LMFDB - Embedded newform 819.2.fm.g.370.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(370,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("819.370");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fm (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			370.5
Character	$\chi$	$=$	819.370
Dual form			819.2.fm.g.622.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.357317 + 1.33353i) q^{2} +(0.0814361 - 0.0470171i) q^{4} +(-2.02925 - 2.02925i) q^{5} +(-2.32989 + 1.25364i) q^{7} +(2.04421 + 2.04421i) q^{8} +O(q^{10})$	\(q+(0.357317 + 1.33353i) q^{2} +(0.0814361 - 0.0470171i) q^{4} +(-2.02925 - 2.02925i) q^{5} +(-2.32989 + 1.25364i) q^{7} +(2.04421 + 2.04421i) q^{8} +(1.98097 - 3.43114i) q^{10} +(-1.37941 + 0.369611i) q^{11} +(-3.54926 - 0.634621i) q^{13} +(-2.50427 - 2.65902i) q^{14} +(-1.90154 + 3.29357i) q^{16} +(2.09909 + 3.63573i) q^{17} +(-1.59577 + 5.95551i) q^{19} +(-0.260663 - 0.0698445i) q^{20} +(-0.985770 - 1.70740i) q^{22} +(-6.77658 - 3.91246i) q^{23} +3.23569i q^{25} +(-0.421928 - 4.95979i) q^{26} +(-0.130794 + 0.211636i) q^{28} +(-0.441485 + 0.764674i) q^{29} +(0.648762 + 0.648762i) q^{31} +(0.513380 + 0.137560i) q^{32} +(-4.09830 + 4.09830i) q^{34} +(7.27187 + 2.18397i) q^{35} +(-7.19341 + 1.92747i) q^{37} -8.51202 q^{38} -8.29643i q^{40} +(-11.4714 + 3.07376i) q^{41} +(0.809734 - 0.467500i) q^{43} +(-0.0949554 + 0.0949554i) q^{44} +(2.79598 - 10.4347i) q^{46} +(2.20935 - 2.20935i) q^{47} +(3.85676 - 5.84170i) q^{49} +(-4.31487 + 1.15617i) q^{50} +(-0.318876 + 0.115195i) q^{52} -2.52486 q^{53} +(3.54919 + 2.04912i) q^{55} +(-7.32550 - 2.20008i) q^{56} +(-1.17746 - 0.315500i) q^{58} +(5.65360 + 1.51488i) q^{59} +(0.0739657 - 0.0427041i) q^{61} +(-0.633327 + 1.09695i) q^{62} +8.33994i q^{64} +(5.91453 + 8.49013i) q^{65} +(0.266684 + 0.995278i) q^{67} +(0.341884 + 0.197387i) q^{68} +(-0.314014 + 10.4776i) q^{70} +(-2.79996 - 0.750247i) q^{71} +(-2.01428 + 2.01428i) q^{73} +(-5.14066 - 8.90388i) q^{74} +(0.150057 + 0.560022i) q^{76} +(2.75050 - 2.59043i) q^{77} +9.43068 q^{79} +(10.5422 - 2.82477i) q^{80} +(-8.19789 - 14.1992i) q^{82} +(1.54040 + 1.54040i) q^{83} +(3.11823 - 11.6374i) q^{85} +(0.912755 + 0.912755i) q^{86} +(-3.57536 - 2.06424i) q^{88} +(1.27469 + 4.75720i) q^{89} +(9.06497 - 2.97091i) q^{91} -0.735811 q^{92} +(3.73567 + 2.15679i) q^{94} +(15.3234 - 8.84698i) q^{95} +(2.37752 - 8.87303i) q^{97} +(9.16814 + 3.05575i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8}+O(q^{10}) $ 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8	$ 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8} + 4 q^{11} + 32 q^{14} + 12 q^{16} + 4 q^{22} + 12 q^{23} + 24 q^{28} - 4 q^{29} - 4 q^{32} + 20 q^{35} + 4 q^{37} - 48 q^{43} - 24 q^{44} + 84 q^{46} + 24 q^{49} + 44 q^{50} - 72 q^{53} - 60 q^{56} - 16 q^{58} - 4 q^{65} - 56 q^{67} + 56 q^{70} - 84 q^{71} + 24 q^{74} - 80 q^{79} + 36 q^{85} + 48 q^{86} - 228 q^{88} - 48 q^{91} - 24 q^{92} + 84 q^{95} + 32 q^{98}+O(q^{100}) $ 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8 + 4 * q^11 + 32 * q^14 + 12 * q^16 + 4 * q^22 + 12 * q^23 + 24 * q^28 - 4 * q^29 - 4 * q^32 + 20 * q^35 + 4 * q^37 - 48 * q^43 - 24 * q^44 + 84 * q^46 + 24 * q^49 + 44 * q^50 - 72 * q^53 - 60 * q^56 - 16 * q^58 - 4 * q^65 - 56 * q^67 + 56 * q^70 - 84 * q^71 + 24 * q^74 - 80 * q^79 + 36 * q^85 + 48 * q^86 - 228 * q^88 - 48 * q^91 - 24 * q^92 + 84 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$-1$

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 $

$2$	0.357317	+	1.33353i	0.252661	+	0.942945i	0.969377	+	0.245579i	$0.0789781\pi$
$2$	0.357317	+	1.33353i	0.252661	+	0.942945i	−0.716715	+	0.697366i	$0.754355\pi$
$3$		0			0
$3$		0			0
$4$	0.0814361	−	0.0470171i	0.0407180	−	0.0235086i
$5$	−2.02925	−	2.02925i	−0.907507	−	0.907507i	0.0885635	−	0.996071i	$-0.471772\pi$
$5$	−2.02925	−	2.02925i	−0.907507	−	0.907507i	−0.996071	+	0.0885635i	$0.971772\pi$
$6$		0			0
$7$	−2.32989	+	1.25364i	−0.880615	+	0.473832i
$7$	−2.32989	+	1.25364i	−0.880615	+	0.473832i
$8$	2.04421	+	2.04421i	0.722739	+	0.722739i
$9$		0			0
$10$	1.98097	−	3.43114i	0.626437	−	1.08502i
$11$	−1.37941	+	0.369611i	−0.415906	+	0.111442i	−0.460703	−	0.887554i	$-0.652403\pi$
$11$	−1.37941	+	0.369611i	−0.415906	+	0.111442i	0.0447966	+	0.998996i	$0.485736\pi$
$12$		0			0
$13$	−3.54926	−	0.634621i	−0.984388	−	0.176012i
$13$	−3.54926	−	0.634621i	−0.984388	−	0.176012i
$14$	−2.50427	−	2.65902i	−0.669295	−	0.710652i
$15$		0			0
$16$	−1.90154	+	3.29357i	−0.475386	+	0.823393i
$17$	2.09909	+	3.63573i	0.509105	+	0.881795i	0.999944	+	0.0105451i	$0.00335669\pi$
$17$	2.09909	+	3.63573i	0.509105	+	0.881795i	−0.490840	+	0.871250i	$0.663310\pi$
$18$		0			0
$19$	−1.59577	+	5.95551i	−0.366096	+	1.36629i	0.499834	+	0.866121i	$0.333394\pi$
$19$	−1.59577	+	5.95551i	−0.366096	+	1.36629i	−0.865929	+	0.500166i	$0.833272\pi$
$20$	−0.260663	−	0.0698445i	−0.0582861	−	0.0156177i
$21$		0			0
$22$	−0.985770	−	1.70740i	−0.210167	−	0.364020i
$23$	−6.77658	−	3.91246i	−1.41302	−	0.815805i	−0.417344	−	0.908748i	$-0.637039\pi$
$23$	−6.77658	−	3.91246i	−1.41302	−	0.815805i	−0.995671	+	0.0929436i	$0.970372\pi$
$24$		0			0
$25$			3.23569i			0.647138i
$26$	−0.421928	−	4.95979i	−0.0827470	−	0.972695i
$27$		0			0
$28$	−0.130794	+	0.211636i	−0.0247178	+	0.0399955i
$29$	−0.441485	+	0.764674i	−0.0819817	+	0.141996i	−0.904101	−	0.427319i	$-0.859458\pi$
$29$	−0.441485	+	0.764674i	−0.0819817	+	0.141996i	0.822119	+	0.569315i	$0.192792\pi$
$30$		0			0
$31$	0.648762	+	0.648762i	0.116521	+	0.116521i	0.762963	−	0.646442i	$-0.223744\pi$
$31$	0.648762	+	0.648762i	0.116521	+	0.116521i	−0.646442	+	0.762963i	$0.723744\pi$
$32$	0.513380	+	0.137560i	0.0907536	+	0.0243174i
$33$		0			0
$34$	−4.09830	+	4.09830i	−0.702853	+	0.702853i
$35$	7.27187	+	2.18397i	1.22917	+	0.369158i
$36$		0			0
$37$	−7.19341	+	1.92747i	−1.18259	+	0.316874i	−0.795953	−	0.605358i	$-0.793030\pi$
$37$	−7.19341	+	1.92747i	−1.18259	+	0.316874i	−0.386637	+	0.922232i	$0.626363\pi$
$38$	−8.51202			−1.38083
$39$		0			0
$40$		−	8.29643i		−	1.31178i
$41$	−11.4714	+	3.07376i	−1.79154	+	0.480041i	−0.992606	−	0.121379i	$-0.961268\pi$
$41$	−11.4714	+	3.07376i	−1.79154	+	0.480041i	−0.798933	+	0.601421i	$0.794602\pi$
$42$		0			0
$43$	0.809734	−	0.467500i	0.123483	−	0.0712931i	−0.436986	−	0.899468i	$-0.643954\pi$
$43$	0.809734	−	0.467500i	0.123483	−	0.0712931i	0.560469	+	0.828175i	$0.310621\pi$
$44$	−0.0949554	+	0.0949554i	−0.0143151	+	0.0143151i
$45$		0			0
$46$	2.79598	−	10.4347i	0.412245	−	1.53852i
$47$	2.20935	−	2.20935i	0.322267	−	0.322267i	−0.527369	−	0.849636i	$-0.676821\pi$
$47$	2.20935	−	2.20935i	0.322267	−	0.322267i	0.849636	+	0.527369i	$0.176821\pi$
$48$		0			0
$49$	3.85676	−	5.84170i	0.550966	−	0.834528i
$50$	−4.31487	+	1.15617i	−0.610215	+	0.163507i
$51$		0			0
$52$	−0.318876	+	0.115195i	−0.0442201	+	0.0159747i
$53$	−2.52486			−0.346816			−0.173408	−	0.984850i	$-0.555478\pi$
$53$	−2.52486			−0.346816			−0.173408	+	0.984850i	$0.555478\pi$
$54$		0			0
$55$	3.54919	+	2.04912i	0.478572	+	0.276304i
$56$	−7.32550	−	2.20008i	−0.978912	−	0.293998i
$57$		0			0
$58$	−1.17746	−	0.315500i	−0.154608	−	0.0414272i
$59$	5.65360	+	1.51488i	0.736035	+	0.197220i	0.607315	−	0.794461i	$-0.292246\pi$
$59$	5.65360	+	1.51488i	0.736035	+	0.197220i	0.128720	+	0.991681i	$0.458913\pi$
$60$		0			0
$61$	0.0739657	−	0.0427041i	0.00947033	−	0.00546770i	−0.495257	−	0.868746i	$-0.664926\pi$
$61$	0.0739657	−	0.0427041i	0.00947033	−	0.00546770i	0.504728	+	0.863279i	$0.331593\pi$
$62$	−0.633327	+	1.09695i	−0.0804326	+	0.139313i
$63$		0			0
$64$			8.33994i			1.04249i
$65$	5.91453	+	8.49013i	0.733607	+	1.05307i
$66$		0			0
$67$	0.266684	+	0.995278i	0.0325806	+	0.121593i	0.980301	−	0.197510i	$-0.0632854\pi$
$67$	0.266684	+	0.995278i	0.0325806	+	0.121593i	−0.947720	+	0.319102i	$0.896619\pi$
