LMFDB - Embedded newform 135.2.q.a.68.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,2,Mod(2,135)] 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("135.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([2, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			68.3
Character	$\chi$	$=$	135.68
Dual form			135.2.q.a.2.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.16608 + 1.66533i) q^{2} +(-0.967587 - 1.43658i) q^{3} +(-0.729546 - 2.00441i) q^{4} +(1.90549 + 1.17008i) q^{5} +(3.52066 + 0.0638164i) q^{6} +(2.43427 - 1.13512i) q^{7} +(0.261271 + 0.0700073i) q^{8} +(-1.12755 + 2.78004i) q^{9} +(-4.17052 + 1.80887i) q^{10} +(4.08386 + 4.86695i) q^{11} +(-2.17361 + 2.98750i) q^{12} +(-1.70687 + 1.19516i) q^{13} +(-0.948196 + 5.37749i) q^{14} +(-0.162811 - 3.86956i) q^{15} +(2.84677 - 2.38873i) q^{16} +(-0.649952 + 0.174154i) q^{17} +(-3.31487 - 5.11948i) q^{18} +(2.70632 - 1.56249i) q^{19} +(0.955177 - 4.67302i) q^{20} +(-3.98606 - 2.39871i) q^{21} +(-12.8672 + 1.12573i) q^{22} +(0.191186 - 0.409999i) q^{23} +(-0.152231 - 0.443076i) q^{24} +(2.26182 + 4.45917i) q^{25} -4.23615i q^{26} +(5.08477 - 1.07011i) q^{27} +(-4.05115 - 4.05115i) q^{28} +(-1.39473 - 7.90988i) q^{29} +(6.63394 + 4.24106i) q^{30} +(-1.53858 + 0.559998i) q^{31} +(0.705611 + 8.06517i) q^{32} +(3.04030 - 10.5760i) q^{33} +(0.467869 - 1.28546i) q^{34} +(5.96666 + 0.685329i) q^{35} +(6.39494 + 0.231909i) q^{36} +(-0.739977 - 2.76163i) q^{37} +(-0.553706 + 6.32889i) q^{38} +(3.36850 + 1.29564i) q^{39} +(0.415936 + 0.439107i) q^{40} +(-9.28604 - 1.63738i) q^{41} +(8.64268 - 3.84102i) q^{42} +(3.51939 + 0.307907i) q^{43} +(6.77601 - 11.7364i) q^{44} +(-5.40142 + 3.97803i) q^{45} +(0.459846 + 0.796477i) q^{46} +(-2.65193 - 5.68707i) q^{47} +(-6.18611 - 1.77833i) q^{48} +(0.137652 - 0.164047i) q^{49} +(-10.0634 - 1.43305i) q^{50} +(0.879072 + 0.765202i) q^{51} +(3.64084 + 2.54934i) q^{52} +(-5.99520 + 5.99520i) q^{53} +(-4.14714 + 9.71563i) q^{54} +(2.08704 + 14.0524i) q^{55} +(0.715470 - 0.126157i) q^{56} +(-4.86325 - 2.37601i) q^{57} +(14.7989 + 6.90084i) q^{58} +(-6.07856 - 5.10051i) q^{59} +(-7.63741 + 3.14936i) q^{60} +(-1.53937 - 0.560286i) q^{61} +(0.861522 - 3.21525i) q^{62} +(0.410911 + 8.04727i) q^{63} +(-7.81729 - 4.51332i) q^{64} +(-4.65087 + 0.280202i) q^{65} +(14.0673 + 17.3955i) q^{66} +(-3.06805 - 4.38163i) q^{67} +(0.823246 + 1.17572i) q^{68} +(-0.773987 + 0.122055i) q^{69} +(-8.09888 + 9.13731i) q^{70} +(2.05039 + 1.18380i) q^{71} +(-0.489220 + 0.647407i) q^{72} +(0.358350 - 1.33738i) q^{73} +(5.46189 + 1.98796i) q^{74} +(4.21746 - 7.56393i) q^{75} +(-5.10626 - 4.28466i) q^{76} +(15.4658 + 7.21181i) q^{77} +(-6.08559 + 4.09885i) q^{78} +(6.73243 - 1.18711i) q^{79} +(8.21952 - 1.22075i) q^{80} +(-6.45726 - 6.26928i) q^{81} +(13.5550 - 13.5550i) q^{82} +(-3.24283 - 2.27065i) q^{83} +(-1.89998 + 9.73966i) q^{84} +(-1.44225 - 0.428647i) q^{85} +(-4.61664 + 5.50190i) q^{86} +(-10.0137 + 9.65714i) q^{87} +(0.726271 + 1.55749i) q^{88} +(-0.428822 - 0.742742i) q^{89} +(-0.326262 - 13.6338i) q^{90} +(-2.79833 + 4.84685i) q^{91} +(-0.961286 - 0.0841016i) q^{92} +(2.29320 + 1.66846i) q^{93} +(12.5632 + 2.21523i) q^{94} +(6.98511 + 0.189288i) q^{95} +(10.9036 - 8.81742i) q^{96} +(-0.340015 + 3.88639i) q^{97} +(0.112680 + 0.420527i) q^{98} +(-18.1351 + 5.86555i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22}+ \cdots + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.16608	+	1.66533i	−0.824540	+	1.17756i	0.157243	+	0.987560i	$0.449739\pi$
$2$	−1.16608	+	1.66533i	−0.824540	+	1.17756i	−0.981783	+	0.190005i	$0.939150\pi$
$3$	−0.967587	−	1.43658i	−0.558637	−	0.829413i
$3$	−0.967587	−	1.43658i	−0.558637	−	0.829413i
$4$	−0.729546	−	2.00441i	−0.364773	−	1.00221i
$5$	1.90549	+	1.17008i	0.852163	+	0.523276i
$5$	1.90549	+	1.17008i	0.852163	+	0.523276i
$6$	3.52066	+	0.0638164i	1.43731	+	0.0260529i
$7$	2.43427	−	1.13512i	0.920067	−	0.429034i	0.0959060	−	0.995390i	$-0.469425\pi$
$7$	2.43427	−	1.13512i	0.920067	−	0.429034i	0.824160	+	0.566356i	$0.191647\pi$
$8$	0.261271	+	0.0700073i	0.0923732	+	0.0247513i
$9$	−1.12755	+	2.78004i	−0.375850	+	0.926680i
$10$	−4.17052	+	1.80887i	−1.31883	+	0.572015i
$11$	4.08386	+	4.86695i	1.23133	+	1.46744i	0.835842	+	0.548970i	$0.184980\pi$
$11$	4.08386	+	4.86695i	1.23133	+	1.46744i	0.395488	+	0.918471i	$0.370576\pi$
$12$	−2.17361	+	2.98750i	−0.627466	+	0.862416i
$13$	−1.70687	+	1.19516i	−0.473401	+	0.331479i	−0.785809	−	0.618469i	$-0.787753\pi$
$13$	−1.70687	+	1.19516i	−0.473401	+	0.331479i	0.312408	+	0.949948i	$0.398864\pi$
$14$	−0.948196	+	5.37749i	−0.253416	+	1.43719i
$15$	−0.162811	−	3.86956i	−0.0420377	−	0.999116i
$16$	2.84677	−	2.38873i	0.711694	−	0.597182i
$17$	−0.649952	+	0.174154i	−0.157637	+	0.0422386i	−0.336774	−	0.941585i	$-0.609336\pi$
$17$	−0.649952	+	0.174154i	−0.157637	+	0.0422386i	0.179138	+	0.983824i	$0.442669\pi$
$18$	−3.31487	−	5.11948i	−0.781322	−	1.20667i
$19$	2.70632	−	1.56249i	0.620871	−	0.358460i	−0.156337	−	0.987704i	$-0.549969\pi$
$19$	2.70632	−	1.56249i	0.620871	−	0.358460i	0.777208	+	0.629243i	$0.216635\pi$
$20$	0.955177	−	4.67302i	0.213584	−	1.04492i
$21$	−3.98606	−	2.39871i	−0.869829	−	0.523441i
$22$	−12.8672	+	1.12573i	−2.74329	+	0.240007i
$23$	0.191186	−	0.409999i	0.0398650	−	0.0854907i	−0.885367	−	0.464893i	$-0.846093\pi$
$23$	0.191186	−	0.409999i	0.0398650	−	0.0854907i	0.925232	+	0.379403i	$0.123870\pi$
$24$	−0.152231	−	0.443076i	−0.0310740	−	0.0904425i
$25$	2.26182	+	4.45917i	0.452364	+	0.891833i
$26$		−	4.23615i		−	0.830778i
$27$	5.08477	−	1.07011i	0.978564	−	0.205942i
$28$	−4.05115	−	4.05115i	−0.765596	−	0.765596i
$29$	−1.39473	−	7.90988i	−0.258994	−	1.46883i	−0.785608	−	0.618724i	$-0.787650\pi$
$29$	−1.39473	−	7.90988i	−0.258994	−	1.46883i	0.526614	−	0.850104i	$-0.323461\pi$
$30$	6.63394	+	4.24106i	1.21119	+	0.774309i
$31$	−1.53858	+	0.559998i	−0.276338	+	0.100579i	−0.476472	−	0.879190i	$-0.658084\pi$
$31$	−1.53858	+	0.559998i	−0.276338	+	0.100579i	0.200134	+	0.979769i	$0.435862\pi$
$32$	0.705611	+	8.06517i	0.124735	+	1.42573i
$33$	3.04030	−	10.5760i	0.529249	−	1.84105i
$34$	0.467869	−	1.28546i	0.0802389	−	0.220455i
$35$	5.96666	+	0.685329i	1.00855	+	0.115842i
$36$	6.39494	+	0.231909i	1.06582	+	0.0386515i
$37$	−0.739977	−	2.76163i	−0.121651	−	0.454009i	0.878047	−	0.478575i	$-0.158846\pi$
$37$	−0.739977	−	2.76163i	−0.121651	−	0.454009i	−0.999698	+	0.0245656i	$0.992180\pi$
$38$	−0.553706	+	6.32889i	−0.0898230	+	1.02668i
$39$	3.36850	+	1.29564i	0.539392	+	0.207468i
$40$	0.415936	+	0.439107i	0.0657653	+	0.0694289i
$41$	−9.28604	−	1.63738i	−1.45024	−	0.255716i	−0.607618	−	0.794229i	$-0.707875\pi$
$41$	−9.28604	−	1.63738i	−1.45024	−	0.255716i	−0.842617	+	0.538514i	$0.818986\pi$
$42$	8.64268	−	3.84102i	1.33359	−	0.592682i
$43$	3.51939	+	0.307907i	0.536702	+	0.0469554i	0.352285	−	0.935893i	$-0.385405\pi$
$43$	3.51939	+	0.307907i	0.536702	+	0.0469554i	0.184417	+	0.982848i	$0.440960\pi$
$44$	6.77601	−	11.7364i	1.02152	−	1.76933i
$45$	−5.40142	+	3.97803i	−0.805196	+	0.593009i
$46$	0.459846	+	0.796477i	0.0678006	+	0.117434i
$47$	−2.65193	−	5.68707i	−0.386823	−	0.829545i	−0.999239	−	0.0390089i	$-0.987580\pi$
$47$	−2.65193	−	5.68707i	−0.386823	−	0.829545i	0.612416	−	0.790536i	$-0.290198\pi$
$48$	−6.18611	−	1.77833i	−0.892888	−	0.256680i
$49$	0.137652	−	0.164047i	0.0196646	−	0.0234353i
$50$	−10.0634	−	1.43305i	−1.42318	−	0.202664i
$51$	0.879072	+	0.765202i	0.123095	+	0.107150i
$52$	3.64084	+	2.54934i	0.504894	+	0.353530i
$53$	−5.99520	+	5.99520i	−0.823504	+	0.823504i	−0.986609	−	0.163105i	$-0.947849\pi$
$53$	−5.99520	+	5.99520i	−0.823504	+	0.823504i	0.163105	+	0.986609i	$0.447849\pi$
$54$	−4.14714	+	9.71563i	−0.564355	+	1.32213i
$55$	2.08704	+	14.0524i	0.281417	+	1.89483i
$56$	0.715470	−	0.126157i	0.0956087	−	0.0168584i
$57$	−4.86325	−	2.37601i	−0.644153	−	0.314710i
$58$	14.7989	+	6.90084i	1.94319	+	0.906125i
$59$	−6.07856	−	5.10051i	−0.791361	−	0.664030i	0.154721	−	0.987958i	$-0.450552\pi$
$59$	−6.07856	−	5.10051i	−0.791361	−	0.664030i	−0.946082	+	0.323928i	$0.894997\pi$
$60$	−7.63741	+	3.14936i	−0.985985	+	0.406581i
$61$	−1.53937	−	0.560286i	−0.197096	−	0.0717372i	0.241586	−	0.970379i	$-0.422332\pi$
$61$	−1.53937	−	0.560286i	−0.197096	−	0.0717372i	−0.438682	+	0.898642i	$0.644555\pi$
$62$	0.861522	−	3.21525i	0.109413	−	0.408337i
$63$	0.410911	+	8.04727i	0.0517700	+	1.01386i
$64$	−7.81729	−	4.51332i	−0.977162	−	0.564165i
$65$	−4.65087	+	0.280202i	−0.576870	+	0.0347547i
$66$	14.0673	+	17.3955i	1.73157	+	2.14124i
$67$	−3.06805	−	4.38163i	−0.374822	−	0.535302i	0.586781	−	0.809746i	$-0.300395\pi$
$67$	−3.06805	−	4.38163i	−0.374822	−	0.535302i	−0.961603	+	0.274444i	$0.911506\pi$
$68$	0.823246	+	1.17572i	0.0998333	+	0.142577i
$69$	−0.773987	+	0.122055i	−0.0931771	+	0.0146937i
$70$	−8.09888	+	9.13731i	−0.968001	+	1.09212i
$71$	2.05039	+	1.18380i	0.243337	+	0.140491i	0.616710	−	0.787191i	$-0.288465\pi$
$71$	2.05039	+	1.18380i	0.243337	+	0.140491i	−0.373372	+	0.927682i	$0.621799\pi$
$72$	−0.489220	+	0.647407i	−0.0576551	+	0.0762976i
$73$	0.358350	−	1.33738i	0.0419417	−	0.156529i	−0.941779	−	0.336232i	$-0.890847\pi$
$73$	0.358350	−	1.33738i	0.0419417	−	0.156529i	0.983721	+	0.179704i	$0.0575139\pi$
$74$	5.46189	+	1.98796i	0.634932	+	0.231096i
$75$	4.21746	−	7.56393i	0.486991	−	0.873407i
$76$	−5.10626	−	4.28466i	−0.585728	−	0.491484i
