LMFDB - Embedded newform 216.2.l.b.179.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(35,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("216.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + \cdots + 256 $ x^16 - 3x^15 + 7x^14 - 12x^13 + 16x^12 - 12x^11 - 8x^10 + 36x^9 - 68x^8 + 72x^7 - 32x^6 - 96x^5 + 256x^4 - 384x^3 + 448x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.5
Root			$1.40985 - 0.111062i$ of defining polynomial
Character	$\chi$	$=$	216.179
Dual form			216.2.l.b.35.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.608741 - 1.27649i) q^{2} +(-1.25887 - 1.55411i) q^{4} +(1.74322 - 3.01934i) q^{5} +(-1.80802 + 1.04386i) q^{7} +(-2.75013 + 0.660890i) q^{8} +O(q^{10})$	\(q+(0.608741 - 1.27649i) q^{2} +(-1.25887 - 1.55411i) q^{4} +(1.74322 - 3.01934i) q^{5} +(-1.80802 + 1.04386i) q^{7} +(-2.75013 + 0.660890i) q^{8} +(-2.79300 - 4.06320i) q^{10} +(0.116985 - 0.0675415i) q^{11} +(2.63890 + 1.52357i) q^{13} +(0.231866 + 2.94336i) q^{14} +(-0.830495 + 3.91283i) q^{16} -4.19800i q^{17} +0.919111 q^{19} +(-6.88686 + 1.09181i) q^{20} +(-0.0150025 - 0.190446i) q^{22} +(0.689877 - 1.19490i) q^{23} +(-3.57762 - 6.19662i) q^{25} +(3.55124 - 2.44108i) q^{26} +(3.89833 + 1.49577i) q^{28} +(4.24111 + 7.34582i) q^{29} +(4.39877 + 2.53963i) q^{31} +(4.48915 + 3.44202i) q^{32} +(-5.35871 - 2.55549i) q^{34} +7.27870i q^{35} -1.61676i q^{37} +(0.559500 - 1.17324i) q^{38} +(-2.79863 + 9.45566i) q^{40} +(-1.79408 - 1.03581i) q^{41} +(5.41106 + 9.37224i) q^{43} +(-0.252236 - 0.0967817i) q^{44} +(-1.10533 - 1.60801i) q^{46} +(-0.205809 - 0.356471i) q^{47} +(-1.32071 + 2.28754i) q^{49} +(-10.0878 + 0.794672i) q^{50} +(-0.954242 - 6.01912i) q^{52} -0.968137 q^{53} -0.470958i q^{55} +(4.28241 - 4.06565i) q^{56} +(11.9586 - 0.942050i) q^{58} +(-3.88770 - 2.24457i) q^{59} +(7.44553 - 4.29868i) q^{61} +(5.91953 - 4.06902i) q^{62} +(7.12645 - 3.63507i) q^{64} +(9.20037 - 5.31183i) q^{65} +(3.15416 - 5.46316i) q^{67} +(-6.52413 + 5.28473i) q^{68} +(9.29121 + 4.43084i) q^{70} -11.9687 q^{71} -4.06264 q^{73} +(-2.06379 - 0.984189i) q^{74} +(-1.15704 - 1.42840i) q^{76} +(-0.141008 + 0.244232i) q^{77} +(-10.8672 + 6.27416i) q^{79} +(10.3665 + 9.32847i) q^{80} +(-2.41434 + 1.65959i) q^{82} +(-5.23875 + 3.02459i) q^{83} +(-12.6752 - 7.31802i) q^{85} +(15.2575 - 1.20192i) q^{86} +(-0.277087 + 0.263062i) q^{88} +8.35848i q^{89} -6.36158 q^{91} +(-2.72547 + 0.432083i) q^{92} +(-0.580317 + 0.0457149i) q^{94} +(1.60221 - 2.77511i) q^{95} +(-0.477065 - 0.826300i) q^{97} +(2.11606 + 3.07840i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 5 q^{4}+O(q^{10}) $ 16 * q + 3 * q^2 - 5 * q^4	$ 16 q + 3 q^{2} - 5 q^{4} - 12 q^{11} + 18 q^{14} + 7 q^{16} - 4 q^{19} - 18 q^{20} - q^{22} - 14 q^{25} - 12 q^{28} - 27 q^{32} - 13 q^{34} + 15 q^{38} - 12 q^{40} + 36 q^{41} + 8 q^{43} + 12 q^{46} + 10 q^{49} - 51 q^{50} - 18 q^{52} + 66 q^{56} + 12 q^{58} - 12 q^{59} + 34 q^{64} + 6 q^{65} - 16 q^{67} + 9 q^{68} + 18 q^{70} - 4 q^{73} + 60 q^{74} - 7 q^{76} - 22 q^{82} - 54 q^{83} + 51 q^{86} - 13 q^{88} - 36 q^{91} - 84 q^{92} + 24 q^{94} + 8 q^{97}+O(q^{100}) $ 16 * q + 3 * q^2 - 5 * q^4 - 12 * q^11 + 18 * q^14 + 7 * q^16 - 4 * q^19 - 18 * q^20 - q^22 - 14 * q^25 - 12 * q^28 - 27 * q^32 - 13 * q^34 + 15 * q^38 - 12 * q^40 + 36 * q^41 + 8 * q^43 + 12 * q^46 + 10 * q^49 - 51 * q^50 - 18 * q^52 + 66 * q^56 + 12 * q^58 - 12 * q^59 + 34 * q^64 + 6 * q^65 - 16 * q^67 + 9 * q^68 + 18 * q^70 - 4 * q^73 + 60 * q^74 - 7 * q^76 - 22 * q^82 - 54 * q^83 + 51 * q^86 - 13 * q^88 - 36 * q^91 - 84 * q^92 + 24 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.608741	−	1.27649i	0.430445	−	0.902617i
$2$	0.608741	−	1.27649i	0.430445	−	0.902617i
$3$		0			0
$3$		0			0
$4$	−1.25887	−	1.55411i	−0.629435	−	0.777053i
$5$	1.74322	−	3.01934i	0.779591	−	1.35029i	−0.152587	−	0.988290i	$-0.548760\pi$
$5$	1.74322	−	3.01934i	0.779591	−	1.35029i	0.932178	−	0.362001i	$-0.117906\pi$
$6$		0			0
$7$	−1.80802	+	1.04386i	−0.683367	+	0.394542i	−0.801122	−	0.598501i	$-0.795763\pi$
$7$	−1.80802	+	1.04386i	−0.683367	+	0.394542i	0.117756	+	0.993043i	$0.462430\pi$
$8$	−2.75013	+	0.660890i	−0.972318	+	0.233660i
$9$		0			0
$10$	−2.79300	−	4.06320i	−0.883225	−	1.28490i
$11$	0.116985	−	0.0675415i	0.0352724	−	0.0203645i	−0.482260	−	0.876028i	$-0.660184\pi$
$11$	0.116985	−	0.0675415i	0.0352724	−	0.0203645i	0.517533	+	0.855664i	$0.326851\pi$
$12$		0			0
$13$	2.63890	+	1.52357i	0.731900	+	0.422563i	0.819117	−	0.573627i	$-0.194464\pi$
$13$	2.63890	+	1.52357i	0.731900	+	0.422563i	−0.0872168	+	0.996189i	$0.527797\pi$
$14$	0.231866	+	2.94336i	0.0619687	+	0.786647i
$15$		0			0
$16$	−0.830495	+	3.91283i	−0.207624	+	0.978209i
$17$		−	4.19800i		−	1.01816i	−0.860718	−	0.509082i	$-0.829985\pi$
$17$		−	4.19800i		−	1.01816i	0.860718	−	0.509082i	$-0.170015\pi$
$18$		0			0
$19$	0.919111			0.210858			0.105429	−	0.994427i	$-0.466378\pi$
$19$	0.919111			0.210858			0.105429	+	0.994427i	$0.466378\pi$
$20$	−6.88686	+	1.09181i	−1.53995	+	0.244136i
$21$		0			0
$22$	−0.0150025	−	0.190446i	−0.00319855	−	0.0406033i
$23$	0.689877	−	1.19490i	0.143849	−	0.249154i	−0.785094	−	0.619377i	$-0.787385\pi$
$23$	0.689877	−	1.19490i	0.143849	−	0.249154i	0.928943	+	0.370223i	$0.120719\pi$
$24$		0			0
$25$	−3.57762	−	6.19662i	−0.715524	−	1.23932i
$26$	3.55124	−	2.44108i	0.696455	−	0.478736i
$27$		0			0
$28$	3.89833	+	1.49577i	0.736715	+	0.282674i
$29$	4.24111	+	7.34582i	0.787555	+	1.36409i	0.927461	+	0.373921i	$0.121987\pi$
$29$	4.24111	+	7.34582i	0.787555	+	1.36409i	−0.139906	+	0.990165i	$0.544680\pi$
$30$		0			0
$31$	4.39877	+	2.53963i	0.790042	+	0.456131i	0.839977	−	0.542621i	$-0.182568\pi$
$31$	4.39877	+	2.53963i	0.790042	+	0.456131i	−0.0499352	+	0.998752i	$0.515901\pi$
$32$	4.48915	+	3.44202i	0.793577	+	0.608470i
$33$		0			0
$34$	−5.35871	−	2.55549i	−0.919012	−	0.438263i
$35$			7.27870i			1.23033i
$36$		0			0
$37$		−	1.61676i		−	0.265794i	−0.991130	−	0.132897i	$-0.957572\pi$
$37$		−	1.61676i		−	0.265794i	0.991130	−	0.132897i	$-0.0424280\pi$
$38$	0.559500	−	1.17324i	0.0907629	−	0.190324i
$39$		0			0
$40$	−2.79863	+	9.45566i	−0.442501	+	1.49507i
$41$	−1.79408	−	1.03581i	−0.280188	−	0.161767i	0.353320	−	0.935502i	$-0.385053\pi$
$41$	−1.79408	−	1.03581i	−0.280188	−	0.161767i	−0.633509	+	0.773736i	$0.718386\pi$
$42$		0			0
$43$	5.41106	+	9.37224i	0.825180	+	1.42925i	0.901782	+	0.432191i	$0.142259\pi$
$43$	5.41106	+	9.37224i	0.825180	+	1.42925i	−0.0766025	+	0.997062i	$0.524407\pi$
$44$	−0.252236	−	0.0967817i	−0.0380260	−	0.0145904i
$45$		0			0
$46$	−1.10533	−	1.60801i	−0.162972	−	0.237088i
$47$	−0.205809	−	0.356471i	−0.0300203	−	0.0519966i	0.850625	−	0.525773i	$-0.176224\pi$
$47$	−0.205809	−	0.356471i	−0.0300203	−	0.0519966i	−0.880645	+	0.473776i	$0.842891\pi$
$48$		0			0
$49$	−1.32071	+	2.28754i	−0.188673	+	0.326791i
$50$	−10.0878	+	0.794672i	−1.42663	+	0.112384i
$51$		0			0
$52$	−0.954242	−	6.01912i	−0.132330	−	0.834701i
$53$	−0.968137			−0.132984			−0.0664919	−	0.997787i	$-0.521181\pi$
$53$	−0.968137			−0.132984			−0.0664919	+	0.997787i	$0.521181\pi$
$54$		0			0
$55$		−	0.470958i		−	0.0635040i
$56$	4.28241	−	4.06565i	0.572261	−	0.543296i
$57$		0			0
$58$	11.9586	−	0.942050i	1.57025	−	0.123697i
$59$	−3.88770	−	2.24457i	−0.506136	−	0.292218i	0.225108	−	0.974334i	$-0.427726\pi$
$59$	−3.88770	−	2.24457i	−0.506136	−	0.292218i	−0.731244	+	0.682116i	$0.761060\pi$
$60$		0			0
$61$	7.44553	−	4.29868i	0.953303	−	0.550390i	0.0591976	−	0.998246i	$-0.481146\pi$
$61$	7.44553	−	4.29868i	0.953303	−	0.550390i	0.894105	+	0.447857i	$0.147812\pi$
$62$	5.91953	−	4.06902i	0.751781	−	0.516766i
$63$		0			0
$64$	7.12645	−	3.63507i	0.890806	−	0.454384i
$65$	9.20037	−	5.31183i	1.14117	−	0.658852i
$66$		0			0
