LMFDB - Embedded newform 819.2.fm.g.622.6

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			622.6
Character	$\chi$	$=$	819.622
Dual form			819.2.fm.g.370.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.357317 - 1.33353i) q^{2} +(0.0814361 + 0.0470171i) q^{4} +(2.02925 - 2.02925i) q^{5} +(1.39092 - 2.25063i) q^{7} +(2.04421 - 2.04421i) q^{8} +O(q^{10})$	\(q+(0.357317 - 1.33353i) q^{2} +(0.0814361 + 0.0470171i) q^{4} +(2.02925 - 2.02925i) q^{5} +(1.39092 - 2.25063i) q^{7} +(2.04421 - 2.04421i) q^{8} +(-1.98097 - 3.43114i) q^{10} +(-1.37941 - 0.369611i) q^{11} +(3.54926 - 0.634621i) q^{13} +(-2.50427 - 2.65902i) q^{14} +(-1.90154 - 3.29357i) q^{16} +(-2.09909 + 3.63573i) q^{17} +(1.59577 + 5.95551i) q^{19} +(0.260663 - 0.0698445i) q^{20} +(-0.985770 + 1.70740i) q^{22} +(-6.77658 + 3.91246i) q^{23} -3.23569i q^{25} +(0.421928 - 4.95979i) q^{26} +(0.219089 - 0.117885i) q^{28} +(-0.441485 - 0.764674i) q^{29} +(-0.648762 + 0.648762i) q^{31} +(0.513380 - 0.137560i) q^{32} +(4.09830 + 4.09830i) q^{34} +(-1.74456 - 7.38961i) q^{35} +(-7.19341 - 1.92747i) q^{37} +8.51202 q^{38} -8.29643i q^{40} +(11.4714 + 3.07376i) q^{41} +(0.809734 + 0.467500i) q^{43} +(-0.0949554 - 0.0949554i) q^{44} +(2.79598 + 10.4347i) q^{46} +(-2.20935 - 2.20935i) q^{47} +(-3.13068 - 6.26090i) q^{49} +(-4.31487 - 1.15617i) q^{50} +(0.318876 + 0.115195i) q^{52} -2.52486 q^{53} +(-3.54919 + 2.04912i) q^{55} +(-1.75743 - 7.44411i) q^{56} +(-1.17746 + 0.315500i) q^{58} +(-5.65360 + 1.51488i) q^{59} +(-0.0739657 - 0.0427041i) q^{61} +(0.633327 + 1.09695i) q^{62} -8.33994i q^{64} +(5.91453 - 8.49013i) q^{65} +(0.266684 - 0.995278i) q^{67} +(-0.341884 + 0.197387i) q^{68} +(-10.4776 - 0.314014i) q^{70} +(-2.79996 + 0.750247i) q^{71} +(2.01428 + 2.01428i) q^{73} +(-5.14066 + 8.90388i) q^{74} +(-0.150057 + 0.560022i) q^{76} +(-2.75050 + 2.59043i) q^{77} +9.43068 q^{79} +(-10.5422 - 2.82477i) q^{80} +(8.19789 - 14.1992i) q^{82} +(-1.54040 + 1.54040i) q^{83} +(3.11823 + 11.6374i) q^{85} +(0.912755 - 0.912755i) q^{86} +(-3.57536 + 2.06424i) q^{88} +(-1.27469 + 4.75720i) q^{89} +(3.50844 - 8.87078i) q^{91} -0.735811 q^{92} +(-3.73567 + 2.15679i) q^{94} +(15.3234 + 8.84698i) q^{95} +(-2.37752 - 8.87303i) q^{97} +(-9.46771 + 1.93771i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$-1$

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	−0.716715	−	0.697366i	$-0.754355\pi$
$2$	0.357317	−	1.33353i	0.252661	−	0.942945i	0.969377	−	0.245579i	$-0.0789781\pi$
$3$		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	$-0.528228\pi$
$5$	2.02925	−	2.02925i	0.907507	−	0.907507i	0.996071	+	0.0885635i	$0.0282276\pi$
$6$		0			0
$7$	1.39092	−	2.25063i	0.525719	−	0.850658i
$7$	1.39092	−	2.25063i	0.525719	−	0.850658i
$8$	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	0.0447966	−	0.998996i	$-0.485736\pi$
$11$	−1.37941	−	0.369611i	−0.415906	−	0.111442i	−0.460703	+	0.887554i	$0.652403\pi$
$12$		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	0.490840	+	0.871250i	$0.336690\pi$
$17$	−2.09909	+	3.63573i	−0.509105	+	0.881795i	−0.999944	+	0.0105451i	$0.996643\pi$
$18$		0			0
$19$	1.59577	+	5.95551i	0.366096	+	1.36629i	0.865929	+	0.500166i	$0.166728\pi$
$19$	1.59577	+	5.95551i	0.366096	+	1.36629i	−0.499834	+	0.866121i	$0.666606\pi$
$20$	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	−0.995671	−	0.0929436i	$-0.970372\pi$
$23$	−6.77658	+	3.91246i	−1.41302	+	0.815805i	−0.417344	+	0.908748i	$0.637039\pi$
$24$		0			0
$25$		−	3.23569i		−	0.647138i
$26$	0.421928	−	4.95979i	0.0827470	−	0.972695i
$27$		0			0
$28$	0.219089	−	0.117885i	0.0414040	−	0.0222783i
$29$	−0.441485	−	0.764674i	−0.0819817	−	0.141996i	0.822119	−	0.569315i	$-0.192792\pi$
$29$	−0.441485	−	0.764674i	−0.0819817	−	0.141996i	−0.904101	+	0.427319i	$0.859458\pi$
$30$		0			0
$31$	−0.648762	+	0.648762i	−0.116521	+	0.116521i	−0.762963	−	0.646442i	$-0.776256\pi$
$31$	−0.648762	+	0.648762i	−0.116521	+	0.116521i	0.646442	+	0.762963i	$0.276256\pi$
$32$	0.513380	−	0.137560i	0.0907536	−	0.0243174i
$33$		0			0
$34$	4.09830	+	4.09830i	0.702853	+	0.702853i
$35$	−1.74456	−	7.38961i	−0.294885	−	1.24907i
$36$		0			0
$37$	−7.19341	−	1.92747i	−1.18259	−	0.316874i	−0.386637	−	0.922232i	$-0.626363\pi$
$37$	−7.19341	−	1.92747i	−1.18259	−	0.316874i	−0.795953	+	0.605358i	$0.793030\pi$
$38$	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	$-0.0387317\pi$
$41$	11.4714	+	3.07376i	1.79154	+	0.480041i	0.798933	+	0.601421i	$0.205398\pi$
$42$		0			0
$43$	0.809734	+	0.467500i	0.123483	+	0.0712931i	0.560469	−	0.828175i	$-0.310621\pi$
$43$	0.809734	+	0.467500i	0.123483	+	0.0712931i	−0.436986	+	0.899468i	$0.643954\pi$
$44$	−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	$-0.323179\pi$
$47$	−2.20935	−	2.20935i	−0.322267	−	0.322267i	−0.849636	+	0.527369i	$0.823179\pi$
$48$		0			0
$49$	−3.13068	−	6.26090i	−0.447240	−	0.894414i
$50$	−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
$56$	−1.75743	−	7.44411i	−0.234847	−	0.994761i
$57$		0			0
$58$	−1.17746	+	0.315500i	−0.154608	+	0.0414272i
$59$	−5.65360	+	1.51488i	−0.736035	+	0.197220i	−0.607315	−	0.794461i	$-0.707754\pi$
$59$	−5.65360	+	1.51488i	−0.736035	+	0.197220i	−0.128720	+	0.991681i	$0.541087\pi$
