LMFDB - Embedded newform 567.2.f.n.379.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(190,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.190"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-2,0,0,4,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.49787136.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			379.3
Root			$0.228425 - 1.39564i$ of defining polynomial
Character	$\chi$	$=$	567.379
Dual form			567.2.f.n.190.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.228425 - 0.395644i) q^{2} +(0.895644 + 1.55130i) q^{4} +(2.18890 + 3.79129i) q^{5} +(0.500000 - 0.866025i) q^{7} +1.73205 q^{8} +2.00000 q^{10} +(1.32288 - 2.29129i) q^{11} +(-2.00000 - 3.46410i) q^{13} +(-0.228425 - 0.395644i) q^{14} +(-1.39564 + 2.41733i) q^{16} +3.46410 q^{17} -3.58258 q^{19} +(-3.92095 + 6.79129i) q^{20} +(-0.604356 - 1.04678i) q^{22} +(1.73205 + 3.00000i) q^{23} +(-7.08258 + 12.2674i) q^{25} -1.82740 q^{26} +1.79129 q^{28} +(-0.913701 + 1.58258i) q^{29} +(-4.58258 - 7.93725i) q^{31} +(2.36965 + 4.10436i) q^{32} +(0.791288 - 1.37055i) q^{34} +4.37780 q^{35} +3.00000 q^{37} +(-0.818350 + 1.41742i) q^{38} +(3.79129 + 6.56670i) q^{40} +(-2.18890 - 3.79129i) q^{41} +(4.29129 - 7.43273i) q^{43} +4.73930 q^{44} +1.58258 q^{46} +(-1.37055 + 2.37386i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(3.23568 + 5.60436i) q^{50} +(3.58258 - 6.20520i) q^{52} -8.66025 q^{53} +11.5826 q^{55} +(0.866025 - 1.50000i) q^{56} +(0.417424 + 0.723000i) q^{58} +(-1.73205 - 3.00000i) q^{59} +(-1.20871 + 2.09355i) q^{61} -4.18710 q^{62} -3.41742 q^{64} +(8.75560 - 15.1652i) q^{65} +(0.291288 + 0.504525i) q^{67} +(3.10260 + 5.37386i) q^{68} +(1.00000 - 1.73205i) q^{70} +11.4014 q^{71} -3.16515 q^{73} +(0.685275 - 1.18693i) q^{74} +(-3.20871 - 5.55765i) q^{76} +(-1.32288 - 2.29129i) q^{77} +(4.29129 - 7.43273i) q^{79} -12.2197 q^{80} -2.00000 q^{82} +(-3.10260 + 5.37386i) q^{83} +(7.58258 + 13.1334i) q^{85} +(-1.96048 - 3.39564i) q^{86} +(2.29129 - 3.96863i) q^{88} +8.75560 q^{89} -4.00000 q^{91} +(-3.10260 + 5.37386i) q^{92} +(0.626136 + 1.08450i) q^{94} +(-7.84190 - 13.5826i) q^{95} +(-3.79129 + 6.56670i) q^{97} -0.456850 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} + 4 q^{7} + 16 q^{10} - 16 q^{13} - 2 q^{16} + 8 q^{19} - 14 q^{22} - 20 q^{25} - 4 q^{28} - 12 q^{34} + 24 q^{37} + 12 q^{40} + 16 q^{43} - 24 q^{46} - 4 q^{49} - 8 q^{52} + 56 q^{55} + 40 q^{58}+ \cdots - 12 q^{97}+O(q^{100}) $ 8 * q - 2 * q^4 + 4 * q^7 + 16 * q^10 - 16 * q^13 - 2 * q^16 + 8 * q^19 - 14 * q^22 - 20 * q^25 - 4 * q^28 - 12 * q^34 + 24 * q^37 + 12 * q^40 + 16 * q^43 - 24 * q^46 - 4 * q^49 - 8 * q^52 + 56 * q^55 + 40 * q^58 - 28 * q^61 - 64 * q^64 - 16 * q^67 + 8 * q^70 + 48 * q^73 - 44 * q^76 + 16 * q^79 - 16 * q^82 + 24 * q^85 - 32 * q^91 + 60 * q^94 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.228425	−	0.395644i	0.161521	−	0.279763i	−0.773893	−	0.633316i	$-0.781693\pi$
$2$	0.228425	−	0.395644i	0.161521	−	0.279763i	0.935414	+	0.353553i	$0.115027\pi$
$3$		0			0
$3$		0			0
$4$	0.895644	+	1.55130i	0.447822	+	0.775650i
$5$	2.18890	+	3.79129i	0.978906	+	1.69552i	0.666390	+	0.745603i	$0.267838\pi$
$5$	2.18890	+	3.79129i	0.978906	+	1.69552i	0.312516	+	0.949913i	$0.398828\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	1.73205			0.612372
$9$		0			0
$10$	2.00000			0.632456
$11$	1.32288	−	2.29129i	0.398862	−	0.690849i	−0.594724	−	0.803930i	$-0.702739\pi$
$11$	1.32288	−	2.29129i	0.398862	−	0.690849i	0.993586	+	0.113081i	$0.0360719\pi$
$12$		0			0
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	0.443227	−	0.896410i	$-0.353834\pi$
$14$	−0.228425	−	0.395644i	−0.0610492	−	0.105740i
$15$		0			0
$16$	−1.39564	+	2.41733i	−0.348911	+	0.604332i
$17$	3.46410			0.840168			0.420084	−	0.907485i	$-0.362001\pi$
$17$	3.46410			0.840168			0.420084	+	0.907485i	$0.362001\pi$
$18$		0			0
$19$	−3.58258			−0.821899			−0.410950	−	0.911658i	$-0.634803\pi$
$19$	−3.58258			−0.821899			−0.410950	+	0.911658i	$0.634803\pi$
$20$	−3.92095	+	6.79129i	−0.876751	+	1.51858i
$21$		0			0
$22$	−0.604356	−	1.04678i	−0.128849	−	0.223173i
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	0.988152	−	0.153481i	$-0.0490483\pi$
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	−0.626994	+	0.779024i	$0.715715\pi$
$24$		0			0
$25$	−7.08258	+	12.2674i	−1.41652	+	2.45348i
$26$	−1.82740			−0.358383
$27$		0			0
$28$	1.79129			0.338522
$29$	−0.913701	+	1.58258i	−0.169670	+	0.293877i	−0.938304	−	0.345812i	$-0.887603\pi$
$29$	−0.913701	+	1.58258i	−0.169670	+	0.293877i	0.768634	+	0.639689i	$0.220937\pi$
$30$		0			0
$31$	−4.58258	−	7.93725i	−0.823055	−	1.42557i	−0.903397	−	0.428806i	$-0.858935\pi$
$31$	−4.58258	−	7.93725i	−0.823055	−	1.42557i	0.0803419	−	0.996767i	$-0.474399\pi$
$32$	2.36965	+	4.10436i	0.418899	+	0.725555i
$33$		0			0
$34$	0.791288	−	1.37055i	0.135705	−	0.235048i
$35$	4.37780			0.739984
$36$		0			0
$37$	3.00000			0.493197			0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000			0.493197			0.246598	+	0.969118i	$0.420687\pi$
$38$	−0.818350	+	1.41742i	−0.132754	+	0.229937i
$39$		0			0
$40$	3.79129	+	6.56670i	0.599455	+	1.03829i
$41$	−2.18890	−	3.79129i	−0.341849	−	0.592100i	0.642927	−	0.765927i	$-0.277720\pi$
$41$	−2.18890	−	3.79129i	−0.341849	−	0.592100i	−0.984776	+	0.173828i	$0.944386\pi$
$42$		0			0
$43$	4.29129	−	7.43273i	0.654415	−	1.13348i	−0.327625	−	0.944808i	$-0.606248\pi$
$43$	4.29129	−	7.43273i	0.654415	−	1.13348i	0.982040	−	0.188673i	$-0.0604185\pi$
$44$	4.73930			0.714477
$45$		0			0
$46$	1.58258			0.233338
$47$	−1.37055	+	2.37386i	−0.199915	+	0.346264i	−0.948501	−	0.316775i	$-0.897400\pi$
$47$	−1.37055	+	2.37386i	−0.199915	+	0.346264i	0.748585	+	0.663038i	$0.230733\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	3.23568	+	5.60436i	0.457594	+	0.792576i
$51$		0			0
$52$	3.58258	−	6.20520i	0.496814	−	0.860507i
$53$	−8.66025			−1.18958			−0.594789	−	0.803882i	$-0.702764\pi$
$53$	−8.66025			−1.18958			−0.594789	+	0.803882i	$0.702764\pi$
$54$		0			0
$55$	11.5826			1.56179
$56$	0.866025	−	1.50000i	0.115728	−	0.200446i
$57$		0			0
$58$	0.417424	+	0.723000i	0.0548105	+	0.0949346i
$59$	−1.73205	−	3.00000i	−0.225494	−	0.390567i	0.730974	−	0.682406i	$-0.239066\pi$
$59$	−1.73205	−	3.00000i	−0.225494	−	0.390567i	−0.956467	+	0.291839i	$0.905733\pi$
$60$		0			0
$61$	−1.20871	+	2.09355i	−0.154760	+	0.268052i	−0.932972	−	0.359950i	$-0.882794\pi$
$61$	−1.20871	+	2.09355i	−0.154760	+	0.268052i	0.778212	+	0.628002i	$0.216127\pi$
$62$	−4.18710			−0.531762
$63$		0			0
$64$	−3.41742			−0.427178
$65$	8.75560	−	15.1652i	1.08600	−	1.88101i
$66$		0			0
$67$	0.291288	+	0.504525i	0.0355865	+	0.0616376i	0.883270	−	0.468865i	$-0.155337\pi$
$67$	0.291288	+	0.504525i	0.0355865	+	0.0616376i	−0.847684	+	0.530502i	$0.822003\pi$
$68$	3.10260	+	5.37386i	0.376246	+	0.651677i
$69$		0			0
$70$	1.00000	−	1.73205i	0.119523	−	0.207020i
$71$	11.4014			1.35309			0.676546	−	0.736400i	$-0.263476\pi$
$71$	11.4014			1.35309			0.676546	+	0.736400i	$0.263476\pi$
