LMFDB - Embedded newform 891.2.k.a.728.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(161,891)] 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("891.161"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.k (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			728.20
Character	$\chi$	$=$	891.728
Dual form			891.2.k.a.809.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.770011 - 2.36985i) q^{2} +(-3.40524 - 2.47406i) q^{4} +(1.34471 - 0.436923i) q^{5} +(1.83962 - 2.53202i) q^{7} +(-4.45339 + 3.23558i) q^{8} -3.52320i q^{10} +(2.44665 - 2.23917i) q^{11} +(5.12091 + 1.66389i) q^{13} +(-4.58399 - 6.30932i) q^{14} +(1.63730 + 5.03909i) q^{16} +(-0.663043 - 2.04064i) q^{17} +(1.17531 + 1.61768i) q^{19} +(-5.66005 - 1.83906i) q^{20} +(-3.42256 - 7.52239i) q^{22} +1.33110i q^{23} +(-2.42774 + 1.76385i) q^{25} +(7.88632 - 10.8546i) q^{26} +(-12.5287 + 4.07083i) q^{28} +(-0.830600 - 0.603467i) q^{29} +(-2.90732 + 8.94782i) q^{31} +2.19325 q^{32} -5.34656 q^{34} +(1.36746 - 4.20862i) q^{35} +(-5.64362 - 4.10033i) q^{37} +(4.73866 - 1.53968i) q^{38} +(-4.57483 + 6.29671i) q^{40} +(-2.59156 + 1.88288i) q^{41} +5.10831i q^{43} +(-13.8713 + 1.57178i) q^{44} +(3.15451 + 1.02496i) q^{46} +(-2.74412 - 3.77695i) q^{47} +(-0.863813 - 2.65854i) q^{49} +(2.31069 + 7.11156i) q^{50} +(-13.3214 - 18.3354i) q^{52} +(4.78123 + 1.55352i) q^{53} +(2.31170 - 4.08004i) q^{55} +17.2283i q^{56} +(-2.06970 + 1.50372i) q^{58} +(6.23944 - 8.58785i) q^{59} +(-2.79366 + 0.907714i) q^{61} +(18.9663 + 13.7799i) q^{62} +(-1.58577 + 4.88050i) q^{64} +7.61314 q^{65} +1.49151 q^{67} +(-2.79082 + 8.58927i) q^{68} +(-8.92084 - 6.48137i) q^{70} +(-10.6126 + 3.44824i) q^{71} +(-5.45572 + 7.50916i) q^{73} +(-14.0628 + 10.2172i) q^{74} -8.41637i q^{76} +(-1.16872 - 10.3142i) q^{77} +(10.0550 + 3.26708i) q^{79} +(4.40339 + 6.06075i) q^{80} +(2.46661 + 7.59144i) q^{82} +(2.10476 + 6.47780i) q^{83} +(-1.78320 - 2.45437i) q^{85} +(12.1059 + 3.93346i) q^{86} +(-3.65088 + 17.8882i) q^{88} -8.06536i q^{89} +(13.6335 - 9.90535i) q^{91} +(3.29322 - 4.53272i) q^{92} +(-11.0638 + 3.59485i) q^{94} +(2.28726 + 1.66179i) q^{95} +(-0.730812 + 2.24921i) q^{97} -6.96550 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) $ 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$

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 $

$2$	0.770011	−	2.36985i	0.544480	−	1.67574i	−0.177742	−	0.984077i	$-0.556879\pi$
$2$	0.770011	−	2.36985i	0.544480	−	1.67574i	0.722222	−	0.691661i	$-0.243121\pi$
$3$		0			0
$3$		0			0
$4$	−3.40524	−	2.47406i	−1.70262	−	1.23703i
$5$	1.34471	−	0.436923i	0.601374	−	0.195398i	0.00752061	−	0.999972i	$-0.497606\pi$
$5$	1.34471	−	0.436923i	0.601374	−	0.195398i	0.593853	+	0.804574i	$0.297606\pi$
$6$		0			0
$7$	1.83962	−	2.53202i	0.695312	−	0.957015i	−0.304677	−	0.952456i	$-0.598549\pi$
$7$	1.83962	−	2.53202i	0.695312	−	0.957015i	0.999990	−	0.00455947i	$-0.00145133\pi$
$8$	−4.45339	+	3.23558i	−1.57451	+	1.14395i
$9$		0			0
$10$		−	3.52320i		−	1.11413i
$11$	2.44665	−	2.23917i	0.737693	−	0.675136i
$11$	2.44665	−	2.23917i	0.737693	−	0.675136i
$12$		0			0
$13$	5.12091	+	1.66389i	1.42029	+	0.461479i	0.915693	−	0.401879i	$-0.131643\pi$
$13$	5.12091	+	1.66389i	1.42029	+	0.461479i	0.504593	+	0.863358i	$0.331643\pi$
$14$	−4.58399	−	6.30932i	−1.22512	−	1.68624i
$15$		0			0
$16$	1.63730	+	5.03909i	0.409325	+	1.25977i
$17$	−0.663043	−	2.04064i	−0.160812	−	0.494927i	0.837892	−	0.545836i	$-0.183788\pi$
$17$	−0.663043	−	2.04064i	−0.160812	−	0.494927i	−0.998703	+	0.0509094i	$0.983788\pi$
$18$		0			0
$19$	1.17531	+	1.61768i	0.269635	+	0.371121i	0.922266	−	0.386555i	$-0.126335\pi$
$19$	1.17531	+	1.61768i	0.269635	+	0.371121i	−0.652632	+	0.757675i	$0.726335\pi$
$20$	−5.66005	−	1.83906i	−1.26562	−	0.411226i
$21$		0			0
$22$	−3.42256	−	7.52239i	−0.729692	−	1.60378i
$23$			1.33110i			0.277554i	0.990324	+	0.138777i	$0.0443171\pi$
$23$			1.33110i			0.277554i	−0.990324	+	0.138777i	$0.955683\pi$
$24$		0			0
$25$	−2.42774	+	1.76385i	−0.485547	+	0.352771i
$26$	7.88632	−	10.8546i	1.54663	−	2.12876i
$27$		0			0
$28$	−12.5287	+	4.07083i	−2.36771	+	0.769315i
$29$	−0.830600	−	0.603467i	−0.154239	−	0.112061i	0.507989	−	0.861363i	$-0.330389\pi$
$29$	−0.830600	−	0.603467i	−0.154239	−	0.112061i	−0.662228	+	0.749302i	$0.730389\pi$
$30$		0			0
$31$	−2.90732	+	8.94782i	−0.522171	+	1.60708i	0.247673	+	0.968844i	$0.420334\pi$
$31$	−2.90732	+	8.94782i	−0.522171	+	1.60708i	−0.769844	+	0.638233i	$0.779666\pi$
$32$	2.19325			0.387716
$33$		0			0
$34$	−5.34656			−0.916927
$35$	1.36746	−	4.20862i	0.231143	−	0.711386i
$36$		0			0
$37$	−5.64362	−	4.10033i	−0.927805	−	0.674090i	0.0176490	−	0.999844i	$-0.494382\pi$
$37$	−5.64362	−	4.10033i	−0.927805	−	0.674090i	−0.945455	+	0.325754i	$0.894382\pi$
$38$	4.73866	−	1.53968i	0.768712	−	0.249770i
$39$		0			0
$40$	−4.57483	+	6.29671i	−0.723344	+	0.995597i
$41$	−2.59156	+	1.88288i	−0.404733	+	0.294056i	−0.771466	−	0.636270i	$-0.780476\pi$
$41$	−2.59156	+	1.88288i	−0.404733	+	0.294056i	0.366733	+	0.930326i	$0.380476\pi$
$42$		0			0
$43$			5.10831i			0.779010i	0.921024	+	0.389505i	$0.127354\pi$
$43$			5.10831i			0.779010i	−0.921024	+	0.389505i	$0.872646\pi$
$44$	−13.8713	+	1.57178i	−2.09117	+	0.236955i
$45$		0			0
$46$	3.15451	+	1.02496i	0.465107	+	0.151122i
$47$	−2.74412	−	3.77695i	−0.400271	−	0.550925i	0.560541	−	0.828127i	$-0.310593\pi$
$47$	−2.74412	−	3.77695i	−0.400271	−	0.550925i	−0.960812	+	0.277201i	$0.910593\pi$
$48$		0			0
$49$	−0.863813	−	2.65854i	−0.123402	−	0.379792i
$50$	2.31069	+	7.11156i	0.326780	+	1.00573i
$51$		0			0
$52$	−13.3214	−	18.3354i	−1.84735	−	2.54266i
$53$	4.78123	+	1.55352i	0.656752	+	0.213392i	0.618389	−	0.785872i	$-0.287786\pi$
$53$	4.78123	+	1.55352i	0.656752	+	0.213392i	0.0383632	+	0.999264i	$0.487786\pi$
$54$		0			0
$55$	2.31170	−	4.08004i	0.311709	−	0.550153i
$56$			17.2283i			2.30223i
$57$		0			0
$58$	−2.06970	+	1.50372i	−0.271765	+	0.197449i
$59$	6.23944	−	8.58785i	0.812306	−	1.11804i	−0.178658	−	0.983911i	$-0.557176\pi$
$59$	6.23944	−	8.58785i	0.812306	−	1.11804i	0.990964	−	0.134131i	$-0.0428245\pi$
$60$		0			0
$61$	−2.79366	+	0.907714i	−0.357691	+	0.116221i	−0.482350	−	0.875979i	$-0.660216\pi$
$61$	−2.79366	+	0.907714i	−0.357691	+	0.116221i	0.124658	+	0.992200i	$0.460216\pi$
$62$	18.9663	+	13.7799i	2.40873	+	1.75004i
$63$		0			0
$64$	−1.58577	+	4.88050i	−0.198221	+	0.610062i
$65$	7.61314			0.944294
$66$		0			0
$67$	1.49151			0.182217			0.0911087	−	0.995841i	$-0.470959\pi$
$67$	1.49151			0.182217			0.0911087	+	0.995841i	$0.470959\pi$
$68$	−2.79082	+	8.58927i	−0.338437	+	1.04160i
$69$		0			0
$70$	−8.92084	−	6.48137i	−1.06624	−	0.774672i
$71$	−10.6126	+	3.44824i	−1.25948	+	0.409231i	−0.861310	−	0.508080i	$-0.830356\pi$
$71$	−10.6126	+	3.44824i	−1.25948	+	0.409231i	−0.398173	+	0.917310i	$0.630356\pi$
$72$		0			0
$73$	−5.45572	+	7.50916i	−0.638544	+	0.878880i	−0.998537	−	0.0540747i	$-0.982779\pi$
$73$	−5.45572	+	7.50916i	−0.638544	+	0.878880i	0.359993	+	0.932955i	$0.382779\pi$
$74$	−14.0628	+	10.2172i	−1.63477	+	1.18773i
$75$		0			0
$76$		−	8.41637i		−	0.965424i
$77$	−1.16872	−	10.3142i	−0.133188	−	1.17541i
$78$		0			0
$79$	10.0550	+	3.26708i	1.13128	+	0.367575i	0.814062	−	0.580778i	$-0.197252\pi$
$79$	10.0550	+	3.26708i	1.13128	+	0.367575i	0.317217	+	0.948353i	$0.397252\pi$
