LMFDB - Embedded newform 260.2.bg.a.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(23,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 10]))

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

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

chi := DirichletCharacter("260.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bg (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{12}]$

Embedding invariants

Embedding label			127.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	260.127
Dual form			260.2.bg.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(1.86603 - 1.23205i) q^{5} +(-2.00000 - 2.00000i) q^{8} +(2.59808 + 1.50000i) q^{9} +O(q^{10})$	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(1.86603 - 1.23205i) q^{5} +(-2.00000 - 2.00000i) q^{8} +(2.59808 + 1.50000i) q^{9} +(-3.00000 + 1.00000i) q^{10} +(-3.59808 - 0.232051i) q^{13} +(2.00000 + 3.46410i) q^{16} +(6.96410 - 1.86603i) q^{17} +(-3.00000 - 3.00000i) q^{18} +(4.46410 - 0.267949i) q^{20} +(1.96410 - 4.59808i) q^{25} +(4.83013 + 1.63397i) q^{26} +(5.76795 - 3.33013i) q^{29} +(-1.46410 - 5.46410i) q^{32} -10.1962 q^{34} +(3.00000 + 5.19615i) q^{36} +(-1.13397 - 0.303848i) q^{37} +(-6.19615 - 1.26795i) q^{40} +(1.66987 - 0.964102i) q^{41} +(6.69615 - 0.401924i) q^{45} +(-6.06218 + 3.50000i) q^{49} +(-4.36603 + 5.56218i) q^{50} +(-6.00000 - 4.00000i) q^{52} +(-10.2942 + 10.2942i) q^{53} +(-9.09808 + 2.43782i) q^{58} +(-7.33013 + 12.6962i) q^{61} +8.00000i q^{64} +(-7.00000 + 4.00000i) q^{65} +(13.9282 + 3.73205i) q^{68} +(-2.19615 - 8.19615i) q^{72} +(-9.83013 - 9.83013i) q^{73} +(1.43782 + 0.830127i) q^{74} +(8.00000 + 4.00000i) q^{80} +(4.50000 + 7.79423i) q^{81} +(-2.63397 + 0.705771i) q^{82} +(10.6962 - 12.0622i) q^{85} +(-5.00000 - 8.66025i) q^{89} +(-9.29423 - 1.90192i) q^{90} +(4.75833 + 17.7583i) q^{97} +(9.56218 - 2.56218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 4 q^{5} - 8 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 + 4 * q^5 - 8 * q^8	$ 4 q - 2 q^{2} + 4 q^{5} - 8 q^{8} - 12 q^{10} - 4 q^{13} + 8 q^{16} + 14 q^{17} - 12 q^{18} + 4 q^{20} - 6 q^{25} + 2 q^{26} + 30 q^{29} + 8 q^{32} - 20 q^{34} + 12 q^{36} - 8 q^{37} - 4 q^{40} + 24 q^{41} + 6 q^{45} - 14 q^{50} - 24 q^{52} - 10 q^{53} - 26 q^{58} - 12 q^{61} - 28 q^{65} + 28 q^{68} + 12 q^{72} - 22 q^{73} + 30 q^{74} + 32 q^{80} + 18 q^{81} - 14 q^{82} + 22 q^{85} - 20 q^{89} - 6 q^{90} - 26 q^{97} + 14 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 4 * q^5 - 8 * q^8 - 12 * q^10 - 4 * q^13 + 8 * q^16 + 14 * q^17 - 12 * q^18 + 4 * q^20 - 6 * q^25 + 2 * q^26 + 30 * q^29 + 8 * q^32 - 20 * q^34 + 12 * q^36 - 8 * q^37 - 4 * q^40 + 24 * q^41 + 6 * q^45 - 14 * q^50 - 24 * q^52 - 10 * q^53 - 26 * q^58 - 12 * q^61 - 28 * q^65 + 28 * q^68 + 12 * q^72 - 22 * q^73 + 30 * q^74 + 32 * q^80 + 18 * q^81 - 14 * q^82 + 22 * q^85 - 20 * q^89 - 6 * q^90 - 26 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$3$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$3$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$	1.86603	−	1.23205i	0.834512	−	0.550990i
$5$	1.86603	−	1.23205i	0.834512	−	0.550990i
$6$		0			0
$7$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$7$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$	2.59808	+	1.50000i	0.866025	+	0.500000i
$10$	−3.00000	+	1.00000i	−0.948683	+	0.316228i
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$		0			0
$13$	−3.59808	−	0.232051i	−0.997927	−	0.0643593i
$13$	−3.59808	−	0.232051i	−0.997927	−	0.0643593i
$14$		0			0
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	6.96410	−	1.86603i	1.68904	−	0.452578i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	6.96410	−	1.86603i	1.68904	−	0.452578i	0.970143	+	0.242536i	$0.0779791\pi$
$18$	−3.00000	−	3.00000i	−0.707107	−	0.707107i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	4.46410	−	0.267949i	0.998203	−	0.0599153i
$21$		0			0
$22$		0			0
$23$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$23$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$24$		0			0
$25$	1.96410	−	4.59808i	0.392820	−	0.919615i
$26$	4.83013	+	1.63397i	0.947266	+	0.320449i
$27$		0			0
$28$		0			0
$29$	5.76795	−	3.33013i	1.07108	−	0.618389i	0.142605	−	0.989780i	$-0.454452\pi$
$29$	5.76795	−	3.33013i	1.07108	−	0.618389i	0.928477	+	0.371391i	$0.121119\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−1.46410	−	5.46410i	−0.258819	−	0.965926i
$33$		0			0
$34$	−10.1962			−1.74863
$35$		0			0
$36$	3.00000	+	5.19615i	0.500000	+	0.866025i
$37$	−1.13397	−	0.303848i	−0.186424	−	0.0499522i	0.164399	−	0.986394i	$-0.447432\pi$
$37$	−1.13397	−	0.303848i	−0.186424	−	0.0499522i	−0.350823	+	0.936442i	$0.614098\pi$
$38$		0			0
$39$		0			0
$40$	−6.19615	−	1.26795i	−0.979698	−	0.200480i
$41$	1.66987	−	0.964102i	0.260790	−	0.150567i	−0.363905	−	0.931436i	$-0.618557\pi$
$41$	1.66987	−	0.964102i	0.260790	−	0.150567i	0.624695	+	0.780869i	$0.285223\pi$
$42$		0			0
$43$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$43$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$44$		0			0
$45$	6.69615	−	0.401924i	0.998203	−	0.0599153i
$46$		0			0
$47$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$47$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$48$		0			0
$49$	−6.06218	+	3.50000i	−0.866025	+	0.500000i
$50$	−4.36603	+	5.56218i	−0.617449	+	0.786611i
$51$		0			0
$52$	−6.00000	−	4.00000i	−0.832050	−	0.554700i