$77$	15.4658	+	7.21181i	1.76249	+	0.821861i
$78$	−6.08559	+	4.09885i	−0.689058	+	0.464103i
$79$	6.73243	−	1.18711i	0.757458	−	0.133560i	0.218435	−	0.975851i	$-0.429905\pi$
$79$	6.73243	−	1.18711i	0.757458	−	0.133560i	0.539023	+	0.842291i	$0.318794\pi$
$80$	8.21952	−	1.22075i	0.918970	−	0.136484i
$81$	−6.45726	−	6.26928i	−0.717473	−	0.696586i
$82$	13.5550	−	13.5550i	1.49690	−	1.49690i
$83$	−3.24283	−	2.27065i	−0.355946	−	0.249236i	0.381902	−	0.924203i	$-0.375269\pi$
$83$	−3.24283	−	2.27065i	−0.355946	−	0.249236i	−0.737848	+	0.674966i	$0.764158\pi$
$84$	−1.89998	+	9.73966i	−0.207305	+	1.06268i
$85$	−1.44225	−	0.428647i	−0.156435	−	0.0464933i
$86$	−4.61664	+	5.50190i	−0.497825	+	0.593285i
$87$	−10.0137	+	9.65714i	−1.07358	+	1.03535i
$88$	0.726271	+	1.55749i	0.0774208	+	0.166029i
$89$	−0.428822	−	0.742742i	−0.0454551	−	0.0787305i	0.842403	−	0.538848i	$-0.181140\pi$
$89$	−0.428822	−	0.742742i	−0.0454551	−	0.0787305i	−0.887858	+	0.460118i	$0.847807\pi$
$90$	−0.326262	−	13.6338i	−0.0343911	−	1.43713i
$91$	−2.79833	+	4.84685i	−0.293345	+	0.508088i
$92$	−0.961286	−	0.0841016i	−0.100221	−	0.00876820i
$93$	2.29320	+	1.66846i	0.237794	+	0.173011i
$94$	12.5632	+	2.21523i	1.29579	+	0.228483i
$95$	6.98511	+	0.189288i	0.716658	+	0.0194205i
$96$	10.9036	−	8.81742i	1.11284	−	0.899924i
$97$	−0.340015	+	3.88639i	−0.0345233	+	0.394603i	0.959199	+	0.282731i	$0.0912403\pi$
$97$	−0.340015	+	3.88639i	−0.0345233	+	0.394603i	−0.993723	+	0.111872i	$0.964315\pi$
$98$	0.112680	+	0.420527i	0.0113824	+	0.0424797i
$99$	−18.1351	+	5.86555i	−1.82264	+	0.589510i
$100$	7.28790	−	7.78678i	0.728790	−	0.778678i
$101$	4.66297	−	12.8114i	0.463983	−	1.27478i	−0.458482	−	0.888704i	$-0.651607\pi$
$101$	4.66297	−	12.8114i	0.463983	−	1.27478i	0.922465	−	0.386080i	$-0.126171\pi$
$102$	−2.29938	+	0.571661i	−0.227672	+	0.0566028i
$103$	0.554178	+	6.33428i	0.0546047	+	0.624135i	0.973356	+	0.229299i	$0.0736432\pi$
$103$	0.554178	+	6.33428i	0.0546047	+	0.624135i	−0.918751	+	0.394837i	$0.870801\pi$
$104$	−0.529626	+	0.192768i	−0.0519341	+	0.0189025i
$105$	−4.78873	−	9.23473i	−0.467332	−	0.901218i
$106$	−2.99312	−	16.9748i	−0.290718	−	1.64874i
$107$	7.42914	+	7.42914i	0.718202	+	0.718202i	0.968237	−	0.250035i	$-0.0804420\pi$
$107$	7.42914	+	7.42914i	0.718202	+	0.718202i	−0.250035	+	0.968237i	$0.580442\pi$
$108$	−5.85451	−	9.41127i	−0.563350	−	0.905600i
$109$		−	2.73749i		−	0.262204i	−0.991369	−	0.131102i	$-0.958148\pi$
$109$		−	2.73749i		−	0.262204i	0.991369	−	0.131102i	$-0.0418515\pi$
$110$	−25.8355	−	12.9105i	−2.46332	−	1.23097i
$111$	−3.25132	+	3.73516i	−0.308602	+	0.354525i
$112$	4.21832	−	9.04622i	0.398594	−	0.854788i
$113$	20.1756	−	1.76514i	1.89796	−	0.166050i	0.922468	−	0.386073i	$-0.126169\pi$
$113$	20.1756	−	1.76514i	1.89796	−	0.166050i	0.975495	+	0.220022i	$0.0706130\pi$
$114$	9.62774	−	5.32830i	0.901721	−	0.499041i
$115$	0.844036	−	0.557549i	0.0787067	−	0.0519917i
$116$	−14.8371	+	8.56623i	−1.37759	+	0.795354i
$117$	−1.39802	−	6.09278i	−0.129247	−	0.563278i
$118$	15.5821	−	4.17521i	1.43445	−	0.384359i
$119$	−1.38447	+	1.16171i	−0.126914	+	0.106494i
$120$	0.228360	−	1.02240i	0.0208463	−	0.0933321i
$121$	−5.09920	+	28.9190i	−0.463564	+	2.62900i
$122$	2.72808	−	1.91022i	0.246989	−	0.172944i
$123$	6.63281	+	14.9245i	0.598061	+	1.34570i
$124$	2.24493	+	2.67541i	0.201601	+	0.240259i
$125$	−0.907697	+	11.1434i	−0.0811869	+	0.996699i
$126$	−13.8805	−	8.69942i	−1.23657	−	0.775006i
$127$	1.38719	+	0.371696i	0.123093	+	0.0329827i	0.319840	−	0.947472i	$-0.396371\pi$
$127$	1.38719	+	0.371696i	0.123093	+	0.0329827i	−0.196747	+	0.980454i	$0.563038\pi$
$128$	1.95682	−	0.912480i	0.172960	−	0.0806526i
$129$	−2.96298	−	5.35383i	−0.260876	−	0.471379i
$130$	4.95664	−	8.07197i	0.434726	−	0.707958i
$131$	−6.84812	−	18.8151i	−0.598323	−	1.64388i	−0.754614	−	0.656168i	$-0.772176\pi$
$131$	−6.84812	−	18.8151i	−0.598323	−	1.64388i	0.156291	−	0.987711i	$-0.450046\pi$
$132$	−23.4167	+	1.62167i	−2.03816	+	0.141148i
$133$	4.81428	−	6.87551i	0.417451	−	0.596182i
$134$	10.8744			0.939409
$135$	10.9411	+	3.91051i	0.941661	+	0.336563i
$136$	−0.182006			−0.0156069
$137$	−7.49837	+	10.7088i	−0.640629	+	0.914913i	−0.999832	−	0.0183463i	$-0.994160\pi$
$137$	−7.49837	+	10.7088i	−0.640629	+	0.914913i	0.359202	+	0.933260i	$0.383049\pi$
$138$	0.699266	−	1.43127i	0.0595254	−	0.121838i
$139$	−4.79900	−	13.1851i	−0.407046	−	1.11835i	−0.958735	−	0.284300i	$-0.908239\pi$
$139$	−4.79900	−	13.1851i	−0.407046	−	1.11835i	0.551690	−	0.834049i	$-0.313983\pi$
$140$	−2.97927	−	12.4596i	−0.251794	−	1.05303i
$141$	−5.60399	+	9.31245i	−0.471941	+	0.784250i
$142$	−4.36232	+	2.03418i	−0.366078	+	0.170705i
$143$	−12.7874	−	3.42638i	−1.06934	−	0.286528i
$144$	3.43087	+	10.6076i	0.285906	+	0.883963i
$145$	6.59756	−	16.7042i	0.547898	−	1.38721i
$146$	1.80932	+	2.15626i	0.149740	+	0.178453i
$147$	−0.368858	−	0.0390188i	−0.0304229	−	0.00321822i
$148$	−4.99559	+	3.49795i	−0.410635	+	0.287530i
$149$	−0.199237	+	1.12993i	−0.0163222	+	0.0925675i	−0.991881	−	0.127173i	$-0.959410\pi$
$149$	−0.199237	+	1.12993i	−0.0163222	+	0.0925675i	0.975558	+	0.219740i	$0.0705209\pi$
$150$	7.67854	+	15.8436i	0.626950	+	1.29362i
$151$	1.20809	−	1.01370i	0.0983127	−	0.0824941i	−0.592307	−	0.805713i	$-0.701783\pi$
$151$	1.20809	−	1.01370i	0.0983127	−	0.0824941i	0.690619	+	0.723219i	$0.257338\pi$
$152$	0.816468	−	0.218772i	0.0662243	−	0.0177447i
$153$	0.248699	−	2.00326i	0.0201061	−	0.161954i
$154$	−30.0443	+	17.3461i	−2.42104	+	1.39779i
$155$	−3.58701	−	0.733193i	−0.288115	−	0.0588914i
$156$	0.139519	−	7.69709i	0.0111705	−	0.616260i
$157$	−13.1978	+	1.15466i	−1.05330	+	0.0921516i	−0.600629	−	0.799528i	$-0.705083\pi$
$157$	−13.1978	+	1.15466i	−1.05330	+	0.0921516i	−0.452668	+	0.891679i	$0.649528\pi$
$158$	−5.87360	+	12.5960i	−0.467278	+	1.00208i
$159$	14.4135	+	2.81174i	1.14306	+	0.222985i
$160$	−8.09236	+	16.1938i	−0.639757	+	1.28023i
$161$		−	1.21507i		−	0.0957606i
$162$	17.9701	−	3.44300i	1.41186	−	0.270507i
$163$	−13.2225	−	13.2225i	−1.03567	−	1.03567i	−0.999340	−	0.0363256i	$-0.988435\pi$
$163$	−13.2225	−	13.2225i	−1.03567	−	1.03567i	−0.0363256	−	0.999340i	$-0.511565\pi$
$164$	3.49261	+	19.8076i	0.272727	+	1.54671i
$165$	18.1681	−	16.5951i	1.41438	−	1.29193i
$166$	7.56276	−	2.75262i	0.586984	−	0.213645i
$167$	−0.657149	−	7.51125i	−0.0508517	−	0.581238i	−0.978287	−	0.207254i	$-0.933547\pi$
$167$	−0.657149	−	7.51125i	−0.0508517	−	0.581238i	0.927435	−	0.373983i	$-0.122008\pi$
$168$	−0.873514	−	0.905766i	−0.0673931	−	0.0698813i
$169$	−2.96127	+	8.13602i	−0.227790	+	0.625848i
$170$	2.39562	−	1.90199i	0.183735	−	0.145876i
$171$	1.29228	+	9.28546i	0.0988233	+	0.710077i
$172$	−1.95039	−	7.27894i	−0.148715	−	0.555014i
$173$	−0.654858	+	7.48506i	−0.0497879	+	0.569078i	0.929800	+	0.368064i	$0.119979\pi$
$173$	−0.654858	+	7.48506i	−0.0497879	+	0.569078i	−0.979588	+	0.201014i	$0.935576\pi$
$174$	−4.40558	−	27.9371i	−0.333986	−	2.11790i
$175$	10.5676	+	8.28737i	0.798832	+	0.626466i
$176$	23.2516	+	4.09989i	1.75266	+	0.309041i
$177$	−1.44579	+	13.6676i	−0.108672	+	1.02732i
$178$	1.73695	+	0.151963i	0.130190	+	0.0113901i
$179$	−6.45949	+	11.1882i	−0.482805	+	0.836242i	−0.999805	−	0.0197428i	$-0.993715\pi$
$179$	−6.45949	+	11.1882i	−0.482805	+	0.836242i	0.517000	+	0.855985i	$0.327049\pi$
$180$	11.9142	+	7.92450i	0.888031	+	0.590658i
$181$	−2.64164	−	4.57545i	−0.196351	−	0.340091i	0.750991	−	0.660312i	$-0.229576\pi$
$181$	−2.64164	−	4.57545i	−0.196351	−	0.340091i	−0.947343	+	0.320222i	$0.896243\pi$
$182$	−4.80853	−	10.3119i	−0.356432	−	0.764371i
$183$	0.684578	+	2.75356i	0.0506055	+	0.203549i
$184$	0.0786542	−	0.0937365i	0.00579847	−	0.00691034i
$185$	1.82131	−	6.12810i	0.133905	−	0.450547i
$186$	−5.45257	+	1.87338i	−0.399802	+	0.137363i
$187$	−3.50191	−	2.45207i	−0.256085	−	0.179313i
$188$	−9.46453	+	9.46453i	−0.690272	+	0.690272i
$189$	11.1630	−	8.37674i	0.811988	−	0.609318i
$190$	−8.46039	+	11.4118i	−0.613782	+	0.827898i
$191$	18.3259	−	3.23135i	1.32602	−	0.233812i	0.534607	−	0.845101i	$-0.320460\pi$
$191$	18.3259	−	3.23135i	1.32602	−	0.233812i	0.791408	+	0.611288i	$0.209348\pi$
$192$	1.08015	+	15.5972i	0.0779530	+	1.12563i
$193$	−5.20146	−	2.42548i	−0.374410	−	0.174590i	0.226300	−	0.974058i	$-0.427337\pi$
$193$	−5.20146	−	2.42548i	−0.374410	−	0.174590i	−0.600709	+	0.799468i	$0.705115\pi$
$194$	−6.07563	−	5.09806i	−0.436205	−	0.366020i
$195$	4.90266	+	6.41025i	0.351087	+	0.459048i
$196$	−0.429242	−	0.156231i	−0.0306601	−	0.0111594i
$197$	4.40513	−	16.4402i	0.313852	−	1.17131i	−0.611201	−	0.791475i	$-0.709313\pi$
$197$	4.40513	−	16.4402i	0.313852	−	1.17131i	0.925053	−	0.379837i	$-0.124020\pi$
$198$	11.3788	−	37.0405i	0.808657	−	2.63236i
$199$	20.0824	+	11.5946i	1.42361	+	0.821920i	0.996605	−	0.0823307i	$-0.0262364\pi$
$199$	20.0824	+	11.5946i	1.42361	+	0.821920i	0.427002	+	0.904251i	$0.359570\pi$
$200$	0.278774	+	1.32339i	0.0197123	+	0.0935781i
$201$	−3.32598	+	8.64713i	−0.234597	+	0.609922i
$202$	15.8978	+	22.7045i	1.11857	+	1.59748i
$203$	−12.3738	−	17.6716i	−0.868469	−	1.24030i
$204$	0.892456	−	2.32027i	0.0624844	−	0.162452i
$205$	−15.7786	−	13.9854i	−1.10203	−	0.976785i
$206$	−11.1949	−	6.46336i	−0.779983	−	0.450324i
$207$	0.924243	+	0.993800i	0.0642393	+	0.0690738i
$208$	−2.00416	+	7.47961i	−0.138963	+	0.518618i
$209$	18.6568	+	6.79052i	1.29052	+	0.469710i
$210$	20.9629	+	2.79359i	1.44658	+	0.192776i
