LMFDB - Embedded newform 567.2.bd.a.17.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(17,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11, 3]))

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

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("567.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.bd (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.20
Character	$\chi$	$=$	567.17
Dual form			567.2.bd.a.467.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.26715 - 0.399760i) q^{2} +(3.10078 - 1.12859i) q^{4} +(1.73217 - 0.630457i) q^{5} +(0.678971 + 2.55715i) q^{7} +(2.59137 - 1.49613i) q^{8} +O(q^{10})$	\(q+(2.26715 - 0.399760i) q^{2} +(3.10078 - 1.12859i) q^{4} +(1.73217 - 0.630457i) q^{5} +(0.678971 + 2.55715i) q^{7} +(2.59137 - 1.49613i) q^{8} +(3.67505 - 2.12179i) q^{10} +(0.0420027 - 0.115401i) q^{11} +(-0.0159063 - 0.0437022i) q^{13} +(2.56157 + 5.52601i) q^{14} +(0.221371 - 0.185752i) q^{16} +(-0.0786230 - 0.136179i) q^{17} +(-6.57855 - 3.79813i) q^{19} +(4.65954 - 3.90982i) q^{20} +(0.0490936 - 0.278423i) q^{22} +(0.957765 + 0.168880i) q^{23} +(-1.22730 + 1.02982i) q^{25} +(-0.0535324 - 0.0927208i) q^{26} +(4.99131 + 7.16286i) q^{28} +(3.33678 - 9.16772i) q^{29} +(-1.56144 - 4.29003i) q^{31} +(-3.41914 + 4.07477i) q^{32} +(-0.232689 - 0.277308i) q^{34} +(2.78826 + 4.00134i) q^{35} +9.37436 q^{37} +(-16.4329 - 5.98109i) q^{38} +(3.54543 - 4.22528i) q^{40} +(-5.76925 + 2.09983i) q^{41} +(1.67890 + 9.52153i) q^{43} -0.405238i q^{44} +2.23891 q^{46} +(-3.91757 - 1.42588i) q^{47} +(-6.07800 + 3.47246i) q^{49} +(-2.37078 + 2.82539i) q^{50} +(-0.0986438 - 0.117559i) q^{52} +(0.141686 + 0.0818025i) q^{53} -0.226376i q^{55} +(5.58527 + 5.61067i) q^{56} +(3.90009 - 22.1185i) q^{58} +(-9.06906 - 7.60984i) q^{59} +(1.03823 - 2.85251i) q^{61} +(-5.25501 - 9.10194i) q^{62} +(-6.41175 + 11.1055i) q^{64} +(-0.0551048 - 0.0656713i) q^{65} +(-1.70755 + 9.68399i) q^{67} +(-0.397483 - 0.333527i) q^{68} +(7.92099 + 7.95701i) q^{70} +(0.863276 + 0.498413i) q^{71} +9.18511i q^{73} +(21.2531 - 3.74749i) q^{74} +(-24.6852 - 4.35266i) q^{76} +(0.323617 + 0.0290528i) q^{77} +(0.451399 + 2.56001i) q^{79} +(0.266342 - 0.461318i) q^{80} +(-12.2403 + 7.06695i) q^{82} +(6.02764 + 2.19388i) q^{83} +(-0.222043 - 0.186316i) q^{85} +(7.61265 + 20.9156i) q^{86} +(-0.0638107 - 0.361889i) q^{88} +(5.30203 - 9.18338i) q^{89} +(0.100953 - 0.0703473i) q^{91} +(3.16041 - 0.557266i) q^{92} +(-9.45173 - 1.66659i) q^{94} +(-13.7897 - 2.43150i) q^{95} +(13.2580 - 2.33775i) q^{97} +(-12.3916 + 10.3023i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} + 51 q^{32} + 18 q^{34} + 9 q^{35} - 6 q^{37} + 9 q^{38} - 9 q^{40} - 12 q^{43} - 6 q^{46} - 45 q^{47} + 30 q^{49} + 9 q^{50} - 9 q^{52} - 45 q^{53} + 51 q^{56} - 3 q^{58} + 9 q^{59} - 63 q^{61} - 99 q^{62} + 18 q^{64} + 102 q^{65} - 3 q^{67} - 144 q^{68} - 15 q^{70} - 18 q^{71} + 33 q^{74} - 36 q^{76} + 57 q^{77} - 21 q^{79} + 72 q^{80} - 18 q^{82} - 90 q^{83} + 9 q^{85} + 33 q^{86} + 45 q^{88} + 9 q^{89} - 21 q^{91} - 150 q^{92} - 9 q^{94} - 27 q^{95} + 180 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	2.26715	−	0.399760i	1.60312	−	0.282673i	0.700674	−	0.713482i	$-0.252883\pi$
$2$	2.26715	−	0.399760i	1.60312	−	0.282673i	0.902443	+	0.430809i	$0.141772\pi$
$3$		0			0
$3$		0			0
$4$	3.10078	−	1.12859i	1.55039	−	0.564295i
$5$	1.73217	−	0.630457i	0.774649	−	0.281949i	0.0757093	−	0.997130i	$-0.475878\pi$
$5$	1.73217	−	0.630457i	0.774649	−	0.281949i	0.698939	+	0.715181i	$0.253656\pi$
$6$		0			0
$7$	0.678971	+	2.55715i	0.256627	+	0.966511i
$7$	0.678971	+	2.55715i	0.256627	+	0.966511i
$8$	2.59137	−	1.49613i	0.916186	−	0.528960i
$9$		0			0
$10$	3.67505	−	2.12179i	1.16215	−	0.670970i
$11$	0.0420027	−	0.115401i	0.0126643	−	0.0347949i	−0.933199	−	0.359359i	$-0.882995\pi$
$11$	0.0420027	−	0.115401i	0.0126643	−	0.0347949i	0.945864	+	0.324564i	$0.105218\pi$
$12$		0			0
$13$	−0.0159063	−	0.0437022i	−0.00441162	−	0.0121208i	0.937467	−	0.348073i	$-0.113164\pi$
$13$	−0.0159063	−	0.0437022i	−0.00441162	−	0.0121208i	−0.941879	+	0.335953i	$0.890942\pi$
$14$	2.56157	+	5.52601i	0.684609	+	1.47689i
$15$		0			0
$16$	0.221371	−	0.185752i	0.0553427	−	0.0464380i
$17$	−0.0786230	−	0.136179i	−0.0190689	−	0.0330283i	0.856334	−	0.516423i	$-0.172737\pi$
$17$	−0.0786230	−	0.136179i	−0.0190689	−	0.0330283i	−0.875402	+	0.483395i	$0.839404\pi$
$18$		0			0
$19$	−6.57855	−	3.79813i	−1.50922	−	0.871350i	−0.999942	−	0.0107502i	$-0.996578\pi$
$19$	−6.57855	−	3.79813i	−1.50922	−	0.871350i	−0.509281	−	0.860600i	$-0.670089\pi$
$20$	4.65954	−	3.90982i	1.04190	−	0.874261i
$21$		0			0
$22$	0.0490936	−	0.278423i	0.0104668	−	0.0593601i
$23$	0.957765	+	0.168880i	0.199708	+	0.0352139i	0.272607	−	0.962125i	$-0.412114\pi$
$23$	0.957765	+	0.168880i	0.199708	+	0.0352139i	−0.0728993	+	0.997339i	$0.523225\pi$
$24$		0			0
$25$	−1.22730	+	1.02982i	−0.245459	+	0.205965i
$26$	−0.0535324	−	0.0927208i	−0.0104986	−	0.0181840i
$27$		0			0
$28$	4.99131	+	7.16286i	0.943269	+	1.35365i
$29$	3.33678	−	9.16772i	0.619624	−	1.70240i	−0.0882816	−	0.996096i	$-0.528138\pi$
$29$	3.33678	−	9.16772i	0.619624	−	1.70240i	0.707906	−	0.706307i	$-0.249640\pi$
$30$		0			0
$31$	−1.56144	−	4.29003i	−0.280444	−	0.770512i	−0.997310	−	0.0733016i	$-0.976646\pi$
$31$	−1.56144	−	4.29003i	−0.280444	−	0.770512i	0.716866	−	0.697211i	$-0.245576\pi$
$32$	−3.41914	+	4.07477i	−0.604424	+	0.720325i
$33$		0			0
$34$	−0.232689	−	0.277308i	−0.0399058	−	0.0475579i
$35$	2.78826	+	4.00134i	0.471303	+	0.676350i
$36$		0			0
$37$	9.37436			1.54113			0.770567	−	0.637358i	$-0.219973\pi$
$37$	9.37436			1.54113			0.770567	+	0.637358i	$0.219973\pi$
$38$	−16.4329	−	5.98109i	−2.66577	−	0.970261i
$39$		0			0
$40$	3.54543	−	4.22528i	0.560582	−	0.668076i
$41$	−5.76925	+	2.09983i	−0.901005	+	0.327939i	−0.750656	−	0.660694i	$-0.770262\pi$
$41$	−5.76925	+	2.09983i	−0.901005	+	0.327939i	−0.150350	+	0.988633i	$0.548040\pi$
$42$		0			0
$43$	1.67890	+	9.52153i	0.256030	+	1.45202i	0.793414	+	0.608682i	$0.208301\pi$
$43$	1.67890	+	9.52153i	0.256030	+	1.45202i	−0.537384	+	0.843338i	$0.680587\pi$
$44$		−	0.405238i		−	0.0610919i
$45$		0			0
$46$	2.23891			0.330109
$47$	−3.91757	−	1.42588i	−0.571436	−	0.207986i	0.0401090	−	0.999195i	$-0.487229\pi$
$47$	−3.91757	−	1.42588i	−0.571436	−	0.207986i	−0.611545	+	0.791210i	$0.709452\pi$
$48$		0			0
$49$	−6.07800	+	3.47246i	−0.868285	+	0.496065i
$50$	−2.37078	+	2.82539i	−0.335279	+	0.399570i
$51$		0			0
$52$	−0.0986438	−	0.117559i	−0.0136794	−	0.0163025i
$53$	0.141686	+	0.0818025i	0.0194621	+	0.0112364i	0.509699	−	0.860353i	$-0.329757\pi$
$53$	0.141686	+	0.0818025i	0.0194621	+	0.0112364i	−0.490237	+	0.871589i	$0.663090\pi$
$54$		0			0
$55$		−	0.226376i		−	0.0305245i
$56$	5.58527	+	5.61067i	0.746364	+	0.749758i
$57$		0			0
$58$	3.90009	−	22.1185i	0.512107	−	2.90430i
$59$	−9.06906	−	7.60984i	−1.18069	−	0.990717i	−0.999974	−	0.00718212i	$-0.997714\pi$
$59$	−9.06906	−	7.60984i	−1.18069	−	0.990717i	−0.180717	−	0.983535i	$-0.557842\pi$
$60$		0			0
$61$	1.03823	−	2.85251i	0.132932	−	0.365227i	−0.855312	−	0.518113i	$-0.826635\pi$
$61$	1.03823	−	2.85251i	0.132932	−	0.365227i	0.988244	+	0.152886i	$0.0488568\pi$
$62$	−5.25501	−	9.10194i	−0.667387	−	1.15595i
$63$		0			0
$64$	−6.41175	+	11.1055i	−0.801469	+	1.38818i
$65$	−0.0551048	−	0.0656713i	−0.00683491	−	0.00814552i
$66$		0			0
$67$	−1.70755	+	9.68399i	−0.208610	+	1.18309i	0.683046	+	0.730375i	$0.260655\pi$
$67$	−1.70755	+	9.68399i	−0.208610	+	1.18309i	−0.891656	+	0.452713i	$0.850456\pi$
$68$	−0.397483	−	0.333527i	−0.0482018	−	0.0404461i
$69$		0			0
$70$	7.92099	+	7.95701i	0.946739	+	0.951045i
$71$	0.863276	+	0.498413i	0.102452	+	0.0591507i	0.550351	−	0.834934i	$-0.314494\pi$
