LMFDB - Embedded newform 432.2.be.b.335.6

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			335.6
Character	$\chi$	$=$	432.335
Dual form			432.2.be.b.383.6

$q$-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	0.00816043	−	0.999967i	$-0.497402\pi$
$7$	−0.862991	−	0.152169i	−0.326180	−	0.0575143i	−0.334340	+	0.942452i	$0.608514\pi$
$8$		0			0
$9$	1.38454	−	2.66140i	0.461514	−	0.887133i
$10$		0			0
$11$	0.855132	−	0.311243i	0.257832	−	0.0938432i	−0.209870	−	0.977729i	$-0.567304\pi$
$11$	0.855132	−	0.311243i	0.257832	−	0.0938432i	0.467702	+	0.883886i	$0.345082\pi$
$12$		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	0.0210701	−	0.999778i	$-0.493293\pi$
$19$	−3.63632	−	2.09943i	−0.834228	−	0.481642i	−0.855298	+	0.518136i	$0.826626\pi$
$20$		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	$0.0131235\pi$
$23$	0.356585	+	2.02229i	0.0743531	+	0.421678i	−0.924797	+	0.380461i	$0.875765\pi$
$24$		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	−0.874702	−	0.484662i	$-0.838943\pi$
$31$	−8.52362	+	1.50294i	−1.53089	+	0.269937i	−0.656187	+	0.754599i	$0.727832\pi$
$32$		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	0.945082	−	0.326834i	$-0.105982\pi$
$43$	0.0722797	+	0.198587i	0.0110226	+	0.0302842i	−0.934059	+	0.357118i	$0.883759\pi$
$44$		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	$0.239893\pi$
$47$	−1.30305	+	7.38995i	−0.190069	+	1.07794i	−0.919268	+	0.393633i	$0.871218\pi$
$48$		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	0.965188	−	0.261556i	$-0.0842358\pi$
$59$	11.8016	+	4.29544i	1.53644	+	0.559218i	0.571252	+	0.820775i	$0.306458\pi$
$60$		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	0.675617	−	0.737253i	$-0.263877\pi$
$67$	−1.37313	−	1.63643i	−0.167755	−	0.199922i	−0.843372	+	0.537331i	$0.819433\pi$
$68$		0			0
$69$	2.34548	+	2.67380i	0.282363	+	0.321887i
$70$		0			0
$71$	1.76808	+	3.06241i	0.209833	+	0.363441i	0.951662	−	0.307148i	$-0.0993747\pi$
$71$	1.76808	+	3.06241i	0.209833	+	0.363441i	−0.741829	+	0.670589i	$0.766041\pi$
$72$		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	−0.809896	−	0.586573i	$-0.800477\pi$
$79$	−0.814135	+	0.970249i	−0.0915974	+	0.109161i	0.718299	+	0.695735i	$0.244921\pi$
$80$		0			0
$81$	−5.16609	−	7.36964i	−0.574010	−	0.818849i
$82$		0			0
$83$	9.32579	+	7.82526i	1.02364	+	0.858934i	0.990080	−	0.140503i	$-0.0448718\pi$
$83$	9.32579	+	7.82526i	1.02364	+	0.858934i	0.0335576	+	0.999437i	$0.489316\pi$
$84$		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	$0.326731\pi$
$103$	−4.35114	+	11.9547i	−0.428730	+	1.17793i	−0.946584	+	0.322458i	$0.895491\pi$
$104$		0			0
$105$	0.0348210	+	1.58620i	0.00339818	+	0.154798i
$106$		0			0
$107$	−5.72690			−0.553641			−0.276820	−	0.960922i	$-0.589281\pi$
$107$	−5.72690			−0.553641			−0.276820	+	0.960922i	$0.589281\pi$
$108$		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	−0.0943395	−	0.995540i	$-0.530074\pi$
$127$	−11.3108	−	6.53030i	−1.00367	−	0.579470i	−0.909333	+	0.416070i	$0.863407\pi$
$128$		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	$-0.786356\pi$
$131$	−2.97506	−	16.8724i	−0.259933	−	1.47415i	0.523154	−	0.852238i	$-0.324755\pi$
