LMFDB - Embedded newform 164.2.o.a.111.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [164,2,Mod(7,164)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(164, base_ring=CyclotomicField(40))

chi = DirichletCharacter(H, H._module([20, 39]))

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

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

chi := DirichletCharacter("164.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 164 = 2^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	164.o (of order $40$, degree $16$, 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:	$1.30954659315$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\Q(\zeta_{40})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{40}]$

Embedding invariants

Embedding label			111.1
Root			$0.891007 - 0.453990i$ of defining polynomial
Character	$\chi$	$=$	164.111
Dual form			164.2.o.a.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.221232 + 1.39680i) q^{2} +(-1.90211 - 0.618034i) q^{4} +(-3.93080 + 2.00284i) q^{5} +(1.28408 - 2.52015i) q^{8} +(-2.12132 - 2.12132i) q^{9} +O(q^{10})$	\(q+(-0.221232 + 1.39680i) q^{2} +(-1.90211 - 0.618034i) q^{4} +(-3.93080 + 2.00284i) q^{5} +(1.28408 - 2.52015i) q^{8} +(-2.12132 - 2.12132i) q^{9} +(-1.92796 - 5.93364i) q^{10} +(1.04080 + 4.33524i) q^{13} +(3.23607 + 2.35114i) q^{16} +(-6.27019 + 5.35525i) q^{17} +(3.43237 - 2.49376i) q^{18} +(8.71465 - 1.38026i) q^{20} +(8.50088 - 11.7005i) q^{25} +(-6.28573 + 0.494697i) q^{26} +(5.72004 + 4.88538i) q^{29} +(-4.00000 + 4.00000i) q^{32} +(-6.09306 - 9.94297i) q^{34} +(2.72394 + 5.34604i) q^{36} +(-2.23416 + 6.87604i) q^{37} +12.4780i q^{40} +(-6.39623 - 0.297142i) q^{41} +(12.5872 + 4.08981i) q^{45} +(3.17793 - 6.23705i) q^{49} +(14.4626 + 14.4626i) q^{50} +(0.699608 - 8.88936i) q^{52} +(2.53572 - 2.96894i) q^{53} +(-8.08936 + 6.90897i) q^{58} +(-6.07643 + 0.962412i) q^{61} +(-4.70228 - 6.47214i) q^{64} +(-12.7740 - 14.9564i) q^{65} +(15.2363 - 6.31110i) q^{68} +(-8.06998 + 2.62210i) q^{72} +(-0.538863 + 0.538863i) q^{73} +(-9.11020 - 4.64188i) q^{74} +(-17.4293 - 2.76053i) q^{80} +9.00000i q^{81} +(1.83010 - 8.86853i) q^{82} +(13.9211 - 33.6086i) q^{85} +(-2.65671 + 1.62803i) q^{89} +(-8.49734 + 16.6770i) q^{90} +(0.439906 + 5.58953i) q^{97} +(8.00886 + 5.81878i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 8 q^{8}+O(q^{10}) $ 16 * q - 4 * q^2 + 8 * q^8	$ 16 q - 4 q^{2} + 8 q^{8} - 8 q^{13} + 16 q^{16} - 4 q^{17} - 20 q^{26} + 20 q^{29} - 64 q^{32} - 48 q^{34} - 20 q^{41} + 56 q^{50} + 96 q^{52} + 28 q^{53} + 12 q^{58} - 44 q^{61} - 112 q^{65} + 32 q^{68} - 36 q^{82} + 56 q^{85} + 32 q^{89} + 48 q^{90} + 36 q^{97}+O(q^{100}) $ 16 * q - 4 * q^2 + 8 * q^8 - 8 * q^13 + 16 * q^16 - 4 * q^17 - 20 * q^26 + 20 * q^29 - 64 * q^32 - 48 * q^34 - 20 * q^41 + 56 * q^50 + 96 * q^52 + 28 * q^53 + 12 * q^58 - 44 * q^61 - 112 * q^65 + 32 * q^68 - 36 * q^82 + 56 * q^85 + 32 * q^89 + 48 * q^90 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/164\mathbb{Z}\right)^\times$.

$n$	$83$	$129$
$\chi(n)$	$-1$	$e\left(\frac{7}{40}\right)$

Coefficient data

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

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

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

$2$	−0.221232	+	1.39680i	−0.156434	+	0.987688i
$2$	−0.221232	+	1.39680i	−0.156434	+	0.987688i
$3$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$3$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$4$	−1.90211	−	0.618034i	−0.951057	−	0.309017i
$5$	−3.93080	+	2.00284i	−1.75791	+	0.895698i	−0.804532	+	0.593910i	$0.797584\pi$
$5$	−3.93080	+	2.00284i	−1.75791	+	0.895698i	−0.953375	+	0.301788i	$0.902416\pi$
$6$		0			0
$7$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$7$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$8$	1.28408	−	2.52015i	0.453990	−	0.891007i
$9$	−2.12132	−	2.12132i	−0.707107	−	0.707107i
$10$	−1.92796	−	5.93364i	−0.609673	−	1.87638i
$11$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$11$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$12$		0			0
$13$	1.04080	+	4.33524i	0.288666	+	1.20238i	0.908581	+	0.417710i	$0.137167\pi$
$13$	1.04080	+	4.33524i	0.288666	+	1.20238i	−0.619915	+	0.784669i	$0.712833\pi$
$14$		0			0
$15$		0			0
$16$	3.23607	+	2.35114i	0.809017	+	0.587785i
$17$	−6.27019	+	5.35525i	−1.52075	+	1.29884i	−0.754294	+	0.656536i	$0.772021\pi$
$17$	−6.27019	+	5.35525i	−1.52075	+	1.29884i	−0.766451	+	0.642303i	$0.777979\pi$
$18$	3.43237	−	2.49376i	0.809017	−	0.587785i
$19$		0			0		0.233445	−	0.972370i	$-0.425000\pi$
$19$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$20$	8.71465	−	1.38026i	1.94865	−	0.308637i
$21$		0			0
$22$		0			0
$23$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$23$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$24$		0			0
$25$	8.50088	−	11.7005i	1.70018	−	2.34009i
$26$	−6.28573	+	0.494697i	−1.23273	+	0.0970181i
$27$		0			0
$28$		0			0
$29$	5.72004	+	4.88538i	1.06219	+	0.907192i	0.995887	−	0.0906081i	$-0.0288811\pi$
$29$	5.72004	+	4.88538i	1.06219	+	0.907192i	0.0662984	+	0.997800i	$0.478881\pi$
$30$		0			0
$31$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$31$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$32$	−4.00000	+	4.00000i	−0.707107	+	0.707107i
$33$		0			0
$34$	−6.09306	−	9.94297i	−1.04495	−	1.70521i
$35$		0			0
$36$	2.72394	+	5.34604i	0.453990	+	0.891007i
$37$	−2.23416	+	6.87604i	−0.367294	+	1.13041i	0.581238	+	0.813733i	$0.302568\pi$
$37$	−2.23416	+	6.87604i	−0.367294	+	1.13041i	−0.948532	+	0.316681i	$0.897432\pi$
$38$		0			0
$39$		0			0
$40$			12.4780i			1.97294i
$41$	−6.39623	−	0.297142i	−0.998923	−	0.0464057i
$41$	−6.39623	−	0.297142i	−0.998923	−	0.0464057i
