LMFDB - Embedded newform 100.2.l.a.3.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,2,Mod(3,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	100.l (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.798504020213$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{20}]$

Embedding invariants

Embedding label			3.1
Root			$-0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	100.3
Dual form			100.2.l.a.67.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.642040 + 1.26007i) q^{2} +(-1.17557 + 1.61803i) q^{4} +(2.20582 - 0.366554i) q^{5} +(-2.79360 - 0.442463i) q^{8} +(-2.85317 + 0.927051i) q^{9} +(1.87811 + 2.54415i) q^{10} +(1.36749 - 2.68384i) q^{13} +(-1.23607 - 3.80423i) q^{16} +(0.846926 - 5.34728i) q^{17} +(-3.00000 - 3.00000i) q^{18} +(-2.00000 + 4.00000i) q^{20} +(4.73128 - 1.61710i) q^{25} +4.25982 q^{26} +(-6.31671 + 8.69421i) q^{29} +(4.00000 - 4.00000i) q^{32} +(7.28173 - 2.36598i) q^{34} +(1.85410 - 5.70634i) q^{36} +(-8.71769 - 4.44189i) q^{37} +(-6.32437 + 0.0480111i) q^{40} +(3.81636 + 11.7455i) q^{41} +(-5.95376 + 3.09075i) q^{45} -7.00000i q^{49} +(5.07533 + 4.92351i) q^{50} +(2.73497 + 5.36768i) q^{52} +(2.26101 + 14.2754i) q^{53} +(-15.0109 - 2.37750i) q^{58} +(-1.18364 + 3.64288i) q^{61} +(7.60845 + 2.47214i) q^{64} +(2.03265 - 6.42133i) q^{65} +(7.65646 + 7.65646i) q^{68} +(8.38081 - 1.32739i) q^{72} +(7.51037 - 3.82672i) q^{73} -13.8368i q^{74} +(-4.12099 - 7.93835i) q^{80} +(7.28115 - 5.29007i) q^{81} +(-12.3500 + 12.3500i) q^{82} +(-0.0918987 - 12.1056i) q^{85} +(-4.34280 - 1.41106i) q^{89} +(-7.71712 - 5.51780i) q^{90} +(1.03093 - 0.163283i) q^{97} +(8.82051 - 4.49428i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 4 q^{5} - 4 q^{8} - 6 q^{10} + 2 q^{13} + 8 q^{16} - 6 q^{17} - 24 q^{18} - 16 q^{20} - 6 q^{25} - 4 q^{26} + 32 q^{32} + 50 q^{34} - 12 q^{36} - 46 q^{37} + 4 q^{40} + 16 q^{41} - 6 q^{45}+ \cdots - 14 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 + 4 * q^5 - 4 * q^8 - 6 * q^10 + 2 * q^13 + 8 * q^16 - 6 * q^17 - 24 * q^18 - 16 * q^20 - 6 * q^25 - 4 * q^26 + 32 * q^32 + 50 * q^34 - 12 * q^36 - 46 * q^37 + 4 * q^40 + 16 * q^41 - 6 * q^45 + 14 * q^50 + 4 * q^52 + 2 * q^53 - 8 * q^58 - 24 * q^61 + 78 * q^65 + 12 * q^68 + 12 * q^72 + 22 * q^73 - 16 * q^80 + 18 * q^81 - 16 * q^82 - 52 * q^85 - 50 * q^89 - 6 * q^90 - 26 * q^97 - 14 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{7}{20}\right)$

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 $

$2$	0.642040	+	1.26007i	0.453990	+	0.891007i
$2$	0.642040	+	1.26007i	0.453990	+	0.891007i
$3$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$3$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$4$	−1.17557	+	1.61803i	−0.587785	+	0.809017i
$5$	2.20582	−	0.366554i	0.986472	−	0.163928i
$5$	2.20582	−	0.366554i	0.986472	−	0.163928i
$6$		0			0
$7$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$7$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$8$	−2.79360	−	0.442463i	−0.987688	−	0.156434i
$9$	−2.85317	+	0.927051i	−0.951057	+	0.309017i
$10$	1.87811	+	2.54415i	0.593910	+	0.804532i
$11$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$11$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$12$		0			0
$13$	1.36749	−	2.68384i	0.379272	−	0.744364i	−0.619915	−	0.784669i	$-0.712833\pi$
$13$	1.36749	−	2.68384i	0.379272	−	0.744364i	0.999187	+	0.0403050i	$0.0128330\pi$
$14$		0			0
$15$		0			0
$16$	−1.23607	−	3.80423i	−0.309017	−	0.951057i
$17$	0.846926	−	5.34728i	0.205410	−	1.29691i	−0.642303	−	0.766451i	$-0.722021\pi$
$17$	0.846926	−	5.34728i	0.205410	−	1.29691i	0.847713	−	0.530456i	$-0.177979\pi$
$18$	−3.00000	−	3.00000i	−0.707107	−	0.707107i
$19$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$19$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$20$	−2.00000	+	4.00000i	−0.447214	+	0.894427i
$21$		0			0
$22$		0			0
$23$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$23$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$24$		0			0
$25$	4.73128	−	1.61710i	0.946255	−	0.323420i
$26$	4.25982			0.835419
$27$		0			0
$28$		0			0
$29$	−6.31671	+	8.69421i	−1.17298	+	1.61447i	−0.532855	+	0.846206i	$0.678881\pi$
$29$	−6.31671	+	8.69421i	−1.17298	+	1.61447i	−0.640129	+	0.768268i	$0.721119\pi$
$30$		0			0
$31$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$31$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$		0			0
$34$	7.28173	−	2.36598i	1.24881	−	0.405762i
$35$		0			0
$36$	1.85410	−	5.70634i	0.309017	−	0.951057i
$37$	−8.71769	−	4.44189i	−1.43318	−	0.730242i	−0.446786	−	0.894641i	$-0.647432\pi$
$37$	−8.71769	−	4.44189i	−1.43318	−	0.730242i	−0.986394	+	0.164399i	$0.947432\pi$
$38$		0			0
$39$		0			0
$40$	−6.32437	+	0.0480111i	−0.999971	+	0.00759122i
$41$	3.81636	+	11.7455i	0.596015	+	1.83434i	0.549609	+	0.835422i	$0.314777\pi$
$41$	3.81636	+	11.7455i	0.596015	+	1.83434i	0.0464057	+	0.998923i	$0.485223\pi$
$42$		0			0
$43$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$43$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$44$		0			0
$45$	−5.95376	+	3.09075i	−0.887535	+	0.460741i
$46$		0			0
$47$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$47$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$48$		0			0
$49$		−	7.00000i		−	1.00000i
$50$	5.07533	+	4.92351i	0.717761	+	0.696290i
$51$		0			0
$52$	2.73497	+	5.36768i	0.379272	+	0.744364i
$53$	2.26101	+	14.2754i	0.310573	+	1.96088i	0.274721	+	0.961524i	$0.411414\pi$
$53$	2.26101	+	14.2754i	0.310573	+	1.96088i	0.0358519	+	0.999357i	$0.488586\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−15.0109	−	2.37750i	−1.97103	−	0.312181i
$59$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$59$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$60$		0			0
