LMFDB - Embedded newform 936.2.dg.e.901.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(829,936)] 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, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.829"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [48,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.10
Character	$\chi$	$=$	936.901
Dual form			936.2.dg.e.829.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.660721 - 1.25038i) q^{2} +(-1.12690 + 1.65230i) q^{4} +0.230393 q^{5} +(-2.89019 + 1.66865i) q^{7} +(2.81057 + 0.317334i) q^{8} +(-0.152225 - 0.288078i) q^{10} +(1.57254 - 2.72371i) q^{11} +(-2.26472 - 2.80553i) q^{13} +(3.99606 + 2.51132i) q^{14} +(-1.46021 - 3.72395i) q^{16} +(0.791692 + 1.37125i) q^{17} +(4.02979 + 6.97979i) q^{19} +(-0.259629 + 0.380679i) q^{20} +(-4.44468 - 0.166652i) q^{22} +(3.40824 - 5.90325i) q^{23} -4.94692 q^{25} +(-2.01163 + 4.68544i) q^{26} +(0.499822 - 6.65587i) q^{28} +(-3.13808 - 1.81177i) q^{29} -9.62991i q^{31} +(-3.69155 + 4.28631i) q^{32} +(1.19150 - 1.89593i) q^{34} +(-0.665879 + 0.384445i) q^{35} +(0.568757 - 0.985115i) q^{37} +(6.06482 - 9.65046i) q^{38} +(0.647535 + 0.0731116i) q^{40} +(-9.84578 - 5.68446i) q^{41} +(5.40070 - 3.11810i) q^{43} +(2.72832 + 5.66765i) q^{44} +(-9.63320 - 0.361194i) q^{46} -8.90552i q^{47} +(2.06880 - 3.58326i) q^{49} +(3.26853 + 6.18552i) q^{50} +(7.18770 - 0.580470i) q^{52} -4.01765i q^{53} +(0.362301 - 0.627524i) q^{55} +(-8.65260 + 3.77270i) q^{56} +(-0.192005 + 5.12086i) q^{58} +(-3.63171 - 6.29031i) q^{59} +(-2.50714 + 1.44750i) q^{61} +(-12.0410 + 6.36268i) q^{62} +(7.79860 + 1.78378i) q^{64} +(-0.521776 - 0.646375i) q^{65} +(0.640338 - 1.10910i) q^{67} +(-3.15788 - 0.237140i) q^{68} +(0.920663 + 0.578590i) q^{70} +(0.987337 - 0.570039i) q^{71} +0.813566i q^{73} +(-1.60756 - 0.0602748i) q^{74} +(-16.0739 - 1.20707i) q^{76} +10.4961i q^{77} -15.4710 q^{79} +(-0.336423 - 0.857971i) q^{80} +(-0.602419 + 16.0668i) q^{82} +12.7265 q^{83} +(0.182400 + 0.315926i) q^{85} +(-7.46716 - 4.69273i) q^{86} +(5.28405 - 7.15616i) q^{88} +(-10.0707 - 5.81429i) q^{89} +(11.2269 + 4.32949i) q^{91} +(5.91323 + 12.2838i) q^{92} +(-11.1353 + 5.88406i) q^{94} +(0.928434 + 1.60809i) q^{95} +(6.94900 - 4.01201i) q^{97} +(-5.84733 - 0.219244i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} - 12 q^{7} - 4 q^{10} + 36 q^{14} - 2 q^{16} - 12 q^{17} - 54 q^{20} - 14 q^{22} - 20 q^{23} + 48 q^{25} + 42 q^{26} + 6 q^{28} + 28 q^{38} - 8 q^{40} + 12 q^{41} - 30 q^{46} + 16 q^{49}+ \cdots - 24 q^{98}+O(q^{100}) $ 48 * q - 2 * q^4 - 12 * q^7 - 4 * q^10 + 36 * q^14 - 2 * q^16 - 12 * q^17 - 54 * q^20 - 14 * q^22 - 20 * q^23 + 48 * q^25 + 42 * q^26 + 6 * q^28 + 28 * q^38 - 8 * q^40 + 12 * q^41 - 30 * q^46 + 16 * q^49 + 84 * q^50 - 28 * q^52 - 68 * q^55 - 18 * q^56 - 24 * q^58 - 24 * q^62 - 68 * q^64 - 12 * q^65 - 4 * q^68 + 12 * q^71 - 54 * q^74 - 54 * q^76 - 192 * q^79 - 78 * q^80 - 6 * q^82 - 10 * q^88 + 48 * q^89 + 12 * q^92 + 54 * q^94 + 20 * q^95 + 144 * q^97 - 24 * q^98

Character values

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

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

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 $

$2$	−0.660721	−	1.25038i	−0.467200	−	0.884151i
$2$	−0.660721	−	1.25038i	−0.467200	−	0.884151i
$3$		0			0
$3$		0			0
$4$	−1.12690	+	1.65230i	−0.563448	+	0.826152i
$5$	0.230393			0.103035			0.0515174	−	0.998672i	$-0.483594\pi$
$5$	0.230393			0.103035			0.0515174	+	0.998672i	$0.483594\pi$
$6$		0			0
$7$	−2.89019	+	1.66865i	−1.09239	+	0.630691i	−0.934211	−	0.356720i	$-0.883895\pi$
$7$	−2.89019	+	1.66865i	−1.09239	+	0.630691i	−0.158177	+	0.987411i	$0.550562\pi$
$8$	2.81057	+	0.317334i	0.993686	+	0.112195i
$9$		0			0
$10$	−0.152225	−	0.288078i	−0.0481379	−	0.0910984i
$11$	1.57254	−	2.72371i	0.474138	−	0.821230i	−0.525424	−	0.850841i	$-0.676093\pi$
$11$	1.57254	−	2.72371i	0.474138	−	0.821230i	0.999562	+	0.0296102i	$0.00942660\pi$
$12$		0			0
$13$	−2.26472	−	2.80553i	−0.628122	−	0.778115i
$13$	−2.26472	−	2.80553i	−0.628122	−	0.778115i
$14$	3.99606	+	2.51132i	1.06799	+	0.671178i
$15$		0			0
$16$	−1.46021	−	3.72395i	−0.365054	−	0.930987i
$17$	0.791692	+	1.37125i	0.192013	+	0.332577i	0.945917	−	0.324408i	$-0.105165\pi$
$17$	0.791692	+	1.37125i	0.192013	+	0.332577i	−0.753904	+	0.656985i	$0.771832\pi$
$18$		0			0
$19$	4.02979	+	6.97979i	0.924496	+	1.60127i	0.792369	+	0.610042i	$0.208847\pi$
$19$	4.02979	+	6.97979i	0.924496	+	1.60127i	0.132127	+	0.991233i	$0.457819\pi$
$20$	−0.259629	+	0.380679i	−0.0580547	+	0.0851224i
$21$		0			0
$22$	−4.44468	−	0.166652i	−0.947609	−	0.0355303i
$23$	3.40824	−	5.90325i	0.710668	−	1.23091i	−0.253939	−	0.967220i	$-0.581726\pi$
$23$	3.40824	−	5.90325i	0.710668	−	1.23091i	0.964607	−	0.263692i	$-0.0849404\pi$
$24$		0			0
$25$	−4.94692			−0.989384
$26$	−2.01163	+	4.68544i	−0.394513	+	0.918890i
$27$		0			0
$28$	0.499822	−	6.65587i	0.0944574	−	1.25784i
$29$	−3.13808	−	1.81177i	−0.582727	−	0.336437i	0.179490	−	0.983760i	$-0.442555\pi$
$29$	−3.13808	−	1.81177i	−0.582727	−	0.336437i	−0.762216	+	0.647323i	$0.775889\pi$
$30$		0			0
$31$		−	9.62991i		−	1.72958i	−0.502132	−	0.864791i	$-0.667451\pi$
$31$		−	9.62991i		−	1.72958i	0.502132	−	0.864791i	$-0.332549\pi$
$32$	−3.69155	+	4.28631i	−0.652580	+	0.757720i
$33$		0			0
$34$	1.19150	−	1.89593i	0.204340	−	0.325149i
$35$	−0.665879	+	0.384445i	−0.112554	+	0.0649831i
$36$		0			0
$37$	0.568757	−	0.985115i	0.0935030	−	0.161952i	−0.815480	−	0.578785i	$-0.803527\pi$
$37$	0.568757	−	0.985115i	0.0935030	−	0.161952i	0.908983	+	0.416834i	$0.136860\pi$
$38$	6.06482	−	9.65046i	0.983844	−	1.56551i
$39$		0			0
$40$	0.647535	+	0.0731116i	0.102384	+	0.0115600i
$41$	−9.84578	−	5.68446i	−1.53765	−	0.887764i	−0.998976	−	0.0452518i	$-0.985591\pi$
$41$	−9.84578	−	5.68446i	−1.53765	−	0.887764i	−0.538677	−	0.842512i	$-0.681076\pi$
$42$		0			0
$43$	5.40070	−	3.11810i	0.823599	−	0.475505i	−0.0280568	−	0.999606i	$-0.508932\pi$
$43$	5.40070	−	3.11810i	0.823599	−	0.475505i	0.851656	+	0.524101i	$0.175599\pi$
$44$	2.72832	+	5.66765i	0.411309	+	0.854430i
$45$		0			0
$46$	−9.63320	−	0.361194i	−1.42034	−	0.0532551i
$47$		−	8.90552i		−	1.29900i	−0.760360	−	0.649501i	$-0.774978\pi$
$47$		−	8.90552i		−	1.29900i	0.760360	−	0.649501i	$-0.225022\pi$
$48$		0			0
$49$	2.06880	−	3.58326i	0.295542	−	0.511894i
$50$	3.26853	+	6.18552i	0.462240	+	0.874765i
$51$		0			0
$52$	7.18770	−	0.580470i	0.996755	−	0.0804967i
$53$		−	4.01765i		−	0.551867i	−0.961177	−	0.275933i	$-0.911013\pi$
$53$		−	4.01765i		−	0.551867i	0.961177	−	0.275933i	$-0.0889869\pi$
$54$		0			0
$55$	0.362301	−	0.627524i	0.0488527	−	0.0846153i
$56$	−8.65260	+	3.77270i	−1.15625	+	0.504149i
$57$		0			0
$58$	−0.192005	+	5.12086i	−0.0252115	+	0.672402i
$59$	−3.63171	−	6.29031i	−0.472809	−	0.818929i	0.526707	−	0.850047i	$-0.323426\pi$
$59$	−3.63171	−	6.29031i	−0.472809	−	0.818929i	−0.999516	+	0.0311183i	$0.990093\pi$
$60$		0			0
$61$	−2.50714	+	1.44750i	−0.321006	+	0.185333i	−0.651841	−	0.758356i	$-0.726003\pi$
$61$	−2.50714	+	1.44750i	−0.321006	+	0.185333i	0.330835	+	0.943689i	$0.392670\pi$
$62$	−12.0410	+	6.36268i	−1.52921	+	0.808061i
$63$		0			0
$64$	7.79860	+	1.78378i	0.974825	+	0.222972i
$65$	−0.521776	−	0.646375i	−0.0647184	−	0.0801730i
$66$		0			0
$67$	0.640338	−	1.10910i	0.0782297	−	0.135498i	−0.824257	−	0.566217i	$-0.808407\pi$
$67$	0.640338	−	1.10910i	0.0782297	−	0.135498i	0.902486	+	0.430719i	$0.141740\pi$
$68$	−3.15788	−	0.237140i	−0.382949	−	0.0287575i
$69$		0			0
$70$	0.920663	+	0.578590i	0.110040	+	0.0691547i
