LMFDB - Embedded newform 252.2.bf.g.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(19,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("252.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.1
Root			$0.0777157 - 1.41208i$ of defining polynomial
Character	$\chi$	$=$	252.199
Dual form			252.2.bf.g.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26175 + 0.638735i) q^{2} +(1.18404 - 1.61185i) q^{4} +(-0.380152 + 0.219481i) q^{5} +(-2.02350 + 1.70453i) q^{7} +(-0.464416 + 2.79004i) q^{8} +O(q^{10})$	\(q+(-1.26175 + 0.638735i) q^{2} +(1.18404 - 1.61185i) q^{4} +(-0.380152 + 0.219481i) q^{5} +(-2.02350 + 1.70453i) q^{7} +(-0.464416 + 2.79004i) q^{8} +(0.339468 - 0.519747i) q^{10} +(1.83249 + 1.05799i) q^{11} +3.84803i q^{13} +(1.46442 - 3.44318i) q^{14} +(-1.19612 - 3.81698i) q^{16} +(4.89158 + 2.82415i) q^{17} +(1.48792 + 2.57715i) q^{19} +(-0.0963438 + 0.872621i) q^{20} +(-2.98792 - 0.164445i) q^{22} +(-4.13127 + 2.38519i) q^{23} +(-2.40366 + 4.16325i) q^{25} +(-2.45787 - 4.85526i) q^{26} +(0.351547 + 5.27981i) q^{28} -7.02285 q^{29} +(3.71264 - 6.43048i) q^{31} +(3.94724 + 4.05208i) q^{32} +(-7.97584 - 0.438962i) q^{34} +(0.395127 - 1.09210i) q^{35} +(2.64335 + 4.57842i) q^{37} +(-3.52350 - 2.30134i) q^{38} +(-0.435811 - 1.16257i) q^{40} +6.81813i q^{41} -4.38646i q^{43} +(3.87505 - 1.70100i) q^{44} +(3.68914 - 5.64831i) q^{46} +(-0.844569 - 1.46284i) q^{47} +(1.18914 - 6.89826i) q^{49} +(0.373604 - 6.78829i) q^{50} +(6.20244 + 4.55620i) q^{52} +(5.35599 - 9.27685i) q^{53} -0.928833 q^{55} +(-3.81596 - 6.43727i) q^{56} +(8.86109 - 4.48574i) q^{58} +(4.05909 - 7.03055i) q^{59} +(5.35787 - 3.09337i) q^{61} +(-0.577061 + 10.4851i) q^{62} +(-7.56863 - 2.59148i) q^{64} +(-0.844569 - 1.46284i) q^{65} +(6.79878 + 3.92528i) q^{67} +(10.3439 - 4.54058i) q^{68} +(0.199011 + 1.63034i) q^{70} -1.16982i q^{71} +(-8.69036 - 5.01738i) q^{73} +(-6.25965 - 4.08843i) q^{74} +(5.91574 + 0.653140i) q^{76} +(-5.51142 + 0.982694i) q^{77} +(-13.4958 + 7.79180i) q^{79} +(1.29246 + 1.18851i) q^{80} +(-4.35498 - 8.60279i) q^{82} +5.49645 q^{83} -2.47939 q^{85} +(2.80178 + 5.53462i) q^{86} +(-3.80287 + 4.62137i) q^{88} +(9.02285 - 5.20934i) q^{89} +(-6.55909 - 7.78650i) q^{91} +(-1.04701 + 9.48314i) q^{92} +(2.00000 + 1.30628i) q^{94} +(-1.13127 - 0.653140i) q^{95} -2.22605i q^{97} +(2.90576 + 9.46343i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - q^{4} + 2 q^{7} - 4 q^{8}+O(q^{10}) $ 8 * q - q^2 - q^4 + 2 * q^7 - 4 * q^8	$ 8 q - q^{2} - q^{4} + 2 q^{7} - 4 q^{8} - 5 q^{10} - 6 q^{11} + 12 q^{14} - 17 q^{16} - 6 q^{19} - 22 q^{20} - 6 q^{22} + 2 q^{25} - 18 q^{26} + 13 q^{28} + 16 q^{29} + 6 q^{31} + 9 q^{32} - 28 q^{34} + 12 q^{35} + 6 q^{37} - 10 q^{38} - 17 q^{40} + 23 q^{44} + 24 q^{46} - 4 q^{47} + 4 q^{49} - 2 q^{50} + 16 q^{52} + 4 q^{53} - 8 q^{55} - 41 q^{56} + 37 q^{58} + 14 q^{59} + 12 q^{61} + 48 q^{62} + 2 q^{64} - 4 q^{65} + 42 q^{67} + 26 q^{68} + 3 q^{70} - 18 q^{73} + 10 q^{74} + 44 q^{76} - 8 q^{77} - 6 q^{79} + 39 q^{80} - 10 q^{82} - 4 q^{83} - 32 q^{85} - 36 q^{86} - 37 q^{88} - 34 q^{91} + 28 q^{92} + 16 q^{94} + 24 q^{95} + 53 q^{98}+O(q^{100}) $ 8 * q - q^2 - q^4 + 2 * q^7 - 4 * q^8 - 5 * q^10 - 6 * q^11 + 12 * q^14 - 17 * q^16 - 6 * q^19 - 22 * q^20 - 6 * q^22 + 2 * q^25 - 18 * q^26 + 13 * q^28 + 16 * q^29 + 6 * q^31 + 9 * q^32 - 28 * q^34 + 12 * q^35 + 6 * q^37 - 10 * q^38 - 17 * q^40 + 23 * q^44 + 24 * q^46 - 4 * q^47 + 4 * q^49 - 2 * q^50 + 16 * q^52 + 4 * q^53 - 8 * q^55 - 41 * q^56 + 37 * q^58 + 14 * q^59 + 12 * q^61 + 48 * q^62 + 2 * q^64 - 4 * q^65 + 42 * q^67 + 26 * q^68 + 3 * q^70 - 18 * q^73 + 10 * q^74 + 44 * q^76 - 8 * q^77 - 6 * q^79 + 39 * q^80 - 10 * q^82 - 4 * q^83 - 32 * q^85 - 36 * q^86 - 37 * q^88 - 34 * q^91 + 28 * q^92 + 16 * q^94 + 24 * q^95 + 53 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.26175	+	0.638735i	−0.892193	+	0.451654i
$2$	−1.26175	+	0.638735i	−0.892193	+	0.451654i
$3$		0			0
$3$		0			0
$4$	1.18404	−	1.61185i	0.592018	−	0.805925i
$5$	−0.380152	+	0.219481i	−0.170009	+	0.0981549i	−0.582590	−	0.812766i	$-0.697961\pi$
$5$	−0.380152	+	0.219481i	−0.170009	+	0.0981549i	0.412581	+	0.910921i	$0.364627\pi$
$6$		0			0
$7$	−2.02350	+	1.70453i	−0.764813	+	0.644253i
$7$	−2.02350	+	1.70453i	−0.764813	+	0.644253i
$8$	−0.464416	+	2.79004i	−0.164196	+	0.986428i
$9$		0			0
$10$	0.339468	−	0.519747i	0.107349	−	0.164358i
$11$	1.83249	+	1.05799i	0.552516	+	0.318995i	0.750136	−	0.661283i	$-0.229988\pi$
$11$	1.83249	+	1.05799i	0.552516	+	0.318995i	−0.197620	+	0.980279i	$0.563321\pi$
$12$		0			0
$13$			3.84803i			1.06725i	0.845721	+	0.533625i	$0.179171\pi$
$13$			3.84803i			1.06725i	−0.845721	+	0.533625i	$0.820829\pi$
$14$	1.46442	−	3.44318i	0.391382	−	0.920228i
$15$		0			0
$16$	−1.19612	−	3.81698i	−0.299029	−	0.954244i
$17$	4.89158	+	2.82415i	1.18638	+	0.684958i	0.957482	−	0.288492i	$-0.0931540\pi$
$17$	4.89158	+	2.82415i	1.18638	+	0.684958i	0.228899	+	0.973450i	$0.426487\pi$
$18$		0			0
$19$	1.48792	+	2.57715i	0.341352	+	0.591240i	0.984684	−	0.174348i	$-0.0557817\pi$
$19$	1.48792	+	2.57715i	0.341352	+	0.591240i	−0.643332	+	0.765588i	$0.722448\pi$
$20$	−0.0963438	+	0.872621i	−0.0215431	+	0.195124i
$21$		0			0
$22$	−2.98792	−	0.164445i	−0.637027	−	0.0350597i
$23$	−4.13127	+	2.38519i	−0.861430	+	0.497347i	−0.864491	−	0.502649i	$-0.832359\pi$
$23$	−4.13127	+	2.38519i	−0.861430	+	0.497347i	0.00306100	+	0.999995i	$0.499026\pi$
$24$		0			0
$25$	−2.40366	+	4.16325i	−0.480731	+	0.832651i
$26$	−2.45787	−	4.85526i	−0.482028	−	0.952194i
$27$		0			0
$28$	0.351547	+	5.27981i	0.0664362	+	0.997791i
$29$	−7.02285			−1.30411			−0.652055	−	0.758172i	$-0.726093\pi$
$29$	−7.02285			−1.30411			−0.652055	+	0.758172i	$0.726093\pi$
$30$		0			0
$31$	3.71264	−	6.43048i	0.666810	−	1.15495i	−0.311981	−	0.950088i	$-0.600993\pi$
$31$	3.71264	−	6.43048i	0.666810	−	1.15495i	0.978791	−	0.204861i	$-0.0656741\pi$
$32$	3.94724	+	4.05208i	0.697779	+	0.716313i
$33$		0			0
$34$	−7.97584	−	0.438962i	−1.36785	−	0.0752813i
$35$	0.395127	−	1.09210i	0.0667887	−	0.184599i
$36$		0			0
$37$	2.64335	+	4.57842i	0.434564	+	0.752688i	0.997260	−	0.0739766i	$-0.0235690\pi$
$37$	2.64335	+	4.57842i	0.434564	+	0.752688i	−0.562696	+	0.826664i	$0.690236\pi$
$38$	−3.52350	−	2.30134i	−0.571588	−	0.373327i
$39$		0			0
$40$	−0.435811	−	1.16257i	−0.0689078	−	0.183818i
$41$			6.81813i			1.06481i	0.846489	+	0.532407i	$0.178712\pi$
$41$			6.81813i			1.06481i	−0.846489	+	0.532407i	$0.821288\pi$
$42$		0			0
$43$		−	4.38646i		−	0.668928i	−0.942408	−	0.334464i	$-0.891445\pi$
$43$		−	4.38646i		−	0.668928i	0.942408	−	0.334464i	$-0.108555\pi$
$44$	3.87505	−	1.70100i	0.584186	−	0.256435i
$45$		0			0
$46$	3.68914	−	5.64831i	0.543934	−	0.832797i
$47$	−0.844569	−	1.46284i	−0.123193	−	0.213377i	0.797832	−	0.602880i	$-0.205980\pi$
$47$	−0.844569	−	1.46284i	−0.123193	−	0.213377i	−0.921025	+	0.389503i	$0.872647\pi$
$48$		0			0
$49$	1.18914	−	6.89826i	0.169877	−	0.985465i
$50$	0.373604	−	6.78829i	0.0528355	−	0.960010i
$51$		0			0
$52$	6.20244	+	4.55620i	0.860124	+	0.631832i
$53$	5.35599	−	9.27685i	0.735702	−	1.27427i	−0.218712	−	0.975789i	$-0.570186\pi$
$53$	5.35599	−	9.27685i	0.735702	−	1.27427i	0.954415	−	0.298484i	$-0.0964811\pi$
$54$		0			0
$55$	−0.928833			−0.125244
$56$	−3.81596	−	6.43727i	−0.509930	−	0.860216i
$57$		0			0
$58$	8.86109	−	4.48574i	1.16352	−	0.589006i
$59$	4.05909	−	7.03055i	0.528448	−	0.915299i	−0.471002	−	0.882132i	$-0.656107\pi$
$59$	4.05909	−	7.03055i	0.528448	−	0.915299i	0.999450	−	0.0331668i	$-0.0105593\pi$
$60$		0			0
$61$	5.35787	−	3.09337i	0.686005	−	0.396065i	−0.116109	−	0.993237i	$-0.537042\pi$
$61$	5.35787	−	3.09337i	0.686005	−	0.396065i	0.802114	+	0.597171i	$0.203709\pi$
$62$	−0.577061	+	10.4851i	−0.0732868	+	1.33160i
$63$		0			0
$64$	−7.56863	−	2.59148i	−0.946079	−	0.323935i