$67$	3.15416	−	5.46316i	0.385342	−	0.667432i	−0.606475	−	0.795103i	$-0.707417\pi$
$67$	3.15416	−	5.46316i	0.385342	−	0.667432i	0.991817	+	0.127671i	$0.0407502\pi$
$68$	−6.52413	+	5.28473i	−0.791168	+	0.640868i
$69$		0			0
$70$	9.29121	+	4.43084i	1.11051	+	0.529587i
$71$	−11.9687			−1.42042			−0.710210	−	0.703990i	$-0.751400\pi$
$71$	−11.9687			−1.42042			−0.710210	+	0.703990i	$0.751400\pi$
$72$		0			0
$73$	−4.06264			−0.475496			−0.237748	−	0.971327i	$-0.576409\pi$
$73$	−4.06264			−0.475496			−0.237748	+	0.971327i	$0.576409\pi$
$74$	−2.06379	−	0.984189i	−0.239910	−	0.114410i
$75$		0			0
$76$	−1.15704	−	1.42840i	−0.132722	−	0.163848i
$77$	−0.141008	+	0.244232i	−0.0160693	+	0.0278329i
$78$		0			0
$79$	−10.8672	+	6.27416i	−1.22265	+	0.705899i	−0.965483	−	0.260468i	$-0.916123\pi$
$79$	−10.8672	+	6.27416i	−1.22265	+	0.705899i	−0.257170	+	0.966366i	$0.582790\pi$
$80$	10.3665	+	9.32847i	1.15900	+	1.04296i
$81$		0			0
$82$	−2.41434	+	1.65959i	−0.266619	+	0.183271i
$83$	−5.23875	+	3.02459i	−0.575027	+	0.331992i	−0.759155	−	0.650910i	$-0.774387\pi$
$83$	−5.23875	+	3.02459i	−0.575027	+	0.331992i	0.184128	+	0.982902i	$0.441054\pi$
$84$		0			0
$85$	−12.6752	−	7.31802i	−1.37482	−	0.793751i
$86$	15.2575	−	1.20192i	1.64526	−	0.129607i
$87$		0			0
$88$	−0.277087	+	0.263062i	−0.0295376	+	0.0280425i
$89$			8.35848i			0.885997i	0.896522	+	0.442999i	$0.146085\pi$
$89$			8.35848i			0.885997i	−0.896522	+	0.442999i	$0.853915\pi$
$90$		0			0
$91$	−6.36158			−0.666875
$92$	−2.72547	+	0.432083i	−0.284150	+	0.0450478i
$93$		0			0
$94$	−0.580317	+	0.0457149i	−0.0598551	+	0.00471513i
$95$	1.60221	−	2.77511i	0.164383	−	0.284720i
$96$		0			0
$97$	−0.477065	−	0.826300i	−0.0484386	−	0.0838981i	0.840790	−	0.541362i	$-0.182091\pi$
$97$	−0.477065	−	0.826300i	−0.0484386	−	0.0838981i	−0.889228	+	0.457464i	$0.848758\pi$
$98$	2.11606	+	3.07840i	0.213754	+	0.310965i
$99$		0			0
$100$	−5.12645	+	13.3607i	−0.512645	+	1.33607i
$101$	−5.35926	−	9.28250i	−0.533266	−	0.923644i	−0.999245	−	0.0388479i	$-0.987631\pi$
$101$	−5.35926	−	9.28250i	−0.533266	−	0.923644i	0.465979	−	0.884796i	$-0.345702\pi$
$102$		0			0
$103$	−7.46070	−	4.30743i	−0.735124	−	0.424424i	0.0851696	−	0.996366i	$-0.472857\pi$
$103$	−7.46070	−	4.30743i	−0.735124	−	0.424424i	−0.820294	+	0.571942i	$0.806190\pi$
$104$	−8.26425	−	2.44600i	−0.810376	−	0.239850i
$105$		0			0
$106$	−0.589344	+	1.23582i	−0.0572422	+	0.120033i
$107$		−	4.80774i		−	0.464781i	−0.972623	−	0.232391i	$-0.925345\pi$
$107$		−	4.80774i		−	0.464781i	0.972623	−	0.232391i	$-0.0746548\pi$
$108$		0			0
$109$			7.16698i			0.686472i	0.939249	+	0.343236i	$0.111523\pi$
$109$			7.16698i			0.686472i	−0.939249	+	0.343236i	$0.888477\pi$
$110$	−0.601175	−	0.286691i	−0.0573198	−	0.0273349i
$111$		0			0
$112$	−2.58290	−	7.94140i	−0.244061	−	0.750392i
$113$	0.213928	+	0.123511i	0.0201246	+	0.0116190i	0.510029	−	0.860157i	$-0.329635\pi$
$113$	0.213928	+	0.123511i	0.0201246	+	0.0116190i	−0.489904	+	0.871776i	$0.662968\pi$
$114$		0			0
$115$	−2.40521	−	4.16595i	−0.224287	−	0.388477i
$116$	6.07719	−	15.8386i	0.564253	−	1.47058i
$117$		0			0
$118$	−5.23178	+	3.59627i	−0.481624	+	0.331063i
$119$	4.38212	+	7.59006i	0.401708	+	0.695779i
$120$		0			0
$121$	−5.49088	+	9.51048i	−0.499171	+	0.864589i
$122$	−0.954837	−	12.1210i	−0.0864469	−	1.09738i
$123$		0			0
$124$	−1.59062	−	10.0332i	−0.142842	−	0.901010i
$125$	−7.51409			−0.672081
$126$		0			0
$127$		−	17.6276i		−	1.56420i	−0.623156	−	0.782098i	$-0.714150\pi$
$127$		−	17.6276i		−	1.56420i	0.623156	−	0.782098i	$-0.285850\pi$
$128$	−0.301983	−	11.3097i	−0.0266918	−	0.999644i
$129$		0			0
$130$	−1.17988	−	14.9777i	−0.103483	−	1.31363i
$131$	12.7802	+	7.37864i	1.11661	+	0.644675i	0.940533	−	0.339702i	$-0.110326\pi$
$131$	12.7802	+	7.37864i	1.11661	+	0.644675i	0.176076	+	0.984377i	$0.443659\pi$
$132$		0			0
$133$	−1.66177	+	0.959423i	−0.144094	+	0.0831925i
$134$	−5.05362	−	7.35191i	−0.436567	−	0.635108i
$135$		0			0
$136$	2.77442	+	11.5450i	0.237904	+	0.989979i
$137$	−14.8589	+	8.57878i	−1.26948	+	0.732934i	−0.974889	−	0.222689i	$-0.928516\pi$
$137$	−14.8589	+	8.57878i	−1.26948	+	0.732934i	−0.294590	+	0.955624i	$0.595183\pi$
$138$		0			0
$139$	−0.607862	+	1.05285i	−0.0515581	+	0.0893013i	−0.890653	−	0.454684i	$-0.849752\pi$
$139$	−0.607862	+	1.05285i	−0.0515581	+	0.0893013i	0.839095	+	0.543986i	$0.183085\pi$
$140$	11.3119	−	9.16294i	0.956028	−	0.774410i
$141$		0			0
$142$	−7.28581	+	15.2779i	−0.611412	+	1.28209i
$143$	0.411617			0.0344211
$144$		0			0
$145$	29.5727			2.45588
$146$	−2.47310	+	5.18593i	−0.204675	+	0.429191i
$147$		0			0
$148$	−2.51262	+	2.03529i	−0.206536	+	0.167300i
$149$	−4.46357	+	7.73113i	−0.365670	+	0.633359i	−0.988883	−	0.148693i	$-0.952493\pi$
$149$	−4.46357	+	7.73113i	−0.365670	+	0.633359i	0.623214	+	0.782052i	$0.285827\pi$
$150$		0			0
$151$	18.9453	−	10.9381i	1.54175	−	0.890127i	0.543017	−	0.839722i	$-0.317282\pi$
$151$	18.9453	−	10.9381i	1.54175	−	0.890127i	0.998729	−	0.0504058i	$-0.0160515\pi$
$152$	−2.52768	+	0.607431i	−0.205022	+	0.0492692i
$153$		0			0
$154$	0.225924	+	0.328670i	0.0182055	+	0.0264850i
$155$	15.3360	−	8.85426i	1.23182	−	0.711191i
$156$		0			0
$157$	−4.85478	−	2.80291i	−0.387454	−	0.223697i	0.293602	−	0.955928i	$-0.405146\pi$
$157$	−4.85478	−	2.80291i	−0.387454	−	0.223697i	−0.681056	+	0.732231i	$0.738479\pi$
$158$	1.39364	+	17.6912i	0.110872	+	1.40744i
$159$		0			0
$160$	18.2182	−	7.55408i	1.44028	−	0.597203i
$161$			2.88054i			0.227018i
$162$		0			0
$163$	−17.1763			−1.34535			−0.672676	−	0.739937i	$-0.734855\pi$
$163$	−17.1763			−1.34535			−0.672676	+	0.739937i	$0.734855\pi$
$164$	0.648749	+	4.09214i	0.0506588	+	0.319543i
$165$		0			0
$166$	0.671832	+	8.52841i	0.0521443	+	0.661933i
$167$	2.31249	−	4.00535i	0.178946	−	0.309943i	−0.762574	−	0.646901i	$-0.776065\pi$
$167$	2.31249	−	4.00535i	0.178946	−	0.309943i	0.941520	+	0.336958i	$0.109398\pi$
$168$		0			0
$169$	−1.85746	−	3.21721i	−0.142881	−	0.247478i
$170$	−17.0573	+	11.7250i	−1.30824	+	0.899267i
$171$		0			0
$172$	7.75363	−	20.2078i	0.591209	−	1.54083i
$173$	−1.52076	−	2.63404i	−0.115621	−	0.200262i	0.802407	−	0.596778i	$-0.203553\pi$
$173$	−1.52076	−	2.63404i	−0.115621	−	0.200262i	−0.918028	+	0.396516i	$0.870219\pi$
$174$		0			0
$175$	12.9368	+	7.46907i	0.977930	+	0.564608i
$176$	0.167123	+	0.513837i	0.0125974	+	0.0387319i
$177$		0			0
$178$	10.6695	+	5.08815i	0.799716	+	0.381373i
$179$		−	17.9997i		−	1.34536i	−0.739935	−	0.672679i	$-0.765144\pi$
$179$		−	17.9997i		−	1.34536i	0.739935	−	0.672679i	$-0.234856\pi$
$180$		0			0
$181$			15.9507i			1.18561i	0.805347	+	0.592804i	$0.201979\pi$
$181$			15.9507i			1.18561i	−0.805347	+	0.592804i	$0.798021\pi$
$182$	−3.87255	+	8.12052i	−0.287053	+	0.601933i
$183$		0			0
$184$	−1.10755	+	3.74207i	−0.0816499	+	0.275869i
$185$	−4.88156	−	2.81837i	−0.358899	−	0.207211i
$186$		0			0
$187$	−0.283539	−	0.491104i	−0.0207344	−	0.0359131i
$188$	−0.294908	+	0.768599i	−0.0215084	+	0.0560558i
$189$		0			0
$190$	−2.56708	−	3.73453i	−0.186235	−	0.270931i
$191$	2.21964	+	3.84452i	0.160607	+	0.278180i	0.935087	−	0.354419i	$-0.115321\pi$
$191$	2.21964	+	3.84452i	0.160607	+	0.278180i	−0.774479	+	0.632599i	$0.781988\pi$
$192$		0			0
$193$	0.673862	−	1.16716i	0.0485057	−	0.0840143i	−0.840753	−	0.541419i	$-0.817887\pi$
$193$	0.673862	−	1.16716i	0.0485057	−	0.0840143i	0.889259	+	0.457404i	$0.151221\pi$
$194$	−1.34518	+	0.105967i	−0.0965780	+	0.00760800i
$195$		0			0
$196$	5.21769	−	0.827187i	0.372692	−	0.0590848i
$197$	9.16835			0.653218			0.326609	−	0.945160i	$-0.394094\pi$
$197$	9.16835			0.653218			0.326609	+	0.945160i	$0.394094\pi$
$198$		0			0
$199$			24.0240i			1.70301i	0.524344	+	0.851507i	$0.324311\pi$
$199$			24.0240i			1.70301i	−0.524344	+	0.851507i	$0.675689\pi$
