LMFDB - Embedded newform 819.2.et.b.136.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (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:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			136.4
Character	$\chi$	$=$	819.136
Dual form			819.2.et.b.271.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.193244 - 0.193244i) q^{2} +1.92531i q^{4} +(0.383199 - 1.43012i) q^{5} +(-2.15474 - 1.53528i) q^{7} +(0.758543 + 0.758543i) q^{8} +O(q^{10})$	\(q+(0.193244 - 0.193244i) q^{2} +1.92531i q^{4} +(0.383199 - 1.43012i) q^{5} +(-2.15474 - 1.53528i) q^{7} +(0.758543 + 0.758543i) q^{8} +(-0.202311 - 0.350412i) q^{10} +(-1.18808 + 4.43396i) q^{11} +(-2.80779 + 2.26193i) q^{13} +(-0.713075 + 0.119706i) q^{14} -3.55746 q^{16} -2.34163 q^{17} +(-1.63673 + 0.438561i) q^{19} +(2.75342 + 0.737778i) q^{20} +(0.627247 + 1.08642i) q^{22} +4.79276i q^{23} +(2.43173 + 1.40396i) q^{25} +(-0.105485 + 0.979692i) q^{26} +(2.95590 - 4.14855i) q^{28} +(2.87534 - 4.98024i) q^{29} +(-5.69764 + 1.52668i) q^{31} +(-2.20454 + 2.20454i) q^{32} +(-0.452505 + 0.452505i) q^{34} +(-3.02133 + 2.49321i) q^{35} +(6.03398 + 6.03398i) q^{37} +(-0.231540 + 0.401038i) q^{38} +(1.37548 - 0.794133i) q^{40} +(0.829479 - 0.222258i) q^{41} +(1.70069 - 0.981895i) q^{43} +(-8.53676 - 2.28742i) q^{44} +(0.926173 + 0.926173i) q^{46} +(-7.75739 - 2.07859i) q^{47} +(2.28581 + 6.61627i) q^{49} +(0.741225 - 0.198611i) q^{50} +(-4.35492 - 5.40588i) q^{52} +(-6.54133 + 11.3299i) q^{53} +(5.88581 + 3.39817i) q^{55} +(-0.469885 - 2.79904i) q^{56} +(-0.406759 - 1.51804i) q^{58} +(-1.09542 + 1.09542i) q^{59} +(-8.45262 - 4.88012i) q^{61} +(-0.806013 + 1.39606i) q^{62} -6.26289i q^{64} +(2.15888 + 4.88224i) q^{65} +(0.526925 + 0.141189i) q^{67} -4.50837i q^{68} +(-0.102055 + 1.06565i) q^{70} +(-1.77061 - 0.474435i) q^{71} +(-0.611552 - 2.28234i) q^{73} +2.33206 q^{74} +(-0.844368 - 3.15123i) q^{76} +(9.36737 - 7.72999i) q^{77} +(-2.13339 - 3.69514i) q^{79} +(-1.36321 + 5.08758i) q^{80} +(0.117342 - 0.203242i) q^{82} +(-3.88518 - 3.88518i) q^{83} +(-0.897309 + 3.34880i) q^{85} +(0.138903 - 0.518394i) q^{86} +(-4.26455 + 2.46214i) q^{88} +(9.92055 - 9.92055i) q^{89} +(9.52276 - 0.563113i) q^{91} -9.22757 q^{92} +(-1.90074 + 1.09739i) q^{94} +2.50878i q^{95} +(0.734114 - 2.73975i) q^{97} +(1.72027 + 0.836835i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8}+O(q^{10}) $ 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8	$ 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 6 q^{10} - 2 q^{11} + 20 q^{14} + 4 q^{16} + 12 q^{17} + 14 q^{19} - 36 q^{20} - 8 q^{22} - 24 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{31} - 10 q^{32} - 12 q^{34} + 20 q^{35} - 10 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{43} + 6 q^{44} + 24 q^{46} + 6 q^{47} - 50 q^{49} - 10 q^{50} - 26 q^{52} - 12 q^{53} + 6 q^{55} - 54 q^{56} - 46 q^{58} - 42 q^{59} + 30 q^{61} - 36 q^{62} - 28 q^{65} - 10 q^{67} - 88 q^{70} + 42 q^{71} + 40 q^{73} - 12 q^{74} - 52 q^{76} + 4 q^{79} - 30 q^{80} - 54 q^{82} - 66 q^{83} - 54 q^{85} + 18 q^{86} - 6 q^{88} + 26 q^{91} + 156 q^{92} - 18 q^{94} - 62 q^{97} + 56 q^{98}+O(q^{100}) $ 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8 - 6 * q^10 - 2 * q^11 + 20 * q^14 + 4 * q^16 + 12 * q^17 + 14 * q^19 - 36 * q^20 - 8 * q^22 - 24 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^31 - 10 * q^32 - 12 * q^34 + 20 * q^35 - 10 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^43 + 6 * q^44 + 24 * q^46 + 6 * q^47 - 50 * q^49 - 10 * q^50 - 26 * q^52 - 12 * q^53 + 6 * q^55 - 54 * q^56 - 46 * q^58 - 42 * q^59 + 30 * q^61 - 36 * q^62 - 28 * q^65 - 10 * q^67 - 88 * q^70 + 42 * q^71 + 40 * q^73 - 12 * q^74 - 52 * q^76 + 4 * q^79 - 30 * q^80 - 54 * q^82 - 66 * q^83 - 54 * q^85 + 18 * q^86 - 6 * q^88 + 26 * q^91 + 156 * q^92 - 18 * q^94 - 62 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.193244	−	0.193244i	0.136644	−	0.136644i	−0.635476	−	0.772120i	$-0.719196\pi$
$2$	0.193244	−	0.193244i	0.136644	−	0.136644i	0.772120	+	0.635476i	$0.219196\pi$
$3$		0			0
$3$		0			0
$4$			1.92531i			0.962657i
$5$	0.383199	−	1.43012i	0.171372	−	0.639568i	−0.825770	−	0.564008i	$-0.809259\pi$
$5$	0.383199	−	1.43012i	0.171372	−	0.639568i	0.997141	−	0.0755602i	$-0.0240745\pi$
$6$		0			0
$7$	−2.15474	−	1.53528i	−0.814415	−	0.580282i
$7$	−2.15474	−	1.53528i	−0.814415	−	0.580282i
$8$	0.758543	+	0.758543i	0.268186	+	0.268186i
$9$		0			0
$10$	−0.202311	−	0.350412i	−0.0639763	−	0.110810i
$11$	−1.18808	+	4.43396i	−0.358218	+	1.33689i	0.518168	+	0.855279i	$0.326614\pi$
$11$	−1.18808	+	4.43396i	−0.358218	+	1.33689i	−0.876386	+	0.481609i	$0.840052\pi$
$12$		0			0
$13$	−2.80779	+	2.26193i	−0.778741	+	0.627346i
$13$	−2.80779	+	2.26193i	−0.778741	+	0.627346i
$14$	−0.713075	+	0.119706i	−0.190577	+	0.0319929i
$15$		0			0
$16$	−3.55746			−0.889365
$17$	−2.34163			−0.567928			−0.283964	−	0.958835i	$-0.591650\pi$
$17$	−2.34163			−0.567928			−0.283964	+	0.958835i	$0.591650\pi$
$18$		0			0
$19$	−1.63673	+	0.438561i	−0.375492	+	0.100613i	−0.441629	−	0.897198i	$-0.645599\pi$
$19$	−1.63673	+	0.438561i	−0.375492	+	0.100613i	0.0661367	+	0.997811i	$0.478933\pi$
$20$	2.75342	+	0.737778i	0.615684	+	0.164972i
$21$		0			0
$22$	0.627247	+	1.08642i	0.133730	+	0.231626i
$23$			4.79276i			0.999360i	0.866210	+	0.499680i	$0.166549\pi$
$23$			4.79276i			0.999360i	−0.866210	+	0.499680i	$0.833451\pi$
$24$		0			0
$25$	2.43173	+	1.40396i	0.486347	+	0.280792i
$26$	−0.105485	+	0.979692i	−0.0206873	+	0.192133i
$27$		0			0
$28$	2.95590	−	4.14855i	0.558613	−	0.784002i
$29$	2.87534	−	4.98024i	0.533938	−	0.924808i	−0.465276	−	0.885166i	$-0.654045\pi$
$29$	2.87534	−	4.98024i	0.533938	−	0.924808i	0.999214	−	0.0396419i	$-0.0126217\pi$
$30$		0			0
$31$	−5.69764	+	1.52668i	−1.02333	+	0.274199i	−0.731187	−	0.682177i	$-0.761033\pi$
$31$	−5.69764	+	1.52668i	−1.02333	+	0.274199i	−0.292139	+	0.956376i	$0.594367\pi$
$32$	−2.20454	+	2.20454i	−0.389712	+	0.389712i
$33$		0			0
$34$	−0.452505	+	0.452505i	−0.0776040	+	0.0776040i
$35$	−3.02133	+	2.49321i	−0.510698	+	0.421430i
$36$		0			0
$37$	6.03398	+	6.03398i	0.991979	+	0.991979i	0.999968	−	0.00798866i	$-0.00254290\pi$
$37$	6.03398	+	6.03398i	0.991979	+	0.991979i	−0.00798866	+	0.999968i	$0.502543\pi$
$38$	−0.231540	+	0.401038i	−0.0375607	+	0.0650570i
$39$		0			0
$40$	1.37548	−	0.794133i	0.217482	−	0.125563i
$41$	0.829479	−	0.222258i	0.129543	−	0.0347109i	−0.193465	−	0.981107i	$-0.561973\pi$
$41$	0.829479	−	0.222258i	0.129543	−	0.0347109i	0.323008	+	0.946396i	$0.395306\pi$
$42$		0			0
$43$	1.70069	−	0.981895i	0.259353	−	0.149738i	−0.364686	−	0.931130i	$-0.618824\pi$
$43$	1.70069	−	0.981895i	0.259353	−	0.149738i	0.624039	+	0.781393i	$0.285490\pi$
$44$	−8.53676	−	2.28742i	−1.28696	−	0.344841i
$45$		0			0
$46$	0.926173	+	0.926173i	0.136557	+	0.136557i
$47$	−7.75739	−	2.07859i	−1.13153	−	0.303193i	−0.355990	−	0.934490i	$-0.615856\pi$
$47$	−7.75739	−	2.07859i	−1.13153	−	0.303193i	−0.775542	+	0.631297i	$0.782523\pi$
$48$		0			0
$49$	2.28581	+	6.61627i	0.326545	+	0.945182i
$50$	0.741225	−	0.198611i	0.104825	−	0.0280878i
$51$		0			0
$52$	−4.35492	−	5.40588i	−0.603918	−	0.749660i
$53$	−6.54133	+	11.3299i	−0.898521	+	1.55628i	−0.0691354	+	0.997607i	$0.522024\pi$
$53$	−6.54133	+	11.3299i	−0.898521	+	1.55628i	−0.829386	+	0.558677i	$0.811309\pi$
$54$		0			0
$55$	5.88581	+	3.39817i	0.793642	+	0.458210i
$56$	−0.469885	−	2.79904i	−0.0627911	−	0.374038i
$57$		0			0
$58$	−0.406759	−	1.51804i	−0.0534100	−	0.199329i
$59$	−1.09542	+	1.09542i	−0.142611	+	0.142611i	−0.774808	−	0.632197i	$-0.782153\pi$
$59$	−1.09542	+	1.09542i	−0.142611	+	0.142611i	0.632197	+	0.774808i	$0.282153\pi$
$60$		0			0
$61$	−8.45262	−	4.88012i	−1.08225	−	0.624836i	−0.150746	−	0.988573i	$-0.548167\pi$
$61$	−8.45262	−	4.88012i	−1.08225	−	0.624836i	−0.931502	+	0.363737i	$0.881501\pi$
$62$	−0.806013	+	1.39606i	−0.102364	+	0.177299i