$71$	0.987337	−	0.570039i	0.117175	−	0.0676512i	−0.440267	−	0.897867i	$-0.645116\pi$
$71$	0.987337	−	0.570039i	0.117175	−	0.0676512i	0.557442	+	0.830216i	$0.311783\pi$
$72$		0			0
$73$			0.813566i			0.0952207i	0.998866	+	0.0476104i	$0.0151606\pi$
$73$			0.813566i			0.0952207i	−0.998866	+	0.0476104i	$0.984839\pi$
$74$	−1.60756	−	0.0602748i	−0.186875	−	0.00700681i
$75$		0			0
$76$	−16.0739	−	1.20707i	−1.84380	−	0.138460i
$77$			10.4961i			1.19614i
$78$		0			0
$79$	−15.4710			−1.74062			−0.870309	−	0.492506i	$-0.836081\pi$
$79$	−15.4710			−1.74062			−0.870309	+	0.492506i	$0.836081\pi$
$80$	−0.336423	−	0.857971i	−0.0376132	−	0.0959240i
$81$		0			0
$82$	−0.602419	+	16.0668i	−0.0665261	+	1.77428i
$83$	12.7265			1.39691			0.698455	−	0.715654i	$-0.253871\pi$
$83$	12.7265			1.39691			0.698455	+	0.715654i	$0.253871\pi$
$84$		0			0
$85$	0.182400	+	0.315926i	0.0197841	+	0.0342670i
$86$	−7.46716	−	4.69273i	−0.805205	−	0.506030i
$87$		0			0
$88$	5.28405	−	7.15616i	0.563282	−	0.762850i
$89$	−10.0707	−	5.81429i	−1.06749	−	0.616314i	−0.139993	−	0.990152i	$-0.544708\pi$
$89$	−10.0707	−	5.81429i	−1.06749	−	0.616314i	−0.927494	+	0.373838i	$0.878041\pi$
$90$		0			0
$91$	11.2269	+	4.32949i	1.17690	+	0.453854i
$92$	5.91323	+	12.2838i	0.616497	+	1.28067i
$93$		0			0
$94$	−11.1353	+	5.88406i	−1.14852	+	0.606895i
$95$	0.928434	+	1.60809i	0.0952553	+	0.164987i
$96$		0			0
$97$	6.94900	−	4.01201i	0.705564	−	0.407358i	−0.103852	−	0.994593i	$-0.533117\pi$
$97$	6.94900	−	4.01201i	0.705564	−	0.407358i	0.809416	+	0.587235i	$0.199784\pi$
$98$	−5.84733	−	0.219244i	−0.590669	−	0.0221469i
$99$		0			0
$100$	5.57466	−	8.17381i	0.557466	−	0.817381i
$101$	9.97844	+	5.76105i	0.992892	+	0.573246i	0.906137	−	0.422983i	$-0.139017\pi$
$101$	9.97844	+	5.76105i	0.992892	+	0.573246i	0.0867543	+	0.996230i	$0.472350\pi$
$102$		0			0
$103$	−0.570336			−0.0561969			−0.0280984	−	0.999605i	$-0.508945\pi$
$103$	−0.570336			−0.0561969			−0.0280984	+	0.999605i	$0.508945\pi$
$104$	−5.47487	−	8.60382i	−0.536856	−	0.843674i
$105$		0			0
$106$	−5.02359	+	2.65455i	−0.487934	+	0.257832i
$107$	1.27986	+	0.738926i	0.123729	+	0.0714347i	0.560587	−	0.828096i	$-0.310576\pi$
$107$	1.27986	+	0.738926i	0.123729	+	0.0714347i	−0.436858	+	0.899530i	$0.643909\pi$
$108$		0			0
$109$	−1.50562			−0.144212			−0.0721062	−	0.997397i	$-0.522972\pi$
$109$	−1.50562			−0.144212			−0.0721062	+	0.997397i	$0.522972\pi$
$110$	−1.02402	−	0.0383954i	−0.0976368	−	0.00366086i
$111$		0			0
$112$	10.4343	+	8.32632i	0.985945	+	0.786763i
$113$	0.0381779	+	0.0661261i	0.00359148	+	0.00622062i	0.867816	−	0.496886i	$-0.165523\pi$
$113$	0.0381779	+	0.0661261i	0.00359148	+	0.00622062i	−0.864224	+	0.503107i	$0.832190\pi$
$114$		0			0
$115$	0.785235	−	1.36007i	0.0732235	−	0.126827i
$116$	6.52988	−	3.14338i	0.606284	−	0.291856i
$117$		0			0
$118$	−5.46572	+	8.69716i	−0.503161	+	0.800638i
$119$	−4.57628	−	2.64211i	−0.419507	−	0.242202i
$120$		0			0
$121$	0.554258	+	0.960004i	0.0503871	+	0.0872731i
$122$	3.46644	+	2.17848i	0.313837	+	0.197230i
$123$		0			0
$124$	15.9115	+	10.8519i	1.42890	+	0.974529i
$125$	−2.29170			−0.204976
$126$		0			0
$127$	3.12007	−	5.40413i	0.276862	−	0.479539i	−0.693741	−	0.720224i	$-0.744039\pi$
$127$	3.12007	−	5.40413i	0.276862	−	0.479539i	0.970603	+	0.240686i	$0.0773723\pi$
$128$	−2.92230	−	10.9298i	−0.258297	−	0.966066i
$129$		0			0
$130$	−0.463465	+	1.07949i	−0.0406486	+	0.0946777i
$131$			15.7714i			1.37795i	0.724783	+	0.688977i	$0.241940\pi$
$131$			15.7714i			1.37795i	−0.724783	+	0.688977i	$0.758060\pi$
$132$		0			0
$133$	−23.2937	−	13.4486i	−2.01982	−	1.16614i
$134$	−1.80988	−	0.0678607i	−0.156349	−	0.00586227i
$135$		0			0
$136$	1.78996	+	4.10522i	0.153488	+	0.352020i
$137$	4.42860	−	2.55686i	0.378361	−	0.218447i	−0.298744	−	0.954333i	$-0.596568\pi$
$137$	4.42860	−	2.55686i	0.378361	−	0.218447i	0.677105	+	0.735886i	$0.263234\pi$
$138$		0			0
$139$	−4.90809	+	2.83369i	−0.416299	+	0.240350i	−0.693492	−	0.720464i	$-0.743929\pi$
$139$	−4.90809	+	2.83369i	−0.416299	+	0.240350i	0.277194	+	0.960814i	$0.410596\pi$
$140$	0.115155	−	1.53346i	0.00973240	−	0.129601i
$141$		0			0
$142$	−1.36512	−	0.857909i	−0.114558	−	0.0719941i
$143$	−11.2028	+	1.75666i	−0.936828	+	0.146899i
$144$		0			0
$145$	−0.722991	−	0.417419i	−0.0600411	−	0.0346648i
$146$	1.01727	−	0.537540i	0.0841896	−	0.0444872i
$147$		0			0
$148$	0.986781	+	2.04988i	0.0811129	+	0.168499i
$149$	−4.50412	−	7.80137i	−0.368992	−	0.639113i	0.620416	−	0.784273i	$-0.286964\pi$
$149$	−4.50412	−	7.80137i	−0.368992	−	0.639113i	−0.989408	+	0.145160i	$0.953630\pi$
$150$		0			0
$151$		−	6.17629i		−	0.502619i	−0.967907	−	0.251310i	$-0.919139\pi$
$151$		−	6.17629i		−	0.502619i	0.967907	−	0.251310i	$-0.0808612\pi$
$152$	9.11106	+	20.8960i	0.739005	+	1.69489i
$153$		0			0
$154$	13.1241	−	6.93497i	1.05757	−	0.558836i
$155$		−	2.21866i		−	0.178207i
$156$		0			0
$157$			10.0557i			0.802532i	0.915961	+	0.401266i	$0.131430\pi$
$157$			10.0557i			0.802532i	−0.915961	+	0.401266i	$0.868570\pi$
$158$	10.2220	+	19.3446i	0.813217	+	1.53897i
$159$		0			0
$160$	−0.850507	+	0.987536i	−0.0672385	+	0.0780715i
$161$			22.7487i			1.79285i
$162$		0			0
$163$	−10.3005	−	17.8410i	−0.806796	−	1.39741i	−0.915072	−	0.403291i	$-0.867866\pi$
$163$	−10.3005	−	17.8410i	−0.806796	−	1.39741i	0.108276	−	0.994121i	$-0.465467\pi$
$164$	20.4876	−	9.86242i	1.59981	−	0.770126i
$165$		0			0
$166$	−8.40864	−	15.9129i	−0.652637	−	1.23508i
$167$	7.97855	+	4.60642i	0.617399	+	0.356455i	0.775856	−	0.630910i	$-0.217318\pi$
$167$	7.97855	+	4.60642i	0.617399	+	0.356455i	−0.158457	+	0.987366i	$0.550652\pi$
$168$		0			0
$169$	−2.74204	+	12.7075i	−0.210926	+	0.977502i
$170$	0.274512	−	0.436808i	0.0210541	−	0.0335017i
$171$		0			0
$172$	−0.933983	+	12.4374i	−0.0712155	+	0.948340i
$173$	−1.65613	+	0.956165i	−0.125913	+	0.0726959i	−0.561634	−	0.827386i	$-0.689827\pi$
$173$	−1.65613	+	0.956165i	−0.125913	+	0.0726959i	0.435721	+	0.900082i	$0.356494\pi$
$174$		0			0
$175$	14.2975	−	8.25468i	1.08079	−	0.623995i
$176$	−12.4392	−	1.87884i	−0.937640	−	0.141623i
$177$		0			0
$178$	−0.616178	+	16.4338i	−0.0461845	+	1.23176i
$179$	11.8443	+	6.83830i	0.885283	+	0.511118i	0.872397	−	0.488799i	$-0.162565\pi$
$179$	11.8443	+	6.83830i	0.885283	+	0.511118i	0.0128863	+	0.999917i	$0.495898\pi$
$180$		0			0
$181$			1.95106i			0.145021i	0.997368	+	0.0725105i	$0.0231011\pi$
$181$			1.95106i			0.145021i	−0.997368	+	0.0725105i	$0.976899\pi$
$182$	−2.00438	−	16.8985i	−0.148574	−	1.25260i
$183$		0			0
$184$	11.4524	−	15.5099i	0.844282	−	1.14341i
$185$	0.131037	−	0.226964i	0.00963407	−	0.0166867i
$186$		0			0
$187$	4.97986			0.364163
$188$	14.7146	+	10.0356i	1.07317	+	0.731920i
$189$		0			0
$190$	1.39729	−	2.22340i	0.101370	−	0.161302i
$191$	−8.22747	−	14.2504i	−0.595318	−	1.03112i	−0.993502	−	0.113816i	$-0.963693\pi$
$191$	−8.22747	−	14.2504i	−0.595318	−	1.03112i	0.398183	−	0.917306i	$-0.369641\pi$
$192$		0			0
$193$	−5.14440	−	2.97012i	−0.370302	−	0.213794i	0.303288	−	0.952899i	$-0.401915\pi$
$193$	−5.14440	−	2.97012i	−0.370302	−	0.213794i	−0.673590	+	0.739105i	$0.735249\pi$
$194$	−9.60788	−	6.03806i	−0.689805	−	0.433508i
$195$		0			0
$196$	3.58932	+	7.45623i	0.256380	+	0.532588i
$197$	3.94646	−	6.83547i	0.281174	−	0.487007i	−0.690500	−	0.723332i	$-0.742610\pi$
$197$	3.94646	−	6.83547i	0.281174	−	0.487007i	0.971674	+	0.236325i	$0.0759430\pi$
$198$		0			0
$199$	8.18855	+	14.1830i	0.580471	+	1.00541i	0.995423	+	0.0955625i	$0.0304650\pi$
$199$	8.18855	+	14.1830i	0.580471	+	1.00541i	−0.414952	+	0.909843i	$0.636202\pi$