$42$		0			0
$43$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$43$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$44$		0			0
$45$	12.5872	+	4.08981i	1.87638	+	0.609673i
$46$		0			0
$47$		0			0		−0.852640	−	0.522499i	$-0.825000\pi$
$47$		0			0		0.852640	+	0.522499i	$0.175000\pi$
$48$		0			0
$49$	3.17793	−	6.23705i	0.453990	−	0.891007i
$50$	14.4626	+	14.4626i	2.04531	+	2.04531i
$51$		0			0
$52$	0.699608	−	8.88936i	0.0970181	−	1.23273i
$53$	2.53572	−	2.96894i	0.348308	−	0.407816i	−0.558403	−	0.829570i	$-0.688586\pi$
$53$	2.53572	−	2.96894i	0.348308	−	0.407816i	0.906710	+	0.421754i	$0.138586\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−8.08936	+	6.90897i	−1.06219	+	0.907192i
$59$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$59$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$60$		0			0
$61$	−6.07643	+	0.962412i	−0.778007	+	0.123224i	−0.532794	−	0.846245i	$-0.678858\pi$
$61$	−6.07643	+	0.962412i	−0.778007	+	0.123224i	−0.245213	+	0.969469i	$0.578858\pi$
$62$		0			0
$63$		0			0
$64$	−4.70228	−	6.47214i	−0.587785	−	0.809017i
$65$	−12.7740	−	14.9564i	−1.58442	−	1.85511i
$66$		0			0
$67$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$67$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$68$	15.2363	−	6.31110i	1.84768	−	0.765333i
$69$		0			0
$70$		0			0
$71$		0			0		−0.996917	−	0.0784591i	$-0.975000\pi$
$71$		0			0		0.996917	+	0.0784591i	$0.0250000\pi$
$72$	−8.06998	+	2.62210i	−0.951057	+	0.309017i
$73$	−0.538863	+	0.538863i	−0.0630691	+	0.0630691i	−0.737938	−	0.674869i	$-0.764200\pi$
$73$	−0.538863	+	0.538863i	−0.0630691	+	0.0630691i	0.674869	+	0.737938i	$0.264200\pi$
$74$	−9.11020	−	4.64188i	−1.05904	−	0.539608i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$79$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$80$	−17.4293	−	2.76053i	−1.94865	−	0.308637i
$81$			9.00000i			1.00000i
$82$	1.83010	−	8.86853i	0.202100	−	0.979365i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$	13.9211	−	33.6086i	1.50996	−	3.64537i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.65671	+	1.62803i	−0.281610	+	0.172571i	−0.656130	−	0.754648i	$-0.727808\pi$
$89$	−2.65671	+	1.62803i	−0.281610	+	0.172571i	0.374519	+	0.927219i	$0.377808\pi$
$90$	−8.49734	+	16.6770i	−0.895698	+	1.75791i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.439906	+	5.58953i	0.0446657	+	0.567531i	0.978011	+	0.208552i	$0.0668751\pi$
$97$	0.439906	+	5.58953i	0.0446657	+	0.567531i	−0.933346	+	0.358979i	$0.883125\pi$
$98$	8.00886	+	5.81878i	0.809017	+	0.587785i
$99$		0			0
$100$	−23.4009	+	17.0018i	−2.34009	+	1.70018i
$101$	0.635944	−	2.64890i	0.0632788	−	0.263575i	−0.931758	−	0.363079i	$-0.881726\pi$
$101$	0.635944	−	2.64890i	0.0632788	−	0.263575i	0.995037	+	0.0995037i	$0.0317255\pi$
$102$		0			0
$103$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$103$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$104$	12.2619	+	2.94382i	1.20238	+	0.288666i
$105$		0			0
$106$	3.58605	+	4.19872i	0.348308	+	0.407816i
$107$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$107$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$108$		0			0
$109$	−14.3809	+	5.95678i	−1.37744	+	0.570556i	−0.943797	−	0.330527i	$-0.892774\pi$
$109$	−14.3809	+	5.95678i	−1.37744	+	0.570556i	−0.433647	+	0.901083i	$0.642774\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	19.6031	−	6.36945i	1.84411	−	0.599187i	0.846324	−	0.532668i	$-0.178811\pi$
$113$	19.6031	−	6.36945i	1.84411	−	0.599187i	0.997785	−	0.0665190i	$-0.0211893\pi$
$114$		0			0
$115$		0			0
$116$	−7.86084	−	12.8277i	−0.729860	−	1.19102i
$117$	6.98856	−	11.4043i	0.646093	−	1.05433i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−10.8646	−	1.72078i	−0.987688	−	0.156434i
$122$		−	8.70049i		−	0.787705i
$123$		0			0
$124$		0			0
$125$	−6.53041	+	41.2314i	−0.584098	+	3.68785i
$126$		0			0
$127$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$127$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$128$	10.0806	−	5.13632i	0.891007	−	0.453990i
$129$		0			0
$130$	23.7171	−	14.5339i	2.08013	−	1.27471i
$131$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$131$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	5.44460	+	22.6784i	0.466870	+	1.94465i
$137$	8.15288	+	19.6828i	0.696548	+	1.68162i	0.731153	+	0.682214i	$0.238983\pi$
$137$	8.15288	+	19.6828i	0.696548	+	1.68162i	−0.0346048	+	0.999401i	$0.511017\pi$
$138$		0			0
$139$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$139$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−1.87721	−	11.8523i	−0.156434	−	0.987688i
$145$	−32.2690	−	7.74709i	−2.67979	−	0.643361i
$146$	−0.633471	−	0.871898i	−0.0524265	−	0.0721588i
$147$		0			0
$148$	8.49926	−	11.6982i	0.698635	−	0.961588i
$149$	−12.3495	+	0.971925i	−1.01171	+	0.0796232i	−0.573462	−	0.819232i	$-0.694400\pi$
$149$	−12.3495	+	0.971925i	−1.01171	+	0.0796232i	−0.438246	+	0.898855i	$0.644400\pi$
$150$		0			0
$151$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$151$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$152$		0			0
$153$	24.6613	+	1.94089i	1.99375	+	0.156911i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	12.8129	+	20.9087i	1.02258	+	1.66870i	0.686955	+	0.726700i	$0.258947\pi$
$157$	12.8129	+	20.9087i	1.02258	+	1.66870i	0.335624	+	0.941996i	$0.391053\pi$
$158$		0			0
$159$		0			0
$160$	7.71183	−	23.7346i	0.609673	−	1.87638i
$161$		0			0
$162$	−12.5712	−	1.99109i	−0.987688	−	0.156434i
$163$		0			0			−	1.00000i	$-0.5\pi$
$163$		0			0				1.00000i	$0.5\pi$
$164$	11.9827	+	4.51828i	0.935692	+	0.352819i
$165$		0			0
$166$		0			0
$167$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$167$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$168$		0			0
$169$	−6.12794	+	3.12234i	−0.471380	+	0.240180i