$211$	−1.99032	−	1.67007i	−0.137019	−	0.114973i	0.571702	−	0.820461i	$-0.306283\pi$
$211$	−1.99032	−	1.67007i	−0.137019	−	0.114973i	−0.708721	+	0.705488i	$0.750728\pi$
$212$	16.3906	+	7.64307i	1.12571	+	0.524928i
$213$	−0.283312	−	4.09099i	−0.0194122	−	0.280310i
$214$	−21.0349	+	3.70902i	−1.43792	+	0.253543i
$215$	6.34591	+	4.70469i	0.432787	+	0.320857i
$216$	1.40342	+	0.0763830i	0.0954905	+	0.00519721i
$217$	−3.10966	+	3.10966i	−0.211097	+	0.211097i
$218$	4.55882	+	3.19212i	0.308762	+	0.216198i
$219$	−2.26800	+	0.779232i	−0.153257	+	0.0526556i
$220$	26.6442	−	14.4352i	1.79635	−	0.973218i
$221$	0.901242	−	1.07406i	0.0606241	−	0.0722490i
$222$	−2.42897	−	9.76999i	−0.163022	−	0.655719i
$223$	2.13291	+	4.57405i	0.142831	+	0.306301i	0.964689	−	0.263390i	$-0.0848406\pi$
$223$	2.13291	+	4.57405i	0.142831	+	0.306301i	−0.821859	+	0.569691i	$0.807063\pi$
$224$	10.8726	+	18.8318i	0.726453	+	1.25825i
$225$	−14.9470	+	1.26002i	−0.996466	+	0.0840010i
$226$	−20.5868	+	35.6573i	−1.36941	+	2.37189i
$227$	19.6926	+	1.72288i	1.30705	+	0.114352i	0.719304	−	0.694696i	$-0.244461\pi$
$227$	19.6926	+	1.72288i	1.30705	+	0.114352i	0.587743	+	0.809048i	$0.300017\pi$
$228$	−1.21453	+	11.4814i	−0.0804341	+	0.760371i
$229$	−24.6362	−	4.34402i	−1.62800	−	0.287061i	−0.716264	−	0.697829i	$-0.754150\pi$
$229$	−24.6362	−	4.34402i	−1.62800	−	0.287061i	−0.911740	+	0.410768i	$0.865261\pi$
$230$	−0.0557080	+	2.05574i	−0.00367328	+	0.135551i
$231$	−4.60410	−	29.1959i	−0.302928	−	1.92095i
$232$	0.189349	−	2.16426i	0.0124313	−	0.142091i
$233$	2.11766	+	7.90321i	0.138732	+	0.517756i	0.999955	+	0.00952771i	$0.00303281\pi$
$233$	2.11766	+	7.90321i	0.138732	+	0.517756i	−0.861222	+	0.508229i	$0.830301\pi$
$234$	11.7767	+	4.77648i	0.769865	+	0.312248i
$235$	1.60110	−	13.9397i	0.104445	−	0.909323i
$236$	−5.78894	+	15.9050i	−0.376828	+	1.03533i
$237$	−8.21960	−	8.52308i	−0.533920	−	0.553633i
$238$	−0.320230	−	3.66024i	−0.0207574	−	0.237258i
$239$	−15.0785	+	5.48812i	−0.975347	+	0.354997i	−0.780029	−	0.625743i	$-0.784796\pi$
$239$	−15.0785	+	5.48812i	−0.975347	+	0.354997i	−0.195317	+	0.980740i	$0.562574\pi$
$240$	−9.70681	−	10.6269i	−0.626572	−	0.685960i
$241$	2.00152	+	11.3512i	0.128929	+	0.731194i	0.978896	+	0.204358i	$0.0655107\pi$
$241$	2.00152	+	11.3512i	0.128929	+	0.731194i	−0.849967	+	0.526836i	$0.823378\pi$
$242$	−42.2136	−	42.2136i	−2.71359	−	2.71359i
$243$	−2.75839	+	15.3425i	−0.176951	+	0.984220i
$244$			3.49429i			0.223699i
$245$	0.454244	−	0.151527i	0.0290206	−	0.00968073i
$246$	−32.5885	−	6.35726i	−2.07777	−	0.405324i
$247$	−2.75190	+	5.90147i	−0.175099	+	0.375501i
$248$	−0.441191	+	0.0385992i	−0.0280157	+	0.00245105i
$249$	−0.124267	+	6.85565i	−0.00787511	+	0.434459i
$250$	−17.4990	−	14.5057i	−1.10674	−	0.917421i
$251$	0.521180	−	0.300903i	0.0328966	−	0.0189928i	−0.483462	−	0.875366i	$-0.660621\pi$
$251$	0.521180	−	0.300903i	0.0328966	−	0.0189928i	0.516358	+	0.856373i	$0.327287\pi$
$252$	15.8302	−	6.69448i	0.997212	−	0.421713i
$253$	2.77622	−	0.743887i	0.174540	−	0.0467677i
$254$	−2.23656	+	1.87670i	−0.140334	+	0.117755i
$255$	0.779719	+	2.48667i	0.0488279	+	0.155722i
$256$	2.37270	−	13.4562i	0.148294	−	0.841014i
$257$	−7.22379	+	5.05815i	−0.450608	+	0.315519i	−0.776758	−	0.629799i	$-0.783137\pi$
$257$	−7.22379	+	5.05815i	−0.450608	+	0.315519i	0.326151	+	0.945318i	$0.394248\pi$
$258$	12.3709	+	1.30863i	0.770181	+	0.0814718i
$259$	−4.93607	−	5.88259i	−0.306713	−	0.365526i
$260$	3.95466	+	9.11784i	0.245258	+	0.565464i
$261$	23.5624	+	5.04141i	1.45848	+	0.312055i
$262$	39.3187	+	10.5354i	2.42912	+	0.650880i
$263$	−10.8388	+	5.05420i	−0.668347	+	0.311656i	−0.727015	−	0.686622i	$-0.759093\pi$
$263$	−10.8388	+	5.05420i	−0.668347	+	0.311656i	0.0586671	+	0.998278i	$0.481315\pi$
$264$	1.53474	−	2.55036i	0.0944568	−	0.156964i
$265$	−18.4387	+	4.40895i	−1.13268	+	0.270840i
$266$	5.83616	+	16.0347i	0.357838	+	0.983152i
$267$	−0.652089	+	1.33471i	−0.0399072	+	0.0816827i
$268$	−6.54431	+	9.34624i	−0.399757	+	0.570913i
$269$	15.6712			0.955492			0.477746	−	0.878498i	$-0.341454\pi$
$269$	15.6712			0.955492			0.477746	+	0.878498i	$0.341454\pi$
$270$	−19.2704	+	13.6606i	−1.17276	+	0.831358i
$271$	15.3544			0.932711			0.466355	−	0.884597i	$-0.345567\pi$
$271$	15.3544			0.932711			0.466355	+	0.884597i	$0.345567\pi$
$272$	−1.43426	+	2.04834i	−0.0869648	+	0.124199i
$273$	9.67054	−	0.669710i	0.585287	−	0.0405327i
$274$	−9.08998	−	24.9745i	−0.549146	−	1.50876i
$275$	−12.4656	+	29.2188i	−0.751704	+	1.76196i
$276$	0.809308	+	1.46234i	0.0487146	+	0.0880227i
$277$	3.92654	−	1.83097i	0.235923	−	0.110013i	−0.301062	−	0.953605i	$-0.597341\pi$
$277$	3.92654	−	1.83097i	0.235923	−	0.110013i	0.536985	+	0.843592i	$0.319563\pi$
$278$	27.5536	+	7.38296i	1.65255	+	0.442800i
$279$	0.178013	−	4.90875i	0.0106574	−	0.293879i
$280$	1.51094	+	0.596767i	0.0902958	+	0.0356636i
$281$	−11.4406	−	13.6344i	−0.682490	−	0.813360i	0.307935	−	0.951407i	$-0.400362\pi$
$281$	−11.4406	−	13.6344i	−0.682490	−	0.813360i	−0.990426	+	0.138047i	$0.955918\pi$
$282$	−8.97361	−	20.1915i	−0.534371	−	1.20239i
$283$	16.2591	−	11.3847i	0.966501	−	0.676752i	0.0201182	−	0.999798i	$-0.493596\pi$
$283$	16.2591	−	11.3847i	0.966501	−	0.676752i	0.946383	+	0.323046i	$0.104707\pi$
$284$	0.876956	−	4.97347i	0.0520378	−	0.295121i
$285$	−6.48678	−	10.2179i	−0.384243	−	0.605254i
$286$	20.6172	−	17.2998i	1.21912	−	1.02296i
$287$	−24.4633	+	6.55492i	−1.44402	+	0.386925i
$288$	−23.2171	−	7.13226i	−1.36808	−	0.420273i
$289$	−14.3303	+	8.27362i	−0.842960	+	0.486683i
$290$	20.1247	+	30.4654i	1.18176	+	1.78899i
$291$	5.91213	−	3.27196i	0.346575	−	0.191806i
$292$	−2.94209	+	0.257400i	−0.172173	+	0.0150632i
$293$	6.95384	−	14.9126i	0.406248	−	0.871201i	−0.591638	−	0.806204i	$-0.701518\pi$
$293$	6.95384	−	14.9126i	0.406248	−	0.871201i	0.997885	−	0.0649974i	$-0.0207039\pi$
$294$	0.495096	−	0.568771i	0.0288746	−	0.0331714i
$295$	−5.61464	−	16.8314i	−0.326897	−	0.979962i
$296$		−	0.773337i		−	0.0449493i
$297$	25.9736	+	20.3772i	1.50714	+	1.18240i
$298$	−1.64938	−	1.64938i	−0.0955460	−	0.0955460i
$299$	0.163687	+	0.928314i	0.00946626	+	0.0536858i
$300$	−18.2380	−	2.93529i	−1.05297	−	0.169469i
$301$	8.91665	−	3.24540i	0.513947	−	0.187061i
$302$	0.279431	+	3.19392i	0.0160795	+	0.183789i
$303$	−22.9165	+	5.69740i	−1.31652	+	0.327307i
$304$	3.97190	−	10.9127i	0.227804	−	0.625887i
$305$	−2.27769	−	2.86881i	−0.130420	−	0.164268i
$306$	3.04609	+	2.75012i	0.174133	+	0.157214i
$307$	0.759611	+	2.83491i	0.0433533	+	0.161797i	0.984209	−	0.177011i	$-0.0566430\pi$
$307$	0.759611	+	2.83491i	0.0433533	+	0.161797i	−0.940856	+	0.338808i	$0.889976\pi$
$308$	3.17243	−	36.2611i	0.180766	−	2.06617i
$309$	8.56351	−	6.92509i	0.487161	−	0.393955i
$310$	5.40372	−	5.11858i	0.306911	−	0.290716i
$311$	−3.75166	−	0.661519i	−0.212737	−	0.0375113i	0.0662637	−	0.997802i	$-0.478892\pi$
$311$	−3.75166	−	0.661519i	−0.212737	−	0.0375113i	−0.279001	+	0.960291i	$0.590003\pi$
$312$	0.789387	+	0.574333i	0.0446902	+	0.0325152i
$313$	0.566450	+	0.0495580i	0.0320177	+	0.00280118i	0.103153	−	0.994665i	$-0.467107\pi$
$313$	0.566450	+	0.0495580i	0.0320177	+	0.00280118i	−0.0711357	+	0.997467i	$0.522662\pi$
$314$	13.4667	−	23.3250i	0.759971	−	1.31631i
$315$	−8.63296	+	15.8148i	−0.486412	+	0.891064i
$316$	−7.29107	−	12.6285i	−0.410155	−	0.710409i
$317$	4.84025	+	10.3800i	0.271856	+	0.582997i	0.994079	−	0.108664i	$-0.0346572\pi$
$317$	4.84025	+	10.3800i	0.271856	+	0.582997i	−0.722223	+	0.691661i	$0.756879\pi$
$318$	−21.4897	+	20.7245i	−1.20508	+	1.16217i
$319$	32.8012	−	39.0909i	1.83651	−	2.18867i
$320$	−9.61487	−	17.7470i	−0.537487	−	0.992086i
$321$	3.48425	−	17.8609i	0.194472	−	0.996900i
$322$	2.02348	+	1.41686i	0.112764	+	0.0789584i
$323$	−1.48686	+	1.48686i	−0.0827312	+	0.0827312i
$324$	−7.85534	+	17.5167i	−0.436408	+	0.973151i
$325$	−9.19007	−	4.90798i	−0.509774	−	0.272246i
$326$	37.4382	−	6.60137i	2.07351	−	0.365616i
$327$	−3.93263	+	2.64876i	−0.217475	+	0.146477i
$328$	−2.31154	−	1.07789i	−0.127634	−	0.0595165i
$329$	−12.9110	−	10.8336i	−0.711806	−	0.597276i
$330$	6.45100	+	49.6070i	0.355116	+	2.73077i
$331$	24.0043	+	8.73685i	1.31940	+	0.480221i	0.903265	−	0.429084i	$-0.141164\pi$
$331$	24.0043	+	8.73685i	1.31940	+	0.480221i	0.416131	+	0.909305i	$0.363386\pi$
$332$	−2.18553	+	8.15650i	−0.119946	+	0.447646i
$333$	8.51181	+	1.05671i	0.466444	+	0.0579076i
$334$	13.2750	+	7.66431i	0.726374	+	0.419372i
$335$	−0.719293	−	11.9391i	−0.0392992	−	0.652300i
$336$	−17.0773	+	2.69303i	−0.931641	+	0.146917i
$337$	−10.1438	−	14.4868i	−0.552566	−	0.789147i	0.441576	−	0.897224i	$-0.354420\pi$
$337$	−10.1438	−	14.4868i	−0.552566	−	0.789147i	−0.994143	+	0.108077i	$0.965531\pi$
$338$	−10.0961	−	14.4187i	−0.549154	−	0.784274i
$339$	−22.0574	−	27.2761i	−1.19800	−	1.48143i
$340$	0.193007	+	3.20359i	0.0104673	+	0.173739i
$341$	−9.00884	−	5.20126i	−0.487856	−	0.281664i
$342$	−16.9702	−	8.67547i	−0.917645	−	0.469116i
$343$	−4.71730	+	17.6052i	−0.254710	+	0.950591i
$344$	0.897959	+	0.326830i	0.0484147	+	0.0176215i
$345$	−1.61764	−	0.673052i	−0.0870910	−	0.0362359i
$346$	−11.7015	−	9.81869i	−0.629075	−	0.527856i
$347$	−2.02390	−	0.943762i	−0.108649	−	0.0506638i	0.367534	−	0.930010i	$-0.380202\pi$
$347$	−2.02390	−	0.943762i	−0.108649	−	0.0506638i	−0.476183	+	0.879346i	$0.657980\pi$
$348$	26.6623	+	13.0262i	1.42925	+	0.698280i
$349$	18.9031	−	3.33312i	1.01186	−	0.178418i	0.356948	−	0.934124i	$-0.383817\pi$
