LMFDB - Embedded newform 567.2.f.n.190.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(190,567)]

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

lf = mfeigenbasis(mf)

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")

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

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			190.2
Root			$-0.228425 - 1.39564i$ of defining polynomial
Character	$\chi$	$=$	567.190
Dual form			567.2.f.n.379.2

$q$-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 $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

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

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	$-0.218307\pi$
$2$	−0.228425	−	0.395644i	−0.161521	−	0.279763i	−0.935414	+	0.353553i	$0.884973\pi$
$3$		0			0
$3$		0			0
$4$	0.895644	−	1.55130i	0.447822	−	0.775650i
$5$	−2.18890	+	3.79129i	−0.978906	+	1.69552i	−0.312516	+	0.949913i	$0.601172\pi$
$5$	−2.18890	+	3.79129i	−0.978906	+	1.69552i	−0.666390	+	0.745603i	$0.732162\pi$
$6$		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	$-0.297261\pi$
$11$	−1.32288	−	2.29129i	−0.398862	−	0.690849i	−0.993586	+	0.113081i	$0.963928\pi$
$12$		0			0
$13$	−2.00000	+	3.46410i	−0.554700	+	0.960769i	0.443227	+	0.896410i	$0.353834\pi$
$13$	−2.00000	+	3.46410i	−0.554700	+	0.960769i	−0.997927	+	0.0643593i	$0.979500\pi$
$14$	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	$-0.637999\pi$
$17$	−3.46410			−0.840168			−0.420084	+	0.907485i	$0.637999\pi$
$18$		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	$-0.950952\pi$
$23$	−1.73205	+	3.00000i	−0.361158	+	0.625543i	0.626994	+	0.779024i	$0.284285\pi$
$24$		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	$-0.112397\pi$
$29$	0.913701	+	1.58258i	0.169670	+	0.293877i	−0.768634	+	0.639689i	$0.779063\pi$
$30$		0			0
$31$	−4.58258	+	7.93725i	−0.823055	+	1.42557i	0.0803419	+	0.996767i	$0.474399\pi$
$31$	−4.58258	+	7.93725i	−0.823055	+	1.42557i	−0.903397	+	0.428806i	$0.858935\pi$
$32$	−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	$-0.722280\pi$
$41$	2.18890	−	3.79129i	0.341849	−	0.592100i	0.984776	+	0.173828i	$0.0556136\pi$
$42$		0			0
$43$	4.29129	+	7.43273i	0.654415	+	1.13348i	0.982040	+	0.188673i	$0.0604185\pi$
$43$	4.29129	+	7.43273i	0.654415	+	1.13348i	−0.327625	+	0.944808i	$0.606248\pi$
$44$	−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	$-0.102600\pi$
$47$	1.37055	+	2.37386i	0.199915	+	0.346264i	−0.748585	+	0.663038i	$0.769267\pi$
$48$		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	$-0.297236\pi$
$53$	8.66025			1.18958			0.594789	+	0.803882i	$0.297236\pi$
$54$		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	$-0.760934\pi$
$59$	1.73205	−	3.00000i	0.225494	−	0.390567i	0.956467	+	0.291839i	$0.0942671\pi$
$60$		0			0
$61$	−1.20871	−	2.09355i	−0.154760	−	0.268052i	0.778212	−	0.628002i	$-0.216127\pi$
$61$	−1.20871	−	2.09355i	−0.154760	−	0.268052i	−0.932972	+	0.359950i	$0.882794\pi$
$62$	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	−0.847684	−	0.530502i	$-0.822003\pi$
$67$	0.291288	−	0.504525i	0.0355865	−	0.0616376i	0.883270	+	0.468865i	$0.155337\pi$
$68$	−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	$-0.736524\pi$
$71$	−11.4014			−1.35309			−0.676546	+	0.736400i	$0.736524\pi$
$72$		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	0.999805	−	0.0197396i	$-0.00628371\pi$
$79$	4.29129	+	7.43273i	0.482808	+	0.836247i	−0.516998	+	0.855987i	$0.672950\pi$
$80$	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	$-0.0560518\pi$
