LMFDB - Embedded newform 1776.2.q.h.1009.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1776,2,Mod(433,1776)] 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("1776.433"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1776, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1776 = 2^{4} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1776.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2,0,-1,0,3,0,-2,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$14.1814313990$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 222)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1009.2
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	1776.1009
Dual form			1776.2.q.h.433.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{3} +(1.18614 + 2.05446i) q^{5} +(-0.686141 - 1.18843i) q^{7} +(-0.500000 + 0.866025i) q^{9} -2.00000 q^{11} +(-0.686141 - 1.18843i) q^{13} +(1.18614 - 2.05446i) q^{15} +(0.813859 - 1.40965i) q^{17} +(2.37228 + 4.10891i) q^{19} +(-0.686141 + 1.18843i) q^{21} +(-0.313859 + 0.543620i) q^{25} +1.00000 q^{27} +4.37228 q^{29} +9.37228 q^{31} +(1.00000 + 1.73205i) q^{33} +(1.62772 - 2.81929i) q^{35} +(-2.55842 - 5.51856i) q^{37} +(-0.686141 + 1.18843i) q^{39} +(2.18614 + 3.78651i) q^{41} +9.37228 q^{43} -2.37228 q^{45} -2.00000 q^{47} +(2.55842 - 4.43132i) q^{49} -1.62772 q^{51} +(-5.74456 + 9.94987i) q^{53} +(-2.37228 - 4.10891i) q^{55} +(2.37228 - 4.10891i) q^{57} +(-2.00000 + 3.46410i) q^{59} +(4.55842 + 7.89542i) q^{61} +1.37228 q^{63} +(1.62772 - 2.81929i) q^{65} +(2.05842 + 3.56529i) q^{67} +(5.74456 + 9.94987i) q^{71} +2.62772 q^{73} +0.627719 q^{75} +(1.37228 + 2.37686i) q^{77} +(0.686141 + 1.18843i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(4.00000 - 6.92820i) q^{83} +3.86141 q^{85} +(-2.18614 - 3.78651i) q^{87} +(-1.81386 + 3.14170i) q^{89} +(-0.941578 + 1.63086i) q^{91} +(-4.68614 - 8.11663i) q^{93} +(-5.62772 + 9.74749i) q^{95} +5.74456 q^{97} +(1.00000 - 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - q^{5} + 3 q^{7} - 2 q^{9} - 8 q^{11} + 3 q^{13} - q^{15} + 9 q^{17} - 2 q^{19} + 3 q^{21} - 7 q^{25} + 4 q^{27} + 6 q^{29} + 26 q^{31} + 4 q^{33} + 18 q^{35} + 7 q^{37} + 3 q^{39} + 3 q^{41}+ \cdots + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - q^5 + 3 * q^7 - 2 * q^9 - 8 * q^11 + 3 * q^13 - q^15 + 9 * q^17 - 2 * q^19 + 3 * q^21 - 7 * q^25 + 4 * q^27 + 6 * q^29 + 26 * q^31 + 4 * q^33 + 18 * q^35 + 7 * q^37 + 3 * q^39 + 3 * q^41 + 26 * q^43 + 2 * q^45 - 8 * q^47 - 7 * q^49 - 18 * q^51 + 2 * q^55 - 2 * q^57 - 8 * q^59 + q^61 - 6 * q^63 + 18 * q^65 - 9 * q^67 + 22 * q^73 + 14 * q^75 - 6 * q^77 - 3 * q^79 - 2 * q^81 + 16 * q^83 - 42 * q^85 - 3 * q^87 - 13 * q^89 - 21 * q^91 - 13 * q^93 - 34 * q^95 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1776\mathbb{Z}\right)^\times$.

$n$	$223$	$593$	$1297$	$1333$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$	1.18614	+	2.05446i	0.530458	+	0.918781i	0.999368	+	0.0355348i	$0.0113134\pi$
$5$	1.18614	+	2.05446i	0.530458	+	0.918781i	−0.468910	+	0.883246i	$0.655353\pi$
$6$		0			0
$7$	−0.686141	−	1.18843i	−0.259337	−	0.449185i	0.706728	−	0.707486i	$-0.250171\pi$
$7$	−0.686141	−	1.18843i	−0.259337	−	0.449185i	−0.966064	+	0.258301i	$0.916837\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$	−0.686141	−	1.18843i	−0.190301	−	0.329611i	0.755049	−	0.655669i	$-0.227613\pi$
$13$	−0.686141	−	1.18843i	−0.190301	−	0.329611i	−0.945350	+	0.326057i	$0.894280\pi$
$14$		0			0
$15$	1.18614	−	2.05446i	0.306260	−	0.530458i
$16$		0			0
$17$	0.813859	−	1.40965i	0.197390	−	0.341889i	−0.750291	−	0.661107i	$-0.770087\pi$
$17$	0.813859	−	1.40965i	0.197390	−	0.341889i	0.947681	+	0.319218i	$0.103420\pi$
$18$		0			0
$19$	2.37228	+	4.10891i	0.544239	+	0.942649i	0.998654	+	0.0518593i	$0.0165147\pi$
$19$	2.37228	+	4.10891i	0.544239	+	0.942649i	−0.454416	+	0.890790i	$0.650152\pi$
$20$		0			0
$21$	−0.686141	+	1.18843i	−0.149728	+	0.259337i
$22$		0			0
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$		0			0
$25$	−0.313859	+	0.543620i	−0.0627719	+	0.108724i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	4.37228			0.811912			0.405956	−	0.913893i	$-0.366939\pi$
$29$	4.37228			0.811912			0.405956	+	0.913893i	$0.366939\pi$
$30$		0			0
$31$	9.37228			1.68331			0.841656	−	0.540015i	$-0.181581\pi$
$31$	9.37228			1.68331			0.841656	+	0.540015i	$0.181581\pi$
$32$		0			0
$33$	1.00000	+	1.73205i	0.174078	+	0.301511i
$34$		0			0
$35$	1.62772	−	2.81929i	0.275135	−	0.476547i
$36$		0			0
$37$	−2.55842	−	5.51856i	−0.420602	−	0.907245i
$37$	−2.55842	−	5.51856i	−0.420602	−	0.907245i
$38$		0			0
$39$	−0.686141	+	1.18843i	−0.109870	+	0.190301i
$40$		0			0
$41$	2.18614	+	3.78651i	0.341418	+	0.591353i	0.984696	−	0.174279i	$-0.0557596\pi$
$41$	2.18614	+	3.78651i	0.341418	+	0.591353i	−0.643278	+	0.765632i	$0.722426\pi$
$42$		0			0
$43$	9.37228			1.42926			0.714630	−	0.699503i	$-0.246595\pi$
$43$	9.37228			1.42926			0.714630	+	0.699503i	$0.246595\pi$
$44$		0			0
$45$	−2.37228			−0.353639
$46$		0			0
$47$	−2.00000			−0.291730			−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000			−0.291730			−0.145865	+	0.989305i	$0.546597\pi$
$48$		0			0
$49$	2.55842	−	4.43132i	0.365489	−	0.633045i
$50$		0			0
$51$	−1.62772			−0.227926
$52$		0			0
$53$	−5.74456	+	9.94987i	−0.789076	+	1.36672i	0.137457	+	0.990508i	$0.456107\pi$
$53$	−5.74456	+	9.94987i	−0.789076	+	1.36672i	−0.926533	+	0.376213i	$0.877226\pi$
$54$		0			0
$55$	−2.37228	−	4.10891i	−0.319878	−	0.554046i
$56$		0			0
$57$	2.37228	−	4.10891i	0.314216	−	0.544239i
$58$		0			0
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	4.55842	+	7.89542i	0.583646	+	1.01090i	0.995043	+	0.0994483i	$0.0317078\pi$
$61$	4.55842	+	7.89542i	0.583646	+	1.01090i	−0.411397	+	0.911456i	$0.634959\pi$
$62$		0			0
$63$	1.37228			0.172891
$64$		0			0
$65$	1.62772	−	2.81929i	0.201894	−	0.349690i
$66$		0			0
$67$	2.05842	+	3.56529i	0.251476	+	0.435570i	0.963932	−	0.266147i	$-0.0857506\pi$
$67$	2.05842	+	3.56529i	0.251476	+	0.435570i	−0.712456	+	0.701717i	$0.752417\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	5.74456	+	9.94987i	0.681754	+	1.18083i	0.974445	+	0.224626i	$0.0721160\pi$
$71$	5.74456	+	9.94987i	0.681754	+	1.18083i	−0.292691	+	0.956207i	$0.594551\pi$
$72$		0			0
$73$	2.62772			0.307551			0.153776	−	0.988106i	$-0.450857\pi$