$72$		0			0
$73$	−3.16515			−0.370453			−0.185226	−	0.982696i	$-0.559302\pi$
$73$	−3.16515			−0.370453			−0.185226	+	0.982696i	$0.559302\pi$
$74$	0.685275	−	1.18693i	0.0796616	−	0.137978i
$75$		0			0
$76$	−3.20871	−	5.55765i	−0.368065	−	0.637506i
$77$	−1.32288	−	2.29129i	−0.150756	−	0.261116i
$78$		0			0
$79$	4.29129	−	7.43273i	0.482808	−	0.836247i	−0.516998	−	0.855987i	$-0.672950\pi$
$79$	4.29129	−	7.43273i	0.482808	−	0.836247i	0.999805	+	0.0197396i	$0.00628371\pi$
$80$	−12.2197			−1.36620
$81$		0			0
$82$	−2.00000			−0.220863
$83$	−3.10260	+	5.37386i	−0.340555	+	0.589858i	−0.984536	−	0.175183i	$-0.943948\pi$
$83$	−3.10260	+	5.37386i	−0.340555	+	0.589858i	0.643981	+	0.765041i	$0.277282\pi$
$84$		0			0
$85$	7.58258	+	13.1334i	0.822446	+	1.42452i
$86$	−1.96048	−	3.39564i	−0.211404	−	0.366162i
$87$		0			0
$88$	2.29129	−	3.96863i	0.244252	−	0.423057i
$89$	8.75560			0.928092			0.464046	−	0.885811i	$-0.346397\pi$
$89$	8.75560			0.928092			0.464046	+	0.885811i	$0.346397\pi$
$90$		0			0
$91$	−4.00000			−0.419314
$92$	−3.10260	+	5.37386i	−0.323469	+	0.560264i
$93$		0			0
$94$	0.626136	+	1.08450i	0.0645810	+	0.111858i
$95$	−7.84190	−	13.5826i	−0.804562	−	1.39354i
$96$		0			0
$97$	−3.79129	+	6.56670i	−0.384947	+	0.666748i	−0.991762	−	0.128096i	$-0.959114\pi$
$97$	−3.79129	+	6.56670i	−0.384947	+	0.666748i	0.606815	+	0.794843i	$0.292447\pi$
$98$	−0.456850			−0.0461488
$99$		0			0
$100$	−25.3739			−2.53739
$101$	0.913701	−	1.58258i	0.0909166	−	0.157472i	−0.816980	−	0.576665i	$-0.804354\pi$
$101$	0.913701	−	1.58258i	0.0909166	−	0.157472i	0.907897	+	0.419193i	$0.137687\pi$
$102$		0			0
$103$	−1.79129	−	3.10260i	−0.176501	−	0.305708i	0.764179	−	0.645004i	$-0.223144\pi$
$103$	−1.79129	−	3.10260i	−0.176501	−	0.305708i	−0.940680	+	0.339296i	$0.889811\pi$
$104$	−3.46410	−	6.00000i	−0.339683	−	0.588348i
$105$		0			0
$106$	−1.97822	+	3.42638i	−0.192142	+	0.332799i
$107$	11.2107			1.08377			0.541887	−	0.840451i	$-0.317710\pi$
$107$	11.2107			1.08377			0.541887	+	0.840451i	$0.317710\pi$
$108$		0			0
$109$	6.00000			0.574696			0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000			0.574696			0.287348	+	0.957826i	$0.407226\pi$
$110$	2.64575	−	4.58258i	0.252262	−	0.436931i
$111$		0			0
$112$	1.39564	+	2.41733i	0.131876	+	0.228416i
$113$	−6.97588	−	12.0826i	−0.656235	−	1.13663i	−0.981583	−	0.191038i	$-0.938814\pi$
$113$	−6.97588	−	12.0826i	−0.656235	−	1.13663i	0.325347	−	0.945595i	$-0.394519\pi$
$114$		0			0
$115$	−7.58258	+	13.1334i	−0.707079	+	1.22470i
$116$	−3.27340			−0.303928
$117$		0			0
$118$	−1.58258			−0.145688
$119$	1.73205	−	3.00000i	0.158777	−	0.275010i
$120$		0			0
$121$	2.00000	+	3.46410i	0.181818	+	0.314918i
$122$	0.552200	+	0.956439i	0.0499939	+	0.0865919i
$123$		0			0
$124$	8.20871	−	14.2179i	0.737164	−	1.27681i
$125$	−40.1232			−3.58873
$126$		0			0
$127$	−7.41742			−0.658190			−0.329095	−	0.944297i	$-0.606744\pi$
$127$	−7.41742			−0.658190			−0.329095	+	0.944297i	$0.606744\pi$
$128$	−5.51993	+	9.56080i	−0.487897	+	0.845063i
$129$		0			0
$130$	−4.00000	−	6.92820i	−0.350823	−	0.607644i
$131$	−9.21245	−	15.9564i	−0.804896	−	1.39412i	−0.916361	−	0.400352i	$-0.868888\pi$
$131$	−9.21245	−	15.9564i	−0.804896	−	1.39412i	0.111465	−	0.993768i	$-0.464446\pi$
$132$		0			0
$133$	−1.79129	+	3.10260i	−0.155324	+	0.269030i
$134$	0.266150			0.0229918
$135$		0			0
$136$	6.00000			0.514496
$137$	−8.80328	+	15.2477i	−0.752115	+	1.30270i	0.194681	+	0.980867i	$0.437633\pi$
$137$	−8.80328	+	15.2477i	−0.752115	+	1.30270i	−0.946796	+	0.321835i	$0.895700\pi$
$138$		0			0
$139$	3.79129	+	6.56670i	0.321573	+	0.556980i	0.980813	−	0.194952i	$-0.0624552\pi$
$139$	3.79129	+	6.56670i	0.321573	+	0.556980i	−0.659240	+	0.751933i	$0.729122\pi$
$140$	3.92095	+	6.79129i	0.331381	+	0.573969i
$141$		0			0
$142$	2.60436	−	4.51088i	0.218553	−	0.378544i
$143$	−10.5830			−0.884995
$144$		0			0
$145$	−8.00000			−0.664364
$146$	−0.723000	+	1.25227i	−0.0598359	+	0.103639i
$147$		0			0
$148$	2.68693	+	4.65390i	0.220864	+	0.382548i
$149$	5.33918	+	9.24773i	0.437402	+	0.757603i	0.997488	−	0.0708313i	$-0.0225652\pi$
$149$	5.33918	+	9.24773i	0.437402	+	0.757603i	−0.560086	+	0.828435i	$0.689232\pi$
$150$		0			0
$151$	10.2913	−	17.8250i	0.837493	−	1.45058i	−0.0544912	−	0.998514i	$-0.517354\pi$
$151$	10.2913	−	17.8250i	0.837493	−	1.45058i	0.891984	−	0.452066i	$-0.149313\pi$
$152$	−6.20520			−0.503308
$153$		0			0
$154$	−1.20871			−0.0974008
$155$	20.0616	−	34.7477i	1.61139	−	2.79100i
$156$		0			0
$157$	−0.417424	−	0.723000i	−0.0333141	−	0.0577017i	0.848888	−	0.528573i	$-0.177273\pi$
$157$	−0.417424	−	0.723000i	−0.0333141	−	0.0577017i	−0.882202	+	0.470872i	$0.843939\pi$
$158$	−1.96048	−	3.39564i	−0.155967	−	0.270143i
$159$		0			0
$160$	−10.3739	+	17.9681i	−0.820126	+	1.42050i
$161$	3.46410			0.273009
$162$		0			0
$163$	14.5826			1.14220			0.571098	−	0.820882i	$-0.306518\pi$
$163$	14.5826			1.14220			0.571098	+	0.820882i	$0.306518\pi$
$164$	3.92095	−	6.79129i	0.306175	−	0.530310i
$165$		0			0
$166$	1.41742	+	2.45505i	0.110013	+	0.190549i
$167$	−1.27520	−	2.20871i	−0.0986780	−	0.170915i	0.812460	−	0.583017i	$-0.198128\pi$
$167$	−1.27520	−	2.20871i	−0.0986780	−	0.170915i	−0.911138	+	0.412102i	$0.864795\pi$
$168$		0			0
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$	6.92820			0.531369
$171$		0			0
$172$	15.3739			1.17225
$173$	5.74835	−	9.95644i	0.437039	−	0.756974i	−0.560420	−	0.828208i	$-0.689360\pi$
$173$	5.74835	−	9.95644i	0.437039	−	0.756974i	0.997460	+	0.0712342i	$0.0226938\pi$
$174$		0			0
$175$	7.08258	+	12.2674i	0.535392	+	0.927327i
$176$	3.69253	+	6.39564i	0.278335	+	0.482090i
$177$		0			0
$178$	2.00000	−	3.46410i	0.149906	−	0.259645i
$179$	1.63670			0.122333			0.0611664	−	0.998128i	$-0.480518\pi$
$179$	1.63670			0.122333			0.0611664	+	0.998128i	$0.480518\pi$
$180$		0			0
$181$	13.1652			0.978558			0.489279	−	0.872127i	$-0.337260\pi$
$181$	13.1652			0.978558			0.489279	+	0.872127i	$0.337260\pi$
$182$	−0.913701	+	1.58258i	−0.0677280	+	0.117308i
$183$		0			0
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$	6.56670	+	11.3739i	0.482794	+	0.836223i
$186$		0			0
$187$	4.58258	−	7.93725i	0.335111	−	0.580429i
$188$	−4.91010			−0.358106
$189$		0			0
$190$	−7.16515			−0.519815
$191$	3.05493	−	5.29129i	0.221047	−	0.382864i	−0.734079	−	0.679064i	$-0.762386\pi$
$191$	3.05493	−	5.29129i	0.221047	−	0.382864i	0.955126	+	0.296200i	$0.0957193\pi$
$192$		0			0
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$	1.73205	+	3.00000i	0.124354	+	0.215387i
$195$		0			0
$196$	0.895644	−	1.55130i	0.0639746	−	0.110807i
$197$	0.0953502			0.00679342			0.00339671	−	0.999994i	$-0.498919\pi$
$197$	0.0953502			0.00679342			0.00339671	+	0.999994i	$0.498919\pi$
$198$		0			0
$199$	−16.7477			−1.18721			−0.593607	−	0.804755i	$-0.702297\pi$
$199$	−16.7477			−1.18721			−0.593607	+	0.804755i	$0.702297\pi$
$200$	−12.2674	+	21.2477i	−0.867435	+	1.50244i
$201$		0			0
$202$	−0.417424	−	0.723000i	−0.0293699	−	0.0508701i
$203$	0.913701	+	1.58258i	0.0641292	+	0.111075i