$80$	4.40339	+	6.06075i	0.492314	+	0.677612i
$81$		0			0
$82$	2.46661	+	7.59144i	0.272391	+	0.838334i
$83$	2.10476	+	6.47780i	0.231028	+	0.711031i	0.997624	+	0.0689006i	$0.0219491\pi$
$83$	2.10476	+	6.47780i	0.231028	+	0.711031i	−0.766596	+	0.642130i	$0.778051\pi$
$84$		0			0
$85$	−1.78320	−	2.45437i	−0.193416	−	0.266214i
$86$	12.1059	+	3.93346i	1.30542	+	0.424156i
$87$		0			0
$88$	−3.65088	+	17.8882i	−0.389185	+	1.90689i
$89$		−	8.06536i		−	0.854927i	−0.904033	−	0.427463i	$-0.859407\pi$
$89$		−	8.06536i		−	0.854927i	0.904033	−	0.427463i	$-0.140593\pi$
$90$		0			0
$91$	13.6335	−	9.90535i	1.42918	−	1.03836i
$92$	3.29322	−	4.53272i	0.343342	−	0.472569i
$93$		0			0
$94$	−11.0638	+	3.59485i	−1.14115	+	0.370781i
$95$	2.28726	+	1.66179i	0.234668	+	0.170496i
$96$		0			0
$97$	−0.730812	+	2.24921i	−0.0742027	+	0.228372i	−0.981278	−	0.192595i	$-0.938309\pi$
$97$	−0.730812	+	2.24921i	−0.0742027	+	0.228372i	0.907076	+	0.420968i	$0.138309\pi$
$98$	−6.96550			−0.703622
$99$		0			0
$100$	12.6309			1.26309
$101$	4.10027	−	12.6193i	0.407992	−	1.25567i	−0.510380	−	0.859949i	$-0.670495\pi$
$101$	4.10027	−	12.6193i	0.407992	−	1.25567i	0.918371	−	0.395720i	$-0.129505\pi$
$102$		0			0
$103$	6.04880	+	4.39471i	0.596006	+	0.433024i	0.844459	−	0.535620i	$-0.179922\pi$
$103$	6.04880	+	4.39471i	0.596006	+	0.433024i	−0.248453	+	0.968644i	$0.579922\pi$
$104$	−28.1890	+	9.15917i	−2.76416	+	0.898131i
$105$		0			0
$106$	7.36320	−	10.1346i	0.715177	−	0.984357i
$107$	−0.791122	+	0.574784i	−0.0764807	+	0.0555664i	−0.625369	−	0.780329i	$-0.715051\pi$
$107$	−0.791122	+	0.574784i	−0.0764807	+	0.0555664i	0.548888	+	0.835896i	$0.315051\pi$
$108$		0			0
$109$			5.38041i			0.515350i	0.966232	+	0.257675i	$0.0829564\pi$
$109$			5.38041i			0.515350i	−0.966232	+	0.257675i	$0.917044\pi$
$110$	−7.88906	−	8.62005i	−0.752193	−	0.821890i
$111$		0			0
$112$	15.7711	+	5.12434i	1.49023	+	0.484205i
$113$	3.13244	+	4.31143i	0.294675	+	0.405585i	0.930526	−	0.366227i	$-0.119351\pi$
$113$	3.13244	+	4.31143i	0.294675	+	0.405585i	−0.635851	+	0.771812i	$0.719351\pi$
$114$		0			0
$115$	0.581589	+	1.78995i	0.0542335	+	0.166913i
$116$	1.33539	+	4.10990i	0.123988	+	0.381595i
$117$		0			0
$118$	−15.5475	−	21.3993i	−1.43126	−	1.96996i
$119$	−6.38669	−	2.07516i	−0.585467	−	0.190230i
$120$		0			0
$121$	0.972210	−	10.9570i	0.0883827	−	0.996087i
$122$			7.31950i			0.662677i
$123$		0			0
$124$	32.0376	−	23.2766i	2.87706	−	2.09030i
$125$	−6.64933	+	9.15201i	−0.594734	+	0.818581i
$126$		0			0
$127$	10.2499	−	3.33040i	0.909534	−	0.295526i	0.183368	−	0.983044i	$-0.441300\pi$
$127$	10.2499	−	3.33040i	0.909534	−	0.295526i	0.726167	+	0.687519i	$0.241300\pi$
$128$	13.8938	+	10.0944i	1.22805	+	0.892227i
$129$		0			0
$130$	5.86221	−	18.0420i	0.514150	−	1.58239i
$131$	17.1948			1.50231			0.751157	−	0.660123i	$-0.229496\pi$
$131$	17.1948			1.50231			0.751157	+	0.660123i	$0.229496\pi$
$132$		0			0
$133$	6.25813			0.542648
$134$	1.14848	−	3.53467i	0.0992138	−	0.305349i
$135$		0			0
$136$	9.55542	+	6.94242i	0.819371	+	0.595308i
$137$	−9.37436	+	3.04592i	−0.800906	+	0.260230i	−0.680741	−	0.732524i	$-0.738342\pi$
$137$	−9.37436	+	3.04592i	−0.800906	+	0.260230i	−0.120165	+	0.992754i	$0.538342\pi$
$138$		0			0
$139$	−1.29891	+	1.78780i	−0.110173	+	0.151639i	−0.860543	−	0.509379i	$-0.829875\pi$
$139$	−1.29891	+	1.78780i	−0.110173	+	0.151639i	0.750370	+	0.661018i	$0.229875\pi$
$140$	−15.0689	+	10.9482i	−1.27355	+	0.925291i
$141$		0			0
$142$			27.8054i			2.33338i
$143$	16.2548	−	7.39566i	1.35930	−	0.618456i
$144$		0			0
$145$	−1.38059	−	0.448580i	−0.114652	−	0.0372525i
$146$	13.5946	+	18.7114i	1.12510	+	1.54857i
$147$		0			0
$148$	9.07347	+	27.9253i	0.745834	+	2.29544i
$149$	−1.68766	−	5.19407i	−0.138258	−	0.425515i	0.857824	−	0.513943i	$-0.171816\pi$
$149$	−1.68766	−	5.19407i	−0.138258	−	0.425515i	−0.996083	+	0.0884279i	$0.971816\pi$
$150$		0			0
$151$	−0.304143	−	0.418617i	−0.0247508	−	0.0340666i	0.796462	−	0.604688i	$-0.206702\pi$
$151$	−0.304143	−	0.418617i	−0.0247508	−	0.0340666i	−0.821213	+	0.570622i	$0.806702\pi$
$152$	−10.4682	−	3.40134i	−0.849086	−	0.275885i
$153$		0			0
$154$	−25.3431	−	5.17237i	−2.04220	−	0.416801i
$155$			13.3025i			1.06848i
$156$		0			0
$157$	10.9121	−	7.92811i	0.870881	−	0.632732i	−0.0599424	−	0.998202i	$-0.519092\pi$
$157$	10.9121	−	7.92811i	0.870881	−	0.632732i	0.930823	+	0.365470i	$0.119092\pi$
$158$	15.4850	−	21.3132i	1.23192	−	1.69559i
$159$		0			0
$160$	2.94929	−	0.958283i	0.233162	−	0.0757589i
$161$	3.37038	+	2.44872i	0.265623	+	0.192986i
$162$		0			0
$163$	−5.94061	+	18.2833i	−0.465305	+	1.43206i	0.393295	+	0.919413i	$0.371335\pi$
$163$	−5.94061	+	18.2833i	−0.465305	+	1.43206i	−0.858599	+	0.512648i	$0.828665\pi$
$164$	13.4832			1.05286
$165$		0			0
$166$	16.9721			1.31729
$167$	−0.182183	+	0.560702i	−0.0140977	+	0.0433884i	−0.957858	−	0.287242i	$-0.907261\pi$
$167$	−0.182183	+	0.560702i	−0.0140977	+	0.0433884i	0.943760	+	0.330631i	$0.107261\pi$
$168$		0			0
$169$	12.9380	+	9.40001i	0.995231	+	0.723078i
$170$	−7.18958	+	2.33604i	−0.551416	+	0.179166i
$171$		0			0
$172$	12.6382	−	17.3950i	0.963657	−	1.32636i
$173$	2.94820	−	2.14199i	0.224148	−	0.162853i	−0.470044	−	0.882643i	$-0.655762\pi$
$173$	2.94820	−	2.14199i	0.224148	−	0.162853i	0.694192	+	0.719790i	$0.255762\pi$
$174$		0			0
$175$			9.39191i			0.709962i
$176$	15.2893	+	8.66270i	1.15247	+	0.652976i
$177$		0			0
$178$	−19.1137	−	6.21042i	−1.43263	−	0.465491i
$179$	−3.36258	−	4.62819i	−0.251331	−	0.345927i	0.664646	−	0.747159i	$-0.268582\pi$
$179$	−3.36258	−	4.62819i	−0.251331	−	0.345927i	−0.915977	+	0.401231i	$0.868582\pi$
$180$		0			0
$181$	−2.48530	−	7.64897i	−0.184731	−	0.568544i	0.815213	−	0.579162i	$-0.196620\pi$
$181$	−2.48530	−	7.64897i	−0.184731	−	0.568544i	−0.999944	+	0.0106182i	$0.996620\pi$
$182$	−12.9762	−	39.9367i	−0.961862	−	2.96031i
$183$		0			0
$184$	−4.30688	−	5.92791i	−0.317507	−	0.437011i
$185$	−9.38058	−	3.04793i	−0.689674	−	0.224089i
$186$		0			0
$187$	−6.19157	−	3.50806i	−0.452773	−	0.256535i
$188$			19.6506i			1.43316i
$189$		0			0
$190$	5.69941	−	4.14086i	0.413478	−	0.300410i
$191$	7.18658	−	9.89147i	0.520002	−	0.715722i	−0.465563	−	0.885015i	$-0.654148\pi$
$191$	7.18658	−	9.89147i	0.520002	−	0.715722i	0.985566	+	0.169293i	$0.0541483\pi$
$192$		0			0
$193$	−15.9375	+	5.17840i	−1.14721	+	0.372750i	−0.820090	−	0.572235i	$-0.806077\pi$
$193$	−15.9375	+	5.17840i	−1.14721	+	0.372750i	−0.327115	+	0.944984i	$0.606077\pi$
$194$	4.76755	+	3.46383i	0.342290	+	0.248689i
$195$		0			0
$196$	−3.63589	+	11.1901i	−0.259706	+	0.799294i
$197$	−6.63610			−0.472803			−0.236401	−	0.971656i	$-0.575968\pi$
$197$	−6.63610			−0.472803			−0.236401	+	0.971656i	$0.575968\pi$
$198$		0			0
$199$	−3.24799			−0.230244			−0.115122	−	0.993351i	$-0.536726\pi$
$199$	−3.24799			−0.230244			−0.115122	+	0.993351i	$0.536726\pi$
$200$	5.10457	−	15.7103i	0.360948	−	1.11088i
$201$		0			0
$202$	−26.7487	−	19.4340i	−1.88203	−	1.36737i
$203$	−3.05598	+	0.992949i	−0.214488	+	0.0696914i
$204$		0			0
$205$	−2.66222	+	3.66424i	−0.185938	+	0.255921i
$206$	15.0725	−	10.9508i	1.05015	−	0.762977i
$207$		0			0
$208$			28.5290i			1.97813i
$209$	6.49784	+	1.32617i	0.449465	+	0.0917329i
$210$		0			0
$211$	−7.59126	−	2.46655i	−0.522604	−	0.169804i	0.0358228	−	0.999358i	$-0.488595\pi$
