LMFDB - Embedded newform 228.2.i.a.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(49,228)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("228.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.1
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	228.49
Dual form			228.2.i.a.121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{3} +(-1.22474 + 2.12132i) q^{5} -3.44949 q^{7} +(-0.500000 - 0.866025i) q^{9} -2.44949 q^{11} +(0.500000 + 0.866025i) q^{13} +(-1.22474 - 2.12132i) q^{15} +(-2.44949 + 4.24264i) q^{17} +(1.00000 - 4.24264i) q^{19} +(1.72474 - 2.98735i) q^{21} +(4.22474 + 7.31747i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +(2.44949 + 4.24264i) q^{29} -9.44949 q^{31} +(1.22474 - 2.12132i) q^{33} +(4.22474 - 7.31747i) q^{35} +8.79796 q^{37} -1.00000 q^{39} +(1.72474 - 2.98735i) q^{43} +2.44949 q^{45} +(-0.550510 - 0.953512i) q^{47} +4.89898 q^{49} +(-2.44949 - 4.24264i) q^{51} +(1.22474 + 2.12132i) q^{53} +(3.00000 - 5.19615i) q^{55} +(3.17423 + 2.98735i) q^{57} +(3.67423 - 6.36396i) q^{59} +(1.05051 + 1.81954i) q^{61} +(1.72474 + 2.98735i) q^{63} -2.44949 q^{65} +(2.27526 + 3.94086i) q^{67} -8.44949 q^{69} +(-3.00000 + 5.19615i) q^{71} +(5.94949 - 10.3048i) q^{73} +1.00000 q^{75} +8.44949 q^{77} +(-6.17423 + 10.6941i) q^{79} +(-0.500000 + 0.866025i) q^{81} -16.8990 q^{83} +(-6.00000 - 10.3923i) q^{85} -4.89898 q^{87} +(1.77526 + 3.07483i) q^{89} +(-1.72474 - 2.98735i) q^{91} +(4.72474 - 8.18350i) q^{93} +(7.77526 + 7.31747i) q^{95} +(-5.34847 + 9.26382i) q^{97} +(1.22474 + 2.12132i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 4 q^{7} - 2 q^{9} + 2 q^{13} + 4 q^{19} + 2 q^{21} + 12 q^{23} - 2 q^{25} + 4 q^{27} - 28 q^{31} + 12 q^{35} - 4 q^{37} - 4 q^{39} + 2 q^{43} - 12 q^{47} + 12 q^{55} - 2 q^{57} + 14 q^{61}+ \cdots + 8 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 - 4 * q^7 - 2 * q^9 + 2 * q^13 + 4 * q^19 + 2 * q^21 + 12 * q^23 - 2 * q^25 + 4 * q^27 - 28 * q^31 + 12 * q^35 - 4 * q^37 - 4 * q^39 + 2 * q^43 - 12 * q^47 + 12 * q^55 - 2 * q^57 + 14 * q^61 + 2 * q^63 + 14 * q^67 - 24 * q^69 - 12 * q^71 + 14 * q^73 + 4 * q^75 + 24 * q^77 - 10 * q^79 - 2 * q^81 - 48 * q^83 - 24 * q^85 + 12 * q^89 - 2 * q^91 + 14 * q^93 + 36 * q^95 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	−1.22474	+	2.12132i	−0.547723	+	0.948683i	0.450708	+	0.892672i	$0.351172\pi$
$5$	−1.22474	+	2.12132i	−0.547723	+	0.948683i	−0.998430	+	0.0560116i	$0.982162\pi$
$6$		0			0
$7$	−3.44949			−1.30378			−0.651892	−	0.758312i	$-0.726025\pi$
$7$	−3.44949			−1.30378			−0.651892	+	0.758312i	$0.726025\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−2.44949			−0.738549			−0.369274	−	0.929320i	$-0.620394\pi$
$11$	−2.44949			−0.738549			−0.369274	+	0.929320i	$0.620394\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$		0			0
$15$	−1.22474	−	2.12132i	−0.316228	−	0.547723i
$16$		0			0
$17$	−2.44949	+	4.24264i	−0.594089	+	1.02899i	0.399586	+	0.916696i	$0.369154\pi$
$17$	−2.44949	+	4.24264i	−0.594089	+	1.02899i	−0.993675	+	0.112296i	$0.964180\pi$
$18$		0			0
$19$	1.00000	−	4.24264i	0.229416	−	0.973329i
$19$	1.00000	−	4.24264i	0.229416	−	0.973329i
$20$		0			0
$21$	1.72474	−	2.98735i	0.376370	−	0.651892i
$22$		0			0
$23$	4.22474	+	7.31747i	0.880920	+	1.52580i	0.850319	+	0.526267i	$0.176409\pi$
$23$	4.22474	+	7.31747i	0.880920	+	1.52580i	0.0306007	+	0.999532i	$0.490258\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	2.44949	+	4.24264i	0.454859	+	0.787839i	0.998680	−	0.0513625i	$-0.0163564\pi$
$29$	2.44949	+	4.24264i	0.454859	+	0.787839i	−0.543821	+	0.839201i	$0.683023\pi$
$30$		0			0
$31$	−9.44949			−1.69718			−0.848589	−	0.529052i	$-0.822548\pi$
$31$	−9.44949			−1.69718			−0.848589	+	0.529052i	$0.822548\pi$
$32$		0			0
$33$	1.22474	−	2.12132i	0.213201	−	0.369274i
$34$		0			0
$35$	4.22474	−	7.31747i	0.714112	−	1.23688i
$36$		0			0
$37$	8.79796			1.44638			0.723188	−	0.690651i	$-0.242676\pi$
$37$	8.79796			1.44638			0.723188	+	0.690651i	$0.242676\pi$
$38$		0			0
$39$	−1.00000			−0.160128
$40$		0			0
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$		0			0
$43$	1.72474	−	2.98735i	0.263021	−	0.455566i	−0.704022	−	0.710178i	$-0.748614\pi$
$43$	1.72474	−	2.98735i	0.263021	−	0.455566i	0.967043	+	0.254612i	$0.0819478\pi$
$44$		0			0
$45$	2.44949			0.365148
$46$		0			0
$47$	−0.550510	−	0.953512i	−0.0803002	−	0.139084i	0.823079	−	0.567927i	$-0.192255\pi$
$47$	−0.550510	−	0.953512i	−0.0803002	−	0.139084i	−0.903379	+	0.428843i	$0.858921\pi$
$48$		0			0
$49$	4.89898			0.699854
$50$		0			0
$51$	−2.44949	−	4.24264i	−0.342997	−	0.594089i
$52$		0			0
$53$	1.22474	+	2.12132i	0.168232	+	0.291386i	0.937798	−	0.347181i	$-0.112861\pi$
$53$	1.22474	+	2.12132i	0.168232	+	0.291386i	−0.769567	+	0.638567i	$0.779528\pi$
$54$		0			0
$55$	3.00000	−	5.19615i	0.404520	−	0.700649i
$56$		0			0
$57$	3.17423	+	2.98735i	0.420438	+	0.395684i
$58$		0			0
$59$	3.67423	−	6.36396i	0.478345	−	0.828517i	−0.521347	−	0.853345i	$-0.674570\pi$
$59$	3.67423	−	6.36396i	0.478345	−	0.828517i	0.999692	+	0.0248275i	$0.00790366\pi$
$60$		0			0
$61$	1.05051	+	1.81954i	0.134504	+	0.232968i	0.925408	−	0.378973i	$-0.123723\pi$
$61$	1.05051	+	1.81954i	0.134504	+	0.232968i	−0.790904	+	0.611940i	$0.790389\pi$
$62$		0			0
$63$	1.72474	+	2.98735i	0.217297	+	0.376370i
$64$		0			0
$65$	−2.44949			−0.303822
$66$		0			0
$67$	2.27526	+	3.94086i	0.277967	+	0.481452i	0.970879	−	0.239569i	$-0.0770062\pi$
$67$	2.27526	+	3.94086i	0.277967	+	0.481452i	−0.692913	+	0.721022i	$0.743673\pi$
$68$		0			0
$69$	−8.44949			−1.01720
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$		0			0
$73$	5.94949	−	10.3048i	0.696335	−	1.20609i	−0.273393	−	0.961902i	$-0.588146\pi$
$73$	5.94949	−	10.3048i	0.696335	−	1.20609i	0.969729	−	0.244185i	$-0.0785206\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	8.44949			0.962909
$78$		0			0
$79$	−6.17423	+	10.6941i	−0.694656	+	1.20318i	0.275641	+	0.961261i	$0.411110\pi$
$79$	−6.17423	+	10.6941i	−0.694656	+	1.20318i	−0.970297	+	0.241918i	$0.922223\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−16.8990			−1.85490			−0.927452	−	0.373942i	$-0.878006\pi$
$83$	−16.8990			−1.85490			−0.927452	+	0.373942i	$0.878006\pi$
$84$		0			0
$85$	−6.00000	−	10.3923i	−0.650791	−	1.12720i