$349$	18.9031	−	3.33312i	1.01186	−	0.178418i	0.654910	+	0.755707i	$0.272706\pi$
$350$	−26.1238	+	7.93475i	−1.39637	+	0.424130i
$351$	−7.40009	+	7.90367i	−0.394988	+	0.421867i
$352$	−36.3712	+	36.3712i	−1.93859	+	1.93859i
$353$	24.3407	+	17.0436i	1.29553	+	0.907137i	0.998855	−	0.0478427i	$-0.0152346\pi$
$353$	24.3407	+	17.0436i	1.29553	+	0.907137i	0.296671	+	0.954980i	$0.404124\pi$
$354$	−21.0751	−	18.3451i	−1.12013	−	0.975032i
$355$	2.52188	+	4.65484i	0.133847	+	0.247053i
$356$	−1.17591	+	1.40140i	−0.0623233	+	0.0742741i
$357$	3.00849	+	0.864856i	0.159226	+	0.0457730i
$358$	−11.0997	−	23.8034i	−0.586638	−	1.25805i
$359$	−14.0984	−	24.4191i	−0.744085	−	1.28879i	−0.950621	−	0.310354i	$-0.899552\pi$
$359$	−14.0984	−	24.4191i	−0.744085	−	1.28879i	0.206536	−	0.978439i	$-0.433781\pi$
$360$	−1.68972	+	0.661204i	−0.0890563	+	0.0348485i
$361$	−4.61724	+	7.99729i	−0.243012	+	0.420910i
$362$	10.7000	+	0.936127i	0.562378	+	0.0492017i
$363$	46.4785	−	20.6562i	2.43949	−	1.08417i
$364$	11.7566	+	2.07300i	0.616212	+	0.108655i
$365$	2.24768	−	2.12907i	0.117649	−	0.111441i
$366$	−5.38386	−	2.07081i	−0.281419	−	0.108243i
$367$	2.09671	−	23.9655i	0.109447	−	1.25099i	−0.720622	−	0.693328i	$-0.756144\pi$
$367$	2.09671	−	23.9655i	0.109447	−	1.25099i	0.830069	−	0.557660i	$-0.188301\pi$
$368$	−0.435114	−	1.62387i	−0.0226819	−	0.0846499i
$369$	15.0225	−	23.9693i	0.782038	−	1.24779i
$370$	8.08152	+	10.1789i	0.420138	+	0.529176i
$371$	−7.78866	+	21.3992i	−0.404367	+	1.11099i
$372$	1.67128	−	5.81373i	0.0866519	−	0.301428i
$373$	0.625791	+	7.15282i	0.0324022	+	0.370359i	0.995033	+	0.0995428i	$0.0317380\pi$
$373$	0.625791	+	7.15282i	0.0324022	+	0.370359i	−0.962631	+	0.270816i	$0.912706\pi$
$374$	8.16699	−	2.97254i	0.422305	−	0.153706i
$375$	16.8868	−	9.47825i	0.872029	−	0.489455i
$376$	−0.294734	−	1.67152i	−0.0151998	−	0.0862021i
$377$	11.8342	+	11.8342i	0.609494	+	0.609494i
$378$	0.933134	+	28.3579i	0.0479952	+	1.45858i
$379$			6.61098i			0.339583i	0.985480	+	0.169792i	$0.0543094\pi$
$379$			6.61098i			0.339583i	−0.985480	+	0.169792i	$0.945691\pi$
$380$	−4.71655	−	14.1391i	−0.241954	−	0.725322i
$381$	−0.808252	−	2.35246i	−0.0414080	−	0.120520i
$382$	−15.9881	+	34.2866i	−0.818023	+	1.75426i
$383$	−9.74694	+	0.852747i	−0.498046	+	0.0435733i	−0.333412	−	0.942781i	$-0.608200\pi$
$383$	−9.74694	+	0.852747i	−0.498046	+	0.0435733i	−0.164634	+	0.986355i	$0.552644\pi$
$384$	−3.20425	−	1.92823i	−0.163516	−	0.0983998i
$385$	21.0315	+	31.8383i	1.07187	+	1.62263i
$386$	10.1045	−	5.83385i	0.514307	−	0.296935i
$387$	−4.82429	+	9.43687i	−0.245232	+	0.479703i
$388$	8.03798	−	2.15377i	0.408067	−	0.109341i
$389$	−7.47118	+	6.26906i	−0.378804	+	0.317854i	−0.812233	−	0.583334i	$-0.801748\pi$
$389$	−7.47118	+	6.26906i	−0.378804	+	0.317854i	0.433429	+	0.901188i	$0.357304\pi$
$390$	−16.3920	+	0.689693i	−0.830043	+	0.0349240i
$391$	−0.0528585	+	0.299776i	−0.00267317	+	0.0151603i
$392$	0.0474490	−	0.0332242i	0.00239654	−	0.00167807i
$393$	−20.4033	+	28.0431i	−1.02921	+	1.41459i
$394$	22.2415	+	26.5064i	1.12051	+	1.33538i
$395$	14.2176	+	5.61546i	0.715366	+	0.282544i
$396$	24.9874	+	32.0710i	1.25566	+	1.61163i
$397$	21.9105	+	5.87091i	1.09966	+	0.294653i	0.762626	−	0.646840i	$-0.223910\pi$
$397$	21.9105	+	5.87091i	1.09966	+	0.294653i	0.337033	+	0.941493i	$0.390577\pi$
$398$	−42.7265	+	19.9237i	−2.14168	+	0.998684i
$399$	−14.5355	−	0.263474i	−0.727685	−	0.0131902i
$400$	17.0906	+	7.29137i	0.854531	+	0.364568i
$401$	10.7416	+	29.5124i	0.536411	+	1.47378i	0.851316	+	0.524654i	$0.175805\pi$
$401$	10.7416	+	29.5124i	0.536411	+	1.47378i	−0.314905	+	0.949123i	$0.601973\pi$
$402$	−10.5220	−	15.6221i	−0.524788	−	0.779157i
$403$	1.95687	−	2.79470i	0.0974788	−	0.139214i
$404$	−29.0812			−1.44684
$405$	−4.96870	−	19.5016i	−0.246897	−	0.969042i
$406$	43.8578			2.17662
$407$	10.4188	−	14.8795i	0.516439	−	0.737551i
$408$	0.176106	+	0.261467i	0.00871856	+	0.0129445i
$409$	9.77070	+	26.8448i	0.483130	+	1.32739i	0.906796	+	0.421570i	$0.138521\pi$
$409$	9.77070	+	26.8448i	0.483130	+	1.32739i	−0.423666	+	0.905818i	$0.639257\pi$
$410$	41.6894	−	9.96853i	2.05889	−	0.492310i
$411$	22.6394	+	0.410367i	1.11672	+	0.0202419i
$412$	12.2922	−	5.73195i	0.605593	−	0.282393i
$413$	−20.5865	−	5.51614i	−1.01300	−	0.271432i
$414$	−2.73274	+	0.380323i	−0.134307	+	0.0186918i
$415$	−3.52234	−	8.12108i	−0.172905	−	0.398648i
$416$	−10.8436	−	12.9229i	−0.531650	−	0.633596i
$417$	−14.2981	+	19.6519i	−0.700182	+	0.962360i
$418$	−33.0637	+	23.1514i	−1.61720	+	1.13237i
$419$	−0.704690	+	3.99650i	−0.0344264	+	0.195242i	−0.997171	−	0.0751721i	$-0.976049\pi$
$419$	−0.704690	+	3.99650i	−0.0344264	+	0.195242i	0.962744	+	0.270414i	$0.0871605\pi$
$420$	−15.0166	+	16.3357i	−0.732735	+	0.797103i
$421$	−7.52582	+	6.31491i	−0.366786	+	0.307770i	−0.807489	−	0.589883i	$-0.799174\pi$
$421$	−7.52582	+	6.31491i	−0.366786	+	0.307770i	0.440703	+	0.897653i	$0.354729\pi$
$422$	5.10208	−	1.36710i	0.248366	−	0.0665493i
$423$	18.8005	−	0.959995i	0.914110	−	0.0466765i
$424$	−1.98608	+	1.14666i	−0.0964525	+	0.0556869i
$425$	−2.24666	−	2.50434i	−0.108979	−	0.121478i
$426$	7.14320	+	4.29860i	0.346089	+	0.208268i
$427$	−4.38323	+	0.383483i	−0.212119	+	0.0185581i
$428$	9.47115	−	20.3110i	0.457805	−	0.981767i
$429$	7.45066	+	21.6855i	0.359721	+	1.04699i
$430$	−15.2347	+	5.08200i	−0.734680	+	0.245076i
$431$		−	3.57709i		−	0.172302i	−0.996282	−	0.0861512i	$-0.972543\pi$
$431$		−	3.57709i		−	0.172302i	0.996282	−	0.0861512i	$-0.0274568\pi$
$432$	11.9190	−	15.1925i	0.573453	−	0.730949i
$433$	0.671243	+	0.671243i	0.0322579	+	0.0322579i	0.723052	−	0.690794i	$-0.242739\pi$
$433$	0.671243	+	0.671243i	0.0322579	+	0.0322579i	−0.690794	+	0.723052i	$0.742739\pi$
$434$	−1.55251	−	8.80470i	−0.0745227	−	0.422639i
$435$	−30.3807	+	6.68479i	−1.45664	+	0.320511i
$436$	−5.48705	+	1.99712i	−0.262782	+	0.0956449i
$437$	−0.123211	−	1.40831i	−0.00589400	−	0.0673688i
$438$	1.34698	−	4.68560i	0.0643611	−	0.223887i
$439$	−11.2524	+	30.9157i	−0.537048	+	1.47553i	0.313479	+	0.949595i	$0.398505\pi$
$439$	−11.2524	+	30.9157i	−0.537048	+	1.47553i	−0.850527	+	0.525932i	$0.823717\pi$
$440$	−0.438488	+	3.81759i	−0.0209041	+	0.181997i
$441$	0.300849	+	0.567650i	0.0143261	+	0.0270310i
$442$	0.737744	+	2.75330i	0.0350909	+	0.130961i
$443$	1.95389	−	22.3331i	0.0928322	−	1.06108i	−0.796752	−	0.604306i	$-0.793450\pi$
$443$	1.95389	−	22.3331i	0.0928322	−	1.06108i	0.889585	−	0.456771i	$-0.150994\pi$
$444$	9.85878	+	3.79202i	0.467877	+	0.179961i
$445$	0.0519496	−	1.91705i	0.00246265	−	0.0908768i
$446$	−10.1044	−	1.78168i	−0.478459	−	0.0843652i
$447$	1.81602	−	0.807085i	0.0858948	−	0.0381738i
$448$	−24.1525	−	2.11307i	−1.14110	−	0.0998333i
$449$	−4.96273	+	8.59571i	−0.234206	+	0.405656i	−0.959042	−	0.283265i	$-0.908582\pi$
$449$	−4.96273	+	8.59571i	−0.234206	+	0.405656i	0.724836	+	0.688922i	$0.241916\pi$
$450$	15.3310	−	26.3609i	0.722709	−	1.24267i
$451$	−29.9538	−	51.8815i	−1.41047	−	2.44301i
$452$	−18.2571	−	39.1525i	−0.858742	−	1.84158i
$453$	−2.62520	−	0.754671i	−0.123343	−	0.0354575i
$454$	−25.8323	+	30.7857i	−1.21237	+	1.44484i
$455$	−11.0034	+	5.96137i	−0.515848	+	0.279473i
$456$	−1.10429	−	0.961244i	−0.0517130	−	0.0450144i
$457$	−28.3019	−	19.8172i	−1.32391	−	0.927010i	−0.324088	−	0.946027i	$-0.605057\pi$
$457$	−28.3019	−	19.8172i	−1.32391	−	0.927010i	−0.999819	+	0.0190173i	$0.993946\pi$
$458$	35.9619	−	35.9619i	1.68039	−	1.68039i
$459$	−3.11849	+	1.58105i	−0.145559	+	0.0737972i
$460$	−1.73332	−	1.28504i	−0.0808164	−	0.0599152i
$461$	−10.2855	+	1.81362i	−0.479046	+	0.0844687i	−0.407957	−	0.913001i	$-0.633759\pi$
$461$	−10.2855	+	1.81362i	−0.479046	+	0.0844687i	−0.0710890	+	0.997470i	$0.522647\pi$
$462$	53.9895	+	26.3773i	2.51182	+	1.22718i
$463$	−16.7427	−	7.80727i	−0.778101	−	0.362835i	−0.00735185	−	0.999973i	$-0.502340\pi$
$463$	−16.7427	−	7.80727i	−0.778101	−	0.362835i	−0.770749	+	0.637138i	$0.780118\pi$
$464$	−22.8650	−	19.1860i	−1.06148	−	0.890689i
$465$	2.41745	+	5.86246i	0.112106	+	0.271865i
$466$	−15.6308	−	5.68914i	−0.724082	−	0.263544i
$467$	−9.96636	+	37.1950i	−0.461188	+	1.72118i	0.208040	+	0.978120i	$0.433292\pi$
$467$	−9.96636	+	37.1950i	−0.461188	+	1.72118i	−0.669228	+	0.743057i	$0.733375\pi$
$468$	−11.1925	+	7.24717i	−0.517374	+	0.335001i
$469$	−12.4421	−	7.18347i	−0.574524	−	0.331702i
$470$	21.3471	+	18.9211i	0.984668	+	0.872763i
$471$	14.4288	+	17.8425i	0.664842	+	0.822139i
$472$	−1.23108	−	1.75816i	−0.0566649	−	0.0809259i
$473$	12.8741	+	18.3862i	0.591953	+	0.845397i
$474$	23.7784	−	3.74977i	1.09218	−	0.172233i
$475$	13.0886	+	8.53384i	0.600547	+	0.391559i
$476$	3.33858	+	1.92753i	0.153024	+	0.0883482i
$477$	−9.90701	−	23.4268i	−0.453611	−	1.07264i
$478$	8.44313	−	31.5102i	0.386180	−	1.44124i
$479$	−13.8251	−	5.03191i	−0.631684	−	0.229914i	0.00628038	−	0.999980i	$-0.498001\pi$
$479$	−13.8251	−	5.03191i	−0.631684	−	0.229914i	−0.637964	+	0.770066i	$0.720223\pi$
$480$	31.0938	−	4.04350i	1.41923	−	0.184560i
$481$	4.56365	+	3.82935i	0.208084	+	0.174604i
$482$	−21.2374	−	9.90315i	−0.967336	−	0.451076i
$483$	−1.74555	+	1.17568i	−0.0794251	+	0.0534954i
$484$	61.6857	−	10.8768i	2.80389	−	0.494402i
$485$	−5.19529	+	7.00765i	−0.235906	+	0.318201i
$486$	−22.3337	−	22.4841i	−1.01308	−	1.01990i
$487$	3.40980	−	3.40980i	0.154513	−	0.154513i	−0.625617	−	0.780130i	$-0.715153\pi$
$487$	3.40980	−	3.40980i	0.154513	−	0.154513i	0.780130	+	0.625617i	$0.215153\pi$
