LMFDB - Embedded newform 819.2.gh.d.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(19,819)]

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, 10, 5]))

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

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

chi := DirichletCharacter("819.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.gh (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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	819.19
Dual form			819.2.gh.d.388.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41061 - 0.377973i) q^{2} +(0.114915 + 0.0663464i) q^{4} +(-1.70489 + 0.456824i) q^{5} +(1.96341 + 1.77342i) q^{7} +(1.92826 + 1.92826i) q^{8} +O(q^{10})$	\(q+(-1.41061 - 0.377973i) q^{2} +(0.114915 + 0.0663464i) q^{4} +(-1.70489 + 0.456824i) q^{5} +(1.96341 + 1.77342i) q^{7} +(1.92826 + 1.92826i) q^{8} +2.57761 q^{10} +(-1.59480 - 1.59480i) q^{11} +(2.06370 + 2.95654i) q^{13} +(-2.09931 - 3.24373i) q^{14} +(-2.12389 - 3.67868i) q^{16} +(-0.813654 + 1.40929i) q^{17} +(-5.08160 - 5.08160i) q^{19} +(-0.226226 - 0.0606172i) q^{20} +(1.64685 + 2.85244i) q^{22} +(5.63098 - 3.25105i) q^{23} +(-1.63217 + 0.942332i) q^{25} +(-1.79359 - 4.95056i) q^{26} +(0.107966 + 0.334058i) q^{28} +(-3.90230 + 6.75898i) q^{29} +(1.68884 - 6.30283i) q^{31} +(0.193962 + 0.723875i) q^{32} +(1.68042 - 1.68042i) q^{34} +(-4.15754 - 2.12655i) q^{35} +(-0.545268 + 2.03497i) q^{37} +(5.24746 + 9.08887i) q^{38} +(-4.16834 - 2.40659i) q^{40} +(-6.84645 + 1.83450i) q^{41} +(-9.48195 + 5.47441i) q^{43} +(-0.0774577 - 0.289076i) q^{44} +(-9.17195 + 2.45762i) q^{46} +(3.34284 + 12.4756i) q^{47} +(0.709963 + 6.96390i) q^{49} +(2.65853 - 0.712352i) q^{50} +(0.0409944 + 0.476671i) q^{52} +(3.00939 + 5.21242i) q^{53} +(3.44750 + 1.99041i) q^{55} +(0.366351 + 7.20557i) q^{56} +(8.05934 - 8.05934i) q^{58} +(-2.02441 - 7.55521i) q^{59} -6.26701i q^{61} +(-4.76460 + 8.25252i) q^{62} +7.40114i q^{64} +(-4.86900 - 4.09784i) q^{65} +(-3.75123 + 3.75123i) q^{67} +(-0.187002 + 0.107966i) q^{68} +(5.06090 + 4.57118i) q^{70} +(-6.88920 - 1.84596i) q^{71} +(-4.55425 - 1.22031i) q^{73} +(1.53832 - 2.66446i) q^{74} +(-0.246808 - 0.921099i) q^{76} +(-0.302997 - 5.95950i) q^{77} +(-4.67565 + 8.09846i) q^{79} +(5.30151 + 5.30151i) q^{80} +10.3511 q^{82} +(-3.82650 - 3.82650i) q^{83} +(0.743393 - 2.77438i) q^{85} +(15.4445 - 4.13835i) q^{86} -6.15037i q^{88} +(-4.91594 - 1.31722i) q^{89} +(-1.19131 + 9.46471i) q^{91} +0.862782 q^{92} -18.8618i q^{94} +(10.9850 + 6.34217i) q^{95} +(-2.57958 + 9.62711i) q^{97} +(1.63068 - 10.0917i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7}+O(q^{10}) $ 40 * q - 8 * q^7	$ 40 q - 8 q^{7} - 4 q^{11} + 18 q^{14} + 32 q^{16} - 4 q^{17} + 14 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} + 24 q^{25} + 32 q^{26} + 16 q^{28} - 8 q^{29} + 14 q^{31} + 26 q^{32} - 24 q^{34} - 26 q^{35} + 36 q^{37} + 8 q^{38} - 30 q^{40} + 2 q^{41} - 66 q^{43} + 32 q^{44} - 26 q^{46} + 4 q^{47} - 14 q^{49} + 20 q^{50} + 2 q^{52} + 8 q^{53} - 42 q^{55} - 46 q^{56} + 24 q^{58} - 14 q^{59} - 24 q^{62} - 28 q^{65} - 44 q^{67} + 18 q^{68} - 4 q^{70} + 6 q^{71} + 14 q^{73} + 20 q^{74} - 64 q^{76} - 24 q^{77} - 20 q^{80} + 48 q^{82} + 12 q^{83} + 2 q^{85} + 60 q^{86} + 2 q^{89} - 14 q^{91} - 236 q^{92} - 24 q^{95} - 62 q^{97} + 88 q^{98}+O(q^{100}) $ 40 * q - 8 * q^7 - 4 * q^11 + 18 * q^14 + 32 * q^16 - 4 * q^17 + 14 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 + 24 * q^25 + 32 * q^26 + 16 * q^28 - 8 * q^29 + 14 * q^31 + 26 * q^32 - 24 * q^34 - 26 * q^35 + 36 * q^37 + 8 * q^38 - 30 * q^40 + 2 * q^41 - 66 * q^43 + 32 * q^44 - 26 * q^46 + 4 * q^47 - 14 * q^49 + 20 * q^50 + 2 * q^52 + 8 * q^53 - 42 * q^55 - 46 * q^56 + 24 * q^58 - 14 * q^59 - 24 * q^62 - 28 * q^65 - 44 * q^67 + 18 * q^68 - 4 * q^70 + 6 * q^71 + 14 * q^73 + 20 * q^74 - 64 * q^76 - 24 * q^77 - 20 * q^80 + 48 * q^82 + 12 * q^83 + 2 * q^85 + 60 * q^86 + 2 * q^89 - 14 * q^91 - 236 * q^92 - 24 * q^95 - 62 * q^97 + 88 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.41061	−	0.377973i	−0.997454	−	0.267267i	−0.277076	−	0.960848i	$-0.589365\pi$
$2$	−1.41061	−	0.377973i	−0.997454	−	0.267267i	−0.720379	+	0.693581i	$0.756032\pi$
$3$		0			0
$3$		0			0
$4$	0.114915	+	0.0663464i	0.0574576	+	0.0331732i
$5$	−1.70489	+	0.456824i	−0.762450	+	0.204298i	−0.619033	−	0.785365i	$-0.712475\pi$
$5$	−1.70489	+	0.456824i	−0.762450	+	0.204298i	−0.143416	+	0.989662i	$0.545809\pi$
$6$		0			0
$7$	1.96341	+	1.77342i	0.742100	+	0.670290i
$7$	1.96341	+	1.77342i	0.742100	+	0.670290i
$8$	1.92826	+	1.92826i	0.681742	+	0.681742i
$9$		0			0
$10$	2.57761			0.815111
$11$	−1.59480	−	1.59480i	−0.480850	−	0.480850i	0.424553	−	0.905403i	$-0.360431\pi$
$11$	−1.59480	−	1.59480i	−0.480850	−	0.480850i	−0.905403	+	0.424553i	$0.860431\pi$
$12$		0			0
$13$	2.06370	+	2.95654i	0.572367	+	0.819998i
$13$	2.06370	+	2.95654i	0.572367	+	0.819998i
$14$	−2.09931	−	3.24373i	−0.561064	−	0.866922i
$15$		0			0
$16$	−2.12389	−	3.67868i	−0.530972	−	0.919671i
$17$	−0.813654	+	1.40929i	−0.197340	+	0.341803i	−0.947665	−	0.319266i	$-0.896564\pi$
$17$	−0.813654	+	1.40929i	−0.197340	+	0.341803i	0.750325	+	0.661069i	$0.229897\pi$
$18$		0			0
$19$	−5.08160	−	5.08160i	−1.16580	−	1.16580i	−0.983185	−	0.182614i	$-0.941544\pi$
$19$	−5.08160	−	5.08160i	−1.16580	−	1.16580i	−0.182614	−	0.983185i	$-0.558456\pi$
$20$	−0.226226	−	0.0606172i	−0.0505858	−	0.0135544i
$21$		0			0
$22$	1.64685	+	2.85244i	0.351111	+	0.608141i
$23$	5.63098	−	3.25105i	1.17414	−	0.677891i	0.219490	−	0.975615i	$-0.429561\pi$
$23$	5.63098	−	3.25105i	1.17414	−	0.677891i	0.954652	+	0.297724i	$0.0962275\pi$
$24$		0			0
$25$	−1.63217	+	0.942332i	−0.326433	+	0.188466i
$26$	−1.79359	−	4.95056i	−0.351751	−	0.970885i
$27$		0			0
$28$	0.107966	+	0.334058i	0.0204036	+	0.0631311i
$29$	−3.90230	+	6.75898i	−0.724638	+	1.25511i	0.234484	+	0.972120i	$0.424660\pi$
$29$	−3.90230	+	6.75898i	−0.724638	+	1.25511i	−0.959123	+	0.282991i	$0.908673\pi$
$30$		0			0
$31$	1.68884	−	6.30283i	0.303324	−	1.13202i	−0.631054	−	0.775739i	$-0.717377\pi$
$31$	1.68884	−	6.30283i	0.303324	−	1.13202i	0.934378	−	0.356283i	$-0.115956\pi$
$32$	0.193962	+	0.723875i	0.0342879	+	0.127964i
$33$		0			0
$34$	1.68042	−	1.68042i	0.288190	−	0.288190i
$35$	−4.15754	−	2.12655i	−0.702752	−	0.359453i
$36$		0			0
$37$	−0.545268	+	2.03497i	−0.0896415	+	0.334547i	−0.996153	−	0.0876352i	$-0.972069\pi$
$37$	−0.545268	+	2.03497i	−0.0896415	+	0.334547i	0.906511	+	0.422182i	$0.138736\pi$
$38$	5.24746	+	9.08887i	0.851251	+	1.47441i
$39$		0			0
$40$	−4.16834	−	2.40659i	−0.659072	−	0.380516i
$41$	−6.84645	+	1.83450i	−1.06924	+	0.286501i	−0.750179	−	0.661235i	$-0.770033\pi$
$41$	−6.84645	+	1.83450i	−1.06924	+	0.286501i	−0.319057	+	0.947736i	$0.603366\pi$
$42$		0			0
$43$	−9.48195	+	5.47441i	−1.44598	+	0.834839i	−0.998239	−	0.0593222i	$-0.981106\pi$
$43$	−9.48195	+	5.47441i	−1.44598	+	0.834839i	−0.447745	+	0.894161i	$0.647773\pi$
$44$	−0.0774577	−	0.289076i	−0.0116772	−	0.0435799i
$45$		0			0
$46$	−9.17195	+	2.45762i	−1.35233	+	0.362356i
$47$	3.34284	+	12.4756i	0.487603	+	1.81976i	0.568043	+	0.822999i	$0.307701\pi$
$47$	3.34284	+	12.4756i	0.487603	+	1.81976i	−0.0804402	+	0.996759i	$0.525633\pi$
$48$		0			0
$49$	0.709963	+	6.96390i	0.101423	+	0.994843i
$50$	2.65853	−	0.712352i	0.375973	−	0.100742i
$51$		0			0
$52$	0.0409944	+	0.476671i	0.00568490	+	0.0661024i
$53$	3.00939	+	5.21242i	0.413371	+	0.715980i	0.995256	−	0.0972910i	$-0.0310178\pi$
$53$	3.00939	+	5.21242i	0.413371	+	0.715980i	−0.581884	+	0.813271i	$0.697684\pi$
$54$		0			0
$55$	3.44750	+	1.99041i	0.464861	+	0.268387i
$56$	0.366351	+	7.20557i	0.0489557	+	0.962885i
$57$		0			0
$58$	8.05934	−	8.05934i	1.05824	−	1.05824i
$59$	−2.02441	−	7.55521i	−0.263556	−	0.983604i	−0.963128	−	0.269042i	$-0.913293\pi$