$71$	0.863276	+	0.498413i	0.102452	+	0.0591507i	−0.447899	+	0.894084i	$0.647827\pi$
$72$		0			0
$73$			9.18511i			1.07504i	0.843252	+	0.537518i	$0.180638\pi$
$73$			9.18511i			1.07504i	−0.843252	+	0.537518i	$0.819362\pi$
$74$	21.2531	−	3.74749i	2.47062	−	0.435637i
$75$		0			0
$76$	−24.6852	−	4.35266i	−2.83158	−	0.499284i
$77$	0.323617	+	0.0290528i	0.0368796	+	0.00331087i
$78$		0			0
$79$	0.451399	+	2.56001i	0.0507864	+	0.288024i	0.999614	−	0.0277696i	$-0.00884048\pi$
$79$	0.451399	+	2.56001i	0.0507864	+	0.288024i	−0.948828	+	0.315793i	$0.897729\pi$
$80$	0.266342	−	0.461318i	0.0297780	−	0.0515769i
$81$		0			0
$82$	−12.2403	+	7.06695i	−1.35172	+	0.780414i
$83$	6.02764	+	2.19388i	0.661619	+	0.240810i	0.650935	−	0.759133i	$-0.274377\pi$
$83$	6.02764	+	2.19388i	0.661619	+	0.240810i	0.0106840	+	0.999943i	$0.496599\pi$
$84$		0			0
$85$	−0.222043	−	0.186316i	−0.0240840	−	0.0202088i
$86$	7.61265	+	20.9156i	0.820893	+	2.25539i
$87$		0			0
$88$	−0.0638107	−	0.361889i	−0.00680225	−	0.0385775i
$89$	5.30203	−	9.18338i	0.562014	−	0.973436i	−0.435307	−	0.900282i	$-0.643360\pi$
$89$	5.30203	−	9.18338i	0.562014	−	0.973436i	0.997321	−	0.0731541i	$-0.0233065\pi$
$90$		0			0
$91$	0.100953	−	0.0703473i	0.0105828	−	0.00737440i
$92$	3.16041	−	0.557266i	0.329496	−	0.0580990i
$93$		0			0
$94$	−9.45173	−	1.66659i	−0.974871	−	0.171896i
$95$	−13.7897	−	2.43150i	−1.41479	−	0.249466i
$96$		0			0
$97$	13.2580	−	2.33775i	1.34615	−	0.237363i	0.546313	−	0.837581i	$-0.316031\pi$
$97$	13.2580	−	2.33775i	1.34615	−	0.237363i	0.799836	+	0.600218i	$0.204920\pi$
$98$	−12.3916	+	10.3023i	−1.25174	+	1.04069i
$99$		0			0
$100$	−2.64332	+	4.57837i	−0.264332	+	0.457837i
$101$	2.41301	+	13.6848i	0.240103	+	1.36169i	0.831595	+	0.555382i	$0.187428\pi$
$101$	2.41301	+	13.6848i	0.240103	+	1.36169i	−0.591492	+	0.806311i	$0.701461\pi$
$102$		0			0
$103$	−2.66808	−	7.33049i	−0.262894	−	0.722295i	−0.998969	−	0.0453951i	$-0.985545\pi$
$103$	−2.66808	−	7.33049i	−0.262894	−	0.722295i	0.736075	−	0.676900i	$-0.236677\pi$
$104$	−0.106603	−	0.0894506i	−0.0104533	−	0.00877135i
$105$		0			0
$106$	0.353925	+	0.128818i	0.0343762	+	0.0125119i
$107$	6.46785	−	3.73421i	0.625271	−	0.361000i	−0.153648	−	0.988126i	$-0.549102\pi$
$107$	6.46785	−	3.73421i	0.625271	−	0.361000i	0.778918	+	0.627126i	$0.215769\pi$
$108$		0			0
$109$	4.37239	−	7.57320i	0.418799	−	0.725381i	−0.577020	−	0.816730i	$-0.695784\pi$
$109$	4.37239	−	7.57320i	0.418799	−	0.725381i	0.995819	+	0.0913488i	$0.0291178\pi$
$110$	−0.0904958	−	0.513227i	−0.00862844	−	0.0489343i
$111$		0			0
$112$	0.625299	+	0.439957i	0.0590852	+	0.0415720i
$113$	−16.2059	−	2.85754i	−1.52453	−	0.268815i	−0.652317	−	0.757947i	$-0.726203\pi$
$113$	−16.2059	−	2.85754i	−1.52453	−	0.268815i	−0.872210	+	0.489131i	$0.837314\pi$
$114$		0			0
$115$	1.76548	−	0.311302i	0.164632	−	0.0290291i
$116$		−	32.1929i		−	2.98904i
$117$		0			0
$118$	−23.6030	−	13.6272i	−2.17283	−	1.25449i
$119$	0.294847	−	0.293512i	0.0270286	−	0.0269062i
$120$		0			0
$121$	8.41494	+	7.06097i	0.764994	+	0.641906i
$122$	1.21350	−	6.88212i	0.109865	−	0.623078i
$123$		0			0
$124$	−9.68338	−	11.5402i	−0.869593	−	1.03634i
$125$	−6.08496	+	10.5395i	−0.544255	+	0.942677i
$126$		0			0
$127$	−2.14737	−	3.71936i	−0.190549	−	0.330040i	0.754884	−	0.655859i	$-0.227693\pi$
$127$	−2.14737	−	3.71936i	−0.190549	−	0.330040i	−0.945432	+	0.325819i	$0.894360\pi$
$128$	−6.45831	+	17.7441i	−0.570839	+	1.56837i
$129$		0			0
$130$	−0.151184	−	0.126858i	−0.0132597	−	0.0111262i
$131$	−0.751230	+	4.26044i	−0.0656353	+	0.372236i	0.934243	+	0.356637i	$0.116077\pi$
$131$	−0.751230	+	4.26044i	−0.0656353	+	0.372236i	−0.999878	+	0.0155992i	$0.995034\pi$
$132$		0			0
$133$	5.24572	−	19.4011i	0.454862	−	1.68229i
$134$			22.6377i			1.95560i
$135$		0			0
$136$	−0.407482	−	0.235260i	−0.0349413	−	0.0201733i
$137$	−1.12676	−	1.34283i	−0.0962660	−	0.114725i	0.715761	−	0.698346i	$-0.246080\pi$
$137$	−1.12676	−	1.34283i	−0.0962660	−	0.114725i	−0.812027	+	0.583620i	$0.801636\pi$
$138$		0			0
$139$	−8.74606	+	10.4232i	−0.741831	+	0.884080i	−0.996555	−	0.0829338i	$-0.973571\pi$
$139$	−8.74606	+	10.4232i	−0.741831	+	0.884080i	0.254724	+	0.967014i	$0.418015\pi$
$140$	13.1617	+	9.26046i	1.11236	+	0.782652i
$141$		0			0
$142$	2.15642	+	0.784874i	0.180963	+	0.0658651i
$143$	−0.00571141			−0.000477612
$144$		0			0
$145$		−	17.9837i		−	1.49347i
$146$	3.67184	+	20.8240i	0.303884	+	1.72341i
$147$		0			0
$148$	29.0678	−	10.5798i	2.38936	−	0.869655i
$149$	5.96077	−	7.10377i	0.488325	−	0.581963i	−0.464465	−	0.885591i	$-0.653753\pi$
$149$	5.96077	−	7.10377i	0.488325	−	0.581963i	0.952791	+	0.303628i	$0.0981979\pi$
$150$		0			0
$151$	−9.17350	−	3.33888i	−0.746529	−	0.271714i	−0.0593846	−	0.998235i	$-0.518914\pi$
$151$	−9.17350	−	3.33888i	−0.746529	−	0.271714i	−0.687144	+	0.726521i	$0.741136\pi$
$152$	−22.7299			−1.84364
$153$		0			0
$154$	0.745303	−	0.0635021i	0.0600582	−	0.00511714i
$155$	−5.40936	−	6.44663i	−0.434490	−	0.517806i
$156$		0			0
$157$	−10.4023	+	12.3970i	−0.830196	+	0.989388i	0.169797	+	0.985479i	$0.445689\pi$
$157$	−10.4023	+	12.3970i	−0.830196	+	0.989388i	−0.999992	+	0.00390940i	$0.998756\pi$
$158$	2.04678	+	5.62348i	0.162833	+	0.447380i
$159$		0			0
$160$	−3.35355	+	9.21381i	−0.265122	+	0.728415i
$161$	0.218444	+	2.56381i	0.0172158	+	0.202057i
$162$		0			0
$163$	5.65656	+	9.79745i	0.443056	+	0.767396i	0.997915	−	0.0645491i	$-0.0205609\pi$
$163$	5.65656	+	9.79745i	0.443056	+	0.767396i	−0.554858	+	0.831945i	$0.687228\pi$
$164$	−15.5193	+	13.0222i	−1.21185	+	1.01687i
$165$		0			0
$166$	14.5426	+	2.56425i	1.12872	+	0.199024i
$167$	0.331914	−	1.88238i	0.0256843	−	0.145663i	−0.969269	−	0.246004i	$-0.920882\pi$
$167$	0.331914	−	1.88238i	0.0256843	−	0.145663i	0.994953	+	0.100341i	$0.0319935\pi$
$168$		0			0
$169$	9.95692	−	8.35485i	0.765917	−	0.642681i
$170$	−0.577887	−	0.333643i	−0.0443219	−	0.0255893i
$171$		0			0
$172$	15.9518	+	27.6293i	1.21631	+	2.10672i
$173$	18.7471	−	15.7306i	1.42531	−	1.19598i	0.476893	−	0.878962i	$-0.341763\pi$
$173$	18.7471	−	15.7306i	1.42531	−	1.19598i	0.948420	−	0.317018i	$-0.102681\pi$
$174$		0			0
$175$	−3.46671	−	2.43915i	−0.262058	−	0.184383i
$176$	−0.0121379	−	0.0333486i	−0.000914928	−	0.00251374i
$177$		0			0
$178$	8.34934	−	22.9396i	0.625810	−	1.71940i
$179$	15.9928	−	9.23345i	1.19536	−	0.690140i	0.235841	−	0.971792i	$-0.424215\pi$
$179$	15.9928	−	9.23345i	1.19536	−	0.690140i	0.959517	+	0.281651i	$0.0908821\pi$
$180$		0			0
$181$	5.58272	−	3.22319i	0.414960	−	0.239577i	−0.277958	−	0.960593i	$-0.589658\pi$
$181$	5.58272	−	3.22319i	0.414960	−	0.239577i	0.692919	+	0.721016i	$0.256324\pi$
$182$	0.200754	−	0.199845i	0.0148809	−	0.0148135i
$183$		0			0
$184$	2.73459	−	0.995308i	0.201596	−	0.0733751i
$185$	16.2380	−	5.91013i	1.19384	−	0.434522i
$186$		0			0
$187$	−0.0190176	+	0.00335332i	−0.00139071	+	0.000245219i
$188$	−13.7567			−1.00331
$189$		0			0
$190$	−32.2354			−2.33860
$191$	−9.88047	+	1.74219i	−0.714926	+	0.126061i	−0.519268	−	0.854612i	$-0.673795\pi$
$191$	−9.88047	+	1.74219i	−0.714926	+	0.126061i	−0.195658	+	0.980672i	$0.562684\pi$
$192$		0			0
$193$	23.1247	−	8.41671i	1.66455	−	0.605848i	0.673485	−	0.739201i	$-0.264797\pi$
$193$	23.1247	−	8.41671i	1.66455	−	0.605848i	0.991069	+	0.133353i	$0.0425745\pi$
$194$	29.1234	−	10.6001i	2.09094	−	0.761040i
$195$		0			0
$196$	−14.9275	+	17.6269i	−1.06625	+	1.25906i
$197$	−12.0988	+	6.98527i	−0.862007	+	0.497680i	−0.864684	−	0.502316i	$-0.832481\pi$
$197$	−12.0988	+	6.98527i	−0.862007	+	0.497680i	0.00267677	+	0.999996i	$0.499148\pi$
$198$		0			0
$199$	11.1535	−	6.43950i	0.790654	−	0.456484i	−0.0495388	−	0.998772i	$-0.515775\pi$
$199$	11.1535	−	6.43950i	0.790654	−	0.456484i	0.840193	+	0.542288i	$0.182442\pi$
