LMFDB - Embedded newform 567.2.e.g.163.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(163,567)] 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([0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.163"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 14x^{12} - 39x^{10} + 77x^{8} - 156x^{6} + 224x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 14x^12 - 39x^10 + 77x^8 - 156x^6 + 224x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.1
Root			$-1.14160 + 0.834713i$ of defining polynomial
Character	$\chi$	$=$	567.163
Dual form			567.2.e.g.487.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.29368 + 2.24073i) q^{2} +(-2.34723 - 4.06553i) q^{4} +(-1.14160 + 1.97731i) q^{5} +(2.45374 + 0.989520i) q^{7} +6.97158 q^{8} +(-2.95374 - 5.11603i) q^{10} +(1.47816 + 2.56025i) q^{11} +4.26843 q^{13} +(-5.39161 + 4.21804i) q^{14} +(-4.32455 + 7.49033i) q^{16} +(0.764218 + 1.32366i) q^{17} +(-3.69033 + 6.39184i) q^{19} +10.7184 q^{20} -7.64909 q^{22} +(3.07601 - 5.32780i) q^{23} +(-0.106508 - 0.184478i) q^{25} +(-5.52200 + 9.56439i) q^{26} +(-1.73659 - 12.2984i) q^{28} -2.34038 q^{29} +(-3.11065 - 5.38780i) q^{31} +(-4.21761 - 7.30512i) q^{32} -3.95462 q^{34} +(-4.75779 + 3.72218i) q^{35} +(-3.58796 + 6.21453i) q^{37} +(-9.54823 - 16.5380i) q^{38} +(-7.95876 + 13.7850i) q^{40} -7.89168 q^{41} +0.834123 q^{43} +(6.93918 - 12.0190i) q^{44} +(7.95876 + 13.7850i) q^{46} +(-2.91322 + 5.04584i) q^{47} +(5.04170 + 4.85605i) q^{49} +0.551152 q^{50} +(-10.0190 - 17.3534i) q^{52} +(-3.71826 - 6.44021i) q^{53} -6.74989 q^{55} +(17.1065 + 6.89851i) q^{56} +(3.02771 - 5.24415i) q^{58} +(2.31179 + 4.00414i) q^{59} +(3.56527 - 6.17523i) q^{61} +16.0968 q^{62} +4.52683 q^{64} +(-4.87285 + 8.44003i) q^{65} +(1.66262 + 2.87974i) q^{67} +(3.58760 - 6.21390i) q^{68} +(-2.18531 - 15.4762i) q^{70} +0.160242 q^{71} +(0.190329 + 0.329659i) q^{73} +(-9.28337 - 16.0793i) q^{74} +34.6483 q^{76} +(1.09361 + 7.74486i) q^{77} +(3.97731 - 6.88891i) q^{79} +(-9.87382 - 17.1020i) q^{80} +(10.2093 - 17.6831i) q^{82} +4.29800 q^{83} -3.48973 q^{85} +(-1.07909 + 1.86904i) q^{86} +(10.3051 + 17.8490i) q^{88} +(3.02828 - 5.24514i) q^{89} +(10.4736 + 4.22370i) q^{91} -28.8804 q^{92} +(-7.53756 - 13.0554i) q^{94} +(-8.42577 - 14.5939i) q^{95} -1.32209 q^{97} +(-17.4034 + 5.01487i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} + 6 q^{7} - 14 q^{10} + 12 q^{13} - 6 q^{16} - 24 q^{19} + 4 q^{22} - 26 q^{28} - 20 q^{31} + 4 q^{37} - 36 q^{40} + 20 q^{43} + 36 q^{46} - 14 q^{49} - 34 q^{52} + 8 q^{55} + 22 q^{58} - 36 q^{61}+ \cdots + 28 q^{97}+O(q^{100}) $ 16 * q - 6 * q^4 + 6 * q^7 - 14 * q^10 + 12 * q^13 - 6 * q^16 - 24 * q^19 + 4 * q^22 - 26 * q^28 - 20 * q^31 + 4 * q^37 - 36 * q^40 + 20 * q^43 + 36 * q^46 - 14 * q^49 - 34 * q^52 + 8 * q^55 + 22 * q^58 - 36 * q^61 + 76 * q^64 + 18 * q^67 - 58 * q^70 - 32 * q^73 + 116 * q^76 + 32 * q^79 + 2 * q^82 + 60 * q^85 + 72 * q^88 - 22 * q^91 - 54 * q^94 + 28 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$	−1.29368	+	2.24073i	−0.914772	+	1.58443i	−0.107538	+	0.994201i	$0.534297\pi$
$2$	−1.29368	+	2.24073i	−0.914772	+	1.58443i	−0.807234	+	0.590231i	$0.799037\pi$
$3$		0			0
$3$		0			0
$4$	−2.34723	−	4.06553i	−1.17362	−	2.03276i
$5$	−1.14160	+	1.97731i	−0.510540	+	0.884281i	0.489386	+	0.872067i	$0.337221\pi$
$5$	−1.14160	+	1.97731i	−0.510540	+	0.884281i	−0.999925	+	0.0122133i	$0.996112\pi$
$6$		0			0
$7$	2.45374	+	0.989520i	0.927427	+	0.374003i
$7$	2.45374	+	0.989520i	0.927427	+	0.374003i
$8$	6.97158			2.46482
$9$		0			0
$10$	−2.95374	−	5.11603i	−0.934055	−	1.61783i
$11$	1.47816	+	2.56025i	0.445682	+	0.771945i	0.998099	−	0.0616233i	$-0.0196277\pi$
$11$	1.47816	+	2.56025i	0.445682	+	0.771945i	−0.552417	+	0.833568i	$0.686294\pi$
$12$		0			0
$13$	4.26843			1.18385			0.591925	−	0.805993i	$-0.298368\pi$
$13$	4.26843			1.18385			0.591925	+	0.805993i	$0.298368\pi$
$14$	−5.39161	+	4.21804i	−1.44097	+	1.12732i
$15$		0			0
$16$	−4.32455	+	7.49033i	−1.08114	+	1.87258i
$17$	0.764218	+	1.32366i	0.185350	+	0.321036i	0.943694	−	0.330818i	$-0.107325\pi$
$17$	0.764218	+	1.32366i	0.185350	+	0.321036i	−0.758344	+	0.651854i	$0.773991\pi$
$18$		0			0
$19$	−3.69033	+	6.39184i	−0.846619	+	1.46639i	0.0375879	+	0.999293i	$0.488033\pi$
$19$	−3.69033	+	6.39184i	−0.846619	+	1.46639i	−0.884207	+	0.467095i	$0.845301\pi$
$20$	10.7184			2.39671
$21$		0			0
$22$	−7.64909			−1.63079
$23$	3.07601	−	5.32780i	0.641392	−	1.11092i	−0.343730	−	0.939068i	$-0.611691\pi$
$23$	3.07601	−	5.32780i	0.641392	−	1.11092i	0.985122	−	0.171855i	$-0.0549761\pi$
$24$		0			0
$25$	−0.106508	−	0.184478i	−0.0213017	−	0.0368956i
$26$	−5.52200	+	9.56439i	−1.08295	+	1.87573i
$27$		0			0
$28$	−1.73659	−	12.2984i	−0.328184	−	2.32418i
$29$	−2.34038			−0.434597			−0.217299	−	0.976105i	$-0.569725\pi$
$29$	−2.34038			−0.434597			−0.217299	+	0.976105i	$0.569725\pi$
$30$		0			0
$31$	−3.11065	−	5.38780i	−0.558689	−	0.967677i	−0.997606	−	0.0691500i	$-0.977971\pi$
$31$	−3.11065	−	5.38780i	−0.558689	−	0.967677i	0.438918	−	0.898527i	$-0.355362\pi$
$32$	−4.21761	−	7.30512i	−0.745575	−	1.29137i
$33$		0			0
$34$	−3.95462			−0.678212
$35$	−4.75779	+	3.72218i	−0.804212	+	0.629163i
$36$		0			0
$37$	−3.58796	+	6.21453i	−0.589857	+	1.02166i	0.404394	+	0.914585i	$0.367483\pi$
$37$	−3.58796	+	6.21453i	−0.589857	+	1.02166i	−0.994251	+	0.107077i	$0.965851\pi$
$38$	−9.54823	−	16.5380i	−1.54893	−	2.68282i
$39$		0			0
$40$	−7.95876	+	13.7850i	−1.25839	+	2.17960i
$41$	−7.89168			−1.23247			−0.616237	−	0.787561i	$-0.711344\pi$
$41$	−7.89168			−1.23247			−0.616237	+	0.787561i	$0.711344\pi$
$42$		0			0
$43$	0.834123			0.127203			0.0636013	−	0.997975i	$-0.479741\pi$
$43$	0.834123			0.127203			0.0636013	+	0.997975i	$0.479741\pi$
$44$	6.93918	−	12.0190i	1.04612	−	1.81193i
$45$		0			0
$46$	7.95876	+	13.7850i	1.17346	+	2.03248i
$47$	−2.91322	+	5.04584i	−0.424936	+	0.736011i	−0.996414	−	0.0846058i	$-0.973037\pi$
$47$	−2.91322	+	5.04584i	−0.424936	+	0.736011i	0.571478	+	0.820617i	$0.306370\pi$
$48$		0			0
$49$	5.04170	+	4.85605i	0.720243	+	0.693722i
$50$	0.551152			0.0779447
$51$		0			0
$52$	−10.0190	−	17.3534i	−1.38939	−	2.40649i
$53$	−3.71826	−	6.44021i	−0.510742	−	0.884631i	−0.999923	−	0.0124487i	$-0.996037\pi$
$53$	−3.71826	−	6.44021i	−0.510742	−	0.884631i	0.489180	−	0.872183i	$-0.337296\pi$
$54$		0			0
$55$	−6.74989			−0.910154
$56$	17.1065	+	6.89851i	2.28595	+	0.921852i
$57$		0			0
$58$	3.02771	−	5.24415i	0.397558	−	0.688590i
$59$	2.31179	+	4.00414i	0.300970	+	0.521295i	0.976356	−	0.216170i	$-0.0693564\pi$
$59$	2.31179	+	4.00414i	0.300970	+	0.521295i	−0.675386	+	0.737464i	$0.736023\pi$
$60$		0			0
$61$	3.56527	−	6.17523i	0.456486	−	0.790657i	−0.542286	−	0.840194i	$-0.682441\pi$
$61$	3.56527	−	6.17523i	0.456486	−	0.790657i	0.998772	+	0.0495366i	$0.0157744\pi$
$62$	16.0968			2.04429
$63$		0			0
$64$	4.52683			0.565853
$65$	−4.87285	+	8.44003i	−0.604403	+	1.04686i
$66$		0			0
$67$	1.66262	+	2.87974i	0.203121	+	0.351816i	0.949533	−	0.313669i	$-0.101558\pi$
$67$	1.66262	+	2.87974i	0.203121	+	0.351816i	−0.746411	+	0.665485i	$0.768225\pi$
$68$	3.58760	−	6.21390i	0.435060	−	0.753546i
$69$		0			0
$70$	−2.18531	−	15.4762i	−0.261194	−	1.84976i