$68$	0.341884	+	0.197387i	0.0414595	+	0.0239366i
$69$		0			0
$70$	−0.314014	+	10.4776i	−0.0375318	+	1.25231i
$71$	−2.79996	−	0.750247i	−0.332294	−	0.0890380i	0.0888143	−	0.996048i	$-0.471692\pi$
$71$	−2.79996	−	0.750247i	−0.332294	−	0.0890380i	−0.421109	+	0.907010i	$0.638359\pi$
$72$		0			0
$73$	−2.01428	+	2.01428i	−0.235754	+	0.235754i	−0.815089	−	0.579335i	$-0.803312\pi$
$73$	−2.01428	+	2.01428i	−0.235754	+	0.235754i	0.579335	+	0.815089i	$0.303312\pi$
$74$	−5.14066	−	8.90388i	−0.597589	−	1.03506i
$75$		0			0
$76$	0.150057	+	0.560022i	0.0172128	+	0.0642389i
$77$	2.75050	−	2.59043i	0.313449	−	0.295207i
$78$		0			0
$79$	9.43068			1.06103			0.530517	−	0.847674i	$-0.321998\pi$
$79$	9.43068			1.06103			0.530517	+	0.847674i	$0.321998\pi$
$80$	10.5422	−	2.82477i	1.17865	−	0.315819i
$81$		0			0
$82$	−8.19789	−	14.1992i	−0.905305	−	1.56803i
$83$	1.54040	+	1.54040i	0.169081	+	0.169081i	0.786575	−	0.617494i	$-0.211852\pi$
$83$	1.54040	+	1.54040i	0.169081	+	0.169081i	−0.617494	+	0.786575i	$0.711852\pi$
$84$		0			0
$85$	3.11823	−	11.6374i	0.338219	−	1.26225i
$86$	0.912755	+	0.912755i	0.0984249	+	0.0984249i
$87$		0			0
$88$	−3.57536	−	2.06424i	−0.381135	−	0.220048i
$89$	1.27469	+	4.75720i	0.135117	+	0.504262i	0.999997	+	0.00228491i	$0.000727309\pi$
$89$	1.27469	+	4.75720i	0.135117	+	0.504262i	−0.864881	+	0.501977i	$0.832606\pi$
$90$		0			0
$91$	9.06497	−	2.97091i	0.950267	−	0.311436i
$92$	−0.735811			−0.0767136
$93$		0			0
$94$	3.73567	+	2.15679i	0.385305	+	0.222456i
$95$	15.3234	−	8.84698i	1.57215	−	0.907681i
$96$		0			0
$97$	2.37752	−	8.87303i	0.241401	−	0.900920i	−0.733758	−	0.679411i	$-0.762235\pi$
$97$	2.37752	−	8.87303i	0.241401	−	0.900920i	0.975158	−	0.221509i	$-0.0710981\pi$
$98$	9.16814	+	3.05575i	0.926122	+	0.308677i
$99$		0			0
$100$	0.152133	+	0.263502i	0.0152133	+	0.0263502i
$101$	3.27488	−	5.67227i	0.325863	−	0.564412i	−0.655824	−	0.754914i	$-0.727678\pi$
$101$	3.27488	−	5.67227i	0.325863	−	0.564412i	0.981687	+	0.190503i	$0.0610118\pi$
$102$		0			0
$103$	9.85541			0.971082			0.485541	−	0.874214i	$-0.338623\pi$
$103$	9.85541			0.971082			0.485541	+	0.874214i	$0.338623\pi$
$104$	−5.95815	−	8.55275i	−0.584245	−	0.838666i
$105$		0			0
$106$	−0.902174	−	3.36696i	−0.0876269	−	0.327028i
$107$	5.29678	−	9.17430i	0.512059	−	0.886913i	−0.487843	−	0.872931i	$-0.662216\pi$
$107$	5.29678	−	9.17430i	0.512059	−	0.886913i	0.999902	−	0.0139814i	$-0.00445058\pi$
$108$		0			0
$109$	11.6691	−	11.6691i	1.11770	−	1.11770i	0.125617	−	0.992079i	$-0.459909\pi$
$109$	11.6691	−	11.6691i	1.11770	−	1.11770i	0.992079	−	0.125617i	$-0.0400911\pi$
$110$	−1.46437	+	5.46512i	−0.139623	+	0.521078i
$111$		0			0
$112$	0.301424	−	10.0575i	0.0284819	−	0.950346i
$113$	0.322118	+	0.557925i	0.0303023	+	0.0524851i	0.880779	−	0.473528i	$-0.157020\pi$
$113$	0.322118	+	0.557925i	0.0303023	+	0.0524851i	−0.850477	+	0.526013i	$0.823686\pi$
$114$		0			0
$115$	5.81201	+	21.6907i	0.541973	+	2.02267i
$116$			0.0830294i			0.00770909i
$117$		0			0
$118$			8.08051i			0.743871i
$119$	−9.44856	−	5.83934i	−0.866148	−	0.535292i
$120$		0			0
$121$	−7.76013	+	4.48031i	−0.705467	+	0.407301i
$122$	0.0833762	+	0.0833762i	0.00754853	+	0.00754853i
$123$		0			0
$124$	0.0833356	+	0.0223297i	0.00748376	+	0.00200527i
$125$	−3.58022	+	3.58022i	−0.320225	+	0.320225i
$126$		0			0
$127$	−14.1284	−	8.15702i	−1.25369	−	0.723819i	−0.281850	−	0.959458i	$-0.590948\pi$
$127$	−14.1284	−	8.15702i	−1.25369	−	0.723819i	−0.971841	+	0.235640i	$0.924282\pi$
$128$	−10.0948	+	2.70488i	−0.892259	+	0.239080i
$129$		0			0
$130$	−9.20845	+	10.9208i	−0.807634	+	0.957821i
$131$			2.35280i			0.205565i	0.994704	+	0.102783i	$0.0327746\pi$
$131$			2.35280i			0.205565i	−0.994704	+	0.102783i	$0.967225\pi$
$132$		0			0
$133$	−3.74811	−	15.8762i	−0.325002	−	1.37664i
$134$	−1.23194	+	0.711259i	−0.106423	+	0.0614435i
$135$		0			0
$136$	−3.14122	+	11.7232i	−0.269358	+	1.00526i
$137$	−2.68838	+	10.0332i	−0.229683	+	0.857190i	0.750790	+	0.660541i	$0.229673\pi$
$137$	−2.68838	+	10.0332i	−0.229683	+	0.857190i	−0.980474	+	0.196650i	$0.936994\pi$
$138$		0			0
$139$	−5.33208	+	3.07848i	−0.452261	+	0.261113i	−0.708784	−	0.705425i	$-0.750756\pi$
$139$	−5.33208	+	3.07848i	−0.452261	+	0.261113i	0.256524	+	0.966538i	$0.417423\pi$
$140$	0.694877	−	0.164049i	0.0587278	−	0.0138647i
$141$		0			0
$142$		−	4.00190i		−	0.335832i
$143$	5.13043	−	0.436445i	0.429028	−	0.0364974i
$144$		0			0
$145$	2.44759	−	0.655831i	0.203262	−	0.0544638i
$146$	−3.40583	−	1.96636i	−0.281869	−	0.162737i
$147$		0			0
$148$	−0.495179	+	0.495179i	−0.0407035	+	0.0407035i
$149$	8.40965	+	2.25336i	0.688945	+	0.184602i	0.586274	−	0.810113i	$-0.300594\pi$
$149$	8.40965	+	2.25336i	0.688945	+	0.184602i	0.102672	+	0.994715i	$0.467261\pi$
$150$		0			0
$151$	9.55198	+	9.55198i	0.777329	+	0.777329i	0.979376	−	0.202047i	$-0.0647593\pi$
$151$	9.55198	+	9.55198i	0.777329	+	0.777329i	−0.202047	+	0.979376i	$0.564759\pi$
$152$	−15.4364	+	8.91223i	−1.25206	+	0.722877i
$153$		0			0
$154$	4.43721	+	2.74226i	0.357561	+	0.220977i
$155$		−	2.63300i		−	0.211487i
$156$		0			0
$157$			6.77973i			0.541081i	0.962709	+	0.270541i	$0.0872024\pi$
$157$			6.77973i			0.541081i	−0.962709	+	0.270541i	$0.912798\pi$
$158$	3.36974	+	12.5761i	0.268082	+	1.00050i
$159$		0			0
$160$	−0.762632	−	1.32092i	−0.0602914	−	0.104428i
$161$	20.6935	+	0.620185i	1.63088	+	0.0488774i
$162$		0			0
$163$	−2.82752	+	10.5525i	−0.221469	+	0.826532i	0.762320	+	0.647200i	$0.224060\pi$
$163$	−2.82752	+	10.5525i	−0.221469	+	0.826532i	−0.983789	+	0.179332i	$0.942606\pi$
$164$	−0.789670	+	0.789670i	−0.0616629	+	0.0616629i
$165$		0			0
$166$	−1.50375	+	2.60458i	−0.116714	+	0.202155i
$167$	4.71387	+	17.5924i	0.364770	+	1.36134i	0.867732	+	0.497032i	$0.165577\pi$
$167$	4.71387	+	17.5924i	0.364770	+	1.36134i	−0.502962	+	0.864308i	$0.667756\pi$
$168$		0			0
$169$	12.1945	+	4.50487i	0.938039	+	0.346529i
$170$	16.6329			1.27569
$171$		0			0
$172$	0.0439610	−	0.0761428i	0.00335200	−	0.00580583i
$173$	−10.0761	−	17.4523i	−0.766070	−	1.32687i	−0.939679	−	0.342058i	$-0.888876\pi$
$173$	−10.0761	−	17.4523i	−0.766070	−	1.32687i	0.173608	−	0.984815i	$-0.444457\pi$
$174$		0			0
$175$	−4.05640	−	7.53880i	−0.306635	−	0.569879i
$176$	1.40566	−	5.24600i	0.105956	−	0.395432i
$177$		0			0
$178$	−5.88838	+	3.39966i	−0.441353	+	0.254815i
$179$	14.3173	+	8.26609i	1.07012	+	0.617837i	0.928216	−	0.372043i	$-0.121343\pi$
$179$	14.3173	+	8.26609i	1.07012	+	0.617837i	0.141909	+	0.989880i	$0.454676\pi$
$180$		0			0
$181$	−13.6897			−1.01755			−0.508774	−	0.860900i	$-0.669901\pi$
$181$	−13.6897			−1.01755			−0.508774	+	0.860900i	$0.669901\pi$
$182$	7.20085	+	11.0268i	0.533763	+	0.817362i
$183$		0			0
$184$	−5.85488	−	21.8507i	−0.431627	−	1.61085i
$185$	18.5085	+	10.6859i	1.36077	+	0.785643i
$186$		0			0
$187$	−4.23930	−	4.23930i	−0.310009	−	0.310009i
$188$	0.0760436	−	0.283799i	0.00554605	−	0.0206981i
$189$		0			0
$190$	17.2730	+	17.2730i	1.25311	+	1.25311i
$191$	−4.07445	−	7.05715i	−0.294817	−	0.510638i	0.680126	−	0.733096i	$-0.261925\pi$
$191$	−4.07445	−	7.05715i	−0.294817	−	0.510638i	−0.974942	+	0.222458i	$0.928592\pi$
$192$		0			0
$193$	−25.8745	+	6.93304i	−1.86249	+	0.499051i	−0.999976	−	0.00698876i	$-0.997775\pi$
$193$	−25.8745	+	6.93304i	−1.86249	+	0.499051i	−0.862510	+	0.506040i	$0.831109\pi$
$194$	12.6819			0.910511
$195$		0			0
$196$	0.0394195	−	0.657059i	0.00281568	−	0.0469328i
$197$	−4.77033	−	17.8031i	−0.339872	−	1.26842i	−0.898490	−	0.438995i	$-0.855335\pi$
$197$	−4.77033	−	17.8031i	−0.339872	−	1.26842i	0.558617	−	0.829426i	$-0.311332\pi$
$198$		0			0
$199$	6.35578	+	11.0085i	0.450550	+	0.780375i	0.998420	−	0.0561884i	$-0.0178947\pi$
$199$	6.35578	+	11.0085i	0.450550	+	0.780375i	−0.547871	+	0.836563i	$0.684561\pi$
