LMFDB - Embedded newform 164.2.o.a.135.1

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			135.1
Root			$-0.891007 + 0.453990i$ of defining polynomial
Character	$\chi$	$=$	164.135
Dual form			164.2.o.a.147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.221232 + 1.39680i) q^{2} +(-1.90211 - 0.618034i) q^{4} +(3.93080 - 2.00284i) q^{5} +(1.28408 - 2.52015i) q^{8} +(2.12132 + 2.12132i) q^{9} +O(q^{10})$	\(q+(-0.221232 + 1.39680i) q^{2} +(-1.90211 - 0.618034i) q^{4} +(3.93080 - 2.00284i) q^{5} +(1.28408 - 2.52015i) q^{8} +(2.12132 + 2.12132i) q^{9} +(1.92796 + 5.93364i) q^{10} +(-5.51107 + 1.32309i) q^{13} +(3.23607 + 2.35114i) q^{16} +(-0.0501224 - 0.0586858i) q^{17} +(-3.43237 + 2.49376i) q^{18} +(-8.71465 + 1.38026i) q^{20} +(8.50088 - 11.7005i) q^{25} +(-0.628873 - 7.99058i) q^{26} +(-5.00599 + 5.86126i) q^{29} +(-4.00000 + 4.00000i) q^{32} +(0.0930611 - 0.0570279i) q^{34} +(-2.72394 - 5.34604i) q^{36} +(2.23416 - 6.87604i) q^{37} -12.4780i q^{40} +(-6.39623 - 0.297142i) q^{41} +(12.5872 + 4.08981i) q^{45} +(-3.17793 + 6.23705i) q^{49} +(14.4626 + 14.4626i) q^{50} +(11.3004 + 0.889360i) q^{52} +(-10.6662 - 9.10978i) q^{53} +(-7.07953 - 8.28907i) q^{58} +(-6.07643 + 0.962412i) q^{61} +(-4.70228 - 6.47214i) q^{64} +(-19.0130 + 16.2386i) q^{65} +(0.0590687 + 0.142604i) q^{68} +(8.06998 - 2.62210i) q^{72} +(0.538863 - 0.538863i) q^{73} +(9.11020 + 4.64188i) q^{74} +(17.4293 + 2.76053i) q^{80} +9.00000i q^{81} +(1.83010 - 8.86853i) q^{82} +(-0.314559 - 0.130295i) q^{85} +(9.72313 + 15.8667i) q^{89} +(-8.49734 + 16.6770i) q^{90} +(18.8247 - 1.48153i) q^{97} +(-8.00886 - 5.81878i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/164\mathbb{Z}\right)^\times$.

$n$	$83$	$129$
$\chi(n)$	$-1$	$e\left(\frac{27}{40}\right)$

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		−0.923880	−	0.382683i	$-0.875000\pi$
$3$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$4$	−1.90211	−	0.618034i	−0.951057	−	0.309017i
$5$	3.93080	−	2.00284i	1.75791	−	0.895698i	0.804532	−	0.593910i	$-0.202416\pi$
$5$	3.93080	−	2.00284i	1.75791	−	0.895698i	0.953375	−	0.301788i	$-0.0975836\pi$
$6$		0			0
$7$		0			0		−0.522499	−	0.852640i	$-0.675000\pi$
$7$		0			0		0.522499	+	0.852640i	$0.325000\pi$
$8$	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		−0.996917	−	0.0784591i	$-0.975000\pi$
$11$		0			0		0.996917	+	0.0784591i	$0.0250000\pi$
$12$		0			0
$13$	−5.51107	+	1.32309i	−1.52850	+	0.366959i	−0.908581	−	0.417710i	$-0.862833\pi$
$13$	−5.51107	+	1.32309i	−1.52850	+	0.366959i	−0.619915	+	0.784669i	$0.712833\pi$
$14$		0			0
$15$		0			0
$16$	3.23607	+	2.35114i	0.809017	+	0.587785i
$17$	−0.0501224	−	0.0586858i	−0.0121565	−	0.0142334i	0.754294	−	0.656536i	$-0.227979\pi$
$17$	−0.0501224	−	0.0586858i	−0.0121565	−	0.0142334i	−0.766451	+	0.642303i	$0.777979\pi$
$18$	−3.43237	+	2.49376i	−0.809017	+	0.587785i
$19$		0			0		−0.972370	−	0.233445i	$-0.925000\pi$
$19$		0			0		0.972370	+	0.233445i	$0.0750000\pi$
$20$	−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
$26$	−0.628873	−	7.99058i	−0.123332	−	1.56708i
$27$		0			0
$28$		0			0
$29$	−5.00599	+	5.86126i	−0.929588	+	1.08841i	0.0662984	+	0.997800i	$0.478881\pi$
$29$	−5.00599	+	5.86126i	−0.929588	+	1.08841i	−0.995887	+	0.0906081i	$0.971119\pi$
$30$		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
$34$	0.0930611	−	0.0570279i	0.0159599	−	0.00978021i
$35$		0			0
$36$	−2.72394	−	5.34604i	−0.453990	−	0.891007i
$37$	2.23416	−	6.87604i	0.367294	−	1.13041i	−0.581238	−	0.813733i	$-0.697432\pi$
$37$	2.23416	−	6.87604i	0.367294	−	1.13041i	0.948532	−	0.316681i	$-0.102568\pi$
$38$		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		0.522499	−	0.852640i	$-0.325000\pi$
$47$		0			0		−0.522499	+	0.852640i	$0.675000\pi$
$48$		0			0
$49$	−3.17793	+	6.23705i	−0.453990	+	0.891007i
$50$	14.4626	+	14.4626i	2.04531	+	2.04531i
$51$		0			0
$52$	11.3004	+	0.889360i	1.56708	+	0.123332i
$53$	−10.6662	−	9.10978i	−1.46511	−	1.25132i	−0.906710	−	0.421754i	$-0.861414\pi$
$53$	−10.6662	−	9.10978i	−1.46511	−	1.25132i	−0.558403	−	0.829570i	$-0.688586\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−7.07953	−	8.28907i	−0.929588	−	1.08841i