$86$		0			0
$87$	−4.89898			−0.525226
$88$		0			0
$89$	1.77526	+	3.07483i	0.188177	+	0.325932i	0.944642	−	0.328102i	$-0.106409\pi$
$89$	1.77526	+	3.07483i	0.188177	+	0.325932i	−0.756466	+	0.654033i	$0.773076\pi$
$90$		0			0
$91$	−1.72474	−	2.98735i	−0.180802	−	0.313159i
$92$		0			0
$93$	4.72474	−	8.18350i	0.489933	−	0.848589i
$94$		0			0
$95$	7.77526	+	7.31747i	0.797724	+	0.750757i
$96$		0			0
$97$	−5.34847	+	9.26382i	−0.543055	+	0.940598i	0.455672	+	0.890148i	$0.349399\pi$
$97$	−5.34847	+	9.26382i	−0.543055	+	0.940598i	−0.998727	+	0.0504506i	$0.983934\pi$
$98$		0			0
$99$	1.22474	+	2.12132i	0.123091	+	0.213201i
$100$		0			0
$101$	−5.44949	−	9.43879i	−0.542244	−	0.939195i	−0.998775	−	0.0494871i	$-0.984241\pi$
$101$	−5.44949	−	9.43879i	−0.542244	−	0.939195i	0.456530	−	0.889708i	$-0.349092\pi$
$102$		0			0
$103$	13.4495			1.32522			0.662609	−	0.748966i	$-0.269449\pi$
$103$	13.4495			1.32522			0.662609	+	0.748966i	$0.269449\pi$
$104$		0			0
$105$	4.22474	+	7.31747i	0.412293	+	0.714112i
$106$		0			0
$107$	3.79796			0.367163			0.183581	−	0.983005i	$-0.441231\pi$
$107$	3.79796			0.367163			0.183581	+	0.983005i	$0.441231\pi$
$108$		0			0
$109$	−4.00000	+	6.92820i	−0.383131	+	0.663602i	−0.991508	−	0.130046i	$-0.958487\pi$
$109$	−4.00000	+	6.92820i	−0.383131	+	0.663602i	0.608377	+	0.793648i	$0.291821\pi$
$110$		0			0
$111$	−4.39898	+	7.61926i	−0.417533	+	0.723188i
$112$		0			0
$113$	−18.2474			−1.71658			−0.858288	−	0.513169i	$-0.828472\pi$
$113$	−18.2474			−1.71658			−0.858288	+	0.513169i	$0.828472\pi$
$114$		0			0
$115$	−20.6969			−1.93000
$116$		0			0
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$		0			0
$119$	8.44949	−	14.6349i	0.774563	−	1.34158i
$120$		0			0
$121$	−5.00000			−0.454545
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.79796			−0.876356
$126$		0			0
$127$	9.34847	+	16.1920i	0.829543	+	1.43681i	0.898398	+	0.439183i	$0.144732\pi$
$127$	9.34847	+	16.1920i	0.829543	+	1.43681i	−0.0688551	+	0.997627i	$0.521935\pi$
$128$		0			0
$129$	1.72474	+	2.98735i	0.151855	+	0.263021i
$130$		0			0
$131$	1.89898	−	3.28913i	0.165915	−	0.287373i	−0.771065	−	0.636756i	$-0.780276\pi$
$131$	1.89898	−	3.28913i	0.165915	−	0.287373i	0.936980	+	0.349384i	$0.113609\pi$
$132$		0			0
$133$	−3.44949	+	14.6349i	−0.299109	+	1.26901i
$134$		0			0
$135$	−1.22474	+	2.12132i	−0.105409	+	0.182574i
$136$		0			0
$137$	6.55051	+	11.3458i	0.559648	+	0.969339i	0.997526	+	0.0703040i	$0.0223969\pi$
$137$	6.55051	+	11.3458i	0.559648	+	0.969339i	−0.437878	+	0.899035i	$0.644270\pi$
$138$		0			0
$139$	4.72474	+	8.18350i	0.400748	+	0.694115i	0.993816	−	0.111037i	$-0.0354171\pi$
$139$	4.72474	+	8.18350i	0.400748	+	0.694115i	−0.593069	+	0.805152i	$0.702084\pi$
$140$		0			0
$141$	1.10102			0.0927227
$142$		0			0
$143$	−1.22474	−	2.12132i	−0.102418	−	0.177394i
$144$		0			0
$145$	−12.0000			−0.996546
$146$		0			0
$147$	−2.44949	+	4.24264i	−0.202031	+	0.349927i
$148$		0			0
$149$	10.2247	−	17.7098i	0.837644	−	1.45084i	−0.0542159	−	0.998529i	$-0.517266\pi$
$149$	10.2247	−	17.7098i	0.837644	−	1.45084i	0.891860	−	0.452312i	$-0.149401\pi$
$150$		0			0
$151$	−6.69694			−0.544989			−0.272495	−	0.962157i	$-0.587849\pi$
$151$	−6.69694			−0.544989			−0.272495	+	0.962157i	$0.587849\pi$
$152$		0			0
$153$	4.89898			0.396059
$154$		0			0
$155$	11.5732	−	20.0454i	0.929583	−	1.61008i
$156$		0			0
$157$	−1.94949	+	3.37662i	−0.155586	+	0.269483i	−0.933272	−	0.359170i	$-0.883060\pi$
$157$	−1.94949	+	3.37662i	−0.155586	+	0.269483i	0.777686	+	0.628653i	$0.216393\pi$
$158$		0			0
$159$	−2.44949			−0.194257
$160$		0			0
$161$	−14.5732	−	25.2415i	−1.14853	−	1.98931i
$162$		0			0
$163$	10.1464			0.794730			0.397365	−	0.917661i	$-0.369925\pi$
$163$	10.1464			0.794730			0.397365	+	0.917661i	$0.369925\pi$
$164$		0			0
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$		0			0
$167$	−2.32577	−	4.02834i	−0.179973	−	0.311723i	0.761898	−	0.647697i	$-0.224268\pi$
$167$	−2.32577	−	4.02834i	−0.179973	−	0.311723i	−0.941871	+	0.335974i	$0.890934\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$	−4.17423	+	1.25529i	−0.319212	+	0.0959948i
$172$		0			0
$173$	−8.44949	+	14.6349i	−0.642403	+	1.11267i	0.342492	+	0.939521i	$0.388729\pi$
$173$	−8.44949	+	14.6349i	−0.642403	+	1.11267i	−0.984895	+	0.173154i	$0.944604\pi$
$174$		0			0
$175$	1.72474	+	2.98735i	0.130378	+	0.225822i
$176$		0			0
$177$	3.67423	+	6.36396i	0.276172	+	0.478345i
$178$		0			0
$179$	−3.55051			−0.265378			−0.132689	−	0.991158i	$-0.542361\pi$
$179$	−3.55051			−0.265378			−0.132689	+	0.991158i	$0.542361\pi$
$180$		0			0
$181$	−5.34847	−	9.26382i	−0.397549	−	0.688574i	0.595874	−	0.803078i	$-0.296806\pi$
$181$	−5.34847	−	9.26382i	−0.397549	−	0.688574i	−0.993423	+	0.114503i	$0.963472\pi$
$182$		0			0
$183$	−2.10102			−0.155312
$184$		0			0
$185$	−10.7753	+	18.6633i	−0.792213	+	1.37215i
$186$		0			0
$187$	6.00000	−	10.3923i	0.438763	−	0.759961i
$188$		0			0
$189$	−3.44949			−0.250913
$190$		0			0
$191$	18.2474			1.32034			0.660170	−	0.751117i	$-0.270484\pi$
$191$	18.2474			1.32034			0.660170	+	0.751117i	$0.270484\pi$
$192$		0			0
$193$	5.94949	−	10.3048i	0.428254	−	0.741757i	−0.568464	−	0.822708i	$-0.692462\pi$
$193$	5.94949	−	10.3048i	0.428254	−	0.741757i	0.996718	+	0.0809508i	$0.0257957\pi$
$194$		0			0
$195$	1.22474	−	2.12132i	0.0877058	−	0.151911i
$196$		0			0
$197$	11.1464			0.794150			0.397075	−	0.917786i	$-0.370025\pi$
$197$	11.1464			0.794150			0.397075	+	0.917786i	$0.370025\pi$
$198$		0			0
$199$	1.17423	+	2.03383i	0.0832393	+	0.144175i	0.904640	−	0.426177i	$-0.140140\pi$
$199$	1.17423	+	2.03383i	0.0832393	+	0.144175i	−0.821400	+	0.570352i	$0.806807\pi$
$200$		0			0
$201$	−4.55051			−0.320968
$202$		0			0
$203$	−8.44949	−	14.6349i	−0.593038	−	1.02717i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	4.22474	−	7.31747i	0.293640	−	0.508600i
$208$		0			0
$209$	−2.44949	+	10.3923i	−0.169435	+	0.718851i
$210$		0			0
$211$	7.17423	−	12.4261i	0.493895	−	0.855451i	−0.506081	−	0.862486i	$-0.668906\pi$
$211$	7.17423	−	12.4261i	0.493895	−	0.855451i	0.999975	+	0.00703553i	$0.00223950\pi$
$212$		0			0
$213$	−3.00000	−	5.19615i	−0.205557	−	0.356034i
$214$		0			0
$215$	4.22474	+	7.31747i	0.288125	+	0.499048i
$216$		0			0
$217$	32.5959			2.21276