$65$	−0.844569	−	1.46284i	−0.104756	−	0.181442i
$66$		0			0
$67$	6.79878	+	3.92528i	0.830604	+	0.479549i	0.854059	−	0.520176i	$-0.174134\pi$
$67$	6.79878	+	3.92528i	0.830604	+	0.479549i	−0.0234557	+	0.999725i	$0.507467\pi$
$68$	10.3439	−	4.54058i	1.25438	−	0.550627i
$69$		0			0
$70$	0.199011	+	1.63034i	0.0237864	+	0.194863i
$71$		−	1.16982i		−	0.138833i	−0.997588	−	0.0694163i	$-0.977886\pi$
$71$		−	1.16982i		−	0.138833i	0.997588	−	0.0694163i	$-0.0221137\pi$
$72$		0			0
$73$	−8.69036	−	5.01738i	−1.01713	−	0.587240i	−0.103858	−	0.994592i	$-0.533119\pi$
$73$	−8.69036	−	5.01738i	−1.01713	−	0.587240i	−0.913271	+	0.407352i	$0.866452\pi$
$74$	−6.25965	−	4.08843i	−0.727669	−	0.475270i
$75$		0			0
$76$	5.91574	+	0.653140i	0.678581	+	0.0749203i
$77$	−5.51142	+	0.982694i	−0.628085	+	0.111988i
$78$		0			0
$79$	−13.4958	+	7.79180i	−1.51840	+	0.876646i	−0.518630	+	0.854999i	$0.673558\pi$
$79$	−13.4958	+	7.79180i	−1.51840	+	0.876646i	−0.999766	+	0.0216472i	$0.993109\pi$
$80$	1.29246	+	1.18851i	0.144501	+	0.132879i
$81$		0			0
$82$	−4.35498	−	8.60279i	−0.480927	−	0.950019i
$83$	5.49645			0.603314			0.301657	−	0.953417i	$-0.402460\pi$
$83$	5.49645			0.603314			0.301657	+	0.953417i	$0.402460\pi$
$84$		0			0
$85$	−2.47939			−0.268928
$86$	2.80178	+	5.53462i	0.302124	+	0.596814i
$87$		0			0
$88$	−3.80287	+	4.62137i	−0.405387	+	0.492640i
$89$	9.02285	−	5.20934i	0.956420	−	0.552189i	0.0613507	−	0.998116i	$-0.480459\pi$
$89$	9.02285	−	5.20934i	0.956420	−	0.552189i	0.895069	+	0.445927i	$0.147126\pi$
$90$		0			0
$91$	−6.55909	−	7.78650i	−0.687579	−	0.816247i
$92$	−1.04701	+	9.48314i	−0.109158	+	0.988686i
$93$		0			0
$94$	2.00000	+	1.30628i	0.206284	+	0.134733i
$95$	−1.13127	−	0.653140i	−0.116066	−	0.0670108i
$96$		0			0
$97$		−	2.22605i		−	0.226021i	−0.993594	−	0.113011i	$-0.963951\pi$
$97$		−	2.22605i		−	0.226021i	0.993594	−	0.113011i	$-0.0360494\pi$
$98$	2.90576	+	9.46343i	0.293526	+	0.955951i
$99$		0			0
$100$	3.86452	+	8.80378i	0.386452	+	0.880378i
$101$	0.664978	+	0.383925i	0.0661678	+	0.0382020i	0.532719	−	0.846292i	$-0.321170\pi$
$101$	0.664978	+	0.383925i	0.0661678	+	0.0382020i	−0.466551	+	0.884494i	$0.654504\pi$
$102$		0			0
$103$	4.31939	+	7.48141i	0.425602	+	0.737165i	0.996476	−	0.0838727i	$-0.0267289\pi$
$103$	4.31939	+	7.48141i	0.425602	+	0.737165i	−0.570874	+	0.821038i	$0.693396\pi$
$104$	−10.7361	−	1.78709i	−1.05277	−	0.175238i
$105$		0			0
$106$	−0.832489	+	15.1261i	−0.0808585	+	1.46918i
$107$	2.20346	−	1.27217i	0.213016	−	0.122985i	−0.389696	−	0.920943i	$-0.627420\pi$
$107$	2.20346	−	1.27217i	0.213016	−	0.122985i	0.602712	+	0.797959i	$0.294087\pi$
$108$		0			0
$109$	3.40366	−	5.89531i	0.326011	−	0.564668i	−0.655705	−	0.755017i	$-0.727629\pi$
$109$	3.40366	−	5.89531i	0.326011	−	0.564668i	0.981716	+	0.190349i	$0.0609620\pi$
$110$	1.17196	−	0.593278i	0.111742	−	0.0565668i
$111$		0			0
$112$	8.92651	+	5.68485i	0.843475	+	0.537168i
$113$	−13.6408			−1.28322			−0.641610	−	0.767031i	$-0.721733\pi$
$113$	−13.6408			−1.28322			−0.641610	+	0.767031i	$0.721733\pi$
$114$		0			0
$115$	1.04701	−	1.81347i	0.0976340	−	0.169107i
$116$	−8.31531	+	11.3198i	−0.772057	+	1.05101i
$117$		0			0
$118$	−0.630909	+	11.4635i	−0.0580799	+	1.05530i
$119$	−14.7120	+	2.62317i	−1.34865	+	0.240465i
$120$		0			0
$121$	−3.26132	−	5.64878i	−0.296484	−	0.513525i
$122$	−4.78446	+	7.32532i	−0.433165	+	0.663203i
$123$		0			0
$124$	−5.96907	−	13.5981i	−0.536038	−	1.22115i
$125$		−	4.30504i		−	0.385054i
$126$		0			0
$127$			3.51914i			0.312273i	0.987735	+	0.156137i	$0.0499040\pi$
$127$			3.51914i			0.312273i	−0.987735	+	0.156137i	$0.950096\pi$
$128$	11.2050	−	1.56454i	0.990392	−	0.138287i
$129$		0			0
$130$	2.00000	+	1.30628i	0.175412	+	0.114568i
$131$	9.80833	+	16.9885i	0.856958	+	1.48429i	0.874817	+	0.484454i	$0.160982\pi$
$131$	9.80833	+	16.9885i	0.856958	+	1.48429i	−0.0178590	+	0.999841i	$0.505685\pi$
$132$		0			0
$133$	−7.40366	−	2.67867i	−0.641978	−	0.232270i
$134$	−11.0856	−	0.610111i	−0.957649	−	0.0527056i
$135$		0			0
$136$	−10.1512	+	12.3361i	−0.870460	+	1.05781i
$137$	−1.68914	+	2.92567i	−0.144313	+	0.249957i	−0.929116	−	0.369788i	$-0.879430\pi$
$137$	−1.68914	+	2.92567i	−0.144313	+	0.249957i	0.784804	+	0.619745i	$0.212764\pi$
$138$		0			0
$139$	16.4481			1.39511			0.697556	−	0.716530i	$-0.254271\pi$
$139$	16.4481			1.39511			0.697556	+	0.716530i	$0.254271\pi$
$140$	−1.29246	−	1.92997i	−0.109233	−	0.163113i
$141$		0			0
$142$	0.747207	+	1.47603i	0.0627042	+	0.123866i
$143$	−4.07117	+	7.05147i	−0.340448	+	0.589673i
$144$		0			0
$145$	2.66975	−	1.54138i	0.221711	−	0.128005i
$146$	14.1699	+	0.779858i	1.17271	+	0.0645415i
$147$		0			0
$148$	10.5095	+	1.16033i	0.863879	+	0.0953786i
$149$	3.23970	+	5.61132i	0.265406	+	0.459697i	0.967670	−	0.252220i	$-0.0811606\pi$
$149$	3.23970	+	5.61132i	0.265406	+	0.459697i	−0.702264	+	0.711917i	$0.747827\pi$
$150$		0			0
$151$	−6.72827	−	3.88457i	−0.547539	−	0.316122i	0.200590	−	0.979675i	$-0.435714\pi$
$151$	−6.72827	−	3.88457i	−0.547539	−	0.316122i	−0.748129	+	0.663554i	$0.769047\pi$
$152$	−7.88137	+	2.95448i	−0.639264	+	0.239640i
$153$		0			0
$154$	6.32637	−	4.76025i	0.509793	−	0.383592i
$155$			3.25942i			0.261803i
$156$		0			0
$157$	7.32996	+	4.23195i	0.584994	+	0.337747i	0.763116	−	0.646262i	$-0.223669\pi$
$157$	7.32996	+	4.23195i	0.584994	+	0.337747i	−0.178121	+	0.984009i	$0.557002\pi$
$158$	12.0515	−	18.4516i	0.958762	−	1.46793i
$159$		0			0
$160$	−2.38990	−	0.674063i	−0.188939	−	0.0532893i
$161$	4.29401	−	11.8683i	0.338415	−	0.935356i
$162$		0			0
$163$	−6.02285	+	3.47729i	−0.471746	+	0.272363i	−0.716970	−	0.697104i	$-0.754472\pi$
$163$	−6.02285	+	3.47729i	−0.471746	+	0.272363i	0.245224	+	0.969466i	$0.421138\pi$
$164$	10.9898	+	8.07291i	0.858159	+	0.630389i
$165$		0			0
$166$	−6.93516	+	3.51077i	−0.538273	+	0.272489i
$167$	−8.12021			−0.628361			−0.314180	−	0.949363i	$-0.601730\pi$
$167$	−8.12021			−0.628361			−0.314180	+	0.949363i	$0.601730\pi$
$168$		0			0
$169$	−1.80731			−0.139024
$170$	3.12838	−	1.58367i	0.239936	−	0.121462i
$171$		0			0
$172$	−7.07031	−	5.19372i	−0.539106	−	0.396018i
$173$	1.22660	−	0.708177i	0.0932565	−	0.0538417i	−0.452646	−	0.891690i	$-0.649520\pi$
$173$	1.22660	−	0.708177i	0.0932565	−	0.0538417i	0.545903	+	0.837848i	$0.316187\pi$
$174$		0			0
$175$	−2.23260	−	12.5215i	−0.168768	−	0.946534i
$176$	1.84645	−	8.26004i	0.139181	−	0.622624i
$177$		0			0
$178$	−8.05721	+	12.3361i	−0.603913	+	0.924630i
$179$	−9.29401	−	5.36590i	−0.694667	−	0.401066i	0.110691	−	0.993855i	$-0.464694\pi$
$179$	−9.29401	−	5.36590i	−0.694667	−	0.401066i	−0.805358	+	0.592789i	$0.798027\pi$
$180$		0			0
$181$		−	1.21426i		−	0.0902549i	−0.998981	−	0.0451275i	$-0.985631\pi$
$181$		−	1.21426i		−	0.0902549i	0.998981	−	0.0451275i	$-0.0143694\pi$
$182$	13.2494	+	5.63511i	0.982114	+	0.417702i
$183$		0			0
$184$	−4.73615	−	12.6341i	−0.349153	−	0.931401i
$185$	−2.00975	−	1.16033i	−0.147760	−	0.0853092i
$186$		0			0
$187$	5.97584	+	10.3505i	0.436997	+	0.756901i
$188$	−3.35787	−	0.370733i	−0.244898	−	0.0270385i
$189$		0			0
$190$	1.84457	+	0.101518i	0.133819	+	0.00736493i
$191$	−5.67473	+	3.27631i	−0.410609	+	0.237065i	−0.691051	−	0.722806i	$-0.742852\pi$
$191$	−5.67473	+	3.27631i	−0.410609	+	0.237065i	0.280442	+	0.959871i	$0.409519\pi$
$192$		0			0
$193$	1.61818	−	2.80276i	0.116479	−	0.201747i	−0.801891	−	0.597470i	$-0.796173\pi$
$193$	1.61818	−	2.80276i	0.116479	−	0.201747i	0.918370	+	0.395723i	$0.129506\pi$
$194$	1.42185	+	2.80872i	0.102083	+	0.201654i
$195$		0			0
$196$	−9.71097	−	10.0845i	−0.693641	−	0.720321i
$197$	19.2554			1.37189			0.685947	−	0.727652i	$-0.259388\pi$
$197$	19.2554			1.37189			0.685947	+	0.727652i	$0.259388\pi$
$198$		0			0
$199$	4.31086	−	7.46663i	0.305589	−	0.529296i	−0.671803	−	0.740730i	$-0.734480\pi$
