LMFDB - Embedded newform 99.2.j.a.35.1

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			35.1
Root			$0.556839 + 1.81878i$ of defining polynomial
Character	$\chi$	$=$	99.35
Dual form			99.2.j.a.17.1

$q$-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 $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

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

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	0.272023	+	0.962291i	$0.412307\pi$
$2$	−0.726437	+	2.23574i	−0.513668	+	1.58091i	−0.785692	+	0.618618i	$0.787693\pi$
$3$		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	$-0.767659\pi$
$5$	−2.13811	+	0.694712i	−0.956190	+	0.310685i	−0.210962	+	0.977494i	$0.567659\pi$
$6$		0			0
$7$	−2.38116	+	3.27739i	−0.899995	+	1.23874i	0.0704753	+	0.997514i	$0.477548\pi$
$7$	−2.38116	+	3.27739i	−0.899995	+	1.23874i	−0.970470	+	0.241223i	$0.922452\pi$
$8$	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	0.849721	−	0.527233i	$-0.176771\pi$
$13$	4.42495	+	1.43775i	1.22726	+	0.398761i	0.377538	+	0.925994i	$0.376771\pi$
$14$	−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	$-0.0970551\pi$
$17$	0.0235753	+	0.0725574i	0.00571786	+	0.0175978i	−0.948157	+	0.317803i	$0.897055\pi$
$18$		0			0
$19$	1.40822	+	1.93825i	0.323068	+	0.444665i	0.939401	−	0.342821i	$-0.111382\pi$
$19$	1.40822	+	1.93825i	0.323068	+	0.444665i	−0.616333	+	0.787486i	$0.711382\pi$
$20$	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	$-0.354625\pi$
$29$	−1.48796	−	1.08107i	−0.276307	−	0.200749i	−0.717305	+	0.696759i	$0.754625\pi$
$30$		0			0
$31$	0.517528	−	1.59279i	0.0929508	−	0.286073i	−0.893763	−	0.448539i	$-0.851945\pi$
$31$	0.517528	−	1.59279i	0.0929508	−	0.286073i	0.986714	+	0.162466i	$0.0519446\pi$
$32$	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	−0.0118571	−	0.999930i	$-0.503774\pi$
$37$	−5.87906	−	4.27138i	−0.966511	−	0.702211i	−0.954654	+	0.297718i	$0.903774\pi$
$38$	−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	$-0.470888\pi$
$41$	6.82980	−	4.96214i	1.06664	−	0.774956i	0.975305	+	0.220864i	$0.0708878\pi$
$42$		0			0
$43$			4.28086i			0.652825i	0.945227	+	0.326413i	$0.105840\pi$
$43$			4.28086i			0.652825i	−0.945227	+	0.326413i	$0.894160\pi$
$44$	−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	$-0.0502328\pi$
$47$	3.65360	+	5.02874i	0.532932	+	0.733518i	−0.454642	+	0.890674i	$0.650233\pi$
$48$		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	$-0.426900\pi$
$53$	−1.16884	−	0.379779i	−0.160552	−	0.0521666i	−0.388190	+	0.921579i	$0.626900\pi$
$54$		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	$-0.787973\pi$
$59$	0.341086	−	0.469465i	0.0444056	−	0.0611191i	0.830642	+	0.556806i	$0.187973\pi$
$60$		0			0
$61$	−3.59710	+	1.16877i	−0.460561	+	0.149645i	−0.530102	−	0.847934i	$-0.677847\pi$
$61$	−3.59710	+	1.16877i	−0.460561	+	0.149645i	0.0695411	+	0.997579i	$0.477847\pi$
$62$	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	$-0.621179\pi$
$71$	−1.06563	+	0.346245i	−0.126467	+	0.0410917i	0.245100	+	0.969498i	$0.421179\pi$
$72$		0			0
$73$	7.82153	−	10.7654i	0.915441	−	1.26000i	−0.0498335	−	0.998758i	$-0.515869\pi$
$73$	7.82153	−	10.7654i	0.915441	−	1.26000i	0.965274	−	0.261239i	$-0.0841309\pi$
$74$	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	0.344107	−	0.938930i	$-0.388182\pi$
$79$	0.627566	+	0.203908i	0.0706066	+	0.0229415i	−0.273501	+	0.961872i	$0.588182\pi$