$83$	3.10260	+	5.37386i	0.340555	+	0.589858i	−0.643981	+	0.765041i	$0.722718\pi$
$84$		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	$-0.653603\pi$
$89$	−8.75560			−0.928092			−0.464046	+	0.885811i	$0.653603\pi$
$90$		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	0.606815	−	0.794843i	$-0.292447\pi$
$97$	−3.79129	−	6.56670i	−0.384947	−	0.666748i	−0.991762	+	0.128096i	$0.959114\pi$
$98$	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	$-0.195646\pi$
$101$	−0.913701	−	1.58258i	−0.0909166	−	0.157472i	−0.907897	+	0.419193i	$0.862313\pi$
$102$		0			0
$103$	−1.79129	+	3.10260i	−0.176501	+	0.305708i	−0.940680	−	0.339296i	$-0.889811\pi$
$103$	−1.79129	+	3.10260i	−0.176501	+	0.305708i	0.764179	+	0.645004i	$0.223144\pi$
$104$	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	$-0.682290\pi$
$107$	−11.2107			−1.08377			−0.541887	+	0.840451i	$0.682290\pi$
$108$		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	−0.325347	−	0.945595i	$-0.605481\pi$
$113$	6.97588	−	12.0826i	0.656235	−	1.13663i	0.981583	−	0.191038i	$-0.0611855\pi$
$114$		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	−0.111465	−	0.993768i	$-0.535554\pi$
$131$	9.21245	−	15.9564i	0.804896	−	1.39412i	0.916361	−	0.400352i	$-0.131112\pi$
$132$		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	0.946796	+	0.321835i	$0.104300\pi$
$137$	8.80328	+	15.2477i	0.752115	+	1.30270i	−0.194681	+	0.980867i	$0.562367\pi$
$138$		0			0
$139$	3.79129	−	6.56670i	0.321573	−	0.556980i	−0.659240	−	0.751933i	$-0.729122\pi$
$139$	3.79129	−	6.56670i	0.321573	−	0.556980i	0.980813	+	0.194952i	$0.0624552\pi$
$140$	−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	$-0.977435\pi$
$149$	−5.33918	+	9.24773i	−0.437402	+	0.757603i	0.560086	+	0.828435i	$0.310768\pi$
$150$		0			0
$151$	10.2913	+	17.8250i	0.837493	+	1.45058i	0.891984	+	0.452066i	$0.149313\pi$
$151$	10.2913	+	17.8250i	0.837493	+	1.45058i	−0.0544912	+	0.998514i	$0.517354\pi$
$152$	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	−0.882202	−	0.470872i	$-0.843939\pi$
$157$	−0.417424	+	0.723000i	−0.0333141	+	0.0577017i	0.848888	+	0.528573i	$0.177273\pi$
$158$	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	$-0.801872\pi$
$167$	1.27520	−	2.20871i	0.0986780	−	0.170915i	0.911138	+	0.412102i	$0.135205\pi$
$168$		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	$-0.310640\pi$
$173$	−5.74835	−	9.95644i	−0.437039	−	0.756974i	−0.997460	+	0.0712342i	$0.977306\pi$
$174$		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	$-0.519482\pi$
$179$	−1.63670			−0.122333			−0.0611664	+	0.998128i	$0.519482\pi$
$180$		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	$-0.237614\pi$
$191$	−3.05493	−	5.29129i	−0.221047	−	0.382864i	−0.955126	+	0.296200i	$0.904281\pi$
$192$		0			0
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$	−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	$-0.501081\pi$
$197$	−0.0953502			−0.00679342			−0.00339671	+	0.999994i	$0.501081\pi$
$198$		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	−0.994248	−	0.107099i	$-0.965844\pi$
$211$	−5.87386	+	10.1738i	−0.404373	+	0.700395i	0.589875	+	0.807495i	$0.299177\pi$
$212$	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	−0.954011	−	0.299770i	$-0.903090\pi$
$223$	−11.0000	−	19.0526i	−0.736614	−	1.27585i	0.217397	−	0.976083i	$-0.430243\pi$
$224$	−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	$-0.0231154\pi$
$227$	6.56670	+	11.3739i	0.435847	+	0.754910i	−0.561517	+	0.827465i	$0.689782\pi$
$228$		0			0
