LMFDB - Embedded newform 800.2.be.a.209.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [800,2,Mod(209,800)] 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("800.209"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(800, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.be (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			209.4
Character	$\chi$	$=$	800.209
Dual form			800.2.be.a.689.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.853735 - 2.62753i) q^{3} +(2.18267 - 0.485731i) q^{5} -2.67391i q^{7} +(-3.74798 + 2.72307i) q^{9} +(-0.305554 + 0.420559i) q^{11} +(4.26356 - 3.09766i) q^{13} +(-3.13970 - 5.32035i) q^{15} +(-6.80346 - 2.21058i) q^{17} +(3.74715 + 1.21752i) q^{19} +(-7.02577 + 2.28281i) q^{21} +(2.11996 - 2.91788i) q^{23} +(4.52813 - 2.12038i) q^{25} +(3.64939 + 2.65144i) q^{27} +(3.63988 - 1.18267i) q^{29} +(-2.54168 + 7.82249i) q^{31} +(1.36589 + 0.443805i) q^{33} +(-1.29880 - 5.83628i) q^{35} +(-1.62286 + 1.17908i) q^{37} +(-11.7791 - 8.55804i) q^{39} +(-5.16753 + 3.75443i) q^{41} -5.41659 q^{43} +(-6.85794 + 7.76408i) q^{45} +(-0.748265 + 0.243126i) q^{47} -0.149804 q^{49} +19.7635i q^{51} +(1.71792 + 5.28721i) q^{53} +(-0.462646 + 1.06636i) q^{55} -10.8852i q^{57} +(-3.67423 - 5.05715i) q^{59} +(4.51387 - 6.21281i) q^{61} +(7.28124 + 10.0218i) q^{63} +(7.80133 - 8.83212i) q^{65} +(-1.98087 + 6.09648i) q^{67} +(-9.47669 - 3.07916i) q^{69} +(-0.885245 - 2.72450i) q^{71} +(-0.839035 + 1.15483i) q^{73} +(-9.43719 - 10.0875i) q^{75} +(1.12454 + 0.817024i) q^{77} +(2.10919 + 6.49143i) q^{79} +(-0.443692 + 1.36554i) q^{81} +(-0.170500 + 0.524746i) q^{83} +(-15.9235 - 1.52032i) q^{85} +(-6.21499 - 8.55421i) q^{87} +(-11.0001 - 7.99206i) q^{89} +(-8.28286 - 11.4004i) q^{91} +22.7237 q^{93} +(8.77019 + 0.837348i) q^{95} +(4.85400 - 1.57716i) q^{97} -2.40829i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79}+ \cdots - 50 q^{97}+O(q^{100}) $ 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$

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			0
$2$		0			0
$3$	−0.853735	−	2.62753i	−0.492904	−	1.51700i	−0.820198	−	0.572080i	$-0.806137\pi$
$3$	−0.853735	−	2.62753i	−0.492904	−	1.51700i	0.327293	−	0.944923i	$-0.393863\pi$
$4$		0			0
$5$	2.18267	−	0.485731i	0.976121	−	0.217225i
$5$	2.18267	−	0.485731i	0.976121	−	0.217225i
$6$		0			0
$7$		−	2.67391i		−	1.01064i	−0.862931	−	0.505322i	$-0.831374\pi$
$7$		−	2.67391i		−	1.01064i	0.862931	−	0.505322i	$-0.168626\pi$
$8$		0			0
$9$	−3.74798	+	2.72307i	−1.24933	+	0.907689i
$10$		0			0
$11$	−0.305554	+	0.420559i	−0.0921280	+	0.126803i	−0.852593	−	0.522576i	$-0.824971\pi$
$11$	−0.305554	+	0.420559i	−0.0921280	+	0.126803i	0.760465	+	0.649379i	$0.224971\pi$
$12$		0			0
$13$	4.26356	−	3.09766i	1.18250	−	0.859136i	0.190047	−	0.981775i	$-0.439136\pi$
$13$	4.26356	−	3.09766i	1.18250	−	0.859136i	0.992451	+	0.122639i	$0.0391359\pi$
$14$		0			0
$15$	−3.13970	−	5.32035i	−0.810666	−	1.37371i
$16$		0			0
$17$	−6.80346	−	2.21058i	−1.65008	−	0.536144i	−0.671324	−	0.741164i	$-0.734274\pi$
$17$	−6.80346	−	2.21058i	−1.65008	−	0.536144i	−0.978758	+	0.205020i	$0.934274\pi$
$18$		0			0
$19$	3.74715	+	1.21752i	0.859654	+	0.279319i	0.705484	−	0.708726i	$-0.250730\pi$
$19$	3.74715	+	1.21752i	0.859654	+	0.279319i	0.154170	+	0.988044i	$0.450730\pi$
$20$		0			0
$21$	−7.02577	+	2.28281i	−1.53315	+	0.498151i
$22$		0			0
$23$	2.11996	−	2.91788i	0.442043	−	0.608420i	−0.528622	−	0.848858i	$-0.677291\pi$
$23$	2.11996	−	2.91788i	0.442043	−	0.608420i	0.970665	+	0.240438i	$0.0772910\pi$
$24$		0			0
$25$	4.52813	−	2.12038i	0.905626	−	0.424077i
$26$		0			0
$27$	3.64939	+	2.65144i	0.702326	+	0.510270i
$28$		0			0
$29$	3.63988	−	1.18267i	0.675910	−	0.219616i	0.0491059	−	0.998794i	$-0.484363\pi$
$29$	3.63988	−	1.18267i	0.675910	−	0.219616i	0.626804	+	0.779177i	$0.284363\pi$
$30$		0			0
$31$	−2.54168	+	7.82249i	−0.456499	+	1.40496i	0.412867	+	0.910791i	$0.364527\pi$
$31$	−2.54168	+	7.82249i	−0.456499	+	1.40496i	−0.869366	+	0.494168i	$0.835473\pi$
$32$		0			0
$33$	1.36589	+	0.443805i	0.237771	+	0.0772566i
$34$		0			0
$35$	−1.29880	−	5.83628i	−0.219538	−	0.986511i
$36$		0			0
$37$	−1.62286	+	1.17908i	−0.266797	+	0.193839i	−0.713138	−	0.701024i	$-0.752727\pi$
$37$	−1.62286	+	1.17908i	−0.266797	+	0.193839i	0.446341	+	0.894863i	$0.352727\pi$
$38$		0			0
$39$	−11.7791	−	8.55804i	−1.88617	−	1.37038i
$40$		0			0
$41$	−5.16753	+	3.75443i	−0.807032	+	0.586343i	−0.912969	−	0.408030i	$-0.866216\pi$
$41$	−5.16753	+	3.75443i	−0.807032	+	0.586343i	0.105936	+	0.994373i	$0.466216\pi$
$42$		0			0
$43$	−5.41659			−0.826022			−0.413011	−	0.910726i	$-0.635523\pi$
$43$	−5.41659			−0.826022			−0.413011	+	0.910726i	$0.635523\pi$
$44$		0			0
$45$	−6.85794	+	7.76408i	−1.02232	+	1.15740i
$46$		0			0
$47$	−0.748265	+	0.243126i	−0.109146	+	0.0354636i	−0.363081	−	0.931758i	$-0.618275\pi$
$47$	−0.748265	+	0.243126i	−0.109146	+	0.0354636i	0.253935	+	0.967221i	$0.418275\pi$
$48$		0			0
$49$	−0.149804			−0.0214006
$50$		0			0
$51$			19.7635i			2.76745i
$52$		0			0
$53$	1.71792	+	5.28721i	0.235974	+	0.726254i	0.996991	+	0.0775214i	$0.0247006\pi$
$53$	1.71792	+	5.28721i	0.235974	+	0.726254i	−0.761016	+	0.648733i	$0.775299\pi$
$54$		0			0
$55$	−0.462646	+	1.06636i	−0.0623832	+	0.143788i
$56$		0			0
$57$		−	10.8852i		−	1.44178i
$58$		0			0
$59$	−3.67423	−	5.05715i	−0.478344	−	0.658385i	0.499841	−	0.866117i	$-0.333392\pi$
$59$	−3.67423	−	5.05715i	−0.478344	−	0.658385i	−0.978186	+	0.207732i	$0.933392\pi$
$60$		0			0
$61$	4.51387	−	6.21281i	0.577941	−	0.795468i	−0.415526	−	0.909581i	$-0.636403\pi$
$61$	4.51387	−	6.21281i	0.577941	−	0.795468i	0.993468	+	0.114113i	$0.0364026\pi$
$62$		0			0
$63$	7.28124	+	10.0218i	0.917350	+	1.26262i
$64$		0			0
$65$	7.80133	−	8.83212i	0.967636	−	1.09549i
$66$		0			0
$67$	−1.98087	+	6.09648i	−0.242001	+	0.744804i	0.754114	+	0.656744i	$0.228067\pi$
$67$	−1.98087	+	6.09648i	−0.242001	+	0.744804i	−0.996115	+	0.0880600i	$0.971933\pi$
$68$		0			0
$69$	−9.47669	−	3.07916i	−1.14086	−	0.370688i
$70$		0			0
$71$	−0.885245	−	2.72450i	−0.105059	−	0.323339i	0.884685	−	0.466189i	$-0.154373\pi$
$71$	−0.885245	−	2.72450i	−0.105059	−	0.323339i	−0.989744	+	0.142850i	$0.954373\pi$
$72$		0			0
$73$	−0.839035	+	1.15483i	−0.0982017	+	0.135163i	−0.855290	−	0.518149i	$-0.826621\pi$
$73$	−0.839035	+	1.15483i	−0.0982017	+	0.135163i	0.757089	+	0.653312i	$0.226621\pi$
$74$		0			0
$75$	−9.43719	−	10.0875i	−1.08971	−	1.16481i
$76$		0			0
$77$	1.12454	+	0.817024i	0.128153	+	0.0931086i
$78$		0			0
$79$	2.10919	+	6.49143i	0.237303	+	0.730342i	0.996808	+	0.0798409i	$0.0254412\pi$
$79$	2.10919	+	6.49143i	0.237303	+	0.730342i	−0.759505	+	0.650501i	$0.774559\pi$
$80$		0			0
$81$	−0.443692	+	1.36554i	−0.0492991	+	0.151727i