$71$	0.160242			0.0190172			0.00950860	−	0.999955i	$-0.496973\pi$
$71$	0.160242			0.0190172			0.00950860	+	0.999955i	$0.496973\pi$
$72$		0			0
$73$	0.190329	+	0.329659i	0.0222763	+	0.0385837i	0.876949	−	0.480584i	$-0.159575\pi$
$73$	0.190329	+	0.329659i	0.0222763	+	0.0385837i	−0.854672	+	0.519168i	$0.826242\pi$
$74$	−9.28337	−	16.0793i	−1.07917	−	1.86918i
$75$		0			0
$76$	34.6483			3.97443
$77$	1.09361	+	7.74486i	0.124628	+	0.882609i
$78$		0			0
$79$	3.97731	−	6.88891i	0.447483	−	0.775063i	−0.550739	−	0.834678i	$-0.685654\pi$
$79$	3.97731	−	6.88891i	0.447483	−	0.775063i	0.998221	+	0.0596151i	$0.0189873\pi$
$80$	−9.87382	−	17.1020i	−1.10393	−	1.91206i
$81$		0			0
$82$	10.2093	−	17.6831i	1.12743	−	1.95277i
$83$	4.29800			0.471767			0.235883	−	0.971781i	$-0.424202\pi$
$83$	4.29800			0.471767			0.235883	+	0.971781i	$0.424202\pi$
$84$		0			0
$85$	−3.48973			−0.378514
$86$	−1.07909	+	1.86904i	−0.116361	+	0.201544i
$87$		0			0
$88$	10.3051	+	17.8490i	1.09853	+	1.90271i
$89$	3.02828	−	5.24514i	0.320997	−	0.555984i	−0.659697	−	0.751532i	$-0.729315\pi$
$89$	3.02828	−	5.24514i	0.320997	−	0.555984i	0.980694	+	0.195548i	$0.0626486\pi$
$90$		0			0
$91$	10.4736	+	4.22370i	1.09794	+	0.442764i
$92$	−28.8804			−3.01099
$93$		0			0
$94$	−7.53756	−	13.0554i	−0.777440	−	1.34657i
$95$	−8.42577	−	14.5939i	−0.864466	−	1.49730i
$96$		0			0
$97$	−1.32209			−0.134238			−0.0671189	−	0.997745i	$-0.521381\pi$
$97$	−1.32209			−0.134238			−0.0671189	+	0.997745i	$0.521381\pi$
$98$	−17.4034	+	5.01487i	−1.75801	+	0.506579i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	9.08101	+	15.7288i	0.903594	+	1.56507i	0.822793	+	0.568341i	$0.192415\pi$
$101$	9.08101	+	15.7288i	0.903594	+	1.56507i	0.0808014	+	0.996730i	$0.474252\pi$
$102$		0			0
$103$	−6.76755	+	11.7217i	−0.666827	+	1.15498i	0.311960	+	0.950095i	$0.399015\pi$
$103$	−6.76755	+	11.7217i	−0.666827	+	1.15498i	−0.978787	+	0.204883i	$0.934319\pi$
$104$	29.7577			2.91798
$105$		0			0
$106$	19.2410			1.86885
$107$	−4.06934	+	7.04830i	−0.393398	+	0.681385i	−0.992895	−	0.118992i	$-0.962034\pi$
$107$	−4.06934	+	7.04830i	−0.393398	+	0.681385i	0.599498	+	0.800377i	$0.295367\pi$
$108$		0			0
$109$	2.74398	+	4.75272i	0.262826	+	0.455228i	0.966992	−	0.254808i	$-0.0820122\pi$
$109$	2.74398	+	4.75272i	0.262826	+	0.455228i	−0.704166	+	0.710036i	$0.748679\pi$
$110$	8.73222	−	15.1246i	0.832584	−	1.44208i
$111$		0			0
$112$	−18.0232	+	14.1001i	−1.70303	+	1.33234i
$113$	−6.25508			−0.588429			−0.294214	−	0.955739i	$-0.595058\pi$
$113$	−6.25508			−0.588429			−0.294214	+	0.955739i	$0.595058\pi$
$114$		0			0
$115$	7.02315	+	12.1645i	0.654912	+	1.13434i
$116$	5.49342	+	9.51487i	0.510051	+	0.883434i
$117$		0			0
$118$	−11.9629			−1.10127
$119$	0.565402	+	4.00414i	0.0518303	+	0.367059i
$120$		0			0
$121$	1.13008	−	1.95735i	0.102734	−	0.177941i
$122$	9.22467	+	15.9776i	0.835162	+	1.44654i
$123$		0			0
$124$	−14.6028	+	25.2929i	−1.31137	+	2.27136i
$125$	−10.9297			−0.977578
$126$		0			0
$127$	−5.60019			−0.496936			−0.248468	−	0.968640i	$-0.579927\pi$
$127$	−5.60019			−0.496936			−0.248468	+	0.968640i	$0.579927\pi$
$128$	2.57894	−	4.46685i	0.227948	−	0.394818i
$129$		0			0
$130$	−12.6079	−	21.8374i	−1.10578	−	1.91527i
$131$	−3.56237	+	6.17020i	−0.311246	+	0.539093i	−0.978632	−	0.205618i	$-0.934080\pi$
$131$	−3.56237	+	6.17020i	−0.311246	+	0.539093i	0.667387	+	0.744711i	$0.267413\pi$
$132$		0			0
$133$	−15.3800	+	12.0323i	−1.33361	+	1.04333i
$134$	−8.60362			−0.743239
$135$		0			0
$136$	5.32780	+	9.22803i	0.456855	+	0.791297i
$137$	−4.43910	−	7.68875i	−0.379258	−	0.656895i	0.611696	−	0.791093i	$-0.290487\pi$
$137$	−4.43910	−	7.68875i	−0.379258	−	0.656895i	−0.990955	+	0.134198i	$0.957154\pi$
$138$		0			0
$139$	8.37099			0.710018			0.355009	−	0.934863i	$-0.384478\pi$
$139$	8.37099			0.710018			0.355009	+	0.934863i	$0.384478\pi$
$140$	26.3002	+	10.6061i	2.22278	+	0.896378i
$141$		0			0
$142$	−0.207302	+	0.359058i	−0.0173964	+	0.0301315i
$143$	6.30943	+	10.9283i	0.527621	+	0.913867i
$144$		0			0
$145$	2.67178	−	4.62766i	0.221879	−	0.384306i
$146$	−0.984900			−0.0815109
$147$		0			0
$148$	33.6871			2.76906
$149$	6.72612	−	11.6500i	0.551025	−	0.954403i	−0.447176	−	0.894446i	$-0.647570\pi$
$149$	6.72612	−	11.6500i	0.551025	−	0.954403i	0.998201	−	0.0599571i	$-0.0190964\pi$
$150$		0			0
$151$	4.51074	+	7.81282i	0.367078	+	0.635799i	0.989107	−	0.147196i	$-0.0470247\pi$
$151$	4.51074	+	7.81282i	0.367078	+	0.635799i	−0.622029	+	0.782994i	$0.713691\pi$
$152$	−25.7274	+	44.5612i	−2.08677	+	3.61439i
$153$		0			0
$154$	−18.7689	−	7.56893i	−1.51244	−	0.609922i
$155$	14.2045			1.14093
$156$		0			0
$157$	−1.46420	−	2.53607i	−0.116856	−	0.202400i	0.801664	−	0.597775i	$-0.203948\pi$
$157$	−1.46420	−	2.53607i	−0.116856	−	0.202400i	−0.918520	+	0.395374i	$0.870615\pi$
$158$	10.2908	+	17.8241i	0.818689	+	1.41801i
$159$		0			0
$160$	19.2593			1.52258
$161$	12.8197	−	10.0293i	1.01033	−	0.790418i
$162$		0			0
$163$	0.602369	−	1.04333i	0.0471812	−	0.0817202i	−0.841470	−	0.540303i	$-0.818310\pi$
$163$	0.602369	−	1.04333i	0.0471812	−	0.0817202i	0.888652	+	0.458583i	$0.151643\pi$
$164$	18.5236	+	32.0839i	1.44645	+	2.50533i
$165$		0			0
$166$	−5.56025	+	9.63064i	−0.431559	+	0.747482i
$167$	14.3693			1.11193			0.555964	−	0.831206i	$-0.312349\pi$
$167$	14.3693			1.11193			0.555964	+	0.831206i	$0.312349\pi$
$168$		0			0
$169$	5.21953			0.401502
$170$	4.51460	−	7.81953i	0.346254	−	0.599730i
$171$		0			0
$172$	−1.95788	−	3.39115i	−0.149287	−	0.258573i
$173$	−2.72184	+	4.71436i	−0.206938	+	0.358426i	−0.950748	−	0.309964i	$-0.899683\pi$
$173$	−2.72184	+	4.71436i	−0.206938	+	0.358426i	0.743811	+	0.668390i	$0.233016\pi$
$174$		0			0
$175$	−0.0787995	−	0.558053i	−0.00595669	−	0.0421849i
$176$	−25.5695			−1.92737
$177$		0			0
$178$	7.83528	+	13.5711i	0.587279	+	1.01720i
$179$	−3.02828	−	5.24514i	−0.226345	−	0.392040i	0.730377	−	0.683044i	$-0.239344\pi$
$179$	−3.02828	−	5.24514i	−0.226345	−	0.392040i	−0.956722	+	0.291004i	$0.906011\pi$
$180$		0			0
$181$	12.7416			0.947076			0.473538	−	0.880773i	$-0.342977\pi$
$181$	12.7416			0.947076			0.473538	+	0.880773i	$0.342977\pi$
$182$	−23.0137	+	18.0044i	−1.70589	+	1.33458i
$183$		0			0
$184$	21.4446	−	37.1432i	1.58092	−	2.73823i
$185$	−8.19204	−	14.1890i	−0.602291	−	1.04320i
$186$		0			0
$187$	−2.25927	+	3.91318i	−0.165215	+	0.286160i
$188$	27.3520			1.99485
$189$		0			0
$190$	43.6011			3.16316
$191$	12.0662	−	20.8993i	0.873079	−	1.51222i	0.0142836	−	0.999898i	$-0.495453\pi$
$191$	12.0662	−	20.8993i	0.873079	−	1.51222i	0.858795	−	0.512319i	$-0.171213\pi$
$192$		0			0
$193$	0.394373	+	0.683075i	0.0283876	+	0.0491688i	0.879870	−	0.475214i	$-0.157629\pi$
$193$	0.394373	+	0.683075i	0.0283876	+	0.0491688i	−0.851483	+	0.524383i	$0.824296\pi$
$194$	1.71036	−	2.96244i	0.122797	−	0.212691i
$195$		0			0
$196$	7.90837	−	31.8955i	0.564883	−	2.27825i
$197$	14.8985			1.06147			0.530736	−	0.847537i	$-0.321915\pi$
$197$	14.8985			1.06147			0.530736	+	0.847537i	$0.321915\pi$
$198$		0			0
$199$	−1.36578	−	2.36561i	−0.0968178	−	0.167693i	0.813548	−	0.581498i	$-0.197533\pi$
$199$	−1.36578	−	2.36561i	−0.0968178	−	0.167693i	−0.910366	+	0.413804i	$0.864200\pi$
$200$	−0.742531	−	1.28610i	−0.0525049	−	0.0909411i
