LMFDB - Embedded newform 720.2.u.a.179.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(179,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 2]))

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

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

chi := DirichletCharacter("720.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.u (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			179.17
Character	$\chi$	$=$	720.179
Dual form			720.2.u.a.539.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.612434 - 1.27473i) q^{2} +(-1.24985 + 1.56137i) q^{4} +(-0.263678 - 2.22047i) q^{5} +2.95946i q^{7} +(2.75577 + 0.636981i) q^{8} +O(q^{10})$	\(q+(-0.612434 - 1.27473i) q^{2} +(-1.24985 + 1.56137i) q^{4} +(-0.263678 - 2.22047i) q^{5} +2.95946i q^{7} +(2.75577 + 0.636981i) q^{8} +(-2.66900 + 1.69601i) q^{10} +(1.04021 - 1.04021i) q^{11} +(0.00780247 - 0.00780247i) q^{13} +(3.77249 - 1.81247i) q^{14} +(-0.875749 - 3.90296i) q^{16} -2.00003 q^{17} +(5.10608 - 5.10608i) q^{19} +(3.79653 + 2.36355i) q^{20} +(-1.96305 - 0.688925i) q^{22} +6.49393 q^{23} +(-4.86095 + 1.17098i) q^{25} +(-0.0147245 - 0.00516751i) q^{26} +(-4.62080 - 3.69888i) q^{28} +(5.45997 - 5.45997i) q^{29} -4.99178i q^{31} +(-4.43886 + 3.50664i) q^{32} +(1.22489 + 2.54949i) q^{34} +(6.57137 - 0.780345i) q^{35} +(3.74547 + 3.74547i) q^{37} +(-9.63598 - 3.38171i) q^{38} +(0.687758 - 6.28705i) q^{40} -10.4245 q^{41} +(-3.52161 + 3.52161i) q^{43} +(0.324047 + 2.92427i) q^{44} +(-3.97710 - 8.27798i) q^{46} -10.6419i q^{47} -1.75838 q^{49} +(4.46968 + 5.47923i) q^{50} +(0.00243062 + 0.0219345i) q^{52} +(2.98006 - 2.98006i) q^{53} +(-2.58404 - 2.03548i) q^{55} +(-1.88512 + 8.15557i) q^{56} +(-10.3038 - 3.61610i) q^{58} +(5.47867 - 5.47867i) q^{59} +(-4.67845 - 4.67845i) q^{61} +(-6.36315 + 3.05713i) q^{62} +(7.18851 + 3.51074i) q^{64} +(-0.0193825 - 0.0152678i) q^{65} +(-2.29404 - 2.29404i) q^{67} +(2.49974 - 3.12279i) q^{68} +(-5.01925 - 7.89879i) q^{70} +0.212315i q^{71} +16.4980 q^{73} +(2.48059 - 7.06830i) q^{74} +(1.59064 + 14.3543i) q^{76} +(3.07847 + 3.07847i) q^{77} -4.54833i q^{79} +(-8.43547 + 2.97370i) q^{80} +(6.38432 + 13.2884i) q^{82} +(-4.68359 + 4.68359i) q^{83} +(0.527365 + 4.44100i) q^{85} +(6.64583 + 2.33233i) q^{86} +(3.52918 - 2.20399i) q^{88} +0.123094 q^{89} +(0.0230911 + 0.0230911i) q^{91} +(-8.11644 + 10.1394i) q^{92} +(-13.5655 + 6.51744i) q^{94} +(-12.6842 - 9.99152i) q^{95} +8.29464i q^{97} +(1.07689 + 2.24145i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) $ 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−0.612434	−	1.27473i	−0.433056	−	0.901367i
$2$	−0.612434	−	1.27473i	−0.433056	−	0.901367i
$3$		0			0
$3$		0			0
$4$	−1.24985	+	1.56137i	−0.624925	+	0.780685i
$5$	−0.263678	−	2.22047i	−0.117921	−	0.993023i
$5$	−0.263678	−	2.22047i	−0.117921	−	0.993023i
$6$		0			0
$7$			2.95946i			1.11857i	0.828976	+	0.559284i	$0.188924\pi$
$7$			2.95946i			1.11857i	−0.828976	+	0.559284i	$0.811076\pi$
$8$	2.75577	+	0.636981i	0.974311	+	0.225207i
$9$		0			0
$10$	−2.66900	+	1.69601i	−0.844012	+	0.536324i
$11$	1.04021	−	1.04021i	0.313636	−	0.313636i	−0.532680	−	0.846317i	$-0.678815\pi$
$11$	1.04021	−	1.04021i	0.313636	−	0.313636i	0.846317	+	0.532680i	$0.178815\pi$
$12$		0			0
$13$	0.00780247	−	0.00780247i	0.00216402	−	0.00216402i	−0.706024	−	0.708188i	$-0.749513\pi$
$13$	0.00780247	−	0.00780247i	0.00216402	−	0.00216402i	0.708188	+	0.706024i	$0.249513\pi$
$14$	3.77249	−	1.81247i	1.00824	−	0.484403i
$15$		0			0
$16$	−0.875749	−	3.90296i	−0.218937	−	0.975739i
$17$	−2.00003			−0.485079			−0.242539	−	0.970142i	$-0.577980\pi$
$17$	−2.00003			−0.485079			−0.242539	+	0.970142i	$0.577980\pi$
$18$		0			0
$19$	5.10608	−	5.10608i	1.17141	−	1.17141i	0.189542	−	0.981873i	$-0.439300\pi$
$19$	5.10608	−	5.10608i	1.17141	−	1.17141i	0.981873	−	0.189542i	$-0.0607003\pi$
$20$	3.79653	+	2.36355i	0.848929	+	0.528506i
$21$		0			0
$22$	−1.96305	−	0.688925i	−0.418524	−	0.146879i
$23$	6.49393			1.35408			0.677039	−	0.735947i	$-0.263263\pi$
$23$	6.49393			1.35408			0.677039	+	0.735947i	$0.263263\pi$
$24$		0			0
$25$	−4.86095	+	1.17098i	−0.972189	+	0.234196i
$26$	−0.0147245	−	0.00516751i	−0.00288771	−	0.00101343i
$27$		0			0
$28$	−4.62080	−	3.69888i	−0.873250	−	0.699022i
$29$	5.45997	−	5.45997i	1.01389	−	1.01389i	0.0139895	−	0.999902i	$-0.495547\pi$
$29$	5.45997	−	5.45997i	1.01389	−	1.01389i	0.999902	−	0.0139895i	$-0.00445315\pi$
$30$		0			0
$31$		−	4.99178i		−	0.896550i	−0.893896	−	0.448275i	$-0.852039\pi$
$31$		−	4.99178i		−	0.896550i	0.893896	−	0.448275i	$-0.147961\pi$
$32$	−4.43886	+	3.50664i	−0.784687	+	0.619892i
$33$		0			0
$34$	1.22489	+	2.54949i	0.210066	+	0.437234i
$35$	6.57137	−	0.780345i	1.11076	−	0.131902i
$36$		0			0
$37$	3.74547	+	3.74547i	0.615752	+	0.615752i	0.944439	−	0.328687i	$-0.106606\pi$
$37$	3.74547	+	3.74547i	0.615752	+	0.615752i	−0.328687	+	0.944439i	$0.606606\pi$
$38$	−9.63598	−	3.38171i	−1.56316	−	0.548586i
$39$		0			0
$40$	0.687758	−	6.28705i	0.108744	−	0.994070i
$41$	−10.4245			−1.62803			−0.814017	−	0.580841i	$-0.802724\pi$
$41$	−10.4245			−1.62803			−0.814017	+	0.580841i	$0.802724\pi$
$42$		0			0
$43$	−3.52161	+	3.52161i	−0.537040	+	0.537040i	−0.922658	−	0.385618i	$-0.873988\pi$
$43$	−3.52161	+	3.52161i	−0.537040	+	0.537040i	0.385618	+	0.922658i	$0.373988\pi$
$44$	0.324047	+	2.92427i	0.0488519	+	0.440850i
$45$		0			0
$46$	−3.97710	−	8.27798i	−0.586391	−	1.22052i
$47$		−	10.6419i		−	1.55228i	−0.630563	−	0.776138i	$-0.717176\pi$
$47$		−	10.6419i		−	1.55228i	0.630563	−	0.776138i	$-0.282824\pi$
$48$		0			0
$49$	−1.75838			−0.251197
$50$	4.46968	+	5.47923i	0.632109	+	0.774880i
$51$		0			0
$52$	0.00243062	+	0.0219345i	0.000337066	+	0.00304176i
$53$	2.98006	−	2.98006i	0.409342	−	0.409342i	−0.472167	−	0.881509i	$-0.656528\pi$
$53$	2.98006	−	2.98006i	0.409342	−	0.409342i	0.881509	+	0.472167i	$0.156528\pi$
$54$		0			0
$55$	−2.58404	−	2.03548i	−0.348432	−	0.274464i
$56$	−1.88512	+	8.15557i	−0.251909	+	1.08983i
$57$		0			0
$58$	−10.3038	−	3.61610i	−1.35296	−	0.474817i
$59$	5.47867	−	5.47867i	0.713262	−	0.713262i	−0.253954	−	0.967216i	$-0.581731\pi$
$59$	5.47867	−	5.47867i	0.713262	−	0.713262i	0.967216	+	0.253954i	$0.0817312\pi$
$60$		0			0
$61$	−4.67845	−	4.67845i	−0.599014	−	0.599014i	0.341037	−	0.940050i	$-0.389222\pi$
$61$	−4.67845	−	4.67845i	−0.599014	−	0.599014i	−0.940050	+	0.341037i	$0.889222\pi$
$62$	−6.36315	+	3.05713i	−0.808120	+	0.388256i
$63$		0			0
$64$	7.18851	+	3.51074i	0.898564	+	0.438843i
$65$	−0.0193825	−	0.0152678i	−0.00240410	−	0.00189374i
$66$		0			0
$67$	−2.29404	−	2.29404i	−0.280261	−	0.280261i	0.552952	−	0.833213i	$-0.313501\pi$
$67$	−2.29404	−	2.29404i	−0.280261	−	0.280261i	−0.833213	+	0.552952i	$0.813501\pi$
$68$	2.49974	−	3.12279i	0.303138	−	0.378693i
$69$		0			0
$70$	−5.01925	−	7.89879i	−0.599916	−	0.944086i
$71$			0.212315i			0.0251971i	0.999921	+	0.0125986i	$0.00401036\pi$
$71$			0.212315i			0.0251971i	−0.999921	+	0.0125986i	$0.995990\pi$
$72$		0			0
$73$	16.4980			1.93094			0.965472	−	0.260505i	$-0.0838891\pi$
$73$	16.4980			1.93094			0.965472	+	0.260505i	$0.0838891\pi$
$74$	2.48059	−	7.06830i	0.288363	−	0.821673i
$75$		0			0
$76$	1.59064	+	14.3543i	0.182459	+	1.64655i
$77$	3.07847	+	3.07847i	0.350824	+	0.350824i
$78$		0			0
$79$		−	4.54833i		−	0.511727i	−0.966713	−	0.255863i	$-0.917640\pi$
