LMFDB - Embedded newform 260.2.bj.a.87.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(3,260)]

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, 4]))

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

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

chi := DirichletCharacter("260.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bj (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			87.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	260.87
Dual form			260.2.bj.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(0.133975 - 2.23205i) q^{5} +(2.00000 - 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})$	\(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(0.133975 - 2.23205i) q^{5} +(2.00000 - 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +(-0.633975 - 3.09808i) q^{10} +(3.23205 - 1.59808i) q^{13} +(2.00000 - 3.46410i) q^{16} +(-2.13397 + 7.96410i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(-2.00000 - 4.00000i) q^{20} +(-4.96410 - 0.598076i) q^{25} +(3.83013 - 3.36603i) q^{26} +(9.23205 + 5.33013i) q^{29} +(1.46410 - 5.46410i) q^{32} +11.6603i q^{34} +(-3.00000 + 5.19615i) q^{36} +(-10.6962 + 2.86603i) q^{37} +(-4.19615 - 4.73205i) q^{40} +(2.33013 - 4.03590i) q^{41} +(3.00000 + 6.00000i) q^{45} +(-6.06218 - 3.50000i) q^{49} +(-7.00000 + 1.00000i) q^{50} +(4.00000 - 6.00000i) q^{52} +(-8.83013 + 8.83013i) q^{53} +(14.5622 + 3.90192i) q^{58} +(-1.33013 - 2.30385i) q^{61} -8.00000i q^{64} +(-3.13397 - 7.42820i) q^{65} +(4.26795 + 15.9282i) q^{68} +(-2.19615 + 8.19615i) q^{72} +(1.16987 - 1.16987i) q^{73} +(-13.5622 + 7.83013i) q^{74} +(-7.46410 - 4.92820i) q^{80} +(4.50000 - 7.79423i) q^{81} +(1.70577 - 6.36603i) q^{82} +(17.4904 + 5.83013i) q^{85} +(13.8564 + 8.00000i) q^{89} +(6.29423 + 7.09808i) q^{90} +(4.75833 - 17.7583i) q^{97} +(-9.56218 - 2.56218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 6 q^{10} + 6 q^{13} + 8 q^{16} - 12 q^{17} - 12 q^{18} - 8 q^{20} - 6 q^{25} - 2 q^{26} + 30 q^{29} - 8 q^{32} - 12 q^{36} - 22 q^{37} + 4 q^{40} - 8 q^{41} + 12 q^{45} - 28 q^{50} + 16 q^{52} - 18 q^{53} + 34 q^{58} + 12 q^{61} - 16 q^{65} + 24 q^{68} + 12 q^{72} + 22 q^{73} - 30 q^{74} - 16 q^{80} + 18 q^{81} + 38 q^{82} + 18 q^{85} - 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 - 12 * q^17 - 12 * q^18 - 8 * q^20 - 6 * q^25 - 2 * q^26 + 30 * q^29 - 8 * q^32 - 12 * q^36 - 22 * q^37 + 4 * q^40 - 8 * q^41 + 12 * q^45 - 28 * q^50 + 16 * q^52 - 18 * q^53 + 34 * q^58 + 12 * q^61 - 16 * q^65 + 24 * q^68 + 12 * q^72 + 22 * q^73 - 30 * q^74 - 16 * q^80 + 18 * q^81 + 38 * q^82 + 18 * q^85 - 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 $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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		−0.258819	−	0.965926i	$-0.583333\pi$
$3$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$	0.133975	−	2.23205i	0.0599153	−	0.998203i
$5$	0.133975	−	2.23205i	0.0599153	−	0.998203i
$6$		0			0
$7$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$7$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$	−2.59808	+	1.50000i	−0.866025	+	0.500000i
$10$	−0.633975	−	3.09808i	−0.200480	−	0.979698i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$		0			0
$13$	3.23205	−	1.59808i	0.896410	−	0.443227i
$13$	3.23205	−	1.59808i	0.896410	−	0.443227i
$14$		0			0
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−2.13397	+	7.96410i	−0.517565	+	1.93158i	−0.242536	+	0.970143i	$0.577979\pi$
$17$	−2.13397	+	7.96410i	−0.517565	+	1.93158i	−0.275029	+	0.961436i	$0.588688\pi$
$18$	−3.00000	+	3.00000i	−0.707107	+	0.707107i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$	−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
$25$	−4.96410	−	0.598076i	−0.992820	−	0.119615i
$26$	3.83013	−	3.36603i	0.751150	−	0.660132i
$27$		0			0
$28$		0			0
$29$	9.23205	+	5.33013i	1.71435	+	0.989780i	0.928477	+	0.371391i	$0.121119\pi$
$29$	9.23205	+	5.33013i	1.71435	+	0.989780i	0.785872	+	0.618389i	$0.212214\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	1.46410	−	5.46410i	0.258819	−	0.965926i
$33$		0			0
$34$			11.6603i			1.99972i
$35$		0			0
$36$	−3.00000	+	5.19615i	−0.500000	+	0.866025i
$37$	−10.6962	+	2.86603i	−1.75844	+	0.471172i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$	−10.6962	+	2.86603i	−1.75844	+	0.471172i	−0.772043	+	0.635571i	$0.780765\pi$
$38$		0			0
$39$		0			0
$40$	−4.19615	−	4.73205i	−0.663470	−	0.748203i
$41$	2.33013	−	4.03590i	0.363905	−	0.630301i	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	2.33013	−	4.03590i	0.363905	−	0.630301i	0.988600	+	0.150567i	$0.0481100\pi$
$42$		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	$-0.750000\pi$
$47$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$48$		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
$53$	−8.83013	+	8.83013i	−1.21291	+	1.21291i	−0.242846	+	0.970065i	$0.578081\pi$