$80$	−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	0.960856	+	0.277048i	$0.0893562\pi$
$83$	3.15542	+	9.71138i	0.346352	+	1.06596i	−0.614504	+	0.788914i	$0.710644\pi$
$84$		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	−0.265551	−	0.964097i	$-0.585554\pi$
$97$	5.08168	−	15.6398i	0.515966	−	1.58798i	0.781517	−	0.623883i	$-0.214446\pi$
$98$	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	$-0.927302\pi$
$101$	−0.532095	+	1.63762i	−0.0529455	+	0.162949i	0.921087	+	0.389356i	$0.127302\pi$
$102$		0			0
$103$	2.61382	+	1.89905i	0.257548	+	0.187119i	0.709065	−	0.705143i	$-0.249117\pi$
$103$	2.61382	+	1.89905i	0.257548	+	0.187119i	−0.451518	+	0.892262i	$0.649117\pi$
$104$	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	$-0.954155\pi$
$107$	−11.9884	+	8.71006i	−1.15896	+	0.842034i	−0.169314	+	0.985562i	$0.554155\pi$
$108$		0			0
$109$			14.9258i			1.42963i	0.699313	+	0.714815i	$0.253489\pi$
$109$			14.9258i			1.42963i	−0.699313	+	0.714815i	$0.746511\pi$
$110$	−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	$-0.377430\pi$
$113$	−6.61055	−	9.09864i	−0.621868	−	0.855928i	−0.997487	+	0.0708461i	$0.977430\pi$
$114$		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	−0.553404	−	0.832913i	$-0.686672\pi$
$127$	−5.76481	+	1.87310i	−0.511544	+	0.166211i	0.0418604	+	0.999123i	$0.486672\pi$
$128$	−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	$-0.398872\pi$
$131$	7.15083			0.624771			0.312385	+	0.949955i	$0.398872\pi$
$132$		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	$-0.749921\pi$
$137$	−10.1026	+	3.28252i	−0.863120	+	0.280445i	−0.156189	+	0.987727i	$0.549921\pi$
$138$		0			0
$139$	−0.0311975	+	0.0429397i	−0.00264614	+	0.00364210i	−0.810338	−	0.585963i	$-0.800716\pi$
$139$	−0.0311975	+	0.0429397i	−0.00264614	+	0.00364210i	0.807692	+	0.589605i	$0.200716\pi$
$140$	−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	0.780883	+	0.624677i	$0.214769\pi$
$149$	6.30238	+	19.3967i	0.516311	+	1.58904i	−0.264572	+	0.964366i	$0.585231\pi$
$150$		0			0
$151$	0.698980	+	0.962063i	0.0568822	+	0.0782916i	0.836510	−	0.547951i	$-0.184592\pi$
$151$	0.698980	+	0.962063i	0.0568822	+	0.0782916i	−0.779628	+	0.626243i	$0.784592\pi$
$152$	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	−0.530428	−	0.847730i	$-0.677969\pi$
$157$	1.40210	−	1.01868i	0.111900	−	0.0812998i	0.642328	+	0.766430i	$0.277969\pi$
$158$	−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	−0.962457	−	0.271435i	$-0.912502\pi$
$163$	−0.309821	+	0.953532i	−0.0242671	+	0.0746864i	0.938190	+	0.346122i	$0.112502\pi$
$164$	−29.7690			−2.32457
$165$		0			0
$166$	−24.0044			−1.86310
$167$	4.17734	−	12.8565i	0.323252	−	0.994868i	−0.648971	−	0.760813i	$-0.724800\pi$
$167$	4.17734	−	12.8565i	0.323252	−	0.994868i	0.972223	−	0.234055i	$-0.0751996\pi$
$168$		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	$-0.607681\pi$
$173$	6.08619	−	4.42188i	0.462724	−	0.336189i	0.794599	+	0.607135i	$0.207681\pi$
$174$		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	$-0.354722\pi$
$179$	−7.34750	−	10.1130i	−0.549178	−	0.755879i	−0.989900	+	0.141765i	$0.954722\pi$
$180$		0			0
$181$	−5.56261	−	17.1200i	−0.413466	−	1.27252i	−0.913616	−	0.406578i	$-0.866722\pi$
$181$	−5.56261	−	17.1200i	−0.413466	−	1.27252i	0.500150	−	0.865939i	$-0.333278\pi$
$182$	−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	−0.0421514	−	0.999111i	$-0.513421\pi$
$191$	12.7297	−	17.5209i	0.921085	−	1.26777i	0.963237	−	0.268654i	$-0.0865788\pi$