$82$		0			0
$83$	−0.170500	+	0.524746i	−0.0187148	+	0.0575984i	−0.959978	−	0.280076i	$-0.909640\pi$
$83$	−0.170500	+	0.524746i	−0.0187148	+	0.0575984i	0.941263	+	0.337674i	$0.109640\pi$
$84$		0			0
$85$	−15.9235	−	1.52032i	−1.72714	−	0.164902i
$86$		0			0
$87$	−6.21499	−	8.55421i	−0.666317	−	0.917107i
$88$		0			0
$89$	−11.0001	−	7.99206i	−1.16601	−	0.847156i	−0.175485	−	0.984482i	$-0.556149\pi$
$89$	−11.0001	−	7.99206i	−1.16601	−	0.847156i	−0.990526	+	0.137326i	$0.956149\pi$
$90$		0			0
$91$	−8.28286	−	11.4004i	−0.868280	−	1.19508i
$92$		0			0
$93$	22.7237			2.35634
$94$		0			0
$95$	8.77019	+	0.837348i	0.899802	+	0.0859101i
$96$		0			0
$97$	4.85400	−	1.57716i	0.492849	−	0.160136i	−0.0520390	−	0.998645i	$-0.516572\pi$
$97$	4.85400	−	1.57716i	0.492849	−	0.160136i	0.544888	+	0.838509i	$0.316572\pi$
$98$		0			0
$99$		−	2.40829i		−	0.242042i
$100$		0			0
$101$		−	1.77393i		−	0.176513i	−0.996098	−	0.0882565i	$-0.971870\pi$
$101$		−	1.77393i		−	0.176513i	0.996098	−	0.0882565i	$-0.0281295\pi$
$102$		0			0
$103$	0.666003	−	0.216398i	0.0656233	−	0.0213223i	−0.276021	−	0.961151i	$-0.589016\pi$
$103$	0.666003	−	0.216398i	0.0656233	−	0.0213223i	0.341645	+	0.939829i	$0.389016\pi$
$104$		0			0
$105$	−14.2261	+	8.39527i	−1.38833	+	0.819295i
$106$		0			0
$107$	20.2036			1.95315			0.976576	−	0.215171i	$-0.0690310\pi$
$107$	20.2036			1.95315			0.976576	+	0.215171i	$0.0690310\pi$
$108$		0			0
$109$	−3.68500	−	5.07197i	−0.352959	−	0.485807i	0.595211	−	0.803569i	$-0.297068\pi$
$109$	−3.68500	−	5.07197i	−0.352959	−	0.485807i	−0.948170	+	0.317763i	$0.897068\pi$
$110$		0			0
$111$	4.48355	+	3.25749i	0.425560	+	0.309188i
$112$		0			0
$113$	−2.03808	−	2.80517i	−0.191726	−	0.263888i	0.702322	−	0.711859i	$-0.252147\pi$
$113$	−2.03808	−	2.80517i	−0.191726	−	0.263888i	−0.894048	+	0.447971i	$0.852147\pi$
$114$		0			0
$115$	3.20988	−	7.39851i	0.299323	−	0.689915i
$116$		0			0
$117$	−7.54461	+	23.2199i	−0.697499	+	2.14668i
$118$		0			0
$119$	−5.91089	+	18.1919i	−0.541851	+	1.66764i
$120$		0			0
$121$	3.31568	+	10.2046i	0.301425	+	0.927692i
$122$		0			0
$123$	14.2766	+	10.3725i	1.28727	+	0.935260i
$124$		0			0
$125$	8.85350	−	6.82756i	0.791881	−	0.610676i
$126$		0			0
$127$	1.99694	−	2.74856i	0.177200	−	0.243895i	−0.711173	−	0.703017i	$-0.751836\pi$
$127$	1.99694	−	2.74856i	0.177200	−	0.243895i	0.888373	+	0.459122i	$0.151836\pi$
$128$		0			0
$129$	4.62433	+	14.2322i	0.407150	+	1.25308i
$130$		0			0
$131$	6.90619	+	2.24396i	0.603397	+	0.196055i	0.594755	−	0.803907i	$-0.297249\pi$
$131$	6.90619	+	2.24396i	0.603397	+	0.196055i	0.00864194	+	0.999963i	$0.497249\pi$
$132$		0			0
$133$	3.25555	−	10.0195i	0.282292	−	0.868804i
$134$		0			0
$135$	9.25332	+	4.01460i	0.796399	+	0.345522i
$136$		0			0
$137$	10.8418	+	14.9224i	0.926276	+	1.27491i	0.961295	+	0.275522i	$0.0888508\pi$
$137$	10.8418	+	14.9224i	0.926276	+	1.27491i	−0.0350190	+	0.999387i	$0.511149\pi$
$138$		0			0
$139$	5.88707	−	8.10286i	0.499335	−	0.687275i	−0.482741	−	0.875763i	$-0.660359\pi$
$139$	5.88707	−	8.10286i	0.499335	−	0.687275i	0.982076	+	0.188488i	$0.0603586\pi$
$140$		0			0
$141$	1.27764	+	1.75852i	0.107597	+	0.148094i
$142$		0			0
$143$			2.73958i			0.229095i
$144$		0			0
$145$	7.37022	−	4.34939i	0.612064	−	0.361197i
$146$		0			0
$147$	0.127893	+	0.393614i	0.0105484	+	0.0324647i
$148$		0			0
$149$		−	22.4904i		−	1.84249i	−0.388984	−	0.921245i	$-0.627174\pi$
$149$		−	22.4904i		−	1.84249i	0.388984	−	0.921245i	$-0.372826\pi$
$150$		0			0
$151$	13.2680			1.07974			0.539869	−	0.841749i	$-0.318474\pi$
$151$	13.2680			1.07974			0.539869	+	0.841749i	$0.318474\pi$
$152$		0			0
$153$	31.5188	−	10.2411i	2.54814	−	0.827942i
$154$		0			0
$155$	−1.74803	+	18.3085i	−0.140406	+	1.47057i
$156$		0			0
$157$	6.77950			0.541063			0.270531	−	0.962711i	$-0.412801\pi$
$157$	6.77950			0.541063			0.270531	+	0.962711i	$0.412801\pi$
$158$		0			0
$159$	12.4256	−	9.02775i	0.985417	−	0.715947i
$160$		0			0
$161$	−7.80215	−	5.66859i	−0.614896	−	0.446748i
$162$		0			0
$163$	11.6472	−	8.46217i	0.912277	−	0.662808i	−0.0293124	−	0.999570i	$-0.509332\pi$
$163$	11.6472	−	8.46217i	0.912277	−	0.662808i	0.941590	+	0.336762i	$0.109332\pi$
$164$		0			0
$165$	3.19687	+	0.305226i	0.248876	+	0.0237618i
$166$		0			0
$167$	−3.69785	−	1.20150i	−0.286148	−	0.0929752i	0.162426	−	0.986721i	$-0.448068\pi$
$167$	−3.69785	−	1.20150i	−0.286148	−	0.0929752i	−0.448574	+	0.893746i	$0.648068\pi$
$168$		0			0
$169$	4.56524	−	14.0504i	0.351172	−	1.08080i
$170$		0			0
$171$	−17.3596	+	5.64048i	−1.32752	+	0.431339i
$172$		0			0
$173$	−1.77044	−	1.28630i	−0.134604	−	0.0977957i	0.518446	−	0.855111i	$-0.326511\pi$
$173$	−1.77044	−	1.28630i	−0.134604	−	0.0977957i	−0.653050	+	0.757315i	$0.726511\pi$
$174$		0			0
$175$	−5.66972	−	12.1078i	−0.428591	−	0.915265i
$176$		0			0
$177$	−10.1510	+	13.9716i	−0.762994	+	1.05017i
$178$		0			0
$179$	8.52431	−	2.76971i	0.637137	−	0.207018i	0.0274027	−	0.999624i	$-0.491276\pi$
$179$	8.52431	−	2.76971i	0.637137	−	0.207018i	0.609734	+	0.792606i	$0.291276\pi$
$180$		0			0
$181$	20.6836	+	6.72051i	1.53740	+	0.499531i	0.950657	−	0.310243i	$-0.100410\pi$
$181$	20.6836	+	6.72051i	1.53740	+	0.499531i	0.586742	+	0.809774i	$0.300410\pi$
$182$		0			0
$183$	−20.1780	−	6.55622i	−1.49160	−	0.484649i
$184$		0			0
$185$	−2.96946	+	3.36182i	−0.218319	+	0.247166i
$186$		0			0
$187$	3.00850	−	2.18581i	0.220004	−	0.159842i
$188$		0			0
$189$	7.08972	−	9.75816i	0.515701	−	0.709801i
$190$		0			0
$191$	−1.35201	+	0.982290i	−0.0978277	+	0.0710760i	−0.635624	−	0.771999i	$-0.719257\pi$
$191$	−1.35201	+	0.982290i	−0.0978277	+	0.0710760i	0.537796	+	0.843075i	$0.319257\pi$
$192$		0			0
$193$			8.56535i			0.616548i	0.951298	+	0.308274i	$0.0997513\pi$
$193$			8.56535i			0.616548i	−0.951298	+	0.308274i	$0.900249\pi$
$194$		0			0
$195$	−29.8669	−	12.9579i	−2.13881	−	0.927936i
$196$		0			0
$197$	3.12786	+	9.62655i	0.222851	+	0.685864i	0.998503	+	0.0547029i	$0.0174212\pi$
$197$	3.12786	+	9.62655i	0.222851	+	0.685864i	−0.775652	+	0.631161i	$0.782579\pi$
$198$		0			0
$199$	17.2203			1.22071			0.610356	−	0.792127i	$-0.291026\pi$
$199$	17.2203			1.22071			0.610356	+	0.792127i	$0.291026\pi$
$200$		0			0
$201$	17.7098			1.24915
$202$		0			0
$203$	−3.16236	−	9.73273i	−0.221954	−	0.683104i
$204$		0			0
$205$	−9.45539	+	10.7047i	−0.660393	+	0.747650i
$206$		0			0
$207$			16.7090i			1.16135i
$208$		0			0
$209$	−1.65700	+	1.20388i	−0.114617	+	0.0832739i
$210$		0			0
$211$	−10.5323	+	14.4965i	−0.725075	+	0.997980i	0.274265	+	0.961654i	$0.411565\pi$
$211$	−10.5323	+	14.4965i	−0.725075	+	0.997980i	−0.999340	+	0.0363260i	$0.988435\pi$
$212$		0			0
$213$	−6.40294	+	4.65201i	−0.438722	+	0.318751i
$214$		0			0
$215$	−11.8226	+	2.63100i	−0.806298	+	0.179433i