$200$	−1.63963	+	4.50484i	−0.115939	+	0.318540i
$201$		0			0
$202$	10.9413	+	30.0610i	0.769827	+	2.11508i
$203$	25.7088	+	2.30801i	1.80440	+	0.161991i
$204$		0			0
$205$	−8.66945	+	7.27453i	−0.605500	+	0.508075i
$206$	−8.97937	−	15.5527i	−0.625623	−	1.08361i
$207$		0			0
$208$	−0.0116390	−	0.00671976i	−0.000807017	−	0.000465931i
$209$	−0.714627	+	0.599643i	−0.0494318	+	0.0414782i
$210$		0			0
$211$	−0.918282	+	5.20784i	−0.0632171	+	0.358522i	0.936747	+	0.350008i	$0.113821\pi$
$211$	−0.918282	+	5.20784i	−0.0632171	+	0.358522i	−0.999964	+	0.00851397i	$0.997290\pi$
$212$	0.531658	+	0.0937457i	0.0365144	+	0.00643848i
$213$		0			0
$214$	13.1708	−	11.0516i	0.900337	−	0.755472i
$215$	8.91106	+	15.4344i	0.607729	+	1.05262i
$216$		0			0
$217$	9.91006	−	6.90565i	0.672739	−	0.468786i
$218$	6.88541	−	18.9175i	0.466339	−	1.28125i
$219$		0			0
$220$	−0.255485	−	0.701940i	−0.0172248	−	0.0473248i
$221$	−0.00470072	+	0.00560210i	−0.000316205	+	0.000376838i
$222$		0			0
$223$	5.38046	+	6.41218i	0.360302	+	0.429392i	0.915495	−	0.402330i	$-0.131800\pi$
$223$	5.38046	+	6.41218i	0.360302	+	0.429392i	−0.555192	+	0.831722i	$0.687355\pi$
$224$	−12.7413	−	5.97659i	−0.851313	−	0.399328i
$225$		0			0
$226$	−37.8836			−2.51998
$227$	18.9673	+	6.90355i	1.25891	+	0.458205i	0.883402	−	0.468616i	$-0.155247\pi$
$227$	18.9673	+	6.90355i	1.25891	+	0.458205i	0.375505	+	0.926820i	$0.377469\pi$
$228$		0			0
$229$	3.73395	−	4.44995i	0.246746	−	0.294061i	−0.628429	−	0.777867i	$-0.716302\pi$
$229$	3.73395	−	4.44995i	0.246746	−	0.294061i	0.875175	+	0.483806i	$0.160746\pi$
$230$	3.87817	−	1.41154i	0.255719	−	0.0930740i
$231$		0			0
$232$	−5.06925	−	28.7491i	−0.332813	−	1.88747i
$233$		−	6.16220i		−	0.403699i	−0.979417	−	0.201850i	$-0.935305\pi$
$233$		−	6.16220i		−	0.403699i	0.979417	−	0.201850i	$-0.0646952\pi$
$234$		0			0
$235$	−7.68484			−0.501304
$236$	−36.7095	−	13.3612i	−2.38959	−	0.869738i
$237$		0			0
$238$	0.551128	−	0.783304i	0.0357243	−	0.0507740i
$239$	−11.9974	+	14.2979i	−0.776046	+	0.924856i	−0.998748	−	0.0500310i	$-0.984068\pi$
$239$	−11.9974	+	14.2979i	−0.776046	+	0.924856i	0.222702	+	0.974887i	$0.428512\pi$
$240$		0			0
$241$	−7.83296	−	9.33496i	−0.504565	−	0.601318i	0.452294	−	0.891869i	$-0.350606\pi$
$241$	−7.83296	−	9.33496i	−0.504565	−	0.601318i	−0.956859	+	0.290551i	$0.906161\pi$
$242$	21.9006	+	12.6443i	1.40782	+	0.812808i
$243$		0			0
$244$		−	10.0167i		−	0.641256i
$245$	−8.33887	+	9.84679i	−0.532751	+	0.629089i
$246$		0			0
$247$	−0.0613462	+	0.347912i	−0.00390336	+	0.0221371i
$248$	−10.4647	−	8.78092i	−0.664509	−	0.557589i
$249$		0			0
$250$	−9.58226	+	26.3270i	−0.606035	+	1.66507i
$251$	1.90241	+	3.29506i	0.120079	+	0.207983i	0.919799	−	0.392391i	$-0.128352\pi$
$251$	1.90241	+	3.29506i	0.120079	+	0.207983i	−0.799720	+	0.600373i	$0.795019\pi$
$252$		0			0
$253$	0.0597177	−	0.103434i	0.00375442	−	0.00650285i
$254$	−6.35527	−	7.57392i	−0.398765	−	0.475230i
$255$		0			0
$256$	−3.09504	+	17.5528i	−0.193440	+	1.09705i
$257$	−16.8941	−	14.1758i	−1.05382	−	0.884262i	−0.0603326	−	0.998178i	$-0.519216\pi$
$257$	−16.8941	−	14.1758i	−1.05382	−	0.884262i	−0.993490	+	0.113916i	$0.963661\pi$
$258$		0			0
$259$	6.36492	+	23.9716i	0.395497	+	1.48952i
$260$	−0.244984	−	0.141441i	−0.0151932	−	0.00877182i
$261$		0			0
$262$			9.95936i			0.615291i
$263$	1.87472	−	0.330563i	0.115600	−	0.0203834i	−0.115549	−	0.993302i	$-0.536863\pi$
$263$	1.87472	−	0.330563i	0.115600	−	0.0203834i	0.231149	+	0.972918i	$0.425752\pi$
$264$		0			0
$265$	0.296997	+	0.0523686i	0.0182444	+	0.00321698i
$266$	4.13705	−	46.0823i	0.253659	−	2.82549i
$267$		0			0
$268$	5.63453	+	31.9550i	0.344184	+	1.95196i
$269$	6.11936	−	10.5990i	0.373104	−	0.646235i	−0.616937	−	0.787012i	$-0.711627\pi$
$269$	6.11936	−	10.5990i	0.373104	−	0.646235i	0.990041	+	0.140777i	$0.0449601\pi$
$270$		0			0
$271$	10.1008	−	5.83167i	0.613577	−	0.354249i	−0.160787	−	0.986989i	$-0.551403\pi$
$271$	10.1008	−	5.83167i	0.613577	−	0.354249i	0.774364	+	0.632740i	$0.218070\pi$
$272$	−0.0427003	−	0.0155416i	−0.00258909	−	0.000942351i
$273$		0			0
$274$	−3.09135	−	2.59395i	−0.186755	−	0.156706i
$275$	0.0672934	+	0.184887i	0.00405794	+	0.0111491i
$276$		0			0
$277$	−3.29023	−	18.6598i	−0.197691	−	1.12116i	−0.908534	−	0.417811i	$-0.862798\pi$
$277$	−3.29023	−	18.6598i	−0.197691	−	1.12116i	0.710843	−	0.703351i	$-0.248314\pi$
$278$	−15.6619	+	27.1272i	−0.939337	+	1.62698i
$279$		0			0
$280$	13.2119	+	6.19735i	0.789563	+	0.370362i
$281$	−0.401346	+	0.0707682i	−0.0239423	+	0.00422168i	−0.185607	−	0.982624i	$-0.559425\pi$
$281$	−0.401346	+	0.0707682i	−0.0239423	+	0.00422168i	0.161664	+	0.986846i	$0.448314\pi$
$282$		0			0
$283$	4.58326	+	0.808153i	0.272447	+	0.0480397i	0.308202	−	0.951321i	$-0.400273\pi$
$283$	4.58326	+	0.808153i	0.272447	+	0.0480397i	−0.0357555	+	0.999361i	$0.511384\pi$
$284$	3.23933	+	0.571182i	0.192219	+	0.0338934i
$285$		0			0
$286$	−0.0129486	+	0.00228319i	−0.000765668	+	0.000135008i
$287$	−9.28674	−	13.3271i	−0.548179	−	0.786673i
$288$		0			0
$289$	8.48764	−	14.7010i	0.499273	−	0.864766i
$290$	−7.18917	−	40.7718i	−0.422162	−	2.39420i
$291$		0			0
$292$	10.3662	+	28.4810i	0.606638	+	1.66672i
$293$	6.35829	+	5.33524i	0.371455	+	0.311688i	0.809337	−	0.587345i	$-0.199827\pi$
$293$	6.35829	+	5.33524i	0.371455	+	0.311688i	−0.437882	+	0.899033i	$0.644271\pi$
$294$		0			0
$295$	−20.5068	−	7.46387i	−1.19395	−	0.434563i
$296$	24.2924	−	14.0252i	1.41197	−	0.815199i
$297$		0			0
$298$	10.6742	−	18.4882i	0.618338	−	1.07099i
$299$	−0.00785408	−	0.0445427i	−0.000454213	−	0.00257597i
$300$		0			0
$301$	−23.2080	+	10.7580i	−1.33769	+	0.620083i
$302$	−22.1325	−	3.90255i	−1.27358	−	0.224567i
$303$		0			0
$304$	−2.16181	+	0.381185i	−0.123988	+	0.0218625i
$305$		−	5.59559i		−	0.320402i
$306$		0			0
$307$	−5.10853	−	2.94941i	−0.291559	−	0.168332i	0.347086	−	0.937833i	$-0.387171\pi$
$307$	−5.10853	−	2.94941i	−0.291559	−	0.168332i	−0.638645	+	0.769502i	$0.720505\pi$
$308$	1.03625	−	0.275145i	0.0590460	−	0.0156778i
$309$		0			0
$310$	−14.8409	−	12.4530i	−0.842909	−	0.707284i
$311$	−2.35699	+	13.3671i	−0.133653	+	0.757981i	0.842136	+	0.539265i	$0.181298\pi$
$311$	−2.35699	+	13.3671i	−0.133653	+	0.757981i	−0.975789	+	0.218716i	$0.929813\pi$
$312$		0			0
$313$	3.67401	+	4.37851i	0.207667	+	0.247488i	0.859817	−	0.510602i	$-0.170577\pi$
$313$	3.67401	+	4.37851i	0.207667	+	0.247488i	−0.652150	+	0.758090i	$0.726133\pi$
$314$	−18.6278	+	32.2643i	−1.05123	+	1.82078i
$315$		0			0
$316$	4.28889	+	7.42858i	0.241269	+	0.417890i
$317$	−0.823688	+	2.26306i	−0.0462629	+	0.127106i	−0.960672	−	0.277684i	$-0.910433\pi$
$317$	−0.823688	+	2.26306i	−0.0462629	+	0.127106i	0.914410	+	0.404790i	$0.132655\pi$
$318$		0			0
$319$	−0.917815	−	0.770138i	−0.0513878	−	0.0431194i
$320$	−4.10470	+	23.2789i	−0.229459	+	1.30133i
$321$		0			0
$322$	1.52015	+	5.72522i	0.0847149	+	0.319054i
$323$			1.19448i			0.0664627i
$324$		0			0
$325$	0.0645273	+	0.0372549i	0.00357933	+	0.00206653i
$326$	16.7409	+	19.9510i	0.927193	+	1.10499i
$327$		0			0
$328$	−11.8086	+	14.0730i	−0.652022	+	0.777049i
$329$	0.986264	−	10.9859i	0.0543745	−	0.605674i
$330$		0			0
$331$	−9.95637	−	3.62382i	−0.547251	−	0.199183i	0.0535735	−	0.998564i	$-0.482939\pi$
$331$	−9.95637	−	3.62382i	−0.547251	−	0.199183i	−0.600825	+	0.799381i	$0.705161\pi$
$332$	21.1664			1.16165
$333$		0			0
$334$		−	4.40032i		−	0.240775i
$335$	3.14758	+	17.8508i	0.171971	+	0.975295i
$336$		0			0
$337$	−21.6242	+	7.87058i	−1.17795	+	0.428738i	−0.855477	−	0.517841i	$-0.826736\pi$
$337$	−21.6242	+	7.87058i	−1.17795	+	0.428738i	−0.322471	+	0.946579i	$0.604514\pi$
$338$	19.2339	−	22.9221i	1.04619	−	1.24680i
$339$		0			0
$340$	−0.898781	−	0.327130i	−0.0487432	−	0.0177411i
$341$	−0.560661			−0.0303615
$342$		0			0
