LMFDB - Embedded newform 297.2.k.a.107.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(107,297)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("297.107"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.k (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(16)] == traces)

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			107.6
Character	$\chi$	$=$	297.107
Dual form			297.2.k.a.161.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.824821 - 0.599267i) q^{2} +(-0.296826 + 0.913536i) q^{4} +(-1.82477 + 2.51158i) q^{5} +(-3.98157 - 1.29369i) q^{7} +(0.932731 + 2.87065i) q^{8} +3.16513i q^{10} +(1.18580 + 3.09740i) q^{11} +(-0.209956 - 0.288980i) q^{13} +(-4.05935 + 1.31896i) q^{14} +(0.935424 + 0.679625i) q^{16} +(2.52248 + 1.83269i) q^{17} +(-0.384024 + 0.124777i) q^{19} +(-1.75278 - 2.41250i) q^{20} +(2.83425 + 1.84418i) q^{22} -2.82276i q^{23} +(-1.43317 - 4.41084i) q^{25} +(-0.346353 - 0.112537i) q^{26} +(2.36367 - 3.25331i) q^{28} +(-1.91796 + 5.90288i) q^{29} +(6.54568 - 4.75571i) q^{31} -4.85793 q^{32} +3.17887 q^{34} +(10.5147 - 7.63935i) q^{35} +(1.01570 - 3.12601i) q^{37} +(-0.241976 + 0.333051i) q^{38} +(-8.91190 - 2.89565i) q^{40} +(2.35035 + 7.23364i) q^{41} +9.26842i q^{43} +(-3.18156 + 0.163887i) q^{44} +(-1.69159 - 2.32827i) q^{46} +(12.0447 - 3.91355i) q^{47} +(8.51614 + 6.18734i) q^{49} +(-3.82538 - 2.77930i) q^{50} +(0.326315 - 0.106026i) q^{52} +(-2.07104 - 2.85055i) q^{53} +(-9.94319 - 2.67380i) q^{55} -12.6364i q^{56} +(1.95543 + 6.01819i) q^{58} +(-11.0755 - 3.59863i) q^{59} +(-0.698776 + 0.961782i) q^{61} +(2.54907 - 7.84522i) q^{62} +(-5.87777 + 4.27045i) q^{64} +1.10892 q^{65} -15.3289 q^{67} +(-2.42297 + 1.76039i) q^{68} +(4.09470 - 12.6022i) q^{70} +(0.357651 - 0.492264i) q^{71} +(10.8303 + 3.51899i) q^{73} +(-1.03554 - 3.18708i) q^{74} -0.387857i q^{76} +(-0.714289 - 13.8666i) q^{77} +(2.84509 + 3.91593i) q^{79} +(-3.41387 + 1.10923i) q^{80} +(6.27351 + 4.55797i) q^{82} +(5.36077 + 3.89483i) q^{83} +(-9.20591 + 2.99118i) q^{85} +(5.55426 + 7.64478i) q^{86} +(-7.78551 + 6.29307i) q^{88} +7.29922i q^{89} +(0.462105 + 1.42221i) q^{91} +(2.57870 + 0.837869i) q^{92} +(7.58943 - 10.4460i) q^{94} +(0.387368 - 1.19220i) q^{95} +(4.20629 - 3.05605i) q^{97} +10.7322 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{4} - 4 q^{16} + 36 q^{22} + 8 q^{25} - 100 q^{28} + 8 q^{31} - 64 q^{34} - 12 q^{37} - 60 q^{40} - 20 q^{46} + 100 q^{52} + 8 q^{55} + 24 q^{58} + 60 q^{61} + 36 q^{64} - 24 q^{67} + 8 q^{70}+ \cdots - 24 q^{97}+O(q^{100}) $ 32 * q - 8 * q^4 - 4 * q^16 + 36 * q^22 + 8 * q^25 - 100 * q^28 + 8 * q^31 - 64 * q^34 - 12 * q^37 - 60 * q^40 - 20 * q^46 + 100 * q^52 + 8 * q^55 + 24 * q^58 + 60 * q^61 + 36 * q^64 - 24 * q^67 + 8 * q^70 + 80 * q^73 - 60 * q^79 + 72 * q^82 - 20 * q^85 - 24 * q^88 + 24 * q^91 + 20 * q^94 - 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$-1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	0.824821	−	0.599267i	0.583236	−	0.423746i	−0.256653	−	0.966504i	$-0.582620\pi$
$2$	0.824821	−	0.599267i	0.583236	−	0.423746i	0.839889	+	0.542758i	$0.182620\pi$
$3$		0			0
$3$		0			0
$4$	−0.296826	+	0.913536i	−0.148413	+	0.456768i
$5$	−1.82477	+	2.51158i	−0.816062	+	1.12321i	0.174297	+	0.984693i	$0.444235\pi$
$5$	−1.82477	+	2.51158i	−0.816062	+	1.12321i	−0.990360	+	0.138520i	$0.955765\pi$
$6$		0			0
$7$	−3.98157	−	1.29369i	−1.50489	−	0.488969i	−0.563451	−	0.826149i	$-0.690527\pi$
$7$	−3.98157	−	1.29369i	−1.50489	−	0.488969i	−0.941440	+	0.337180i	$0.890527\pi$
$8$	0.932731	+	2.87065i	0.329770	+	1.01493i
$9$		0			0
$10$			3.16513i			1.00090i
$11$	1.18580	+	3.09740i	0.357533	+	0.933900i
$11$	1.18580	+	3.09740i	0.357533	+	0.933900i
$12$		0			0
$13$	−0.209956	−	0.288980i	−0.0582315	−	0.0801487i	0.778908	−	0.627138i	$-0.215774\pi$
$13$	−0.209956	−	0.288980i	−0.0582315	−	0.0801487i	−0.837140	+	0.546989i	$0.815774\pi$
$14$	−4.05935	+	1.31896i	−1.08491	+	0.352507i
$15$		0			0
$16$	0.935424	+	0.679625i	0.233856	+	0.169906i
$17$	2.52248	+	1.83269i	0.611792	+	0.444493i	0.850045	−	0.526710i	$-0.176575\pi$
$17$	2.52248	+	1.83269i	0.611792	+	0.444493i	−0.238253	+	0.971203i	$0.576575\pi$
$18$		0			0
$19$	−0.384024	+	0.124777i	−0.0881011	+	0.0286258i	−0.352736	−	0.935723i	$-0.614749\pi$
$19$	−0.384024	+	0.124777i	−0.0881011	+	0.0286258i	0.264635	+	0.964349i	$0.414749\pi$
$20$	−1.75278	−	2.41250i	−0.391934	−	0.539451i
$21$		0			0
$22$	2.83425	+	1.84418i	0.604263	+	0.393181i
$23$		−	2.82276i		−	0.588587i	−0.955715	−	0.294293i	$-0.904916\pi$
$23$		−	2.82276i		−	0.588587i	0.955715	−	0.294293i	$-0.0950843\pi$
$24$		0			0
$25$	−1.43317	−	4.41084i	−0.286634	−	0.882168i
$26$	−0.346353	−	0.112537i	−0.0679254	−	0.0220703i
$27$		0			0
$28$	2.36367	−	3.25331i	0.446691	−	0.614817i
$29$	−1.91796	+	5.90288i	−0.356157	+	1.09614i	0.599179	+	0.800615i	$0.295494\pi$
$29$	−1.91796	+	5.90288i	−0.356157	+	1.09614i	−0.955336	+	0.295522i	$0.904506\pi$
$30$		0			0
$31$	6.54568	−	4.75571i	1.17564	−	0.854151i	0.183966	−	0.982933i	$-0.441107\pi$
$31$	6.54568	−	4.75571i	1.17564	−	0.854151i	0.991673	+	0.128781i	$0.0411065\pi$
$32$	−4.85793			−0.858769
$33$		0			0
$34$	3.17887			0.545171
$35$	10.5147	−	7.63935i	1.77730	−	1.29129i
$36$		0			0
$37$	1.01570	−	3.12601i	0.166981	−	0.513914i	−0.832196	−	0.554481i	$-0.812917\pi$
$37$	1.01570	−	3.12601i	0.166981	−	0.513914i	0.999177	+	0.0405678i	$0.0129167\pi$
$38$	−0.241976	+	0.333051i	−0.0392537	+	0.0540281i
$39$		0			0
$40$	−8.91190	−	2.89565i	−1.40910	−	0.457843i
$41$	2.35035	+	7.23364i	0.367063	+	1.12971i	0.948679	+	0.316241i	$0.102421\pi$
$41$	2.35035	+	7.23364i	0.367063	+	1.12971i	−0.581615	+	0.813464i	$0.697579\pi$
$42$		0			0
$43$			9.26842i			1.41342i	0.707503	+	0.706710i	$0.249821\pi$
$43$			9.26842i			1.41342i	−0.707503	+	0.706710i	$0.750179\pi$
$44$	−3.18156	+	0.163887i	−0.479639	+	0.0247069i
$45$		0			0
$46$	−1.69159	−	2.32827i	−0.249411	−	0.343285i
$47$	12.0447	−	3.91355i	1.75689	−	0.570850i	0.760024	−	0.649896i	$-0.225187\pi$
$47$	12.0447	−	3.91355i	1.75689	−	0.570850i	0.996871	+	0.0790459i	$0.0251874\pi$
$48$		0			0
$49$	8.51614	+	6.18734i	1.21659	+	0.883905i
$50$	−3.82538	−	2.77930i	−0.540991	−	0.393053i
$51$		0			0
$52$	0.326315	−	0.106026i	0.0452517	−	0.0147032i
$53$	−2.07104	−	2.85055i	−0.284480	−	0.391553i	0.642731	−	0.766092i	$-0.277801\pi$
$53$	−2.07104	−	2.85055i	−0.284480	−	0.391553i	−0.927211	+	0.374539i	$0.877801\pi$
$54$		0			0
$55$	−9.94319	−	2.67380i	−1.34074	−	0.360535i
$56$		−	12.6364i		−	1.68861i
$57$		0			0
$58$	1.95543	+	6.01819i	0.256760	+	0.790227i
$59$	−11.0755	−	3.59863i	−1.44190	−	0.468502i	−0.519412	−	0.854524i	$-0.673849\pi$
$59$	−11.0755	−	3.59863i	−1.44190	−	0.468502i	−0.922490	+	0.386022i	$0.873849\pi$
$60$		0			0
$61$	−0.698776	+	0.961782i	−0.0894691	+	0.123144i	−0.851405	−	0.524509i	$-0.824249\pi$
$61$	−0.698776	+	0.961782i	−0.0894691	+	0.123144i	0.761936	+	0.647652i	$0.224249\pi$
$62$	2.54907	−	7.84522i	0.323732	−	0.996345i
$63$		0			0
$64$	−5.87777	+	4.27045i	−0.734721	+	0.533806i
$65$	1.10892			0.137545
$66$		0			0
$67$	−15.3289			−1.87272			−0.936362	−	0.351035i	$-0.885830\pi$
$67$	−15.3289			−1.87272			−0.936362	+	0.351035i	$0.885830\pi$
$68$	−2.42297	+	1.76039i	−0.293828	+	0.213479i
$69$		0			0
$70$	4.09470	−	12.6022i	0.489410	−	1.50625i
$71$	0.357651	−	0.492264i	0.0424453	−	0.0584210i	−0.787267	−	0.616612i	$-0.788505\pi$
$71$	0.357651	−	0.492264i	0.0424453	−	0.0584210i	0.829712	+	0.558192i	$0.188505\pi$
$72$		0			0
