LMFDB - Embedded newform 260.2.bg.b.147.1

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			147.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	260.147
Dual form			260.2.bg.b.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(2.00000 + 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})$	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(2.00000 + 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +(2.36603 + 2.09808i) q^{10} +(0.232051 + 3.59808i) q^{13} +(2.00000 - 3.46410i) q^{16} +(-1.86603 + 6.96410i) q^{17} +(3.00000 + 3.00000i) q^{18} +(2.00000 - 4.00000i) q^{20} +(1.96410 - 4.59808i) q^{25} +(4.83013 - 1.63397i) q^{26} +(-5.76795 - 3.33013i) q^{29} +(-5.46410 - 1.46410i) q^{32} +10.1962 q^{34} +(3.00000 - 5.19615i) q^{36} +(-0.303848 - 1.13397i) q^{37} +(-6.19615 - 1.26795i) q^{40} +(1.66987 + 0.964102i) q^{41} +(3.00000 - 6.00000i) q^{45} +(6.06218 + 3.50000i) q^{49} +(-7.00000 - 1.00000i) q^{50} +(-4.00000 - 6.00000i) q^{52} +(-10.2942 + 10.2942i) q^{53} +(-2.43782 + 9.09808i) q^{58} +(-7.33013 - 12.6962i) q^{61} +8.00000i q^{64} +(-4.86603 - 6.42820i) q^{65} +(-3.73205 - 13.9282i) q^{68} +(-8.19615 - 2.19615i) q^{72} +(9.83013 + 9.83013i) q^{73} +(-1.43782 + 0.830127i) q^{74} +(0.535898 + 8.92820i) q^{80} +(4.50000 - 7.79423i) q^{81} +(0.705771 - 2.63397i) q^{82} +(-5.09808 - 15.2942i) q^{85} +(5.00000 - 8.66025i) q^{89} +(-9.29423 - 1.90192i) q^{90} +(17.7583 + 4.75833i) q^{97} +(2.56218 - 9.56218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 6 q^{10} - 6 q^{13} + 8 q^{16} - 4 q^{17} + 12 q^{18} + 8 q^{20} - 6 q^{25} + 2 q^{26} - 30 q^{29} - 8 q^{32} + 20 q^{34} + 12 q^{36} - 22 q^{37} - 4 q^{40} + 24 q^{41} + 12 q^{45} - 28 q^{50} - 16 q^{52} - 10 q^{53} - 34 q^{58} - 12 q^{61} - 16 q^{65} - 8 q^{68} - 12 q^{72} + 22 q^{73} - 30 q^{74} + 16 q^{80} + 18 q^{81} + 34 q^{82} - 10 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 + 6 * q^10 - 6 * q^13 + 8 * q^16 - 4 * q^17 + 12 * q^18 + 8 * q^20 - 6 * q^25 + 2 * q^26 - 30 * q^29 - 8 * q^32 + 20 * q^34 + 12 * q^36 - 22 * q^37 - 4 * q^40 + 24 * q^41 + 12 * q^45 - 28 * q^50 - 16 * q^52 - 10 * q^53 - 34 * q^58 - 12 * q^61 - 16 * q^65 - 8 * q^68 - 12 * q^72 + 22 * q^73 - 30 * q^74 + 16 * q^80 + 18 * q^81 + 34 * q^82 - 10 * 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 $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i
$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i
$3$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$3$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$4$	−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		−0.965926	−	0.258819i	$-0.916667\pi$
$7$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	−2.59808	+	1.50000i	−0.866025	+	0.500000i
$10$	2.36603	+	2.09808i	0.748203	+	0.663470i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$		0			0
$13$	0.232051	+	3.59808i	0.0643593	+	0.997927i
$13$	0.232051	+	3.59808i	0.0643593	+	0.997927i
$14$		0			0
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−1.86603	+	6.96410i	−0.452578	+	1.68904i	0.242536	+	0.970143i	$0.422021\pi$
$17$	−1.86603	+	6.96410i	−0.452578	+	1.68904i	−0.695113	+	0.718900i	$0.744646\pi$
$18$	3.00000	+	3.00000i	0.707107	+	0.707107i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	2.00000	−	4.00000i	0.447214	−	0.894427i
$21$		0			0
$22$		0			0
$23$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$23$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$24$		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	$-0.545548\pi$
$29$	−5.76795	−	3.33013i	−1.07108	−	0.618389i	−0.928477	+	0.371391i	$0.878881\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−5.46410	−	1.46410i	−0.965926	−	0.258819i
$33$		0			0
$34$	10.1962			1.74863
$35$		0			0
$36$	3.00000	−	5.19615i	0.500000	−	0.866025i
$37$	−0.303848	−	1.13397i	−0.0499522	−	0.186424i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	−0.303848	−	1.13397i	−0.0499522	−	0.186424i	−0.986394	+	0.164399i	$0.947432\pi$
$38$		0			0
$39$		0			0
$40$	−6.19615	−	1.26795i	−0.979698	−	0.200480i
$41$	1.66987	+	0.964102i	0.260790	+	0.150567i	0.624695	−	0.780869i	$-0.285223\pi$
$41$	1.66987	+	0.964102i	0.260790	+	0.150567i	−0.363905	+	0.931436i	$0.618557\pi$
$42$		0			0
$43$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$43$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$44$		0			0
$45$	3.00000	−	6.00000i	0.447214	−	0.894427i
$46$		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