$53$	−10.2942	+	10.2942i	−1.41402	+	1.41402i	−0.695344	+	0.718677i	$0.744748\pi$
$53$	−10.2942	+	10.2942i	−1.41402	+	1.41402i	−0.718677	+	0.695344i	$0.755252\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−9.09808	+	2.43782i	−1.19464	+	0.320102i
$59$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$59$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$60$		0			0
$61$	−7.33013	+	12.6962i	−0.938527	+	1.62558i	−0.170305	+	0.985391i	$0.554475\pi$
$61$	−7.33013	+	12.6962i	−0.938527	+	1.62558i	−0.768221	+	0.640184i	$0.778858\pi$
$62$		0			0
$63$		0			0
$64$			8.00000i			1.00000i
$65$	−7.00000	+	4.00000i	−0.868243	+	0.496139i
$66$		0			0
$67$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$67$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$68$	13.9282	+	3.73205i	1.68904	+	0.452578i
$69$		0			0
$70$		0			0
$71$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$71$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$72$	−2.19615	−	8.19615i	−0.258819	−	0.965926i
$73$	−9.83013	−	9.83013i	−1.15053	−	1.15053i	−0.986447	−	0.164083i	$-0.947534\pi$
$73$	−9.83013	−	9.83013i	−1.15053	−	1.15053i	−0.164083	−	0.986447i	$-0.552466\pi$
$74$	1.43782	+	0.830127i	0.167143	+	0.0965003i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	8.00000	+	4.00000i	0.894427	+	0.447214i
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	−2.63397	+	0.705771i	−0.290874	+	0.0779394i
$83$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$83$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$84$		0			0
$85$	10.6962	−	12.0622i	1.16016	−	1.30833i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	−0.999388	−	0.0349934i	$-0.988859\pi$
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	0.469389	−	0.882992i	$-0.344474\pi$
$90$	−9.29423	−	1.90192i	−0.979698	−	0.200480i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	4.75833	+	17.7583i	0.483135	+	1.80309i	0.588315	+	0.808632i	$0.299792\pi$
$97$	4.75833	+	17.7583i	0.483135	+	1.80309i	−0.105180	+	0.994453i	$0.533542\pi$
$98$	9.56218	−	2.56218i	0.965926	−	0.258819i
$99$		0			0
$100$	8.00000	−	6.00000i	0.800000	−	0.600000i
$101$	−8.16025	−	14.1340i	−0.811976	−	1.40638i	−0.911479	−	0.411346i	$-0.865059\pi$
$101$	−8.16025	−	14.1340i	−0.811976	−	1.40638i	0.0995037	−	0.995037i	$-0.468274\pi$
$102$		0			0
$103$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$103$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$104$	6.73205	+	7.66025i	0.660132	+	0.751150i
$105$		0			0
$106$	17.8301	−	10.2942i	1.73182	−	0.999864i
$107$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$107$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$108$		0			0
$109$	−20.0000			−1.91565			−0.957826	−	0.287348i	$-0.907226\pi$
$109$	−20.0000			−1.91565			−0.957826	+	0.287348i	$0.907226\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.06218	+	11.4282i	0.288065	+	1.07507i	0.946570	+	0.322498i	$0.104523\pi$
$113$	3.06218	+	11.4282i	0.288065	+	1.07507i	−0.658505	+	0.752577i	$0.728811\pi$
$114$		0			0
$115$		0			0
$116$	13.3205			1.23678
$117$	−9.00000	−	6.00000i	−0.832050	−	0.554700i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	14.6603	−	14.6603i	1.32728	−	1.32728i
$123$		0			0
$124$		0			0
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$127$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$128$	2.92820	−	10.9282i	0.258819	−	0.965926i
$129$		0			0
$130$	11.0263	−	2.90192i	0.967069	−	0.254516i
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−17.6603	−	10.1962i	−1.51435	−	0.874313i
$137$	6.03590	+	22.5263i	0.515682	+	1.92455i	0.341743	+	0.939793i	$0.388983\pi$
$137$	6.03590	+	22.5263i	0.515682	+	1.92455i	0.173939	+	0.984757i	$0.444351\pi$
$138$		0			0
$139$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$139$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$			12.0000i			1.00000i
$145$	6.66025	−	13.3205i	0.553104	−	1.10621i
$146$	9.83013	+	17.0263i	0.813547	+	1.40910i
$147$		0			0
$148$	−1.66025	−	1.66025i	−0.136472	−	0.136472i
$149$	1.06218	−	1.83975i	0.0870170	−	0.150718i	−0.819232	−	0.573462i	$-0.805600\pi$
$149$	1.06218	−	1.83975i	0.0870170	−	0.150718i	0.906249	+	0.422744i	$0.138933\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$		0			0
$153$	20.8923	+	5.59808i	1.68904	+	0.452578i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	12.2224	+	12.2224i	0.975456	+	0.975456i	0.999706	−	0.0242497i	$-0.00771967\pi$
$157$	12.2224	+	12.2224i	0.975456	+	0.975456i	−0.0242497	+	0.999706i	$0.507720\pi$
$158$		0			0
$159$		0			0
$160$	−9.46410	−	8.39230i	−0.748203	−	0.663470i
$161$		0			0
$162$	−3.29423	−	12.2942i	−0.258819	−	0.965926i
$163$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$163$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$164$	3.85641			0.301135
$165$		0			0
$166$		0			0
$167$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$167$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$168$		0			0
$169$	12.8923	+	1.66987i	0.991716	+	0.128452i
$170$	−19.0263	+	12.5622i	−1.45925	+	0.963475i
$171$		0			0
$172$		0			0
$173$	−5.49038	−	20.4904i	−0.417426	−	1.55785i	−0.779926	−	0.625871i	$-0.784744\pi$
$173$	−5.49038	−	20.4904i	−0.417426	−	1.55785i	0.362500	−	0.931984i	$-0.381923\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	3.66025	+	13.6603i	0.274348	+	1.02388i
$179$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$179$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$180$	12.0000	+	6.00000i	0.894427	+	0.447214i
