LMFDB - Embedded newform 819.2.fm.e.748.4

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			748.4
Character	$\chi$	$=$	819.748
Dual form			819.2.fm.e.496.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.604240 + 0.161906i) q^{2} +(-1.39316 + 0.804341i) q^{4} +(-0.965431 + 0.965431i) q^{5} +(2.12303 + 1.57884i) q^{7} +(1.59624 - 1.59624i) q^{8} +O(q^{10})$	\(q+(-0.604240 + 0.161906i) q^{2} +(-1.39316 + 0.804341i) q^{4} +(-0.965431 + 0.965431i) q^{5} +(2.12303 + 1.57884i) q^{7} +(1.59624 - 1.59624i) q^{8} +(0.427043 - 0.739660i) q^{10} +(-1.26706 - 4.72873i) q^{11} +(1.35196 - 3.34249i) q^{13} +(-1.53844 - 0.610269i) q^{14} +(0.902609 - 1.56336i) q^{16} +(2.72530 + 4.72035i) q^{17} +(4.47375 + 1.19874i) q^{19} +(0.568463 - 2.12153i) q^{20} +(1.53121 + 2.65214i) q^{22} +(3.14262 + 1.81439i) q^{23} +3.13589i q^{25} +(-0.275740 + 2.23855i) q^{26} +(-4.22764 - 0.491938i) q^{28} +(-1.00956 + 1.74861i) q^{29} +(-5.91069 + 5.91069i) q^{31} +(-1.46081 + 5.45180i) q^{32} +(-2.41098 - 2.41098i) q^{34} +(-3.57390 + 0.525376i) q^{35} +(-2.84395 - 10.6138i) q^{37} -2.89730 q^{38} +3.08212i q^{40} +(1.08400 + 4.04553i) q^{41} +(-0.669160 + 0.386339i) q^{43} +(5.56872 + 5.56872i) q^{44} +(-2.19266 - 0.587521i) q^{46} +(5.65938 + 5.65938i) q^{47} +(2.01452 + 6.70386i) q^{49} +(-0.507717 - 1.89483i) q^{50} +(0.805003 + 5.74405i) q^{52} +6.72661 q^{53} +(5.78852 + 3.34200i) q^{55} +(5.90909 - 0.868657i) q^{56} +(0.326908 - 1.22004i) q^{58} +(-3.87661 + 14.4677i) q^{59} +(0.210912 - 0.121770i) q^{61} +(2.61450 - 4.52844i) q^{62} +0.0797289i q^{64} +(1.92172 + 4.53216i) q^{65} +(5.55533 - 1.48855i) q^{67} +(-7.59354 - 4.38413i) q^{68} +(2.07443 - 0.896088i) q^{70} +(0.711167 - 2.65411i) q^{71} +(2.17212 + 2.17212i) q^{73} +(3.43686 + 5.95281i) q^{74} +(-7.19684 + 1.92839i) q^{76} +(4.77591 - 12.0397i) q^{77} +8.38955 q^{79} +(0.637914 + 2.38073i) q^{80} +(-1.30999 - 2.26897i) q^{82} +(11.2487 - 11.2487i) q^{83} +(-7.18826 - 1.92609i) q^{85} +(0.341782 - 0.341782i) q^{86} +(-9.57073 - 5.52567i) q^{88} +(-3.25716 + 0.872754i) q^{89} +(8.14751 - 4.96167i) q^{91} -5.83756 q^{92} +(-4.33591 - 2.50334i) q^{94} +(-5.47640 + 3.16180i) q^{95} +(9.46128 + 2.53514i) q^{97} +(-2.30264 - 3.72458i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 32 q^{28} + 18 q^{29} - 14 q^{31} + 8 q^{32} - 66 q^{34} - 22 q^{35} - 24 q^{37} - 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} + 28 q^{47} + 8 q^{49} - 70 q^{50} + 28 q^{52} + 80 q^{53} + 60 q^{55} + 54 q^{56} - 4 q^{58} + 42 q^{59} + 36 q^{61} - 52 q^{62} - 14 q^{65} + 26 q^{67} + 72 q^{68} - 116 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} + 148 q^{91} + 4 q^{92} - 60 q^{95} - 40 q^{97} - 36 q^{98}+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 - 32 * q^28 + 18 * q^29 - 14 * q^31 + 8 * q^32 - 66 * q^34 - 22 * q^35 - 24 * q^37 - 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 + 28 * q^47 + 8 * q^49 - 70 * q^50 + 28 * q^52 + 80 * q^53 + 60 * q^55 + 54 * q^56 - 4 * q^58 + 42 * q^59 + 36 * q^61 - 52 * q^62 - 14 * q^65 + 26 * q^67 + 72 * q^68 - 116 * 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 + 148 * q^91 + 4 * q^92 - 60 * q^95 - 40 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$-1$

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	−0.466041	−	0.884763i	$-0.654320\pi$
$2$	−0.604240	+	0.161906i	−0.427262	+	0.114484i	0.0387787	+	0.999248i	$0.487653\pi$
$3$		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	$-0.848755\pi$
$5$	−0.965431	+	0.965431i	−0.431754	+	0.431754i	0.457471	+	0.889225i	$0.348755\pi$
$6$		0			0
$7$	2.12303	+	1.57884i	0.802430	+	0.596746i
$7$	2.12303	+	1.57884i	0.802430	+	0.596746i
$8$	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	−0.842791	−	0.538240i	$-0.819089\pi$
$11$	−1.26706	−	4.72873i	−0.382033	−	1.42577i	0.460759	−	0.887525i	$-0.347577\pi$
$12$		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	0.980358	+	0.197225i	$0.0631931\pi$
$17$	2.72530	+	4.72035i	0.660981	+	1.14485i	−0.319377	+	0.947628i	$0.603474\pi$
$18$		0			0
$19$	4.47375	+	1.19874i	1.02635	+	0.275010i	0.732446	−	0.680825i	$-0.238379\pi$
$19$	4.47375	+	1.19874i	1.02635	+	0.275010i	0.293904	+	0.955835i	$0.405045\pi$
$20$	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	0.790477	−	0.612492i	$-0.209833\pi$
$23$	3.14262	+	1.81439i	0.655282	+	0.378327i	−0.135195	+	0.990819i	$0.543166\pi$
$24$		0			0
$25$			3.13589i			0.627177i
$26$	−0.275740	+	2.23855i	−0.0540771	+	0.439016i
$27$		0			0
$28$	−4.22764	−	0.491938i	−0.798950	−	0.0929676i
$29$	−1.00956	+	1.74861i	−0.187471	+	0.324710i	−0.944406	−	0.328780i	$-0.893362\pi$
$29$	−1.00956	+	1.74861i	−0.187471	+	0.324710i	0.756935	+	0.653490i	$0.226696\pi$
$30$		0			0
$31$	−5.91069	+	5.91069i	−1.06159	+	1.06159i	−0.0636160	+	0.997974i	$0.520263\pi$
$31$	−5.91069	+	5.91069i	−1.06159	+	1.06159i	−0.997974	+	0.0636160i	$0.979737\pi$
$32$	−1.46081	+	5.45180i	−0.258236	+	0.963751i
$33$		0			0
$34$	−2.41098	−	2.41098i	−0.413480	−	0.413480i
$35$	−3.57390	+	0.525376i	−0.604100	+	0.0888048i
$36$		0			0
$37$	−2.84395	−	10.6138i	−0.467543	−	1.74489i	−0.648317	−	0.761370i	$-0.724527\pi$
$37$	−2.84395	−	10.6138i	−0.467543	−	1.74489i	0.180774	−	0.983525i	$-0.442140\pi$
$38$	−2.89730			−0.470004
$39$		0			0
$40$			3.08212i			0.487327i
$41$	1.08400	+	4.04553i	0.169292	+	0.631806i	0.997454	+	0.0713169i	$0.0227201\pi$