$216$		0			0
$217$	20.9166	+	6.79623i	1.41991	+	0.461358i
$218$		0			0
$219$	3.75067	+	1.21867i	0.253447	+	0.0823498i
$220$		0			0
$221$	−35.8546	+	11.6499i	−2.41184	+	0.783654i
$222$		0			0
$223$	3.76665	−	5.18435i	0.252233	−	0.347170i	−0.664058	−	0.747681i	$-0.731167\pi$
$223$	3.76665	−	5.18435i	0.252233	−	0.347170i	0.916292	+	0.400511i	$0.131167\pi$
$224$		0			0
$225$	−11.1974	+	20.2776i	−0.746493	+	1.35184i
$226$		0			0
$227$	−21.6339	−	15.7179i	−1.43589	−	1.04324i	−0.988881	−	0.148706i	$-0.952489\pi$
$227$	−21.6339	−	15.7179i	−1.43589	−	1.04324i	−0.447009	−	0.894529i	$-0.647511\pi$
$228$		0			0
$229$	−1.64026	+	0.532952i	−0.108391	+	0.0352185i	−0.362711	−	0.931902i	$-0.618149\pi$
$229$	−1.64026	+	0.532952i	−0.108391	+	0.0352185i	0.254319	+	0.967120i	$0.418149\pi$
$230$		0			0
$231$	1.18670	−	3.65228i	0.0780789	−	0.240302i
$232$		0			0
$233$	−25.2733	−	8.21180i	−1.65571	−	0.537973i	−0.675743	−	0.737137i	$-0.736177\pi$
$233$	−25.2733	−	8.21180i	−1.65571	−	0.537973i	−0.979966	+	0.199164i	$0.936177\pi$
$234$		0			0
$235$	−1.51512	+	0.894120i	−0.0988358	+	0.0583260i
$236$		0			0
$237$	15.2557	−	11.0839i	0.990964	−	0.719978i
$238$		0			0
$239$	10.8304	+	7.86871i	0.700557	+	0.508985i	0.880114	−	0.474763i	$-0.157466\pi$
$239$	10.8304	+	7.86871i	0.700557	+	0.508985i	−0.179556	+	0.983748i	$0.557466\pi$
$240$		0			0
$241$	9.29368	−	6.75225i	0.598658	−	0.434951i	−0.246744	−	0.969081i	$-0.579361\pi$
$241$	9.29368	−	6.75225i	0.598658	−	0.434951i	0.845402	+	0.534130i	$0.179361\pi$
$242$		0			0
$243$	17.4995			1.12259
$244$		0			0
$245$	−0.326973	+	0.0727644i	−0.0208895	+	0.00464875i
$246$		0			0
$247$	19.7476	−	6.41640i	1.25651	−	0.408266i
$248$		0			0
$249$	1.52435			0.0966015
$250$		0			0
$251$			10.3951i			0.656130i	0.944655	+	0.328065i	$0.106397\pi$
$251$			10.3951i			0.656130i	−0.944655	+	0.328065i	$0.893603\pi$
$252$		0			0
$253$	0.579377	+	1.78314i	0.0364251	+	0.112105i
$254$		0			0
$255$	9.59976	+	43.1373i	0.601160	+	2.70136i
$256$		0			0
$257$		−	5.90778i		−	0.368517i	−0.982878	−	0.184258i	$-0.941012\pi$
$257$		−	5.90778i		−	0.368517i	0.982878	−	0.184258i	$-0.0589884\pi$
$258$		0			0
$259$	3.15275	+	4.33939i	0.195902	+	0.269637i
$260$		0			0
$261$	−10.4217	+	14.3443i	−0.645089	+	0.887889i
$262$		0			0
$263$	−3.28152	−	4.51662i	−0.202347	−	0.278507i	0.695769	−	0.718266i	$-0.255064\pi$
$263$	−3.28152	−	4.51662i	−0.202347	−	0.278507i	−0.898116	+	0.439759i	$0.855064\pi$
$264$		0			0
$265$	6.31782	+	10.7058i	0.388100	+	0.657653i
$266$		0			0
$267$	−11.6082	+	35.7262i	−0.710407	+	2.18641i
$268$		0			0
$269$	2.00902	+	0.652770i	0.122492	+	0.0398001i	0.369622	−	0.929182i	$-0.379487\pi$
$269$	2.00902	+	0.652770i	0.122492	+	0.0398001i	−0.247130	+	0.968982i	$0.579487\pi$
$270$		0			0
$271$	−5.94944	−	18.3105i	−0.361403	−	1.11228i	−0.952203	−	0.305466i	$-0.901188\pi$
$271$	−5.94944	−	18.3105i	−0.361403	−	1.11228i	0.590800	−	0.806818i	$-0.298812\pi$
$272$		0			0
$273$	−22.8834	+	31.4963i	−1.38497	+	1.90625i
$274$		0			0
$275$	−0.491842	+	2.55224i	−0.0296592	+	0.153906i
$276$		0			0
$277$	−16.0691	−	11.6749i	−0.965498	−	0.701476i	−0.0110772	−	0.999939i	$-0.503526\pi$
$277$	−16.0691	−	11.6749i	−0.965498	−	0.701476i	−0.954421	+	0.298463i	$0.903526\pi$
$278$		0			0
$279$	−11.7750	−	36.2397i	−0.704950	−	2.16961i
$280$		0			0
$281$	−3.83866	+	11.8142i	−0.228995	+	0.704775i	0.768866	+	0.639410i	$0.220821\pi$
$281$	−3.83866	+	11.8142i	−0.228995	+	0.704775i	−0.997861	+	0.0653651i	$0.979179\pi$
$282$		0			0
$283$	0.0965181	−	0.297052i	0.00573740	−	0.0176579i	−0.948147	−	0.317833i	$-0.897045\pi$
$283$	0.0965181	−	0.297052i	0.00573740	−	0.0176579i	0.953884	+	0.300175i	$0.0970450\pi$
$284$		0			0
$285$	−5.28726	−	23.7588i	−0.313190	−	1.40735i
$286$		0			0
$287$	10.0390	+	13.8175i	0.592584	+	0.815622i
$288$		0			0
$289$	27.6471	+	20.0868i	1.62630	+	1.18158i
$290$		0			0
$291$	−8.28807	−	11.4075i	−0.485855	−	0.668722i
$292$		0			0
$293$	−10.1550			−0.593262			−0.296631	−	0.954992i	$-0.595863\pi$
$293$	−10.1550			−0.593262			−0.296631	+	0.954992i	$0.595863\pi$
$294$		0			0
$295$	−10.4761	−	9.25342i	−0.609940	−	0.538755i
$296$		0			0
$297$	−2.23017	+	0.724627i	−0.129408	+	0.0420471i
$298$		0			0
$299$		−	19.0075i		−	1.09923i
$300$		0			0
$301$			14.4835i			0.834814i
$302$		0			0
$303$	−4.66106	+	1.51447i	−0.267771	+	0.0870040i
$304$		0			0
$305$	6.83455	−	15.7531i	0.391345	−	0.902017i
$306$		0			0
$307$	30.2858			1.72850			0.864250	−	0.503062i	$-0.167793\pi$
$307$	30.2858			1.72850			0.864250	+	0.503062i	$0.167793\pi$
$308$		0			0
$309$	−1.13718	−	1.56520i	−0.0646920	−	0.0890408i
$310$		0			0
$311$	−20.4723	−	14.8740i	−1.16088	−	0.843426i	−0.170988	−	0.985273i	$-0.554696\pi$
$311$	−20.4723	−	14.8740i	−1.16088	−	0.843426i	−0.989889	+	0.141847i	$0.954696\pi$
$312$		0			0
$313$	−15.0000	−	20.6458i	−0.847852	−	1.16697i	−0.984332	−	0.176325i	$-0.943579\pi$
$313$	−15.0000	−	20.6458i	−0.847852	−	1.16697i	0.136480	−	0.990643i	$-0.456421\pi$
$314$		0			0
$315$	20.7605	+	18.3375i	1.16972	+	1.03320i
$316$		0			0
$317$	−8.30209	+	25.5512i	−0.466292	+	1.43510i	0.391059	+	0.920366i	$0.372109\pi$
$317$	−8.30209	+	25.5512i	−0.466292	+	1.43510i	−0.857351	+	0.514733i	$0.827891\pi$
$318$		0			0
$319$	−0.614799	+	1.89216i	−0.0344221	+	0.105940i
$320$		0			0
$321$	−17.2485	−	53.0854i	−0.962717	−	2.96294i
$322$		0			0
$323$	−22.8021	−	16.5667i	−1.26874	−	0.921797i
$324$		0			0
$325$	12.7377	−	23.0670i	0.706562	−	1.27953i
$326$		0			0
$327$	−10.1807	+	14.0126i	−0.562995	+	0.774897i
$328$		0			0
$329$	0.650098	+	2.00079i	0.0358410	+	0.110307i
$330$		0			0
$331$	−11.4630	−	3.72455i	−0.630063	−	0.204720i	−0.0234603	−	0.999725i	$-0.507468\pi$
$331$	−11.4630	−	3.72455i	−0.630063	−	0.204720i	−0.606603	+	0.795005i	$0.707468\pi$
$332$		0			0
$333$	2.87175	−	8.83833i	0.157371	−	0.484337i
$334$		0			0
$335$	−1.36234	+	14.2688i	−0.0744324	+	0.779588i
$336$		0			0
$337$	−8.18324	−	11.2633i	−0.445769	−	0.613549i	0.525713	−	0.850662i	$-0.323799\pi$
$337$	−8.18324	−	11.2633i	−0.445769	−	0.613549i	−0.971482	+	0.237113i	$0.923799\pi$
$338$		0			0
$339$	−5.63068	+	7.74997i	−0.305817	+	0.420921i
$340$		0			0
$341$	−2.51320	−	3.45912i	−0.136097	−	0.187322i
$342$		0			0
$343$		−	18.3168i		−	0.989015i
$344$		0			0
$345$	−22.1802	−	2.11769i	−1.19414	−	0.114012i
$346$		0			0
$347$	4.69862	+	14.4609i	0.252235	+	0.776300i	0.994362	+	0.106041i	$0.0338173\pi$
$347$	4.69862	+	14.4609i	0.252235	+	0.776300i	−0.742127	+	0.670260i	$0.766183\pi$
$348$		0			0
$349$			23.4212i			1.25371i	0.779136	+	0.626854i	$0.215658\pi$
$349$			23.4212i			1.25371i	−0.779136	+	0.626854i	$0.784342\pi$
$350$		0			0
$351$	23.7727			1.26889
$352$		0			0
$353$	−4.26001	+	1.38416i	−0.226738	+	0.0736715i	−0.420182	−	0.907440i	$-0.638034\pi$