$63$		0			0
$64$		−	6.26289i		−	0.782861i
$65$	2.15888	+	4.88224i	0.267776	+	0.605567i
$66$		0			0
$67$	0.526925	+	0.141189i	0.0643742	+	0.0172490i	0.290862	−	0.956765i	$-0.406058\pi$
$67$	0.526925	+	0.141189i	0.0643742	+	0.0172490i	−0.226488	+	0.974014i	$0.572724\pi$
$68$		−	4.50837i		−	0.546720i
$69$		0			0
$70$	−0.102055	+	1.06565i	−0.0121979	+	0.127370i
$71$	−1.77061	−	0.474435i	−0.210133	−	0.0563050i	0.152217	−	0.988347i	$-0.451359\pi$
$71$	−1.77061	−	0.474435i	−0.210133	−	0.0563050i	−0.362350	+	0.932042i	$0.618025\pi$
$72$		0			0
$73$	−0.611552	−	2.28234i	−0.0715768	−	0.267128i	0.920859	−	0.389897i	$-0.127489\pi$
$73$	−0.611552	−	2.28234i	−0.0715768	−	0.267128i	−0.992435	+	0.122769i	$0.960823\pi$
$74$	2.33206			0.271096
$75$		0			0
$76$	−0.844368	−	3.15123i	−0.0968557	−	0.361470i
$77$	9.36737	−	7.72999i	1.06751	−	0.880915i
$78$		0			0
$79$	−2.13339	−	3.69514i	−0.240025	−	0.415736i	0.720696	−	0.693251i	$-0.243822\pi$
$79$	−2.13339	−	3.69514i	−0.240025	−	0.415736i	−0.960721	+	0.277516i	$0.910489\pi$
$80$	−1.36321	+	5.08758i	−0.152412	+	0.568809i
$81$		0			0
$82$	0.117342	−	0.203242i	0.0129582	−	0.0224443i
$83$	−3.88518	−	3.88518i	−0.426454	−	0.426454i	0.460965	−	0.887419i	$-0.347504\pi$
$83$	−3.88518	−	3.88518i	−0.426454	−	0.426454i	−0.887419	+	0.460965i	$0.847504\pi$
$84$		0			0
$85$	−0.897309	+	3.34880i	−0.0973268	+	0.363228i
$86$	0.138903	−	0.518394i	0.0149783	−	0.0558998i
$87$		0			0
$88$	−4.26455	+	2.46214i	−0.454603	+	0.262465i
$89$	9.92055	−	9.92055i	1.05158	−	1.05158i	0.0529806	−	0.998596i	$-0.483128\pi$
$89$	9.92055	−	9.92055i	1.05158	−	1.05158i	0.998596	−	0.0529806i	$-0.0168721\pi$
$90$		0			0
$91$	9.52276	−	0.563113i	0.998256	−	0.0590303i
$92$	−9.22757			−0.962041
$93$		0			0
$94$	−1.90074	+	1.09739i	−0.196047	+	0.113188i
$95$			2.50878i			0.257395i
$96$		0			0
$97$	0.734114	−	2.73975i	0.0745380	−	0.278180i	−0.918590	−	0.395212i	$-0.870671\pi$
$97$	0.734114	−	2.73975i	0.0745380	−	0.278180i	0.993128	+	0.117032i	$0.0373380\pi$
$98$	1.72027	+	0.836835i	0.173774	+	0.0845331i
$99$		0			0
$100$	−2.70307	+	4.68185i	−0.270307	+	0.468185i
$101$	5.32015	+	9.21476i	0.529374	+	0.916903i	0.999413	+	0.0342575i	$0.0109066\pi$
$101$	5.32015	+	9.21476i	0.529374	+	0.916903i	−0.470039	+	0.882646i	$0.655760\pi$
$102$		0			0
$103$	8.60773	+	14.9090i	0.848145	+	1.46903i	0.882862	+	0.469633i	$0.155614\pi$
$103$	8.60773	+	14.9090i	0.848145	+	1.46903i	−0.0347173	+	0.999397i	$0.511053\pi$
$104$	−3.84560	−	0.414061i	−0.377092	−	0.0406020i
$105$		0			0
$106$	0.925366	+	3.45351i	0.0898794	+	0.335435i
$107$	4.05690			0.392195			0.196097	−	0.980584i	$-0.437173\pi$
$107$	4.05690			0.392195			0.196097	+	0.980584i	$0.437173\pi$
$108$		0			0
$109$	−2.05022	−	7.65154i	−0.196376	−	0.732885i	−0.991906	−	0.126971i	$-0.959474\pi$
$109$	−2.05022	−	7.65154i	−0.196376	−	0.732885i	0.795531	−	0.605914i	$-0.207192\pi$
$110$	1.79407	−	0.480721i	0.171058	−	0.0458349i
$111$		0			0
$112$	7.66540	+	5.46171i	0.724312	+	0.516083i
$113$	9.23138	+	15.9892i	0.868415	+	1.50414i	0.863616	+	0.504150i	$0.168194\pi$
$113$	9.23138	+	15.9892i	0.868415	+	1.50414i	0.00479920	+	0.999988i	$0.498472\pi$
$114$		0			0
$115$	6.85421	+	1.83658i	0.639159	+	0.171262i
$116$	9.58853	+	5.53594i	0.890272	+	0.513999i
$117$		0			0
$118$			0.423366i			0.0389740i
$119$	5.04560	+	3.59506i	0.462529	+	0.329559i
$120$		0			0
$121$	−8.72217	−	5.03575i	−0.792925	−	0.457795i
$122$	−2.57647	+	0.690364i	−0.233263	+	0.0625026i
$123$		0			0
$124$	−2.93933	−	10.9697i	−0.263960	−	0.985112i
$125$	8.17426	−	8.17426i	0.731128	−	0.731128i
$126$		0			0
$127$	−2.52084	−	1.45541i	−0.223689	−	0.129147i	0.383968	−	0.923346i	$-0.374557\pi$
$127$	−2.52084	−	1.45541i	−0.223689	−	0.129147i	−0.607657	+	0.794200i	$0.707890\pi$
$128$	−5.61935	−	5.61935i	−0.496685	−	0.496685i
$129$		0			0
$130$	1.36065	+	0.526273i	0.119337	+	0.0461572i
$131$	8.58252	−	4.95512i	0.749858	−	0.432931i	−0.0757847	−	0.997124i	$-0.524146\pi$
$131$	8.58252	−	4.95512i	0.749858	−	0.432931i	0.825643	+	0.564194i	$0.190813\pi$
$132$		0			0
$133$	4.20005	+	1.56786i	0.364191	+	0.135951i
$134$	0.129109	−	0.0745412i	0.0111533	−	0.00643938i
$135$		0			0
$136$	−1.77623	−	1.77623i	−0.152310	−	0.152310i
$137$	0.385142	+	0.385142i	0.0329049	+	0.0329049i	0.723368	−	0.690463i	$-0.242593\pi$
$137$	0.385142	+	0.385142i	0.0329049	+	0.0329049i	−0.690463	+	0.723368i	$0.742593\pi$
$138$		0			0
$139$	3.32499	−	1.91968i	0.282022	−	0.162825i	−0.352317	−	0.935881i	$-0.614606\pi$
$139$	3.32499	−	1.91968i	0.282022	−	0.162825i	0.634338	+	0.773056i	$0.281273\pi$
$140$	−4.80022	−	5.81700i	−0.405692	−	0.491627i
$141$		0			0
$142$	−0.433842	+	0.250479i	−0.0364072	+	0.0210197i
$143$	−6.69342	−	15.1370i	−0.559732	−	1.26582i
$144$		0			0
$145$	−6.02050	−	6.02050i	−0.499975	−	0.499975i
$146$	−0.559228	−	0.322870i	−0.0462820	−	0.0267210i
$147$		0			0
$148$	−11.6173	+	11.6173i	−0.954936	+	0.954936i
$149$	−6.05379	−	22.5930i	−0.495946	−	1.85089i	−0.524668	−	0.851307i	$-0.675811\pi$
$149$	−6.05379	−	22.5930i	−0.495946	−	1.85089i	0.0287228	−	0.999587i	$-0.490856\pi$
$150$		0			0
$151$	6.36774	−	1.70623i	0.518200	−	0.138851i	0.00976596	−	0.999952i	$-0.496891\pi$
$151$	6.36774	−	1.70623i	0.518200	−	0.138851i	0.508434	+	0.861101i	$0.330225\pi$
$152$	−1.57420	−	0.908865i	−0.127685	−	0.0737187i
$153$		0			0
$154$	0.316413	−	3.30396i	0.0254973	−	0.266241i
$155$			8.73331i			0.701476i
$156$		0			0
$157$	9.49287	+	5.48071i	0.757613	+	0.437408i	0.828438	−	0.560081i	$-0.189230\pi$
$157$	9.49287	+	5.48071i	0.757613	+	0.437408i	−0.0708249	+	0.997489i	$0.522563\pi$
$158$	−1.12633	−	0.301799i	−0.0896058	−	0.0240098i
$159$		0			0
$160$	2.30798	+	3.99754i	0.182462	+	0.316033i
$161$	7.35825	−	10.3272i	0.579911	−	0.813894i
$162$		0			0
$163$	−3.73496	+	1.00078i	−0.292544	+	0.0783870i	−0.402106	−	0.915593i	$-0.631722\pi$
$163$	−3.73496	+	1.00078i	−0.292544	+	0.0783870i	0.109562	+	0.993980i	$0.465055\pi$
$164$	0.427917	+	1.59701i	0.0334147	+	0.124705i
$165$		0			0
$166$	−1.50158			−0.116545
$167$	6.30900	+	23.5455i	0.488205	+	1.82201i	0.565172	+	0.824973i	$0.308810\pi$
$167$	6.30900	+	23.5455i	0.488205	+	1.82201i	−0.0769673	+	0.997034i	$0.524524\pi$
$168$		0			0
$169$	2.76737	−	12.7020i	0.212875	−	0.977079i
$170$	0.473736	+	0.820535i	0.0363339	+	0.0629322i
$171$		0			0
$172$	1.89046	+	3.27436i	0.144146	+	0.249668i
$173$	2.39991	−	4.15677i	0.182462	−	0.316033i	−0.760257	−	0.649623i	$-0.774927\pi$
$173$	2.39991	−	4.15677i	0.182462	−	0.316033i	0.942718	+	0.333590i	$0.108260\pi$
$174$		0			0
$175$	−3.08427	−	6.75857i	−0.233149	−	0.510900i
$176$	4.22653	−	15.7736i	0.318587	−	1.18898i
$177$		0			0
$178$		−	3.83417i		−	0.287383i
$179$	9.64786	−	5.57019i	0.721115	−	0.416336i	−0.0940481	−	0.995568i	$-0.529981\pi$
$179$	9.64786	−	5.57019i	0.721115	−	0.416336i	0.815163	+	0.579232i	$0.196647\pi$
$180$		0			0
$181$	4.32449			0.321437			0.160718	−	0.987000i	$-0.448619\pi$
$181$	4.32449			0.321437			0.160718	+	0.987000i	$0.448619\pi$
$182$	1.73140	−	1.94903i	0.128340	−	0.144472i
$183$		0			0
$184$	−3.63552	+	3.63552i	−0.268014	+	0.268014i
$185$	10.9415	−	6.31708i	0.804435	−	0.464441i
$186$		0			0
$187$	2.78203	−	10.3827i	0.203442	−	0.759256i
$188$	4.00193	−	14.9354i	0.291871	−	1.08928i
$189$		0			0
$190$	0.484806	+	0.484806i	0.0351715	+	0.0351715i
$191$	−3.15973	+	5.47282i	−0.228630	+	0.395999i	−0.957402	−	0.288757i	$-0.906758\pi$
$191$	−3.15973	+	5.47282i	−0.228630	+	0.395999i	0.728772	+	0.684756i	$0.240091\pi$
$192$		0			0
$193$	3.08313	−	11.5064i	0.221929	−	0.828250i	−0.761683	−	0.647950i	$-0.775627\pi$
$193$	3.08313	−	11.5064i	0.221929	−	0.828250i	0.983612	−	0.180300i	$-0.0577068\pi$
$194$	−0.387577	−	0.671304i	−0.0278264	−	0.0481968i
$195$		0			0
$196$	−12.7384	+	4.40091i	−0.909886	+	0.314351i
$197$	0.533499	+	1.99105i	0.0380103	+	0.141856i	0.982323	−	0.187192i	$-0.0599387\pi$
$197$	0.533499	+	1.99105i	0.0380103	+	0.141856i	−0.944313	+	0.329048i	$0.893272\pi$