$50$	−7.00000	−	1.00000i	−0.989949	−	0.141421i
$51$		0			0
$52$	−4.00000	−	6.00000i	−0.554700	−	0.832050i
$53$	−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
$58$	−2.43782	+	9.09808i	−0.320102	+	1.19464i
$59$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$59$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$60$		0			0
$61$	−7.33013	−	12.6962i	−0.938527	−	1.62558i	−0.768221	−	0.640184i	$-0.778858\pi$
$61$	−7.33013	−	12.6962i	−0.938527	−	1.62558i	−0.170305	−	0.985391i	$-0.554475\pi$
$62$		0			0
$63$		0			0
$64$			8.00000i			1.00000i
$65$	−4.86603	−	6.42820i	−0.603556	−	0.797320i
$66$		0			0
$67$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$67$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$68$	−3.73205	−	13.9282i	−0.452578	−	1.68904i
$69$		0			0
$70$		0			0
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$	−8.19615	−	2.19615i	−0.965926	−	0.258819i
$73$	9.83013	+	9.83013i	1.15053	+	1.15053i	0.986447	+	0.164083i	$0.0524664\pi$
$73$	9.83013	+	9.83013i	1.15053	+	1.15053i	0.164083	+	0.986447i	$0.447534\pi$
$74$	−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	$0.5\pi$
$80$	0.535898	+	8.92820i	0.0599153	+	0.998203i
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$	0.705771	−	2.63397i	0.0779394	−	0.290874i
$83$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$83$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$84$		0			0
$85$	−5.09808	−	15.2942i	−0.552964	−	1.65889i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.00000	−	8.66025i	0.529999	−	0.917985i	−0.469389	−	0.882992i	$-0.655526\pi$
$89$	5.00000	−	8.66025i	0.529999	−	0.917985i	0.999388	−	0.0349934i	$-0.0111410\pi$
$90$	−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
$97$	17.7583	+	4.75833i	1.80309	+	0.483135i	0.994453	−	0.105180i	$-0.0335417\pi$
$97$	17.7583	+	4.75833i	1.80309	+	0.483135i	0.808632	+	0.588315i	$0.200208\pi$
$98$	2.56218	−	9.56218i	0.258819	−	0.965926i
$99$		0			0
$100$	1.19615	+	9.92820i	0.119615	+	0.992820i
$101$	−8.16025	+	14.1340i	−0.811976	+	1.40638i	0.0995037	+	0.995037i	$0.468274\pi$
$101$	−8.16025	+	14.1340i	−0.811976	+	1.40638i	−0.911479	+	0.411346i	$0.865059\pi$
$102$		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		0.965926	−	0.258819i	$-0.0833333\pi$
$107$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$108$		0			0
$109$	20.0000			1.91565			0.957826	−	0.287348i	$-0.0927736\pi$
$109$	20.0000			1.91565			0.957826	+	0.287348i	$0.0927736\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−11.4282	−	3.06218i	−1.07507	−	0.288065i	−0.322498	−	0.946570i	$-0.604523\pi$
$113$	−11.4282	−	3.06218i	−1.07507	−	0.288065i	−0.752577	+	0.658505i	$0.771189\pi$
$114$		0			0
$115$		0			0
$116$	13.3205			1.23678
$117$	−6.00000	−	9.00000i	−0.554700	−	0.832050i
$118$		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		0.965926	−	0.258819i	$-0.0833333\pi$
$127$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$128$	10.9282	−	2.92820i	0.965926	−	0.258819i
$129$		0			0
$130$	−7.00000	+	9.00000i	−0.613941	+	0.789352i
$131$		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
$137$	22.5263	+	6.03590i	1.92455	+	0.515682i	0.984757	+	0.173939i	$0.0556494\pi$
$137$	22.5263	+	6.03590i	1.92455	+	0.515682i	0.939793	+	0.341743i	$0.111017\pi$
$138$		0			0
$139$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$139$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$			12.0000i			1.00000i
$145$	14.8660	−	0.892305i	1.23456	−	0.0741019i
$146$	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	$-0.194400\pi$
$149$	−1.06218	−	1.83975i	−0.0870170	−	0.150718i	−0.906249	+	0.422744i	$0.861067\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$		0			0
$153$	−5.59808	−	20.8923i	−0.452578	−	1.68904i
$154$		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
$160$	12.0000	−	4.00000i	0.948683	−	0.316228i
$161$		0			0
$162$	−12.2942	−	3.29423i	−0.965926	−	0.258819i
$163$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$163$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$164$	−3.85641			−0.301135
$165$		0			0
$166$		0			0
$167$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$167$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$168$		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
$173$	20.4904	+	5.49038i	1.55785	+	0.417426i	0.931984	−	0.362500i	$-0.118077\pi$
$173$	20.4904	+	5.49038i	1.55785	+	0.417426i	0.625871	+	0.779926i	$0.284744\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−13.6603	−	3.66025i	−1.02388	−	0.274348i
