LMFDB - Embedded newform 99.2.j.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(8,99)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("99.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.j (of order $10$, 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:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 $ x^16 + 2x^14 - 16x^12 - 72x^10 + 26x^8 + 360x^6 + 725x^4 + 1000*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			17.4
Root			$-0.556839 + 1.81878i$ of defining polynomial
Character	$\chi$	$=$	99.17
Dual form			99.2.j.a.35.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.726437 + 2.23574i) q^{2} +(-2.85280 + 2.07268i) q^{4} +(2.13811 + 0.694712i) q^{5} +(-2.38116 - 3.27739i) q^{7} +(-2.90269 - 2.10893i) q^{8} +O(q^{10})$	\(q+(0.726437 + 2.23574i) q^{2} +(-2.85280 + 2.07268i) q^{4} +(2.13811 + 0.694712i) q^{5} +(-2.38116 - 3.27739i) q^{7} +(-2.90269 - 2.10893i) q^{8} +5.28492i q^{10} +(-3.31656 - 0.0200544i) q^{11} +(4.42495 - 1.43775i) q^{13} +(5.59763 - 7.70448i) q^{14} +(0.427051 - 1.31433i) q^{16} +(-0.0235753 + 0.0725574i) q^{17} +(1.40822 - 1.93825i) q^{19} +(-7.53950 + 2.44973i) q^{20} +(-2.36444 - 7.42955i) q^{22} +3.22717i q^{23} +(0.0437835 + 0.0318106i) q^{25} +(6.42889 + 8.84860i) q^{26} +(13.5860 + 4.41435i) q^{28} +(1.48796 - 1.08107i) q^{29} +(0.517528 + 1.59279i) q^{31} -3.92711 q^{32} -0.179346 q^{34} +(-2.81433 - 8.66162i) q^{35} +(-5.87906 + 4.27138i) q^{37} +(5.35641 + 1.74040i) q^{38} +(-4.74115 - 6.52564i) q^{40} +(-6.82980 - 4.96214i) q^{41} -4.28086i q^{43} +(9.50306 - 6.81697i) q^{44} +(-7.21513 + 2.34434i) q^{46} +(-3.65360 + 5.02874i) q^{47} +(-2.90822 + 8.95058i) q^{49} +(-0.0393143 + 0.120997i) q^{50} +(-9.64348 + 13.2731i) q^{52} +(1.16884 - 0.379779i) q^{53} +(-7.07723 - 2.34694i) q^{55} +14.5349i q^{56} +(3.49789 + 2.54137i) q^{58} +(-0.341086 - 0.469465i) q^{59} +(-3.59710 - 1.16877i) q^{61} +(-3.18511 + 2.31412i) q^{62} +(-3.70690 - 11.4087i) q^{64} +10.4598 q^{65} +12.9984 q^{67} +(-0.0831326 - 0.255856i) q^{68} +(17.3207 - 12.5842i) q^{70} +(1.06563 + 0.346245i) q^{71} +(7.82153 + 10.7654i) q^{73} +(-13.8205 - 10.0412i) q^{74} +8.44824i q^{76} +(7.83155 + 10.9174i) q^{77} +(0.627566 - 0.203908i) q^{79} +(1.82616 - 2.51349i) q^{80} +(6.13265 - 18.8744i) q^{82} +(-3.15542 + 9.71138i) q^{83} +(-0.100813 + 0.138757i) q^{85} +(9.57090 - 3.10977i) q^{86} +(9.58466 + 7.05260i) q^{88} -6.58983i q^{89} +(-15.2486 - 11.0787i) q^{91} +(-6.68890 - 9.20649i) q^{92} +(-13.8971 - 4.51544i) q^{94} +(4.35745 - 3.16587i) q^{95} +(5.08168 + 15.6398i) q^{97} -22.1238 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4}+O(q^{10}) $ 16 * q - 4 * q^4	$ 16 q - 4 q^{4} - 20 q^{16} - 48 q^{22} - 32 q^{25} + 40 q^{28} + 16 q^{31} + 40 q^{34} - 12 q^{37} + 60 q^{40} - 40 q^{46} - 24 q^{49} - 40 q^{52} + 16 q^{55} + 12 q^{58} + 36 q^{64} + 96 q^{67} + 76 q^{70} - 20 q^{73} - 12 q^{82} - 100 q^{85} - 12 q^{88} - 72 q^{91} - 80 q^{94} + 60 q^{97}+O(q^{100}) $ 16 * q - 4 * q^4 - 20 * q^16 - 48 * q^22 - 32 * q^25 + 40 * q^28 + 16 * q^31 + 40 * q^34 - 12 * q^37 + 60 * q^40 - 40 * q^46 - 24 * q^49 - 40 * q^52 + 16 * q^55 + 12 * q^58 + 36 * q^64 + 96 * q^67 + 76 * q^70 - 20 * q^73 - 12 * q^82 - 100 * q^85 - 12 * q^88 - 72 * q^91 - 80 * q^94 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.726437	+	2.23574i	0.513668	+	1.58091i	0.785692	+	0.618618i	$0.212307\pi$
$2$	0.726437	+	2.23574i	0.513668	+	1.58091i	−0.272023	+	0.962291i	$0.587693\pi$
$3$		0			0
$3$		0			0
$4$	−2.85280	+	2.07268i	−1.42640	+	1.03634i
$5$	2.13811	+	0.694712i	0.956190	+	0.310685i	0.745228	−	0.666809i	$-0.232341\pi$
$5$	2.13811	+	0.694712i	0.956190	+	0.310685i	0.210962	+	0.977494i	$0.432341\pi$
$6$		0			0
$7$	−2.38116	−	3.27739i	−0.899995	−	1.23874i	−0.970470	−	0.241223i	$-0.922452\pi$
$7$	−2.38116	−	3.27739i	−0.899995	−	1.23874i	0.0704753	−	0.997514i	$-0.477548\pi$
$8$	−2.90269	−	2.10893i	−1.02626	−	0.745618i
$9$		0			0
$10$			5.28492i			1.67124i
$11$	−3.31656	−	0.0200544i	−0.999982	−	0.00604662i
$11$	−3.31656	−	0.0200544i	−0.999982	−	0.00604662i
$12$		0			0
$13$	4.42495	−	1.43775i	1.22726	−	0.398761i	0.377538	−	0.925994i	$-0.376771\pi$
$13$	4.42495	−	1.43775i	1.22726	−	0.398761i	0.849721	+	0.527233i	$0.176771\pi$
$14$	5.59763	−	7.70448i	1.49603	−	2.05911i
$15$		0			0
$16$	0.427051	−	1.31433i	0.106763	−	0.328582i
$17$	−0.0235753	+	0.0725574i	−0.00571786	+	0.0175978i	−0.953875	−	0.300205i	$-0.902945\pi$
$17$	−0.0235753	+	0.0725574i	−0.00571786	+	0.0175978i	0.948157	+	0.317803i	$0.102945\pi$
$18$		0			0
$19$	1.40822	−	1.93825i	0.323068	−	0.444665i	−0.616333	−	0.787486i	$-0.711382\pi$
$19$	1.40822	−	1.93825i	0.323068	−	0.444665i	0.939401	+	0.342821i	$0.111382\pi$
$20$	−7.53950	+	2.44973i	−1.68588	+	0.547777i
$21$		0			0
$22$	−2.36444	−	7.42955i	−0.504100	−	1.58399i
$23$			3.22717i			0.672912i	0.941699	+	0.336456i	$0.109228\pi$
$23$			3.22717i			0.672912i	−0.941699	+	0.336456i	$0.890772\pi$
$24$		0			0
$25$	0.0437835	+	0.0318106i	0.00875670	+	0.00636211i
$26$	6.42889	+	8.84860i	1.26081	+	1.73535i
$27$		0			0
$28$	13.5860	+	4.41435i	2.56750	+	0.834233i
$29$	1.48796	−	1.08107i	0.276307	−	0.200749i	−0.440998	−	0.897508i	$-0.645375\pi$
$29$	1.48796	−	1.08107i	0.276307	−	0.200749i	0.717305	+	0.696759i	$0.245375\pi$
$30$		0			0
$31$	0.517528	+	1.59279i	0.0929508	+	0.286073i	0.986714	−	0.162466i	$-0.0519446\pi$
$31$	0.517528	+	1.59279i	0.0929508	+	0.286073i	−0.893763	+	0.448539i	$0.851945\pi$
$32$	−3.92711			−0.694222
$33$		0			0
$34$	−0.179346			−0.0307575
$35$	−2.81433	−	8.66162i	−0.475709	−	1.46408i
$36$		0			0
$37$	−5.87906	+	4.27138i	−0.966511	+	0.702211i	−0.954654	−	0.297718i	$-0.903774\pi$
$37$	−5.87906	+	4.27138i	−0.966511	+	0.702211i	−0.0118571	+	0.999930i	$0.503774\pi$
$38$	5.35641	+	1.74040i	0.868925	+	0.282331i
$39$		0			0
$40$	−4.74115	−	6.52564i	−0.749642	−	1.03179i
$41$	−6.82980	−	4.96214i	−1.06664	−	0.774956i	−0.0913313	−	0.995821i	$-0.529112\pi$
$41$	−6.82980	−	4.96214i	−1.06664	−	0.774956i	−0.975305	+	0.220864i	$0.929112\pi$
$42$		0			0
$43$		−	4.28086i		−	0.652825i	−0.945227	−	0.326413i	$-0.894160\pi$
$43$		−	4.28086i		−	0.652825i	0.945227	−	0.326413i	$-0.105840\pi$
$44$	9.50306	−	6.81697i	1.43264	−	1.02770i
$45$		0			0
$46$	−7.21513	+	2.34434i	−1.06381	+	0.345654i
$47$	−3.65360	+	5.02874i	−0.532932	+	0.733518i	−0.987574	−	0.157157i	$-0.949767\pi$
$47$	−3.65360	+	5.02874i	−0.532932	+	0.733518i	0.454642	+	0.890674i	$0.349767\pi$
$48$		0			0
$49$	−2.90822	+	8.95058i	−0.415460	+	1.27865i
$50$	−0.0393143	+	0.120997i	−0.00555988	+	0.0171116i
$51$		0			0
$52$	−9.64348	+	13.2731i	−1.33731	+	1.84065i
$53$	1.16884	−	0.379779i	0.160552	−	0.0521666i	−0.227638	−	0.973746i	$-0.573100\pi$
$53$	1.16884	−	0.379779i	0.160552	−	0.0521666i	0.388190	+	0.921579i	$0.373100\pi$
$54$		0			0
$55$	−7.07723	−	2.34694i	−0.954294	−	0.316461i
$56$			14.5349i			1.94231i
$57$		0			0
$58$	3.49789	+	2.54137i	0.459296	+	0.333698i
$59$	−0.341086	−	0.469465i	−0.0444056	−	0.0611191i	0.786237	−	0.617925i	$-0.212027\pi$
$59$	−0.341086	−	0.469465i	−0.0444056	−	0.0611191i	−0.830642	+	0.556806i	$0.812027\pi$
$60$		0			0
$61$	−3.59710	−	1.16877i	−0.460561	−	0.149645i	0.0695411	−	0.997579i	$-0.477847\pi$
$61$	−3.59710	−	1.16877i	−0.460561	−	0.149645i	−0.530102	+	0.847934i	$0.677847\pi$
$62$	−3.18511	+	2.31412i	−0.404510	+	0.293893i
$63$		0			0
$64$	−3.70690	−	11.4087i	−0.463363	−	1.42608i
$65$	10.4598			1.29738
$66$		0			0
$67$	12.9984			1.58801			0.794003	−	0.607914i	$-0.207993\pi$
$67$	12.9984			1.58801			0.794003	+	0.607914i	$0.207993\pi$
$68$	−0.0831326	−	0.255856i	−0.0100813	−	0.0310271i
$69$		0			0
