LMFDB - Embedded newform 2736.2.s.w.1873.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(577,2736)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2736, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("2736.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.s (of order $3$, degree $2$, not 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:	$21.8470699930$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1873.2
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	2736.1873
Dual form			2736.2.s.w.577.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61803 - 2.80252i) q^{5} +2.23607 q^{7} +O(q^{10})$	$q+(1.61803 - 2.80252i) q^{5} +2.23607 q^{7} +5.23607 q^{11} +(1.50000 + 2.59808i) q^{13} +(3.23607 - 5.60503i) q^{17} +(2.00000 - 3.87298i) q^{19} +(2.85410 + 4.94345i) q^{23} +(-2.73607 - 4.73901i) q^{25} +(-2.00000 - 3.46410i) q^{29} +2.23607 q^{31} +(3.61803 - 6.26662i) q^{35} -7.47214 q^{37} +(-5.23607 + 9.06914i) q^{41} +(-5.35410 + 9.27358i) q^{43} +(5.47214 + 9.47802i) q^{47} -2.00000 q^{49} +(4.85410 + 8.40755i) q^{53} +(8.47214 - 14.6742i) q^{55} +(3.85410 - 6.67550i) q^{59} +(-0.736068 - 1.27491i) q^{61} +9.70820 q^{65} +(0.354102 + 0.613323i) q^{67} +(3.00000 - 5.19615i) q^{71} +(-3.26393 + 5.65330i) q^{73} +11.7082 q^{77} +(-3.11803 + 5.40059i) q^{79} -5.52786 q^{83} +(-10.4721 - 18.1383i) q^{85} +(-2.61803 - 4.53457i) q^{89} +(3.35410 + 5.80948i) q^{91} +(-7.61803 - 11.8717i) q^{95} +(-3.00000 + 5.19615i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5}+O(q^{10}) $ 4 * q + 2 * q^5	$ 4 q + 2 q^{5} + 12 q^{11} + 6 q^{13} + 4 q^{17} + 8 q^{19} - 2 q^{23} - 2 q^{25} - 8 q^{29} + 10 q^{35} - 12 q^{37} - 12 q^{41} - 8 q^{43} + 4 q^{47} - 8 q^{49} + 6 q^{53} + 16 q^{55} + 2 q^{59} + 6 q^{61} + 12 q^{65} - 12 q^{67} + 12 q^{71} - 22 q^{73} + 20 q^{77} - 8 q^{79} - 40 q^{83} - 24 q^{85} - 6 q^{89} - 26 q^{95} - 12 q^{97}+O(q^{100}) $ 4 * q + 2 * q^5 + 12 * q^11 + 6 * q^13 + 4 * q^17 + 8 * q^19 - 2 * q^23 - 2 * q^25 - 8 * q^29 + 10 * q^35 - 12 * q^37 - 12 * q^41 - 8 * q^43 + 4 * q^47 - 8 * q^49 + 6 * q^53 + 16 * q^55 + 2 * q^59 + 6 * q^61 + 12 * q^65 - 12 * q^67 + 12 * q^71 - 22 * q^73 + 20 * q^77 - 8 * q^79 - 40 * q^83 - 24 * q^85 - 6 * q^89 - 26 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.61803	−	2.80252i	0.723607	−	1.25332i	−0.235938	−	0.971768i	$-0.575816\pi$
$5$	1.61803	−	2.80252i	0.723607	−	1.25332i	0.959545	−	0.281556i	$-0.0908504\pi$
$6$		0			0
$7$	2.23607			0.845154			0.422577	−	0.906327i	$-0.361126\pi$
$7$	2.23607			0.845154			0.422577	+	0.906327i	$0.361126\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	5.23607			1.57873			0.789367	−	0.613922i	$-0.210409\pi$
$11$	5.23607			1.57873			0.789367	+	0.613922i	$0.210409\pi$
$12$		0			0
$13$	1.50000	+	2.59808i	0.416025	+	0.720577i	0.995535	−	0.0943882i	$-0.0300895\pi$
$13$	1.50000	+	2.59808i	0.416025	+	0.720577i	−0.579510	+	0.814965i	$0.696756\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.23607	−	5.60503i	0.784862	−	1.35942i	−0.144220	−	0.989546i	$-0.546067\pi$
$17$	3.23607	−	5.60503i	0.784862	−	1.35942i	0.929082	−	0.369875i	$-0.120599\pi$
$18$		0			0
$19$	2.00000	−	3.87298i	0.458831	−	0.888523i
$19$	2.00000	−	3.87298i	0.458831	−	0.888523i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.85410	+	4.94345i	0.595121	+	1.03078i	0.993530	+	0.113572i	$0.0362294\pi$
$23$	2.85410	+	4.94345i	0.595121	+	1.03078i	−0.398408	+	0.917208i	$0.630437\pi$
$24$		0			0
$25$	−2.73607	−	4.73901i	−0.547214	−	0.947802i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	0.618389	−	0.785872i	$-0.287786\pi$
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	−0.989780	+	0.142605i	$0.954452\pi$
$30$		0			0
$31$	2.23607			0.401610			0.200805	−	0.979631i	$-0.435644\pi$
$31$	2.23607			0.401610			0.200805	+	0.979631i	$0.435644\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.61803	−	6.26662i	0.611559	−	1.05925i
$36$		0			0
$37$	−7.47214			−1.22841			−0.614206	−	0.789146i	$-0.710524\pi$
$37$	−7.47214			−1.22841			−0.614206	+	0.789146i	$0.710524\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.23607	+	9.06914i	−0.817736	+	1.41636i	0.0896098	+	0.995977i	$0.471438\pi$
$41$	−5.23607	+	9.06914i	−0.817736	+	1.41636i	−0.907346	+	0.420384i	$0.861895\pi$
$42$		0			0
$43$	−5.35410	+	9.27358i	−0.816493	+	1.41421i	0.0917581	+	0.995781i	$0.470751\pi$
$43$	−5.35410	+	9.27358i	−0.816493	+	1.41421i	−0.908251	+	0.418426i	$0.862582\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.47214	+	9.47802i	0.798193	+	1.38251i	0.920792	+	0.390055i	$0.127544\pi$
$47$	5.47214	+	9.47802i	0.798193	+	1.38251i	−0.122599	+	0.992456i	$0.539123\pi$
$48$		0			0
$49$	−2.00000			−0.285714
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.85410	+	8.40755i	0.666762	+	1.15487i	0.978804	+	0.204798i	$0.0656537\pi$
$53$	4.85410	+	8.40755i	0.666762	+	1.15487i	−0.312042	+	0.950068i	$0.601013\pi$
$54$		0			0
$55$	8.47214	−	14.6742i	1.14238	−	1.97866i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.85410	−	6.67550i	0.501761	−	0.869076i	−0.498237	−	0.867041i	$-0.666019\pi$
$59$	3.85410	−	6.67550i	0.501761	−	0.869076i	0.999998	−	0.00203501i	$-0.000647765\pi$
$60$		0			0
$61$	−0.736068	−	1.27491i	−0.0942438	−	0.163235i	0.815049	−	0.579392i	$-0.196710\pi$
$61$	−0.736068	−	1.27491i	−0.0942438	−	0.163235i	−0.909293	+	0.416157i	$0.863377\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.70820			1.20415
$66$		0			0
$67$	0.354102	+	0.613323i	0.0432604	+	0.0749293i	0.886845	−	0.462067i	$-0.152892\pi$
$67$	0.354102	+	0.613323i	0.0432604	+	0.0749293i	−0.843584	+	0.536997i	$0.819559\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$		0			0
$73$	−3.26393	+	5.65330i	−0.382014	+	0.661668i	−0.991350	−	0.131244i	$-0.958103\pi$
$73$	−3.26393	+	5.65330i	−0.382014	+	0.661668i	0.609336	+	0.792912i	$0.291436\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	11.7082			1.33427
