LMFDB - Embedded newform 864.2.bf.a.49.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(49,864)] 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("864.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bf (of order $18$, degree $6$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.19
Character	$\chi$	$=$	864.49
Dual form			864.2.bf.a.529.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.195652 + 1.72096i) q^{3} +(-1.34802 - 3.70366i) q^{5} +(-0.00177522 - 0.0100678i) q^{7} +(-2.92344 + 0.673422i) q^{9} +(0.343808 - 0.944604i) q^{11} +(-2.57400 + 3.06757i) q^{13} +(6.11013 - 3.04453i) q^{15} +(-0.948987 + 1.64369i) q^{17} +(-3.76245 + 2.17225i) q^{19} +(0.0169790 - 0.00502488i) q^{21} +(-1.19728 + 6.79010i) q^{23} +(-8.06972 + 6.77130i) q^{25} +(-1.73091 - 4.89938i) q^{27} +(-3.82827 - 4.56236i) q^{29} +(-1.38501 + 7.85480i) q^{31} +(1.69290 + 0.406867i) q^{33} +(-0.0348946 + 0.0201464i) q^{35} +(-6.65823 - 3.84413i) q^{37} +(-5.78279 - 3.82958i) q^{39} +(4.44753 + 3.73192i) q^{41} +(-1.42511 + 3.91546i) q^{43} +(6.43499 + 9.91964i) q^{45} +(-1.37530 - 7.79973i) q^{47} +(6.57775 - 2.39411i) q^{49} +(-3.01441 - 1.31158i) q^{51} -2.25567i q^{53} -3.96195 q^{55} +(-4.47450 - 6.05004i) q^{57} +(2.24610 + 6.17111i) q^{59} +(0.106836 - 0.0188381i) q^{61} +(0.0119696 + 0.0282371i) q^{63} +(14.8311 + 5.39806i) q^{65} +(2.47342 - 2.94771i) q^{67} +(-11.9198 - 0.731973i) q^{69} +(-0.442665 + 0.766718i) q^{71} +(-7.26116 - 12.5767i) q^{73} +(-13.2320 - 12.5629i) q^{75} +(-0.0101204 - 0.00178450i) q^{77} +(-2.46319 + 2.06686i) q^{79} +(8.09301 - 3.93742i) q^{81} +(-9.76904 - 11.6423i) q^{83} +(7.36694 + 1.29899i) q^{85} +(7.10265 - 7.48096i) q^{87} +(-1.45362 - 2.51775i) q^{89} +(0.0354530 + 0.0204688i) q^{91} +(-13.7888 - 0.846748i) q^{93} +(13.1172 + 11.0066i) q^{95} +(-12.0217 - 4.37554i) q^{97} +(-0.368984 + 2.99302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) $ 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.195652	+	1.72096i	0.112960	+	0.993600i
$3$	0.195652	+	1.72096i	0.112960	+	0.993600i
$4$		0			0
$5$	−1.34802	−	3.70366i	−0.602854	−	1.65633i	−0.745462	−	0.666548i	$-0.767771\pi$
$5$	−1.34802	−	3.70366i	−0.602854	−	1.65633i	0.142608	−	0.989779i	$-0.454451\pi$
$6$		0			0
$7$	−0.00177522	−	0.0100678i	−0.000670970	−	0.00380526i	0.984470	−	0.175550i	$-0.0561705\pi$
$7$	−0.00177522	−	0.0100678i	−0.000670970	−	0.00380526i	−0.985141	+	0.171745i	$0.945059\pi$
$8$		0			0
$9$	−2.92344	+	0.673422i	−0.974480	+	0.224474i
$10$		0			0
$11$	0.343808	−	0.944604i	0.103662	−	0.284809i	−0.877009	−	0.480474i	$-0.840465\pi$
$11$	0.343808	−	0.944604i	0.103662	−	0.284809i	0.980671	+	0.195666i	$0.0626867\pi$
$12$		0			0
$13$	−2.57400	+	3.06757i	−0.713899	+	0.850792i	−0.994023	−	0.109172i	$-0.965180\pi$
$13$	−2.57400	+	3.06757i	−0.713899	+	0.850792i	0.280124	+	0.959964i	$0.409624\pi$
$14$		0			0
$15$	6.11013	−	3.04453i	1.57763	−	0.786094i
$16$		0			0
$17$	−0.948987	+	1.64369i	−0.230163	+	0.398654i	−0.957856	−	0.287249i	$-0.907259\pi$
$17$	−0.948987	+	1.64369i	−0.230163	+	0.398654i	0.727693	+	0.685903i	$0.240593\pi$
$18$		0			0
$19$	−3.76245	+	2.17225i	−0.863166	+	0.498349i	−0.865071	−	0.501649i	$-0.832727\pi$
$19$	−3.76245	+	2.17225i	−0.863166	+	0.498349i	0.00190536	+	0.999998i	$0.499394\pi$
$20$		0			0
$21$	0.0169790	−	0.00502488i	0.00370511	−	0.00109652i
$22$		0			0
$23$	−1.19728	+	6.79010i	−0.249650	+	1.41583i	0.559792	+	0.828633i	$0.310881\pi$
$23$	−1.19728	+	6.79010i	−0.249650	+	1.41583i	−0.809442	+	0.587200i	$0.800230\pi$
$24$		0			0
$25$	−8.06972	+	6.77130i	−1.61394	+	1.35426i
$26$		0			0
$27$	−1.73091	−	4.89938i	−0.333115	−	0.942886i
$28$		0			0
$29$	−3.82827	−	4.56236i	−0.710892	−	0.847208i	0.282820	−	0.959173i	$-0.408730\pi$
$29$	−3.82827	−	4.56236i	−0.710892	−	0.847208i	−0.993712	+	0.111965i	$0.964286\pi$
$30$		0			0
$31$	−1.38501	+	7.85480i	−0.248756	+	1.41076i	0.562850	+	0.826559i	$0.309705\pi$
$31$	−1.38501	+	7.85480i	−0.248756	+	1.41076i	−0.811606	+	0.584205i	$0.801406\pi$
$32$		0			0
$33$	1.69290	+	0.406867i	0.294696	+	0.0708264i
$34$		0			0
$35$	−0.0348946	+	0.0201464i	−0.00589826	+	0.00340536i
$36$		0			0
$37$	−6.65823	−	3.84413i	−1.09461	−	0.631971i	−0.159807	−	0.987148i	$-0.551087\pi$
$37$	−6.65823	−	3.84413i	−1.09461	−	0.631971i	−0.934799	+	0.355177i	$0.884421\pi$
$38$		0			0
$39$	−5.78279	−	3.82958i	−0.925988	−	0.613224i
$40$		0			0
$41$	4.44753	+	3.73192i	0.694588	+	0.582828i	0.920228	−	0.391382i	$-0.128003\pi$
$41$	4.44753	+	3.73192i	0.694588	+	0.582828i	−0.225641	+	0.974211i	$0.572447\pi$
$42$		0			0
$43$	−1.42511	+	3.91546i	−0.217327	+	0.597102i	−0.999668	−	0.0257481i	$-0.991803\pi$
$43$	−1.42511	+	3.91546i	−0.217327	+	0.597102i	0.782341	+	0.622850i	$0.214025\pi$
$44$		0			0
$45$	6.43499	+	9.91964i	0.959272	+	1.47873i
$46$		0			0
$47$	−1.37530	−	7.79973i	−0.200608	−	1.13771i	−0.904202	−	0.427105i	$-0.859534\pi$
$47$	−1.37530	−	7.79973i	−0.200608	−	1.13771i	0.703594	−	0.710602i	$-0.251578\pi$
$48$		0			0
$49$	6.57775	−	2.39411i	0.939679	−	0.342015i
$50$		0			0
$51$	−3.01441	−	1.31158i	−0.422102	−	0.183658i
$52$		0			0
$53$		−	2.25567i		−	0.309840i	−0.987927	−	0.154920i	$-0.950488\pi$
$53$		−	2.25567i		−	0.309840i	0.987927	−	0.154920i	$-0.0495120\pi$
$54$		0			0
$55$	−3.96195			−0.534230
$56$		0			0
$57$	−4.47450	−	6.05004i	−0.592663	−	0.801348i
$58$		0			0
$59$	2.24610	+	6.17111i	0.292417	+	0.803410i	0.995712	+	0.0925111i	$0.0294894\pi$
$59$	2.24610	+	6.17111i	0.292417	+	0.803410i	−0.703294	+	0.710899i	$0.748288\pi$
$60$		0			0
$61$	0.106836	−	0.0188381i	0.0136789	−	0.00241197i	−0.166805	−	0.985990i	$-0.553345\pi$
$61$	0.106836	−	0.0188381i	0.0136789	−	0.00241197i	0.180483	+	0.983578i	$0.442234\pi$
$62$		0			0
$63$	0.0119696	+	0.0282371i	0.00150803	+	0.00355754i
$64$		0			0
$65$	14.8311	+	5.39806i	1.83957	+	0.669547i
$66$		0			0
$67$	2.47342	−	2.94771i	0.302177	−	0.360120i	−0.593494	−	0.804839i	$-0.702252\pi$
$67$	2.47342	−	2.94771i	0.302177	−	0.360120i	0.895670	+	0.444718i	$0.146696\pi$
$68$		0			0
$69$	−11.9198	−	0.731973i	−1.43497	−	0.0881192i
$70$		0			0
$71$	−0.442665	+	0.766718i	−0.0525346	+	0.0909926i	−0.891097	−	0.453813i	$-0.850063\pi$
$71$	−0.442665	+	0.766718i	−0.0525346	+	0.0909926i	0.838562	+	0.544806i	$0.183397\pi$
$72$		0			0
$73$	−7.26116	−	12.5767i	−0.849854	−	1.47199i	−0.881338	−	0.472486i	$-0.843357\pi$
$73$	−7.26116	−	12.5767i	−0.849854	−	1.47199i	0.0314838	−	0.999504i	$-0.489977\pi$
$74$		0			0
$75$	−13.2320	−	12.5629i	−1.52790	−	1.45064i
$76$		0			0
$77$	−0.0101204	−	0.00178450i	−0.00115333	−	0.000203362i
$78$		0			0
$79$	−2.46319	+	2.06686i	−0.277131	+	0.232540i	−0.770750	−	0.637138i	$-0.780118\pi$
$79$	−2.46319	+	2.06686i	−0.277131	+	0.232540i	0.493619	+	0.869678i	$0.335674\pi$
$80$		0			0
$81$	8.09301	−	3.93742i	0.899223	−	0.437491i
$82$		0			0