$53$	−8.83013	+	8.83013i	−1.21291	+	1.21291i	−0.970065	+	0.242846i	$0.921919\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	14.5622	+	3.90192i	1.91211	+	0.512348i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	−1.33013	−	2.30385i	−0.170305	−	0.294977i	0.768221	−	0.640184i	$-0.221142\pi$
$61$	−1.33013	−	2.30385i	−0.170305	−	0.294977i	−0.938527	+	0.345207i	$0.887809\pi$
$62$		0			0
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	−3.13397	−	7.42820i	−0.388722	−	0.921355i
$66$		0			0
$67$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$67$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$68$	4.26795	+	15.9282i	0.517565	+	1.93158i
$69$		0			0
$70$		0			0
$71$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$71$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$72$	−2.19615	+	8.19615i	−0.258819	+	0.965926i
$73$	1.16987	−	1.16987i	0.136923	−	0.136923i	−0.635323	−	0.772246i	$-0.719133\pi$
$73$	1.16987	−	1.16987i	0.136923	−	0.136923i	0.772246	+	0.635323i	$0.219133\pi$
$74$	−13.5622	+	7.83013i	−1.57657	+	0.910234i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	−7.46410	−	4.92820i	−0.834512	−	0.550990i
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$	1.70577	−	6.36603i	0.188371	−	0.703010i
$83$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$83$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$84$		0			0
$85$	17.4904	+	5.83013i	1.89710	+	0.632366i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	13.8564	+	8.00000i	1.46878	+	0.847998i	0.999388	−	0.0349934i	$-0.0111410\pi$
$89$	13.8564	+	8.00000i	1.46878	+	0.847998i	0.469389	+	0.882992i	$0.344474\pi$
$90$	6.29423	+	7.09808i	0.663470	+	0.748203i
$91$		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	−0.105180	−	0.994453i	$-0.533542\pi$
$97$	4.75833	−	17.7583i	0.483135	−	1.80309i	0.588315	−	0.808632i	$-0.299792\pi$
$98$	−9.56218	−	2.56218i	−0.965926	−	0.258819i
$99$		0			0
$100$	−9.19615	+	3.92820i	−0.919615	+	0.392820i
$101$	9.16025	−	15.8660i	0.911479	−	1.57873i	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	9.16025	−	15.8660i	0.911479	−	1.57873i	0.811976	−	0.583691i	$-0.198392\pi$
$102$		0			0
$103$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$103$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$104$	3.26795	−	9.66025i	0.320449	−	0.947266i
$105$		0			0
$106$	−8.83013	+	15.2942i	−0.857658	+	1.48551i
$107$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$107$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$108$		0			0
$109$		−	6.00000i		−	0.574696i	−0.957826	−	0.287348i	$-0.907226\pi$
$109$		−	6.00000i		−	0.574696i	0.957826	−	0.287348i	$-0.0927736\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−18.4282	−	4.93782i	−1.73358	−	0.464511i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$	−18.4282	−	4.93782i	−1.73358	−	0.464511i	−0.981003	+	0.193993i	$0.937856\pi$
$114$		0			0
$115$		0			0
$116$	21.3205			1.97956
$117$	−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
$122$	−2.66025	−	2.66025i	−0.240848	−	0.240848i
$123$		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	$0.916667\pi$
$128$	−2.92820	−	10.9282i	−0.258819	−	0.965926i
$129$		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
$136$	11.6603	+	20.1962i	0.999859	+	1.73181i
$137$	−3.47372	+	12.9641i	−0.296780	+	1.10760i	0.643013	+	0.765855i	$0.277684\pi$
$137$	−3.47372	+	12.9641i	−0.296780	+	1.10760i	−0.939793	+	0.341743i	$0.888983\pi$
$138$		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
$145$	13.1340	−	19.8923i	1.09072	−	1.65197i
$146$	1.16987	−	2.02628i	0.0968194	−	0.167696i
$147$		0			0
$148$	−15.6603	+	15.6603i	−1.28726	+	1.28726i
$149$	8.93782	−	5.16025i	0.732215	−	0.422744i	−0.0870170	−	0.996207i	$-0.527733\pi$
$149$	8.93782	−	5.16025i	0.732215	−	0.422744i	0.819232	+	0.573462i	$0.194400\pi$
$150$		0			0
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		0			0
$153$	−6.40192	−	23.8923i	−0.517565	−	1.93158i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	4.16987	+	4.16987i	0.332792	+	0.332792i	0.853646	−	0.520854i	$-0.174386\pi$
$157$	4.16987	+	4.16987i	0.332792	+	0.332792i	−0.520854	+	0.853646i	$0.674386\pi$
$158$		0			0
$159$		0			0
$160$	−12.0000	−	4.00000i	−0.948683	−	0.316228i
$161$		0			0
$162$	3.29423	−	12.2942i	0.258819	−	0.965926i
$163$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$163$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$164$		−	9.32051i		−	0.727809i
$165$		0			0
$166$		0			0
$167$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$167$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$168$		0			0
$169$	7.89230	−	10.3301i	0.607100	−	0.794625i
$170$	26.0263	+	1.56218i	1.99612	+	0.119814i
$171$		0			0
$172$		0			0
$173$	15.0263	+	4.02628i	1.14243	+	0.306112i	0.779926	−	0.625871i	$-0.215256\pi$
$173$	15.0263	+	4.02628i	1.14243	+	0.306112i	0.362500	+	0.931984i	$0.381923\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	21.8564	+	5.85641i	1.63821	+	0.438956i
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$	11.1962	+	7.39230i	0.834512	+	0.550990i