$78$		0			0
$79$	−3.11803	+	5.40059i	−0.350806	+	0.607614i	−0.986391	−	0.164417i	$-0.947426\pi$
$79$	−3.11803	+	5.40059i	−0.350806	+	0.607614i	0.635585	+	0.772031i	$0.280759\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−5.52786			−0.606762			−0.303381	−	0.952869i	$-0.598115\pi$
$83$	−5.52786			−0.606762			−0.303381	+	0.952869i	$0.598115\pi$
$84$		0			0
$85$	−10.4721	−	18.1383i	−1.13586	−	1.96737i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.61803	−	4.53457i	−0.277511	−	0.480663i	0.693255	−	0.720693i	$-0.256176\pi$
$89$	−2.61803	−	4.53457i	−0.277511	−	0.480663i	−0.970766	+	0.240030i	$0.922843\pi$
$90$		0			0
$91$	3.35410	+	5.80948i	0.351605	+	0.608998i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−7.61803	−	11.8717i	−0.781594	−	1.21801i
$96$		0			0
$97$	−3.00000	+	5.19615i	−0.304604	+	0.527589i	−0.977173	−	0.212445i	$-0.931857\pi$
$97$	−3.00000	+	5.19615i	−0.304604	+	0.527589i	0.672569	+	0.740034i	$0.265191\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.23607	−	10.8012i	−0.620512	−	1.07476i	−0.989390	−	0.145281i	$-0.953592\pi$
$101$	−6.23607	−	10.8012i	−0.620512	−	1.07476i	0.368879	−	0.929478i	$-0.379742\pi$
$102$		0			0
$103$	−8.23607			−0.811524			−0.405762	−	0.913979i	$-0.632994\pi$
$103$	−8.23607			−0.811524			−0.405762	+	0.913979i	$0.632994\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.472136			0.0456431			0.0228216	−	0.999740i	$-0.492735\pi$
$107$	0.472136			0.0456431			0.0228216	+	0.999740i	$0.492735\pi$
$108$		0			0
$109$	2.23607	−	3.87298i	0.214176	−	0.370965i	−0.738841	−	0.673880i	$-0.764627\pi$
$109$	2.23607	−	3.87298i	0.214176	−	0.370965i	0.953018	+	0.302915i	$0.0979599\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−15.7082			−1.47770			−0.738852	−	0.673868i	$-0.764632\pi$
$113$	−15.7082			−1.47770			−0.738852	+	0.673868i	$0.764632\pi$
$114$		0			0
$115$	18.4721			1.72254
$116$		0			0
$117$		0			0
$118$		0			0
$119$	7.23607	−	12.5332i	0.663329	−	1.14892i
$120$		0			0
$121$	16.4164			1.49240
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.52786			−0.136656
$126$		0			0
$127$	−0.763932	−	1.32317i	−0.0677880	−	0.117412i	0.830139	−	0.557556i	$-0.188261\pi$
$127$	−0.763932	−	1.32317i	−0.0677880	−	0.117412i	−0.897927	+	0.440144i	$0.854927\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.527864	+	0.914287i	−0.0461197	+	0.0798817i	−0.888164	−	0.459527i	$-0.848019\pi$
$131$	−0.527864	+	0.914287i	−0.0461197	+	0.0798817i	0.842044	+	0.539409i	$0.181352\pi$
$132$		0			0
$133$	4.47214	−	8.66025i	0.387783	−	0.750939i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.47214	−	12.9421i	−0.638388	−	1.10572i	−0.985787	−	0.168002i	$-0.946268\pi$
$137$	−7.47214	−	12.9421i	−0.638388	−	1.10572i	0.347399	−	0.937717i	$-0.387065\pi$
$138$		0			0
$139$	6.59017	+	11.4145i	0.558971	+	0.968166i	0.997583	+	0.0694894i	$0.0221370\pi$
$139$	6.59017	+	11.4145i	0.558971	+	0.968166i	−0.438612	+	0.898677i	$0.644530\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	7.85410	+	13.6037i	0.656793	+	1.13760i
$144$		0			0
$145$	−12.9443			−1.07496
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.14590	−	7.18091i	0.339645	−	0.588283i	−0.644721	−	0.764418i	$-0.723026\pi$
$149$	4.14590	−	7.18091i	0.339645	−	0.588283i	0.984366	+	0.176135i	$0.0563597\pi$
$150$		0			0
$151$	2.47214			0.201180			0.100590	−	0.994928i	$-0.467927\pi$
$151$	2.47214			0.201180			0.100590	+	0.994928i	$0.467927\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.61803	−	6.26662i	0.290607	−	0.503347i
$156$		0			0
$157$	8.50000	−	14.7224i	0.678374	−	1.17498i	−0.297097	−	0.954847i	$-0.596018\pi$
$157$	8.50000	−	14.7224i	0.678374	−	1.17498i	0.975470	−	0.220131i	$-0.0706483\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.38197	+	11.0539i	0.502969	+	0.871169i
$162$		0			0
$163$	−15.1803			−1.18902			−0.594508	−	0.804090i	$-0.702653\pi$
$163$	−15.1803			−1.18902			−0.594508	+	0.804090i	$0.702653\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.85410	−	6.67550i	−0.298239	−	0.516566i	0.677494	−	0.735528i	$-0.263066\pi$
$167$	−3.85410	−	6.67550i	−0.298239	−	0.516566i	−0.975733	+	0.218963i	$0.929733\pi$
$168$		0			0
$169$	2.00000	−	3.46410i	0.153846	−	0.266469i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.9443	−	18.9560i	0.832078	−	1.44120i	−0.0643102	−	0.997930i	$-0.520485\pi$
$173$	10.9443	−	18.9560i	0.832078	−	1.44120i	0.896388	−	0.443271i	$-0.146182\pi$
$174$		0			0
$175$	−6.11803	−	10.5967i	−0.462480	−	0.801039i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.76393			−0.655047			−0.327524	−	0.944843i	$-0.606214\pi$
$179$	−8.76393			−0.655047			−0.327524	+	0.944843i	$0.606214\pi$
$180$		0			0
$181$	−2.52786	−	4.37839i	−0.187895	−	0.325443i	0.756653	−	0.653816i	$-0.226833\pi$
$181$	−2.52786	−	4.37839i	−0.187895	−	0.325443i	−0.944548	+	0.328373i	$0.893500\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−12.0902	+	20.9408i	−0.888887	+	1.53960i
$186$		0			0
$187$	16.9443	−	29.3483i	1.23909	−	2.14616i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−18.6525			−1.34965			−0.674823	−	0.737980i	$-0.735780\pi$
$191$	−18.6525			−1.34965			−0.674823	+	0.737980i	$0.735780\pi$
$192$		0			0
$193$	−8.44427	+	14.6259i	−0.607832	+	1.05280i	0.383765	+	0.923431i	$0.374627\pi$
$193$	−8.44427	+	14.6259i	−0.607832	+	1.05280i	−0.991597	+	0.129365i	$0.958706\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−0.291796			−0.0207896			−0.0103948	−	0.999946i	$-0.503309\pi$
$197$	−0.291796			−0.0207896			−0.0103948	+	0.999946i	$0.503309\pi$
$198$		0			0
$199$	−6.82624	−	11.8234i	−0.483899	−	0.838138i	0.515930	−	0.856631i	$-0.327447\pi$
$199$	−6.82624	−	11.8234i	−0.483899	−	0.838138i	−0.999829	+	0.0184929i	$0.994113\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.47214	−	7.74597i	−0.313882	−	0.543660i
