LMFDB - Embedded newform 666.2.f.g.433.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(343,666)] 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("666.343"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2,0,-2,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.31803677462$
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			433.1
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	666.433
Dual form			666.2.f.g.343.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.18614 + 2.05446i) q^{5} +(0.686141 - 1.18843i) q^{7} +1.00000 q^{8} +2.37228 q^{10} -2.00000 q^{11} +(-0.686141 + 1.18843i) q^{13} -1.37228 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.813859 - 1.40965i) q^{17} +(-2.37228 + 4.10891i) q^{19} +(-1.18614 - 2.05446i) q^{20} +(1.00000 + 1.73205i) q^{22} +(-0.313859 - 0.543620i) q^{25} +1.37228 q^{26} +(0.686141 + 1.18843i) q^{28} -4.37228 q^{29} -9.37228 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.813859 + 1.40965i) q^{34} +(1.62772 + 2.81929i) q^{35} +(-2.55842 + 5.51856i) q^{37} +4.74456 q^{38} +(-1.18614 + 2.05446i) q^{40} +(-2.18614 + 3.78651i) q^{41} -9.37228 q^{43} +(1.00000 - 1.73205i) q^{44} -2.00000 q^{47} +(2.55842 + 4.43132i) q^{49} +(-0.313859 + 0.543620i) q^{50} +(-0.686141 - 1.18843i) q^{52} +(5.74456 + 9.94987i) q^{53} +(2.37228 - 4.10891i) q^{55} +(0.686141 - 1.18843i) q^{56} +(2.18614 + 3.78651i) q^{58} +(-2.00000 - 3.46410i) q^{59} +(4.55842 - 7.89542i) q^{61} +(4.68614 + 8.11663i) q^{62} +1.00000 q^{64} +(-1.62772 - 2.81929i) q^{65} +(-2.05842 + 3.56529i) q^{67} +1.62772 q^{68} +(1.62772 - 2.81929i) q^{70} +(5.74456 - 9.94987i) q^{71} +2.62772 q^{73} +(6.05842 - 0.543620i) q^{74} +(-2.37228 - 4.10891i) q^{76} +(-1.37228 + 2.37686i) q^{77} +(-0.686141 + 1.18843i) q^{79} +2.37228 q^{80} +4.37228 q^{82} +(4.00000 + 6.92820i) q^{83} +3.86141 q^{85} +(4.68614 + 8.11663i) q^{86} -2.00000 q^{88} +(1.81386 + 3.14170i) q^{89} +(0.941578 + 1.63086i) q^{91} +(1.00000 + 1.73205i) q^{94} +(-5.62772 - 9.74749i) q^{95} +5.74456 q^{97} +(2.55842 - 4.43132i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + q^{5} - 3 q^{7} + 4 q^{8} - 2 q^{10} - 8 q^{11} + 3 q^{13} + 6 q^{14} - 2 q^{16} - 9 q^{17} + 2 q^{19} + q^{20} + 4 q^{22} - 7 q^{25} - 6 q^{26} - 3 q^{28} - 6 q^{29} - 26 q^{31}+ \cdots - 7 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + q^5 - 3 * q^7 + 4 * q^8 - 2 * q^10 - 8 * q^11 + 3 * q^13 + 6 * q^14 - 2 * q^16 - 9 * q^17 + 2 * q^19 + q^20 + 4 * q^22 - 7 * q^25 - 6 * q^26 - 3 * q^28 - 6 * q^29 - 26 * q^31 - 2 * q^32 - 9 * q^34 + 18 * q^35 + 7 * q^37 - 4 * q^38 + q^40 - 3 * q^41 - 26 * q^43 + 4 * q^44 - 8 * q^47 - 7 * q^49 - 7 * q^50 + 3 * q^52 - 2 * q^55 - 3 * q^56 + 3 * q^58 - 8 * q^59 + q^61 + 13 * q^62 + 4 * q^64 - 18 * q^65 + 9 * q^67 + 18 * q^68 + 18 * q^70 + 22 * q^73 + 7 * q^74 + 2 * q^76 + 6 * q^77 + 3 * q^79 - 2 * q^80 + 6 * q^82 + 16 * q^83 - 42 * q^85 + 13 * q^86 - 8 * q^88 + 13 * q^89 + 21 * q^91 + 4 * q^94 - 34 * q^95 - 7 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.18614	+	2.05446i	−0.530458	+	0.918781i	0.468910	+	0.883246i	$0.344647\pi$
$5$	−1.18614	+	2.05446i	−0.530458	+	0.918781i	−0.999368	+	0.0355348i	$0.988687\pi$
$6$		0			0
$7$	0.686141	−	1.18843i	0.259337	−	0.449185i	−0.706728	−	0.707486i	$-0.749829\pi$
$7$	0.686141	−	1.18843i	0.259337	−	0.449185i	0.966064	+	0.258301i	$0.0831627\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	2.37228			0.750181
$11$	−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	−0.945350	−	0.326057i	$-0.894280\pi$
$13$	−0.686141	+	1.18843i	−0.190301	+	0.329611i	0.755049	+	0.655669i	$0.227613\pi$
$14$	−1.37228			−0.366758
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.813859	−	1.40965i	−0.197390	−	0.341889i	0.750291	−	0.661107i	$-0.229913\pi$
$17$	−0.813859	−	1.40965i	−0.197390	−	0.341889i	−0.947681	+	0.319218i	$0.896580\pi$
$18$		0			0
$19$	−2.37228	+	4.10891i	−0.544239	+	0.942649i	0.454416	+	0.890790i	$0.349848\pi$
$19$	−2.37228	+	4.10891i	−0.544239	+	0.942649i	−0.998654	+	0.0518593i	$0.983485\pi$
$20$	−1.18614	−	2.05446i	−0.265229	−	0.459390i
$21$		0			0
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$		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
$26$	1.37228			0.269127
$27$		0			0
$28$	0.686141	+	1.18843i	0.129668	+	0.224592i
$29$	−4.37228			−0.811912			−0.405956	−	0.913893i	$-0.633061\pi$
$29$	−4.37228			−0.811912			−0.405956	+	0.913893i	$0.633061\pi$
$30$		0			0
$31$	−9.37228			−1.68331			−0.841656	−	0.540015i	$-0.818419\pi$
$31$	−9.37228			−1.68331			−0.841656	+	0.540015i	$0.818419\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−0.813859	+	1.40965i	−0.139576	+	0.241752i
$35$	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
$38$	4.74456			0.769670
$39$		0			0
$40$	−1.18614	+	2.05446i	−0.187545	+	0.324838i
$41$	−2.18614	+	3.78651i	−0.341418	+	0.591353i	−0.984696	−	0.174279i	$-0.944240\pi$
$41$	−2.18614	+	3.78651i	−0.341418	+	0.591353i	0.643278	+	0.765632i	$0.277574\pi$
$42$		0			0
$43$	−9.37228			−1.42926			−0.714630	−	0.699503i	$-0.753405\pi$
$43$	−9.37228			−1.42926			−0.714630	+	0.699503i	$0.753405\pi$
$44$	1.00000	−	1.73205i	0.150756	−	0.261116i
$45$		0			0
$46$		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
$50$	−0.313859	+	0.543620i	−0.0443864	+	0.0768795i
$51$		0			0
$52$	−0.686141	−	1.18843i	−0.0951506	−	0.164806i
$53$	5.74456	+	9.94987i	0.789076	+	1.36672i	0.926533	+	0.376213i	$0.122774\pi$
$53$	5.74456	+	9.94987i	0.789076	+	1.36672i	−0.137457	+	0.990508i	$0.543893\pi$
$54$		0			0
$55$	2.37228	−	4.10891i	0.319878	−	0.554046i
$56$	0.686141	−	1.18843i	0.0916894	−	0.158811i
$57$		0			0
$58$	2.18614	+	3.78651i	0.287054	+	0.497193i
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	0.705965	−	0.708247i	$-0.250514\pi$
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	−0.966342	+	0.257260i	$0.917180\pi$
$60$		0			0
$61$	4.55842	−	7.89542i	0.583646	−	1.01090i	−0.411397	−	0.911456i	$-0.634959\pi$
$61$	4.55842	−	7.89542i	0.583646	−	1.01090i	0.995043	−	0.0994483i	$-0.0317078\pi$
$62$	4.68614	+	8.11663i	0.595140	+	1.03081i
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.62772	−	2.81929i	−0.201894	−	0.349690i
$66$		0			0
$67$	−2.05842	+	3.56529i	−0.251476	+	0.435570i	−0.963932	−	0.266147i	$-0.914249\pi$
$67$	−2.05842	+	3.56529i	−0.251476	+	0.435570i	0.712456	+	0.701717i	$0.247583\pi$
$68$	1.62772			0.197390
$69$		0			0
$70$	1.62772	−	2.81929i	0.194550	−	0.336970i
$71$	5.74456	−	9.94987i	0.681754	−	1.18083i	−0.292691	−	0.956207i	$-0.594551\pi$
$71$	5.74456	−	9.94987i	0.681754	−	1.18083i	0.974445	−	0.224626i	$-0.0721160\pi$
$72$		0			0
$73$	2.62772			0.307551			0.153776	−	0.988106i	$-0.450857\pi$
