LMFDB - Embedded newform 567.2.e.g.487.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(163,567)]

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([0, 2]))

N = Newforms(chi, 2, names="a")

//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: 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:	$16$
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			487.8
Root			$1.14160 + 0.834713i$ of defining polynomial
Character	$\chi$	$=$	567.487
Dual form			567.2.e.g.163.8

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

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

Coefficient data

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

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

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

$2$	1.29368	+	2.24073i	0.914772	+	1.58443i	0.807234	+	0.590231i	$0.200963\pi$
$2$	1.29368	+	2.24073i	0.914772	+	1.58443i	0.107538	+	0.994201i	$0.465703\pi$
$3$		0			0
$3$		0			0
$4$	−2.34723	+	4.06553i	−1.17362	+	2.03276i
$5$	1.14160	+	1.97731i	0.510540	+	0.884281i	0.999925	+	0.0122133i	$0.00388772\pi$
$5$	1.14160	+	1.97731i	0.510540	+	0.884281i	−0.489386	+	0.872067i	$0.662779\pi$
$6$		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	$-0.980372\pi$
$11$	−1.47816	+	2.56025i	−0.445682	+	0.771945i	0.552417	+	0.833568i	$0.313706\pi$
$12$		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	$-0.892675\pi$
$17$	−0.764218	+	1.32366i	−0.185350	+	0.321036i	0.758344	+	0.651854i	$0.226009\pi$
$18$		0			0
$19$	−3.69033	−	6.39184i	−0.846619	−	1.46639i	−0.884207	−	0.467095i	$-0.845301\pi$
$19$	−3.69033	−	6.39184i	−0.846619	−	1.46639i	0.0375879	−	0.999293i	$-0.488033\pi$
$20$	−10.7184			−2.39671
$21$		0			0
$22$	−7.64909			−1.63079
$23$	−3.07601	−	5.32780i	−0.641392	−	1.11092i	−0.985122	−	0.171855i	$-0.945024\pi$
$23$	−3.07601	−	5.32780i	−0.641392	−	1.11092i	0.343730	−	0.939068i	$-0.388309\pi$
$24$		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	$-0.430275\pi$
$29$	2.34038			0.434597			0.217299	+	0.976105i	$0.430275\pi$
$30$		0			0
$31$	−3.11065	+	5.38780i	−0.558689	+	0.967677i	0.438918	+	0.898527i	$0.355362\pi$
$31$	−3.11065	+	5.38780i	−0.558689	+	0.967677i	−0.997606	+	0.0691500i	$0.977971\pi$
$32$	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	−0.994251	−	0.107077i	$-0.965851\pi$
$37$	−3.58796	−	6.21453i	−0.589857	−	1.02166i	0.404394	−	0.914585i	$-0.367483\pi$
$38$	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	$-0.288656\pi$
$41$	7.89168			1.23247			0.616237	+	0.787561i	$0.288656\pi$
$42$		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	$-0.0269631\pi$
$47$	2.91322	+	5.04584i	0.424936	+	0.736011i	−0.571478	+	0.820617i	$0.693630\pi$
$48$		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	−0.489180	−	0.872183i	$-0.662704\pi$
$53$	3.71826	−	6.44021i	0.510742	−	0.884631i	0.999923	−	0.0124487i	$-0.00396266\pi$
$54$		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	$-0.930644\pi$
$59$	−2.31179	+	4.00414i	−0.300970	+	0.521295i	0.675386	+	0.737464i	$0.263977\pi$
$60$		0			0
$61$	3.56527	+	6.17523i	0.456486	+	0.790657i	0.998772	−	0.0495366i	$-0.0157744\pi$
$61$	3.56527	+	6.17523i	0.456486	+	0.790657i	−0.542286	+	0.840194i	$0.682441\pi$