$204$		0			0
$205$	16.9443	+	29.3483i	1.18344	+	2.04978i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	10.4721	−	20.2792i	0.724373	−	1.40274i
$210$		0			0
$211$	−11.5902	+	20.0748i	−0.797900	+	1.38200i	0.123081	+	0.992397i	$0.460723\pi$
$211$	−11.5902	+	20.0748i	−0.797900	+	1.38200i	−0.920981	+	0.389607i	$0.872611\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	17.3262	+	30.0099i	1.18164	+	2.04666i
$216$		0			0
$217$	5.00000			0.339422
$218$		0			0
$219$		0			0
$220$		0			0
$221$	19.4164			1.30609
$222$		0			0
$223$	−3.88197	+	6.72376i	−0.259956	+	0.450256i	−0.966230	−	0.257682i	$-0.917041\pi$
$223$	−3.88197	+	6.72376i	−0.259956	+	0.450256i	0.706274	+	0.707938i	$0.250375\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	16.7639			1.11266			0.556331	−	0.830961i	$-0.312209\pi$
$227$	16.7639			1.11266			0.556331	+	0.830961i	$0.312209\pi$
$228$		0			0
$229$	14.8885			0.983863			0.491931	−	0.870634i	$-0.336291\pi$
$229$	14.8885			0.983863			0.491931	+	0.870634i	$0.336291\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.70820	−	8.15485i	0.308445	−	0.534242i	−0.669578	−	0.742742i	$-0.733525\pi$
$233$	4.70820	−	8.15485i	0.308445	−	0.534242i	0.978022	+	0.208500i	$0.0668582\pi$
$234$		0			0
$235$	35.4164			2.31031
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−9.70820			−0.627972			−0.313986	−	0.949428i	$-0.601664\pi$
$239$	−9.70820			−0.627972			−0.313986	+	0.949428i	$0.601664\pi$
$240$		0			0
$241$	6.73607	+	11.6672i	0.433908	+	0.751551i	0.997206	−	0.0747029i	$-0.0238009\pi$
$241$	6.73607	+	11.6672i	0.433908	+	0.751551i	−0.563298	+	0.826254i	$0.690468\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.23607	+	5.60503i	−0.206745	+	0.358092i
$246$		0			0
$247$	13.0623	−	0.613323i	0.831135	−	0.0390248i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.23607	−	3.87298i	−0.141139	−	0.244461i	0.786787	−	0.617225i	$-0.211743\pi$
$251$	−2.23607	−	3.87298i	−0.141139	−	0.244461i	−0.927926	+	0.372765i	$0.878410\pi$
$252$		0			0
$253$	14.9443	+	25.8842i	0.939538	+	1.62733i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.38197	−	4.12569i	−0.148583	−	0.257353i	0.782121	−	0.623127i	$-0.214138\pi$
$257$	−2.38197	−	4.12569i	−0.148583	−	0.257353i	−0.930704	+	0.365773i	$0.880805\pi$
$258$		0			0
$259$	−16.7082			−1.03820
$260$		0			0
$261$		0			0
$262$		0			0
$263$	11.4721	−	19.8703i	0.707402	−	1.22526i	−0.258415	−	0.966034i	$-0.583200\pi$
$263$	11.4721	−	19.8703i	0.707402	−	1.22526i	0.965818	−	0.259223i	$-0.0834663\pi$
$264$		0			0
$265$	31.4164			1.92989
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−15.5623	+	26.9547i	−0.948851	+	1.64346i	−0.200999	+	0.979591i	$0.564419\pi$
$269$	−15.5623	+	26.9547i	−0.948851	+	1.64346i	−0.747852	+	0.663866i	$0.768915\pi$
$270$		0			0
$271$	−5.52786	+	9.57454i	−0.335794	+	0.581612i	−0.983637	−	0.180162i	$-0.942338\pi$
$271$	−5.52786	+	9.57454i	−0.335794	+	0.581612i	0.647843	+	0.761774i	$0.275671\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−14.3262	−	24.8138i	−0.863905	−	1.49633i
$276$		0			0
$277$	30.9443			1.85926			0.929631	−	0.368493i	$-0.120126\pi$
$277$	30.9443			1.85926			0.929631	+	0.368493i	$0.120126\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−13.7984	−	23.8995i	−0.823142	−	1.42572i	−0.903331	−	0.428944i	$-0.858886\pi$
$281$	−13.7984	−	23.8995i	−0.823142	−	1.42572i	0.0801891	−	0.996780i	$-0.474448\pi$
$282$		0			0
$283$	−0.472136	+	0.817763i	−0.0280656	+	0.0486110i	−0.879717	−	0.475498i	$-0.842268\pi$
$283$	−0.472136	+	0.817763i	−0.0280656	+	0.0486110i	0.851651	+	0.524109i	$0.175601\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−11.7082	+	20.2792i	−0.691113	+	1.19704i
$288$		0			0
$289$	−12.4443	−	21.5541i	−0.732016	−	1.26789i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.05573			0.295359			0.147679	−	0.989035i	$-0.452820\pi$
$293$	5.05573			0.295359			0.147679	+	0.989035i	$0.452820\pi$
$294$		0			0
$295$	−12.4721	−	21.6024i	−0.726156	−	1.25774i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−8.56231	+	14.8303i	−0.495171	+	0.857661i
$300$		0			0
$301$	−11.9721	+	20.7363i	−0.690062	+	1.19522i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−4.76393			−0.272782
$306$		0			0
$307$	−5.52786	+	9.57454i	−0.315492	+	0.546448i	−0.979542	−	0.201240i	$-0.935503\pi$
$307$	−5.52786	+	9.57454i	−0.315492	+	0.546448i	0.664050	+	0.747688i	$0.268836\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.65248			0.490637			0.245318	−	0.969443i	$-0.421107\pi$
$311$	8.65248			0.490637			0.245318	+	0.969443i	$0.421107\pi$
$312$		0			0
$313$	−5.76393	−	9.98342i	−0.325797	−	0.564296i	0.655877	−	0.754868i	$-0.272299\pi$
$313$	−5.76393	−	9.98342i	−0.325797	−	0.564296i	−0.981673	+	0.190572i	$0.938966\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.79837	+	13.5072i	0.438000	+	0.758639i	0.997535	−	0.0701680i	$-0.0223535\pi$
$317$	7.79837	+	13.5072i	0.438000	+	0.758639i	−0.559535	+	0.828807i	$0.689020\pi$
$318$		0			0
$319$	−10.4721	−	18.1383i	−0.586327	−	1.01555i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−15.2361	−	23.7433i	−0.847757	−	1.32111i
$324$		0			0
$325$	8.20820	−	14.2170i	0.455309	−	0.788619i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	12.2361	+	21.1935i	0.674596	+	1.16844i
$330$		0			0
$331$	0.819660			0.0450526			0.0225263	−	0.999746i	$-0.492829\pi$
$331$	0.819660			0.0450526			0.0225263	+	0.999746i	$0.492829\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.29180			0.125214
$336$		0			0
$337$	−12.6803	+	21.9630i	−0.690742	+	1.19640i	0.280853	+	0.959751i	$0.409383\pi$
$337$	−12.6803	+	21.9630i	−0.690742	+	1.19640i	−0.971595	+	0.236650i	$0.923951\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	11.7082			0.634035
$342$		0			0
$343$	−20.1246			−1.08663
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.38197	+	7.58979i	−0.235236	+	0.407441i	−0.959341	−	0.282249i	$-0.908920\pi$