$41$	1.08400	+	4.04553i	0.169292	+	0.631806i	−0.828162	+	0.560489i	$0.810613\pi$
$42$		0			0
$43$	−0.669160	+	0.386339i	−0.102046	+	0.0589162i	−0.550154	−	0.835063i	$-0.685431\pi$
$43$	−0.669160	+	0.386339i	−0.102046	+	0.0589162i	0.448109	+	0.893979i	$0.352098\pi$
$44$	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	$-0.0515964\pi$
$47$	5.65938	+	5.65938i	0.825506	+	0.825506i	−0.161386	+	0.986891i	$0.551596\pi$
$48$		0			0
$49$	2.01452	+	6.70386i	0.287788	+	0.957694i
$50$	−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
$56$	5.90909	−	0.868657i	0.789635	−	0.116079i
$57$		0			0
$58$	0.326908	−	1.22004i	0.0429251	−	0.160199i
$59$	−3.87661	+	14.4677i	−0.504692	+	1.88354i	−0.0376705	+	0.999290i	$0.511994\pi$
$59$	−3.87661	+	14.4677i	−0.504692	+	1.88354i	−0.467022	+	0.884246i	$0.654673\pi$
$60$		0			0
$61$	0.210912	−	0.121770i	0.0270046	−	0.0155911i	−0.486437	−	0.873716i	$-0.661704\pi$
$61$	0.210912	−	0.121770i	0.0270046	−	0.0155911i	0.513442	+	0.858125i	$0.328370\pi$
$62$	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	0.0970245	−	0.995282i	$-0.469067\pi$
$67$	5.55533	−	1.48855i	0.678691	−	0.181855i	0.581667	+	0.813427i	$0.302401\pi$
$68$	−7.59354	−	4.38413i	−0.920852	−	0.531654i
$69$		0			0
$70$	2.07443	−	0.896088i	0.247942	−	0.107103i
$71$	0.711167	−	2.65411i	0.0844000	−	0.314985i	−0.910800	−	0.412848i	$-0.864534\pi$
$71$	0.711167	−	2.65411i	0.0844000	−	0.314985i	0.995200	+	0.0978630i	$0.0312007\pi$
$72$		0			0
$73$	2.17212	+	2.17212i	0.254228	+	0.254228i	0.822701	−	0.568474i	$-0.192466\pi$
$73$	2.17212	+	2.17212i	0.254228	+	0.254228i	−0.568474	+	0.822701i	$0.692466\pi$
$74$	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	0.272563	−	0.962138i	$-0.412129\pi$
$83$	11.2487	−	11.2487i	1.23470	−	1.23470i	0.962138	−	0.272563i	$-0.0878713\pi$
$84$		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	$-0.640529\pi$
$89$	−3.25716	+	0.872754i	−0.345259	+	0.0925118i	0.0820228	+	0.996630i	$0.473862\pi$
$90$		0			0
$91$	8.14751	−	4.96167i	0.854091	−	0.520124i
$92$	−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	$-0.251003\pi$
$97$	9.46128	+	2.53514i	0.960648	+	0.257405i	0.255773	+	0.966737i	$0.417670\pi$
$98$	−2.30264	−	3.72458i	−0.232602	−	0.376239i
$99$		0			0
$100$	−2.52232	−	4.36879i	−0.252232	−	0.436879i
$101$	1.30615	−	2.26231i	0.129966	−	0.225108i	−0.793697	−	0.608313i	$-0.791846\pi$
$101$	1.30615	−	2.26231i	0.129966	−	0.225108i	0.923663	+	0.383205i	$0.125180\pi$
$102$		0			0
$103$	−16.7503			−1.65046			−0.825230	−	0.564797i	$-0.808954\pi$
$103$	−16.7503			−1.65046			−0.825230	+	0.564797i	$0.808954\pi$
$104$	−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	0.437520	+	0.899209i	$0.355857\pi$
$107$	−5.79246	+	10.0328i	−0.559978	+	0.969910i	−0.997498	+	0.0707014i	$0.977476\pi$
$108$		0			0
$109$	3.99577	+	3.99577i	0.382725	+	0.382725i	0.872083	−	0.489358i	$-0.162769\pi$
$109$	3.99577	+	3.99577i	0.382725	+	0.382725i	−0.489358	+	0.872083i	$0.662769\pi$
$110$	−4.03874	−	1.08218i	−0.385079	−	0.103182i
$111$		0			0
$112$	4.38457	−	1.89399i	0.414303	−	0.178965i
$113$	−1.65445	−	2.86558i	−0.155637	−	0.269571i	0.777654	−	0.628693i	$-0.216410\pi$
$113$	−1.65445	−	2.86558i	−0.155637	−	0.269571i	−0.933291	+	0.359121i	$0.883076\pi$
$114$		0			0
$115$	−4.78566	+	1.28231i	−0.446265	+	0.119576i
$116$		−	3.24813i		−	0.301581i
$117$		0			0
$118$		−	9.36961i		−	0.862543i
$119$	−1.66680	+	14.3243i	−0.152796	+	1.31310i
$120$		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	0.991505	−	0.130071i	$-0.0415205\pi$
$127$	15.4911	+	8.94379i	1.37461	+	0.793633i	0.383108	+	0.923704i	$0.374854\pi$
$128$	−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
$133$	7.60530	+	9.60831i	0.659463	+	0.833146i
$134$	−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	0.346977	−	0.937874i	$-0.387208\pi$
$137$	2.08965	+	0.559921i	0.178531	+	0.0478373i	−0.168446	+	0.985711i	$0.553875\pi$
$138$		0			0
$139$	1.11782	−	0.645374i	0.0948124	−	0.0547399i	−0.451844	−	0.892097i	$-0.649234\pi$
$139$	1.11782	−	0.645374i	0.0948124	−	0.0547399i	0.546657	+	0.837357i	$0.315900\pi$
$140$	4.55643	−	3.60657i	0.385089	−	0.304811i
$141$		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	−0.951269	−	0.308363i	$-0.900219\pi$
$149$	0.326352	−	1.21796i	0.0267358	−	0.0997793i	0.978004	+	0.208584i	$0.0668854\pi$
$150$		0			0
$151$	5.35713	−	5.35713i	0.435957	−	0.435957i	−0.454692	−	0.890649i	$-0.650251\pi$
$151$	5.35713	−	5.35713i	0.435957	−	0.435957i	0.890649	+	0.454692i	$0.150251\pi$
$152$	9.05468	−	5.22772i	0.734431	−	0.424024i
$153$		0			0
$154$	−0.936497	+	8.04812i	−0.0754651	+	0.648536i
$155$		−	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
$161$	3.80724	+	8.81372i	0.300053	+	0.694618i
$162$		0			0
$163$	−11.3293	−	3.03568i	−0.887379	−	0.237773i	−0.213791	−	0.976879i	$-0.568581\pi$
$163$	−11.3293	−	3.03568i	−0.887379	−	0.237773i	−0.673588	+	0.739107i	$0.735248\pi$
$164$	−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	$-0.493623\pi$
$167$	6.94320	−	1.86042i	0.537281	−	0.143964i	0.517248	+	0.855835i	$0.326956\pi$
$168$		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	0.995441	+	0.0953789i	$0.0304063\pi$
$173$	7.63293	+	13.2206i	0.580321	+	1.00515i	−0.415120	+	0.909767i	$0.636260\pi$
$174$		0			0
$175$	−4.95107	+	6.65758i	−0.374266	+	0.503266i
$176$	−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	−0.465330	−	0.885137i	$-0.654065\pi$
