LMFDB - Embedded newform 888.2.br.a.569.36

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [888,2,Mod(473,888)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(888, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 6, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("888.473"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 888 = 2^{3} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	888.br (of order $12$, degree $4$, 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:	$7.09071569949$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			569.36
Character	$\chi$	$=$	888.569
Dual form			888.2.br.a.785.36

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.70811 - 0.287007i) q^{3} +(-0.721322 + 2.69201i) q^{5} +(2.47898 + 4.29371i) q^{7} +(2.83525 - 0.980478i) q^{9} -1.92072 q^{11} +(1.17839 + 0.315747i) q^{13} +(-0.459467 + 4.80526i) q^{15} +(-5.26023 + 1.40947i) q^{17} +(-4.56995 - 1.22452i) q^{19} +(5.46668 + 6.62264i) q^{21} +(-2.41576 - 2.41576i) q^{23} +(-2.39648 - 1.38361i) q^{25} +(4.56151 - 2.48850i) q^{27} +(3.35285 - 3.35285i) q^{29} +(2.96309 + 2.96309i) q^{31} +(-3.28079 + 0.551260i) q^{33} +(-13.3469 + 3.57628i) q^{35} +(-5.71600 - 2.08022i) q^{37} +(2.10343 + 0.201125i) q^{39} +(2.27871 + 3.94685i) q^{41} +(3.86120 - 3.86120i) q^{43} +(0.594327 + 8.33977i) q^{45} -1.47732i q^{47} +(-8.79066 + 15.2259i) q^{49} +(-8.58050 + 3.91726i) q^{51} +(11.0443 + 6.37642i) q^{53} +(1.38545 - 5.17059i) q^{55} +(-8.15741 - 0.779992i) q^{57} +(10.7362 - 2.87675i) q^{59} +(2.65045 - 9.89160i) q^{61} +(11.2384 + 9.74319i) q^{63} +(-1.69999 + 2.94447i) q^{65} +(8.89621 - 5.13623i) q^{67} +(-4.81971 - 3.43303i) q^{69} +(1.72584 - 0.996416i) q^{71} -0.224313i q^{73} +(-4.49054 - 1.67554i) q^{75} +(-4.76141 - 8.24701i) q^{77} +(7.22868 + 1.93692i) q^{79} +(7.07732 - 5.55981i) q^{81} +(13.1112 + 7.56973i) q^{83} -15.1773i q^{85} +(4.76473 - 6.68931i) q^{87} +(-1.85313 - 6.91598i) q^{89} +(1.56546 + 5.84238i) q^{91} +(5.91169 + 4.21084i) q^{93} +(6.59281 - 11.4191i) q^{95} +(-10.0950 + 10.0950i) q^{97} +(-5.44572 + 1.88322i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) $ 152 * q + 4 * q^13 - 12 * q^15 + 4 * q^19 - 44 * q^31 - 12 * q^39 + 28 * q^43 + 20 * q^45 - 80 * q^49 - 12 * q^51 - 8 * q^55 - 40 * q^57 - 28 * q^61 + 48 * q^63 + 56 * q^69 + 64 * q^75 + 20 * q^79 + 16 * q^81 + 56 * q^87 + 52 * q^91 + 40 * q^93 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.70811	−	0.287007i	0.986176	−	0.165704i
$3$	1.70811	−	0.287007i	0.986176	−	0.165704i
$4$		0			0
$5$	−0.721322	+	2.69201i	−0.322585	+	1.20390i	0.594133	+	0.804367i	$0.297495\pi$
$5$	−0.721322	+	2.69201i	−0.322585	+	1.20390i	−0.916718	+	0.399536i	$0.869171\pi$
$6$		0			0
$7$	2.47898	+	4.29371i	0.936965	+	1.62287i	0.771091	+	0.636725i	$0.219711\pi$
$7$	2.47898	+	4.29371i	0.936965	+	1.62287i	0.165874	+	0.986147i	$0.446955\pi$
$8$		0			0
$9$	2.83525	−	0.980478i	0.945084	−	0.326826i
$10$		0			0
$11$	−1.92072			−0.579118			−0.289559	−	0.957160i	$-0.593509\pi$
$11$	−1.92072			−0.579118			−0.289559	+	0.957160i	$0.593509\pi$
$12$		0			0
$13$	1.17839	+	0.315747i	0.326825	+	0.0875726i	0.418501	−	0.908216i	$-0.362556\pi$
$13$	1.17839	+	0.315747i	0.326825	+	0.0875726i	−0.0916757	+	0.995789i	$0.529222\pi$
$14$		0			0
$15$	−0.459467	+	4.80526i	−0.118634	+	1.24071i
$16$		0			0
$17$	−5.26023	+	1.40947i	−1.27579	+	0.341848i	−0.832247	−	0.554404i	$-0.812946\pi$
$17$	−5.26023	+	1.40947i	−1.27579	+	0.341848i	−0.443545	+	0.896252i	$0.646279\pi$
$18$		0			0
$19$	−4.56995	−	1.22452i	−1.04842	−	0.280923i	−0.306821	−	0.951767i	$-0.599265\pi$
$19$	−4.56995	−	1.22452i	−1.04842	−	0.280923i	−0.741598	+	0.670844i	$0.765932\pi$
$20$		0			0
$21$	5.46668	+	6.62264i	1.19293	+	1.44518i
$22$		0			0
$23$	−2.41576	−	2.41576i	−0.503720	−	0.503720i	0.408872	−	0.912592i	$-0.365922\pi$
$23$	−2.41576	−	2.41576i	−0.503720	−	0.503720i	−0.912592	+	0.408872i	$0.865922\pi$
$24$		0			0
$25$	−2.39648	−	1.38361i	−0.479296	−	0.276721i
$26$		0			0
$27$	4.56151	−	2.48850i	0.877863	−	0.478912i
$28$		0			0
$29$	3.35285	−	3.35285i	0.622608	−	0.622608i	−0.323589	−	0.946198i	$-0.604890\pi$
$29$	3.35285	−	3.35285i	0.622608	−	0.622608i	0.946198	+	0.323589i	$0.104890\pi$
$30$		0			0
$31$	2.96309	+	2.96309i	0.532186	+	0.532186i	0.921222	−	0.389037i	$-0.127192\pi$
$31$	2.96309	+	2.96309i	0.532186	+	0.532186i	−0.389037	+	0.921222i	$0.627192\pi$
$32$		0			0
$33$	−3.28079	+	0.551260i	−0.571112	+	0.0959621i
$34$		0			0
$35$	−13.3469	+	3.57628i	−2.25603	+	0.604502i
$36$		0			0
$37$	−5.71600	−	2.08022i	−0.939705	−	0.341986i
$37$	−5.71600	−	2.08022i	−0.939705	−	0.341986i
$38$		0			0
$39$	2.10343	+	0.201125i	0.336818	+	0.0322057i
$40$		0			0
$41$	2.27871	+	3.94685i	0.355875	+	0.616394i	0.987267	−	0.159070i	$-0.0508494\pi$
$41$	2.27871	+	3.94685i	0.355875	+	0.616394i	−0.631392	+	0.775464i	$0.717516\pi$
$42$		0			0
$43$	3.86120	−	3.86120i	0.588827	−	0.588827i	−0.348486	−	0.937314i	$-0.613304\pi$
$43$	3.86120	−	3.86120i	0.588827	−	0.588827i	0.937314	+	0.348486i	$0.113304\pi$
$44$		0			0
$45$	0.594327	+	8.33977i	0.0885971	+	1.24322i
$46$		0			0
$47$		−	1.47732i		−	0.215489i	−0.994179	−	0.107745i	$-0.965637\pi$
$47$		−	1.47732i		−	0.215489i	0.994179	−	0.107745i	$-0.0343629\pi$
$48$		0			0
$49$	−8.79066	+	15.2259i	−1.25581	+	2.17512i
$50$		0			0
$51$	−8.58050	+	3.91726i	−1.20151	+	0.548525i
$52$		0			0
$53$	11.0443	+	6.37642i	1.51705	+	0.875869i	0.999799	+	0.0200345i	$0.00637760\pi$
$53$	11.0443	+	6.37642i	1.51705	+	0.875869i	0.517250	+	0.855834i	$0.326956\pi$
$54$		0			0
$55$	1.38545	−	5.17059i	0.186815	−	0.697202i
$56$		0			0
$57$	−8.15741	−	0.779992i	−1.08048	−	0.103312i
$58$		0			0
$59$	10.7362	−	2.87675i	1.39773	−	0.374521i	0.520201	−	0.854044i	$-0.325857\pi$
$59$	10.7362	−	2.87675i	1.39773	−	0.374521i	0.877529	+	0.479523i	$0.159190\pi$
$60$		0			0
$61$	2.65045	−	9.89160i	0.339355	−	1.26649i	−0.559715	−	0.828685i	$-0.689090\pi$
$61$	2.65045	−	9.89160i	0.339355	−	1.26649i	0.899070	−	0.437804i	$-0.144244\pi$
$62$		0			0
$63$	11.2384	+	9.74319i	1.41591	+	1.22753i
$64$		0			0
$65$	−1.69999	+	2.94447i	−0.210858	+	0.365216i
$66$		0			0
$67$	8.89621	−	5.13623i	1.08684	−	0.627490i	0.154110	−	0.988054i	$-0.450749\pi$
$67$	8.89621	−	5.13623i	1.08684	−	0.627490i	0.932735	+	0.360564i	$0.117416\pi$
$68$		0			0
$69$	−4.81971	−	3.43303i	−0.580224	−	0.413288i
$70$		0			0
$71$	1.72584	−	0.996416i	0.204820	−	0.118253i	−0.394082	−	0.919075i	$-0.628937\pi$
$71$	1.72584	−	0.996416i	0.204820	−	0.118253i	0.598902	+	0.800823i	$0.295604\pi$
$72$		0			0
$73$		−	0.224313i		−	0.0262539i	−0.999914	−	0.0131269i	$-0.995821\pi$
$73$		−	0.224313i		−	0.0262539i	0.999914	−	0.0131269i	$-0.00417855\pi$