$200$	13.9342	+	14.6771i	0.985297	+	1.03783i
$201$		0			0
$202$	−15.1114	+	1.19042i	−1.06324	+	0.0837573i
$203$	−15.3360	−	8.85426i	−1.07638	−	0.621447i
$204$		0			0
$205$	−6.25494	+	3.61129i	−0.436864	+	0.252224i
$206$	−10.0400	+	6.90142i	−0.699523	+	0.480844i
$207$		0			0
$208$	−8.15308	+	9.06028i	−0.565314	+	0.628217i
$209$	0.107522	−	0.0620781i	0.00743748	−	0.00429403i
$210$		0			0
$211$	10.1275	−	17.5414i	0.697208	−	1.20760i	−0.272223	−	0.962234i	$-0.587759\pi$
$211$	10.1275	−	17.5414i	0.697208	−	1.20760i	0.969431	−	0.245365i	$-0.0789078\pi$
$212$	1.21876	+	1.50459i	0.0837046	+	0.103336i
$213$		0			0
$214$	−6.13704	−	2.92666i	−0.419520	−	0.200063i
$215$	37.7307			2.57321
$216$		0			0
$217$	−10.6041			−0.719852
$218$	9.14860	+	4.36283i	0.619622	+	0.295488i
$219$		0			0
$220$	−0.731919	+	0.592875i	−0.0493460	+	0.0399716i
$221$	6.39595	−	11.0781i	0.430238	−	0.745194i
$222$		0			0
$223$	−0.521119	+	0.300868i	−0.0348967	+	0.0201476i	−0.517347	−	0.855776i	$-0.673080\pi$
$223$	−0.521119	+	0.300868i	−0.0348967	+	0.0201476i	0.482450	+	0.875923i	$0.339747\pi$
$224$	−11.7095	−	1.53720i	−0.782371	−	0.102708i
$225$		0			0
$226$	0.287888	−	0.197891i	0.0191500	−	0.0131635i
$227$	−9.23720	+	5.33310i	−0.613095	+	0.353970i	−0.774176	−	0.632971i	$-0.781835\pi$
$227$	−9.23720	+	5.33310i	−0.613095	+	0.353970i	0.161081	+	0.986941i	$0.448502\pi$
$228$		0			0
$229$	22.1574	+	12.7926i	1.46420	+	0.845356i	0.999201	−	0.0399555i	$-0.0127216\pi$
$229$	22.1574	+	12.7926i	1.46420	+	0.845356i	0.464998	+	0.885312i	$0.346055\pi$
$230$	−6.78196	+	0.534254i	−0.447189	+	0.0352276i
$231$		0			0
$232$	−16.5184	−	17.3991i	−1.08449	−	1.14231i
$233$			4.71086i			0.308619i	0.988023	+	0.154309i	$0.0493152\pi$
$233$			4.71086i			0.308619i	−0.988023	+	0.154309i	$0.950685\pi$
$234$		0			0
$235$	−1.43508			−0.0936141
$236$	1.40581	+	8.86752i	0.0915108	+	0.577226i
$237$		0			0
$238$	12.3562	−	0.973371i	0.800936	−	0.0630943i
$239$	−7.51034	+	13.0083i	−0.485803	+	0.841436i	−0.999867	−	0.0163162i	$-0.994806\pi$
$239$	−7.51034	+	13.0083i	−0.485803	+	0.841436i	0.514064	+	0.857752i	$0.328139\pi$
$240$		0			0
$241$	12.8731	+	22.2969i	0.829230	+	1.43627i	0.898643	+	0.438681i	$0.144554\pi$
$241$	12.8731	+	22.2969i	0.829230	+	1.43627i	−0.0694129	+	0.997588i	$0.522113\pi$
$242$	8.79754	+	12.7985i	0.565527	+	0.822717i
$243$		0			0
$244$	−16.0536	−	6.15968i	−1.02772	−	0.394333i
$245$	4.60458	+	7.97536i	0.294176	+	0.509527i
$246$		0			0
$247$	2.42544	+	1.40033i	0.154327	+	0.0891009i
$248$	−13.7756	−	4.07721i	−0.874752	−	0.258903i
$249$		0			0
$250$	−4.57413	+	9.59169i	−0.289294	+	0.606631i
$251$			5.30436i			0.334808i	0.985888	+	0.167404i	$0.0535385\pi$
$251$			5.30436i			0.334808i	−0.985888	+	0.167404i	$0.946462\pi$
$252$		0			0
$253$		−	0.186381i		−	0.0117177i
$254$	−22.5015	−	10.7306i	−1.41187	−	0.673300i
$255$		0			0
$256$	−14.6206	−	6.49918i	−0.913785	−	0.406199i
$257$	21.4984	+	12.4121i	1.34104	+	0.774248i	0.986959	−	0.160969i	$-0.0514619\pi$
$257$	21.4984	+	12.4121i	1.34104	+	0.774248i	0.354077	+	0.935216i	$0.384795\pi$
$258$		0			0
$259$	1.68767	+	2.92314i	0.104867	+	0.181635i
$260$	−19.8372	−	7.61145i	−1.23025	−	0.472042i
$261$		0			0
$262$	17.1986	−	11.8221i	1.06253	−	0.730374i
$263$	−9.95859	−	17.2488i	−0.614073	−	1.06361i	−0.990546	−	0.137178i	$-0.956197\pi$
$263$	−9.95859	−	17.2488i	−0.614073	−	1.06361i	0.376473	−	0.926427i	$-0.377137\pi$
$264$		0			0
$265$	−1.68767	+	2.92314i	−0.103673	+	0.179567i
$266$	0.213110	+	2.70528i	0.0130666	+	0.165871i
$267$		0			0
$268$	−12.4610	+	1.97551i	−0.761177	+	0.120673i
$269$	2.35540			0.143611			0.0718057	−	0.997419i	$-0.477124\pi$
$269$	2.35540			0.143611			0.0718057	+	0.997419i	$0.477124\pi$
$270$		0			0
$271$		−	12.0774i		−	0.733648i	−0.930290	−	0.366824i	$-0.880445\pi$
$271$		−	12.0774i		−	0.733648i	0.930290	−	0.366824i	$-0.119555\pi$
$272$	16.4261	+	3.48642i	0.995977	+	0.211395i
$273$		0			0
$274$	1.90555	+	24.1895i	0.115118	+	1.46134i
$275$	−0.837057	−	0.483275i	−0.0504764	−	0.0291426i
$276$		0			0
$277$	14.5504	−	8.40069i	0.874250	−	0.504748i	0.00549164	−	0.999985i	$-0.498252\pi$
$277$	14.5504	−	8.40069i	0.874250	−	0.504748i	0.868758	+	0.495237i	$0.164919\pi$
$278$	0.973922	+	1.41684i	0.0584120	+	0.0849765i
$279$		0			0
$280$	−4.81042	−	20.0174i	−0.287478	−	1.19627i
$281$	−11.9853	+	6.91973i	−0.714984	+	0.412796i	−0.812904	−	0.582398i	$-0.802115\pi$
$281$	−11.9853	+	6.91973i	−0.714984	+	0.412796i	0.0979194	+	0.995194i	$0.468781\pi$
$282$		0			0
$283$	2.58123	−	4.47082i	0.153438	−	0.265763i	−0.779051	−	0.626960i	$-0.784299\pi$
$283$	2.58123	−	4.47082i	0.153438	−	0.265763i	0.932489	+	0.361198i	$0.117632\pi$
$284$	15.0670	+	18.6006i	0.894061	+	1.10374i
$285$		0			0
$286$	0.250568	−	0.525426i	0.0148164	−	0.0310691i
$287$	4.32497			0.255295
$288$		0			0
$289$	−0.623177			−0.0366574
$290$	18.0021	−	37.7494i	1.05712	−	2.21672i
$291$		0			0
$292$	5.11434	+	6.31378i	0.299294	+	0.369486i
$293$	−5.41881	+	9.38566i	−0.316571	+	0.548316i	−0.979770	−	0.200126i	$-0.935865\pi$
$293$	−5.41881	+	9.38566i	−0.316571	+	0.548316i	0.663200	+	0.748443i	$0.269198\pi$
$294$		0			0
$295$	−13.5542	+	7.82554i	−0.789158	+	0.455620i
$296$	1.06850	+	4.44631i	0.0621054	+	0.258436i
$297$		0			0
$298$	7.15158	+	10.4040i	0.414280	+	0.602686i
$299$	3.64104	−	2.10215i	0.210567	−	0.121571i
$300$		0			0
$301$	−19.5666	−	11.2968i	−1.12780	−	0.651136i
$302$	−2.42960	−	30.8420i	−0.139808	−	1.77476i
$303$		0			0
$304$	−0.763317	+	3.59633i	−0.0437792	+	0.206264i
$305$		−	29.9742i		−	1.71632i
$306$		0			0
$307$	16.6551			0.950557			0.475279	−	0.879835i	$-0.342347\pi$
$307$	16.6551			0.950557			0.475279	+	0.879835i	$0.342347\pi$
$308$	0.557074	−	0.0883158i	0.0317422	−	0.00503226i
$309$		0			0
$310$	−1.96674	−	24.9663i	−0.111703	−	1.41799i
$311$	−6.47216	+	11.2101i	−0.367002	+	0.635667i	−0.989095	−	0.147277i	$-0.952949\pi$
$311$	−6.47216	+	11.2101i	−0.367002	+	0.635667i	0.622093	+	0.782943i	$0.286283\pi$
$312$		0			0
$313$	−13.3593	−	23.1390i	−0.755112	−	1.30789i	−0.945318	−	0.326149i	$-0.894249\pi$
$313$	−13.3593	−	23.1390i	−0.755112	−	1.30789i	0.190206	−	0.981744i	$-0.439084\pi$
$314$	−6.53320	+	4.49085i	−0.368690	+	0.253433i
$315$		0			0
$316$	23.4311	+	8.99039i	1.31810	+	0.505749i
$317$	−12.5342	−	21.7098i	−0.703990	−	1.21935i	−0.967055	−	0.254568i	$-0.918067\pi$
$317$	−12.5342	−	21.7098i	−0.703990	−	1.21935i	0.263065	−	0.964778i	$-0.415267\pi$
$318$		0			0
$319$	0.992296	+	0.572902i	0.0555579	+	0.0320764i
$320$	1.44743	−	27.8539i	0.0809139	−	1.55708i
$321$		0			0
$322$	3.67699	+	1.75350i	0.204911	+	0.0977189i
$323$		−	3.85842i		−	0.214688i
$324$		0			0
$325$		−	21.8030i		−	1.20941i
$326$	−10.4559	+	21.9254i	−0.579100	+	1.21434i
$327$		0			0
$328$	5.61851	+	1.66293i	0.310230	+	0.0918199i
$329$	0.744211	+	0.429671i	0.0410297	+	0.0236885i
$330$		0			0
$331$	−8.47956	−	14.6870i	−0.466079	−	0.807272i	0.533171	−	0.846008i	$-0.321000\pi$
$331$	−8.47956	−	14.6870i	−0.466079	−	0.807272i	−0.999249	+	0.0387357i	$0.987667\pi$
$332$	11.2954	+	4.33400i	0.619917	+	0.237859i
$333$		0			0
$334$	−3.70510	−	5.39010i	−0.202734	−	0.294933i
$335$	−10.9968	−	19.0470i	−0.600818	−	1.04065i
$336$		0			0
$337$	4.47220	−	7.74608i	0.243616	−	0.421956i	−0.718125	−	0.695914i	$-0.755000\pi$
$337$	4.47220	−	7.74608i	0.243616	−	0.421956i	0.961742	+	0.273958i	$0.0883329\pi$
$338$	−5.23746	+	0.412585i	−0.284880	+	0.0224417i
$339$		0			0
$340$	4.58342	+	28.9110i	0.248571	+	1.56792i
$341$	0.686122			0.0371556
$342$		0			0
$343$		−	20.1286i		−	1.08684i
$344$	−21.0752	−	22.1988i	−1.13630	−	1.19688i
$345$		0			0
$346$	−4.28808	+	0.337797i	−0.230529	+	0.0181601i
$347$	4.29330	+	2.47874i	0.230476	+	0.133066i	0.610792	−	0.791791i	$-0.290851\pi$
