LMFDB - Embedded newform 432.2.be.c.335.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 7]))

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

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

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.be (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			335.1
Character	$\chi$	$=$	432.335
Dual form			432.2.be.c.383.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.48063 + 0.898737i) q^{3} +(0.357520 - 0.982277i) q^{5} +(0.862991 + 0.152169i) q^{7} +(1.38454 - 2.66140i) q^{9} +O(q^{10})$	\(q+(-1.48063 + 0.898737i) q^{3} +(0.357520 - 0.982277i) q^{5} +(0.862991 + 0.152169i) q^{7} +(1.38454 - 2.66140i) q^{9} +(-0.855132 + 0.311243i) q^{11} +(0.662306 - 0.555741i) q^{13} +(0.353454 + 1.77571i) q^{15} +(4.52256 - 2.61110i) q^{17} +(3.63632 + 2.09943i) q^{19} +(-1.41453 + 0.550297i) q^{21} +(-0.356585 - 2.02229i) q^{23} +(2.99317 + 2.51157i) q^{25} +(0.341901 + 5.18489i) q^{27} +(0.526265 - 0.627178i) q^{29} +(8.52362 - 1.50294i) q^{31} +(0.986410 - 1.22937i) q^{33} +(0.458008 - 0.793293i) q^{35} +(1.44045 + 2.49493i) q^{37} +(-0.481166 + 1.41809i) q^{39} +(5.04026 + 6.00675i) q^{41} +(-0.0722797 - 0.198587i) q^{43} +(-2.11923 - 2.31151i) q^{45} +(1.30305 - 7.38995i) q^{47} +(-5.85625 - 2.13150i) q^{49} +(-4.34955 + 7.93067i) q^{51} -8.58900i q^{53} +0.951252i q^{55} +(-7.27088 + 0.159613i) q^{57} +(-11.8016 - 4.29544i) q^{59} +(-1.82666 + 10.3595i) q^{61} +(1.59983 - 2.08608i) q^{63} +(-0.309104 - 0.849256i) q^{65} +(1.37313 + 1.63643i) q^{67} +(2.34548 + 2.67380i) q^{69} +(-1.76808 - 3.06241i) q^{71} +(-0.656039 + 1.13629i) q^{73} +(-6.68903 - 1.02863i) q^{75} +(-0.785333 + 0.138475i) q^{77} +(0.814135 - 0.970249i) q^{79} +(-5.16609 - 7.36964i) q^{81} +(-9.32579 - 7.82526i) q^{83} +(-0.947921 - 5.37593i) q^{85} +(-0.215536 + 1.40159i) q^{87} +(4.27725 + 2.46947i) q^{89} +(0.656130 - 0.378817i) q^{91} +(-11.2696 + 9.88581i) q^{93} +(3.36228 - 2.82128i) q^{95} +(-13.6037 + 4.95134i) q^{97} +(-0.355626 + 2.70678i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q + 3 * q^5 + 6 * q^9	$ 36 q + 3 q^{5} + 6 q^{9} + 18 q^{11} - 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} - 27 q^{31} + 27 q^{33} - 27 q^{35} + 45 q^{39} + 18 q^{41} + 27 q^{45} - 45 q^{47} + 63 q^{51} - 9 q^{57} - 54 q^{59} + 63 q^{63} - 57 q^{65} - 63 q^{69} - 36 q^{71} + 9 q^{73} + 45 q^{75} - 81 q^{77} - 54 q^{81} + 27 q^{83} - 36 q^{85} - 45 q^{87} - 63 q^{89} - 27 q^{91} - 63 q^{93} + 72 q^{95} - 99 q^{99}+O(q^{100}) $ 36 * q + 3 * q^5 + 6 * q^9 + 18 * q^11 - 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 - 27 * q^31 + 27 * q^33 - 27 * q^35 + 45 * q^39 + 18 * q^41 + 27 * q^45 - 45 * q^47 + 63 * q^51 - 9 * q^57 - 54 * q^59 + 63 * q^63 - 57 * q^65 - 63 * q^69 - 36 * q^71 + 9 * q^73 + 45 * q^75 - 81 * q^77 - 54 * q^81 + 27 * q^83 - 36 * q^85 - 45 * q^87 - 63 * q^89 - 27 * q^91 - 63 * q^93 + 72 * q^95 - 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.48063	+	0.898737i	−0.854843	+	0.518886i
$3$	−1.48063	+	0.898737i	−0.854843	+	0.518886i
$4$		0			0
$5$	0.357520	−	0.982277i	0.159888	−	0.439288i	−0.833718	−	0.552190i	$-0.813792\pi$
$5$	0.357520	−	0.982277i	0.159888	−	0.439288i	0.993606	+	0.112902i	$0.0360146\pi$
$6$		0			0
$7$	0.862991	+	0.152169i	0.326180	+	0.0575143i	0.334340	−	0.942452i	$-0.391486\pi$
$7$	0.862991	+	0.152169i	0.326180	+	0.0575143i	−0.00816043	+	0.999967i	$0.502598\pi$
$8$		0			0
$9$	1.38454	−	2.66140i	0.461514	−	0.887133i
$10$		0			0
$11$	−0.855132	+	0.311243i	−0.257832	+	0.0938432i	−0.467702	−	0.883886i	$-0.654918\pi$
$11$	−0.855132	+	0.311243i	−0.257832	+	0.0938432i	0.209870	+	0.977729i	$0.432696\pi$
$12$		0			0
$13$	0.662306	−	0.555741i	0.183691	−	0.154135i	−0.546306	−	0.837586i	$-0.683966\pi$
$13$	0.662306	−	0.555741i	0.183691	−	0.154135i	0.729996	+	0.683451i	$0.239522\pi$
$14$		0			0
$15$	0.353454	+	1.77571i	0.0912615	+	0.458486i
$16$		0			0
$17$	4.52256	−	2.61110i	1.09688	−	0.633285i	0.161481	−	0.986876i	$-0.448373\pi$
$17$	4.52256	−	2.61110i	1.09688	−	0.633285i	0.935400	+	0.353591i	$0.115040\pi$
$18$		0			0
$19$	3.63632	+	2.09943i	0.834228	+	0.481642i	0.855298	−	0.518136i	$-0.173374\pi$
$19$	3.63632	+	2.09943i	0.834228	+	0.481642i	−0.0210701	+	0.999778i	$0.506707\pi$
$20$		0			0
$21$	−1.41453	+	0.550297i	−0.308676	+	0.120085i
$22$		0			0
$23$	−0.356585	−	2.02229i	−0.0743531	−	0.421678i	−0.999150	−	0.0412169i	$-0.986877\pi$
$23$	−0.356585	−	2.02229i	−0.0743531	−	0.421678i	0.924797	−	0.380461i	$-0.124235\pi$
$24$		0			0
$25$	2.99317	+	2.51157i	0.598635	+	0.502314i
$26$		0			0
$27$	0.341901	+	5.18489i	0.0657990	+	0.997833i
$28$		0			0
$29$	0.526265	−	0.627178i	0.0977250	−	0.116464i	−0.714965	−	0.699160i	$-0.753558\pi$
$29$	0.526265	−	0.627178i	0.0977250	−	0.116464i	0.812690	+	0.582696i	$0.198002\pi$
$30$		0			0
$31$	8.52362	−	1.50294i	1.53089	−	0.269937i	0.656187	−	0.754599i	$-0.272168\pi$
$31$	8.52362	−	1.50294i	1.53089	−	0.269937i	0.874702	+	0.484662i	$0.161057\pi$
$32$		0			0
$33$	0.986410	−	1.22937i	0.171712	−	0.214007i
$34$		0			0
$35$	0.458008	−	0.793293i	0.0774175	−	0.134091i
$36$		0			0
$37$	1.44045	+	2.49493i	0.236808	+	0.410163i	0.959797	−	0.280697i	$-0.0905655\pi$
$37$	1.44045	+	2.49493i	0.236808	+	0.410163i	−0.722989	+	0.690860i	$0.757232\pi$
$38$		0			0
$39$	−0.481166	+	1.41809i	−0.0770483	+	0.227076i
$40$		0			0
$41$	5.04026	+	6.00675i	0.787157	+	0.938097i	0.999233	−	0.0391564i	$-0.0124671\pi$
$41$	5.04026	+	6.00675i	0.787157	+	0.938097i	−0.212077	+	0.977253i	$0.568023\pi$
$42$		0			0
$43$	−0.0722797	−	0.198587i	−0.0110226	−	0.0302842i	0.934059	−	0.357118i	$-0.116241\pi$
$43$	−0.0722797	−	0.198587i	−0.0110226	−	0.0302842i	−0.945082	+	0.326834i	$0.894018\pi$
$44$		0			0
$45$	−2.11923	−	2.31151i	−0.315916	−	0.344579i
$46$		0			0
$47$	1.30305	−	7.38995i	0.190069	−	1.07794i	−0.729198	−	0.684302i	$-0.760107\pi$
$47$	1.30305	−	7.38995i	0.190069	−	1.07794i	0.919268	−	0.393633i	$-0.128782\pi$
$48$		0			0
$49$	−5.85625	−	2.13150i	−0.836607	−	0.304500i
$50$		0			0
$51$	−4.34955	+	7.93067i	−0.609059	+	1.11052i
$52$		0			0
$53$		−	8.58900i		−	1.17979i	−0.807480	−	0.589895i	$-0.799169\pi$
$53$		−	8.58900i		−	1.17979i	0.807480	−	0.589895i	$-0.200831\pi$
$54$		0			0
$55$			0.951252i			0.128267i
$56$		0			0
$57$	−7.27088	+	0.159613i	−0.963052	+	0.0211413i
$58$		0			0
$59$	−11.8016	−	4.29544i	−1.53644	−	0.559218i	−0.571252	−	0.820775i	$-0.693542\pi$
$59$	−11.8016	−	4.29544i	−1.53644	−	0.559218i	−0.965188	+	0.261556i	$0.915764\pi$
$60$		0			0
$61$	−1.82666	+	10.3595i	−0.233880	+	1.32640i	0.611079	+	0.791570i	$0.290736\pi$
$61$	−1.82666	+	10.3595i	−0.233880	+	1.32640i	−0.844959	+	0.534831i	$0.820375\pi$
$62$		0			0
$63$	1.59983	−	2.08608i	0.201560	−	0.262821i
$64$		0			0
$65$	−0.309104	−	0.849256i	−0.0383396	−	0.105337i
$66$		0			0
$67$	1.37313	+	1.63643i	0.167755	+	0.199922i	0.843372	−	0.537331i	$-0.180567\pi$
$67$	1.37313	+	1.63643i	0.167755	+	0.199922i	−0.675617	+	0.737253i	$0.736123\pi$