$347$	−4.38197	+	7.58979i	−0.235236	+	0.407441i	0.724105	+	0.689690i	$0.242253\pi$
$348$		0			0
$349$	−13.0000			−0.695874			−0.347937	−	0.937518i	$-0.613118\pi$
$349$	−13.0000			−0.695874			−0.347937	+	0.937518i	$0.613118\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−8.76393			−0.466457			−0.233229	−	0.972422i	$-0.574929\pi$
$353$	−8.76393			−0.466457			−0.233229	+	0.972422i	$0.574929\pi$
$354$		0			0
$355$	−9.70820	−	16.8151i	−0.515258	−	0.892453i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	0.472136	−	0.817763i	0.0249184	−	0.0431599i	−0.853297	−	0.521425i	$-0.825401\pi$
$359$	0.472136	−	0.817763i	0.0249184	−	0.0431599i	0.878216	+	0.478265i	$0.158734\pi$
$360$		0			0
$361$	−11.0000	−	15.4919i	−0.578947	−	0.815365i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	10.5623	+	18.2945i	0.552856	+	0.957575i
$366$		0			0
$367$	10.3541	+	17.9338i	0.540480	+	0.936138i	0.998876	+	0.0473907i	$0.0150906\pi$
$367$	10.3541	+	17.9338i	0.540480	+	0.936138i	−0.458397	+	0.888748i	$0.651576\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	10.8541	+	18.7999i	0.563517	+	0.976040i
$372$		0			0
$373$	2.94427			0.152449			0.0762243	−	0.997091i	$-0.475713\pi$
$373$	2.94427			0.152449			0.0762243	+	0.997091i	$0.475713\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.00000	−	10.3923i	0.309016	−	0.535231i
$378$		0			0
$379$	−33.6525			−1.72861			−0.864306	−	0.502967i	$-0.832242\pi$
$379$	−33.6525			−1.72861			−0.864306	+	0.502967i	$0.832242\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.145898	+	0.252703i	−0.00745504	+	0.0129125i	−0.869729	−	0.493530i	$-0.835706\pi$
$383$	−0.145898	+	0.252703i	−0.00745504	+	0.0129125i	0.862274	+	0.506442i	$0.169040\pi$
$384$		0			0
$385$	18.9443	−	32.8124i	0.965489	−	1.67228i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	8.38197	+	14.5180i	0.424983	+	0.736091i	0.996419	−	0.0845551i	$-0.0269469\pi$
$389$	8.38197	+	14.5180i	0.424983	+	0.736091i	−0.571436	+	0.820646i	$0.693614\pi$
$390$		0			0
$391$	36.9443			1.86835
$392$		0			0
$393$		0			0
$394$		0			0
$395$	10.0902	+	17.4767i	0.507692	+	0.879348i
$396$		0			0
$397$	−4.44427	+	7.69770i	−0.223052	+	0.386337i	−0.955733	−	0.294235i	$-0.904935\pi$
$397$	−4.44427	+	7.69770i	−0.223052	+	0.386337i	0.732682	+	0.680572i	$0.238269\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	10.1459	−	17.5732i	0.506662	−	0.877564i	−0.493308	−	0.869855i	$-0.664213\pi$
$401$	10.1459	−	17.5732i	0.506662	−	0.877564i	0.999970	−	0.00770974i	$-0.00245411\pi$
$402$		0			0
$403$	3.35410	+	5.80948i	0.167080	+	0.289391i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−39.1246			−1.93934
$408$		0			0
$409$	−16.7082	−	28.9395i	−0.826168	−	1.43096i	−0.901024	−	0.433770i	$-0.857183\pi$
$409$	−16.7082	−	28.9395i	−0.826168	−	1.43096i	0.0748562	−	0.997194i	$-0.476150\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	8.61803	−	14.9269i	0.424066	−	0.734503i
$414$		0			0
$415$	−8.94427	+	15.4919i	−0.439057	+	0.760469i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	12.6525			0.618114			0.309057	−	0.951044i	$-0.399987\pi$
$419$	12.6525			0.618114			0.309057	+	0.951044i	$0.399987\pi$
$420$		0			0
$421$	8.23607	−	14.2653i	0.401401	−	0.695248i	−0.592494	−	0.805575i	$-0.701857\pi$
$421$	8.23607	−	14.2653i	0.401401	−	0.695248i	0.993895	+	0.110327i	$0.0351899\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−35.4164			−1.71795
$426$		0			0
$427$	−1.64590	−	2.85078i	−0.0796506	−	0.137959i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	19.4721	+	33.7267i	0.937940	+	1.62456i	0.769306	+	0.638881i	$0.220602\pi$
$431$	19.4721	+	33.7267i	0.937940	+	1.62456i	0.168634	+	0.985679i	$0.446064\pi$
$432$		0			0
$433$	15.2639	+	26.4379i	0.733538	+	1.27052i	0.955362	+	0.295438i	$0.0954656\pi$
$433$	15.2639	+	26.4379i	0.733538	+	1.27052i	−0.221824	+	0.975087i	$0.571201\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	24.8541	−	1.16699i	1.18893	−	0.0558247i
$438$		0			0
$439$	0.826238	−	1.43109i	0.0394342	−	0.0683020i	−0.845635	−	0.533762i	$-0.820778\pi$
$439$	0.826238	−	1.43109i	0.0394342	−	0.0683020i	0.885069	+	0.465460i	$0.154111\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12.4721	−	21.6024i	−0.592569	−	1.02636i	−0.993885	−	0.110420i	$-0.964780\pi$
$443$	−12.4721	−	21.6024i	−0.592569	−	1.02636i	0.401316	−	0.915940i	$-0.368553\pi$
$444$		0			0
$445$	−16.9443			−0.803236
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−25.8885			−1.22176			−0.610878	−	0.791725i	$-0.709183\pi$
$449$	−25.8885			−1.22176			−0.610878	+	0.791725i	$0.709183\pi$
$450$		0			0
$451$	−27.4164	+	47.4866i	−1.29099	+	2.23606i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	21.7082			1.01770
$456$		0			0
$457$	−34.4164			−1.60993			−0.804966	−	0.593321i	$-0.797816\pi$
$457$	−34.4164			−1.60993			−0.804966	+	0.593321i	$0.797816\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.14590	+	10.6450i	−0.286243	+	0.495787i	−0.972910	−	0.231185i	$-0.925740\pi$
$461$	−6.14590	+	10.6450i	−0.286243	+	0.495787i	0.686667	+	0.726972i	$0.259073\pi$
$462$		0			0
$463$	36.2361			1.68403			0.842016	−	0.539452i	$-0.181369\pi$
$463$	36.2361			1.68403			0.842016	+	0.539452i	$0.181369\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.41641			−0.158093			−0.0790463	−	0.996871i	$-0.525187\pi$
$467$	−3.41641			−0.158093			−0.0790463	+	0.996871i	$0.525187\pi$
$468$		0			0
$469$	0.791796	+	1.37143i	0.0365617	+	0.0633268i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−28.0344	+	48.5571i	−1.28903	+	2.23266i
$474$		0			0
$475$	−23.8262	+	1.11873i	−1.09322	+	0.0513308i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.94427	+	6.83168i	0.180218	+	0.312147i	0.941955	−	0.335740i	$-0.108986\pi$
$479$	3.94427	+	6.83168i	0.180218	+	0.312147i	−0.761736	+	0.647887i	$0.775653\pi$