$79$		−	4.54833i		−	0.511727i	0.966713	−	0.255863i	$-0.0823597\pi$
$80$	−8.43547	+	2.97370i	−0.943114	+	0.332469i
$81$		0			0
$82$	6.38432	+	13.2884i	0.705030	+	1.46746i
$83$	−4.68359	+	4.68359i	−0.514090	+	0.514090i	−0.915777	−	0.401687i	$-0.868424\pi$
$83$	−4.68359	+	4.68359i	−0.514090	+	0.514090i	0.401687	+	0.915777i	$0.368424\pi$
$84$		0			0
$85$	0.527365	+	4.44100i	0.0572008	+	0.481694i
$86$	6.64583	+	2.33233i	0.716639	+	0.251502i
$87$		0			0
$88$	3.52918	−	2.20399i	0.376212	−	0.234946i
$89$	0.123094			0.0130479			0.00652395	−	0.999979i	$-0.497923\pi$
$89$	0.123094			0.0130479			0.00652395	+	0.999979i	$0.497923\pi$
$90$		0			0
$91$	0.0230911	+	0.0230911i	0.00242060	+	0.00242060i
$92$	−8.11644	+	10.1394i	−0.846197	+	1.05711i
$93$		0			0
$94$	−13.5655	+	6.51744i	−1.39917	+	0.672223i
$95$	−12.6842	−	9.99152i	−1.30138	−	1.02511i
$96$		0			0
$97$			8.29464i			0.842193i	0.907016	+	0.421096i	$0.138355\pi$
$97$			8.29464i			0.842193i	−0.907016	+	0.421096i	$0.861645\pi$
$98$	1.07689	+	2.24145i	0.108782	+	0.226420i
$99$		0			0
$100$	4.24713	−	9.05328i	0.424713	−	0.905328i
$101$	−7.95152	−	7.95152i	−0.791205	−	0.791205i	0.190485	−	0.981690i	$-0.438994\pi$
$101$	−7.95152	−	7.95152i	−0.791205	−	0.791205i	−0.981690	+	0.190485i	$0.938994\pi$
$102$		0			0
$103$		−	6.14632i		−	0.605615i	−0.953052	−	0.302808i	$-0.902076\pi$
$103$		−	6.14632i		−	0.605615i	0.953052	−	0.302808i	$-0.0979240\pi$
$104$	0.0264718	−	0.0165318i	0.00259578	−	0.00162107i
$105$		0			0
$106$	−5.62384	−	1.97367i	−0.546236	−	0.191699i
$107$	5.83941	+	5.83941i	0.564517	+	0.564517i	0.930587	−	0.366070i	$-0.119297\pi$
$107$	5.83941	+	5.83941i	0.564517	+	0.564517i	−0.366070	+	0.930587i	$0.619297\pi$
$108$		0			0
$109$	10.9696	+	10.9696i	1.05070	+	1.05070i	0.998644	+	0.0520513i	$0.0165759\pi$
$109$	10.9696	+	10.9696i	1.05070	+	1.05070i	0.0520513	+	0.998644i	$0.483424\pi$
$110$	−1.01212	+	4.54054i	−0.0965021	+	0.432924i
$111$		0			0
$112$	11.5506	−	2.59174i	1.09143	−	0.244896i
$113$	−9.95287			−0.936288			−0.468144	−	0.883652i	$-0.655077\pi$
$113$	−9.95287			−0.936288			−0.468144	+	0.883652i	$0.655077\pi$
$114$		0			0
$115$	−1.71231	−	14.4196i	−0.159674	−	1.34463i
$116$	1.70089	+	15.3492i	0.157923	+	1.42514i
$117$		0			0
$118$	−10.3391	−	3.62848i	−0.951794	−	0.334029i
$119$		−	5.91900i		−	0.542594i
$120$		0			0
$121$			8.83591i			0.803264i
$122$	−3.09850	+	8.82897i	−0.280525	+	0.799337i
$123$		0			0
$124$	7.79401	+	6.23897i	0.699923	+	0.560276i
$125$	3.88185	+	10.4848i	0.347203	+	0.937790i
$126$		0			0
$127$	0.542244			0.0481164			0.0240582	−	0.999711i	$-0.492341\pi$
$127$	0.542244			0.0481164			0.0240582	+	0.999711i	$0.492341\pi$
$128$	0.0727470	−	11.3135i	0.00642998	−	0.999979i
$129$		0			0
$130$	−0.00759176	+	0.0340578i	−0.000665841	+	0.00298707i
$131$	5.55272	+	5.55272i	0.485143	+	0.485143i	0.906770	−	0.421626i	$-0.138541\pi$
$131$	5.55272	+	5.55272i	0.485143	+	0.485143i	−0.421626	+	0.906770i	$0.638541\pi$
$132$		0			0
$133$	15.1112	+	15.1112i	1.31031	+	1.31031i
$134$	−1.51932	+	4.32922i	−0.131250	+	0.373987i
$135$		0			0
$136$	−5.51162	−	1.27398i	−0.472617	−	0.109243i
$137$			5.80371i			0.495844i	0.968780	+	0.247922i	$0.0797477\pi$
$137$			5.80371i			0.495844i	−0.968780	+	0.247922i	$0.920252\pi$
$138$		0			0
$139$	6.27873	+	6.27873i	0.532555	+	0.532555i	0.921332	−	0.388777i	$-0.127102\pi$
$139$	6.27873	+	6.27873i	0.532555	+	0.532555i	−0.388777	+	0.921332i	$0.627102\pi$
$140$	−6.99483	+	11.2357i	−0.591171	+	0.949586i
$141$		0			0
$142$	0.270643	−	0.130029i	0.0227119	−	0.0109118i
$143$		−	0.0162325i		−	0.00135743i
$144$		0			0
$145$	−13.5634	−	10.6840i	−1.12638	−	0.887259i
$146$	−10.1039	−	21.0304i	−0.836207	−	1.74049i
$147$		0			0
$148$	−10.5293	+	1.16679i	−0.865506	+	0.0959092i
$149$	−12.6568	−	12.6568i	−1.03689	−	1.03689i	−0.999293	−	0.0375933i	$-0.988031\pi$
$149$	−12.6568	−	12.6568i	−1.03689	−	1.03689i	−0.0375933	−	0.999293i	$-0.511969\pi$
$150$		0			0
$151$	17.1332			1.39428			0.697140	−	0.716935i	$-0.254456\pi$
$151$	17.1332			1.39428			0.697140	+	0.716935i	$0.254456\pi$
$152$	17.3236	−	10.8187i	1.40513	−	0.877512i
$153$		0			0
$154$	2.03884	−	5.80956i	0.164295	−	0.468147i
$155$	−11.0841	+	1.31622i	−0.890294	+	0.105722i
$156$		0			0
$157$	−4.80235	+	4.80235i	−0.383269	+	0.383269i	−0.872279	−	0.489009i	$-0.837358\pi$
$157$	−4.80235	+	4.80235i	−0.383269	+	0.383269i	0.489009	+	0.872279i	$0.337358\pi$
$158$	−5.79787	+	2.78555i	−0.461254	+	0.221606i
$159$		0			0
$160$	8.95681	+	8.93171i	0.708098	+	0.706114i
$161$			19.2185i			1.51463i
$162$		0			0
$163$	−0.778039	−	0.778039i	−0.0609407	−	0.0609407i	0.675980	−	0.736920i	$-0.263721\pi$
$163$	−0.778039	−	0.778039i	−0.0609407	−	0.0609407i	−0.736920	+	0.675980i	$0.763721\pi$
$164$	13.0291	−	16.2765i	1.01740	−	1.27098i
$165$		0			0
$166$	8.83867	+	3.10190i	0.686014	+	0.240754i
$167$	−5.26638			−0.407525			−0.203763	−	0.979020i	$-0.565317\pi$
$167$	−5.26638			−0.407525			−0.203763	+	0.979020i	$0.565317\pi$
$168$		0			0
$169$			12.9999i			0.999991i
$170$	5.33808	−	3.39206i	0.409412	−	0.260159i
$171$		0			0
$172$	−1.09705	−	9.90001i	−0.0836492	−	0.754869i
$173$	8.51881	+	8.51881i	0.647673	+	0.647673i	0.952430	−	0.304757i	$-0.0985752\pi$
$173$	8.51881	+	8.51881i	0.647673	+	0.647673i	−0.304757	+	0.952430i	$0.598575\pi$
$174$		0			0
$175$	−3.46546	−	14.3858i	−0.261964	−	1.08746i
$176$	−4.97088	−	3.14894i	−0.374694	−	0.237361i
$177$		0			0
$178$	−0.0753866	−	0.156911i	−0.00565047	−	0.0117609i
$179$	10.2479	+	10.2479i	0.765966	+	0.765966i	0.977394	−	0.211428i	$-0.0678114\pi$
$179$	10.2479	+	10.2479i	0.765966	+	0.765966i	−0.211428	+	0.977394i	$0.567811\pi$
$180$		0			0
$181$	−0.590728	+	0.590728i	−0.0439085	+	0.0439085i	−0.728720	−	0.684812i	$-0.759884\pi$
$181$	−0.590728	+	0.590728i	−0.0439085	+	0.0439085i	0.684812	+	0.728720i	$0.259884\pi$
$182$	0.0152930	−	0.0435765i	0.00113359	−	0.00323011i
$183$		0			0
$184$	17.8958	+	4.13651i	1.31929	+	0.304947i
$185$	7.32909	−	9.30429i	0.538846	−	0.684065i
$186$		0			0
$187$	−2.08046	+	2.08046i	−0.152138	+	0.152138i
$188$	16.6159	+	13.3007i	1.21184	+	0.970057i
$189$		0			0
$190$	−4.96818	+	22.2881i	−0.360430	+	1.61695i
$191$	15.2046			1.10017			0.550083	−	0.835110i	$-0.314596\pi$
$191$	15.2046			1.10017			0.550083	+	0.835110i	$0.314596\pi$
$192$		0			0
$193$		−	12.4277i		−	0.894566i	−0.894392	−	0.447283i	$-0.852392\pi$
$193$		−	12.4277i		−	0.894566i	0.894392	−	0.447283i	$-0.147608\pi$
$194$	10.5734	−	5.07991i	0.759125	−	0.364717i
$195$		0			0
$196$	2.19771	−	2.74547i	0.156979	−	0.196105i
$197$	7.54210	−	7.54210i	0.537352	−	0.537352i	−0.385398	−	0.922750i	$-0.625936\pi$
$197$	7.54210	−	7.54210i	0.537352	−	0.537352i	0.922750	+	0.385398i	$0.125936\pi$
$198$		0			0
$199$	10.0231			0.710517			0.355258	−	0.934768i	$-0.384393\pi$
$199$	10.0231			0.710517			0.355258	+	0.934768i	$0.384393\pi$
$200$	−14.1415	+	0.130615i	−0.999957	+	0.00923585i
$201$		0			0
$202$	−5.26622	+	15.0058i	−0.370530	+	1.05580i
$203$	16.1585	+	16.1585i	1.13411	+	1.13411i
$204$		0			0
$205$	2.74872	+	23.1473i	0.191979	+	1.61668i
$206$	−7.83488	+	3.76421i	−0.545882	+	0.262265i
$207$		0			0
$208$	−0.0372857	−	0.0236197i	−0.00258530	−	0.00163773i
$209$		−	10.6228i		−	0.734796i
$210$		0			0
$211$	−15.9950	+	15.9950i	−1.10114	+	1.10114i	−0.106867	+	0.994273i	$0.534082\pi$