$181$	−8.32051			−0.618458			−0.309229	−	0.950988i	$-0.600071\pi$
$181$	−8.32051			−0.618458			−0.309229	+	0.950988i	$0.600071\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.96410	+	24.2583i	0.364968	+	1.78351i
$186$		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
$193$	−1.89230	−	7.06218i	−0.136211	−	0.508347i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−1.89230	−	7.06218i	−0.136211	−	0.508347i	0.863779	−	0.503871i	$-0.168091\pi$
$194$		−	26.0000i		−	1.86669i
$195$		0			0
$196$	−14.0000			−1.00000
$197$	−17.7583	+	4.75833i	−1.26523	+	0.339017i	−0.828201	−	0.560431i	$-0.810635\pi$
$197$	−17.7583	+	4.75833i	−1.26523	+	0.339017i	−0.437028	+	0.899448i	$0.643969\pi$
$198$		0			0
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$	−11.1244	+	8.73205i	−0.786611	+	0.617449i
$201$		0			0
$202$	6.70577	−	25.0263i	0.471816	−	1.76084i
$203$		0			0
$204$		0			0
$205$	−8.69615	−	5.74167i	−0.607366	−	0.401016i
$206$		0			0
$207$		0			0
$208$	0.928203	−	14.3923i	0.0643593	−	0.997927i
$209$		0			0
$210$		0			0
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$	−6.46410	+	24.1244i	−0.443956	+	1.65687i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−2.19615	−	8.19615i	−0.148742	−	0.555113i
$219$		0			0
$220$		0			0
$221$	5.83013	+	29.1506i	0.392177	+	1.96088i
$222$		0			0
$223$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$223$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$224$		0			0
$225$	13.7942	−	5.89230i	0.919615	−	0.392820i
$226$	−26.9808			−1.79473
$227$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$227$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$228$		0			0
$229$			4.00000i			0.264327i	0.991228	+	0.132164i	$0.0421925\pi$
$229$			4.00000i			0.264327i	−0.991228	+	0.132164i	$0.957808\pi$
$230$		0			0
$231$		0			0
$232$	29.1244	−	7.80385i	1.91211	−	0.512348i
$233$	−21.0000	+	21.0000i	−1.37576	+	1.37576i	−0.524097	+	0.851658i	$0.675597\pi$
$233$	−21.0000	+	21.0000i	−1.37576	+	1.37576i	−0.851658	+	0.524097i	$0.824403\pi$
$234$	−4.90192	+	14.4904i	−0.320449	+	0.947266i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	10.9904	+	19.0359i	0.707953	+	1.22621i	0.965615	+	0.259975i	$0.0837143\pi$
$241$	10.9904	+	19.0359i	0.707953	+	1.22621i	−0.257663	+	0.966235i	$0.582952\pi$
$242$	−11.0000	−	11.0000i	−0.707107	−	0.707107i
$243$		0			0
$244$	−4.60770	−	2.66025i	−0.294977	−	0.170305i
$245$	−8.62436	+	13.0622i	−0.550990	+	0.834512i
$246$		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	$-0.666667\pi$
$251$		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
$257$	6.13397	−	1.64359i	0.382627	−	0.102525i	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	6.13397	−	1.64359i	0.382627	−	0.102525i	0.445005	+	0.895528i	$0.353202\pi$
$258$		0			0
$259$		0			0
$260$	−12.8564	−	9.73205i	−0.797320	−	0.603556i
$261$	−31.9808			−1.97956
$262$		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
$265$	18.5263	+	20.8923i	1.13806	+	1.28340i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−22.5167	+	13.0000i	−1.37287	+	0.792624i	−0.991288	−	0.131713i	$-0.957952\pi$
$269$	−22.5167	+	13.0000i	−1.37287	+	0.792624i	−0.381577	+	0.924337i	$0.624619\pi$
$270$		0			0
$271$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$271$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$272$	23.3205	+	23.3205i	1.41401	+	1.41401i
$273$		0			0
$274$			18.9808i			1.14667i
$275$		0			0
$276$		0			0
$277$	−2.62436	+	9.79423i	−0.157682	+	0.588478i	0.841178	+	0.540758i	$0.181862\pi$
$277$	−2.62436	+	9.79423i	−0.157682	+	0.588478i	−0.998861	+	0.0477206i	$0.984804\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−24.6603			−1.47111			−0.735554	−	0.677466i	$-0.763078\pi$
$281$	−24.6603			−1.47111			−0.735554	+	0.677466i	$0.763078\pi$
$282$		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
$288$	4.39230	+	16.3923i	0.258819	+	0.965926i
$289$	−44.1506	−	25.4904i	−2.59710	−	1.49943i
$290$	10.6603	−	31.9808i	0.625992	−	1.87798i
$291$		0			0
$292$	0.856406	−	3.19615i	0.0501174	−	0.187041i
$293$	30.7224	+	8.23205i	1.79482	+	0.480922i	0.993151	−	0.116841i	$-0.0372769\pi$
$293$	30.7224	+	8.23205i	1.79482	+	0.480922i	0.801673	+	0.597763i	$0.203944\pi$
$294$		0			0
$295$		0			0
$296$	−15.6603	+	27.1244i	−0.910234	+	1.57657i
$297$		0			0
$298$	10.3205	−	10.3205i	0.597851	−	0.597851i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−5.32051	+	2.66025i	−0.304651	+	0.152326i
$306$	−17.4904	−	30.2942i	−0.999859	−	1.73181i
$307$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$307$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$	−1.00000	+	1.00000i	−0.0565233	+	0.0565233i	−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−1.00000	+	1.00000i	−0.0565233	+	0.0565233i	0.678280	+	0.734803i	$0.262726\pi$
$314$	7.22243	+	4.16987i	0.407585	+	0.235320i
$315$		0			0
$316$		0			0
$317$	20.1506	+	20.1506i	1.13177	+	1.13177i	0.989882	+	0.141890i	$0.0453179\pi$
$317$	20.1506	+	20.1506i	1.13177	+	1.13177i	0.141890	+	0.989882i	$0.454682\pi$
$318$		0			0
$319$		0			0