$170$	43.8648	+	26.8804i	3.36428	+	2.06163i
$171$		0			0
$172$		0			0
$173$	0.0824082	+	0.0824082i	0.00626538	+	0.00626538i	0.710233	−	0.703967i	$-0.248590\pi$
$173$	0.0824082	+	0.0824082i	0.00626538	+	0.00626538i	−0.703967	+	0.710233i	$0.748590\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−1.68629	−	4.07107i	−0.126393	−	0.305139i
$179$		0			0		−0.0784591	−	0.996917i	$-0.525000\pi$
$179$		0			0		0.0784591	+	0.996917i	$0.475000\pi$
$180$	−21.4145	−	15.5586i	−1.59615	−	1.15967i
$181$	0.531027	−	0.453540i	0.0394709	−	0.0337113i	−0.629494	−	0.777005i	$-0.716738\pi$
$181$	0.531027	−	0.453540i	0.0394709	−	0.0337113i	0.668965	+	0.743294i	$0.266738\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.98959	−	31.5030i	−0.366842	−	2.31615i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$191$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$192$		0			0
$193$	14.6119	+	12.4797i	1.05178	+	0.898309i	0.994980	−	0.100076i	$-0.0319087\pi$
$193$	14.6119	+	12.4797i	1.05178	+	0.898309i	0.0568050	+	0.998385i	$0.481909\pi$
$194$	−7.90479	−	0.622121i	−0.567531	−	0.0446657i
$195$		0			0
$196$	−9.89949	+	9.89949i	−0.707107	+	0.707107i
$197$	5.66283	+	2.88536i	0.403460	+	0.205573i	0.643932	−	0.765083i	$-0.277302\pi$
$197$	5.66283	+	2.88536i	0.403460	+	0.205573i	−0.240472	+	0.970656i	$0.577302\pi$
$198$		0			0
$199$		0			0		0.522499	−	0.852640i	$-0.325000\pi$
$199$		0			0		−0.522499	+	0.852640i	$0.675000\pi$
$200$	−18.5711	−	36.4478i	−1.31317	−	2.57725i
$201$		0			0
$202$	3.55930	+	1.47431i	0.250431	+	0.103732i
$203$		0			0
$204$		0			0
$205$	25.7374	−	11.6426i	1.79758	−	0.813156i
$206$		0			0
$207$		0			0
$208$	−6.82466	+	16.4762i	−0.473205	+	1.14242i
$209$		0			0
$210$		0			0
$211$		0			0		−0.852640	−	0.522499i	$-0.825000\pi$
$211$		0			0		0.852640	+	0.522499i	$0.175000\pi$
$212$	−6.65813	+	4.08011i	−0.457282	+	0.280223i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−5.13892	−	21.4052i	−0.348052	−	1.44974i
$219$		0			0
$220$		0			0
$221$	−29.7423	−	21.6090i	−2.00068	−	1.45358i
$222$		0			0
$223$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$223$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$224$		0			0
$225$	−42.8535	+	6.78733i	−2.85690	+	0.452488i
$226$	4.56002	+	28.7908i	0.303328	+	1.91514i
$227$		0			0		−0.972370	−	0.233445i	$-0.925000\pi$
$227$		0			0		0.972370	+	0.233445i	$0.0750000\pi$
$228$		0			0
$229$	19.6272	+	22.9805i	1.29700	+	1.51859i	0.689552	+	0.724236i	$0.257808\pi$
$229$	19.6272	+	22.9805i	1.29700	+	1.51859i	0.607450	+	0.794358i	$0.292192\pi$
$230$		0			0
$231$		0			0
$232$	19.6569	−	8.14214i	1.29054	−	0.534557i
$233$	−26.4749	+	6.35606i	−1.73443	+	0.416400i	−0.972806	−	0.231621i	$-0.925597\pi$
$233$	−26.4749	+	6.35606i	−1.73443	+	0.416400i	−0.761623	+	0.648020i	$0.775597\pi$
$234$	14.3835	+	12.2846i	0.940276	+	0.803071i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.522499	−	0.852640i	$-0.675000\pi$
$239$		0			0		0.522499	+	0.852640i	$0.325000\pi$
$240$		0			0
$241$	5.71780	+	11.2218i	0.368316	+	0.722861i	0.998566	−	0.0535313i	$-0.0170477\pi$
$241$	5.71780	+	11.2218i	0.368316	+	0.722861i	−0.630250	+	0.776392i	$0.717048\pi$
$242$	4.80718	−	14.7950i	0.309017	−	0.951057i
$243$		0			0
$244$	12.1529	+	1.92482i	0.778007	+	0.123224i
$245$			30.8815i			1.97294i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−56.1474	−	18.2434i	−3.55107	−	1.15381i
$251$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$251$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	4.94427	+	15.2169i	0.309017	+	0.951057i
$257$	2.25953	−	28.7100i	0.140945	−	1.79088i	−0.367740	−	0.929928i	$-0.619869\pi$
$257$	2.25953	−	28.7100i	0.140945	−	1.79088i	0.508686	−	0.860952i	$-0.330131\pi$
$258$		0			0
$259$		0			0
$260$	15.0540	+	36.3435i	0.933607	+	2.25393i
$261$	−1.77059	−	22.4975i	−0.109597	−	1.39256i
$262$		0			0
$263$		0			0		0.760406	−	0.649448i	$-0.225000\pi$
$263$		0			0		−0.760406	+	0.649448i	$0.775000\pi$
$264$		0			0
$265$	−4.02107	+	16.7490i	−0.247012	+	1.02888i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	6.45781	+	8.88842i	0.393740	+	0.541936i	0.959159	−	0.282867i	$-0.0912856\pi$
$269$	6.45781	+	8.88842i	0.393740	+	0.541936i	−0.565419	+	0.824804i	$0.691286\pi$
$270$		0			0
$271$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$271$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$272$	−32.8817	+	2.58785i	−1.99375	+	0.156911i
$273$		0			0
$274$	−29.2967	+	7.03350i	−1.76988	+	0.424910i
$275$		0			0
$276$		0			0
$277$	−23.6237	+	7.67581i	−1.41941	+	0.461195i	−0.915415	−	0.402511i	$-0.868138\pi$
$277$	−23.6237	+	7.67581i	−1.41941	+	0.461195i	−0.503997	+	0.863706i	$0.668138\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	16.1073	−	26.2847i	0.960882	−	1.56802i	0.145289	−	0.989389i	$-0.453589\pi$
$281$	16.1073	−	26.2847i	0.960882	−	1.56802i	0.815592	−	0.578627i	$-0.196411\pi$
$282$		0			0
$283$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$283$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	16.9706			1.00000
$289$	7.97723	−	50.3662i	0.469249	−	2.96272i
$290$	17.9601	−	43.3595i	1.05465	−	2.54616i
$291$		0			0
$292$	1.35801	−	0.691943i	0.0794717	−	0.0404929i
$293$	−26.4999	−	16.2391i	−1.54814	−	0.948700i	−0.993151	−	0.116841i	$-0.962723\pi$
$293$	−26.4999	−	16.2391i	−1.54814	−	0.948700i	−0.554987	−	0.831859i	$-0.687277\pi$
$294$		0			0
$295$		0			0
$296$	14.4598	+	14.4598i	0.840459	+	0.840459i
$297$		0			0
$298$	1.37451	−	17.4648i	0.0796232	−	1.01171i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	21.9577	−	15.9532i	1.25729	−	0.913476i
$306$	−8.16689	+	34.0176i	−0.466870	+	1.94465i
$307$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$307$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.649448	−	0.760406i	$-0.725000\pi$