$201$		0			0
$202$	−46.9918			−3.30633
$203$	−5.74269	−	2.31585i	−0.403057	−	0.162541i
$204$		0			0
$205$	9.00916	−	15.6043i	0.629227	−	1.08985i
$206$	−17.5101	−	30.3285i	−1.21999	−	2.11308i
$207$		0			0
$208$	−18.4590	+	31.9720i	−1.27990	+	2.21686i
$209$	−21.8196			−1.50929
$210$		0			0
$211$	−9.17592			−0.631696			−0.315848	−	0.948810i	$-0.602289\pi$
$211$	−9.17592			−0.631696			−0.315848	+	0.948810i	$0.602289\pi$
$212$	−17.4552	+	30.2334i	−1.19883	+	2.07644i
$213$		0			0
$214$	−10.5289	−	18.2365i	−0.719739	−	1.24662i
$215$	−0.952236	+	1.64932i	−0.0649419	+	0.112483i
$216$		0			0
$217$	−2.30139	−	16.2983i	−0.156229	−	1.10640i
$218$	−14.1994			−0.961703
$219$		0			0
$220$	15.8436	+	27.4418i	1.06817	+	1.85013i
$221$	3.26201	+	5.64997i	0.219427	+	0.380058i
$222$		0			0
$223$	−28.3427			−1.89797			−0.948985	−	0.315322i	$-0.897887\pi$
$223$	−28.3427			−1.89797			−0.948985	+	0.315322i	$0.897887\pi$
$224$	−3.12037	−	22.0983i	−0.208489	−	1.47650i
$225$		0			0
$226$	8.09210	−	14.0159i	0.538278	−	0.932326i
$227$	1.03599	+	1.79438i	0.0687608	+	0.119097i	0.898356	−	0.439268i	$-0.144762\pi$
$227$	1.03599	+	1.79438i	0.0687608	+	0.119097i	−0.829595	+	0.558365i	$0.811429\pi$
$228$		0			0
$229$	7.84268	−	13.5839i	0.518259	−	0.897650i	−0.481516	−	0.876437i	$-0.659914\pi$
$229$	7.84268	−	13.5839i	0.518259	−	0.897650i	0.999775	−	0.0212133i	$-0.00675290\pi$
$230$	−36.3429			−2.39638
$231$		0			0
$232$	−16.3161			−1.07121
$233$	14.6262	−	25.3334i	0.958196	−	1.65964i	0.231317	−	0.972878i	$-0.425696\pi$
$233$	14.6262	−	25.3334i	0.958196	−	1.65964i	0.726879	−	0.686766i	$-0.240970\pi$
$234$		0			0
$235$	−6.65147	−	11.5207i	−0.433894	−	0.751526i
$236$	10.8526	−	18.7973i	0.706446	−	1.22360i
$237$		0			0
$238$	−9.70363	−	3.91318i	−0.628993	−	0.253654i
$239$	17.7212			1.14629			0.573144	−	0.819454i	$-0.305723\pi$
$239$	17.7212			1.14629			0.573144	+	0.819454i	$0.305723\pi$
$240$		0			0
$241$	13.2036	+	22.8694i	0.850520	+	1.47314i	0.880739	+	0.473601i	$0.157046\pi$
$241$	13.2036	+	22.8694i	0.850520	+	1.47314i	−0.0302190	+	0.999543i	$0.509620\pi$
$242$	2.92393	+	5.06439i	0.187957	+	0.325551i
$243$		0			0
$244$	−33.4741			−2.14296
$245$	−15.3575	+	4.42534i	−0.981158	+	0.282725i
$246$		0			0
$247$	−15.7519	+	27.2831i	−1.00227	+	1.73598i
$248$	−21.6861	−	37.5615i	−1.37707	−	2.38515i
$249$		0			0
$250$	14.1395	−	24.4904i	0.894261	−	1.54891i
$251$	−8.81798			−0.556586			−0.278293	−	0.960496i	$-0.589769\pi$
$251$	−8.81798			−0.556586			−0.278293	+	0.960496i	$0.589769\pi$
$252$		0			0
$253$	18.1873			1.14343
$254$	7.24487	−	12.5485i	0.454584	−	0.787362i
$255$		0			0
$256$	11.1995	+	19.3981i	0.699968	+	1.21238i
$257$	4.59835	−	7.96458i	0.286837	−	0.496817i	−0.686216	−	0.727398i	$-0.740729\pi$
$257$	4.59835	−	7.96458i	0.286837	−	0.496817i	0.973053	+	0.230581i	$0.0740627\pi$
$258$		0			0
$259$	−14.9533	+	11.6985i	−0.929154	+	0.726909i
$260$	45.7509			2.83735
$261$		0			0
$262$	−9.21716	−	15.9646i	−0.569438	−	0.986295i
$263$	−0.127303	−	0.220495i	−0.00784982	−	0.0135963i	0.862074	−	0.506783i	$-0.169165\pi$
$263$	−0.127303	−	0.220495i	−0.00784982	−	0.0135963i	−0.869924	+	0.493186i	$0.835832\pi$
$264$		0			0
$265$	16.9791			1.04302
$266$	−7.06420	−	50.0282i	−0.433134	−	3.06743i
$267$		0			0
$268$	7.80512	−	13.5189i	0.476773	−	0.825796i
$269$	0.489721	+	0.848222i	0.0298588	+	0.0517170i	0.880569	−	0.473919i	$-0.157161\pi$
$269$	0.489721	+	0.848222i	0.0298588	+	0.0517170i	−0.850710	+	0.525636i	$0.823828\pi$
$270$		0			0
$271$	−7.02445	+	12.1667i	−0.426705	+	0.739075i	−0.996578	−	0.0826580i	$-0.973659\pi$
$271$	−7.02445	+	12.1667i	−0.426705	+	0.739075i	0.569873	+	0.821733i	$0.306992\pi$
$272$	−13.2196			−0.801555
$273$		0			0
$274$	22.9712			1.38774
$275$	0.314873	−	0.545376i	0.0189876	−	0.0328874i
$276$		0			0
$277$	−12.7093	−	22.0132i	−0.763630	−	1.32265i	−0.940968	−	0.338496i	$-0.890082\pi$
$277$	−12.7093	−	22.0132i	−0.763630	−	1.32265i	0.177337	−	0.984150i	$-0.443252\pi$
$278$	−10.8294	+	18.7571i	−0.649505	+	1.12498i
$279$		0			0
$280$	−33.1693	+	25.9494i	−1.98224	+	1.55078i
$281$	29.3811			1.75273			0.876366	−	0.481646i	$-0.159961\pi$
$281$	29.3811			1.75273			0.876366	+	0.481646i	$0.159961\pi$
$282$		0			0
$283$	1.53844	+	2.66466i	0.0914510	+	0.158398i	0.908122	−	0.418706i	$-0.137516\pi$
$283$	1.53844	+	2.66466i	0.0914510	+	0.158398i	−0.816671	+	0.577104i	$0.804183\pi$
$284$	−0.376125	−	0.651467i	−0.0223189	−	0.0386575i
$285$		0			0
$286$	−32.6496			−1.93061
$287$	−19.3642	−	7.80898i	−1.14303	−	0.460949i
$288$		0			0
$289$	7.33194	−	12.6993i	0.431291	−	0.747017i
$290$	6.91287	+	11.9734i	0.405938	+	0.703105i
$291$		0			0
$292$	0.893492	−	1.54757i	0.0522876	−	0.0905649i
$293$	17.0163			0.994105			0.497053	−	0.867720i	$-0.334416\pi$
$293$	17.0163			0.994105			0.497053	+	0.867720i	$0.334416\pi$
$294$		0			0
$295$	−10.5566			−0.614628
$296$	−25.0137	+	43.3251i	−1.45389	+	2.51822i
$297$		0			0
$298$	17.4029	+	30.1428i	1.00812	+	1.74612i
$299$	13.1297	−	22.7414i	0.759313	−	1.31517i
$300$		0			0
$301$	2.04672	+	0.825381i	0.117971	+	0.0475742i
$302$	−23.3419			−1.34317
$303$		0			0
$304$	−31.9180	−	55.2836i	−1.83062	−	3.17073i
$305$	8.14024	+	14.0993i	0.466109	+	0.807324i
$306$		0			0
$307$	24.2396			1.38343			0.691714	−	0.722172i	$-0.256856\pi$
$307$	24.2396			1.38343			0.691714	+	0.722172i	$0.256856\pi$
$308$	28.9200	−	22.6251i	1.64787	−	1.28918i
$309$		0			0
$310$	−18.3761	+	31.8283i	−1.04369	+	1.80773i
$311$	10.9807	+	19.0192i	0.622661	+	1.07848i	0.988988	+	0.147994i	$0.0472816\pi$
$311$	10.9807	+	19.0192i	0.622661	+	1.07848i	−0.366328	+	0.930486i	$0.619385\pi$
$312$		0			0
$313$	1.24073	−	2.14900i	0.0701300	−	0.121469i	−0.828828	−	0.559503i	$-0.810992\pi$
$313$	1.24073	−	2.14900i	0.0701300	−	0.121469i	0.898958	+	0.438035i	$0.144325\pi$
$314$	7.57685			0.427586
$315$		0			0
$316$	−37.3427			−2.10069
$317$	9.73961	−	16.8695i	0.547031	−	0.947486i	−0.451445	−	0.892299i	$-0.649091\pi$
$317$	9.73961	−	16.8695i	0.547031	−	0.947486i	0.998476	−	0.0551868i	$-0.0175754\pi$
$318$		0			0
$319$	−3.45946	−	5.99195i	−0.193692	−	0.335485i
$320$	−5.16783	+	8.95095i	−0.288891	+	0.500373i
$321$		0			0
$322$	5.88824	+	41.7001i	0.328139	+	2.32386i
$323$	−11.2809			−0.627684
$324$		0			0
$325$	−0.454624	−	0.787432i	−0.0252180	−	0.0436789i
$326$	1.55855	+	2.69949i	0.0863201	+	0.149511i
$327$		0			0
$328$	−55.0175			−3.03783
$329$	−12.1412	+	9.49851i	−0.669368	+	0.523670i
$330$		0			0
$331$	−1.28856	+	2.23185i	−0.0708256	+	0.122674i	−0.899263	−	0.437408i	$-0.855897\pi$
$331$	−1.28856	+	2.23185i	−0.0708256	+	0.122674i	0.828438	+	0.560081i	$0.189230\pi$
$332$	−10.0884	−	17.4736i	−0.553673	−	0.958990i
$333$		0			0
$334$	−18.5893	+	32.1976i	−1.01716	+	1.76178i
$335$	−7.59220			−0.414806
$336$		0			0
$337$	−24.1520			−1.31564			−0.657822	−	0.753173i	$-0.728522\pi$
$337$	−24.1520			−1.31564			−0.657822	+	0.753173i	$0.728522\pi$
$338$	−6.75242	+	11.6955i	−0.367283	+	0.636153i
$339$		0			0
$340$	8.19121	+	14.1876i	0.444231	+	0.769430i
$341$	9.19608	−	15.9281i	0.497996	−	0.862554i
$342$		0			0
$343$	7.56588	+	16.9044i	0.408519	+	0.912750i
$344$	5.81515			0.313532
$345$		0			0
$346$	−7.04240	−	12.1978i	−0.378602	−	0.655757i