$192$		0			0
$193$	−4.93306	+	1.60285i	−0.355090	+	0.115376i	−0.481129	−	0.876650i	$-0.659773\pi$
$193$	−4.93306	+	1.60285i	−0.355090	+	0.115376i	0.126040	+	0.992025i	$0.459773\pi$
$194$	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	$-0.441307\pi$
$197$	5.14679			0.366693			0.183347	+	0.983048i	$0.441307\pi$
$198$		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	−0.377506	−	0.926007i	$-0.623218\pi$
$211$	−17.8262	−	5.79210i	−1.22721	−	0.398744i	−0.849702	+	0.527263i	$0.823218\pi$
$212$	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	−0.429100	−	0.903257i	$-0.641169\pi$
$223$	4.44037	−	3.22612i	0.297349	−	0.216037i	0.726449	+	0.687220i	$0.241169\pi$
$224$	−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	$-0.149007\pi$
$227$	11.1352	+	8.09016i	0.739066	+	0.536963i	−0.153352	+	0.988172i	$0.549007\pi$
$228$		0			0
$229$	−6.53035	+	20.0983i	−0.431538	+	1.32814i	0.465056	+	0.885281i	$0.346034\pi$
$229$	−6.53035	+	20.0983i	−0.431538	+	1.32814i	−0.896593	+	0.442855i	$0.853966\pi$
$230$	17.0554			1.12460
$231$		0			0
$232$	−6.59897			−0.433244
$233$	4.62458	−	14.2330i	0.302967	−	0.932435i	−0.677462	−	0.735558i	$-0.736920\pi$
$233$	4.62458	−	14.2330i	0.302967	−	0.932435i	0.980428	−	0.196877i	$-0.0630800\pi$
$234$		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	$-0.755931\pi$
$239$	−4.37274	+	3.17698i	−0.282849	+	0.205502i	0.437310	+	0.899311i	$0.355931\pi$
$240$		0			0
$241$			11.7091i			0.754252i	0.926162	+	0.377126i	$0.123088\pi$
$241$			11.7091i			0.754252i	−0.926162	+	0.377126i	$0.876912\pi$
$242$	−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	$-0.652750\pi$
$251$	−21.4920	−	6.98319i	−1.35657	−	0.440775i	−0.894895	+	0.446276i	$0.852750\pi$
$252$		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	−0.0891801	+	0.996016i	$0.528425\pi$
$257$	−16.1737	+	22.2612i	−1.00889	+	1.38862i	−0.919709	+	0.392601i	$0.871575\pi$
$258$		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	$-0.950213\pi$
$263$	−32.0386			−1.97559			−0.987793	+	0.155773i	$0.950213\pi$
$264$		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	$-0.291532\pi$
$269$	25.7177	−	8.35619i	1.56804	−	0.509486i	0.958940	+	0.283610i	$0.0915322\pi$
$270$		0			0
$271$	8.74690	−	12.0391i	0.531336	−	0.731322i	−0.455997	−	0.889981i	$-0.650717\pi$
$271$	8.74690	−	12.0391i	0.531336	−	0.731322i	0.987333	+	0.158660i	$0.0507172\pi$
$272$	−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	0.0750927	−	0.997177i	$-0.476075\pi$
$277$	−7.49418	−	2.43501i	−0.450282	−	0.146305i	−0.525374	+	0.850871i	$0.676075\pi$
$278$	−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	−0.931763	−	0.363068i	$-0.881729\pi$
$281$	−6.56034	−	20.1906i	−0.391357	−	1.20447i	0.540406	−	0.841405i	$-0.318271\pi$
$282$		0			0
$283$	−2.52460	−	3.47482i	−0.150072	−	0.206556i	0.727362	−	0.686254i	$-0.240746\pi$
$283$	−2.52460	−	3.47482i	−0.150072	−	0.206556i	−0.877434	+	0.479698i	$0.840746\pi$
$284$	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	$-0.488349\pi$
$293$	−15.4486	−	11.2241i	−0.902518	−	0.655717i	−0.939111	+	0.343613i	$0.888349\pi$
$294$		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	$0.0169250\pi$
$307$			1.86240i			0.106293i	−0.998587	+	0.0531463i	$0.983075\pi$
$308$	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	$-0.281708\pi$
$311$	−5.26339	−	7.24443i	−0.298459	−	0.410794i	−0.931739	+	0.363129i	$0.881708\pi$
$312$		0			0