$68$		0			0
$69$	2.34548	+	2.67380i	0.282363	+	0.321887i
$70$		0			0
$71$	−1.76808	−	3.06241i	−0.209833	−	0.363441i	0.741829	−	0.670589i	$-0.233959\pi$
$71$	−1.76808	−	3.06241i	−0.209833	−	0.363441i	−0.951662	+	0.307148i	$0.900625\pi$
$72$		0			0
$73$	−0.656039	+	1.13629i	−0.0767835	+	0.132993i	−0.901860	−	0.432027i	$-0.857798\pi$
$73$	−0.656039	+	1.13629i	−0.0767835	+	0.132993i	0.825077	+	0.565020i	$0.191132\pi$
$74$		0			0
$75$	−6.68903	−	1.02863i	−0.772383	−	0.118777i
$76$		0			0
$77$	−0.785333	+	0.138475i	−0.0894970	+	0.0157807i
$78$		0			0
$79$	0.814135	−	0.970249i	0.0915974	−	0.109161i	−0.718299	−	0.695735i	$-0.755079\pi$
$79$	0.814135	−	0.970249i	0.0915974	−	0.109161i	0.809896	+	0.586573i	$0.199523\pi$
$80$		0			0
$81$	−5.16609	−	7.36964i	−0.574010	−	0.818849i
$82$		0			0
$83$	−9.32579	−	7.82526i	−1.02364	−	0.858934i	−0.0335576	−	0.999437i	$-0.510684\pi$
$83$	−9.32579	−	7.82526i	−1.02364	−	0.858934i	−0.990080	+	0.140503i	$0.955128\pi$
$84$		0			0
$85$	−0.947921	−	5.37593i	−0.102816	−	0.583101i
$86$		0			0
$87$	−0.215536	+	1.40159i	−0.0231079	+	0.150267i
$88$		0			0
$89$	4.27725	+	2.46947i	0.453388	+	0.261764i	0.709260	−	0.704947i	$-0.249029\pi$
$89$	4.27725	+	2.46947i	0.453388	+	0.261764i	−0.255872	+	0.966711i	$0.582363\pi$
$90$		0			0
$91$	0.656130	−	0.378817i	0.0687812	−	0.0397108i
$92$		0			0
$93$	−11.2696	+	9.88581i	−1.16860	+	1.02511i
$94$		0			0
$95$	3.36228	−	2.82128i	0.344962	−	0.289458i
$96$		0			0
$97$	−13.6037	+	4.95134i	−1.38125	+	0.502733i	−0.922556	−	0.385863i	$-0.873904\pi$
$97$	−13.6037	+	4.95134i	−1.38125	+	0.502733i	−0.458691	+	0.888596i	$0.651681\pi$
$98$		0			0
$99$	−0.355626	+	2.70678i	−0.0357417	+	0.272041i
$100$		0			0
$101$	−17.0598	−	3.00811i	−1.69752	−	0.299318i	−0.760691	−	0.649114i	$-0.775140\pi$
$101$	−17.0598	−	3.00811i	−1.69752	−	0.299318i	−0.936826	+	0.349797i	$0.886251\pi$
$102$		0			0
$103$	4.35114	−	11.9547i	0.428730	−	1.17793i	−0.517853	−	0.855469i	$-0.673269\pi$
$103$	4.35114	−	11.9547i	0.428730	−	1.17793i	0.946584	−	0.322458i	$-0.104509\pi$
$104$		0			0
$105$	0.0348210	+	1.58620i	0.00339818	+	0.154798i
$106$		0			0
$107$	5.72690			0.553641			0.276820	−	0.960922i	$-0.410719\pi$
$107$	5.72690			0.553641			0.276820	+	0.960922i	$0.410719\pi$
$108$		0			0
$109$	18.7360			1.79459			0.897294	−	0.441434i	$-0.145530\pi$
$109$	18.7360			1.79459			0.897294	+	0.441434i	$0.145530\pi$
$110$		0			0
$111$	−4.37505	−	2.39948i	−0.415262	−	0.227749i
$112$		0			0
$113$	−2.64000	+	7.25335i	−0.248351	+	0.682337i	0.751397	+	0.659851i	$0.229381\pi$
$113$	−2.64000	+	7.25335i	−0.248351	+	0.682337i	−0.999747	+	0.0224866i	$0.992842\pi$
$114$		0			0
$115$	−2.11394	−	0.372745i	−0.197126	−	0.0347586i
$116$		0			0
$117$	−0.562057	−	2.53211i	−0.0519622	−	0.234093i
$118$		0			0
$119$	4.30026	−	1.56516i	0.394204	−	0.143478i
$120$		0			0
$121$	−7.79211	+	6.53836i	−0.708374	+	0.594396i
$122$		0			0
$123$	−12.8613	−	4.36391i	−1.15966	−	0.393481i
$124$		0			0
$125$	8.06354	−	4.65549i	0.721225	−	0.416399i
$126$		0			0
$127$	11.3108	+	6.53030i	1.00367	+	0.579470i	0.909333	−	0.416070i	$-0.136593\pi$
$127$	11.3108	+	6.53030i	1.00367	+	0.579470i	0.0943395	+	0.995540i	$0.469926\pi$
$128$		0			0
$129$	0.285497	+	0.229074i	0.0251366	+	0.0201688i
$130$		0			0
$131$	2.97506	+	16.8724i	0.259933	+	1.47415i	0.783087	+	0.621913i	$0.213644\pi$
$131$	2.97506	+	16.8724i	0.259933	+	1.47415i	−0.523154	+	0.852238i	$0.675245\pi$
$132$		0			0
$133$	2.81864	+	2.36512i	0.244407	+	0.205082i
$134$		0			0
$135$	5.21524	+	1.51786i	0.448856	+	0.130637i
$136$		0			0
$137$	−4.25955	+	5.07633i	−0.363917	+	0.433700i	−0.916670	−	0.399646i	$-0.869133\pi$
$137$	−4.25955	+	5.07633i	−0.363917	+	0.433700i	0.552752	+	0.833346i	$0.313578\pi$
$138$		0			0
$139$	−5.35032	+	0.943406i	−0.453808	+	0.0800187i	−0.395880	−	0.918302i	$-0.629561\pi$
$139$	−5.35032	+	0.943406i	−0.453808	+	0.0800187i	−0.0579280	+	0.998321i	$0.518449\pi$
$140$		0			0
$141$	4.71229	+	12.1129i	0.396847	+	1.02009i
$142$		0			0
$143$	−0.393389	+	0.681369i	−0.0328968	+	0.0569790i
$144$		0			0
$145$	−0.427913	−	0.741167i	−0.0355362	−	0.0615506i
$146$		0			0
$147$	10.5866	−	2.10726i	0.873169	−	0.173804i
$148$		0			0
$149$	9.57370	+	11.4095i	0.784308	+	0.934702i	0.999120	−	0.0419534i	$-0.0133581\pi$
$149$	9.57370	+	11.4095i	0.784308	+	0.934702i	−0.214811	+	0.976656i	$0.568914\pi$
$150$		0			0
$151$	−2.94957	−	8.10389i	−0.240033	−	0.659485i	−0.999955	−	0.00947108i	$-0.996985\pi$
$151$	−2.94957	−	8.10389i	−0.240033	−	0.659485i	0.759922	−	0.650014i	$-0.225237\pi$
$152$		0			0
$153$	−0.687507	−	15.6515i	−0.0555816	−	1.26535i
$154$		0			0
$155$	1.57106	−	8.90990i	0.126190	−	0.715660i
$156$		0			0
$157$	−6.78417	−	2.46924i	−0.541436	−	0.197066i	0.0568016	−	0.998385i	$-0.481910\pi$
$157$	−6.78417	−	2.46924i	−0.541436	−	0.197066i	−0.598237	+	0.801319i	$0.704132\pi$
$158$		0			0
$159$	7.71926	+	12.7172i	0.612177	+	1.00854i
$160$		0			0
$161$		−	1.79948i		−	0.141819i
$162$		0			0
$163$			2.30077i			0.180210i	0.995932	+	0.0901051i	$0.0287203\pi$
$163$			2.30077i			0.180210i	−0.995932	+	0.0901051i	$0.971280\pi$
$164$		0			0
$165$	−0.854926	−	1.40845i	−0.0665559	−	0.109648i
$166$		0			0
$167$	−16.6973	−	6.07731i	−1.29207	−	0.470277i	−0.397667	−	0.917530i	$-0.630180\pi$
$167$	−16.6973	−	6.07731i	−1.29207	−	0.470277i	−0.894407	+	0.447253i	$0.852402\pi$
$168$		0			0
$169$	−2.12762	+	12.0664i	−0.163663	+	0.928182i
$170$		0			0
$171$	10.6220	−	6.77094i	0.812288	−	0.517787i
$172$		0			0
$173$	−3.83276	−	10.5304i	−0.291399	−	0.800613i	−0.995863	−	0.0908727i	$-0.971034\pi$
$173$	−3.83276	−	10.5304i	−0.291399	−	0.800613i	0.704463	−	0.709741i	$-0.251188\pi$
$174$		0			0
$175$	2.20090	+	2.62293i	0.166372	+	0.198275i
$176$		0			0
$177$	21.3343	−	4.24659i	1.60359	−	0.319194i
$178$		0			0
$179$	10.9900	+	19.0352i	0.821431	+	1.42276i	0.904616	+	0.426227i	$0.140157\pi$
$179$	10.9900	+	19.0352i	0.821431	+	1.42276i	−0.0831849	+	0.996534i	$0.526509\pi$
$180$		0			0
$181$	9.50948	−	16.4709i	0.706834	−	1.22427i	−0.259191	−	0.965826i	$-0.583456\pi$
$181$	9.50948	−	16.4709i	0.706834	−	1.22427i	0.966025	−	0.258447i	$-0.0832107\pi$
$182$		0			0
$183$	−6.60588	−	16.9803i	−0.488320	−	1.25522i
$184$		0			0
$185$	2.96570	−	0.522932i	0.218042	−	0.0384468i
$186$		0			0
$187$	−3.05470	+	3.64045i	−0.223382	+	0.266216i
$188$		0			0
$189$	−0.493920	+	4.52654i	−0.0359274	+	0.329258i
$190$		0			0
$191$	11.7943	+	9.89655i	0.853402	+	0.716089i	0.960536	−	0.278155i	$-0.0897230\pi$
$191$	11.7943	+	9.89655i	0.853402	+	0.716089i	−0.107134	+	0.994245i	$0.534167\pi$
$192$		0			0
$193$	−3.48037	−	19.7381i	−0.250522	−	1.42078i	−0.807310	−	0.590127i	$-0.799078\pi$
$193$	−3.48037	−	19.7381i	−0.250522	−	1.42078i	0.556788	−	0.830655i	$-0.312034\pi$
$194$		0			0
$195$	1.22093	+	0.979633i	0.0874324	+	0.0701529i
$196$		0			0
$197$	−6.20995	−	3.58532i	−0.442441	−	0.255443i	0.262192	−	0.965016i	$-0.415555\pi$