$218$		0			0
$219$	5.94949	+	10.3048i	0.402029	+	0.696335i
$220$		0			0
$221$	−4.89898			−0.329541
$222$		0			0
$223$	−8.62372	+	14.9367i	−0.577487	+	1.00024i	0.418279	+	0.908319i	$0.362633\pi$
$223$	−8.62372	+	14.9367i	−0.577487	+	1.00024i	−0.995767	+	0.0919188i	$0.970700\pi$
$224$		0			0
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$		0			0
$227$	25.3485			1.68244			0.841218	−	0.540695i	$-0.181839\pi$
$227$	25.3485			1.68244			0.841218	+	0.540695i	$0.181839\pi$
$228$		0			0
$229$	20.7980			1.37437			0.687184	−	0.726484i	$-0.258847\pi$
$229$	20.7980			1.37437			0.687184	+	0.726484i	$0.258847\pi$
$230$		0			0
$231$	−4.22474	+	7.31747i	−0.277968	+	0.481454i
$232$		0			0
$233$	11.4495	−	19.8311i	0.750081	−	1.29918i	−0.197702	−	0.980262i	$-0.563348\pi$
$233$	11.4495	−	19.8311i	0.750081	−	1.29918i	0.947783	−	0.318916i	$-0.103319\pi$
$234$		0			0
$235$	2.69694			0.175929
$236$		0			0
$237$	−6.17423	−	10.6941i	−0.401060	−	0.694656i
$238$		0			0
$239$	11.1464			0.721003			0.360501	−	0.932759i	$-0.382606\pi$
$239$	11.1464			0.721003			0.360501	+	0.932759i	$0.382606\pi$
$240$		0			0
$241$	7.05051	+	12.2118i	0.454163	+	0.786634i	0.998640	−	0.0521423i	$-0.0166049\pi$
$241$	7.05051	+	12.2118i	0.454163	+	0.786634i	−0.544476	+	0.838776i	$0.683272\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−6.00000	+	10.3923i	−0.383326	+	0.663940i
$246$		0			0
$247$	4.17423	−	1.25529i	0.265600	−	0.0798725i
$248$		0			0
$249$	8.44949	−	14.6349i	0.535465	−	0.927452i
$250$		0			0
$251$	11.4495	+	19.8311i	0.722685	+	1.25173i	0.959920	+	0.280275i	$0.0904258\pi$
$251$	11.4495	+	19.8311i	0.722685	+	1.25173i	−0.237234	+	0.971452i	$0.576241\pi$
$252$		0			0
$253$	−10.3485	−	17.9241i	−0.650603	−	1.12688i
$254$		0			0
$255$	12.0000			0.751469
$256$		0			0
$257$	−13.2247	−	22.9059i	−0.824937	−	1.42883i	−0.901967	−	0.431804i	$-0.857877\pi$
$257$	−13.2247	−	22.9059i	−0.824937	−	1.42883i	0.0770306	−	0.997029i	$-0.475456\pi$
$258$		0			0
$259$	−30.3485			−1.88576
$260$		0			0
$261$	2.44949	−	4.24264i	0.151620	−	0.262613i
$262$		0			0
$263$	−6.79796	+	11.7744i	−0.419180	+	0.726041i	−0.995857	−	0.0909309i	$-0.971016\pi$
$263$	−6.79796	+	11.7744i	−0.419180	+	0.726041i	0.576677	+	0.816972i	$0.304349\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$		0			0
$267$	−3.55051			−0.217288
$268$		0			0
$269$	−5.57321	+	9.65309i	−0.339805	+	0.588559i	−0.984396	−	0.175968i	$-0.943694\pi$
$269$	−5.57321	+	9.65309i	−0.339805	+	0.588559i	0.644591	+	0.764528i	$0.277028\pi$
$270$		0			0
$271$	2.00000	−	3.46410i	0.121491	−	0.210429i	−0.798865	−	0.601511i	$-0.794566\pi$
$271$	2.00000	−	3.46410i	0.121491	−	0.210429i	0.920356	+	0.391082i	$0.127899\pi$
$272$		0			0
$273$	3.44949			0.208773
$274$		0			0
$275$	1.22474	+	2.12132i	0.0738549	+	0.127920i
$276$		0			0
$277$	−30.6969			−1.84440			−0.922200	−	0.386713i	$-0.873610\pi$
$277$	−30.6969			−1.84440			−0.922200	+	0.386713i	$0.873610\pi$
$278$		0			0
$279$	4.72474	+	8.18350i	0.282863	+	0.489933i
$280$		0			0
$281$	−12.1237	−	20.9989i	−0.723241	−	1.25269i	−0.959694	−	0.281047i	$-0.909318\pi$
$281$	−12.1237	−	20.9989i	−0.723241	−	1.25269i	0.236453	−	0.971643i	$-0.424015\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$		0			0
$285$	−10.2247	+	3.07483i	−0.605662	+	0.182137i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−3.50000	−	6.06218i	−0.205882	−	0.356599i
$290$		0			0
$291$	−5.34847	−	9.26382i	−0.313533	−	0.543055i
$292$		0			0
$293$	−3.79796			−0.221879			−0.110940	−	0.993827i	$-0.535386\pi$
$293$	−3.79796			−0.221879			−0.110940	+	0.993827i	$0.535386\pi$
$294$		0			0
$295$	9.00000	+	15.5885i	0.524000	+	0.907595i
$296$		0			0
$297$	−2.44949			−0.142134
$298$		0			0
$299$	−4.22474	+	7.31747i	−0.244323	+	0.423180i
$300$		0			0
$301$	−5.94949	+	10.3048i	−0.342923	+	0.593960i
$302$		0			0
$303$	10.8990			0.626130
$304$		0			0
$305$	−5.14643			−0.294684
$306$		0			0
$307$	−1.00000	+	1.73205i	−0.0570730	+	0.0988534i	−0.893150	−	0.449758i	$-0.851510\pi$
$307$	−1.00000	+	1.73205i	−0.0570730	+	0.0988534i	0.836077	+	0.548612i	$0.184843\pi$
$308$		0			0
$309$	−6.72474	+	11.6476i	−0.382557	+	0.662609i
$310$		0			0
$311$	−29.1464			−1.65274			−0.826371	−	0.563126i	$-0.809599\pi$
$311$	−29.1464			−1.65274			−0.826371	+	0.563126i	$0.809599\pi$
$312$		0			0
$313$	2.00000	+	3.46410i	0.113047	+	0.195803i	0.916997	−	0.398894i	$-0.130606\pi$
$313$	2.00000	+	3.46410i	0.113047	+	0.195803i	−0.803951	+	0.594696i	$0.797272\pi$
$314$		0			0
$315$	−8.44949			−0.476075
$316$		0			0
$317$	14.5732	+	25.2415i	0.818513	+	1.41771i	0.906778	+	0.421609i	$0.138535\pi$
$317$	14.5732	+	25.2415i	0.818513	+	1.41771i	−0.0882643	+	0.996097i	$0.528132\pi$
$318$		0			0
$319$	−6.00000	−	10.3923i	−0.335936	−	0.581857i
$320$		0			0
$321$	−1.89898	+	3.28913i	−0.105991	+	0.183581i
$322$		0			0
$323$	15.5505	+	14.6349i	0.865254	+	0.814310i
$324$		0			0
$325$	0.500000	−	0.866025i	0.0277350	−	0.0480384i
$326$		0			0
$327$	−4.00000	−	6.92820i	−0.221201	−	0.383131i
$328$		0			0
$329$	1.89898	+	3.28913i	0.104694	+	0.181336i
$330$		0			0
$331$	−11.0454			−0.607111			−0.303555	−	0.952814i	$-0.598174\pi$
$331$	−11.0454			−0.607111			−0.303555	+	0.952814i	$0.598174\pi$
$332$		0			0
$333$	−4.39898	−	7.61926i	−0.241063	−	0.417533i
$334$		0			0
$335$	−11.1464			−0.608994
$336$		0			0
$337$	−0.601021	+	1.04100i	−0.0327397	+	0.0567068i	−0.881931	−	0.471379i	$-0.843757\pi$
$337$	−0.601021	+	1.04100i	−0.0327397	+	0.0567068i	0.849191	+	0.528085i	$0.177090\pi$
$338$		0			0
$339$	9.12372	−	15.8028i	0.495533	−	0.858288i
$340$		0			0
$341$	23.1464			1.25345
$342$		0			0
$343$	7.24745			0.391325
$344$		0			0
$345$	10.3485	−	17.9241i	0.557143	−	0.965000i
$346$		0			0
$347$	−8.02270	+	13.8957i	−0.430681	+	0.745962i	−0.996932	−	0.0782711i	$-0.975060\pi$
$347$	−8.02270	+	13.8957i	−0.430681	+	0.745962i	0.566251	+	0.824233i	$0.308393\pi$
$348$		0			0
$349$	−2.59592			−0.138956			−0.0694782	−	0.997583i	$-0.522133\pi$
$349$	−2.59592			−0.138956			−0.0694782	+	0.997583i	$0.522133\pi$
$350$		0			0
$351$	0.500000	+	0.866025i	0.0266880	+	0.0462250i
$352$		0			0
$353$	4.65153			0.247576			0.123788	−	0.992309i	$-0.460496\pi$
$353$	4.65153			0.247576			0.123788	+	0.992309i	$0.460496\pi$
$354$		0			0