$313$	5.29558	+	16.2981i	0.299324	+	0.921224i	0.981735	+	0.190255i	$0.0609316\pi$
$313$	5.29558	+	16.2981i	0.299324	+	0.921224i	−0.682411	+	0.730969i	$0.739068\pi$
$314$	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	$-0.121859\pi$
$317$	25.9678	+	8.43746i	1.45850	+	0.473895i	0.530888	+	0.847442i	$0.321859\pi$
$318$		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	−0.987218	−	0.159377i	$-0.949051\pi$
$337$	−9.74004	+	13.4060i	−0.530574	+	0.730272i	0.456644	+	0.889650i	$0.349051\pi$
$338$	−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	$-0.121531\pi$
$347$	−0.778158	−	2.39492i	−0.0417737	−	0.128566i	−0.969768	+	0.244027i	$0.921531\pi$
$348$		0			0
$349$	5.13104	+	7.06228i	0.274658	+	0.378035i	0.923955	−	0.382500i	$-0.124937\pi$
$349$	5.13104	+	7.06228i	0.274658	+	0.378035i	−0.649297	+	0.760535i	$0.724937\pi$
$350$	−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	$-0.163047\pi$
$359$	12.7871	+	9.29040i	0.674880	+	0.490329i	−0.196775	+	0.980449i	$0.563047\pi$
$360$		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	−0.225608	−	0.974218i	$-0.572437\pi$
$367$	−23.4075	−	17.0065i	−1.22186	−	0.887734i	−0.996253	+	0.0864843i	$0.972437\pi$
$368$	−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	$-0.945265\pi$
$373$		−	6.60935i		−	0.342219i	0.985252	−	0.171109i	$-0.0547352\pi$
$374$	−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	0.962594	−	0.270948i	$-0.0873370\pi$
$379$	0.478524	+	1.47275i	0.0245801	+	0.0756498i	−0.938014	+	0.346597i	$0.887337\pi$
$380$	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	$-0.287842\pi$
$383$	12.8467	+	4.17415i	0.656436	+	0.213289i	0.0381861	+	0.999271i	$0.487842\pi$
$384$		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	$-0.676012\pi$
$389$	8.80471	−	12.1186i	0.446416	−	0.614440i	0.971623	+	0.236535i	$0.0760119\pi$
$390$		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	$-0.364025\pi$
$401$	25.7211	−	8.35730i	1.28445	−	0.417343i	0.870146	+	0.492795i	$0.164025\pi$
$402$		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	0.161915	−	0.986805i	$-0.448233\pi$
$409$	−5.80668	−	1.88670i	−0.287122	−	0.0932915i	−0.449037	+	0.893513i	$0.648233\pi$
$410$	−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	−0.832971	−	0.553317i	$-0.813362\pi$
$421$	−11.5751	+	8.40982i	−0.564137	+	0.409870i	0.268834	+	0.963187i	$0.413362\pi$
$422$	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	$-0.832781\pi$
$431$	2.68944	−	8.27725i	0.129546	−	0.398701i	0.994702	+	0.102802i	$0.0327807\pi$
$432$		0			0
$433$	30.3812	+	22.0733i	1.46003	+	1.06077i	0.983355	+	0.181693i	$0.0581576\pi$
$433$	30.3812	+	22.0733i	1.46003	+	1.06077i	0.476673	+	0.879080i	$0.341842\pi$
$434$	−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	$-0.717861\pi$
$439$		−	32.4669i		−	1.54956i	0.632232	−	0.774779i	$-0.282139\pi$
$440$	−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	$-0.347549\pi$
$443$	−11.0630	−	15.2269i	−0.525618	−	0.723451i	−0.986455	+	0.164034i	$0.947549\pi$
$444$		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	$-0.454509\pi$
$449$	−6.86840	−	2.23168i	−0.324140	−	0.105319i	−0.466567	+	0.884486i	$0.654509\pi$
$450$		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	−0.213587	−	0.976924i	$-0.568515\pi$
$457$	4.01554	−	1.30473i	0.187839	−	0.0610326i	0.401426	+	0.915891i	$0.368515\pi$
$458$	−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	$-0.392783\pi$
$461$	14.1922			0.660997			0.330499	+	0.943806i	$0.392783\pi$