$197$	−6.20995	−	3.58532i	−0.442441	−	0.255443i	−0.704632	+	0.709572i	$0.748888\pi$
$198$		0			0
$199$	−15.1085	+	8.72292i	−1.07102	+	0.618352i	−0.928459	−	0.371435i	$-0.878866\pi$
$199$	−15.1085	+	8.72292i	−1.07102	+	0.618352i	−0.142558	+	0.989787i	$0.545533\pi$
$200$		0			0
$201$	−3.50382	−	1.18887i	−0.247141	−	0.0838565i
$202$		0			0
$203$	0.549599	−	0.461168i	0.0385743	−	0.0323677i
$204$		0			0
$205$	7.70229	−	2.80340i	0.537951	−	0.195798i
$206$		0			0
$207$	−5.87584	−	1.85094i	−0.408399	−	0.128649i
$208$		0			0
$209$	−3.76296	−	0.663512i	−0.260289	−	0.0458961i
$210$		0			0
$211$	−0.945207	+	2.59694i	−0.0650708	+	0.178780i	−0.967967	−	0.251079i	$-0.919215\pi$
$211$	−0.945207	+	2.59694i	−0.0650708	+	0.178780i	0.902896	+	0.429859i	$0.141437\pi$
$212$		0			0
$213$	5.37018	+	2.94526i	0.367959	+	0.201806i
$214$		0			0
$215$	−0.220909			−0.0150659
$216$		0			0
$217$	7.58451			0.514870
$218$		0			0
$219$	−0.0498766	−	2.27204i	−0.00337035	−	0.153530i
$220$		0			0
$221$	1.54422	−	4.24272i	0.103876	−	0.285396i
$222$		0			0
$223$	−24.2380	−	4.27381i	−1.62309	−	0.286195i	−0.713177	−	0.700984i	$-0.752744\pi$
$223$	−24.2380	−	4.27381i	−1.62309	−	0.286195i	−0.909918	+	0.414789i	$0.863855\pi$
$224$		0			0
$225$	10.8285	−	4.48865i	0.721898	−	0.299244i
$226$		0			0
$227$	4.15263	−	1.51143i	0.275620	−	0.100317i	−0.200512	−	0.979691i	$-0.564261\pi$
$227$	4.15263	−	1.51143i	0.275620	−	0.100317i	0.476132	+	0.879374i	$0.342038\pi$
$228$		0			0
$229$	13.7629	−	11.5484i	0.909477	−	0.763142i	−0.0625423	−	0.998042i	$-0.519921\pi$
$229$	13.7629	−	11.5484i	0.909477	−	0.763142i	0.972019	+	0.234900i	$0.0754764\pi$
$230$		0			0
$231$	1.03834	−	0.910839i	0.0683175	−	0.0599288i
$232$		0			0
$233$	8.65324	−	4.99595i	0.566893	−	0.327296i	−0.189015	−	0.981974i	$-0.560529\pi$
$233$	8.65324	−	4.99595i	0.566893	−	0.327296i	0.755907	+	0.654679i	$0.227196\pi$
$234$		0			0
$235$	−6.79312	−	3.92201i	−0.443134	−	0.255844i
$236$		0			0
$237$	−0.333436	+	2.16827i	−0.0216590	+	0.140845i
$238$		0			0
$239$	4.63317	+	26.2760i	0.299695	+	1.69965i	0.647482	+	0.762080i	$0.275822\pi$
$239$	4.63317	+	26.2760i	0.299695	+	1.69965i	−0.347787	+	0.937573i	$0.613067\pi$
$240$		0			0
$241$	−5.01164	−	4.20527i	−0.322828	−	0.270885i	0.466942	−	0.884288i	$-0.345356\pi$
$241$	−5.01164	−	4.20527i	−0.322828	−	0.270885i	−0.789770	+	0.613403i	$0.789800\pi$
$242$		0			0
$243$	14.2724	+	6.26876i	0.915578	+	0.402141i
$244$		0			0
$245$	−4.18745	+	4.99041i	−0.267526	+	0.318825i
$246$		0			0
$247$	3.57509	−	0.630385i	0.227478	−	0.0401104i
$248$		0			0
$249$	20.8409	+	3.20490i	1.32074	+	0.203102i
$250$		0			0
$251$	0.963757	−	1.66928i	0.0608318	−	0.105364i	−0.834006	−	0.551756i	$-0.813958\pi$
$251$	0.963757	−	1.66928i	0.0608318	−	0.105364i	0.894837	+	0.446392i	$0.147291\pi$
$252$		0			0
$253$	0.934352	+	1.61834i	0.0587422	+	0.101744i
$254$		0			0
$255$	6.23507	+	7.10784i	0.390455	+	0.445110i
$256$		0			0
$257$	19.6622	+	23.4325i	1.22649	+	1.46168i	0.842807	+	0.538215i	$0.180901\pi$
$257$	19.6622	+	23.4325i	1.22649	+	1.46168i	0.383687	+	0.923463i	$0.374654\pi$
$258$		0			0
$259$	0.863443	+	2.37229i	0.0536517	+	0.147407i
$260$		0			0
$261$	−0.940535	−	2.26896i	−0.0582177	−	0.140445i
$262$		0			0
$263$	−2.25823	+	12.8071i	−0.139249	+	0.789718i	0.832558	+	0.553938i	$0.186876\pi$
$263$	−2.25823	+	12.8071i	−0.139249	+	0.789718i	−0.971807	+	0.235780i	$0.924236\pi$
$264$		0			0
$265$	−8.43678	−	3.07074i	−0.518267	−	0.188634i
$266$		0			0
$267$	−8.55245	+	0.187747i	−0.523401	+	0.0114899i
$268$		0			0
$269$		−	12.5617i		−	0.765899i	−0.923769	−	0.382950i	$-0.874908\pi$
$269$		−	12.5617i		−	0.765899i	0.923769	−	0.382950i	$-0.125092\pi$
$270$		0			0
$271$			22.0527i			1.33961i	0.742539	+	0.669803i	$0.233621\pi$
$271$			22.0527i			1.33961i	−0.742539	+	0.669803i	$0.766379\pi$
$272$		0			0
$273$	−0.631031	+	1.15058i	−0.0381917	+	0.0696361i
$274$		0			0
$275$	−3.34127	−	1.21612i	−0.201486	−	0.0733349i
$276$		0			0
$277$	0.542604	−	3.07726i	0.0326019	−	0.184895i	−0.964158	−	0.265329i	$-0.914520\pi$
$277$	0.542604	−	3.07726i	0.0326019	−	0.184895i	0.996760	+	0.0804340i	$0.0256306\pi$
$278$		0			0
$279$	7.80138	−	24.7657i	0.467056	−	1.48268i
$280$		0			0
$281$	−2.09238	−	5.74876i	−0.124821	−	0.342942i	0.861505	−	0.507749i	$-0.169522\pi$
$281$	−2.09238	−	5.74876i	−0.124821	−	0.342942i	−0.986326	+	0.164807i	$0.947300\pi$
$282$		0			0
$283$	−9.26570	−	11.0424i	−0.550789	−	0.656404i	0.416781	−	0.909007i	$-0.363158\pi$
$283$	−9.26570	−	11.0424i	−0.550789	−	0.656404i	−0.967570	+	0.252602i	$0.918714\pi$
$284$		0			0
$285$	−2.44270	+	7.19909i	−0.144693	+	0.426437i
$286$		0			0
$287$	3.43566	+	5.95074i	0.202801	+	0.351261i
$288$		0			0
$289$	5.13568	−	8.89527i	0.302099	−	0.523251i
$290$		0			0
$291$	15.6921	−	19.5573i	0.919888	−	1.14647i
$292$		0			0
$293$	−28.7692	+	5.07278i	−1.68071	+	0.296355i	−0.930895	−	0.365288i	$-0.880971\pi$
$293$	−28.7692	+	5.07278i	−1.68071	+	0.296355i	−0.749819	+	0.661643i	$0.769860\pi$
$294$		0			0
$295$	−8.43862	+	10.0568i	−0.491316	+	0.585527i
$296$		0			0
$297$	−1.90613	−	4.32735i	−0.110605	−	0.251098i
$298$		0			0
$299$	−1.36004	−	1.14121i	−0.0786531	−	0.0659978i
$300$		0			0
$301$	−0.0321581	−	0.182378i	−0.00185356	−	0.0105121i
$302$		0			0
$303$	27.9628	−	10.8784i	1.60642	−	0.624948i
$304$		0			0
$305$	9.52286	+	5.49802i	0.545277	+	0.314816i
$306$		0			0
$307$	5.30538	−	3.06306i	0.302794	−	0.174818i	−0.340903	−	0.940098i	$-0.610733\pi$
$307$	5.30538	−	3.06306i	0.302794	−	0.174818i	0.643697	+	0.765280i	$0.277400\pi$
$308$		0			0
$309$	4.30166	+	21.6110i	0.244713	+	1.22941i
$310$		0			0
$311$	20.5489	−	17.2426i	1.16522	−	0.977739i	0.165260	−	0.986250i	$-0.447154\pi$
$311$	20.5489	−	17.2426i	1.16522	−	0.977739i	0.999964	+	0.00851113i	$0.00270921\pi$
$312$		0			0
$313$	−8.31736	+	3.02727i	−0.470125	+	0.171111i	−0.566209	−	0.824262i	$-0.691590\pi$
$313$	−8.31736	+	3.02727i	−0.470125	+	0.171111i	0.0960841	+	0.995373i	$0.469368\pi$
$314$		0			0
$315$	−1.47714	−	2.31729i	−0.0832273	−	0.130565i
$316$		0			0
$317$	−16.2536	−	2.86595i	−0.912894	−	0.160968i	−0.302577	−	0.953125i	$-0.597847\pi$
$317$	−16.2536	−	2.86595i	−0.912894	−	0.160968i	−0.610317	+	0.792157i	$0.708958\pi$
$318$		0			0
$319$	−0.254821	+	0.700116i	−0.0142673	+	0.0391990i
$320$		0			0
$321$	−8.47944	+	5.14698i	−0.473276	+	0.287277i
$322$		0			0
$323$	21.9273			1.22007
$324$		0			0
$325$	3.37818			0.187388
$326$		0			0
$327$	−27.7412	+	16.8388i	−1.53409	+	0.931187i
$328$		0			0
$329$	2.24904	−	6.17918i	0.123994	−	0.340669i
$330$		0			0
$331$	1.90388	+	0.335705i	0.104646	+	0.0184520i	0.225726	−	0.974191i	$-0.427525\pi$
$331$	1.90388	+	0.335705i	0.104646	+	0.0184520i	−0.121080	+	0.992643i	$0.538636\pi$
$332$		0			0
$333$	8.63435	−	0.379272i	0.473160	−	0.0207840i
$334$		0			0
$335$	2.09835	−	0.763738i	0.114645	−	0.0417274i
$336$		0			0
$337$	−5.93398	+	4.97920i	−0.323244	+	0.271234i	−0.789941	−	0.613183i	$-0.789889\pi$
