LMFDB - Embedded newform 819.2.fm.f.496.4

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 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			496.4
Character	$\chi$	$=$	819.496
Dual form			819.2.fm.f.748.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.604240 - 0.161906i) q^{2} +(-1.39316 - 0.804341i) q^{4} +(0.965431 + 0.965431i) q^{5} +(2.62802 + 0.305802i) q^{7} +(1.59624 + 1.59624i) q^{8} +O(q^{10})$	\(q+(-0.604240 - 0.161906i) q^{2} +(-1.39316 - 0.804341i) q^{4} +(0.965431 + 0.965431i) q^{5} +(2.62802 + 0.305802i) q^{7} +(1.59624 + 1.59624i) q^{8} +(-0.427043 - 0.739660i) q^{10} +(-1.26706 + 4.72873i) q^{11} +(-1.35196 - 3.34249i) q^{13} +(-1.53844 - 0.610269i) q^{14} +(0.902609 + 1.56336i) q^{16} +(-2.72530 + 4.72035i) q^{17} +(-4.47375 + 1.19874i) q^{19} +(-0.568463 - 2.12153i) q^{20} +(1.53121 - 2.65214i) q^{22} +(3.14262 - 1.81439i) q^{23} -3.13589i q^{25} +(0.275740 + 2.23855i) q^{26} +(-3.41528 - 2.53985i) q^{28} +(-1.00956 - 1.74861i) q^{29} +(5.91069 + 5.91069i) q^{31} +(-1.46081 - 5.45180i) q^{32} +(2.41098 - 2.41098i) q^{34} +(2.24194 + 2.83240i) q^{35} +(-2.84395 + 10.6138i) q^{37} +2.89730 q^{38} +3.08212i q^{40} +(-1.08400 + 4.04553i) q^{41} +(-0.669160 - 0.386339i) q^{43} +(5.56872 - 5.56872i) q^{44} +(-2.19266 + 0.587521i) q^{46} +(-5.65938 + 5.65938i) q^{47} +(6.81297 + 1.60731i) q^{49} +(-0.507717 + 1.89483i) q^{50} +(-0.805003 + 5.74405i) q^{52} +6.72661 q^{53} +(-5.78852 + 3.34200i) q^{55} +(3.70682 + 4.68309i) q^{56} +(0.326908 + 1.22004i) q^{58} +(3.87661 + 14.4677i) q^{59} +(-0.210912 - 0.121770i) q^{61} +(-2.61450 - 4.52844i) q^{62} -0.0797289i q^{64} +(1.92172 - 4.53216i) q^{65} +(5.55533 + 1.48855i) q^{67} +(7.59354 - 4.38413i) q^{68} +(-0.896088 - 2.07443i) q^{70} +(0.711167 + 2.65411i) q^{71} +(-2.17212 + 2.17212i) q^{73} +(3.43686 - 5.95281i) q^{74} +(7.19684 + 1.92839i) q^{76} +(-4.77591 + 12.0397i) q^{77} +8.38955 q^{79} +(-0.637914 + 2.38073i) q^{80} +(1.30999 - 2.26897i) q^{82} +(-11.2487 - 11.2487i) q^{83} +(-7.18826 + 1.92609i) q^{85} +(0.341782 + 0.341782i) q^{86} +(-9.57073 + 5.52567i) q^{88} +(3.25716 + 0.872754i) q^{89} +(-2.53083 - 9.19755i) q^{91} -5.83756 q^{92} +(4.33591 - 2.50334i) q^{94} +(-5.47640 - 3.16180i) q^{95} +(-9.46128 + 2.53514i) q^{97} +(-3.85643 - 2.07426i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.604240	−	0.161906i	−0.427262	−	0.114484i	0.0387787	−	0.999248i	$-0.487653\pi$
$2$	−0.604240	−	0.161906i	−0.427262	−	0.114484i	−0.466041	+	0.884763i	$0.654320\pi$
$3$		0			0
$3$		0			0
$4$	−1.39316	−	0.804341i	−0.696579	−	0.402170i
$5$	0.965431	+	0.965431i	0.431754	+	0.431754i	0.889225	−	0.457471i	$-0.151245\pi$
$5$	0.965431	+	0.965431i	0.431754	+	0.431754i	−0.457471	+	0.889225i	$0.651245\pi$
$6$		0			0
$7$	2.62802	+	0.305802i	0.993298	+	0.115582i
$7$	2.62802	+	0.305802i	0.993298	+	0.115582i
$8$	1.59624	+	1.59624i	0.564357	+	0.564357i
$9$		0			0
$10$	−0.427043	−	0.739660i	−0.135043	−	0.233901i
$11$	−1.26706	+	4.72873i	−0.382033	+	1.42577i	0.460759	+	0.887525i	$0.347577\pi$
$11$	−1.26706	+	4.72873i	−0.382033	+	1.42577i	−0.842791	+	0.538240i	$0.819089\pi$
$12$		0			0
$13$	−1.35196	−	3.34249i	−0.374966	−	0.927039i
$13$	−1.35196	−	3.34249i	−0.374966	−	0.927039i
$14$	−1.53844	−	0.610269i	−0.411166	−	0.163101i
$15$		0			0
$16$	0.902609	+	1.56336i	0.225652	+	0.390841i
$17$	−2.72530	+	4.72035i	−0.660981	+	1.14485i	0.319377	+	0.947628i	$0.396526\pi$
$17$	−2.72530	+	4.72035i	−0.660981	+	1.14485i	−0.980358	+	0.197225i	$0.936807\pi$
$18$		0			0
$19$	−4.47375	+	1.19874i	−1.02635	+	0.275010i	−0.732446	−	0.680825i	$-0.761621\pi$
$19$	−4.47375	+	1.19874i	−1.02635	+	0.275010i	−0.293904	+	0.955835i	$0.594955\pi$
$20$	−0.568463	−	2.12153i	−0.127112	−	0.474389i
$21$		0			0
$22$	1.53121	−	2.65214i	0.326456	−	0.565439i
$23$	3.14262	−	1.81439i	0.655282	−	0.378327i	−0.135195	−	0.990819i	$-0.543166\pi$
$23$	3.14262	−	1.81439i	0.655282	−	0.378327i	0.790477	+	0.612492i	$0.209833\pi$
$24$		0			0
$25$		−	3.13589i		−	0.627177i
$26$	0.275740	+	2.23855i	0.0540771	+	0.439016i
$27$		0			0
$28$	−3.41528	−	2.53985i	−0.645427	−	0.479987i
$29$	−1.00956	−	1.74861i	−0.187471	−	0.324710i	0.756935	−	0.653490i	$-0.226696\pi$
$29$	−1.00956	−	1.74861i	−0.187471	−	0.324710i	−0.944406	+	0.328780i	$0.893362\pi$
$30$		0			0
$31$	5.91069	+	5.91069i	1.06159	+	1.06159i	0.997974	+	0.0636160i	$0.0202633\pi$
$31$	5.91069	+	5.91069i	1.06159	+	1.06159i	0.0636160	+	0.997974i	$0.479737\pi$
$32$	−1.46081	−	5.45180i	−0.258236	−	0.963751i
$33$		0			0
$34$	2.41098	−	2.41098i	0.413480	−	0.413480i
$35$	2.24194	+	2.83240i	0.378957	+	0.478763i
$36$		0			0
$37$	−2.84395	+	10.6138i	−0.467543	+	1.74489i	0.180774	+	0.983525i	$0.442140\pi$
$37$	−2.84395	+	10.6138i	−0.467543	+	1.74489i	−0.648317	+	0.761370i	$0.724527\pi$
$38$	2.89730			0.470004
$39$		0			0
$40$			3.08212i			0.487327i
$41$	−1.08400	+	4.04553i	−0.169292	+	0.631806i	0.828162	+	0.560489i	$0.189387\pi$
$41$	−1.08400	+	4.04553i	−0.169292	+	0.631806i	−0.997454	+	0.0713169i	$0.977280\pi$
$42$		0			0
$43$	−0.669160	−	0.386339i	−0.102046	−	0.0589162i	0.448109	−	0.893979i	$-0.352098\pi$
$43$	−0.669160	−	0.386339i	−0.102046	−	0.0589162i	−0.550154	+	0.835063i	$0.685431\pi$
$44$	5.56872	−	5.56872i	0.839517	−	0.839517i
$45$		0			0
$46$	−2.19266	+	0.587521i	−0.323290	+	0.0866252i
$47$	−5.65938	+	5.65938i	−0.825506	+	0.825506i	−0.986891	−	0.161386i	$-0.948404\pi$
$47$	−5.65938	+	5.65938i	−0.825506	+	0.825506i	0.161386	+	0.986891i	$0.448404\pi$
$48$		0			0
$49$	6.81297	+	1.60731i	0.973281	+	0.229615i
$50$	−0.507717	+	1.89483i	−0.0718021	+	0.267969i
$51$		0			0
$52$	−0.805003	+	5.74405i	−0.111634	+	0.796556i
$53$	6.72661			0.923971			0.461986	−	0.886887i	$-0.347137\pi$
$53$	6.72661			0.923971			0.461986	+	0.886887i	$0.347137\pi$
$54$		0			0
$55$	−5.78852	+	3.34200i	−0.780524	+	0.450636i
$56$	3.70682	+	4.68309i	0.495345	+	0.625804i
$57$		0			0
$58$	0.326908	+	1.22004i	0.0429251	+	0.160199i
$59$	3.87661	+	14.4677i	0.504692	+	1.88354i	0.467022	+	0.884246i	$0.345327\pi$
$59$	3.87661	+	14.4677i	0.504692	+	1.88354i	0.0376705	+	0.999290i	$0.488006\pi$
$60$		0			0
$61$	−0.210912	−	0.121770i	−0.0270046	−	0.0155911i	0.486437	−	0.873716i	$-0.338296\pi$
$61$	−0.210912	−	0.121770i	−0.0270046	−	0.0155911i	−0.513442	+	0.858125i	$0.671630\pi$
$62$	−2.61450	−	4.52844i	−0.332042	−	0.575113i
$63$		0			0
$64$		−	0.0797289i		−	0.00996611i
$65$	1.92172	−	4.53216i	0.238360	−	0.562146i
$66$		0			0
$67$	5.55533	+	1.48855i	0.678691	+	0.181855i	0.581667	−	0.813427i	$-0.302401\pi$
$67$	5.55533	+	1.48855i	0.678691	+	0.181855i	0.0970245	+	0.995282i	$0.469067\pi$
$68$	7.59354	−	4.38413i	0.920852	−	0.531654i
$69$		0			0
$70$	−0.896088	−	2.07443i	−0.107103	−	0.247942i
$71$	0.711167	+	2.65411i	0.0844000	+	0.314985i	0.995200	−	0.0978630i	$-0.0312007\pi$
$71$	0.711167	+	2.65411i	0.0844000	+	0.314985i	−0.910800	+	0.412848i	$0.864534\pi$
$72$		0			0
$73$	−2.17212	+	2.17212i	−0.254228	+	0.254228i	−0.822701	−	0.568474i	$-0.807534\pi$
$73$	−2.17212	+	2.17212i	−0.254228	+	0.254228i	0.568474	+	0.822701i	$0.307534\pi$
$74$	3.43686	−	5.95281i	0.399527	−	0.692001i
$75$		0			0
$76$	7.19684	+	1.92839i	0.825535	+	0.221201i
$77$	−4.77591	+	12.0397i	−0.544266	+	1.37205i
$78$		0			0
$79$	8.38955			0.943898			0.471949	−	0.881626i	$-0.343551\pi$
$79$	8.38955			0.943898			0.471949	+	0.881626i	$0.343551\pi$
$80$	−0.637914	+	2.38073i	−0.0713209	+	0.266173i
$81$		0			0