$347$	4.29330	+	2.47874i	0.230476	+	0.133066i	−0.380315	+	0.924857i	$0.624185\pi$
$348$		0			0
$349$	−22.9731	+	13.2635i	−1.22972	+	0.709980i	−0.966972	−	0.254884i	$-0.917963\pi$
$349$	−22.9731	+	13.2635i	−1.22972	+	0.709980i	−0.262749	+	0.964864i	$0.584629\pi$
$350$	17.4094	−	11.9670i	0.930570	−	0.639664i
$351$		0			0
$352$	0.757644	+	0.0994621i	0.0403825	+	0.00530135i
$353$	28.7458	−	16.5964i	1.52998	−	0.883337i	0.530623	−	0.847608i	$-0.321958\pi$
$353$	28.7458	−	16.5964i	1.52998	−	0.883337i	0.999362	−	0.0357291i	$-0.0113753\pi$
$354$		0			0
$355$	−20.8640	+	36.1375i	−1.10735	+	1.91798i
$356$	12.9900	−	10.5222i	0.688467	−	0.557678i
$357$		0			0
$358$	−22.9764	−	10.9571i	−1.21434	−	0.579102i
$359$	−20.6138			−1.08795			−0.543977	−	0.839100i	$-0.683082\pi$
$359$	−20.6138			−1.08795			−0.543977	+	0.839100i	$0.683082\pi$
$360$		0			0
$361$	−18.1552			−0.955539
$362$	20.3610	+	9.70986i	1.07015	+	0.510339i
$363$		0			0
$364$	8.00840	+	9.88658i	0.419754	+	0.518198i
$365$	−7.08207	+	12.2665i	−0.370693	+	0.642058i
$366$		0			0
$367$	−10.1478	+	5.85881i	−0.529708	+	0.305827i	−0.740898	−	0.671618i	$-0.765600\pi$
$367$	−10.1478	+	5.85881i	−0.529708	+	0.305827i	0.211189	+	0.977445i	$0.432266\pi$
$368$	4.10251	+	3.69174i	0.213858	+	0.192445i
$369$		0			0
$370$	−6.56923	+	4.51562i	−0.341518	+	0.234756i
$371$	1.75041	−	1.01060i	0.0908767	−	0.0524677i
$372$		0			0
$373$	3.02771	+	1.74805i	0.156769	+	0.0905105i	0.576332	−	0.817216i	$-0.304483\pi$
$373$	3.02771	+	1.74805i	0.156769	+	0.0905105i	−0.419563	+	0.907726i	$0.637817\pi$
$374$	−0.799492	+	0.0629806i	−0.0413408	+	0.00325665i
$375$		0			0
$376$	0.801589	+	0.844325i	0.0413388	+	0.0435427i
$377$			25.8466i			1.33117i
$378$		0			0
$379$	20.1604			1.03557			0.517785	−	0.855511i	$-0.326757\pi$
$379$	20.1604			1.03557			0.517785	+	0.855511i	$0.326757\pi$
$380$	−6.32979	+	1.00350i	−0.324711	+	0.0514782i
$381$		0			0
$382$	6.25869	−	0.493033i	0.320222	−	0.0252258i
$383$	5.33120	−	9.23391i	0.272412	−	0.471831i	−0.697067	−	0.717006i	$-0.745512\pi$
$383$	5.33120	−	9.23391i	0.272412	−	0.471831i	0.969479	+	0.245175i	$0.0788454\pi$
$384$		0			0
$385$	0.491614	+	0.851501i	0.0250550	+	0.0433965i
$386$	−1.07967	−	1.57068i	−0.0549537	−	0.0799455i
$387$		0			0
$388$	−0.683597	+	1.78161i	−0.0347044	+	0.0904477i
$389$	8.34122	+	14.4474i	0.422917	+	0.732513i	0.996223	−	0.0868277i	$-0.0276730\pi$
$389$	8.34122	+	14.4474i	0.422917	+	0.732513i	−0.573307	+	0.819341i	$0.694340\pi$
$390$		0			0
$391$	−5.01619	−	2.89610i	−0.253680	−	0.146462i
$392$	2.12032	−	7.16388i	0.107092	−	0.361831i
$393$		0			0
$394$	5.58115	−	11.7033i	0.281174	−	0.589605i
$395$			43.7489i			2.20125i
$396$		0			0
$397$		−	22.9869i		−	1.15368i	−0.816857	−	0.576840i	$-0.804285\pi$
$397$		−	22.9869i		−	1.15368i	0.816857	−	0.576840i	$-0.195715\pi$
$398$	30.6664	+	14.6244i	1.53717	+	0.733053i
$399$		0			0
$400$	27.2175	−	8.85237i	1.36088	−	0.442618i
$401$	−27.3094	−	15.7671i	−1.36377	−	0.787371i	−0.373644	−	0.927572i	$-0.621892\pi$
$401$	−27.3094	−	15.7671i	−1.36377	−	0.787371i	−0.990123	+	0.140201i	$0.955225\pi$
$402$		0			0
$403$	7.73862	+	13.4037i	0.385488	+	0.667685i
$404$	−7.67940	+	20.0143i	−0.382064	+	0.995749i
$405$		0			0
$406$	−20.6381	+	14.1864i	−1.02425	+	0.704058i
$407$	−0.109199	−	0.189137i	−0.00541277	−	0.00937519i
$408$		0			0
$409$	3.59259	−	6.22255i	0.177642	−	0.307686i	−0.763430	−	0.645890i	$-0.776486\pi$
$409$	3.59259	−	6.22255i	0.177642	−	0.307686i	0.941073	+	0.338205i	$0.109820\pi$
$410$	0.802152	+	10.1827i	0.0396155	+	0.502889i
$411$		0			0
$412$	2.69783	+	17.0172i	0.132913	+	0.838378i
$413$	9.37205			0.461169
$414$		0			0
$415$			21.0901i			1.03527i
$416$	6.60227	+	15.9227i	0.323703	+	0.780675i
$417$		0			0
$418$	−0.0137890	−	0.175041i	−0.000674442	−	0.00856154i
$419$	12.5999	+	7.27453i	0.615543	+	0.355384i	0.775132	−	0.631800i	$-0.217683\pi$
$419$	12.5999	+	7.27453i	0.615543	+	0.355384i	−0.159589	+	0.987184i	$0.551017\pi$
$420$		0			0
$421$	−9.38587	+	5.41893i	−0.457439	+	0.264103i	−0.710967	−	0.703225i	$-0.751742\pi$
$421$	−9.38587	+	5.41893i	−0.457439	+	0.264103i	0.253528	+	0.967328i	$0.418409\pi$
$422$	−16.2264	−	23.6059i	−0.789890	−	1.14912i
$423$		0			0
$424$	2.66250	−	0.639832i	0.129303	−	0.0310730i
$425$	−26.0134	+	15.0188i	−1.26183	+	0.728520i
$426$		0			0
$427$	−8.97444	+	15.5442i	−0.434304	+	0.752236i
$428$	−7.47173	+	6.05231i	−0.361160	+	0.292550i
$429$		0			0
$430$	22.9682	−	48.1629i	1.10762	−	2.32262i
$431$	−10.8604			−0.523129			−0.261565	−	0.965186i	$-0.584238\pi$
$431$	−10.8604			−0.523129			−0.261565	+	0.965186i	$0.584238\pi$
$432$		0			0
$433$	9.41382			0.452399			0.226200	−	0.974081i	$-0.427370\pi$
$433$	9.41382			0.452399			0.226200	+	0.974081i	$0.427370\pi$
$434$	−6.45513	+	13.5360i	−0.309856	+	0.649750i
$435$		0			0
$436$	11.1383	−	9.02229i	0.533426	−	0.432090i
$437$	0.634073	−	1.09825i	0.0303318	−	0.0525363i
$438$		0			0
$439$	9.25745	−	5.34479i	0.441834	−	0.255093i	−0.262541	−	0.964921i	$-0.584561\pi$
$439$	9.25745	−	5.34479i	0.441834	−	0.255093i	0.704375	+	0.709828i	$0.251227\pi$
$440$	0.311252	+	1.29520i	0.0148383	+	0.0617461i
$441$		0			0
$442$	−10.2477	−	14.9081i	−0.487431	−	0.709105i
$443$	−18.9818	+	10.9592i	−0.901854	+	0.520686i	−0.877801	−	0.479025i	$-0.840990\pi$
$443$	−18.9818	+	10.9592i	−0.901854	+	0.520686i	−0.0240526	+	0.999711i	$0.507657\pi$
$444$		0			0
$445$	25.2371	+	14.5707i	1.19635	+	0.690715i
$446$	0.0668299	+	0.848356i	0.00316449	+	0.0401708i
$447$		0			0
$448$	−9.09025	+	14.0113i	−0.429474	+	0.661971i
$449$		−	18.7436i		−	0.884565i	−0.896876	−	0.442282i	$-0.854169\pi$
$449$		−	18.7436i		−	0.884565i	0.896876	−	0.442282i	$-0.145831\pi$
$450$		0			0
$451$	−0.279841			−0.0131772
$452$	−0.0773574	−	0.487951i	−0.00363859	−	0.0229513i
$453$		0			0
$454$	1.18461	+	15.0377i	0.0555963	+	0.705754i
$455$	−11.0896	+	19.2078i	−0.519890	+	0.900475i
$456$		0			0
$457$	−0.00912370	−	0.0158027i	−0.000426789	−	0.000739220i	0.865812	−	0.500370i	$-0.166803\pi$
$457$	−0.00912370	−	0.0158027i	−0.000426789	−	0.000739220i	−0.866239	+	0.499630i	$0.833469\pi$
$458$	29.8177	−	20.4964i	1.39329	−	0.957732i
$459$		0			0
$460$	−3.44648	+	8.98234i	−0.160693	+	0.418804i
$461$	−1.25915	−	2.18091i	−0.0586444	−	0.101575i	0.835213	−	0.549927i	$-0.185344\pi$
$461$	−1.25915	−	2.18091i	−0.0586444	−	0.101575i	−0.893857	+	0.448352i	$0.852011\pi$
$462$		0			0
$463$	−23.9003	−	13.7988i	−1.11074	−	0.641286i	−0.171719	−	0.985146i	$-0.554932\pi$
$463$	−23.9003	−	13.7988i	−1.11074	−	0.641286i	−0.939021	+	0.343860i	$0.888265\pi$
$464$	−32.2652	+	10.4941i	−1.49788	+	0.487177i
$465$		0			0
$466$	6.01338	+	2.86769i	0.278565	+	0.132843i
$467$		−	28.4629i		−	1.31711i	−0.752533	−	0.658554i	$-0.771168\pi$
$467$		−	28.4629i		−	1.31711i	0.752533	−	0.658554i	$-0.228832\pi$
$468$		0			0
$469$			13.1700i			0.608134i
$470$	−0.873590	+	1.83187i	−0.0402957	+	0.0844977i
$471$		0			0
$472$	12.1751	+	3.60351i	0.560405	+	0.165865i
$473$	1.26603	+	0.730942i	0.0582121	+	0.0336088i
$474$		0			0
$475$	−3.28823	−	5.69538i	−0.150874	−	0.261322i
$476$	6.27924	−	16.3652i	0.287808	−	0.750097i
$477$		0			0
$478$	12.0331	+	17.5056i	0.550383	+	0.800686i
$479$	19.1602	+	33.1865i	0.875454	+	1.51633i	0.856279	+	0.516514i	$0.172771\pi$
$479$	19.1602	+	33.1865i	0.875454	+	1.51633i	0.0191747	+	0.999816i	$0.493896\pi$
$480$		0			0
$481$	2.46325	−	4.26648i	0.112315	−	0.194535i
$482$	36.2982	−	2.85942i	1.65334	−	0.130243i
$483$		0			0
$484$	21.6926	−	3.43904i	0.986027	−	0.156320i
$485$	−3.32651			−0.151049
$486$		0			0
$487$			2.25659i			0.102256i	0.998692	+	0.0511280i	$0.0162817\pi$
$487$			2.25659i			0.102256i	−0.998692	+	0.0511280i	$0.983718\pi$
$488$	−17.6352	+	16.7426i	−0.798310	+	0.757903i
$489$		0			0