$59$	−2.02441	−	7.55521i	−0.263556	−	0.983604i	0.699572	−	0.714562i	$-0.253374\pi$
$60$		0			0
$61$		−	6.26701i		−	0.802408i	−0.915989	−	0.401204i	$-0.868592\pi$
$61$		−	6.26701i		−	0.802408i	0.915989	−	0.401204i	$-0.131408\pi$
$62$	−4.76460	+	8.25252i	−0.605104	+	1.04807i
$63$		0			0
$64$			7.40114i			0.925142i
$65$	−4.86900	−	4.09784i	−0.603925	−	0.508274i
$66$		0			0
$67$	−3.75123	+	3.75123i	−0.458285	+	0.458285i	−0.898092	−	0.439807i	$-0.855047\pi$
$67$	−3.75123	+	3.75123i	−0.458285	+	0.458285i	0.439807	+	0.898092i	$0.355047\pi$
$68$	−0.187002	+	0.107966i	−0.0226774	+	0.0130928i
$69$		0			0
$70$	5.06090	+	4.57118i	0.604893	+	0.546360i
$71$	−6.88920	−	1.84596i	−0.817598	−	0.219075i	−0.174302	−	0.984692i	$-0.555767\pi$
$71$	−6.88920	−	1.84596i	−0.817598	−	0.219075i	−0.643296	+	0.765617i	$0.722434\pi$
$72$		0			0
$73$	−4.55425	−	1.22031i	−0.533035	−	0.142826i	−0.0177454	−	0.999843i	$-0.505649\pi$
$73$	−4.55425	−	1.22031i	−0.533035	−	0.142826i	−0.515289	+	0.857016i	$0.672315\pi$
$74$	1.53832	−	2.66446i	0.178827	−	0.309737i
$75$		0			0
$76$	−0.246808	−	0.921099i	−0.0283108	−	0.105657i
$77$	−0.302997	−	5.95950i	−0.0345297	−	0.679148i
$78$		0			0
$79$	−4.67565	+	8.09846i	−0.526052	+	0.911148i	0.473488	+	0.880800i	$0.342995\pi$
$79$	−4.67565	+	8.09846i	−0.526052	+	0.911148i	−0.999539	+	0.0303476i	$0.990339\pi$
$80$	5.30151	+	5.30151i	0.592726	+	0.592726i
$81$		0			0
$82$	10.3511			1.14309
$83$	−3.82650	−	3.82650i	−0.420013	−	0.420013i	0.465195	−	0.885208i	$-0.345984\pi$
$83$	−3.82650	−	3.82650i	−0.420013	−	0.420013i	−0.885208	+	0.465195i	$0.845984\pi$
$84$		0			0
$85$	0.743393	−	2.77438i	0.0806322	−	0.300924i
$86$	15.4445	−	4.13835i	1.66543	−	0.446250i
$87$		0			0
$88$		−	6.15037i		−	0.655631i
$89$	−4.91594	−	1.31722i	−0.521089	−	0.139625i	−0.0113186	−	0.999936i	$-0.503603\pi$
$89$	−4.91594	−	1.31722i	−0.521089	−	0.139625i	−0.509770	+	0.860311i	$0.670270\pi$
$90$		0			0
$91$	−1.19131	+	9.46471i	−0.124883	+	0.992171i
$92$	0.862782			0.0899512
$93$		0			0
$94$		−	18.8618i		−	1.94545i
$95$	10.9850	+	6.34217i	1.12703	+	0.650693i
$96$		0			0
$97$	−2.57958	+	9.62711i	−0.261916	+	0.977485i	0.702195	+	0.711985i	$0.252204\pi$
$97$	−2.57958	+	9.62711i	−0.261916	+	0.977485i	−0.964111	+	0.265500i	$0.914463\pi$
$98$	1.63068	−	10.0917i	0.164724	−	1.01942i
$99$		0			0
$100$	−0.250081			−0.0250081
$101$	−6.81498			−0.678115			−0.339058	−	0.940766i	$-0.610108\pi$
$101$	−6.81498			−0.678115			−0.339058	+	0.940766i	$0.610108\pi$
$102$		0			0
$103$	−5.66334	+	9.80919i	−0.558025	+	0.966528i	0.439636	+	0.898176i	$0.355107\pi$
$103$	−5.66334	+	9.80919i	−0.558025	+	0.966528i	−0.997661	+	0.0683520i	$0.978226\pi$
$104$	−1.72164	+	9.68032i	−0.168821	+	0.949233i
$105$		0			0
$106$	−2.27493	−	8.49017i	−0.220961	−	0.824638i
$107$	−2.27413	−	3.93890i	−0.219848	−	0.380788i	0.734913	−	0.678161i	$-0.237223\pi$
$107$	−2.27413	−	3.93890i	−0.219848	−	0.380788i	−0.954761	+	0.297373i	$0.903889\pi$
$108$		0			0
$109$	−2.02887	−	0.543633i	−0.194330	−	0.0520706i	0.160341	−	0.987062i	$-0.448741\pi$
$109$	−2.02887	−	0.543633i	−0.194330	−	0.0520706i	−0.354671	+	0.934991i	$0.615407\pi$
$110$	−4.11077	−	4.11077i	−0.391946	−	0.391946i
$111$		0			0
$112$	2.35378	−	10.9893i	0.222412	−	1.03839i
$113$	3.95721	+	6.85409i	0.372263	+	0.644779i	0.989913	−	0.141674i	$-0.0452486\pi$
$113$	3.95721	+	6.85409i	0.372263	+	0.644779i	−0.617650	+	0.786453i	$0.711915\pi$
$114$		0			0
$115$	−8.11505	+	8.11505i	−0.756732	+	0.756732i
$116$	−0.896867	+	0.517807i	−0.0832720	+	0.0480771i
$117$		0			0
$118$			11.4226i			1.05154i
$119$	−4.09680	+	1.32406i	−0.375553	+	0.121377i
$120$		0			0
$121$		−	5.91323i		−	0.537566i
$122$	−2.36876	+	8.84032i	−0.214457	+	0.800365i
$123$		0			0
$124$	0.612243	−	0.612243i	0.0549811	−	0.0549811i
$125$	8.59251	−	8.59251i	0.768538	−	0.768538i
$126$		0			0
$127$	14.3203	+	8.26781i	1.27072	+	0.733650i	0.975123	−	0.221664i	$-0.0711487\pi$
$127$	14.3203	+	8.26781i	1.27072	+	0.733650i	0.295595	+	0.955313i	$0.404482\pi$
$128$	3.18535	−	11.8879i	0.281548	−	1.05075i
$129$		0			0
$130$	5.31940	+	7.62081i	0.466542	+	0.668389i
$131$	−11.0979	−	6.40737i	−0.969628	−	0.559815i	−0.0705050	−	0.997511i	$-0.522461\pi$
$131$	−11.0979	−	6.40737i	−0.969628	−	0.559815i	−0.899123	+	0.437697i	$0.855794\pi$
$132$		0			0
$133$	−0.965457	−	18.9891i	−0.0837157	−	1.64656i
$134$	6.70939	−	3.87367i	0.579603	−	0.334634i
$135$		0			0
$136$	−4.28641	+	1.14854i	−0.367556	+	0.0984864i
$137$	−8.51271	+	2.28097i	−0.727290	+	0.194877i	−0.603422	−	0.797422i	$-0.706197\pi$
$137$	−8.51271	+	2.28097i	−0.727290	+	0.194877i	−0.123868	+	0.992299i	$0.539530\pi$
$138$		0			0
$139$	10.9213	−	6.30540i	0.926330	−	0.534817i	0.0406813	−	0.999172i	$-0.487047\pi$
$139$	10.9213	−	6.30540i	0.926330	−	0.534817i	0.885649	+	0.464355i	$0.153714\pi$
$140$	−0.336676	−	0.520211i	−0.0284543	−	0.0439659i
$141$		0			0
$142$	9.02028	+	5.20786i	0.756965	+	0.437034i
$143$	1.42391	−	8.00628i	0.119074	−	0.669519i
$144$		0			0
$145$	3.56532	−	13.3060i	0.296084	−	1.10500i
$146$	5.96304	+	3.44276i	0.493505	+	0.284925i
$147$		0			0
$148$	−0.197672	+	0.197672i	−0.0162486	+	0.0162486i
$149$	−5.24546	+	5.24546i	−0.429725	+	0.429725i	−0.888535	−	0.458810i	$-0.848276\pi$
$149$	−5.24546	+	5.24546i	−0.429725	+	0.429725i	0.458810	+	0.888535i	$0.348276\pi$
$150$		0			0
$151$	−3.65054	+	13.6240i	−0.297077	+	1.10871i	0.642477	+	0.766305i	$0.277907\pi$
$151$	−3.65054	+	13.6240i	−0.297077	+	1.10871i	−0.939554	+	0.342401i	$0.888760\pi$
$152$		−	19.5973i		−	1.58955i
$153$		0			0
$154$	−1.82511	+	8.52107i	−0.147072	+	0.686647i
$155$			11.5171i			0.925078i
$156$		0			0
$157$	−4.64586	+	2.68229i	−0.370780	+	0.214070i	−0.673799	−	0.738915i	$-0.735339\pi$
$157$	−4.64586	+	2.68229i	−0.370780	+	0.214070i	0.303019	+	0.952984i	$0.402005\pi$
$158$	9.65653	−	9.65653i	0.768232	−	0.768232i
$159$		0			0
$160$	−0.661367	−	1.14552i	−0.0522856	−	0.0905614i
$161$	16.8214	+	3.60295i	1.32571	+	0.283952i
$162$		0			0
$163$	−11.3721	−	11.3721i	−0.890731	−	0.890731i	0.103861	−	0.994592i	$-0.466880\pi$
$163$	−11.3721	−	11.3721i	−0.890731	−	0.890731i	−0.994592	+	0.103861i	$0.966880\pi$
$164$	−0.908474	−	0.243425i	−0.0709399	−	0.0190083i
$165$		0			0
$166$	3.95140	+	6.84402i	0.306688	+	0.531199i
$167$	−1.36025	−	5.07654i	−0.105260	−	0.392834i	0.893115	−	0.449829i	$-0.148515\pi$
$167$	−1.36025	−	5.07654i	−0.105260	−	0.392834i	−0.998375	+	0.0569944i	$0.981848\pi$
$168$		0			0
$169$	−4.48231	+	12.2028i	−0.344793	+	0.938679i
$170$	−2.09728	+	3.63259i	−0.160854	+	0.278607i
$171$		0			0
$172$	−1.45283			−0.110777
$173$	−5.71254			−0.434316			−0.217158	−	0.976136i	$-0.569679\pi$
$173$	−5.71254			−0.434316			−0.217158	+	0.976136i	$0.569679\pi$
$174$		0			0
$175$	−4.87576	−	1.04433i	−0.368573	−	0.0789441i
$176$	−2.47959	+	9.25394i	−0.186906	+	0.697542i
$177$		0			0
$178$	6.43662	+	3.71618i	0.482445	+	0.278540i
$179$			5.98541i			0.447371i	0.974661	+	0.223685i	$0.0718088\pi$
$179$			5.98541i			0.447371i	−0.974661	+	0.223685i	$0.928191\pi$
$180$		0			0
$181$	14.3000			1.06291			0.531455	−	0.847086i	$-0.321645\pi$
$181$	14.3000			1.06291			0.531455	+	0.847086i	$0.321645\pi$
$182$	5.25788	−	12.9008i	0.389740	−	0.956268i
$183$		0			0
$184$	17.1268	+	4.58913i	1.26261	+	0.338315i
$185$		−	3.71849i		−	0.273389i
$186$		0			0
$187$	3.54515	−	0.949920i	0.259247	−	0.0694650i
$188$	−0.443570	+	1.65543i	−0.0323507	+	0.120734i
$189$		0			0
$190$	−13.0984	−	13.0984i	−0.950255	−	0.950255i
$191$	7.65775			0.554096			0.277048	−	0.960856i	$-0.410644\pi$
$191$	7.65775			0.554096			0.277048	+	0.960856i	$0.410644\pi$
$192$		0			0
$193$	−4.55803	−	4.55803i	−0.328094	−	0.328094i	0.523767	−	0.851861i	$-0.324526\pi$
$193$	−4.55803	−	4.55803i	−0.328094	−	0.328094i	−0.851861	+	0.523767i	$0.824526\pi$
$194$	7.27757	−	12.6051i	0.522499	−	0.904995i