$59$		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
$65$	−19.0130	+	16.2386i	−2.35827	+	2.01415i
$66$		0			0
$67$		0			0		−0.0784591	−	0.996917i	$-0.525000\pi$
$67$		0			0		0.0784591	+	0.996917i	$0.475000\pi$
$68$	0.0590687	+	0.142604i	0.00716313	+	0.0172933i
$69$		0			0
$70$		0			0
$71$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$71$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$72$	8.06998	−	2.62210i	0.951057	−	0.309017i
$73$	0.538863	−	0.538863i	0.0630691	−	0.0630691i	−0.674869	−	0.737938i	$-0.735800\pi$
$73$	0.538863	−	0.538863i	0.0630691	−	0.0630691i	0.737938	+	0.674869i	$0.235800\pi$
$74$	9.11020	+	4.64188i	1.05904	+	0.539608i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$79$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$80$	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
$85$	−0.314559	−	0.130295i	−0.0341188	−	0.0141325i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	9.72313	+	15.8667i	1.03065	+	1.68187i	0.656130	+	0.754648i	$0.272192\pi$
$89$	9.72313	+	15.8667i	1.03065	+	1.68187i	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
$97$	18.8247	−	1.48153i	1.91136	−	0.150427i	0.933346	−	0.358979i	$-0.116875\pi$
$97$	18.8247	−	1.48153i	1.91136	−	0.150427i	0.978011	+	0.208552i	$0.0668751\pi$
$98$	−8.00886	−	5.81878i	−0.809017	−	0.587785i
$99$		0			0
$100$	−23.4009	+	17.0018i	−2.34009	+	1.70018i
$101$	19.3641	+	4.64890i	1.92680	+	0.462583i	0.995037	+	0.0995037i	$0.0317255\pi$
$101$	19.3641	+	4.64890i	1.92680	+	0.462583i	0.931758	+	0.363079i	$0.118274\pi$
$102$		0			0
$103$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$103$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$104$	−3.74227	+	15.5877i	−0.366959	+	1.52850i
$105$		0			0
$106$	15.0843	−	12.8832i	1.46511	−	1.25132i
$107$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$107$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$108$		0			0
$109$	−5.32612	−	12.8584i	−0.510149	−	1.23161i	−0.943797	−	0.330527i	$-0.892774\pi$
$109$	−5.32612	−	12.8584i	−0.510149	−	1.23161i	0.433647	−	0.901083i	$-0.357226\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−19.6031	+	6.36945i	−1.84411	+	0.599187i	−0.846324	+	0.532668i	$0.821189\pi$
$113$	−19.6031	+	6.36945i	−1.84411	+	0.599187i	−0.997785	+	0.0665190i	$0.978811\pi$
$114$		0			0
$115$		0			0
$116$	13.1444	−	8.05490i	1.22043	−	0.747879i
$117$	−14.4974	−	8.88404i	−1.34029	−	0.821330i
$118$		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
$130$	−18.4758	−	30.1498i	−1.62044	−	2.64432i
$131$		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
$136$	−0.212258	+	0.0509586i	−0.0182010	+	0.00436967i
$137$	−8.96296	+	3.71258i	−0.765757	+	0.317187i	−0.731153	−	0.682214i	$-0.761017\pi$
$137$	−8.96296	+	3.71258i	−0.765757	+	0.317187i	−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
$145$	−7.93835	+	33.0656i	−0.659244	+	2.74595i
$146$	0.633471	+	0.871898i	0.0524265	+	0.0721588i
$147$		0			0
$148$	−8.49926	+	11.6982i	−0.698635	+	0.961588i
$149$	−1.65053	−	20.9719i	−0.135216	−	1.71809i	−0.573462	−	0.819232i	$-0.694400\pi$
$149$	−1.65053	−	20.9719i	−0.135216	−	1.71809i	0.438246	−	0.898855i	$-0.355600\pi$
$150$		0			0
$151$		0			0		−0.233445	−	0.972370i	$-0.575000\pi$
$151$		0			0		0.233445	+	0.972370i	$0.425000\pi$
$152$		0			0
$153$	0.0181657	−	0.230817i	0.00146861	−	0.0186605i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	4.40217	−	2.69765i	0.351331	−	0.215296i	−0.335624	−	0.941996i	$-0.608947\pi$
$157$	4.40217	−	2.69765i	0.351331	−	0.215296i	0.686955	+	0.726700i	$0.258947\pi$
$158$		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		−0.923880	−	0.382683i	$-0.875000\pi$
$167$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$168$		0			0
$169$	17.0382	−	8.68141i	1.31063	−	0.667801i
$170$	0.251587	−	0.410552i	0.0192958	−	0.0314879i
$171$		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
$178$	−24.3137	+	10.0711i	−1.82239	+	0.754858i
$179$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$179$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$180$	−21.4145	−	15.5586i	−1.59615	−	1.15967i
$181$	17.4690	+	20.4535i	1.29846	+	1.52030i	0.668965	+	0.743294i	$0.266738\pi$