$70$	17.3207	−	12.5842i	2.07022	−	1.50410i
$71$	1.06563	+	0.346245i	0.126467	+	0.0410917i	0.371567	−	0.928406i	$-0.378821\pi$
$71$	1.06563	+	0.346245i	0.126467	+	0.0410917i	−0.245100	+	0.969498i	$0.578821\pi$
$72$		0			0
$73$	7.82153	+	10.7654i	0.915441	+	1.26000i	0.965274	+	0.261239i	$0.0841309\pi$
$73$	7.82153	+	10.7654i	0.915441	+	1.26000i	−0.0498335	+	0.998758i	$0.515869\pi$
$74$	−13.8205	−	10.0412i	−1.60660	−	1.16726i
$75$		0			0
$76$			8.44824i			0.969079i
$77$	7.83155	+	10.9174i	0.892488	+	1.24416i
$78$		0			0
$79$	0.627566	−	0.203908i	0.0706066	−	0.0229415i	−0.273501	−	0.961872i	$-0.588182\pi$
$79$	0.627566	−	0.203908i	0.0706066	−	0.0229415i	0.344107	+	0.938930i	$0.388182\pi$
$80$	1.82616	−	2.51349i	0.204171	−	0.281017i
$81$		0			0
$82$	6.13265	−	18.8744i	0.677238	−	2.08432i
$83$	−3.15542	+	9.71138i	−0.346352	+	1.06596i	0.614504	+	0.788914i	$0.289356\pi$
$83$	−3.15542	+	9.71138i	−0.346352	+	1.06596i	−0.960856	+	0.277048i	$0.910644\pi$
$84$		0			0
$85$	−0.100813	+	0.138757i	−0.0109347	+	0.0150503i
$86$	9.57090	−	3.10977i	1.03206	−	0.335336i
$87$		0			0
$88$	9.58466	+	7.05260i	1.02173	+	0.751810i
$89$		−	6.58983i		−	0.698520i	−0.937026	−	0.349260i	$-0.886433\pi$
$89$		−	6.58983i		−	0.698520i	0.937026	−	0.349260i	$-0.113567\pi$
$90$		0			0
$91$	−15.2486	−	11.0787i	−1.59849	−	1.16137i
$92$	−6.68890	−	9.20649i	−0.697366	−	0.959843i
$93$		0			0
$94$	−13.8971	−	4.51544i	−1.43337	−	0.465732i
$95$	4.35745	−	3.16587i	0.447065	−	0.324812i
$96$		0			0
$97$	5.08168	+	15.6398i	0.515966	+	1.58798i	0.781517	+	0.623883i	$0.214446\pi$
$97$	5.08168	+	15.6398i	0.515966	+	1.58798i	−0.265551	+	0.964097i	$0.585554\pi$
$98$	−22.1238			−2.23485
$99$		0			0
$100$	−0.190839			−0.0190839
$101$	0.532095	+	1.63762i	0.0529455	+	0.162949i	0.974033	−	0.226406i	$-0.0726977\pi$
$101$	0.532095	+	1.63762i	0.0529455	+	0.162949i	−0.921087	+	0.389356i	$0.872698\pi$
$102$		0			0
$103$	2.61382	−	1.89905i	0.257548	−	0.187119i	−0.451518	−	0.892262i	$-0.649117\pi$
$103$	2.61382	−	1.89905i	0.257548	−	0.187119i	0.709065	+	0.705143i	$0.249117\pi$
$104$	−15.8763	−	5.15854i	−1.55680	−	0.505836i
$105$		0			0
$106$	1.69818	+	2.33734i	0.164941	+	0.227022i
$107$	11.9884	+	8.71006i	1.15896	+	0.842034i	0.989646	−	0.143529i	$-0.0458449\pi$
$107$	11.9884	+	8.71006i	1.15896	+	0.842034i	0.169314	+	0.985562i	$0.445845\pi$
$108$		0			0
$109$		−	14.9258i		−	1.42963i	−0.699313	−	0.714815i	$-0.746511\pi$
$109$		−	14.9258i		−	1.42963i	0.699313	−	0.714815i	$-0.253489\pi$
$110$	0.105986	−	17.5278i	0.0101053	−	1.67121i
$111$		0			0
$112$	−5.32444	+	1.73002i	−0.503112	+	0.163471i
$113$	6.61055	−	9.09864i	0.621868	−	0.855928i	−0.375619	−	0.926774i	$-0.622570\pi$
$113$	6.61055	−	9.09864i	0.621868	−	0.855928i	0.997487	+	0.0708461i	$0.0225699\pi$
$114$		0			0
$115$	−2.24196	+	6.90004i	−0.209064	+	0.643432i
$116$	−2.00415	+	6.16813i	−0.186080	+	0.572697i
$117$		0			0
$118$	0.801825	−	1.10362i	0.0738139	−	0.101596i
$119$	0.293935	−	0.0955054i	0.0269450	−	0.00875497i
$120$		0			0
$121$	10.9992	+	0.133023i	0.999927	+	0.0120930i
$122$		−	8.89122i		−	0.804973i
$123$		0			0
$124$	−4.77775	−	3.47124i	−0.429054	−	0.311726i
$125$	−6.53559	−	8.99547i	−0.584561	−	0.804580i
$126$		0			0
$127$	−5.76481	−	1.87310i	−0.511544	−	0.166211i	0.0418604	−	0.999123i	$-0.486672\pi$
$127$	−5.76481	−	1.87310i	−0.511544	−	0.166211i	−0.553404	+	0.832913i	$0.686672\pi$
$128$	16.4598	−	11.9588i	1.45486	−	1.05701i
$129$		0			0
$130$	7.59840	+	23.3855i	0.666424	+	2.05104i
$131$	−7.15083			−0.624771			−0.312385	−	0.949955i	$-0.601128\pi$
$131$	−7.15083			−0.624771			−0.312385	+	0.949955i	$0.601128\pi$
$132$		0			0
$133$	−9.70560			−0.841582
$134$	9.44251	+	29.0611i	0.815709	+	2.51049i
$135$		0			0
$136$	0.221450	−	0.160893i	0.0189892	−	0.0137964i
$137$	10.1026	+	3.28252i	0.863120	+	0.280445i	0.706931	−	0.707283i	$-0.250079\pi$
$137$	10.1026	+	3.28252i	0.863120	+	0.280445i	0.156189	+	0.987727i	$0.450079\pi$
$138$		0			0
$139$	−0.0311975	−	0.0429397i	−0.00264614	−	0.00364210i	0.807692	−	0.589605i	$-0.200716\pi$
$139$	−0.0311975	−	0.0429397i	−0.00264614	−	0.00364210i	−0.810338	+	0.585963i	$0.800716\pi$
$140$	25.9815	+	18.8767i	2.19584	+	1.59537i
$141$		0			0
$142$			2.63400i			0.221041i
$143$	−14.7044	+	4.67966i	−1.22965	+	0.391333i
$144$		0			0
$145$	3.93244	−	1.27773i	0.326572	−	0.106110i
$146$	−18.3868	+	25.3073i	−1.52171	+	2.09445i
$147$		0			0
$148$	7.91856	−	24.3708i	0.650901	−	2.00327i
$149$	−6.30238	+	19.3967i	−0.516311	+	1.58904i	0.264572	+	0.964366i	$0.414769\pi$
$149$	−6.30238	+	19.3967i	−0.516311	+	1.58904i	−0.780883	+	0.624677i	$0.785231\pi$
$150$		0			0
$151$	0.698980	−	0.962063i	0.0568822	−	0.0782916i	−0.779628	−	0.626243i	$-0.784592\pi$
$151$	0.698980	−	0.962063i	0.0568822	−	0.0782916i	0.836510	+	0.547951i	$0.184592\pi$
$152$	−8.17525	+	2.65630i	−0.663101	+	0.215454i
$153$		0			0
$154$	−18.7194	+	25.4401i	−1.50845	+	2.05003i
$155$			3.76508i			0.302419i
$156$		0			0
$157$	1.40210	+	1.01868i	0.111900	+	0.0812998i	0.642328	−	0.766430i	$-0.277969\pi$
$157$	1.40210	+	1.01868i	0.111900	+	0.0812998i	−0.530428	+	0.847730i	$0.677969\pi$
$158$	0.911773	+	1.25495i	0.0725368	+	0.0998383i
$159$		0			0
$160$	−8.39658	−	2.72822i	−0.663808	−	0.215684i
$161$	10.5767	−	7.68443i	0.833561	−	0.605618i
$162$		0			0
$163$	−0.309821	−	0.953532i	−0.0242671	−	0.0746864i	0.938190	−	0.346122i	$-0.112502\pi$
$163$	−0.309821	−	0.953532i	−0.0242671	−	0.0746864i	−0.962457	+	0.271435i	$0.912502\pi$
$164$	29.7690			2.32457
$165$		0			0
$166$	−24.0044			−1.86310
$167$	−4.17734	−	12.8565i	−0.323252	−	0.994868i	−0.972223	−	0.234055i	$-0.924800\pi$
$167$	−4.17734	−	12.8565i	−0.323252	−	0.994868i	0.648971	−	0.760813i	$-0.275200\pi$
$168$		0			0
$169$	6.99579	−	5.08274i	0.538138	−	0.390980i
$170$	−0.383460	−	0.124594i	−0.0294100	−	0.00955590i
$171$		0			0
$172$	8.87286	+	12.2124i	0.676549	+	0.931190i
$173$	−6.08619	−	4.42188i	−0.462724	−	0.336189i	0.331875	−	0.943324i	$-0.392319\pi$
$173$	−6.08619	−	4.42188i	−0.462724	−	0.336189i	−0.794599	+	0.607135i	$0.792319\pi$
$174$		0			0
$175$		−	0.219242i		−	0.0165731i
$176$	−1.44270	+	4.35049i	−0.108748	+	0.327930i
$177$		0			0
$178$	14.7332	−	4.78709i	1.10430	−	0.358808i
$179$	7.34750	−	10.1130i	0.549178	−	0.755879i	−0.440722	−	0.897643i	$-0.645278\pi$
$179$	7.34750	−	10.1130i	0.549178	−	0.755879i	0.989900	+	0.141765i	$0.0452777\pi$
$180$		0			0
$181$	−5.56261	+	17.1200i	−0.413466	+	1.27252i	0.500150	+	0.865939i	$0.333278\pi$
$181$	−5.56261	+	17.1200i	−0.413466	+	1.27252i	−0.913616	+	0.406578i	$0.866722\pi$
$182$	13.6921	−	42.1399i	1.01492	−	3.12362i
$183$		0			0
$184$	6.80587	−	9.36748i	0.501736	−	0.690580i
$185$	−15.5374	+	5.04842i	−1.14233	+	0.371167i
$186$		0			0
$187$	0.0796442	−	0.240168i	0.00582416	−	0.0175629i
$188$		−	21.9187i		−	1.59859i
$189$		0			0
$190$	10.2435	+	7.44233i	0.743141	+	0.539924i
$191$	−12.7297	−	17.5209i	−0.921085	−	1.26777i	−0.963237	−	0.268654i	$-0.913421\pi$
$191$	−12.7297	−	17.5209i	−0.921085	−	1.26777i	0.0421514	−	0.999111i	$-0.486579\pi$
$192$		0			0
$193$	−4.93306	−	1.60285i	−0.355090	−	0.115376i	0.126040	−	0.992025i	$-0.459773\pi$
$193$	−4.93306	−	1.60285i	−0.355090	−	0.115376i	−0.481129	+	0.876650i	$0.659773\pi$
$194$	−31.2750	+	22.7226i	−2.24542	+	1.63139i
$195$		0			0
$196$	−10.2551	−	31.5620i	−0.732509	−	2.25443i
$197$	−5.14679			−0.366693			−0.183347	−	0.983048i	$-0.558693\pi$
$197$	−5.14679			−0.366693			−0.183347	+	0.983048i	$0.558693\pi$
$198$		0			0
$199$	24.2595			1.71971			0.859855	−	0.510539i	$-0.170554\pi$
$199$	24.2595			1.71971			0.859855	+	0.510539i	$0.170554\pi$
$200$	−0.0600037	−	0.184672i	−0.00424290	−	0.0130583i