$488$	−0.362969	−	0.254154i	−0.0164308	−	0.0115050i
$489$	−6.20132	+	31.7891i	−0.280433	+	1.43755i
$490$	−0.277340	+	0.933158i	−0.0125289	+	0.0421558i
$491$	−4.15599	+	4.95292i	−0.187557	+	0.223522i	−0.851627	−	0.524149i	$-0.824383\pi$
$491$	−4.15599	+	4.95292i	−0.187557	+	0.223522i	0.664069	+	0.747671i	$0.268828\pi$
$492$	25.0759	−	24.1830i	1.13051	−	1.09025i
$493$	2.28404	+	4.89815i	0.102868	+	0.220602i
$494$	−6.61896	−	11.4644i	−0.297801	−	0.515806i
$495$	−41.4195	−	10.0427i	−1.86167	−	0.451388i
$496$	−3.04231	+	5.26944i	−0.136604	+	0.236605i
$497$	6.33496	+	0.554237i	0.284162	+	0.0248609i
$498$	−11.2720	−	8.20115i	−0.505110	−	0.367502i
$499$	24.8022	+	4.37330i	1.11030	+	0.195776i	0.698578	−	0.715534i	$-0.253816\pi$
$499$	24.8022	+	4.37330i	1.11030	+	0.195776i	0.411722	+	0.911309i	$0.364927\pi$
$500$	22.9982	−	6.31025i	1.02851	−	0.282203i
$501$	−10.1547	+	8.21183i	−0.453678	+	0.366878i
$502$	−0.106632	+	1.21881i	−0.00475922	+	0.0543982i
$503$	−10.0577	−	37.5360i	−0.448452	−	1.67365i	−0.706657	−	0.707556i	$-0.749798\pi$
$503$	−10.0577	−	37.5360i	−0.448452	−	1.67365i	0.258205	−	0.966090i	$-0.416869\pi$
$504$	−0.456008	+	2.13128i	−0.0203122	+	0.0949349i
$505$	23.8757	−	18.9560i	1.06245	−	0.843532i
$506$	−1.99847	+	5.49075i	−0.0888428	+	0.244094i
$507$	14.5534	−	3.61819i	0.646338	−	0.160690i
$508$	−0.266986	−	3.05166i	−0.0118456	−	0.135396i
$509$	−5.50573	+	2.00392i	−0.244037	+	0.0888223i	−0.461143	−	0.887326i	$-0.652561\pi$
$509$	−5.50573	+	2.00392i	−0.244037	+	0.0888223i	0.217106	+	0.976148i	$0.430338\pi$
$510$	−5.05034	−	1.60116i	−0.223633	−	0.0709006i
$511$	−0.645765	−	3.66231i	−0.0285669	−	0.162011i
$512$	22.6957	+	22.6957i	1.00302	+	1.00302i
$513$	12.0890	−	10.8410i	0.533740	−	0.478640i
$514$		−	17.9282i		−	0.790777i
$515$	−6.35564	+	12.7184i	−0.280063	+	0.560438i
$516$	−8.56964	+	9.84490i	−0.377258	+	0.433397i
$517$	16.8486	−	36.1320i	0.741002	−	1.58908i
$518$	15.5523	−	1.36065i	0.683327	−	0.0597834i
$519$	11.3866	−	6.30168i	0.499814	−	0.276613i
$520$	−1.23475	−	0.252387i	−0.0541476	−	0.0110679i
$521$	16.6908	−	9.63645i	0.731238	−	0.422180i	−0.0876370	−	0.996152i	$-0.527932\pi$
$521$	16.6908	−	9.63645i	0.731238	−	0.422180i	0.818875	+	0.573972i	$0.194598\pi$
$522$	−35.8712	+	33.3605i	−1.57004	+	1.46015i
$523$	−21.0483	+	5.63988i	−0.920379	+	0.246615i	−0.687747	−	0.725950i	$-0.741400\pi$
$523$	−21.0483	+	5.63988i	−0.920379	+	0.246615i	−0.232631	+	0.972565i	$0.574734\pi$
$524$	−32.7171	+	27.4529i	−1.42925	+	1.19929i
$525$	1.68048	−	23.1999i	0.0733423	−	1.01253i
$526$	4.22192	−	23.9437i	0.184084	−	1.04399i
$527$	0.902479	−	0.631923i	0.0393126	−	0.0275270i
$528$	−16.6081	−	37.3700i	−0.722777	−	1.62632i
$529$	14.6526	+	17.4623i	0.637068	+	0.759228i
$530$	14.1585	−	35.8476i	0.615008	−	1.55712i
$531$	21.0335	−	11.1475i	0.912777	−	0.483762i
$532$	−17.2936	−	4.63380i	−0.749772	−	0.200901i
$533$	17.8070	−	8.30354i	0.771307	−	0.359666i
$534$	−1.46234	−	2.64231i	−0.0632816	−	0.114344i
$535$	5.46349	+	22.8489i	0.236207	+	0.987844i
$536$	−0.494847	−	1.35958i	−0.0213741	−	0.0587249i
$537$	22.3229	−	1.54592i	0.963302	−	0.0667112i
$538$	−18.2738	+	26.0978i	−0.787841	+	1.12515i
$539$	1.36056			0.0586036
$540$	−0.143784	−	24.7834i	−0.00618746	−	1.06651i
$541$	17.4882			0.751877			0.375938	−	0.926645i	$-0.377320\pi$
$541$	17.4882			0.751877			0.375938	+	0.926645i	$0.377320\pi$
$542$	−17.9043	+	25.5700i	−0.769057	+	1.09833i
$543$	−4.01701	+	8.22208i	−0.172386	+	0.352843i
$544$	−1.86319	−	5.11909i	−0.0798838	−	0.219479i
$545$	3.20308	−	5.21627i	0.137205	−	0.223440i
$546$	−10.1613	+	16.8855i	−0.434863	+	0.722635i
$547$	−32.7524	+	15.2727i	−1.40039	+	0.653013i	−0.968523	−	0.248924i	$-0.919923\pi$
$547$	−32.7524	+	15.2727i	−1.40039	+	0.653013i	−0.431868	+	0.901937i	$0.642145\pi$
$548$	26.9352	+	7.21727i	1.15062	+	0.308306i
$549$	3.29334	−	3.64777i	0.140556	−	0.155683i
$550$	−34.1230	−	54.8306i	−1.45501	−	2.33798i
$551$	−16.1337	−	19.2274i	−0.687319	−	0.819115i
$552$	−0.210765	−	0.0222953i	−0.00897076	−	0.000948951i
$553$	15.0410	−	10.5318i	0.639610	−	0.447859i
$554$	−1.52946	+	8.67402i	−0.0649807	+	0.368524i
$555$	−10.5658	+	3.31301i	−0.448494	+	0.140629i
$556$	−22.9273	+	19.2383i	−0.972336	+	0.815887i
$557$	−3.51852	+	0.942784i	−0.149084	+	0.0399470i	−0.332589	−	0.943072i	$-0.607922\pi$
$557$	−3.51852	+	0.942784i	−0.149084	+	0.0399470i	0.183505	+	0.983019i	$0.441256\pi$
$558$	7.96710	+	6.02042i	0.337274	+	0.254865i
$559$	−6.37515	+	3.68069i	−0.269640	+	0.155677i
$560$	18.6228	−	12.3018i	0.786957	−	0.519844i
$561$	−0.134195	+	7.40338i	−0.00566574	+	0.312571i
$562$	36.0464	−	3.15365i	1.52053	−	0.133029i
$563$	−3.66170	+	7.85254i	−0.154322	+	0.330945i	−0.968235	−	0.250042i	$-0.919556\pi$
$563$	−3.66170	+	7.85254i	−0.154322	+	0.330945i	0.813913	+	0.580987i	$0.197333\pi$
$564$	22.7543	+	4.43884i	0.958131	+	0.186909i
$565$	40.5099	+	20.2437i	1.70426	+	0.851657i
$566$			40.3521i			1.69613i
$567$	−22.8351	−	7.93136i	−0.958982	−	0.333086i
$568$	0.452834	+	0.452834i	0.0190005	+	0.0190005i
$569$	6.84317	+	38.8095i	0.286881	+	1.62698i	0.698490	+	0.715620i	$0.253856\pi$
$569$	6.84317	+	38.8095i	0.286881	+	1.62698i	−0.411609	+	0.911361i	$0.635033\pi$
$570$	24.5802	+	1.11218i	1.02955	+	0.0465843i
$571$	−4.05495	+	1.47588i	−0.169694	+	0.0617636i	−0.425470	−	0.904972i	$-0.639891\pi$
$571$	−4.05495	+	1.47588i	−0.169694	+	0.0617636i	0.255776	+	0.966736i	$0.417669\pi$
$572$	2.46114	+	28.1310i	0.102905	+	1.17621i
$573$	−22.3740	−	23.2001i	−0.934687	−	0.969198i
$574$	17.6100	−	48.3830i	0.735026	−	2.01947i
$575$	2.26068	−	0.0748157i	0.0942770	−	0.00312003i
$576$	21.3616	−	16.6434i	0.890067	−	0.693475i
$577$	−7.86919	−	29.3682i	−0.327598	−	1.22261i	−0.911674	−	0.410915i	$-0.865209\pi$
$577$	−7.86919	−	29.3682i	−0.327598	−	1.22261i	0.584075	−	0.811699i	$-0.301457\pi$
$578$	2.93195	−	33.5123i	0.121953	−	1.39393i
$579$	1.54846	+	9.81921i	0.0643517	+	0.408072i
$580$	−38.2953	−	1.03775i	−1.59012	−	0.0430904i
$581$	−10.4714	−	1.84638i	−0.434425	−	0.0766009i
$582$	−1.44509	+	13.6610i	−0.0599011	+	0.566266i
$583$	−53.6619	−	4.69481i	−2.22245	−	0.194439i
$584$	0.187253	−	0.324332i	0.00774858	−	0.0134209i
$585$	4.46513	−	13.2456i	0.184610	−	0.547637i
$586$	16.7256	+	28.9696i	0.690929	+	1.19672i
$587$	−8.32785	−	17.8591i	−0.343727	−	0.737126i	0.656119	−	0.754657i	$-0.272197\pi$
$587$	−8.32785	−	17.8591i	−0.343727	−	0.737126i	−0.999846	+	0.0175318i	$0.994419\pi$
$588$	0.190889	+	0.767809i	0.00787214	+	0.0316639i
$589$	−3.28890	+	3.91956i	−0.135517	+	0.161503i
$590$	34.5769	+	10.2765i	1.42351	+	0.423075i
$591$	−27.8800	+	9.57894i	−1.14683	+	0.394025i
$592$	−8.70333	−	6.09413i	−0.357705	−	0.250467i
$593$	1.60584	−	1.60584i	0.0659438	−	0.0659438i	−0.673366	−	0.739310i	$-0.735152\pi$
$593$	1.60584	−	1.60584i	0.0659438	−	0.0659438i	0.739310	+	0.673366i	$0.235152\pi$
$594$	−64.2219	+	19.4933i	−2.63506	+	0.799821i
$595$	−3.99740	+	0.593688i	−0.163877	+	0.0243388i
$596$	2.41020	−	0.424983i	0.0987255	−	0.0174080i
$597$	−2.77488	−	40.0689i	−0.113568	−	1.63991i
$598$	−1.73682	−	0.809892i	−0.0710238	−	0.0331190i
$599$	16.1072	+	13.5155i	0.658122	+	0.552230i	0.909523	−	0.415653i	$-0.136447\pi$
$599$	16.1072	+	13.5155i	0.658122	+	0.552230i	−0.251401	+	0.967883i	$0.580891\pi$
$600$	1.63143	−	1.68098i	0.0666029	−	0.0686258i
$601$	−25.6301	−	9.32859i	−1.04547	−	0.380521i	−0.238521	−	0.971137i	$-0.576662\pi$
$601$	−25.6301	−	9.32859i	−1.04547	−	0.380521i	−0.806952	+	0.590616i	$0.798885\pi$
$602$	−4.99284	+	18.6335i	−0.203493	+	0.759446i
$603$	15.6405	−	3.58880i	0.636931	−	0.146147i
$604$	−2.91323	−	1.68196i	−0.118538	−	0.0684378i
$605$	−43.5541	+	49.1385i	−1.77073	+	1.99777i
$606$	17.2343	−	44.8071i	0.700097	−	1.82016i
$607$	19.2596	+	27.5055i	0.781721	+	1.11641i	0.990373	+	0.138424i	$0.0442036\pi$
$607$	19.2596	+	27.5055i	0.781721	+	1.11641i	−0.208652	+	0.977990i	$0.566908\pi$
$608$	14.5114	+	20.7244i	0.588513	+	0.840484i
$609$	−13.4140	+	34.8748i	−0.543564	+	1.41320i
$610$	7.43346	−	0.447844i	0.300972	−	0.0181327i
$611$	11.3235	+	6.53761i	0.458099	+	0.264484i
$612$	−4.19680	+	0.962976i	−0.169645	+	0.0389260i
$613$	−11.4584	+	42.7632i	−0.462799	+	1.72719i	0.201288	+	0.979532i	$0.435487\pi$
$613$	−11.4584	+	42.7632i	−0.462799	+	1.72719i	−0.664086	+	0.747656i	$0.731179\pi$
$614$	−5.60681	−	2.04071i	−0.226272	−	0.0823564i
$615$	−4.82406	+	36.1995i	−0.194525	+	1.45970i
$616$	3.53588	+	2.96695i	0.142464	+	0.119542i
$617$	−12.8604	−	5.99691i	−0.517741	−	0.241427i	0.146141	−	0.989264i	$-0.453315\pi$
$617$	−12.8604	−	5.99691i	−0.517741	−	0.241427i	−0.663882	+	0.747837i	$0.731092\pi$
$618$	1.54684	+	22.3362i	0.0622231	+	0.898495i
$619$	−21.7592	+	3.83673i	−0.874576	+	0.154211i	−0.592878	−	0.805292i	$-0.702009\pi$
$619$	−21.7592	+	3.83673i	−0.874576	+	0.154211i	−0.281697	+	0.959503i	$0.590897\pi$
$620$	1.14727	+	7.72473i	0.0460753	+	0.310233i
$621$	0.533392	−	2.28934i	0.0214043	−	0.0918681i
$622$	5.47637	−	5.47637i	0.219582	−	0.219582i
$623$	−1.88697	−	1.32127i	−0.0755998	−	0.0529355i
$624$	12.6843	−	4.35803i	0.507778	−	0.174461i
$625$	−14.7683	+	20.1717i	−0.590733	+	0.806867i
$626$	−0.743054	+	0.885537i	−0.0296984	+	0.0353932i
$627$	−8.29691	−	33.3725i	−0.331347	−	1.33277i
$628$	11.9428	+	25.6114i	0.476569	+	1.02201i
$629$	0.961899	+	1.66606i	0.0383534	+	0.0664301i
$630$	−16.2702	−	32.8180i	−0.648220	−	1.30750i