$73$	10.8303	+	3.51899i	1.26760	+	0.411867i	0.864195	−	0.503157i	$-0.167828\pi$
$73$	10.8303	+	3.51899i	1.26760	+	0.411867i	0.403401	+	0.915023i	$0.367828\pi$
$74$	−1.03554	−	3.18708i	−0.120380	−	0.370490i
$75$		0			0
$76$		−	0.387857i		−	0.0444902i
$77$	−0.714289	−	13.8666i	−0.0814007	−	1.58024i
$78$		0			0
$79$	2.84509	+	3.91593i	0.320098	+	0.440577i	0.938497	−	0.345287i	$-0.112219\pi$
$79$	2.84509	+	3.91593i	0.320098	+	0.440577i	−0.618399	+	0.785864i	$0.712219\pi$
$80$	−3.41387	+	1.10923i	−0.381682	+	0.124016i
$81$		0			0
$82$	6.27351	+	4.55797i	0.692793	+	0.503343i
$83$	5.36077	+	3.89483i	0.588421	+	0.427513i	0.841750	−	0.539867i	$-0.181526\pi$
$83$	5.36077	+	3.89483i	0.588421	+	0.427513i	−0.253329	+	0.967380i	$0.581526\pi$
$84$		0			0
$85$	−9.20591	+	2.99118i	−0.998521	+	0.324439i
$86$	5.55426	+	7.64478i	0.598931	+	0.824358i
$87$		0			0
$88$	−7.78551	+	6.29307i	−0.829938	+	0.670844i
$89$			7.29922i			0.773716i	0.922139	+	0.386858i	$0.126440\pi$
$89$			7.29922i			0.773716i	−0.922139	+	0.386858i	$0.873560\pi$
$90$		0			0
$91$	0.462105	+	1.42221i	0.0484418	+	0.149088i
$92$	2.57870	+	0.837869i	0.268848	+	0.0873539i
$93$		0			0
$94$	7.58943	−	10.4460i	0.782790	−	1.07742i
$95$	0.387368	−	1.19220i	0.0397431	−	0.122317i
$96$		0			0
$97$	4.20629	−	3.05605i	0.427084	−	0.310295i	−0.353398	−	0.935473i	$-0.614974\pi$
$97$	4.20629	−	3.05605i	0.427084	−	0.310295i	0.780482	+	0.625178i	$0.214974\pi$
$98$	10.7322			1.08411
$99$		0			0
$100$	4.45487			0.445487
$101$	−6.58321	+	4.78298i	−0.655054	+	0.475924i	−0.864989	−	0.501791i	$-0.832675\pi$
$101$	−6.58321	+	4.78298i	−0.655054	+	0.475924i	0.209935	+	0.977715i	$0.432675\pi$
$102$		0			0
$103$	4.26514	−	13.1268i	0.420257	−	1.29342i	−0.487207	−	0.873287i	$-0.661984\pi$
$103$	4.26514	−	13.1268i	0.420257	−	1.29342i	0.907463	−	0.420131i	$-0.138016\pi$
$104$	0.633729	−	0.872253i	0.0621422	−	0.0855315i
$105$		0			0
$106$	−3.41648	−	1.11008i	−0.331838	−	0.107821i
$107$	1.25282	+	3.85579i	0.121115	+	0.372753i	0.993173	−	0.116649i	$-0.0372151\pi$
$107$	1.25282	+	3.85579i	0.121115	+	0.372753i	−0.872058	+	0.489402i	$0.837215\pi$
$108$		0			0
$109$			5.57814i			0.534289i	0.963656	+	0.267145i	$0.0860801\pi$
$109$			5.57814i			0.534289i	−0.963656	+	0.267145i	$0.913920\pi$
$110$	−9.80367	+	3.75323i	−0.934743	+	0.357856i
$111$		0			0
$112$	−2.84523	−	3.91612i	−0.268849	−	0.370039i
$113$	6.92887	−	2.25133i	0.651814	−	0.211787i	0.0356000	−	0.999366i	$-0.488666\pi$
$113$	6.92887	−	2.25133i	0.651814	−	0.211787i	0.616214	+	0.787579i	$0.288666\pi$
$114$		0			0
$115$	7.08960	+	5.15090i	0.661109	+	0.480324i
$116$	−4.82319	−	3.50426i	−0.447822	−	0.325362i
$117$		0			0
$118$	−11.2918	+	3.66893i	−1.03950	+	0.337753i
$119$	−7.67250	−	10.5603i	−0.703337	−	0.968061i
$120$		0			0
$121$	−8.18774	+	7.34581i	−0.744340	+	0.667801i
$122$			1.21205i			0.109734i
$123$		0			0
$124$	2.40159	+	7.39133i	0.215669	+	0.663761i
$125$	−1.06931	−	0.347441i	−0.0956422	−	0.0310760i
$126$		0			0
$127$	8.05590	−	11.0880i	0.714846	−	0.983901i	−0.284834	−	0.958577i	$-0.591938\pi$
$127$	8.05590	−	11.0880i	0.714846	−	0.983901i	0.999679	−	0.0253237i	$-0.00806165\pi$
$128$	0.713400	−	2.19562i	0.0630562	−	0.194067i
$129$		0			0
$130$	0.914661	−	0.664540i	0.0802210	−	0.0582840i
$131$	18.5282			1.61882			0.809409	−	0.587246i	$-0.199788\pi$
$131$	18.5282			1.61882			0.809409	+	0.587246i	$0.199788\pi$
$132$		0			0
$133$	1.69044			0.146580
$134$	−12.6436	+	9.18612i	−1.09224	+	0.793560i
$135$		0			0
$136$	−2.90822	+	8.95058i	−0.249378	+	0.767506i
$137$	−11.4214	+	15.7202i	−0.975793	+	1.34306i	−0.0367271	+	0.999325i	$0.511693\pi$
$137$	−11.4214	+	15.7202i	−0.975793	+	1.34306i	−0.939066	+	0.343738i	$0.888307\pi$
$138$		0			0
$139$	3.34590	+	1.08715i	0.283796	+	0.0922108i	0.447456	−	0.894306i	$-0.352330\pi$
$139$	3.34590	+	1.08715i	0.283796	+	0.0922108i	−0.163660	+	0.986517i	$0.552330\pi$
$140$	3.85780	+	11.8731i	0.326043	+	1.00346i
$141$		0			0
$142$		−	0.620358i		−	0.0520593i
$143$	0.646120	−	0.992993i	0.0540312	−	0.0830382i
$144$		0			0
$145$	−11.3257	−	15.5885i	−0.940550	−	1.29456i
$146$	11.0419	−	3.58773i	0.913835	−	0.296923i
$147$		0			0
$148$	2.55424	+	1.85576i	0.209957	+	0.152543i
$149$	0.00772996	+	0.00561615i	0.000633263	+	0.000460093i	0.588102	−	0.808787i	$-0.299875\pi$
$149$	0.00772996	+	0.00561615i	0.000633263	+	0.000460093i	−0.587469	+	0.809247i	$0.699875\pi$
$150$		0			0
$151$	−0.366897	+	0.119212i	−0.0298577	+	0.00970135i	−0.323908	−	0.946089i	$-0.604997\pi$
$151$	−0.366897	+	0.119212i	−0.0298577	+	0.00970135i	0.294050	+	0.955790i	$0.404997\pi$
$152$	−0.716382	−	0.986015i	−0.0581062	−	0.0799764i
$153$		0			0
$154$	−8.89894	−	11.0094i	−0.717097	−	0.887161i
$155$			25.1181i			2.01753i
$156$		0			0
$157$	0.905149	+	2.78576i	0.0722388	+	0.222328i	0.980657	−	0.195735i	$-0.0627092\pi$
$157$	0.905149	+	2.78576i	0.0722388	+	0.222328i	−0.908418	+	0.418063i	$0.862709\pi$
$158$	4.69338	+	1.52497i	0.373385	+	0.121320i
$159$		0			0
$160$	8.86461	−	12.2011i	0.700809	−	0.964581i
$161$	−3.65178	+	11.2390i	−0.287801	+	0.885759i
$162$		0			0
$163$	10.8005	−	7.84704i	0.845962	−	0.614627i	−0.0780678	−	0.996948i	$-0.524875\pi$
$163$	10.8005	−	7.84704i	0.845962	−	0.614627i	0.924030	+	0.382321i	$0.124875\pi$
$164$	−7.30584			−0.570490
$165$		0			0
$166$	6.75572			0.524346
$167$	−6.21321	+	4.51416i	−0.480792	+	0.349316i	−0.801632	−	0.597817i	$-0.796035\pi$
$167$	−6.21321	+	4.51416i	−0.480792	+	0.349316i	0.320840	+	0.947133i	$0.396035\pi$
$168$		0			0
$169$	3.97779	−	12.2424i	0.305984	−	0.941722i
$170$	−5.80071	+	7.98399i	−0.444894	+	0.612344i
$171$		0			0
$172$	−8.46704	−	2.75111i	−0.645605	−	0.209770i
$173$	−3.83729	−	11.8100i	−0.291744	−	0.897894i	−0.984296	−	0.176527i	$-0.943514\pi$
$173$	−3.83729	−	11.8100i	−0.291744	−	0.897894i	0.692552	−	0.721368i	$-0.256486\pi$
$174$		0			0
$175$			19.4161i			1.46772i
$176$	−0.995840	+	3.70328i	−0.0750643	+	0.279145i
$177$		0			0
$178$	4.37418	+	6.02055i	0.327859	+	0.451259i
$179$	−5.04243	+	1.63838i	−0.376889	+	0.122459i	−0.491335	−	0.870971i	$-0.663491\pi$
$179$	−5.04243	+	1.63838i	−0.376889	+	0.122459i	0.114446	+	0.993429i	$0.463491\pi$
$180$		0			0
$181$	13.8366	+	10.0529i	1.02846	+	0.747224i	0.968001	−	0.250947i	$-0.0807419\pi$
$181$	13.8366	+	10.0529i	1.02846	+	0.747224i	0.0604641	+	0.998170i	$0.480742\pi$
$182$	1.23344	+	0.896147i	0.0914287	+	0.0664268i
$183$		0			0
$184$	8.10317	−	2.63288i	0.597374	−	0.194098i
$185$	5.99781	+	8.25528i	0.440968	+	0.606940i
$186$		0			0
$187$	−2.68540	+	9.98634i	−0.196376	+	0.730274i
$188$			12.1649i			0.887215i
$189$		0			0
$190$	−0.394935	−	1.21549i	−0.0286516	−	0.0881806i
$191$	8.44267	+	2.74319i	0.610890	+	0.198490i	0.598092	−	0.801428i	$-0.295926\pi$
$191$	8.44267	+	2.74319i	0.610890	+	0.198490i	0.0127989	+	0.999918i	$0.495926\pi$
$192$		0			0
$193$	0.848302	−	1.16759i	0.0610621	−	0.0840448i	−0.777394	−	0.629014i	$-0.783459\pi$
$193$	0.848302	−	1.16759i	0.0610621	−	0.0840448i	0.838456	+	0.544969i	$0.183459\pi$
$194$	1.63805	−	5.04139i	0.117605	−	0.361951i
$195$		0			0
$196$	−8.18017	+	5.94324i	−0.584298	+	0.424517i
$197$	−18.4552			−1.31488			−0.657441	−	0.753506i	$-0.728361\pi$
$197$	−18.4552			−1.31488			−0.657441	+	0.753506i	$0.728361\pi$
$198$		0			0
$199$	18.3392			1.30003			0.650016	−	0.759921i	$-0.274762\pi$
$199$	18.3392			1.30003			0.650016	+	0.759921i	$0.274762\pi$
$200$	11.3252	−	8.22826i	0.800815	−	0.581826i
$201$		0			0
$202$	−2.56368	+	7.89020i	−0.180380	+	0.555153i
$203$	15.2730	−	21.0215i	1.07195	−	1.47542i