$73$	2.62772			0.307551			0.153776	+	0.988106i	$0.450857\pi$
$74$		0			0
$75$	0.627719			0.0724827
$76$		0			0
$77$	1.37228	+	2.37686i	0.156386	+	0.270868i
$78$		0			0
$79$	0.686141	+	1.18843i	0.0771969	+	0.133709i	0.902039	−	0.431653i	$-0.142070\pi$
$79$	0.686141	+	1.18843i	0.0771969	+	0.133709i	−0.824843	+	0.565362i	$0.808736\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	4.00000	−	6.92820i	0.439057	−	0.760469i	−0.558560	−	0.829464i	$-0.688646\pi$
$83$	4.00000	−	6.92820i	0.439057	−	0.760469i	0.997617	+	0.0689950i	$0.0219793\pi$
$84$		0			0
$85$	3.86141			0.418828
$86$		0			0
$87$	−2.18614	−	3.78651i	−0.234379	−	0.405956i
$88$		0			0
$89$	−1.81386	+	3.14170i	−0.192269	+	0.333019i	−0.946002	−	0.324162i	$-0.894918\pi$
$89$	−1.81386	+	3.14170i	−0.192269	+	0.333019i	0.753733	+	0.657181i	$0.228251\pi$
$90$		0			0
$91$	−0.941578	+	1.63086i	−0.0987042	+	0.170961i
$92$		0			0
$93$	−4.68614	−	8.11663i	−0.485930	−	0.841656i
$94$		0			0
$95$	−5.62772	+	9.74749i	−0.577392	+	1.00007i
$96$		0			0
$97$	5.74456			0.583272			0.291636	−	0.956529i	$-0.405800\pi$
$97$	5.74456			0.583272			0.291636	+	0.956529i	$0.405800\pi$
$98$		0			0
$99$	1.00000	−	1.73205i	0.100504	−	0.174078i
$100$		0			0
$101$	13.8614			1.37926			0.689631	−	0.724161i	$-0.257773\pi$
$101$	13.8614			1.37926			0.689631	+	0.724161i	$0.257773\pi$
$102$		0			0
$103$	−12.7446			−1.25576			−0.627880	−	0.778311i	$-0.716077\pi$
$103$	−12.7446			−1.25576			−0.627880	+	0.778311i	$0.716077\pi$
$104$		0			0
$105$	−3.25544			−0.317698
$106$		0			0
$107$	2.37228	+	4.10891i	0.229337	+	0.397223i	0.957612	−	0.288062i	$-0.0930109\pi$
$107$	2.37228	+	4.10891i	0.229337	+	0.397223i	−0.728275	+	0.685285i	$0.759678\pi$
$108$		0			0
$109$	2.12772	−	3.68532i	0.203798	−	0.352989i	−0.745951	−	0.666001i	$-0.768005\pi$
$109$	2.12772	−	3.68532i	0.203798	−	0.352989i	0.949749	+	0.313012i	$0.101338\pi$
$110$		0			0
$111$	−3.50000	+	4.97494i	−0.332205	+	0.472200i
$112$		0			0
$113$	7.74456	−	13.4140i	0.728547	−	1.26188i	−0.228950	−	0.973438i	$-0.573529\pi$
$113$	7.74456	−	13.4140i	0.728547	−	1.26188i	0.957497	−	0.288443i	$-0.0931374\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.37228			0.126867
$118$		0			0
$119$	−2.23369			−0.204762
$120$		0			0
$121$	−7.00000			−0.636364
$122$		0			0
$123$	2.18614	−	3.78651i	0.197118	−	0.341418i
$124$		0			0
$125$	10.3723			0.927725
$126$		0			0
$127$	4.31386	−	7.47182i	0.382793	−	0.663017i	−0.608667	−	0.793426i	$-0.708296\pi$
$127$	4.31386	−	7.47182i	0.382793	−	0.663017i	0.991460	+	0.130408i	$0.0416289\pi$
$128$		0			0
$129$	−4.68614	−	8.11663i	−0.412592	−	0.714630i
$130$		0			0
$131$	5.37228	−	9.30506i	0.469378	−	0.812987i	−0.530009	−	0.847992i	$-0.677811\pi$
$131$	5.37228	−	9.30506i	0.469378	−	0.812987i	0.999387	+	0.0350049i	$0.0111447\pi$
$132$		0			0
$133$	3.25544	−	5.63858i	0.282282	−	0.488927i
$134$		0			0
$135$	1.18614	+	2.05446i	0.102087	+	0.176819i
$136$		0			0
$137$	10.3723			0.886164			0.443082	−	0.896481i	$-0.353885\pi$
$137$	10.3723			0.886164			0.443082	+	0.896481i	$0.353885\pi$
$138$		0			0
$139$	−4.31386	+	7.47182i	−0.365897	+	0.633752i	−0.988920	−	0.148452i	$-0.952571\pi$
$139$	−4.31386	+	7.47182i	−0.365897	+	0.633752i	0.623023	+	0.782204i	$0.285904\pi$
$140$		0			0
$141$	1.00000	+	1.73205i	0.0842152	+	0.145865i
$142$		0			0
$143$	1.37228	+	2.37686i	0.114756	+	0.198763i
$144$		0			0
$145$	5.18614	+	8.98266i	0.430686	+	0.745969i
$146$		0			0
$147$	−5.11684			−0.422030
$148$		0			0
$149$	1.62772			0.133348			0.0666740	−	0.997775i	$-0.478761\pi$
$149$	1.62772			0.133348			0.0666740	+	0.997775i	$0.478761\pi$
$150$		0			0
$151$	−9.68614	−	16.7769i	−0.788247	−	1.36528i	−0.927040	−	0.374962i	$-0.877656\pi$
$151$	−9.68614	−	16.7769i	−0.788247	−	1.36528i	0.138793	−	0.990321i	$-0.455678\pi$
$152$		0			0
$153$	0.813859	+	1.40965i	0.0657966	+	0.113963i
$154$		0			0
$155$	11.1168	+	19.2549i	0.892926	+	1.54659i
$156$		0			0
$157$	−3.24456	+	5.61975i	−0.258944	+	0.448505i	−0.965959	−	0.258694i	$-0.916708\pi$
$157$	−3.24456	+	5.61975i	−0.258944	+	0.448505i	0.707015	+	0.707198i	$0.250041\pi$
$158$		0			0
$159$	11.4891			0.911147
$160$		0			0
$161$		0			0
$162$		0			0
$163$	12.3723	−	21.4294i	0.969072	−	1.67848i	0.270819	−	0.962630i	$-0.412705\pi$
$163$	12.3723	−	21.4294i	0.969072	−	1.67848i	0.698253	−	0.715852i	$-0.253961\pi$
$164$		0			0
$165$	−2.37228	+	4.10891i	−0.184682	+	0.319878i
$166$		0			0
$167$	−0.744563	−	1.28962i	−0.0576160	−	0.0997938i	0.835779	−	0.549066i	$-0.185017\pi$
$167$	−0.744563	−	1.28962i	−0.0576160	−	0.0997938i	−0.893395	+	0.449273i	$0.851683\pi$
$168$		0			0
$169$	5.55842	−	9.62747i	0.427571	−	0.740575i
$170$		0			0
$171$	−4.74456			−0.362826
$172$		0			0
$173$	−11.5584	+	20.0198i	−0.878771	+	1.52208i	−0.0260794	+	0.999660i	$0.508302\pi$
$173$	−11.5584	+	20.0198i	−0.878771	+	1.52208i	−0.852691	+	0.522415i	$0.825031\pi$
$174$		0			0
$175$	0.861407			0.0651162
$176$		0			0
$177$	4.00000			0.300658
$178$		0			0
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	2.12772	+	3.68532i	0.158152	+	0.273927i	0.934202	−	0.356744i	$-0.116113\pi$
$181$	2.12772	+	3.68532i	0.158152	+	0.273927i	−0.776050	+	0.630671i	$0.782780\pi$
$182$		0			0
$183$	4.55842	−	7.89542i	0.336968	−	0.583646i
$184$		0			0
$185$	8.30298	−	11.8020i	0.610448	−	0.867697i
$186$		0			0
$187$	−1.62772	+	2.81929i	−0.119031	+	0.206167i
$188$		0			0
$189$	−0.686141	−	1.18843i	−0.0499094	−	0.0864456i
$190$		0			0
$191$	22.7446			1.64574			0.822869	−	0.568231i	$-0.192372\pi$
$191$	22.7446			1.64574			0.822869	+	0.568231i	$0.192372\pi$
$192$		0			0
$193$	−18.4891			−1.33088			−0.665438	−	0.746453i	$-0.731755\pi$
$193$	−18.4891			−1.33088			−0.665438	+	0.746453i	$0.731755\pi$
$194$		0			0
$195$	−3.25544			−0.233127
$196$		0			0
$197$	−6.81386	+	11.8020i	−0.485467	+	0.840854i	−0.999861	−	0.0167003i	$-0.994684\pi$
$197$	−6.81386	+	11.8020i	−0.485467	+	0.840854i	0.514393	+	0.857554i	$0.328017\pi$
$198$		0			0
$199$	6.62772			0.469827			0.234913	−	0.972016i	$-0.424519\pi$
$199$	6.62772			0.469827			0.234913	+	0.972016i	$0.424519\pi$
$200$		0			0
$201$	2.05842	−	3.56529i	0.145190	−	0.251476i
$202$		0			0
$203$	−3.00000	−	5.19615i	−0.210559	−	0.364698i
$204$		0			0
$205$	−5.18614	+	8.98266i	−0.362216	+	0.627376i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−4.74456	−	8.21782i	−0.328188	−	0.568439i
$210$		0			0