$631$	6.92272	−	11.9905i	0.275589	−	0.477334i	−0.694694	−	0.719305i	$-0.744460\pi$
$631$	6.92272	−	11.9905i	0.275589	−	0.477334i	0.970284	+	0.241971i	$0.0777937\pi$
$632$	1.84210	+	0.161162i	0.0732746	+	0.00641070i
$633$	−0.473399	+	4.47520i	−0.0188159	+	0.177873i
$634$	−22.9301	−	4.04320i	−0.910672	−	0.160576i
$635$	2.20837	+	2.33139i	0.0876363	+	0.0925183i
$636$	−4.87943	−	30.9418i	−0.193482	−	1.22692i
$637$	−0.0388909	+	0.444525i	−0.00154091	+	0.0176127i
$638$	26.8506	+	100.208i	1.06302	+	3.96726i
$639$	−5.60293	+	4.36539i	−0.221648	+	0.172692i
$640$	4.79639	+	0.550912i	0.189594	+	0.0217767i
$641$	−7.88689	+	21.6691i	−0.311513	+	0.855876i	0.680838	+	0.732434i	$0.261616\pi$
$641$	−7.88689	+	21.6691i	−0.311513	+	0.855876i	−0.992352	+	0.123442i	$0.960607\pi$
$642$	25.6814	+	26.6296i	1.01356	+	1.05099i
$643$	0.640026	+	7.31553i	0.0252402	+	0.288496i	0.998316	+	0.0580110i	$0.0184758\pi$
$643$	0.640026	+	7.31553i	0.0252402	+	0.288496i	−0.973076	+	0.230485i	$0.925969\pi$
$644$	−2.43549	+	0.886446i	−0.0959718	+	0.0349309i
$645$	0.618467	−	13.6686i	0.0243521	−	0.538202i
$646$	−0.742320	−	4.20990i	−0.0292062	−	0.165636i
$647$	24.4108	+	24.4108i	0.959686	+	0.959686i	0.999218	−	0.0395324i	$-0.0125868\pi$
$647$	24.4108	+	24.4108i	0.959686	+	0.959686i	−0.0395324	+	0.999218i	$0.512587\pi$
$648$	−1.24820	−	2.09004i	−0.0490338	−	0.0821043i
$649$		−	50.4138i		−	1.97892i
$650$	18.8897	−	9.58142i	0.740915	−	0.375814i
$651$	7.47615	+	1.45842i	0.293013	+	0.0571601i
$652$	−16.8569	+	36.1497i	−0.660167	+	1.41573i
$653$	9.15617	−	0.801061i	0.358309	−	0.0313480i	0.0934196	−	0.995627i	$-0.470220\pi$
$653$	9.15617	−	0.801061i	0.358309	−	0.0313480i	0.264889	+	0.964279i	$0.414665\pi$
$654$	0.174697	−	9.63778i	0.00683118	−	0.376867i
$655$	8.96608	−	43.8649i	0.350334	−	1.71394i
$656$	−30.3465	+	17.5206i	−1.18483	+	0.684063i
$657$	3.31392	+	2.50419i	0.129288	+	0.0976979i
$658$	33.0967	−	8.86823i	1.29024	−	0.345720i
$659$	23.2374	−	19.4985i	0.905199	−	0.759552i	−0.0660005	−	0.997820i	$-0.521024\pi$
$659$	23.2374	−	19.4985i	0.905199	−	0.759552i	0.971200	+	0.238267i	$0.0765795\pi$
$660$	−46.5179	−	24.3094i	−1.81071	−	0.946240i
$661$	1.43027	−	8.11147i	0.0556311	−	0.315500i	−0.944276	−	0.329156i	$-0.893236\pi$
$661$	1.43027	−	8.11147i	0.0556311	−	0.315500i	0.999907	+	0.0136561i	$0.00434700\pi$
$662$	−42.5405	+	29.7872i	−1.65338	+	1.15771i
$663$	−2.41501	−	0.255466i	−0.0937910	−	0.00992147i
$664$	−0.688294	−	0.820277i	−0.0267110	−	0.0318329i
$665$	17.2185	−	7.46815i	0.667705	−	0.289602i
$666$	−11.6852	+	12.9427i	−0.452792	+	0.501521i
$667$	−3.50970	−	0.940421i	−0.135896	−	0.0364132i
$668$	−14.5762	+	6.79699i	−0.563970	+	0.262984i
$669$	4.50723	−	7.48990i	0.174260	−	0.289576i
$670$	20.7212	+	12.7240i	0.800529	+	0.491570i
$671$	−3.55969	−	9.78018i	−0.137420	−	0.377560i
$672$	16.5334	−	33.8408i	0.637788	−	1.30544i
$673$	5.98326	−	8.54498i	0.230638	−	0.329385i	−0.687107	−	0.726557i	$-0.741119\pi$
$673$	5.98326	−	8.54498i	0.230638	−	0.329385i	0.917744	+	0.397172i	$0.130008\pi$
$674$	35.9537			1.38488
$675$	16.2726	+	20.2534i	0.626334	+	0.779555i
$676$	18.4683			0.710319
$677$	22.7690	−	32.5175i	0.875083	−	1.24975i	−0.0921212	−	0.995748i	$-0.529365\pi$
$677$	22.7690	−	32.5175i	0.875083	−	1.24975i	0.967204	−	0.254000i	$-0.0817464\pi$
$678$	71.1442	−	4.92692i	2.73228	−	0.189217i
$679$	3.58382	+	9.84647i	0.137535	+	0.377873i
$680$	−0.346811	−	0.212961i	−0.0132996	−	0.00816670i
$681$	−16.5793	−	29.9572i	−0.635319	−	1.14796i
$682$	19.1668	−	8.93762i	0.733934	−	0.342239i
$683$	0.911173	+	0.244148i	0.0348651	+	0.00934207i	0.276209	−	0.961097i	$-0.410922\pi$
$683$	0.911173	+	0.244148i	0.0348651	+	0.00934207i	−0.241344	+	0.970440i	$0.577588\pi$
$684$	17.6691	−	9.36443i	0.675595	−	0.358058i
$685$	−26.8183	+	11.6318i	−1.02467	+	0.444430i
$686$	−23.8177	−	28.3848i	−0.909364	−	1.08374i
$687$	17.5971	+	39.5952i	0.671371	+	1.51065i
$688$	10.7544	−	7.53032i	0.410008	−	0.287091i
$689$	3.06779	−	17.3983i	0.116873	−	0.662822i
$690$	3.00715	−	1.90908i	0.114480	−	0.0726774i
$691$	−8.89879	+	7.46697i	−0.338526	+	0.284057i	−0.796163	−	0.605082i	$-0.793140\pi$
$691$	−8.89879	+	7.46697i	−0.338526	+	0.284057i	0.457637	+	0.889139i	$0.348696\pi$
$692$	15.4809	−	4.14809i	0.588495	−	0.157687i
$693$	−37.4876	+	34.8638i	−1.42403	+	1.32437i
$694$	3.93170	−	2.26997i	0.149245	−	0.0861668i
$695$	6.28321	−	30.7394i	0.238336	−	1.16601i
$696$	−3.29236	+	1.82210i	−0.124797	+	0.0690665i
$697$	6.32063	−	0.552984i	0.239411	−	0.0209458i
$698$	−16.4917	+	35.3665i	−0.624219	+	1.33864i
$699$	9.30461	−	10.6892i	0.351933	−	0.404304i
$700$	8.90178	−	27.2277i	0.336456	−	1.02911i
$701$		−	27.3341i		−	1.03240i	−0.856469	−	0.516198i	$-0.827347\pi$
$701$		−	27.3341i		−	1.03240i	0.856469	−	0.516198i	$-0.172653\pi$
$702$	−4.53314	−	21.5399i	−0.171092	−	0.812969i
$703$	−6.31764	−	6.31764i	−0.238274	−	0.238274i
$704$	−9.95862	−	56.4781i	−0.375330	−	2.12860i
$705$	−21.5747	+	11.1877i	−0.812550	+	0.421353i
$706$	−56.7662	+	20.6612i	−2.13643	+	0.777595i
$707$	−3.19154	−	36.4794i	−0.120030	−	1.37195i
$708$	28.4502	−	7.07315i	1.06922	−	0.265825i
$709$	−10.1733	+	27.9510i	−0.382068	+	1.04972i	0.588417	+	0.808558i	$0.299751\pi$
$709$	−10.1733	+	27.9510i	−0.382068	+	1.04972i	−0.970484	+	0.241164i	$0.922471\pi$
$710$	−10.6925	−	1.22814i	−0.401284	−	0.0460914i
$711$	−4.29095	+	20.0550i	−0.160923	+	0.752120i
$712$	−0.0600414	−	0.224078i	−0.00225015	−	0.00839766i
$713$	−0.0645563	+	0.737882i	−0.00241765	+	0.0276339i
$714$	−4.94840	+	4.00164i	−0.185189	+	0.149758i
$715$	−20.3572	−	21.4913i	−0.761318	−	0.803728i
$716$	27.1382	+	4.78519i	1.01420	+	0.178831i
$717$	22.4739	+	16.3513i	0.839303	+	0.610650i
$718$	57.1057	+	4.99610i	2.13116	+	0.186453i
$719$	−4.04581	+	7.00756i	−0.150883	+	0.261338i	−0.931552	−	0.363607i	$-0.881545\pi$
$719$	−4.04581	+	7.00756i	−0.150883	+	0.261338i	0.780669	+	0.624945i	$0.214878\pi$
$720$	−5.87419	+	24.2271i	−0.218918	+	0.902889i
$721$	8.53917	+	14.7903i	0.318015	+	0.550819i
$722$	−7.93406	−	17.0147i	−0.295275	−	0.633220i
$723$	14.3703	−	13.8586i	0.534437	−	0.515407i
$724$	−7.24389	+	8.63293i	−0.269217	+	0.320840i
$725$	32.1169	−	24.1101i	1.19279	−	0.895425i
$726$	−19.7981	+	101.489i	−0.734776	+	3.76660i
$727$	37.2574	+	26.0879i	1.38180	+	0.967546i	0.999045	+	0.0436958i	$0.0139132\pi$
$727$	37.2574	+	26.0879i	1.38180	+	0.967546i	0.382754	+	0.923850i	$0.374976\pi$
$728$	−1.07044	+	1.07044i	−0.0396730	+	0.0396730i
$729$	24.7097	−	10.8825i	0.915175	−	0.403056i
$730$	0.924644	+	6.22578i	0.0342226	+	0.230427i
$731$	−2.34106	+	0.412792i	−0.0865872	+	0.0152677i
$732$	5.01984	−	3.38103i	0.185539	−	0.124966i
$733$	24.5512	+	11.4484i	0.906819	+	0.422857i	0.819339	−	0.573309i	$-0.194341\pi$
$733$	24.5512	+	11.4484i	0.906819	+	0.422857i	0.0874805	+	0.996166i	$0.472118\pi$
$734$	37.4655	+	31.4373i	1.38288	+	1.16037i
$735$	−0.657202	−	0.505944i	−0.0242413	−	0.0186620i
$736$	3.44161	+	1.25265i	0.126860	+	0.0461731i
$737$	8.79571	−	32.8260i	0.323994	−	1.20916i
$738$	22.3995	+	52.9674i	0.824536	+	1.94976i
$739$	13.2893	+	7.67257i	0.488854	+	0.282240i	0.724099	−	0.689696i	$-0.242256\pi$
$739$	13.2893	+	7.67257i	0.488854	+	0.282240i	−0.235245	+	0.971936i	$0.575589\pi$
$740$	−13.6120	+	0.820081i	−0.500386	+	0.0301468i
$741$	11.1407	−	1.75684i	0.409262	−	0.0645393i
$742$	−26.5545	−	37.9237i	−0.974846	−	1.39222i
$743$	21.9611	+	31.3637i	0.805674	+	1.15062i	0.985956	+	0.167007i	$0.0534101\pi$
$743$	21.9611	+	31.3637i	0.805674	+	1.15062i	−0.180282	+	0.983615i	$0.557701\pi$
$744$	0.482342	+	0.596460i	0.0176835	+	0.0218673i
$745$	−1.70176	+	1.91995i	−0.0623475	+	0.0703417i
$746$	−12.6415	−	7.29858i	−0.462839	−	0.267220i
$747$	9.96896	−	6.45491i	0.364745	−	0.236173i
$748$	−2.36014	+	8.80816i	−0.0862953	+	0.322058i
$749$	26.5175	+	9.65157i	0.968927	+	0.352661i
$750$	−3.90683	+	39.1744i	−0.142657	+	1.43045i
$751$	−6.83954	−	5.73906i	−0.249578	−	0.209421i	0.509412	−	0.860523i	$-0.329863\pi$
$751$	−6.83954	−	5.73906i	−0.249578	−	0.209421i	−0.758991	+	0.651101i	$0.774307\pi$
$752$	−21.1343	−	9.85508i	−0.770688	−	0.359378i
$753$	−0.936559	−	0.457569i	−0.0341301	−	0.0166747i
$754$	−33.5075	+	5.90827i	−1.22027	+	0.215167i
$755$	3.48812	−	0.518050i	0.126946	−	0.0188538i
$756$	−24.9343	−	16.2640i	−0.906853	−	0.591516i
$757$	−12.0849	+	12.0849i	−0.439232	+	0.439232i	−0.891753	−	0.452522i	$-0.850525\pi$
$757$	−12.0849	+	12.0849i	−0.439232	+	0.439232i	0.452522	+	0.891753i	$0.350525\pi$
$758$	−11.0094	−	7.70890i	−0.399881	−	0.280000i
$759$	−3.75489	−	3.26850i	−0.136294	−	0.118639i
$760$	1.81176	+	0.538465i	0.0657193	+	0.0195322i
$761$	−28.7638	+	34.2794i	−1.04269	+	1.24263i	−0.0732447	+	0.997314i	$0.523335\pi$
$761$	−28.7638	+	34.2794i	−1.04269	+	1.24263i	−0.969444	+	0.245314i	$0.921109\pi$
$762$	4.86010	+	1.39714i	0.176063	+	0.0506131i
$763$	−3.10737	−	6.66378i	−0.112494	−	0.241245i
$764$	−19.8465	−	34.3752i	−0.718022	−	1.24365i
$765$	2.81787	−	3.52621i	0.101880	−	0.127490i
$766$	9.94557	−	17.2262i	0.359348	−	0.622409i
$767$	16.4713	+	1.44105i	0.594743	+	0.0520333i
$768$	−21.6268	+	9.61149i	−0.780390	+	0.346825i
$769$	−22.4692	−	3.96193i	−0.810262	−	0.142871i	−0.246857	−	0.969052i	$-0.579398\pi$
$769$	−22.4692	−	3.96193i	−0.810262	−	0.142871i	−0.563405	+	0.826181i	$0.690509\pi$
$770$	−77.5455	−	2.10139i	−2.79455	−	0.0757287i
$771$	14.2561	+	5.48338i	0.513421	+	0.197479i
$772$	−1.06696	+	12.1954i	−0.0384006	+	0.438921i