$353$	−4.26001	+	1.38416i	−0.226738	+	0.0736715i	0.193445	+	0.981111i	$0.438034\pi$
$354$		0			0
$355$	−3.25558	−	5.51671i	−0.172788	−	0.292797i
$356$		0			0
$357$	52.8459			2.79690
$358$		0			0
$359$	7.45656	−	5.41751i	0.393542	−	0.285925i	−0.373363	−	0.927685i	$-0.621795\pi$
$359$	7.45656	−	5.41751i	0.393542	−	0.285925i	0.766906	+	0.641760i	$0.221795\pi$
$360$		0			0
$361$	−2.81258	−	2.04346i	−0.148030	−	0.107550i
$362$		0			0
$363$	23.9822	−	17.4241i	1.25874	−	0.914527i
$364$		0			0
$365$	−1.27040	+	2.92817i	−0.0664959	+	0.153267i
$366$		0			0
$367$	32.3311	+	10.5050i	1.68767	+	0.548357i	0.986375	−	0.164513i	$-0.0526053\pi$
$367$	32.3311	+	10.5050i	1.68767	+	0.548357i	0.701296	+	0.712871i	$0.252605\pi$
$368$		0			0
$369$	9.14424	−	28.1431i	0.476030	−	1.46507i
$370$		0			0
$371$	14.1375	−	4.59356i	0.733984	−	0.238486i
$372$		0			0
$373$	20.7909	+	15.1054i	1.07651	+	0.782130i	0.977071	−	0.212914i	$-0.0682953\pi$
$373$	20.7909	+	15.1054i	1.07651	+	0.782130i	0.0994385	+	0.995044i	$0.468295\pi$
$374$		0			0
$375$	−25.4981	−	17.4339i	−1.31672	−	0.900281i
$376$		0			0
$377$	11.8554	−	16.3175i	0.610582	−	0.840394i
$378$		0			0
$379$	−23.6500	+	7.68435i	−1.21482	+	0.394719i	−0.845193	−	0.534462i	$-0.820514\pi$
$379$	−23.6500	+	7.68435i	−1.21482	+	0.394719i	−0.369627	+	0.929180i	$0.620514\pi$
$380$		0			0
$381$	−8.92676	−	2.90048i	−0.457332	−	0.148596i
$382$		0			0
$383$	−5.06647	−	1.64620i	−0.258885	−	0.0841167i	0.176699	−	0.984265i	$-0.443458\pi$
$383$	−5.06647	−	1.64620i	−0.258885	−	0.0841167i	−0.435584	+	0.900148i	$0.643458\pi$
$384$		0			0
$385$	2.85135	+	1.23708i	0.145318	+	0.0630472i
$386$		0			0
$387$	20.3013	−	14.7497i	1.03197	−	0.749771i
$388$		0			0
$389$	6.84259	−	9.41801i	0.346933	−	0.477512i	−0.599517	−	0.800362i	$-0.704641\pi$
$389$	6.84259	−	9.41801i	0.346933	−	0.477512i	0.946450	+	0.322850i	$0.104641\pi$
$390$		0			0
$391$	−20.8733	+	15.1653i	−1.05561	+	0.766944i
$392$		0			0
$393$		−	20.0619i		−	1.01199i
$394$		0			0
$395$	7.75676	+	13.1442i	0.390285	+	0.661355i
$396$		0			0
$397$	−1.22834	−	3.78044i	−0.0616486	−	0.189735i	0.915489	−	0.402343i	$-0.131804\pi$
$397$	−1.22834	−	3.78044i	−0.0616486	−	0.189735i	−0.977137	+	0.212608i	$0.931804\pi$
$398$		0			0
$399$	−29.1060			−1.45712
$400$		0			0
$401$	14.8970			0.743920			0.371960	−	0.928249i	$-0.378686\pi$
$401$	14.8970			0.743920			0.371960	+	0.928249i	$0.378686\pi$
$402$		0			0
$403$	13.3948	+	41.2249i	0.667241	+	2.05356i
$404$		0			0
$405$	−0.305148	+	3.19605i	−0.0151629	+	0.158813i
$406$		0			0
$407$		−	1.04278i		−	0.0516888i
$408$		0			0
$409$	−9.86001	+	7.16371i	−0.487546	+	0.354223i	−0.804240	−	0.594305i	$-0.797427\pi$
$409$	−9.86001	+	7.16371i	−0.487546	+	0.354223i	0.316694	+	0.948528i	$0.397427\pi$
$410$		0			0
$411$	29.9531	−	41.2269i	1.47748	−	2.03357i
$412$		0			0
$413$	−13.5224	+	9.82457i	−0.665392	+	0.483436i
$414$		0			0
$415$	−0.117261	+	1.22817i	−0.00575613	+	0.0602883i
$416$		0			0
$417$	−26.3165	−	8.55074i	−1.28872	−	0.418732i
$418$		0			0
$419$	−11.9484	−	3.88226i	−0.583716	−	0.189661i	0.00224856	−	0.999997i	$-0.499284\pi$
$419$	−11.9484	−	3.88226i	−0.583716	−	0.189661i	−0.585965	+	0.810337i	$0.699284\pi$
$420$		0			0
$421$	6.83134	−	2.21964i	0.332939	−	0.108179i	−0.137777	−	0.990463i	$-0.543996\pi$
$421$	6.83134	−	2.21964i	0.332939	−	0.108179i	0.470716	+	0.882285i	$0.343996\pi$
$422$		0			0
$423$	2.14243	−	2.94881i	0.104169	−	0.143376i
$424$		0			0
$425$	−35.4942	+	4.41616i	−1.72172	+	0.214215i
$426$		0			0
$427$	−16.6125	−	12.0697i	−0.803935	−	0.584093i
$428$		0			0
$429$	7.19832	−	2.33888i	0.347538	−	0.112922i
$430$		0			0
$431$	−7.56243	+	23.2748i	−0.364269	+	1.12111i	0.586168	+	0.810190i	$0.300636\pi$
$431$	−7.56243	+	23.2748i	−0.364269	+	1.12111i	−0.950437	+	0.310916i	$0.899364\pi$
$432$		0			0
$433$	−0.422614	−	0.137316i	−0.0203095	−	0.00659896i	0.298845	−	0.954302i	$-0.403399\pi$
$433$	−0.422614	−	0.137316i	−0.0203095	−	0.00659896i	−0.319154	+	0.947703i	$0.603399\pi$
$434$		0			0
$435$	−17.7203	−	15.6522i	−0.849626	−	0.750467i
$436$		0			0
$437$	11.4964	−	8.35262i	0.549947	−	0.399560i
$438$		0			0
$439$	20.5740	+	14.9479i	0.981941	+	0.713422i	0.958142	−	0.286295i	$-0.0924236\pi$
$439$	20.5740	+	14.9479i	0.981941	+	0.713422i	0.0237998	+	0.999717i	$0.492424\pi$
$440$		0			0
$441$	0.561462	−	0.407926i	0.0267363	−	0.0194251i
$442$		0			0
$443$	1.21860			0.0578973			0.0289486	−	0.999581i	$-0.490784\pi$
$443$	1.21860			0.0578973			0.0289486	+	0.999581i	$0.490784\pi$
$444$		0			0
$445$	−27.8917	−	12.1010i	−1.32219	−	0.573640i
$446$		0			0
$447$	−59.0943	+	19.2009i	−2.79506	+	0.908171i
$448$		0			0
$449$	5.21381			0.246055			0.123027	−	0.992403i	$-0.460740\pi$
$449$	5.21381			0.246055			0.123027	+	0.992403i	$0.460740\pi$
$450$		0			0
$451$		−	3.32043i		−	0.156353i
$452$		0			0
$453$	−11.3274	−	34.8622i	−0.532208	−	1.63797i
$454$		0			0
$455$	−23.6163	−	20.8601i	−1.10715	−	0.977935i
$456$		0			0
$457$			29.9606i			1.40150i	0.713408	+	0.700749i	$0.247151\pi$
$457$			29.9606i			1.40150i	−0.713408	+	0.700749i	$0.752849\pi$
$458$		0			0
$459$	−18.9673	−	26.1062i	−0.885317	−	1.21853i
$460$		0			0
$461$	14.3867	−	19.8016i	0.670055	−	0.922251i	−0.329707	−	0.944083i	$-0.606950\pi$
$461$	14.3867	−	19.8016i	0.670055	−	0.922251i	0.999762	+	0.0218322i	$0.00694996\pi$
$462$		0			0
$463$	19.5394	+	26.8937i	0.908072	+	1.24985i	0.967821	+	0.251641i	$0.0809702\pi$
$463$	19.5394	+	26.8937i	0.908072	+	1.24985i	−0.0597482	+	0.998213i	$0.519030\pi$
$464$		0			0
$465$	49.5984	−	11.0376i	2.30007	−	0.511857i
$466$		0			0
$467$	−6.61921	+	20.3718i	−0.306301	+	0.942697i	0.672888	+	0.739744i	$0.265054\pi$
$467$	−6.61921	+	20.3718i	−0.306301	+	0.942697i	−0.979189	+	0.202952i	$0.934946\pi$
$468$		0			0
$469$	16.3015	+	5.29666i	0.752731	+	0.244577i
$470$		0			0
$471$	−5.78790	−	17.8133i	−0.266692	−	0.820794i
$472$		0			0
$473$	1.65506	−	2.27799i	0.0760997	−	0.104742i
$474$		0			0
$475$	19.5492	−	2.43229i	0.896978	−	0.111601i
$476$		0			0
$477$	−20.8362	−	15.1384i	−0.954022	−	0.693138i
$478$		0			0
$479$	2.03109	+	6.25104i	0.0928026	+	0.285617i	0.986675	−	0.162705i	$-0.0520218\pi$
$479$	2.03109	+	6.25104i	0.0928026	+	0.285617i	−0.893872	+	0.448322i	$0.852022\pi$
$480$		0			0
$481$	−3.26679	+	10.0541i	−0.148953	+	0.458429i
$482$		0			0
$483$	−8.23341	+	25.3398i	−0.374633	+	1.15300i
$484$		0			0
$485$	9.82863	−	5.80017i	0.446295	−	0.263372i
$486$		0			0
$487$	−13.2598	−	18.2506i	−0.600860	−	0.827013i	0.394927	−	0.918713i	$-0.370770\pi$
$487$	−13.2598	−	18.2506i	−0.600860	−	0.827013i	−0.995787	+	0.0917000i	$0.970770\pi$
$488$		0			0
$489$	−32.1782	−	23.3788i	−1.45515	−	1.05723i
$490$		0			0
$491$	16.2270	+	22.3345i	0.732313	+	1.00794i	0.999024	+	0.0441661i	$0.0140631\pi$