$83$	−9.76904	−	11.6423i	−1.07229	−	1.27791i	−0.958712	−	0.284378i	$-0.908213\pi$
$83$	−9.76904	−	11.6423i	−1.07229	−	1.27791i	−0.113579	−	0.993529i	$-0.536232\pi$
$84$		0			0
$85$	7.36694	+	1.29899i	0.799057	+	0.140895i
$86$		0			0
$87$	7.10265	−	7.48096i	0.761483	−	0.802043i
$88$		0			0
$89$	−1.45362	−	2.51775i	−0.154084	−	0.266881i	0.778641	−	0.627469i	$-0.215909\pi$
$89$	−1.45362	−	2.51775i	−0.154084	−	0.266881i	−0.932725	+	0.360588i	$0.882576\pi$
$90$		0			0
$91$	0.0354530	+	0.0204688i	0.00371649	+	0.00214572i
$92$		0			0
$93$	−13.7888	−	0.846748i	−1.42983	−	0.0878037i
$94$		0			0
$95$	13.1172	+	11.0066i	1.34579	+	1.12925i
$96$		0			0
$97$	−12.0217	−	4.37554i	−1.22062	−	0.444269i	−0.350244	−	0.936658i	$-0.613901\pi$
$97$	−12.0217	−	4.37554i	−1.22062	−	0.444269i	−0.870375	+	0.492389i	$0.836124\pi$
$98$		0			0
$99$	−0.368984	+	2.99302i	−0.0370843	+	0.300810i
$100$		0			0
$101$	8.25225	−	1.45509i	0.821129	−	0.144787i	0.252727	−	0.967538i	$-0.418673\pi$
$101$	8.25225	−	1.45509i	0.821129	−	0.144787i	0.568403	+	0.822751i	$0.307562\pi$
$102$		0			0
$103$	−6.53199	+	2.37745i	−0.643617	+	0.234257i	−0.643147	−	0.765743i	$-0.722372\pi$
$103$	−6.53199	+	2.37745i	−0.643617	+	0.234257i	−0.000469418		1.00000i	$0.500149\pi$
$104$		0			0
$105$	−0.0414985	−	0.0561107i	−0.00404984	−	0.00547584i
$106$		0			0
$107$			14.2756i			1.38007i	0.723776	+	0.690035i	$0.242405\pi$
$107$			14.2756i			1.38007i	−0.723776	+	0.690035i	$0.757595\pi$
$108$		0			0
$109$			4.88426i			0.467827i	0.972257	+	0.233914i	$0.0751533\pi$
$109$			4.88426i			0.467827i	−0.972257	+	0.233914i	$0.924847\pi$
$110$		0			0
$111$	5.31292	−	12.2107i	0.504280	−	1.15899i
$112$		0			0
$113$	4.20463	−	1.53036i	0.395538	−	0.143964i	−0.136591	−	0.990628i	$-0.543614\pi$
$113$	4.20463	−	1.53036i	0.395538	−	0.143964i	0.532129	+	0.846663i	$0.321392\pi$
$114$		0			0
$115$	26.7622	−	4.71889i	2.49559	−	0.440039i
$116$		0			0
$117$	5.45916	−	10.7013i	0.504700	−	0.989331i
$118$		0			0
$119$	0.0182330	+	0.00663627i	0.00167142	+	0.000608346i
$120$		0			0
$121$	7.65242	+	6.42114i	0.695674	+	0.583740i
$122$		0			0
$123$	−5.55233	+	8.38420i	−0.500637	+	0.755978i
$124$		0			0
$125$	18.8902	+	10.9063i	1.68959	+	0.975485i
$126$		0			0
$127$	0.733337	+	1.27018i	0.0650731	+	0.112710i	0.896726	−	0.442585i	$-0.145939\pi$
$127$	0.733337	+	1.27018i	0.0650731	+	0.112710i	−0.831653	+	0.555295i	$0.812605\pi$
$128$		0			0
$129$	−7.01720	−	1.68650i	−0.617830	−	0.148488i
$130$		0			0
$131$	−11.2373	−	1.98143i	−0.981805	−	0.173119i	−0.340366	−	0.940293i	$-0.610551\pi$
$131$	−11.2373	−	1.98143i	−0.981805	−	0.173119i	−0.641439	+	0.767174i	$0.721662\pi$
$132$		0			0
$133$	0.0285489	+	0.0340233i	0.00247551	+	0.00295019i
$134$		0			0
$135$	−15.8123	+	13.0152i	−1.36091	+	1.12017i
$136$		0			0
$137$	3.27137	−	2.74501i	0.279492	−	0.234522i	−0.492255	−	0.870451i	$-0.663827\pi$
$137$	3.27137	−	2.74501i	0.279492	−	0.234522i	0.771748	+	0.635929i	$0.219383\pi$
$138$		0			0
$139$	1.04893	+	0.184955i	0.0889693	+	0.0156877i	0.217956	−	0.975959i	$-0.430061\pi$
$139$	1.04893	+	0.184955i	0.0889693	+	0.0156877i	−0.128986	+	0.991646i	$0.541172\pi$
$140$		0			0
$141$	13.1540	−	3.89288i	1.10776	−	0.327840i
$142$		0			0
$143$	2.01268	+	3.48606i	0.168309	+	0.291519i
$144$		0			0
$145$	−11.7368	+	20.3288i	−0.974690	+	1.68821i
$146$		0			0
$147$	5.40712	+	10.8517i	0.445972	+	0.895030i
$148$		0			0
$149$	−1.34236	+	1.59976i	−0.109970	+	0.131058i	−0.818222	−	0.574903i	$-0.805040\pi$
$149$	−1.34236	+	1.59976i	−0.109970	+	0.131058i	0.708251	+	0.705960i	$0.249484\pi$
$150$		0			0
$151$	−9.89970	−	3.60320i	−0.805626	−	0.293224i	−0.0938105	−	0.995590i	$-0.529905\pi$
$151$	−9.89970	−	3.60320i	−0.805626	−	0.293224i	−0.711816	+	0.702366i	$0.752127\pi$
$152$		0			0
$153$	1.66741	−	5.44431i	0.134802	−	0.440146i
$154$		0			0
$155$	30.9586	−	5.45883i	2.48665	−	0.438464i
$156$		0			0
$157$	7.61747	+	20.9288i	0.607940	+	1.67030i	0.734720	+	0.678371i	$0.237314\pi$
$157$	7.61747	+	20.9288i	0.607940	+	1.67030i	−0.126779	+	0.991931i	$0.540464\pi$
$158$		0			0
$159$	3.88193	−	0.441328i	0.307857	−	0.0349996i
$160$		0			0
$161$	0.0704866			0.00555512
$162$		0			0
$163$		−	8.64571i		−	0.677184i	−0.940933	−	0.338592i	$-0.890049\pi$
$163$		−	8.64571i		−	0.677184i	0.940933	−	0.338592i	$-0.109951\pi$
$164$		0			0
$165$	−0.775166	−	6.81838i	−0.0603466	−	0.530810i
$166$		0			0
$167$	7.93163	−	2.88688i	0.613768	−	0.223393i	−0.0163833	−	0.999866i	$-0.505215\pi$
$167$	7.93163	−	2.88688i	0.613768	−	0.223393i	0.630151	+	0.776473i	$0.282993\pi$
$168$		0			0
$169$	−0.527105	−	2.98936i	−0.0405465	−	0.229951i
$170$		0			0
$171$	9.53646	−	8.88417i	0.729271	−	0.679389i
$172$		0			0
$173$	−4.65008	+	12.7760i	−0.353539	+	0.971340i	0.627685	+	0.778467i	$0.284003\pi$
$173$	−4.65008	+	12.7760i	−0.353539	+	0.971340i	−0.981224	+	0.192872i	$0.938220\pi$
$174$		0			0
$175$	0.0824974	+	0.0692236i	0.00623622	+	0.00523281i
$176$		0			0
$177$	−10.1808	+	5.07285i	−0.765236	+	0.381299i
$178$		0			0
$179$	−0.257187	−	0.148487i	−0.0192231	−	0.0110985i	0.490358	−	0.871521i	$-0.336866\pi$
$179$	−0.257187	−	0.148487i	−0.0192231	−	0.0110985i	−0.509581	+	0.860423i	$0.670199\pi$
$180$		0			0
$181$	1.63626	−	0.944694i	0.121622	−	0.0702186i	−0.437955	−	0.898997i	$-0.644297\pi$
$181$	1.63626	−	0.944694i	0.121622	−	0.0702186i	0.559577	+	0.828778i	$0.310964\pi$
$182$		0			0
$183$	0.0533224	+	0.180175i	0.00394170	+	0.0133189i
$184$		0			0
$185$	−5.26192	+	29.8418i	−0.386864	+	2.19401i
$186$		0			0
$187$	1.22637	+	1.46153i	0.0896811	+	0.106878i
$188$		0			0
$189$	−0.0462531	+	0.0261239i	−0.00336442	+	0.00190024i
$190$		0			0
$191$	−10.6897	+	8.96976i	−0.773483	+	0.649029i	−0.941598	−	0.336738i	$-0.890676\pi$
$191$	−10.6897	+	8.96976i	−0.773483	+	0.649029i	0.168116	+	0.985767i	$0.446232\pi$
$192$		0			0
$193$	1.65530	−	9.38768i	0.119151	−	0.675740i	−0.865460	−	0.500979i	$-0.832974\pi$
$193$	1.65530	−	9.38768i	0.119151	−	0.675740i	0.984611	−	0.174761i	$-0.0559153\pi$
$194$		0			0
$195$	−6.38814	+	26.5799i	−0.457465	+	1.90342i
$196$		0			0
$197$	7.61046	−	4.39390i	0.542223	−	0.313052i	−0.203757	−	0.979022i	$-0.565315\pi$
$197$	7.61046	−	4.39390i	0.542223	−	0.313052i	0.745979	+	0.665969i	$0.231982\pi$
$198$		0			0
$199$	−4.70991	+	8.15780i	−0.333876	+	0.578291i	−0.983268	−	0.182163i	$-0.941690\pi$
$199$	−4.70991	+	8.15780i	−0.333876	+	0.578291i	0.649392	+	0.760454i	$0.275023\pi$
$200$		0			0
$201$	5.55684	+	3.67995i	0.391949	+	0.259563i
$202$		0			0
$203$	−0.0391368	+	0.0466414i	−0.00274686	+	0.00327358i
$204$		0			0
$205$	7.82640	−	21.5029i	0.546619	−	1.50182i
$206$		0			0
$207$	−1.07243	−	20.6567i	−0.0745393	−	1.43574i
$208$		0			0
$209$	0.758358	+	4.30086i	0.0524567	+	0.297497i
$210$		0			0
$211$	4.12560	+	11.3350i	0.284018	+	0.780333i	0.996873	+	0.0790214i	$0.0251795\pi$
$211$	4.12560	+	11.3350i	0.284018	+	0.780333i	−0.712855	+	0.701311i	$0.752598\pi$