$73$	2.62772			0.307551			0.153776	+	0.988106i	$0.450857\pi$
$74$	6.05842	−	0.543620i	0.704277	−	0.0631946i
$75$		0			0
$76$	−2.37228	−	4.10891i	−0.272119	−	0.471325i
$77$	−1.37228	+	2.37686i	−0.156386	+	0.270868i
$78$		0			0
$79$	−0.686141	+	1.18843i	−0.0771969	+	0.133709i	−0.902039	−	0.431653i	$-0.857930\pi$
$79$	−0.686141	+	1.18843i	−0.0771969	+	0.133709i	0.824843	+	0.565362i	$0.191264\pi$
$80$	2.37228			0.265229
$81$		0			0
$82$	4.37228			0.482838
$83$	4.00000	+	6.92820i	0.439057	+	0.760469i	0.997617	−	0.0689950i	$-0.0219793\pi$
$83$	4.00000	+	6.92820i	0.439057	+	0.760469i	−0.558560	+	0.829464i	$0.688646\pi$
$84$		0			0
$85$	3.86141			0.418828
$86$	4.68614	+	8.11663i	0.505320	+	0.875239i
$87$		0			0
$88$	−2.00000			−0.213201
$89$	1.81386	+	3.14170i	0.192269	+	0.333019i	0.946002	−	0.324162i	$-0.105082\pi$
$89$	1.81386	+	3.14170i	0.192269	+	0.333019i	−0.753733	+	0.657181i	$0.771749\pi$
$90$		0			0
$91$	0.941578	+	1.63086i	0.0987042	+	0.170961i
$92$		0			0
$93$		0			0
$94$	1.00000	+	1.73205i	0.103142	+	0.178647i
$95$	−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	$0.405800\pi$
$98$	2.55842	−	4.43132i	0.258440	−	0.447631i
$99$		0			0
$100$	0.627719			0.0627719
$101$	−13.8614			−1.37926			−0.689631	−	0.724161i	$-0.742227\pi$
$101$	−13.8614			−1.37926			−0.689631	+	0.724161i	$0.742227\pi$
$102$		0			0
$103$	12.7446			1.25576			0.627880	−	0.778311i	$-0.283923\pi$
$103$	12.7446			1.25576			0.627880	+	0.778311i	$0.283923\pi$
$104$	−0.686141	+	1.18843i	−0.0672816	+	0.116535i
$105$		0			0
$106$	5.74456	−	9.94987i	0.557961	−	0.966417i
$107$	2.37228	−	4.10891i	0.229337	−	0.397223i	−0.728275	−	0.685285i	$-0.759678\pi$
$107$	2.37228	−	4.10891i	0.229337	−	0.397223i	0.957612	+	0.288062i	$0.0930109\pi$
$108$		0			0
$109$	2.12772	+	3.68532i	0.203798	+	0.352989i	0.949749	−	0.313012i	$-0.101338\pi$
$109$	2.12772	+	3.68532i	0.203798	+	0.352989i	−0.745951	+	0.666001i	$0.768005\pi$
$110$	−4.74456			−0.452376
$111$		0			0
$112$	−1.37228			−0.129668
$113$	−7.74456	−	13.4140i	−0.728547	−	1.26188i	−0.957497	−	0.288443i	$-0.906863\pi$
$113$	−7.74456	−	13.4140i	−0.728547	−	1.26188i	0.228950	−	0.973438i	$-0.426471\pi$
$114$		0			0
$115$		0			0
$116$	2.18614	−	3.78651i	0.202978	−	0.351568i
$117$		0			0
$118$	−2.00000	+	3.46410i	−0.184115	+	0.318896i
$119$	−2.23369			−0.204762
$120$		0			0
$121$	−7.00000			−0.636364
$122$	−9.11684			−0.825400
$123$		0			0
$124$	4.68614	−	8.11663i	0.420828	−	0.728895i
$125$	−10.3723			−0.927725
$126$		0			0
$127$	−4.31386	−	7.47182i	−0.382793	−	0.663017i	0.608667	−	0.793426i	$-0.291704\pi$
$127$	−4.31386	−	7.47182i	−0.382793	−	0.663017i	−0.991460	+	0.130408i	$0.958371\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−1.62772	+	2.81929i	−0.142760	+	0.247268i
$131$	5.37228	+	9.30506i	0.469378	+	0.812987i	0.999387	−	0.0350049i	$-0.0111447\pi$
$131$	5.37228	+	9.30506i	0.469378	+	0.812987i	−0.530009	+	0.847992i	$0.677811\pi$
$132$		0			0
$133$	3.25544	+	5.63858i	0.282282	+	0.488927i
$134$	4.11684			0.355641
$135$		0			0
$136$	−0.813859	−	1.40965i	−0.0697879	−	0.120876i
$137$	−10.3723			−0.886164			−0.443082	−	0.896481i	$-0.646115\pi$
$137$	−10.3723			−0.886164			−0.443082	+	0.896481i	$0.646115\pi$
$138$		0			0
$139$	4.31386	+	7.47182i	0.365897	+	0.633752i	0.988920	−	0.148452i	$-0.0474290\pi$
$139$	4.31386	+	7.47182i	0.365897	+	0.633752i	−0.623023	+	0.782204i	$0.714096\pi$
$140$	−3.25544			−0.275135
$141$		0			0
$142$	−11.4891			−0.964146
$143$	1.37228	−	2.37686i	0.114756	−	0.198763i
$144$		0			0
$145$	5.18614	−	8.98266i	0.430686	−	0.745969i
$146$	−1.31386	−	2.27567i	−0.108736	−	0.188336i
$147$		0			0
$148$	−3.50000	−	4.97494i	−0.287698	−	0.408937i
$149$	−1.62772			−0.133348			−0.0666740	−	0.997775i	$-0.521239\pi$
$149$	−1.62772			−0.133348			−0.0666740	+	0.997775i	$0.521239\pi$
$150$		0			0
$151$	9.68614	−	16.7769i	0.788247	−	1.36528i	−0.138793	−	0.990321i	$-0.544322\pi$
$151$	9.68614	−	16.7769i	0.788247	−	1.36528i	0.927040	−	0.374962i	$-0.122344\pi$
$152$	−2.37228	+	4.10891i	−0.192417	+	0.333277i
$153$		0			0
$154$	2.74456			0.221163
$155$	11.1168	−	19.2549i	0.892926	−	1.54659i
$156$		0			0
$157$	−3.24456	−	5.61975i	−0.258944	−	0.448505i	0.707015	−	0.707198i	$-0.250041\pi$
$157$	−3.24456	−	5.61975i	−0.258944	−	0.448505i	−0.965959	+	0.258694i	$0.916708\pi$
$158$	1.37228			0.109173
$159$		0			0
$160$	−1.18614	−	2.05446i	−0.0937727	−	0.162419i
$161$		0			0
$162$		0			0
$163$	−12.3723	−	21.4294i	−0.969072	−	1.67848i	−0.698253	−	0.715852i	$-0.746039\pi$
$163$	−12.3723	−	21.4294i	−0.969072	−	1.67848i	−0.270819	−	0.962630i	$-0.587295\pi$
$164$	−2.18614	−	3.78651i	−0.170709	−	0.295676i
$165$		0			0
$166$	4.00000	−	6.92820i	0.310460	−	0.537733i
$167$	−0.744563	+	1.28962i	−0.0576160	+	0.0997938i	−0.893395	−	0.449273i	$-0.851683\pi$
$167$	−0.744563	+	1.28962i	−0.0576160	+	0.0997938i	0.835779	+	0.549066i	$0.185017\pi$
$168$		0			0
$169$	5.55842	+	9.62747i	0.427571	+	0.740575i
$170$	−1.93070	−	3.34408i	−0.148078	−	0.256479i
$171$		0			0
$172$	4.68614	−	8.11663i	0.357315	−	0.618888i
$173$	11.5584	+	20.0198i	0.878771	+	1.52208i	0.852691	+	0.522415i	$0.174969\pi$
$173$	11.5584	+	20.0198i	0.878771	+	1.52208i	0.0260794	+	0.999660i	$0.491698\pi$
$174$		0			0
$175$	−0.861407			−0.0651162
$176$	1.00000	+	1.73205i	0.0753778	+	0.130558i
$177$		0			0
$178$	1.81386	−	3.14170i	0.135955	−	0.235480i
$179$	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	−0.776050	−	0.630671i	$-0.782780\pi$
$181$	2.12772	−	3.68532i	0.158152	−	0.273927i	0.934202	+	0.356744i	$0.116113\pi$
$182$	0.941578	−	1.63086i	0.0697944	−	0.120887i
$183$		0			0
$184$		0			0
$185$	−8.30298	−	11.8020i	−0.610448	−	0.867697i
$186$		0			0
$187$	1.62772	+	2.81929i	0.119031	+	0.206167i
$188$	1.00000	−	1.73205i	0.0729325	−	0.126323i
$189$		0			0
$190$	−5.62772	+	9.74749i	−0.408278	+	0.707158i
$191$	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	$0.731755\pi$
$194$	−2.87228	−	4.97494i	−0.206218	−	0.357180i
$195$		0			0
$196$	−5.11684			−0.365489
$197$	6.81386	+	11.8020i	0.485467	+	0.840854i	0.999861	−	0.0167003i	$-0.00531612\pi$
$197$	6.81386	+	11.8020i	0.485467	+	0.840854i	−0.514393	+	0.857554i	$0.671983\pi$
$198$		0			0
$199$	−6.62772			−0.469827			−0.234913	−	0.972016i	$-0.575481\pi$
$199$	−6.62772			−0.469827			−0.234913	+	0.972016i	$0.575481\pi$
$200$	−0.313859	−	0.543620i	−0.0221932	−	0.0384398i
$201$		0			0
$202$	6.93070	+	12.0043i	0.487643	+	0.844622i
$203$	−3.00000	+	5.19615i	−0.210559	+	0.364698i
$204$		0			0
$205$	−5.18614	−	8.98266i	−0.362216	−	0.627376i
$206$	−6.37228	−	11.0371i	−0.443978	−	0.768992i
$207$		0			0
$208$	1.37228			0.0951506
$209$	4.74456	−	8.21782i	0.328188	−	0.568439i
$210$		0			0