$179$	−19.5943	−	11.3128i	−1.46455	−	0.845557i	−0.999216	+	0.0395805i	$0.987398\pi$
$180$		0			0
$181$	−1.46318			−0.108758			−0.0543788	−	0.998520i	$-0.517318\pi$
$181$	−1.46318			−0.108758			−0.0543788	+	0.998520i	$0.517318\pi$
$182$	−4.11972	+	4.31716i	−0.305374	+	0.320009i
$183$		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	0.931179	−	0.364561i	$-0.118781\pi$
$191$	2.07125	+	3.58751i	0.149870	+	0.259583i	−0.781309	+	0.624144i	$0.785448\pi$
$192$		0			0
$193$	0.316568	+	1.18145i	0.0227871	+	0.0850425i	0.976383	−	0.216047i	$-0.0693164\pi$
$193$	0.316568	+	1.18145i	0.0227871	+	0.0850425i	−0.953596	+	0.301089i	$0.902650\pi$
$194$	−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	0.162678	−	0.986679i	$-0.447987\pi$
$197$	11.1850	−	2.99702i	0.796901	−	0.213529i	0.634223	+	0.773150i	$0.281320\pi$
$198$		0			0
$199$	1.08128	+	1.87283i	0.0766498	+	0.132761i	0.901803	−	0.432148i	$-0.142244\pi$
$199$	1.08128	+	1.87283i	0.0766498	+	0.132761i	−0.825153	+	0.564910i	$0.808911\pi$
$200$	5.00563	+	5.00563i	0.353952	+	0.353952i
$201$		0			0
$202$	−0.422944	+	1.57845i	−0.0297583	+	0.111059i
$203$	−4.90412	+	2.11842i	−0.344202	+	0.148684i
$204$		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	0.366603	+	0.930378i	$0.380521\pi$
$211$	−9.04131	+	15.6600i	−0.622429	+	1.07808i	−0.989032	+	0.147701i	$0.952813\pi$
$212$	−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
$217$	−21.8806	+	3.21653i	−1.48535	+	0.218352i
$218$	−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	−0.856611	−	0.515963i	$-0.827434\pi$
$223$	−5.56628	−	20.7736i	−0.372746	−	1.39111i	0.483865	−	0.875142i	$-0.339232\pi$
$224$	−11.7089	+	9.26796i	−0.782331	+	0.619241i
$225$		0			0
$226$	1.46363	+	1.46363i	0.0973595	+	0.0973595i
$227$	−2.73398	−	0.732566i	−0.181460	−	0.0486221i	0.166945	−	0.985966i	$-0.446610\pi$
$227$	−2.73398	−	0.732566i	−0.181460	−	0.0486221i	−0.348405	+	0.937344i	$0.613277\pi$
$228$		0			0
$229$	−0.121782	−	0.121782i	−0.00804759	−	0.00804759i	0.703072	−	0.711119i	$-0.251811\pi$
$229$	−0.121782	−	0.121782i	−0.00804759	−	0.00804759i	−0.711119	+	0.703072i	$0.751811\pi$
$230$	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	$0.0922984\pi$
$233$			8.72869i			0.571835i	−0.958254	+	0.285918i	$0.907702\pi$
$234$		0			0
$235$	−10.9275			−0.712830
$236$	−6.23623	−	23.2739i	−0.405944	−	1.51500i
$237$		0			0
$238$	−1.31203	−	8.92515i	−0.0850462	−	0.578532i
$239$	15.9007	+	15.9007i	1.02853	+	1.02853i	0.999581	+	0.0289485i	$0.00921587\pi$
$239$	15.9007	+	15.9007i	1.02853	+	1.02853i	0.0289485	+	0.999581i	$0.490784\pi$
$240$		0			0
$241$	2.48430	−	9.27155i	0.160028	−	0.597233i	−0.838594	−	0.544757i	$-0.816622\pi$
$241$	2.48430	−	9.27155i	0.160028	−	0.597233i	0.998622	−	0.0524761i	$-0.0167113\pi$
$242$	5.73545	−	5.73545i	0.368689	−	0.368689i
$243$		0			0
$244$	−0.195890	+	0.339291i	−0.0125406	+	0.0217209i
$245$	−8.41699	−	4.52724i	−0.537742	−	0.289235i
$246$		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	$-0.224839\pi$
$251$	−2.87929	−	4.98708i	−0.181739	−	0.314782i	−0.942473	+	0.334282i	$0.891506\pi$
$252$		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	−0.272406	−	0.962182i	$-0.587819\pi$
$257$	11.1749	−	19.3555i	0.697071	−	1.20736i	0.969477	−	0.245181i	$-0.0788473\pi$
$258$		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	0.447382	+	0.894343i	$0.352357\pi$
$263$	−8.93301	+	15.4724i	−0.550833	+	0.954071i	−0.998215	+	0.0597277i	$0.980977\pi$
$264$		0			0
$265$	−6.49408	+	6.49408i	−0.398928	+	0.398928i
$266$	−6.15106	−	4.57438i	−0.377146	−	0.280473i
$267$		0			0
$268$	−6.54216	+	6.54216i	−0.399626	+	0.399626i
$269$	7.06977	−	4.08173i	0.431051	−	0.248868i	−0.268743	−	0.963212i	$-0.586608\pi$
$269$	7.06977	−	4.08173i	0.431051	−	0.248868i	0.699794	+	0.714344i	$0.253275\pi$
$270$		0			0
$271$	17.9820	−	4.81826i	1.09233	−	0.292688i	0.332691	−	0.943036i	$-0.392044\pi$
$271$	17.9820	−	4.81826i	1.09233	−	0.292688i	0.759637	+	0.650348i	$0.225377\pi$
$272$	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	−0.632846	−	0.774278i	$-0.718113\pi$
$277$	−4.63889	+	2.67826i	−0.278724	+	0.160921i	0.354122	+	0.935199i	$0.384780\pi$
$278$	−0.570942	+	0.570942i	−0.0342428	+	0.0342428i
$279$		0			0
$280$	−4.86619	+	6.54344i	−0.290810	+	0.391046i
$281$	11.1684	−	11.1684i	0.666249	−	0.666249i	−0.290597	−	0.956846i	$-0.593854\pi$
$281$	11.1684	−	11.1684i	0.666249	−	0.666249i	0.956846	+	0.290597i	$0.0938539\pi$
$282$		0			0
$283$	−10.7122	+	18.5541i	−0.636775	+	1.10293i	0.349361	+	0.936988i	$0.386399\pi$
$283$	−10.7122	+	18.5541i	−0.636775	+	1.10293i	−0.986136	+	0.165938i	$0.946935\pi$
$284$	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	$-0.868551\pi$
$293$	1.33426	−	4.97953i	0.0779484	−	0.290907i	0.993886	+	0.110414i	$0.0352177\pi$
$294$		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
$301$	−2.03061	−	0.236287i	−0.117043	−	0.0136193i
$302$	−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	−0.999672	−	0.0256108i	$-0.991847\pi$
$307$	−17.9644	−	17.9644i	−1.02528	−	1.02528i	−0.0256108	−	0.999672i	$-0.508153\pi$
$308$	3.03043	+	20.6147i	0.172675	+	1.17463i
$309$		0			0
$310$	1.84778	+	6.89602i	0.104947	+	0.391667i
$311$	−7.22402			−0.409637			−0.204818	−	0.978800i	$-0.565660\pi$
$311$	−7.22402			−0.409637			−0.204818	+	0.978800i	$0.565660\pi$
$312$		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	0.701263	−	0.712902i	$-0.252620\pi$