$200$	−6.61444	+	6.61444i	−0.467712	+	0.467712i
$201$		0			0
$202$	8.73428	+	2.34034i	0.614542	+	0.164666i
$203$	0.0699820	−	2.33507i	0.00491178	−	0.163890i
$204$		0			0
$205$	29.5158	+	17.0410i	2.06147	+	1.19019i
$206$	3.52150	+	13.1424i	0.245355	+	0.915677i
$207$		0			0
$208$	8.83925	−	10.4830i	0.612892	−	0.726864i
$209$		−	8.80488i		−	0.609046i
$210$		0			0
$211$	−2.26459	+	3.92239i	−0.155901	+	0.270028i	−0.933387	−	0.358872i	$-0.883161\pi$
$211$	−2.26459	+	3.92239i	−0.155901	+	0.270028i	0.777486	+	0.628900i	$0.216495\pi$
$212$	−0.205614	+	0.118712i	−0.0141217	+	0.00815314i
$213$		0			0
$214$	14.1268	+	3.78526i	0.965688	+	0.258755i
$215$	−2.59182	−	0.694477i	−0.176761	−	0.0473629i
$216$		0			0
$217$	−2.32486	−	0.698227i	−0.157822	−	0.0473988i
$218$	19.7306	+	11.3915i	1.33632	+	0.771527i
$219$		0			0
$220$	0.385376			0.0259820
$221$	−5.14291	−	14.2363i	−0.345950	−	0.957637i
$222$		0			0
$223$	−22.4788	+	6.02318i	−1.50529	+	0.403342i	−0.914868	−	0.403752i	$-0.867706\pi$
$223$	−22.4788	+	6.02318i	−1.50529	+	0.403342i	−0.590423	+	0.807094i	$0.701039\pi$
$224$	−1.36857	+	0.323096i	−0.0914414	+	0.0215878i
$225$		0			0
$226$	−0.628909	+	0.628909i	−0.0418344	+	0.0418344i
$227$	2.69786	−	10.0685i	0.179063	−	0.668273i	−0.816761	−	0.576977i	$-0.804232\pi$
$227$	2.69786	−	10.0685i	0.179063	−	0.668273i	0.995824	−	0.0912961i	$-0.0291010\pi$
$228$		0			0
$229$	−1.36381	+	1.36381i	−0.0901234	+	0.0901234i	−0.750731	−	0.660608i	$-0.770299\pi$
$229$	−1.36381	+	1.36381i	−0.0901234	+	0.0901234i	0.660608	+	0.750731i	$0.270299\pi$
$230$	−26.8484	+	15.5009i	−1.77033	+	1.02210i
$231$		0			0
$232$	−2.46565	+	0.660668i	−0.161878	+	0.0433750i
$233$			8.59532i			0.563098i	0.959547	+	0.281549i	$0.0908482\pi$
$233$			8.59532i			0.563098i	−0.959547	+	0.281549i	$0.909152\pi$
$234$		0			0
$235$	−8.96665			−0.584920
$236$	0.531632	−	0.142450i	0.0346063	−	0.00927273i
$237$		0			0
$238$	4.41078	−	14.6864i	0.285908	−	0.951978i
$239$	6.45158	−	6.45158i	0.417318	−	0.417318i	−0.466960	−	0.884278i	$-0.654651\pi$
$239$	6.45158	−	6.45158i	0.417318	−	0.417318i	0.884278	+	0.466960i	$0.154651\pi$
$240$		0			0
$241$	4.21497	+	1.12940i	0.271510	+	0.0727509i	0.392005	−	0.919963i	$-0.371782\pi$
$241$	4.21497	+	1.12940i	0.271510	+	0.0727509i	−0.120495	+	0.992714i	$0.538448\pi$
$242$	−8.74744	−	8.74744i	−0.562307	−	0.562307i
$243$		0			0
$244$	0.00401565	−	0.00695531i	0.000257076	−	0.000445268i
$245$	−19.6806	+	4.02793i	−1.25735	+	0.257335i
$246$		0			0
$247$	9.44331	−	20.1249i	0.600863	−	1.28052i
$248$			2.65242i			0.168429i
$249$		0			0
$250$	−6.05359	−	3.49504i	−0.382863	−	0.221046i
$251$	2.27953	+	3.94826i	0.143883	+	0.249212i	0.928956	−	0.370191i	$-0.120708\pi$
$251$	2.27953	+	3.94826i	0.143883	+	0.249212i	−0.785073	+	0.619403i	$0.787375\pi$
$252$		0			0
$253$	10.7937	+	2.89218i	0.678597	+	0.181830i
$254$	5.82929	−	21.7552i	0.365762	−	1.36504i
$255$		0			0
$256$	1.12588	+	1.95008i	0.0703674	+	0.121880i
$257$	−4.31666	+	7.47667i	−0.269266	+	0.466382i	−0.968672	−	0.248342i	$-0.920114\pi$
$257$	−4.31666	+	7.47667i	−0.269266	+	0.466382i	0.699407	+	0.714724i	$0.253448\pi$
$258$		0			0
$259$	14.3435	−	13.5088i	0.891261	−	0.839393i
$260$	0.880838	+	0.413319i	0.0546272	+	0.0256330i
$261$		0			0
$262$	−3.13752	+	0.840697i	−0.193837	+	0.0519384i
$263$	−6.53143	+	11.3128i	−0.402745	+	0.697575i	−0.994056	−	0.108868i	$-0.965277\pi$
$263$	−6.53143	+	11.3128i	−0.402745	+	0.697575i	0.591311	+	0.806444i	$0.298611\pi$
$264$		0			0
$265$	5.12356	+	5.12356i	0.314738	+	0.314738i
$266$	19.8321	−	10.6710i	1.21598	−	0.654283i
$267$		0			0
$268$	0.0685128	+	0.0685128i	0.00418509	+	0.00418509i
$269$	−10.8756	+	6.27901i	−0.663095	+	0.382838i	−0.793455	−	0.608629i	$-0.791720\pi$
$269$	−10.8756	+	6.27901i	−0.663095	+	0.382838i	0.130360	+	0.991467i	$0.458387\pi$
$270$		0			0
$271$	−1.19419	−	4.45677i	−0.0725418	−	0.270730i	0.920123	−	0.391630i	$-0.128089\pi$
$271$	−1.19419	−	4.45677i	−0.0725418	−	0.270730i	−0.992665	+	0.120900i	$0.961422\pi$
$272$	−15.9661			−0.968085
$273$		0			0
$274$	−14.3401			−0.866315
$275$	−1.19595	−	4.46333i	−0.0721182	−	0.269149i
$276$		0			0
$277$	−1.44840	+	0.836232i	−0.0870257	+	0.0502443i	−0.542881	−	0.839809i	$-0.682667\pi$
$277$	−1.44840	+	0.836232i	−0.0870257	+	0.0502443i	0.455856	+	0.890054i	$0.349333\pi$
$278$	−6.01047	−	6.01047i	−0.360484	−	0.360484i
$279$		0			0
$280$	10.4008	+	19.3298i	0.621564	+	1.15517i
$281$	13.9259	+	13.9259i	0.830749	+	0.830749i	0.987619	−	0.156870i	$-0.0501403\pi$
$281$	13.9259	+	13.9259i	0.830749	+	0.830749i	−0.156870	+	0.987619i	$0.550140\pi$
$282$		0			0
$283$	16.4969	−	28.5736i	0.980642	−	1.69852i	0.320744	−	0.947166i	$-0.396067\pi$
$283$	16.4969	−	28.5736i	0.980642	−	1.69852i	0.659897	−	0.751356i	$-0.270600\pi$
$284$	−0.263292	+	0.0705490i	−0.0156235	+	0.00418631i
$285$		0			0
$286$	2.41520	+	6.68561i	0.142814	+	0.395329i
$287$	22.8738	−	21.5426i	1.35020	−	1.27162i
$288$		0			0
$289$	−0.312374	+	0.541047i	−0.0183749	+	0.0318263i
$290$	1.74913	+	3.02959i	0.102713	+	0.177904i
$291$		0			0
$292$	−0.0693294	+	0.258741i	−0.00405720	+	0.0151417i
$293$	−21.2120	−	5.68375i	−1.23922	−	0.332048i	−0.421057	−	0.907034i	$-0.638341\pi$
$293$	−21.2120	−	5.68375i	−1.23922	−	0.332048i	−0.818163	+	0.574986i	$0.805007\pi$
$294$		0			0
$295$	−8.39849	−	14.5466i	−0.488979	−	0.846936i
$296$	−18.6450	−	10.7647i	−1.08372	−	0.625686i
$297$		0			0
$298$			12.0196i			0.696279i
$299$	21.5689	+	18.1869i	1.24736	+	1.05178i
$300$		0			0
$301$	−1.30051	+	2.10434i	−0.0749602	+	0.121292i
$302$	−9.32472	+	16.1509i	−0.536578	+	0.929380i
$303$		0			0
$304$	−16.5805	−	16.5805i	−0.950955	−	0.950955i
$305$	−0.236752	−	0.0634374i	−0.0135564	−	0.00363242i
$306$		0			0
$307$	13.7833	−	13.7833i	0.786656	−	0.786656i	−0.194289	−	0.980944i	$-0.562240\pi$
$307$	13.7833	−	13.7833i	0.786656	−	0.786656i	0.980944	+	0.194289i	$0.0622399\pi$
$308$	0.102195	−	0.340275i	0.00582312	−	0.0193890i
$309$		0			0
$310$	3.51117	−	0.940815i	0.199421	−	0.0534347i
$311$	25.8267			1.46450			0.732248	−	0.681038i	$-0.238471\pi$
$311$	25.8267			1.46450			0.732248	+	0.681038i	$0.238471\pi$
$312$		0			0
$313$			28.6662i			1.62031i	0.586216	+	0.810155i	$0.300617\pi$
$313$			28.6662i			1.62031i	−0.586216	+	0.810155i	$0.699383\pi$
$314$	−9.04094	+	2.42251i	−0.510210	+	0.136710i
$315$		0			0
$316$	0.767998	−	0.443404i	0.0432033	−	0.0249434i
$317$	−8.81498	+	8.81498i	−0.495098	+	0.495098i	−0.909908	−	0.414810i	$-0.863848\pi$
$317$	−8.81498	+	8.81498i	−0.495098	+	0.495098i	0.414810	+	0.909908i	$0.363848\pi$
$318$		0			0
$319$	0.326355	−	1.21797i	0.0182724	−	0.0681934i
$320$	16.9238	−	16.9238i	0.946069	−	0.946069i
$321$		0			0
$322$	6.56711	+	27.8169i	0.365971	+	1.55018i
$323$	−25.0023	+	6.69935i	−1.39117	+	0.372762i
$324$		0			0
$325$	2.05344	−	11.4843i	0.113904	−	0.637035i
$326$	−15.0823			−0.835331
$327$		0			0
$328$	−29.7335	−	17.1667i	−1.64176	−	0.947870i
$329$	−2.37781	+	7.91729i	−0.131093	+	0.436494i
$330$		0			0
$331$	−28.9319	−	7.75229i	−1.59024	−	0.426104i	−0.648166	−	0.761499i	$-0.724464\pi$
$331$	−28.9319	−	7.75229i	−1.59024	−	0.426104i	−0.942078	+	0.335395i	$0.891130\pi$
$332$	0.197870	+	0.0530190i	0.0108595	+	0.00290980i
$333$		0			0
$334$	−21.7756	+	12.5721i	−1.19151	+	0.687916i
$335$	1.47850	−	2.56083i	0.0807789	−	0.139913i
$336$		0			0
$337$			13.4402i			0.732137i	0.930588	+	0.366068i	$0.119296\pi$
$337$			13.4402i			0.732137i	−0.930588	+	0.366068i	$0.880704\pi$
$338$	−1.65005	+	17.8714i	−0.0897511	+	0.972074i
$339$		0			0
$340$	−0.293220	−	1.09431i	−0.0159021	−	0.0593474i
$341$	−1.13470	−	0.655117i	−0.0614472	−	0.0354766i
$342$		0			0
$343$	−1.66242	+	18.4455i	−0.0897621	+	0.995963i
$344$	2.61094	+	0.699599i	0.140772	+	0.0377199i
$345$		0			0
$346$	19.6727	−	19.6727i	1.05761	−	1.05761i
$347$	−7.24936	−	12.5563i	−0.389166	−	0.674055i	0.603172	−	0.797611i	$-0.293903\pi$
