LMFDB - Embedded newform 980.2.x.a.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(67,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("980.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$1$
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			67.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	980.67
Dual form			980.2.x.a.863.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(1.23205 - 1.86603i) q^{5} +(-2.00000 + 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})$	\(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(1.23205 - 1.86603i) q^{5} +(-2.00000 + 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +(-2.09808 - 2.36603i) q^{10} +(-5.00000 + 5.00000i) q^{13} +(2.00000 + 3.46410i) q^{16} +(-6.83013 + 1.83013i) q^{17} +(1.09808 + 4.09808i) q^{18} +(-4.00000 + 2.00000i) q^{20} +(-1.96410 - 4.59808i) q^{25} +(5.00000 + 8.66025i) q^{26} -4.00000i q^{29} +(5.46410 - 1.46410i) q^{32} +10.0000i q^{34} +6.00000 q^{36} +(2.56218 - 9.56218i) q^{37} +(1.26795 + 6.19615i) q^{40} -10.0000 q^{41} +(-0.401924 + 6.69615i) q^{45} +(-7.00000 + 1.00000i) q^{50} +(13.6603 - 3.66025i) q^{52} +(3.29423 + 12.2942i) q^{53} +(-5.46410 - 1.46410i) q^{58} +(-5.00000 - 8.66025i) q^{61} -8.00000i q^{64} +(3.16987 + 15.4904i) q^{65} +(13.6603 + 3.66025i) q^{68} +(2.19615 - 8.19615i) q^{72} +(1.83013 + 6.83013i) q^{73} +(-12.1244 - 7.00000i) q^{74} +(8.92820 + 0.535898i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-3.66025 + 13.6603i) q^{82} +(-5.00000 + 15.0000i) q^{85} +(8.66025 - 5.00000i) q^{89} +(9.00000 + 3.00000i) q^{90} +(-5.00000 - 5.00000i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{5} - 8 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^5 - 8 * q^8	$ 4 q - 2 q^{2} - 2 q^{5} - 8 q^{8} + 2 q^{10} - 20 q^{13} + 8 q^{16} - 10 q^{17} - 6 q^{18} - 16 q^{20} + 6 q^{25} + 20 q^{26} + 8 q^{32} + 24 q^{36} - 14 q^{37} + 12 q^{40} - 40 q^{41} - 12 q^{45} - 28 q^{50} + 20 q^{52} - 18 q^{53} - 8 q^{58} - 20 q^{61} + 30 q^{65} + 20 q^{68} - 12 q^{72} - 10 q^{73} + 8 q^{80} + 18 q^{81} + 20 q^{82} - 20 q^{85} + 36 q^{90} - 20 q^{97}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^5 - 8 * q^8 + 2 * q^10 - 20 * q^13 + 8 * q^16 - 10 * q^17 - 6 * q^18 - 16 * q^20 + 6 * q^25 + 20 * q^26 + 8 * q^32 + 24 * q^36 - 14 * q^37 + 12 * q^40 - 40 * q^41 - 12 * q^45 - 28 * q^50 + 20 * q^52 - 18 * q^53 - 8 * q^58 - 20 * q^61 + 30 * q^65 + 20 * q^68 - 12 * q^72 - 10 * q^73 + 8 * q^80 + 18 * q^81 + 20 * q^82 - 20 * q^85 + 36 * q^90 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.366025	−	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
$5$	1.23205	−	1.86603i	0.550990	−	0.834512i
$5$	1.23205	−	1.86603i	0.550990	−	0.834512i
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	−2.59808	+	1.50000i	−0.866025	+	0.500000i
$10$	−2.09808	−	2.36603i	−0.663470	−	0.748203i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$		0			0
$13$	−5.00000	+	5.00000i	−1.38675	+	1.38675i	−0.554700	+	0.832050i	$0.687167\pi$
$13$	−5.00000	+	5.00000i	−1.38675	+	1.38675i	−0.832050	+	0.554700i	$0.812833\pi$
$14$		0			0
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−6.83013	+	1.83013i	−1.65655	+	0.443871i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−6.83013	+	1.83013i	−1.65655	+	0.443871i	−0.695113	+	0.718900i	$0.744646\pi$
$18$	1.09808	+	4.09808i	0.258819	+	0.965926i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$	−4.00000	+	2.00000i	−0.894427	+	0.447214i
$21$		0			0
$22$		0			0
$23$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$23$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$24$		0			0
$25$	−1.96410	−	4.59808i	−0.392820	−	0.919615i
$26$	5.00000	+	8.66025i	0.980581	+	1.69842i
$27$		0			0
$28$		0			0
$29$		−	4.00000i		−	0.742781i	−0.928477	−	0.371391i	$-0.878881\pi$
$29$		−	4.00000i		−	0.742781i	0.928477	−	0.371391i	$-0.121119\pi$
$30$		0			0
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	5.46410	−	1.46410i	0.965926	−	0.258819i
$33$		0			0
$34$			10.0000i			1.71499i
$35$		0			0
$36$	6.00000			1.00000
$37$	2.56218	−	9.56218i	0.421219	−	1.57201i	−0.350823	−	0.936442i	$-0.614098\pi$
$37$	2.56218	−	9.56218i	0.421219	−	1.57201i	0.772043	−	0.635571i	$-0.219235\pi$
$38$		0			0
$39$		0			0
$40$	1.26795	+	6.19615i	0.200480	+	0.979698i
$41$	−10.0000			−1.56174			−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000			−1.56174			−0.780869	+	0.624695i	$0.785223\pi$
$42$		0			0
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$		0			0
$45$	−0.401924	+	6.69615i	−0.0599153	+	0.998203i
$46$		0			0
$47$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$47$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$48$		0			0
$49$		0			0
$50$	−7.00000	+	1.00000i	−0.989949	+	0.141421i
$51$		0			0
$52$	13.6603	−	3.66025i	1.89434	−	0.507586i
$53$	3.29423	+	12.2942i	0.452497	+	1.68874i	0.695344	+	0.718677i	$0.255252\pi$
$53$	3.29423	+	12.2942i	0.452497	+	1.68874i	−0.242846	+	0.970065i	$0.578081\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−5.46410	−	1.46410i	−0.717472	−	0.192246i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$		0			0
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	3.16987	+	15.4904i	0.393174	+	1.92135i