$211$	−15.9950	+	15.9950i	−1.10114	+	1.10114i	−0.994273	+	0.106867i	$0.965918\pi$
$212$	0.928345	+	8.37759i	0.0637590	+	0.575375i
$213$		0			0
$214$	3.86739	−	11.0199i	0.264370	−	0.753305i
$215$	8.74819	+	6.89104i	0.596621	+	0.469965i
$216$		0			0
$217$	14.7729			1.00285
$218$	7.26507	−	20.7014i	0.492052	−	1.40207i
$219$		0			0
$220$	6.40780	−	1.49060i	0.432014	−	0.100496i
$221$	−0.0156052	+	0.0156052i	−0.00104972	+	0.00104972i
$222$		0			0
$223$	26.9611			1.80545			0.902724	−	0.430221i	$-0.141564\pi$
$223$	26.9611			1.80545			0.902724	+	0.430221i	$0.141564\pi$
$224$	−10.3777	−	13.1366i	−0.693392	−	0.877726i
$225$		0			0
$226$	6.09547	+	12.6872i	0.405465	+	0.843939i
$227$	−4.80422	+	4.80422i	−0.318867	+	0.318867i	−0.848332	−	0.529465i	$-0.822393\pi$
$227$	−4.80422	+	4.80422i	−0.318867	+	0.318867i	0.529465	+	0.848332i	$0.322393\pi$
$228$		0			0
$229$	−3.77289	+	3.77289i	−0.249320	+	0.249320i	−0.820691	−	0.571372i	$-0.806412\pi$
$229$	−3.77289	+	3.77289i	−0.249320	+	0.249320i	0.571372	+	0.820691i	$0.306412\pi$
$230$	−17.3323	+	11.0137i	−1.14286	+	0.726225i
$231$		0			0
$232$	18.5243	−	11.5685i	1.21618	−	0.759511i
$233$			12.2685i			0.803737i	0.915697	+	0.401868i	$0.131639\pi$
$233$			12.2685i			0.803737i	−0.915697	+	0.401868i	$0.868361\pi$
$234$		0			0
$235$	−23.6299	+	2.80603i	−1.54145	+	0.183045i
$236$	1.70671	+	15.4018i	0.111097	+	1.00257i
$237$		0			0
$238$	−7.54510	+	3.62499i	−0.489076	+	0.234974i
$239$	−12.4166			−0.803164			−0.401582	−	0.915823i	$-0.631540\pi$
$239$	−12.4166			−0.803164			−0.401582	+	0.915823i	$0.631540\pi$
$240$		0			0
$241$	−16.6958			−1.07547			−0.537735	−	0.843114i	$-0.680720\pi$
$241$	−16.6958			−1.07547			−0.537735	+	0.843114i	$0.680720\pi$
$242$	11.2634	−	5.41141i	0.724036	−	0.347858i
$243$		0			0
$244$	13.1521	−	1.45743i	0.841979	−	0.0933021i
$245$	0.463646	+	3.90442i	0.0296212	+	0.249444i
$246$		0			0
$247$		−	0.0796800i		−	0.00506992i
$248$	3.17967	−	13.7562i	0.201909	−	0.873518i
$249$		0			0
$250$	10.9879	−	11.3695i	0.694935	−	0.719073i
$251$	18.3923	−	18.3923i	1.16091	−	1.16091i	0.176634	−	0.984277i	$-0.443479\pi$
$251$	18.3923	−	18.3923i	1.16091	−	1.16091i	0.984277	−	0.176634i	$-0.0565207\pi$
$252$		0			0
$253$	6.75507	−	6.75507i	0.424688	−	0.424688i
$254$	−0.332089	−	0.691212i	−0.0208371	−	0.0433705i
$255$		0			0
$256$	−14.4661	+	6.83602i	−0.904133	+	0.427251i
$257$	−29.8867			−1.86428			−0.932142	−	0.362094i	$-0.882062\pi$
$257$	−29.8867			−1.86428			−0.932142	+	0.362094i	$0.882062\pi$
$258$		0			0
$259$	−11.0846	+	11.0846i	−0.688761	+	0.688761i
$260$	0.0480638	−	0.0111808i	0.00298079	−	0.000693401i
$261$		0			0
$262$	3.67752	−	10.4789i	0.227198	−	0.647386i
$263$	−17.6640			−1.08921			−0.544605	−	0.838693i	$-0.683320\pi$
$263$	−17.6640			−1.08921			−0.544605	+	0.838693i	$0.683320\pi$
$264$		0			0
$265$	−7.40289	−	5.83134i	−0.454756	−	0.358216i
$266$	10.0080	−	28.5173i	0.613632	−	1.74851i
$267$		0			0
$268$	6.44905	−	0.714637i	0.393938	−	0.0436534i
$269$	0.0280978	−	0.0280978i	0.00171315	−	0.00171315i	−0.706250	−	0.707963i	$-0.749614\pi$
$269$	0.0280978	−	0.0280978i	0.00171315	−	0.00171315i	0.707963	+	0.706250i	$0.249614\pi$
$270$		0			0
$271$		−	13.7422i		−	0.834779i	−0.908728	−	0.417390i	$-0.862945\pi$
$271$		−	13.7422i		−	0.834779i	0.908728	−	0.417390i	$-0.137055\pi$
$272$	1.75152	+	7.80603i	0.106202	+	0.473310i
$273$		0			0
$274$	7.39813	−	3.55439i	0.446938	−	0.214728i
$275$	−3.83836	+	6.27449i	−0.231462	+	0.378366i
$276$		0			0
$277$	−23.0188	−	23.0188i	−1.38306	−	1.38306i	−0.839126	−	0.543937i	$-0.816933\pi$
$277$	−23.0188	−	23.0188i	−1.38306	−	1.38306i	−0.543937	−	0.839126i	$-0.683067\pi$
$278$	4.15835	−	11.8490i	0.249401	−	0.710654i
$279$		0			0
$280$	18.6062	+	2.03539i	1.11194	+	0.121638i
$281$	−19.3294			−1.15309			−0.576547	−	0.817064i	$-0.695600\pi$
$281$	−19.3294			−1.15309			−0.576547	+	0.817064i	$0.695600\pi$
$282$		0			0
$283$	2.78511	−	2.78511i	0.165557	−	0.165557i	−0.619466	−	0.785023i	$-0.712651\pi$
$283$	2.78511	−	2.78511i	0.165557	−	0.165557i	0.785023	+	0.619466i	$0.212651\pi$
$284$	−0.331502	−	0.265362i	−0.0196710	−	0.0157463i
$285$		0			0
$286$	−0.0206920	+	0.00994132i	−0.00122354	+	0.000587842i
$287$		−	30.8509i		−	1.82107i
$288$		0			0
$289$	−12.9999			−0.764699
$290$	−5.31252	+	23.8328i	−0.311962	+	1.39951i
$291$		0			0
$292$	−20.6200	+	25.7595i	−1.20670	+	1.50746i
$293$	−17.8866	+	17.8866i	−1.04495	+	1.04495i	−0.0460045	+	0.998941i	$0.514649\pi$
$293$	−17.8866	+	17.8866i	−1.04495	+	1.04495i	−0.998941	+	0.0460045i	$0.985351\pi$
$294$		0			0
$295$	−13.6098	−	10.7206i	−0.792394	−	0.624178i
$296$	7.93585	+	12.7074i	0.461262	+	0.738605i
$297$		0			0
$298$	−8.38250	+	23.8854i	−0.485585	+	1.38365i
$299$	0.0506687	−	0.0506687i	0.00293025	−	0.00293025i
$300$		0			0
$301$	−10.4220	−	10.4220i	−0.600716	−	0.600716i
$302$	−10.4929	−	21.8401i	−0.603801	−	1.25676i
$303$		0			0
$304$	−24.4004	−	15.4572i	−1.39946	−	0.886529i
$305$	−9.15473	+	11.6219i	−0.524198	+	0.665470i
$306$		0			0
$307$	−23.4113	−	23.4113i	−1.33615	−	1.33615i	−0.899754	−	0.436397i	$-0.856254\pi$
$307$	−23.4113	−	23.4113i	−1.33615	−	1.33615i	−0.436397	−	0.899754i	$-0.643746\pi$
$308$	−8.65425	+	0.959002i	−0.493121	+	0.0546442i
$309$		0			0
$310$	8.46608	+	13.3231i	0.480841	+	0.756699i
$311$			24.0385i			1.36310i	0.731772	+	0.681549i	$0.238693\pi$
$311$			24.0385i			1.36310i	−0.731772	+	0.681549i	$0.761307\pi$
$312$		0			0
$313$	−17.7757			−1.00474			−0.502371	−	0.864652i	$-0.667539\pi$
$313$	−17.7757			−1.00474			−0.502371	+	0.864652i	$0.667539\pi$
$314$	9.06280	+	3.18056i	0.511444	+	0.179489i
$315$		0			0
$316$	7.10162	+	5.68473i	0.399497	+	0.319791i
$317$	4.69302	+	4.69302i	0.263586	+	0.263586i	0.826509	−	0.562923i	$-0.190323\pi$
$317$	4.69302	+	4.69302i	0.263586	+	0.263586i	−0.562923	+	0.826509i	$0.690323\pi$
$318$		0			0
$319$		−	11.3591i		−	0.635987i
$320$	5.90003	−	16.8876i	0.329822	−	0.944043i
$321$		0			0
$322$	24.4983	−	11.7700i	1.36524	−	0.655919i
$323$	−10.2123	+	10.2123i	−0.568228	+	0.568228i
$324$		0			0
$325$	−0.0287909	+	0.0470639i	−0.00159703	+	0.00261064i
$326$	−0.515289	+	1.46828i	−0.0285392	+	0.0813207i
$327$		0			0
$328$	−28.7275	−	6.64021i	−1.58621	−	0.366644i
$329$	31.4942			1.73633
$330$		0			0
$331$	20.1568	+	20.1568i	1.10792	+	1.10792i	0.993424	+	0.114494i	$0.0365247\pi$
$331$	20.1568	+	20.1568i	1.10792	+	1.10792i	0.114494	+	0.993424i	$0.463475\pi$
$332$	−1.45903	−	13.1666i	−0.0800745	−	0.722610i
$333$		0			0
$334$	3.22531	+	6.71320i	0.176481	+	0.367330i
$335$	−4.48895	+	5.69873i	−0.245258	+	0.311355i
$336$		0			0
$337$		−	22.5791i		−	1.22996i	−0.788542	−	0.614980i	$-0.789164\pi$
$337$		−	22.5791i		−	1.22996i	0.788542	−	0.614980i	$-0.210836\pi$
$338$	16.5713	−	7.96156i	0.901359	−	0.433052i
$339$		0			0
$340$	−7.59317	−	4.72718i	−0.411798	−	0.256367i
$341$	−5.19252	−	5.19252i	−0.281191	−	0.281191i
$342$		0			0
$343$			15.5124i			0.837588i
$344$	−11.9479	+	7.46154i	−0.644189	+	0.402299i
$345$		0			0
$346$	5.64194	−	16.0764i	0.303313	−	0.864270i
$347$	8.61782	+	8.61782i	0.462629	+	0.462629i	0.899516	−	0.436887i	$-0.143919\pi$
$347$	8.61782	+	8.61782i	0.462629	+	0.462629i	−0.436887	+	0.899516i	$0.643919\pi$
$348$		0			0
$349$	11.4945	+	11.4945i	0.615284	+	0.615284i	0.944318	−	0.329034i	$-0.106723\pi$
$349$	11.4945	+	11.4945i	0.615284	+	0.615284i	−0.329034	+	0.944318i	$0.606723\pi$