$211$	−7.59126	−	2.46655i	−0.522604	−	0.169804i	−0.558427	+	0.829554i	$0.688595\pi$
$212$	−12.4378	−	17.1191i	−0.854230	−	1.17575i
$213$		0			0
$214$	0.752979	+	2.31743i	0.0514726	+	0.158416i
$215$	2.23194	+	6.86921i	0.152217	+	0.468476i
$216$		0			0
$217$	17.3077	+	23.8220i	1.17492	+	1.61715i
$218$	12.7508	+	4.14298i	0.863591	+	0.280598i
$219$		0			0
$220$	−17.9661	+	8.17428i	−1.21128	+	0.551110i
$221$		−	11.5531i		−	0.777149i
$222$		0			0
$223$	11.2464	−	8.17099i	0.753115	−	0.547170i	−0.143676	−	0.989625i	$-0.545892\pi$
$223$	11.2464	−	8.17099i	0.753115	−	0.547170i	0.896791	+	0.442455i	$0.145892\pi$
$224$	4.03476	−	5.55336i	0.269583	−	0.371050i
$225$		0			0
$226$	12.6295	−	4.10356i	0.840099	−	0.272965i
$227$	−16.8532	−	12.2446i	−1.11859	−	0.812702i	−0.134594	−	0.990901i	$-0.542973\pi$
$227$	−16.8532	−	12.2446i	−1.11859	−	0.812702i	−0.983995	+	0.178198i	$0.942973\pi$
$228$		0			0
$229$	4.57791	−	14.0893i	0.302517	−	0.931050i	−0.678076	−	0.734992i	$-0.737186\pi$
$229$	4.57791	−	14.0893i	0.302517	−	0.931050i	0.980592	−	0.196058i	$-0.0628141\pi$
$230$	4.68974			0.309232
$231$		0			0
$232$	5.65155			0.371042
$233$	5.72371	−	17.6158i	0.374972	−	1.15405i	−0.568525	−	0.822666i	$-0.692486\pi$
$233$	5.72371	−	17.6158i	0.374972	−	1.15405i	0.943497	−	0.331380i	$-0.107514\pi$
$234$		0			0
$235$	−5.34029	−	3.87995i	−0.348362	−	0.253100i
$236$	−42.4936	+	13.8070i	−2.76610	+	0.898760i
$237$		0			0
$238$	−9.83565	+	13.5376i	−0.637550	+	0.877513i
$239$	−19.1098	+	13.8841i	−1.23611	+	0.898086i	−0.997333	−	0.0729883i	$-0.976746\pi$
$239$	−19.1098	+	13.8841i	−1.23611	+	0.898086i	−0.238777	+	0.971074i	$0.576746\pi$
$240$		0			0
$241$		−	10.3796i		−	0.668607i	−0.942466	−	0.334303i	$-0.891499\pi$
$241$		−	10.3796i		−	0.668607i	0.942466	−	0.334303i	$-0.108501\pi$
$242$	−25.2177	−	10.7410i	−1.62106	−	0.690456i
$243$		0			0
$244$	11.7588	+	3.82067i	0.752781	+	0.244593i
$245$	−2.32316	−	3.19755i	−0.148421	−	0.204284i
$246$		0			0
$247$	3.32704	+	10.2396i	0.211694	+	0.651528i
$248$	−16.0039	−	49.2550i	−1.01625	−	3.12770i
$249$		0			0
$250$	16.5689	+	22.8051i	1.04791	+	1.44232i
$251$	−6.21725	−	2.02011i	−0.392429	−	0.127508i	0.106154	−	0.994350i	$-0.466146\pi$
$251$	−6.21725	−	2.02011i	−0.392429	−	0.127508i	−0.498584	+	0.866842i	$0.666146\pi$
$252$		0			0
$253$	2.98056	+	3.25674i	0.187386	+	0.204749i
$254$		−	26.8553i		−	1.68505i
$255$		0			0
$256$	26.3174	−	19.1207i	1.64484	−	1.19504i
$257$	−6.26782	+	8.62691i	−0.390976	+	0.538132i	−0.958451	−	0.285259i	$-0.907920\pi$
$257$	−6.26782	+	8.62691i	−0.390976	+	0.538132i	0.567475	+	0.823391i	$0.307920\pi$
$258$		0			0
$259$	−20.7643	+	6.74672i	−1.29023	+	0.419221i
$260$	−25.9246	−	18.8353i	−1.60778	−	1.16812i
$261$		0			0
$262$	13.2402	−	40.7491i	0.817981	−	2.51749i
$263$	−20.1385			−1.24179			−0.620897	−	0.783892i	$-0.713232\pi$
$263$	−20.1385			−1.24179			−0.620897	+	0.783892i	$0.713232\pi$
$264$		0			0
$265$	7.10814			0.436650
$266$	4.81883	−	14.8308i	0.295461	−	0.909337i
$267$		0			0
$268$	−5.07897	−	3.69009i	−0.310247	−	0.225408i
$269$	9.24045	−	3.00240i	0.563400	−	0.183060i	−0.0134505	−	0.999910i	$-0.504282\pi$
$269$	9.24045	−	3.00240i	0.563400	−	0.183060i	0.576850	+	0.816850i	$0.304282\pi$
$270$		0			0
$271$	−13.7884	+	18.9781i	−0.837584	+	1.15284i	0.148880	+	0.988855i	$0.452433\pi$
$271$	−13.7884	+	18.9781i	−0.837584	+	1.15284i	−0.986464	+	0.163980i	$0.947567\pi$
$272$	9.19735	−	6.68227i	0.557671	−	0.405172i
$273$		0			0
$274$			24.5612i			1.48380i
$275$	−1.99025	+	9.75166i	−0.120017	+	0.588047i
$276$		0			0
$277$	−16.5873	−	5.38954i	−0.996634	−	0.323826i	−0.235114	−	0.971968i	$-0.575546\pi$
$277$	−16.5873	−	5.38954i	−0.996634	−	0.323826i	−0.761520	+	0.648142i	$0.775546\pi$
$278$	3.23665	+	4.45486i	0.194121	+	0.267185i
$279$		0			0
$280$	7.52746	+	23.1671i	0.449852	+	1.38450i
$281$	7.08550	+	21.8069i	0.422685	+	1.30089i	0.905193	+	0.425000i	$0.139726\pi$
$281$	7.08550	+	21.8069i	0.422685	+	1.30089i	−0.482508	+	0.875892i	$0.660274\pi$
$282$		0			0
$283$	12.7186	+	17.5056i	0.756041	+	1.04060i	0.997533	+	0.0701981i	$0.0223631\pi$
$283$	12.7186	+	17.5056i	0.756041	+	1.04060i	−0.241492	+	0.970403i	$0.577637\pi$
$284$	44.6696	+	14.5140i	2.65065	+	0.861250i
$285$		0			0
$286$	−5.01022	−	44.2162i	−0.296261	−	2.61456i
$287$			10.0257i			0.591796i
$288$		0			0
$289$	10.0287	−	7.28629i	0.589925	−	0.428605i
$290$	−2.12614	+	2.92637i	−0.124851	+	0.171843i
$291$		0			0
$292$	37.1561	−	12.0728i	2.17440	−	0.706505i
$293$	−15.7384	−	11.4347i	−0.919450	−	0.668020i	0.0239370	−	0.999713i	$-0.492380\pi$
$293$	−15.7384	−	11.4347i	−0.919450	−	0.668020i	−0.943387	+	0.331694i	$0.892380\pi$
$294$		0			0
$295$	4.63801	−	14.2743i	0.270036	−	0.831084i
$296$	38.4002			2.23196
$297$		0			0
$298$	−13.6087			−0.788331
$299$	−2.21480	+	6.81645i	−0.128085	+	0.394205i
$300$		0			0
$301$	12.9344	+	9.39736i	0.745524	+	0.541655i
$302$	−1.22625	+	0.398434i	−0.0705630	+	0.0229273i
$303$		0			0
$304$	−6.22728	+	8.57112i	−0.357159	+	0.491587i
$305$	−3.36006	+	2.44123i	−0.192397	+	0.139784i
$306$		0			0
$307$			2.08212i			0.118833i	0.998233	+	0.0594164i	$0.0189240\pi$
$307$			2.08212i			0.118833i	−0.998233	+	0.0594164i	$0.981076\pi$
$308$	−21.5382	+	38.0139i	−1.22725	+	2.16604i
$309$		0			0
$310$	31.5250	+	10.2431i	1.79050	+	0.581769i
$311$	7.69423	+	10.5902i	0.436300	+	0.600515i	0.969385	−	0.245546i	$-0.0789674\pi$
$311$	7.69423	+	10.5902i	0.436300	+	0.600515i	−0.533085	+	0.846062i	$0.678967\pi$
$312$		0			0
$313$	0.926030	+	2.85003i	0.0523423	+	0.161093i	0.973811	−	0.227360i	$-0.0730095\pi$
$313$	0.926030	+	2.85003i	0.0523423	+	0.161093i	−0.921468	+	0.388453i	$0.873009\pi$
$314$	−10.3860	−	31.9648i	−0.586116	−	1.80388i
$315$		0			0
$316$	−26.1569	−	36.0019i	−1.47144	−	2.02526i
$317$	30.3708	+	9.86806i	1.70579	+	0.554245i	0.989624	−	0.143683i	$-0.0458946\pi$
$317$	30.3708	+	9.86806i	1.70579	+	0.554245i	0.716168	+	0.697928i	$0.245895\pi$
$318$		0			0
$319$	−3.38346	+	0.383385i	−0.189437	+	0.0214655i
$320$			7.25573i			0.405607i
$321$		0			0
$322$	8.39834	−	6.10175i	0.468021	−	0.340037i
$323$	2.52181	−	3.47097i	0.140317	−	0.193130i
$324$		0			0
$325$	−15.3671	+	4.99306i	−0.852412	+	0.276965i
$326$	38.7544	+	28.1567i	2.14641	+	1.55946i
$327$		0			0
$328$	5.44902	−	16.7704i	0.300872	−	0.925988i
$329$	−14.6115			−0.805557
$330$		0			0
$331$	26.3584			1.44879			0.724395	−	0.689385i	$-0.242119\pi$
$331$	26.3584			1.44879			0.724395	+	0.689385i	$0.242119\pi$
$332$	8.85919	−	27.2658i	0.486211	−	1.49640i
$333$		0			0
$334$	1.18850	+	0.863494i	0.0650317	+	0.0472483i
$335$	2.00566	−	0.651677i	0.109581	−	0.0356049i
$336$		0			0
$337$	−2.46455	+	3.39217i	−0.134253	+	0.184783i	−0.870850	−	0.491548i	$-0.836431\pi$
$337$	−2.46455	+	3.39217i	−0.134253	+	0.184783i	0.736598	+	0.676331i	$0.236431\pi$
$338$	32.2390	−	23.4230i	1.75357	−	1.27404i
$339$		0			0
$340$			12.7695i			0.692522i
$341$	12.9225	+	28.4022i	0.699793	+	1.53807i
$342$		0			0
$343$	12.5154	+	4.06651i	0.675769	+	0.219571i
$344$	−16.5283	−	22.7493i	−0.891148	−	1.22656i
$345$		0			0
$346$	−2.80606	−	8.63616i	−0.150855	−	0.464283i
$347$	10.6218	+	32.6905i	0.570208	+	1.75492i	0.651947	+	0.758265i	$0.273953\pi$
$347$	10.6218	+	32.6905i	0.570208	+	1.75492i	−0.0817393	+	0.996654i	$0.526047\pi$
$348$		0			0
