LMFDB - Embedded newform 252.2.bf.f.19.4

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			19.4
Root			$0.0777157 - 1.41208i$ of defining polynomial
Character	$\chi$	$=$	252.19
Dual form			252.2.bf.f.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18404 + 0.773342i) q^{2} +(0.803884 + 1.83133i) q^{4} +(-0.380152 - 0.219481i) q^{5} +(2.02350 + 1.70453i) q^{7} +(-0.464416 + 2.79004i) q^{8} +O(q^{10})$	\(q+(1.18404 + 0.773342i) q^{2} +(0.803884 + 1.83133i) q^{4} +(-0.380152 - 0.219481i) q^{5} +(2.02350 + 1.70453i) q^{7} +(-0.464416 + 2.79004i) q^{8} +(-0.280380 - 0.553861i) q^{10} +(-1.83249 + 1.05799i) q^{11} -3.84803i q^{13} +(1.07772 + 3.58309i) q^{14} +(-2.70754 + 2.94435i) q^{16} +(4.89158 - 2.82415i) q^{17} +(-1.48792 + 2.57715i) q^{19} +(0.0963438 - 0.872621i) q^{20} +(-2.98792 - 0.164445i) q^{22} +(4.13127 + 2.38519i) q^{23} +(-2.40366 - 4.16325i) q^{25} +(2.97584 - 4.55620i) q^{26} +(-1.49490 + 5.07595i) q^{28} -7.02285 q^{29} +(-3.71264 - 6.43048i) q^{31} +(-5.48282 + 1.39237i) q^{32} +(7.97584 + 0.438962i) q^{34} +(-0.395127 - 1.09210i) q^{35} +(2.64335 - 4.57842i) q^{37} +(-3.75477 + 1.90077i) q^{38} +(0.788909 - 0.958709i) q^{40} -6.81813i q^{41} -4.38646i q^{43} +(-3.41063 - 2.50539i) q^{44} +(3.04701 + 6.01904i) q^{46} +(0.844569 - 1.46284i) q^{47} +(1.18914 + 6.89826i) q^{49} +(0.373604 - 6.78829i) q^{50} +(7.04701 - 3.09337i) q^{52} +(5.35599 + 9.27685i) q^{53} +0.928833 q^{55} +(-5.69546 + 4.85404i) q^{56} +(-8.31531 - 5.43106i) q^{58} +(-4.05909 - 7.03055i) q^{59} +(5.35787 + 3.09337i) q^{61} +(0.577061 - 10.4851i) q^{62} +(-7.56863 - 2.59148i) q^{64} +(-0.844569 + 1.46284i) q^{65} +(-6.79878 + 3.92528i) q^{67} +(9.10422 + 6.68780i) q^{68} +(0.376724 - 1.59866i) q^{70} -1.16982i q^{71} +(-8.69036 + 5.01738i) q^{73} +(6.67051 - 3.37680i) q^{74} +(-5.91574 - 0.653140i) q^{76} +(-5.51142 - 0.982694i) q^{77} +(13.4958 + 7.79180i) q^{79} +(1.67551 - 0.525049i) q^{80} +(5.27275 - 8.07291i) q^{82} -5.49645 q^{83} -2.47939 q^{85} +(3.39223 - 5.19372i) q^{86} +(-2.10079 - 5.60406i) q^{88} +(9.02285 + 5.20934i) q^{89} +(6.55909 - 7.78650i) q^{91} +(-1.04701 + 9.48314i) q^{92} +(2.13127 - 1.07891i) q^{94} +(1.13127 - 0.653140i) q^{95} +2.22605i q^{97} +(-3.92673 + 9.08740i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 13 q^{10} + 6 q^{11} + 10 q^{14} + 7 q^{16} + 6 q^{19} + 22 q^{20} - 6 q^{22} + 2 q^{25} - 12 q^{26} - 7 q^{28} + 16 q^{29} - 6 q^{31} - 21 q^{32} + 28 q^{34} - 12 q^{35} + 6 q^{37} - 8 q^{38} - 13 q^{40} - 19 q^{44} - 12 q^{46} + 4 q^{47} + 4 q^{49} - 2 q^{50} + 20 q^{52} + 4 q^{53} + 8 q^{55} + q^{56} - 23 q^{58} - 14 q^{59} + 12 q^{61} - 48 q^{62} + 2 q^{64} - 4 q^{65} - 42 q^{67} + 10 q^{68} + 35 q^{70} - 18 q^{73} + 28 q^{74} - 44 q^{76} - 8 q^{77} + 6 q^{79} + 33 q^{80} - 14 q^{82} + 4 q^{83} - 32 q^{85} + 42 q^{86} + 11 q^{88} + 34 q^{91} + 28 q^{92} - 16 q^{94} - 24 q^{95} + 19 q^{98}+O(q^{100}) $ 8 * q - q^2 - q^4 - 2 * q^7 - 4 * q^8 - 13 * q^10 + 6 * q^11 + 10 * q^14 + 7 * q^16 + 6 * q^19 + 22 * q^20 - 6 * q^22 + 2 * q^25 - 12 * q^26 - 7 * q^28 + 16 * q^29 - 6 * q^31 - 21 * q^32 + 28 * q^34 - 12 * q^35 + 6 * q^37 - 8 * q^38 - 13 * q^40 - 19 * q^44 - 12 * q^46 + 4 * q^47 + 4 * q^49 - 2 * q^50 + 20 * q^52 + 4 * q^53 + 8 * q^55 + q^56 - 23 * q^58 - 14 * q^59 + 12 * q^61 - 48 * q^62 + 2 * q^64 - 4 * q^65 - 42 * q^67 + 10 * q^68 + 35 * q^70 - 18 * q^73 + 28 * q^74 - 44 * q^76 - 8 * q^77 + 6 * q^79 + 33 * q^80 - 14 * q^82 + 4 * q^83 - 32 * q^85 + 42 * q^86 + 11 * q^88 + 34 * q^91 + 28 * q^92 - 16 * q^94 - 24 * q^95 + 19 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.18404	+	0.773342i	0.837240	+	0.546835i
$2$	1.18404	+	0.773342i	0.837240	+	0.546835i
$3$		0			0
$3$		0			0
$4$	0.803884	+	1.83133i	0.401942	+	0.915665i
$5$	−0.380152	−	0.219481i	−0.170009	−	0.0981549i	0.412581	−	0.910921i	$-0.364627\pi$
$5$	−0.380152	−	0.219481i	−0.170009	−	0.0981549i	−0.582590	+	0.812766i	$0.697961\pi$
$6$		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
$10$	−0.280380	−	0.553861i	−0.0886640	−	0.175146i
$11$	−1.83249	+	1.05799i	−0.552516	+	0.318995i	−0.750136	−	0.661283i	$-0.770012\pi$
$11$	−1.83249	+	1.05799i	−0.552516	+	0.318995i	0.197620	+	0.980279i	$0.436679\pi$
$12$		0			0
$13$		−	3.84803i		−	1.06725i	−0.845721	−	0.533625i	$-0.820829\pi$
$13$		−	3.84803i		−	1.06725i	0.845721	−	0.533625i	$-0.179171\pi$
$14$	1.07772	+	3.58309i	0.288032	+	0.957621i
$15$		0			0
$16$	−2.70754	+	2.94435i	−0.676885	+	0.736089i
$17$	4.89158	−	2.82415i	1.18638	−	0.684958i	0.228899	−	0.973450i	$-0.426487\pi$
$17$	4.89158	−	2.82415i	1.18638	−	0.684958i	0.957482	+	0.288492i	$0.0931540\pi$
$18$		0			0
$19$	−1.48792	+	2.57715i	−0.341352	+	0.591240i	−0.984684	−	0.174348i	$-0.944218\pi$
$19$	−1.48792	+	2.57715i	−0.341352	+	0.591240i	0.643332	+	0.765588i	$0.277552\pi$
$20$	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	$-0.167641\pi$
$23$	4.13127	+	2.38519i	0.861430	+	0.497347i	−0.00306100	+	0.999995i	$0.500974\pi$
$24$		0			0
$25$	−2.40366	−	4.16325i	−0.480731	−	0.832651i
$26$	2.97584	−	4.55620i	0.583610	−	0.893545i
$27$		0			0
$28$	−1.49490	+	5.07595i	−0.282509	+	0.959265i
$29$	−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	−0.978791	−	0.204861i	$-0.934326\pi$
$31$	−3.71264	−	6.43048i	−0.666810	−	1.15495i	0.311981	−	0.950088i	$-0.399007\pi$
$32$	−5.48282	+	1.39237i	−0.969235	+	0.246138i
$33$		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	−0.562696	−	0.826664i	$-0.690236\pi$
$37$	2.64335	−	4.57842i	0.434564	−	0.752688i	0.997260	+	0.0739766i	$0.0235690\pi$
$38$	−3.75477	+	1.90077i	−0.609105	+	0.308346i
$39$		0			0
$40$	0.788909	−	0.958709i	0.124738	−	0.151585i
$41$		−	6.81813i		−	1.06481i	−0.846489	−	0.532407i	$-0.821288\pi$
$41$		−	6.81813i		−	1.06481i	0.846489	−	0.532407i	$-0.178712\pi$
$42$		0			0
$43$		−	4.38646i		−	0.668928i	−0.942408	−	0.334464i	$-0.891445\pi$
$43$		−	4.38646i		−	0.668928i	0.942408	−	0.334464i	$-0.108555\pi$
$44$	−3.41063	−	2.50539i	−0.514173	−	0.377702i
$45$		0			0
$46$	3.04701	+	6.01904i	0.449257	+	0.887459i
$47$	0.844569	−	1.46284i	0.123193	−	0.213377i	−0.797832	−	0.602880i	$-0.794020\pi$
$47$	0.844569	−	1.46284i	0.123193	−	0.213377i	0.921025	+	0.389503i	$0.127353\pi$
$48$		0			0
$49$	1.18914	+	6.89826i	0.169877	+	0.985465i
$50$	0.373604	−	6.78829i	0.0528355	−	0.960010i
$51$		0			0
$52$	7.04701	−	3.09337i	0.977244	−	0.428973i
