LMFDB - Embedded newform 720.2.u.a.179.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("720.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			179.7
Character	$\chi$	$=$	720.179
Dual form			720.2.u.a.539.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23687 + 0.685679i) q^{2} +(1.05969 - 1.69619i) q^{4} +(-2.19631 + 0.419806i) q^{5} +0.263783i q^{7} +(-0.147653 + 2.82457i) q^{8} +(2.42869 - 2.02521i) q^{10} +(0.913594 - 0.913594i) q^{11} +(1.49018 - 1.49018i) q^{13} +(-0.180870 - 0.326265i) q^{14} +(-1.75412 - 3.59487i) q^{16} -2.90538 q^{17} +(-0.296217 + 0.296217i) q^{19} +(-1.61533 + 4.17022i) q^{20} +(-0.503563 + 1.75643i) q^{22} +3.14640 q^{23} +(4.64753 - 1.84404i) q^{25} +(-0.821369 + 2.86493i) q^{26} +(0.447426 + 0.279528i) q^{28} +(2.43765 - 2.43765i) q^{29} +2.53546i q^{31} +(4.63454 + 3.24361i) q^{32} +(3.59358 - 1.99216i) q^{34} +(-0.110738 - 0.579348i) q^{35} +(1.53556 + 1.53556i) q^{37} +(0.163272 - 0.569491i) q^{38} +(-0.861481 - 6.26561i) q^{40} +10.7792 q^{41} +(4.51269 - 4.51269i) q^{43} +(-0.581504 - 2.51775i) q^{44} +(-3.89169 + 2.15742i) q^{46} -6.67809i q^{47} +6.93042 q^{49} +(-4.48396 + 5.46755i) q^{50} +(-0.948500 - 4.10674i) q^{52} +(-2.95356 + 2.95356i) q^{53} +(-1.62300 + 2.39006i) q^{55} +(-0.745073 - 0.0389483i) q^{56} +(-1.34361 + 4.68649i) q^{58} +(9.76773 - 9.76773i) q^{59} +(-1.02388 - 1.02388i) q^{61} +(-1.73851 - 3.13603i) q^{62} +(-7.95640 - 0.834111i) q^{64} +(-2.64730 + 3.89847i) q^{65} +(-3.67191 - 3.67191i) q^{67} +(-3.07880 + 4.92808i) q^{68} +(0.534215 + 0.640647i) q^{70} +7.85546i q^{71} +12.4323 q^{73} +(-2.95219 - 0.846384i) q^{74} +(0.188543 + 0.816337i) q^{76} +(0.240990 + 0.240990i) q^{77} +10.7196i q^{79} +(5.36174 + 7.15904i) q^{80} +(-13.3324 + 7.39107i) q^{82} +(3.50410 - 3.50410i) q^{83} +(6.38111 - 1.21970i) q^{85} +(-2.48735 + 8.67586i) q^{86} +(2.44561 + 2.71540i) q^{88} +13.2383 q^{89} +(0.393083 + 0.393083i) q^{91} +(3.33421 - 5.33690i) q^{92} +(4.57903 + 8.25992i) q^{94} +(0.526229 - 0.774936i) q^{95} +11.1057i q^{97} +(-8.57202 + 4.75204i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) $ 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

Character values

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

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

Coefficient data

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

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

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

$2$	−1.23687	+	0.685679i	−0.874598	+	0.484848i
$2$	−1.23687	+	0.685679i	−0.874598	+	0.484848i
$3$		0			0
$3$		0			0
$4$	1.05969	−	1.69619i	0.529844	−	0.848095i
$5$	−2.19631	+	0.419806i	−0.982218	+	0.187743i
$5$	−2.19631	+	0.419806i	−0.982218	+	0.187743i
$6$		0			0
$7$			0.263783i			0.0997006i	0.998757	+	0.0498503i	$0.0158744\pi$
$7$			0.263783i			0.0997006i	−0.998757	+	0.0498503i	$0.984126\pi$
$8$	−0.147653	+	2.82457i	−0.0522031	+	0.998636i
$9$		0			0
$10$	2.42869	−	2.02521i	0.768019	−	0.640427i
$11$	0.913594	−	0.913594i	0.275459	−	0.275459i	−0.555834	−	0.831293i	$-0.687601\pi$
$11$	0.913594	−	0.913594i	0.275459	−	0.275459i	0.831293	+	0.555834i	$0.187601\pi$
$12$		0			0
$13$	1.49018	−	1.49018i	0.413300	−	0.413300i	−0.469586	−	0.882887i	$-0.655597\pi$
$13$	1.49018	−	1.49018i	0.413300	−	0.413300i	0.882887	+	0.469586i	$0.155597\pi$
$14$	−0.180870	−	0.326265i	−0.0483397	−	0.0871979i
$15$		0			0
$16$	−1.75412	−	3.59487i	−0.438531	−	0.898716i
$17$	−2.90538			−0.704659			−0.352329	−	0.935876i	$-0.614610\pi$
$17$	−2.90538			−0.704659			−0.352329	+	0.935876i	$0.614610\pi$
$18$		0			0
$19$	−0.296217	+	0.296217i	−0.0679568	+	0.0679568i	−0.740268	−	0.672312i	$-0.765302\pi$
$19$	−0.296217	+	0.296217i	−0.0679568	+	0.0679568i	0.672312	+	0.740268i	$0.265302\pi$
$20$	−1.61533	+	4.17022i	−0.361199	+	0.932489i
$21$		0			0
$22$	−0.503563	+	1.75643i	−0.107360	+	0.374472i
$23$	3.14640			0.656070			0.328035	−	0.944666i	$-0.393614\pi$
$23$	3.14640			0.656070			0.328035	+	0.944666i	$0.393614\pi$
$24$		0			0
$25$	4.64753	−	1.84404i	0.929505	−	0.368809i
$26$	−0.821369	+	2.86493i	−0.161084	+	0.561860i
$27$		0			0
$28$	0.447426	+	0.279528i	0.0845556	+	0.0528258i
$29$	2.43765	−	2.43765i	0.452660	−	0.452660i	−0.443577	−	0.896236i	$-0.646291\pi$
$29$	2.43765	−	2.43765i	0.452660	−	0.452660i	0.896236	+	0.443577i	$0.146291\pi$
$30$		0			0
$31$			2.53546i			0.455382i	0.973733	+	0.227691i	$0.0731177\pi$
$31$			2.53546i			0.455382i	−0.973733	+	0.227691i	$0.926882\pi$
$32$	4.63454	+	3.24361i	0.819279	+	0.573395i
$33$		0			0
$34$	3.59358	−	1.99216i	0.616293	−	0.341653i
$35$	−0.110738	−	0.579348i	−0.0187181	−	0.0979277i
$36$		0			0
$37$	1.53556	+	1.53556i	0.252444	+	0.252444i	0.821972	−	0.569528i	$-0.192874\pi$
$37$	1.53556	+	1.53556i	0.252444	+	0.252444i	−0.569528	+	0.821972i	$0.692874\pi$
$38$	0.163272	−	0.569491i	0.0264861	−	0.0923836i
$39$		0			0
$40$	−0.861481	−	6.26561i	−0.136212	−	0.990680i
$41$	10.7792			1.68343			0.841713	−	0.539925i	$-0.181547\pi$
$41$	10.7792			1.68343			0.841713	+	0.539925i	$0.181547\pi$
$42$		0			0
$43$	4.51269	−	4.51269i	0.688178	−	0.688178i	−0.273651	−	0.961829i	$-0.588231\pi$
$43$	4.51269	−	4.51269i	0.688178	−	0.688178i	0.961829	+	0.273651i	$0.0882313\pi$
$44$	−0.581504	−	2.51775i	−0.0876651	−	0.379566i
$45$		0			0
$46$	−3.89169	+	2.15742i	−0.573798	+	0.318095i
$47$		−	6.67809i		−	0.974100i	−0.873374	−	0.487050i	$-0.838073\pi$
$47$		−	6.67809i		−	0.974100i	0.873374	−	0.487050i	$-0.161927\pi$
$48$		0			0
$49$	6.93042			0.990060
$50$	−4.48396	+	5.46755i	−0.634127	+	0.773229i
$51$		0			0
$52$	−0.948500	−	4.10674i	−0.131533	−	0.569503i
$53$	−2.95356	+	2.95356i	−0.405703	+	0.405703i	−0.880237	−	0.474534i	$-0.842617\pi$
$53$	−2.95356	+	2.95356i	−0.405703	+	0.405703i	0.474534	+	0.880237i	$0.342617\pi$
$54$		0			0
$55$	−1.62300	+	2.39006i	−0.218845	+	0.322276i
$56$	−0.745073	−	0.0389483i	−0.0995646	−	0.00520468i
$57$		0			0
$58$	−1.34361	+	4.68649i	−0.176424	+	0.615367i
$59$	9.76773	−	9.76773i	1.27165	−	1.27165i	0.326428	−	0.945222i	$-0.394155\pi$
$59$	9.76773	−	9.76773i	1.27165	−	1.27165i	0.945222	−	0.326428i	$-0.105845\pi$
$60$		0			0
$61$	−1.02388	−	1.02388i	−0.131095	−	0.131095i	0.638515	−	0.769610i	$-0.279549\pi$
$61$	−1.02388	−	1.02388i	−0.131095	−	0.131095i	−0.769610	+	0.638515i	$0.779549\pi$
$62$	−1.73851	−	3.13603i	−0.220791	−	0.398277i
$63$		0			0
$64$	−7.95640	−	0.834111i	−0.994550	−	0.104264i
$65$	−2.64730	+	3.89847i	−0.328357	+	0.483545i
$66$		0			0
$67$	−3.67191	−	3.67191i	−0.448595	−	0.448595i	0.446292	−	0.894887i	$-0.352744\pi$
$67$	−3.67191	−	3.67191i	−0.448595	−	0.448595i	−0.894887	+	0.446292i	$0.852744\pi$
$68$	−3.07880	+	4.92808i	−0.373359	+	0.597618i
$69$		0			0
$70$	0.534215	+	0.640647i	0.0638509	+	0.0765720i
$71$			7.85546i			0.932272i	0.884713	+	0.466136i	$0.154354\pi$
$71$			7.85546i			0.932272i	−0.884713	+	0.466136i	$0.845646\pi$
$72$		0			0
$73$	12.4323			1.45509			0.727543	−	0.686062i	$-0.240662\pi$
$73$	12.4323			1.45509			0.727543	+	0.686062i	$0.240662\pi$
$74$	−2.95219	−	0.846384i	−0.343185	−	0.0983901i
$75$		0			0
$76$	0.188543	+	0.816337i	0.0216273	+	0.0936403i
$77$	0.240990	+	0.240990i	0.0274634	+	0.0274634i
$78$		0			0
$79$			10.7196i			1.20605i	0.797724	+	0.603023i	$0.206037\pi$