$181$	−26.3205			−1.95639			−0.978194	−	0.207693i	$-0.933404\pi$
$181$	−26.3205			−1.95639			−0.978194	+	0.207693i	$0.933404\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.49038	+	0.830127i	−0.183096	+	0.0610322i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$		0			0
$193$	−5.06218	+	18.8923i	−0.364384	+	1.35990i	0.503871	+	0.863779i	$0.331909\pi$
$193$	−5.06218	+	18.8923i	−0.364384	+	1.35990i	−0.868255	+	0.496119i	$0.834758\pi$
$194$		−	26.0000i		−	1.86669i
$195$		0			0
$196$	−14.0000			−1.00000
$197$	−17.7583	−	4.75833i	−1.26523	−	0.339017i	−0.437028	−	0.899448i	$-0.643969\pi$
$197$	−17.7583	−	4.75833i	−1.26523	−	0.339017i	−0.828201	+	0.560431i	$0.810635\pi$
$198$		0			0
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	−13.1244	+	5.26795i	−0.928032	+	0.372500i
$201$		0			0
$202$	5.97372	+	22.2942i	0.420310	+	1.56862i
$203$		0			0
$204$		0			0
$205$	1.92820	−	3.85641i	0.134672	−	0.269343i
$206$		0			0
$207$		0			0
$208$	−6.39230	−	12.9282i	−0.443227	−	0.896410i
$209$		0			0
$210$		0			0
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$	−28.1244	+	7.53590i	−1.93159	+	0.517568i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	27.3205	+	7.32051i	1.85038	+	0.495807i
$219$		0			0
$220$		0			0
$221$	−25.4904	+	5.09808i	−1.71467	+	0.342934i
$222$		0			0
$223$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$223$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$224$		0			0
$225$	12.0000	−	9.00000i	0.800000	−	0.600000i
$226$		−	16.7321i		−	1.11300i
$227$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$227$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$228$		0			0
$229$	30.0000			1.98246			0.991228	−	0.132164i	$-0.0421925\pi$
$229$	30.0000			1.98246			0.991228	+	0.132164i	$0.0421925\pi$
$230$		0			0
$231$		0			0
$232$	−18.1962	−	4.87564i	−1.19464	−	0.320102i
$233$	−5.00000	+	5.00000i	−0.327561	+	0.327561i	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−5.00000	+	5.00000i	−0.327561	+	0.327561i	0.524097	+	0.851658i	$0.324403\pi$
$234$	10.0981	+	11.4904i	0.660132	+	0.751150i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	6.99038	+	4.03590i	0.450290	+	0.259975i	0.707953	−	0.706260i	$-0.249619\pi$
$241$	6.99038	+	4.03590i	0.450290	+	0.259975i	−0.257663	+	0.966235i	$0.582952\pi$
$242$	−11.0000	+	11.0000i	−0.707107	+	0.707107i
$243$		0			0
$244$	−25.3923	+	14.6603i	−1.62558	+	0.938527i
$245$	−7.00000	+	14.0000i	−0.447214	+	0.894427i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−1.29423	+	15.7583i	−0.0818542	+	0.996644i
$251$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$251$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	2.64359	−	9.86603i	0.164903	−	0.615426i	−0.833150	−	0.553047i	$-0.813465\pi$
$257$	2.64359	−	9.86603i	0.164903	−	0.615426i	0.998053	−	0.0623783i	$-0.0198685\pi$
$258$		0			0
$259$		0			0
$260$	−16.1244	−	0.0717968i	−0.999990	−	0.00445265i
$261$	19.9808			1.23678
$262$		0			0
$263$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$263$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$264$		0			0
$265$	−6.52628	+	31.8923i	−0.400906	+	1.95913i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−22.5167	−	13.0000i	−1.37287	−	0.792624i	−0.381577	−	0.924337i	$-0.624619\pi$
$269$	−22.5167	−	13.0000i	−1.37287	−	0.792624i	−0.991288	+	0.131713i	$0.957952\pi$
$270$		0			0
$271$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$271$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$272$	20.3923	+	20.3923i	1.23647	+	1.23647i
$273$		0			0
$274$		−	32.9808i		−	1.99244i
$275$		0			0
$276$		0			0
$277$	23.7942	−	6.37564i	1.42966	−	0.383075i	0.540758	−	0.841178i	$-0.318138\pi$
$277$	23.7942	−	6.37564i	1.42966	−	0.383075i	0.888899	+	0.458103i	$0.151471\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	32.7128i		−	1.95148i	−0.218926	−	0.975741i	$-0.570255\pi$
$281$		−	32.7128i		−	1.95148i	0.218926	−	0.975741i	$-0.429745\pi$
$282$		0			0
$283$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$283$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	4.39230	−	16.3923i	0.258819	−	0.965926i
$289$	30.2942	−	17.4904i	1.78201	−	1.02885i
$290$	−13.9737	+	15.7583i	−0.820565	+	0.925361i
$291$		0			0
$292$	−7.19615	−	26.8564i	−0.421123	−	1.57165i
$293$	4.76795	−	1.27757i	0.278547	−	0.0746363i	−0.116841	−	0.993151i	$-0.537277\pi$
$293$	4.76795	−	1.27757i	0.278547	−	0.0746363i	0.395388	+	0.918514i	$0.370610\pi$
$294$		0			0
$295$		0			0
$296$	1.66025	+	2.87564i	0.0965003	+	0.167143i
$297$		0			0
$298$	−2.12436	+	2.12436i	−0.123061	+	0.123061i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.96410	+	32.7224i	0.112464	+	1.87368i
$306$	−26.4904	−	15.2942i	−1.51435	−	0.874313i
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$	25.0000	−	25.0000i	1.41308	−	1.41308i	0.678280	−	0.734803i	$-0.262726\pi$
$313$	25.0000	−	25.0000i	1.41308	−	1.41308i	0.734803	−	0.678280i	$-0.237274\pi$
$314$	−12.2224	−	21.1699i	−0.689752	−	1.19469i
$315$		0			0
$316$		0			0
$317$	23.1506	−	23.1506i	1.30027	−	1.30027i	0.372061	−	0.928208i	$-0.378651\pi$
$317$	23.1506	−	23.1506i	1.30027	−	1.30027i	0.928208	−	0.372061i	$-0.121349\pi$
$318$		0			0
$319$		0			0
$320$	9.85641	+	14.9282i	0.550990	+	0.834512i
$321$		0			0
$322$		0			0
$323$		0			0
$324$			18.0000i			1.00000i
$325$	−8.13397	+	16.0885i	−0.451192	+	0.892427i
$326$		0			0
$327$		0			0
$328$	−5.26795	−	1.41154i	−0.290874	−	0.0779394i
$329$		0			0