$347$	−7.24936	−	12.5563i	−0.389166	−	0.674055i	−0.992338	+	0.123556i	$0.960570\pi$
$348$		0			0
$349$	5.68220	+	21.2063i	0.304161	+	1.13515i	0.933665	+	0.358148i	$0.116592\pi$
$349$	5.68220	+	21.2063i	0.304161	+	1.13515i	−0.629504	+	0.776998i	$0.716742\pi$
$350$	8.60376	−	8.10305i	0.459890	−	0.433126i
$351$		0			0
$352$	−0.759003			−0.0404550
$353$	−11.1538	+	2.98864i	−0.593655	+	0.159069i	−0.543123	−	0.839653i	$-0.682758\pi$
$353$	−11.1538	+	2.98864i	−0.593655	+	0.159069i	−0.0505316	+	0.998722i	$0.516092\pi$
$354$		0			0
$355$	4.15938	+	7.20425i	0.220757	+	0.382362i
$356$	0.327476	+	0.327476i	0.0173562	+	0.0173562i
$357$		0			0
$358$	−5.90723	+	22.0461i	−0.312207	+	1.16517i
$359$	0.631018	+	0.631018i	0.0333039	+	0.0333039i	0.723563	−	0.690259i	$-0.242503\pi$
$359$	0.631018	+	0.631018i	0.0333039	+	0.0333039i	−0.690259	+	0.723563i	$0.742503\pi$
$360$		0			0
$361$	−16.4671	−	9.50729i	−0.866690	−	0.500384i
$362$	−4.89156	−	18.2556i	−0.257095	−	0.959491i
$363$		0			0
$364$	0.598532	−	0.668148i	0.0313716	−	0.0350205i
$365$	8.17495			0.427897
$366$		0			0
$367$	12.5341	+	7.23654i	0.654273	+	0.377744i	0.790091	−	0.612989i	$-0.210033\pi$
$367$	12.5341	+	7.23654i	0.654273	+	0.377744i	−0.135819	+	0.990734i	$0.543366\pi$
$368$	25.7720	−	14.8794i	1.34346	−	0.775645i
$369$		0			0
$370$	−7.63651	+	28.4998i	−0.397003	+	1.48164i
$371$	5.88263	−	3.16527i	0.305411	−	0.164332i
$372$		0			0
$373$	−10.4635	−	18.1233i	−0.541778	−	0.938387i	−0.998802	−	0.0489327i	$-0.984418\pi$
$373$	−10.4635	−	18.1233i	−0.541778	−	0.938387i	0.457024	−	0.889454i	$-0.348915\pi$
$374$	4.13844	−	7.16800i	0.213994	−	0.370648i
$375$		0			0
$376$	9.03278			0.465830
$377$	2.05222	−	2.43385i	0.105695	−	0.125350i
$378$		0			0
$379$	−5.53128	−	20.6430i	−0.284123	−	1.06036i	−0.949478	−	0.313834i	$-0.898387\pi$
$379$	−5.53128	−	20.6430i	−0.284123	−	1.06036i	0.665355	−	0.746527i	$-0.268280\pi$
$380$	0.831920	−	1.44093i	0.0426766	−	0.0739180i
$381$		0			0
$382$	7.95502	−	7.95502i	0.407014	−	0.407014i
$383$	−4.63937	+	17.3144i	−0.237061	+	0.884723i	0.740148	+	0.672444i	$0.234755\pi$
$383$	−4.63937	+	17.3144i	−0.237061	+	0.884723i	−0.977209	+	0.212279i	$0.931911\pi$
$384$		0			0
$385$	−10.8381	−	0.324817i	−0.552360	−	0.0165542i
$386$	−18.4908	−	32.0270i	−0.941156	−	1.63013i
$387$		0			0
$388$	−0.223569	−	0.834369i	−0.0113500	−	0.0423587i
$389$		−	4.86154i		−	0.246490i	−0.992376	−	0.123245i	$-0.960670\pi$
$389$		−	4.86154i		−	0.246490i	0.992376	−	0.123245i	$-0.0393301\pi$
$390$		0			0
$391$		−	32.8505i		−	1.66132i
$392$	19.8257	−	4.05763i	1.00135	−	0.204942i
$393$		0			0
$394$	22.0364	−	12.7227i	1.11018	−	0.640962i
$395$	−19.1372	−	19.1372i	−0.962896	−	0.962896i
$396$		0			0
$397$	−18.8967	−	5.06335i	−0.948397	−	0.254122i	−0.248715	−	0.968577i	$-0.580008\pi$
$397$	−18.8967	−	5.06335i	−0.948397	−	0.254122i	−0.699682	+	0.714455i	$0.746675\pi$
$398$	−12.4091	+	12.4091i	−0.622014	+	0.622014i
$399$		0			0
$400$	−10.6570	−	6.15281i	−0.532849	−	0.307640i
$401$	−4.15019	+	1.11204i	−0.207251	+	0.0555327i	−0.360951	−	0.932585i	$-0.617548\pi$
$401$	−4.15019	+	1.11204i	−0.207251	+	0.0555327i	0.153700	+	0.988118i	$0.450881\pi$
$402$		0			0
$403$	−1.89091	−	2.71434i	−0.0941928	−	0.135211i
$404$		−	0.615903i		−	0.0306423i
$405$		0			0
$406$	3.13888	−	0.741037i	0.155780	−	0.0367771i
$407$	9.21022	−	5.31752i	0.456534	−	0.263580i
$408$		0			0
$409$	7.85062	−	29.2989i	0.388188	−	1.44874i	−0.444891	−	0.895585i	$-0.646758\pi$
$409$	7.85062	−	29.2989i	0.388188	−	1.44874i	0.833079	−	0.553154i	$-0.186576\pi$
$410$	−12.1781	+	45.4491i	−0.601432	+	2.24457i
$411$		0			0
$412$	0.802586	−	0.463373i	0.0395406	−	0.0228288i
$413$	−15.0714	+	3.55810i	−0.741613	+	0.175083i
$414$		0			0
$415$		−	6.25172i		−	0.306885i
$416$	−1.73482	−	0.814037i	−0.0850566	−	0.0399115i
$417$		0			0
$418$	11.7415	−	3.14613i	0.574297	−	0.153882i
$419$	−6.87240	−	3.96778i	−0.335739	−	0.193839i	0.322647	−	0.946519i	$-0.395427\pi$
$419$	−6.87240	−	3.96778i	−0.335739	−	0.193839i	−0.658386	+	0.752680i	$0.728761\pi$
$420$		0			0
$421$	−5.98090	+	5.98090i	−0.291491	+	0.291491i	−0.837669	−	0.546178i	$-0.816082\pi$
$421$	−5.98090	+	5.98090i	−0.291491	+	0.291491i	0.546178	+	0.837669i	$0.316082\pi$
$422$	−6.03978	−	1.61835i	−0.294012	−	0.0787802i
$423$		0			0
$424$	−5.16134	−	5.16134i	−0.250657	−	0.250657i
$425$	−11.7641	+	6.79201i	−0.570643	+	0.329461i
$426$		0			0
$427$	−0.118796	+	0.192222i	−0.00574894	+	0.00930229i
$428$		−	0.996159i		−	0.0481511i
$429$		0			0
$430$		−	3.70441i		−	0.178643i
$431$	−0.149741	−	0.558842i	−0.00721278	−	0.0269185i	0.962226	−	0.272253i	$-0.0877688\pi$
$431$	−0.149741	−	0.558842i	−0.00721278	−	0.0269185i	−0.969438	+	0.245335i	$0.921102\pi$
$432$		0			0
$433$	−4.11334	−	7.12452i	−0.197675	−	0.342382i	0.750099	−	0.661325i	$-0.230006\pi$
$433$	−4.11334	−	7.12452i	−0.197675	−	0.342382i	−0.947774	+	0.318943i	$0.896672\pi$
$434$	0.100392	−	3.34975i	0.00481897	−	0.160793i
$435$		0			0
$436$	0.401638	−	1.49893i	0.0192350	−	0.0717858i
$437$	34.1146	−	34.1146i	1.63192	−	1.63192i
$438$		0			0
$439$	−6.36168	+	11.0188i	−0.303626	+	0.525896i	−0.976955	−	0.213447i	$-0.931531\pi$
$439$	−6.36168	+	11.0188i	−0.303626	+	0.525896i	0.673328	+	0.739344i	$0.264864\pi$
$440$	3.06645	+	11.4441i	0.146187	+	0.545578i
$441$		0			0
$442$	17.1468	−	11.9451i	0.815591	−	0.568169i
$443$	2.23067			0.105982			0.0529912	−	0.998595i	$-0.483124\pi$
$443$	2.23067			0.105982			0.0529912	+	0.998595i	$0.483124\pi$
$444$		0			0
$445$	7.06688	−	12.2402i	0.335002	−	0.580241i
$446$	−16.0641	−	27.8239i	−0.760658	−	1.31750i
$447$		0			0
$448$	−10.4553	−	19.4311i	−0.493967	−	0.918034i
$449$	−10.0883	+	37.6500i	−0.476096	+	1.77682i	0.141088	+	0.989997i	$0.454940\pi$
$449$	−10.0883	+	37.6500i	−0.476096	+	1.77682i	−0.617184	+	0.786819i	$0.711727\pi$
$450$		0			0
$451$	14.6877	−	8.47994i	0.691616	−	0.399305i
$452$	0.0524641	+	0.0302901i	0.00246770	+	0.00142473i
$453$		0			0
$454$	14.3906			0.675387
$455$	−24.4238	−	12.3664i	−1.14500	−	0.579744i
$456$		0			0
$457$	5.96003	+	22.2431i	0.278798	+	1.04049i	0.953253	+	0.302174i	$0.0977122\pi$
$457$	5.96003	+	22.2431i	0.278798	+	1.04049i	−0.674455	+	0.738316i	$0.735621\pi$
$458$	−2.30600	−	1.33137i	−0.107752	−	0.0622107i
$459$		0			0
$460$	1.49314	+	1.49314i	0.0696182	+	0.0696182i
$461$	7.81461	−	29.1645i	0.363962	−	1.35833i	−0.504859	−	0.863202i	$-0.668456\pi$
$461$	7.81461	−	29.1645i	0.363962	−	1.35833i	0.868822	−	0.495125i	$-0.164878\pi$
$462$		0			0
$463$	2.19856	+	2.19856i	0.102176	+	0.102176i	0.756347	−	0.654171i	$-0.226982\pi$
$463$	2.19856	+	2.19856i	0.102176	+	0.102176i	−0.654171	+	0.756347i	$0.726982\pi$
$464$	−1.67901	−	2.90812i	−0.0779459	−	0.135006i
$465$		0			0
$466$	−11.4621	+	3.07126i	−0.530971	+	0.142273i
$467$	−21.1712			−0.979688			−0.489844	−	0.871810i	$-0.662946\pi$
$467$	−21.1712			−0.979688			−0.489844	+	0.871810i	$0.662946\pi$
$468$		0			0
$469$	−1.86907	−	1.98456i	−0.0863055	−	0.0916384i
$470$	−3.20394	−	11.9573i	−0.147787	−	0.551547i
$471$		0			0
$472$	8.46043	+	14.6539i	0.389423	+	0.674500i
$473$	−0.944158	+	0.944158i	−0.0434125	+	0.0434125i
$474$		0			0
$475$	−19.2702	−	5.16343i	−0.884176	−	0.236914i
$476$	−1.04400	−	0.0312888i	−0.0478518	−	0.00143412i
$477$		0			0
$478$	10.9086	+	6.29809i	0.498948	+	0.288068i
$479$	6.21539	+	23.1962i	0.283988	+	1.05986i	0.949575	+	0.313539i	$0.101515\pi$
$479$	6.21539	+	23.1962i	0.283988	+	1.05986i	−0.665587	+	0.746320i	$0.731819\pi$
$480$		0			0
$481$	26.7545	−	2.27600i	1.21990	−	0.103777i
$482$			6.02432i			0.274400i
$483$		0			0
$484$	−0.421303	+	0.729719i	−0.0191501	+	0.0331690i
$485$	−22.8302	+	13.1810i	−1.03666	+	0.598518i
$486$		0			0
$487$	32.9158	+	8.81975i	1.49156	+	0.399661i	0.910262	−	0.414032i	$-0.135880\pi$