$199$	4.31086	−	7.46663i	0.305589	−	0.529296i	0.977392	+	0.211434i	$0.0678133\pi$
$200$	−10.4993	−	8.63978i	−0.742416	−	0.610925i
$201$		0			0
$202$	−1.08426	−	0.0596741i	−0.0762886	−	0.00419865i
$203$	14.2108	−	11.9707i	0.997400	−	0.840177i
$204$		0			0
$205$	−1.49645	−	2.59193i	−0.104517	−	0.181028i
$206$	−10.2286	−	6.68073i	−0.712663	−	0.465469i
$207$		0			0
$208$	14.6878	−	4.60269i	1.01842	−	0.319139i
$209$			6.29681i			0.435559i
$210$		0			0
$211$		−	6.09787i		−	0.419795i	−0.977723	−	0.209897i	$-0.932687\pi$
$211$		−	6.09787i		−	0.419795i	0.977723	−	0.209897i	$-0.0673130\pi$
$212$	−8.61120	−	19.6172i	−0.591419	−	1.34731i
$213$		0			0
$214$	−1.96764	+	3.01258i	−0.134505	+	0.205936i
$215$	0.962744	+	1.66752i	0.0656586	+	0.113724i
$216$		0			0
$217$	3.44842	+	19.3404i	0.234094	+	1.31291i
$218$	−0.529035	+	9.61245i	−0.0358308	+	0.651037i
$219$		0			0
$220$	−1.09977	+	1.49714i	−0.0741466	+	0.100937i
$221$	−10.8674	+	18.8229i	−0.731022	+	1.26617i
$222$		0			0
$223$	2.44944			0.164027			0.0820134	−	0.996631i	$-0.473865\pi$
$223$	2.44944			0.164027			0.0820134	+	0.996631i	$0.473865\pi$
$224$	−14.8941	−	1.47120i	−0.995157	−	0.0982988i
$225$		0			0
$226$	17.2113	−	8.71286i	1.14488	−	0.579571i
$227$	11.6398	−	20.1607i	0.772561	−	1.33811i	−0.163595	−	0.986528i	$-0.552309\pi$
$227$	11.6398	−	20.1607i	0.772561	−	1.33811i	0.936155	−	0.351587i	$-0.114358\pi$
$228$		0			0
$229$	−10.1385	+	5.85346i	−0.669970	+	0.386808i	−0.796065	−	0.605211i	$-0.793089\pi$
$229$	−10.1385	+	5.85346i	−0.669970	+	0.386808i	0.126095	+	0.992018i	$0.459756\pi$
$230$	−0.162738	+	2.95691i	−0.0107306	+	0.194973i
$231$		0			0
$232$	3.26153	−	19.5940i	0.214130	−	1.28641i
$233$	−4.08426	−	7.07415i	−0.267569	−	0.463443i	0.700664	−	0.713491i	$-0.252887\pi$
$233$	−4.08426	−	7.07415i	−0.267569	−	0.463443i	−0.968234	+	0.250048i	$0.919554\pi$
$234$		0			0
$235$	0.642129	+	0.370733i	0.0418879	+	0.0241840i
$236$	−6.52607	−	14.8671i	−0.424811	−	0.967763i
$237$		0			0
$238$	16.8874	−	12.7068i	1.09465	−	0.823662i
$239$		−	18.1984i		−	1.17716i	−0.808439	−	0.588579i	$-0.799687\pi$
$239$		−	18.1984i		−	1.17716i	0.808439	−	0.588579i	$-0.200313\pi$
$240$		0			0
$241$	25.0409	+	14.4574i	1.61303	+	0.931282i	0.988663	+	0.150149i	$0.0479753\pi$
$241$	25.0409	+	14.4574i	1.61303	+	0.931282i	0.624364	+	0.781133i	$0.285358\pi$
$242$	7.72305	+	5.04424i	0.496456	+	0.324256i
$243$		0			0
$244$	1.35787	−	12.2987i	0.0869288	−	0.787346i
$245$	1.06198	+	2.88338i	0.0678476	+	0.184212i
$246$		0			0
$247$	−9.91696	+	5.72556i	−0.631001	+	0.364309i
$248$	16.2171	+	13.3448i	1.02979	+	0.847398i
$249$		0			0
$250$	2.74978	+	5.43189i	0.173911	+	0.343543i
$251$	20.3586			1.28502			0.642512	−	0.766276i	$-0.277892\pi$
$251$	20.3586			1.28502			0.642512	+	0.766276i	$0.277892\pi$
$252$		0			0
$253$	−10.0940			−0.634605
$254$	−2.24780	−	4.44028i	−0.141039	−	0.278608i
$255$		0			0
$256$	−13.1386	+	9.13109i	−0.821163	+	0.570693i
$257$	−18.4350	+	10.6435i	−1.14995	+	0.663922i	−0.948874	−	0.315655i	$-0.897776\pi$
$257$	−18.4350	+	10.6435i	−1.14995	+	0.663922i	−0.201072	+	0.979577i	$0.564442\pi$
$258$		0			0
$259$	−13.1529	−	4.75877i	−0.817281	−	0.295696i
$260$	−3.35787	−	0.370733i	−0.208246	−	0.0229919i
$261$		0			0
$262$	−23.2268	−	15.1704i	−1.43496	−	0.937230i
$263$	17.4760	+	10.0898i	1.07762	+	0.622164i	0.930253	−	0.366918i	$-0.119587\pi$
$263$	17.4760	+	10.0898i	1.07762	+	0.622164i	0.147366	+	0.989082i	$0.452920\pi$
$264$		0			0
$265$			4.70215i			0.288851i
$266$	11.0525	−	1.34915i	0.677675	−	0.0827217i
$267$		0			0
$268$	14.3770	−	6.31094i	0.878213	−	0.385502i
$269$	−14.1764	−	8.18475i	−0.864351	−	0.499033i	0.00111621	−	0.999999i	$-0.499645\pi$
$269$	−14.1764	−	8.18475i	−0.864351	−	0.499033i	−0.865467	+	0.500966i	$0.832978\pi$
$270$		0			0
$271$	6.72696	+	11.6514i	0.408634	+	0.707775i	0.994737	−	0.102462i	$-0.0326720\pi$
$271$	6.72696	+	11.6514i	0.408634	+	0.707775i	−0.586103	+	0.810236i	$0.699339\pi$
$272$	4.92883	−	22.0490i	0.298854	−	1.33692i
$273$		0			0
$274$	0.262545	−	4.77038i	0.0158609	−	0.288189i
$275$	−8.80935	+	5.08608i	−0.531224	+	0.306702i
$276$		0			0
$277$	−1.40366	+	2.43120i	−0.0843375	+	0.146077i	−0.905109	−	0.425180i	$-0.860211\pi$
$277$	−1.40366	+	2.43120i	−0.0843375	+	0.146077i	0.820771	+	0.571257i	$0.193544\pi$
$278$	−20.7535	+	10.5060i	−1.24471	+	0.630107i
$279$		0			0
$280$	2.86350	+	1.60961i	0.171127	+	0.0961926i
$281$	25.4502			1.51823			0.759115	−	0.650957i	$-0.225632\pi$
$281$	25.4502			1.51823			0.759115	+	0.650957i	$0.225632\pi$
$282$		0			0
$283$	−2.36975	+	4.10452i	−0.140867	+	0.243988i	−0.927823	−	0.373020i	$-0.878322\pi$
$283$	−2.36975	+	4.10452i	−0.140867	+	0.243988i	0.786957	+	0.617008i	$0.211656\pi$
$284$	−1.88558	−	1.38511i	−0.111889	−	0.0821914i
$285$		0			0
$286$	0.632787	−	11.4976i	0.0374175	−	0.679867i
$287$	−11.6217	−	13.7965i	−0.686009	−	0.814382i
$288$		0			0
$289$	7.45168	+	12.9067i	0.438334	+	0.759217i
$290$	−2.38403	+	3.65010i	−0.139995	+	0.214341i
$291$		0			0
$292$	−18.3770	+	8.06679i	−1.07543	+	0.472073i
$293$			3.22818i			0.188592i	0.995544	+	0.0942960i	$0.0300600\pi$
$293$			3.22818i			0.188592i	−0.995544	+	0.0942960i	$0.969940\pi$
$294$		0			0
$295$			3.56357i			0.207479i
$296$	−14.0016	+	5.24876i	−0.813826	+	0.305078i
$297$		0			0
$298$	−7.67183	−	5.01079i	−0.444417	−	0.290267i
$299$	−9.17828	−	15.8972i	−0.530794	−	0.919362i
$300$		0			0
$301$	7.47686	+	8.87601i	0.430959	+	0.511605i
$302$	10.9706	+	0.603784i	0.631288	+	0.0347439i
$303$		0			0
$304$	8.05721	−	8.76193i	0.462113	−	0.502531i
$305$	−1.35787	+	2.35190i	−0.0777515	+	0.134669i
$306$		0			0
$307$	5.45523			0.311347			0.155673	−	0.987809i	$-0.450245\pi$
$307$	5.45523			0.311347			0.155673	+	0.987809i	$0.450245\pi$
$308$	−4.94177	+	10.0471i	−0.281584	+	0.572488i
$309$		0			0
$310$	−2.08190	−	4.11258i	−0.118244	−	0.233579i
$311$	−15.2625	+	26.4355i	−0.865460	+	1.49902i	0.00113066	+	0.999999i	$0.499640\pi$
$311$	−15.2625	+	26.4355i	−0.865460	+	1.49902i	−0.866590	+	0.499020i	$0.833693\pi$
$312$		0			0
$313$	−16.3093	+	9.41621i	−0.921859	+	0.532235i	−0.884228	−	0.467056i	$-0.845315\pi$
$313$	−16.3093	+	9.41621i	−0.921859	+	0.532235i	−0.0376312	+	0.999292i	$0.511981\pi$
$314$	−11.9517	−	0.657778i	−0.674472	−	0.0371206i
$315$		0			0
$316$	−3.42030	+	30.9790i	−0.192407	+	1.74270i
$317$	8.58259	+	14.8655i	0.482046	+	0.834929i	0.999788	−	0.0206085i	$-0.00656034\pi$
$317$	8.58259	+	14.8655i	0.482046	+	0.834929i	−0.517741	+	0.855537i	$0.673227\pi$
$318$		0			0
$319$	−12.8693	−	7.43009i	−0.720542	−	0.416005i
$320$	3.44601	−	0.676014i	0.192638	−	0.0377904i
$321$		0			0
$322$	2.16274	+	17.7176i	0.120525	+	0.987365i
$323$			16.8085i			0.935248i
$324$		0			0
$325$	−16.0203	−	9.24933i	−0.888647	−	0.513061i
$326$	5.37827	−	8.23448i	0.297875	−	0.456066i
$327$		0			0
$328$	−19.0228	−	3.16645i	−1.05036	−	0.174838i
$329$	4.20244	+	1.52046i	0.231688	+	0.0838256i
$330$		0			0
$331$	18.6081	−	10.7434i	1.02280	−	0.590511i	0.107883	−	0.994164i	$-0.465593\pi$
$331$	18.6081	−	10.7434i	1.02280	−	0.590511i	0.914912	+	0.403652i	$0.132259\pi$
$332$	6.50800	−	8.85945i	0.357173	−	0.486225i
$333$		0			0
$334$	10.2457	−	5.18666i	0.560619	−	0.283801i
$335$	−3.44610			−0.188280
$336$		0			0
$337$	5.91046			0.321964			0.160982	−	0.986957i	$-0.448534\pi$
$337$	5.91046			0.321964			0.160982	+	0.986957i	$0.448534\pi$
$338$	2.28038	−	1.15439i	0.124036	−	0.0627907i
$339$		0			0
$340$	−2.93569	+	3.99640i	−0.159210	+	0.216735i
$341$	13.6068	−	7.85586i	0.736847	−	0.425419i
$342$		0			0
$343$	9.35208	+	15.9856i	0.504965	+	0.863140i
$344$	12.2384	+	2.03714i	0.659850	+	0.109835i
$345$		0			0
$346$	−1.09533	+	1.67701i	−0.0588851	+	0.0901569i
$347$	2.43838	+	1.40780i	0.130899	+	0.0755746i	0.564020	−	0.825761i	$-0.309254\pi$
$347$	2.43838	+	1.40780i	0.130899	+	0.0755746i	−0.433121	+	0.901336i	$0.642588\pi$
$348$		0			0