$204$		0			0
$205$	−22.4567	−	7.29664i	−1.56845	−	0.509619i
$206$	−4.34846	−	13.3832i	−0.302972	−	0.932451i
$207$		0			0
$208$		−	0.413011i		−	0.0286372i
$209$	−0.841860	−	1.04151i	−0.0582327	−	0.0720429i
$210$		0			0
$211$	−2.69098	−	3.70382i	−0.185255	−	0.254981i	0.706281	−	0.707932i	$-0.250372\pi$
$211$	−2.69098	−	3.70382i	−0.185255	−	0.254981i	−0.891536	+	0.452950i	$0.850372\pi$
$212$	3.21882	−	1.04586i	0.221069	−	0.0718298i
$213$		0			0
$214$	3.34400	+	2.42956i	0.228591	+	0.166081i
$215$	−23.2784	−	16.9127i	−1.58757	−	1.15344i
$216$		0			0
$217$	−32.2145	+	10.4671i	−2.18686	+	0.710555i
$218$	3.34280	+	4.60097i	0.226403	+	0.311617i
$219$		0			0
$220$	5.39401	−	8.28981i	0.363664	−	0.558899i
$221$		−	1.11373i		−	0.0749178i
$222$		0			0
$223$	−3.37290	−	10.3807i	−0.225866	−	0.695145i	−0.998203	−	0.0599311i	$-0.980912\pi$
$223$	−3.37290	−	10.3807i	−0.225866	−	0.695145i	0.772336	−	0.635214i	$-0.219088\pi$
$224$	19.3422	+	6.28466i	1.29235	+	0.419911i
$225$		0			0
$226$	4.36593	−	6.00919i	0.290418	−	0.399725i
$227$	−0.871552	+	2.68236i	−0.0578470	+	0.178035i	−0.975805	−	0.218643i	$-0.929837\pi$
$227$	−0.871552	+	2.68236i	−0.0578470	+	0.178035i	0.917958	+	0.396678i	$0.129837\pi$
$228$		0			0
$229$	−1.61091	+	1.17039i	−0.106452	+	0.0773419i	−0.639738	−	0.768593i	$-0.720957\pi$
$229$	−1.61091	+	1.17039i	−0.106452	+	0.0773419i	0.533286	+	0.845935i	$0.320957\pi$
$230$	8.93442			0.589118
$231$		0			0
$232$	−18.7341			−1.22995
$233$	19.6843	−	14.3015i	1.28956	−	0.936923i	0.289768	−	0.957097i	$-0.406422\pi$
$233$	19.6843	−	14.3015i	1.28956	−	0.936923i	0.999796	+	0.0201739i	$0.00642200\pi$
$234$		0			0
$235$	−12.1496	+	37.3925i	−0.792550	+	2.43922i
$236$	6.57497	−	9.04967i	0.427994	−	0.589083i
$237$		0			0
$238$	−12.6569	−	4.11247i	−0.820424	−	0.266572i
$239$	−3.09950	−	9.53927i	−0.200490	−	0.617044i	−0.999869	−	0.0162167i	$-0.994838\pi$
$239$	−3.09950	−	9.53927i	−0.200490	−	0.617044i	0.799379	−	0.600828i	$-0.205162\pi$
$240$		0			0
$241$			17.3175i			1.11552i	0.830002	+	0.557760i	$0.188339\pi$
$241$			17.3175i			1.11552i	−0.830002	+	0.557760i	$0.811661\pi$
$242$	−2.35131	+	10.9656i	−0.151148	+	0.704897i
$243$		0			0
$244$	−0.671208	−	0.923839i	−0.0429697	−	0.0591427i
$245$	−31.0800	+	10.0985i	−1.98563	+	0.645170i
$246$		0			0
$247$	0.116686	+	0.0847776i	0.00742457	+	0.00539427i
$248$	19.7574	+	14.3546i	1.25459	+	0.911516i
$249$		0			0
$250$	−1.09020	+	0.354228i	−0.0689503	+	0.0224033i
$251$	−9.57729	−	13.1820i	−0.604513	−	0.832041i	0.391599	−	0.920136i	$-0.371922\pi$
$251$	−9.57729	−	13.1820i	−0.604513	−	0.832041i	−0.996112	+	0.0880949i	$0.971922\pi$
$252$		0			0
$253$	8.74322	−	3.34724i	0.549681	−	0.210439i
$254$		−	13.9733i		−	0.876760i
$255$		0			0
$256$	−5.21755	−	16.0580i	−0.326097	−	1.00362i
$257$	−7.06641	−	2.29602i	−0.440790	−	0.143221i	0.0802098	−	0.996778i	$-0.474441\pi$
$257$	−7.06641	−	2.29602i	−0.440790	−	0.143221i	−0.521000	+	0.853557i	$0.674441\pi$
$258$		0			0
$259$	−8.08819	+	11.1324i	−0.502575	+	0.691736i
$260$	−0.329156	+	1.01304i	−0.0204134	+	0.0628260i
$261$		0			0
$262$	15.2825	−	11.1034i	0.944153	−	0.685968i
$263$	−1.62422			−0.100154			−0.0500769	−	0.998745i	$-0.515947\pi$
$263$	−1.62422			−0.100154			−0.0500769	+	0.998745i	$0.515947\pi$
$264$		0			0
$265$	10.9386			0.671951
$266$	1.39431	−	1.01303i	0.0854906	−	0.0621126i
$267$		0			0
$268$	4.55002	−	14.0035i	0.277937	−	0.855401i
$269$	−7.63802	+	10.5128i	−0.465699	+	0.640979i	−0.975678	−	0.219207i	$-0.929653\pi$
$269$	−7.63802	+	10.5128i	−0.465699	+	0.640979i	0.509980	+	0.860186i	$0.329653\pi$
$270$		0			0
$271$	7.28021	+	2.36548i	0.442241	+	0.143693i	0.521669	−	0.853148i	$-0.325309\pi$
$271$	7.28021	+	2.36548i	0.442241	+	0.143693i	−0.0794282	+	0.996841i	$0.525309\pi$
$272$	1.11405	+	3.42869i	0.0675491	+	0.207895i
$273$		0			0
$274$			19.8108i			1.19681i
$275$	11.9627	−	9.66949i	0.721376	−	0.583092i
$276$		0			0
$277$	−9.92682	−	13.6631i	−0.596445	−	0.820936i	0.398932	−	0.916980i	$-0.369381\pi$
$277$	−9.92682	−	13.6631i	−0.596445	−	0.820936i	−0.995377	+	0.0960447i	$0.969381\pi$
$278$	3.41126	−	1.10839i	0.204594	−	0.0664766i
$279$		0			0
$280$	31.7373	+	23.0585i	1.89666	+	1.37801i
$281$	−8.77929	−	6.37853i	−0.523729	−	0.380511i	0.294278	−	0.955720i	$-0.404921\pi$
$281$	−8.77929	−	6.37853i	−0.523729	−	0.380511i	−0.818007	+	0.575209i	$0.804921\pi$
$282$		0			0
$283$	16.6540	−	5.41121i	0.989978	−	0.321663i	0.231124	−	0.972924i	$-0.425760\pi$
$283$	16.6540	−	5.41121i	0.989978	−	0.321663i	0.758854	+	0.651261i	$0.225760\pi$
$284$	0.343541	+	0.472844i	0.0203854	+	0.0280581i
$285$		0			0
$286$	−0.0621353	−	1.20624i	−0.00367414	−	0.0713264i
$287$		−	31.8419i		−	1.87957i
$288$		0			0
$289$	−2.24913	−	6.92210i	−0.132302	−	0.407182i
$290$	−18.6834	−	6.07060i	−1.09713	−	0.356478i
$291$		0			0
$292$	−6.42945	+	8.84939i	−0.376255	+	0.517871i
$293$	4.03222	−	12.4099i	0.235565	−	0.724994i	−0.761481	−	0.648187i	$-0.775528\pi$
$293$	4.03222	−	12.4099i	0.235565	−	0.724994i	0.997046	−	0.0768068i	$-0.0244725\pi$
$294$		0			0
$295$	29.2484	−	21.2502i	1.70291	−	1.23724i
$296$	9.92108			0.576651
$297$		0			0
$298$	0.00974141			0.000564305
$299$	−0.815723	+	0.592657i	−0.0471745	+	0.0342743i
$300$		0			0
$301$	11.9905	−	36.9028i	0.691119	−	2.12704i
$302$	−0.231185	+	0.318198i	−0.0133032	+	0.0183103i
$303$		0			0
$304$	−0.444027	−	0.144273i	−0.0254667	−	0.00827462i
$305$	−1.14049	−	3.51007i	−0.0653042	−	0.200986i
$306$		0			0
$307$		−	27.5790i		−	1.57402i	−0.616941	−	0.787009i	$-0.711628\pi$
$307$		−	27.5790i		−	1.57402i	0.616941	−	0.787009i	$-0.288372\pi$
$308$	12.8796	+	3.46343i	0.733885	+	0.197347i
$309$		0			0
$310$	15.0525	+	20.7179i	0.854922	+	1.17670i
$311$	7.24629	−	2.35446i	0.410899	−	0.133509i	−0.0962709	−	0.995355i	$-0.530692\pi$
$311$	7.24629	−	2.35446i	0.410899	−	0.133509i	0.507170	+	0.861846i	$0.330692\pi$
$312$		0			0
$313$	−10.7999	−	7.84660i	−0.610448	−	0.443516i	0.239124	−	0.970989i	$-0.423140\pi$
$313$	−10.7999	−	7.84660i	−0.610448	−	0.443516i	−0.849572	+	0.527473i	$0.823140\pi$
$314$	2.41600	+	1.75533i	0.136343	+	0.0990589i
$315$		0			0
$316$	−4.42184	+	1.43674i	−0.248748	+	0.0808232i
$317$	4.50648	+	6.20264i	0.253109	+	0.348375i	0.916597	−	0.399812i	$-0.130925\pi$
$317$	4.50648	+	6.20264i	0.253109	+	0.348375i	−0.663488	+	0.748187i	$0.730925\pi$
$318$		0			0
$319$	−20.5579	+	1.05897i	−1.15102	+	0.0592909i
$320$		−	22.5551i		−	1.26087i
$321$		0			0
$322$	3.72312	+	11.4586i	0.207481	+	0.638561i
$323$	−1.19737	−	0.389049i	−0.0666235	−	0.0216473i
$324$		0			0
$325$	−0.973743	+	1.34024i	−0.0540136	+	0.0743433i
$326$	4.20602	−	12.9448i	0.232950	−	0.716946i
$327$		0			0
$328$	−18.5730	+	13.4941i	−1.02552	+	0.745087i
$329$	−53.0196			−2.92306
$330$		0			0
$331$	−7.32587			−0.402666			−0.201333	−	0.979523i	$-0.564527\pi$
$331$	−7.32587			−0.402666			−0.201333	+	0.979523i	$0.564527\pi$
$332$	−5.14928	+	3.74117i	−0.282604	+	0.205324i
$333$		0			0
$334$	−2.41959	+	7.44675i	−0.132394	+	0.407468i
$335$	27.9718	−	38.4998i	1.52826	−	2.10347i
$336$		0			0
$337$	6.87849	+	2.23496i	0.374695	+	0.121746i	0.490310	−	0.871548i	$-0.336884\pi$
$337$	6.87849	+	2.23496i	0.374695	+	0.121746i	−0.115614	+	0.993294i	$0.536884\pi$
$338$	−4.05550	−	12.4815i	−0.220590	−	0.678906i
$339$		0			0
$340$		−	9.29779i		−	0.504243i
$341$	22.4922	+	14.6352i	1.21802	+	0.792542i
$342$		0			0
$343$	−8.67788	−	11.9441i	−0.468561	−	0.644919i
$344$	−26.6064	+	8.64494i	−1.43452	+	0.466104i
$345$		0			0