$195$		0			0
$196$	−0.380444	+	0.847362i	−0.0271746	+	0.0605259i
$197$	−5.31612	−	19.8400i	−0.378758	−	1.41354i	−0.847775	−	0.530355i	$-0.822059\pi$
$197$	−5.31612	−	19.8400i	−0.378758	−	1.41354i	0.469017	−	0.883189i	$-0.344608\pi$
$198$		0			0
$199$	3.37252	−	5.84137i	0.239071	−	0.414084i	−0.721377	−	0.692543i	$-0.756490\pi$
$199$	3.37252	−	5.84137i	0.239071	−	0.414084i	0.960448	+	0.278459i	$0.0898237\pi$
$200$	−4.96430	−	1.33018i	−0.351029	−	0.0940579i
$201$		0			0
$202$	9.61329	+	2.57587i	0.676389	+	0.181238i
$203$	−19.6483	+	6.35024i	−1.37904	+	0.445699i
$204$		0			0
$205$	10.8344	−	6.25524i	0.756707	−	0.436885i
$206$	11.6964	−	11.6964i	0.814926	−	0.814926i
$207$		0			0
$208$	6.49313	−	13.8711i	0.450217	−	0.961785i
$209$			16.2083i			1.12115i
$210$		0			0
$211$	8.08382	−	14.0016i	0.556513	−	0.963910i	−0.441271	−	0.897374i	$-0.645472\pi$
$211$	8.08382	−	14.0016i	0.556513	−	0.963910i	0.997784	−	0.0665355i	$-0.0211946\pi$
$212$			0.798648i			0.0548514i
$213$		0			0
$214$	1.71911	+	6.41582i	0.117516	+	0.438577i
$215$	13.6648	−	13.6648i	0.931934	−	0.931934i
$216$		0			0
$217$	14.4935	−	9.38003i	0.983879	−	0.636758i
$218$	2.65647	+	1.53371i	0.179919	+	0.103876i
$219$		0			0
$220$	0.264114	+	0.457458i	0.0178065	+	0.0308418i
$221$	−5.84576	+	0.502744i	−0.393228	+	0.0338182i
$222$		0			0
$223$	6.29395	−	1.68646i	0.421474	−	0.112934i	−0.0418472	−	0.999124i	$-0.513324\pi$
$223$	6.29395	−	1.68646i	0.421474	−	0.112934i	0.463321	+	0.886190i	$0.346658\pi$
$224$	−0.902908	+	1.76524i	−0.0603281	+	0.117945i
$225$		0			0
$226$	−2.99144	−	11.1642i	−0.198987	−	0.742631i
$227$	10.1500	−	2.71970i	0.673682	−	0.180513i	0.0942692	−	0.995547i	$-0.469949\pi$
$227$	10.1500	−	2.71970i	0.673682	−	0.180513i	0.579413	+	0.815034i	$0.303282\pi$
$228$		0			0
$229$	1.12133	+	4.18487i	0.0740997	+	0.276544i	0.993028	−	0.117881i	$-0.0376103\pi$
$229$	1.12133	+	4.18487i	0.0740997	+	0.276544i	−0.918928	+	0.394425i	$0.870944\pi$
$230$	14.5145	−	8.37993i	0.957055	−	0.552556i
$231$		0			0
$232$	−20.5577	+	5.50841i	−1.34968	+	0.361645i
$233$	13.8386	+	7.98973i	0.906598	+	0.523425i	0.879335	−	0.476204i	$-0.157987\pi$
$233$	13.8386	+	7.98973i	0.906598	+	0.523425i	0.0272631	+	0.999628i	$0.491321\pi$
$234$		0			0
$235$	−11.3983	−	19.7425i	−0.743545	−	1.28786i
$236$	0.268625	−	1.00252i	0.0174860	−	0.0652586i
$237$		0			0
$238$	6.27946	−	0.319265i	0.407037	−	0.0206949i
$239$	1.84753	−	1.84753i	0.119507	−	0.119507i	−0.644824	−	0.764331i	$-0.723069\pi$
$239$	1.84753	−	1.84753i	0.119507	−	0.119507i	0.764331	+	0.644824i	$0.223069\pi$
$240$		0			0
$241$	−5.09222	−	19.0044i	−0.328019	−	1.22418i	−0.911242	−	0.411871i	$-0.864875\pi$
$241$	−5.09222	−	19.0044i	−0.328019	−	1.22418i	0.583223	−	0.812312i	$-0.301791\pi$
$242$	−2.23504	+	8.34128i	−0.143674	+	0.536198i
$243$		0			0
$244$	0.415793	−	0.720175i	0.0266184	−	0.0461045i
$245$	−4.39169	−	11.5484i	−0.280575	−	0.737797i
$246$		0			0
$247$	4.53709	−	25.5108i	0.288688	−	1.62322i
$248$	15.4100	−	8.89696i	0.978536	−	0.564958i
$249$		0			0
$250$	−15.3684	+	8.87298i	−0.971986	+	0.561176i
$251$	3.65679	+	6.33375i	0.230815	+	0.399783i	0.958048	−	0.286608i	$-0.0925276\pi$
$251$	3.65679	+	6.33375i	0.230815	+	0.399783i	−0.727234	+	0.686390i	$0.759194\pi$
$252$		0			0
$253$	−14.1651	−	3.79552i	−0.890550	−	0.238622i
$254$	−17.0754	−	17.0754i	−1.07140	−	1.07140i
$255$		0			0
$256$	−1.58546	+	2.74610i	−0.0990912	+	0.171631i
$257$	−4.71541	−	8.16733i	−0.294139	−	0.509464i	0.680645	−	0.732613i	$-0.261700\pi$
$257$	−4.71541	−	8.16733i	−0.294139	−	0.509464i	−0.974784	+	0.223149i	$0.928366\pi$
$258$		0			0
$259$	−4.67944	+	3.02849i	−0.290766	+	0.188181i
$260$	−0.287645	−	0.793944i	−0.0178390	−	0.0492383i
$261$		0			0
$262$	13.2330	+	13.2330i	0.817539	+	0.817539i
$263$	4.60736			0.284102			0.142051	−	0.989859i	$-0.454630\pi$
$263$	4.60736			0.284102			0.142051	+	0.989859i	$0.454630\pi$
$264$		0			0
$265$	−7.51183	−	7.51183i	−0.461448	−	0.461448i
$266$	−5.81546	+	27.1512i	−0.356569	+	1.66474i
$267$		0			0
$268$	−0.679954	+	0.182193i	−0.0415348	+	0.0111292i
$269$	11.7137	+	6.76289i	0.714195	+	0.412341i	0.812612	−	0.582805i	$-0.198045\pi$
$269$	11.7137	+	6.76289i	0.714195	+	0.412341i	−0.0984174	+	0.995145i	$0.531378\pi$
$270$		0			0
$271$	−17.1433	−	4.59354i	−1.04138	−	0.279038i	−0.302697	−	0.953087i	$-0.597887\pi$
$271$	−17.1433	−	4.59354i	−1.04138	−	0.279038i	−0.738687	+	0.674049i	$0.764554\pi$
$272$	6.91244			0.419128
$273$		0			0
$274$	12.8703			0.777522
$275$	4.10581	+	1.10015i	0.247590	+	0.0663415i
$276$		0			0
$277$	10.0049	+	5.77632i	0.601135	+	0.347065i	0.769488	−	0.638661i	$-0.220511\pi$
$277$	10.0049	+	5.77632i	0.601135	+	0.347065i	−0.168353	+	0.985727i	$0.553845\pi$
$278$	−17.7890	+	4.76654i	−1.06691	+	0.285878i
$279$		0			0
$280$	−3.91626	−	12.1173i	−0.234042	−	0.724150i
$281$	11.8978	+	11.8978i	0.709764	+	0.709764i	0.966486	−	0.256721i	$-0.0826422\pi$
$281$	11.8978	+	11.8978i	0.709764	+	0.709764i	−0.256721	+	0.966486i	$0.582642\pi$
$282$		0			0
$283$	21.6412			1.28644			0.643219	−	0.765682i	$-0.277598\pi$
$283$	21.6412			1.28644			0.643219	+	0.765682i	$0.277598\pi$
$284$	−0.669202	−	0.669202i	−0.0397099	−	0.0397099i
$285$		0			0
$286$	−5.03474	+	10.7556i	−0.297711	+	0.635990i
$287$	−16.6957	−	8.53975i	−0.985518	−	0.504086i
$288$		0			0
$289$	7.17594	+	12.4291i	0.422114	+	0.731123i
$290$	−10.0586	+	17.4220i	−0.590661	+	1.02305i
$291$		0			0
$292$	−0.442390	−	0.442390i	−0.0258889	−	0.0258889i
$293$	−9.50719	−	2.54744i	−0.555416	−	0.148823i	−0.0298165	−	0.999555i	$-0.509492\pi$
$293$	−9.50719	−	2.54744i	−0.555416	−	0.148823i	−0.525600	+	0.850732i	$0.676159\pi$
$294$		0			0
$295$	6.90280	+	11.9560i	0.401896	+	0.696105i
$296$	−4.97536	+	2.87253i	−0.289187	+	0.166962i
$297$		0			0
$298$	9.38196	−	5.41668i	0.543482	−	0.313780i
$299$	21.2325	+	9.93907i	1.22791	+	0.574791i
$300$		0			0
$301$	−28.3254	−	6.06697i	−1.63265	−	0.349694i
$302$	10.2990	−	17.8384i	0.592641	−	1.02648i
$303$		0			0
$304$	−7.90084	+	29.4863i	−0.453144	+	1.69116i
$305$	2.86292	+	10.6846i	0.163930	+	0.611796i
$306$		0			0
$307$	−16.2375	+	16.2375i	−0.926725	+	0.926725i	−0.997493	−	0.0707682i	$-0.977455\pi$
$307$	−16.2375	+	16.2375i	−0.926725	+	0.926725i	0.0707682	+	0.997493i	$0.477455\pi$
$308$	0.360572	−	0.704940i	0.0205455	−	0.0401677i
$309$		0			0
$310$	4.35316	−	16.2462i	0.247243	−	0.922723i
$311$	6.35536	+	11.0078i	0.360379	+	0.624195i	0.988023	−	0.154305i	$-0.0493139\pi$
$311$	6.35536	+	11.0078i	0.360379	+	0.624195i	−0.627644	+	0.778501i	$0.715981\pi$
$312$		0			0
$313$	1.51101	+	0.872380i	0.0854072	+	0.0493099i	0.542095	−	0.840317i	$-0.317631\pi$
$313$	1.51101	+	0.872380i	0.0854072	+	0.0493099i	−0.456688	+	0.889627i	$0.650964\pi$
$314$	7.56734	−	2.02766i	0.427049	−	0.114428i
$315$		0			0
$316$	−1.07461	+	0.620425i	−0.0604514	+	0.0349016i
$317$	6.21636	+	23.1998i	0.349146	+	1.30303i	0.887694	+	0.460434i	$0.152306\pi$
$317$	6.21636	+	23.1998i	0.349146	+	1.30303i	−0.538548	+	0.842595i	$0.681027\pi$
$318$		0			0
$319$	17.0026	−	4.55583i	0.951963	−	0.255078i
$320$	−3.38101	−	12.6181i	−0.189004	−	0.705374i
$321$		0			0
$322$	−22.3667	−	11.4404i	−1.24645	−	0.637549i
$323$	11.2961	−	3.02678i	0.628532	−	0.168415i
$324$		0			0
$325$	−6.15435	−	2.88089i	−0.341382	−	0.159803i
$326$	11.7433	+	20.3400i	0.650400	+	1.12653i
$327$		0			0
$328$	−16.7391	−	9.66433i	−0.924263	−	0.533623i
$329$	−15.5612	+	30.4230i	−0.857916	+	1.67728i
$330$		0			0
$331$	−10.9866	+	10.9866i	−0.603879	+	0.603879i	−0.941340	−	0.337461i	$-0.890432\pi$
$331$	−10.9866	+	10.9866i	−0.603879	+	0.603879i	0.337461	+	0.941340i	$0.390432\pi$
$332$	−0.185849	−	0.693597i	−0.0101998	−	0.0380661i
$333$		0			0
$334$			7.67517i			0.419967i
$335$	4.68178	−	8.10908i	0.255793	−	0.443046i
$336$		0			0
$337$		−	4.66674i		−	0.254213i	−0.991889	−	0.127107i	$-0.959431\pi$