$200$	−13.9037	−	1.56983i	−0.983137	−	0.111004i
$201$		0			0
$202$	0.610536	−	16.2833i	0.0429572	−	1.14569i
$203$	12.0929			0.848752
$204$		0			0
$205$	−2.26840	−	1.30966i	−0.158432	−	0.0914706i
$206$	0.376833	+	0.713136i	0.0262552	+	0.0496866i
$207$		0			0
$208$	−7.14067	+	12.5304i	−0.495117	+	0.868826i
$209$	25.3479			1.75335
$210$		0			0
$211$	12.5801	+	7.26314i	0.866052	+	0.500016i	0.866034	−	0.499984i	$-0.166661\pi$
$211$	12.5801	+	7.26314i	0.866052	+	0.500016i	1.79224e−5		1.00000i	$0.499994\pi$
$212$	6.63838	+	4.52747i	0.455926	+	0.310948i
$213$		0			0
$214$	0.0783088	−	2.08853i	0.00535308	−	0.142769i
$215$	1.24428	−	0.718387i	0.0848594	−	0.0489936i
$216$		0			0
$217$	16.0690	+	27.8322i	1.09083	+	1.88938i
$218$	0.994795	+	1.88260i	0.0673760	+	0.127506i
$219$		0			0
$220$	0.628585	+	1.30579i	0.0423792	+	0.0880360i
$221$	2.05413	−	5.32662i	0.138175	−	0.358307i
$222$		0			0
$223$	20.0347	+	11.5670i	1.34162	+	0.774585i	0.987045	−	0.160442i	$-0.0512919\pi$
$223$	20.0347	+	11.5670i	1.34162	+	0.774585i	0.354576	+	0.935027i	$0.384625\pi$
$224$	3.51692	−	18.5482i	0.234984	−	1.23930i
$225$		0			0
$226$	0.0574577	−	0.0914278i	0.00382203	−	0.00608169i
$227$	−10.2158	−	17.6943i	−0.678048	−	1.17441i	−0.975568	−	0.219699i	$-0.929493\pi$
$227$	−10.2158	−	17.6943i	−0.678048	−	1.17441i	0.297519	−	0.954716i	$-0.403841\pi$
$228$		0			0
$229$	6.70980			0.443396			0.221698	−	0.975115i	$-0.428840\pi$
$229$	6.70980			0.443396			0.221698	+	0.975115i	$0.428840\pi$
$230$	−2.21942	−	0.0832164i	−0.146344	−	0.00548713i
$231$		0			0
$232$	−8.24485	−	6.08793i	−0.541301	−	0.399692i
$233$	9.35304			0.612738			0.306369	−	0.951913i	$-0.400886\pi$
$233$	9.35304			0.612738			0.306369	+	0.951913i	$0.400886\pi$
$234$		0			0
$235$		−	2.05177i		−	0.133843i
$236$	14.4861	+	1.08783i	0.942962	+	0.0708117i
$237$		0			0
$238$	−0.280002	+	7.46778i	−0.0181498	+	0.484064i
$239$			8.79465i			0.568879i	0.958694	+	0.284439i	$0.0918074\pi$
$239$			8.79465i			0.568879i	−0.958694	+	0.284439i	$0.908193\pi$
$240$		0			0
$241$	−16.6492	+	9.61245i	−1.07247	+	0.619192i	−0.928856	−	0.370441i	$-0.879206\pi$
$241$	−16.6492	+	9.61245i	−1.07247	+	0.619192i	−0.143616	+	0.989633i	$0.545873\pi$
$242$	0.834158	−	1.32733i	0.0536217	−	0.0853238i
$243$		0			0
$244$	0.433578	−	5.77373i	0.0277570	−	0.369625i
$245$	0.476636	−	0.825557i	0.0304511	−	0.0527429i
$246$		0			0
$247$	10.4557	−	27.1130i	0.665280	−	1.72516i
$248$	3.05590	−	27.0655i	0.194050	−	1.71866i
$249$		0			0
$250$	1.51417	+	2.86549i	0.0957648	+	0.181230i
$251$	18.3517	−	10.5953i	1.15835	−	0.668772i	0.207440	−	0.978248i	$-0.433487\pi$
$251$	18.3517	−	10.5953i	1.15835	−	0.668772i	0.950907	+	0.309476i	$0.100154\pi$
$252$		0			0
$253$	−10.7192	−	18.5661i	−0.673909	−	1.16724i
$254$	−8.81870	−	0.330654i	−0.553335	−	0.0207471i
$255$		0			0
$256$	−11.7355	+	10.8755i	−0.733472	+	0.679720i
$257$	−2.53390	+	4.38885i	−0.158061	+	0.273769i	−0.934169	−	0.356830i	$-0.883857\pi$
$257$	−2.53390	+	4.38885i	−0.158061	+	0.273769i	0.776109	+	0.630599i	$0.217191\pi$
$258$		0			0
$259$			3.79623i			0.235886i
$260$	1.65600	−	0.133736i	0.102700	−	0.00829396i
$261$		0			0
$262$	19.7202	−	10.4205i	1.21832	−	0.643781i
$263$	−2.69479	+	4.66751i	−0.166168	+	0.287811i	−0.937069	−	0.349143i	$-0.886473\pi$
$263$	−2.69479	+	4.66751i	−0.166168	+	0.287811i	0.770902	+	0.636954i	$0.219806\pi$
$264$		0			0
$265$		−	0.925638i		−	0.0568615i
$266$	−1.42524	+	38.0117i	−0.0873869	+	2.33065i
$267$		0			0
$268$	1.11097	+	2.30787i	0.0678634	+	0.140975i
$269$	−13.0916	+	7.55845i	−0.798210	+	0.460847i	−0.842845	−	0.538156i	$-0.819121\pi$
$269$	−13.0916	+	7.55845i	−0.798210	+	0.460847i	0.0446347	+	0.999003i	$0.485788\pi$
$270$		0			0
$271$	1.44092	+	0.831915i	0.0875296	+	0.0505352i	0.543126	−	0.839651i	$-0.317241\pi$
$271$	1.44092	+	0.831915i	0.0875296	+	0.0505352i	−0.455596	+	0.890186i	$0.650574\pi$
$272$	3.95042	−	4.95054i	0.239530	−	0.300170i
$273$		0			0
$274$	−6.12311	−	3.84806i	−0.369911	−	0.232470i
$275$	−7.77921	+	13.4740i	−0.469104	+	0.812512i
$276$		0			0
$277$	13.9650	−	8.06272i	0.839078	−	0.484442i	−0.0178730	−	0.999840i	$-0.505689\pi$
$277$	13.9650	−	8.06272i	0.839078	−	0.484442i	0.856951	+	0.515399i	$0.172356\pi$
$278$	6.78606	+	4.26469i	0.407001	+	0.255779i
$279$		0			0
$280$	−1.99350	+	0.869204i	−0.119134	+	0.0519449i
$281$		−	23.9271i		−	1.42737i	−0.700466	−	0.713686i	$-0.747024\pi$
$281$		−	23.9271i		−	1.42737i	0.700466	−	0.713686i	$-0.252976\pi$
$282$		0			0
$283$	7.67135	+	4.42906i	0.456015	+	0.263280i	0.710367	−	0.703831i	$-0.248529\pi$
$283$	7.67135	+	4.42906i	0.456015	+	0.263280i	−0.254352	+	0.967112i	$0.581862\pi$
$284$	−0.170747	+	2.27376i	−0.0101320	+	0.134923i
$285$		0			0
$286$	9.59843	+	12.8471i	0.567567	+	0.759666i
$287$	37.9416			2.23962
$288$		0			0
$289$	7.24645	−	12.5512i	0.426262	−	0.738307i
$290$	−0.0442366	+	1.17981i	−0.00259766	+	0.0692808i
$291$		0			0
$292$	−1.34426	−	0.916804i	−0.0786668	−	0.0536519i
$293$	−12.1437	−	21.0335i	−0.709441	−	1.22879i	−0.965065	−	0.262012i	$-0.915614\pi$
$293$	−12.1437	−	21.0335i	−0.709441	−	1.22879i	0.255623	−	0.966776i	$-0.417719\pi$
$294$		0			0
$295$	−0.836721	−	1.44924i	−0.0487158	−	0.0843782i
$296$	1.91114	−	2.58825i	0.111083	−	0.150439i
$297$		0			0
$298$	−6.77870	+	10.7864i	−0.392680	+	0.624839i
$299$	−24.2805	+	3.80729i	−1.40418	+	0.220182i
$300$		0			0
$301$	−10.4060	+	18.0238i	−0.599794	+	1.03887i
$302$	−7.72270	+	4.08080i	−0.444391	+	0.234824i
$303$		0			0
$304$	20.1080	−	25.1987i	1.15327	−	1.44524i
$305$	−0.577627	+	0.333493i	−0.0330748	+	0.0190957i
$306$		0			0
$307$	32.3797			1.84801			0.924004	−	0.382383i	$-0.124897\pi$
$307$	32.3797			1.84801			0.924004	+	0.382383i	$0.124897\pi$
$308$	−17.3427	−	11.8280i	−0.988191	−	0.673961i
$309$		0			0
$310$	−2.77417	+	1.46592i	−0.157562	+	0.0832585i
$311$	−16.7587			−0.950298			−0.475149	−	0.879905i	$-0.657606\pi$
$311$	−16.7587			−0.950298			−0.475149	+	0.879905i	$0.657606\pi$
$312$		0			0
$313$	−12.2059			−0.689921			−0.344960	−	0.938617i	$-0.612108\pi$
$313$	−12.2059			−0.689921			−0.344960	+	0.938617i	$0.612108\pi$
$314$	12.5734	−	6.64401i	0.709560	−	0.374943i
$315$		0			0
$316$	17.4341	−	25.5627i	0.980747	−	1.43801i
$317$	−30.0086			−1.68545			−0.842725	−	0.538345i	$-0.819050\pi$
$317$	−30.0086			−1.68545			−0.842725	+	0.538345i	$0.819050\pi$
$318$		0			0
$319$	−9.86948	+	5.69815i	−0.552585	+	0.319035i
$320$	1.79674	+	0.410970i	0.100441	+	0.0229739i
$321$		0			0
$322$	28.4445	−	15.0305i	1.58515	−	0.837619i
$323$	−6.38070	+	11.0517i	−0.355031	+	0.614932i
$324$		0			0
$325$	11.2034	+	13.8788i	0.621453	+	0.769855i
$326$	−15.5022	+	24.6674i	−0.858588	+	1.36620i
$327$		0			0
$328$	−25.8684	−	19.1010i	−1.42834	−	1.05468i
$329$	14.8602	+	25.7386i	0.819269	+	1.41902i
$330$		0			0
$331$	2.48978	+	4.31242i	0.136851	+	0.237032i	0.926303	−	0.376780i	$-0.122969\pi$
$331$	2.48978	+	4.31242i	0.136851	+	0.237032i	−0.789452	+	0.613812i	$0.789635\pi$
$332$	−14.3414	+	21.0280i	−0.787086	+	1.15406i
$333$		0			0
$334$	0.488172	−	13.0198i	0.0267116	−	0.712410i
$335$	0.147529	−	0.255528i	0.00806038	−	0.0139610i
$336$		0			0
$337$	−14.3686			−0.782707			−0.391353	−	0.920240i	$-0.627993\pi$
$337$	−14.3686			−0.782707			−0.391353	+	0.920240i	$0.627993\pi$
$338$	17.7009	−	4.96754i	0.962805	−	0.270198i
$339$		0			0
$340$	−0.727552	−	0.0546354i	−0.0394570	−	0.00296302i
$341$	−26.2291	−	15.1434i	−1.42039	−	0.820060i
$342$		0			0
$343$		−	9.55273i		−	0.515799i
$344$	16.1685	−	7.04980i	0.871748	−	0.380100i
$345$		0			0
$346$	2.28981	+	1.43903i	0.123101	+	0.0773626i