$66$		0			0
$67$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$67$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$68$	13.6603	+	3.66025i	1.65655	+	0.443871i
$69$		0			0
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	2.19615	−	8.19615i	0.258819	−	0.965926i
$73$	1.83013	+	6.83013i	0.214200	+	0.799406i	0.986447	+	0.164083i	$0.0524664\pi$
$73$	1.83013	+	6.83013i	0.214200	+	0.799406i	−0.772246	+	0.635323i	$0.780867\pi$
$74$	−12.1244	−	7.00000i	−1.40943	−	0.813733i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	8.92820	+	0.535898i	0.998203	+	0.0599153i
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$	−3.66025	+	13.6603i	−0.404207	+	1.50852i
$83$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$83$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$84$		0			0
$85$	−5.00000	+	15.0000i	−0.542326	+	1.62698i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	8.66025	−	5.00000i	0.917985	−	0.529999i	0.0349934	−	0.999388i	$-0.488859\pi$
$89$	8.66025	−	5.00000i	0.917985	−	0.529999i	0.882992	+	0.469389i	$0.155526\pi$
$90$	9.00000	+	3.00000i	0.948683	+	0.316228i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.00000	−	5.00000i	−0.507673	−	0.507673i	0.406138	−	0.913812i	$-0.366875\pi$
$97$	−5.00000	−	5.00000i	−0.507673	−	0.507673i	−0.913812	+	0.406138i	$0.866875\pi$
$98$		0			0
$99$		0			0
$100$	−1.19615	+	9.92820i	−0.119615	+	0.992820i
$101$	−10.0000	+	17.3205i	−0.995037	+	1.72345i	−0.411346	+	0.911479i	$0.634941\pi$
$101$	−10.0000	+	17.3205i	−0.995037	+	1.72345i	−0.583691	+	0.811976i	$0.698392\pi$
$102$		0			0
$103$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$103$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$104$		−	20.0000i		−	1.96116i
$105$		0			0
$106$	18.0000			1.74831
$107$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$107$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$108$		0			0
$109$	−5.19615	−	3.00000i	−0.497701	−	0.287348i	0.230063	−	0.973176i	$-0.426107\pi$
$109$	−5.19615	−	3.00000i	−0.497701	−	0.287348i	−0.727764	+	0.685828i	$0.759440\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.00000	+	1.00000i	−0.0940721	+	0.0940721i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$	−1.00000	+	1.00000i	−0.0940721	+	0.0940721i	0.658505	+	0.752577i	$0.271189\pi$
$114$		0			0
$115$		0			0
$116$	−4.00000	+	6.92820i	−0.371391	+	0.643268i
$117$	5.49038	−	20.4904i	0.507586	−	1.89434i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−5.50000	−	9.52628i	−0.500000	−	0.866025i
$122$	−13.6603	+	3.66025i	−1.23674	+	0.331384i
$123$		0			0
$124$		0			0
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$127$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$128$	−10.9282	−	2.92820i	−0.965926	−	0.258819i
$129$		0			0
$130$	22.3205	+	1.33975i	1.95764	+	0.117503i
$131$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$131$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	10.0000	−	17.3205i	0.857493	−	1.48522i
$137$	−9.56218	+	2.56218i	−0.816952	+	0.218902i	−0.643013	−	0.765855i	$-0.722316\pi$
$137$	−9.56218	+	2.56218i	−0.816952	+	0.218902i	−0.173939	+	0.984757i	$0.555649\pi$
$138$		0			0
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−10.3923	−	6.00000i	−0.866025	−	0.500000i
$145$	−7.46410	−	4.92820i	−0.619860	−	0.409265i
$146$	10.0000			0.827606
$147$		0			0
$148$	−14.0000	+	14.0000i	−1.15079	+	1.15079i
$149$	12.1244	−	7.00000i	0.993266	−	0.573462i	0.0870170	−	0.996207i	$-0.472267\pi$
$149$	12.1244	−	7.00000i	0.993266	−	0.573462i	0.906249	+	0.422744i	$0.138933\pi$
$150$		0			0
$151$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$151$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$152$		0			0
$153$	15.0000	−	15.0000i	1.21268	−	1.21268i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	6.83013	−	1.83013i	0.545103	−	0.146060i	0.0242497	−	0.999706i	$-0.492280\pi$
$157$	6.83013	−	1.83013i	0.545103	−	0.146060i	0.520854	+	0.853646i	$0.325614\pi$
$158$		0			0
$159$		0			0
$160$	4.00000	−	12.0000i	0.316228	−	0.948683i
$161$		0			0
$162$	−9.00000	−	9.00000i	−0.707107	−	0.707107i
$163$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$163$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$164$	17.3205	+	10.0000i	1.35250	+	0.780869i
$165$		0			0
$166$		0			0
$167$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$167$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$168$		0			0
$169$		−	37.0000i		−	2.84615i
$170$	18.6603	+	12.3205i	1.43118	+	0.944940i
$171$		0			0
$172$		0			0
$173$	−20.4904	−	5.49038i	−1.55785	−	0.417426i	−0.625871	−	0.779926i	$-0.715256\pi$
$173$	−20.4904	−	5.49038i	−1.55785	−	0.417426i	−0.931984	+	0.362500i	$0.881923\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−3.66025	−	13.6603i	−0.274348	−	1.02388i
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$	7.39230	−	11.1962i	0.550990	−	0.834512i
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−14.6865	−	16.5622i	−1.07978	−	1.21768i
$186$		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
$193$	6.95448	+	25.9545i	0.500595	+	1.86824i	0.496119	+	0.868255i	$0.334758\pi$
$193$	6.95448	+	25.9545i	0.500595	+	1.86824i	0.00447566	+	0.999990i	$0.498575\pi$