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$	0.803848	+	13.3923i	0.0599153	+	0.998203i
$181$	−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
$185$	1.96410	+	1.74167i	0.144404	+	0.128050i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$191$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$192$		0			0
$193$	−18.8923	+	5.06218i	−1.35990	+	0.364384i	−0.863779	−	0.503871i	$-0.831909\pi$
$193$	−18.8923	+	5.06218i	−1.35990	+	0.364384i	−0.496119	+	0.868255i	$0.665242\pi$
$194$		−	26.0000i		−	1.86669i
$195$		0			0
$196$	−14.0000			−1.00000
$197$	−4.75833	−	17.7583i	−0.339017	−	1.26523i	−0.899448	−	0.437028i	$-0.856031\pi$
$197$	−4.75833	−	17.7583i	−0.339017	−	1.26523i	0.560431	−	0.828201i	$-0.310635\pi$
$198$		0			0
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$	13.1244	−	5.26795i	0.928032	−	0.372500i
$201$		0			0
$202$	22.2942	+	5.97372i	1.56862	+	0.420310i
$203$		0			0
$204$		0			0
$205$	−4.30385	+	0.258330i	−0.300594	+	0.0180426i
$206$		0			0
$207$		0			0
$208$	12.9282	+	6.39230i	0.896410	+	0.443227i
$209$		0			0
$210$		0			0
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$	7.53590	−	28.1244i	0.517568	−	1.93159i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−7.32051	−	27.3205i	−0.495807	−	1.85038i
$219$		0			0
$220$		0			0
$221$	−25.4904	−	5.09808i	−1.71467	−	0.342934i
$222$		0			0
$223$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$223$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$224$		0			0
$225$	1.79423	+	14.8923i	0.119615	+	0.992820i
$226$			16.7321i			1.11300i
$227$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$227$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$228$		0			0
$229$	−30.0000			−1.98246			−0.991228	−	0.132164i	$-0.957808\pi$
$229$	−30.0000			−1.98246			−0.991228	+	0.132164i	$0.957808\pi$
$230$		0			0
$231$		0			0
$232$	−4.87564	−	18.1962i	−0.320102	−	1.19464i
$233$	−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	−0.257663	−	0.966235i	$-0.582952\pi$
$241$	6.99038	−	4.03590i	0.450290	−	0.259975i	0.707953	+	0.706260i	$0.249619\pi$
$242$	11.0000	−	11.0000i	0.707107	−	0.707107i
$243$		0			0
$244$	25.3923	+	14.6603i	1.62558	+	0.938527i
$245$	−15.6244	+	0.937822i	−0.998203	+	0.0599153i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	14.2942	−	6.75833i	0.904046	−	0.427434i
$251$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$251$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−9.86603	+	2.64359i	−0.615426	+	0.164903i	−0.553047	−	0.833150i	$-0.686535\pi$
$257$	−9.86603	+	2.64359i	−0.615426	+	0.164903i	−0.0623783	+	0.998053i	$0.519869\pi$
$258$		0			0
$259$		0			0
$260$	14.8564	+	6.26795i	0.921355	+	0.388722i
$261$	19.9808			1.23678
$262$		0			0
$263$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$263$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$264$		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	$-0.375381\pi$
$269$	22.5167	−	13.0000i	1.37287	−	0.792624i	0.991288	+	0.131713i	$0.0420477\pi$
$270$		0			0
$271$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$271$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$272$	20.3923	+	20.3923i	1.23647	+	1.23647i
$273$		0			0
$274$		−	32.9808i		−	1.99244i
$275$		0			0
$276$		0			0
$277$	−6.37564	+	23.7942i	−0.383075	+	1.42966i	0.458103	+	0.888899i	$0.348529\pi$
$277$	−6.37564	+	23.7942i	−0.383075	+	1.42966i	−0.841178	+	0.540758i	$0.818138\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			32.7128i			1.95148i	0.218926	+	0.975741i	$0.429745\pi$
$281$			32.7128i			1.95148i	−0.218926	+	0.975741i	$0.570255\pi$
$282$		0			0
$283$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$283$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	16.3923	−	4.39230i	0.965926	−	0.258819i
$289$	−30.2942	−	17.4904i	−1.78201	−	1.02885i
$290$	−6.66025	−	19.9808i	−0.391104	−	1.17331i
$291$		0			0
$292$	−26.8564	−	7.19615i	−1.57165	−	0.421123i
$293$	1.27757	−	4.76795i	0.0746363	−	0.278547i	−0.918514	−	0.395388i	$-0.870610\pi$
$293$	1.27757	−	4.76795i	0.0746363	−	0.278547i	0.993151	+	0.116841i	$0.0372769\pi$
$294$		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
$305$	29.3205	+	14.6603i	1.67889	+	0.839444i
$306$	−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	$0.621349\pi$
$317$	−23.1506	+	23.1506i	−1.30027	+	1.30027i	−0.928208	+	0.372061i	$0.878651\pi$
$318$		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
$325$	17.0000	+	6.00000i	0.942990	+	0.332820i
$326$		0			0