$317$	−0.207227	−	0.207227i	−0.0116390	−	0.0116390i	−0.712902	+	0.701263i	$0.752620\pi$
$318$		0			0
$319$	9.54790	+	2.55835i	0.534580	+	0.143240i
$320$	−0.0769727	−	0.0769727i	−0.00430291	−	0.00430291i
$321$		0			0
$322$	−3.72748	−	4.70919i	−0.207724	−	0.262433i
$323$	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
$329$	3.07977	+	20.9503i	0.169793	+	1.15503i
$330$		0			0
$331$	−3.35420	+	12.5180i	−0.184363	+	0.688054i	0.810403	+	0.585873i	$0.199248\pi$
$331$	−3.35420	+	12.5180i	−0.184363	+	0.688054i	−0.994766	+	0.102180i	$0.967418\pi$
$332$	−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	$-0.760529\pi$
$337$		−	25.0887i		−	1.36667i	0.730105	−	0.683335i	$-0.239471\pi$
$338$	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
$343$	−6.30746	+	17.4131i	−0.340571	+	0.940219i
$344$	−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	0.627649	−	0.778497i	$-0.284017\pi$
$347$	−6.71302	−	11.6273i	−0.360374	−	0.624185i	−0.988022	+	0.154311i	$0.950684\pi$
$348$		0			0
$349$	5.30405	−	1.42122i	0.283919	−	0.0760760i	−0.114049	−	0.993475i	$-0.536382\pi$
$349$	5.30405	−	1.42122i	0.283919	−	0.0760760i	0.397968	+	0.917399i	$0.369715\pi$
$350$	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	$-0.108133\pi$
$353$	−0.756952	−	2.82498i	−0.0402885	−	0.150359i	−0.983140	+	0.182855i	$0.941466\pi$
$354$		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	0.0420147	−	0.999117i	$-0.486622\pi$
$359$	19.7266	−	19.7266i	1.04113	−	1.04113i	0.999117	−	0.0420147i	$-0.0133776\pi$
$360$		0			0
$361$	2.12302	+	1.22573i	0.111738	+	0.0645120i
$362$	0.884114	−	0.236898i	0.0464680	−	0.0124511i
$363$		0			0
$364$	−7.35990	+	13.4658i	−0.385763	+	0.705798i
$365$	−4.19407			−0.219527
$366$		0			0
$367$	−14.4392	−	8.33648i	−0.753720	−	0.435161i	0.0733163	−	0.997309i	$-0.476642\pi$
$367$	−14.4392	−	8.33648i	−0.753720	−	0.435161i	−0.827037	+	0.562148i	$0.809975\pi$
$368$	5.67312	−	3.27538i	0.295732	−	0.170741i
$369$		0			0
$370$	−9.06508	−	2.42898i	−0.471271	−	0.126277i
$371$	14.2808	+	10.6203i	0.741422	+	0.551376i
$372$		0			0
$373$	17.1121	+	29.6390i	0.886030	+	1.53465i	0.844529	+	0.535511i	$0.179881\pi$
$373$	17.1121	+	29.6390i	0.886030	+	1.53465i	0.0415014	+	0.999138i	$0.486786\pi$
$374$	−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	−0.546057	−	0.837748i	$-0.683872\pi$
$379$	−11.6824	+	3.13028i	−0.600082	+	0.160792i	−0.0540253	+	0.998540i	$0.517205\pi$
$380$	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	$-0.739157\pi$
$383$	−32.0791	−	8.59556i	−1.63916	−	0.439213i	−0.956550	+	0.291567i	$0.905823\pi$
$384$		0			0
$385$	7.01271	+	16.2343i	0.357401	+	0.827378i
$386$	−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	$-0.774209\pi$
$389$		−	25.6927i		−	1.30267i	0.758789	−	0.651337i	$-0.225791\pi$
$390$		0			0
$391$			19.7790i			1.00027i
$392$	13.9166	+	7.48533i	0.702897	+	0.378066i
$393$		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	−0.848652	−	0.528952i	$-0.822585\pi$
$397$	3.00423	−	11.2120i	0.150778	−	0.562712i	0.999430	−	0.0337600i	$-0.0107482\pi$
$398$	−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	−0.850191	−	0.526475i	$-0.823513\pi$
$401$	−7.55225	−	28.1854i	−0.377141	−	1.40751i	0.473049	−	0.881036i	$-0.343153\pi$
$402$		0			0
$403$	11.7654	+	27.7474i	0.586075	+	1.38220i
$404$			4.20234i			0.209074i
$405$		0			0
$406$	2.62028	−	2.07404i	0.130042	−	0.102933i
$407$	−46.5862	+	26.8966i	−2.30919	+	1.33321i
$408$		0			0
$409$	2.36962	+	0.634939i	0.117170	+	0.0313957i	0.316928	−	0.948450i	$-0.397349\pi$
$409$	2.36962	+	0.634939i	0.117170	+	0.0313957i	−0.199757	+	0.979845i	$0.564015\pi$
$410$	3.45523	+	0.925827i	0.170642	+	0.0457233i
$411$		0			0
$412$	23.3359	−	13.4730i	1.14968	−	0.663766i
$413$	−31.0724	+	24.5948i	−1.52897	+	1.21023i
$414$		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	$-0.522957\pi$
$419$	−19.8935	−	11.4855i	−0.971861	−	0.561104i	−0.899803	+	0.436296i	$0.856290\pi$
$420$		0			0
$421$	1.61471	+	1.61471i	0.0786962	+	0.0786962i	0.745359	−	0.666663i	$-0.232278\pi$
$421$	1.61471	+	1.61471i	0.0786962	+	0.0786962i	−0.666663	+	0.745359i	$0.732278\pi$
$422$	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
$427$	0.640030	+	0.0744753i	0.0309732	+	0.00360411i
$428$		−	18.6364i		−	0.900826i
$429$		0			0
$430$			0.659934i			0.0318249i
$431$	−18.1238	+	4.85625i	−0.872991	+	0.233917i	−0.667381	−	0.744717i	$-0.732585\pi$
$431$	−18.1238	+	4.85625i	−0.872991	+	0.233917i	−0.205610	+	0.978634i	$0.565918\pi$
$432$		0			0
$433$	2.29346	+	3.97239i	0.110217	+	0.190901i	0.915858	−	0.401503i	$-0.131512\pi$
$433$	2.29346	+	3.97239i	0.110217	+	0.190901i	−0.805641	+	0.592404i	$0.798179\pi$
$434$	12.7004	−	5.48614i	0.609636	−	0.263343i
$435$		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	$-0.844691\pi$
$439$	−0.747446	+	1.29461i	−0.0356737	+	0.0617886i	0.847637	+	0.530576i	$0.178024\pi$
$440$	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
$448$	−0.125879	+	0.169267i	−0.00594724	+	0.00799711i
$449$	18.3337	+	4.91250i	0.865221	+	0.231835i	0.664020	−	0.747715i	$-0.268849\pi$
$449$	18.3337	+	4.91250i	0.865221	+	0.231835i	0.201201	+	0.979550i	$0.435516\pi$
$450$		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
$455$	−3.07571	+	12.6560i	−0.144191	+	0.593323i
$456$		0			0
$457$	9.41753	−	2.52342i	0.440533	−	0.118041i	−0.0317331	−	0.999496i	$-0.510103\pi$