$487$	32.9158	+	8.81975i	1.49156	+	0.399661i	0.581294	+	0.813694i	$0.302547\pi$
$488$	0.238498	+	0.0639053i	0.0107963	+	0.00289286i
$489$		0			0
$490$	−12.4035	−	24.8053i	−0.560335	−	1.12059i
$491$	−12.2688	−	7.08337i	−0.553681	−	0.319668i	0.196924	−	0.980419i	$-0.436905\pi$
$491$	−12.2688	−	7.08337i	−0.553681	−	0.319668i	−0.750605	+	0.660751i	$0.770238\pi$
$492$		0			0
$493$	−3.70687			−0.166949
$494$	30.2114	+	5.40191i	1.35927	+	0.243043i
$495$		0			0
$496$	−3.37039	+	0.903094i	−0.151335	+	0.0405501i
$497$	7.46414	−	1.76216i	0.334812	−	0.0790436i
$498$		0			0
$499$	−21.0854	+	21.0854i	−0.943912	+	0.943912i	−0.998509	−	0.0545964i	$-0.982613\pi$
$499$	−21.0854	+	21.0854i	−0.943912	+	0.943912i	0.0545964	+	0.998509i	$0.482613\pi$
$500$	−0.123227	+	0.459891i	−0.00551090	+	0.0205670i
$501$		0			0
$502$	−4.45059	+	4.45059i	−0.198640	+	0.198640i
$503$	11.8147	−	6.82122i	0.526791	−	0.304143i	−0.212918	−	0.977070i	$-0.568297\pi$
$503$	11.8147	−	6.82122i	0.526791	−	0.304143i	0.739709	+	0.672927i	$0.234963\pi$
$504$		0			0
$505$	−18.1560	+	4.86488i	−0.807930	+	0.216484i
$506$			15.4272i			0.685821i
$507$		0			0
$508$	−1.53408			−0.0680638
$509$	2.57869	−	0.690957i	0.114298	−	0.0306261i	−0.201216	−	0.979547i	$-0.564489\pi$
$509$	2.57869	−	0.690957i	0.114298	−	0.0306261i	0.315515	+	0.948921i	$0.397823\pi$
$510$		0			0
$511$	2.16786	−	7.21824i	0.0959005	−	0.319316i
$512$	−16.9779	+	16.9779i	−0.750326	+	0.750326i
$513$		0			0
$514$	−11.5127	−	3.08483i	−0.507806	−	0.136066i
$515$	−19.9991	−	19.9991i	−0.881264	−	0.881264i
$516$		0			0
$517$	−2.23099	+	3.86419i	−0.0981190	+	0.169947i
$518$	23.1394	+	14.3005i	1.01669	+	0.628328i
$519$		0			0
$520$	−5.26509	+	29.4462i	−0.230889	+	1.29130i
$521$		−	15.5467i		−	0.681111i	−0.940224	−	0.340556i	$-0.889385\pi$
$521$		−	15.5467i		−	0.681111i	0.940224	−	0.340556i	$-0.110615\pi$
$522$		0			0
$523$	0.102601	+	0.0592367i	0.00448643	+	0.00259024i	0.502242	−	0.864727i	$-0.332509\pi$
$523$	0.102601	+	0.0592367i	0.00448643	+	0.00259024i	−0.497755	+	0.867318i	$0.665842\pi$
$524$	0.110622	+	0.191603i	0.00483255	+	0.00837022i
$525$		0			0
$526$	−17.4197	−	4.66758i	−0.759533	−	0.203516i
$527$	−0.996915	+	3.72054i	−0.0434263	+	0.162069i
$528$		0			0
$529$	19.1147	+	33.1077i	0.831075	+	1.43946i
$530$	−5.00166	+	8.66313i	−0.217258	+	0.376302i
$531$		0			0
$532$	−1.05168	−	1.11667i	−0.0455963	−	0.0484138i
$533$	42.6658	−	3.62957i	1.84806	−	0.157214i
$534$		0			0
$535$	−29.3654	+	7.86844i	−1.26958	+	0.340182i
$536$	−1.48940	+	2.57972i	−0.0643324	+	0.111427i
$537$		0			0
$538$	−12.2592	−	12.2592i	−0.528534	−	0.528534i
$539$	−3.16088	+	9.48357i	−0.136149	+	0.408486i
$540$		0			0
$541$	−3.27270	−	3.27270i	−0.140705	−	0.140705i	0.633246	−	0.773951i	$-0.281722\pi$
$541$	−3.27270	−	3.27270i	−0.140705	−	0.140705i	−0.773951	+	0.633246i	$0.781722\pi$
$542$	5.51652	−	3.18496i	0.236955	−	0.136806i
$543$		0			0
$544$	0.577501	+	2.15526i	0.0247602	+	0.0924062i
$545$	−47.3589			−2.02863
$546$		0			0
$547$	29.4860			1.26073			0.630365	−	0.776299i	$-0.282905\pi$
$547$	29.4860			1.26073			0.630365	+	0.776299i	$0.282905\pi$
$548$	0.252800	+	0.943461i	0.0107991	+	0.0403026i
$549$		0			0
$550$	5.52463	−	3.18965i	0.235571	−	0.136007i
$551$	−3.84951	−	3.84951i	−0.163995	−	0.163995i
$552$		0			0
$553$	−21.9724	+	11.8227i	−0.934363	+	0.502753i
$554$	−1.63267	−	1.63267i	−0.0693657	−	0.0693657i
$555$		0			0
$556$	−0.289482	+	0.501398i	−0.0122768	+	0.0212640i
$557$	1.31037	−	0.351113i	0.0555222	−	0.0148771i	−0.230951	−	0.972965i	$-0.574184\pi$
$557$	1.31037	−	0.351113i	0.0555222	−	0.0148771i	0.286473	+	0.958088i	$0.407517\pi$
$558$		0			0
$559$	−3.17064	+	1.14541i	−0.134104	+	0.0484455i
$560$	−21.0208	+	19.7975i	−0.888293	+	0.836598i
$561$		0			0
$562$	−13.5946	+	23.5465i	−0.573453	+	0.993249i
$563$	−16.4050	−	28.4143i	−0.691388	−	1.19752i	−0.971383	−	0.237517i	$-0.923666\pi$
$563$	−16.4050	−	28.4143i	−0.691388	−	1.19752i	0.279995	−	0.960001i	$-0.409667\pi$
$564$		0			0
$565$	0.478510	−	1.78582i	0.0201311	−	0.0751302i
$566$	43.9982	+	11.7893i	1.84938	+	0.495541i
$567$		0			0
$568$	−4.19005	−	7.25739i	−0.175811	−	0.304513i
$569$	25.8745	+	14.9387i	1.08472	+	0.626261i	0.932165	−	0.362034i	$-0.117918\pi$
$569$	25.8745	+	14.9387i	1.08472	+	0.626261i	0.152552	+	0.988296i	$0.451251\pi$
$570$		0			0
$571$		−	0.740021i		−	0.0309689i	−0.999880	−	0.0154844i	$-0.995071\pi$
$571$		−	0.740021i		−	0.0309689i	0.999880	−	0.0154844i	$-0.00492905\pi$
$572$	0.397282	−	0.276761i	0.0166112	−	0.0115719i
$573$		0			0
$574$	36.9008	+	22.8052i	1.54021	+	0.951872i
$575$	12.6595	−	21.9269i	0.527938	−	0.914416i
$576$		0			0
$577$	−24.1189	−	24.1189i	−1.00408	−	1.00408i	−0.999992	−	0.00409020i	$-0.998698\pi$
$577$	−24.1189	−	24.1189i	−1.00408	−	1.00408i	−0.00409020	−	0.999992i	$-0.501302\pi$
$578$	−0.833116	−	0.223233i	−0.0346531	−	0.00928526i
$579$		0			0
$580$	0.168487	−	0.168487i	0.00699605	−	0.00699605i
$581$	−5.52008	−	1.65785i	−0.229012	−	0.0687793i
$582$		0			0
$583$	3.48280	−	0.933213i	0.144243	−	0.0386498i
$584$	−8.23524			−0.340777
$585$		0			0
$586$		−	30.3177i		−	1.25241i
$587$	11.9740	−	3.20842i	0.494219	−	0.132426i	−0.00309648	−	0.999995i	$-0.500986\pi$
$587$	11.9740	−	3.20842i	0.494219	−	0.132426i	0.497316	+	0.867569i	$0.334319\pi$
$588$		0			0
$589$	−4.89899	+	2.82843i	−0.201859	+	0.116543i
$590$	16.3973	−	16.3973i	0.675068	−	0.675068i
$591$		0			0
$592$	7.33034	−	27.3572i	0.301275	−	1.12437i
$593$	−16.1631	+	16.1631i	−0.663739	+	0.663739i	−0.956259	−	0.292520i	$-0.905506\pi$
$593$	−16.1631	+	16.1631i	−0.663739	+	0.663739i	0.292520	+	0.956259i	$0.405506\pi$
$594$		0			0
$595$	7.32400	+	31.0229i	0.300255	+	1.27182i
$596$	0.790795	−	0.211893i	0.0323922	−	0.00867948i
$597$		0			0
$598$	−16.5458	+	35.2612i	−0.676607	+	1.44194i
$599$	−2.49403			−0.101903			−0.0509516	−	0.998701i	$-0.516225\pi$
$599$	−2.49403			−0.101903			−0.0509516	+	0.998701i	$0.516225\pi$
$600$		0			0
$601$	18.5873	+	10.7314i	0.758193	+	0.437743i	0.828647	−	0.559772i	$-0.189111\pi$
$601$	18.5873	+	10.7314i	0.758193	+	0.437743i	−0.0704537	+	0.997515i	$0.522445\pi$
$602$	−3.27089	−	0.982348i	−0.133311	−	0.0400375i
$603$		0			0
$604$	1.22698	+	0.328769i	0.0499252	+	0.0133774i
$605$	24.8389	+	6.65556i	1.00984	+	0.270587i
$606$		0			0
$607$	−13.8907	+	8.01981i	−0.563807	+	0.325514i	−0.754672	−	0.656102i	$-0.772204\pi$
$607$	−13.8907	+	8.01981i	−0.563807	+	0.325514i	0.190865	+	0.981616i	$0.438871\pi$
$608$	−1.63848	+	2.83793i	−0.0664490	+	0.115093i
$609$		0			0
$610$		−	0.338382i		−	0.0137007i
$611$	−9.24368	+	6.43947i	−0.373959	+	0.260513i
$612$		0			0
$613$	−1.78927	−	6.67764i	−0.0722679	−	0.269707i	0.920332	−	0.391138i	$-0.127918\pi$
$613$	−1.78927	−	6.67764i	−0.0722679	−	0.269707i	−0.992600	+	0.121431i	$0.961252\pi$
$614$	23.3054	+	13.4554i	0.940530	+	0.543015i
$615$		0			0
$616$	10.9180	+	0.327213i	0.439899	+	0.0131838i
$617$	−26.9254	−	7.21463i	−1.08397	−	0.290450i	−0.327751	−	0.944764i	$-0.606291\pi$
$617$	−26.9254	−	7.21463i	−1.08397	−	0.290450i	−0.756223	+	0.654314i	$0.772957\pi$
$618$		0			0
$619$	−9.80302	+	9.80302i	−0.394017	+	0.394017i	−0.876116	−	0.482100i	$-0.839874\pi$
$619$	−9.80302	+	9.80302i	−0.394017	+	0.394017i	0.482100	+	0.876116i	$0.339874\pi$
$620$	−0.123796	−	0.214421i	−0.00497177	−	0.00861136i
$621$		0			0
$622$	9.22831	+	34.4405i	0.370022	+	1.38094i
$623$	−8.93371	−	9.48575i	−0.357922	−	0.380038i
$624$		0			0
$625$	30.7088			1.22835
$626$	−38.2271	+	10.2429i	−1.52786	+	0.409390i
$627$		0			0
$628$	0.318763	+	0.552115i	0.0127200	+	0.0220318i
$629$	−22.1074	−	22.1074i	−0.881480	−	0.881480i
$630$		0			0
$631$	6.69536	−	24.9874i	0.266538	−	0.994733i	−0.694764	−	0.719237i	$-0.744491\pi$
$631$	6.69536	−	24.9874i	0.266538	−	0.994733i	0.961302	−	0.275496i	$-0.0888419\pi$
$632$	19.2783	+	19.2783i	0.766851	+	0.766851i
$633$		0			0