$491$	16.2270	+	22.3345i	0.732313	+	1.00794i	−0.266711	+	0.963777i	$0.585937\pi$
$492$		0			0
$493$	−27.3782			−1.23305
$494$		0			0
$495$	−1.16978	−	5.25652i	−0.0525778	−	0.236263i
$496$		0			0
$497$	−7.28509	+	2.36707i	−0.326781	+	0.106177i
$498$		0			0
$499$		−	15.6614i		−	0.701101i	−0.936544	−	0.350551i	$-0.885994\pi$
$499$		−	15.6614i		−	0.701101i	0.936544	−	0.350551i	$-0.114006\pi$
$500$		0			0
$501$			10.7420i			0.479916i
$502$		0			0
$503$	−15.7968	+	5.13269i	−0.704344	+	0.228855i	−0.639222	−	0.769022i	$-0.720744\pi$
$503$	−15.7968	+	5.13269i	−0.704344	+	0.228855i	−0.0651216	+	0.997877i	$0.520744\pi$
$504$		0			0
$505$	−0.861655	−	3.87192i	−0.0383431	−	0.172298i
$506$		0			0
$507$	−40.8152			−1.81267
$508$		0			0
$509$	7.12293	+	9.80387i	0.315718	+	0.434549i	0.937154	−	0.348916i	$-0.113450\pi$
$509$	7.12293	+	9.80387i	0.315718	+	0.434549i	−0.621436	+	0.783465i	$0.713450\pi$
$510$		0			0
$511$	3.08792	+	2.24351i	0.136602	+	0.0992469i
$512$		0			0
$513$	10.4466	+	14.3785i	0.461230	+	0.634828i
$514$		0			0
$515$	1.34856	−	0.795824i	0.0594245	−	0.0350682i
$516$		0			0
$517$	0.126387	−	0.388978i	0.00555847	−	0.0171072i
$518$		0			0
$519$	−1.86830	+	5.75005i	−0.0820094	+	0.252399i
$520$		0			0
$521$	6.53479	+	20.1120i	0.286294	+	0.881123i	0.986008	+	0.166700i	$0.0533110\pi$
$521$	6.53479	+	20.1120i	0.286294	+	0.881123i	−0.699713	+	0.714424i	$0.746689\pi$
$522$		0			0
$523$	19.5338	+	14.1922i	0.854155	+	0.620580i	0.926289	−	0.376815i	$-0.122981\pi$
$523$	19.5338	+	14.1922i	0.854155	+	0.620580i	−0.0721334	+	0.997395i	$0.522981\pi$
$524$		0			0
$525$	−26.9732	+	25.2342i	−1.17721	+	1.10131i
$526$		0			0
$527$	34.5844	−	47.6014i	1.50652	−	2.07355i
$528$		0			0
$529$	3.08762	+	9.50271i	0.134244	+	0.413161i
$530$		0			0
$531$	27.5419	+	8.94891i	1.19522	+	0.388350i
$532$		0			0
$533$	−10.4021	+	32.0145i	−0.450566	+	1.38670i
$534$		0			0
$535$	44.0978	−	9.81350i	1.90651	−	0.424275i
$536$		0			0
$537$	−14.5550	−	20.0332i	−0.628095	−	0.864498i
$538$		0			0
$539$	0.0457732	−	0.0630014i	0.00197159	−	0.00271366i
$540$		0			0
$541$	−4.93039	−	6.78610i	−0.211974	−	0.291757i	0.689769	−	0.724029i	$-0.257712\pi$
$541$	−4.93039	−	6.78610i	−0.211974	−	0.291757i	−0.901743	+	0.432272i	$0.857712\pi$
$542$		0			0
$543$		−	60.0842i		−	2.57846i
$544$		0			0
$545$	−10.5068	−	9.28054i	−0.450061	−	0.397535i
$546$		0			0
$547$	−6.01158	−	18.5017i	−0.257037	−	0.791077i	−0.993422	−	0.114514i	$-0.963469\pi$
$547$	−6.01158	−	18.5017i	−0.257037	−	0.791077i	0.736385	−	0.676563i	$-0.236531\pi$
$548$		0			0
$549$			35.5770i			1.51839i
$550$		0			0
$551$	15.0791			0.642391
$552$		0			0
$553$	17.3575	−	5.63979i	0.738116	−	0.239828i
$554$		0			0
$555$	11.3684	+	4.93224i	0.482562	+	0.209362i
$556$		0			0
$557$	−16.0914			−0.681815			−0.340907	−	0.940097i	$-0.610734\pi$
$557$	−16.0914			−0.681815			−0.340907	+	0.940097i	$0.610734\pi$
$558$		0			0
$559$	−23.0939	+	16.7787i	−0.976770	+	0.709665i
$560$		0			0
$561$	−8.31173	−	6.03882i	−0.350921	−	0.254959i
$562$		0			0
$563$	−21.5684	+	15.6704i	−0.909000	+	0.660427i	−0.940762	−	0.339068i	$-0.889888\pi$
$563$	−21.5684	+	15.6704i	−0.909000	+	0.660427i	0.0317617	+	0.999495i	$0.489888\pi$
$564$		0			0
$565$	−5.81101	−	5.13282i	−0.244471	−	0.215939i
$566$		0			0
$567$	3.65134	+	1.18639i	0.153342	+	0.0498238i
$568$		0			0
$569$	0.701887	−	2.16018i	0.0294246	−	0.0905597i	−0.935266	−	0.353946i	$-0.884840\pi$
$569$	0.701887	−	2.16018i	0.0294246	−	0.0905597i	0.964690	+	0.263387i	$0.0848395\pi$
$570$		0			0
$571$	−26.3024	+	8.54617i	−1.10072	+	0.357646i	−0.802380	−	0.596813i	$-0.796433\pi$
$571$	−26.3024	+	8.54617i	−1.10072	+	0.357646i	−0.298342	+	0.954459i	$0.596433\pi$
$572$		0			0
$573$	3.73525	+	2.71382i	0.156042	+	0.113371i
$574$		0			0
$575$	3.41245	−	17.7077i	0.142309	−	0.738461i
$576$		0			0
$577$	−7.01351	+	9.65326i	−0.291976	+	0.401871i	−0.929655	−	0.368432i	$-0.879895\pi$
$577$	−7.01351	+	9.65326i	−0.291976	+	0.401871i	0.637679	+	0.770302i	$0.279895\pi$
$578$		0			0
$579$	22.5057	−	7.31254i	0.935305	−	0.303899i
$580$		0			0
$581$	1.40312	+	0.455903i	0.0582114	+	0.0189140i
$582$		0			0
$583$	−2.74850	−	0.893042i	−0.113831	−	0.0369860i
$584$		0			0
$585$	−5.18879	+	54.3462i	−0.214530	+	2.24694i
$586$		0			0
$587$	−32.6376	+	23.7126i	−1.34710	+	0.978723i	−0.347946	+	0.937515i	$0.613121\pi$
$587$	−32.6376	+	23.7126i	−1.34710	+	0.978723i	−0.999151	+	0.0412086i	$0.986879\pi$
$588$		0			0
$589$	−19.0481	+	26.2174i	−0.784863	+	1.08027i
$590$		0			0
$591$	22.6237	−	16.4371i	0.930613	−	0.676130i
$592$		0			0
$593$		−	5.46839i		−	0.224560i	−0.993677	−	0.112280i	$-0.964185\pi$
$593$		−	5.46839i		−	0.224560i	0.993677	−	0.112280i	$-0.0358153\pi$
$594$		0			0
$595$	−4.06520	+	42.5780i	−0.166657	+	1.74553i
$596$		0			0
$597$	−14.7015	−	45.2467i	−0.601694	−	1.85182i
$598$		0			0
$599$	−27.9052			−1.14017			−0.570087	−	0.821584i	$-0.693091\pi$
$599$	−27.9052			−1.14017			−0.570087	+	0.821584i	$0.693091\pi$
$600$		0			0
$601$	13.3613			0.545018			0.272509	−	0.962153i	$-0.412146\pi$
$601$	13.3613			0.545018			0.272509	+	0.962153i	$0.412146\pi$
$602$		0			0
$603$	−9.17688	−	28.2435i	−0.373712	−	1.15017i
$604$		0			0
$605$	12.1937	+	20.6628i	0.495746	+	0.840063i
$606$		0			0
$607$		−	31.7630i		−	1.28922i	−0.764511	−	0.644611i	$-0.777019\pi$
$607$		−	31.7630i		−	1.28922i	0.764511	−	0.644611i	$-0.222981\pi$
$608$		0			0
$609$	−22.8732	+	16.6183i	−0.926869	+	0.673409i
$610$		0			0
$611$	−2.43715	+	3.35445i	−0.0985966	+	0.135707i
$612$		0			0
$613$	31.8620	−	23.1491i	1.28690	−	0.934985i	0.287158	−	0.957883i	$-0.407289\pi$
$613$	31.8620	−	23.1491i	1.28690	−	0.934985i	0.999738	+	0.0228985i	$0.00728944\pi$
$614$		0			0
$615$	36.1993	+	15.7053i	1.45970	+	0.633298i
$616$		0			0
$617$	16.4548	+	5.34648i	0.662445	+	0.215241i	0.620893	−	0.783895i	$-0.286770\pi$
$617$	16.4548	+	5.34648i	0.662445	+	0.215241i	0.0415512	+	0.999136i	$0.486770\pi$
$618$		0			0
$619$	−19.9635	−	6.48655i	−0.802402	−	0.260716i	−0.121026	−	0.992649i	$-0.538618\pi$
$619$	−19.9635	−	6.48655i	−0.802402	−	0.260716i	−0.681377	+	0.731933i	$0.738618\pi$
$620$		0			0
$621$	15.4732	−	5.02753i	0.620916	−	0.201748i
$622$		0			0
$623$	−21.3701	+	29.4134i	−0.856173	+	1.17842i
$624$		0			0
$625$	16.0079	−	19.2028i	0.640318	−	0.768110i
$626$		0			0
$627$	4.57786	+	3.32601i	0.182822	+	0.132828i
$628$		0			0
$629$	13.6475	−	4.43435i	0.544163	−	0.176809i
$630$		0			0
$631$	−4.33588	+	13.3445i	−0.172609	+	0.531235i	−0.999516	−	0.0311029i	$-0.990098\pi$
$631$	−4.33588	+	13.3445i	−0.172609	+	0.531235i	0.826907	+	0.562338i	$0.190098\pi$
$632$		0			0
$633$	47.0818	+	15.2978i	1.87133	+	0.608032i
$634$		0			0
$635$	3.02362	−	6.96918i	0.119989	−	0.276563i