$198$		0			0
$199$	−18.5628			−1.31588			−0.657942	−	0.753068i	$-0.728573\pi$
$199$	−18.5628			−1.31588			−0.657942	+	0.753068i	$0.728573\pi$
$200$	0.779609	+	2.90954i	0.0551267	+	0.205736i
$201$		0			0
$202$	2.80878	+	0.752611i	0.197625	+	0.0529536i
$203$	−13.8417	+	6.31666i	−0.971497	+	0.443343i
$204$		0			0
$205$		−	1.27142i		−	0.0887999i
$206$	4.54447	+	1.21769i	0.316628	+	0.0848403i
$207$		0			0
$208$	9.98860	−	8.04671i	0.692585	−	0.557939i
$209$		−	7.77825i		−	0.538033i
$210$		0			0
$211$	−1.40368	+	2.43124i	−0.0966332	+	0.167374i	−0.910289	−	0.413973i	$-0.864141\pi$
$211$	−1.40368	+	2.43124i	−0.0966332	+	0.167374i	0.813656	+	0.581347i	$0.197474\pi$
$212$	−21.8136	−	12.5941i	−1.49817	−	0.864967i
$213$		0			0
$214$	0.783971	−	0.783971i	0.0535911	−	0.0535911i
$215$	−0.752522	−	2.80845i	−0.0513216	−	0.191535i
$216$		0			0
$217$	14.6208	+	5.45789i	0.992525	+	0.370506i
$218$	−1.87481	−	1.08242i	−0.126978	−	0.0733108i
$219$		0			0
$220$	−6.54255	+	11.3320i	−0.441099	+	0.764005i
$221$	6.57480	−	5.29659i	0.442269	−	0.356287i
$222$		0			0
$223$	−15.6678	+	4.19816i	−1.04919	+	0.281130i	−0.741917	−	0.670491i	$-0.766083\pi$
$223$	−15.6678	+	4.19816i	−1.04919	+	0.281130i	−0.307274	+	0.951621i	$0.599417\pi$
$224$	8.13482	−	1.36562i	0.543530	−	0.0912444i
$225$		0			0
$226$	4.87373	+	1.30591i	0.324196	+	0.0868679i
$227$	−1.24111	−	1.24111i	−0.0823752	−	0.0823752i	0.664719	−	0.747094i	$-0.268551\pi$
$227$	−1.24111	−	1.24111i	−0.0823752	−	0.0823752i	−0.747094	+	0.664719i	$0.768551\pi$
$228$		0			0
$229$	10.7645	+	2.88434i	0.711338	+	0.190602i	0.596304	−	0.802759i	$-0.296635\pi$
$229$	10.7645	+	2.88434i	0.711338	+	0.190602i	0.115034	+	0.993362i	$0.463302\pi$
$230$	1.67944	−	0.969627i	0.110739	−	0.0639353i
$231$		0			0
$232$	5.95880	−	1.59666i	0.391214	−	0.104826i
$233$	−17.6370	+	10.1827i	−1.15544	+	0.667091i	−0.950206	−	0.311623i	$-0.899128\pi$
$233$	−17.6370	+	10.1827i	−1.15544	+	0.667091i	−0.205230	+	0.978714i	$0.565794\pi$
$234$		0			0
$235$	−5.94525	+	10.2975i	−0.387825	+	0.671733i
$236$	−2.10902	−	2.10902i	−0.137286	−	0.137286i
$237$		0			0
$238$	1.66976	−	0.280308i	0.108234	−	0.0181697i
$239$	−14.6160	+	14.6160i	−0.945430	+	0.945430i	−0.998586	−	0.0531558i	$-0.983072\pi$
$239$	−14.6160	+	14.6160i	−0.945430	+	0.945430i	0.0531558	+	0.998586i	$0.483072\pi$
$240$		0			0
$241$	10.0956	−	10.0956i	0.650314	−	0.650314i	−0.302755	−	0.953069i	$-0.597906\pi$
$241$	10.0956	−	10.0956i	0.650314	−	0.650314i	0.953069	+	0.302755i	$0.0979063\pi$
$242$	−2.65863	+	0.712379i	−0.170904	+	0.0457935i
$243$		0			0
$244$	9.39577	−	16.2740i	0.601503	−	1.04183i
$245$	10.3380	−	0.733634i	0.660468	−	0.0468702i
$246$		0			0
$247$	3.60361	−	4.93356i	0.229292	−	0.313915i
$248$	−5.47995	−	3.16385i	−0.347977	−	0.200905i
$249$		0			0
$250$		−	3.15925i		−	0.199809i
$251$	3.24540	+	5.62120i	0.204848	+	0.354807i	0.950084	−	0.311993i	$-0.100997\pi$
$251$	3.24540	+	5.62120i	0.204848	+	0.354807i	−0.745236	+	0.666801i	$0.767663\pi$
$252$		0			0
$253$	−21.2509	−	5.69416i	−1.33603	−	0.357989i
$254$	−0.768387	+	0.205889i	−0.0482129	+	0.0129186i
$255$		0			0
$256$	10.3540			0.647123
$257$	22.1961			1.38455			0.692277	−	0.721632i	$-0.256608\pi$
$257$	22.1961			1.38455			0.692277	+	0.721632i	$0.256608\pi$
$258$		0			0
$259$	−3.73779	−	22.2655i	−0.232255	−	1.38351i
$260$	−9.39984	+	4.15652i	−0.582953	+	0.257776i
$261$		0			0
$262$	0.700973	−	2.61607i	0.0433062	−	0.161621i
$263$	5.05320	+	8.75240i	0.311594	+	0.539696i	0.978708	−	0.205260i	$-0.0658039\pi$
$263$	5.05320	+	8.75240i	0.311594	+	0.539696i	−0.667114	+	0.744956i	$0.732471\pi$
$264$		0			0
$265$	13.6965	+	13.6965i	0.841368	+	0.841368i
$266$	1.11461	−	0.508655i	0.0683414	−	0.0311876i
$267$		0			0
$268$	−0.271834	+	1.01450i	−0.0166049	+	0.0619702i
$269$			10.3582i			0.631552i	0.948834	+	0.315776i	$0.102265\pi$
$269$			10.3582i			0.631552i	−0.948834	+	0.315776i	$0.897735\pi$
$270$		0			0
$271$	−2.31182	+	2.31182i	−0.140433	+	0.140433i	−0.773828	−	0.633395i	$-0.781661\pi$
$271$	−2.31182	+	2.31182i	−0.140433	+	0.140433i	0.633395	+	0.773828i	$0.281661\pi$
$272$	8.33024			0.505095
$273$		0			0
$274$	0.148853			0.00899252
$275$	−9.11419	+	9.11419i	−0.549606	+	0.549606i
$276$		0			0
$277$			16.6626i			1.00116i	0.865690	+	0.500580i	$0.166880\pi$
$277$			16.6626i			1.00116i	−0.865690	+	0.500580i	$0.833120\pi$
$278$	0.271567	−	1.01350i	0.0162875	−	0.0607857i
$279$		0			0
$280$	−4.18302	−	0.400598i	−0.249983	−	0.0239403i
$281$	−8.02095	−	8.02095i	−0.478490	−	0.478490i	0.426159	−	0.904648i	$-0.359866\pi$
$281$	−8.02095	−	8.02095i	−0.478490	−	0.478490i	−0.904648	+	0.426159i	$0.859866\pi$
$282$		0			0
$283$	7.22018	+	12.5057i	0.429195	+	0.743388i	0.996802	−	0.0799119i	$-0.0254639\pi$
$283$	7.22018	+	12.5057i	0.429195	+	0.743388i	−0.567607	+	0.823300i	$0.692131\pi$
$284$	0.913435	−	3.40899i	0.0542024	−	0.202286i
$285$		0			0
$286$	−4.21859	−	1.63166i	−0.249450	−	0.0964823i
$287$	−2.12854	−	0.794576i	−0.125644	−	0.0469023i
$288$		0			0
$289$	−11.5168			−0.677458
$290$	−2.32685			−0.136637
$291$		0			0
$292$	4.39423	−	1.17743i	0.257153	−	0.0689039i
$293$	−15.9091	−	4.26283i	−0.929420	−	0.249037i	−0.237812	−	0.971311i	$-0.576430\pi$
$293$	−15.9091	−	4.26283i	−0.929420	−	0.249037i	−0.691607	+	0.722274i	$0.743097\pi$
$294$		0			0
$295$	1.14681	+	1.98634i	0.0667701	+	0.115649i
$296$			9.15406i			0.532069i
$297$		0			0
$298$	−5.53583	−	3.19611i	−0.320682	−	0.185146i
$299$	−10.8409	−	13.4571i	−0.626944	−	0.778243i
$300$		0			0
$301$	−5.17204	−	0.495314i	−0.298111	−	0.0285494i
$302$	0.900809	−	1.56025i	0.0518357	−	0.0897821i
$303$		0			0
$304$	5.82261	−	1.56016i	0.333950	−	0.0894816i
$305$	−10.2182	+	10.2182i	−0.585092	+	0.585092i
$306$		0			0
$307$	−8.27574	+	8.27574i	−0.472322	+	0.472322i	−0.902665	−	0.430344i	$-0.858392\pi$
$307$	−8.27574	+	8.27574i	−0.472322	+	0.472322i	0.430344	+	0.902665i	$0.358392\pi$
$308$	14.8827	+	18.0351i	0.848018	+	1.02765i
$309$		0			0
$310$	1.68766	+	1.68766i	0.0958526	+	0.0958526i
$311$	−6.45124	+	11.1739i	−0.365816	+	0.633612i	−0.988907	−	0.148538i	$-0.952543\pi$
$311$	−6.45124	+	11.1739i	−0.365816	+	0.633612i	0.623091	+	0.782150i	$0.285877\pi$
$312$		0			0
$313$	5.16307	−	2.98090i	0.291834	−	0.168490i	−0.346935	−	0.937889i	$-0.612777\pi$
$313$	5.16307	−	2.98090i	0.291834	−	0.168490i	0.638769	+	0.769399i	$0.279444\pi$
$314$	2.89355	−	0.775325i	0.163293	−	0.0437541i
$315$		0			0
$316$	7.11430	−	4.10744i	0.400211	−	0.231062i
$317$	12.4965	+	3.34843i	0.701873	+	0.188066i	0.592070	−	0.805887i	$-0.298311\pi$
$317$	12.4965	+	3.34843i	0.701873	+	0.188066i	0.109804	+	0.993953i	$0.464978\pi$
$318$		0			0
$319$	18.6660	+	18.6660i	1.04510	+	1.04510i
$320$	−8.95667	−	2.39993i	−0.500693	−	0.134160i
$321$		0			0
$322$	−0.573725	−	3.41760i	−0.0319724	−	0.190455i
$323$	3.83262	−	1.02695i	0.213253	−	0.0571409i
$324$		0			0
$325$	−10.0035	+	1.55837i	−0.554892	+	0.0864429i
$326$	−0.528363	+	0.915152i	−0.0292633	+	0.0506856i
$327$		0			0
$328$	0.797788	+	0.460603i	0.0440505	+	0.0254325i
$329$	13.5239	+	16.3886i	0.745599	+	0.903533i
$330$		0			0
$331$	−2.58639	−	9.65252i	−0.142161	−	0.530551i	−0.999865	−	0.0164080i	$-0.994777\pi$
$331$	−2.58639	−	9.65252i	−0.142161	−	0.530551i	0.857705	−	0.514142i	$-0.171890\pi$
$332$	7.48019	−	7.48019i	0.410529	−	0.410529i
$333$		0			0
$334$	5.76920	+	3.33085i	0.315677	+	0.182256i
$335$	0.403834	−	0.699462i	0.0220638	−	0.0382157i
$336$		0			0
$337$			17.5327i			0.955069i	0.878613	+	0.477534i	$0.158469\pi$
$337$			17.5327i			0.955069i	−0.878613	+	0.477534i	$0.841531\pi$
$338$	−1.91981	−	2.98937i	−0.104424	−	0.162600i
$339$		0			0
$340$	−6.44749	−	1.72760i	−0.349664	−	0.0936923i
$341$		−	27.0769i		−	1.46630i
$342$		0			0
$343$	5.23251	−	17.7657i	0.282529	−	0.959259i
$344$	2.03486	+	0.545238i	0.109712	+	0.0293973i
$345$		0			0
$346$	−0.339502	−	1.26704i	−0.0182517	−	0.0681164i