$53$	5.35599	+	9.27685i	0.735702	+	1.27427i	0.954415	+	0.298484i	$0.0964811\pi$
$53$	5.35599	+	9.27685i	0.735702	+	1.27427i	−0.218712	+	0.975789i	$0.570186\pi$
$54$		0			0
$55$	0.928833			0.125244
$56$	−5.69546	+	4.85404i	−0.761088	+	0.648649i
$57$		0			0
$58$	−8.31531	−	5.43106i	−1.09185	−	0.713134i
$59$	−4.05909	−	7.03055i	−0.528448	−	0.915299i	−0.999450	−	0.0331668i	$-0.989441\pi$
$59$	−4.05909	−	7.03055i	−0.528448	−	0.915299i	0.471002	−	0.882132i	$-0.343893\pi$
$60$		0			0
$61$	5.35787	+	3.09337i	0.686005	+	0.396065i	0.802114	−	0.597171i	$-0.203709\pi$
$61$	5.35787	+	3.09337i	0.686005	+	0.396065i	−0.116109	+	0.993237i	$0.537042\pi$
$62$	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	$-0.825866\pi$
$67$	−6.79878	+	3.92528i	−0.830604	+	0.479549i	0.0234557	+	0.999725i	$0.492533\pi$
$68$	9.10422	+	6.68780i	1.10405	+	0.811015i
$69$		0			0
$70$	0.376724	−	1.59866i	0.0450271	−	0.191076i
$71$		−	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	−0.913271	−	0.407352i	$-0.866452\pi$
$73$	−8.69036	+	5.01738i	−1.01713	+	0.587240i	−0.103858	+	0.994592i	$0.533119\pi$
$74$	6.67051	−	3.37680i	0.775431	−	0.392545i
$75$		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	0.999766	+	0.0216472i	$0.00689107\pi$
$79$	13.4958	+	7.79180i	1.51840	+	0.876646i	0.518630	+	0.854999i	$0.326442\pi$
$80$	1.67551	−	0.525049i	0.187327	−	0.0587023i
$81$		0			0
$82$	5.27275	−	8.07291i	0.582277	−	0.891504i
$83$	−5.49645			−0.603314			−0.301657	−	0.953417i	$-0.597540\pi$
$83$	−5.49645			−0.603314			−0.301657	+	0.953417i	$0.597540\pi$
$84$		0			0
$85$	−2.47939			−0.268928
$86$	3.39223	−	5.19372i	0.365794	−	0.560054i
$87$		0			0
$88$	−2.10079	−	5.60406i	−0.223945	−	0.597395i
$89$	9.02285	+	5.20934i	0.956420	+	0.552189i	0.895069	−	0.445927i	$-0.147126\pi$
$89$	9.02285	+	5.20934i	0.956420	+	0.552189i	0.0613507	+	0.998116i	$0.480459\pi$
$90$		0			0
$91$	6.55909	−	7.78650i	0.687579	−	0.816247i
$92$	−1.04701	+	9.48314i	−0.109158	+	0.988686i
$93$		0			0
$94$	2.13127	−	1.07891i	0.219824	−	0.111281i
$95$	1.13127	−	0.653140i	0.116066	−	0.0670108i
$96$		0			0
$97$			2.22605i			0.226021i	0.993594	+	0.113011i	$0.0360494\pi$
$97$			2.22605i			0.226021i	−0.993594	+	0.113011i	$0.963951\pi$
$98$	−3.92673	+	9.08740i	−0.396660	+	0.917966i
$99$		0			0
$100$	5.69203	−	7.74866i	0.569203	−	0.774866i
$101$	0.664978	−	0.383925i	0.0661678	−	0.0382020i	−0.466551	−	0.884494i	$-0.654504\pi$
$101$	0.664978	−	0.383925i	0.0661678	−	0.0382020i	0.532719	+	0.846292i	$0.321170\pi$
$102$		0			0
$103$	−4.31939	+	7.48141i	−0.425602	+	0.737165i	−0.996476	−	0.0838727i	$-0.973271\pi$
$103$	−4.31939	+	7.48141i	−0.425602	+	0.737165i	0.570874	+	0.821038i	$0.306604\pi$
$104$	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	$-0.372580\pi$
$107$	−2.20346	−	1.27217i	−0.213016	−	0.122985i	−0.602712	+	0.797959i	$0.705913\pi$
$108$		0			0
$109$	3.40366	+	5.89531i	0.326011	+	0.564668i	0.981716	−	0.190349i	$-0.0609620\pi$
$109$	3.40366	+	5.89531i	0.326011	+	0.564668i	−0.655705	+	0.755017i	$0.727629\pi$
$110$	1.09977	+	0.718306i	0.104859	+	0.0684878i
$111$		0			0
$112$	−10.4975	+	1.34282i	−0.991917	+	0.126885i
$113$	−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
$116$	−5.64556	−	12.8612i	−0.524177	−	1.19413i
$117$		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
$122$	3.95168	+	7.80613i	0.357768	+	0.706734i
$123$		0			0
$124$	8.79180	−	11.9684i	0.789527	−	1.07480i
$125$			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	$0.950096\pi$
$128$	−6.95744	−	8.92155i	−0.614956	−	0.788561i
$129$		0			0
$130$	−2.13127	+	1.07891i	−0.186925	+	0.0946267i
$131$	−9.80833	+	16.9885i	−0.856958	+	1.48429i	0.0178590	+	0.999841i	$0.494315\pi$
$131$	−9.80833	+	16.9885i	−0.856958	+	1.48429i	−0.874817	+	0.484454i	$0.839018\pi$
$132$		0			0
$133$	−7.40366	+	2.67867i	−0.641978	+	0.232270i
$134$	−11.0856	−	0.610111i	−0.957649	−	0.0527056i
$135$		0			0
$136$	5.60777	+	14.9593i	0.480862	+	1.28275i
$137$	−1.68914	−	2.92567i	−0.144313	−	0.249957i	0.784804	−	0.619745i	$-0.212764\pi$
$137$	−1.68914	−	2.92567i	−0.144313	−	0.249957i	−0.929116	+	0.369788i	$0.879430\pi$
$138$		0			0
$139$	−16.4481			−1.39511			−0.697556	−	0.716530i	$-0.745729\pi$
$139$	−16.4481			−1.39511			−0.697556	+	0.716530i	$0.745729\pi$
$140$	1.68236	−	1.60153i	0.142186	−	0.135354i
$141$		0			0
$142$	0.904674	−	1.38511i	0.0759186	−	0.116236i
$143$	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	−0.702264	−	0.711917i	$-0.747827\pi$
$149$	3.23970	−	5.61132i	0.265406	−	0.459697i	0.967670	+	0.252220i	$0.0811606\pi$
$150$		0			0
$151$	6.72827	−	3.88457i	0.547539	−	0.316122i	−0.200590	−	0.979675i	$-0.564286\pi$
$151$	6.72827	−	3.88457i	0.547539	−	0.316122i	0.748129	+	0.663554i	$0.230953\pi$
$152$	−6.49935	−	5.34823i	−0.527167	−	0.433799i
$153$		0			0
$154$	−5.76577	−	5.42576i	−0.464619	−	0.437220i
$155$			3.25942i			0.261803i
$156$		0			0
$157$	7.32996	−	4.23195i	0.584994	−	0.337747i	−0.178121	−	0.984009i	$-0.557002\pi$
$157$	7.32996	−	4.23195i	0.584994	−	0.337747i	0.763116	+	0.646262i	$0.223669\pi$
$158$	9.95378	+	19.6626i	0.791881	+	1.56428i
$159$		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	$-0.245528\pi$
$163$	6.02285	+	3.47729i	0.471746	+	0.272363i	−0.245224	+	0.969466i	$0.578862\pi$
$164$	12.4862	−	5.48099i	0.975012	−	0.427993i
$165$		0			0
$166$	−6.50800	−	4.25064i	−0.505118	−	0.329913i
$167$	8.12021			0.628361			0.314180	−	0.949363i	$-0.398270\pi$
$167$	8.12021			0.628361			0.314180	+	0.949363i	$0.398270\pi$
$168$		0			0
$169$	−1.80731			−0.139024
$170$	−2.93569	−	1.91742i	−0.225157	−	0.147059i
$171$		0			0
$172$	8.03305	−	3.52620i	0.612514	−	0.268870i
$173$	1.22660	+	0.708177i	0.0932565	+	0.0538417i	0.545903	−	0.837848i	$-0.316187\pi$
$173$	1.22660	+	0.708177i	0.0932565	+	0.0538417i	−0.452646	+	0.891690i	$0.649520\pi$
$174$		0			0
$175$	2.23260	−	12.5215i	0.168768	−	0.946534i
$176$	1.84645	−	8.26004i	0.139181	−	0.622624i
$177$		0			0
$178$	6.65478	+	13.1458i	0.498797	+	0.985320i
$179$	9.29401	−	5.36590i	0.694667	−	0.401066i	−0.110691	−	0.993855i	$-0.535306\pi$
$179$	9.29401	−	5.36590i	0.694667	−	0.401066i	0.805358	+	0.592789i	$0.201973\pi$
$180$		0			0
$181$			1.21426i			0.0902549i	0.998981	+	0.0451275i	$0.0143694\pi$
$181$			1.21426i			0.0902549i	−0.998981	+	0.0451275i	$0.985631\pi$
$182$	13.7878	−	4.14708i	1.02202	−	0.307402i
$183$		0			0