$337$	−5.93398	+	4.97920i	−0.323244	+	0.271234i	0.466696	+	0.884418i	$0.345444\pi$
$338$		0			0
$339$	−2.60998	−	13.1122i	−0.141755	−	0.712157i
$340$		0			0
$341$	−6.82104	+	3.93813i	−0.369380	+	0.213262i
$342$		0			0
$343$	−10.0419	−	5.79767i	−0.542209	−	0.313045i
$344$		0			0
$345$	3.46497	−	1.34798i	0.186548	−	0.0725728i
$346$		0			0
$347$	3.62921	+	20.5823i	0.194826	+	1.10491i	0.912666	+	0.408706i	$0.134020\pi$
$347$	3.62921	+	20.5823i	0.194826	+	1.10491i	−0.717840	+	0.696208i	$0.754869\pi$
$348$		0			0
$349$	3.68709	+	3.09384i	0.197365	+	0.165609i	0.736115	−	0.676857i	$-0.236658\pi$
$349$	3.68709	+	3.09384i	0.197365	+	0.165609i	−0.538749	+	0.842466i	$0.681103\pi$
$350$		0			0
$351$	3.10790	+	3.24398i	0.165887	+	0.173151i
$352$		0			0
$353$	−18.0088	+	21.4620i	−0.958510	+	1.14231i	0.0312417	+	0.999512i	$0.490054\pi$
$353$	−18.0088	+	21.4620i	−0.958510	+	1.14231i	−0.989752	+	0.142796i	$0.954391\pi$
$354$		0			0
$355$	−3.64026	+	0.641876i	−0.193205	+	0.0340672i
$356$		0			0
$357$	−4.96042	+	6.18223i	−0.262533	+	0.327198i
$358$		0			0
$359$	−14.8329	+	25.6913i	−0.782849	+	1.35593i	0.147427	+	0.989073i	$0.452901\pi$
$359$	−14.8329	+	25.6913i	−0.782849	+	1.35593i	−0.930276	+	0.366861i	$0.880432\pi$
$360$		0			0
$361$	−0.684806	−	1.18612i	−0.0360424	−	0.0624273i
$362$		0			0
$363$	5.66098	−	16.6840i	0.297124	−	0.875681i
$364$		0			0
$365$	0.881607	+	1.05066i	0.0461454	+	0.0549940i
$366$		0			0
$367$	−5.16356	−	14.1868i	−0.269536	−	0.740543i	−0.998435	−	0.0559224i	$-0.982190\pi$
$367$	−5.16356	−	14.1868i	−0.269536	−	0.740543i	0.728899	−	0.684621i	$-0.240032\pi$
$368$		0			0
$369$	22.9648	−	5.09755i	1.19550	−	0.265368i
$370$		0			0
$371$	1.30698	−	7.41223i	0.0678549	−	0.384824i
$372$		0			0
$373$	−11.0141	−	4.00882i	−0.570291	−	0.207569i	0.0407481	−	0.999169i	$-0.487026\pi$
$373$	−11.0141	−	4.00882i	−0.570291	−	0.207569i	−0.611039	+	0.791601i	$0.709248\pi$
$374$		0			0
$375$	−7.75507	+	14.1401i	−0.400470	+	0.730190i
$376$		0			0
$377$		−	0.707851i		−	0.0364562i
$378$		0			0
$379$		−	21.9951i		−	1.12981i	−0.825155	−	0.564906i	$-0.808913\pi$
$379$		−	21.9951i		−	1.12981i	0.825155	−	0.564906i	$-0.191087\pi$
$380$		0			0
$381$	−22.6162	+	0.496479i	−1.15866	+	0.0254354i
$382$		0			0
$383$	−17.1381	−	6.23776i	−0.875716	−	0.318735i	−0.135236	−	0.990813i	$-0.543179\pi$
$383$	−17.1381	−	6.23776i	−0.875716	−	0.318735i	−0.740480	+	0.672079i	$0.765402\pi$
$384$		0			0
$385$	−0.144751	+	0.820922i	−0.00737718	+	0.0418381i
$386$		0			0
$387$	−0.628593	−	0.0825868i	−0.0319532	−	0.00419812i
$388$		0			0
$389$	4.30124	+	11.8176i	0.218082	+	0.599174i	0.999698	−	0.0245854i	$-0.00782655\pi$
$389$	4.30124	+	11.8176i	0.218082	+	0.599174i	−0.781616	+	0.623760i	$0.785604\pi$
$390$		0			0
$391$	−6.89309	−	8.21487i	−0.348599	−	0.415444i
$392$		0			0
$393$	−19.5689	−	22.3081i	−0.987118	−	1.12529i
$394$		0			0
$395$	−0.661984	−	1.14659i	−0.0333080	−	0.0576912i
$396$		0			0
$397$	−4.83557	+	8.37546i	−0.242690	+	0.420352i	−0.961480	−	0.274876i	$-0.911363\pi$
$397$	−4.83557	+	8.37546i	−0.242690	+	0.420352i	0.718789	+	0.695228i	$0.244697\pi$
$398$		0			0
$399$	−6.29899	−	0.968655i	−0.315344	−	0.0484934i
$400$		0			0
$401$	−23.9107	+	4.21610i	−1.19404	+	0.210542i	−0.735122	−	0.677935i	$-0.762875\pi$
$401$	−23.9107	+	4.21610i	−1.19404	+	0.210542i	−0.458921	+	0.888477i	$0.651764\pi$
$402$		0			0
$403$	4.81000	−	5.73233i	0.239603	−	0.285548i
$404$		0			0
$405$	−9.08601	+	2.43974i	−0.451487	+	0.121232i
$406$		0			0
$407$	−2.00830	−	1.68516i	−0.0995477	−	0.0835304i
$408$		0			0
$409$	0.524727	+	2.97587i	0.0259461	+	0.147148i	0.995029	−	0.0995891i	$-0.0317528\pi$
$409$	0.524727	+	2.97587i	0.0259461	+	0.147148i	−0.969083	+	0.246737i	$0.920642\pi$
$410$		0			0
$411$	1.74453	−	11.3444i	0.0860514	−	0.559577i
$412$		0			0
$413$	−9.53106	−	5.50276i	−0.468993	−	0.270773i
$414$		0			0
$415$	−11.0207	+	6.36282i	−0.540986	+	0.312339i
$416$		0			0
$417$	7.07398	−	6.20537i	0.346414	−	0.303878i
$418$		0			0
$419$	4.03376	−	3.38472i	0.197062	−	0.165355i	−0.538917	−	0.842359i	$-0.681166\pi$
$419$	4.03376	−	3.38472i	0.197062	−	0.165355i	0.735979	+	0.677004i	$0.236722\pi$
$420$		0			0
$421$	−2.10173	+	0.764966i	−0.102432	+	0.0372822i	−0.392728	−	0.919655i	$-0.628469\pi$
$421$	−2.10173	+	0.764966i	−0.102432	+	0.0372822i	0.290296	+	0.956937i	$0.406246\pi$
$422$		0			0
$423$	−17.8635	−	13.6996i	−0.868553	−	0.666099i
$424$		0			0
$425$	20.0948	+	3.54325i	0.974739	+	0.171873i
$426$		0			0
$427$	−3.15279	+	8.66222i	−0.152574	+	0.419194i
$428$		0			0
$429$	−0.0299081	−	1.36241i	−0.00144398	−	0.0657778i
$430$		0			0
$431$	−16.1724			−0.778995			−0.389498	−	0.921028i	$-0.627351\pi$
$431$	−16.1724			−0.778995			−0.389498	+	0.921028i	$0.627351\pi$
$432$		0			0
$433$	−24.5777			−1.18113			−0.590564	−	0.806991i	$-0.701094\pi$
$433$	−24.5777			−1.18113			−0.590564	+	0.806991i	$0.701094\pi$
$434$		0			0
$435$	1.29970	+	0.712814i	0.0623156	+	0.0341768i
$436$		0			0
$437$	2.94901	−	8.10233i	0.141070	−	0.387587i
$438$		0			0
$439$	−11.9050	−	2.09917i	−0.568195	−	0.100188i	−0.117832	−	0.993034i	$-0.537594\pi$
$439$	−11.9050	−	2.09917i	−0.568195	−	0.100188i	−0.450363	+	0.892845i	$0.648705\pi$
$440$		0			0
$441$	−13.7810	+	12.6347i	−0.656238	+	0.601651i
$442$		0			0
$443$	−1.19218	+	0.433918i	−0.0566422	+	0.0206161i	−0.370186	−	0.928958i	$-0.620706\pi$
$443$	−1.19218	+	0.433918i	−0.0566422	+	0.0206161i	0.313544	+	0.949574i	$0.398484\pi$
$444$		0			0
$445$	3.95491	−	3.31856i	0.187481	−	0.157315i
$446$		0			0
$447$	−24.4293	−	8.28902i	−1.15546	−	0.392057i
$448$		0			0
$449$	−12.4201	+	7.17076i	−0.586142	+	0.338409i	−0.763570	−	0.645724i	$-0.776555\pi$
$449$	−12.4201	+	7.17076i	−0.586142	+	0.338409i	0.177429	+	0.984134i	$0.443222\pi$
$450$		0			0
$451$	−6.17964	−	3.56782i	−0.290988	−	0.168002i
$452$		0			0
$453$	11.6505	+	9.34798i	0.547388	+	0.439207i
$454$		0			0
$455$	−0.137524	−	0.779937i	−0.00644722	−	0.0365640i
$456$		0			0
$457$	2.18801	+	1.83596i	0.102351	+	0.0858825i	0.692527	−	0.721392i	$-0.256497\pi$
$457$	2.18801	+	1.83596i	0.102351	+	0.0858825i	−0.590176	+	0.807274i	$0.700942\pi$
$458$		0			0
$459$	15.0845	+	22.5562i	0.704086	+	1.05283i
$460$		0			0
$461$	16.1365	−	19.2307i	0.751551	−	0.895664i	−0.245731	−	0.969338i	$-0.579028\pi$
$461$	16.1365	−	19.2307i	0.751551	−	0.895664i	0.997282	+	0.0736740i	$0.0234724\pi$
$462$		0			0
$463$	21.9130	−	3.86385i	1.01838	−	0.179568i	0.360556	−	0.932738i	$-0.382587\pi$
$463$	21.9130	−	3.86385i	1.01838	−	0.179568i	0.657827	+	0.753169i	$0.271476\pi$
$464$		0			0
$465$	5.68150	+	14.6042i	0.263473	+	0.677256i
$466$		0			0
$467$	16.0152	−	27.7392i	0.741097	−	1.28362i	−0.210899	−	0.977508i	$-0.567639\pi$
$467$	16.0152	−	27.7392i	0.741097	−	1.28362i	0.951996	−	0.306110i	$-0.0990276\pi$
$468$		0			0
$469$	0.935986	+	1.62117i	0.0432198	+	0.0748589i
$470$		0			0
$471$	12.2641	−	2.44116i	0.565098	−	0.112483i
$472$		0			0
$473$	0.123617	+	0.147322i	0.00568394	+	0.00677385i
$474$		0			0