$211$	−13.3723			−0.920586			−0.460293	−	0.887767i	$-0.652256\pi$
$211$	−13.3723			−0.920586			−0.460293	+	0.887767i	$0.652256\pi$
$212$		0			0
$213$	5.74456	−	9.94987i	0.393611	−	0.681754i
$214$		0			0
$215$	11.1168	+	19.2549i	0.758162	+	1.31318i
$216$		0			0
$217$	−6.43070	−	11.1383i	−0.436545	−	0.756117i
$218$		0			0
$219$	−1.31386	−	2.27567i	−0.0887824	−	0.153776i
$220$		0			0
$221$	−2.23369			−0.150254
$222$		0			0
$223$	−18.1168			−1.21319			−0.606597	−	0.795010i	$-0.707466\pi$
$223$	−18.1168			−1.21319			−0.606597	+	0.795010i	$0.707466\pi$
$224$		0			0
$225$	−0.313859	−	0.543620i	−0.0209240	−	0.0362414i
$226$		0			0
$227$	−5.74456	−	9.94987i	−0.381280	−	0.660396i	0.609965	−	0.792428i	$-0.291183\pi$
$227$	−5.74456	−	9.94987i	−0.381280	−	0.660396i	−0.991246	+	0.132032i	$0.957850\pi$
$228$		0			0
$229$	6.87228	+	11.9031i	0.454133	+	0.786582i	0.998638	−	0.0521761i	$-0.0166157\pi$
$229$	6.87228	+	11.9031i	0.454133	+	0.786582i	−0.544505	+	0.838758i	$0.683282\pi$
$230$		0			0
$231$	1.37228	−	2.37686i	0.0902895	−	0.156386i
$232$		0			0
$233$	−28.6060			−1.87404			−0.937020	−	0.349277i	$-0.886427\pi$
$233$	−28.6060			−1.87404			−0.937020	+	0.349277i	$0.886427\pi$
$234$		0			0
$235$	−2.37228	−	4.10891i	−0.154751	−	0.268036i
$236$		0			0
$237$	0.686141	−	1.18843i	0.0445696	−	0.0771969i
$238$		0			0
$239$	−11.1168	+	19.2549i	−0.719089	+	1.24550i	0.242272	+	0.970208i	$0.422107\pi$
$239$	−11.1168	+	19.2549i	−0.719089	+	1.24550i	−0.961361	+	0.275290i	$0.911226\pi$
$240$		0			0
$241$	−12.0584	−	20.8858i	−0.776751	−	1.34537i	−0.933805	−	0.357783i	$-0.883533\pi$
$241$	−12.0584	−	20.8858i	−0.776751	−	1.34537i	0.157054	−	0.987590i	$-0.449800\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	12.1386			0.775506
$246$		0			0
$247$	3.25544	−	5.63858i	0.207139	−	0.358774i
$248$		0			0
$249$	−8.00000			−0.506979
$250$		0			0
$251$	12.7446			0.804430			0.402215	−	0.915545i	$-0.368240\pi$
$251$	12.7446			0.804430			0.402215	+	0.915545i	$0.368240\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−1.93070	−	3.34408i	−0.120905	−	0.209414i
$256$		0			0
$257$	−9.93070	+	17.2005i	−0.619460	+	1.07294i	0.370124	+	0.928982i	$0.379315\pi$
$257$	−9.93070	+	17.2005i	−0.619460	+	1.07294i	−0.989584	+	0.143954i	$0.954018\pi$
$258$		0			0
$259$	−4.80298	+	6.82701i	−0.298443	+	0.424210i
$260$		0			0
$261$	−2.18614	+	3.78651i	−0.135319	+	0.234379i
$262$		0			0
$263$	−13.3723	−	23.1615i	−0.824570	−	1.42820i	−0.902247	−	0.431219i	$-0.858084\pi$
$263$	−13.3723	−	23.1615i	−0.824570	−	1.42820i	0.0776771	−	0.996979i	$-0.475250\pi$
$264$		0			0
$265$	−27.2554			−1.67429
$266$		0			0
$267$	3.62772			0.222013
$268$		0			0
$269$	2.00000			0.121942			0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000			0.121942			0.0609711	+	0.998140i	$0.480580\pi$
$270$		0			0
$271$	9.43070	−	16.3345i	0.572874	−	0.992248i	−0.423395	−	0.905945i	$-0.639162\pi$
$271$	9.43070	−	16.3345i	0.572874	−	0.992248i	0.996269	−	0.0863022i	$-0.0275051\pi$
$272$		0			0
$273$	1.88316			0.113974
$274$		0			0
$275$	0.627719	−	1.08724i	0.0378529	−	0.0655631i
$276$		0			0
$277$	1.06930	+	1.85208i	0.0642478	+	0.111280i	0.896360	−	0.443327i	$-0.146202\pi$
$277$	1.06930	+	1.85208i	0.0642478	+	0.111280i	−0.832112	+	0.554607i	$0.812869\pi$
$278$		0			0
$279$	−4.68614	+	8.11663i	−0.280552	+	0.485930i
$280$		0			0
$281$	3.55842	−	6.16337i	0.212278	−	0.367676i	−0.740149	−	0.672443i	$-0.765245\pi$
$281$	3.55842	−	6.16337i	0.212278	−	0.367676i	0.952427	+	0.304767i	$0.0985785\pi$
$282$		0			0
$283$	−0.0584220	−	0.101190i	−0.00347283	−	0.00601511i	0.864284	−	0.503005i	$-0.167772\pi$
$283$	−0.0584220	−	0.101190i	−0.00347283	−	0.00601511i	−0.867757	+	0.496989i	$0.834439\pi$
$284$		0			0
$285$	11.2554			0.666715
$286$		0			0
$287$	3.00000	−	5.19615i	0.177084	−	0.306719i
$288$		0			0
$289$	7.17527	+	12.4279i	0.422074	+	0.731054i
$290$		0			0
$291$	−2.87228	−	4.97494i	−0.168376	−	0.291636i
$292$		0			0
$293$	16.5584	+	28.6800i	0.967353	+	1.67551i	0.703155	+	0.711037i	$0.251774\pi$
$293$	16.5584	+	28.6800i	0.967353	+	1.67551i	0.264199	+	0.964468i	$0.414893\pi$
$294$		0			0
$295$	−9.48913			−0.552478
$296$		0			0
$297$	−2.00000			−0.116052
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−6.43070	−	11.1383i	−0.370660	−	0.642001i
$302$		0			0
$303$	−6.93070	−	12.0043i	−0.398159	−	0.689631i
$304$		0			0
$305$	−10.8139	+	18.7302i	−0.619200	+	1.07249i
$306$		0			0
$307$	8.11684			0.463253			0.231626	−	0.972805i	$-0.425595\pi$
$307$	8.11684			0.463253			0.231626	+	0.972805i	$0.425595\pi$
$308$		0			0
$309$	6.37228	+	11.0371i	0.362506	+	0.627880i
$310$		0			0
$311$	−14.4891	+	25.0959i	−0.821603	+	1.42306i	0.0828852	+	0.996559i	$0.473587\pi$
$311$	−14.4891	+	25.0959i	−0.821603	+	1.42306i	−0.904488	+	0.426499i	$0.859747\pi$
$312$		0			0
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	−0.519300	−	0.854592i	$-0.673807\pi$
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	0.999748	+	0.0224310i	$0.00714060\pi$
$314$		0			0
$315$	1.62772	+	2.81929i	0.0917116	+	0.158849i
$316$		0			0
$317$	6.44158	−	11.1571i	0.361795	−	0.626647i	−0.626461	−	0.779453i	$-0.715497\pi$
$317$	6.44158	−	11.1571i	0.361795	−	0.626647i	0.988256	+	0.152805i	$0.0488307\pi$
$318$		0			0
$319$	−8.74456			−0.489602
$320$		0			0
$321$	2.37228	−	4.10891i	0.132408	−	0.229337i
$322$		0			0
$323$	7.72281			0.429709
$324$		0			0
$325$	0.861407			0.0477822
$326$		0			0
$327$	−4.25544			−0.235326
$328$		0			0
$329$	1.37228	+	2.37686i	0.0756563	+	0.131041i
$330$		0			0
$331$	−17.8030	+	30.8357i	−0.978541	+	1.69488i	−0.310822	+	0.950468i	$0.600604\pi$
$331$	−17.8030	+	30.8357i	−0.978541	+	1.69488i	−0.667719	+	0.744414i	$0.732729\pi$
$332$		0			0
$333$	6.05842	+	0.543620i	0.331999	+	0.0297902i
$334$		0			0
$335$	−4.88316	+	8.45787i	−0.266795	+	0.462103i
$336$		0			0
$337$	−14.8723	−	25.7595i	−0.810145	−	1.40321i	−0.912762	−	0.408491i	$-0.866055\pi$
$337$	−14.8723	−	25.7595i	−0.810145	−	1.40321i	0.102618	−	0.994721i	$-0.467278\pi$
$338$		0			0
$339$	−15.4891			−0.841254
$340$		0			0
$341$	−18.7446			−1.01507
$342$		0			0
$343$	−16.6277			−0.897812
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−26.7446			−1.43572			−0.717862	−	0.696186i	$-0.754879\pi$
$347$	−26.7446			−1.43572			−0.717862	+	0.696186i	$0.754879\pi$
$348$		0			0
$349$	4.55842	−	7.89542i	0.244007	−	0.422632i	−0.717845	−	0.696203i	$-0.754871\pi$