$61$	−1.18364	+	3.64288i	−0.151550	+	0.466423i	−0.997795	−	0.0663709i	$-0.978858\pi$
$61$	−1.18364	+	3.64288i	−0.151550	+	0.466423i	0.846245	+	0.532794i	$0.178858\pi$
$62$		0			0
$63$		0			0
$64$	7.60845	+	2.47214i	0.951057	+	0.309017i
$65$	2.03265	−	6.42133i	0.252120	−	0.796468i
$66$		0			0
$67$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$67$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$68$	7.65646	+	7.65646i	0.928483	+	0.928483i
$69$		0			0
$70$		0			0
$71$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$71$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$72$	8.38081	−	1.32739i	0.987688	−	0.156434i
$73$	7.51037	−	3.82672i	0.879022	−	0.447884i	0.0445966	−	0.999005i	$-0.485800\pi$
$73$	7.51037	−	3.82672i	0.879022	−	0.447884i	0.834425	+	0.551121i	$0.185800\pi$
$74$		−	13.8368i		−	1.60850i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$79$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$80$	−4.12099	−	7.93835i	−0.460741	−	0.887535i
$81$	7.28115	−	5.29007i	0.809017	−	0.587785i
$82$	−12.3500	+	12.3500i	−1.36383	+	1.36383i
$83$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$83$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$84$		0			0
$85$	−0.0918987	−	12.1056i	−0.00996782	−	1.31303i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.34280	−	1.41106i	−0.460336	−	0.149572i	0.0696627	−	0.997571i	$-0.477808\pi$
$89$	−4.34280	−	1.41106i	−0.460336	−	0.149572i	−0.529999	+	0.847998i	$0.677808\pi$
$90$	−7.71712	−	5.51780i	−0.813456	−	0.581627i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	1.03093	−	0.163283i	0.104675	−	0.0165788i	−0.103877	−	0.994590i	$-0.533125\pi$
$97$	1.03093	−	0.163283i	0.104675	−	0.0165788i	0.208552	+	0.978011i	$0.433125\pi$
$98$	8.82051	−	4.49428i	0.891007	−	0.453990i
$99$		0			0
$100$	−2.94542	+	9.55638i	−0.294542	+	0.955638i
$101$	−18.4031			−1.83118			−0.915588	−	0.402117i	$-0.868274\pi$
$101$	−18.4031			−1.83118			−0.915588	+	0.402117i	$0.868274\pi$
$102$		0			0
$103$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$103$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$104$	−5.00772	+	6.89253i	−0.491047	+	0.675868i
$105$		0			0
$106$	−16.5364	+	12.0144i	−1.60616	+	1.16694i
$107$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$107$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$108$		0			0
$109$	15.7969	−	5.13271i	1.51307	−	0.491625i	0.569269	−	0.822152i	$-0.307226\pi$
$109$	15.7969	−	5.13271i	1.51307	−	0.491625i	0.943797	+	0.330527i	$0.107226\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	9.35764	−	18.3654i	0.880293	−	1.72767i	0.221788	−	0.975095i	$-0.428811\pi$
$113$	9.35764	−	18.3654i	0.880293	−	1.72767i	0.658505	−	0.752577i	$-0.271189\pi$
$114$		0			0
$115$		0			0
$116$	−6.64178	−	20.4413i	−0.616674	−	1.89793i
$117$	−1.41361	+	8.92519i	−0.130688	+	0.825134i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−8.89919	−	6.46564i	−0.809017	−	0.587785i
$122$	−5.35024	+	0.847395i	−0.484388	+	0.0767196i
$123$		0			0
$124$		0			0
$125$	9.84359	−	5.30130i	0.880437	−	0.474163i
$126$		0			0
$127$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$127$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$128$	1.76985	+	11.1744i	0.156434	+	0.987688i
$129$		0			0
$130$	9.39639	−	1.56145i	0.824118	−	0.136948i
$131$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$131$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−4.73195	+	14.5635i	−0.405762	+	1.24881i
$137$	18.2457	+	9.29667i	1.55884	+	0.794268i	0.999401	−	0.0346048i	$-0.0110173\pi$
$137$	18.2457	+	9.29667i	1.55884	+	0.794268i	0.559437	+	0.828873i	$0.311017\pi$
$138$		0			0
$139$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$139$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	7.05342	+	9.70820i	0.587785	+	0.809017i
$145$	−10.7466	+	21.4933i	−0.892459	+	1.78492i
$146$	9.64390	+	7.00671i	0.798135	+	0.579879i
$147$		0			0
$148$	17.4354	−	8.88377i	1.43318	−	0.730242i
$149$		−	0.429467i		−	0.0351833i	−0.999845	−	0.0175917i	$-0.994400\pi$
$149$		−	0.429467i		−	0.0351833i	0.999845	−	0.0175917i	$-0.00559989\pi$
$150$		0			0
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		0			0
$153$	2.54078	+	16.0418i	0.205410	+	1.29691i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−10.0086	+	10.0086i	−0.798771	+	0.798771i	−0.982902	−	0.184131i	$-0.941053\pi$
$157$	−10.0086	+	10.0086i	−0.798771	+	0.798771i	0.184131	+	0.982902i	$0.441053\pi$
$158$		0			0
$159$		0			0
$160$	7.35706	−	10.2895i	0.581627	−	0.813456i
$161$		0			0
$162$	11.3407	+	5.77836i	0.891007	+	0.453990i
$163$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$163$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$164$	−23.4911	−	7.63271i	−1.83434	−	0.596015i
$165$		0			0
$166$		0			0
$167$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$167$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$168$		0			0
$169$	2.30822	+	3.17699i	0.177555	+	0.244384i
$170$	15.1949	−	7.88806i	1.16540	−	0.604987i
$171$		0			0
$172$		0			0
$173$	−22.2592	+	11.3417i	−1.69234	+	0.862290i	−0.703967	+	0.710233i	$0.748590\pi$
$173$	−22.2592	+	11.3417i	−1.69234	+	0.862290i	−0.988372	+	0.152057i	$0.951410\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−1.01021	−	6.37821i	−0.0757184	−	0.478067i
$179$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$179$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$180$	1.99814	−	13.2668i	0.148932	−	0.988847i
$181$	19.8884	−	14.4498i	1.47829	−	1.07404i	0.500193	−	0.865914i	$-0.333262\pi$
$181$	19.8884	−	14.4498i	1.47829	−	1.07404i	0.978101	−	0.208130i	$-0.0667377\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−20.8578	−	6.60250i	−1.53350	−	0.485425i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$191$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$192$		0			0