$347$	5.35002	−	3.08884i	0.287204	−	0.165817i	−0.349476	−	0.936945i	$-0.613640\pi$
$347$	5.35002	−	3.08884i	0.287204	−	0.165817i	0.636680	+	0.771128i	$0.280307\pi$
$348$		0			0
$349$	−12.8064	+	22.1813i	−0.685510	+	1.18734i	0.287766	+	0.957701i	$0.407088\pi$
$349$	−12.8064	+	22.1813i	−0.685510	+	1.18734i	−0.973276	+	0.229638i	$0.926246\pi$
$350$	−19.7682	−	12.4233i	−1.05665	−	0.664053i
$351$		0			0
$352$	5.86958	+	16.7951i	0.312850	+	0.895182i
$353$	−6.78643	−	3.91815i	−0.361205	−	0.208542i	0.308404	−	0.951255i	$-0.400205\pi$
$353$	−6.78643	−	3.91815i	−0.361205	−	0.208542i	−0.669609	+	0.742713i	$0.733538\pi$
$354$		0			0
$355$	0.227475	−	0.131333i	0.0120731	−	0.00697043i
$356$	20.9556	−	10.0877i	1.11064	−	0.534646i
$357$		0			0
$358$	0.724699	−	19.3280i	0.0383015	−	1.02152i
$359$			27.9638i			1.47587i	0.674870	+	0.737937i	$0.264200\pi$
$359$			27.9638i			1.47587i	−0.674870	+	0.737937i	$0.735800\pi$
$360$		0			0
$361$	−22.9783	+	39.7997i	−1.20939	+	2.09472i
$362$	2.43956	−	1.28910i	0.128220	−	0.0677538i
$363$		0			0
$364$	−19.8052	+	13.6714i	−1.03808	+	0.716578i
$365$			0.187440i			0.00981105i
$366$		0			0
$367$	−11.9144	+	20.6364i	−0.621929	+	1.07721i	0.367198	+	0.930143i	$0.380317\pi$
$367$	−11.9144	+	20.6364i	−0.621929	+	1.07721i	−0.989126	+	0.147069i	$0.953016\pi$
$368$	−26.9601	−	4.07210i	−1.40539	−	0.212273i
$369$		0			0
$370$	−0.370370	−	0.0138869i	−0.0192546	−	0.000721945i
$371$	6.70406	+	11.6118i	0.348057	+	0.602853i
$372$		0			0
$373$	−10.4787	+	6.04988i	−0.542567	+	0.313251i	−0.746118	−	0.665813i	$-0.768085\pi$
$373$	−10.4787	+	6.04988i	−0.542567	+	0.313251i	0.203552	+	0.979064i	$0.434751\pi$
$374$	−3.29030	−	6.22671i	−0.170137	−	0.321975i
$375$		0			0
$376$	2.82603	−	25.0296i	0.145741	−	1.29080i
$377$	2.02390	+	12.9071i	0.104236	+	0.664752i
$378$		0			0
$379$	7.11999	−	12.3322i	0.365729	−	0.633462i	−0.623164	−	0.782092i	$-0.714153\pi$
$379$	7.11999	−	12.3322i	0.365729	−	0.633462i	0.988893	+	0.148630i	$0.0474862\pi$
$380$	−3.70331	−	0.278100i	−0.189976	−	0.0142662i
$381$		0			0
$382$	−12.3823	+	19.7030i	−0.633535	+	1.00809i
$383$	−20.4692	+	11.8179i	−1.04593	+	0.603866i	−0.921506	−	0.388363i	$-0.873041\pi$
$383$	−20.4692	+	11.8179i	−1.04593	+	0.603866i	−0.124421	+	0.992230i	$0.539707\pi$
$384$		0			0
$385$			2.41822i			0.123244i
$386$	−0.314763	+	8.39487i	−0.0160210	+	0.427288i
$387$		0			0
$388$	−1.20174	+	16.0030i	−0.0610092	+	0.812427i
$389$			16.4521i			0.834152i	0.908872	+	0.417076i	$0.136945\pi$
$389$			16.4521i			0.834152i	−0.908872	+	0.417076i	$0.863055\pi$
$390$		0			0
$391$	10.7931			0.545831
$392$	6.95158	−	9.41450i	0.351108	−	0.475504i
$393$		0			0
$394$	−11.1544	−	0.418232i	−0.561952	−	0.0210702i
$395$	−3.56440			−0.179344
$396$		0			0
$397$	−2.08064	−	3.60378i	−0.104424	−	0.180868i	0.809078	−	0.587701i	$-0.199967\pi$
$397$	−2.08064	−	3.60378i	−0.104424	−	0.180868i	−0.913503	+	0.406832i	$0.866633\pi$
$398$	12.3238	−	19.6098i	0.617735	−	0.982950i
$399$		0			0
$400$	7.22356	+	18.4221i	0.361178	+	0.921103i
$401$	9.32403	+	5.38323i	0.465620	+	0.268826i	0.714404	−	0.699733i	$-0.246698\pi$
$401$	9.32403	+	5.38323i	0.465620	+	0.268826i	−0.248785	+	0.968559i	$0.580031\pi$
$402$		0			0
$403$	−27.0170	+	21.8091i	−1.34581	+	1.08639i
$404$	−20.7637	+	9.99531i	−1.03303	+	0.497285i
$405$		0			0
$406$	−7.99000	−	15.1206i	−0.396537	−	0.750425i
$407$	−1.78878	−	3.09826i	−0.0886666	−	0.153575i
$408$		0			0
$409$	26.0298	−	15.0283i	1.28709	−	0.743103i	0.308958	−	0.951076i	$-0.400020\pi$
$409$	26.0298	−	15.0283i	1.28709	−	0.743103i	0.978135	+	0.207972i	$0.0666864\pi$
$410$	−0.138793	+	3.70168i	−0.00685450	+	0.182813i
$411$		0			0
$412$	0.642709	−	0.942368i	0.0316640	−	0.0464272i
$413$	20.9927	+	12.1201i	1.03298	+	0.596392i
$414$		0			0
$415$	2.93209			0.143930
$416$	20.3857	+	0.649453i	0.999493	+	0.0318421i
$417$		0			0
$418$	−16.7479	−	31.6945i	−0.819167	−	1.55023i
$419$	−13.7149	−	7.91829i	−0.670016	−	0.386834i	0.126067	−	0.992022i	$-0.459765\pi$
$419$	−13.7149	−	7.91829i	−0.670016	−	0.386834i	−0.796083	+	0.605188i	$0.793098\pi$
$420$		0			0
$421$	23.2913			1.13515			0.567574	−	0.823322i	$-0.307882\pi$
$421$	23.2913			1.13515			0.567574	+	0.823322i	$0.307882\pi$
$422$	0.769722	−	20.5289i	0.0374695	−	0.999329i
$423$		0			0
$424$	1.27494	−	11.2919i	0.0619165	−	0.548382i
$425$	−3.91643	−	6.78346i	−0.189975	−	0.329046i
$426$		0			0
$427$	4.83073	−	8.36708i	0.233776	−	0.404911i
$428$	−2.66320	+	1.28202i	−0.128730	+	0.0619688i
$429$		0			0
$430$	−1.72038	−	1.08117i	−0.0829641	−	0.0521387i
$431$	−6.94958	−	4.01234i	−0.334750	−	0.193268i	0.323198	−	0.946331i	$-0.395242\pi$
$431$	−6.94958	−	4.01234i	−0.334750	−	0.193268i	−0.657948	+	0.753064i	$0.728575\pi$
$432$		0			0
$433$	−15.2699	−	26.4483i	−0.733825	−	1.27102i	−0.955237	−	0.295842i	$-0.904400\pi$
$433$	−15.2699	−	26.4483i	−0.733825	−	1.27102i	0.221412	−	0.975180i	$-0.428934\pi$
$434$	24.1838	−	38.4816i	1.16086	−	1.84718i
$435$		0			0
$436$	1.69668	−	2.48774i	0.0812561	−	0.119141i
$437$	54.9379			2.62804
$438$		0			0
$439$	−5.57038	+	9.64818i	−0.265860	+	0.460482i	−0.967788	−	0.251765i	$-0.918989\pi$
$439$	−5.57038	+	9.64818i	−0.265860	+	0.460482i	0.701929	+	0.712247i	$0.252322\pi$
$440$	1.21741	−	1.64873i	0.0580376	−	0.0786001i
$441$		0			0
$442$	−8.01750	+	0.950977i	−0.381354	+	0.0452333i
$443$		−	1.48868i		−	0.0707295i	−0.999374	−	0.0353647i	$-0.988741\pi$
$443$		−	1.48868i		−	0.0707295i	0.999374	−	0.0353647i	$-0.0112593\pi$
$444$		0			0
$445$	−2.32021	−	1.33957i	−0.109988	−	0.0635018i
$446$	1.22583	−	32.6935i	0.0580449	−	1.54808i
$447$		0			0
$448$	−25.5159	+	7.85768i	−1.20551	+	0.371241i
$449$	−23.5031	+	13.5695i	−1.10918	+	0.640384i	−0.938616	−	0.344963i	$-0.887891\pi$
$449$	−23.5031	+	13.5695i	−1.10918	+	0.640384i	−0.170561	+	0.985347i	$0.554558\pi$
$450$		0			0
$451$	−30.9657	+	17.8781i	−1.45812	+	0.841845i
$452$	−0.152283	−	0.0114357i	−0.00716279	−	0.000537889i
$453$		0			0
$454$	−15.3748	+	24.4647i	−0.721576	+	1.14818i
$455$	2.58661	+	0.997483i	0.121262	+	0.0467627i
$456$		0			0
$457$	21.3528	+	12.3281i	0.998843	+	0.576682i	0.907906	−	0.419174i	$-0.137680\pi$
$457$	21.3528	+	12.3281i	0.998843	+	0.576682i	0.0909374	+	0.995857i	$0.471014\pi$
$458$	−4.43331	−	8.38979i	−0.207155	−	0.392029i
$459$		0			0
$460$	1.36237	+	2.83010i	0.0635206	+	0.131954i
$461$	−3.67379	−	6.36319i	−0.171105	−	0.296363i	0.767701	−	0.640808i	$-0.221401\pi$
$461$	−3.67379	−	6.36319i	−0.171105	−	0.296363i	−0.938807	+	0.344445i	$0.888067\pi$
$462$		0			0
$463$		−	13.6798i		−	0.635756i	−0.948132	−	0.317878i	$-0.897030\pi$
$463$		−	13.6798i		−	0.635756i	0.948132	−	0.317878i	$-0.102970\pi$
$464$	−2.16467	+	14.3316i	−0.100492	+	0.665328i
$465$		0			0
$466$	−6.17975	−	11.6948i	−0.286271	−	0.541753i
$467$			29.4078i			1.36083i	0.732826	+	0.680416i	$0.238201\pi$
$467$			29.4078i			1.36083i	−0.732826	+	0.680416i	$0.761799\pi$
$468$		0			0
$469$			4.27400i			0.197355i
$470$	−2.56549	+	1.35565i	−0.118337	+	0.0625313i
$471$		0			0
$472$	−8.21105	−	18.8318i	−0.377944	−	0.866805i
$473$		−	19.6133i		−	0.901820i
$474$		0			0
$475$	−19.9350	−	34.5285i	−0.914682	−	1.58428i
$476$	9.52256	−	4.58401i	0.436466	−	0.210108i
$477$		0			0
$478$	10.9966	−	5.81081i	0.502975	−	0.265780i
$479$	3.66802	+	2.11773i	0.167596	+	0.0967616i	0.581452	−	0.813581i	$-0.302485\pi$
$479$	3.66802	+	2.11773i	0.167596	+	0.0967616i	−0.413856	+	0.910342i	$0.635818\pi$
$480$		0			0
$481$	−4.05185	+	0.635349i	−0.184749	+	0.0289694i
$482$	23.0197	+	14.4667i	1.04852	+	0.658941i
$483$		0			0
$484$	−2.21081	−	0.166020i	−0.100491	−	0.00754638i
$485$	1.60100	−	0.924338i	0.0726977	−	0.0419720i