$74$		0			0
$75$	−4.49054	−	1.67554i	−0.518523	−	0.193475i
$76$		0			0
$77$	−4.76141	−	8.24701i	−0.542614	−	0.939834i
$78$		0			0
$79$	7.22868	+	1.93692i	0.813290	+	0.217921i	0.641411	−	0.767197i	$-0.278349\pi$
$79$	7.22868	+	1.93692i	0.813290	+	0.217921i	0.171879	+	0.985118i	$0.445016\pi$
$80$		0			0
$81$	7.07732	−	5.55981i	0.786369	−	0.617757i
$82$		0			0
$83$	13.1112	+	7.56973i	1.43914	+	0.830886i	0.997790	−	0.0664499i	$-0.0211673\pi$
$83$	13.1112	+	7.56973i	1.43914	+	0.830886i	0.441348	+	0.897336i	$0.354501\pi$
$84$		0			0
$85$		−	15.1773i		−	1.64621i
$86$		0			0
$87$	4.76473	−	6.68931i	0.510832	−	0.717170i
$88$		0			0
$89$	−1.85313	−	6.91598i	−0.196432	−	0.733093i	−0.991892	−	0.127087i	$-0.959437\pi$
$89$	−1.85313	−	6.91598i	−0.196432	−	0.733093i	0.795460	−	0.606006i	$-0.207229\pi$
$90$		0			0
$91$	1.56546	+	5.84238i	0.164105	+	0.612448i
$92$		0			0
$93$	5.91169	+	4.21084i	0.613014	+	0.436643i
$94$		0			0
$95$	6.59281	−	11.4191i	0.676408	−	1.17157i
$96$		0			0
$97$	−10.0950	+	10.0950i	−1.02499	+	1.02499i	−0.0253127	+	0.999680i	$0.508058\pi$
$97$	−10.0950	+	10.0950i	−1.02499	+	1.02499i	−0.999680	+	0.0253127i	$0.991942\pi$
$98$		0			0
$99$	−5.44572	+	1.88322i	−0.547315	+	0.189271i
$100$		0			0
$101$	−4.21631			−0.419538			−0.209769	−	0.977751i	$-0.567271\pi$
$101$	−4.21631			−0.419538			−0.209769	+	0.977751i	$0.567271\pi$
$102$		0			0
$103$	9.01132	+	9.01132i	0.887912	+	0.887912i	0.994322	−	0.106411i	$-0.0339358\pi$
$103$	9.01132	+	9.01132i	0.887912	+	0.887912i	−0.106411	+	0.994322i	$0.533936\pi$
$104$		0			0
$105$	−21.7714	+	9.93931i	−2.12467	+	0.969978i
$106$		0			0
$107$	1.97635	−	1.14104i	0.191061	−	0.110309i	−0.401418	−	0.915895i	$-0.631483\pi$
$107$	1.97635	−	1.14104i	0.191061	−	0.110309i	0.592479	+	0.805586i	$0.298149\pi$
$108$		0			0
$109$	3.10557	+	11.5901i	0.297459	+	1.11013i	0.939244	+	0.343249i	$0.111527\pi$
$109$	3.10557	+	11.5901i	0.297459	+	1.11013i	−0.641785	+	0.766885i	$0.721806\pi$
$110$		0			0
$111$	−10.3606	−	1.91270i	−0.983383	−	0.181545i
$112$		0			0
$113$	−2.88305	−	10.7597i	−0.271214	−	1.01218i	−0.958336	−	0.285643i	$-0.907793\pi$
$113$	−2.88305	−	10.7597i	−0.271214	−	1.01218i	0.687122	−	0.726542i	$-0.258874\pi$
$114$		0			0
$115$	8.24577	−	4.76070i	0.768922	−	0.443937i
$116$		0			0
$117$	3.65061	−	0.260158i	0.337499	−	0.0240516i
$118$		0			0
$119$	−19.0919	−	19.0919i	−1.75015	−	1.75015i
$120$		0			0
$121$	−7.31085			−0.664622
$122$		0			0
$123$	5.02506	+	6.08763i	0.453095	+	0.548903i
$124$		0			0
$125$	−4.40012	+	4.40012i	−0.393559	+	0.393559i
$126$		0			0
$127$	6.59143	−	11.4167i	0.584895	−	1.01307i	−0.409994	−	0.912088i	$-0.634469\pi$
$127$	6.59143	−	11.4167i	0.584895	−	1.01307i	0.994889	−	0.100979i	$-0.0321976\pi$
$128$		0			0
$129$	5.48715	−	7.70353i	0.483116	−	0.678258i
$130$		0			0
$131$	−4.07459	−	15.2066i	−0.355999	−	1.32861i	−0.879223	−	0.476410i	$-0.841938\pi$
$131$	−4.07459	−	15.2066i	−0.355999	−	1.32861i	0.523224	−	0.852195i	$-0.324729\pi$
$132$		0			0
$133$	−6.07109	−	22.6576i	−0.526431	−	1.96467i
$134$		0			0
$135$	3.40875	+	14.0746i	0.293378	+	1.21135i
$136$		0			0
$137$			17.3055i			1.47851i	0.673428	+	0.739253i	$0.264821\pi$
$137$			17.3055i			1.47851i	−0.673428	+	0.739253i	$0.735179\pi$
$138$		0			0
$139$	−0.856960	−	0.494766i	−0.0726864	−	0.0419655i	0.463216	−	0.886245i	$-0.346695\pi$
$139$	−0.856960	−	0.494766i	−0.0726864	−	0.0419655i	−0.535903	+	0.844280i	$0.680029\pi$
$140$		0			0
$141$	−0.424002	−	2.52342i	−0.0357074	−	0.212510i
$142$		0			0
$143$	−2.26335	−	0.606462i	−0.189270	−	0.0507149i
$144$		0			0
$145$	6.60741	+	11.4444i	0.548716	+	0.950404i
$146$		0			0
$147$	−10.6454	+	28.5304i	−0.878021	+	2.35315i
$148$		0			0
$149$		−	16.0092i		−	1.31153i	−0.754966	−	0.655764i	$-0.772346\pi$
$149$		−	16.0092i		−	1.31153i	0.754966	−	0.655764i	$-0.227654\pi$
$150$		0			0
$151$	−1.88466	+	1.08811i	−0.153371	+	0.0885488i	−0.574721	−	0.818349i	$-0.694890\pi$
$151$	−1.88466	+	1.08811i	−0.153371	+	0.0885488i	0.421350	+	0.906898i	$0.361556\pi$
$152$		0			0
$153$	−13.5321	+	9.15375i	−1.09401	+	0.740037i
$154$		0			0
$155$	−10.1140	+	5.83931i	−0.812375	+	0.469025i
$156$		0			0
$157$	−10.4581	+	18.1139i	−0.834647	+	1.44565i	0.0596710	+	0.998218i	$0.480995\pi$
$157$	−10.4581	+	18.1139i	−0.834647	+	1.44565i	−0.894318	+	0.447432i	$0.852338\pi$
$158$		0			0
$159$	20.6949	+	7.72181i	1.64121	+	0.612380i
$160$		0			0
$161$	4.38396	−	16.3612i	0.345505	−	1.28944i
$162$		0			0
$163$	−1.03808	+	0.278154i	−0.0813091	+	0.0217867i	−0.299244	−	0.954177i	$-0.596735\pi$
$163$	−1.03808	+	0.278154i	−0.0813091	+	0.0217867i	0.217935	+	0.975963i	$0.430068\pi$
$164$		0			0
$165$	0.882507	−	9.22955i	0.0687030	−	0.718519i
$166$		0			0
$167$	0.724622	−	2.70432i	0.0560729	−	0.209267i	−0.932205	−	0.361930i	$-0.882118\pi$
$167$	0.724622	−	2.70432i	0.0560729	−	0.209267i	0.988278	+	0.152663i	$0.0487848\pi$
$168$		0			0
$169$	−9.96943	−	5.75586i	−0.766880	−	0.442758i
$170$		0			0
$171$	−14.1576	+	1.00893i	−1.08266	+	0.0771548i
$172$		0			0
$173$	−6.83093	+	11.8315i	−0.519346	+	0.899534i	0.480401	+	0.877049i	$0.340491\pi$
$173$	−6.83093	+	11.8315i	−0.519346	+	0.899534i	−0.999747	+	0.0224848i	$0.992842\pi$
$174$		0			0
$175$		−	13.7197i		−	1.03711i
$176$		0			0
$177$	17.5129	−	7.99515i	1.31635	−	0.600953i
$178$		0			0
$179$	−6.71510	+	6.71510i	−0.501910	+	0.501910i	−0.912031	−	0.410121i	$-0.865487\pi$
$179$	−6.71510	+	6.71510i	−0.501910	+	0.501910i	0.410121	+	0.912031i	$0.365487\pi$
$180$		0			0
$181$	7.39113	+	12.8018i	0.549378	+	0.951551i	0.998317	+	0.0579889i	$0.0184688\pi$
$181$	7.39113	+	12.8018i	0.549378	+	0.951551i	−0.448939	+	0.893563i	$0.648198\pi$
$182$		0			0
$183$	1.68828	−	17.6566i	0.124801	−	1.30521i
$184$		0			0
$185$	9.72304	−	13.8870i	0.714852	−	1.02099i
$186$		0			0
$187$	10.1034	−	2.70720i	0.738834	−	0.197970i
$188$		0			0
$189$	21.9928	+	13.4169i	1.59974	+	0.975935i
$190$		0			0
$191$	−9.13195	−	9.13195i	−0.660765	−	0.660765i	0.294796	−	0.955560i	$-0.404748\pi$
$191$	−9.13195	−	9.13195i	−0.660765	−	0.660765i	−0.955560	+	0.294796i	$0.904748\pi$
$192$		0			0
$193$	8.05716	−	8.05716i	0.579967	−	0.579967i	−0.354927	−	0.934894i	$-0.615494\pi$
$193$	8.05716	−	8.05716i	0.579967	−	0.579967i	0.934894	+	0.354927i	$0.115494\pi$
$194$		0			0
$195$	−2.05868	+	5.51737i	−0.147425	+	0.395107i
$196$		0			0
$197$	4.50413	+	2.60046i	0.320906	+	0.185275i	0.651796	−	0.758394i	$-0.274016\pi$
$197$	4.50413	+	2.60046i	0.320906	+	0.185275i	−0.330890	+	0.943669i	$0.607349\pi$
$198$		0			0
$199$	−5.87203	−	5.87203i	−0.416257	−	0.416257i	0.467654	−	0.883911i	$-0.345099\pi$
$199$	−5.87203	−	5.87203i	−0.416257	−	0.416257i	−0.883911	+	0.467654i	$0.845099\pi$
$200$		0			0
$201$	13.7215	−	11.3265i	0.967842	−	0.798910i