$475$	5.61126	+	15.4168i	0.257462	+	0.707372i
$476$		0			0
$477$	−22.8588	−	11.8918i	−1.04663	−	0.544490i
$478$		0			0
$479$	−4.52904	+	25.6855i	−0.206937	+	1.17360i	0.687425	+	0.726256i	$0.258741\pi$
$479$	−4.52904	+	25.6855i	−0.206937	+	1.17360i	−0.894362	+	0.447344i	$0.852370\pi$
$480$		0			0
$481$	2.34055	+	0.851890i	0.106720	+	0.0388428i
$482$		0			0
$483$	1.61726	+	2.66437i	0.0735880	+	0.121233i
$484$		0			0
$485$			15.1328i			0.687145i
$486$		0			0
$487$			12.8151i			0.580706i	0.956920	+	0.290353i	$0.0937727\pi$
$487$			12.8151i			0.580706i	−0.956920	+	0.290353i	$0.906227\pi$
$488$		0			0
$489$	−2.06779	−	3.40659i	−0.0935086	−	0.154051i
$490$		0			0
$491$	−32.9705	−	12.0003i	−1.48794	−	0.541566i	−0.535033	−	0.844831i	$-0.679701\pi$
$491$	−32.9705	−	12.0003i	−1.48794	−	0.541566i	−0.952906	+	0.303266i	$0.901923\pi$
$492$		0			0
$493$	0.742439	−	4.21058i	0.0334378	−	0.189635i
$494$		0			0
$495$	2.53166	+	1.31705i	0.113790	+	0.0591969i
$496$		0			0
$497$	−1.05984	−	2.91188i	−0.0475402	−	0.130616i
$498$		0			0
$499$	3.47692	+	4.14363i	0.155648	+	0.185494i	0.838233	−	0.545312i	$-0.183589\pi$
$499$	3.47692	+	4.14363i	0.155648	+	0.185494i	−0.682585	+	0.730806i	$0.739144\pi$
$500$		0			0
$501$	30.1844	−	6.00821i	1.34854	−	0.268427i
$502$		0			0
$503$	−8.89978	−	15.4149i	−0.396822	−	0.687315i	0.596510	−	0.802606i	$-0.296554\pi$
$503$	−8.89978	−	15.4149i	−0.396822	−	0.687315i	−0.993332	+	0.115290i	$0.963220\pi$
$504$		0			0
$505$	−9.05402	+	15.6820i	−0.402899	+	0.697841i
$506$		0			0
$507$	−7.69426	−	19.7780i	−0.341714	−	0.878372i
$508$		0			0
$509$	4.55607	−	0.803358i	0.201944	−	0.0356082i	−0.0717610	−	0.997422i	$-0.522862\pi$
$509$	4.55607	−	0.803358i	0.201944	−	0.0356082i	0.273705	+	0.961814i	$0.411751\pi$
$510$		0			0
$511$	−0.739064	+	0.880782i	−0.0326942	+	0.0389635i
$512$		0			0
$513$	−9.64204	+	19.5717i	−0.425707	+	0.864112i
$514$		0			0
$515$	−10.1872	−	8.54805i	−0.448900	−	0.376672i
$516$		0			0
$517$	1.18579	+	6.72495i	0.0521510	+	0.295763i
$518$		0			0
$519$	15.1390	+	12.1470i	0.664528	+	0.533196i
$520$		0			0
$521$	−6.04248	−	3.48863i	−0.264726	−	0.152839i	0.361763	−	0.932270i	$-0.382175\pi$
$521$	−6.04248	−	3.48863i	−0.264726	−	0.152839i	−0.626488	+	0.779431i	$0.715508\pi$
$522$		0			0
$523$	29.9008	−	17.2632i	1.30747	−	0.754869i	0.325798	−	0.945440i	$-0.394367\pi$
$523$	29.9008	−	17.2632i	1.30747	−	0.754869i	0.981673	+	0.190571i	$0.0610338\pi$
$524$		0			0
$525$	−5.61605	−	1.90556i	−0.245104	−	0.0831656i
$526$		0			0
$527$	34.6242	−	29.0532i	1.50826	−	1.26558i
$528$		0			0
$529$	17.6504	−	6.42422i	0.767409	−	0.279314i
$530$		0			0
$531$	−27.7717	+	25.4616i	−1.20519	+	1.10494i
$532$		0			0
$533$	6.67639	+	1.17723i	0.289186	+	0.0509914i
$534$		0			0
$535$	2.04748	−	5.62541i	0.0885203	−	0.243208i
$536$		0			0
$537$	−33.3798	−	18.3071i	−1.44045	−	0.790008i
$538$		0			0
$539$	5.67128			0.244279
$540$		0			0
$541$	−7.84296			−0.337195			−0.168598	−	0.985685i	$-0.553924\pi$
$541$	−7.84296			−0.337195			−0.168598	+	0.985685i	$0.553924\pi$
$542$		0			0
$543$	0.722977	+	32.9339i	0.0310259	+	1.41333i
$544$		0			0
$545$	6.69851	−	18.4040i	0.286932	−	0.788340i
$546$		0			0
$547$	44.9004	+	7.91716i	1.91980	+	0.338513i	0.998708	−	0.0508207i	$-0.0161837\pi$
$547$	44.9004	+	7.91716i	1.91980	+	0.338513i	0.921097	+	0.389334i	$0.127295\pi$
$548$		0			0
$549$	25.0417	+	19.2047i	1.06875	+	0.819636i
$550$		0			0
$551$	3.23038	−	1.17576i	0.137619	−	0.0500892i
$552$		0			0
$553$	0.850233	−	0.713430i	0.0361556	−	0.0303381i
$554$		0			0
$555$	−3.92113	+	3.43965i	−0.166443	+	0.146005i
$556$		0			0
$557$	15.3982	−	8.89017i	0.652444	−	0.376689i	−0.136948	−	0.990578i	$-0.543729\pi$
$557$	15.3982	−	8.89017i	0.652444	−	0.376689i	0.789392	+	0.613890i	$0.210396\pi$
$558$		0			0
$559$	−0.158234	−	0.0913565i	−0.00669259	−	0.00386397i
$560$		0			0
$561$	1.25108	−	8.13553i	0.0528205	−	0.343483i
$562$		0			0
$563$	5.94955	+	33.7416i	0.250744	+	1.42204i	0.806766	+	0.590871i	$0.201216\pi$
$563$	5.94955	+	33.7416i	0.250744	+	1.42204i	−0.556022	+	0.831167i	$0.687673\pi$
$564$		0			0
$565$	6.18095	+	5.18643i	0.260034	+	0.218195i
$566$		0			0
$567$	−3.33686	−	7.14605i	−0.140135	−	0.300106i
$568$		0			0
$569$	7.97000	−	9.49828i	0.334120	−	0.398189i	−0.572660	−	0.819793i	$-0.694088\pi$
$569$	7.97000	−	9.49828i	0.334120	−	0.398189i	0.906780	+	0.421604i	$0.138533\pi$
$570$		0			0
$571$	−31.1551	+	5.49348i	−1.30380	+	0.229895i	−0.782056	−	0.623208i	$-0.785829\pi$
$571$	−31.1551	+	5.49348i	−1.30380	+	0.229895i	−0.521743	+	0.853103i	$0.674718\pi$
$572$		0			0
$573$	−26.3573	−	4.05322i	−1.10109	−	0.169326i
$574$		0			0
$575$	4.01182	−	6.94867i	0.167304	−	0.289780i
$576$		0			0
$577$	1.81116	+	3.13703i	0.0753997	+	0.130596i	0.901260	−	0.433279i	$-0.142643\pi$
$577$	1.81116	+	3.13703i	0.0753997	+	0.130596i	−0.825860	+	0.563875i	$0.809310\pi$
$578$		0			0
$579$	22.8925	+	26.0970i	0.951381	+	1.08455i
$580$		0			0
$581$	−6.85731	−	8.17223i	−0.284489	−	0.339041i
$582$		0			0
$583$	2.67326	+	7.34473i	0.110715	+	0.304188i
$584$		0			0
$585$	−2.68818	−	0.353182i	−0.111142	−	0.0146023i
$586$		0			0
$587$	4.78428	−	27.1330i	0.197468	−	1.11990i	−0.711391	−	0.702797i	$-0.751934\pi$
$587$	4.78428	−	27.1330i	0.197468	−	1.11990i	0.908859	−	0.417103i	$-0.136954\pi$
$588$		0			0
$589$	34.1499	+	12.4296i	1.40712	+	0.512151i
$590$		0			0
$591$	12.4169	−	0.272581i	0.510764	−	0.0112125i
$592$		0			0
$593$			10.7012i			0.439445i	0.975562	+	0.219723i	$0.0705152\pi$
$593$			10.7012i			0.439445i	−0.975562	+	0.219723i	$0.929485\pi$
$594$		0			0
$595$		−	4.78362i		−	0.196109i
$596$		0			0
$597$	14.5306	−	26.4941i	0.594697	−	1.08433i
$598$		0			0
$599$	−11.5378	−	4.19943i	−0.471423	−	0.171584i	0.0953740	−	0.995442i	$-0.469595\pi$
$599$	−11.5378	−	4.19943i	−0.471423	−	0.171584i	−0.566797	+	0.823858i	$0.691818\pi$
$600$		0			0
$601$	1.12791	−	6.39667i	0.0460082	−	0.260926i	−0.953124	−	0.302581i	$-0.902152\pi$
$601$	1.12791	−	6.39667i	0.0460082	−	0.260926i	0.999132	+	0.0416548i	$0.0132630\pi$
$602$		0			0
$603$	6.25636	−	1.38874i	0.254779	−	0.0565537i
$604$		0			0
$605$	3.63665	+	9.99161i	0.147851	+	0.406217i
$606$		0			0
$607$	25.3826	+	30.2499i	1.03025	+	1.22780i	0.973326	+	0.229425i	$0.0736846\pi$
$607$	25.3826	+	30.2499i	1.03025	+	1.22780i	0.0569233	+	0.998379i	$0.481871\pi$
$608$		0			0
$609$	−0.399285	+	1.17677i	−0.0161798	+	0.0476850i
$610$		0			0
$611$	−3.24388	−	5.61857i	−0.131233	−	0.227303i
$612$		0			0
$613$	0.172794	−	0.299289i	0.00697910	−	0.0120882i	−0.862515	−	0.506032i	$-0.831112\pi$
$613$	0.172794	−	0.299289i	0.00697910	−	0.0120882i	0.869494	+	0.493944i	$0.164445\pi$
$614$		0			0
$615$	−8.88473	+	11.0731i	−0.358267	+	0.446512i
$616$		0			0
$617$	11.0241	−	1.94385i	0.443814	−	0.0782564i	0.0527246	−	0.998609i	$-0.483209\pi$
$617$	11.0241	−	1.94385i	0.443814	−	0.0782564i	0.391089	+	0.920353i	$0.372098\pi$
$618$		0			0
$619$	6.45918	−	7.69775i	0.259616	−	0.309399i	−0.620453	−	0.784243i	$-0.713051\pi$
