i
$800$	−2.06601	−	9.73602i	−0.0730444	−	0.344220i
$801$		0			0
$802$	6.69568	+	13.4907i	0.236433	+	0.476372i
$803$	35.8558	+	20.7013i	1.26532	+	0.730534i
$804$		0			0
$805$		−	9.20142i		−	0.324308i
$806$	−14.6937	+	21.4201i	−0.517564	+	0.754490i
$807$		0			0
$808$	27.7287	+	23.9446i	0.975492	+	0.842368i
$809$	18.9274	−	32.7832i	0.665452	−	1.15260i	−0.313711	−	0.949519i	$-0.601572\pi$
$809$	18.9274	−	32.7832i	0.665452	−	1.15260i	0.979163	−	0.203078i	$-0.0650943\pi$
$810$		0			0
$811$		−	16.1872i		−	0.568409i	−0.958764	−	0.284205i	$-0.908270\pi$
$811$		−	16.1872i		−	0.568409i	0.958764	−	0.284205i	$-0.0917295\pi$
$812$	1.97203	−	0.828649i	0.0692046	−	0.0290799i
$813$		0			0
$814$	40.0271	+	2.52101i	1.40295	+	0.0883615i
$815$	−14.1603	−	24.5264i	−0.496015	−	0.859122i
$816$		0			0
$817$	−24.6576	+	42.7082i	−0.862659	+	1.49417i
$818$	−0.766080	−	0.0482498i	−0.0267854	−	0.00168702i
$819$		0			0
$820$	−6.86645	+	54.2943i	−0.239787	+	1.89604i
$821$	23.9391	+	13.8212i	0.835479	+	0.482364i	0.855725	−	0.517431i	$-0.173111\pi$
$821$	23.9391	+	13.8212i	0.835479	+	0.482364i	−0.0202456	+	0.999795i	$0.506445\pi$
$822$		0			0
$823$	−16.9386	−	29.3385i	−0.590442	−	1.02268i	−0.994173	−	0.107797i	$-0.965620\pi$
$823$	−16.9386	−	29.3385i	−0.590442	−	1.02268i	0.403731	−	0.914878i	$-0.367713\pi$
$824$	−18.3679	−	3.50774i	−0.639878	−	0.122198i
$825$		0			0
$826$	−8.30426	+	4.12157i	−0.288942	+	0.143408i
$827$		−	1.10220i		−	0.0383272i	−0.999816	−	0.0191636i	$-0.993900\pi$
$827$		−	1.10220i		−	0.0383272i	0.999816	−	0.0191636i	$-0.00610034\pi$
$828$		0			0
$829$	17.1870	+	9.92292i	0.596929	+	0.344637i	0.767833	−	0.640650i	$-0.221335\pi$
$829$	17.1870	+	9.92292i	0.596929	+	0.344637i	−0.170903	+	0.985288i	$0.554669\pi$
$830$	−1.89349	+	2.84952i	−0.0657241	+	0.0989082i
$831$		0			0
$832$	−26.6548	−	11.0237i	−0.924088	−	0.382179i
$833$	17.1810			0.595286
$834$		0			0
$835$	−30.0877	−	17.3712i	−1.04123	−	0.601154i
$836$	10.9048	+	25.9513i	0.377150	+	0.897544i
$837$		0			0
$838$	26.1060	−	12.9569i	0.901818	−	0.447590i
$839$	8.38043	+	14.5153i	0.289325	+	0.501125i	0.973649	−	0.228053i	$-0.0732359\pi$
$839$	8.38043	+	14.5153i	0.289325	+	0.501125i	−0.684324	+	0.729178i	$0.739903\pi$
$840$		0			0
$841$	−12.9175	−	22.3737i	−0.445430	−	0.771508i
$842$	2.52298	+	1.67651i	0.0869478	+	0.0577764i
$843$		0			0
$844$	5.30493	−	41.9471i	0.182603	−	1.44388i
$845$	0.997279	−	33.7838i	0.0343074	−	1.16220i
$846$		0			0
$847$	−0.979528	+	1.69659i	−0.0336570	+	0.0582956i
$848$	17.1927	+	16.8455i	0.590401	+	0.578477i
$849$		0			0
$850$	−6.42686	−	0.404781i	−0.220439	−	0.0138839i
$851$	51.9663	−	30.0027i	1.78138	−	1.02848i
$852$		0			0
$853$			12.5392i			0.429333i	0.976687	+	0.214666i	$0.0688664\pi$
$853$			12.5392i			0.429333i	−0.976687	+	0.214666i	$0.931134\pi$