$181$	17.4690	+	20.4535i	1.29846	+	1.52030i	0.629494	+	0.777005i	$0.283262\pi$
$182$		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		−0.382683	−	0.923880i	$-0.625000\pi$
$191$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$192$		0			0
$193$	13.0335	−	15.2603i	0.938175	−	1.09846i	−0.0568050	−	0.998385i	$-0.518091\pi$
$193$	13.0335	−	15.2603i	0.938175	−	1.09846i	0.994980	−	0.100076i	$-0.0319087\pi$
$194$	−2.09521	+	26.6221i	−0.150427	+	1.91136i
$195$		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		−0.852640	−	0.522499i	$-0.825000\pi$
$199$		0			0		0.852640	+	0.522499i	$0.175000\pi$
$200$	−18.5711	−	36.4478i	−1.31317	−	2.57725i
$201$		0			0
$202$	−10.7775	+	26.0193i	−0.758305	+	1.83071i
$203$		0			0
$204$		0			0
$205$	−25.7374	+	11.6426i	−1.79758	+	0.813156i
$206$		0			0
$207$		0			0
$208$	−20.9450	−	8.67569i	−1.45227	−	0.601551i
$209$		0			0
$210$		0			0
$211$		0			0		0.522499	−	0.852640i	$-0.325000\pi$
$211$		0			0		−0.522499	+	0.852640i	$0.675000\pi$
$212$	14.6581	+	23.9199i	1.00672	+	1.64283i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	19.1389	−	4.59485i	1.29625	−	0.311202i
$219$		0			0
$220$		0			0
$221$	0.353875	+	0.257105i	0.0238042	+	0.0172948i
$222$		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		0.233445	−	0.972370i	$-0.425000\pi$
$227$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$228$		0			0
$229$	1.24242	−	1.06113i	0.0821017	−	0.0701215i	−0.607450	−	0.794358i	$-0.707808\pi$
$229$	1.24242	−	1.06113i	0.0821017	−	0.0701215i	0.689552	+	0.724236i	$0.257808\pi$
$230$		0			0
$231$		0			0
$232$	8.34315	+	20.1421i	0.547754	+	1.32240i
$233$	3.22357	+	13.4271i	0.211183	+	0.879641i	0.972806	+	0.231621i	$0.0744028\pi$
$233$	3.22357	+	13.4271i	0.211183	+	0.879641i	−0.761623	+	0.648020i	$0.775597\pi$
$234$	15.6165	−	18.2846i	1.02089	−	1.19530i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$239$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$240$		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
$257$	−14.0502	−	1.10577i	−0.876426	−	0.0689762i	−0.367740	−	0.929928i	$-0.619869\pi$
$257$	−14.0502	−	1.10577i	−0.876426	−	0.0689762i	−0.508686	+	0.860952i	$0.669869\pi$
$258$		0			0
$259$		0			0
$260$	46.2008	−	19.1370i	2.86525	−	1.18683i
$261$	−23.0529	+	1.81430i	−1.42694	+	0.112303i
$262$		0			0
$263$		0			0		−0.649448	−	0.760406i	$-0.725000\pi$
$263$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$264$		0			0
$265$	−60.1721	−	14.4460i	−3.69634	−	0.887413i
$266$		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	$0.700000\pi$
$272$	−0.0242209	−	0.307756i	−0.00146861	−	0.0186605i
$273$		0			0
$274$	−3.20285	−	13.3408i	−0.193491	−	0.805949i
$275$		0			0
$276$		0			0
$277$	23.6237	−	7.67581i	1.41941	−	0.461195i	0.503997	−	0.863706i	$-0.331862\pi$
$277$	23.6237	−	7.67581i	1.41941	−	0.461195i	0.915415	+	0.402511i	$0.131862\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	11.2363	+	6.88563i	0.670303	+	0.410762i	0.815592	−	0.578627i	$-0.196411\pi$
$281$	11.2363	+	6.88563i	0.670303	+	0.410762i	−0.145289	+	0.989389i	$0.546411\pi$
$282$		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
$289$	2.65845	−	16.7848i	0.156380	−	0.987342i
$290$	−44.4299	−	18.4035i	−2.60901	−	1.08069i
$291$		0			0
$292$	−1.35801	+	0.691943i	−0.0794717	+	0.0404929i
$293$	−7.50015	+	12.2391i	−0.438163	+	0.715018i	−0.993151	−	0.116841i	$-0.962723\pi$
$293$	−7.50015	+	12.2391i	−0.438163	+	0.715018i	0.554987	+	0.831859i	$0.312723\pi$
$294$		0			0
$295$		0			0
$296$	−14.4598	−	14.4598i	−0.840459	−	0.840459i
$297$		0			0
$298$	29.6588	+	2.33420i	1.71809	+	0.135216i
$299$		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
$306$	0.318387	+	0.0764379i	0.0182010	+	0.00436967i
$307$		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		0.760406	−	0.649448i	$-0.225000\pi$
$311$		0			0		−0.760406	+	0.649448i	$0.775000\pi$
$312$		0			0
$313$	−0.959032	−	12.1857i	−0.0542077	−	0.688774i	−0.962647	−	0.270758i	$-0.912726\pi$
$313$	−0.959032	−	12.1857i	−0.0542077	−	0.688774i	0.908440	−	0.418016i	$-0.137274\pi$
$314$	2.79419	+	6.74577i	0.157685	+	0.380686i
$315$		0			0
$316$		0			0
$317$	2.73928	−	34.8058i	0.153853	−	1.95489i	−0.119145	−	0.992877i	$-0.538015\pi$