$462$		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	$-0.684206\pi$
$467$	−10.7476	+	3.49210i	−0.497338	+	0.161595i	0.0495980	+	0.998769i	$0.484206\pi$
$468$		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	0.972198	+	0.234161i	$0.0752341\pi$
$479$	7.07597	+	21.7776i	0.323309	+	0.995044i	−0.648889	+	0.760883i	$0.724766\pi$
$480$		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	−0.440893	−	0.897560i	$-0.645338\pi$
$487$	6.10169	−	4.43314i	0.276494	−	0.200885i	0.717387	+	0.696675i	$0.245338\pi$
$488$	−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	0.995373	+	0.0960820i	$0.0306311\pi$
$491$	30.8965	+	22.4476i	1.39434	+	1.01305i	0.398967	+	0.916965i	$0.369369\pi$
$492$		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	0.724079	−	0.689717i	$-0.242265\pi$
$499$	6.51994	+	4.73701i	0.291873	+	0.212058i	−0.432207	+	0.901775i	$0.642265\pi$
$500$	−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	$-0.897347\pi$
$503$	−21.0846	+	15.3188i	−0.940115	+	0.683033i	0.00833362	+	0.999965i	$0.497347\pi$
$504$		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	0.999197	+	0.0400639i	$0.0127561\pi$
$509$	16.4364	+	22.6228i	0.728531	+	1.00274i	−0.270666	+	0.962673i	$0.587244\pi$
$510$		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	0.156088	+	0.987743i	$0.450112\pi$
$521$	−18.9804	+	26.1242i	−0.831545	+	1.14452i	−0.987633	+	0.156781i	$0.949888\pi$
$522$		0			0
$523$	16.5104	−	5.36454i	0.721948	−	0.234575i	0.0750804	−	0.997177i	$-0.476079\pi$
$523$	16.5104	−	5.36454i	0.721948	−	0.234575i	0.646868	+	0.762602i	$0.276079\pi$
$524$	−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	0.0956753	−	0.995413i	$-0.469499\pi$
$541$	−9.58312	−	3.11375i	−0.412011	−	0.133870i	−0.507686	+	0.861542i	$0.669499\pi$
$542$	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	0.995675	−	0.0929023i	$-0.0296144\pi$
$547$	14.0244	+	19.3029i	0.599639	+	0.825333i	−0.396036	+	0.918235i	$0.629614\pi$
$548$	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	−0.999359	−	0.0357950i	$-0.988604\pi$
$557$	−31.6776	−	23.0151i	−1.34222	−	0.975181i	−0.342862	−	0.939386i	$-0.611396\pi$
$558$		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	$-0.866260\pi$
$563$	1.55147	−	4.77494i	0.0653868	−	0.201240i	0.978412	+	0.206663i	$0.0662603\pi$
$564$		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	$-0.636126\pi$
$569$	7.69308	−	5.58935i	0.322511	−	0.234318i	0.737246	+	0.675624i	$0.236126\pi$
$570$		0			0
$571$			39.8291i			1.66680i	0.552673	+	0.833398i	$0.313608\pi$
$571$			39.8291i			1.66680i	−0.552673	+	0.833398i	$0.686392\pi$
$572$	−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	0.831262	−	0.555881i	$-0.187619\pi$
$577$	−4.03506	−	12.4186i	−0.167982	−	0.516994i	−0.999244	+	0.0388866i	$0.987619\pi$
$578$	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	$-0.963063\pi$
$587$	−13.9608	+	19.2153i	−0.576222	+	0.793102i	0.417053	+	0.908882i	$0.363063\pi$
$588$		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	$-0.223843\pi$
$593$	37.1489			1.52552			0.762761	+	0.646680i	$0.223843\pi$
$594$		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	$-0.584479\pi$
$599$	2.26902	−	0.737248i	0.0927095	−	0.0301231i	0.355004	+	0.934865i	$0.384479\pi$
$600$		0			0
$601$	3.99333	−	5.49635i	0.162891	−	0.224201i	−0.719767	−	0.694216i	$-0.755751\pi$
$601$	3.99333	−	5.49635i	0.162891	−	0.224201i	0.882658	+	0.470015i	$0.155751\pi$