$202$		0			0
$203$	22.7078	+	6.08454i	1.59378	+	0.427051i
$204$		0			0
$205$	−12.2686	+	3.28737i	−0.856879	+	0.229600i
$206$		0			0
$207$	−9.21787	−	4.48068i	−0.640686	−	0.311429i
$208$		0			0
$209$	8.77759	+	2.35195i	0.607159	+	0.162688i
$210$		0			0
$211$	−21.9236			−1.50928			−0.754642	−	0.656137i	$-0.772189\pi$
$211$	−21.9236			−1.50928			−0.754642	+	0.656137i	$0.772189\pi$
$212$		0			0
$213$	2.66194	−	2.19731i	0.182393	−	0.150557i
$214$		0			0
$215$	7.60922	+	13.1795i	0.518944	+	0.898838i
$216$		0			0
$217$	−5.37722	+	20.0681i	−0.365030	+	1.36231i
$218$		0			0
$219$	−0.0643795	−	0.383151i	−0.00435037	−	0.0258909i
$220$		0			0
$221$	−6.64361			−0.446898
$222$		0			0
$223$	3.91097			0.261898			0.130949	−	0.991389i	$-0.458198\pi$
$223$	3.91097			0.261898			0.130949	+	0.991389i	$0.458198\pi$
$224$		0			0
$225$	−8.15122	−	1.57318i	−0.543415	−	0.104879i
$226$		0			0
$227$	6.76248	−	25.2379i	0.448841	−	1.67510i	−0.256749	−	0.966478i	$-0.582651\pi$
$227$	6.76248	−	25.2379i	0.448841	−	1.67510i	0.705590	−	0.708620i	$-0.250682\pi$
$228$		0			0
$229$	−3.10369	−	5.37576i	−0.205098	−	0.355240i	0.745066	−	0.666991i	$-0.232418\pi$
$229$	−3.10369	−	5.37576i	−0.205098	−	0.355240i	−0.950164	+	0.311751i	$0.899085\pi$
$230$		0			0
$231$	−10.5000	−	12.7202i	−0.690846	−	0.836928i
$232$		0			0
$233$	1.67385			0.109658			0.0548288	−	0.998496i	$-0.482539\pi$
$233$	1.67385			0.109658			0.0548288	+	0.998496i	$0.482539\pi$
$234$		0			0
$235$	3.97696	+	1.06562i	0.259428	+	0.0695135i
$236$		0			0
$237$	12.9033	+	1.23378i	0.838157	+	0.0801425i
$238$		0			0
$239$	−4.06296	+	1.08867i	−0.262811	+	0.0704199i	−0.387818	−	0.921736i	$-0.626771\pi$
$239$	−4.06296	+	1.08867i	−0.262811	+	0.0704199i	0.125007	+	0.992156i	$0.460105\pi$
$240$		0			0
$241$	−2.89541	−	0.775822i	−0.186510	−	0.0499751i	0.164355	−	0.986401i	$-0.447446\pi$
$241$	−2.89541	−	0.775822i	−0.186510	−	0.0499751i	−0.350865	+	0.936426i	$0.614112\pi$
$242$		0			0
$243$	10.4931	−	11.5280i	0.673134	−	0.739521i
$244$		0			0
$245$	−34.6473	−	34.6473i	−2.21353	−	2.21353i
$246$		0			0
$247$	−4.99853	−	2.88590i	−0.318049	−	0.183626i
$248$		0			0
$249$	24.5678	+	9.16691i	1.55692	+	0.580929i
$250$		0			0
$251$	13.3139	−	13.3139i	0.840366	−	0.840366i	−0.148541	−	0.988906i	$-0.547458\pi$
$251$	13.3139	−	13.3139i	0.840366	−	0.840366i	0.988906	+	0.148541i	$0.0474575\pi$
$252$		0			0
$253$	4.63998	+	4.63998i	0.291713	+	0.291713i
$254$		0			0
$255$	−4.35599	−	25.9244i	−0.272782	−	1.62345i
$256$		0			0
$257$	−16.8305	+	4.50971i	−1.04985	+	0.281308i	−0.742192	−	0.670188i	$-0.766214\pi$
$257$	−16.8305	+	4.50971i	−1.04985	+	0.281308i	−0.307663	+	0.951495i	$0.599547\pi$
$258$		0			0
$259$	−5.23799	−	29.6997i	−0.325473	−	1.84545i
$260$		0			0
$261$	6.21878	−	12.7936i	0.384933	−	0.791902i
$262$		0			0
$263$	−13.9576	−	24.1753i	−0.860662	−	1.49071i	−0.871291	−	0.490766i	$-0.836717\pi$
$263$	−13.9576	−	24.1753i	−0.860662	−	1.49071i	0.0106295	−	0.999944i	$-0.496616\pi$
$264$		0			0
$265$	−25.1319	+	25.1319i	−1.54384	+	1.54384i
$266$		0			0
$267$	−5.15028	−	11.2814i	−0.315192	−	0.690409i
$268$		0			0
$269$		−	19.4076i		−	1.18330i	−0.806194	−	0.591651i	$-0.798476\pi$
$269$		−	19.4076i		−	1.18330i	0.806194	−	0.591651i	$-0.201524\pi$
$270$		0			0
$271$	10.0772	−	17.4542i	0.612147	−	1.06027i	−0.378731	−	0.925507i	$-0.623639\pi$
$271$	10.0772	−	17.4542i	0.612147	−	1.06027i	0.990878	−	0.134763i	$-0.0430273\pi$
$272$		0			0
$273$	4.35078	+	9.53011i	0.263321	+	0.576788i
$274$		0			0
$275$	4.60296	+	2.65752i	0.277569	+	0.160254i
$276$		0			0
$277$	5.55031	−	20.7140i	0.333486	−	1.24458i	−0.572016	−	0.820242i	$-0.693839\pi$
$277$	5.55031	−	20.7140i	0.333486	−	1.24458i	0.905502	−	0.424343i	$-0.139495\pi$
$278$		0			0
$279$	11.3063	+	5.49586i	0.676893	+	0.329028i
$280$		0			0
$281$	−7.00447	+	1.87684i	−0.417852	+	0.111963i	−0.461618	−	0.887079i	$-0.652731\pi$
$281$	−7.00447	+	1.87684i	−0.417852	+	0.111963i	0.0437663	+	0.999042i	$0.486064\pi$
$282$		0			0
$283$	−5.82300	+	21.7317i	−0.346141	+	1.29182i	0.545132	+	0.838350i	$0.316480\pi$
$283$	−5.82300	+	21.7317i	−0.346141	+	1.29182i	−0.891273	+	0.453467i	$0.850187\pi$
$284$		0			0
$285$	7.98386	−	21.3972i	0.472923	−	1.26746i
$286$		0			0
$287$	−11.2978	+	19.5683i	−0.666886	+	1.15508i
$288$		0			0
$289$	10.9609	−	6.32830i	0.644761	−	0.372253i
$290$		0			0
$291$	−14.3460	+	20.1407i	−0.840977	+	1.18067i
$292$		0			0
$293$	9.51177	−	5.49162i	0.555684	−	0.320824i	−0.195728	−	0.980658i	$-0.562707\pi$
$293$	9.51177	−	5.49162i	0.555684	−	0.320824i	0.751411	+	0.659834i	$0.229373\pi$
$294$		0			0
$295$			30.9769i			1.80355i
$296$		0			0
$297$	−8.76137	+	4.77971i	−0.508386	+	0.277347i
$298$		0			0
$299$	−2.08392	−	3.60946i	−0.120516	−	0.208740i
$300$		0			0
$301$	26.1507	+	7.00706i	1.50730	+	0.403880i
$302$		0			0
$303$	−7.20190	+	1.21011i	−0.413738	+	0.0695191i
$304$		0			0
$305$	24.7164	+	14.2700i	1.41526	+	0.817100i
$306$		0			0
$307$			3.91476i			0.223427i	0.993740	+	0.111714i	$0.0356339\pi$
$307$			3.91476i			0.223427i	−0.993740	+	0.111714i	$0.964366\pi$
$308$		0			0
$309$	17.9786	+	12.8060i	1.02277	+	0.728506i
$310$		0			0
$311$	5.82053	+	21.7225i	0.330052	+	1.23177i	0.909135	+	0.416502i	$0.136744\pi$
$311$	5.82053	+	21.7225i	0.330052	+	1.23177i	−0.579083	+	0.815268i	$0.696589\pi$
$312$		0			0
$313$	−3.53236	−	13.1829i	−0.199661	−	0.745144i	−0.991011	−	0.133781i	$-0.957288\pi$
$313$	−3.53236	−	13.1829i	−0.199661	−	0.745144i	0.791350	−	0.611363i	$-0.209379\pi$
$314$		0			0
$315$	−34.3353	+	23.2260i	−1.93457	+	1.30863i
$316$		0			0
$317$	13.5652	−	23.4957i	0.761899	−	1.31965i	−0.179972	−	0.983672i	$-0.557601\pi$
$317$	13.5652	−	23.4957i	0.761899	−	1.31965i	0.941871	−	0.335976i	$-0.109066\pi$
$318$		0			0
$319$	−6.43987	+	6.43987i	−0.360564	+	0.360564i
$320$		0			0
$321$	3.04832	−	2.51625i	0.170141	−	0.140443i
$322$		0			0
$323$	25.7649			1.43360
$324$		0			0
$325$	−2.38710	−	2.38710i	−0.132413	−	0.132413i
$326$		0			0
$327$	8.63109	+	18.9059i	0.477301	+	1.04550i
$328$		0			0
$329$	6.34319	−	3.66224i	0.349711	−	0.201906i
$330$		0			0
$331$	−1.23512	−	4.60953i	−0.0678883	−	0.253362i	0.923639	−	0.383265i	$-0.125200\pi$
$331$	−1.23512	−	4.60953i	−0.0678883	−	0.253362i	−0.991527	+	0.129902i	$0.958534\pi$
$332$		0			0
$333$	−18.2459	−	0.293523i	−0.999871	−	0.0160850i
$334$		0			0
$335$	7.40974	+	27.6535i	0.404838	+	1.51087i
$336$		0			0
$337$	−3.98358	+	2.29992i	−0.216999	+	0.125285i	−0.604560	−	0.796560i	$-0.706651\pi$
$337$	−3.98358	+	2.29992i	−0.216999	+	0.125285i	0.387561	+	0.921844i	$0.373318\pi$
$338$		0			0
$339$	−8.01265	−	17.5512i	−0.435188	−	0.953251i
$340$		0			0
$341$	−5.69125	−	5.69125i	−0.308198	−	0.308198i
$342$		0			0