$634$	−14.9047	−	8.60525i	−0.591943	−	0.341758i
$635$	12.1174	+	45.2226i	0.480863	+	1.79460i
$636$		0			0
$637$	−17.3959	+	18.2861i	−0.689251	+	0.724523i
$638$	1.74081			0.0689193
$639$		0			0
$640$	25.9736	+	14.9959i	1.02670	+	0.592764i
$641$	10.8902	−	6.28745i	0.430136	−	0.248339i	−0.269269	−	0.963065i	$-0.586782\pi$
$641$	10.8902	−	6.28745i	0.430136	−	0.248339i	0.699405	+	0.714726i	$0.253449\pi$
$642$		0			0
$643$	6.40174	−	23.8916i	0.252460	−	0.942193i	−0.717026	−	0.697046i	$-0.754497\pi$
$643$	6.40174	−	23.8916i	0.252460	−	0.942193i	0.969486	−	0.245147i	$-0.0788361\pi$
$644$	1.71436	−	0.922445i	0.0675552	−	0.0363494i
$645$		0			0
$646$	−17.8675	−	30.9474i	−0.702988	−	1.21761i
$647$	17.3117	−	29.9848i	0.680595	−	1.17883i	−0.294205	−	0.955742i	$-0.595055\pi$
$647$	17.3117	−	29.9848i	0.680595	−	1.17883i	0.974800	−	0.223083i	$-0.0716120\pi$
$648$		0			0
$649$	−8.35852			−0.328100
$650$	16.0483	−	1.36523i	0.629468	−	0.0535487i
$651$		0			0
$652$	0.265884	+	0.992293i	0.0104128	+	0.0388612i
$653$	−13.7001	+	23.7293i	−0.536127	+	0.928600i	0.462980	+	0.886368i	$0.346780\pi$
$653$	−13.7001	+	23.7293i	−0.536127	+	0.928600i	−0.999108	+	0.0422314i	$0.986553\pi$
$654$		0			0
$655$	4.77442	−	4.77442i	0.186552	−	0.186552i
$656$	11.6898	−	43.6269i	0.456410	−	1.70335i
$657$		0			0
$658$	−11.4075	−	0.341884i	−0.444712	−	0.0133280i
$659$	−2.14617	−	3.71728i	−0.0836031	−	0.144805i	0.821192	−	0.570652i	$-0.193309\pi$
$659$	−2.14617	−	3.71728i	−0.0836031	−	0.144805i	−0.904795	+	0.425847i	$0.859976\pi$
$660$		0			0
$661$	3.93734	+	14.6944i	0.153145	+	0.571544i	0.999257	+	0.0385395i	$0.0122705\pi$
$661$	3.93734	+	14.6944i	0.153145	+	0.571544i	−0.846112	+	0.533005i	$0.821063\pi$
$662$		−	41.3515i		−	1.60717i
$663$		0			0
$664$			6.29783i			0.244403i
$665$	−24.6109	+	39.8226i	−0.954370	+	1.54425i
$666$		0			0
$667$	5.98352	−	3.45459i	0.231683	−	0.133762i
$668$	1.21102	+	1.21102i	0.0468559	+	0.0468559i
$669$		0			0
$670$	3.94323	+	1.05658i	0.152340	+	0.0408194i
$671$	−0.0862447	+	0.0862447i	−0.00332944	+	0.00332944i
$672$		0			0
$673$	26.3013	+	15.1851i	1.01384	+	0.585341i	0.912314	−	0.409492i	$-0.134294\pi$
$673$	26.3013	+	15.1851i	1.01384	+	0.585341i	0.101526	+	0.994833i	$0.467627\pi$
$674$	−17.9229	+	4.80243i	−0.690365	+	0.184983i
$675$		0			0
$676$	1.20488	−	0.206492i	0.0463415	−	0.00794200i
$677$			36.6725i			1.40944i	0.709486	+	0.704720i	$0.248927\pi$
$677$			36.6725i			1.40944i	−0.709486	+	0.704720i	$0.751073\pi$
$678$		0			0
$679$	5.58425	+	23.6537i	0.214304	+	0.907747i
$680$	30.1636	−	17.4150i	1.15672	−	0.667834i
$681$		0			0
$682$	0.468169	−	1.74723i	0.0179271	−	0.0669049i
$683$	−4.14330	+	15.4630i	−0.158539	+	0.591676i	0.840237	+	0.542219i	$0.182416\pi$
$683$	−4.14330	+	15.4630i	−0.158539	+	0.591676i	−0.998776	+	0.0494567i	$0.984251\pi$
$684$		0			0
$685$	25.8151	−	14.9044i	0.986346	−	0.569467i
$686$	−25.1916	+	4.37401i	−0.961818	+	0.167001i
$687$		0			0
$688$			3.55589i			0.135567i
$689$	8.96137	+	1.60233i	0.341401	+	0.0610438i
$690$		0			0
$691$	−17.4509	+	4.67596i	−0.663864	+	0.177882i	−0.574989	−	0.818161i	$-0.694994\pi$
$691$	−17.4509	+	4.67596i	−0.663864	+	0.177882i	−0.0888748	+	0.996043i	$0.528327\pi$
$692$	−1.64111	−	0.947497i	−0.0623858	−	0.0360184i
$693$		0			0
$694$	14.1538	−	14.1538i	0.537270	−	0.537270i
$695$	17.0671	+	4.57311i	0.647391	+	0.173468i
$696$		0			0
$697$	−35.2550	−	35.2550i	−1.33538	−	1.33538i
$698$	−26.2487	+	15.1547i	−0.993530	+	0.573615i
$699$		0			0
$700$	−0.684790	−	0.423210i	−0.0258826	−	0.0159958i
$701$			37.6363i			1.42150i	0.703444	+	0.710751i	$0.251645\pi$
$701$			37.6363i			1.42150i	−0.703444	+	0.710751i	$0.748355\pi$
$702$		0			0
$703$		−	45.9162i		−	1.73176i
$704$	−3.08253	−	11.5042i	−0.116177	−	0.433579i
$705$		0			0
$706$	−7.97086	−	13.8059i	−0.299987	−	0.519593i
$707$	−0.519119	+	17.3213i	−0.0195235	+	0.651434i
$708$		0			0
$709$	−2.98398	+	11.1364i	−0.112066	+	0.418235i	−0.999051	−	0.0435634i	$-0.986129\pi$
$709$	−2.98398	+	11.1364i	−0.112066	+	0.418235i	0.886985	+	0.461798i	$0.152796\pi$
$710$	−8.12084	+	8.12084i	−0.304770	+	0.304770i
$711$		0			0
$712$	−7.11900	+	12.3305i	−0.266796	+	0.462104i
$713$	−1.85813	−	6.93465i	−0.0695876	−	0.259705i
$714$		0			0
$715$	−11.2966	−	9.52526i	−0.422468	−	0.356225i
$716$	1.55459			0.0580978
$717$		0			0
$718$	−0.616005	+	1.06695i	−0.0229891	+	0.0398183i
$719$	23.0965	+	40.0043i	0.861355	+	1.49191i	0.870622	+	0.491953i	$0.163717\pi$
$719$	23.0965	+	40.0043i	0.861355	+	1.49191i	−0.00926691	+	0.999957i	$0.502950\pi$
$720$		0			0
$721$	−22.9620	+	12.3552i	−0.855149	+	0.460130i
$722$	6.79424	−	25.3564i	0.252855	−	0.943669i
$723$		0			0
$724$	−1.11484	+	0.643651i	−0.0414325	+	0.0239211i
$725$	−2.47425	−	1.42851i	−0.0918913	−	0.0530534i
$726$		0			0
$727$	−3.27502			−0.121464			−0.0607318	−	0.998154i	$-0.519343\pi$
$727$	−3.27502			−0.121464			−0.0607318	+	0.998154i	$0.519343\pi$
$728$	24.6039	+	12.4576i	0.911882	+	0.461708i
$729$		0			0
$730$	2.92105	+	10.9015i	0.108113	+	0.403483i
$731$	3.39941	+	1.96265i	0.125732	+	0.0725913i
$732$		0			0
$733$	23.8639	+	23.8639i	0.881432	+	0.881432i	0.993680	−	0.112248i	$-0.0358052\pi$
$733$	23.8639	+	23.8639i	0.881432	+	0.881432i	−0.112248	+	0.993680i	$0.535805\pi$
$734$	−5.17148	+	19.3002i	−0.190883	+	0.712384i
$735$		0			0
$736$	−2.94077	−	2.94077i	−0.108398	−	0.108398i
$737$	−0.735730	−	1.27432i	−0.0271010	−	0.0469403i
$738$		0			0
$739$	2.04383	−	0.547643i	0.0751836	−	0.0201454i	−0.221031	−	0.975267i	$-0.570942\pi$
$739$	2.04383	−	0.547643i	0.0751836	−	0.0201454i	0.296215	+	0.955121i	$0.404276\pi$
$740$	2.00968			0.0738774
$741$		0			0
$742$	6.32293	+	6.71364i	0.232122	+	0.246465i
$743$	7.14174	+	26.6533i	0.262005	+	0.977816i	0.964058	+	0.265692i	$0.0856003\pi$
$743$	7.14174	+	26.6533i	0.262005	+	0.977816i	−0.702053	+	0.712125i	$0.747733\pi$
$744$		0			0
$745$	−12.4926	−	21.6379i	−0.457695	−	0.792751i
$746$	20.4291	−	20.4291i	0.747961	−	0.747961i
$747$		0			0
$748$	−0.544552	−	0.145912i	−0.0199108	−	0.00533508i
$749$	−0.839621	+	28.0154i	−0.0306791	+	1.02366i
$750$		0			0
$751$	−6.52544	−	3.76747i	−0.238117	−	0.137477i	0.376194	−	0.926541i	$-0.377233\pi$
$751$	−6.52544	−	3.76747i	−0.238117	−	0.137477i	−0.614311	+	0.789064i	$0.710566\pi$
$752$	3.07548	+	11.4778i	0.112151	+	0.418554i
$753$		0			0
$754$	3.97890	+	1.86703i	0.144903	+	0.0679934i
$755$		−	38.7667i		−	1.41086i
$756$		0			0
$757$	−21.0971	+	36.5412i	−0.766786	+	1.32811i	0.172512	+	0.985007i	$0.444812\pi$
$757$	−21.0971	+	36.5412i	−0.766786	+	1.32811i	−0.939297	+	0.343104i	$0.888522\pi$
$758$	25.5516	−	14.7522i	0.928075	−	0.535824i
$759$		0			0
$760$	49.4095	+	13.2392i	1.79227	+	0.480237i
$761$	1.64757	+	0.441464i	0.0597243	+	0.0160031i	0.288557	−	0.957463i	$-0.406824\pi$
$761$	1.64757	+	0.441464i	0.0597243	+	0.0160031i	−0.228833	+	0.973466i	$0.573491\pi$
$762$		0			0
$763$	−12.5588	+	41.8165i	−0.454659	+	1.51386i
$764$	−0.663614	−	0.383138i	−0.0240087	−	0.0138614i
$765$		0			0
$766$	−24.7469			−0.894141
$767$	−19.1047	−	8.96458i	−0.689831	−	0.323692i
$768$		0			0
$769$	−3.49612	+	0.936782i	−0.126073	+	0.0337812i	−0.321304	−	0.946976i	$-0.604121\pi$
$769$	−3.49612	+	0.936782i	−0.126073	+	0.0337812i	0.195231	+	0.980757i	$0.437454\pi$
$770$	−3.43948	−	14.5689i	−0.123950	−	0.525027i
$771$		0			0
$772$	−1.78114	+	1.78114i	−0.0641048	+	0.0641048i
$773$	−6.91718	+	25.8153i	−0.248794	+	0.928510i	0.722645	+	0.691219i	$0.242926\pi$
$773$	−6.91718	+	25.8153i	−0.248794	+	0.928510i	−0.971439	+	0.237291i	$0.923741\pi$
$774$		0			0
$775$	−2.09919	+	2.09919i	−0.0754052	+	0.0754052i
$776$	22.9985	−	13.2782i	0.825600	−	0.476660i
$777$		0			0
$778$	6.48299	−	1.73711i	0.232426	−	0.0622785i
$779$		−	73.2233i		−	2.62350i
$780$		0			0
$781$	4.13958			0.148126
$782$	43.8069	−	11.7380i	1.56653	−	0.419751i