$349$		−	9.54077i		−	0.510705i	−0.966848	−	0.255353i	$-0.917808\pi$
$349$		−	9.54077i		−	0.510705i	0.966848	−	0.255353i	$-0.0821916\pi$
$350$	10.8149	+	14.3730i	0.578080	+	0.768267i
$351$		0			0
$352$	2.94622	+	11.6015i	0.157034	+	0.618363i
$353$	−8.63351	−	4.98456i	−0.459516	−	0.265301i	0.252325	−	0.967643i	$-0.418805\pi$
$353$	−8.63351	−	4.98456i	−0.459516	−	0.265301i	−0.711841	+	0.702341i	$0.752138\pi$
$354$		0			0
$355$	0.256754	+	0.444711i	0.0136271	+	0.0236028i
$356$	2.28670	−	20.7115i	0.121195	−	1.09771i
$357$		0			0
$358$	15.1541	+	0.834029i	0.800920	+	0.0440798i
$359$	−6.00000	+	3.46410i	−0.316668	+	0.182828i	−0.649906	−	0.760014i	$-0.725192\pi$
$359$	−6.00000	+	3.46410i	−0.316668	+	0.182828i	0.333238	+	0.942843i	$0.391859\pi$
$360$		0			0
$361$	5.07218	−	8.78528i	0.266957	−	0.462383i
$362$	0.775587	+	1.53209i	0.0407639	+	0.0805248i
$363$		0			0
$364$	−20.3169	+	1.35276i	−1.06489	+	0.0709040i
$365$	4.40488			0.230562
$366$		0			0
$367$	8.95234	−	15.5059i	0.467308	−	0.809402i	−0.531994	−	0.846748i	$-0.678557\pi$
$367$	8.95234	−	15.5059i	0.467308	−	0.809402i	0.999302	+	0.0373465i	$0.0118905\pi$
$368$	14.0457	+	12.9160i	0.732183	+	0.673293i
$369$		0			0
$370$	3.27695	+	0.180352i	0.170361	+	0.00937604i
$371$	4.97482	+	27.9012i	0.258280	+	1.44856i
$372$		0			0
$373$	−7.23716	−	12.5351i	−0.374726	−	0.649045i	0.615560	−	0.788090i	$-0.288930\pi$
$373$	−7.23716	−	12.5351i	−0.374726	−	0.649045i	−0.990286	+	0.139045i	$0.955597\pi$
$374$	−14.1512	−	9.24274i	−0.731742	−	0.477931i
$375$		0			0
$376$	4.47360	−	1.67701i	0.230708	−	0.0864854i
$377$		−	27.0241i		−	1.39181i
$378$		0			0
$379$		−	21.5969i		−	1.10936i	−0.832064	−	0.554679i	$-0.812841\pi$
$379$		−	21.5969i		−	1.10936i	0.832064	−	0.554679i	$-0.187159\pi$
$380$	−2.39223	+	1.05010i	−0.122719	+	0.0538689i
$381$		0			0
$382$	5.06741	−	7.75853i	0.259271	−	0.396961i
$383$	0.318169	+	0.551085i	0.0162577	+	0.0281591i	0.874040	−	0.485854i	$-0.161491\pi$
$383$	0.318169	+	0.551085i	0.0162577	+	0.0281591i	−0.857782	+	0.514013i	$0.828158\pi$
$384$		0			0
$385$	1.87950	−	1.58323i	0.0957881	−	0.0806887i
$386$	−0.251515	+	4.56997i	−0.0128018	+	0.232606i
$387$		0			0
$388$	−3.58806	−	2.63572i	−0.182156	−	0.133809i
$389$	−0.509547	+	0.882561i	−0.0258351	+	0.0447476i	−0.878654	−	0.477459i	$-0.841558\pi$
$389$	−0.509547	+	0.882561i	−0.0258351	+	0.0447476i	0.852819	+	0.522207i	$0.174891\pi$
$390$		0			0
$391$	−26.9446			−1.36265
$392$	18.6942	+	6.52140i	0.944197	+	0.329381i
$393$		0			0
$394$	−24.2956	+	12.2991i	−1.22399	+	0.619621i
$395$	3.42030	−	5.92414i	0.172094	−	0.298076i
$396$		0			0
$397$	25.8035	−	14.8976i	1.29504	−	0.747691i	0.315496	−	0.948927i	$-0.397829\pi$
$397$	25.8035	−	14.8976i	1.29504	−	0.747691i	0.979543	+	0.201236i	$0.0644957\pi$
$398$	−0.670043	+	12.1745i	−0.0335862	+	0.610254i
$399$		0			0
$400$	18.7661	+	4.19496i	0.938305	+	0.209748i
$401$	−3.39513	−	5.88053i	−0.169545	−	0.293660i	0.768715	−	0.639591i	$-0.220896\pi$
$401$	−3.39513	−	5.88053i	−0.169545	−	0.293660i	−0.938260	+	0.345931i	$0.887563\pi$
$402$		0			0
$403$	24.7447	+	14.2863i	1.23262	+	0.711654i
$404$	1.40619	−	0.617263i	0.0699605	−	0.0307100i
$405$		0			0
$406$	−10.2844	+	24.1809i	−0.510405	+	1.20008i
$407$			11.1865i			0.554496i
$408$		0			0
$409$	3.21574	+	1.85661i	0.159008	+	0.0918034i	0.577393	−	0.816467i	$-0.304070\pi$
$409$	3.21574	+	1.85661i	0.159008	+	0.0918034i	−0.418384	+	0.908270i	$0.637404\pi$
$410$	3.54370	+	2.31454i	0.175011	+	0.114307i
$411$		0			0
$412$	17.1732	+	1.89605i	0.846064	+	0.0934116i
$413$	3.77021	+	21.1452i	0.185520	+	1.04049i
$414$		0			0
$415$	−2.08949	+	1.20637i	−0.102569	+	0.0592182i
$416$	−15.5925	+	15.1891i	−0.764485	+	0.744705i
$417$		0			0
$418$	−4.02199	−	7.94501i	−0.196722	−	0.388603i
$419$	−20.7082			−1.01166			−0.505832	−	0.862632i	$-0.668814\pi$
$419$	−20.7082			−1.01166			−0.505832	+	0.862632i	$0.668814\pi$
$420$		0			0
$421$	15.6579			0.763118			0.381559	−	0.924344i	$-0.375387\pi$
$421$	15.6579			0.763118			0.381559	+	0.924344i	$0.375387\pi$
$422$	3.89492	+	7.69400i	0.189602	+	0.374538i
$423$		0			0
$424$	23.3954	+	19.2518i	1.13618	+	0.934948i
$425$	−23.5153	+	13.5766i	−1.14066	+	0.658561i
$426$		0			0
$427$	−5.56893	+	15.3921i	−0.269499	+	0.744876i
$428$	0.558433	−	5.05793i	0.0269929	−	0.244484i
$429$		0			0
$430$	−2.27985	−	1.48906i	−0.109944	−	0.0718089i
$431$	−10.2723	−	5.93071i	−0.494799	−	0.285672i	0.231764	−	0.972772i	$-0.425550\pi$
$431$	−10.2723	−	5.93071i	−0.494799	−	0.285672i	−0.726563	+	0.687100i	$0.758884\pi$
$432$		0			0
$433$		−	16.9269i		−	0.813454i	−0.913550	−	0.406727i	$-0.866670\pi$
$433$		−	16.9269i		−	0.813454i	0.913550	−	0.406727i	$-0.133330\pi$
$434$	−16.7045	−	22.2002i	−0.801839	−	1.06564i
$435$		0			0
$436$	−5.47229	−	12.4664i	−0.262075	−	0.597034i
$437$	−12.2940	−	7.09795i	−0.588102	−	0.339541i
$438$		0			0
$439$	−1.17640	−	2.03759i	−0.0561467	−	0.0972489i	0.836586	−	0.547836i	$-0.184548\pi$
$439$	−1.17640	−	2.03759i	−0.0561467	−	0.0972489i	−0.892733	+	0.450587i	$0.851215\pi$
$440$	0.431365	−	2.59148i	0.0205645	−	0.123544i
$441$		0			0
$442$	1.68914	−	30.6913i	0.0803441	−	1.45983i
$443$	1.38904	−	0.801965i	0.0659955	−	0.0381025i	−0.466639	−	0.884448i	$-0.654535\pi$
$443$	1.38904	−	0.801965i	0.0659955	−	0.0381025i	0.532635	+	0.846345i	$0.321202\pi$
$444$		0			0
$445$	−2.28670	+	3.96069i	−0.108400	+	0.187755i
$446$	−3.09059	+	1.56454i	−0.146344	+	0.0740833i
$447$		0			0
$448$	19.7324	−	7.65711i	0.932269	−	0.361765i
$449$	−1.35208			−0.0638086			−0.0319043	−	0.999491i	$-0.510157\pi$
$449$	−1.35208			−0.0638086			−0.0319043	+	0.999491i	$0.510157\pi$
$450$		0			0
$451$	−7.21350	+	12.4942i	−0.339670	+	0.588327i
$452$	−16.1512	+	21.9869i	−0.759690	+	1.03418i
$453$		0			0
$454$	−1.80919	+	32.8726i	−0.0849095	+	1.54279i
$455$	4.20244	+	1.52046i	0.197013	+	0.0712802i
$456$		0			0
$457$	−11.0734	−	19.1797i	−0.517992	−	0.897189i	−0.999782	−	0.0209017i	$-0.993346\pi$
$457$	−11.0734	−	19.1797i	−0.517992	−	0.897189i	0.481789	−	0.876287i	$-0.339987\pi$
$458$	9.05345	−	13.8614i	0.423040	−	0.647702i
$459$		0			0
$460$	−1.68335	−	3.83484i	−0.0784864	−	0.178800i
$461$		−	30.7842i		−	1.43376i	−0.697195	−	0.716882i	$-0.745569\pi$
$461$		−	30.7842i		−	1.43376i	0.697195	−	0.716882i	$-0.254431\pi$
$462$		0			0
$463$			13.8120i			0.641897i	0.947097	+	0.320948i	$0.104002\pi$
$463$			13.8120i			0.641897i	−0.947097	+	0.320948i	$0.895998\pi$
$464$	8.40014	+	26.8060i	0.389967	+	1.24444i
$465$		0			0
$466$	9.67183	+	6.31707i	0.448039	+	0.292632i
$467$	8.51330	+	14.7455i	0.393949	+	0.682339i	0.992966	−	0.118397i	$-0.0377754\pi$
$467$	8.51330	+	14.7455i	0.393949	+	0.682339i	−0.599018	+	0.800736i	$0.704442\pi$
$468$		0			0
$469$	−20.4481	+	3.64593i	−0.944207	+	0.168353i
$470$	−1.04701	−	0.0576236i	−0.0482949	−	0.00265798i
$471$		0			0
$472$	17.7304	+	14.5901i	0.816107	+	0.671564i
$473$	4.64082	−	8.03814i	0.213385	−	0.369594i
$474$		0			0
$475$	−14.3058			−0.656395
$476$	−13.1914	+	26.8194i	−0.604626	+	1.22927i
$477$		0			0
$478$	11.6240	+	22.9619i	0.531668	+	1.05025i
$479$	15.8903	−	27.5227i	0.726045	−	1.25755i	−0.232498	−	0.972597i	$-0.574690\pi$
$479$	15.8903	−	27.5227i	0.726045	−	1.25755i	0.958543	−	0.284950i	$-0.0919769\pi$
$480$		0			0
$481$	−17.6179	+	10.1717i	−0.803306	+	0.463789i
$482$	−40.8299	−	2.24713i	−1.85975	−	0.102354i
$483$		0			0
$484$	−12.9665	−	1.43160i	−0.589386	−	0.0650726i
$485$	0.488575	+	0.846237i	0.0221851	+	0.0384257i
$486$		0			0
$487$	−4.99690	−	2.88496i	−0.226431	−	0.130730i	0.382493	−	0.923958i	$-0.375065\pi$
$487$	−4.99690	−	2.88496i	−0.226431	−	0.130730i	−0.608925	+	0.793228i	$0.708399\pi$
$488$	6.14233	+	16.3853i	0.278050	+	0.741727i
$489$		0			0
$490$	−3.18167	−	2.95979i	−0.143733	−	0.133709i
$491$		−	22.6443i		−	1.02192i	−0.859603	−	0.510962i	$-0.829289\pi$