$184$	−8.57341	+	10.4187i	−0.632040	+	0.768076i
$185$	−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	$-0.257148\pi$
$191$	5.67473	+	3.27631i	0.410609	+	0.237065i	−0.280442	+	0.959871i	$0.590481\pi$
$192$		0			0
$193$	1.61818	+	2.80276i	0.116479	+	0.201747i	0.918370	−	0.395723i	$-0.129506\pi$
$193$	1.61818	+	2.80276i	0.116479	+	0.201747i	−0.801891	+	0.597470i	$0.796173\pi$
$194$	−1.72150	+	2.63572i	−0.123596	+	0.189234i
$195$		0			0
$196$	−11.6771	+	7.72310i	−0.834076	+	0.551650i
$197$	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	$-0.265520\pi$
$199$	−4.31086	−	7.46663i	−0.305589	−	0.529296i	−0.977392	+	0.211434i	$0.932187\pi$
$200$	12.7319	−	4.77281i	0.900284	−	0.337489i
$201$		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
$206$	−10.9000	+	5.51789i	−0.759439	+	0.384450i
$207$		0			0
$208$	11.3300	+	10.4187i	0.785591	+	0.722406i
$209$		−	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	$-0.0673130\pi$
$212$	−12.6834	+	17.2661i	−0.871098	+	1.18584i
$213$		0			0
$214$	−1.62515	−	3.21032i	−0.111093	−	0.219453i
$215$	−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
$220$	0.746674	+	1.70100i	0.0503408	+	0.114681i
$221$	−10.8674	−	18.8229i	−0.731022	−	1.26617i
$222$		0			0
$223$	−2.44944			−0.164027			−0.0820134	−	0.996631i	$-0.526135\pi$
$223$	−2.44944			−0.164027			−0.0820134	+	0.996631i	$0.526135\pi$
$224$	−13.4678	−	6.52818i	−0.899858	−	0.436182i
$225$		0			0
$226$	−16.1512	−	10.5490i	−1.07436	−	0.701710i
$227$	−11.6398	−	20.1607i	−0.772561	−	1.33811i	−0.936155	−	0.351587i	$-0.885642\pi$
$227$	−11.6398	−	20.1607i	−0.772561	−	1.33811i	0.163595	−	0.986528i	$-0.447691\pi$
$228$		0			0
$229$	−10.1385	−	5.85346i	−0.669970	−	0.386808i	0.126095	−	0.992018i	$-0.459756\pi$
$229$	−10.1385	−	5.85346i	−0.669970	−	0.386808i	−0.796065	+	0.605211i	$0.793089\pi$
$230$	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	−0.968234	−	0.250048i	$-0.919554\pi$
$233$	−4.08426	+	7.07415i	−0.267569	+	0.463443i	0.700664	+	0.713491i	$0.252887\pi$
$234$		0			0
$235$	−0.642129	+	0.370733i	−0.0418879	+	0.0241840i
$236$	9.61221	−	13.0853i	0.625702	−	0.851779i
$237$		0			0
$238$	15.3909	+	14.4833i	0.997645	+	0.938814i
$239$		−	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	0.624364	−	0.781133i	$-0.285358\pi$
$241$	25.0409	−	14.4574i	1.61303	−	0.931282i	0.988663	−	0.150149i	$-0.0479753\pi$
$242$	−8.22996	+	4.16624i	−0.529042	+	0.267816i
$243$		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
$248$	19.6655	−	7.37199i	1.24876	−	0.468122i
$249$		0			0
$250$	−3.32927	+	5.09732i	−0.210561	+	0.322383i
$251$	−20.3586			−1.28502			−0.642512	−	0.766276i	$-0.722108\pi$
$251$	−20.3586			−1.28502			−0.642512	+	0.766276i	$0.722108\pi$
$252$		0			0
$253$	−10.0940			−0.634605
$254$	−2.72150	+	4.16679i	−0.170762	+	0.261447i
$255$		0			0
$256$	−1.33845	−	15.9439i	−0.0836531	−	0.996495i
$257$	−18.4350	−	10.6435i	−1.14995	−	0.663922i	−0.201072	−	0.979577i	$-0.564442\pi$
$257$	−18.4350	−	10.6435i	−1.14995	−	0.663922i	−0.948874	+	0.315655i	$0.897776\pi$
$258$		0			0
$259$	13.1529	−	4.75877i	0.817281	−	0.295696i
$260$	−3.35787	−	0.370733i	−0.208246	−	0.0229919i
$261$		0			0
$262$	−24.7514	+	12.5298i	−1.52914	+	0.774096i
$263$	−17.4760	+	10.0898i	−1.07762	+	0.622164i	−0.930253	−	0.366918i	$-0.880413\pi$
$263$	−17.4760	+	10.0898i	−1.07762	+	0.622164i	−0.147366	+	0.989082i	$0.547080\pi$
$264$		0			0
$265$		−	4.70215i		−	0.288851i
$266$	−10.8377	−	2.55391i	−0.664504	−	0.156590i
$267$		0			0
$268$	−12.6539	−	9.29535i	−0.772961	−	0.567804i
$269$	−14.1764	+	8.18475i	−0.864351	+	0.499033i	−0.865467	−	0.500966i	$-0.832978\pi$
$269$	−14.1764	+	8.18475i	−0.864351	+	0.499033i	0.00111621	+	0.999999i	$0.499645\pi$
$270$		0			0
$271$	−6.72696	+	11.6514i	−0.408634	+	0.707775i	−0.994737	−	0.102462i	$-0.967328\pi$
$271$	−6.72696	+	11.6514i	−0.408634	+	0.707775i	0.586103	+	0.810236i	$0.300661\pi$
$272$	−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	0.820771	−	0.571257i	$-0.193544\pi$
$277$	−1.40366	−	2.43120i	−0.0843375	−	0.146077i	−0.905109	+	0.425180i	$0.860211\pi$
$278$	−19.4752	−	12.7200i	−1.16804	−	0.762897i
$279$		0			0
$280$	3.23051	−	0.595229i	0.193060	−	0.0355718i
$281$	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	$-0.121678\pi$
$283$	2.36975	+	4.10452i	0.140867	+	0.243988i	−0.786957	+	0.617008i	$0.788344\pi$
$284$	2.14233	−	0.940403i	0.127124	−	0.0558027i
$285$		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
$290$	1.96907	+	3.88968i	0.115628	+	0.228410i
$291$		0			0
$292$	−16.1745	−	11.8815i	−0.946543	−	0.695314i
$293$		−	3.22818i		−	0.188592i	−0.995544	−	0.0942960i	$-0.969940\pi$
$293$		−	3.22818i		−	0.188592i	0.995544	−	0.0942960i	$-0.0300600\pi$
$294$		0			0
$295$			3.56357i			0.207479i
$296$	11.5464	+	9.50135i	0.671118	+	0.552255i
$297$		0			0
$298$	8.17539	−	4.13861i	0.473587	−	0.239743i
$299$	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
$304$	−3.55945	−	11.3587i	−0.204148	−	0.651467i
$305$	−1.35787	−	2.35190i	−0.0777515	−	0.134669i
$306$		0			0
$307$	−5.45523			−0.311347			−0.155673	−	0.987809i	$-0.549755\pi$
$307$	−5.45523			−0.311347			−0.155673	+	0.987809i	$0.549755\pi$
$308$	−2.63091	−	10.8832i	−0.149910	−	0.620128i
$309$		0			0
$310$	−2.52064	+	3.85927i	−0.143163	+	0.219192i
$311$	15.2625	+	26.4355i	0.865460	+	1.49902i	0.866590	+	0.499020i	$0.166307\pi$
$311$	15.2625	+	26.4355i	0.865460	+	1.49902i	−0.00113066	+	0.999999i	$0.500360\pi$
$312$		0			0
$313$	−16.3093	−	9.41621i	−0.921859	−	0.532235i	−0.0376312	−	0.999292i	$-0.511981\pi$
$313$	−16.3093	−	9.41621i	−0.921859	−	0.532235i	−0.884228	+	0.467056i	$0.845315\pi$
$314$	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	−0.517741	−	0.855537i	$-0.673227\pi$
$317$	8.58259	−	14.8655i	0.482046	−	0.834929i	0.999788	+	0.0206085i	$0.00656034\pi$
$318$		0			0
$319$	12.8693	−	7.43009i	0.720542	−	0.416005i
$320$	2.30845	+	2.64633i	0.129046	+	0.147934i
$321$		0			0
$322$	−4.09402	+	17.3733i	−0.228151	+	0.968175i
$323$			16.8085i			0.935248i
$324$		0			0
$325$	−16.0203	+	9.24933i	−0.888647	+	0.513061i
$326$	4.44214	+	8.77496i	0.246027	+	0.486000i
$327$		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	$-0.534407\pi$
$331$	−18.6081	−	10.7434i	−1.02280	−	0.590511i	−0.914912	+	0.403652i	$0.867741\pi$
$332$	−4.41851	−	10.0658i	−0.242497	−	0.552433i
$333$		0			0
$334$	9.61462	+	6.27970i	0.526089	+	0.343610i