$337$		−	4.66674i		−	0.254213i	0.991889	−	0.127107i	$-0.0405691\pi$
$338$	10.9351	−	15.5193i	0.594793	−	0.844137i
$339$		0			0
$340$	0.269497	−	0.269497i	0.0146155	−	0.0146155i
$341$	−12.7451	+	7.35839i	−0.690187	+	0.398479i
$342$		0			0
$343$	−10.9560	+	14.9321i	−0.591567	+	0.806256i
$344$	−28.8397	−	7.72757i	−1.55493	−	0.416643i
$345$		0			0
$346$	8.05818	+	2.15918i	0.433211	+	0.116078i
$347$	−16.7637	+	29.0355i	−0.899921	+	1.55871i	−0.0723277	+	0.997381i	$0.523043\pi$
$347$	−16.7637	+	29.0355i	−0.899921	+	1.55871i	−0.827593	+	0.561328i	$0.810291\pi$
$348$		0			0
$349$	1.15161	+	4.29785i	0.0616440	+	0.230059i	0.989874	−	0.141948i	$-0.0453365\pi$
$349$	1.15161	+	4.29785i	0.0616440	+	0.230059i	−0.928230	+	0.372007i	$0.878670\pi$
$350$	6.48309	+	3.31606i	0.346536	+	0.177251i
$351$		0			0
$352$	0.845106	−	1.46377i	0.0450443	−	0.0780190i
$353$	−19.3433	−	19.3433i	−1.02954	−	1.02954i	−0.999550	−	0.0299886i	$-0.990453\pi$
$353$	−19.3433	−	19.3433i	−1.02954	−	1.02954i	−0.0299886	−	0.999550i	$-0.509547\pi$
$354$		0			0
$355$	12.5886			0.668134
$356$	−0.477524	−	0.477524i	−0.0253087	−	0.0253087i
$357$		0			0
$358$	2.26232	−	8.44310i	0.119567	−	0.446232i
$359$	31.7614	−	8.51045i	1.67630	−	0.449164i	0.709505	−	0.704701i	$-0.248919\pi$
$359$	31.7614	−	8.51045i	1.67630	−	0.449164i	0.966799	+	0.255537i	$0.0822521\pi$
$360$		0			0
$361$			32.6453i			1.71817i
$362$	−20.1718	−	5.40501i	−1.06020	−	0.284081i
$363$		0			0
$364$	−0.764849	+	1.00860i	−0.0400890	+	0.0528651i
$365$	8.32196			0.435591
$366$		0			0
$367$			13.1452i			0.686173i	0.939304	+	0.343086i	$0.111472\pi$
$367$			13.1452i			0.686173i	−0.939304	+	0.343086i	$0.888528\pi$
$368$	−23.9192	−	13.8097i	−1.24687	−	0.719883i
$369$		0			0
$370$	−1.40549	+	5.24535i	−0.0730678	+	0.272693i
$371$	−3.33513	+	15.5710i	−0.173152	+	0.808407i
$372$		0			0
$373$	−13.5493			−0.701556			−0.350778	−	0.936459i	$-0.614083\pi$
$373$	−13.5493			−0.701556			−0.350778	+	0.936459i	$0.614083\pi$
$374$	−5.35988			−0.277153
$375$		0			0
$376$	−17.6104	+	30.5021i	−0.908186	+	1.57302i
$377$	−28.0364	+	2.41117i	−1.44395	+	0.124181i
$378$		0			0
$379$	3.10819	+	11.5999i	0.159657	+	0.595848i	0.998661	+	0.0517233i	$0.0164714\pi$
$379$	3.10819	+	11.5999i	0.159657	+	0.595848i	−0.839005	+	0.544124i	$0.816862\pi$
$380$	0.841560	+	1.45762i	0.0431711	+	0.0747745i
$381$		0			0
$382$	−10.8021	−	2.89442i	−0.552685	−	0.148091i
$383$	−5.62895	−	5.62895i	−0.287626	−	0.287626i	0.548515	−	0.836141i	$-0.315193\pi$
$383$	−5.62895	−	5.62895i	−0.287626	−	0.287626i	−0.836141	+	0.548515i	$0.815193\pi$
$384$		0			0
$385$	3.23902	+	10.0219i	0.165076	+	0.510762i
$386$	4.70680	+	8.15242i	0.239570	+	0.414947i
$387$		0			0
$388$	−0.935156	+	0.935156i	−0.0474754	+	0.0474754i
$389$	−26.9226	+	15.5438i	−1.36503	+	0.788100i	−0.990288	−	0.139029i	$-0.955602\pi$
$389$	−26.9226	+	15.5438i	−1.36503	+	0.788100i	−0.374742	+	0.927129i	$0.622269\pi$
$390$		0			0
$391$			10.5809i			0.535100i
$392$	−12.0592	+	14.7972i	−0.609082	+	0.747371i
$393$		0			0
$394$			29.9960i			1.51118i
$395$	4.27189	−	15.9429i	0.214942	−	0.802176i
$396$		0			0
$397$	−5.72844	+	5.72844i	−0.287502	+	0.287502i	−0.836092	−	0.548590i	$-0.815165\pi$
$397$	−5.72844	+	5.72844i	−0.287502	+	0.287502i	0.548590	+	0.836092i	$0.315165\pi$
$398$	−6.96519	+	6.96519i	−0.349134	+	0.349134i
$399$		0			0
$400$	6.93308	+	4.00282i	0.346654	+	0.200141i
$401$	4.32020	−	16.1232i	0.215740	−	0.805154i	−0.770164	−	0.637846i	$-0.779826\pi$
$401$	4.32020	−	16.1232i	0.215740	−	0.805154i	0.985905	−	0.167309i	$-0.0535076\pi$
$402$		0			0
$403$	22.1199	−	8.01401i	1.10187	−	0.399206i
$404$	−0.783145	−	0.452149i	−0.0389629	−	0.0224952i
$405$		0			0
$406$	30.1164	−	1.53120i	1.49465	−	0.0759922i
$407$	4.11496	−	2.37577i	0.203971	−	0.117763i
$408$		0			0
$409$	16.8910	−	4.52593i	0.835206	−	0.223793i	0.184223	−	0.982885i	$-0.441023\pi$
$409$	16.8910	−	4.52593i	0.835206	−	0.223793i	0.650984	+	0.759092i	$0.274357\pi$
$410$	−17.6475	+	4.72862i	−0.871546	+	0.233530i
$411$		0			0
$412$	−1.30161	+	0.751484i	−0.0641256	+	0.0370229i
$413$	9.42380	−	18.4241i	0.463715	−	0.906591i
$414$		0			0
$415$	8.27179	+	4.77572i	0.406046	+	0.234431i
$416$	−1.73989	+	2.06732i	−0.0853052	+	0.101359i
$417$		0			0
$418$	6.12628	−	22.8636i	0.299646	−	1.11829i
$419$	−12.1131	−	6.99350i	−0.591764	−	0.341655i	0.174031	−	0.984740i	$-0.444321\pi$
$419$	−12.1131	−	6.99350i	−0.591764	−	0.341655i	−0.765795	+	0.643085i	$0.777654\pi$
$420$		0			0
$421$	11.2239	−	11.2239i	0.547020	−	0.547020i	−0.378558	−	0.925578i	$-0.623580\pi$
$421$	11.2239	−	11.2239i	0.547020	−	0.547020i	0.925578	+	0.378558i	$0.123580\pi$
$422$	−16.6954	+	16.6954i	−0.812718	+	0.812718i
$423$		0			0
$424$	−4.24800	+	15.8538i	−0.206301	+	0.769926i
$425$		−	3.06693i		−	0.148768i
$426$		0			0
$427$	11.1140	−	12.3047i	0.537846	−	0.595467i
$428$		−	0.603520i		−	0.0291722i
$429$		0			0
$430$	−24.4407	+	14.1109i	−1.17864	+	0.680486i
$431$	20.5510	−	20.5510i	0.989905	−	0.989905i	−0.0100445	−	0.999950i	$-0.503197\pi$
$431$	20.5510	−	20.5510i	0.989905	−	0.989905i	0.999950	+	0.0100445i	$0.00319731\pi$
$432$		0			0
$433$	−14.2229	−	24.6348i	−0.683508	−	1.18387i	−0.973903	−	0.226964i	$-0.927120\pi$
$433$	−14.2229	−	24.6348i	−0.683508	−	1.18387i	0.290395	−	0.956907i	$-0.406213\pi$
$434$	−23.9900	+	7.75346i	−1.15156	+	0.372178i
$435$		0			0
$436$	−0.197080	−	0.197080i	−0.00943841	−	0.00943841i
$437$	−45.1349	−	12.0939i	−2.15910	−	0.578528i
$438$		0			0
$439$	−16.3048	−	28.2408i	−0.778186	−	1.34786i	−0.932986	−	0.359912i	$-0.882807\pi$
$439$	−16.3048	−	28.2408i	−0.778186	−	1.34786i	0.154800	−	0.987946i	$-0.450527\pi$
$440$	2.80963	+	10.4857i	0.133944	+	0.499886i
$441$		0			0
$442$	8.43613	+	1.50036i	0.401266	+	0.0713649i
$443$	6.08812	−	10.5449i	0.289255	−	0.501005i	−0.684377	−	0.729128i	$-0.739926\pi$
$443$	6.08812	−	10.5449i	0.289255	−	0.501005i	0.973632	+	0.228124i	$0.0732591\pi$
$444$		0			0
$445$	8.98287			0.425829
$446$	−9.51577			−0.450585
$447$		0			0
$448$	−13.1253	+	14.5315i	−0.620113	+	0.686547i
$449$	0.322297	−	1.20283i	0.0152101	−	0.0567650i	−0.957904	−	0.287090i	$-0.907312\pi$
$449$	0.322297	−	1.20283i	0.0152101	−	0.0567650i	0.973114	+	0.230325i	$0.0739789\pi$
$450$		0			0
$451$	13.8444	+	7.99306i	0.651906	+	0.376378i
$452$			1.05019i			0.0493966i
$453$		0			0
$454$	−15.3458			−0.720212
$455$	−2.29265	−	16.6805i	−0.107481	−	0.781994i
$456$		0			0
$457$	−7.36967	−	1.97470i	−0.344738	−	0.0923724i	0.0822955	−	0.996608i	$-0.473775\pi$
$457$	−7.36967	−	1.97470i	−0.344738	−	0.0923724i	−0.427034	+	0.904236i	$0.640442\pi$
$458$		−	6.32707i		−	0.295644i
$459$		0			0
$460$	−1.47095	+	0.394139i	−0.0685833	+	0.0183768i
$461$	−0.143143	+	0.534215i	−0.00666682	+	0.0248809i	−0.969179	−	0.246357i	$-0.920766\pi$
$461$	−0.143143	+	0.534215i	−0.00666682	+	0.0248809i	0.962512	+	0.271238i	$0.0874331\pi$
$462$		0			0
$463$	28.5117	+	28.5117i	1.32505	+	1.32505i	0.909627	+	0.415426i	$0.136367\pi$
$463$	28.5117	+	28.5117i	1.32505	+	1.32505i	0.415426	+	0.909627i	$0.363633\pi$
$464$	33.1522			1.53905
$465$		0			0
$466$	−16.5010	−	16.5010i	−0.764396	−	0.764396i
$467$	−15.3705	+	26.6225i	−0.711262	+	1.23194i	0.253121	+	0.967435i	$0.418543\pi$
$467$	−15.3705	+	26.6225i	−0.711262	+	1.23194i	−0.964384	+	0.264508i	$0.914791\pi$
$468$		0			0
$469$	−14.0177	+	0.712699i	−0.647277	+	0.0329094i
$470$	8.61652	+	32.1573i	0.397450	+	1.48330i
$471$		0			0
$472$	10.6648	−	18.4720i	0.490887	−	0.850241i
$473$	23.8524	+	6.39123i	1.09673	+	0.293869i
$474$		0			0
$475$	13.0826	+	3.50546i	0.600269	+	0.160842i
$476$	−0.558632	−	0.119652i	−0.0256048	−	0.00548426i
$477$		0			0
$478$	−3.30447	+	1.90784i	−0.151143	+	0.0872624i
$479$	−3.20616	+	3.20616i	−0.146493	+	0.146493i	−0.776550	−	0.630056i	$-0.783032\pi$