$602$	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	−0.605575	−	0.795788i	$-0.707057\pi$
$607$	−38.5143	−	12.5141i	−1.56325	−	0.507930i	−0.957673	+	0.287859i	$0.907057\pi$
$608$	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	0.811415	−	0.584471i	$-0.198698\pi$
$613$	0.119072	+	0.163888i	0.00480926	+	0.00661938i	−0.806606	+	0.591090i	$0.798698\pi$
$614$	−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	−0.874161	−	0.485636i	$-0.838588\pi$
$619$	−16.9785	+	12.3356i	−0.682424	+	0.495810i	0.191737	+	0.981446i	$0.438588\pi$
$620$	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	0.905378	−	0.424606i	$-0.139587\pi$
$631$	19.6268	+	14.2597i	0.781332	+	0.567671i	−0.124047	+	0.992276i	$0.539587\pi$
$632$	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	$-0.303256\pi$
$641$	−9.48633	−	13.0568i	−0.374688	−	0.515713i	−0.954167	+	0.299273i	$0.903256\pi$
$642$		0			0
$643$	3.88866	+	11.9681i	0.153354	+	0.471975i	0.997990	−	0.0633656i	$-0.0201834\pi$
$643$	3.88866	+	11.9681i	0.153354	+	0.471975i	−0.844637	+	0.535340i	$0.820183\pi$
$644$	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	$-0.197295\pi$
$647$	28.7701	+	9.34797i	1.13107	+	0.367507i	0.317087	+	0.948396i	$0.397295\pi$
$648$		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	$-0.925232\pi$
$653$	−11.5162	+	15.8507i	−0.450664	+	0.620286i	0.521876	+	0.853021i	$0.325232\pi$
$654$		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	$-0.491633\pi$
$659$	1.34943			0.0525664			0.0262832	+	0.999655i	$0.491633\pi$
$660$		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	0.679252	−	0.733905i	$-0.262304\pi$
$673$	20.6864	+	6.72140i	0.797400	+	0.259091i	0.118148	+	0.992996i	$0.462304\pi$
$674$	−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	−0.998339	−	0.0576121i	$-0.981651\pi$
$677$	−5.84208	−	17.9801i	−0.224529	−	0.691030i	0.773810	−	0.633418i	$-0.218349\pi$
$678$		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	0.648375	+	0.761321i	$0.275449\pi$
$691$	−8.50814	+	26.1854i	−0.323665	+	0.996138i	−0.972040	+	0.234817i	$0.924551\pi$
$692$	−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	$-0.763101\pi$
$701$	−8.43699	+	6.12983i	−0.318661	+	0.231521i	0.416943	+	0.908933i	$0.363101\pi$
$702$		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	−0.997425	−	0.0717239i	$-0.977150\pi$
$709$	−6.19477	−	19.0655i	−0.232649	−	0.716021i	0.764775	−	0.644297i	$-0.222850\pi$
$710$	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	$-0.861140\pi$
$719$	−6.01752	+	8.28241i	−0.224416	+	0.308882i	0.681931	+	0.731417i	$0.261140\pi$
$720$		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	−0.722270	−	0.691611i	$-0.756901\pi$
$733$	4.29622	−	5.91324i	0.158685	−	0.218411i	0.880955	+	0.473200i	$0.156901\pi$
$734$	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	0.0701229	−	0.997538i	$-0.477661\pi$
$739$	−12.4909	−	4.05854i	−0.459485	−	0.149296i	−0.529608	+	0.848243i	$0.677661\pi$
$740$	−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	−0.924183	−	0.381950i	$-0.875253\pi$
$743$	−10.9307	−	33.6412i	−0.401008	−	1.23418i	0.523175	−	0.852225i	$-0.324747\pi$
$744$		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	−0.192677	−	0.981262i	$-0.561717\pi$
$751$	18.6629	−	13.5594i	0.681018	−	0.494789i	0.873695	+	0.486473i	$0.161717\pi$
$752$	−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	−0.880874	−	0.473350i	$-0.843044\pi$
$757$	3.02640	−	9.31430i	0.109996	−	0.338534i	0.990871	+	0.134816i	$0.0430445\pi$