$347$	26.2542			1.40940			0.704700	−	0.709506i	$-0.251082\pi$
$347$	26.2542			1.40940			0.704700	+	0.709506i	$0.251082\pi$
$348$		0			0
$349$	2.90133	+	10.8279i	0.155304	+	0.579604i	0.999079	+	0.0429064i	$0.0136617\pi$
$349$	2.90133	+	10.8279i	0.155304	+	0.579604i	−0.843775	+	0.536698i	$0.819672\pi$
$350$	−1.90207	−	0.710035i	−0.101670	−	0.0379530i
$351$		0			0
$352$	−7.15569	−	12.3940i	−0.381399	−	0.660603i
$353$	−1.81273	+	6.76519i	−0.0964817	+	0.360075i	−0.997240	−	0.0742463i	$-0.976345\pi$
$353$	−1.81273	+	6.76519i	−0.0964817	+	0.360075i	0.900758	+	0.434321i	$0.143012\pi$
$354$		0			0
$355$	−1.35699	+	2.35038i	−0.0720218	+	0.124745i
$356$	19.1002	+	19.1002i	1.01231	+	1.01231i
$357$		0			0
$358$	0.787984	−	2.94080i	0.0416463	−	0.155426i
$359$	−1.32297	+	4.93737i	−0.0698234	+	0.260585i	−0.992010	−	0.126161i	$-0.959734\pi$
$359$	−1.32297	+	4.93737i	−0.0698234	+	0.260585i	0.922186	+	0.386746i	$0.126401\pi$
$360$		0			0
$361$	−13.9679	+	8.06438i	−0.735154	+	0.424441i
$362$	0.835682	−	0.835682i	0.0439225	−	0.0439225i
$363$		0			0
$364$	1.08417	+	18.3343i	0.0568259	+	0.960978i
$365$	−3.49837			−0.183113
$366$		0			0
$367$	15.9153	−	9.18868i	0.830770	−	0.479645i	−0.0233461	−	0.999727i	$-0.507432\pi$
$367$	15.9153	−	9.18868i	0.830770	−	0.479645i	0.854116	+	0.520082i	$0.174099\pi$
$368$		−	17.0501i		−	0.888796i
$369$		0			0
$370$	0.893642	−	3.33512i	0.0464582	−	0.173385i
$371$	31.4895	−	14.3702i	1.63485	−	0.746066i
$372$		0			0
$373$	−10.4260	+	18.0583i	−0.539837	+	0.935025i	0.459075	+	0.888397i	$0.348181\pi$
$373$	−10.4260	+	18.0583i	−0.539837	+	0.935025i	−0.998912	+	0.0466277i	$0.985153\pi$
$374$	−1.46878	−	2.54400i	−0.0759487	−	0.131547i
$375$		0			0
$376$	−4.30762	−	7.46101i	−0.222148	−	0.384772i
$377$	3.19158	+	20.4873i	0.164375	+	1.05515i
$378$		0			0
$379$	7.22021	+	26.9462i	0.370877	+	1.38413i	0.859276	+	0.511512i	$0.170914\pi$
$379$	7.22021	+	26.9462i	0.370877	+	1.38413i	−0.488399	+	0.872620i	$0.662419\pi$
$380$	−4.83018			−0.247783
$381$		0			0
$382$	0.446990	+	1.66819i	0.0228700	+	0.0853520i
$383$	−23.7412	+	6.36142i	−1.21312	+	0.325054i	−0.807984	−	0.589204i	$-0.799441\pi$
$383$	−23.7412	+	6.36142i	−1.21312	+	0.325054i	−0.405132	+	0.914258i	$0.632775\pi$
$384$		0			0
$385$	−7.46523	−	16.3586i	−0.380464	−	0.833710i
$386$	−1.62775	−	2.81934i	−0.0828502	−	0.143501i
$387$		0			0
$388$	5.27488	+	1.41340i	0.267792	+	0.0717545i
$389$	−21.2079	−	12.2444i	−1.07528	−	0.620815i	−0.145663	−	0.989334i	$-0.546532\pi$
$389$	−21.2079	−	12.2444i	−1.07528	−	0.620815i	−0.929620	+	0.368519i	$0.879865\pi$
$390$		0			0
$391$		−	11.2229i		−	0.567565i
$392$	−3.28484	+	6.75262i	−0.165909	+	0.341059i
$393$		0			0
$394$	0.487853	+	0.281662i	0.0245777	+	0.0141899i
$395$	−6.10199	+	1.63502i	−0.307025	+	0.0822670i
$396$		0			0
$397$	−5.01142	−	18.7029i	−0.251516	−	0.938671i	−0.969996	−	0.243122i	$-0.921828\pi$
$397$	−5.01142	−	18.7029i	−0.251516	−	0.938671i	0.718480	−	0.695548i	$-0.244838\pi$
$398$	−3.58716	+	3.58716i	−0.179808	+	0.179808i
$399$		0			0
$400$	−8.65079	−	4.99454i	−0.432539	−	0.249727i
$401$	9.35345	+	9.35345i	0.467089	+	0.467089i	0.900970	−	0.433881i	$-0.142856\pi$
$401$	9.35345	+	9.35345i	0.467089	+	0.467089i	−0.433881	+	0.900970i	$0.642856\pi$
$402$		0			0
$403$	12.5445	−	17.1742i	0.624888	−	0.855509i
$404$	−17.7413	+	10.2430i	−0.882663	+	0.509606i
$405$		0			0
$406$	−1.45417	+	3.89548i	−0.0721691	+	0.193330i
$407$	−33.9232	+	19.5856i	−1.68151	+	0.970821i
$408$		0			0
$409$	17.6086	+	17.6086i	0.870691	+	0.870691i	0.992548	−	0.121857i	$-0.0388848\pi$
$409$	17.6086	+	17.6086i	0.870691	+	0.870691i	−0.121857	+	0.992548i	$0.538885\pi$
$410$	−0.245694	−	0.245694i	−0.0121340	−	0.0121340i
$411$		0			0
$412$	−28.7045	+	16.5726i	−1.41417	+	0.816472i
$413$	4.04212	−	0.678566i	0.198900	−	0.0333900i
$414$		0			0
$415$	−7.04506	+	4.06747i	−0.345828	+	0.199664i
$416$	1.20338	−	11.1764i	0.0590006	−	0.547969i
$417$		0			0
$418$	−1.50310	−	1.50310i	−0.0735190	−	0.0735190i
$419$	−13.9899	−	8.07708i	−0.683452	−	0.394591i	0.117703	−	0.993049i	$-0.462447\pi$
$419$	−13.9899	−	8.07708i	−0.683452	−	0.394591i	−0.801154	+	0.598458i	$0.795780\pi$
$420$		0			0
$421$	−12.8050	+	12.8050i	−0.624080	+	0.624080i	−0.946572	−	0.322492i	$-0.895479\pi$
$421$	−12.8050	+	12.8050i	−0.624080	+	0.624080i	0.322492	+	0.946572i	$0.395479\pi$
$422$	0.198570	+	0.741075i	0.00966626	+	0.0360750i
$423$		0			0
$424$	−13.5561	+	3.63235i	−0.658343	+	0.176403i
$425$	−5.69421	−	3.28755i	−0.276210	−	0.159470i
$426$		0			0
$427$	10.7208	+	23.4926i	0.518818	+	1.13689i
$428$			7.81080i			0.377549i
$429$		0			0
$430$	−0.688136	−	0.397296i	−0.0331849	−	0.0191593i
$431$	21.5984	+	5.78727i	1.04036	+	0.278763i	0.738261	−	0.674515i	$-0.235647\pi$
$431$	21.5984	+	5.78727i	1.04036	+	0.278763i	0.302096	+	0.953278i	$0.402314\pi$
$432$		0			0
$433$	−9.21467	−	15.9603i	−0.442829	−	0.767002i	0.555069	−	0.831804i	$-0.312692\pi$
$433$	−9.21467	−	15.9603i	−0.442829	−	0.767002i	−0.997898	+	0.0648019i	$0.979358\pi$
$434$	3.88009	−	1.77068i	0.186250	−	0.0849953i
$435$		0			0
$436$	14.7316	−	3.94732i	0.705517	−	0.189043i
$437$	−2.10192	−	7.84448i	−0.100549	−	0.375252i
$438$		0			0
$439$	−15.6000			−0.744546			−0.372273	−	0.928123i	$-0.621421\pi$
$439$	−15.6000			−0.744546			−0.372273	+	0.928123i	$0.621421\pi$
$440$	1.88698	+	7.04230i	0.0899582	+	0.335729i
$441$		0			0
$442$	0.247006	−	2.29407i	0.0117489	−	0.109118i
$443$	−14.7949	−	25.6255i	−0.702926	−	1.21750i	−0.967435	−	0.253120i	$-0.918543\pi$
$443$	−14.7949	−	25.6255i	−0.702926	−	1.21750i	0.264509	−	0.964383i	$-0.414790\pi$
$444$		0			0
$445$	−10.3860	−	17.9891i	−0.492344	−	0.852765i
$446$	−2.21643	+	3.83897i	−0.104951	+	0.181781i
$447$		0			0
$448$	−9.61531	+	13.4949i	−0.454280	+	0.637574i
$449$	2.50811	−	9.36041i	0.118365	−	0.441745i	−0.881151	−	0.472834i	$-0.843231\pi$
$449$	2.50811	−	9.36041i	0.118365	−	0.441745i	0.999517	+	0.0310893i	$0.00989763\pi$
$450$		0			0
$451$			3.94193i			0.185618i
$452$	−30.7843	+	17.7733i	−1.44797	+	0.835986i
$453$		0			0
$454$	−0.479673			−0.0225122
$455$	2.84379	−	13.8344i	0.133319	−	0.648569i
$456$		0			0
$457$	24.5102	−	24.5102i	1.14654	−	1.14654i	0.159312	−	0.987228i	$-0.449073\pi$
$457$	24.5102	−	24.5102i	1.14654	−	1.14654i	0.987228	−	0.159312i	$-0.0509275\pi$
$458$	2.63756	−	1.52279i	0.123245	−	0.0711555i
$459$		0			0
$460$	−3.53599	+	13.1965i	−0.164867	+	0.615291i
$461$	−2.45042	+	9.14508i	−0.114127	+	0.425929i	−0.999220	−	0.0394858i	$-0.987428\pi$
$461$	−2.45042	+	9.14508i	−0.114127	+	0.425929i	0.885093	+	0.465414i	$0.154095\pi$
$462$		0			0
$463$	3.59580	+	3.59580i	0.167111	+	0.167111i	0.785708	−	0.618597i	$-0.212299\pi$
$463$	3.59580	+	3.59580i	0.167111	+	0.167111i	−0.618597	+	0.785708i	$0.712299\pi$
$464$	−10.2289	+	17.7170i	−0.474866	+	0.822491i
$465$		0			0
$466$	−1.44049	+	5.37598i	−0.0667294	+	0.249038i
$467$	12.0623	+	20.8926i	0.558179	+	0.966794i	0.997649	+	0.0685368i	$0.0218331\pi$
$467$	12.0623	+	20.8926i	0.558179	+	0.966794i	−0.439470	+	0.898257i	$0.644834\pi$
$468$		0			0
$469$	−0.918622	−	1.11321i	−0.0424180	−	0.0514031i
$470$	0.841041	+	3.13881i	0.0387943	+	0.144782i
$471$		0			0
$472$	−1.66184			−0.0764926
$473$	2.33313	+	8.70736i	0.107277	+	0.400365i
$474$		0			0
$475$	−4.59582	−	1.23145i	−0.210871	−	0.0565027i
$476$	−6.92162	+	9.71436i	−0.317252	+	0.445257i
$477$		0			0
$478$			5.64891i			0.258375i
$479$	23.6619	+	6.34020i	1.08114	+	0.289691i	0.755063	−	0.655652i	$-0.227606\pi$
$479$	23.6619	+	6.34020i	1.08114	+	0.289691i	0.326078	+	0.945343i	$0.394273\pi$
$480$		0			0
$481$	−30.5905	−	3.29373i	−1.39481	−	0.150181i
$482$		−	3.90182i		−	0.177723i
$483$		0			0
$484$	9.69539	−	16.7929i	0.440700	−	0.763314i
$485$	−3.63686	−	2.09974i	−0.165141	−	0.0953443i
$486$		0			0
$487$	−27.0263	+	27.0263i	−1.22468	+	1.22468i	−0.258727	+	0.965951i	$0.583303\pi$
$487$	−27.0263	+	27.0263i	−1.22468	+	1.22468i	−0.965951	+	0.258727i	$0.916697\pi$