$479$	−3.20616	+	3.20616i	−0.146493	+	0.146493i	0.630056	+	0.776550i	$0.283032\pi$
$480$		0			0
$481$	−7.14174	+	2.58745i	−0.325635	+	0.117978i
$482$			28.7326i			1.30873i
$483$		0			0
$484$	0.392321	−	0.679520i	0.0178328	−	0.0308873i
$485$		−	17.5916i		−	0.798792i
$486$		0			0
$487$	5.72908	+	21.3812i	0.259609	+	0.968876i	0.965468	+	0.260523i	$0.0838949\pi$
$487$	5.72908	+	21.3812i	0.259609	+	0.968876i	−0.705858	+	0.708353i	$0.749438\pi$
$488$	12.0844	−	12.0844i	0.547035	−	0.547035i
$489$		0			0
$490$	1.83001	+	17.9502i	0.0826713	+	0.810907i
$491$	23.7750	+	13.7265i	1.07295	+	0.619469i	0.928986	−	0.370114i	$-0.120681\pi$
$491$	23.7750	+	13.7265i	1.07295	+	0.619469i	0.143965	+	0.989583i	$0.454015\pi$
$492$		0			0
$493$	−6.35024	−	10.9989i	−0.286000	−	0.495367i
$494$	−16.0425	+	34.2710i	−0.721785	+	1.54193i
$495$		0			0
$496$	−26.7730	+	7.17381i	−1.20214	+	0.322114i
$497$	−10.2527	−	15.8418i	−0.459896	−	0.710603i
$498$		0			0
$499$	8.08079	+	30.1579i	0.361746	+	1.35005i	0.871779	+	0.489900i	$0.162967\pi$
$499$	8.08079	+	30.1579i	0.361746	+	1.35005i	−0.510033	+	0.860155i	$0.670367\pi$
$500$	1.55749	−	0.417329i	0.0696532	−	0.0186635i
$501$		0			0
$502$	−2.76433	−	10.3166i	−0.123378	−	0.460454i
$503$	33.4708	−	19.3244i	1.49239	−	0.861633i	0.492429	−	0.870352i	$-0.336109\pi$
$503$	33.4708	−	19.3244i	1.49239	−	0.861633i	0.999962	+	0.00871978i	$0.00277563\pi$
$504$		0			0
$505$	11.6188	−	3.11324i	0.517029	−	0.138537i
$506$	18.5468	+	10.7080i	0.824507	+	0.476029i
$507$		0			0
$508$	1.09708	+	1.90020i	0.0486750	+	0.0843076i
$509$	−2.14731	+	8.01388i	−0.0951779	+	0.355209i	−0.997046	−	0.0768019i	$-0.975529\pi$
$509$	−2.14731	+	8.01388i	−0.0951779	+	0.355209i	0.901868	+	0.432011i	$0.142196\pi$
$510$		0			0
$511$	−6.77775	−	10.4726i	−0.299830	−	0.463279i
$512$	−14.1307	+	14.1307i	−0.624493	+	0.624493i
$513$		0			0
$514$	3.56459	+	13.3032i	0.157227	+	0.586781i
$515$	5.17429	−	19.3107i	0.228007	−	0.850932i
$516$		0			0
$517$	14.5650	−	25.2273i	0.640567	−	1.10950i
$518$	7.74556	−	2.50333i	0.340321	−	0.109990i
$519$		0			0
$520$	−1.48699	−	17.2904i	−0.0652090	−	0.758232i
$521$	−23.3799	+	13.4984i	−1.02429	+	0.591375i	−0.915344	−	0.402672i	$-0.868082\pi$
$521$	−23.3799	+	13.4984i	−1.02429	+	0.591375i	−0.108948	+	0.994047i	$0.534748\pi$
$522$		0			0
$523$	5.97993	−	3.45251i	0.261484	−	0.150968i	−0.363527	−	0.931584i	$-0.618428\pi$
$523$	5.97993	−	3.45251i	0.261484	−	0.150968i	0.625011	+	0.780616i	$0.285094\pi$
$524$	−0.850212	−	1.47261i	−0.0371417	−	0.0643313i
$525$		0			0
$526$	−6.49920	−	1.74145i	−0.283378	−	0.0759310i
$527$	7.50838	+	7.50838i	0.327070	+	0.327070i
$528$		0			0
$529$	9.63866	−	16.6946i	0.419072	−	0.725854i
$530$	7.75702	+	13.4356i	0.336944	+	0.583603i
$531$		0			0
$532$	1.14891	−	2.24619i	0.0498116	−	0.0973847i
$533$	−19.5528	−	16.4560i	−0.846925	−	0.712788i
$534$		0			0
$535$	5.67652	+	5.67652i	0.245417	+	0.245417i
$536$	−14.4667			−0.624865
$537$		0			0
$538$	−13.9673	−	13.9673i	−0.602172	−	0.602172i
$539$	9.97378	−	12.2383i	0.429601	−	0.527140i
$540$		0			0
$541$	3.68111	−	0.986350i	0.158263	−	0.0424065i	−0.178817	−	0.983882i	$-0.557227\pi$
$541$	3.68111	−	0.986350i	0.158263	−	0.0424065i	0.337081	+	0.941476i	$0.390560\pi$
$542$	22.4464	+	12.9594i	0.964155	+	0.556655i
$543$		0			0
$544$	−1.17797	−	0.315635i	−0.0505049	−	0.0135328i
$545$	3.70734			0.158805
$546$		0			0
$547$	6.54169			0.279702			0.139851	−	0.990173i	$-0.455338\pi$
$547$	6.54169			0.279702			0.139851	+	0.990173i	$0.455338\pi$
$548$	−1.12957	−	0.302669i	−0.0482530	−	0.0129294i
$549$		0			0
$550$	−5.37588	−	3.10377i	−0.229228	−	0.132345i
$551$	54.1763	−	14.5165i	2.30799	−	0.618424i
$552$		0			0
$553$	−23.5422	+	7.60872i	−1.00112	+	0.323556i
$554$	−11.9297	−	11.9297i	−0.506845	−	0.506845i
$555$		0			0
$556$	1.67336			0.0709664
$557$	−0.230073	−	0.230073i	−0.00974850	−	0.00974850i	0.702216	−	0.711964i	$-0.252194\pi$
$557$	−0.230073	−	0.230073i	−0.00974850	−	0.00974850i	−0.711964	+	0.702216i	$0.752194\pi$
$558$		0			0
$559$	−35.7532	−	16.7363i	−1.51220	−	0.707870i
$560$	1.00724	+	19.8108i	0.0425635	+	0.837160i
$561$		0			0
$562$	−12.2862	−	21.2803i	−0.518261	−	0.897654i
$563$	−1.18117	+	2.04585i	−0.0497804	+	0.0862222i	−0.889842	−	0.456269i	$-0.849185\pi$
$563$	−1.18117	+	2.04585i	−0.0497804	+	0.0862222i	0.840062	+	0.542491i	$0.182519\pi$
$564$		0			0
$565$	−9.87772	−	9.87772i	−0.415559	−	0.415559i
$566$	−30.5274	−	8.17980i	−1.28316	−	0.343823i
$567$		0			0
$568$	−9.72468	−	16.8436i	−0.408038	−	0.706743i
$569$	5.30051	−	3.06025i	0.222209	−	0.128292i	−0.384764	−	0.923015i	$-0.625717\pi$
$569$	5.30051	−	3.06025i	0.222209	−	0.128292i	0.606973	+	0.794723i	$0.292384\pi$
$570$		0			0
$571$	34.6029	−	19.9780i	1.44808	−	0.836052i	0.449718	−	0.893171i	$-0.351525\pi$
$571$	34.6029	−	19.9780i	1.44808	−	0.836052i	0.998367	+	0.0571186i	$0.0181913\pi$
$572$	0.694817	−	0.825573i	0.0290518	−	0.0345189i
$573$		0			0
$574$	20.3234	+	18.3568i	0.848284	+	0.766199i
$575$	−6.12714	+	10.6125i	−0.255519	+	0.442572i
$576$		0			0
$577$	−5.69221	+	21.2436i	−0.236970	+	0.884383i	0.740281	+	0.672297i	$0.234692\pi$
$577$	−5.69221	+	21.2436i	−0.236970	+	0.884383i	−0.977251	+	0.212086i	$0.931974\pi$
$578$	−5.42461	−	20.2449i	−0.225634	−	0.842078i
$579$		0			0
$580$	1.29251	−	1.29251i	0.0536687	−	0.0536687i
$581$	−0.726999	−	14.2990i	−0.0301610	−	0.593221i
$582$		0			0
$583$	3.51339	−	13.1121i	0.145510	−	0.543049i
$584$	−6.42870	−	11.1348i	−0.266021	−	0.460763i
$585$		0			0
$586$	12.4481	+	7.18692i	0.514226	+	0.296889i
$587$	24.8029	−	6.64591i	1.02372	−	0.274306i	0.292371	−	0.956305i	$-0.405556\pi$
$587$	24.8029	−	6.64591i	1.02372	−	0.274306i	0.731353	+	0.681999i	$0.238889\pi$
$588$		0			0
$589$	−40.6105	+	23.4465i	−1.67332	+	0.966094i
$590$	−5.21814	−	19.4743i	−0.214827	−	0.801746i
$591$		0			0
$592$	8.64409	−	2.31618i	0.355270	−	0.0951943i
$593$	−0.190725	−	0.711795i	−0.00783213	−	0.0292299i	0.961899	−	0.273404i	$-0.0881497\pi$
$593$	−0.190725	−	0.711795i	−0.00783213	−	0.0292299i	−0.969731	+	0.244174i	$0.921483\pi$
$594$		0			0
$595$	6.37972	−	4.12890i	0.261543	−	0.169268i
$596$	−0.950801	+	0.254766i	−0.0389463	+	0.0104356i
$597$		0			0
$598$	−26.1942	−	22.0455i	−1.07116	−	0.901507i
$599$	8.17923	+	14.1669i	0.334194	+	0.578842i	0.983330	−	0.181831i	$-0.0582024\pi$
$599$	8.17923	+	14.1669i	0.334194	+	0.578842i	−0.649135	+	0.760673i	$0.724869\pi$
$600$		0			0
$601$	2.40336	+	1.38758i	0.0980349	+	0.0566005i	0.548216	−	0.836337i	$-0.315307\pi$
$601$	2.40336	+	1.38758i	0.0980349	+	0.0566005i	−0.450181	+	0.892937i	$0.648641\pi$
$602$	37.6630	+	19.2644i	1.53503	+	0.785157i
$603$		0			0
$604$	−1.32341	+	1.32341i	−0.0538486	+	0.0538486i
$605$	2.70130	+	10.0814i	0.109824	+	0.409867i
$606$		0			0
$607$		−	1.50128i		−	0.0609351i	−0.999536	−	0.0304676i	$-0.990300\pi$
$607$		−	1.50128i		−	0.0609351i	0.999536	−	0.0304676i	$-0.00969963\pi$
$608$	2.69281	−	4.66408i	0.109208	−	0.189153i
$609$		0			0
$610$		−	16.1539i		−	0.654051i
$611$	−29.9862	+	35.6292i	−1.21311	+	1.44140i
$612$		0			0
$613$	0.0719018	−	0.0719018i	0.00290408	−	0.00290408i	−0.705653	−	0.708557i	$-0.749346\pi$
$613$	0.0719018	−	0.0719018i	0.00290408	−	0.00290408i	0.708557	+	0.705653i	$0.249346\pi$
$614$	29.0422	−	16.7675i	1.17205	−	0.676682i
$615$		0			0
$616$	10.9072	−	12.0757i	0.439463	−	0.486544i
$617$	33.4006	+	8.94965i	1.34466	+	0.360299i	0.858159	−	0.513383i	$-0.171608\pi$
$617$	33.4006	+	8.94965i	1.34466	+	0.360299i	0.486496	+	0.873683i	$0.338275\pi$
$618$		0			0
$619$	4.56014	+	1.22189i	0.183287	+	0.0491117i	0.349295	−	0.937013i	$-0.386421\pi$
$619$	4.56014	+	1.22189i	0.183287	+	0.0491117i	−0.166008	+	0.986124i	$0.553088\pi$
$620$	−0.764120	+	1.32349i	−0.0306878	+	0.0531528i
$621$		0			0
$622$	−4.80430	−	17.9299i	−0.192635	−	0.718924i
$623$	−7.31602	−	11.3043i	−0.293110	−	0.452896i
$624$		0			0