$343$	−52.4617			−2.83266
$344$		0			0
$345$	12.7183	−	10.4984i	0.684730	−	0.565213i
$346$		0			0
$347$	11.2615	−	11.2615i	0.604549	−	0.604549i	−0.336967	−	0.941516i	$-0.609401\pi$
$347$	11.2615	−	11.2615i	0.604549	−	0.604549i	0.941516	+	0.336967i	$0.109401\pi$
$348$		0			0
$349$	0.445357	−	0.771380i	0.0238394	−	0.0412910i	−0.853860	−	0.520503i	$-0.825744\pi$
$349$	0.445357	−	0.771380i	0.0238394	−	0.0412910i	0.877699	+	0.479212i	$0.159078\pi$
$350$		0			0
$351$	6.16095	−	1.49213i	0.328847	−	0.0796439i
$352$		0			0
$353$	4.73922	+	17.6870i	0.252243	+	0.941385i	0.969603	+	0.244682i	$0.0786837\pi$
$353$	4.73922	+	17.6870i	0.252243	+	0.941385i	−0.717360	+	0.696703i	$0.754650\pi$
$354$		0			0
$355$	1.43747	+	5.36472i	0.0762931	+	0.284730i
$356$		0			0
$357$	−38.0904	−	27.1314i	−2.01596	−	1.43595i
$358$		0			0
$359$			17.9479i			0.947253i	0.880726	+	0.473626i	$0.157055\pi$
$359$			17.9479i			0.947253i	−0.880726	+	0.473626i	$0.842945\pi$
$360$		0			0
$361$	2.93057	+	1.69196i	0.154240	+	0.0890507i
$362$		0			0
$363$	−12.4877	+	2.09827i	−0.655434	+	0.110130i
$364$		0			0
$365$	0.603853	+	0.161802i	0.0316071	+	0.00846910i
$366$		0			0
$367$	−2.58182	−	4.47184i	−0.134770	−	0.233428i	0.790740	−	0.612152i	$-0.209696\pi$
$367$	−2.58182	−	4.47184i	−0.134770	−	0.233428i	−0.925509	+	0.378725i	$0.876363\pi$
$368$		0			0
$369$	10.3305	+	8.95609i	0.537786	+	0.466235i
$370$		0			0
$371$			63.2280i			3.28264i
$372$		0			0
$373$	18.9668	−	10.9505i	0.982064	−	0.566995i	0.0791714	−	0.996861i	$-0.474773\pi$
$373$	18.9668	−	10.9505i	0.982064	−	0.566995i	0.902893	+	0.429866i	$0.141439\pi$
$374$		0			0
$375$	−6.25301	+	8.77874i	−0.322904	+	0.453332i
$376$		0			0
$377$	5.00960	−	2.89229i	0.258008	−	0.148961i
$378$		0			0
$379$	7.76446	−	13.4484i	0.398834	−	0.690800i	−0.594749	−	0.803912i	$-0.702748\pi$
$379$	7.76446	−	13.4484i	0.398834	−	0.690800i	0.993582	+	0.113112i	$0.0360818\pi$
$380$		0			0
$381$	7.98219	−	21.3927i	0.408940	−	1.09598i
$382$		0			0
$383$	−0.679403	+	2.53557i	−0.0347159	+	0.129561i	−0.981109	−	0.193456i	$-0.938030\pi$
$383$	−0.679403	+	2.53557i	−0.0347159	+	0.129561i	0.946393	+	0.323017i	$0.104697\pi$
$384$		0			0
$385$	25.6355	−	6.86902i	1.30651	−	0.350078i
$386$		0			0
$387$	7.16166	−	14.7333i	0.364047	−	0.748936i
$388$		0			0
$389$	−3.54108	+	13.2155i	−0.179540	+	0.670052i	0.816194	+	0.577778i	$0.196080\pi$
$389$	−3.54108	+	13.2155i	−0.179540	+	0.670052i	−0.995734	+	0.0922739i	$0.970586\pi$
$390$		0			0
$391$	16.1124	+	9.30248i	0.814837	+	0.470447i
$392$		0			0
$393$	−11.3242	−	24.8050i	−0.571232	−	1.25125i
$394$		0			0
$395$	−10.4284	+	18.0625i	−0.524710	+	0.908825i
$396$		0			0
$397$		−	7.72923i		−	0.387919i	−0.981010	−	0.193959i	$-0.937867\pi$
$397$		−	7.72923i		−	0.387919i	0.981010	−	0.193959i	$-0.0621330\pi$
$398$		0			0
$399$	−16.8730	−	36.9592i	−0.844706	−	1.85027i
$400$		0			0
$401$	−27.9698	+	27.9698i	−1.39675	+	1.39675i	−0.587579	+	0.809167i	$0.699919\pi$
$401$	−27.9698	+	27.9698i	−1.39675	+	1.39675i	−0.809167	+	0.587579i	$0.800081\pi$
$402$		0			0
$403$	2.55607	+	4.42724i	0.127327	+	0.220537i
$404$		0			0
$405$	9.86203	+	23.0626i	0.490048	+	1.14599i
$406$		0			0
$407$	10.9788	+	3.99551i	0.544200	+	0.198050i
$408$		0			0
$409$	−21.1464	+	5.66616i	−1.04562	+	0.280174i	−0.740441	−	0.672121i	$-0.765384\pi$
$409$	−21.1464	+	5.66616i	−1.04562	+	0.280174i	−0.305181	+	0.952294i	$0.598717\pi$
$410$		0			0
$411$	4.96680	+	29.5596i	0.244994	+	1.45807i
$412$		0			0
$413$	38.9667	+	38.9667i	1.91742	+	1.91742i
$414$		0			0
$415$	−29.8352	+	29.8352i	−1.46455	+	1.46455i
$416$		0			0
$417$	−1.60578	−	0.599159i	−0.0786354	−	0.0293410i
$418$		0			0
$419$	−22.0009	−	12.7022i	−1.07482	−	0.620545i	−0.145323	−	0.989384i	$-0.546422\pi$
$419$	−22.0009	−	12.7022i	−1.07482	−	0.620545i	−0.929493	+	0.368839i	$0.879755\pi$
$420$		0			0
$421$	−9.68216	−	9.68216i	−0.471880	−	0.471880i	0.430643	−	0.902522i	$-0.358287\pi$
$421$	−9.68216	−	9.68216i	−0.471880	−	0.471880i	−0.902522	+	0.430643i	$0.858287\pi$
$422$		0			0
$423$	−1.44848	−	4.18857i	−0.0704275	−	0.203655i
$424$		0			0
$425$	14.5562	+	3.90032i	0.706078	+	0.189193i
$426$		0			0
$427$	49.0421	−	13.1408i	2.37331	−	0.635927i
$428$		0			0
$429$	−4.04009	−	0.386304i	−0.195058	−	0.0186509i
$430$		0			0
$431$	17.7983	+	4.76904i	0.857313	+	0.229716i	0.660594	−	0.750743i	$-0.270305\pi$
$431$	17.7983	+	4.76904i	0.857313	+	0.229716i	0.196719	+	0.980460i	$0.436971\pi$
$432$		0			0
$433$	6.48199			0.311504			0.155752	−	0.987796i	$-0.450220\pi$
$433$	6.48199			0.311504			0.155752	+	0.987796i	$0.450220\pi$
$434$		0			0
$435$	14.5708	+	17.6518i	0.698616	+	0.846341i
$436$		0			0
$437$	8.08176	+	13.9980i	0.386603	+	0.669616i
$438$		0			0
$439$	−2.19803	+	8.20317i	−0.104906	+	0.391516i	−0.998335	−	0.0576903i	$-0.981626\pi$
$439$	−2.19803	+	8.20317i	−0.104906	+	0.391516i	0.893428	+	0.449206i	$0.148293\pi$
$440$		0			0
$441$	−9.99511	+	51.7882i	−0.475958	+	2.46611i
$442$		0			0
$443$	−28.3775			−1.34826			−0.674128	−	0.738614i	$-0.735480\pi$
$443$	−28.3775			−1.34826			−0.674128	+	0.738614i	$0.735480\pi$
$444$		0			0
$445$	19.9546			0.945938
$446$		0			0
$447$	−4.59477	−	27.3455i	−0.217325	−	1.29340i
$448$		0			0
$449$	0.210024	−	0.783819i	0.00991163	−	0.0369907i	−0.960793	−	0.277267i	$-0.910571\pi$
$449$	0.210024	−	0.783819i	0.00991163	−	0.0369907i	0.970705	+	0.240276i	$0.0772380\pi$
$450$		0			0
$451$	−4.37677	−	7.58078i	−0.206094	−	0.356965i
$452$		0			0
$453$	−2.90690	+	2.39951i	−0.136578	+	0.112739i
$454$		0			0
$455$	−16.8569			−0.790266
$456$		0			0
$457$	−10.8225	−	2.89987i	−0.506254	−	0.135650i	−0.00335304	−	0.999994i	$-0.501067\pi$
$457$	−10.8225	−	2.89987i	−0.506254	−	0.135650i	−0.502901	+	0.864344i	$0.667734\pi$
$458$		0			0
$459$	−20.4871	+	19.5194i	−0.956256	+	0.911088i
$460$		0			0
$461$	−22.8495	+	6.12250i	−1.06421	+	0.285153i	−0.748111	−	0.663574i	$-0.769039\pi$
$461$	−22.8495	+	6.12250i	−1.06421	+	0.285153i	−0.316096	+	0.948727i	$0.602372\pi$
$462$		0			0
$463$	31.0582	+	8.32201i	1.44340	+	0.386757i	0.893721	−	0.448623i	$-0.148085\pi$
$463$	31.0582	+	8.32201i	1.44340	+	0.386757i	0.549674	+	0.835379i	$0.314752\pi$
$464$		0			0
$465$	−15.5998	+	12.8770i	−0.723425	+	0.597155i
$466$		0			0
$467$	−8.15245	−	8.15245i	−0.377250	−	0.377250i	0.492859	−	0.870109i	$-0.335952\pi$
$467$	−8.15245	−	8.15245i	−0.377250	−	0.377250i	−0.870109	+	0.492859i	$0.835952\pi$
$468$		0			0
$469$	44.1070	+	25.4652i	2.03667	+	1.17587i
$470$		0			0
$471$	−12.6647	+	33.9421i	−0.583558	+	1.56397i
$472$		0			0
$473$	−7.41627	+	7.41627i	−0.341001	+	0.341001i
$474$		0			0
$475$	9.25755	+	9.25755i	0.424765	+	0.424765i
$476$		0			0
$477$	37.5653	+	7.25009i	1.72000	+	0.331959i
$478$		0			0