$211$	13.3723			0.920586			0.460293	−	0.887767i	$-0.347744\pi$
$211$	13.3723			0.920586			0.460293	+	0.887767i	$0.347744\pi$
$212$	−11.4891			−0.789076
$213$		0			0
$214$	−4.74456			−0.324332
$215$	11.1168	−	19.2549i	0.758162	−	1.31318i
$216$		0			0
$217$	−6.43070	+	11.1383i	−0.436545	+	0.756117i
$218$	2.12772	−	3.68532i	0.144107	−	0.249601i
$219$		0			0
$220$	2.37228	+	4.10891i	0.159939	+	0.277023i
$221$	2.23369			0.150254
$222$		0			0
$223$	18.1168			1.21319			0.606597	−	0.795010i	$-0.292534\pi$
$223$	18.1168			1.21319			0.606597	+	0.795010i	$0.292534\pi$
$224$	0.686141	+	1.18843i	0.0458447	+	0.0794054i
$225$		0			0
$226$	−7.74456	+	13.4140i	−0.515161	+	0.892284i
$227$	−5.74456	+	9.94987i	−0.381280	+	0.660396i	−0.991246	−	0.132032i	$-0.957850\pi$
$227$	−5.74456	+	9.94987i	−0.381280	+	0.660396i	0.609965	+	0.792428i	$0.291183\pi$
$228$		0			0
$229$	6.87228	−	11.9031i	0.454133	−	0.786582i	−0.544505	−	0.838758i	$-0.683282\pi$
$229$	6.87228	−	11.9031i	0.454133	−	0.786582i	0.998638	+	0.0521761i	$0.0166157\pi$
$230$		0			0
$231$		0			0
$232$	−4.37228			−0.287054
$233$	28.6060			1.87404			0.937020	−	0.349277i	$-0.113573\pi$
$233$	28.6060			1.87404			0.937020	+	0.349277i	$0.113573\pi$
$234$		0			0
$235$	2.37228	−	4.10891i	0.154751	−	0.268036i
$236$	4.00000			0.260378
$237$		0			0
$238$	1.11684	+	1.93443i	0.0723942	+	0.125391i
$239$	−11.1168	−	19.2549i	−0.719089	−	1.24550i	−0.961361	−	0.275290i	$-0.911226\pi$
$239$	−11.1168	−	19.2549i	−0.719089	−	1.24550i	0.242272	−	0.970208i	$-0.422107\pi$
$240$		0			0
$241$	−12.0584	+	20.8858i	−0.776751	+	1.34537i	0.157054	+	0.987590i	$0.449800\pi$
$241$	−12.0584	+	20.8858i	−0.776751	+	1.34537i	−0.933805	+	0.357783i	$0.883533\pi$
$242$	3.50000	+	6.06218i	0.224989	+	0.389692i
$243$		0			0
$244$	4.55842	+	7.89542i	0.291823	+	0.505452i
$245$	−12.1386			−0.775506
$246$		0			0
$247$	−3.25544	−	5.63858i	−0.207139	−	0.358774i
$248$	−9.37228			−0.595140
$249$		0			0
$250$	5.18614	+	8.98266i	0.328000	+	0.568113i
$251$	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
$254$	−4.31386	+	7.47182i	−0.270676	+	0.468824i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.93070	+	17.2005i	0.619460	+	1.07294i	0.989584	+	0.143954i	$0.0459818\pi$
$257$	9.93070	+	17.2005i	0.619460	+	1.07294i	−0.370124	+	0.928982i	$0.620685\pi$
$258$		0			0
$259$	4.80298	+	6.82701i	0.298443	+	0.424210i
$260$	3.25544			0.201894
$261$		0			0
$262$	5.37228	−	9.30506i	0.331901	−	0.574869i
$263$	−13.3723	+	23.1615i	−0.824570	+	1.42820i	0.0776771	+	0.996979i	$0.475250\pi$
$263$	−13.3723	+	23.1615i	−0.824570	+	1.42820i	−0.902247	+	0.431219i	$0.858084\pi$
$264$		0			0
$265$	−27.2554			−1.67429
$266$	3.25544	−	5.63858i	0.199604	−	0.345724i
$267$		0			0
$268$	−2.05842	−	3.56529i	−0.125738	−	0.217785i
$269$	−2.00000			−0.121942			−0.0609711	−	0.998140i	$-0.519420\pi$
$269$	−2.00000			−0.121942			−0.0609711	+	0.998140i	$0.519420\pi$
$270$		0			0
$271$	−9.43070	−	16.3345i	−0.572874	−	0.992248i	−0.996269	−	0.0863022i	$-0.972495\pi$
$271$	−9.43070	−	16.3345i	−0.572874	−	0.992248i	0.423395	−	0.905945i	$-0.360838\pi$
$272$	−0.813859	+	1.40965i	−0.0493475	+	0.0854723i
$273$		0			0
$274$	5.18614	+	8.98266i	0.313306	+	0.542662i
$275$	0.627719	+	1.08724i	0.0378529	+	0.0655631i
$276$		0			0
$277$	1.06930	−	1.85208i	0.0642478	−	0.111280i	−0.832112	−	0.554607i	$-0.812869\pi$
$277$	1.06930	−	1.85208i	0.0642478	−	0.111280i	0.896360	+	0.443327i	$0.146202\pi$
$278$	4.31386	−	7.47182i	0.258728	−	0.448130i
$279$		0			0
$280$	1.62772	+	2.81929i	0.0972748	+	0.168485i
$281$	−3.55842	−	6.16337i	−0.212278	−	0.367676i	0.740149	−	0.672443i	$-0.234755\pi$
$281$	−3.55842	−	6.16337i	−0.212278	−	0.367676i	−0.952427	+	0.304767i	$0.901421\pi$
$282$		0			0
$283$	0.0584220	−	0.101190i	0.00347283	−	0.00601511i	−0.864284	−	0.503005i	$-0.832228\pi$
$283$	0.0584220	−	0.101190i	0.00347283	−	0.00601511i	0.867757	+	0.496989i	$0.165561\pi$
$284$	5.74456	+	9.94987i	0.340877	+	0.590416i
$285$		0			0
$286$	−2.74456			−0.162289
$287$	3.00000	+	5.19615i	0.177084	+	0.306719i
$288$		0			0
$289$	7.17527	−	12.4279i	0.422074	−	0.731054i
$290$	−10.3723			−0.609081
$291$		0			0
$292$	−1.31386	+	2.27567i	−0.0768878	+	0.133174i
$293$	−16.5584	+	28.6800i	−0.967353	+	1.67551i	−0.264199	+	0.964468i	$0.585107\pi$
$293$	−16.5584	+	28.6800i	−0.967353	+	1.67551i	−0.703155	+	0.711037i	$0.748226\pi$
$294$		0			0
$295$	9.48913			0.552478
$296$	−2.55842	+	5.51856i	−0.148705	+	0.320760i
$297$		0			0
$298$	0.813859	+	1.40965i	0.0471456	+	0.0816586i
$299$		0			0
$300$		0			0
$301$	−6.43070	+	11.1383i	−0.370660	+	0.642001i
$302$	−19.3723			−1.11475
$303$		0			0
$304$	4.74456			0.272119
$305$	10.8139	+	18.7302i	0.619200	+	1.07249i
$306$		0			0
$307$	−8.11684			−0.463253			−0.231626	−	0.972805i	$-0.574405\pi$
$307$	−8.11684			−0.463253			−0.231626	+	0.972805i	$0.574405\pi$
$308$	−1.37228	−	2.37686i	−0.0781930	−	0.135434i
$309$		0			0
$310$	−22.2337			−1.26279
$311$	−14.4891	−	25.0959i	−0.821603	−	1.42306i	−0.904488	−	0.426499i	$-0.859747\pi$
$311$	−14.4891	−	25.0959i	−0.821603	−	1.42306i	0.0828852	−	0.996559i	$-0.473587\pi$
$312$		0			0
$313$	8.50000	+	14.7224i	0.480448	+	0.832161i	0.999748	−	0.0224310i	$-0.00714060\pi$
$313$	8.50000	+	14.7224i	0.480448	+	0.832161i	−0.519300	+	0.854592i	$0.673807\pi$
$314$	−3.24456	+	5.61975i	−0.183101	+	0.317141i
$315$		0			0
$316$	−0.686141	−	1.18843i	−0.0385984	−	0.0668544i
$317$	−6.44158	−	11.1571i	−0.361795	−	0.626647i	0.626461	−	0.779453i	$-0.284503\pi$
$317$	−6.44158	−	11.1571i	−0.361795	−	0.626647i	−0.988256	+	0.152805i	$0.951169\pi$
$318$		0			0
$319$	8.74456			0.489602
$320$	−1.18614	+	2.05446i	−0.0663073	+	0.114848i
$321$		0			0
$322$		0			0
$323$	7.72281			0.429709
$324$		0			0
$325$	0.861407			0.0477822
$326$	−12.3723	+	21.4294i	−0.685237	+	1.18687i
$327$		0			0
$328$	−2.18614	+	3.78651i	−0.120709	+	0.209075i
$329$	−1.37228	+	2.37686i	−0.0756563	+	0.131041i
$330$		0			0
$331$	17.8030	+	30.8357i	0.978541	+	1.69488i	0.667719	+	0.744414i	$0.267271\pi$
$331$	17.8030	+	30.8357i	0.978541	+	1.69488i	0.310822	+	0.950468i	$0.399396\pi$
$332$	−8.00000			−0.439057
$333$		0			0
$334$	1.48913			0.0814813
$335$	−4.88316	−	8.45787i	−0.266795	−	0.462103i
$336$		0			0
$337$	−14.8723	+	25.7595i	−0.810145	+	1.40321i	0.102618	+	0.994721i	$0.467278\pi$
$337$	−14.8723	+	25.7595i	−0.810145	+	1.40321i	−0.912762	+	0.408491i	$0.866055\pi$
$338$	5.55842	−	9.62747i	0.302338	−	0.523665i
$339$		0			0
$340$	−1.93070	+	3.34408i	−0.104707	+	0.181358i
$341$	18.7446			1.01507
$342$		0			0
$343$	16.6277			0.897812
$344$	−9.37228			−0.505320
$345$		0			0
$346$	11.5584	−	20.0198i	0.621385	−	1.07627i
$347$	−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	0.961852	−	0.273571i	$-0.0882048\pi$