$347$	−18.1212	−	31.3868i	−0.972797	−	1.68493i	−0.687022	−	0.726637i	$-0.741082\pi$
$347$	−18.1212	−	31.3868i	−0.972797	−	1.68493i	−0.285775	−	0.958297i	$-0.592251\pi$
$348$		0			0
$349$	35.2938			1.88923			0.944617	−	0.328173i	$-0.106433\pi$
$349$	35.2938			1.88923			0.944617	+	0.328173i	$0.106433\pi$
$350$	1.35239	+	0.545376i	0.0722881	+	0.0291516i
$351$		0			0
$352$	12.4686	−	21.5963i	0.664579	−	1.15109i
$353$	1.46109	+	2.53069i	0.0777662	+	0.134695i	0.902286	−	0.431138i	$-0.141888\pi$
$353$	1.46109	+	2.53069i	0.0777662	+	0.134695i	−0.824520	+	0.565833i	$0.808555\pi$
$354$		0			0
$355$	−0.182932	+	0.316848i	−0.00970903	+	0.0168165i
$356$	−28.4324			−1.50691
$357$		0			0
$358$	15.6706			0.828215
$359$	−0.196714	+	0.340719i	−0.0103822	+	0.0179825i	−0.871170	−	0.490982i	$-0.836638\pi$
$359$	−0.196714	+	0.340719i	−0.0103822	+	0.0179825i	0.860788	+	0.508964i	$0.169971\pi$
$360$		0			0
$361$	−17.7371	−	30.7215i	−0.933529	−	1.61692i
$362$	−16.4836	+	28.5504i	−0.866359	+	1.50058i
$363$		0			0
$364$	−7.41251	−	52.4949i	−0.388521	−	2.75148i
$365$	−0.869118			−0.0454917
$366$		0			0
$367$	4.61567	+	7.99457i	0.240936	+	0.417313i	0.960981	−	0.276614i	$-0.0892123\pi$
$367$	4.61567	+	7.99457i	0.240936	+	0.417313i	−0.720045	+	0.693927i	$0.755879\pi$
$368$	26.6047	+	46.0807i	1.38686	+	2.40212i
$369$		0			0
$370$	42.3916			2.20384
$371$	−2.75093	−	19.4819i	−0.142821	−	1.01145i
$372$		0			0
$373$	10.7622	−	18.6407i	0.557245	−	0.965177i	−0.440480	−	0.897763i	$-0.645192\pi$
$373$	10.7622	−	18.6407i	0.557245	−	0.965177i	0.997725	−	0.0674147i	$-0.0214751\pi$
$374$	−5.84557	−	10.1248i	−0.302267	−	0.523542i
$375$		0			0
$376$	−20.3097	+	35.1775i	−1.04739	+	1.81414i
$377$	−9.98975			−0.514498
$378$		0			0
$379$	−18.2445			−0.937159			−0.468579	−	0.883421i	$-0.655234\pi$
$379$	−18.2445			−0.937159			−0.468579	+	0.883421i	$0.655234\pi$
$380$	−39.5545	+	68.5104i	−2.02910	+	3.51451i
$381$		0			0
$382$	31.2197	+	54.0740i	1.59734	+	2.76667i
$383$	−3.12982	+	5.42101i	−0.159926	+	0.277001i	−0.934842	−	0.355064i	$-0.884459\pi$
$383$	−3.12982	+	5.42101i	−0.159926	+	0.277001i	0.774915	+	0.632065i	$0.217792\pi$
$384$		0			0
$385$	−16.5625	−	6.67914i	−0.844102	−	0.340401i
$386$	−2.04078			−0.103873
$387$		0			0
$388$	3.10325	+	5.37499i	0.157544	+	0.272874i
$389$	11.3104	+	19.5902i	0.573460	+	0.993262i	0.996207	+	0.0870142i	$0.0277325\pi$
$389$	11.3104	+	19.5902i	0.573460	+	0.993262i	−0.422747	+	0.906248i	$0.638934\pi$
$390$		0			0
$391$	9.40296			0.475528
$392$	35.1486	+	33.8543i	1.77527	+	1.70990i
$393$		0			0
$394$	−19.2739	+	33.3834i	−0.971006	+	1.68183i
$395$	9.08101	+	15.7288i	0.456915	+	0.791400i
$396$		0			0
$397$	10.6077	−	18.3730i	0.532384	−	0.922115i	−0.466902	−	0.884309i	$-0.654630\pi$
$397$	10.6077	−	18.3730i	0.532384	−	0.922115i	0.999285	−	0.0378060i	$-0.0120369\pi$
$398$	7.06756			0.354265
$399$		0			0
$400$	1.84240			0.0921200
$401$	−2.13721	+	3.70176i	−0.106727	+	0.184857i	−0.914443	−	0.404716i	$-0.867370\pi$
$401$	−2.13721	+	3.70176i	−0.106727	+	0.184857i	0.807715	+	0.589573i	$0.200704\pi$
$402$		0			0
$403$	−13.2776	−	22.9975i	−0.661404	−	1.14559i
$404$	42.6305	−	73.8382i	2.12095	−	3.67359i
$405$		0			0
$406$	12.6184	−	9.87180i	0.626241	−	0.489929i
$407$	−21.2143			−1.05156
$408$		0			0
$409$	−17.6627	−	30.5926i	−0.873363	−	1.51271i	−0.858497	−	0.512819i	$-0.828601\pi$
$409$	−17.6627	−	30.5926i	−0.873363	−	1.51271i	−0.0148660	−	0.999889i	$-0.504732\pi$
$410$	23.3100	+	40.3741i	1.15120	+	1.99394i
$411$		0			0
$412$	63.5401			3.13040
$413$	1.71036	+	12.1127i	0.0841615	+	0.596026i
$414$		0			0
$415$	−4.90660	+	8.49849i	−0.240856	+	0.417174i
$416$	−18.0026	−	31.1814i	−0.882650	−	1.52879i
$417$		0			0
$418$	28.2277	−	48.8917i	1.38066	−	2.39137i
$419$	−3.74901			−0.183151			−0.0915755	−	0.995798i	$-0.529190\pi$
$419$	−3.74901			−0.183151			−0.0915755	+	0.995798i	$0.529190\pi$
$420$		0			0
$421$	24.5327			1.19565			0.597825	−	0.801627i	$-0.296032\pi$
$421$	24.5327			1.19565			0.597825	+	0.801627i	$0.296032\pi$
$422$	11.8707	−	20.5607i	0.577858	−	1.00088i
$423$		0			0
$424$	−25.9221	−	44.8984i	−1.25889	−	2.18046i
$425$	0.162791	−	0.281963i	0.00789653	−	0.0136772i
$426$		0			0
$427$	14.8588	−	11.6245i	0.719066	−	0.562550i
$428$	38.2067			1.84679
$429$		0			0
$430$	−2.46378	−	4.26740i	−0.118814	−	0.205792i
$431$	12.1284	+	21.0071i	0.584206	+	1.01187i	0.994974	+	0.100135i	$0.0319273\pi$
$431$	12.1284	+	21.0071i	0.584206	+	1.01187i	−0.410768	+	0.911740i	$0.634739\pi$
$432$		0			0
$433$	8.60056			0.413317			0.206658	−	0.978413i	$-0.433741\pi$
$433$	8.60056			0.413317			0.206658	+	0.978413i	$0.433741\pi$
$434$	39.4973	+	15.9281i	1.89593	+	0.764572i
$435$		0			0
$436$	12.8815	−	22.3115i	0.616914	−	1.06853i
$437$	22.7030	+	39.3227i	1.08603	+	1.88106i
$438$		0			0
$439$	−13.2792	+	23.0002i	−0.633780	+	1.09774i	0.352992	+	0.935626i	$0.385164\pi$
$439$	−13.2792	+	23.0002i	−0.633780	+	1.09774i	−0.986772	+	0.162113i	$0.948169\pi$
$440$	−47.0573			−2.24337
$441$		0			0
$442$	−16.8801			−0.802902
$443$	−13.8041	+	23.9094i	−0.655853	+	1.13597i	0.325826	+	0.945430i	$0.394358\pi$
$443$	−13.8041	+	23.9094i	−0.655853	+	1.13597i	−0.981679	+	0.190542i	$0.938976\pi$
$444$		0			0
$445$	6.91419	+	11.9757i	0.327764	+	0.567704i
$446$	36.6665	−	63.5083i	1.73621	−	3.00720i
$447$		0			0
$448$	11.1077	+	4.47938i	0.524788	+	0.211631i
$449$	15.6315			0.737695			0.368847	−	0.929490i	$-0.379753\pi$
$449$	15.6315			0.737695			0.368847	+	0.929490i	$0.379753\pi$
$450$		0			0
$451$	−11.6652	−	20.2047i	−0.549292	−	0.951402i
$452$	14.6821	+	25.4302i	0.690590	+	1.19614i
$453$		0			0
$454$	−5.36095			−0.251602
$455$	−20.3083	+	15.8879i	−0.952067	+	0.744835i
$456$		0			0
$457$	16.4677	−	28.5230i	0.770328	−	1.33425i	−0.167055	−	0.985948i	$-0.553426\pi$
$457$	16.4677	−	28.5230i	0.770328	−	1.33425i	0.937383	−	0.348300i	$-0.113241\pi$
$458$	20.2919	+	35.1466i	0.948178	+	1.64229i
$459$		0			0
$460$	32.9700	−	57.1057i	1.53723	−	2.66256i
$461$	−34.9181			−1.62630			−0.813149	−	0.582055i	$-0.802249\pi$
$461$	−34.9181			−1.62630			−0.813149	+	0.582055i	$0.802249\pi$
$462$		0			0
$463$	3.10256			0.144188			0.0720940	−	0.997398i	$-0.477032\pi$
$463$	3.10256			0.144188			0.0720940	+	0.997398i	$0.477032\pi$
$464$	10.1211	−	17.5302i	0.469859	−	0.813820i
$465$		0			0
$466$	37.8434	+	65.5467i	1.75306	+	3.03639i
$467$	−5.26376	+	9.11710i	−0.243578	+	0.421889i	−0.961731	−	0.273996i	$-0.911654\pi$
$467$	−5.26376	+	9.11710i	−0.243578	+	0.421889i	0.718153	+	0.695885i	$0.244988\pi$
$468$		0			0
$469$	1.23008	+	8.71134i	0.0567998	+	0.402252i
$470$	34.4196			1.58766
$471$		0			0
$472$	16.1168	+	27.9152i	0.741837	+	1.28490i
$473$	1.23297	+	2.13556i	0.0566919	+	0.0981933i
$474$		0			0
$475$	1.57220			0.0721376
$476$	14.9518	−	11.6973i	0.685315	−	0.536145i
$477$		0			0
$478$	−22.9256	+	39.7083i	−1.04859	+	1.81622i
$479$	−8.48903	−	14.7034i	−0.387874	−	0.671817i	0.604289	−	0.796765i	$-0.293457\pi$
$479$	−8.48903	−	14.7034i	−0.387874	−	0.671817i	−0.992163	+	0.124948i	$0.960124\pi$
$480$		0			0
$481$	−15.3150	+	26.5263i	−0.698302	+	1.20950i
$482$	−68.3253			−3.11213
$483$		0			0
$484$	−10.6102			−0.482283
$485$	1.50930	−	2.61418i	0.0685337	−	0.118704i
$486$		0			0