$79$			10.7196i			1.20605i	−0.797724	+	0.603023i	$0.793963\pi$
$80$	5.36174	+	7.15904i	0.599460	+	0.800404i
$81$		0			0
$82$	−13.3324	+	7.39107i	−1.47232	+	0.816207i
$83$	3.50410	−	3.50410i	0.384625	−	0.384625i	−0.488140	−	0.872765i	$-0.662325\pi$
$83$	3.50410	−	3.50410i	0.384625	−	0.384625i	0.872765	+	0.488140i	$0.162325\pi$
$84$		0			0
$85$	6.38111	−	1.21970i	0.692129	−	0.132295i
$86$	−2.48735	+	8.67586i	−0.268217	+	0.935542i
$87$		0			0
$88$	2.44561	+	2.71540i	0.260703	+	0.289463i
$89$	13.2383			1.40326			0.701629	−	0.712542i	$-0.252456\pi$
$89$	13.2383			1.40326			0.701629	+	0.712542i	$0.252456\pi$
$90$		0			0
$91$	0.393083	+	0.393083i	0.0412063	+	0.0412063i
$92$	3.33421	−	5.33690i	0.347615	−	0.556410i
$93$		0			0
$94$	4.57903	+	8.25992i	0.472291	+	0.851946i
$95$	0.526229	−	0.774936i	0.0539900	−	0.0795068i
$96$		0			0
$97$			11.1057i			1.12761i	0.825908	+	0.563804i	$0.190663\pi$
$97$			11.1057i			1.12761i	−0.825908	+	0.563804i	$0.809337\pi$
$98$	−8.57202	+	4.75204i	−0.865905	+	0.480029i
$99$		0			0
$100$	1.79708	−	9.83720i	0.179708	−	0.983720i
$101$	0.625096	+	0.625096i	0.0621994	+	0.0621994i	0.737522	−	0.675323i	$-0.235996\pi$
$101$	0.625096	+	0.625096i	0.0621994	+	0.0621994i	−0.675323	+	0.737522i	$0.735996\pi$
$102$		0			0
$103$		−	7.47669i		−	0.736701i	−0.929687	−	0.368350i	$-0.879923\pi$
$103$		−	7.47669i		−	0.736701i	0.929687	−	0.368350i	$-0.120077\pi$
$104$	3.98908	+	4.42914i	0.391161	+	0.434312i
$105$		0			0
$106$	1.62797	−	5.67837i	0.158123	−	0.551532i
$107$	−10.7929	−	10.7929i	−1.04339	−	1.04339i	−0.999015	−	0.0443705i	$-0.985872\pi$
$107$	−10.7929	−	10.7929i	−1.04339	−	1.04339i	−0.0443705	−	0.999015i	$-0.514128\pi$
$108$		0			0
$109$	−0.260948	−	0.260948i	−0.0249942	−	0.0249942i	0.694499	−	0.719493i	$-0.255626\pi$
$109$	−0.260948	−	0.260948i	−0.0249942	−	0.0249942i	−0.719493	+	0.694499i	$0.755626\pi$
$110$	0.368621	−	4.06905i	0.0351466	−	0.387969i
$111$		0			0
$112$	0.948264	−	0.462707i	0.0896025	−	0.0437217i
$113$	3.88893			0.365839			0.182920	−	0.983128i	$-0.441445\pi$
$113$	3.88893			0.365839			0.182920	+	0.983128i	$0.441445\pi$
$114$		0			0
$115$	−6.91046	+	1.32088i	−0.644404	+	0.123173i
$116$	−1.55157	−	6.71786i	−0.144059	−	0.623738i
$117$		0			0
$118$	−5.38387	+	18.7789i	−0.495625	+	1.72874i
$119$		−	0.766390i		−	0.0702549i
$120$		0			0
$121$			9.33069i			0.848245i
$122$	1.96846	+	0.564353i	0.178216	+	0.0510942i
$123$		0			0
$124$	4.30063	+	2.68680i	0.386208	+	0.241282i
$125$	−9.43325	+	6.00115i	−0.843736	+	0.536759i
$126$		0			0
$127$	−18.1176			−1.60768			−0.803840	−	0.594846i	$-0.797213\pi$
$127$	−18.1176			−1.60768			−0.803840	+	0.594846i	$0.797213\pi$
$128$	10.4130	−	4.42385i	0.920384	−	0.391017i
$129$		0			0
$130$	0.601262	−	6.63709i	0.0527342	−	0.582111i
$131$	−14.0610	−	14.0610i	−1.22851	−	1.22851i	−0.964526	−	0.263988i	$-0.914962\pi$
$131$	−14.0610	−	14.0610i	−1.22851	−	1.22851i	−0.263988	−	0.964526i	$-0.585038\pi$
$132$		0			0
$133$	−0.0781369	−	0.0781369i	−0.00677533	−	0.00677533i
$134$	7.05942	+	2.02392i	0.609841	+	0.174840i
$135$		0			0
$136$	0.428988	−	8.20646i	0.0367854	−	0.703698i
$137$		−	10.3404i		−	0.883440i	−0.897153	−	0.441720i	$-0.854368\pi$
$137$		−	10.3404i		−	0.883440i	0.897153	−	0.441720i	$-0.145632\pi$
$138$		0			0
$139$	11.8106	+	11.8106i	1.00176	+	1.00176i	0.999998	+	0.00176137i	$0.000560663\pi$
$139$	11.8106	+	11.8106i	1.00176	+	1.00176i	0.00176137	+	0.999998i	$0.499439\pi$
$140$	−1.10003	−	0.426096i	−0.0929697	−	0.0360117i
$141$		0			0
$142$	−5.38633	−	9.71618i	−0.452011	−	0.815363i
$143$		−	2.72283i		−	0.227695i
$144$		0			0
$145$	−4.33048	+	6.37716i	−0.359627	+	0.529594i
$146$	−15.3771	+	8.52454i	−1.27262	+	0.705496i
$147$		0			0
$148$	4.23181	−	0.977386i	0.347853	−	0.0803407i
$149$	−5.72046	−	5.72046i	−0.468639	−	0.468639i	0.432835	−	0.901473i	$-0.357513\pi$
$149$	−5.72046	−	5.72046i	−0.468639	−	0.468639i	−0.901473	+	0.432835i	$0.857513\pi$
$150$		0			0
$151$	−14.9974			−1.22047			−0.610234	−	0.792221i	$-0.708925\pi$
$151$	−14.9974			−1.22047			−0.610234	+	0.792221i	$0.708925\pi$
$152$	−0.792948	−	0.880422i	−0.0643166	−	0.0714117i
$153$		0			0
$154$	−0.463316	−	0.132831i	−0.0373350	−	0.0107039i
$155$	−1.06440	−	5.56865i	−0.0854948	−	0.447285i
$156$		0			0
$157$	−0.0261720	+	0.0261720i	−0.00208875	+	0.00208875i	−0.708150	−	0.706062i	$-0.750470\pi$
$157$	−0.0261720	+	0.0261720i	−0.00208875	+	0.00208875i	0.706062	+	0.708150i	$0.250470\pi$
$158$	−7.35019	−	13.2587i	−0.584750	−	1.05481i
$159$		0			0
$160$	−11.5406	−	5.17836i	−0.912362	−	0.409385i
$161$			0.829967i			0.0654106i
$162$		0			0
$163$	−17.1126	−	17.1126i	−1.34036	−	1.34036i	−0.895700	−	0.444659i	$-0.853325\pi$
$163$	−17.1126	−	17.1126i	−1.34036	−	1.34036i	−0.444659	−	0.895700i	$-0.646675\pi$
$164$	11.4226	−	18.2836i	0.891953	−	1.42771i
$165$		0			0
$166$	−1.93142	+	6.73680i	−0.149907	+	0.522877i
$167$	19.4611			1.50594			0.752971	−	0.658053i	$-0.228620\pi$
$167$	19.4611			1.50594			0.752971	+	0.658053i	$0.228620\pi$
$168$		0			0
$169$			8.55875i			0.658365i
$170$	−7.05628	+	5.88400i	−0.541192	+	0.451282i
$171$		0			0
$172$	−2.87233	−	12.4364i	−0.219013	−	0.948268i
$173$	11.3427	+	11.3427i	0.862367	+	0.862367i	0.991613	−	0.129245i	$-0.0412555\pi$
$173$	11.3427	+	11.3427i	0.862367	+	0.862367i	−0.129245	+	0.991613i	$0.541256\pi$
$174$		0			0
$175$	0.486428	+	1.22594i	0.0367705	+	0.0926722i
$176$	−4.88680	−	1.68169i	−0.368356	−	0.126762i
$177$		0			0
$178$	−16.3741	+	9.07724i	−1.22729	+	0.680368i
$179$	−4.50621	−	4.50621i	−0.336810	−	0.336810i	0.518356	−	0.855165i	$-0.326544\pi$
$179$	−4.50621	−	4.50621i	−0.336810	−	0.336810i	−0.855165	+	0.518356i	$0.826544\pi$
$180$		0			0
$181$	10.0971	−	10.0971i	0.750512	−	0.750512i	−0.224062	−	0.974575i	$-0.571932\pi$
$181$	10.0971	−	10.0971i	0.750512	−	0.750512i	0.974575	+	0.224062i	$0.0719320\pi$
$182$	−0.755721	−	0.216663i	−0.0560178	−	0.0160601i
$183$		0			0
$184$	−0.464575	+	8.88723i	−0.0342489	+	0.655176i
$185$	−4.01719	−	2.72792i	−0.295350	−	0.200561i
$186$		0			0
$187$	−2.65434	+	2.65434i	−0.194104	+	0.194104i
$188$	−11.3273	−	7.07669i	−0.826129	−	0.516121i
$189$		0			0
$190$	−0.119519	+	1.31932i	−0.00867080	+	0.0957134i
$191$	−23.8545			−1.72605			−0.863025	−	0.505161i	$-0.831433\pi$
$191$	−23.8545			−1.72605			−0.863025	+	0.505161i	$0.831433\pi$
$192$		0			0
$193$		−	13.8585i		−	0.997560i	−0.866729	−	0.498780i	$-0.833782\pi$
$193$		−	13.8585i		−	0.997560i	0.866729	−	0.498780i	$-0.166218\pi$
$194$	−7.61492	−	13.7362i	−0.546719	−	0.986205i
$195$		0			0
$196$	7.34408	−	11.7553i	0.524577	−	0.839665i
$197$	−11.9818	+	11.9818i	−0.853664	+	0.853664i	−0.990582	−	0.136918i	$-0.956280\pi$
$197$	−11.9818	+	11.9818i	−0.853664	+	0.853664i	0.136918	+	0.990582i	$0.456280\pi$
$198$		0			0
$199$	−11.4336			−0.810507			−0.405253	−	0.914204i	$-0.632817\pi$
$199$	−11.4336			−0.810507			−0.405253	+	0.914204i	$0.632817\pi$
$200$	4.52242	+	13.3995i	0.319783	+	0.947491i
$201$		0			0
$202$	−1.20178	−	0.344546i	−0.0845567	−	0.0242422i
$203$	0.643010	+	0.643010i	0.0451304	+	0.0451304i
$204$		0			0
$205$	−23.6744	+	4.52517i	−1.65349	+	0.316051i
$206$	5.12661	+	9.24769i	0.357188	+	0.644317i
$207$		0			0
$208$	−7.97093	−	2.74303i	−0.552685	−	0.190195i
$209$			0.541243i			0.0374386i
$210$		0			0
$211$	6.45820	−	6.45820i	0.444601	−	0.444601i	−0.448954	−	0.893555i	$-0.648203\pi$