$327$		0			0
$328$	1.41154	+	5.26795i	0.0779394	+	0.290874i
$329$		0			0
$330$		0			0
$331$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$331$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$332$		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	$0.670235\pi$
$338$	7.00000	+	17.0000i	0.380750	+	0.924678i
$339$		0			0
$340$	24.1244	+	21.3923i	1.30833	+	1.16016i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		−	30.0000i		−	1.61281i
$347$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$347$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$348$		0			0
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	−0.968253	−	0.249973i	$-0.919578\pi$
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	0.700609	+	0.713545i	$0.252912\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−23.4282	+	6.27757i	−1.24696	+	0.334121i	−0.821160	−	0.570697i	$-0.806673\pi$
$353$	−23.4282	+	6.27757i	−1.24696	+	0.334121i	−0.425797	+	0.904819i	$0.640006\pi$
$354$		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			$\pi$
$360$	18.0000	−	6.00000i	0.948683	−	0.316228i
$361$	−9.50000	+	16.4545i	−0.500000	+	0.866025i
$362$	9.63397	+	35.9545i	0.506350	+	1.88973i
$363$		0			0
$364$		0			0
$365$	−30.4545	−	6.23205i	−1.59406	−	0.326200i
$366$		0			0
$367$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$367$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$368$		0			0
$369$	−5.78461			−0.301135
$370$	1.66025	−	3.32051i	0.0863125	−	0.172625i
$371$		0			0
$372$		0			0
$373$	−4.06218	−	1.08846i	−0.210332	−	0.0563582i	0.152115	−	0.988363i	$-0.451392\pi$
$373$	−4.06218	−	1.08846i	−0.210332	−	0.0563582i	−0.362446	+	0.932005i	$0.618058\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	10.6436	−	21.5263i	0.548173	−	1.10866i
$378$		0			0
$379$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$379$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$383$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$384$		0			0
$385$		0			0
$386$	13.8301	+	23.9545i	0.703935	+	1.21925i
$387$		0			0
$388$	−35.5167	+	9.51666i	−1.80309	+	0.483135i
$389$		−	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
$392$	5.12436	+	19.1244i	0.258819	+	0.965926i
$393$		0			0
$394$	−22.5167	+	13.0000i	−1.13437	+	0.654931i
$395$		0			0
$396$		0			0
$397$	−17.7583	−	4.75833i	−0.891265	−	0.238814i	−0.216004	−	0.976392i	$-0.569302\pi$
$397$	−17.7583	−	4.75833i	−0.891265	−	0.238814i	−0.675261	+	0.737579i	$0.735969\pi$
$398$		0			0
$399$		0			0
$400$	−12.0000	−	16.0000i	−0.600000	−	0.800000i
$401$	15.8205	+	9.13397i	0.790038	+	0.456129i	0.839976	−	0.542623i	$-0.182569\pi$
$401$	15.8205	+	9.13397i	0.790038	+	0.456129i	−0.0499376	+	0.998752i	$0.515902\pi$
$402$		0			0
$403$		0			0
$404$		−	32.6410i		−	1.62395i
$405$	1.20577	+	20.0885i	0.0599153	+	0.998203i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	7.40192	+	12.8205i	0.366002	+	0.633933i	0.988936	−	0.148340i	$-0.0473931\pi$
$409$	7.40192	+	12.8205i	0.366002	+	0.633933i	−0.622935	+	0.782274i	$0.714060\pi$
$410$	1.92820	+	5.78461i	0.0952272	+	0.285682i
$411$		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	$-0.833333\pi$
$419$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$420$		0			0
$421$		−	39.2487i		−	1.91287i	−0.291953	−	0.956433i	$-0.594305\pi$
$421$		−	39.2487i		−	1.91287i	0.291953	−	0.956433i	$-0.405695\pi$
$422$		0			0
$423$		0			0
$424$	−41.1769			−1.99973
$425$	28.3564	+	22.2583i	1.37549	+	1.07969i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$		0			0
$433$	37.7224	+	10.1077i	1.81282	+	0.485745i	0.995857	−	0.0909384i	$-0.0289866\pi$
$433$	37.7224	+	10.1077i	1.81282	+	0.485745i	0.816968	+	0.576683i	$0.195653\pi$
$434$		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	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$	−21.0000			−1.00000
$442$	2.36603	+	36.6865i	0.112540	+	1.74500i
$443$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$443$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$444$		0			0
$445$	1.33975	+	22.3205i	0.0635100	+	1.05809i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	20.0000	+	34.6410i	0.943858	+	1.63481i	0.758021	+	0.652230i	$0.226166\pi$
$449$	20.0000	+	34.6410i	0.943858	+	1.63481i	0.185837	+	0.982581i	$0.440500\pi$
$450$	19.6865	−	7.90192i	0.928032	−	0.372500i
$451$		0			0
$452$	22.8564	−	6.12436i	1.07507	−	0.288065i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−11.0359	−	41.1865i	−0.516238	−	1.92662i	−0.329125	−	0.944286i	$-0.606754\pi$