$355$	−7.34847	−	12.7279i	−0.390016	−	0.675528i
$356$		0			0
$357$	8.44949	+	14.6349i	0.447194	+	0.774563i
$358$		0			0
$359$	−16.8990	+	29.2699i	−0.891894	+	1.54481i	−0.0542918	+	0.998525i	$0.517290\pi$
$359$	−16.8990	+	29.2699i	−0.891894	+	1.54481i	−0.837602	+	0.546281i	$0.816043\pi$
$360$		0			0
$361$	−17.0000	−	8.48528i	−0.894737	−	0.446594i
$362$		0			0
$363$	2.50000	−	4.33013i	0.131216	−	0.227273i
$364$		0			0
$365$	14.5732	+	25.2415i	0.762797	+	1.32120i
$366$		0			0
$367$	1.72474	+	2.98735i	0.0900309	+	0.155938i	0.907524	−	0.420000i	$-0.137970\pi$
$367$	1.72474	+	2.98735i	0.0900309	+	0.155938i	−0.817493	+	0.575939i	$0.804637\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.22474	−	7.31747i	−0.219338	−	0.379904i
$372$		0			0
$373$	10.6969			0.553866			0.276933	−	0.960889i	$-0.410682\pi$
$373$	10.6969			0.553866			0.276933	+	0.960889i	$0.410682\pi$
$374$		0			0
$375$	4.89898	−	8.48528i	0.252982	−	0.438178i
$376$		0			0
$377$	−2.44949	+	4.24264i	−0.126155	+	0.218507i
$378$		0			0
$379$	35.2474			1.81054			0.905270	−	0.424837i	$-0.139669\pi$
$379$	35.2474			1.81054			0.905270	+	0.424837i	$0.139669\pi$
$380$		0			0
$381$	−18.6969			−0.957873
$382$		0			0
$383$	−11.0227	+	19.0919i	−0.563234	+	0.975550i	0.433978	+	0.900924i	$0.357110\pi$
$383$	−11.0227	+	19.0919i	−0.563234	+	0.975550i	−0.997212	+	0.0746261i	$0.976224\pi$
$384$		0			0
$385$	−10.3485	+	17.9241i	−0.527407	+	0.913495i
$386$		0			0
$387$	−3.44949			−0.175347
$388$		0			0
$389$	7.47219	+	12.9422i	0.378855	+	0.656197i	0.990896	−	0.134630i	$-0.0429845\pi$
$389$	7.47219	+	12.9422i	0.378855	+	0.656197i	−0.612041	+	0.790826i	$0.709651\pi$
$390$		0			0
$391$	−41.3939			−2.09338
$392$		0			0
$393$	1.89898	+	3.28913i	0.0957908	+	0.165915i
$394$		0			0
$395$	−15.1237	−	26.1951i	−0.760957	−	1.31802i
$396$		0			0
$397$	14.3990	−	24.9398i	0.722664	−	1.25169i	−0.237264	−	0.971445i	$-0.576251\pi$
$397$	14.3990	−	24.9398i	0.722664	−	1.25169i	0.959928	−	0.280246i	$-0.0904159\pi$
$398$		0			0
$399$	−10.9495	−	10.3048i	−0.548160	−	0.515886i
$400$		0			0
$401$	−7.77526	+	13.4671i	−0.388278	+	0.672517i	−0.992218	−	0.124513i	$-0.960263\pi$
$401$	−7.77526	+	13.4671i	−0.388278	+	0.672517i	0.603940	+	0.797030i	$0.293597\pi$
$402$		0			0
$403$	−4.72474	−	8.18350i	−0.235356	−	0.407649i
$404$		0			0
$405$	−1.22474	−	2.12132i	−0.0608581	−	0.105409i
$406$		0			0
$407$	−21.5505			−1.06822
$408$		0			0
$409$	16.6969	+	28.9199i	0.825610	+	1.43000i	0.901452	+	0.432879i	$0.142502\pi$
$409$	16.6969	+	28.9199i	0.825610	+	1.43000i	−0.0758414	+	0.997120i	$0.524164\pi$
$410$		0			0
$411$	−13.1010			−0.646226
$412$		0			0
$413$	−12.6742	+	21.9524i	−0.623658	+	1.08021i
$414$		0			0
$415$	20.6969	−	35.8481i	1.01597	−	1.75972i
$416$		0			0
$417$	−9.44949			−0.462744
$418$		0			0
$419$	−0.247449			−0.0120887			−0.00604433	−	0.999982i	$-0.501924\pi$
$419$	−0.247449			−0.0120887			−0.00604433	+	0.999982i	$0.501924\pi$
$420$		0			0
$421$	8.00000	−	13.8564i	0.389896	−	0.675320i	−0.602539	−	0.798089i	$-0.705844\pi$
$421$	8.00000	−	13.8564i	0.389896	−	0.675320i	0.992435	+	0.122769i	$0.0391776\pi$
$422$		0			0
$423$	−0.550510	+	0.953512i	−0.0267667	+	0.0463613i
$424$		0			0
$425$	4.89898			0.237635
$426$		0			0
$427$	−3.62372	−	6.27647i	−0.175364	−	0.303740i
$428$		0			0
$429$	2.44949			0.118262
$430$		0			0
$431$	−11.4495	−	19.8311i	−0.551503	−	0.955230i	−0.998166	−	0.0605286i	$-0.980721\pi$
$431$	−11.4495	−	19.8311i	−0.551503	−	0.955230i	0.446664	−	0.894702i	$-0.352612\pi$
$432$		0			0
$433$	14.3990	+	24.9398i	0.691971	+	1.19853i	0.971191	+	0.238302i	$0.0765907\pi$
$433$	14.3990	+	24.9398i	0.691971	+	1.19853i	−0.279220	+	0.960227i	$0.590076\pi$
$434$		0			0
$435$	6.00000	−	10.3923i	0.287678	−	0.498273i
$436$		0			0
$437$	35.2702	−	10.6066i	1.68720	−	0.507383i
$438$		0			0
$439$	14.5227	−	25.1541i	0.693131	−	1.20054i	−0.277676	−	0.960675i	$-0.589564\pi$
$439$	14.5227	−	25.1541i	0.693131	−	1.20054i	0.970807	−	0.239863i	$-0.0771025\pi$
$440$		0			0
$441$	−2.44949	−	4.24264i	−0.116642	−	0.202031i
$442$		0			0
$443$	8.44949	+	14.6349i	0.401447	+	0.695327i	0.993901	−	0.110277i	$-0.0351739\pi$
$443$	8.44949	+	14.6349i	0.401447	+	0.695327i	−0.592453	+	0.805605i	$0.701841\pi$
$444$		0			0
$445$	−8.69694			−0.412274
$446$		0			0
$447$	10.2247	+	17.7098i	0.483614	+	0.837644i
$448$		0			0
$449$	28.8990			1.36383			0.681914	−	0.731433i	$-0.261148\pi$
$449$	28.8990			1.36383			0.681914	+	0.731433i	$0.261148\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	3.34847	−	5.79972i	0.157325	−	0.272495i
$454$		0			0
$455$	8.44949			0.396118
$456$		0			0
$457$	−3.20204			−0.149785			−0.0748926	−	0.997192i	$-0.523861\pi$
$457$	−3.20204			−0.149785			−0.0748926	+	0.997192i	$0.523861\pi$
$458$		0			0
$459$	−2.44949	+	4.24264i	−0.114332	+	0.198030i
$460$		0			0
$461$	20.0227	−	34.6803i	0.932550	−	1.61522i	0.153605	−	0.988132i	$-0.450912\pi$
$461$	20.0227	−	34.6803i	0.932550	−	1.61522i	0.778945	−	0.627092i	$-0.215755\pi$
$462$		0			0
$463$	0.348469			0.0161947			0.00809737	−	0.999967i	$-0.497422\pi$
$463$	0.348469			0.0161947			0.00809737	+	0.999967i	$0.497422\pi$
$464$		0			0
$465$	11.5732	+	20.0454i	0.536695	+	0.929583i
$466$		0			0
$467$		0			0			−	1.00000i	$-0.5\pi$
$467$		0			0				1.00000i	$0.5\pi$
$468$		0			0
$469$	−7.84847	−	13.5939i	−0.362409	−	0.627710i
$470$		0			0
$471$	−1.94949	−	3.37662i	−0.0898277	−	0.155586i
$472$		0			0
$473$	−4.22474	+	7.31747i	−0.194254	+	0.336458i
$474$		0			0
$475$	−4.17423	+	1.25529i	−0.191527	+	0.0575969i
$476$		0			0
$477$	1.22474	−	2.12132i	0.0560772	−	0.0971286i
$478$		0			0
$479$	−11.6969	−	20.2597i	−0.534447	−	0.925689i	−0.999190	−	0.0402434i	$-0.987187\pi$
$479$	−11.6969	−	20.2597i	−0.534447	−	0.925689i	0.464743	−	0.885446i	$-0.346147\pi$
$480$		0			0
$481$	4.39898	+	7.61926i	0.200576	+	0.347408i
$482$		0			0
$483$	29.1464			1.32621
$484$		0			0
$485$	−13.1010	−	22.6916i	−0.594887	−	1.03037i
$486$		0			0
$487$	22.6969			1.02850			0.514248	−	0.857641i	$-0.328071\pi$
$487$	22.6969			1.02850			0.514248	+	0.857641i	$0.328071\pi$
$488$		0			0
$489$	−5.07321	+	8.78706i	−0.229419	+	0.397365i
$490$		0			0
$491$	6.79796	−	11.7744i	0.306788	−	0.531372i	−0.670870	−	0.741575i	$-0.734079\pi$