$204$		0			0
$205$	9.58258	−	16.5975i	0.669276	−	1.15922i
$206$	−1.63670			−0.114034
$207$		0			0
$208$	11.1652			0.774164
$209$	−4.73930	+	8.20871i	−0.327824	+	0.567808i
$210$		0			0
$211$	−5.87386	−	10.1738i	−0.404373	−	0.700395i	0.589875	−	0.807495i	$-0.299177\pi$
$211$	−5.87386	−	10.1738i	−0.404373	−	0.700395i	−0.994248	+	0.107099i	$0.965844\pi$
$212$	−7.75650	−	13.4347i	−0.532719	−	0.922696i
$213$		0			0
$214$	2.56080	−	4.43543i	0.175052	−	0.303200i
$215$	37.5728			2.56244
$216$		0			0
$217$	−9.16515			−0.622171
$218$	1.37055	−	2.37386i	0.0928254	−	0.160778i
$219$		0			0
$220$	10.3739	+	17.9681i	0.699406	+	1.21141i
$221$	−6.92820	−	12.0000i	−0.466041	−	0.807207i
$222$		0			0
$223$	−11.0000	+	19.0526i	−0.736614	+	1.27585i	0.217397	+	0.976083i	$0.430243\pi$
$223$	−11.0000	+	19.0526i	−0.736614	+	1.27585i	−0.954011	+	0.299770i	$0.903090\pi$
$224$	4.73930			0.316658
$225$		0			0
$226$	−6.37386			−0.423983
$227$	−6.56670	+	11.3739i	−0.435847	+	0.754910i	−0.997364	−	0.0725554i	$-0.976885\pi$
$227$	−6.56670	+	11.3739i	−0.435847	+	0.754910i	0.561517	+	0.827465i	$0.310218\pi$
$228$		0			0
$229$	−10.9564	−	18.9771i	−0.724022	−	1.25404i	−0.959375	−	0.282133i	$-0.908958\pi$
$229$	−10.9564	−	18.9771i	−0.724022	−	1.25404i	0.235353	−	0.971910i	$-0.424375\pi$
$230$	3.46410	+	6.00000i	0.228416	+	0.395628i
$231$		0			0
$232$	−1.58258	+	2.74110i	−0.103901	+	0.179962i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$	−12.0000			−0.782794
$236$	3.10260	−	5.37386i	0.201962	−	0.349809i
$237$		0			0
$238$	−0.791288	−	1.37055i	−0.0512916	−	0.0888396i
$239$	12.6289	+	21.8739i	0.816894	+	1.41490i	0.907960	+	0.419058i	$0.137639\pi$
$239$	12.6289	+	21.8739i	0.816894	+	1.41490i	−0.0910652	+	0.995845i	$0.529027\pi$
$240$		0			0
$241$	−9.20871	+	15.9500i	−0.593185	+	1.02743i	0.400615	+	0.916247i	$0.368797\pi$
$241$	−9.20871	+	15.9500i	−0.593185	+	1.02743i	−0.993800	+	0.111181i	$0.964537\pi$
$242$	1.82740			0.117470
$243$		0			0
$244$	−4.33030			−0.277219
$245$	2.18890	−	3.79129i	0.139844	−	0.242216i
$246$		0			0
$247$	7.16515	+	12.4104i	0.455908	+	0.789655i
$248$	−7.93725	−	13.7477i	−0.504016	−	0.872982i
$249$		0			0
$250$	−9.16515	+	15.8745i	−0.579655	+	1.00399i
$251$	−7.84190			−0.494977			−0.247488	−	0.968891i	$-0.579605\pi$
$251$	−7.84190			−0.494977			−0.247488	+	0.968891i	$0.579605\pi$
$252$		0			0
$253$	9.16515			0.576208
$254$	−1.69433	+	2.93466i	−0.106311	+	0.184137i
$255$		0			0
$256$	−0.895644	−	1.55130i	−0.0559777	−	0.0969563i
$257$	5.10080	+	8.83485i	0.318179	+	0.551103i	0.980108	−	0.198464i	$-0.0635953\pi$
$257$	5.10080	+	8.83485i	0.318179	+	0.551103i	−0.661929	+	0.749567i	$0.730262\pi$
$258$		0			0
$259$	1.50000	−	2.59808i	0.0932055	−	0.161437i
$260$	31.3676			1.94534
$261$		0			0
$262$	−8.41742			−0.520030
$263$	−2.14123	+	3.70871i	−0.132034	+	0.228689i	−0.924460	−	0.381278i	$-0.875484\pi$
$263$	−2.14123	+	3.70871i	−0.132034	+	0.228689i	0.792427	+	0.609967i	$0.208817\pi$
$264$		0			0
$265$	−18.9564	−	32.8335i	−1.16448	−	2.01695i
$266$	0.818350	+	1.41742i	0.0501763	+	0.0869079i
$267$		0			0
$268$	−0.521780	+	0.903750i	−0.0318728	+	0.0552053i
$269$	6.92820			0.422420			0.211210	−	0.977441i	$-0.432260\pi$
$269$	6.92820			0.422420			0.211210	+	0.977441i	$0.432260\pi$
$270$		0			0
$271$	8.74773			0.531387			0.265693	−	0.964058i	$-0.414399\pi$
$271$	8.74773			0.531387			0.265693	+	0.964058i	$0.414399\pi$
$272$	−4.83465	+	8.37386i	−0.293144	+	0.507740i
$273$		0			0
$274$	4.02178	+	6.96593i	0.242965	+	0.420827i
$275$	18.7387	+	32.4564i	1.12999	+	1.95720i
$276$		0			0
$277$	−3.50000	+	6.06218i	−0.210295	+	0.364241i	−0.951807	−	0.306699i	$-0.900776\pi$
$277$	−3.50000	+	6.06218i	−0.210295	+	0.364241i	0.741512	+	0.670940i	$0.234109\pi$
$278$	3.46410			0.207763
$279$		0			0
$280$	7.58258			0.453146
$281$	−14.8178	+	25.6652i	−0.883955	+	1.53105i	−0.0370478	+	0.999313i	$0.511795\pi$
$281$	−14.8178	+	25.6652i	−0.883955	+	1.53105i	−0.846907	+	0.531741i	$0.821538\pi$
$282$		0			0
$283$	−8.79129	−	15.2270i	−0.522588	−	0.905149i	−0.999655	−	0.0262816i	$-0.991633\pi$
$283$	−8.79129	−	15.2270i	−0.522588	−	0.905149i	0.477067	−	0.878867i	$-0.341700\pi$
$284$	10.2116	+	17.6869i	0.605944	+	1.04953i
$285$		0			0
$286$	−2.41742	+	4.18710i	−0.142945	+	0.247589i
$287$	−4.37780			−0.258413
$288$		0			0
$289$	−5.00000			−0.294118
$290$	−1.82740	+	3.16515i	−0.107309	+	0.185864i
$291$		0			0
$292$	−2.83485	−	4.91010i	−0.165897	−	0.287342i
$293$	−10.8492	−	18.7913i	−0.633814	−	1.09780i	−0.986765	−	0.162157i	$-0.948155\pi$
$293$	−10.8492	−	18.7913i	−0.633814	−	1.09780i	0.352951	−	0.935642i	$-0.385178\pi$
$294$		0			0
$295$	7.58258	−	13.1334i	0.441475	−	0.764656i
$296$	5.19615			0.302020
$297$		0			0
$298$	4.87841			0.282599
$299$	6.92820	−	12.0000i	0.400668	−	0.693978i
$300$		0			0
$301$	−4.29129	−	7.43273i	−0.247346	−	0.428415i
$302$	−4.70158	−	8.14337i	−0.270545	−	0.468598i
$303$		0			0
$304$	5.00000	−	8.66025i	0.286770	−	0.496700i
$305$	−10.5830			−0.605981
$306$		0			0
$307$	16.3303			0.932020			0.466010	−	0.884780i	$-0.345691\pi$
$307$	16.3303			0.932020			0.466010	+	0.884780i	$0.345691\pi$
$308$	2.36965	−	4.10436i	0.135023	−	0.233867i
$309$		0			0
$310$	−9.16515	−	15.8745i	−0.520546	−	0.901611i
$311$	9.02175	+	15.6261i	0.511577	+	0.886077i	0.999910	+	0.0134197i	$0.00427174\pi$
$311$	9.02175	+	15.6261i	0.511577	+	0.886077i	−0.488333	+	0.872657i	$0.662395\pi$
$312$		0			0
$313$	0.582576	−	1.00905i	0.0329291	−	0.0570349i	−0.849091	−	0.528246i	$-0.822850\pi$
$313$	0.582576	−	1.00905i	0.0329291	−	0.0570349i	0.882020	+	0.471211i	$0.156183\pi$
$314$	−0.381401			−0.0215237
$315$		0			0
$316$	15.3739			0.864847
$317$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$317$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$318$		0			0
$319$	2.41742	+	4.18710i	0.135350	+	0.234433i
$320$	−7.48040	−	12.9564i	−0.418167	−	0.724287i
$321$		0			0
$322$	0.791288	−	1.37055i	0.0440967	−	0.0763778i
$323$	−12.4104			−0.690533
$324$		0			0
$325$	56.6606			3.14296
$326$	3.33103	−	5.76951i	0.184489	−	0.319543i
$327$		0			0
$328$	−3.79129	−	6.56670i	−0.209339	−	0.362586i
$329$	1.37055	+	2.37386i	0.0755609	+	0.130875i
$330$		0			0
$331$	−7.16515	+	12.4104i	−0.393832	+	0.682138i	−0.992951	−	0.118522i	$-0.962184\pi$
$331$	−7.16515	+	12.4104i	−0.393832	+	0.682138i	0.599119	+	0.800660i	$0.295518\pi$
$332$	−11.1153			−0.610032
$333$		0			0
$334$	−1.16515			−0.0637542
$335$	−1.27520	+	2.20871i	−0.0696716	+	0.120675i
$336$		0			0
$337$	10.0826	+	17.4635i	0.549233	+	0.951299i	0.998327	+	0.0578150i	$0.0184133\pi$
$337$	10.0826	+	17.4635i	0.549233	+	0.951299i	−0.449094	+	0.893484i	$0.648253\pi$
$338$	0.685275	+	1.18693i	0.0372741	+	0.0645606i
$339$		0			0
$340$	−13.5826	+	23.5257i	−0.736619	+	1.27586i
$341$	−24.2487			−1.31314
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	7.43273	−	12.8739i	0.400746	−	0.694112i
$345$		0			0
$346$	−2.62614	−	4.54860i	−0.141182	−	0.244534i
$347$	18.0157	+	31.2042i	0.967135	+	1.67513i	0.703765	+	0.710432i	$0.251501\pi$