$349$	4.55842	−	7.89542i	0.244007	−	0.422632i	0.961852	+	0.273571i	$0.0882048\pi$
$350$		0			0
$351$	−0.686141	−	1.18843i	−0.0366235	−	0.0634337i
$352$		0			0
$353$	−15.3030	+	26.5055i	−0.814496	+	1.41075i	0.0951938	+	0.995459i	$0.469653\pi$
$353$	−15.3030	+	26.5055i	−0.814496	+	1.41075i	−0.909689	+	0.415289i	$0.863680\pi$
$354$		0			0
$355$	−13.6277	+	23.6039i	−0.723284	+	1.25276i
$356$		0			0
$357$	1.11684	+	1.93443i	0.0591097	+	0.102381i
$358$		0			0
$359$	−12.2337			−0.645669			−0.322835	−	0.946455i	$-0.604636\pi$
$359$	−12.2337			−0.645669			−0.322835	+	0.946455i	$0.604636\pi$
$360$		0			0
$361$	−1.75544	+	3.04051i	−0.0923914	+	0.160027i
$362$		0			0
$363$	3.50000	+	6.06218i	0.183702	+	0.318182i
$364$		0			0
$365$	3.11684	+	5.39853i	0.163143	+	0.282572i
$366$		0			0
$367$	3.05842	+	5.29734i	0.159648	+	0.276519i	0.934742	−	0.355327i	$-0.115631\pi$
$367$	3.05842	+	5.29734i	0.159648	+	0.276519i	−0.775094	+	0.631846i	$0.782297\pi$
$368$		0			0
$369$	−4.37228			−0.227612
$370$		0			0
$371$	15.7663			0.818546
$372$		0			0
$373$	15.5000	+	26.8468i	0.802560	+	1.39007i	0.917926	+	0.396751i	$0.129862\pi$
$373$	15.5000	+	26.8468i	0.802560	+	1.39007i	−0.115367	+	0.993323i	$0.536804\pi$
$374$		0			0
$375$	−5.18614	−	8.98266i	−0.267811	−	0.463863i
$376$		0			0
$377$	−3.00000	−	5.19615i	−0.154508	−	0.267615i
$378$		0			0
$379$	−13.8614	+	24.0087i	−0.712013	+	1.23324i	0.252088	+	0.967704i	$0.418883\pi$
$379$	−13.8614	+	24.0087i	−0.712013	+	1.23324i	−0.964100	+	0.265538i	$0.914451\pi$
$380$		0			0
$381$	−8.62772			−0.442011
$382$		0			0
$383$	−3.11684	−	5.39853i	−0.159263	−	0.275852i	0.775340	−	0.631544i	$-0.217579\pi$
$383$	−3.11684	−	5.39853i	−0.159263	−	0.275852i	−0.934603	+	0.355692i	$0.884245\pi$
$384$		0			0
$385$	−3.25544	+	5.63858i	−0.165912	+	0.287369i
$386$		0			0
$387$	−4.68614	+	8.11663i	−0.238210	+	0.412592i
$388$		0			0
$389$	−3.44158	−	5.96099i	−0.174495	−	0.302234i	0.765491	−	0.643446i	$-0.222496\pi$
$389$	−3.44158	−	5.96099i	−0.174495	−	0.302234i	−0.939986	+	0.341212i	$0.889163\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−10.7446			−0.541991
$394$		0			0
$395$	−1.62772	+	2.81929i	−0.0818994	+	0.141854i
$396$		0			0
$397$	−19.0000			−0.953583			−0.476791	−	0.879017i	$-0.658200\pi$
$397$	−19.0000			−0.953583			−0.476791	+	0.879017i	$0.658200\pi$
$398$		0			0
$399$	−6.51087			−0.325951
$400$		0			0
$401$	−3.25544			−0.162569			−0.0812844	−	0.996691i	$-0.525902\pi$
$401$	−3.25544			−0.162569			−0.0812844	+	0.996691i	$0.525902\pi$
$402$		0			0
$403$	−6.43070	−	11.1383i	−0.320336	−	0.554838i
$404$		0			0
$405$	1.18614	−	2.05446i	0.0589398	−	0.102087i
$406$		0			0
$407$	5.11684	+	11.0371i	0.253633	+	0.547089i
$408$		0			0
$409$	11.8723	−	20.5634i	0.587047	−	1.01679i	−0.407570	−	0.913174i	$-0.633624\pi$
$409$	11.8723	−	20.5634i	0.587047	−	1.01679i	0.994617	−	0.103621i	$-0.0330428\pi$
$410$		0			0
$411$	−5.18614	−	8.98266i	−0.255813	−	0.443082i
$412$		0			0
$413$	5.48913			0.270102
$414$		0			0
$415$	18.9783			0.931606
$416$		0			0
$417$	8.62772			0.422501
$418$		0			0
$419$	9.74456	−	16.8781i	0.476053	−	0.824548i	−0.523571	−	0.851982i	$-0.675400\pi$
$419$	9.74456	−	16.8781i	0.476053	−	0.824548i	0.999624	+	0.0274343i	$0.00873369\pi$
$420$		0			0
$421$	−11.6277			−0.566700			−0.283350	−	0.959017i	$-0.591446\pi$
$421$	−11.6277			−0.566700			−0.283350	+	0.959017i	$0.591446\pi$
$422$		0			0
$423$	1.00000	−	1.73205i	0.0486217	−	0.0842152i
$424$		0			0
$425$	0.510875	+	0.884861i	0.0247811	+	0.0429221i
$426$		0			0
$427$	6.25544	−	10.8347i	0.302722	−	0.524330i
$428$		0			0
$429$	1.37228	−	2.37686i	0.0662544	−	0.114756i
$430$		0			0
$431$	4.48913	+	7.77539i	0.216234	+	0.374528i	0.953653	−	0.300907i	$-0.0972894\pi$
$431$	4.48913	+	7.77539i	0.216234	+	0.374528i	−0.737420	+	0.675435i	$0.763956\pi$
$432$		0			0
$433$	7.62772			0.366565			0.183282	−	0.983060i	$-0.441328\pi$
$433$	7.62772			0.366565			0.183282	+	0.983060i	$0.441328\pi$
$434$		0			0
$435$	5.18614	−	8.98266i	0.248656	−	0.430686i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	4.31386	+	7.47182i	0.205889	+	0.356611i	0.950416	−	0.310982i	$-0.100658\pi$
$439$	4.31386	+	7.47182i	0.205889	+	0.356611i	−0.744526	+	0.667593i	$0.767325\pi$
$440$		0			0
$441$	2.55842	+	4.43132i	0.121830	+	0.211015i
$442$		0			0
$443$	5.48913			0.260796			0.130398	−	0.991462i	$-0.458374\pi$
$443$	5.48913			0.260796			0.130398	+	0.991462i	$0.458374\pi$
$444$		0			0
$445$	−8.60597			−0.407962
$446$		0			0
$447$	−0.813859	−	1.40965i	−0.0384942	−	0.0666740i
$448$		0			0
$449$	−12.4891	−	21.6318i	−0.589398	−	1.02087i	−0.994311	−	0.106513i	$-0.966032\pi$
$449$	−12.4891	−	21.6318i	−0.589398	−	1.02087i	0.404913	−	0.914355i	$-0.367302\pi$
$450$		0			0
$451$	−4.37228	−	7.57301i	−0.205883	−	0.356599i
$452$		0			0
$453$	−9.68614	+	16.7769i	−0.455095	+	0.788247i
$454$		0			0
$455$	−4.46738			−0.209434
$456$		0			0
$457$	−12.0475	−	20.8670i	−0.563560	−	0.976115i	−0.997182	−	0.0750203i	$-0.976098\pi$
$457$	−12.0475	−	20.8670i	−0.563560	−	0.976115i	0.433622	−	0.901095i	$-0.357235\pi$
$458$		0			0
$459$	0.813859	−	1.40965i	0.0379877	−	0.0657966i
$460$		0			0
$461$	10.4891	−	18.1677i	0.488527	−	0.846154i	−0.511386	−	0.859351i	$-0.670868\pi$
$461$	10.4891	−	18.1677i	0.488527	−	0.846154i	0.999913	+	0.0131973i	$0.00420095\pi$
$462$		0			0
$463$	−0.0584220	−	0.101190i	−0.00271510	−	0.00470269i	0.864665	−	0.502350i	$-0.167531\pi$
$463$	−0.0584220	−	0.101190i	−0.00271510	−	0.00470269i	−0.867380	+	0.497647i	$0.834198\pi$
$464$		0			0
$465$	11.1168	−	19.2549i	0.515531	−	0.892926i
$466$		0			0
$467$	−14.7446			−0.682297			−0.341148	−	0.940009i	$-0.610816\pi$
$467$	−14.7446			−0.682297			−0.341148	+	0.940009i	$0.610816\pi$
$468$		0			0
$469$	2.82473	−	4.89258i	0.130434	−	0.225918i
$470$		0			0
$471$	6.48913			0.299003
$472$		0			0
$473$	−18.7446			−0.861876
$474$		0			0
$475$	−2.97825			−0.136652
$476$		0			0
$477$	−5.74456	−	9.94987i	−0.263025	−	0.455573i
$478$		0			0
$479$	−0.116844	+	0.202380i	−0.00533874	+	0.00924696i	−0.868682	−	0.495369i	$-0.835033\pi$
$479$	−0.116844	+	0.202380i	−0.00533874	+	0.00924696i	0.863344	+	0.504616i	$0.168366\pi$
$480$		0			0
$481$	−4.80298	+	6.82701i	−0.218997	+	0.311285i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	6.81386	+	11.8020i	0.309401	+	0.535899i
$486$		0			0