$346$	−10.2424	−	7.44154i	−0.550635	−	0.400060i
$347$	19.9795	+	14.5160i	1.07256	+	0.779259i	0.976370	−	0.216104i	$-0.0693351\pi$
$347$	19.9795	+	14.5160i	1.07256	+	0.779259i	0.0961877	+	0.995363i	$0.469335\pi$
$348$		0			0
$349$	13.4331	−	4.36468i	0.719058	−	0.233636i	0.0734433	−	0.997299i	$-0.476601\pi$
$349$	13.4331	−	4.36468i	0.719058	−	0.233636i	0.645615	+	0.763663i	$0.276601\pi$
$350$	11.6355	+	16.0148i	0.621942	+	0.856029i
$351$		0			0
$352$	−5.76055	−	15.0469i	−0.307039	−	0.802005i
$353$			15.0649i			0.801823i	0.916117	+	0.400911i	$0.131307\pi$
$353$			15.0649i			0.801823i	−0.916117	+	0.400911i	$0.868693\pi$
$354$		0			0
$355$	0.583731	+	1.79654i	0.0309812	+	0.0953503i
$356$	−6.66810	−	2.16660i	−0.353409	−	0.114829i
$357$		0			0
$358$	−3.17727	+	4.37314i	−0.167924	+	0.231127i
$359$	−2.21156	+	6.80649i	−0.116722	+	0.359233i	−0.992302	−	0.123840i	$-0.960479\pi$
$359$	−2.21156	+	6.80649i	−0.116722	+	0.359233i	0.875580	+	0.483072i	$0.160479\pi$
$360$		0			0
$361$	−15.2394	+	11.0721i	−0.802075	+	0.582741i
$362$	17.4371			0.916471
$363$		0			0
$364$	−1.43641			−0.0752883
$365$	−28.6011	+	20.7799i	−1.49705	+	1.08767i
$366$		0			0
$367$	1.31179	−	4.03727i	0.0684747	−	0.210744i	−0.910964	−	0.412486i	$-0.864660\pi$
$367$	1.31179	−	4.03727i	0.0684747	−	0.210744i	0.979439	+	0.201743i	$0.0646605\pi$
$368$	1.91842	−	2.64048i	0.100005	−	0.137645i
$369$		0			0
$370$	9.89424	+	3.21483i	0.514377	+	0.167131i
$371$	4.55828	+	14.0289i	0.236654	+	0.728346i
$372$		0			0
$373$			20.3457i			1.05346i	0.850032	+	0.526730i	$0.176582\pi$
$373$			20.3457i			1.05346i	−0.850032	+	0.526730i	$0.823418\pi$
$374$	3.76951	+	9.84622i	0.194917	+	0.509136i
$375$		0			0
$376$	22.4689	+	30.9257i	1.15874	+	1.59487i
$377$	2.10850	−	0.685095i	0.108593	−	0.0352842i
$378$		0			0
$379$	−23.6596	−	17.1897i	−1.21531	−	0.882977i	−0.219611	−	0.975587i	$-0.570479\pi$
$379$	−23.6596	−	17.1897i	−1.21531	−	0.882977i	−0.995702	+	0.0926103i	$0.970479\pi$
$380$	0.974134	+	0.707749i	0.0499720	+	0.0363068i
$381$		0			0
$382$	8.60760	−	2.79678i	0.440403	−	0.143096i
$383$	−2.88647	−	3.97288i	−0.147492	−	0.203005i	0.728878	−	0.684643i	$-0.240042\pi$
$383$	−2.88647	−	3.97288i	−0.147492	−	0.203005i	−0.876370	+	0.481638i	$0.840042\pi$
$384$		0			0
$385$	36.1304	+	23.5093i	1.84138	+	1.19815i
$386$		−	1.47141i		−	0.0748929i
$387$		0			0
$388$	1.54328	+	4.74972i	0.0783480	+	0.241130i
$389$	16.3036	+	5.29736i	0.826625	+	0.268587i	0.691623	−	0.722259i	$-0.256896\pi$
$389$	16.3036	+	5.29736i	0.826625	+	0.268587i	0.135002	+	0.990845i	$0.456896\pi$
$390$		0			0
$391$	5.17325	−	7.12037i	0.261623	−	0.360093i
$392$	−9.81842	+	30.2180i	−0.495905	+	1.52624i
$393$		0			0
$394$	−15.2223	+	11.0596i	−0.766887	+	0.557176i
$395$	−15.0268			−0.756082
$396$		0			0
$397$	−7.94416			−0.398706			−0.199353	−	0.979928i	$-0.563884\pi$
$397$	−7.94416			−0.398706			−0.199353	+	0.979928i	$0.563884\pi$
$398$	15.1266	−	10.9901i	0.758226	−	0.550883i
$399$		0			0
$400$	1.65710	−	5.10003i	0.0828549	−	0.255001i
$401$	−3.78746	+	5.21299i	−0.189137	+	0.260324i	−0.893046	−	0.449966i	$-0.851436\pi$
$401$	−3.78746	+	5.21299i	−0.189137	+	0.260324i	0.703909	+	0.710290i	$0.251436\pi$
$402$		0			0
$403$	−2.74862	−	0.893079i	−0.136918	−	0.0444874i
$404$	−2.41536	−	7.43371i	−0.120169	−	0.369841i
$405$		0			0
$406$		−	26.4916i		−	1.31475i
$407$	10.8869	−	0.560803i	0.539645	−	0.0277980i
$408$		0			0
$409$	−9.38469	−	12.9169i	−0.464043	−	0.638700i	0.511298	−	0.859403i	$-0.329165\pi$
$409$	−9.38469	−	12.9169i	−0.464043	−	0.638700i	−0.975341	+	0.220703i	$0.929165\pi$
$410$	−22.8954	+	7.43917i	−1.13072	+	0.367395i
$411$		0			0
$412$	10.7258	+	7.79272i	0.528420	+	0.383920i
$413$	39.4422	+	28.6564i	1.94082	+	1.41009i
$414$		0			0
$415$	−19.5644	+	6.35685i	−0.960377	+	0.312045i
$416$	1.01995	+	1.40385i	0.0500074	+	0.0688292i
$417$		0			0
$418$	−1.31853	−	0.354562i	−0.0644913	−	0.0173422i
$419$			3.64302i			0.177973i	0.996033	+	0.0889865i	$0.0283628\pi$
$419$			3.64302i			0.177973i	−0.996033	+	0.0889865i	$0.971637\pi$
$420$		0			0
$421$	4.08027	+	12.5578i	0.198860	+	0.612029i	0.999910	+	0.0134311i	$0.00427537\pi$
$421$	4.08027	+	12.5578i	0.198860	+	0.612029i	−0.801049	+	0.598598i	$0.795725\pi$
$422$	−4.43916	−	1.44237i	−0.216095	−	0.0702135i
$423$		0			0
$424$	6.25120	−	8.60405i	0.303585	−	0.417849i
$425$	4.46856	−	13.7528i	0.216757	−	0.667110i
$426$		0			0
$427$	4.02647	−	2.92540i	0.194855	−	0.141570i
$428$	−3.89427			−0.188237
$429$		0			0
$430$	−29.3358			−1.41470
$431$	−12.5748	+	9.13610i	−0.605705	+	0.440071i	−0.847899	−	0.530157i	$-0.822133\pi$
$431$	−12.5748	+	9.13610i	−0.605705	+	0.440071i	0.242194	+	0.970228i	$0.422133\pi$
$432$		0			0
$433$	−3.84495	+	11.8336i	−0.184777	+	0.568684i	−0.999944	−	0.0105407i	$-0.996645\pi$
$433$	−3.84495	+	11.8336i	−0.184777	+	0.568684i	0.815168	+	0.579225i	$0.196645\pi$
$434$	−20.2986	+	27.9386i	−0.974363	+	1.34110i
$435$		0			0
$436$	−5.09584	−	1.65574i	−0.244046	−	0.0792954i
$437$	0.352215	+	1.08401i	0.0168488	+	0.0518551i
$438$		0			0
$439$			11.4700i			0.547434i	0.961810	+	0.273717i	$0.0882532\pi$
$439$			11.4700i			0.547434i	−0.961810	+	0.273717i	$0.911747\pi$
$440$	−1.59878	−	31.0374i	−0.0762190	−	1.47965i
$441$		0			0
$442$	−0.667424	−	0.918630i	−0.0317461	−	0.0436948i
$443$	−6.99176	+	2.27176i	−0.332189	+	0.107935i	−0.470362	−	0.882473i	$-0.655877\pi$
$443$	−6.99176	+	2.27176i	−0.332189	+	0.107935i	0.138174	+	0.990408i	$0.455877\pi$
$444$		0			0
$445$	−18.3326	−	13.3194i	−0.869048	−	0.631400i
$446$	−9.00288	−	6.54097i	−0.426299	−	0.309724i
$447$		0			0
$448$	28.9274	−	9.39908i	1.36669	−	0.444065i
$449$	2.58876	+	3.56312i	0.122171	+	0.168154i	0.865722	−	0.500525i	$-0.166860\pi$
$449$	2.58876	+	3.56312i	0.122171	+	0.168154i	−0.743551	+	0.668680i	$0.766860\pi$
$450$		0			0
$451$	−19.6184	+	15.8577i	−0.923794	+	0.746708i
$452$			6.99803i			0.329160i
$453$		0			0
$454$	0.888578	+	2.73476i	0.0417030	+	0.128349i
$455$	−4.41524	−	1.43460i	−0.206990	−	0.0672550i
$456$		0			0
$457$	3.70372	−	5.09773i	0.173253	−	0.238462i	−0.713556	−	0.700598i	$-0.752917\pi$
$457$	3.70372	−	5.09773i	0.173253	−	0.238462i	0.886809	+	0.462136i	$0.152917\pi$
$458$	−0.627333	+	1.93073i	−0.0293133	+	0.0902172i
$459$		0			0
$460$	−6.80991	+	4.94769i	−0.317514	+	0.230687i
$461$	−10.3190			−0.480604			−0.240302	−	0.970698i	$-0.577246\pi$
$461$	−10.3190			−0.480604			−0.240302	+	0.970698i	$0.577246\pi$
$462$		0			0
$463$	1.69322			0.0786908			0.0393454	−	0.999226i	$-0.487473\pi$
$463$	1.69322			0.0786908			0.0393454	+	0.999226i	$0.487473\pi$
$464$	−5.80585	+	4.21820i	−0.269530	+	0.195825i
$465$		0			0
$466$	7.66563	−	23.5924i	0.355103	−	1.09290i
$467$	14.1753	−	19.5106i	0.655953	−	0.902842i	−0.343386	−	0.939194i	$-0.611574\pi$
$467$	14.1753	−	19.5106i	0.655953	−	0.902842i	0.999339	+	0.0363528i	$0.0115740\pi$
$468$		0			0
$469$	61.0331	+	19.8309i	2.81825	+	0.915704i
$470$	12.3869	+	38.1229i	0.571365	+	1.75848i
$471$		0			0
$472$		−	35.1504i		−	1.61793i
$473$	−28.7080	+	10.9905i	−1.31999	+	0.505345i
$474$		0			0
$475$	1.10074	+	1.51504i	0.0505055	+	0.0695149i
$476$	11.9246	−	3.87454i	0.546564	−	0.177589i
$477$		0			0
$478$	−8.27311	−	6.01076i	−0.378403	−	0.274926i
$479$	−30.1685	−	21.9187i	−1.37843	−	1.00149i	−0.997025	−	0.0770852i	$-0.975439\pi$
$479$	−30.1685	−	21.9187i	−1.37843	−	1.00149i	−0.381410	−	0.924406i	$-0.624561\pi$
$480$		0			0
$481$	−1.11661	+	0.362809i	−0.0509130	+	0.0165426i
$482$	10.3778	+	14.2839i	0.472698	+	0.650612i
$483$		0			0