$457$	9.41753	−	2.52342i	0.440533	−	0.118041i	0.472267	+	0.881456i	$0.343436\pi$
$458$	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	$-0.296313\pi$
$461$	15.3121	+	4.10288i	0.713157	+	0.191090i	0.116041	+	0.993244i	$0.462980\pi$
$462$		0			0
$463$	18.1402	−	18.1402i	0.843045	−	0.843045i	−0.146209	−	0.989254i	$-0.546707\pi$
$463$	18.1402	−	18.1402i	0.843045	−	0.843045i	0.989254	+	0.146209i	$0.0467071\pi$
$464$	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	$-0.620158\pi$
$467$	−15.9305			−0.737174			−0.368587	+	0.929593i	$0.620158\pi$
$468$		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
$476$	−9.19946	−	21.2966i	−0.421657	−	0.976130i
$477$		0			0
$478$	−12.1822	−	7.03341i	−0.557202	−	0.321701i
$479$	−8.19612	+	2.19614i	−0.374490	+	0.100344i	−0.441155	−	0.897431i	$-0.645431\pi$
$479$	−8.19612	+	2.19614i	−0.374490	+	0.100344i	0.0666644	+	0.997775i	$0.478764\pi$
$480$		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	−0.970571	−	0.240813i	$-0.922586\pi$
$487$	−0.212412	+	0.792734i	−0.00962533	+	0.0359222i	0.960946	+	0.276735i	$0.0892526\pi$
$488$	0.142292	−	0.531043i	0.00644128	−	0.0240392i
$489$		0			0
$490$	5.81886	+	1.37278i	0.262869	+	0.0620158i
$491$	28.7764	+	16.6141i	1.29866	+	0.749782i	0.980173	−	0.198145i	$-0.0634917\pi$
$491$	28.7764	+	16.6141i	1.29866	+	0.749782i	0.318488	+	0.947927i	$0.396825\pi$
$492$		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
$497$	5.70025	−	4.51194i	0.255691	−	0.202388i
$498$		0			0
$499$	−2.26621	−	2.26621i	−0.101449	−	0.101449i	0.654560	−	0.756010i	$-0.272854\pi$
$499$	−2.26621	−	2.26621i	−0.101449	−	0.101449i	−0.756010	+	0.654560i	$0.772854\pi$
$500$	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	$-0.741858\pi$
$503$	−9.09104	+	5.24871i	−0.405349	+	0.234028i	0.283440	+	0.958990i	$0.408524\pi$
$504$		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	0.999894	+	0.0145680i	$0.00463731\pi$
$509$	3.18662	+	11.8926i	0.141244	+	0.527131i	−0.858649	+	0.512563i	$0.828696\pi$
$510$		0			0
$511$	1.18204	+	8.04092i	0.0522905	+	0.355709i
$512$	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
$518$	−2.10200	+	18.0643i	−0.0923565	+	0.793698i
$519$		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	$-0.624552\pi$
$523$	−31.3912	−	18.1237i	−1.37264	−	0.792495i	−0.991260	+	0.131923i	$0.957885\pi$
$524$	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
$539$	29.1482	−	18.0203i	1.25550	−	0.776189i
$540$		0			0
$541$	15.3940	−	15.3940i	0.661840	−	0.661840i	−0.293974	−	0.955813i	$-0.594978\pi$
$541$	15.3940	−	15.3940i	0.661840	−	0.661840i	0.955813	+	0.293974i	$0.0949778\pi$
$542$	−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
$553$	17.8113	+	13.2458i	0.757412	+	0.563268i
$554$	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	0.946315	+	0.323247i	$0.104775\pi$
$557$	6.80662	+	25.4027i	0.288406	+	1.07634i	−0.657909	+	0.753098i	$0.728559\pi$
$558$		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	−0.637050	−	0.770822i	$-0.719846\pi$
$563$	−23.3973	−	40.5252i	−0.986077	−	1.70794i	−0.349027	−	0.937113i	$-0.613488\pi$
$564$		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	0.614282	−	0.789087i	$-0.289446\pi$
$569$	5.67847	+	3.27847i	0.238054	+	0.137441i	−0.376228	+	0.926527i	$0.622779\pi$
$570$		0			0
$571$			12.2503i			0.512659i	0.966590	+	0.256329i	$0.0825132\pi$
$571$			12.2503i			0.512659i	−0.966590	+	0.256329i	$0.917487\pi$
$572$	26.1421	−	11.0847i	1.09305	−	0.463474i
$573$		0			0
$574$	0.801194	−	6.88535i	0.0334412	−	0.287389i
$575$	−5.68973	+	9.85491i	−0.237278	+	0.410978i
$576$		0			0
$577$	25.5329	−	25.5329i	1.06295	−	1.06295i	0.0650684	−	0.997881i	$-0.479273\pi$
$577$	25.5329	−	25.5329i	1.06295	−	1.06295i	0.997881	−	0.0650684i	$-0.0207266\pi$
$578$	2.05765	−	7.67925i	0.0855869	−	0.319415i
$579$		0			0
$580$	3.13585	+	3.13585i	0.130209	+	0.130209i
$581$	41.6411	−	6.12139i	1.72756	−	0.253958i
$582$		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	$-0.134202\pi$
$587$	−1.99568	−	7.44800i	−0.0823707	−	0.307412i	−0.994803	+	0.101815i	$0.967535\pi$
$588$		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	$-0.305197\pi$
$593$	−5.94198	−	5.94198i	−0.244008	−	0.244008i	−0.818506	+	0.574498i	$0.805197\pi$
$594$		0			0
$595$	−12.2199	−	15.4383i	−0.500967	−	0.632907i
$596$	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	$-0.292968\pi$
$601$	5.37026	+	3.10052i	0.219058	+	0.126473i	−0.386456	+	0.922308i	$0.626301\pi$
$602$	1.26523	−	0.185994i	0.0515671	−	0.00758054i
$603$		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	$-0.813551\pi$
$607$	−19.0001	+	10.9697i	−0.771192	+	0.445248i	0.0621079	+	0.998069i	$0.480218\pi$
$608$	−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	−0.330073	−	0.943955i	$-0.607073\pi$
$613$	−3.56397	+	0.954962i	−0.143947	+	0.0385706i	0.186126	+	0.982526i	$0.440407\pi$
$614$	13.7633	+	7.94627i	0.555443	+	0.320685i
$615$		0			0
$616$	−11.5948	−	26.8418i	−0.467168	−	1.08149i
$617$	−1.16293	+	4.34013i	−0.0468180	+	0.174727i	−0.985376	−	0.170395i	$-0.945496\pi$
$617$	−1.16293	+	4.34013i	−0.0468180	+	0.174727i	0.938558	+	0.345122i	$0.112162\pi$
$618$		0			0
$619$	−6.43883	−	6.43883i	−0.258798	−	0.258798i	0.565767	−	0.824565i	$-0.308580\pi$
$619$	−6.43883	−	6.43883i	−0.258798	−	0.258798i	−0.824565	+	0.565767i	$0.808580\pi$
$620$	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	−0.264586	−	0.964362i	$-0.585235\pi$