$347$	18.0157	+	31.2042i	0.967135	+	1.67513i	0.263370	+	0.964695i	$0.415166\pi$
$348$		0			0
$349$	12.3739	−	21.4322i	0.662358	−	1.14724i	−0.317637	−	0.948212i	$-0.602889\pi$
$349$	12.3739	−	21.4322i	0.662358	−	1.14724i	0.979994	−	0.199025i	$-0.0637774\pi$
$350$	6.47135			0.345908
$351$		0			0
$352$	12.5390			0.668332
$353$	−17.8727	+	30.9564i	−0.951268	+	1.64765i	−0.208583	+	0.978005i	$0.566885\pi$
$353$	−17.8727	+	30.9564i	−0.951268	+	1.64765i	−0.742686	+	0.669640i	$0.766448\pi$
$354$		0			0
$355$	24.9564	+	43.2258i	1.32455	+	2.29419i
$356$	7.84190	+	13.5826i	0.415620	+	0.719875i
$357$		0			0
$358$	0.373864	−	0.647551i	0.0197593	−	0.0342241i
$359$	30.3586			1.60226			0.801132	−	0.598488i	$-0.204232\pi$
$359$	30.3586			1.60226			0.801132	+	0.598488i	$0.204232\pi$
$360$		0			0
$361$	−6.16515			−0.324482
$362$	3.00725	−	5.20871i	0.158058	−	0.273764i
$363$		0			0
$364$	−3.58258	−	6.20520i	−0.187778	−	0.325241i
$365$	−6.92820	−	12.0000i	−0.362639	−	0.628109i
$366$		0			0
$367$	4.41742	−	7.65120i	0.230588	−	0.399390i	−0.727394	−	0.686221i	$-0.759268\pi$
$367$	4.41742	−	7.65120i	0.230588	−	0.399390i	0.957981	+	0.286831i	$0.0926018\pi$
$368$	−9.66930			−0.504047
$369$		0			0
$370$	6.00000			0.311925
$371$	−4.33013	+	7.50000i	−0.224809	+	0.389381i
$372$		0			0
$373$	3.66515	+	6.34823i	0.189774	+	0.328699i	0.945175	−	0.326564i	$-0.105891\pi$
$373$	3.66515	+	6.34823i	0.189774	+	0.328699i	−0.755401	+	0.655263i	$0.772558\pi$
$374$	−2.09355	−	3.62614i	−0.108255	−	0.187503i
$375$		0			0
$376$	−2.37386	+	4.11165i	−0.122423	+	0.212042i
$377$	7.30960			0.376464
$378$		0			0
$379$	−28.9129			−1.48515			−0.742577	−	0.669760i	$-0.766397\pi$
$379$	−28.9129			−1.48515			−0.742577	+	0.669760i	$0.766397\pi$
$380$	14.0471	−	24.3303i	0.720601	−	1.24812i
$381$		0			0
$382$	−1.39564	−	2.41733i	−0.0714074	−	0.123681i
$383$	9.66930	+	16.7477i	0.494078	+	0.855769i	0.999977	−	0.00682424i	$-0.00217224\pi$
$383$	9.66930	+	16.7477i	0.494078	+	0.855769i	−0.505898	+	0.862593i	$0.668839\pi$
$384$		0			0
$385$	5.79129	−	10.0308i	0.295151	−	0.511217i
$386$	−6.39590			−0.325543
$387$		0			0
$388$	−13.5826			−0.689551
$389$	15.8745	−	27.4955i	0.804869	−	1.39407i	−0.111510	−	0.993763i	$-0.535569\pi$
$389$	15.8745	−	27.4955i	0.804869	−	1.39407i	0.916379	−	0.400312i	$-0.131098\pi$
$390$		0			0
$391$	6.00000	+	10.3923i	0.303433	+	0.525561i
$392$	−0.866025	−	1.50000i	−0.0437409	−	0.0757614i
$393$		0			0
$394$	0.0217804	−	0.0377247i	0.00109728	−	0.00190054i
$395$	37.5728			1.89049
$396$		0			0
$397$	−1.58258			−0.0794272			−0.0397136	−	0.999211i	$-0.512645\pi$
$397$	−1.58258			−0.0794272			−0.0397136	+	0.999211i	$0.512645\pi$
$398$	−3.82560	+	6.62614i	−0.191760	+	0.332138i
$399$		0			0
$400$	−19.7695	−	34.2418i	−0.988475	−	1.71209i
$401$	−7.07123	−	12.2477i	−0.353120	−	0.611622i	0.633674	−	0.773600i	$-0.281546\pi$
$401$	−7.07123	−	12.2477i	−0.353120	−	0.611622i	−0.986794	+	0.161978i	$0.948213\pi$
$402$		0			0
$403$	−18.3303	+	31.7490i	−0.913097	+	1.58153i
$404$	3.27340			0.162858
$405$		0			0
$406$	0.834849			0.0414328
$407$	3.96863	−	6.87386i	0.196718	−	0.340725i
$408$		0			0
$409$	−4.62614	−	8.01270i	−0.228748	−	0.396203i	0.728690	−	0.684844i	$-0.240130\pi$
$409$	−4.62614	−	8.01270i	−0.228748	−	0.396203i	−0.957437	+	0.288642i	$0.906796\pi$
$410$	−4.37780	−	7.58258i	−0.216204	−	0.374477i
$411$		0			0
$412$	3.20871	−	5.55765i	0.158082	−	0.273806i
$413$	−3.46410			−0.170457
$414$		0			0
$415$	−27.1652			−1.33348
$416$	9.47860	−	16.4174i	0.464727	−	0.804930i
$417$		0			0
$418$	2.16515	+	3.75015i	0.105901	+	0.183426i
$419$	−9.30780	−	16.1216i	−0.454716	−	0.787591i	0.543956	−	0.839114i	$-0.316926\pi$
$419$	−9.30780	−	16.1216i	−0.454716	−	0.787591i	−0.998672	+	0.0515226i	$0.983593\pi$
$420$		0			0
$421$	8.08258	−	13.9994i	0.393921	−	0.682291i	−0.599042	−	0.800718i	$-0.704452\pi$
$421$	8.08258	−	13.9994i	0.393921	−	0.682291i	0.992963	+	0.118427i	$0.0377851\pi$
$422$	−5.36695			−0.261259
$423$		0			0
$424$	−15.0000			−0.728464
$425$	−24.5348	+	42.4955i	−1.19011	+	2.06133i
$426$		0			0
$427$	1.20871	+	2.09355i	0.0584937	+	0.101314i
$428$	10.0408	+	17.3911i	0.485338	+	0.840630i
$429$		0			0
$430$	8.58258	−	14.8655i	0.413889	−	0.716876i
$431$	−36.6591			−1.76581			−0.882904	−	0.469554i	$-0.844415\pi$
$431$	−36.6591			−1.76581			−0.882904	+	0.469554i	$0.844415\pi$
$432$		0			0
$433$	−21.9129			−1.05307			−0.526533	−	0.850155i	$-0.676508\pi$
$433$	−21.9129			−1.05307			−0.526533	+	0.850155i	$0.676508\pi$
$434$	−2.09355	+	3.62614i	−0.100494	+	0.174060i
$435$		0			0
$436$	5.37386	+	9.30780i	0.257361	+	0.445763i
$437$	−6.20520	−	10.7477i	−0.296835	−	0.514134i
$438$		0			0
$439$	−12.7913	+	22.1552i	−0.610495	+	1.05741i	0.380662	+	0.924714i	$0.375696\pi$
$439$	−12.7913	+	22.1552i	−0.610495	+	1.05741i	−0.991157	+	0.132694i	$0.957637\pi$
$440$	20.0616			0.956400
$441$		0			0
$442$	−6.33030			−0.301102
$443$	−8.66025	+	15.0000i	−0.411461	+	0.712672i	−0.995050	−	0.0993779i	$-0.968315\pi$
$443$	−8.66025	+	15.0000i	−0.411461	+	0.712672i	0.583589	+	0.812049i	$0.301648\pi$
$444$		0			0
$445$	19.1652	+	33.1950i	0.908515	+	1.57359i
$446$	5.02535	+	8.70417i	0.237957	+	0.412154i
$447$		0			0
$448$	−1.70871	+	2.95958i	−0.0807291	+	0.139827i
$449$	26.5529			1.25311			0.626554	−	0.779378i	$-0.284465\pi$
$449$	26.5529			1.25311			0.626554	+	0.779378i	$0.284465\pi$
$450$		0			0
$451$	−11.5826			−0.545402
$452$	12.4958	−	21.6434i	0.587753	−	1.01802i
$453$		0			0
$454$	3.00000	+	5.19615i	0.140797	+	0.243868i
$455$	−8.75560	−	15.1652i	−0.410469	−	0.710953i
$456$		0			0
$457$	−15.6652	+	27.1328i	−0.732785	+	1.26922i	0.222904	+	0.974841i	$0.428447\pi$
$457$	−15.6652	+	27.1328i	−0.732785	+	1.26922i	−0.955688	+	0.294380i	$0.904887\pi$
$458$	−10.0109			−0.467779
$459$		0			0
$460$	−27.1652			−1.26658
$461$	−6.66205	+	11.5390i	−0.310283	+	0.537426i	−0.978424	−	0.206609i	$-0.933757\pi$
$461$	−6.66205	+	11.5390i	−0.310283	+	0.537426i	0.668141	+	0.744035i	$0.267090\pi$
$462$		0			0
$463$	−10.4564	−	18.1111i	−0.485952	−	0.841693i	0.513918	−	0.857839i	$-0.328194\pi$
$463$	−10.4564	−	18.1111i	−0.485952	−	0.841693i	−0.999870	+	0.0161460i	$0.994860\pi$
$464$	−2.55040	−	4.41742i	−0.118399	−	0.205074i
$465$		0			0
$466$		0			0
$467$	−6.20520			−0.287143			−0.143571	−	0.989640i	$-0.545859\pi$
$467$	−6.20520			−0.287143			−0.143571	+	0.989640i	$0.545859\pi$
$468$		0			0
$469$	0.582576			0.0269008
$470$	−2.74110	+	4.74773i	−0.126438	+	0.218996i
$471$		0			0
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	−11.3537	−	19.6652i	−0.522043	−	0.904205i
$474$		0			0
$475$	25.3739	−	43.9488i	1.16423	−	2.01651i
$476$	6.20520			0.284415
$477$		0			0
$478$	11.5390			0.527782
$479$	12.3151	−	21.3303i	0.562689	−	0.974606i	−0.434571	−	0.900637i	$-0.643100\pi$
$479$	12.3151	−	21.3303i	0.562689	−	0.974606i	0.997261	−	0.0739690i	$-0.0235666\pi$
$480$		0			0
$481$	−6.00000	−	10.3923i	−0.273576	−	0.473848i
$482$	4.20700	+	7.28674i	0.191624	+	0.331902i