$349$	−12.2424	−	16.8502i	−0.655321	−	0.901972i	0.343994	−	0.938972i	$-0.388220\pi$
$349$	−12.2424	−	16.8502i	−0.655321	−	0.901972i	−0.999315	+	0.0369999i	$0.988220\pi$
$350$	22.2574	+	7.23188i	1.18971	+	0.386560i
$351$		0			0
$352$	5.36612	−	4.91107i	0.286015	−	0.261761i
$353$		−	8.27728i		−	0.440555i	−0.975437	−	0.220278i	$-0.929304\pi$
$353$		−	8.27728i		−	0.440555i	0.975437	−	0.220278i	$-0.0706963\pi$
$354$		0			0
$355$	−12.7643	+	9.27378i	−0.677457	+	0.492201i
$356$	−19.9542	+	27.4645i	−1.05757	+	1.45562i
$357$		0			0
$358$	−13.5574	+	4.40505i	−0.716529	+	0.232814i
$359$	10.3031	+	7.48561i	0.543774	+	0.395075i	0.825485	−	0.564424i	$-0.190902\pi$
$359$	10.3031	+	7.48561i	0.543774	+	0.395075i	−0.281711	+	0.959499i	$0.590902\pi$
$360$		0			0
$361$	4.63580	−	14.2675i	0.243989	−	0.750922i
$362$	−20.0406			−1.05331
$363$		0			0
$364$	−70.9319			−3.71784
$365$	−4.05545	+	12.4814i	−0.212272	+	0.653306i
$366$		0			0
$367$	17.0169	+	12.3635i	0.888274	+	0.645369i	0.935427	−	0.353519i	$-0.115015\pi$
$367$	17.0169	+	12.3635i	0.888274	+	0.645369i	−0.0471537	+	0.998888i	$0.515015\pi$
$368$	−6.70753	+	2.17941i	−0.349654	+	0.113610i
$369$		0			0
$370$	−14.4463	+	19.8836i	−0.751027	+	1.03370i
$371$	12.7292	−	9.24830i	0.660867	−	0.480148i
$372$		0			0
$373$		−	16.5055i		−	0.854622i	−0.904105	−	0.427311i	$-0.859461\pi$
$373$		−	16.5055i		−	0.854622i	0.904105	−	0.427311i	$-0.140539\pi$
$374$	−13.0812	+	11.9719i	−0.676411	+	0.619050i
$375$		0			0
$376$	24.4412	+	7.94144i	1.26046	+	0.409549i
$377$	−3.24933	−	4.47232i	−0.167349	−	0.230336i
$378$		0			0
$379$	−4.41092	−	13.5754i	−0.226574	−	0.697322i	−0.998128	−	0.0611588i	$-0.980520\pi$
$379$	−4.41092	−	13.5754i	−0.226574	−	0.697322i	0.771554	−	0.636163i	$-0.219480\pi$
$380$	−3.67731	−	11.3176i	−0.188642	−	0.580580i
$381$		0			0
$382$	−17.9076	−	24.6477i	−0.916231	−	1.26108i
$383$	−9.65933	−	3.13851i	−0.493569	−	0.160370i	0.0516479	−	0.998665i	$-0.483553\pi$
$383$	−9.65933	−	3.13851i	−0.493569	−	0.160370i	−0.545217	+	0.838295i	$0.683553\pi$
$384$		0			0
$385$	−6.07812	−	13.3590i	−0.309770	−	0.680838i
$386$			41.7569i			2.12537i
$387$		0			0
$388$	8.05326	−	5.85103i	0.408842	−	0.297041i
$389$	−12.1545	+	16.7293i	−0.616260	+	0.848209i	−0.997074	−	0.0764426i	$-0.975644\pi$
$389$	−12.1545	+	16.7293i	−0.616260	+	0.848209i	0.380814	+	0.924652i	$0.375644\pi$
$390$		0			0
$391$	2.71629	−	0.882577i	0.137369	−	0.0446338i
$392$	12.4488	+	9.04459i	0.628760	+	0.456821i
$393$		0			0
$394$	−5.10987	+	15.7266i	−0.257432	+	0.792293i
$395$	14.9486			0.752144
$396$		0			0
$397$	33.6048			1.68658			0.843288	−	0.537463i	$-0.180617\pi$
$397$	33.6048			1.68658			0.843288	+	0.537463i	$0.180617\pi$
$398$	−2.50099	+	7.69725i	−0.125363	+	0.385828i
$399$		0			0
$400$	−12.8631	−	9.34562i	−0.643157	−	0.467281i
$401$	−3.41170	+	1.10853i	−0.170372	+	0.0553573i	−0.392961	−	0.919555i	$-0.628549\pi$
$401$	−3.41170	+	1.10853i	−0.170372	+	0.0553573i	0.222589	+	0.974912i	$0.428549\pi$
$402$		0			0
$403$	−29.7763	+	40.9836i	−1.48326	+	2.04154i
$404$	−45.1833	+	32.8276i	−2.24795	+	1.63323i
$405$		0			0
$406$			8.00681i			0.397371i
$407$	−22.9893	+	2.60496i	−1.13954	+	0.129123i
$408$		0			0
$409$	3.61277	+	1.17386i	0.178640	+	0.0580437i	0.396971	−	0.917831i	$-0.370061\pi$
$409$	3.61277	+	1.17386i	0.178640	+	0.0580437i	−0.218331	+	0.975875i	$0.570061\pi$
$410$	6.63376	+	9.13058i	0.327618	+	0.450927i
$411$		0			0
$412$	−9.72489	−	29.9301i	−0.479111	−	1.47455i
$413$	−10.2664	−	31.5968i	−0.505178	−	1.55478i
$414$		0			0
$415$	5.66060	+	7.79115i	0.277868	+	0.382453i
$416$	11.2314	+	3.64932i	0.550667	+	0.178923i
$417$		0			0
$418$	8.14623	−	14.3777i	0.398445	−	0.703238i
$419$		−	9.01381i		−	0.440354i	−0.975460	−	0.220177i	$-0.929337\pi$
$419$		−	9.01381i		−	0.440354i	0.975460	−	0.220177i	$-0.0706634\pi$
$420$		0			0
$421$	−7.16120	+	5.20292i	−0.349016	+	0.253575i	−0.748456	−	0.663185i	$-0.769204\pi$
$421$	−7.16120	+	5.20292i	−0.349016	+	0.253575i	0.399440	+	0.916759i	$0.369204\pi$
$422$	−11.6907	+	16.0909i	−0.569095	+	0.783292i
$423$		0			0
$424$	−26.3192	+	8.55162i	−1.27817	+	0.415303i
$425$	5.20908	+	3.78462i	0.252677	+	0.183581i
$426$		0			0
$427$	−2.84092	+	8.74346i	−0.137482	+	0.423126i
$428$	4.11601			0.198955
$429$		0			0
$430$	17.9976			0.867922
$431$	−11.5395	+	35.5149i	−0.555837	+	1.71069i	0.137886	+	0.990448i	$0.455969\pi$
$431$	−11.5395	+	35.5149i	−0.555837	+	1.71069i	−0.693723	+	0.720242i	$0.744031\pi$
$432$		0			0
$433$	−32.3699	−	23.5181i	−1.55560	−	1.13021i	−0.939504	−	0.342537i	$-0.888714\pi$
$433$	−32.3699	−	23.5181i	−1.55560	−	1.13021i	−0.616095	−	0.787672i	$-0.711286\pi$
$434$	69.7818	−	22.6735i	3.34963	−	1.08836i
$435$		0			0
$436$	13.3114	−	18.3216i	0.637502	−	0.877446i
$437$	−2.15329	+	1.56446i	−0.103006	+	0.0748381i
$438$		0			0
$439$		−	13.2574i		−	0.632739i	−0.948636	−	0.316370i	$-0.897536\pi$
$439$		−	13.2574i		−	0.632739i	0.948636	−	0.316370i	$-0.102464\pi$
$440$	2.90641	+	25.6497i	0.138558	+	1.22280i
$441$		0			0
$442$	−27.3792	−	8.89606i	−1.30230	−	0.423142i
$443$	2.35618	+	3.24301i	0.111946	+	0.154080i	0.861313	−	0.508074i	$-0.169642\pi$
$443$	2.35618	+	3.24301i	0.111946	+	0.154080i	−0.749368	+	0.662154i	$0.769642\pi$
$444$		0			0
$445$	−3.52395	−	10.8456i	−0.167051	−	0.514130i
$446$	−10.7042	−	32.9441i	−0.506858	−	1.55995i
$447$		0			0
$448$	9.44032	+	12.9935i	0.446013	+	0.613884i
$449$	20.8754	+	6.78284i	0.985172	+	0.320102i	0.756925	−	0.653501i	$-0.226701\pi$
$449$	20.8754	+	6.78284i	0.985172	+	0.320102i	0.228247	+	0.973603i	$0.426701\pi$
$450$		0			0
$451$	−2.12455	+	10.4097i	−0.100041	+	0.490173i
$452$		−	22.4313i		−	1.05508i
$453$		0			0
$454$	−41.9951	+	30.5112i	−1.97093	+	1.43196i
$455$	14.0053	−	19.2767i	0.656579	−	0.903704i
$456$		0			0
$457$	16.9733	−	5.51496i	0.793978	−	0.257979i	0.116181	−	0.993228i	$-0.462935\pi$
$457$	16.9733	−	5.51496i	0.793978	−	0.257979i	0.677797	+	0.735249i	$0.262935\pi$
$458$	−29.8646	−	21.6979i	−1.39548	−	1.01388i
$459$		0			0
$460$	2.44797	−	7.53409i	0.114137	−	0.351279i
$461$	11.5454			0.537722			0.268861	−	0.963179i	$-0.413353\pi$
$461$	11.5454			0.537722			0.268861	+	0.963179i	$0.413353\pi$
$462$		0			0
$463$	14.4101			0.669693			0.334846	−	0.942273i	$-0.391316\pi$
$463$	14.4101			0.669693			0.334846	+	0.942273i	$0.391316\pi$
$464$	1.68098	−	5.17353i	0.0780376	−	0.240175i
$465$		0			0
$466$	−37.3394	−	27.1287i	−1.72971	−	1.25671i
$467$	−22.0042	+	7.14959i	−1.01823	+	0.330844i	−0.770128	−	0.637890i	$-0.779808\pi$
$467$	−22.0042	+	7.14959i	−1.01823	+	0.330844i	−0.248104	+	0.968733i	$0.579808\pi$
$468$		0			0
$469$	2.74382	−	3.77655i	0.126698	−	0.174385i
$470$	−13.3070	+	9.66809i	−0.613805	+	0.445956i
$471$		0			0
$472$			58.4332i			2.68961i
$473$	11.4384	+	12.4983i	0.525938	+	0.574670i
$474$		0			0
$475$	−5.70669	−	1.85422i	−0.261841	−	0.0850773i
$476$	16.6142	+	22.8675i	0.761510	+	1.04813i
$477$		0			0
$478$	18.1884	+	55.9783i	0.831920	+	2.56039i
$479$	0.138470	+	0.426167i	0.00632686	+	0.0194721i	0.954170	−	0.299265i	$-0.0967414\pi$
$479$	0.138470	+	0.426167i	0.00632686	+	0.0194721i	−0.947843	+	0.318737i	$0.896741\pi$
$480$		0			0
$481$	−22.0780	−	30.3878i	−1.00667	−	1.38556i
$482$	−24.5980	−	7.99239i	−1.12041	−	0.364043i
$483$		0			0
$484$	−30.4187	+	34.9058i	−1.38267	+	1.58663i
$485$			3.34385i			0.151836i