$60$		0			0
$61$	−0.0739657	−	0.0427041i	−0.00947033	−	0.00546770i	0.495257	−	0.868746i	$-0.335074\pi$
$61$	−0.0739657	−	0.0427041i	−0.00947033	−	0.00546770i	−0.504728	+	0.863279i	$0.668407\pi$
$62$	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	−0.947720	−	0.319102i	$-0.896619\pi$
$67$	0.266684	−	0.995278i	0.0325806	−	0.121593i	0.980301	+	0.197510i	$0.0632854\pi$
$68$	−0.341884	+	0.197387i	−0.0414595	+	0.0239366i
$69$		0			0
$70$	−10.4776	−	0.314014i	−1.25231	−	0.0375318i
$71$	−2.79996	+	0.750247i	−0.332294	+	0.0890380i	−0.421109	−	0.907010i	$-0.638359\pi$
$71$	−2.79996	+	0.750247i	−0.332294	+	0.0890380i	0.0888143	+	0.996048i	$0.471692\pi$
$72$		0			0
$73$	2.01428	+	2.01428i	0.235754	+	0.235754i	0.815089	−	0.579335i	$-0.196688\pi$
$73$	2.01428	+	2.01428i	0.235754	+	0.235754i	−0.579335	+	0.815089i	$0.696688\pi$
$74$	−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	$-0.788148\pi$
$83$	−1.54040	+	1.54040i	−0.169081	+	0.169081i	0.617494	+	0.786575i	$0.288148\pi$
$84$		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	0.864881	+	0.501977i	$0.167394\pi$
$89$	−1.27469	+	4.75720i	−0.135117	+	0.504262i	−0.999997	+	0.00228491i	$0.999273\pi$
$90$		0			0
$91$	3.50844	−	8.87078i	0.367785	−	0.929911i
$92$	−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	−0.975158	−	0.221509i	$-0.928902\pi$
$97$	−2.37752	−	8.87303i	−0.241401	−	0.900920i	0.733758	−	0.679411i	$-0.237765\pi$
$98$	−9.46771	+	1.93771i	−0.956383	+	0.195738i
$99$		0			0
$100$	0.152133	−	0.263502i	0.0152133	−	0.0263502i
$101$	−3.27488	−	5.67227i	−0.325863	−	0.564412i	0.655824	−	0.754914i	$-0.272322\pi$
$101$	−3.27488	−	5.67227i	−0.325863	−	0.564412i	−0.981687	+	0.190503i	$0.938988\pi$
$102$		0			0
$103$	−9.85541			−0.971082			−0.485541	−	0.874214i	$-0.661377\pi$
$103$	−9.85541			−0.971082			−0.485541	+	0.874214i	$0.661377\pi$
$104$	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	0.999902	+	0.0139814i	$0.00445058\pi$
$107$	5.29678	+	9.17430i	0.512059	+	0.886913i	−0.487843	+	0.872931i	$0.662216\pi$
$108$		0			0
$109$	11.6691	+	11.6691i	1.11770	+	1.11770i	0.992079	+	0.125617i	$0.0400911\pi$
$109$	11.6691	+	11.6691i	1.11770	+	1.11770i	0.125617	+	0.992079i	$0.459909\pi$
$110$	1.46437	+	5.46512i	0.139623	+	0.521078i
$111$		0			0
$112$	−10.0575	−	0.301424i	−0.950346	−	0.0284819i
$113$	0.322118	−	0.557925i	0.0303023	−	0.0524851i	−0.850477	−	0.526013i	$-0.823686\pi$
$113$	0.322118	−	0.557925i	0.0303023	−	0.0524851i	0.880779	+	0.473528i	$0.157020\pi$
$114$		0			0
$115$	−5.81201	+	21.6907i	−0.541973	+	2.02267i
$116$		−	0.0830294i		−	0.00770909i
$117$		0			0
$118$			8.08051i			0.743871i
$119$	5.26302	+	9.78130i	0.482461	+	0.896650i
$120$		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	−0.971841	−	0.235640i	$-0.924282\pi$
$127$	−14.1284	+	8.15702i	−1.25369	+	0.723819i	−0.281850	+	0.959458i	$0.590948\pi$
$128$	−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
$133$	15.6232	+	4.69215i	1.35471	+	0.406861i
$134$	−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	−0.980474	−	0.196650i	$-0.936994\pi$
$137$	−2.68838	−	10.0332i	−0.229683	−	0.857190i	0.750790	−	0.660541i	$-0.229673\pi$
$138$		0			0
$139$	5.33208	+	3.07848i	0.452261	+	0.261113i	0.708784	−	0.705425i	$-0.249244\pi$
$139$	5.33208	+	3.07848i	0.452261	+	0.261113i	−0.256524	+	0.966538i	$0.582577\pi$
$140$	0.205368	−	0.683805i	0.0173568	−	0.0577921i
$141$		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	0.102672	−	0.994715i	$-0.467261\pi$
$149$	8.40965	−	2.25336i	0.688945	−	0.184602i	0.586274	+	0.810113i	$0.300594\pi$
$150$		0			0
$151$	9.55198	−	9.55198i	0.777329	−	0.777329i	−0.202047	−	0.979376i	$-0.564759\pi$
$151$	9.55198	−	9.55198i	0.777329	−	0.777329i	0.979376	+	0.202047i	$0.0647593\pi$
$152$	15.4364	+	8.91223i	1.25206	+	0.722877i
$153$		0			0
$154$	2.47161	+	4.59347i	0.199168	+	0.370152i
$155$			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
$161$	−0.620185	+	20.6935i	−0.0488774	+	1.63088i
$162$		0			0
$163$	−2.82752	−	10.5525i	−0.221469	−	0.826532i	−0.983789	−	0.179332i	$-0.942606\pi$
$163$	−2.82752	−	10.5525i	−0.221469	−	0.826532i	0.762320	−	0.647200i	$-0.224060\pi$
$164$	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	0.502962	+	0.864308i	$0.332244\pi$
$167$	−4.71387	+	17.5924i	−0.364770	+	1.36134i	−0.867732	+	0.497032i	$0.834423\pi$
$168$		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	−0.173608	−	0.984815i	$-0.555543\pi$
$173$	10.0761	−	17.4523i	0.766070	−	1.32687i	0.939679	−	0.342058i	$-0.111124\pi$
$174$		0			0
$175$	−7.28234	−	4.50059i	−0.550493	−	0.340213i
$176$	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	0.141909	−	0.989880i	$-0.454676\pi$
$179$	14.3173	−	8.26609i	1.07012	−	0.617837i	0.928216	+	0.372043i	$0.121343\pi$
$180$		0			0
$181$	13.6897			1.01755			0.508774	−	0.860900i	$-0.330099\pi$
$181$	13.6897			1.01755			0.508774	+	0.860900i	$0.330099\pi$
$182$	−10.5758	−	7.84828i	−0.783930	−	0.581753i
$183$		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	−0.974942	−	0.222458i	$-0.928592\pi$
$191$	−4.07445	+	7.05715i	−0.294817	+	0.510638i	0.680126	+	0.733096i	$0.261925\pi$
$192$		0			0
$193$	−25.8745	−	6.93304i	−1.86249	−	0.499051i	−0.862510	−	0.506040i	$-0.831109\pi$