$350$	−16.2155	+	13.2278i	−0.866756	+	0.707057i
$351$		0			0
$352$	−0.969707	+	8.26502i	−0.0516855	+	0.440527i
$353$	−17.2352			−0.917336			−0.458668	−	0.888608i	$-0.651673\pi$
$353$	−17.2352			−0.917336			−0.458668	+	0.888608i	$0.651673\pi$
$354$		0			0
$355$	0.471438	−	0.0559829i	0.0250213	−	0.00297126i
$356$	−0.153849	+	0.192195i	−0.00815396	+	0.0101863i
$357$		0			0
$358$	6.78711	−	19.3395i	0.358710	−	1.02212i
$359$		−	2.27145i		−	0.119882i	−0.998202	−	0.0599412i	$-0.980909\pi$
$359$		−	2.27145i		−	0.119882i	0.998202	−	0.0599412i	$-0.0190913\pi$
$360$		0			0
$361$		−	33.1441i		−	1.74442i
$362$	1.11480	+	0.391234i	0.0585925	+	0.0205628i
$363$		0			0
$364$	−0.0649140	+	0.00719331i	−0.00340242	+	0.000377032i
$365$	−4.35017	−	36.6333i	−0.227698	−	1.91747i
$366$		0			0
$367$	−31.1335			−1.62516			−0.812579	−	0.582852i	$-0.801937\pi$
$367$	−31.1335			−1.62516			−0.812579	+	0.582852i	$0.801937\pi$
$368$	−5.68705	−	25.3455i	−0.296458	−	1.32123i
$369$		0			0
$370$	−16.3490	−	3.64432i	−0.849944	−	0.189459i
$371$	8.81934	+	8.81934i	0.457877	+	0.457877i
$372$		0			0
$373$	20.3199	+	20.3199i	1.05212	+	1.05212i	0.998565	+	0.0535601i	$0.0170569\pi$
$373$	20.3199	+	20.3199i	1.05212	+	1.05212i	0.0535601	+	0.998565i	$0.482943\pi$
$374$	3.92616	+	1.37787i	0.203017	+	0.0712480i
$375$		0			0
$376$	6.77867	−	29.3265i	0.349583	−	1.51240i
$377$		−	0.0852026i		−	0.00438816i
$378$		0			0
$379$	−9.61527	−	9.61527i	−0.493903	−	0.493903i	0.415630	−	0.909534i	$-0.363561\pi$
$379$	−9.61527	−	9.61527i	−0.493903	−	0.493903i	−0.909534	+	0.415630i	$0.863561\pi$
$380$	31.4538	−	7.31689i	1.61355	−	0.375348i
$381$		0			0
$382$	−9.31180	−	19.3817i	−0.476433	−	0.991653i
$383$			1.17749i			0.0601668i	0.999547	+	0.0300834i	$0.00957728\pi$
$383$			1.17749i			0.0601668i	−0.999547	+	0.0300834i	$0.990423\pi$
$384$		0			0
$385$	6.02391	−	7.64736i	0.307007	−	0.389746i
$386$	−15.8419	+	7.61115i	−0.806333	+	0.387397i
$387$		0			0
$388$	−12.9510	−	10.3671i	−0.657487	−	0.526307i
$389$	23.7967	+	23.7967i	1.20654	+	1.20654i	0.972139	+	0.234403i	$0.0753137\pi$
$389$	23.7967	+	23.7967i	1.20654	+	1.20654i	0.234403	+	0.972139i	$0.424686\pi$
$390$		0			0
$391$	−12.9881			−0.656834
$392$	−4.84568	−	1.12005i	−0.244744	−	0.0565712i
$393$		0			0
$394$	−14.2331	−	4.99507i	−0.717055	−	0.251648i
$395$	−10.0994	+	1.19930i	−0.508156	+	0.0603431i
$396$		0			0
$397$	−5.88396	+	5.88396i	−0.295308	+	0.295308i	−0.839173	−	0.543865i	$-0.816960\pi$
$397$	−5.88396	+	5.88396i	−0.295308	+	0.295308i	0.543865	+	0.839173i	$0.316960\pi$
$398$	−6.13847	−	12.7767i	−0.307693	−	0.640436i
$399$		0			0
$400$	8.82725	+	17.9466i	0.441362	+	0.897329i
$401$			15.4433i			0.771202i	0.922666	+	0.385601i	$0.126006\pi$
$401$			15.4433i			0.771202i	−0.922666	+	0.385601i	$0.873994\pi$
$402$		0			0
$403$	−0.0389482	−	0.0389482i	−0.00194015	−	0.00194015i
$404$	22.3535	−	2.47705i	1.11213	−	0.123238i
$405$		0			0
$406$	10.7017	−	30.4938i	0.531115	−	1.51338i
$407$	7.79218			0.386244
$408$		0			0
$409$		−	8.72546i		−	0.431446i	−0.976455	−	0.215723i	$-0.930789\pi$
$409$		−	8.72546i		−	0.431446i	0.976455	−	0.215723i	$-0.0692109\pi$
$410$	27.8230	−	17.6800i	1.37408	−	0.873154i
$411$		0			0
$412$	9.59668	+	7.68198i	0.472795	+	0.378464i
$413$	16.2139	+	16.2139i	0.797833	+	0.797833i
$414$		0			0
$415$	11.6347	+	9.16479i	0.571125	+	0.449882i
$416$	−0.00727361	+	0.0619945i	−0.000356618	+	0.00303953i
$417$		0			0
$418$	−13.5412	+	6.50578i	−0.662321	+	0.318208i
$419$	−4.83085	−	4.83085i	−0.236003	−	0.236003i	0.579190	−	0.815193i	$-0.303369\pi$
$419$	−4.83085	−	4.83085i	−0.236003	−	0.236003i	−0.815193	+	0.579190i	$0.803369\pi$
$420$		0			0
$421$	20.2440	−	20.2440i	0.986633	−	0.986633i	−0.0132784	−	0.999912i	$-0.504227\pi$
$421$	20.2440	−	20.2440i	0.986633	−	0.986633i	0.999912	+	0.0132784i	$0.00422678\pi$
$422$	30.1851	+	10.5934i	1.46939	+	0.515676i
$423$		0			0
$424$	10.1106	−	6.31410i	0.491013	−	0.306640i
$425$	9.72204	−	2.34199i	0.471588	−	0.113603i
$426$		0			0
$427$	13.8456	−	13.8456i	0.670038	−	0.670038i
$428$	−16.4159	+	1.81909i	−0.793491	+	0.0879290i
$429$		0			0
$430$	3.42650	−	15.3718i	0.165241	−	0.741296i
$431$	6.63538			0.319615			0.159808	−	0.987148i	$-0.448913\pi$
$431$	6.63538			0.319615			0.159808	+	0.987148i	$0.448913\pi$
$432$		0			0
$433$		−	2.17952i		−	0.104741i	−0.998628	−	0.0523706i	$-0.983322\pi$
$433$		−	2.17952i		−	0.104741i	0.998628	−	0.0523706i	$-0.0166777\pi$
$434$	−9.04745	−	18.8314i	−0.434291	−	0.903938i
$435$		0			0
$436$	−30.8379	+	3.41724i	−1.47687	+	0.163656i
$437$	33.1585	−	33.1585i	1.58619	−	1.58619i
$438$		0			0
$439$	−18.1795			−0.867661			−0.433830	−	0.900995i	$-0.642838\pi$
$439$	−18.1795			−0.867661			−0.433830	+	0.900995i	$0.642838\pi$
$440$	−5.82446	−	7.25529i	−0.277670	−	0.345883i
$441$		0			0
$442$	0.0294495	+	0.0103352i	0.00140077	+	0.000491595i
$443$	−20.1844	−	20.1844i	−0.958989	−	0.958989i	0.0402025	−	0.999192i	$-0.487200\pi$
$443$	−20.1844	−	20.1844i	−0.958989	−	0.958989i	−0.999192	+	0.0402025i	$0.987200\pi$
$444$		0			0
$445$	−0.0324571	−	0.273325i	−0.00153862	−	0.0129569i
$446$	−16.5119	−	34.3680i	−0.781860	−	1.62737i
$447$		0			0
$448$	−10.3899	+	21.2741i	−0.490876	+	1.00511i
$449$			31.3405i			1.47905i	0.673129	+	0.739525i	$0.264950\pi$
$449$			31.3405i			1.47905i	−0.673129	+	0.739525i	$0.735050\pi$
$450$		0			0
$451$	−10.8437	+	10.8437i	−0.510611	+	0.510611i
$452$	12.4396	−	15.5401i	0.585110	−	0.730945i
$453$		0			0
$454$	9.06633	+	3.18180i	0.425504	+	0.149329i
$455$	0.0451843	−	0.0573616i	0.00211827	−	0.00268915i
$456$		0			0
$457$	−15.6212			−0.730727			−0.365364	−	0.930865i	$-0.619055\pi$
$457$	−15.6212			−0.730727			−0.365364	+	0.930865i	$0.619055\pi$
$458$	7.12005	+	2.49876i	0.332698	+	0.116759i
$459$		0			0
$460$	24.6544	+	15.3487i	1.14952	+	0.715638i
$461$	−9.98698	+	9.98698i	−0.465140	+	0.465140i	−0.900336	−	0.435196i	$-0.856679\pi$
$461$	−9.98698	+	9.98698i	−0.465140	+	0.465140i	0.435196	+	0.900336i	$0.356679\pi$
$462$		0			0
$463$	27.8119			1.29253			0.646264	−	0.763114i	$-0.276330\pi$
$463$	27.8119			1.29253			0.646264	+	0.763114i	$0.276330\pi$
$464$	−26.0916	−	16.5285i	−1.21127	−	0.767315i
$465$		0			0
$466$	15.6390	−	7.51365i	0.724462	−	0.348063i
$467$	−10.4295	+	10.4295i	−0.482620	+	0.482620i	−0.905967	−	0.423348i	$-0.860855\pi$
$467$	−10.4295	+	10.4295i	−0.482620	+	0.482620i	0.423348	+	0.905967i	$0.360855\pi$
$468$		0			0
$469$	6.78911	−	6.78911i	0.313492	−	0.313492i
$470$	18.0487	+	28.4032i	0.832524	+	1.31014i
$471$		0			0
$472$	18.5878	−	11.6081i	0.855571	−	0.534308i
$473$			7.32645i			0.336871i
$474$		0			0
$475$	−18.8413	+	30.7995i	−0.864497	+	1.41318i
$476$	9.24175	+	7.39786i	0.423595	+	0.339081i
$477$		0			0
$478$	7.60435	+	15.8278i	0.347815	+	0.723946i
$479$	−23.5450			−1.07580			−0.537900	−	0.843009i	$-0.680782\pi$
$479$	−23.5450			−1.07580			−0.537900	+	0.843009i	$0.680782\pi$
$480$		0			0
$481$	0.0584478			0.00266499
$482$	10.2251	+	21.2825i	0.465739	+	0.969393i
$483$		0			0
$484$	−13.7961	−	11.0436i	−0.627096	−	0.501980i
$485$	18.4180	−	2.18712i	0.836317	−	0.0993119i
$486$		0			0
$487$			15.4005i			0.697865i	0.937148	+	0.348932i	$0.113456\pi$
$487$			15.4005i			0.697865i	−0.937148	+	0.348932i	$0.886544\pi$
$488$	−9.91263	−	15.8728i	−0.448724	−	0.718527i
$489$		0			0