$486$		0			0
$487$	−34.5579	+	19.9520i	−1.56597	+	0.904112i	−0.569337	+	0.822104i	$0.692800\pi$
$487$	−34.5579	+	19.9520i	−1.56597	+	0.904112i	−0.996632	+	0.0820078i	$0.973867\pi$
$488$	−7.50582	+	3.27269i	−0.339773	+	0.148148i
$489$		0			0
$490$	−1.34718	−	0.0505122i	−0.0608595	−	0.00228191i
$491$	−23.5208	−	13.5798i	−1.06148	−	0.612846i	−0.135639	−	0.990758i	$-0.543309\pi$
$491$	−23.5208	−	13.5798i	−1.06148	−	0.612846i	−0.925841	+	0.377913i	$0.876642\pi$
$492$		0			0
$493$		−	5.73745i		−	0.258402i
$494$	−40.8098	+	4.84056i	−1.83612	+	0.217787i
$495$		0			0
$496$	−35.8612	+	14.0617i	−1.61022	+	0.631390i
$497$	−1.90239	+	3.29504i	−0.0853340	+	0.147803i
$498$		0			0
$499$	−12.6803			−0.567649			−0.283825	−	0.958876i	$-0.591603\pi$
$499$	−12.6803			−0.567649			−0.283825	+	0.958876i	$0.591603\pi$
$500$	2.58251	−	3.78658i	0.115493	−	0.169341i
$501$		0			0
$502$	−25.3735	−	15.9460i	−1.13248	−	0.711704i
$503$	3.49953	+	6.06136i	0.156036	+	0.270263i	0.933436	−	0.358744i	$-0.116795\pi$
$503$	3.49953	+	6.06136i	0.156036	+	0.270263i	−0.777400	+	0.629007i	$0.783462\pi$
$504$		0			0
$505$	2.29896	+	1.32731i	0.102302	+	0.0590643i
$506$	−16.1323	+	25.6701i	−0.717170	+	1.14117i
$507$		0			0
$508$	5.41326	+	11.2452i	0.240175	+	0.498925i
$509$	−7.65922	+	13.2662i	−0.339489	+	0.588012i	−0.984337	−	0.176299i	$-0.943587\pi$
$509$	−7.65922	+	13.2662i	−0.339489	+	0.588012i	0.644848	+	0.764311i	$0.276921\pi$
$510$		0			0
$511$	−1.35756	−	2.35136i	−0.0600549	−	0.104018i
$512$	21.3524	+	7.48820i	0.943654	+	0.330935i
$513$		0			0
$514$	7.16193	+	0.268534i	0.315899	+	0.0118445i
$515$	−0.131401			−0.00579024
$516$		0			0
$517$	−24.2561	−	14.0042i	−1.06678	−	0.615906i
$518$	4.74672	−	2.50825i	0.208559	−	0.110206i
$519$		0			0
$520$	−1.26137	−	1.98226i	−0.0553148	−	0.0869278i
$521$	−30.3448			−1.32943			−0.664715	−	0.747097i	$-0.731447\pi$
$521$	−30.3448			−1.32943			−0.664715	+	0.747097i	$0.731447\pi$
$522$		0			0
$523$	−19.0473	−	10.9970i	−0.832879	−	0.480863i	0.0219582	−	0.999759i	$-0.493010\pi$
$523$	−19.0473	−	10.9970i	−0.832879	−	0.480863i	−0.854837	+	0.518896i	$0.826343\pi$
$524$	−26.0591	−	17.7727i	−1.13840	−	0.776405i
$525$		0			0
$526$	7.61666	+	0.285584i	0.332102	+	0.0124521i
$527$	13.2050	−	7.62392i	0.575219	−	0.332103i
$528$		0			0
$529$	−11.7322	−	20.3208i	−0.510097	−	0.883514i
$530$	−1.15740	+	0.611589i	−0.0502742	+	0.0265657i
$531$		0			0
$532$	48.4707	−	23.3331i	2.10147	−	1.01162i
$533$	6.35003	+	40.4964i	0.275050	+	1.75409i
$534$		0			0
$535$	0.294870	+	0.170243i	0.0127483	+	0.00736026i
$536$	2.15167	−	2.91399i	0.0929379	−	0.125865i
$537$		0			0
$538$	18.1008	+	11.3755i	0.780383	+	0.490431i
$539$	−6.50651	−	11.2696i	−0.280255	−	0.485416i
$540$		0			0
$541$	−1.38788			−0.0596694			−0.0298347	−	0.999555i	$-0.509498\pi$
$541$	−1.38788			−0.0596694			−0.0298347	+	0.999555i	$0.509498\pi$
$542$	0.0881634	−	2.35136i	0.00378694	−	0.100999i
$543$		0			0
$544$	−8.80017	−	1.66860i	−0.377304	−	0.0715407i
$545$	−0.346884			−0.0148589
$546$		0			0
$547$			2.42593i			0.103725i	0.998654	+	0.0518626i	$0.0165158\pi$
$547$			2.42593i			0.103725i	−0.998654	+	0.0518626i	$0.983484\pi$
$548$	−0.765871	+	10.1987i	−0.0327164	+	0.435667i
$549$		0			0
$550$	21.9875	+	0.824413i	0.937549	+	0.0351531i
$551$		−	29.2042i		−	1.24414i
$552$		0			0
$553$	44.7140	−	25.8156i	1.90143	−	1.09779i
$554$	−19.3084	−	12.1344i	−0.820337	−	0.515540i
$555$		0			0
$556$	0.848792	−	11.3029i	0.0359968	−	0.479351i
$557$	15.3441	−	26.5767i	0.650148	−	1.12609i	−0.332938	−	0.942949i	$-0.608040\pi$
$557$	15.3441	−	26.5767i	0.650148	−	1.12609i	0.983087	−	0.183141i	$-0.0586266\pi$
$558$		0			0
$559$	−20.9790	−	8.09022i	−0.887318	−	0.342180i
$560$	2.40398	+	1.91832i	0.101587	+	0.0810640i
$561$		0			0
$562$	−29.9180	+	15.8092i	−1.26201	+	0.666869i
$563$	34.3455	−	19.8294i	1.44749	−	0.835709i	0.449159	−	0.893452i	$-0.351724\pi$
$563$	34.3455	−	19.8294i	1.44749	−	0.835709i	0.998331	+	0.0577430i	$0.0183904\pi$
$564$		0			0
$565$	0.00879592	+	0.0152350i	0.000370047	+	0.000640941i
$566$	0.469376	−	12.5185i	0.0197293	−	0.526191i
$567$		0			0
$568$	2.95587	−	1.28882i	0.124026	−	0.0540776i
$569$	4.59173	−	7.95311i	0.192495	−	0.333412i	−0.753581	−	0.657355i	$-0.771675\pi$
$569$	4.59173	−	7.95311i	0.192495	−	0.333412i	0.946077	+	0.323943i	$0.105009\pi$
$570$		0			0
$571$			12.4846i			0.522463i	0.965276	+	0.261232i	$0.0841286\pi$
$571$			12.4846i			0.522463i	−0.965276	+	0.261232i	$0.915871\pi$
$572$	9.72189	−	20.4900i	0.406493	−	0.856732i
$573$		0			0
$574$	−25.0688	−	47.4413i	−1.04635	−	1.98016i
$575$	−16.8603	+	29.2029i	−0.703123	+	1.21784i
$576$		0			0
$577$		−	29.8603i		−	1.24310i	−0.783375	−	0.621550i	$-0.786503\pi$
$577$		−	29.8603i		−	1.24310i	0.783375	−	0.621550i	$-0.213497\pi$
$578$	−20.4817	−	0.767953i	−0.851925	−	0.0319426i
$579$		0			0
$580$	1.50444	−	0.724213i	0.0624684	−	0.0300713i
$581$	−36.7819	+	21.2360i	−1.52597	+	0.881019i
$582$		0			0
$583$	−10.9429	−	6.31790i	−0.453210	−	0.261661i
$584$	−0.258173	+	2.28658i	−0.0106833	+	0.0946195i
$585$		0			0
$586$	−18.2762	+	29.0815i	−0.754984	+	1.20134i
$587$	18.2451	−	31.6014i	0.753054	−	1.30433i	−0.193282	−	0.981143i	$-0.561913\pi$
$587$	18.2451	−	31.6014i	0.753054	−	1.30433i	0.946336	−	0.323185i	$-0.104754\pi$
$588$		0			0
$589$	67.2148	−	38.8065i	2.76954	−	1.59899i
$590$	−1.25926	+	2.00376i	−0.0518431	+	0.0824936i
$591$		0			0
$592$	−4.49902	−	0.679540i	−0.184909	−	0.0279289i
$593$			26.4261i			1.08519i	0.839995	+	0.542594i	$0.182558\pi$
$593$			26.4261i			1.08519i	−0.839995	+	0.542594i	$0.817442\pi$
$594$		0			0
$595$	−1.05434	−	0.608724i	−0.0432238	−	0.0249553i
$596$	17.9659	+	1.34915i	0.735912	+	0.0552633i
$597$		0			0
$598$	20.8032	+	27.8443i	0.850706	+	1.13864i
$599$	−7.29146			−0.297921			−0.148960	−	0.988843i	$-0.547593\pi$
$599$	−7.29146			−0.297921			−0.148960	+	0.988843i	$0.547593\pi$
$600$		0			0
$601$	0.117332	−	0.203224i	0.00478606	−	0.00828970i	−0.863622	−	0.504139i	$-0.831810\pi$
$601$	0.117332	−	0.203224i	0.00478606	−	0.00828970i	0.868409	+	0.495849i	$0.165143\pi$
$602$	29.4120	+	1.10279i	1.19875	+	0.0449466i
$603$		0			0
$604$	10.2051	+	6.96003i	0.415240	+	0.283200i
$605$	0.127697	+	0.221178i	0.00519163	+	0.00899216i
$606$		0			0
$607$	7.42041	+	12.8525i	0.301185	+	0.521668i	0.976405	−	0.215949i	$-0.0692845\pi$
$607$	7.42041	+	12.8525i	0.301185	+	0.521668i	−0.675220	+	0.737617i	$0.735951\pi$
$608$	−44.7937	−	8.49334i	−1.81663	−	0.344450i
$609$		0			0
$610$	0.798643	+	0.501906i	0.0323361	+	0.0203216i
$611$	−24.9847	+	20.1685i	−1.01077	+	0.815932i
$612$		0			0
$613$	0.235744	−	0.408321i	0.00952163	−	0.0164919i	−0.861225	−	0.508223i	$-0.830302\pi$
$613$	0.235744	−	0.408321i	0.00952163	−	0.0164919i	0.870747	+	0.491731i	$0.163636\pi$
$614$	−21.3940	−	40.4869i	−0.863390	−	1.63392i
$615$		0			0
$616$	−3.33076	+	29.4999i	−0.134200	+	1.18859i
$617$	28.2097	−	16.2869i	1.13568	−	0.655685i	0.190323	−	0.981721i	$-0.439046\pi$
$617$	28.2097	−	16.2869i	1.13568	−	0.655685i	0.945357	+	0.326036i	$0.105713\pi$
$618$		0			0
$619$	9.28369			0.373143			0.186571	−	0.982441i	$-0.440262\pi$
$619$	9.28369			0.373143			0.186571	+	0.982441i	$0.440262\pi$
$620$	3.66590	+	2.50020i	0.147226	+	0.100410i
$621$		0			0
$622$	11.0728	+	20.9547i	0.443979	+	0.840207i
$623$	38.8081			1.55481
$624$		0			0
$625$	24.2066			0.968264
$626$	8.06473	+	15.2621i	0.322331	+	0.609995i
$627$		0			0
$628$	−16.6151	−	11.3317i	−0.663014	−	0.452185i
$629$	1.80112			0.0718153
$630$		0			0
$631$	3.76004	−	2.17086i	0.149685	−	0.0864205i	−0.423287	−	0.905996i	$-0.639124\pi$