$636$		0			0
$637$	−0.638698	+	0.464041i	−0.0253061	+	0.0183860i
$638$		0			0
$639$	10.7369	+	7.80081i	0.424745	+	0.308595i
$640$		0			0
$641$	−38.2200	+	27.7684i	−1.50960	+	1.09679i	−0.543242	+	0.839576i	$0.682803\pi$
$641$	−38.2200	+	27.7684i	−1.50960	+	1.09679i	−0.966355	+	0.257210i	$0.917197\pi$
$642$		0			0
$643$	−35.9924			−1.41940			−0.709702	−	0.704502i	$-0.751170\pi$
$643$	−35.9924			−1.41940			−0.709702	+	0.704502i	$0.751170\pi$
$644$		0			0
$645$	17.0064	+	28.8181i	0.669628	+	1.13471i
$646$		0			0
$647$	0.591058	−	0.192046i	0.0232369	−	0.00755012i	−0.297375	−	0.954761i	$-0.596111\pi$
$647$	0.591058	−	0.192046i	0.0232369	−	0.00755012i	0.320612	+	0.947210i	$0.396111\pi$
$648$		0			0
$649$	3.24951			0.127554
$650$		0			0
$651$		−	60.7612i		−	2.38142i
$652$		0			0
$653$	2.23277	+	6.87175i	0.0873749	+	0.268912i	0.985192	−	0.171457i	$-0.0548475\pi$
$653$	2.23277	+	6.87175i	0.0873749	+	0.268912i	−0.897817	+	0.440369i	$0.854848\pi$
$654$		0			0
$655$	16.1639	+	1.54328i	0.631577	+	0.0603008i
$656$		0			0
$657$		−	6.61304i		−	0.257999i
$658$		0			0
$659$	14.7715	+	20.3312i	0.575415	+	0.791991i	0.993183	−	0.116563i	$-0.0371875\pi$
$659$	14.7715	+	20.3312i	0.575415	+	0.791991i	−0.417768	+	0.908554i	$0.637188\pi$
$660$		0			0
$661$	−1.96163	+	2.69996i	−0.0762987	+	0.105016i	−0.845461	−	0.534038i	$-0.820674\pi$
$661$	−1.96163	+	2.69996i	−0.0762987	+	0.105016i	0.769162	+	0.639054i	$0.220674\pi$
$662$		0			0
$663$	61.2206	+	84.2630i	2.37761	+	3.27250i
$664$		0			0
$665$	2.23899	−	23.4507i	0.0868245	−	0.909379i
$666$		0			0
$667$	4.26553	−	13.1280i	0.165162	−	0.508317i
$668$		0			0
$669$	−16.8377	−	5.47091i	−0.650984	−	0.211518i
$670$		0			0
$671$	1.23362	+	3.79670i	0.0476234	+	0.146570i
$672$		0			0
$673$	−19.4876	+	26.8224i	−0.751191	+	1.03393i	0.246705	+	0.969091i	$0.420652\pi$
$673$	−19.4876	+	26.8224i	−0.751191	+	1.03393i	−0.997896	+	0.0648353i	$0.979348\pi$
$674$		0			0
$675$	22.1470	+	4.26795i	0.852439	+	0.164273i
$676$		0			0
$677$	9.80817	+	7.12605i	0.376959	+	0.273876i	0.760091	−	0.649817i	$-0.225155\pi$
$677$	9.80817	+	7.12605i	0.376959	+	0.273876i	−0.383132	+	0.923694i	$0.625155\pi$
$678$		0			0
$679$	−4.21719	−	12.9792i	−0.161841	−	0.498095i
$680$		0			0
$681$	−22.8297	+	70.2625i	−0.874835	+	2.69247i
$682$		0			0
$683$	12.5862	−	38.7363i	0.481597	−	1.48220i	−0.355253	−	0.934770i	$-0.615605\pi$
$683$	12.5862	−	38.7363i	0.481597	−	1.48220i	0.836850	−	0.547432i	$-0.184395\pi$
$684$		0			0
$685$	30.9124	+	27.3046i	1.18110	+	1.04326i
$686$		0			0
$687$	2.80069	+	3.85482i	0.106853	+	0.147071i
$688$		0			0
$689$	23.7024	+	17.2208i	0.902990	+	0.656061i
$690$		0			0
$691$	−4.49348	−	6.18474i	−0.170940	−	0.235279i	0.714948	−	0.699177i	$-0.246450\pi$
$691$	−4.49348	−	6.18474i	−0.170940	−	0.235279i	−0.885888	+	0.463899i	$0.846450\pi$
$692$		0			0
$693$	−6.43956			−0.244619
$694$		0			0
$695$	8.91375	−	20.5454i	0.338118	−	0.779332i
$696$		0			0
$697$	43.4565	−	14.1199i	1.64603	−	0.534829i
$698$		0			0
$699$			73.4170i			2.77689i
$700$		0			0
$701$			41.0013i			1.54860i	0.632820	+	0.774299i	$0.281897\pi$
$701$			41.0013i			1.54860i	−0.632820	+	0.774299i	$0.718103\pi$
$702$		0			0
$703$	−7.51666	+	2.44231i	−0.283496	+	0.0921135i
$704$		0			0
$705$	3.64284	+	3.21769i	0.137197	+	0.121185i
$706$		0			0
$707$	−4.74334			−0.178392
$708$		0			0
$709$	18.4825	+	25.4390i	0.694125	+	0.955382i	0.999995	+	0.00330817i	$0.00105303\pi$
$709$	18.4825	+	25.4390i	0.694125	+	0.955382i	−0.305869	+	0.952074i	$0.598947\pi$
$710$		0			0
$711$	−25.5818	−	18.5863i	−0.959393	−	0.697040i
$712$		0			0
$713$	17.4368	+	23.9997i	0.653013	+	0.898796i
$714$		0			0
$715$	1.33070	+	5.97961i	0.0497653	+	0.223625i
$716$		0			0
$717$	11.4290	−	35.1748i	0.426824	−	1.31363i
$718$		0			0
$719$	0.494184	−	1.52094i	0.0184300	−	0.0567216i	−0.941419	−	0.337240i	$-0.890506\pi$
$719$	0.494184	−	1.52094i	0.0184300	−	0.0567216i	0.959849	+	0.280519i	$0.0905065\pi$
$720$		0			0
$721$	−0.578628	−	1.78083i	−0.0215492	−	0.0663217i
$722$		0			0
$723$	−25.6761	−	18.6548i	−0.954903	−	0.693778i
$724$		0			0
$725$	13.9742	−	13.0732i	0.518987	−	0.485528i
$726$		0			0
$727$	−29.8436	+	41.0762i	−1.10684	+	1.52343i	−0.280843	+	0.959754i	$0.590614\pi$
$727$	−29.8436	+	41.0762i	−1.10684	+	1.52343i	−0.825995	+	0.563678i	$0.809386\pi$
$728$		0			0
$729$	−13.6089	−	41.8837i	−0.504032	−	1.55125i
$730$		0			0
$731$	36.8515	+	11.9738i	1.36300	+	0.442867i
$732$		0			0
$733$	6.55606	−	20.1775i	0.242154	−	0.745272i	−0.753938	−	0.656946i	$-0.771848\pi$
$733$	6.55606	−	20.1775i	0.242154	−	0.745272i	0.996092	−	0.0883266i	$-0.0281519\pi$
$734$		0			0
$735$	0.470339	+	0.797009i	0.0173487	+	0.0293981i
$736$		0			0
$737$	−1.95867	−	2.69588i	−0.0721485	−	0.0993039i
$738$		0			0
$739$	14.2869	−	19.6642i	0.525551	−	0.723358i	−0.460894	−	0.887455i	$-0.652471\pi$
$739$	14.2869	−	19.6642i	0.525551	−	0.723358i	0.986444	+	0.164097i	$0.0524710\pi$
$740$		0			0
$741$	−33.7185	−	46.4096i	−1.23868	−	1.70490i
$742$		0			0
$743$		−	11.2680i		−	0.413384i	−0.978406	−	0.206692i	$-0.933730\pi$
$743$		−	11.2680i		−	0.413384i	0.978406	−	0.206692i	$-0.0662698\pi$
$744$		0			0
$745$	−10.9243	−	49.0893i	−0.400236	−	1.79849i
$746$		0			0
$747$	−0.789887	−	2.43102i	−0.0289005	−	0.0889465i
$748$		0			0
$749$		−	54.0226i		−	1.97394i
$750$		0			0
$751$	8.71647			0.318068			0.159034	−	0.987273i	$-0.449162\pi$
$751$	8.71647			0.318068			0.159034	+	0.987273i	$0.449162\pi$
$752$		0			0
$753$	27.3133	−	8.87463i	0.995352	−	0.323409i
$754$		0			0
$755$	28.9598	−	6.44470i	1.05396	−	0.234547i
$756$		0			0
$757$	−38.5500			−1.40112			−0.700562	−	0.713592i	$-0.747067\pi$
$757$	−38.5500			−1.40112			−0.700562	+	0.713592i	$0.747067\pi$
$758$		0			0
$759$	4.19061	−	3.04466i	0.152110	−	0.110514i
$760$		0			0
$761$	22.7571	+	16.5340i	0.824944	+	0.599357i	0.918124	−	0.396292i	$-0.129703\pi$
$761$	22.7571	+	16.5340i	0.824944	+	0.599357i	−0.0931801	+	0.995649i	$0.529703\pi$
$762$		0			0
$763$	−13.5620	+	9.85338i	−0.490978	+	0.356716i
$764$		0			0
$765$	63.8209	−	37.6626i	2.30745	−	1.36169i
$766$		0			0
$767$	−31.3306	−	10.1799i	−1.13128	−	0.367576i
$768$		0			0
$769$	−1.71576	+	5.28055i	−0.0618717	+	0.190422i	−0.977215	−	0.212254i	$-0.931920\pi$
$769$	−1.71576	+	5.28055i	−0.0618717	+	0.190422i	0.915343	+	0.402675i	$0.131920\pi$
$770$		0			0
$771$	−15.5228	+	5.04368i	−0.559041	+	0.181644i
$772$		0			0
$773$	−26.9230	−	19.5607i	−0.968353	−	0.703549i	−0.0132772	−	0.999912i	$-0.504226\pi$
$773$	−26.9230	−	19.5607i	−0.968353	−	0.703549i	−0.955076	+	0.296362i	$0.904226\pi$
$774$		0			0
$775$	5.07762	+	40.8106i	0.182393	+	1.46596i
$776$		0			0
$777$	8.71025	−	11.9886i	0.312478	−	0.430090i
$778$		0			0
$779$	−23.9346	+	7.77682i	−0.857545	+	0.278633i