$330$		0			0
$331$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$331$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$332$		0			0
$333$	−2.49038	−	2.49038i	−0.136472	−	0.136472i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	6.43782	+	6.43782i	0.350691	+	0.350691i	0.860366	−	0.509676i	$-0.170235\pi$
$337$	6.43782	+	6.43782i	0.350691	+	0.350691i	−0.509676	+	0.860366i	$0.670235\pi$
$338$	−17.0000	−	7.00000i	−0.924678	−	0.380750i
$339$		0			0
$340$	30.5885	−	10.1962i	1.65889	−	0.552964i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$			30.0000i			1.61281i
$347$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$347$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$348$		0			0
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	0.968253	−	0.249973i	$-0.0804216\pi$
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	−0.700609	+	0.713545i	$0.747088\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.27757	+	23.4282i	−0.334121	+	1.24696i	0.570697	+	0.821160i	$0.306673\pi$
$353$	−6.27757	+	23.4282i	−0.334121	+	1.24696i	−0.904819	+	0.425797i	$0.859994\pi$
$354$		0			0
$355$		0			0
$356$		−	20.0000i		−	1.06000i
$357$		0			0
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$	−14.1962	−	12.5885i	−0.748203	−	0.663470i
$361$	−9.50000	−	16.4545i	−0.500000	−	0.866025i
$362$	35.9545	+	9.63397i	1.88973	+	0.506350i
$363$		0			0
$364$		0			0
$365$	−30.4545	−	6.23205i	−1.59406	−	0.326200i
$366$		0			0
$367$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$367$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$368$		0			0
$369$	5.78461			0.301135
$370$	3.70577	−	0.222432i	0.192654	−	0.0115637i
$371$		0			0
$372$		0			0
$373$	1.08846	+	4.06218i	0.0563582	+	0.210332i	0.988363	−	0.152115i	$-0.0486083\pi$
$373$	1.08846	+	4.06218i	0.0563582	+	0.210332i	−0.932005	+	0.362446i	$0.881942\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−21.5263	+	10.6436i	−1.10866	+	0.548173i
$378$		0			0
$379$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$379$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$383$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$384$		0			0
$385$		0			0
$386$	13.8301	−	23.9545i	0.703935	−	1.21925i
$387$		0			0
$388$	−9.51666	+	35.5167i	−0.483135	+	1.80309i
$389$		−	0.320508i		−	0.0162504i	−0.999967	−	0.00812520i	$-0.997414\pi$
$389$		−	0.320508i		−	0.0162504i	0.999967	−	0.00812520i	$-0.00258636\pi$
$390$		0			0
$391$		0			0
$392$	19.1244	+	5.12436i	0.965926	+	0.258819i
$393$		0			0
$394$	22.5167	+	13.0000i	1.13437	+	0.654931i
$395$		0			0
$396$		0			0
$397$	−4.75833	−	17.7583i	−0.238814	−	0.891265i	−0.976392	−	0.216004i	$-0.930698\pi$
$397$	−4.75833	−	17.7583i	−0.238814	−	0.891265i	0.737579	−	0.675261i	$-0.235969\pi$
$398$		0			0
$399$		0			0
$400$	19.8564	−	2.39230i	0.992820	−	0.119615i
$401$	15.8205	−	9.13397i	0.790038	−	0.456129i	−0.0499376	−	0.998752i	$-0.515902\pi$
$401$	15.8205	−	9.13397i	0.790038	−	0.456129i	0.839976	+	0.542623i	$0.182569\pi$
$402$		0			0
$403$		0			0
$404$		−	32.6410i		−	1.62395i
$405$	18.0000	+	9.00000i	0.894427	+	0.447214i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−7.40192	+	12.8205i	−0.366002	+	0.633933i	−0.988936	−	0.148340i	$-0.952607\pi$
$409$	−7.40192	+	12.8205i	−0.366002	+	0.633933i	0.622935	+	0.782274i	$0.285940\pi$
$410$	−4.04552	+	4.56218i	−0.199794	+	0.225310i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	4.00000	+	20.0000i	0.196116	+	0.980581i
$417$		0			0
$418$		0			0
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$		0			0
$421$			39.2487i			1.91287i	0.291953	+	0.956433i	$0.405695\pi$
$421$			39.2487i			1.91287i	−0.291953	+	0.956433i	$0.594305\pi$
$422$		0			0
$423$		0			0
$424$	41.1769			1.99973
$425$	5.09808	−	35.6865i	0.247293	−	1.73105i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$431$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$432$		0			0
$433$	−10.1077	−	37.7224i	−0.485745	−	1.81282i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$	−10.1077	−	37.7224i	−0.485745	−	1.81282i	0.0909384	−	0.995857i	$-0.471013\pi$
$434$		0			0
$435$		0			0
$436$	−34.6410	−	20.0000i	−1.65900	−	0.957826i
$437$		0			0
$438$		0			0
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$	−21.0000			−1.00000
$442$	36.6865	+	2.36603i	1.74500	+	0.112540i
$443$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$443$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$444$		0			0
$445$	−20.0000	−	10.0000i	−0.948091	−	0.474045i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−20.0000	+	34.6410i	−0.943858	+	1.63481i	−0.185837	+	0.982581i	$0.559500\pi$
$449$	−20.0000	+	34.6410i	−0.943858	+	1.63481i	−0.758021	+	0.652230i	$0.773834\pi$
$450$	−19.6865	+	7.90192i	−0.928032	+	0.372500i
$451$		0			0
$452$	−6.12436	+	22.8564i	−0.288065	+	1.07507i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−41.1865	−	11.0359i	−1.92662	−	0.516238i	−0.982339	−	0.187112i	$-0.940087\pi$
$457$	−41.1865	−	11.0359i	−1.92662	−	0.516238i	−0.944286	−	0.329125i	$-0.893246\pi$
$458$	−40.9808	−	10.9808i	−1.91491	−	0.513097i
$459$		0			0
$460$		0			0
$461$	37.1603	+	21.4545i	1.73073	+	0.999235i	0.884918	+	0.465746i	$0.154214\pi$
$461$	37.1603	+	21.4545i	1.73073	+	0.999235i	0.845807	+	0.533488i	$0.179119\pi$
$462$		0			0
$463$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$463$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$464$	23.0718	+	13.3205i	1.07108	+	0.618389i
$465$		0			0