$631$	3.76004	−	2.17086i	0.149685	−	0.0864205i	0.572972	+	0.819575i	$0.305790\pi$
$632$	−43.4822	−	4.90946i	−1.72963	−	0.195288i
$633$		0			0
$634$	19.8273	+	37.5221i	0.787443	+	1.49019i
$635$	0.718843	−	1.24507i	0.0285264	−	0.0494092i
$636$		0			0
$637$	−14.7382	+	2.31102i	−0.583949	+	0.0915659i
$638$	13.6458	+	8.57571i	0.540243	+	0.339516i
$639$		0			0
$640$	−0.673276	−	2.51814i	−0.0266136	−	0.0995384i
$641$	16.3563	+	28.3299i	0.646035	+	1.11897i	0.984061	+	0.177829i	$0.0569073\pi$
$641$	16.3563	+	28.3299i	0.646035	+	1.11897i	−0.338026	+	0.941137i	$0.609759\pi$
$642$		0			0
$643$	3.40535	+	5.89823i	0.134294	+	0.232604i	0.925327	−	0.379169i	$-0.123790\pi$
$643$	3.40535	+	5.89823i	0.134294	+	0.232604i	−0.791034	+	0.611773i	$0.790457\pi$
$644$	−37.5877	−	25.6354i	−1.48116	−	1.01018i
$645$		0			0
$646$	18.0347	+	0.676204i	0.709564	+	0.0266049i
$647$	12.5284	−	21.6999i	0.492543	−	0.853110i	−0.507420	−	0.861699i	$-0.669401\pi$
$647$	12.5284	−	21.6999i	0.492543	−	0.853110i	0.999963	+	0.00858905i	$0.00273401\pi$
$648$		0			0
$649$	−22.8440			−0.896705
$650$	9.95137	−	23.1785i	0.390325	−	0.909135i
$651$		0			0
$652$	41.0863	+	3.08537i	1.60906	+	0.120832i
$653$	41.6685	+	24.0573i	1.63062	+	0.941436i	0.983903	+	0.178702i	$0.0571898\pi$
$653$	41.6685	+	24.0573i	1.63062	+	0.941436i	0.646712	+	0.762734i	$0.276144\pi$
$654$		0			0
$655$			3.63362i			0.141977i
$656$	−6.79169	+	44.9657i	−0.265171	+	1.75562i
$657$		0			0
$658$	22.3646	−	35.5869i	0.871862	−	1.38732i
$659$	−18.7319	+	10.8148i	−0.729690	+	0.421287i	−0.818309	−	0.574779i	$-0.805088\pi$
$659$	−18.7319	+	10.8148i	−0.729690	+	0.421287i	0.0886189	+	0.996066i	$0.471755\pi$
$660$		0			0
$661$	−10.4554	+	18.1092i	−0.406666	+	0.704366i	−0.994514	−	0.104605i	$-0.966642\pi$
$661$	−10.4554	+	18.1092i	−0.406666	+	0.704366i	0.587848	+	0.808972i	$0.299975\pi$
$662$	3.74711	−	5.96247i	0.145636	−	0.231738i
$663$		0			0
$664$	35.7686	+	4.03854i	1.38809	+	0.156726i
$665$	−5.36670	−	3.09847i	−0.208112	−	0.120153i
$666$		0			0
$667$	−21.3907	+	12.3499i	−0.828250	+	0.478190i
$668$	−16.6022	+	7.99204i	−0.642358	+	0.309221i
$669$		0			0
$670$	−0.416983	−	0.0156346i	−0.0161094	−	0.000604018i
$671$			9.10496i			0.351493i
$672$		0			0
$673$	−8.64625	+	14.9757i	−0.333288	+	0.577272i	−0.983155	−	0.182776i	$-0.941492\pi$
$673$	−8.64625	+	14.9757i	−0.333288	+	0.577272i	0.649866	+	0.760049i	$0.274825\pi$
$674$	9.49363	+	17.9662i	0.365681	+	0.692031i
$675$		0			0
$676$	−17.9067	−	18.8507i	−0.688719	−	0.725028i
$677$		−	5.72652i		−	0.220088i	−0.993927	−	0.110044i	$-0.964901\pi$
$677$		−	5.72652i		−	0.220088i	0.993927	−	0.110044i	$-0.0350992\pi$
$678$		0			0
$679$	−13.3893	+	23.1909i	−0.513833	+	0.889986i
$680$	0.412394	+	0.945814i	0.0158146	+	0.0362703i
$681$		0			0
$682$	−1.60484	+	42.8019i	−0.0614526	+	1.63897i
$683$	17.8037	+	30.8369i	0.681238	+	1.17994i	0.974603	+	0.223939i	$0.0718917\pi$
$683$	17.8037	+	30.8369i	0.681238	+	1.17994i	−0.293365	+	0.956001i	$0.594775\pi$
$684$		0			0
$685$	1.02032	−	0.589081i	0.0389844	−	0.0225076i
$686$	−11.9445	+	6.31169i	−0.456044	+	0.240981i
$687$		0			0
$688$	−19.4978	−	15.5588i	−0.743347	−	0.593175i
$689$	−11.2717	+	9.09887i	−0.429416	+	0.346639i
$690$		0			0
$691$	14.8409	−	25.7052i	0.564575	−	0.977873i	−0.432514	−	0.901627i	$-0.642373\pi$
$691$	14.8409	−	25.7052i	0.564575	−	0.977873i	0.997089	−	0.0762454i	$-0.0242933\pi$
$692$	0.286406	−	3.81392i	0.0108875	−	0.144984i
$693$		0			0
$694$	−7.39709	−	4.64869i	−0.280790	−	0.176462i
$695$	−1.13079	+	0.652861i	−0.0428933	+	0.0247644i
$696$		0			0
$697$		−	18.0014i		−	0.681851i
$698$	36.1965	+	1.35718i	1.37006	+	0.0513699i
$699$		0			0
$700$	−2.47258	+	32.9260i	−0.0934546	+	1.24449i
$701$		−	23.7944i		−	0.898704i	−0.893355	−	0.449352i	$-0.851655\pi$
$701$		−	23.7944i		−	0.898704i	0.893355	−	0.449352i	$-0.148345\pi$
$702$		0			0
$703$	9.16787			0.345773
$704$	17.1221	−	18.4361i	0.645313	−	0.694836i
$705$		0			0
$706$	−0.415232	+	11.0744i	−0.0156274	+	0.416791i
$707$	−38.4528			−1.44617
$708$		0			0
$709$	−4.26282	−	7.38342i	−0.160093	−	0.277290i	0.774809	−	0.632196i	$-0.217846\pi$
$709$	−4.26282	−	7.38342i	−0.160093	−	0.277290i	−0.934902	+	0.354906i	$0.884513\pi$
$710$	−0.314514	−	0.197656i	−0.0118035	−	0.00741790i
$711$		0			0
$712$	−26.4592	−	19.5372i	−0.991600	−	0.732189i
$713$	−56.8477	−	32.8211i	−2.12896	−	1.22916i
$714$		0			0
$715$	−2.58105	+	0.404721i	−0.0965259	+	0.0151357i
$716$	−24.6462	+	11.8643i	−0.921072	+	0.443390i
$717$		0			0
$718$	34.9654	−	18.4763i	1.30490	−	0.689529i
$719$	6.37676	+	11.0449i	0.237813	+	0.411904i	0.960086	−	0.279703i	$-0.0902361\pi$
$719$	6.37676	+	11.0449i	0.237813	+	0.411904i	−0.722273	+	0.691608i	$0.756903\pi$
$720$		0			0
$721$	1.64838	−	0.951692i	0.0613888	−	0.0354429i
$722$	64.9469	+	2.43516i	2.41707	+	0.0906274i
$723$		0			0
$724$	−3.22374	−	2.19864i	−0.119809	−	0.0817117i
$725$	15.5238	+	8.96268i	0.576540	+	0.332866i
$726$		0			0
$727$	28.1255			1.04312			0.521559	−	0.853216i	$-0.325351\pi$
$727$	28.1255			1.04312			0.521559	+	0.853216i	$0.325351\pi$
$728$	30.1802	+	15.7310i	1.11855	+	0.583030i
$729$		0			0
$730$	0.234371	−	0.123845i	0.00867446	−	0.00458373i
$731$	8.55138	+	4.93714i	0.316284	+	0.182607i
$732$		0			0
$733$	49.4380			1.82604			0.913018	−	0.407920i	$-0.133746\pi$
$733$	49.4380			1.82604			0.913018	+	0.407920i	$0.133746\pi$
$734$	33.6755	+	1.26265i	1.24298	+	0.0466053i
$735$		0			0
$736$	12.7215	+	36.4009i	0.468919	+	1.34176i
$737$	−2.01391	−	3.48819i	−0.0741833	−	0.128489i
$738$		0			0
$739$	−14.0277	+	24.2967i	−0.516018	+	0.893769i	0.483809	+	0.875173i	$0.339253\pi$
$739$	−14.0277	+	24.2967i	−0.516018	+	0.893769i	−0.999827	+	0.0185956i	$0.994081\pi$
$740$	0.227347	+	0.472278i	0.00835745	+	0.0173613i
$741$		0			0
$742$	10.0896	−	16.0548i	0.370401	−	0.589389i
$743$	2.05615	+	1.18712i	0.0754328	+	0.0435512i	0.537242	−	0.843428i	$-0.319466\pi$
$743$	2.05615	+	1.18712i	0.0754328	+	0.0435512i	−0.461809	+	0.886979i	$0.652800\pi$
$744$		0			0
$745$	−1.03772	−	1.79738i	−0.0380191	−	0.0658509i
$746$	14.4881	+	9.10506i	0.530449	+	0.333360i
$747$		0			0
$748$	−5.61178	+	8.22823i	−0.205187	+	0.300854i
$749$	−4.93204			−0.180213
$750$		0			0
$751$	2.48319	−	4.30101i	0.0906130	−	0.156946i	−0.817156	−	0.576416i	$-0.804451\pi$
$751$	2.48319	−	4.30101i	0.0906130	−	0.156946i	0.907769	+	0.419470i	$0.137784\pi$
$752$	−33.1637	+	13.0040i	−1.20935	+	0.474206i
$753$		0			0
$754$	14.8016	−	11.0587i	0.539042	−	0.402733i
$755$		−	1.42297i		−	0.0517873i
$756$		0			0
$757$	3.10991	+	1.79551i	0.113032	+	0.0652589i	0.555450	−	0.831550i	$-0.312546\pi$
$757$	3.10991	+	1.79551i	0.113032	+	0.0652589i	−0.442418	+	0.896809i	$0.645879\pi$
$758$	−20.1242	−	0.754551i	−0.730945	−	0.0274065i
$759$		0			0
$760$	2.09912	+	4.81429i	0.0761432	+	0.174632i
$761$	30.1976	−	17.4346i	1.09466	−	0.632004i	0.159849	−	0.987142i	$-0.448899\pi$
$761$	30.1976	−	17.4346i	1.09466	−	0.632004i	0.934814	+	0.355138i	$0.115566\pi$
$762$		0			0
$763$	4.35153	−	2.51236i	0.157536	−	0.0909534i
$764$	32.8175	+	2.46442i	1.18729	+	0.0891597i
$765$		0			0
$766$	28.3013	+	17.7859i	1.02257	+	0.642631i
$767$	−9.42285	+	24.4347i	−0.340239	+	0.882286i
$768$		0			0
$769$	−3.53352	−	2.04008i	−0.127422	−	0.0735670i	0.434934	−	0.900462i	$-0.356772\pi$
$769$	−3.53352	−	2.04008i	−0.127422	−	0.0735670i	−0.562356	+	0.826895i	$0.690105\pi$
$770$	3.02369	−	1.59777i	0.108966	−	0.0575795i
$771$		0			0
$772$	10.7047	−	5.15310i	0.385272	−	0.185464i
$773$	−7.40633	−	12.8281i	−0.266387	−	0.461396i	0.701539	−	0.712631i	$-0.252497\pi$