$484$	−4.28033	−	9.66022i	−0.194561	−	0.439101i
$485$			16.1410i			0.732927i
$486$		0			0
$487$	11.7540	+	36.1751i	0.532624	+	1.63925i	0.748727	+	0.662879i	$0.230665\pi$
$487$	11.7540	+	36.1751i	0.532624	+	1.63925i	−0.216102	+	0.976371i	$0.569335\pi$
$488$	−3.41271	−	1.10886i	−0.154486	−	0.0501956i
$489$		0			0
$490$	−19.5837	+	26.9547i	−0.884703	+	1.21769i
$491$	−8.84932	+	27.2354i	−0.399364	+	1.22912i	0.526146	+	0.850394i	$0.323637\pi$
$491$	−8.84932	+	27.2354i	−0.399364	+	1.22912i	−0.925510	+	0.378723i	$0.876363\pi$
$492$		0			0
$493$	−15.6562	+	11.3749i	−0.705119	+	0.512299i
$494$	0.147050			0.00661608
$495$		0			0
$496$	9.35509			0.420056
$497$	−2.06085	+	1.49729i	−0.0924416	+	0.0671628i
$498$		0			0
$499$	−4.75621	+	14.6381i	−0.212917	+	0.655292i	0.786378	+	0.617746i	$0.211954\pi$
$499$	−4.75621	+	14.6381i	−0.212917	+	0.655292i	−0.999295	+	0.0375457i	$0.988046\pi$
$500$	0.634799	−	0.873726i	0.0283891	−	0.0390742i
$501$		0			0
$502$	−15.7991	−	5.13344i	−0.705148	−	0.229117i
$503$	1.24129	+	3.82031i	0.0553466	+	0.170339i	0.974909	−	0.222606i	$-0.0714563\pi$
$503$	1.24129	+	3.82031i	0.0553466	+	0.170339i	−0.919562	+	0.392945i	$0.871456\pi$
$504$		0			0
$505$		−	25.2621i		−	1.12415i
$506$	5.20569	−	8.00040i	0.231421	−	0.355661i
$507$		0			0
$508$	7.73809	+	10.6506i	0.343322	+	0.472542i
$509$	19.9081	−	6.46855i	0.882413	−	0.286713i	0.167454	−	0.985880i	$-0.446445\pi$
$509$	19.9081	−	6.46855i	0.882413	−	0.286713i	0.714959	+	0.699167i	$0.246445\pi$
$510$		0			0
$511$	−38.5693	−	28.0222i	−1.70620	−	1.23963i
$512$	−10.1912	−	7.40431i	−0.450390	−	0.327227i
$513$		0			0
$514$	−7.20445	+	2.34087i	−0.317775	+	0.103251i
$515$	25.1860	+	34.6656i	1.10983	+	1.52755i
$516$		0			0
$517$	26.4044	+	32.6664i	1.16127	+	1.43667i
$518$			14.0293i			0.616410i
$519$		0			0
$520$	1.03432	+	3.18332i	0.0453581	+	0.139598i
$521$	34.9601	+	11.3592i	1.53163	+	0.497656i	0.949052	−	0.315120i	$-0.102045\pi$
$521$	34.9601	+	11.3592i	1.53163	+	0.497656i	0.582576	+	0.812776i	$0.302045\pi$
$522$		0			0
$523$	−3.90101	+	5.36927i	−0.170579	+	0.234782i	−0.885744	−	0.464173i	$-0.846351\pi$
$523$	−3.90101	+	5.36927i	−0.170579	+	0.234782i	0.715165	+	0.698955i	$0.246351\pi$
$524$	−5.49965	+	16.9262i	−0.240253	+	0.739424i
$525$		0			0
$526$	−1.33969	+	0.973344i	−0.0584134	+	0.0424398i
$527$	25.2271			1.09891
$528$		0			0
$529$	15.0320			0.653566
$530$	9.02236	−	6.55513i	0.391906	−	0.284737i
$531$		0			0
$532$	−0.501766	+	1.54428i	−0.0217543	+	0.0669529i
$533$	1.59691	−	2.19796i	0.0691698	−	0.0952040i
$534$		0			0
$535$	−11.9702	−	3.88937i	−0.517519	−	0.168152i
$536$	−14.2978	−	44.0040i	−0.617569	−	1.90068i
$537$		0			0
$538$			13.2484i			0.571180i
$539$	−9.06616	+	33.7148i	−0.390507	+	1.45220i
$540$		0			0
$541$	−0.307811	−	0.423665i	−0.0132338	−	0.0182148i	0.802349	−	0.596855i	$-0.203583\pi$
$541$	−0.307811	−	0.423665i	−0.0132338	−	0.0182148i	−0.815583	+	0.578641i	$0.803583\pi$
$542$	7.42243	−	2.41169i	0.318821	−	0.103591i
$543$		0			0
$544$	−12.2540	−	8.90308i	−0.525388	−	0.381717i
$545$	−14.0100	−	10.1788i	−0.600121	−	0.436013i
$546$		0			0
$547$	32.3165	−	10.5003i	1.38175	−	0.448958i	0.478507	−	0.878084i	$-0.341178\pi$
$547$	32.3165	−	10.5003i	1.38175	−	0.448958i	0.903245	+	0.429125i	$0.141178\pi$
$548$	−10.9708	−	15.1000i	−0.468648	−	0.645039i
$549$		0			0
$550$	4.07245	−	15.1444i	0.173650	−	0.645761i
$551$		−	2.50616i		−	0.106766i
$552$		0			0
$553$	−6.26192	−	19.2722i	−0.266284	−	0.819538i
$554$	−16.3757	−	5.32079i	−0.695737	−	0.226059i
$555$		0			0
$556$	−1.98630	+	2.73391i	−0.0842379	+	0.115944i
$557$	9.71173	−	29.8896i	0.411499	−	1.26646i	−0.503846	−	0.863794i	$-0.668082\pi$
$557$	9.71173	−	29.8896i	0.411499	−	1.26646i	0.915345	−	0.402671i	$-0.131918\pi$
$558$		0			0
$559$	2.67839	−	1.94596i	0.113284	−	0.0823055i
$560$	15.0276			0.635030
$561$		0			0
$562$	−11.0638			−0.466698
$563$	2.42568	−	1.76236i	0.102230	−	0.0742746i	−0.535496	−	0.844538i	$-0.679875\pi$
$563$	2.42568	−	1.76236i	0.102230	−	0.0742746i	0.637726	+	0.770263i	$0.279875\pi$
$564$		0			0
$565$	−6.98922	+	21.5106i	−0.294038	+	0.904957i
$566$	10.4938	−	14.4435i	0.441088	−	0.607105i
$567$		0			0
$568$	1.74671	+	0.567541i	0.0732903	+	0.0238135i
$569$	−12.7004	−	39.0879i	−0.532429	−	1.63865i	−0.749139	−	0.662413i	$-0.769533\pi$
$569$	−12.7004	−	39.0879i	−0.532429	−	1.63865i	0.216710	−	0.976236i	$-0.430467\pi$
$570$		0			0
$571$		−	13.4398i		−	0.562438i	−0.959644	−	0.281219i	$-0.909261\pi$
$571$		−	13.4398i		−	0.562438i	0.959644	−	0.281219i	$-0.0907387\pi$
$572$	0.715350	+	0.885000i	0.0299103	+	0.0370037i
$573$		0			0
$574$	−19.0818	−	26.2638i	−0.796459	−	1.09623i
$575$	−12.4508	+	4.04550i	−0.519233	+	0.168709i
$576$		0			0
$577$	−6.44828	−	4.68495i	−0.268445	−	0.195037i	0.445417	−	0.895323i	$-0.353056\pi$
$577$	−6.44828	−	4.68495i	−0.268445	−	0.195037i	−0.713862	+	0.700287i	$0.753056\pi$
$578$	−6.00332	−	4.36167i	−0.249705	−	0.181421i
$579$		0			0
$580$	17.6024	−	5.71938i	0.730902	−	0.237484i
$581$	−16.3056	−	22.4427i	−0.676470	−	0.931080i
$582$		0			0
$583$	6.37343	−	9.79504i	0.263960	−	0.405669i
$584$			34.3724i			1.42234i
$585$		0			0
$586$	−4.11099	−	12.6523i	−0.169823	−	0.522662i
$587$	22.5693	+	7.33321i	0.931534	+	0.302674i	0.735190	−	0.677861i	$-0.237093\pi$
$587$	22.5693	+	7.33321i	0.931534	+	0.302674i	0.196344	+	0.980535i	$0.437093\pi$
$588$		0			0
$589$	−1.92029	+	2.64306i	−0.0791243	+	0.108905i
$590$	11.3902	−	35.0553i	0.468925	−	1.44320i
$591$		0			0
$592$	3.07463	−	2.23385i	0.126367	−	0.0918107i
$593$	29.4804			1.21062			0.605308	−	0.795991i	$-0.293050\pi$
$593$	29.4804			1.21062			0.605308	+	0.795991i	$0.293050\pi$
$594$		0			0
$595$	40.5236			1.66131
$596$	−0.00742501	+	0.00539459i	−0.000304140	+	0.000220971i
$597$		0			0
$598$	−0.317665	+	0.977672i	−0.0129903	+	0.0399800i
$599$	−17.5649	+	24.1760i	−0.717681	+	0.987803i	0.281917	+	0.959439i	$0.409030\pi$
$599$	−17.5649	+	24.1760i	−0.717681	+	0.987803i	−0.999598	+	0.0283643i	$0.990970\pi$
$600$		0			0
$601$	6.33078	+	2.05699i	0.258238	+	0.0839066i	0.435275	−	0.900298i	$-0.356651\pi$
$601$	6.33078	+	2.05699i	0.258238	+	0.0839066i	−0.177037	+	0.984204i	$0.556651\pi$
$602$	−12.2247	−	37.6237i	−0.498241	−	1.53343i
$603$		0			0
$604$		−	0.370559i		−	0.0150778i
$605$	−3.50886	−	33.9686i	−0.142656	−	1.38102i
$606$		0			0
$607$	18.8649	+	25.9653i	0.765702	+	1.05390i	0.996718	+	0.0809482i	$0.0257948\pi$
$607$	18.8649	+	25.9653i	0.765702	+	1.05390i	−0.231017	+	0.972950i	$0.574205\pi$
$608$	1.86556	−	0.606157i	0.0756585	−	0.0245829i
$609$		0			0
$610$	−3.04417	−	2.21172i	−0.123255	−	0.0895498i
$611$	−3.65979	−	2.65900i	−0.148059	−	0.107571i
$612$		0			0
$613$	10.3905	−	3.37608i	0.419668	−	0.136358i	−0.0915678	−	0.995799i	$-0.529188\pi$
$613$	10.3905	−	3.37608i	0.419668	−	0.136358i	0.511236	+	0.859440i	$0.329188\pi$
$614$	−16.5272	−	22.7478i	−0.666984	−	0.918025i
$615$		0			0
$616$	39.1398	−	14.9843i	1.57699	−	0.603733i
$617$		−	7.05166i		−	0.283889i	−0.989875	−	0.141945i	$-0.954665\pi$
$617$		−	7.05166i		−	0.283889i	0.989875	−	0.141945i	$-0.0453355\pi$
$618$		0			0
$619$	−11.9984	−	36.9273i	−0.482257	−	1.48423i	−0.835915	−	0.548859i	$-0.815062\pi$
$619$	−11.9984	−	36.9273i	−0.482257	−	1.48423i	0.353658	−	0.935375i	$-0.384938\pi$
$620$	−22.9463	−	7.45570i	−0.921545	−	0.299428i
$621$		0			0
$622$	4.56594	−	6.28448i	0.183077	−	0.251985i
$623$	9.44293	−	29.0623i	0.378323	−	1.16436i
$624$		0			0
$625$	21.5843	−	15.6819i	0.863372	−	0.627277i
$626$	−13.6102			−0.543974
$627$		0			0