$625$	−6.01236	+	10.4137i	−0.240494	+	0.416549i
$626$	−1.80171	−	1.80171i	−0.0720108	−	0.0720108i
$627$		0			0
$628$	−0.711840			−0.0284055
$629$	−2.42420	−	2.42420i	−0.0966592	−	0.0966592i
$630$		0			0
$631$	4.26964	−	15.9345i	0.169972	−	0.634343i	−0.827382	−	0.561640i	$-0.810171\pi$
$631$	4.26964	−	15.9345i	0.169972	−	0.634343i	0.997354	−	0.0727032i	$-0.0231626\pi$
$632$	−24.6318	+	6.60006i	−0.979799	+	0.262536i
$633$		0			0
$634$		−	35.0755i		−	1.39303i
$635$	−28.1914	−	7.55386i	−1.11874	−	0.299766i
$636$		0			0
$637$	−19.1239	+	16.4704i	−0.757718	+	0.652582i
$638$	−25.7061			−1.01771
$639$		0			0
$640$			21.7227i			0.858664i
$641$	9.72481	+	5.61462i	0.384107	+	0.221764i	0.679604	−	0.733580i	$-0.262152\pi$
$641$	9.72481	+	5.61462i	0.384107	+	0.221764i	−0.295497	+	0.955344i	$0.595485\pi$
$642$		0			0
$643$	10.7511	−	40.1236i	0.423982	−	1.58232i	−0.342155	−	0.939644i	$-0.611157\pi$
$643$	10.7511	−	40.1236i	0.423982	−	1.58232i	0.766136	−	0.642678i	$-0.222177\pi$
$644$	1.69399	+	1.53007i	0.0667527	+	0.0602934i
$645$		0			0
$646$	−17.0785			−0.671944
$647$	28.7294			1.12947			0.564735	−	0.825273i	$-0.308979\pi$
$647$	28.7294			1.12947			0.564735	+	0.825273i	$0.308979\pi$
$648$		0			0
$649$	−8.82051	+	15.2776i	−0.346235	+	0.599697i
$650$	7.59250	+	6.38999i	0.297803	+	0.250636i
$651$		0			0
$652$	−0.552330	−	2.06132i	−0.0216309	−	0.0807277i
$653$	−8.47378	−	14.6770i	−0.331605	−	0.574356i	0.651222	−	0.758887i	$-0.274257\pi$
$653$	−8.47378	−	14.6770i	−0.331605	−	0.574356i	−0.982827	+	0.184531i	$0.940923\pi$
$654$		0			0
$655$	21.8477	+	5.85408i	0.853661	+	0.228738i
$656$	21.2897	+	21.2897i	0.831221	+	0.831221i
$657$		0			0
$658$	33.4499	−	37.0335i	1.30401	−	1.44371i
$659$	−6.53667	−	11.3218i	−0.254632	−	0.441036i	0.710163	−	0.704037i	$-0.248621\pi$
$659$	−6.53667	−	11.3218i	−0.254632	−	0.441036i	−0.964796	+	0.263001i	$0.915288\pi$
$660$		0			0
$661$	−9.42539	+	9.42539i	−0.366605	+	0.366605i	−0.866238	−	0.499632i	$-0.833468\pi$
$661$	−9.42539	+	9.42539i	−0.366605	+	0.366605i	0.499632	+	0.866238i	$0.333468\pi$
$662$	19.6505	−	11.3452i	0.763739	−	0.440945i
$663$		0			0
$664$		−	14.7569i		−	0.572680i
$665$	10.3207	+	31.9332i	0.400218	+	1.23832i
$666$		0			0
$667$			50.7463i			1.96490i
$668$	0.180496	−	0.673620i	0.00698360	−	0.0260631i
$669$		0			0
$670$	−9.66919	+	9.66919i	−0.373553	+	0.373553i
$671$	−9.99462	+	9.99462i	−0.385838	+	0.385838i
$672$		0			0
$673$	26.6155	+	15.3665i	1.02595	+	0.592334i	0.915823	−	0.401583i	$-0.131540\pi$
$673$	26.6155	+	15.3665i	1.02595	+	0.592334i	0.110130	+	0.993917i	$0.464873\pi$
$674$	−1.76390	+	6.58296i	−0.0679429	+	0.253566i
$675$		0			0
$676$	−1.32470	+	1.10491i	−0.0509500	+	0.0424964i
$677$	−8.46296	−	4.88609i	−0.325258	−	0.187788i	0.328476	−	0.944512i	$-0.393465\pi$
$677$	−8.46296	−	4.88609i	−0.325258	−	0.187788i	−0.653734	+	0.756725i	$0.726798\pi$
$678$		0			0
$679$	−22.1377	+	14.3273i	−0.849566	+	0.549831i
$680$	6.78317	−	3.91626i	0.260123	−	0.150182i
$681$		0			0
$682$	20.7597	−	5.56254i	0.794930	−	0.213001i
$683$	−23.6182	+	6.32848i	−0.903726	+	0.242153i	−0.680616	−	0.732640i	$-0.738288\pi$
$683$	−23.6182	+	6.32848i	−0.903726	+	0.242153i	−0.223110	+	0.974793i	$0.571621\pi$
$684$		0			0
$685$	13.4712	−	7.77761i	0.514709	−	0.297167i
$686$	21.0986	−	16.9223i	0.805547	−	0.646097i
$687$		0			0
$688$	40.2772	+	23.2541i	1.53555	+	0.886553i
$689$	−9.20027	+	19.6542i	−0.350502	+	0.748767i
$690$		0			0
$691$	9.73031	−	36.3140i	0.370158	−	1.38145i	−0.490133	−	0.871648i	$-0.663052\pi$
$691$	9.73031	−	36.3140i	0.370158	−	1.38145i	0.860291	−	0.509803i	$-0.170282\pi$
$692$	−0.656458	−	0.379006i	−0.0249548	−	0.0144077i
$693$		0			0
$694$	34.6217	−	34.6217i	1.31422	−	1.31422i
$695$	−15.7391	+	15.7391i	−0.597018	+	0.597018i
$696$		0			0
$697$	2.98530	−	11.1413i	0.113076	−	0.422006i
$698$		−	6.49788i		−	0.245948i
$699$		0			0
$700$	−0.491012	−	0.443499i	−0.0185585	−	0.0167627i
$701$		−	41.9982i		−	1.58625i	−0.609058	−	0.793125i	$-0.708452\pi$
$701$		−	41.9982i		−	1.58625i	0.609058	−	0.793125i	$-0.291548\pi$
$702$		0			0
$703$	13.1117	−	7.57006i	0.494518	−	0.285510i
$704$	11.8033	−	11.8033i	0.444855	−	0.444855i
$705$		0			0
$706$	19.9747	+	34.5971i	0.751756	+	1.30208i
$707$	−13.3806	−	12.0858i	−0.503229	−	0.454534i
$708$		0			0
$709$	13.5329	+	13.5329i	0.508238	+	0.508238i	0.913985	−	0.405748i	$-0.132989\pi$
$709$	13.5329	+	13.5329i	0.508238	+	0.508238i	−0.405748	+	0.913985i	$0.632989\pi$
$710$	−17.7577	−	4.75815i	−0.666433	−	0.178570i
$711$		0			0
$712$	−6.93925	−	12.0191i	−0.260060	−	0.450436i
$713$	−10.9810	−	40.9816i	−0.411242	−	1.53477i
$714$		0			0
$715$	1.22985	+	14.3003i	0.0459936	+	0.534801i
$716$	−0.397111	+	0.687816i	−0.0148407	+	0.0257049i
$717$		0			0
$718$	−48.0198			−1.79208
$719$	−12.7618			−0.475934			−0.237967	−	0.971273i	$-0.576481\pi$
$719$	−12.7618			−0.475934			−0.237967	+	0.971273i	$0.576481\pi$
$720$		0			0
$721$	−28.5153	+	9.21599i	−1.06196	+	0.343221i
$722$	12.3390	−	46.0499i	0.459211	−	1.71380i
$723$		0			0
$724$	1.64329	+	0.948753i	0.0610723	+	0.0352601i
$725$		−	14.7090i		−	0.546280i
$726$		0			0
$727$	3.92873			0.145708			0.0728542	−	0.997343i	$-0.476789\pi$
$727$	3.92873			0.145708			0.0728542	+	0.997343i	$0.476789\pi$
$728$	−20.5475	+	15.9532i	−0.761543	+	0.591267i
$729$		0			0
$730$	−11.7391	−	3.14547i	−0.434482	−	0.116419i
$731$		−	17.8171i		−	0.658989i
$732$		0			0
$733$	30.7075	−	8.22804i	1.13421	−	0.303910i	0.357587	−	0.933880i	$-0.383600\pi$
$733$	30.7075	−	8.22804i	1.13421	−	0.303910i	0.776619	+	0.629970i	$0.216933\pi$
$734$	4.96852	−	18.5428i	0.183391	−	0.684426i
$735$		0			0
$736$	3.44555	+	3.44555i	0.127005	+	0.127005i
$737$	11.9649			0.440733
$738$		0			0
$739$	−18.1407	−	18.1407i	−0.667317	−	0.667317i	0.289777	−	0.957094i	$-0.406419\pi$
$739$	−18.1407	−	18.1407i	−0.667317	−	0.667317i	−0.957094	+	0.289777i	$0.906419\pi$
$740$	0.246708	−	0.427311i	0.00906917	−	0.0157083i
$741$		0			0
$742$	10.5900	−	20.7041i	0.388771	−	0.760072i
$743$	3.90299	+	14.5661i	0.143187	+	0.534380i	0.999829	+	0.0184698i	$0.00587945\pi$
$743$	3.90299	+	14.5661i	0.143187	+	0.534380i	−0.856643	+	0.515910i	$0.827454\pi$
$744$		0			0
$745$	6.54668	−	11.3392i	0.239852	−	0.415436i
$746$	19.1128	+	5.12126i	0.699770	+	0.187503i
$747$		0			0
$748$	0.470416	+	0.126047i	0.0172001	+	0.00460875i
$749$	2.52028	−	11.7667i	0.0920891	−	0.429944i
$750$		0			0
$751$	−40.3147	+	23.2757i	−1.47110	+	0.849341i	−0.999473	−	0.0324554i	$-0.989667\pi$
$751$	−40.3147	+	23.2757i	−1.47110	+	0.849341i	−0.471629	+	0.881797i	$0.656334\pi$
$752$	38.7941	−	38.7941i	1.41468	−	1.41468i
$753$		0			0
$754$	40.4598	+	7.19576i	1.47346	+	0.262054i
$755$		−	24.8951i		−	0.906025i
$756$		0			0
$757$	1.12340	−	1.94578i	0.0408306	−	0.0707207i	−0.844888	−	0.534943i	$-0.820333\pi$
$757$	1.12340	−	1.94578i	0.0408306	−	0.0707207i	0.885719	+	0.464223i	$0.153666\pi$
$758$		−	17.5378i		−	0.637002i
$759$		0			0
$760$	8.95249	+	33.4112i	0.324741	+	1.21195i
$761$	29.4999	−	29.4999i	1.06937	−	1.06937i	0.0719617	−	0.997407i	$-0.477074\pi$
$761$	29.4999	−	29.4999i	1.06937	−	1.06937i	0.997407	−	0.0719617i	$-0.0229259\pi$
$762$		0			0
$763$	−3.01941	−	4.66541i	−0.109310	−	0.168899i
$764$	0.879993	+	0.508064i	0.0318370	+	0.0183811i
$765$		0			0
$766$	5.81268	+	10.0679i	0.210021	+	0.363766i
$767$	18.1595	−	21.5769i	0.655703	−	0.779097i
$768$		0			0
$769$	−30.8135	+	8.25646i	−1.11116	+	0.297736i	−0.767303	−	0.641285i	$-0.778402\pi$
$769$	−30.8135	+	8.25646i	−1.11116	+	0.297736i	−0.343861	+	0.939020i	$0.611735\pi$
$770$	−0.781008	−	15.3612i	−0.0281456	−	0.553581i
$771$		0			0
$772$	−0.221378	−	0.826196i	−0.00796758	−	0.0297354i
$773$	−31.6927	+	8.49203i	−1.13991	+	0.305437i	−0.778913	−	0.627132i	$-0.784229\pi$
$773$	−31.6927	+	8.49203i	−1.13991	+	0.305437i	−0.360993	+	0.932569i	$0.617562\pi$