$335$	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	$0.448534\pi$
$338$	−2.13992	−	1.39767i	−0.116397	−	0.0760233i
$339$		0			0
$340$	−1.99314	−	4.54058i	−0.108093	−	0.246248i
$341$	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
$346$	0.904674	+	1.78709i	0.0486356	+	0.0960744i
$347$	−2.43838	+	1.40780i	−0.130899	+	0.0755746i	−0.564020	−	0.825761i	$-0.690746\pi$
$347$	−2.43838	+	1.40780i	−0.130899	+	0.0755746i	0.433121	+	0.901336i	$0.357412\pi$
$348$		0			0
$349$			9.54077i			0.510705i	0.966848	+	0.255353i	$0.0821916\pi$
$349$			9.54077i			0.510705i	−0.966848	+	0.255353i	$0.917808\pi$
$350$	12.3269	−	13.0993i	0.658898	−	0.700188i
$351$		0			0
$352$	8.57410	−	8.35226i	0.457001	−	0.445177i
$353$	−8.63351	+	4.98456i	−0.459516	+	0.265301i	−0.711841	−	0.702341i	$-0.752138\pi$
$353$	−8.63351	+	4.98456i	−0.459516	+	0.265301i	0.252325	+	0.967643i	$0.418805\pi$
$354$		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	$-0.274808\pi$
$359$	6.00000	+	3.46410i	0.316668	+	0.182828i	−0.333238	+	0.942843i	$0.608141\pi$
$360$		0			0
$361$	5.07218	+	8.78528i	0.266957	+	0.462383i
$362$	−0.939035	+	1.43772i	−0.0493546	+	0.0755650i
$363$		0			0
$364$	19.5324	+	5.75241i	1.02378	+	0.301508i
$365$	4.40488			0.230562
$366$		0			0
$367$	−8.95234	−	15.5059i	−0.467308	−	0.809402i	0.531994	−	0.846748i	$-0.321443\pi$
$367$	−8.95234	−	15.5059i	−0.467308	−	0.809402i	−0.999302	+	0.0373465i	$0.988109\pi$
$368$	−18.2084	+	5.70593i	−0.949180	+	0.297442i
$369$		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	−0.990286	−	0.139045i	$-0.955597\pi$
$373$	−7.23716	+	12.5351i	−0.374726	+	0.649045i	0.615560	+	0.788090i	$0.288930\pi$
$374$	−15.0801	+	7.63395i	−0.779771	+	0.394742i
$375$		0			0
$376$	3.68914	+	3.03574i	0.190253	+	0.156557i
$377$			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	$-0.187159\pi$
$380$	2.10553	+	1.54668i	0.108011	+	0.0793432i
$381$		0			0
$382$	4.18538	+	8.26777i	0.214143	+	0.423016i
$383$	−0.318169	+	0.551085i	−0.0162577	+	0.0281591i	−0.874040	−	0.485854i	$-0.838509\pi$
$383$	−0.318169	+	0.551085i	−0.0162577	+	0.0281591i	0.857782	+	0.514013i	$0.171842\pi$
$384$		0			0
$385$	1.87950	+	1.58323i	0.0957881	+	0.0806887i
$386$	−0.251515	+	4.56997i	−0.0128018	+	0.232606i
$387$		0			0
$388$	−4.07663	+	1.78949i	−0.206960	+	0.0908474i
$389$	−0.509547	−	0.882561i	−0.0258351	−	0.0447476i	0.852819	−	0.522207i	$-0.174891\pi$
$389$	−0.509547	−	0.882561i	−0.0258351	−	0.0447476i	−0.878654	+	0.477459i	$0.841558\pi$
$390$		0			0
$391$	26.9446			1.36265
$392$	−19.7987	+	0.114075i	−0.999983	+	0.00576166i
$393$		0			0
$394$	22.7991	+	14.8910i	1.14860	+	0.750200i
$395$	−3.42030	−	5.92414i	−0.172094	−	0.298076i
$396$		0			0
$397$	25.8035	+	14.8976i	1.29504	+	0.747691i	0.979543	−	0.201236i	$-0.0644957\pi$
$397$	25.8035	+	14.8976i	1.29504	+	0.747691i	0.315496	+	0.948927i	$0.397829\pi$
$398$	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	−0.938260	−	0.345931i	$-0.887563\pi$
$401$	−3.39513	+	5.88053i	−0.169545	+	0.293660i	0.768715	+	0.639591i	$0.220896\pi$
$402$		0			0
$403$	−24.7447	+	14.2863i	−1.23262	+	0.711654i
$404$	1.23766	+	0.909163i	0.0615759	+	0.0452326i
$405$		0			0
$406$	−7.56863	−	25.1635i	−0.375625	−	1.24884i
$407$			11.1865i			0.554496i
$408$		0			0
$409$	3.21574	−	1.85661i	0.159008	−	0.0918034i	−0.418384	−	0.908270i	$-0.637404\pi$
$409$	3.21574	−	1.85661i	0.159008	−	0.0918034i	0.577393	+	0.816467i	$0.304070\pi$
$410$	−3.77630	+	1.91167i	−0.186498	+	0.0944106i
$411$		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
$416$	5.35787	+	21.0980i	0.262691	+	1.03442i
$417$		0			0
$418$	4.86959	−	7.45565i	0.238179	−	0.364668i
$419$	20.7082			1.01166			0.505832	−	0.862632i	$-0.331186\pi$
$419$	20.7082			1.01166			0.505832	+	0.862632i	$0.331186\pi$
$420$		0			0
$421$	15.6579			0.763118			0.381559	−	0.924344i	$-0.375387\pi$
$421$	15.6579			0.763118			0.381559	+	0.924344i	$0.375387\pi$
$422$	4.71574	−	7.22010i	0.229559	−	0.351469i
$423$		0			0
$424$	−28.3702	+	10.6351i	−1.37778	+	0.516486i
$425$	−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
$430$	−2.42949	+	1.22988i	−0.117160	+	0.0593099i
$431$	10.2723	−	5.93071i	0.494799	−	0.285672i	−0.231764	−	0.972772i	$-0.574450\pi$
$431$	10.2723	−	5.93071i	0.494799	−	0.285672i	0.726563	+	0.687100i	$0.241116\pi$
$432$		0			0
$433$			16.9269i			0.813454i	0.913550	+	0.406727i	$0.133330\pi$
$433$			16.9269i			0.813454i	−0.913550	+	0.406727i	$0.866670\pi$
$434$	19.0398	−	20.2330i	0.913941	−	0.971213i
$435$		0			0
$436$	−8.06011	+	10.9724i	−0.386009	+	0.525481i
$437$	−12.2940	+	7.09795i	−0.588102	+	0.339541i
$438$		0			0
$439$	1.17640	−	2.03759i	0.0561467	−	0.0972489i	−0.836586	−	0.547836i	$-0.815452\pi$
$439$	1.17640	−	2.03759i	0.0561467	−	0.0972489i	0.892733	+	0.450587i	$0.148785\pi$
$440$	−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	$-0.345465\pi$
$443$	−1.38904	−	0.801965i	−0.0659955	−	0.0381025i	−0.532635	+	0.846345i	$0.678798\pi$
$444$		0			0
$445$	−2.28670	−	3.96069i	−0.108400	−	0.187755i
$446$	−2.90023	−	1.89426i	−0.137330	−	0.0896956i
$447$		0			0
$448$	−10.8979	−	18.1449i	−0.514877	−	0.857264i
$449$	−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
$452$	−10.9656	−	24.9808i	−0.515780	−	1.17500i
$453$		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	0.481789	+	0.876287i	$0.339987\pi$
$457$	−11.0734	+	19.1797i	−0.517992	+	0.897189i	−0.999782	+	0.0209017i	$0.993346\pi$
$458$	−7.47762	−	14.7712i	−0.349406	−	0.690214i
$459$		0			0
$460$	2.47939	−	3.37524i	0.115602	−	0.157371i
$461$			30.7842i			1.43376i	0.697195	+	0.716882i	$0.254431\pi$
$461$			30.7842i			1.43376i	−0.697195	+	0.716882i	$0.745569\pi$
$462$		0			0
$463$			13.8120i			0.641897i	0.947097	+	0.320948i	$0.104002\pi$
$463$			13.8120i			0.641897i	−0.947097	+	0.320948i	$0.895998\pi$
$464$	19.0146	−	20.6778i	0.882733	−	0.959941i
$465$		0			0
$466$	−10.3067	+	5.21752i	−0.477447	+	0.241697i
$467$	−8.51330	+	14.7455i	−0.393949	+	0.682339i	−0.992966	−	0.118397i	$-0.962225\pi$
$467$	−8.51330	+	14.7455i	−0.393949	+	0.682339i	0.599018	+	0.800736i	$0.295558\pi$
$468$		0			0
$469$	−20.4481	−	3.64593i	−0.944207	−	0.168353i
$470$	−1.04701	−	0.0576236i	−0.0482949	−	0.00265798i
$471$		0			0
$472$	21.5006	−	8.05991i	0.989646	−	0.370987i
$473$	4.64082	+	8.03814i	0.213385	+	0.369594i
$474$		0			0
$475$	14.3058			0.656395