$211$	6.45820	−	6.45820i	0.444601	−	0.444601i	0.893555	+	0.448954i	$0.148203\pi$
$212$	1.87995	+	8.13966i	0.129115	+	0.559034i
$213$		0			0
$214$	20.7498	+	5.94891i	1.41843	+	0.406659i
$215$	−8.01679	+	11.8057i	−0.546741	+	0.805142i
$216$		0			0
$217$	−0.668811			−0.0454019
$218$	0.501684	+	0.143832i	0.0339783	+	0.00974150i
$219$		0			0
$220$	2.33413	+	5.28564i	0.157367	+	0.356358i
$221$	−4.32953	+	4.32953i	−0.291236	+	0.291236i
$222$		0			0
$223$	0.620487			0.0415509			0.0207754	−	0.999784i	$-0.493386\pi$
$223$	0.620487			0.0415509			0.0207754	+	0.999784i	$0.493386\pi$
$224$	−0.855609	+	1.22251i	−0.0571678	+	0.0816826i
$225$		0			0
$226$	−4.81009	+	2.66656i	−0.319962	+	0.177377i
$227$	−10.0579	+	10.0579i	−0.667564	+	0.667564i	−0.957152	−	0.289588i	$-0.906482\pi$
$227$	−10.0579	+	10.0579i	−0.667564	+	0.667564i	0.289588	+	0.957152i	$0.406482\pi$
$228$		0			0
$229$	14.9831	−	14.9831i	0.990113	−	0.990113i	−0.00983872	−	0.999952i	$-0.503132\pi$
$229$	14.9831	−	14.9831i	0.990113	−	0.990113i	0.999952	+	0.00983872i	$0.00313181\pi$
$230$	7.64164	−	6.37211i	0.503875	−	0.420165i
$231$		0			0
$232$	6.52538	+	7.24523i	0.428412	+	0.475673i
$233$			2.07914i			0.136209i	0.997678	+	0.0681046i	$0.0216952\pi$
$233$			2.07914i			0.136209i	−0.997678	+	0.0681046i	$0.978305\pi$
$234$		0			0
$235$	2.80350	+	14.6671i	0.182880	+	0.956779i
$236$	−6.21718	−	26.9187i	−0.404704	−	1.75226i
$237$		0			0
$238$	0.525498	+	0.947924i	0.0340630	+	0.0614448i
$239$	13.2816			0.859113			0.429557	−	0.903040i	$-0.358670\pi$
$239$	13.2816			0.859113			0.429557	+	0.903040i	$0.358670\pi$
$240$		0			0
$241$	−3.84064			−0.247397			−0.123699	−	0.992320i	$-0.539476\pi$
$241$	−3.84064			−0.247397			−0.123699	+	0.992320i	$0.539476\pi$
$242$	−6.39786	−	11.5408i	−0.411270	−	0.741873i
$243$		0			0
$244$	−2.82170	+	0.651704i	−0.180641	+	0.0417210i
$245$	−15.2213	+	2.90943i	−0.972455	+	0.185877i
$246$		0			0
$247$			0.882830i			0.0561731i
$248$	−7.16159	−	0.374368i	−0.454761	−	0.0237724i
$249$		0			0
$250$	7.55283	−	13.8908i	0.477683	−	0.878532i
$251$	−10.6627	+	10.6627i	−0.673022	+	0.673022i	−0.958412	−	0.285389i	$-0.907877\pi$
$251$	−10.6627	+	10.6627i	−0.673022	+	0.673022i	0.285389	+	0.958412i	$0.407877\pi$
$252$		0			0
$253$	2.87453	−	2.87453i	0.180720	−	0.180720i
$254$	22.4091	−	12.4229i	1.40607	−	0.779481i
$255$		0			0
$256$	−9.84611	+	12.6117i	−0.615382	+	0.788229i
$257$	−11.6239			−0.725081			−0.362540	−	0.931968i	$-0.618090\pi$
$257$	−11.6239			−0.725081			−0.362540	+	0.931968i	$0.618090\pi$
$258$		0			0
$259$	−0.405054	+	0.405054i	−0.0251688	+	0.0251688i
$260$	3.80723	+	8.62148i	0.236115	+	0.534682i
$261$		0			0
$262$	27.0329	+	7.75027i	1.67010	+	0.478813i
$263$	29.3422			1.80932			0.904658	−	0.426138i	$-0.140126\pi$
$263$	29.3422			1.80932			0.904658	+	0.426138i	$0.140126\pi$
$264$		0			0
$265$	5.24701	−	7.72685i	0.322321	−	0.474657i
$266$	0.150222	+	0.0430682i	0.00921070	+	0.00264068i
$267$		0			0
$268$	−10.1193	+	2.33718i	−0.618137	+	0.142766i
$269$	−8.91793	+	8.91793i	−0.543736	+	0.543736i	−0.924622	−	0.380886i	$-0.875619\pi$
$269$	−8.91793	+	8.91793i	−0.543736	+	0.543736i	0.380886	+	0.924622i	$0.375619\pi$
$270$		0			0
$271$		−	31.2790i		−	1.90007i	−0.312150	−	0.950033i	$-0.601049\pi$
$271$		−	31.2790i		−	1.90007i	0.312150	−	0.950033i	$-0.398951\pi$
$272$	5.09640	+	10.4445i	0.309014	+	0.633288i
$273$		0			0
$274$	7.09020	+	12.7897i	0.428335	+	0.772655i
$275$	2.56124	−	5.93066i	0.154449	−	0.357632i
$276$		0			0
$277$	4.04579	+	4.04579i	0.243088	+	0.243088i	0.818126	−	0.575038i	$-0.195013\pi$
$277$	4.04579	+	4.04579i	0.243088	+	0.243088i	−0.575038	+	0.818126i	$0.695013\pi$
$278$	−22.7064	−	6.50986i	−1.36184	−	0.390436i
$279$		0			0
$280$	1.65276	−	0.227244i	0.0987713	−	0.0135804i
$281$	19.2114			1.14606			0.573029	−	0.819535i	$-0.305768\pi$
$281$	19.2114			1.14606			0.573029	+	0.819535i	$0.305768\pi$
$282$		0			0
$283$	10.0809	−	10.0809i	0.599247	−	0.599247i	−0.340865	−	0.940112i	$-0.610720\pi$
$283$	10.0809	−	10.0809i	0.599247	−	0.599247i	0.940112	+	0.340865i	$0.110720\pi$
$284$	13.3244	+	8.32434i	0.790655	+	0.493959i
$285$		0			0
$286$	1.86699	+	3.36778i	0.110397	+	0.199141i
$287$			2.84337i			0.167839i
$288$		0			0
$289$	−8.55875			−0.503456
$290$	0.983552	−	10.8570i	0.0577562	−	0.637547i
$291$		0			0
$292$	13.1743	−	21.0875i	0.770969	−	1.23405i
$293$	−4.81368	+	4.81368i	−0.281218	+	0.281218i	−0.833595	−	0.552376i	$-0.813721\pi$
$293$	−4.81368	+	4.81368i	−0.281218	+	0.281218i	0.552376	+	0.833595i	$0.313721\pi$
$294$		0			0
$295$	−17.3524	+	25.5535i	−1.01029	+	1.48778i
$296$	−4.56402	+	4.11056i	−0.265278	+	0.238922i
$297$		0			0
$298$	10.9979	+	3.15306i	0.637089	+	0.182652i
$299$	4.68869	−	4.68869i	0.271154	−	0.271154i
$300$		0			0
$301$	1.19037	+	1.19037i	0.0686118	+	0.0686118i
$302$	18.5498	−	10.2834i	1.06742	−	0.591742i
$303$		0			0
$304$	1.58446	+	0.545259i	0.0908750	+	0.0312727i
$305$	2.67859	+	1.81893i	0.153376	+	0.104152i
$306$		0			0
$307$	17.1791	+	17.1791i	0.980465	+	0.980465i	0.999813	−	0.0193480i	$-0.00615904\pi$
$307$	17.1791	+	17.1791i	0.980465	+	0.980465i	−0.0193480	+	0.999813i	$0.506159\pi$
$308$	0.664140	−	0.153391i	0.0378429	−	0.00874026i
$309$		0			0
$310$	5.13483	+	6.15785i	0.291639	+	0.349743i
$311$			16.6032i			0.941479i	0.882272	+	0.470740i	$0.156013\pi$
$311$			16.6032i			0.941479i	−0.882272	+	0.470740i	$0.843987\pi$
$312$		0			0
$313$	10.8345			0.612404			0.306202	−	0.951967i	$-0.400942\pi$
$313$	10.8345			0.612404			0.306202	+	0.951967i	$0.400942\pi$
$314$	0.0144257	−	0.0503169i	0.000814090	−	0.00283954i
$315$		0			0
$316$	18.1824	+	11.3594i	1.02284	+	0.639017i
$317$	15.3464	+	15.3464i	0.861942	+	0.861942i	0.991564	−	0.129621i	$-0.0413762\pi$
$317$	15.3464	+	15.3464i	0.861942	+	0.861942i	−0.129621	+	0.991564i	$0.541376\pi$
$318$		0			0
$319$		−	4.45404i		−	0.249378i
$320$	17.8249	−	1.50818i	0.996440	−	0.0843098i
$321$		0			0
$322$	−0.569091	−	1.02656i	−0.0317142	−	0.0572080i
$323$	0.860623	−	0.860623i	0.0478863	−	0.0478863i
$324$		0			0
$325$	4.17768	−	9.67358i	0.231736	−	0.536594i
$326$	32.8997	+	9.43226i	1.82215	+	0.522405i
$327$		0			0
$328$	−1.59158	+	30.4466i	−0.0878801	+	1.68113i
$329$	1.76157			0.0971183
$330$		0			0
$331$	−6.23806	−	6.23806i	−0.342875	−	0.342875i	0.514572	−	0.857447i	$-0.327951\pi$
$331$	−6.23806	−	6.23806i	−0.342875	−	0.342875i	−0.857447	+	0.514572i	$0.827951\pi$
$332$	−2.23037	−	9.65687i	−0.122407	−	0.529990i
$333$		0			0
$334$	−24.0708	+	13.3440i	−1.31709	+	0.730154i
$335$	9.60613	+	6.52315i	0.524839	+	0.356398i
$336$		0			0
$337$			8.87003i			0.483181i	0.970378	+	0.241591i	$0.0776691\pi$
$337$			8.87003i			0.483181i	−0.970378	+	0.241591i	$0.922331\pi$
$338$	−5.86856	−	10.5861i	−0.319207	−	0.575805i
$339$		0			0
$340$	4.69315	−	12.1161i	0.254522	−	0.657087i
$341$	2.31638	+	2.31638i	0.125439	+	0.125439i
$342$		0			0
$343$			3.67461i			0.198410i
$344$	12.0801	+	13.4127i	0.651315	+	0.723165i
$345$		0			0
$346$	−21.8068	−	6.25196i	−1.17234	−	0.336107i
$347$	11.3990	+	11.3990i	0.611932	+	0.611932i	0.943449	−	0.331517i	$-0.107560\pi$
$347$	11.3990	+	11.3990i	0.611932	+	0.611932i	−0.331517	+	0.943449i	$0.607560\pi$
$348$		0			0
$349$	−11.5358	−	11.5358i	−0.617496	−	0.617496i	0.327393	−	0.944888i	$-0.393830\pi$