$631$	−24.5144	−	6.56863i	−0.975905	−	0.261493i	−0.711319	+	0.702869i	$0.751902\pi$
$632$	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
$637$	25.1311	+	2.32985i	0.995730	+	0.0923121i
$638$	−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	−0.924625	−	0.380879i	$-0.875621\pi$
$641$	−26.7633	+	15.4518i	−1.05709	+	0.610309i	−0.132461	+	0.991188i	$0.542288\pi$
$642$		0			0
$643$	−22.1486	−	5.93469i	−0.873454	−	0.234041i	−0.205873	−	0.978579i	$-0.566004\pi$
$643$	−22.1486	−	5.93469i	−0.873454	−	0.234041i	−0.667581	+	0.744537i	$0.732670\pi$
$644$	−12.3933	−	9.21659i	−0.488365	−	0.363185i
$645$		0			0
$646$	−7.89601	−	13.6763i	−0.310664	−	0.538086i
$647$	9.66194	−	16.7350i	0.379850	−	0.657919i	−0.611190	−	0.791484i	$-0.709309\pi$
$647$	9.66194	−	16.7350i	0.379850	−	0.657919i	0.991040	+	0.133564i	$0.0426423\pi$
$648$		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	−0.994239	−	0.107189i	$-0.965815\pi$
$653$	−10.3312	+	17.8942i	−0.404291	+	0.700253i	0.589947	+	0.807442i	$0.299148\pi$
$654$		0			0
$655$	14.8618	+	14.8618i	0.580700	+	0.580700i
$656$	7.30306	+	1.95685i	0.285137	+	0.0764022i
$657$		0			0
$658$	−5.25289	−	12.1604i	−0.204779	−	0.474061i
$659$	−11.5048	−	19.9270i	−0.448165	−	0.776245i	0.550102	−	0.835098i	$-0.314589\pi$
$659$	−11.5048	−	19.9270i	−0.448165	−	0.776245i	−0.998267	+	0.0588532i	$0.981256\pi$
$660$		0			0
$661$	27.9076	−	7.47783i	1.08548	−	0.290854i	0.328642	−	0.944455i	$-0.393409\pi$
$661$	27.9076	−	7.47783i	1.08548	−	0.290854i	0.756839	+	0.653601i	$0.226743\pi$
$662$		−	8.10696i		−	0.315086i
$663$		0			0
$664$		−	35.9112i		−	1.39362i
$665$	−16.6186	−	1.93377i	−0.644440	−	0.0749884i
$666$		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	0.420876	−	0.907118i	$-0.361723\pi$
$673$	−4.00219	−	2.31066i	−0.154273	−	0.0890695i	−0.575149	+	0.818049i	$0.695056\pi$
$674$	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
$679$	16.0840	+	20.3201i	0.617247	+	0.779812i
$680$	−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	−0.286877	−	0.957967i	$-0.592617\pi$
$683$	−26.5081	−	7.10282i	−1.01430	−	0.271782i	−0.727426	+	0.686186i	$0.759284\pi$
$684$		0			0
$685$	−2.55798	+	1.47685i	−0.0977355	+	0.0564276i
$686$	0.991938	−	11.5429i	0.0378724	−	0.440710i
$687$		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	0.818289	+	0.574807i	$0.194923\pi$
$691$	10.4368	+	38.9506i	0.397033	+	1.48175i	−0.421255	+	0.906942i	$0.638410\pi$
$692$	−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
$700$	1.54266	−	13.2574i	0.0583071	−	0.501083i
$701$		−	17.7693i		−	0.671135i	−0.942016	−	0.335568i	$-0.891072\pi$
$701$		−	17.7693i		−	0.671135i	0.942016	−	0.335568i	$-0.108928\pi$
$702$		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
$707$	6.34482	−	2.74076i	0.238621	−	0.103077i
$708$		0			0
$709$	13.1479	+	3.52297i	0.493780	+	0.132308i	0.497112	−	0.867687i	$-0.334394\pi$
$709$	13.1479	+	3.52297i	0.493780	+	0.132308i	−0.00333188	+	0.999994i	$0.501061\pi$
$710$	−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	−0.999070	−	0.0431147i	$-0.986272\pi$
$719$	−14.3958	−	24.9343i	−0.536873	−	0.929892i	0.462197	−	0.886777i	$-0.347061\pi$
$720$		0			0
$721$	−35.5615	−	26.4461i	−1.32438	−	0.984905i
$722$	−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	$-0.730389\pi$
$727$	−35.7112			−1.32445			−0.662227	+	0.749303i	$0.730389\pi$
$728$	5.08537	−	20.9254i	0.188476	−	0.775548i
$729$		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	$-0.792441\pi$
$733$	−5.08991	+	5.08991i	−0.188000	+	0.188000i	0.606831	+	0.794831i	$0.292441\pi$
$734$	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	0.912439	−	0.409212i	$-0.134196\pi$
$739$	−2.23899	−	8.35601i	−0.0823624	−	0.307381i	−0.994802	+	0.101831i	$0.967530\pi$
$740$	−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	−0.261892	−	0.965097i	$-0.584347\pi$
$743$	−0.167623	+	0.0449143i	−0.00614947	+	0.00164775i	0.255743	+	0.966745i	$0.417680\pi$
$744$		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
$749$	−28.1378	+	12.1546i	−1.02813	+	0.444120i
$750$		0			0
$751$	5.40946	+	3.12315i	0.197394	+	0.113965i	0.595439	−	0.803400i	$-0.296978\pi$
$751$	5.40946	+	3.12315i	0.197394	+	0.113965i	−0.398045	+	0.917366i	$0.630311\pi$
$752$	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	−0.750372	−	0.661016i	$-0.770126\pi$
$757$	5.42762	−	9.40091i	0.197270	−	0.341682i	0.947642	+	0.319334i	$0.103459\pi$
$758$	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	0.798796	+	0.601602i	$0.205471\pi$
$761$	−5.34573	+	19.9505i	−0.193783	+	0.723206i	−0.992579	+	0.121604i	$0.961196\pi$
$762$		0			0
$763$	2.17445	+	14.7918i	0.0787204	+	0.535500i
$764$	−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	−0.956491	−	0.291760i	$-0.905759\pi$
$769$	−7.59897	−	28.3597i	−0.274026	−	1.02268i	0.682466	−	0.730918i	$-0.260908\pi$
$770$	−6.86579	−	8.67403i	−0.247426	−	0.312590i
$771$		0			0
$772$	−1.39132	−	1.39132i	−0.0500745	−	0.0500745i
$773$	−14.8539	−	3.98008i	−0.534257	−	0.143154i	−0.0184036	−	0.999831i	$-0.505858\pi$
$773$	−14.8539	−	3.98008i	−0.534257	−	0.143154i	−0.515853	+	0.856677i	$0.672525\pi$
$774$		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
$784$	12.2989	+	2.90154i	0.439246	+	0.103626i
$785$	−7.19500	−	7.19500i	−0.256801	−	0.256801i
$786$		0			0
$787$	−8.72193	+	32.5507i	−0.310903	+	1.16031i	0.616841	+	0.787088i	$0.288412\pi$