$783$		0			0
$784$	11.9062	+	23.8108i	0.425223	+	0.850384i
$785$	13.7577	−	13.7577i	0.491035	−	0.491035i
$786$		0			0
$787$	42.5173	+	11.3925i	1.51558	+	0.406098i	0.918284	−	0.395923i	$-0.129575\pi$
$787$	42.5173	+	11.3925i	1.51558	+	0.406098i	0.597296	+	0.802021i	$0.296242\pi$
$788$	−1.22553	−	1.22553i	−0.0436577	−	0.0436577i
$789$		0			0
$790$	18.6819	−	32.3580i	0.664672	−	1.15124i
$791$	−1.44994	−	0.896081i	−0.0515538	−	0.0318610i
$792$		0			0
$793$	−0.289624	+	0.104628i	−0.0102849	+	0.00371544i
$794$		−	27.0084i		−	0.958493i
$795$		0			0
$796$	1.03518	+	0.597662i	0.0366910	+	0.0211836i
$797$	6.94770	+	12.0338i	0.246100	+	0.426258i	0.962440	−	0.271493i	$-0.0875175\pi$
$797$	6.94770	+	12.0338i	0.246100	+	0.426258i	−0.716340	+	0.697751i	$0.754184\pi$
$798$		0			0
$799$	12.6703	+	3.39499i	0.448241	+	0.120106i
$800$	−0.445101	+	1.66114i	−0.0157367	+	0.0587301i
$801$		0			0
$802$	−2.96587	−	5.13704i	−0.104728	−	0.181395i
$803$	2.03401	−	3.52301i	0.0717787	−	0.124324i
$804$		0			0
$805$	−40.7338	−	43.2508i	−1.43568	−	1.52439i
$806$	2.94399	−	3.49146i	0.103698	−	0.122981i
$807$		0			0
$808$	18.2899	−	4.90076i	0.643436	−	0.172408i
$809$	−22.2022	+	38.4554i	−0.780589	+	1.35202i	0.151010	+	0.988532i	$0.451747\pi$
$809$	−22.2022	+	38.4554i	−0.780589	+	1.35202i	−0.931599	+	0.363488i	$0.881586\pi$
$810$		0			0
$811$	9.49597	+	9.49597i	0.333449	+	0.333449i	0.853895	−	0.520446i	$-0.174234\pi$
$811$	9.49597	+	9.49597i	0.333449	+	0.333449i	−0.520446	+	0.853895i	$0.674234\pi$
$812$	−0.104089	−	0.193449i	−0.00365282	−	0.00678874i
$813$		0			0
$814$	10.3820	+	10.3820i	0.363890	+	0.363890i
$815$	27.1513	−	15.6758i	0.951068	−	0.549099i
$816$		0			0
$817$	1.49205	+	5.56840i	0.0522002	+	0.194814i
$818$	41.8760			1.46416
$819$		0			0
$820$	3.20487			0.111919
$821$	−13.3053	−	49.6560i	−0.464358	−	1.73301i	−0.659009	−	0.752135i	$-0.729024\pi$
$821$	−13.3053	−	49.6560i	−0.464358	−	1.73301i	0.194651	−	0.980873i	$-0.437643\pi$
$822$		0			0
$823$	22.4979	−	12.9892i	0.784227	−	0.452774i	−0.0536991	−	0.998557i	$-0.517101\pi$
$823$	22.4979	−	12.9892i	0.784227	−	0.452774i	0.837926	+	0.545783i	$0.183768\pi$
$824$	20.1466	+	20.1466i	0.701839	+	0.701839i
$825$		0			0
$826$	−10.1301	−	18.8267i	−0.352470	−	0.655064i
$827$	1.05853	+	1.05853i	0.0368089	+	0.0368089i	0.725272	−	0.688463i	$-0.241714\pi$
$827$	1.05853	+	1.05853i	0.0368089	+	0.0368089i	−0.688463	+	0.725272i	$0.741714\pi$
$828$		0			0
$829$	7.34482	−	12.7216i	0.255096	−	0.441839i	−0.709826	−	0.704378i	$-0.751226\pi$
$829$	7.34482	−	12.7216i	0.255096	−	0.441839i	0.964922	+	0.262538i	$0.0845596\pi$
$830$	8.33682	−	2.23385i	0.289375	−	0.0775379i
$831$		0			0
$832$	5.29270	−	29.6006i	0.183491	−	1.02622i
$833$	29.3345	+	1.75989i	1.01638	+	0.0609767i
$834$		0			0
$835$	26.1337	−	45.2649i	0.904395	−	1.56646i
$836$	−0.413980	−	0.717035i	−0.0143178	−	0.0247992i
$837$		0			0
$838$	2.83551	−	10.5823i	0.0979511	−	0.365559i
$839$	18.7042	+	5.01177i	0.645740	+	0.173025i	0.566802	−	0.823854i	$-0.308180\pi$
$839$	18.7042	+	5.01177i	0.645740	+	0.173025i	0.0789379	+	0.996880i	$0.474847\pi$
$840$		0			0
$841$	14.1102	+	24.4396i	0.486558	+	0.842743i
$842$	−10.1128	−	5.83860i	−0.348509	−	0.201211i
$843$		0			0
$844$			0.425898i			0.0146600i
$845$	−15.6042	−	33.8872i	−0.536800	−	1.16575i
$846$		0			0
$847$	12.4635	−	20.1671i	0.428252	−	0.692949i
$848$	4.80113	−	8.31579i	0.164871	−	0.285566i
$849$		0			0
$850$	−13.2608	−	13.2608i	−0.454843	−	0.454843i
$851$	56.2879	+	15.0823i	1.92953	+	0.517015i
$852$		0			0
$853$	−16.7852	+	16.7852i	−0.574713	+	0.574713i	−0.933442	−	0.358728i	$-0.883210\pi$
$853$	−16.7852	+	16.7852i	−0.574713	+	0.574713i	0.358728	+	0.933442i	$0.383210\pi$
$854$	−0.298781	−	0.0897332i	−0.0102241	−	0.00307061i
$855$		0			0
$856$	29.5820	−	7.92647i	1.01109	−	0.270921i
$857$	−51.1432			−1.74702			−0.873508	−	0.486809i	$-0.838161\pi$
$857$	−51.1432			−1.74702			−0.873508	+	0.486809i	$0.838161\pi$
$858$		0			0
$859$			15.0880i			0.514795i	0.966306	+	0.257397i	$0.0828649\pi$
$859$			15.0880i			0.514795i	−0.966306	+	0.257397i	$0.917135\pi$
$860$	−0.243720	+	0.0653047i	−0.00831079	+	0.00222687i
$861$		0			0
$862$	0.691725	−	0.399367i	0.0235602	−	0.0136025i
$863$	9.33430	−	9.33430i	0.317743	−	0.317743i	−0.530156	−	0.847900i	$-0.677867\pi$
$863$	9.33430	−	9.33430i	0.317743	−	0.317743i	0.847900	+	0.530156i	$0.177867\pi$
$864$		0			0
$865$	−14.9681	+	55.8619i	−0.508932	+	1.89936i
$866$	8.03096	−	8.03096i	0.272903	−	0.272903i
$867$		0			0
$868$	−0.222156	+	0.0524473i	−0.00754047	+	0.00178018i
$869$	−13.0087	+	3.48568i	−0.441291	+	0.118244i
$870$		0			0
$871$	−0.314907	−	3.70174i	−0.0106702	−	0.125429i
$872$	47.7082			1.61560
$873$		0			0
$874$	57.6824	+	33.3030i	1.95114	+	1.12649i
$875$	3.85320	−	12.8298i	0.130262	−	0.433728i
$876$		0			0
$877$	−37.6430	−	10.0864i	−1.27111	−	0.340594i	−0.440655	−	0.897676i	$-0.645254\pi$
$877$	−37.6430	−	10.0864i	−1.27111	−	0.340594i	−0.830457	+	0.557083i	$0.811921\pi$
$878$	−16.9669	−	4.54627i	−0.572606	−	0.153429i
$879$		0			0
$880$	−13.4979	+	7.79300i	−0.455013	+	0.262702i
$881$	−14.6029	+	25.2929i	−0.491983	+	0.852140i	−0.999957	−	0.00923231i	$-0.997061\pi$
$881$	−14.6029	+	25.2929i	−0.491983	+	0.852140i	0.507974	+	0.861372i	$0.330395\pi$
$882$		0			0
$883$			2.58799i			0.0870929i	0.999051	+	0.0435464i	$0.0138656\pi$
$883$			2.58799i			0.0870929i	−0.999051	+	0.0435464i	$0.986134\pi$
$884$	−1.08817	−	0.917543i	−0.0365991	−	0.0308603i
$885$		0			0
$886$	0.797057	+	2.97466i	0.0267776	+	0.0999355i
$887$	−32.6723	−	18.8634i	−1.09703	−	0.633370i	−0.161590	−	0.986858i	$-0.551662\pi$
$887$	−32.6723	−	18.8634i	−1.09703	−	0.633370i	−0.935439	+	0.353488i	$0.884996\pi$
$888$		0			0
$889$	43.1435	+	1.29301i	1.44699	+	0.0433662i
$890$	18.8477	+	5.05023i	0.631777	+	0.169284i
$891$		0			0
$892$	−1.54739	+	1.54739i	−0.0518105	+	0.0518105i
$893$	9.63220	+	16.6835i	0.322329	+	0.558291i
$894$		0			0
$895$	−12.2794	−	45.8273i	−0.410454	−	1.53184i
$896$	20.1287	−	18.9573i	0.672453	−	0.633319i
$897$		0			0
$898$	−53.8120			−1.79573
$899$	−0.782510	+	0.209673i	−0.0260982	+	0.00699298i
$900$		0			0
$901$	−5.29990	−	9.17970i	−0.176565	−	0.305820i
$902$	16.5564	+	16.5564i	0.551267	+	0.551267i
$903$		0			0
$904$	−0.482039	+	1.79900i	−0.0160324	+	0.0598337i
$905$	27.7798	+	27.7798i	0.923432	+	0.923432i
$906$		0			0
$907$	−44.9567	−	25.9558i	−1.49276	−	0.861847i	−0.492798	−	0.870144i	$-0.664026\pi$
$907$	−44.9567	−	25.9558i	−1.49276	−	0.861847i	−0.999966	+	0.00829638i	$0.997359\pi$
$908$	−0.253691	−	0.946788i	−0.00841904	−	0.0314203i
$909$		0			0
$910$	7.76382	−	36.9884i	0.257368	−	1.22615i
$911$	−15.0311			−0.498003			−0.249002	−	0.968503i	$-0.580102\pi$
$911$	−15.0311			−0.498003			−0.249002	+	0.968503i	$0.580102\pi$
$912$		0			0
$913$	−2.69419	−	1.55549i	−0.0891647	−	0.0514792i
$914$	−27.5322	+	15.8957i	−0.910683	+	0.525783i
$915$		0			0
$916$	−0.0469410	+	0.175186i	−0.00155098	+	0.00578832i
$917$	−2.94957	−	5.48177i	−0.0974035	−	0.181024i
$918$		0			0
$919$	−1.62567	−	2.81574i	−0.0536259	−	0.0928828i	0.837966	−	0.545722i	$-0.183745\pi$
$919$	−1.62567	−	2.81574i	−0.0536259	−	0.0928828i	−0.891592	+	0.452839i	$0.850411\pi$
$920$	−32.4595	+	56.2215i	−1.07016	+	1.85357i
$921$		0			0
$922$	41.6839			1.37279
$923$	9.46167	+	4.43974i	0.311435	+	0.146136i
$924$		0			0
$925$	−6.23669	−	23.2757i	−0.205061	−	0.765299i
$926$	−2.14626	+	3.71742i	−0.0705303	+	0.122162i
$927$		0			0
$928$	−0.331838	+	0.331838i	−0.0108931	+	0.0108931i
$929$	11.0712	−	41.3182i	0.363234	−	1.35561i	−0.506566	−	0.862201i	$-0.669085\pi$
$929$	11.0712	−	41.3182i	0.363234	−	1.35561i	0.869799	−	0.493405i	$-0.164248\pi$
$930$		0			0
$931$	28.6358	+	32.2910i	0.938499	+	1.05829i
$932$	0.404128	+	0.699969i	0.0132376	+	0.0229283i
$933$		0			0
$934$	−7.56484	−	28.2324i	−0.247529	−	0.923791i