$487$	37.4891			1.69879			0.849397	−	0.527754i	$-0.176966\pi$
$487$	37.4891			1.69879			0.849397	+	0.527754i	$0.176966\pi$
$488$		0			0
$489$	−24.7446			−1.11899
$490$		0			0
$491$	−6.00000			−0.270776			−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000			−0.270776			−0.135388	+	0.990793i	$0.543228\pi$
$492$		0			0
$493$	3.55842	−	6.16337i	0.160263	−	0.277584i
$494$		0			0
$495$	4.74456			0.213252
$496$		0			0
$497$	7.88316	−	13.6540i	0.353608	−	0.612467i
$498$		0			0
$499$	−13.1168	−	22.7190i	−0.587191	−	1.01704i	−0.994598	−	0.103798i	$-0.966901\pi$
$499$	−13.1168	−	22.7190i	−0.587191	−	1.01704i	0.407408	−	0.913246i	$-0.366433\pi$
$500$		0			0
$501$	−0.744563	+	1.28962i	−0.0332646	+	0.0576160i
$502$		0			0
$503$	−11.0000	+	19.0526i	−0.490466	+	0.849512i	−0.999940	−	0.0109744i	$-0.996507\pi$
$503$	−11.0000	+	19.0526i	−0.490466	+	0.849512i	0.509474	+	0.860486i	$0.329840\pi$
$504$		0			0
$505$	16.4416	+	28.4776i	0.731641	+	1.26724i
$506$		0			0
$507$	−11.1168			−0.493716
$508$		0			0
$509$	−2.18614	+	3.78651i	−0.0968990	+	0.167834i	−0.910400	−	0.413730i	$-0.864226\pi$
$509$	−2.18614	+	3.78651i	−0.0968990	+	0.167834i	0.813501	+	0.581564i	$0.197559\pi$
$510$		0			0
$511$	−1.80298	−	3.12286i	−0.0797593	−	0.138147i
$512$		0			0
$513$	2.37228	+	4.10891i	0.104739	+	0.181413i
$514$		0			0
$515$	−15.1168	−	26.1831i	−0.666128	−	1.15377i
$516$		0			0
$517$	4.00000			0.175920
$518$		0			0
$519$	23.1168			1.01472
$520$		0			0
$521$	−10.3723	−	17.9653i	−0.454418	−	0.787075i	0.544237	−	0.838932i	$-0.316819\pi$
$521$	−10.3723	−	17.9653i	−0.454418	−	0.787075i	−0.998655	+	0.0518569i	$0.983486\pi$
$522$		0			0
$523$	0.941578	+	1.63086i	0.0411723	+	0.0713126i	0.885877	−	0.463920i	$-0.153557\pi$
$523$	0.941578	+	1.63086i	0.0411723	+	0.0713126i	−0.844705	+	0.535232i	$0.820224\pi$
$524$		0			0
$525$	−0.430703	−	0.746000i	−0.0187974	−	0.0325581i
$526$		0			0
$527$	7.62772	−	13.2116i	0.332269	−	0.575506i
$528$		0			0
$529$	−23.0000			−1.00000
$530$		0			0
$531$	−2.00000	−	3.46410i	−0.0867926	−	0.150329i
$532$		0			0
$533$	3.00000	−	5.19615i	0.129944	−	0.225070i
$534$		0			0
$535$	−5.62772	+	9.74749i	−0.243307	+	0.421421i
$536$		0			0
$537$	−6.00000	−	10.3923i	−0.258919	−	0.448461i
$538$		0			0
$539$	−5.11684	+	8.86263i	−0.220398	+	0.381741i
$540$		0			0
$541$	−5.74456			−0.246978			−0.123489	−	0.992346i	$-0.539408\pi$
$541$	−5.74456			−0.246978			−0.123489	+	0.992346i	$0.539408\pi$
$542$		0			0
$543$	2.12772	−	3.68532i	0.0913091	−	0.158152i
$544$		0			0
$545$	10.0951			0.432426
$546$		0			0
$547$	39.0951			1.67159			0.835793	−	0.549045i	$-0.185008\pi$
$547$	39.0951			1.67159			0.835793	+	0.549045i	$0.185008\pi$
$548$		0			0
$549$	−9.11684			−0.389097
$550$		0			0
$551$	10.3723	+	17.9653i	0.441874	+	0.765348i
$552$		0			0
$553$	0.941578	−	1.63086i	0.0400400	−	0.0693513i
$554$		0			0
$555$	−14.3723	−	1.28962i	−0.610069	−	0.0547413i
$556$		0			0
$557$	−1.55842	+	2.69927i	−0.0660325	+	0.114372i	−0.897152	−	0.441723i	$-0.854367\pi$
$557$	−1.55842	+	2.69927i	−0.0660325	+	0.114372i	0.831119	+	0.556095i	$0.187701\pi$
$558$		0			0
$559$	−6.43070	−	11.1383i	−0.271990	−	0.471100i
$560$		0			0
$561$	3.25544			0.137445
$562$		0			0
$563$	−13.2554			−0.558650			−0.279325	−	0.960197i	$-0.590111\pi$
$563$	−13.2554			−0.558650			−0.279325	+	0.960197i	$0.590111\pi$
$564$		0			0
$565$	36.7446			1.54586
$566$		0			0
$567$	−0.686141	+	1.18843i	−0.0288152	+	0.0499094i
$568$		0			0
$569$	15.6277			0.655148			0.327574	−	0.944826i	$-0.393769\pi$
$569$	15.6277			0.655148			0.327574	+	0.944826i	$0.393769\pi$
$570$		0			0
$571$	17.9198	−	31.0381i	0.749921	−	1.29890i	−0.197938	−	0.980214i	$-0.563425\pi$
$571$	17.9198	−	31.0381i	0.749921	−	1.29890i	0.947860	−	0.318688i	$-0.103242\pi$
$572$		0			0
$573$	−11.3723	−	19.6974i	−0.475084	−	0.822869i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	6.48913	−	11.2395i	0.270146	−	0.467906i	−0.698753	−	0.715363i	$-0.746261\pi$
$577$	6.48913	−	11.2395i	0.270146	−	0.467906i	0.968899	+	0.247457i	$0.0795948\pi$
$578$		0			0
$579$	9.24456	+	16.0121i	0.384191	+	0.665438i
$580$		0			0
$581$	−10.9783			−0.455455
$582$		0			0
$583$	11.4891	−	19.8997i	0.475831	−	0.824163i
$584$		0			0
$585$	1.62772	+	2.81929i	0.0672979	+	0.116563i
$586$		0			0
$587$	−1.37228	−	2.37686i	−0.0566401	−	0.0981036i	0.836315	−	0.548249i	$-0.184705\pi$
$587$	−1.37228	−	2.37686i	−0.0566401	−	0.0981036i	−0.892955	+	0.450146i	$0.851372\pi$
$588$		0			0
$589$	22.2337	+	38.5099i	0.916123	+	1.58677i
$590$		0			0
$591$	13.6277			0.560569
$592$		0			0
$593$	14.3723			0.590199			0.295099	−	0.955467i	$-0.404647\pi$
$593$	14.3723			0.590199			0.295099	+	0.955467i	$0.404647\pi$
$594$		0			0
$595$	−2.64947	−	4.58901i	−0.108618	−	0.188131i
$596$		0			0
$597$	−3.31386	−	5.73977i	−0.135627	−	0.234913i
$598$		0			0
$599$	3.62772	+	6.28339i	0.148225	+	0.256732i	0.930571	−	0.366111i	$-0.119311\pi$
$599$	3.62772	+	6.28339i	0.148225	+	0.256732i	−0.782347	+	0.622843i	$0.785977\pi$
$600$		0			0
$601$	8.50000	−	14.7224i	0.346722	−	0.600541i	−0.638943	−	0.769254i	$-0.720628\pi$
$601$	8.50000	−	14.7224i	0.346722	−	0.600541i	0.985665	+	0.168714i	$0.0539613\pi$
$602$		0			0
$603$	−4.11684			−0.167651
$604$		0			0
$605$	−8.30298	−	14.3812i	−0.337564	−	0.584679i
$606$		0			0
$607$	23.8614	−	41.3292i	0.968505	−	1.67750i	0.268616	−	0.963247i	$-0.413434\pi$
$607$	23.8614	−	41.3292i	0.968505	−	1.67750i	0.699889	−	0.714252i	$-0.253233\pi$
$608$		0			0
$609$	−3.00000	+	5.19615i	−0.121566	+	0.210559i
$610$		0			0
$611$	1.37228	+	2.37686i	0.0555166	+	0.0961575i
$612$		0			0
$613$	−8.93070	+	15.4684i	−0.360708	+	0.624764i	−0.988077	−	0.153957i	$-0.950798\pi$
$613$	−8.93070	+	15.4684i	−0.360708	+	0.624764i	0.627370	+	0.778721i	$0.284131\pi$
$614$		0			0
$615$	10.3723			0.418251
$616$		0			0
$617$	11.8614	−	20.5446i	0.477522	−	0.827093i	−0.522146	−	0.852856i	$-0.674868\pi$
$617$	11.8614	−	20.5446i	0.477522	−	0.827093i	0.999668	+	0.0257634i	$0.00820166\pi$
$618$		0			0
$619$	−33.8397			−1.36013			−0.680065	−	0.733152i	$-0.738049\pi$
$619$	−33.8397			−1.36013			−0.680065	+	0.733152i	$0.738049\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.97825			0.199449
$624$		0			0
$625$	13.8723	+	24.0275i	0.554891	+	0.961100i
$626$		0			0
$627$	−4.74456	+	8.21782i	−0.189480	+	0.328188i
$628$		0			0
$629$	−9.86141	−	0.884861i	−0.393200	−	0.0352817i