$212$		0			0
$213$	−1.40610	−	0.611800i	−0.0963445	−	0.0419198i
$214$		0			0
$215$	16.4226			1.12001
$216$		0			0
$217$	0.0815391			0.00553524
$218$		0			0
$219$	20.2234	−	14.9569i	1.36657	−	1.01069i
$220$		0			0
$221$	−2.59946	−	7.14195i	−0.174858	−	0.480420i
$222$		0			0
$223$	−0.616341	−	3.49544i	−0.0412732	−	0.234072i	0.957192	−	0.289454i	$-0.0934736\pi$
$223$	−0.616341	−	3.49544i	−0.0412732	−	0.234072i	−0.998465	+	0.0553815i	$0.982362\pi$
$224$		0			0
$225$	19.0314	−	25.2298i	1.26876	−	1.68199i
$226$		0			0
$227$	3.72066	−	10.2224i	0.246949	−	0.678486i	−0.752846	−	0.658197i	$-0.771319\pi$
$227$	3.72066	−	10.2224i	0.246949	−	0.678486i	0.999794	−	0.0202886i	$-0.00645849\pi$
$228$		0			0
$229$	−5.05083	+	6.01935i	−0.333769	+	0.397770i	−0.906661	−	0.421861i	$-0.861377\pi$
$229$	−5.05083	+	6.01935i	−0.333769	+	0.397770i	0.572892	+	0.819631i	$0.305821\pi$
$230$		0			0
$231$	0.00109098	−	0.0177660i	7.17811e−5	−	0.00116892i
$232$		0			0
$233$	12.0985	−	20.9553i	0.792602	−	1.37283i	−0.131749	−	0.991283i	$-0.542059\pi$
$233$	12.0985	−	20.9553i	0.792602	−	1.37283i	0.924351	−	0.381544i	$-0.124608\pi$
$234$		0			0
$235$	−27.0336	+	15.6079i	−1.76348	+	1.01814i
$236$		0			0
$237$	−4.03893	−	3.83468i	−0.262357	−	0.249089i
$238$		0			0
$239$	5.23764	−	29.7041i	0.338795	−	1.92140i	−0.0471684	−	0.998887i	$-0.515020\pi$
$239$	5.23764	−	29.7041i	0.338795	−	1.92140i	0.385963	−	0.922514i	$-0.373869\pi$
$240$		0			0
$241$	−1.91756	+	1.60903i	−0.123521	+	0.103647i	−0.702456	−	0.711727i	$-0.747913\pi$
$241$	−1.91756	+	1.60903i	−0.123521	+	0.103647i	0.578935	+	0.815374i	$0.303469\pi$
$242$		0			0
$243$	8.35958	+	13.1574i	0.536267	+	0.844048i
$244$		0			0
$245$	−17.7339	−	21.1344i	−1.13298	−	1.35023i
$246$		0			0
$247$	3.02101	−	17.1330i	0.192222	−	1.09015i
$248$		0			0
$249$	18.1246	−	19.0900i	1.14860	−	1.20978i
$250$		0			0
$251$	14.5027	−	8.37314i	0.915402	−	0.528508i	0.0332368	−	0.999448i	$-0.489418\pi$
$251$	14.5027	−	8.37314i	0.915402	−	0.528508i	0.882165	+	0.470940i	$0.156085\pi$
$252$		0			0
$253$	6.00232	+	3.46544i	0.377363	+	0.217870i
$254$		0			0
$255$	−0.794157	+	12.9324i	−0.0497320	+	0.809858i
$256$		0			0
$257$	−20.4870	−	17.1907i	−1.27795	−	1.07232i	−0.993524	−	0.113626i	$-0.963753\pi$
$257$	−20.4870	−	17.1907i	−1.27795	−	1.07232i	−0.284423	−	0.958699i	$-0.591802\pi$
$258$		0			0
$259$	−0.0268820	+	0.0738578i	−0.00167037	+	0.00458930i
$260$		0			0
$261$	14.2641	+	10.7597i	0.882927	+	0.666011i
$262$		0			0
$263$	0.762315	+	4.32330i	0.0470064	+	0.266586i	0.999249	−	0.0387571i	$-0.0123398\pi$
$263$	0.762315	+	4.32330i	0.0470064	+	0.266586i	−0.952242	+	0.305343i	$0.901229\pi$
$264$		0			0
$265$	−8.35424	+	3.04070i	−0.513197	+	0.186788i
$266$		0			0
$267$	4.04855	−	2.99424i	0.247767	−	0.183244i
$268$		0			0
$269$			0.741050i			0.0451826i	0.999745	+	0.0225913i	$0.00719165\pi$
$269$			0.741050i			0.0451826i	−0.999745	+	0.0225913i	$0.992808\pi$
$270$		0			0
$271$	14.1450			0.859245			0.429622	−	0.903009i	$-0.358647\pi$
$271$	14.1450			0.859245			0.429622	+	0.903009i	$0.358647\pi$
$272$		0			0
$273$	−0.0282897	+	0.0650182i	−0.00171217	+	0.00393508i
$274$		0			0
$275$	3.62176	+	9.95071i	0.218400	+	0.600050i
$276$		0			0
$277$	−8.42697	+	1.48590i	−0.506327	+	0.0892792i	−0.420976	−	0.907072i	$-0.638312\pi$
$277$	−8.42697	+	1.48590i	−0.506327	+	0.0892792i	−0.0853514	+	0.996351i	$0.527201\pi$
$278$		0			0
$279$	−1.24059	−	23.8958i	−0.0742724	−	1.43060i
$280$		0			0
$281$	−17.6483	−	6.42344i	−1.05281	−	0.383191i	−0.243086	−	0.970005i	$-0.578160\pi$
$281$	−17.6483	−	6.42344i	−1.05281	−	0.383191i	−0.809722	+	0.586814i	$0.800382\pi$
$282$		0			0
$283$	−16.5234	+	19.6918i	−0.982214	+	1.17056i	0.00313343	+	0.999995i	$0.499003\pi$
$283$	−16.5234	+	19.6918i	−0.982214	+	1.17056i	−0.985347	+	0.170562i	$0.945442\pi$
$284$		0			0
$285$	−16.3756	+	24.7276i	−0.970005	+	1.46474i
$286$		0			0
$287$	0.0296768	−	0.0514017i	0.00175177	−	0.00303415i
$288$		0			0
$289$	6.69885	+	11.6027i	0.394050	+	0.682514i
$290$		0			0
$291$	5.17808	−	21.5450i	0.303544	−	1.26299i
$292$		0			0
$293$	−14.3663	−	2.53317i	−0.839288	−	0.147989i	−0.262550	−	0.964918i	$-0.584564\pi$
$293$	−14.3663	−	2.53317i	−0.839288	−	0.147989i	−0.576738	+	0.816929i	$0.695675\pi$
$294$		0			0
$295$	19.8279	−	16.6376i	1.15442	−	0.968678i
$296$		0			0
$297$	−5.22308	−	0.0494167i	−0.303074	−	0.00286745i
$298$		0			0
$299$	−17.7473	−	21.1504i	−1.02635	−	1.22316i
$300$		0			0
$301$	0.0419499	+	0.00739689i	0.00241795	+	0.000426350i
$302$		0			0
$303$	4.11874	+	13.9171i	0.236615	+	0.799518i
$304$		0			0
$305$	−0.213787	−	0.370290i	−0.0122414	−	0.0212028i
$306$		0			0
$307$	−8.07578	−	4.66255i	−0.460909	−	0.266106i	0.251517	−	0.967853i	$-0.419070\pi$
$307$	−8.07578	−	4.66255i	−0.460909	−	0.266106i	−0.712426	+	0.701747i	$0.752404\pi$
$308$		0			0
$309$	−5.36951	−	10.7762i	−0.305461	−	0.613035i
$310$		0			0
$311$	6.15253	+	5.16259i	0.348878	+	0.292743i	0.800339	−	0.599547i	$-0.204653\pi$
$311$	6.15253	+	5.16259i	0.348878	+	0.292743i	−0.451461	+	0.892291i	$0.649097\pi$
$312$		0			0
$313$	31.0694	+	11.3083i	1.75615	+	0.639185i	0.999886	−	0.0150840i	$-0.00480156\pi$
$313$	31.0694	+	11.3083i	1.75615	+	0.639185i	0.756261	+	0.654269i	$0.227024\pi$
$314$		0			0
$315$	0.0884452	−	0.0823956i	0.00498332	−	0.00464247i
$316$		0			0
$317$	25.6721	−	4.52669i	1.44189	−	0.254244i	0.602650	−	0.798006i	$-0.294112\pi$
$317$	25.6721	−	4.52669i	1.44189	−	0.254244i	0.839240	+	0.543762i	$0.183000\pi$
$318$		0			0
$319$	−5.62581	+	2.04763i	−0.314985	+	0.114645i
$320$		0			0
$321$	−24.5677	+	2.79305i	−1.37124	+	0.155893i
$322$		0			0
$323$		−	8.24576i		−	0.458806i
$324$		0			0
$325$		−	42.1838i		−	2.33993i
$326$		0			0
$327$	−8.40564	+	0.955617i	−0.464833	+	0.0528457i
$328$		0			0
$329$	−0.0760844	+	0.0276925i	−0.00419467	+	0.00152674i
$330$		0			0
$331$	−2.73256	+	0.481823i	−0.150195	+	0.0264834i	−0.248240	−	0.968699i	$-0.579852\pi$
$331$	−2.73256	+	0.481823i	−0.150195	+	0.0264834i	0.0980451	+	0.995182i	$0.468741\pi$
$332$		0			0
$333$	22.0537	+	6.75429i	1.20853	+	0.370133i
$334$		0			0
$335$	−14.2516	−	5.18714i	−0.778645	−	0.283404i
$336$		0			0
$337$	−10.0326	−	8.41837i	−0.546512	−	0.458578i	0.327246	−	0.944939i	$-0.393879\pi$
$337$	−10.0326	−	8.41837i	−0.546512	−	0.458578i	−0.873758	+	0.486361i	$0.838324\pi$
$338$		0			0
$339$	3.45634	+	6.93660i	0.187723	+	0.376744i
$340$		0			0
$341$	6.94350	+	4.00883i	0.376012	+	0.217090i
$342$		0			0
$343$	−0.0715611	−	0.123947i	−0.00386393	−	0.00669253i
$344$		0			0
$345$	13.3571	+	45.1335i	0.719124	+	2.42991i
$346$		0			0
$347$	−14.2864	−	2.51907i	−0.766932	−	0.135231i	−0.223523	−	0.974699i	$-0.571756\pi$
$347$	−14.2864	−	2.51907i	−0.766932	−	0.135231i	−0.543409	+	0.839468i	$0.682867\pi$
$348$		0			0
$349$	15.0245	+	17.9055i	0.804242	+	0.958459i	0.999753	−	0.0222430i	$-0.00708074\pi$