$132$		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	0.0579280	−	0.998321i	$-0.481551\pi$
$139$	5.35032	−	0.943406i	0.453808	−	0.0800187i	0.395880	+	0.918302i	$0.370439\pi$
$140$		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	$0.00301478\pi$
$151$	2.94957	+	8.10389i	0.240033	+	0.659485i	−0.759922	+	0.650014i	$0.774763\pi$
$152$		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	$-0.971280\pi$
$163$		−	2.30077i		−	0.180210i	0.995932	−	0.0901051i	$-0.0287203\pi$
$164$		0			0
$165$	−0.854926	−	1.40845i	−0.0665559	−	0.109648i
$166$		0			0
$167$	16.6973	+	6.07731i	1.29207	+	0.470277i	0.894407	−	0.447253i	$-0.147598\pi$
$167$	16.6973	+	6.07731i	1.29207	+	0.470277i	0.397667	+	0.917530i	$0.369820\pi$
$168$		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	$-0.859843\pi$
$179$	−10.9900	−	19.0352i	−0.821431	−	1.42276i	0.0831849	−	0.996534i	$-0.473491\pi$
$180$		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	0.107134	−	0.994245i	$-0.465833\pi$
$191$	−11.7943	−	9.89655i	−0.853402	−	0.716089i	−0.960536	+	0.278155i	$0.910277\pi$
$192$		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	0.142558	−	0.989787i	$-0.454467\pi$
$199$	15.1085	−	8.72292i	1.07102	−	0.618352i	0.928459	+	0.371435i	$0.121134\pi$
$200$		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	−0.902896	−	0.429859i	$-0.858563\pi$
$211$	0.945207	−	2.59694i	0.0650708	−	0.178780i	0.967967	+	0.251079i	$0.0807854\pi$
$212$		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	0.909918	−	0.414789i	$-0.136145\pi$
$223$	24.2380	+	4.27381i	1.62309	+	0.286195i	0.713177	+	0.700984i	$0.247256\pi$
$224$		0			0
$225$	10.8285	−	4.48865i	0.721898	−	0.299244i
$226$		0			0
$227$	−4.15263	+	1.51143i	−0.275620	+	0.100317i	−0.476132	−	0.879374i	$-0.657962\pi$
$227$	−4.15263	+	1.51143i	−0.275620	+	0.100317i	0.200512	+	0.979691i	$0.435739\pi$
$228$		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	$-0.724178\pi$
$239$	−4.63317	−	26.2760i	−0.299695	−	1.69965i	0.347787	−	0.937573i	$-0.386933\pi$
$240$		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	−0.894837	−	0.446392i	$-0.852709\pi$
$251$	−0.963757	+	1.66928i	−0.0608318	+	0.105364i	0.834006	+	0.551756i	$0.186042\pi$
$252$		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	$-0.813124\pi$
$263$	2.25823	−	12.8071i	0.139249	−	0.789718i	0.971807	−	0.235780i	$-0.0757644\pi$
$264$		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	$-0.766379\pi$
$271$		−	22.0527i		−	1.33961i	0.742539	−	0.669803i	$-0.233621\pi$
$272$		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	0.967570	−	0.252602i	$-0.0812864\pi$
$283$	9.26570	+	11.0424i	0.550789	+	0.656404i	−0.416781	+	0.909007i	$0.636842\pi$
$284$		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	−0.643697	−	0.765280i	$-0.722600\pi$
$307$	−5.30538	+	3.06306i	−0.302794	+	0.174818i	0.340903	+	0.940098i	$0.389267\pi$
$308$		0			0
$309$	4.30166	+	21.6110i	0.244713	+	1.22941i
$310$		0			0
$311$	−20.5489	+	17.2426i	−1.16522	+	0.977739i	−0.999964	−	0.00851113i	$-0.997291\pi$
$311$	−20.5489	+	17.2426i	−1.16522	+	0.977739i	−0.165260	+	0.986250i	$0.552846\pi$
$312$		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	0.121080	−	0.992643i	$-0.461364\pi$