$311$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$312$		0			0
$313$	33.1029	−	2.60526i	1.87109	−	0.147258i	0.908440	−	0.418016i	$-0.137274\pi$
$313$	33.1029	−	2.60526i	1.87109	−	0.147258i	0.962647	+	0.270758i	$0.0872744\pi$
$314$	−32.0399	+	13.2714i	−1.80812	+	0.748947i
$315$		0			0
$316$		0			0
$317$	6.98192	+	0.549489i	0.392144	+	0.0308624i	0.272999	−	0.962014i	$-0.411985\pi$
$317$	6.98192	+	0.549489i	0.392144	+	0.0308624i	0.119145	+	0.992877i	$0.461985\pi$
$318$		0			0
$319$		0			0
$320$	31.4464	+	16.0227i	1.75791	+	0.895698i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	5.56231	−	17.1190i	0.309017	−	0.951057i
$325$	59.5719	+	24.6755i	3.30446	+	1.36875i
$326$		0			0
$327$		0			0
$328$	−8.96210	+	15.7379i	−0.494849	+	0.868979i
$329$		0			0
$330$		0			0
$331$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$331$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$332$		0			0
$333$	19.3257	−	9.84692i	1.05904	−	0.539608i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−3.00296	−	3.00296i	−0.163581	−	0.163581i	0.620570	−	0.784151i	$-0.286901\pi$
$337$	−3.00296	−	3.00296i	−0.163581	−	0.163581i	−0.784151	+	0.620570i	$0.786901\pi$
$338$	−3.00560	−	9.25028i	−0.163483	−	0.503149i
$339$		0			0
$340$	−47.2509	+	55.3237i	−2.56254	+	3.00035i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.133339	+	0.0968766i	−0.00716836	+	0.00520812i
$347$		0			0		0.233445	−	0.972370i	$-0.425000\pi$
$347$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$348$		0			0
$349$	2.04461	+	12.9092i	0.109446	+	0.691013i	0.980009	+	0.198956i	$0.0637549\pi$
$349$	2.04461	+	12.9092i	0.109446	+	0.691013i	−0.870563	+	0.492057i	$0.836245\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	18.2675	−	25.1430i	0.972279	−	1.33823i	0.0313912	−	0.999507i	$-0.490006\pi$
$353$	18.2675	−	25.1430i	0.972279	−	1.33823i	0.940887	−	0.338719i	$-0.109994\pi$
$354$		0			0
$355$		0			0
$356$	6.05954	−	1.45477i	0.321155	−	0.0771025i
$357$		0			0
$358$		0			0
$359$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$359$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$360$	26.4698	−	26.4698i	1.39508	−	1.39508i
$361$	−16.9291	−	8.62582i	−0.891007	−	0.453990i
$362$	0.516025	+	0.842077i	0.0271217	+	0.0442586i
$363$		0			0
$364$		0			0
$365$	1.03890	−	3.19742i	0.0543787	−	0.167361i
$366$		0			0
$367$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$367$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$368$		0			0
$369$	12.9381	+	14.1988i	0.673531	+	0.739159i
$370$	45.1073			2.34502
$371$		0			0
$372$		0			0
$373$	−28.4478	−	9.24325i	−1.47297	−	0.478598i	−0.540967	−	0.841044i	$-0.681942\pi$
$373$	−28.4478	−	9.24325i	−1.47297	−	0.478598i	−0.932005	+	0.362446i	$0.881942\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−15.2259	+	29.8824i	−0.784172	+	1.53902i
$378$		0			0
$379$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$379$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$383$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$384$		0			0
$385$		0			0
$386$	−20.6643	+	17.6490i	−1.05178	+	0.898309i
$387$		0			0
$388$	2.61777	−	10.9038i	0.132897	−	0.553557i
$389$	−24.7639	+	3.92221i	−1.25558	+	0.198864i	−0.748557	−	0.663070i	$-0.769253\pi$
$389$	−24.7639	+	3.92221i	−1.25558	+	0.198864i	−0.507020	+	0.861934i	$0.669253\pi$
$390$		0			0
$391$		0			0
$392$	−11.6376	−	16.0177i	−0.587785	−	0.809017i
$393$		0			0
$394$	−5.28307	+	7.27152i	−0.266157	+	0.366334i
$395$		0			0
$396$		0			0
$397$	−2.72022	+	0.653067i	−0.136524	+	0.0327765i	−0.301131	−	0.953583i	$-0.597364\pi$
$397$	−2.72022	+	0.653067i	−0.136524	+	0.0327765i	0.164607	+	0.986359i	$0.447364\pi$
$398$		0			0
$399$		0			0
$400$	55.0188	−	17.8767i	2.75094	−	0.893835i
$401$	−15.4810	+	15.4810i	−0.773082	+	0.773082i	−0.978644	−	0.205562i	$-0.934098\pi$
$401$	−15.4810	+	15.4810i	−0.773082	+	0.773082i	0.205562	+	0.978644i	$0.434098\pi$
$402$		0			0
$403$		0			0
$404$	−2.84675	+	4.64547i	−0.141631	+	0.231121i
$405$	−18.0256	−	35.3772i	−0.895698	−	1.75791i
$406$		0			0
$407$		0			0
$408$		0			0
$409$			32.9163i			1.62761i	0.581140	+	0.813804i	$0.302607\pi$
$409$			32.9163i			1.62761i	−0.581140	+	0.813804i	$0.697393\pi$
$410$	10.5685	+	38.5258i	0.521942	+	1.90265i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−21.5041	−	13.1778i	−1.05433	−	0.646093i
$417$		0			0
$418$		0			0
$419$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$419$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$420$		0			0
$421$	2.80158	−	35.5975i	0.136541	−	1.73492i	−0.423015	−	0.906123i	$-0.639028\pi$
$421$	2.80158	−	35.5975i	0.136541	−	1.73492i	0.559556	−	0.828793i	$-0.310972\pi$
$422$		0			0
$423$		0			0
$424$	−4.22611	−	10.2027i	−0.205238	−	0.495489i
$425$	9.35672	+	118.888i	0.453868	+	5.76694i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$431$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$432$		0			0
$433$	−7.87616	−	10.8406i	−0.378504	−	0.520967i	0.576683	−	0.816968i	$-0.304347\pi$
$433$	−7.87616	−	10.8406i	−0.378504	−	0.520967i	−0.955188	+	0.296001i	$0.904347\pi$
$434$		0			0
$435$		0			0
$436$	31.0357	−	2.44256i	1.48634	−	0.116977i
$437$		0			0
$438$		0			0
$439$		0			0		−0.760406	−	0.649448i	$-0.775000\pi$
$439$		0			0		0.760406	+	0.649448i	$0.225000\pi$
$440$		0			0
$441$	−19.9722	+	6.48936i	−0.951057	+	0.309017i
$442$	36.7635	−	36.7635i	1.74866	−	1.74866i
$443$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$443$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$444$		0			0
$445$	7.18229	−	11.7204i	0.340473	−	0.555602i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	36.8580	+	5.83774i	1.73944	+	0.275500i	0.943858	−	0.330350i	$-0.107167\pi$