$62$	−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	−0.746411	−	0.665485i	$-0.768225\pi$
$67$	1.66262	−	2.87974i	0.203121	−	0.351816i	0.949533	+	0.313669i	$0.101558\pi$
$68$	−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	$-0.503027\pi$
$71$	−0.160242			−0.0190172			−0.00950860	+	0.999955i	$0.503027\pi$
$72$		0			0
$73$	0.190329	−	0.329659i	0.0222763	−	0.0385837i	−0.854672	−	0.519168i	$-0.826242\pi$
$73$	0.190329	−	0.329659i	0.0222763	−	0.0385837i	0.876949	+	0.480584i	$0.159575\pi$
$74$	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	0.998221	−	0.0596151i	$-0.0189873\pi$
$79$	3.97731	+	6.88891i	0.447483	+	0.775063i	−0.550739	+	0.834678i	$0.685654\pi$
$80$	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	$-0.575798\pi$
$83$	−4.29800			−0.471767			−0.235883	+	0.971781i	$0.575798\pi$
$84$		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	$-0.270685\pi$
$89$	−3.02828	−	5.24514i	−0.320997	−	0.555984i	−0.980694	+	0.195548i	$0.937351\pi$
$90$		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	−0.0808014	+	0.996730i	$0.525748\pi$
$101$	−9.08101	+	15.7288i	−0.903594	+	1.56507i	−0.822793	+	0.568341i	$0.807585\pi$
$102$		0			0
$103$	−6.76755	−	11.7217i	−0.666827	−	1.15498i	−0.978787	−	0.204883i	$-0.934319\pi$
$103$	−6.76755	−	11.7217i	−0.666827	−	1.15498i	0.311960	−	0.950095i	$-0.399015\pi$
$104$	−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	$-0.0379662\pi$
$107$	4.06934	+	7.04830i	0.393398	+	0.681385i	−0.599498	+	0.800377i	$0.704633\pi$
$108$		0			0
$109$	2.74398	−	4.75272i	0.262826	−	0.455228i	−0.704166	−	0.710036i	$-0.748679\pi$
$109$	2.74398	−	4.75272i	0.262826	−	0.455228i	0.966992	+	0.254808i	$0.0820122\pi$
$110$	−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	$-0.404942\pi$
$113$	6.25508			0.588429			0.294214	+	0.955739i	$0.404942\pi$
$114$		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	$-0.0659205\pi$
$131$	3.56237	+	6.17020i	0.311246	+	0.539093i	−0.667387	+	0.744711i	$0.732587\pi$
$132$		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	$-0.709513\pi$
$137$	4.43910	−	7.68875i	0.379258	−	0.656895i	0.990955	+	0.134198i	$0.0428459\pi$
$138$		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	−0.998201	−	0.0599571i	$-0.980904\pi$
$149$	−6.72612	−	11.6500i	−0.551025	−	0.954403i	0.447176	−	0.894446i	$-0.352430\pi$
$150$		0			0
$151$	4.51074	−	7.81282i	0.367078	−	0.635799i	−0.622029	−	0.782994i	$-0.713691\pi$
$151$	4.51074	−	7.81282i	0.367078	−	0.635799i	0.989107	+	0.147196i	$0.0470247\pi$
$152$	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	−0.918520	−	0.395374i	$-0.870615\pi$
$157$	−1.46420	+	2.53607i	−0.116856	+	0.202400i	0.801664	+	0.597775i	$0.203948\pi$
$158$	−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	0.888652	−	0.458583i	$-0.151643\pi$
$163$	0.602369	+	1.04333i	0.0471812	+	0.0817202i	−0.841470	+	0.540303i	$0.818310\pi$
$164$	−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	$-0.687651\pi$
$167$	−14.3693			−1.11193			−0.555964	+	0.831206i	$0.687651\pi$
$168$		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	$-0.100317\pi$
$173$	2.72184	+	4.71436i	0.206938	+	0.358426i	−0.743811	+	0.668390i	$0.766984\pi$