$201$		0			0
$202$	−3.27477	+	2.37926i	−0.230412	+	0.167404i
$203$	−7.08615	−	2.30243i	−0.497350	−	0.161599i
$204$		0			0
$205$	−11.1556	−	15.3543i	−0.779139	−	1.07239i
$206$	6.14457	+	4.46429i	0.428113	+	0.311042i
$207$		0			0
$208$		−	6.42982i		−	0.445828i
$209$	−4.70933	+	6.40009i	−0.325751	+	0.442704i
$210$		0			0
$211$	−17.8262	+	5.79210i	−1.22721	+	0.398744i	−0.849702	−	0.527263i	$-0.823218\pi$
$211$	−17.8262	+	5.79210i	−1.22721	+	0.398744i	−0.377506	+	0.926007i	$0.623218\pi$
$212$	−2.54730	+	3.50606i	−0.174950	+	0.240797i
$213$		0			0
$214$	−10.7647	+	33.1302i	−0.735857	+	2.26474i
$215$	2.97397	−	9.15293i	0.202823	−	0.624225i
$216$		0			0
$217$	3.98787	−	5.48883i	0.270714	−	0.372606i
$218$	33.3702	−	10.8426i	2.26012	−	0.734356i
$219$		0			0
$220$	25.0544	−	7.97350i	1.68917	−	0.537573i
$221$			0.354958i			0.0238771i
$222$		0			0
$223$	4.44037	+	3.22612i	0.297349	+	0.216037i	0.726449	−	0.687220i	$-0.241169\pi$
$223$	4.44037	+	3.22612i	0.297349	+	0.216037i	−0.429100	+	0.903257i	$0.641169\pi$
$224$	9.35109	+	12.8707i	0.624796	+	0.859958i
$225$		0			0
$226$	25.1444	+	8.16990i	1.67258	+	0.543454i
$227$	−11.1352	+	8.09016i	−0.739066	+	0.536963i	−0.892419	−	0.451209i	$-0.850993\pi$
$227$	−11.1352	+	8.09016i	−0.739066	+	0.536963i	0.153352	+	0.988172i	$0.450993\pi$
$228$		0			0
$229$	−6.53035	−	20.0983i	−0.431538	−	1.32814i	−0.896593	−	0.442855i	$-0.853966\pi$
$229$	−6.53035	−	20.0983i	−0.431538	−	1.32814i	0.465056	−	0.885281i	$-0.346034\pi$
$230$	−17.0554			−1.12460
$231$		0			0
$232$	−6.59897			−0.433244
$233$	−4.62458	−	14.2330i	−0.302967	−	0.932435i	−0.980428	−	0.196877i	$-0.936920\pi$
$233$	−4.62458	−	14.2330i	−0.302967	−	0.932435i	0.677462	−	0.735558i	$-0.263080\pi$
$234$		0			0
$235$	−11.3053	+	8.21378i	−0.737477	+	0.535808i
$236$	1.94610	+	0.632327i	0.126680	+	0.0411610i
$237$		0			0
$238$	0.427051	+	0.587785i	0.0276816	+	0.0381005i
$239$	4.37274	+	3.17698i	0.282849	+	0.205502i	0.720159	−	0.693809i	$-0.244069\pi$
$239$	4.37274	+	3.17698i	0.282849	+	0.205502i	−0.437310	+	0.899311i	$0.644069\pi$
$240$		0			0
$241$		−	11.7091i		−	0.754252i	−0.926162	−	0.377126i	$-0.876912\pi$
$241$		−	11.7091i		−	0.754252i	0.926162	−	0.377126i	$-0.123088\pi$
$242$	7.69281	+	24.6880i	0.494513	+	1.58700i
$243$		0			0
$244$	12.6843	−	4.12137i	0.812028	−	0.263844i
$245$	−12.4362	+	17.1169i	−0.794518	+	1.09356i
$246$		0			0
$247$	3.44458	−	10.6013i	0.219173	−	0.674546i
$248$	1.85685	−	5.71479i	0.117910	−	0.362890i
$249$		0			0
$250$	15.3639	−	21.1465i	0.971696	−	1.33743i
$251$	21.4920	−	6.98319i	1.35657	−	0.440775i	0.461671	−	0.887051i	$-0.347250\pi$
$251$	21.4920	−	6.98319i	1.35657	−	0.440775i	0.894895	+	0.446276i	$0.147250\pi$
$252$		0			0
$253$	0.0647190	−	10.7031i	0.00406885	−	0.672900i
$254$		−	14.2493i		−	0.894081i
$255$		0			0
$256$	19.2841	+	14.0107i	1.20526	+	0.875671i
$257$	16.1737	+	22.2612i	1.00889	+	1.38862i	0.919709	+	0.392601i	$0.128425\pi$
$257$	16.1737	+	22.2612i	1.00889	+	1.38862i	0.0891801	+	0.996016i	$0.471575\pi$
$258$		0			0
$259$	27.9980	+	9.09709i	1.73971	+	0.565266i
$260$	−29.8398	+	21.6799i	−1.85059	+	1.34453i
$261$		0			0
$262$	−5.19462	−	15.9874i	−0.320925	−	0.987705i
$263$	32.0386			1.97559			0.987793	−	0.155773i	$-0.0497868\pi$
$263$	32.0386			1.97559			0.987793	+	0.155773i	$0.0497868\pi$
$264$		0			0
$265$	2.76294			0.169726
$266$	−7.05051	−	21.6992i	−0.432294	−	1.33046i
$267$		0			0
$268$	−37.0818	+	26.9415i	−2.26513	+	1.64572i
$269$	−25.7177	−	8.35619i	−1.56804	−	0.509486i	−0.609097	−	0.793096i	$-0.708468\pi$
$269$	−25.7177	−	8.35619i	−1.56804	−	0.509486i	−0.958940	+	0.283610i	$0.908468\pi$
$270$		0			0
$271$	8.74690	+	12.0391i	0.531336	+	0.731322i	0.987333	−	0.158660i	$-0.0507172\pi$
$271$	8.74690	+	12.0391i	0.531336	+	0.731322i	−0.455997	+	0.889981i	$0.650717\pi$
$272$	0.0852963	+	0.0619714i	0.00517185	+	0.00375757i
$273$		0			0
$274$			24.9713i			1.50857i
$275$	−0.144573	−	0.106380i	−0.00871807	−	0.00641495i
$276$		0			0
$277$	−7.49418	+	2.43501i	−0.450282	+	0.146305i	−0.525374	−	0.850871i	$-0.676075\pi$
$277$	−7.49418	+	2.43501i	−0.450282	+	0.146305i	0.0750927	+	0.997177i	$0.476075\pi$
$278$	0.0733391	−	0.100943i	0.00439859	−	0.00605414i
$279$		0			0
$280$	−10.0976	+	31.0772i	−0.603447	+	1.85722i
$281$	6.56034	−	20.1906i	0.391357	−	1.20447i	−0.540406	−	0.841405i	$-0.681729\pi$
$281$	6.56034	−	20.1906i	0.391357	−	1.20447i	0.931763	−	0.363068i	$-0.118271\pi$
$282$		0			0
$283$	−2.52460	+	3.47482i	−0.150072	+	0.206556i	−0.877434	−	0.479698i	$-0.840746\pi$
$283$	−2.52460	+	3.47482i	−0.150072	+	0.206556i	0.727362	+	0.686254i	$0.240746\pi$
$284$	−3.75769	+	1.22095i	−0.222978	+	0.0724499i
$285$		0			0
$286$	−21.1444	−	29.4759i	−1.25029	−	1.74295i
$287$			34.1996i			2.01874i
$288$		0			0
$289$	13.7486	+	9.98893i	0.808740	+	0.587584i
$290$	5.71335	+	7.86374i	0.335499	+	0.461775i
$291$		0			0
$292$	−44.6265	−	14.5000i	−2.61157	−	0.848550i
$293$	15.4486	−	11.2241i	0.902518	−	0.655717i	−0.0365938	−	0.999330i	$-0.511651\pi$
$293$	15.4486	−	11.2241i	0.902518	−	0.655717i	0.939111	+	0.343613i	$0.111651\pi$
$294$		0			0
$295$	−0.403135	−	1.24072i	−0.0234714	−	0.0722376i
$296$	26.0731			1.51547
$297$		0			0
$298$	−47.9444			−2.77735
$299$	4.63988	+	14.2801i	0.268331	+	0.825838i
$300$		0			0
$301$	−14.0300	+	10.1934i	−0.808678	+	0.587539i
$302$	2.65869	+	0.863861i	0.152990	+	0.0497096i
$303$		0			0
$304$	−1.94611	−	2.67860i	−0.111617	−	0.153628i
$305$	−6.87902	−	4.99790i	−0.393891	−	0.286179i
$306$		0			0
$307$		−	1.86240i		−	0.106293i	−0.998587	−	0.0531463i	$-0.983075\pi$
$307$		−	1.86240i		−	0.106293i	0.998587	−	0.0531463i	$-0.0169250\pi$
$308$	−44.9702	−	14.9129i	−2.56241	−	0.849742i
$309$		0			0
$310$	−8.41775	+	2.73509i	−0.478096	+	0.155343i
$311$	5.26339	−	7.24443i	0.298459	−	0.410794i	−0.633279	−	0.773923i	$-0.718292\pi$
$311$	5.26339	−	7.24443i	0.298459	−	0.410794i	0.931739	+	0.363129i	$0.118292\pi$
$312$		0			0
$313$	5.29558	−	16.2981i	0.299324	−	0.921224i	−0.682411	−	0.730969i	$-0.739068\pi$
$313$	5.29558	−	16.2981i	0.299324	−	0.921224i	0.981735	−	0.190255i	$-0.0609316\pi$
$314$	−1.25898	+	3.87474i	−0.0710483	+	0.218664i
$315$		0			0
$316$	−1.36768	+	1.88245i	−0.0769381	+	0.105896i
$317$	−25.9678	+	8.43746i	−1.45850	+	0.473895i	−0.927611	−	0.373547i	$-0.878141\pi$
$317$	−25.9678	+	8.43746i	−1.45850	+	0.473895i	−0.530888	+	0.847442i	$0.678141\pi$
$318$		0			0
$319$	−4.95659	+	3.55558i	−0.277516	+	0.199075i
$320$		−	26.9682i		−	1.50757i
$321$		0			0
$322$	24.8637	+	18.0645i	1.38560	+	1.00670i
$323$	0.107435	+	0.147872i	0.00597785	+	0.00822781i
$324$		0			0
$325$	0.239475	+	0.0778102i	0.0132837	+	0.00431614i
$326$	1.90679	−	1.38536i	0.105607	−	0.0767281i
$327$		0			0
$328$	9.35999	+	28.8071i	0.516819	+	1.59061i
$329$	25.1809			1.38827
$330$		0			0
$331$	−5.87217			−0.322764			−0.161382	−	0.986892i	$-0.551595\pi$
$331$	−5.87217			−0.322764			−0.161382	+	0.986892i	$0.551595\pi$
$332$	−11.1268	−	34.2448i	−0.610663	−	1.87943i
$333$		0			0
$334$	25.7093	−	18.6789i	1.40675	−	1.02206i
$335$	27.7919	+	9.03014i	1.51844	+	0.493370i
$336$		0			0
$337$	−9.74004	−	13.4060i	−0.530574	−	0.730272i	0.456644	−	0.889650i	$-0.349051\pi$
$337$	−9.74004	−	13.4060i	−0.530574	−	0.730272i	−0.987218	+	0.159377i	$0.949051\pi$
$338$	16.4457	+	11.9485i	0.894528	+	0.649912i
$339$		0			0
$340$		−	0.604800i		−	0.0327999i
$341$	−1.68447	−	5.29296i	−0.0912193	−	0.286630i
$342$		0			0
$343$	9.28988	−	3.01847i	0.501606	−	0.162982i
$344$	−9.02802	+	12.4260i	−0.486758	+	0.669965i
$345$		0			0
$346$	5.46494	−	16.8194i	0.293797	−	0.904215i
$347$	0.778158	−	2.39492i	0.0417737	−	0.128566i	−0.927995	−	0.372593i	$-0.878469\pi$