$317$	2.73928	−	34.8058i	0.153853	−	1.95489i	0.272999	−	0.962014i	$-0.411985\pi$
$318$		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
$325$	−31.3682	+	75.7294i	−1.73999	+	4.20071i
$326$		0			0
$327$		0			0
$328$	−8.96210	+	15.7379i	−0.494849	+	0.868979i
$329$		0			0
$330$		0			0
$331$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$331$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$332$		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	0.784151	−	0.620570i	$-0.213099\pi$
$337$	3.00296	+	3.00296i	0.163581	+	0.163581i	−0.620570	+	0.784151i	$0.713099\pi$
$338$	8.35682	+	25.7196i	0.454551	+	1.39896i
$339$		0			0
$340$	0.517801	+	0.442244i	0.0280817	+	0.0239840i
$341$		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		−0.972370	−	0.233445i	$-0.925000\pi$
$347$		0			0		0.972370	+	0.233445i	$0.0750000\pi$
$348$		0			0
$349$	−2.04461	−	12.9092i	−0.109446	−	0.691013i	−0.980009	−	0.198956i	$-0.936245\pi$
$349$	−2.04461	−	12.9092i	−0.109446	−	0.691013i	0.870563	−	0.492057i	$-0.163755\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−18.2675	+	25.1430i	−0.972279	+	1.33823i	−0.0313912	+	0.999507i	$0.509994\pi$
$353$	−18.2675	+	25.1430i	−0.972279	+	1.33823i	−0.940887	+	0.338719i	$0.890006\pi$
$354$		0			0
$355$		0			0
$356$	−8.68833	−	36.1895i	−0.460480	−	1.91804i
$357$		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
$362$	−32.4342	+	19.8757i	−1.70471	+	1.04465i
$363$		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
$377$	19.8334	−	38.9252i	1.02147	−	2.00475i
$378$		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		0.923880	−	0.382683i	$-0.125000\pi$
$383$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$384$		0			0
$385$		0			0
$386$	18.4322	+	21.5813i	0.938175	+	1.09846i
$387$		0			0
$388$	−36.7223	−	8.81625i	−1.86429	−	0.447577i
$389$	−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
$397$	−9.27978	−	38.6531i	−0.465739	−	1.93994i	−0.301131	−	0.953583i	$-0.597364\pi$
$397$	−9.27978	−	38.6531i	−0.465739	−	1.93994i	−0.164607	−	0.986359i	$-0.552636\pi$
$398$		0			0
$399$		0			0
$400$	55.0188	−	17.8767i	2.75094	−	0.893835i
$401$	15.4810	−	15.4810i	0.773082	−	0.773082i	−0.205562	−	0.978644i	$-0.565902\pi$
$401$	15.4810	−	15.4810i	0.773082	−	0.773082i	0.978644	+	0.205562i	$0.0659023\pi$
$402$		0			0
$403$		0			0
$404$	−33.9594	−	20.8104i	−1.68955	−	1.03535i
$405$	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	$-0.697393\pi$
$409$		−	32.9163i		−	1.62761i	0.581140	−	0.813804i	$-0.302607\pi$
$410$	−10.5685	−	38.5258i	−0.521942	−	1.90265i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	16.7519	−	27.3366i	0.821330	−	1.34029i
$417$		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
$421$	−20.1607	−	1.58668i	−0.982570	−	0.0773300i	−0.423015	−	0.906123i	$-0.639028\pi$
$421$	−20.1607	−	1.58668i	−0.982570	−	0.0773300i	−0.559556	+	0.828793i	$0.689028\pi$
$422$		0			0
$423$		0			0
$424$	−36.6542	+	15.1827i	−1.78009	+	0.737336i
$425$	−1.11273	+	0.0875741i	−0.0539756	+	0.00424797i
$426$		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
$436$	2.18396	+	27.7498i	0.104593	+	1.32898i
$437$		0			0
$438$		0			0
$439$		0			0		0.649448	−	0.760406i	$-0.275000\pi$
$439$		0			0		−0.649448	+	0.760406i	$0.725000\pi$
$440$		0			0
$441$	−19.9722	+	6.48936i	−0.951057	+	0.309017i
$442$	−0.437413	+	0.437413i	−0.0208056	+	0.0208056i
$443$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$443$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$444$		0			0
$445$	69.9982	+	42.8949i	3.31823	+	2.03341i
$446$		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
$457$	−11.0736	+	18.0705i	−0.518002	+	0.845302i	−0.999515	−	0.0311368i	$-0.990087\pi$
$457$	−11.0736	+	18.0705i	−0.518002	+	0.845302i	0.481514	+	0.876439i	$0.340087\pi$
$458$	1.20733	+	1.97018i	0.0564146	+	0.0920603i
$459$		0			0
$460$		0			0
$461$	10.8378	+	33.3552i	0.504765	+	1.55351i	0.801165	+	0.598444i	$0.204214\pi$
$461$	10.8378	+	33.3552i	0.504765	+	1.55351i	−0.296399	+	0.955064i	$0.595786\pi$
$462$		0			0
$463$		0			0		−0.760406	−	0.649448i	$-0.775000\pi$
$463$		0			0		0.760406	+	0.649448i	$0.225000\pi$
$464$	−29.9803	+	7.19764i	−1.39180	+	0.334142i
$465$		0			0