$193$	−18.3102	−	18.3102i	−1.31800	−	1.31800i	−0.915357	−	0.402644i	$-0.868091\pi$
$193$	−18.3102	−	18.3102i	−1.31800	−	1.31800i	−0.402644	−	0.915357i	$-0.631909\pi$
$194$	0.867644	+	1.19421i	0.0622932	+	0.0857392i
$195$		0			0
$196$	11.3262	+	8.22899i	0.809017	+	0.587785i
$197$	2.37518	−	0.376192i	0.169225	−	0.0268026i	−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	2.37518	−	0.376192i	0.169225	−	0.0268026i	0.240472	+	0.970656i	$0.422698\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−13.9328	+	2.42412i	−0.985200	+	0.171412i
$201$		0			0
$202$	−11.8155	−	23.1893i	−0.831337	−	1.63159i
$203$		0			0
$204$		0			0
$205$	12.7236	+	24.5096i	0.888652	+	1.71183i
$206$		0			0
$207$		0			0
$208$	−11.9002	−	1.88481i	−0.825134	−	0.130688i
$209$		0			0
$210$		0			0
$211$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$211$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$212$	−25.7561	−	13.1234i	−1.76894	−	0.901318i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	16.6098	+	16.6098i	1.12496	+	1.12496i
$219$		0			0
$220$		0			0
$221$	−13.1931	−	9.58535i	−0.887464	−	0.644780i
$222$		0			0
$223$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$223$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$224$		0			0
$225$	−12.0000	+	9.00000i	−0.800000	+	0.600000i
$226$	29.1497			1.93901
$227$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$227$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$228$		0			0
$229$	12.2669	−	16.8839i	0.810617	−	1.11572i	−0.180611	−	0.983555i	$-0.557808\pi$
$229$	12.2669	−	16.8839i	0.810617	−	1.11572i	0.991228	−	0.132164i	$-0.0421925\pi$
$230$		0			0
$231$		0			0
$232$	21.4933	−	21.4933i	1.41110	−	1.41110i
$233$	−19.6257	−	3.10840i	−1.28572	−	0.203638i	−0.524097	−	0.851658i	$-0.675597\pi$
$233$	−19.6257	−	3.10840i	−1.28572	−	0.203638i	−0.761623	+	0.648020i	$0.775597\pi$
$234$	−12.1540	+	3.94907i	−0.794531	+	0.258159i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$239$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$240$		0			0
$241$	8.05285	+	24.7841i	0.518729	+	1.59649i	0.776392	+	0.630250i	$0.217048\pi$
$241$	8.05285	+	24.7841i	0.518729	+	1.59649i	−0.257663	+	0.966235i	$0.582952\pi$
$242$	2.43355	−	15.3648i	0.156434	−	0.987688i
$243$		0			0
$244$	−4.50285	−	6.19764i	−0.288265	−	0.396763i
$245$	−2.56587	−	15.4407i	−0.163928	−	0.986472i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	13.0000	+	9.00000i	0.822192	+	0.569210i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−12.9443	+	9.40456i	−0.809017	+	0.587785i
$257$	22.5701	−	22.5701i	1.40788	−	1.40788i	0.637106	−	0.770776i	$-0.280131\pi$
$257$	22.5701	−	22.5701i	1.40788	−	1.40788i	0.770776	−	0.637106i	$-0.219869\pi$
$258$		0			0
$259$		0			0
$260$	8.00040	+	10.8376i	0.496164	+	0.672121i
$261$	9.96268	−	30.6620i	0.616674	−	1.89793i
$262$		0			0
$263$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$263$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$264$		0			0
$265$	10.2201	+	30.6602i	0.627814	+	1.88344i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	19.2736	+	26.5278i	1.17513	+	1.61743i	0.609711	+	0.792624i	$0.291286\pi$
$269$	19.2736	+	26.5278i	1.17513	+	1.61743i	0.565419	+	0.824804i	$0.308714\pi$
$270$		0			0
$271$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$271$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$272$	−21.3891	+	3.38771i	−1.29691	+	0.205410i
$273$		0			0
$274$			28.9598i			1.74953i
$275$		0			0
$276$		0			0
$277$	−1.51015	−	2.96383i	−0.0907359	−	0.178079i	0.841178	−	0.540758i	$-0.181862\pi$
$277$	−1.51015	−	2.96383i	−0.0907359	−	0.178079i	−0.931914	+	0.362678i	$0.881862\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	16.1890	−	11.7620i	0.965754	−	0.701661i	0.0112742	−	0.999936i	$-0.496411\pi$
$281$	16.1890	−	11.7620i	0.965754	−	0.701661i	0.954480	+	0.298275i	$0.0964112\pi$
$282$		0			0
$283$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$283$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−7.70447	+	15.1209i	−0.453990	+	0.891007i
$289$	−11.7082	−	3.80422i	−0.688717	−	0.223778i
$290$	−33.9829	+	0.257979i	−1.99554	+	0.0151490i
$291$		0			0
$292$	−2.63720	+	16.6506i	−0.154330	+	0.974403i
$293$	−8.39452	−	8.39452i	−0.490413	−	0.490413i	0.418023	−	0.908436i	$-0.362723\pi$
$293$	−8.39452	−	8.39452i	−0.490413	−	0.490413i	−0.908436	+	0.418023i	$0.862723\pi$
$294$		0			0
$295$		0			0
$296$	22.3884	+	16.2661i	1.30130	+	0.945450i
$297$		0			0
$298$	0.541160	−	0.275735i	0.0313486	−	0.0159729i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.27559	+	8.46941i	−0.0730403	+	0.484957i
$306$	−18.5826	+	13.5011i	−1.06230	+	0.771805i
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$311$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$312$		0			0
$313$	0.642040	−	1.26007i	0.0362902	−	0.0712236i	−0.872149	−	0.489240i	$-0.837274\pi$
$313$	0.642040	−	1.26007i	0.0362902	−	0.0712236i	0.908440	+	0.418016i	$0.137274\pi$
$314$	−19.0374	−	6.18564i	−1.07434	−	0.349076i
$315$		0			0
$316$		0			0
$317$	−0.663695	+	4.19041i	−0.0372768	+	0.235357i	−0.999291	−	0.0376418i	$-0.988015\pi$
$317$	−0.663695	+	4.19041i	−0.0372768	+	0.235357i	0.962014	+	0.272999i	$0.0880154\pi$
$318$		0			0
$319$		0			0
$320$	17.6890	+	2.66418i	0.988847	+	0.148932i
$321$		0			0
$322$		0			0
$323$		0			0
$324$			18.0000i			1.00000i
$325$	2.12991	−	14.9094i	0.118146	−	0.827023i
$326$		0			0
$327$		0			0
$328$	−5.46442	−	34.5010i	−0.301722	−	1.90500i
$329$		0			0
$330$		0			0
$331$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$331$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$332$		0			0