$347$	0.778158	−	2.39492i	0.0417737	−	0.128566i	0.969768	+	0.244027i	$0.0784686\pi$
$348$		0			0
$349$	5.13104	−	7.06228i	0.274658	−	0.378035i	−0.649297	−	0.760535i	$-0.724937\pi$
$349$	5.13104	−	7.06228i	0.274658	−	0.378035i	0.923955	+	0.382500i	$0.124937\pi$
$350$	0.490168	−	0.159265i	0.0262006	−	0.00851308i
$351$		0			0
$352$	13.0245	+	0.0787558i	0.694210	+	0.00419770i
$353$			0.536500i			0.0285550i	0.999898	+	0.0142775i	$0.00454483\pi$
$353$			0.536500i			0.0285550i	−0.999898	+	0.0142775i	$0.995455\pi$
$354$		0			0
$355$	2.03789	+	1.48062i	0.108160	+	0.0785829i
$356$	13.6586	+	18.7995i	0.723905	+	0.996370i
$357$		0			0
$358$	27.9475	+	9.08069i	1.47707	+	0.479929i
$359$	−12.7871	+	9.29040i	−0.674880	+	0.490329i	−0.871655	−	0.490120i	$-0.836953\pi$
$359$	−12.7871	+	9.29040i	−0.674880	+	0.490329i	0.196775	+	0.980449i	$0.436953\pi$
$360$		0			0
$361$	4.09760	+	12.6111i	0.215663	+	0.663742i
$362$	−42.3167			−2.22412
$363$		0			0
$364$	66.4639			3.48365
$365$	9.24439	+	28.4513i	0.483873	+	1.48921i
$366$		0			0
$367$	−23.4075	+	17.0065i	−1.22186	+	0.887734i	−0.996253	−	0.0864843i	$-0.972437\pi$
$367$	−23.4075	+	17.0065i	−1.22186	+	0.887734i	−0.225608	+	0.974218i	$0.572437\pi$
$368$	4.24157	+	1.37817i	0.221107	+	0.0718420i
$369$		0			0
$370$	−22.5739	−	31.0703i	−1.17356	−	1.61527i
$371$	−4.02788	−	2.92642i	−0.209117	−	0.151932i
$372$		0			0
$373$			6.60935i			0.342219i	0.985252	+	0.171109i	$0.0547352\pi$
$373$			6.60935i			0.342219i	−0.985252	+	0.171109i	$0.945265\pi$
$374$	0.594811	+	0.00359666i	0.0307570	+	0.000185979i
$375$		0			0
$376$	21.2105	−	6.89171i	1.09385	−	0.355413i
$377$	5.02984	−	6.92297i	0.259050	−	0.356551i
$378$		0			0
$379$	0.478524	−	1.47275i	0.0245801	−	0.0756498i	−0.938014	−	0.346597i	$-0.887337\pi$
$379$	0.478524	−	1.47275i	0.0245801	−	0.0756498i	0.962594	+	0.270948i	$0.0873370\pi$
$380$	−5.86909	+	18.0632i	−0.301078	+	0.926623i
$381$		0			0
$382$	29.9249	−	41.1880i	1.53109	−	2.10736i
$383$	−12.8467	+	4.17415i	−0.656436	+	0.213289i	−0.618250	−	0.785982i	$-0.712158\pi$
$383$	−12.8467	+	4.17415i	−0.656436	+	0.213289i	−0.0381861	+	0.999271i	$0.512158\pi$
$384$		0			0
$385$	9.16021	+	28.7833i	0.466847	+	1.46693i
$386$		−	12.1934i		−	0.620629i
$387$		0			0
$388$	−46.9133	−	34.0845i	−2.38166	−	1.73038i
$389$	−8.80471	−	12.1186i	−0.446416	−	0.614440i	0.525206	−	0.850975i	$-0.323988\pi$
$389$	−8.80471	−	12.1186i	−0.446416	−	0.614440i	−0.971623	+	0.236535i	$0.923988\pi$
$390$		0			0
$391$	−0.234155	−	0.0760817i	−0.0118417	−	0.00384762i
$392$	27.3178	−	19.8475i	1.37976	−	1.00245i
$393$		0			0
$394$	−3.73882	−	11.5069i	−0.188359	−	0.579709i
$395$	1.48346			0.0746409
$396$		0			0
$397$	−20.7132			−1.03956			−0.519782	−	0.854299i	$-0.673987\pi$
$397$	−20.7132			−1.03956			−0.519782	+	0.854299i	$0.673987\pi$
$398$	17.6230	+	54.2380i	0.883360	+	2.71870i
$399$		0			0
$400$	0.0605073	−	0.0439611i	0.00302537	−	0.00219806i
$401$	−25.7211	−	8.35730i	−1.28445	−	0.417343i	−0.414305	−	0.910138i	$-0.635975\pi$
$401$	−25.7211	−	8.35730i	−1.28445	−	0.417343i	−0.870146	+	0.492795i	$0.835975\pi$
$402$		0			0
$403$	4.58007	+	6.30392i	0.228149	+	0.314021i
$404$	−4.91223	−	3.56894i	−0.244392	−	0.177561i
$405$		0			0
$406$		−	17.5154i		−	0.869273i
$407$	19.5839	−	14.0484i	0.970739	−	0.696354i
$408$		0			0
$409$	−5.80668	+	1.88670i	−0.287122	+	0.0932915i	−0.449037	−	0.893513i	$-0.648233\pi$
$409$	−5.80668	+	1.88670i	−0.287122	+	0.0932915i	0.161915	+	0.986805i	$0.448233\pi$
$410$	26.2245	−	36.0949i	1.29514	−	1.78260i
$411$		0			0
$412$	−3.52058	+	10.8352i	−0.173447	+	0.533814i
$413$	−0.726437	+	2.23574i	−0.0357456	+	0.110014i
$414$		0			0
$415$	−13.4932	+	18.5718i	−0.662357	+	0.911656i
$416$	−17.3773	+	5.64622i	−0.851991	+	0.276829i
$417$		0			0
$418$	−17.7300	−	5.87958i	−0.867202	−	0.287580i
$419$		−	35.6619i		−	1.74220i	−0.491110	−	0.871098i	$-0.663409\pi$
$419$		−	35.6619i		−	1.74220i	0.491110	−	0.871098i	$-0.336591\pi$
$420$		0			0
$421$	−11.5751	−	8.40982i	−0.564137	−	0.409870i	0.268834	−	0.963187i	$-0.413362\pi$
$421$	−11.5751	−	8.40982i	−0.564137	−	0.409870i	−0.832971	+	0.553317i	$0.813362\pi$
$422$	−25.8993	−	35.6473i	−1.26076	−	1.73528i
$423$		0			0
$424$	−4.19370	−	1.36262i	−0.203664	−	0.0661745i
$425$	−0.00334030	+	0.00242687i	−0.000162028	+	0.000117721i
$426$		0			0
$427$	4.73477	+	14.5721i	0.229131	+	0.705194i
$428$	−52.2536			−2.52577
$429$		0			0
$430$	22.6240			1.09103
$431$	−2.68944	−	8.27725i	−0.129546	−	0.398701i	0.865156	−	0.501503i	$-0.167219\pi$
$431$	−2.68944	−	8.27725i	−0.129546	−	0.398701i	−0.994702	+	0.102802i	$0.967219\pi$
$432$		0			0
$433$	30.3812	−	22.0733i	1.46003	−	1.06077i	0.476673	−	0.879080i	$-0.341842\pi$
$433$	30.3812	−	22.0733i	1.46003	−	1.06077i	0.983355	−	0.181693i	$-0.0581576\pi$
$434$	15.1685	+	4.92856i	0.728113	+	0.236578i
$435$		0			0
$436$	30.9364	+	42.5803i	1.48158	+	2.03923i
$437$	6.25507	+	4.54458i	0.299221	+	0.217397i
$438$		0			0
$439$			32.4669i			1.54956i	0.632232	+	0.774779i	$0.282139\pi$
$439$			32.4669i			1.54956i	−0.632232	+	0.774779i	$0.717861\pi$
$440$	15.5935	+	21.7378i	0.743390	+	1.03631i
$441$		0			0
$442$	−0.793595	+	0.257855i	−0.0377474	+	0.0122649i
$443$	11.0630	−	15.2269i	0.525618	−	0.723451i	−0.460837	−	0.887485i	$-0.652451\pi$
$443$	11.0630	−	15.2269i	0.525618	−	0.723451i	0.986455	+	0.164034i	$0.0524506\pi$
$444$		0			0
$445$	4.57804	−	14.0897i	0.217020	−	0.667918i
$446$	−3.98712	+	12.2711i	−0.188796	+	0.581053i
$447$		0			0
$448$	−28.5639	+	39.3149i	−1.34952	+	1.85745i
$449$	6.86840	−	2.23168i	0.324140	−	0.105319i	−0.142427	−	0.989805i	$-0.545491\pi$
$449$	6.86840	−	2.23168i	0.324140	−	0.105319i	0.466567	+	0.884486i	$0.345491\pi$
$450$		0			0
$451$	22.5520	+	16.5942i	1.06193	+	0.781392i
$452$			39.6582i			1.86536i
$453$		0			0
$454$	−26.1765	−	19.0183i	−1.22852	−	0.892575i
$455$	−24.9065	−	34.2809i	−1.16764	−	1.60711i
$456$		0			0
$457$	4.01554	+	1.30473i	0.187839	+	0.0610326i	0.401426	−	0.915891i	$-0.368515\pi$
$457$	4.01554	+	1.30473i	0.187839	+	0.0610326i	−0.213587	+	0.976924i	$0.568515\pi$
$458$	40.1908	−	29.2004i	1.87799	−	1.36444i
$459$		0			0
$460$	−7.90572	−	24.3313i	−0.368606	−	1.13445i
$461$	−14.1922			−0.660997			−0.330499	−	0.943806i	$-0.607217\pi$
$461$	−14.1922			−0.660997			−0.330499	+	0.943806i	$0.607217\pi$
$462$		0			0
$463$	−40.3784			−1.87654			−0.938271	−	0.345902i	$-0.887573\pi$
$463$	−40.3784			−1.87654			−0.938271	+	0.345902i	$0.887573\pi$
$464$	−0.785440	−	2.41734i	−0.0364632	−	0.112222i
$465$		0			0
$466$	28.4619	−	20.6788i	1.31847	−	0.957925i
$467$	10.7476	+	3.49210i	0.497338	+	0.161595i	0.546936	−	0.837174i	$-0.315794\pi$
$467$	10.7476	+	3.49210i	0.497338	+	0.161595i	−0.0495980	+	0.998769i	$0.515794\pi$
$468$		0			0
$469$	−30.9513	−	42.6008i	−1.42920	−	1.96712i
$470$	−26.5765	−	19.3090i	−1.22588	−	0.890656i
$471$		0			0
$472$			2.08203i			0.0958334i
$473$	−0.0858500	+	14.1977i	−0.00394739	+	0.652813i
$474$		0			0
$475$	0.123314	−	0.0400671i	0.00565802	−	0.00183840i
$476$	−0.640587	+	0.881692i	−0.0293612	+	0.0404123i
$477$		0			0
$478$	−3.92639	+	12.0842i	−0.179589	+	0.552718i
$479$	−7.07597	+	21.7776i	−0.323309	+	0.995044i	0.648889	+	0.760883i	$0.275234\pi$
$479$	−7.07597	+	21.7776i	−0.323309	+	0.995044i	−0.972198	+	0.234161i	$0.924766\pi$
$480$		0			0
$481$	−19.8733	+	27.3533i	−0.906145	+	1.24720i
$482$	26.1786	−	8.50595i	1.19240	−	0.387436i
$483$		0			0
$484$	−31.6542	+	22.4183i	−1.43883	+	1.01902i
$485$			36.9698i			1.67871i
$486$		0			0
$487$	6.10169	+	4.43314i	0.276494	+	0.200885i	0.717387	−	0.696675i	$-0.245338\pi$
$487$	6.10169	+	4.43314i	0.276494	+	0.200885i	−0.440893	+	0.897560i	$0.645338\pi$