$193$	−25.8745	−	6.93304i	−1.86249	−	0.499051i	−0.999976	+	0.00698876i	$0.997775\pi$
$194$	−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	0.558617	+	0.829426i	$0.311332\pi$
$197$	−4.77033	+	17.8031i	−0.339872	+	1.26842i	−0.898490	+	0.438995i	$0.855335\pi$
$198$		0			0
$199$	−6.35578	+	11.0085i	−0.450550	+	0.780375i	−0.998420	−	0.0561884i	$-0.982105\pi$
$199$	−6.35578	+	11.0085i	−0.450550	+	0.780375i	0.547871	+	0.836563i	$0.315439\pi$
$200$	−6.61444	−	6.61444i	−0.467712	−	0.467712i
$201$		0			0
$202$	−8.73428	+	2.34034i	−0.614542	+	0.164666i
$203$	−2.33507	−	0.0699820i	−0.163890	−	0.00491178i
$204$		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	0.777486	−	0.628900i	$-0.216495\pi$
$211$	−2.26459	−	3.92239i	−0.155901	−	0.270028i	−0.933387	+	0.358872i	$0.883161\pi$
$212$	−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
$217$	0.557747	+	2.36250i	0.0378623	+	0.160377i
$218$	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	$-0.132294\pi$
$223$	22.4788	+	6.02318i	1.50529	+	0.403342i	0.590423	+	0.807094i	$0.298961\pi$
$224$	0.404475	−	1.34676i	0.0270251	−	0.0899844i
$225$		0			0
$226$	−0.628909	−	0.628909i	−0.0418344	−	0.0418344i
$227$	−2.69786	−	10.0685i	−0.179063	−	0.668273i	−0.995824	−	0.0912961i	$-0.970899\pi$
$227$	−2.69786	−	10.0685i	−0.179063	−	0.668273i	0.816761	−	0.576977i	$-0.195768\pi$
$228$		0			0
$229$	1.36381	+	1.36381i	0.0901234	+	0.0901234i	0.750731	−	0.660608i	$-0.229701\pi$
$229$	1.36381	+	1.36381i	0.0901234	+	0.0901234i	−0.660608	+	0.750731i	$0.729701\pi$
$230$	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	$-0.909152\pi$
$233$		−	8.59532i		−	0.563098i	0.959547	−	0.281549i	$-0.0908482\pi$
$234$		0			0
$235$	−8.96665			−0.584920
$236$	−0.531632	−	0.142450i	−0.0346063	−	0.00927273i
$237$		0			0
$238$	14.9242	−	3.52335i	0.967391	−	0.228385i
$239$	6.45158	+	6.45158i	0.417318	+	0.417318i	0.884278	−	0.466960i	$-0.154651\pi$
$239$	6.45158	+	6.45158i	0.417318	+	0.417318i	−0.466960	+	0.884278i	$0.654651\pi$
$240$		0			0
$241$	−4.21497	+	1.12940i	−0.271510	+	0.0727509i	−0.392005	−	0.919963i	$-0.628218\pi$
$241$	−4.21497	+	1.12940i	−0.271510	+	0.0727509i	0.120495	+	0.992714i	$0.461552\pi$
$242$	−8.74744	+	8.74744i	−0.562307	+	0.562307i
$243$		0			0
$244$	−0.00401565	−	0.00695531i	−0.000257076	−	0.000445268i
$245$	−19.0578	−	6.35199i	−1.21756	−	0.405814i
$246$		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	$-0.879292\pi$
$251$	−2.27953	+	3.94826i	−0.143883	+	0.249212i	0.785073	+	0.619403i	$0.212625\pi$
$252$		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	$-0.0798857\pi$
$257$	4.31666	+	7.47667i	0.269266	+	0.466382i	−0.699407	+	0.714724i	$0.746552\pi$
$258$		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	0.591311	−	0.806444i	$-0.298611\pi$
$263$	−6.53143	−	11.3128i	−0.402745	−	0.697575i	−0.994056	+	0.108868i	$0.965277\pi$
$264$		0			0
$265$	−5.12356	+	5.12356i	−0.314738	+	0.314738i
$266$	11.8395	−	19.1574i	0.725929	−	1.17462i
$267$		0			0
$268$	0.0685128	−	0.0685128i	0.00418509	−	0.00418509i
$269$	10.8756	+	6.27901i	0.663095	+	0.382838i	0.793455	−	0.608629i	$-0.208280\pi$
$269$	10.8756	+	6.27901i	0.663095	+	0.382838i	−0.130360	+	0.991467i	$0.541613\pi$
$270$		0			0
$271$	1.19419	−	4.45677i	0.0725418	−	0.270730i	−0.920123	−	0.391630i	$-0.871911\pi$
$271$	1.19419	−	4.45677i	0.0725418	−	0.270730i	0.992665	+	0.120900i	$0.0385781\pi$
$272$	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	0.455856	−	0.890054i	$-0.349333\pi$
$277$	−1.44840	−	0.836232i	−0.0870257	−	0.0502443i	−0.542881	+	0.839809i	$0.682667\pi$
$278$	6.01047	−	6.01047i	0.360484	−	0.360484i
$279$		0			0
$280$	−18.6722	−	11.5397i	−1.11588	−	0.689628i
$281$	13.9259	−	13.9259i	0.830749	−	0.830749i	−0.156870	−	0.987619i	$-0.550140\pi$
$281$	13.9259	−	13.9259i	0.830749	−	0.830749i	0.987619	+	0.156870i	$0.0501403\pi$
$282$		0			0
$283$	−16.4969	−	28.5736i	−0.980642	−	1.69852i	−0.659897	−	0.751356i	$-0.729400\pi$
$283$	−16.4969	−	28.5736i	−0.980642	−	1.69852i	−0.320744	−	0.947166i	$-0.603933\pi$
$284$	−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	$-0.361659\pi$
$293$	21.2120	−	5.68375i	1.23922	−	0.332048i	0.818163	+	0.574986i	$0.194993\pi$
$294$		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
$301$	2.17845	−	1.17216i	0.125564	−	0.0675620i
$302$	−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	$-0.437760\pi$
$307$	−13.7833	−	13.7833i	−0.786656	−	0.786656i	−0.980944	+	0.194289i	$0.937760\pi$
$308$	−0.345785	+	0.0816340i	−0.0197029	+	0.00465153i
$309$		0			0
$310$	3.51117	+	0.940815i	0.199421	+	0.0534347i
$311$	−25.8267			−1.46450			−0.732248	−	0.681038i	$-0.761529\pi$
$311$	−25.8267			−1.46450			−0.732248	+	0.681038i	$0.761529\pi$
$312$		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	0.414810	−	0.909908i	$-0.363848\pi$
$317$	−8.81498	−	8.81498i	−0.495098	−	0.495098i	−0.909908	+	0.414810i	$0.863848\pi$
$318$		0			0
$319$	0.326355	+	1.21797i	0.0182724	+	0.0681934i
$320$	−16.9238	−	16.9238i	−0.946069	−	0.946069i
$321$		0			0
$322$	27.3737	+	8.22118i	1.52548	+	0.458148i
$323$	−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
$329$	−8.04548	+	1.89940i	−0.443561	+	0.104717i
$330$		0			0