$343$	−13.0064	−	13.1846i	−0.702278	−	0.711903i
$344$	18.5961	+	22.1619i	1.00263	+	1.19489i
$345$		0			0
$346$	36.2139	−	43.1581i	1.94687	−	2.32019i
$347$	−1.31719	−	3.61896i	−0.0707106	−	0.194276i	0.899303	−	0.437326i	$-0.144074\pi$
$347$	−1.31719	−	3.61896i	−0.0707106	−	0.194276i	−0.970014	+	0.243050i	$0.921852\pi$
$348$		0			0
$349$	0.721690	−	1.98283i	0.0386312	−	0.106138i	−0.918877	−	0.394543i	$-0.870903\pi$
$349$	0.721690	−	1.98283i	0.0386312	−	0.106138i	0.957508	+	0.288405i	$0.0931250\pi$
$350$	−8.83462	−	4.14408i	−0.472230	−	0.221510i
$351$		0			0
$352$	0.326622	+	0.565725i	0.0174090	+	0.0301533i
$353$	−9.41323	+	7.89864i	−0.501016	+	0.420402i	−0.857955	−	0.513726i	$-0.828265\pi$
$353$	−9.41323	+	7.89864i	−0.501016	+	0.420402i	0.356939	+	0.934128i	$0.383820\pi$
$354$		0			0
$355$	1.80957	+	0.319075i	0.0960418	+	0.0169348i
$356$	6.07613	−	34.4594i	0.322034	−	1.82635i
$357$		0			0
$358$	32.5669	−	27.3269i	1.72122	−	1.44427i
$359$	26.4895	+	15.2937i	1.39806	+	0.807170i	0.994189	−	0.107646i	$-0.0343313\pi$
$359$	26.4895	+	15.2937i	1.39806	+	0.807170i	0.403871	+	0.914816i	$0.367665\pi$
$360$		0			0
$361$	19.3516	+	33.5179i	1.01850	+	1.76410i
$362$	11.3684	−	9.53919i	0.597508	−	0.501369i
$363$		0			0
$364$	0.233640	−	0.332066i	0.0122460	−	0.0174050i
$365$	5.79082	+	15.9102i	0.303105	+	0.832775i
$366$		0			0
$367$	−4.68686	+	12.8771i	−0.244652	+	0.672177i	0.755208	+	0.655485i	$0.227536\pi$
$367$	−4.68686	+	12.8771i	−0.244652	+	0.672177i	−0.999861	+	0.0166920i	$0.994687\pi$
$368$	0.243391	−	0.140522i	0.0126876	−	0.00732520i
$369$		0			0
$370$	34.4513	−	19.8904i	1.79104	−	1.03405i
$371$	−0.112980	+	0.417853i	−0.00586564	+	0.0216939i
$372$		0			0
$373$	10.9812	−	3.99683i	0.568585	−	0.206948i	−0.0416995	−	0.999130i	$-0.513277\pi$
$373$	10.9812	−	3.99683i	0.568585	−	0.206948i	0.610285	+	0.792182i	$0.291055\pi$
$374$	−0.0417753	+	0.0152050i	−0.00216015	+	0.000786230i
$375$		0			0
$376$	−12.2851	+	2.16620i	−0.633558	+	0.111713i
$377$	−0.453725			−0.0233681
$378$		0			0
$379$	−12.7028			−0.652500			−0.326250	−	0.945283i	$-0.605785\pi$
$379$	−12.7028			−0.652500			−0.326250	+	0.945283i	$0.605785\pi$
$380$	−45.5030	+	8.02340i	−2.33425	+	0.411592i
$381$		0			0
$382$	−21.7040	+	7.89963i	−1.11048	+	0.404180i
$383$	7.52651	−	2.73942i	0.384587	−	0.139978i	−0.142489	−	0.989796i	$-0.545511\pi$
$383$	7.52651	−	2.73942i	0.384587	−	0.139978i	0.527076	+	0.849818i	$0.323288\pi$
$384$		0			0
$385$	0.578876	−	0.153702i	0.0295022	−	0.00783340i
$386$	49.0625	−	28.3263i	2.49722	−	1.44177i
$387$		0			0
$388$	38.4719	−	22.2117i	1.95311	−	1.12763i
$389$	4.38258	−	12.0411i	0.222206	−	0.610506i	−0.777628	−	0.628724i	$-0.783577\pi$
$389$	4.38258	−	12.0411i	0.222206	−	0.610506i	0.999834	+	0.0182189i	$0.00579958\pi$
$390$		0			0
$391$	−0.0523045	−	0.143705i	−0.00264515	−	0.00726749i
$392$	−10.5551	+	18.0919i	−0.533112	+	0.913776i
$393$		0			0
$394$	−24.6375	+	20.6733i	−1.24122	+	1.04151i
$395$	2.39588	+	4.14978i	0.120550	+	0.208798i
$396$		0			0
$397$	8.65774	+	4.99855i	0.434520	+	0.250870i	0.701270	−	0.712896i	$-0.252617\pi$
$397$	8.65774	+	4.99855i	0.434520	+	0.250870i	−0.266750	+	0.963766i	$0.585950\pi$
$398$	22.7125	−	19.0581i	1.13848	−	0.955294i
$399$		0			0
$400$	−0.0803954	+	0.455945i	−0.00401977	+	0.0227973i
$401$	−36.5039	−	6.43662i	−1.82292	−	0.321429i	−0.845698	−	0.533662i	$-0.820815\pi$
$401$	−36.5039	−	6.43662i	−1.82292	−	0.321429i	−0.977219	+	0.212233i	$0.931926\pi$
$402$		0			0
$403$	−0.162647	+	0.136477i	−0.00810203	+	0.00679841i
$404$	22.9268	+	39.7104i	1.14065	+	1.97566i
$405$		0			0
$406$	59.2083	−	5.04473i	2.93846	−	0.250366i
$407$	0.393748	−	1.08181i	0.0195174	−	0.0536236i
$408$		0			0
$409$	−0.800841	−	2.20029i	−0.0395990	−	0.108797i	0.918317	−	0.395845i	$-0.129548\pi$
$409$	−0.800841	−	2.20029i	−0.0395990	−	0.108797i	−0.957916	+	0.287048i	$0.907326\pi$
$410$	−16.7469	+	19.9581i	−0.827069	+	0.985663i
$411$		0			0
$412$	−16.5462	−	19.7190i	−0.815175	−	0.971488i
$413$	13.3019	−	28.3578i	0.654542	−	1.39539i
$414$		0			0
$415$	11.8240			0.580419
$416$	0.232462	+	0.0846094i	0.0113974	+	0.00414832i
$417$		0			0
$418$	−1.38045	+	1.64516i	−0.0675202	+	0.0804674i
$419$	−28.6465	+	10.4265i	−1.39947	+	0.509366i	−0.928022	−	0.372526i	$-0.878492\pi$
$419$	−28.6465	+	10.4265i	−1.39947	+	0.509366i	−0.471451	+	0.881892i	$0.656270\pi$
$420$		0			0
$421$	0.369085	+	2.09318i	0.0179881	+	0.102015i	0.992480	−	0.122407i	$-0.0390614\pi$
$421$	0.369085	+	2.09318i	0.0179881	+	0.102015i	−0.974492	+	0.224423i	$0.927950\pi$
$422$			12.1740i			0.592623i
$423$		0			0
$424$	0.489547			0.0237745
$425$	0.236734	+	0.0861641i	0.0114833	+	0.00417957i
$426$		0			0
$427$	7.99922	+	0.718132i	0.387109	+	0.0347528i
$428$	15.8410	−	18.8785i	0.765702	−	0.912528i
$429$		0			0
$430$	26.3728	+	31.4298i	1.27181	+	1.51568i
$431$	1.02928	+	0.594254i	0.0495786	+	0.0286242i	0.524584	−	0.851358i	$-0.324221\pi$
$431$	1.02928	+	0.594254i	0.0495786	+	0.0286242i	−0.475006	+	0.879983i	$0.657554\pi$
$432$		0			0
$433$			11.1104i			0.533930i	0.963706	+	0.266965i	$0.0860208\pi$
$433$			11.1104i			0.533930i	−0.963706	+	0.266965i	$0.913979\pi$
$434$	19.7070	−	19.6178i	0.945966	−	0.941684i
$435$		0			0
$436$	5.01076	−	28.4175i	0.239972	−	1.36095i
$437$	−5.65928	−	4.74870i	−0.270720	−	0.227161i
$438$		0			0
$439$	1.90318	−	5.22894i	0.0908337	−	0.249564i	−0.885954	−	0.463773i	$-0.846495\pi$
$439$	1.90318	−	5.22894i	0.0908337	−	0.249564i	0.976788	+	0.214209i	$0.0687175\pi$
$440$	−0.338686	−	0.586622i	−0.0161462	−	0.0279661i
$441$		0			0
$442$	−0.00841775	+	0.0145800i	−0.000400391	+	0.000693498i
$443$	−17.4915	−	20.8455i	−0.831046	−	0.990402i	−0.999989	−	0.00477585i	$-0.998480\pi$
$443$	−17.4915	−	20.8455i	−0.831046	−	0.990402i	0.168943	−	0.985626i	$-0.445965\pi$
$444$		0			0
$445$	3.39427	−	19.2498i	0.160904	−	0.912530i
$446$	14.7616	+	12.3865i	0.698984	+	0.586517i
$447$		0			0
$448$	−32.7517	−	8.85549i	−1.54737	−	0.418382i
$449$	21.3299	+	12.3148i	1.00662	+	0.581171i	0.910200	−	0.414170i	$-0.135928\pi$
$449$	21.3299	+	12.3148i	1.00662	+	0.581171i	0.0964182	+	0.995341i	$0.469261\pi$
$450$		0			0
$451$			0.753979i			0.0355035i
$452$	−53.4760	+	9.42926i	−2.51530	+	0.443515i
$453$		0			0
$454$	45.7616	+	8.06900i	2.14770	+	0.378697i
$455$	0.130517	−	0.185500i	0.00611871	−	0.00869637i
$456$		0			0
$457$	−1.22308	−	6.93645i	−0.0572134	−	0.324473i	0.942746	−	0.333512i	$-0.108234\pi$
$457$	−1.22308	−	6.93645i	−0.0572134	−	0.324473i	−0.999959	+	0.00903894i	$0.997123\pi$
$458$	6.68651	−	11.5814i	0.312440	−	0.541162i
$459$		0			0
$460$	5.12303	−	2.95778i	0.238863	−	0.137907i
$461$	6.82236	+	2.48314i	0.317749	+	0.115651i	0.495971	−	0.868339i	$-0.334812\pi$
$461$	6.82236	+	2.48314i	0.317749	+	0.115651i	−0.178222	+	0.983990i	$0.557034\pi$
$462$		0			0
$463$	6.25076	+	5.24501i	0.290498	+	0.243756i	0.776376	−	0.630270i	$-0.217056\pi$
$463$	6.25076	+	5.24501i	0.290498	+	0.243756i	−0.485878	+	0.874026i	$0.661500\pi$
$464$	−0.964258	−	2.64928i	−0.0447645	−	0.122990i
$465$		0			0
$466$	−2.46340	−	13.9706i	−0.114115	−	0.647177i
$467$	−6.38140	+	11.0529i	−0.295296	+	0.511468i	−0.975054	−	0.221969i	$-0.928752\pi$
$467$	−6.38140	+	11.0529i	−0.295296	+	0.511468i	0.679758	+	0.733437i	$0.262085\pi$
$468$		0			0
$469$	−25.9228	+	2.20870i	−1.19700	+	0.101988i
$470$	−17.4227	+	3.07209i	−0.803649	+	0.141705i
$471$		0			0
$472$	−34.8865	−	6.15144i	−1.60578	−	0.283143i
$473$	1.16932	+	0.206182i	0.0537653	+	0.00948027i
$474$		0			0
$475$	11.9852	−	2.11332i	0.549920	−	0.0969657i
$476$	0.582999	−	1.24288i	0.0267217	−	0.0569672i
$477$		0			0
$478$	−21.4841	+	37.2116i	−0.982661	+	1.70202i
$479$	3.46023	+	19.6239i	0.158102	+	0.896640i	0.955895	+	0.293709i	$0.0948895\pi$