$82$	1.30999	−	2.26897i	0.144664	−	0.250565i
$83$	−11.2487	−	11.2487i	−1.23470	−	1.23470i	−0.962138	−	0.272563i	$-0.912129\pi$
$83$	−11.2487	−	11.2487i	−1.23470	−	1.23470i	−0.272563	−	0.962138i	$-0.587871\pi$
$84$		0			0
$85$	−7.18826	+	1.92609i	−0.779676	+	0.208914i
$86$	0.341782	+	0.341782i	0.0368553	+	0.0368553i
$87$		0			0
$88$	−9.57073	+	5.52567i	−1.02024	+	0.589038i
$89$	3.25716	+	0.872754i	0.345259	+	0.0925118i	0.427281	−	0.904119i	$-0.359471\pi$
$89$	3.25716	+	0.872754i	0.345259	+	0.0925118i	−0.0820228	+	0.996630i	$0.526138\pi$
$90$		0			0
$91$	−2.53083	−	9.19755i	−0.265304	−	0.964165i
$92$	−5.83756			−0.608608
$93$		0			0
$94$	4.33591	−	2.50334i	0.447215	−	0.258200i
$95$	−5.47640	−	3.16180i	−0.561867	−	0.324394i
$96$		0			0
$97$	−9.46128	+	2.53514i	−0.960648	+	0.257405i	−0.704874	−	0.709332i	$-0.748997\pi$
$97$	−9.46128	+	2.53514i	−0.960648	+	0.257405i	−0.255773	+	0.966737i	$0.582330\pi$
$98$	−3.85643	−	2.07426i	−0.389559	−	0.209532i
$99$		0			0
$100$	−2.52232	+	4.36879i	−0.252232	+	0.436879i
$101$	−1.30615	−	2.26231i	−0.129966	−	0.225108i	0.793697	−	0.608313i	$-0.208154\pi$
$101$	−1.30615	−	2.26231i	−0.129966	−	0.225108i	−0.923663	+	0.383205i	$0.874820\pi$
$102$		0			0
$103$	16.7503			1.65046			0.825230	−	0.564797i	$-0.191046\pi$
$103$	16.7503			1.65046			0.825230	+	0.564797i	$0.191046\pi$
$104$	3.17736	−	7.49347i	0.311566	−	0.734795i
$105$		0			0
$106$	−4.06449	−	1.08908i	−0.394778	−	0.105780i
$107$	−5.79246	−	10.0328i	−0.559978	−	0.969910i	−0.997498	−	0.0707014i	$-0.977476\pi$
$107$	−5.79246	−	10.0328i	−0.559978	−	0.969910i	0.437520	−	0.899209i	$-0.355857\pi$
$108$		0			0
$109$	3.99577	−	3.99577i	0.382725	−	0.382725i	−0.489358	−	0.872083i	$-0.662769\pi$
$109$	3.99577	−	3.99577i	0.382725	−	0.382725i	0.872083	+	0.489358i	$0.162769\pi$
$110$	4.03874	−	1.08218i	0.385079	−	0.103182i
$111$		0			0
$112$	1.89399	+	4.38457i	0.178965	+	0.414303i
$113$	−1.65445	+	2.86558i	−0.155637	+	0.269571i	−0.933291	−	0.359121i	$-0.883076\pi$
$113$	−1.65445	+	2.86558i	−0.155637	+	0.269571i	0.777654	+	0.628693i	$0.216410\pi$
$114$		0			0
$115$	4.78566	+	1.28231i	0.446265	+	0.119576i
$116$			3.24813i			0.301581i
$117$		0			0
$118$		−	9.36961i		−	0.862543i
$119$	−8.60562	+	11.5718i	−0.788876	+	1.06078i
$120$		0			0
$121$	−11.2292	−	6.48316i	−1.02083	−	0.589378i
$122$	0.107726	+	0.107726i	0.00975309	+	0.00975309i
$123$		0			0
$124$	−3.48032	−	12.9887i	−0.312542	−	1.16642i
$125$	7.85464	−	7.85464i	0.702540	−	0.702540i
$126$		0			0
$127$	15.4911	−	8.94379i	1.37461	−	0.793633i	0.383108	−	0.923704i	$-0.374854\pi$
$127$	15.4911	−	8.94379i	1.37461	−	0.793633i	0.991505	+	0.130071i	$0.0415205\pi$
$128$	−2.93452	+	10.9518i	−0.259377	+	0.968009i
$129$		0			0
$130$	−1.89496	+	2.42738i	−0.166199	+	0.212895i
$131$		−	15.3940i		−	1.34498i	−0.740107	−	0.672489i	$-0.765225\pi$
$131$		−	15.3940i		−	1.34498i	0.740107	−	0.672489i	$-0.234775\pi$
$132$		0			0
$133$	−12.1237	+	1.78223i	−1.05126	+	0.154539i
$134$	−3.11574	−	1.79888i	−0.269159	−	0.155399i
$135$		0			0
$136$	−11.8851	+	3.18459i	−1.01914	+	0.273077i
$137$	2.08965	−	0.559921i	0.178531	−	0.0478373i	−0.168446	−	0.985711i	$-0.553875\pi$
$137$	2.08965	−	0.559921i	0.178531	−	0.0478373i	0.346977	+	0.937874i	$0.387208\pi$
$138$		0			0
$139$	−1.11782	−	0.645374i	−0.0948124	−	0.0547399i	0.451844	−	0.892097i	$-0.350766\pi$
$139$	−1.11782	−	0.645374i	−0.0948124	−	0.0547399i	−0.546657	+	0.837357i	$0.684100\pi$
$140$	−0.845163	−	5.74927i	−0.0714293	−	0.485902i
$141$		0			0
$142$		−	1.71886i		−	0.144244i
$143$	17.5187	−	2.15792i	1.46499	−	0.180454i
$144$		0			0
$145$	0.713503	−	2.66283i	0.0592532	−	0.221136i
$146$	1.66416	−	0.960803i	0.137727	−	0.0795166i
$147$		0			0
$148$	12.4992	−	12.4992i	1.02743	−	1.02743i
$149$	0.326352	+	1.21796i	0.0267358	+	0.0997793i	0.978004	−	0.208584i	$-0.0668854\pi$
$149$	0.326352	+	1.21796i	0.0267358	+	0.0997793i	−0.951269	+	0.308363i	$0.900219\pi$
$150$		0			0
$151$	5.35713	+	5.35713i	0.435957	+	0.435957i	0.890649	−	0.454692i	$-0.150251\pi$
$151$	5.35713	+	5.35713i	0.435957	+	0.435957i	−0.454692	+	0.890649i	$0.650251\pi$
$152$	−9.05468	−	5.22772i	−0.734431	−	0.424024i
$153$		0			0
$154$	4.83509	−	6.50163i	0.389623	−	0.523916i
$155$			11.4127i			0.916692i
$156$		0			0
$157$			7.45263i			0.594785i	0.954755	+	0.297392i	$0.0961169\pi$
$157$			7.45263i			0.594785i	−0.954755	+	0.297392i	$0.903883\pi$
$158$	−5.06930	−	1.35831i	−0.403292	−	0.108062i
$159$		0			0
$160$	3.85303	−	6.67364i	0.304609	−	0.527598i
$161$	8.81372	−	3.80724i	0.694618	−	0.300053i
$162$		0			0
$163$	−11.3293	+	3.03568i	−0.887379	+	0.237773i	−0.673588	−	0.739107i	$-0.735248\pi$
$163$	−11.3293	+	3.03568i	−0.887379	+	0.237773i	−0.213791	+	0.976879i	$0.568581\pi$
$164$	4.76417	−	4.76417i	0.372019	−	0.372019i
$165$		0			0
$166$	4.97567	+	8.61811i	0.386187	+	0.668895i
$167$	−6.94320	−	1.86042i	−0.537281	−	0.143964i	−0.0200325	−	0.999799i	$-0.506377\pi$
$167$	−6.94320	−	1.86042i	−0.537281	−	0.143964i	−0.517248	+	0.855835i	$0.673044\pi$
$168$		0			0
$169$	−9.34441	+	9.03780i	−0.718801	+	0.695216i
$170$	4.65527			0.357043
$171$		0			0
$172$	0.621497	+	1.07646i	0.0473887	+	0.0820796i
$173$	−7.63293	+	13.2206i	−0.580321	+	1.00515i	0.415120	+	0.909767i	$0.363740\pi$
$173$	−7.63293	+	13.2206i	−0.580321	+	1.00515i	−0.995441	+	0.0953789i	$0.969594\pi$
$174$		0			0
$175$	0.958961	−	8.24117i	0.0724906	−	0.622974i
$176$	−8.53638	+	2.28732i	−0.643454	+	0.172413i
$177$		0			0
$178$	−1.82680	−	1.05471i	−0.136925	−	0.0790535i
$179$	−19.5943	+	11.3128i	−1.46455	+	0.845557i	−0.999216	−	0.0395805i	$-0.987398\pi$
$179$	−19.5943	+	11.3128i	−1.46455	+	0.845557i	−0.465330	+	0.885137i	$0.654065\pi$
$180$		0			0
$181$	1.46318			0.108758			0.0543788	−	0.998520i	$-0.482682\pi$
$181$	1.46318			0.108758			0.0543788	+	0.998520i	$0.482682\pi$
$182$	0.0400969	+	5.96728i	0.00297218	+	0.442324i
$183$		0			0
$184$	7.91260	+	2.12018i	0.583325	+	0.156301i
$185$	−12.9925	+	7.50123i	−0.955229	+	0.551502i
$186$		0			0
$187$	−18.8682	−	18.8682i	−1.37978	−	1.37978i
$188$	12.4365	−	3.33235i	0.907024	−	0.243036i
$189$		0			0
$190$	2.79715	+	2.79715i	0.202926	+	0.202926i
$191$	2.07125	−	3.58751i	0.149870	−	0.259583i	−0.781309	−	0.624144i	$-0.785448\pi$
$191$	2.07125	−	3.58751i	0.149870	−	0.259583i	0.931179	+	0.364561i	$0.118781\pi$
$192$		0			0
$193$	0.316568	−	1.18145i	0.0227871	−	0.0850425i	−0.953596	−	0.301089i	$-0.902650\pi$
$193$	0.316568	−	1.18145i	0.0227871	−	0.0850425i	0.976383	+	0.216047i	$0.0693164\pi$
$194$	6.12733			0.439917
$195$		0			0
$196$	−8.19873	−	7.71918i	−0.585623	−	0.551370i
$197$	11.1850	+	2.99702i	0.796901	+	0.213529i	0.634223	−	0.773150i	$-0.281320\pi$
$197$	11.1850	+	2.99702i	0.796901	+	0.213529i	0.162678	+	0.986679i	$0.447987\pi$
$198$		0			0
$199$	−1.08128	+	1.87283i	−0.0766498	+	0.132761i	−0.901803	−	0.432148i	$-0.857756\pi$
$199$	−1.08128	+	1.87283i	−0.0766498	+	0.132761i	0.825153	+	0.564910i	$0.191089\pi$
$200$	5.00563	−	5.00563i	0.353952	−	0.353952i
$201$		0			0
$202$	0.422944	+	1.57845i	0.0297583	+	0.111059i
$203$	−2.11842	−	4.90412i	−0.148684	−	0.344202i
$204$		0			0
$205$	−4.95221	+	2.85916i	−0.345877	+	0.199692i
$206$	−10.1212	−	2.71197i	−0.705179	−	0.188952i
$207$		0			0
$208$	4.00523	−	5.13056i	0.277713	−	0.355740i
$209$		−	22.6741i		−	1.56840i
$210$		0			0
$211$	−9.04131	−	15.6600i	−0.622429	−	1.07808i	−0.989032	−	0.147701i	$-0.952813\pi$
$211$	−9.04131	−	15.6600i	−0.622429	−	1.07808i	0.366603	−	0.930378i	$-0.380521\pi$