$486$		0			0
$487$	3.32024	−	2.41230i	0.150455	−	0.109312i	−0.510011	−	0.860168i	$-0.670359\pi$
$487$	3.32024	−	2.41230i	0.150455	−	0.109312i	0.660466	+	0.750856i	$0.270359\pi$
$488$	9.50426	−	13.0815i	0.430238	−	0.592171i
$489$		0			0
$490$	−9.36659	+	3.04339i	−0.423139	+	0.137486i
$491$	−20.0205	−	14.5457i	−0.903512	−	0.656440i	0.0358534	−	0.999357i	$-0.488585\pi$
$491$	−20.0205	−	14.5457i	−0.903512	−	0.656440i	−0.939366	+	0.342917i	$0.888585\pi$
$492$		0			0
$493$	−0.680732	+	2.09508i	−0.0306586	+	0.0943576i
$494$	26.8281			1.20705
$495$		0			0
$496$	−49.8490			−2.23829
$497$	−10.7921	+	33.2148i	−0.484094	+	1.48989i
$498$		0			0
$499$	−1.25981	−	0.915304i	−0.0563967	−	0.0409746i	0.559230	−	0.829013i	$-0.311097\pi$
$499$	−1.25981	−	0.915304i	−0.0563967	−	0.0409746i	−0.615626	+	0.788038i	$0.711097\pi$
$500$	45.2852	−	14.7140i	2.02521	−	0.658032i
$501$		0			0
$502$	−9.57471	+	13.1785i	−0.427340	+	0.588183i
$503$	−3.60435	+	2.61872i	−0.160710	+	0.116763i	−0.665234	−	0.746635i	$-0.731668\pi$
$503$	−3.60435	+	2.61872i	−0.160710	+	0.116763i	0.504524	+	0.863398i	$0.331668\pi$
$504$		0			0
$505$		−	18.7609i		−	0.834847i
$506$	10.0131	−	4.55577i	0.445135	−	0.202529i
$507$		0			0
$508$	−43.1431	−	14.0181i	−1.91417	−	0.621951i
$509$	17.0148	+	23.4188i	0.754167	+	1.03802i	0.997677	+	0.0681234i	$0.0217011\pi$
$509$	17.0148	+	23.4188i	0.754167	+	1.03802i	−0.243510	+	0.969898i	$0.578299\pi$
$510$		0			0
$511$	8.97689	+	27.6280i	0.397114	+	1.22219i
$512$	−14.4346	−	44.4253i	−0.637927	−	1.96334i
$513$		0			0
$514$	15.6182	+	21.4966i	0.688890	+	0.948176i
$515$	10.0540	+	3.26676i	0.443034	+	0.143951i
$516$		0			0
$517$	−15.1712	−	3.09634i	−0.667227	−	0.136177i
$518$			54.4033i			2.39034i
$519$		0			0
$520$	−33.9043	+	24.6329i	−1.48680	+	1.08022i
$521$	−24.7832	+	34.1112i	−1.08577	+	1.49444i	−0.232769	+	0.972532i	$0.574779\pi$
$521$	−24.7832	+	34.1112i	−1.08577	+	1.49444i	−0.853003	+	0.521905i	$0.825221\pi$
$522$		0			0
$523$	−12.4929	+	4.05920i	−0.546277	+	0.177496i	−0.569137	−	0.822242i	$-0.692723\pi$
$523$	−12.4929	+	4.05920i	−0.546277	+	0.177496i	0.0228601	+	0.999739i	$0.492723\pi$
$524$	−58.5524	−	42.5408i	−2.55788	−	1.85840i
$525$		0			0
$526$	−15.5069	+	47.7253i	−0.676133	+	2.08092i
$527$	20.1869			0.879357
$528$		0			0
$529$	21.2282			0.922964
$530$	5.47335	−	16.8452i	0.237747	−	0.731711i
$531$		0			0
$532$	−21.3105	−	15.4829i	−0.923925	−	0.671271i
$533$	−16.4040	+	5.32999i	−0.710537	+	0.230867i
$534$		0			0
$535$	−0.812695	+	1.11858i	−0.0351359	+	0.0483604i
$536$	−6.64229	+	4.82591i	−0.286903	+	0.208447i
$537$		0			0
$538$		−	24.2104i		−	1.04378i
$539$	−8.06639	−	4.57030i	−0.347444	−	0.196857i
$540$		0			0
$541$	−9.06438	−	2.94519i	−0.389708	−	0.126624i	0.107608	−	0.994193i	$-0.465681\pi$
$541$	−9.06438	−	2.94519i	−0.389708	−	0.126624i	−0.497316	+	0.867570i	$0.665681\pi$
$542$	34.3580	+	47.2897i	1.47580	+	2.03127i
$543$		0			0
$544$	−1.45422	−	4.47563i	−0.0623492	−	0.191891i
$545$	2.35083	+	7.23510i	0.100698	+	0.309918i
$546$		0			0
$547$	−14.3438	−	19.7426i	−0.613298	−	0.844132i	0.383546	−	0.923522i	$-0.374703\pi$
$547$	−14.3438	−	19.7426i	−0.613298	−	0.844132i	−0.996844	+	0.0793899i	$0.974703\pi$
$548$	39.4578	+	12.8206i	1.68555	+	0.547669i
$549$		0			0
$550$	21.5775	+	12.2255i	0.920066	+	0.521297i
$551$		−	2.05290i		−	0.0874567i
$552$		0			0
$553$	26.7698	−	19.4494i	1.13837	−	0.827071i
$554$	−25.5448	+	35.1594i	−1.08530	+	1.49378i
$555$		0			0
$556$	8.84625	−	2.87432i	0.375164	−	0.121898i
$557$	−10.0179	−	7.27845i	−0.424473	−	0.308398i	0.354962	−	0.934881i	$-0.384494\pi$
$557$	−10.0179	−	7.27845i	−0.424473	−	0.308398i	−0.779435	+	0.626483i	$0.784494\pi$
$558$		0			0
$559$	−8.49964	+	26.1592i	−0.359497	+	1.10642i
$560$	23.4465			0.990797
$561$		0			0
$562$	57.1351			2.41010
$563$	−0.905863	+	2.78796i	−0.0381776	+	0.117499i	−0.968329	−	0.249678i	$-0.919675\pi$
$563$	−0.905863	+	2.78796i	−0.0381776	+	0.117499i	0.930151	+	0.367176i	$0.119675\pi$
$564$		0			0
$565$	6.09599	+	4.42900i	0.256460	+	0.186329i
$566$	51.2792	−	16.6616i	2.15542	−	0.700340i
$567$		0			0
$568$	36.1049	−	49.6942i	1.51493	−	2.08512i
$569$	−10.3399	+	7.51236i	−0.433470	+	0.314935i	−0.783035	−	0.621978i	$-0.786329\pi$
$569$	−10.3399	+	7.51236i	−0.433470	+	0.314935i	0.349565	+	0.936912i	$0.386329\pi$
$570$		0			0
$571$		−	0.673079i		−	0.0281675i	−0.999901	−	0.0140837i	$-0.995517\pi$
$571$		−	0.673079i		−	0.0281675i	0.999901	−	0.0140837i	$-0.00448314\pi$
$572$	−73.6489	−	15.0313i	−3.07941	−	0.628489i
$573$		0			0
$574$	23.7593	+	7.71988i	0.991695	+	0.322221i
$575$	−2.34787	−	3.23156i	−0.0979128	−	0.134765i
$576$		0			0
$577$	−7.29562	−	22.4536i	−0.303721	−	0.934756i	−0.980151	−	0.198250i	$-0.936474\pi$
$577$	−7.29562	−	22.4536i	−0.303721	−	0.934756i	0.676431	−	0.736506i	$-0.263526\pi$
$578$	−9.54520	−	29.3771i	−0.397028	−	1.22193i
$579$		0			0
$580$	3.59143	+	4.94317i	0.149126	+	0.205254i
$581$	20.2739	+	6.58739i	0.841104	+	0.273291i
$582$		0			0
$583$	15.1766	−	6.90509i	0.628550	−	0.285979i
$584$		−	51.0936i		−	2.11427i
$585$		0			0
$586$	−39.2172	+	28.4930i	−1.62005	+	1.17703i
$587$	−7.62469	+	10.4945i	−0.314705	+	0.433154i	−0.936841	−	0.349755i	$-0.886265\pi$
$587$	−7.62469	+	10.4945i	−0.314705	+	0.433154i	0.622137	+	0.782909i	$0.286265\pi$
$588$		0			0
$589$	−17.8917	+	5.81337i	−0.737215	+	0.239536i
$590$	−30.2567	−	21.9828i	−1.24565	−	0.905018i
$591$		0			0
$592$	11.4216	−	35.1522i	0.469426	−	1.44475i
$593$	−35.3371			−1.45112			−0.725561	−	0.688158i	$-0.758419\pi$
$593$	−35.3371			−1.45112			−0.725561	+	0.688158i	$0.758419\pi$
$594$		0			0
$595$	−9.49495			−0.389255
$596$	−7.10354	+	21.8624i	−0.290972	+	0.895521i
$597$		0			0
$598$	14.4486	+	10.4975i	0.590845	+	0.429274i
$599$	23.6836	−	7.69526i	0.967685	−	0.314420i	0.217804	−	0.975993i	$-0.430111\pi$
$599$	23.6836	−	7.69526i	0.967685	−	0.314420i	0.749881	+	0.661573i	$0.230111\pi$
$600$		0			0
$601$	18.8457	−	25.9389i	0.768734	−	1.05807i	−0.227703	−	0.973731i	$-0.573122\pi$
$601$	18.8457	−	25.9389i	0.768734	−	1.05807i	0.996437	−	0.0843409i	$-0.0268785\pi$
$602$	32.2300	−	23.4164i	1.31360	−	0.954383i
$603$		0			0
$604$			2.17796i			0.0886200i
$605$	−3.48001	−	15.1587i	−0.141482	−	0.616290i
$606$		0			0
$607$	−22.8234	−	7.41576i	−0.926372	−	0.300997i	−0.193294	−	0.981141i	$-0.561917\pi$
$607$	−22.8234	−	7.41576i	−0.926372	−	0.300997i	−0.733078	+	0.680144i	$0.761917\pi$
$608$	2.57775	+	3.54797i	0.104542	+	0.143889i
$609$		0			0
$610$	3.19806	+	9.84262i	0.129486	+	0.398516i
$611$	−7.76797	−	23.9073i	−0.314258	−	0.967188i
$612$		0			0
$613$	−21.1678	−	29.1350i	−0.854959	−	1.17675i	−0.982748	−	0.184949i	$-0.940788\pi$
$613$	−21.1678	−	29.1350i	−0.854959	−	1.17675i	0.127789	−	0.991801i	$-0.459212\pi$
$614$	4.93431	+	1.60326i	0.199133	+	0.0647021i
$615$		0			0
$616$	38.5772	+	42.1517i	1.55432	+	1.69834i
$617$		−	46.1210i		−	1.85676i	−0.371630	−	0.928381i	$-0.621201\pi$
$617$		−	46.1210i		−	1.85676i	0.371630	−	0.928381i	$-0.378799\pi$
$618$		0			0
$619$	−36.0313	+	26.1783i	−1.44822	+	1.05219i	−0.461979	+	0.886891i	$0.652861\pi$
$619$	−36.0313	+	26.1783i	−1.44822	+	1.05219i	−0.986243	+	0.165304i	$0.947139\pi$
$620$	32.9112	−	45.2983i	1.32174	−	1.81923i
$621$		0			0
$622$	31.0219	−	10.0796i	1.24386	−	0.404156i
$623$	−20.4217	−	14.8372i	−0.818178	−	0.594441i