$331$	−1.90388	−	0.335705i	−0.104646	−	0.0184520i	−0.225726	+	0.974191i	$0.572475\pi$
$332$		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	$-0.865980\pi$
$347$	−3.62921	−	20.5823i	−0.194826	−	1.10491i	0.717840	−	0.696208i	$-0.245131\pi$
$348$		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	$-0.547099\pi$
$359$	14.8329	−	25.6913i	0.782849	−	1.35593i	0.930276	−	0.366861i	$-0.119568\pi$
$360$		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	$0.0178099\pi$
$367$	5.16356	+	14.1868i	0.269536	+	0.740543i	−0.728899	+	0.684621i	$0.759968\pi$
$368$		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	$0.191087\pi$
$379$			21.9951i			1.12981i	−0.825155	+	0.564906i	$0.808913\pi$
$380$		0			0
$381$	−22.6162	+	0.496479i	−1.15866	+	0.0254354i
$382$		0			0
$383$	17.1381	+	6.23776i	0.875716	+	0.318735i	0.740480	−	0.672079i	$-0.234598\pi$
$383$	17.1381	+	6.23776i	0.875716	+	0.318735i	0.135236	+	0.990813i	$0.456821\pi$
$384$		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	−0.735979	−	0.677004i	$-0.763278\pi$
$419$	−4.03376	+	3.38472i	−0.197062	+	0.165355i	0.538917	+	0.842359i	$0.318834\pi$
$420$		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	$-0.372649\pi$
$431$	16.1724			0.778995			0.389498	+	0.921028i	$0.372649\pi$
$432$		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	0.450363	−	0.892845i	$-0.351295\pi$
$439$	11.9050	+	2.09917i	0.568195	+	0.100188i	0.117832	+	0.993034i	$0.462406\pi$
$440$		0			0
$441$	−13.7810	+	12.6347i	−0.656238	+	0.601651i
$442$		0			0
$443$	1.19218	−	0.433918i	0.0566422	−	0.0206161i	−0.313544	−	0.949574i	$-0.601516\pi$
$443$	1.19218	−	0.433918i	0.0566422	−	0.0206161i	0.370186	+	0.928958i	$0.379294\pi$
$444$		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	−0.657827	−	0.753169i	$-0.728524\pi$
$463$	−21.9130	+	3.86385i	−1.01838	+	0.179568i	−0.360556	+	0.932738i	$0.617413\pi$
$464$		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	$0.432361\pi$
$467$	−16.0152	+	27.7392i	−0.741097	+	1.28362i	−0.951996	+	0.306110i	$0.900972\pi$
$468$		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	$-0.741259\pi$
$479$	4.52904	−	25.6855i	0.206937	−	1.17360i	0.894362	−	0.447344i	$-0.147630\pi$
$480$		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	$-0.906227\pi$
$487$		−	12.8151i		−	0.580706i	0.956920	−	0.290353i	$-0.0937727\pi$
$488$		0			0
$489$	−2.06779	−	3.40659i	−0.0935086	−	0.154051i
$490$		0			0
$491$	32.9705	+	12.0003i	1.48794	+	0.541566i	0.952906	−	0.303266i	$-0.0980769\pi$
$491$	32.9705	+	12.0003i	1.48794	+	0.541566i	0.535033	+	0.844831i	$0.320299\pi$
$492$		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	0.682585	−	0.730806i	$-0.260856\pi$
$499$	−3.47692	−	4.14363i	−0.155648	−	0.185494i	−0.838233	+	0.545312i	$0.816411\pi$
$500$		0			0
$501$	30.1844	−	6.00821i	1.34854	−	0.268427i
$502$		0			0
$503$	8.89978	+	15.4149i	0.396822	+	0.687315i	0.993332	−	0.115290i	$-0.0367798\pi$
$503$	8.89978	+	15.4149i	0.396822	+	0.687315i	−0.596510	+	0.802606i	$0.703446\pi$
$504$		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	−0.981673	−	0.190571i	$-0.938966\pi$
$523$	−29.9008	+	17.2632i	−1.30747	+	0.754869i	−0.325798	+	0.945440i	$0.605633\pi$