$331$	−28.9319	+	7.75229i	−1.59024	+	0.426104i	−0.942078	−	0.335395i	$-0.891130\pi$
$331$	−28.9319	+	7.75229i	−1.59024	+	0.426104i	−0.648166	+	0.761499i	$0.724464\pi$
$332$	−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	$-0.880704\pi$
$337$		−	13.4402i		−	0.732137i	0.930588	−	0.366068i	$-0.119296\pi$
$338$	−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
$343$	−18.4455	−	1.66242i	−0.995963	−	0.0897621i
$344$	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	−0.992338	−	0.123556i	$-0.960570\pi$
$347$	−7.24936	+	12.5563i	−0.389166	+	0.674055i	0.603172	+	0.797611i	$0.293903\pi$
$348$		0			0
$349$	−5.68220	+	21.2063i	−0.304161	+	1.13515i	0.629504	+	0.776998i	$0.283258\pi$
$349$	−5.68220	+	21.2063i	−0.304161	+	1.13515i	−0.933665	+	0.358148i	$0.883408\pi$
$350$	−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	$-0.317242\pi$
$353$	11.1538	+	2.98864i	0.593655	+	0.159069i	0.0505316	+	0.998722i	$0.483908\pi$
$354$		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	−0.690259	−	0.723563i	$-0.742503\pi$
$359$	0.631018	−	0.631018i	0.0333039	−	0.0333039i	0.723563	+	0.690259i	$0.242503\pi$
$360$		0			0
$361$	−16.4671	+	9.50729i	−0.866690	+	0.500384i
$362$	4.89156	−	18.2556i	0.257095	−	0.959491i
$363$		0			0
$364$	0.702793	−	0.557445i	0.0368364	−	0.0292181i
$365$	8.17495			0.427897
$366$		0			0
$367$	−12.5341	+	7.23654i	−0.654273	+	0.377744i	−0.790091	−	0.612989i	$-0.789967\pi$
$367$	−12.5341	+	7.23654i	−0.654273	+	0.377744i	0.135819	+	0.990734i	$0.456634\pi$
$368$	25.7720	+	14.8794i	1.34346	+	0.775645i
$369$		0			0
$370$	7.63651	+	28.4998i	0.397003	+	1.48164i
$371$	−3.51187	+	5.68252i	−0.182327	+	0.295022i
$372$		0			0
$373$	−10.4635	+	18.1233i	−0.541778	+	0.938387i	0.457024	+	0.889454i	$0.348915\pi$
$373$	−10.4635	+	18.1233i	−0.541778	+	0.938387i	−0.998802	+	0.0489327i	$0.984418\pi$
$374$	−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	0.665355	+	0.746527i	$0.268280\pi$
$379$	−5.53128	+	20.6430i	−0.284123	+	1.06036i	−0.949478	+	0.313834i	$0.898387\pi$
$380$	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	0.977209	+	0.212279i	$0.0680886\pi$
$383$	4.63937	+	17.3144i	0.237061	+	0.884723i	−0.740148	+	0.672444i	$0.765245\pi$
$384$		0			0
$385$	−0.324817	+	10.8381i	−0.0165542	+	0.552360i
$386$	−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	$0.0393301\pi$
$389$			4.86154i			0.246490i	−0.992376	+	0.123245i	$0.960670\pi$
$390$		0			0
$391$		−	32.8505i		−	1.66132i
$392$	−19.1984	−	6.39884i	−0.969665	−	0.323190i
$393$		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	$-0.419992\pi$
$397$	18.8967	−	5.06335i	0.948397	−	0.254122i	0.699682	+	0.714455i	$0.253325\pi$
$398$	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	0.153700	−	0.988118i	$-0.450881\pi$
$401$	−4.15019	−	1.11204i	−0.207251	−	0.0555327i	−0.360951	+	0.932585i	$0.617548\pi$
$402$		0			0
$403$	−1.89091	+	2.71434i	−0.0941928	+	0.135211i
$404$		−	0.615903i		−	0.0306423i
$405$		0			0
$406$	−0.927683	+	3.08887i	−0.0460401	+	0.153298i
$407$	9.21022	+	5.31752i	0.456534	+	0.263580i
$408$		0			0
$409$	−7.85062	−	29.2989i	−0.388188	−	1.44874i	−0.833079	−	0.553154i	$-0.813424\pi$
$409$	−7.85062	−	29.2989i	−0.388188	−	1.44874i	0.444891	−	0.895585i	$-0.353242\pi$
$410$	−12.1781	−	45.4491i	−0.601432	−	2.24457i
$411$		0			0
$412$	−0.802586	−	0.463373i	−0.0395406	−	0.0228288i
$413$	−4.45428	+	14.8312i	−0.219181	+	0.729797i
$414$		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	$-0.604573\pi$
$419$	6.87240	−	3.96778i	0.335739	−	0.193839i	0.658386	+	0.752680i	$0.271239\pi$
$420$		0			0
$421$	−5.98090	−	5.98090i	−0.291491	−	0.291491i	0.546178	−	0.837669i	$-0.316082\pi$
$421$	−5.98090	−	5.98090i	−0.291491	−	0.291491i	−0.837669	+	0.546178i	$0.816082\pi$
$422$	−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
$427$	−0.198992	+	0.107071i	−0.00962987	+	0.00518155i
$428$			0.996159i			0.0481511i
$429$		0			0
$430$		−	3.70441i		−	0.178643i
$431$	−0.149741	+	0.558842i	−0.00721278	+	0.0269185i	−0.969438	−	0.245335i	$-0.921102\pi$
$431$	−0.149741	+	0.558842i	−0.00721278	+	0.0269185i	0.962226	+	0.272253i	$0.0877688\pi$
$432$		0			0
$433$	4.11334	−	7.12452i	0.197675	−	0.342382i	−0.750099	−	0.661325i	$-0.769994\pi$
$433$	4.11334	−	7.12452i	0.197675	−	0.342382i	0.947774	+	0.318943i	$0.103328\pi$
$434$	3.34975	+	0.100392i	0.160793	+	0.00481897i
$435$		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	$-0.0684692\pi$
$439$	6.36168	+	11.0188i	0.303626	+	0.525896i	−0.673328	+	0.739344i	$0.735136\pi$
$440$	−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
$448$	−18.7701	−	11.6002i	−0.886805	−	0.548058i
$449$	−10.0883	−	37.6500i	−0.476096	−	1.77682i	−0.617184	−	0.786819i	$-0.711727\pi$
$449$	−10.0883	−	37.6500i	−0.476096	−	1.77682i	0.141088	−	0.989997i	$-0.454940\pi$
$450$		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
$455$	−10.8815	−	25.1205i	−0.510133	−	1.17767i
$456$		0			0
$457$	5.96003	−	22.2431i	0.278798	−	1.04049i	−0.674455	−	0.738316i	$-0.735621\pi$
$457$	5.96003	−	22.2431i	0.278798	−	1.04049i	0.953253	−	0.302174i	$-0.0977122\pi$
$458$	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	−0.868822	−	0.495125i	$-0.835122\pi$
$461$	−7.81461	−	29.1645i	−0.363962	−	1.35833i	0.504859	−	0.863202i	$-0.331544\pi$