$487$	6.60283	+	11.4364i	0.299203	+	0.518235i	0.975954	−	0.217977i	$-0.0699459\pi$
$487$	6.60283	+	11.4364i	0.299203	+	0.518235i	−0.676751	+	0.736212i	$0.736613\pi$
$488$	24.8556	−	43.0511i	1.12516	−	1.94883i
$489$		0			0
$490$	9.95183	−	40.1370i	0.449578	−	1.81321i
$491$	15.7834			0.712293			0.356147	−	0.934430i	$-0.384090\pi$
$491$	15.7834			0.712293			0.356147	+	0.934430i	$0.384090\pi$
$492$		0			0
$493$	−1.78856	−	3.09787i	−0.0805526	−	0.139521i
$494$	−40.7560	−	70.5915i	−1.83370	−	3.17606i
$495$		0			0
$496$	53.8085			2.41608
$497$	0.393192	+	0.158562i	0.0176371	+	0.00711249i
$498$		0			0
$499$	−21.4729	+	37.1922i	−0.961261	+	1.66495i	−0.241919	+	0.970296i	$0.577777\pi$
$499$	−21.4729	+	37.1922i	−0.961261	+	1.66495i	−0.719342	+	0.694656i	$0.755556\pi$
$500$	25.6545	+	44.4348i	1.14730	+	1.98719i
$501$		0			0
$502$	11.4077	−	19.7587i	0.509149	−	0.881873i
$503$	−37.7173			−1.68173			−0.840866	−	0.541243i	$-0.817954\pi$
$503$	−37.7173			−1.68173			−0.840866	+	0.541243i	$0.817954\pi$
$504$		0			0
$505$	−41.4676			−1.84528
$506$	−23.5287	+	40.7529i	−1.04598	+	1.81169i
$507$		0			0
$508$	13.1450	+	22.7677i	0.583213	+	1.01015i
$509$	−17.4964	+	30.3046i	−0.775513	+	1.34323i	0.158992	+	0.987280i	$0.449176\pi$
$509$	−17.4964	+	30.3046i	−0.775513	+	1.34323i	−0.934506	+	0.355949i	$0.884158\pi$
$510$		0			0
$511$	0.140813	+	0.997232i	0.00622922	+	0.0441149i
$512$	−47.6386			−2.10535
$513$		0			0
$514$	11.8976	+	20.6073i	0.524782	+	0.908949i
$515$	−15.4517	−	26.7631i	−0.680883	−	1.17932i
$516$		0			0
$517$	−17.2248			−0.757547
$518$	−6.86824	−	48.6404i	−0.301773	−	2.13714i
$519$		0			0
$520$	−33.9715	+	58.8403i	−1.48975	+	2.58032i
$521$	6.97005	+	12.0725i	0.305363	+	0.528905i	0.977342	−	0.211665i	$-0.0678887\pi$
$521$	6.97005	+	12.0725i	0.305363	+	0.528905i	−0.671979	+	0.740570i	$0.734555\pi$
$522$		0			0
$523$	−13.4103	+	23.2274i	−0.586393	+	1.01566i	0.408308	+	0.912844i	$0.366119\pi$
$523$	−13.4103	+	23.2274i	−0.586393	+	1.01566i	−0.994700	+	0.102817i	$0.967214\pi$
$524$	33.4469			1.46113
$525$		0			0
$526$	0.658757			0.0287232
$527$	4.75442	−	8.23490i	0.207106	−	0.358718i
$528$		0			0
$529$	−7.42366	−	12.8582i	−0.322768	−	0.559050i
$530$	−21.9656	+	38.0455i	−0.954123	+	1.65259i
$531$		0			0
$532$	85.0179	+	34.2851i	3.68599	+	1.48645i
$533$	−33.6851			−1.45907
$534$		0			0
$535$	−9.29112	−	16.0927i	−0.401690	−	0.695748i
$536$	11.5911	+	20.0763i	0.500658	+	0.867166i
$537$		0			0
$538$	−2.53418			−0.109256
$539$	−4.98026	+	20.0860i	−0.214515	+	0.865167i
$540$		0			0
$541$	−11.6251	+	20.1353i	−0.499802	+	0.865683i	−1.00000		0.000228285i	$-0.999927\pi$
$541$	−11.6251	+	20.1353i	−0.499802	+	0.865683i	0.500198	+	0.865911i	$0.333261\pi$
$542$	−18.1748	−	31.4797i	−0.780676	−	1.35217i
$543$		0			0
$544$	6.44635	−	11.1654i	0.276385	−	0.478713i
$545$	−12.5301			−0.536732
$546$		0			0
$547$	15.7425			0.673102			0.336551	−	0.941665i	$-0.390740\pi$
$547$	15.7425			0.673102			0.336551	+	0.941665i	$0.390740\pi$
$548$	−20.8392	+	36.0946i	−0.890208	+	1.54189i
$549$		0			0
$550$	0.814692	+	1.41109i	0.0347386	+	0.0601690i
$551$	8.63677	−	14.9593i	0.367939	−	0.637288i
$552$		0			0
$553$	16.5760	−	12.9680i	0.704884	−	0.551454i
$554$	65.7675			2.79419
$555$		0			0
$556$	−19.6487	−	34.0325i	−0.833289	−	1.44330i
$557$	2.06405	+	3.57504i	0.0874565	+	0.151479i	0.906435	−	0.422345i	$-0.138793\pi$
$557$	2.06405	+	3.57504i	0.0874565	+	0.151479i	−0.818979	+	0.573824i	$0.805459\pi$
$558$		0			0
$559$	3.56040			0.150589
$560$	−7.30508	−	51.7341i	−0.308696	−	2.18617i
$561$		0			0
$562$	−38.0099	+	65.8351i	−1.60335	+	2.77709i
$563$	−0.342707	−	0.593585i	−0.0144434	−	0.0250166i	0.858713	−	0.512456i	$-0.171264\pi$
$563$	−0.342707	−	0.593585i	−0.0144434	−	0.0250166i	−0.873157	+	0.487440i	$0.837931\pi$
$564$		0			0
$565$	7.14081	−	12.3683i	0.300416	−	0.520336i
$566$	−7.96104			−0.334627
$567$		0			0
$568$	1.11714			0.0468740
$569$	9.25223	−	16.0253i	0.387874	−	0.671817i	−0.604290	−	0.796765i	$-0.706543\pi$
$569$	9.25223	−	16.0253i	0.387874	−	0.671817i	0.992163	+	0.124948i	$0.0398763\pi$
$570$		0			0
$571$	−17.2741	−	29.9197i	−0.722901	−	1.25210i	−0.959832	−	0.280574i	$-0.909475\pi$
$571$	−17.2741	−	29.9197i	−0.722901	−	1.25210i	0.236932	−	0.971526i	$-0.423858\pi$
$572$	29.6194	−	51.3024i	1.23845	−	2.14506i
$573$		0			0
$574$	42.5489	−	33.2874i	1.77596	−	1.38939i
$575$	−1.31048			−0.0546509
$576$		0			0
$577$	−0.246628	−	0.427172i	−0.0102673	−	0.0177834i	0.860846	−	0.508865i	$-0.169935\pi$
$577$	−0.246628	−	0.427172i	−0.0102673	−	0.0177834i	−0.871113	+	0.491082i	$0.836602\pi$
$578$	18.9704	+	32.8577i	0.789066	+	1.36670i
$579$		0			0
$580$	−25.0852			−1.04160
$581$	10.5462	+	4.25295i	0.437529	+	0.176442i
$582$		0			0
$583$	10.9924	−	19.0394i	0.455258	−	0.788529i
$584$	1.32689	+	2.29824i	0.0549071	+	0.0951019i
$585$		0			0
$586$	−22.0138	+	38.1290i	−0.909380	+	1.57509i
$587$	37.6412			1.55362			0.776810	−	0.629735i	$-0.216836\pi$
$587$	37.6412			1.55362			0.776810	+	0.629735i	$0.216836\pi$
$588$		0			0
$589$	45.9172			1.89199
$590$	13.6569	−	23.6544i	0.562244	−	0.973836i
$591$		0			0
$592$	−31.0326	−	53.7500i	−1.27543	−	2.20911i
$593$	12.5475	−	21.7328i	0.515262	−	0.892460i	−0.484581	−	0.874746i	$-0.661028\pi$
$593$	12.5475	−	21.7328i	0.515262	−	0.892460i	0.999843	−	0.0177137i	$-0.00563874\pi$
$594$		0			0
$595$	−8.56290	−	3.45316i	−0.351044	−	0.141566i
$596$	−63.1511			−2.58677
$597$		0			0
$598$	33.9715	+	58.8403i	1.38920	+	2.40616i
$599$	−0.269218	−	0.466300i	−0.0110000	−	0.0190525i	0.860473	−	0.509496i	$-0.170168\pi$
$599$	−0.269218	−	0.466300i	−0.0110000	−	0.0190525i	−0.871473	+	0.490444i	$0.836835\pi$
$600$		0			0
$601$	−36.1040			−1.47271			−0.736357	−	0.676593i	$-0.763456\pi$
$601$	−36.1040			−1.47271			−0.736357	+	0.676593i	$0.763456\pi$
$602$	−4.49726	+	3.51836i	−0.183295	+	0.143398i
$603$		0			0
$604$	21.1755	−	36.6770i	0.861619	−	1.49237i
$605$	2.58020	+	4.46903i	0.104900	+	0.181692i
$606$		0			0
$607$	11.1768	−	19.3588i	0.453652	−	0.785749i	−0.544957	−	0.838464i	$-0.683454\pi$
$607$	11.1768	−	19.3588i	0.453652	−	0.785749i	0.998610	+	0.0527149i	$0.0167875\pi$
$608$	62.2575			2.52487
$609$		0			0
$610$	−42.1236			−1.70553
$611$	−12.4349	+	21.5378i	−0.503061	+	0.871328i
$612$		0			0
$613$	12.2687	+	21.2500i	0.495529	+	0.858281i	0.999987	−	0.00515549i	$-0.00164105\pi$
$613$	12.2687	+	21.2500i	0.495529	+	0.858281i	−0.504458	+	0.863436i	$0.668308\pi$
$614$	−31.3584	+	54.3143i	−1.26552	+	2.19195i
$615$		0			0
$616$	7.62418	+	53.9939i	0.307187	+	2.17548i
$617$	−30.1527			−1.21390			−0.606950	−	0.794740i	$-0.707607\pi$
$617$	−30.1527			−1.21390			−0.606950	+	0.794740i	$0.707607\pi$
$618$		0			0
$619$	−11.8047	−	20.4463i	−0.474471	−	0.821808i	0.525102	−	0.851039i	$-0.324027\pi$
$619$	−11.8047	−	20.4463i	−0.474471	−	0.821808i	−0.999573	+	0.0292318i	$0.990694\pi$
$620$	−33.3412	−	57.7487i	−1.33902	−	2.31924i
$621$		0			0
$622$	−56.8224			−2.27837
$623$	12.6208	−	9.87368i	0.505642	−	0.395581i
$624$		0			0
$625$	13.0099	−	22.5337i	0.520394	−	0.901349i
$626$	3.21021	+	5.56025i	0.128306	+	0.222232i
$627$		0			0
$628$	−6.87364	+	11.9055i	−0.274288	+	0.475081i
$629$	−10.9679			−0.437320
$630$		0			0