$619$	6.45918	−	7.69775i	0.259616	−	0.309399i	0.880070	+	0.474845i	$0.157496\pi$
$620$		0			0
$621$	10.3635	−	2.54028i	0.415871	−	0.101938i
$622$		0			0
$623$	3.31546	+	2.78200i	0.132831	+	0.111458i
$624$		0			0
$625$	1.70238	+	9.65469i	0.0680953	+	0.386188i
$626$		0			0
$627$	6.16788	−	2.39950i	0.246322	−	0.0958267i
$628$		0			0
$629$	13.0290	+	7.52230i	0.519500	+	0.299934i
$630$		0			0
$631$	30.2407	−	17.4595i	1.20386	−	0.695050i	0.242451	−	0.970164i	$-0.422049\pi$
$631$	30.2407	−	17.4595i	1.20386	−	0.695050i	0.961412	+	0.275113i	$0.0887154\pi$
$632$		0			0
$633$	−0.934459	−	4.69460i	−0.0371414	−	0.186594i
$634$		0			0
$635$	10.4584	−	8.77564i	0.415029	−	0.348251i
$636$		0			0
$637$	−5.06319	+	1.84285i	−0.200611	+	0.0730164i
$638$		0			0
$639$	−10.5983	+	0.465539i	−0.419261	+	0.0184164i
$640$		0			0
$641$	36.8418	+	6.49620i	1.45516	+	0.256585i	0.844606	−	0.535388i	$-0.179834\pi$
$641$	36.8418	+	6.49620i	1.45516	+	0.256585i	0.610557	+	0.791972i	$0.290946\pi$
$642$		0			0
$643$	−2.88367	+	7.92281i	−0.113721	+	0.312445i	−0.983476	−	0.181038i	$-0.942054\pi$
$643$	−2.88367	+	7.92281i	−0.113721	+	0.312445i	0.869755	+	0.493483i	$0.164277\pi$
$644$		0			0
$645$	0.327085	−	0.198539i	0.0128790	−	0.00781747i
$646$		0			0
$647$	−34.7421			−1.36585			−0.682927	−	0.730487i	$-0.739293\pi$
$647$	−34.7421			−1.36585			−0.682927	+	0.730487i	$0.739293\pi$
$648$		0			0
$649$	11.4289			0.448622
$650$		0			0
$651$	−11.2299	+	6.81649i	−0.440133	+	0.267159i
$652$		0			0
$653$	12.1343	−	33.3388i	0.474853	−	1.30465i	−0.438958	−	0.898508i	$-0.644652\pi$
$653$	12.1343	−	33.3388i	0.474853	−	1.30465i	0.913811	−	0.406140i	$-0.133126\pi$
$654$		0			0
$655$	17.6370	+	3.10989i	0.689136	+	0.121513i
$656$		0			0
$657$	2.11581	+	3.31922i	0.0825458	+	0.129495i
$658$		0			0
$659$	−23.3441	+	8.49655i	−0.909356	+	0.330978i	−0.753996	−	0.656879i	$-0.771876\pi$
$659$	−23.3441	+	8.49655i	−0.909356	+	0.330978i	−0.155360	+	0.987858i	$0.549654\pi$
$660$		0			0
$661$	−20.4085	+	17.1248i	−0.793800	+	0.666078i	−0.946683	−	0.322167i	$-0.895589\pi$
$661$	−20.4085	+	17.1248i	−0.793800	+	0.666078i	0.152883	+	0.988244i	$0.451144\pi$
$662$		0			0
$663$	1.52666	+	7.66975i	0.0592907	+	0.297868i
$664$		0			0
$665$	3.33092	−	1.92311i	0.129168	−	0.0745750i
$666$		0			0
$667$	−1.45600	−	0.840621i	−0.0563765	−	0.0325490i
$668$		0			0
$669$	39.7285	−	15.4556i	1.53599	−	0.597549i
$670$		0			0
$671$	−1.66229	−	9.42729i	−0.0641719	−	0.363937i
$672$		0			0
$673$	−20.2278	−	16.9732i	−0.779726	−	0.654267i	0.163454	−	0.986551i	$-0.447736\pi$
$673$	−20.2278	−	16.9732i	−0.779726	−	0.654267i	−0.943180	+	0.332284i	$0.892181\pi$
$674$		0			0
$675$	−11.9989	+	16.3780i	−0.461836	+	0.630389i
$676$		0			0
$677$	19.7326	−	23.5164i	0.758385	−	0.903808i	−0.239360	−	0.970931i	$-0.576938\pi$
$677$	19.7326	−	23.5164i	0.758385	−	0.903808i	0.997745	+	0.0671230i	$0.0213820\pi$
$678$		0			0
$679$	−12.4933	+	2.20291i	−0.479449	+	0.0845399i
$680$		0			0
$681$	−4.79013	+	5.97000i	−0.183558	+	0.228771i
$682$		0			0
$683$	−3.64903	+	6.32031i	−0.139626	+	0.241840i	−0.927355	−	0.374182i	$-0.877923\pi$
$683$	−3.64903	+	6.32031i	−0.139626	+	0.241840i	0.787729	+	0.616022i	$0.211257\pi$
$684$		0			0
$685$	3.46349	+	5.99894i	0.132333	+	0.229208i
$686$		0			0
$687$	−9.99876	+	29.4682i	−0.381477	+	1.12428i
$688$		0			0
$689$	−4.77326	−	5.68855i	−0.181847	−	0.216716i
$690$		0			0
$691$	7.71959	+	21.2094i	0.293667	+	0.806843i	0.995523	+	0.0945240i	$0.0301329\pi$
$691$	7.71959	+	21.2094i	0.293667	+	0.806843i	−0.701856	+	0.712319i	$0.747645\pi$
$692$		0			0
$693$	−0.718788	+	2.28181i	−0.0273045	+	0.0866787i
$694$		0			0
$695$	−0.986159	+	5.59279i	−0.0374072	+	0.212147i
$696$		0			0
$697$	38.4791	+	14.0052i	1.45750	+	0.530486i
$698$		0			0
$699$	−8.32222	+	15.1742i	−0.314775	+	0.573940i
$700$		0			0
$701$			17.4254i			0.658149i	0.944304	+	0.329075i	$0.106737\pi$
$701$			17.4254i			0.658149i	−0.944304	+	0.329075i	$0.893263\pi$
$702$		0			0
$703$			12.0965i			0.456226i
$704$		0			0
$705$	13.5830	−	0.298178i	0.511564	−	0.0112300i
$706$		0			0
$707$	−14.2647	−	5.19194i	−0.536481	−	0.195263i
$708$		0			0
$709$	7.38273	−	41.8695i	0.277264	−	1.57244i	−0.454413	−	0.890791i	$-0.650151\pi$
$709$	7.38273	−	41.8695i	0.277264	−	1.57244i	0.731677	−	0.681652i	$-0.238738\pi$
$710$		0			0
$711$	−1.45501	−	3.51009i	−0.0545673	−	0.131639i
$712$		0			0
$713$	−6.07880	−	16.7014i	−0.227653	−	0.625471i
$714$		0			0
$715$	0.528649	+	0.630020i	0.0197704	+	0.0235614i
$716$		0			0
$717$	−30.4753	−	34.7411i	−1.13812	−	1.29743i
$718$		0			0
$719$	−15.9720	−	27.6643i	−0.595655	−	1.03170i	−0.993454	−	0.114232i	$-0.963559\pi$
$719$	−15.9720	−	27.6643i	−0.595655	−	1.03170i	0.397799	−	0.917472i	$-0.369774\pi$
$720$		0			0
$721$	5.57412	−	9.65466i	0.207591	−	0.359558i
$722$		0			0
$723$	11.1998	+	1.72230i	0.416526	+	0.0640531i
$724$		0			0
$725$	3.15041	−	0.555501i	0.117003	−	0.0206308i
$726$		0			0
$727$	21.2524	−	25.3276i	0.788207	−	0.939348i	−0.211066	−	0.977472i	$-0.567694\pi$
$727$	21.2524	−	25.3276i	0.788207	−	0.939348i	0.999273	+	0.0381237i	$0.0121381\pi$
$728$		0			0
$729$	−26.7662	+	3.54544i	−0.991341	+	0.131313i
$730$		0			0
$731$	−0.845420	−	0.709391i	−0.0312690	−	0.0262378i
$732$		0			0
$733$	7.27308	+	41.2477i	0.268637	+	1.52352i	0.758473	+	0.651704i	$0.225946\pi$
$733$	7.27308	+	41.2477i	0.268637	+	1.52352i	−0.489836	+	0.871815i	$0.662943\pi$
$734$		0			0
$735$	1.71501	−	11.1524i	0.0632589	−	0.411362i
$736$		0			0
$737$	−1.68353	−	0.971989i	−0.0620138	−	0.0358037i
$738$		0			0
$739$	−18.0221	+	10.4051i	−0.662953	+	0.382756i	−0.793401	−	0.608699i	$-0.791692\pi$
$739$	−18.0221	+	10.4051i	−0.662953	+	0.382756i	0.130448	+	0.991455i	$0.458358\pi$
$740$		0			0
$741$	−4.72684	+	4.14644i	−0.173645	+	0.152323i
$742$		0			0
$743$	34.8189	−	29.2165i	1.27738	−	1.07185i	0.283783	−	0.958888i	$-0.408410\pi$
$743$	34.8189	−	29.2165i	1.27738	−	1.07185i	0.993599	−	0.112963i	$-0.0360341\pi$
$744$		0			0
$745$	14.6301	−	5.32491i	0.536004	−	0.195090i
$746$		0			0
$747$	−33.7381	+	13.9852i	−1.23441	+	0.511693i
$748$		0			0
$749$	4.94227	+	0.871455i	0.180587	+	0.0318423i
$750$		0			0
$751$	8.29032	−	22.7775i	0.302518	−	0.831162i	−0.691543	−	0.722336i	$-0.743069\pi$
$751$	8.29032	−	22.7775i	0.302518	−	0.831162i	0.994061	−	0.108826i	$-0.0347091\pi$
$752$		0			0
$753$	0.0732715	+	3.33775i	0.00267016	+	0.121634i
$754$		0			0
$755$	−9.01480			−0.328082
$756$		0			0
$757$	−52.0732			−1.89263			−0.946317	−	0.323240i	$-0.895228\pi$
$757$	−52.0732			−1.89263			−0.946317	+	0.323240i	$0.895228\pi$
$758$		0			0
$759$	−2.83790	−	1.55644i	−0.103009	−	0.0564950i
$760$		0			0
$761$	15.6086	−	42.8843i	0.565811	−	1.55455i	−0.245170	−	0.969480i	$-0.578844\pi$
$761$	15.6086	−	42.8843i	0.565811	−	1.55455i	0.810981	−	0.585073i	$-0.198934\pi$
$762$		0			0
$763$	16.1690	+	2.85104i	0.585359	+	0.103215i
$764$		0			0
$765$	−15.6199	−	4.92040i	−0.564739	−	0.177897i
$766$		0			0