$462$		0			0
$463$	2.19856	−	2.19856i	0.102176	−	0.102176i	−0.654171	−	0.756347i	$-0.726982\pi$
$463$	2.19856	−	2.19856i	0.102176	−	0.102176i	0.756347	+	0.654171i	$0.226982\pi$
$464$	−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	$-0.337054\pi$
$467$	21.1712			0.979688			0.489844	+	0.871810i	$0.337054\pi$
$468$		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
$476$	−0.0312888	+	1.04400i	−0.00143412	+	0.0478518i
$477$		0			0
$478$	10.9086	−	6.29809i	0.498948	−	0.288068i
$479$	−6.21539	+	23.1962i	−0.283988	+	1.05986i	0.665587	+	0.746320i	$0.268181\pi$
$479$	−6.21539	+	23.1962i	−0.283988	+	1.05986i	−0.949575	+	0.313539i	$0.898485\pi$
$480$		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	0.581294	−	0.813694i	$-0.302547\pi$
$487$	32.9158	−	8.81975i	1.49156	−	0.399661i	0.910262	+	0.414032i	$0.135880\pi$
$488$	−0.238498	+	0.0639053i	−0.0107963	+	0.00289286i
$489$		0			0
$490$	−15.2802	+	23.1444i	−0.690291	+	1.04556i
$491$	−12.2688	+	7.08337i	−0.553681	+	0.319668i	−0.750605	−	0.660751i	$-0.770238\pi$
$491$	−12.2688	+	7.08337i	−0.553681	+	0.319668i	0.196924	+	0.980419i	$0.436905\pi$
$492$		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
$497$	−2.20600	+	7.34521i	−0.0989524	+	0.329478i
$498$		0			0
$499$	−21.0854	−	21.0854i	−0.943912	−	0.943912i	0.0545964	−	0.998509i	$-0.482613\pi$
$499$	−21.0854	−	21.0854i	−0.943912	−	0.943912i	−0.998509	+	0.0545964i	$0.982613\pi$
$500$	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	$-0.431703\pi$
$503$	−11.8147	−	6.82122i	−0.526791	−	0.304143i	−0.739709	+	0.672927i	$0.765037\pi$
$504$		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	$-0.435511\pi$
$509$	−2.57869	−	0.690957i	−0.114298	−	0.0306261i	−0.315515	+	0.948921i	$0.602177\pi$
$510$		0			0
$511$	7.33511	−	1.73170i	0.324486	−	0.0766058i
$512$	−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
$518$	12.8891	+	23.9543i	0.566315	+	1.05249i
$519$		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	$-0.667491\pi$
$523$	−0.102601	+	0.0592367i	−0.00448643	+	0.00259024i	0.497755	+	0.867318i	$0.334158\pi$
$524$	−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
$539$	2.00438	+	9.79345i	0.0863347	+	0.421834i
$540$		0			0
$541$	−3.27270	+	3.27270i	−0.140705	+	0.140705i	−0.773951	−	0.633246i	$-0.781722\pi$
$541$	−3.27270	+	3.27270i	−0.140705	+	0.140705i	0.633246	+	0.773951i	$0.281722\pi$
$542$	−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
$553$	13.1173	−	21.2250i	0.557806	−	0.902578i
$554$	−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	0.286473	−	0.958088i	$-0.407517\pi$
$557$	1.31037	+	0.351113i	0.0555222	+	0.0148771i	−0.230951	+	0.972965i	$0.574184\pi$
$558$		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	−0.279995	−	0.960001i	$-0.590333\pi$
$563$	16.4050	−	28.4143i	0.691388	−	1.19752i	0.971383	−	0.237517i	$-0.0763337\pi$
$564$		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	0.152552	−	0.988296i	$-0.451251\pi$
$569$	25.8745	−	14.9387i	1.08472	−	0.626261i	0.932165	+	0.362034i	$0.117918\pi$
$570$		0			0
$571$			0.740021i			0.0309689i	0.999880	+	0.0154844i	$0.00492905\pi$
$571$			0.740021i			0.0309689i	−0.999880	+	0.0154844i	$0.995071\pi$
$572$	−0.397282	−	0.276761i	−0.0166112	−	0.0115719i
$573$		0			0
$574$	−20.5544	−	38.2003i	−0.857926	−	1.59445i
$575$	12.6595	+	21.9269i	0.527938	+	0.914416i
$576$		0			0
$577$	24.1189	−	24.1189i	1.00408	−	1.00408i	0.00409020	−	0.999992i	$-0.498698\pi$
$577$	24.1189	−	24.1189i	1.00408	−	1.00408i	0.999992	−	0.00409020i	$-0.00130196\pi$
$578$	−0.833116	+	0.223233i	−0.0346531	+	0.00928526i
$579$		0			0
$580$	−0.168487	−	0.168487i	−0.00699605	−	0.00699605i
$581$	1.32430	+	5.60946i	0.0549412	+	0.232719i
$582$		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	$-0.499014\pi$
$587$	−11.9740	−	3.20842i	−0.494219	−	0.132426i	−0.497316	+	0.867569i	$0.665681\pi$
$588$		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	$-0.0944938\pi$
$593$	16.1631	+	16.1631i	0.663739	+	0.663739i	−0.292520	+	0.956259i	$0.594494\pi$
$594$		0			0
$595$	30.5287	+	9.16870i	1.25155	+	0.375880i
$596$	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	$-0.810889\pi$
$601$	−18.5873	+	10.7314i	−0.758193	+	0.437743i	0.0704537	+	0.997515i	$0.477555\pi$
$602$	−0.784704	−	3.32384i	−0.0319822	−	0.135470i
$603$		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	$-0.227796\pi$
$607$	13.8907	+	8.01981i	0.563807	+	0.325514i	−0.190865	+	0.981616i	$0.561129\pi$
$608$	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	−0.992600	−	0.121431i	$-0.961252\pi$
$613$	−1.78927	+	6.67764i	−0.0722679	+	0.269707i	0.920332	+	0.391138i	$0.127918\pi$
$614$	−23.3054	+	13.4554i	−0.940530	+	0.543015i
$615$		0			0
$616$	−0.327213	+	10.9180i	−0.0131838	+	0.439899i
$617$	−26.9254	+	7.21463i	−1.08397	+	0.290450i	−0.756223	−	0.654314i	$-0.772957\pi$
$617$	−26.9254	+	7.21463i	−1.08397	+	0.290450i	−0.327751	+	0.944764i	$0.606291\pi$
$618$		0			0
$619$	9.80302	+	9.80302i	0.394017	+	0.394017i	0.876116	−	0.482100i	$-0.160126\pi$
$619$	9.80302	+	9.80302i	0.394017	+	0.394017i	−0.482100	+	0.876116i	$0.660126\pi$
$620$	−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	0.961302	+	0.275496i	$0.0888419\pi$