$194$	−8.66025	+	5.00000i	−0.621770	+	0.358979i
$195$		0			0
$196$		0			0
$197$	13.0000	+	13.0000i	0.926212	+	0.926212i	0.997459	−	0.0712470i	$-0.0226979\pi$
$197$	13.0000	+	13.0000i	0.926212	+	0.926212i	−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	13.1244	+	5.26795i	0.928032	+	0.372500i
$201$		0			0
$202$	20.0000	+	20.0000i	1.40720	+	1.40720i
$203$		0			0
$204$		0			0
$205$	−12.3205	+	18.6603i	−0.860502	+	1.30329i
$206$		0			0
$207$		0			0
$208$	−27.3205	−	7.32051i	−1.89434	−	0.507586i
$209$		0			0
$210$		0			0
$211$		0			0		1.00000			$0$
$211$		0			0		−1.00000			$\pi$
$212$	6.58846	−	24.5885i	0.452497	−	1.68874i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−6.00000	+	6.00000i	−0.406371	+	0.406371i
$219$		0			0
$220$		0			0
$221$	25.0000	−	43.3013i	1.68168	−	2.91276i
$222$		0			0
$223$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$223$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$224$		0			0
$225$	12.0000	+	9.00000i	0.800000	+	0.600000i
$226$	1.00000	+	1.73205i	0.0665190	+	0.115214i
$227$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$227$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$228$		0			0
$229$	−25.9808	+	15.0000i	−1.71686	+	0.991228i	−0.792347	+	0.610071i	$0.791141\pi$
$229$	−25.9808	+	15.0000i	−1.71686	+	0.991228i	−0.924510	+	0.381157i	$0.875526\pi$
$230$		0			0
$231$		0			0
$232$	8.00000	+	8.00000i	0.525226	+	0.525226i
$233$	−28.6865	−	7.68653i	−1.87932	−	0.503562i	−0.999606	−	0.0280525i	$-0.991069\pi$
$233$	−28.6865	−	7.68653i	−1.87932	−	0.503562i	−0.879711	−	0.475509i	$-0.842264\pi$
$234$	−25.9808	−	15.0000i	−1.69842	−	0.980581i
$235$		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
$241$	15.0000	−	25.9808i	0.966235	−	1.67357i	0.259975	−	0.965615i	$-0.416286\pi$
$241$	15.0000	−	25.9808i	0.966235	−	1.67357i	0.706260	−	0.707953i	$-0.250381\pi$
$242$	−15.0263	+	4.02628i	−0.965926	+	0.258819i
$243$		0			0
$244$			20.0000i			1.28037i
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−6.75833	+	14.2942i	−0.427434	+	0.904046i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−5.49038	+	20.4904i	−0.342481	+	1.27815i	0.553047	+	0.833150i	$0.313465\pi$
$257$	−5.49038	+	20.4904i	−0.342481	+	1.27815i	−0.895528	+	0.445005i	$0.853202\pi$
$258$		0			0
$259$		0			0
$260$	10.0000	−	30.0000i	0.620174	−	1.86052i
$261$	6.00000	+	10.3923i	0.371391	+	0.643268i
$262$		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
$265$	27.0000	+	9.00000i	1.65860	+	0.552866i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−17.3205	−	10.0000i	−1.05605	−	0.609711i	−0.131713	−	0.991288i	$-0.542048\pi$
$269$	−17.3205	−	10.0000i	−1.05605	−	0.609711i	−0.924337	+	0.381577i	$0.875381\pi$
$270$		0			0
$271$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$271$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$272$	−20.0000	−	20.0000i	−1.21268	−	1.21268i
$273$		0			0
$274$			14.0000i			0.845771i
$275$		0			0
$276$		0			0
$277$	−31.4186	+	8.41858i	−1.88776	+	0.505824i	−0.888899	+	0.458103i	$0.848529\pi$
$277$	−31.4186	+	8.41858i	−1.88776	+	0.505824i	−0.998861	+	0.0477206i	$0.984804\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−32.0000			−1.90896			−0.954480	−	0.298275i	$-0.903589\pi$
$281$	−32.0000			−1.90896			−0.954480	+	0.298275i	$0.903589\pi$
$282$		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
$288$	−12.0000	+	12.0000i	−0.707107	+	0.707107i
$289$	28.5788	−	16.5000i	1.68111	−	0.970588i
$290$	−9.46410	+	8.39230i	−0.555751	+	0.492813i
$291$		0			0
$292$	3.66025	−	13.6603i	0.214200	−	0.799406i
$293$	−15.0000	+	15.0000i	−0.876309	+	0.876309i	−0.993151	−	0.116841i	$-0.962723\pi$
$293$	−15.0000	+	15.0000i	−0.876309	+	0.876309i	0.116841	+	0.993151i	$0.462723\pi$
$294$		0			0
$295$		0			0
$296$	14.0000	+	24.2487i	0.813733	+	1.40943i
$297$		0			0
$298$	−5.12436	−	19.1244i	−0.296846	−	1.10784i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−22.3205	−	1.33975i	−1.27807	−	0.0767136i
$306$	−15.0000	−	25.9808i	−0.857493	−	1.48522i
$307$		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		0.500000	−	0.866025i	$-0.333333\pi$
$311$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$312$		0			0
$313$	34.1506	+	9.15064i	1.93031	+	0.517224i	0.975499	+	0.220006i	$0.0706077\pi$
$313$	34.1506	+	9.15064i	1.93031	+	0.517224i	0.954810	+	0.297218i	$0.0960589\pi$
$314$		−	10.0000i		−	0.564333i
$315$		0			0
$316$		0			0
$317$	1.09808	−	4.09808i	0.0616741	−	0.230171i	−0.928208	−	0.372061i	$-0.878651\pi$
$317$	1.09808	−	4.09808i	0.0616741	−	0.230171i	0.989882	+	0.141890i	$0.0453179\pi$
$318$		0			0
$319$		0			0
$320$	−14.9282	−	9.85641i	−0.834512	−	0.550990i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−15.5885	+	9.00000i	−0.866025	+	0.500000i
$325$	32.8109	+	13.1699i	1.82002	+	0.730533i
$326$		0			0
$327$		0			0
$328$	20.0000	−	20.0000i	1.10432	−	1.10432i
$329$		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
$333$	7.68653	+	28.6865i	0.421219	+	1.57201i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	7.00000	+	7.00000i	0.381314	+	0.381314i	0.871576	−	0.490261i	$-0.163099\pi$
$337$	7.00000	+	7.00000i	0.381314	+	0.381314i	−0.490261	+	0.871576i	$0.663099\pi$