$449$	36.8580	+	5.83774i	1.73944	+	0.275500i	0.795579	+	0.605850i	$0.207167\pi$
$450$		−	61.3594i		−	2.89251i
$451$		0			0
$452$	−41.2239			−1.93901
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	31.6608	+	19.4017i	1.48103	+	0.907576i	0.999515	+	0.0311368i	$0.00991277\pi$
$457$	31.6608	+	19.4017i	1.48103	+	0.907576i	0.481514	+	0.876439i	$0.340087\pi$
$458$	−36.4414	+	22.3313i	−1.70279	+	1.04347i
$459$		0			0
$460$		0			0
$461$	−10.8378	−	33.3552i	−0.504765	−	1.55351i	−0.801165	−	0.598444i	$-0.795786\pi$
$461$	−10.8378	−	33.3552i	−0.504765	−	1.55351i	0.296399	−	0.955064i	$-0.404214\pi$
$462$		0			0
$463$		0			0		0.649448	−	0.760406i	$-0.275000\pi$
$463$		0			0		−0.649448	+	0.760406i	$0.725000\pi$
$464$	7.02423	+	29.2580i	0.326092	+	1.35827i
$465$		0			0
$466$	−3.02107	−	38.3864i	−0.139949	−	1.77821i
$467$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$467$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$468$	−20.3413	+	17.3731i	−0.940276	+	0.803071i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−11.6771	+	0.919012i	−0.534660	+	0.0420787i
$478$		0			0
$479$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$479$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$480$		0			0
$481$	−32.1346	−	2.52905i	−1.46521	−	0.115315i
$482$	−16.9396	+	5.50402i	−0.771579	+	0.250701i
$483$		0			0
$484$	19.6021	+	9.98779i	0.891007	+	0.453990i
$485$	−12.9241	−	21.0903i	−0.586855	−	0.957660i
$486$		0			0
$487$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$487$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$488$	−5.37720	+	16.5493i	−0.243414	+	0.749152i
$489$		0			0
$490$	−43.1353	−	6.83196i	−1.94865	−	0.308637i
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$		0			0
$493$	−62.0282			−2.79361
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$499$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$500$	37.9040	−	74.3908i	1.69512	−	3.32686i
$501$		0			0
$502$		0			0
$503$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$503$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$504$		0			0
$505$	2.80556	+	11.6860i	0.124846	+	0.520019i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	32.5006	−	27.7582i	1.44056	−	1.23036i	0.512107	−	0.858922i	$-0.328865\pi$
$509$	32.5006	−	27.7582i	1.44056	−	1.23036i	0.928458	−	0.371437i	$-0.121135\pi$
$510$		0			0
$511$		0			0
$512$	−22.3488	+	3.53971i	−0.987688	+	0.156434i
$513$		0			0
$514$	39.6023	+	9.50767i	1.74678	+	0.419366i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−54.0951	+	12.9871i	−2.37223	+	0.569521i
$521$	−29.0099	−	24.7768i	−1.27095	−	1.08549i	−0.992138	−	0.125146i	$-0.960060\pi$
$521$	−29.0099	−	24.7768i	−1.27095	−	1.08549i	−0.278810	−	0.960346i	$-0.589940\pi$
$522$	31.8163	+	2.50399i	1.39256	+	0.109597i
$523$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$523$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−7.10739	+	21.8743i	−0.309017	+	0.951057i
$530$	−22.5054	−	9.32204i	−0.977572	−	0.404924i
$531$		0			0
$532$		0			0
$533$	−5.36900	−	28.0384i	−0.232557	−	1.21448i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−13.8440	+	7.05389i	−0.596859	+	0.304115i
$539$		0			0
$540$		0			0
$541$	−10.0890	+	19.8008i	−0.433761	+	0.851305i	0.565879	+	0.824488i	$0.308537\pi$
$541$	−10.0890	+	19.8008i	−0.433761	+	0.851305i	−0.999640	+	0.0268165i	$0.991463\pi$
$542$		0			0
$543$		0			0
$544$	3.65977	−	46.5018i	0.156911	−	1.99375i
$545$	44.5981	−	52.2176i	1.91037	−	2.23676i
$546$		0			0
$547$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$547$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$548$	−3.34306	−	42.4777i	−0.142809	−	1.81456i
$549$	14.9316	+	10.8485i	0.637267	+	0.463001i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−5.49528	−	34.6958i	−0.233472	−	1.47408i
$555$		0			0
$556$		0			0
$557$	15.8415	+	18.5480i	0.671227	+	0.785906i	0.986617	−	0.163057i	$-0.0521353\pi$
$557$	15.8415	+	18.5480i	0.671227	+	0.785906i	−0.315390	+	0.948962i	$0.602135\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	33.1511	+	28.3137i	1.39840	+	1.19434i
$563$		0			0		−0.996917	−	0.0784591i	$-0.975000\pi$
$563$		0			0		0.996917	+	0.0784591i	$0.0250000\pi$
$564$		0			0
$565$	−64.2990	+	64.2990i	−2.70508	+	2.70508i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	16.8377	+	33.0458i	0.705872	+	1.38535i	0.913376	+	0.407117i	$0.133466\pi$
$569$	16.8377	+	33.0458i	0.705872	+	1.38535i	−0.207504	+	0.978234i	$0.566534\pi$
$570$		0			0
$571$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$571$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−3.75443	+	23.7045i	−0.156434	+	0.987688i
$577$	−8.94509	+	21.5954i	−0.372389	+	0.899027i	0.620956	+	0.783846i	$0.286745\pi$
$577$	−8.94509	+	21.5954i	−0.372389	+	0.899027i	−0.993345	+	0.115181i	$0.963255\pi$
$578$	68.5868	+	22.2852i	2.85284	+	0.926943i
$579$		0			0
$580$	56.5913	+	34.6792i	2.34982	+	1.43997i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.666071	+	2.04996i	0.0275622	+	0.0848278i
$585$	−4.62963	+	58.8250i	−0.191411	+	2.43211i
$586$	28.5455	−	33.4224i	1.17920	−	1.38067i
$587$		0			0		−0.233445	−	0.972370i	$-0.575000\pi$
$587$		0			0		0.233445	+	0.972370i	$0.425000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−23.3964	+	16.9985i	−0.961588	+	0.698635i
$593$	−9.81430	+	40.8795i	−0.403025	+	1.67872i	0.289383	+	0.957214i	$0.406550\pi$
$593$	−9.81430	+	40.8795i	−0.403025	+	1.67872i	−0.692408	+	0.721507i	$0.743450\pi$
$594$		0			0
$595$		0			0
$596$	24.0908	+	5.78368i	0.986797	+	0.236909i
$597$		0			0
$598$		0			0
$599$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$599$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$600$		0			0
$601$	43.4846	−	18.0119i	1.77378	−	0.734722i	0.779685	−	0.626172i	$-0.215379\pi$