$488$	7.97641	+	10.9786i	0.361075	+	0.496977i
$489$		0			0
$490$	−47.3031	−	15.3697i	−2.13694	−	0.694333i
$491$	−30.8965	+	22.4476i	−1.39434	+	1.01305i	−0.398967	+	0.916965i	$0.630631\pi$
$491$	−30.8965	+	22.4476i	−1.39434	+	1.01305i	−0.995373	+	0.0960820i	$0.969369\pi$
$492$		0			0
$493$	0.0433602	+	0.133449i	0.00195285	+	0.00601024i
$494$	26.2041			1.17898
$495$		0			0
$496$	2.31446			0.103922
$497$	−1.40266	−	4.31695i	−0.0629181	−	0.193642i
$498$		0			0
$499$	6.51994	−	4.73701i	0.291873	−	0.212058i	−0.432207	−	0.901775i	$-0.642265\pi$
$499$	6.51994	−	4.73701i	0.291873	−	0.212058i	0.724079	+	0.689717i	$0.242265\pi$
$500$	37.2895	+	12.1161i	1.66764	+	0.541848i
$501$		0			0
$502$	31.2252	+	42.9778i	1.39365	+	1.91820i
$503$	21.0846	+	15.3188i	0.940115	+	0.683033i	0.948448	−	0.316932i	$-0.102653\pi$
$503$	21.0846	+	15.3188i	0.940115	+	0.683033i	−0.00833362	+	0.999965i	$0.502653\pi$
$504$		0			0
$505$			3.87106i			0.172260i
$506$	23.9765	−	7.63045i	1.06588	−	0.339215i
$507$		0			0
$508$	20.3282	−	6.60503i	0.901917	−	0.293051i
$509$	−16.4364	+	22.6228i	−0.728531	+	1.00274i	0.270666	+	0.962673i	$0.412756\pi$
$509$	−16.4364	+	22.6228i	−0.728531	+	1.00274i	−0.999197	+	0.0400639i	$0.987244\pi$
$510$		0			0
$511$	16.6581	−	51.2684i	0.736911	−	2.26798i
$512$	−4.74153	+	14.5929i	−0.209548	+	0.644922i
$513$		0			0
$514$	−38.0212	+	52.3316i	−1.67704	+	2.30825i
$515$	6.90792	−	2.24452i	0.304399	−	0.0989054i
$516$		0			0
$517$	12.2182	−	16.6049i	0.537357	−	0.730282i
$518$			69.2047i			3.04068i
$519$		0			0
$520$	−30.3616	−	22.0590i	−1.33144	−	0.967351i
$521$	18.9804	+	26.1242i	0.831545	+	1.14452i	0.987633	+	0.156781i	$0.0501117\pi$
$521$	18.9804	+	26.1242i	0.831545	+	1.14452i	−0.156088	+	0.987743i	$0.549888\pi$
$522$		0			0
$523$	16.5104	+	5.36454i	0.721948	+	0.234575i	0.646868	−	0.762602i	$-0.276079\pi$
$523$	16.5104	+	5.36454i	0.721948	+	0.234575i	0.0750804	+	0.997177i	$0.476079\pi$
$524$	20.3999	−	14.8214i	0.891173	−	0.647475i
$525$		0			0
$526$	23.2740	+	71.6301i	1.01480	+	3.12322i
$527$	−0.127769			−0.00556572
$528$		0			0
$529$	12.5853			0.547189
$530$	2.00710	+	6.17722i	0.0871828	+	0.268321i
$531$		0			0
$532$	27.6881	−	20.1166i	1.20043	−	0.872166i
$533$	−37.3558	−	12.1376i	−1.61806	−	0.525740i
$534$		0			0
$535$	19.5814	+	26.9515i	0.846578	+	1.16522i
$536$	−37.7303	−	27.4126i	−1.62970	−	1.18405i
$537$		0			0
$538$		−	63.5684i		−	2.74063i
$539$	9.82480	−	29.6269i	0.423184	−	1.27612i
$540$		0			0
$541$	−9.58312	+	3.11375i	−0.412011	+	0.133870i	−0.507686	−	0.861542i	$-0.669499\pi$
$541$	−9.58312	+	3.11375i	−0.412011	+	0.133870i	0.0956753	+	0.995413i	$0.469499\pi$
$542$	−20.5622	+	28.3014i	−0.883222	+	1.21565i
$543$		0			0
$544$	0.0925830	−	0.284941i	0.00396946	−	0.0122168i
$545$	10.3691	−	31.9129i	0.444165	−	1.36700i
$546$		0			0
$547$	14.0244	−	19.3029i	0.599639	−	0.825333i	−0.396036	−	0.918235i	$-0.629614\pi$
$547$	14.0244	−	19.3029i	0.599639	−	0.825333i	0.995675	+	0.0929023i	$0.0296144\pi$
$548$	−35.6242	+	11.5750i	−1.52179	+	0.494460i
$549$		0			0
$550$	0.132815	−	0.400506i	0.00566325	−	0.0170776i
$551$		−	4.40642i		−	0.187720i
$552$		0			0
$553$	−2.16262	−	1.57124i	−0.0919640	−	0.0668158i
$554$	−10.8881	−	14.9862i	−0.462591	−	0.636702i
$555$		0			0
$556$	0.178001	+	0.0578359i	0.00754891	+	0.00245279i
$557$	31.6776	−	23.0151i	1.34222	−	0.975181i	0.342862	−	0.939386i	$-0.388604\pi$
$557$	31.6776	−	23.0151i	1.34222	−	0.975181i	0.999359	−	0.0357950i	$-0.0113963\pi$
$558$		0			0
$559$	−6.15482	−	18.9426i	−0.260321	−	0.801185i
$560$	−12.5861			−0.531859
$561$		0			0
$562$	49.9068			2.10519
$563$	−1.55147	−	4.77494i	−0.0653868	−	0.201240i	0.913025	−	0.407903i	$-0.133740\pi$
$563$	−1.55147	−	4.77494i	−0.0653868	−	0.201240i	−0.978412	+	0.206663i	$0.933740\pi$
$564$		0			0
$565$	20.4550	−	14.8614i	0.860548	−	0.625225i
$566$	−9.60276	−	3.12012i	−0.403634	−	0.131149i
$567$		0			0
$568$	−2.36299	−	3.25238i	−0.0991489	−	0.136467i
$569$	−7.69308	−	5.58935i	−0.322511	−	0.234318i	0.414735	−	0.909942i	$-0.363874\pi$
$569$	−7.69308	−	5.58935i	−0.322511	−	0.234318i	−0.737246	+	0.675624i	$0.763874\pi$
$570$		0			0
$571$		−	39.8291i		−	1.66680i	−0.552673	−	0.833398i	$-0.686392\pi$
$571$		−	39.8291i		−	1.66680i	0.552673	−	0.833398i	$-0.313608\pi$
$572$	32.2494	−	43.8278i	1.34842	−	1.83253i
$573$		0			0
$574$	−76.4614	+	24.8438i	−3.19144	+	1.03696i
$575$	−0.102658	+	0.141297i	−0.00428115	+	0.00589249i
$576$		0			0
$577$	−4.03506	+	12.4186i	−0.167982	+	0.516994i	−0.999244	−	0.0388866i	$-0.987619\pi$
$577$	−4.03506	+	12.4186i	−0.167982	+	0.516994i	0.831262	+	0.555881i	$0.187619\pi$
$578$	−12.3452	+	37.9946i	−0.513493	+	1.58037i
$579$		0			0
$580$	−8.57016	+	11.7958i	−0.355856	+	0.489794i
$581$	39.3415	−	12.7828i	1.63216	−	0.530321i
$582$		0			0
$583$	−3.88415	+	1.23612i	−0.160865	+	0.0511949i
$584$		−	47.7437i		−	1.97565i
$585$		0			0
$586$	36.3166	+	26.3855i	1.50022	+	1.08998i
$587$	13.9608	+	19.2153i	0.576222	+	0.793102i	0.993275	−	0.115780i	$-0.0369369\pi$
$587$	13.9608	+	19.2153i	0.576222	+	0.793102i	−0.417053	+	0.908882i	$0.636937\pi$
$588$		0			0
$589$	3.81602	+	1.23990i	0.157236	+	0.0510891i
$590$	2.48108	−	1.80261i	0.102145	−	0.0742123i
$591$		0			0
$592$	3.10334	+	9.55111i	0.127547	+	0.392548i
$593$	−37.1489			−1.52552			−0.762761	−	0.646680i	$-0.776157\pi$
$593$	−37.1489			−1.52552			−0.762761	+	0.646680i	$0.776157\pi$
$594$		0			0
$595$	0.694814			0.0284846
$596$	−22.2238	−	68.3979i	−0.910323	−	2.80169i
$597$		0			0
$598$	−28.5560	+	20.7471i	−1.16774	+	0.848414i
$599$	−2.26902	−	0.737248i	−0.0927095	−	0.0301231i	0.262295	−	0.964988i	$-0.415521\pi$
$599$	−2.26902	−	0.737248i	−0.0927095	−	0.0301231i	−0.355004	+	0.934865i	$0.615521\pi$
$600$		0			0
$601$	3.99333	+	5.49635i	0.162891	+	0.224201i	0.882658	−	0.470015i	$-0.155751\pi$
$601$	3.99333	+	5.49635i	0.162891	+	0.224201i	−0.719767	+	0.694216i	$0.755751\pi$
$602$	−32.9818	−	23.9627i	−1.34424	−	0.976646i
$603$		0			0
$604$			4.19334i			0.170624i
$605$	23.4250	+	7.92570i	0.952363	+	0.322225i
$606$		0			0
$607$	−38.5143	+	12.5141i	−1.56325	+	0.507930i	−0.957673	−	0.287859i	$-0.907057\pi$
$607$	−38.5143	+	12.5141i	−1.56325	+	0.507930i	−0.605575	+	0.795788i	$0.707057\pi$
$608$	−5.53025	+	7.61173i	−0.224281	+	0.308696i
$609$		0			0
$610$	6.17684	−	19.0104i	0.250093	−	0.769707i
$611$	−8.93688	+	27.5049i	−0.361547	+	1.11273i
$612$		0			0
$613$	0.119072	−	0.163888i	0.00480926	−	0.00661938i	−0.806606	−	0.591090i	$-0.798698\pi$
$613$	0.119072	−	0.163888i	0.00480926	−	0.00661938i	0.811415	+	0.584471i	$0.198698\pi$
$614$	4.16384	−	1.35291i	0.168039	−	0.0545991i
$615$		0			0
$616$	0.291489	−	48.2060i	0.0117444	−	1.94228i
$617$		−	8.08426i		−	0.325460i	−0.986671	−	0.162730i	$-0.947970\pi$
$617$		−	8.08426i		−	0.325460i	0.986671	−	0.162730i	$-0.0520299\pi$
$618$		0			0
$619$	−16.9785	−	12.3356i	−0.682424	−	0.495810i	0.191737	−	0.981446i	$-0.438588\pi$
$619$	−16.9785	−	12.3356i	−0.682424	−	0.495810i	−0.874161	+	0.485636i	$0.838588\pi$
$620$	−7.80381	−	10.7410i	−0.313409	−	0.431370i
$621$		0			0
$622$	20.0202	+	6.50496i	0.802737	+	0.260825i
$623$	−21.5974	+	15.6914i	−0.865282	+	0.628664i
$624$		0			0
$625$	−7.80814	−	24.0310i	−0.312326	−	0.961239i
$626$	40.2853			1.61012
$627$		0			0
$628$	−6.11131			−0.243868
$629$	−0.171320	−	0.527268i	−0.00683097	−	0.0210236i
$630$		0			0
$631$	19.6268	−	14.2597i	0.781332	−	0.567671i	−0.124047	−	0.992276i	$-0.539587\pi$
$631$	19.6268	−	14.2597i	0.781332	−	0.567671i	0.905378	+	0.424606i	$0.139587\pi$
$632$	−2.25165	−	0.731607i	−0.0895660	−	0.0291018i
$633$		0			0
$634$	−37.7280	−	51.9281i	−1.49837	−	2.06233i