$480$		0			0
$481$	−11.2082	−	19.4132i	−0.511050	−	0.885165i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	9.70820	+	16.8151i	0.440827	+	0.763534i
$486$		0			0
$487$	1.52786			0.0692341			0.0346171	−	0.999401i	$-0.488979\pi$
$487$	1.52786			0.0692341			0.0346171	+	0.999401i	$0.488979\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	7.00000	−	12.1244i	0.315906	−	0.547165i	−0.663724	−	0.747978i	$-0.731025\pi$
$491$	7.00000	−	12.1244i	0.315906	−	0.547165i	0.979630	+	0.200813i	$0.0643584\pi$
$492$		0			0
$493$	−25.8885			−1.16596
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.70820	−	11.6190i	0.300904	−	0.521181i
$498$		0			0
$499$	−3.40983	+	5.90600i	−0.152645	+	0.264389i	−0.932199	−	0.361946i	$-0.882112\pi$
$499$	−3.40983	+	5.90600i	−0.152645	+	0.264389i	0.779554	+	0.626335i	$0.215446\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−10.9443	−	18.9560i	−0.487981	−	0.845208i	0.511923	−	0.859031i	$-0.328933\pi$
$503$	−10.9443	−	18.9560i	−0.487981	−	0.845208i	−0.999904	+	0.0138232i	$0.995600\pi$
$504$		0			0
$505$	−40.3607			−1.79603
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.47214	+	12.9421i	0.331197	+	0.573649i	0.982747	−	0.184956i	$-0.0592143\pi$
$509$	7.47214	+	12.9421i	0.331197	+	0.573649i	−0.651550	+	0.758606i	$0.725881\pi$
$510$		0			0
$511$	−7.29837	+	12.6412i	−0.322861	+	0.559212i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−13.3262	+	23.0817i	−0.587224	+	1.01710i
$516$		0			0
$517$	28.6525	+	49.6275i	1.26013	+	2.18262i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	26.7639			1.17255			0.586275	−	0.810112i	$-0.300594\pi$
$521$	26.7639			1.17255			0.586275	+	0.810112i	$0.300594\pi$
$522$		0			0
$523$	−10.0623	−	17.4284i	−0.439994	−	0.762092i	0.557695	−	0.830046i	$-0.311686\pi$
$523$	−10.0623	−	17.4284i	−0.439994	−	0.762092i	−0.997688	+	0.0679545i	$0.978353\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	7.23607	−	12.5332i	0.315208	−	0.545956i
$528$		0			0
$529$	−4.79180	+	8.29963i	−0.208339	+	0.360854i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−31.4164			−1.36080
$534$		0			0
$535$	0.763932	−	1.32317i	0.0330277	−	0.0572056i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−10.4721			−0.451067
$540$		0			0
$541$	−3.44427	−	5.96565i	−0.148081	−	0.256483i	0.782437	−	0.622729i	$-0.213976\pi$
$541$	−3.44427	−	5.96565i	−0.148081	−	0.256483i	−0.930518	+	0.366246i	$0.880643\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−7.23607	−	12.5332i	−0.309959	−	0.536865i
$546$		0			0
$547$	−10.4098	−	18.0304i	−0.445092	−	0.770922i	0.552966	−	0.833204i	$-0.313496\pi$
$547$	−10.4098	−	18.0304i	−0.445092	−	0.770922i	−0.998059	+	0.0622812i	$0.980162\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−17.4164	+	0.817763i	−0.741964	+	0.0348379i
$552$		0			0
$553$	−6.97214	+	12.0761i	−0.296485	+	0.513528i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	3.94427	+	6.83168i	0.167124	+	0.289468i	0.937408	−	0.348234i	$-0.113219\pi$
$557$	3.94427	+	6.83168i	0.167124	+	0.289468i	−0.770283	+	0.637702i	$0.779885\pi$
$558$		0			0
$559$	−32.1246			−1.35873
$560$		0			0
$561$		0			0
$562$		0			0
$563$	9.41641			0.396854			0.198427	−	0.980116i	$-0.436417\pi$
$563$	9.41641			0.396854			0.198427	+	0.980116i	$0.436417\pi$
$564$		0			0
$565$	−25.4164	+	44.0225i	−1.06928	+	1.85204i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−16.3607			−0.685875			−0.342938	−	0.939358i	$-0.611422\pi$
$569$	−16.3607			−0.685875			−0.342938	+	0.939358i	$0.611422\pi$
$570$		0			0
$571$	30.2361			1.26534			0.632670	−	0.774421i	$-0.281959\pi$
$571$	30.2361			1.26534			0.632670	+	0.774421i	$0.281959\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	15.6180	−	27.0512i	0.651317	−	1.12811i
$576$		0			0
$577$	−23.3050			−0.970198			−0.485099	−	0.874459i	$-0.661216\pi$
$577$	−23.3050			−0.970198			−0.485099	+	0.874459i	$0.661216\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−12.3607			−0.512807
$582$		0			0
$583$	25.4164	+	44.0225i	1.05264	+	1.82323i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−18.5066	+	32.0543i	−0.763848	+	1.32302i	0.177005	+	0.984210i	$0.443359\pi$
$587$	−18.5066	+	32.0543i	−0.763848	+	1.32302i	−0.940853	+	0.338814i	$0.889974\pi$
$588$		0			0
$589$	4.47214	−	8.66025i	0.184271	−	0.356840i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−17.2705	−	29.9134i	−0.709215	−	1.22840i	−0.965149	−	0.261702i	$-0.915716\pi$
$593$	−17.2705	−	29.9134i	−0.709215	−	1.22840i	0.255934	−	0.966694i	$-0.417617\pi$
$594$		0			0
$595$	−23.4164	−	40.5584i	−0.959979	−	1.66273i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−8.79837	−	15.2392i	−0.359492	−	0.622658i	0.628384	−	0.777903i	$-0.283717\pi$
$599$	−8.79837	−	15.2392i	−0.359492	−	0.622658i	−0.987876	+	0.155245i	$0.950383\pi$
$600$		0			0
$601$	10.4164			0.424894			0.212447	−	0.977173i	$-0.431857\pi$
$601$	10.4164			0.424894			0.212447	+	0.977173i	$0.431857\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	26.5623	−	46.0073i	1.07991	−	1.87046i
$606$		0			0
$607$	−23.2918			−0.945385			−0.472692	−	0.881227i	$-0.656718\pi$
$607$	−23.2918			−0.945385			−0.472692	+	0.881227i	$0.656718\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−16.4164	+	28.4341i	−0.664137	+	1.15032i
$612$		0			0
$613$	15.4721	−	26.7985i	0.624914	−	1.08238i	−0.363644	−	0.931538i	$-0.618467\pi$
$613$	15.4721	−	26.7985i	0.624914	−	1.08238i	0.988558	−	0.150844i	$-0.0481992\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	10.9098	+	18.8964i	0.439213	+	0.760740i	0.997629	−	0.0688216i	$-0.0219239\pi$
$617$	10.9098	+	18.8964i	0.439213	+	0.760740i	−0.558416	+	0.829561i	$0.688591\pi$
$618$		0			0
$619$	−6.70820			−0.269625			−0.134813	−	0.990871i	$-0.543043\pi$
$619$	−6.70820			−0.269625			−0.134813	+	0.990871i	$0.543043\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−5.85410	−	10.1396i	−0.234540	−	0.406235i