$631$	−7.41460			−0.295171			−0.147585	−	0.989049i	$-0.547150\pi$
$631$	−7.41460			−0.295171			−0.147585	+	0.989049i	$0.547150\pi$
$632$	27.7281	−	48.0265i	1.10297	−	1.91039i
$633$		0			0
$634$	25.2000	+	43.6476i	1.00082	+	1.73347i
$635$	6.39318	−	11.0733i	0.253706	−	0.439431i
$636$		0			0
$637$	21.5202	+	20.7277i	0.852660	+	0.821263i
$638$	17.9018			0.708738
$639$		0			0
$640$	5.88824	+	10.1987i	0.232753	+	0.403140i
$641$	9.34588	+	16.1875i	0.369140	+	0.639369i	0.989431	−	0.145002i	$-0.0463190\pi$
$641$	9.34588	+	16.1875i	0.369140	+	0.639369i	−0.620291	+	0.784372i	$0.712986\pi$
$642$		0			0
$643$	36.4204			1.43628			0.718141	−	0.695897i	$-0.244993\pi$
$643$	36.4204			1.43628			0.718141	+	0.695897i	$0.244993\pi$
$644$	−70.8652	−	28.5778i	−2.79248	−	1.12612i
$645$		0			0
$646$	14.5939	−	25.2773i	0.574188	−	0.994522i
$647$	8.33593	+	14.4383i	0.327719	+	0.567626i	0.982059	−	0.188574i	$-0.0603867\pi$
$647$	8.33593	+	14.4383i	0.327719	+	0.567626i	−0.654340	+	0.756201i	$0.727053\pi$
$648$		0			0
$649$	−6.83440	+	11.8375i	−0.268274	+	0.464664i
$650$	2.35256			0.0922749
$651$		0			0
$652$	−5.65561			−0.221491
$653$	4.30535	−	7.45708i	0.168481	−	0.291818i	−0.769405	−	0.638761i	$-0.779447\pi$
$653$	4.30535	−	7.45708i	0.168481	−	0.291818i	0.937886	+	0.346943i	$0.112780\pi$
$654$		0			0
$655$	−8.13361	−	14.0878i	−0.317807	−	0.550457i
$656$	34.1280	−	59.1113i	1.33247	−	2.30791i
$657$		0			0
$658$	−5.57662	−	39.4933i	−0.217399	−	1.53961i
$659$	14.6903			0.572253			0.286126	−	0.958192i	$-0.407632\pi$
$659$	14.6903			0.572253			0.286126	+	0.958192i	$0.407632\pi$
$660$		0			0
$661$	−4.06201	−	7.03561i	−0.157994	−	0.273654i	0.776151	−	0.630547i	$-0.217169\pi$
$661$	−4.06201	−	7.03561i	−0.157994	−	0.273654i	−0.934145	+	0.356893i	$0.883836\pi$
$662$	−3.33397	−	5.77461i	−0.129579	−	0.224437i
$663$		0			0
$664$	29.9638			1.16282
$665$	−6.23375	−	44.1470i	−0.241735	−	1.71195i
$666$		0			0
$667$	−7.19902	+	12.4691i	−0.278747	+	0.482805i
$668$	−33.7281	−	58.4187i	−1.30498	−	2.26029i
$669$		0			0
$670$	9.82190	−	17.0120i	0.379453	−	0.657232i
$671$	21.0802			0.813792
$672$		0			0
$673$	−13.1516			−0.506958			−0.253479	−	0.967341i	$-0.581575\pi$
$673$	−13.1516			−0.506958			−0.253479	+	0.967341i	$0.581575\pi$
$674$	31.2451	−	54.1180i	1.20351	−	2.08455i
$675$		0			0
$676$	−12.2515	−	21.2202i	−0.471210	−	0.816160i
$677$	−5.40967	+	9.36982i	−0.207910	+	0.360111i	−0.951056	−	0.309018i	$-0.900000\pi$
$677$	−5.40967	+	9.36982i	−0.207910	+	0.360111i	0.743146	+	0.669130i	$0.233333\pi$
$678$		0			0
$679$	−3.24406	−	1.30823i	−0.124496	−	0.0502054i
$680$	−24.3289			−0.932971
$681$		0			0
$682$	23.7936	+	41.2118i	0.911105	+	1.57808i
$683$	−0.684640	−	1.18583i	−0.0261970	−	0.0453746i	0.852630	−	0.522516i	$-0.175006\pi$
$683$	−0.684640	−	1.18583i	−0.0261970	−	0.0453746i	−0.878827	+	0.477141i	$0.841673\pi$
$684$		0			0
$685$	20.2708			0.774506
$686$	−47.6659	−	4.91584i	−1.81989	−	0.187688i
$687$		0			0
$688$	−3.60720	+	6.24786i	−0.137523	+	0.238197i
$689$	−15.8711	−	27.4896i	−0.604642	−	1.04727i
$690$		0			0
$691$	17.9215	−	31.0409i	0.681765	−	1.18085i	−0.292677	−	0.956211i	$-0.594546\pi$
$691$	17.9215	−	31.0409i	0.681765	−	1.18085i	0.974442	−	0.224640i	$-0.0721207\pi$
$692$	25.5552			0.971462
$693$		0			0
$694$	93.7724			3.55955
$695$	−9.55634	+	16.5521i	−0.362493	+	0.627855i
$696$		0			0
$697$	−6.03097	−	10.4459i	−0.228439	−	0.395668i
$698$	−45.6590	+	79.0838i	−1.72822	+	2.99336i
$699$		0			0
$700$	−2.08382	+	1.63024i	−0.0787610	+	0.0616174i
$701$	29.6235			1.11886			0.559431	−	0.828877i	$-0.311020\pi$
$701$	29.6235			1.11886			0.559431	+	0.828877i	$0.311020\pi$
$702$		0			0
$703$	−26.4815	−	45.8673i	−0.998769	−	1.72992i
$704$	6.69138	+	11.5898i	0.252191	+	0.436807i
$705$		0			0
$706$	−7.56077			−0.284553
$707$	6.71853	+	47.5802i	0.252676	+	1.78944i
$708$		0			0
$709$	7.63863	−	13.2305i	0.286875	−	0.496882i	−0.686187	−	0.727425i	$-0.740717\pi$
$709$	7.63863	−	13.2305i	0.286875	−	0.496882i	0.973062	+	0.230543i	$0.0740503\pi$
$710$	−0.473313	−	0.819802i	−0.0177631	−	0.0307666i
$711$		0			0
$712$	21.1119	−	36.5669i	0.791202	−	1.37040i
$713$	−38.2735			−1.43335
$714$		0			0
$715$	−28.8114			−1.07749
$716$	−14.2162	+	24.6231i	−0.531284	+	0.920210i
$717$		0			0
$718$	−0.508972	−	0.881565i	−0.0189947	−	0.0328997i
$719$	−1.00538	+	1.74138i	−0.0374945	+	0.0649424i	−0.884164	−	0.467177i	$-0.845271\pi$
$719$	−1.00538	+	1.74138i	−0.0374945	+	0.0649424i	0.846669	+	0.532120i	$0.178604\pi$
$720$		0			0
$721$	−28.2047	+	22.0655i	−1.05040	+	0.821763i
$722$	91.7845			3.41587
$723$		0			0
$724$	−29.9075	−	51.8014i	−1.11150	−	1.92518i
$725$	0.249270	+	0.431748i	0.00925765	+	0.0160347i
$726$		0			0
$727$	20.5029			0.760411			0.380206	−	0.924902i	$-0.375853\pi$
$727$	20.5029			0.760411			0.380206	+	0.924902i	$0.375853\pi$
$728$	73.0178	+	29.4458i	2.70622	+	1.09134i
$729$		0			0
$730$	1.12436	−	1.94745i	0.0416146	−	0.0720785i
$731$	0.637452	+	1.10410i	0.0235770	+	0.0408366i
$732$		0			0
$733$	−2.31427	+	4.00844i	−0.0854797	+	0.148055i	−0.905596	−	0.424142i	$-0.860576\pi$
$733$	−2.31427	+	4.00844i	−0.0854797	+	0.148055i	0.820116	+	0.572198i	$0.193909\pi$
$734$	−23.8849			−0.881606
$735$		0			0
$736$	−51.8936			−1.91282
$737$	−4.91524	+	8.51345i	−0.181055	+	0.313597i
$738$		0			0
$739$	11.6640	+	20.2026i	0.429066	+	0.743164i	0.996790	−	0.0800546i	$-0.0255095\pi$
$739$	11.6640	+	20.2026i	0.429066	+	0.743164i	−0.567725	+	0.823219i	$0.692176\pi$
$740$	−38.4573	+	66.6099i	−1.41372	+	2.44863i
$741$		0			0
$742$	47.2125	+	19.0394i	1.73322	+	0.698957i
$743$	−52.2565			−1.91711			−0.958553	−	0.284913i	$-0.908035\pi$
$743$	−52.2565			−1.91711			−0.958553	+	0.284913i	$0.908035\pi$
$744$		0			0
$745$	15.3571	+	26.5993i	0.562640	+	0.974521i
$746$	27.8458	+	48.2303i	1.01951	+	1.76584i
$747$		0			0
$748$	21.2122			0.775594
$749$	−16.9595	+	13.2680i	−0.619688	+	0.484803i
$750$		0			0
$751$	3.09378	−	5.35858i	0.112894	−	0.195538i	−0.804042	−	0.594572i	$-0.797321\pi$
$751$	3.09378	−	5.35858i	0.112894	−	0.195538i	0.916936	+	0.399035i	$0.130655\pi$
$752$	−25.1967	−	43.6419i	−0.918829	−	1.59146i
$753$		0			0
$754$	12.9236	−	22.3843i	0.470649	−	0.815188i
$755$	−20.5979			−0.749633
$756$		0			0
$757$	20.9175			0.760260			0.380130	−	0.924933i	$-0.375879\pi$
$757$	20.9175			0.760260			0.380130	+	0.924933i	$0.375879\pi$
$758$	23.6026	−	40.8810i	0.857287	−	1.48486i
$759$		0			0
$760$	−58.7409	−	101.742i	−2.13076	−	3.69058i
$761$	−16.9572	+	29.3707i	−0.614696	+	1.06469i	0.375741	+	0.926725i	$0.377388\pi$
$761$	−16.9572	+	29.3707i	−0.614696	+	1.06469i	−0.990438	+	0.137961i	$0.955945\pi$
$762$		0			0
$763$	2.03012	+	14.3772i	0.0734952	+	0.520488i
$764$	−113.289			−4.09864
$765$		0			0
$766$	−8.09800	−	14.0261i	−0.292593	−	0.506785i
$767$	9.86773	+	17.0914i	0.356303	+	0.617135i
$768$		0			0
$769$	−8.50784			−0.306800			−0.153400	−	0.988164i	$-0.549022\pi$
$769$	−8.50784			−0.306800			−0.153400	+	0.988164i	$0.549022\pi$
$770$	36.3927	−	28.4713i	1.31150	−	1.02603i
$771$		0			0
$772$	1.85137	−	3.20667i	0.0666324	−	0.115411i
$773$	−22.7870	−	39.4682i	−0.819590	−	1.41957i	−0.905985	−	0.423310i	$-0.860868\pi$
$773$	−22.7870	−	39.4682i	−0.819590	−	1.41957i	0.0863952	−	0.996261i	$-0.472465\pi$