$229$	−10.9564	+	18.9771i	−0.724022	+	1.25404i	0.235353	+	0.971910i	$0.424375\pi$
$229$	−10.9564	+	18.9771i	−0.724022	+	1.25404i	−0.959375	+	0.282133i	$0.908958\pi$
$230$	−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	0.0910652	+	0.995845i	$0.470973\pi$
$239$	−12.6289	+	21.8739i	−0.816894	+	1.41490i	−0.907960	+	0.419058i	$0.862361\pi$
$240$		0			0
$241$	−9.20871	−	15.9500i	−0.593185	−	1.02743i	−0.993800	−	0.111181i	$-0.964537\pi$
$241$	−9.20871	−	15.9500i	−0.593185	−	1.02743i	0.400615	−	0.916247i	$-0.368797\pi$
$242$	−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	$-0.420395\pi$
$251$	7.84190			0.494977			0.247488	+	0.968891i	$0.420395\pi$
$252$		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	$-0.936405\pi$
$257$	−5.10080	+	8.83485i	−0.318179	+	0.551103i	0.661929	+	0.749567i	$0.269738\pi$
$258$		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	$-0.124516\pi$
$263$	2.14123	+	3.70871i	0.132034	+	0.228689i	−0.792427	+	0.609967i	$0.791183\pi$
$264$		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	$-0.567740\pi$
$269$	−6.92820			−0.422420			−0.211210	+	0.977441i	$0.567740\pi$
$270$		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	0.741512	−	0.670940i	$-0.234109\pi$
$277$	−3.50000	−	6.06218i	−0.210295	−	0.364241i	−0.951807	+	0.306699i	$0.900776\pi$
$278$	−3.46410			−0.207763
$279$		0			0
$280$	7.58258			0.453146
$281$	14.8178	+	25.6652i	0.883955	+	1.53105i	0.846907	+	0.531741i	$0.178462\pi$
$281$	14.8178	+	25.6652i	0.883955	+	1.53105i	0.0370478	+	0.999313i	$0.488205\pi$
$282$		0			0
$283$	−8.79129	+	15.2270i	−0.522588	+	0.905149i	0.477067	+	0.878867i	$0.341700\pi$
$283$	−8.79129	+	15.2270i	−0.522588	+	0.905149i	−0.999655	+	0.0262816i	$0.991633\pi$
$284$	−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	−0.352951	−	0.935642i	$-0.614822\pi$
$293$	10.8492	−	18.7913i	0.633814	−	1.09780i	0.986765	−	0.162157i	$-0.0518450\pi$
$294$		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	0.488333	+	0.872657i	$0.337605\pi$
$311$	−9.02175	+	15.6261i	−0.511577	+	0.886077i	−0.999910	+	0.0134197i	$0.995728\pi$
$312$		0			0
$313$	0.582576	+	1.00905i	0.0329291	+	0.0570349i	0.882020	−	0.471211i	$-0.156183\pi$
$313$	0.582576	+	1.00905i	0.0329291	+	0.0570349i	−0.849091	+	0.528246i	$0.822850\pi$
$314$	0.381401			0.0215237
$315$		0			0
$316$	15.3739			0.864847
$317$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$317$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$318$		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	0.599119	−	0.800660i	$-0.295518\pi$
$331$	−7.16515	−	12.4104i	−0.393832	−	0.682138i	−0.992951	+	0.118522i	$0.962184\pi$
$332$	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	−0.449094	−	0.893484i	$-0.648253\pi$
$337$	10.0826	−	17.4635i	0.549233	−	0.951299i	0.998327	−	0.0578150i	$-0.0184133\pi$
$338$	−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	−0.263370	+	0.964695i	$0.584834\pi$
$347$	−18.0157	+	31.2042i	−0.967135	+	1.67513i	−0.703765	+	0.710432i	$0.748499\pi$
$348$		0			0
$349$	12.3739	+	21.4322i	0.662358	+	1.14724i	0.979994	+	0.199025i	$0.0637774\pi$
$349$	12.3739	+	21.4322i	0.662358	+	1.14724i	−0.317637	+	0.948212i	$0.602889\pi$
$350$	−6.47135			−0.345908
$351$		0			0
$352$	12.5390			0.668332
$353$	17.8727	+	30.9564i	0.951268	+	1.64765i	0.742686	+	0.669640i	$0.233552\pi$
$353$	17.8727	+	30.9564i	0.951268	+	1.64765i	0.208583	+	0.978005i	$0.433115\pi$
$354$		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	$-0.795768\pi$
$359$	−30.3586			−1.60226			−0.801132	+	0.598488i	$0.795768\pi$