$479$	3.46023	+	19.6239i	0.158102	+	0.896640i	−0.797793	+	0.602931i	$0.793999\pi$
$480$		0			0
$481$	−0.149111	−	0.409680i	−0.00679890	−	0.0186798i
$482$	−21.4902	−	18.0325i	−0.978854	−	0.821356i
$483$		0			0
$484$	34.0618	+	12.3975i	1.54826	+	0.563522i
$485$	21.4913	−	12.4080i	0.975869	−	0.563418i
$486$		0			0
$487$	−16.5334	+	28.6367i	−0.749200	+	1.29765i	0.199007	+	0.979998i	$0.436228\pi$
$487$	−16.5334	+	28.6367i	−0.749200	+	1.29765i	−0.948207	+	0.317654i	$0.897105\pi$
$488$	−1.57728	−	8.94522i	−0.0714003	−	0.404931i
$489$		0			0
$490$	−14.9691	+	25.6577i	−0.676236	+	1.15910i
$491$	−1.71158	−	0.301798i	−0.0772427	−	0.0136200i	0.134893	−	0.990860i	$-0.456931\pi$
$491$	−1.71158	−	0.301798i	−0.0772427	−	0.0136200i	−0.212136	+	0.977240i	$0.568042\pi$
$492$		0			0
$493$	−1.51080	+	0.266394i	−0.0680429	+	0.0119978i
$494$			0.813291i			0.0365917i
$495$		0			0
$496$	−1.14254	−	0.659646i	−0.0513015	−	0.0296190i
$497$	−0.688375	+	2.54593i	−0.0308778	+	0.114201i
$498$		0			0
$499$	−26.2943	−	22.0635i	−1.17709	−	0.987699i	−0.999994	−	0.00350565i	$-0.998884\pi$
$499$	−26.2943	−	22.0635i	−1.17709	−	0.987699i	−0.177100	−	0.984193i	$-0.556671\pi$
$500$	−6.97336	+	39.5479i	−0.311858	+	1.76864i
$501$		0			0
$502$	5.63027	+	6.70990i	0.251291	+	0.299478i
$503$	−6.14413	+	10.6419i	−0.273953	+	0.474501i	−0.969870	−	0.243621i	$-0.921665\pi$
$503$	−6.14413	+	10.6419i	−0.273953	+	0.474501i	0.695917	+	0.718122i	$0.254998\pi$
$504$		0			0
$505$	12.8074	+	22.1831i	0.569924	+	0.987137i
$506$	0.0940402	−	0.258373i	0.00418060	−	0.0114861i
$507$		0			0
$508$	−10.8562	−	9.10940i	−0.481664	−	0.404164i
$509$	−4.54581	+	25.7805i	−0.201489	+	1.14270i	0.701380	+	0.712787i	$0.252568\pi$
$509$	−4.54581	+	25.7805i	−0.201489	+	1.14270i	−0.902869	+	0.429915i	$0.858544\pi$
$510$		0			0
$511$	−23.4877	+	6.23643i	−1.03903	+	0.275883i
$512$			3.26654i			0.144362i
$513$		0			0
$514$	−43.9683	−	25.3851i	−1.93936	−	1.11969i
$515$	−9.24312	−	11.0155i	−0.407301	−	0.485402i
$516$		0			0
$517$	−0.329097	+	0.392203i	−0.0144737	+	0.0172490i
$518$	24.0131	+	51.8028i	1.05508	+	2.27608i
$519$		0			0
$520$	−0.241049	−	0.0877347i	−0.0105707	−	0.00384742i
$521$	−14.2660			−0.625004			−0.312502	−	0.949917i	$-0.601167\pi$
$521$	−14.2660			−0.625004			−0.312502	+	0.949917i	$0.601167\pi$
$522$		0			0
$523$		−	20.0974i		−	0.878798i	−0.898292	−	0.439399i	$-0.855191\pi$
$523$		−	20.0974i		−	0.878798i	0.898292	−	0.439399i	$-0.144809\pi$
$524$	2.47889	+	14.0585i	0.108291	+	0.614148i
$525$		0			0
$526$	4.11812	−	1.49887i	0.179559	−	0.0653540i
$527$	−0.461447	+	0.549931i	−0.0201009	+	0.0239554i
$528$		0			0
$529$	−20.7241	−	7.54297i	−0.901049	−	0.327955i
$530$	0.694271			0.0301572
$531$		0			0
$532$	−5.63012	−	66.0789i	−0.244097	−	2.86488i
$533$	0.183535	+	0.218728i	0.00794978	+	0.00947418i
$534$		0			0
$535$	8.84913	−	10.5460i	0.382581	−	0.455943i
$536$	10.0636	+	27.6495i	0.434681	+	1.19428i
$537$		0			0
$538$	9.63644	−	26.4759i	0.415457	−	1.14146i
$539$	0.145434	+	0.847262i	0.00626430	+	0.0364942i
$540$		0			0
$541$	3.47620	+	6.02095i	0.149453	+	0.258861i	0.931026	−	0.364954i	$-0.118915\pi$
$541$	3.47620	+	6.02095i	0.149453	+	0.258861i	−0.781572	+	0.623815i	$0.785582\pi$
$542$	20.5687	−	17.2592i	0.883500	−	0.741344i
$543$		0			0
$544$	0.823721	+	0.145244i	0.0353167	+	0.00622730i
$545$	2.79913	−	15.8747i	0.119902	−	0.679996i
$546$		0			0
$547$	−10.1175	+	8.48957i	−0.432592	+	0.362988i	−0.832929	−	0.553380i	$-0.813338\pi$
$547$	−10.1175	+	8.48957i	−0.432592	+	0.362988i	0.400337	+	0.916368i	$0.368893\pi$
$548$	−5.00934	−	2.89215i	−0.213989	−	0.123546i
$549$		0			0
$550$	0.226475	+	0.392266i	0.00965691	+	0.0167263i
$551$	−56.7713	+	47.6368i	−2.41854	+	2.02940i
$552$		0			0
$553$	−6.23984	+	2.89247i	−0.265345	+	0.123000i
$554$	−14.9189	−	40.9894i	−0.633844	−	1.74147i
$555$		0			0
$556$	−15.3561	+	42.1906i	−0.651244	+	1.78928i
$557$	−36.7504	+	21.2178i	−1.55716	+	0.899028i	−0.559636	+	0.828738i	$0.689059\pi$
$557$	−36.7504	+	21.2178i	−1.55716	+	0.899028i	−0.997527	+	0.0702901i	$0.977608\pi$
$558$		0			0
$559$	0.389407	−	0.224824i	0.0164702	−	0.00950905i
$560$	1.36050	+	0.367854i	0.0574915	+	0.0155447i
$561$		0			0
$562$	−0.881622	+	0.320884i	−0.0371890	+	0.0135357i
$563$	29.1497	−	10.6096i	1.22852	−	0.447143i	0.355426	−	0.934704i	$-0.384336\pi$
$563$	29.1497	−	10.6096i	1.22852	−	0.447143i	0.873089	+	0.487561i	$0.162113\pi$
$564$		0			0
$565$	−29.8730	+	5.26741i	−1.25676	+	0.221602i
$566$	10.7140			0.450344
$567$		0			0
$568$	2.98275			0.125154
$569$	−11.2726	+	1.98767i	−0.472573	+	0.0833273i	−0.404862	−	0.914378i	$-0.632681\pi$
$569$	−11.2726	+	1.98767i	−0.472573	+	0.0833273i	−0.0677106	+	0.997705i	$0.521569\pi$
$570$		0			0
$571$	−14.2946	+	5.20281i	−0.598210	+	0.217731i	−0.623337	−	0.781954i	$-0.714223\pi$
$571$	−14.2946	+	5.20281i	−0.598210	+	0.217731i	0.0251265	+	0.999684i	$0.492001\pi$
$572$	−0.0177098	+	0.00644584i	−0.000740484	+	0.000269514i
$573$		0			0
$574$	−26.3821	−	26.5020i	−1.10117	−	1.10617i
$575$	−1.34938	+	0.779063i	−0.0562729	+	0.0324892i
$576$		0			0
$577$	−14.5184	+	8.38222i	−0.604410	+	0.348956i	−0.770775	−	0.637108i	$-0.780131\pi$
$577$	−14.5184	+	8.38222i	−0.604410	+	0.348956i	0.166364	+	0.986064i	$0.446797\pi$
$578$	13.3659	−	36.7224i	0.555947	−	1.52745i
$579$		0			0
$580$	−20.2963	−	55.7635i	−0.842756	−	2.31545i
$581$	−1.51748	+	16.9031i	−0.0629558	+	0.701260i
$582$		0			0
$583$	0.0153913	−	0.0129149i	0.000637443	−	0.000534879i
$584$	13.7421	+	23.8020i	0.568651	+	0.984933i
$585$		0			0
$586$	16.5480	+	9.55400i	0.683592	+	0.394672i
$587$	1.10643	−	0.928404i	0.0456672	−	0.0383193i	−0.619668	−	0.784864i	$-0.712733\pi$
$587$	1.10643	−	0.928404i	0.0456672	−	0.0383193i	0.665336	+	0.746544i	$0.268288\pi$
$588$		0			0
$589$	−6.02205	+	34.1528i	−0.248134	+	1.40724i
$590$	−49.4758	−	8.72391i	−2.03689	−	0.359158i
$591$		0			0
$592$	2.07521	−	1.74131i	0.0852905	−	0.0715672i
$593$	−17.6222	−	30.5226i	−0.723657	−	1.25341i	−0.959524	−	0.281626i	$-0.909126\pi$
$593$	−17.6222	−	30.5226i	−0.723657	−	1.25341i	0.235867	−	0.971785i	$-0.424207\pi$
$594$		0			0
$595$	0.325677	−	0.694300i	0.0133515	−	0.0284635i
$596$	10.4658	−	28.7545i	0.428695	−	1.17783i
$597$		0			0
$598$	−0.0356128	−	0.0978453i	−0.00145631	−	0.00400119i
$599$	27.9181	−	33.2715i	1.14070	−	1.35944i	0.217069	−	0.976156i	$-0.430350\pi$
$599$	27.9181	−	33.2715i	1.14070	−	1.35944i	0.923633	−	0.383279i	$-0.125205\pi$
$600$		0			0
$601$	12.1502	+	14.4801i	0.495618	+	0.590655i	0.954637	−	0.297772i	$-0.0962434\pi$
$601$	12.1502	+	14.4801i	0.495618	+	0.590655i	−0.459019	+	0.888427i	$0.651799\pi$
$602$	−48.3154	+	33.6677i	−1.96919	+	1.37219i
$603$		0			0
$604$	−32.2132			−1.31074
$605$	19.0277	+	6.92552i	0.773587	+	0.281563i
$606$		0			0
$607$	−1.36629	+	1.62828i	−0.0554560	+	0.0660899i	−0.793059	−	0.609144i	$-0.791513\pi$
$607$	−1.36629	+	1.62828i	−0.0554560	+	0.0660899i	0.737603	+	0.675234i	$0.235957\pi$
$608$	37.9695	−	13.8198i	1.53987	−	0.560465i
$609$		0			0
$610$	−2.23689	−	12.6860i	−0.0905691	−	0.513643i
$611$			0.193887i			0.00784383i
$612$		0			0
$613$	−18.2547			−0.737301			−0.368650	−	0.929568i	$-0.620180\pi$
$613$	−18.2547			−0.737301			−0.368650	+	0.929568i	$0.620180\pi$
$614$	−12.7609	−	4.64457i	−0.514987	−	0.187440i
$615$		0			0
$616$	0.882077	−	0.408885i	0.0355399	−	0.0164745i
$617$	5.58064	−	6.65075i	0.224668	−	0.267749i	−0.641922	−	0.766770i	$-0.721863\pi$
$617$	5.58064	−	6.65075i	0.224668	−	0.267749i	0.866590	+	0.499021i	$0.166307\pi$
$618$		0			0
$619$	−25.2770	−	30.1239i	−1.01597	−	1.21078i	−0.977372	−	0.211527i	$-0.932156\pi$
$619$	−25.2770	−	30.1239i	−1.01597	−	1.21078i	−0.0385946	−	0.999255i	$-0.512288\pi$
$620$	−24.0488	−	13.8846i	−0.965824	−	0.557619i
$621$		0			0
$622$			31.2476i			1.25291i