$854$	−1.62564	+	0.806836i	−0.0556281	+	0.0276093i
$855$		0			0
$856$	−21.9409	−	18.9467i	−0.749924	−	0.647583i
$857$	−34.8182			−1.18937			−0.594684	−	0.803960i	$-0.702723\pi$
$857$	−34.8182			−1.18937			−0.594684	+	0.803960i	$0.702723\pi$
$858$		0			0
$859$		−	33.1090i		−	1.12966i	−0.825206	−	0.564832i	$-0.808941\pi$
$859$		−	33.1090i		−	1.12966i	0.825206	−	0.564832i	$-0.191059\pi$
$860$	30.6534	−	40.3730i	1.04527	−	1.37671i
$861$		0			0
$862$	−7.20293	−	14.5127i	−0.245333	−	0.494304i
$863$	48.3902			1.64722			0.823611	−	0.567155i	$-0.191956\pi$
$863$	48.3902			1.64722			0.823611	+	0.567155i	$0.191956\pi$
$864$		0			0
$865$	−8.50735	−	14.7352i	−0.289259	−	0.501011i
$866$	−23.0023	−	1.44875i	−0.781650	−	0.0492305i
$867$		0			0
$868$	−3.70384	+	4.87826i	−0.125717	+	0.165579i
$869$	18.8902	+	10.9062i	0.640805	+	0.369969i
$870$		0			0
$871$	−12.1201	−	7.23804i	−0.410673	−	0.245252i
$872$	−5.74025	+	30.0583i	−0.194389	+	1.01790i
$873$		0			0
$874$	35.0776	+	23.3089i	1.18652	+	0.788436i
$875$	−4.38641	+	2.53249i	−0.148288	+	0.0856139i
$876$		0			0
$877$	36.8042	−	21.2489i	1.24279	−	0.717524i	0.273127	−	0.961978i	$-0.411942\pi$
$877$	36.8042	−	21.2489i	1.24279	−	0.717524i	0.969661	+	0.244454i	$0.0786087\pi$
$878$	1.68815	+	3.40134i	0.0569723	+	0.114790i
$879$		0			0
$880$	−7.77360	−	27.8711i	−0.262048	−	0.939534i
$881$	−0.254151	+	0.440202i	−0.00856257	+	0.0148308i	−0.870275	−	0.492566i	$-0.836059\pi$
$881$	−0.254151	+	0.440202i	−0.00856257	+	0.0148308i	0.861712	+	0.507397i	$0.169392\pi$
$882$		0			0
$883$			47.2885i			1.59139i	0.605700	+	0.795693i	$0.292893\pi$
$883$			47.2885i			1.59139i	−0.605700	+	0.795693i	$0.707107\pi$
$884$	−11.5035	+	14.6957i	−0.386906	+	0.494271i
$885$		0			0
$886$	17.2769	+	11.4804i	0.580430	+	0.385693i
$887$	−5.21481	+	9.03232i	−0.175096	+	0.303276i	−0.940195	−	0.340638i	$-0.889357\pi$
$887$	−5.21481	+	9.03232i	−0.175096	+	0.303276i	0.765098	+	0.643914i	$0.222690\pi$
$888$		0			0
$889$	−11.0752			−0.371450
$890$	7.75878	−	3.85084i	0.260075	−	0.129080i
$891$		0			0
$892$	−16.0201	−	2.02601i	−0.536391	−	0.0678358i
$893$	−9.37295	+	5.41147i	−0.313654	+	0.181088i
$894$		0			0
$895$	20.3890	−	35.3147i	0.681528	−	1.18044i
$896$	−6.15283	−	2.89887i	−0.205552	−	0.0968443i
$897$		0			0
$898$	−1.85307	−	0.116711i	−0.0618377	−	0.00389470i
$899$	−7.84870	−	4.53145i	−0.261769	−	0.151132i
$900$		0			0
$901$	13.4871	−	7.78677i	0.449320	−	0.259415i
$902$	−2.60315	+	41.3311i	−0.0866753	+	1.37618i
$903$		0			0
$904$	8.84468	+	25.4151i	0.294170	+	0.845293i
$905$	−12.1107			−0.402573
$906$		0			0
$907$	−20.2878	−	11.7132i	−0.673646	−	0.388930i	0.123811	−	0.992306i	$-0.460488\pi$
$907$	−20.2878	−	11.7132i	−0.673646	−	0.388930i	−0.797457	+	0.603376i	$0.793822\pi$