$174$		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	$-0.760656\pi$
$179$	3.02828	−	5.24514i	0.226345	−	0.392040i	0.956722	+	0.291004i	$0.0939891\pi$
$180$		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	−0.858795	−	0.512319i	$-0.828787\pi$
$191$	−12.0662	−	20.8993i	−0.873079	−	1.51222i	−0.0142836	−	0.999898i	$-0.504547\pi$
$192$		0			0
$193$	0.394373	−	0.683075i	0.0283876	−	0.0491688i	−0.851483	−	0.524383i	$-0.824296\pi$
$193$	0.394373	−	0.683075i	0.0283876	−	0.0491688i	0.879870	+	0.475214i	$0.157629\pi$
$194$	−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	$-0.678085\pi$
$197$	−14.8985			−1.06147			−0.530736	+	0.847537i	$0.678085\pi$
$198$		0			0
$199$	−1.36578	+	2.36561i	−0.0968178	+	0.167693i	−0.910366	−	0.413804i	$-0.864200\pi$
$199$	−1.36578	+	2.36561i	−0.0968178	+	0.167693i	0.813548	+	0.581498i	$0.197533\pi$
$200$	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	$-0.855238\pi$
$227$	−1.03599	+	1.79438i	−0.0687608	+	0.119097i	0.829595	+	0.558365i	$0.188571\pi$
$228$		0			0
$229$	7.84268	+	13.5839i	0.518259	+	0.897650i	0.999775	+	0.0212133i	$0.00675290\pi$
$229$	7.84268	+	13.5839i	0.518259	+	0.897650i	−0.481516	+	0.876437i	$0.659914\pi$
$230$	36.3429			2.39638
$231$		0			0
$232$	−16.3161			−1.07121
$233$	−14.6262	−	25.3334i	−0.958196	−	1.65964i	−0.726879	−	0.686766i	$-0.759030\pi$
$233$	−14.6262	−	25.3334i	−0.958196	−	1.65964i	−0.231317	−	0.972878i	$-0.574304\pi$
$234$		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	$-0.694277\pi$
$239$	−17.7212			−1.14629			−0.573144	+	0.819454i	$0.694277\pi$
$240$		0			0
$241$	13.2036	−	22.8694i	0.850520	−	1.47314i	−0.0302190	−	0.999543i	$-0.509620\pi$
$241$	13.2036	−	22.8694i	0.850520	−	1.47314i	0.880739	−	0.473601i	$-0.157046\pi$
$242$	−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	$-0.410231\pi$
$251$	8.81798			0.556586			0.278293	+	0.960496i	$0.410231\pi$
$252$		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	$-0.259271\pi$
$257$	−4.59835	−	7.96458i	−0.286837	−	0.496817i	−0.973053	+	0.230581i	$0.925937\pi$
$258$		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	$-0.830835\pi$
$263$	0.127303	−	0.220495i	0.00784982	−	0.0135963i	0.869924	+	0.493186i	$0.164168\pi$
$264$		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	$-0.842839\pi$
$269$	−0.489721	+	0.848222i	−0.0298588	+	0.0517170i	0.850710	+	0.525636i	$0.176172\pi$
$270$		0			0
$271$	−7.02445	−	12.1667i	−0.426705	−	0.739075i	0.569873	−	0.821733i	$-0.306992\pi$
$271$	−7.02445	−	12.1667i	−0.426705	−	0.739075i	−0.996578	+	0.0826580i	$0.973659\pi$
$272$	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	0.177337	+	0.984150i	$0.443252\pi$
$277$	−12.7093	+	22.0132i	−0.763630	+	1.32265i	−0.940968	+	0.338496i	$0.890082\pi$
$278$	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	$-0.840039\pi$
$281$	−29.3811			−1.75273			−0.876366	+	0.481646i	$0.840039\pi$
$282$		0			0
$283$	1.53844	−	2.66466i	0.0914510	−	0.158398i	−0.816671	−	0.577104i	$-0.804183\pi$
$283$	1.53844	−	2.66466i	0.0914510	−	0.158398i	0.908122	+	0.418706i	$0.137516\pi$
$284$	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	$-0.665584\pi$
$293$	−17.0163			−0.994105			−0.497053	+	0.867720i	$0.665584\pi$