$476$	7.02285	+	29.0512i	0.321892	+	1.33156i
$477$		0			0
$478$	14.0736	−	21.5476i	0.643712	−	0.985565i
$479$	−15.8903	−	27.5227i	−0.726045	−	1.25755i	−0.958543	−	0.284950i	$-0.908023\pi$
$479$	−15.8903	−	27.5227i	−0.726045	−	1.25755i	0.232498	−	0.972597i	$-0.425310\pi$
$480$		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	$-0.624935\pi$
$487$	4.99690	−	2.88496i	0.226431	−	0.130730i	0.608925	+	0.793228i	$0.291601\pi$
$488$	−11.1189	+	13.5121i	−0.503329	+	0.611662i
$489$		0			0
$490$	3.48727	−	2.59275i	0.157539	−	0.117129i
$491$		−	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
$494$	7.31422	+	14.4485i	0.329083	+	0.650067i
$495$		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	$-0.190012\pi$
$499$	16.8383	+	9.72159i	0.753785	+	0.435198i	−0.0732749	+	0.997312i	$0.523345\pi$
$500$	−7.88394	+	3.46075i	−0.352581	+	0.154769i
$501$		0			0
$502$	−24.1053	−	15.7442i	−1.07587	−	0.702696i
$503$	−11.7570			−0.524217			−0.262108	−	0.965038i	$-0.584418\pi$
$503$	−11.7570			−0.524217			−0.262108	+	0.965038i	$0.584418\pi$
$504$		0			0
$505$	−0.337057			−0.0149989
$506$	−11.9517	−	7.80613i	−0.531317	−	0.347025i
$507$		0			0
$508$	−6.44470	+	2.82898i	−0.285937	+	0.125516i
$509$	17.4476	+	10.0734i	0.773350	+	0.446494i	0.834068	−	0.551661i	$-0.186006\pi$
$509$	17.4476	+	10.0734i	0.773350	+	0.446494i	−0.0607186	+	0.998155i	$0.519339\pi$
$510$		0			0
$511$	−26.1373	−	4.66031i	−1.15624	−	0.206160i
$512$	10.7453	−	19.9133i	0.474881	−	0.880050i
$513$		0			0
$514$	−13.5967	−	26.8588i	−0.599725	−	1.18469i
$515$	3.28405	−	1.89605i	0.144713	−	0.0835499i
$516$		0			0
$517$			3.57417i			0.157192i
$518$	19.2537	+	4.53713i	0.845958	+	0.199350i
$519$		0			0
$520$	−3.68914	−	3.03574i	−0.161779	−	0.133126i
$521$	31.0965	−	17.9536i	1.36236	−	0.786559i	0.372423	−	0.928063i	$-0.378527\pi$
$521$	31.0965	−	17.9536i	1.36236	−	0.786559i	0.989938	+	0.141504i	$0.0451937\pi$
$522$		0			0
$523$	22.6480	−	39.2276i	0.990330	−	1.71530i	0.375017	−	0.927018i	$-0.377637\pi$
$523$	22.6480	−	39.2276i	0.990330	−	1.71530i	0.615312	−	0.788283i	$-0.289030\pi$
$524$	−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
$530$	3.63637	−	5.56752i	0.157954	−	0.241838i
$531$		0			0
$532$	−10.8572	−	11.4052i	−0.470720	−	0.494478i
$533$	−26.2364			−1.13642
$534$		0			0
$535$	0.558433	+	0.967234i	0.0241432	+	0.0418172i
$536$	−7.79422	−	20.7918i	−0.336659	−	0.898070i
$537$		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	−0.228732	−	0.973490i	$-0.573458\pi$
$541$	16.9491	−	29.3568i	0.728701	−	1.26215i	0.957432	−	0.288657i	$-0.0932089\pi$
$542$	−16.9755	+	8.59349i	−0.729161	+	0.369122i
$543$		0			0
$544$	−22.8874	+	22.2952i	−0.981288	+	0.955899i
$545$		−	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	$0.946448\pi$
$548$	4.00000	−	5.44527i	0.170872	−	0.232610i
$549$		0			0
$550$	6.49731	+	12.8347i	0.277046	+	0.547275i
$551$	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
$556$	−13.2224	−	30.1220i	−0.560754	−	1.27746i
$557$	7.69701	+	13.3316i	0.326133	+	0.564879i	0.981741	−	0.190223i	$-0.0609210\pi$
$557$	7.69701	+	13.3316i	0.326133	+	0.564879i	−0.655608	+	0.755101i	$0.727588\pi$
$558$		0			0
$559$	−16.8792			−0.713914
$560$	4.28536	+	1.79352i	0.181089	+	0.0757899i
$561$		0			0
$562$	30.1339	+	19.6817i	1.27112	+	0.830222i
$563$	8.22052	+	14.2384i	0.346453	+	0.600075i	0.985617	−	0.168996i	$-0.0540525\pi$
$563$	8.22052	+	14.2384i	0.346453	+	0.600075i	−0.639163	+	0.769071i	$0.720719\pi$
$564$		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	0.151363	+	0.988478i	$0.451634\pi$
$569$	−18.6146	+	32.2415i	−0.780366	+	1.35163i	−0.931729	+	0.363155i	$0.881700\pi$
$570$		0			0
$571$	−17.9660	+	10.3727i	−0.751854	+	0.434083i	−0.826363	−	0.563137i	$-0.809594\pi$
$571$	−17.9660	+	10.3727i	−0.751854	+	0.434083i	0.0745095	+	0.997220i	$0.476261\pi$
$572$	−9.64082	+	13.1242i	−0.403103	+	0.548751i
$573$		0			0
$574$	24.4300	−	7.34801i	1.01969	−	0.306700i
$575$		−	22.9327i		−	0.956361i
$576$		0			0
$577$	−13.3550	+	7.71054i	−0.555978	+	0.320994i	−0.751530	−	0.659699i	$-0.770684\pi$
$577$	−13.3550	+	7.71054i	−0.555978	+	0.320994i	0.195552	+	0.980693i	$0.437350\pi$
$578$	18.8044	−	9.51929i	0.782158	−	0.395950i
$579$		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
$584$	−9.96274	−	26.5766i	−0.412261	−	1.09975i
$585$		0			0
$586$	2.49648	−	3.82228i	0.103129	−	0.157897i
$587$	34.0410			1.40502			0.702512	−	0.711672i	$-0.252062\pi$
$587$	34.0410			1.40502			0.702512	+	0.711672i	$0.252062\pi$
$588$		0			0
$589$	22.0965			0.910469
$590$	−2.75586	+	4.21940i	−0.113457	+	0.173710i
$591$		0			0
$592$	6.32351	+	20.1792i	0.259895	+	0.829361i
$593$	−27.5697	−	15.9173i	−1.13215	−	0.653647i	−0.187675	−	0.982231i	$-0.560095\pi$
$593$	−27.5697	−	15.9173i	−1.13215	−	0.653647i	−0.944475	+	0.328584i	$0.893429\pi$
$594$		0			0
$595$	−5.01706	−	4.22620i	−0.205679	−	0.173257i
$596$	12.8805	+	1.42210i	0.527606	+	0.0582516i
$597$		0			0
$598$	23.1614	−	11.7250i	0.947141	−	0.479470i
$599$	−18.0000	+	10.3923i	−0.735460	+	0.424618i	−0.820416	−	0.571767i	$-0.806258\pi$
$599$	−18.0000	+	10.3923i	−0.735460	+	0.424618i	0.0849563	+	0.996385i	$0.472925\pi$
$600$		0			0
$601$		−	15.8614i		−	0.646999i	−0.946228	−	0.323499i	$-0.895141\pi$
$601$		−	15.8614i		−	0.646999i	0.946228	−	0.323499i	$-0.104859\pi$
$602$	15.7171	−	4.72735i	0.640580	−	0.192673i
$603$		0			0
$604$	12.5227	+	9.19894i	0.509541	+	0.374300i
$605$	2.47960	−	1.43160i	0.100810	−	0.0582027i
$606$		0			0
$607$	21.7151	−	37.6116i	0.881388	−	1.52661i	0.0315900	−	0.999501i	$-0.489943\pi$
$607$	21.7151	−	37.6116i	0.881388	−	1.52661i	0.849798	−	0.527108i	$-0.176724\pi$
$608$	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	0.665668	−	0.746248i	$-0.268147\pi$
$613$	−7.76030	−	13.4412i	−0.313436	−	0.542887i	−0.979104	+	0.203361i	$0.934813\pi$
$614$	−6.45919	−	4.21876i	−0.260672	−	0.170255i
$615$		0			0
$616$	5.30135	−	14.9207i	0.213598	−	0.601173i
$617$	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	$-0.0603448\pi$
$619$	8.15665	+	14.1277i	0.327844	+	0.567842i	−0.654240	+	0.756287i	$0.727011\pi$
$620$	−5.96907	+	2.62019i	−0.239724	+	0.105229i
$621$		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
$626$	−12.0289	−	23.7618i	−0.480772	−	0.949714i
$627$		0			0
$628$	13.6425	+	10.0216i	0.544397	+	0.399904i
$629$		−	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	$0.817066\pi$