$491$		−	22.6443i		−	1.02192i	0.859603	−	0.510962i	$-0.170711\pi$
$492$		0			0
$493$	−34.3528	−	19.8336i	−1.54717	−	0.893261i
$494$	8.85563	−	13.5585i	0.398434	−	0.610028i
$495$		0			0
$496$	−28.9858	−	6.47946i	−1.30150	−	0.290936i
$497$	1.99400	+	2.36714i	0.0894433	+	0.106181i
$498$		0			0
$499$	−16.8383	+	9.72159i	−0.753785	+	0.435198i	−0.827060	−	0.562114i	$-0.809988\pi$
$499$	−16.8383	+	9.72159i	−0.753785	+	0.435198i	0.0732749	+	0.997312i	$0.476655\pi$
$500$	−6.93907	−	5.09732i	−0.310325	−	0.227959i
$501$		0			0
$502$	−25.6875	+	13.0037i	−1.14649	+	0.580385i
$503$	11.7570			0.524217			0.262108	−	0.965038i	$-0.415582\pi$
$503$	11.7570			0.524217			0.262108	+	0.965038i	$0.415582\pi$
$504$		0			0
$505$	−0.337057			−0.0149989
$506$	12.7361	−	6.44740i	0.566191	−	0.286622i
$507$		0			0
$508$	5.67232	+	4.16679i	0.251669	+	0.184871i
$509$	17.4476	−	10.0734i	0.773350	−	0.446494i	−0.0607186	−	0.998155i	$-0.519339\pi$
$509$	17.4476	−	10.0734i	0.773350	−	0.446494i	0.834068	+	0.551661i	$0.186006\pi$
$510$		0			0
$511$	26.1373	−	4.66031i	1.15624	−	0.206160i
$512$	10.7453	−	19.9133i	0.474881	−	0.880050i
$513$		0			0
$514$	16.4621	−	25.2045i	0.726112	−	1.11172i
$515$	−3.28405	−	1.89605i	−0.144713	−	0.0835499i
$516$		0			0
$517$		−	3.57417i		−	0.157192i
$518$	19.6353	−	2.39682i	0.862725	−	0.105310i
$519$		0			0
$520$	4.47360	−	1.67701i	0.196180	−	0.0735419i
$521$	31.0965	+	17.9536i	1.36236	+	0.786559i	0.989938	−	0.141504i	$-0.0451937\pi$
$521$	31.0965	+	17.9536i	1.36236	+	0.786559i	0.372423	+	0.928063i	$0.378527\pi$
$522$		0			0
$523$	−22.6480	−	39.2276i	−0.990330	−	1.71530i	−0.615312	−	0.788283i	$-0.710970\pi$
$523$	−22.6480	−	39.2276i	−0.990330	−	1.71530i	−0.375017	−	0.927018i	$-0.622363\pi$
$524$	38.9964	+	4.30548i	1.70356	+	0.188086i
$525$		0			0
$526$	−28.4951	−	1.56827i	−1.24245	−	0.0683799i
$527$	36.3213	−	20.9701i	1.58218	−	0.913473i
$528$		0			0
$529$	−0.121725	+	0.210835i	−0.00529241	+	0.00916672i
$530$	−3.00343	−	5.93295i	−0.130461	−	0.257711i
$531$		0			0
$532$	−13.0838	+	8.76193i	−0.567255	+	0.379878i
$533$	−26.2364			−1.13642
$534$		0			0
$535$	−0.558433	+	0.967234i	−0.0241432	+	0.0418172i
$536$	−14.1091	+	17.1459i	−0.609422	+	0.740590i
$537$		0			0
$538$	23.1150	+	1.27217i	0.996558	+	0.0548470i
$539$	9.47736	−	11.3829i	0.408219	−	0.490296i
$540$		0			0
$541$	16.9491	+	29.3568i	0.728701	+	1.26215i	0.957432	+	0.288657i	$0.0932089\pi$
$541$	16.9491	+	29.3568i	0.728701	+	1.26215i	−0.228732	+	0.973490i	$0.573458\pi$
$542$	−15.9299	−	10.4045i	−0.684249	−	0.446911i
$543$		0			0
$544$	7.86452	+	30.9686i	0.337189	+	1.32777i
$545$			2.98815i			0.127998i
$546$		0			0
$547$			7.83251i			0.334894i	0.985881	+	0.167447i	$0.0535523\pi$
$547$			7.83251i			0.334894i	−0.985881	+	0.167447i	$0.946448\pi$
$548$	2.71574	+	6.18674i	0.116011	+	0.264284i
$549$		0			0
$550$	7.86656	−	12.0442i	0.335431	−	0.513567i
$551$	−10.4494	−	18.0990i	−0.445161	−	0.771042i
$552$		0			0
$553$	14.0274	−	38.7708i	0.596506	−	1.64870i
$554$	0.218172	−	3.96414i	0.00926925	−	0.168420i
$555$		0			0
$556$	19.4752	−	26.5119i	0.825932	−	1.12436i
$557$	7.69701	−	13.3316i	0.326133	−	0.564879i	−0.655608	−	0.755101i	$-0.727588\pi$
$557$	7.69701	−	13.3316i	0.326133	−	0.564879i	0.981741	+	0.190223i	$0.0609210\pi$
$558$		0			0
$559$	16.8792			0.713914
$560$	−4.64115	−	0.201909i	−0.196124	−	0.00853223i
$561$		0			0
$562$	−32.1118	+	16.2559i	−1.35455	+	0.685714i
$563$	−8.22052	+	14.2384i	−0.346453	+	0.600075i	−0.985617	−	0.168996i	$-0.945947\pi$
$563$	−8.22052	+	14.2384i	−0.346453	+	0.600075i	0.639163	+	0.769071i	$0.279281\pi$
$564$		0			0
$565$	5.18559	−	2.99390i	0.218159	−	0.125954i
$566$	0.368333	−	6.69252i	0.0154822	−	0.281308i
$567$		0			0
$568$	3.26385	+	0.543286i	0.136948	+	0.0227958i
$569$	−18.6146	−	32.2415i	−0.780366	−	1.35163i	−0.931729	−	0.363155i	$-0.881700\pi$
$569$	−18.6146	−	32.2415i	−0.780366	−	1.35163i	0.151363	−	0.988478i	$-0.451634\pi$
$570$		0			0
$571$	17.9660	+	10.3727i	0.751854	+	0.434083i	0.826363	−	0.563137i	$-0.190406\pi$
$571$	17.9660	+	10.3727i	0.751854	+	0.434083i	−0.0745095	+	0.997220i	$0.523739\pi$
$572$	6.54549	+	14.9113i	0.273681	+	0.623473i
$573$		0			0
$574$	23.4760	+	9.98458i	0.979871	+	0.416748i
$575$		−	22.9327i		−	0.956361i
$576$		0			0
$577$	−13.3550	−	7.71054i	−0.555978	−	0.320994i	0.195552	−	0.980693i	$-0.437350\pi$
$577$	−13.3550	−	7.71054i	−0.555978	−	0.320994i	−0.751530	+	0.659699i	$0.770684\pi$
$578$	−17.6461	−	11.5254i	−0.733982	−	0.479393i
$579$		0			0
$580$	0.676608	−	6.12829i	0.0280946	−	0.254463i
$581$	−11.1221	+	9.36888i	−0.461422	+	0.388687i
$582$		0			0
$583$	19.6296	−	11.3332i	0.812975	−	0.469371i
$584$	18.0346	−	21.9163i	0.746279	−	0.906902i
$585$		0			0
$586$	−2.06195	−	4.07316i	−0.0851783	−	0.168261i
$587$	−34.0410			−1.40502			−0.702512	−	0.711672i	$-0.747938\pi$
$587$	−34.0410			−1.40502			−0.702512	+	0.711672i	$0.747938\pi$
$588$		0			0
$589$	22.0965			0.910469
$590$	−2.27618	−	4.49634i	−0.0937086	−	0.185111i
$591$		0			0
$592$	14.3140	−	15.5659i	0.588300	−	0.639756i
$593$	−27.5697	+	15.9173i	−1.13215	+	0.653647i	−0.944475	−	0.328584i	$-0.893429\pi$
$593$	−27.5697	+	15.9173i	−1.13215	+	0.653647i	−0.187675	+	0.982231i	$0.560095\pi$
$594$		0			0
$595$	5.01706	−	4.22620i	0.205679	−	0.173257i
$596$	12.8805	+	1.42210i	0.527606	+	0.0582516i
$597$		0			0
$598$	21.7348	+	14.1959i	0.888804	+	0.580514i
$599$	18.0000	+	10.3923i	0.735460	+	0.424618i	0.820416	−	0.571767i	$-0.193742\pi$
$599$	18.0000	+	10.3923i	0.735460	+	0.424618i	−0.0849563	+	0.996385i	$0.527075\pi$
$600$		0			0
$601$			15.8614i			0.646999i	0.946228	+	0.323499i	$0.104859\pi$
$601$			15.8614i			0.646999i	−0.946228	+	0.323499i	$0.895141\pi$
$602$	−15.1034	−	6.42360i	−0.615567	−	0.261806i
$603$		0			0
$604$	−14.2279	+	6.24549i	−0.578923	+	0.254125i
$605$	2.47960	+	1.43160i	0.100810	+	0.0582027i
$606$		0			0
$607$	−21.7151	−	37.6116i	−0.881388	−	1.52661i	−0.849798	−	0.527108i	$-0.823276\pi$
$607$	−21.7151	−	37.6116i	−0.881388	−	1.52661i	−0.0315900	−	0.999501i	$-0.510057\pi$
$608$	−4.56965	+	16.2018i	−0.185324	+	0.657070i
$609$		0			0
$610$	0.211056	−	3.83484i	0.00854539	−	0.155268i
$611$	5.62903	−	3.24992i	0.227726	−	0.131478i
$612$		0			0
$613$	−7.76030	+	13.4412i	−0.313436	+	0.542887i	−0.979104	−	0.203361i	$-0.934813\pi$
$613$	−7.76030	+	13.4412i	−0.313436	+	0.542887i	0.665668	+	0.746248i	$0.268147\pi$
$614$	−6.88315	+	3.48445i	−0.277781	+	0.140621i
$615$		0			0
$616$	−0.182159	−	15.8335i	−0.00733939	−	0.637949i
$617$	19.8053			0.797330			0.398665	−	0.917097i	$-0.369474\pi$
$617$	19.8053			0.797330			0.398665	+	0.917097i	$0.369474\pi$
$618$		0			0
$619$	−8.15665	+	14.1277i	−0.327844	+	0.567842i	−0.982084	−	0.188445i	$-0.939655\pi$
$619$	−8.15665	+	14.1277i	−0.327844	+	0.567842i	0.654240	+	0.756287i	$0.272989\pi$
$620$	5.25369	+	3.85927i	0.210993	+	0.154992i
$621$		0			0
$622$	2.37228	−	43.1038i	0.0951197	−	1.72830i
$623$	−9.37827	+	25.9209i	−0.375733	+	1.03850i
$624$		0			0
$625$	−11.0734	−	19.1797i	−0.442936	−	0.767188i
$626$	14.5639	−	22.2983i	0.582090	−	0.891218i
$627$		0			0
$628$	15.5002	−	6.80400i	0.618526	−	0.271509i
$629$			29.8609i			1.19063i
$630$		0			0
$631$			27.3095i			1.08717i	0.839353	+	0.543587i	$0.182934\pi$
$631$			27.3095i			1.08717i	−0.839353	+	0.543587i	$0.817066\pi$
$632$	−15.4718	−	41.2724i	−0.615433	−	1.64173i
$633$		0			0
$634$	−20.3242	−	13.2746i	−0.807177	−	0.527200i
$635$	−0.772384	−	1.33781i	−0.0306511	−	0.0530893i
$636$		0			0
$637$	26.5447	+	4.57583i	1.05174	+	0.181301i
$638$	20.9837	+	1.15487i	0.830753	+	0.0457217i
$639$		0			0
$640$	−3.91622	+	3.05405i	−0.154802	+	0.120722i
$641$	4.89533	−	8.47896i	0.193354	−	0.334899i	−0.753006	−	0.658014i	$-0.771397\pi$
$641$	4.89533	−	8.47896i	0.193354	−	0.334899i	0.946360	+	0.323115i	$0.104730\pi$
$642$		0			0
$643$	−7.26458			−0.286487			−0.143244	−	0.989687i	$-0.545753\pi$