$333$	28.9909	+	4.59171i	1.58869	+	0.251624i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−8.82051	−	4.49428i	−0.480484	−	0.244819i	0.196934	−	0.980417i	$-0.436901\pi$
$337$	−8.82051	−	4.49428i	−0.480484	−	0.244819i	−0.677419	+	0.735598i	$0.736901\pi$
$338$	−2.52127	+	4.94827i	−0.137139	+	0.269151i
$339$		0			0
$340$	19.6953	+	14.0823i	1.06813	+	0.763718i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−28.5826	−	20.7665i	−1.53661	−	1.11641i
$347$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$347$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$348$		0			0
$349$			1.61405i			0.0863979i	0.999066	+	0.0431990i	$0.0137549\pi$
$349$			1.61405i			0.0863979i	−0.999066	+	0.0431990i	$0.986245\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.99109	−	12.5712i	−0.105975	−	0.669099i	−0.982291	−	0.187362i	$-0.940006\pi$
$353$	−1.99109	−	12.5712i	−0.105975	−	0.669099i	0.876316	−	0.481736i	$-0.159994\pi$
$354$		0			0
$355$		0			0
$356$	7.38842	−	5.36800i	0.391585	−	0.284503i
$357$		0			0
$358$		0			0
$359$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$359$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$360$	18.0000	−	6.00000i	0.948683	−	0.316228i
$361$	−5.87132	+	18.0701i	−0.309017	+	0.951057i
$362$	30.9769	+	15.7835i	1.62811	+	0.829564i
$363$		0			0
$364$		0			0
$365$	15.1638	−	11.1940i	0.793710	−	0.585921i
$366$		0			0
$367$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$367$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$368$		0			0
$369$	−21.7774	−	29.9741i	−1.13369	−	1.56039i
$370$	−5.07193	−	30.5215i	−0.263677	−	1.58674i
$371$		0			0
$372$		0			0
$373$	−13.8608	+	7.06243i	−0.717685	+	0.365679i	−0.774387	−	0.632712i	$-0.781942\pi$
$373$	−13.8608	+	7.06243i	−0.717685	+	0.365679i	0.0567016	+	0.998391i	$0.481942\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	14.6959	+	28.8423i	0.756876	+	1.48545i
$378$		0			0
$379$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$379$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$383$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$384$		0			0
$385$		0			0
$386$	11.3164	−	34.8282i	0.575987	−	1.77271i
$387$		0			0
$388$	−0.947730	+	1.86002i	−0.0481137	+	0.0944284i
$389$	14.9800	+	4.86729i	0.759515	+	0.246781i	0.663070	−	0.748557i	$-0.269253\pi$
$389$	14.9800	+	4.86729i	0.759515	+	0.246781i	0.0964443	+	0.995338i	$0.469253\pi$
$390$		0			0
$391$		0			0
$392$	−3.09724	+	19.5552i	−0.156434	+	0.987688i
$393$		0			0
$394$	1.99899	+	2.75137i	0.100708	+	0.138612i
$395$		0			0
$396$		0			0
$397$	−18.1584	+	2.87601i	−0.911345	+	0.144343i	−0.594464	−	0.804122i	$-0.702636\pi$
$397$	−18.1584	+	2.87601i	−0.911345	+	0.144343i	−0.316881	+	0.948465i	$0.602636\pi$
$398$		0			0
$399$		0			0
$400$	−12.0000	−	16.0000i	−0.600000	−	0.800000i
$401$	−25.1294			−1.25490			−0.627452	−	0.778655i	$-0.715902\pi$
$401$	−25.1294			−1.25490			−0.627452	+	0.778655i	$0.715902\pi$
$402$		0			0
$403$		0			0
$404$	21.6341	−	29.7768i	1.07634	−	1.48145i
$405$	14.1218	−	14.3379i	0.701719	−	0.712454i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−37.9437	+	12.3287i	−1.87619	+	0.609613i	−0.887259	+	0.461272i	$0.847393\pi$
$409$	−37.9437	+	12.3287i	−1.87619	+	0.609613i	−0.988936	+	0.148340i	$0.952607\pi$
$410$	−22.7149	+	31.7688i	−1.12181	+	1.56895i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−5.26543	−	16.2053i	−0.258159	−	0.794531i
$417$		0			0
$418$		0			0
$419$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$419$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$420$		0			0
$421$	−16.0826	−	11.6847i	−0.783819	−	0.569478i	0.122304	−	0.992493i	$-0.460972\pi$
$421$	−16.0826	−	11.6847i	−0.783819	−	0.569478i	−0.906123	+	0.423015i	$0.860972\pi$
$422$		0			0
$423$		0			0
$424$		−	40.8803i		−	1.98532i
$425$	−4.64006	−	26.6690i	−0.225076	−	1.29364i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$431$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$432$		0			0
$433$	36.8762	+	5.84061i	1.77216	+	0.280682i	0.955188	−	0.296001i	$-0.0956533\pi$
$433$	36.8762	+	5.84061i	1.77216	+	0.280682i	0.816968	+	0.576683i	$0.195653\pi$
$434$		0			0
$435$		0			0
$436$	−10.2654	+	31.5937i	−0.491625	+	1.51307i
$437$		0			0
$438$		0			0
$439$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$439$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$440$		0			0
$441$	6.48936	+	19.9722i	0.309017	+	0.951057i
$442$	3.60775	−	22.7785i	0.171603	−	1.08346i
$443$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$443$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$444$		0			0
$445$	−10.0967	−	1.52068i	−0.478628	−	0.0720871i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			33.7160i			1.59116i	0.605850	+	0.795579i	$0.292833\pi$
$449$			33.7160i			1.59116i	−0.605850	+	0.795579i	$0.707167\pi$
$450$	−19.0451	−	9.34253i	−0.897796	−	0.440411i
$451$		0			0
$452$	18.7153	+	36.7308i	0.880293	+	1.72767i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−17.0000	+	17.0000i	−0.795226	+	0.795226i	−0.982339	−	0.187112i	$-0.940087\pi$
$457$	−17.0000	+	17.0000i	−0.795226	+	0.795226i	0.187112	+	0.982339i	$0.440087\pi$
$458$	29.1507	+	4.61702i	1.36212	+	0.215739i
$459$		0			0
$460$		0			0
$461$	−9.50653	+	29.2581i	−0.442763	+	1.36269i	0.442155	+	0.896939i	$0.354214\pi$
$461$	−9.50653	+	29.2581i	−0.442763	+	1.36269i	−0.884918	+	0.465746i	$0.845786\pi$
$462$		0			0
$463$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$463$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$464$	40.8826	+	13.2836i	1.89793	+	0.616674i
$465$		0			0
$466$	−8.68364	−	26.7255i	−0.402262	−	1.23804i