$479$	9.95114	−	2.66640i	0.454679	−	0.121831i	−0.0242087	−	0.999707i	$-0.507707\pi$
$479$	9.95114	−	2.66640i	0.454679	−	0.121831i	0.478888	+	0.877876i	$0.341040\pi$
$480$		0			0
$481$	−6.07883	−	4.25611i	−0.277171	−	0.194062i
$482$		0			0
$483$	2.79249	−	29.2048i	0.127063	−	1.32887i
$484$		0			0
$485$	−19.8941	−	34.4576i	−0.903344	−	1.56464i
$486$		0			0
$487$	−21.5256	+	21.5256i	−0.975417	+	0.975417i	−0.999705	−	0.0242876i	$-0.992268\pi$
$487$	−21.5256	+	21.5256i	−0.975417	+	0.975417i	0.0242876	+	0.999705i	$0.492268\pi$
$488$		0			0
$489$	−1.69333	+	0.773054i	−0.0765749	+	0.0349587i
$490$		0			0
$491$			20.8288i			0.939991i	0.882669	+	0.469996i	$0.155745\pi$
$491$			20.8288i			0.939991i	−0.882669	+	0.469996i	$0.844255\pi$
$492$		0			0
$493$	−12.9110	+	22.3625i	−0.581482	+	1.00716i
$494$		0			0
$495$	−1.14153	−	16.0183i	−0.0513082	−	0.719971i
$496$		0			0
$497$	8.55665	+	4.94018i	0.383818	+	0.221598i
$498$		0			0
$499$	11.4490	−	42.7281i	0.512526	−	1.91277i	0.120851	−	0.992671i	$-0.461438\pi$
$499$	11.4490	−	42.7281i	0.512526	−	1.91277i	0.391676	−	0.920103i	$-0.371896\pi$
$500$		0			0
$501$	0.461569	−	4.82725i	0.0206214	−	0.215665i
$502$		0			0
$503$	6.23253	−	1.67000i	0.277895	−	0.0744617i	−0.117180	−	0.993111i	$-0.537385\pi$
$503$	6.23253	−	1.67000i	0.277895	−	0.0744617i	0.395075	+	0.918649i	$0.370719\pi$
$504$		0			0
$505$	3.04131	−	11.3503i	0.135337	−	0.505083i
$506$		0			0
$507$	−18.6808	−	6.97031i	−0.829645	−	0.309562i
$508$		0			0
$509$	−8.31526	+	14.4025i	−0.368568	+	0.638378i	−0.989342	−	0.145612i	$-0.953485\pi$
$509$	−8.31526	+	14.4025i	−0.368568	+	0.638378i	0.620774	+	0.783989i	$0.286818\pi$
$510$		0			0
$511$	0.963136	−	0.556067i	0.0426066	−	0.0245990i
$512$		0			0
$513$	−23.8931	+	5.78669i	−1.05491	+	0.255489i
$514$		0			0
$515$	−30.7586	+	17.7585i	−1.35539	+	0.782532i
$516$		0			0
$517$			2.83751i			0.124794i
$518$		0			0
$519$	−8.27222	+	22.1700i	−0.363110	+	0.973156i
$520$		0			0
$521$	16.0261	+	27.7580i	0.702116	+	1.21610i	0.967722	+	0.252020i	$0.0810947\pi$
$521$	16.0261	+	27.7580i	0.702116	+	1.21610i	−0.265606	+	0.964082i	$0.585572\pi$
$522$		0			0
$523$	−13.7697	−	3.68958i	−0.602107	−	0.161334i	−0.0551262	−	0.998479i	$-0.517556\pi$
$523$	−13.7697	−	3.68958i	−0.602107	−	0.161334i	−0.546980	+	0.837145i	$0.684223\pi$
$524$		0			0
$525$	−3.93766	−	23.4347i	−0.171854	−	1.02278i
$526$		0			0
$527$	−19.7629	−	11.4101i	−0.860885	−	0.497032i
$528$		0			0
$529$		−	11.3283i		−	0.492533i
$530$		0			0
$531$	27.6192	−	18.6829i	1.19857	−	0.810769i
$532$		0			0
$533$	1.43900	+	5.37041i	0.0623299	+	0.232618i
$534$		0			0
$535$	1.64612	+	6.14340i	0.0711679	+	0.265602i
$536$		0			0
$537$	−9.54282	+	13.3974i	−0.411803	+	0.578140i
$538$		0			0
$539$	16.8844	−	29.2446i	0.727261	−	1.25965i
$540$		0			0
$541$	21.3040	−	21.3040i	0.915930	−	0.915930i	−0.0808004	−	0.996730i	$-0.525748\pi$
$541$	21.3040	−	21.3040i	0.915930	−	0.915930i	0.996730	+	0.0808004i	$0.0257476\pi$
$542$		0			0
$543$	16.2991	+	19.7455i	0.699459	+	0.847363i
$544$		0			0
$545$	−33.4409			−1.43245
$546$		0			0
$547$	3.39928	+	3.39928i	0.145343	+	0.145343i	0.776034	−	0.630691i	$-0.217229\pi$
$547$	3.39928	+	3.39928i	0.145343	+	0.145343i	−0.630691	+	0.776034i	$0.717229\pi$
$548$		0			0
$549$	−2.18381	−	30.6439i	−0.0932029	−	1.30785i
$550$		0			0
$551$	−19.4280	+	11.2167i	−0.827660	+	0.477850i
$552$		0			0
$553$	9.60316	+	35.8395i	0.408368	+	1.52405i
$554$		0			0
$555$	12.6223	−	26.5111i	0.535787	−	1.12533i
$556$		0			0
$557$	9.75975	+	36.4239i	0.413534	+	1.54333i	0.787754	+	0.615990i	$0.211244\pi$
$557$	9.75975	+	36.4239i	0.413534	+	1.54333i	−0.374220	+	0.927340i	$0.622089\pi$
$558$		0			0
$559$	5.76915	−	3.33082i	0.244009	−	0.140879i
$560$		0			0
$561$	16.4807	−	7.52394i	0.695816	−	0.317661i
$562$		0			0
$563$	−18.6142	−	18.6142i	−0.784496	−	0.784496i	0.196090	−	0.980586i	$-0.437175\pi$
$563$	−18.6142	−	18.6142i	−0.784496	−	0.784496i	−0.980586	+	0.196090i	$0.937175\pi$
$564$		0			0
$565$	31.0447			1.30606
$566$		0			0
$567$	41.4168	+	16.6054i	1.73934	+	0.697360i
$568$		0			0
$569$	19.4214	−	19.4214i	0.814189	−	0.814189i	−0.171070	−	0.985259i	$-0.554722\pi$
$569$	19.4214	−	19.4214i	0.814189	−	0.814189i	0.985259	+	0.171070i	$0.0547224\pi$
$570$		0			0
$571$	−1.66614	+	2.88583i	−0.0697256	+	0.120768i	−0.898780	−	0.438399i	$-0.855546\pi$
$571$	−1.66614	+	2.88583i	−0.0697256	+	0.120768i	0.829055	+	0.559167i	$0.188879\pi$
$572$		0			0
$573$	−18.2193	−	12.9774i	−0.761121	−	0.542139i
$574$		0			0
$575$	2.44685	+	9.13176i	0.102041	+	0.380821i
$576$		0			0
$577$	−7.79900	−	29.1063i	−0.324677	−	1.21171i	−0.914637	−	0.404277i	$-0.867523\pi$
$577$	−7.79900	−	29.1063i	−0.324677	−	1.21171i	0.589960	−	0.807432i	$-0.299143\pi$
$578$		0			0
$579$	11.4500	−	16.0750i	0.475847	−	0.668052i
$580$		0			0
$581$			75.0608i			3.11405i
$582$		0			0
$583$	−21.2129	−	12.2473i	−0.878551	−	0.507231i
$584$		0			0
$585$	−1.93291	+	10.0151i	−0.0799161	+	0.414074i
$586$		0			0
$587$	5.28887	+	1.41715i	0.218295	+	0.0584919i	0.366309	−	0.930493i	$-0.380621\pi$
$587$	5.28887	+	1.41715i	0.218295	+	0.0584919i	−0.148014	+	0.988985i	$0.547288\pi$
$588$		0			0
$589$	−9.91282	−	17.1695i	−0.408451	−	0.707457i
$590$		0			0
$591$	8.43988	+	3.14914i	0.347170	+	0.129538i
$592$		0			0
$593$		−	20.3806i		−	0.836931i	−0.908233	−	0.418465i	$-0.862568\pi$
$593$		−	20.3806i		−	0.836931i	0.908233	−	0.418465i	$-0.137432\pi$
$594$		0			0
$595$	65.1668	−	37.6241i	2.67158	−	1.54244i
$596$		0			0
$597$	−11.7154	−	8.34473i	−0.479478	−	0.341527i
$598$		0			0
$599$	17.5372	−	10.1251i	0.716551	−	0.413701i	−0.0969307	−	0.995291i	$-0.530903\pi$
$599$	17.5372	−	10.1251i	0.716551	−	0.413701i	0.813482	+	0.581590i	$0.197569\pi$
$600$		0			0
$601$	−14.6260	+	25.3330i	−0.596607	+	1.03335i	0.396711	+	0.917943i	$0.370151\pi$
$601$	−14.6260	+	25.3330i	−0.596607	+	1.03335i	−0.993318	+	0.115410i	$0.963182\pi$
$602$		0			0
$603$	20.1870	−	23.2850i	0.822080	−	0.948240i
$604$		0			0
$605$	5.27347	−	19.6809i	0.214397	−	0.800141i
$606$		0			0
$607$	−13.3809	+	3.58539i	−0.543112	+	0.145527i	−0.519937	−	0.854205i	$-0.674044\pi$
$607$	−13.3809	+	3.58539i	−0.543112	+	0.145527i	−0.0231758	+	0.999731i	$0.507378\pi$
$608$		0			0
$609$	40.5336	+	3.87573i	1.64251	+	0.157052i
$610$		0			0
$611$	0.466460	−	1.74085i	0.0188709	−	0.0704273i
$612$		0			0
$613$	2.69388	+	1.55531i	0.108805	+	0.0628184i	0.553415	−	0.832906i	$-0.313324\pi$
$613$	2.69388	+	1.55531i	0.108805	+	0.0628184i	−0.444610	+	0.895724i	$0.646658\pi$
$614$		0			0
$615$	−20.0126	+	9.13637i	−0.806987	+	0.368414i
$616$		0			0
$617$	−0.533514	+	0.924073i	−0.0214785	+	0.0372018i	−0.876565	−	0.481284i	$-0.840171\pi$
$617$	−0.533514	+	0.924073i	−0.0214785	+	0.0372018i	0.855086	+	0.518486i	$0.173504\pi$