$483$		0			0
$484$	−3.58258	+	6.20520i	−0.162844	+	0.282055i
$485$	−33.1950			−1.50731
$486$		0			0
$487$	−6.58258			−0.298285			−0.149142	−	0.988816i	$-0.547651\pi$
$487$	−6.58258			−0.298285			−0.149142	+	0.988816i	$0.547651\pi$
$488$	−2.09355	+	3.62614i	−0.0947706	+	0.164147i
$489$		0			0
$490$	−1.00000	−	1.73205i	−0.0451754	−	0.0782461i
$491$	−11.2107	−	19.4174i	−0.505930	−	0.876296i	−0.999976	−	0.00686071i	$-0.997816\pi$
$491$	−11.2107	−	19.4174i	−0.505930	−	0.876296i	0.494047	−	0.869435i	$-0.335517\pi$
$492$		0			0
$493$	−3.16515	+	5.48220i	−0.142551	+	0.246906i
$494$	6.54680			0.294555
$495$		0			0
$496$	25.5826			1.14869
$497$	5.70068	−	9.87386i	0.255710	−	0.442903i
$498$		0			0
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	0.998233	−	0.0594153i	$-0.0189236\pi$
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	−0.550572	+	0.834788i	$0.685590\pi$
$500$	−35.9361	−	62.2432i	−1.60711	−	2.78360i
$501$		0			0
$502$	−1.79129	+	3.10260i	−0.0799491	+	0.138476i
$503$	−5.48220			−0.244439			−0.122220	−	0.992503i	$-0.539001\pi$
$503$	−5.48220			−0.244439			−0.122220	+	0.992503i	$0.539001\pi$
$504$		0			0
$505$	8.00000			0.355995
$506$	2.09355	−	3.62614i	0.0930697	−	0.161201i
$507$		0			0
$508$	−6.64337	−	11.5067i	−0.294752	−	0.510525i
$509$	9.57395	+	16.5826i	0.424358	+	0.735010i	0.996360	−	0.0852424i	$-0.0271665\pi$
$509$	9.57395	+	16.5826i	0.424358	+	0.735010i	−0.572002	+	0.820252i	$0.693833\pi$
$510$		0			0
$511$	−1.58258	+	2.74110i	−0.0700090	+	0.121259i
$512$	−22.8981			−1.01196
$513$		0			0
$514$	4.66061			0.205570
$515$	7.84190	−	13.5826i	0.345556	−	0.598520i
$516$		0			0
$517$	3.62614	+	6.28065i	0.159477	+	0.276223i
$518$	−0.685275	−	1.18693i	−0.0301093	−	0.0521508i
$519$		0			0
$520$	15.1652	−	26.2668i	0.665036	−	1.15188i
$521$	3.46410			0.151765			0.0758825	−	0.997117i	$-0.475823\pi$
$521$	3.46410			0.151765			0.0758825	+	0.997117i	$0.475823\pi$
$522$		0			0
$523$	−6.41742			−0.280614			−0.140307	−	0.990108i	$-0.544809\pi$
$523$	−6.41742			−0.280614			−0.140307	+	0.990108i	$0.544809\pi$
$524$	16.5022	−	28.5826i	0.720900	−	1.24864i
$525$		0			0
$526$	0.978220	+	1.69433i	0.0426524	+	0.0738761i
$527$	−15.8745	−	27.4955i	−0.691504	−	1.19772i
$528$		0			0
$529$	5.50000	−	9.52628i	0.239130	−	0.414186i
$530$	−17.3205			−0.752355
$531$		0			0
$532$	−6.41742			−0.278231
$533$	−8.75560	+	15.1652i	−0.379247	+	0.656876i
$534$		0			0
$535$	24.5390	+	42.5028i	1.06091	+	1.83756i
$536$	0.504525	+	0.873864i	0.0217922	+	0.0377452i
$537$		0			0
$538$	1.58258	−	2.74110i	0.0682297	−	0.118177i
$539$	−2.64575			−0.113961
$540$		0			0
$541$	11.0000			0.472927			0.236463	−	0.971640i	$-0.424012\pi$
$541$	11.0000			0.472927			0.236463	+	0.971640i	$0.424012\pi$
$542$	1.99820	−	3.46099i	0.0858301	−	0.148662i
$543$		0			0
$544$	8.20871	+	14.2179i	0.351946	+	0.609588i
$545$	13.1334	+	22.7477i	0.562573	+	0.974406i
$546$		0			0
$547$	6.45644	−	11.1829i	0.276057	−	0.478145i	−0.694344	−	0.719643i	$-0.744305\pi$
$547$	6.45644	−	11.1829i	0.276057	−	0.478145i	0.970401	+	0.241498i	$0.0776387\pi$
$548$	−31.5384			−1.34725
$549$		0			0
$550$	17.1216			0.730067
$551$	3.27340	−	5.66970i	0.139452	−	0.241537i
$552$		0			0
$553$	−4.29129	−	7.43273i	−0.182484	−	0.316072i
$554$	1.59898	+	2.76951i	0.0679340	+	0.117665i
$555$		0			0
$556$	−6.79129	+	11.7629i	−0.288015	+	0.498856i
$557$	12.5058			0.529886			0.264943	−	0.964264i	$-0.414647\pi$
$557$	12.5058			0.529886			0.264943	+	0.964264i	$0.414647\pi$
$558$		0			0
$559$	−34.3303			−1.45202
$560$	−6.10985	+	10.5826i	−0.258188	+	0.447195i
$561$		0			0
$562$	6.76951	+	11.7251i	0.285554	+	0.494595i
$563$	20.8800	+	36.1652i	0.879985	+	1.52418i	0.851355	+	0.524589i	$0.175781\pi$
$563$	20.8800	+	36.1652i	0.879985	+	1.52418i	0.0286300	+	0.999590i	$0.490886\pi$
$564$		0			0
$565$	30.5390	−	52.8951i	1.28479	−	2.22531i
$566$	−8.03260			−0.337636
$567$		0			0
$568$	19.7477			0.828596
$569$	−5.96683	+	10.3348i	−0.250142	+	0.433259i	−0.963565	−	0.267475i	$-0.913811\pi$
$569$	−5.96683	+	10.3348i	−0.250142	+	0.433259i	0.713422	+	0.700734i	$0.247144\pi$
$570$		0			0
$571$	0.417424	+	0.723000i	0.0174687	+	0.0302566i	0.874628	−	0.484795i	$-0.161106\pi$
$571$	0.417424	+	0.723000i	0.0174687	+	0.0302566i	−0.857159	+	0.515052i	$0.827773\pi$
$572$	−9.47860	−	16.4174i	−0.396320	−	0.686447i
$573$		0			0
$574$	−1.00000	+	1.73205i	−0.0417392	+	0.0722944i
$575$	−49.0695			−2.04634
$576$		0			0
$577$	32.7477			1.36331			0.681653	−	0.731676i	$-0.261261\pi$
$577$	32.7477			1.36331			0.681653	+	0.731676i	$0.261261\pi$
$578$	−1.14213	+	1.97822i	−0.0475062	+	0.0822831i
$579$		0			0
$580$	−7.16515	−	12.4104i	−0.297517	−	0.515314i
$581$	3.10260	+	5.37386i	0.128718	+	0.222945i
$582$		0			0
$583$	−11.4564	+	19.8431i	−0.474477	+	0.821819i
$584$	−5.48220			−0.226855
$585$		0			0
$586$	−9.91288			−0.409497
$587$	4.28245	−	7.41742i	0.176756	−	0.306150i	−0.764012	−	0.645202i	$-0.776773\pi$
$587$	4.28245	−	7.41742i	0.176756	−	0.306150i	0.940767	+	0.339052i	$0.110106\pi$
$588$		0			0
$589$	16.4174	+	28.4358i	0.676468	+	1.17168i
$590$	−3.46410	−	6.00000i	−0.142615	−	0.247016i
$591$		0			0
$592$	−4.18693	+	7.25198i	−0.172082	+	0.298054i
$593$	−43.5873			−1.78992			−0.894958	−	0.446150i	$-0.852795\pi$
$593$	−43.5873			−1.78992			−0.894958	+	0.446150i	$0.852795\pi$
$594$		0			0
$595$	15.1652			0.621711
$596$	−9.56400	+	16.5653i	−0.391757	+	0.678543i
$597$		0			0
$598$	−3.16515	−	5.48220i	−0.129433	−	0.224184i
$599$	−2.23658	−	3.87386i	−0.0913840	−	0.158282i	0.816710	−	0.577049i	$-0.195796\pi$
$599$	−2.23658	−	3.87386i	−0.0913840	−	0.158282i	−0.908094	+	0.418767i	$0.862462\pi$
$600$		0			0
$601$	−2.20871	+	3.82560i	−0.0900952	+	0.156050i	−0.907551	−	0.419942i	$-0.862050\pi$
$601$	−2.20871	+	3.82560i	−0.0900952	+	0.156050i	0.817456	+	0.575991i	$0.195384\pi$
$602$	−3.92095			−0.159806
$603$		0			0
$604$	36.8693			1.50019
$605$	−8.75560	+	15.1652i	−0.355966	+	0.616551i
$606$		0			0
$607$	−10.7913	−	18.6911i	−0.438005	−	0.758647i	0.559531	−	0.828810i	$-0.310981\pi$
$607$	−10.7913	−	18.6911i	−0.438005	−	0.758647i	−0.997536	+	0.0701630i	$0.977648\pi$
$608$	−8.48945	−	14.7042i	−0.344293	−	0.596333i
$609$		0			0
$610$	−2.41742	+	4.18710i	−0.0978786	+	0.169531i
$611$	10.9644			0.443572
$612$		0			0
$613$	1.00000			0.0403896			0.0201948	−	0.999796i	$-0.493571\pi$
$613$	1.00000			0.0403896			0.0201948	+	0.999796i	$0.493571\pi$
$614$	3.73025	−	6.46099i	0.150541	−	0.260744i
$615$		0			0
$616$	−2.29129	−	3.96863i	−0.0923186	−	0.159901i
$617$	−12.4104	−	21.4955i	−0.499624	−	0.865374i	0.500376	−	0.865808i	$-0.333195\pi$
$617$	−12.4104	−	21.4955i	−0.499624	−	0.865374i	−1.00000		0.000433948i	$0.999862\pi$
$618$		0			0
$619$	13.9564	−	24.1733i	0.560957	−	0.971605i	−0.436457	−	0.899725i	$-0.643767\pi$
$619$	13.9564	−	24.1733i	0.560957	−	0.971605i	0.997413	−	0.0718801i	$-0.0228999\pi$
$620$	71.8722			2.88646
$621$		0			0
$622$	8.24318			0.330521
$623$	4.37780	−	7.58258i	0.175393	−	0.303789i
$624$		0			0
$625$	−52.4129	−	90.7818i	−2.09652	−	3.63127i