$349$	4.55842	+	7.89542i	0.244007	+	0.422632i	−0.717845	+	0.696203i	$0.754871\pi$
$350$	0.430703	+	0.746000i	0.0230221	+	0.0398754i
$351$		0			0
$352$	1.00000	−	1.73205i	0.0533002	−	0.0923186i
$353$	15.3030	+	26.5055i	0.814496	+	1.41075i	0.909689	+	0.415289i	$0.136320\pi$
$353$	15.3030	+	26.5055i	0.814496	+	1.41075i	−0.0951938	+	0.995459i	$0.530347\pi$
$354$		0			0
$355$	13.6277	+	23.6039i	0.723284	+	1.25276i
$356$	−3.62772			−0.192269
$357$		0			0
$358$	−6.00000	−	10.3923i	−0.317110	−	0.549250i
$359$	−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
$362$	−4.25544			−0.223661
$363$		0			0
$364$	−1.88316			−0.0987042
$365$	−3.11684	+	5.39853i	−0.163143	+	0.282572i
$366$		0			0
$367$	−3.05842	+	5.29734i	−0.159648	+	0.276519i	−0.934742	−	0.355327i	$-0.884369\pi$
$367$	−3.05842	+	5.29734i	−0.159648	+	0.276519i	0.775094	+	0.631846i	$0.217703\pi$
$368$		0			0
$369$		0			0
$370$	−6.06930	+	13.0916i	−0.315528	+	0.680598i
$371$	15.7663			0.818546
$372$		0			0
$373$	15.5000	−	26.8468i	0.802560	−	1.39007i	−0.115367	−	0.993323i	$-0.536804\pi$
$373$	15.5000	−	26.8468i	0.802560	−	1.39007i	0.917926	−	0.396751i	$-0.129862\pi$
$374$	1.62772	−	2.81929i	0.0841673	−	0.145782i
$375$		0			0
$376$	−2.00000			−0.103142
$377$	3.00000	−	5.19615i	0.154508	−	0.267615i
$378$		0			0
$379$	13.8614	+	24.0087i	0.712013	+	1.23324i	0.964100	+	0.265538i	$0.0855495\pi$
$379$	13.8614	+	24.0087i	0.712013	+	1.23324i	−0.252088	+	0.967704i	$0.581117\pi$
$380$	11.2554			0.577392
$381$		0			0
$382$	−11.3723	−	19.6974i	−0.581857	−	1.00781i
$383$	−3.11684	+	5.39853i	−0.159263	+	0.275852i	−0.934603	−	0.355692i	$-0.884245\pi$
$383$	−3.11684	+	5.39853i	−0.159263	+	0.275852i	0.775340	+	0.631544i	$0.217579\pi$
$384$		0			0
$385$	−3.25544	−	5.63858i	−0.165912	−	0.287369i
$386$	9.24456	+	16.0121i	0.470536	+	0.814992i
$387$		0			0
$388$	−2.87228	+	4.97494i	−0.145818	+	0.252564i
$389$	3.44158	−	5.96099i	0.174495	−	0.302234i	−0.765491	−	0.643446i	$-0.777504\pi$
$389$	3.44158	−	5.96099i	0.174495	−	0.302234i	0.939986	+	0.341212i	$0.110837\pi$
$390$		0			0
$391$		0			0
$392$	2.55842	+	4.43132i	0.129220	+	0.223815i
$393$		0			0
$394$	6.81386	−	11.8020i	0.343277	−	0.594574i
$395$	−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	$0.658200\pi$
$398$	3.31386	+	5.73977i	0.166109	+	0.287709i
$399$		0			0
$400$	−0.313859	+	0.543620i	−0.0156930	+	0.0271810i
$401$	3.25544			0.162569			0.0812844	−	0.996691i	$-0.474098\pi$
$401$	3.25544			0.162569			0.0812844	+	0.996691i	$0.474098\pi$
$402$		0			0
$403$	6.43070	−	11.1383i	0.320336	−	0.554838i
$404$	6.93070	−	12.0043i	0.344815	−	0.597238i
$405$		0			0
$406$	6.00000			0.297775
$407$	5.11684	−	11.0371i	0.253633	−	0.547089i
$408$		0			0
$409$	11.8723	+	20.5634i	0.587047	+	1.01679i	0.994617	+	0.103621i	$0.0330428\pi$
$409$	11.8723	+	20.5634i	0.587047	+	1.01679i	−0.407570	+	0.913174i	$0.633624\pi$
$410$	−5.18614	+	8.98266i	−0.256125	+	0.443622i
$411$		0			0
$412$	−6.37228	+	11.0371i	−0.313940	+	0.543760i
$413$	−5.48913			−0.270102
$414$		0			0
$415$	−18.9783			−0.931606
$416$	−0.686141	−	1.18843i	−0.0336408	−	0.0582676i
$417$		0			0
$418$	−9.48913			−0.464128
$419$	9.74456	+	16.8781i	0.476053	+	0.824548i	0.999624	−	0.0274343i	$-0.00873369\pi$
$419$	9.74456	+	16.8781i	0.476053	+	0.824548i	−0.523571	+	0.851982i	$0.675400\pi$
$420$		0			0
$421$	−11.6277			−0.566700			−0.283350	−	0.959017i	$-0.591446\pi$
$421$	−11.6277			−0.566700			−0.283350	+	0.959017i	$0.591446\pi$
$422$	−6.68614	−	11.5807i	−0.325476	−	0.563741i
$423$		0			0
$424$	5.74456	+	9.94987i	0.278981	+	0.483209i
$425$	−0.510875	+	0.884861i	−0.0247811	+	0.0429221i
$426$		0			0
$427$	−6.25544	−	10.8347i	−0.302722	−	0.524330i
$428$	2.37228	+	4.10891i	0.114669	+	0.198612i
$429$		0			0
$430$	−22.2337			−1.07220
$431$	4.48913	−	7.77539i	0.216234	−	0.374528i	−0.737420	−	0.675435i	$-0.763956\pi$
$431$	4.48913	−	7.77539i	0.216234	−	0.374528i	0.953653	+	0.300907i	$0.0972894\pi$
$432$		0			0
$433$	7.62772			0.366565			0.183282	−	0.983060i	$-0.441328\pi$
$433$	7.62772			0.366565			0.183282	+	0.983060i	$0.441328\pi$
$434$	12.8614			0.617367
$435$		0			0
$436$	−4.25544			−0.203798
$437$		0			0
$438$		0			0
$439$	−4.31386	+	7.47182i	−0.205889	+	0.356611i	−0.950416	−	0.310982i	$-0.899342\pi$
$439$	−4.31386	+	7.47182i	−0.205889	+	0.356611i	0.744526	+	0.667593i	$0.232675\pi$
$440$	2.37228	−	4.10891i	0.113094	−	0.195885i
$441$		0			0
$442$	−1.11684	−	1.93443i	−0.0531229	−	0.0920115i
$443$	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
$446$	−9.05842	−	15.6896i	−0.428929	−	0.742926i
$447$		0			0
$448$	0.686141	−	1.18843i	0.0324171	−	0.0561481i
$449$	12.4891	−	21.6318i	0.589398	−	1.02087i	−0.404913	−	0.914355i	$-0.632698\pi$
$449$	12.4891	−	21.6318i	0.589398	−	1.02087i	0.994311	−	0.106513i	$-0.0339684\pi$
$450$		0			0
$451$	4.37228	−	7.57301i	0.205883	−	0.356599i
$452$	15.4891			0.728547
$453$		0			0
$454$	11.4891			0.539211
$455$	−4.46738			−0.209434
$456$		0			0
$457$	−12.0475	+	20.8670i	−0.563560	+	0.976115i	0.433622	+	0.901095i	$0.357235\pi$
$457$	−12.0475	+	20.8670i	−0.563560	+	0.976115i	−0.997182	+	0.0750203i	$0.976098\pi$
$458$	−13.7446			−0.642241
$459$		0			0
$460$		0			0
$461$	−10.4891	−	18.1677i	−0.488527	−	0.846154i	0.511386	−	0.859351i	$-0.329132\pi$
$461$	−10.4891	−	18.1677i	−0.488527	−	0.846154i	−0.999913	+	0.0131973i	$0.995799\pi$
$462$		0			0
$463$	0.0584220	−	0.101190i	0.00271510	−	0.00470269i	−0.864665	−	0.502350i	$-0.832469\pi$
$463$	0.0584220	−	0.101190i	0.00271510	−	0.00470269i	0.867380	+	0.497647i	$0.165802\pi$
$464$	2.18614	+	3.78651i	0.101489	+	0.175784i
$465$		0			0
$466$	−14.3030	−	24.7735i	−0.662573	−	1.14761i
$467$	−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
$470$	−4.74456			−0.218850
$471$		0			0
$472$	−2.00000	−	3.46410i	−0.0920575	−	0.159448i
$473$	18.7446			0.861876
$474$		0			0
$475$	2.97825			0.136652
$476$	1.11684	−	1.93443i	0.0511905	−	0.0886645i
$477$		0			0
$478$	−11.1168	+	19.2549i	−0.508473	+	0.880700i
$479$	−0.116844	−	0.202380i	−0.00533874	−	0.00924696i	0.863344	−	0.504616i	$-0.168366\pi$
$479$	−0.116844	−	0.202380i	−0.00533874	−	0.00924696i	−0.868682	+	0.495369i	$0.835033\pi$
$480$		0			0
$481$	−4.80298	−	6.82701i	−0.218997	−	0.311285i
$482$	24.1168			1.09849
$483$		0			0
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	−6.81386	+	11.8020i	−0.309401	+	0.535899i
$486$		0			0
$487$	−37.4891			−1.69879			−0.849397	−	0.527754i	$-0.823034\pi$
$487$	−37.4891			−1.69879			−0.849397	+	0.527754i	$0.823034\pi$
$488$	4.55842	−	7.89542i	0.206350	−	0.357409i
$489$		0			0
$490$	6.06930	+	10.5123i	0.274183	+	0.474899i
$491$	−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