$349$	15.0245	+	17.9055i	0.804242	+	0.958459i	−0.195510	+	0.980702i	$0.562636\pi$
$350$		0			0
$351$	19.4846	+	7.30130i	1.04001	+	0.389714i
$352$		0			0
$353$	−26.1780	+	21.9660i	−1.39332	+	1.16913i	−0.429340	+	0.903143i	$0.641254\pi$
$353$	−26.1780	+	21.9660i	−1.39332	+	1.16913i	−0.963976	+	0.265988i	$0.914302\pi$
$354$		0			0
$355$	3.43638	+	0.605927i	0.182384	+	0.0321593i
$356$		0			0
$357$	−0.00785346	+	0.0326768i	−0.000415649	+	0.00172944i
$358$		0			0
$359$	13.5391	+	23.4504i	0.714565	+	1.23766i	0.963127	+	0.269047i	$0.0867088\pi$
$359$	13.5391	+	23.4504i	0.714565	+	1.23766i	−0.248562	+	0.968616i	$0.579958\pi$
$360$		0			0
$361$	−0.0626343	+	0.108486i	−0.00329654	+	0.00570978i
$362$		0			0
$363$	−9.55334	+	14.4259i	−0.501420	+	0.757161i
$364$		0			0
$365$	−36.7916	+	43.8465i	−1.92576	+	2.29503i
$366$		0			0
$367$	−4.30354	−	1.56636i	−0.224643	−	0.0817633i	0.227247	−	0.973837i	$-0.427028\pi$
$367$	−4.30354	−	1.56636i	−0.224643	−	0.0817633i	−0.451890	+	0.892074i	$0.649250\pi$
$368$		0			0
$369$	−15.5152	−	7.91498i	−0.807691	−	0.412038i
$370$		0			0
$371$	−0.0227096	+	0.00400432i	−0.00117902	+	0.000207894i
$372$		0			0
$373$	5.86591	+	16.1165i	0.303725	+	0.834479i	0.993845	+	0.110783i	$0.0353359\pi$
$373$	5.86591	+	16.1165i	0.303725	+	0.834479i	−0.690119	+	0.723696i	$0.742442\pi$
$374$		0			0
$375$	−15.0734	+	34.6432i	−0.778385	+	1.78897i
$376$		0			0
$377$	23.8493			1.22830
$378$		0			0
$379$		−	0.380673i		−	0.0195538i	−0.999952	−	0.00977692i	$-0.996888\pi$
$379$		−	0.380673i		−	0.0195538i	0.999952	−	0.00977692i	$-0.00311214\pi$
$380$		0			0
$381$	−2.04245	+	1.51056i	−0.104638	+	0.0773884i
$382$		0			0
$383$	−34.6697	+	12.6187i	−1.77154	+	0.644788i	−0.771578	+	0.636135i	$0.780532\pi$
$383$	−34.6697	+	12.6187i	−1.77154	+	0.644788i	−0.999963	+	0.00865253i	$0.997246\pi$
$384$		0			0
$385$	0.00703334	+	0.0398880i	0.000358452	+	0.00203288i
$386$		0			0
$387$	1.52947	−	12.4063i	0.0777473	−	0.630649i
$388$		0			0
$389$	2.44660	−	6.72197i	0.124047	−	0.340817i	−0.862088	−	0.506758i	$-0.830844\pi$
$389$	2.44660	−	6.72197i	0.124047	−	0.340817i	0.986136	+	0.165941i	$0.0530660\pi$
$390$		0			0
$391$	−10.0246	−	8.41167i	−0.506968	−	0.425397i
$392$		0			0
$393$	1.21138	−	19.7266i	0.0611060	−	0.995077i
$394$		0			0
$395$	10.9754	+	6.33665i	0.552233	+	0.318832i
$396$		0			0
$397$	−22.6986	+	13.1051i	−1.13921	+	0.657724i	−0.946235	−	0.323479i	$-0.895147\pi$
$397$	−22.6986	+	13.1051i	−1.13921	+	0.657724i	−0.192976	+	0.981203i	$0.561814\pi$
$398$		0			0
$399$	−0.0529672	+	0.0557885i	−0.00265168	+	0.00279292i
$400$		0			0
$401$	3.00071	−	17.0179i	0.149848	−	0.849832i	−0.813497	−	0.581569i	$-0.802439\pi$
$401$	3.00071	−	17.0179i	0.149848	−	0.849832i	0.963346	−	0.268263i	$-0.0864497\pi$
$402$		0			0
$403$	−20.5302	−	24.4669i	−1.02268	−	1.21878i
$404$		0			0
$405$	−25.4924	−	24.6660i	−1.26673	−	1.22566i
$406$		0			0
$407$	−5.92033	+	4.96775i	−0.293460	+	0.246242i
$408$		0			0
$409$	−4.27076	+	24.2207i	−0.211176	+	1.19764i	0.676245	+	0.736677i	$0.263606\pi$
$409$	−4.27076	+	24.2207i	−0.211176	+	1.19764i	−0.887421	+	0.460960i	$0.847505\pi$
$410$		0			0
$411$	5.36412	+	5.09285i	0.264592	+	0.251212i
$412$		0			0
$413$	0.0581420	−	0.0335683i	0.00286098	−	0.00165179i
$414$		0			0
$415$	−29.9502	+	51.8753i	−1.47020	+	2.54646i
$416$		0			0
$417$	−0.113075	+	1.84136i	−0.00553731	+	0.0901720i
$418$		0			0
$419$	−8.86909	+	10.5698i	−0.433283	+	0.516367i	−0.937867	−	0.346996i	$-0.887202\pi$
$419$	−8.86909	+	10.5698i	−0.433283	+	0.516367i	0.504583	+	0.863363i	$0.331646\pi$
$420$		0			0
$421$	12.5029	−	34.3515i	0.609355	−	1.67419i	−0.122281	−	0.992496i	$-0.539021\pi$
$421$	12.5029	−	34.3515i	0.609355	−	1.67419i	0.731637	−	0.681695i	$-0.238757\pi$
$422$		0			0
$423$	9.27312	+	21.8759i	0.450875	+	1.06364i
$424$		0			0
$425$	−3.47188	−	19.6900i	−0.168411	−	0.955106i
$426$		0			0
$427$	−0.000379315	−	0.00104216i	−1.83563e−5	−	5.04336e-5i
$428$		0			0
$429$	−5.60561	+	4.14581i	−0.270641	+	0.200162i
$430$		0			0
$431$	−7.44743			−0.358730			−0.179365	−	0.983783i	$-0.557404\pi$
$431$	−7.44743			−0.358730			−0.179365	+	0.983783i	$0.557404\pi$
$432$		0			0
$433$	20.9407			1.00634			0.503172	−	0.864186i	$-0.332166\pi$
$433$	20.9407			1.00634			0.503172	+	0.864186i	$0.332166\pi$
$434$		0			0
$435$	−37.2815	−	16.2213i	−1.78751	−	0.777751i
$436$		0			0
$437$	−10.2451	−	28.1482i	−0.490090	−	1.34651i
$438$		0			0
$439$	−4.88555	−	27.7073i	−0.233174	−	1.32240i	−0.846424	−	0.532509i	$-0.821249\pi$
$439$	−4.88555	−	27.7073i	−0.233174	−	1.32240i	0.613250	−	0.789889i	$-0.289862\pi$
$440$		0			0
$441$	−17.6174	+	11.4286i	−0.838925	+	0.544220i
$442$		0			0
$443$	−5.98423	+	16.4415i	−0.284319	+	0.781161i	0.712515	+	0.701657i	$0.247556\pi$
$443$	−5.98423	+	16.4415i	−0.284319	+	0.781161i	−0.996835	+	0.0795043i	$0.974666\pi$
$444$		0			0
$445$	−7.36537	+	8.77771i	−0.349152	+	0.416103i
$446$		0			0
$447$	−3.01577	−	1.99716i	−0.142641	−	0.0944624i
$448$		0			0
$449$	−2.99357	+	5.18501i	−0.141275	+	0.244696i	−0.927977	−	0.372637i	$-0.878454\pi$
$449$	−2.99357	+	5.18501i	−0.141275	+	0.244696i	0.786702	+	0.617333i	$0.211787\pi$
$450$		0			0
$451$	5.05428	−	2.91809i	0.237997	−	0.137408i
$452$		0			0
$453$	4.26407	−	17.7420i	0.200344	−	0.833593i
$454$		0			0
$455$	0.0280181	−	0.158899i	0.00131351	−	0.00744928i
$456$		0			0
$457$	18.6279	−	15.6306i	0.871375	−	0.731170i	−0.0930125	−	0.995665i	$-0.529650\pi$
$457$	18.6279	−	15.6306i	0.871375	−	0.731170i	0.964387	+	0.264495i	$0.0852052\pi$
$458$		0			0
$459$	9.69570	+	1.80436i	0.452556	+	0.0842201i
$460$		0			0
$461$	10.3010	+	12.2762i	0.479764	+	0.571761i	0.950584	−	0.310469i	$-0.100486\pi$
$461$	10.3010	+	12.2762i	0.479764	+	0.571761i	−0.470819	+	0.882230i	$0.656042\pi$
$462$		0			0
$463$	−0.124840	+	0.708003i	−0.00580181	+	0.0329037i	−0.987571	−	0.157172i	$-0.949762\pi$
$463$	−0.124840	+	0.708003i	−0.00580181	+	0.0329037i	0.981769	+	0.190076i	$0.0608734\pi$
$464$		0			0
$465$	15.4516	+	52.2106i	0.716550	+	2.42121i
$466$		0			0
$467$	−16.8793	+	9.74528i	−0.781082	+	0.450958i	−0.836814	−	0.547488i	$-0.815584\pi$
$467$	−16.8793	+	9.74528i	−0.781082	+	0.450958i	0.0557318	+	0.998446i	$0.482251\pi$
$468$		0			0
$469$	−0.0340678	−	0.0196690i	−0.00157310	−	0.000908231i
$470$		0			0
$471$	−34.5274	+	17.2042i	−1.59094	+	0.792726i
$472$		0			0
$473$	3.20859	+	2.69233i	0.147531	+	0.123794i
$474$		0			0
$475$	15.6530	−	43.0062i	0.718207	−	1.97326i
$476$		0			0
$477$	1.51902	+	6.59432i	0.0695511	+	0.301933i
$478$		0			0
$479$	−1.69552	−	9.61575i	−0.0774701	−	0.439355i	−0.998729	−	0.0504046i	$-0.983949\pi$
$479$	−1.69552	−	9.61575i	−0.0774701	−	0.439355i	0.921259	−	0.388950i	$-0.127162\pi$
$480$		0			0
$481$	28.9304	−	10.5298i	1.31911	−	0.480118i
$482$		0			0
$483$	0.0137909	+	0.121305i	0.000627507	+	0.00551957i