$349$	−11.5358	−	11.5358i	−0.617496	−	0.617496i	−0.944888	+	0.327393i	$0.893830\pi$
$350$	−1.44225	−	1.18279i	−0.0770914	−	0.0632228i
$351$		0			0
$352$	7.19743	−	1.27075i	0.383624	−	0.0677310i
$353$	20.5642			1.09452			0.547260	−	0.836963i	$-0.315671\pi$
$353$	20.5642			1.09452			0.547260	+	0.836963i	$0.315671\pi$
$354$		0			0
$355$	−3.29777	−	17.2530i	−0.175027	−	0.915695i
$356$	14.0285	−	22.4547i	0.743508	−	1.19010i
$357$		0			0
$358$	8.66339	+	2.48377i	0.457875	+	0.131271i
$359$			18.8141i			0.992972i	0.868045	+	0.496486i	$0.165377\pi$
$359$			18.8141i			0.992972i	−0.868045	+	0.496486i	$0.834623\pi$
$360$		0			0
$361$			18.8245i			0.990764i
$362$	−5.56542	+	19.4122i	−0.292512	+	1.02028i
$363$		0			0
$364$	1.08329	−	0.250198i	0.0567798	−	0.0131139i
$365$	−27.3051	+	5.21914i	−1.42921	+	0.273182i
$366$		0			0
$367$	12.1654			0.635031			0.317515	−	0.948253i	$-0.397151\pi$
$367$	12.1654			0.635031			0.317515	+	0.948253i	$0.397151\pi$
$368$	−5.51917	−	11.3109i	−0.287707	−	0.589621i
$369$		0			0
$370$	6.83922	+	0.619574i	0.355554	+	0.0322101i
$371$	−0.779099	−	0.779099i	−0.0404488	−	0.0404488i
$372$		0			0
$373$	−14.7424	−	14.7424i	−0.763330	−	0.763330i	0.213592	−	0.976923i	$-0.431484\pi$
$373$	−14.7424	−	14.7424i	−0.763330	−	0.763330i	−0.976923	+	0.213592i	$0.931484\pi$
$374$	1.46304	−	5.10309i	0.0756522	−	0.263875i
$375$		0			0
$376$	18.8627	+	0.986038i	0.972772	+	0.0508510i
$377$		−	7.26505i		−	0.374169i
$378$		0			0
$379$	1.59803	+	1.59803i	0.0820853	+	0.0820853i	0.746957	−	0.664872i	$-0.231514\pi$
$379$	1.59803	+	1.59803i	0.0820853	+	0.0820853i	−0.664872	+	0.746957i	$0.731514\pi$
$380$	−0.756800	−	1.71378i	−0.0388230	−	0.0879148i
$381$		0			0
$382$	29.5049	−	16.3565i	1.50960	−	0.836873i
$383$			24.9035i			1.27251i	0.771479	+	0.636255i	$0.219517\pi$
$383$			24.9035i			1.27251i	−0.771479	+	0.636255i	$0.780483\pi$
$384$		0			0
$385$	−0.630458	−	0.428120i	−0.0321311	−	0.0218190i
$386$	9.50252	+	17.1412i	0.483665	+	0.872464i
$387$		0			0
$388$	18.8373	+	11.7685i	0.956319	+	0.597457i
$389$	−11.9793	−	11.9793i	−0.607375	−	0.607375i	0.334884	−	0.942259i	$-0.391303\pi$
$389$	−11.9793	−	11.9793i	−0.607375	−	0.607375i	−0.942259	+	0.334884i	$0.891303\pi$
$390$		0			0
$391$	−9.14150			−0.462306
$392$	−1.02329	+	19.5755i	−0.0516842	+	0.988710i
$393$		0			0
$394$	6.60422	−	23.0355i	0.332716	−	1.16051i
$395$	−4.50014	−	23.5435i	−0.226427	−	1.18460i
$396$		0			0
$397$	16.0845	−	16.0845i	0.807258	−	0.807258i	−0.176960	−	0.984218i	$-0.556626\pi$
$397$	16.0845	−	16.0845i	0.807258	−	0.807258i	0.984218	+	0.176960i	$0.0566264\pi$
$398$	14.1419	−	7.83978i	0.708868	−	0.392973i
$399$		0			0
$400$	−14.7814	−	13.4725i	−0.739071	−	0.673627i
$401$			3.56411i			0.177983i	0.996032	+	0.0889915i	$0.0283644\pi$
$401$			3.56411i			0.177983i	−0.996032	+	0.0889915i	$0.971636\pi$
$402$		0			0
$403$	3.77828	+	3.77828i	0.188210	+	0.188210i
$404$	1.72269	−	0.397875i	0.0857069	−	0.0197950i
$405$		0			0
$406$	−1.23622	−	0.354420i	−0.0613524	−	0.0175896i
$407$	2.80575			0.139076
$408$		0			0
$409$		−	0.455458i		−	0.0225209i	−0.999937	−	0.0112605i	$-0.996416\pi$
$409$		−	0.455458i		−	0.0225209i	0.999937	−	0.0112605i	$-0.00358439\pi$
$410$	26.1793	−	21.8301i	1.29290	−	1.07811i
$411$		0			0
$412$	−12.6819	−	7.92296i	−0.624792	−	0.390336i
$413$	2.57656	+	2.57656i	0.126784	+	0.126784i
$414$		0			0
$415$	−6.22503	+	9.16712i	−0.305575	+	0.449996i
$416$	11.7398	−	2.07273i	0.575593	−	0.101624i
$417$		0			0
$418$	−0.371119	−	0.669447i	−0.0181520	−	0.0327437i
$419$	−7.20612	−	7.20612i	−0.352042	−	0.352042i	0.508827	−	0.860869i	$-0.330079\pi$
$419$	−7.20612	−	7.20612i	−0.352042	−	0.352042i	−0.860869	+	0.508827i	$0.830079\pi$
$420$		0			0
$421$	−13.9138	+	13.9138i	−0.678119	+	0.678119i	−0.959574	−	0.281455i	$-0.909183\pi$
$421$	−13.9138	+	13.9138i	−0.678119	+	0.678119i	0.281455	+	0.959574i	$0.409183\pi$
$422$	−3.55969	+	12.4162i	−0.173283	+	0.604411i
$423$		0			0
$424$	−7.90645	−	8.77865i	−0.383971	−	0.426329i
$425$	−13.5028	+	5.35766i	−0.654984	+	0.259885i
$426$		0			0
$427$	0.270083	−	0.270083i	0.0130702	−	0.0130702i
$428$	−29.7438	+	6.86968i	−1.43772	+	0.332059i
$429$		0			0
$430$	1.82080	−	20.0990i	0.0878067	−	0.969262i
$431$	−20.2896			−0.977314			−0.488657	−	0.872476i	$-0.662513\pi$
$431$	−20.2896			−0.977314			−0.488657	+	0.872476i	$0.662513\pi$
$432$		0			0
$433$		−	13.2049i		−	0.634587i	−0.948327	−	0.317294i	$-0.897226\pi$
$433$		−	13.2049i		−	0.634587i	0.948327	−	0.317294i	$-0.102774\pi$
$434$	0.827232	−	0.458590i	0.0397084	−	0.0220130i
$435$		0			0
$436$	−0.719140	+	0.166094i	−0.0344406	+	0.00795445i
$437$	−0.932017	+	0.932017i	−0.0445844	+	0.0445844i
$438$		0			0
$439$	4.81740			0.229922			0.114961	−	0.993370i	$-0.463326\pi$
$439$	4.81740			0.229922			0.114961	+	0.993370i	$0.463326\pi$
$440$	−6.51126	−	4.93718i	−0.310412	−	0.235371i
$441$		0			0
$442$	2.38639	−	8.32373i	0.113509	−	0.395920i
$443$	9.16428	+	9.16428i	0.435408	+	0.435408i	0.890463	−	0.455055i	$-0.150380\pi$
$443$	9.16428	+	9.16428i	0.435408	+	0.435408i	−0.455055	+	0.890463i	$0.650380\pi$
$444$		0			0
$445$	−29.0754	+	5.55752i	−1.37831	+	0.263452i
$446$	−0.767461	+	0.425455i	−0.0363403	+	0.0201459i
$447$		0			0
$448$	0.220024	−	2.09876i	0.0103952	−	0.0991572i
$449$		−	3.67981i		−	0.173661i	−0.996223	−	0.0868305i	$-0.972326\pi$
$449$		−	3.67981i		−	0.173661i	0.996223	−	0.0868305i	$-0.0276739\pi$
$450$		0			0
$451$	9.84780	−	9.84780i	0.463715	−	0.463715i
$452$	4.12105	−	6.59636i	0.193838	−	0.310267i
$453$		0			0
$454$	5.54379	−	19.3367i	0.260183	−	0.907517i
$455$	−1.02835	−	0.698312i	−0.0482098	−	0.0327374i
$456$		0			0
$457$	−18.1968			−0.851212			−0.425606	−	0.904908i	$-0.639939\pi$
$457$	−18.1968			−0.851212			−0.425606	+	0.904908i	$0.639939\pi$
$458$	−8.25854	+	28.8058i	−0.385896	+	1.34601i
$459$		0			0
$460$	−5.08248	+	13.1212i	−0.236972	+	0.611778i
$461$	20.4826	−	20.4826i	0.953971	−	0.953971i	−0.0450155	−	0.998986i	$-0.514334\pi$
$461$	20.4826	−	20.4826i	0.953971	−	0.953971i	0.998986	+	0.0450155i	$0.0143337\pi$
$462$		0			0
$463$	22.5416			1.04760			0.523799	−	0.851842i	$-0.324514\pi$
$463$	22.5416			1.04760			0.523799	+	0.851842i	$0.324514\pi$
$464$	−13.0389	−	4.48708i	−0.605318	−	0.208308i
$465$		0			0
$466$	−1.42562	−	2.57163i	−0.0660408	−	0.119128i
$467$	−26.2704	+	26.2704i	−1.21565	+	1.21565i	−0.246507	+	0.969141i	$0.579283\pi$
$467$	−26.2704	+	26.2704i	−1.21565	+	1.21565i	−0.969141	+	0.246507i	$0.920717\pi$
$468$		0			0
$469$	0.968587	−	0.968587i	0.0447252	−	0.0447252i
$470$	−13.5245	−	16.2190i	−0.623839	−	0.748128i
$471$		0			0
$472$	26.1474	+	29.0319i	1.20353	+	1.33630i
$473$		−	8.24552i		−	0.379130i
$474$		0			0
$475$	−0.830438	+	1.92291i	−0.0381031	+	0.0882292i
$476$	−1.29994	−	0.812135i	−0.0595828	−	0.0372241i
$477$		0			0
$478$	−16.4276	+	9.10690i	−0.751379	+	0.416540i
$479$	−0.723719			−0.0330676			−0.0165338	−	0.999863i	$-0.505263\pi$
$479$	−0.723719			−0.0330676			−0.0165338	+	0.999863i	$0.505263\pi$
$480$		0			0
$481$	4.57651			0.208671
$482$	4.75036	−	2.63344i	0.216373	−	0.119950i
$483$		0			0
$484$	15.8266	+	9.88762i	0.719392	+	0.449437i
$485$	−4.66222	−	24.3914i	−0.211701	−	1.10756i
$486$		0			0
$487$		−	15.0222i		−	0.680719i	−0.940295	−	0.340360i	$-0.889451\pi$
$487$		−	15.0222i		−	0.680719i	0.940295	−	0.340360i	$-0.110549\pi$