$780$		0			0
$781$	1.41631	+	0.460185i	0.0506794	+	0.0164667i
$782$		0			0
$783$	16.4191	+	5.33491i	0.586773	+	0.190654i
$784$		0			0
$785$	14.7974	−	3.29301i	0.528143	−	0.117533i
$786$		0			0
$787$	17.2535	−	12.5354i	0.615021	−	0.446839i	−0.236158	−	0.971715i	$-0.575888\pi$
$787$	17.2535	−	12.5354i	0.615021	−	0.446839i	0.851179	+	0.524876i	$0.175888\pi$
$788$		0			0
$789$	−9.06600	+	12.4783i	−0.322758	+	0.444239i
$790$		0			0
$791$	−7.50078	+	5.44963i	−0.266697	+	0.193767i
$792$		0			0
$793$		−	40.4711i		−	1.43717i
$794$		0			0
$795$	22.7361	−	25.7402i	0.806365	−	0.912909i
$796$		0			0
$797$	−0.373055	−	1.14814i	−0.0132143	−	0.0406694i	0.944232	−	0.329281i	$-0.106806\pi$
$797$	−0.373055	−	1.14814i	−0.0132143	−	0.0406694i	−0.957446	+	0.288612i	$0.906806\pi$
$798$		0			0
$799$	5.62824			0.199113
$800$		0			0
$801$	62.9912			2.22568
$802$		0			0
$803$	−0.229305	−	0.705728i	−0.00809199	−	0.0249046i
$804$		0			0
$805$	−19.7830	−	8.58295i	−0.697258	−	0.302509i
$806$		0			0
$807$		−	5.83604i		−	0.205438i
$808$		0			0
$809$	−8.23313	+	5.98172i	−0.289462	+	0.210306i	−0.723034	−	0.690813i	$-0.757253\pi$
$809$	−8.23313	+	5.98172i	−0.289462	+	0.210306i	0.433572	+	0.901119i	$0.357253\pi$
$810$		0			0
$811$	9.04159	−	12.4447i	0.317493	−	0.436992i	−0.620206	−	0.784439i	$-0.712951\pi$
$811$	9.04159	−	12.4447i	0.317493	−	0.436992i	0.937700	+	0.347447i	$0.112951\pi$
$812$		0			0
$813$	−43.0321	+	31.2646i	−1.50920	+	1.09650i
$814$		0			0
$815$	21.3117	−	24.1276i	0.746515	−	0.845151i
$816$		0			0
$817$	−20.2967	−	6.59481i	−0.710093	−	0.230723i
$818$		0			0
$819$	62.0880	+	20.1736i	2.16953	+	0.704923i
$820$		0			0
$821$	49.2854	−	16.0138i	1.72007	−	0.558885i	0.728115	−	0.685455i	$-0.240397\pi$
$821$	49.2854	−	16.0138i	1.72007	−	0.558885i	0.991958	+	0.126570i	$0.0403968\pi$
$822$		0			0
$823$	15.1546	−	20.8585i	0.528256	−	0.727082i	−0.458607	−	0.888639i	$-0.651651\pi$
$823$	15.1546	−	20.8585i	0.528256	−	0.727082i	0.986863	+	0.161557i	$0.0516515\pi$
$824$		0			0
$825$	7.12598	−	0.886608i	0.248095	−	0.0308677i
$826$		0			0
$827$	−2.88316	−	2.09474i	−0.100257	−	0.0728411i	0.536527	−	0.843883i	$-0.319736\pi$
$827$	−2.88316	−	2.09474i	−0.100257	−	0.0728411i	−0.636784	+	0.771042i	$0.719736\pi$
$828$		0			0
$829$	−25.3530	+	8.23770i	−0.880547	+	0.286107i	−0.714184	−	0.699958i	$-0.753202\pi$
$829$	−25.3530	+	8.23770i	−0.880547	+	0.286107i	−0.166362	+	0.986065i	$0.553202\pi$
$830$		0			0
$831$	−16.9573	+	52.1892i	−0.588243	+	1.81042i
$832$		0			0
$833$	1.01919	+	0.331153i	0.0353127	+	0.0114738i
$834$		0			0
$835$	−8.65481	−	0.826332i	−0.299512	−	0.0285964i
$836$		0			0
$837$	−30.0164	+	21.8082i	−1.03752	+	0.753802i
$838$		0			0
$839$	2.07141	+	1.50497i	0.0715131	+	0.0519573i	0.622967	−	0.782248i	$-0.285927\pi$
$839$	2.07141	+	1.50497i	0.0715131	+	0.0519573i	−0.551454	+	0.834205i	$0.685927\pi$
$840$		0			0
$841$	−11.6114	+	8.43621i	−0.400395	+	0.290904i
$842$		0			0
$843$	34.3193			1.18202
$844$		0			0
$845$	3.13973	−	32.8848i	0.108010	−	1.13127i
$846$		0			0
$847$	27.2862	−	8.86584i	0.937566	−	0.304634i
$848$		0			0
$849$	−0.862913			−0.0296151
$850$		0			0
$851$			7.23492i			0.248010i
$852$		0			0
$853$	0.926669	+	2.85199i	0.0317285	+	0.0976504i	0.965667	−	0.259784i	$-0.0836515\pi$
$853$	0.926669	+	2.85199i	0.0317285	+	0.0976504i	−0.933938	+	0.357435i	$0.883651\pi$
$854$		0			0
$855$	−35.1506	+	20.7434i	−1.20213	+	0.709411i
$856$		0			0
$857$			6.92518i			0.236560i	0.992980	+	0.118280i	$0.0377380\pi$
$857$			6.92518i			0.236560i	−0.992980	+	0.118280i	$0.962262\pi$
$858$		0			0
$859$	15.0901	+	20.7697i	0.514866	+	0.708653i	0.984730	−	0.174086i	$-0.0556971\pi$
$859$	15.0901	+	20.7697i	0.514866	+	0.708653i	−0.469864	+	0.882739i	$0.655697\pi$
$860$		0			0
$861$	27.7352	−	38.1743i	0.945214	−	1.30098i
$862$		0			0
$863$	−8.57489	−	11.8023i	−0.291893	−	0.401756i	0.637735	−	0.770256i	$-0.279871\pi$
$863$	−8.57489	−	11.8023i	−0.291893	−	0.401756i	−0.929628	+	0.368500i	$0.879871\pi$
$864$		0			0
$865$	−4.48910	−	1.94762i	−0.152634	−	0.0662210i
$866$		0			0
$867$	29.1753	−	89.7924i	0.990846	−	3.04951i
$868$		0			0
$869$	−3.37450	−	1.09644i	−0.114472	−	0.0371942i
$870$		0			0
$871$	10.4393	+	32.1288i	0.353721	+	1.08864i
$872$		0			0
$873$	−13.8980	+	19.1289i	−0.470376	+	0.647417i
$874$		0			0
$875$	−18.2563	−	23.6735i	−0.617175	−	0.800309i
$876$		0			0
$877$	29.6831	+	21.5661i	1.00233	+	0.728234i	0.962586	−	0.270976i	$-0.0873463\pi$
$877$	29.6831	+	21.5661i	1.00233	+	0.728234i	0.0397424	+	0.999210i	$0.487346\pi$
$878$		0			0
$879$	8.66968	+	26.6825i	0.292421	+	0.899980i
$880$		0			0
$881$	7.66494	−	23.5903i	0.258238	−	0.794776i	−0.734936	−	0.678137i	$-0.762788\pi$
$881$	7.66494	−	23.5903i	0.258238	−	0.794776i	0.993174	−	0.116639i	$-0.0372122\pi$
$882$		0			0
$883$	3.12800	−	9.62701i	0.105266	−	0.323975i	−0.884527	−	0.466489i	$-0.845519\pi$
$883$	3.12800	−	9.62701i	0.105266	−	0.323975i	0.989793	+	0.142514i	$0.0455187\pi$
$884$		0			0
$885$	−15.3698	+	35.4261i	−0.516651	+	1.19084i
$886$		0			0
$887$	6.68404	+	9.19979i	0.224428	+	0.308899i	0.906351	−	0.422525i	$-0.138856\pi$
$887$	6.68404	+	9.19979i	0.224428	+	0.308899i	−0.681923	+	0.731424i	$0.738856\pi$
$888$		0			0
$889$	−7.34939	−	5.33965i	−0.246491	−	0.179086i
$890$		0			0
$891$	−0.438720	−	0.603846i	−0.0146977	−	0.0202296i
$892$		0			0
$893$	−3.09987			−0.103733
$894$		0			0
$895$	17.2604	−	10.1859i	0.576953	−	0.340477i
$896$		0			0
$897$	−49.9426	+	16.2273i	−1.66754	+	0.541815i
$898$		0			0
$899$			31.4789i			1.04988i
$900$		0			0
$901$		−	39.7689i		−	1.32489i
$902$		0			0
$903$	38.0557	−	12.3651i	1.26642	−	0.411483i
$904$		0			0
$905$	48.4099	+	4.62201i	1.60920	+	0.153641i
$906$		0			0
$907$	16.5101			0.548207			0.274104	−	0.961700i	$-0.411619\pi$
$907$	16.5101			0.548207			0.274104	+	0.961700i	$0.411619\pi$
$908$		0			0
$909$	4.83054	+	6.64867i	0.160219	+	0.220523i
$910$		0			0
$911$	10.4321	+	7.57935i	0.345630	+	0.251115i	0.747033	−	0.664786i	$-0.231477\pi$
$911$	10.4321	+	7.57935i	0.345630	+	0.251115i	−0.401403	+	0.915901i	$0.631477\pi$
$912$		0			0
$913$	−0.168590	−	0.232044i	−0.00557950	−	0.00767953i
$914$		0			0
$915$	−47.2265	−	4.50902i	−1.56126	−	0.149064i
$916$		0			0
$917$	6.00014	−	18.4665i	0.198142	−	0.609819i
$918$		0			0
$919$	−6.83471	+	21.0351i	−0.225456	+	0.693883i	0.772789	+	0.634663i	$0.218861\pi$
$919$	−6.83471	+	21.0351i	−0.225456	+	0.693883i	−0.998245	+	0.0592194i	$0.981139\pi$
$920$		0			0
$921$	−25.8560	−	79.5767i	−0.851985	−	2.62214i
$922$		0			0
$923$	−12.2139	−	8.87390i	−0.402025	−	0.292088i
$924$		0			0
$925$	−4.84843	+	8.78011i	−0.159416	+	0.288688i
$926$		0			0
$927$	−1.90690	+	2.62463i	−0.0626309	+	0.0862040i
$928$		0			0