$490$	4.69311	−	2.98222i	0.212013	−	0.134723i
$491$	11.9089	−	11.9089i	0.537443	−	0.537443i	−0.385334	−	0.922777i	$-0.625914\pi$
$491$	11.9089	−	11.9089i	0.537443	−	0.537443i	0.922777	+	0.385334i	$0.125914\pi$
$492$		0			0
$493$	−10.9201	+	10.9201i	−0.491817	+	0.491817i
$494$	−0.101570	+	0.0487987i	−0.00456986	+	0.00219556i
$495$		0			0
$496$	−19.4827	+	4.37154i	−0.874798	+	0.196288i
$497$	−0.628336			−0.0281847
$498$		0			0
$499$	16.4502	−	16.4502i	0.736411	−	0.736411i	−0.235471	−	0.971881i	$-0.575663\pi$
$499$	16.4502	−	16.4502i	0.736411	−	0.736411i	0.971881	+	0.235471i	$0.0756631\pi$
$500$	−21.2224	−	7.04345i	−0.949094	−	0.314993i
$501$		0			0
$502$	−34.7092	−	12.1811i	−1.54915	−	0.543667i
$503$	11.4298			0.509632			0.254816	−	0.966990i	$-0.417985\pi$
$503$	11.4298			0.509632			0.254816	+	0.966990i	$0.417985\pi$
$504$		0			0
$505$	−15.5594	+	19.7527i	−0.692386	+	0.878985i
$506$	−12.7479	−	4.47383i	−0.566713	−	0.198886i
$507$		0			0
$508$	−0.677724	+	0.846643i	−0.0300691	+	0.0375637i
$509$	26.8748	−	26.8748i	1.19120	−	1.19120i	0.214473	−	0.976730i	$-0.431197\pi$
$509$	26.8748	−	26.8748i	1.19120	−	1.19120i	0.976730	−	0.214473i	$-0.0688034\pi$
$510$		0			0
$511$			48.8251i			2.15990i
$512$	17.5736	+	14.2537i	0.776650	+	0.629932i
$513$		0			0
$514$	18.3036	+	38.0974i	0.807339	+	1.68040i
$515$	−13.6477	+	1.62065i	−0.601390	+	0.0714145i
$516$		0			0
$517$	−11.0698	−	11.0698i	−0.486850	−	0.486850i
$518$	20.9183	+	7.34121i	0.919098	+	0.322554i
$519$		0			0
$520$	−0.0436883	−	0.0544207i	−0.00191586	−	0.00238651i
$521$	−18.0720			−0.791749			−0.395874	−	0.918305i	$-0.629558\pi$
$521$	−18.0720			−0.791749			−0.395874	+	0.918305i	$0.629558\pi$
$522$		0			0
$523$	10.2127	−	10.2127i	0.446571	−	0.446571i	−0.447642	−	0.894213i	$-0.647736\pi$
$523$	10.2127	−	10.2127i	0.446571	−	0.446571i	0.894213	+	0.447642i	$0.147736\pi$
$524$	−15.6099	+	1.72978i	−0.681922	+	0.0755657i
$525$		0			0
$526$	10.8180	+	22.5168i	0.471689	+	0.981778i
$527$			9.98371i			0.434897i
$528$		0			0
$529$	19.1711			0.833526
$530$	−2.89958	+	13.0080i	−0.125950	+	0.565030i
$531$		0			0
$532$	−42.4809	+	4.70743i	−1.84178	+	0.204093i
$533$	−0.0813369	+	0.0813369i	−0.00352309	+	0.00352309i
$534$		0			0
$535$	11.4265	−	14.5059i	0.494010	−	0.627147i
$536$	−4.86058	−	7.78310i	−0.209945	−	0.336179i
$537$		0			0
$538$	−0.0530249	−	0.0186089i	−0.00228607	−	0.000802287i
$539$	−1.82909	+	1.82909i	−0.0787844	+	0.0787844i
$540$		0			0
$541$	−4.93323	−	4.93323i	−0.212096	−	0.212096i	0.593061	−	0.805157i	$-0.297919\pi$
$541$	−4.93323	−	4.93323i	−0.212096	−	0.212096i	−0.805157	+	0.593061i	$0.797919\pi$
$542$	−17.5175	+	8.41618i	−0.752442	+	0.361506i
$543$		0			0
$544$	8.87785	−	7.01339i	0.380635	−	0.300697i
$545$	21.4652	−	27.2500i	0.919466	−	1.16726i
$546$		0			0
$547$	25.5794	+	25.5794i	1.09370	+	1.09370i	0.995130	+	0.0985674i	$0.0314260\pi$
$547$	25.5794	+	25.5794i	1.09370	+	1.09370i	0.0985674	+	0.995130i	$0.468574\pi$
$548$	−9.06173	−	7.25377i	−0.387098	−	0.309865i
$549$		0			0
$550$	10.3490	+	1.05014i	0.441283	+	0.0447782i
$551$		−	55.7581i		−	2.37538i
$552$		0			0
$553$	13.4606			0.572402
$554$	−15.2451	+	43.4401i	−0.647704	+	1.84559i
$555$		0			0
$556$	−17.6509	+	1.95595i	−0.748565	+	0.0829506i
$557$	−4.34156	−	4.34156i	−0.183958	−	0.183958i	0.609120	−	0.793078i	$-0.291523\pi$
$557$	−4.34156	−	4.34156i	−0.183958	−	0.183958i	−0.793078	+	0.609120i	$0.791523\pi$
$558$		0			0
$559$			0.0549545i			0.00232433i
$560$	−8.80052	−	24.9644i	−0.371890	−	1.05494i
$561$		0			0
$562$	11.8380	+	24.6396i	0.499354	+	1.03936i
$563$	−16.4606	+	16.4606i	−0.693731	+	0.693731i	−0.963051	−	0.269320i	$-0.913201\pi$
$563$	−16.4606	+	16.4606i	−0.693731	+	0.693731i	0.269320	+	0.963051i	$0.413201\pi$
$564$		0			0
$565$	2.62436	+	22.1000i	0.110408	+	0.929755i
$566$	−5.25594	−	1.84455i	−0.220924	−	0.0775324i
$567$		0			0
$568$	−0.135240	+	0.585090i	−0.00567457	+	0.0245499i
$569$	−27.5819			−1.15629			−0.578146	−	0.815933i	$-0.696224\pi$
$569$	−27.5819			−1.15629			−0.578146	+	0.815933i	$0.696224\pi$
$570$		0			0
$571$	4.33390	+	4.33390i	0.181368	+	0.181368i	0.791952	−	0.610584i	$-0.209065\pi$
$571$	4.33390	+	4.33390i	0.181368	+	0.181368i	−0.610584	+	0.791952i	$0.709065\pi$
$572$	0.0253449	+	0.0202882i	0.00105972	+	0.000848291i
$573$		0			0
$574$	−39.3264	+	18.8941i	−1.64145	+	0.788625i
$575$	−31.5666	+	7.60425i	−1.31642	+	0.317119i
$576$		0			0
$577$			32.4805i			1.35218i	0.736819	+	0.676090i	$0.236327\pi$
$577$			32.4805i			1.35218i	−0.736819	+	0.676090i	$0.763673\pi$
$578$	7.96156	+	16.5713i	0.331157	+	0.689274i
$579$		0			0
$580$	33.6339	−	7.82401i	1.39657	−	0.324874i
$581$	−13.8609	−	13.8609i	−0.575046	−	0.575046i
$582$		0			0
$583$		−	6.19979i		−	0.256769i
$584$	45.4647	+	10.5089i	1.88134	+	0.434862i
$585$		0			0
$586$	33.7548	+	11.8461i	1.39440	+	0.489360i
$587$	30.2712	+	30.2712i	1.24942	+	1.24942i	0.955975	+	0.293450i	$0.0948033\pi$
$587$	30.2712	+	30.2712i	1.24942	+	1.24942i	0.293450	+	0.955975i	$0.405197\pi$
$588$		0			0
$589$	−25.4884	−	25.4884i	−1.05023	−	1.05023i
$590$	−5.33072	+	23.9144i	−0.219462	+	0.984542i
$591$		0			0
$592$	11.3383	−	17.8985i	0.466002	−	0.735624i
$593$	38.4245			1.57790			0.788952	−	0.614455i	$-0.210624\pi$
$593$	38.4245			1.57790			0.788952	+	0.614455i	$0.210624\pi$
$594$		0			0
$595$	−13.1429	+	1.56071i	−0.538808	+	0.0639830i
$596$	35.5811	−	3.94284i	1.45746	−	0.161505i
$597$		0			0
$598$	−0.0956199	−	0.0335575i	−0.00391019	−	0.00137227i
$599$			20.1491i			0.823269i	0.911349	+	0.411635i	$0.135042\pi$
$599$			20.1491i			0.823269i	−0.911349	+	0.411635i	$0.864958\pi$
$600$		0			0
$601$		−	3.75831i		−	0.153305i	−0.997058	−	0.0766524i	$-0.975577\pi$
$601$		−	3.75831i		−	0.153305i	0.997058	−	0.0766524i	$-0.0244232\pi$
$602$	−6.90243	+	19.6681i	−0.281322	+	0.801610i
$603$		0			0
$604$	−21.4139	+	26.7513i	−0.871321	+	1.08849i
$605$	19.6198	−	2.32984i	0.797660	−	0.0947214i
$606$		0			0
$607$	−1.55683			−0.0631899			−0.0315949	−	0.999501i	$-0.510059\pi$
$607$	−1.55683			−0.0631899			−0.0315949	+	0.999501i	$0.510059\pi$
$608$	−4.75998	+	40.5703i	−0.193043	+	1.64534i
$609$		0			0
$610$	20.4214	+	4.55210i	0.826840	+	0.184309i
$611$	−0.0830329	−	0.0830329i	−0.00335915	−	0.00335915i
$612$		0			0
$613$	−19.5306	−	19.5306i	−0.788832	−	0.788832i	0.192471	−	0.981303i	$-0.438350\pi$
$613$	−19.5306	−	19.5306i	−0.788832	−	0.788832i	−0.981303	+	0.192471i	$0.938350\pi$
$614$	−15.5051	+	44.1808i	−0.625734	+	1.78299i
$615$		0			0
$616$	6.52262	+	10.4445i	0.262804	+	0.420819i
$617$		−	4.07636i		−	0.164108i	−0.996628	−	0.0820540i	$-0.973852\pi$
$617$		−	4.07636i		−	0.164108i	0.996628	−	0.0820540i	$-0.0261480\pi$
$618$		0			0
$619$	5.05003	+	5.05003i	0.202978	+	0.202978i	0.801275	−	0.598297i	$-0.204156\pi$
$619$	5.05003	+	5.05003i	0.202978	+	0.202978i	−0.598297	+	0.801275i	$0.704156\pi$
$620$	11.7983	−	18.9514i	0.473832	−	0.761107i
$621$		0			0
$622$	30.6425	−	14.7220i	1.22865	−	0.590298i
$623$			0.364290i			0.0145950i
$624$		0			0
$625$	22.2576	−	11.3841i	0.890305	−	0.455365i
$626$	10.8864	+	22.6592i	0.435110	+	0.905642i
$627$		0			0
$628$	−1.49603	−	13.5005i	−0.0596979	−	0.538727i
$629$	−7.49105	−	7.49105i	−0.298688	−	0.298688i
$630$		0			0
$631$	−0.782254			−0.0311411			−0.0155705	−	0.999879i	$-0.504956\pi$
$631$	−0.782254			−0.0311411			−0.0155705	+	0.999879i	$0.504956\pi$