$488$	3.04321	−	2.74085i	0.137760	−	0.124072i
$489$		0			0
$490$	16.8318	−	14.0355i	0.760385	−	0.634061i
$491$	3.04102	−	3.04102i	0.137239	−	0.137239i	−0.635150	−	0.772389i	$-0.719062\pi$
$491$	3.04102	−	3.04102i	0.137239	−	0.137239i	0.772389	+	0.635150i	$0.219062\pi$
$492$		0			0
$493$	−7.08230	+	7.08230i	−0.318971	+	0.318971i
$494$	−0.605338	−	1.09194i	−0.0272355	−	0.0491289i
$495$		0			0
$496$	9.11464	−	4.44751i	0.409260	−	0.199699i
$497$	−2.07214			−0.0929481
$498$		0			0
$499$	11.3545	−	11.3545i	0.508298	−	0.508298i	−0.405706	−	0.914004i	$-0.632974\pi$
$499$	11.3545	−	11.3545i	0.508298	−	0.508298i	0.914004	+	0.405706i	$0.132974\pi$
$500$	0.182782	+	22.3599i	0.00817426	+	0.999967i
$501$		0			0
$502$	5.87716	−	20.4995i	0.262310	−	0.914938i
$503$	−24.8256			−1.10692			−0.553459	−	0.832876i	$-0.686692\pi$
$503$	−24.8256			−1.10692			−0.553459	+	0.832876i	$0.686692\pi$
$504$		0			0
$505$	−1.63532	−	1.11048i	−0.0727708	−	0.0494159i
$506$	−1.58441	+	5.52643i	−0.0704357	+	0.245680i
$507$		0			0
$508$	−19.1990	+	30.7309i	−0.851820	+	1.36347i
$509$	−22.3544	+	22.3544i	−0.990841	+	0.990841i	−0.999958	−	0.00911778i	$-0.997098\pi$
$509$	−22.3544	+	22.3544i	−0.990841	+	0.990841i	0.00911778	+	0.999958i	$0.497098\pi$
$510$		0			0
$511$			3.27942i			0.145073i
$512$	3.53079	−	22.3502i	0.156040	−	0.987751i
$513$		0			0
$514$	14.3773	−	7.97029i	0.634154	−	0.351554i
$515$	3.13876	+	16.4211i	0.138310	+	0.723601i
$516$		0			0
$517$	−6.10106	−	6.10106i	−0.268324	−	0.268324i
$518$	0.223262	−	0.778736i	0.00980955	−	0.0342157i
$519$		0			0
$520$	−10.6206	−	8.05310i	−0.465745	−	0.353152i
$521$	30.7334			1.34646			0.673228	−	0.739435i	$-0.264907\pi$
$521$	30.7334			1.34646			0.673228	+	0.739435i	$0.264907\pi$
$522$		0			0
$523$	12.6215	−	12.6215i	0.551898	−	0.551898i	−0.375090	−	0.926988i	$-0.622388\pi$
$523$	12.6215	−	12.6215i	0.551898	−	0.551898i	0.926988	+	0.375090i	$0.122388\pi$
$524$	−38.7504	+	8.94984i	−1.69282	+	0.390976i
$525$		0			0
$526$	−36.2924	+	20.1193i	−1.58242	+	0.877244i
$527$		−	7.36649i		−	0.320889i
$528$		0			0
$529$	−13.1002			−0.569572
$530$	−1.19172	+	13.1549i	−0.0517648	+	0.571411i
$531$		0			0
$532$	−0.215336	+	0.0497343i	−0.00933599	+	0.00215626i
$533$	16.0629	−	16.0629i	0.695761	−	0.695761i
$534$		0			0
$535$	28.2353	+	19.1735i	1.22072	+	0.828944i
$536$	10.9137	−	9.82940i	0.471402	−	0.424566i
$537$		0			0
$538$	4.91547	−	17.1451i	0.211921	−	0.739180i
$539$	6.33159	−	6.33159i	0.272721	−	0.272721i
$540$		0			0
$541$	18.0279	+	18.0279i	0.775081	+	0.775081i	0.978990	−	0.203909i	$-0.0653645\pi$
$541$	18.0279	+	18.0279i	0.775081	+	0.775081i	−0.203909	+	0.978990i	$0.565365\pi$
$542$	21.4474	+	38.6880i	0.921244	+	1.66179i
$543$		0			0
$544$	−13.4651	−	9.42393i	−0.577312	−	0.404048i
$545$	0.682668	+	0.463574i	0.0292423	+	0.0198573i
$546$		0			0
$547$	26.0749	+	26.0749i	1.11488	+	1.11488i	0.992480	+	0.122403i	$0.0390600\pi$
$547$	26.0749	+	26.0749i	1.11488	+	1.11488i	0.122403	+	0.992480i	$0.460940\pi$
$548$	−17.5393	−	10.9576i	−0.749241	−	0.468086i
$549$		0			0
$550$	0.898608	+	9.09164i	0.0383168	+	0.387669i
$551$			1.44414i			0.0615226i
$552$		0			0
$553$	−2.82764			−0.120244
$554$	−7.77823	−	2.23000i	−0.330465	−	0.0947435i
$555$		0			0
$556$	32.5485	−	7.51745i	1.38036	−	0.318811i
$557$	23.2849	+	23.2849i	0.986612	+	0.986612i	0.999912	−	0.0132999i	$-0.00423361\pi$
$557$	23.2849	+	23.2849i	0.986612	+	0.986612i	−0.0132999	+	0.999912i	$0.504234\pi$
$558$		0			0
$559$		−	13.4494i		−	0.568849i
$560$	−1.88843	+	1.41433i	−0.0798008	+	0.0597665i
$561$		0			0
$562$	−23.7620	+	13.1729i	−1.00234	+	0.555664i
$563$	−2.08207	+	2.08207i	−0.0877489	+	0.0877489i	−0.749619	−	0.661870i	$-0.769763\pi$
$563$	−2.08207	+	2.08207i	−0.0877489	+	0.0877489i	0.661870	+	0.749619i	$0.269763\pi$
$564$		0			0
$565$	−8.54127	+	1.63259i	−0.359334	+	0.0686837i
$566$	−5.55648	+	19.3810i	−0.233556	+	0.814644i
$567$		0			0
$568$	−22.1883	−	1.15988i	−0.931001	−	0.0486675i
$569$	−22.4930			−0.942957			−0.471478	−	0.881878i	$-0.656279\pi$
$569$	−22.4930			−0.942957			−0.471478	+	0.881878i	$0.656279\pi$
$570$		0			0
$571$	−17.5867	−	17.5867i	−0.735979	−	0.735979i	0.235818	−	0.971797i	$-0.424223\pi$
$571$	−17.5867	−	17.5867i	−0.735979	−	0.735979i	−0.971797	+	0.235818i	$0.924223\pi$
$572$	−4.61844	−	2.88535i	−0.193107	−	0.120643i
$573$		0			0
$574$	−1.94964	−	3.51687i	−0.0813763	−	0.146791i
$575$	14.6230	−	5.80211i	0.609821	−	0.241965i
$576$		0			0
$577$			24.8497i			1.03450i	0.855833	+	0.517252i	$0.173045\pi$
$577$			24.8497i			1.03450i	−0.855833	+	0.517252i	$0.826955\pi$
$578$	10.5861	−	5.86856i	0.440322	−	0.244100i
$579$		0			0
$580$	6.22792	+	14.1031i	0.258600	+	0.585600i
$581$	0.924321	+	0.924321i	0.0383473	+	0.0383473i
$582$		0			0
$583$			5.39671i			0.223509i
$584$	−1.83566	+	35.1158i	−0.0759600	+	1.45310i
$585$		0			0
$586$	2.65325	−	9.25454i	0.109605	−	0.382301i
$587$	−22.8896	−	22.8896i	−0.944753	−	0.944753i	0.0537988	−	0.998552i	$-0.482867\pi$
$587$	−22.8896	−	22.8896i	−0.944753	−	0.944753i	−0.998552	+	0.0537988i	$0.982867\pi$
$588$		0			0
$589$	−0.751046	−	0.751046i	−0.0309463	−	0.0309463i
$590$	3.94113	−	43.5045i	0.162254	−	1.79105i
$591$		0			0
$592$	2.82657	−	8.21368i	0.116171	−	0.337580i
$593$	13.3090			0.546536			0.273268	−	0.961938i	$-0.411895\pi$
$593$	13.3090			0.546536			0.273268	+	0.961938i	$0.411895\pi$
$594$		0			0
$595$	0.321735	+	1.68323i	0.0131899	+	0.0690056i
$596$	−15.7649	+	3.64109i	−0.645756	+	0.149145i
$597$		0			0
$598$	−2.58436	+	9.01424i	−0.105682	+	0.368620i
$599$			7.33982i			0.299897i	0.988694	+	0.149948i	$0.0479108\pi$
$599$			7.33982i			0.299897i	−0.988694	+	0.149948i	$0.952089\pi$
$600$		0			0
$601$			27.4748i			1.12072i	0.828250	+	0.560359i	$0.189337\pi$
$601$			27.4748i			1.12072i	−0.828250	+	0.560359i	$0.810663\pi$
$602$	−2.28854	−	0.656119i	−0.0932740	−	0.0267414i
$603$		0			0
$604$	−15.8925	+	25.4384i	−0.646658	+	1.03507i
$605$	−3.91708	−	20.4931i	−0.159252	−	0.833162i
$606$		0			0
$607$	−27.4473			−1.11405			−0.557026	−	0.830495i	$-0.688058\pi$
$607$	−27.4473			−1.11405			−0.557026	+	0.830495i	$0.688058\pi$
$608$	−2.33364	+	0.412017i	−0.0946416	+	0.0167095i
$609$		0			0
$610$	−4.56027	−	0.413121i	−0.184640	−	0.0167268i
$611$	−9.95153	−	9.95153i	−0.402596	−	0.402596i
$612$		0			0
$613$	−17.6219	−	17.6219i	−0.711742	−	0.711742i	0.255158	−	0.966899i	$-0.417873\pi$
$613$	−17.6219	−	17.6219i	−0.711742	−	0.711742i	−0.966899	+	0.255158i	$0.917873\pi$
$614$	−33.0277	−	9.46896i	−1.33289	−	0.382136i
$615$		0			0
$616$	−0.716277	+	0.645111i	−0.0288596	+	0.0259923i
$617$		−	41.8102i		−	1.68322i	−0.540088	−	0.841608i	$-0.681609\pi$
$617$		−	41.8102i		−	1.68322i	0.540088	−	0.841608i	$-0.318391\pi$
$618$		0			0
$619$	1.39925	+	1.39925i	0.0562406	+	0.0562406i	0.734668	−	0.678427i	$-0.237338\pi$
$619$	1.39925	+	1.39925i	0.0562406	+	0.0562406i	−0.678427	+	0.734668i	$0.737338\pi$
$620$	−10.5734	−	4.09561i	−0.424639	−	0.164483i
$621$		0			0
$622$	−11.3844	−	20.5359i	−0.456475	−	0.823416i
$623$			3.49204i			0.139906i
$624$		0			0
$625$	18.1990	−	17.1405i	0.727960	−	0.685620i
$626$	−13.4009	+	7.42901i	−0.535607	+	0.296923i
$627$		0			0
$628$	0.0166585	+	0.0721267i	0.000664747	+	0.00287817i
$629$	−4.46139	−	4.46139i	−0.177887	−	0.177887i