$360$		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	0.957981	−	0.286831i	$-0.0926018\pi$
$367$	4.41742	+	7.65120i	0.230588	+	0.399390i	−0.727394	+	0.686221i	$0.759268\pi$
$368$	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	−0.755401	−	0.655263i	$-0.772558\pi$
$373$	3.66515	−	6.34823i	0.189774	−	0.328699i	0.945175	+	0.326564i	$0.105891\pi$
$374$	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	$-0.997828\pi$
$383$	−9.66930	+	16.7477i	−0.494078	+	0.855769i	0.505898	+	0.862593i	$0.331161\pi$
$384$		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	−0.916379	−	0.400312i	$-0.868902\pi$
$389$	−15.8745	−	27.4955i	−0.804869	−	1.39407i	0.111510	−	0.993763i	$-0.464431\pi$
$390$		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	$-0.718454\pi$
$401$	7.07123	−	12.2477i	0.353120	−	0.611622i	0.986794	+	0.161978i	$0.0517873\pi$
$402$		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	−0.957437	−	0.288642i	$-0.906796\pi$
$409$	−4.62614	+	8.01270i	−0.228748	+	0.396203i	0.728690	+	0.684844i	$0.240130\pi$
$410$	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	$-0.683074\pi$
$419$	9.30780	−	16.1216i	0.454716	−	0.787591i	0.998672	+	0.0515226i	$0.0164074\pi$
$420$		0			0
$421$	8.08258	+	13.9994i	0.393921	+	0.682291i	0.992963	−	0.118427i	$-0.0377851\pi$
$421$	8.08258	+	13.9994i	0.393921	+	0.682291i	−0.599042	+	0.800718i	$0.704452\pi$
$422$	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	$-0.155585\pi$
$431$	36.6591			1.76581			0.882904	+	0.469554i	$0.155585\pi$
$432$		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	−0.991157	−	0.132694i	$-0.957637\pi$
$439$	−12.7913	−	22.1552i	−0.610495	−	1.05741i	0.380662	−	0.924714i	$-0.375696\pi$
$440$	−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	$-0.0316853\pi$
$443$	8.66025	+	15.0000i	0.411461	+	0.712672i	−0.583589	+	0.812049i	$0.698352\pi$
$444$		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	$-0.715535\pi$
$449$	−26.5529			−1.25311			−0.626554	+	0.779378i	$0.715535\pi$
$450$		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	−0.955688	−	0.294380i	$-0.904887\pi$
$457$	−15.6652	−	27.1328i	−0.732785	−	1.26922i	0.222904	−	0.974841i	$-0.428447\pi$
$458$	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	$-0.0662429\pi$
$461$	6.66205	+	11.5390i	0.310283	+	0.537426i	−0.668141	+	0.744035i	$0.732910\pi$
$462$		0			0
$463$	−10.4564	+	18.1111i	−0.485952	+	0.841693i	−0.999870	−	0.0161460i	$-0.994860\pi$
$463$	−10.4564	+	18.1111i	−0.485952	+	0.841693i	0.513918	+	0.857839i	$0.328194\pi$
$464$	2.55040	−	4.41742i	0.118399	−	0.205074i
$465$		0			0
$466$		0			0
$467$	6.20520			0.287143			0.143571	−	0.989640i	$-0.454141\pi$
$467$	6.20520			0.287143			0.143571	+	0.989640i	$0.454141\pi$
$468$		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	−0.997261	−	0.0739690i	$-0.976433\pi$
$479$	−12.3151	−	21.3303i	−0.562689	−	0.974606i	0.434571	−	0.900637i	$-0.356900\pi$
$480$		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	−0.494047	−	0.869435i	$-0.664483\pi$
$491$	11.2107	−	19.4174i	0.505930	−	0.876296i	0.999976	−	0.00686071i	$-0.00218385\pi$
$492$		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	−0.550572	−	0.834788i	$-0.685590\pi$
$499$	10.0000	−	17.3205i	0.447661	−	0.775372i	0.998233	+	0.0594153i	$0.0189236\pi$
$500$	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	$-0.460999\pi$
$503$	5.48220			0.244439			0.122220	+	0.992503i	$0.460999\pi$
$504$		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	$-0.972834\pi$
$509$	−9.57395	+	16.5826i	−0.424358	+	0.735010i	0.572002	+	0.820252i	$0.306167\pi$