$773$	−7.40633	−	12.8281i	−0.266387	−	0.461396i	−0.967926	+	0.251235i	$0.919163\pi$
$774$		0			0
$775$			47.6384i			1.71122i
$776$	20.8038	−	9.07087i	0.746812	−	0.325625i
$777$		0			0
$778$	20.5713	−	10.8702i	0.737517	−	0.389716i
$779$		−	91.6287i		−	3.28294i
$780$		0			0
$781$		−	3.58563i		−	0.128304i
$782$	−7.13123	−	13.4955i	−0.255012	−	0.482597i
$783$		0			0
$784$	−16.3647	−	2.47176i	−0.584455	−	0.0882770i
$785$			2.31676i			0.0826888i
$786$		0			0
$787$	18.0243	+	31.2189i	0.642496	+	1.11283i	0.984874	+	0.173273i	$0.0554342\pi$
$787$	18.0243	+	31.2189i	0.642496	+	1.11283i	−0.342378	+	0.939562i	$0.611232\pi$
$788$	6.84702	+	14.2236i	0.243915	+	0.506695i
$789$		0			0
$790$	2.35507	+	4.45685i	0.0837897	+	0.158568i
$791$	−0.220683	−	0.127411i	−0.00784658	−	0.00453022i
$792$		0			0
$793$	9.73898	+	3.75568i	0.345841	+	0.133368i
$794$	−3.13136	+	4.98268i	−0.111128	+	0.176829i
$795$		0			0
$796$	−32.6623	−	2.45277i	−1.15768	−	0.0869361i
$797$	−11.3573	+	6.55713i	−0.402295	+	0.232265i	−0.687474	−	0.726209i	$-0.741280\pi$
$797$	−11.3573	+	6.55713i	−0.402295	+	0.232265i	0.285179	+	0.958474i	$0.407947\pi$
$798$		0			0
$799$	12.2117	−	7.05042i	0.432019	−	0.249426i
$800$	18.2618	−	21.2040i	0.645652	−	0.749676i
$801$		0			0
$802$	0.570496	−	15.2154i	0.0201449	−	0.537274i
$803$	2.21592	+	1.27936i	0.0781982	+	0.0451477i
$804$		0			0
$805$			5.24113i			0.184726i
$806$	45.1203	+	19.3718i	1.58930	+	0.682343i
$807$		0			0
$808$	26.2169	+	19.3583i	0.922308	+	0.681024i
$809$	−7.48145	+	12.9583i	−0.263034	+	0.455588i	−0.967047	−	0.254599i	$-0.918056\pi$
$809$	−7.48145	+	12.9583i	−0.263034	+	0.455588i	0.704013	+	0.710187i	$0.251390\pi$
$810$		0			0
$811$	−20.9684			−0.736299			−0.368150	−	0.929767i	$-0.620009\pi$
$811$	−20.9684			−0.736299			−0.368150	+	0.929767i	$0.620009\pi$
$812$	−13.6274	+	19.9811i	−0.478227	+	0.701198i
$813$		0			0
$814$	−2.69211	+	4.28374i	−0.0943585	+	0.150145i
$815$	−2.37316	−	4.11043i	−0.0831281	−	0.143982i
$816$		0			0
$817$	43.5273	+	25.1305i	1.52283	+	0.879206i
$818$	−35.9896	−	22.6176i	−1.25835	−	0.790807i
$819$		0			0
$820$	4.72020	−	2.27223i	0.164837	−	0.0793498i
$821$	12.5793	−	21.7880i	0.439021	−	0.760407i	−0.558593	−	0.829442i	$-0.688659\pi$
$821$	12.5793	−	21.7880i	0.439021	−	0.760407i	0.997614	+	0.0690347i	$0.0219919\pi$
$822$		0			0
$823$	−4.64806	−	8.05068i	−0.162021	−	0.280629i	0.773572	−	0.633708i	$-0.218468\pi$
$823$	−4.64806	−	8.05068i	−0.162021	−	0.280629i	−0.935593	+	0.353079i	$0.885135\pi$
$824$	−1.60297	−	0.180987i	−0.0558421	−	0.00630499i
$825$		0			0
$826$	1.28445	−	34.2568i	0.0446917	−	1.19195i
$827$	22.5483			0.784080			0.392040	−	0.919948i	$-0.371769\pi$
$827$	22.5483			0.784080			0.392040	+	0.919948i	$0.371769\pi$
$828$		0			0
$829$	4.07023	+	2.34995i	0.141365	+	0.0816171i	0.569014	−	0.822328i	$-0.307325\pi$
$829$	4.07023	+	2.34995i	0.141365	+	0.0816171i	−0.427649	+	0.903945i	$0.640658\pi$
$830$	−1.93729	−	3.66622i	−0.0672444	−	0.127256i
$831$		0			0
$832$	−12.6572	−	25.9190i	−0.438810	−	0.898580i
$833$	6.55139			0.226992
$834$		0			0
$835$	1.83820	+	1.06129i	0.0636136	+	0.0367273i
$836$	−28.5645	+	41.8825i	−0.987923	+	1.44854i
$837$		0			0
$838$	−0.839152	+	22.3806i	−0.0289880	+	0.773124i
$839$	38.2396	−	22.0776i	1.32018	−	0.762205i	0.336421	−	0.941712i	$-0.390784\pi$
$839$	38.2396	−	22.0776i	1.32018	−	0.762205i	0.983757	+	0.179507i	$0.0574503\pi$
$840$		0			0
$841$	−7.93498	−	13.7438i	−0.273620	−	0.473924i
$842$	−15.3890	−	29.1229i	−0.530341	−	1.00364i
$843$		0			0
$844$	−26.1774	+	12.6014i	−0.901064	+	0.433758i
$845$	−0.631747	+	2.92772i	−0.0217328	+	0.100717i
$846$		0			0
$847$	−3.20382	−	1.84973i	−0.110085	−	0.0635574i
$848$	−14.9615	+	5.86663i	−0.513780	+	0.201461i
$849$		0			0
$850$	−5.89423	+	9.37901i	−0.202170	+	0.321697i
$851$	−3.87692	−	6.71502i	−0.132899	−	0.230188i
$852$		0			0
$853$	−2.24836			−0.0769825			−0.0384912	−	0.999259i	$-0.512255\pi$
$853$	−2.24836			−0.0769825			−0.0384912	+	0.999259i	$0.512255\pi$
$854$	−13.6538	−	0.511944i	−0.467223	−	0.0175184i
$855$		0			0
$856$	3.36264	+	2.48295i	0.114933	+	0.0848654i
$857$	−23.3922			−0.799062			−0.399531	−	0.916720i	$-0.630827\pi$
$857$	−23.3922			−0.799062			−0.399531	+	0.916720i	$0.630827\pi$
$858$		0			0
$859$		−	23.3254i		−	0.795854i	−0.917417	−	0.397927i	$-0.869730\pi$
$859$		−	23.3254i		−	0.795854i	0.917417	−	0.397927i	$-0.130270\pi$
$860$	−0.215183	+	2.86548i	−0.00733768	+	0.0977121i
$861$		0			0
$862$	−0.425214	+	11.3406i	−0.0144828	+	0.386264i
$863$		−	51.3259i		−	1.74715i	−0.486687	−	0.873577i	$-0.661795\pi$
$863$		−	51.3259i		−	1.74715i	0.486687	−	0.873577i	$-0.338205\pi$
$864$		0			0
$865$	−0.381560	+	0.220294i	−0.0129734	+	0.00749021i
$866$	−22.9812	+	36.5681i	−0.780933	+	1.24263i
$867$		0			0
$868$	−64.0954	−	4.81323i	−2.17554	−	0.163372i
$869$	−24.3286	+	42.1384i	−0.825292	+	1.42945i
$870$		0			0
$871$	−4.56180	+	0.715311i	−0.154571	+	0.0242374i
$872$	−4.23165	−	0.477785i	−0.143302	−	0.0161798i
$873$		0			0
$874$	−36.2987	−	68.6933i	−1.22782	−	2.32358i
$875$	6.62344	−	3.82405i	0.223913	−	0.129276i
$876$		0			0
$877$	−5.20754	−	9.01972i	−0.175846	−	0.304574i	0.764608	−	0.644496i	$-0.222933\pi$
$877$	−5.20754	−	9.01972i	−0.175846	−	0.304574i	−0.940454	+	0.339922i	$0.889599\pi$
$878$	15.7443	+	0.590329i	0.531346	+	0.0199226i
$879$		0			0
$880$	−2.86590	−	0.432871i	−0.0966096	−	0.0145921i
$881$	20.8219	−	36.0645i	0.701507	−	1.21505i	−0.266431	−	0.963854i	$-0.585844\pi$
$881$	20.8219	−	36.0645i	0.701507	−	1.21505i	0.967938	−	0.251191i	$-0.0808222\pi$
$882$		0			0
$883$		−	20.2048i		−	0.679945i	−0.940435	−	0.339972i	$-0.889582\pi$
$883$		−	20.2048i		−	0.679945i	0.940435	−	0.339972i	$-0.110418\pi$
$884$	6.48641	+	9.39658i	0.218162	+	0.316041i
$885$		0			0
$886$	−1.86142	+	0.983604i	−0.0625356	+	0.0330448i
$887$	−12.6955	+	21.9892i	−0.426273	+	0.738326i	−0.996538	−	0.0831341i	$-0.973507\pi$
$887$	−12.6955	+	21.9892i	−0.426273	+	0.738326i	0.570265	+	0.821460i	$0.306840\pi$
$888$		0			0
$889$			20.8253i			0.698457i
$890$	−0.141963	+	3.78622i	−0.00475861	+	0.126914i
$891$		0			0
$892$	−41.6892	+	20.0685i	−1.39586	+	0.671945i
$893$	62.1587	−	35.8873i	2.08006	−	1.20092i
$894$		0			0
$895$	2.72884	+	1.57550i	0.0912150	+	0.0526630i
$896$	26.6840	+	26.7128i	0.891450	+	0.892414i
$897$		0			0
$898$	32.4960	+	20.4221i	1.08440	+	0.681493i
$899$	−17.4472	+	30.2194i	−0.581896	+	1.00787i
$900$		0			0
$901$	5.50920	−	3.18074i	0.183538	−	0.105966i
$902$	42.8140	+	26.9065i	1.42555	+	0.895887i
$903$		0			0
$904$	0.0863176	+	0.197967i	0.00287088	+	0.00658429i
$905$			0.449510i			0.0149422i
$906$		0			0
$907$	−19.8890	−	11.4829i	−0.660405	−	0.381285i	0.132027	−	0.991246i	$-0.457852\pi$
$907$	−19.8890	−	11.4829i	−0.660405	−	0.381285i	−0.792431	+	0.609961i	$0.791185\pi$
$908$	40.7486	+	3.06001i	1.35229	+	0.101550i
$909$		0			0
$910$	−0.461794	−	3.89330i	−0.0153083	−	0.129062i
$911$	−25.4657			−0.843717			−0.421859	−	0.906662i	$-0.638622\pi$
$911$	−25.4657			−0.843717			−0.421859	+	0.906662i	$0.638622\pi$
$912$		0			0
$913$	20.0128	−	34.6632i	0.662328	−	1.14719i
$914$	1.30648	−	34.8445i	0.0432147	−	1.15255i
$915$		0			0
$916$	−7.56124	+	11.0866i	−0.249831	+	0.366313i
$917$	−26.3170	−	45.5823i	−0.869063	−	1.50526i
$918$		0			0
$919$	−10.3095	−	17.8566i	−0.340079	−	0.589034i	0.644368	−	0.764715i	$-0.277120\pi$
$919$	−10.3095	−	17.8566i	−0.340079	−	0.589034i	−0.984447	+	0.175682i	$0.943787\pi$
$920$	2.63855	−	3.57338i	0.0869905	−	0.117811i
$921$		0			0
$922$	−5.52905	+	8.79792i	−0.182090	+	0.289744i
$923$	−3.83531	−	1.47903i	−0.126241	−	0.0486827i
$924$		0			0