$494$	−3.25544	+	5.63858i	−0.146469	+	0.253692i
$495$		0			0
$496$	4.68614	+	8.11663i	0.210414	+	0.364448i
$497$	−7.88316	−	13.6540i	−0.353608	−	0.612467i
$498$		0			0
$499$	13.1168	−	22.7190i	0.587191	−	1.01704i	−0.407408	−	0.913246i	$-0.633567\pi$
$499$	13.1168	−	22.7190i	0.587191	−	1.01704i	0.994598	−	0.103798i	$-0.0330994\pi$
$500$	5.18614	−	8.98266i	0.231931	−	0.401717i
$501$		0			0
$502$	−6.37228	−	11.0371i	−0.284409	−	0.492611i
$503$	−11.0000	−	19.0526i	−0.490466	−	0.849512i	0.509474	−	0.860486i	$-0.329840\pi$
$503$	−11.0000	−	19.0526i	−0.490466	−	0.849512i	−0.999940	+	0.0109744i	$0.996507\pi$
$504$		0			0
$505$	16.4416	−	28.4776i	0.731641	−	1.26724i
$506$		0			0
$507$		0			0
$508$	8.62772			0.382793
$509$	2.18614	+	3.78651i	0.0968990	+	0.167834i	0.910400	−	0.413730i	$-0.135774\pi$
$509$	2.18614	+	3.78651i	0.0968990	+	0.167834i	−0.813501	+	0.581564i	$0.802441\pi$
$510$		0			0
$511$	1.80298	−	3.12286i	0.0797593	−	0.138147i
$512$	1.00000			0.0441942
$513$		0			0
$514$	9.93070	−	17.2005i	0.438025	−	0.758681i
$515$	−15.1168	+	26.1831i	−0.666128	+	1.15377i
$516$		0			0
$517$	4.00000			0.175920
$518$	3.51087	−	7.57301i	0.154259	−	0.332739i
$519$		0			0
$520$	−1.62772	−	2.81929i	−0.0713802	−	0.123634i
$521$	10.3723	−	17.9653i	0.454418	−	0.787075i	−0.544237	−	0.838932i	$-0.683181\pi$
$521$	10.3723	−	17.9653i	0.454418	−	0.787075i	0.998655	+	0.0518569i	$0.0165140\pi$
$522$		0			0
$523$	−0.941578	+	1.63086i	−0.0411723	+	0.0713126i	−0.885877	−	0.463920i	$-0.846443\pi$
$523$	−0.941578	+	1.63086i	−0.0411723	+	0.0713126i	0.844705	+	0.535232i	$0.179776\pi$
$524$	−10.7446			−0.469378
$525$		0			0
$526$	26.7446			1.16612
$527$	7.62772	+	13.2116i	0.332269	+	0.575506i
$528$		0			0
$529$	−23.0000			−1.00000
$530$	13.6277	+	23.6039i	0.591950	+	1.02529i
$531$		0			0
$532$	−6.51087			−0.282282
$533$	−3.00000	−	5.19615i	−0.129944	−	0.225070i
$534$		0			0
$535$	5.62772	+	9.74749i	0.243307	+	0.421421i
$536$	−2.05842	+	3.56529i	−0.0889103	+	0.153997i
$537$		0			0
$538$	1.00000	+	1.73205i	0.0431131	+	0.0746740i
$539$	−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	$0.539408\pi$
$542$	−9.43070	+	16.3345i	−0.405083	+	0.701625i
$543$		0			0
$544$	1.62772			0.0697879
$545$	−10.0951			−0.432426
$546$		0			0
$547$	−39.0951			−1.67159			−0.835793	−	0.549045i	$-0.814992\pi$
$547$	−39.0951			−1.67159			−0.835793	+	0.549045i	$0.814992\pi$
$548$	5.18614	−	8.98266i	0.221541	−	0.383720i
$549$		0			0
$550$	0.627719	−	1.08724i	0.0267660	−	0.0463601i
$551$	10.3723	−	17.9653i	0.441874	−	0.765348i
$552$		0			0
$553$	0.941578	+	1.63086i	0.0400400	+	0.0693513i
$554$	−2.13859			−0.0908601
$555$		0			0
$556$	−8.62772			−0.365897
$557$	1.55842	+	2.69927i	0.0660325	+	0.114372i	0.897152	−	0.441723i	$-0.145633\pi$
$557$	1.55842	+	2.69927i	0.0660325	+	0.114372i	−0.831119	+	0.556095i	$0.812299\pi$
$558$		0			0
$559$	6.43070	−	11.1383i	0.271990	−	0.471100i
$560$	1.62772	−	2.81929i	0.0687837	−	0.119137i
$561$		0			0
$562$	−3.55842	+	6.16337i	−0.150103	+	0.259986i
$563$	−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
$566$	−0.116844			−0.00491132
$567$		0			0
$568$	5.74456	−	9.94987i	0.241036	−	0.417487i
$569$	−15.6277			−0.655148			−0.327574	−	0.944826i	$-0.606231\pi$
$569$	−15.6277			−0.655148			−0.327574	+	0.944826i	$0.606231\pi$
$570$		0			0
$571$	−17.9198	−	31.0381i	−0.749921	−	1.29890i	−0.947860	−	0.318688i	$-0.896758\pi$
$571$	−17.9198	−	31.0381i	−0.749921	−	1.29890i	0.197938	−	0.980214i	$-0.436575\pi$
$572$	1.37228	+	2.37686i	0.0573780	+	0.0993815i
$573$		0			0
$574$	3.00000	−	5.19615i	0.125218	−	0.216883i
$575$		0			0
$576$		0			0
$577$	6.48913	+	11.2395i	0.270146	+	0.467906i	0.968899	−	0.247457i	$-0.0795948\pi$
$577$	6.48913	+	11.2395i	0.270146	+	0.467906i	−0.698753	+	0.715363i	$0.746261\pi$
$578$	−14.3505			−0.596903
$579$		0			0
$580$	5.18614	+	8.98266i	0.215343	+	0.372985i
$581$	10.9783			0.455455
$582$		0			0
$583$	−11.4891	−	19.8997i	−0.475831	−	0.824163i
$584$	2.62772			0.108736
$585$		0			0
$586$	33.1168			1.36804
$587$	−1.37228	+	2.37686i	−0.0566401	+	0.0981036i	−0.892955	−	0.450146i	$-0.851372\pi$
$587$	−1.37228	+	2.37686i	−0.0566401	+	0.0981036i	0.836315	+	0.548249i	$0.184705\pi$
$588$		0			0
$589$	22.2337	−	38.5099i	0.916123	−	1.58677i
$590$	−4.74456	−	8.21782i	−0.195331	−	0.338322i
$591$		0			0
$592$	6.05842	−	0.543620i	0.249000	−	0.0223427i
$593$	−14.3723			−0.590199			−0.295099	−	0.955467i	$-0.595353\pi$
$593$	−14.3723			−0.590199			−0.295099	+	0.955467i	$0.595353\pi$
$594$		0			0
$595$	2.64947	−	4.58901i	0.108618	−	0.188131i
$596$	0.813859	−	1.40965i	0.0333370	−	0.0577413i
$597$		0			0
$598$		0			0
$599$	3.62772	−	6.28339i	0.148225	−	0.256732i	−0.782347	−	0.622843i	$-0.785977\pi$
$599$	3.62772	−	6.28339i	0.148225	−	0.256732i	0.930571	+	0.366111i	$0.119311\pi$
$600$		0			0
$601$	8.50000	+	14.7224i	0.346722	+	0.600541i	0.985665	−	0.168714i	$-0.0539613\pi$
$601$	8.50000	+	14.7224i	0.346722	+	0.600541i	−0.638943	+	0.769254i	$0.720628\pi$
$602$	12.8614			0.524192
$603$		0			0
$604$	9.68614	+	16.7769i	0.394123	+	0.682642i
$605$	8.30298	−	14.3812i	0.337564	−	0.584679i
$606$		0			0
$607$	−23.8614	−	41.3292i	−0.968505	−	1.67750i	−0.699889	−	0.714252i	$-0.746767\pi$
$607$	−23.8614	−	41.3292i	−0.968505	−	1.67750i	−0.268616	−	0.963247i	$-0.586566\pi$
$608$	−2.37228	−	4.10891i	−0.0962087	−	0.166638i
$609$		0			0
$610$	10.8139	−	18.7302i	0.437840	−	0.758362i
$611$	1.37228	−	2.37686i	0.0555166	−	0.0961575i
$612$		0			0
$613$	−8.93070	−	15.4684i	−0.360708	−	0.624764i	0.627370	−	0.778721i	$-0.284131\pi$
$613$	−8.93070	−	15.4684i	−0.360708	−	0.624764i	−0.988077	+	0.153957i	$0.950798\pi$
$614$	4.05842	+	7.02939i	0.163785	+	0.283683i
$615$		0			0
$616$	−1.37228	+	2.37686i	−0.0552908	+	0.0957665i
$617$	−11.8614	−	20.5446i	−0.477522	−	0.827093i	0.522146	−	0.852856i	$-0.325132\pi$
$617$	−11.8614	−	20.5446i	−0.477522	−	0.827093i	−0.999668	+	0.0257634i	$0.991798\pi$
$618$		0			0
$619$	33.8397			1.36013			0.680065	−	0.733152i	$-0.261951\pi$
$619$	33.8397			1.36013			0.680065	+	0.733152i	$0.261951\pi$
$620$	11.1168	+	19.2549i	0.446463	+	0.773297i
$621$		0			0
$622$	−14.4891	+	25.0959i	−0.580961	+	1.00625i
$623$	4.97825			0.199449
$624$		0			0
$625$	13.8723	−	24.0275i	0.554891	−	0.961100i
$626$	8.50000	−	14.7224i	0.339728	−	0.588427i
$627$		0			0
$628$	6.48913			0.258944
$629$	9.86141	−	0.884861i	0.393200	−	0.0352817i
$630$		0			0
$631$	21.0584	+	36.4743i	0.838323	+	1.45202i	0.891296	+	0.453421i	$0.149797\pi$
$631$	21.0584	+	36.4743i	0.838323	+	1.45202i	−0.0529738	+	0.998596i	$0.516870\pi$
$632$	−0.686141	+	1.18843i	−0.0272932	+	0.0472732i
$633$		0			0
$634$	−6.44158	+	11.1571i	−0.255828	+	0.443107i