$510$		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	$-0.524177\pi$
$521$	−3.46410			−0.151765			−0.0758825	+	0.997117i	$0.524177\pi$
$522$		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	0.970401	−	0.241498i	$-0.0776387\pi$
$547$	6.45644	+	11.1829i	0.276057	+	0.478145i	−0.694344	+	0.719643i	$0.744305\pi$
$548$	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	$-0.585353\pi$
$557$	−12.5058			−0.529886			−0.264943	+	0.964264i	$0.585353\pi$
$558$		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	−0.0286300	+	0.999590i	$0.509114\pi$
$563$	−20.8800	+	36.1652i	−0.879985	+	1.52418i	−0.851355	+	0.524589i	$0.824219\pi$
$564$		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	$-0.0861892\pi$
$569$	5.96683	+	10.3348i	0.250142	+	0.433259i	−0.713422	+	0.700734i	$0.752856\pi$
$570$		0			0
$571$	0.417424	−	0.723000i	0.0174687	−	0.0302566i	−0.857159	−	0.515052i	$-0.827773\pi$
$571$	0.417424	−	0.723000i	0.0174687	−	0.0302566i	0.874628	+	0.484795i	$0.161106\pi$
$572$	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	$-0.223227\pi$
$587$	−4.28245	−	7.41742i	−0.176756	−	0.306150i	−0.940767	+	0.339052i	$0.889894\pi$
$588$		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	$-0.147205\pi$
$593$	43.5873			1.78992			0.894958	+	0.446150i	$0.147205\pi$
$594$		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	$-0.804204\pi$
$599$	2.23658	−	3.87386i	0.0913840	−	0.158282i	0.908094	+	0.418767i	$0.137538\pi$
$600$		0			0
$601$	−2.20871	−	3.82560i	−0.0900952	−	0.156050i	0.817456	−	0.575991i	$-0.195384\pi$
$601$	−2.20871	−	3.82560i	−0.0900952	−	0.156050i	−0.907551	+	0.419942i	$0.862050\pi$
$602$	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	−0.997536	−	0.0701630i	$-0.977648\pi$
$607$	−10.7913	+	18.6911i	−0.438005	+	0.758647i	0.559531	+	0.828810i	$0.310981\pi$
$608$	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	$-0.666805\pi$
$617$	12.4104	−	21.4955i	0.499624	−	0.865374i	1.00000		0.000433948i	$0.000138130\pi$
$618$		0			0
$619$	13.9564	+	24.1733i	0.560957	+	0.971605i	0.997413	+	0.0718801i	$0.0228999\pi$
$619$	13.9564	+	24.1733i	0.560957	+	0.971605i	−0.436457	+	0.899725i	$0.643767\pi$
$620$	−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	$-0.0897023\pi$
$641$	6.06218	+	10.5000i	0.239442	+	0.414725i	−0.721113	+	0.692818i	$0.756369\pi$
$642$		0			0
$643$	17.1652	−	29.7309i	0.676927	−	1.17247i	−0.298974	−	0.954261i	$-0.596644\pi$
$643$	17.1652	−	29.7309i	0.676927	−	1.17247i	0.975901	−	0.218212i	$-0.0700223\pi$
$644$	−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	$-0.571338\pi$
$647$	−11.3060			−0.444485			−0.222242	+	0.974991i	$0.571338\pi$
$648$		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	$-0.757093\pi$
$653$	6.06218	−	10.5000i	0.237231	−	0.410897i	0.959919	+	0.280278i	$0.0904267\pi$
$654$		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	$-0.126314\pi$
$659$	3.24563	+	5.62159i	0.126432	+	0.218986i	−0.795860	+	0.605481i	$0.792981\pi$
$660$		0			0
$661$	4.00000	−	6.92820i	0.155582	−	0.269476i	−0.777689	−	0.628649i	$-0.783608\pi$
$661$	4.00000	−	6.92820i	0.155582	−	0.269476i	0.933271	+	0.359174i	$0.116941\pi$
$662$	−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	−0.998329	−	0.0577870i	$-0.981596\pi$
$673$	−14.2477	−	24.6778i	−0.549210	−	0.951259i	0.449119	−	0.893472i	$-0.351738\pi$
$674$	−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	$-0.0936143\pi$
$677$	5.91915	+	10.2523i	0.227492	+	0.394027i	−0.729573	+	0.683903i	$0.760281\pi$