$320$	−17.8564	−	1.07180i	−0.998203	−	0.0599153i
$321$		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
$328$	−3.41154	−	12.7321i	−0.188371	−	0.703010i
$329$		0			0
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$		0			0
$333$	23.4904	−	23.4904i	1.28726	−	1.28726i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−18.1506	−	18.1506i	−0.988728	−	0.988728i	0.0112091	−	0.999937i	$-0.496432\pi$
$337$	−18.1506	−	18.1506i	−0.988728	−	0.988728i	−0.999937	+	0.0112091i	$0.996432\pi$
$338$	7.00000	−	17.0000i	0.380750	−	0.924678i
$339$		0			0
$340$	36.1244	−	7.39230i	1.95912	−	0.400904i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	22.0000			1.18273
$347$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$347$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$348$		0			0
$349$	31.1769	+	18.0000i	1.66886	+	0.963518i	0.968253	+	0.249973i	$0.0804216\pi$
$349$	31.1769	+	18.0000i	1.66886	+	0.963518i	0.700609	+	0.713545i	$0.252912\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−9.57180	−	35.7224i	−0.509455	−	1.90131i	−0.425797	−	0.904819i	$-0.640006\pi$
$353$	−9.57180	−	35.7224i	−0.509455	−	1.90131i	−0.0836583	−	0.996495i	$-0.526660\pi$
$354$		0			0
$355$		0			0
$356$	32.0000			1.69600
$357$		0			0
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$	18.0000	+	6.00000i	0.948683	+	0.316228i
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	−11.3660	+	3.04552i	−0.597385	+	0.160069i
$363$		0			0
$364$		0			0
$365$	−2.45448	−	2.76795i	−0.128473	−	0.144881i
$366$		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
$369$			13.9808i			0.727809i
$370$	15.6603	+	31.3205i	0.814138	+	1.62828i
$371$		0			0
$372$		0			0
$373$	22.0622	+	5.91154i	1.14234	+	0.306088i	0.779890	−	0.625917i	$-0.215275\pi$
$373$	22.0622	+	5.91154i	1.14234	+	0.306088i	0.362446	+	0.932005i	$0.381942\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	38.3564	+	2.47372i	1.97546	+	0.127403i
$378$		0			0
$379$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$379$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$383$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$384$		0			0
$385$		0			0
$386$	−5.16987	−	8.95448i	−0.263140	−	0.455771i
$387$		0			0
$388$	−9.51666	−	35.5167i	−0.483135	−	1.80309i
$389$		−	34.3205i		−	1.74012i	−0.492947	−	0.870059i	$-0.664080\pi$
$389$		−	34.3205i		−	1.74012i	0.492947	−	0.870059i	$-0.335920\pi$
$390$		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	−0.737579	−	0.675261i	$-0.764031\pi$
$397$	4.75833	−	17.7583i	0.238814	−	0.891265i	0.976392	−	0.216004i	$-0.0693024\pi$
$398$		0			0
$399$		0			0
$400$	−12.0000	+	16.0000i	−0.600000	+	0.800000i
$401$	−16.8205	+	29.1340i	−0.839976	+	1.45488i	0.0499376	+	0.998752i	$0.484098\pi$
$401$	−16.8205	+	29.1340i	−0.839976	+	1.45488i	−0.889914	+	0.456129i	$0.849236\pi$
$402$		0			0
$403$		0			0
$404$		−	36.6410i		−	1.82296i
$405$	−16.7942	−	11.0885i	−0.834512	−	0.550990i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−27.4019	+	15.8205i	−1.35494	+	0.782274i	−0.988936	−	0.148340i	$-0.952607\pi$
$409$	−27.4019	+	15.8205i	−1.35494	+	0.782274i	−0.366002	+	0.930614i	$0.619274\pi$
$410$	−13.9808	−	4.66025i	−0.690461	−	0.230154i
$411$		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
$421$	39.9808			1.94854			0.974272	−	0.225377i	$-0.0723615\pi$
$421$	39.9808			1.94854			0.974272	+	0.225377i	$0.0723615\pi$
$422$		0			0
$423$		0			0
$424$			35.3205i			1.71532i
$425$	15.3564	−	38.2583i	0.744895	−	1.85580i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$		0			0
$433$	25.7224	+	6.89230i	1.23614	+	0.331223i	0.816968	−	0.576683i	$-0.195653\pi$
$433$	25.7224	+	6.89230i	1.23614	+	0.331223i	0.419173	+	0.907906i	$0.362320\pi$
$434$		0			0
$435$		0			0
$436$	−6.00000	−	10.3923i	−0.287348	−	0.497701i
$437$		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
$442$	18.6340	+	37.6865i	0.886328	+	1.79257i
$443$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$443$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$444$		0			0
$445$	19.7128	−	29.8564i	0.934477	−	1.41533i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	12.1244	−	7.00000i	0.572184	−	0.330350i	−0.185837	−	0.982581i	$-0.559500\pi$
$449$	12.1244	−	7.00000i	0.572184	−	0.330350i	0.758021	+	0.652230i	$0.226166\pi$
$450$	16.6865	−	13.0981i	0.786611	−	0.617449i
$451$		0			0
$452$	−36.8564	+	9.87564i	−1.73358	+	0.464511i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	17.9641	−	4.81347i	0.840325	−	0.225164i	0.187112	−	0.982339i	$-0.440087\pi$
$457$	17.9641	−	4.81347i	0.840325	−	0.225164i	0.653213	+	0.757174i	$0.273421\pi$
$458$	1.46410	+	5.46410i	0.0684130	+	0.255321i
$459$		0			0
$460$		0			0
$461$	−18.1603	−	31.4545i	−0.845807	−	1.46498i	−0.884918	−	0.465746i	$-0.845786\pi$
$461$	−18.1603	−	31.4545i	−0.845807	−	1.46498i	0.0391109	−	0.999235i	$-0.487547\pi$
$462$		0			0
$463$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$463$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$464$	36.9282	−	21.3205i	1.71435	−	0.989780i