$467$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$467$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$468$	−12.7795	−	12.7795i	−0.590731	−	0.590731i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−19.6851	−	38.6342i	−0.901318	−	1.76894i
$478$		0			0
$479$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$479$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$480$		0			0
$481$	−23.8426	+	17.3227i	−1.08713	+	0.789847i
$482$	−26.0596	+	26.0596i	−1.18698	+	1.18698i
$483$		0			0
$484$	20.9232	−	6.79837i	0.951057	−	0.309017i
$485$	2.21418	−	0.738062i	0.100541	−	0.0335137i
$486$		0			0
$487$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$487$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$488$	4.91847	−	9.65305i	0.222649	−	0.436973i
$489$		0			0
$490$	17.8091	−	13.1468i	0.804532	−	0.593910i
$491$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$491$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$492$		0			0
$493$	41.1406	+	41.1406i	1.85288	+	1.85288i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	−2.99415	+	22.1593i	−0.133902	+	0.990995i
$501$		0			0
$502$		0			0
$503$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$503$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$504$		0			0
$505$	−40.5939	+	6.74572i	−1.80641	+	0.300181i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	21.9764	−	7.14055i	0.974085	−	0.316499i	0.221621	−	0.975133i	$-0.428865\pi$
$509$	21.9764	−	7.14055i	0.974085	−	0.316499i	0.752464	+	0.658633i	$0.228865\pi$
$510$		0			0
$511$		0			0
$512$	−20.1612	−	10.2726i	−0.891007	−	0.453990i
$513$		0			0
$514$	42.9308	+	13.9491i	1.89360	+	0.615267i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−8.51964	+	17.0393i	−0.373611	+	0.747222i
$521$	33.4203	+	24.2813i	1.46417	+	1.06378i	0.982252	+	0.187566i	$0.0600600\pi$
$521$	33.4203	+	24.2813i	1.46417	+	1.06378i	0.481919	+	0.876216i	$0.339940\pi$
$522$	45.0328	−	7.13249i	1.97103	−	0.312181i
$523$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$523$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	13.5191	−	18.6074i	0.587785	−	0.809017i
$530$	−32.0725	+	32.5631i	−1.39314	+	1.41445i
$531$		0			0
$532$		0			0
$533$	36.7420	+	5.81936i	1.59147	+	0.252064i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−21.0526	+	41.3180i	−0.907641	+	1.78135i
$539$		0			0
$540$		0			0
$541$	−1.86721	−	5.74668i	−0.0802776	−	0.247069i	0.902861	−	0.429934i	$-0.141463\pi$
$541$	−1.86721	−	5.74668i	−0.0802776	−	0.247069i	−0.983138	+	0.182865i	$0.941463\pi$
$542$		0			0
$543$		0			0
$544$	−18.0014	−	24.7768i	−0.771805	−	1.06230i
$545$	32.9636	−	17.1122i	1.41201	−	0.733008i
$546$		0			0
$547$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$547$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$548$	−36.4915	+	18.5933i	−1.55884	+	0.794268i
$549$		−	11.4911i		−	0.490426i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	2.76507	−	3.80579i	0.117477	−	0.161693i
$555$		0			0
$556$		0			0
$557$	5.44228	−	5.44228i	0.230597	−	0.230597i	−0.582345	−	0.812942i	$-0.697865\pi$
$557$	5.44228	−	5.44228i	0.230597	−	0.230597i	0.812942	+	0.582345i	$0.197865\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	25.2149	+	12.8477i	1.06363	+	0.541946i
$563$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$563$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$564$		0			0
$565$	13.9094	−	43.9408i	0.585171	−	1.84860i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−27.0832	−	37.2768i	−1.13539	−	1.56273i	−0.777408	−	0.628997i	$-0.783466\pi$
$569$	−27.0832	−	37.2768i	−1.13539	−	1.56273i	−0.357979	−	0.933730i	$-0.616534\pi$
$570$		0			0
$571$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$571$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−24.0000			−1.00000
$577$	−14.7669	−	28.9817i	−0.614754	−	1.20652i	−0.963097	−	0.269156i	$-0.913255\pi$
$577$	−14.7669	−	28.9817i	−0.614754	−	1.20652i	0.348342	−	0.937367i	$-0.386745\pi$
$578$	−2.72352	−	17.1956i	−0.113284	−	0.715244i
$579$		0			0
$580$	−22.1434	−	42.6553i	−0.919455	−	1.77116i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−22.6742	+	7.36729i	−0.938264	+	0.304861i
$585$	0.153389	+	20.2055i	0.00634185	+	0.835395i
$586$	5.18810	−	15.9673i	0.214319	−	0.659605i
$587$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$587$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−6.12228	+	38.6546i	−0.251624	+	1.58869i
$593$	−23.8454	−	23.8454i	−0.979212	−	0.979212i	0.0205761	−	0.999788i	$-0.493450\pi$
$593$	−23.8454	−	23.8454i	−0.979212	−	0.979212i	−0.999788	+	0.0205761i	$0.993450\pi$
$594$		0			0
$595$		0			0
$596$	0.694892	+	0.504869i	0.0284639	+	0.0206802i
$597$		0			0
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	44.7107			1.82379			0.911893	−	0.410428i	$-0.134621\pi$
$601$	44.7107			1.82379			0.911893	+	0.410428i	$0.134621\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−22.0000	−	11.0000i	−0.894427	−	0.447214i
$606$		0			0
$607$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$607$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$608$		0			0
$609$		0			0
$610$	−11.4911	+	3.83035i	−0.465259	+	0.155086i
$611$		0			0
$612$	−28.9431	−	14.7473i	−1.16996	−	0.596122i
$613$	−21.1732	+	41.5547i	−0.855176	+	1.67838i	−0.128162	+	0.991753i	$0.540908\pi$
$613$	−21.1732	+	41.5547i	−0.855176	+	1.67838i	−0.727013	+	0.686624i	$0.759092\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.08823	−	32.1258i	0.204844	−	1.29334i	−0.644136	−	0.764911i	$-0.722783\pi$
$617$	5.08823	−	32.1258i	0.204844	−	1.29334i	0.848980	−	0.528425i	$-0.177217\pi$
$618$		0			0
$619$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$619$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	19.7700	−	15.3019i	0.790799	−	0.612076i