$773$	−10.7667	−	40.1817i	−0.387250	−	1.44524i	−0.834589	−	0.550872i	$-0.814295\pi$
$773$	−10.7667	−	40.1817i	−0.387250	−	1.44524i	0.447339	−	0.894364i	$-0.352372\pi$
$774$	−10.0900	−	19.0381i	−0.362678	−	0.684311i
$775$	−5.97713	−	5.59418i	−0.214705	−	0.200949i
$776$	−0.360912	+	0.991598i	−0.0129560	+	0.0355963i
$777$	−3.67475	+	12.7830i	−0.131831	+	0.458588i
$778$	−1.72809	−	19.7522i	−0.0619550	−	0.708149i
$779$	−27.6893	+	10.0781i	−0.992074	+	0.361085i
$780$	9.27207	−	14.5035i	0.331993	−	0.519309i
$781$	2.61204	+	14.8136i	0.0934662	+	0.530073i
$782$	−0.437588	−	0.437588i	−0.0156481	−	0.0156481i
$783$	−15.5563	−	38.7274i	−0.555936	−	1.38401i
$784$		−	0.795819i		−	0.0284221i
$785$	−26.4993	−	13.2423i	−0.945802	−	0.472637i
$786$	−22.9092	−	66.6785i	−0.817145	−	2.37834i
$787$	−0.237611	+	0.509559i	−0.00846992	+	0.0181638i	−0.910497	−	0.413515i	$-0.864301\pi$
$787$	−0.237611	+	0.509559i	−0.00846992	+	0.0181638i	0.902027	+	0.431679i	$0.142079\pi$
$788$	−36.1666	+	3.16416i	−1.28838	+	0.112719i
$789$	17.7482	+	10.6804i	0.631854	+	0.380234i
$790$	−25.9304	+	17.1290i	−0.922562	+	0.609421i
$791$	47.1092	−	27.1985i	1.67501	−	0.967068i
$792$	−5.14880	+	0.262909i	−0.182955	+	0.00934208i
$793$	3.29714	−	0.883467i	0.117085	−	0.0313728i
$794$	−35.3263	+	29.6423i	−1.25368	+	1.05197i
$795$	24.1749	+	22.2227i	0.857394	+	0.788158i
$796$	8.58929	−	48.7123i	0.304439	−	1.72656i
$797$	41.9854	−	29.3985i	1.48720	−	1.04135i	0.502998	−	0.864288i	$-0.332230\pi$
$797$	41.9854	−	29.3985i	1.48720	−	1.04135i	0.984200	−	0.177060i	$-0.0566585\pi$
$798$	17.3882	−	23.8991i	0.615537	−	0.846020i
$799$	2.71405	+	3.23448i	0.0960162	+	0.114428i
$800$	−34.3679	+	21.3884i	−1.21509	+	0.756194i
$801$	2.54837	−	0.354664i	0.0900423	−	0.0125314i
$802$	−61.6733	−	16.5253i	−2.17776	−	0.583529i
$803$	7.97242	−	3.71760i	0.281341	−	0.131191i
$804$	19.7589	+	0.358154i	0.696841	+	0.0126311i
$805$	1.42173	−	2.31530i	0.0501092	−	0.0816037i
$806$	2.37224	+	6.51767i	0.0835585	+	0.229575i
$807$	−15.1633	−	22.5131i	−0.533773	−	0.792497i
$808$	2.11519	−	3.02081i	0.0744122	−	0.106272i
$809$	−10.4010			−0.365681			−0.182841	−	0.983143i	$-0.558529\pi$
$809$	−10.4010			−0.365681			−0.182841	+	0.983143i	$0.558529\pi$
$810$	38.2704	+	14.4658i	1.34469	+	0.508276i
$811$	3.01122			0.105738			0.0528692	−	0.998601i	$-0.483163\pi$
$811$	3.01122			0.105738			0.0528692	+	0.998601i	$0.483163\pi$
$812$	−26.3939	+	37.6944i	−0.926244	+	1.32281i
$813$	−14.8567	−	22.0578i	−0.521046	−	0.773602i
$814$	12.6302	+	34.7013i	0.442690	+	1.21628i
$815$	−9.72401	−	40.6668i	−0.340617	−	1.42450i
$816$	4.33038	+	0.0784935i	0.151594	+	0.00274782i
$817$	10.0057	−	4.66573i	0.350055	−	0.163233i
$818$	−56.0987	−	15.0316i	−1.96145	−	0.525568i
$819$	−10.3192	−	13.2445i	−0.360581	−	0.462802i
$820$	−16.5213	+	41.8299i	−0.576949	+	1.46076i
$821$	23.3489	+	27.8262i	0.814883	+	0.971140i	0.999933	−	0.0115894i	$-0.00368910\pi$
$821$	23.3489	+	27.8262i	0.814883	+	0.971140i	−0.185050	+	0.982729i	$0.559245\pi$
$822$	−27.0826	+	37.2235i	−0.944616	+	1.29832i
$823$	6.71249	−	4.70013i	0.233983	−	0.163836i	−0.450705	−	0.892673i	$-0.648827\pi$
$823$	6.71249	−	4.70013i	0.233983	−	0.163836i	0.684688	+	0.728836i	$0.259939\pi$
$824$	−0.298656	+	1.69376i	−0.0104042	+	0.0590049i
$825$	54.0368	−	10.3638i	1.88132	−	0.360822i
$826$	33.1916	−	27.8511i	1.15488	−	0.969063i
$827$	8.08092	−	2.16528i	0.281001	−	0.0752940i	−0.115566	−	0.993300i	$-0.536868\pi$
$827$	8.08092	−	2.16528i	0.281001	−	0.0752940i	0.396567	+	0.918006i	$0.370201\pi$
$828$	1.31770	−	2.57758i	0.0457934	−	0.0895772i
$829$	24.2355	−	13.9924i	0.841734	−	0.485975i	−0.0161192	−	0.999870i	$-0.505131\pi$
$829$	24.2355	−	13.9924i	0.841734	−	0.485975i	0.857853	+	0.513895i	$0.171798\pi$
$830$	17.6316	+	3.60394i	0.612001	+	0.125095i
$831$	−6.42961	−	3.86918i	−0.223041	−	0.134220i
$832$	18.7373	−	1.63930i	0.649598	−	0.0568325i
$833$	−0.0608977	+	0.130596i	−0.00210998	+	0.00452487i
$834$	−16.0542	−	46.7267i	−0.555913	−	1.61801i
$835$	7.53657	−	15.0816i	0.260814	−	0.521919i
$836$		−	42.3499i		−	1.46470i
$837$	−7.22408	+	4.49391i	−0.249701	+	0.155332i
$838$	−5.83376	−	5.83376i	−0.201524	−	0.201524i
$839$	−4.76834	−	27.0426i	−0.164621	−	0.933615i	−0.949454	−	0.313907i	$-0.898362\pi$
$839$	−4.76834	−	27.0426i	−0.164621	−	0.933615i	0.784832	−	0.619708i	$-0.212749\pi$
$840$	−0.604657	−	2.74801i	−0.0208627	−	0.0948155i
$841$	−33.3699	+	12.1457i	−1.15069	+	0.418816i
$842$	−1.74073	−	19.8966i	−0.0599895	−	0.685683i
$843$	−8.51718	+	29.6279i	−0.293347	+	1.02044i
$844$	−1.89549	+	5.20781i	−0.0652454	+	0.179260i
$845$	−15.1625	+	12.0382i	−0.521605	+	0.414127i
$846$	−20.3241	+	32.4284i	−0.698756	+	1.11491i
$847$	20.4137	+	76.1848i	0.701421	+	2.61774i
$848$	−2.74608	+	31.3879i	−0.0943009	+	1.07786i
$849$	−32.0872	−	12.3418i	−1.10123	−	0.423570i
$850$	6.79032	−	0.821174i	0.232906	−	0.0281660i
$851$	−1.27374	−	0.224595i	−0.0436632	−	0.00769900i
$852$	−7.99334	+	3.55244i	−0.273847	+	0.121705i
$853$	16.5834	+	1.45086i	0.567806	+	0.0496766i	0.367444	−	0.930045i	$-0.380233\pi$
$853$	16.5834	+	1.45086i	0.567806	+	0.0496766i	0.200361	+	0.979722i	$0.435788\pi$
$854$	4.47255	−	7.74669i	0.153048	−	0.265086i
$855$	−8.40230	+	19.2055i	−0.287353	+	0.656813i
$856$	1.42092	+	2.46111i	0.0485662	+	0.0841191i
$857$	−4.59299	−	9.84971i	−0.156894	−	0.336460i	0.812111	−	0.583504i	$-0.198319\pi$
$857$	−4.59299	−	9.84971i	−0.156894	−	0.336460i	−0.969004	+	0.247044i	$0.920541\pi$
$858$	−44.8016	−	12.8792i	−1.52950	−	0.439688i
$859$	−0.275808	+	0.328695i	−0.00941045	+	0.0112149i	−0.770729	−	0.637163i	$-0.780108\pi$
$859$	−0.275808	+	0.328695i	−0.00941045	+	0.0112149i	0.761319	+	0.648378i	$0.224552\pi$
$860$	4.80050	−	16.1521i	0.163696	−	0.550782i
$861$	33.0871	+	28.8012i	1.12760	+	0.981541i
$862$	5.95703	+	4.17115i	0.202897	+	0.142070i
$863$	7.52083	−	7.52083i	0.256012	−	0.256012i	−0.567418	−	0.823430i	$-0.692058\pi$
$863$	7.52083	−	7.52083i	0.256012	−	0.256012i	0.823430	+	0.567418i	$0.192058\pi$
$864$	12.2185	+	40.2544i	0.415681	+	1.36948i
$865$	−10.0060	+	13.4965i	−0.340213	+	0.458895i
$866$	−1.90056	+	0.335120i	−0.0645837	+	0.0113878i
$867$	25.7516	+	12.5813i	0.874570	+	0.427283i
$868$	8.50167	+	3.96439i	0.288565	+	0.134560i
$869$	33.2719	+	27.9184i	1.12867	+	0.947068i
$870$	24.2938	−	58.3888i	0.823637	−	1.97957i
$871$	10.4735	+	3.81206i	0.354883	+	0.129167i
$872$	0.191644	−	0.715226i	0.00648989	−	0.0242206i
$873$	−10.4209	−	5.32736i	−0.352696	−	0.180304i
$874$	2.48898	+	1.43701i	0.0841909	+	0.0486077i
$875$	10.4395	+	28.1564i	0.352920	+	0.951861i
$876$	3.21651	+	3.97751i	0.108676	+	0.134388i
$877$	−2.81136	−	4.01504i	−0.0949330	−	0.135578i	0.768876	−	0.639398i	$-0.220816\pi$
$877$	−2.81136	−	4.01504i	−0.0949330	−	0.135578i	−0.863809	+	0.503820i	$0.831928\pi$
$878$	−38.3637	−	54.7890i	−1.29471	−	1.84904i
$879$	−28.1516	+	4.43942i	−0.949530	+	0.149738i
$880$	39.5087	+	35.0186i	1.33184	+	1.18048i
$881$	−0.734747	−	0.424206i	−0.0247542	−	0.0142919i	0.487572	−	0.873083i	$-0.337883\pi$
$881$	−0.734747	−	0.424206i	−0.0247542	−	0.0142919i	−0.512326	+	0.858791i	$0.671216\pi$
$882$	−1.29614	−	0.160911i	−0.0436432	−	0.00541817i
$883$	−9.09767	+	33.9530i	−0.306161	+	1.14261i	0.625781	+	0.779999i	$0.284781\pi$
$883$	−9.09767	+	33.9530i	−0.306161	+	1.14261i	−0.931941	+	0.362609i	$0.881886\pi$
$884$	−2.81035	−	1.02288i	−0.0945223	−	0.0344033i
$885$	−18.7471	+	24.3518i	−0.630176	+	0.818575i
$886$	34.9135	+	29.2959i	1.17294	+	0.984216i
$887$	−20.1843	−	9.41211i	−0.677724	−	0.316028i	0.0531048	−	0.998589i	$-0.483088\pi$
$887$	−20.1843	−	9.41211i	−0.677724	−	0.316028i	−0.730828	+	0.682561i	$0.760866\pi$
$888$	−1.11096	+	0.748271i	−0.0372815	+	0.0251103i
$889$	3.79871	−	0.669814i	0.127405	−	0.0224649i
$890$	3.13194	+	2.32194i	0.104983	+	0.0778314i
$891$	4.14177	−	57.0300i	0.138754	−	1.91058i
$892$	7.61222	−	7.61222i	0.254876	−	0.254876i
$893$	−16.0630	−	11.2474i	−0.537526	−	0.376380i
$894$	−0.773556	+	3.96539i	−0.0258716	+	0.132623i
$895$	−25.3996	+	13.7609i	−0.849014	+	0.459975i
$896$	3.72765	−	4.44244i	0.124532	−	0.148412i
$897$	1.17522	−	1.13337i	0.0392395	−	0.0378423i
$898$	−8.52775	−	18.2878i	−0.284575	−	0.610272i
$899$	6.57542	+	11.3890i	0.219303	+	0.379843i
$900$	13.4301	+	29.0407i	0.447670	+	0.968022i
$901$	2.85250	−	4.94068i	0.0950307	−	0.164598i
$902$	121.328	+	10.6148i	4.03979	+	0.353435i
$903$	−13.2899	−	9.66932i	−0.442261	−	0.321775i
$904$	5.39488	+	0.951262i	0.179431	+	0.0316385i
$905$	0.320021	−	11.8094i	0.0106379	−	0.392559i
$906$	4.31796	−	3.49182i	0.143454	−	0.116008i
$907$	4.43286	−	50.6679i	0.147191	−	1.68240i	−0.460060	−	0.887888i	$-0.652172\pi$
$907$	4.43286	−	50.6679i	0.147191	−	1.68240i	0.607250	−	0.794511i	$-0.292273\pi$
$908$	−10.9133	−	40.7291i	−0.362171	−	1.35164i
$909$	30.3585	+	27.4088i	1.00693	+	0.909092i
$910$	2.90316	−	25.2757i	0.0962388	−	0.837881i
$911$	−1.01302	+	2.78325i	−0.0335629	+	0.0922132i	−0.955342	−	0.295502i	$-0.904513\pi$
$911$	−1.01302	+	2.78325i	−0.0335629	+	0.0922132i	0.921779	+	0.387715i	$0.126735\pi$
$912$	−19.5202	+	4.85302i	−0.646378	+	0.160700i
$913$	−2.19209	−	25.0557i	−0.0725476	−	0.829223i
$914$	66.0043	−	24.0236i	2.18323	−	0.794630i
$915$	−1.91743	+	6.04791i	−0.0633883	+	0.199938i
$916$	9.26601	+	52.5502i	0.306158	+	1.73631i
$917$	−38.0275	−	38.0275i	−1.25578	−	1.25578i
$918$	1.00343	−	7.03694i	0.0331180	−	0.232254i