$624$		0			0
$625$	11.2082	−	19.4132i	0.448328	−	0.776527i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−24.1803	+	41.8816i	−0.964133	+	1.66993i
$630$		0			0
$631$	−19.5902	−	33.9312i	−0.779872	−	1.35078i	−0.932015	−	0.362420i	$-0.881951\pi$
$631$	−19.5902	−	33.9312i	−0.779872	−	1.35078i	0.152143	−	0.988359i	$-0.451383\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−4.94427			−0.196207
$636$		0			0
$637$	−3.00000	−	5.19615i	−0.118864	−	0.205879i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.29180	+	16.0939i	−0.367004	+	0.635669i	−0.989096	−	0.147275i	$-0.952950\pi$
$641$	−9.29180	+	16.0939i	−0.367004	+	0.635669i	0.622092	+	0.782944i	$0.286283\pi$
$642$		0			0
$643$	6.11803	−	10.5967i	0.241272	−	0.417895i	−0.719805	−	0.694176i	$-0.755769\pi$
$643$	6.11803	−	10.5967i	0.241272	−	0.417895i	0.961077	+	0.276281i	$0.0891022\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−15.0557			−0.591902			−0.295951	−	0.955203i	$-0.595636\pi$
$647$	−15.0557			−0.591902			−0.295951	+	0.955203i	$0.595636\pi$
$648$		0			0
$649$	20.1803	−	34.9534i	0.792148	−	1.37204i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	17.4164			0.681557			0.340778	−	0.940144i	$-0.389309\pi$
$653$	17.4164			0.681557			0.340778	+	0.940144i	$0.389309\pi$
$654$		0			0
$655$	1.70820	+	2.95870i	0.0667451	+	0.115606i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	17.0902	+	29.6010i	0.665739	+	1.15309i	0.979085	+	0.203454i	$0.0652167\pi$
$659$	17.0902	+	29.6010i	0.665739	+	1.15309i	−0.313346	+	0.949639i	$0.601450\pi$
$660$		0			0
$661$	−8.41641	−	14.5776i	−0.327360	−	0.567005i	0.654627	−	0.755952i	$-0.272826\pi$
$661$	−8.41641	−	14.5776i	−0.327360	−	0.567005i	−0.981987	+	0.188947i	$0.939492\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−17.0344	−	26.5458i	−0.660567	−	1.02940i
$666$		0			0
$667$	11.4164	−	19.7738i	0.442045	−	0.765645i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.85410	−	6.67550i	−0.148786	−	0.257705i
$672$		0			0
$673$	−26.3050			−1.01398			−0.506991	−	0.861952i	$-0.669242\pi$
$673$	−26.3050			−1.01398			−0.506991	+	0.861952i	$0.669242\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−0.111456			−0.00428361			−0.00214180	−	0.999998i	$-0.500682\pi$
$677$	−0.111456			−0.00428361			−0.00214180	+	0.999998i	$0.500682\pi$
$678$		0			0
$679$	−6.70820	+	11.6190i	−0.257437	+	0.445894i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	30.2918			1.15908			0.579542	−	0.814943i	$-0.303232\pi$
$683$	30.2918			1.15908			0.579542	+	0.814943i	$0.303232\pi$
$684$		0			0
$685$	−48.3607			−1.84777
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−14.5623	+	25.2227i	−0.554780	+	0.960907i
$690$		0			0
$691$	32.9443			1.25326			0.626630	−	0.779317i	$-0.284434\pi$
$691$	32.9443			1.25326			0.626630	+	0.779317i	$0.284434\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	42.6525			1.61790
$696$		0			0
$697$	33.8885	+	58.6967i	1.28362	+	2.22330i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	3.79837	−	6.57898i	0.143463	−	0.248485i	−0.785336	−	0.619070i	$-0.787510\pi$
$701$	3.79837	−	6.57898i	0.143463	−	0.248485i	0.928798	+	0.370586i	$0.120843\pi$
$702$		0			0
$703$	−14.9443	+	28.9395i	−0.563634	+	1.09147i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−13.9443	−	24.1522i	−0.524428	−	0.908336i
$708$		0			0
$709$	−0.319660	−	0.553668i	−0.0120051	−	0.0207934i	0.859960	−	0.510361i	$-0.170488\pi$
$709$	−0.319660	−	0.553668i	−0.0120051	−	0.0207934i	−0.871966	+	0.489567i	$0.837155\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	6.38197	+	11.0539i	0.239007	+	0.413971i
$714$		0			0
$715$	50.8328			1.90104
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−5.03444	+	8.71991i	−0.187753	+	0.325198i	−0.944501	−	0.328509i	$-0.893454\pi$
$719$	−5.03444	+	8.71991i	−0.187753	+	0.325198i	0.756748	+	0.653707i	$0.226787\pi$
$720$		0			0
$721$	−18.4164			−0.685863
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−10.9443	+	18.9560i	−0.406460	+	0.704009i
$726$		0			0
$727$	8.29837	−	14.3732i	0.307770	−	0.533073i	−0.670104	−	0.742267i	$-0.733751\pi$
$727$	8.29837	−	14.3732i	0.307770	−	0.533073i	0.977874	+	0.209194i	$0.0670841\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	34.6525	+	60.0198i	1.28167	+	2.21991i
$732$		0			0
$733$	13.0557			0.482224			0.241112	−	0.970497i	$-0.422488\pi$
$733$	13.0557			0.482224			0.241112	+	0.970497i	$0.422488\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.85410	+	3.21140i	0.0682967	+	0.118293i
$738$		0			0
$739$	17.2984	−	29.9617i	0.636331	−	1.10216i	−0.349901	−	0.936787i	$-0.613785\pi$
$739$	17.2984	−	29.9617i	0.636331	−	1.10216i	0.986231	−	0.165371i	$-0.0528821\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−8.90983	+	15.4323i	−0.326870	+	0.566155i	−0.981889	−	0.189457i	$-0.939327\pi$
$743$	−8.90983	+	15.4323i	−0.326870	+	0.566155i	0.655019	+	0.755612i	$0.272661\pi$
$744$		0			0
$745$	−13.4164	−	23.2379i	−0.491539	−	0.851371i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.05573			0.0385755
$750$		0			0
$751$	18.0066	+	31.1883i	0.657069	+	1.13808i	0.981371	+	0.192124i	$0.0615375\pi$
$751$	18.0066	+	31.1883i	0.657069	+	1.13808i	−0.324301	+	0.945954i	$0.605129\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	4.00000	−	6.92820i	0.145575	−	0.252143i
$756$		0			0
$757$	−21.7361	+	37.6480i	−0.790011	+	1.36834i	0.135949	+	0.990716i	$0.456592\pi$
$757$	−21.7361	+	37.6480i	−0.790011	+	1.36834i	−0.925959	+	0.377623i	$0.876742\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−29.2361			−1.05981			−0.529903	−	0.848058i	$-0.677772\pi$
$761$	−29.2361			−1.05981			−0.529903	+	0.848058i	$0.677772\pi$
$762$		0			0
$763$	5.00000	−	8.66025i	0.181012	−	0.313522i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	23.1246			0.834981
$768$		0			0