$212$	−9.37124	−	5.41049i	−0.643619	−	0.371594i
$213$		0			0
$214$	1.87566	+	7.00006i	0.128218	+	0.478515i
$215$	−0.273043	−	1.01901i	−0.0186214	−	0.0694960i
$216$		0			0
$217$	13.7259	+	17.3409i	0.931774	+	1.17718i
$218$	−3.06134	+	1.76746i	−0.207340	+	0.119708i
$219$		0			0
$220$	10.7524			0.724929
$221$	19.4622	+	2.72754i	1.30917	+	0.183474i
$222$		0			0
$223$	5.56628	−	20.7736i	0.372746	−	1.39111i	−0.483865	−	0.875142i	$-0.660768\pi$
$223$	5.56628	−	20.7736i	0.372746	−	1.39111i	0.856611	−	0.515963i	$-0.172566\pi$
$224$	−2.17185	−	14.7742i	−0.145113	−	0.987140i
$225$		0			0
$226$	1.46363	−	1.46363i	0.0973595	−	0.0973595i
$227$	2.73398	−	0.732566i	0.181460	−	0.0486221i	−0.166945	−	0.985966i	$-0.553390\pi$
$227$	2.73398	−	0.732566i	0.181460	−	0.0486221i	0.348405	+	0.937344i	$0.386723\pi$
$228$		0			0
$229$	0.121782	−	0.121782i	0.00804759	−	0.00804759i	−0.703072	−	0.711119i	$-0.748189\pi$
$229$	0.121782	−	0.121782i	0.00804759	−	0.00804759i	0.711119	+	0.703072i	$0.248189\pi$
$230$	−2.68407	−	1.54965i	−0.176982	−	0.102181i
$231$		0			0
$232$	1.17971	−	4.40272i	0.0774514	−	0.289053i
$233$		−	8.72869i		−	0.571835i	−0.958254	−	0.285918i	$-0.907702\pi$
$233$		−	8.72869i		−	0.571835i	0.958254	−	0.285918i	$-0.0922984\pi$
$234$		0			0
$235$	−10.9275			−0.712830
$236$	6.23623	−	23.2739i	0.405944	−	1.51500i
$237$		0			0
$238$	7.07339	−	5.59882i	0.458500	−	0.362918i
$239$	15.9007	−	15.9007i	1.02853	−	1.02853i	0.0289485	−	0.999581i	$-0.490784\pi$
$239$	15.9007	−	15.9007i	1.02853	−	1.02853i	0.999581	−	0.0289485i	$-0.00921587\pi$
$240$		0			0
$241$	−2.48430	−	9.27155i	−0.160028	−	0.597233i	−0.998622	−	0.0524761i	$-0.983289\pi$
$241$	−2.48430	−	9.27155i	−0.160028	−	0.597233i	0.838594	−	0.544757i	$-0.183378\pi$
$242$	5.73545	+	5.73545i	0.368689	+	0.368689i
$243$		0			0
$244$	0.195890	+	0.339291i	0.0125406	+	0.0217209i
$245$	5.02571	+	8.12920i	0.321081	+	0.519355i
$246$		0			0
$247$	10.0551	+	13.3328i	0.639791	+	0.848347i
$248$			18.8698i			1.19823i
$249$		0			0
$250$	−6.01779	+	3.47437i	−0.380599	+	0.219739i
$251$	2.87929	−	4.98708i	0.181739	−	0.314782i	−0.760734	−	0.649064i	$-0.775161\pi$
$251$	2.87929	−	4.98708i	0.181739	−	0.314782i	0.942473	+	0.334282i	$0.108494\pi$
$252$		0			0
$253$	4.59789	+	17.1596i	0.289067	+	1.07881i
$254$	−10.8084	+	2.89610i	−0.678178	+	0.181717i
$255$		0			0
$256$	3.46658	−	6.00429i	0.216661	−	0.375268i
$257$	−11.1749	−	19.3555i	−0.697071	−	1.20736i	−0.969477	−	0.245181i	$-0.921153\pi$
$257$	−11.1749	−	19.3555i	−0.697071	−	1.20736i	0.272406	−	0.962182i	$-0.412181\pi$
$258$		0			0
$259$	−10.7197	+	27.0235i	−0.666089	+	1.67916i
$260$	−6.32266	+	4.76831i	−0.392115	+	0.295718i
$261$		0			0
$262$	−2.49237	+	9.30166i	−0.153979	+	0.574658i
$263$	−8.93301	−	15.4724i	−0.550833	−	0.954071i	−0.998215	−	0.0597277i	$-0.980977\pi$
$263$	−8.93301	−	15.4724i	−0.550833	−	0.954071i	0.447382	−	0.894343i	$-0.352357\pi$
$264$		0			0
$265$	6.49408	+	6.49408i	0.398928	+	0.398928i
$266$	7.61417	+	0.886001i	0.466854	+	0.0543242i
$267$		0			0
$268$	−6.54216	−	6.54216i	−0.399626	−	0.399626i
$269$	−7.06977	−	4.08173i	−0.431051	−	0.248868i	0.268743	−	0.963212i	$-0.413392\pi$
$269$	−7.06977	−	4.08173i	−0.431051	−	0.248868i	−0.699794	+	0.714344i	$0.746725\pi$
$270$		0			0
$271$	−17.9820	−	4.81826i	−1.09233	−	0.292688i	−0.332691	−	0.943036i	$-0.607956\pi$
$271$	−17.9820	−	4.81826i	−1.09233	−	0.292688i	−0.759637	+	0.650348i	$0.774623\pi$
$272$	−9.83950			−0.596607
$273$		0			0
$274$	−1.35331			−0.0817562
$275$	14.8288	+	3.97335i	0.894208	+	0.239602i
$276$		0			0
$277$	−4.63889	−	2.67826i	−0.278724	−	0.160921i	0.354122	−	0.935199i	$-0.384780\pi$
$277$	−4.63889	−	2.67826i	−0.278724	−	0.160921i	−0.632846	+	0.774278i	$0.718113\pi$
$278$	0.570942	+	0.570942i	0.0342428	+	0.0342428i
$279$		0			0
$280$	−0.942520	+	8.09988i	−0.0563264	+	0.484061i
$281$	11.1684	+	11.1684i	0.666249	+	0.666249i	0.956846	−	0.290597i	$-0.0938539\pi$
$281$	11.1684	+	11.1684i	0.666249	+	0.666249i	−0.290597	+	0.956846i	$0.593854\pi$
$282$		0			0
$283$	10.7122	+	18.5541i	0.636775	+	1.10293i	0.986136	+	0.165938i	$0.0530653\pi$
$283$	10.7122	+	18.5541i	0.636775	+	1.10293i	−0.349361	+	0.936988i	$0.613601\pi$
$284$	1.14404	−	4.26962i	0.0678863	−	0.253355i
$285$		0			0
$286$	−10.9349	−	1.53248i	−0.646593	−	0.0906172i
$287$	−4.08590	+	10.3002i	−0.241183	+	0.608004i
$288$		0			0
$289$	−6.35448	−	11.0063i	−0.373793	−	0.647428i
$290$	−0.862254	+	1.49347i	−0.0506333	+	0.0876994i
$291$		0			0
$292$	4.77324	−	1.27898i	0.279332	−	0.0748469i
$293$	−1.33426	−	4.97953i	−0.0779484	−	0.290907i	0.915937	−	0.401321i	$-0.131449\pi$
$293$	−1.33426	−	4.97953i	−0.0779484	−	0.290907i	−0.993886	+	0.110414i	$0.964782\pi$
$294$		0			0
$295$	−10.2250	+	17.7102i	−0.595321	+	1.03113i
$296$	−21.4818	+	12.4025i	−1.24860	+	0.720882i
$297$		0			0
$298$		−	0.788779i		−	0.0456927i
$299$	−10.3133	−	8.05119i	−0.596433	−	0.465612i
$300$		0			0
$301$	−1.64042	−	1.21994i	−0.0945523	−	0.0703160i
$302$	−2.36964	−	4.10434i	−0.136357	−	0.236178i
$303$		0			0
$304$	−5.91212	−	5.91212i	−0.339083	−	0.339083i
$305$	−0.0860606	−	0.321182i	−0.00492781	−	0.0183908i
$306$		0			0
$307$	17.9644	−	17.9644i	1.02528	−	1.02528i	0.0256108	−	0.999672i	$-0.491847\pi$
$307$	17.9644	−	17.9644i	1.02528	−	1.02528i	0.999672	−	0.0256108i	$-0.00815305\pi$
$308$	16.3376	−	12.9318i	0.930924	−	0.736857i
$309$		0			0
$310$	1.84778	−	6.89602i	0.104947	−	0.391667i
$311$	7.22402			0.409637			0.204818	−	0.978800i	$-0.434340\pi$
$311$	7.22402			0.409637			0.204818	+	0.978800i	$0.434340\pi$
$312$		0			0
$313$			20.9613i			1.18480i	0.805643	+	0.592401i	$0.201820\pi$
$313$			20.9613i			1.18480i	−0.805643	+	0.592401i	$0.798180\pi$
$314$	1.20662	−	4.50318i	0.0680936	−	0.254129i
$315$		0			0
$316$	−11.6880	−	6.74806i	−0.657500	−	0.379608i
$317$	−0.207227	+	0.207227i	−0.0116390	+	0.0116390i	−0.712902	−	0.701263i	$-0.752620\pi$
$317$	−0.207227	+	0.207227i	−0.0116390	+	0.0116390i	0.701263	+	0.712902i	$0.252620\pi$
$318$		0			0
$319$	9.54790	−	2.55835i	0.534580	−	0.143240i
$320$	0.0769727	−	0.0769727i	0.00430291	−	0.00430291i
$321$		0			0
$322$	−5.94201	+	0.873497i	−0.331135	+	0.0486781i
$323$	6.53384	−	24.3846i	0.363552	−	1.35680i
$324$		0			0
$325$	−10.4817	+	4.23959i	−0.581417	+	0.235170i
$326$	7.33711			0.406365
$327$		0			0
$328$	−8.18797	+	4.72733i	−0.452105	+	0.261023i
$329$	−16.6036	+	13.1423i	−0.915387	+	0.724559i
$330$		0			0
$331$	−3.35420	−	12.5180i	−0.184363	−	0.688054i	−0.994766	−	0.102180i	$-0.967418\pi$
$331$	−3.35420	−	12.5180i	−0.184363	−	0.688054i	0.810403	−	0.585873i	$-0.199248\pi$
$332$	6.62342	+	24.7189i	0.363507	+	1.35663i
$333$		0			0
$334$	3.89414	+	2.24828i	0.213078	+	0.123021i
$335$	3.92620	+	6.80037i	0.214511	+	0.371544i
$336$		0			0
$337$			25.0887i			1.36667i	0.730105	+	0.683335i	$0.239471\pi$
$337$			25.0887i			1.36667i	−0.730105	+	0.683335i	$0.760529\pi$
$338$	7.10954	−	3.94809i	0.386708	−	0.214748i
$339$		0			0
$340$	11.5636	+	3.09846i	0.627125	+	0.168038i
$341$	−35.4392	+	20.4608i	−1.91914	+	1.10802i
$342$		0			0
$343$	17.4131	+	6.30746i	0.940219	+	0.340571i
$344$	−0.451449	−	1.68483i	−0.0243405	−	0.0908401i
$345$		0			0
$346$	6.75261	−	6.75261i	0.363023	−	0.363023i
$347$	−6.71302	+	11.6273i	−0.360374	+	0.624185i	−0.988022	−	0.154311i	$-0.950684\pi$
$347$	−6.71302	+	11.6273i	−0.360374	+	0.624185i	0.627649	+	0.778497i	$0.284017\pi$
$348$		0			0