$466$	−19.4682	+	1.53218i	−0.901847	+	0.0709769i
$467$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$467$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$468$	22.0851	+	25.8584i	1.02089	+	1.19530i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−3.30163	−	41.9511i	−0.151171	−	1.92081i
$478$		0			0
$479$		0			0		−0.233445	−	0.972370i	$-0.575000\pi$
$479$		0			0		0.233445	+	0.972370i	$0.425000\pi$
$480$		0			0
$481$	−3.21499	+	40.8503i	−0.146591	+	1.86262i
$482$	−16.9396	+	5.50402i	−0.771579	+	0.250701i
$483$		0			0
$484$	−19.6021	−	9.98779i	−0.891007	−	0.453990i
$485$	71.0288	−	43.5265i	3.22525	−	1.97644i
$486$		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
$493$	0.594885			0.0267923
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.522499	−	0.852640i	$-0.675000\pi$
$499$		0			0		0.522499	+	0.852640i	$0.325000\pi$
$500$	−37.9040	+	74.3908i	−1.69512	+	3.32686i
$501$		0			0
$502$		0			0
$503$		0			0		−0.996917	−	0.0784591i	$-0.975000\pi$
$503$		0			0		0.996917	+	0.0784591i	$0.0250000\pi$
$504$		0			0
$505$	85.4272	−	20.5093i	3.80146	−	0.912650i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−9.39331	−	10.9982i	−0.416351	−	0.487485i	0.512107	−	0.858922i	$-0.328865\pi$
$509$	−9.39331	−	10.9982i	−0.416351	−	0.487485i	−0.928458	+	0.371437i	$0.878865\pi$
$510$		0			0
$511$		0			0
$512$	−22.3488	+	3.53971i	−0.987688	+	0.156434i
$513$		0			0
$514$	4.65289	−	19.3807i	0.205230	−	0.854846i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	16.5095	+	68.7671i	0.723990	+	3.01564i
$521$	−16.2820	+	19.0638i	−0.713328	+	0.835200i	−0.992138	−	0.125146i	$-0.960060\pi$
$521$	−16.2820	+	19.0638i	−0.713328	+	0.835200i	0.278810	+	0.960346i	$0.410060\pi$
$522$	2.56581	−	32.6017i	0.112303	−	1.42694i
$523$		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
$530$	33.4902	−	80.8525i	1.45472	−	3.51201i
$531$		0			0
$532$		0			0
$533$	35.6432	−	6.82522i	1.54388	−	0.295633i
$534$		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	$-0.691463\pi$
$541$	10.0890	−	19.8008i	0.433761	−	0.851305i	0.999640	−	0.0268165i	$-0.00853697\pi$
$542$		0			0
$543$		0			0
$544$	0.435233	+	0.0342536i	0.0186605	+	0.00146861i
$545$	−46.6892	−	39.8763i	−1.99995	−	1.70811i
$546$		0			0
$547$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$547$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$548$	19.3431	−	1.52233i	0.826295	−	0.0650308i
$549$	−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
$557$	−30.7285	+	26.2446i	−1.30201	+	1.11202i	−0.315390	+	0.948962i	$0.602135\pi$
$557$	−30.7285	+	26.2446i	−1.30201	+	1.11202i	−0.986617	+	0.163057i	$0.947865\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−12.1037	+	14.1716i	−0.510564	+	0.597793i
$563$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$563$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$564$		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	$-0.866534\pi$
$569$	−16.8377	−	33.0458i	−0.705872	−	1.38535i	0.207504	−	0.978234i	$-0.433466\pi$
$570$		0			0
$571$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$571$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	3.75443	−	23.7045i	0.156434	−	0.987688i
$577$	38.7768	+	16.0619i	1.61430	+	0.668665i	0.993345	−	0.115181i	$-0.0367448\pi$
$577$	38.7768	+	16.0619i	1.61430	+	0.668665i	0.620956	+	0.783846i	$0.286745\pi$
$578$	22.8569	+	7.42667i	0.950723	+	0.308909i
$579$		0			0
$580$	35.5353	−	57.9884i	1.47552	−	2.40784i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.666071	−	2.04996i	−0.0275622	−	0.0848278i
$585$	−74.7799	−	5.88530i	−3.09177	−	0.243327i
$586$	−15.4364	−	13.1839i	−0.637671	−	0.544622i
$587$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$587$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	23.3964	−	16.9985i	0.961588	−	0.698635i
$593$	23.9082	+	5.73984i	0.981790	+	0.235707i	0.692408	−	0.721507i	$-0.256550\pi$
$593$	23.9082	+	5.73984i	0.981790	+	0.235707i	0.289383	+	0.957214i	$0.406550\pi$
$594$		0			0
$595$		0			0
$596$	−9.82187	+	40.9111i	−0.402320	+	1.67578i
$597$		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
$601$	5.25624	+	12.6897i	0.214406	+	0.517623i	0.994091	−	0.108550i	$-0.0346206\pi$