$626$	2.00000			0.0799361
$627$		0			0
$628$	−4.42843	−	27.9600i	−0.176713	−	1.11573i
$629$	−31.1353	+	42.8540i	−1.24144	+	1.70870i
$630$		0			0
$631$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$631$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$632$		0			0
$633$		0			0
$634$	−5.70634	+	1.85410i	−0.226628	+	0.0736358i
$635$		0			0
$636$		0			0
$637$	−18.7869	−	9.57240i	−0.744364	−	0.379272i
$638$		0			0
$639$		0			0
$640$	8.00000	+	24.0000i	0.316228	+	0.948683i
$641$	−2.47214	−	7.60845i	−0.0976435	−	0.300516i	0.890290	−	0.455394i	$-0.150502\pi$
$641$	−2.47214	−	7.60845i	−0.0976435	−	0.300516i	−0.987934	+	0.154878i	$0.950502\pi$
$642$		0			0
$643$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$643$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$647$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$648$	−22.6813	+	11.5567i	−0.891007	+	0.453990i
$649$		0			0
$650$	20.1544	−	6.88856i	0.790520	−	0.270192i
$651$		0			0
$652$		0			0
$653$	−7.97942	−	50.3800i	−0.312259	−	1.97152i	−0.217789	−	0.975996i	$-0.569885\pi$
$653$	−7.97942	−	50.3800i	−0.312259	−	1.97152i	−0.0944693	−	0.995528i	$-0.530115\pi$
$654$		0			0
$655$		0			0
$656$	39.9654	−	29.0366i	1.56039	−	1.13369i
$657$	−17.8808	+	17.8808i	−0.697596	+	0.697596i
$658$		0			0
$659$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$659$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$660$		0			0
$661$	3.70820	−	11.4127i	0.144232	−	0.443902i	−0.852679	−	0.522435i	$-0.825024\pi$
$661$	3.70820	−	11.4127i	0.144232	−	0.443902i	0.996911	+	0.0785333i	$0.0250237\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	12.8274	+	39.4787i	0.497053	+	1.52977i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	37.6608	−	19.1891i	1.45172	−	0.739687i	0.462566	−	0.886585i	$-0.346929\pi$
$673$	37.6608	−	19.1891i	1.45172	−	0.739687i	0.989152	+	0.146898i	$0.0469288\pi$
$674$		−	14.0000i		−	0.539260i
$675$		0			0
$676$	−7.85395			−0.302075
$677$	17.3351	+	34.0220i	0.666241	+	1.30757i	0.938477	+	0.345341i	$0.112237\pi$
$677$	17.3351	+	34.0220i	0.666241	+	1.30757i	−0.272237	+	0.962230i	$0.587763\pi$
$678$		0			0
$679$		0			0
$680$	−5.09955	+	33.8589i	−0.195559	+	1.29843i
$681$		0			0
$682$		0			0
$683$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$683$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$684$		0			0
$685$	43.6545	+	13.8187i	1.66795	+	0.527986i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	41.4049	+	13.4533i	1.57740	+	0.512529i
$690$		0			0
$691$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$691$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$692$	7.81613	−	49.3491i	0.297125	−	1.87597i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	66.0389	−	10.4595i	2.50140	−	0.396183i
$698$	−2.03382	+	1.03628i	−0.0769811	+	0.0392238i
$699$		0			0
$700$		0			0
$701$	−36.1910			−1.36692			−0.683458	−	0.729990i	$-0.739525\pi$
$701$	−36.1910			−1.36692			−0.683458	+	0.729990i	$0.739525\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	14.5623	−	10.5801i	0.548060	−	0.398189i
$707$		0			0
$708$		0			0
$709$	−50.6250	+	16.4491i	−1.90126	+	0.617758i	−0.941393	+	0.337311i	$0.890483\pi$
$709$	−50.6250	+	16.4491i	−1.90126	+	0.617758i	−0.959870	+	0.280447i	$0.909517\pi$
$710$		0			0
$711$		0			0
$712$	11.5077	+	5.86348i	0.431270	+	0.219743i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$719$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$720$	19.1172	+	18.8291i	0.712454	+	0.701719i
$721$		0			0
$722$	−26.5392	+	4.20340i	−0.987688	+	0.156434i
$723$		0			0
$724$			49.1669i			1.82727i
$725$	−15.8267	+	51.3495i	−0.587789	+	1.90707i
$726$		0			0
$727$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$727$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$728$		0			0
$729$	−15.8702	+	21.8435i	−0.587785	+	0.809017i
$730$	23.8410	+	11.9205i	0.882397	+	0.441198i
$731$		0			0
$732$		0			0
$733$	−40.5073	−	6.41572i	−1.49617	−	0.236970i	−0.645943	−	0.763386i	$-0.723536\pi$
$733$	−40.5073	−	6.41572i	−1.49617	−	0.236970i	−0.850227	+	0.526416i	$0.823536\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	23.7875	−	46.6857i	0.875632	−	1.71852i
$739$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$739$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$740$	35.2029	−	25.9870i	1.29409	−	0.955301i
$741$		0			0
$742$		0			0
$743$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$743$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$744$		0			0
$745$	−0.157423	−	0.947327i	−0.00576752	−	0.0347074i
$746$	−17.7984	−	12.9313i	−0.651645	−	0.473448i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		1.00000			$0$
$751$		0			0		−1.00000			$\pi$
$752$		0			0
$753$		0			0
$754$	−26.9080	+	37.0358i	−0.979933	+	1.34876i
$755$		0			0
$756$		0			0
$757$	−6.81919	+	6.81919i	−0.247848	+	0.247848i	−0.820087	−	0.572239i	$-0.806075\pi$
$757$	−6.81919	+	6.81919i	−0.247848	+	0.247848i	0.572239	+	0.820087i	$0.306075\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.23457	−	6.87731i	0.0810033	−	0.249302i	−0.902351	−	0.431003i	$-0.858160\pi$
$761$	2.23457	−	6.87731i	0.0810033	−	0.249302i	0.983354	+	0.181700i	$0.0581600\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	11.4847	+	34.4541i	0.415230	+	1.24569i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	14.1068	+	19.4164i	0.508706	+	0.700174i	0.983700	−	0.179815i	$-0.0575500\pi$
$769$	14.1068	+	19.4164i	0.508706	+	0.700174i	−0.474995	+	0.879989i	$0.657550\pi$
$770$		0			0
$771$		0			0
$772$	51.1516	−	8.10162i	1.84099	−	0.291584i
$773$	−43.4607	+	22.1443i	−1.56317	+	0.796476i	−0.999563	−	0.0295658i	$-0.990588\pi$
$773$	−43.4607	+	22.1443i	−1.56317	+	0.796476i	−0.563609	+	0.826042i	$0.690588\pi$