$349$	−5.30405	−	1.42122i	−0.283919	−	0.0760760i	0.114049	−	0.993475i	$-0.463618\pi$
$349$	−5.30405	−	1.42122i	−0.283919	−	0.0760760i	−0.397968	+	0.917399i	$0.630285\pi$
$350$	−1.91373	+	4.82438i	−0.102293	+	0.257874i
$351$		0			0
$352$	27.6310			1.47274
$353$	0.756952	−	2.82498i	0.0402885	−	0.150359i	−0.942851	−	0.333213i	$-0.891867\pi$
$353$	0.756952	−	2.82498i	0.0402885	−	0.150359i	0.983140	+	0.182855i	$0.0585338\pi$
$354$		0			0
$355$	−1.87578	+	3.24894i	−0.0995560	+	0.172436i
$356$	−3.83575	−	3.83575i	−0.203295	−	0.203295i
$357$		0			0
$358$	13.6713	−	3.66320i	0.722548	−	0.193606i
$359$	19.7266	+	19.7266i	1.04113	+	1.04113i	0.999117	+	0.0420147i	$0.0133776\pi$
$359$	19.7266	+	19.7266i	1.04113	+	1.04113i	0.0420147	+	0.999117i	$0.486622\pi$
$360$		0			0
$361$	2.12302	−	1.22573i	0.111738	−	0.0645120i
$362$	−0.884114	−	0.236898i	−0.0464680	−	0.0124511i
$363$		0			0
$364$	−3.87211	+	14.8493i	−0.202954	+	0.778315i
$365$	−4.19407			−0.219527
$366$		0			0
$367$	14.4392	−	8.33648i	0.753720	−	0.435161i	−0.0733163	−	0.997309i	$-0.523358\pi$
$367$	14.4392	−	8.33648i	0.753720	−	0.435161i	0.827037	+	0.562148i	$0.190025\pi$
$368$	5.67312	+	3.27538i	0.295732	+	0.170741i
$369$		0			0
$370$	9.06508	−	2.42898i	0.471271	−	0.126277i
$371$	17.6777	+	2.05701i	0.917779	+	0.106795i
$372$		0			0
$373$	17.1121	−	29.6390i	0.886030	−	1.53465i	0.0415014	−	0.999138i	$-0.486786\pi$
$373$	17.1121	−	29.6390i	0.886030	−	1.53465i	0.844529	−	0.535511i	$-0.179881\pi$
$374$	8.34603	+	14.4557i	0.431563	+	0.747489i
$375$		0			0
$376$	−18.0675			−0.931760
$377$	−4.47983	+	5.73850i	−0.230723	+	0.295548i
$378$		0			0
$379$	−11.6824	−	3.13028i	−0.600082	−	0.160792i	−0.0540253	−	0.998540i	$-0.517205\pi$
$379$	−11.6824	−	3.13028i	−0.600082	−	0.160792i	−0.546057	+	0.837748i	$0.683872\pi$
$380$	5.08633	+	8.80978i	0.260923	+	0.451932i
$381$		0			0
$382$	−1.83237	+	1.83237i	−0.0937521	+	0.0937521i
$383$	32.0791	−	8.59556i	1.63916	−	0.439213i	0.682614	−	0.730780i	$-0.260843\pi$
$383$	32.0791	−	8.59556i	1.63916	−	0.439213i	0.956550	+	0.291567i	$0.0941766\pi$
$384$		0			0
$385$	−16.2343	+	7.01271i	−0.827378	+	0.357401i
$386$	−0.382566	+	0.662623i	−0.0194721	+	0.0337266i
$387$		0			0
$388$	15.2202	+	4.07824i	0.772688	+	0.207041i
$389$			25.6927i			1.30267i	0.758789	+	0.651337i	$0.225791\pi$
$389$			25.6927i			1.30267i	−0.758789	+	0.651337i	$0.774209\pi$
$390$		0			0
$391$			19.7790i			1.00027i
$392$	8.30950	+	13.4408i	0.419693	+	0.678863i
$393$		0			0
$394$	−6.27321	−	3.62184i	−0.316040	−	0.182466i
$395$	8.09953	+	8.09953i	0.407532	+	0.407532i
$396$		0			0
$397$	−3.00423	−	11.2120i	−0.150778	−	0.562712i	−0.999430	−	0.0337600i	$-0.989252\pi$
$397$	−3.00423	−	11.2120i	−0.150778	−	0.562712i	0.848652	−	0.528952i	$-0.177415\pi$
$398$	0.956572	−	0.956572i	0.0479486	−	0.0479486i
$399$		0			0
$400$	4.90253	−	2.83048i	0.245127	−	0.141524i
$401$	−7.55225	+	28.1854i	−0.377141	+	1.40751i	0.473049	+	0.881036i	$0.343153\pi$
$401$	−7.55225	+	28.1854i	−0.377141	+	1.40751i	−0.850191	+	0.526475i	$0.823513\pi$
$402$		0			0
$403$	11.7654	−	27.7474i	0.586075	−	1.38220i
$404$			4.20234i			0.209074i
$405$		0			0
$406$	0.486030	+	3.30625i	0.0241213	+	0.164086i
$407$	−46.5862	−	26.8966i	−2.30919	−	1.33321i
$408$		0			0
$409$	−2.36962	+	0.634939i	−0.117170	+	0.0313957i	−0.316928	−	0.948450i	$-0.602651\pi$
$409$	−2.36962	+	0.634939i	−0.117170	+	0.0313957i	0.199757	+	0.979845i	$0.435985\pi$
$410$	3.45523	−	0.925827i	0.170642	−	0.0457233i
$411$		0			0
$412$	−23.3359	−	13.4730i	−1.14968	−	0.663766i
$413$	5.76355	+	39.2069i	0.283606	+	1.92925i
$414$		0			0
$415$		−	21.7196i		−	1.06617i
$416$	−16.2476	+	12.2533i	−0.796605	+	0.600769i
$417$		0			0
$418$	−3.67105	+	13.7006i	−0.179557	+	0.670116i
$419$	19.8935	−	11.4855i	0.971861	−	0.561104i	0.0720579	−	0.997400i	$-0.477043\pi$
$419$	19.8935	−	11.4855i	0.971861	−	0.561104i	0.899803	+	0.436296i	$0.143710\pi$
$420$		0			0
$421$	1.61471	−	1.61471i	0.0786962	−	0.0786962i	−0.666663	−	0.745359i	$-0.732278\pi$
$421$	1.61471	−	1.61471i	0.0786962	−	0.0786962i	0.745359	+	0.666663i	$0.232278\pi$
$422$	2.92767	+	10.9262i	0.142517	+	0.531881i
$423$		0			0
$424$	10.7373	+	10.7373i	0.521450	+	0.521450i
$425$	14.8025	+	8.54622i	0.718026	+	0.414552i
$426$		0			0
$427$	−0.517044	−	0.384512i	−0.0250215	−	0.0186079i
$428$			18.6364i			0.900826i
$429$		0			0
$430$			0.659934i			0.0318249i
$431$	−18.1238	−	4.85625i	−0.872991	−	0.233917i	−0.205610	−	0.978634i	$-0.565918\pi$
$431$	−18.1238	−	4.85625i	−0.872991	−	0.233917i	−0.667381	+	0.744717i	$0.732585\pi$
$432$		0			0
$433$	−2.29346	+	3.97239i	−0.110217	+	0.190901i	−0.915858	−	0.401503i	$-0.868488\pi$
$433$	−2.29346	+	3.97239i	−0.110217	+	0.190901i	0.805641	+	0.592404i	$0.201821\pi$
$434$	−5.48614	−	12.7004i	−0.263343	−	0.609636i
$435$		0			0
$436$	−8.78070	+	2.35278i	−0.420519	+	0.112678i
$437$	−11.8843	+	11.8843i	−0.568505	+	0.568505i
$438$		0			0
$439$	0.747446	+	1.29461i	0.0356737	+	0.0617886i	0.883311	−	0.468787i	$-0.155309\pi$
$439$	0.747446	+	1.29461i	0.0356737	+	0.0617886i	−0.847637	+	0.530576i	$0.821976\pi$
$440$	−14.5745	−	3.90523i	−0.694814	−	0.186175i
$441$		0			0
$442$	−11.3182	−	4.79912i	−0.538353	−	0.228271i
$443$	−5.15152			−0.244756			−0.122378	−	0.992484i	$-0.539052\pi$
$443$	−5.15152			−0.244756			−0.122378	+	0.992484i	$0.539052\pi$
$444$		0			0
$445$	2.30198	+	3.98715i	0.109124	+	0.189009i
$446$	−6.72673	+	11.6510i	−0.318520	+	0.551693i
$447$		0			0
$448$	0.0243813	−	0.209529i	0.00115191	−	0.00989932i
$449$	18.3337	−	4.91250i	0.865221	−	0.231835i	0.201201	−	0.979550i	$-0.435516\pi$
$449$	18.3337	−	4.91250i	0.865221	−	0.231835i	0.664020	+	0.747715i	$0.268849\pi$
$450$		0			0
$451$	−17.7567	−	10.2519i	−0.836132	−	0.482741i
$452$	4.60981	−	2.66147i	0.216827	−	0.125185i
$453$		0			0
$454$	−1.77058			−0.0830976
$455$	6.43625	−	11.3229i	0.301736	−	0.530828i
$456$		0			0
$457$	9.41753	+	2.52342i	0.440533	+	0.118041i	0.472267	−	0.881456i	$-0.343436\pi$
$457$	9.41753	+	2.52342i	0.440533	+	0.118041i	−0.0317331	+	0.999496i	$0.510103\pi$
$458$	−0.0933028	+	0.0538684i	−0.00435975	+	0.00251710i
$459$		0			0
$460$	−5.63577	−	5.63577i	−0.262769	−	0.262769i
$461$	−15.3121	+	4.10288i	−0.713157	+	0.191090i	−0.597117	−	0.802154i	$-0.703687\pi$
$461$	−15.3121	+	4.10288i	−0.713157	+	0.191090i	−0.116041	+	0.993244i	$0.537020\pi$
$462$		0			0
$463$	18.1402	+	18.1402i	0.843045	+	0.843045i	0.989254	−	0.146209i	$-0.0467071\pi$
$463$	18.1402	+	18.1402i	0.843045	+	0.843045i	−0.146209	+	0.989254i	$0.546707\pi$
$464$	1.82248	−	3.15663i	0.0846065	−	0.146543i
$465$		0			0
$466$	−1.41322	+	5.27422i	−0.0654663	+	0.244323i
$467$	15.9305			0.737174			0.368587	−	0.929593i	$-0.379842\pi$
$467$	15.9305			0.737174			0.368587	+	0.929593i	$0.379842\pi$
$468$		0			0
$469$	14.1443	+	5.61076i	0.653123	+	0.259081i
$470$	6.60282	+	1.76922i	0.304565	+	0.0816080i
$471$		0			0
$472$	−16.9060	+	29.2820i	−0.778160	+	1.34781i
$473$	2.67476	−	2.67476i	0.122986	−	0.122986i
$474$		0			0
$475$	3.75911	+	14.0292i	0.172480	+	0.643703i
$476$	21.2966	−	9.19946i	0.976130	−	0.421657i
$477$		0			0
$478$	−12.1822	+	7.03341i	−0.557202	+	0.321701i
$479$	8.19612	+	2.19614i	0.374490	+	0.100344i	0.441155	−	0.897431i	$-0.354569\pi$
$479$	8.19612	+	2.19614i	0.374490	+	0.100344i	−0.0666644	+	0.997775i	$0.521236\pi$
$480$		0			0
$481$	39.3213	−	4.84352i	1.79290	−	0.220845i
$482$			6.00446i			0.273496i
$483$		0			0
$484$	10.4293	+	18.0641i	0.474061	+	0.821098i
$485$	−11.5817	−	6.68671i	−0.525899	−	0.303628i