$488$	−2.70989	−	10.1135i	−0.122671	−	0.457815i
$489$		0			0
$490$	1.85598	−	2.13952i	0.0838446	−	0.0966537i
$491$	−10.2155	−	5.89793i	−0.461020	−	0.266170i	0.251453	−	0.967869i	$-0.419092\pi$
$491$	−10.2155	−	5.89793i	−0.461020	−	0.266170i	−0.712473	+	0.701700i	$0.752425\pi$
$492$		0			0
$493$	−6.73298	+	11.6619i	−0.303238	+	0.525224i
$494$	−0.257005	−	1.64976i	−0.0115632	−	0.0742261i
$495$		0			0
$496$	20.2691	−	5.43109i	0.910110	−	0.243863i
$497$	3.08682	+	3.74068i	0.138463	+	0.167792i
$498$		0			0
$499$	−14.7901	−	3.96298i	−0.662094	−	0.177408i	−0.0879031	−	0.996129i	$-0.528017\pi$
$499$	−14.7901	−	3.96298i	−0.662094	−	0.177408i	−0.574191	+	0.818722i	$0.694683\pi$
$500$	15.7380	+	15.7380i	0.703825	+	0.703825i
$501$		0			0
$502$	1.71342	+	0.459109i	0.0764736	+	0.0204910i
$503$	−21.5683	+	12.4524i	−0.961682	+	0.555227i	−0.896690	−	0.442659i	$-0.854035\pi$
$503$	−21.5683	+	12.4524i	−0.961682	+	0.555227i	−0.0649915	+	0.997886i	$0.520702\pi$
$504$		0			0
$505$	15.2169	−	4.07735i	0.677142	−	0.181440i
$506$	−5.20697	+	3.00625i	−0.231478	+	0.133644i
$507$		0			0
$508$	2.80212	−	4.85341i	0.124324	−	0.215335i
$509$	−23.6813	−	23.6813i	−1.04966	−	1.04966i	−0.998701	−	0.0509546i	$-0.983774\pi$
$509$	−23.6813	−	23.6813i	−1.04966	−	1.04966i	−0.0509546	−	0.998701i	$-0.516226\pi$
$510$		0			0
$511$	−2.18631	+	5.85677i	−0.0967165	+	0.259088i
$512$	13.2395	−	13.2395i	0.585111	−	0.585111i
$513$		0			0
$514$	4.28926	−	4.28926i	0.189191	−	0.189191i
$515$	24.6201	−	6.59694i	1.08489	−	0.290696i
$516$		0			0
$517$	18.4327	−	31.9264i	0.810670	−	1.40412i
$518$	−5.02498	−	3.58037i	−0.220785	−	0.157312i
$519$		0			0
$520$	−2.06579	+	5.34099i	−0.0905907	+	0.234218i
$521$	−19.8845	−	11.4803i	−0.871155	−	0.502962i	−0.00342331	−	0.999994i	$-0.501090\pi$
$521$	−19.8845	−	11.4803i	−0.871155	−	0.502962i	−0.867732	+	0.497032i	$0.834423\pi$
$522$		0			0
$523$			3.37998i			0.147796i	0.997266	+	0.0738980i	$0.0235439\pi$
$523$			3.37998i			0.147796i	−0.997266	+	0.0738980i	$0.976456\pi$
$524$	9.54015	+	16.5240i	0.416764	+	0.721856i
$525$		0			0
$526$	2.66785	+	0.714848i	0.116324	+	0.0311688i
$527$	13.3417	−	3.57491i	0.581175	−	0.155725i
$528$		0			0
$529$	0.0294194			0.00127910
$530$	5.29353			0.229936
$531$		0			0
$532$	−3.01863	+	8.08642i	−0.130874	+	0.350591i
$533$	−1.82627	+	2.50027i	−0.0791046	+	0.108299i
$534$		0			0
$535$	1.55460	−	5.80184i	0.0672111	−	0.250835i
$536$	0.292598	+	0.506794i	0.0126383	+	0.0218902i
$537$		0			0
$538$	2.00167	+	2.00167i	0.0862979	+	0.0862979i
$539$	−32.0520	+	2.27457i	−1.38058	+	0.0979726i
$540$		0			0
$541$	−8.32634	+	31.0743i	−0.357977	+	1.33599i	0.518719	+	0.854945i	$0.326409\pi$
$541$	−8.32634	+	31.0743i	−0.357977	+	1.33599i	−0.876696	+	0.481044i	$0.840258\pi$
$542$			0.893492i			0.0383788i
$543$		0			0
$544$	5.16222	−	5.16222i	0.221328	−	0.221328i
$545$	−11.7282			−0.502383
$546$		0			0
$547$	−13.1782			−0.563460			−0.281730	−	0.959494i	$-0.590908\pi$
$547$	−13.1782			−0.563460			−0.281730	+	0.959494i	$0.590908\pi$
$548$	−0.741519	+	0.741519i	−0.0316761	+	0.0316761i
$549$		0			0
$550$			3.52252i			0.150201i
$551$	−2.52203	+	9.41234i	−0.107442	+	0.400979i
$552$		0			0
$553$	−1.07618	+	11.2374i	−0.0457639	+	0.477864i
$554$	3.21995	+	3.21995i	0.136803	+	0.136803i
$555$		0			0
$556$	3.69599	+	6.40164i	0.156745	+	0.271490i
$557$	1.05682	−	3.94410i	0.0447788	−	0.167117i	−0.939916	−	0.341407i	$-0.889097\pi$
$557$	1.05682	−	3.94410i	0.0447788	−	0.167117i	0.984694	+	0.174290i	$0.0557632\pi$
$558$		0			0
$559$	−2.55421	+	6.60379i	−0.108032	+	0.279311i
$560$	10.7483	−	8.86951i	0.454197	−	0.374805i
$561$		0			0
$562$	−3.10000			−0.130766
$563$	−20.4603			−0.862298			−0.431149	−	0.902281i	$-0.641892\pi$
$563$	−20.4603			−0.862298			−0.431149	+	0.902281i	$0.641892\pi$
$564$		0			0
$565$	26.4039	−	7.07491i	1.11082	−	0.297644i
$566$	3.81191	+	1.02140i	0.160227	+	0.0429326i
$567$		0			0
$568$	−0.983208	−	1.70297i	−0.0412545	−	0.0714549i
$569$		−	9.24906i		−	0.387741i	−0.981027	−	0.193870i	$-0.937896\pi$
$569$		−	9.24906i		−	0.387741i	0.981027	−	0.193870i	$-0.0621041\pi$
$570$		0			0
$571$	35.2658	+	20.3607i	1.47583	+	0.852069i	0.999628	−	0.0272690i	$-0.00868107\pi$
$571$	35.2658	+	20.3607i	1.47583	+	0.852069i	0.476198	+	0.879338i	$0.342014\pi$
$572$	29.1434	−	12.8869i	1.21855	−	0.538830i
$573$		0			0
$574$	−0.564875	+	0.257781i	−0.0235774	+	0.0107596i
$575$	−6.72885	+	11.6547i	−0.280613	+	0.486035i
$576$		0			0
$577$	10.5574	−	2.82885i	0.439511	−	0.117767i	−0.0322762	−	0.999479i	$-0.510276\pi$
$577$	10.5574	−	2.82885i	0.439511	−	0.117767i	0.471788	+	0.881712i	$0.343609\pi$
$578$	−2.22555	+	2.22555i	−0.0925706	+	0.0925706i
$579$		0			0
$580$	11.5914	−	11.5914i	0.481305	−	0.481305i
$581$	2.40670	+	14.3364i	0.0998469	+	0.594774i
$582$		0			0
$583$	−42.4648	−	42.4648i	−1.75871	−	1.75871i
$584$	1.26737	−	2.19515i	0.0524441	−	0.0908358i
$585$		0			0
$586$	−3.89810	+	2.25057i	−0.161029	+	0.0929703i
$587$	−15.6037	+	4.18099i	−0.644033	+	0.172568i	−0.566029	−	0.824385i	$-0.691521\pi$
$587$	−15.6037	+	4.18099i	−0.644033	+	0.172568i	−0.0780032	+	0.996953i	$0.524854\pi$
$588$		0			0
$589$	8.65597	−	4.99753i	0.356663	−	0.205920i
$590$	0.605463	+	0.162233i	0.0249265	+	0.00667904i
$591$		0			0
$592$	−21.4656	−	21.4656i	−0.882232	−	0.882232i
$593$	44.6856	+	11.9735i	1.83502	+	0.491691i	0.998423	−	0.0561324i	$-0.0178769\pi$
$593$	44.6856	+	11.9735i	1.83502	+	0.491691i	0.836594	+	0.547824i	$0.184544\pi$
$594$		0			0
$595$	7.07482	−	5.83818i	0.290040	−	0.239342i
$596$	43.4987	−	11.6554i	1.78178	−	0.477425i
$597$		0			0
$598$	−4.69543	−	0.505564i	−0.192011	−	0.0206741i
$599$	−5.89887	+	10.2171i	−0.241021	+	0.417461i	−0.961005	−	0.276529i	$-0.910816\pi$
$599$	−5.89887	+	10.2171i	−0.241021	+	0.417461i	0.719984	+	0.693990i	$0.244149\pi$
$600$		0			0
$601$	11.5727	+	6.68152i	0.472062	+	0.272545i	0.717102	−	0.696968i	$-0.245468\pi$
$601$	11.5727	+	6.68152i	0.472062	+	0.272545i	−0.245041	+	0.969513i	$0.578801\pi$
$602$	−1.09518	+	0.903748i	−0.0446363	+	0.0368340i
$603$		0			0
$604$	3.28503	+	12.2599i	0.133666	+	0.498848i
$605$	−10.5440	+	10.5440i	−0.428676	+	0.428676i
$606$		0			0
$607$	29.5465	+	17.0587i	1.19926	+	0.692392i	0.960390	−	0.278660i	$-0.0898904\pi$
$607$	29.5465	+	17.0587i	1.19926	+	0.692392i	0.238868	+	0.971052i	$0.423224\pi$
$608$	2.64142	−	4.57508i	0.107124	−	0.185544i
$609$		0			0
$610$			3.94921i			0.159899i
$611$	26.4827	−	11.7104i	1.07138	−	0.473753i
$612$		0			0
$613$	3.92990	+	1.05301i	0.158727	+	0.0425308i	0.337307	−	0.941395i	$-0.390484\pi$
$613$	3.92990	+	1.05301i	0.158727	+	0.0425308i	−0.178580	+	0.983925i	$0.557150\pi$
$614$			3.19847i			0.129080i
$615$		0			0
$616$	12.9691	+	1.24202i	0.522540	+	0.0500424i
$617$	17.7169	+	4.74724i	0.713257	+	0.191117i	0.597161	−	0.802121i	$-0.296295\pi$
$617$	17.7169	+	4.74724i	0.713257	+	0.191117i	0.116096	+	0.993238i	$0.462962\pi$
$618$		0			0
$619$	−9.38547	−	35.0270i	−0.377234	−	1.40786i	−0.850053	−	0.526697i	$-0.823430\pi$
$619$	−9.38547	−	35.0270i	−0.377234	−	1.40786i	0.472820	−	0.881159i	$-0.343236\pi$
$620$	−16.8144			−0.675281
$621$		0			0
$622$	0.912620	+	3.40595i	0.0365927	+	0.136566i
$623$	−36.6071	+	6.14536i	−1.46663	+	0.246209i
$624$		0			0
$625$	−1.53798	−	2.66385i	−0.0615191	−	0.106554i
$626$	0.421691	−	1.57377i	0.0168542	−	0.0629006i
$627$		0			0
$628$	−10.5521	+	18.2767i	−0.421074	+	0.729321i
$629$	−14.1293	−	14.1293i	−0.563373	−	0.563373i
$630$		0			0
$631$	6.52992	−	24.3700i	0.259952	−	0.970153i	−0.705316	−	0.708893i	$-0.749195\pi$
$631$	6.52992	−	24.3700i	0.259952	−	0.970153i	0.965268	−	0.261261i	$-0.0841383\pi$
$632$	1.18465	−	4.42119i	0.0471230	−	0.175866i
$633$		0			0
$634$	3.06194	−	1.76781i	0.121605	−	0.0702087i
$635$	−3.04739	+	3.04739i	−0.120932	+	0.120932i
$636$		0			0
$637$	−21.3836	−	13.4068i	−0.847249	−	0.531195i
$638$	7.21420			0.285613
$639$		0			0