$601$	43.4846	−	18.0119i	1.77378	−	0.734722i	0.994091	−	0.108550i	$-0.0346206\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	46.1529	−	14.9960i	1.87638	−	0.609673i
$606$		0			0
$607$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$607$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$608$		0			0
$609$		0			0
$610$	17.4257	+	34.1999i	0.705546	+	1.38471i
$611$		0			0
$612$	−45.7090	−	18.9333i	−1.84768	−	0.765333i
$613$	−20.9502	−	3.31818i	−0.846169	−	0.134020i	−0.281729	−	0.959494i	$-0.590908\pi$
$613$	−20.9502	−	3.31818i	−0.846169	−	0.134020i	−0.564440	+	0.825474i	$0.690908\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.87420	+	37.0882i	−0.236486	+	1.49312i	0.528425	+	0.848980i	$0.322783\pi$
$617$	−5.87420	+	37.0882i	−0.236486	+	1.49312i	−0.764911	+	0.644136i	$0.777217\pi$
$618$		0			0
$619$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$619$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−34.5644	−	106.378i	−1.38258	−	4.25513i
$626$	−3.68439	+	46.8146i	−0.147258	+	1.87109i
$627$		0			0
$628$	−11.4492	−	47.6895i	−0.456874	−	1.90302i
$629$	−22.8143	−	55.0786i	−0.909666	−	2.19613i
$630$		0			0
$631$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$631$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$632$		0			0
$633$		0			0
$634$	−2.31215	+	9.63080i	−0.0918272	+	0.382488i
$635$		0			0
$636$		0			0
$637$	30.3467	+	7.28559i	1.20238	+	0.288666i
$638$		0			0
$639$		0			0
$640$	−29.3375	+	40.3796i	−1.15967	+	1.59615i
$641$	46.6068	−	3.66804i	1.84086	−	0.144879i	0.890290	−	0.455394i	$-0.150502\pi$
$641$	46.6068	−	3.66804i	1.84086	−	0.144879i	0.950568	+	0.310515i	$0.100502\pi$
$642$		0			0
$643$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$643$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$647$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$648$	22.6813	+	11.5567i	0.891007	+	0.453990i
$649$		0			0
$650$	−47.6460	+	77.7512i	−1.86883	+	3.04965i
$651$		0			0
$652$		0			0
$653$	44.6661	+	18.5013i	1.74792	+	0.724012i	0.998049	+	0.0624287i	$0.0198846\pi$
$653$	44.6661	+	18.5013i	1.74792	+	0.724012i	0.749871	+	0.661584i	$0.230115\pi$
$654$		0			0
$655$		0			0
$656$	−20.0000	−	16.0000i	−0.780869	−	0.624695i
$657$	2.28620			0.0891932
$658$		0			0
$659$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$659$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$660$		0			0
$661$	23.9356	−	12.1958i	0.930986	−	0.474361i	0.0783849	−	0.996923i	$-0.475024\pi$
$661$	23.9356	−	12.1958i	0.930986	−	0.474361i	0.852601	+	0.522562i	$0.175024\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	9.47875	+	29.1726i	0.367294	+	1.13041i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−15.4491	+	13.1948i	−0.595519	+	0.508621i	−0.895345	−	0.445373i	$-0.853071\pi$
$673$	−15.4491	+	13.1948i	−0.595519	+	0.508621i	0.299827	+	0.953994i	$0.403071\pi$
$674$	4.85889	−	3.53019i	0.187157	−	0.135978i
$675$		0			0
$676$	13.5857	−	2.15177i	0.522528	−	0.0827604i
$677$	−7.63978	−	48.2356i	−0.293620	−	1.85385i	−0.487899	−	0.872900i	$-0.662237\pi$
$677$	−7.63978	−	48.2356i	−0.293620	−	1.85385i	0.194279	−	0.980946i	$-0.437763\pi$
$678$		0			0
$679$		0			0
$680$	−66.8228	−	78.2395i	−2.56254	−	3.00035i
$681$		0			0
$682$		0			0
$683$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$683$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$684$		0			0
$685$	−71.4689	−	61.0402i	−2.73069	−	2.33223i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	15.5102	+	7.90287i	0.590893	+	0.301075i
$690$		0			0
$691$		0			0		0.522499	−	0.852640i	$-0.325000\pi$
$691$		0			0		−0.522499	+	0.852640i	$0.675000\pi$
$692$	−0.105819	−	0.207681i	−0.00402262	−	0.00789483i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	41.6968	−	32.3903i	1.57938	−	1.22687i
$698$	−18.4839			−0.699626
$699$		0			0
$700$		0			0
$701$	47.3583	+	15.3876i	1.78870	+	0.581183i	0.999459	−	0.0329027i	$-0.0104752\pi$
$701$	47.3583	+	15.3876i	1.78870	+	0.581183i	0.789239	+	0.614086i	$0.210475\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	31.0785	+	31.0785i	1.16965	+	1.16965i
$707$		0			0
$708$		0			0
$709$	−23.2378	+	27.2080i	−0.872716	+	1.02182i	0.126837	+	0.991924i	$0.459517\pi$
$709$	−23.2378	+	27.2080i	−0.872716	+	1.02182i	−0.999553	+	0.0298952i	$0.990483\pi$
$710$		0			0
$711$		0			0
$712$	0.691459	+	8.78582i	0.0259135	+	0.329262i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.972370	−	0.233445i	$-0.925000\pi$
$719$		0			0		0.972370	+	0.233445i	$0.0750000\pi$
$720$	31.1172	+	42.8291i	1.15967	+	1.59615i
$721$		0			0
$722$	15.7938	−	21.7383i	0.587785	−	0.809017i
$723$		0			0
$724$	−1.29038	+	0.534491i	−0.0479564	+	0.0198642i
$725$	105.786	−	25.3971i	3.92881	−	0.943224i
$726$		0			0
$727$		0			0		−0.996917	−	0.0784591i	$-0.975000\pi$
$727$		0			0		0.996917	+	0.0784591i	$0.0250000\pi$
$728$		0			0
$729$	19.0919	−	19.0919i	0.707107	−	0.707107i
$730$	4.23632	+	2.15851i	0.156793	+	0.0798902i
$731$		0			0
$732$		0			0
$733$	21.0190	+	41.2522i	0.776356	+	1.52368i	0.850227	+	0.526416i	$0.176464\pi$
$733$	21.0190	+	41.2522i	0.776356	+	1.52368i	−0.0738717	+	0.997268i	$0.523536\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−22.6952	+	14.9308i	−0.835422	+	0.549609i
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$	−9.97917	+	63.0060i	−0.366842	+	2.31615i
$741$		0			0
$742$		0			0
$743$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$743$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$744$		0			0
$745$	46.5967	−	28.5545i	1.70717	−	1.04616i
$746$	19.2046	−	37.6911i	0.703129	−	1.37997i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.233445	−	0.972370i	$-0.575000\pi$
$751$		0			0		0.233445	+	0.972370i	$0.425000\pi$
$752$		0			0