$486$		0			0
$487$	−0.212412	−	0.792734i	−0.00962533	−	0.0359222i	0.960946	−	0.276735i	$-0.0892526\pi$
$487$	−0.212412	−	0.792734i	−0.00962533	−	0.0359222i	−0.970571	+	0.240813i	$0.922586\pi$
$488$	−0.142292	−	0.531043i	−0.00644128	−	0.0240392i
$489$		0			0
$490$	−1.72057	−	5.72567i	−0.0777274	−	0.258660i
$491$	28.7764	−	16.6141i	1.29866	−	0.749782i	0.318488	−	0.947927i	$-0.396825\pi$
$491$	28.7764	−	16.6141i	1.29866	−	0.749782i	0.980173	+	0.198145i	$0.0634917\pi$
$492$		0			0
$493$	11.0054			0.495660
$494$	−3.91703	−	9.68419i	−0.176236	−	0.435712i
$495$		0			0
$496$	−3.90552	+	14.5756i	−0.175363	+	0.654463i
$497$	1.05733	+	7.19253i	0.0474276	+	0.322629i
$498$		0			0
$499$	−2.26621	+	2.26621i	−0.101449	+	0.101449i	−0.756010	−	0.654560i	$-0.772854\pi$
$499$	−2.26621	+	2.26621i	−0.101449	+	0.101449i	0.654560	+	0.756010i	$0.272854\pi$
$500$	−17.2606	+	4.62495i	−0.771916	+	0.206834i
$501$		0			0
$502$	−2.54722	+	2.54722i	−0.113688	+	0.113688i
$503$	9.09104	+	5.24871i	0.405349	+	0.234028i	0.688789	−	0.724961i	$-0.258142\pi$
$503$	9.09104	+	5.24871i	0.405349	+	0.234028i	−0.283440	+	0.958990i	$0.591476\pi$
$504$		0			0
$505$	0.923111	−	3.44510i	0.0410779	−	0.153305i
$506$		−	11.1129i		−	0.494029i
$507$		0			0
$508$	−28.7754			−1.27670
$509$	−3.18662	+	11.8926i	−0.141244	+	0.527131i	0.858649	+	0.512563i	$0.171304\pi$
$509$	−3.18662	+	11.8926i	−0.141244	+	0.527131i	−0.999894	+	0.0145680i	$0.995363\pi$
$510$		0			0
$511$	−6.37262	+	5.04414i	−0.281908	+	0.223140i
$512$	12.9677	−	12.9677i	0.573099	−	0.573099i
$513$		0			0
$514$	3.61856	+	13.5046i	0.159608	+	0.595664i
$515$	16.1713	+	16.1713i	0.712592	+	0.712592i
$516$		0			0
$517$	−19.5909	−	33.9325i	−0.861607	−	1.49235i
$518$	10.8525	−	14.5931i	0.476832	−	0.641185i
$519$		0			0
$520$	10.3020	−	4.16691i	0.451771	−	0.182731i
$521$		−	10.4773i		−	0.459019i	−0.973306	−	0.229509i	$-0.926288\pi$
$521$		−	10.4773i		−	0.459019i	0.973306	−	0.229509i	$-0.0737122\pi$
$522$		0			0
$523$	31.3912	−	18.1237i	1.37264	−	0.792495i	0.381381	−	0.924418i	$-0.375448\pi$
$523$	31.3912	−	18.1237i	1.37264	−	0.792495i	0.991260	+	0.131923i	$0.0421151\pi$
$524$	−12.3820	+	21.4463i	−0.540911	+	0.936885i
$525$		0			0
$526$	2.89261	+	10.7954i	0.126124	+	0.470700i
$527$	−44.0089	+	11.7921i	−1.91706	+	0.513674i
$528$		0			0
$529$	−4.91595	+	8.51467i	−0.213737	+	0.370203i
$530$	−2.87255	−	4.97541i	−0.124776	−	0.216118i
$531$		0			0
$532$	18.3237	+	7.26865i	0.794435	+	0.315136i
$533$	14.9876	−	1.84615i	0.649187	−	0.0799656i
$534$		0			0
$535$	4.09379	−	15.2782i	0.176990	−	0.660535i
$536$	6.49157	+	11.2437i	0.280393	+	0.485655i
$537$		0			0
$538$	3.61098	+	3.61098i	0.155680	+	0.155680i
$539$	−16.2330	+	30.1801i	−0.699203	+	1.29995i
$540$		0			0
$541$	15.3940	+	15.3940i	0.661840	+	0.661840i	0.955813	−	0.293974i	$-0.0949778\pi$
$541$	15.3940	+	15.3940i	0.661840	+	0.661840i	−0.293974	+	0.955813i	$0.594978\pi$
$542$	10.0853	+	5.82276i	0.433202	+	0.250109i
$543$		0			0
$544$	29.7155	+	7.96225i	1.27404	+	0.341379i
$545$	7.71528			0.330486
$546$		0			0
$547$	−1.98911			−0.0850480			−0.0425240	−	0.999095i	$-0.513540\pi$
$547$	−1.98911			−0.0850480			−0.0425240	+	0.999095i	$0.513540\pi$
$548$	−3.36159	−	0.900735i	−0.143600	−	0.0384775i
$549$		0			0
$550$	−8.31681	−	4.80171i	−0.354630	−	0.204746i
$551$	6.61267	+	6.61267i	0.281709	+	0.281709i
$552$		0			0
$553$	22.0479	+	2.56554i	0.937572	+	0.109098i
$554$	2.36938	+	2.36938i	0.100665	+	0.100665i
$555$		0			0
$556$	1.03820	+	1.79822i	0.0440296	+	0.0762614i
$557$	6.80662	−	25.4027i	0.288406	−	1.07634i	−0.657909	−	0.753098i	$-0.728559\pi$
$557$	6.80662	−	25.4027i	0.288406	−	1.07634i	0.946315	−	0.323247i	$-0.104775\pi$
$558$		0			0
$559$	−0.386658	+	2.75897i	−0.0163539	+	0.116692i
$560$	−2.40448	+	6.06152i	−0.101608	+	0.256146i
$561$		0			0
$562$	−4.94015	−	8.55659i	−0.208388	−	0.360938i
$563$	23.3973	−	40.5252i	0.986077	−	1.70794i	0.349027	−	0.937113i	$-0.386512\pi$
$563$	23.3973	−	40.5252i	0.986077	−	1.70794i	0.637050	−	0.770822i	$-0.280154\pi$
$564$		0			0
$565$	−4.36378	+	1.16927i	−0.183585	+	0.0491916i
$566$	−3.46873	−	12.9455i	−0.145802	−	0.544139i
$567$		0			0
$568$	−3.10141	+	5.37180i	−0.130132	+	0.225396i
$569$	5.67847	−	3.27847i	0.238054	−	0.137441i	−0.376228	−	0.926527i	$-0.622779\pi$
$569$	5.67847	−	3.27847i	0.238054	−	0.137441i	0.614282	+	0.789087i	$0.289446\pi$
$570$		0			0
$571$		−	12.2503i		−	0.512659i	−0.966590	−	0.256329i	$-0.917487\pi$
$571$		−	12.2503i		−	0.512659i	0.966590	−	0.256329i	$-0.0825132\pi$
$572$	−26.1421	−	11.0847i	−1.09305	−	0.463474i
$573$		0			0
$574$	4.13653	−	5.56229i	0.172655	−	0.232165i
$575$	−5.68973	−	9.85491i	−0.237278	−	0.410978i
$576$		0			0
$577$	−25.5329	−	25.5329i	−1.06295	−	1.06295i	−0.997881	−	0.0650684i	$-0.979273\pi$
$577$	−25.5329	−	25.5329i	−1.06295	−	1.06295i	−0.0650684	−	0.997881i	$-0.520727\pi$
$578$	2.05765	+	7.67925i	0.0855869	+	0.319415i
$579$		0			0
$580$	−3.13585	+	3.13585i	−0.130209	+	0.130209i
$581$	−26.1218	−	33.0016i	−1.08372	−	1.36914i
$582$		0			0
$583$	−8.52302	+	31.8083i	−0.352987	+	1.31737i
$584$	−6.93447			−0.286950
$585$		0			0
$586$			3.22485i			0.133217i
$587$	1.99568	−	7.44800i	0.0823707	−	0.307412i	−0.912433	−	0.409227i	$-0.865798\pi$
$587$	1.99568	−	7.44800i	0.0823707	−	0.307412i	0.994803	+	0.101815i	$0.0324651\pi$
$588$		0			0
$589$	−33.5283	−	19.3576i	−1.38151	−	0.797616i
$590$	9.04571	−	9.04571i	0.372406	−	0.372406i
$591$		0			0
$592$	−19.1602	+	5.13395i	−0.787479	+	0.211004i
$593$	5.94198	−	5.94198i	0.244008	−	0.244008i	−0.574498	−	0.818506i	$-0.694803\pi$
$593$	5.94198	−	5.94198i	0.244008	−	0.244008i	0.818506	+	0.574498i	$0.194803\pi$
$594$		0			0
$595$	−19.4799	+	2.86361i	−0.798597	+	0.117397i
$596$	0.524996	−	1.95931i	0.0215047	−	0.0802566i
$597$		0			0
$598$	4.92816	+	6.53462i	0.201528	+	0.267221i
$599$	−28.6135			−1.16912			−0.584558	−	0.811352i	$-0.698732\pi$
$599$	−28.6135			−1.16912			−0.584558	+	0.811352i	$0.698732\pi$
$600$		0			0
$601$	−5.37026	+	3.10052i	−0.219058	+	0.126473i	−0.605514	−	0.795835i	$-0.707032\pi$
$601$	−5.37026	+	3.10052i	−0.219058	+	0.126473i	0.386456	+	0.922308i	$0.373699\pi$
$602$	0.793692	+	1.00273i	0.0323485	+	0.0408681i
$603$		0			0
$604$	−3.15437	−	11.7723i	−0.128350	−	0.479007i
$605$	−4.58194	−	17.1000i	−0.186282	−	0.695215i
$606$		0			0
$607$	19.0001	+	10.9697i	0.771192	+	0.445248i	0.833300	−	0.552822i	$-0.186449\pi$
$607$	19.0001	+	10.9697i	0.771192	+	0.445248i	−0.0621079	+	0.998069i	$0.519782\pi$
$608$	13.0706	+	22.6389i	0.530082	+	0.918128i
$609$		0			0
$610$			0.208005i			0.00842187i
$611$	26.5676	+	11.2651i	1.07481	+	0.455739i
$612$		0			0
$613$	−3.56397	−	0.954962i	−0.143947	−	0.0385706i	0.186126	−	0.982526i	$-0.440407\pi$
$613$	−3.56397	−	0.954962i	−0.143947	−	0.0385706i	−0.330073	+	0.943955i	$0.607073\pi$
$614$	−13.7633	+	7.94627i	−0.555443	+	0.320685i
$615$		0			0
$616$	−26.8418	+	11.5948i	−1.08149	+	0.467168i
$617$	−1.16293	−	4.34013i	−0.0468180	−	0.174727i	0.938558	−	0.345122i	$-0.112162\pi$
$617$	−1.16293	−	4.34013i	−0.0468180	−	0.174727i	−0.985376	+	0.170395i	$0.945496\pi$
$618$		0			0
$619$	6.43883	−	6.43883i	0.258798	−	0.258798i	−0.565767	−	0.824565i	$-0.691420\pi$
$619$	6.43883	−	6.43883i	0.258798	−	0.258798i	0.824565	+	0.565767i	$0.191420\pi$
$620$	9.17971	−	15.8997i	0.368666	−	0.638548i
$621$		0			0
$622$	−4.36504	−	1.16961i	−0.175022	−	0.0468970i
$623$	8.29300	+	3.28966i	0.332252	+	0.131798i