$640$	−10.1897	+	5.88301i	−0.402782	+	0.232546i
$641$		−	11.3468i		−	0.448171i	−0.974570	−	0.224085i	$-0.928061\pi$
$641$		−	11.3468i		−	0.448171i	0.974570	−	0.224085i	$-0.0719394\pi$
$642$		0			0
$643$	−2.92632	+	10.9212i	−0.115403	+	0.430690i	−0.999317	−	0.0369602i	$-0.988233\pi$
$643$	−2.92632	+	10.9212i	−0.115403	+	0.430690i	0.883914	+	0.467650i	$0.154899\pi$
$644$	19.8830	+	14.1669i	0.783501	+	0.558255i
$645$		0			0
$646$	0.542179	−	0.939082i	0.0213318	−	0.0369477i
$647$	−9.64081	−	16.6984i	−0.379020	−	0.656481i	0.611900	−	0.790935i	$-0.290405\pi$
$647$	−9.64081	−	16.6984i	−0.379020	−	0.656481i	−0.990920	+	0.134454i	$0.957072\pi$
$648$		0			0
$649$	−3.55560	−	6.15848i	−0.139569	−	0.241741i
$650$	−1.63196	+	2.23425i	−0.0640108	+	0.0876346i
$651$		0			0
$652$	−1.92681	−	7.19096i	−0.0754598	−	0.281620i
$653$	−3.98817			−0.156069			−0.0780346	−	0.996951i	$-0.524864\pi$
$653$	−3.98817			−0.156069			−0.0780346	+	0.996951i	$0.524864\pi$
$654$		0			0
$655$	−3.79759	−	14.1728i	−0.148384	−	0.553777i
$656$	−2.95084	+	0.790674i	−0.115211	+	0.0308706i
$657$		0			0
$658$	5.78042	+	0.553578i	0.225344	+	0.0215807i
$659$	13.3526	+	23.1273i	0.520143	+	0.900913i	0.999726	+	0.0234170i	$0.00745455\pi$
$659$	13.3526	+	23.1273i	0.520143	+	0.900913i	−0.479583	+	0.877496i	$0.659212\pi$
$660$		0			0
$661$	13.7159	+	3.67516i	0.533486	+	0.142947i	0.515498	−	0.856891i	$-0.327607\pi$
$661$	13.7159	+	3.67516i	0.533486	+	0.142947i	0.0179886	+	0.999838i	$0.494274\pi$
$662$	−2.36509	−	1.36549i	−0.0919220	−	0.0530712i
$663$		0			0
$664$		−	5.89415i		−	0.228738i
$665$	3.85168	−	5.40576i	0.149362	−	0.209627i
$666$		0			0
$667$	23.8691	+	13.7808i	0.924216	+	0.533596i
$668$	−45.3325	+	12.1468i	−1.75397	+	0.469974i
$669$		0			0
$670$	−0.0571282	−	0.213205i	−0.00220705	−	0.00823684i
$671$	31.6806	−	31.6806i	1.22302	−	1.22302i
$672$		0			0
$673$	34.5521	+	19.9487i	1.33189	+	0.768965i	0.985589	−	0.169159i	$-0.0541052\pi$
$673$	34.5521	+	19.9487i	1.33189	+	0.768965i	0.346298	+	0.938124i	$0.387439\pi$
$674$	3.38809	+	3.38809i	0.130505	+	0.130505i
$675$		0			0
$676$	24.4554	+	5.32806i	0.940592	+	0.204926i
$677$	−5.68825	+	3.28411i	−0.218617	+	0.126219i	−0.605310	−	0.795990i	$-0.706951\pi$
$677$	−5.68825	+	3.28411i	−0.218617	+	0.126219i	0.386693	+	0.922209i	$0.373617\pi$
$678$		0			0
$679$	−5.78812	+	4.77638i	−0.222128	+	0.183301i
$680$	−3.22086	+	1.85956i	−0.123514	+	0.0713110i
$681$		0			0
$682$	−5.23244	−	5.23244i	−0.200361	−	0.200361i
$683$	−8.25678	−	8.25678i	−0.315937	−	0.315937i	0.531267	−	0.847204i	$-0.321716\pi$
$683$	−8.25678	−	8.25678i	−0.315937	−	0.315937i	−0.847204	+	0.531267i	$0.821716\pi$
$684$		0			0
$685$	0.698384	−	0.403212i	0.0266839	−	0.0154060i
$686$	−2.42197	−	4.44427i	−0.0924711	−	0.169683i
$687$		0			0
$688$	−6.05014	+	3.49305i	−0.230659	+	0.133171i
$689$	−7.26076	−	46.6080i	−0.276613	−	1.77563i
$690$		0			0
$691$	13.9233	+	13.9233i	0.529669	+	0.529669i	0.920474	−	0.390805i	$-0.127803\pi$
$691$	13.9233	+	13.9233i	0.529669	+	0.529669i	−0.390805	+	0.920474i	$0.627803\pi$
$692$	8.00308	+	4.62058i	0.304231	+	0.175648i
$693$		0			0
$694$	5.07347	−	5.07347i	0.192586	−	0.192586i
$695$	−1.47124	−	5.49074i	−0.0558073	−	0.208276i
$696$		0			0
$697$	−1.94233	+	0.520446i	−0.0735710	+	0.0197133i
$698$	2.65309	+	1.53176i	0.100421	+	0.0579780i
$699$		0			0
$700$	13.0124	−	5.93820i	0.491821	−	0.224443i
$701$			1.58634i			0.0599153i	0.999551	+	0.0299577i	$0.00953725\pi$
$701$			1.58634i			0.0599153i	−0.999551	+	0.0299577i	$0.990463\pi$
$702$		0			0
$703$	−12.5223	−	7.22974i	−0.472287	−	0.272675i
$704$	27.7694	+	7.44078i	1.04660	+	0.280435i
$705$		0			0
$706$	0.957033	+	1.65763i	0.0360184	+	0.0623857i
$707$	2.68373	−	28.0234i	0.100932	−	1.05393i
$708$		0			0
$709$	16.6679	−	4.46614i	0.625975	−	0.167730i	0.0681325	−	0.997676i	$-0.478296\pi$
$709$	16.6679	−	4.46614i	0.625975	−	0.167730i	0.557843	+	0.829947i	$0.311629\pi$
$710$	0.191966	+	0.716428i	0.00720437	+	0.0268871i
$711$		0			0
$712$	15.0503			0.564035
$713$	−7.31700	−	27.3074i	−0.274024	−	1.02267i
$714$		0			0
$715$	−24.2125	+	3.77191i	−0.905498	+	0.141061i
$716$	10.7244	+	18.5751i	0.400788	+	0.694186i
$717$		0			0
$718$	0.698463	+	1.20977i	0.0260664	+	0.0451483i
$719$	−11.5856	+	20.0668i	−0.432069	+	0.748365i	−0.997051	−	0.0767379i	$-0.975550\pi$
$719$	−11.5856	+	20.0668i	−0.432069	+	0.748365i	0.564983	+	0.825103i	$0.308883\pi$
$720$		0			0
$721$	4.34215	−	45.3404i	0.161710	−	1.68856i
$722$	−1.14082	+	4.25761i	−0.0424570	+	0.158452i
$723$		0			0
$724$			8.32600i			0.309433i
$725$	13.9841	−	8.07374i	0.519358	−	0.299851i
$726$		0			0
$727$	−18.3365			−0.680062			−0.340031	−	0.940414i	$-0.610438\pi$
$727$	−18.3365			−0.680062			−0.340031	+	0.940414i	$0.610438\pi$
$728$	7.65057	+	6.79628i	0.283549	+	0.251887i
$729$		0			0
$730$	−0.676038	+	0.676038i	−0.0250213	+	0.0250213i
$731$	−3.98239	+	2.29923i	−0.147294	+	0.0850401i
$732$		0			0
$733$	−5.26026	+	19.6316i	−0.194292	+	0.725108i	0.798157	+	0.602450i	$0.205809\pi$
$733$	−5.26026	+	19.6316i	−0.194292	+	0.725108i	−0.992449	+	0.122658i	$0.960858\pi$
$734$	1.29987	−	4.85119i	0.0479791	−	0.179061i
$735$		0			0
$736$	−10.5659	−	10.5659i	−0.389463	−	0.389463i
$737$	−1.25205	+	2.16862i	−0.0461200	+	0.0798822i
$738$		0			0
$739$	−8.59704	+	32.0846i	−0.316247	+	1.18025i	0.606576	+	0.795026i	$0.292543\pi$
$739$	−8.59704	+	32.0846i	−0.316247	+	1.18025i	−0.922823	+	0.385225i	$0.874124\pi$
$740$	12.1624	+	21.0658i	0.447097	+	0.774395i
$741$		0			0
$742$	3.30819	−	8.86212i	0.121448	−	0.325339i
$743$	−1.88756	−	7.04445i	−0.0692477	−	0.258436i	0.922620	−	0.385711i	$-0.126044\pi$
$743$	−1.88756	−	7.04445i	−0.0692477	−	0.258436i	−0.991868	+	0.127275i	$0.959377\pi$
$744$		0			0
$745$	−34.6305			−1.26876
$746$	1.47491	+	5.50442i	0.0540001	+	0.201531i
$747$		0			0
$748$	19.9899	+	5.35628i	0.730903	+	0.195845i
$749$	−8.74156	−	6.22848i	−0.319410	−	0.227584i
$750$		0			0
$751$			7.15760i			0.261185i	0.991436	+	0.130592i	$0.0416879\pi$
$751$			7.15760i			0.261185i	−0.991436	+	0.130592i	$0.958312\pi$
$752$	27.5966	+	7.39449i	1.00634	+	0.269649i
$753$		0			0
$754$	4.57580	+	3.34229i	0.166641	+	0.121719i
$755$		−	9.76045i		−	0.355219i
$756$		0			0
$757$	7.08185	−	12.2661i	0.257394	−	0.445820i	−0.708149	−	0.706063i	$-0.750469\pi$
$757$	7.08185	−	12.2661i	0.257394	−	0.445820i	0.965543	+	0.260243i	$0.0838027\pi$
$758$	6.60245	+	3.81192i	0.239812	+	0.138455i
$759$		0			0
$760$	−1.90302	+	1.90302i	−0.0690296	+	0.0690296i
$761$	−3.73637	−	13.9443i	−0.135443	−	0.505481i	−0.999996	−	0.00293843i	$-0.999065\pi$
$761$	−3.73637	−	13.9443i	−0.135443	−	0.505481i	0.864552	−	0.502543i	$-0.167602\pi$
$762$		0			0
$763$	−7.32958	+	19.6348i	−0.265349	+	0.710826i
$764$	−10.5369	−	6.08348i	−0.381212	−	0.220093i
$765$		0			0
$766$	−3.35853	+	5.81714i	−0.121349	+	0.210182i
$767$	0.597949	−	5.55346i	0.0215907	−	0.200524i
$768$		0			0
$769$	−48.9223	+	13.1087i	−1.76418	+	0.472711i	−0.987559	−	0.157252i	$-0.949737\pi$
$769$	−48.9223	+	13.1087i	−1.76418	+	0.472711i	−0.776625	+	0.629963i	$0.783070\pi$
$770$	−4.60381	−	1.71858i	−0.165910	−	0.0619334i
$771$		0			0
$772$	22.1535	+	5.93600i	0.797320	+	0.213641i
$773$	8.28259	+	8.28259i	0.297904	+	0.297904i	0.840192	−	0.542288i	$-0.182442\pi$
$773$	8.28259	+	8.28259i	0.297904	+	0.297904i	−0.542288	+	0.840192i	$0.682442\pi$
$774$		0			0
$775$	−15.9985	−	4.28679i	−0.574684	−	0.153986i
$776$	2.63508	−	1.52136i	0.0945938	−	0.0546137i
$777$		0			0
$778$	−6.46445	+	1.73215i	−0.231762	+	0.0621004i
$779$	−1.26016	+	0.727555i	−0.0451500	+	0.0260674i
$780$		0			0
$781$	4.20725	−	7.28716i	0.150547	−	0.260755i
$782$	−2.16875	−	2.16875i	−0.0775544	−	0.0775544i
$783$		0			0
$784$	−8.13169	−	23.5371i	−0.290417	−	0.840611i
$785$	11.4757	−	11.4757i	0.409586	−	0.409586i
$786$		0			0
$787$	−24.8664	+	24.8664i	−0.886390	+	0.886390i	−0.994174	−	0.107784i	$-0.965624\pi$
$787$	−24.8664	+	24.8664i	−0.886390	+	0.886390i	0.107784	+	0.994174i	$0.465624\pi$