$774$		0			0
$775$	3.18289	+	11.8787i	0.114333	+	0.426696i
$776$	−23.5376	+	13.5895i	−0.844951	+	0.487833i
$777$		0			0
$778$	43.8525	−	11.7502i	1.57219	−	0.421267i
$779$	44.1131	+	25.4687i	1.58052	+	0.912511i
$780$		0			0
$781$	8.04297	+	13.9308i	0.287800	+	0.498484i
$782$	3.99930	−	14.9256i	0.143015	−	0.533738i
$783$		0			0
$784$	24.1101	−	17.4023i	0.861076	−	0.621510i
$785$	6.69534	−	6.69534i	0.238967	−	0.238967i
$786$		0			0
$787$	−9.81127	−	36.6162i	−0.349734	−	1.30523i	−0.886983	−	0.461802i	$-0.847203\pi$
$787$	−9.81127	−	36.6162i	−0.349734	−	1.30523i	0.537249	−	0.843424i	$-0.319464\pi$
$788$	0.705411	−	2.63263i	0.0251292	−	0.0937835i
$789$		0			0
$790$	−12.0520	+	20.8746i	−0.428790	+	0.742686i
$791$	−4.38555	+	20.4752i	−0.155932	+	0.728014i
$792$		0			0
$793$	18.5287	−	12.9332i	0.657973	−	0.459272i
$794$	10.2458	−	5.91542i	0.363610	−	0.209930i
$795$		0			0
$796$	0.775107	−	0.447508i	0.0274729	−	0.0158615i
$797$	20.1772	+	34.9479i	0.714712	+	1.23792i	0.963071	+	0.269249i	$0.0867756\pi$
$797$	20.1772	+	34.9479i	0.714712	+	1.23792i	−0.248358	+	0.968668i	$0.579891\pi$
$798$		0			0
$799$	−20.3017	−	5.43982i	−0.718222	−	0.192447i
$800$	−0.998709	−	0.998709i	−0.0353097	−	0.0353097i
$801$		0			0
$802$	−12.1883	+	21.1107i	−0.430382	+	0.745444i
$803$	5.31697	+	9.20926i	0.187632	+	0.324988i
$804$		0			0
$805$	−30.3246	+	1.54178i	−1.06880	+	0.0543408i
$806$	−34.2316	+	2.94397i	−1.20576	+	0.103697i
$807$		0			0
$808$	−13.1410	−	13.1410i	−0.462300	−	0.462300i
$809$	21.1048			0.742005			0.371003	−	0.928632i	$-0.379014\pi$
$809$	21.1048			0.742005			0.371003	+	0.928632i	$0.379014\pi$
$810$		0			0
$811$	−12.9178	−	12.9178i	−0.453607	−	0.453607i	0.442943	−	0.896550i	$-0.353934\pi$
$811$	−12.9178	−	12.9178i	−0.453607	−	0.453607i	−0.896550	+	0.442943i	$0.853934\pi$
$812$	−2.67921	−	0.573855i	−0.0940217	−	0.0201384i
$813$		0			0
$814$	−6.70260	+	1.79596i	−0.234926	+	0.0629482i
$815$	24.5832	+	14.1931i	0.861112	+	0.497163i
$816$		0			0
$817$	76.0022	+	20.3647i	2.65898	+	0.712472i
$818$	−25.5373			−0.892892
$819$		0			0
$820$	1.66005			0.0579715
$821$	−47.4052	−	12.7022i	−1.65445	−	0.443309i	−0.693598	−	0.720363i	$-0.743975\pi$
$821$	−47.4052	−	12.7022i	−1.65445	−	0.443309i	−0.960854	+	0.277054i	$0.910642\pi$
$822$		0			0
$823$	17.3304	+	10.0057i	0.604100	+	0.348778i	0.770653	−	0.637255i	$-0.219930\pi$
$823$	17.3304	+	10.0057i	0.604100	+	0.348778i	−0.166553	+	0.986033i	$0.553264\pi$
$824$	−29.8350	+	7.99427i	−1.03935	+	0.278493i
$825$		0			0
$826$	−20.2571	+	22.4273i	−0.704836	+	0.780347i
$827$	33.6816	+	33.6816i	1.17122	+	1.17122i	0.981918	+	0.189306i	$0.0606239\pi$
$827$	33.6816	+	33.6816i	1.17122	+	1.17122i	0.189306	+	0.981918i	$0.439376\pi$
$828$		0			0
$829$	−47.3709			−1.64526			−0.822629	−	0.568578i	$-0.807494\pi$
$829$	−47.3709			−1.64526			−0.822629	+	0.568578i	$0.807494\pi$
$830$	−9.86320	−	9.86320i	−0.342357	−	0.342357i
$831$		0			0
$832$	−21.8818	+	15.2737i	−0.758614	+	0.529520i
$833$	−10.3918	−	4.66566i	−0.360055	−	0.161656i
$834$		0			0
$835$	4.63817	+	8.03354i	0.160510	+	0.278012i
$836$	−1.07536	+	1.86258i	−0.0371921	+	0.0644186i
$837$		0			0
$838$	14.4436	+	14.4436i	0.498944	+	0.498944i
$839$	14.4591	+	3.87431i	0.499184	+	0.133756i	0.499621	−	0.866244i	$-0.333473\pi$
$839$	14.4591	+	3.87431i	0.499184	+	0.133756i	−0.000437384		1.00000i	$0.500139\pi$
$840$		0			0
$841$	−15.9559	−	27.6363i	−0.550202	−	0.952977i
$842$	−20.0749	+	11.5903i	−0.691827	+	0.399427i
$843$		0			0
$844$	1.85791	−	1.07266i	0.0639519	−	0.0369226i
$845$	2.06730	−	22.8521i	0.0711173	−	0.786136i
$846$		0			0
$847$	10.4866	−	11.6101i	0.360325	−	0.398928i
$848$	12.7832	−	22.1412i	0.438978	−	0.760332i
$849$		0			0
$850$	−1.15921	+	4.32625i	−0.0397607	+	0.148389i
$851$	3.54539	+	13.2316i	0.121534	+	0.453572i
$852$		0			0
$853$	−4.30446	+	4.30446i	−0.147382	+	0.147382i	−0.776947	−	0.629565i	$-0.783233\pi$
$853$	−4.30446	+	4.30446i	−0.147382	+	0.147382i	0.629565	+	0.776947i	$0.283233\pi$
$854$	−20.3284	+	13.1564i	−0.695625	+	0.450202i
$855$		0			0
$856$	3.21012	−	11.9803i	0.109719	−	0.409479i
$857$	2.53847	+	4.39675i	0.0867124	+	0.150190i	0.906120	−	0.423022i	$-0.139031\pi$
$857$	2.53847	+	4.39675i	0.0867124	+	0.150190i	−0.819407	+	0.573212i	$0.805697\pi$
$858$		0			0
$859$	13.0902	+	7.55762i	0.446631	+	0.257863i	0.706406	−	0.707807i	$-0.250315\pi$
$859$	13.0902	+	7.55762i	0.446631	+	0.257863i	−0.259775	+	0.965669i	$0.583648\pi$
$860$	2.47691	−	0.663686i	0.0844620	−	0.0226315i
$861$		0			0
$862$	−36.7572	+	21.2218i	−1.25195	+	0.722816i
$863$	8.82787	+	32.9461i	0.300504	+	1.12150i	0.936747	+	0.350008i	$0.113821\pi$
$863$	8.82787	+	32.9461i	0.300504	+	1.12150i	−0.636243	+	0.771489i	$0.719512\pi$
$864$		0			0
$865$	9.73925	−	2.60962i	0.331144	−	0.0887298i
$866$	10.7517	+	40.1260i	0.365359	+	1.36354i
$867$		0			0
$868$	2.28785	−	0.116321i	0.0776547	−	0.00394818i
$869$	20.3721	−	5.45870i	0.691078	−	0.185174i
$870$		0			0
$871$	−18.8321	−	3.34927i	−0.638100	−	0.113486i
$872$	−2.86391	−	4.96044i	−0.0969843	−	0.167982i
$873$		0			0
$874$	59.0968	+	34.1195i	1.99898	+	1.15411i
$875$	32.1088	−	1.63250i	1.08547	−	0.0551885i
$876$		0			0
$877$	11.9907	−	11.9907i	0.404897	−	0.404897i	−0.475058	−	0.879955i	$-0.657573\pi$
$877$	11.9907	−	11.9907i	0.404897	−	0.404897i	0.879955	+	0.475058i	$0.157573\pi$
$878$	12.3255	+	45.9996i	0.415967	+	1.55241i
$879$		0			0
$880$		−	16.9097i		−	0.570025i
$881$	−13.1115	+	22.7097i	−0.441737	+	0.765111i	−0.997819	−	0.0660169i	$-0.978971\pi$
$881$	−13.1115	+	22.7097i	−0.441737	+	0.765111i	0.556082	+	0.831128i	$0.312304\pi$
$882$		0			0
$883$		−	46.6268i		−	1.56912i	−0.620054	−	0.784559i	$-0.712889\pi$
$883$		−	46.6268i		−	1.56912i	0.620054	−	0.784559i	$-0.287111\pi$
$884$	−0.705123	−	0.330072i	−0.0237158	−	0.0111015i
$885$		0			0
$886$	−12.5737	+	12.5737i	−0.422421	+	0.422421i
$887$	−41.0807	+	23.7179i	−1.37935	+	0.796371i	−0.992082	−	0.125594i	$-0.959916\pi$
$887$	−41.0807	+	23.7179i	−1.37935	+	0.796371i	−0.387273	+	0.921965i	$0.626583\pi$
$888$		0			0
$889$	13.4543	+	41.6290i	0.451242	+	1.39619i
$890$	−12.6714	−	3.39528i	−0.424745	−	0.113810i
$891$		0			0
$892$	0.835162	+	0.223781i	0.0279633	+	0.00749274i
$893$	46.4092	−	80.3831i	1.55303	−	2.68992i
$894$		0			0
$895$	−2.73428	−	10.2045i	−0.0913969	−	0.341098i
$896$	27.3364	−	17.6918i	0.913244	−	0.591043i
$897$		0			0
$898$	−0.909273	+	1.57491i	−0.0303428	+	0.0525553i
$899$	36.0103	+	36.0103i	1.20101	+	1.20101i
$900$		0			0
$901$	−9.79440			−0.326299
$902$	−16.5079	−	16.5079i	−0.549653	−	0.549653i
$903$		0			0
$904$	−5.58593	+	20.8470i	−0.185785	+	0.693360i
$905$	−24.3799	+	6.53258i	−0.810416	+	0.217150i
$906$		0			0
$907$			28.3652i			0.941850i	0.882173	+	0.470925i	$0.156080\pi$
$907$			28.3652i			0.941850i	−0.882173	+	0.470925i	$0.843920\pi$
$908$	1.34684	+	0.360884i	0.0446964	+	0.0119764i
$909$		0			0
$910$	−3.07073	+	24.3963i	−0.101794	+	0.808730i
$911$	−25.8520			−0.856515			−0.428258	−	0.903657i	$-0.640872\pi$
$911$	−25.8520			−0.856515			−0.428258	+	0.903657i	$0.640872\pi$
$912$		0			0
$913$			12.2050i			0.403926i
$914$	9.64937	+	5.57106i	0.319173	+	0.184274i
$915$		0			0
$916$	−0.148793	+	0.555302i	−0.00491625	+	0.0183477i
$917$	−10.4268	−	32.2615i	−0.344322	−	1.06537i
$918$		0			0
$919$	7.15708			0.236090			0.118045	−	0.993008i	$-0.462337\pi$
$919$	7.15708			0.236090			0.118045	+	0.993008i	$0.462337\pi$
$920$	−31.2958			−1.03179
$921$		0			0
$922$	0.403838	−	0.699467i	0.0132997	−	0.0230357i
$923$	−8.75958	−	24.1777i	−0.288325	−	0.795820i
$924$		0			0
$925$	−1.02765	−	3.83523i	−0.0337888	−	0.126102i
$926$	−29.4424	−	50.9957i	−0.967536	−	1.67582i
$927$		0			0
$928$	−5.64955	−	1.51379i	−0.185456	−	0.0496927i
$929$	31.3926	+	31.3926i	1.02996	+	1.02996i	0.999537	+	0.0304195i	$0.00968434\pi$