$466$	8.66025	−	5.00000i	0.401179	−	0.231621i
$467$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$467$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$468$	−9.58846	−	19.3923i	−0.443227	−	0.896410i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−42.1865	+	11.3038i	−1.93159	+	0.517568i
$478$		0			0
$479$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$479$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$480$		0			0
$481$	4.00962	+	1.35641i	0.182823	+	0.0618468i
$482$	−8.07180	−	8.07180i	−0.367660	−	0.367660i
$483$		0			0
$484$	19.0526	−	11.0000i	0.866025	−	0.500000i
$485$	30.7583	+	27.2750i	1.39666	+	1.23849i
$486$		0			0
$487$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$487$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$488$	40.0526	−	10.7321i	1.81309	−	0.485817i
$489$		0			0
$490$	14.6865	−	16.5622i	0.663470	−	0.748203i
$491$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$491$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$492$		0			0
$493$	33.9545	−	33.9545i	1.52923	−	1.52923i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	7.53590	−	21.0526i	0.337016	−	0.941499i
$501$		0			0
$502$		0			0
$503$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$503$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$504$		0			0
$505$	−32.6410	−	16.3205i	−1.45251	−	0.726253i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−21.5526	−	37.3301i	−0.955300	−	1.65463i	−0.733679	−	0.679496i	$-0.762199\pi$
$509$	−21.5526	−	37.3301i	−0.955300	−	1.65463i	−0.221621	−	0.975133i	$-0.571135\pi$
$510$		0			0
$511$		0			0
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$		0			0
$514$	−7.22243	+	12.5096i	−0.318568	+	0.551776i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	22.0000	+	6.00000i	0.964764	+	0.263117i
$521$	45.6410			1.99957			0.999785	−	0.0207541i	$-0.00660670\pi$
$521$	45.6410			1.99957			0.999785	+	0.0207541i	$0.00660670\pi$
$522$	−27.2942	−	7.31347i	−1.19464	−	0.320102i
$523$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$523$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	19.9186	+	11.5000i	0.866025	+	0.500000i
$530$	20.5885	−	41.1769i	0.894305	−	1.78861i
$531$		0			0
$532$		0			0
$533$	−6.23205	+	3.08142i	−0.269940	+	0.133471i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	26.0000	+	26.0000i	1.12094	+	1.12094i
$539$		0			0
$540$		0			0
$541$			26.3731i			1.13387i	0.823764	+	0.566933i	$0.191870\pi$
$541$			26.3731i			1.13387i	−0.823764	+	0.566933i	$0.808130\pi$
$542$		0			0
$543$		0			0
$544$	−20.3923	−	35.3205i	−0.874313	−	1.51435i
$545$	−37.3205	+	24.6410i	−1.59863	+	1.05551i
$546$		0			0
$547$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$547$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$548$	−12.0718	+	45.0526i	−0.515682	+	1.92455i
$549$	−38.0885	+	21.9904i	−1.62558	+	0.938527i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−34.8372			−1.48009
$555$		0			0
$556$		0			0
$557$	−16.6244	−	4.45448i	−0.704397	−	0.188742i	−0.111198	−	0.993798i	$-0.535469\pi$
$557$	−16.6244	−	4.45448i	−0.704397	−	0.188742i	−0.593199	+	0.805056i	$0.702135\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−11.9737	+	44.6865i	−0.505081	+	1.88499i
$563$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$563$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$564$		0			0
$565$	19.7942	+	17.5526i	0.832749	+	0.738442i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−22.5167	+	13.0000i	−0.943948	+	0.544988i	−0.891196	−	0.453619i	$-0.850133\pi$
$569$	−22.5167	+	13.0000i	−0.943948	+	0.544988i	−0.0527519	+	0.998608i	$0.516799\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−12.0000	+	20.7846i	−0.500000	+	0.866025i
$577$	−10.1506	+	10.1506i	−0.422576	+	0.422576i	−0.886090	−	0.463513i	$-0.846589\pi$
$577$	−10.1506	+	10.1506i	−0.422576	+	0.422576i	0.463513	+	0.886090i	$0.346589\pi$
$578$	−47.7846	+	12.8038i	−1.98758	+	0.532570i
$579$		0			0
$580$	24.8564	−	16.4115i	1.03211	−	0.681452i
$581$		0			0
$582$		0			0
$583$		0			0
$584$			39.3205i			1.62709i
$585$	−24.1865	−	0.107695i	−0.999990	−	0.00445265i
$586$	−6.98076			−0.288373
$587$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$587$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.21539	−	4.53590i	−0.0499522	−	0.186424i
$593$	28.4904	+	28.4904i	1.16996	+	1.16996i	0.982219	+	0.187741i	$0.0601166\pi$
$593$	28.4904	+	28.4904i	1.16996	+	1.16996i	0.187741	+	0.982219i	$0.439883\pi$
$594$		0			0
$595$		0			0
$596$	3.67949	−	2.12436i	0.150718	−	0.0870170i
$597$		0			0
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	−16.3301	−	28.2846i	−0.666120	−	1.15375i	−0.978980	−	0.203954i	$-0.934621\pi$
$601$	−16.3301	−	28.2846i	−0.666120	−	1.15375i	0.312861	−	0.949799i	$-0.398713\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.47372	−	24.5526i	−0.0599153	−	0.998203i
$606$		0			0
$607$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$607$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$608$		0			0
$609$		0			0
$610$	9.29423	−	45.4186i	0.376312	−	1.83894i
$611$		0			0
$612$	30.5885	+	30.5885i	1.23647	+	1.23647i
$613$	−10.9115	+	40.7224i	−0.440713	+	1.64476i	0.286300	+	0.958140i	$0.407575\pi$
$613$	−10.9115	+	40.7224i	−0.440713	+	1.64476i	−0.727013	+	0.686624i	$0.759092\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−11.6436	−	43.4545i	−0.468753	−	1.74941i	−0.644136	−	0.764911i	$-0.722783\pi$