$626$	−0.266150	−	0.460985i	−0.0106375	−	0.0184247i
$627$		0			0
$628$	0.747727	−	1.29510i	0.0298376	−	0.0516802i
$629$	10.3923			0.414368
$630$		0			0
$631$	−31.1652			−1.24067			−0.620333	−	0.784339i	$-0.713002\pi$
$631$	−31.1652			−1.24067			−0.620333	+	0.784339i	$0.713002\pi$
$632$	7.43273	−	12.8739i	0.295658	−	0.512095i
$633$		0			0
$634$		0			0
$635$	−16.2360	−	28.1216i	−0.644306	−	1.11597i
$636$		0			0
$637$	−2.00000	+	3.46410i	−0.0792429	+	0.137253i
$638$	2.20880			0.0874473
$639$		0			0
$640$	−48.3303			−1.91042
$641$	−6.06218	+	10.5000i	−0.239442	+	0.414725i	−0.960554	−	0.278093i	$-0.910298\pi$
$641$	−6.06218	+	10.5000i	−0.239442	+	0.414725i	0.721113	+	0.692818i	$0.243631\pi$
$642$		0			0
$643$	17.1652	+	29.7309i	0.676927	+	1.17247i	0.975901	+	0.218212i	$0.0700223\pi$
$643$	17.1652	+	29.7309i	0.676927	+	1.17247i	−0.298974	+	0.954261i	$0.596644\pi$
$644$	3.10260	+	5.37386i	0.122260	+	0.211760i
$645$		0			0
$646$	−2.83485	+	4.91010i	−0.111536	+	0.193185i
$647$	11.3060			0.444485			0.222242	−	0.974991i	$-0.428662\pi$
$647$	11.3060			0.444485			0.222242	+	0.974991i	$0.428662\pi$
$648$		0			0
$649$	−9.16515			−0.359764
$650$	12.9427	−	22.4174i	0.507655	−	0.879284i
$651$		0			0
$652$	13.0608	+	22.6220i	0.511500	+	0.885944i
$653$	−6.06218	−	10.5000i	−0.237231	−	0.410897i	0.722687	−	0.691175i	$-0.242907\pi$
$653$	−6.06218	−	10.5000i	−0.237231	−	0.410897i	−0.959919	+	0.280278i	$0.909573\pi$
$654$		0			0
$655$	40.3303	−	69.8541i	1.57584	−	2.72943i
$656$	12.2197			0.477099
$657$		0			0
$658$	1.25227			0.0488187
$659$	−3.24563	+	5.62159i	−0.126432	+	0.218986i	−0.922292	−	0.386495i	$-0.873686\pi$
$659$	−3.24563	+	5.62159i	−0.126432	+	0.218986i	0.795860	+	0.605481i	$0.207019\pi$
$660$		0			0
$661$	4.00000	+	6.92820i	0.155582	+	0.269476i	0.933271	−	0.359174i	$-0.116941\pi$
$661$	4.00000	+	6.92820i	0.155582	+	0.269476i	−0.777689	+	0.628649i	$0.783608\pi$
$662$	3.27340	+	5.66970i	0.127224	+	0.220359i
$663$		0			0
$664$	−5.37386	+	9.30780i	−0.208546	+	0.361213i
$665$	−15.6838			−0.608192
$666$		0			0
$667$	−6.33030			−0.245110
$668$	2.28425	−	3.95644i	0.0883803	−	0.153079i
$669$		0			0
$670$	0.582576	+	1.00905i	0.0225069	+	0.0389830i
$671$	3.19795	+	5.53901i	0.123456	+	0.213831i
$672$		0			0
$673$	−14.2477	+	24.6778i	−0.549210	+	0.951259i	0.449119	+	0.893472i	$0.351738\pi$
$673$	−14.2477	+	24.6778i	−0.549210	+	0.951259i	−0.998329	+	0.0577870i	$0.981596\pi$
$674$	9.21245			0.354850
$675$		0			0
$676$	−5.37386			−0.206687
$677$	−5.91915	+	10.2523i	−0.227492	+	0.394027i	−0.957064	−	0.289877i	$-0.906386\pi$
$677$	−5.91915	+	10.2523i	−0.227492	+	0.394027i	0.729573	+	0.683903i	$0.239719\pi$
$678$		0			0
$679$	3.79129	+	6.56670i	0.145496	+	0.252007i
$680$	13.1334	+	22.7477i	0.503643	+	0.872336i
$681$		0			0
$682$	−5.53901	+	9.59386i	−0.212100	+	0.367368i
$683$	4.47315			0.171160			0.0855802	−	0.996331i	$-0.472726\pi$
$683$	4.47315			0.171160			0.0855802	+	0.996331i	$0.472726\pi$
$684$		0			0
$685$	−77.0780			−2.94500
$686$	−0.228425	+	0.395644i	−0.00872131	+	0.0151058i
$687$		0			0
$688$	11.9782	+	20.7469i	0.456665	+	0.790968i
$689$	17.3205	+	30.0000i	0.659859	+	1.14291i
$690$		0			0
$691$	−5.41742	+	9.38325i	−0.206089	+	0.356956i	−0.950479	−	0.310789i	$-0.899407\pi$
$691$	−5.41742	+	9.38325i	−0.206089	+	0.356956i	0.744390	+	0.667745i	$0.232740\pi$
$692$	20.5939			0.782863
$693$		0			0
$694$	16.4610			0.624850
$695$	−16.5975	+	28.7477i	−0.629579	+	1.09046i
$696$		0			0
$697$	−7.58258	−	13.1334i	−0.287211	−	0.497463i
$698$	−5.65300	−	9.79129i	−0.213969	−	0.370606i
$699$		0			0
$700$	−12.6869	+	21.9744i	−0.479521	+	0.830555i
$701$	−29.4449			−1.11212			−0.556059	−	0.831143i	$-0.687687\pi$
$701$	−29.4449			−1.11212			−0.556059	+	0.831143i	$0.687687\pi$
$702$		0			0
$703$	−10.7477			−0.405358
$704$	−4.52083	+	7.83030i	−0.170385	+	0.295116i
$705$		0			0
$706$	8.16515	+	14.1425i	0.307300	+	0.532258i
$707$	−0.913701	−	1.58258i	−0.0343632	−	0.0595189i
$708$		0			0
$709$	−7.50000	+	12.9904i	−0.281668	+	0.487864i	−0.971796	−	0.235824i	$-0.924221\pi$
$709$	−7.50000	+	12.9904i	−0.281668	+	0.487864i	0.690127	+	0.723688i	$0.257554\pi$
$710$	22.8027			0.855770
$711$		0			0
$712$	15.1652			0.568338
$713$	15.8745	−	27.4955i	0.594505	−	1.02971i
$714$		0			0
$715$	−23.1652	−	40.1232i	−0.866328	−	1.50052i
$716$	1.46590	+	2.53901i	0.0547833	+	0.0948874i
$717$		0			0
$718$	6.93466	−	12.0112i	0.258799	−	0.448253i
$719$	49.0695			1.82998			0.914992	−	0.403471i	$-0.132197\pi$
$719$	49.0695			1.82998			0.914992	+	0.403471i	$0.132197\pi$
$720$		0			0
$721$	−3.58258			−0.133422
$722$	−1.40828	+	2.43920i	−0.0524106	+	0.0907778i
$723$		0			0
$724$	11.7913	+	20.4231i	0.438220	+	0.759019i
$725$	−12.9427	−	22.4174i	−0.480680	−	0.832562i
$726$		0			0
$727$	−23.1216	+	40.0478i	−0.857532	+	1.48529i	0.0167434	+	0.999860i	$0.494670\pi$
$727$	−23.1216	+	40.0478i	−0.857532	+	1.48529i	−0.874276	+	0.485430i	$0.838663\pi$
$728$	−6.92820			−0.256776
$729$		0			0
$730$	−6.33030			−0.234295
$731$	14.8655	−	25.7477i	0.549819	−	0.952314i
$732$		0			0
$733$	−5.37386	−	9.30780i	−0.198488	−	0.343792i	0.749550	−	0.661947i	$-0.230270\pi$
$733$	−5.37386	−	9.30780i	−0.198488	−	0.343792i	−0.948038	+	0.318156i	$0.896936\pi$
$734$	−2.01810	−	3.49545i	−0.0744895	−	0.129020i
$735$		0			0
$736$	−8.20871	+	14.2179i	−0.302577	+	0.524079i
$737$	1.54135			0.0567764
$738$		0			0
$739$	−19.4174			−0.714281			−0.357141	−	0.934051i	$-0.616248\pi$
$739$	−19.4174			−0.714281			−0.357141	+	0.934051i	$0.616248\pi$
$740$	−11.7629	+	20.3739i	−0.432411	+	0.748958i
$741$		0			0
$742$	1.97822	+	3.42638i	0.0726227	+	0.125786i
$743$	6.70973	+	11.6216i	0.246156	+	0.426355i	0.962456	−	0.271438i	$-0.0874991\pi$
$743$	6.70973	+	11.6216i	0.246156	+	0.426355i	−0.716300	+	0.697793i	$0.754166\pi$
$744$		0			0
$745$	−23.3739	+	40.4847i	−0.856352	+	1.48325i
$746$	3.34885			0.122610
$747$		0			0
$748$	16.4174			0.600280
$749$	5.60533	−	9.70871i	0.204814	−	0.354749i
$750$		0			0
$751$	4.70871	+	8.15573i	0.171823	+	0.297607i	0.939057	−	0.343761i	$-0.111701\pi$
$751$	4.70871	+	8.15573i	0.171823	+	0.297607i	−0.767234	+	0.641367i	$0.778368\pi$
$752$	−3.82560	−	6.62614i	−0.139505	−	0.241630i
$753$		0			0
$754$	1.66970	−	2.89200i	0.0608068	−	0.105320i
$755$	90.1064			3.27931
$756$		0			0
$757$	−6.83485			−0.248417			−0.124208	−	0.992256i	$-0.539639\pi$
$757$	−6.83485			−0.248417			−0.124208	+	0.992256i	$0.539639\pi$
$758$	−6.60443	+	11.4392i	−0.239884	+	0.415491i
$759$		0			0
$760$	−13.5826	−	23.5257i	−0.492692	−	0.853367i
$761$	15.2270	+	26.3739i	0.551977	+	0.956052i	0.998132	+	0.0610962i	$0.0194596\pi$
$761$	15.2270	+	26.3739i	0.551977	+	0.956052i	−0.446155	+	0.894956i	$0.647207\pi$
$762$		0			0
$763$	3.00000	−	5.19615i	0.108607	−	0.188113i
$764$	10.9445			0.395958
$765$		0			0
$766$	8.83485			0.319216
$767$	−6.92820	+	12.0000i	−0.250163	+	0.433295i
$768$		0			0
$769$	22.5390	+	39.0387i	0.812778	+	1.40777i	0.910913	+	0.412599i	$0.135379\pi$