$635$	−11.0245	−	8.00977i	−0.437494	−	0.317858i
$636$		0			0
$637$			43.7871i			1.73491i
$638$	−11.5500	−	8.49876i	−0.457270	−	0.336469i
$639$		0			0
$640$	43.5007	−	14.1342i	1.71952	−	0.558705i
$641$	9.48633	−	13.0568i	0.374688	−	0.515713i	−0.579480	−	0.814987i	$-0.696744\pi$
$641$	9.48633	−	13.0568i	0.374688	−	0.515713i	0.954167	+	0.299273i	$0.0967442\pi$
$642$		0			0
$643$	3.88866	−	11.9681i	0.153354	−	0.471975i	−0.844637	−	0.535340i	$-0.820183\pi$
$643$	3.88866	−	11.9681i	0.153354	−	0.471975i	0.997990	+	0.0633656i	$0.0201834\pi$
$644$	−14.2459	+	43.8443i	−0.561366	+	1.72771i
$645$		0			0
$646$	−0.252558	+	0.347617i	−0.00993678	+	0.0136768i
$647$	−28.7701	+	9.34797i	−1.13107	+	0.367507i	−0.813982	−	0.580890i	$-0.802705\pi$
$647$	−28.7701	+	9.34797i	−1.13107	+	0.367507i	−0.317087	+	0.948396i	$0.602705\pi$
$648$		0			0
$649$	1.12182	+	1.56385i	0.0440352	+	0.0613865i
$650$			0.591929i			0.0232174i
$651$		0			0
$652$	2.86023	+	2.07808i	0.112015	+	0.0813837i
$653$	11.5162	+	15.8507i	0.450664	+	0.620286i	0.972540	−	0.232735i	$-0.0747676\pi$
$653$	11.5162	+	15.8507i	0.450664	+	0.620286i	−0.521876	+	0.853021i	$0.674768\pi$
$654$		0			0
$655$	−15.2892	−	4.96777i	−0.597399	−	0.194107i
$656$	−9.43855	+	6.85751i	−0.368514	+	0.267741i
$657$		0			0
$658$	18.2924	+	56.2981i	0.713111	+	2.19473i
$659$	−1.34943			−0.0525664			−0.0262832	−	0.999655i	$-0.508367\pi$
$659$	−1.34943			−0.0525664			−0.0262832	+	0.999655i	$0.508367\pi$
$660$		0			0
$661$	28.7859			1.11964			0.559821	−	0.828614i	$-0.310870\pi$
$661$	28.7859			1.11964			0.559821	+	0.828614i	$0.310870\pi$
$662$	−4.26576	−	13.1287i	−0.165794	−	0.510260i
$663$		0			0
$664$	29.6398	−	21.5346i	1.15025	−	0.835703i
$665$	−20.7516	−	6.74260i	−0.804712	−	0.261467i
$666$		0			0
$667$	3.48879	+	4.80191i	0.135086	+	0.185931i
$668$	38.5646	+	28.0188i	1.49211	+	1.08408i
$669$		0			0
$670$			68.6954i			2.65394i
$671$	11.9066	+	3.94843i	0.459648	+	0.152428i
$672$		0			0
$673$	20.6864	−	6.72140i	0.797400	−	0.259091i	0.118148	−	0.992996i	$-0.462304\pi$
$673$	20.6864	−	6.72140i	0.797400	−	0.259091i	0.679252	+	0.733905i	$0.262304\pi$
$674$	22.8969	−	31.5149i	0.881955	−	1.21391i
$675$		0			0
$676$	−9.42270	+	29.0001i	−0.362411	+	1.11539i
$677$	5.84208	−	17.9801i	0.224529	−	0.691030i	−0.773810	−	0.633418i	$-0.781651\pi$
$677$	5.84208	−	17.9801i	0.224529	−	0.691030i	0.998339	−	0.0576121i	$-0.0183487\pi$
$678$		0			0
$679$	39.1574	−	53.8955i	1.50272	−	2.06832i
$680$	0.585258	−	0.190162i	0.0224436	−	0.00729237i
$681$		0			0
$682$	10.6100	−	7.61105i	0.406279	−	0.291442i
$683$			33.7466i			1.29128i	0.763642	+	0.645640i	$0.223409\pi$
$683$			33.7466i			1.29128i	−0.763642	+	0.645640i	$0.776591\pi$
$684$		0			0
$685$	19.3199	+	14.0367i	0.738176	+	0.536316i
$686$	13.4970	+	18.5771i	0.515319	+	0.709275i
$687$		0			0
$688$	−5.62645	−	1.82815i	−0.214507	−	0.0696974i
$689$	4.62602	−	3.36100i	0.176237	−	0.128044i
$690$		0			0
$691$	−8.50814	−	26.1854i	−0.323665	−	0.996138i	−0.972040	−	0.234817i	$-0.924551\pi$
$691$	−8.50814	−	26.1854i	−0.323665	−	0.996138i	0.648375	−	0.761321i	$-0.275449\pi$
$692$	26.5278			1.00844
$693$		0			0
$694$	5.91971			0.224709
$695$	−0.0368728	−	0.113483i	−0.00139867	−	0.00430465i
$696$		0			0
$697$	0.521055	−	0.378569i	0.0197364	−	0.0143393i
$698$	19.5168	+	6.34140i	0.738722	+	0.240025i
$699$		0			0
$700$	0.454418	+	0.625453i	0.0171754	+	0.0236399i
$701$	8.43699	+	6.12983i	0.318661	+	0.231521i	0.735604	−	0.677412i	$-0.236899\pi$
$701$	8.43699	+	6.12983i	0.318661	+	0.231521i	−0.416943	+	0.908933i	$0.636899\pi$
$702$		0			0
$703$			17.4101i			0.656636i
$704$	12.0654	+	37.9119i	0.454731	+	1.42886i
$705$		0			0
$706$	−1.19948	+	0.389734i	−0.0451429	+	0.0146678i
$707$	4.10011	−	5.64332i	0.154201	−	0.212239i
$708$		0			0
$709$	−6.19477	+	19.0655i	−0.232649	+	0.716021i	0.764775	+	0.644297i	$0.222850\pi$
$709$	−6.19477	+	19.0655i	−0.232649	+	0.716021i	−0.997425	+	0.0717239i	$0.977150\pi$
$710$	−1.82988	+	5.63178i	−0.0686740	+	0.211357i
$711$		0			0
$712$	−13.8975	+	19.1282i	−0.520829	+	0.716860i
$713$	−5.14021	+	1.67015i	−0.192502	+	0.0625478i
$714$		0			0
$715$	−34.6907	−	0.209765i	−1.29736	−	0.00784477i
$716$			44.0793i			1.64732i
$717$		0			0
$718$	−30.0600	−	21.8399i	−1.12183	−	0.815057i
$719$	6.01752	+	8.28241i	0.224416	+	0.308882i	0.906347	−	0.422535i	$-0.138860\pi$
$719$	6.01752	+	8.28241i	0.224416	+	0.308882i	−0.681931	+	0.731417i	$0.738860\pi$
$720$		0			0
$721$	−12.4479	−	4.04456i	−0.463583	−	0.150627i
$722$	−25.2185	+	18.3223i	−0.938537	+	0.681887i
$723$		0			0
$724$	−19.6152	−	60.3694i	−0.728993	−	2.24361i
$725$	0.0995374			0.00369673
$726$		0			0
$727$	−14.4456			−0.535759			−0.267880	−	0.963452i	$-0.586323\pi$
$727$	−14.4456			−0.535759			−0.267880	+	0.963452i	$0.586323\pi$
$728$	20.8976	+	64.3163i	0.774517	+	2.38372i
$729$		0			0
$730$	−56.8943	+	41.3361i	−2.10575	+	1.52992i
$731$	0.310608	+	0.100923i	0.0114883	+	0.00373276i
$732$		0			0
$733$	4.29622	+	5.91324i	0.158685	+	0.218411i	0.880955	−	0.473200i	$-0.156901\pi$
$733$	4.29622	+	5.91324i	0.158685	+	0.218411i	−0.722270	+	0.691611i	$0.756901\pi$
$734$	−55.0263	−	39.9789i	−2.03106	−	1.47565i
$735$		0			0
$736$		−	12.6735i		−	0.467151i
$737$	−43.1100	−	0.260675i	−1.58798	−	0.00960207i
$738$		0			0
$739$	−12.4909	+	4.05854i	−0.459485	+	0.149296i	−0.529608	−	0.848243i	$-0.677661\pi$
$739$	−12.4909	+	4.05854i	−0.459485	+	0.149296i	0.0701229	+	0.997538i	$0.477661\pi$
$740$	33.8614	−	46.6062i	1.24477	−	1.71328i
$741$		0			0
$742$	3.61673	−	11.1312i	0.132774	−	0.408638i
$743$	10.9307	−	33.6412i	0.401008	−	1.23418i	−0.523175	−	0.852225i	$-0.675253\pi$
$743$	10.9307	−	33.6412i	0.401008	−	1.23418i	0.924183	−	0.381950i	$-0.124747\pi$
$744$		0			0
$745$	−26.9503	+	37.0939i	−0.987383	+	1.35902i
$746$	−14.7768	+	4.80127i	−0.541017	+	0.175787i
$747$		0			0
$748$	0.270584	+	0.850230i	0.00989352	+	0.0310875i
$749$		−	60.0306i		−	2.19347i
$750$		0			0
$751$	18.6629	+	13.5594i	0.681018	+	0.494789i	0.873695	−	0.486473i	$-0.161717\pi$
$751$	18.6629	+	13.5594i	0.681018	+	0.494789i	−0.192677	+	0.981262i	$0.561717\pi$
$752$	5.04914	+	6.94955i	0.184123	+	0.253424i
$753$		0			0
$754$	19.1318	+	6.21631i	0.696741	+	0.226385i
$755$	2.16285	−	1.57140i	0.0787141	−	0.0571892i
$756$		0			0
$757$	3.02640	+	9.31430i	0.109996	+	0.338534i	0.990871	−	0.134816i	$-0.0430445\pi$
$757$	3.02640	+	9.31430i	0.109996	+	0.338534i	−0.880874	+	0.473350i	$0.843044\pi$
$758$	3.64030			0.132222
$759$		0			0
$760$	−19.3249			−0.700988
$761$	14.9642	+	46.0550i	0.542452	+	1.66949i	0.726973	+	0.686666i	$0.240926\pi$
$761$	14.9642	+	46.0550i	0.542452	+	1.66949i	−0.184522	+	0.982828i	$0.559074\pi$
$762$		0			0
$763$	−48.9176	+	35.5407i	−1.77094	+	1.28666i
$764$	72.6303	+	23.5990i	2.62767	+	0.853783i
$765$		0			0
$766$	−18.6646	−	25.6897i	−0.674381	−	0.928205i
$767$	−2.18426	−	1.58696i	−0.0788691	−	0.0573017i
$768$		0			0
$769$			33.4223i			1.20524i	0.798029	+	0.602619i	$0.205876\pi$
$769$			33.4223i			1.20524i	−0.798029	+	0.602619i	$0.794124\pi$
$770$	−57.6977	+	41.3891i	−2.07928	+	1.49156i
$771$		0			0
$772$	17.3952	−	5.65205i	0.626068	−	0.203422i
$773$	−3.82924	+	5.27050i	−0.137728	+	0.189567i	−0.872310	−	0.488954i	$-0.837379\pi$
$773$	−3.82924	+	5.27050i	−0.137728	+	0.189567i	0.734581	+	0.678521i	$0.237379\pi$
$774$		0			0
$775$	−0.0280083	+	0.0862007i	−0.00100609	+	0.00309642i
$776$	18.2326	−	56.1143i	0.654514	−	2.01439i
$777$		0			0
$778$	20.6981	−	28.4885i	0.742063	−	1.02136i
$779$	−19.2357	+	6.25007i	−0.689192	+	0.223932i
$780$		0			0
$781$	−3.52729	−	1.16971i	−0.126216	−	0.0418556i
$782$		−	0.578780i		−	0.0206971i