$929$	11.8169	+	36.3687i	0.387701	+	1.19322i	0.934502	+	0.355958i	$0.115845\pi$
$929$	11.8169	+	36.3687i	0.387701	+	1.19322i	−0.546801	+	0.837262i	$0.684155\pi$
$930$		0			0
$931$	−0.561337	−	0.182390i	−0.0183971	−	0.00597758i
$932$		0			0
$933$	−21.6039	+	66.4899i	−0.707279	+	2.17678i
$934$		0			0
$935$	5.50487	−	6.23222i	0.180028	−	0.203816i
$936$		0			0
$937$	−8.14697	−	11.2133i	−0.266150	−	0.366324i	0.654935	−	0.755685i	$-0.272696\pi$
$937$	−8.14697	−	11.2133i	−0.266150	−	0.366324i	−0.921085	+	0.389361i	$0.872696\pi$
$938$		0			0
$939$	−41.4413	+	57.0390i	−1.35238	+	1.86140i
$940$		0			0
$941$	23.3206	+	32.0981i	0.760230	+	1.04637i	0.997195	+	0.0748487i	$0.0238474\pi$
$941$	23.3206	+	32.0981i	0.760230	+	1.04637i	−0.236965	+	0.971518i	$0.576153\pi$
$942$		0			0
$943$			23.0375i			0.750203i
$944$		0			0
$945$	10.7347	−	24.7426i	0.349200	−	0.804876i
$946$		0			0
$947$	−9.93611	−	30.5802i	−0.322880	−	0.993724i	−0.972388	−	0.233369i	$-0.925025\pi$
$947$	−9.93611	−	30.5802i	−0.322880	−	0.993724i	0.649508	−	0.760355i	$-0.274975\pi$
$948$		0			0
$949$			7.52274i			0.244199i
$950$		0			0
$951$	74.2243			2.40689
$952$		0			0
$953$	2.59539	−	0.843293i	0.0840729	−	0.0273169i	−0.266679	−	0.963786i	$-0.585926\pi$
$953$	2.59539	−	0.843293i	0.0840729	−	0.0273169i	0.350751	+	0.936469i	$0.385926\pi$
$954$		0			0
$955$	−2.47386	+	2.80073i	−0.0800522	+	0.0906295i
$956$		0			0
$957$	5.49657			0.177679
$958$		0			0
$959$	39.9013	−	28.9900i	1.28848	−	0.936135i
$960$		0			0
$961$	−29.6516	−	21.5432i	−0.956504	−	0.694941i
$962$		0			0
$963$	−75.7226	+	55.0157i	−2.44013	+	1.77286i
$964$		0			0
$965$	4.16046	+	18.6954i	0.133930	+	0.601825i
$966$		0			0
$967$	−18.5861	−	6.03899i	−0.597689	−	0.194201i	−0.00547963	−	0.999985i	$-0.501744\pi$
$967$	−18.5861	−	6.03899i	−0.597689	−	0.194201i	−0.592210	+	0.805784i	$0.701744\pi$
$968$		0			0
$969$	−24.0625	+	74.0568i	−0.772999	+	2.37905i
$970$		0			0
$971$	5.24830	−	1.70528i	0.168426	−	0.0547250i	−0.223590	−	0.974683i	$-0.571778\pi$
$971$	5.24830	−	1.70528i	0.168426	−	0.0547250i	0.392016	+	0.919958i	$0.371778\pi$
$972$		0			0
$973$	−21.6663	−	15.7415i	−0.694591	−	0.504650i
$974$		0			0
$975$	−71.4838	−	13.7756i	−2.28931	−	0.441173i
$976$		0			0
$977$	−0.133245	+	0.183396i	−0.00426289	+	0.00586736i	−0.811143	−	0.584848i	$-0.801154\pi$
$977$	−0.133245	+	0.183396i	−0.00426289	+	0.00586736i	0.806880	+	0.590715i	$0.201154\pi$
$978$		0			0
$979$	6.72226	−	2.18420i	0.214844	−	0.0698072i
$980$		0			0
$981$	27.6227	+	8.97514i	0.881923	+	0.286554i
$982$		0			0
$983$	−36.7510	−	11.9411i	−1.17217	−	0.380862i	−0.342720	−	0.939438i	$-0.611348\pi$
$983$	−36.7510	−	11.9411i	−1.17217	−	0.380862i	−0.829454	+	0.558575i	$0.811348\pi$
$984$		0			0
$985$	11.5030	+	19.4923i	0.366516	+	0.621077i
$986$		0			0
$987$	4.70213	−	3.41630i	0.149670	−	0.108742i
$988$		0			0
$989$	−11.4830	+	15.8049i	−0.365137	+	0.502568i
$990$		0			0
$991$	−41.5262	+	30.1706i	−1.31912	+	0.958400i	−0.319181	+	0.947694i	$0.603408\pi$
$991$	−41.5262	+	30.1706i	−1.31912	+	0.958400i	−0.999943	+	0.0107060i	$0.996592\pi$
$992$		0			0
$993$			33.2991i			1.05672i
$994$		0			0
$995$	37.5862	−	8.36441i	1.19156	−	0.265170i
$996$		0			0
$997$	6.00849	+	18.4922i	0.190291	+	0.585655i	0.999999	−	0.00117756i	$-0.000374828\pi$
$997$	6.00849	+	18.4922i	0.190291	+	0.585655i	−0.809709	+	0.586832i	$0.800375\pi$
$998$		0			0
$999$	−9.04872			−0.286289

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.be.a.209.4		112
4.3	odd	2		200.2.o.a.109.8	✓	112
8.3	odd	2		200.2.o.a.109.11	yes	112
8.5	even	2	inner	800.2.be.a.209.25		112
20.3	even	4		1000.2.t.b.701.44		224
20.7	even	4		1000.2.t.b.701.13		224
20.19	odd	2		1000.2.o.a.549.21		112
25.14	even	10	inner	800.2.be.a.689.25		112
40.3	even	4		1000.2.t.b.701.48		224
40.19	odd	2		1000.2.o.a.549.18		112
40.27	even	4		1000.2.t.b.701.9		224
100.11	odd	10		1000.2.o.a.949.18		112
100.23	even	20		1000.2.t.b.301.48		224
100.27	even	20		1000.2.t.b.301.9		224
100.39	odd	10		200.2.o.a.189.11	yes	112
200.11	odd	10		1000.2.o.a.949.21		112
200.27	even	20		1000.2.t.b.301.13		224
200.123	even	20		1000.2.t.b.301.44		224
200.139	odd	10		200.2.o.a.189.8	yes	112
200.189	even	10	inner	800.2.be.a.689.4		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.8	✓	112	4.3	odd	2
200.2.o.a.109.11	yes	112	8.3	odd	2
200.2.o.a.189.8	yes	112	200.139	odd	10
200.2.o.a.189.11	yes	112	100.39	odd	10
800.2.be.a.209.4		112	1.1	even	1	trivial
800.2.be.a.209.25		112	8.5	even	2	inner
800.2.be.a.689.4		112	200.189	even	10	inner
800.2.be.a.689.25		112	25.14	even	10	inner
1000.2.o.a.549.18		112	40.19	odd	2
1000.2.o.a.549.21		112	20.19	odd	2
1000.2.o.a.949.18		112	100.11	odd	10
1000.2.o.a.949.21		112	200.11	odd	10
1000.2.t.b.301.9		224	100.27	even	20
1000.2.t.b.301.13		224	200.27	even	20
1000.2.t.b.301.44		224	200.123	even	20
1000.2.t.b.301.48		224	100.23	even	20
1000.2.t.b.701.9		224	40.27	even	4
1000.2.t.b.701.13		224	20.7	even	4
1000.2.t.b.701.44		224	20.3	even	4
1000.2.t.b.701.48		224	40.3	even	4

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:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.be (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.853735 - 2.62753i) q^{3} +(2.18267 - 0.485731i) q^{5} -2.67391i q^{7} +(-3.74798 + 2.72307i) q^{9} +(-0.305554 + 0.420559i) q^{11} +(4.26356 - 3.09766i) q^{13} +(-3.13970 - 5.32035i) q^{15} +(-6.80346 - 2.21058i) q^{17} +(3.74715 + 1.21752i) q^{19} +(-7.02577 + 2.28281i) q^{21} +(2.11996 - 2.91788i) q^{23} +(4.52813 - 2.12038i) q^{25} +(3.64939 + 2.65144i) q^{27} +(3.63988 - 1.18267i) q^{29} +(-2.54168 + 7.82249i) q^{31} +(1.36589 + 0.443805i) q^{33} +(-1.29880 - 5.83628i) q^{35} +(-1.62286 + 1.17908i) q^{37} +(-11.7791 - 8.55804i) q^{39} +(-5.16753 + 3.75443i) q^{41} -5.41659 q^{43} +(-6.85794 + 7.76408i) q^{45} +(-0.748265 + 0.243126i) q^{47} -0.149804 q^{49} +19.7635i q^{51} +(1.71792 + 5.28721i) q^{53} +(-0.462646 + 1.06636i) q^{55} -10.8852i q^{57} +(-3.67423 - 5.05715i) q^{59} +(4.51387 - 6.21281i) q^{61} +(7.28124 + 10.0218i) q^{63} +(7.80133 - 8.83212i) q^{65} +(-1.98087 + 6.09648i) q^{67} +(-9.47669 - 3.07916i) q^{69} +(-0.885245 - 2.72450i) q^{71} +(-0.839035 + 1.15483i) q^{73} +(-9.43719 - 10.0875i) q^{75} +(1.12454 + 0.817024i) q^{77} +(2.10919 + 6.49143i) q^{79} +(-0.443692 + 1.36554i) q^{81} +(-0.170500 + 0.524746i) q^{83} +(-15.9235 - 1.52032i) q^{85} +(-6.21499 - 8.55421i) q^{87} +(-11.0001 - 7.99206i) q^{89} +(-8.28286 - 11.4004i) q^{91} +22.7237 q^{93} +(8.77019 + 0.837348i) q^{95} +(4.85400 - 1.57716i) q^{97} -2.40829i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79}+ \cdots - 50 q^{97}+O(q^{100}) \) 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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