$484$		0			0
$485$			50.4227i			2.28958i
$486$		0			0
$487$	40.7197			1.84519			0.922594	−	0.385773i	$-0.126065\pi$
$487$	40.7197			1.84519			0.922594	+	0.385773i	$0.126065\pi$
$488$		0			0
$489$	14.8790	−	1.69155i	0.672850	−	0.0764947i
$490$		0			0
$491$	4.27622	+	11.7488i	0.192983	+	0.530217i	0.998012	−	0.0630180i	$-0.0200726\pi$
$491$	4.27622	+	11.7488i	0.192983	+	0.530217i	−0.805029	+	0.593235i	$0.797850\pi$
$492$		0			0
$493$	11.1321	−	1.96289i	0.501365	−	0.0884041i
$494$		0			0
$495$	11.5825	−	2.66807i	0.520596	−	0.119921i
$496$		0			0
$497$	0.00850497	+	0.00309555i	0.000381500	+	0.000138855i
$498$		0			0
$499$	2.94192	−	3.50604i	0.131698	−	0.156952i	−0.696165	−	0.717882i	$-0.745112\pi$
$499$	2.94192	−	3.50604i	0.131698	−	0.156952i	0.827863	+	0.560930i	$0.189556\pi$
$500$		0			0
$501$	6.52006	+	13.0852i	0.291295	+	0.584605i
$502$		0			0
$503$	9.68900	−	16.7818i	0.432011	−	0.748265i	−0.565035	−	0.825067i	$-0.691137\pi$
$503$	9.68900	−	16.7818i	0.432011	−	0.748265i	0.997046	+	0.0768015i	$0.0244708\pi$
$504$		0			0
$505$	−16.5134	−	28.6020i	−0.734836	−	1.27277i
$506$		0			0
$507$	5.04145	−	1.49200i	0.223899	−	0.0662622i
$508$		0			0
$509$	−2.30682	−	0.406755i	−0.102248	−	0.0180291i	0.122290	−	0.992494i	$-0.460976\pi$
$509$	−2.30682	−	0.406755i	−0.102248	−	0.0180291i	−0.224538	+	0.974465i	$0.572087\pi$
$510$		0			0
$511$	−0.113729	+	0.0954301i	−0.00503108	+	0.00422158i
$512$		0			0
$513$	17.1552	+	14.6737i	0.757420	+	0.647860i
$514$		0			0
$515$	17.6105	+	20.9874i	0.776014	+	0.924817i
$516$		0			0
$517$	−7.84049	−	1.38249i	−0.344824	−	0.0608018i
$518$		0			0
$519$	−22.8968	−	5.50296i	−1.00506	−	0.241553i
$520$		0			0
$521$	−3.33988	−	5.78485i	−0.146323	−	0.253439i	0.783543	−	0.621338i	$-0.213411\pi$
$521$	−3.33988	−	5.78485i	−0.146323	−	0.253439i	−0.929866	+	0.367899i	$0.880077\pi$
$522$		0			0
$523$	−25.4719	−	14.7062i	−1.11381	−	0.643057i	−0.173994	−	0.984747i	$-0.555667\pi$
$523$	−25.4719	−	14.7062i	−1.11381	−	0.643057i	−0.939813	+	0.341690i	$0.889001\pi$
$524$		0			0
$525$	−0.102990	+	0.155519i	−0.00449487	+	0.00678740i
$526$		0			0
$527$	−11.5965	−	9.73065i	−0.505153	−	0.423874i
$528$		0			0
$529$	−23.0590	−	8.39280i	−1.00257	−	0.364904i
$530$		0			0
$531$	−10.7221	−	16.5283i	−0.465299	−	0.717267i
$532$		0			0
$533$	−22.8959	+	4.03716i	−0.991731	+	0.174869i
$534$		0			0
$535$	52.8718	−	19.2438i	2.28585	−	0.831980i
$536$		0			0
$537$	0.205222	−	0.471662i	0.00885598	−	0.0203537i
$538$		0			0
$539$		−	7.03648i		−	0.303083i
$540$		0			0
$541$		−	1.09392i		−	0.0470312i	−0.999723	−	0.0235156i	$-0.992514\pi$
$541$		−	1.09392i		−	0.0470312i	0.999723	−	0.0235156i	$-0.00748594\pi$
$542$		0			0
$543$	1.94592	+	2.63111i	0.0835076	+	0.112912i
$544$		0			0
$545$	18.0896	−	6.58409i	0.774875	−	0.282031i
$546$		0			0
$547$	11.4033	−	2.01070i	0.487568	−	0.0859714i	0.0755403	−	0.997143i	$-0.475932\pi$
$547$	11.4033	−	2.01070i	0.487568	−	0.0859714i	0.412028	+	0.911171i	$0.364821\pi$
$548$		0			0
$549$	−0.299643	+	0.127018i	−0.0127884	+	0.00542098i
$550$		0			0
$551$	24.3143	+	8.84968i	1.03582	+	0.377009i
$552$		0			0
$553$	0.0251814	+	0.0211297i	0.00107082	+	0.000898528i
$554$		0			0
$555$	−52.3862	−	3.21695i	−2.22367	−	0.136552i
$556$		0			0
$557$	−11.9979	−	6.92697i	−0.508366	−	0.293505i	0.223796	−	0.974636i	$-0.428155\pi$
$557$	−11.9979	−	6.92697i	−0.508366	−	0.293505i	−0.732162	+	0.681131i	$0.761488\pi$
$558$		0			0
$559$	−8.34273	−	14.4500i	−0.352860	−	0.611171i
$560$		0			0
$561$	−2.27530	+	2.39649i	−0.0960633	+	0.101180i
$562$		0			0
$563$	−29.5384	−	5.20841i	−1.24489	−	0.219508i	−0.487882	−	0.872910i	$-0.662230\pi$
$563$	−29.5384	−	5.20841i	−1.24489	−	0.219508i	−0.757012	+	0.653401i	$0.773341\pi$
$564$		0			0
$565$	−11.3359	−	13.5096i	−0.476903	−	0.568351i
$566$		0			0
$567$	−0.0540079	−	0.0744888i	−0.00226812	−	0.00312823i
$568$		0			0
$569$	−13.1491	+	11.0334i	−0.551241	+	0.462546i	−0.875361	−	0.483470i	$-0.839376\pi$
$569$	−13.1491	+	11.0334i	−0.551241	+	0.462546i	0.324120	+	0.946016i	$0.394932\pi$
$570$		0			0
$571$	16.7116	+	2.94670i	0.699357	+	0.123316i	0.512012	−	0.858978i	$-0.328900\pi$
$571$	16.7116	+	2.94670i	0.699357	+	0.123316i	0.187346	+	0.982294i	$0.440012\pi$
$572$		0			0
$573$	−17.5281	−	16.6417i	−0.732248	−	0.695218i
$574$		0			0
$575$	−36.3161	−	62.9013i	−1.51449	−	2.62317i
$576$		0			0
$577$	−4.49809	+	7.79092i	−0.187258	+	0.324340i	−0.944335	−	0.328985i	$-0.893293\pi$
$577$	−4.49809	+	7.79092i	−0.187258	+	0.324340i	0.757077	+	0.653326i	$0.226627\pi$
$578$		0			0
$579$	16.4797	+	1.01199i	0.684874	+	0.0420570i
$580$		0			0
$581$	−0.0998698	+	0.119020i	−0.00414330	+	0.00493779i
$582$		0			0
$583$	−2.13072	−	0.775517i	−0.0882453	−	0.0321186i
$584$		0			0
$585$	−46.9929	−	5.79335i	−1.94292	−	0.239526i
$586$		0			0
$587$	−29.2734	+	5.16169i	−1.20824	+	0.213046i	−0.741258	−	0.671220i	$-0.765771\pi$
$587$	−29.2734	+	5.16169i	−1.20824	+	0.213046i	−0.466984	+	0.884266i	$0.654660\pi$
$588$		0			0
$589$	−11.8516	−	32.5619i	−0.488336	−	1.34169i
$590$		0			0
$591$	9.05075	+	12.2376i	0.372298	+	0.503390i
$592$		0			0
$593$	−21.5451			−0.884750			−0.442375	−	0.896830i	$-0.645864\pi$
$593$	−21.5451			−0.884750			−0.442375	+	0.896830i	$0.645864\pi$
$594$		0			0
$595$		−	0.0764747i		−	0.00313516i
$596$		0			0
$597$	−14.9608	−	6.50949i	−0.612304	−	0.266416i
$598$		0			0
$599$	10.2586	−	3.73384i	0.419156	−	0.152560i	−0.123827	−	0.992304i	$-0.539517\pi$
$599$	10.2586	−	3.73384i	0.419156	−	0.152560i	0.542983	+	0.839743i	$0.317295\pi$
$600$		0			0
$601$	−2.62710	−	14.8990i	−0.107162	−	0.607744i	−0.990335	−	0.138697i	$-0.955709\pi$
$601$	−2.62710	−	14.8990i	−0.107162	−	0.607744i	0.883173	−	0.469047i	$-0.155403\pi$
$602$		0			0
$603$	−5.24585	+	10.2831i	−0.213628	+	0.418761i
$604$		0			0
$605$	13.4661	−	36.9978i	0.547475	−	1.50417i
$606$		0			0
$607$	18.8283	+	15.7988i	0.764216	+	0.641253i	0.939221	−	0.343314i	$-0.111550\pi$
$607$	18.8283	+	15.7988i	0.764216	+	0.641253i	−0.175005	+	0.984568i	$0.555994\pi$
$608$		0			0
$609$	−0.0879254	−	0.0582275i	−0.00356292	−	0.00235950i
$610$		0			0
$611$	27.4663	+	15.8577i	1.11117	+	0.641532i
$612$		0			0
$613$	−15.6018	+	9.00768i	−0.630149	+	0.363817i	−0.780810	−	0.624769i	$-0.785193\pi$
$613$	−15.6018	+	9.00768i	−0.630149	+	0.363817i	0.150661	+	0.988586i	$0.451860\pi$
$614$		0			0
$615$	38.5369	+	9.26187i	1.55396	+	0.373475i
$616$		0			0
$617$	−4.06887	+	23.0757i	−0.163807	+	0.928994i	0.786480	+	0.617616i	$0.211902\pi$
$617$	−4.06887	+	23.0757i	−0.163807	+	0.928994i	−0.950286	+	0.311378i	$0.899210\pi$
$618$		0			0
$619$	21.6871	+	25.8457i	0.871679	+	1.03883i	0.998897	+	0.0469514i	$0.0149506\pi$
$619$	21.6871	+	25.8457i	0.871679	+	1.03883i	−0.127219	+	0.991875i	$0.540605\pi$
$620$		0			0
$621$	35.3397	−	5.88716i	1.41813	−	0.236244i
$622$		0			0
$623$	−0.0227676	+	0.0191043i	−0.000912166	+	0.000765398i