$758$	−3.64030			−0.132222
$759$		0			0
$760$	−19.3249			−0.700988
$761$	−14.9642	+	46.0550i	−0.542452	+	1.66949i	0.184522	+	0.982828i	$0.440926\pi$
$761$	−14.9642	+	46.0550i	−0.542452	+	1.66949i	−0.726973	+	0.686666i	$0.759074\pi$
$762$		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	$-0.794124\pi$
$769$		−	33.4223i		−	1.20524i	0.798029	−	0.602619i	$-0.205876\pi$
$770$	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	$-0.162621\pi$
$773$	3.82924	+	5.27050i	0.137728	+	0.189567i	−0.734581	+	0.678521i	$0.762621\pi$
$774$		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	0.226911	−	0.973916i	$-0.427137\pi$
$787$	27.5749	−	8.95962i	0.982939	−	0.319376i	0.756028	+	0.654539i	$0.227137\pi$
$788$	−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	$-0.759032\pi$
$797$	−25.7264	+	8.35900i	−0.911274	+	0.296091i	−0.184392	+	0.982853i	$0.559032\pi$
$798$		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	−0.871262	−	0.490818i	$-0.836698\pi$
$809$	−12.9385	−	39.8205i	−0.454892	−	1.40001i	0.416370	−	0.909195i	$-0.363302\pi$
$810$		0			0
$811$	−7.51871	−	10.3486i	−0.264018	−	0.363389i	0.656341	−	0.754464i	$-0.272103\pi$
$811$	−7.51871	−	10.3486i	−0.264018	−	0.363389i	−0.920359	+	0.391075i	$0.872103\pi$
$812$	−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	$-0.366370\pi$
$821$	−9.59682	−	6.97250i	−0.334931	−	0.243342i	−0.742520	+	0.669824i	$0.766370\pi$
$822$		0			0
$823$	8.11976	−	24.9900i	0.283037	−	0.871098i	−0.703943	−	0.710256i	$-0.748579\pi$
$823$	8.11976	−	24.9900i	0.283037	−	0.871098i	0.986980	−	0.160842i	$-0.0514210\pi$
$824$	11.5921			0.403829
$825$		0			0
$826$	−5.52626			−0.192283
$827$	−7.99992	+	24.6212i	−0.278184	+	0.856163i	0.710175	+	0.704025i	$0.248616\pi$
$827$	−7.99992	+	24.6212i	−0.278184	+	0.856163i	−0.988359	+	0.152138i	$0.951384\pi$
$828$		0			0
$829$	−14.0195	−	10.1858i	−0.486918	−	0.353766i	0.317080	−	0.948399i	$-0.397298\pi$
$829$	−14.0195	−	10.1858i	−0.486918	−	0.353766i	−0.803998	+	0.594632i	$0.797298\pi$
$830$	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	$-0.380065\pi$
$839$	−18.2513	−	25.1207i	−0.630104	−	0.867264i	−0.998039	+	0.0625873i	$0.980065\pi$
$840$		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	−0.303812	−	0.952732i	$-0.598260\pi$
$853$	0.303737	−	0.0986902i	0.0103998	−	0.00337909i	0.314212	+	0.949353i	$0.398260\pi$
$854$	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	$-0.572651\pi$
$857$	−13.2476			−0.452528			−0.226264	+	0.974066i	$0.572651\pi$
$858$		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	$-0.967252\pi$
$863$	−51.0889	+	16.5998i	−1.73909	+	0.565063i	−0.744374	+	0.667763i	$0.767252\pi$
$864$		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	−0.978147	−	0.207916i	$-0.933332\pi$
$877$	−25.8716	−	35.6092i	−0.873623	−	1.20244i	0.104524	−	0.994522i	$-0.466668\pi$
$878$	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	−0.452634	−	0.891696i	$-0.649516\pi$
$883$	7.59369	−	5.51714i	0.255548	−	0.185667i	0.708182	+	0.706030i	$0.249516\pi$
$884$	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	$-0.166916\pi$
$887$	19.5658	+	14.2154i	0.656957	+	0.477307i	−0.208677	+	0.977985i	$0.566916\pi$
$888$		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	−0.948282	−	0.317428i	$-0.897181\pi$
$907$	−11.0734	−	34.0803i	−0.367685	−	1.13162i	0.580597	−	0.814191i	$-0.302819\pi$
$908$	−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	$-0.446352\pi$