$632$	−28.0071	+	34.0352i	−1.11406	+	1.35385i
$633$		0			0
$634$	21.6582	−	10.9640i	0.860157	−	0.435436i
$635$	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
$640$	0.686775	+	4.91857i	0.0271472	+	0.194424i
$641$	4.89533	+	8.47896i	0.193354	+	0.334899i	0.946360	−	0.323115i	$-0.104730\pi$
$641$	4.89533	+	8.47896i	0.193354	+	0.334899i	−0.753006	+	0.658014i	$0.771397\pi$
$642$		0			0
$643$	7.26458			0.286487			0.143244	−	0.989687i	$-0.454247\pi$
$643$	7.26458			0.286487			0.143244	+	0.989687i	$0.454247\pi$
$644$	−18.2829	+	17.4045i	−0.720449	+	0.685834i
$645$		0			0
$646$	−12.9987	+	19.9018i	−0.511427	+	0.783027i
$647$	23.0419	+	39.9098i	0.905872	+	1.56902i	0.819742	+	0.572733i	$0.194117\pi$
$647$	23.0419	+	39.9098i	0.905872	+	1.56902i	0.0861302	+	0.996284i	$0.472550\pi$
$648$		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	−0.924700	−	0.380696i	$-0.875684\pi$
$653$	−3.38990	+	5.87149i	−0.132657	+	0.229769i	0.792043	+	0.610465i	$0.209018\pi$
$654$		0			0
$655$	7.45732	−	4.30548i	0.291381	−	0.168229i
$656$	20.0750	+	18.4604i	0.783797	+	0.720756i
$657$		0			0
$658$	6.15168	+	1.44964i	0.239817	+	0.0565130i
$659$			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	0.113019	−	0.993593i	$-0.463948\pi$
$661$	26.4813	−	15.2890i	1.03000	−	0.594674i	0.916986	+	0.398919i	$0.130615\pi$
$662$	−13.7244	−	27.1110i	−0.533413	−	1.05370i
$663$		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
$668$	6.52771	+	14.8708i	0.252565	+	0.575368i
$669$		0			0
$670$	4.08030	+	2.66501i	0.157636	+	0.102958i
$671$	−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	$0.539230\pi$
$674$	6.99821	+	4.57081i	0.269561	+	0.176061i
$675$		0			0
$676$	−1.45287	−	3.30979i	−0.0558796	−	0.127299i
$677$	10.8219	+	6.24801i	0.415919	+	0.240131i	0.693330	−	0.720621i	$-0.256143\pi$
$677$	10.8219	+	6.24801i	0.415919	+	0.240131i	−0.277411	+	0.960751i	$0.589476\pi$
$678$		0			0
$679$	−3.79437	+	4.50442i	−0.145615	+	0.172864i
$680$	1.15147	−	6.91760i	0.0441569	−	0.265278i
$681$		0			0
$682$	10.0356	+	19.8243i	0.384284	+	0.759112i
$683$	39.1917	−	22.6273i	1.49963	−	0.865811i	0.499629	−	0.866240i	$-0.333470\pi$
$683$	39.1917	−	22.6273i	1.49963	−	0.865811i	1.00000		0.000428478i	$0.000136389\pi$
$684$		0			0
$685$			1.48293i			0.0566600i
$686$	−23.4355	+	11.6951i	−0.894772	+	0.446523i
$687$		0			0
$688$	12.9153	+	11.8765i	0.492391	+	0.452788i
$689$	35.6976	−	20.6100i	1.35997	−	0.785179i
$690$		0			0
$691$	5.29654	−	9.17388i	0.201490	−	0.348991i	−0.747519	−	0.664241i	$-0.768755\pi$
$691$	5.29654	−	9.17388i	0.201490	−	0.348991i	0.949009	+	0.315250i	$0.102088\pi$
$692$	−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
$698$	−7.37827	+	11.2966i	−0.279272	+	0.427583i
$699$		0			0
$700$	24.7257	−	5.97720i	0.934544	−	0.225917i
$701$	−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
$704$	16.6112	−	3.25867i	0.626058	−	0.122816i
$705$		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	−0.307401	−	0.951580i	$-0.599459\pi$
$709$	17.8506	−	30.9181i	0.670392	−	1.16115i	0.977793	−	0.209573i	$-0.0672074\pi$
$710$	−0.647920	+	0.327995i	−0.0243160	+	0.0123094i
$711$		0			0
$712$	−18.7246	+	22.7548i	−0.701735	+	0.852772i
$713$		−	35.4214i		−	1.32654i
$714$		0			0
$715$		−	3.57417i		−	0.133667i
$716$	17.2980	+	12.7068i	0.646458	+	0.474877i
$717$		0			0
$718$	4.42528	+	8.74167i	0.165150	+	0.326236i
$719$	−6.40447	+	11.0929i	−0.238846	+	0.413694i	−0.960384	−	0.278682i	$-0.910103\pi$
$719$	−6.40447	+	11.0929i	−0.238846	+	0.413694i	0.721537	+	0.692376i	$0.243436\pi$
$720$		0			0
$721$	−21.4926	+	7.77611i	−0.800427	+	0.289598i
$722$	−0.788376	+	14.3246i	−0.0293403	+	0.533107i
$723$		0			0
$724$	−2.22370	+	0.976121i	−0.0826433	+	0.0362772i
$725$	16.8805	+	29.2379i	0.626927	+	1.08587i
$726$		0			0
$727$	−19.3286			−0.716860			−0.358430	−	0.933557i	$-0.616688\pi$
$727$	−19.3286			−0.716860			−0.358430	+	0.933557i	$0.616688\pi$
$728$	18.6785	+	21.9163i	0.692271	+	0.812272i
$729$		0			0
$730$	5.21554	+	3.40648i	0.193036	+	0.126079i
$731$	−12.3880	−	21.4567i	−0.458188	−	0.793604i
$732$		0			0
$733$	−32.6407	−	18.8451i	−1.20561	−	0.696061i	−0.243815	−	0.969822i	$-0.578399\pi$
$733$	−32.6407	−	18.8451i	−1.20561	−	0.696061i	−0.961798	+	0.273761i	$0.911732\pi$
$734$	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	$-0.584587\pi$
$739$	12.0072	−	6.93237i	0.441693	−	0.255011i	0.704315	+	0.709887i	$0.251254\pi$
$740$	−3.74056	−	2.74775i	−0.137506	−	0.101009i
$741$		0			0
$742$	−27.4676	+	29.1888i	−1.00837	+	1.07155i
$743$			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
$746$	−18.2630	+	9.24525i	−0.668656	+	0.338493i
$747$		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	$-0.512170\pi$
$751$	−25.2868	−	14.5993i	−0.922728	−	0.532737i	−0.884504	+	0.466532i	$0.845503\pi$
$752$	2.02040	+	6.44740i	0.0736765	+	0.235112i
$753$		0			0
$754$	−20.8989	+	31.9975i	−0.761092	+	1.16528i
$755$	−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	$0.562895\pi$
$758$	16.7018	−	25.5715i	0.606636	−	0.928799i
$759$		0			0
$760$	1.29691	+	3.45962i	0.0470437	+	0.125494i
$761$	0.203165	+	0.117298i	0.00736474	+	0.00425204i	0.503678	−	0.863892i	$-0.331980\pi$
$761$	0.203165	+	0.117298i	0.00736474	+	0.00425204i	−0.496313	+	0.868144i	$0.665313\pi$
$762$		0			0
$763$	−3.16143	+	17.7308i	−0.114451	+	0.641899i
$764$	−1.43817	+	13.0261i	−0.0520313	+	0.471267i
$765$		0			0
$766$	−0.802901	+	0.406451i	−0.0290100	+	0.0146857i
$767$	−27.0537	+	15.6195i	−0.976854	+	0.563987i
$768$		0			0
$769$		−	34.8540i		−	1.25687i	−0.777863	−	0.628434i	$-0.783696\pi$
$769$		−	34.8540i		−	1.25687i	0.777863	−	0.628434i	$-0.216304\pi$
$770$	1.00102	+	3.32809i	0.0360742	+	0.119936i
$771$		0			0
$772$	−3.83196	+	5.21651i	−0.137915	+	0.187746i
$773$	−17.0362	+	9.83583i	−0.612748	+	0.353770i	−0.774040	−	0.633137i	$-0.781767\pi$
$773$	−17.0362	+	9.83583i	−0.612748	+	0.353770i	0.161292	+	0.986907i	$0.448434\pi$
$774$		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
$782$	31.9034	+	20.8374i	1.14086	+	0.745143i
$783$		0			0
$784$	−23.5306	−	15.1761i	−0.840377	−	0.542002i
$785$	−3.71533			−0.132606
$786$		0			0
$787$	19.4781	+	33.7370i	0.694319	+	1.20260i	0.970410	+	0.241464i	$0.0776275\pi$
$787$	19.4781	+	33.7370i	0.694319	+	1.20260i	−0.276091	+	0.961131i	$0.589039\pi$
$788$	15.4791	+	35.2631i	0.551422	+	1.25620i
$789$		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