$457$	−11.0359	−	41.1865i	−0.516238	−	1.92662i	−0.187112	−	0.982339i	$-0.559913\pi$
$458$	10.9808	+	40.9808i	0.513097	+	1.91491i
$459$		0			0
$460$		0			0
$461$	37.1603	−	21.4545i	1.73073	−	0.999235i	0.845807	−	0.533488i	$-0.179119\pi$
$461$	37.1603	−	21.4545i	1.73073	−	0.999235i	0.884918	−	0.465746i	$-0.154214\pi$
$462$		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	$0.250000\pi$
$468$	19.3923	+	9.58846i	0.896410	+	0.443227i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	11.3038	−	42.1865i	0.517568	−	1.93159i
$478$		0			0
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$		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
$485$	−39.0000	+	13.0000i	−1.77090	+	0.590300i
$486$		0			0
$487$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$487$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$488$	10.7321	−	40.0526i	0.485817	−	1.81309i
$489$		0			0
$490$	7.00000	+	21.0000i	0.316228	+	0.948683i
$491$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$491$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$492$		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			$\pi$
$500$	−14.4641	−	17.0526i	−0.646854	−	0.762614i
$501$		0			0
$502$		0			0
$503$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$503$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$504$		0			0
$505$	−2.18653	−	36.4282i	−0.0972995	−	1.62103i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	21.5526	−	37.3301i	0.955300	−	1.65463i	0.221621	−	0.975133i	$-0.428865\pi$
$509$	21.5526	−	37.3301i	0.955300	−	1.65463i	0.733679	−	0.679496i	$-0.237801\pi$
$510$		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
$520$	3.12436	−	22.5885i	0.137012	−	0.990569i
$521$	45.6410			1.99957			0.999785	−	0.0207541i	$-0.00660670\pi$
$521$	45.6410			1.99957			0.999785	+	0.0207541i	$0.00660670\pi$
$522$	−7.31347	−	27.2942i	−0.320102	−	1.19464i
$523$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$523$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−19.9186	+	11.5000i	−0.866025	+	0.500000i
$530$	−45.9545	+	2.75833i	−1.99614	+	0.119814i
$531$		0			0
$532$		0			0
$533$	−3.08142	+	6.23205i	−0.133471	+	0.269940i
$534$		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	$-0.808130\pi$
$541$		−	26.3731i		−	1.13387i	0.823764	−	0.566933i	$-0.191870\pi$
$542$		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	$0.250000\pi$
$548$	−45.0526	+	12.0718i	−1.92455	+	0.515682i
$549$	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
$557$	−4.45448	−	16.6244i	−0.188742	−	0.704397i	−0.993798	−	0.111198i	$-0.964531\pi$
$557$	−4.45448	−	16.6244i	−0.188742	−	0.704397i	0.805056	−	0.593199i	$-0.202135\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	44.6865	−	11.9737i	1.88499	−	0.505081i
$563$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$563$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$564$		0			0
$565$	25.0981	−	8.36603i	1.05588	−	0.351961i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	22.5167	+	13.0000i	0.943948	+	0.544988i	0.891196	−	0.453619i	$-0.149867\pi$
$569$	22.5167	+	13.0000i	0.943948	+	0.544988i	0.0527519	+	0.998608i	$0.483201\pi$
$570$		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	−0.463513	−	0.886090i	$-0.653411\pi$
$577$	10.1506	−	10.1506i	0.422576	−	0.422576i	0.886090	+	0.463513i	$0.153411\pi$
$578$	−12.8038	+	47.7846i	−0.532570	+	1.98758i
$579$		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
$585$	22.2846	+	9.40192i	0.921355	+	0.388722i
$586$	−6.98076			−0.288373
$587$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$587$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−4.53590	−	1.21539i	−0.186424	−	0.0499522i
$593$	−28.4904	−	28.4904i	−1.16996	−	1.16996i	−0.982219	−	0.187741i	$-0.939883\pi$
$593$	−28.4904	−	28.4904i	−1.16996	−	1.16996i	−0.187741	−	0.982219i	$-0.560117\pi$
$594$		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	0.312861	+	0.949799i	$0.398713\pi$
$601$	−16.3301	+	28.2846i	−0.666120	+	1.15375i	−0.978980	+	0.203954i	$0.934621\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−22.0000	−	11.0000i	−0.894427	−	0.447214i
$606$		0			0
$607$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$607$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$608$		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
$613$	−40.7224	+	10.9115i	−1.64476	+	0.440713i	−0.958140	−	0.286300i	$-0.907575\pi$