$624$		0			0
$625$	−0.306137	+	0.942193i	−0.0122455	+	0.0376877i
$626$	7.46720			0.298449
$627$		0			0
$628$	−56.7730			−2.26549
$629$	−4.62532	+	14.2353i	−0.184424	+	0.567598i
$630$		0			0
$631$	29.7072	+	21.5835i	1.18262	+	0.859227i	0.992465	−	0.122527i	$-0.0390997\pi$
$631$	29.7072	+	21.5835i	1.18262	+	0.859227i	0.190159	+	0.981753i	$0.439100\pi$
$632$	−55.3498	+	17.9842i	−2.20170	+	0.715375i
$633$		0			0
$634$	46.7717	−	64.3757i	1.85754	−	2.55668i
$635$	12.3281	−	8.95687i	0.489225	−	0.355443i
$636$		0			0
$637$		−	15.0514i		−	0.596360i
$638$	−1.69673	+	8.31350i	−0.0671743	+	0.329135i
$639$		0			0
$640$	23.0936	+	7.50356i	0.912854	+	0.296604i
$641$	−20.6516	−	28.4245i	−0.815690	−	1.12270i	−0.990420	−	0.138084i	$-0.955906\pi$
$641$	−20.6516	−	28.4245i	−0.815690	−	1.12270i	0.174731	−	0.984616i	$-0.444094\pi$
$642$		0			0
$643$	1.51014	+	4.64774i	0.0595542	+	0.183289i	0.976408	−	0.215934i	$-0.0692797\pi$
$643$	1.51014	+	4.64774i	0.0595542	+	0.183289i	−0.916854	+	0.399224i	$0.869280\pi$
$644$	−5.41869	−	16.6770i	−0.213526	−	0.657166i
$645$		0			0
$646$	−6.28387	−	8.64900i	−0.247235	−	0.340290i
$647$	−13.2744	−	4.31311i	−0.521870	−	0.169566i	0.0362237	−	0.999344i	$-0.488467\pi$
$647$	−13.2744	−	4.31311i	−0.521870	−	0.169566i	−0.558094	+	0.829778i	$0.688467\pi$
$648$		0			0
$649$	−3.96395	−	34.9827i	−0.155599	−	1.37319i
$650$			40.2624i			1.57922i
$651$		0			0
$652$	65.4632	−	47.5618i	2.56374	−	1.86266i
$653$	7.12220	−	9.80287i	0.278713	−	0.383616i	−0.646594	−	0.762834i	$-0.723807\pi$
$653$	7.12220	−	9.80287i	0.278713	−	0.383616i	0.925307	+	0.379218i	$0.123807\pi$
$654$		0			0
$655$	23.1220	−	7.51280i	0.903452	−	0.293550i
$656$	−13.7311	−	9.97625i	−0.536111	−	0.389507i
$657$		0			0
$658$	−11.2510	+	34.6270i	−0.438610	+	1.34990i
$659$	48.0441			1.87153			0.935767	−	0.352619i	$-0.114709\pi$
$659$	48.0441			1.87153			0.935767	+	0.352619i	$0.114709\pi$
$660$		0			0
$661$	−1.17993			−0.0458941			−0.0229470	−	0.999737i	$-0.507305\pi$
$661$	−1.17993			−0.0458941			−0.0229470	+	0.999737i	$0.507305\pi$
$662$	20.2963	−	62.4655i	0.788838	−	2.42779i
$663$		0			0
$664$	−30.3327	−	22.0380i	−1.17714	−	0.855241i
$665$	8.41538	−	2.73432i	0.326334	−	0.106032i
$666$		0			0
$667$	0.803275	−	1.10561i	0.0311029	−	0.0428095i
$668$	2.00759	−	1.45860i	0.0776758	−	0.0564348i
$669$		0			0
$670$		−	5.25491i		−	0.203015i
$671$	−4.80258	+	8.47634i	−0.185401	+	0.327226i
$672$		0			0
$673$	−23.3681	−	7.59277i	−0.900776	−	0.292680i	−0.178219	−	0.983991i	$-0.557033\pi$
$673$	−23.3681	−	7.59277i	−0.900776	−	0.292680i	−0.722557	+	0.691311i	$0.757033\pi$
$674$	6.14120	+	8.45263i	0.236550	+	0.325583i
$675$		0			0
$676$	−20.8009	−	64.0187i	−0.800036	−	2.46226i
$677$	−12.9744	−	39.9311i	−0.498647	−	1.53468i	−0.811195	−	0.584776i	$-0.801183\pi$
$677$	−12.9744	−	39.9311i	−0.498647	−	1.53468i	0.312548	−	0.949902i	$-0.398817\pi$
$678$		0			0
$679$	4.35063	+	5.98813i	0.166962	+	0.229803i
$680$	15.8826	+	5.16057i	0.609070	+	0.197899i
$681$		0			0
$682$	77.2595	−	8.75441i	2.95842	−	0.335224i
$683$		−	45.5024i		−	1.74110i	−0.492081	−	0.870550i	$-0.663764\pi$
$683$		−	45.5024i		−	1.74110i	0.492081	−	0.870550i	$-0.336236\pi$
$684$		0			0
$685$	−11.2750	+	8.19176i	−0.430795	+	0.312991i
$686$	19.2740	−	26.5284i	0.735886	−	1.01286i
$687$		0			0
$688$	−25.7412	+	8.36383i	−0.981375	+	0.318868i
$689$	21.8994	+	15.9108i	0.834300	+	0.606154i
$690$		0			0
$691$	−14.5126	+	44.6653i	−0.552087	+	1.69915i	0.151429	+	0.988468i	$0.451613\pi$
$691$	−14.5126	+	44.6653i	−0.552087	+	1.69915i	−0.703515	+	0.710680i	$0.748387\pi$
$692$	−15.3388			−0.583092
$693$		0			0
$694$	85.6506			3.25125
$695$	−0.965534	+	2.97161i	−0.0366248	+	0.112719i
$696$		0			0
$697$	5.56058	+	4.04000i	0.210622	+	0.153026i
$698$	−49.3593	+	16.0378i	−1.86828	+	0.607040i
$699$		0			0
$700$	23.2361	−	31.9818i	0.878242	−	1.20880i
$701$	7.98290	−	5.79992i	0.301510	−	0.219060i	−0.426735	−	0.904377i	$-0.640336\pi$
$701$	7.98290	−	5.79992i	0.301510	−	0.219060i	0.728245	+	0.685317i	$0.240336\pi$
$702$		0			0
$703$		−	13.9487i		−	0.526086i
$704$	7.04845	+	15.4917i	0.265649	+	0.583865i
$705$		0			0
$706$	−19.6159	−	6.37360i	−0.738255	−	0.239874i
$707$	−24.4095	−	33.5968i	−0.918013	−	1.26354i
$708$		0			0
$709$	−8.25559	−	25.4081i	−0.310045	−	0.954221i	−0.977746	−	0.209791i	$-0.932721\pi$
$709$	−8.25559	−	25.4081i	−0.310045	−	0.954221i	0.667701	−	0.744430i	$-0.267279\pi$
$710$	12.1489	+	37.3903i	0.455938	+	1.40323i
$711$		0			0
$712$	26.0961	+	35.9182i	0.977992	+	1.34609i
$713$	−11.9105	−	3.86994i	−0.446050	−	0.144930i
$714$		0			0
$715$	18.6267	−	17.0471i	0.696599	−	0.637527i
$716$			24.0793i			0.899887i
$717$		0			0
$718$	25.6732	−	18.6527i	0.958117	−	0.696113i
$719$	16.7605	−	23.0689i	0.625061	−	0.860323i	−0.372648	−	0.927973i	$-0.621550\pi$
$719$	16.7605	−	23.0689i	0.625061	−	0.860323i	0.997709	+	0.0676497i	$0.0215500\pi$
$720$		0			0
$721$	22.2550	−	7.23110i	0.828821	−	0.269300i
$722$	−30.2423	−	21.9723i	−1.12550	−	0.817725i
$723$		0			0
$724$	−10.4609	+	32.1954i	−0.388777	+	1.19653i
$725$	3.08091			0.114422
$726$		0			0
$727$	1.96659			0.0729369			0.0364684	−	0.999335i	$-0.488389\pi$
$727$	1.96659			0.0729369			0.0364684	+	0.999335i	$0.488389\pi$
$728$	−28.6660	+	88.2247i	−1.06243	+	3.26983i
$729$		0			0
$730$	26.4563	+	19.2216i	0.979191	+	0.711424i
$731$	10.4242	−	3.38703i	0.385553	−	0.125274i
$732$		0			0
$733$	−27.4707	+	37.8102i	−1.01465	+	1.39655i	−0.0987701	+	0.995110i	$0.531491\pi$
$733$	−27.4707	+	37.8102i	−1.01465	+	1.39655i	−0.915884	+	0.401442i	$0.868509\pi$
$734$	42.4028	−	30.8074i	1.56512	−	1.13712i
$735$		0			0
$736$			2.91944i			0.107612i
$737$	3.64921	−	3.33976i	0.134421	−	0.123022i
$738$		0			0
$739$	16.2275	+	5.27262i	0.596937	+	0.193957i	0.591874	−	0.806031i	$-0.298388\pi$
$739$	16.2275	+	5.27262i	0.596937	+	0.193957i	0.00506302	+	0.999987i	$0.498388\pi$
$740$	24.4024	+	33.5870i	0.897050	+	1.23468i
$741$		0			0
$742$	−12.1155	−	37.2876i	−0.444773	−	1.36887i
$743$	−12.7736	−	39.3132i	−0.468619	−	1.44226i	−0.854374	−	0.519659i	$-0.826059\pi$
$743$	−12.7736	−	39.3132i	−0.468619	−	1.44226i	0.385755	−	0.922601i	$-0.373941\pi$
$744$		0			0
$745$	−4.53883	−	6.24716i	−0.166290	−	0.228878i
$746$	−39.1155	−	12.7094i	−1.43212	−	0.465325i
$747$		0			0
$748$	12.4047	+	27.2641i	0.453560	+	0.996874i
$749$			3.06053i			0.111829i
$750$		0			0
$751$	−36.8341	+	26.7615i	−1.34409	+	0.976542i	−0.344812	+	0.938672i	$0.612057\pi$
$751$	−36.8341	+	26.7615i	−1.34409	+	0.976542i	−0.999283	+	0.0378703i	$0.987943\pi$
$752$	14.5395	−	20.0119i	0.530200	−	0.729757i
$753$		0			0
$754$	−13.1008	+	4.25670i	−0.477102	+	0.155020i
$755$	−0.591889	−	0.430032i	−0.0215410	−	0.0156505i
$756$		0			0
$757$	−13.3554	+	41.1036i	−0.485409	+	1.49393i	0.345979	+	0.938242i	$0.387547\pi$
$757$	−13.3554	+	41.1036i	−0.485409	+	1.49393i	−0.831388	+	0.555692i	$0.812453\pi$
$758$	−35.5682			−1.29189
$759$		0			0
$760$	−15.5629			−0.564525
$761$	−6.15029	+	18.9287i	−0.222948	+	0.686163i	0.775546	+	0.631292i	$0.217475\pi$
$761$	−6.15029	+	18.9287i	−0.222948	+	0.686163i	−0.998493	+	0.0548715i	$0.982525\pi$
$762$		0			0
$763$	13.6233	+	9.89793i	0.493198	+	0.358329i
$764$	−48.9441	+	15.9029i	−1.77074	+	0.575347i
$765$		0			0
$766$	−14.8756	+	20.4745i	−0.537477	+	0.739774i
$767$	46.2408	−	33.5959i	1.66966	−	1.21308i