$491$	6.79796	−	11.7744i	0.306788	−	0.531372i	0.977658	+	0.210203i	$0.0674125\pi$
$492$		0			0
$493$	−24.0000			−1.08091
$494$		0			0
$495$	−6.00000			−0.269680
$496$		0			0
$497$	10.3485	−	17.9241i	0.464192	−	0.804005i
$498$		0			0
$499$	5.52270	−	9.56560i	0.247230	−	0.428215i	−0.715526	−	0.698586i	$-0.753813\pi$
$499$	5.52270	−	9.56560i	0.247230	−	0.428215i	0.962756	+	0.270371i	$0.0871463\pi$
$500$		0			0
$501$	4.65153			0.207815
$502$		0			0
$503$	3.55051	+	6.14966i	0.158309	+	0.274200i	0.934259	−	0.356595i	$-0.116062\pi$
$503$	3.55051	+	6.14966i	0.158309	+	0.274200i	−0.775950	+	0.630795i	$0.782729\pi$
$504$		0			0
$505$	26.6969			1.18800
$506$		0			0
$507$	6.00000	+	10.3923i	0.266469	+	0.461538i
$508$		0			0
$509$	1.89898	+	3.28913i	0.0841708	+	0.145788i	0.905038	−	0.425332i	$-0.139843\pi$
$509$	1.89898	+	3.28913i	0.0841708	+	0.145788i	−0.820867	+	0.571120i	$0.806509\pi$
$510$		0			0
$511$	−20.5227	+	35.5464i	−0.907871	+	1.57248i
$512$		0			0
$513$	1.00000	−	4.24264i	0.0441511	−	0.187317i
$514$		0			0
$515$	−16.4722	+	28.5307i	−0.725852	+	1.25721i
$516$		0			0
$517$	1.34847	+	2.33562i	0.0593056	+	0.102720i
$518$		0			0
$519$	−8.44949	−	14.6349i	−0.370891	−	0.642403i
$520$		0			0
$521$	8.94439			0.391861			0.195930	−	0.980618i	$-0.437227\pi$
$521$	8.94439			0.391861			0.195930	+	0.980618i	$0.437227\pi$
$522$		0			0
$523$	9.07321	+	15.7153i	0.396744	+	0.687181i	0.993322	−	0.115374i	$-0.0368068\pi$
$523$	9.07321	+	15.7153i	0.396744	+	0.687181i	−0.596578	+	0.802555i	$0.703473\pi$
$524$		0			0
$525$	−3.44949			−0.150548
$526$		0			0
$527$	23.1464	−	40.0908i	1.00827	−	1.74638i
$528$		0			0
$529$	−24.1969	+	41.9103i	−1.05204	+	1.82219i
$530$		0			0
$531$	−7.34847			−0.318896
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−4.65153	+	8.05669i	−0.201103	+	0.348321i
$536$		0			0
$537$	1.77526	−	3.07483i	0.0766079	−	0.132689i
$538$		0			0
$539$	−12.0000			−0.516877
$540$		0			0
$541$	−6.05051	−	10.4798i	−0.260132	−	0.450561i	0.706145	−	0.708067i	$-0.250433\pi$
$541$	−6.05051	−	10.4798i	−0.260132	−	0.450561i	−0.966277	+	0.257506i	$0.917099\pi$
$542$		0			0
$543$	10.6969			0.459050
$544$		0			0
$545$	−9.79796	−	16.9706i	−0.419698	−	0.726939i
$546$		0			0
$547$	1.72474	+	2.98735i	0.0737448	+	0.127730i	0.900540	−	0.434774i	$-0.143172\pi$
$547$	1.72474	+	2.98735i	0.0737448	+	0.127730i	−0.826795	+	0.562503i	$0.809838\pi$
$548$		0			0
$549$	1.05051	−	1.81954i	0.0448347	−	0.0776560i
$550$		0			0
$551$	20.4495	−	6.14966i	0.871178	−	0.261985i
$552$		0			0
$553$	21.2980	−	36.8891i	0.905681	−	1.56869i
$554$		0			0
$555$	−10.7753	−	18.6633i	−0.457384	−	0.792213i
$556$		0			0
$557$	−6.55051	−	11.3458i	−0.277554	−	0.480738i	0.693222	−	0.720724i	$-0.256190\pi$
$557$	−6.55051	−	11.3458i	−0.277554	−	0.480738i	−0.970776	+	0.239986i	$0.922857\pi$
$558$		0			0
$559$	3.44949			0.145898
$560$		0			0
$561$	6.00000	+	10.3923i	0.253320	+	0.438763i
$562$		0			0
$563$	−1.59592			−0.0672599			−0.0336300	−	0.999434i	$-0.510707\pi$
$563$	−1.59592			−0.0672599			−0.0336300	+	0.999434i	$0.510707\pi$
$564$		0			0
$565$	22.3485	−	38.7087i	0.940207	−	1.62849i
$566$		0			0
$567$	1.72474	−	2.98735i	0.0724325	−	0.125457i
$568$		0			0
$569$	−14.2020			−0.595381			−0.297690	−	0.954663i	$-0.596216\pi$
$569$	−14.2020			−0.595381			−0.297690	+	0.954663i	$0.596216\pi$
$570$		0			0
$571$	−10.5505			−0.441525			−0.220763	−	0.975328i	$-0.570855\pi$
$571$	−10.5505			−0.441525			−0.220763	+	0.975328i	$0.570855\pi$
$572$		0			0
$573$	−9.12372	+	15.8028i	−0.381149	+	0.660170i
$574$		0			0
$575$	4.22474	−	7.31747i	0.176184	−	0.305160i
$576$		0			0
$577$	−21.3939			−0.890639			−0.445319	−	0.895372i	$-0.646910\pi$
$577$	−21.3939			−0.890639			−0.445319	+	0.895372i	$0.646910\pi$
$578$		0			0
$579$	5.94949	+	10.3048i	0.247252	+	0.428254i
$580$		0			0
$581$	58.2929			2.41840
$582$		0			0
$583$	−3.00000	−	5.19615i	−0.124247	−	0.215203i
$584$		0			0
$585$	1.22474	+	2.12132i	0.0506370	+	0.0877058i
$586$		0			0
$587$	−10.7753	+	18.6633i	−0.444742	+	0.770316i	−0.998034	−	0.0626711i	$-0.980038\pi$
$587$	−10.7753	+	18.6633i	−0.444742	+	0.770316i	0.553292	+	0.832987i	$0.313371\pi$
$588$		0			0
$589$	−9.44949	+	40.0908i	−0.389359	+	1.65191i
$590$		0			0
$591$	−5.57321	+	9.65309i	−0.229251	+	0.397075i
$592$		0			0
$593$	0.426786	+	0.739215i	0.0175260	+	0.0303559i	0.874655	−	0.484745i	$-0.161088\pi$
$593$	0.426786	+	0.739215i	0.0175260	+	0.0303559i	−0.857129	+	0.515101i	$0.827754\pi$
$594$		0			0
$595$	20.6969	+	35.8481i	0.848492	+	1.46963i
$596$		0			0
$597$	−2.34847			−0.0961164
$598$		0			0
$599$	2.32577	+	4.02834i	0.0950282	+	0.164594i	0.909620	−	0.415440i	$-0.136373\pi$
$599$	2.32577	+	4.02834i	0.0950282	+	0.164594i	−0.814592	+	0.580034i	$0.803039\pi$
$600$		0			0
$601$	−4.79796			−0.195713			−0.0978564	−	0.995201i	$-0.531199\pi$
$601$	−4.79796			−0.195713			−0.0978564	+	0.995201i	$0.531199\pi$
$602$		0			0
$603$	2.27526	−	3.94086i	0.0926556	−	0.160484i
$604$		0			0
$605$	6.12372	−	10.6066i	0.248965	−	0.431220i
$606$		0			0
$607$	−12.1464			−0.493008			−0.246504	−	0.969142i	$-0.579282\pi$
$607$	−12.1464			−0.493008			−0.246504	+	0.969142i	$0.579282\pi$
$608$		0			0
$609$	16.8990			0.684781
$610$		0			0
$611$	0.550510	−	0.953512i	0.0222713	−	0.0385750i
$612$		0			0
$613$	−2.65153	+	4.59259i	−0.107094	+	0.185493i	−0.914592	−	0.404378i	$-0.867488\pi$
$613$	−2.65153	+	4.59259i	−0.107094	+	0.185493i	0.807498	+	0.589871i	$0.200821\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−8.02270	−	13.8957i	−0.322982	−	0.559421i	0.658120	−	0.752913i	$-0.271352\pi$
$617$	−8.02270	−	13.8957i	−0.322982	−	0.559421i	−0.981102	+	0.193492i	$0.938019\pi$
$618$		0			0
$619$	5.85357			0.235275			0.117637	−	0.993057i	$-0.462468\pi$
$619$	5.85357			0.235275			0.117637	+	0.993057i	$0.462468\pi$
$620$		0			0
$621$	4.22474	+	7.31747i	0.169533	+	0.293640i
$622$		0			0
$623$	−6.12372	−	10.6066i	−0.245342	−	0.424945i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$	−7.77526	−	7.31747i	−0.310514	−	0.292232i
$628$		0			0
$629$	−21.5505	+	37.3266i	−0.859275	+	1.48831i
$630$		0			0
$631$	−20.0732	−	34.7678i	−0.799102	−	1.38409i	−0.920202	−	0.391445i	$-0.871975\pi$
$631$	−20.0732	−	34.7678i	−0.799102	−	1.38409i	0.121099	−	0.992640i	$-0.461358\pi$
$632$		0			0