$465$		0			0
$466$	−21.0000	+	36.3731i	−0.972806	+	1.68495i
$467$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$467$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$468$	−1.39230	+	21.5885i	−0.0643593	+	0.997927i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	9.69615	−	36.1865i	0.443956	−	1.65687i
$478$		0			0
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$		0			0
$481$	−29.9904	+	26.3564i	−1.36744	+	1.20175i
$482$	21.9808	+	21.9808i	1.00120	+	1.00120i
$483$		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		0.258819	−	0.965926i	$-0.416667\pi$
$487$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$488$	−7.26795	−	1.94744i	−0.329005	−	0.0881565i
$489$		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
$493$	−62.1506	+	62.1506i	−2.79912	+	2.79912i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	7.53590	+	21.0526i	0.337016	+	0.941499i
$501$		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
$505$	−34.1865	−	22.5718i	−1.52128	−	1.00443i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	26.5526	+	15.3301i	1.17692	+	0.679496i	0.955300	−	0.295637i	$-0.0955319\pi$
$509$	26.5526	+	15.3301i	1.17692	+	0.679496i	0.221621	+	0.975133i	$0.428865\pi$
$510$		0			0
$511$		0			0
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$		0			0
$514$	7.77757	−	4.49038i	0.343054	−	0.198062i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−21.1244	−	8.58846i	−0.926364	−	0.376629i
$521$	23.6410			1.03573			0.517866	−	0.855462i	$-0.326727\pi$
$521$	23.6410			1.03573			0.517866	+	0.855462i	$0.326727\pi$
$522$	−43.6865	+	11.7058i	−1.91211	+	0.512348i
$523$		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
$530$	32.9545	+	21.7583i	1.43145	+	0.945121i
$531$		0			0
$532$		0			0
$533$	1.08142	−	16.7679i	0.0468413	−	0.726301i
$534$		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
$541$	−3.67949			−0.158194			−0.0790969	−	0.996867i	$-0.525204\pi$
$541$	−3.67949			−0.158194			−0.0790969	+	0.996867i	$0.525204\pi$
$542$		0			0
$543$		0			0
$544$	40.3923	+	23.3205i	1.73181	+	0.999859i
$545$	−13.3923	−	0.803848i	−0.573663	−	0.0344330i
$546$		0			0
$547$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$547$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$548$	6.94744	+	25.9282i	0.296780	+	1.10760i
$549$	6.91154	+	3.99038i	0.294977	+	0.170305i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$			14.3397i			0.609237i
$555$		0			0
$556$		0			0
$557$	28.4545	−	7.62436i	1.20566	−	0.323054i	0.400599	−	0.916253i	$-0.368802\pi$
$557$	28.4545	−	7.62436i	1.20566	−	0.323054i	0.805056	+	0.593199i	$0.202135\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−33.6865	+	9.02628i	−1.42098	+	0.380751i
$563$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$563$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$564$		0			0
$565$	−13.4904	+	40.4711i	−0.567545	+	1.70263i
$566$		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
$577$	−33.1506	−	33.1506i	−1.38008	−	1.38008i	−0.844459	−	0.535620i	$-0.820078\pi$
$577$	−33.1506	−	33.1506i	−1.38008	−	1.38008i	−0.535620	−	0.844459i	$-0.679922\pi$
$578$	−69.6410	−	18.6603i	−2.89668	−	0.776164i
$579$		0			0
$580$	2.85641	−	47.5885i	0.118606	−	1.97600i
$581$		0			0
$582$		0			0
$583$		0			0
$584$		−	4.67949i		−	0.193639i
$585$	19.2846	+	14.5981i	0.797320	+	0.603556i
$586$	44.9808			1.85814
$587$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$587$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−11.4641	+	42.7846i	−0.471172	+	1.75844i
$593$	2.50962	−	2.50962i	0.103058	−	0.103058i	−0.653698	−	0.756756i	$-0.726783\pi$
$593$	2.50962	−	2.50962i	0.103058	−	0.103058i	0.756756	+	0.653698i	$0.226783\pi$
$594$		0			0
$595$		0			0
$596$	10.3205	−	17.8756i	0.422744	−	0.732215i
$597$		0			0
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	−7.66987	+	13.2846i	−0.312861	+	0.541891i	−0.978980	−	0.203954i	$-0.934621\pi$
$601$	−7.66987	+	13.2846i	−0.312861	+	0.541891i	0.666120	+	0.745845i	$0.267954\pi$
$602$		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
$610$	−6.29423	+	5.58142i	−0.254846	+	0.225985i
$611$		0			0
$612$	−34.9808	−	34.9808i	−1.41401	−	1.41401i
$613$	11.2776	+	42.0885i	0.455497	+	1.69994i	0.686624	+	0.727013i	$0.259092\pi$
$613$	11.2776	+	42.0885i	0.455497	+	1.69994i	−0.231127	+	0.972924i	$0.574241\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	10.5455	−	39.3564i	0.424547	−	1.58443i	−0.340365	−	0.940294i	$-0.610551\pi$
$617$	10.5455	−	39.3564i	0.424547	−	1.58443i	0.764911	−	0.644136i	$-0.222783\pi$
$618$		0			0
$619$		0			0			−	1.00000i	$-0.5\pi$
$619$		0			0				1.00000i	$0.5\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$	−1.00000	+	1.73205i	−0.0399680	+	0.0692267i
$627$		0			0
$628$	11.3923	+	3.05256i	0.454602	+	0.121810i
$629$		−	91.3013i		−	3.64042i
$630$		0			0
$631$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$631$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$632$		0			0
$633$		0			0
$634$	34.9019	+	20.1506i	1.38613	+	0.800284i