$774$		0			0
$775$		0			0
$776$	−2.95225			−0.105979
$777$		0			0
$778$	3.48459	+	22.0009i	0.124929	+	0.788769i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−26.6296	+	8.65248i	−0.951057	+	0.309017i
$785$	−18.4084	+	25.7458i	−0.657025	+	0.918906i
$786$		0			0
$787$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$787$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$788$	−2.18350	+	4.28536i	−0.0777840	+	0.152660i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	8.15830	+	8.15830i	0.289710	+	0.289710i
$794$	−15.2824	−	21.0344i	−0.542353	−	0.746484i
$795$		0			0
$796$		0			0
$797$	−54.1267	+	8.57282i	−1.91726	+	0.303665i	−0.996297	−	0.0859751i	$-0.972599\pi$
$797$	−54.1267	+	8.57282i	−1.91726	+	0.303665i	−0.920967	+	0.389640i	$0.872599\pi$
$798$		0			0
$799$		0			0
$800$	12.4567	−	25.3935i	0.440411	−	0.897796i
$801$	13.6989			0.484026
$802$	−16.1341	−	31.6649i	−0.569715	−	1.11813i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	51.4110	+	8.14270i	1.80863	+	0.286459i
$809$	−7.41290	+	2.40860i	−0.260624	+	0.0846818i	−0.436414	−	0.899746i	$-0.643752\pi$
$809$	−7.41290	+	2.40860i	−0.260624	+	0.0846818i	0.175791	+	0.984428i	$0.443752\pi$
$810$	27.1335	+	8.58905i	0.953375	+	0.301788i
$811$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$811$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−39.8964	−	39.8964i	−1.39494	−	1.39494i
$819$		0			0
$820$	−54.6149	−	8.22565i	−1.90723	−	0.287252i
$821$	22.6525	+	16.4580i	0.790577	+	0.574388i	0.908135	−	0.418678i	$-0.137507\pi$
$821$	22.6525	+	16.4580i	0.790577	+	0.574388i	−0.117558	+	0.993066i	$0.537507\pi$
$822$		0			0
$823$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$823$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$827$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$828$		0			0
$829$	18.7687	−	25.8329i	0.651864	−	0.897213i	−0.347314	−	0.937749i	$-0.612906\pi$
$829$	18.7687	−	25.8329i	0.651864	−	0.897213i	0.999178	+	0.0405353i	$0.0129063\pi$
$830$		0			0
$831$		0			0
$832$	17.0393	−	17.0393i	0.590731	−	0.590731i
$833$	−37.4310	−	5.92848i	−1.29691	−	0.205410i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$839$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$840$		0			0
$841$	−26.7269	−	82.2570i	−0.921618	−	2.83645i
$842$	4.39791	−	27.7673i	0.151562	−	0.956926i
$843$		0			0
$844$		0			0
$845$	6.25605	+	6.16178i	0.215214	+	0.211972i
$846$		0			0
$847$		0			0
$848$	51.5122	−	26.2468i	1.76894	−	0.901318i
$849$		0			0
$850$	30.6259	−	22.9694i	1.05046	−	0.787844i
$851$		0			0
$852$		0			0
$853$	−6.68801	−	42.2264i	−0.228993	−	1.44580i	−0.787505	−	0.616308i	$-0.788628\pi$
$853$	−6.68801	−	42.2264i	−0.228993	−	1.44580i	0.558512	−	0.829496i	$-0.311372\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	33.0000	−	33.0000i	1.12726	−	1.12726i	0.136637	−	0.990621i	$-0.456370\pi$
$857$	33.0000	−	33.0000i	1.12726	−	1.12726i	0.990621	−	0.136637i	$-0.0436295\pi$
$858$		0			0
$859$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$859$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$863$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$864$		0			0
$865$	−44.9425	+	33.1768i	−1.52809	+	1.12805i
$866$	16.3164	+	50.2166i	0.554452	+	1.70643i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−46.4012	+	7.34923i	−1.57134	+	0.248876i
$873$	−2.79004	+	1.42159i	−0.0944284	+	0.0481137i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	25.1550	+	49.3695i	0.849425	+	1.66709i	0.739506	+	0.673150i	$0.235059\pi$
$877$	25.1550	+	49.3695i	0.849425	+	1.66709i	0.109919	+	0.993941i	$0.464941\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−25.8885	+	18.8091i	−0.872207	+	0.633696i	−0.931178	−	0.364564i	$-0.881218\pi$
$881$	−25.8885	+	18.8091i	−0.872207	+	0.633696i	0.0589711	+	0.998260i	$0.481218\pi$
$882$	−21.0000	+	21.0000i	−0.707107	+	0.707107i
$883$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$883$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$884$	31.0188	−	10.0786i	1.04328	−	0.338981i
$885$		0			0
$886$		0			0
$887$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$887$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$888$		0			0
$889$		0			0
$890$	−4.56629	−	13.6989i	−0.153062	−	0.459187i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−42.4847	+	21.6470i	−1.41773	+	0.722370i
$899$		0			0
$900$	−0.455460	−	29.9965i	−0.0151820	−	0.999885i
$901$	78.2497			2.60687
$902$		0			0
$903$		0			0
$904$	−34.2676	+	47.1653i	−1.13972	+	1.56869i
$905$	38.5736	−	39.1638i	1.28223	−	1.30185i
$906$		0			0
$907$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$907$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$908$		0			0
$909$	52.5072	−	17.0606i	1.74155	−	0.565865i
$910$		0			0
$911$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$911$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$912$		0			0
$913$		0			0
$914$	−32.3359	−	10.5066i	−1.06958	−	0.347527i
$915$		0			0
$916$	12.8981	+	39.6964i	0.426166	+	1.31161i
$917$		0			0
$918$		0			0
$919$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$919$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$920$		0			0
$921$		0			0
$922$	−42.9709	+	6.80592i	−1.41517	+	0.224141i
$923$		0			0
$924$		0			0
$925$	−48.4288	−	6.91840i	−1.59233	−	0.227476i
$926$		0			0
$927$		0			0
$928$	9.50999	+	60.0437i	0.312181	+	1.97103i
$929$	30.7159	−	42.2768i	1.00776	−	1.38706i	0.0873137	−	0.996181i	$-0.472172\pi$
$929$	30.7159	−	42.2768i	1.00776	−	1.38706i	0.920443	−	0.390877i	$-0.127828\pi$
$930$		0			0
$931$		0			0
$932$	28.1009	−	28.1009i	0.920474	−	0.920474i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	7.89814	−	24.3080i	0.258159	−	0.794531i