$613$	−40.7224	+	10.9115i	−1.64476	+	0.440713i	−0.686624	+	0.727013i	$0.740908\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−43.4545	−	11.6436i	−1.74941	−	0.468753i	−0.764911	−	0.644136i	$-0.777217\pi$
$617$	−43.4545	−	11.6436i	−1.74941	−	0.468753i	−0.984500	+	0.175382i	$0.943884\pi$
$618$		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
$628$	−33.3923	−	8.94744i	−1.33250	−	0.357042i
$629$	8.46410			0.337486
$630$		0			0
$631$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$631$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$632$		0			0
$633$		0			0
$634$	40.0981	+	23.1506i	1.59250	+	0.919429i
$635$		0			0
$636$		0			0
$637$	−11.1865	+	22.6244i	−0.443227	+	0.896410i
$638$		0			0
$639$		0			0
$640$	−16.7846	+	18.9282i	−0.663470	+	0.748203i
$641$	−23.6506	−	40.9641i	−0.934144	−	1.61798i	−0.776153	−	0.630544i	$-0.782832\pi$
$641$	−23.6506	−	40.9641i	−0.934144	−	1.61798i	−0.157991	−	0.987441i	$-0.550502\pi$
$642$		0			0
$643$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$643$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$647$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$648$	24.5885	−	6.58846i	0.965926	−	0.258819i
$649$		0			0
$650$	1.97372	−	25.4186i	0.0774157	−	0.996999i
$651$		0			0
$652$		0			0
$653$	12.8109	+	47.8109i	0.501329	+	1.87098i	0.491220	+	0.871036i	$0.336551\pi$
$653$	12.8109	+	47.8109i	0.501329	+	1.87098i	0.0101092	+	0.999949i	$0.496782\pi$
$654$		0			0
$655$		0			0
$656$	6.67949	−	3.85641i	0.260790	−	0.150567i
$657$	−40.2846	−	10.7942i	−1.57165	−	0.421123i
$658$		0			0
$659$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$659$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$660$		0			0
$661$	30.6506	+	17.6962i	1.19217	+	0.688301i	0.958799	−	0.284087i	$-0.0916904\pi$
$661$	30.6506	+	17.6962i	1.19217	+	0.688301i	0.233373	+	0.972387i	$0.425024\pi$
$662$		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
$673$	−9.89230	−	36.9186i	−0.381320	−	1.42311i	−0.843886	−	0.536522i	$-0.819738\pi$
$673$	−9.89230	−	36.9186i	−0.381320	−	1.42311i	0.462566	−	0.886585i	$-0.346929\pi$
$674$	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
$680$	20.3923	−	40.7846i	0.782009	−	1.56402i
$681$		0			0
$682$		0			0
$683$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$683$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$684$		0			0
$685$	−49.4711	+	16.4904i	−1.89020	+	0.630065i
$686$		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	$-0.833333\pi$
$691$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$692$	−40.9808	+	10.9808i	−1.55785	+	0.417426i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−9.83013	+	9.83013i	−0.372343	+	0.372343i
$698$	13.6603	+	3.66025i	0.517048	+	0.138543i
$699$		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	0.563337	+	0.826227i	$0.309517\pi$
$709$	26.5526	+	45.9904i	0.997202	+	1.72721i	0.433865	+	0.900978i	$0.357149\pi$
$710$		0			0
$711$		0			0
$712$	27.3205	−	7.32051i	1.02388	−	0.274348i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	−14.7846	−	22.3923i	−0.550990	−	0.834512i
$721$		0			0
$722$	25.9545	+	6.95448i	0.965926	+	0.258819i
$723$		0			0
$724$	45.5885	−	26.3205i	1.69428	−	0.978194i
$725$	−26.6410	+	19.9808i	−0.989423	+	0.742067i
$726$		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
$730$	2.63397	+	43.8827i	0.0974878	+	1.62417i
$731$		0			0
$732$		0			0
$733$	36.1506	+	36.1506i	1.33525	+	1.33525i	0.900595	+	0.434659i	$0.143131\pi$
$733$	36.1506	+	36.1506i	1.33525	+	1.33525i	0.434659	+	0.900595i	$0.356869\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	2.11731	+	7.90192i	0.0779394	+	0.290874i
$739$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$739$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$740$	−5.14359	−	1.05256i	−0.189082	−	0.0386928i
$741$		0			0
$742$		0			0
$743$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$743$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$744$		0			0
$745$	4.24871	+	2.12436i	0.155661	+	0.0778304i
$746$			5.94744i			0.217751i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$		0			0
$753$		0			0
$754$	−33.3013	−	6.66025i	−1.21276	−	0.242552i
$755$		0			0
$756$		0			0
$757$	−47.8109	+	12.8109i	−1.73772	+	0.465620i	−0.981937	−	0.189207i	$-0.939408\pi$
$757$	−47.8109	+	12.8109i	−1.73772	+	0.465620i	−0.755779	+	0.654827i	$0.772742\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	34.6410	−	20.0000i	1.25574	−	0.724999i	0.283493	−	0.958974i	$-0.408507\pi$