$490$	12.9835	−	1.02278i	0.586534	−	0.0462047i
$491$	17.7659	+	10.2572i	0.801765	+	0.462899i	0.844088	−	0.536205i	$-0.180142\pi$
$491$	17.7659	+	10.2572i	0.801765	+	0.462899i	−0.0423228	+	0.999104i	$0.513476\pi$
$492$		0			0
$493$	30.8377	−	17.8042i	1.38886	−	0.801860i
$494$	3.26398	−	2.24362i	0.146853	−	0.100945i
$495$		0			0
$496$	−13.5903	+	15.1025i	−0.610223	+	0.678123i
$497$	21.6396	−	12.4936i	0.970667	−	0.560415i
$498$		0			0
$499$	1.87815	−	3.25306i	0.0840777	−	0.145627i	−0.820920	−	0.571043i	$-0.806539\pi$
$499$	1.87815	−	3.25306i	0.0840777	−	0.145627i	0.904998	+	0.425416i	$0.139872\pi$
$500$	9.45926	+	11.6777i	0.423031	+	0.522243i
$501$		0			0
$502$	6.77098	+	3.22898i	0.302204	+	0.144116i
$503$	−33.3322			−1.48621			−0.743104	−	0.669175i	$-0.766647\pi$
$503$	−33.3322			−1.48621			−0.743104	+	0.669175i	$0.766647\pi$
$504$		0			0
$505$	−37.3694			−1.66292
$506$	−0.237914	−	0.113458i	−0.0105766	−	0.00504382i
$507$		0			0
$508$	−27.3952	+	22.1908i	−1.21546	+	0.984559i
$509$	3.41788	−	5.91994i	0.151495	−	0.262397i	−0.780282	−	0.625427i	$-0.784925\pi$
$509$	3.41788	−	5.91994i	0.151495	−	0.262397i	0.931777	+	0.363031i	$0.118258\pi$
$510$		0			0
$511$	7.34533	−	4.24083i	0.324938	−	0.187603i
$512$	−17.1963	+	14.7067i	−0.759976	+	0.649951i
$513$		0			0
$514$	28.9310	−	19.8868i	1.27609	−	0.877171i
$515$	−26.0112	+	15.0176i	−1.14619	+	0.661754i
$516$		0			0
$517$	−0.0481531	−	0.0278012i	−0.00211777	−	0.00122270i
$518$	4.75872	−	0.374872i	0.209086	−	0.0164709i
$519$		0			0
$520$	−21.7917	+	20.6887i	−0.955629	+	0.907259i
$521$		−	19.9468i		−	0.873887i	−0.899489	−	0.436943i	$-0.856061\pi$
$521$		−	19.9468i		−	0.873887i	0.899489	−	0.436943i	$-0.143939\pi$
$522$		0			0
$523$	−5.50358			−0.240655			−0.120327	−	0.992734i	$-0.538394\pi$
$523$	−5.50358			−0.240655			−0.120327	+	0.992734i	$0.538394\pi$
$524$	−4.62138	−	29.1505i	−0.201886	−	1.27345i
$525$		0			0
$526$	−28.0802	+	2.21204i	−1.22435	+	0.0964493i
$527$	10.6614	−	18.4660i	0.464416	−	0.804392i
$528$		0			0
$529$	10.5481	+	18.2699i	0.458615	+	0.794344i
$530$	2.70401	+	3.93374i	0.117455	+	0.170871i
$531$		0			0
$532$	3.58300	+	1.37478i	0.155343	+	0.0596042i
$533$	−3.15627	−	5.46682i	−0.136713	−	0.236794i
$534$		0			0
$535$	−14.5162	−	8.38093i	−0.627590	−	0.362339i
$536$	−5.06380	+	17.1090i	−0.218723	+	0.738995i
$537$		0			0
$538$	1.43383	−	3.00665i	0.0618168	−	0.129626i
$539$			0.356811i			0.0153690i
$540$		0			0
$541$		−	12.1375i		−	0.521831i	−0.965362	−	0.260915i	$-0.915976\pi$
$541$		−	12.1375i		−	0.521831i	0.965362	−	0.260915i	$-0.0840243\pi$
$542$	−15.4167	−	7.35199i	−0.662203	−	0.315795i
$543$		0			0
$544$	14.4496	−	18.8454i	0.619522	−	0.807992i
$545$	21.6396	+	12.4936i	0.926937	+	0.535167i
$546$		0			0
$547$	5.02439	+	8.70250i	0.214827	+	0.372092i	0.953219	−	0.302280i	$-0.0977477\pi$
$547$	5.02439	+	8.70250i	0.214827	+	0.372092i	−0.738392	+	0.674372i	$0.764414\pi$
$548$	32.0377	+	12.2927i	1.36858	+	0.525119i
$549$		0			0
$550$	−1.12645	+	0.774308i	−0.0480319	+	0.0330166i
$551$	3.89805	+	6.75163i	0.166063	+	0.287629i
$552$		0			0
$553$	13.0987	−	22.6876i	0.557013	−	0.964775i
$554$	−1.86599	−	23.6873i	−0.0792782	−	1.00638i
$555$		0			0
$556$	2.40146	−	0.380715i	0.101844	−	0.0161459i
$557$	15.4323			0.653887			0.326944	−	0.945044i	$-0.393981\pi$
$557$	15.4323			0.653887			0.326944	+	0.945044i	$0.393981\pi$
$558$		0			0
$559$			32.9766i			1.39476i
$560$	−28.4804	−	6.04493i	−1.20352	−	0.255445i
$561$		0			0
$562$	1.53703	+	19.5115i	0.0648358	+	0.823043i
$563$	−5.08901	−	2.93814i	−0.214476	−	0.123828i	0.388914	−	0.921274i	$-0.372850\pi$
$563$	−5.08901	−	2.93814i	−0.214476	−	0.123828i	−0.603390	+	0.797446i	$0.706184\pi$
$564$		0			0
$565$	0.745845	−	0.430614i	0.0313779	−	0.0181161i
$566$	−4.13567	−	6.01649i	−0.173835	−	0.252892i
$567$		0			0
$568$	32.9154	−	7.90997i	1.38110	−	0.331895i
$569$	28.3228	−	16.3522i	1.18735	−	0.685519i	0.229650	−	0.973273i	$-0.426242\pi$
$569$	28.3228	−	16.3522i	1.18735	−	0.685519i	0.957704	+	0.287754i	$0.0929087\pi$
$570$		0			0
$571$	16.4253	−	28.4495i	0.687377	−	1.19057i	−0.285306	−	0.958437i	$-0.592095\pi$
$571$	16.4253	−	28.4495i	0.687377	−	1.19057i	0.972683	−	0.232136i	$-0.0745715\pi$
$572$	−0.518172	−	0.639697i	−0.0216659	−	0.0267471i
$573$		0			0
$574$	2.63279	−	5.52080i	0.109890	−	0.230434i
$575$	−9.87246			−0.411710
$576$		0			0
$577$	−16.7158			−0.695887			−0.347943	−	0.937516i	$-0.613120\pi$
$577$	−16.7158			−0.695887			−0.347943	+	0.937516i	$0.613120\pi$
$578$	−0.379353	+	0.795481i	−0.0157790	+	0.0330876i
$579$		0			0
$580$	−37.2282	−	45.9592i	−1.54582	−	1.90835i
$581$	6.31450	−	10.9370i	0.261970	−	0.453745i
$582$		0			0
$583$	−0.113258	+	0.0653894i	−0.00469066	+	0.00270815i
$584$	11.1728	−	2.68496i	0.462334	−	0.111104i
$585$		0			0
$586$	8.68208	+	12.6305i	0.358653	+	0.521762i
$587$	23.7005	−	13.6835i	0.978222	−	0.564777i	0.0764895	−	0.997070i	$-0.475629\pi$
$587$	23.7005	−	13.6835i	0.978222	−	0.564777i	0.901733	+	0.432293i	$0.142296\pi$
$588$		0			0
$589$	4.04296	+	2.33420i	0.166587	+	0.0961791i
$590$	1.73823	+	22.0656i	0.0715620	+	0.908426i
$591$		0			0
$592$	6.32612	+	1.34271i	0.260002	+	0.0551852i
$593$			25.6865i			1.05482i	0.849612	+	0.527408i	$0.176836\pi$
$593$			25.6865i			1.05482i	−0.849612	+	0.527408i	$0.823164\pi$
$594$		0			0
$595$	30.5560			1.25267
$596$	17.6341	−	2.79562i	0.722319	−	0.114513i
$597$		0			0
$598$	−0.466937	−	5.92743i	−0.0190945	−	0.242390i
$599$	19.9859	−	34.6166i	0.816601	−	1.41439i	−0.0915718	−	0.995798i	$-0.529189\pi$
$599$	19.9859	−	34.6166i	0.816601	−	1.41439i	0.908173	−	0.418596i	$-0.137478\pi$
$600$		0			0
$601$	2.01867	+	3.49645i	0.0823434	+	0.142623i	0.904256	−	0.426991i	$-0.140426\pi$
$601$	2.01867	+	3.49645i	0.0823434	+	0.142623i	−0.821913	+	0.569613i	$0.807093\pi$
$602$	−26.3313	+	18.0998i	−1.07318	+	0.737694i
$603$		0			0
$604$	−40.8486	−	15.6734i	−1.66210	−	0.637742i
$605$	19.1436	+	33.1577i	0.778298	+	1.34805i
$606$		0			0
$607$	11.2251	+	6.48081i	0.455612	+	0.263048i	0.710198	−	0.704002i	$-0.248606\pi$
$607$	11.2251	+	6.48081i	0.455612	+	0.263048i	−0.254585	+	0.967050i	$0.581939\pi$
$608$	4.12603	+	3.16360i	0.167332	+	0.128301i
$609$		0			0
$610$	−38.2618	−	18.2465i	−1.54918	−	0.738779i
$611$		−	1.25426i		−	0.0507418i
$612$		0			0
$613$		−	22.0890i		−	0.892167i	−0.894991	−	0.446084i	$-0.852818\pi$
$613$		−	22.0890i		−	0.892167i	0.894991	−	0.446084i	$-0.147182\pi$
$614$	10.1386	−	21.2601i	0.409162	−	0.857989i
$615$		0			0
$616$	0.226379	−	0.764862i	0.00912106	−	0.0308172i
$617$	−20.0171	−	11.5569i	−0.805859	−	0.465263i	0.0396569	−	0.999213i	$-0.487374\pi$
$617$	−20.0171	−	11.5569i	−0.805859	−	0.465263i	−0.845516	+	0.533951i	$0.820707\pi$
$618$		0			0
$619$	−2.24675	−	3.89149i	−0.0903046	−	0.156412i	0.817335	−	0.576163i	$-0.195451\pi$
$619$	−2.24675	−	3.89149i	−0.0903046	−	0.156412i	−0.907639	+	0.419751i	$0.862117\pi$
$620$	−33.0665	−	12.6875i	−1.32798	−	0.509541i
$621$		0			0
$622$	10.3698	+	15.0857i	0.415789	+	0.604882i
$623$	−8.72509	−	15.1123i	−0.349563	−	0.605461i
$624$		0			0
$625$	4.78939	−	8.29547i	0.191576	−	0.331819i
$626$	−37.6691	+	2.96741i	−1.50556	+	0.118602i
$627$		0			0
$628$	1.75552	+	11.0734i	0.0700528	+	0.441875i
$629$	−6.78716			−0.270622
$630$		0			0
$631$			30.8693i			1.22889i	0.788961	+	0.614443i	$0.210619\pi$
$631$			30.8693i			1.22889i	−0.788961	+	0.614443i	$0.789381\pi$
$632$	25.7396	−	24.4368i	1.02387	−	0.972043i
$633$		0			0
$634$	−35.3425	+	2.78413i	−1.40363	+	0.110572i
$635$	−53.2237	−	30.7287i	−2.11212	−	1.21943i
$636$		0			0
$637$	−6.97046	+	4.02440i	−0.276180	+	0.159452i
$638$	1.33536	−	0.917910i	0.0528673	−	0.0363404i
$639$		0			0
$640$	−34.6742	−	18.8034i	−1.37062	−	0.743271i
$641$	−23.7137	+	13.6911i	−0.936633	+	0.540766i	−0.888903	−	0.458095i	$-0.848532\pi$