$628$	−2.81357			−0.112274
$629$	8.29111	−	6.02384i	0.330588	−	0.240186i
$630$		0			0
$631$	−9.93575	+	30.5791i	−0.395536	+	1.21733i	0.533007	+	0.846111i	$0.321062\pi$
$631$	−9.93575	+	30.5791i	−0.395536	+	1.21733i	−0.928543	+	0.371224i	$0.878938\pi$
$632$	−8.58757	+	11.8198i	−0.341595	+	0.470166i
$633$		0			0
$634$	7.43409	+	2.41548i	0.295245	+	0.0959310i
$635$	13.1482	+	40.4661i	0.521772	+	1.60585i
$636$		0			0
$637$		−	3.76007i		−	0.148979i
$638$	−16.3220	+	13.1931i	−0.646193	+	0.522321i
$639$		0			0
$640$	4.21268	+	5.79826i	0.166521	+	0.229196i
$641$	29.7968	−	9.68156i	1.17690	−	0.382399i	0.345687	−	0.938350i	$-0.387646\pi$
$641$	29.7968	−	9.68156i	1.17690	−	0.382399i	0.831215	+	0.555951i	$0.187646\pi$
$642$		0			0
$643$	8.64773	+	6.28295i	0.341033	+	0.247775i	0.745098	−	0.666955i	$-0.232403\pi$
$643$	8.64773	+	6.28295i	0.341033	+	0.247775i	−0.404064	+	0.914731i	$0.632403\pi$
$644$	−9.18331	−	6.67207i	−0.361873	−	0.262916i
$645$		0			0
$646$	−1.22076	+	0.396649i	−0.0480302	+	0.0156060i
$647$	−14.2861	−	19.6631i	−0.561644	−	0.773037i	0.429890	−	0.902881i	$-0.358552\pi$
$647$	−14.2861	−	19.6631i	−0.561644	−	0.773037i	−0.991534	+	0.129844i	$0.958552\pi$
$648$		0			0
$649$	−1.98692	−	38.5724i	−0.0779936	−	1.51410i
$650$			1.68899i			0.0662477i
$651$		0			0
$652$	3.96268	+	12.1959i	0.155190	+	0.477627i
$653$	45.2693	+	14.7089i	1.77152	+	0.575603i	0.998287	−	0.0585131i	$-0.0186359\pi$
$653$	45.2693	+	14.7089i	1.77152	+	0.575603i	0.773238	+	0.634116i	$0.218636\pi$
$654$		0			0
$655$	−33.8097	+	46.5351i	−1.32106	+	1.81828i
$656$	−2.71759	+	8.36388i	−0.106104	+	0.326555i
$657$		0			0
$658$	−43.7316	+	31.7729i	−1.70484	+	1.23864i
$659$	23.1371			0.901292			0.450646	−	0.892703i	$-0.351194\pi$
$659$	23.1371			0.901292			0.450646	+	0.892703i	$0.351194\pi$
$660$		0			0
$661$	−18.8879			−0.734656			−0.367328	−	0.930091i	$-0.619727\pi$
$661$	−18.8879			−0.734656			−0.367328	+	0.930091i	$0.619727\pi$
$662$	−6.04253	+	4.39016i	−0.234850	+	0.170628i
$663$		0			0
$664$	−6.18054	+	19.0217i	−0.239851	+	0.738187i
$665$	−3.08466	+	4.24568i	−0.119618	+	0.164640i
$666$		0			0
$667$	16.6624	+	5.41395i	0.645172	+	0.209629i
$668$	−2.27961	−	7.01591i	−0.0882006	−	0.271454i
$669$		0			0
$670$		−	48.5180i		−	1.87441i
$671$	−3.80763	−	1.02390i	−0.146992	−	0.0395272i
$672$		0			0
$673$	17.1502	+	23.6053i	0.661093	+	0.909916i	0.999517	−	0.0310774i	$-0.00989382\pi$
$673$	17.1502	+	23.6053i	0.661093	+	0.909916i	−0.338424	+	0.940994i	$0.609894\pi$
$674$	7.01286	−	2.27862i	0.270125	−	0.0877691i
$675$		0			0
$676$	10.0032	+	7.26772i	0.384737	+	0.279528i
$677$	12.9133	+	9.38207i	0.496299	+	0.360582i	0.807601	−	0.589729i	$-0.200765\pi$
$677$	12.9133	+	9.38207i	0.496299	+	0.360582i	−0.311303	+	0.950311i	$0.600765\pi$
$678$		0			0
$679$	−20.7012	+	6.72624i	−0.794440	+	0.258129i
$680$	−17.1733	−	23.6370i	−0.658565	−	0.906437i
$681$		0			0
$682$	27.3225	−	1.40742i	1.04623	−	0.0538930i
$683$		−	4.33022i		−	0.165691i	−0.996562	−	0.0828457i	$-0.973599\pi$
$683$		−	4.33022i		−	0.165691i	0.996562	−	0.0828457i	$-0.0264009\pi$
$684$		0			0
$685$	−18.6411	−	57.3714i	−0.712239	−	2.19205i
$686$	−14.3154	−	4.65135i	−0.546564	−	0.177589i
$687$		0			0
$688$	−6.29905	+	8.66990i	−0.240149	+	0.330537i
$689$	−0.388923	+	1.19698i	−0.0148168	+	0.0456014i
$690$		0			0
$691$	18.4551	−	13.4084i	0.702065	−	0.510080i	−0.178539	−	0.983933i	$-0.557137\pi$
$691$	18.4551	−	13.4084i	0.702065	−	0.510080i	0.880604	+	0.473853i	$0.157137\pi$
$692$	11.9278			0.453428
$693$		0			0
$694$	25.1785			0.955763
$695$	−8.83597	+	6.41971i	−0.335167	+	0.243513i
$696$		0			0
$697$	−7.32830	+	22.5542i	−0.277579	+	0.854301i
$698$	8.46430	−	11.6501i	0.320379	−	0.440963i
$699$		0			0
$700$	−17.7374	−	5.76322i	−0.670409	−	0.217829i
$701$	11.9110	+	36.6583i	0.449872	+	1.38456i	0.877052	+	0.480396i	$0.159507\pi$
$701$	11.9110	+	36.6583i	0.449872	+	1.38456i	−0.427180	+	0.904167i	$0.640493\pi$
$702$		0			0
$703$			1.32720i			0.0500563i
$704$	−20.1972	−	13.1419i	−0.761209	−	0.495303i
$705$		0			0
$706$	9.02790	+	12.4258i	0.339769	+	0.467652i
$707$	32.3992	−	10.5271i	1.21850	−	0.395914i
$708$		0			0
$709$	−20.8948	−	15.1809i	−0.784719	−	0.570132i	0.121672	−	0.992570i	$-0.461174\pi$
$709$	−20.8948	−	15.1809i	−0.784719	−	0.570132i	−0.906392	+	0.422438i	$0.861174\pi$
$710$	1.55808	+	1.13201i	0.0584737	+	0.0424836i
$711$		0			0
$712$	−20.9535	+	6.80821i	−0.785266	+	0.255148i
$713$	−13.4243	−	18.4769i	−0.502742	−	0.691965i
$714$		0			0
$715$	1.31496	+	3.43477i	0.0491768	+	0.128453i
$716$		−	5.09276i		−	0.190325i
$717$		0			0
$718$	2.25477	+	6.93945i	0.0841471	+	0.258978i
$719$	−28.7908	−	9.35469i	−1.07371	−	0.348871i	−0.281781	−	0.959479i	$-0.590925\pi$
$719$	−28.7908	−	9.35469i	−1.07371	−	0.348871i	−0.791933	+	0.610608i	$0.790925\pi$
$720$		0			0
$721$	−33.9639	+	46.7473i	−1.26488	+	1.74096i
$722$	−5.93465	+	18.2650i	−0.220865	+	0.679752i
$723$		0			0
$724$	−13.2907	+	9.65627i	−0.493945	+	0.358872i
$725$	28.7854			1.06906
$726$		0			0
$727$	−41.0564			−1.52270			−0.761349	−	0.648342i	$-0.775463\pi$
$727$	−41.0564			−1.52270			−0.761349	+	0.648342i	$0.775463\pi$
$728$	−3.65166	+	2.65309i	−0.135340	+	0.0983299i
$729$		0			0
$730$	−11.1381	+	34.2795i	−0.412239	+	1.26874i
$731$	−16.9861	+	23.3794i	−0.628255	+	0.864719i
$732$		0			0
$733$	−9.44935	−	3.07028i	−0.349020	−	0.113403i	0.129260	−	0.991611i	$-0.458740\pi$
$733$	−9.44935	−	3.07028i	−0.349020	−	0.113403i	−0.478280	+	0.878207i	$0.658740\pi$
$734$	−1.33741	−	4.11613i	−0.0493648	−	0.151929i
$735$		0			0
$736$			13.7128i			0.505460i
$737$	−18.1771	−	47.4797i	−0.669562	−	1.74894i
$738$		0			0
$739$	−16.1574	−	22.2387i	−0.594359	−	0.818065i	0.400818	−	0.916158i	$-0.368726\pi$
$739$	−16.1574	−	22.2387i	−0.594359	−	0.818065i	−0.995177	+	0.0980925i	$0.968726\pi$
$740$	−9.32181	+	3.02884i	−0.342676	+	0.111342i
$741$		0			0
$742$	12.1669	+	8.83974i	0.446659	+	0.324517i
$743$	−23.2314	−	16.8786i	−0.852278	−	0.619216i	0.0734953	−	0.997296i	$-0.476585\pi$
$743$	−23.2314	−	16.8786i	−0.852278	−	0.619216i	−0.925773	+	0.378079i	$0.876585\pi$
$744$		0			0
$745$	−0.0282108	+	0.00916626i	−0.00103356	+	0.000335826i
$746$	12.1925	+	16.7816i	0.446400	+	0.614417i
$747$		0			0
$748$	−8.32579	−	5.41742i	−0.304421	−	0.198080i
$749$		−	16.9729i		−	0.620175i
$750$		0			0
$751$	8.86258	+	27.2762i	0.323400	+	0.995323i	0.972158	+	0.234328i	$0.0752889\pi$
$751$	8.86258	+	27.2762i	0.323400	+	0.995323i	−0.648758	+	0.760995i	$0.724711\pi$
$752$	13.9266	+	4.52503i	0.507851	+	0.165011i
$753$		0			0
$754$	1.32858	−	1.82864i	0.0483842	−	0.0665951i
$755$	0.370092	−	1.13903i	0.0134690	−	0.0414534i
$756$		0			0
$757$	23.4351	−	17.0266i	0.851763	−	0.618842i	−0.0738684	−	0.997268i	$-0.523534\pi$
$757$	23.4351	−	17.0266i	0.851763	−	0.618842i	0.925632	+	0.378426i	$0.123534\pi$
$758$	−29.8162			−1.08297
$759$		0			0
$760$	3.78369			0.137249
$761$	36.3686	−	26.4234i	1.31836	−	0.957846i	0.318411	−	0.947953i	$-0.396851\pi$
$761$	36.3686	−	26.4234i	1.31836	−	0.957846i	0.999951	−	0.00989298i	$-0.00314908\pi$
$762$		0			0
$763$	7.21639	−	22.2098i	0.261251	−	0.804047i
$764$	−5.01201	+	6.89844i	−0.181328	+	0.249577i
$765$		0			0
$766$	−4.76164	−	1.54715i	−0.172045	−	0.0559008i
$767$	1.28543	+	3.95615i	0.0464142	+	0.142848i
$768$		0			0
$769$			1.08812i			0.0392388i	0.999808	+	0.0196194i	$0.00624544\pi$
$769$			1.08812i			0.0392388i	−0.999808	+	0.0196194i	$0.993755\pi$
$770$	43.8895	−	2.26082i	1.58167	−	0.0814742i
$771$		0			0