$633$	7.17423	+	12.4261i	0.285150	+	0.493895i
$634$		0			0
$635$	−45.7980			−1.81744
$636$		0			0
$637$	2.44949	+	4.24264i	0.0970523	+	0.168100i
$638$		0			0
$639$	6.00000			0.237356
$640$		0			0
$641$	−17.6969	+	30.6520i	−0.698987	+	1.21068i	0.269831	+	0.962908i	$0.413032\pi$
$641$	−17.6969	+	30.6520i	−0.698987	+	1.21068i	−0.968818	+	0.247773i	$0.920301\pi$
$642$		0			0
$643$	−17.8712	+	30.9538i	−0.704770	+	1.22070i	0.262004	+	0.965067i	$0.415617\pi$
$643$	−17.8712	+	30.9538i	−0.704770	+	1.22070i	−0.966774	+	0.255631i	$0.917717\pi$
$644$		0			0
$645$	−8.44949			−0.332698
$646$		0			0
$647$	−4.89898			−0.192599			−0.0962994	−	0.995352i	$-0.530701\pi$
$647$	−4.89898			−0.192599			−0.0962994	+	0.995352i	$0.530701\pi$
$648$		0			0
$649$	−9.00000	+	15.5885i	−0.353281	+	0.611900i
$650$		0			0
$651$	−16.2980	+	28.2289i	−0.638767	+	1.10638i
$652$		0			0
$653$	13.1010			0.512683			0.256341	−	0.966586i	$-0.417483\pi$
$653$	13.1010			0.512683			0.256341	+	0.966586i	$0.417483\pi$
$654$		0			0
$655$	4.65153	+	8.05669i	0.181750	+	0.314801i
$656$		0			0
$657$	−11.8990			−0.464223
$658$		0			0
$659$	−19.2247	−	33.2982i	−0.748890	−	1.29712i	−0.948355	−	0.317210i	$-0.897254\pi$
$659$	−19.2247	−	33.2982i	−0.748890	−	1.29712i	0.199466	−	0.979905i	$-0.436079\pi$
$660$		0			0
$661$	17.0000	+	29.4449i	0.661223	+	1.14527i	0.980294	+	0.197542i	$0.0632958\pi$
$661$	17.0000	+	29.4449i	0.661223	+	1.14527i	−0.319071	+	0.947731i	$0.603371\pi$
$662$		0			0
$663$	2.44949	−	4.24264i	0.0951303	−	0.164771i
$664$		0			0
$665$	−26.8207	−	25.2415i	−1.04006	−	0.978825i
$666$		0			0
$667$	−20.6969	+	35.8481i	−0.801389	+	1.38805i
$668$		0			0
$669$	−8.62372	−	14.9367i	−0.333412	−	0.577487i
$670$		0			0
$671$	−2.57321	−	4.45694i	−0.0993378	−	0.172058i
$672$		0			0
$673$	5.00000			0.192736			0.0963679	−	0.995346i	$-0.469277\pi$
$673$	5.00000			0.192736			0.0963679	+	0.995346i	$0.469277\pi$
$674$		0			0
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$		0			0
$677$	37.5959			1.44493			0.722464	−	0.691408i	$-0.243009\pi$
$677$	37.5959			1.44493			0.722464	+	0.691408i	$0.243009\pi$
$678$		0			0
$679$	18.4495	−	31.9555i	0.708026	−	1.22634i
$680$		0			0
$681$	−12.6742	+	21.9524i	−0.485678	+	0.841218i
$682$		0			0
$683$	−23.1464			−0.885673			−0.442837	−	0.896602i	$-0.646028\pi$
$683$	−23.1464			−0.885673			−0.442837	+	0.896602i	$0.646028\pi$
$684$		0			0
$685$	−32.0908			−1.22613
$686$		0			0
$687$	−10.3990	+	18.0116i	−0.396746	+	0.687184i
$688$		0			0
$689$	−1.22474	+	2.12132i	−0.0466591	+	0.0808159i
$690$		0			0
$691$	37.3939			1.42253			0.711265	−	0.702924i	$-0.248123\pi$
$691$	37.3939			1.42253			0.711265	+	0.702924i	$0.248123\pi$
$692$		0			0
$693$	−4.22474	−	7.31747i	−0.160485	−	0.277968i
$694$		0			0
$695$	−23.1464			−0.877994
$696$		0			0
$697$		0			0
$698$		0			0
$699$	11.4495	+	19.8311i	0.433059	+	0.750081i
$700$		0			0
$701$	9.92168	−	17.1849i	0.374737	−	0.649063i	−0.615551	−	0.788097i	$-0.711066\pi$
$701$	9.92168	−	17.1849i	0.374737	−	0.649063i	0.990288	+	0.139034i	$0.0443997\pi$
$702$		0			0
$703$	8.79796	−	37.3266i	0.331821	−	1.40780i
$704$		0			0
$705$	−1.34847	+	2.33562i	−0.0507863	+	0.0879644i
$706$		0			0
$707$	18.7980	+	32.5590i	0.706970	+	1.22451i
$708$		0			0
$709$	−6.84847	−	11.8619i	−0.257200	−	0.445483i	0.708291	−	0.705921i	$-0.249466\pi$
$709$	−6.84847	−	11.8619i	−0.257200	−	0.445483i	−0.965491	+	0.260438i	$0.916133\pi$
$710$		0			0
$711$	12.3485			0.463104
$712$		0			0
$713$	−39.9217	−	69.1464i	−1.49508	−	2.58955i
$714$		0			0
$715$	6.00000			0.224387
$716$		0			0
$717$	−5.57321	+	9.65309i	−0.208135	+	0.360501i
$718$		0			0
$719$	6.67423	−	11.5601i	0.248907	−	0.431119i	−0.714316	−	0.699823i	$-0.753262\pi$
$719$	6.67423	−	11.5601i	0.248907	−	0.431119i	0.963223	+	0.268704i	$0.0865953\pi$
$720$		0			0
$721$	−46.3939			−1.72780
$722$		0			0
$723$	−14.1010			−0.524423
$724$		0			0
$725$	2.44949	−	4.24264i	0.0909718	−	0.157568i
$726$		0			0
$727$	−6.17423	+	10.6941i	−0.228990	+	0.396622i	−0.957509	−	0.288404i	$-0.906876\pi$
$727$	−6.17423	+	10.6941i	−0.228990	+	0.396622i	0.728519	+	0.685025i	$0.240209\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	8.44949	+	14.6349i	0.312516	+	0.541293i
$732$		0			0
$733$	−30.6969			−1.13382			−0.566909	−	0.823781i	$-0.691861\pi$
$733$	−30.6969			−1.13382			−0.566909	+	0.823781i	$0.691861\pi$
$734$		0			0
$735$	−6.00000	−	10.3923i	−0.221313	−	0.383326i
$736$		0			0
$737$	−5.57321	−	9.65309i	−0.205292	−	0.355576i
$738$		0			0
$739$	2.27526	−	3.94086i	0.0836966	−	0.144967i	−0.821138	−	0.570729i	$-0.806661\pi$
$739$	2.27526	−	3.94086i	0.0836966	−	0.144967i	0.904835	+	0.425762i	$0.139994\pi$
$740$		0			0
$741$	−1.00000	+	4.24264i	−0.0367359	+	0.155857i
$742$		0			0
$743$	2.32577	−	4.02834i	0.0853241	−	0.147786i	−0.820205	−	0.572069i	$-0.806141\pi$
$743$	2.32577	−	4.02834i	0.0853241	−	0.147786i	0.905529	+	0.424284i	$0.139474\pi$
$744$		0			0
$745$	25.0454	+	43.3799i	0.917593	+	1.58932i
$746$		0			0
$747$	8.44949	+	14.6349i	0.309151	+	0.535465i
$748$		0			0
$749$	−13.1010			−0.478701
$750$		0			0
$751$	11.2753	+	19.5293i	0.411440	+	0.712635i	0.995047	−	0.0994010i	$-0.0316927\pi$
$751$	11.2753	+	19.5293i	0.411440	+	0.712635i	−0.583608	+	0.812036i	$0.698359\pi$
$752$		0			0
$753$	−22.8990			−0.834485
$754$		0			0
$755$	8.20204	−	14.2064i	0.298503	−	0.517022i
$756$		0			0
$757$	−19.9495	+	34.5535i	−0.725077	+	1.25587i	0.233866	+	0.972269i	$0.424862\pi$
$757$	−19.9495	+	34.5535i	−0.725077	+	1.25587i	−0.958943	+	0.283601i	$0.908471\pi$
$758$		0			0
$759$	20.6969			0.751251
$760$		0			0
$761$	16.0454			0.581646			0.290823	−	0.956777i	$-0.406071\pi$
$761$	16.0454			0.581646			0.290823	+	0.956777i	$0.406071\pi$
$762$		0			0
$763$	13.7980	−	23.8988i	0.499520	−	0.865193i
$764$		0			0
$765$	−6.00000	+	10.3923i	−0.216930	+	0.375735i
$766$		0			0
$767$	7.34847			0.265338
$768$		0			0
$769$	6.50000	+	11.2583i	0.234396	+	0.405986i	0.959097	−	0.283078i	$-0.0913554\pi$
$769$	6.50000	+	11.2583i	0.234396	+	0.405986i	−0.724701	+	0.689063i	$0.758022\pi$
$770$		0			0
$771$	26.4495			0.952555
$772$		0			0
$773$	6.79796	+	11.7744i	0.244506	+	0.423496i	0.961992	−	0.273076i	$-0.0880410\pi$
$773$	6.79796	+	11.7744i	0.244506	+	0.423496i	−0.717487	+	0.696572i	$0.754708\pi$