$768$		0			0
$769$		−	39.9620i		−	1.44107i	−0.693419	−	0.720534i	$-0.743897\pi$
$769$		−	39.9620i		−	1.44107i	0.693419	−	0.720534i	$-0.256103\pi$
$770$	−36.3391	+	4.11765i	−1.30957	+	0.148390i
$771$		0			0
$772$	67.0827	+	21.7965i	2.41436	+	0.784473i
$773$	0.983134	+	1.35317i	0.0353609	+	0.0486701i	0.826331	−	0.563184i	$-0.190424\pi$
$773$	0.983134	+	1.35317i	0.0353609	+	0.0486701i	−0.790970	+	0.611854i	$0.790424\pi$
$774$		0			0
$775$	−8.72443	−	26.8510i	−0.313391	−	0.964518i
$776$	−4.02289	−	12.3812i	−0.144413	−	0.444459i
$777$		0			0
$778$	30.2868	+	41.6862i	1.08583	+	1.49452i
$779$	−6.09177	−	1.97934i	−0.218260	−	0.0709171i
$780$		0			0
$781$	−18.2441	+	32.2001i	−0.652826	+	1.15221i
$782$		−	7.11680i		−	0.254496i
$783$		0			0
$784$	11.9823	−	8.70566i	0.427940	−	0.310916i
$785$	11.2097	−	15.4288i	0.400090	−	0.550677i
$786$		0			0
$787$	8.94317	−	2.90581i	0.318790	−	0.103581i	−0.145251	−	0.989395i	$-0.546399\pi$
$787$	8.94317	−	2.90581i	0.318790	−	0.103581i	0.464041	+	0.885814i	$0.346399\pi$
$788$	22.5975	+	16.4181i	0.805004	+	0.584870i
$789$		0			0
$790$	11.5106	−	35.4259i	0.409528	−	1.26040i
$791$	16.6791			0.593042
$792$		0			0
$793$	−15.8164			−0.561657
$794$	25.8761	−	79.6383i	0.918307	−	2.82626i
$795$		0			0
$796$	11.0602	+	8.03570i	0.392018	+	0.284818i
$797$	−28.0643	+	9.11865i	−0.994089	+	0.322999i	−0.760501	−	0.649337i	$-0.775047\pi$
$797$	−28.0643	+	9.11865i	−0.994089	+	0.322999i	−0.233588	+	0.972336i	$0.575047\pi$
$798$		0			0
$799$	−5.88792	+	8.10403i	−0.208300	+	0.286700i
$800$	−5.32464	+	3.86857i	−0.188254	+	0.136775i
$801$		0			0
$802$			8.93881i			0.315640i
$803$	3.46605	+	30.5886i	0.122314	+	1.07945i
$804$		0			0
$805$	5.60209	+	1.82023i	0.197448	+	0.0641547i
$806$	74.1969	+	102.123i	2.61347	+	3.59714i
$807$		0			0
$808$	22.5707	+	69.4655i	0.794034	+	2.44379i
$809$	16.3139	+	50.2091i	0.573567	+	1.76526i	0.641008	+	0.767534i	$0.278516\pi$
$809$	16.3139	+	50.2091i	0.573567	+	1.76526i	−0.0674416	+	0.997723i	$0.521484\pi$
$810$		0			0
$811$	9.82048	+	13.5167i	0.344844	+	0.474636i	0.945848	−	0.324609i	$-0.105233\pi$
$811$	9.82048	+	13.5167i	0.344844	+	0.474636i	−0.601005	+	0.799245i	$0.705233\pi$
$812$	12.8630	+	4.17944i	0.451402	+	0.146669i
$813$		0			0
$814$	−11.5287	+	56.4871i	−0.404080	+	1.97987i
$815$			27.1814i			0.952123i
$816$		0			0
$817$	−8.26360	+	6.00385i	−0.289107	+	0.210048i
$818$	5.56375	−	7.65785i	0.194532	−	0.267750i
$819$		0			0
$820$	18.1311	−	5.89114i	0.633164	−	0.205727i
$821$	14.8119	+	10.7615i	0.516940	+	0.375579i	0.815450	−	0.578828i	$-0.196490\pi$
$821$	14.8119	+	10.7615i	0.516940	+	0.375579i	−0.298510	+	0.954407i	$0.596490\pi$
$822$		0			0
$823$	−3.52189	+	10.8393i	−0.122766	+	0.377833i	−0.993487	−	0.113942i	$-0.963652\pi$
$823$	−3.52189	+	10.8393i	−0.122766	+	0.377833i	0.870722	+	0.491776i	$0.163652\pi$
$824$	−41.1571			−1.43377
$825$		0			0
$826$	−82.7850			−2.88046
$827$	−5.84858	+	18.0001i	−0.203375	+	0.625924i	0.796401	+	0.604769i	$0.206734\pi$
$827$	−5.84858	+	18.0001i	−0.203375	+	0.625924i	−0.999776	+	0.0211551i	$0.993266\pi$
$828$		0			0
$829$	13.0466	+	9.47891i	0.453127	+	0.329216i	0.790829	−	0.612037i	$-0.209650\pi$
$829$	13.0466	+	9.47891i	0.453127	+	0.329216i	−0.337702	+	0.941253i	$0.609650\pi$
$830$	22.8226	−	7.41551i	0.792184	−	0.257396i
$831$		0			0
$832$	−16.2412	+	22.3541i	−0.563062	+	0.774988i
$833$	−4.85238	+	3.52546i	−0.168125	+	0.122150i
$834$		0			0
$835$			0.833583i			0.0288473i
$836$	−18.8457	−	20.5919i	−0.651792	−	0.712187i
$837$		0			0
$838$	−21.3614	−	6.94074i	−0.737917	−	0.239764i
$839$	−13.6484	−	18.7854i	−0.471196	−	0.648546i	0.505587	−	0.862775i	$-0.331276\pi$
$839$	−13.6484	−	18.7854i	−0.471196	−	0.648546i	−0.976783	+	0.214230i	$0.931276\pi$
$840$		0			0
$841$	−8.63577	−	26.5782i	−0.297785	−	0.916488i
$842$	6.81593	+	20.9773i	0.234893	+	0.722925i
$843$		0			0
$844$	19.7477	+	27.1804i	0.679745	+	0.935588i
$845$	21.5050	+	6.98739i	0.739794	+	0.240374i
$846$		0			0
$847$	−25.9548	−	22.6183i	−0.891816	−	0.777175i
$848$			26.6366i			0.914705i
$849$		0			0
$850$	12.9800	−	9.43054i	0.445211	−	0.323465i
$851$	5.45795	−	7.51223i	0.187096	−	0.257516i
$852$		0			0
$853$	−23.5404	+	7.64874i	−0.806008	+	0.261888i	−0.682906	−	0.730506i	$-0.739284\pi$
$853$	−23.5404	+	7.64874i	−0.806008	+	0.261888i	−0.123102	+	0.992394i	$0.539284\pi$
$854$	18.5332	+	13.4651i	0.634191	+	0.460767i
$855$		0			0
$856$	1.66342	−	5.11947i	0.0568544	−	0.174980i
$857$	8.41752			0.287537			0.143769	−	0.989611i	$-0.454078\pi$
$857$	8.41752			0.287537			0.143769	+	0.989611i	$0.454078\pi$
$858$		0			0
$859$	52.6551			1.79657			0.898285	−	0.439414i	$-0.144814\pi$
$859$	52.6551			1.79657			0.898285	+	0.439414i	$0.144814\pi$
$860$	9.39449	−	28.9133i	0.320350	−	0.985934i
$861$		0			0
$862$	75.2794	+	54.6937i	2.56403	+	1.86287i
$863$	37.6211	−	12.2238i	1.28064	−	0.416104i	0.411832	−	0.911260i	$-0.364889\pi$
$863$	37.6211	−	12.2238i	1.28064	−	0.416104i	0.868804	+	0.495156i	$0.164889\pi$
$864$		0			0
$865$	3.02860	−	4.16851i	0.102975	−	0.141733i
$866$	−80.6597	+	58.6027i	−2.74093	+	1.99140i
$867$		0			0
$868$		−	123.940i		−	4.20680i
$869$	31.9167	−	14.5215i	1.08270	−	0.492610i
$870$		0			0
$871$	7.63791	+	2.48171i	0.258801	+	0.0840894i
$872$	−17.4087	−	23.9611i	−0.589534	−	0.811424i
$873$		0			0
$874$	2.04947	+	6.30763i	0.0693245	+	0.213359i
$875$	10.9409	+	33.6725i	0.369869	+	1.13834i
$876$		0			0
$877$	22.5627	+	31.0548i	0.761887	+	1.04865i	0.997055	+	0.0766925i	$0.0244360\pi$
$877$	22.5627	+	31.0548i	0.761887	+	1.04865i	−0.235168	+	0.971955i	$0.575564\pi$
$878$	−31.4180	−	10.2083i	−1.06031	−	0.344514i
$879$		0			0
$880$	24.3446	+	4.96859i	0.820657	+	0.167491i
$881$		−	25.4083i		−	0.856026i	−0.903772	−	0.428013i	$-0.859214\pi$
$881$		−	25.4083i		−	0.856026i	0.903772	−	0.428013i	$-0.140786\pi$
$882$		0			0
$883$	4.42613	−	3.21577i	0.148951	−	0.108219i	−0.510814	−	0.859691i	$-0.670656\pi$
$883$	4.42613	−	3.21577i	0.148951	−	0.108219i	0.659765	+	0.751472i	$0.270656\pi$
$884$	−28.5831	+	39.3413i	−0.961355	+	1.32319i
$885$		0			0
$886$	9.49974	−	3.08665i	0.319150	−	0.103698i
$887$	−3.40029	−	2.47046i	−0.114171	−	0.0829499i	0.529235	−	0.848475i	$-0.322479\pi$
$887$	−3.40029	−	2.47046i	−0.114171	−	0.0829499i	−0.643406	+	0.765526i	$0.722479\pi$
$888$		0			0
$889$	10.4233	−	32.0798i	0.349588	−	1.07592i
$890$	−28.4159			−0.952504
$891$		0			0
$892$	−58.5123			−1.95914
$893$	2.88470	−	8.87819i	0.0965328	−	0.297097i
$894$		0			0
$895$	−6.54387	−	4.75440i	−0.218737	−	0.158922i
$896$	51.1185	−	16.6094i	1.70775	−	0.554882i
$897$		0			0
$898$	32.1486	−	44.2488i	1.07281	−	1.47660i
$899$	7.81454	−	5.67759i	0.260629	−	0.189358i
$900$		0			0
$901$		−	10.7868i		−	0.359360i
$902$	23.0335	+	13.0504i	0.766931	+	0.434532i
$903$		0			0
$904$	−27.8999	−	9.06523i	−0.927938	−	0.301505i
$905$	−6.68403	−	9.19978i	−0.222185	−	0.305811i
$906$		0			0
$907$	−12.1741	−	37.4681i	−0.404236	−	1.24411i	−0.921532	−	0.388303i	$-0.873061\pi$
$907$	−12.1741	−	37.4681i	−0.404236	−	1.24411i	0.517296	−	0.855806i	$-0.326939\pi$
$908$	27.0956	+	83.3917i	0.899199	+	2.76745i
$909$		0			0
$910$	−34.8986	−	48.0338i	−1.15688	−	1.59230i
$911$	7.47258	+	2.42799i	0.247578	+	0.0804429i	0.430177	−	0.902745i	$-0.358451\pi$
$911$	7.47258	+	2.42799i	0.247578	+	0.0804429i	−0.182599	+	0.983187i	$0.558451\pi$