$794$	19.0313	+	37.5943i	0.675395	+	1.33417i
$795$		0			0
$796$	10.2084	−	13.8969i	0.361828	−	0.492563i
$797$			20.4557i			0.724579i	0.932066	+	0.362289i	$0.118005\pi$
$797$			20.4557i			0.724579i	−0.932066	+	0.362289i	$0.881995\pi$
$798$		0			0
$799$		−	9.54077i		−	0.337528i
$800$	18.9756	+	19.4796i	0.670889	+	0.688708i
$801$		0			0
$802$	−8.56762	+	4.33717i	−0.302533	+	0.153151i
$803$	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
$808$	0.762340	+	2.03362i	0.0268190	+	0.0715424i
$809$	−24.4650	−	42.3746i	−0.860143	−	1.48981i	−0.871790	−	0.489879i	$-0.837041\pi$
$809$	−24.4650	−	42.3746i	−0.860143	−	1.48981i	0.0116472	−	0.999932i	$-0.496292\pi$
$810$		0			0
$811$	51.9424			1.82394			0.911972	−	0.410253i	$-0.134560\pi$
$811$	51.9424			1.82394			0.911972	+	0.410253i	$0.134560\pi$
$812$	10.4985	−	35.6476i	0.368423	−	1.25099i
$813$		0			0
$814$	−8.65102	+	13.2453i	−0.303218	+	0.464246i
$815$	−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	−0.449281	−	0.893391i	$-0.648320\pi$
$821$	15.7322	−	27.2490i	0.549059	−	0.950998i	0.998339	−	0.0576069i	$-0.0183470\pi$
$822$		0			0
$823$	35.9504	−	20.7560i	1.25315	−	0.723507i	0.281417	−	0.959586i	$-0.409196\pi$
$823$	35.9504	−	20.7560i	1.25315	−	0.723507i	0.971734	+	0.236078i	$0.0758622\pi$
$824$	−18.8674	−	15.5258i	−0.657278	−	0.540865i
$825$		0			0
$826$	20.8165	−	22.1210i	0.724300	−	0.769688i
$827$			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	−0.336553	−	0.941664i	$-0.609261\pi$
$829$	8.94508	−	5.16444i	0.310675	−	0.179369i	0.647229	+	0.762296i	$0.275928\pi$
$830$	1.54110	+	3.04427i	0.0534922	+	0.105668i
$831$		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
$836$	11.5315	−	5.06191i	0.398827	−	0.175070i
$837$		0			0
$838$	24.5193	+	16.0145i	0.847005	+	0.553213i
$839$	−10.4794			−0.361789			−0.180894	−	0.983503i	$-0.557899\pi$
$839$	−10.4794			−0.361789			−0.180894	+	0.983503i	$0.557899\pi$
$840$		0			0
$841$	20.3204			0.700704
$842$	18.5395	+	12.1089i	0.638913	+	0.417300i
$843$		0			0
$844$	11.1672	−	4.90198i	0.384392	−	0.168733i
$845$	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
$850$	−17.3437	−	34.2606i	−0.594883	−	1.17513i
$851$	21.8408	−	12.6098i	0.748693	−	0.432258i
$852$		0			0
$853$		−	25.5157i		−	0.873642i	−0.899548	−	0.436821i	$-0.856104\pi$
$853$		−	25.5157i		−	0.873642i	0.899548	−	0.436821i	$-0.143896\pi$
$854$	−5.30955	+	22.5315i	−0.181689	+	0.771012i
$855$		0			0
$856$	4.57272	−	5.55692i	0.156292	−	0.189931i
$857$	9.99828	−	5.77251i	0.341535	−	0.197185i	−0.319416	−	0.947615i	$-0.603487\pi$
$857$	9.99828	−	5.77251i	0.341535	−	0.197185i	0.660951	+	0.750429i	$0.270153\pi$
$858$		0			0
$859$	−16.4552	+	28.5013i	−0.561445	+	0.972452i	0.435925	+	0.899983i	$0.356421\pi$
$859$	−16.4552	+	28.5013i	−0.561445	+	0.972452i	−0.997371	+	0.0724689i	$0.976912\pi$
$860$	−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	−0.955546	−	0.294842i	$-0.904733\pi$
$863$	−49.6075	−	28.6409i	−1.68866	−	0.974948i	−0.733114	−	0.680106i	$-0.761934\pi$
$864$		0			0
$865$	−0.310863	−	0.538430i	−0.0105696	−	0.0183072i
$866$	−13.0903	+	20.0420i	−0.444825	+	0.681056i
$867$		0			0
$868$	38.1908	−	9.23226i	1.29628	−	0.313363i
$869$	−32.9745			−1.11858
$870$		0			0
$871$	15.1046	+	26.1619i	0.511799	+	0.886462i
$872$	−18.0288	+	6.75846i	−0.610534	+	0.228870i
$873$		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	0.421289	+	0.906926i	$0.361578\pi$
$877$	−17.0215	+	29.4822i	−0.574777	+	0.995542i	−0.996066	+	0.0886159i	$0.971756\pi$
$878$	2.96866	−	1.50282i	0.100187	−	0.0507177i
$879$		0			0
$880$	−2.51485	+	2.73481i	−0.0847757	+	0.0921906i
$881$		−	23.4638i		−	0.790514i	−0.918571	−	0.395257i	$-0.870656\pi$
$881$		−	23.4638i		−	0.790514i	0.918571	−	0.395257i	$-0.129344\pi$
$882$		0			0
$883$			8.14468i			0.274090i	0.990565	+	0.137045i	$0.0437606\pi$
$883$			8.14468i			0.274090i	−0.990565	+	0.137045i	$0.956239\pi$
$884$	25.7348	−	35.0333i	0.865556	−	1.17830i
$885$		0			0
$886$	−1.02449	−	2.02376i	−0.0344183	−	0.0679896i
$887$	14.6109	−	25.3068i	0.490585	−	0.849718i	−0.509356	−	0.860556i	$-0.670116\pi$
$887$	14.6109	−	25.3068i	0.490585	−	0.849718i	0.999941	+	0.0108376i	$0.00344978\pi$
$888$		0			0
$889$	−5.99849	+	7.12099i	−0.201183	+	0.238830i
$890$	0.355425	−	6.45800i	0.0119139	−	0.216473i
$891$		0			0
$892$	−1.96907	−	4.48574i	−0.0659293	−	0.150194i
$893$	2.51330	+	4.35317i	0.0841044	+	0.145673i
$894$		0			0
$895$	−4.71085			−0.157466
$896$	1.12867	−	29.9120i	0.0377062	−	0.999289i
$897$		0			0
$898$	−1.60091	−	1.04562i	−0.0534231	−	0.0348928i
$899$	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	0.625231	−	0.780440i	$-0.285005\pi$
$907$	48.5997	−	28.0591i	1.61373	−	0.931686i	0.988496	−	0.151246i	$-0.0483286\pi$
$908$	27.5639	−	37.5232i	0.914740	−	1.24525i
$909$		0			0
$910$	−6.15168	−	1.44964i	−0.203926	−	0.0480552i
$911$		−	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
$914$	−27.9438	+	14.1459i	−0.924298	+	0.467906i
$915$		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	$-0.552488\pi$
$919$	−33.3617	−	19.2614i	−1.10050	−	0.635375i	−0.936353	+	0.351060i	$0.885821\pi$
$920$	5.54590	−	2.07899i	0.182843	−	0.0685422i
$921$		0			0
$922$	−23.8067	+	36.4496i	−0.784033	+	1.20040i
$923$	−4.50151			−0.148169
$924$		0			0
$925$	−25.4148			−0.835635
$926$	−10.6814	+	16.3539i	−0.351012	+	0.537422i
$927$		0			0
$928$	38.5050	−	9.77839i	1.26399	−	0.320991i
$929$	41.3034	+	23.8465i	1.35512	+	0.782379i	0.988961	−	0.148173i	$-0.0473394\pi$
$929$	41.3034	+	23.8465i	1.35512	+	0.782379i	0.366159	+	0.930552i	$0.380673\pi$
$930$		0			0
$931$	−19.5472	−	7.19947i	−0.640634	−	0.235953i
$932$	−16.2384	−	1.79284i	−0.531906	−	0.0587263i
$933$		0			0
$934$	−21.4834	+	10.8755i	−0.702957	+	0.355857i
$935$	4.54346	−	2.62317i	0.148587	−	0.0857867i
$936$		0			0
$937$			6.18932i			0.202196i	0.994876	+	0.101098i	$0.0322356\pi$
$937$			6.18932i			0.202196i	−0.994876	+	0.101098i	$0.967764\pi$
$938$	−21.3918	−	20.1303i	−0.698466	−	0.657278i
$939$		0			0
$940$	−1.19513	−	0.877924i	−0.0389809	−	0.0286347i
$941$	6.33052	−	3.65493i	0.206369	−	0.119147i	−0.393254	−	0.919430i	$-0.628651\pi$
$941$	6.33052	−	3.65493i	0.206369	−	0.119147i	0.599623	+	0.800283i	$0.295317\pi$
$942$		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	$-0.253795\pi$
$947$	13.1805	+	7.60978i	0.428309	+	0.247285i	−0.270317	+	0.962771i	$0.587128\pi$