$635$		0			0
$636$		0			0
$637$	−25.1865	−	1.62436i	−0.997927	−	0.0643593i
$638$		0			0
$639$		0			0
$640$	−24.7846	+	5.07180i	−0.979698	+	0.200480i
$641$	19.6506	+	34.0359i	0.776153	+	1.34434i	0.934144	+	0.356897i	$0.116165\pi$
$641$	19.6506	+	34.0359i	0.776153	+	1.34434i	−0.157991	+	0.987441i	$0.550502\pi$
$642$		0			0
$643$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$643$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$644$		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	$0.916667\pi$
$648$	−6.58846	−	24.5885i	−0.258819	−	0.965926i
$649$		0			0
$650$	−21.0263	+	14.4186i	−0.824719	+	0.565543i
$651$		0			0
$652$		0			0
$653$	3.29423	+	12.2942i	0.128913	+	0.481110i	0.999949	−	0.0101092i	$-0.00321793\pi$
$653$	3.29423	+	12.2942i	0.128913	+	0.481110i	−0.871036	+	0.491220i	$0.836551\pi$
$654$		0			0
$655$		0			0
$656$	−9.32051	−	16.1436i	−0.363905	−	0.630301i
$657$	−1.28461	+	4.79423i	−0.0501174	+	0.187041i
$658$		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
$661$	24.6506	−	42.6962i	0.958799	−	1.66069i	0.233373	−	0.972387i	$-0.425024\pi$
$661$	24.6506	−	42.6962i	0.958799	−	1.66069i	0.725426	−	0.688301i	$-0.241643\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	23.4904	−	40.6865i	0.910234	−	1.57657i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	13.1077	+	48.9186i	0.505265	+	1.88567i	0.462566	+	0.886585i	$0.346929\pi$
$673$	13.1077	+	48.9186i	0.505265	+	1.88567i	0.0426985	+	0.999088i	$0.486405\pi$
$674$	−31.4378	−	18.1506i	−1.21094	−	0.699136i
$675$		0			0
$676$	3.33975	−	25.7846i	0.128452	−	0.991716i
$677$	−27.0000	−	27.0000i	−1.03769	−	1.03769i	−0.999261	−	0.0384331i	$-0.987763\pi$
$677$	−27.0000	−	27.0000i	−1.03769	−	1.03769i	−0.0384331	−	0.999261i	$-0.512237\pi$
$678$		0			0
$679$		0			0
$680$	46.6410	−	23.3205i	1.78860	−	0.894301i
$681$		0			0
$682$		0			0
$683$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$683$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$684$		0			0
$685$	28.4711	+	9.49038i	1.08783	+	0.362609i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−14.4282	+	42.6506i	−0.549671	+	1.62486i
$690$		0			0
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$	30.0526	−	8.05256i	1.14243	−	0.306112i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	27.1699	+	27.1699i	1.02913	+	1.02913i
$698$	49.1769	+	13.1769i	1.86137	+	0.498754i
$699$		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
$706$	−26.1506	−	45.2942i	−0.984192	−	1.70467i
$707$		0			0
$708$		0			0
$709$	−41.5526	+	23.9904i	−1.56054	+	0.900978i	−0.563337	+	0.826227i	$0.690483\pi$
$709$	−41.5526	+	23.9904i	−1.56054	+	0.900978i	−0.997202	+	0.0747503i	$0.976184\pi$
$710$		0			0
$711$		0			0
$712$	43.7128	−	11.7128i	1.63821	−	0.438956i
$713$		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	$0.833333\pi$
$720$	26.7846	+	1.60770i	0.998203	+	0.0599153i
$721$		0			0
$722$	6.95448	−	25.9545i	0.258819	−	0.965926i
$723$		0			0
$724$	−14.4115	+	8.32051i	−0.535601	+	0.309229i
$725$	−42.6410	−	31.9808i	−1.58365	−	1.18774i
$726$		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
$730$	−4.36603	−	2.88269i	−0.161594	−	0.106693i
$731$		0			0
$732$		0			0
$733$	7.15064	−	7.15064i	0.264115	−	0.264115i	−0.562609	−	0.826723i	$-0.690202\pi$
$733$	7.15064	−	7.15064i	0.264115	−	0.264115i	0.826723	+	0.562609i	$0.190202\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	5.11731	+	19.0981i	0.188371	+	0.703010i
$739$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$739$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$740$	32.8564	+	37.0526i	1.20783	+	1.36208i
$741$		0			0
$742$		0			0
$743$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$743$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$744$		0			0
$745$	−10.3205	−	20.6410i	−0.378114	−	0.756228i
$746$	32.3013			1.18263
$747$		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
$754$	53.3013	−	10.6603i	1.94112	−	0.388224i
$755$		0			0
$756$		0			0
$757$	23.2224	−	6.22243i	0.844034	−	0.226158i	0.189207	−	0.981937i	$-0.439408\pi$
$757$	23.2224	−	6.22243i	0.844034	−	0.226158i	0.654827	+	0.755779i	$0.272742\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	19.0000	+	32.9090i	0.688749	+	1.19295i	0.972243	+	0.233975i	$0.0751733\pi$
$761$	19.0000	+	32.9090i	0.688749	+	1.19295i	−0.283493	+	0.958974i	$0.591493\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−54.1865	+	11.0885i	−1.95912	+	0.400904i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−20.7846	−	12.0000i	−0.749512	−	0.432731i	0.0760054	−	0.997107i	$-0.475783\pi$
$769$	−20.7846	−	12.0000i	−0.749512	−	0.432731i	−0.825518	+	0.564376i	$0.809117\pi$
$770$		0			0
$771$		0			0
$772$	−10.3397	−	10.3397i	−0.372136	−	0.372136i
$773$	−53.2750	−	14.2750i	−1.91617	−	0.513436i	−0.990997	−	0.133887i	$-0.957254\pi$
$773$	−53.2750	−	14.2750i	−1.91617	−	0.513436i	−0.925172	−	0.379549i	$-0.876079\pi$
$774$		0			0
$775$		0			0
$776$	−26.0000	−	45.0333i	−0.933346	−	1.61660i
$777$		0			0