$774$		0			0
$775$	−0.662620	+	1.14769i	−0.0238020	+	0.0412263i
$776$	−9.21704			−0.330873
$777$		0			0
$778$	−58.5283			−2.09834
$779$	29.1229	−	50.4424i	1.04344	−	1.80729i
$780$		0			0
$781$	0.236863	+	0.410259i	0.00847563	+	0.0146802i
$782$	−12.1645	+	21.0695i	−0.435000	+	0.753442i
$783$		0			0
$784$	−58.1765	+	16.7638i	−2.07773	+	0.598707i
$785$	6.68614			0.238638
$786$		0			0
$787$	4.16234	+	7.20939i	0.148372	+	0.256987i	0.930626	−	0.365972i	$-0.119264\pi$
$787$	4.16234	+	7.20939i	0.148372	+	0.256987i	−0.782254	+	0.622959i	$0.785930\pi$
$788$	−34.9702	−	60.5702i	−1.24576	−	2.15772i
$789$		0			0
$790$	−46.9918			−1.67189
$791$	−15.3484	−	6.18953i	−0.545725	−	0.220074i
$792$		0			0
$793$	15.2181	−	26.3586i	0.540412	−	0.936020i
$794$	27.4459	+	47.5377i	0.974019	+	1.68705i
$795$		0			0
$796$	−6.41162	+	11.1053i	−0.227254	+	0.393615i
$797$	39.2773			1.39127			0.695637	−	0.718394i	$-0.255122\pi$
$797$	39.2773			1.39127			0.695637	+	0.718394i	$0.255122\pi$
$798$		0			0
$799$	−8.90533			−0.315048
$800$	−0.898421	+	1.55611i	−0.0317640	+	0.0550168i
$801$		0			0
$802$	−5.52975	−	9.57781i	−0.195262	−	0.338204i
$803$	−0.562673	+	0.974578i	−0.0198563	+	0.0343921i
$804$		0			0
$805$	5.19604	+	36.7980i	0.183136	+	1.29696i
$806$	68.7080			2.42014
$807$		0			0
$808$	63.3090	+	109.654i	2.22720	+	3.85763i
$809$	11.4525	+	19.8364i	0.402649	+	0.697409i	0.994045	−	0.108973i	$-0.0347561\pi$
$809$	11.4525	+	19.8364i	0.402649	+	0.697409i	−0.591395	+	0.806382i	$0.701423\pi$
$810$		0			0
$811$	−17.0254			−0.597842			−0.298921	−	0.954278i	$-0.596627\pi$
$811$	−17.0254			−0.597842			−0.298921	+	0.954278i	$0.596627\pi$
$812$	4.06427	+	28.7829i	0.142628	+	1.01008i
$813$		0			0
$814$	27.4446	−	47.5355i	0.961934	−	1.66612i
$815$	1.37533	+	2.38214i	0.0481758	+	0.0834429i
$816$		0			0
$817$	−3.07819	+	5.33158i	−0.107692	+	0.186528i
$818$	91.3996			3.19571
$819$		0			0
$820$	−84.5864			−2.95389
$821$	16.3565	−	28.3303i	0.570845	−	0.988733i	−0.425634	−	0.904895i	$-0.639949\pi$
$821$	16.3565	−	28.3303i	0.570845	−	0.988733i	0.996479	−	0.0838376i	$-0.0267177\pi$
$822$		0			0
$823$	13.9457	+	24.1547i	0.486118	+	0.841981i	0.999873	−	0.0159561i	$-0.00507920\pi$
$823$	13.9457	+	24.1547i	0.486118	+	0.841981i	−0.513755	+	0.857937i	$0.671746\pi$
$824$	−47.1805	+	81.7190i	−1.64361	+	2.84682i
$825$		0			0
$826$	−29.3539	−	11.8375i	−1.02135	−	0.411880i
$827$	17.5753			0.611153			0.305576	−	0.952168i	$-0.401151\pi$
$827$	17.5753			0.611153			0.305576	+	0.952168i	$0.401151\pi$
$828$		0			0
$829$	0.997731	+	1.72812i	0.0346526	+	0.0600201i	0.882832	−	0.469690i	$-0.155634\pi$
$829$	0.997731	+	1.72812i	0.0346526	+	0.0600201i	−0.848179	+	0.529710i	$0.822301\pi$
$830$	−12.6952	−	21.9887i	−0.440656	−	0.763239i
$831$		0			0
$832$	19.3225			0.669886
$833$	−2.57482	+	10.3846i	−0.0892124	+	0.359805i
$834$		0			0
$835$	−16.4040	+	28.4126i	−0.567684	+	0.983257i
$836$	51.2157	+	88.7082i	1.77133	+	3.06804i
$837$		0			0
$838$	4.85003	−	8.40049i	0.167541	−	0.290190i
$839$	22.6524			0.782046			0.391023	−	0.920381i	$-0.372121\pi$
$839$	22.6524			0.782046			0.391023	+	0.920381i	$0.372121\pi$
$840$		0			0
$841$	−23.5226			−0.811125
$842$	−31.7375	+	54.9710i	−1.09375	+	1.89443i
$843$		0			0
$844$	21.5380	+	37.3050i	0.741369	+	1.28409i
$845$	−5.95863	+	10.3206i	−0.204983	+	0.355041i
$846$		0			0
$847$	4.70976	−	3.68460i	0.161829	−	0.126605i
$848$	64.3191			2.20873
$849$		0			0
$850$	0.421200	+	0.729541i	0.0144471	+	0.0250230i
$851$	22.0732	+	38.2319i	0.756659	+	1.31057i
$852$		0			0
$853$	−13.3024			−0.455465			−0.227732	−	0.973724i	$-0.573131\pi$
$853$	−13.3024			−0.455465			−0.227732	+	0.973724i	$0.573131\pi$
$854$	6.82481	+	48.3329i	0.233540	+	1.65392i
$855$		0			0
$856$	−28.3697	+	49.1377i	−0.969656	+	1.67949i
$857$	12.1665	+	21.0729i	0.415599	+	0.719838i	0.995491	−	0.0948550i	$-0.0302387\pi$
$857$	12.1665	+	21.0729i	0.415599	+	0.719838i	−0.579892	+	0.814693i	$0.696905\pi$
$858$		0			0
$859$	−7.80925	+	13.5260i	−0.266448	+	0.461502i	−0.967942	−	0.251174i	$-0.919183\pi$
$859$	−7.80925	+	13.5260i	−0.266448	+	0.461502i	0.701494	+	0.712676i	$0.252517\pi$
$860$	8.94048			0.304868
$861$		0			0
$862$	−62.7614			−2.13766
$863$	−18.3558	+	31.7931i	−0.624838	+	1.08225i	0.363735	+	0.931503i	$0.381502\pi$
$863$	−18.3558	+	31.7931i	−0.624838	+	1.08225i	−0.988572	+	0.150748i	$0.951832\pi$
$864$		0			0
$865$	−6.21451	−	10.7638i	−0.211300	−	0.365982i
$866$	−11.1264	+	19.2715i	−0.378091	+	0.654872i
$867$		0			0
$868$	−60.8594	+	47.6123i	−2.06570	+	1.61607i
$869$	23.5164			0.797740
$870$		0			0
$871$	7.09678	+	12.2920i	0.240465	+	0.416498i
$872$	19.1299	+	33.1339i	0.647820	+	1.12206i
$873$		0			0
$874$	−117.482			−3.97388
$875$	−26.8186	−	10.8151i	−0.906633	−	0.365617i
$876$		0			0
$877$	25.0992	−	43.4730i	0.847538	−	1.46798i	−0.0358600	−	0.999357i	$-0.511417\pi$
$877$	25.0992	−	43.4730i	0.847538	−	1.46798i	0.883398	−	0.468623i	$-0.155250\pi$
$878$	−34.3581	−	59.5099i	−1.15953	−	2.00836i
$879$		0			0
$880$	29.1902	−	50.5589i	0.984001	−	1.70434i
$881$	51.6426			1.73989			0.869943	−	0.493153i	$-0.164156\pi$
$881$	51.6426			1.73989			0.869943	+	0.493153i	$0.164156\pi$
$882$		0			0
$883$	−4.77954			−0.160844			−0.0804222	−	0.996761i	$-0.525627\pi$
$883$	−4.77954			−0.160844			−0.0804222	+	0.996761i	$0.525627\pi$
$884$	15.3134	−	26.5236i	0.515046	−	0.892086i
$885$		0			0
$886$	−35.7163	−	61.8625i	−1.19991	−	2.07831i
$887$	15.5782	−	26.9823i	0.523066	−	0.905976i	−0.476574	−	0.879134i	$-0.658122\pi$
$887$	15.5782	−	26.9823i	0.523066	−	0.905976i	0.999640	−	0.0268420i	$-0.00854509\pi$
$888$		0			0
$889$	−13.7414	−	5.54150i	−0.460872	−	0.185856i
$890$	−35.7791			−1.19932
$891$		0			0
$892$	66.5270	+	115.228i	2.22749	+	3.85812i
$893$	−21.5015	−	37.2416i	−0.719519	−	1.24624i
$894$		0			0
$895$	13.8284			0.462232
$896$	10.7481	−	8.40860i	0.359069	−	0.280911i
$897$		0			0
$898$	−20.2222	+	35.0258i	−0.674823	+	1.16883i
$899$	7.28009	+	12.6095i	0.242805	+	0.420550i
$900$		0			0
$901$	5.68312	−	9.84345i	0.189332	−	0.327933i
$902$	60.3642			2.00991
$903$		0			0
$904$	−43.6078			−1.45037
$905$	−14.5458	+	25.1941i	−0.483520	+	0.837481i
$906$		0			0
$907$	11.1185	+	19.2578i	0.369184	+	0.639445i	0.989438	−	0.144955i	$-0.0463039\pi$
$907$	11.1185	+	19.2578i	0.369184	+	0.639445i	−0.620254	+	0.784401i	$0.712971\pi$
$908$	4.86340	−	8.42366i	0.161398	−	0.279549i
$909$		0			0
$910$	−9.32784	−	66.0592i	−0.309215	−	2.18984i
$911$	2.03370			0.0673794			0.0336897	−	0.999432i	$-0.489274\pi$
$911$	2.03370			0.0673794			0.0336897	+	0.999432i	$0.489274\pi$
$912$		0			0
$913$	6.35314	+	11.0040i	0.210258	+	0.364178i
$914$	42.6081	+	73.7993i	1.40935	+	2.44107i
$915$		0			0
$916$	−73.6344			−2.43295
$917$	−14.8467	+	11.6151i	−0.490280	+	0.383563i
$918$		0			0
$919$	23.8031	−	41.2282i	0.785193	−	1.35999i	−0.143691	−	0.989623i	$-0.545897\pi$
$919$	23.8031	−	41.2282i	0.785193	−	1.35999i	0.928884	−	0.370371i	$-0.120769\pi$
$920$	48.9624	+	84.8054i	1.61424	+	2.79595i
$921$		0			0
$922$	45.1730	−	78.2419i	1.48769	−	2.57676i
$923$	0.683981			0.0225135
$924$		0			0
$925$	1.52859			0.0502597
$926$	−4.01373	+	6.95198i	−0.131899	+	0.228456i
$927$		0			0
$928$	9.87080	+	17.0967i	0.324025	+	0.561228i