$772$	0.814836	+	1.12153i	0.0293266	+	0.0403646i
$773$	5.28257	−	1.71641i	0.190001	−	0.0617350i	−0.212471	−	0.977167i	$-0.568151\pi$
$773$	5.28257	−	1.71641i	0.190001	−	0.0617350i	0.402472	+	0.915432i	$0.368151\pi$
$774$		0			0
$775$	−30.3578	−	22.0562i	−1.09048	−	0.792282i
$776$	12.6962	+	9.22433i	0.455767	+	0.331134i
$777$		0			0
$778$	16.6221	−	5.40084i	0.595930	−	0.193629i
$779$	−1.80518	−	2.48462i	−0.0646774	−	0.0890207i
$780$		0			0
$781$	1.94884	+	0.524058i	0.0697350	+	0.0187523i
$782$		−	8.97319i		−	0.320881i
$783$		0			0
$784$	3.76113	+	11.5756i	0.134326	+	0.413413i
$785$	−8.64836	−	2.81002i	−0.308673	−	0.100294i
$786$		0			0
$787$	−14.2392	+	19.5986i	−0.507573	+	0.698615i	−0.983508	−	0.180866i	$-0.942110\pi$
$787$	−14.2392	+	19.5986i	−0.507573	+	0.698615i	0.475935	+	0.879481i	$0.342110\pi$
$788$	5.47799	−	16.8595i	0.195145	−	0.600596i
$789$		0			0
$790$	−12.3944	+	9.00509i	−0.440974	+	0.320387i
$791$	−30.5003			−1.08447
$792$		0			0
$793$	0.424649			0.0150797
$794$	−6.55251	+	4.76068i	−0.232540	+	0.168950i
$795$		0			0
$796$	−5.44355	+	16.7535i	−0.192942	+	0.593813i
$797$	6.31956	−	8.69813i	0.223850	−	0.308104i	−0.682289	−	0.731082i	$-0.739015\pi$
$797$	6.31956	−	8.69813i	0.223850	−	0.308104i	0.906140	+	0.422979i	$0.139015\pi$
$798$		0			0
$799$	37.5548	+	12.2023i	1.32859	+	0.431686i
$800$	6.96224	+	21.4276i	0.246152	+	0.757579i
$801$		0			0
$802$			6.56948i			0.231976i
$803$	1.94295	+	37.7187i	0.0685653	+	1.33106i
$804$		0			0
$805$	−21.5641	−	29.6804i	−0.760034	−	1.04610i
$806$	−2.80231	+	0.910525i	−0.0987071	+	0.0320719i
$807$		0			0
$808$	−19.8706	−	14.4369i	−0.699047	−	0.507887i
$809$	12.6347	+	9.17967i	0.444213	+	0.322740i	0.787307	−	0.616561i	$-0.211475\pi$
$809$	12.6347	+	9.17967i	0.444213	+	0.322740i	−0.343093	+	0.939301i	$0.611475\pi$
$810$		0			0
$811$	51.9356	−	16.8749i	1.82370	−	0.592557i	0.824043	−	0.566528i	$-0.191714\pi$
$811$	51.9356	−	16.8749i	1.82370	−	0.592557i	0.999661	−	0.0260296i	$-0.00828640\pi$
$812$	14.6705	+	20.1922i	0.514832	+	0.708606i
$813$		0			0
$814$	8.64370	−	6.98675i	0.302961	−	0.244885i
$815$			41.4454i			1.45177i
$816$		0			0
$817$	−1.15648	−	3.55929i	−0.0404602	−	0.124524i
$818$	−15.4814	−	5.03020i	−0.541294	−	0.175877i
$819$		0			0
$820$	13.3315	−	18.3492i	0.465556	−	0.640782i
$821$	−6.21259	+	19.1204i	−0.216821	+	0.667306i	0.782198	+	0.623029i	$0.214098\pi$
$821$	−6.21259	+	19.1204i	−0.216821	+	0.667306i	−0.999019	+	0.0442767i	$0.985902\pi$
$822$		0			0
$823$	32.3767	−	23.5230i	1.12858	−	0.819962i	0.143093	−	0.989709i	$-0.454295\pi$
$823$	32.3767	−	23.5230i	1.12858	−	0.819962i	0.985488	+	0.169748i	$0.0542953\pi$
$824$	41.6606			1.45132
$825$		0			0
$826$	49.7056			1.72948
$827$	−36.6966	+	26.6617i	−1.27607	+	0.927117i	−0.999427	−	0.0338566i	$-0.989221\pi$
$827$	−36.6966	+	26.6617i	−1.27607	+	0.927117i	−0.276640	+	0.960974i	$0.589221\pi$
$828$		0			0
$829$	−11.8926	+	36.6018i	−0.413049	+	1.27123i	0.500936	+	0.865484i	$0.332989\pi$
$829$	−11.8926	+	36.6018i	−0.413049	+	1.27123i	−0.913985	+	0.405749i	$0.867011\pi$
$830$	−12.3276	+	16.9675i	−0.427899	+	0.588952i
$831$		0			0
$832$	2.46815	+	0.801951i	0.0855678	+	0.0278027i
$833$	10.1423	+	31.2149i	0.351411	+	1.08153i
$834$		0			0
$835$		−	23.8423i		−	0.825096i
$836$	1.20135	−	0.459922i	0.0415494	−	0.0159067i
$837$		0			0
$838$	2.18314	+	3.00484i	0.0754154	+	0.103800i
$839$	5.64290	−	1.83349i	0.194814	−	0.0632990i	−0.209985	−	0.977705i	$-0.567341\pi$
$839$	5.64290	−	1.83349i	0.194814	−	0.0632990i	0.404799	+	0.914406i	$0.367341\pi$
$840$		0			0
$841$	−7.70391	−	5.59722i	−0.265652	−	0.193008i
$842$	10.8910	+	7.91275i	0.375328	+	0.272691i
$843$		0			0
$844$	4.18233	−	1.35892i	0.143962	−	0.0467760i
$845$	23.4892	+	32.3301i	0.808053	+	1.11219i
$846$		0			0
$847$	42.1032	−	18.6555i	1.44668	−	0.641009i
$848$		−	4.07401i		−	0.139902i
$849$		0			0
$850$	−4.55586	−	14.0215i	−0.156265	−	0.480933i
$851$	−8.82400	−	2.86709i	−0.302483	−	0.0982826i
$852$		0			0
$853$	1.84244	−	2.53590i	0.0630839	−	0.0868275i	−0.776309	−	0.630352i	$-0.782911\pi$
$853$	1.84244	−	2.53590i	0.0630839	−	0.0868275i	0.839393	+	0.543525i	$0.182911\pi$
$854$	1.56802	−	4.82587i	0.0536565	−	0.165138i
$855$		0			0
$856$	−9.90009	+	7.19283i	−0.338378	+	0.245846i
$857$	−42.4553			−1.45025			−0.725124	−	0.688619i	$-0.758217\pi$
$857$	−42.4553			−1.45025			−0.725124	+	0.688619i	$0.758217\pi$
$858$		0			0
$859$	1.01620			0.0346723			0.0173361	−	0.999850i	$-0.494481\pi$
$859$	1.01620			0.0346723			0.0173361	+	0.999850i	$0.494481\pi$
$860$	22.3600	−	16.2455i	0.762471	−	0.553967i
$861$		0			0
$862$	−4.89696	+	15.0713i	−0.166791	+	0.513331i
$863$	−6.08271	+	8.37213i	−0.207058	+	0.284991i	−0.899898	−	0.436101i	$-0.856359\pi$
$863$	−6.08271	+	8.37213i	−0.207058	+	0.284991i	0.692840	+	0.721091i	$0.256359\pi$
$864$		0			0
$865$	36.6638	+	11.9128i	1.24661	+	0.405048i
$866$	3.92006	+	12.0647i	0.133209	+	0.409976i
$867$		0			0
$868$		−	32.5360i		−	1.10434i
$869$	−8.75548	+	13.4559i	−0.297009	+	0.456460i
$870$		0			0
$871$	3.21840	+	4.42975i	0.109051	+	0.150096i
$872$	−16.0129	+	5.20291i	−0.542265	+	0.176193i
$873$		0			0
$874$	0.940125	+	0.683041i	0.0318002	+	0.0231042i
$875$	3.80806	+	2.76672i	0.128736	+	0.0935321i
$876$		0			0
$877$	−27.9173	+	9.07089i	−0.942701	+	0.306302i	−0.739746	−	0.672886i	$-0.765054\pi$
$877$	−27.9173	+	9.07089i	−0.942701	+	0.306302i	−0.202955	+	0.979188i	$0.565054\pi$
$878$	6.87361	+	9.46071i	0.231973	+	0.319284i
$879$		0			0
$880$	−7.48392	−	9.25878i	−0.252283	−	0.312113i
$881$		−	28.0964i		−	0.946592i	−0.880903	−	0.473296i	$-0.843064\pi$
$881$		−	28.0964i		−	0.946592i	0.880903	−	0.473296i	$-0.156936\pi$
$882$		0			0
$883$	−3.44111	−	10.5906i	−0.115802	−	0.356403i	0.876311	−	0.481746i	$-0.159997\pi$
$883$	−3.44111	−	10.5906i	−0.115802	−	0.356403i	−0.992114	+	0.125342i	$0.959997\pi$
$884$	1.01744	+	0.330585i	0.0342201	+	0.0111188i
$885$		0			0
$886$	−4.40556	+	6.06373i	−0.148008	+	0.203715i
$887$	−7.35421	+	22.6339i	−0.246930	+	0.759973i	0.748383	+	0.663267i	$0.230831\pi$
$887$	−7.35421	+	22.6339i	−0.246930	+	0.759973i	−0.995313	+	0.0967061i	$0.969169\pi$
$888$		0			0
$889$	−46.4196	+	33.7258i	−1.55686	+	1.13113i
$890$	−23.1030			−0.774414
$891$		0			0
$892$	10.4843			0.351042
$893$	−4.13711	+	3.00579i	−0.138443	+	0.100585i
$894$		0			0
$895$	5.08634	−	15.6541i	0.170018	−	0.523260i
$896$	−5.68090	+	7.81909i	−0.189786	+	0.261217i
$897$		0			0
$898$	4.27053	+	1.38758i	0.142509	+	0.0463041i
$899$	15.5180	+	47.7596i	0.517556	+	1.59287i
$900$		0			0
$901$		−	10.9860i		−	0.365998i
$902$	−6.67869	+	24.8364i	−0.222376	+	0.826962i
$903$		0			0
$904$	12.9256	+	17.7905i	0.429898	+	0.591703i
$905$	−50.4972	+	16.4075i	−1.67858	+	0.545405i
$906$		0			0
$907$	0.945921	+	0.687252i	0.0314088	+	0.0228198i	0.603379	−	0.797455i	$-0.293821\pi$
$907$	0.945921	+	0.687252i	0.0314088	+	0.0228198i	−0.571970	+	0.820274i	$0.693821\pi$
$908$	−2.19174	−	1.59239i	−0.0727353	−	0.0528453i
$909$		0			0
$910$	−4.50149	+	1.46262i	−0.149223	+	0.0484855i
$911$	0.840855	+	1.15734i	0.0278588	+	0.0383443i	0.822719	−	0.568448i	$-0.192456\pi$
$911$	0.840855	+	1.15734i	0.0278588	+	0.0383443i	−0.794860	+	0.606792i	$0.792456\pi$
$912$		0			0
$913$	−5.70701	+	21.2229i	−0.188874	+	0.702377i
$914$		−	6.42424i		−	0.212495i
$915$		0			0
$916$	−0.591038	−	1.81903i	−0.0195285	−	0.0601024i
$917$	−73.7713	−	23.9698i	−2.43614	−	0.791551i
$918$		0			0
$919$	−7.86498	+	10.8252i	−0.259442	+	0.357091i	−0.918790	−	0.394747i	$-0.870832\pi$