$937$	10.7515	+	5.47817i	0.351237	+	0.178964i	0.620703	−	0.784046i	$-0.286847\pi$
$937$	10.7515	+	5.47817i	0.351237	+	0.178964i	−0.269466	+	0.963010i	$0.586847\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−11.4164	−	35.1359i	−0.372163	−	1.14540i	−0.945373	−	0.325991i	$-0.894302\pi$
$941$	−11.4164	−	35.1359i	−0.372163	−	1.14540i	0.573210	−	0.819408i	$-0.305698\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$947$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$948$		0			0
$949$		−	25.3896i		−	0.824182i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	5.95900	+	37.6236i	0.193031	+	1.21875i	0.873813	+	0.486263i	$0.161640\pi$
$953$	5.95900	+	37.6236i	0.193031	+	1.21875i	−0.680782	+	0.732486i	$0.738360\pi$
$954$	36.0433	−	49.6093i	1.16694	−	1.60616i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	9.57953	−	29.4828i	0.309017	−	0.951057i
$962$	−37.1358	−	18.9216i	−1.19731	−	0.610058i
$963$		0			0
$964$	−49.5682	−	16.1057i	−1.59649	−	0.518729i
$965$	−47.1008	−	33.6774i	−1.51623	−	1.08411i
$966$		0			0
$967$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$967$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$968$	22.0000	+	22.0000i	0.707107	+	0.707107i
$969$		0			0
$970$	2.35161	+	2.31617i	0.0755055	+	0.0743678i
$971$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$971$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	15.3214			0.490426
$977$	−0.816016	−	1.60152i	−0.0261067	−	0.0512372i	0.877585	−	0.479421i	$-0.159153\pi$
$977$	−0.816016	−	1.60152i	−0.0261067	−	0.0512372i	−0.903691	+	0.428184i	$0.859153\pi$
$978$		0			0
$979$		0			0
$980$	28.0000	+	14.0000i	0.894427	+	0.447214i
$981$	−40.3128	+	29.2890i	−1.28709	+	0.935126i
$982$		0			0
$983$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$983$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$984$		0			0
$985$	5.10133	−	1.70044i	0.162542	−	0.0541806i
$986$	−25.4263	+	78.2541i	−0.809738	+	2.49212i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$991$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	51.6817	−	8.18557i	1.63678	−	0.259240i	0.730807	−	0.682585i	$-0.239144\pi$
$997$	51.6817	−	8.18557i	1.63678	−	0.259240i	0.905969	+	0.423345i	$0.139144\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.2.l.a.3.1	✓	8
3.2	odd	2		900.2.bj.a.703.1		8
4.3	odd	2	CM	100.2.l.a.3.1	✓	8
5.2	odd	4		500.2.l.c.7.1		8
5.3	odd	4		500.2.l.a.7.1		8
5.4	even	2		500.2.l.b.243.1		8
12.11	even	2		900.2.bj.a.703.1		8
20.3	even	4		500.2.l.a.7.1		8
20.7	even	4		500.2.l.c.7.1		8
20.19	odd	2		500.2.l.b.243.1		8
25.6	even	5		500.2.l.c.143.1		8
25.8	odd	20		500.2.l.b.107.1		8
25.17	odd	20	inner	100.2.l.a.67.1	yes	8
25.19	even	10		500.2.l.a.143.1		8
75.17	even	20		900.2.bj.a.667.1		8
100.19	odd	10		500.2.l.a.143.1		8
100.31	odd	10		500.2.l.c.143.1		8
100.67	even	20	inner	100.2.l.a.67.1	yes	8
100.83	even	20		500.2.l.b.107.1		8
300.167	odd	20		900.2.bj.a.667.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.l.a.3.1	✓	8	1.1	even	1	trivial
100.2.l.a.3.1	✓	8	4.3	odd	2	CM
100.2.l.a.67.1	yes	8	25.17	odd	20	inner
100.2.l.a.67.1	yes	8	100.67	even	20	inner
500.2.l.a.7.1		8	5.3	odd	4
500.2.l.a.7.1		8	20.3	even	4
500.2.l.a.143.1		8	25.19	even	10
500.2.l.a.143.1		8	100.19	odd	10
500.2.l.b.107.1		8	25.8	odd	20
500.2.l.b.107.1		8	100.83	even	20
500.2.l.b.243.1		8	5.4	even	2
500.2.l.b.243.1		8	20.19	odd	2
500.2.l.c.7.1		8	5.2	odd	4
500.2.l.c.7.1		8	20.7	even	4
500.2.l.c.143.1		8	25.6	even	5
500.2.l.c.143.1		8	100.31	odd	10
900.2.bj.a.667.1		8	75.17	even	20
900.2.bj.a.667.1		8	300.167	odd	20
900.2.bj.a.703.1		8	3.2	odd	2
900.2.bj.a.703.1		8	12.11	even	2

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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	100.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.642040 + 1.26007i) q^{2} +(-1.17557 + 1.61803i) q^{4} +(2.20582 - 0.366554i) q^{5} +(-2.79360 - 0.442463i) q^{8} +(-2.85317 + 0.927051i) q^{9} +(1.87811 + 2.54415i) q^{10} +(1.36749 - 2.68384i) q^{13} +(-1.23607 - 3.80423i) q^{16} +(0.846926 - 5.34728i) q^{17} +(-3.00000 - 3.00000i) q^{18} +(-2.00000 + 4.00000i) q^{20} +(4.73128 - 1.61710i) q^{25} +4.25982 q^{26} +(-6.31671 + 8.69421i) q^{29} +(4.00000 - 4.00000i) q^{32} +(7.28173 - 2.36598i) q^{34} +(1.85410 - 5.70634i) q^{36} +(-8.71769 - 4.44189i) q^{37} +(-6.32437 + 0.0480111i) q^{40} +(3.81636 + 11.7455i) q^{41} +(-5.95376 + 3.09075i) q^{45} -7.00000i q^{49} +(5.07533 + 4.92351i) q^{50} +(2.73497 + 5.36768i) q^{52} +(2.26101 + 14.2754i) q^{53} +(-15.0109 - 2.37750i) q^{58} +(-1.18364 + 3.64288i) q^{61} +(7.60845 + 2.47214i) q^{64} +(2.03265 - 6.42133i) q^{65} +(7.65646 + 7.65646i) q^{68} +(8.38081 - 1.32739i) q^{72} +(7.51037 - 3.82672i) q^{73} -13.8368i q^{74} +(-4.12099 - 7.93835i) q^{80} +(7.28115 - 5.29007i) q^{81} +(-12.3500 + 12.3500i) q^{82} +(-0.0918987 - 12.1056i) q^{85} +(-4.34280 - 1.41106i) q^{89} +(-7.71712 - 5.51780i) q^{90} +(1.03093 - 0.163283i) q^{97} +(8.82051 - 4.49428i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 4 q^{5} - 4 q^{8} - 6 q^{10} + 2 q^{13} + 8 q^{16} - 6 q^{17} - 24 q^{18} - 16 q^{20} - 6 q^{25} - 4 q^{26} + 32 q^{32} + 50 q^{34} - 12 q^{36} - 46 q^{37} + 4 q^{40} + 16 q^{41} - 6 q^{45}+ \cdots - 14 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 4 * q^5 - 4 * q^8 - 6 * q^10 + 2 * q^13 + 8 * q^16 - 6 * q^17 - 24 * q^18 - 16 * q^20 - 6 * q^25 - 4 * q^26 + 32 * q^32 + 50 * q^34 - 12 * q^36 - 46 * q^37 + 4 * q^40 + 16 * q^41 - 6 * q^45 + 14 * q^50 + 4 * q^52 + 2 * q^53 - 8 * q^58 - 24 * q^61 + 78 * q^65 + 12 * q^68 + 12 * q^72 + 22 * q^73 - 16 * q^80 + 18 * q^81 - 16 * q^82 - 52 * q^85 - 50 * q^89 - 6 * q^90 - 26 * q^97 - 14 * q^98

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