$911$	−8.33061	−	2.70678i	−0.276005	−	0.0896796i	−0.443749	+	0.896151i	$0.646352\pi$
$912$		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	−0.876477	−	0.481443i	$-0.840113\pi$
$919$	−39.4876	+	12.8303i	−1.30258	+	0.423233i	−0.426100	+	0.904676i	$0.640113\pi$
$920$	−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	$-0.948552\pi$
$929$	−51.5363	+	16.7451i	−1.69085	+	0.549390i	−0.703883	+	0.710316i	$0.748552\pi$
$930$		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	0.0260393	−	0.999661i	$-0.491710\pi$
$937$	−16.5444	−	5.37559i	−0.540480	−	0.175613i	−0.566520	+	0.824048i	$0.691710\pi$
$938$	−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	0.999029	+	0.0440486i	$0.0140256\pi$
$941$	6.64708	+	20.4576i	0.216689	+	0.666899i	−0.782341	+	0.622851i	$0.785974\pi$
$942$		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	$-0.351959\pi$
$953$	−8.11741	−	5.89765i	−0.262949	−	0.191043i	−0.711446	+	0.702741i	$0.751959\pi$
$954$		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	$-0.977863\pi$
$967$		−	4.32167i		−	0.138976i	0.997583	−	0.0694878i	$-0.0221365\pi$
$968$	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	0.856640	+	0.515914i	$0.172548\pi$
$971$	33.7344	+	46.4314i	1.08259	+	1.49005i	0.225947	+	0.974140i	$0.427452\pi$
$972$		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	$-0.382423\pi$
$977$	3.28130	+	1.06616i	0.104978	+	0.0341095i	−0.256057	+	0.966662i	$0.582423\pi$
$978$		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	$-0.794747\pi$
$983$	0.608167	−	0.837070i	0.0193975	−	0.0266984i	0.818606	+	0.574356i	$0.194747\pi$
$984$		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	−0.903321	−	0.428965i	$-0.858878\pi$
$997$	−6.82690	+	9.39642i	−0.216210	+	0.297588i	0.687111	+	0.726552i	$0.258878\pi$
$998$	−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.35.1	yes	16
3.2	odd	2	inner	99.2.j.a.35.4	yes	16
4.3	odd	2		1584.2.cd.c.1025.1		16
9.2	odd	6		891.2.u.c.134.1		32
9.4	even	3		891.2.u.c.431.1		32
9.5	odd	6		891.2.u.c.431.4		32
9.7	even	3		891.2.u.c.134.4		32
11.4	even	5		1089.2.d.g.1088.4		16
11.6	odd	10	inner	99.2.j.a.17.4	yes	16
11.7	odd	10		1089.2.d.g.1088.14		16
12.11	even	2		1584.2.cd.c.1025.4		16
33.17	even	10	inner	99.2.j.a.17.1	✓	16
33.26	odd	10		1089.2.d.g.1088.13		16
33.29	even	10		1089.2.d.g.1088.3		16
44.39	even	10		1584.2.cd.c.17.4		16
99.50	even	30		891.2.u.c.512.4		32
99.61	odd	30		891.2.u.c.215.4		32
99.83	even	30		891.2.u.c.215.1		32
99.94	odd	30		891.2.u.c.512.1		32
132.83	odd	10		1584.2.cd.c.17.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.17.1	✓	16	33.17	even	10	inner
99.2.j.a.17.4	yes	16	11.6	odd	10	inner
99.2.j.a.35.1	yes	16	1.1	even	1	trivial
99.2.j.a.35.4	yes	16	3.2	odd	2	inner
891.2.u.c.134.1		32	9.2	odd	6
891.2.u.c.134.4		32	9.7	even	3
891.2.u.c.215.1		32	99.83	even	30
891.2.u.c.215.4		32	99.61	odd	30
891.2.u.c.431.1		32	9.4	even	3
891.2.u.c.431.4		32	9.5	odd	6
891.2.u.c.512.1		32	99.94	odd	30
891.2.u.c.512.4		32	99.50	even	30
1089.2.d.g.1088.3		16	33.29	even	10
1089.2.d.g.1088.4		16	11.4	even	5
1089.2.d.g.1088.13		16	33.26	odd	10
1089.2.d.g.1088.14		16	11.7	odd	10
1584.2.cd.c.17.1		16	132.83	odd	10
1584.2.cd.c.17.4		16	44.39	even	10
1584.2.cd.c.1025.1		16	4.3	odd	2
1584.2.cd.c.1025.4		16	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
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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