$753$		0			0
$754$	−38.3714	−	27.8785i	−1.39740	−	1.01527i
$755$		0			0
$756$		0			0
$757$	8.15479	−	33.9671i	0.296391	−	1.23456i	−0.603117	−	0.797652i	$-0.706075\pi$
$757$	8.15479	−	33.9671i	0.296391	−	1.23456i	0.899508	−	0.436904i	$-0.143925\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−25.7388	−	35.4265i	−0.933032	−	1.28421i	−0.958665	−	0.284537i	$-0.908160\pi$
$761$	−25.7388	−	35.4265i	−0.933032	−	1.28421i	0.0256326	−	0.999671i	$-0.491840\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−100.826	+	41.7634i	−3.64537	+	1.50996i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−38.1720	+	12.4028i	−1.37652	+	0.447258i	−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−38.1720	+	12.4028i	−1.37652	+	0.447258i	−0.474995	+	0.879989i	$0.657550\pi$
$770$		0			0
$771$		0			0
$772$	−20.0805	−	32.7684i	−0.722714	−	1.17936i
$773$	−25.2105	+	41.1399i	−0.906760	+	1.47970i	−0.0295658	+	0.999563i	$0.509412\pi$
$773$	−25.2105	+	41.1399i	−0.906760	+	1.47970i	−0.877194	+	0.480135i	$0.840588\pi$
$774$		0			0
$775$		0			0
$776$	14.6513	+	6.06878i	0.525952	+	0.217856i
$777$		0			0
$778$		−	35.4579i		−	1.27123i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	24.9482	−	12.7117i	0.891007	−	0.453990i
$785$	−92.2416	−	56.5258i	−3.29225	−	2.01749i
$786$		0			0
$787$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$787$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$788$	−8.98809	−	8.98809i	−0.320188	−	0.320188i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−10.4966	−	25.3411i	−0.372746	−	0.899888i
$794$	−0.310406	−	3.94409i	−0.0110159	−	0.139970i
$795$		0			0
$796$		0			0
$797$	−39.1267	+	28.4272i	−1.38594	+	1.00694i	−0.389640	+	0.920967i	$0.627401\pi$
$797$	−39.1267	+	28.4272i	−1.38594	+	1.00694i	−0.996297	+	0.0859751i	$0.972599\pi$
$798$		0			0
$799$		0			0
$800$	12.7983	+	80.8053i	0.452488	+	2.85690i
$801$	9.08931	+	2.18215i	0.321155	+	0.0771025i
$802$	−18.1990	−	25.0487i	−0.642627	−	0.884501i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−5.85901	−	5.00407i	−0.206119	−	0.176042i
$809$	−14.3186	−	1.12690i	−0.503415	−	0.0396197i	−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−14.3186	−	1.12690i	−0.503415	−	0.0396197i	−0.327625	+	0.944808i	$0.606248\pi$
$810$	53.4028	−	17.3516i	1.87638	−	0.609673i
$811$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$811$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−45.9776	−	7.28213i	−1.60757	−	0.254614i
$819$		0			0
$820$	−56.1510	+	6.23900i	−1.96088	+	0.217875i
$821$	31.8386			1.11117			0.555587	−	0.831458i	$-0.312493\pi$
$821$	31.8386			1.11117			0.555587	+	0.831458i	$0.312493\pi$
$822$		0			0
$823$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$823$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$827$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$828$		0			0
$829$	−40.6851	−	40.6851i	−1.41305	−	1.41305i	−0.735188	−	0.677863i	$-0.762906\pi$
$829$	−40.6851	−	40.6851i	−1.41305	−	1.41305i	−0.677863	−	0.735188i	$-0.737094\pi$
$830$		0			0
$831$		0			0
$832$	23.1641	−	27.1217i	0.803071	−	0.940276i
$833$	13.4747	+	56.1261i	0.466870	+	1.94465i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.233445	−	0.972370i	$-0.425000\pi$
$839$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$840$		0			0
$841$	4.31537	+	27.2462i	0.148806	+	0.939523i
$842$	49.1029	+	11.7886i	1.69220	+	0.406260i
$843$		0			0
$844$		0			0
$845$	17.8341	−	24.5466i	0.613513	−	0.844428i
$846$		0			0
$847$		0			0
$848$	15.1862	−	3.64587i	0.521495	−	0.125200i
$849$		0			0
$850$	−168.134	−	13.2324i	−5.76694	−	0.453868i
$851$		0			0
$852$		0			0
$853$	−6.30037	−	3.21020i	−0.215720	−	0.109915i	0.342792	−	0.939411i	$-0.388628\pi$
$853$	−6.30037	−	3.21020i	−0.215720	−	0.109915i	−0.558512	+	0.829496i	$0.688628\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−17.3156	+	53.2919i	−0.591490	+	1.82042i	−0.0200121	+	0.999800i	$0.506370\pi$
$857$	−17.3156	+	53.2919i	−0.591490	+	1.82042i	−0.571477	+	0.820618i	$0.693630\pi$
$858$		0			0
$859$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$859$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$863$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$864$		0			0
$865$	−0.488980	−	0.158879i	−0.0166258	−	0.00540206i
$866$	16.8846	−	8.60316i	0.573764	−	0.292347i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−3.45430	+	43.8910i	−0.116977	+	1.48634i
$873$	10.9240	−	12.7904i	0.369722	−	0.432888i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	32.2552	+	23.4347i	1.08918	+	0.791335i	0.979260	−	0.202606i	$-0.0649409\pi$
$877$	32.2552	+	23.4347i	1.08918	+	0.791335i	0.109919	+	0.993941i	$0.464941\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	12.5712	−	1.99109i	0.423535	−	0.0670814i	0.0589711	−	0.998260i	$-0.481218\pi$
$881$	12.5712	−	1.99109i	0.423535	−	0.0670814i	0.364564	+	0.931178i	$0.381218\pi$
$882$	−4.64587	−	29.3328i	−0.156434	−	0.987688i
$883$		0			0		−0.972370	−	0.233445i	$-0.925000\pi$
$883$		0			0		0.972370	+	0.233445i	$0.0750000\pi$
$884$	43.2181	+	59.4846i	1.45358	+	2.00068i
$885$		0			0
$886$		0			0
$887$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$887$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$888$		0			0
$889$		0			0
$890$	14.7822	+	12.6252i	0.495500	+	0.423197i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−16.3083	+	50.1919i	−0.544216	+	1.67492i
$899$		0			0
$900$	85.7070	+	13.5747i	2.85690	+	0.452488i
$901$			32.1953i			1.07258i
$902$		0			0
$903$		0			0
$904$	9.12004	−	57.5817i	0.303328	−	1.91514i
$905$	−1.17899	+	2.84634i	−0.0391910	+	0.0946154i
$906$		0			0
$907$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$907$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$908$		0			0