$624$		0			0
$625$	5.78239	−	32.7936i	0.231296	−	1.31174i
$626$		0			0
$627$	−7.25326	+	2.14658i	−0.289667	+	0.0857263i
$628$		0			0
$629$	12.6372	−	7.29606i	0.503876	−	0.290913i
$630$		0			0
$631$	3.55095	−	6.15043i	0.141361	−	0.244845i	−0.786648	−	0.617401i	$-0.788185\pi$
$631$	3.55095	−	6.15043i	0.141361	−	0.244845i	0.928009	+	0.372557i	$0.121519\pi$
$632$		0			0
$633$	−18.6999	+	9.31773i	−0.743256	+	0.370346i
$634$		0			0
$635$	3.71575	−	4.42826i	0.147455	−	0.175730i
$636$		0			0
$637$	−9.58703	+	26.3402i	−0.379852	+	1.04363i
$638$		0			0
$639$	0.777779	−	2.53955i	0.0307685	−	0.100463i
$640$		0			0
$641$	−0.826096	−	4.68502i	−0.0326288	−	0.185047i	0.964137	−	0.265404i	$-0.0855052\pi$
$641$	−0.826096	−	4.68502i	−0.0326288	−	0.185047i	−0.996766	+	0.0803565i	$0.974394\pi$
$642$		0			0
$643$	5.88956	+	16.1814i	0.232262	+	0.638134i	0.999997	−	0.00263392i	$-0.000838403\pi$
$643$	5.88956	+	16.1814i	0.232262	+	0.638134i	−0.767735	+	0.640768i	$0.778616\pi$
$644$		0			0
$645$	3.21313	+	28.2628i	0.126517	+	1.11284i
$646$		0			0
$647$	−38.9704			−1.53208			−0.766042	−	0.642791i	$-0.777776\pi$
$647$	−38.9704			−1.53208			−0.766042	+	0.642791i	$0.777776\pi$
$648$		0			0
$649$	6.60148			0.259131
$650$		0			0
$651$	0.0159533	+	0.140326i	0.000625260	+	0.00549981i
$652$		0			0
$653$	7.50821	+	20.6286i	0.293819	+	0.807261i	0.995499	+	0.0947692i	$0.0302113\pi$
$653$	7.50821	+	20.6286i	0.293819	+	0.807261i	−0.701680	+	0.712492i	$0.747566\pi$
$654$		0			0
$655$	7.80953	+	44.2901i	0.305144	+	1.73056i
$656$		0			0
$657$	29.6970	+	31.8774i	1.15859	+	1.24366i
$658$		0			0
$659$	10.8064	−	29.6905i	0.420960	−	1.15658i	−0.530199	−	0.847873i	$-0.677883\pi$
$659$	10.8064	−	29.6905i	0.420960	−	1.15658i	0.951158	−	0.308703i	$-0.0998950\pi$
$660$		0			0
$661$	−0.564964	+	0.673298i	−0.0219746	+	0.0261883i	−0.776920	−	0.629600i	$-0.783219\pi$
$661$	−0.564964	+	0.673298i	−0.0219746	+	0.0261883i	0.754945	+	0.655788i	$0.227663\pi$
$662$		0			0
$663$	11.7825	−	5.87092i	0.457593	−	0.228008i
$664$		0			0
$665$	0.0875262	−	0.151600i	0.00339412	−	0.00587879i
$666$		0			0
$667$	35.5624	−	20.5319i	1.37698	−	0.795000i
$668$		0			0
$669$	5.89494	−	1.74459i	0.227912	−	0.0674498i
$670$		0			0
$671$	0.0189365	−	0.107394i	0.000731036	−	0.00414591i
$672$		0			0
$673$	2.60760	−	2.18804i	0.100516	−	0.0843426i	−0.591145	−	0.806565i	$-0.701324\pi$
$673$	2.60760	−	2.18804i	0.100516	−	0.0843426i	0.691661	+	0.722223i	$0.256879\pi$
$674$		0			0
$675$	47.1432	+	27.8161i	1.81454	+	1.07064i
$676$		0			0
$677$	−12.0910	−	14.4095i	−0.464695	−	0.553802i	0.481900	−	0.876226i	$-0.339947\pi$
$677$	−12.0910	−	14.4095i	−0.464695	−	0.553802i	−0.946595	+	0.322424i	$0.895502\pi$
$678$		0			0
$679$	−0.0227108	+	0.128799i	−0.000871561	+	0.00494287i
$680$		0			0
$681$	18.3204	+	4.40308i	0.702038	+	0.168726i
$682$		0			0
$683$	−19.4488	+	11.2288i	−0.744188	+	0.429657i	−0.823590	−	0.567186i	$-0.808032\pi$
$683$	−19.4488	+	11.2288i	−0.744188	+	0.429657i	0.0794021	+	0.996843i	$0.474699\pi$
$684$		0			0
$685$	−14.5765	−	8.41573i	−0.556938	−	0.321548i
$686$		0			0
$687$	−11.3473	−	7.51461i	−0.432926	−	0.286700i
$688$		0			0
$689$	6.91944	+	5.80610i	0.263610	+	0.221195i
$690$		0			0
$691$	−14.6665	+	40.2960i	−0.557941	+	1.53293i	0.264677	+	0.964337i	$0.414735\pi$
$691$	−14.6665	+	40.2960i	−0.557941	+	1.53293i	−0.822618	+	0.568594i	$0.807488\pi$
$692$		0			0
$693$	0.0307881	−	0.00159842i	0.00116954	−	6.07191e-5i
$694$		0			0
$695$	−0.728974	−	4.13422i	−0.0276515	−	0.156820i
$696$		0			0
$697$	−10.3548	+	3.76883i	−0.392215	+	0.142755i
$698$		0			0
$699$	38.4304	+	16.7212i	1.45357	+	0.632455i
$700$		0			0
$701$		−	30.9274i		−	1.16811i	−0.811714	−	0.584055i	$-0.801465\pi$
$701$		−	30.9274i		−	1.16811i	0.811714	−	0.584055i	$-0.198535\pi$
$702$		0			0
$703$	33.4017			1.25977
$704$		0			0
$705$	−32.1498	−	43.4702i	−1.21083	−	1.63718i
$706$		0			0
$707$	−0.0292991	−	0.0804987i	−0.00110191	−	0.00302746i
$708$		0			0
$709$	−10.5402	+	1.85852i	−0.395845	+	0.0697982i	−0.368028	−	0.929815i	$-0.619967\pi$
$709$	−10.5402	+	1.85852i	−0.395845	+	0.0697982i	−0.0278175	+	0.999613i	$0.508856\pi$
$710$		0			0
$711$	5.80913	−	7.70112i	0.217859	−	0.288815i
$712$		0			0
$713$	−51.6766	−	18.8088i	−1.93531	−	0.704394i
$714$		0			0
$715$	10.1981	−	12.1536i	0.381386	−	0.454518i
$716$		0			0
$717$	52.1445	+	3.20211i	1.94737	+	0.119585i
$718$		0			0
$719$	−7.98318	+	13.8273i	−0.297723	+	0.515671i	−0.975615	−	0.219491i	$-0.929560\pi$
$719$	−7.98318	+	13.8273i	−0.297723	+	0.515671i	0.677892	+	0.735161i	$0.262894\pi$
$720$		0			0
$721$	0.0355314	+	0.0615422i	0.00132326	+	0.00229195i
$722$		0			0
$723$	−3.14426	−	2.98525i	−0.116936	−	0.111023i
$724$		0			0
$725$	61.7861	+	10.8946i	2.29468	+	0.404614i
$726$		0			0
$727$	−18.0652	+	15.1585i	−0.670002	+	0.562198i	−0.913066	−	0.407812i	$-0.866292\pi$
$727$	−18.0652	+	15.1585i	−0.670002	+	0.562198i	0.243064	+	0.970010i	$0.421847\pi$
$728$		0			0
$729$	−21.0079	+	16.9608i	−0.778069	+	0.628178i
$730$		0			0
$731$	−5.08341	−	6.05817i	−0.188017	−	0.224069i
$732$		0			0
$733$	−5.12011	−	0.902813i	−0.189115	−	0.0333462i	0.0782882	−	0.996931i	$-0.475055\pi$
$733$	−5.12011	−	0.902813i	−0.189115	−	0.0333462i	−0.267404	+	0.963585i	$0.586166\pi$
$734$		0			0
$735$	32.9020	−	34.6544i	1.21361	−	1.27825i
$736$		0			0
$737$	−1.93404	−	3.34985i	−0.0712412	−	0.123393i
$738$		0			0
$739$	10.5638	+	6.09903i	0.388596	+	0.224356i	0.681552	−	0.731770i	$-0.261305\pi$
$739$	10.5638	+	6.09903i	0.388596	+	0.224356i	−0.292955	+	0.956126i	$0.594639\pi$
$740$		0			0
$741$	30.0763	+	1.84694i	1.10488	+	0.0678489i
$742$		0			0
$743$	11.5486	+	9.69040i	0.423676	+	0.355506i	0.829559	−	0.558419i	$-0.188592\pi$
$743$	11.5486	+	9.69040i	0.423676	+	0.355506i	−0.405883	+	0.913925i	$0.633036\pi$
$744$		0			0
$745$	7.73451	+	2.81513i	0.283371	+	0.103138i
$746$		0			0
$747$	36.3994	+	27.4568i	1.33178	+	1.00459i
$748$		0			0
$749$	0.143723	−	0.0253422i	0.00525153	−	0.000925986i
$750$		0			0
$751$	1.35242	−	0.492239i	0.0493504	−	0.0179621i	−0.317227	−	0.948350i	$-0.602752\pi$
$751$	1.35242	−	0.492239i	0.0493504	−	0.0179621i	0.366577	+	0.930388i	$0.380529\pi$
$752$		0			0
$753$	17.2474	+	23.3204i	0.628529	+	0.849843i
$754$		0			0
$755$			41.5223i			1.51115i
$756$		0			0
$757$			15.3476i			0.557818i	0.960318	+	0.278909i	$0.0899727\pi$
$757$			15.3476i			0.557818i	−0.960318	+	0.278909i	$0.910027\pi$
$758$		0			0
$759$	−4.78953	+	11.0078i	−0.173849	+	0.399558i
$760$		0			0
$761$	−3.86991	+	1.40853i	−0.140284	+	0.0510593i	−0.411208	−	0.911541i	$-0.634893\pi$
$761$	−3.86991	+	1.40853i	−0.140284	+	0.0510593i	0.270924	+	0.962601i	$0.412671\pi$
$762$		0			0
$763$	0.0491736	−	0.00867063i	0.00178020	−	0.000313898i
$764$		0			0
$765$	−22.4116	+	1.16354i	−0.810292	+	0.0420679i
$766$		0			0
$767$	−24.7118	−	8.99435i	−0.892291	−	0.324767i