$623$	27.0832	+	7.32281i	1.08506	+	0.293382i
$624$		0			0
$625$	−2.50446	+	14.2035i	−0.100178	+	0.568140i
$626$	10.0799	+	8.45803i	0.402873	+	0.338051i
$627$		0			0
$628$	−18.2641	+	50.1803i	−0.728818	+	2.00241i
$629$	−0.737040	−	1.27659i	−0.0293877	−	0.0509010i
$630$		0			0
$631$	5.26401	−	9.11753i	0.209557	−	0.362963i	−0.742018	−	0.670380i	$-0.766131\pi$
$631$	5.26401	−	9.11753i	0.209557	−	0.362963i	0.951575	+	0.307417i	$0.0994645\pi$
$632$	4.99984	+	5.95857i	0.198883	+	0.237019i
$633$		0			0
$634$	−0.962742	+	5.45998i	−0.0382354	+	0.216844i
$635$	−6.06451	−	5.08873i	−0.240663	−	0.201940i
$636$		0			0
$637$	0.248433	+	0.210388i	0.00984326	+	0.00833587i
$638$	−2.38869	−	1.37911i	−0.0945693	−	0.0545996i
$639$		0			0
$640$			34.8074i			1.37588i
$641$	12.1516	−	2.14265i	0.479958	−	0.0846295i	0.0715652	−	0.997436i	$-0.477201\pi$
$641$	12.1516	−	2.14265i	0.479958	−	0.0846295i	0.408392	+	0.912806i	$0.366089\pi$
$642$		0			0
$643$	−22.7208	−	4.00630i	−0.896023	−	0.157993i	−0.293372	−	0.955998i	$-0.594778\pi$
$643$	−22.7208	−	4.00630i	−0.896023	−	0.157993i	−0.602650	+	0.798005i	$0.705889\pi$
$644$	3.57084	+	7.70327i	0.140711	+	0.303551i
$645$		0			0
$646$	0.477505	+	2.70807i	0.0187872	+	0.106547i
$647$	−19.2253	+	33.2993i	−0.755826	+	1.30913i	0.189137	+	0.981951i	$0.439431\pi$
$647$	−19.2253	+	33.2993i	−0.755826	+	1.30913i	−0.944963	+	0.327178i	$0.893902\pi$
$648$		0			0
$649$	−1.25911	+	0.726949i	−0.0494245	+	0.0285352i
$650$	0.161186	+	0.0586669i	0.00632224	+	0.00230111i
$651$		0			0
$652$	28.5970	+	23.9958i	1.11995	+	0.939747i
$653$	−4.84634	−	13.3152i	−0.189652	−	0.521064i	0.808028	−	0.589144i	$-0.200535\pi$
$653$	−4.84634	−	13.3152i	−0.189652	−	0.521064i	−0.997680	+	0.0680800i	$0.978313\pi$
$654$		0			0
$655$	1.38477	+	7.85341i	0.0541074	+	0.306858i
$656$	−0.887094	+	1.53649i	−0.0346352	+	0.0599899i
$657$		0			0
$658$	−2.15572	−	25.3010i	−0.0840389	−	0.986336i
$659$	−39.3185	+	6.93292i	−1.53163	+	0.270068i	−0.874993	−	0.484136i	$-0.839134\pi$
$659$	−39.3185	+	6.93292i	−1.53163	+	0.270068i	−0.656640	+	0.754204i	$0.728023\pi$
$660$		0			0
$661$	24.1288	+	4.25455i	0.938500	+	0.165483i	0.621918	−	0.783082i	$-0.286354\pi$
$661$	24.1288	+	4.25455i	0.938500	+	0.165483i	0.316582	+	0.948565i	$0.397465\pi$
$662$	−24.0212	−	4.23559i	−0.933612	−	0.164621i
$663$		0			0
$664$	18.9021	−	3.33296i	0.733545	−	0.129344i
$665$	−3.14512	−	36.9132i	−0.121962	−	1.43143i
$666$		0			0
$667$	4.74409	−	8.21701i	0.183692	−	0.318164i
$668$	−1.09524	−	6.21143i	−0.0423762	−	0.240327i
$669$		0			0
$670$	14.2721	+	39.2122i	0.551379	+	1.51490i
$671$	−0.285576	−	0.239627i	−0.0110245	−	0.00925068i
$672$		0			0
$673$	−12.2850	−	4.47136i	−0.473551	−	0.172358i	0.0942095	−	0.995552i	$-0.469968\pi$
$673$	−12.2850	−	4.47136i	−0.473551	−	0.172358i	−0.567760	+	0.823194i	$0.692190\pi$
$674$	−45.8791	+	26.4883i	−1.76720	+	1.02029i
$675$		0			0
$676$	21.4450	−	37.1438i	0.824807	−	1.42861i
$677$	−4.73038	−	26.8273i	−0.181803	−	1.03106i	−0.929994	−	0.367575i	$-0.880188\pi$
$677$	−4.73038	−	26.8273i	−0.181803	−	1.03106i	0.748191	−	0.663484i	$-0.230923\pi$
$678$		0			0
$679$	14.9798	+	32.3155i	0.574872	+	1.24015i
$680$	−0.854147	−	0.150609i	−0.0327551	−	0.00577560i
$681$		0			0
$682$	−1.27110	+	0.224130i	−0.0486730	+	0.00858237i
$683$			46.5851i			1.78253i	0.453482	+	0.891265i	$0.350182\pi$
$683$			46.5851i			1.78253i	−0.453482	+	0.891265i	$0.649818\pi$
$684$		0			0
$685$	−2.79834	−	1.61562i	−0.106919	−	0.0617297i
$686$	−34.7581	−	24.6921i	−1.32707	−	0.942749i
$687$		0			0
$688$	2.14030	+	1.79593i	0.0815983	+	0.0684691i
$689$	0.00132125	−	0.00749317i	5.03355e−5	−	0.000285467i
$690$		0			0
$691$	5.79402	+	6.90504i	0.220415	+	0.262680i	0.864909	−	0.501929i	$-0.167376\pi$
$691$	5.79402	+	6.90504i	0.220415	+	0.262680i	−0.644494	+	0.764610i	$0.722932\pi$
$692$	40.3770	−	69.9350i	1.53490	−	2.65853i
$693$		0			0
$694$	−4.43299	−	7.67816i	−0.168274	−	0.291459i
$695$	−8.57829	+	23.5687i	−0.325393	+	0.894010i
$696$		0			0
$697$	0.739549	+	0.620555i	0.0280124	+	0.0235052i
$698$	0.843525	−	4.78387i	0.0319279	−	0.181072i
$699$		0			0
$700$	−13.5023	−	3.65078i	−0.510339	−	0.137987i
$701$		−	28.1670i		−	1.06385i	−0.846790	−	0.531927i	$-0.821468\pi$
$701$		−	28.1670i		−	1.06385i	0.846790	−	0.531927i	$-0.178532\pi$
$702$		0			0
$703$	−61.6697	−	35.6050i	−2.32592	−	1.34287i
$704$	1.01228	+	1.20639i	0.0381517	+	0.0454674i
$705$		0			0
$706$	−18.1837	+	21.6704i	−0.684351	+	0.815578i
$707$	−33.3558	+	15.4620i	−1.25447	+	0.581509i
$708$		0			0
$709$	33.4746	+	12.1838i	1.25717	+	0.457571i	0.882817	−	0.469717i	$-0.155644\pi$
$709$	33.4746	+	12.1838i	1.25717	+	0.457571i	0.374349	+	0.927288i	$0.377866\pi$
$710$	4.23011			0.158753
$711$		0			0
$712$		−	31.7300i		−	1.18913i
$713$	−0.770997	−	4.37254i	−0.0288741	−	0.163753i
$714$		0			0
$715$	−0.00989312	+	0.00360080i	−0.000369982	+	0.000134662i
$716$	39.1693	−	46.6802i	1.46383	−	1.74452i
$717$		0			0
$718$	66.1694	+	24.0837i	2.46942	+	0.898795i
$719$	−9.13804			−0.340791			−0.170396	−	0.985376i	$-0.554505\pi$
$719$	−9.13804			−0.340791			−0.170396	+	0.985376i	$0.554505\pi$
$720$		0			0
$721$	16.9336	−	11.7999i	0.630640	−	0.439450i
$722$	57.2720	+	68.2541i	2.13144	+	2.54016i
$723$		0			0
$724$	13.6731	−	16.2950i	0.508157	−	0.605598i
$725$	5.34592	+	14.6878i	0.198542	+	0.545491i
$726$		0			0
$727$	3.56316	−	9.78970i	0.132150	−	0.363080i	−0.855915	−	0.517117i	$-0.827005\pi$
$727$	3.56316	−	9.78970i	0.132150	−	0.363080i	0.988065	+	0.154037i	$0.0492275\pi$
$728$	0.156358	−	0.333334i	0.00579501	−	0.0123542i
$729$		0			0
$730$	19.4889	+	33.7558i	0.721317	+	1.24936i
$731$	1.16463	−	0.977242i	0.0430755	−	0.0361446i
$732$		0			0
$733$	27.3550	+	4.82343i	1.01038	+	0.178157i	0.654250	−	0.756279i	$-0.272985\pi$
$733$	27.3550	+	4.82343i	1.01038	+	0.178157i	0.356131	+	0.934436i	$0.384096\pi$
$734$	−5.47810	+	31.0678i	−0.202200	+	1.14673i
$735$		0			0
$736$	−3.96288	+	3.32525i	−0.146074	+	0.122570i
$737$	1.04583	+	0.603808i	0.0385235	+	0.0222415i
$738$		0			0
$739$	17.8396	+	30.8992i	0.656242	+	1.13664i	0.981581	+	0.191047i	$0.0611882\pi$
$739$	17.8396	+	30.8992i	0.656242	+	1.13664i	−0.325339	+	0.945597i	$0.605479\pi$
$740$	43.6802	−	36.6520i	1.60571	−	1.34735i
$741$		0			0
$742$	−0.0891020	+	0.992502i	−0.00327104	+	0.0364359i
$743$	−2.30236	−	6.32568i	−0.0844653	−	0.232067i	0.890269	−	0.455436i	$-0.150517\pi$
$743$	−2.30236	−	6.32568i	−0.0844653	−	0.232067i	−0.974734	+	0.223369i	$0.928294\pi$
$744$		0			0
$745$	5.84643	−	16.0629i	0.214197	−	0.588500i
$746$	23.2983	−	13.4513i	0.853010	−	0.492486i
$747$		0			0
$748$	−0.0551849	+	0.0318610i	−0.00201776	+	0.00116495i
$749$	13.9404	+	14.0038i	0.509372	+	0.511688i
$750$		0			0
$751$	44.9691	−	16.3674i	1.64095	−	0.597256i	0.653742	−	0.756717i	$-0.273198\pi$
$751$	44.9691	−	16.3674i	1.64095	−	0.597256i	0.987204	+	0.159462i	$0.0509759\pi$
$752$	−1.13209	+	0.412049i	−0.0412832	+	0.0150259i
$753$		0			0
$754$	−1.02866	+	0.181381i	−0.0374617	+	0.00660551i
$755$	−17.9951			−0.654907
$756$		0			0
$757$	35.1225			1.27655			0.638274	−	0.769809i	$-0.279649\pi$
$757$	35.1225			1.27655			0.638274	+	0.769809i	$0.279649\pi$
$758$	−28.7992	+	5.07808i	−1.04603	+	0.184444i
$759$		0			0
$760$	−39.3720	+	14.3302i	−1.42817	+	0.519812i
$761$	32.1441	−	11.6995i	1.16522	−	0.424106i	0.314262	−	0.949336i	$-0.398243\pi$
$761$	32.1441	−	11.6995i	1.16522	−	0.424106i	0.850960	+	0.525230i	$0.176021\pi$
$762$		0			0
$763$	22.3345	+	6.03886i	0.808564	+	0.218621i
$764$	−28.6709	+	16.5532i	−1.03728	+	0.598872i
$765$		0			0
$766$	15.9686	−	9.21948i	0.576969	−	0.333113i
$767$	−0.188312	+	0.517383i	−0.00679955	+	0.0186816i
$768$		0			0
$769$	3.20130	+	8.79549i	0.115442	+	0.317174i	0.983935	−	0.178528i	$-0.0571334\pi$