$601$	5.25624	+	12.6897i	0.214406	+	0.517623i	−0.779685	+	0.626172i	$0.784621\pi$
$602$		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
$612$	−0.177206	+	0.427813i	−0.00716313	+	0.0172933i
$613$	20.9502	+	3.31818i	0.846169	+	0.134020i	0.564440	−	0.825474i	$-0.309092\pi$
$613$	20.9502	+	3.31818i	0.846169	+	0.134020i	0.281729	+	0.959494i	$0.409092\pi$
$614$		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
$626$	17.2331	+	1.35628i	0.688774	+	0.0542077i
$627$		0			0
$628$	−10.0407	+	2.41055i	−0.400666	+	0.0961914i
$629$	−0.515508	+	0.213530i	−0.0205546	+	0.00851401i
$630$		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
$634$	48.0109	+	11.5264i	1.90676	+	0.457771i
$635$		0			0
$636$		0			0
$637$	9.26164	−	38.5775i	0.366959	−	1.52850i
$638$		0			0
$639$		0			0
$640$	29.3375	−	40.3796i	1.15967	−	1.59615i
$641$	−1.52613	−	19.3913i	−0.0602783	−	0.765909i	−0.950568	−	0.310515i	$-0.899498\pi$
$641$	−1.52613	−	19.3913i	−0.0602783	−	0.765909i	0.890290	−	0.455394i	$-0.150502\pi$
$642$		0			0
$643$		0			0		−0.233445	−	0.972370i	$-0.575000\pi$
$643$		0			0		0.233445	+	0.972370i	$0.425000\pi$
$644$		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
$650$	−98.8394	−	60.5689i	−3.87680	−	2.37571i
$651$		0			0
$652$		0			0
$653$	−6.34191	+	15.3107i	−0.248178	+	0.599155i	−0.998049	−	0.0624287i	$-0.980115\pi$
$653$	−6.34191	+	15.3107i	−0.248178	+	0.599155i	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		−0.923880	−	0.382683i	$-0.875000\pi$
$659$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$660$		0			0
$661$	−23.9356	+	12.1958i	−0.930986	+	0.474361i	−0.852601	−	0.522562i	$-0.824976\pi$
$661$	−23.9356	+	12.1958i	−0.930986	+	0.474361i	−0.0783849	+	0.996923i	$0.524976\pi$
$662$		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
$673$	−31.0054	−	36.3027i	−1.19517	−	1.39937i	−0.895345	−	0.445373i	$-0.853071\pi$
$673$	−31.0054	−	36.3027i	−1.19517	−	1.39937i	−0.299827	−	0.953994i	$-0.596929\pi$
$674$	−4.85889	+	3.53019i	−0.187157	+	0.135978i
$675$		0			0
$676$	−37.7741	+	5.98282i	−1.45285	+	0.230109i
$677$	7.63978	+	48.2356i	0.293620	+	1.85385i	0.487899	+	0.872900i	$0.337763\pi$
$677$	7.63978	+	48.2356i	0.293620	+	1.85385i	−0.194279	+	0.980946i	$0.562237\pi$
$678$		0			0
$679$		0			0
$680$	−0.732281	+	0.625427i	−0.0280817	+	0.0239840i
$681$		0			0
$682$		0			0
$683$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$683$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$684$		0			0
$685$	−27.7959	+	32.5448i	−1.06203	+	1.24347i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	70.8351	+	36.0923i	2.69860	+	1.37501i
$690$		0			0
$691$		0			0		−0.852640	−	0.522499i	$-0.825000\pi$
$691$		0			0		0.852640	+	0.522499i	$0.175000\pi$
$692$	−0.105819	−	0.207681i	−0.00402262	−	0.00789483i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.303156	+	0.390261i	0.0114829	+	0.0147822i
$698$	18.4839			0.699626
$699$		0			0
$700$		0			0
$701$	−47.3583	−	15.3876i	−1.78870	−	0.581183i	−0.789239	−	0.614086i	$-0.789525\pi$
$701$	−47.3583	−	15.3876i	−1.78870	−	0.581183i	−0.999459	+	0.0329027i	$0.989525\pi$
$702$		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
$709$	−29.9925	−	25.6160i	−1.12639	−	0.962028i	−0.126837	−	0.991924i	$-0.540483\pi$
$709$	−29.9925	−	25.6160i	−1.12639	−	0.962028i	−0.999553	+	0.0298952i	$0.990483\pi$
$710$		0			0
$711$		0			0
$712$	52.4717	−	4.12961i	1.96646	−	0.154764i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.233445	−	0.972370i	$-0.425000\pi$
$719$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$720$	31.1172	+	42.8291i	1.15967	+	1.59615i
$721$		0			0
$722$	−15.7938	+	21.7383i	−0.587785	+	0.809017i
$723$		0			0
$724$	−20.5870	−	49.7014i	−0.765109	−	1.84714i
$725$	26.0241	+	108.398i	0.966510	+	4.02580i
$726$		0			0
$727$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$727$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$728$		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
$745$	−48.4913	−	79.1307i	−1.77659	−	2.89912i
$746$	19.2046	−	37.6911i	0.703129	−	1.37997i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$751$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$752$		0			0
$753$		0			0