$929$	31.3926	+	31.3926i	1.02996	+	1.02996i	0.0304195	+	0.999537i	$0.490316\pi$
$930$		0			0
$931$	31.7800	−	38.9955i	1.04155	−	1.27803i
$932$	1.06018	+	1.83628i	0.0347273	+	0.0601495i
$933$		0			0
$934$	31.7444	−	31.7444i	1.03871	−	1.03871i
$935$	−5.61014	+	3.23902i	−0.183471	+	0.105927i
$936$		0			0
$937$			7.95395i			0.259844i	0.991524	+	0.129922i	$0.0414727\pi$
$937$			7.95395i			0.259844i	−0.991524	+	0.129922i	$0.958527\pi$
$938$	20.0429	+	4.29297i	0.654425	+	0.140170i
$939$		0			0
$940$		−	3.02495i		−	0.0986631i
$941$	10.6078	−	39.5887i	0.345803	−	1.29055i	−0.545869	−	0.837871i	$-0.683800\pi$
$941$	10.6078	−	39.5887i	0.345803	−	1.29055i	0.891671	−	0.452683i	$-0.149533\pi$
$942$		0			0
$943$	−32.5882	+	32.5882i	−1.06122	+	1.06122i
$944$	−23.4936	+	23.4936i	−0.764651	+	0.764651i
$945$		0			0
$946$	−31.2308	−	18.0311i	−1.01540	−	0.586242i
$947$	−13.6972	+	51.1188i	−0.445100	+	1.66114i	0.270571	+	0.962700i	$0.412787\pi$
$947$	−13.6972	+	51.1188i	−0.445100	+	1.66114i	−0.715672	+	0.698437i	$0.753879\pi$
$948$		0			0
$949$	−5.79070	−	15.9832i	−0.187974	−	0.518836i
$950$	−17.1295	−	9.88971i	−0.555754	−	0.320864i
$951$		0			0
$952$	−10.4528	−	5.34654i	−0.338778	−	0.173282i
$953$	32.1309	−	18.5508i	1.04082	−	0.600920i	0.120757	−	0.992682i	$-0.461468\pi$
$953$	32.1309	−	18.5508i	1.04082	−	0.600920i	0.920066	+	0.391763i	$0.128135\pi$
$954$		0			0
$955$	−13.0556	+	3.49824i	−0.422470	+	0.113201i
$956$	0.334887	−	0.0897326i	0.0108310	−	0.00290216i
$957$		0			0
$958$	5.73450	−	3.31081i	0.185273	−	0.106968i
$959$	−20.7591	−	10.6181i	−0.670345	−	0.342877i
$960$		0			0
$961$	−10.0267	−	5.78893i	−0.323442	−	0.186740i
$962$	11.0522	−	0.950506i	0.356338	−	0.0306456i
$963$		0			0
$964$	0.675701	−	2.52175i	0.0217629	−	0.0812201i
$965$	9.85315	+	5.68872i	0.317184	+	0.183126i
$966$		0			0
$967$	−18.4234	+	18.4234i	−0.592456	+	0.592456i	−0.938294	−	0.345838i	$-0.887595\pi$
$967$	−18.4234	+	18.4234i	−0.592456	+	0.592456i	0.345838	+	0.938294i	$0.387595\pi$
$968$	11.4022	−	11.4022i	0.366481	−	0.366481i
$969$		0			0
$970$	−6.64913	+	24.8149i	−0.213491	+	0.796758i
$971$			30.7246i			0.986000i	0.870029	+	0.493000i	$0.164100\pi$
$971$			30.7246i			0.986000i	−0.870029	+	0.493000i	$0.835900\pi$
$972$		0			0
$973$	32.6251	+	6.98791i	1.04591	+	0.224022i
$974$		−	32.3261i		−	1.03579i
$975$		0			0
$976$	−23.0543	+	13.3104i	−0.737951	+	0.426056i
$977$	−6.55679	+	6.55679i	−0.209770	+	0.209770i	−0.804170	−	0.594400i	$-0.797390\pi$
$977$	−6.55679	+	6.55679i	−0.209770	+	0.209770i	0.594400	+	0.804170i	$0.297390\pi$
$978$		0			0
$979$	5.73924	+	9.94065i	0.183427	+	0.317704i
$980$	0.261520	−	1.61846i	0.00835394	−	0.0516997i
$981$		0			0
$982$	−28.3491	−	28.3491i	−0.904656	−	0.904656i
$983$	−31.3616	−	8.40332i	−1.00028	−	0.268024i	−0.278718	−	0.960373i	$-0.589909\pi$
$983$	−31.3616	−	8.40332i	−1.00028	−	0.268024i	−0.721563	+	0.692349i	$0.756576\pi$
$984$		0			0
$985$	18.1268	+	31.3965i	0.577568	+	1.00038i
$986$	4.80043	+	17.9155i	0.152877	+	0.570544i
$987$		0			0
$988$	2.21393	−	2.63057i	0.0704346	−	0.0836895i
$989$	−35.5951	+	61.6526i	−1.13186	+	1.96044i
$990$		0			0
$991$	−23.8883			−0.758836			−0.379418	−	0.925225i	$-0.623876\pi$
$991$	−23.8883			−0.758836			−0.379418	+	0.925225i	$0.623876\pi$
$992$	4.89003			0.155259
$993$		0			0
$994$	8.47479	+	26.2219i	0.268804	+	0.831709i
$995$	−3.08129	+	11.4995i	−0.0976835	+	0.364560i
$996$		0			0
$997$	−16.3534	−	9.44164i	−0.517918	−	0.299020i	0.218165	−	0.975912i	$-0.429993\pi$
$997$	−16.3534	−	9.44164i	−0.517918	−	0.299020i	−0.736082	+	0.676892i	$0.763326\pi$
$998$		−	45.5955i		−	1.44330i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.gh.d.19.3		40
3.2	odd	2		273.2.cg.b.19.8	yes	40
7.3	odd	6		819.2.et.d.136.8		40
13.11	odd	12		819.2.et.d.271.8		40
21.17	even	6		273.2.bt.b.136.3	✓	40
39.11	even	12		273.2.bt.b.271.3	yes	40
91.24	even	12	inner	819.2.gh.d.388.3		40
273.206	odd	12		273.2.cg.b.115.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.136.3	✓	40	21.17	even	6
273.2.bt.b.271.3	yes	40	39.11	even	12
273.2.cg.b.19.8	yes	40	3.2	odd	2
273.2.cg.b.115.8	yes	40	273.206	odd	12
819.2.et.d.136.8		40	7.3	odd	6
819.2.et.d.271.8		40	13.11	odd	12
819.2.gh.d.19.3		40	1.1	even	1	trivial
819.2.gh.d.388.3		40	91.24	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.41061 - 0.377973i) q^{2} +(0.114915 + 0.0663464i) q^{4} +(-1.70489 + 0.456824i) q^{5} +(1.96341 + 1.77342i) q^{7} +(1.92826 + 1.92826i) q^{8} +O(q^{10})\)	\(q+(-1.41061 - 0.377973i) q^{2} +(0.114915 + 0.0663464i) q^{4} +(-1.70489 + 0.456824i) q^{5} +(1.96341 + 1.77342i) q^{7} +(1.92826 + 1.92826i) q^{8} +2.57761 q^{10} +(-1.59480 - 1.59480i) q^{11} +(2.06370 + 2.95654i) q^{13} +(-2.09931 - 3.24373i) q^{14} +(-2.12389 - 3.67868i) q^{16} +(-0.813654 + 1.40929i) q^{17} +(-5.08160 - 5.08160i) q^{19} +(-0.226226 - 0.0606172i) q^{20} +(1.64685 + 2.85244i) q^{22} +(5.63098 - 3.25105i) q^{23} +(-1.63217 + 0.942332i) q^{25} +(-1.79359 - 4.95056i) q^{26} +(0.107966 + 0.334058i) q^{28} +(-3.90230 + 6.75898i) q^{29} +(1.68884 - 6.30283i) q^{31} +(0.193962 + 0.723875i) q^{32} +(1.68042 - 1.68042i) q^{34} +(-4.15754 - 2.12655i) q^{35} +(-0.545268 + 2.03497i) q^{37} +(5.24746 + 9.08887i) q^{38} +(-4.16834 - 2.40659i) q^{40} +(-6.84645 + 1.83450i) q^{41} +(-9.48195 + 5.47441i) q^{43} +(-0.0774577 - 0.289076i) q^{44} +(-9.17195 + 2.45762i) q^{46} +(3.34284 + 12.4756i) q^{47} +(0.709963 + 6.96390i) q^{49} +(2.65853 - 0.712352i) q^{50} +(0.0409944 + 0.476671i) q^{52} +(3.00939 + 5.21242i) q^{53} +(3.44750 + 1.99041i) q^{55} +(0.366351 + 7.20557i) q^{56} +(8.05934 - 8.05934i) q^{58} +(-2.02441 - 7.55521i) q^{59} -6.26701i q^{61} +(-4.76460 + 8.25252i) q^{62} +7.40114i q^{64} +(-4.86900 - 4.09784i) q^{65} +(-3.75123 + 3.75123i) q^{67} +(-0.187002 + 0.107966i) q^{68} +(5.06090 + 4.57118i) q^{70} +(-6.88920 - 1.84596i) q^{71} +(-4.55425 - 1.22031i) q^{73} +(1.53832 - 2.66446i) q^{74} +(-0.246808 - 0.921099i) q^{76} +(-0.302997 - 5.95950i) q^{77} +(-4.67565 + 8.09846i) q^{79} +(5.30151 + 5.30151i) q^{80} +10.3511 q^{82} +(-3.82650 - 3.82650i) q^{83} +(0.743393 - 2.77438i) q^{85} +(15.4445 - 4.13835i) q^{86} -6.15037i q^{88} +(-4.91594 - 1.31722i) q^{89} +(-1.19131 + 9.46471i) q^{91} +0.862782 q^{92} -18.8618i q^{94} +(10.9850 + 6.34217i) q^{95} +(-2.57958 + 9.62711i) q^{97} +(1.63068 - 10.0917i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7}+O(q^{10}) \) 40 * q - 8 * q^7	\( 40 q - 8 q^{7} - 4 q^{11} + 18 q^{14} + 32 q^{16} - 4 q^{17} + 14 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} + 24 q^{25} + 32 q^{26} + 16 q^{28} - 8 q^{29} + 14 q^{31} + 26 q^{32} - 24 q^{34} - 26 q^{35} + 36 q^{37} + 8 q^{38} - 30 q^{40} + 2 q^{41} - 66 q^{43} + 32 q^{44} - 26 q^{46} + 4 q^{47} - 14 q^{49} + 20 q^{50} + 2 q^{52} + 8 q^{53} - 42 q^{55} - 46 q^{56} + 24 q^{58} - 14 q^{59} - 24 q^{62} - 28 q^{65} - 44 q^{67} + 18 q^{68} - 4 q^{70} + 6 q^{71} + 14 q^{73} + 20 q^{74} - 64 q^{76} - 24 q^{77} - 20 q^{80} + 48 q^{82} + 12 q^{83} + 2 q^{85} + 60 q^{86} + 2 q^{89} - 14 q^{91} - 236 q^{92} - 24 q^{95} - 62 q^{97} + 88 q^{98}+O(q^{100}) \) 40 * q - 8 * q^7 - 4 * q^11 + 18 * q^14 + 32 * q^16 - 4 * q^17 + 14 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 + 24 * q^25 + 32 * q^26 + 16 * q^28 - 8 * q^29 + 14 * q^31 + 26 * q^32 - 24 * q^34 - 26 * q^35 + 36 * q^37 + 8 * q^38 - 30 * q^40 + 2 * q^41 - 66 * q^43 + 32 * q^44 - 26 * q^46 + 4 * q^47 - 14 * q^49 + 20 * q^50 + 2 * q^52 + 8 * q^53 - 42 * q^55 - 46 * q^56 + 24 * q^58 - 14 * q^59 - 24 * q^62 - 28 * q^65 - 44 * q^67 + 18 * q^68 - 4 * q^70 + 6 * q^71 + 14 * q^73 + 20 * q^74 - 64 * q^76 - 24 * q^77 - 20 * q^80 + 48 * q^82 + 12 * q^83 + 2 * q^85 + 60 * q^86 + 2 * q^89 - 14 * q^91 - 236 * q^92 - 24 * q^95 - 62 * q^97 + 88 * q^98

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