$643$	−7.26458			−0.286487			−0.143244	+	0.989687i	$0.545753\pi$
$644$	−14.0457	−	20.9738i	−0.553478	−	0.826485i
$645$		0			0
$646$	−10.7361	−	21.2081i	−0.422408	−	0.834422i
$647$	−23.0419	+	39.9098i	−0.905872	+	1.56902i	−0.0861302	+	0.996284i	$0.527450\pi$
$647$	−23.0419	+	39.9098i	−0.905872	+	1.56902i	−0.819742	+	0.572733i	$0.805883\pi$
$648$		0			0
$649$	14.8765	−	8.58893i	0.583952	−	0.337145i
$650$	26.1215	+	1.43764i	1.02457	+	0.0563887i
$651$		0			0
$652$	−1.52640	+	13.8252i	−0.0597784	+	0.541435i
$653$	−3.38990	−	5.87149i	−0.132657	−	0.229769i	0.792043	−	0.610465i	$-0.209018\pi$
$653$	−3.38990	−	5.87149i	−0.132657	−	0.229769i	−0.924700	+	0.380696i	$0.875684\pi$
$654$		0			0
$655$	−7.45732	−	4.30548i	−0.291381	−	0.168229i
$656$	26.0246	−	8.15527i	1.01609	−	0.318410i
$657$		0			0
$658$	−6.27361	+	0.765800i	−0.244571	+	0.0298540i
$659$			29.3184i			1.14208i	0.820921	+	0.571041i	$0.193460\pi$
$659$			29.3184i			1.14208i	−0.820921	+	0.571041i	$0.806540\pi$
$660$		0			0
$661$	26.4813	+	15.2890i	1.03000	+	0.594674i	0.916986	−	0.398919i	$-0.130615\pi$
$661$	26.4813	+	15.2890i	1.03000	+	0.594674i	0.113019	+	0.993593i	$0.463948\pi$
$662$	−16.6167	+	25.4412i	−0.645825	+	0.988799i
$663$		0			0
$664$	−2.55264	+	15.3353i	−0.0990617	+	0.595125i
$665$	3.40243	−	0.606658i	0.131941	−	0.0235252i
$666$		0			0
$667$	29.0133	−	16.7508i	1.12340	−	0.648595i
$668$	−9.61462	+	13.0886i	−0.372001	+	0.506411i
$669$		0			0
$670$	4.34812	−	2.20114i	0.167982	−	0.0850375i
$671$	13.0910			0.505372
$672$		0			0
$673$	−6.37827			−0.245864			−0.122932	−	0.992415i	$-0.539230\pi$
$673$	−6.37827			−0.245864			−0.122932	+	0.992415i	$0.539230\pi$
$674$	−7.45754	+	3.77522i	−0.287254	+	0.145416i
$675$		0			0
$676$	−2.13992	+	2.91312i	−0.0823048	+	0.112043i
$677$	10.8219	−	6.24801i	0.415919	−	0.240131i	−0.277411	−	0.960751i	$-0.589476\pi$
$677$	10.8219	−	6.24801i	0.415919	−	0.240131i	0.693330	+	0.720621i	$0.256143\pi$
$678$		0			0
$679$	3.79437	+	4.50442i	0.145615	+	0.172864i
$680$	1.15147	−	6.91760i	0.0441569	−	0.265278i
$681$		0			0
$682$	−12.1505	+	18.6033i	−0.465268	+	0.712355i
$683$	−39.1917	−	22.6273i	−1.49963	−	0.865811i	−0.499629	−	0.866240i	$-0.666530\pi$
$683$	−39.1917	−	22.6273i	−1.49963	−	0.865811i	−1.00000		0.000428478i	$0.999864\pi$
$684$		0			0
$685$		−	1.48293i		−	0.0566600i
$686$	−22.0105	−	14.1963i	−0.840367	−	0.542019i
$687$		0			0
$688$	−16.7430	+	5.24671i	−0.638321	+	0.200029i
$689$	35.6976	+	20.6100i	1.35997	+	0.785179i
$690$		0			0
$691$	−5.29654	−	9.17388i	−0.201490	−	0.348991i	0.747519	−	0.664241i	$-0.231245\pi$
$691$	−5.29654	−	9.17388i	−0.201490	−	0.348991i	−0.949009	+	0.315250i	$0.897912\pi$
$692$	0.310863	−	2.81560i	0.0118172	−	0.107033i
$693$		0			0
$694$	−3.97584	−	0.218816i	−0.150921	−	0.00830615i
$695$	−6.25279	+	3.61005i	−0.237182	+	0.136937i
$696$		0			0
$697$	−19.2554	+	33.3514i	−0.729352	+	1.26327i
$698$	6.09402	+	12.0381i	0.230662	+	0.455648i
$699$		0			0
$700$	−22.8262	−	11.2273i	−0.862749	−	0.424351i
$701$	−29.6566			−1.12011			−0.560057	−	0.828454i	$-0.689221\pi$
$701$	−29.6566			−1.12011			−0.560057	+	0.828454i	$0.689221\pi$
$702$		0			0
$703$	−7.86620	+	13.6246i	−0.296679	+	0.513863i
$704$	−11.1277	−	12.7564i	−0.419390	−	0.480774i
$705$		0			0
$706$	14.0772	+	0.774757i	0.529801	+	0.0291584i
$707$	−2.00000	+	0.356603i	−0.0752177	+	0.0134114i
$708$		0			0
$709$	17.8506	+	30.9181i	0.670392	+	1.16115i	0.977793	+	0.209573i	$0.0672074\pi$
$709$	17.8506	+	30.9181i	0.670392	+	1.16115i	−0.307401	+	0.951580i	$0.599459\pi$
$710$	−0.608012	−	0.397117i	−0.0228183	−	0.0149036i
$711$		0			0
$712$	10.3439	+	27.5934i	0.387655	+	1.03411i
$713$			35.4214i			1.32654i
$714$		0			0
$715$		−	3.57417i		−	0.133667i
$716$	−19.6535	+	8.62712i	−0.734485	+	0.322411i
$717$		0			0
$718$	5.35787	−	8.20324i	0.199954	−	0.306142i
$719$	6.40447	+	11.0929i	0.238846	+	0.413694i	0.960384	−	0.278682i	$-0.0898974\pi$
$719$	6.40447	+	11.0929i	0.238846	+	0.413694i	−0.721537	+	0.692376i	$0.756564\pi$
$720$		0			0
$721$	−21.4926	−	7.77611i	−0.800427	−	0.289598i
$722$	−0.788376	+	14.3246i	−0.0293403	+	0.533107i
$723$		0			0
$724$	−1.95720	−	1.43772i	−0.0727387	−	0.0534325i
$725$	16.8805	−	29.2379i	0.626927	−	1.08587i
$726$		0			0
$727$	19.3286			0.716860			0.358430	−	0.933557i	$-0.383312\pi$
$727$	19.3286			0.716860			0.358430	+	0.933557i	$0.383312\pi$
$728$	24.7708	−	14.6839i	0.918066	−	0.544223i
$729$		0			0
$730$	−5.55786	+	2.81355i	−0.205706	+	0.104134i
$731$	12.3880	−	21.4567i	0.458188	−	0.793604i
$732$		0			0
$733$	−32.6407	+	18.8451i	−1.20561	+	0.696061i	−0.961798	−	0.273761i	$-0.911732\pi$
$733$	−32.6407	+	18.8451i	−1.20561	+	0.696061i	−0.243815	+	0.969822i	$0.578399\pi$
$734$	−1.39147	+	25.2828i	−0.0513602	+	0.933204i
$735$		0			0
$736$	−25.9721	−	7.32532i	−0.957344	−	0.270015i
$737$	8.30580	+	14.3861i	0.305948	+	0.529917i
$738$		0			0
$739$	−12.0072	−	6.93237i	−0.441693	−	0.255011i	0.262623	−	0.964899i	$-0.415413\pi$
$739$	−12.0072	−	6.93237i	−0.441693	−	0.255011i	−0.704315	+	0.709887i	$0.748746\pi$
$740$	−4.24990	+	1.86554i	−0.156229	+	0.0685787i
$741$		0			0
$742$	−24.0985	−	32.0268i	−0.884682	−	1.17574i
$743$			18.9927i			0.696773i	0.937351	+	0.348387i	$0.113270\pi$
$743$			18.9927i			0.696773i	−0.937351	+	0.348387i	$0.886730\pi$
$744$		0			0
$745$	−2.46315	−	1.42210i	−0.0902430	−	0.0521018i
$746$	17.1381	+	11.1936i	0.627471	+	0.409827i
$747$		0			0
$748$	23.7590	+	2.62317i	0.868715	+	0.0959125i
$749$	−2.29026	+	6.33010i	−0.0836841	+	0.231297i
$750$		0			0
$751$	25.2868	−	14.5993i	0.922728	−	0.532737i	0.0382233	−	0.999269i	$-0.487830\pi$
$751$	25.2868	−	14.5993i	0.922728	−	0.532737i	0.884504	+	0.466532i	$0.154497\pi$
$752$	−4.57341	+	4.97342i	−0.166775	+	0.181362i
$753$		0			0
$754$	17.2612	+	34.0977i	0.628617	+	1.24177i
$755$	3.41036			0.124116
$756$		0			0
$757$	−10.8022			−0.392614			−0.196307	−	0.980542i	$-0.562895\pi$
$757$	−10.8022			−0.392614			−0.196307	+	0.980542i	$0.562895\pi$
$758$	13.7947	+	27.2499i	0.501045	+	0.989762i
$759$		0			0
$760$	2.34767	−	2.85296i	0.0851589	−	0.103488i
$761$	0.203165	−	0.117298i	0.00736474	−	0.00425204i	−0.496313	−	0.868144i	$-0.665313\pi$
$761$	0.203165	−	0.117298i	0.00736474	−	0.00425204i	0.503678	+	0.863892i	$0.331980\pi$
$762$		0			0
$763$	3.16143	+	17.7308i	0.114451	+	0.641899i
$764$	−1.43817	+	13.0261i	−0.0520313	+	0.471267i
$765$		0			0
$766$	−0.753448	−	0.492107i	−0.0272232	−	0.0177806i
$767$	27.0537	+	15.6195i	0.976854	+	0.563987i
$768$		0			0
$769$			34.8540i			1.25687i	0.777863	+	0.628434i	$0.216304\pi$
$769$			34.8540i			1.25687i	−0.777863	+	0.628434i	$0.783696\pi$
$770$	−1.36020	+	3.19814i	−0.0490181	+	0.115253i
$771$		0			0
$772$	−2.60165	−	5.92683i	−0.0936355	−	0.213311i
$773$	−17.0362	−	9.83583i	−0.612748	−	0.353770i	0.161292	−	0.986907i	$-0.448434\pi$
$773$	−17.0362	−	9.83583i	−0.612748	−	0.353770i	−0.774040	+	0.633137i	$0.781767\pi$
$774$		0			0
$775$	17.8478	+	30.9133i	0.641113	+	1.11044i
$776$	6.21076	+	1.03381i	0.222953	+	0.0371118i
$777$		0			0
$778$	0.0791996	−	1.43904i	0.00283944	−	0.0515920i
$779$	−17.5714	+	10.1448i	−0.629560	+	0.363476i
$780$		0			0
$781$	1.23766	−	2.14369i	0.0442870	−	0.0767073i
$782$	33.9974	−	17.2104i	1.21574	−	0.615444i
$783$		0			0
$784$	−27.7528	+	3.71221i	−0.991172	+	0.132579i
$785$	−3.71533			−0.132606
$786$		0			0
$787$	−19.4781	+	33.7370i	−0.694319	+	1.20260i	0.276091	+	0.961131i	$0.410961\pi$
$787$	−19.4781	+	33.7370i	−0.694319	+	1.20260i	−0.970410	+	0.241464i	$0.922373\pi$
$788$	22.7991	−	31.0369i	0.812186	−	1.10564i
$789$		0			0
$790$	−0.531622	+	9.65946i	−0.0189143	+	0.343668i
$791$	27.6023	−	23.2512i	0.981423	−	0.826718i
$792$		0			0
$793$	11.9034	+	20.6172i	0.422701	+	0.732139i
$794$	−23.0419	+	35.2787i	−0.817728	+	1.25199i
$795$		0			0