$787$	−8.72193	+	32.5507i	−0.310903	+	1.16031i	−0.927744	+	0.373218i	$0.878254\pi$
$788$	−13.1719	+	13.1719i	−0.469230	+	0.469230i
$789$		0			0
$790$	3.58270	−	6.20542i	0.127467	−	0.220779i
$791$	1.01187	−	8.69583i	0.0359778	−	0.309188i
$792$		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	$-0.253916\pi$
$797$	−7.64170	−	13.2358i	−0.270683	−	0.468837i	−0.969037	+	0.246916i	$0.920583\pi$
$798$		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	−0.338955	−	0.940803i	$-0.610073\pi$
$809$	18.3537	−	31.7895i	0.645282	−	1.11766i	0.984236	−	0.176858i	$-0.0565933\pi$
$810$		0			0
$811$	−15.9213	+	15.9213i	−0.559073	+	0.559073i	−0.929044	−	0.369970i	$-0.879368\pi$
$811$	−15.9213	+	15.9213i	−0.559073	+	0.559073i	0.369970	+	0.929044i	$0.379368\pi$
$812$	5.12828	−	6.89588i	0.179967	−	0.241998i
$813$		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	−0.703532	−	0.710664i	$-0.748395\pi$
$821$	−27.4347	+	7.35110i	−0.957477	+	0.256555i	−0.253945	+	0.967219i	$0.581728\pi$
$822$		0			0
$823$	44.7888	−	25.8588i	1.56124	−	0.901382i	0.564107	−	0.825702i	$-0.309221\pi$
$823$	44.7888	−	25.8588i	1.56124	−	0.901382i	0.997132	−	0.0756800i	$-0.0241127\pi$
$824$	−26.7376	+	26.7376i	−0.931448	+	0.931448i
$825$		0			0
$826$	14.7931	−	19.8920i	0.514719	−	0.692130i
$827$	5.62199	−	5.62199i	0.195496	−	0.195496i	−0.602570	−	0.798066i	$-0.705857\pi$
$827$	5.62199	−	5.62199i	0.195496	−	0.195496i	0.798066	+	0.602570i	$0.205857\pi$
$828$		0			0
$829$	9.16413	−	15.8727i	0.318284	−	0.551283i	−0.661846	−	0.749639i	$-0.730227\pi$
$829$	9.16413	−	15.8727i	0.318284	−	0.551283i	0.980130	+	0.198356i	$0.0635603\pi$
$830$	−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	−0.855475	−	0.517844i	$-0.826735\pi$
$839$	4.18001	−	15.6000i	0.144310	−	0.538572i	0.999785	−	0.0207282i	$-0.00659846\pi$
$840$		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
$847$	−34.0758	−	3.96513i	−1.17086	−	0.136243i
$848$	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	$-0.0220464\pi$
$853$	27.1149	+	27.1149i	0.928397	+	0.928397i	−0.0692053	+	0.997602i	$0.522046\pi$
$854$	−0.398789	+	0.0586234i	−0.0136463	+	0.00200605i
$855$		0			0
$856$	6.76866	+	25.2610i	0.231348	+	0.863403i
$857$	−39.5227			−1.35007			−0.675035	−	0.737785i	$-0.735872\pi$
$857$	−39.5227			−1.35007			−0.675035	+	0.737785i	$0.735872\pi$
$858$		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	0.956421	+	0.291991i	$0.0943176\pi$
$863$	36.6744	+	36.6744i	1.24841	+	1.24841i	0.291991	+	0.956421i	$0.405682\pi$
$864$		0			0
$865$	−20.1327	−	5.39453i	−0.684531	−	0.183420i
$866$	−2.02895	−	2.02895i	−0.0689466	−	0.0689466i
$867$		0			0
$868$	27.8960	−	22.0806i	0.946851	−	0.749464i
$869$	−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
$875$	−4.27440	−	29.0769i	−0.144501	−	0.982977i
$876$		0			0
$877$	4.12095	−	15.3796i	0.139155	−	0.519332i	−0.860792	−	0.508957i	$-0.830031\pi$
$877$	4.12095	−	15.3796i	0.139155	−	0.519332i	0.999946	−	0.0103742i	$-0.00330228\pi$
$878$	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	0.130668	+	0.991426i	$0.458288\pi$
$881$	−23.5454	+	40.7819i	−0.793266	+	1.37398i	−0.923934	+	0.382551i	$0.875046\pi$
$882$		0			0
$883$			25.4763i			0.857347i	0.903460	+	0.428673i	$0.141019\pi$
$883$			25.4763i			0.857347i	−0.903460	+	0.428673i	$0.858981\pi$
$884$	−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	$-0.115114\pi$
$887$	32.6585	+	18.8554i	1.09657	+	0.633103i	0.161249	+	0.986914i	$0.448448\pi$
$888$		0			0
$889$	18.7672	+	43.4459i	0.629433	+	1.45713i
$890$	−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	−0.406162	−	0.913801i	$-0.633133\pi$
$907$	−42.1816	−	24.3536i	−1.40062	−	0.808647i	−0.994456	+	0.105154i	$0.966467\pi$
$908$	4.39809	−	1.17847i	0.145956	−	0.0391088i
$909$		0			0
$910$	−0.190613	−	8.14523i	−0.00631876	−	0.270012i
$911$	−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
$917$	24.3047	−	32.6819i	0.802611	−	1.07925i
$918$		0			0
$919$	−22.9530	−	39.7557i	−0.757148	−	1.31142i	−0.944299	−	0.329088i	$-0.893259\pi$
$919$	−22.9530	−	39.7557i	−0.757148	−	1.31142i	0.187151	−	0.982331i	$-0.440075\pi$
$920$	−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	$-0.285292\pi$
$929$	23.6180	+	6.32841i	0.774880	+	0.207629i	0.150354	+	0.988632i	$0.451959\pi$
$930$		0			0
$931$	0.976272	+	32.4063i	0.0319960	+	1.06207i
$932$	−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	$0.940605\pi$
$938$	−9.45496	−	1.10020i	−0.308715	−	0.0359228i
$939$		0			0
$940$	15.2237	−	8.78942i	0.496543	−	0.286679i
$941$	31.2382	−	31.2382i	1.01834	−	1.01834i	0.0185076	−	0.999829i	$-0.494108\pi$
$941$	31.2382	−	31.2382i	1.01834	−	1.01834i	0.999829	−	0.0185076i	$-0.00589150\pi$
$942$		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	0.998679	+	0.0513927i	$0.0163660\pi$
$947$	4.90816	+	18.3175i	0.159494	+	0.595239i	−0.839185	+	0.543847i	$0.816967\pi$
$948$		0			0
$949$	10.1969	−	4.32367i	0.331005	−	0.140352i
$950$		−	9.08561i		−	0.294776i
$951$		0			0
$952$	20.2044	+	25.5256i	0.654828	+	0.827290i
$953$	−20.5939	+	11.8899i	−0.667103	+	0.385152i	−0.794978	−	0.606638i	$-0.792518\pi$
$953$	−20.5939	+	11.8899i	−0.667103	+	0.385152i	0.127875	+	0.991790i	$0.459184\pi$
$954$		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
$959$	3.55237	+	4.48796i	0.114712	+	0.144924i
$960$		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	0.777771	−	0.628548i	$-0.216350\pi$
$967$	4.64032	+	4.64032i	0.149223	+	0.149223i	−0.628548	+	0.777771i	$0.716350\pi$