$524$		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	−0.921097	−	0.389334i	$-0.872705\pi$
$547$	−44.9004	−	7.91716i	−1.91980	−	0.338513i	−0.998708	+	0.0508207i	$0.983816\pi$
$548$		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	$-0.798784\pi$
$563$	−5.94955	−	33.7416i	−0.250744	−	1.42204i	0.556022	−	0.831167i	$-0.312327\pi$
$564$		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	0.521743	−	0.853103i	$-0.325282\pi$
$571$	31.1551	−	5.49348i	1.30380	−	0.229895i	0.782056	+	0.623208i	$0.214171\pi$
$572$		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	$0.248066\pi$
$587$	−4.78428	+	27.1330i	−0.197468	+	1.11990i	−0.908859	+	0.417103i	$0.863046\pi$
$588$		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	0.566797	−	0.823858i	$-0.308182\pi$
$599$	11.5378	+	4.19943i	0.471423	+	0.171584i	−0.0953740	+	0.995442i	$0.530405\pi$
$600$		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	$-0.926315\pi$
$607$	−25.3826	−	30.2499i	−1.03025	−	1.22780i	−0.0569233	−	0.998379i	$-0.518129\pi$
$608$		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	−0.880070	−	0.474845i	$-0.842504\pi$
$619$	−6.45918	+	7.69775i	−0.259616	+	0.309399i	0.620453	+	0.784243i	$0.286949\pi$
$620$		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	−0.961412	−	0.275113i	$-0.911285\pi$
$631$	−30.2407	+	17.4595i	−1.20386	+	0.695050i	−0.242451	+	0.970164i	$0.577951\pi$
$632$		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	−0.869755	−	0.493483i	$-0.835723\pi$
$643$	2.88367	−	7.92281i	0.113721	−	0.312445i	0.983476	+	0.181038i	$0.0579457\pi$
$644$		0			0
$645$	0.327085	−	0.198539i	0.0128790	−	0.00781747i
$646$		0			0
$647$	34.7421			1.36585			0.682927	−	0.730487i	$-0.260707\pi$
$647$	34.7421			1.36585			0.682927	+	0.730487i	$0.260707\pi$
$648$		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	0.155360	−	0.987858i	$-0.450346\pi$
$659$	23.3441	−	8.49655i	0.909356	−	0.330978i	0.753996	+	0.656879i	$0.228124\pi$
$660$		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	−0.787729	−	0.616022i	$-0.788743\pi$
$683$	3.64903	−	6.32031i	0.139626	−	0.241840i	0.927355	+	0.374182i	$0.122077\pi$
$684$		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	$-0.969867\pi$
$691$	−7.71959	−	21.2094i	−0.293667	−	0.806843i	0.701856	−	0.712319i	$-0.252355\pi$
$692$		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	$0.0364407\pi$
$719$	15.9720	+	27.6643i	0.595655	+	1.03170i	−0.397799	+	0.917472i	$0.630226\pi$
$720$		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	−0.999273	−	0.0381237i	$-0.987862\pi$
$727$	−21.2524	+	25.3276i	−0.788207	+	0.939348i	0.211066	+	0.977472i	$0.432306\pi$
$728$		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	−0.130448	−	0.991455i	$-0.541642\pi$
$739$	18.0221	−	10.4051i	0.662953	−	0.382756i	0.793401	+	0.608699i	$0.208308\pi$
$740$		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	$0.591590\pi$
$743$	−34.8189	+	29.2165i	−1.27738	+	1.07185i	−0.993599	+	0.112963i	$0.963966\pi$
$744$		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	$0.256931\pi$
$751$	−8.29032	+	22.7775i	−0.302518	+	0.831162i	−0.994061	+	0.108826i	$0.965291\pi$
$752$		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	−0.514499	−	0.857491i	$-0.672022\pi$