$630$		0			0
$631$	33.0559			1.31593			0.657967	−	0.753047i	$-0.271417\pi$
$631$	33.0559			1.31593			0.657967	+	0.753047i	$0.271417\pi$
$632$	−30.2782	−	1.58277i	−1.20440	−	0.0629594i
$633$		0			0
$634$	−29.5043	−	8.45880i	−1.17176	−	0.335942i
$635$	39.7919	−	7.60589i	1.57909	−	0.301830i
$636$		0			0
$637$	10.3275	−	10.3275i	0.409192	−	0.409192i
$638$	3.05404	+	5.50906i	0.120911	+	0.218106i
$639$		0			0
$640$	−21.0129	+	14.0876i	−0.830607	+	0.556859i
$641$		−	8.31451i		−	0.328404i	−0.986427	−	0.164202i	$-0.947495\pi$
$641$		−	8.31451i		−	0.328404i	0.986427	−	0.164202i	$-0.0525048\pi$
$642$		0			0
$643$	−17.1504	−	17.1504i	−0.676344	−	0.676344i	0.282827	−	0.959171i	$-0.408728\pi$
$643$	−17.1504	−	17.1504i	−0.676344	−	0.676344i	−0.959171	+	0.282827i	$0.908728\pi$
$644$	1.40778	+	0.879506i	0.0554744	+	0.0346574i
$645$		0			0
$646$	−0.474366	+	1.65459i	−0.0186637	+	0.0650989i
$647$	−5.95293			−0.234034			−0.117017	−	0.993130i	$-0.537333\pi$
$647$	−5.95293			−0.234034			−0.117017	+	0.993130i	$0.537333\pi$
$648$		0			0
$649$		−	17.8475i		−	0.700575i
$650$	1.46573	+	14.8295i	0.0574908	+	0.581661i
$651$		0			0
$652$	−47.1601	+	10.8922i	−1.84693	+	0.426571i
$653$	−24.1739	−	24.1739i	−0.945997	−	0.945997i	0.0526174	−	0.998615i	$-0.483244\pi$
$653$	−24.1739	−	24.1739i	−0.945997	−	0.945997i	−0.998615	+	0.0526174i	$0.983244\pi$
$654$		0			0
$655$	36.7851	+	24.9793i	1.43731	+	0.976024i
$656$	−18.9080	−	38.7497i	−0.738234	−	1.51292i
$657$		0			0
$658$	−2.17883	+	1.20787i	−0.0849395	+	0.0470877i
$659$	25.0108	+	25.0108i	0.974284	+	0.974284i	0.999678	−	0.0253938i	$-0.00808397\pi$
$659$	25.0108	+	25.0108i	0.974284	+	0.974284i	−0.0253938	+	0.999678i	$0.508084\pi$
$660$		0			0
$661$	−28.8800	+	28.8800i	−1.12330	+	1.12330i	−0.132061	+	0.991242i	$0.542159\pi$
$661$	−28.8800	+	28.8800i	−1.12330	+	1.12330i	−0.991242	+	0.132061i	$0.957841\pi$
$662$	11.9930	+	3.43835i	0.466120	+	0.133635i
$663$		0			0
$664$	9.38018	+	10.4150i	0.364022	+	0.404179i
$665$	0.204415	+	0.138810i	0.00792687	+	0.00538283i
$666$		0			0
$667$	7.66982	−	7.66982i	0.296977	−	0.296977i
$668$	20.6227	−	33.0097i	0.797915	−	1.27718i
$669$		0			0
$670$	−16.3543	−	1.48156i	−0.631822	−	0.0572376i
$671$	−1.87083			−0.0722224
$672$		0			0
$673$		−	26.0623i		−	1.00463i	−0.864685	−	0.502315i	$-0.832482\pi$
$673$		−	26.0623i		−	1.00463i	0.864685	−	0.502315i	$-0.167518\pi$
$674$	−6.08199	−	10.9711i	−0.234270	−	0.422589i
$675$		0			0
$676$	14.5173	+	9.06961i	0.558357	+	0.348831i
$677$	9.70043	−	9.70043i	0.372818	−	0.372818i	−0.495685	−	0.868503i	$-0.665083\pi$
$677$	9.70043	−	9.70043i	0.372818	−	0.372818i	0.868503	+	0.495685i	$0.165083\pi$
$678$		0			0
$679$	−2.92948			−0.112423
$680$	2.50293	+	18.2040i	0.0959830	+	0.698091i
$681$		0			0
$682$	−4.45335	−	1.27677i	−0.170528	−	0.0488899i
$683$	−8.36855	−	8.36855i	−0.320214	−	0.320214i	0.528635	−	0.848849i	$-0.322704\pi$
$683$	−8.36855	−	8.36855i	−0.320214	−	0.320214i	−0.848849	+	0.528635i	$0.822704\pi$
$684$		0			0
$685$	4.34096	+	22.7107i	0.165860	+	0.867731i
$686$	−2.51960	−	4.54501i	−0.0961988	−	0.173529i
$687$		0			0
$688$	−24.1383	−	8.30670i	−0.920264	−	0.316690i
$689$			8.80266i			0.335355i
$690$		0			0
$691$	16.7998	−	16.7998i	0.639095	−	0.639095i	−0.311237	−	0.950332i	$-0.600743\pi$
$691$	16.7998	−	16.7998i	0.639095	−	0.639095i	0.950332	+	0.311237i	$0.100743\pi$
$692$	31.2590	−	7.21963i	1.18829	−	0.274449i
$693$		0			0
$694$	−21.9152	−	6.28303i	−0.831889	−	0.238501i
$695$	−30.8978	−	20.9815i	−1.17202	−	0.795873i
$696$		0			0
$697$	−31.3177			−1.18624
$698$	22.1781	+	6.35840i	0.839452	+	0.240669i
$699$		0			0
$700$	2.59489	+	0.474038i	0.0980774	+	0.0179170i
$701$	26.5344	−	26.5344i	1.00219	−	1.00219i	0.00219271	−	0.999998i	$-0.499302\pi$
$701$	26.5344	−	26.5344i	1.00219	−	1.00219i	0.999998	−	0.00219271i	$-0.000697963\pi$
$702$		0			0
$703$	−0.909716			−0.0343106
$704$	−8.03095	+	6.50688i	−0.302678	+	0.245237i
$705$		0			0
$706$	−25.4352	+	14.1004i	−0.957265	+	0.530676i
$707$	−0.164890	+	0.164890i	−0.00620131	+	0.00620131i
$708$		0			0
$709$	−32.4351	+	32.4351i	−1.21813	+	1.21813i	−0.249840	+	0.968287i	$0.580378\pi$
$709$	−32.4351	+	32.4351i	−1.21813	+	1.21813i	−0.968287	+	0.249840i	$0.919622\pi$
$710$	15.9089	+	19.0785i	0.597052	+	0.716003i
$711$		0			0
$712$	−1.95467	+	37.3925i	−0.0732545	+	1.40135i
$713$			7.97758i			0.298763i
$714$		0			0
$715$	1.14306	+	5.98017i	0.0427480	+	0.223646i
$716$	−12.4186	+	2.86821i	−0.464103	+	0.107190i
$717$		0			0
$718$	−12.9005	−	23.2706i	−0.481441	−	0.868452i
$719$	8.81868			0.328881			0.164441	−	0.986387i	$-0.447418\pi$
$719$	8.81868			0.328881			0.164441	+	0.986387i	$0.447418\pi$
$720$		0			0
$721$	1.97222			0.0734495
$722$	−12.9076	−	23.2834i	−0.480370	−	0.866520i
$723$		0			0
$724$	−6.42683	−	27.8264i	−0.238851	−	1.03416i
$725$	6.83390	−	15.8242i	0.253805	−	0.587695i
$726$		0			0
$727$		−	10.5815i		−	0.392448i	−0.980559	−	0.196224i	$-0.937132\pi$
$727$		−	10.5815i		−	0.392448i	0.980559	−	0.196224i	$-0.0628679\pi$
$728$	−1.16833	+	1.05225i	−0.0433012	+	0.0389990i
$729$		0			0
$730$	30.1941	−	25.1779i	1.11753	−	0.931876i
$731$	−13.1111	+	13.1111i	−0.484931	+	0.484931i
$732$		0			0
$733$	0.891694	−	0.891694i	0.0329355	−	0.0329355i	−0.690447	−	0.723383i	$-0.742586\pi$
$733$	0.891694	−	0.891694i	0.0329355	−	0.0329355i	0.723383	+	0.690447i	$0.242586\pi$
$734$	−15.0471	+	8.34159i	−0.555397	+	0.307894i
$735$		0			0
$736$	14.5821	+	10.2057i	0.537505	+	0.376187i
$737$	−6.70927			−0.247139
$738$		0			0
$739$	−22.1859	+	22.1859i	−0.816120	+	0.816120i	−0.985543	−	0.169423i	$-0.945810\pi$
$739$	−22.1859	+	22.1859i	−0.816120	+	0.816120i	0.169423	+	0.985543i	$0.445810\pi$
$740$	−8.88405	+	3.92318i	−0.326584	+	0.144219i
$741$		0			0
$742$	1.49786	+	0.429431i	0.0549880	+	0.0157649i
$743$	7.89487			0.289635			0.144817	−	0.989458i	$-0.453741\pi$
$743$	7.89487			0.289635			0.144817	+	0.989458i	$0.453741\pi$
$744$		0			0
$745$	14.9654	+	10.1624i	0.548289	+	0.372322i
$746$	28.3429	+	8.12583i	1.03771	+	0.297508i
$747$		0			0
$748$	1.68949	+	7.31504i	0.0617740	+	0.267464i
$749$	2.84697	−	2.84697i	0.104026	−	0.104026i
$750$		0			0
$751$		−	4.43117i		−	0.161696i	−0.996726	−	0.0808478i	$-0.974237\pi$
$751$		−	4.43117i		−	0.161696i	0.996726	−	0.0808478i	$-0.0257628\pi$
$752$	−24.0068	+	11.7142i	−0.875439	+	0.427173i
$753$		0			0
$754$	4.98149	+	8.98591i	0.181415	+	0.327248i
$755$	32.9388	−	6.29598i	1.19877	−	0.229134i
$756$		0			0
$757$	−22.8329	−	22.8329i	−0.829876	−	0.829876i	0.157623	−	0.987499i	$-0.449617\pi$
$757$	−22.8329	−	22.8329i	−0.829876	−	0.829876i	−0.987499	+	0.157623i	$0.949617\pi$
$758$	−3.07229	−	0.880817i	−0.111591	−	0.0319927i
$759$		0			0
$760$	2.11116	+	1.60079i	0.0765799	+	0.0580669i
$761$	18.3941			0.666784			0.333392	−	0.942788i	$-0.391807\pi$
$761$	18.3941			0.666784			0.333392	+	0.942788i	$0.391807\pi$
$762$		0			0
$763$	0.0688335	−	0.0688335i	0.00249194	−	0.00249194i
$764$	−25.2783	+	40.4617i	−0.914537	+	1.46385i
$765$		0			0
$766$	−17.0758	−	30.8024i	−0.616975	−	1.11294i
$767$		−	29.1113i		−	1.05115i
$768$		0			0
$769$	12.2959			0.443402			0.221701	−	0.975115i	$-0.428839\pi$
$769$	12.2959			0.443402			0.221701	+	0.975115i	$0.428839\pi$
$770$	1.07335	+	0.0972358i	0.0386807	+	0.00350414i
$771$		0			0
$772$	−23.5067	−	14.6857i	−0.846026	−	0.528551i