$678$		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	$-0.527274\pi$
$683$	−4.47315			−0.171160			−0.0855802	+	0.996331i	$0.527274\pi$
$684$		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	0.744390	−	0.667745i	$-0.232740\pi$
$691$	−5.41742	−	9.38325i	−0.206089	−	0.356956i	−0.950479	+	0.310789i	$0.899407\pi$
$692$	−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	$-0.312313\pi$
$701$	29.4449			1.11212			0.556059	+	0.831143i	$0.312313\pi$
$702$		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	0.690127	−	0.723688i	$-0.257554\pi$
$709$	−7.50000	−	12.9904i	−0.281668	−	0.487864i	−0.971796	+	0.235824i	$0.924221\pi$
$710$	−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	$-0.867803\pi$
$719$	−49.0695			−1.82998			−0.914992	+	0.403471i	$0.867803\pi$
$720$		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	−0.874276	−	0.485430i	$-0.838663\pi$
$727$	−23.1216	−	40.0478i	−0.857532	−	1.48529i	0.0167434	−	0.999860i	$-0.494670\pi$
$728$	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	−0.948038	−	0.318156i	$-0.896936\pi$
$733$	−5.37386	+	9.30780i	−0.198488	+	0.343792i	0.749550	+	0.661947i	$0.230270\pi$
$734$	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	$-0.912501\pi$
$743$	−6.70973	+	11.6216i	−0.246156	+	0.426355i	0.716300	+	0.697793i	$0.245834\pi$
$744$		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	−0.767234	−	0.641367i	$-0.778368\pi$
$751$	4.70871	−	8.15573i	0.171823	−	0.297607i	0.939057	+	0.343761i	$0.111701\pi$
$752$	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	0.446155	+	0.894956i	$0.352793\pi$
$761$	−15.2270	+	26.3739i	−0.551977	+	0.956052i	−0.998132	+	0.0610962i	$0.980540\pi$
$762$		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	−0.0981351	−	0.995173i	$-0.531288\pi$
$769$	22.5390	−	39.0387i	0.812778	−	1.40777i	0.910913	−	0.412599i	$-0.135379\pi$
$770$	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	$-0.307896\pi$
$773$	31.5583			1.13507			0.567537	+	0.823348i	$0.307896\pi$
$774$		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	−0.240628	+	0.970617i	$0.577353\pi$
$787$	−26.9564	+	46.6899i	−0.960893	+	1.66432i	−0.720265	+	0.693699i	$0.755980\pi$
$788$	−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	−0.0680737	+	0.997680i	$0.521685\pi$
$797$	−25.3531	+	43.9129i	−0.898053	+	1.55547i	−0.829980	+	0.557794i	$0.811648\pi$
$798$		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	$-0.556852\pi$
$809$	−10.1063			−0.355317			−0.177658	+	0.984092i	$0.556852\pi$
$810$		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	0.994549	+	0.104272i	$0.0332512\pi$
$821$	16.8359	+	29.1606i	0.587576	+	1.01771i	−0.406972	+	0.913440i	$0.633416\pi$
$822$		0			0
$823$	−6.00000	+	10.3923i	−0.209147	+	0.362253i	−0.951446	−	0.307816i	$-0.900402\pi$
$823$	−6.00000	+	10.3923i	−0.209147	+	0.362253i	0.742299	+	0.670069i	$0.233735\pi$
$824$	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	$-0.355280\pi$
$827$	25.2578			0.878298			0.439149	+	0.898414i	$0.355280\pi$
$828$		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	−0.976893	−	0.213727i	$-0.931440\pi$
$839$	−19.5094	−	33.7913i	−0.673540	−	1.16660i	0.303354	−	0.952878i	$-0.401894\pi$
$840$		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	0.736032	−	0.676947i	$-0.236697\pi$
$853$	−6.37386	−	11.0399i	−0.218237	−	0.377997i	−0.954269	+	0.298949i	$0.903364\pi$
$854$	−1.10440			−0.0377918
$855$		0			0
$856$	19.4174			0.663674
$857$	−20.1570	−	34.9129i	−0.688549	−	1.19260i	−0.972307	−	0.233706i	$-0.924915\pi$