$618$		0			0
$619$			17.7026i			0.711528i	0.934576	+	0.355764i	$0.115779\pi$
$619$			17.7026i			0.711528i	−0.934576	+	0.355764i	$0.884221\pi$
$620$		0			0
$621$	−17.0311	−	5.00788i	−0.683434	−	0.200959i
$622$		0			0
$623$	25.1014	−	25.1014i	1.00567	−	1.00567i
$624$		0			0
$625$	−15.5893	−	27.0015i	−0.623572	−	1.08006i
$626$		0			0
$627$	15.6681	+	1.49814i	0.625723	+	0.0598301i
$628$		0			0
$629$	32.9995	+	2.88586i	1.31578	+	0.115067i
$630$		0			0
$631$	14.8571	−	3.98096i	0.591453	−	0.158479i	0.0493357	−	0.998782i	$-0.484290\pi$
$631$	14.8571	−	3.98096i	0.591453	−	0.158479i	0.542117	+	0.840303i	$0.317623\pi$
$632$		0			0
$633$	−37.4479	+	6.29224i	−1.48842	+	0.250094i
$634$		0			0
$635$	25.9793	+	25.9793i	1.03096	+	1.03096i
$636$		0			0
$637$	−15.1663	+	15.1663i	−0.600911	+	0.600911i
$638$		0			0
$639$	3.91624	−	4.51724i	0.154924	−	0.178699i
$640$		0			0
$641$	−18.8919	−	10.9072i	−0.746184	−	0.430809i	0.0781297	−	0.996943i	$-0.475105\pi$
$641$	−18.8919	−	10.9072i	−0.746184	−	0.430809i	−0.824313	+	0.566134i	$0.808439\pi$
$642$		0			0
$643$	−15.0996	−	15.0996i	−0.595471	−	0.595471i	0.343633	−	0.939104i	$-0.388342\pi$
$643$	−15.0996	−	15.0996i	−0.595471	−	0.595471i	−0.939104	+	0.343633i	$0.888342\pi$
$644$		0			0
$645$	16.7800	+	20.3282i	0.660711	+	0.800421i
$646$		0			0
$647$	−6.67640	−	1.78894i	−0.262476	−	0.0703303i	0.125181	−	0.992134i	$-0.460049\pi$
$647$	−6.67640	−	1.78894i	−0.262476	−	0.0703303i	−0.387657	+	0.921804i	$0.626716\pi$
$648$		0			0
$649$	−20.6212	+	5.52542i	−0.809451	+	0.216892i
$650$		0			0
$651$	−3.42518	+	35.8217i	−0.134243	+	1.40396i
$652$		0			0
$653$	−39.5401	−	10.5947i	−1.54732	−	0.414604i	−0.618699	−	0.785628i	$-0.712340\pi$
$653$	−39.5401	−	10.5947i	−1.54732	−	0.414604i	−0.928623	+	0.371024i	$0.879007\pi$
$654$		0			0
$655$	43.8753			1.71435
$656$		0			0
$657$	−0.219934	−	0.635984i	−0.00858045	−	0.0248121i
$658$		0			0
$659$	−17.4226	−	30.1768i	−0.678687	−	1.17552i	−0.975377	−	0.220546i	$-0.929216\pi$
$659$	−17.4226	−	30.1768i	−0.678687	−	1.17552i	0.296690	−	0.954974i	$-0.404117\pi$
$660$		0			0
$661$	−2.52526	+	9.42439i	−0.0982212	+	0.366566i	−0.997488	−	0.0708338i	$-0.977434\pi$
$661$	−2.52526	+	9.42439i	−0.0982212	+	0.366566i	0.899267	+	0.437400i	$0.144101\pi$
$662$		0			0
$663$	−11.3480	+	1.90677i	−0.440720	+	0.0740527i
$664$		0			0
$665$	65.3737			2.53508
$666$		0			0
$667$	−16.1993			−0.627240
$668$		0			0
$669$	6.68036	−	1.12248i	0.258278	−	0.0433975i
$670$		0			0
$671$	−5.09076	+	18.9990i	−0.196526	+	0.733447i
$672$		0			0
$673$	−19.6955	−	34.1137i	−0.759207	−	1.31499i	−0.943255	−	0.332068i	$-0.892254\pi$
$673$	−19.6955	−	34.1137i	−0.759207	−	1.31499i	0.184048	−	0.982917i	$-0.441080\pi$
$674$		0			0
$675$	−14.3747	−	0.347701i	−0.553281	−	0.0133830i
$676$		0			0
$677$	3.38167			0.129968			0.0649841	−	0.997886i	$-0.479300\pi$
$677$	3.38167			0.129968			0.0649841	+	0.997886i	$0.479300\pi$
$678$		0			0
$679$	−68.3703	−	18.3198i	−2.62381	−	0.703049i
$680$		0			0
$681$	4.30756	−	45.0499i	0.165066	−	1.72632i
$682$		0			0
$683$	24.3154	−	6.51529i	0.930402	−	0.249301i	0.238376	−	0.971173i	$-0.423385\pi$
$683$	24.3154	−	6.51529i	0.930402	−	0.249301i	0.692026	+	0.721872i	$0.256718\pi$
$684$		0			0
$685$	−46.5865	−	12.4828i	−1.77998	−	0.476944i
$686$		0			0
$687$	−6.84432	−	8.29158i	−0.261127	−	0.316343i
$688$		0			0
$689$	11.0011	+	11.0011i	0.419108	+	0.419108i
$690$		0			0
$691$	−34.4374	−	19.8824i	−1.31006	−	0.756364i	−0.327954	−	0.944694i	$-0.606359\pi$
$691$	−34.4374	−	19.8824i	−1.31006	−	0.756364i	−0.982106	+	0.188330i	$0.939693\pi$
$692$		0			0
$693$	−21.5858	−	18.7139i	−0.819978	−	0.710882i
$694$		0			0
$695$	1.95006	−	1.95006i	0.0739699	−	0.0739699i
$696$		0			0
$697$	−17.5495	−	17.5495i	−0.664736	−	0.664736i
$698$		0			0
$699$	2.85911	−	0.480407i	0.108142	−	0.0181707i
$700$		0			0
$701$	−23.5982	+	6.32311i	−0.891290	+	0.238821i	−0.675272	−	0.737569i	$-0.735974\pi$
$701$	−23.5982	+	6.32311i	−0.891290	+	0.238821i	−0.216018	+	0.976389i	$0.569307\pi$
$702$		0			0
$703$	23.5746	+	16.5058i	0.889134	+	0.622529i
$704$		0			0
$705$	7.09890	+	0.678780i	0.267360	+	0.0255643i
$706$		0			0
$707$	−10.4521	−	18.1036i	−0.393093	−	0.680857i
$708$		0			0
$709$	8.52427	−	8.52427i	0.320135	−	0.320135i	−0.528684	−	0.848819i	$-0.677314\pi$
$709$	8.52427	−	8.52427i	0.320135	−	0.320135i	0.848819	+	0.528684i	$0.177314\pi$
$710$		0			0
$711$	22.3943	−	1.59591i	0.839850	−	0.0598513i
$712$		0			0
$713$		−	14.3162i		−	0.536145i
$714$		0			0
$715$	3.26520	−	5.65549i	0.122112	−	0.211503i
$716$		0			0
$717$	−6.62751	+	3.02566i	−0.247509	+	0.112995i
$718$		0			0
$719$	33.6559	+	19.4313i	1.25515	+	0.724664i	0.972129	−	0.234448i	$-0.0753283\pi$
$719$	33.6559	+	19.4313i	1.25515	+	0.724664i	0.283026	+	0.959112i	$0.408662\pi$
$720$		0			0
$721$	−16.3532	+	61.0309i	−0.609024	+	2.27291i
$722$		0			0
$723$	−5.16833	−	0.494183i	−0.192212	−	0.0183789i
$724$		0			0
$725$	−12.6741	+	3.39600i	−0.470702	+	0.126124i
$726$		0			0
$727$	−11.5281	+	43.0234i	−0.427553	+	1.59565i	0.330732	+	0.943725i	$0.392704\pi$
$727$	−11.5281	+	43.0234i	−0.427553	+	1.59565i	−0.758285	+	0.651923i	$0.773962\pi$
$728$		0			0
$729$	14.6147	−	22.7026i	0.541286	−	0.840838i
$730$		0			0
$731$	−14.8685	+	25.7530i	−0.549932	+	0.952511i
$732$		0			0
$733$	12.0889	−	6.97954i	0.446514	−	0.257795i	−0.259843	−	0.965651i	$-0.583671\pi$
$733$	12.0889	−	6.97954i	0.446514	−	0.257795i	0.706357	+	0.707856i	$0.250337\pi$
$734$		0			0
$735$	−69.1252	−	49.2372i	−2.54972	−	1.81614i
$736$		0			0
$737$	−17.0871	+	9.86524i	−0.629411	+	0.363391i
$738$		0			0
$739$		−	29.7117i		−	1.09296i	−0.837471	−	0.546482i	$-0.815967\pi$
$739$		−	29.7117i		−	1.09296i	0.837471	−	0.546482i	$-0.184033\pi$
$740$		0			0
$741$	−9.36630	−	3.49481i	−0.344080	−	0.128385i
$742$		0			0
$743$	18.0722	+	31.3020i	0.663005	+	1.14836i	0.979822	+	0.199872i	$0.0640526\pi$
$743$	18.0722	+	31.3020i	0.663005	+	1.14836i	−0.316817	+	0.948487i	$0.602614\pi$
$744$		0			0
$745$	43.0970	+	11.5478i	1.57895	+	0.423079i
$746$		0			0
$747$	44.5954	+	8.60690i	1.63166	+	0.314910i
$748$		0			0
$749$	9.79863	+	5.65724i	0.358034	+	0.206711i
$750$		0			0
$751$			42.5201i			1.55158i	0.630992	+	0.775789i	$0.282648\pi$
$751$			42.5201i			1.55158i	−0.630992	+	0.775789i	$0.717352\pi$
$752$		0			0
$753$	18.9204	−	26.5627i	0.689496	−	0.968000i
$754$		0			0
$755$	−1.56975	−	5.85838i	−0.0571290	−	0.213208i
$756$		0			0
$757$	9.47819	+	35.3731i	0.344491	+	1.28566i	0.893206	+	0.449648i	$0.148451\pi$
$757$	9.47819	+	35.3731i	0.344491	+	1.28566i	−0.548715	+	0.836009i	$0.684883\pi$
$758$		0			0
$759$	9.25729	+	6.59387i	0.336018	+	0.239342i
$760$		0			0