$769$	3.20130	+	8.79549i	0.115442	+	0.317174i	−0.868493	+	0.495701i	$0.834911\pi$
$770$	1.25095	−	0.579878i	0.0450812	−	0.0208973i
$771$		0			0
$772$	62.2056	−	52.1967i	2.23883	−	1.87860i
$773$	−10.0564	−	17.4182i	−0.361703	−	0.626488i	0.626538	−	0.779391i	$-0.284471\pi$
$773$	−10.0564	−	17.4182i	−0.361703	−	0.626488i	−0.988241	+	0.152903i	$0.951138\pi$
$774$		0			0
$775$	6.33433	+	3.65712i	0.227536	+	0.131368i
$776$	30.8589	−	25.8936i	1.10777	−	0.929528i
$777$		0			0
$778$	5.12245	−	29.0509i	0.183649	−	1.04152i
$779$	45.9287	+	8.09848i	1.64557	+	0.290158i
$780$		0			0
$781$	0.0937775	−	0.0786887i	0.00335562	−	0.00281570i
$782$	−0.176030	−	0.304892i	−0.00629481	−	0.0109029i
$783$		0			0
$784$	−0.700474	+	1.89770i	−0.0250169	+	0.0677750i
$785$	−10.2028	+	28.0319i	−0.364153	+	1.00050i
$786$		0			0
$787$	16.4562	+	45.2130i	0.586600	+	1.61167i	0.776675	+	0.629901i	$0.216905\pi$
$787$	16.4562	+	45.2130i	0.586600	+	1.61167i	−0.190075	+	0.981769i	$0.560873\pi$
$788$	−29.6323	+	35.3144i	−1.05561	+	1.25802i
$789$		0			0
$790$	7.09073	+	8.45040i	0.252277	+	0.300652i
$791$	−3.69621	−	43.3812i	−0.131422	−	1.54246i
$792$		0			0
$793$	−0.141176			−0.00501329
$794$	21.6266	+	7.87145i	0.767500	+	0.279347i
$795$		0			0
$796$	27.3171	−	32.5552i	0.968229	−	1.15389i
$797$	−30.7365	+	11.1872i	−1.08874	+	0.396270i	−0.823155	−	0.567817i	$-0.807788\pi$
$797$	−30.7365	+	11.1872i	−1.08874	+	0.396270i	−0.265588	+	0.964087i	$0.585566\pi$
$798$		0			0
$799$	0.113836	+	0.645597i	0.00402724	+	0.0228396i
$800$		−	8.52206i		−	0.301300i
$801$		0			0
$802$	−85.3329			−3.01321
$803$	1.05998	+	0.385800i	0.0374057	+	0.0136146i
$804$		0			0
$805$	1.99476	+	4.30323i	0.0703059	+	0.151669i
$806$	−0.314187	+	0.374434i	−0.0110668	+	0.0131889i
$807$		0			0
$808$	26.7272	+	31.8523i	0.940261	+	1.12056i
$809$	−2.72104	−	1.57099i	−0.0956666	−	0.0552332i	0.451403	−	0.892320i	$-0.350924\pi$
$809$	−2.72104	−	1.57099i	−0.0956666	−	0.0552332i	−0.547070	+	0.837087i	$0.684257\pi$
$810$		0			0
$811$			36.4973i			1.28159i	0.767711	+	0.640797i	$0.221396\pi$
$811$			36.4973i			1.28159i	−0.767711	+	0.640797i	$0.778604\pi$
$812$	82.3220	−	21.8581i	2.88894	−	0.767067i
$813$		0			0
$814$	0.460221	−	2.61004i	0.0161307	−	0.0914819i
$815$	15.9750	+	13.4046i	0.559579	+	0.469543i
$816$		0			0
$817$	25.1192	−	69.0146i	0.878811	−	2.41451i
$818$	−2.69521	−	4.66825i	−0.0942360	−	0.163221i
$819$		0			0
$820$	−18.6721	+	32.3409i	−0.652056	+	1.12939i
$821$	29.5789	+	35.2508i	1.03231	+	1.23026i	0.972706	+	0.232039i	$0.0745398\pi$
$821$	29.5789	+	35.2508i	1.03231	+	1.23026i	0.0596053	+	0.998222i	$0.481016\pi$
$822$		0			0
$823$	7.37331	−	41.8161i	0.257017	−	1.45762i	−0.533823	−	0.845596i	$-0.679245\pi$
$823$	7.37331	−	41.8161i	0.257017	−	1.45762i	0.790841	−	0.612022i	$-0.209644\pi$
$824$	−17.8813	−	15.0042i	−0.622925	−	0.522696i
$825$		0			0
$826$	18.8210	−	69.6089i	0.654867	−	2.42200i
$827$	9.94149	+	5.73972i	0.345699	+	0.199590i	0.662789	−	0.748806i	$-0.269372\pi$
$827$	9.94149	+	5.73972i	0.345699	+	0.199590i	−0.317090	+	0.948395i	$0.602706\pi$
$828$		0			0
$829$			37.3804i			1.29827i	0.760671	+	0.649137i	$0.224870\pi$
$829$			37.3804i			1.29827i	−0.760671	+	0.649137i	$0.775130\pi$
$830$	26.8068	−	4.72677i	0.930479	−	0.164069i
$831$		0			0
$832$	0.587321	+	0.103561i	0.0203617	+	0.00359032i
$833$	0.950746	+	0.554680i	0.0329414	+	0.0192185i
$834$		0			0
$835$	−0.611828	−	3.46985i	−0.0211732	−	0.120079i
$836$	−1.53915	+	2.66588i	−0.0532325	+	0.0922014i
$837$		0			0
$838$	−60.7778	+	35.0901i	−2.09954	+	1.21217i
$839$	−14.8437	−	5.40267i	−0.512462	−	0.186521i	0.0728286	−	0.997344i	$-0.476797\pi$
$839$	−14.8437	−	5.40267i	−0.512462	−	0.186521i	−0.585291	+	0.810824i	$0.699020\pi$
$840$		0			0
$841$	−50.6977	−	42.5404i	−1.74820	−	1.46691i
$842$	1.67354	+	4.59801i	0.0576740	+	0.158458i
$843$		0			0
$844$	3.03013	+	17.1847i	0.104301	+	0.591522i
$845$	11.9797	−	20.7494i	0.412113	−	0.713801i
$846$		0			0
$847$	−12.3424	+	26.3124i	−0.424091	+	0.904105i
$848$	0.0465601	−	0.00820980i	0.00159888	−	0.000281926i
$849$		0			0
$850$	0.571156	+	0.100710i	0.0195905	+	0.00345433i
$851$	8.97843	+	1.58314i	0.307777	+	0.0542694i
$852$		0			0
$853$	−30.8230	+	5.43493i	−1.05536	+	0.186089i	−0.674297	−	0.738460i	$-0.735553\pi$
$853$	−30.8230	+	5.43493i	−1.05536	+	0.186089i	−0.381064	+	0.924549i	$0.624442\pi$
$854$	18.4225	−	1.56965i	0.630406	−	0.0537125i
$855$		0			0
$856$	11.1737	−	19.3534i	0.381909	−	0.661486i
$857$	4.62895	+	26.2521i	0.158122	+	0.896754i	0.955876	+	0.293771i	$0.0949103\pi$
$857$	4.62895	+	26.2521i	0.158122	+	0.896754i	−0.797754	+	0.602983i	$0.793979\pi$
$858$		0			0
$859$	−9.73550	−	26.7481i	−0.332171	−	0.912633i	−0.987546	−	0.157329i	$-0.949712\pi$
$859$	−9.73550	−	26.7481i	−0.332171	−	0.912633i	0.655375	−	0.755304i	$-0.272511\pi$
$860$	45.0503	+	37.8017i	1.53620	+	1.28903i
$861$		0			0
$862$	2.57109	+	0.935799i	0.0875716	+	0.0318734i
$863$	−2.69995	+	1.55882i	−0.0919074	+	0.0530628i	−0.545249	−	0.838274i	$-0.683565\pi$
$863$	−2.69995	+	1.55882i	−0.0919074	+	0.0530628i	0.453342	+	0.891337i	$0.350232\pi$
$864$		0			0
$865$	22.5555	−	39.0673i	0.766911	−	1.32833i
$866$	4.44148	+	25.1889i	0.150928	+	0.855953i
$867$		0			0
$868$	22.9352	−	32.5973i	0.778473	−	1.10642i
$869$	0.314389	+	0.0554353i	0.0106649	+	0.00188051i
$870$		0			0
$871$	0.450373	−	0.0794129i	0.0152603	−	0.00269080i
$872$		−	26.1666i		−	0.886112i
$873$		0			0
$874$	−14.7288	−	8.50367i	−0.498208	−	0.287641i
$875$	−31.0824	−	8.40414i	−1.05078	−	0.284112i
$876$		0			0
$877$	4.99322	+	4.18981i	0.168609	+	0.141480i	0.723188	−	0.690651i	$-0.242676\pi$
$877$	4.99322	+	4.18981i	0.168609	+	0.141480i	−0.554579	+	0.832131i	$0.687121\pi$
$878$	2.22447	−	12.6156i	0.0750723	−	0.425756i
$879$		0			0
$880$	−0.0420497	−	0.0501129i	−0.00141750	−	0.00168931i
$881$	−0.192986	+	0.334261i	−0.00650186	+	0.0112615i	−0.869258	−	0.494359i	$-0.835403\pi$
$881$	−0.192986	+	0.334261i	−0.00650186	+	0.0112615i	0.862756	+	0.505620i	$0.168736\pi$
$882$		0			0
$883$	6.61385	+	11.4555i	0.222574	+	0.385509i	0.955589	−	0.294704i	$-0.0952209\pi$
$883$	6.61385	+	11.4555i	0.222574	+	0.385509i	−0.733015	+	0.680212i	$0.761888\pi$
$884$	−0.00825341	+	0.0226761i	−0.000277592	+	0.000762678i
$885$		0			0
$886$	−47.9890	−	40.2676i	−1.61222	−	1.35282i
$887$	4.11247	−	23.3230i	0.138083	−	0.783109i	−0.834580	−	0.550887i	$-0.814289\pi$
$887$	4.11247	−	23.3230i	0.138083	−	0.783109i	0.972663	−	0.232221i	$-0.0745994\pi$
$888$		0			0
$889$	8.05295	−	8.01649i	0.270087	−	0.268864i
$890$		−	44.9992i		−	1.50838i
$891$		0			0
$892$	23.9203	+	13.8104i	0.800912	+	0.462407i
$893$	20.3563	+	24.2596i	0.681196	+	0.811818i
$894$		0			0
$895$	21.8809	−	26.0767i	0.731398	−	0.871647i
$896$	−49.7592	−	4.46714i	−1.66234	−	0.149237i
$897$		0			0
$898$	53.2809	+	19.3927i	1.77801	+	0.647142i
$899$	−44.5400			−1.48549
$900$		0			0
$901$		−	0.0257262i		−	0.000857064i
$902$	0.301410	+	1.70938i	0.0100359	+	0.0569162i
$903$		0			0
$904$	−46.2708	+	16.8412i	−1.53894	+	0.560129i
$905$	7.63812	−	9.10276i	0.253900	−	0.302586i
$906$		0			0
$907$	−11.8281	−	4.30507i	−0.392745	−	0.142948i	0.138096	−	0.990419i	$-0.455902\pi$
$907$	−11.8281	−	4.30507i	−0.392745	−	0.142948i	−0.530841	+	0.847471i	$0.678124\pi$
$908$	66.6048			2.21036
$909$		0			0
$910$	0.221745	−	0.472731i	0.00735079	−	0.0156709i
$911$	−12.9220	−	15.3999i	−0.428125	−	0.510220i	0.508255	−	0.861207i	$-0.330291\pi$
$911$	−12.9220	−	15.3999i	−0.428125	−	0.510220i	−0.936380	+	0.350987i	$0.885846\pi$
$912$		0			0
$913$	0.506354	−	0.603450i	0.0167579	−	0.0199713i
$914$	−5.54583	−	15.2370i	−0.183440	−	0.503996i
$915$		0			0
$916$	6.55597	−	18.0124i	0.216615	−	0.595146i
$917$	−11.4046	+	0.971709i	−0.376614	+	0.0320886i
$918$		0			0