$617$	−11.6436	−	43.4545i	−0.468753	−	1.74941i	0.175382	−	0.984500i	$-0.443884\pi$
$618$		0			0
$619$		0			0		1.00000			$0$
$619$		0			0		−1.00000			$\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$	−43.3013	+	25.0000i	−1.73067	+	0.999201i
$627$		0			0
$628$	8.94744	+	33.3923i	0.357042	+	1.33250i
$629$	−8.46410			−0.337486
$630$		0			0
$631$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$631$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$632$		0			0
$633$		0			0
$634$	−40.0981	+	23.1506i	−1.59250	+	0.919429i
$635$		0			0
$636$		0			0
$637$	22.6244	−	11.1865i	0.896410	−	0.443227i
$638$		0			0
$639$		0			0
$640$	−8.00000	−	24.0000i	−0.316228	−	0.948683i
$641$	−23.6506	+	40.9641i	−0.934144	+	1.61798i	−0.157991	+	0.987441i	$0.550502\pi$
$641$	−23.6506	+	40.9641i	−0.934144	+	1.61798i	−0.776153	+	0.630544i	$0.782832\pi$
$642$		0			0
$643$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$643$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$647$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$648$	6.58846	−	24.5885i	0.258819	−	0.965926i
$649$		0			0
$650$	17.0000	−	19.0000i	0.666795	−	0.745241i
$651$		0			0
$652$		0			0
$653$	−47.8109	−	12.8109i	−1.87098	−	0.501329i	−0.999949	−	0.0101092i	$-0.996782\pi$
$653$	−47.8109	−	12.8109i	−1.87098	−	0.501329i	−0.871036	−	0.491220i	$-0.836551\pi$
$654$		0			0
$655$		0			0
$656$	6.67949	+	3.85641i	0.260790	+	0.150567i
$657$	−10.7942	−	40.2846i	−0.421123	−	1.57165i
$658$		0			0
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$		0			0
$661$	30.6506	−	17.6962i	1.19217	−	0.688301i	0.233373	−	0.972387i	$-0.425024\pi$
$661$	30.6506	−	17.6962i	1.19217	−	0.688301i	0.958799	+	0.284087i	$0.0916904\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	2.49038	+	4.31347i	0.0965003	+	0.167143i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	36.9186	+	9.89230i	1.42311	+	0.381320i	0.886585	−	0.462566i	$-0.153071\pi$
$673$	36.9186	+	9.89230i	1.42311	+	0.381320i	0.536522	+	0.843886i	$0.319738\pi$
$674$	−6.43782	−	11.1506i	−0.247976	−	0.429506i
$675$		0			0
$676$	20.6603	+	15.7846i	0.794625	+	0.607100i
$677$	25.0000	+	25.0000i	0.960828	+	0.960828i	0.999261	−	0.0384331i	$-0.0122367\pi$
$677$	25.0000	+	25.0000i	0.960828	+	0.960828i	−0.0384331	+	0.999261i	$0.512237\pi$
$678$		0			0
$679$		0			0
$680$	−45.5167	+	2.73205i	−1.74548	+	0.104769i
$681$		0			0
$682$		0			0
$683$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$683$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$684$		0			0
$685$	39.0167	+	34.5981i	1.49075	+	1.32192i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	39.4282	−	34.6506i	1.50209	−	1.32008i
$690$		0			0
$691$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$691$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$692$	10.9808	−	40.9808i	0.417426	−	1.55785i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	9.83013	−	9.83013i	0.372343	−	0.372343i
$698$	−3.66025	−	13.6603i	−0.138543	−	0.517048i
$699$		0			0
$700$		0			0
$701$	52.0000			1.96401			0.982006	−	0.188847i	$-0.0604752\pi$
$701$	52.0000			1.96401			0.982006	+	0.188847i	$0.0604752\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	17.1506	−	29.7058i	0.645473	−	1.11799i
$707$		0			0
$708$		0			0
$709$	−26.5526	+	45.9904i	−0.997202	+	1.72721i	−0.433865	+	0.900978i	$0.642851\pi$
$709$	−26.5526	+	45.9904i	−0.997202	+	1.72721i	−0.563337	+	0.826227i	$0.690483\pi$
$710$		0			0
$711$		0			0
$712$	−7.32051	+	27.3205i	−0.274348	+	1.02388i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$	14.7846	+	22.3923i	0.550990	+	0.834512i
$721$		0			0
$722$	6.95448	+	25.9545i	0.258819	+	0.965926i
$723$		0			0
$724$	−45.5885	−	26.3205i	−1.69428	−	0.978194i
$725$	−3.98334	−	33.0622i	−0.147938	−	1.22790i
$726$		0			0
$727$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$727$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$	39.3205	+	19.6603i	1.45532	+	0.727659i
$731$		0			0
$732$		0			0
$733$	−36.1506	−	36.1506i	−1.33525	−	1.33525i	−0.900595	−	0.434659i	$-0.856869\pi$
$733$	−36.1506	−	36.1506i	−1.33525	−	1.33525i	−0.434659	−	0.900595i	$-0.643131\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−7.90192	−	2.11731i	−0.290874	−	0.0779394i
$739$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$739$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$740$	−5.14359	−	1.05256i	−0.189082	−	0.0386928i
$741$		0			0
$742$		0			0
$743$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$743$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$744$		0			0
$745$	−0.284610	−	4.74167i	−0.0104273	−	0.173721i
$746$		−	5.94744i		−	0.217751i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$		0			0
$753$		0			0
$754$	33.3013	−	6.66025i	1.21276	−	0.242552i
$755$		0			0
$756$		0			0
$757$	12.8109	−	47.8109i	0.465620	−	1.73772i	−0.189207	−	0.981937i	$-0.560592\pi$
$757$	12.8109	−	47.8109i	0.465620	−	1.73772i	0.654827	−	0.755779i	$-0.272742\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	34.6410	+	20.0000i	1.25574	+	0.724999i	0.972243	−	0.233975i	$-0.0751733\pi$
$761$	34.6410	+	20.0000i	1.25574	+	0.724999i	0.283493	+	0.958974i	$0.408507\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	45.8827	−	15.2942i	1.65889	−	0.552964i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.825518	+	0.564376i	$0.190883\pi$
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.0760054	+	0.997107i	$0.475783\pi$
$770$		0			0
$771$		0			0
$772$	−27.6603	+	27.6603i	−0.995514	+	0.995514i