$857$	−20.1570	−	34.9129i	−0.688549	−	1.19260i	0.283759	−	0.958896i	$-0.408418\pi$
$858$		0			0
$859$	−13.1652	+	22.8027i	−0.449189	+	0.778018i	−0.998333	−	0.0577091i	$-0.981620\pi$
$859$	−13.1652	+	22.8027i	−0.449189	+	0.778018i	0.549144	+	0.835728i	$0.314954\pi$
$860$	−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	$-0.513305\pi$
$863$	−2.45505			−0.0835709			−0.0417855	+	0.999127i	$0.513305\pi$
$864$		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	−0.954652	−	0.297724i	$-0.903772\pi$
$877$	−6.50000	+	11.2583i	−0.219489	+	0.380167i	0.735163	+	0.677891i	$0.237106\pi$
$878$	−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	$-0.618010\pi$
$881$	−21.5076			−0.724610			−0.362305	+	0.932060i	$0.618010\pi$
$882$		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	$-0.707182\pi$
$887$	11.4967	−	19.9129i	0.386022	−	0.668609i	0.991910	+	0.126940i	$0.0405157\pi$
$888$		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	0.669525	−	0.742790i	$-0.266498\pi$
$907$	−9.29129	−	16.0930i	−0.308512	−	0.534359i	−0.978037	+	0.208431i	$0.933164\pi$
$908$	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	$-0.119318\pi$
$911$	4.47315	+	7.74773i	0.148202	+	0.256694i	−0.782361	+	0.622825i	$0.785985\pi$
$912$		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	$-0.154342\pi$
$929$	1.17985	+	2.04356i	0.0387096	+	0.0670471i	−0.846022	+	0.533149i	$0.821009\pi$
$930$		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	−0.464324	−	0.885665i	$-0.653703\pi$
$941$	16.4068	−	28.4174i	0.534847	−	0.926382i	0.999171	−	0.0407162i	$-0.0129640\pi$
$942$		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	0.975430	+	0.220308i	$0.0707063\pi$
$947$	20.8800	+	36.1652i	0.678508	+	1.17521i	−0.296923	+	0.954901i	$0.595960\pi$
$948$		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	$-0.518853\pi$
$953$	−3.65480			−0.118391			−0.0591953	+	0.998246i	$0.518853\pi$
$954$		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	−0.896390	−	0.443266i	$-0.853820\pi$
$967$	−2.00000	+	3.46410i	−0.0643157	+	0.111398i	0.832075	+	0.554664i	$0.187153\pi$
$968$	−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	$-0.308868\pi$
$971$	35.2131			1.13004			0.565021	+	0.825076i	$0.308868\pi$
$972$		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	$-0.963297\pi$
$977$	−12.4104	+	21.4955i	−0.397044	+	0.687701i	0.596316	+	0.802750i	$0.296631\pi$
$978$		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	0.966096	+	0.258181i	$0.0831232\pi$
$983$	22.1552	+	38.3739i	0.706640	+	1.22394i	−0.259457	+	0.965755i	$0.583543\pi$
$984$		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	0.806823	−	0.590794i	$-0.201185\pi$
$997$	−3.41742	−	5.91915i	−0.108231	−	0.187461i	−0.915054	+	0.403332i	$0.867852\pi$
$998$	−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.190.2		8
3.2	odd	2	inner	567.2.f.n.190.3		8
9.2	odd	6	inner	567.2.f.n.379.3		8
9.4	even	3		567.2.a.i.1.3	yes	4
9.5	odd	6		567.2.a.i.1.2	✓	4
9.7	even	3	inner	567.2.f.n.379.2		8
36.23	even	6		9072.2.a.ci.1.1		4
36.31	odd	6		9072.2.a.ci.1.4		4
63.13	odd	6		3969.2.a.u.1.3		4
63.41	even	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	9.5	odd	6
567.2.a.i.1.3	yes	4	9.4	even	3
567.2.f.n.190.2		8	1.1	even	1	trivial
567.2.f.n.190.3		8	3.2	odd	2	inner
567.2.f.n.379.2		8	9.7	even	3	inner
567.2.f.n.379.3		8	9.2	odd	6	inner
3969.2.a.u.1.2		4	63.41	even	6
3969.2.a.u.1.3		4	63.13	odd	6
9072.2.a.ci.1.1		4	36.23	even	6
9072.2.a.ci.1.4		4	36.31	odd	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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