$631$	6.69536	+	24.9874i	0.266538	+	0.994733i	−0.694764	+	0.719237i	$0.744491\pi$
$632$	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
$637$	−15.0849	−	20.2348i	−0.597685	−	0.801731i
$638$	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	0.699405	−	0.714726i	$-0.253449\pi$
$641$	10.8902	+	6.28745i	0.430136	+	0.248339i	−0.269269	+	0.963065i	$0.586782\pi$
$642$		0			0
$643$	−6.40174	−	23.8916i	−0.252460	−	0.942193i	−0.969486	−	0.245147i	$-0.921164\pi$
$643$	−6.40174	−	23.8916i	−0.252460	−	0.942193i	0.717026	−	0.697046i	$-0.245503\pi$
$644$	−1.02346	+	1.65604i	−0.0403298	+	0.0652571i
$645$		0			0
$646$	−17.8675	+	30.9474i	−0.702988	+	1.21761i
$647$	−17.3117	−	29.9848i	−0.680595	−	1.17883i	−0.974800	−	0.223083i	$-0.928388\pi$
$647$	−17.3117	−	29.9848i	−0.680595	−	1.17883i	0.294205	−	0.955742i	$-0.404945\pi$
$648$		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	−0.999108	−	0.0422314i	$-0.986553\pi$
$653$	−13.7001	−	23.7293i	−0.536127	−	0.928600i	0.462980	−	0.886368i	$-0.346780\pi$
$654$		0			0
$655$	4.77442	+	4.77442i	0.186552	+	0.186552i
$656$	−11.6898	−	43.6269i	−0.456410	−	1.70335i
$657$		0			0
$658$	−0.341884	+	11.4075i	−0.0133280	+	0.444712i
$659$	−2.14617	+	3.71728i	−0.0836031	+	0.144805i	−0.904795	−	0.425847i	$-0.859976\pi$
$659$	−2.14617	+	3.71728i	−0.0836031	+	0.144805i	0.821192	+	0.570652i	$0.193309\pi$
$660$		0			0
$661$	−3.93734	+	14.6944i	−0.153145	+	0.571544i	0.846112	+	0.533005i	$0.178937\pi$
$661$	−3.93734	+	14.6944i	−0.153145	+	0.571544i	−0.999257	+	0.0385395i	$0.987729\pi$
$662$			41.3515i			1.60717i
$663$		0			0
$664$			6.29783i			0.244403i
$665$	41.2250	−	22.1819i	1.59864	−	0.860178i
$666$		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	0.101526	−	0.994833i	$-0.467627\pi$
$673$	26.3013	−	15.1851i	1.01384	−	0.585341i	0.912314	+	0.409492i	$0.134294\pi$
$674$	−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
$679$	−23.2769	−	6.99076i	−0.893284	−	0.268281i
$680$	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	−0.998776	−	0.0494567i	$-0.984251\pi$
$683$	−4.14330	−	15.4630i	−0.158539	−	0.591676i	0.840237	−	0.542219i	$-0.182416\pi$
$684$		0			0
$685$	−25.8151	−	14.9044i	−0.986346	−	0.569467i
$686$	−8.80777	+	24.0035i	−0.336282	+	0.916459i
$687$		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	$-0.305006\pi$
$691$	17.4509	+	4.67596i	0.663864	+	0.177882i	0.0888748	+	0.996043i	$0.471673\pi$
$692$	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
$700$	−0.381441	−	0.708905i	−0.0144171	−	0.0267941i
$701$		−	37.6363i		−	1.42150i	−0.703444	−	0.710751i	$-0.748355\pi$
$701$		−	37.6363i		−	1.42150i	0.703444	−	0.710751i	$-0.251645\pi$
$702$		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
$707$	−17.3213	−	0.519119i	−0.651434	−	0.0195235i
$708$		0			0
$709$	−2.98398	−	11.1364i	−0.112066	−	0.418235i	0.886985	−	0.461798i	$-0.152796\pi$
$709$	−2.98398	−	11.1364i	−0.112066	−	0.418235i	−0.999051	+	0.0435634i	$0.986129\pi$
$710$	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	0.00926691	+	0.999957i	$0.497050\pi$
$719$	−23.0965	+	40.0043i	−0.861355	+	1.49191i	−0.870622	+	0.491953i	$0.836283\pi$
$720$		0			0
$721$	−13.7081	+	22.1809i	−0.510516	+	0.826059i
$722$	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	$-0.480657\pi$
$727$	3.27502			0.121464			0.0607318	+	0.998154i	$0.480657\pi$
$728$	−10.9618	−	25.3058i	−0.406270	−	0.937895i
$729$		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	$-0.964195\pi$
$733$	−23.8639	+	23.8639i	−0.881432	+	0.881432i	0.112248	+	0.993680i	$0.464195\pi$
$734$	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	0.296215	−	0.955121i	$-0.404276\pi$
$739$	2.04383	+	0.547643i	0.0751836	+	0.0201454i	−0.221031	+	0.975267i	$0.570942\pi$
$740$	−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	−0.702053	−	0.712125i	$-0.747733\pi$
$743$	7.14174	−	26.6533i	0.262005	−	0.977816i	0.964058	−	0.265692i	$-0.0856003\pi$
$744$		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
$749$	28.0154	+	0.839621i	1.02366	+	0.0306791i
$750$		0			0
$751$	−6.52544	+	3.76747i	−0.238117	+	0.137477i	−0.614311	−	0.789064i	$-0.710566\pi$
$751$	−6.52544	+	3.76747i	−0.238117	+	0.137477i	0.376194	+	0.926541i	$0.377233\pi$
$752$	−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	−0.939297	−	0.343104i	$-0.888522\pi$
$757$	−21.0971	−	36.5412i	−0.766786	−	1.32811i	0.172512	−	0.985007i	$-0.444812\pi$
$758$	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	$-0.593176\pi$
$761$	−1.64757	+	0.441464i	−0.0597243	+	0.0160031i	0.228833	+	0.973466i	$0.426509\pi$
$762$		0			0
$763$	42.4936	−	10.0320i	1.53837	−	0.363184i
$764$	−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	$-0.395879\pi$
$769$	3.49612	+	0.936782i	0.126073	+	0.0337812i	−0.195231	+	0.980757i	$0.562546\pi$
$770$	14.3368	+	4.30578i	0.516662	+	0.155170i
$771$		0			0
$772$	−1.78114	−	1.78114i	−0.0641048	−	0.0641048i
$773$	6.91718	+	25.8153i	0.248794	+	0.928510i	0.971439	+	0.237291i	$0.0762595\pi$
$773$	6.91718	+	25.8153i	0.248794	+	0.928510i	−0.722645	+	0.691219i	$0.757074\pi$
$774$		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
$784$	−14.6676	+	22.2165i	−0.523843	+	0.793446i
$785$	13.7577	+	13.7577i	0.491035	+	0.491035i