$624$		0			0
$625$	−0.513208			−0.0205283
$626$	3.39375	−	12.6656i	0.135641	−	0.506221i
$627$		0			0
$628$	5.99445	−	10.3827i	0.239205	−	0.414315i
$629$	−42.3502	−	42.3502i	−1.68861	−	1.68861i
$630$		0			0
$631$	−24.5144	+	6.56863i	−0.975905	+	0.261493i	−0.711319	−	0.702869i	$-0.751902\pi$
$631$	−24.5144	+	6.56863i	−0.975905	+	0.261493i	−0.264586	+	0.964362i	$0.585235\pi$
$632$	13.3918	+	13.3918i	0.532696	+	0.532696i
$633$		0			0
$634$	0.158766	−	0.0916634i	0.00630539	−	0.00364042i
$635$	23.5902	+	6.32097i	0.936148	+	0.250840i
$636$		0			0
$637$	−3.83845	−	24.9453i	−0.152085	−	0.988367i
$638$	−6.18343			−0.244804
$639$		0			0
$640$	−13.4063	+	7.74011i	−0.529929	+	0.305955i
$641$	−26.7633	−	15.4518i	−1.05709	−	0.610309i	−0.132461	−	0.991188i	$-0.542288\pi$
$641$	−26.7633	−	15.4518i	−1.05709	−	0.610309i	−0.924625	+	0.380879i	$0.875621\pi$
$642$		0			0
$643$	22.1486	−	5.93469i	0.873454	−	0.234041i	0.205873	−	0.978579i	$-0.433996\pi$
$643$	22.1486	−	5.93469i	0.873454	−	0.234041i	0.667581	+	0.744537i	$0.267330\pi$
$644$	−15.3412	−	1.78514i	−0.604529	−	0.0703444i
$645$		0			0
$646$	−7.89601	+	13.6763i	−0.310664	+	0.538086i
$647$	−9.66194	−	16.7350i	−0.379850	−	0.657919i	0.611190	−	0.791484i	$-0.290691\pi$
$647$	−9.66194	−	16.7350i	−0.379850	−	0.657919i	−0.991040	+	0.133564i	$0.957358\pi$
$648$		0			0
$649$	−73.3258			−2.87829
$650$	7.01984	−	0.864690i	0.275341	−	0.0339159i
$651$		0			0
$652$	18.2252	+	4.88344i	0.713755	+	0.191250i
$653$	−10.3312	−	17.8942i	−0.404291	−	0.700253i	0.589947	−	0.807442i	$-0.299148\pi$
$653$	−10.3312	−	17.8942i	−0.404291	−	0.700253i	−0.994239	+	0.107189i	$0.965815\pi$
$654$		0			0
$655$	14.8618	−	14.8618i	0.580700	−	0.580700i
$656$	−7.30306	+	1.95685i	−0.285137	+	0.0764022i
$657$		0			0
$658$	12.1604	−	5.25289i	0.474061	−	0.204779i
$659$	−11.5048	+	19.9270i	−0.448165	+	0.776245i	−0.998267	−	0.0588532i	$-0.981256\pi$
$659$	−11.5048	+	19.9270i	−0.448165	+	0.776245i	0.550102	+	0.835098i	$0.314589\pi$
$660$		0			0
$661$	−27.9076	−	7.47783i	−1.08548	−	0.290854i	−0.328642	−	0.944455i	$-0.606591\pi$
$661$	−27.9076	−	7.47783i	−1.08548	−	0.290854i	−0.756839	+	0.653601i	$0.773257\pi$
$662$			8.10696i			0.315086i
$663$		0			0
$664$		−	35.9112i		−	1.39362i
$665$	−13.4252	−	9.98397i	−0.520607	−	0.387162i
$666$		0			0
$667$	−6.34535	−	3.66349i	−0.245693	−	0.141851i
$668$	8.17656	+	8.17656i	0.316361	+	0.316361i
$669$		0			0
$670$	−1.27135	−	4.74473i	−0.0491164	−	0.183305i
$671$	0.843058	−	0.843058i	0.0325459	−	0.0325459i
$672$		0			0
$673$	−4.00219	+	2.31066i	−0.154273	+	0.0890695i	−0.575149	−	0.818049i	$-0.695056\pi$
$673$	−4.00219	+	2.31066i	−0.154273	+	0.0890695i	0.420876	+	0.907118i	$0.361723\pi$
$674$	4.06200	−	15.1596i	0.156462	−	0.583926i
$675$		0			0
$676$	20.2877	−	5.07500i	0.780297	−	0.195192i
$677$			21.5334i			0.827596i	0.910369	+	0.413798i	$0.135798\pi$
$677$			21.5334i			0.827596i	−0.910369	+	0.413798i	$0.864202\pi$
$678$		0			0
$679$	−25.6397	+	3.76912i	−0.983961	+	0.144646i
$680$	−14.5487	−	8.39970i	−0.557918	−	0.322114i
$681$		0			0
$682$	24.7265	−	6.62545i	0.946827	−	0.253701i
$683$	−26.5081	+	7.10282i	−1.01430	+	0.271782i	−0.727426	−	0.686186i	$-0.759284\pi$
$683$	−26.5081	+	7.10282i	−1.01430	+	0.271782i	−0.286877	+	0.957967i	$0.592617\pi$
$684$		0			0
$685$	2.55798	+	1.47685i	0.0977355	+	0.0564276i
$686$	−9.50047	−	6.63049i	−0.362730	−	0.253153i
$687$		0			0
$688$		−	1.39485i		−	0.0531783i
$689$	−9.09410	−	22.4836i	−0.346458	−	0.856557i
$690$		0			0
$691$	−10.4368	+	38.9506i	−0.397033	+	1.48175i	0.421255	+	0.906942i	$0.361590\pi$
$691$	−10.4368	+	38.9506i	−0.397033	+	1.48175i	−0.818289	+	0.574807i	$0.805077\pi$
$692$	21.2678	−	12.2790i	0.808479	−	0.466776i
$693$		0			0
$694$	5.93879	−	5.93879i	0.225433	−	0.225433i
$695$	−0.456115	−	1.70224i	−0.0173014	−	0.0645698i
$696$		0			0
$697$	−16.1421	−	16.1421i	−0.611426	−	0.611426i
$698$	2.97482	+	1.71751i	0.112598	+	0.0650087i
$699$		0			0
$700$	−7.96469	+	10.7099i	−0.301037	+	0.404797i
$701$			17.7693i			0.671135i	0.942016	+	0.335568i	$0.108928\pi$
$701$			17.7693i			0.671135i	−0.942016	+	0.335568i	$0.891072\pi$
$702$		0			0
$703$		−	50.8926i		−	1.91945i
$704$	0.377016	+	0.101021i	0.0142093	+	0.00380738i
$705$		0			0
$706$	−0.914760	+	1.58441i	−0.0344275	+	0.0596301i
$707$	−2.74076	−	6.34482i	−0.103077	−	0.238621i
$708$		0			0
$709$	13.1479	−	3.52297i	0.493780	−	0.132308i	−0.00333188	−	0.999994i	$-0.501061\pi$
$709$	13.1479	−	3.52297i	0.493780	−	0.132308i	0.497112	+	0.867687i	$0.334394\pi$
$710$	1.65944	−	1.65944i	0.0622777	−	0.0622777i
$711$		0			0
$712$	3.80610	+	6.59235i	0.142639	+	0.247059i
$713$	29.2994	+	7.85074i	1.09727	+	0.294013i
$714$		0			0
$715$	18.9964	+	14.8298i	0.710427	+	0.554603i
$716$	36.3973			1.36023
$717$		0			0
$718$	−8.72576	−	15.1135i	−0.325642	−	0.564029i
$719$	14.3958	−	24.9343i	0.536873	−	0.929892i	−0.462197	−	0.886777i	$-0.652939\pi$
$719$	14.3958	−	24.9343i	0.536873	−	0.929892i	0.999070	−	0.0431147i	$-0.0137281\pi$
$720$		0			0
$721$	44.0202	+	5.12229i	1.63940	+	0.190764i
$722$	−1.48127	+	0.396904i	−0.0551271	+	0.0147713i
$723$		0			0
$724$	−2.03845	−	1.17690i	−0.0757583	−	0.0437391i
$725$	−5.48345	+	3.16587i	−0.203650	+	0.117578i
$726$		0			0
$727$	35.7112			1.32445			0.662227	−	0.749303i	$-0.269611\pi$
$727$	35.7112			1.32445			0.662227	+	0.749303i	$0.269611\pi$
$728$	10.6417	−	18.7213i	0.394407	−	0.693859i
$729$		0			0
$730$	2.53422	+	0.679043i	0.0937957	+	0.0251325i
$731$	3.64732	−	2.10578i	0.134901	−	0.0778850i
$732$		0			0
$733$	5.08991	+	5.08991i	0.188000	+	0.188000i	0.794831	−	0.606831i	$-0.207559\pi$
$733$	5.08991	+	5.08991i	0.188000	+	0.188000i	−0.606831	+	0.794831i	$0.707559\pi$
$734$	−10.0745	+	2.69944i	−0.371855	+	0.0996383i
$735$		0			0
$736$	−14.4825	−	14.4825i	−0.533831	−	0.533831i
$737$	−14.0779	+	24.3836i	−0.518565	+	0.898180i
$738$		0			0
$739$	−2.23899	+	8.35601i	−0.0823624	+	0.307381i	−0.994802	−	0.101831i	$-0.967530\pi$
$739$	−2.23899	+	8.35601i	−0.0823624	+	0.307381i	0.912439	+	0.409212i	$0.134196\pi$
$740$	24.1342			0.887190
$741$		0			0
$742$	−10.3485	−	4.10504i	−0.379906	−	0.150701i
$743$	−0.167623	−	0.0449143i	−0.00614947	−	0.00164775i	0.255743	−	0.966745i	$-0.417680\pi$
$743$	−0.167623	−	0.0449143i	−0.00614947	−	0.00164775i	−0.261892	+	0.965097i	$0.584347\pi$
$744$		0			0
$745$	−0.860788	+	1.49093i	−0.0315368	+	0.0546234i
$746$	−15.1385	+	15.1385i	−0.554260	+	0.554260i
$747$		0			0
$748$	11.1099	+	41.4628i	0.406219	+	1.51603i
$749$	−12.1546	−	28.1378i	−0.444120	−	1.02813i
$750$		0			0
$751$	5.40946	−	3.12315i	0.197394	−	0.113965i	−0.398045	−	0.917366i	$-0.630311\pi$
$751$	5.40946	−	3.12315i	0.197394	−	0.113965i	0.595439	+	0.803400i	$0.296978\pi$
$752$	−13.9559	−	3.73947i	−0.508919	−	0.136364i
$753$		0			0
$754$	3.63599	−	2.74212i	0.132415	−	0.0998622i
$755$			10.3439i			0.376452i
$756$		0			0
$757$	5.42762	+	9.40091i	0.197270	+	0.341682i	0.947642	−	0.319334i	$-0.103459\pi$
$757$	5.42762	+	9.40091i	0.197270	+	0.341682i	−0.750372	+	0.661016i	$0.770126\pi$
$758$	6.55213	+	3.78288i	0.237984	+	0.137400i
$759$		0			0
$760$	−3.69466	−	13.7887i	−0.134020	−	0.500168i
$761$	5.34573	+	19.9505i	0.193783	+	0.723206i	0.992579	+	0.121604i	$0.0388039\pi$
$761$	5.34573	+	19.9505i	0.193783	+	0.723206i	−0.798796	+	0.601602i	$0.794529\pi$
$762$		0			0
$763$	11.7229	−	9.27904i	0.424397	−	0.335924i
$764$	−5.77116	+	3.33198i	−0.208793	+	0.120547i
$765$		0			0
$766$	−20.7751			−0.750635