$632$	2.89720	−	12.5341i	0.115244	−	0.498581i
$633$		0			0
$634$	3.10815	−	8.85648i	0.123440	−	0.351736i
$635$	−0.142978	−	1.20404i	−0.00567391	−	0.0477807i
$636$		0			0
$637$	−0.0137197	+	0.0137197i	−0.000543593	+	0.000543593i
$638$	−14.4797	+	6.95668i	−0.573257	+	0.275418i
$639$		0			0
$640$	−25.1404	+	2.82159i	−0.993761	+	0.111533i
$641$		−	2.92420i		−	0.115499i	−0.998331	−	0.0577495i	$-0.981608\pi$
$641$		−	2.92420i		−	0.115499i	0.998331	−	0.0577495i	$-0.0183925\pi$
$642$		0			0
$643$	30.2222	+	30.2222i	1.19185	+	1.19185i	0.976548	+	0.215301i	$0.0690732\pi$
$643$	30.2222	+	30.2222i	1.19185	+	1.19185i	0.215301	+	0.976548i	$0.430927\pi$
$644$	−30.0072	−	24.0202i	−1.18245	−	0.946530i
$645$		0			0
$646$	19.2723	+	6.76353i	0.758257	+	0.266108i
$647$	−48.8394			−1.92007			−0.960037	−	0.279871i	$-0.909708\pi$
$647$	−48.8394			−1.92007			−0.960037	+	0.279871i	$0.909708\pi$
$648$		0			0
$649$		−	11.3980i		−	0.447410i
$650$	0.0776261	+	0.00787693i	0.00304475	+	0.000308959i
$651$		0			0
$652$	2.18724	−	0.242374i	0.0856588	−	0.00949210i
$653$	4.18933	+	4.18933i	0.163941	+	0.163941i	0.784310	−	0.620369i	$-0.213017\pi$
$653$	4.18933	+	4.18933i	0.163941	+	0.163941i	−0.620369	+	0.784310i	$0.713017\pi$
$654$		0			0
$655$	10.8655	−	13.7938i	0.424550	−	0.538967i
$656$	9.12925	+	40.6864i	0.356437	+	1.58854i
$657$		0			0
$658$	−19.2881	−	40.1464i	−0.751928	−	1.56507i
$659$	−13.0512	−	13.0512i	−0.508402	−	0.508402i	0.405634	−	0.914036i	$-0.367051\pi$
$659$	−13.0512	−	13.0512i	−0.508402	−	0.508402i	−0.914036	+	0.405634i	$0.867051\pi$
$660$		0			0
$661$	8.41832	−	8.41832i	0.327435	−	0.327435i	−0.524175	−	0.851610i	$-0.675626\pi$
$661$	8.41832	−	8.41832i	0.327435	−	0.327435i	0.851610	+	0.524175i	$0.175626\pi$
$662$	13.3497	−	38.0391i	0.518850	−	1.47843i
$663$		0			0
$664$	−15.8902	+	9.92352i	−0.616660	+	0.385107i
$665$	29.5694	−	37.5384i	1.14665	−	1.45568i
$666$		0			0
$667$	35.4567	−	35.4567i	1.37289	−	1.37289i
$668$	6.58219	−	8.22277i	0.254673	−	0.318149i
$669$		0			0
$670$	10.0135	+	2.23209i	0.386855	+	0.0862330i
$671$	−9.73317			−0.375745
$672$		0			0
$673$		−	8.96622i		−	0.345622i	−0.984955	−	0.172811i	$-0.944715\pi$
$673$		−	8.96622i		−	0.345622i	0.984955	−	0.172811i	$-0.0552850\pi$
$674$	−28.7821	+	13.8282i	−1.10865	+	0.532642i
$675$		0			0
$676$	−20.2976	−	16.2479i	−0.780677	−	0.624919i
$677$	16.5376	−	16.5376i	0.635590	−	0.635590i	−0.313874	−	0.949464i	$-0.601627\pi$
$677$	16.5376	−	16.5376i	0.635590	−	0.635590i	0.949464	+	0.313874i	$0.101627\pi$
$678$		0			0
$679$	−24.5476			−0.942051
$680$	−1.37554	+	12.5743i	−0.0527495	+	0.482202i
$681$		0			0
$682$	−3.43896	+	9.79910i	−0.131685	+	0.375227i
$683$	3.42707	+	3.42707i	0.131133	+	0.131133i	0.769627	−	0.638494i	$-0.220442\pi$
$683$	3.42707	+	3.42707i	0.131133	+	0.131133i	−0.638494	+	0.769627i	$0.720442\pi$
$684$		0			0
$685$	12.8869	−	1.53031i	0.492385	−	0.0584702i
$686$	19.7740	−	9.50029i	0.754974	−	0.362723i
$687$		0			0
$688$	16.8287	+	10.6606i	0.641589	+	0.406433i
$689$		−	0.0465036i		−	0.00177165i
$690$		0			0
$691$	18.7477	−	18.7477i	0.713195	−	0.713195i	−0.254008	−	0.967202i	$-0.581749\pi$
$691$	18.7477	−	18.7477i	0.713195	−	0.713195i	0.967202	+	0.254008i	$0.0817489\pi$
$692$	−23.9483	+	2.65377i	−0.910376	+	0.100881i
$693$		0			0
$694$	5.70751	−	16.2632i	0.216654	−	0.617343i
$695$	12.2862	−	15.5973i	0.466040	−	0.591639i
$696$		0			0
$697$	20.8493			0.789725
$698$	7.61269	−	21.6919i	0.288145	−	0.821050i
$699$		0			0
$700$	26.7928	+	12.5692i	1.01267	+	0.475070i
$701$	−28.2156	+	28.2156i	−1.06569	+	1.06569i	−0.0680026	+	0.997685i	$0.521663\pi$
$701$	−28.2156	+	28.2156i	−1.06569	+	1.06569i	−0.997685	+	0.0680026i	$0.978337\pi$
$702$		0			0
$703$	38.2493			1.44260
$704$	11.1295	−	3.82567i	0.419459	−	0.144185i
$705$		0			0
$706$	10.5554	+	21.9701i	0.397258	+	0.826857i
$707$	23.5322	−	23.5322i	0.885018	−	0.885018i
$708$		0			0
$709$	10.7577	−	10.7577i	0.404013	−	0.404013i	−0.475631	−	0.879645i	$-0.657780\pi$
$709$	10.7577	−	10.7577i	0.404013	−	0.404013i	0.879645	+	0.475631i	$0.157780\pi$
$710$	−0.360087	−	0.566668i	−0.0135138	−	0.0212667i
$711$		0			0
$712$	0.339217	+	0.0784082i	0.0127127	+	0.00293847i
$713$		−	32.4162i		−	1.21400i
$714$		0			0
$715$	−0.0360437	+	0.00428015i	−0.00134796	+	0.000160069i
$716$	−28.8092	+	3.19242i	−1.07665	+	0.119307i
$717$		0			0
$718$	−2.89547	+	1.39111i	−0.108058	+	0.0519158i
$719$	1.68057			0.0626748			0.0313374	−	0.999509i	$-0.490023\pi$
$719$	1.68057			0.0626748			0.0313374	+	0.999509i	$0.490023\pi$
$720$		0			0
$721$	18.1898			0.677422
$722$	−42.2496	+	20.2985i	−1.57237	+	0.755433i
$723$		0			0
$724$	−0.184023	−	1.66067i	−0.00683916	−	0.0617182i
$725$	−20.1471	+	32.9342i	−0.748246	+	1.22314i
$726$		0			0
$727$			33.3069i			1.23528i	0.786460	+	0.617641i	$0.211912\pi$
$727$			33.3069i			1.23528i	−0.786460	+	0.617641i	$0.788088\pi$
$728$	0.0489250	+	0.0783422i	0.00181328	+	0.00290355i
$729$		0			0
$730$	−44.0332	+	27.9807i	−1.62974	+	1.03561i
$731$	7.04332	−	7.04332i	0.260507	−	0.260507i
$732$		0			0
$733$	9.28476	−	9.28476i	0.342941	−	0.342941i	−0.514531	−	0.857472i	$-0.672034\pi$
$733$	9.28476	−	9.28476i	0.342941	−	0.342941i	0.857472	+	0.514531i	$0.172034\pi$
$734$	19.0672	+	39.6867i	0.703784	+	1.46486i
$735$		0			0
$736$	−28.8256	+	22.7719i	−1.06253	+	0.839382i
$737$	−4.77258			−0.175800
$738$		0			0
$739$	−24.0117	+	24.0117i	−0.883286	+	0.883286i	−0.993867	−	0.110581i	$-0.964729\pi$
$739$	−24.0117	+	24.0117i	−0.883286	+	0.883286i	0.110581	+	0.993867i	$0.464729\pi$
$740$	5.36717	+	23.0724i	0.197301	+	0.848158i
$741$		0			0
$742$	5.84098	−	16.6435i	0.214429	−	0.611002i
$743$	25.5380			0.936897			0.468448	−	0.883491i	$-0.344813\pi$
$743$	25.5380			0.936897			0.468448	+	0.883491i	$0.344813\pi$
$744$		0			0
$745$	−24.7667	+	31.4414i	−0.907382	+	1.15192i
$746$	13.4577	−	38.3469i	0.492722	−	1.40398i
$747$		0			0
$748$	−0.648103	−	5.84863i	−0.0236970	−	0.213847i
$749$	−17.2815	+	17.2815i	−0.631451	+	0.631451i
$750$		0			0
$751$			38.6627i			1.41082i	0.708799	+	0.705411i	$0.249238\pi$
$751$			38.6627i			1.41082i	−0.708799	+	0.705411i	$0.750762\pi$
$752$	−41.5348	+	9.31961i	−1.51462	+	0.339851i
$753$		0			0
$754$	−0.108610	+	0.0521809i	−0.00395534	+	0.00190032i
$755$	−4.51766	−	38.0437i	−0.164414	−	1.38455i
$756$		0			0
$757$	−28.0622	−	28.0622i	−1.01994	−	1.01994i	−0.999797	−	0.0201412i	$-0.993588\pi$
$757$	−28.0622	−	28.0622i	−1.01994	−	1.01994i	−0.0201412	−	0.999797i	$-0.506412\pi$
$758$	−6.36812	+	18.1455i	−0.231300	+	0.659076i
$759$		0			0
$760$	−28.5904	−	35.6139i	−1.03708	−	1.29185i
$761$	12.1544			0.440597			0.220299	−	0.975432i	$-0.429297\pi$
$761$	12.1544			0.440597			0.220299	+	0.975432i	$0.429297\pi$
$762$		0			0
$763$	−32.4640	+	32.4640i	−1.17528	+	1.17528i
$764$	−19.0035	+	23.7400i	−0.687521	+	0.858882i
$765$		0			0
$766$	1.50097	−	0.721132i	0.0542323	−	0.0260556i
$767$		−	0.0854944i		−	0.00308702i
$768$		0			0
$769$	−0.0426731			−0.00153883			−0.000769416	−	1.00000i	$-0.500245\pi$
$769$	−0.0426731			−0.00153883			−0.000769416		1.00000i	$0.500245\pi$
$770$	−13.4375	−	2.99533i	−0.484255	−	0.107944i
$771$		0			0
$772$	19.4042	+	15.5328i	0.698374	+	0.559037i
$773$	4.96973	−	4.96973i	0.178749	−	0.178749i	−0.612061	−	0.790810i	$-0.709659\pi$
$773$	4.96973	−	4.96973i	0.178749	−	0.178749i	0.790810	+	0.612061i	$0.209659\pi$