$786$		0			0
$787$	−42.5173	+	11.3925i	−1.51558	+	0.406098i	−0.918284	−	0.395923i	$-0.870425\pi$
$787$	−42.5173	+	11.3925i	−1.51558	+	0.406098i	−0.597296	+	0.802021i	$0.703758\pi$
$788$	−1.22553	+	1.22553i	−0.0436577	+	0.0436577i
$789$		0			0
$790$	−18.6819	−	32.3580i	−0.664672	−	1.15124i
$791$	−0.807642	−	1.50100i	−0.0287164	−	0.0533693i
$792$		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	$-0.912483\pi$
$797$	−6.94770	+	12.0338i	−0.246100	+	0.426258i	0.716340	+	0.697751i	$0.245816\pi$
$798$		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	−0.931599	−	0.363488i	$-0.881586\pi$
$809$	−22.2022	−	38.4554i	−0.780589	−	1.35202i	0.151010	−	0.988532i	$-0.451747\pi$
$810$		0			0
$811$	−9.49597	+	9.49597i	−0.333449	+	0.333449i	−0.853895	−	0.520446i	$-0.825766\pi$
$811$	−9.49597	+	9.49597i	−0.333449	+	0.333449i	0.520446	+	0.853895i	$0.325766\pi$
$812$	−0.186869	−	0.115487i	−0.00655780	−	0.00405281i
$813$		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	0.194651	+	0.980873i	$0.437643\pi$
$821$	−13.3053	+	49.6560i	−0.464358	+	1.73301i	−0.659009	+	0.752135i	$0.729024\pi$
$822$		0			0
$823$	22.4979	+	12.9892i	0.784227	+	0.452774i	0.837926	−	0.545783i	$-0.183768\pi$
$823$	22.4979	+	12.9892i	0.784227	+	0.452774i	−0.0536991	+	0.998557i	$0.517101\pi$
$824$	−20.1466	+	20.1466i	−0.701839	+	0.701839i
$825$		0			0
$826$	18.1862	+	11.2393i	0.632780	+	0.391067i
$827$	1.05853	−	1.05853i	0.0368089	−	0.0368089i	−0.688463	−	0.725272i	$-0.741714\pi$
$827$	1.05853	−	1.05853i	0.0368089	−	0.0368089i	0.725272	+	0.688463i	$0.241714\pi$
$828$		0			0
$829$	−7.34482	−	12.7216i	−0.255096	−	0.441839i	0.709826	−	0.704378i	$-0.248774\pi$
$829$	−7.34482	−	12.7216i	−0.255096	−	0.441839i	−0.964922	+	0.262538i	$0.915440\pi$
$830$	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	$-0.691820\pi$
$839$	−18.7042	+	5.01177i	−0.645740	+	0.173025i	−0.0789379	+	0.996880i	$0.525153\pi$
$840$		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
$847$	−20.8773	+	11.2334i	−0.717351	+	0.385985i
$848$	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	$-0.116790\pi$
$853$	16.7852	+	16.7852i	0.574713	+	0.574713i	−0.358728	+	0.933442i	$0.616790\pi$
$854$	0.0716793	+	0.303619i	0.00245282	+	0.0103896i
$855$		0			0
$856$	29.5820	+	7.92647i	1.01109	+	0.270921i
$857$	51.1432			1.74702			0.873508	−	0.486809i	$-0.161839\pi$
$857$	51.1432			1.74702			0.873508	+	0.486809i	$0.161839\pi$
$858$		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	0.847900	−	0.530156i	$-0.177867\pi$
$863$	9.33430	+	9.33430i	0.317743	+	0.317743i	−0.530156	+	0.847900i	$0.677867\pi$
$864$		0			0
$865$	−14.9681	−	55.8619i	−0.508932	−	1.89936i
$866$	−8.03096	−	8.03096i	−0.272903	−	0.272903i
$867$		0			0
$868$	−0.0656573	+	0.218616i	−0.00222855	+	0.00742033i
$869$	−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
$875$	13.0376	−	3.07795i	0.440750	−	0.104054i
$876$		0			0
$877$	−37.6430	+	10.0864i	−1.27111	+	0.340594i	−0.830457	−	0.557083i	$-0.811921\pi$
$877$	−37.6430	+	10.0864i	−1.27111	+	0.340594i	−0.440655	+	0.897676i	$0.645254\pi$
$878$	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	$-0.00293878\pi$
$881$	14.6029	+	25.2929i	0.491983	+	0.852140i	−0.507974	+	0.861372i	$0.669605\pi$
$882$		0			0
$883$		−	2.58799i		−	0.0870929i	−0.999051	−	0.0435464i	$-0.986134\pi$
$883$		−	2.58799i		−	0.0870929i	0.999051	−	0.0435464i	$-0.0138656\pi$
$884$	−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	$-0.448338\pi$
$887$	32.6723	−	18.8634i	1.09703	−	0.633370i	0.935439	+	0.353488i	$0.115004\pi$
$888$		0			0
$889$	−1.29301	+	43.1435i	−0.0433662	+	1.44699i
$890$	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	−0.999966	−	0.00829638i	$-0.997359\pi$
$907$	−44.9567	+	25.9558i	−1.49276	+	0.861847i	−0.492798	+	0.870144i	$0.664026\pi$
$908$	0.253691	−	0.946788i	0.00841904	−	0.0314203i
$909$		0			0
$910$	−37.3870	+	5.53479i	−1.23937	+	0.183476i
$911$	−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
$917$	5.29529	+	3.27256i	0.174866	+	0.108070i
$918$		0			0
$919$	−1.62567	+	2.81574i	−0.0536259	+	0.0928828i	−0.891592	−	0.452839i	$-0.850411\pi$
$919$	−1.62567	+	2.81574i	−0.0536259	+	0.0928828i	0.837966	+	0.545722i	$0.183745\pi$
$920$	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	−0.869799	−	0.493405i	$-0.835752\pi$
$929$	−11.0712	−	41.3182i	−0.363234	−	1.35561i	0.506566	−	0.862201i	$-0.330915\pi$
$930$		0			0
$931$	32.2910	−	28.6358i	1.05829	−	0.938499i
$932$	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	$0.921529\pi$
$938$	−3.31431	+	1.78333i	−0.108216	+	0.0582278i
$939$		0			0
$940$	−0.730209	−	0.421586i	−0.0238168	−	0.0137506i
$941$	−8.04957	+	8.04957i	−0.262409	+	0.262409i	−0.826032	−	0.563623i	$-0.809407\pi$
$941$	−8.04957	+	8.04957i	−0.262409	+	0.262409i	0.563623	+	0.826032i	$0.309407\pi$
$942$		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	−0.283885	−	0.958858i	$-0.591623\pi$
$947$	−31.0554	−	8.32128i	−1.00917	−	0.270405i	−0.725281	+	0.688453i	$0.758290\pi$
$948$		0			0
$949$	8.42752	+	5.87091i	0.273569	+	0.190578i
$950$		−	27.5423i		−	0.893589i
$951$		0			0
$952$	30.7538	+	9.23632i	0.996737	+	0.299351i
$953$	−32.4604	−	18.7410i	−1.05150	−	0.607081i	−0.128428	−	0.991719i	$-0.540993\pi$