$773$	16.8697	−	16.8697i	0.606762	−	0.606762i	−0.335337	−	0.942098i	$-0.608850\pi$
$773$	16.8697	−	16.8697i	0.606762	−	0.606762i	0.942098	+	0.335337i	$0.108850\pi$
$774$		0			0
$775$	4.67551	+	11.7836i	0.167949	+	0.423280i
$776$	−31.3687	−	1.63978i	−1.12607	−	0.0588647i
$777$		0			0
$778$	23.0308	+	6.60287i	0.825694	+	0.236724i
$779$	−3.19298	+	3.19298i	−0.114400	+	0.114400i
$780$		0			0
$781$	7.17670	+	7.17670i	0.256803	+	0.256803i
$782$	11.3068	−	6.26814i	0.404332	−	0.224148i
$783$		0			0
$784$	−12.1568	−	24.9139i	−0.434171	−	0.889783i
$785$	0.0464945	−	0.0684688i	0.00165946	−	0.00244376i
$786$		0			0
$787$	32.0462	+	32.0462i	1.14232	+	1.14232i	0.988024	+	0.154299i	$0.0493118\pi$
$787$	32.0462	+	32.0462i	1.14232	+	1.14232i	0.154299	+	0.988024i	$0.450688\pi$
$788$	7.62641	+	33.0203i	0.271680	+	1.17630i
$789$		0			0
$790$	21.7094	+	26.0345i	0.772384	+	0.926267i
$791$			1.02583i			0.0364744i
$792$		0			0
$793$	−3.05153			−0.108363
$794$	−8.86560	+	30.9232i	−0.314628	+	1.09742i
$795$		0			0
$796$	−12.1161	+	19.3936i	−0.429442	+	0.687387i
$797$	−16.6812	−	16.6812i	−0.590879	−	0.590879i	0.346990	−	0.937869i	$-0.387204\pi$
$797$	−16.6812	−	16.6812i	−0.590879	−	0.590879i	−0.937869	+	0.346990i	$0.887204\pi$
$798$		0			0
$799$			19.4024i			0.686408i
$800$	27.5205	+	6.52846i	0.972997	+	0.230816i
$801$		0			0
$802$	−2.44383	−	4.40833i	−0.0862948	−	0.155664i
$803$	11.3580	−	11.3580i	0.400816	−	0.400816i
$804$		0			0
$805$	−0.348425	−	1.82286i	−0.0122804	−	0.0642475i
$806$	−7.26393	−	2.08255i	−0.255861	−	0.0733547i
$807$		0			0
$808$	−1.85792	+	1.67333i	−0.0653616	+	0.0588676i
$809$	−26.5382			−0.933032			−0.466516	−	0.884513i	$-0.654491\pi$
$809$	−26.5382			−0.933032			−0.466516	+	0.884513i	$0.654491\pi$
$810$		0			0
$811$	19.0246	+	19.0246i	0.668044	+	0.668044i	0.957263	−	0.289219i	$-0.0933955\pi$
$811$	19.0246	+	19.0246i	0.668044	+	0.668044i	−0.289219	+	0.957263i	$0.593396\pi$
$812$	1.77206	−	0.409277i	0.0621870	−	0.0143628i
$813$		0			0
$814$	−3.47035	+	1.92385i	−0.121636	+	0.0674308i
$815$	44.7684	+	30.4005i	1.56817	+	1.06488i
$816$		0			0
$817$			2.67347i			0.0935328i
$818$	0.312298	+	0.563341i	0.0109192	+	0.0196968i
$819$		0			0
$820$	−17.4119	+	44.9516i	−0.608051	+	1.56978i
$821$	8.92298	+	8.92298i	0.311414	+	0.311414i	0.845457	−	0.534043i	$-0.179328\pi$
$821$	8.92298	+	8.92298i	0.311414	+	0.311414i	−0.534043	+	0.845457i	$0.679328\pi$
$822$		0			0
$823$			28.4770i			0.992646i	0.868138	+	0.496323i	$0.165317\pi$
$823$			28.4770i			0.992646i	−0.868138	+	0.496323i	$0.834683\pi$
$824$	21.1185	+	1.10395i	0.735696	+	0.0384581i
$825$		0			0
$826$	−4.95356	−	1.42017i	−0.172356	−	0.0494141i
$827$	14.8892	+	14.8892i	0.517748	+	0.517748i	0.916889	−	0.399141i	$-0.130692\pi$
$827$	14.8892	+	14.8892i	0.517748	+	0.517748i	−0.399141	+	0.916889i	$0.630692\pi$
$828$		0			0
$829$	11.4041	+	11.4041i	0.396082	+	0.396082i	0.876849	−	0.480767i	$-0.159642\pi$
$829$	11.4041	+	11.4041i	0.396082	+	0.396082i	−0.480767	+	0.876849i	$0.659642\pi$
$830$	1.41385	−	15.6069i	0.0490754	−	0.541723i
$831$		0			0
$832$	−13.0994	+	10.6135i	−0.454140	+	0.367956i
$833$	−20.1355			−0.697654
$834$		0			0
$835$	−42.7425	+	8.16987i	−1.47916	+	0.282730i
$836$	0.918052	+	0.573549i	0.0317515	+	0.0198366i
$837$		0			0
$838$	13.8541	+	3.97193i	0.478582	+	0.137208i
$839$		−	16.2531i		−	0.561118i	−0.959837	−	0.280559i	$-0.909480\pi$
$839$		−	16.2531i		−	0.561118i	0.959837	−	0.280559i	$-0.0905199\pi$
$840$		0			0
$841$			17.1157i			0.590198i
$842$	7.66916	−	26.7500i	0.264297	−	0.921867i
$843$		0			0
$844$	−4.11066	−	17.7980i	−0.141495	−	0.612633i
$845$	−3.59301	−	18.7976i	−0.123603	−	0.646659i
$846$		0			0
$847$	−2.46128			−0.0845705
$848$	15.7986	+	5.43675i	0.542525	+	0.186699i
$849$		0			0
$850$	13.0276	−	15.8853i	0.446843	−	0.544862i
$851$	4.83149	+	4.83149i	0.165621	+	0.165621i
$852$		0			0
$853$	23.0418	+	23.0418i	0.788935	+	0.788935i	0.981320	−	0.192385i	$-0.0616222\pi$
$853$	23.0418	+	23.0418i	0.788935	+	0.788935i	−0.192385	+	0.981320i	$0.561622\pi$
$854$	−0.148867	+	0.519247i	−0.00509412	+	0.0177683i
$855$		0			0
$856$	32.0788	−	28.8916i	1.09643	−	0.987495i
$857$		−	30.7846i		−	1.05158i	−0.850614	−	0.525791i	$-0.823769\pi$
$857$		−	30.7846i		−	1.05158i	0.850614	−	0.525791i	$-0.176231\pi$
$858$		0			0
$859$	−18.4753	−	18.4753i	−0.630370	−	0.630370i	0.317791	−	0.948161i	$-0.397059\pi$
$859$	−18.4753	−	18.4753i	−0.630370	−	0.630370i	−0.948161	+	0.317791i	$0.897059\pi$
$860$	11.5294	+	26.1084i	0.393150	+	0.890288i
$861$		0			0
$862$	25.0955	−	13.9121i	0.854757	−	0.473849i
$863$		−	25.8775i		−	0.880879i	−0.897782	−	0.440440i	$-0.854823\pi$
$863$		−	25.8775i		−	0.880879i	0.897782	−	0.440440i	$-0.145177\pi$
$864$		0			0
$865$	−29.6737	−	20.1503i	−1.00894	−	0.685129i
$866$	9.05433	+	16.3327i	0.307679	+	0.555009i
$867$		0			0
$868$	−0.708732	+	1.13443i	−0.0240559	+	0.0385051i
$869$	9.79333	+	9.79333i	0.332216	+	0.332216i
$870$		0			0
$871$	−10.9436			−0.370809
$872$	0.775595	−	0.698535i	0.0262649	−	0.0236554i
$873$		0			0
$874$	0.513718	−	1.79185i	0.0173768	−	0.0606101i
$875$	−1.58300	−	2.48833i	−0.0535152	−	0.0841209i
$876$		0			0
$877$	21.3569	−	21.3569i	0.721171	−	0.721171i	−0.247673	−	0.968844i	$-0.579666\pi$
$877$	21.3569	−	21.3569i	0.721171	−	0.721171i	0.968844	+	0.247673i	$0.0796658\pi$
$878$	−5.95850	+	3.30319i	−0.201090	+	0.111477i
$879$		0			0
$880$	11.4389	+	1.64200i	0.385605	+	0.0553519i
$881$		−	38.6737i		−	1.30295i	−0.758670	−	0.651475i	$-0.774151\pi$
$881$		−	38.6737i		−	1.30295i	0.758670	−	0.651475i	$-0.225849\pi$
$882$		0			0
$883$	31.7478	+	31.7478i	1.06840	+	1.06840i	0.997482	+	0.0709157i	$0.0225921\pi$
$883$	31.7478	+	31.7478i	1.06840	+	1.06840i	0.0709157	+	0.997482i	$0.477408\pi$
$884$	2.75576	+	11.9317i	0.0926861	+	0.401305i
$885$		0			0
$886$	−17.6188	−	5.05126i	−0.591914	−	0.169700i
$887$	16.1784			0.543217			0.271609	−	0.962408i	$-0.412444\pi$
$887$	16.1784			0.543217			0.271609	+	0.962408i	$0.412444\pi$
$888$		0			0
$889$		−	4.77912i		−	0.160287i
$890$	32.1518	−	26.8103i	1.07773	−	0.898684i
$891$		0			0
$892$	0.657523	−	1.05246i	0.0220155	−	0.0352391i
$893$	1.97816	+	1.97816i	0.0661967	+	0.0661967i
$894$		0			0
$895$	11.7887	+	8.00528i	0.394054	+	0.267587i
$896$	1.16694	+	2.74676i	0.0389846	+	0.0917628i
$897$		0			0
$898$	2.52317	+	4.55144i	0.0841993	+	0.151884i
$899$	6.18056	+	6.18056i	0.206133	+	0.206133i
$900$		0			0
$901$	8.58123	−	8.58123i	0.285882	−	0.285882i
$902$	−5.42800	+	18.9329i	−0.180733	+	0.630395i
$903$		0			0
$904$	−0.574210	+	10.9845i	−0.0190979	+	0.365340i
$905$	−17.9375	+	26.4152i	−0.596264	+	0.878070i
$906$		0			0
$907$	−28.4899	+	28.4899i	−0.945992	+	0.945992i	−0.998614	−	0.0526227i	$-0.983242\pi$
$907$	−28.4899	+	28.4899i	−0.945992	+	0.945992i	0.0526227	+	0.998614i	$0.483242\pi$
$908$	6.40185	+	27.7182i	0.212453	+	0.919862i
$909$		0			0
$910$	1.75075	+	0.158603i	0.0580368	+	0.00525763i
$911$	−2.49312			−0.0826008			−0.0413004	−	0.999147i	$-0.513150\pi$
$911$	−2.49312			−0.0826008			−0.0413004	+	0.999147i	$0.513150\pi$
$912$		0			0
$913$		−	6.40264i		−	0.211897i
$914$	22.5071	−	12.4772i	0.744469	−	0.412709i
$915$		0			0
$916$	−9.53679	−	41.2917i	−0.315104	−	1.36432i
$917$	3.70905	−	3.70905i	0.122484	−	0.122484i
$918$		0			0