$761$	−24.7152	+	42.8080i	−0.895926	+	1.55179i	−0.0632720	+	0.997996i	$0.520154\pi$
$761$	−24.7152	+	42.8080i	−0.895926	+	1.55179i	−0.832654	+	0.553793i	$0.813180\pi$
$762$		0			0
$763$	−42.0661	+	42.0661i	−1.52290	+	1.52290i
$764$		0			0
$765$	−14.8810	−	43.0314i	−0.538023	−	1.55580i
$766$		0			0
$767$	13.5597			0.489612
$768$		0			0
$769$	8.24607	+	8.24607i	0.297361	+	0.297361i	0.839979	−	0.542619i	$-0.182567\pi$
$769$	8.24607	+	8.24607i	0.297361	+	0.297361i	−0.542619	+	0.839979i	$0.682567\pi$
$770$		0			0
$771$	−27.4539	+	12.5335i	−0.988727	+	0.451384i
$772$		0			0
$773$	16.8847	−	9.74840i	0.607301	−	0.350626i	−0.164607	−	0.986359i	$-0.552636\pi$
$773$	16.8847	−	9.74840i	0.607301	−	0.350626i	0.771908	+	0.635734i	$0.219302\pi$
$774$		0			0
$775$	−3.00122	−	11.2007i	−0.107807	−	0.402342i
$776$		0			0
$777$	−17.4711	−	49.2269i	−0.626771	−	1.76601i
$778$		0			0
$779$	−5.58064	−	20.8272i	−0.199947	−	0.746214i
$780$		0			0
$781$	−3.31486	+	1.91383i	−0.118615	+	0.0684823i
$782$		0			0
$783$	6.95048	−	23.6376i	0.248390	−	0.844739i
$784$		0			0
$785$	−41.2193	−	41.2193i	−1.47118	−	1.47118i
$786$		0			0
$787$	−16.6388			−0.593109			−0.296555	−	0.955016i	$-0.595838\pi$
$787$	−16.6388			−0.593109			−0.296555	+	0.955016i	$0.595838\pi$
$788$		0			0
$789$	−30.7795	−	37.2880i	−1.09578	−	1.32749i
$790$		0			0
$791$	39.0520	−	39.0520i	1.38853	−	1.38853i
$792$		0			0
$793$	6.24649	−	10.8192i	0.221819	−	0.384203i
$794$		0			0
$795$	−35.7149	+	50.1409i	−1.26668	+	1.77832i
$796$		0			0
$797$	−0.986720	−	3.68249i	−0.0349514	−	0.130440i	0.946246	−	0.323449i	$-0.104842\pi$
$797$	−0.986720	−	3.68249i	−0.0349514	−	0.130440i	−0.981197	+	0.193008i	$0.938176\pi$
$798$		0			0
$799$	2.08224	+	7.77104i	0.0736644	+	0.274919i
$800$		0			0
$801$	−12.0351	−	17.7916i	−0.425238	−	0.628636i
$802$		0			0
$803$			0.430842i			0.0152041i
$804$		0			0
$805$	40.8822	+	23.6033i	1.44091	+	0.831908i
$806$		0			0
$807$	−5.57013	−	33.1502i	−0.196078	−	1.16694i
$808$		0			0
$809$	4.24758	+	1.13813i	0.149337	+	0.0400147i	0.332713	−	0.943028i	$-0.392036\pi$
$809$	4.24758	+	1.13813i	0.149337	+	0.0400147i	−0.183376	+	0.983043i	$0.558703\pi$
$810$		0			0
$811$	13.0119	+	22.5373i	0.456910	+	0.791392i	0.998796	−	0.0490605i	$-0.0156227\pi$
$811$	13.0119	+	22.5373i	0.456910	+	0.791392i	−0.541886	+	0.840452i	$0.682289\pi$
$812$		0			0
$813$	12.2034	−	32.7059i	0.427994	−	1.14705i
$814$		0			0
$815$		−	2.99517i		−	0.104916i
$816$		0			0
$817$	−22.3736	+	12.9174i	−0.782753	+	0.451923i
$818$		0			0
$819$	10.1668	+	15.0297i	0.355257	+	0.525181i
$820$		0			0
$821$	44.2394	−	25.5416i	1.54397	−	0.891409i	0.545383	−	0.838187i	$-0.316384\pi$
$821$	44.2394	−	25.5416i	1.54397	−	0.891409i	0.998583	−	0.0532217i	$-0.0169490\pi$
$822$		0			0
$823$	16.0862	−	27.8622i	0.560731	−	0.971214i	−0.436702	−	0.899606i	$-0.643854\pi$
$823$	16.0862	−	27.8622i	0.560731	−	0.971214i	0.997433	−	0.0716080i	$-0.0228131\pi$
$824$		0			0
$825$	8.62507	+	3.21824i	0.300286	+	0.112045i
$826$		0			0
$827$	−1.96110	+	7.31892i	−0.0681941	+	0.254504i	−0.991604	−	0.129311i	$-0.958723\pi$
$827$	−1.96110	+	7.31892i	−0.0681941	+	0.254504i	0.923410	+	0.383815i	$0.125390\pi$
$828$		0			0
$829$	−24.4831	+	6.56022i	−0.850332	+	0.227846i	−0.657564	−	0.753399i	$-0.728413\pi$
$829$	−24.4831	+	6.56022i	−0.850332	+	0.227846i	−0.192768	+	0.981244i	$0.561746\pi$
$830$		0			0
$831$	3.53543	−	36.9747i	0.122643	−	1.28264i
$832$		0			0
$833$	24.7804	−	92.4817i	0.858590	−	3.20430i
$834$		0			0
$835$	6.75738	+	3.90137i	0.233849	+	0.135013i
$836$		0			0
$837$	20.8898	+	6.14250i	0.722056	+	0.212316i
$838$		0			0
$839$	−8.54351	+	14.7978i	−0.294955	+	0.510877i	−0.974974	−	0.222317i	$-0.928638\pi$
$839$	−8.54351	+	14.7978i	−0.294955	+	0.510877i	0.680020	+	0.733194i	$0.261971\pi$
$840$		0			0
$841$			6.51683i			0.224718i
$842$		0			0
$843$	−11.4257	+	5.21618i	−0.393523	+	0.179655i
$844$		0			0
$845$	22.6860	−	22.6860i	0.780421	−	0.780421i
$846$		0			0
$847$	−18.1234	−	31.3907i	−0.622728	−	1.07860i
$848$		0			0
$849$	−3.70913	+	38.7913i	−0.127297	+	1.33132i
$850$		0			0
$851$	8.78317	+	18.8338i	0.301083	+	0.645613i
$852$		0			0
$853$	−24.2153	+	6.48848i	−0.829118	+	0.222161i	−0.648329	−	0.761361i	$-0.724532\pi$
$853$	−24.2153	+	6.48848i	−0.829118	+	0.222161i	−0.180789	+	0.983522i	$0.557865\pi$
$854$		0			0
$855$	7.49613	−	38.8401i	0.256362	−	1.32830i
$856$		0			0
$857$	−21.6253	−	21.6253i	−0.738705	−	0.738705i	0.233622	−	0.972327i	$-0.424942\pi$
$857$	−21.6253	−	21.6253i	−0.738705	−	0.738705i	−0.972327	+	0.233622i	$0.924942\pi$
$858$		0			0
$859$	15.2693	−	15.2693i	0.520982	−	0.520982i	−0.396886	−	0.917868i	$-0.629909\pi$
$859$	15.2693	−	15.2693i	0.520982	−	0.520982i	0.917868	+	0.396886i	$0.129909\pi$
$860$		0			0
$861$	−13.6815	+	36.6673i	−0.466265	+	1.24962i
$862$		0			0
$863$	−42.2340	−	24.3838i	−1.43766	−	0.830034i	−0.439974	−	0.898010i	$-0.645012\pi$
$863$	−42.2340	−	24.3838i	−1.43766	−	0.830034i	−0.997687	+	0.0679763i	$0.978346\pi$
$864$		0			0
$865$	−26.9233	−	26.9233i	−0.915418	−	0.915418i
$866$		0			0
$867$	16.9062	−	13.9553i	0.574164	−	0.473946i
$868$		0			0
$869$	−13.8843	−	3.72028i	−0.470991	−	0.126202i
$870$		0			0
$871$	12.1049	−	3.24350i	0.410159	−	0.109902i
$872$		0			0
$873$	−18.7240	+	38.5198i	−0.633710	+	1.30370i
$874$		0			0
$875$	−29.8007	−	7.98506i	−1.00745	−	0.269944i
$876$		0			0
$877$	11.9504			0.403536			0.201768	−	0.979433i	$-0.435331\pi$
$877$	11.9504			0.403536			0.201768	+	0.979433i	$0.435331\pi$
$878$		0			0
$879$	14.6710	−	12.1102i	0.494840	−	0.408468i
$880$		0			0
$881$	25.0140	+	43.3255i	0.842743	+	1.45967i	0.887567	+	0.460679i	$0.152394\pi$
$881$	25.0140	+	43.3255i	0.842743	+	1.45967i	−0.0448240	+	0.998995i	$0.514273\pi$
$882$		0			0
$883$	−12.4342	+	46.4051i	−0.418444	+	1.56166i	0.359391	+	0.933187i	$0.382984\pi$
$883$	−12.4342	+	46.4051i	−0.418444	+	1.56166i	−0.777835	+	0.628468i	$0.783682\pi$
$884$		0			0
$885$	8.89061	+	52.9119i	0.298855	+	1.77861i
$886$		0			0
$887$	51.3182			1.72310			0.861548	−	0.507677i	$-0.169496\pi$
$887$	51.3182			1.72310			0.861548	+	0.507677i	$0.169496\pi$
$888$		0			0
$889$	65.3600			2.19211
$890$		0			0
$891$	−13.5935	+	10.6788i	−0.455401	+	0.357754i
$892$		0			0
$893$	−1.80900	+	6.75128i	−0.0605359	+	0.225923i
$894$		0			0
$895$	−13.2334	−	22.9209i	−0.442343	−	0.766160i
$896$		0			0
$897$	−4.59550	−	5.56724i	−0.153439	−	0.185885i
$898$		0			0
$899$	19.8695			0.662686
$900$		0			0
$901$	−67.0829	−	17.9748i	−2.23485	−	0.598827i
$902$		0			0
$903$	46.6793	+	4.46336i	1.55339	+	0.148531i
$904$		0			0
$905$	−39.7940	+	10.6628i	−1.32280	+	0.354442i
$906$		0			0
$907$	46.1179	+	12.3573i	1.53132	+	0.410316i	0.923449	−	0.383720i	$-0.125357\pi$