$641$	−23.7137	+	13.6911i	−0.936633	+	0.540766i	−0.0477300	+	0.998860i	$0.515199\pi$
$642$		0			0
$643$	−19.9857	+	34.6162i	−0.788158	+	1.36513i	0.138937	+	0.990301i	$0.455631\pi$
$643$	−19.9857	+	34.6162i	−0.788158	+	1.36513i	−0.927094	+	0.374828i	$0.877702\pi$
$644$	4.47667	−	3.62622i	0.176405	−	0.142893i
$645$		0			0
$646$	−4.92525	−	2.34878i	−0.193781	−	0.0924115i
$647$	30.9768			1.21782			0.608912	−	0.793238i	$-0.291606\pi$
$647$	30.9768			1.21782			0.608912	+	0.793238i	$0.291606\pi$
$648$		0			0
$649$	−0.606405			−0.0238035
$650$	−27.8314	−	13.2724i	−1.09164	−	0.520586i
$651$		0			0
$652$	21.6227	+	26.6938i	0.846812	+	1.04541i
$653$	−2.78891	+	4.83053i	−0.109138	+	0.189033i	−0.915421	−	0.402497i	$-0.868143\pi$
$653$	−2.78891	+	4.83053i	−0.109138	+	0.189033i	0.806283	+	0.591530i	$0.201476\pi$
$654$		0			0
$655$	44.5573	−	25.7252i	1.74100	−	1.00517i
$656$	5.54294	−	6.15970i	0.216415	−	0.240496i
$657$		0			0
$658$	1.00150	−	0.688423i	0.0390427	−	0.0268375i
$659$	5.69959	−	3.29066i	0.222025	−	0.128186i	−0.384863	−	0.922974i	$-0.625751\pi$
$659$	5.69959	−	3.29066i	0.222025	−	0.128186i	0.606887	+	0.794788i	$0.292418\pi$
$660$		0			0
$661$	−26.9562	−	15.5632i	−1.04847	−	0.605337i	−0.126253	−	0.991998i	$-0.540295\pi$
$661$	−26.9562	−	15.5632i	−1.04847	−	0.605337i	−0.922222	+	0.386661i	$0.873628\pi$
$662$	−23.9097	+	1.88351i	−0.929278	+	0.0732046i
$663$		0			0
$664$	12.4083	−	11.7803i	0.481536	−	0.457163i
$665$			6.68993i			0.259425i
$666$		0			0
$667$	11.7034			0.453157
$668$	−9.13587	+	1.44836i	−0.353477	+	0.0560386i
$669$		0			0
$670$	−31.0075	+	2.44264i	−1.19792	+	0.0943674i
$671$	0.580679	−	1.00576i	0.0224168	−	0.0388271i
$672$		0			0
$673$	−3.54087	−	6.13297i	−0.136491	−	0.236409i	0.789675	−	0.613525i	$-0.210249\pi$
$673$	−3.54087	−	6.13297i	−0.136491	−	0.236409i	−0.926166	+	0.377116i	$0.876916\pi$
$674$	−7.16541	−	10.4241i	−0.276001	−	0.401521i
$675$		0			0
$676$	−2.66159	+	6.93674i	−0.102369	+	0.266798i
$677$	−3.18253	−	5.51231i	−0.122315	−	0.211855i	0.798365	−	0.602173i	$-0.205698\pi$
$677$	−3.18253	−	5.51231i	−0.122315	−	0.211855i	−0.920680	+	0.390318i	$0.872365\pi$
$678$		0			0
$679$	1.72508	+	0.995978i	0.0662026	+	0.0382221i
$680$	39.6948	+	11.7486i	1.52223	+	0.450539i
$681$		0			0
$682$	0.417670	−	0.875829i	0.0159934	−	0.0335372i
$683$			51.9104i			1.98630i	0.116864	+	0.993148i	$0.462716\pi$
$683$			51.9104i			1.98630i	−0.116864	+	0.993148i	$0.537284\pi$
$684$		0			0
$685$			59.8187i			2.28556i
$686$	−25.6940	−	12.2531i	−0.981002	−	0.467825i
$687$		0			0
$688$	−41.1659	+	13.3890i	−1.56943	+	0.510451i
$689$	−2.55482	−	1.47503i	−0.0973309	−	0.0561940i
$690$		0			0
$691$	−17.9150	−	31.0297i	−0.681519	−	1.18043i	−0.974517	−	0.224313i	$-0.927986\pi$
$691$	−17.9150	−	31.0297i	−0.681519	−	1.18043i	0.292998	−	0.956113i	$-0.405347\pi$
$692$	−2.17913	+	5.67933i	−0.0828382	+	0.215896i
$693$		0			0
$694$	5.77760	−	3.97146i	0.219315	−	0.150755i
$695$	2.11927	+	3.67068i	0.0803885	+	0.139237i
$696$		0			0
$697$	−4.34834	+	7.53154i	−0.164705	+	0.285277i
$698$	2.94614	+	37.3990i	0.111513	+	1.41557i
$699$		0			0
$700$	−4.67802	−	29.5077i	−0.176813	−	1.11529i
$701$	−19.0081			−0.717927			−0.358964	−	0.933352i	$-0.616870\pi$
$701$	−19.0081			−0.717927			−0.358964	+	0.933352i	$0.616870\pi$
$702$		0			0
$703$		−	1.48598i		−	0.0560449i
$704$	0.588171	−	0.906580i	0.0221675	−	0.0341680i
$705$		0			0
$706$	−3.68645	−	46.7967i	−0.138741	−	1.76122i
$707$	19.3793	+	11.1886i	0.728832	+	0.420792i
$708$		0			0
$709$	−38.5758	+	22.2717i	−1.44874	+	0.836433i	−0.998407	−	0.0564260i	$-0.982030\pi$
$709$	−38.5758	+	22.2717i	−1.44874	+	0.836433i	−0.450337	+	0.892859i	$0.648696\pi$
$710$	33.4285	+	48.6311i	1.25455	+	1.82509i
$711$		0			0
$712$	−5.52404	−	22.9869i	−0.207022	−	0.861472i
$713$	6.06922	−	3.50407i	0.227294	−	0.131228i
$714$		0			0
$715$	0.717538	−	1.24281i	0.0268344	−	0.0464786i
$716$	−27.9734	+	22.6592i	−1.04541	+	0.846815i
$717$		0			0
$718$	−12.5485	+	26.3134i	−0.468304	+	0.982006i
$719$	40.5385			1.51183			0.755915	−	0.654670i	$-0.227192\pi$
$719$	40.5385			1.51183			0.755915	+	0.654670i	$0.227192\pi$
$720$		0			0
$721$	17.9854			0.669813
$722$	−11.0518	+	23.1750i	−0.411307	+	0.862485i
$723$		0			0
$724$	24.7891	−	20.0799i	0.921281	−	0.746263i
$725$	30.3462	−	52.5611i	1.12703	−	1.95207i
$726$		0			0
$727$	−16.5719	+	9.56779i	−0.614618	+	0.354850i	−0.774770	−	0.632243i	$-0.782135\pi$
$727$	−16.5719	+	9.56779i	−0.614618	+	0.354850i	0.160153	+	0.987092i	$0.448801\pi$
$728$	17.4952	−	4.20431i	0.648415	−	0.155822i
$729$		0			0
$730$	11.3470	+	16.5073i	0.419970	+	0.610964i
$731$	39.3446	−	22.7156i	1.45521	−	0.840168i
$732$		0			0
$733$	25.4597	+	14.6992i	0.940377	+	0.542927i	0.890078	−	0.455807i	$-0.150649\pi$
$733$	25.4597	+	14.6992i	0.940377	+	0.542927i	0.0502985	+	0.998734i	$0.483983\pi$
$734$	1.30138	+	16.5200i	0.0480347	+	0.609765i
$735$		0			0
$736$	7.20984	−	2.98952i	0.265758	−	0.110195i
$737$		−	0.852146i		−	0.0313892i
$738$		0			0
$739$	−0.807511			−0.0297048			−0.0148524	−	0.999890i	$-0.504728\pi$
$739$	−0.807511			−0.0297048			−0.0148524	+	0.999890i	$0.504728\pi$
$740$	1.76520	+	11.1344i	0.0648900	+	0.409309i
$741$		0			0
$742$	−0.224478	−	2.84958i	−0.00824084	−	0.104611i
$743$	13.2127	−	22.8850i	0.484725	−	0.839569i	−0.515121	−	0.857118i	$-0.672253\pi$
$743$	13.2127	−	22.8850i	0.484725	−	0.839569i	0.999846	+	0.0175489i	$0.00558629\pi$
$744$		0			0
$745$	15.5620	+	26.9541i	0.570146	+	0.987521i
$746$	4.07446	−	2.80074i	0.149177	−	0.102542i
$747$		0			0
$748$	−0.406289	+	1.05889i	−0.0148554	+	0.0387167i
$749$	5.01860	+	8.69248i	0.183376	+	0.317616i
$750$		0			0
$751$	−2.08658	−	1.20469i	−0.0761405	−	0.0439597i	0.461446	−	0.887168i	$-0.347331\pi$
$751$	−2.08658	−	1.20469i	−0.0761405	−	0.0439597i	−0.537587	+	0.843208i	$0.680664\pi$
$752$	1.56573	−	0.509248i	0.0570965	−	0.0185703i
$753$		0			0
$754$	32.9930	+	15.7339i	1.20153	+	0.572993i
$755$		−	76.2698i		−	2.77574i
$756$		0			0
$757$			3.61528i			0.131400i	0.997839	+	0.0656998i	$0.0209280\pi$
$757$			3.61528i			0.131400i	−0.997839	+	0.0656998i	$0.979072\pi$
$758$	12.2725	−	25.7346i	0.445756	−	0.934723i
$759$		0			0
$760$	−2.57225	+	8.69080i	−0.0933052	+	0.315249i
$761$	−7.79878	−	4.50263i	−0.282706	−	0.163220i	0.351942	−	0.936022i	$-0.385521\pi$
$761$	−7.79878	−	4.50263i	−0.282706	−	0.163220i	−0.634648	+	0.772802i	$0.718855\pi$
$762$		0			0
$763$	−7.48133	−	12.9580i	−0.270842	−	0.469112i
$764$	3.18057	−	8.28930i	0.115069	−	0.299896i
$765$		0			0
$766$	−8.54171	−	12.4263i	−0.308624	−	0.448981i
$767$	−6.83951	−	11.8464i	−0.246961	−	0.427748i
$768$		0			0
$769$	7.58489	−	13.1374i	0.273518	−	0.473747i	−0.696242	−	0.717807i	$-0.745146\pi$
$769$	7.58489	−	13.1374i	0.273518	−	0.473747i	0.969760	+	0.244060i	$0.0784794\pi$
$770$	1.38620	−	0.109199i	0.0499552	−	0.00393526i
$771$		0			0
$772$	−2.66220	+	0.422053i	−0.0958147	+	0.0151900i
$773$	−31.6926			−1.13990			−0.569952	−	0.821678i	$-0.693038\pi$
$773$	−31.6926			−1.13990			−0.569952	+	0.821678i	$0.693038\pi$
$774$		0			0
$775$		−	36.3433i		−	1.30549i
$776$	1.85808	+	1.95715i	0.0667014	+	0.0702575i
$777$		0			0
$778$	23.5197	−	1.85278i	0.843221	−	0.0664254i
$779$	−1.64896	−	0.952026i	−0.0590800	−	0.0341099i
$780$		0			0
$781$	−1.40016	+	0.808381i	−0.0501016	+	0.0289262i
$782$	−6.75042	+	4.64016i	−0.241394	+	0.165932i
$783$		0			0
$784$	−7.85392	−	7.06752i	−0.280497	−	0.252411i
$785$	−16.9259	+	9.77217i	−0.604111	+	0.348784i
$786$		0			0
$787$	10.3290	−	17.8904i	0.368189	−	0.637723i	−0.621093	−	0.783737i	$-0.713311\pi$
$787$	10.3290	−	17.8904i	0.368189	−	0.637723i	0.989283	+	0.146014i	$0.0466444\pi$
$788$	−11.5418	−	14.2486i	−0.411158	−	0.507585i
$789$		0			0