$754$	49.9830	+	36.3148i	1.82027	+	1.32251i
$755$		0			0
$756$		0			0
$757$	−41.3427	−	9.92550i	−1.50263	−	0.360748i	−0.603117	−	0.797652i	$-0.706075\pi$
$757$	−41.3427	−	9.92550i	−1.50263	−	0.360748i	−0.899508	+	0.436904i	$0.856075\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	25.7388	+	35.4265i	0.933032	+	1.28421i	0.958665	+	0.284537i	$0.0918400\pi$
$761$	25.7388	+	35.4265i	0.933032	+	1.28421i	−0.0256326	+	0.999671i	$0.508160\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.390884	−	0.943678i	−0.0141325	−	0.0341188i
$766$		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
$772$	−34.2227	+	20.9717i	−1.23170	+	0.754787i
$773$	23.5665	+	14.4416i	0.847629	+	0.519428i	0.877194	−	0.480135i	$-0.159412\pi$
$773$	23.5665	+	14.4416i	0.847629	+	0.519428i	−0.0295658	+	0.999563i	$0.509412\pi$
$774$		0			0
$775$		0			0
$776$	20.4387	−	49.3434i	0.733706	−	1.77132i
$777$		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
$785$	11.9011	−	19.4208i	0.424767	−	0.693157i
$786$		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
$793$	32.2143	−	13.3436i	1.14396	−	0.473845i
$794$	56.0437	−	4.41073i	1.98892	−	0.156531i
$795$		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
$801$	−13.0325	+	54.2842i	−0.460480	+	1.91804i
$802$	18.1990	+	25.0487i	0.642627	+	0.884501i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	36.5809	−	42.8307i	1.28691	−	1.50678i
$809$	4.31861	−	54.8731i	0.151834	−	1.92924i	−0.175791	−	0.984428i	$-0.556248\pi$
$809$	4.31861	−	54.8731i	0.151834	−	1.92924i	0.327625	−	0.944808i	$-0.393752\pi$
$810$	−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	$-0.687507\pi$
$821$	−31.8386			−1.11117			−0.555587	+	0.831458i	$0.687507\pi$
$822$		0			0
$823$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$823$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.522499	−	0.852640i	$-0.675000\pi$
$827$		0			0		0.522499	+	0.852640i	$0.325000\pi$
$828$		0			0
$829$	40.6851	+	40.6851i	1.41305	+	1.41305i	0.735188	+	0.677863i	$0.237094\pi$
$829$	40.6851	+	40.6851i	1.41305	+	1.41305i	0.677863	+	0.735188i	$0.262906\pi$
$830$		0			0
$831$		0			0
$832$	34.4778	+	29.4468i	1.19530	+	1.02089i
$833$	0.525312	−	0.126116i	0.0182010	−	0.00436967i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.972370	−	0.233445i	$-0.925000\pi$
$839$		0			0		0.972370	+	0.233445i	$0.0750000\pi$
$840$		0			0
$841$	−4.75783	−	30.0398i	−0.164063	−	1.03585i
$842$	6.67645	−	27.8094i	0.230086	−	0.958376i
$843$		0			0
$844$		0			0
$845$	49.5864	−	68.2498i	1.70582	−	2.34786i
$846$		0			0
$847$		0			0
$848$	−13.0981	−	54.5576i	−0.449791	−	1.87351i
$849$		0			0
$850$	0.123849	−	1.57364i	0.00424797	−	0.0539756i
$851$		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	$-0.493630\pi$
$857$	17.3156	−	53.2919i	0.591490	−	1.82042i	0.571477	−	0.820618i	$-0.306370\pi$
$858$		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
$872$	−39.2442	−	3.08858i	−1.32898	−	0.104593i
$873$	43.0760	+	36.7904i	1.45790	+	1.24517i
$874$		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		0.233445	−	0.972370i	$-0.425000\pi$
$883$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$884$	−0.514210	−	0.707749i	−0.0172948	−	0.0238042i
$885$		0			0
$886$		0			0
$887$		0			0		−0.0784591	−	0.996917i	$-0.525000\pi$
$887$		0			0		0.0784591	+	0.996917i	$0.475000\pi$
$888$		0			0
$889$		0			0
$890$	−75.4015	+	88.2839i	−2.52747	+	2.95928i
$891$		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
$901$			1.08256i			0.0360652i
$902$		0			0
$903$		0			0
$904$	−9.12004	+	57.5817i	−0.303328	+	1.91514i
$905$	109.632	+	45.4112i	3.64430	+	1.50952i
$906$		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
$909$	31.2156	+	50.9392i	1.03535	+	1.68955i
$910$		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
$914$	−22.7911	−	19.4654i	−0.753861	−	0.643859i
$915$		0			0
$916$	−3.01905	+	1.25053i	−0.0997521	+	0.0413187i
$917$		0			0
$918$		0			0
$919$		0			0		−0.649448	−	0.760406i	$-0.725000\pi$
$919$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$920$		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
$928$	−3.42108	−	43.4690i	−0.112303	−	1.42694i
$929$	−0.207272	−	0.500399i	−0.00680038	−	0.0164176i	0.920443	−	0.390877i	$-0.127828\pi$