$338$	−50.5429	−	13.5429i	−2.74917	−	0.736639i
$339$		0			0
$340$	23.6603	−	20.9808i	1.28316	−	1.13784i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−15.0000	+	25.9808i	−0.806405	+	1.39673i
$347$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$347$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$348$		0			0
$349$		−	10.0000i		−	0.535288i	−0.963518	−	0.267644i	$-0.913755\pi$
$349$		−	10.0000i		−	0.535288i	0.963518	−	0.267644i	$-0.0862451\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−9.15064	−	34.1506i	−0.487039	−	1.81765i	−0.570697	−	0.821160i	$-0.693327\pi$
$353$	−9.15064	−	34.1506i	−0.487039	−	1.81765i	0.0836583	−	0.996495i	$-0.473340\pi$
$354$		0			0
$355$		0			0
$356$	−20.0000			−1.06000
$357$		0			0
$358$		0			0
$359$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$	−12.5885	−	14.1962i	−0.663470	−	0.748203i
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	7.32051	−	27.3205i	0.384757	−	1.43593i
$363$		0			0
$364$		0			0
$365$	15.0000	+	5.00000i	0.785136	+	0.261712i
$366$		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
$369$	25.9808	−	15.0000i	1.35250	−	0.780869i
$370$	−28.0000	+	14.0000i	−1.45565	+	0.727825i
$371$		0			0
$372$		0			0
$373$	15.0263	+	4.02628i	0.778031	+	0.208473i	0.625917	−	0.779890i	$-0.284725\pi$
$373$	15.0263	+	4.02628i	0.778031	+	0.208473i	0.152115	+	0.988363i	$0.451392\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	20.0000	+	20.0000i	1.03005	+	1.03005i
$378$		0			0
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$		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
$386$	38.0000			1.93415
$387$		0			0
$388$	3.66025	+	13.6603i	0.185821	+	0.693494i
$389$	29.4449	+	17.0000i	1.49291	+	0.861934i	0.999967	−	0.00812520i	$-0.00258636\pi$
$389$	29.4449	+	17.0000i	1.49291	+	0.861934i	0.492947	+	0.870059i	$0.335920\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	22.5167	−	13.0000i	1.13437	−	0.654931i
$395$		0			0
$396$		0			0
$397$	−9.15064	+	34.1506i	−0.459257	+	1.71397i	0.216004	+	0.976392i	$0.430698\pi$
$397$	−9.15064	+	34.1506i	−0.459257	+	1.71397i	−0.675261	+	0.737579i	$0.735969\pi$
$398$		0			0
$399$		0			0
$400$	12.0000	−	16.0000i	0.600000	−	0.800000i
$401$	1.00000	+	1.73205i	0.0499376	+	0.0864945i	0.889914	−	0.456129i	$-0.150764\pi$
$401$	1.00000	+	1.73205i	0.0499376	+	0.0864945i	−0.839976	+	0.542623i	$0.817431\pi$
$402$		0			0
$403$		0			0
$404$	34.6410	−	20.0000i	1.72345	−	0.995037i
$405$	−9.00000	−	18.0000i	−0.447214	−	0.894427i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	34.6410	+	20.0000i	1.71289	+	0.988936i	0.930614	+	0.366002i	$0.119274\pi$
$409$	34.6410	+	20.0000i	1.71289	+	0.988936i	0.782274	+	0.622935i	$0.214060\pi$
$410$	20.9808	+	23.6603i	1.03617	+	1.16850i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−20.0000	+	34.6410i	−0.980581	+	1.69842i
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−28.0000			−1.36464			−0.682318	−	0.731055i	$-0.739028\pi$
$421$	−28.0000			−1.36464			−0.682318	+	0.731055i	$0.739028\pi$
$422$		0			0
$423$		0			0
$424$	−31.1769	−	18.0000i	−1.51408	−	0.874157i
$425$	21.8301	+	27.8109i	1.05892	+	1.34903i
$426$		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
$433$	5.00000	−	5.00000i	0.240285	−	0.240285i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$	5.00000	−	5.00000i	0.240285	−	0.240285i	0.816968	+	0.576683i	$0.195653\pi$
$434$		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	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$		0			0
$442$	−50.0000	−	50.0000i	−2.37826	−	2.37826i
$443$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$443$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$444$		0			0
$445$	1.33975	−	22.3205i	0.0635100	−	1.05809i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			14.0000i			0.660701i	0.943858	+	0.330350i	$0.107167\pi$
$449$			14.0000i			0.660701i	−0.943858	+	0.330350i	$0.892833\pi$
$450$	16.6865	−	13.0981i	0.786611	−	0.617449i
$451$		0			0
$452$	2.73205	−	0.732051i	0.128505	−	0.0344328i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−6.22243	+	23.2224i	−0.291073	+	1.08630i	0.653213	+	0.757174i	$0.273421\pi$
$457$	−6.22243	+	23.2224i	−0.291073	+	1.08630i	−0.944286	+	0.329125i	$0.893246\pi$
$458$	10.9808	+	40.9808i	0.513097	+	1.91491i
$459$		0			0
$460$		0			0
$461$	−20.0000			−0.931493			−0.465746	−	0.884918i	$-0.654214\pi$
$461$	−20.0000			−0.931493			−0.465746	+	0.884918i	$0.654214\pi$
$462$		0			0
$463$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$463$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$464$	13.8564	−	8.00000i	0.643268	−	0.371391i
$465$		0			0
$466$	−21.0000	+	36.3731i	−0.972806	+	1.68495i
$467$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$467$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$468$	−30.0000	+	30.0000i	−1.38675	+	1.38675i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−27.0000	−	27.0000i	−1.23625	−	1.23625i
$478$		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
$481$	35.0000	+	60.6218i	1.59586	+	2.76412i
$482$	−30.0000	−	30.0000i	−1.36646	−	1.36646i
$483$		0			0
$484$			22.0000i			1.00000i
$485$	−15.4904	+	3.16987i	−0.703382	+	0.143937i
$486$		0			0