$907$	46.1179	+	12.3573i	1.53132	+	0.410316i	0.607870	+	0.794036i	$0.292024\pi$
$908$		0			0
$909$	−11.9543	+	4.13400i	−0.396499	+	0.137116i
$910$		0			0
$911$	10.4296	+	10.4296i	0.345549	+	0.345549i	0.858448	−	0.512900i	$-0.171429\pi$
$911$	10.4296	+	10.4296i	0.345549	+	0.345549i	−0.512900	+	0.858448i	$0.671429\pi$
$912$		0			0
$913$	−25.1828	−	14.5393i	−0.833430	−	0.481181i
$914$		0			0
$915$	46.3139	+	17.2809i	1.53109	+	0.571290i
$916$		0			0
$917$	55.1919	−	55.1919i	1.82260	−	1.82260i
$918$		0			0
$919$	−11.9016	−	11.9016i	−0.392599	−	0.392599i	0.483014	−	0.875613i	$-0.339542\pi$
$919$	−11.9016	−	11.9016i	−0.392599	−	0.392599i	−0.875613	+	0.483014i	$0.839542\pi$
$920$		0			0
$921$	1.12357	+	6.68683i	0.0370227	+	0.220338i
$922$		0			0
$923$	2.34832	−	0.629231i	0.0772960	−	0.0207114i
$924$		0			0
$925$	10.8201	+	12.8939i	0.355762	+	0.423949i
$926$		0			0
$927$	34.3848	+	16.7140i	1.12934	+	0.548959i
$928$		0			0
$929$	−1.89260	−	3.27808i	−0.0620943	−	0.107550i	0.833307	−	0.552810i	$-0.186445\pi$
$929$	−1.89260	−	3.27808i	−0.0620943	−	0.107550i	−0.895401	+	0.445260i	$0.853111\pi$
$930$		0			0
$931$	58.8172	−	58.8172i	1.92766	−	1.92766i
$932$		0			0
$933$	16.1766	+	35.4338i	0.529598	+	1.16005i
$934$		0			0
$935$			29.1512i			0.953347i
$936$		0			0
$937$	19.1831	−	33.2261i	0.626685	−	1.08545i	−0.361528	−	0.932361i	$-0.617745\pi$
$937$	19.1831	−	33.2261i	0.626685	−	1.08545i	0.988213	−	0.153088i	$-0.0489219\pi$
$938$		0			0
$939$	−9.81725	−	21.5041i	−0.320374	−	0.701758i
$940$		0			0
$941$	9.57980	+	5.53090i	0.312293	+	0.180302i	0.647952	−	0.761681i	$-0.275626\pi$
$941$	9.57980	+	5.53090i	0.312293	+	0.180302i	−0.335659	+	0.941983i	$0.608959\pi$
$942$		0			0
$943$	4.02981	−	15.0394i	0.131229	−	0.489752i
$944$		0			0
$945$	−51.9822	+	49.5269i	−1.69098	+	1.61111i
$946$		0			0
$947$	−8.43525	+	2.26022i	−0.274109	+	0.0734473i	−0.393255	−	0.919429i	$-0.628651\pi$
$947$	−8.43525	+	2.26022i	−0.274109	+	0.0734473i	0.119146	+	0.992877i	$0.461984\pi$
$948$		0			0
$949$	0.0708263	−	0.264327i	0.00229912	−	0.00858043i
$950$		0			0
$951$	16.4274	−	44.0264i	0.532695	−	1.42765i
$952$		0			0
$953$	−17.7007	+	30.6586i	−0.573383	+	0.993129i	0.422832	+	0.906208i	$0.361036\pi$
$953$	−17.7007	+	30.6586i	−0.573383	+	0.993129i	−0.996215	+	0.0869208i	$0.972297\pi$
$954$		0			0
$955$	31.1704	−	17.9962i	1.00865	−	0.582344i
$956$		0			0
$957$	−9.15169	+	12.8483i	−0.295832	+	0.415326i
$958$		0			0
$959$	−74.3048	+	42.8999i	−2.39943	+	1.38531i
$960$		0			0
$961$		−	13.4403i		−	0.433557i
$962$		0			0
$963$	4.48467	−	5.17291i	0.144517	−	0.166695i
$964$		0			0
$965$	15.8781	+	27.5017i	0.511135	+	0.885313i
$966$		0			0
$967$	4.20839	+	1.12764i	0.135333	+	0.0362623i	0.325850	−	0.945422i	$-0.394350\pi$
$967$	4.20839	+	1.12764i	0.135333	+	0.0362623i	−0.190517	+	0.981684i	$0.561016\pi$
$968$		0			0
$969$	44.0092	−	7.39473i	1.41378	−	0.237553i
$970$		0			0
$971$	−4.37165	−	2.52398i	−0.140293	−	0.0809982i	0.428211	−	0.903679i	$-0.359144\pi$
$971$	−4.37165	−	2.52398i	−0.140293	−	0.0809982i	−0.568504	+	0.822681i	$0.692477\pi$
$972$		0			0
$973$		−	4.90606i		−	0.157281i
$974$		0			0
$975$	−4.76254	−	3.39231i	−0.152524	−	0.108641i
$976$		0			0
$977$	13.4778	+	50.3000i	0.431195	+	1.60924i	0.750012	+	0.661424i	$0.230048\pi$
$977$	13.4778	+	50.3000i	0.431195	+	1.60924i	−0.318818	+	0.947816i	$0.603286\pi$
$978$		0			0
$979$	3.55934	+	13.2836i	0.113757	+	0.424547i
$980$		0			0
$981$	20.1689	+	29.8160i	0.643945	+	0.951952i
$982$		0			0
$983$	12.1562	−	21.0551i	0.387721	−	0.671553i	−0.604422	−	0.796665i	$-0.706596\pi$
$983$	12.1562	−	21.0551i	0.387721	−	0.671553i	0.992143	+	0.125112i	$0.0399290\pi$
$984$		0			0
$985$	−10.2494	+	10.2494i	−0.326572	+	0.326572i
$986$		0			0
$987$	9.78375	−	8.07604i	0.311420	−	0.257063i
$988$		0			0
$989$	−18.6554			−0.593208
$990$		0			0
$991$	−3.71444	−	3.71444i	−0.117993	−	0.117993i	0.645645	−	0.763638i	$-0.276589\pi$
$991$	−3.71444	−	3.71444i	−0.117993	−	0.117993i	−0.763638	+	0.645645i	$0.776589\pi$
$992$		0			0
$993$	−3.43268	−	7.51907i	−0.108933	−	0.238611i
$994$		0			0
$995$	20.0432	−	11.5719i	0.635411	−	0.366855i
$996$		0			0
$997$	−6.98549	−	26.0702i	−0.221233	−	0.825652i	−0.983879	−	0.178836i	$-0.942767\pi$
$997$	−6.98549	−	26.0702i	−0.221233	−	0.825652i	0.762646	−	0.646816i	$-0.223900\pi$
$998$		0			0
$999$	−31.2502	+	4.73535i	−0.988713	+	0.149820i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.br.a.569.36	yes	152
3.2	odd	2	inner	888.2.br.a.569.29	✓	152
37.8	odd	12	inner	888.2.br.a.785.29	yes	152
111.8	even	12	inner	888.2.br.a.785.36	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.br.a.569.29	✓	152	3.2	odd	2	inner
888.2.br.a.569.36	yes	152	1.1	even	1	trivial
888.2.br.a.785.29	yes	152	37.8	odd	12	inner
888.2.br.a.785.36	yes	152	111.8	even	12	inner

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:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.70811 - 0.287007i) q^{3} +(-0.721322 + 2.69201i) q^{5} +(2.47898 + 4.29371i) q^{7} +(2.83525 - 0.980478i) q^{9} -1.92072 q^{11} +(1.17839 + 0.315747i) q^{13} +(-0.459467 + 4.80526i) q^{15} +(-5.26023 + 1.40947i) q^{17} +(-4.56995 - 1.22452i) q^{19} +(5.46668 + 6.62264i) q^{21} +(-2.41576 - 2.41576i) q^{23} +(-2.39648 - 1.38361i) q^{25} +(4.56151 - 2.48850i) q^{27} +(3.35285 - 3.35285i) q^{29} +(2.96309 + 2.96309i) q^{31} +(-3.28079 + 0.551260i) q^{33} +(-13.3469 + 3.57628i) q^{35} +(-5.71600 - 2.08022i) q^{37} +(2.10343 + 0.201125i) q^{39} +(2.27871 + 3.94685i) q^{41} +(3.86120 - 3.86120i) q^{43} +(0.594327 + 8.33977i) q^{45} -1.47732i q^{47} +(-8.79066 + 15.2259i) q^{49} +(-8.58050 + 3.91726i) q^{51} +(11.0443 + 6.37642i) q^{53} +(1.38545 - 5.17059i) q^{55} +(-8.15741 - 0.779992i) q^{57} +(10.7362 - 2.87675i) q^{59} +(2.65045 - 9.89160i) q^{61} +(11.2384 + 9.74319i) q^{63} +(-1.69999 + 2.94447i) q^{65} +(8.89621 - 5.13623i) q^{67} +(-4.81971 - 3.43303i) q^{69} +(1.72584 - 0.996416i) q^{71} -0.224313i q^{73} +(-4.49054 - 1.67554i) q^{75} +(-4.76141 - 8.24701i) q^{77} +(7.22868 + 1.93692i) q^{79} +(7.07732 - 5.55981i) q^{81} +(13.1112 + 7.56973i) q^{83} -15.1773i q^{85} +(4.76473 - 6.68931i) q^{87} +(-1.85313 - 6.91598i) q^{89} +(1.56546 + 5.84238i) q^{91} +(5.91169 + 4.21084i) q^{93} +(6.59281 - 11.4191i) q^{95} +(-10.0950 + 10.0950i) q^{97} +(-5.44572 + 1.88322i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) \) 152 * q + 4 * q^13 - 12 * q^15 + 4 * q^19 - 44 * q^31 - 12 * q^39 + 28 * q^43 + 20 * q^45 - 80 * q^49 - 12 * q^51 - 8 * q^55 - 40 * q^57 - 28 * q^61 + 48 * q^63 + 56 * q^69 + 64 * q^75 + 20 * q^79 + 16 * q^81 + 56 * q^87 + 52 * q^91 + 40 * q^93 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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