$761$	34.6410	−	20.0000i	1.25574	−	0.724999i	0.972243	+	0.233975i	$0.0751733\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	36.1865	+	32.0885i	1.30833	+	1.16016i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−25.0000	+	43.3013i	−0.901523	+	1.56148i	−0.0760054	+	0.997107i	$0.524217\pi$
$769$	−25.0000	+	43.3013i	−0.901523	+	1.56148i	−0.825518	+	0.564376i	$0.809117\pi$
$770$		0			0
$771$		0			0
$772$	27.6603	−	27.6603i	0.995514	−	0.995514i
$773$	14.2750	−	53.2750i	0.513436	−	1.91617i	0.133887	−	0.990997i	$-0.457254\pi$
$773$	14.2750	−	53.2750i	0.513436	−	1.91617i	0.379549	−	0.925172i	$-0.376079\pi$
$774$		0			0
$775$		0			0
$776$	26.0000	+	45.0333i	0.933346	+	1.61660i
$777$		0			0
$778$	−0.437822	+	0.117314i	−0.0156967	+	0.00420591i
$779$		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		−0.965926	−	0.258819i	$-0.916667\pi$
$787$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$788$	26.0000	+	26.0000i	0.926212	+	0.926212i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	43.9808	−	29.3205i	1.56180	−	1.04120i
$794$			26.0000i			0.922705i
$795$		0			0
$796$		0			0
$797$	−5.49038	+	20.4904i	−0.194479	+	0.725807i	0.797922	+	0.602761i	$0.205933\pi$
$797$	−5.49038	+	20.4904i	−0.194479	+	0.725807i	−0.992401	+	0.123045i	$0.960734\pi$
$798$		0			0
$799$		0			0
$800$	−17.4641	+	22.2487i	−0.617449	+	0.786611i
$801$			30.0000i			1.06000i
$802$	6.68653	−	24.9545i	0.236110	−	0.881173i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−44.5885	+	11.9474i	−1.56862	+	0.420310i
$809$	−16.7487	−	9.66987i	−0.588853	−	0.339975i	0.175791	−	0.984428i	$-0.443752\pi$
$809$	−16.7487	−	9.66987i	−0.588853	−	0.339975i	−0.764644	+	0.644453i	$0.777085\pi$
$810$	27.0000	−	9.00000i	0.948683	−	0.316228i
$811$		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	0.999914	+	0.0131101i	$0.00417319\pi$
$821$	43.3013	+	25.0000i	1.51122	+	0.872506i	0.511311	+	0.859396i	$0.329160\pi$
$822$		0			0
$823$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$823$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$824$		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	$-0.279573\pi$
$829$	8.38269	+	4.83975i	0.291143	+	0.168091i	−0.347314	+	0.937749i	$0.612906\pi$
$830$		0			0
$831$		0			0
$832$	−28.7846	+	1.85641i	−0.997927	+	0.0643593i
$833$	−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	$-0.666667\pi$
$839$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$840$		0			0
$841$	7.67949	+	13.3013i	0.264810	+	0.458664i
$842$	−53.6147	+	14.3660i	−1.84769	+	0.495086i
$843$		0			0
$844$		0			0
$845$	22.0000	−	19.0000i	0.756823	−	0.653620i
$846$		0			0
$847$		0			0
$848$	15.0718	+	56.2487i	0.517568	+	1.93159i
$849$		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	0.927491	−	0.373845i	$-0.121961\pi$
$853$	16.1699	+	16.1699i	0.553646	+	0.553646i	−0.373845	+	0.927491i	$0.621961\pi$
$854$		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
$865$	−45.0000	+	15.0000i	−1.53005	+	0.510015i
$866$		−	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
$873$	−53.2750	+	14.2750i	−1.80309	+	0.483135i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	25.6962	+	6.88526i	0.867697	+	0.232499i	0.665092	−	0.746762i	$-0.268392\pi$
$877$	25.6962	+	6.88526i	0.867697	+	0.232499i	0.202606	+	0.979260i	$0.435059\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−29.6506	+	51.3564i	−0.998955	+	1.73024i	−0.459902	+	0.887970i	$0.652115\pi$
$881$	−29.6506	+	51.3564i	−0.998955	+	1.73024i	−0.539054	+	0.842271i	$0.681218\pi$
$882$	7.68653	+	28.6865i	0.258819	+	0.965926i
$883$		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		0.965926	−	0.258819i	$-0.0833333\pi$
$887$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$888$		0			0
$889$		0			0
$890$	30.0000	−	10.0000i	1.00560	−	0.335201i
$891$		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
$900$	−18.0000	−	24.0000i	−0.600000	−	0.800000i
$901$	−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		0.965926	−	0.258819i	$-0.0833333\pi$
$907$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$908$		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	$-0.166667\pi$
$919$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$920$		0			0
$921$		0			0
$922$	−42.9090	−	42.9090i	−1.41313	−	1.41313i
$923$		0			0
$924$		0			0
$925$	−5.81089	−	0.830127i	−0.191061	−	0.0272944i
$926$		0			0
$927$		0			0
$928$	26.6410	+	26.6410i	0.874534	+	0.874534i
$929$	−29.9186	−	51.8205i	−0.981597	−	1.70018i	−0.656179	−	0.754606i	$-0.727828\pi$
$929$	−29.9186	−	51.8205i	−0.981597	−	1.70018i	−0.325418	−	0.945570i	$-0.605505\pi$