$925$	−2.81359	+	4.87329i	−0.0925104	+	0.160233i
$926$	−17.1050	+	9.03856i	−0.562105	+	0.297026i
$927$		0			0
$928$	19.3502	−	6.76254i	0.635201	−	0.221991i
$929$	13.2006	−	7.62136i	0.433097	−	0.250049i	−0.267568	−	0.963539i	$-0.586220\pi$
$929$	13.2006	−	7.62136i	0.433097	−	0.250049i	0.700665	+	0.713490i	$0.252887\pi$
$930$		0			0
$931$	33.3472			1.09291
$932$	−10.5399	+	15.4541i	−0.345246	+	0.506215i
$933$		0			0
$934$	36.7709	−	19.4304i	1.20318	−	0.635781i
$935$	1.14732			0.0375215
$936$		0			0
$937$	44.7527			1.46201			0.731004	−	0.682373i	$-0.239052\pi$
$937$	44.7527			1.46201			0.731004	+	0.682373i	$0.239052\pi$
$938$	5.34412	−	2.82392i	0.174492	−	0.0922043i
$939$		0			0
$940$	3.39014	+	2.31213i	0.110574	+	0.0754133i
$941$	20.4855			0.667807			0.333904	−	0.942607i	$-0.391634\pi$
$941$	20.4855			0.667807			0.333904	+	0.942607i	$0.391634\pi$
$942$		0			0
$943$	−67.1136	+	38.7481i	−2.18552	+	1.26181i
$944$	−18.1217	+	22.7095i	−0.589811	+	0.739131i
$945$		0			0
$946$	−24.5240	+	12.9589i	−0.797345	+	0.421330i
$947$	−17.4837	+	30.2826i	−0.568143	+	0.984052i	0.428607	+	0.903491i	$0.359004\pi$
$947$	−17.4837	+	30.2826i	−0.568143	+	0.984052i	−0.996750	+	0.0805608i	$0.974329\pi$
$948$		0			0
$949$	2.28249	−	1.84250i	0.0740927	−	0.0598102i
$950$	−30.0022	+	47.7400i	−0.973400	+	1.54889i
$951$		0			0
$952$	−12.0235	−	8.87806i	−0.389684	−	0.287739i
$953$	−16.0909	−	27.8703i	−0.521236	−	0.902808i	−0.999695	−	0.0246977i	$-0.992138\pi$
$953$	−16.0909	−	27.8703i	−0.521236	−	0.902808i	0.478459	−	0.878110i	$-0.341196\pi$
$954$		0			0
$955$	−1.89555	−	3.28319i	−0.0613385	−	0.106241i
$956$	−14.5314	−	9.91065i	−0.469980	−	0.320533i
$957$		0			0
$958$	0.224430	−	5.98564i	0.00725099	−	0.193387i
$959$	−8.53300	+	14.7796i	−0.275545	+	0.477258i
$960$		0			0
$961$	−61.7351			−1.99145
$962$	3.47157	+	4.64656i	0.111928	+	0.149811i
$963$		0			0
$964$	2.87928	−	38.3418i	0.0927352	−	1.23491i
$965$	−1.18523	−	0.684295i	−0.0381540	−	0.0220282i
$966$		0			0
$967$			20.7493i			0.667251i	0.942706	+	0.333626i	$0.108272\pi$
$967$			20.7493i			0.667251i	−0.942706	+	0.333626i	$0.891728\pi$
$968$	1.25314	+	2.87404i	0.0402774	+	0.0923752i
$969$		0			0
$970$	−2.21359	−	1.39113i	−0.0710740	−	0.0446664i
$971$	−16.3626	+	9.44693i	−0.525099	+	0.303166i	−0.739019	−	0.673685i	$-0.764710\pi$
$971$	−16.3626	+	9.44693i	−0.525099	+	0.303166i	0.213919	+	0.976851i	$0.431377\pi$
$972$		0			0
$973$	9.45687	−	16.3798i	0.303173	−	0.525112i
$974$	47.7807	+	30.0278i	1.53099	+	0.962152i
$975$		0			0
$976$	9.05136	+	7.22279i	0.289727	+	0.231196i
$977$	−31.6318	−	18.2627i	−1.01199	−	0.584274i	−0.100218	−	0.994966i	$-0.531954\pi$
$977$	−31.6318	−	18.2627i	−1.01199	−	0.584274i	−0.911774	+	0.410691i	$0.865287\pi$
$978$		0			0
$979$	−31.6729	+	18.2864i	−1.01227	+	0.584435i
$980$	0.826953	+	1.71786i	0.0264160	+	0.0548751i
$981$		0			0
$982$	−1.43913	+	38.3824i	−0.0459246	+	1.22483i
$983$			38.2418i			1.21972i	0.792508	+	0.609862i	$0.208775\pi$
$983$			38.2418i			1.21972i	−0.792508	+	0.609862i	$0.791225\pi$
$984$		0			0
$985$	0.909236	−	1.57484i	0.0289707	−	0.0501787i
$986$	−7.17399	+	3.79086i	−0.228466	+	0.120725i
$987$		0			0
$988$	33.0165	+	47.8295i	1.05039	+	1.52166i
$989$		−	42.5089i		−	1.35170i
$990$		0			0
$991$	16.1451	−	27.9641i	0.512866	−	0.888309i	−0.487023	−	0.873389i	$-0.661917\pi$
$991$	16.1451	−	27.9641i	0.512866	−	0.888309i	0.999889	−	0.0149201i	$-0.00474939\pi$
$992$	41.2768	+	35.5493i	1.31054	+	1.12869i
$993$		0			0
$994$	5.37700	+	0.201609i	0.170548	+	0.00639465i
$995$	1.88658	+	3.26766i	0.0598088	+	0.103592i
$996$		0			0
$997$	18.9701	−	10.9524i	0.600789	−	0.346866i	−0.168563	−	0.985691i	$-0.553913\pi$
$997$	18.9701	−	10.9524i	0.600789	−	0.346866i	0.769352	+	0.638825i	$0.220579\pi$
$998$	8.37816	+	15.8552i	0.265206	+	0.501888i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.dg.e.901.10		48
3.2	odd	2		312.2.bk.b.277.15	yes	48
8.5	even	2	inner	936.2.dg.e.901.2		48
12.11	even	2		1248.2.ca.b.433.18		48
13.10	even	6	inner	936.2.dg.e.829.2		48
24.5	odd	2		312.2.bk.b.277.23	yes	48
24.11	even	2		1248.2.ca.b.433.7		48
39.23	odd	6		312.2.bk.b.205.23	yes	48
104.101	even	6	inner	936.2.dg.e.829.10		48
156.23	even	6		1248.2.ca.b.49.7		48
312.101	odd	6		312.2.bk.b.205.15	✓	48
312.179	even	6		1248.2.ca.b.49.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.b.205.15	✓	48	312.101	odd	6
312.2.bk.b.205.23	yes	48	39.23	odd	6
312.2.bk.b.277.15	yes	48	3.2	odd	2
312.2.bk.b.277.23	yes	48	24.5	odd	2
936.2.dg.e.829.2		48	13.10	even	6	inner
936.2.dg.e.829.10		48	104.101	even	6	inner
936.2.dg.e.901.2		48	8.5	even	2	inner
936.2.dg.e.901.10		48	1.1	even	1	trivial
1248.2.ca.b.49.7		48	156.23	even	6
1248.2.ca.b.49.18		48	312.179	even	6
1248.2.ca.b.433.7		48	24.11	even	2
1248.2.ca.b.433.18		48	12.11	even	2

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.dg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.660721 - 1.25038i) q^{2} +(-1.12690 + 1.65230i) q^{4} +0.230393 q^{5} +(-2.89019 + 1.66865i) q^{7} +(2.81057 + 0.317334i) q^{8} +(-0.152225 - 0.288078i) q^{10} +(1.57254 - 2.72371i) q^{11} +(-2.26472 - 2.80553i) q^{13} +(3.99606 + 2.51132i) q^{14} +(-1.46021 - 3.72395i) q^{16} +(0.791692 + 1.37125i) q^{17} +(4.02979 + 6.97979i) q^{19} +(-0.259629 + 0.380679i) q^{20} +(-4.44468 - 0.166652i) q^{22} +(3.40824 - 5.90325i) q^{23} -4.94692 q^{25} +(-2.01163 + 4.68544i) q^{26} +(0.499822 - 6.65587i) q^{28} +(-3.13808 - 1.81177i) q^{29} -9.62991i q^{31} +(-3.69155 + 4.28631i) q^{32} +(1.19150 - 1.89593i) q^{34} +(-0.665879 + 0.384445i) q^{35} +(0.568757 - 0.985115i) q^{37} +(6.06482 - 9.65046i) q^{38} +(0.647535 + 0.0731116i) q^{40} +(-9.84578 - 5.68446i) q^{41} +(5.40070 - 3.11810i) q^{43} +(2.72832 + 5.66765i) q^{44} +(-9.63320 - 0.361194i) q^{46} -8.90552i q^{47} +(2.06880 - 3.58326i) q^{49} +(3.26853 + 6.18552i) q^{50} +(7.18770 - 0.580470i) q^{52} -4.01765i q^{53} +(0.362301 - 0.627524i) q^{55} +(-8.65260 + 3.77270i) q^{56} +(-0.192005 + 5.12086i) q^{58} +(-3.63171 - 6.29031i) q^{59} +(-2.50714 + 1.44750i) q^{61} +(-12.0410 + 6.36268i) q^{62} +(7.79860 + 1.78378i) q^{64} +(-0.521776 - 0.646375i) q^{65} +(0.640338 - 1.10910i) q^{67} +(-3.15788 - 0.237140i) q^{68} +(0.920663 + 0.578590i) q^{70} +(0.987337 - 0.570039i) q^{71} +0.813566i q^{73} +(-1.60756 - 0.0602748i) q^{74} +(-16.0739 - 1.20707i) q^{76} +10.4961i q^{77} -15.4710 q^{79} +(-0.336423 - 0.857971i) q^{80} +(-0.602419 + 16.0668i) q^{82} +12.7265 q^{83} +(0.182400 + 0.315926i) q^{85} +(-7.46716 - 4.69273i) q^{86} +(5.28405 - 7.15616i) q^{88} +(-10.0707 - 5.81429i) q^{89} +(11.2269 + 4.32949i) q^{91} +(5.91323 + 12.2838i) q^{92} +(-11.1353 + 5.88406i) q^{94} +(0.928434 + 1.60809i) q^{95} +(6.94900 - 4.01201i) q^{97} +(-5.84733 - 0.219244i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} - 12 q^{7} - 4 q^{10} + 36 q^{14} - 2 q^{16} - 12 q^{17} - 54 q^{20} - 14 q^{22} - 20 q^{23} + 48 q^{25} + 42 q^{26} + 6 q^{28} + 28 q^{38} - 8 q^{40} + 12 q^{41} - 30 q^{46} + 16 q^{49}+ \cdots - 24 q^{98}+O(q^{100}) \) 48 * q - 2 * q^4 - 12 * q^7 - 4 * q^10 + 36 * q^14 - 2 * q^16 - 12 * q^17 - 54 * q^20 - 14 * q^22 - 20 * q^23 + 48 * q^25 + 42 * q^26 + 6 * q^28 + 28 * q^38 - 8 * q^40 + 12 * q^41 - 30 * q^46 + 16 * q^49 + 84 * q^50 - 28 * q^52 - 68 * q^55 - 18 * q^56 - 24 * q^58 - 24 * q^62 - 68 * q^64 - 12 * q^65 - 4 * q^68 + 12 * q^71 - 54 * q^74 - 54 * q^76 - 192 * q^79 - 78 * q^80 - 6 * q^82 - 10 * q^88 + 48 * q^89 + 12 * q^92 + 54 * q^94 + 20 * q^95 + 144 * q^97 - 24 * q^98

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