$635$	20.4674			0.812223
$636$		0			0
$637$	−7.02175			−0.278212
$638$	−4.37228	−	7.57301i	−0.173100	−	0.299818i
$639$		0			0
$640$	2.37228			0.0937727
$641$	−7.55842	−	13.0916i	−0.298540	−	0.517086i	0.677262	−	0.735742i	$-0.263166\pi$
$641$	−7.55842	−	13.0916i	−0.298540	−	0.517086i	−0.975802	+	0.218656i	$0.929833\pi$
$642$		0			0
$643$	17.6060			0.694312			0.347156	−	0.937807i	$-0.387147\pi$
$643$	17.6060			0.694312			0.347156	+	0.937807i	$0.387147\pi$
$644$		0			0
$645$		0			0
$646$	−3.86141	−	6.68815i	−0.151925	−	0.263142i
$647$	−19.8614	+	34.4010i	−0.780832	+	1.35244i	0.150625	+	0.988591i	$0.451871\pi$
$647$	−19.8614	+	34.4010i	−0.780832	+	1.35244i	−0.931457	+	0.363851i	$0.881462\pi$
$648$		0			0
$649$	4.00000	+	6.92820i	0.157014	+	0.271956i
$650$	−0.430703	−	0.746000i	−0.0168936	−	0.0292605i
$651$		0			0
$652$	24.7446			0.969072
$653$	−13.4198	+	23.2438i	−0.525158	+	0.909601i	0.474412	+	0.880303i	$0.342661\pi$
$653$	−13.4198	+	23.2438i	−0.525158	+	0.909601i	−0.999571	+	0.0292984i	$0.990673\pi$
$654$		0			0
$655$	−25.4891			−0.995943
$656$	4.37228			0.170709
$657$		0			0
$658$	2.74456			0.106994
$659$	3.88316	−	6.72582i	0.151266	−	0.262001i	−0.780427	−	0.625247i	$-0.784998\pi$
$659$	3.88316	−	6.72582i	0.151266	−	0.262001i	0.931693	+	0.363246i	$0.118332\pi$
$660$		0			0
$661$	−9.98913	+	17.3017i	−0.388532	+	0.672957i	−0.992252	−	0.124239i	$-0.960351\pi$
$661$	−9.98913	+	17.3017i	−0.388532	+	0.672957i	0.603720	+	0.797196i	$0.293684\pi$
$662$	17.8030	−	30.8357i	0.691933	−	1.19846i
$663$		0			0
$664$	4.00000	+	6.92820i	0.155230	+	0.268866i
$665$	−15.4456			−0.598956
$666$		0			0
$667$		0			0
$668$	−0.744563	−	1.28962i	−0.0288080	−	0.0498969i
$669$		0			0
$670$	−4.88316	+	8.45787i	−0.188653	+	0.326756i
$671$	−9.11684	+	15.7908i	−0.351952	+	0.609598i
$672$		0			0
$673$	6.48913	−	11.2395i	0.250137	−	0.433251i	−0.713426	−	0.700731i	$-0.752858\pi$
$673$	6.48913	−	11.2395i	0.250137	−	0.433251i	0.963563	+	0.267480i	$0.0861909\pi$
$674$	29.7446			1.14572
$675$		0			0
$676$	−11.1168			−0.427571
$677$	29.1168			1.11905			0.559526	−	0.828813i	$-0.310983\pi$
$677$	29.1168			1.11905			0.559526	+	0.828813i	$0.310983\pi$
$678$		0			0
$679$	3.94158	−	6.82701i	0.151264	−	0.261997i
$680$	3.86141			0.148078
$681$		0			0
$682$	−9.37228	−	16.2333i	−0.358883	−	0.621604i
$683$	7.11684	+	12.3267i	0.272318	+	0.471669i	0.969455	−	0.245269i	$-0.0788762\pi$
$683$	7.11684	+	12.3267i	0.272318	+	0.471669i	−0.697137	+	0.716938i	$0.745543\pi$
$684$		0			0
$685$	12.3030	−	21.3094i	0.470073	−	0.814190i
$686$	−8.31386	−	14.4000i	−0.317425	−	0.549796i
$687$		0			0
$688$	4.68614	+	8.11663i	0.178657	+	0.309444i
$689$	−15.7663			−0.600649
$690$		0			0
$691$	7.31386	+	12.6680i	0.278232	+	0.481913i	0.970946	−	0.239301i	$-0.0769182\pi$
$691$	7.31386	+	12.6680i	0.278232	+	0.481913i	−0.692713	+	0.721213i	$0.743585\pi$
$692$	−23.1168			−0.878771
$693$		0			0
$694$	13.3723	+	23.1615i	0.507605	+	0.879197i
$695$	−20.4674			−0.776372
$696$		0			0
$697$	7.11684			0.269570
$698$	4.55842	−	7.89542i	0.172539	−	0.298846i
$699$		0			0
$700$	0.430703	−	0.746000i	0.0162791	−	0.0281962i
$701$	21.1168	+	36.5754i	0.797572	+	1.38144i	0.921193	+	0.389106i	$0.127216\pi$
$701$	21.1168	+	36.5754i	0.797572	+	1.38144i	−0.123621	+	0.992330i	$0.539451\pi$
$702$		0			0
$703$	−16.6060	−	23.6039i	−0.626306	−	0.890238i
$704$	−2.00000			−0.0753778
$705$		0			0
$706$	15.3030	−	26.5055i	0.575935	−	0.997549i
$707$	−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	$0.632977\pi$
$710$	13.6277	−	23.6039i	0.511439	−	0.885839i
$711$		0			0
$712$	1.81386	+	3.14170i	0.0679773	+	0.117740i
$713$		0			0
$714$		0			0
$715$	3.25544	+	5.63858i	0.121746	+	0.210871i
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$		0			0
$718$	6.11684	+	10.5947i	0.228279	+	0.395390i
$719$	−21.6060	−	37.4226i	−0.805767	−	1.39563i	−0.915772	−	0.401698i	$-0.868420\pi$
$719$	−21.6060	−	37.4226i	−0.805767	−	1.39563i	0.110006	−	0.993931i	$-0.464913\pi$
$720$		0			0
$721$	8.74456	−	15.1460i	0.325665	−	0.564068i
$722$	−1.75544	+	3.04051i	−0.0653306	+	0.113156i
$723$		0			0
$724$	2.12772	+	3.68532i	0.0790760	+	0.136964i
$725$	1.37228	+	2.37686i	0.0509652	+	0.0882744i
$726$		0			0
$727$	−14.5475	+	25.1971i	−0.539539	+	0.934508i	0.459390	+	0.888235i	$0.348068\pi$
$727$	−14.5475	+	25.1971i	−0.539539	+	0.934508i	−0.998929	+	0.0462738i	$0.985265\pi$
$728$	0.941578	+	1.63086i	0.0348972	+	0.0604437i
$729$		0			0
$730$	6.23369			0.230719
$731$	7.62772	+	13.2116i	0.282121	+	0.488649i
$732$		0			0
$733$	−4.68614	+	8.11663i	−0.173087	+	0.299795i	−0.939497	−	0.342556i	$-0.888707\pi$
$733$	−4.68614	+	8.11663i	−0.173087	+	0.299795i	0.766411	+	0.642351i	$0.222041\pi$
$734$	6.11684			0.225777
$735$		0			0
$736$		0			0
$737$	4.11684	−	7.13058i	0.151646	−	0.262658i
$738$		0			0
$739$	−24.4674			−0.900047			−0.450023	−	0.893017i	$-0.648584\pi$
$739$	−24.4674			−0.900047			−0.450023	+	0.893017i	$0.648584\pi$
$740$	14.3723	−	1.28962i	0.528336	−	0.0474074i
$741$		0			0
$742$	−7.88316	−	13.6540i	−0.289400	−	0.501255i
$743$	6.25544	−	10.8347i	0.229490	−	0.397488i	−0.728167	−	0.685399i	$-0.759628\pi$
$743$	6.25544	−	10.8347i	0.229490	−	0.397488i	0.957657	+	0.287912i	$0.0929609\pi$
$744$		0			0
$745$	1.93070	−	3.34408i	0.0707355	−	0.122517i
$746$	−31.0000			−1.13499
$747$		0			0
$748$	−3.25544			−0.119031
$749$	−3.25544	−	5.63858i	−0.118951	−	0.206029i
$750$		0			0
$751$	15.8832			0.579585			0.289792	−	0.957090i	$-0.406414\pi$
$751$	15.8832			0.579585			0.289792	+	0.957090i	$0.406414\pi$
$752$	1.00000	+	1.73205i	0.0364662	+	0.0631614i
$753$		0			0
$754$	−6.00000			−0.218507
$755$	22.9783	+	39.7995i	0.836264	+	1.44845i
$756$		0			0
$757$	10.1277	+	17.5417i	0.368098	+	0.637565i	0.989268	−	0.146111i	$-0.0466757\pi$
$757$	10.1277	+	17.5417i	0.368098	+	0.637565i	−0.621170	+	0.783676i	$0.713342\pi$
$758$	13.8614	−	24.0087i	0.503469	−	0.872034i
$759$		0			0
$760$	−5.62772	−	9.74749i	−0.204139	−	0.353579i
$761$	11.9307	+	20.6646i	0.432488	+	0.749091i	0.997087	−	0.0762746i	$-0.0243026\pi$
$761$	11.9307	+	20.6646i	0.432488	+	0.749091i	−0.564599	+	0.825365i	$0.690969\pi$
$762$		0			0
$763$	5.83966			0.211410
$764$	−11.3723	+	19.6974i	−0.411435	+	0.712626i
$765$		0			0
$766$	6.23369			0.225232
$767$	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	$0.477695\pi$
$770$	−3.25544	+	5.63858i	−0.117318	+	0.203200i
$771$		0			0
$772$	9.24456	−	16.0121i	0.332719	−	0.576286i
$773$	2.06930	−	3.58413i	0.0744274	−	0.128912i	−0.826410	−	0.563069i	$-0.809620\pi$
$773$	2.06930	−	3.58413i	0.0744274	−	0.128912i	0.900837	+	0.434157i	$0.142954\pi$
$774$		0			0
$775$	2.94158	+	5.09496i	0.105665	+	0.183016i
$776$	5.74456			0.206218
$777$		0			0