$768$		0			0
$769$	36.4911	+	30.6197i	1.31590	+	1.10417i	0.987156	+	0.159757i	$0.0510710\pi$
$769$	36.4911	+	30.6197i	1.31590	+	1.10417i	0.328748	+	0.944418i	$0.393373\pi$
$770$		0			0
$771$	25.5762	−	38.6209i	0.921104	−	1.39090i
$772$		0			0
$773$	−4.04314	−	2.33431i	−0.145422	−	0.0839592i	0.425524	−	0.904947i	$-0.360090\pi$
$773$	−4.04314	−	2.33431i	−0.145422	−	0.0839592i	−0.570945	+	0.820988i	$0.693423\pi$
$774$		0			0
$775$	−42.0105	−	72.7644i	−1.50906	−	2.61377i
$776$		0			0
$777$	−0.132366	−	0.0318126i	−0.00474861	−	0.00114127i
$778$		0			0
$779$	−24.8403	−	4.38001i	−0.889996	−	0.156930i
$780$		0			0
$781$	0.572053	+	0.681746i	0.0204697	+	0.0243948i
$782$		0			0
$783$	−15.7263	+	26.6532i	−0.562013	+	0.952508i
$784$		0			0
$785$	67.2447	−	56.4250i	2.40007	−	2.01390i
$786$		0			0
$787$	−16.1106	−	2.84073i	−0.574279	−	0.101261i	−0.121037	−	0.992648i	$-0.538622\pi$
$787$	−16.1106	−	2.84073i	−0.574279	−	0.101261i	−0.453243	+	0.891387i	$0.649733\pi$
$788$		0			0
$789$	−7.29111	+	2.15778i	−0.259570	+	0.0768191i
$790$		0			0
$791$	−0.0228715	−	0.0396145i	−0.000813215	−	0.00140853i
$792$		0			0
$793$	−0.217209	+	0.376216i	−0.00771330	+	0.0133598i
$794$		0			0
$795$	−6.86746	−	13.7824i	−0.243564	−	0.488813i
$796$		0			0
$797$	6.71611	−	8.00395i	0.237897	−	0.283514i	−0.633866	−	0.773443i	$-0.718533\pi$
$797$	6.71611	−	8.00395i	0.237897	−	0.283514i	0.871762	+	0.489929i	$0.162977\pi$
$798$		0			0
$799$	14.1255	+	5.14126i	0.499725	+	0.181885i
$800$		0			0
$801$	5.94509	+	6.38159i	0.210059	+	0.225482i
$802$		0			0
$803$	−14.3764	+	2.53495i	−0.507333	+	0.0894566i
$804$		0			0
$805$	−0.0950175	−	0.261058i	−0.00334893	−	0.00920110i
$806$		0			0
$807$	−1.27532	+	0.144988i	−0.0448934	+	0.00510383i
$808$		0			0
$809$	5.87774			0.206650			0.103325	−	0.994648i	$-0.467052\pi$
$809$	5.87774			0.206650			0.103325	+	0.994648i	$0.467052\pi$
$810$		0			0
$811$		−	40.3341i		−	1.41632i	−0.706052	−	0.708160i	$-0.749525\pi$
$811$		−	40.3341i		−	1.41632i	0.706052	−	0.708160i	$-0.250475\pi$
$812$		0			0
$813$	2.76750	+	24.3430i	0.0970603	+	0.853745i
$814$		0			0
$815$	−32.0208	+	11.6546i	−1.12164	+	0.408243i
$816$		0			0
$817$	−3.14346	−	17.8274i	−0.109976	−	0.623703i
$818$		0			0
$819$	−0.117429	−	0.0359645i	−0.00410330	−	0.00125670i
$820$		0			0
$821$	8.31903	−	22.8563i	0.290336	−	0.797692i	−0.705681	−	0.708530i	$-0.749359\pi$
$821$	8.31903	−	22.8563i	0.290336	−	0.797692i	0.996017	−	0.0891622i	$-0.0284190\pi$
$822$		0			0
$823$	22.0384	+	18.4924i	0.768211	+	0.644605i	0.940250	−	0.340485i	$-0.110591\pi$
$823$	22.0384	+	18.4924i	0.768211	+	0.644605i	−0.172039	+	0.985090i	$0.555036\pi$
$824$		0			0
$825$	−16.4162	+	8.17981i	−0.571539	+	0.284784i
$826$		0			0
$827$	12.6598	+	7.30915i	0.440225	+	0.254164i	0.703693	−	0.710504i	$-0.251533\pi$
$827$	12.6598	+	7.30915i	0.440225	+	0.254164i	−0.263468	+	0.964668i	$0.584866\pi$
$828$		0			0
$829$	−38.2098	+	22.0604i	−1.32708	+	0.766191i	−0.984847	−	0.173424i	$-0.944517\pi$
$829$	−38.2098	+	22.0604i	−1.32708	+	0.766191i	−0.342234	+	0.939615i	$0.611184\pi$
$830$		0			0
$831$	−4.20594	−	14.2118i	−0.145903	−	0.493002i
$832$		0			0
$833$	−2.30702	+	13.0838i	−0.0799336	+	0.453326i
$834$		0			0
$835$	−21.3840	−	25.4845i	−0.740025	−	0.881927i
$836$		0			0
$837$	40.8810	−	6.81028i	1.41305	−	0.235398i
$838$		0			0
$839$	28.2388	−	23.6951i	0.974911	−	0.818047i	−0.00840301	−	0.999965i	$-0.502675\pi$
$839$	28.2388	−	23.6951i	0.974911	−	0.818047i	0.983314	+	0.181917i	$0.0582303\pi$
$840$		0			0
$841$	−1.12364	+	6.37246i	−0.0387461	+	0.219740i
$842$		0			0
$843$	7.60159	−	31.6288i	0.261813	−	1.08935i
$844$		0			0
$845$	−10.3610	+	5.98194i	−0.356430	+	0.205785i
$846$		0			0
$847$	0.0510619	−	0.0884417i	0.00175451	−	0.00303889i
$848$		0			0
$849$	−37.1218	−	24.5834i	−1.27402	−	0.843701i
$850$		0			0
$851$	34.0738	−	40.6075i	1.16803	−	1.39201i
$852$		0			0
$853$	−12.7574	+	35.0506i	−0.436804	+	1.20011i	0.504756	+	0.863262i	$0.331583\pi$
$853$	−12.7574	+	35.0506i	−0.436804	+	1.20011i	−0.941560	+	0.336846i	$0.890640\pi$
$854$		0			0
$855$	−45.7593	−	23.3438i	−1.56494	−	0.798340i
$856$		0			0
$857$	−2.38265	−	13.5127i	−0.0813899	−	0.461585i	−0.998077	−	0.0619803i	$-0.980258\pi$
$857$	−2.38265	−	13.5127i	−0.0813899	−	0.461585i	0.916687	−	0.399605i	$-0.130853\pi$
$858$		0			0
$859$	10.4655	+	28.7538i	0.357079	+	0.981067i	0.980038	+	0.198812i	$0.0637083\pi$
$859$	10.4655	+	28.7538i	0.357079	+	0.981067i	−0.622958	+	0.782255i	$0.714069\pi$
$860$		0			0
$861$	0.0942669	+	0.0410158i	0.00321261	+	0.00139782i
$862$		0			0
$863$	7.80840			0.265801			0.132900	−	0.991129i	$-0.457571\pi$
$863$	7.80840			0.265801			0.132900	+	0.991129i	$0.457571\pi$
$864$		0			0
$865$	53.5863			1.82199
$866$		0			0
$867$	−18.6573	+	13.7986i	−0.633634	+	0.468625i
$868$		0			0
$869$	1.10550	+	3.03735i	0.0375016	+	0.103035i
$870$		0			0
$871$	2.67573	+	15.1748i	0.0906636	+	0.514179i
$872$		0			0
$873$	38.0913	+	4.69596i	1.28920	+	0.158934i
$874$		0			0
$875$	0.0762675	−	0.209543i	0.00257831	−	0.00708385i
$876$		0			0
$877$	22.5373	−	26.8589i	0.761029	−	0.906959i	−0.236883	−	0.971538i	$-0.576126\pi$
$877$	22.5373	−	26.8589i	0.761029	−	0.906959i	0.997913	+	0.0645787i	$0.0205703\pi$
$878$		0			0
$879$	1.54869	−	25.2195i	0.0522359	−	0.850633i
$880$		0			0
$881$	−17.3596	+	30.0677i	−0.584859	+	1.01301i	0.410034	+	0.912070i	$0.365517\pi$
$881$	−17.3596	+	30.0677i	−0.584859	+	1.01301i	−0.994893	+	0.100936i	$0.967816\pi$
$882$		0			0
$883$	−48.4749	+	27.9870i	−1.63131	+	0.941837i	−0.647620	+	0.761963i	$0.724236\pi$
$883$	−48.4749	+	27.9870i	−1.63131	+	0.941837i	−0.983690	+	0.179874i	$0.942431\pi$
$884$		0			0
$885$	32.5121	+	30.8679i	1.09288	+	1.03761i
$886$		0			0
$887$	−5.13500	+	29.1221i	−0.172417	+	0.977823i	0.768667	+	0.639649i	$0.220920\pi$
$887$	−5.13500	+	29.1221i	−0.172417	+	0.977823i	−0.941084	+	0.338174i	$0.890191\pi$
$888$		0			0
$889$	0.0114860	−	0.00963792i	0.000385229	−	0.000323245i
$890$		0			0
$891$	−0.936863	−	8.99840i	−0.0313861	−	0.301458i
$892$		0			0
$893$	22.1175	+	26.3586i	0.740134	+	0.882057i
$894$		0			0
$895$	−0.203252	+	1.15270i	−0.00679396	+	0.0385305i
$896$		0			0
$897$	32.9269	−	34.6807i	1.09940	−	1.15795i
$898$		0			0
$899$	41.1386	−	23.7514i	1.37205	−	0.792154i
$900$		0			0
$901$	3.70763	+	2.14060i	0.123519	+	0.0713138i
$902$		0			0
$903$	−0.00452220	+	0.0736415i	−0.000150489	+	0.00245063i
$904$		0			0
$905$	−5.70454	−	4.78668i	−0.189625	−	0.159115i
$906$		0			0
$907$	11.8324	−	32.5093i	0.392889	−	1.07945i	−0.572787	−	0.819704i	$-0.694138\pi$
$907$	11.8324	−	32.5093i	0.392889	−	1.07945i	0.965676	−	0.259749i	$-0.0836399\pi$
$908$		0			0
$909$	−23.1451	+	9.81113i	−0.767673	+	0.325414i
$910$		0			0
$911$	2.10465	+	11.9361i	0.0697303	+	0.395460i	0.999619	+	0.0276180i	$0.00879219\pi$