$908$	36.5139	+	27.7234i	1.21176	+	0.920032i
$909$		0			0
$910$	0.618267	−	7.94570i	0.0204953	−	0.263397i
$911$	−53.8994			−1.78577			−0.892883	−	0.450289i	$-0.851321\pi$
$911$	−53.8994			−1.78577			−0.892883	+	0.450289i	$0.851321\pi$
$912$		0			0
$913$	−1.29447	+	2.24210i	−0.0428409	+	0.0742025i
$914$	−12.3700	−	24.9235i	−0.409165	−	0.824397i
$915$		0			0
$916$	−1.09654	+	0.460769i	−0.0362308	+	0.0152242i
$917$	0.414330	−	0.239214i	0.0136824	−	0.00789953i
$918$		0			0
$919$	−21.8643	−	37.8701i	−0.721237	−	1.24922i	−0.960504	−	0.278265i	$-0.910241\pi$
$919$	−21.8643	−	37.8701i	−0.721237	−	1.24922i	0.239268	−	0.970954i	$-0.423093\pi$
$920$	−32.7654	−	28.2940i	−1.08024	−	0.932825i
$921$		0			0
$922$	1.04086	−	16.5261i	0.0342789	−	0.544260i
$923$	0.810918	+	1.45367i	0.0266917	+	0.0478482i
$924$		0			0
$925$	15.5308	+	8.96670i	0.510649	+	0.294823i
$926$	15.7255	−	23.6653i	0.516772	−	0.777690i
$927$		0			0
$928$	3.11315	−	9.57026i	0.102194	−	0.314159i
$929$	2.52459	+	4.37272i	0.0828291	+	0.143464i	0.904464	−	0.426550i	$-0.140271\pi$
$929$	2.52459	+	4.37272i	0.0828291	+	0.143464i	−0.821635	+	0.570014i	$0.806938\pi$
$930$		0			0
$931$		−	33.5820i		−	1.10061i
$932$	−0.0732825	−	0.174398i	−0.00240045	−	0.00571260i
$933$		0			0
$934$	44.8148	+	29.7793i	1.46639	+	0.974408i
$935$	−18.7212			−0.612249
$936$		0			0
$937$	44.5775			1.45628			0.728141	−	0.685427i	$-0.240385\pi$
$937$	44.5775			1.45628			0.728141	+	0.685427i	$0.240385\pi$
$938$	−2.77247	−	1.84230i	−0.0905243	−	0.0601531i
$939$		0			0
$940$	10.2563	−	4.30971i	0.334523	−	0.140567i
$941$			58.1679i			1.89622i	0.317943	+	0.948110i	$0.397008\pi$
$941$			58.1679i			1.89622i	−0.317943	+	0.948110i	$0.602992\pi$
$942$		0			0
$943$	30.9802	+	53.6593i	1.00885	+	1.74739i
$944$	−10.8587	+	42.2444i	−0.353421	+	1.37494i
$945$		0			0
$946$	21.2299	−	31.9488i	0.690243	−	1.03875i
$947$	−8.18618	−	4.72629i	−0.266015	−	0.153584i	0.361060	−	0.932542i	$-0.382415\pi$
$947$	−8.18618	−	4.72629i	−0.266015	−	0.153584i	−0.627075	+	0.778959i	$0.715748\pi$
$948$		0			0
$949$	53.6471	+	0.791642i	1.74146	+	0.0256978i
$950$	−0.791186	+	12.5620i	−0.0256695	+	0.407564i
$951$		0			0
$952$	−2.87617	+	3.33070i	−0.0932170	+	0.107949i
$953$	−9.38165	−	16.2495i	−0.303901	−	0.526373i	0.673115	−	0.739538i	$-0.264956\pi$
$953$	−9.38165	−	16.2495i	−0.303901	−	0.526373i	−0.977016	+	0.213165i	$0.931623\pi$
$954$		0			0
$955$	−19.5542	+	11.2897i	−0.632761	+	0.365325i
$956$	−11.9079	−	28.3386i	−0.385131	−	0.916537i
$957$		0			0
$958$	6.24457	+	12.5818i	0.201753	+	0.406498i
$959$	−1.06916	+	1.85184i	−0.0345250	+	0.0597991i
$960$		0			0
$961$	−5.04906			−0.162873
$962$	46.8903	−	22.4165i	1.51181	−	0.722737i
$963$		0			0
$964$	12.1450	−	15.9959i	0.391163	−	0.515194i