$778$	−6.88316			−0.246773
$779$	−10.3723	−	17.9653i	−0.371626	−	0.643674i
$780$		0			0
$781$	−11.4891	+	19.8997i	−0.411113	+	0.712069i
$782$		0			0
$783$		0			0
$784$	2.55842	−	4.43132i	0.0913722	−	0.158261i
$785$	15.3940			0.549437
$786$		0			0
$787$	−6.11684			−0.218042			−0.109021	−	0.994039i	$-0.534772\pi$
$787$	−6.11684			−0.218042			−0.109021	+	0.994039i	$0.534772\pi$
$788$	−13.6277			−0.485467
$789$		0			0
$790$	−1.62772	+	2.81929i	−0.0579116	+	0.100306i
$791$	−21.2554			−0.755756
$792$		0			0
$793$	6.25544	+	10.8347i	0.222137	+	0.384753i
$794$	9.50000	+	16.4545i	0.337142	+	0.583948i
$795$		0			0
$796$	3.31386	−	5.73977i	0.117457	−	0.203441i
$797$	−20.6060	−	35.6906i	−0.729901	−	1.26423i	−0.956925	−	0.290336i	$-0.906233\pi$
$797$	−20.6060	−	35.6906i	−0.729901	−	1.26423i	0.227024	−	0.973889i	$-0.427100\pi$
$798$		0			0
$799$	1.62772	+	2.81929i	0.0575845	+	0.0997394i
$800$	0.627719			0.0221932
$801$		0			0
$802$	−1.62772	−	2.81929i	−0.0574767	−	0.0995526i
$803$	−5.25544			−0.185460
$804$		0			0
$805$		0			0
$806$	−12.8614			−0.453024
$807$		0			0
$808$	−13.8614			−0.487643
$809$	−26.4891	+	45.8805i	−0.931308	+	1.61307i	−0.150219	+	0.988653i	$0.547998\pi$
$809$	−26.4891	+	45.8805i	−0.931308	+	1.61307i	−0.781089	+	0.624420i	$0.785335\pi$
$810$		0			0
$811$	−5.48913	+	9.50744i	−0.192749	+	0.333852i	−0.946160	−	0.323698i	$-0.895074\pi$
$811$	−5.48913	+	9.50744i	−0.192749	+	0.333852i	0.753411	+	0.657550i	$0.228407\pi$
$812$	−3.00000	−	5.19615i	−0.105279	−	0.182349i
$813$		0			0
$814$	−12.1168	+	1.08724i	−0.424695	+	0.0381078i
$815$	58.7011			2.05621
$816$		0			0
$817$	22.2337	−	38.5099i	0.777858	−	1.34729i
$818$	11.8723	−	20.5634i	0.415105	−	0.718982i
$819$		0			0
$820$	10.3723			0.362216
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	−0.991616	−	0.129217i	$-0.958754\pi$
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	0.607714	+	0.794156i	$0.292087\pi$
$822$		0			0
$823$	23.9198	+	41.4304i	0.833793	+	1.44417i	0.895010	+	0.446047i	$0.147169\pi$
$823$	23.9198	+	41.4304i	0.833793	+	1.44417i	−0.0612167	+	0.998124i	$0.519498\pi$
$824$	12.7446			0.443978
$825$		0			0
$826$	2.74456	+	4.75372i	0.0954955	+	0.165403i
$827$	16.0000	−	27.7128i	0.556375	−	0.963669i	−0.441421	−	0.897300i	$-0.645525\pi$
$827$	16.0000	−	27.7128i	0.556375	−	0.963669i	0.997795	−	0.0663686i	$-0.0211413\pi$
$828$		0			0
$829$	−19.4307	−	33.6550i	−0.674856	−	1.16889i	−0.976511	−	0.215468i	$-0.930872\pi$
$829$	−19.4307	−	33.6550i	−0.674856	−	1.16889i	0.301655	−	0.953417i	$-0.402461\pi$
$830$	9.48913	+	16.4356i	0.329372	+	0.570490i
$831$		0			0
$832$	−0.686141	+	1.18843i	−0.0237876	+	0.0412014i
$833$	4.16439	−	7.21294i	0.144288	−	0.249913i
$834$		0			0
$835$	−1.76631	−	3.05934i	−0.0611257	−	0.105873i
$836$	4.74456	+	8.21782i	0.164094	+	0.284219i
$837$		0			0
$838$	9.74456	−	16.8781i	0.336620	−	0.583044i
$839$	2.00000	+	3.46410i	0.0690477	+	0.119594i	0.898482	−	0.439010i	$-0.144671\pi$
$839$	2.00000	+	3.46410i	0.0690477	+	0.119594i	−0.829435	+	0.558604i	$0.811337\pi$
$840$		0			0
$841$	−9.88316			−0.340798
$842$	5.81386	+	10.0699i	0.200359	+	0.347032i
$843$		0			0
$844$	−6.68614	+	11.5807i	−0.230146	+	0.398625i
$845$	−26.3723			−0.907234
$846$		0			0
$847$	−4.80298	+	8.31901i	−0.165033	+	0.285845i
$848$	5.74456	−	9.94987i	0.197269	−	0.341680i
$849$		0			0
$850$	1.02175			0.0350457
$851$		0			0
$852$		0			0
$853$	17.3030	+	29.9696i	0.592443	+	1.02614i	0.993902	+	0.110264i	$0.0351698\pi$
$853$	17.3030	+	29.9696i	0.592443	+	1.02614i	−0.401459	+	0.915877i	$0.631497\pi$
$854$	−6.25544	+	10.8347i	−0.214057	+	0.370757i
$855$		0			0
$856$	2.37228	−	4.10891i	0.0810829	−	0.140440i
$857$	−30.8397			−1.05346			−0.526731	−	0.850032i	$-0.676583\pi$
$857$	−30.8397			−1.05346			−0.526731	+	0.850032i	$0.676583\pi$
$858$		0			0
$859$	37.6060			1.28310			0.641550	−	0.767082i	$-0.278292\pi$
$859$	37.6060			1.28310			0.641550	+	0.767082i	$0.278292\pi$
$860$	11.1168	+	19.2549i	0.379081	+	0.656588i
$861$		0			0
$862$	−8.97825			−0.305800
$863$	−13.3723	−	23.1615i	−0.455198	−	0.788426i	0.543502	−	0.839408i	$-0.317098\pi$
$863$	−13.3723	−	23.1615i	−0.455198	−	0.788426i	−0.998700	+	0.0509824i	$0.983765\pi$
$864$		0			0
$865$	−54.8397			−1.86460
$866$	−3.81386	−	6.60580i	−0.129600	−	0.224474i
$867$		0			0
$868$	−6.43070	−	11.1383i	−0.218272	−	0.378059i
$869$	1.37228	−	2.37686i	0.0465515	−	0.0806295i
$870$		0			0
$871$	−2.82473	−	4.89258i	−0.0957125	−	0.165779i
$872$	2.12772	+	3.68532i	0.0720536	+	0.124801i
$873$		0			0
$874$		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	$0.791764\pi$
$878$	8.62772			0.291171
$879$		0			0
$880$	−4.74456			−0.159939
$881$	−3.55842	+	6.16337i	−0.119886	+	0.207649i	−0.919722	−	0.392569i	$-0.871586\pi$
$881$	−3.55842	+	6.16337i	−0.119886	+	0.207649i	0.799836	+	0.600218i	$0.204920\pi$
$882$		0			0
$883$	3.48913	−	6.04334i	0.117418	−	0.203375i	−0.801325	−	0.598229i	$-0.795871\pi$
$883$	3.48913	−	6.04334i	0.117418	−	0.203375i	0.918744	+	0.394854i	$0.129205\pi$
$884$	−1.11684	+	1.93443i	−0.0375635	+	0.0650619i
$885$		0			0
$886$	−2.74456	−	4.75372i	−0.0922054	−	0.159704i
$887$	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
$890$	4.30298	+	7.45299i	0.144236	+	0.249825i
$891$		0			0
$892$	−9.05842	+	15.6896i	−0.303298	+	0.525328i
$893$	4.74456	−	8.21782i	0.158771	−	0.274999i
$894$		0			0
$895$	−14.2337	+	24.6535i	−0.475780	+	0.824075i
$896$	−1.37228			−0.0458447
$897$		0			0
$898$	−24.9783			−0.833535
$899$	40.9783			1.36670
$900$		0			0
$901$	9.35053	−	16.1956i	0.311511	−	0.539554i
$902$	−8.74456			−0.291162
$903$		0			0
$904$	−7.74456	−	13.4140i	−0.257580	−	0.446142i
$905$	5.04755	+	8.74261i	0.167786	+	0.290614i
$906$		0			0
$907$	−10.1753	+	17.6241i	−0.337864	+	0.585198i	−0.984031	−	0.177998i	$-0.943038\pi$
$907$	−10.1753	+	17.6241i	−0.337864	+	0.585198i	0.646167	+	0.763196i	$0.276371\pi$
$908$	−5.74456	−	9.94987i	−0.190640	−	0.330198i
$909$		0			0
$910$	2.23369	+	3.86886i	0.0740460	+	0.128251i
$911$	−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
$914$	24.0951			0.796995
$915$		0			0
$916$	6.87228	+	11.9031i	0.227067	+	0.393291i
$917$	14.7446			0.486908
$918$		0			0
$919$	−23.6060			−0.778689			−0.389345	−	0.921092i	$-0.627298\pi$
$919$	−23.6060			−0.778689			−0.389345	+	0.921092i	$0.627298\pi$
$920$		0			0
$921$		0			0
$922$	−10.4891	+	18.1677i	−0.345441	+	0.598321i
$923$	7.88316	+	13.6540i	0.259477	+	0.449428i
$924$		0			0
$925$	3.80298	−	0.341241i	0.125041	−	0.0112199i
$926$	−0.116844			−0.00383973
$927$		0			0
$928$	2.18614	−	3.78651i	0.0717636	−	0.124298i
$929$	−4.69702	+	8.13547i	−0.154104	+	0.266916i	−0.932732	−	0.360569i	$-0.882582\pi$