$294$		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	0.366328	+	0.930486i	$0.380615\pi$
$311$	−10.9807	+	19.0192i	−0.622661	+	1.07848i	−0.988988	+	0.147994i	$0.952718\pi$
$312$		0			0
$313$	1.24073	+	2.14900i	0.0701300	+	0.121469i	0.898958	−	0.438035i	$-0.144325\pi$
$313$	1.24073	+	2.14900i	0.0701300	+	0.121469i	−0.828828	+	0.559503i	$0.810992\pi$
$314$	−7.57685			−0.427586
$315$		0			0
$316$	−37.3427			−2.10069
$317$	−9.73961	−	16.8695i	−0.547031	−	0.947486i	−0.998476	−	0.0551868i	$-0.982425\pi$
$317$	−9.73961	−	16.8695i	−0.547031	−	0.947486i	0.451445	−	0.892299i	$-0.350909\pi$
$318$		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	0.828438	−	0.560081i	$-0.189230\pi$
$331$	−1.28856	−	2.23185i	−0.0708256	−	0.122674i	−0.899263	+	0.437408i	$0.855897\pi$
$332$	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	0.285775	−	0.958297i	$-0.407749\pi$
$347$	18.1212	−	31.3868i	0.972797	−	1.68493i	0.687022	−	0.726637i	$-0.258918\pi$
$348$		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	$-0.858112\pi$
$353$	−1.46109	+	2.53069i	−0.0777662	+	0.134695i	0.824520	+	0.565833i	$0.191445\pi$
$354$		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	$-0.163362\pi$
$359$	0.196714	+	0.340719i	0.0103822	+	0.0179825i	−0.860788	+	0.508964i	$0.830029\pi$
$360$		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	−0.720045	−	0.693927i	$-0.755879\pi$
$367$	4.61567	−	7.99457i	0.240936	−	0.417313i	0.960981	+	0.276614i	$0.0892123\pi$
$368$	−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	0.997725	+	0.0674147i	$0.0214751\pi$
$373$	10.7622	+	18.6407i	0.557245	+	0.965177i	−0.440480	+	0.897763i	$0.645192\pi$
$374$	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	$-0.115541\pi$
$383$	3.12982	+	5.42101i	0.159926	+	0.277001i	−0.774915	+	0.632065i	$0.782208\pi$
$384$		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	0.422747	+	0.906248i	$0.361066\pi$
$389$	−11.3104	+	19.5902i	−0.573460	+	0.993262i	−0.996207	+	0.0870142i	$0.972267\pi$
$390$		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	0.999285	+	0.0378060i	$0.0120369\pi$
$397$	10.6077	+	18.3730i	0.532384	+	0.922115i	−0.466902	+	0.884309i	$0.654630\pi$
$398$	−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	$-0.132630\pi$
$401$	2.13721	+	3.70176i	0.106727	+	0.184857i	−0.807715	+	0.589573i	$0.799296\pi$
$402$		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	−0.0148660	+	0.999889i	$0.504732\pi$
$409$	−17.6627	+	30.5926i	−0.873363	+	1.51271i	−0.858497	+	0.512819i	$0.828601\pi$
$410$	−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	$-0.470810\pi$
$419$	3.74901			0.183151			0.0915755	+	0.995798i	$0.470810\pi$
$420$		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	0.410768	+	0.911740i	$0.365261\pi$
$431$	−12.1284	+	21.0071i	−0.584206	+	1.01187i	−0.994974	+	0.100135i	$0.968073\pi$
$432$		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	−0.986772	−	0.162113i	$-0.948169\pi$
$439$	−13.2792	−	23.0002i	−0.633780	−	1.09774i	0.352992	−	0.935626i	$-0.385164\pi$
$440$	47.0573			2.24337
$441$		0			0
$442$	−16.8801			−0.802902
$443$	13.8041	+	23.9094i	0.655853	+	1.13597i	0.981679	+	0.190542i	$0.0610244\pi$
$443$	13.8041	+	23.9094i	0.655853	+	1.13597i	−0.325826	+	0.945430i	$0.605642\pi$