$774$		0			0
$775$	5.84526	+	24.2648i	0.209968	+	0.871616i
$776$	−5.28353	+	22.8581i	−0.189667	+	0.820558i
$777$		0			0
$778$	15.7604	−	44.9082i	0.565037	−	1.61004i
$779$	−53.2283	+	53.2283i	−1.90710	+	1.90710i
$780$		0			0
$781$	0.220853	+	0.220853i	0.00790274	+	0.00790274i
$782$	7.95432	+	16.5562i	0.284446	+	0.592049i
$783$		0			0
$784$	1.53990	+	6.86286i	0.0549963	+	0.245102i
$785$	11.9297	+	9.39719i	0.425791	+	0.335400i
$786$		0			0
$787$	16.8577	+	16.8577i	0.600911	+	0.600911i	0.940554	−	0.339643i	$-0.110306\pi$
$787$	16.8577	+	16.8577i	0.600911	+	0.600911i	−0.339643	+	0.940554i	$0.610306\pi$
$788$	2.34951	+	21.2025i	0.0836978	+	0.755308i
$789$		0			0
$790$	7.71399	+	12.1395i	0.274451	+	0.431904i
$791$		−	29.4551i		−	1.04730i
$792$		0			0
$793$	−0.0730069			−0.00259255
$794$	11.1040	+	3.89690i	0.394065	+	0.138296i
$795$		0			0
$796$	−12.5273	+	15.6497i	−0.444020	+	0.554689i
$797$	0.0286009	+	0.0286009i	0.00101310	+	0.00101310i	0.707613	−	0.706600i	$-0.249772\pi$
$797$	0.0286009	+	0.0286009i	0.00101310	+	0.00101310i	−0.706600	+	0.707613i	$0.749772\pi$
$798$		0			0
$799$			21.2841i			0.752976i
$800$	17.4709	−	22.2434i	0.617688	−	0.786423i
$801$		0			0
$802$	19.6860	−	9.45801i	0.695136	−	0.333974i
$803$	17.1615	−	17.1615i	0.605614	−	0.605614i
$804$		0			0
$805$	42.6740	−	5.06750i	1.50406	−	0.178606i
$806$	−0.0257951	+	0.0735014i	−0.000908593	+	0.00258898i
$807$		0			0
$808$	−16.8476	−	26.9775i	−0.592695	−	0.949065i
$809$	1.19014			0.0418431			0.0209216	−	0.999781i	$-0.493340\pi$
$809$	1.19014			0.0418431			0.0209216	+	0.999781i	$0.493340\pi$
$810$		0			0
$811$	13.9807	+	13.9807i	0.490928	+	0.490928i	0.908598	−	0.417671i	$-0.137153\pi$
$811$	13.9807	+	13.9807i	0.490928	+	0.490928i	−0.417671	+	0.908598i	$0.637153\pi$
$812$	−45.4252	+	5.03370i	−1.59411	+	0.176648i
$813$		0			0
$814$	−4.77219	−	9.93289i	−0.167265	−	0.348148i
$815$	−1.52246	+	1.93276i	−0.0533294	+	0.0677017i
$816$		0			0
$817$			35.9632i			1.25819i
$818$	−11.1226	+	5.34377i	−0.388892	+	0.186840i
$819$		0			0
$820$	−39.5769	−	24.6389i	−1.38209	−	0.860426i
$821$	13.0285	+	13.0285i	0.454699	+	0.454699i	0.896911	−	0.442212i	$-0.145806\pi$
$821$	13.0285	+	13.0285i	0.454699	+	0.454699i	−0.442212	+	0.896911i	$0.645806\pi$
$822$		0			0
$823$		−	44.1886i		−	1.54032i	−0.637851	−	0.770160i	$-0.720177\pi$
$823$		−	44.1886i		−	1.54032i	0.637851	−	0.770160i	$-0.279823\pi$
$824$	3.91509	−	16.9378i	0.136389	−	0.590058i
$825$		0			0
$826$	10.7383	−	30.5982i	0.373634	−	1.06465i
$827$	−14.3077	−	14.3077i	−0.497528	−	0.497528i	0.413139	−	0.910668i	$-0.364432\pi$
$827$	−14.3077	−	14.3077i	−0.497528	−	0.497528i	−0.910668	+	0.413139i	$0.864432\pi$
$828$		0			0
$829$	−1.86701	−	1.86701i	−0.0648439	−	0.0648439i	0.673941	−	0.738785i	$-0.264600\pi$
$829$	−1.86701	−	1.86701i	−0.0648439	−	0.0648439i	−0.738785	+	0.673941i	$0.764600\pi$
$830$	4.55710	−	20.4439i	0.158179	−	0.709618i
$831$		0			0
$832$	0.0834806	−	0.0286957i	0.00289417	−	0.000994844i
$833$	3.51681			0.121850
$834$		0			0
$835$	1.38863	+	11.6938i	0.0480556	+	0.404682i
$836$	16.5862	+	13.2769i	0.573644	+	0.459193i
$837$		0			0
$838$	−3.19943	+	9.11659i	−0.110523	+	0.314927i
$839$			11.8696i			0.409786i	0.978784	+	0.204893i	$0.0656846\pi$
$839$			11.8696i			0.409786i	−0.978784	+	0.204893i	$0.934315\pi$
$840$		0			0
$841$		−	30.6226i		−	1.05595i
$842$	−38.2037	−	13.4075i	−1.31659	−	0.462051i
$843$		0			0
$844$	−4.98275	−	44.9654i	−0.171513	−	1.54777i
$845$	28.8658	−	3.42779i	0.993014	−	0.117919i
$846$		0			0
$847$	−26.1495			−0.898507
$848$	−14.2408	−	9.02124i	−0.489031	−	0.309791i
$849$		0			0
$850$	−8.93950	−	10.9586i	−0.306622	−	0.375878i
$851$	24.3228	+	24.3228i	0.833775	+	0.833775i
$852$		0			0
$853$	11.7299	+	11.7299i	0.401626	+	0.401626i	0.878806	−	0.477180i	$-0.158341\pi$
$853$	11.7299	+	11.7299i	0.401626	+	0.401626i	−0.477180	+	0.878806i	$0.658341\pi$
$854$	−26.1289	−	9.16986i	−0.894114	−	0.313786i
$855$		0			0
$856$	12.3725	+	19.8116i	0.422882	+	0.677148i
$857$			19.0655i			0.651266i	0.945496	+	0.325633i	$0.105577\pi$
$857$			19.0655i			0.651266i	−0.945496	+	0.325633i	$0.894423\pi$
$858$		0			0
$859$	−22.2411	−	22.2411i	−0.758858	−	0.758858i	0.217256	−	0.976115i	$-0.430289\pi$
$859$	−22.2411	−	22.2411i	−0.758858	−	0.758858i	−0.976115	+	0.217256i	$0.930289\pi$
$860$	−21.6934	+	5.04638i	−0.739738	+	0.172080i
$861$		0			0
$862$	−4.06373	−	8.45829i	−0.138411	−	0.288091i
$863$			39.9598i			1.36025i	0.733097	+	0.680124i	$0.238074\pi$
$863$			39.9598i			1.36025i	−0.733097	+	0.680124i	$0.761926\pi$
$864$		0			0
$865$	16.6695	−	21.1620i	0.566781	−	0.719529i
$866$	−2.77829	+	1.33481i	−0.0944103	+	0.0453588i
$867$		0			0
$868$	−18.4640	+	23.0660i	−0.626708	+	0.782912i
$869$	−4.73123	−	4.73123i	−0.160496	−	0.160496i
$870$		0			0
$871$	−0.0357983			−0.00121298
$872$	23.2422	+	37.2170i	0.787081	+	1.26033i
$873$		0			0
$874$	−62.5754	−	21.9606i	−2.11664	−	0.742829i
$875$	−31.0293	+	11.4882i	−1.04898	+	0.388370i
$876$		0			0
$877$	24.1486	−	24.1486i	0.815442	−	0.815442i	−0.170002	−	0.985444i	$-0.554377\pi$
$877$	24.1486	−	24.1486i	0.815442	−	0.815442i	0.985444	+	0.170002i	$0.0543774\pi$
$878$	11.1337	+	23.1739i	0.375746	+	0.782081i
$879$		0			0
$880$	−5.68141	+	11.8680i	−0.191520	+	0.400069i
$881$		−	31.7726i		−	1.07045i	−0.844711	−	0.535223i	$-0.820228\pi$
$881$		−	31.7726i		−	1.07045i	0.844711	−	0.535223i	$-0.179772\pi$
$882$		0			0
$883$	1.59278	+	1.59278i	0.0536012	+	0.0536012i	0.733399	−	0.679798i	$-0.237933\pi$
$883$	1.59278	+	1.59278i	0.0536012	+	0.0536012i	−0.679798	+	0.733399i	$0.737933\pi$
$884$	−0.00486131	−	0.0438696i	−0.000163504	−	0.00147549i
$885$		0			0
$886$	−13.3680	+	38.0911i	−0.449105	+	1.27970i
$887$	8.63569			0.289958			0.144979	−	0.989435i	$-0.453689\pi$
$887$	8.63569			0.289958			0.144979	+	0.989435i	$0.453689\pi$
$888$		0			0
$889$			1.60475i			0.0538215i
$890$	−0.328537	+	0.208767i	−0.0110126	+	0.00699790i
$891$		0			0
$892$	−33.6973	+	42.0962i	−1.12827	+	1.40948i
$893$	−54.3382	−	54.3382i	−1.81836	−	1.81836i
$894$		0			0
$895$	20.0530	−	25.4573i	0.670298	−	0.850944i
$896$	33.4817	+	0.215291i	1.11855	+	0.00719238i
$897$		0			0
$898$	39.9506	−	19.1940i	1.33317	−	0.640512i
$899$	−27.2550	−	27.2550i	−0.909004	−	0.909004i
$900$		0			0
$901$	−5.96020	+	5.96020i	−0.198563	+	0.198563i
$902$	20.4638	+	7.18171i	0.681371	+	0.239125i
$903$		0			0
$904$	−27.4278	−	6.33979i	−0.912235	−	0.210858i
$905$	1.46745	+	1.15593i	0.0487798	+	0.0384244i
$906$		0			0
$907$	12.8316	−	12.8316i	0.426068	−	0.426068i	−0.461219	−	0.887286i	$-0.652588\pi$
$907$	12.8316	−	12.8316i	0.426068	−	0.426068i	0.887286	+	0.461219i	$0.152588\pi$
$908$	−1.49661	−	13.5057i	−0.0496667	−	0.448203i
$909$		0			0
$910$	−0.100793	−	0.0224675i	−0.00334124	−	0.000744789i
$911$	52.5129			1.73983			0.869915	−	0.493202i	$-0.164174\pi$
$911$	52.5129			1.73983			0.869915	+	0.493202i	$0.164174\pi$
$912$		0			0
$913$			9.74386i			0.322475i
$914$	9.56693	+	19.9127i	0.316446	+	0.658653i
$915$		0			0
$916$	−1.17533	−	10.6064i	−0.0388340	−	0.350446i
$917$	−16.4330	+	16.4330i	−0.542666	+	0.542666i
$918$		0			0
$919$	43.7005			1.44155			0.720773	−	0.693172i	$-0.243787\pi$
$919$	43.7005			1.44155			0.720773	+	0.693172i	$0.243787\pi$
$920$	4.46625	−	40.8276i	0.147248	−	1.34605i
$921$		0			0