$965$	−3.55159	−	2.05051i	−0.114330	−	0.0660083i
$966$		0			0
$967$	13.9692			0.449218			0.224609	−	0.974449i	$-0.427889\pi$
$967$	13.9692			0.449218			0.224609	+	0.974449i	$0.427889\pi$
$968$	3.02940	+	8.70496i	0.0973687	+	0.279788i
$969$		0			0
$970$	2.73250	−	43.3849i	0.0877353	−	1.39301i
$971$	−10.8263	+	6.25059i	−0.347434	+	0.200591i	−0.663555	−	0.748128i	$-0.730953\pi$
$971$	−10.8263	+	6.25059i	−0.347434	+	0.200591i	0.316121	+	0.948719i	$0.397620\pi$
$972$		0			0
$973$	−1.11927	−	0.646212i	−0.0358822	−	0.0207166i
$974$	33.1572	+	2.08833i	1.06243	+	0.0669144i
$975$		0			0
$976$	−2.12569	+	8.26973i	−0.0680418	+	0.264707i
$977$	7.03484	−	12.1847i	0.225065	−	0.389823i	−0.731274	−	0.682084i	$-0.761074\pi$
$977$	7.03484	−	12.1847i	0.225065	−	0.389823i	0.956339	+	0.292260i	$0.0944074\pi$
$978$		0			0
$979$	5.67646	−	3.27731i	0.181421	−	0.104743i
$980$	−4.33104	+	34.2464i	−0.138350	+	1.09396i
$981$		0			0
$982$	−38.9877	+	19.3503i	−1.24415	+	0.617494i
$983$	42.4961			1.35541			0.677707	−	0.735332i	$-0.262974\pi$
$983$	42.4961			1.35541			0.677707	+	0.735332i	$0.262974\pi$
$984$		0			0
$985$	33.2422	−	57.5771i	1.05918	−	1.83456i
$986$	−5.42328	−	3.60375i	−0.172713	−	0.114767i
$987$		0			0
$988$	28.7243	+	22.4849i	0.913842	+	0.715339i
$989$		−	57.3916i		−	1.82495i
$990$		0			0
$991$	4.71260	−	8.16245i	0.149701	−	0.259289i	−0.781416	−	0.624010i	$-0.785502\pi$
$991$	4.71260	−	8.16245i	0.149701	−	0.259289i	0.931117	+	0.364721i	$0.118836\pi$
$992$	5.98188	+	28.1895i	0.189925	+	0.895017i
$993$		0			0
$994$	0.174497	+	0.351581i	0.00553470	+	0.0111515i
$995$	46.6148	−	26.9131i	1.47779	−	0.853201i
$996$		0			0
$997$	−6.28844	+	3.63063i	−0.199157	+	0.114983i	−0.596262	−	0.802790i	$-0.703348\pi$
$997$	−6.28844	+	3.63063i	−0.199157	+	0.114983i	0.397105	+	0.917773i	$0.370015\pi$
$998$	5.43910	+	3.61426i	0.172172	+	0.114408i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.be.a.685.9		24
3.2	odd	2		104.2.r.a.61.4	yes	24
8.5	even	2	inner	936.2.be.a.685.8		24
12.11	even	2		416.2.z.a.113.3		24
13.3	even	3	inner	936.2.be.a.757.8		24
24.5	odd	2		104.2.r.a.61.5	yes	24
24.11	even	2		416.2.z.a.113.10		24
39.29	odd	6		104.2.r.a.29.5	yes	24
104.29	even	6	inner	936.2.be.a.757.9		24
156.107	even	6		416.2.z.a.81.10		24
312.29	odd	6		104.2.r.a.29.4	✓	24
312.107	even	6		416.2.z.a.81.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.r.a.29.4	✓	24	312.29	odd	6
104.2.r.a.29.5	yes	24	39.29	odd	6
104.2.r.a.61.4	yes	24	3.2	odd	2
104.2.r.a.61.5	yes	24	24.5	odd	2
416.2.z.a.81.3		24	312.107	even	6
416.2.z.a.81.10		24	156.107	even	6
416.2.z.a.113.3		24	12.11	even	2
416.2.z.a.113.10		24	24.11	even	2
936.2.be.a.685.8		24	8.5	even	2	inner
936.2.be.a.685.9		24	1.1	even	1	trivial
936.2.be.a.757.8		24	13.3	even	3	inner