$769$	22.5390	+	39.0387i	0.812778	+	1.40777i	−0.0981351	+	0.995173i	$0.531288\pi$
$770$	−2.64575	−	4.58258i	−0.0953463	−	0.165145i
$771$		0			0
$772$	12.5390	−	21.7182i	0.451289	−	0.781656i
$773$	−31.5583			−1.13507			−0.567537	−	0.823348i	$-0.692104\pi$
$773$	−31.5583			−1.13507			−0.567537	+	0.823348i	$0.692104\pi$
$774$		0			0
$775$	129.826			4.66348
$776$	−6.56670	+	11.3739i	−0.235731	+	0.408298i
$777$		0			0
$778$	−7.25227	−	12.5613i	−0.260007	−	0.450345i
$779$	7.84190	+	13.5826i	0.280965	+	0.486646i
$780$		0			0
$781$	15.0826	−	26.1238i	0.539697	−	0.934783i
$782$	5.48220			0.196043
$783$		0			0
$784$	2.79129			0.0996889
$785$	1.82740	−	3.16515i	0.0652227	−	0.112969i
$786$		0			0
$787$	−26.9564	−	46.6899i	−0.960893	−	1.66432i	−0.720265	−	0.693699i	$-0.755980\pi$
$787$	−26.9564	−	46.6899i	−0.960893	−	1.66432i	−0.240628	−	0.970617i	$-0.577353\pi$
$788$	0.0853998	+	0.147917i	0.00304224	+	0.00526932i
$789$		0			0
$790$	8.58258	−	14.8655i	0.305354	−	0.528889i
$791$	−13.9518			−0.496067
$792$		0			0
$793$	9.66970			0.343381
$794$	−0.361500	+	0.626136i	−0.0128292	+	0.0222208i
$795$		0			0
$796$	−15.0000	−	25.9808i	−0.531661	−	0.920864i
$797$	25.3531	+	43.9129i	0.898053	+	1.55547i	0.829980	+	0.557794i	$0.188352\pi$
$797$	25.3531	+	43.9129i	0.898053	+	1.55547i	0.0680737	+	0.997680i	$0.478315\pi$
$798$		0			0
$799$	−4.74773	+	8.22330i	−0.167963	+	0.290920i
$800$	−67.1329			−2.37351
$801$		0			0
$802$	−6.46099			−0.228145
$803$	−4.18710	+	7.25227i	−0.147760	+	0.255927i
$804$		0			0
$805$	7.58258	+	13.1334i	0.267251	+	0.462892i
$806$	8.37420	+	14.5045i	0.294969	+	0.510901i
$807$		0			0
$808$	1.58258	−	2.74110i	0.0556748	−	0.0964316i
$809$	10.1063			0.355317			0.177658	−	0.984092i	$-0.443148\pi$
$809$	10.1063			0.355317			0.177658	+	0.984092i	$0.443148\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$	−1.63670	+	2.83485i	−0.0574369	+	0.0994837i
$813$		0			0
$814$	−1.81307	−	3.14033i	−0.0635480	−	0.110068i
$815$	31.9198	+	55.2867i	1.11810	+	1.93661i
$816$		0			0
$817$	−15.3739	+	26.6283i	−0.537863	+	0.931607i
$818$	−4.22690			−0.147790
$819$		0			0
$820$	34.3303			1.19887
$821$	−16.8359	+	29.1606i	−0.587576	+	1.01771i	0.406972	+	0.913440i	$0.366584\pi$
$821$	−16.8359	+	29.1606i	−0.587576	+	1.01771i	−0.994549	+	0.104272i	$0.966749\pi$
$822$		0			0
$823$	−6.00000	−	10.3923i	−0.209147	−	0.362253i	0.742299	−	0.670069i	$-0.233735\pi$
$823$	−6.00000	−	10.3923i	−0.209147	−	0.362253i	−0.951446	+	0.307816i	$0.900402\pi$
$824$	−3.10260	−	5.37386i	−0.108084	−	0.187207i
$825$		0			0
$826$	−0.791288	+	1.37055i	−0.0275324	+	0.0476876i
$827$	−25.2578			−0.878298			−0.439149	−	0.898414i	$-0.644720\pi$
$827$	−25.2578			−0.878298			−0.439149	+	0.898414i	$0.644720\pi$
$828$		0			0
$829$	−10.3303			−0.358786			−0.179393	−	0.983777i	$-0.557413\pi$
$829$	−10.3303			−0.358786			−0.179393	+	0.983777i	$0.557413\pi$
$830$	−6.20520	+	10.7477i	−0.215386	+	0.373059i
$831$		0			0
$832$	6.83485	+	11.8383i	0.236956	+	0.410419i
$833$	−1.73205	−	3.00000i	−0.0600120	−	0.103944i
$834$		0			0
$835$	5.58258	−	9.66930i	0.193193	−	0.334620i
$836$	−16.9789			−0.587228
$837$		0			0
$838$	−8.50455			−0.293785
$839$	19.5094	−	33.7913i	0.673540	−	1.16660i	−0.303354	−	0.952878i	$-0.598106\pi$
$839$	19.5094	−	33.7913i	0.673540	−	1.16660i	0.976893	−	0.213727i	$-0.0685602\pi$
$840$		0			0
$841$	12.8303	+	22.2227i	0.442424	+	0.766301i
$842$	−3.69253	−	6.39564i	−0.127253	−	0.220408i
$843$		0			0
$844$	10.5218	−	18.2243i	0.362175	−	0.627305i
$845$	−13.1334			−0.451803
$846$		0			0
$847$	4.00000			0.137442
$848$	12.0866	−	20.9347i	0.415057	−	0.718899i
$849$		0			0
$850$	11.2087	+	19.4141i	0.384456	+	0.665897i
$851$	5.19615	+	9.00000i	0.178122	+	0.308516i
$852$		0			0
$853$	−6.37386	+	11.0399i	−0.218237	+	0.377997i	−0.954269	−	0.298949i	$-0.903364\pi$
$853$	−6.37386	+	11.0399i	−0.218237	+	0.377997i	0.736032	+	0.676947i	$0.236697\pi$
$854$	1.10440			0.0377918
$855$		0			0
$856$	19.4174			0.663674
$857$	20.1570	−	34.9129i	0.688549	−	1.19260i	−0.283759	−	0.958896i	$-0.591582\pi$
$857$	20.1570	−	34.9129i	0.688549	−	1.19260i	0.972307	−	0.233706i	$-0.0750852\pi$
$858$		0			0
$859$	−13.1652	−	22.8027i	−0.449189	−	0.778018i	0.549144	−	0.835728i	$-0.314954\pi$
$859$	−13.1652	−	22.8027i	−0.449189	−	0.778018i	−0.998333	+	0.0577091i	$0.981620\pi$
$860$	33.6519	+	58.2867i	1.14752	+	1.98756i
$861$		0			0
$862$	−8.37386	+	14.5040i	−0.285215	+	0.494007i
$863$	2.45505			0.0835709			0.0417855	−	0.999127i	$-0.486695\pi$
$863$	2.45505			0.0835709			0.0417855	+	0.999127i	$0.486695\pi$
$864$		0			0
$865$	50.3303			1.71128
$866$	−5.00545	+	8.66970i	−0.170092	+	0.294608i
$867$		0			0
$868$	−8.20871	−	14.2179i	−0.278622	−	0.482587i
$869$	−11.3537	−	19.6652i	−0.385147	−	0.667095i
$870$		0			0
$871$	1.16515	−	2.01810i	0.0394796	−	0.0683808i
$872$	10.3923			0.351928
$873$		0			0
$874$	−5.66970			−0.191780
$875$	−20.0616	+	34.7477i	−0.678206	+	1.17469i
$876$		0			0
$877$	−6.50000	−	11.2583i	−0.219489	−	0.380167i	0.735163	−	0.677891i	$-0.237106\pi$
$877$	−6.50000	−	11.2583i	−0.219489	−	0.380167i	−0.954652	+	0.297724i	$0.903772\pi$
$878$	5.84370	+	10.1216i	0.197215	+	0.341587i
$879$		0			0
$880$	−16.1652	+	27.9989i	−0.544927	+	0.943841i
$881$	21.5076			0.724610			0.362305	−	0.932060i	$-0.381990\pi$
$881$	21.5076			0.724610			0.362305	+	0.932060i	$0.381990\pi$
$882$		0			0
$883$	48.9129			1.64605			0.823025	−	0.568006i	$-0.192285\pi$
$883$	48.9129			1.64605			0.823025	+	0.568006i	$0.192285\pi$
$884$	12.4104	−	21.4955i	0.417407	−	0.722970i
$885$		0			0
$886$	3.95644	+	6.85275i	0.132919	+	0.230223i
$887$	−11.4967	−	19.9129i	−0.386022	−	0.668609i	0.605889	−	0.795549i	$-0.292818\pi$
$887$	−11.4967	−	19.9129i	−0.386022	−	0.668609i	−0.991910	+	0.126940i	$0.959484\pi$
$888$		0			0
$889$	−3.70871	+	6.42368i	−0.124386	+	0.215443i
$890$	17.5112			0.586977
$891$		0			0
$892$	−39.4083			−1.31949
$893$	4.91010	−	8.50455i	0.164310	−	0.284594i
$894$		0			0
$895$	3.58258	+	6.20520i	0.119752	+	0.207417i
$896$	5.51993	+	9.56080i	0.184408	+	0.319404i
$897$		0			0
$898$	6.06534	−	10.5055i	0.202403	−	0.350572i
$899$	16.7484			0.558591
$900$		0			0
$901$	−30.0000			−0.999445
$902$	−2.64575	+	4.58258i	−0.0880939	+	0.152583i
$903$		0			0
$904$	−12.0826	−	20.9276i	−0.401860	−	0.696043i
$905$	28.8172	+	49.9129i	0.957917	+	1.65916i
$906$		0			0
$907$	−9.29129	+	16.0930i	−0.308512	+	0.534359i	−0.978037	−	0.208431i	$-0.933164\pi$
$907$	−9.29129	+	16.0930i	−0.308512	+	0.534359i	0.669525	+	0.742790i	$0.266498\pi$
$908$	−23.5257			−0.780728
$909$		0			0
$910$	−8.00000			−0.265197
$911$	−4.47315	+	7.74773i	−0.148202	+	0.256694i	−0.930563	−	0.366132i	$-0.880682\pi$
$911$	−4.47315	+	7.74773i	−0.148202	+	0.256694i	0.782361	+	0.622825i	$0.214015\pi$
$912$		0			0
$913$	8.20871	+	14.2179i	0.271669	+	0.470544i
$914$	7.15663	+	12.3956i	0.236720	+	0.410011i
$915$		0			0
$916$	19.6261	−	33.9935i	0.648466	−	1.12318i
$917$	−18.4249			−0.608444
$918$		0			0
$919$	16.0780			0.530365			0.265183	−	0.964198i	$-0.414568\pi$