$783$		0			0
$784$	10.5220	+	7.64471i	0.375787	+	0.273025i
$785$	2.29014	+	3.15211i	0.0817386	+	0.112503i
$786$		0			0
$787$	27.5749	+	8.95962i	0.982939	+	0.319376i	0.756028	−	0.654539i	$-0.227137\pi$
$787$	27.5749	+	8.95962i	0.982939	+	0.319376i	0.226911	+	0.973916i	$0.427137\pi$
$788$	14.6828	−	10.6676i	0.523052	−	0.380019i
$789$		0			0
$790$	1.07764	+	3.31663i	0.0383407	+	0.118000i
$791$	−45.5606			−1.61995
$792$		0			0
$793$	−17.5974			−0.624901
$794$	−15.0468	−	46.3093i	−0.533991	−	1.64346i
$795$		0			0
$796$	−69.2075	+	50.2822i	−2.45299	+	1.78220i
$797$	25.7264	+	8.35900i	0.911274	+	0.296091i	0.726882	−	0.686762i	$-0.240968\pi$
$797$	25.7264	+	8.35900i	0.911274	+	0.296091i	0.184392	+	0.982853i	$0.440968\pi$
$798$		0			0
$799$	−0.278738	−	0.383650i	−0.00986103	−	0.0135725i
$800$	−0.171943	−	0.124924i	−0.00607910	−	0.00441672i
$801$		0			0
$802$		−	63.5768i		−	2.24498i
$803$	−25.7247	−	35.8610i	−0.907805	−	1.26551i
$804$		0			0
$805$	27.9526	−	9.08234i	0.985199	−	0.320110i
$806$	−10.7668	+	14.8193i	−0.379245	+	0.521986i
$807$		0			0
$808$	1.90911	−	5.87565i	0.0671624	−	0.206705i
$809$	12.9385	−	39.8205i	0.454892	−	1.40001i	−0.416370	−	0.909195i	$-0.636698\pi$
$809$	12.9385	−	39.8205i	0.454892	−	1.40001i	0.871262	−	0.490818i	$-0.163302\pi$
$810$		0			0
$811$	−7.51871	+	10.3486i	−0.264018	+	0.363389i	−0.920359	−	0.391075i	$-0.872103\pi$
$811$	−7.51871	+	10.3486i	−0.264018	+	0.363389i	0.656341	+	0.754464i	$0.272103\pi$
$812$	24.9876	−	8.11895i	0.876891	−	0.284919i
$813$		0			0
$814$	45.6351	+	33.5793i	1.59951	+	1.17695i
$815$		−	2.25399i		−	0.0789538i
$816$		0			0
$817$	−8.29738	−	6.02840i	−0.290289	−	0.210907i
$818$	−8.43637	−	11.6117i	−0.294971	−	0.405992i
$819$		0			0
$820$	63.6493	+	20.6809i	2.22273	+	0.722208i
$821$	9.59682	−	6.97250i	0.334931	−	0.243342i	−0.407589	−	0.913166i	$-0.633630\pi$
$821$	9.59682	−	6.97250i	0.334931	−	0.243342i	0.742520	+	0.669824i	$0.233630\pi$
$822$		0			0
$823$	8.11976	+	24.9900i	0.283037	+	0.871098i	0.986980	+	0.160842i	$0.0514210\pi$
$823$	8.11976	+	24.9900i	0.283037	+	0.871098i	−0.703943	+	0.710256i	$0.748579\pi$
$824$	−11.5921			−0.403829
$825$		0			0
$826$	−5.52626			−0.192283
$827$	7.99992	+	24.6212i	0.278184	+	0.856163i	0.988359	+	0.152138i	$0.0486159\pi$
$827$	7.99992	+	24.6212i	0.278184	+	0.856163i	−0.710175	+	0.704025i	$0.751384\pi$
$828$		0			0
$829$	−14.0195	+	10.1858i	−0.486918	+	0.353766i	−0.803998	−	0.594632i	$-0.797298\pi$
$829$	−14.0195	+	10.1858i	−0.486918	+	0.353766i	0.317080	+	0.948399i	$0.397298\pi$
$830$	−51.3238	−	16.6761i	−1.78148	−	0.578837i
$831$		0			0
$832$	−32.8057	−	45.1531i	−1.13733	−	1.56540i
$833$	−0.580869	−	0.422026i	−0.0201259	−	0.0146223i
$834$		0			0
$835$		−	30.3907i		−	1.05171i
$836$	0.169424	−	28.0191i	0.00585965	−	0.969061i
$837$		0			0
$838$	79.7307	−	25.9061i	2.75425	−	0.894911i
$839$	18.2513	−	25.1207i	0.630104	−	0.867264i	−0.367935	−	0.929851i	$-0.619935\pi$
$839$	18.2513	−	25.1207i	0.630104	−	0.867264i	0.998039	+	0.0625873i	$0.0199352\pi$
$840$		0			0
$841$	−7.91617	+	24.3635i	−0.272971	+	0.840120i
$842$	10.3936	−	31.9882i	0.358187	−	1.10239i
$843$		0			0
$844$	38.8495	−	53.4718i	1.33726	−	1.84058i
$845$	18.4888	−	6.00737i	0.636033	−	0.206660i
$846$		0			0
$847$	−25.7549	−	36.3654i	−0.884949	−	1.24953i
$848$		−	1.69842i		−	0.0583241i
$849$		0			0
$850$	−0.00785238	−	0.00570509i	−0.000269334	−	0.000195683i
$851$	−13.7845	−	18.9727i	−0.472527	−	0.650377i
$852$		0			0
$853$	0.303737	+	0.0986902i	0.0103998	+	0.00337909i	0.314212	−	0.949353i	$-0.398260\pi$
$853$	0.303737	+	0.0986902i	0.0103998	+	0.00337909i	−0.303812	+	0.952732i	$0.598260\pi$
$854$	−29.1400	+	21.1714i	−0.997150	+	0.724472i
$855$		0			0
$856$	−16.4296	−	50.5652i	−0.561553	−	1.72828i
$857$	13.2476			0.452528			0.226264	−	0.974066i	$-0.427349\pi$
$857$	13.2476			0.452528			0.226264	+	0.974066i	$0.427349\pi$
$858$		0			0
$859$	−8.58152			−0.292798			−0.146399	−	0.989226i	$-0.546768\pi$
$859$	−8.58152			−0.292798			−0.146399	+	0.989226i	$0.546768\pi$
$860$	10.4870	+	32.2756i	0.357603	+	1.10059i
$861$		0			0
$862$	16.5521	−	12.0258i	0.563766	−	0.409600i
$863$	51.0889	+	16.5998i	1.73909	+	0.565063i	0.994712	−	0.102700i	$-0.0327482\pi$
$863$	51.0889	+	16.5998i	1.73909	+	0.565063i	0.744374	+	0.667763i	$0.232748\pi$
$864$		0			0
$865$	−9.94098	−	13.6826i	−0.338004	−	0.465222i
$866$	71.4202	+	51.8898i	2.42696	+	1.76329i
$867$		0			0
$868$			23.9241i			0.812037i
$869$	−2.08545	+	0.663690i	−0.0707441	+	0.0225141i
$870$		0			0
$871$	57.5172	−	18.6885i	1.94889	−	0.633234i
$872$	−31.4774	+	43.3249i	−1.06596	+	1.46717i
$873$		0			0
$874$	−5.61659	+	17.2861i	−0.189984	+	0.584710i
$875$	−13.9193	+	42.8394i	−0.470560	+	1.44823i
$876$		0			0
$877$	−25.8716	+	35.6092i	−0.873623	+	1.20244i	0.104524	+	0.994522i	$0.466668\pi$
$877$	−25.8716	+	35.6092i	−0.873623	+	1.20244i	−0.978147	+	0.207916i	$0.933332\pi$
$878$	−72.5876	+	23.5851i	−2.44971	+	0.795959i
$879$		0			0
$880$	−6.10698	+	8.29954i	−0.205866	+	0.279777i
$881$			7.44194i			0.250725i	0.992111	+	0.125363i	$0.0400095\pi$
$881$			7.44194i			0.250725i	−0.992111	+	0.125363i	$0.959991\pi$
$882$		0			0
$883$	7.59369	+	5.51714i	0.255548	+	0.185667i	0.708182	−	0.706030i	$-0.249516\pi$
$883$	7.59369	+	5.51714i	0.255548	+	0.185667i	−0.452634	+	0.891696i	$0.649516\pi$
$884$	−0.735715	−	1.01262i	−0.0247448	−	0.0340582i
$885$		0			0
$886$	42.0799	+	13.6726i	1.41370	+	0.459340i
$887$	−19.5658	+	14.2154i	−0.656957	+	0.477307i	−0.865634	−	0.500678i	$-0.833084\pi$
$887$	−19.5658	+	14.2154i	−0.656957	+	0.477307i	0.208677	+	0.977985i	$0.433084\pi$
$888$		0			0
$889$	7.58806	+	23.3537i	0.254496	+	0.783257i
$890$	34.8267			1.16739
$891$		0			0
$892$	−19.3542			−0.648026
$893$	4.60189	+	14.1632i	0.153996	+	0.473952i
$894$		0			0
$895$	22.7353	−	16.5182i	0.759958	−	0.552142i
$896$	−78.3870	−	25.4695i	−2.61873	−	0.850875i
$897$		0			0
$898$	9.97892	+	13.7348i	0.333001	+	0.458336i
$899$	2.49197	+	1.81052i	0.0831119	+	0.0603843i
$900$		0			0
$901$			0.0937613i			0.00312364i
$902$	−20.7178	+	62.4750i	−0.689829	+	2.08019i
$903$		0			0
$904$	−38.3767	+	12.4693i	−1.27639	+	0.414724i
$905$	−23.7869	+	32.7399i	−0.790703	+	1.08831i
$906$		0			0
$907$	−11.0734	+	34.0803i	−0.367685	+	1.13162i	0.580597	+	0.814191i	$0.302819\pi$
$907$	−11.0734	+	34.0803i	−0.367685	+	1.13162i	−0.948282	+	0.317428i	$0.897181\pi$
$908$	14.9980	−	46.1592i	0.497728	−	1.53185i
$909$		0			0
$910$	58.5502	−	80.5875i	1.94092	−	2.67145i
$911$	8.33061	−	2.70678i	0.276005	−	0.0896796i	−0.167744	−	0.985831i	$-0.553648\pi$
$911$	8.33061	−	2.70678i	0.276005	−	0.0896796i	0.443749	+	0.896151i	$0.353648\pi$
$912$		0			0
$913$	10.6599	−	32.1451i	0.352791	−	1.06385i
$914$			9.92552i			0.328307i
$915$		0			0
$916$	60.2872	+	43.8012i	1.99195	+	1.44723i
$917$	17.0273	+	23.4360i	0.562290	+	0.773926i
$918$		0			0
$919$	−39.4876	−	12.8303i	−1.30258	−	0.423233i	−0.426100	−	0.904676i	$-0.640113\pi$
$919$	−39.4876	−	12.8303i	−1.30258	−	0.423233i	−0.876477	+	0.481443i	$0.840113\pi$
$920$	21.0594	−	15.3005i	0.694307	−	0.504444i
$921$		0			0
$922$	−10.3097	−	31.7301i	−0.339533	−	1.04498i
$923$	5.21318			0.171594
$924$		0			0
$925$	−0.393281			−0.0129310
$926$	−29.3323	−	90.2756i	−0.963920	−	2.96664i
$927$		0			0
$928$	−5.84339	+	4.24547i	−0.191819	+	0.139364i
$929$	51.5363	+	16.7451i	1.69085	+	0.549390i	0.986967	−	0.160925i	$-0.0514478\pi$
$929$	51.5363	+	16.7451i	1.69085	+	0.549390i	0.703883	+	0.710316i	$0.251448\pi$
$930$		0			0
$931$	13.2531	+	18.2413i	0.434351	+	0.597833i
$932$	42.6935	+	31.0186i	1.39847	+	1.01605i
$933$		0			0
$934$			26.5656i			0.869253i