$787$	−19.7690	+	3.48581i	−0.704690	+	0.124256i	−0.190191	+	0.981747i	$0.560911\pi$
$788$		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	$0.312886\pi$
$811$			47.3956i			1.66428i	−0.554562	+	0.832142i	$0.687114\pi$
$812$		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	0.712830	−	0.701337i	$-0.247413\pi$
$823$	−2.91567	−	3.47476i	−0.101634	−	0.121122i	−0.814464	+	0.580214i	$0.802969\pi$
$824$		0			0
$825$	6.04016	−	1.20229i	0.210291	−	0.0418585i
$826$		0			0
$827$	11.8188	+	20.4707i	0.410979	+	0.711837i	0.994997	−	0.0999041i	$-0.0318536\pi$
$827$	11.8188	+	20.4707i	0.410979	+	0.711837i	−0.584018	+	0.811741i	$0.698520\pi$
$828$		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	0.0118681	−	0.999930i	$-0.496222\pi$
$839$	−28.1200	−	23.5955i	−0.970809	−	0.814606i	−0.982678	+	0.185324i	$0.940667\pi$
$840$		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	$-0.711251\pi$
$859$	10.6165	−	29.1686i	0.362231	−	0.995220i	0.978239	−	0.207481i	$-0.0665265\pi$
$860$		0			0
$861$	−10.4351	−	5.72310i	−0.355627	−	0.195043i
$862$		0			0
$863$	0.703740			0.0239556			0.0119778	−	0.999928i	$-0.496187\pi$
$863$	0.703740			0.0239556			0.0119778	+	0.999928i	$0.496187\pi$
$864$		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	0.869095	−	0.494645i	$-0.164702\pi$
$883$	26.0089	+	15.0162i	0.875268	+	0.505336i	0.00617240	+	0.999981i	$0.498035\pi$
$884$		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	$0.272051\pi$
$887$	8.86313	+	50.2653i	0.297595	+	1.68774i	−0.358870	+	0.933387i	$0.616838\pi$
$888$		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	$-0.798578\pi$
$907$	−17.1302	−	47.0648i	−0.568798	−	1.56276i	0.237585	−	0.971367i	$-0.423644\pi$
$908$		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	$-0.857868\pi$
$911$	2.81605	−	15.9706i	0.0932998	−	0.529130i	0.995255	−	0.0973001i	$-0.0310207\pi$
$912$		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	$0.0526163\pi$
$919$			9.97650i			0.329094i	−0.986369	+	0.164547i	$0.947384\pi$
$920$		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	0.908586	−	0.417697i	$-0.137163\pi$
$947$	20.1568	+	16.9136i	0.655010	+	0.549618i	−0.253577	+	0.967315i	$0.581607\pi$
$948$		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	$-0.693734\pi$
$967$	12.2396	−	33.6280i	0.393598	−	1.08140i	0.965346	−	0.260973i	$-0.0840433\pi$
$968$		0			0
$969$	−32.4662	+	19.7069i	−1.04296	+	0.633075i
$970$		0			0
$971$	20.7054			0.664469			0.332234	−	0.943197i	$-0.392197\pi$
$971$	20.7054			0.664469			0.332234	+	0.943197i	$0.392197\pi$
$972$		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	−0.578793	−	0.815475i	$-0.696476\pi$
$983$	−15.6136	+	5.68289i	−0.497997	+	0.181256i	0.0807960	+	0.996731i	$0.474254\pi$
$984$		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	0.698762	−	0.715354i	$-0.253735\pi$
$991$	13.4933	+	7.79036i	0.428629	+	0.247469i	−0.270134	+	0.962823i	$0.587068\pi$
$992$		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.b.335.6	✓	36
4.3	odd	2		432.2.be.c.335.1	yes	36
27.5	odd	18		432.2.be.c.383.1	yes	36
108.59	even	18	inner	432.2.be.b.383.6	yes	36

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

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