$909$	−6.96820	+	4.27012i	−0.231121	+	0.141631i
$910$		0			0
$911$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$911$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$912$		0			0
$913$		0			0
$914$	−34.1048	+	39.9316i	−1.12809	+	1.32082i
$915$		0			0
$916$	−23.1304	−	55.8418i	−0.764251	−	1.84506i
$917$		0			0
$918$		0			0
$919$		0			0		0.760406	−	0.649448i	$-0.225000\pi$
$919$		0			0		−0.760406	+	0.649448i	$0.775000\pi$
$920$		0			0
$921$		0			0
$922$	48.9883	−	7.75899i	1.61334	−	0.255529i
$923$		0			0
$924$		0			0
$925$	61.4605	+	84.5931i	2.02081	+	2.78140i
$926$		0			0
$927$		0			0
$928$	−42.4217	+	3.33866i	−1.39256	+	0.109597i
$929$	56.3166	−	23.3271i	1.84769	−	0.765337i	0.920443	−	0.390877i	$-0.127828\pi$
$929$	56.3166	−	23.3271i	1.84769	−	0.765337i	0.927243	−	0.374460i	$-0.122172\pi$
$930$		0			0
$931$		0			0
$932$	54.2865	+	4.27244i	1.77821	+	0.139949i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−19.7666	−	32.2562i	−0.646093	−	1.05433i
$937$	30.7690	−	50.2104i	1.00518	−	1.64030i	0.269466	−	0.963010i	$-0.413153\pi$
$937$	30.7690	−	50.2104i	1.00518	−	1.64030i	0.735713	−	0.677294i	$-0.236847\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−60.0102	−	9.50467i	−1.95628	−	0.309844i	−0.999840	−	0.0178992i	$-0.994302\pi$
$941$	−60.0102	−	9.50467i	−1.95628	−	0.309844i	−0.956435	−	0.291944i	$-0.905698\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$947$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$948$		0			0
$949$	−2.89695	−	1.77525i	−0.0940388	−	0.0576271i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	6.55524	+	20.1750i	0.212345	+	0.653531i	0.999331	+	0.0365605i	$0.0116402\pi$
$953$	6.55524	+	20.1750i	0.212345	+	0.653531i	−0.786986	+	0.616970i	$0.788360\pi$
$954$	1.29968	−	16.5140i	0.0420787	−	0.534660i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	25.0795	−	18.2213i	0.809017	−	0.587785i
$962$	10.6418	−	44.3262i	0.343104	−	1.42913i
$963$		0			0
$964$	−3.94044	−	24.8790i	−0.126913	−	0.801297i
$965$	−82.4312	−	19.7900i	−2.65355	−	0.637062i
$966$		0			0
$967$		0			0		−0.649448	−	0.760406i	$-0.725000\pi$
$967$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$968$	−18.2876	+	25.1707i	−0.587785	+	0.809017i
$969$		0			0
$970$	32.3182	−	13.3866i	1.03767	−	0.429818i
$971$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$971$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−21.9265	−	11.1721i	−0.701850	−	0.357611i
$977$	8.53519	+	13.9282i	0.273065	+	0.445601i	0.959548	−	0.281544i	$-0.0908466\pi$
$977$	8.53519	+	13.9282i	0.273065	+	0.445601i	−0.686483	+	0.727145i	$0.740847\pi$
$978$		0			0
$979$		0			0
$980$	19.0858	−	58.7400i	0.609673	−	1.87638i
$981$	43.1428	+	17.8703i	1.37744	+	0.570556i
$982$		0			0
$983$		0			0			−	1.00000i	$-0.5\pi$
$983$		0			0				1.00000i	$0.5\pi$
$984$		0			0
$985$	−28.0384			−0.893376
$986$	13.7226	−	86.6411i	0.437017	−	2.75922i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$991$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−10.8771	−	45.3063i	−0.344481	−	1.43487i	−0.828589	−	0.559857i	$-0.810856\pi$
$997$	−10.8771	−	45.3063i	−0.344481	−	1.43487i	0.484108	−	0.875008i	$-0.339144\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	164.2.o.a.111.1	yes	16
4.3	odd	2	CM	164.2.o.a.111.1	yes	16
41.17	odd	40	inner	164.2.o.a.99.1	✓	16
164.99	even	40	inner	164.2.o.a.99.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.2.o.a.99.1	✓	16	41.17	odd	40	inner
164.2.o.a.99.1	✓	16	164.99	even	40	inner
164.2.o.a.111.1	yes	16	1.1	even	1	trivial
164.2.o.a.111.1	yes	16	4.3	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	164.o (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.221232 + 1.39680i) q^{2} +(-1.90211 - 0.618034i) q^{4} +(-3.93080 + 2.00284i) q^{5} +(1.28408 - 2.52015i) q^{8} +(-2.12132 - 2.12132i) q^{9} +O(q^{10})\)	\(q+(-0.221232 + 1.39680i) q^{2} +(-1.90211 - 0.618034i) q^{4} +(-3.93080 + 2.00284i) q^{5} +(1.28408 - 2.52015i) q^{8} +(-2.12132 - 2.12132i) q^{9} +(-1.92796 - 5.93364i) q^{10} +(1.04080 + 4.33524i) q^{13} +(3.23607 + 2.35114i) q^{16} +(-6.27019 + 5.35525i) q^{17} +(3.43237 - 2.49376i) q^{18} +(8.71465 - 1.38026i) q^{20} +(8.50088 - 11.7005i) q^{25} +(-6.28573 + 0.494697i) q^{26} +(5.72004 + 4.88538i) q^{29} +(-4.00000 + 4.00000i) q^{32} +(-6.09306 - 9.94297i) q^{34} +(2.72394 + 5.34604i) q^{36} +(-2.23416 + 6.87604i) q^{37} +12.4780i q^{40} +(-6.39623 - 0.297142i) q^{41} +(12.5872 + 4.08981i) q^{45} +(3.17793 - 6.23705i) q^{49} +(14.4626 + 14.4626i) q^{50} +(0.699608 - 8.88936i) q^{52} +(2.53572 - 2.96894i) q^{53} +(-8.08936 + 6.90897i) q^{58} +(-6.07643 + 0.962412i) q^{61} +(-4.70228 - 6.47214i) q^{64} +(-12.7740 - 14.9564i) q^{65} +(15.2363 - 6.31110i) q^{68} +(-8.06998 + 2.62210i) q^{72} +(-0.538863 + 0.538863i) q^{73} +(-9.11020 - 4.64188i) q^{74} +(-17.4293 - 2.76053i) q^{80} +9.00000i q^{81} +(1.83010 - 8.86853i) q^{82} +(13.9211 - 33.6086i) q^{85} +(-2.65671 + 1.62803i) q^{89} +(-8.49734 + 16.6770i) q^{90} +(0.439906 + 5.58953i) q^{97} +(8.00886 + 5.81878i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 8 q^{8}+O(q^{10}) \) 16 * q - 4 * q^2 + 8 * q^8	\( 16 q - 4 q^{2} + 8 q^{8} - 8 q^{13} + 16 q^{16} - 4 q^{17} - 20 q^{26} + 20 q^{29} - 64 q^{32} - 48 q^{34} - 20 q^{41} + 56 q^{50} + 96 q^{52} + 28 q^{53} + 12 q^{58} - 44 q^{61} - 112 q^{65} + 32 q^{68} - 36 q^{82} + 56 q^{85} + 32 q^{89} + 48 q^{90} + 36 q^{97}+O(q^{100}) \) 16 * q - 4 * q^2 + 8 * q^8 - 8 * q^13 + 16 * q^16 - 4 * q^17 - 20 * q^26 + 20 * q^29 - 64 * q^32 - 48 * q^34 - 20 * q^41 + 56 * q^50 + 96 * q^52 + 28 * q^53 + 12 * q^58 - 44 * q^61 - 112 * q^65 + 32 * q^68 - 36 * q^82 + 56 * q^85 + 32 * q^89 + 48 * q^90 + 36 * q^97

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