$487$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$487$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$488$	27.3205	+	7.32051i	1.23674	+	0.331384i
$489$		0			0
$490$		0			0
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$	7.32051	+	27.3205i	0.329699	+	1.23045i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$499$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$500$	17.0526	+	14.4641i	0.762614	+	0.646854i
$501$		0			0
$502$		0			0
$503$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$503$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$504$		0			0
$505$	20.0000	+	40.0000i	0.889988	+	1.77998i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−8.66025	+	5.00000i	−0.383859	+	0.221621i	−0.679496	−	0.733679i	$-0.737801\pi$
$509$	−8.66025	+	5.00000i	−0.383859	+	0.221621i	0.295637	+	0.955300i	$0.404468\pi$
$510$		0			0
$511$		0			0
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$		0			0
$514$	25.9808	+	15.0000i	1.14596	+	0.661622i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−37.3205	−	24.6410i	−1.63661	−	1.08058i
$521$	20.0000	−	34.6410i	0.876216	−	1.51765i	0.0207541	−	0.999785i	$-0.493393\pi$
$521$	20.0000	−	34.6410i	0.876216	−	1.51765i	0.855462	−	0.517866i	$-0.173273\pi$
$522$	16.3923	−	4.39230i	0.717472	−	0.192246i
$523$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$523$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	19.9186	+	11.5000i	0.866025	+	0.500000i
$530$	22.1769	−	33.5885i	0.963304	−	1.45899i
$531$		0			0
$532$		0			0
$533$	50.0000	−	50.0000i	2.16574	−	2.16574i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−20.0000	+	20.0000i	−0.862261	+	0.862261i
$539$		0			0
$540$		0			0
$541$	−21.0000	−	36.3731i	−0.902861	−	1.56380i	−0.823764	−	0.566933i	$-0.808130\pi$
$541$	−21.0000	−	36.3731i	−0.902861	−	1.56380i	−0.0790969	−	0.996867i	$-0.525204\pi$
$542$		0			0
$543$		0			0
$544$	−34.6410	+	20.0000i	−1.48522	+	0.857493i
$545$	−12.0000	+	6.00000i	−0.514024	+	0.257012i
$546$		0			0
$547$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$547$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$548$	19.1244	+	5.12436i	0.816952	+	0.218902i
$549$	25.9808	+	15.0000i	1.10883	+	0.640184i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$			46.0000i			1.95435i
$555$		0			0
$556$		0			0
$557$	−45.0788	+	12.0788i	−1.91005	+	0.511797i	−0.916253	+	0.400599i	$0.868802\pi$
$557$	−45.0788	+	12.0788i	−1.91005	+	0.511797i	−0.993798	+	0.111198i	$0.964531\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−11.7128	+	43.7128i	−0.494075	+	1.84391i
$563$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$563$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$564$		0			0
$565$	0.633975	+	3.09808i	0.0266715	+	0.130337i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	22.5167	−	13.0000i	0.943948	−	0.544988i	0.0527519	−	0.998608i	$-0.483201\pi$
$569$	22.5167	−	13.0000i	0.943948	−	0.544988i	0.891196	+	0.453619i	$0.149867\pi$
$570$		0			0
$571$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$571$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	12.0000	+	20.7846i	0.500000	+	0.866025i
$577$	34.1506	−	9.15064i	1.42171	−	0.380946i	0.535620	−	0.844459i	$-0.320078\pi$
$577$	34.1506	−	9.15064i	1.42171	−	0.380946i	0.886090	+	0.463513i	$0.153411\pi$
$578$	−12.0788	−	45.0788i	−0.502413	−	1.87503i
$579$		0			0
$580$	8.00000	+	16.0000i	0.332182	+	0.664364i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−17.3205	−	10.0000i	−0.716728	−	0.413803i
$585$	−31.4711	−	35.4904i	−1.30117	−	1.46735i
$586$	15.0000	+	25.9808i	0.619644	+	1.07326i
$587$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$587$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	38.2487	−	10.2487i	1.57201	−	0.421219i
$593$	20.4904	+	5.49038i	0.841439	+	0.225463i	0.653698	−	0.756756i	$-0.273217\pi$
$593$	20.4904	+	5.49038i	0.841439	+	0.225463i	0.187741	+	0.982219i	$0.439883\pi$
$594$		0			0
$595$		0			0
$596$	−28.0000			−1.14692
$597$		0			0
$598$		0			0
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−24.5526	−	1.47372i	−0.998203	−	0.0599153i
$606$		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
$610$	−10.0000	+	30.0000i	−0.404888	+	1.21466i
$611$		0			0
$612$	−40.9808	+	10.9808i	−1.65655	+	0.443871i
$613$	0.366025	+	1.36603i	0.0147836	+	0.0551732i	0.972924	−	0.231127i	$-0.0742412\pi$
$613$	0.366025	+	1.36603i	0.0147836	+	0.0551732i	−0.958140	+	0.286300i	$0.907575\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.00000	−	3.00000i	−0.120775	−	0.120775i	0.644136	−	0.764911i	$-0.277217\pi$
$617$	−3.00000	−	3.00000i	−0.120775	−	0.120775i	−0.764911	+	0.644136i	$0.777217\pi$
$618$		0			0
$619$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$619$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	25.0000	−	43.3013i	0.999201	−	1.73067i
$627$		0			0
$628$	−13.6603	−	3.66025i	−0.545103	−	0.146060i
$629$			70.0000i			2.79108i
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$		0			0
$634$	−5.19615	−	3.00000i	−0.206366	−	0.119145i
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−18.9282	+	16.7846i	−0.748203	+	0.663470i
$641$	−4.00000	+	6.92820i	−0.157991	+	0.273648i	−0.934144	−	0.356897i	$-0.883835\pi$