$919$			4.33194i			0.142897i	0.997444	+	0.0714487i	$0.0227622\pi$
$919$			4.33194i			0.142897i	−0.997444	+	0.0714487i	$0.977238\pi$
$920$	0.259555	−	0.0865825i	0.00855726	−	0.00285454i
$921$	3.33759	−	3.83426i	0.109977	−	0.126343i
$922$	8.97345	−	19.2436i	0.295525	−	0.633755i
$923$	−4.91459	+	0.429971i	−0.161766	+	0.0141527i
$924$	−55.1617	+	30.5283i	−1.81469	+	1.00431i
$925$	10.6409	−	9.54599i	0.349870	−	0.313870i
$926$	32.5250	−	18.7783i	1.06884	−	0.617093i
$927$	−18.2344	−	5.60159i	−0.598897	−	0.183980i
$928$	62.8104	−	16.8300i	2.06185	−	0.552472i
$929$	24.5535	−	20.6028i	0.805574	−	0.675957i	−0.143973	−	0.989582i	$-0.545988\pi$
$929$	24.5535	−	20.6028i	0.805574	−	0.675957i	0.949547	+	0.313625i	$0.101543\pi$
$930$	−12.5819	−	2.81023i	−0.412575	−	0.0921512i
$931$	0.116207	−	0.659044i	0.00380854	−	0.0215993i
$932$	14.2963	−	10.0104i	0.468292	−	0.327902i
$933$	2.67973	+	6.02966i	0.0877304	+	0.197402i
$934$	−50.3203	−	59.9694i	−1.64653	−	1.96226i
$935$	−3.80376	−	8.76992i	−0.124396	−	0.286807i
$936$	0.0612774	−	1.68974i	0.00200291	−	0.0552308i
$937$	14.2207	+	3.81043i	0.464571	+	0.124481i	0.483509	−	0.875339i	$-0.339362\pi$
$937$	14.2207	+	3.81043i	0.464571	+	0.124481i	−0.0189383	+	0.999821i	$0.506029\pi$
$938$	26.4713	−	12.3438i	0.864318	−	0.403038i
$939$	−0.476896	−	0.861705i	−0.0155629	−	0.0281207i
$940$	−29.1089	+	6.96034i	−0.949427	+	0.227021i
$941$	−0.647073	−	1.77782i	−0.0210940	−	0.0579552i	0.928699	−	0.370835i	$-0.120928\pi$
$941$	−0.647073	−	1.77782i	−0.0210940	−	0.0579552i	−0.949793	+	0.312880i	$0.898706\pi$
$942$	−46.5386	+	3.22292i	−1.51631	+	0.105008i
$943$	−2.44668	+	3.49422i	−0.0796749	+	0.113788i
$944$	−29.4880			−0.959753
$945$	31.0725	−	2.90023i	1.01079	−	0.0943446i
$946$	−45.6312			−1.48360
$947$	−19.1689	+	27.3760i	−0.622906	+	0.889601i	−0.999321	−	0.0368497i	$-0.988268\pi$
$947$	−19.1689	+	27.3760i	−0.622906	+	0.889601i	0.376415	+	0.926451i	$0.377157\pi$
$948$	−11.0872	+	22.6934i	−0.360095	+	0.737048i
$949$	0.986732	+	2.71103i	0.0320307	+	0.0880036i
$950$	−29.4739	+	11.8457i	−0.956261	+	0.384327i
$951$	10.2283	−	16.9969i	0.331676	−	0.551164i
$952$	−0.443050	+	0.206598i	−0.0143593	+	0.00669587i
$953$	17.5785	+	4.71015i	0.569424	+	0.152577i	0.532032	−	0.846724i	$-0.321428\pi$
$953$	17.5785	+	4.71015i	0.569424	+	0.152577i	0.0373915	+	0.999301i	$0.488095\pi$
$954$	50.5656	+	10.8190i	1.63712	+	0.350278i
$955$	38.7008	+	15.2855i	1.25233	+	0.494626i
$956$	22.0009	+	26.2197i	0.711560	+	0.848004i
$957$	−87.8954	−	9.29781i	−2.84125	−	0.300555i
$958$	24.5009	−	17.1557i	0.791587	−	0.554275i
$959$	−6.09731	+	34.5796i	−0.196893	+	1.11663i
$960$	−16.1918	+	30.9843i	−0.522588	+	1.00001i
$961$	−21.6937	+	18.2032i	−0.699798	+	0.587200i
$962$	−11.6987	+	3.13465i	−0.377181	+	0.101065i
$963$	−29.0301	+	12.2766i	−0.935481	+	0.395607i
$964$	21.2922	−	12.2931i	0.685777	−	0.395934i
$965$	−7.07335	−	10.7079i	−0.227699	−	0.344699i
$966$	0.0775412	−	4.27784i	0.00249485	−	0.137637i
$967$	42.2870	−	3.69964i	1.35986	−	0.118972i	0.616231	−	0.787566i	$-0.288659\pi$
$967$	42.2870	−	3.69964i	1.35986	−	0.118972i	0.743628	+	0.668593i	$0.233103\pi$
$968$	−3.35682	+	7.19871i	−0.107892	+	0.231375i
$969$	3.57467	+	0.697335i	0.114835	+	0.0224016i
$970$	−5.61194	−	16.8233i	−0.180189	−	0.540164i
$971$		−	8.10739i		−	0.260179i	−0.991502	−	0.130089i	$-0.958474\pi$
$971$		−	8.10739i		−	0.260179i	0.991502	−	0.130089i	$-0.0415264\pi$
$972$	32.7650	−	5.66408i	1.05094	−	0.181675i
$973$	−26.6487	−	26.6487i	−0.854319	−	0.854319i
$974$	1.70235	+	9.65451i	0.0545468	+	0.309350i
$975$	1.84147	+	17.9512i	0.0589743	+	0.574899i
$976$	−5.72061	+	2.08213i	−0.183112	+	0.0666475i
$977$	3.67792	+	42.0388i	0.117667	+	1.34494i	0.793808	+	0.608168i	$0.208095\pi$
$977$	3.67792	+	42.0388i	0.117667	+	1.34494i	−0.676141	+	0.736772i	$0.736349\pi$
$978$	−45.7081	−	47.3958i	−1.46159	−	1.51555i
$979$	1.86364	−	5.12031i	0.0595622	−	0.163646i
$980$	−0.635115	−	0.799945i	−0.0202880	−	0.0255533i
$981$	7.61033	+	3.08666i	0.242979	+	0.0985495i
$982$	−3.40203	−	12.6966i	−0.108563	−	0.405163i
$983$	−1.24906	+	14.2769i	−0.0398390	+	0.455362i	0.949908	+	0.312530i	$0.101176\pi$
$983$	−1.24906	+	14.2769i	−0.0398390	+	0.455362i	−0.989747	+	0.142832i	$0.954379\pi$
$984$	0.688138	+	4.36368i	0.0219370	+	0.139109i
$985$	27.6303	−	26.1723i	0.880373	−	0.833918i
$986$	−10.8204	−	1.90793i	−0.344592	−	0.0607608i
$987$	−3.07089	+	29.0302i	−0.0977475	+	0.924041i
$988$	13.8366	+	1.21055i	0.440201	+	0.0385126i
$989$	0.799099	−	1.38408i	0.0254099	−	0.0440112i
$990$	65.0227	−	57.2665i	2.06656	−	1.82005i
$991$	15.7989	+	27.3646i	0.501870	+	0.869265i	0.999998	+	0.00216080i	$0.000687805\pi$
$991$	15.7989	+	27.3646i	0.501870	+	0.869265i	−0.498128	+	0.867104i	$0.665979\pi$
$992$	−5.60212	−	12.0138i	−0.177867	−	0.381438i
$993$	−10.6750	−	42.9379i	−0.338761	−	1.36259i
$994$	−8.31002	+	9.90350i	−0.263578	+	0.314120i
$995$	24.7004	+	45.5916i	0.783055	+	1.44535i
$996$	13.8322	−	4.75243i	0.438290	−	0.150586i
$997$	−10.1346	−	7.09629i	−0.320965	−	0.224742i	0.401979	−	0.915649i	$-0.368322\pi$
$997$	−10.1346	−	7.09629i	−0.320965	−	0.224742i	−0.722944	+	0.690907i	$0.757211\pi$
$998$	−36.2043	+	36.2043i	−1.14603	+	1.14603i
$999$	−6.71785	−	13.2504i	−0.212543	−	0.419224i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.68.3	yes	192
3.2	odd	2		405.2.r.a.233.14		192
5.2	odd	4	inner	135.2.q.a.122.3	yes	192
5.3	odd	4		675.2.ba.b.257.14		192
5.4	even	2		675.2.ba.b.68.14		192
15.2	even	4		405.2.r.a.152.14		192
27.2	odd	18	inner	135.2.q.a.83.3	yes	192
27.25	even	9		405.2.r.a.8.14		192
135.2	even	36	inner	135.2.q.a.2.3	✓	192
135.29	odd	18		675.2.ba.b.218.14		192
135.52	odd	36		405.2.r.a.332.14		192
135.83	even	36		675.2.ba.b.407.14		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.3	✓	192	135.2	even	36	inner
135.2.q.a.68.3	yes	192	1.1	even	1	trivial
135.2.q.a.83.3	yes	192	27.2	odd	18	inner
135.2.q.a.122.3	yes	192	5.2	odd	4	inner
405.2.r.a.8.14		192	27.25	even	9
405.2.r.a.152.14		192	15.2	even	4
405.2.r.a.233.14		192	3.2	odd	2
405.2.r.a.332.14		192	135.52	odd	36
675.2.ba.b.68.14		192	5.4	even	2
675.2.ba.b.218.14		192	135.29	odd	18
675.2.ba.b.257.14		192	5.3	odd	4
675.2.ba.b.407.14		192	135.83	even	36

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16608 + 1.66533i) q^{2} +(-0.967587 - 1.43658i) q^{3} +(-0.729546 - 2.00441i) q^{4} +(1.90549 + 1.17008i) q^{5} +(3.52066 + 0.0638164i) q^{6} +(2.43427 - 1.13512i) q^{7} +(0.261271 + 0.0700073i) q^{8} +(-1.12755 + 2.78004i) q^{9} +(-4.17052 + 1.80887i) q^{10} +(4.08386 + 4.86695i) q^{11} +(-2.17361 + 2.98750i) q^{12} +(-1.70687 + 1.19516i) q^{13} +(-0.948196 + 5.37749i) q^{14} +(-0.162811 - 3.86956i) q^{15} +(2.84677 - 2.38873i) q^{16} +(-0.649952 + 0.174154i) q^{17} +(-3.31487 - 5.11948i) q^{18} +(2.70632 - 1.56249i) q^{19} +(0.955177 - 4.67302i) q^{20} +(-3.98606 - 2.39871i) q^{21} +(-12.8672 + 1.12573i) q^{22} +(0.191186 - 0.409999i) q^{23} +(-0.152231 - 0.443076i) q^{24} +(2.26182 + 4.45917i) q^{25} -4.23615i q^{26} +(5.08477 - 1.07011i) q^{27} +(-4.05115 - 4.05115i) q^{28} +(-1.39473 - 7.90988i) q^{29} +(6.63394 + 4.24106i) q^{30} +(-1.53858 + 0.559998i) q^{31} +(0.705611 + 8.06517i) q^{32} +(3.04030 - 10.5760i) q^{33} +(0.467869 - 1.28546i) q^{34} +(5.96666 + 0.685329i) q^{35} +(6.39494 + 0.231909i) q^{36} +(-0.739977 - 2.76163i) q^{37} +(-0.553706 + 6.32889i) q^{38} +(3.36850 + 1.29564i) q^{39} +(0.415936 + 0.439107i) q^{40} +(-9.28604 - 1.63738i) q^{41} +(8.64268 - 3.84102i) q^{42} +(3.51939 + 0.307907i) q^{43} +(6.77601 - 11.7364i) q^{44} +(-5.40142 + 3.97803i) q^{45} +(0.459846 + 0.796477i) q^{46} +(-2.65193 - 5.68707i) q^{47} +(-6.18611 - 1.77833i) q^{48} +(0.137652 - 0.164047i) q^{49} +(-10.0634 - 1.43305i) q^{50} +(0.879072 + 0.765202i) q^{51} +(3.64084 + 2.54934i) q^{52} +(-5.99520 + 5.99520i) q^{53} +(-4.14714 + 9.71563i) q^{54} +(2.08704 + 14.0524i) q^{55} +(0.715470 - 0.126157i) q^{56} +(-4.86325 - 2.37601i) q^{57} +(14.7989 + 6.90084i) q^{58} +(-6.07856 - 5.10051i) q^{59} +(-7.63741 + 3.14936i) q^{60} +(-1.53937 - 0.560286i) q^{61} +(0.861522 - 3.21525i) q^{62} +(0.410911 + 8.04727i) q^{63} +(-7.81729 - 4.51332i) q^{64} +(-4.65087 + 0.280202i) q^{65} +(14.0673 + 17.3955i) q^{66} +(-3.06805 - 4.38163i) q^{67} +(0.823246 + 1.17572i) q^{68} +(-0.773987 + 0.122055i) q^{69} +(-8.09888 + 9.13731i) q^{70} +(2.05039 + 1.18380i) q^{71} +(-0.489220 + 0.647407i) q^{72} +(0.358350 - 1.33738i) q^{73} +(5.46189 + 1.98796i) q^{74} +(4.21746 - 7.56393i) q^{75} +(-5.10626 - 4.28466i) q^{76} +(15.4658 + 7.21181i) q^{77} +(-6.08559 + 4.09885i) q^{78} +(6.73243 - 1.18711i) q^{79} +(8.21952 - 1.22075i) q^{80} +(-6.45726 - 6.26928i) q^{81} +(13.5550 - 13.5550i) q^{82} +(-3.24283 - 2.27065i) q^{83} +(-1.89998 + 9.73966i) q^{84} +(-1.44225 - 0.428647i) q^{85} +(-4.61664 + 5.50190i) q^{86} +(-10.0137 + 9.65714i) q^{87} +(0.726271 + 1.55749i) q^{88} +(-0.428822 - 0.742742i) q^{89} +(-0.326262 - 13.6338i) q^{90} +(-2.79833 + 4.84685i) q^{91} +(-0.961286 - 0.0841016i) q^{92} +(2.29320 + 1.66846i) q^{93} +(12.5632 + 2.21523i) q^{94} +(6.98511 + 0.189288i) q^{95} +(10.9036 - 8.81742i) q^{96} +(-0.340015 + 3.88639i) q^{97} +(0.112680 + 0.420527i) q^{98} +(-18.1351 + 5.86555i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22}+ \cdots + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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