$767$	−10.2034	+	3.71374i	−0.368425	+	0.134096i
$768$		0			0
$769$	9.50115	−	7.97241i	0.342620	−	0.287493i	−0.455198	−	0.890390i	$-0.650432\pi$
$769$	9.50115	−	7.97241i	0.342620	−	0.287493i	0.797819	+	0.602897i	$0.205987\pi$
$770$		0			0
$771$	−50.1721	−	17.0237i	−1.80691	−	0.613095i
$772$		0			0
$773$	−40.5127	+	23.3900i	−1.45714	+	0.841280i	−0.998870	−	0.0475339i	$-0.984864\pi$
$773$	−40.5127	+	23.3900i	−1.45714	+	0.841280i	−0.458269	+	0.888813i	$0.651530\pi$
$774$		0			0
$775$	29.2874	+	16.9091i	1.05204	+	0.607393i
$776$		0			0
$777$	−3.41051	−	2.73648i	−0.122351	−	0.0981707i
$778$		0			0
$779$	5.71724	+	32.4241i	0.204842	+	1.16171i
$780$		0			0
$781$	2.46509	+	2.06846i	0.0882080	+	0.0740153i
$782$		0			0
$783$	3.43178	+	2.51419i	0.122642	+	0.0898500i
$784$		0			0
$785$	−4.85095	+	5.78114i	−0.173138	+	0.206338i
$786$		0			0
$787$	19.7690	−	3.48581i	0.704690	−	0.124256i	0.190191	−	0.981747i	$-0.439089\pi$
$787$	19.7690	−	3.48581i	0.704690	−	0.124256i	0.514499	+	0.857491i	$0.327978\pi$
$788$		0			0
$789$	−8.16658	−	20.9921i	−0.290738	−	0.747339i
$790$		0			0
$791$	−3.38203	+	5.85785i	−0.120251	+	0.208281i
$792$		0			0
$793$	4.54740	+	7.87632i	0.161483	+	0.279696i
$794$		0			0
$795$	15.2516	−	3.03582i	0.540917	−	0.107669i
$796$		0			0
$797$	7.88321	+	9.39484i	0.279238	+	0.332782i	0.887374	−	0.461050i	$-0.152527\pi$
$797$	7.88321	+	9.39484i	0.279238	+	0.332782i	−0.608137	+	0.793832i	$0.708083\pi$
$798$		0			0
$799$	−13.4028	−	36.8239i	−0.474157	−	1.30274i
$800$		0			0
$801$	12.4943	−	7.96439i	0.441464	−	0.281408i
$802$		0			0
$803$	0.207337	−	1.17587i	0.00731677	−	0.0414954i
$804$		0			0
$805$	−1.76759	−	0.643351i	−0.0622994	−	0.0226751i
$806$		0			0
$807$	11.2897	+	18.5992i	0.397415	+	0.654724i
$808$		0			0
$809$		−	8.67342i		−	0.304941i	−0.988308	−	0.152471i	$-0.951277\pi$
$809$		−	8.67342i		−	0.304941i	0.988308	−	0.152471i	$-0.0487230\pi$
$810$		0			0
$811$		−	47.3956i		−	1.66428i	−0.554562	−	0.832142i	$-0.687114\pi$
$811$		−	47.3956i		−	1.66428i	0.554562	−	0.832142i	$-0.312886\pi$
$812$		0			0
$813$	−19.8196	−	32.6519i	−0.695103	−	1.14515i
$814$		0			0
$815$	2.25999	+	0.822570i	0.0791641	+	0.0288134i
$816$		0			0
$817$	0.154087	−	0.873871i	0.00539082	−	0.0305729i
$818$		0			0
$819$	−0.0997431	−	2.27071i	−0.00348531	−	0.0793451i
$820$		0			0
$821$	16.6304	+	45.6917i	0.580405	+	1.59465i	0.787490	+	0.616327i	$0.211380\pi$
$821$	16.6304	+	45.6917i	0.580405	+	1.59465i	−0.207085	+	0.978323i	$0.566398\pi$
$822$		0			0
$823$	2.91567	+	3.47476i	0.101634	+	0.121122i	0.814464	−	0.580214i	$-0.197031\pi$
$823$	2.91567	+	3.47476i	0.101634	+	0.121122i	−0.712830	+	0.701337i	$0.752587\pi$
$824$		0			0
$825$	6.04016	−	1.20229i	0.210291	−	0.0418585i
$826$		0			0
$827$	−11.8188	−	20.4707i	−0.410979	−	0.711837i	0.584018	−	0.811741i	$-0.301480\pi$
$827$	−11.8188	−	20.4707i	−0.410979	−	0.711837i	−0.994997	+	0.0999041i	$0.968146\pi$
$828$		0			0
$829$	−16.9769	+	29.4048i	−0.589631	+	1.02127i	0.404650	+	0.914472i	$0.367394\pi$
$829$	−16.9769	+	29.4048i	−0.589631	+	1.02127i	−0.994281	+	0.106799i	$0.965940\pi$
$830$		0			0
$831$	1.96225	+	5.04395i	0.0680698	+	0.174973i
$832$		0			0
$833$	−32.0508	+	5.65142i	−1.11049	+	0.195810i
$834$		0			0
$835$	−11.9392	+	14.2286i	−0.413173	+	0.492401i
$836$		0			0
$837$	10.7068	+	43.6802i	0.370083	+	1.50981i
$838$		0			0
$839$	28.1200	+	23.5955i	0.970809	+	0.814606i	0.982678	−	0.185324i	$-0.0593334\pi$
$839$	28.1200	+	23.5955i	0.970809	+	0.814606i	−0.0118681	+	0.999930i	$0.503778\pi$
$840$		0			0
$841$	4.91940	+	27.8993i	0.169634	+	0.962045i
$842$		0			0
$843$	8.26467	+	6.63130i	0.284650	+	0.228394i
$844$		0			0
$845$	11.0918	+	6.40388i	0.381571	+	0.220300i
$846$		0			0
$847$	−7.71946	+	4.45683i	−0.265244	+	0.153138i
$848$		0			0
$849$	23.6433	+	8.02235i	0.811437	+	0.275326i
$850$		0			0
$851$	4.53183	−	3.80266i	0.155349	−	0.130354i
$852$		0			0
$853$	−6.93434	+	2.52389i	−0.237427	+	0.0864164i	−0.457993	−	0.888956i	$-0.651432\pi$
$853$	−6.93434	+	2.52389i	−0.237427	+	0.0864164i	0.220566	+	0.975372i	$0.429209\pi$
$854$		0			0
$855$	−2.85335	−	12.8545i	−0.0975825	−	0.439616i
$856$		0			0
$857$	23.7926	+	4.19528i	0.812741	+	0.143308i	0.564546	−	0.825402i	$-0.309051\pi$
$857$	23.7926	+	4.19528i	0.812741	+	0.143308i	0.248195	+	0.968710i	$0.420163\pi$
$858$		0			0
$859$	−10.6165	+	29.1686i	−0.362231	+	0.995220i	0.616009	+	0.787739i	$0.288749\pi$
$859$	−10.6165	+	29.1686i	−0.362231	+	0.995220i	−0.978239	+	0.207481i	$0.933474\pi$
$860$		0			0
$861$	−10.4351	−	5.72310i	−0.355627	−	0.195043i
$862$		0			0
$863$	−0.703740			−0.0239556			−0.0119778	−	0.999928i	$-0.503813\pi$
$863$	−0.703740			−0.0239556			−0.0119778	+	0.999928i	$0.503813\pi$
$864$		0			0
$865$	−11.7141			−0.398291
$866$		0			0
$867$	0.390450	+	17.7862i	0.0132604	+	0.604053i
$868$		0			0
$869$	−0.394210	+	1.08308i	−0.0133727	+	0.0367411i
$870$		0			0
$871$	1.81886	+	0.320715i	0.0616299	+	0.0108670i
$872$		0			0
$873$	−5.65740	+	43.0602i	−0.191474	+	1.45737i
$874$		0			0
$875$	7.66718	−	2.79063i	0.259198	−	0.0943404i
$876$		0			0
$877$	−1.09474	+	0.918593i	−0.0369666	+	0.0310187i	−0.661084	−	0.750312i	$-0.729903\pi$
$877$	−1.09474	+	0.918593i	−0.0369666	+	0.0310187i	0.624117	+	0.781331i	$0.285459\pi$
$878$		0			0
$879$	38.0375	−	33.3669i	1.28297	−	1.12544i
$880$		0			0
$881$	−45.8116	+	26.4494i	−1.54343	+	0.891102i	−0.544815	+	0.838556i	$0.683400\pi$
$881$	−45.8116	+	26.4494i	−1.54343	+	0.891102i	−0.998619	+	0.0525451i	$0.983267\pi$
$882$		0			0
$883$	−26.0089	−	15.0162i	−0.875268	−	0.505336i	−0.00617240	−	0.999981i	$-0.501965\pi$
$883$	−26.0089	−	15.0162i	−0.875268	−	0.505336i	−0.869095	+	0.494645i	$0.835298\pi$
$884$		0			0
$885$	3.45611	−	22.4745i	0.116176	−	0.755471i
$886$		0			0
$887$	−8.86313	−	50.2653i	−0.297595	−	1.68774i	−0.656465	−	0.754356i	$-0.727949\pi$
$887$	−8.86313	−	50.2653i	−0.297595	−	1.68774i	0.358870	−	0.933387i	$-0.383162\pi$
$888$		0			0
$889$	8.76743	+	7.35674i	0.294050	+	0.246737i
$890$		0			0
$891$	6.71143	+	4.69411i	0.224841	+	0.157258i
$892$		0			0
$893$	20.2530	−	24.1365i	0.677740	−	0.807699i
$894$		0			0
$895$	22.6270	−	3.98976i	0.756338	−	0.133363i
$896$		0			0
$897$	3.03937	+	0.467392i	0.101481	+	0.0156058i
$898$		0			0
$899$	3.54307	−	6.13678i	0.118168	−	0.204673i
$900$		0			0
$901$	−22.4267	−	38.8443i	−0.747143	−	1.29409i
$902$		0			0
$903$	0.211524	+	0.241132i	0.00703907	+	0.00802438i
$904$		0			0
$905$	−12.7792	−	15.2296i	−0.424794	−	0.506250i
$906$		0			0
$907$	17.1302	+	47.0648i	0.568798	+	1.56276i	0.806383	+	0.591393i	$0.201422\pi$
$907$	17.1302	+	47.0648i	0.568798	+	1.56276i	−0.237585	+	0.971367i	$0.576356\pi$
$908$		0			0
$909$	−31.6258	+	41.2382i	−1.04896	+	1.36778i
$910$		0			0
$911$	−2.81605	+	15.9706i	−0.0932998	+	0.529130i	0.901955	+	0.431829i	$0.142132\pi$
$911$	−2.81605	+	15.9706i	−0.0932998	+	0.529130i	−0.995255	+	0.0973001i	$0.968979\pi$
$912$		0			0
$913$	10.4103	+	3.78905i	0.344532	+	0.125399i
$914$		0			0