$774$		0			0
$775$	4.72474	+	8.18350i	0.169718	+	0.293960i
$776$		0			0
$777$	15.1742	−	26.2825i	0.544373	−	0.942881i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	7.34847	−	12.7279i	0.262949	−	0.455441i
$782$		0			0
$783$	2.44949	+	4.24264i	0.0875376	+	0.151620i
$784$		0			0
$785$	−4.77526	−	8.27098i	−0.170436	−	0.295204i
$786$		0			0
$787$	−42.1464			−1.50236			−0.751179	−	0.660099i	$-0.770514\pi$
$787$	−42.1464			−1.50236			−0.751179	+	0.660099i	$0.770514\pi$
$788$		0			0
$789$	−6.79796	−	11.7744i	−0.242014	−	0.419180i
$790$		0			0
$791$	62.9444			2.23804
$792$		0			0
$793$	−1.05051	+	1.81954i	−0.0373047	+	0.0646137i
$794$		0			0
$795$	3.00000	−	5.19615i	0.106399	−	0.184289i
$796$		0			0
$797$	−40.2929			−1.42725			−0.713623	−	0.700530i	$-0.752947\pi$
$797$	−40.2929			−1.42725			−0.713623	+	0.700530i	$0.752947\pi$
$798$		0			0
$799$	5.39388			0.190822
$800$		0			0
$801$	1.77526	−	3.07483i	0.0627256	−	0.108644i
$802$		0			0
$803$	−14.5732	+	25.2415i	−0.514278	+	0.890755i
$804$		0			0
$805$	71.3939			2.51630
$806$		0			0
$807$	−5.57321	−	9.65309i	−0.196186	−	0.339805i
$808$		0			0
$809$	50.4495			1.77371			0.886855	−	0.462048i	$-0.152885\pi$
$809$	50.4495			1.77371			0.886855	+	0.462048i	$0.152885\pi$
$810$		0			0
$811$	18.0454	+	31.2556i	0.633660	+	1.09753i	0.986797	+	0.161960i	$0.0517815\pi$
$811$	18.0454	+	31.2556i	0.633660	+	1.09753i	−0.353137	+	0.935571i	$0.614885\pi$
$812$		0			0
$813$	2.00000	+	3.46410i	0.0701431	+	0.121491i
$814$		0			0
$815$	−12.4268	+	21.5238i	−0.435291	+	0.753947i
$816$		0			0
$817$	−10.9495	−	10.3048i	−0.383074	−	0.360520i
$818$		0			0
$819$	−1.72474	+	2.98735i	−0.0602675	+	0.104386i
$820$		0			0
$821$	−13.3485	−	23.1202i	−0.465865	−	0.806901i	0.533375	−	0.845879i	$-0.320923\pi$
$821$	−13.3485	−	23.1202i	−0.465865	−	0.806901i	−0.999240	+	0.0389772i	$0.987590\pi$
$822$		0			0
$823$	−17.3485	−	30.0484i	−0.604730	−	1.04742i	−0.992094	−	0.125496i	$-0.959948\pi$
$823$	−17.3485	−	30.0484i	−0.604730	−	1.04742i	0.387365	−	0.921927i	$-0.373385\pi$
$824$		0			0
$825$	−2.44949			−0.0852803
$826$		0			0
$827$	−2.44949	−	4.24264i	−0.0851771	−	0.147531i	0.820290	−	0.571948i	$-0.193812\pi$
$827$	−2.44949	−	4.24264i	−0.0851771	−	0.147531i	−0.905467	+	0.424417i	$0.860479\pi$
$828$		0			0
$829$	−15.6969			−0.545177			−0.272589	−	0.962131i	$-0.587880\pi$
$829$	−15.6969			−0.545177			−0.272589	+	0.962131i	$0.587880\pi$
$830$		0			0
$831$	15.3485	−	26.5843i	0.532432	−	0.922200i
$832$		0			0
$833$	−12.0000	+	20.7846i	−0.415775	+	0.720144i
$834$		0			0
$835$	11.3939			0.394301
$836$		0			0
$837$	−9.44949			−0.326622
$838$		0			0
$839$	−0.426786	+	0.739215i	−0.0147343	+	0.0255205i	−0.873299	−	0.487185i	$-0.838024\pi$
$839$	−0.426786	+	0.739215i	−0.0147343	+	0.0255205i	0.858564	+	0.512706i	$0.171357\pi$
$840$		0			0
$841$	2.50000	−	4.33013i	0.0862069	−	0.149315i
$842$		0			0
$843$	24.2474			0.835126
$844$		0			0
$845$	14.6969	+	25.4558i	0.505590	+	0.875708i
$846$		0			0
$847$	17.2474			0.592629
$848$		0			0
$849$	2.00000	+	3.46410i	0.0686398	+	0.118888i
$850$		0			0
$851$	37.1691	+	64.3788i	1.27414	+	2.20688i
$852$		0			0
$853$	4.29796	−	7.44428i	0.147159	−	0.254887i	−0.783017	−	0.622000i	$-0.786320\pi$
$853$	4.29796	−	7.44428i	0.147159	−	0.254887i	0.930176	+	0.367113i	$0.119654\pi$
$854$		0			0
$855$	2.44949	−	10.3923i	0.0837708	−	0.355409i
$856$		0			0
$857$	22.5959	−	39.1373i	0.771862	−	1.33690i	−0.164680	−	0.986347i	$-0.552659\pi$
$857$	22.5959	−	39.1373i	0.771862	−	1.33690i	0.936541	−	0.350557i	$-0.114008\pi$
$858$		0			0
$859$	−15.7247	−	27.2361i	−0.536521	−	0.929282i	−0.999088	−	0.0426978i	$-0.986405\pi$
$859$	−15.7247	−	27.2361i	−0.536521	−	0.929282i	0.462567	−	0.886585i	$-0.346929\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−22.8990			−0.779490			−0.389745	−	0.920923i	$-0.627437\pi$
$863$	−22.8990			−0.779490			−0.389745	+	0.920923i	$0.627437\pi$
$864$		0			0
$865$	−20.6969	−	35.8481i	−0.703717	−	1.21887i
$866$		0			0
$867$	7.00000			0.237732
$868$		0			0
$869$	15.1237	−	26.1951i	0.513037	−	0.888607i
$870$		0			0
$871$	−2.27526	+	3.94086i	−0.0770941	+	0.133531i
$872$		0			0
$873$	10.6969			0.362037
$874$		0			0
$875$	33.7980			1.14258
$876$		0			0
$877$	−4.39898	+	7.61926i	−0.148543	+	0.257284i	−0.930689	−	0.365811i	$-0.880792\pi$
$877$	−4.39898	+	7.61926i	−0.148543	+	0.257284i	0.782146	+	0.623095i	$0.214125\pi$
$878$		0			0
$879$	1.89898	−	3.28913i	0.0640510	−	0.110940i
$880$		0			0
$881$	−2.44949			−0.0825254			−0.0412627	−	0.999148i	$-0.513138\pi$
$881$	−2.44949			−0.0825254			−0.0412627	+	0.999148i	$0.513138\pi$
$882$		0			0
$883$	14.8258	+	25.6790i	0.498927	+	0.864166i	0.999999	−	0.00123886i	$-0.000394342\pi$
$883$	14.8258	+	25.6790i	0.498927	+	0.864166i	−0.501073	+	0.865405i	$0.667061\pi$
$884$		0			0
$885$	−18.0000			−0.605063
$886$		0			0
$887$	9.92168	+	17.1849i	0.333138	+	0.577011i	0.983125	−	0.182934i	$-0.0585593\pi$
$887$	9.92168	+	17.1849i	0.333138	+	0.577011i	−0.649988	+	0.759945i	$0.725226\pi$
$888$		0			0
$889$	−32.2474	−	55.8542i	−1.08154	−	1.87329i
$890$		0			0
$891$	1.22474	−	2.12132i	0.0410305	−	0.0710669i
$892$		0			0
$893$	−4.59592	+	1.38211i	−0.153797	+	0.0462504i
$894$		0			0
$895$	4.34847	−	7.53177i	0.145353	−	0.251759i
$896$		0			0
$897$	−4.22474	−	7.31747i	−0.141060	−	0.244323i
$898$		0			0
$899$	−23.1464	−	40.0908i	−0.771977	−	1.33710i
$900$		0			0
$901$	−12.0000			−0.399778
$902$		0			0
$903$	−5.94949	−	10.3048i	−0.197987	−	0.342923i
$904$		0			0
$905$	26.2020			0.870985
$906$		0			0
$907$	20.0000	−	34.6410i	0.664089	−	1.15024i	−0.315442	−	0.948945i	$-0.602153\pi$
$907$	20.0000	−	34.6410i	0.664089	−	1.15024i	0.979531	−	0.201291i	$-0.0645138\pi$
$908$		0			0
$909$	−5.44949	+	9.43879i	−0.180748	+	0.313065i
$910$		0			0
$911$	17.3939			0.576285			0.288142	−	0.957588i	$-0.406962\pi$
$911$	17.3939			0.576285			0.288142	+	0.957588i	$0.406962\pi$
$912$		0			0
$913$	41.3939			1.36994
$914$		0			0
$915$	2.57321	−	4.45694i	0.0850678	−	0.147342i
$916$		0			0
$917$	−6.55051	+	11.3458i	−0.216317	+	0.374672i
$918$		0			0
$919$	0.348469			0.0114949			0.00574747	−	0.999983i	$-0.498171\pi$
$919$	0.348469			0.0114949			0.00574747	+	0.999983i	$0.498171\pi$
$920$		0			0
$921$	−1.00000	−	1.73205i	−0.0329511	−	0.0570730i