$444$		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	$-0.620247\pi$
$449$	−15.6315			−0.737695			−0.368847	+	0.929490i	$0.620247\pi$
$450$		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	0.937383	+	0.348300i	$0.113241\pi$
$457$	16.4677	+	28.5230i	0.770328	+	1.33425i	−0.167055	+	0.985948i	$0.553426\pi$
$458$	−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	$-0.197751\pi$
$461$	34.9181			1.62630			0.813149	+	0.582055i	$0.197751\pi$
$462$		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	$-0.0883455\pi$
$467$	5.26376	+	9.11710i	0.243578	+	0.421889i	−0.718153	+	0.695885i	$0.755012\pi$
$468$		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	$-0.706543\pi$
$479$	8.48903	−	14.7034i	0.387874	−	0.671817i	0.992163	+	0.124948i	$0.0398763\pi$
$480$		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	−0.676751	−	0.736212i	$-0.736613\pi$
$487$	6.60283	−	11.4364i	0.299203	−	0.518235i	0.975954	+	0.217977i	$0.0699459\pi$
$488$	−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	$-0.615910\pi$
$491$	−15.7834			−0.712293			−0.356147	+	0.934430i	$0.615910\pi$
$492$		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	−0.719342	−	0.694656i	$-0.755556\pi$
$499$	−21.4729	−	37.1922i	−0.961261	−	1.66495i	−0.241919	−	0.970296i	$-0.577777\pi$
$500$	−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	$-0.182046\pi$
$503$	37.7173			1.68173			0.840866	+	0.541243i	$0.182046\pi$
$504$		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	0.934506	+	0.355949i	$0.115842\pi$
$509$	17.4964	+	30.3046i	0.775513	+	1.34323i	−0.158992	+	0.987280i	$0.550824\pi$
$510$		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	$-0.932111\pi$
$521$	−6.97005	+	12.0725i	−0.305363	+	0.528905i	0.671979	+	0.740570i	$0.265445\pi$
$522$		0			0
$523$	−13.4103	−	23.2274i	−0.586393	−	1.01566i	−0.994700	−	0.102817i	$-0.967214\pi$
$523$	−13.4103	−	23.2274i	−0.586393	−	1.01566i	0.408308	−	0.912844i	$-0.366119\pi$
$524$	−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	0.500198	−	0.865911i	$-0.333261\pi$
$541$	−11.6251	−	20.1353i	−0.499802	−	0.865683i	−1.00000		0.000228285i	$0.999927\pi$
$542$	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	$-0.861207\pi$
$557$	−2.06405	+	3.57504i	−0.0874565	+	0.151479i	0.818979	+	0.573824i	$0.194541\pi$
$558$		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	$-0.828736\pi$
$563$	0.342707	−	0.593585i	0.0144434	−	0.0250166i	0.873157	+	0.487440i	$0.162069\pi$
$564$		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	$-0.293457\pi$
$569$	−9.25223	−	16.0253i	−0.387874	−	0.671817i	−0.992163	+	0.124948i	$0.960124\pi$
$570$		0			0
$571$	−17.2741	+	29.9197i	−0.722901	+	1.25210i	0.236932	+	0.971526i	$0.423858\pi$
$571$	−17.2741	+	29.9197i	−0.722901	+	1.25210i	−0.959832	+	0.280574i	$0.909475\pi$
$572$	−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	−0.871113	−	0.491082i	$-0.836602\pi$
$577$	−0.246628	+	0.427172i	−0.0102673	+	0.0177834i	0.860846	+	0.508865i	$0.169935\pi$
$578$	−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	$-0.783164\pi$
$587$	−37.6412			−1.55362			−0.776810	+	0.629735i	$0.783164\pi$