$796$	−6.93087	−	15.7892i	−0.245658	−	0.559634i
$797$		−	20.4557i		−	0.724579i	−0.932066	−	0.362289i	$-0.881995\pi$
$797$		−	20.4557i		−	0.724579i	0.932066	−	0.362289i	$-0.118005\pi$
$798$		0			0
$799$		−	9.54077i		−	0.337528i
$800$	−26.3576	+	6.69355i	−0.931883	+	0.236653i
$801$		0			0
$802$	8.03991	+	5.25119i	0.283899	+	0.185426i
$803$	−10.6167	−	18.3886i	−0.374654	−	0.648919i
$804$		0			0
$805$	0.972496	+	5.45423i	0.0342760	+	0.192236i
$806$	−40.3468	−	2.22055i	−1.42116	−	0.0782154i
$807$		0			0
$808$	−1.37999	+	1.67701i	−0.0485480	+	0.0589972i
$809$	−24.4650	+	42.3746i	−0.860143	+	1.48981i	0.0116472	+	0.999932i	$0.496292\pi$
$809$	−24.4650	+	42.3746i	−0.860143	+	1.48981i	−0.871790	+	0.489879i	$0.837041\pi$
$810$		0			0
$811$	−51.9424			−1.82394			−0.911972	−	0.410253i	$-0.865440\pi$
$811$	−51.9424			−1.82394			−0.911972	+	0.410253i	$0.865440\pi$
$812$	−2.46886	−	37.0793i	−0.0866401	−	1.30123i
$813$		0			0
$814$	−7.14523	−	14.1146i	−0.250440	−	0.494718i
$815$	1.52640	−	2.64380i	0.0534674	−	0.0926083i
$816$		0			0
$817$	11.3046	−	6.52670i	0.395497	−	0.228340i
$818$	−5.24335	−	0.288575i	−0.183329	−	0.0100898i
$819$		0			0
$820$	−5.94965	−	0.656884i	−0.207771	−	0.0229394i
$821$	15.7322	+	27.2490i	0.549059	+	0.950998i	0.998339	+	0.0576069i	$0.0183470\pi$
$821$	15.7322	+	27.2490i	0.549059	+	0.950998i	−0.449281	+	0.893391i	$0.648320\pi$
$822$		0			0
$823$	−35.9504	−	20.7560i	−1.25315	−	0.723507i	−0.281417	−	0.959586i	$-0.590804\pi$
$823$	−35.9504	−	20.7560i	−1.25315	−	0.723507i	−0.971734	+	0.236078i	$0.924138\pi$
$824$	−22.8794	+	8.57678i	−0.797042	+	0.298786i
$825$		0			0
$826$	−18.2632	−	24.2718i	−0.635459	−	0.844524i
$827$			38.6850i			1.34521i	0.740003	+	0.672604i	$0.234824\pi$
$827$			38.6850i			1.34521i	−0.740003	+	0.672604i	$0.765176\pi$
$828$		0			0
$829$	8.94508	+	5.16444i	0.310675	+	0.179369i	0.647229	−	0.762296i	$-0.275928\pi$
$829$	8.94508	+	5.16444i	0.310675	+	0.179369i	−0.336553	+	0.941664i	$0.609261\pi$
$830$	1.86587	−	2.85676i	0.0647652	−	0.0991597i
$831$		0			0
$832$	9.97209	−	29.1243i	0.345720	−	1.00970i
$833$	25.2985	−	30.3850i	0.876541	−	1.05278i
$834$		0			0
$835$	3.08692	−	1.78223i	0.106827	−	0.0616767i
$836$	10.1495	+	7.45565i	0.351028	+	0.257859i
$837$		0			0
$838$	26.1287	−	13.2271i	0.902599	−	0.456921i
$839$	10.4794			0.361789			0.180894	−	0.983503i	$-0.442101\pi$
$839$	10.4794			0.361789			0.180894	+	0.983503i	$0.442101\pi$
$840$		0			0
$841$	20.3204			0.700704
$842$	−19.7564	+	10.0012i	−0.680849	+	0.344665i
$843$		0			0
$844$	−9.82885	−	7.22010i	−0.338323	−	0.248526i
$845$	0.687054	−	0.396671i	0.0236354	−	0.0136459i
$846$		0			0
$847$	16.2278	+	5.87129i	0.557595	+	0.201740i
$848$	−41.8159	−	9.34751i	−1.43596	−	0.320995i
$849$		0			0
$850$	20.9987	−	32.1503i	0.720249	−	1.10275i
$851$	−21.8408	−	12.6098i	−0.748693	−	0.432258i
$852$		0			0
$853$			25.5157i			0.873642i	0.899548	+	0.436821i	$0.143896\pi$
$853$			25.5157i			0.873642i	−0.899548	+	0.436821i	$0.856104\pi$
$854$	−2.80487	−	22.9781i	−0.0959806	−	0.786294i
$855$		0			0
$856$	2.52607	+	6.73855i	0.0863394	+	0.230319i
$857$	9.99828	+	5.77251i	0.341535	+	0.197185i	0.660951	−	0.750429i	$-0.270153\pi$
$857$	9.99828	+	5.77251i	0.341535	+	0.197185i	−0.319416	+	0.947615i	$0.603487\pi$
$858$		0			0
$859$	16.4552	+	28.5013i	0.561445	+	0.972452i	0.997371	+	0.0724689i	$0.0230878\pi$
$859$	16.4552	+	28.5013i	0.561445	+	0.972452i	−0.435925	+	0.899983i	$0.643579\pi$
$860$	3.82772	+	0.422608i	0.130524	+	0.0144108i
$861$		0			0
$862$	16.7492	+	0.921819i	0.570481	+	0.0313973i
$863$	49.6075	−	28.6409i	1.68866	−	0.974948i	0.733114	−	0.680106i	$-0.238066\pi$
$863$	49.6075	−	28.6409i	1.68866	−	0.974948i	0.955546	−	0.294842i	$-0.0952671\pi$
$864$		0			0
$865$	−0.310863	+	0.538430i	−0.0105696	+	0.0183072i
$866$	10.8118	+	21.3575i	0.367399	+	0.725758i
$867$		0			0
$868$	35.2569	+	17.3414i	1.19670	+	0.588606i
$869$	−32.9745			−1.11858
$870$		0			0
$871$	−15.1046	+	26.1619i	−0.511799	+	0.886462i
$872$	14.8674	+	12.2342i	0.503474	+	0.414303i
$873$		0			0
$874$	20.0457	+	1.10324i	0.678056	+	0.0373178i
$875$	7.33808	+	8.71126i	0.248072	+	0.294494i
$876$		0			0
$877$	−17.0215	−	29.4822i	−0.574777	−	0.995542i	−0.996066	−	0.0886159i	$-0.971756\pi$
$877$	−17.0215	−	29.4822i	−0.574777	−	0.995542i	0.421289	−	0.906926i	$-0.361578\pi$
$878$	2.78581	+	1.81952i	0.0940165	+	0.0614060i
$879$		0			0
$880$	1.11099	+	3.54533i	0.0374515	+	0.119513i
$881$			23.4638i			0.790514i	0.918571	+	0.395257i	$0.129344\pi$
$881$			23.4638i			0.790514i	−0.918571	+	0.395257i	$0.870656\pi$
$882$		0			0
$883$			8.14468i			0.274090i	0.990565	+	0.137045i	$0.0437606\pi$
$883$			8.14468i			0.274090i	−0.990565	+	0.137045i	$0.956239\pi$
$884$	17.4723	+	39.8037i	0.587657	+	1.33874i
$885$		0			0
$886$	−1.24039	+	1.89911i	−0.0416716	+	0.0638019i
$887$	−14.6109	−	25.3068i	−0.490585	−	0.849718i	0.509356	−	0.860556i	$-0.329884\pi$
$887$	−14.6109	−	25.3068i	−0.490585	−	0.849718i	−0.999941	+	0.0108376i	$0.996550\pi$
$888$		0			0
$889$	−5.99849	−	7.12099i	−0.201183	−	0.238830i
$890$	0.355425	−	6.45800i	0.0119139	−	0.216473i
$891$		0			0
$892$	2.90023	−	3.94813i	0.0971068	−	0.132193i
$893$	2.51330	−	4.35317i	0.0841044	−	0.145673i
$894$		0			0
$895$	4.71085			0.157466
$896$	−20.0066	+	22.2652i	−0.668372	+	0.743827i
$897$		0			0
$898$	1.70599	−	0.863620i	0.0569296	−	0.0288194i
$899$	−26.0733	+	45.1603i	−0.869594	+	1.50618i
$900$		0			0
$901$	52.3985	−	30.2523i	1.74565	−	1.00785i
$902$	1.12120	−	20.3720i	0.0373320	−	0.678314i
$903$		0			0
$904$	6.33502	−	38.0584i	0.210700	−	1.26580i
$905$	0.266506	+	0.461602i	0.00885896	+	0.0153442i
$906$		0			0
$907$	−48.5997	−	28.0591i	−1.61373	−	0.931686i	−0.988496	−	0.151246i	$-0.951671\pi$
$907$	−48.5997	−	28.0591i	−1.61373	−	0.931686i	−0.625231	−	0.780440i	$-0.714995\pi$
$908$	−18.7141	−	42.6326i	−0.621049	−	1.41481i
$909$		0			0
$910$	−6.27361	+	0.765800i	−0.207968	+	0.0253860i
$911$		−	43.1536i		−	1.42974i	−0.699256	−	0.714871i	$-0.746485\pi$
$911$		−	43.1536i		−	1.42974i	0.699256	−	0.714871i	$-0.253515\pi$
$912$		0			0
$913$	10.0722	+	5.81518i	0.333341	+	0.192454i
$914$	26.2226	+	17.1271i	0.867368	+	0.566513i
$915$		0			0
$916$	−2.56945	+	23.2724i	−0.0848969	+	0.768943i
$917$	−48.8047	−	17.6577i	−1.61167	−	0.583110i
$918$		0			0
$919$	33.3617	−	19.2614i	1.10050	−	0.635375i	0.164149	−	0.986435i	$-0.447512\pi$
$919$	33.3617	−	19.2614i	1.10050	−	0.635375i	0.936353	+	0.351060i	$0.114179\pi$
$920$	4.57341	+	3.76340i	0.150781	+	0.124076i
$921$		0			0
$922$	19.6629	+	38.8420i	0.647565	+	1.27919i
$923$	4.50151			0.148169
$924$		0			0
$925$	−25.4148			−0.835635
$926$	−8.82219	−	17.4273i	−0.289915	−	0.572696i
$927$		0			0
$928$	−27.7208	−	28.4571i	−0.909981	−	0.934151i
$929$	41.3034	−	23.8465i	1.35512	−	0.782379i	0.366159	−	0.930552i	$-0.380673\pi$
$929$	41.3034	−	23.8465i	1.35512	−	0.782379i	0.988961	+	0.148173i	$0.0473394\pi$
$930$		0			0
$931$	19.5472	−	7.19947i	0.640634	−	0.235953i
$932$	−16.2384	−	1.79284i	−0.531906	−	0.0587263i
$933$		0			0
$934$	−20.1601	−	13.1674i	−0.659659	−	0.430850i
$935$	−4.54346	−	2.62317i	−0.148587	−	0.0857867i
$936$		0			0
$937$		−	6.18932i		−	0.202196i	−0.994876	−	0.101098i	$-0.967764\pi$
$937$		−	6.18932i		−	0.202196i	0.994876	−	0.101098i	$-0.0322356\pi$
$938$	23.4717	−	17.6612i	0.766378	−	0.576658i
$939$		0			0
$940$	1.35787	−	0.596054i	0.0442889	−	0.0194411i
$941$	6.33052	+	3.65493i	0.206369	+	0.119147i	0.599623	−	0.800283i	$-0.295317\pi$
$941$	6.33052	+	3.65493i	0.206369	+	0.119147i	−0.393254	+	0.919430i	$0.628651\pi$
$942$		0			0
$943$	−16.2625	−	28.1676i	−0.529581	−	0.917262i
$944$	−31.6906	−	7.08409i	−1.03144	−	0.230568i
$945$		0			0
$946$	−0.721329	+	13.1064i	−0.0234524	+	0.426125i
$947$	−13.1805	+	7.60978i	−0.428309	+	0.247285i	−0.698626	−	0.715487i	$-0.746205\pi$
$947$	−13.1805	+	7.60978i	−0.428309	+	0.247285i	0.270317	+	0.962771i	$0.412872\pi$