$935$			17.2052i			0.562670i
$936$		0			0
$937$			14.9401i			0.488071i	0.969766	+	0.244035i	$0.0784713\pi$
$937$			14.9401i			0.488071i	−0.969766	+	0.244035i	$0.921529\pi$
$938$	1.97861	−	3.20156i	0.0646040	−	0.104535i
$939$		0			0
$940$	−0.730209	+	0.421586i	−0.0238168	+	0.0137506i
$941$	8.04957	+	8.04957i	0.262409	+	0.262409i	0.826032	−	0.563623i	$-0.190593\pi$
$941$	8.04957	+	8.04957i	0.262409	+	0.262409i	−0.563623	+	0.826032i	$0.690593\pi$
$942$		0			0
$943$	89.7632	+	24.0520i	2.92309	+	0.783240i
$944$	−15.7399	+	15.7399i	−0.512291	+	0.512291i
$945$		0			0
$946$	−1.59642	−	0.921695i	−0.0519042	−	0.0299669i
$947$	−31.0554	+	8.32128i	−1.00917	+	0.270405i	−0.725281	−	0.688453i	$-0.758290\pi$
$947$	−31.0554	+	8.32128i	−1.00917	+	0.270405i	−0.283885	+	0.958858i	$0.591623\pi$
$948$		0			0
$949$	8.42752	−	5.87091i	0.273569	−	0.190578i
$950$		−	27.5423i		−	0.893589i
$951$		0			0
$952$	−7.37802	−	31.2517i	−0.239123	−	1.01287i
$953$	−32.4604	+	18.7410i	−1.05150	+	0.607081i	−0.923068	−	0.384638i	$-0.874326\pi$
$953$	−32.4604	+	18.7410i	−1.05150	+	0.607081i	−0.128428	+	0.991719i	$0.540993\pi$
$954$		0			0
$955$	−6.05264	+	22.5888i	−0.195859	+	0.730955i
$956$	0.222056	−	0.828726i	0.00718182	−	0.0268029i
$957$		0			0
$958$	−28.7118	+	16.5768i	−0.927636	+	0.535571i
$959$	−6.31438	−	26.7464i	−0.203902	−	0.863686i
$960$		0			0
$961$		−	30.1582i		−	0.972846i
$962$	12.5950	+	34.8646i	0.406077	+	1.12408i
$963$		0			0
$964$	0.396352	−	0.106202i	0.0127656	−	0.00342054i
$965$	66.5746	+	38.4368i	2.14311	+	1.23733i
$966$		0			0
$967$	10.9130	−	10.9130i	0.350939	−	0.350939i	−0.509520	−	0.860459i	$-0.670177\pi$
$967$	10.9130	−	10.9130i	0.350939	−	0.350939i	0.860459	+	0.509520i	$0.170177\pi$
$968$	−25.0221	−	6.70465i	−0.804240	−	0.215496i
$969$		0			0
$970$	−25.7348	−	25.7348i	−0.826295	−	0.826295i
$971$	1.54608	−	0.892628i	0.0496160	−	0.0286458i	−0.474987	−	0.879993i	$-0.657547\pi$
$971$	1.54608	−	0.892628i	0.0496160	−	0.0286458i	0.524603	+	0.851347i	$0.324214\pi$
$972$		0			0
$973$	8.56383	−	13.8570i	0.274544	−	0.444236i
$974$			47.0455i			1.50743i
$975$		0			0
$976$			0.324815i			0.0103971i
$977$	0.587766	+	2.19357i	0.0188043	+	0.0701786i	0.974690	−	0.223559i	$-0.0717675\pi$
$977$	0.587766	+	2.19357i	0.0188043	+	0.0701786i	−0.955886	+	0.293737i	$0.905101\pi$
$978$		0			0
$979$	−3.51662	−	6.09097i	−0.112392	−	0.194668i
$980$	−1.41333	+	1.25334i	−0.0451471	+	0.0400366i
$981$		0			0
$982$	5.06202	−	18.8917i	0.161535	−	0.602858i
$983$	−30.2896	+	30.2896i	−0.966088	+	0.966088i	−0.999444	−	0.0333560i	$-0.989380\pi$
$983$	−30.2896	+	30.2896i	−0.966088	+	0.966088i	0.0333560	+	0.999444i	$0.489380\pi$
$984$		0			0
$985$	−26.4468	+	45.8071i	−0.842664	+	1.45954i
$986$	−1.32453	−	4.94320i	−0.0421815	−	0.157424i
$987$		0			0
$988$	−0.177191	−	2.08289i	−0.00563721	−	0.0662657i
$989$	−7.31631			−0.232645
$990$		0			0
$991$	−26.6800	+	46.2112i	−0.847519	+	1.46795i	0.0358964	+	0.999356i	$0.488571\pi$
$991$	−26.6800	+	46.2112i	−0.847519	+	1.46795i	−0.883415	+	0.468591i	$0.844762\pi$
$992$	0.243818	+	0.422305i	0.00774123	+	0.0134082i
$993$		0			0
$994$	5.01695	+	9.32397i	0.159128	+	0.295738i
$995$	9.44159	−	35.2365i	0.299319	−	1.11707i
$996$		0			0
$997$	40.7247	−	23.5124i	1.28976	−	0.744645i	0.311152	−	0.950360i	$-0.399285\pi$
$997$	40.7247	−	23.5124i	1.28976	−	0.744645i	0.978612	+	0.205715i	$0.0659519\pi$
$998$	−35.6521	−	20.5837i	−1.12855	−	0.651567i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.g.370.5		32
3.2	odd	2		91.2.bc.a.6.4	yes	32
7.6	odd	2	inner	819.2.fm.g.370.6		32
13.11	odd	12	inner	819.2.fm.g.622.6		32
21.2	odd	6		637.2.bb.b.227.3		32
21.5	even	6		637.2.bb.b.227.4		32
21.11	odd	6		637.2.x.b.19.5		32
21.17	even	6		637.2.x.b.19.6		32
21.20	even	2		91.2.bc.a.6.3	✓	32
39.11	even	12		91.2.bc.a.76.3	yes	32
91.76	even	12	inner	819.2.fm.g.622.5		32
273.11	even	12		637.2.bb.b.362.4		32
273.89	odd	12		637.2.x.b.570.6		32
273.128	even	12		637.2.x.b.570.5		32
273.167	odd	12		91.2.bc.a.76.4	yes	32
273.206	odd	12		637.2.bb.b.362.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.6.3	✓	32	21.20	even	2
91.2.bc.a.6.4	yes	32	3.2	odd	2
91.2.bc.a.76.3	yes	32	39.11	even	12
91.2.bc.a.76.4	yes	32	273.167	odd	12
637.2.x.b.19.5		32	21.11	odd	6
637.2.x.b.19.6		32	21.17	even	6
637.2.x.b.570.5		32	273.128	even	12
637.2.x.b.570.6		32	273.89	odd	12
637.2.bb.b.227.3		32	21.2	odd	6
637.2.bb.b.227.4		32	21.5	even	6
637.2.bb.b.362.3		32	273.206	odd	12
637.2.bb.b.362.4		32	273.11	even	12
819.2.fm.g.370.5		32	1.1	even	1	trivial
819.2.fm.g.370.6		32	7.6	odd	2	inner
819.2.fm.g.622.5		32	91.76	even	12	inner
819.2.fm.g.622.6		32	13.11	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.357317 + 1.33353i) q^{2} +(0.0814361 - 0.0470171i) q^{4} +(-2.02925 - 2.02925i) q^{5} +(-2.32989 + 1.25364i) q^{7} +(2.04421 + 2.04421i) q^{8} +O(q^{10})\)	\(q+(0.357317 + 1.33353i) q^{2} +(0.0814361 - 0.0470171i) q^{4} +(-2.02925 - 2.02925i) q^{5} +(-2.32989 + 1.25364i) q^{7} +(2.04421 + 2.04421i) q^{8} +(1.98097 - 3.43114i) q^{10} +(-1.37941 + 0.369611i) q^{11} +(-3.54926 - 0.634621i) q^{13} +(-2.50427 - 2.65902i) q^{14} +(-1.90154 + 3.29357i) q^{16} +(2.09909 + 3.63573i) q^{17} +(-1.59577 + 5.95551i) q^{19} +(-0.260663 - 0.0698445i) q^{20} +(-0.985770 - 1.70740i) q^{22} +(-6.77658 - 3.91246i) q^{23} +3.23569i q^{25} +(-0.421928 - 4.95979i) q^{26} +(-0.130794 + 0.211636i) q^{28} +(-0.441485 + 0.764674i) q^{29} +(0.648762 + 0.648762i) q^{31} +(0.513380 + 0.137560i) q^{32} +(-4.09830 + 4.09830i) q^{34} +(7.27187 + 2.18397i) q^{35} +(-7.19341 + 1.92747i) q^{37} -8.51202 q^{38} -8.29643i q^{40} +(-11.4714 + 3.07376i) q^{41} +(0.809734 - 0.467500i) q^{43} +(-0.0949554 + 0.0949554i) q^{44} +(2.79598 - 10.4347i) q^{46} +(2.20935 - 2.20935i) q^{47} +(3.85676 - 5.84170i) q^{49} +(-4.31487 + 1.15617i) q^{50} +(-0.318876 + 0.115195i) q^{52} -2.52486 q^{53} +(3.54919 + 2.04912i) q^{55} +(-7.32550 - 2.20008i) q^{56} +(-1.17746 - 0.315500i) q^{58} +(5.65360 + 1.51488i) q^{59} +(0.0739657 - 0.0427041i) q^{61} +(-0.633327 + 1.09695i) q^{62} +8.33994i q^{64} +(5.91453 + 8.49013i) q^{65} +(0.266684 + 0.995278i) q^{67} +(0.341884 + 0.197387i) q^{68} +(-0.314014 + 10.4776i) q^{70} +(-2.79996 - 0.750247i) q^{71} +(-2.01428 + 2.01428i) q^{73} +(-5.14066 - 8.90388i) q^{74} +(0.150057 + 0.560022i) q^{76} +(2.75050 - 2.59043i) q^{77} +9.43068 q^{79} +(10.5422 - 2.82477i) q^{80} +(-8.19789 - 14.1992i) q^{82} +(1.54040 + 1.54040i) q^{83} +(3.11823 - 11.6374i) q^{85} +(0.912755 + 0.912755i) q^{86} +(-3.57536 - 2.06424i) q^{88} +(1.27469 + 4.75720i) q^{89} +(9.06497 - 2.97091i) q^{91} -0.735811 q^{92} +(3.73567 + 2.15679i) q^{94} +(15.3234 - 8.84698i) q^{95} +(2.37752 - 8.87303i) q^{97} +(9.16814 + 3.05575i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8}+O(q^{10}) \) 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8	\( 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8} + 4 q^{11} + 32 q^{14} + 12 q^{16} + 4 q^{22} + 12 q^{23} + 24 q^{28} - 4 q^{29} - 4 q^{32} + 20 q^{35} + 4 q^{37} - 48 q^{43} - 24 q^{44} + 84 q^{46} + 24 q^{49} + 44 q^{50} - 72 q^{53} - 60 q^{56} - 16 q^{58} - 4 q^{65} - 56 q^{67} + 56 q^{70} - 84 q^{71} + 24 q^{74} - 80 q^{79} + 36 q^{85} + 48 q^{86} - 228 q^{88} - 48 q^{91} - 24 q^{92} + 84 q^{95} + 32 q^{98}+O(q^{100}) \) 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8 + 4 * q^11 + 32 * q^14 + 12 * q^16 + 4 * q^22 + 12 * q^23 + 24 * q^28 - 4 * q^29 - 4 * q^32 + 20 * q^35 + 4 * q^37 - 48 * q^43 - 24 * q^44 + 84 * q^46 + 24 * q^49 + 44 * q^50 - 72 * q^53 - 60 * q^56 - 16 * q^58 - 4 * q^65 - 56 * q^67 + 56 * q^70 - 84 * q^71 + 24 * q^74 - 80 * q^79 + 36 * q^85 + 48 * q^86 - 228 * q^88 - 48 * q^91 - 24 * q^92 + 84 * q^95 + 32 * q^98

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