$788$	−3.83339	+	1.02715i	−0.136559	+	0.0365908i
$789$		0			0
$790$	−0.863215	+	1.49513i	−0.0307118	+	0.0531944i
$791$	4.65674	−	48.6254i	0.165575	−	1.72892i
$792$		0			0
$793$	34.7717	−	5.41685i	1.23478	−	0.192358i
$794$	−4.58265	−	2.64579i	−0.162632	−	0.0938956i
$795$		0			0
$796$		−	35.7393i		−	1.26675i
$797$	−4.21417	−	7.29915i	−0.149273	−	0.258549i	0.781686	−	0.623673i	$-0.214360\pi$
$797$	−4.21417	−	7.29915i	−0.149273	−	0.258549i	−0.930959	+	0.365123i	$0.881027\pi$
$798$		0			0
$799$	18.1649	+	4.86727i	0.642629	+	0.172192i
$800$	−8.45596	+	2.26577i	−0.298963	+	0.0801069i
$801$		0			0
$802$	3.61499			0.127650
$803$	10.8464			0.382761
$804$		0			0
$805$	−11.9494	−	14.4805i	−0.421160	−	0.510371i
$806$	−0.894660	−	5.74297i	−0.0315130	−	0.202288i
$807$		0			0
$808$	−2.95424	+	11.0254i	−0.103930	+	0.387871i
$809$	19.4561	+	33.6989i	0.684040	+	1.18479i	0.973738	+	0.227673i	$0.0731118\pi$
$809$	19.4561	+	33.6989i	0.684040	+	1.18479i	−0.289698	+	0.957118i	$0.593555\pi$
$810$		0			0
$811$	−33.4503	−	33.4503i	−1.17460	−	1.17460i	−0.981101	−	0.193499i	$-0.938016\pi$
$811$	−33.4503	−	33.4503i	−1.17460	−	1.17460i	−0.193499	−	0.981101i	$-0.561984\pi$
$812$	−12.1616	−	26.6496i	−0.426787	−	0.935218i
$813$		0			0
$814$	−2.77066	+	10.3402i	−0.0971116	+	0.362425i
$815$			5.72492i			0.200535i
$816$		0			0
$817$	−2.35296	+	2.35296i	−0.0823196	+	0.0823196i
$818$	6.80553			0.237950
$819$		0			0
$820$	2.44788			0.0854838
$821$	33.6195	−	33.6195i	1.17333	−	1.17333i	0.191918	−	0.981411i	$-0.438529\pi$
$821$	33.6195	−	33.6195i	1.17333	−	1.17333i	0.981411	−	0.191918i	$-0.0614709\pi$
$822$		0			0
$823$		−	36.4458i		−	1.27042i	−0.772340	−	0.635210i	$-0.780914\pi$
$823$		−	36.4458i		−	1.27042i	0.772340	−	0.635210i	$-0.219086\pi$
$824$	−4.77980	+	17.8385i	−0.166512	+	0.621433i
$825$		0			0
$826$	0.649987	−	0.912244i	0.0226159	−	0.0317410i
$827$	−4.04107	−	4.04107i	−0.140522	−	0.140522i	0.633347	−	0.773868i	$-0.281681\pi$
$827$	−4.04107	−	4.04107i	−0.140522	−	0.140522i	−0.773868	+	0.633347i	$0.781681\pi$
$828$		0			0
$829$	−17.7840	−	30.8028i	−0.617664	−	1.06983i	−0.989911	−	0.141692i	$-0.954746\pi$
$829$	−17.7840	−	30.8028i	−0.617664	−	1.06983i	0.372247	−	0.928134i	$-0.378588\pi$
$830$	−0.575402	+	2.14743i	−0.0199725	+	0.0745383i
$831$		0			0
$832$	14.1662	+	17.5849i	0.491124	+	0.609646i
$833$	−5.35252	−	15.4928i	−0.185454	−	0.536795i
$834$		0			0
$835$	36.0904			1.24896
$836$	14.9756			0.517941
$837$		0			0
$838$	−4.26431	+	1.14262i	−0.147308	+	0.0394711i
$839$	14.5158	+	3.88950i	0.501142	+	0.134280i	0.500530	−	0.865719i	$-0.333139\pi$
$839$	14.5158	+	3.88950i	0.501142	+	0.134280i	0.000611847		1.00000i	$0.499805\pi$
$840$		0			0
$841$	−2.03520	−	3.52507i	−0.0701793	−	0.121554i
$842$			4.94900i			0.170554i
$843$		0			0
$844$	−4.68090	−	2.70252i	−0.161123	−	0.0930246i
$845$	−17.1049	−	8.82507i	−0.588428	−	0.303592i
$846$		0			0
$847$	11.0627	+	24.2417i	0.380119	+	0.832956i
$848$	23.2705	−	40.3057i	0.799113	−	1.38410i
$849$		0			0
$850$	−1.73567	+	0.465072i	−0.0595331	+	0.0159518i
$851$	−28.9194	+	28.9194i	−0.991345	+	0.991345i
$852$		0			0
$853$	11.5963	−	11.5963i	0.397050	−	0.397050i	−0.480141	−	0.877191i	$-0.659415\pi$
$853$	11.5963	−	11.5963i	0.397050	−	0.397050i	0.877191	+	0.480141i	$0.159415\pi$
$854$	6.61154	+	2.46806i	0.226242	+	0.0844553i
$855$		0			0
$856$	3.07733	+	3.07733i	0.105181	+	0.105181i
$857$	23.4161	−	40.5579i	0.799880	−	1.38543i	−0.119814	−	0.992796i	$-0.538230\pi$
$857$	23.4161	−	40.5579i	0.799880	−	1.38543i	0.919694	−	0.392637i	$-0.128437\pi$
$858$		0			0
$859$	−17.1191	+	9.88371i	−0.584095	+	0.337228i	−0.762759	−	0.646683i	$-0.776156\pi$
$859$	−17.1191	+	9.88371i	−0.584095	+	0.337228i	0.178664	+	0.983910i	$0.442823\pi$
$860$	5.40715	−	1.44884i	0.184382	−	0.0494050i
$861$		0			0
$862$	5.29211	−	3.05540i	0.180250	−	0.104067i
$863$	6.94395	+	1.86062i	0.236375	+	0.0633364i	0.375062	−	0.927000i	$-0.377622\pi$
$863$	6.94395	+	1.86062i	0.236375	+	0.0633364i	−0.138687	+	0.990336i	$0.544288\pi$
$864$		0			0
$865$	−5.02502	−	5.02502i	−0.170856	−	0.170856i
$866$	−4.86491	−	1.30355i	−0.165316	−	0.0442964i
$867$		0			0
$868$	−10.5082	+	28.1496i	−0.356670	+	0.955461i
$869$	18.9187	−	5.06925i	0.641773	−	0.171963i
$870$		0			0
$871$	−1.79886	+	0.795437i	−0.0609519	+	0.0269523i
$872$	4.24884	−	7.35921i	0.143884	−	0.249214i
$873$		0			0
$874$	−1.92208	−	1.10971i	−0.0650154	−	0.0375366i
$875$	−30.1632	+	5.06361i	−1.01970	+	0.171181i
$876$		0			0
$877$	−8.22456	−	30.6945i	−0.277724	−	1.03648i	−0.953994	−	0.299825i	$-0.903072\pi$
$877$	−8.22456	−	30.6945i	−0.277724	−	1.03648i	0.676270	−	0.736653i	$-0.263595\pi$
$878$	−3.01460	+	3.01460i	−0.101738	+	0.101738i
$879$		0			0
$880$	−20.9385	−	12.0889i	−0.705838	−	0.407516i
$881$	8.45038	−	14.6365i	0.284701	−	0.493116i	−0.687836	−	0.725866i	$-0.741439\pi$
$881$	8.45038	−	14.6365i	0.284701	−	0.493116i	0.972537	+	0.232750i	$0.0747725\pi$
$882$		0			0
$883$		−	21.1502i		−	0.711760i	−0.934532	−	0.355880i	$-0.884181\pi$
$883$		−	21.1502i		−	0.711760i	0.934532	−	0.355880i	$-0.115819\pi$
$884$	10.1976	+	12.6585i	0.342982	+	0.425753i
$885$		0			0
$886$	−7.81099	−	2.09295i	−0.262415	−	0.0703140i
$887$		−	10.2044i		−	0.342631i	−0.985216	−	0.171316i	$-0.945198\pi$
$887$		−	10.2044i		−	0.342631i	0.985216	−	0.171316i	$-0.0548018\pi$
$888$		0			0
$889$	3.19730	+	7.00623i	0.107234	+	0.234982i
$890$	−5.48332	−	1.46925i	−0.183801	−	0.0492494i
$891$		0			0
$892$	−8.08278	−	30.1654i	−0.270632	−	1.01001i
$893$	13.6084			0.455387
$894$		0			0
$895$	−4.26898	−	15.9321i	−0.142696	−	0.532550i
$896$	3.48095	+	20.7355i	0.116290	+	0.692726i
$897$		0			0
$898$	−1.32416	−	2.29352i	−0.0441879	−	0.0765357i
$899$	−8.77944	+	32.7653i	−0.292811	+	1.09278i
$900$		0			0
$901$	15.3174	−	26.5304i	0.510295	−	0.883857i
$902$	0.761755	+	0.761755i	0.0253637	+	0.0253637i
$903$		0			0
$904$	−5.12611	+	19.1309i	−0.170492	+	0.636285i
$905$	1.65714	−	6.18453i	0.0550852	−	0.205581i
$906$		0			0
$907$	13.5900	−	7.84622i	0.451250	−	0.260529i	−0.257108	−	0.966383i	$-0.582770\pi$
$907$	13.5900	−	7.84622i	0.451250	−	0.260529i	0.708358	+	0.705853i	$0.249436\pi$
$908$	2.38952	−	2.38952i	0.0792990	−	0.0792990i
$909$		0			0
$910$	−2.12388	−	3.22297i	−0.0704059	−	0.106840i
$911$	23.8232			0.789296			0.394648	−	0.918832i	$-0.370866\pi$
$911$	23.8232			0.789296			0.394648	+	0.918832i	$0.370866\pi$
$912$		0			0
$913$	21.8426	−	12.6108i	0.722885	−	0.417358i
$914$		−	9.47291i		−	0.313336i
$915$		0			0
$916$	−5.55326	+	20.7250i	−0.183485	+	0.684774i
$917$	−26.1006	−	2.49960i	−0.861918	−	0.0825439i
$918$		0			0
$919$	4.01647	−	6.95674i	0.132491	−	0.229482i	−0.792145	−	0.610333i	$-0.791036\pi$
$919$	4.01647	−	6.95674i	0.132491	−	0.229482i	0.924636	+	0.380851i	$0.124369\pi$
$920$	3.80609	+	6.59234i	0.125483	+	0.217343i
$921$		0			0
$922$	1.29370	+	2.24076i	0.0426058	+	0.0737955i
$923$	6.04465	−	2.67289i	0.198962	−	0.0879791i
$924$		0			0
$925$	6.20155	+	23.1445i	0.203906	+	0.760986i
$926$	1.38973			0.0456695
$927$		0			0
$928$	4.64034	+	17.3180i	0.152327	+	0.568491i
$929$	12.3985	−	3.32217i	0.406781	−	0.108997i	−0.0496256	−	0.998768i	$-0.515803\pi$
$929$	12.3985	−	3.32217i	0.406781	−	0.108997i	0.456407	+	0.889771i	$0.349136\pi$
$930$		0			0
$931$	−6.64291	−	9.82661i	−0.217713	−	0.322054i
$932$	−19.6049	−	33.9567i	−0.642180	−	1.11229i
$933$		0			0
$934$	6.36835	+	1.70639i	0.208379	+	0.0558349i
$935$	−13.7824	−	7.95725i	−0.450732	−	0.260230i
$936$		0			0
$937$			19.3918i			0.633501i	0.948509	+	0.316751i	$0.102592\pi$
$937$			19.3918i			0.633501i	−0.948509	+	0.316751i	$0.897408\pi$
$938$	−0.392638	−	0.0376021i	−0.0128201	−	0.00122775i
$939$		0			0
$940$	−19.8259	−	11.4465i	−0.646648	−	0.373342i
$941$	2.57085	−	0.688857i	0.0838073	−	0.0224561i	−0.216672	−	0.976245i	$-0.569520\pi$
$941$	2.57085	−	0.688857i	0.0838073	−	0.0224561i	0.300479	+	0.953788i	$0.402853\pi$