$769$	24.3885	+	42.2422i	0.879473	+	1.52329i	0.851920	+	0.523672i	$0.175438\pi$
$769$	24.3885	+	42.2422i	0.879473	+	1.52329i	0.0275536	+	0.999620i	$0.491228\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−19.6525	−	34.0391i	−0.706850	−	1.22430i	−0.966020	−	0.258469i	$-0.916782\pi$
$773$	−19.6525	−	34.0391i	−0.706850	−	1.22430i	0.259169	−	0.965832i	$-0.416551\pi$
$774$		0			0
$775$	−6.11803	−	10.5967i	−0.219766	−	0.380646i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	24.6525	+	38.4175i	0.883267	+	1.37645i
$780$		0			0
$781$	15.7082	−	27.2074i	0.562084	−	0.973558i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−27.5066	−	47.6428i	−0.981752	−	1.70044i
$786$		0			0
$787$	42.0132			1.49761			0.748804	−	0.662792i	$-0.230629\pi$
$787$	42.0132			1.49761			0.748804	+	0.662792i	$0.230629\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−35.1246			−1.24889
$792$		0			0
$793$	2.20820	−	3.82472i	0.0784156	−	0.135820i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	50.3607			1.78387			0.891933	−	0.452167i	$-0.149349\pi$
$797$	50.3607			1.78387			0.891933	+	0.452167i	$0.149349\pi$
$798$		0			0
$799$	70.8328			2.50588
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−17.0902	+	29.6010i	−0.603099	+	1.04460i
$804$		0			0
$805$	41.3050			1.45581
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−10.0689			−0.354003			−0.177002	−	0.984211i	$-0.556640\pi$
$809$	−10.0689			−0.354003			−0.177002	+	0.984211i	$0.556640\pi$
$810$		0			0
$811$	17.2361	+	29.8537i	0.605240	+	1.04831i	0.992013	+	0.126132i	$0.0402563\pi$
$811$	17.2361	+	29.8537i	0.605240	+	1.04831i	−0.386773	+	0.922175i	$0.626410\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−24.5623	+	42.5432i	−0.860380	+	1.49022i
$816$		0			0
$817$	25.2082	+	39.2835i	0.881923	+	1.37436i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−22.9443	−	39.7406i	−0.800761	−	1.38696i	−0.919116	−	0.393987i	$-0.871096\pi$
$821$	−22.9443	−	39.7406i	−0.800761	−	1.38696i	0.118355	−	0.992971i	$-0.462238\pi$
$822$		0			0
$823$	27.1246	+	46.9812i	0.945505	+	1.63766i	0.754738	+	0.656026i	$0.227764\pi$
$823$	27.1246	+	46.9812i	0.945505	+	1.63766i	0.190767	+	0.981635i	$0.438903\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$827$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$828$		0			0
$829$	−10.4164			−0.361777			−0.180888	−	0.983504i	$-0.557897\pi$
$829$	−10.4164			−0.361777			−0.180888	+	0.983504i	$0.557897\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−6.47214	+	11.2101i	−0.224246	+	0.388406i
$834$		0			0
$835$	−24.9443			−0.863232
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−4.67376	+	8.09519i	−0.161356	+	0.279477i	−0.935355	−	0.353710i	$-0.884920\pi$
$839$	−4.67376	+	8.09519i	−0.161356	+	0.279477i	0.773999	+	0.633187i	$0.218253\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.47214	−	11.2101i	−0.222648	−	0.385638i
$846$		0			0
$847$	36.7082			1.26131
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−21.3262	−	36.9381i	−0.731054	−	1.26622i
$852$		0			0
$853$	9.26393	−	16.0456i	0.317191	−	0.549391i	−0.662710	−	0.748876i	$-0.730594\pi$
$853$	9.26393	−	16.0456i	0.317191	−	0.549391i	0.979901	+	0.199485i	$0.0639270\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−23.9443	+	41.4727i	−0.817921	+	1.41668i	0.0892908	+	0.996006i	$0.471540\pi$
$857$	−23.9443	+	41.4727i	−0.817921	+	1.41668i	−0.907212	+	0.420675i	$0.861793\pi$
$858$		0			0
$859$	−4.11803	−	7.13264i	−0.140506	−	0.243363i	0.787182	−	0.616721i	$-0.211539\pi$
$859$	−4.11803	−	7.13264i	−0.140506	−	0.243363i	−0.927687	+	0.373359i	$0.878206\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	3.88854			0.132368			0.0661838	−	0.997807i	$-0.478918\pi$
$863$	3.88854			0.132368			0.0661838	+	0.997807i	$0.478918\pi$
$864$		0			0
$865$	−35.4164	−	61.3430i	−1.20419	−	2.08573i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−16.3262	+	28.2779i	−0.553830	+	0.959261i
$870$		0			0
$871$	−1.06231	+	1.83997i	−0.0359949	+	0.0623449i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−3.41641			−0.115496
$876$		0			0
$877$	−4.73607	+	8.20311i	−0.159926	+	0.276999i	−0.934842	−	0.355065i	$-0.884459\pi$
$877$	−4.73607	+	8.20311i	−0.159926	+	0.276999i	0.774916	+	0.632064i	$0.217792\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−6.87539			−0.231638			−0.115819	−	0.993270i	$-0.536949\pi$
$881$	−6.87539			−0.231638			−0.115819	+	0.993270i	$0.536949\pi$
$882$		0			0
$883$	20.5344	+	35.5667i	0.691039	+	1.19691i	0.971498	+	0.237049i	$0.0761801\pi$
$883$	20.5344	+	35.5667i	0.691039	+	1.19691i	−0.280459	+	0.959866i	$0.590487\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.3262	−	28.2779i	−0.548181	−	0.949478i	−0.998399	−	0.0565593i	$-0.981987\pi$
$887$	−16.3262	−	28.2779i	−0.548181	−	0.949478i	0.450218	−	0.892919i	$-0.351346\pi$
$888$		0			0
$889$	−1.70820	−	2.95870i	−0.0572913	−	0.0992315i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	47.6525	−	2.23746i	1.59463	−	0.0748736i
$894$		0			0
$895$	−14.1803	+	24.5611i	−0.473996	+	0.820986i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.47214	−	7.74597i	−0.149154	−	0.258342i
$900$		0			0
$901$	62.8328			2.09326
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−16.3607			−0.543847
$906$		0			0
$907$	−6.94427	+	12.0278i	−0.230581	+	0.399378i	−0.957979	−	0.286838i	$-0.907396\pi$
$907$	−6.94427	+	12.0278i	−0.230581	+	0.399378i	0.727398	+	0.686215i	$0.240729\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−7.41641			−0.245717			−0.122858	−	0.992424i	$-0.539206\pi$
$911$	−7.41641			−0.245717			−0.122858	+	0.992424i	$0.539206\pi$
$912$		0			0
$913$	−28.9443			−0.957916
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.18034	+	2.04441i	−0.0389783	+	0.0675123i
$918$		0			0
$919$	−29.6525			−0.978145			−0.489072	−	0.872243i	$-0.662665\pi$