$915$	−19.0411	+	0.417998i	−0.629480	+	0.0138186i
$916$		0			0
$917$			15.0135i			0.495788i
$918$		0			0
$919$		−	9.97650i		−	0.329094i	−0.986369	−	0.164547i	$-0.947384\pi$
$919$		−	9.97650i		−	0.329094i	0.986369	−	0.164547i	$-0.0526163\pi$
$920$		0			0
$921$	−5.10242	+	9.30341i	−0.168131	+	0.306558i
$922$		0			0
$923$	−2.87291	−	1.04566i	−0.0945631	−	0.0344182i
$924$		0			0
$925$	−1.95468	+	11.0855i	−0.0642694	+	0.364490i
$926$		0			0
$927$	−25.7918	−	28.1318i	−0.847113	−	0.923971i
$928$		0			0
$929$	−8.44030	−	23.1895i	−0.276917	−	0.760824i	−0.997708	−	0.0676708i	$-0.978443\pi$
$929$	−8.44030	−	23.1895i	−0.276917	−	0.760824i	0.720791	−	0.693153i	$-0.243779\pi$
$930$		0			0
$931$	−16.8202	−	20.0456i	−0.551261	−	0.656967i
$932$		0			0
$933$	−14.9288	+	43.9981i	−0.488748	+	1.44043i
$934$		0			0
$935$	2.48381	+	4.30209i	0.0812294	+	0.140693i
$936$		0			0
$937$	−19.9913	+	34.6259i	−0.653087	+	1.13118i	0.329282	+	0.944231i	$0.393193\pi$
$937$	−19.9913	+	34.6259i	−0.653087	+	1.13118i	−0.982370	+	0.186949i	$0.940140\pi$
$938$		0			0
$939$	9.59422	−	11.9574i	0.313096	−	0.390215i
$940$		0			0
$941$	−22.3585	+	3.94241i	−0.728867	+	0.128519i	−0.525754	−	0.850636i	$-0.676217\pi$
$941$	−22.3585	+	3.94241i	−0.728867	+	0.128519i	−0.203113	+	0.979155i	$0.565106\pi$
$942$		0			0
$943$	10.3501	−	12.3348i	0.337047	−	0.401677i
$944$		0			0
$945$	4.26973	+	2.10349i	0.138894	+	0.0684267i
$946$		0			0
$947$	−20.1568	−	16.9136i	−0.655010	−	0.549618i	0.253577	−	0.967315i	$-0.418393\pi$
$947$	−20.1568	−	16.9136i	−0.655010	−	0.549618i	−0.908586	+	0.417697i	$0.862837\pi$
$948$		0			0
$949$	0.196985	+	1.11716i	0.00639442	+	0.0362646i
$950$		0			0
$951$	26.6413	−	10.3643i	0.863905	−	0.336086i
$952$		0			0
$953$	−26.6869	−	15.4077i	−0.864473	−	0.499104i	0.00103472	−	0.999999i	$-0.499671\pi$
$953$	−26.6869	−	15.4077i	−0.864473	−	0.499104i	−0.865508	+	0.500896i	$0.833004\pi$
$954$		0			0
$955$	13.9378	−	8.04701i	0.451018	−	0.260395i
$956$		0			0
$957$	−0.251924	−	1.26563i	−0.00814354	−	0.0409121i
$958$		0			0
$959$	−4.44841	+	3.73266i	−0.143647	+	0.120534i
$960$		0			0
$961$	41.2629	−	15.0185i	1.33106	−	0.484466i
$962$		0			0
$963$	7.92914	−	15.2416i	0.255513	−	0.491153i
$964$		0			0
$965$	−20.6326	−	3.63809i	−0.664188	−	0.117114i
$966$		0			0
$967$	−12.2396	+	33.6280i	−0.393598	+	1.08140i	0.571748	+	0.820429i	$0.306266\pi$
$967$	−12.2396	+	33.6280i	−0.393598	+	1.08140i	−0.965346	+	0.260973i	$0.915957\pi$
$968$		0			0
$969$	−32.4662	+	19.7069i	−1.04296	+	0.633075i
$970$		0			0
$971$	−20.7054			−0.664469			−0.332234	−	0.943197i	$-0.607803\pi$
$971$	−20.7054			−0.664469			−0.332234	+	0.943197i	$0.607803\pi$
$972$		0			0
$973$	−4.76084			−0.152625
$974$		0			0
$975$	−5.00184	+	3.03610i	−0.160187	+	0.0972329i
$976$		0			0
$977$	1.72029	−	4.72646i	0.0550369	−	0.151213i	−0.909128	−	0.416518i	$-0.863250\pi$
$977$	1.72029	−	4.72646i	0.0550369	−	0.151213i	0.964165	+	0.265305i	$0.0854726\pi$
$978$		0			0
$979$	−4.42622	−	0.780462i	−0.141463	−	0.0249437i
$980$		0			0
$981$	25.9408	−	49.8641i	0.828227	−	1.59204i
$982$		0			0
$983$	15.6136	−	5.68289i	0.497997	−	0.181256i	−0.0807960	−	0.996731i	$-0.525746\pi$
$983$	15.6136	−	5.68289i	0.497997	−	0.181256i	0.578793	+	0.815475i	$0.303524\pi$
$984$		0			0
$985$	−5.74196	+	4.81808i	−0.182954	+	0.153517i
$986$		0			0
$987$	2.22346	+	11.1704i	0.0707736	+	0.355557i
$988$		0			0
$989$	−0.375828	+	0.216984i	−0.0119506	+	0.00689969i
$990$		0			0
$991$	−13.4933	−	7.79036i	−0.428629	−	0.247469i	0.270134	−	0.962823i	$-0.412932\pi$
$991$	−13.4933	−	7.79036i	−0.428629	−	0.247469i	−0.698762	+	0.715354i	$0.746265\pi$
$992$		0			0
$993$	−3.12065	+	1.21403i	−0.0990308	+	0.0385261i
$994$		0			0
$995$	3.16673	+	17.9594i	0.100392	+	0.569351i
$996$		0			0
$997$	−36.2831	−	30.4451i	−1.14910	−	0.964207i	−0.149399	−	0.988777i	$-0.547734\pi$
$997$	−36.2831	−	30.4451i	−1.14910	−	0.964207i	−0.999698	+	0.0245702i	$0.992178\pi$
$998$		0			0
$999$	−12.4434	+	8.32158i	−0.393693	+	0.263283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.c.335.1	yes	36
4.3	odd	2		432.2.be.b.335.6	✓	36
27.5	odd	18		432.2.be.b.383.6	yes	36
108.59	even	18	inner	432.2.be.c.383.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.335.6	✓	36	4.3	odd	2
432.2.be.b.383.6	yes	36	27.5	odd	18
432.2.be.c.335.1	yes	36	1.1	even	1	trivial
432.2.be.c.383.1	yes	36	108.59	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.48063 + 0.898737i) q^{3} +(0.357520 - 0.982277i) q^{5} +(0.862991 + 0.152169i) q^{7} +(1.38454 - 2.66140i) q^{9} +O(q^{10})\)	\(q+(-1.48063 + 0.898737i) q^{3} +(0.357520 - 0.982277i) q^{5} +(0.862991 + 0.152169i) q^{7} +(1.38454 - 2.66140i) q^{9} +(-0.855132 + 0.311243i) q^{11} +(0.662306 - 0.555741i) q^{13} +(0.353454 + 1.77571i) q^{15} +(4.52256 - 2.61110i) q^{17} +(3.63632 + 2.09943i) q^{19} +(-1.41453 + 0.550297i) q^{21} +(-0.356585 - 2.02229i) q^{23} +(2.99317 + 2.51157i) q^{25} +(0.341901 + 5.18489i) q^{27} +(0.526265 - 0.627178i) q^{29} +(8.52362 - 1.50294i) q^{31} +(0.986410 - 1.22937i) q^{33} +(0.458008 - 0.793293i) q^{35} +(1.44045 + 2.49493i) q^{37} +(-0.481166 + 1.41809i) q^{39} +(5.04026 + 6.00675i) q^{41} +(-0.0722797 - 0.198587i) q^{43} +(-2.11923 - 2.31151i) q^{45} +(1.30305 - 7.38995i) q^{47} +(-5.85625 - 2.13150i) q^{49} +(-4.34955 + 7.93067i) q^{51} -8.58900i q^{53} +0.951252i q^{55} +(-7.27088 + 0.159613i) q^{57} +(-11.8016 - 4.29544i) q^{59} +(-1.82666 + 10.3595i) q^{61} +(1.59983 - 2.08608i) q^{63} +(-0.309104 - 0.849256i) q^{65} +(1.37313 + 1.63643i) q^{67} +(2.34548 + 2.67380i) q^{69} +(-1.76808 - 3.06241i) q^{71} +(-0.656039 + 1.13629i) q^{73} +(-6.68903 - 1.02863i) q^{75} +(-0.785333 + 0.138475i) q^{77} +(0.814135 - 0.970249i) q^{79} +(-5.16609 - 7.36964i) q^{81} +(-9.32579 - 7.82526i) q^{83} +(-0.947921 - 5.37593i) q^{85} +(-0.215536 + 1.40159i) q^{87} +(4.27725 + 2.46947i) q^{89} +(0.656130 - 0.378817i) q^{91} +(-11.2696 + 9.88581i) q^{93} +(3.36228 - 2.82128i) q^{95} +(-13.6037 + 4.95134i) q^{97} +(-0.355626 + 2.70678i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q + 3 * q^5 + 6 * q^9	\( 36 q + 3 q^{5} + 6 q^{9} + 18 q^{11} - 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} - 27 q^{31} + 27 q^{33} - 27 q^{35} + 45 q^{39} + 18 q^{41} + 27 q^{45} - 45 q^{47} + 63 q^{51} - 9 q^{57} - 54 q^{59} + 63 q^{63} - 57 q^{65} - 63 q^{69} - 36 q^{71} + 9 q^{73} + 45 q^{75} - 81 q^{77} - 54 q^{81} + 27 q^{83} - 36 q^{85} - 45 q^{87} - 63 q^{89} - 27 q^{91} - 63 q^{93} + 72 q^{95} - 99 q^{99}+O(q^{100}) \) 36 * q + 3 * q^5 + 6 * q^9 + 18 * q^11 - 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 - 27 * q^31 + 27 * q^33 - 27 * q^35 + 45 * q^39 + 18 * q^41 + 27 * q^45 - 45 * q^47 + 63 * q^51 - 9 * q^57 - 54 * q^59 + 63 * q^63 - 57 * q^65 - 63 * q^69 - 36 * q^71 + 9 * q^73 + 45 * q^75 - 81 * q^77 - 54 * q^81 + 27 * q^83 - 36 * q^85 - 45 * q^87 - 63 * q^89 - 27 * q^91 - 63 * q^93 + 72 * q^95 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more