$588$		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	−0.999843	−	0.0177137i	$-0.994361\pi$
$593$	−12.5475	−	21.7328i	−0.515262	−	0.892460i	0.484581	−	0.874746i	$-0.338972\pi$
$594$		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	$-0.829832\pi$
$599$	0.269218	−	0.466300i	0.0110000	−	0.0190525i	0.871473	+	0.490444i	$0.163165\pi$
$600$		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	0.998610	−	0.0527149i	$-0.0167875\pi$
$607$	11.1768	+	19.3588i	0.453652	+	0.785749i	−0.544957	+	0.838464i	$0.683454\pi$
$608$	−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	−0.504458	−	0.863436i	$-0.668308\pi$
$613$	12.2687	−	21.2500i	0.495529	−	0.858281i	0.999987	+	0.00515549i	$0.00164105\pi$
$614$	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	$-0.292393\pi$
$617$	30.1527			1.21390			0.606950	+	0.794740i	$0.292393\pi$
$618$		0			0
$619$	−11.8047	+	20.4463i	−0.474471	+	0.821808i	−0.999573	−	0.0292318i	$-0.990694\pi$
$619$	−11.8047	+	20.4463i	−0.474471	+	0.821808i	0.525102	+	0.851039i	$0.324027\pi$
$620$	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	$-0.953681\pi$
$641$	−9.34588	+	16.1875i	−0.369140	+	0.639369i	0.620291	+	0.784372i	$0.287014\pi$
$642$		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	$-0.939613\pi$
$647$	−8.33593	+	14.4383i	−0.327719	+	0.567626i	0.654340	+	0.756201i	$0.272947\pi$
$648$		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	$-0.220553\pi$
$653$	−4.30535	−	7.45708i	−0.168481	−	0.291818i	−0.937886	+	0.346943i	$0.887220\pi$
$654$		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	$-0.592368\pi$
$659$	−14.6903			−0.572253			−0.286126	+	0.958192i	$0.592368\pi$
$660$		0			0
$661$	−4.06201	+	7.03561i	−0.157994	+	0.273654i	−0.934145	−	0.356893i	$-0.883836\pi$
$661$	−4.06201	+	7.03561i	−0.157994	+	0.273654i	0.776151	+	0.630547i	$0.217169\pi$
$662$	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	$-0.100000\pi$
$677$	5.40967	+	9.36982i	0.207910	+	0.360111i	−0.743146	+	0.669130i	$0.766667\pi$
$678$		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	$-0.824994\pi$
$683$	0.684640	−	1.18583i	0.0261970	−	0.0453746i	0.878827	+	0.477141i	$0.158327\pi$
$684$		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	0.974442	+	0.224640i	$0.0721207\pi$
$691$	17.9215	+	31.0409i	0.681765	+	1.18085i	−0.292677	+	0.956211i	$0.594546\pi$
$692$	−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	$-0.688980\pi$
$701$	−29.6235			−1.11886			−0.559431	+	0.828877i	$0.688980\pi$
$702$		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	0.973062	−	0.230543i	$-0.0740503\pi$
$709$	7.63863	+	13.2305i	0.286875	+	0.496882i	−0.686187	+	0.727425i	$0.740717\pi$
$710$	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	$-0.154729\pi$
$719$	1.00538	+	1.74138i	0.0374945	+	0.0649424i	−0.846669	+	0.532120i	$0.821396\pi$
$720$		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	0.820116	−	0.572198i	$-0.193909\pi$
$733$	−2.31427	−	4.00844i	−0.0854797	−	0.148055i	−0.905596	+	0.424142i	$0.860576\pi$
$734$	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	−0.567725	−	0.823219i	$-0.692176\pi$
$739$	11.6640	−	20.2026i	0.429066	−	0.743164i	0.996790	+	0.0800546i	$0.0255095\pi$
$740$	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	$-0.0919647\pi$