$767$	43.1171	−	32.5173i	1.55687	−	1.17413i
$768$		0			0
$769$	7.59897	−	28.3597i	0.274026	−	1.02268i	−0.682466	−	0.730918i	$-0.739092\pi$
$769$	7.59897	−	28.3597i	0.274026	−	1.02268i	0.956491	−	0.291760i	$-0.0942410\pi$
$770$	10.9448	−	1.60893i	0.394424	−	0.0579817i
$771$		0			0
$772$	−1.39132	+	1.39132i	−0.0500745	+	0.0500745i
$773$	14.8539	−	3.98008i	0.534257	−	0.143154i	0.0184036	−	0.999831i	$-0.494142\pi$
$773$	14.8539	−	3.98008i	0.534257	−	0.143154i	0.515853	+	0.856677i	$0.327475\pi$
$774$		0			0
$775$	18.5352	−	18.5352i	0.665805	−	0.665805i
$776$	−19.1492	−	11.0558i	−0.687416	−	0.396880i
$777$		0			0
$778$	4.15980	−	15.5246i	0.149136	−	0.556583i
$779$		−	19.3981i		−	0.695011i
$780$		0			0
$781$	−13.4517			−0.481338
$782$	3.20234	−	11.9513i	0.114515	−	0.427377i
$783$		0			0
$784$	3.63664	+	12.1019i	0.129880	+	0.432212i
$785$	−7.19500	+	7.19500i	−0.256801	+	0.256801i
$786$		0			0
$787$	8.72193	+	32.5507i	0.310903	+	1.16031i	0.927744	+	0.373218i	$0.121746\pi$
$787$	8.72193	+	32.5507i	0.310903	+	1.16031i	−0.616841	+	0.787088i	$0.711588\pi$
$788$	−13.1719	−	13.1719i	−0.469230	−	0.469230i
$789$		0			0
$790$	−3.58270	−	6.20542i	−0.127467	−	0.220779i
$791$	−5.22421	+	7.02487i	−0.185752	+	0.249776i
$792$		0			0
$793$	−0.121871	+	0.869600i	−0.00432776	+	0.0308804i
$794$			7.26111i			0.257687i
$795$		0			0
$796$	3.01278	−	1.73943i	0.106785	−	0.0616525i
$797$	7.64170	−	13.2358i	0.270683	−	0.468837i	−0.698354	−	0.715753i	$-0.746084\pi$
$797$	7.64170	−	13.2358i	0.270683	−	0.468837i	0.969037	+	0.246916i	$0.0794171\pi$
$798$		0			0
$799$	−11.2908	−	42.1378i	−0.399439	−	1.49073i
$800$	−17.0962	+	4.58092i	−0.604443	+	0.161960i
$801$		0			0
$802$	9.12674	−	15.8080i	0.322276	−	0.558199i
$803$	−7.51917	−	13.0236i	−0.265346	−	0.459592i
$804$		0			0
$805$	12.1847	+	4.83341i	0.429453	+	0.170355i
$806$	−11.6016	+	14.8612i	−0.408648	+	0.523463i
$807$		0			0
$808$	1.52627	−	5.69612i	0.0536940	−	0.200389i
$809$	18.3537	+	31.7895i	0.645282	+	1.11766i	0.984236	+	0.176858i	$0.0565933\pi$
$809$	18.3537	+	31.7895i	0.645282	+	1.11766i	−0.338955	+	0.940803i	$0.610073\pi$
$810$		0			0
$811$	15.9213	+	15.9213i	0.559073	+	0.559073i	0.929044	−	0.369970i	$-0.120632\pi$
$811$	15.9213	+	15.9213i	0.559073	+	0.559073i	−0.369970	+	0.929044i	$0.620632\pi$
$812$	−0.993285	+	8.53615i	−0.0348575	+	0.299560i
$813$		0			0
$814$	23.7945	+	23.7945i	0.833998	+	0.833998i
$815$	−13.8684	−	8.00692i	−0.485789	−	0.280470i
$816$		0			0
$817$	3.45678	+	0.926240i	0.120937	+	0.0324050i
$818$	1.53462			0.0536568
$819$		0			0
$820$	9.19895			0.321241
$821$	−27.4347	−	7.35110i	−0.957477	−	0.256555i	−0.253945	−	0.967219i	$-0.581728\pi$
$821$	−27.4347	−	7.35110i	−0.957477	−	0.256555i	−0.703532	+	0.710664i	$0.748395\pi$
$822$		0			0
$823$	44.7888	+	25.8588i	1.56124	+	0.901382i	0.997132	+	0.0756800i	$0.0241127\pi$
$823$	44.7888	+	25.8588i	1.56124	+	0.901382i	0.564107	+	0.825702i	$0.309221\pi$
$824$	26.7376	+	26.7376i	0.931448	+	0.931448i
$825$		0			0
$826$	2.86525	−	24.6235i	0.0996947	−	0.856762i
$827$	5.62199	+	5.62199i	0.195496	+	0.195496i	0.798066	−	0.602570i	$-0.205857\pi$
$827$	5.62199	+	5.62199i	0.195496	+	0.195496i	−0.602570	+	0.798066i	$0.705857\pi$
$828$		0			0
$829$	−9.16413	−	15.8727i	−0.318284	−	0.551283i	0.661846	−	0.749639i	$-0.269773\pi$
$829$	−9.16413	−	15.8727i	−0.318284	−	0.551283i	−0.980130	+	0.198356i	$0.936440\pi$
$830$	−3.51652	+	13.1238i	−0.122060	+	0.455535i
$831$		0			0
$832$	−0.266493	+	0.107790i	−0.00923897	+	0.00373695i
$833$	−26.1544	+	27.7792i	−0.906197	+	0.962493i
$834$		0			0
$835$	−4.90707	−	8.49929i	−0.169816	−	0.294130i
$836$	−18.2377	+	31.5886i	−0.630763	+	1.09251i
$837$		0			0
$838$	−13.8800	+	3.71914i	−0.479477	+	0.128475i
$839$	−4.18001	−	15.6000i	−0.144310	−	0.538572i	−0.999785	−	0.0207282i	$-0.993402\pi$
$839$	−4.18001	−	15.6000i	−0.144310	−	0.538572i	0.855475	−	0.517844i	$-0.173265\pi$
$840$		0			0
$841$	12.4616	−	21.5841i	0.429709	−	0.744278i
$842$	−1.23710	+	0.714242i	−0.0426334	+	0.0246144i
$843$		0			0
$844$			29.0892i			1.00129i
$845$	−17.7468	−	0.296011i	−0.610507	−	0.0101831i
$846$		0			0
$847$	−27.5279	−	20.4718i	−0.945870	−	0.703419i
$848$	6.07150	+	10.5161i	0.208496	+	0.361126i
$849$		0			0
$850$	−7.56057	−	7.56057i	−0.259325	−	0.259325i
$851$	10.3201	+	38.5152i	0.353769	+	1.32028i
$852$		0			0
$853$	−27.1149	+	27.1149i	−0.928397	+	0.928397i	−0.997602	−	0.0692053i	$-0.977954\pi$
$853$	−27.1149	+	27.1149i	−0.928397	+	0.928397i	0.0692053	+	0.997602i	$0.477954\pi$
$854$	0.250164	+	0.316050i	0.00856044	+	0.0108150i
$855$		0			0
$856$	6.76866	−	25.2610i	0.231348	−	0.863403i
$857$	39.5227			1.35007			0.675035	−	0.737785i	$-0.264128\pi$
$857$	39.5227			1.35007			0.675035	+	0.737785i	$0.264128\pi$
$858$		0			0
$859$			11.5991i			0.395757i	0.980227	+	0.197878i	$0.0634051\pi$
$859$			11.5991i			0.395757i	−0.980227	+	0.197878i	$0.936595\pi$
$860$	−0.439240	+	1.63926i	−0.0149779	+	0.0558985i
$861$		0			0
$862$	10.1648	+	5.86867i	0.346216	+	0.199888i
$863$	36.6744	−	36.6744i	1.24841	−	1.24841i	0.291991	−	0.956421i	$-0.405682\pi$
$863$	36.6744	−	36.6744i	1.24841	−	1.24841i	0.956421	−	0.291991i	$-0.0943176\pi$
$864$		0			0
$865$	−20.1327	+	5.39453i	−0.684531	+	0.183420i
$866$	2.02895	−	2.02895i	0.0689466	−	0.0689466i
$867$		0			0
$868$	−5.17436	−	35.1989i	−0.175629	−	1.19473i
$869$	−10.6301	+	39.6719i	−0.360600	+	1.34578i
$870$		0			0
$871$	−2.53513	−	20.5811i	−0.0858997	−	0.697362i
$872$	12.7564			0.431987
$873$		0			0
$874$	9.10513	−	5.25685i	0.307986	−	0.177816i
$875$	23.0441	−	18.2402i	0.779033	−	0.616630i
$876$		0			0
$877$	4.12095	+	15.3796i	0.139155	+	0.519332i	0.999946	+	0.0103742i	$0.00330228\pi$
$877$	4.12095	+	15.3796i	0.139155	+	0.519332i	−0.860792	+	0.508957i	$0.830031\pi$
$878$	−0.242031	−	0.903273i	−0.00816816	−	0.0304840i
$879$		0			0
$880$	−10.4495	−	6.03304i	−0.352254	−	0.203374i
$881$	23.5454	+	40.7819i	0.793266	+	1.37398i	0.923934	+	0.382551i	$0.124954\pi$
$881$	23.5454	+	40.7819i	0.793266	+	1.37398i	−0.130668	+	0.991426i	$0.541712\pi$
$882$		0			0
$883$		−	25.4763i		−	0.857347i	−0.903460	−	0.428673i	$-0.858981\pi$
$883$		−	25.4763i		−	0.857347i	0.903460	−	0.428673i	$-0.141019\pi$
$884$	−24.9201	−	19.4541i	−0.838152	−	0.654313i
$885$		0			0
$886$	3.11275	+	0.834059i	0.104575	+	0.0280208i
$887$	−32.6585	+	18.8554i	−1.09657	+	0.633103i	−0.935317	−	0.353811i	$-0.884886\pi$
$887$	−32.6585	+	18.8554i	−1.09657	+	0.633103i	−0.161249	+	0.986914i	$0.551552\pi$
$888$		0			0
$889$	43.4459	−	18.7672i	1.45713	−	0.629433i
$890$	−0.745407	−	2.78190i	−0.0249861	−	0.0932494i
$891$		0			0
$892$	−24.4638	+	24.4638i	−0.819108	+	0.819108i
$893$	18.5346	−	32.1028i	0.620235	−	1.07428i
$894$		0			0
$895$	−29.8387	−	7.99524i	−0.997396	−	0.267251i
$896$	−11.0610	+	27.8841i	−0.369524	+	0.931542i
$897$		0			0
$898$	−11.8733			−0.396218
$899$	4.36830	−	16.3027i	0.145691	−	0.543726i
$900$		0			0
$901$	−18.3320	+	31.7520i	−0.610728	+	1.05781i
$902$	9.06949	+	9.06949i	0.301981	+	0.301981i
$903$		0			0
$904$	−7.21506	+	1.93327i	−0.239969	+	0.0642996i
$905$	1.41260	+	1.41260i	0.0469565	+	0.0469565i
$906$		0			0
$907$	−42.1816	+	24.3536i	−1.40062	+	0.808647i	−0.994456	−	0.105154i	$-0.966467\pi$
$907$	−42.1816	+	24.3536i	−1.40062	+	0.808647i	−0.406162	+	0.913801i	$0.633133\pi$
$908$	−4.39809	−	1.17847i	−0.145956	−	0.0391088i
$909$		0			0
$910$	−5.72228	+	5.79971i	−0.189692	+	0.192258i
$911$	−1.75858			−0.0582644			−0.0291322	−	0.999576i	$-0.509274\pi$