$630$		0			0
$631$	−21.0584	+	36.4743i	−0.838323	+	1.45202i	0.0529738	+	0.998596i	$0.483130\pi$
$631$	−21.0584	+	36.4743i	−0.838323	+	1.45202i	−0.891296	+	0.453421i	$0.850203\pi$
$632$		0			0
$633$	6.68614	+	11.5807i	0.265750	+	0.460293i
$634$		0			0
$635$	20.4674			0.812223
$636$		0			0
$637$	−7.02175			−0.278212
$638$		0			0
$639$	−11.4891			−0.454503
$640$		0			0
$641$	7.55842	−	13.0916i	0.298540	−	0.517086i	−0.677262	−	0.735742i	$-0.736834\pi$
$641$	7.55842	−	13.0916i	0.298540	−	0.517086i	0.975802	+	0.218656i	$0.0701671\pi$
$642$		0			0
$643$	−17.6060			−0.694312			−0.347156	−	0.937807i	$-0.612853\pi$
$643$	−17.6060			−0.694312			−0.347156	+	0.937807i	$0.612853\pi$
$644$		0			0
$645$	11.1168	−	19.2549i	0.437725	−	0.758162i
$646$		0			0
$647$	−19.8614	−	34.4010i	−0.780832	−	1.35244i	−0.931457	−	0.363851i	$-0.881462\pi$
$647$	−19.8614	−	34.4010i	−0.780832	−	1.35244i	0.150625	−	0.988591i	$-0.451871\pi$
$648$		0			0
$649$	4.00000	−	6.92820i	0.157014	−	0.271956i
$650$		0			0
$651$	−6.43070	+	11.1383i	−0.252039	+	0.436545i
$652$		0			0
$653$	13.4198	+	23.2438i	0.525158	+	0.909601i	0.999571	+	0.0292984i	$0.00932729\pi$
$653$	13.4198	+	23.2438i	0.525158	+	0.909601i	−0.474412	+	0.880303i	$0.657339\pi$
$654$		0			0
$655$	25.4891			0.995943
$656$		0			0
$657$	−1.31386	+	2.27567i	−0.0512585	+	0.0887824i
$658$		0			0
$659$	3.88316	+	6.72582i	0.151266	+	0.262001i	0.931693	−	0.363246i	$-0.118332\pi$
$659$	3.88316	+	6.72582i	0.151266	+	0.262001i	−0.780427	+	0.625247i	$0.784998\pi$
$660$		0			0
$661$	−9.98913	−	17.3017i	−0.388532	−	0.672957i	0.603720	−	0.797196i	$-0.293684\pi$
$661$	−9.98913	−	17.3017i	−0.388532	−	0.672957i	−0.992252	+	0.124239i	$0.960351\pi$
$662$		0			0
$663$	1.11684	+	1.93443i	0.0433746	+	0.0751271i
$664$		0			0
$665$	15.4456			0.598956
$666$		0			0
$667$		0			0
$668$		0			0
$669$	9.05842	+	15.6896i	0.350219	+	0.606597i
$670$		0			0
$671$	−9.11684	−	15.7908i	−0.351952	−	0.609598i
$672$		0			0
$673$	6.48913	+	11.2395i	0.250137	+	0.433251i	0.963563	−	0.267480i	$-0.0861909\pi$
$673$	6.48913	+	11.2395i	0.250137	+	0.433251i	−0.713426	+	0.700731i	$0.752858\pi$
$674$		0			0
$675$	−0.313859	+	0.543620i	−0.0120805	+	0.0209240i
$676$		0			0
$677$	−29.1168			−1.11905			−0.559526	−	0.828813i	$-0.689017\pi$
$677$	−29.1168			−1.11905			−0.559526	+	0.828813i	$0.689017\pi$
$678$		0			0
$679$	−3.94158	−	6.82701i	−0.151264	−	0.261997i
$680$		0			0
$681$	−5.74456	+	9.94987i	−0.220132	+	0.381280i
$682$		0			0
$683$	7.11684	−	12.3267i	0.272318	−	0.471669i	−0.697137	−	0.716938i	$-0.745543\pi$
$683$	7.11684	−	12.3267i	0.272318	−	0.471669i	0.969455	+	0.245269i	$0.0788762\pi$
$684$		0			0
$685$	12.3030	+	21.3094i	0.470073	+	0.814190i
$686$		0			0
$687$	6.87228	−	11.9031i	0.262194	−	0.454133i
$688$		0			0
$689$	15.7663			0.600649
$690$		0			0
$691$	−7.31386	+	12.6680i	−0.278232	+	0.481913i	−0.970946	−	0.239301i	$-0.923082\pi$
$691$	−7.31386	+	12.6680i	−0.278232	+	0.481913i	0.692713	+	0.721213i	$0.256415\pi$
$692$		0			0
$693$	−2.74456			−0.104257
$694$		0			0
$695$	−20.4674			−0.776372
$696$		0			0
$697$	7.11684			0.269570
$698$		0			0
$699$	14.3030	+	24.7735i	0.540989	+	0.937020i
$700$		0			0
$701$	−21.1168	+	36.5754i	−0.797572	+	1.38144i	0.123621	+	0.992330i	$0.460549\pi$
$701$	−21.1168	+	36.5754i	−0.797572	+	1.38144i	−0.921193	+	0.389106i	$0.872784\pi$
$702$		0			0
$703$	16.6060	−	23.6039i	0.626306	−	0.890238i
$704$		0			0
$705$	−2.37228	+	4.10891i	−0.0893453	+	0.154751i
$706$		0			0
$707$	−9.51087	−	16.4733i	−0.357693	−	0.619543i
$708$		0			0
$709$	−21.6060			−0.811429			−0.405715	−	0.914000i	$-0.632977\pi$
$709$	−21.6060			−0.811429			−0.405715	+	0.914000i	$0.632977\pi$
$710$		0			0
$711$	−1.37228			−0.0514646
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−3.25544	+	5.63858i	−0.121746	+	0.210871i
$716$		0			0
$717$	22.2337			0.830332
$718$		0			0
$719$	−21.6060	+	37.4226i	−0.805767	+	1.39563i	0.110006	+	0.993931i	$0.464913\pi$
$719$	−21.6060	+	37.4226i	−0.805767	+	1.39563i	−0.915772	+	0.401698i	$0.868420\pi$
$720$		0			0
$721$	8.74456	+	15.1460i	0.325665	+	0.564068i
$722$		0			0
$723$	−12.0584	+	20.8858i	−0.448458	+	0.776751i
$724$		0			0
$725$	−1.37228	+	2.37686i	−0.0509652	+	0.0882744i
$726$		0			0
$727$	14.5475	+	25.1971i	0.539539	+	0.934508i	0.998929	+	0.0462738i	$0.0147347\pi$
$727$	14.5475	+	25.1971i	0.539539	+	0.934508i	−0.459390	+	0.888235i	$0.651932\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	7.62772	−	13.2116i	0.282121	−	0.488649i
$732$		0			0
$733$	−4.68614	−	8.11663i	−0.173087	−	0.299795i	0.766411	−	0.642351i	$-0.222041\pi$
$733$	−4.68614	−	8.11663i	−0.173087	−	0.299795i	−0.939497	+	0.342556i	$0.888707\pi$
$734$		0			0
$735$	−6.06930	−	10.5123i	−0.223869	−	0.387753i
$736$		0			0
$737$	−4.11684	−	7.13058i	−0.151646	−	0.262658i
$738$		0			0
$739$	24.4674			0.900047			0.450023	−	0.893017i	$-0.351416\pi$
$739$	24.4674			0.900047			0.450023	+	0.893017i	$0.351416\pi$
$740$		0			0
$741$	−6.51087			−0.239183
$742$		0			0
$743$	6.25544	+	10.8347i	0.229490	+	0.397488i	0.957657	−	0.287912i	$-0.0929609\pi$
$743$	6.25544	+	10.8347i	0.229490	+	0.397488i	−0.728167	+	0.685399i	$0.759628\pi$
$744$		0			0
$745$	1.93070	+	3.34408i	0.0707355	+	0.122517i
$746$		0			0
$747$	4.00000	+	6.92820i	0.146352	+	0.253490i
$748$		0			0
$749$	3.25544	−	5.63858i	0.118951	−	0.206029i
$750$		0			0
$751$	−15.8832			−0.579585			−0.289792	−	0.957090i	$-0.593586\pi$
$751$	−15.8832			−0.579585			−0.289792	+	0.957090i	$0.593586\pi$
$752$		0			0
$753$	−6.37228	−	11.0371i	−0.232219	−	0.402215i
$754$		0			0
$755$	22.9783	−	39.7995i	0.836264	−	1.44845i
$756$		0			0
$757$	10.1277	−	17.5417i	0.368098	−	0.637565i	−0.621170	−	0.783676i	$-0.713342\pi$
$757$	10.1277	−	17.5417i	0.368098	−	0.637565i	0.989268	+	0.146111i	$0.0466757\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−11.9307	+	20.6646i	−0.432488	+	0.749091i	−0.997087	−	0.0762746i	$-0.975697\pi$
$761$	−11.9307	+	20.6646i	−0.432488	+	0.749091i	0.564599	+	0.825365i	$0.309031\pi$
$762$		0			0
$763$	−5.83966			−0.211410
$764$		0			0
$765$	−1.93070	+	3.34408i	−0.0698047	+	0.120905i
$766$		0			0
$767$	5.48913			0.198201
$768$		0			0
$769$	3.88316			0.140030			0.0700151	−	0.997546i	$-0.477695\pi$
$769$	3.88316			0.140030			0.0700151	+	0.997546i	$0.477695\pi$
$770$		0			0
$771$	19.8614			0.715291
$772$		0			0