$942$		0			0
$943$	1.06523	+	3.97550i	0.0346887	+	0.129460i
$944$	3.89691	−	3.89691i	0.126834	−	0.126834i
$945$		0			0
$946$	2.13351	+	1.23178i	0.0693663	+	0.0400487i
$947$	−14.2267	−	14.2267i	−0.462307	−	0.462307i	0.437104	−	0.899411i	$-0.356004\pi$
$947$	−14.2267	−	14.2267i	−0.462307	−	0.462307i	−0.899411	+	0.437104i	$0.856004\pi$
$948$		0			0
$949$	6.87961	+	5.02506i	0.223321	+	0.163120i
$950$	−1.12608	+	0.650145i	−0.0365350	+	0.0210935i
$951$		0			0
$952$	1.10030	+	6.55431i	0.0356608	+	0.212426i
$953$	−24.0417	+	13.8805i	−0.778788	+	0.449634i	−0.836001	−	0.548728i	$-0.815112\pi$
$953$	−24.0417	+	13.8805i	−0.778788	+	0.449634i	0.0572123	+	0.998362i	$0.481779\pi$
$954$		0			0
$955$	6.61597	+	6.61597i	0.214088	+	0.214088i
$956$	−28.1404	−	28.1404i	−0.910125	−	0.910125i
$957$		0			0
$958$	5.79773	−	3.34732i	0.187316	−	0.108147i
$959$	−0.238579	−	1.42118i	−0.00770413	−	0.0458924i
$960$		0			0
$961$	3.28554	−	1.89691i	0.105985	−	0.0611906i
$962$	−6.54793	+	5.27495i	−0.211114	+	0.170071i
$963$		0			0
$964$	19.4372	+	19.4372i	0.626029	+	0.626029i
$965$	−15.2741	−	8.81849i	−0.491690	−	0.283877i
$966$		0			0
$967$	−4.10934	+	4.10934i	−0.132147	+	0.132147i	−0.770087	−	0.637939i	$-0.779787\pi$
$967$	−4.10934	+	4.10934i	−0.132147	+	0.132147i	0.637939	+	0.770087i	$0.279787\pi$
$968$	−2.79631	−	10.4360i	−0.0898768	−	0.335425i
$969$		0			0
$970$	−1.10856	+	0.297038i	−0.0355938	+	0.00953733i
$971$	18.8523	+	10.8844i	0.604999	+	0.349296i	0.771006	−	0.636828i	$-0.219754\pi$
$971$	18.8523	+	10.8844i	0.604999	+	0.349296i	−0.166007	+	0.986125i	$0.553087\pi$
$972$		0			0
$973$	−10.1117	−	0.968378i	−0.324167	−	0.0310448i
$974$			10.4453i			0.334690i
$975$		0			0
$976$	30.0699	+	17.3608i	0.962513	+	0.555707i
$977$	−8.93483	−	2.39408i	−0.285850	−	0.0765934i	0.113045	−	0.993590i	$-0.463940\pi$
$977$	−8.93483	−	2.39408i	−0.285850	−	0.0765934i	−0.398895	+	0.916996i	$0.630606\pi$
$978$		0			0
$979$	32.2009	+	55.7736i	1.02915	+	1.78253i
$980$	1.41248	+	19.9038i	0.0451199	+	0.635804i
$981$		0			0
$982$	−3.11383	+	0.834347i	−0.0993662	+	0.0266251i
$983$	14.2329	+	53.1178i	0.453958	+	1.69420i	0.691132	+	0.722729i	$0.257112\pi$
$983$	14.2329	+	53.1178i	0.453958	+	1.69420i	−0.237174	+	0.971467i	$0.576221\pi$
$984$		0			0
$985$	3.05187			0.0972406
$986$	0.952477	+	3.55469i	0.0303331	+	0.113205i
$987$		0			0
$988$	9.49865	+	6.93808i	0.302192	+	0.220730i
$989$	4.70599	+	8.15101i	0.149642	+	0.259187i
$990$		0			0
$991$	2.34950	+	4.06946i	0.0746345	+	0.129271i	0.900927	−	0.433970i	$-0.142888\pi$
$991$	2.34950	+	4.06946i	0.0746345	+	0.129271i	−0.826293	+	0.563241i	$0.809554\pi$
$992$	9.19506	−	15.9263i	0.291944	−	0.505661i
$993$		0			0
$994$	1.31937	+	0.126353i	0.0418480	+	0.00400769i
$995$	−7.11326	+	26.5470i	−0.225505	+	0.841598i
$996$		0			0
$997$			16.8903i			0.534921i	0.963569	+	0.267461i	$0.0861845\pi$
$997$			16.8903i			0.534921i	−0.963569	+	0.267461i	$0.913816\pi$
$998$	−3.62391	+	2.09227i	−0.114713	+	0.0662295i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.b.136.4		28
3.2	odd	2		91.2.ba.a.45.4	yes	28
7.5	odd	6		819.2.gh.b.19.4		28
13.11	odd	12		819.2.gh.b.388.4		28
21.2	odd	6		637.2.x.a.19.4		28
21.5	even	6		91.2.w.a.19.4	✓	28
21.11	odd	6		637.2.bd.b.97.4		28
21.17	even	6		637.2.bd.a.97.4		28
21.20	even	2		637.2.bb.a.227.4		28
39.11	even	12		91.2.w.a.24.4	yes	28
91.89	even	12	inner	819.2.et.b.271.4		28
273.11	even	12		637.2.bd.a.440.4		28
273.89	odd	12		91.2.ba.a.89.4	yes	28
273.128	even	12		637.2.bb.a.362.4		28
273.167	odd	12		637.2.x.a.570.4		28
273.206	odd	12		637.2.bd.b.440.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.4	✓	28	21.5	even	6
91.2.w.a.24.4	yes	28	39.11	even	12
91.2.ba.a.45.4	yes	28	3.2	odd	2
91.2.ba.a.89.4	yes	28	273.89	odd	12
637.2.x.a.19.4		28	21.2	odd	6
637.2.x.a.570.4		28	273.167	odd	12
637.2.bb.a.227.4		28	21.20	even	2
637.2.bb.a.362.4		28	273.128	even	12
637.2.bd.a.97.4		28	21.17	even	6
637.2.bd.a.440.4		28	273.11	even	12
637.2.bd.b.97.4		28	21.11	odd	6
637.2.bd.b.440.4		28	273.206	odd	12
819.2.et.b.136.4		28	1.1	even	1	trivial
819.2.et.b.271.4		28	91.89	even	12	inner
819.2.gh.b.19.4		28	7.5	odd	6
819.2.gh.b.388.4		28	13.11	odd	12

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.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.193244 - 0.193244i) q^{2} +1.92531i q^{4} +(0.383199 - 1.43012i) q^{5} +(-2.15474 - 1.53528i) q^{7} +(0.758543 + 0.758543i) q^{8} +O(q^{10})\)	\(q+(0.193244 - 0.193244i) q^{2} +1.92531i q^{4} +(0.383199 - 1.43012i) q^{5} +(-2.15474 - 1.53528i) q^{7} +(0.758543 + 0.758543i) q^{8} +(-0.202311 - 0.350412i) q^{10} +(-1.18808 + 4.43396i) q^{11} +(-2.80779 + 2.26193i) q^{13} +(-0.713075 + 0.119706i) q^{14} -3.55746 q^{16} -2.34163 q^{17} +(-1.63673 + 0.438561i) q^{19} +(2.75342 + 0.737778i) q^{20} +(0.627247 + 1.08642i) q^{22} +4.79276i q^{23} +(2.43173 + 1.40396i) q^{25} +(-0.105485 + 0.979692i) q^{26} +(2.95590 - 4.14855i) q^{28} +(2.87534 - 4.98024i) q^{29} +(-5.69764 + 1.52668i) q^{31} +(-2.20454 + 2.20454i) q^{32} +(-0.452505 + 0.452505i) q^{34} +(-3.02133 + 2.49321i) q^{35} +(6.03398 + 6.03398i) q^{37} +(-0.231540 + 0.401038i) q^{38} +(1.37548 - 0.794133i) q^{40} +(0.829479 - 0.222258i) q^{41} +(1.70069 - 0.981895i) q^{43} +(-8.53676 - 2.28742i) q^{44} +(0.926173 + 0.926173i) q^{46} +(-7.75739 - 2.07859i) q^{47} +(2.28581 + 6.61627i) q^{49} +(0.741225 - 0.198611i) q^{50} +(-4.35492 - 5.40588i) q^{52} +(-6.54133 + 11.3299i) q^{53} +(5.88581 + 3.39817i) q^{55} +(-0.469885 - 2.79904i) q^{56} +(-0.406759 - 1.51804i) q^{58} +(-1.09542 + 1.09542i) q^{59} +(-8.45262 - 4.88012i) q^{61} +(-0.806013 + 1.39606i) q^{62} -6.26289i q^{64} +(2.15888 + 4.88224i) q^{65} +(0.526925 + 0.141189i) q^{67} -4.50837i q^{68} +(-0.102055 + 1.06565i) q^{70} +(-1.77061 - 0.474435i) q^{71} +(-0.611552 - 2.28234i) q^{73} +2.33206 q^{74} +(-0.844368 - 3.15123i) q^{76} +(9.36737 - 7.72999i) q^{77} +(-2.13339 - 3.69514i) q^{79} +(-1.36321 + 5.08758i) q^{80} +(0.117342 - 0.203242i) q^{82} +(-3.88518 - 3.88518i) q^{83} +(-0.897309 + 3.34880i) q^{85} +(0.138903 - 0.518394i) q^{86} +(-4.26455 + 2.46214i) q^{88} +(9.92055 - 9.92055i) q^{89} +(9.52276 - 0.563113i) q^{91} -9.22757 q^{92} +(-1.90074 + 1.09739i) q^{94} +2.50878i q^{95} +(0.734114 - 2.73975i) q^{97} +(1.72027 + 0.836835i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8}+O(q^{10}) \) 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8	\( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 6 q^{10} - 2 q^{11} + 20 q^{14} + 4 q^{16} + 12 q^{17} + 14 q^{19} - 36 q^{20} - 8 q^{22} - 24 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{31} - 10 q^{32} - 12 q^{34} + 20 q^{35} - 10 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{43} + 6 q^{44} + 24 q^{46} + 6 q^{47} - 50 q^{49} - 10 q^{50} - 26 q^{52} - 12 q^{53} + 6 q^{55} - 54 q^{56} - 46 q^{58} - 42 q^{59} + 30 q^{61} - 36 q^{62} - 28 q^{65} - 10 q^{67} - 88 q^{70} + 42 q^{71} + 40 q^{73} - 12 q^{74} - 52 q^{76} + 4 q^{79} - 30 q^{80} - 54 q^{82} - 66 q^{83} - 54 q^{85} + 18 q^{86} - 6 q^{88} + 26 q^{91} + 156 q^{92} - 18 q^{94} - 62 q^{97} + 56 q^{98}+O(q^{100}) \) 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8 - 6 * q^10 - 2 * q^11 + 20 * q^14 + 4 * q^16 + 12 * q^17 + 14 * q^19 - 36 * q^20 - 8 * q^22 - 24 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^31 - 10 * q^32 - 12 * q^34 + 20 * q^35 - 10 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^43 + 6 * q^44 + 24 * q^46 + 6 * q^47 - 50 * q^49 - 10 * q^50 - 26 * q^52 - 12 * q^53 + 6 * q^55 - 54 * q^56 - 46 * q^58 - 42 * q^59 + 30 * q^61 - 36 * q^62 - 28 * q^65 - 10 * q^67 - 88 * q^70 + 42 * q^71 + 40 * q^73 - 12 * q^74 - 52 * q^76 + 4 * q^79 - 30 * q^80 - 54 * q^82 - 66 * q^83 - 54 * q^85 + 18 * q^86 - 6 * q^88 + 26 * q^91 + 156 * q^92 - 18 * q^94 - 62 * q^97 + 56 * q^98

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