$919$	−7.86498	+	10.8252i	−0.259442	+	0.357091i	0.659348	+	0.751838i	$0.270832\pi$
$920$	−8.17374	+	25.1562i	−0.269480	+	0.829375i
$921$		0			0
$922$	−8.51133	+	6.18384i	−0.280306	+	0.203654i
$923$	−0.217346			−0.00715402
$924$		0			0
$925$	−15.2440			−0.501221
$926$	1.39661	−	1.01469i	0.0458953	−	0.0333449i
$927$		0			0
$928$	9.31732	−	28.6758i	0.305856	−	0.941328i
$929$	32.4134	−	44.6132i	1.06345	−	1.46371i	0.186912	−	0.982377i	$-0.440152\pi$
$929$	32.4134	−	44.6132i	1.06345	−	1.46371i	0.876537	−	0.481335i	$-0.159848\pi$
$930$		0			0
$931$	−4.04243	−	1.31347i	−0.132485	−	0.0430471i
$932$	7.22213	+	22.2274i	0.236569	+	0.728083i
$933$		0			0
$934$		−	24.5875i		−	0.804528i
$935$	−20.1813	−	24.9674i	−0.659998	−	0.816521i
$936$		0			0
$937$	14.4585	+	19.9004i	0.472339	+	0.650118i	0.977010	−	0.213193i	$-0.0683863\pi$
$937$	14.4585	+	19.9004i	0.472339	+	0.650118i	−0.504671	+	0.863312i	$0.668386\pi$
$938$	62.2254	−	20.2183i	2.03173	−	0.660149i
$939$		0			0
$940$	−30.5531	−	22.1981i	−0.996532	−	0.724023i
$941$	17.6381	+	12.8149i	0.574987	+	0.417752i	0.836913	−	0.547335i	$-0.184358\pi$
$941$	17.6381	+	12.8149i	0.574987	+	0.417752i	−0.261926	+	0.965088i	$0.584358\pi$
$942$		0			0
$943$	20.4189	−	6.63449i	0.664929	−	0.216049i
$944$	−7.91453	−	10.8934i	−0.257596	−	0.354550i
$945$		0			0
$946$	−17.0927	+	26.2690i	−0.555731	+	0.854078i
$947$		−	47.5553i		−	1.54534i	−0.634809	−	0.772669i	$-0.718921\pi$
$947$		−	47.5553i		−	1.54534i	0.634809	−	0.772669i	$-0.281079\pi$
$948$		0			0
$949$	−1.25698	−	3.86859i	−0.0408034	−	0.125580i
$950$	1.81583	+	0.589999i	0.0589133	+	0.0191421i
$951$		0			0
$952$	23.1585	−	31.8750i	0.750573	−	1.03307i
$953$	−13.1907	+	40.5969i	−0.427290	+	1.31506i	0.473495	+	0.880797i	$0.342992\pi$
$953$	−13.1907	+	40.5969i	−0.427290	+	1.31506i	−0.900785	+	0.434266i	$0.857008\pi$
$954$		0			0
$955$	−22.2957	+	16.1988i	−0.721472	+	0.524180i
$956$	9.63448			0.311601
$957$		0			0
$958$	−38.0188			−1.22833
$959$	65.8119	−	47.8152i	2.12518	−	1.54403i
$960$		0			0
$961$	10.6496	−	32.7760i	0.343534	−	1.05729i
$962$	−0.703584	+	0.968400i	−0.0226845	+	0.0312225i
$963$		0			0
$964$	−15.8202	−	5.14029i	−0.509534	−	0.165558i
$965$	1.38454	+	4.26116i	0.0445698	+	0.137172i
$966$		0			0
$967$		−	1.49173i		−	0.0479709i	−0.999712	−	0.0239855i	$-0.992364\pi$
$967$		−	1.49173i		−	0.0479709i	0.999712	−	0.0239855i	$-0.00763554\pi$
$968$	−28.7242	−	16.6525i	−0.923232	−	0.535231i
$969$		0			0
$970$	9.67280	+	13.3135i	0.310575	+	0.427470i
$971$	2.12249	−	0.689639i	0.0681140	−	0.0221316i	−0.274762	−	0.961512i	$-0.588599\pi$
$971$	2.12249	−	0.689639i	0.0681140	−	0.0221316i	0.342876	+	0.939381i	$0.388599\pi$
$972$		0			0
$973$	−11.9155	−	8.65712i	−0.381994	−	0.277535i
$974$	31.3735	+	22.7942i	1.00527	+	0.730373i
$975$		0			0
$976$	−1.30730	+	0.424769i	−0.0418458	+	0.0135965i
$977$	25.9944	+	35.7782i	0.831635	+	1.14465i	0.987616	+	0.156887i	$0.0501460\pi$
$977$	25.9944	+	35.7782i	0.831635	+	1.14465i	−0.155981	+	0.987760i	$0.549854\pi$
$978$		0			0
$979$	−22.6086	+	8.65544i	−0.722573	+	0.276629i
$980$		−	31.3902i		−	1.00272i
$981$		0			0
$982$	9.02219	+	27.7674i	0.287910	+	0.886095i
$983$	−40.5465	−	13.1744i	−1.29323	−	0.420197i	−0.420010	−	0.907519i	$-0.637974\pi$
$983$	−40.5465	−	13.1744i	−1.29323	−	0.420197i	−0.873222	+	0.487323i	$0.837974\pi$
$984$		0			0
$985$	33.6766	−	46.3518i	1.07303	−	1.47689i
$986$	−6.09695	+	18.7645i	−0.194166	+	0.597583i
$987$		0			0
$988$	−0.112083	+	0.0814330i	−0.00356583	+	0.00259073i
$989$	26.1625			0.831920
$990$		0			0
$991$	−1.45490			−0.0462164			−0.0231082	−	0.999733i	$-0.507356\pi$
$991$	−1.45490			−0.0462164			−0.0231082	+	0.999733i	$0.507356\pi$
$992$	−31.7984	+	23.1029i	−1.00960	+	0.733519i
$993$		0			0
$994$	−0.802551	+	2.47000i	−0.0254554	+	0.0783436i
$995$	−33.4649	+	46.0604i	−1.06091	+	1.46021i
$996$		0			0
$997$	49.9163	+	16.2188i	1.58086	+	0.513654i	0.962279	−	0.272064i	$-0.0877063\pi$
$997$	49.9163	+	16.2188i	1.58086	+	0.513654i	0.618585	+	0.785718i	$0.287706\pi$
$998$	4.84912	+	14.9241i	0.153496	+	0.472413i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.k.a.107.6	yes	32
3.2	odd	2	inner	297.2.k.a.107.3	✓	32
9.2	odd	6		891.2.u.e.701.6		64
9.4	even	3		891.2.u.e.107.6		64
9.5	odd	6		891.2.u.e.107.3		64
9.7	even	3		891.2.u.e.701.3		64
11.7	odd	10	inner	297.2.k.a.161.3	yes	32
33.29	even	10	inner	297.2.k.a.161.6	yes	32
99.7	odd	30		891.2.u.e.458.3		64
99.29	even	30		891.2.u.e.458.6		64
99.40	odd	30		891.2.u.e.755.6		64
99.95	even	30		891.2.u.e.755.3		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.k.a.107.3	✓	32	3.2	odd	2	inner
297.2.k.a.107.6	yes	32	1.1	even	1	trivial
297.2.k.a.161.3	yes	32	11.7	odd	10	inner
297.2.k.a.161.6	yes	32	33.29	even	10	inner
891.2.u.e.107.3		64	9.5	odd	6
891.2.u.e.107.6		64	9.4	even	3
891.2.u.e.458.3		64	99.7	odd	30
891.2.u.e.458.6		64	99.29	even	30
891.2.u.e.701.3		64	9.7	even	3
891.2.u.e.701.6		64	9.2	odd	6
891.2.u.e.755.3		64	99.95	even	30
891.2.u.e.755.6		64	99.40	odd	30

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.824821 - 0.599267i) q^{2} +(-0.296826 + 0.913536i) q^{4} +(-1.82477 + 2.51158i) q^{5} +(-3.98157 - 1.29369i) q^{7} +(0.932731 + 2.87065i) q^{8} +3.16513i q^{10} +(1.18580 + 3.09740i) q^{11} +(-0.209956 - 0.288980i) q^{13} +(-4.05935 + 1.31896i) q^{14} +(0.935424 + 0.679625i) q^{16} +(2.52248 + 1.83269i) q^{17} +(-0.384024 + 0.124777i) q^{19} +(-1.75278 - 2.41250i) q^{20} +(2.83425 + 1.84418i) q^{22} -2.82276i q^{23} +(-1.43317 - 4.41084i) q^{25} +(-0.346353 - 0.112537i) q^{26} +(2.36367 - 3.25331i) q^{28} +(-1.91796 + 5.90288i) q^{29} +(6.54568 - 4.75571i) q^{31} -4.85793 q^{32} +3.17887 q^{34} +(10.5147 - 7.63935i) q^{35} +(1.01570 - 3.12601i) q^{37} +(-0.241976 + 0.333051i) q^{38} +(-8.91190 - 2.89565i) q^{40} +(2.35035 + 7.23364i) q^{41} +9.26842i q^{43} +(-3.18156 + 0.163887i) q^{44} +(-1.69159 - 2.32827i) q^{46} +(12.0447 - 3.91355i) q^{47} +(8.51614 + 6.18734i) q^{49} +(-3.82538 - 2.77930i) q^{50} +(0.326315 - 0.106026i) q^{52} +(-2.07104 - 2.85055i) q^{53} +(-9.94319 - 2.67380i) q^{55} -12.6364i q^{56} +(1.95543 + 6.01819i) q^{58} +(-11.0755 - 3.59863i) q^{59} +(-0.698776 + 0.961782i) q^{61} +(2.54907 - 7.84522i) q^{62} +(-5.87777 + 4.27045i) q^{64} +1.10892 q^{65} -15.3289 q^{67} +(-2.42297 + 1.76039i) q^{68} +(4.09470 - 12.6022i) q^{70} +(0.357651 - 0.492264i) q^{71} +(10.8303 + 3.51899i) q^{73} +(-1.03554 - 3.18708i) q^{74} -0.387857i q^{76} +(-0.714289 - 13.8666i) q^{77} +(2.84509 + 3.91593i) q^{79} +(-3.41387 + 1.10923i) q^{80} +(6.27351 + 4.55797i) q^{82} +(5.36077 + 3.89483i) q^{83} +(-9.20591 + 2.99118i) q^{85} +(5.55426 + 7.64478i) q^{86} +(-7.78551 + 6.29307i) q^{88} +7.29922i q^{89} +(0.462105 + 1.42221i) q^{91} +(2.57870 + 0.837869i) q^{92} +(7.58943 - 10.4460i) q^{94} +(0.387368 - 1.19220i) q^{95} +(4.20629 - 3.05605i) q^{97} +10.7322 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{4} - 4 q^{16} + 36 q^{22} + 8 q^{25} - 100 q^{28} + 8 q^{31} - 64 q^{34} - 12 q^{37} - 60 q^{40} - 20 q^{46} + 100 q^{52} + 8 q^{55} + 24 q^{58} + 60 q^{61} + 36 q^{64} - 24 q^{67} + 8 q^{70}+ \cdots - 24 q^{97}+O(q^{100}) \) 32 * q - 8 * q^4 - 4 * q^16 + 36 * q^22 + 8 * q^25 - 100 * q^28 + 8 * q^31 - 64 * q^34 - 12 * q^37 - 60 * q^40 - 20 * q^46 + 100 * q^52 + 8 * q^55 + 24 * q^58 + 60 * q^61 + 36 * q^64 - 24 * q^67 + 8 * q^70 + 80 * q^73 - 60 * q^79 + 72 * q^82 - 20 * q^85 - 24 * q^88 + 24 * q^91 + 20 * q^94 - 24 * q^97

Introduction

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