$641$	−4.00000	+	6.92820i	−0.157991	+	0.273648i	0.776153	+	0.630544i	$0.217168\pi$
$642$		0			0
$643$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$643$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$644$		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
$650$	30.0000	−	40.0000i	1.17670	−	1.56893i
$651$		0			0
$652$		0			0
$653$	12.2942	+	3.29423i	0.481110	+	0.128913i	0.491220	−	0.871036i	$-0.336551\pi$
$653$	12.2942	+	3.29423i	0.481110	+	0.128913i	−0.0101092	+	0.999949i	$0.503218\pi$
$654$		0			0
$655$		0			0
$656$	−20.0000	−	34.6410i	−0.780869	−	1.35250i
$657$	−15.0000	−	15.0000i	−0.585206	−	0.585206i
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−25.0000	+	43.3013i	−0.972387	+	1.68422i	−0.284087	+	0.958799i	$0.591690\pi$
$661$	−25.0000	+	43.3013i	−0.972387	+	1.68422i	−0.688301	+	0.725426i	$0.741643\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	42.0000			1.62747
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	11.0000	−	11.0000i	0.424019	−	0.424019i	−0.462566	−	0.886585i	$-0.653071\pi$
$673$	11.0000	−	11.0000i	0.424019	−	0.424019i	0.886585	+	0.462566i	$0.153071\pi$
$674$	12.1244	−	7.00000i	0.467013	−	0.269630i
$675$		0			0
$676$	−37.0000	+	64.0859i	−1.42308	+	2.46484i
$677$	9.15064	−	34.1506i	0.351687	−	1.31252i	−0.532915	−	0.846169i	$-0.678903\pi$
$677$	9.15064	−	34.1506i	0.351687	−	1.31252i	0.884602	−	0.466347i	$-0.154430\pi$
$678$		0			0
$679$		0			0
$680$	−20.0000	−	40.0000i	−0.766965	−	1.53393i
$681$		0			0
$682$		0			0
$683$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$683$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$684$		0			0
$685$	−7.00000	+	21.0000i	−0.267456	+	0.802369i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−77.9423	−	45.0000i	−2.96936	−	1.71436i
$690$		0			0
$691$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$691$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$692$	30.0000	+	30.0000i	1.14043	+	1.14043i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	68.3013	−	18.3013i	2.58710	−	0.693210i
$698$	−13.6603	−	3.66025i	−0.517048	−	0.138543i
$699$		0			0
$700$		0			0
$701$	−52.0000			−1.96401			−0.982006	−	0.188847i	$-0.939525\pi$
$701$	−52.0000			−1.96401			−0.982006	+	0.188847i	$0.939525\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−50.0000			−1.88177
$707$		0			0
$708$		0			0
$709$	−38.1051	+	22.0000i	−1.43107	+	0.826227i	−0.997202	−	0.0747503i	$-0.976184\pi$
$709$	−38.1051	+	22.0000i	−1.43107	+	0.826227i	−0.433865	+	0.900978i	$0.642851\pi$
$710$		0			0
$711$		0			0
$712$	−7.32051	+	27.3205i	−0.274348	+	1.02388i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	−24.0000	+	12.0000i	−0.894427	+	0.447214i
$721$		0			0
$722$	−19.0000	−	19.0000i	−0.707107	−	0.707107i
$723$		0			0
$724$	−34.6410	−	20.0000i	−1.28742	−	0.743294i
$725$	−18.3923	+	7.85641i	−0.683073	+	0.291780i
$726$		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
$730$	12.3205	−	18.6603i	0.456002	−	0.690647i
$731$		0			0
$732$		0			0
$733$	−34.1506	−	9.15064i	−1.26138	−	0.337986i	−0.434659	−	0.900595i	$-0.643131\pi$
$733$	−34.1506	−	9.15064i	−1.26138	−	0.337986i	−0.826723	+	0.562609i	$0.809798\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−10.9808	−	40.9808i	−0.404207	−	1.50852i
$739$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$739$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$740$	8.87564	+	43.3731i	0.326275	+	1.59443i
$741$		0			0
$742$		0			0
$743$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$743$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$744$		0			0
$745$	1.87564	−	31.2487i	0.0687183	−	1.14486i
$746$	11.0000	−	19.0526i	0.402739	−	0.697564i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$		0			0
$753$		0			0
$754$	34.6410	−	20.0000i	1.26155	−	0.728357i
$755$		0			0
$756$		0			0
$757$	17.0000	+	17.0000i	0.617876	+	0.617876i	0.944986	−	0.327111i	$-0.106075\pi$
$757$	17.0000	+	17.0000i	0.617876	+	0.617876i	−0.327111	+	0.944986i	$0.606075\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−20.0000	−	34.6410i	−0.724999	−	1.25574i	−0.958974	−	0.283493i	$-0.908507\pi$
$761$	−20.0000	−	34.6410i	−0.724999	−	1.25574i	0.233975	−	0.972243i	$-0.424827\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−9.50962	−	46.4711i	−0.343821	−	1.68017i
$766$		0			0
$767$		0			0
$768$		0			0
$769$		−	50.0000i		−	1.80305i	−0.432731	−	0.901523i	$-0.642450\pi$
$769$		−	50.0000i		−	1.80305i	0.432731	−	0.901523i	$-0.357550\pi$
$770$		0			0
$771$		0			0
$772$	13.9090	−	51.9090i	0.500595	−	1.86824i
$773$	−1.83013	−	6.83013i	−0.0658251	−	0.245663i	0.925172	−	0.379549i	$-0.123921\pi$
$773$	−1.83013	−	6.83013i	−0.0658251	−	0.245663i	−0.990997	+	0.133887i	$0.957254\pi$
$774$		0			0
$775$		0			0
$776$	20.0000			0.717958
$777$		0			0
$778$	34.0000	−	34.0000i	1.21896	−	1.21896i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.00000	−	15.0000i	0.178458	−	0.535373i
$786$		0			0
$787$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$787$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$788$	−9.51666	−	35.5167i	−0.339017	−	1.26523i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	68.3013	+	18.3013i	2.42545	+	0.649897i