$929$	15.6050	−	27.0287i	0.511985	−	0.886784i	−0.487919	−	0.872889i	$-0.662244\pi$
$929$	15.6050	−	27.0287i	0.511985	−	0.886784i	0.999903	−	0.0138945i	$-0.00442289\pi$
$930$		0			0
$931$	−49.6446	+	14.3053i	−1.62704	+	0.468837i
$932$	−137.325			−4.49822
$933$		0			0
$934$	−13.6193	−	23.5893i	−0.445637	−	0.771865i
$935$	−5.15838	−	8.93458i	−0.168697	−	0.292192i
$936$		0			0
$937$	−18.0157			−0.588548			−0.294274	−	0.955721i	$-0.595078\pi$
$937$	−18.0157			−0.588548			−0.294274	+	0.955721i	$0.595078\pi$
$938$	−21.1111	−	8.51345i	−0.689300	−	0.277974i
$939$		0			0
$940$	−31.2251	+	54.0835i	−1.01845	+	1.76401i
$941$	−21.8559	−	37.8555i	−0.712481	−	1.23405i	−0.963923	−	0.266181i	$-0.914238\pi$
$941$	−21.8559	−	37.8555i	−0.712481	−	1.23405i	0.251442	−	0.967872i	$-0.419095\pi$
$942$		0			0
$943$	−24.2749	+	42.0453i	−0.790499	+	1.36918i
$944$	−39.9898			−1.30156
$945$		0			0
$946$	−6.38028			−0.207441
$947$	−22.2393	+	38.5197i	−0.722681	+	1.25172i	0.237240	+	0.971451i	$0.423757\pi$
$947$	−22.2393	+	38.5197i	−0.722681	+	1.25172i	−0.959921	+	0.280270i	$0.909576\pi$
$948$		0			0
$949$	0.812405	+	1.40713i	0.0263718	+	0.0456773i
$950$	−2.03393	+	3.52288i	−0.0659895	+	0.114297i
$951$		0			0
$952$	3.94174	+	27.9152i	0.127753	+	0.904736i
$953$	−52.3118			−1.69454			−0.847272	−	0.531159i	$-0.821757\pi$
$953$	−52.3118			−1.69454			−0.847272	+	0.531159i	$0.821757\pi$
$954$		0			0
$955$	27.5496	+	47.7172i	0.891483	+	1.54409i
$956$	−41.5958	−	72.0460i	−1.34530	−	2.33013i
$957$		0			0
$958$	43.9285			1.41927
$959$	−3.28424	−	23.2588i	−0.106054	−	0.751066i
$960$		0			0
$961$	−3.85225	+	6.67230i	−0.124266	+	0.215236i
$962$	−39.6254	−	68.6333i	−1.27758	−	2.21283i
$963$		0			0
$964$	61.9840	−	107.359i	1.99637	−	3.45781i
$965$	−1.80087			−0.0579720
$966$		0			0
$967$	0.663672			0.0213423			0.0106711	−	0.999943i	$-0.496603\pi$
$967$	0.663672			0.0213423			0.0106711	+	0.999943i	$0.496603\pi$
$968$	7.87843	−	13.6458i	0.253222	−	0.438594i
$969$		0			0
$970$	3.90511	+	6.76385i	0.125385	+	0.217174i
$971$	29.2598	−	50.6795i	0.938993	−	1.62638i	0.171639	−	0.985160i	$-0.445094\pi$
$971$	29.2598	−	50.6795i	0.938993	−	1.62638i	0.767354	−	0.641224i	$-0.221573\pi$
$972$		0			0
$973$	20.5403	+	8.28326i	0.658490	+	0.265549i
$974$	−34.1679			−1.09481
$975$		0			0
$976$	30.8364	+	53.4101i	0.987048	+	1.70962i
$977$	−27.0201	−	46.8002i	−0.864450	−	1.49727i	−0.867593	−	0.497276i	$-0.834334\pi$
$977$	−27.0201	−	46.8002i	−0.864450	−	1.49727i	0.00314297	−	0.999995i	$-0.499000\pi$
$978$		0			0
$979$	17.9052			0.572252
$980$	54.0391	+	52.0492i	1.72622	+	1.66265i
$981$		0			0
$982$	−20.4187	+	35.3662i	−0.651586	+	1.12858i
$983$	10.9261	+	18.9245i	0.348487	+	0.603597i	0.985981	−	0.166858i	$-0.0533622\pi$
$983$	10.9261	+	18.9245i	0.348487	+	0.603597i	−0.637494	+	0.770455i	$0.720029\pi$
$984$		0			0
$985$	−17.0081	+	29.4589i	−0.541924	+	0.938640i
$986$	9.25532			0.294749
$987$		0			0
$988$	147.894			4.70513
$989$	2.56577	−	4.44404i	0.0815867	−	0.141312i
$990$		0			0
$991$	6.91507	+	11.9773i	0.219664	+	0.380470i	0.954705	−	0.297553i	$-0.0961704\pi$
$991$	6.91507	+	11.9773i	0.219664	+	0.380470i	−0.735041	+	0.678023i	$0.762837\pi$
$992$	−26.2390	+	45.4473i	−0.833089	+	1.44295i
$993$		0			0
$994$	−0.863961	+	0.675906i	−0.0274032	+	0.0214384i
$995$	6.23672			0.197717
$996$		0			0
$997$	3.13701	+	5.43346i	0.0993501	+	0.172079i	0.911416	−	0.411487i	$-0.134990\pi$
$997$	3.13701	+	5.43346i	0.0993501	+	0.172079i	−0.812066	+	0.583566i	$0.801657\pi$
$998$	−55.5584	−	96.2299i	−1.75867	−	3.04611i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.e.g.163.1	✓	16
3.2	odd	2	inner	567.2.e.g.163.8	yes	16
7.2	even	3		3969.2.a.bg.1.8		8
7.4	even	3	inner	567.2.e.g.487.1	yes	16
7.5	odd	6		3969.2.a.bf.1.8		8
9.2	odd	6		567.2.h.l.352.1		16
9.4	even	3		567.2.g.l.541.1		16
9.5	odd	6		567.2.g.l.541.8		16
9.7	even	3		567.2.h.l.352.8		16
21.2	odd	6		3969.2.a.bg.1.1		8
21.5	even	6		3969.2.a.bf.1.1		8
21.11	odd	6	inner	567.2.e.g.487.8	yes	16
63.4	even	3		567.2.h.l.298.8		16
63.11	odd	6		567.2.g.l.109.8		16
63.25	even	3		567.2.g.l.109.1		16
63.32	odd	6		567.2.h.l.298.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.g.163.1	✓	16	1.1	even	1	trivial
567.2.e.g.163.8	yes	16	3.2	odd	2	inner
567.2.e.g.487.1	yes	16	7.4	even	3	inner
567.2.e.g.487.8	yes	16	21.11	odd	6	inner
567.2.g.l.109.1		16	63.25	even	3
567.2.g.l.109.8		16	63.11	odd	6
567.2.g.l.541.1		16	9.4	even	3
567.2.g.l.541.8		16	9.5	odd	6
567.2.h.l.298.1		16	63.32	odd	6
567.2.h.l.298.8		16	63.4	even	3
567.2.h.l.352.1		16	9.2	odd	6
567.2.h.l.352.8		16	9.7	even	3
3969.2.a.bf.1.1		8	21.5	even	6
3969.2.a.bf.1.8		8	7.5	odd	6
3969.2.a.bg.1.1		8	21.2	odd	6
3969.2.a.bg.1.8		8	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29368 + 2.24073i) q^{2} +(-2.34723 - 4.06553i) q^{4} +(-1.14160 + 1.97731i) q^{5} +(2.45374 + 0.989520i) q^{7} +6.97158 q^{8} +(-2.95374 - 5.11603i) q^{10} +(1.47816 + 2.56025i) q^{11} +4.26843 q^{13} +(-5.39161 + 4.21804i) q^{14} +(-4.32455 + 7.49033i) q^{16} +(0.764218 + 1.32366i) q^{17} +(-3.69033 + 6.39184i) q^{19} +10.7184 q^{20} -7.64909 q^{22} +(3.07601 - 5.32780i) q^{23} +(-0.106508 - 0.184478i) q^{25} +(-5.52200 + 9.56439i) q^{26} +(-1.73659 - 12.2984i) q^{28} -2.34038 q^{29} +(-3.11065 - 5.38780i) q^{31} +(-4.21761 - 7.30512i) q^{32} -3.95462 q^{34} +(-4.75779 + 3.72218i) q^{35} +(-3.58796 + 6.21453i) q^{37} +(-9.54823 - 16.5380i) q^{38} +(-7.95876 + 13.7850i) q^{40} -7.89168 q^{41} +0.834123 q^{43} +(6.93918 - 12.0190i) q^{44} +(7.95876 + 13.7850i) q^{46} +(-2.91322 + 5.04584i) q^{47} +(5.04170 + 4.85605i) q^{49} +0.551152 q^{50} +(-10.0190 - 17.3534i) q^{52} +(-3.71826 - 6.44021i) q^{53} -6.74989 q^{55} +(17.1065 + 6.89851i) q^{56} +(3.02771 - 5.24415i) q^{58} +(2.31179 + 4.00414i) q^{59} +(3.56527 - 6.17523i) q^{61} +16.0968 q^{62} +4.52683 q^{64} +(-4.87285 + 8.44003i) q^{65} +(1.66262 + 2.87974i) q^{67} +(3.58760 - 6.21390i) q^{68} +(-2.18531 - 15.4762i) q^{70} +0.160242 q^{71} +(0.190329 + 0.329659i) q^{73} +(-9.28337 - 16.0793i) q^{74} +34.6483 q^{76} +(1.09361 + 7.74486i) q^{77} +(3.97731 - 6.88891i) q^{79} +(-9.87382 - 17.1020i) q^{80} +(10.2093 - 17.6831i) q^{82} +4.29800 q^{83} -3.48973 q^{85} +(-1.07909 + 1.86904i) q^{86} +(10.3051 + 17.8490i) q^{88} +(3.02828 - 5.24514i) q^{89} +(10.4736 + 4.22370i) q^{91} -28.8804 q^{92} +(-7.53756 - 13.0554i) q^{94} +(-8.42577 - 14.5939i) q^{95} -1.32209 q^{97} +(-17.4034 + 5.01487i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} + 6 q^{7} - 14 q^{10} + 12 q^{13} - 6 q^{16} - 24 q^{19} + 4 q^{22} - 26 q^{28} - 20 q^{31} + 4 q^{37} - 36 q^{40} + 20 q^{43} + 36 q^{46} - 14 q^{49} - 34 q^{52} + 8 q^{55} + 22 q^{58} - 36 q^{61}+ \cdots + 28 q^{97}+O(q^{100}) \) 16 * q - 6 * q^4 + 6 * q^7 - 14 * q^10 + 12 * q^13 - 6 * q^16 - 24 * q^19 + 4 * q^22 - 26 * q^28 - 20 * q^31 + 4 * q^37 - 36 * q^40 + 20 * q^43 + 36 * q^46 - 14 * q^49 - 34 * q^52 + 8 * q^55 + 22 * q^58 - 36 * q^61 + 76 * q^64 + 18 * q^67 - 58 * q^70 - 32 * q^73 + 116 * q^76 + 32 * q^79 + 2 * q^82 + 60 * q^85 + 72 * q^88 - 22 * q^91 - 54 * q^94 + 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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