$922$	18.8470	+	6.61430i	0.620694	+	0.217830i
$923$	0.00165658	+	0.00165658i	5.45270e−5	+	5.45270e-5i
$924$		0			0
$925$	−22.5924	−	13.8207i	−0.742833	−	0.454421i
$926$	−17.0329	−	35.4525i	−0.559737	−	1.16504i
$927$		0			0
$928$	−5.08989	+	43.3822i	−0.167084	+	1.42409i
$929$		−	11.4938i		−	0.377099i	−0.982064	−	0.188550i	$-0.939621\pi$
$929$		−	11.4938i		−	0.377099i	0.982064	−	0.188550i	$-0.0603786\pi$
$930$		0			0
$931$	−8.97840	+	8.97840i	−0.294255	+	0.294255i
$932$	−19.1557	−	15.3338i	−0.627465	−	0.502275i
$933$		0			0
$934$	19.6821	+	6.90737i	0.644019	+	0.226016i
$935$	5.16816	+	4.07102i	0.169017	+	0.133137i
$936$		0			0
$937$	53.9308			1.76184			0.880922	−	0.473261i	$-0.156923\pi$
$937$	53.9308			1.76184			0.880922	+	0.473261i	$0.156923\pi$
$938$	−12.8121	−	4.49637i	−0.418331	−	0.146812i
$939$		0			0
$940$	25.1526	−	40.4022i	0.820388	−	1.31777i
$941$	−6.98130	+	6.98130i	−0.227584	+	0.227584i	−0.811683	−	0.584099i	$-0.801448\pi$
$941$	−6.98130	+	6.98130i	−0.227584	+	0.227584i	0.584099	+	0.811683i	$0.301448\pi$
$942$		0			0
$943$	−67.6960			−2.20448
$944$	−26.1810	−	16.5851i	−0.852118	−	0.539798i
$945$		0			0
$946$	9.33922	−	4.48697i	0.303644	−	0.145884i
$947$	5.16523	−	5.16523i	0.167847	−	0.167847i	−0.618185	−	0.786032i	$-0.712132\pi$
$947$	5.16523	−	5.16523i	0.167847	−	0.167847i	0.786032	+	0.618185i	$0.212132\pi$
$948$		0			0
$949$	0.128725	−	0.128725i	0.00417860	−	0.00417860i
$950$	50.7999	+	5.15481i	1.64817	+	0.167244i
$951$		0			0
$952$	3.77029	−	16.3114i	0.122196	−	0.528655i
$953$			20.7891i			0.673424i	0.941608	+	0.336712i	$0.109315\pi$
$953$			20.7891i			0.673424i	−0.941608	+	0.336712i	$0.890685\pi$
$954$		0			0
$955$	−4.00912	−	33.7613i	−0.129732	−	1.09249i
$956$	15.5189	−	19.3869i	0.501917	−	0.627018i
$957$		0			0
$958$	14.4198	+	30.0134i	0.465881	+	0.969690i
$959$	−17.1758			−0.554636
$960$		0			0
$961$	6.08216			0.196199
$962$	−0.0357954	−	0.0745050i	−0.00115409	−	0.00240214i
$963$		0			0
$964$	20.8672	−	26.0683i	0.672088	−	0.839603i
$965$	−27.5953	+	3.27692i	−0.888325	+	0.105488i
$966$		0			0
$967$			50.2701i			1.61658i	0.588786	+	0.808289i	$0.299606\pi$
$967$			50.2701i			1.61658i	−0.588786	+	0.808289i	$0.700394\pi$
$968$	−5.62830	+	24.3497i	−0.180901	+	0.782629i
$969$		0			0
$970$	−14.0678	−	22.1384i	−0.451688	−	0.710821i
$971$	19.7427	−	19.7427i	0.633574	−	0.633574i	−0.315388	−	0.948963i	$-0.602135\pi$
$971$	19.7427	−	19.7427i	0.633574	−	0.633574i	0.948963	+	0.315388i	$0.102135\pi$
$972$		0			0
$973$	−18.5816	+	18.5816i	−0.595700	+	0.595700i
$974$	19.6315	−	9.43181i	0.629032	−	0.302215i
$975$		0			0
$976$	−14.1626	+	22.3569i	−0.453334	+	0.715627i
$977$	−29.6872			−0.949779			−0.474889	−	0.880045i	$-0.657512\pi$
$977$	−29.6872			−0.949779			−0.474889	+	0.880045i	$0.657512\pi$
$978$		0			0
$979$	0.128044	−	0.128044i	0.00409229	−	0.00409229i
$980$	−6.67572	−	4.15601i	−0.213248	−	0.132759i
$981$		0			0
$982$	−22.4741	−	7.88719i	−0.717176	−	0.251690i
$983$	0.250996			0.00800552			0.00400276	−	0.999992i	$-0.498726\pi$
$983$	0.250996			0.00800552			0.00400276	+	0.999992i	$0.498726\pi$
$984$		0			0
$985$	−18.7357	−	14.7583i	−0.596968	−	0.470238i
$986$	20.6080	+	7.23230i	0.656292	+	0.230323i
$987$		0			0
$988$	0.124410	+	0.0995881i	0.00395801	+	0.00316832i
$989$	−22.8691	+	22.8691i	−0.727194	+	0.727194i
$990$		0			0
$991$			33.2980i			1.05775i	0.848701	+	0.528873i	$0.177385\pi$
$991$			33.2980i			1.05775i	−0.848701	+	0.528873i	$0.822615\pi$
$992$	17.5044	+	22.1578i	0.555764	+	0.703511i
$993$		0			0
$994$	0.384814	+	0.800956i	0.0122056	+	0.0254048i
$995$	−2.64287	−	22.2559i	−0.0837845	−	0.705559i
$996$		0			0
$997$	−14.4987	−	14.4987i	−0.459180	−	0.459180i	0.439207	−	0.898386i	$-0.355260\pi$
$997$	−14.4987	−	14.4987i	−0.459180	−	0.459180i	−0.898386	+	0.439207i	$0.855260\pi$
$998$	−31.0441	−	10.8948i	−0.982684	−	0.344869i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.u.a.179.17	✓	96
3.2	odd	2	inner	720.2.u.a.179.32	yes	96
4.3	odd	2		2880.2.u.a.2159.23		96
5.4	even	2	inner	720.2.u.a.179.31	yes	96
12.11	even	2		2880.2.u.a.2159.26		96
15.14	odd	2	inner	720.2.u.a.179.18	yes	96
16.5	even	4		2880.2.u.a.719.47		96
16.11	odd	4	inner	720.2.u.a.539.18	yes	96
20.19	odd	2		2880.2.u.a.2159.2		96
48.5	odd	4		2880.2.u.a.719.2		96
48.11	even	4	inner	720.2.u.a.539.31	yes	96
60.59	even	2		2880.2.u.a.2159.47		96
80.59	odd	4	inner	720.2.u.a.539.32	yes	96
80.69	even	4		2880.2.u.a.719.26		96
240.59	even	4	inner	720.2.u.a.539.17	yes	96
240.149	odd	4		2880.2.u.a.719.23		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.17	✓	96	1.1	even	1	trivial
720.2.u.a.179.18	yes	96	15.14	odd	2	inner
720.2.u.a.179.31	yes	96	5.4	even	2	inner
720.2.u.a.179.32	yes	96	3.2	odd	2	inner
720.2.u.a.539.17	yes	96	240.59	even	4	inner
720.2.u.a.539.18	yes	96	16.11	odd	4	inner
720.2.u.a.539.31	yes	96	48.11	even	4	inner
720.2.u.a.539.32	yes	96	80.59	odd	4	inner
2880.2.u.a.719.2		96	48.5	odd	4
2880.2.u.a.719.23		96	240.149	odd	4
2880.2.u.a.719.26		96	80.69	even	4
2880.2.u.a.719.47		96	16.5	even	4
2880.2.u.a.2159.2		96	20.19	odd	2
2880.2.u.a.2159.23		96	4.3	odd	2
2880.2.u.a.2159.26		96	12.11	even	2
2880.2.u.a.2159.47		96	60.59	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.612434 - 1.27473i) q^{2} +(-1.24985 + 1.56137i) q^{4} +(-0.263678 - 2.22047i) q^{5} +2.95946i q^{7} +(2.75577 + 0.636981i) q^{8} +O(q^{10})\)	\(q+(-0.612434 - 1.27473i) q^{2} +(-1.24985 + 1.56137i) q^{4} +(-0.263678 - 2.22047i) q^{5} +2.95946i q^{7} +(2.75577 + 0.636981i) q^{8} +(-2.66900 + 1.69601i) q^{10} +(1.04021 - 1.04021i) q^{11} +(0.00780247 - 0.00780247i) q^{13} +(3.77249 - 1.81247i) q^{14} +(-0.875749 - 3.90296i) q^{16} -2.00003 q^{17} +(5.10608 - 5.10608i) q^{19} +(3.79653 + 2.36355i) q^{20} +(-1.96305 - 0.688925i) q^{22} +6.49393 q^{23} +(-4.86095 + 1.17098i) q^{25} +(-0.0147245 - 0.00516751i) q^{26} +(-4.62080 - 3.69888i) q^{28} +(5.45997 - 5.45997i) q^{29} -4.99178i q^{31} +(-4.43886 + 3.50664i) q^{32} +(1.22489 + 2.54949i) q^{34} +(6.57137 - 0.780345i) q^{35} +(3.74547 + 3.74547i) q^{37} +(-9.63598 - 3.38171i) q^{38} +(0.687758 - 6.28705i) q^{40} -10.4245 q^{41} +(-3.52161 + 3.52161i) q^{43} +(0.324047 + 2.92427i) q^{44} +(-3.97710 - 8.27798i) q^{46} -10.6419i q^{47} -1.75838 q^{49} +(4.46968 + 5.47923i) q^{50} +(0.00243062 + 0.0219345i) q^{52} +(2.98006 - 2.98006i) q^{53} +(-2.58404 - 2.03548i) q^{55} +(-1.88512 + 8.15557i) q^{56} +(-10.3038 - 3.61610i) q^{58} +(5.47867 - 5.47867i) q^{59} +(-4.67845 - 4.67845i) q^{61} +(-6.36315 + 3.05713i) q^{62} +(7.18851 + 3.51074i) q^{64} +(-0.0193825 - 0.0152678i) q^{65} +(-2.29404 - 2.29404i) q^{67} +(2.49974 - 3.12279i) q^{68} +(-5.01925 - 7.89879i) q^{70} +0.212315i q^{71} +16.4980 q^{73} +(2.48059 - 7.06830i) q^{74} +(1.59064 + 14.3543i) q^{76} +(3.07847 + 3.07847i) q^{77} -4.54833i q^{79} +(-8.43547 + 2.97370i) q^{80} +(6.38432 + 13.2884i) q^{82} +(-4.68359 + 4.68359i) q^{83} +(0.527365 + 4.44100i) q^{85} +(6.64583 + 2.33233i) q^{86} +(3.52918 - 2.20399i) q^{88} +0.123094 q^{89} +(0.0230911 + 0.0230911i) q^{91} +(-8.11644 + 10.1394i) q^{92} +(-13.5655 + 6.51744i) q^{94} +(-12.6842 - 9.99152i) q^{95} +8.29464i q^{97} +(1.07689 + 2.24145i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) \) 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

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