$743$	52.2565			1.91711			0.958553	+	0.284913i	$0.0919647\pi$
$744$		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	0.916936	−	0.399035i	$-0.130655\pi$
$751$	3.09378	+	5.35858i	0.112894	+	0.195538i	−0.804042	+	0.594572i	$0.797321\pi$
$752$	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	0.990438	+	0.137961i	$0.0440548\pi$
$761$	16.9572	+	29.3707i	0.614696	+	1.06469i	−0.375741	+	0.926725i	$0.622612\pi$
$762$		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	−0.0863952	−	0.996261i	$-0.527535\pi$
$773$	22.7870	−	39.4682i	0.819590	−	1.41957i	0.905985	−	0.423310i	$-0.139132\pi$
$774$		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	−0.782254	−	0.622959i	$-0.785930\pi$
$787$	4.16234	−	7.20939i	0.148372	−	0.256987i	0.930626	+	0.365972i	$0.119264\pi$
$788$	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	$-0.744878\pi$
$797$	−39.2773			−1.39127			−0.695637	+	0.718394i	$0.744878\pi$
$798$		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	$-0.965244\pi$
$809$	−11.4525	+	19.8364i	−0.402649	+	0.697409i	0.591395	+	0.806382i	$0.298577\pi$
$810$		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	−0.996479	−	0.0838376i	$-0.973282\pi$
$821$	−16.3565	−	28.3303i	−0.570845	−	0.988733i	0.425634	−	0.904895i	$-0.360051\pi$
$822$		0			0
$823$	13.9457	−	24.1547i	0.486118	−	0.841981i	−0.513755	−	0.857937i	$-0.671746\pi$
$823$	13.9457	−	24.1547i	0.486118	−	0.841981i	0.999873	+	0.0159561i	$0.00507920\pi$
$824$	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	$-0.598849\pi$
$827$	−17.5753			−0.611153			−0.305576	+	0.952168i	$0.598849\pi$
$828$		0			0
$829$	0.997731	−	1.72812i	0.0346526	−	0.0600201i	−0.848179	−	0.529710i	$-0.822301\pi$
$829$	0.997731	−	1.72812i	0.0346526	−	0.0600201i	0.882832	+	0.469690i	$0.155634\pi$
$830$	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	$-0.627879\pi$
$839$	−22.6524			−0.782046			−0.391023	+	0.920381i	$0.627879\pi$
$840$		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	$-0.969761\pi$
$857$	−12.1665	+	21.0729i	−0.415599	+	0.719838i	0.579892	+	0.814693i	$0.303095\pi$
$858$		0			0
$859$	−7.80925	−	13.5260i	−0.266448	−	0.461502i	0.701494	−	0.712676i	$-0.252517\pi$
$859$	−7.80925	−	13.5260i	−0.266448	−	0.461502i	−0.967942	+	0.251174i	$0.919183\pi$
$860$	−8.94048			−0.304868
$861$		0			0
$862$	−62.7614			−2.13766
$863$	18.3558	+	31.7931i	0.624838	+	1.08225i	0.988572	+	0.150748i	$0.0481682\pi$
$863$	18.3558	+	31.7931i	0.624838	+	1.08225i	−0.363735	+	0.931503i	$0.618498\pi$
$864$		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	0.883398	+	0.468623i	$0.155250\pi$
$877$	25.0992	+	43.4730i	0.847538	+	1.46798i	−0.0358600	+	0.999357i	$0.511417\pi$
$878$	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	$-0.835844\pi$
$881$	−51.6426			−1.73989			−0.869943	+	0.493153i	$0.835844\pi$
$882$		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	−0.999640	−	0.0268420i	$-0.991455\pi$
$887$	−15.5782	−	26.9823i	−0.523066	−	0.905976i	0.476574	−	0.879134i	$-0.341878\pi$
$888$		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	−0.620254	−	0.784401i	$-0.712971\pi$
$907$	11.1185	−	19.2578i	0.369184	−	0.639445i	0.989438	+	0.144955i	$0.0463039\pi$