$948$		0			0
$949$	19.3070	−	33.4407i	0.626732	−	1.08553i
$950$	18.0504	−	9.13761i	0.585631	−	0.296463i
$951$		0			0
$952$	−0.486248	−	42.2653i	−0.0157594	−	1.36982i
$953$	−17.5899			−0.569792			−0.284896	−	0.958558i	$-0.591959\pi$
$953$	−17.5899			−0.569792			−0.284896	+	0.958558i	$0.591959\pi$
$954$		0			0
$955$	1.43817	−	2.49099i	0.0465382	−	0.0806066i
$956$	−29.3331	−	21.5476i	−0.948701	−	0.696899i
$957$		0			0
$958$	−2.46985	+	44.8765i	−0.0797971	+	1.44990i
$959$	−1.56893	−	8.79930i	−0.0506633	−	0.284144i
$960$		0			0
$961$	−12.0674	−	20.9014i	−0.389271	−	0.674238i
$962$	15.7324	−	24.0873i	0.507233	−	0.776606i
$963$		0			0
$964$	52.9525	−	23.2441i	1.70548	−	0.748643i
$965$			1.42063i			0.0457318i
$966$		0			0
$967$		−	15.0905i		−	0.485279i	−0.970117	−	0.242640i	$-0.921987\pi$
$967$		−	15.0905i		−	0.485279i	0.970117	−	0.242640i	$-0.0780132\pi$
$968$	17.2749	−	6.47583i	0.555237	−	0.208141i
$969$		0			0
$970$	−1.15698	−	0.755672i	−0.0371485	−	0.0242632i
$971$	−22.4660	−	38.9123i	−0.720968	−	1.24875i	−0.960612	−	0.277893i	$-0.910364\pi$
$971$	−22.4660	−	38.9123i	−0.720968	−	1.24875i	0.239644	−	0.970861i	$-0.422969\pi$
$972$		0			0
$973$	−33.2829	+	28.0364i	−1.06700	+	0.898805i
$974$	8.14757	+	0.448413i	0.261065	+	0.0143681i
$975$		0			0
$976$	−18.2159	−	16.7508i	−0.583078	−	0.536181i
$977$	6.04122	−	10.4637i	0.193276	−	0.334763i	−0.753058	−	0.657954i	$-0.771422\pi$
$977$	6.04122	−	10.4637i	0.193276	−	0.334763i	0.946334	+	0.323191i	$0.104755\pi$
$978$		0			0
$979$	22.0457			0.704584
$980$	5.90500	+	1.70227i	0.188628	+	0.0543770i
$981$		0			0
$982$	14.4637	+	28.5715i	0.461556	+	0.911755i
$983$	8.67473	−	15.0251i	0.276681	−	0.479225i	−0.693877	−	0.720094i	$-0.744099\pi$
$983$	8.67473	−	15.0251i	0.276681	−	0.479225i	0.970558	+	0.240868i	$0.0774322\pi$
$984$		0			0
$985$	−7.32000	+	4.22620i	−0.233235	+	0.134658i
$986$	56.0131	+	3.08276i	1.78382	+	0.0981752i
$987$		0			0
$988$	−2.51330	+	22.7639i	−0.0799588	+	0.724216i
$989$	10.4625	+	18.1216i	0.332689	+	0.576235i
$990$		0			0
$991$	42.5136	+	24.5452i	1.35049	+	0.779705i	0.988318	−	0.152407i	$-0.0487025\pi$
$991$	42.5136	+	24.5452i	1.35049	+	0.779705i	0.362171	+	0.932112i	$0.382036\pi$
$992$	40.7115	−	10.3387i	1.29259	−	0.328255i
$993$		0			0
$994$	−4.02791	−	1.71311i	−0.127758	−	0.0543365i
$995$			3.78461i			0.119980i
$996$		0			0
$997$	7.88043	+	4.54977i	0.249576	+	0.144093i	0.619570	−	0.784941i	$-0.287307\pi$
$997$	7.88043	+	4.54977i	0.249576	+	0.144093i	−0.369994	+	0.929034i	$0.620640\pi$
$998$	15.0362	−	23.0214i	0.475963	−	0.728730i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bf.g.199.1		8
3.2	odd	2		84.2.o.a.31.4	yes	8
4.3	odd	2		252.2.bf.f.199.4		8
7.3	odd	6		1764.2.b.j.1567.3		8
7.4	even	3		1764.2.b.i.1567.3		8
7.5	odd	6		252.2.bf.f.19.4		8
12.11	even	2		84.2.o.b.31.1	yes	8
21.2	odd	6		588.2.o.b.19.1		8
21.5	even	6		84.2.o.b.19.1	yes	8
21.11	odd	6		588.2.b.b.391.6		8
21.17	even	6		588.2.b.a.391.6		8
21.20	even	2		588.2.o.d.31.4		8
24.5	odd	2		1344.2.bl.j.703.3		8
24.11	even	2		1344.2.bl.i.703.3		8
28.3	even	6		1764.2.b.i.1567.4		8
28.11	odd	6		1764.2.b.j.1567.4		8
28.19	even	6	inner	252.2.bf.g.19.1		8
84.11	even	6		588.2.b.a.391.5		8
84.23	even	6		588.2.o.d.19.4		8
84.47	odd	6		84.2.o.a.19.4	✓	8
84.59	odd	6		588.2.b.b.391.5		8
84.83	odd	2		588.2.o.b.31.1		8
168.5	even	6		1344.2.bl.i.1279.3		8
168.131	odd	6		1344.2.bl.j.1279.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.4	✓	8	84.47	odd	6
84.2.o.a.31.4	yes	8	3.2	odd	2
84.2.o.b.19.1	yes	8	21.5	even	6
84.2.o.b.31.1	yes	8	12.11	even	2
252.2.bf.f.19.4		8	7.5	odd	6
252.2.bf.f.199.4		8	4.3	odd	2
252.2.bf.g.19.1		8	28.19	even	6	inner
252.2.bf.g.199.1		8	1.1	even	1	trivial
588.2.b.a.391.5		8	84.11	even	6
588.2.b.a.391.6		8	21.17	even	6
588.2.b.b.391.5		8	84.59	odd	6
588.2.b.b.391.6		8	21.11	odd	6
588.2.o.b.19.1		8	21.2	odd	6
588.2.o.b.31.1		8	84.83	odd	2
588.2.o.d.19.4		8	84.23	even	6
588.2.o.d.31.4		8	21.20	even	2
1344.2.bl.i.703.3		8	24.11	even	2
1344.2.bl.i.1279.3		8	168.5	even	6
1344.2.bl.j.703.3		8	24.5	odd	2
1344.2.bl.j.1279.3		8	168.131	odd	6
1764.2.b.i.1567.3		8	7.4	even	3
1764.2.b.i.1567.4		8	28.3	even	6
1764.2.b.j.1567.3		8	7.3	odd	6
1764.2.b.j.1567.4		8	28.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26175 + 0.638735i) q^{2} +(1.18404 - 1.61185i) q^{4} +(-0.380152 + 0.219481i) q^{5} +(-2.02350 + 1.70453i) q^{7} +(-0.464416 + 2.79004i) q^{8} +O(q^{10})\)	\(q+(-1.26175 + 0.638735i) q^{2} +(1.18404 - 1.61185i) q^{4} +(-0.380152 + 0.219481i) q^{5} +(-2.02350 + 1.70453i) q^{7} +(-0.464416 + 2.79004i) q^{8} +(0.339468 - 0.519747i) q^{10} +(1.83249 + 1.05799i) q^{11} +3.84803i q^{13} +(1.46442 - 3.44318i) q^{14} +(-1.19612 - 3.81698i) q^{16} +(4.89158 + 2.82415i) q^{17} +(1.48792 + 2.57715i) q^{19} +(-0.0963438 + 0.872621i) q^{20} +(-2.98792 - 0.164445i) q^{22} +(-4.13127 + 2.38519i) q^{23} +(-2.40366 + 4.16325i) q^{25} +(-2.45787 - 4.85526i) q^{26} +(0.351547 + 5.27981i) q^{28} -7.02285 q^{29} +(3.71264 - 6.43048i) q^{31} +(3.94724 + 4.05208i) q^{32} +(-7.97584 - 0.438962i) q^{34} +(0.395127 - 1.09210i) q^{35} +(2.64335 + 4.57842i) q^{37} +(-3.52350 - 2.30134i) q^{38} +(-0.435811 - 1.16257i) q^{40} +6.81813i q^{41} -4.38646i q^{43} +(3.87505 - 1.70100i) q^{44} +(3.68914 - 5.64831i) q^{46} +(-0.844569 - 1.46284i) q^{47} +(1.18914 - 6.89826i) q^{49} +(0.373604 - 6.78829i) q^{50} +(6.20244 + 4.55620i) q^{52} +(5.35599 - 9.27685i) q^{53} -0.928833 q^{55} +(-3.81596 - 6.43727i) q^{56} +(8.86109 - 4.48574i) q^{58} +(4.05909 - 7.03055i) q^{59} +(5.35787 - 3.09337i) q^{61} +(-0.577061 + 10.4851i) q^{62} +(-7.56863 - 2.59148i) q^{64} +(-0.844569 - 1.46284i) q^{65} +(6.79878 + 3.92528i) q^{67} +(10.3439 - 4.54058i) q^{68} +(0.199011 + 1.63034i) q^{70} -1.16982i q^{71} +(-8.69036 - 5.01738i) q^{73} +(-6.25965 - 4.08843i) q^{74} +(5.91574 + 0.653140i) q^{76} +(-5.51142 + 0.982694i) q^{77} +(-13.4958 + 7.79180i) q^{79} +(1.29246 + 1.18851i) q^{80} +(-4.35498 - 8.60279i) q^{82} +5.49645 q^{83} -2.47939 q^{85} +(2.80178 + 5.53462i) q^{86} +(-3.80287 + 4.62137i) q^{88} +(9.02285 - 5.20934i) q^{89} +(-6.55909 - 7.78650i) q^{91} +(-1.04701 + 9.48314i) q^{92} +(2.00000 + 1.30628i) q^{94} +(-1.13127 - 0.653140i) q^{95} -2.22605i q^{97} +(2.90576 + 9.46343i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - q^{4} + 2 q^{7} - 4 q^{8}+O(q^{10}) \) 8 * q - q^2 - q^4 + 2 * q^7 - 4 * q^8	\( 8 q - q^{2} - q^{4} + 2 q^{7} - 4 q^{8} - 5 q^{10} - 6 q^{11} + 12 q^{14} - 17 q^{16} - 6 q^{19} - 22 q^{20} - 6 q^{22} + 2 q^{25} - 18 q^{26} + 13 q^{28} + 16 q^{29} + 6 q^{31} + 9 q^{32} - 28 q^{34} + 12 q^{35} + 6 q^{37} - 10 q^{38} - 17 q^{40} + 23 q^{44} + 24 q^{46} - 4 q^{47} + 4 q^{49} - 2 q^{50} + 16 q^{52} + 4 q^{53} - 8 q^{55} - 41 q^{56} + 37 q^{58} + 14 q^{59} + 12 q^{61} + 48 q^{62} + 2 q^{64} - 4 q^{65} + 42 q^{67} + 26 q^{68} + 3 q^{70} - 18 q^{73} + 10 q^{74} + 44 q^{76} - 8 q^{77} - 6 q^{79} + 39 q^{80} - 10 q^{82} - 4 q^{83} - 32 q^{85} - 36 q^{86} - 37 q^{88} - 34 q^{91} + 28 q^{92} + 16 q^{94} + 24 q^{95} + 53 q^{98}+O(q^{100}) \) 8 * q - q^2 - q^4 + 2 * q^7 - 4 * q^8 - 5 * q^10 - 6 * q^11 + 12 * q^14 - 17 * q^16 - 6 * q^19 - 22 * q^20 - 6 * q^22 + 2 * q^25 - 18 * q^26 + 13 * q^28 + 16 * q^29 + 6 * q^31 + 9 * q^32 - 28 * q^34 + 12 * q^35 + 6 * q^37 - 10 * q^38 - 17 * q^40 + 23 * q^44 + 24 * q^46 - 4 * q^47 + 4 * q^49 - 2 * q^50 + 16 * q^52 + 4 * q^53 - 8 * q^55 - 41 * q^56 + 37 * q^58 + 14 * q^59 + 12 * q^61 + 48 * q^62 + 2 * q^64 - 4 * q^65 + 42 * q^67 + 26 * q^68 + 3 * q^70 - 18 * q^73 + 10 * q^74 + 44 * q^76 - 8 * q^77 - 6 * q^79 + 39 * q^80 - 10 * q^82 - 4 * q^83 - 32 * q^85 - 36 * q^86 - 37 * q^88 - 34 * q^91 + 28 * q^92 + 16 * q^94 + 24 * q^95 + 53 * q^98

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