$778$	−12.5622	−	46.8827i	−0.450376	−	1.68083i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−24.2487	+	14.0000i	−0.866025	+	0.500000i
$785$	9.86603	−	8.74871i	0.352134	−	0.312255i
$786$		0			0
$787$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$787$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$788$	−26.0000	+	26.0000i	−0.926212	+	0.926212i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−7.98076	−	5.32051i	−0.283405	−	0.188937i
$794$		−	26.0000i		−	0.922705i
$795$		0			0
$796$		0			0
$797$	−13.5429	+	50.5429i	−0.479716	+	1.79032i	0.123045	+	0.992401i	$0.460734\pi$
$797$	−13.5429	+	50.5429i	−0.479716	+	1.79032i	−0.602761	+	0.797922i	$0.705933\pi$
$798$		0			0
$799$		0			0
$800$	−10.5359	+	26.2487i	−0.372500	+	0.928032i
$801$	−48.0000			−1.69600
$802$	−12.3135	+	45.9545i	−0.434804	+	1.62271i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−13.4115	−	50.0526i	−0.471816	−	1.76084i
$809$	−31.7487	−	18.3301i	−1.11623	−	0.644453i	−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−31.7487	−	18.3301i	−1.11623	−	0.644453i	−0.940435	+	0.339975i	$0.889582\pi$
$810$	−27.0000	−	9.00000i	−0.948683	−	0.316228i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−31.6410	+	31.6410i	−1.10630	+	1.10630i
$819$		0			0
$820$	−20.8038	−	1.24871i	−0.726502	−	0.0436069i
$821$	14.0000	−	24.2487i	0.488603	−	0.846286i	−0.511311	−	0.859396i	$-0.670840\pi$
$821$	14.0000	−	24.2487i	0.488603	−	0.846286i	0.999914	+	0.0131101i	$0.00417319\pi$
$822$		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	$-0.750000\pi$
$827$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$828$		0			0
$829$	38.3827	+	22.1603i	1.33309	+	0.769657i	0.985771	−	0.168091i	$-0.0537604\pi$
$829$	38.3827	+	22.1603i	1.33309	+	0.769657i	0.347314	+	0.937749i	$0.387094\pi$
$830$		0			0
$831$		0			0
$832$	−12.7846	−	25.8564i	−0.443227	−	0.896410i
$833$	40.8109	−	40.8109i	1.41401	−	1.41401i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$		0			0
$841$	42.3205	+	73.3013i	1.45933	+	2.52763i
$842$	54.6147	−	14.6340i	1.88215	−	0.504320i
$843$		0			0
$844$		0			0
$845$	−22.0000	−	19.0000i	−0.756823	−	0.653620i
$846$		0			0
$847$		0			0
$848$	12.9282	+	48.2487i	0.443956	+	1.65687i
$849$		0			0
$850$	6.97372	−	57.8827i	0.239197	−	1.98536i
$851$		0			0
$852$		0			0
$853$	24.8301	−	24.8301i	0.850167	−	0.850167i	−0.139986	−	0.990153i	$-0.544706\pi$
$853$	24.8301	−	24.8301i	0.850167	−	0.850167i	0.990153	+	0.139986i	$0.0447058\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	5.15064	+	5.15064i	0.175942	+	0.175942i	0.789584	−	0.613642i	$-0.210296\pi$
$857$	5.15064	+	5.15064i	0.175942	+	0.175942i	−0.613642	+	0.789584i	$0.710296\pi$
$858$		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	$-0.250000\pi$
$863$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$864$		0			0
$865$	11.0000	−	33.0000i	0.374011	−	1.12203i
$866$	37.6603			1.27975
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−12.0000	−	12.0000i	−0.406371	−	0.406371i
$873$	14.2750	+	53.2750i	0.483135	+	1.80309i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−15.3038	+	57.1147i	−0.516774	+	1.92863i	−0.202606	+	0.979260i	$0.564941\pi$
$877$	−15.3038	+	57.1147i	−0.516774	+	1.92863i	−0.314169	+	0.949367i	$0.601726\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−13.6506	+	23.6436i	−0.459902	+	0.796573i	−0.998955	−	0.0456985i	$-0.985449\pi$
$881$	−13.6506	+	23.6436i	−0.459902	+	0.796573i	0.539054	+	0.842271i	$0.318782\pi$
$882$	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	$0.750000\pi$
$884$	39.2487	+	44.6603i	1.32008	+	1.50209i
$885$		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
$890$	16.0000	−	48.0000i	0.536321	−	1.60896i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	14.0000	−	14.0000i	0.467186	−	0.467186i
$899$		0			0
$900$	18.0000	−	24.0000i	0.600000	−	0.800000i
$901$	−51.4808	−	89.1673i	−1.71507	−	2.97059i
$902$		0			0
$903$		0			0
$904$	−46.7321	+	26.9808i	−1.55428	+	0.897367i
$905$	−1.11474	+	18.5718i	−0.0370551	+	0.617347i
$906$		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
$909$			54.9615i			1.82296i
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$	22.7776	−	13.1506i	0.753415	−	0.434984i
$915$		0			0
$916$	4.00000	+	6.92820i	0.132164	+	0.228914i
$917$		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
$922$	−36.3205	−	36.3205i	−1.19615	−	1.19615i
$923$		0			0
$924$		0			0
$925$	54.8109	−	7.83013i	1.80217	−	0.257453i
$926$		0			0
$927$		0			0
$928$	42.6410	−	42.6410i	1.39976	−	1.39976i
$929$	49.9186	−	28.8205i	1.63778	−	0.945570i	0.656179	−	0.754606i	$-0.272172\pi$
$929$	49.9186	−	28.8205i	1.63778	−	0.945570i	0.981597	−	0.190965i	$-0.0611616\pi$
$930$		0			0
$931$		0			0
$932$	−15.3731	+	57.3731i	−0.503562	+	1.87932i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	6.00000	+	30.0000i	0.196116	+	0.980581i
$937$	−17.1699	−	17.1699i	−0.560915	−	0.560915i	0.368652	−	0.929567i	$-0.379819\pi$