$968$	−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	$-0.764056\pi$
$971$	−16.2568	+	9.38587i	−0.521706	+	0.301207i	0.215926	+	0.976410i	$0.430723\pi$
$972$		0			0
$973$	3.39211	+	0.394714i	0.108746	+	0.0126539i
$974$		−	0.513392i		−	0.0164501i
$975$		0			0
$976$		−	0.439644i		−	0.0140727i
$977$	17.6749	−	4.73598i	0.565471	−	0.151517i	0.0352523	−	0.999378i	$-0.488777\pi$
$977$	17.6749	−	4.73598i	0.565471	−	0.151517i	0.530219	+	0.847861i	$0.322110\pi$
$978$		0			0
$979$	8.25404	+	14.2964i	0.263800	+	0.456915i
$980$	15.3676	−	0.462966i	0.490901	−	0.0147889i
$981$		0			0
$982$	−20.0777	−	5.37982i	−0.640707	−	0.171677i
$983$	−31.0006	−	31.0006i	−0.988766	−	0.988766i	0.0111712	−	0.999938i	$-0.496444\pi$
$983$	−31.0006	−	31.0006i	−0.988766	−	0.988766i	−0.999938	+	0.0111712i	$0.996444\pi$
$984$		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	−0.218991	−	0.975727i	$-0.570277\pi$
$991$	23.1539	−	40.1038i	0.735509	−	1.27394i	0.954500	−	0.298212i	$-0.0963901\pi$
$992$	−23.5895	−	40.8582i	−0.748968	−	1.29725i
$993$		0			0
$994$	−2.71381	+	3.64919i	−0.0860768	+	0.115745i
$995$	−2.85199	−	0.764187i	−0.0904140	−	0.0242264i
$996$		0			0
$997$	−39.3257	+	22.7047i	−1.24546	+	0.719065i	−0.970200	−	0.242305i	$-0.922096\pi$
$997$	−39.3257	+	22.7047i	−1.24546	+	0.719065i	−0.275257	+	0.961371i	$0.588763\pi$
$998$	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.e.748.4		32
3.2	odd	2		273.2.by.d.202.5	yes	32
7.6	odd	2		819.2.fm.f.748.4		32
13.2	odd	12		819.2.fm.f.496.4		32
21.20	even	2		273.2.by.c.202.5	✓	32
39.2	even	12		273.2.by.c.223.5	yes	32
91.41	even	12	inner	819.2.fm.e.496.4		32
273.41	odd	12		273.2.by.d.223.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.202.5	✓	32	21.20	even	2
273.2.by.c.223.5	yes	32	39.2	even	12
273.2.by.d.202.5	yes	32	3.2	odd	2
273.2.by.d.223.5	yes	32	273.41	odd	12
819.2.fm.e.496.4		32	91.41	even	12	inner
819.2.fm.e.748.4		32	1.1	even	1	trivial
819.2.fm.f.496.4		32	13.2	odd	12
819.2.fm.f.748.4		32	7.6	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.604240 + 0.161906i) q^{2} +(-1.39316 + 0.804341i) q^{4} +(-0.965431 + 0.965431i) q^{5} +(2.12303 + 1.57884i) q^{7} +(1.59624 - 1.59624i) q^{8} +O(q^{10})\)	\(q+(-0.604240 + 0.161906i) q^{2} +(-1.39316 + 0.804341i) q^{4} +(-0.965431 + 0.965431i) q^{5} +(2.12303 + 1.57884i) q^{7} +(1.59624 - 1.59624i) q^{8} +(0.427043 - 0.739660i) q^{10} +(-1.26706 - 4.72873i) q^{11} +(1.35196 - 3.34249i) q^{13} +(-1.53844 - 0.610269i) q^{14} +(0.902609 - 1.56336i) q^{16} +(2.72530 + 4.72035i) q^{17} +(4.47375 + 1.19874i) q^{19} +(0.568463 - 2.12153i) q^{20} +(1.53121 + 2.65214i) q^{22} +(3.14262 + 1.81439i) q^{23} +3.13589i q^{25} +(-0.275740 + 2.23855i) q^{26} +(-4.22764 - 0.491938i) q^{28} +(-1.00956 + 1.74861i) q^{29} +(-5.91069 + 5.91069i) q^{31} +(-1.46081 + 5.45180i) q^{32} +(-2.41098 - 2.41098i) q^{34} +(-3.57390 + 0.525376i) q^{35} +(-2.84395 - 10.6138i) q^{37} -2.89730 q^{38} +3.08212i q^{40} +(1.08400 + 4.04553i) q^{41} +(-0.669160 + 0.386339i) q^{43} +(5.56872 + 5.56872i) q^{44} +(-2.19266 - 0.587521i) q^{46} +(5.65938 + 5.65938i) q^{47} +(2.01452 + 6.70386i) q^{49} +(-0.507717 - 1.89483i) q^{50} +(0.805003 + 5.74405i) q^{52} +6.72661 q^{53} +(5.78852 + 3.34200i) q^{55} +(5.90909 - 0.868657i) q^{56} +(0.326908 - 1.22004i) q^{58} +(-3.87661 + 14.4677i) q^{59} +(0.210912 - 0.121770i) q^{61} +(2.61450 - 4.52844i) q^{62} +0.0797289i q^{64} +(1.92172 + 4.53216i) q^{65} +(5.55533 - 1.48855i) q^{67} +(-7.59354 - 4.38413i) q^{68} +(2.07443 - 0.896088i) q^{70} +(0.711167 - 2.65411i) q^{71} +(2.17212 + 2.17212i) q^{73} +(3.43686 + 5.95281i) q^{74} +(-7.19684 + 1.92839i) q^{76} +(4.77591 - 12.0397i) q^{77} +8.38955 q^{79} +(0.637914 + 2.38073i) q^{80} +(-1.30999 - 2.26897i) q^{82} +(11.2487 - 11.2487i) q^{83} +(-7.18826 - 1.92609i) q^{85} +(0.341782 - 0.341782i) q^{86} +(-9.57073 - 5.52567i) q^{88} +(-3.25716 + 0.872754i) q^{89} +(8.14751 - 4.96167i) q^{91} -5.83756 q^{92} +(-4.33591 - 2.50334i) q^{94} +(-5.47640 + 3.16180i) q^{95} +(9.46128 + 2.53514i) q^{97} +(-2.30264 - 3.72458i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 2 q^{10} + 4 q^{11} + 6 q^{13} - 34 q^{14} + 14 q^{16} + 8 q^{17} + 2 q^{19} - 44 q^{20} - 4 q^{22} + 18 q^{23} + 28 q^{26} - 32 q^{28} + 18 q^{29} - 14 q^{31} + 8 q^{32} - 66 q^{34} - 22 q^{35} - 24 q^{37} - 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} + 28 q^{47} + 8 q^{49} - 70 q^{50} + 28 q^{52} + 80 q^{53} + 60 q^{55} + 54 q^{56} - 4 q^{58} + 42 q^{59} + 36 q^{61} - 52 q^{62} - 14 q^{65} + 26 q^{67} + 72 q^{68} - 116 q^{70} + 4 q^{71} + 12 q^{73} + 18 q^{74} - 48 q^{76} - 28 q^{77} - 4 q^{79} + 98 q^{80} + 20 q^{82} + 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} + 54 q^{89} + 148 q^{91} + 4 q^{92} - 60 q^{95} - 40 q^{97} - 36 q^{98}+O(q^{100}) \) 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 - 32 * q^28 + 18 * q^29 - 14 * q^31 + 8 * q^32 - 66 * q^34 - 22 * q^35 - 24 * q^37 - 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 + 28 * q^47 + 8 * q^49 - 70 * q^50 + 28 * q^52 + 80 * q^53 + 60 * q^55 + 54 * q^56 - 4 * q^58 + 42 * q^59 + 36 * q^61 - 52 * q^62 - 14 * q^65 + 26 * q^67 + 72 * q^68 - 116 * 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 + 148 * q^91 + 4 * q^92 - 60 * q^95 - 40 * q^97 - 36 * q^98

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