$911$	2.10465	+	11.9361i	0.0697303	+	0.395460i	−0.929888	+	0.367842i	$0.880097\pi$
$912$		0			0
$913$	−14.3560	+	5.22516i	−0.475115	+	0.172928i
$914$		0			0
$915$	0.595428	−	0.440368i	0.0196843	−	0.0145581i
$916$		0			0
$917$			0.116652i			0.00385218i
$918$		0			0
$919$	−11.2018			−0.369514			−0.184757	−	0.982784i	$-0.559150\pi$
$919$	−11.2018			−0.369514			−0.184757	+	0.982784i	$0.559150\pi$
$920$		0			0
$921$	6.44404	−	14.8104i	0.212338	−	0.488018i
$922$		0			0
$923$	−1.21254	−	3.33144i	−0.0399114	−	0.109656i
$924$		0			0
$925$	79.7598	−	14.0638i	2.62249	−	0.462415i
$926$		0			0
$927$	17.4949	−	11.3491i	0.574607	−	0.372754i
$928$		0			0
$929$	33.5582	+	12.2142i	1.10101	+	0.400734i	0.827687	−	0.561189i	$-0.189656\pi$
$929$	33.5582	+	12.2142i	1.10101	+	0.400734i	0.273320	+	0.961923i	$0.411878\pi$
$930$		0			0
$931$	−19.5479	+	23.2962i	−0.640656	+	0.763504i
$932$		0			0
$933$	−7.68087	+	11.5984i	−0.251460	+	0.379713i
$934$		0			0
$935$	3.75984	−	6.51224i	0.122960	−	0.212973i
$936$		0			0
$937$	−13.9023	−	24.0795i	−0.454169	−	0.786643i	0.544471	−	0.838779i	$-0.316730\pi$
$937$	−13.9023	−	24.0795i	−0.454169	−	0.786643i	−0.998640	+	0.0521363i	$0.983397\pi$
$938$		0			0
$939$	−13.3825	+	55.6819i	−0.436720	+	1.81711i
$940$		0			0
$941$	−17.4040	−	3.06880i	−0.567355	−	0.100040i	−0.117390	−	0.993086i	$-0.537453\pi$
$941$	−17.4040	−	3.06880i	−0.567355	−	0.100040i	−0.449965	+	0.893046i	$0.648564\pi$
$942$		0			0
$943$	−30.6650	+	25.7310i	−0.998591	+	0.837917i
$944$		0			0
$945$	0.159104	+	0.136090i	0.00517567	+	0.00442701i
$946$		0			0
$947$	31.1472	+	37.1197i	1.01215	+	1.20623i	0.978383	+	0.206800i	$0.0663049\pi$
$947$	31.1472	+	37.1197i	1.01215	+	1.20623i	0.0337637	+	0.999430i	$0.489251\pi$
$948$		0			0
$949$	57.2701	+	10.0983i	1.85907	+	0.327804i
$950$		0			0
$951$	12.8131	+	43.2951i	0.415493	+	1.40394i
$952$		0			0
$953$	6.84000	+	11.8472i	0.221569	+	0.383770i	0.955285	−	0.295688i	$-0.0955487\pi$
$953$	6.84000	+	11.8472i	0.221569	+	0.383770i	−0.733715	+	0.679457i	$0.762215\pi$
$954$		0			0
$955$	47.6310	+	27.4998i	1.54130	+	0.889871i
$956$		0			0
$957$	−4.62460	−	9.28120i	−0.149492	−	0.300018i
$958$		0			0
$959$	−0.0334435	−	0.0280625i	−0.00107995	−	0.000906184i
$960$		0			0
$961$	−30.6492	−	11.1554i	−0.988684	−	0.359852i
$962$		0			0
$963$	−9.61347	−	41.7337i	−0.309790	−	1.34485i
$964$		0			0
$965$	−37.0002	+	6.52413i	−1.19108	+	0.210019i
$966$		0			0
$967$	−28.0120	+	10.1955i	−0.900806	+	0.327867i	−0.750576	−	0.660785i	$-0.770224\pi$
$967$	−28.0120	+	10.1955i	−0.900806	+	0.327867i	−0.150230	+	0.988651i	$0.548001\pi$
$968$		0			0
$969$	14.1907	−	1.61330i	0.455870	−	0.0518268i
$970$		0			0
$971$		−	31.5563i		−	1.01269i	−0.862331	−	0.506345i	$-0.830996\pi$
$971$		−	31.5563i		−	1.01269i	0.862331	−	0.506345i	$-0.169004\pi$
$972$		0			0
$973$		−	0.0108888i		−	0.000349078i
$974$		0			0
$975$	72.5968	−	8.25336i	2.32496	−	0.264319i
$976$		0			0
$977$	26.2819	−	9.56585i	0.840834	−	0.306039i	0.114536	−	0.993419i	$-0.463462\pi$
$977$	26.2819	−	9.56585i	0.840834	−	0.306039i	0.726297	+	0.687381i	$0.241240\pi$
$978$		0			0
$979$	−2.87804	+	0.507477i	−0.0919827	+	0.0162190i
$980$		0			0
$981$	−3.28917	−	14.2788i	−0.105015	−	0.455888i
$982$		0			0
$983$	−23.5384	−	8.56727i	−0.750758	−	0.273253i	−0.0618331	−	0.998087i	$-0.519695\pi$
$983$	−23.5384	−	8.56727i	−0.750758	−	0.273253i	−0.688925	+	0.724833i	$0.741917\pi$
$984$		0			0
$985$	−26.5326	−	22.2635i	−0.845398	−	0.709373i
$986$		0			0
$987$	−0.0625439	−	0.125521i	−0.00199079	−	0.00399536i
$988$		0			0
$989$	−24.8801	−	14.3645i	−0.791141	−	0.456766i
$990$		0			0
$991$	−11.3147	−	19.5976i	−0.359422	−	0.622537i	0.628442	−	0.777856i	$-0.283693\pi$
$991$	−11.3147	−	19.5976i	−0.359422	−	0.622537i	−0.987864	+	0.155319i	$0.950359\pi$
$992$		0			0
$993$	−1.36383	−	4.60836i	−0.0432799	−	0.146242i
$994$		0			0
$995$	36.5628	+	6.44700i	1.15912	+	0.204384i
$996$		0			0
$997$	6.16806	+	7.35081i	0.195344	+	0.232802i	0.854821	−	0.518922i	$-0.173667\pi$
$997$	6.16806	+	7.35081i	0.195344	+	0.232802i	−0.659477	+	0.751725i	$0.729222\pi$
$998$		0			0
$999$	−7.30904	+	39.2751i	−0.231248	+	1.24261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bf.a.49.19		204
4.3	odd	2		216.2.t.a.157.4	✓	204
8.3	odd	2		216.2.t.a.157.13	yes	204
8.5	even	2	inner	864.2.bf.a.49.16		204
12.11	even	2		648.2.t.a.37.31		204
24.11	even	2		648.2.t.a.37.22		204
27.16	even	9	inner	864.2.bf.a.529.16		204
108.11	even	18		648.2.t.a.613.22		204
108.43	odd	18		216.2.t.a.205.13	yes	204
216.11	even	18		648.2.t.a.613.31		204
216.43	odd	18		216.2.t.a.205.4	yes	204
216.205	even	18	inner	864.2.bf.a.529.19		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.4	✓	204	4.3	odd	2
216.2.t.a.157.13	yes	204	8.3	odd	2
216.2.t.a.205.4	yes	204	216.43	odd	18
216.2.t.a.205.13	yes	204	108.43	odd	18
648.2.t.a.37.22		204	24.11	even	2
648.2.t.a.37.31		204	12.11	even	2
648.2.t.a.613.22		204	108.11	even	18
648.2.t.a.613.31		204	216.11	even	18
864.2.bf.a.49.16		204	8.5	even	2	inner
864.2.bf.a.49.19		204	1.1	even	1	trivial
864.2.bf.a.529.16		204	27.16	even	9	inner
864.2.bf.a.529.19		204	216.205	even	18	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bf (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.195652 + 1.72096i) q^{3} +(-1.34802 - 3.70366i) q^{5} +(-0.00177522 - 0.0100678i) q^{7} +(-2.92344 + 0.673422i) q^{9} +(0.343808 - 0.944604i) q^{11} +(-2.57400 + 3.06757i) q^{13} +(6.11013 - 3.04453i) q^{15} +(-0.948987 + 1.64369i) q^{17} +(-3.76245 + 2.17225i) q^{19} +(0.0169790 - 0.00502488i) q^{21} +(-1.19728 + 6.79010i) q^{23} +(-8.06972 + 6.77130i) q^{25} +(-1.73091 - 4.89938i) q^{27} +(-3.82827 - 4.56236i) q^{29} +(-1.38501 + 7.85480i) q^{31} +(1.69290 + 0.406867i) q^{33} +(-0.0348946 + 0.0201464i) q^{35} +(-6.65823 - 3.84413i) q^{37} +(-5.78279 - 3.82958i) q^{39} +(4.44753 + 3.73192i) q^{41} +(-1.42511 + 3.91546i) q^{43} +(6.43499 + 9.91964i) q^{45} +(-1.37530 - 7.79973i) q^{47} +(6.57775 - 2.39411i) q^{49} +(-3.01441 - 1.31158i) q^{51} -2.25567i q^{53} -3.96195 q^{55} +(-4.47450 - 6.05004i) q^{57} +(2.24610 + 6.17111i) q^{59} +(0.106836 - 0.0188381i) q^{61} +(0.0119696 + 0.0282371i) q^{63} +(14.8311 + 5.39806i) q^{65} +(2.47342 - 2.94771i) q^{67} +(-11.9198 - 0.731973i) q^{69} +(-0.442665 + 0.766718i) q^{71} +(-7.26116 - 12.5767i) q^{73} +(-13.2320 - 12.5629i) q^{75} +(-0.0101204 - 0.00178450i) q^{77} +(-2.46319 + 2.06686i) q^{79} +(8.09301 - 3.93742i) q^{81} +(-9.76904 - 11.6423i) q^{83} +(7.36694 + 1.29899i) q^{85} +(7.10265 - 7.48096i) q^{87} +(-1.45362 - 2.51775i) q^{89} +(0.0354530 + 0.0204688i) q^{91} +(-13.7888 - 0.846748i) q^{93} +(13.1172 + 11.0066i) q^{95} +(-12.0217 - 4.37554i) q^{97} +(-0.368984 + 2.99302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) \) 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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