$790$	55.8452	+	26.6318i	1.98688	+	0.947515i
$791$	−0.515713			−0.0183367
$792$		0			0
$793$	26.1974			0.930297
$794$	−29.3427	−	13.9931i	−1.04133	−	0.496596i
$795$		0			0
$796$	37.3358	−	30.2430i	1.32333	−	1.07194i
$797$	−17.8453	+	30.9089i	−0.632112	+	1.09485i	0.355007	+	0.934864i	$0.384479\pi$
$797$	−17.8453	+	30.9089i	−0.632112	+	1.09485i	−0.987119	+	0.159987i	$0.948855\pi$
$798$		0			0
$799$	−1.49646	+	0.863984i	−0.0529411	+	0.0305655i
$800$	5.26843	−	40.1318i	0.186267	−	1.41887i
$801$		0			0
$802$	−36.7510	+	25.2622i	−1.29772	+	0.892040i
$803$	−0.475269	+	0.274397i	−0.0167719	+	0.00968325i
$804$		0			0
$805$	8.69734	+	5.02141i	0.306541	+	0.176981i
$806$	21.8205	−	1.71893i	0.768595	−	0.0605466i
$807$		0			0
$808$	20.8734	+	21.9862i	0.734323	+	0.773473i
$809$			18.7528i			0.659314i	0.944101	+	0.329657i	$0.106933\pi$
$809$			18.7528i			0.659314i	−0.944101	+	0.329657i	$0.893067\pi$
$810$		0			0
$811$	−33.9206			−1.19111			−0.595556	−	0.803314i	$-0.703068\pi$
$811$	−33.9206			−1.19111			−0.595556	+	0.803314i	$0.703068\pi$
$812$	5.54559	+	34.9802i	0.194612	+	1.22756i
$813$		0			0
$814$	−0.307906	+	0.0242555i	−0.0107921	+	0.000850156i
$815$	−29.9421	+	51.8612i	−1.04882	+	1.81662i
$816$		0			0
$817$	4.97337	+	8.61412i	0.173996	+	0.301370i
$818$	−5.75609	−	8.37384i	−0.201257	−	0.292785i
$819$		0			0
$820$	13.4865	+	5.17470i	0.470969	+	0.180708i
$821$	−5.34636	−	9.26017i	−0.186589	−	0.323182i	0.757522	−	0.652810i	$-0.226410\pi$
$821$	−5.34636	−	9.26017i	−0.186589	−	0.323182i	−0.944111	+	0.329628i	$0.893077\pi$
$822$		0			0
$823$	33.4172	+	19.2934i	1.16485	+	0.672527i	0.952462	−	0.304658i	$-0.0985421\pi$
$823$	33.4172	+	19.2934i	1.16485	+	0.672527i	0.212390	+	0.977185i	$0.431875\pi$
$824$	23.3646	+	6.91531i	0.813946	+	0.240906i
$825$		0			0
$826$	5.70515	−	11.9634i	0.198508	−	0.416259i
$827$		−	0.214418i		−	0.00745604i	−0.999993	−	0.00372802i	$-0.998813\pi$
$827$		−	0.214418i		−	0.00745604i	0.999993	−	0.00372802i	$-0.00118667\pi$
$828$		0			0
$829$		−	35.5733i		−	1.23551i	−0.786369	−	0.617757i	$-0.788042\pi$
$829$		−	35.5733i		−	1.23551i	0.786369	−	0.617757i	$-0.211958\pi$
$830$	26.9214	+	12.8384i	0.934454	+	0.445627i
$831$		0			0
$832$	24.3443	+	1.26505i	0.843987	+	0.0438579i
$833$	9.60309	+	5.54434i	0.332727	+	0.192100i
$834$		0			0
$835$	−8.06235	−	13.9644i	−0.279009	−	0.483258i
$836$	−0.231833	−	0.0889531i	−0.00801810	−	0.00307651i
$837$		0			0
$838$	16.9559	−	11.6553i	0.585733	−	0.402627i
$839$	20.5867	+	35.6571i	0.710730	+	1.23102i	0.964583	+	0.263778i	$0.0849687\pi$
$839$	20.5867	+	35.6571i	0.710730	+	1.23102i	−0.253853	+	0.967243i	$0.581698\pi$
$840$		0			0
$841$	−21.4741	+	37.1942i	−0.740486	+	1.28256i
$842$	1.20367	+	15.2797i	0.0414813	+	0.526574i
$843$		0			0
$844$	−40.0104	+	6.34306i	−1.37722	+	0.218337i
$845$	−12.9518			−0.445556
$846$		0			0
$847$		−	22.9268i		−	0.787775i
$848$	0.804033	−	3.78816i	0.0276106	−	0.130086i
$849$		0			0
$850$	3.33603	+	42.3485i	0.114425	+	1.45254i
$851$	−1.93187	−	1.11537i	−0.0662237	−	0.0382343i
$852$		0			0
$853$	30.9858	−	17.8897i	1.06093	−	0.612530i	0.135243	−	0.990812i	$-0.456819\pi$
$853$	30.9858	−	17.8897i	1.06093	−	0.612530i	0.925690	+	0.378282i	$0.123485\pi$
$854$	14.3789	+	20.9182i	0.492037	+	0.715806i
$855$		0			0
$856$	3.17739	+	13.2219i	0.108601	+	0.451915i
$857$	−26.3688	+	15.2241i	−0.900742	+	0.520044i	−0.877441	−	0.479685i	$-0.840751\pi$
$857$	−26.3688	+	15.2241i	−0.900742	+	0.520044i	−0.0233014	+	0.999728i	$0.507418\pi$
$858$		0			0
$859$	−11.7147	+	20.2904i	−0.399700	+	0.692301i	−0.993689	−	0.112172i	$-0.964219\pi$
$859$	−11.7147	+	20.2904i	−0.399700	+	0.692301i	0.593989	+	0.804473i	$0.297552\pi$
$860$	−47.4980	−	58.6375i	−1.61967	−	1.99952i
$861$		0			0
$862$	−6.61119	+	13.8633i	−0.225178	+	0.472185i
$863$	−32.2240			−1.09692			−0.548458	−	0.836178i	$-0.684785\pi$
$863$	−32.2240			−1.09692			−0.548458	+	0.836178i	$0.684785\pi$
$864$		0			0
$865$	−10.6041			−0.360549
$866$	5.73058	−	12.0167i	0.194733	−	0.408343i
$867$		0			0
$868$	13.3491	+	16.4799i	0.453100	+	0.559363i
$869$	−0.847532	+	1.46797i	−0.0287506	+	0.0497974i
$870$		0			0
$871$	16.6470	−	9.61117i	0.564063	−	0.325662i
$872$	−4.73659	−	19.7101i	−0.160401	−	0.667470i
$873$		0			0
$874$	−1.01592	−	1.47794i	−0.0343640	−	0.0499920i
$875$	13.5856	−	7.84366i	0.459278	−	0.265164i
$876$		0			0
$877$	1.74081	+	1.00506i	0.0587829	+	0.0339384i	0.529103	−	0.848557i	$-0.322528\pi$
$877$	1.74081	+	1.00506i	0.0587829	+	0.0339384i	−0.470320	+	0.882496i	$0.655862\pi$
$878$	−1.18720	−	15.0707i	−0.0400661	−	0.508610i
$879$		0			0
$880$	1.84278	+	0.391128i	0.0621201	+	0.0131849i
$881$			21.6545i			0.729558i	0.931094	+	0.364779i	$0.118855\pi$
$881$			21.6545i			0.729558i	−0.931094	+	0.364779i	$0.881145\pi$
$882$		0			0
$883$	−23.3462			−0.785664			−0.392832	−	0.919610i	$-0.628505\pi$
$883$	−23.3462			−0.785664			−0.392832	+	0.919610i	$0.628505\pi$
$884$	−25.2682	+	4.00591i	−0.849862	+	0.134733i
$885$		0			0
$886$	2.43429	+	30.9015i	0.0817814	+	1.03815i
$887$	−24.4901	+	42.4181i	−0.822297	+	1.42426i	0.0816710	+	0.996659i	$0.473974\pi$
$887$	−24.4901	+	42.4181i	−0.822297	+	1.42426i	−0.903968	+	0.427600i	$0.859359\pi$
$888$		0			0
$889$	18.4007	+	31.8710i	0.617141	+	1.06892i
$890$	33.9622	−	23.3453i	1.13842	−	0.782535i
$891$		0			0
$892$	1.12360	+	0.431121i	0.0376210	+	0.0144350i
$893$	−0.189161	−	0.327636i	−0.00633003	−	0.0109639i
$894$		0			0
$895$	−54.3471	−	31.3773i	−1.81662	−	1.04883i
$896$	12.3517	+	20.1329i	0.412642	+	0.672592i
$897$		0			0
$898$	−23.9261	−	11.4100i	−0.798423	−	0.380756i
$899$			43.0834i			1.43691i
$900$		0			0
$901$			4.06424i			0.135399i
$902$	−0.170351	+	0.357215i	−0.00567206	+	0.0118940i
$903$		0			0
$904$	−0.669956	−	0.198289i	−0.0222824	−	0.00659500i
$905$	48.1607	+	27.8056i	1.60092	+	0.924289i
$906$		0			0
$907$	−9.93443	−	17.2069i	−0.329867	−	0.571347i	0.652618	−	0.757687i	$-0.273671\pi$
$907$	−9.93443	−	17.2069i	−0.329867	−	0.571347i	−0.982485	+	0.186340i	$0.940337\pi$
$908$	19.9166	+	7.64192i	0.660957	+	0.253606i
$909$		0			0
$910$	17.7679	+	25.8484i	0.589001	+	0.856866i
$911$	24.0672	+	41.6857i	0.797383	+	1.38111i	0.921315	+	0.388817i	$0.127116\pi$
$911$	24.0672	+	41.6857i	0.797383	+	1.38111i	−0.123932	+	0.992291i	$0.539550\pi$
$912$		0			0
$913$	−0.408571	+	0.707665i	−0.0135217	+	0.0234203i
$914$	−0.0257260	+	0.00202659i	−0.000850941	+	6.70335e-5i
$915$		0			0
$916$	−8.01223	−	50.5391i	−0.264731	−	1.66986i
$917$	−30.8091			−1.01741
$918$		0			0
$919$		−	34.3644i		−	1.13358i	−0.823864	−	0.566788i	$-0.808186\pi$
$919$		−	34.3644i		−	1.13358i	0.823864	−	0.566788i	$-0.191814\pi$
$920$	9.36789	+	9.86733i	0.308850	+	0.325316i
$921$		0			0
$922$	−3.55041	+	0.279686i	−0.116927	+	0.00921098i
$923$	−31.5841	−	18.2351i	−1.03960	−	0.600216i
$924$		0			0
$925$	−10.0185	+	5.78416i	−0.329405	+	0.190182i
$926$	−32.1632	+	22.1086i	−1.05695	+	0.726535i
$927$		0			0
$928$	−6.24550	+	47.5745i	−0.205019	+	1.56171i
$929$	−15.1165	+	8.72750i	−0.495955	+	0.286340i	−0.727042	−	0.686593i	$-0.759105\pi$
$929$	−15.1165	+	8.72750i	−0.495955	+	0.286340i	0.231086	+	0.972933i	$0.425772\pi$
$930$		0			0
$931$	−1.21388	+	2.10250i	−0.0397833	+	0.0689067i
$932$	7.32118	−	5.93036i	0.239813	−	0.194255i
$933$		0			0
$934$	−36.3328	−	17.3266i	−1.18884	−	0.566942i
$935$	−1.97708			−0.0646574
$936$		0			0
$937$	42.3068			1.38210			0.691051	−	0.722806i	$-0.257148\pi$
$937$	42.3068			1.38210			0.691051	+	0.722806i	$0.257148\pi$
$938$	16.8114	+	8.01712i	0.548912	+	0.261768i
$939$		0			0
$940$	1.80657	+	2.23026i	0.0589240	+	0.0727431i
$941$	11.6752	−	20.2221i	0.380602	−	0.659222i	−0.610546	−	0.791980i	$-0.709050\pi$
$941$	11.6752	−	20.2221i	0.380602	−	0.659222i	0.991148	+	0.132758i	$0.0423835\pi$