$930$		0			0
$931$		0			0
$932$	3.66025	−	13.6603i	0.119896	−	0.447456i
$933$		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	$-0.894302\pi$
$941$		−	20.0000i		−	0.651981i	0.945373	−	0.325991i	$-0.105698\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$947$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$948$		0			0
$949$	−33.0885	+	37.6506i	−1.07410	+	1.22219i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−20.4904	−	5.49038i	−0.663749	−	0.177851i	−0.0888114	−	0.996048i	$-0.528307\pi$
$953$	−20.4904	−	5.49038i	−0.663749	−	0.177851i	−0.574937	+	0.818198i	$0.694974\pi$
$954$	−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
$962$	−3.32051	−	4.98076i	−0.107057	−	0.160586i
$963$		0			0
$964$	−8.07180	+	13.9808i	−0.259975	+	0.450290i
$965$	29.0167	−	32.7224i	0.934079	−	1.05337i
$966$		0			0
$967$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$967$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$968$	−8.05256	+	30.0526i	−0.258819	+	0.965926i
$969$		0			0
$970$	32.0333	+	48.5167i	1.02853	+	1.55778i
$971$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$971$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−58.6410			−1.87705
$977$	−6.15321	−	22.9641i	−0.196859	−	0.734687i	−0.991778	−	0.127971i	$-0.959153\pi$
$977$	−6.15321	−	22.9641i	−0.196859	−	0.734687i	0.794919	−	0.606715i	$-0.207513\pi$
$978$		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
$985$	30.7583	+	27.2750i	0.980042	+	0.869053i
$986$	−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	$-0.333333\pi$
$991$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−7.15321	+	26.6962i	−0.226545	+	0.845476i	0.755235	+	0.655454i	$0.227523\pi$
$997$	−7.15321	+	26.6962i	−0.226545	+	0.845476i	−0.981780	+	0.190022i	$0.939144\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bg.a.43.1	✓	4	5.3	odd	4
260.2.bg.a.43.1	✓	4	20.3	even	4
260.2.bg.a.127.1	yes	4	13.10	even	6
260.2.bg.a.127.1	yes	4	52.23	odd	6
260.2.bg.b.23.1	yes	4	65.23	odd	12	inner
260.2.bg.b.23.1	yes	4	260.23	even	12	inner
260.2.bg.b.147.1	yes	4	1.1	even	1	trivial
260.2.bg.b.147.1	yes	4	4.3	odd	2	CM

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)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(2.00000 + 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(2.00000 + 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +(2.36603 + 2.09808i) q^{10} +(0.232051 + 3.59808i) q^{13} +(2.00000 - 3.46410i) q^{16} +(-1.86603 + 6.96410i) q^{17} +(3.00000 + 3.00000i) q^{18} +(2.00000 - 4.00000i) q^{20} +(1.96410 - 4.59808i) q^{25} +(4.83013 - 1.63397i) q^{26} +(-5.76795 - 3.33013i) q^{29} +(-5.46410 - 1.46410i) q^{32} +10.1962 q^{34} +(3.00000 - 5.19615i) q^{36} +(-0.303848 - 1.13397i) q^{37} +(-6.19615 - 1.26795i) q^{40} +(1.66987 + 0.964102i) q^{41} +(3.00000 - 6.00000i) q^{45} +(6.06218 + 3.50000i) q^{49} +(-7.00000 - 1.00000i) q^{50} +(-4.00000 - 6.00000i) q^{52} +(-10.2942 + 10.2942i) q^{53} +(-2.43782 + 9.09808i) q^{58} +(-7.33013 - 12.6962i) q^{61} +8.00000i q^{64} +(-4.86603 - 6.42820i) q^{65} +(-3.73205 - 13.9282i) q^{68} +(-8.19615 - 2.19615i) q^{72} +(9.83013 + 9.83013i) q^{73} +(-1.43782 + 0.830127i) q^{74} +(0.535898 + 8.92820i) q^{80} +(4.50000 - 7.79423i) q^{81} +(0.705771 - 2.63397i) q^{82} +(-5.09808 - 15.2942i) q^{85} +(5.00000 - 8.66025i) q^{89} +(-9.29423 - 1.90192i) q^{90} +(17.7583 + 4.75833i) q^{97} +(2.56218 - 9.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{5} + 8 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 4 * q^5 + 8 * q^8	\( 4 q + 2 q^{2} - 4 q^{5} + 8 q^{8} + 6 q^{10} - 6 q^{13} + 8 q^{16} - 4 q^{17} + 12 q^{18} + 8 q^{20} - 6 q^{25} + 2 q^{26} - 30 q^{29} - 8 q^{32} + 20 q^{34} + 12 q^{36} - 22 q^{37} - 4 q^{40} + 24 q^{41} + 12 q^{45} - 28 q^{50} - 16 q^{52} - 10 q^{53} - 34 q^{58} - 12 q^{61} - 16 q^{65} - 8 q^{68} - 12 q^{72} + 22 q^{73} - 30 q^{74} + 16 q^{80} + 18 q^{81} + 34 q^{82} - 10 q^{85} + 20 q^{89} - 6 q^{90} + 26 q^{97} - 14 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^5 + 8 * q^8 + 6 * q^10 - 6 * q^13 + 8 * q^16 - 4 * q^17 + 12 * q^18 + 8 * q^20 - 6 * q^25 + 2 * q^26 - 30 * q^29 - 8 * q^32 + 20 * q^34 + 12 * q^36 - 22 * q^37 - 4 * q^40 + 24 * q^41 + 12 * q^45 - 28 * q^50 - 16 * q^52 - 10 * q^53 - 34 * q^58 - 12 * q^61 - 16 * q^65 - 8 * q^68 - 12 * q^72 + 22 * q^73 - 30 * q^74 + 16 * q^80 + 18 * q^81 + 34 * q^82 - 10 * q^85 + 20 * q^89 - 6 * q^90 + 26 * q^97 - 14 * q^98

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