$919$	−4.76251	−	8.24891i	−0.157101	−	0.272106i	0.776721	−	0.629845i	$-0.216881\pi$
$919$	−4.76251	−	8.24891i	−0.157101	−	0.272106i	−0.933822	+	0.357738i	$0.883548\pi$
$920$	4.10926	−	3.44808i	0.135478	−	0.113680i
$921$		0			0
$922$	16.4600	+	2.90234i	0.542081	+	0.0955834i
$923$	0.00805021	−	0.0456550i	0.000264976	−	0.00150275i
$924$		0			0
$925$	−11.5051	+	9.65393i	−0.378286	+	0.317419i
$926$	16.2682	+	9.39243i	0.534605	+	0.308654i
$927$		0			0
$928$	25.9475	+	44.9423i	0.851767	+	1.47530i
$929$	37.3866	−	31.3711i	1.22661	−	1.02925i	0.228163	−	0.973623i	$-0.426728\pi$
$929$	37.3866	−	31.3711i	1.22661	−	1.02925i	0.998452	−	0.0556286i	$-0.0177163\pi$
$930$		0			0
$931$	53.1733	+	0.241271i	1.74268	+	0.00790735i
$932$	−6.95460	−	19.1076i	−0.227805	−	0.625890i
$933$		0			0
$934$	−10.0491	+	27.6096i	−0.328816	+	0.903415i
$935$	−0.0308276	+	0.0177983i	−0.00100817	+	0.000582067i
$936$		0			0
$937$	14.6214	−	8.44169i	0.477661	−	0.275778i	−0.241780	−	0.970331i	$-0.577731\pi$
$937$	14.6214	−	8.44169i	0.477661	−	0.275778i	0.719441	+	0.694553i	$0.244398\pi$
$938$	−57.8879	+	15.3703i	−1.89011	+	0.501859i
$939$		0			0
$940$	−23.8290	+	8.67304i	−0.777215	+	0.282883i
$941$	−8.57887	+	3.12245i	−0.279663	+	0.101789i	−0.478044	−	0.878336i	$-0.658654\pi$
$941$	−8.57887	+	3.12245i	−0.279663	+	0.101789i	0.198381	+	0.980125i	$0.436432\pi$
$942$		0			0
$943$	−5.88021	+	1.03684i	−0.191486	+	0.0337641i
$944$	−3.42117			−0.111349
$945$		0			0
$946$	2.73344			0.0888718
$947$	39.6423	−	6.99001i	1.28820	−	0.227145i	0.512743	−	0.858542i	$-0.328629\pi$
$947$	39.6423	−	6.99001i	1.28820	−	0.227145i	0.775460	+	0.631397i	$0.217518\pi$
$948$		0			0
$949$	0.401410	−	0.146101i	0.0130303	−	0.00474265i
$950$	26.3275	−	9.58242i	0.854177	−	0.310895i
$951$		0			0
$952$	0.324925	−	1.20172i	0.0105309	−	0.0389481i
$953$	15.4047	−	8.89392i	0.499008	−	0.288102i	−0.229296	−	0.973357i	$-0.573642\pi$
$953$	15.4047	−	8.89392i	0.499008	−	0.288102i	0.728304	+	0.685254i	$0.240309\pi$
$954$		0			0
$955$	−16.0162	+	9.24698i	−0.518274	+	0.299225i
$956$	−21.0647	+	57.8748i	−0.681281	+	1.87180i
$957$		0			0
$958$	15.6897	+	43.1071i	0.506911	+	1.39273i
$959$	2.66876	−	3.79304i	0.0861788	−	0.122484i
$960$		0			0
$961$	7.78112	−	6.52913i	0.251004	−	0.210617i
$962$	−0.501832	−	0.869198i	−0.0161797	−	0.0280241i
$963$		0			0
$964$	−34.8236	−	20.1054i	−1.12159	−	0.647552i
$965$	34.7495	−	29.1583i	1.11863	−	0.938639i
$966$		0			0
$967$	−2.19010	+	12.4206i	−0.0704287	+	0.399421i	0.929131	+	0.369751i	$0.120557\pi$
$967$	−2.19010	+	12.4206i	−0.0704287	+	0.399421i	−0.999560	+	0.0296704i	$0.990554\pi$
$968$	32.3703	+	5.70775i	1.04042	+	0.183454i
$969$		0			0
$970$	43.7638	−	36.7221i	1.40517	−	1.17908i
$971$	−9.58786	−	16.6067i	−0.307689	−	0.532933i	0.670167	−	0.742210i	$-0.266222\pi$
$971$	−9.58786	−	16.6067i	−0.307689	−	0.532933i	−0.977856	+	0.209277i	$0.932889\pi$
$972$		0			0
$973$	−32.5918	−	15.2879i	−1.04485	−	0.490109i
$974$	−26.0359	+	71.5330i	−0.834244	+	2.29207i
$975$		0			0
$976$	−0.300026	−	0.824316i	−0.00960361	−	0.0263857i
$977$	−15.8858	+	18.9319i	−0.508232	+	0.605687i	−0.957756	−	0.287581i	$-0.907149\pi$
$977$	−15.8858	+	18.9319i	−0.508232	+	0.605687i	0.449525	+	0.893268i	$0.351593\pi$
$978$		0			0
$979$	−0.837076	−	0.997588i	−0.0267531	−	0.0318831i
$980$	−14.7440	+	39.9439i	−0.470979	+	1.27596i
$981$		0			0
$982$	−4.00106			−0.127679
$983$	−15.9748	−	5.81436i	−0.509518	−	0.185449i	0.0744521	−	0.997225i	$-0.476279\pi$
$983$	−15.9748	−	5.81436i	−0.509518	−	0.185449i	−0.583970	+	0.811775i	$0.698501\pi$
$984$		0			0
$985$	−16.5533	+	19.7275i	−0.527432	+	0.628569i
$986$	−3.31871	+	1.20791i	−0.105689	+	0.0384678i
$987$		0			0
$988$	0.202429	+	1.14803i	0.00644012	+	0.0365237i
$989$			9.40292i			0.298996i
$990$		0			0
$991$	−2.84408			−0.0903450			−0.0451725	−	0.998979i	$-0.514384\pi$
$991$	−2.84408			−0.0903450			−0.0451725	+	0.998979i	$0.514384\pi$
$992$	22.8197	+	8.30569i	0.724526	+	0.263706i
$993$		0			0
$994$	−0.542888	+	6.04719i	−0.0172194	+	0.191805i
$995$	15.2600	−	18.1861i	0.483774	−	0.576539i
$996$		0			0
$997$	22.6186	+	26.9558i	0.716339	+	0.853700i	0.994270	−	0.106901i	$-0.0340929\pi$
$997$	22.6186	+	26.9558i	0.716339	+	0.853700i	−0.277930	+	0.960601i	$0.589648\pi$
$998$	−68.4332	−	39.5099i	−2.16621	−	1.25066i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.bd.a.17.20		132
3.2	odd	2		189.2.bd.a.185.3	yes	132
7.5	odd	6		567.2.ba.a.341.3		132
21.5	even	6		189.2.ba.a.131.20	yes	132
27.7	even	9		189.2.ba.a.101.20	✓	132
27.20	odd	18		567.2.ba.a.143.3		132
189.47	even	18	inner	567.2.bd.a.467.20		132
189.61	odd	18		189.2.bd.a.47.3	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.20	✓	132	27.7	even	9
189.2.ba.a.131.20	yes	132	21.5	even	6
189.2.bd.a.47.3	yes	132	189.61	odd	18
189.2.bd.a.185.3	yes	132	3.2	odd	2
567.2.ba.a.143.3		132	27.20	odd	18
567.2.ba.a.341.3		132	7.5	odd	6
567.2.bd.a.17.20		132	1.1	even	1	trivial
567.2.bd.a.467.20		132	189.47	even	18	inner

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.bd (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.26715 - 0.399760i) q^{2} +(3.10078 - 1.12859i) q^{4} +(1.73217 - 0.630457i) q^{5} +(0.678971 + 2.55715i) q^{7} +(2.59137 - 1.49613i) q^{8} +O(q^{10})\)	\(q+(2.26715 - 0.399760i) q^{2} +(3.10078 - 1.12859i) q^{4} +(1.73217 - 0.630457i) q^{5} +(0.678971 + 2.55715i) q^{7} +(2.59137 - 1.49613i) q^{8} +(3.67505 - 2.12179i) q^{10} +(0.0420027 - 0.115401i) q^{11} +(-0.0159063 - 0.0437022i) q^{13} +(2.56157 + 5.52601i) q^{14} +(0.221371 - 0.185752i) q^{16} +(-0.0786230 - 0.136179i) q^{17} +(-6.57855 - 3.79813i) q^{19} +(4.65954 - 3.90982i) q^{20} +(0.0490936 - 0.278423i) q^{22} +(0.957765 + 0.168880i) q^{23} +(-1.22730 + 1.02982i) q^{25} +(-0.0535324 - 0.0927208i) q^{26} +(4.99131 + 7.16286i) q^{28} +(3.33678 - 9.16772i) q^{29} +(-1.56144 - 4.29003i) q^{31} +(-3.41914 + 4.07477i) q^{32} +(-0.232689 - 0.277308i) q^{34} +(2.78826 + 4.00134i) q^{35} +9.37436 q^{37} +(-16.4329 - 5.98109i) q^{38} +(3.54543 - 4.22528i) q^{40} +(-5.76925 + 2.09983i) q^{41} +(1.67890 + 9.52153i) q^{43} -0.405238i q^{44} +2.23891 q^{46} +(-3.91757 - 1.42588i) q^{47} +(-6.07800 + 3.47246i) q^{49} +(-2.37078 + 2.82539i) q^{50} +(-0.0986438 - 0.117559i) q^{52} +(0.141686 + 0.0818025i) q^{53} -0.226376i q^{55} +(5.58527 + 5.61067i) q^{56} +(3.90009 - 22.1185i) q^{58} +(-9.06906 - 7.60984i) q^{59} +(1.03823 - 2.85251i) q^{61} +(-5.25501 - 9.10194i) q^{62} +(-6.41175 + 11.1055i) q^{64} +(-0.0551048 - 0.0656713i) q^{65} +(-1.70755 + 9.68399i) q^{67} +(-0.397483 - 0.333527i) q^{68} +(7.92099 + 7.95701i) q^{70} +(0.863276 + 0.498413i) q^{71} +9.18511i q^{73} +(21.2531 - 3.74749i) q^{74} +(-24.6852 - 4.35266i) q^{76} +(0.323617 + 0.0290528i) q^{77} +(0.451399 + 2.56001i) q^{79} +(0.266342 - 0.461318i) q^{80} +(-12.2403 + 7.06695i) q^{82} +(6.02764 + 2.19388i) q^{83} +(-0.222043 - 0.186316i) q^{85} +(7.61265 + 20.9156i) q^{86} +(-0.0638107 - 0.361889i) q^{88} +(5.30203 - 9.18338i) q^{89} +(0.100953 - 0.0703473i) q^{91} +(3.16041 - 0.557266i) q^{92} +(-9.45173 - 1.66659i) q^{94} +(-13.7897 - 2.43150i) q^{95} +(13.2580 - 2.33775i) q^{97} +(-12.3916 + 10.3023i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} + 51 q^{32} + 18 q^{34} + 9 q^{35} - 6 q^{37} + 9 q^{38} - 9 q^{40} - 12 q^{43} - 6 q^{46} - 45 q^{47} + 30 q^{49} + 9 q^{50} - 9 q^{52} - 45 q^{53} + 51 q^{56} - 3 q^{58} + 9 q^{59} - 63 q^{61} - 99 q^{62} + 18 q^{64} + 102 q^{65} - 3 q^{67} - 144 q^{68} - 15 q^{70} - 18 q^{71} + 33 q^{74} - 36 q^{76} + 57 q^{77} - 21 q^{79} + 72 q^{80} - 18 q^{82} - 90 q^{83} + 9 q^{85} + 33 q^{86} + 45 q^{88} + 9 q^{89} - 21 q^{91} - 150 q^{92} - 9 q^{94} - 27 q^{95} + 180 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more