$942$		0			0
$943$	−2.47539	+	1.42917i	−0.0806097	+	0.0465400i
$944$	12.0113	−	13.3478i	0.390936	−	0.434435i
$945$		0			0
$946$	1.70373	−	1.17112i	0.0553929	−	0.0380765i
$947$	−28.1206	+	16.2354i	−0.913796	+	0.527580i	−0.881651	−	0.471903i	$-0.843567\pi$
$947$	−28.1206	+	16.2354i	−0.913796	+	0.527580i	−0.0321454	+	0.999483i	$0.510234\pi$
$948$		0			0
$949$	−10.7209	−	6.18973i	−0.348016	−	0.200927i
$950$	−9.27179	+	0.730392i	−0.300816	+	0.0236970i
$951$		0			0
$952$	−17.0676	−	17.9776i	−0.553164	−	0.582656i
$953$		−	11.0705i		−	0.358607i	−0.983794	−	0.179304i	$-0.942616\pi$
$953$		−	11.0705i		−	0.358607i	0.983794	−	0.179304i	$-0.0573844\pi$
$954$		0			0
$955$	15.4772			0.500832
$956$	29.6708	−	4.70387i	0.959622	−	0.152134i
$957$		0			0
$958$	54.0260	−	4.25593i	1.74550	−	0.137503i
$959$	17.9101	−	31.0212i	0.578347	−	1.00173i
$960$		0			0
$961$	−2.60055	−	4.50429i	−0.0838888	−	0.145300i
$962$	−3.94665	−	5.74151i	−0.127245	−	0.185114i
$963$		0			0
$964$	18.4462	−	48.0751i	0.594111	−	1.54839i
$965$	−2.34938	−	4.06924i	−0.0756291	−	0.130993i
$966$		0			0
$967$	40.9201	+	23.6252i	1.31590	+	0.759736i	0.983066	−	0.183249i	$-0.0586616\pi$
$967$	40.9201	+	23.6252i	1.31590	+	0.759736i	0.332835	+	0.942985i	$0.391995\pi$
$968$	8.81525	−	29.7839i	0.283333	−	0.957292i
$969$		0			0
$970$	−2.02498	+	4.24627i	−0.0650183	+	0.136339i
$971$		−	33.9428i		−	1.08928i	−0.838671	−	0.544638i	$-0.816667\pi$
$971$		−	33.9428i		−	1.08928i	0.838671	−	0.544638i	$-0.183333\pi$
$972$		0			0
$973$		−	2.53809i		−	0.0813674i
$974$	2.88053	+	1.37368i	0.0922981	+	0.0440156i
$975$		0			0
$976$	10.6365	+	32.7032i	0.340468	+	1.04680i
$977$	−26.9476	−	15.5582i	−0.862131	−	0.497752i	0.00259421	−	0.999997i	$-0.499174\pi$
$977$	−26.9476	−	15.5582i	−0.862131	−	0.497752i	−0.864725	+	0.502245i	$0.832508\pi$
$978$		0			0
$979$	0.564544	+	0.977819i	0.0180429	+	0.0312512i
$980$	6.59800	−	17.1959i	0.210765	−	0.549304i
$981$		0			0
$982$	23.9080	−	16.4341i	0.762936	−	0.524434i
$983$	−18.2288	−	31.5733i	−0.581410	−	1.00703i	−0.995313	−	0.0967103i	$-0.969168\pi$
$983$	−18.2288	−	31.5733i	−0.581410	−	1.00703i	0.413903	−	0.910321i	$-0.364165\pi$
$984$		0			0
$985$	15.9824	−	27.6824i	0.509243	−	0.882034i
$986$	−3.95472	−	50.2023i	−0.125944	−	1.59877i
$987$		0			0
$988$	−0.877054	−	5.53223i	−0.0279028	−	0.176004i
$989$	14.9319			0.474806
$990$		0			0
$991$			21.5164i			0.683490i	0.939793	+	0.341745i	$0.111018\pi$
$991$			21.5164i			0.683490i	−0.939793	+	0.341745i	$0.888982\pi$
$992$	11.0053	+	26.5415i	0.349418	+	0.842692i
$993$		0			0
$994$	−2.77512	−	35.2281i	−0.0880215	−	1.11737i
$995$	72.5365	+	41.8790i	2.29956	+	1.32765i
$996$		0			0
$997$	−49.4923	+	28.5744i	−1.56744	+	0.904961i	−0.570971	+	0.820970i	$0.693433\pi$
$997$	−49.4923	+	28.5744i	−1.56744	+	0.904961i	−0.996467	+	0.0839906i	$0.973233\pi$
$998$	−3.00920	−	4.37772i	−0.0952544	−	0.138574i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.l.b.179.5		16
3.2	odd	2		72.2.l.b.59.4	yes	16
4.3	odd	2		864.2.p.b.719.8		16
8.3	odd	2	inner	216.2.l.b.179.8		16
8.5	even	2		864.2.p.b.719.1		16
9.2	odd	6	inner	216.2.l.b.35.8		16
9.4	even	3		648.2.f.b.323.10		16
9.5	odd	6		648.2.f.b.323.7		16
9.7	even	3		72.2.l.b.11.1	✓	16
12.11	even	2		288.2.p.b.239.7		16
24.5	odd	2		288.2.p.b.239.8		16
24.11	even	2		72.2.l.b.59.1	yes	16
36.7	odd	6		288.2.p.b.47.8		16
36.11	even	6		864.2.p.b.143.1		16
36.23	even	6		2592.2.f.b.1295.16		16
36.31	odd	6		2592.2.f.b.1295.2		16
72.5	odd	6		2592.2.f.b.1295.1		16
72.11	even	6	inner	216.2.l.b.35.5		16
72.13	even	6		2592.2.f.b.1295.15		16
72.29	odd	6		864.2.p.b.143.8		16
72.43	odd	6		72.2.l.b.11.4	yes	16
72.59	even	6		648.2.f.b.323.9		16
72.61	even	6		288.2.p.b.47.7		16
72.67	odd	6		648.2.f.b.323.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.l.b.11.1	✓	16	9.7	even	3
72.2.l.b.11.4	yes	16	72.43	odd	6
72.2.l.b.59.1	yes	16	24.11	even	2
72.2.l.b.59.4	yes	16	3.2	odd	2
216.2.l.b.35.5		16	72.11	even	6	inner
216.2.l.b.35.8		16	9.2	odd	6	inner
216.2.l.b.179.5		16	1.1	even	1	trivial
216.2.l.b.179.8		16	8.3	odd	2	inner
288.2.p.b.47.7		16	72.61	even	6
288.2.p.b.47.8		16	36.7	odd	6
288.2.p.b.239.7		16	12.11	even	2
288.2.p.b.239.8		16	24.5	odd	2
648.2.f.b.323.7		16	9.5	odd	6
648.2.f.b.323.8		16	72.67	odd	6
648.2.f.b.323.9		16	72.59	even	6
648.2.f.b.323.10		16	9.4	even	3
864.2.p.b.143.1		16	36.11	even	6
864.2.p.b.143.8		16	72.29	odd	6
864.2.p.b.719.1		16	8.5	even	2
864.2.p.b.719.8		16	4.3	odd	2
2592.2.f.b.1295.1		16	72.5	odd	6
2592.2.f.b.1295.2		16	36.31	odd	6
2592.2.f.b.1295.15		16	72.13	even	6
2592.2.f.b.1295.16		16	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.608741 - 1.27649i) q^{2} +(-1.25887 - 1.55411i) q^{4} +(1.74322 - 3.01934i) q^{5} +(-1.80802 + 1.04386i) q^{7} +(-2.75013 + 0.660890i) q^{8} +O(q^{10})\)	\(q+(0.608741 - 1.27649i) q^{2} +(-1.25887 - 1.55411i) q^{4} +(1.74322 - 3.01934i) q^{5} +(-1.80802 + 1.04386i) q^{7} +(-2.75013 + 0.660890i) q^{8} +(-2.79300 - 4.06320i) q^{10} +(0.116985 - 0.0675415i) q^{11} +(2.63890 + 1.52357i) q^{13} +(0.231866 + 2.94336i) q^{14} +(-0.830495 + 3.91283i) q^{16} -4.19800i q^{17} +0.919111 q^{19} +(-6.88686 + 1.09181i) q^{20} +(-0.0150025 - 0.190446i) q^{22} +(0.689877 - 1.19490i) q^{23} +(-3.57762 - 6.19662i) q^{25} +(3.55124 - 2.44108i) q^{26} +(3.89833 + 1.49577i) q^{28} +(4.24111 + 7.34582i) q^{29} +(4.39877 + 2.53963i) q^{31} +(4.48915 + 3.44202i) q^{32} +(-5.35871 - 2.55549i) q^{34} +7.27870i q^{35} -1.61676i q^{37} +(0.559500 - 1.17324i) q^{38} +(-2.79863 + 9.45566i) q^{40} +(-1.79408 - 1.03581i) q^{41} +(5.41106 + 9.37224i) q^{43} +(-0.252236 - 0.0967817i) q^{44} +(-1.10533 - 1.60801i) q^{46} +(-0.205809 - 0.356471i) q^{47} +(-1.32071 + 2.28754i) q^{49} +(-10.0878 + 0.794672i) q^{50} +(-0.954242 - 6.01912i) q^{52} -0.968137 q^{53} -0.470958i q^{55} +(4.28241 - 4.06565i) q^{56} +(11.9586 - 0.942050i) q^{58} +(-3.88770 - 2.24457i) q^{59} +(7.44553 - 4.29868i) q^{61} +(5.91953 - 4.06902i) q^{62} +(7.12645 - 3.63507i) q^{64} +(9.20037 - 5.31183i) q^{65} +(3.15416 - 5.46316i) q^{67} +(-6.52413 + 5.28473i) q^{68} +(9.29121 + 4.43084i) q^{70} -11.9687 q^{71} -4.06264 q^{73} +(-2.06379 - 0.984189i) q^{74} +(-1.15704 - 1.42840i) q^{76} +(-0.141008 + 0.244232i) q^{77} +(-10.8672 + 6.27416i) q^{79} +(10.3665 + 9.32847i) q^{80} +(-2.41434 + 1.65959i) q^{82} +(-5.23875 + 3.02459i) q^{83} +(-12.6752 - 7.31802i) q^{85} +(15.2575 - 1.20192i) q^{86} +(-0.277087 + 0.263062i) q^{88} +8.35848i q^{89} -6.36158 q^{91} +(-2.72547 + 0.432083i) q^{92} +(-0.580317 + 0.0457149i) q^{94} +(1.60221 - 2.77511i) q^{95} +(-0.477065 - 0.826300i) q^{97} +(2.11606 + 3.07840i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 5 q^{4}+O(q^{10}) \) 16 * q + 3 * q^2 - 5 * q^4	\( 16 q + 3 q^{2} - 5 q^{4} - 12 q^{11} + 18 q^{14} + 7 q^{16} - 4 q^{19} - 18 q^{20} - q^{22} - 14 q^{25} - 12 q^{28} - 27 q^{32} - 13 q^{34} + 15 q^{38} - 12 q^{40} + 36 q^{41} + 8 q^{43} + 12 q^{46} + 10 q^{49} - 51 q^{50} - 18 q^{52} + 66 q^{56} + 12 q^{58} - 12 q^{59} + 34 q^{64} + 6 q^{65} - 16 q^{67} + 9 q^{68} + 18 q^{70} - 4 q^{73} + 60 q^{74} - 7 q^{76} - 22 q^{82} - 54 q^{83} + 51 q^{86} - 13 q^{88} - 36 q^{91} - 84 q^{92} + 24 q^{94} + 8 q^{97}+O(q^{100}) \) 16 * q + 3 * q^2 - 5 * q^4 - 12 * q^11 + 18 * q^14 + 7 * q^16 - 4 * q^19 - 18 * q^20 - q^22 - 14 * q^25 - 12 * q^28 - 27 * q^32 - 13 * q^34 + 15 * q^38 - 12 * q^40 + 36 * q^41 + 8 * q^43 + 12 * q^46 + 10 * q^49 - 51 * q^50 - 18 * q^52 + 66 * q^56 + 12 * q^58 - 12 * q^59 + 34 * q^64 + 6 * q^65 - 16 * q^67 + 9 * q^68 + 18 * q^70 - 4 * q^73 + 60 * q^74 - 7 * q^76 - 22 * q^82 - 54 * q^83 + 51 * q^86 - 13 * q^88 - 36 * q^91 - 84 * q^92 + 24 * q^94 + 8 * q^97

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