$937$	−17.1699	−	17.1699i	−0.560915	−	0.560915i	−0.929567	+	0.368652i	$0.879819\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−58.0000			−1.89075			−0.945373	−	0.325991i	$-0.894302\pi$
$941$	−58.0000			−1.89075			−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	$-0.0833333\pi$
$947$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$948$		0			0
$949$	1.91154	−	5.65064i	0.0620513	−	0.183427i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	56.0070	+	15.0070i	1.81425	+	0.486126i	0.996048	−	0.0888114i	$-0.0283068\pi$
$953$	56.0070	+	15.0070i	1.81425	+	0.486126i	0.818198	+	0.574937i	$0.194974\pi$
$954$		−	52.9808i		−	1.71532i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	31.0000			1.00000
$962$	−31.3205	+	46.9808i	−1.00981	+	1.51472i
$963$		0			0
$964$	38.0718	+	21.9808i	1.22621	+	0.707953i
$965$	−16.0167	+	3.27757i	−0.515595	+	0.105509i
$966$		0			0
$967$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$967$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$968$	−30.0526	−	8.05256i	−0.965926	−	0.258819i
$969$		0			0
$970$	−58.0333	−	3.48334i	−1.86334	−	0.111843i
$971$		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
$976$	−10.6410			−0.340611
$977$	−59.8468	+	16.0359i	−1.91467	+	0.513034i	−0.922890	+	0.385063i	$0.874180\pi$
$977$	−59.8468	+	16.0359i	−1.91467	+	0.513034i	−0.991778	+	0.127971i	$0.959153\pi$
$978$		0			0
$979$		0			0
$980$	−1.87564	+	31.2487i	−0.0599153	+	0.998203i
$981$	9.00000	+	15.5885i	0.287348	+	0.497701i
$982$		0			0
$983$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$983$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$984$		0			0
$985$	8.24167	+	40.2750i	0.262601	+	1.28327i
$986$	−62.1506	+	107.648i	−1.97928	+	3.42821i
$987$		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
$997$	−1.15321	+	4.30385i	−0.0365226	+	0.136304i	−0.981780	−	0.190022i	$-0.939144\pi$
$997$	−1.15321	+	4.30385i	−0.0365226	+	0.136304i	0.945257	+	0.326326i	$0.105811\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bj.a.87.1	yes	4
4.3	odd	2	CM	260.2.bj.a.87.1	yes	4
5.3	odd	4		260.2.bj.b.243.1	yes	4
13.3	even	3		260.2.bj.b.107.1	yes	4
20.3	even	4		260.2.bj.b.243.1	yes	4
52.3	odd	6		260.2.bj.b.107.1	yes	4
65.3	odd	12	inner	260.2.bj.a.3.1	✓	4
260.3	even	12	inner	260.2.bj.a.3.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bj.a.3.1	✓	4	65.3	odd	12	inner
260.2.bj.a.3.1	✓	4	260.3	even	12	inner
260.2.bj.a.87.1	yes	4	1.1	even	1	trivial
260.2.bj.a.87.1	yes	4	4.3	odd	2	CM
260.2.bj.b.107.1	yes	4	13.3	even	3
260.2.bj.b.107.1	yes	4	52.3	odd	6
260.2.bj.b.243.1	yes	4	5.3	odd	4
260.2.bj.b.243.1	yes	4	20.3	even	4

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.bj (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(0.133975 - 2.23205i) q^{5} +(2.00000 - 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})\)	\(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(0.133975 - 2.23205i) q^{5} +(2.00000 - 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +(-0.633975 - 3.09808i) q^{10} +(3.23205 - 1.59808i) q^{13} +(2.00000 - 3.46410i) q^{16} +(-2.13397 + 7.96410i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(-2.00000 - 4.00000i) q^{20} +(-4.96410 - 0.598076i) q^{25} +(3.83013 - 3.36603i) q^{26} +(9.23205 + 5.33013i) q^{29} +(1.46410 - 5.46410i) q^{32} +11.6603i q^{34} +(-3.00000 + 5.19615i) q^{36} +(-10.6962 + 2.86603i) q^{37} +(-4.19615 - 4.73205i) q^{40} +(2.33013 - 4.03590i) q^{41} +(3.00000 + 6.00000i) q^{45} +(-6.06218 - 3.50000i) q^{49} +(-7.00000 + 1.00000i) q^{50} +(4.00000 - 6.00000i) q^{52} +(-8.83013 + 8.83013i) q^{53} +(14.5622 + 3.90192i) q^{58} +(-1.33013 - 2.30385i) q^{61} -8.00000i q^{64} +(-3.13397 - 7.42820i) q^{65} +(4.26795 + 15.9282i) q^{68} +(-2.19615 + 8.19615i) q^{72} +(1.16987 - 1.16987i) q^{73} +(-13.5622 + 7.83013i) q^{74} +(-7.46410 - 4.92820i) q^{80} +(4.50000 - 7.79423i) q^{81} +(1.70577 - 6.36603i) q^{82} +(17.4904 + 5.83013i) q^{85} +(13.8564 + 8.00000i) q^{89} +(6.29423 + 7.09808i) q^{90} +(4.75833 - 17.7583i) q^{97} +(-9.56218 - 2.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 4 q^{5} + 8 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 + 4 * q^5 + 8 * q^8	\( 4 q + 2 q^{2} + 4 q^{5} + 8 q^{8} - 6 q^{10} + 6 q^{13} + 8 q^{16} - 12 q^{17} - 12 q^{18} - 8 q^{20} - 6 q^{25} - 2 q^{26} + 30 q^{29} - 8 q^{32} - 12 q^{36} - 22 q^{37} + 4 q^{40} - 8 q^{41} + 12 q^{45} - 28 q^{50} + 16 q^{52} - 18 q^{53} + 34 q^{58} + 12 q^{61} - 16 q^{65} + 24 q^{68} + 12 q^{72} + 22 q^{73} - 30 q^{74} - 16 q^{80} + 18 q^{81} + 38 q^{82} + 18 q^{85} - 6 q^{90} - 26 q^{97} - 14 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 4 * q^5 + 8 * q^8 - 6 * q^10 + 6 * q^13 + 8 * q^16 - 12 * q^17 - 12 * q^18 - 8 * q^20 - 6 * q^25 - 2 * q^26 + 30 * q^29 - 8 * q^32 - 12 * q^36 - 22 * q^37 + 4 * q^40 - 8 * q^41 + 12 * q^45 - 28 * q^50 + 16 * q^52 - 18 * q^53 + 34 * q^58 + 12 * q^61 - 16 * q^65 + 24 * q^68 + 12 * q^72 + 22 * q^73 - 30 * q^74 - 16 * q^80 + 18 * q^81 + 38 * q^82 + 18 * q^85 - 6 * q^90 - 26 * q^97 - 14 * q^98

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