$912$		0			0
$913$	19.6545	+	11.1360i	0.650470	+	0.368547i
$914$		−	44.4708i		−	1.47096i
$915$		0			0
$916$	−50.4467	+	36.6517i	−1.66681	+	1.21101i
$917$	31.6319	−	43.5376i	1.04458	−	1.43774i
$918$		0			0
$919$	−39.9674	+	12.9862i	−1.31840	+	0.428376i	−0.881947	−	0.471349i	$-0.843767\pi$
$919$	−39.9674	+	12.9862i	−1.31840	+	0.428376i	−0.436458	+	0.899725i	$0.643767\pi$
$920$	−8.38155	−	6.08955i	−0.276332	−	0.200767i
$921$		0			0
$922$	8.89008	−	27.3609i	0.292779	−	0.901082i
$923$	−60.0836			−1.97768
$924$		0			0
$925$	20.9336			0.688293
$926$	11.0959	−	34.1497i	0.364635	−	1.12223i
$927$		0			0
$928$	−1.82172	−	1.32355i	−0.0598007	−	0.0434478i
$929$	−19.0322	+	6.18393i	−0.624426	+	0.202888i	−0.604104	−	0.796905i	$-0.706469\pi$
$929$	−19.0322	+	6.18393i	−0.624426	+	0.202888i	−0.0203214	+	0.999793i	$0.506469\pi$
$930$		0			0
$931$	3.28541	−	4.52199i	0.107675	−	0.148202i
$932$	−63.0730	+	45.8252i	−2.06602	+	1.50105i
$933$		0			0
$934$			57.6519i			1.88643i
$935$	−9.85864	−	2.01209i	−0.322412	−	0.0658023i
$936$		0			0
$937$	−39.0020	−	12.6725i	−1.27414	−	0.413993i	−0.407627	−	0.913149i	$-0.633643\pi$
$937$	−39.0020	−	12.6725i	−1.27414	−	0.413993i	−0.866512	+	0.499156i	$0.833643\pi$
$938$	−6.83708	−	9.41044i	−0.223239	−	0.307262i
$939$		0			0
$940$	8.58579	+	26.4243i	0.280038	+	0.861867i
$941$	−4.72947	−	14.5558i	−0.154176	−	0.474506i	0.843900	−	0.536500i	$-0.180254\pi$
$941$	−4.72947	−	14.5558i	−0.154176	−	0.474506i	−0.998077	+	0.0619941i	$0.980254\pi$
$942$		0			0
$943$	−2.50630	−	3.44962i	−0.0816163	−	0.112335i
$944$	53.4908	+	17.3802i	1.74098	+	0.565677i
$945$		0			0
$946$	38.4267	−	17.4835i	1.24936	−	0.568437i
$947$			35.5222i			1.15432i	0.816632	+	0.577158i	$0.195838\pi$
$947$			35.5222i			1.15432i	−0.816632	+	0.577158i	$0.804162\pi$
$948$		0			0
$949$	−40.4326	+	29.3760i	−1.31250	+	0.953586i
$950$	−8.78844	+	12.0962i	−0.285135	+	0.392454i
$951$		0			0
$952$	35.1568	−	11.4231i	1.13944	−	0.370226i
$953$	−24.4990	−	17.7996i	−0.793602	−	0.576585i	0.115428	−	0.993316i	$-0.463176\pi$
$953$	−24.4990	−	17.7996i	−0.793602	−	0.576585i	−0.909030	+	0.416730i	$0.863176\pi$
$954$		0			0
$955$	5.34206	−	16.4412i	0.172865	−	0.532024i
$956$	99.4235			3.21559
$957$		0			0
$958$	1.11658			0.0360750
$959$	−9.53297	+	29.3395i	−0.307836	+	0.947420i
$960$		0			0
$961$	−46.5315	−	33.8071i	−1.50102	−	1.09055i
$962$	−89.0148	+	28.9227i	−2.86995	+	0.932504i
$963$		0			0
$964$	−25.6796	+	35.3450i	−0.827085	+	1.13838i
$965$	−19.1688	+	13.9269i	−0.617064	+	0.448324i
$966$		0			0
$967$			19.8481i			0.638272i	0.947709	+	0.319136i	$0.103393\pi$
$967$			19.8481i			0.638272i	−0.947709	+	0.319136i	$0.896607\pi$
$968$	31.1224	+	51.9412i	1.00031	+	1.66945i
$969$		0			0
$970$	7.92442	+	2.57480i	0.254438	+	0.0826718i
$971$	−2.26406	−	3.11621i	−0.0726570	−	0.100004i	0.771142	−	0.636663i	$-0.219686\pi$
$971$	−2.26406	−	3.11621i	−0.0726570	−	0.100004i	−0.843799	+	0.536660i	$0.819686\pi$
$972$		0			0
$973$	2.13725	+	6.57777i	0.0685170	+	0.210874i
$974$	−3.16016	−	9.72598i	−0.101258	−	0.311640i
$975$		0			0
$976$	−9.14811	−	12.5913i	−0.292824	−	0.403037i
$977$	5.90797	+	1.91962i	0.189013	+	0.0614140i	0.401994	−	0.915642i	$-0.368317\pi$
$977$	5.90797	+	1.91962i	0.189013	+	0.0614140i	−0.212981	+	0.977056i	$0.568317\pi$
$978$		0			0
$979$	−18.0597	−	19.7331i	−0.577192	−	0.630674i
$980$			16.6361i			0.531420i
$981$		0			0
$982$	−49.8873	+	36.2452i	−1.59197	+	1.15663i
$983$	17.0697	−	23.4944i	0.544438	−	0.749355i	−0.444806	−	0.895627i	$-0.646727\pi$
$983$	17.0697	−	23.4944i	0.544438	−	0.749355i	0.989244	+	0.146272i	$0.0467275\pi$
$984$		0			0
$985$	−8.92364	+	2.89947i	−0.284331	+	0.0923847i
$986$	4.44085	+	3.22647i	0.141426	+	0.102752i
$987$		0			0
$988$	14.0039	−	43.0995i	0.445523	−	1.37118i
$989$	−6.79967			−0.216217
$990$		0			0
$991$	−0.476493			−0.0151363			−0.00756816	−	0.999971i	$-0.502409\pi$
$991$	−0.476493			−0.0151363			−0.00756816	+	0.999971i	$0.502409\pi$
$992$	−6.37649	+	19.6248i	−0.202454	+	0.623089i
$993$		0			0
$994$	70.4041	+	51.1515i	2.23308	+	1.62243i
$995$	−4.36761	+	1.41912i	−0.138463	+	0.0449892i
$996$		0			0
$997$	−15.1911	+	20.9087i	−0.481107	+	0.662187i	−0.978717	−	0.205214i	$-0.934211\pi$
$997$	−15.1911	+	20.9087i	−0.481107	+	0.662187i	0.497610	+	0.867401i	$0.334211\pi$
$998$	−3.13920	+	2.28076i	−0.0993696	+	0.0721963i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.k.a.728.20		80
3.2	odd	2	inner	891.2.k.a.728.1		80
9.2	odd	6		297.2.t.a.233.10		80
9.4	even	3		297.2.t.a.35.10		80
9.5	odd	6		99.2.p.a.2.1	✓	80
9.7	even	3		99.2.p.a.68.1	yes	80
11.6	odd	10	inner	891.2.k.a.809.1		80
33.17	even	10	inner	891.2.k.a.809.20		80
99.50	even	30		99.2.p.a.83.1	yes	80
99.61	odd	30		99.2.p.a.50.1	yes	80
99.83	even	30		297.2.t.a.17.10		80
99.94	odd	30		297.2.t.a.116.10		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.2.1	✓	80	9.5	odd	6
99.2.p.a.50.1	yes	80	99.61	odd	30
99.2.p.a.68.1	yes	80	9.7	even	3
99.2.p.a.83.1	yes	80	99.50	even	30
297.2.t.a.17.10		80	99.83	even	30
297.2.t.a.35.10		80	9.4	even	3
297.2.t.a.116.10		80	99.94	odd	30
297.2.t.a.233.10		80	9.2	odd	6
891.2.k.a.728.1		80	3.2	odd	2	inner
891.2.k.a.728.20		80	1.1	even	1	trivial
891.2.k.a.809.1		80	11.6	odd	10	inner
891.2.k.a.809.20		80	33.17	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.770011 - 2.36985i) q^{2} +(-3.40524 - 2.47406i) q^{4} +(1.34471 - 0.436923i) q^{5} +(1.83962 - 2.53202i) q^{7} +(-4.45339 + 3.23558i) q^{8} -3.52320i q^{10} +(2.44665 - 2.23917i) q^{11} +(5.12091 + 1.66389i) q^{13} +(-4.58399 - 6.30932i) q^{14} +(1.63730 + 5.03909i) q^{16} +(-0.663043 - 2.04064i) q^{17} +(1.17531 + 1.61768i) q^{19} +(-5.66005 - 1.83906i) q^{20} +(-3.42256 - 7.52239i) q^{22} +1.33110i q^{23} +(-2.42774 + 1.76385i) q^{25} +(7.88632 - 10.8546i) q^{26} +(-12.5287 + 4.07083i) q^{28} +(-0.830600 - 0.603467i) q^{29} +(-2.90732 + 8.94782i) q^{31} +2.19325 q^{32} -5.34656 q^{34} +(1.36746 - 4.20862i) q^{35} +(-5.64362 - 4.10033i) q^{37} +(4.73866 - 1.53968i) q^{38} +(-4.57483 + 6.29671i) q^{40} +(-2.59156 + 1.88288i) q^{41} +5.10831i q^{43} +(-13.8713 + 1.57178i) q^{44} +(3.15451 + 1.02496i) q^{46} +(-2.74412 - 3.77695i) q^{47} +(-0.863813 - 2.65854i) q^{49} +(2.31069 + 7.11156i) q^{50} +(-13.3214 - 18.3354i) q^{52} +(4.78123 + 1.55352i) q^{53} +(2.31170 - 4.08004i) q^{55} +17.2283i q^{56} +(-2.06970 + 1.50372i) q^{58} +(6.23944 - 8.58785i) q^{59} +(-2.79366 + 0.907714i) q^{61} +(18.9663 + 13.7799i) q^{62} +(-1.58577 + 4.88050i) q^{64} +7.61314 q^{65} +1.49151 q^{67} +(-2.79082 + 8.58927i) q^{68} +(-8.92084 - 6.48137i) q^{70} +(-10.6126 + 3.44824i) q^{71} +(-5.45572 + 7.50916i) q^{73} +(-14.0628 + 10.2172i) q^{74} -8.41637i q^{76} +(-1.16872 - 10.3142i) q^{77} +(10.0550 + 3.26708i) q^{79} +(4.40339 + 6.06075i) q^{80} +(2.46661 + 7.59144i) q^{82} +(2.10476 + 6.47780i) q^{83} +(-1.78320 - 2.45437i) q^{85} +(12.1059 + 3.93346i) q^{86} +(-3.65088 + 17.8882i) q^{88} -8.06536i q^{89} +(13.6335 - 9.90535i) q^{91} +(3.29322 - 4.53272i) q^{92} +(-11.0638 + 3.59485i) q^{94} +(2.28726 + 1.66179i) q^{95} +(-0.730812 + 2.24921i) q^{97} -6.96550 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) \) 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

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