$948$		0			0
$949$	19.3070	+	33.4407i	0.626732	+	1.08553i
$950$	16.9386	+	11.0633i	0.549560	+	0.358940i
$951$		0			0
$952$	−14.1512	+	39.8288i	−0.458644	+	1.29086i
$953$	−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
$956$	33.3273	−	14.6294i	1.07788	−	0.473150i
$957$		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
$962$	−12.9940	−	25.6683i	−0.418944	−	0.827579i
$963$		0			0
$964$	46.6062	+	34.2361i	1.50109	+	1.10267i
$965$		−	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	$-0.0780132\pi$
$968$	−14.2457	−	11.7226i	−0.457874	−	0.376779i
$969$		0			0
$970$	1.23292	−	0.624140i	0.0395867	−	0.0200399i
$971$	22.4660	−	38.9123i	0.720968	−	1.24875i	−0.239644	−	0.970861i	$-0.577031\pi$
$971$	22.4660	−	38.9123i	0.720968	−	1.24875i	0.960612	−	0.277893i	$-0.0896360\pi$
$972$		0			0
$973$	−33.2829	−	28.0364i	−1.06700	−	0.898805i
$974$	8.14757	+	0.448413i	0.261065	+	0.0143681i
$975$		0			0
$976$	−23.6146	+	7.40005i	−0.755886	+	0.236870i
$977$	6.04122	+	10.4637i	0.193276	+	0.334763i	0.946334	−	0.323191i	$-0.104755\pi$
$977$	6.04122	+	10.4637i	0.193276	+	0.334763i	−0.753058	+	0.657954i	$0.771422\pi$
$978$		0			0
$979$	−22.0457			−0.704584
$980$	6.13413	−	0.373063i	0.195948	−	0.0119170i
$981$		0			0
$982$	17.5118	−	26.8117i	0.558825	−	0.855597i
$983$	−8.67473	−	15.0251i	−0.276681	−	0.479225i	0.693877	−	0.720094i	$-0.255901\pi$
$983$	−8.67473	−	15.0251i	−0.276681	−	0.479225i	−0.970558	+	0.240868i	$0.922568\pi$
$984$		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	$-0.951298\pi$
$991$	−42.5136	+	24.5452i	−1.35049	+	0.779705i	−0.362171	+	0.932112i	$0.617964\pi$
$992$	29.3093	+	30.0878i	0.930573	+	0.955289i
$993$		0			0
$994$	4.19158	−	1.26074i	0.132949	−	0.0399882i
$995$			3.78461i			0.119980i
$996$		0			0
$997$	7.88043	−	4.54977i	0.249576	−	0.144093i	−0.369994	−	0.929034i	$-0.620640\pi$
$997$	7.88043	−	4.54977i	0.249576	−	0.144093i	0.619570	+	0.784941i	$0.287307\pi$
$998$	12.4190	+	24.5325i	0.393117	+	0.776562i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.4	✓	8	12.11	even	2
84.2.o.a.31.4	yes	8	21.17	even	6
84.2.o.b.19.1	yes	8	3.2	odd	2
84.2.o.b.31.1	yes	8	84.59	odd	6
252.2.bf.f.19.4		8	1.1	even	1	trivial
252.2.bf.f.199.4		8	28.3	even	6	inner
252.2.bf.g.19.1		8	4.3	odd	2
252.2.bf.g.199.1		8	7.3	odd	6
588.2.b.a.391.5		8	84.47	odd	6
588.2.b.a.391.6		8	21.2	odd	6
588.2.b.b.391.5		8	84.23	even	6
588.2.b.b.391.6		8	21.5	even	6
588.2.o.b.19.1		8	21.20	even	2
588.2.o.b.31.1		8	84.11	even	6
588.2.o.d.19.4		8	84.83	odd	2
588.2.o.d.31.4		8	21.11	odd	6
1344.2.bl.i.703.3		8	168.59	odd	6
1344.2.bl.i.1279.3		8	24.5	odd	2
1344.2.bl.j.703.3		8	168.101	even	6
1344.2.bl.j.1279.3		8	24.11	even	2
1764.2.b.i.1567.3		8	7.5	odd	6
1764.2.b.i.1567.4		8	28.23	odd	6
1764.2.b.j.1567.3		8	7.2	even	3
1764.2.b.j.1567.4		8	28.19	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18404 + 0.773342i) q^{2} +(0.803884 + 1.83133i) q^{4} +(-0.380152 - 0.219481i) q^{5} +(2.02350 + 1.70453i) q^{7} +(-0.464416 + 2.79004i) q^{8} +O(q^{10})\)	\(q+(1.18404 + 0.773342i) q^{2} +(0.803884 + 1.83133i) q^{4} +(-0.380152 - 0.219481i) q^{5} +(2.02350 + 1.70453i) q^{7} +(-0.464416 + 2.79004i) q^{8} +(-0.280380 - 0.553861i) q^{10} +(-1.83249 + 1.05799i) q^{11} -3.84803i q^{13} +(1.07772 + 3.58309i) q^{14} +(-2.70754 + 2.94435i) q^{16} +(4.89158 - 2.82415i) q^{17} +(-1.48792 + 2.57715i) q^{19} +(0.0963438 - 0.872621i) q^{20} +(-2.98792 - 0.164445i) q^{22} +(4.13127 + 2.38519i) q^{23} +(-2.40366 - 4.16325i) q^{25} +(2.97584 - 4.55620i) q^{26} +(-1.49490 + 5.07595i) q^{28} -7.02285 q^{29} +(-3.71264 - 6.43048i) q^{31} +(-5.48282 + 1.39237i) q^{32} +(7.97584 + 0.438962i) q^{34} +(-0.395127 - 1.09210i) q^{35} +(2.64335 - 4.57842i) q^{37} +(-3.75477 + 1.90077i) q^{38} +(0.788909 - 0.958709i) q^{40} -6.81813i q^{41} -4.38646i q^{43} +(-3.41063 - 2.50539i) q^{44} +(3.04701 + 6.01904i) q^{46} +(0.844569 - 1.46284i) q^{47} +(1.18914 + 6.89826i) q^{49} +(0.373604 - 6.78829i) q^{50} +(7.04701 - 3.09337i) q^{52} +(5.35599 + 9.27685i) q^{53} +0.928833 q^{55} +(-5.69546 + 4.85404i) q^{56} +(-8.31531 - 5.43106i) q^{58} +(-4.05909 - 7.03055i) q^{59} +(5.35787 + 3.09337i) q^{61} +(0.577061 - 10.4851i) q^{62} +(-7.56863 - 2.59148i) q^{64} +(-0.844569 + 1.46284i) q^{65} +(-6.79878 + 3.92528i) q^{67} +(9.10422 + 6.68780i) q^{68} +(0.376724 - 1.59866i) q^{70} -1.16982i q^{71} +(-8.69036 + 5.01738i) q^{73} +(6.67051 - 3.37680i) q^{74} +(-5.91574 - 0.653140i) q^{76} +(-5.51142 - 0.982694i) q^{77} +(13.4958 + 7.79180i) q^{79} +(1.67551 - 0.525049i) q^{80} +(5.27275 - 8.07291i) q^{82} -5.49645 q^{83} -2.47939 q^{85} +(3.39223 - 5.19372i) q^{86} +(-2.10079 - 5.60406i) q^{88} +(9.02285 + 5.20934i) q^{89} +(6.55909 - 7.78650i) q^{91} +(-1.04701 + 9.48314i) q^{92} +(2.13127 - 1.07891i) q^{94} +(1.13127 - 0.653140i) q^{95} +2.22605i q^{97} +(-3.92673 + 9.08740i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - q^{4} - 2 q^{7} - 4 q^{8}+O(q^{10}) \) 8 * q - q^2 - q^4 - 2 * q^7 - 4 * q^8	\( 8 q - q^{2} - q^{4} - 2 q^{7} - 4 q^{8} - 13 q^{10} + 6 q^{11} + 10 q^{14} + 7 q^{16} + 6 q^{19} + 22 q^{20} - 6 q^{22} + 2 q^{25} - 12 q^{26} - 7 q^{28} + 16 q^{29} - 6 q^{31} - 21 q^{32} + 28 q^{34} - 12 q^{35} + 6 q^{37} - 8 q^{38} - 13 q^{40} - 19 q^{44} - 12 q^{46} + 4 q^{47} + 4 q^{49} - 2 q^{50} + 20 q^{52} + 4 q^{53} + 8 q^{55} + q^{56} - 23 q^{58} - 14 q^{59} + 12 q^{61} - 48 q^{62} + 2 q^{64} - 4 q^{65} - 42 q^{67} + 10 q^{68} + 35 q^{70} - 18 q^{73} + 28 q^{74} - 44 q^{76} - 8 q^{77} + 6 q^{79} + 33 q^{80} - 14 q^{82} + 4 q^{83} - 32 q^{85} + 42 q^{86} + 11 q^{88} + 34 q^{91} + 28 q^{92} - 16 q^{94} - 24 q^{95} + 19 q^{98}+O(q^{100}) \) 8 * q - q^2 - q^4 - 2 * q^7 - 4 * q^8 - 13 * q^10 + 6 * q^11 + 10 * q^14 + 7 * q^16 + 6 * q^19 + 22 * q^20 - 6 * q^22 + 2 * q^25 - 12 * q^26 - 7 * q^28 + 16 * q^29 - 6 * q^31 - 21 * q^32 + 28 * q^34 - 12 * q^35 + 6 * q^37 - 8 * q^38 - 13 * q^40 - 19 * q^44 - 12 * q^46 + 4 * q^47 + 4 * q^49 - 2 * q^50 + 20 * q^52 + 4 * q^53 + 8 * q^55 + q^56 - 23 * q^58 - 14 * q^59 + 12 * q^61 - 48 * q^62 + 2 * q^64 - 4 * q^65 - 42 * q^67 + 10 * q^68 + 35 * q^70 - 18 * q^73 + 28 * q^74 - 44 * q^76 - 8 * q^77 + 6 * q^79 + 33 * q^80 - 14 * q^82 + 4 * q^83 - 32 * q^85 + 42 * q^86 + 11 * q^88 + 34 * q^91 + 28 * q^92 - 16 * q^94 - 24 * q^95 + 19 * q^98

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