$919$	16.0780			0.530365			0.265183	+	0.964198i	$0.414568\pi$
$920$	−13.1334	+	22.7477i	−0.432996	+	0.749970i
$921$		0			0
$922$	3.04356	+	5.27160i	0.100234	+	0.173611i
$923$	−22.8027	−	39.4955i	−0.750560	−	1.30001i
$924$		0			0
$925$	−21.2477	+	36.8021i	−0.698621	+	1.21005i
$926$	−9.55405			−0.313966
$927$		0			0
$928$	−8.66061			−0.284298
$929$	−1.17985	+	2.04356i	−0.0387096	+	0.0670471i	−0.884731	−	0.466102i	$-0.845658\pi$
$929$	−1.17985	+	2.04356i	−0.0387096	+	0.0670471i	0.846022	+	0.533149i	$0.178991\pi$
$930$		0			0
$931$	1.79129	+	3.10260i	0.0587071	+	0.101684i
$932$		0			0
$933$		0			0
$934$	−1.41742	+	2.45505i	−0.0463795	+	0.0803317i
$935$	40.1232			1.31217
$936$		0			0
$937$	33.4955			1.09425			0.547124	−	0.837051i	$-0.315722\pi$
$937$	33.4955			1.09425			0.547124	+	0.837051i	$0.315722\pi$
$938$	0.133075	−	0.230493i	0.00434505	−	0.00752585i
$939$		0			0
$940$	−10.7477	−	18.6156i	−0.350552	−	0.607174i
$941$	−16.4068	−	28.4174i	−0.534847	−	0.926382i	−0.999171	−	0.0407162i	$-0.987036\pi$
$941$	−16.4068	−	28.4174i	−0.534847	−	0.926382i	0.464324	−	0.885665i	$-0.346297\pi$
$942$		0			0
$943$	7.58258	−	13.1334i	0.246923	−	0.427683i
$944$	9.66930			0.314709
$945$		0			0
$946$	−10.3739			−0.337283
$947$	−20.8800	+	36.1652i	−0.678508	+	1.17521i	0.296923	+	0.954901i	$0.404040\pi$
$947$	−20.8800	+	36.1652i	−0.678508	+	1.17521i	−0.975430	+	0.220308i	$0.929294\pi$
$948$		0			0
$949$	6.33030	+	10.9644i	0.205490	+	0.355920i
$950$	−11.5921	−	20.0780i	−0.376096	−	0.651417i
$951$		0			0
$952$	3.00000	−	5.19615i	0.0972306	−	0.168408i
$953$	3.65480			0.118391			0.0591953	−	0.998246i	$-0.481147\pi$
$953$	3.65480			0.118391			0.0591953	+	0.998246i	$0.481147\pi$
$954$		0			0
$955$	26.7477			0.865536
$956$	−22.6220	+	39.1824i	−0.731647	+	1.26725i
$957$		0			0
$958$	−5.62614	−	9.74475i	−0.181772	−	0.314839i
$959$	8.80328	+	15.2477i	0.284273	+	0.492375i
$960$		0			0
$961$	−26.5000	+	45.8993i	−0.854839	+	1.48062i
$962$	−5.48220			−0.176753
$963$		0			0
$964$	−32.9909			−1.06257
$965$	30.6446	−	53.0780i	0.986485	−	1.70864i
$966$		0			0
$967$	−2.00000	−	3.46410i	−0.0643157	−	0.111398i	0.832075	−	0.554664i	$-0.187153\pi$
$967$	−2.00000	−	3.46410i	−0.0643157	−	0.111398i	−0.896390	+	0.443266i	$0.853820\pi$
$968$	3.46410	+	6.00000i	0.111340	+	0.192847i
$969$		0			0
$970$	−7.58258	+	13.1334i	−0.243462	+	0.421688i
$971$	−35.2131			−1.13004			−0.565021	−	0.825076i	$-0.691132\pi$
$971$	−35.2131			−1.13004			−0.565021	+	0.825076i	$0.691132\pi$
$972$		0			0
$973$	7.58258			0.243086
$974$	−1.50363	+	2.60436i	−0.0481793	+	0.0834490i
$975$		0			0
$976$	−3.37386	−	5.84370i	−0.107995	−	0.187052i
$977$	12.4104	+	21.4955i	0.397044	+	0.687701i	0.993360	−	0.115050i	$-0.0367027\pi$
$977$	12.4104	+	21.4955i	0.397044	+	0.687701i	−0.596316	+	0.802750i	$0.703369\pi$
$978$		0			0
$979$	11.5826	−	20.0616i	0.370181	−	0.641172i
$980$	7.84190			0.250500
$981$		0			0
$982$	−10.2432			−0.326873
$983$	−22.1552	+	38.3739i	−0.706640	+	1.22394i	0.259457	+	0.965755i	$0.416457\pi$
$983$	−22.1552	+	38.3739i	−0.706640	+	1.22394i	−0.966096	+	0.258181i	$0.916877\pi$
$984$		0			0
$985$	0.208712	+	0.361500i	0.00665012	+	0.0115183i
$986$	1.44600	+	2.50455i	0.0460500	+	0.0797610i
$987$		0			0
$988$	−12.8348	+	22.2306i	−0.408331	+	0.707250i
$989$	29.7309			0.945388
$990$		0			0
$991$	−35.7477			−1.13556			−0.567782	−	0.823179i	$-0.692198\pi$
$991$	−35.7477			−1.13556			−0.567782	+	0.823179i	$0.692198\pi$
$992$	21.7182	−	37.6170i	0.689554	−	1.19434i
$993$		0			0
$994$	−2.60436	−	4.51088i	−0.0826052	−	0.143076i
$995$	−36.6591	−	63.4955i	−1.16217	−	2.01294i
$996$		0			0
$997$	−3.41742	+	5.91915i	−0.108231	+	0.187461i	−0.915054	−	0.403332i	$-0.867852\pi$
$997$	−3.41742	+	5.91915i	−0.108231	+	0.187461i	0.806823	+	0.590794i	$0.201185\pi$
$998$	9.13701			0.289227
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.f.n.379.3		8
3.2	odd	2	inner	567.2.f.n.379.2		8
9.2	odd	6		567.2.a.i.1.3	yes	4
9.4	even	3	inner	567.2.f.n.190.3		8
9.5	odd	6	inner	567.2.f.n.190.2		8
9.7	even	3		567.2.a.i.1.2	✓	4
36.7	odd	6		9072.2.a.ci.1.1		4
36.11	even	6		9072.2.a.ci.1.4		4
63.20	even	6		3969.2.a.u.1.3		4
63.34	odd	6		3969.2.a.u.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.a.i.1.2	✓	4	9.7	even	3
567.2.a.i.1.3	yes	4	9.2	odd	6
567.2.f.n.190.2		8	9.5	odd	6	inner
567.2.f.n.190.3		8	9.4	even	3	inner
567.2.f.n.379.2		8	3.2	odd	2	inner
567.2.f.n.379.3		8	1.1	even	1	trivial
3969.2.a.u.1.2		4	63.34	odd	6
3969.2.a.u.1.3		4	63.20	even	6
9072.2.a.ci.1.1		4	36.7	odd	6
9072.2.a.ci.1.4		4	36.11	even	6

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.228425 - 0.395644i) q^{2} +(0.895644 + 1.55130i) q^{4} +(2.18890 + 3.79129i) q^{5} +(0.500000 - 0.866025i) q^{7} +1.73205 q^{8} +2.00000 q^{10} +(1.32288 - 2.29129i) q^{11} +(-2.00000 - 3.46410i) q^{13} +(-0.228425 - 0.395644i) q^{14} +(-1.39564 + 2.41733i) q^{16} +3.46410 q^{17} -3.58258 q^{19} +(-3.92095 + 6.79129i) q^{20} +(-0.604356 - 1.04678i) q^{22} +(1.73205 + 3.00000i) q^{23} +(-7.08258 + 12.2674i) q^{25} -1.82740 q^{26} +1.79129 q^{28} +(-0.913701 + 1.58258i) q^{29} +(-4.58258 - 7.93725i) q^{31} +(2.36965 + 4.10436i) q^{32} +(0.791288 - 1.37055i) q^{34} +4.37780 q^{35} +3.00000 q^{37} +(-0.818350 + 1.41742i) q^{38} +(3.79129 + 6.56670i) q^{40} +(-2.18890 - 3.79129i) q^{41} +(4.29129 - 7.43273i) q^{43} +4.73930 q^{44} +1.58258 q^{46} +(-1.37055 + 2.37386i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(3.23568 + 5.60436i) q^{50} +(3.58258 - 6.20520i) q^{52} -8.66025 q^{53} +11.5826 q^{55} +(0.866025 - 1.50000i) q^{56} +(0.417424 + 0.723000i) q^{58} +(-1.73205 - 3.00000i) q^{59} +(-1.20871 + 2.09355i) q^{61} -4.18710 q^{62} -3.41742 q^{64} +(8.75560 - 15.1652i) q^{65} +(0.291288 + 0.504525i) q^{67} +(3.10260 + 5.37386i) q^{68} +(1.00000 - 1.73205i) q^{70} +11.4014 q^{71} -3.16515 q^{73} +(0.685275 - 1.18693i) q^{74} +(-3.20871 - 5.55765i) q^{76} +(-1.32288 - 2.29129i) q^{77} +(4.29129 - 7.43273i) q^{79} -12.2197 q^{80} -2.00000 q^{82} +(-3.10260 + 5.37386i) q^{83} +(7.58258 + 13.1334i) q^{85} +(-1.96048 - 3.39564i) q^{86} +(2.29129 - 3.96863i) q^{88} +8.75560 q^{89} -4.00000 q^{91} +(-3.10260 + 5.37386i) q^{92} +(0.626136 + 1.08450i) q^{94} +(-7.84190 - 13.5826i) q^{95} +(-3.79129 + 6.56670i) q^{97} -0.456850 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} + 4 q^{7} + 16 q^{10} - 16 q^{13} - 2 q^{16} + 8 q^{19} - 14 q^{22} - 20 q^{25} - 4 q^{28} - 12 q^{34} + 24 q^{37} + 12 q^{40} + 16 q^{43} - 24 q^{46} - 4 q^{49} - 8 q^{52} + 56 q^{55} + 40 q^{58}+ \cdots - 12 q^{97}+O(q^{100}) \) 8 * q - 2 * q^4 + 4 * q^7 + 16 * q^10 - 16 * q^13 - 2 * q^16 + 8 * q^19 - 14 * q^22 - 20 * q^25 - 4 * q^28 - 12 * q^34 + 24 * q^37 + 12 * q^40 + 16 * q^43 - 24 * q^46 - 4 * q^49 - 8 * q^52 + 56 * q^55 + 40 * q^58 - 28 * q^61 - 64 * q^64 - 16 * q^67 + 8 * q^70 + 48 * q^73 - 44 * q^76 + 16 * q^79 - 16 * q^82 + 24 * q^85 - 32 * q^91 + 60 * q^94 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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