$794$	43.3013	+	25.0000i	1.53670	+	0.887217i
$795$		0			0
$796$		0			0
$797$	−15.0000	−	15.0000i	−0.531327	−	0.531327i	0.389640	−	0.920967i	$-0.372599\pi$
$797$	−15.0000	−	15.0000i	−0.531327	−	0.531327i	−0.920967	+	0.389640i	$0.872599\pi$
$798$		0			0
$799$		0			0
$800$	−17.4641	−	22.2487i	−0.617449	−	0.786611i
$801$	−15.0000	+	25.9808i	−0.529999	+	0.917985i
$802$	2.73205	−	0.732051i	0.0964721	−	0.0258496i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−14.6410	−	54.6410i	−0.515069	−	1.92226i
$809$	48.4974	+	28.0000i	1.70508	+	0.984428i	0.940435	+	0.339975i	$0.110418\pi$
$809$	48.4974	+	28.0000i	1.70508	+	0.984428i	0.764644	+	0.644453i	$0.222915\pi$
$810$	−27.8827	+	5.70577i	−0.979698	+	0.200480i
$811$		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
$818$	40.0000	−	40.0000i	1.39857	−	1.39857i
$819$		0			0
$820$	40.0000	−	20.0000i	1.39686	−	0.698430i
$821$	14.0000	+	24.2487i	0.488603	+	0.846286i	0.999914	−	0.0131101i	$-0.00417319\pi$
$821$	14.0000	+	24.2487i	0.488603	+	0.846286i	−0.511311	+	0.859396i	$0.670840\pi$
$822$		0			0
$823$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$823$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$827$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$828$		0			0
$829$	17.3205	+	10.0000i	0.601566	+	0.347314i	0.769657	−	0.638457i	$-0.220427\pi$
$829$	17.3205	+	10.0000i	0.601566	+	0.347314i	−0.168091	+	0.985771i	$0.553760\pi$
$830$		0			0
$831$		0			0
$832$	40.0000	+	40.0000i	1.38675	+	1.38675i
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	13.0000			0.448276
$842$	−10.2487	+	38.2487i	−0.353194	+	1.31814i
$843$		0			0
$844$		0			0
$845$	−69.0429	−	45.5859i	−2.37515	−	1.56820i
$846$		0			0
$847$		0			0
$848$	−36.0000	+	36.0000i	−1.23625	+	1.23625i
$849$		0			0
$850$	45.9808	−	19.6410i	1.57713	−	0.673681i
$851$		0			0
$852$		0			0
$853$	5.00000	−	5.00000i	0.171197	−	0.171197i	−0.616308	−	0.787505i	$-0.711372\pi$
$853$	5.00000	−	5.00000i	0.171197	−	0.171197i	0.787505	+	0.616308i	$0.211372\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−34.1506	+	9.15064i	−1.16656	+	0.312580i	−0.789584	−	0.613642i	$-0.789704\pi$
$857$	−34.1506	+	9.15064i	−1.16656	+	0.312580i	−0.376979	+	0.926222i	$0.623037\pi$
$858$		0			0
$859$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$859$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$863$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$864$		0			0
$865$	−35.4904	+	31.4711i	−1.20671	+	1.07005i
$866$	−5.00000	−	8.66025i	−0.169907	−	0.294287i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	16.3923	−	4.39230i	0.555113	−	0.148742i
$873$	20.4904	+	5.49038i	0.693494	+	0.185821i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−8.41858	+	31.4186i	−0.284275	+	1.06093i	0.665092	+	0.746762i	$0.268392\pi$
$877$	−8.41858	+	31.4186i	−0.284275	+	1.06093i	−0.949367	+	0.314169i	$0.898274\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	50.0000			1.68454			0.842271	−	0.539054i	$-0.181218\pi$
$881$	50.0000			1.68454			0.842271	+	0.539054i	$0.181218\pi$
$882$		0			0
$883$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$883$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$884$	−86.6025	+	50.0000i	−2.91276	+	1.68168i
$885$		0			0
$886$		0			0
$887$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$887$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$888$		0			0
$889$		0			0
$890$	−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
$898$	19.1244	+	5.12436i	0.638188	+	0.171002i
$899$		0			0
$900$	−11.7846	−	27.5885i	−0.392820	−	0.919615i
$901$	−45.0000	−	77.9423i	−1.49917	−	2.59663i
$902$		0			0
$903$		0			0
$904$		−	4.00000i		−	0.133038i
$905$	24.6410	−	37.3205i	0.819095	−	1.24058i
$906$		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
$909$		−	60.0000i		−	1.99007i
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$	29.4449	+	17.0000i	0.973950	+	0.562310i
$915$		0			0
$916$	60.0000			1.98246
$917$		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
$922$	−7.32051	+	27.3205i	−0.241088	+	0.899753i
$923$		0			0
$924$		0			0
$925$	−49.0000	+	7.00000i	−1.61111	+	0.230159i
$926$		0			0
$927$		0			0
$928$	−5.85641	−	21.8564i	−0.192246	−	0.717472i
$929$	−34.6410	+	20.0000i	−1.13653	+	0.656179i	−0.945570	−	0.325418i	$-0.894495\pi$
$929$	−34.6410	+	20.0000i	−1.13653	+	0.656179i	−0.190965	+	0.981597i	$0.561162\pi$
$930$		0			0
$931$		0			0
$932$	42.0000	+	42.0000i	1.37576	+	1.37576i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	30.0000	+	51.9615i	0.980581	+	1.69842i
$937$	5.00000	+	5.00000i	0.163343	+	0.163343i	0.784046	−	0.620703i	$-0.213153\pi$
$937$	5.00000	+	5.00000i	0.163343	+	0.163343i	−0.620703	+	0.784046i	$0.713153\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.0000	−	17.3205i	0.325991	−	0.564632i	−0.655722	−	0.755003i	$-0.727636\pi$
$941$	10.0000	−	17.3205i	0.325991	−	0.564632i	0.981712	+	0.190370i	$0.0609689\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$947$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$948$		0			0
$949$	−43.3013	−	25.0000i	−1.40562	−	0.811534i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−41.0000	+	41.0000i	−1.32812	+	1.32812i	−0.421111	+	0.907009i	$0.638360\pi$