$929$	−4.69702	+	8.13547i	−0.154104	+	0.266916i	0.778628	+	0.627485i	$0.215916\pi$
$930$		0			0
$931$	−24.2772			−0.795653
$932$	−14.3030	+	24.7735i	−0.468510	+	0.811483i
$933$		0			0
$934$	7.37228	+	12.7692i	0.241228	+	0.417820i
$935$	−7.72281			−0.252563
$936$		0			0
$937$	23.9891	+	41.5504i	0.783691	+	1.35739i	0.929778	+	0.368120i	$0.119999\pi$
$937$	23.9891	+	41.5504i	0.783691	+	1.35739i	−0.146088	+	0.989272i	$0.546668\pi$
$938$	2.82473	−	4.89258i	0.0922308	−	0.159748i
$939$		0			0
$940$	2.37228	+	4.10891i	0.0773753	+	0.134018i
$941$	−28.1644	−	48.7822i	−0.918133	−	1.59025i	−0.802249	−	0.596990i	$-0.796363\pi$
$941$	−28.1644	−	48.7822i	−0.918133	−	1.59025i	−0.115884	−	0.993263i	$-0.536970\pi$
$942$		0			0
$943$		0			0
$944$	−2.00000	+	3.46410i	−0.0650945	+	0.112747i
$945$		0			0
$946$	−9.37228	−	16.2333i	−0.304719	−	0.527789i
$947$	21.6060	+	37.4226i	0.702100	+	1.21607i	0.967728	+	0.251997i	$0.0810872\pi$
$947$	21.6060	+	37.4226i	0.702100	+	1.21607i	−0.265628	+	0.964075i	$0.585579\pi$
$948$		0			0
$949$	−1.80298	+	3.12286i	−0.0585274	+	0.101372i
$950$	−1.48913	−	2.57924i	−0.0483136	−	0.0836816i
$951$		0			0
$952$	−2.23369			−0.0723942
$953$	−25.8614	−	44.7933i	−0.837733	−	1.45100i	−0.891786	−	0.452458i	$-0.850547\pi$
$953$	−25.8614	−	44.7933i	−0.837733	−	1.45100i	0.0540525	−	0.998538i	$-0.482786\pi$
$954$		0			0
$955$	−26.9783	+	46.7277i	−0.872996	+	1.51207i
$956$	22.2337			0.719089
$957$		0			0
$958$	−0.116844	+	0.202380i	−0.00377506	+	0.00653859i
$959$	−7.11684	+	12.3267i	−0.229815	+	0.398051i
$960$		0			0
$961$	56.8397			1.83354
$962$	−3.51087	+	7.57301i	−0.113195	+	0.244164i
$963$		0			0
$964$	−12.0584	−	20.8858i	−0.388376	−	0.672686i
$965$	21.9307	−	37.9851i	0.705974	−	1.22278i
$966$		0			0
$967$	3.80298	−	6.58696i	0.122296	−	0.211822i	−0.798377	−	0.602158i	$-0.794308\pi$
$967$	3.80298	−	6.58696i	0.122296	−	0.211822i	0.920673	+	0.390336i	$0.127641\pi$
$968$	−7.00000			−0.224989
$969$		0			0
$970$	13.6277			0.437560
$971$	22.9783	+	39.7995i	0.737407	+	1.27723i	0.953659	+	0.300889i	$0.0972834\pi$
$971$	22.9783	+	39.7995i	0.737407	+	1.27723i	−0.216252	+	0.976338i	$0.569383\pi$
$972$		0			0
$973$	11.8397			0.379562
$974$	18.7446	+	32.4665i	0.600615	+	1.04029i
$975$		0			0
$976$	−9.11684			−0.291823
$977$	−1.62772	−	2.81929i	−0.0520753	−	0.0901971i	0.838813	−	0.544420i	$-0.183250\pi$
$977$	−1.62772	−	2.81929i	−0.0520753	−	0.0901971i	−0.890888	+	0.454223i	$0.849917\pi$
$978$		0			0
$979$	−3.62772	−	6.28339i	−0.115942	−	0.200818i
$980$	6.06930	−	10.5123i	0.193877	−	0.335804i
$981$		0			0
$982$	3.00000	+	5.19615i	0.0957338	+	0.165816i
$983$	−10.3723	−	17.9653i	−0.330824	−	0.573005i	0.651849	−	0.758348i	$-0.273993\pi$
$983$	−10.3723	−	17.9653i	−0.330824	−	0.573005i	−0.982674	+	0.185344i	$0.940660\pi$
$984$		0			0
$985$	−32.3288			−1.03008
$986$	3.55842	−	6.16337i	0.113323	−	0.196282i
$987$		0			0
$988$	6.51087			0.207139
$989$		0			0
$990$		0			0
$991$	−17.7663			−0.564366			−0.282183	−	0.959361i	$-0.591058\pi$
$991$	−17.7663			−0.564366			−0.282183	+	0.959361i	$0.591058\pi$
$992$	4.68614	−	8.11663i	0.148785	−	0.257703i
$993$		0			0
$994$	−7.88316	+	13.6540i	−0.250039	+	0.433079i
$995$	7.86141	−	13.6164i	0.249223	−	0.431667i
$996$		0			0
$997$	26.4891	+	45.8805i	0.838919	+	1.45305i	0.890799	+	0.454397i	$0.150145\pi$
$997$	26.4891	+	45.8805i	0.838919	+	1.45305i	−0.0518802	+	0.998653i	$0.516521\pi$
$998$	−26.2337			−0.830413
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.f.g.433.1		4
3.2	odd	2		222.2.e.c.211.2	yes	4
12.11	even	2		1776.2.q.h.433.2		4
37.10	even	3	inner	666.2.f.g.343.1		4
111.11	odd	6		8214.2.a.o.1.2		2
111.26	odd	6		8214.2.a.m.1.1		2
111.47	odd	6		222.2.e.c.121.2	✓	4
444.47	even	6		1776.2.q.h.1009.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
222.2.e.c.121.2	✓	4	111.47	odd	6
222.2.e.c.211.2	yes	4	3.2	odd	2
666.2.f.g.343.1		4	37.10	even	3	inner
666.2.f.g.433.1		4	1.1	even	1	trivial
1776.2.q.h.433.2		4	12.11	even	2
1776.2.q.h.1009.2		4	444.47	even	6
8214.2.a.m.1.1		2	111.26	odd	6
8214.2.a.o.1.2		2	111.11	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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.18614 + 2.05446i) q^{5} +(0.686141 - 1.18843i) q^{7} +1.00000 q^{8} +2.37228 q^{10} -2.00000 q^{11} +(-0.686141 + 1.18843i) q^{13} -1.37228 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.813859 - 1.40965i) q^{17} +(-2.37228 + 4.10891i) q^{19} +(-1.18614 - 2.05446i) q^{20} +(1.00000 + 1.73205i) q^{22} +(-0.313859 - 0.543620i) q^{25} +1.37228 q^{26} +(0.686141 + 1.18843i) q^{28} -4.37228 q^{29} -9.37228 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.813859 + 1.40965i) q^{34} +(1.62772 + 2.81929i) q^{35} +(-2.55842 + 5.51856i) q^{37} +4.74456 q^{38} +(-1.18614 + 2.05446i) q^{40} +(-2.18614 + 3.78651i) q^{41} -9.37228 q^{43} +(1.00000 - 1.73205i) q^{44} -2.00000 q^{47} +(2.55842 + 4.43132i) q^{49} +(-0.313859 + 0.543620i) q^{50} +(-0.686141 - 1.18843i) q^{52} +(5.74456 + 9.94987i) q^{53} +(2.37228 - 4.10891i) q^{55} +(0.686141 - 1.18843i) q^{56} +(2.18614 + 3.78651i) q^{58} +(-2.00000 - 3.46410i) q^{59} +(4.55842 - 7.89542i) q^{61} +(4.68614 + 8.11663i) q^{62} +1.00000 q^{64} +(-1.62772 - 2.81929i) q^{65} +(-2.05842 + 3.56529i) q^{67} +1.62772 q^{68} +(1.62772 - 2.81929i) q^{70} +(5.74456 - 9.94987i) q^{71} +2.62772 q^{73} +(6.05842 - 0.543620i) q^{74} +(-2.37228 - 4.10891i) q^{76} +(-1.37228 + 2.37686i) q^{77} +(-0.686141 + 1.18843i) q^{79} +2.37228 q^{80} +4.37228 q^{82} +(4.00000 + 6.92820i) q^{83} +3.86141 q^{85} +(4.68614 + 8.11663i) q^{86} -2.00000 q^{88} +(1.81386 + 3.14170i) q^{89} +(0.941578 + 1.63086i) q^{91} +(1.00000 + 1.73205i) q^{94} +(-5.62772 - 9.74749i) q^{95} +5.74456 q^{97} +(2.55842 - 4.43132i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + q^{5} - 3 q^{7} + 4 q^{8} - 2 q^{10} - 8 q^{11} + 3 q^{13} + 6 q^{14} - 2 q^{16} - 9 q^{17} + 2 q^{19} + q^{20} + 4 q^{22} - 7 q^{25} - 6 q^{26} - 3 q^{28} - 6 q^{29} - 26 q^{31}+ \cdots - 7 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + q^5 - 3 * q^7 + 4 * q^8 - 2 * q^10 - 8 * q^11 + 3 * q^13 + 6 * q^14 - 2 * q^16 - 9 * q^17 + 2 * q^19 + q^20 + 4 * q^22 - 7 * q^25 - 6 * q^26 - 3 * q^28 - 6 * q^29 - 26 * q^31 - 2 * q^32 - 9 * q^34 + 18 * q^35 + 7 * q^37 - 4 * q^38 + q^40 - 3 * q^41 - 26 * q^43 + 4 * q^44 - 8 * q^47 - 7 * q^49 - 7 * q^50 + 3 * q^52 - 2 * q^55 - 3 * q^56 + 3 * q^58 - 8 * q^59 + q^61 + 13 * q^62 + 4 * q^64 - 18 * q^65 + 9 * q^67 + 18 * q^68 + 18 * q^70 + 22 * q^73 + 7 * q^74 + 2 * q^76 + 6 * q^77 + 3 * q^79 - 2 * q^80 + 6 * q^82 + 16 * q^83 - 42 * q^85 + 13 * q^86 - 8 * q^88 + 13 * q^89 + 21 * q^91 + 4 * q^94 - 34 * q^95 - 7 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more