$929$	−0.207272	−	0.500399i	−0.00680038	−	0.0164176i	−0.927243	+	0.374460i	$0.877828\pi$
$930$		0			0
$931$		0			0
$932$	2.16683	−	27.5322i	0.0709769	−	0.901847i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−41.0050	+	25.1279i	−1.34029	+	0.821330i
$937$	−14.2720	−	8.74590i	−0.466246	−	0.285716i	0.269466	−	0.963010i	$-0.413153\pi$
$937$	−14.2720	−	8.74590i	−0.466246	−	0.285716i	−0.735713	+	0.677294i	$0.763153\pi$
$938$		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
$949$	−2.25675	+	3.68268i	−0.0732571	+	0.119545i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−6.55524	−	20.1750i	−0.212345	−	0.653531i	−0.999331	−	0.0365605i	$-0.988360\pi$
$953$	−6.55524	−	20.1750i	−0.212345	−	0.653531i	0.786986	−	0.616970i	$-0.211640\pi$
$954$	59.3279	+	4.66921i	1.92081	+	0.151171i
$955$		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
$962$	−56.3486	−	13.5281i	−1.81675	−	0.436164i
$963$		0			0
$964$	−3.94044	−	24.8790i	−0.126913	−	0.801297i
$965$	20.6682	−	86.0894i	0.665334	−	2.77131i
$966$		0			0
$967$		0			0		0.760406	−	0.649448i	$-0.225000\pi$
$967$		0			0		−0.760406	+	0.649448i	$0.775000\pi$
$968$	18.2876	−	25.1707i	0.587785	−	0.809017i
$969$		0			0
$970$	45.0841	+	108.843i	1.44756	+	3.49472i
$971$		0			0		−0.233445	−	0.972370i	$-0.575000\pi$
$971$		0			0		0.233445	+	0.972370i	$0.425000\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−21.9265	−	11.1721i	−0.701850	−	0.357611i
$977$	−51.4500	+	31.5286i	−1.64603	+	1.00869i	−0.686483	+	0.727145i	$0.740847\pi$
$977$	−51.4500	+	31.5286i	−1.64603	+	1.00869i	−0.959548	+	0.281544i	$0.909153\pi$
$978$		0			0
$979$		0			0
$980$	19.0858	−	58.7400i	0.609673	−	1.87638i
$981$	15.9783	−	38.5751i	0.510149	−	1.23161i
$982$		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
$986$	−0.131607	+	0.830936i	−0.00419123	+	0.0264624i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.522499	−	0.852640i	$-0.675000\pi$
$991$		0			0		0.522499	+	0.852640i	$0.325000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	41.4488	−	9.95098i	1.31270	−	0.315151i	0.484108	−	0.875008i	$-0.339144\pi$
$997$	41.4488	−	9.95098i	1.31270	−	0.315151i	0.828589	+	0.559857i	$0.189144\pi$
$998$		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.135.1	✓	16
4.3	odd	2	CM	164.2.o.a.135.1	✓	16
41.24	odd	40	inner	164.2.o.a.147.1	yes	16
164.147	even	40	inner	164.2.o.a.147.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.2.o.a.135.1	✓	16	1.1	even	1	trivial
164.2.o.a.135.1	✓	16	4.3	odd	2	CM
164.2.o.a.147.1	yes	16	41.24	odd	40	inner
164.2.o.a.147.1	yes	16	164.147	even	40	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.221232 + 1.39680i) q^{2} +(-1.90211 - 0.618034i) q^{4} +(3.93080 - 2.00284i) q^{5} +(1.28408 - 2.52015i) q^{8} +(2.12132 + 2.12132i) q^{9} +O(q^{10})\)	\(q+(-0.221232 + 1.39680i) q^{2} +(-1.90211 - 0.618034i) q^{4} +(3.93080 - 2.00284i) q^{5} +(1.28408 - 2.52015i) q^{8} +(2.12132 + 2.12132i) q^{9} +(1.92796 + 5.93364i) q^{10} +(-5.51107 + 1.32309i) q^{13} +(3.23607 + 2.35114i) q^{16} +(-0.0501224 - 0.0586858i) q^{17} +(-3.43237 + 2.49376i) q^{18} +(-8.71465 + 1.38026i) q^{20} +(8.50088 - 11.7005i) q^{25} +(-0.628873 - 7.99058i) q^{26} +(-5.00599 + 5.86126i) q^{29} +(-4.00000 + 4.00000i) q^{32} +(0.0930611 - 0.0570279i) q^{34} +(-2.72394 - 5.34604i) q^{36} +(2.23416 - 6.87604i) q^{37} -12.4780i q^{40} +(-6.39623 - 0.297142i) q^{41} +(12.5872 + 4.08981i) q^{45} +(-3.17793 + 6.23705i) q^{49} +(14.4626 + 14.4626i) q^{50} +(11.3004 + 0.889360i) q^{52} +(-10.6662 - 9.10978i) q^{53} +(-7.07953 - 8.28907i) q^{58} +(-6.07643 + 0.962412i) q^{61} +(-4.70228 - 6.47214i) q^{64} +(-19.0130 + 16.2386i) q^{65} +(0.0590687 + 0.142604i) q^{68} +(8.06998 - 2.62210i) q^{72} +(0.538863 - 0.538863i) q^{73} +(9.11020 + 4.64188i) q^{74} +(17.4293 + 2.76053i) q^{80} +9.00000i q^{81} +(1.83010 - 8.86853i) q^{82} +(-0.314559 - 0.130295i) q^{85} +(9.72313 + 15.8667i) q^{89} +(-8.49734 + 16.6770i) q^{90} +(18.8247 - 1.48153i) q^{97} +(-8.00886 - 5.81878i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 8 q^{8}+O(q^{10}) \) 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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