$953$	−41.0000	+	41.0000i	−1.32812	+	1.32812i	−0.907009	+	0.421111i	$0.861640\pi$
$954$	−46.7654	+	27.0000i	−1.51408	+	0.874157i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−15.5000	−	26.8468i	−0.500000	−	0.866025i
$962$	95.6218	−	25.6218i	3.08297	−	0.826079i
$963$		0			0
$964$	−51.9615	+	30.0000i	−1.67357	+	0.966235i
$965$	57.0000	+	19.0000i	1.83489	+	0.611632i
$966$		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
$970$	−1.33975	+	22.3205i	−0.0430167	+	0.716668i
$971$		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
$976$	20.0000	−	34.6410i	0.640184	−	1.10883i
$977$	−36.8827	+	9.88269i	−1.17998	+	0.316175i	−0.794919	−	0.606715i	$-0.792487\pi$
$977$	−36.8827	+	9.88269i	−1.17998	+	0.316175i	−0.385063	+	0.922890i	$0.625820\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	18.0000			0.574696
$982$		0			0
$983$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$983$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$984$		0			0
$985$	40.2750	−	8.24167i	1.28327	−	0.262601i
$986$	40.0000			1.27386
$987$		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
$997$	−34.1506	+	9.15064i	−1.08156	+	0.289804i	−0.755235	−	0.655454i	$-0.772477\pi$
$997$	−34.1506	+	9.15064i	−1.08156	+	0.289804i	−0.326326	+	0.945257i	$0.605811\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.a.67.1		4
4.3	odd	2	CM	980.2.x.a.67.1		4
5.3	odd	4	inner	980.2.x.a.263.1		4
7.2	even	3	inner	980.2.x.a.667.1		4
7.3	odd	6		980.2.k.b.687.1	✓	2
7.4	even	3		980.2.k.c.687.1	yes	2
7.5	odd	6		980.2.x.b.667.1		4
7.6	odd	2		980.2.x.b.67.1		4
20.3	even	4	inner	980.2.x.a.263.1		4
28.3	even	6		980.2.k.b.687.1	✓	2
28.11	odd	6		980.2.k.c.687.1	yes	2
28.19	even	6		980.2.x.b.667.1		4
28.23	odd	6	inner	980.2.x.a.667.1		4
28.27	even	2		980.2.x.b.67.1		4
35.3	even	12		980.2.k.b.883.1	yes	2
35.13	even	4		980.2.x.b.263.1		4
35.18	odd	12		980.2.k.c.883.1	yes	2
35.23	odd	12	inner	980.2.x.a.863.1		4
35.33	even	12		980.2.x.b.863.1		4
140.3	odd	12		980.2.k.b.883.1	yes	2
140.23	even	12	inner	980.2.x.a.863.1		4
140.83	odd	4		980.2.x.b.263.1		4
140.103	odd	12		980.2.x.b.863.1		4
140.123	even	12		980.2.k.c.883.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.k.b.687.1	✓	2	7.3	odd	6
980.2.k.b.687.1	✓	2	28.3	even	6
980.2.k.b.883.1	yes	2	35.3	even	12
980.2.k.b.883.1	yes	2	140.3	odd	12
980.2.k.c.687.1	yes	2	7.4	even	3
980.2.k.c.687.1	yes	2	28.11	odd	6
980.2.k.c.883.1	yes	2	35.18	odd	12
980.2.k.c.883.1	yes	2	140.123	even	12
980.2.x.a.67.1		4	1.1	even	1	trivial
980.2.x.a.67.1		4	4.3	odd	2	CM
980.2.x.a.263.1		4	5.3	odd	4	inner
980.2.x.a.263.1		4	20.3	even	4	inner
980.2.x.a.667.1		4	7.2	even	3	inner
980.2.x.a.667.1		4	28.23	odd	6	inner
980.2.x.a.863.1		4	35.23	odd	12	inner
980.2.x.a.863.1		4	140.23	even	12	inner
980.2.x.b.67.1		4	7.6	odd	2
980.2.x.b.67.1		4	28.27	even	2
980.2.x.b.263.1		4	35.13	even	4
980.2.x.b.263.1		4	140.83	odd	4
980.2.x.b.667.1		4	7.5	odd	6
980.2.x.b.667.1		4	28.19	even	6
980.2.x.b.863.1		4	35.33	even	12
980.2.x.b.863.1		4	140.103	odd	12

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(1.23205 - 1.86603i) q^{5} +(-2.00000 + 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(1.23205 - 1.86603i) q^{5} +(-2.00000 + 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +(-2.09808 - 2.36603i) q^{10} +(-5.00000 + 5.00000i) q^{13} +(2.00000 + 3.46410i) q^{16} +(-6.83013 + 1.83013i) q^{17} +(1.09808 + 4.09808i) q^{18} +(-4.00000 + 2.00000i) q^{20} +(-1.96410 - 4.59808i) q^{25} +(5.00000 + 8.66025i) q^{26} -4.00000i q^{29} +(5.46410 - 1.46410i) q^{32} +10.0000i q^{34} +6.00000 q^{36} +(2.56218 - 9.56218i) q^{37} +(1.26795 + 6.19615i) q^{40} -10.0000 q^{41} +(-0.401924 + 6.69615i) q^{45} +(-7.00000 + 1.00000i) q^{50} +(13.6603 - 3.66025i) q^{52} +(3.29423 + 12.2942i) q^{53} +(-5.46410 - 1.46410i) q^{58} +(-5.00000 - 8.66025i) q^{61} -8.00000i q^{64} +(3.16987 + 15.4904i) q^{65} +(13.6603 + 3.66025i) q^{68} +(2.19615 - 8.19615i) q^{72} +(1.83013 + 6.83013i) q^{73} +(-12.1244 - 7.00000i) q^{74} +(8.92820 + 0.535898i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-3.66025 + 13.6603i) q^{82} +(-5.00000 + 15.0000i) q^{85} +(8.66025 - 5.00000i) q^{89} +(9.00000 + 3.00000i) q^{90} +(-5.00000 - 5.00000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{5} - 8 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^5 - 8 * q^8	\( 4 q - 2 q^{2} - 2 q^{5} - 8 q^{8} + 2 q^{10} - 20 q^{13} + 8 q^{16} - 10 q^{17} - 6 q^{18} - 16 q^{20} + 6 q^{25} + 20 q^{26} + 8 q^{32} + 24 q^{36} - 14 q^{37} + 12 q^{40} - 40 q^{41} - 12 q^{45} - 28 q^{50} + 20 q^{52} - 18 q^{53} - 8 q^{58} - 20 q^{61} + 30 q^{65} + 20 q^{68} - 12 q^{72} - 10 q^{73} + 8 q^{80} + 18 q^{81} + 20 q^{82} - 20 q^{85} + 36 q^{90} - 20 q^{97}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^5 - 8 * q^8 + 2 * q^10 - 20 * q^13 + 8 * q^16 - 10 * q^17 - 6 * q^18 - 16 * q^20 + 6 * q^25 + 20 * q^26 + 8 * q^32 + 24 * q^36 - 14 * q^37 + 12 * q^40 - 40 * q^41 - 12 * q^45 - 28 * q^50 + 20 * q^52 - 18 * q^53 - 8 * q^58 - 20 * q^61 + 30 * q^65 + 20 * q^68 - 12 * q^72 - 10 * q^73 + 8 * q^80 + 18 * q^81 + 20 * q^82 - 20 * q^85 + 36 * q^90 - 20 * q^97

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