$773$	−2.06930	−	3.58413i	−0.0744274	−	0.128912i	0.826410	−	0.563069i	$-0.190380\pi$
$773$	−2.06930	−	3.58413i	−0.0744274	−	0.128912i	−0.900837	+	0.434157i	$0.857046\pi$
$774$		0			0
$775$	−2.94158	+	5.09496i	−0.105665	+	0.183016i
$776$		0			0
$777$	8.31386	+	0.746000i	0.298258	+	0.0267626i
$778$		0			0
$779$	−10.3723	+	17.9653i	−0.371626	+	0.643674i
$780$		0			0
$781$	−11.4891	−	19.8997i	−0.411113	−	0.712069i
$782$		0			0
$783$	4.37228			0.156253
$784$		0			0
$785$	−15.3940			−0.549437
$786$		0			0
$787$	6.11684			0.218042			0.109021	−	0.994039i	$-0.465228\pi$
$787$	6.11684			0.218042			0.109021	+	0.994039i	$0.465228\pi$
$788$		0			0
$789$	−13.3723	+	23.1615i	−0.476066	+	0.824570i
$790$		0			0
$791$	−21.2554			−0.755756
$792$		0			0
$793$	6.25544	−	10.8347i	0.222137	−	0.384753i
$794$		0			0
$795$	13.6277	+	23.6039i	0.483325	+	0.837144i
$796$		0			0
$797$	20.6060	−	35.6906i	0.729901	−	1.26423i	−0.227024	−	0.973889i	$-0.572900\pi$
$797$	20.6060	−	35.6906i	0.729901	−	1.26423i	0.956925	−	0.290336i	$-0.0937671\pi$
$798$		0			0
$799$	−1.62772	+	2.81929i	−0.0575845	+	0.0997394i
$800$		0			0
$801$	−1.81386	−	3.14170i	−0.0640896	−	0.111006i
$802$		0			0
$803$	−5.25544			−0.185460
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.00000	−	1.73205i	−0.0352017	−	0.0609711i
$808$		0			0
$809$	26.4891	+	45.8805i	0.931308	+	1.61307i	0.781089	+	0.624420i	$0.214665\pi$
$809$	26.4891	+	45.8805i	0.931308	+	1.61307i	0.150219	+	0.988653i	$0.452002\pi$
$810$		0			0
$811$	5.48913	+	9.50744i	0.192749	+	0.333852i	0.946160	−	0.323698i	$-0.104926\pi$
$811$	5.48913	+	9.50744i	0.192749	+	0.333852i	−0.753411	+	0.657550i	$0.771593\pi$
$812$		0			0
$813$	−18.8614			−0.661498
$814$		0			0
$815$	58.7011			2.05621
$816$		0			0
$817$	22.2337	+	38.5099i	0.777858	+	1.34729i
$818$		0			0
$819$	−0.941578	−	1.63086i	−0.0329014	−	0.0569869i
$820$		0			0
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	0.991616	−	0.129217i	$-0.0412465\pi$
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	−0.607714	+	0.794156i	$0.707913\pi$
$822$		0			0
$823$	−23.9198	+	41.4304i	−0.833793	+	1.44417i	0.0612167	+	0.998124i	$0.480502\pi$
$823$	−23.9198	+	41.4304i	−0.833793	+	1.44417i	−0.895010	+	0.446047i	$0.852831\pi$
$824$		0			0
$825$	−1.25544			−0.0437087
$826$		0			0
$827$	16.0000	+	27.7128i	0.556375	+	0.963669i	0.997795	+	0.0663686i	$0.0211413\pi$
$827$	16.0000	+	27.7128i	0.556375	+	0.963669i	−0.441421	+	0.897300i	$0.645525\pi$
$828$		0			0
$829$	−19.4307	+	33.6550i	−0.674856	+	1.16889i	0.301655	+	0.953417i	$0.402461\pi$
$829$	−19.4307	+	33.6550i	−0.674856	+	1.16889i	−0.976511	+	0.215468i	$0.930872\pi$
$830$		0			0
$831$	1.06930	−	1.85208i	0.0370935	−	0.0642478i
$832$		0			0
$833$	−4.16439	−	7.21294i	−0.144288	−	0.249913i
$834$		0			0
$835$	1.76631	−	3.05934i	0.0611257	−	0.105873i
$836$		0			0
$837$	9.37228			0.323953
$838$		0			0
$839$	2.00000	−	3.46410i	0.0690477	−	0.119594i	−0.829435	−	0.558604i	$-0.811337\pi$
$839$	2.00000	−	3.46410i	0.0690477	−	0.119594i	0.898482	+	0.439010i	$0.144671\pi$
$840$		0			0
$841$	−9.88316			−0.340798
$842$		0			0
$843$	−7.11684			−0.245117
$844$		0			0
$845$	26.3723			0.907234
$846$		0			0
$847$	4.80298	+	8.31901i	0.165033	+	0.285845i
$848$		0			0
$849$	−0.0584220	+	0.101190i	−0.00200504	+	0.00347283i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	17.3030	−	29.9696i	0.592443	−	1.02614i	−0.401459	−	0.915877i	$-0.631497\pi$
$853$	17.3030	−	29.9696i	0.592443	−	1.02614i	0.993902	−	0.110264i	$-0.0351698\pi$
$854$		0			0
$855$	−5.62772	−	9.74749i	−0.192464	−	0.333357i
$856$		0			0
$857$	30.8397			1.05346			0.526731	−	0.850032i	$-0.323417\pi$
$857$	30.8397			1.05346			0.526731	+	0.850032i	$0.323417\pi$
$858$		0			0
$859$	−37.6060			−1.28310			−0.641550	−	0.767082i	$-0.721708\pi$
$859$	−37.6060			−1.28310			−0.641550	+	0.767082i	$0.721708\pi$
$860$		0			0
$861$	−6.00000			−0.204479
$862$		0			0
$863$	−13.3723	+	23.1615i	−0.455198	+	0.788426i	−0.998700	−	0.0509824i	$-0.983765\pi$
$863$	−13.3723	+	23.1615i	−0.455198	+	0.788426i	0.543502	+	0.839408i	$0.317098\pi$
$864$		0			0
$865$	−54.8397			−1.86460
$866$		0			0
$867$	7.17527	−	12.4279i	0.243685	−	0.422074i
$868$		0			0
$869$	−1.37228	−	2.37686i	−0.0465515	−	0.0806295i
$870$		0			0
$871$	2.82473	−	4.89258i	0.0957125	−	0.165779i
$872$		0			0
$873$	−2.87228	+	4.97494i	−0.0972120	+	0.168376i
$874$		0			0
$875$	−7.11684	−	12.3267i	−0.240593	−	0.416720i
$876$		0			0
$877$	−47.0000			−1.58708			−0.793539	−	0.608520i	$-0.791764\pi$
$877$	−47.0000			−1.58708			−0.793539	+	0.608520i	$0.791764\pi$
$878$		0			0
$879$	16.5584	−	28.6800i	0.558502	−	0.967353i
$880$		0			0
$881$	3.55842	+	6.16337i	0.119886	+	0.207649i	0.919722	−	0.392569i	$-0.128414\pi$
$881$	3.55842	+	6.16337i	0.119886	+	0.207649i	−0.799836	+	0.600218i	$0.795080\pi$
$882$		0			0
$883$	−3.48913	−	6.04334i	−0.117418	−	0.203375i	0.801325	−	0.598229i	$-0.204129\pi$
$883$	−3.48913	−	6.04334i	−0.117418	−	0.203375i	−0.918744	+	0.394854i	$0.870795\pi$
$884$		0			0
$885$	4.74456	+	8.21782i	0.159487	+	0.276239i
$886$		0			0
$887$	20.0000			0.671534			0.335767	−	0.941945i	$-0.391004\pi$
$887$	20.0000			0.671534			0.335767	+	0.941945i	$0.391004\pi$
$888$		0			0
$889$	−11.8397			−0.397089
$890$		0			0
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$		0			0
$893$	−4.74456	−	8.21782i	−0.158771	−	0.274999i
$894$		0			0
$895$	14.2337	+	24.6535i	0.475780	+	0.824075i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	40.9783			1.36670
$900$		0			0
$901$	9.35053	+	16.1956i	0.311511	+	0.539554i
$902$		0			0
$903$	−6.43070	+	11.1383i	−0.214000	+	0.370660i
$904$		0			0
$905$	−5.04755	+	8.74261i	−0.167786	+	0.290614i
$906$		0			0
$907$	10.1753	+	17.6241i	0.337864	+	0.585198i	0.984031	−	0.177998i	$-0.0569622\pi$
$907$	10.1753	+	17.6241i	0.337864	+	0.585198i	−0.646167	+	0.763196i	$0.723629\pi$
$908$		0			0
$909$	−6.93070	+	12.0043i	−0.229877	+	0.398159i
$910$		0			0
$911$	−21.7228			−0.719709			−0.359854	−	0.933008i	$-0.617174\pi$
$911$	−21.7228			−0.719709			−0.359854	+	0.933008i	$0.617174\pi$
$912$		0			0
$913$	−8.00000	+	13.8564i	−0.264761	+	0.458580i
$914$		0			0
$915$	21.6277			0.714990
$916$		0			0
$917$	−14.7446			−0.486908
$918$		0			0
$919$	23.6060			0.778689			0.389345	−	0.921092i	$-0.372702\pi$
$919$	23.6060			0.778689			0.389345	+	0.921092i	$0.372702\pi$
$920$		0			0