$953$	−32.4604	−	18.7410i	−1.05150	−	0.607081i	−0.923068	+	0.384638i	$0.874326\pi$
$954$		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
$959$	−26.3202	−	7.90479i	−0.849925	−	0.255259i
$960$		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	0.860459	−	0.509520i	$-0.170177\pi$
$967$	10.9130	+	10.9130i	0.350939	+	0.350939i	−0.509520	+	0.860459i	$0.670177\pi$
$968$	−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	$-0.342453\pi$
$971$	−1.54608	−	0.892628i	−0.0496160	−	0.0286458i	−0.524603	+	0.851347i	$0.675786\pi$
$972$		0			0
$973$	14.3450	−	7.71862i	0.459880	−	0.247447i
$974$		−	47.0455i		−	1.50743i
$975$		0			0
$976$			0.324815i			0.0103971i
$977$	0.587766	−	2.19357i	0.0188043	−	0.0701786i	−0.955886	−	0.293737i	$-0.905101\pi$
$977$	0.587766	−	2.19357i	0.0188043	−	0.0701786i	0.974690	+	0.223559i	$0.0717675\pi$
$978$		0			0
$979$	3.51662	−	6.09097i	0.112392	−	0.194668i
$980$	−1.25334	−	1.41333i	−0.0400366	−	0.0451471i
$981$		0			0
$982$	5.06202	+	18.8917i	0.161535	+	0.602858i
$983$	30.2896	+	30.2896i	0.966088	+	0.966088i	0.999444	−	0.0333560i	$-0.0106195\pi$
$983$	30.2896	+	30.2896i	0.966088	+	0.966088i	−0.0333560	+	0.999444i	$0.510620\pi$
$984$		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	−0.883415	−	0.468591i	$-0.844762\pi$
$991$	−26.6800	−	46.2112i	−0.847519	−	1.46795i	0.0358964	−	0.999356i	$-0.488571\pi$
$992$	−0.243818	+	0.422305i	−0.00774123	+	0.0134082i
$993$		0			0
$994$	9.00679	+	5.56632i	0.285678	+	0.176553i
$995$	9.44159	+	35.2365i	0.299319	+	1.11707i
$996$		0			0
$997$	−40.7247	−	23.5124i	−1.28976	−	0.744645i	−0.311152	−	0.950360i	$-0.600715\pi$
$997$	−40.7247	−	23.5124i	−1.28976	−	0.744645i	−0.978612	+	0.205715i	$0.934048\pi$
$998$	−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.622.6		32
3.2	odd	2		91.2.bc.a.76.3	yes	32
7.6	odd	2	inner	819.2.fm.g.622.5		32
13.6	odd	12	inner	819.2.fm.g.370.5		32
21.2	odd	6		637.2.x.b.570.5		32
21.5	even	6		637.2.x.b.570.6		32
21.11	odd	6		637.2.bb.b.362.4		32
21.17	even	6		637.2.bb.b.362.3		32
21.20	even	2		91.2.bc.a.76.4	yes	32
39.32	even	12		91.2.bc.a.6.4	yes	32
91.6	even	12	inner	819.2.fm.g.370.6		32
273.32	even	12		637.2.x.b.19.5		32
273.110	odd	12		637.2.bb.b.227.4		32
273.149	even	12		637.2.bb.b.227.3		32
273.188	odd	12		91.2.bc.a.6.3	✓	32
273.227	odd	12		637.2.x.b.19.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.6.3	✓	32	273.188	odd	12
91.2.bc.a.6.4	yes	32	39.32	even	12
91.2.bc.a.76.3	yes	32	3.2	odd	2
91.2.bc.a.76.4	yes	32	21.20	even	2
637.2.x.b.19.5		32	273.32	even	12
637.2.x.b.19.6		32	273.227	odd	12
637.2.x.b.570.5		32	21.2	odd	6
637.2.x.b.570.6		32	21.5	even	6
637.2.bb.b.227.3		32	273.149	even	12
637.2.bb.b.227.4		32	273.110	odd	12
637.2.bb.b.362.3		32	21.17	even	6
637.2.bb.b.362.4		32	21.11	odd	6
819.2.fm.g.370.5		32	13.6	odd	12	inner
819.2.fm.g.370.6		32	91.6	even	12	inner
819.2.fm.g.622.5		32	7.6	odd	2	inner
819.2.fm.g.622.6		32	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.357317 - 1.33353i) q^{2} +(0.0814361 + 0.0470171i) q^{4} +(2.02925 - 2.02925i) q^{5} +(1.39092 - 2.25063i) q^{7} +(2.04421 - 2.04421i) q^{8} +O(q^{10})\)	\(q+(0.357317 - 1.33353i) q^{2} +(0.0814361 + 0.0470171i) q^{4} +(2.02925 - 2.02925i) q^{5} +(1.39092 - 2.25063i) q^{7} +(2.04421 - 2.04421i) q^{8} +(-1.98097 - 3.43114i) q^{10} +(-1.37941 - 0.369611i) q^{11} +(3.54926 - 0.634621i) q^{13} +(-2.50427 - 2.65902i) q^{14} +(-1.90154 - 3.29357i) q^{16} +(-2.09909 + 3.63573i) q^{17} +(1.59577 + 5.95551i) q^{19} +(0.260663 - 0.0698445i) q^{20} +(-0.985770 + 1.70740i) q^{22} +(-6.77658 + 3.91246i) q^{23} -3.23569i q^{25} +(0.421928 - 4.95979i) q^{26} +(0.219089 - 0.117885i) q^{28} +(-0.441485 - 0.764674i) q^{29} +(-0.648762 + 0.648762i) q^{31} +(0.513380 - 0.137560i) q^{32} +(4.09830 + 4.09830i) q^{34} +(-1.74456 - 7.38961i) q^{35} +(-7.19341 - 1.92747i) q^{37} +8.51202 q^{38} -8.29643i q^{40} +(11.4714 + 3.07376i) q^{41} +(0.809734 + 0.467500i) q^{43} +(-0.0949554 - 0.0949554i) q^{44} +(2.79598 + 10.4347i) q^{46} +(-2.20935 - 2.20935i) q^{47} +(-3.13068 - 6.26090i) q^{49} +(-4.31487 - 1.15617i) q^{50} +(0.318876 + 0.115195i) q^{52} -2.52486 q^{53} +(-3.54919 + 2.04912i) q^{55} +(-1.75743 - 7.44411i) q^{56} +(-1.17746 + 0.315500i) q^{58} +(-5.65360 + 1.51488i) q^{59} +(-0.0739657 - 0.0427041i) q^{61} +(0.633327 + 1.09695i) q^{62} -8.33994i q^{64} +(5.91453 - 8.49013i) q^{65} +(0.266684 - 0.995278i) q^{67} +(-0.341884 + 0.197387i) q^{68} +(-10.4776 - 0.314014i) q^{70} +(-2.79996 + 0.750247i) q^{71} +(2.01428 + 2.01428i) q^{73} +(-5.14066 + 8.90388i) q^{74} +(-0.150057 + 0.560022i) q^{76} +(-2.75050 + 2.59043i) q^{77} +9.43068 q^{79} +(-10.5422 - 2.82477i) q^{80} +(8.19789 - 14.1992i) q^{82} +(-1.54040 + 1.54040i) q^{83} +(3.11823 + 11.6374i) q^{85} +(0.912755 - 0.912755i) q^{86} +(-3.57536 + 2.06424i) q^{88} +(-1.27469 + 4.75720i) q^{89} +(3.50844 - 8.87078i) q^{91} -0.735811 q^{92} +(-3.73567 + 2.15679i) q^{94} +(15.3234 + 8.84698i) q^{95} +(-2.37752 - 8.87303i) q^{97} +(-9.46771 + 1.93771i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8}+O(q^{10}) \) 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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