$919$	−29.6525			−0.978145			−0.489072	+	0.872243i	$0.662665\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	18.0000			0.592477
$924$		0			0
$925$	20.4443	+	35.4105i	0.672204	+	1.16429i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−10.0902	+	17.4767i	−0.331048	+	0.573392i	−0.982718	−	0.185111i	$-0.940735\pi$
$929$	−10.0902	+	17.4767i	−0.331048	+	0.573392i	0.651670	+	0.758503i	$0.274069\pi$
$930$		0			0
$931$	−4.00000	+	7.74597i	−0.131095	+	0.253864i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−54.8328	−	94.9732i	−1.79322	−	3.10596i
$936$		0			0
$937$	3.44427	+	5.96565i	0.112519	+	0.194889i	0.916785	−	0.399380i	$-0.130775\pi$
$937$	3.44427	+	5.96565i	0.112519	+	0.194889i	−0.804266	+	0.594269i	$0.797441\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−23.4164	−	40.5584i	−0.763353	−	1.32217i	−0.941113	−	0.338092i	$-0.890218\pi$
$941$	−23.4164	−	40.5584i	−0.763353	−	1.32217i	0.177760	−	0.984074i	$-0.443115\pi$
$942$		0			0
$943$	−59.7771			−1.94661
$944$		0			0
$945$		0			0
$946$		0			0
$947$	17.9443	−	31.0804i	0.583110	−	1.00998i	−0.411998	−	0.911185i	$-0.635169\pi$
$947$	17.9443	−	31.0804i	0.583110	−	1.00998i	0.995108	−	0.0987921i	$-0.0314979\pi$
$948$		0			0
$949$	−19.5836			−0.635710
$950$		0			0
$951$		0			0
$952$		0			0
$953$	26.2148	−	45.4053i	0.849180	−	1.47082i	−0.0327609	−	0.999463i	$-0.510430\pi$
$953$	26.2148	−	45.4053i	0.849180	−	1.47082i	0.881941	−	0.471360i	$-0.156237\pi$
$954$		0			0
$955$	−30.1803	+	52.2739i	−0.976613	+	1.69154i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−16.7082	−	28.9395i	−0.539536	−	0.934504i
$960$		0			0
$961$	−26.0000			−0.838710
$962$		0			0
$963$		0			0
$964$		0			0
$965$	27.3262	+	47.3304i	0.879663	+	1.52362i
$966$		0			0
$967$	−1.35410	+	2.34537i	−0.0435450	+	0.0754221i	−0.886976	−	0.461815i	$-0.847199\pi$
$967$	−1.35410	+	2.34537i	−0.0435450	+	0.0754221i	0.843431	+	0.537237i	$0.180532\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	24.4164	−	42.2905i	0.783560	−	1.35717i	−0.146296	−	0.989241i	$-0.546735\pi$
$971$	24.4164	−	42.2905i	0.783560	−	1.35717i	0.929856	−	0.367925i	$-0.119932\pi$
$972$		0			0
$973$	14.7361	+	25.5236i	0.472417	+	0.818250i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.41641			−0.0453149			−0.0226575	−	0.999743i	$-0.507213\pi$
$977$	−1.41641			−0.0453149			−0.0226575	+	0.999743i	$0.507213\pi$
$978$		0			0
$979$	−13.7082	−	23.7433i	−0.438116	−	0.758839i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−10.1459	+	17.5732i	−0.323604	+	0.560498i	−0.981229	−	0.192847i	$-0.938228\pi$
$983$	−10.1459	+	17.5732i	−0.323604	+	0.560498i	0.657625	+	0.753346i	$0.271561\pi$
$984$		0			0
$985$	−0.472136	+	0.817763i	−0.0150435	+	0.0260561i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−61.1246			−1.94365
$990$		0			0
$991$	−1.06231	+	1.83997i	−0.0337453	+	0.0584485i	−0.882405	−	0.470491i	$-0.844077\pi$
$991$	−1.06231	+	1.83997i	−0.0337453	+	0.0584485i	0.848660	+	0.528939i	$0.177410\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−44.1803			−1.40061
$996$		0			0
$997$	−1.50000	−	2.59808i	−0.0475055	−	0.0822819i	0.841295	−	0.540576i	$-0.181794\pi$
$997$	−1.50000	−	2.59808i	−0.0475055	−	0.0822819i	−0.888800	+	0.458295i	$0.848460\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.s.w.1873.2		4
3.2	odd	2		912.2.q.h.49.1		4
4.3	odd	2		1368.2.s.i.505.2		4
12.11	even	2		456.2.q.e.49.1	✓	4
19.7	even	3	inner	2736.2.s.w.577.2		4
57.26	odd	6		912.2.q.h.577.1		4
76.7	odd	6		1368.2.s.i.577.2		4
228.11	even	6		8664.2.a.s.1.2		2
228.83	even	6		456.2.q.e.121.1	yes	4
228.179	odd	6		8664.2.a.w.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.q.e.49.1	✓	4	12.11	even	2
456.2.q.e.121.1	yes	4	228.83	even	6
912.2.q.h.49.1		4	3.2	odd	2
912.2.q.h.577.1		4	57.26	odd	6
1368.2.s.i.505.2		4	4.3	odd	2
1368.2.s.i.577.2		4	76.7	odd	6
2736.2.s.w.577.2		4	19.7	even	3	inner
2736.2.s.w.1873.2		4	1.1	even	1	trivial
8664.2.a.s.1.2		2	228.11	even	6
8664.2.a.w.1.2		2	228.179	odd	6

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:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.s (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.61803 - 2.80252i) q^{5} +2.23607 q^{7} +O(q^{10})\)	\(q+(1.61803 - 2.80252i) q^{5} +2.23607 q^{7} +5.23607 q^{11} +(1.50000 + 2.59808i) q^{13} +(3.23607 - 5.60503i) q^{17} +(2.00000 - 3.87298i) q^{19} +(2.85410 + 4.94345i) q^{23} +(-2.73607 - 4.73901i) q^{25} +(-2.00000 - 3.46410i) q^{29} +2.23607 q^{31} +(3.61803 - 6.26662i) q^{35} -7.47214 q^{37} +(-5.23607 + 9.06914i) q^{41} +(-5.35410 + 9.27358i) q^{43} +(5.47214 + 9.47802i) q^{47} -2.00000 q^{49} +(4.85410 + 8.40755i) q^{53} +(8.47214 - 14.6742i) q^{55} +(3.85410 - 6.67550i) q^{59} +(-0.736068 - 1.27491i) q^{61} +9.70820 q^{65} +(0.354102 + 0.613323i) q^{67} +(3.00000 - 5.19615i) q^{71} +(-3.26393 + 5.65330i) q^{73} +11.7082 q^{77} +(-3.11803 + 5.40059i) q^{79} -5.52786 q^{83} +(-10.4721 - 18.1383i) q^{85} +(-2.61803 - 4.53457i) q^{89} +(3.35410 + 5.80948i) q^{91} +(-7.61803 - 11.8717i) q^{95} +(-3.00000 + 5.19615i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5}+O(q^{10}) \) 4 * q + 2 * q^5	\( 4 q + 2 q^{5} + 12 q^{11} + 6 q^{13} + 4 q^{17} + 8 q^{19} - 2 q^{23} - 2 q^{25} - 8 q^{29} + 10 q^{35} - 12 q^{37} - 12 q^{41} - 8 q^{43} + 4 q^{47} - 8 q^{49} + 6 q^{53} + 16 q^{55} + 2 q^{59} + 6 q^{61} + 12 q^{65} - 12 q^{67} + 12 q^{71} - 22 q^{73} + 20 q^{77} - 8 q^{79} - 40 q^{83} - 24 q^{85} - 6 q^{89} - 26 q^{95} - 12 q^{97}+O(q^{100}) \) 4 * q + 2 * q^5 + 12 * q^11 + 6 * q^13 + 4 * q^17 + 8 * q^19 - 2 * q^23 - 2 * q^25 - 8 * q^29 + 10 * q^35 - 12 * q^37 - 12 * q^41 - 8 * q^43 + 4 * q^47 - 8 * q^49 + 6 * q^53 + 16 * q^55 + 2 * q^59 + 6 * q^61 + 12 * q^65 - 12 * q^67 + 12 * q^71 - 22 * q^73 + 20 * q^77 - 8 * q^79 - 40 * q^83 - 24 * q^85 - 6 * q^89 - 26 * q^95 - 12 * q^97

Introduction

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