$919$	22.3205			0.736287			0.368143	−	0.929769i	$-0.379994\pi$
$919$	22.3205			0.736287			0.368143	+	0.929769i	$0.379994\pi$
$920$	−2.71056	−	19.7141i	−0.0893647	−	0.649955i
$921$		0			0
$922$	−11.2898	+	39.3788i	−0.371810	+	1.29687i
$923$	11.7060	+	11.7060i	0.385308	+	0.385308i
$924$		0			0
$925$	9.96819	+	4.30491i	0.327752	+	0.141545i
$926$	−27.8810	+	15.4563i	−0.916228	+	0.507927i
$927$		0			0
$928$	19.2042	−	3.39060i	0.630408	−	0.111302i
$929$			6.44533i			0.211464i	0.994395	+	0.105732i	$0.0337186\pi$
$929$			6.44533i			0.211464i	−0.994395	+	0.105732i	$0.966281\pi$
$930$		0			0
$931$	−2.05291	+	2.05291i	−0.0672813	+	0.0672813i
$932$	3.52662	+	2.20324i	0.115518	+	0.0721696i
$933$		0			0
$934$	14.4800	−	50.5061i	0.473799	−	1.65261i
$935$	4.71544	−	6.94405i	0.154211	−	0.227095i
$936$		0			0
$937$	−56.5439			−1.84721			−0.923605	−	0.383346i	$-0.874772\pi$
$937$	−56.5439			−1.84721			−0.923605	+	0.383346i	$0.874772\pi$
$938$	−0.533875	+	1.86216i	−0.0174316	+	0.0608015i
$939$		0			0
$940$	27.8491	+	10.7873i	0.908337	+	0.351844i
$941$	1.57877	−	1.57877i	0.0514663	−	0.0514663i	−0.680905	−	0.732372i	$-0.738413\pi$
$941$	1.57877	−	1.57877i	0.0514663	−	0.0514663i	0.732372	+	0.680905i	$0.238413\pi$
$942$		0			0
$943$	33.9157			1.10445
$944$	−52.2475	−	17.9799i	−1.70051	−	0.585195i
$945$		0			0
$946$	5.65378	+	10.1986i	0.183820	+	0.331586i
$947$	−12.1004	+	12.1004i	−0.393210	+	0.393210i	−0.875830	−	0.482620i	$-0.839685\pi$
$947$	−12.1004	+	12.1004i	−0.393210	+	0.393210i	0.482620	+	0.875830i	$0.339685\pi$
$948$		0			0
$949$	18.5263	−	18.5263i	0.601388	−	0.601388i
$950$	−0.291358	−	2.94780i	−0.00945290	−	0.0956394i
$951$		0			0
$952$	2.16472	+	0.113160i	0.0701591	+	0.00366752i
$953$			25.9757i			0.841435i	0.907192	+	0.420718i	$0.138222\pi$
$953$			25.9757i			0.841435i	−0.907192	+	0.420718i	$0.861778\pi$
$954$		0			0
$955$	52.3918	−	10.0143i	1.69536	−	0.324054i
$956$	14.0743	−	22.5281i	0.455196	−	0.728610i
$957$		0			0
$958$	0.895146	−	0.496239i	0.0289208	−	0.0160328i
$959$	2.72762			0.0880795
$960$		0			0
$961$	24.5714			0.792627
$962$	−5.66054	+	3.13801i	−0.182503	+	0.101174i
$963$		0			0
$964$	−4.06988	+	6.51445i	−0.131082	+	0.209816i
$965$	5.81790	+	30.4376i	0.187285	+	0.979822i
$966$		0			0
$967$		−	61.3307i		−	1.97226i	−0.165969	−	0.986131i	$-0.553075\pi$
$967$		−	61.3307i		−	1.97226i	0.165969	−	0.986131i	$-0.446925\pi$
$968$	−26.3552	−	1.37770i	−0.847088	−	0.0442810i
$969$		0			0
$970$	22.4913	+	26.9722i	0.722151	+	0.866025i
$971$	−30.0810	+	30.0810i	−0.965346	+	0.965346i	−0.999419	−	0.0340737i	$-0.989152\pi$
$971$	−30.0810	+	30.0810i	−0.965346	+	0.965346i	0.0340737	+	0.999419i	$0.489152\pi$
$972$		0			0
$973$	−3.11543	+	3.11543i	−0.0998760	+	0.0998760i
$974$	10.3004	+	18.5804i	0.330046	+	0.595356i
$975$		0			0
$976$	−1.88470	+	5.47674i	−0.0603279	+	0.175306i
$977$	−33.3131			−1.06578			−0.532891	−	0.846184i	$-0.678894\pi$
$977$	−33.3131			−1.06578			−0.532891	+	0.846184i	$0.678894\pi$
$978$		0			0
$979$	12.0944	−	12.0944i	0.386540	−	0.386540i
$980$	−11.1949	+	28.9014i	−0.357608	+	0.923220i
$981$		0			0
$982$	−1.67618	+	5.84650i	−0.0534889	+	0.186569i
$983$	−54.1424			−1.72687			−0.863437	−	0.504456i	$-0.831693\pi$
$983$	−54.1424			−1.72687			−0.863437	+	0.504456i	$0.831693\pi$
$984$		0			0
$985$	21.2856	−	31.3456i	0.678215	−	0.998754i
$986$	3.90369	−	13.6161i	0.124319	−	0.433624i
$987$		0			0
$988$	1.49745	+	0.935524i	0.0476402	+	0.0297630i
$989$	14.1987	−	14.1987i	0.451493	−	0.451493i
$990$		0			0
$991$		−	39.3653i		−	1.25048i	−0.780433	−	0.625240i	$-0.785001\pi$
$991$		−	39.3653i		−	1.25048i	0.780433	−	0.625240i	$-0.214999\pi$
$992$	−8.22405	+	11.7507i	−0.261114	+	0.373085i
$993$		0			0
$994$	2.56296	−	1.42082i	0.0812922	−	0.0450657i
$995$	25.1117	−	4.79989i	0.796094	−	0.152167i
$996$		0			0
$997$	28.9457	+	28.9457i	0.916720	+	0.916720i	0.996789	−	0.0800697i	$-0.0255143\pi$
$997$	28.9457	+	28.9457i	0.916720	+	0.916720i	−0.0800697	+	0.996789i	$0.525514\pi$
$998$	−6.25849	+	21.8296i	−0.198109	+	0.691004i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.u.a.179.7	✓	96
3.2	odd	2	inner	720.2.u.a.179.42	yes	96
4.3	odd	2		2880.2.u.a.2159.4		96
5.4	even	2	inner	720.2.u.a.179.41	yes	96
12.11	even	2		2880.2.u.a.2159.45		96
15.14	odd	2	inner	720.2.u.a.179.8	yes	96
16.5	even	4		2880.2.u.a.719.21		96
16.11	odd	4	inner	720.2.u.a.539.8	yes	96
20.19	odd	2		2880.2.u.a.2159.28		96
48.5	odd	4		2880.2.u.a.719.28		96
48.11	even	4	inner	720.2.u.a.539.41	yes	96
60.59	even	2		2880.2.u.a.2159.21		96
80.59	odd	4	inner	720.2.u.a.539.42	yes	96
80.69	even	4		2880.2.u.a.719.45		96
240.59	even	4	inner	720.2.u.a.539.7	yes	96
240.149	odd	4		2880.2.u.a.719.4		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.7	✓	96	1.1	even	1	trivial
720.2.u.a.179.8	yes	96	15.14	odd	2	inner
720.2.u.a.179.41	yes	96	5.4	even	2	inner
720.2.u.a.179.42	yes	96	3.2	odd	2	inner
720.2.u.a.539.7	yes	96	240.59	even	4	inner
720.2.u.a.539.8	yes	96	16.11	odd	4	inner
720.2.u.a.539.41	yes	96	48.11	even	4	inner
720.2.u.a.539.42	yes	96	80.59	odd	4	inner
2880.2.u.a.719.4		96	240.149	odd	4
2880.2.u.a.719.21		96	16.5	even	4
2880.2.u.a.719.28		96	48.5	odd	4
2880.2.u.a.719.45		96	80.69	even	4
2880.2.u.a.2159.4		96	4.3	odd	2
2880.2.u.a.2159.21		96	60.59	even	2
2880.2.u.a.2159.28		96	20.19	odd	2
2880.2.u.a.2159.45		96	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.23687 + 0.685679i) q^{2} +(1.05969 - 1.69619i) q^{4} +(-2.19631 + 0.419806i) q^{5} +0.263783i q^{7} +(-0.147653 + 2.82457i) q^{8} +(2.42869 - 2.02521i) q^{10} +(0.913594 - 0.913594i) q^{11} +(1.49018 - 1.49018i) q^{13} +(-0.180870 - 0.326265i) q^{14} +(-1.75412 - 3.59487i) q^{16} -2.90538 q^{17} +(-0.296217 + 0.296217i) q^{19} +(-1.61533 + 4.17022i) q^{20} +(-0.503563 + 1.75643i) q^{22} +3.14640 q^{23} +(4.64753 - 1.84404i) q^{25} +(-0.821369 + 2.86493i) q^{26} +(0.447426 + 0.279528i) q^{28} +(2.43765 - 2.43765i) q^{29} +2.53546i q^{31} +(4.63454 + 3.24361i) q^{32} +(3.59358 - 1.99216i) q^{34} +(-0.110738 - 0.579348i) q^{35} +(1.53556 + 1.53556i) q^{37} +(0.163272 - 0.569491i) q^{38} +(-0.861481 - 6.26561i) q^{40} +10.7792 q^{41} +(4.51269 - 4.51269i) q^{43} +(-0.581504 - 2.51775i) q^{44} +(-3.89169 + 2.15742i) q^{46} -6.67809i q^{47} +6.93042 q^{49} +(-4.48396 + 5.46755i) q^{50} +(-0.948500 - 4.10674i) q^{52} +(-2.95356 + 2.95356i) q^{53} +(-1.62300 + 2.39006i) q^{55} +(-0.745073 - 0.0389483i) q^{56} +(-1.34361 + 4.68649i) q^{58} +(9.76773 - 9.76773i) q^{59} +(-1.02388 - 1.02388i) q^{61} +(-1.73851 - 3.13603i) q^{62} +(-7.95640 - 0.834111i) q^{64} +(-2.64730 + 3.89847i) q^{65} +(-3.67191 - 3.67191i) q^{67} +(-3.07880 + 4.92808i) q^{68} +(0.534215 + 0.640647i) q^{70} +7.85546i q^{71} +12.4323 q^{73} +(-2.95219 - 0.846384i) q^{74} +(0.188543 + 0.816337i) q^{76} +(0.240990 + 0.240990i) q^{77} +10.7196i q^{79} +(5.36174 + 7.15904i) q^{80} +(-13.3324 + 7.39107i) q^{82} +(3.50410 - 3.50410i) q^{83} +(6.38111 - 1.21970i) q^{85} +(-2.48735 + 8.67586i) q^{86} +(2.44561 + 2.71540i) q^{88} +13.2383 q^{89} +(0.393083 + 0.393083i) q^{91} +(3.33421 - 5.33690i) q^{92} +(4.57903 + 8.25992i) q^{94} +(0.526229 - 0.774936i) q^{95} +11.1057i q^{97} +(-8.57202 + 4.75204i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) \) 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more