$911$	−1.75858			−0.0582644			−0.0291322	+	0.999576i	$0.509274\pi$
$912$		0			0
$913$	67.4446	−	38.9392i	2.23209	−	1.28870i
$914$	−5.28189	−	3.04950i	−0.174709	−	0.100868i
$915$		0			0
$916$	−0.267616	+	0.0717075i	−0.00884229	+	0.00236928i
$917$	4.70751	−	40.4557i	0.155456	−	1.33596i
$918$		0			0
$919$	−22.9530	+	39.7557i	−0.757148	+	1.31142i	0.187151	+	0.982331i	$0.440075\pi$
$919$	−22.9530	+	39.7557i	−0.757148	+	1.31142i	−0.944299	+	0.329088i	$0.893259\pi$
$920$	5.59219	+	9.68596i	0.184369	+	0.319337i
$921$		0			0
$922$	9.91648			0.326582
$923$	7.90986	−	5.96531i	0.260356	−	0.196351i
$924$		0			0
$925$	33.2836	+	8.91831i	1.09436	+	0.293232i
$926$	−8.02401	−	13.8980i	−0.263685	−	0.456717i
$927$		0			0
$928$	−8.05832	+	8.05832i	−0.264527	+	0.264527i
$929$	−23.6180	+	6.32841i	−0.774880	+	0.207629i	−0.624526	−	0.781004i	$-0.714708\pi$
$929$	−23.6180	+	6.32841i	−0.774880	+	0.207629i	−0.150354	+	0.988632i	$0.548041\pi$
$930$		0			0
$931$	−32.4063	+	0.976272i	−1.06207	+	0.0319960i
$932$	−7.02084	+	12.1604i	−0.229975	+	0.398329i
$933$		0			0
$934$	−9.62582	−	2.57923i	−0.314966	−	0.0843950i
$935$		−	36.4318i		−	1.19145i
$936$		0			0
$937$			11.3574i			0.371031i	0.982641	+	0.185515i	$0.0593955\pi$
$937$			11.3574i			0.371031i	−0.982641	+	0.185515i	$0.940605\pi$
$938$	−7.63814	−	5.68028i	−0.249394	−	0.185468i
$939$		0			0
$940$	15.2237	+	8.78942i	0.496543	+	0.286679i
$941$	−31.2382	−	31.2382i	−1.01834	−	1.01834i	−0.999829	−	0.0185076i	$-0.994108\pi$
$941$	−31.2382	−	31.2382i	−1.01834	−	1.01834i	−0.0185076	−	0.999829i	$-0.505892\pi$
$942$		0			0
$943$	3.93360	+	14.6804i	0.128096	+	0.478059i
$944$	−19.1192	+	19.1192i	−0.622278	+	0.622278i
$945$		0			0
$946$	−2.04925	+	1.18314i	−0.0666270	+	0.0384671i
$947$	4.90816	−	18.3175i	0.159494	−	0.595239i	−0.839185	−	0.543847i	$-0.816967\pi$
$947$	4.90816	−	18.3175i	0.159494	−	0.595239i	0.998679	−	0.0513927i	$-0.0163660\pi$
$948$		0			0
$949$	10.1969	+	4.32367i	0.331005	+	0.140352i
$950$		−	9.08561i		−	0.294776i
$951$		0			0
$952$	−32.2080	+	4.73469i	−1.04387	+	0.153452i
$953$	−20.5939	−	11.8899i	−0.667103	−	0.385152i	0.127875	−	0.991790i	$-0.459184\pi$
$953$	−20.5939	−	11.8899i	−0.667103	−	0.385152i	−0.794978	+	0.606638i	$0.792518\pi$
$954$		0			0
$955$	5.46314	−	1.46384i	0.176783	−	0.0473689i
$956$	−34.9417	+	9.36261i	−1.13010	+	0.302808i
$957$		0			0
$958$	−4.59685	−	2.65399i	−0.148518	−	0.0857466i
$959$	5.66288	−	0.832463i	0.182864	−	0.0268816i
$960$		0			0
$961$			38.8724i			1.25395i
$962$	−24.5437	−	3.43969i	−0.791320	−	0.110900i
$963$		0			0
$964$	−3.99645	+	14.9150i	−0.128717	+	0.480379i
$965$	1.44623	−	0.834982i	0.0465558	−	0.0268790i
$966$		0			0
$967$	4.64032	−	4.64032i	0.149223	−	0.149223i	−0.628548	−	0.777771i	$-0.716350\pi$
$967$	4.64032	−	4.64032i	0.149223	−	0.149223i	0.777771	+	0.628548i	$0.216350\pi$
$968$	−7.57577	−	28.2732i	−0.243495	−	0.908734i
$969$		0			0
$970$	5.91552	+	5.91552i	0.189936	+	0.189936i
$971$	16.2568	+	9.38587i	0.521706	+	0.301207i	0.737632	−	0.675203i	$-0.235944\pi$
$971$	16.2568	+	9.38587i	0.521706	+	0.301207i	−0.215926	+	0.976410i	$0.569277\pi$
$972$		0			0
$973$	−2.74030	−	2.03789i	−0.0878500	−	0.0653317i
$974$			0.513392i			0.0164501i
$975$		0			0
$976$		−	0.439644i		−	0.0140727i
$977$	17.6749	+	4.73598i	0.565471	+	0.151517i	0.530219	−	0.847861i	$-0.322110\pi$
$977$	17.6749	+	4.73598i	0.565471	+	0.151517i	0.0352523	+	0.999378i	$0.488777\pi$
$978$		0			0
$979$	−8.25404	+	14.2964i	−0.263800	+	0.456915i
$980$	−0.462966	−	15.3676i	−0.0147889	−	0.490901i
$981$		0			0
$982$	−20.0777	+	5.37982i	−0.640707	+	0.171677i
$983$	31.0006	−	31.0006i	0.988766	−	0.988766i	−0.0111712	−	0.999938i	$-0.503556\pi$
$983$	31.0006	−	31.0006i	0.988766	−	0.988766i	0.999938	+	0.0111712i	$0.00355597\pi$
$984$		0			0
$985$	7.90497	+	13.6918i	0.251873	+	0.436257i
$986$	−6.64992	−	1.78184i	−0.211777	−	0.0567453i
$987$		0			0
$988$	−3.28423	−	26.6625i	−0.104485	−	0.848246i
$989$	−2.80389			−0.0891585
$990$		0			0
$991$	23.1539	+	40.1038i	0.735509	+	1.27394i	0.954500	+	0.298212i	$0.0963901\pi$
$991$	23.1539	+	40.1038i	0.735509	+	1.27394i	−0.218991	+	0.975727i	$0.570277\pi$
$992$	23.5895	−	40.8582i	0.748968	−	1.29725i
$993$		0			0
$994$	0.525631	−	4.51720i	0.0166720	−	0.143277i
$995$	−2.85199	+	0.764187i	−0.0904140	+	0.0242264i
$996$		0			0
$997$	39.3257	+	22.7047i	1.24546	+	0.719065i	0.970200	−	0.242305i	$-0.0779036\pi$
$997$	39.3257	+	22.7047i	1.24546	+	0.719065i	0.275257	+	0.961371i	$0.411237\pi$
$998$	1.73624	−	1.00242i	0.0549598	−	0.0317311i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.f.496.4		32
3.2	odd	2		273.2.by.c.223.5	yes	32
7.6	odd	2		819.2.fm.e.496.4		32
13.7	odd	12		819.2.fm.e.748.4		32
21.20	even	2		273.2.by.d.223.5	yes	32
39.20	even	12		273.2.by.d.202.5	yes	32
91.20	even	12	inner	819.2.fm.f.748.4		32
273.20	odd	12		273.2.by.c.202.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.202.5	✓	32	273.20	odd	12
273.2.by.c.223.5	yes	32	3.2	odd	2
273.2.by.d.202.5	yes	32	39.20	even	12
273.2.by.d.223.5	yes	32	21.20	even	2
819.2.fm.e.496.4		32	7.6	odd	2
819.2.fm.e.748.4		32	13.7	odd	12
819.2.fm.f.496.4		32	1.1	even	1	trivial
819.2.fm.f.748.4		32	91.20	even	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)

\(f(q)\)	\(=\)	\(q+(-0.604240 - 0.161906i) q^{2} +(-1.39316 - 0.804341i) q^{4} +(0.965431 + 0.965431i) q^{5} +(2.62802 + 0.305802i) q^{7} +(1.59624 + 1.59624i) q^{8} +O(q^{10})\)	\(q+(-0.604240 - 0.161906i) q^{2} +(-1.39316 - 0.804341i) q^{4} +(0.965431 + 0.965431i) q^{5} +(2.62802 + 0.305802i) q^{7} +(1.59624 + 1.59624i) q^{8} +(-0.427043 - 0.739660i) q^{10} +(-1.26706 + 4.72873i) q^{11} +(-1.35196 - 3.34249i) q^{13} +(-1.53844 - 0.610269i) q^{14} +(0.902609 + 1.56336i) q^{16} +(-2.72530 + 4.72035i) q^{17} +(-4.47375 + 1.19874i) q^{19} +(-0.568463 - 2.12153i) q^{20} +(1.53121 - 2.65214i) q^{22} +(3.14262 - 1.81439i) q^{23} -3.13589i q^{25} +(0.275740 + 2.23855i) q^{26} +(-3.41528 - 2.53985i) q^{28} +(-1.00956 - 1.74861i) q^{29} +(5.91069 + 5.91069i) q^{31} +(-1.46081 - 5.45180i) q^{32} +(2.41098 - 2.41098i) q^{34} +(2.24194 + 2.83240i) q^{35} +(-2.84395 + 10.6138i) q^{37} +2.89730 q^{38} +3.08212i q^{40} +(-1.08400 + 4.04553i) q^{41} +(-0.669160 - 0.386339i) q^{43} +(5.56872 - 5.56872i) q^{44} +(-2.19266 + 0.587521i) q^{46} +(-5.65938 + 5.65938i) q^{47} +(6.81297 + 1.60731i) q^{49} +(-0.507717 + 1.89483i) q^{50} +(-0.805003 + 5.74405i) q^{52} +6.72661 q^{53} +(-5.78852 + 3.34200i) q^{55} +(3.70682 + 4.68309i) q^{56} +(0.326908 + 1.22004i) q^{58} +(3.87661 + 14.4677i) q^{59} +(-0.210912 - 0.121770i) q^{61} +(-2.61450 - 4.52844i) q^{62} -0.0797289i q^{64} +(1.92172 - 4.53216i) q^{65} +(5.55533 + 1.48855i) q^{67} +(7.59354 - 4.38413i) q^{68} +(-0.896088 - 2.07443i) q^{70} +(0.711167 + 2.65411i) q^{71} +(-2.17212 + 2.17212i) q^{73} +(3.43686 - 5.95281i) q^{74} +(7.19684 + 1.92839i) q^{76} +(-4.77591 + 12.0397i) q^{77} +8.38955 q^{79} +(-0.637914 + 2.38073i) q^{80} +(1.30999 - 2.26897i) q^{82} +(-11.2487 - 11.2487i) q^{83} +(-7.18826 + 1.92609i) q^{85} +(0.341782 + 0.341782i) q^{86} +(-9.57073 + 5.52567i) q^{88} +(3.25716 + 0.872754i) q^{89} +(-2.53083 - 9.19755i) q^{91} -5.83756 q^{92} +(4.33591 - 2.50334i) q^{94} +(-5.47640 - 3.16180i) q^{95} +(-9.46128 + 2.53514i) q^{97} +(-3.85643 - 2.07426i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

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