$773$	53.2750	−	14.2750i	1.91617	−	0.513436i	0.925172	−	0.379549i	$-0.123921\pi$
$773$	53.2750	−	14.2750i	1.91617	−	0.513436i	0.990997	−	0.133887i	$-0.0427458\pi$
$774$		0			0
$775$		0			0
$776$	26.0000	−	45.0333i	0.933346	−	1.61660i
$777$		0			0
$778$	−0.117314	+	0.437822i	−0.00420591	+	0.0156967i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−24.2487	−	14.0000i	−0.866025	−	0.500000i
$785$	37.8660	+	7.74871i	1.35150	+	0.276563i
$786$		0			0
$787$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$787$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$788$	−26.0000	−	26.0000i	−0.926212	−	0.926212i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	29.3205	−	43.9808i	1.04120	−	1.56180i
$794$			26.0000i			0.922705i
$795$		0			0
$796$		0			0
$797$	20.4904	−	5.49038i	0.725807	−	0.194479i	0.123045	−	0.992401i	$-0.460734\pi$
$797$	20.4904	−	5.49038i	0.725807	−	0.194479i	0.602761	+	0.797922i	$0.294067\pi$
$798$		0			0
$799$		0			0
$800$	−28.0000	−	4.00000i	−0.989949	−	0.141421i
$801$		−	30.0000i		−	1.06000i
$802$	−24.9545	+	6.68653i	−0.881173	+	0.236110i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−11.9474	+	44.5885i	−0.420310	+	1.56862i
$809$	16.7487	−	9.66987i	0.588853	−	0.339975i	−0.175791	−	0.984428i	$-0.556248\pi$
$809$	16.7487	−	9.66987i	0.588853	−	0.339975i	0.764644	+	0.644453i	$0.222915\pi$
$810$	−21.2942	−	18.8827i	−0.748203	−	0.663470i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	14.8038	−	14.8038i	0.517604	−	0.517604i
$819$		0			0
$820$	7.19615	−	4.75129i	0.251301	−	0.165922i
$821$	43.3013	−	25.0000i	1.51122	−	0.872506i	0.511311	−	0.859396i	$-0.329160\pi$
$821$	43.3013	−	25.0000i	1.51122	−	0.872506i	0.999914	−	0.0131101i	$-0.00417319\pi$
$822$		0			0
$823$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$823$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$827$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$828$		0			0
$829$	−8.38269	+	4.83975i	−0.291143	+	0.168091i	−0.638457	−	0.769657i	$-0.720427\pi$
$829$	−8.38269	+	4.83975i	−0.291143	+	0.168091i	0.347314	+	0.937749i	$0.387094\pi$
$830$		0			0
$831$		0			0
$832$	1.85641	−	28.7846i	0.0643593	−	0.997927i
$833$	−35.6865	+	35.6865i	−1.23647	+	1.23647i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$839$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$840$		0			0
$841$	7.67949	−	13.3013i	0.264810	−	0.458664i
$842$	14.3660	−	53.6147i	0.495086	−	1.84769i
$843$		0			0
$844$		0			0
$845$	26.1147	−	12.7679i	0.898374	−	0.439231i
$846$		0			0
$847$		0			0
$848$	−56.2487	−	15.0718i	−1.93159	−	0.517568i
$849$		0			0
$850$	−20.0263	+	46.8827i	−0.686896	+	1.60806i
$851$		0			0
$852$		0			0
$853$	−16.1699	−	16.1699i	−0.553646	−	0.553646i	0.373845	−	0.927491i	$-0.378039\pi$
$853$	−16.1699	−	16.1699i	−0.553646	−	0.553646i	−0.927491	+	0.373845i	$0.878039\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	16.0788	+	16.0788i	0.549243	+	0.549243i	0.926222	−	0.376979i	$-0.123037\pi$
$857$	16.0788	+	16.0788i	0.549243	+	0.549243i	−0.376979	+	0.926222i	$0.623037\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$863$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$864$		0			0
$865$	−35.4904	−	31.4711i	−1.20671	−	1.07005i
$866$			55.2295i			1.87677i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	40.0000	+	40.0000i	1.35457	+	1.35457i
$873$	−14.2750	+	53.2750i	−0.483135	+	1.80309i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.88526	+	25.6962i	0.232499	+	0.867697i	0.979260	+	0.202606i	$0.0649409\pi$
$877$	6.88526	+	25.6962i	0.232499	+	0.867697i	−0.746762	+	0.665092i	$0.768392\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−29.6506	−	51.3564i	−0.998955	−	1.73024i	−0.539054	−	0.842271i	$-0.681218\pi$
$881$	−29.6506	−	51.3564i	−0.998955	−	1.73024i	−0.459902	−	0.887970i	$-0.652115\pi$
$882$	28.6865	+	7.68653i	0.965926	+	0.258819i
$883$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$883$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$884$	−49.2487	−	16.6603i	−1.65641	−	0.560345i
$885$		0			0
$886$		0			0
$887$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$887$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$888$		0			0
$889$		0			0
$890$	23.6603	+	20.9808i	0.793094	+	0.703277i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	40.0000	−	40.0000i	1.33482	−	1.33482i
$899$		0			0
$900$	29.7846	−	3.58846i	0.992820	−	0.119615i
$901$	−52.4808	+	90.8993i	−1.74839	+	3.02830i
$902$		0			0
$903$		0			0
$904$	16.7321	−	28.9808i	0.556500	−	0.963886i
$905$	−49.1147	+	32.4282i	−1.63263	+	1.07795i
$906$		0			0
$907$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$907$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$908$		0			0
$909$		−	48.9615i		−	1.62395i
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$	52.2224	+	30.1506i	1.72736	+	0.997294i
$915$		0			0
$916$	51.9615	+	30.0000i	1.71686	+	0.991228i
$917$		0			0
$918$		0			0
$919$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$919$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$920$		0			0
$921$		0			0
$922$	−42.9090	−	42.9090i	−1.41313	−	1.41313i
$923$		0			0
$924$		0			0
$925$	−3.62436	+	4.61731i	−0.119168	+	0.151816i
$926$		0			0
$927$		0			0
$928$	−26.6410	−	26.6410i	−0.874534	−	0.874534i
$929$	29.9186	−	51.8205i	0.981597	−	1.70018i	0.325418	−	0.945570i	$-0.394495\pi$
$929$	29.9186	−	51.8205i	0.981597	−	1.70018i	0.656179	−	0.754606i	$-0.272172\pi$
$930$		0			0
$931$		0			0