$922$		0			0
$923$	−6.00000			−0.197492
$924$		0			0
$925$	−4.39898	−	7.61926i	−0.144638	−	0.250520i
$926$		0			0
$927$	−6.72474	−	11.6476i	−0.220870	−	0.382557i
$928$		0			0
$929$	−29.2702	+	50.6974i	−0.960323	+	1.66333i	−0.238634	+	0.971110i	$0.576700\pi$
$929$	−29.2702	+	50.6974i	−0.960323	+	1.66333i	−0.721689	+	0.692218i	$0.756634\pi$
$930$		0			0
$931$	4.89898	−	20.7846i	0.160558	−	0.681188i
$932$		0			0
$933$	14.5732	−	25.2415i	0.477106	−	0.826371i
$934$		0			0
$935$	14.6969	+	25.4558i	0.480641	+	0.832495i
$936$		0			0
$937$	−8.74745	−	15.1510i	−0.285767	−	0.494962i	0.687028	−	0.726631i	$-0.258915\pi$
$937$	−8.74745	−	15.1510i	−0.285767	−	0.494962i	−0.972795	+	0.231668i	$0.925582\pi$
$938$		0			0
$939$	−4.00000			−0.130535
$940$		0			0
$941$	−8.20204	−	14.2064i	−0.267379	−	0.463114i	0.700805	−	0.713353i	$-0.252824\pi$
$941$	−8.20204	−	14.2064i	−0.267379	−	0.463114i	−0.968184	+	0.250239i	$0.919491\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	4.22474	−	7.31747i	0.137431	−	0.238037i
$946$		0			0
$947$	−7.89898	+	13.6814i	−0.256682	+	0.444587i	−0.965351	−	0.260954i	$-0.915963\pi$
$947$	−7.89898	+	13.6814i	−0.256682	+	0.444587i	0.708669	+	0.705541i	$0.249296\pi$
$948$		0			0
$949$	11.8990			0.386257
$950$		0			0
$951$	−29.1464			−0.945138
$952$		0			0
$953$	−12.6742	+	21.9524i	−0.410559	+	0.711109i	−0.994951	−	0.100363i	$-0.968000\pi$
$953$	−12.6742	+	21.9524i	−0.410559	+	0.711109i	0.584392	+	0.811471i	$0.301333\pi$
$954$		0			0
$955$	−22.3485	+	38.7087i	−0.723179	+	1.25258i
$956$		0			0
$957$	12.0000			0.387905
$958$		0			0
$959$	−22.5959	−	39.1373i	−0.729660	−	1.26381i
$960$		0			0
$961$	58.2929			1.88041
$962$		0			0
$963$	−1.89898	−	3.28913i	−0.0611938	−	0.105991i
$964$		0			0
$965$	14.5732	+	25.2415i	0.469128	+	0.812554i
$966$		0			0
$967$	13.9722	−	24.2005i	0.449315	−	0.778237i	−0.549026	−	0.835805i	$-0.685001\pi$
$967$	13.9722	−	24.2005i	0.449315	−	0.778237i	0.998342	+	0.0575680i	$0.0183346\pi$
$968$		0			0
$969$	−20.4495	+	6.14966i	−0.656932	+	0.197556i
$970$		0			0
$971$	6.55051	−	11.3458i	0.210216	−	0.364105i	−0.741566	−	0.670880i	$-0.765917\pi$
$971$	6.55051	−	11.3458i	0.210216	−	0.364105i	0.951782	+	0.306775i	$0.0992500\pi$
$972$		0			0
$973$	−16.2980	−	28.2289i	−0.522489	−	0.904977i
$974$		0			0
$975$	0.500000	+	0.866025i	0.0160128	+	0.0277350i
$976$		0			0
$977$	−37.5959			−1.20280			−0.601400	−	0.798948i	$-0.705390\pi$
$977$	−37.5959			−1.20280			−0.601400	+	0.798948i	$0.705390\pi$
$978$		0			0
$979$	−4.34847	−	7.53177i	−0.138978	−	0.240716i
$980$		0			0
$981$	8.00000			0.255420
$982$		0			0
$983$	−14.5732	+	25.2415i	−0.464813	+	0.805080i	−0.999193	−	0.0401642i	$-0.987212\pi$
$983$	−14.5732	+	25.2415i	−0.464813	+	0.805080i	0.534380	+	0.845245i	$0.320545\pi$
$984$		0			0
$985$	−13.6515	+	23.6451i	−0.434974	+	0.753397i
$986$		0			0
$987$	−3.79796			−0.120890
$988$		0			0
$989$	29.1464			0.926802
$990$		0			0
$991$	−18.9722	+	32.8608i	−0.602672	+	1.04386i	0.389743	+	0.920924i	$0.372564\pi$
$991$	−18.9722	+	32.8608i	−0.602672	+	1.04386i	−0.992415	+	0.122934i	$0.960770\pi$
$992$		0			0
$993$	5.52270	−	9.56560i	0.175258	−	0.303555i
$994$		0			0
$995$	−5.75255			−0.182368
$996$		0			0
$997$	1.84847	+	3.20164i	0.0585416	+	0.101397i	0.893811	−	0.448444i	$-0.148022\pi$
$997$	1.84847	+	3.20164i	0.0585416	+	0.101397i	−0.835269	+	0.549841i	$0.814688\pi$
$998$		0			0
$999$	8.79796			0.278355

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.i.a.49.1	✓	4
3.2	odd	2		684.2.k.f.505.2		4
4.3	odd	2		912.2.q.i.49.1		4
12.11	even	2		2736.2.s.t.1873.2		4
19.7	even	3	inner	228.2.i.a.121.1	yes	4
19.8	odd	6		4332.2.a.g.1.2		2
19.11	even	3		4332.2.a.l.1.2		2
57.26	odd	6		684.2.k.f.577.2		4
76.7	odd	6		912.2.q.i.577.1		4
228.83	even	6		2736.2.s.t.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.i.a.49.1	✓	4	1.1	even	1	trivial
228.2.i.a.121.1	yes	4	19.7	even	3	inner
684.2.k.f.505.2		4	3.2	odd	2
684.2.k.f.577.2		4	57.26	odd	6
912.2.q.i.49.1		4	4.3	odd	2
912.2.q.i.577.1		4	76.7	odd	6
2736.2.s.t.577.2		4	228.83	even	6
2736.2.s.t.1873.2		4	12.11	even	2
4332.2.a.g.1.2		2	19.8	odd	6
4332.2.a.l.1.2		2	19.11	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-1.22474 + 2.12132i) q^{5} -3.44949 q^{7} +(-0.500000 - 0.866025i) q^{9} -2.44949 q^{11} +(0.500000 + 0.866025i) q^{13} +(-1.22474 - 2.12132i) q^{15} +(-2.44949 + 4.24264i) q^{17} +(1.00000 - 4.24264i) q^{19} +(1.72474 - 2.98735i) q^{21} +(4.22474 + 7.31747i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +(2.44949 + 4.24264i) q^{29} -9.44949 q^{31} +(1.22474 - 2.12132i) q^{33} +(4.22474 - 7.31747i) q^{35} +8.79796 q^{37} -1.00000 q^{39} +(1.72474 - 2.98735i) q^{43} +2.44949 q^{45} +(-0.550510 - 0.953512i) q^{47} +4.89898 q^{49} +(-2.44949 - 4.24264i) q^{51} +(1.22474 + 2.12132i) q^{53} +(3.00000 - 5.19615i) q^{55} +(3.17423 + 2.98735i) q^{57} +(3.67423 - 6.36396i) q^{59} +(1.05051 + 1.81954i) q^{61} +(1.72474 + 2.98735i) q^{63} -2.44949 q^{65} +(2.27526 + 3.94086i) q^{67} -8.44949 q^{69} +(-3.00000 + 5.19615i) q^{71} +(5.94949 - 10.3048i) q^{73} +1.00000 q^{75} +8.44949 q^{77} +(-6.17423 + 10.6941i) q^{79} +(-0.500000 + 0.866025i) q^{81} -16.8990 q^{83} +(-6.00000 - 10.3923i) q^{85} -4.89898 q^{87} +(1.77526 + 3.07483i) q^{89} +(-1.72474 - 2.98735i) q^{91} +(4.72474 - 8.18350i) q^{93} +(7.77526 + 7.31747i) q^{95} +(-5.34847 + 9.26382i) q^{97} +(1.22474 + 2.12132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 4 q^{7} - 2 q^{9} + 2 q^{13} + 4 q^{19} + 2 q^{21} + 12 q^{23} - 2 q^{25} + 4 q^{27} - 28 q^{31} + 12 q^{35} - 4 q^{37} - 4 q^{39} + 2 q^{43} - 12 q^{47} + 12 q^{55} - 2 q^{57} + 14 q^{61}+ \cdots + 8 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 - 4 * q^7 - 2 * q^9 + 2 * q^13 + 4 * q^19 + 2 * q^21 + 12 * q^23 - 2 * q^25 + 4 * q^27 - 28 * q^31 + 12 * q^35 - 4 * q^37 - 4 * q^39 + 2 * q^43 - 12 * q^47 + 12 * q^55 - 2 * q^57 + 14 * q^61 + 2 * q^63 + 14 * q^67 - 24 * q^69 - 12 * q^71 + 14 * q^73 + 4 * q^75 + 24 * q^77 - 10 * q^79 - 2 * q^81 - 48 * q^83 - 24 * q^85 + 12 * q^89 - 2 * q^91 + 14 * q^93 + 36 * q^95 + 8 * q^97

Introduction

L-functions

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Database

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