$908$	−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	$-0.510726\pi$
$911$	−2.03370			−0.0673794			−0.0336897	+	0.999432i	$0.510726\pi$
$912$		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	0.928884	+	0.370371i	$0.120769\pi$
$919$	23.8031	+	41.2282i	0.785193	+	1.35999i	−0.143691	+	0.989623i	$0.545897\pi$
$920$	−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	−0.999903	−	0.0138945i	$-0.995577\pi$
$929$	−15.6050	−	27.0287i	−0.511985	−	0.886784i	0.487919	−	0.872889i	$-0.337756\pi$
$930$		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	−0.251442	−	0.967872i	$-0.580905\pi$
$941$	21.8559	−	37.8555i	0.712481	−	1.23405i	0.963923	−	0.266181i	$-0.0857618\pi$
$942$		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	0.959921	+	0.280270i	$0.0904239\pi$
$947$	22.2393	+	38.5197i	0.722681	+	1.25172i	−0.237240	+	0.971451i	$0.576243\pi$
$948$		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	$-0.178243\pi$
$953$	52.3118			1.69454			0.847272	+	0.531159i	$0.178243\pi$
$954$		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	−0.767354	−	0.641224i	$-0.778427\pi$
$971$	−29.2598	−	50.6795i	−0.938993	−	1.62638i	−0.171639	−	0.985160i	$-0.554906\pi$
$972$		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	−0.00314297	−	0.999995i	$-0.501000\pi$
$977$	27.0201	−	46.8002i	0.864450	−	1.49727i	0.867593	−	0.497276i	$-0.165666\pi$
$978$		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	$-0.946638\pi$
$983$	−10.9261	+	18.9245i	−0.348487	+	0.603597i	0.637494	+	0.770455i	$0.279971\pi$
$984$		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	−0.735041	−	0.678023i	$-0.762837\pi$
$991$	6.91507	−	11.9773i	0.219664	−	0.380470i	0.954705	+	0.297553i	$0.0961704\pi$
$992$	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	−0.812066	−	0.583566i	$-0.801657\pi$
$997$	3.13701	−	5.43346i	0.0993501	−	0.172079i	0.911416	+	0.411487i	$0.134990\pi$
$998$	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.487.8	yes	16
3.2	odd	2	inner	567.2.e.g.487.1	yes	16
7.2	even	3	inner	567.2.e.g.163.8	yes	16
7.3	odd	6		3969.2.a.bf.1.1		8
7.4	even	3		3969.2.a.bg.1.1		8
9.2	odd	6		567.2.g.l.109.1		16
9.4	even	3		567.2.h.l.298.1		16
9.5	odd	6		567.2.h.l.298.8		16
9.7	even	3		567.2.g.l.109.8		16
21.2	odd	6	inner	567.2.e.g.163.1	✓	16
21.11	odd	6		3969.2.a.bg.1.8		8
21.17	even	6		3969.2.a.bf.1.8		8
63.2	odd	6		567.2.h.l.352.8		16
63.16	even	3		567.2.h.l.352.1		16
63.23	odd	6		567.2.g.l.541.1		16
63.58	even	3		567.2.g.l.541.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.g.163.1	✓	16	21.2	odd	6	inner
567.2.e.g.163.8	yes	16	7.2	even	3	inner
567.2.e.g.487.1	yes	16	3.2	odd	2	inner
567.2.e.g.487.8	yes	16	1.1	even	1	trivial
567.2.g.l.109.1		16	9.2	odd	6
567.2.g.l.109.8		16	9.7	even	3
567.2.g.l.541.1		16	63.23	odd	6
567.2.g.l.541.8		16	63.58	even	3
567.2.h.l.298.1		16	9.4	even	3
567.2.h.l.298.8		16	9.5	odd	6
567.2.h.l.352.1		16	63.16	even	3
567.2.h.l.352.8		16	63.2	odd	6
3969.2.a.bf.1.1		8	7.3	odd	6
3969.2.a.bf.1.8		8	21.17	even	6
3969.2.a.bg.1.1		8	7.4	even	3
3969.2.a.bg.1.8		8	21.11	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.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

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