$932$	−13.6603	+	3.66025i	−0.447456	+	0.119896i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	6.00000	+	30.0000i	0.196116	+	0.980581i
$937$	−34.7391	−	34.7391i	−1.13488	−	1.13488i	−0.989355	−	0.145522i	$-0.953514\pi$
$937$	−34.7391	−	34.7391i	−1.13488	−	1.13488i	−0.145522	−	0.989355i	$-0.546486\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$			20.0000i			0.651981i	0.945373	+	0.325991i	$0.105698\pi$
$941$			20.0000i			0.651981i	−0.945373	+	0.325991i	$0.894302\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$947$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$948$		0			0
$949$	33.0885	+	37.6506i	1.07410	+	1.22219i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	5.49038	+	20.4904i	0.177851	+	0.663749i	0.996048	+	0.0888114i	$0.0283068\pi$
$953$	5.49038	+	20.4904i	0.177851	+	0.663749i	−0.818198	+	0.574937i	$0.805026\pi$
$954$	61.7654			1.99973
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−31.0000			−1.00000
$962$	−4.98076	−	3.32051i	−0.160586	−	0.107057i
$963$		0			0
$964$	8.07180	+	13.9808i	0.259975	+	0.450290i
$965$	13.8301	+	41.4904i	0.445208	+	1.33562i
$966$		0			0
$967$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$967$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$968$	−30.0526	+	8.05256i	−0.965926	+	0.258819i
$969$		0			0
$970$	−32.0333	−	48.5167i	−1.02853	−	1.55778i
$971$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$971$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−58.6410			−1.87705
$977$	−22.9641	−	6.15321i	−0.734687	−	0.196859i	−0.127971	−	0.991778i	$-0.540847\pi$
$977$	−22.9641	−	6.15321i	−0.734687	−	0.196859i	−0.606715	+	0.794919i	$0.707513\pi$
$978$		0			0
$979$		0			0
$980$	−26.1244	+	17.2487i	−0.834512	+	0.550990i
$981$	−51.9615	−	30.0000i	−1.65900	−	0.957826i
$982$		0			0
$983$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$983$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$984$		0			0
$985$	−39.0000	+	13.0000i	−1.24264	+	0.414214i
$986$	−58.8109	+	33.9545i	−1.87292	+	1.08133i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$991$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	26.6962	−	7.15321i	0.845476	−	0.226545i	0.190022	−	0.981780i	$-0.439144\pi$
$997$	26.6962	−	7.15321i	0.845476	−	0.226545i	0.655454	+	0.755235i	$0.272477\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bg.a.127.1	yes	4
4.3	odd	2	CM	260.2.bg.a.127.1	yes	4
5.3	odd	4		260.2.bg.b.23.1	yes	4
13.4	even	6		260.2.bg.b.147.1	yes	4
20.3	even	4		260.2.bg.b.23.1	yes	4
52.43	odd	6		260.2.bg.b.147.1	yes	4
65.43	odd	12	inner	260.2.bg.a.43.1	✓	4
260.43	even	12	inner	260.2.bg.a.43.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bg.a.43.1	✓	4	65.43	odd	12	inner
260.2.bg.a.43.1	✓	4	260.43	even	12	inner
260.2.bg.a.127.1	yes	4	1.1	even	1	trivial
260.2.bg.a.127.1	yes	4	4.3	odd	2	CM
260.2.bg.b.23.1	yes	4	5.3	odd	4
260.2.bg.b.23.1	yes	4	20.3	even	4
260.2.bg.b.147.1	yes	4	13.4	even	6
260.2.bg.b.147.1	yes	4	52.43	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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(1.86603 - 1.23205i) q^{5} +(-2.00000 - 2.00000i) q^{8} +(2.59808 + 1.50000i) q^{9} +O(q^{10})\)	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(1.86603 - 1.23205i) q^{5} +(-2.00000 - 2.00000i) q^{8} +(2.59808 + 1.50000i) q^{9} +(-3.00000 + 1.00000i) q^{10} +(-3.59808 - 0.232051i) q^{13} +(2.00000 + 3.46410i) q^{16} +(6.96410 - 1.86603i) q^{17} +(-3.00000 - 3.00000i) q^{18} +(4.46410 - 0.267949i) q^{20} +(1.96410 - 4.59808i) q^{25} +(4.83013 + 1.63397i) q^{26} +(5.76795 - 3.33013i) q^{29} +(-1.46410 - 5.46410i) q^{32} -10.1962 q^{34} +(3.00000 + 5.19615i) q^{36} +(-1.13397 - 0.303848i) q^{37} +(-6.19615 - 1.26795i) q^{40} +(1.66987 - 0.964102i) q^{41} +(6.69615 - 0.401924i) q^{45} +(-6.06218 + 3.50000i) q^{49} +(-4.36603 + 5.56218i) q^{50} +(-6.00000 - 4.00000i) q^{52} +(-10.2942 + 10.2942i) q^{53} +(-9.09808 + 2.43782i) q^{58} +(-7.33013 + 12.6962i) q^{61} +8.00000i q^{64} +(-7.00000 + 4.00000i) q^{65} +(13.9282 + 3.73205i) q^{68} +(-2.19615 - 8.19615i) q^{72} +(-9.83013 - 9.83013i) q^{73} +(1.43782 + 0.830127i) q^{74} +(8.00000 + 4.00000i) q^{80} +(4.50000 + 7.79423i) q^{81} +(-2.63397 + 0.705771i) q^{82} +(10.6962 - 12.0622i) q^{85} +(-5.00000 - 8.66025i) q^{89} +(-9.29423 - 1.90192i) q^{90} +(4.75833 + 17.7583i) q^{97} +(9.56218 - 2.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 4 q^{5} - 8 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 + 4 * q^5 - 8 * q^8	\( 4 q - 2 q^{2} + 4 q^{5} - 8 q^{8} - 12 q^{10} - 4 q^{13} + 8 q^{16} + 14 q^{17} - 12 q^{18} + 4 q^{20} - 6 q^{25} + 2 q^{26} + 30 q^{29} + 8 q^{32} - 20 q^{34} + 12 q^{36} - 8 q^{37} - 4 q^{40} + 24 q^{41} + 6 q^{45} - 14 q^{50} - 24 q^{52} - 10 q^{53} - 26 q^{58} - 12 q^{61} - 28 q^{65} + 28 q^{68} + 12 q^{72} - 22 q^{73} + 30 q^{74} + 32 q^{80} + 18 q^{81} - 14 q^{82} + 22 q^{85} - 20 q^{89} - 6 q^{90} - 26 q^{97} + 14 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 4 * q^5 - 8 * q^8 - 12 * q^10 - 4 * q^13 + 8 * q^16 + 14 * q^17 - 12 * q^18 + 4 * q^20 - 6 * q^25 + 2 * q^26 + 30 * q^29 + 8 * q^32 - 20 * q^34 + 12 * q^36 - 8 * q^37 - 4 * q^40 + 24 * q^41 + 6 * q^45 - 14 * q^50 - 24 * q^52 - 10 * q^53 - 26 * q^58 - 12 * q^61 - 28 * q^65 + 28 * q^68 + 12 * q^72 - 22 * q^73 + 30 * q^74 + 32 * q^80 + 18 * q^81 - 14 * q^82 + 22 * q^85 - 20 * q^89 - 6 * q^90 - 26 * q^97 + 14 * q^98

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