936.2.be.a.757.9		24	104.29	even	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.782694 - 1.17788i) q^{2} +(-0.774781 - 1.84383i) q^{4} -2.59989i q^{5} +(-0.300588 - 0.520633i) q^{7} +(-2.77822 - 0.530559i) q^{8} +(-3.06235 - 2.03492i) q^{10} +(-2.40956 - 1.39116i) q^{11} +(-3.60516 - 0.0531995i) q^{13} +(-0.848509 - 0.0534414i) q^{14} +(-2.79943 + 2.85713i) q^{16} +(1.29402 + 2.24132i) q^{17} +(4.38088 - 2.52930i) q^{19} +(-4.79376 + 2.01435i) q^{20} +(-3.52456 + 1.74931i) q^{22} +(-2.94353 + 5.09835i) q^{23} -1.75942 q^{25} +(-2.88440 + 4.20479i) q^{26} +(-0.727070 + 0.957610i) q^{28} +(-1.54071 - 0.889530i) q^{29} +5.09421 q^{31} +(1.17425 + 5.53364i) q^{32} +(3.65282 + 0.230064i) q^{34} +(-1.35359 + 0.781495i) q^{35} +(-8.82719 - 5.09638i) q^{37} +(0.449684 - 7.13981i) q^{38} +(-1.37940 + 7.22306i) q^{40} +(5.26242 - 9.11477i) q^{41} +(-8.44267 + 4.87438i) q^{43} +(-0.698182 + 5.52066i) q^{44} +(3.70134 + 7.45756i) q^{46} -2.13951 q^{47} +(3.31929 - 5.74919i) q^{49} +(-1.37709 + 2.07238i) q^{50} +(2.69512 + 6.68852i) q^{52} -6.01748i q^{53} +(-3.61686 + 6.26458i) q^{55} +(0.558872 + 1.60591i) q^{56} +(-2.25366 + 1.11854i) q^{58} +(9.44349 - 5.45220i) q^{59} +(1.84865 - 1.06732i) q^{61} +(3.98720 - 6.00034i) q^{62} +(7.43701 + 2.94802i) q^{64} +(-0.138313 + 9.37301i) q^{65} +(3.39076 + 1.95766i) q^{67} +(3.13002 - 4.12249i) q^{68} +(-0.138942 + 2.20603i) q^{70} +(-0.230832 - 0.399814i) q^{71} -14.8806 q^{73} +(-12.9119 + 6.40843i) q^{74} +(-8.05784 - 6.11795i) q^{76} +1.67266i q^{77} -7.83968 q^{79} +(7.42823 + 7.27820i) q^{80} +(-6.61721 - 13.3325i) q^{82} -0.930501i q^{83} +(5.82717 - 3.36432i) q^{85} +(-0.866614 + 13.7596i) q^{86} +(5.95619 + 5.14336i) q^{88} +(-1.17791 + 2.04019i) q^{89} +(1.05597 + 1.89296i) q^{91} +(11.6811 + 1.47727i) q^{92} +(-1.67458 + 2.52008i) q^{94} +(-6.57591 - 11.3898i) q^{95} +(5.91151 + 10.2390i) q^{97} +(-4.17383 - 8.40957i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8} - 3 q^{10} - 8 q^{14} - q^{16} + 11 q^{20} - 2 q^{22} + 14 q^{23} - 12 q^{25} + 3 q^{26} - 4 q^{28} - 8 q^{31} + 21 q^{32} + 14 q^{34} - 12 q^{38} + 54 q^{40}+ \cdots + 17 q^{98}+O(q^{100}) \) 24 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8 - 3 * q^10 - 8 * q^14 - q^16 + 11 * q^20 - 2 * q^22 + 14 * q^23 - 12 * q^25 + 3 * q^26 - 4 * q^28 - 8 * q^31 + 21 * q^32 + 14 * q^34 - 12 * q^38 + 54 * q^40 + 4 * q^41 + 24 * q^46 + 8 * q^47 + 6 * q^49 - 32 * q^50 - 4 * q^52 + 8 * q^55 - 8 * q^56 + 33 * q^58 + 14 * q^62 + 26 * q^64 - 30 * q^65 - 23 * q^68 - 16 * q^70 - 30 * q^71 - 12 * q^73 + 7 * q^74 + 14 * q^76 - 48 * q^79 - 29 * q^80 - q^82 + 96 * q^86 + 4 * q^88 + 22 * q^89 + 80 * q^92 - 42 * q^94 - 60 * q^95 + 2 * q^97 + 17 * q^98

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