$935$	0.337136	−	0.458176i	0.0110255	−	0.0149839i
$936$		0			0
$937$	−16.5444	+	5.37559i	−0.540480	+	0.175613i	−0.566520	−	0.824048i	$-0.691710\pi$
$937$	−16.5444	+	5.37559i	−0.540480	+	0.175613i	0.0260393	+	0.999661i	$0.491710\pi$
$938$	72.7602	−	100.146i	2.37571	−	3.26988i
$939$		0			0
$940$	15.2272	−	46.8646i	0.496657	−	1.52855i
$941$	−6.64708	+	20.4576i	−0.216689	+	0.666899i	0.782341	+	0.622851i	$0.214026\pi$
$941$	−6.64708	+	20.4576i	−0.216689	+	0.666899i	−0.999029	+	0.0440486i	$0.985974\pi$
$942$		0			0
$943$	16.0137	−	22.0410i	0.521478	−	0.717753i
$944$	−0.762692	+	0.247814i	−0.0248235	+	0.00806564i
$945$		0			0
$946$	−31.8049	+	10.1218i	−1.03407	+	0.329089i
$947$		−	44.7887i		−	1.45544i	−0.685875	−	0.727719i	$-0.740580\pi$
$947$		−	44.7887i		−	1.45544i	0.685875	−	0.727719i	$-0.259420\pi$
$948$		0			0
$949$	50.0878	+	36.3909i	1.62592	+	1.18130i
$950$	0.179159	+	0.246592i	0.00581269	+	0.00800049i
$951$		0			0
$952$	−1.05462	−	0.342666i	−0.0341803	−	0.0111059i
$953$	8.11741	−	5.89765i	0.262949	−	0.191043i	−0.448497	−	0.893784i	$-0.648041\pi$
$953$	8.11741	−	5.89765i	0.262949	−	0.191043i	0.711446	+	0.702741i	$0.248041\pi$
$954$		0			0
$955$	−15.0454	−	46.3049i	−0.486857	−	1.49839i
$956$	−19.0594			−0.616425
$957$		0			0
$958$	−53.8294			−1.73915
$959$	−13.2977	−	40.9262i	−0.429406	−	1.32158i
$960$		0			0
$961$	22.8104	−	16.5727i	0.735819	−	0.534604i
$962$	−75.5916	−	24.5612i	−2.43717	−	0.791884i
$963$		0			0
$964$	24.2693	+	33.4039i	0.781662	+	1.07587i
$965$	−9.43388	−	6.85412i	−0.303688	−	0.220642i
$966$		0			0
$967$			4.32167i			0.138976i	0.997583	+	0.0694878i	$0.0221365\pi$
$967$			4.32167i			0.138976i	−0.997583	+	0.0694878i	$0.977863\pi$
$968$	−31.6467	−	23.5826i	−1.01716	−	0.757974i
$969$		0			0
$970$	−82.6550	+	26.8562i	−2.65389	+	0.862302i
$971$	−33.7344	+	46.4314i	−1.08259	+	1.49005i	−0.225947	+	0.974140i	$0.572548\pi$
$971$	−33.7344	+	46.4314i	−1.08259	+	1.49005i	−0.856640	+	0.515914i	$0.827452\pi$
$972$		0			0
$973$	−0.0664437	+	0.204493i	−0.00213009	+	0.00655574i
$974$	−5.47886	+	16.8622i	−0.175554	+	0.540300i
$975$		0			0
$976$	−3.07229	+	4.22864i	−0.0983416	+	0.135356i
$977$	−3.28130	+	1.06616i	−0.104978	+	0.0341095i	−0.361035	−	0.932552i	$-0.617577\pi$
$977$	−3.28130	+	1.06616i	−0.104978	+	0.0341095i	0.256057	+	0.966662i	$0.417577\pi$
$978$		0			0
$979$	−0.132155	+	21.8556i	−0.00422369	+	0.698508i
$980$		−	74.6073i		−	2.38324i
$981$		0			0
$982$	−72.6315	−	52.7699i	−2.31776	−	1.68395i
$983$	−0.608167	−	0.837070i	−0.0193975	−	0.0266984i	0.799208	−	0.601054i	$-0.205253\pi$
$983$	−0.608167	−	0.837070i	−0.0193975	−	0.0266984i	−0.818606	+	0.574356i	$0.805253\pi$
$984$		0			0
$985$	−11.0044	−	3.57554i	−0.350628	−	0.113926i
$986$	−0.266859	+	0.193884i	−0.00849853	+	0.00617454i
$987$		0			0
$988$	12.1465	+	37.3830i	0.386431	+	1.18931i
$989$	13.8151			0.439294
$990$		0			0
$991$	9.78910			0.310961			0.155481	−	0.987839i	$-0.450307\pi$
$991$	9.78910			0.310961			0.155481	+	0.987839i	$0.450307\pi$
$992$	−2.03239	−	6.25506i	−0.0645285	−	0.198598i
$993$		0			0
$994$	8.63265	−	6.27199i	0.273811	−	0.198935i
$995$	51.8693	+	16.8534i	1.64437	+	0.534288i
$996$		0			0
$997$	−6.82690	−	9.39642i	−0.216210	−	0.297588i	0.687111	−	0.726552i	$-0.258878\pi$
$997$	−6.82690	−	9.39642i	−0.216210	−	0.297588i	−0.903321	+	0.428965i	$0.858878\pi$
$998$	15.3271	+	11.1358i	0.485170	+	0.352496i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.j.a.17.4	yes	16
3.2	odd	2	inner	99.2.j.a.17.1	✓	16
4.3	odd	2		1584.2.cd.c.17.4		16
9.2	odd	6		891.2.u.c.215.1		32
9.4	even	3		891.2.u.c.512.1		32
9.5	odd	6		891.2.u.c.512.4		32
9.7	even	3		891.2.u.c.215.4		32
11.2	odd	10	inner	99.2.j.a.35.1	yes	16
11.3	even	5		1089.2.d.g.1088.14		16
11.8	odd	10		1089.2.d.g.1088.4		16
12.11	even	2		1584.2.cd.c.17.1		16
33.2	even	10	inner	99.2.j.a.35.4	yes	16
33.8	even	10		1089.2.d.g.1088.13		16
33.14	odd	10		1089.2.d.g.1088.3		16
44.35	even	10		1584.2.cd.c.1025.1		16
99.2	even	30		891.2.u.c.134.1		32
99.13	odd	30		891.2.u.c.431.1		32
99.68	even	30		891.2.u.c.431.4		32
99.79	odd	30		891.2.u.c.134.4		32
132.35	odd	10		1584.2.cd.c.1025.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.17.1	✓	16	3.2	odd	2	inner
99.2.j.a.17.4	yes	16	1.1	even	1	trivial
99.2.j.a.35.1	yes	16	11.2	odd	10	inner
99.2.j.a.35.4	yes	16	33.2	even	10	inner
891.2.u.c.134.1		32	99.2	even	30
891.2.u.c.134.4		32	99.79	odd	30
891.2.u.c.215.1		32	9.2	odd	6
891.2.u.c.215.4		32	9.7	even	3
891.2.u.c.431.1		32	99.13	odd	30
891.2.u.c.431.4		32	99.68	even	30
891.2.u.c.512.1		32	9.4	even	3
891.2.u.c.512.4		32	9.5	odd	6
1089.2.d.g.1088.3		16	33.14	odd	10
1089.2.d.g.1088.4		16	11.8	odd	10
1089.2.d.g.1088.13		16	33.8	even	10
1089.2.d.g.1088.14		16	11.3	even	5
1584.2.cd.c.17.1		16	12.11	even	2
1584.2.cd.c.17.4		16	4.3	odd	2
1584.2.cd.c.1025.1		16	44.35	even	10
1584.2.cd.c.1025.4		16	132.35	odd	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.726437 + 2.23574i) q^{2} +(-2.85280 + 2.07268i) q^{4} +(2.13811 + 0.694712i) q^{5} +(-2.38116 - 3.27739i) q^{7} +(-2.90269 - 2.10893i) q^{8} +O(q^{10})\)	\(q+(0.726437 + 2.23574i) q^{2} +(-2.85280 + 2.07268i) q^{4} +(2.13811 + 0.694712i) q^{5} +(-2.38116 - 3.27739i) q^{7} +(-2.90269 - 2.10893i) q^{8} +5.28492i q^{10} +(-3.31656 - 0.0200544i) q^{11} +(4.42495 - 1.43775i) q^{13} +(5.59763 - 7.70448i) q^{14} +(0.427051 - 1.31433i) q^{16} +(-0.0235753 + 0.0725574i) q^{17} +(1.40822 - 1.93825i) q^{19} +(-7.53950 + 2.44973i) q^{20} +(-2.36444 - 7.42955i) q^{22} +3.22717i q^{23} +(0.0437835 + 0.0318106i) q^{25} +(6.42889 + 8.84860i) q^{26} +(13.5860 + 4.41435i) q^{28} +(1.48796 - 1.08107i) q^{29} +(0.517528 + 1.59279i) q^{31} -3.92711 q^{32} -0.179346 q^{34} +(-2.81433 - 8.66162i) q^{35} +(-5.87906 + 4.27138i) q^{37} +(5.35641 + 1.74040i) q^{38} +(-4.74115 - 6.52564i) q^{40} +(-6.82980 - 4.96214i) q^{41} -4.28086i q^{43} +(9.50306 - 6.81697i) q^{44} +(-7.21513 + 2.34434i) q^{46} +(-3.65360 + 5.02874i) q^{47} +(-2.90822 + 8.95058i) q^{49} +(-0.0393143 + 0.120997i) q^{50} +(-9.64348 + 13.2731i) q^{52} +(1.16884 - 0.379779i) q^{53} +(-7.07723 - 2.34694i) q^{55} +14.5349i q^{56} +(3.49789 + 2.54137i) q^{58} +(-0.341086 - 0.469465i) q^{59} +(-3.59710 - 1.16877i) q^{61} +(-3.18511 + 2.31412i) q^{62} +(-3.70690 - 11.4087i) q^{64} +10.4598 q^{65} +12.9984 q^{67} +(-0.0831326 - 0.255856i) q^{68} +(17.3207 - 12.5842i) q^{70} +(1.06563 + 0.346245i) q^{71} +(7.82153 + 10.7654i) q^{73} +(-13.8205 - 10.0412i) q^{74} +8.44824i q^{76} +(7.83155 + 10.9174i) q^{77} +(0.627566 - 0.203908i) q^{79} +(1.82616 - 2.51349i) q^{80} +(6.13265 - 18.8744i) q^{82} +(-3.15542 + 9.71138i) q^{83} +(-0.100813 + 0.138757i) q^{85} +(9.57090 - 3.10977i) q^{86} +(9.58466 + 7.05260i) q^{88} -6.58983i q^{89} +(-15.2486 - 11.0787i) q^{91} +(-6.68890 - 9.20649i) q^{92} +(-13.8971 - 4.51544i) q^{94} +(4.35745 - 3.16587i) q^{95} +(5.08168 + 15.6398i) q^{97} -22.1238 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4}+O(q^{10}) \) 16 * q - 4 * q^4	\( 16 q - 4 q^{4} - 20 q^{16} - 48 q^{22} - 32 q^{25} + 40 q^{28} + 16 q^{31} + 40 q^{34} - 12 q^{37} + 60 q^{40} - 40 q^{46} - 24 q^{49} - 40 q^{52} + 16 q^{55} + 12 q^{58} + 36 q^{64} + 96 q^{67} + 76 q^{70} - 20 q^{73} - 12 q^{82} - 100 q^{85} - 12 q^{88} - 72 q^{91} - 80 q^{94} + 60 q^{97}+O(q^{100}) \) 16 * q - 4 * q^4 - 20 * q^16 - 48 * q^22 - 32 * q^25 + 40 * q^28 + 16 * q^31 + 40 * q^34 - 12 * q^37 + 60 * q^40 - 40 * q^46 - 24 * q^49 - 40 * q^52 + 16 * q^55 + 12 * q^58 + 36 * q^64 + 96 * q^67 + 76 * q^70 - 20 * q^73 - 12 * q^82 - 100 * q^85 - 12 * q^88 - 72 * q^91 - 80 * q^94 + 60 * q^97

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