$921$	−4.05842	−	7.02939i	−0.133730	−	0.231626i
$922$		0			0
$923$	7.88316	−	13.6540i	0.259477	−	0.449428i
$924$		0			0
$925$	3.80298	+	0.341241i	0.125041	+	0.0112199i
$926$		0			0
$927$	6.37228	−	11.0371i	0.209293	−	0.362506i
$928$		0			0
$929$	4.69702	+	8.13547i	0.154104	+	0.266916i	0.932732	−	0.360569i	$-0.117418\pi$
$929$	4.69702	+	8.13547i	0.154104	+	0.266916i	−0.778628	+	0.627485i	$0.784084\pi$
$930$		0			0
$931$	24.2772			0.795653
$932$		0			0
$933$	28.9783			0.948705
$934$		0			0
$935$	−7.72281			−0.252563
$936$		0			0
$937$	23.9891	−	41.5504i	0.783691	−	1.35739i	−0.146088	−	0.989272i	$-0.546668\pi$
$937$	23.9891	−	41.5504i	0.783691	−	1.35739i	0.929778	−	0.368120i	$-0.119999\pi$
$938$		0			0
$939$	−17.0000			−0.554774
$940$		0			0
$941$	28.1644	−	48.7822i	0.918133	−	1.59025i	0.115884	−	0.993263i	$-0.463030\pi$
$941$	28.1644	−	48.7822i	0.918133	−	1.59025i	0.802249	−	0.596990i	$-0.203637\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	1.62772	−	2.81929i	0.0529497	−	0.0917116i
$946$		0			0
$947$	21.6060	−	37.4226i	0.702100	−	1.21607i	−0.265628	−	0.964075i	$-0.585579\pi$
$947$	21.6060	−	37.4226i	0.702100	−	1.21607i	0.967728	−	0.251997i	$-0.0810872\pi$
$948$		0			0
$949$	−1.80298	−	3.12286i	−0.0585274	−	0.101372i
$950$		0			0
$951$	−12.8832			−0.417765
$952$		0			0
$953$	25.8614	−	44.7933i	0.837733	−	1.45100i	−0.0540525	−	0.998538i	$-0.517214\pi$
$953$	25.8614	−	44.7933i	0.837733	−	1.45100i	0.891786	−	0.452458i	$-0.149453\pi$
$954$		0			0
$955$	26.9783	+	46.7277i	0.872996	+	1.51207i
$956$		0			0
$957$	4.37228	+	7.57301i	0.141336	+	0.244801i
$958$		0			0
$959$	−7.11684	−	12.3267i	−0.229815	−	0.398051i
$960$		0			0
$961$	56.8397			1.83354
$962$		0			0
$963$	−4.74456			−0.152891
$964$		0			0
$965$	−21.9307	−	37.9851i	−0.705974	−	1.22278i
$966$		0			0
$967$	−3.80298	−	6.58696i	−0.122296	−	0.211822i	0.798377	−	0.602158i	$-0.205692\pi$
$967$	−3.80298	−	6.58696i	−0.122296	−	0.211822i	−0.920673	+	0.390336i	$0.872359\pi$
$968$		0			0
$969$	−3.86141	−	6.68815i	−0.124046	−	0.214854i
$970$		0			0
$971$	22.9783	−	39.7995i	0.737407	−	1.27723i	−0.216252	−	0.976338i	$-0.569383\pi$
$971$	22.9783	−	39.7995i	0.737407	−	1.27723i	0.953659	−	0.300889i	$-0.0972834\pi$
$972$		0			0
$973$	11.8397			0.379562
$974$		0			0
$975$	−0.430703	−	0.746000i	−0.0137935	−	0.0238911i
$976$		0			0
$977$	1.62772	−	2.81929i	0.0520753	−	0.0901971i	−0.838813	−	0.544420i	$-0.816750\pi$
$977$	1.62772	−	2.81929i	0.0520753	−	0.0901971i	0.890888	+	0.454223i	$0.150083\pi$
$978$		0			0
$979$	3.62772	−	6.28339i	0.115942	−	0.200818i
$980$		0			0
$981$	2.12772	+	3.68532i	0.0679328	+	0.117663i
$982$		0			0
$983$	−10.3723	+	17.9653i	−0.330824	+	0.573005i	−0.982674	−	0.185344i	$-0.940660\pi$
$983$	−10.3723	+	17.9653i	−0.330824	+	0.573005i	0.651849	+	0.758348i	$0.273993\pi$
$984$		0			0
$985$	−32.3288			−1.03008
$986$		0			0
$987$	1.37228	−	2.37686i	0.0436802	−	0.0756563i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	17.7663			0.564366			0.282183	−	0.959361i	$-0.408942\pi$
$991$	17.7663			0.564366			0.282183	+	0.959361i	$0.408942\pi$
$992$		0			0
$993$	35.6060			1.12992
$994$		0			0
$995$	7.86141	+	13.6164i	0.249223	+	0.431667i
$996$		0			0
$997$	26.4891	−	45.8805i	0.838919	−	1.45305i	−0.0518802	−	0.998653i	$-0.516521\pi$
$997$	26.4891	−	45.8805i	0.838919	−	1.45305i	0.890799	−	0.454397i	$-0.150145\pi$
$998$		0			0
$999$	−2.55842	−	5.51856i	−0.0809449	−	0.174599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1776.2.q.h.1009.2		4
4.3	odd	2		222.2.e.c.121.2	✓	4
12.11	even	2		666.2.f.g.343.1		4
37.26	even	3	inner	1776.2.q.h.433.2		4
148.27	odd	6		8214.2.a.o.1.2		2
148.47	odd	6		8214.2.a.m.1.1		2
148.63	odd	6		222.2.e.c.211.2	yes	4
444.359	even	6		666.2.f.g.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
222.2.e.c.121.2	✓	4	4.3	odd	2
222.2.e.c.211.2	yes	4	148.63	odd	6
666.2.f.g.343.1		4	12.11	even	2
666.2.f.g.433.1		4	444.359	even	6
1776.2.q.h.433.2		4	37.26	even	3	inner
1776.2.q.h.1009.2		4	1.1	even	1	trivial
8214.2.a.m.1.1		2	148.47	odd	6
8214.2.a.o.1.2		2	148.27	odd	6

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:	\( N \)	\(=\)	\( 1776 = 2^{4} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1776.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(1.18614 + 2.05446i) q^{5} +(-0.686141 - 1.18843i) q^{7} +(-0.500000 + 0.866025i) q^{9} -2.00000 q^{11} +(-0.686141 - 1.18843i) q^{13} +(1.18614 - 2.05446i) q^{15} +(0.813859 - 1.40965i) q^{17} +(2.37228 + 4.10891i) q^{19} +(-0.686141 + 1.18843i) q^{21} +(-0.313859 + 0.543620i) q^{25} +1.00000 q^{27} +4.37228 q^{29} +9.37228 q^{31} +(1.00000 + 1.73205i) q^{33} +(1.62772 - 2.81929i) q^{35} +(-2.55842 - 5.51856i) q^{37} +(-0.686141 + 1.18843i) q^{39} +(2.18614 + 3.78651i) q^{41} +9.37228 q^{43} -2.37228 q^{45} -2.00000 q^{47} +(2.55842 - 4.43132i) q^{49} -1.62772 q^{51} +(-5.74456 + 9.94987i) q^{53} +(-2.37228 - 4.10891i) q^{55} +(2.37228 - 4.10891i) q^{57} +(-2.00000 + 3.46410i) q^{59} +(4.55842 + 7.89542i) q^{61} +1.37228 q^{63} +(1.62772 - 2.81929i) q^{65} +(2.05842 + 3.56529i) q^{67} +(5.74456 + 9.94987i) q^{71} +2.62772 q^{73} +0.627719 q^{75} +(1.37228 + 2.37686i) q^{77} +(0.686141 + 1.18843i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(4.00000 - 6.92820i) q^{83} +3.86141 q^{85} +(-2.18614 - 3.78651i) q^{87} +(-1.81386 + 3.14170i) q^{89} +(-0.941578 + 1.63086i) q^{91} +(-4.68614 - 8.11663i) q^{93} +(-5.62772 + 9.74749i) q^{95} +5.74456 q^{97} +(1.00000 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - q^{5} + 3 q^{7} - 2 q^{9} - 8 q^{11} + 3 q^{13} - q^{15} + 9 q^{17} - 2 q^{19} + 3 q^{21} - 7 q^{25} + 4 q^{27} + 6 q^{29} + 26 q^{31} + 4 q^{33} + 18 q^{35} + 7 q^{37} + 3 q^{39} + 3 q^{41}+ \cdots + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - q^5 + 3 * q^7 - 2 * q^9 - 8 * q^11 + 3 * q^13 - q^15 + 9 * q^17 - 2 * q^19 + 3 * q^21 - 7 * q^25 + 4 * q^27 + 6 * q^29 + 26 * q^31 + 4 * q^33 + 18 * q^35 + 7 * q^37 + 3 * q^39 + 3 * q^41 + 26 * q^43 + 2 * q^45 - 8 * q^47 - 7 * q^49 - 18 * q^51 + 2 * q^55 - 2 * q^57 - 8 * q^59 + q^61 - 6 * q^63 + 18 * q^65 - 9 * q^67 + 22 * q^73 + 14 * q^75 - 6 * q^77 - 3 * q^79 - 2 * q^81 + 16 * q^83 - 42 * q^85 - 3 * q^87 - 13 * q^89 - 21 * q^91 - 13 * q^93 - 34 * q^95 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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