LMFDB - Embedded newform 2610.2.b.f.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2610,2,Mod(289,2610)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2610, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2610.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2610 = 2 \cdot 3^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2610.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,8,0,8,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$20.8409549276$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.75200995984.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 10x^{6} + 30x^{4} + 27x^{2} + 4 $ x^8 + 10x^6 + 30x^4 + 27*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 290)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			289.1
Root			$1.83507i$ of defining polynomial
Character	$\chi$	$=$	2610.289
Dual form			2610.2.b.f.289.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.82635 - 1.29013i) q^{5} +2.99580i q^{7} +1.00000 q^{8} +(-1.82635 - 1.29013i) q^{10} -1.08988i q^{11} -1.37471i q^{13} +2.99580i q^{14} +1.00000 q^{16} -0.212256 q^{17} +6.70297i q^{19} +(-1.82635 - 1.29013i) q^{20} -1.08988i q^{22} +1.06384i q^{23} +(1.67114 + 4.71246i) q^{25} -1.37471i q^{26} +2.99580i q^{28} +(-2.49749 - 4.77101i) q^{29} +4.22738i q^{31} +1.00000 q^{32} -0.212256 q^{34} +(3.86496 - 5.47139i) q^{35} -5.72993 q^{37} +6.70297i q^{38} +(-1.82635 - 1.29013i) q^{40} +10.3731i q^{41} +10.8599 q^{43} -1.08988i q^{44} +1.06384i q^{46} -6.38765 q^{47} -1.97480 q^{49} +(1.67114 + 4.71246i) q^{50} -1.37471i q^{52} +10.0993i q^{53} +(-1.40608 + 1.99050i) q^{55} +2.99580i q^{56} +(-2.49749 - 4.77101i) q^{58} +5.28523 q^{59} -3.38530i q^{61} +4.22738i q^{62} +1.00000 q^{64} +(-1.77356 + 2.51071i) q^{65} +10.2314i q^{67} -0.212256 q^{68} +(3.86496 - 5.47139i) q^{70} +5.04538 q^{71} +3.51767 q^{73} -5.72993 q^{74} +6.70297i q^{76} +3.26505 q^{77} -8.85669i q^{79} +(-1.82635 - 1.29013i) q^{80} +10.3731i q^{82} +12.4112i q^{83} +(0.387654 + 0.273837i) q^{85} +10.8599 q^{86} -1.08988i q^{88} +2.95876i q^{89} +4.11836 q^{91} +1.06384i q^{92} -6.38765 q^{94} +(8.64769 - 12.2420i) q^{95} -16.0605 q^{97} -1.97480 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{4} + q^{5} + 8 q^{8} + q^{10} + 8 q^{16} - 2 q^{17} + q^{20} + 5 q^{25} + 4 q^{29} + 8 q^{32} - 2 q^{34} + 16 q^{37} + q^{40} + 8 q^{43} - 6 q^{47} - 6 q^{49} + 5 q^{50} + 11 q^{55}+ \cdots - 6 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^4 + q^5 + 8 * q^8 + q^10 + 8 * q^16 - 2 * q^17 + q^20 + 5 * q^25 + 4 * q^29 + 8 * q^32 - 2 * q^34 + 16 * q^37 + q^40 + 8 * q^43 - 6 * q^47 - 6 * q^49 + 5 * q^50 + 11 * q^55 + 4 * q^58 + 18 * q^59 + 8 * q^64 + 15 * q^65 - 2 * q^68 + 12 * q^71 - 34 * q^73 + 16 * q^74 + 40 * q^77 + q^80 - 42 * q^85 + 8 * q^86 - 20 * q^91 - 6 * q^94 - 10 * q^95 - 14 * q^97 - 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2610\mathbb{Z}\right)^\times$.

$n$	$901$	$1451$	$1567$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.82635	−	1.29013i	−0.816770	−	0.576963i
$5$	−1.82635	−	1.29013i	−0.816770	−	0.576963i
$6$		0			0
$7$			2.99580i			1.13230i	0.824301	+	0.566152i	$0.191569\pi$
$7$			2.99580i			1.13230i	−0.824301	+	0.566152i	$0.808431\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.82635	−	1.29013i	−0.577544	−	0.407974i
$11$		−	1.08988i		−	0.328611i	−0.986410	−	0.164305i	$-0.947462\pi$
$11$		−	1.08988i		−	0.328611i	0.986410	−	0.164305i	$-0.0525382\pi$
$12$		0			0
$13$		−	1.37471i		−	0.381277i	−0.981660	−	0.190638i	$-0.938944\pi$
$13$		−	1.37471i		−	0.381277i	0.981660	−	0.190638i	$-0.0610558\pi$
$14$			2.99580i			0.800660i
$15$		0			0
$16$	1.00000			0.250000
$17$	−0.212256			−0.0514796			−0.0257398	−	0.999669i	$-0.508194\pi$
$17$	−0.212256			−0.0514796			−0.0257398	+	0.999669i	$0.508194\pi$
$18$		0			0
$19$			6.70297i			1.53777i	0.639390	+	0.768883i	$0.279187\pi$
$19$			6.70297i			1.53777i	−0.639390	+	0.768883i	$0.720813\pi$
$20$	−1.82635	−	1.29013i	−0.408385	−	0.288482i
$21$		0			0
$22$		−	1.08988i		−	0.232363i
$23$			1.06384i			0.221826i	0.993830	+	0.110913i	$0.0353776\pi$
$23$			1.06384i			0.221826i	−0.993830	+	0.110913i	$0.964622\pi$
$24$		0			0
$25$	1.67114	+	4.71246i	0.334227	+	0.942493i
$26$		−	1.37471i		−	0.269603i
$27$		0			0
$28$			2.99580i			0.566152i
$29$	−2.49749	−	4.77101i	−0.463772	−	0.885954i
$29$	−2.49749	−	4.77101i	−0.463772	−	0.885954i
$30$		0			0
$31$			4.22738i			0.759259i	0.925139	+	0.379630i	$0.123949\pi$
$31$			4.22738i			0.759259i	−0.925139	+	0.379630i	$0.876051\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−0.212256			−0.0364016
$35$	3.86496	−	5.47139i	0.653298	−	0.924833i
$36$		0			0
$37$	−5.72993			−0.941994			−0.470997	−	0.882135i	$-0.656106\pi$
$37$	−5.72993			−0.941994			−0.470997	+	0.882135i	$0.656106\pi$
$38$			6.70297i			1.08736i
$39$		0			0
$40$	−1.82635	−	1.29013i	−0.288772	−	0.203987i
$41$			10.3731i			1.62001i	0.586426	+	0.810003i	$0.300535\pi$
$41$			10.3731i			1.62001i	−0.586426	+	0.810003i	$0.699465\pi$
$42$		0			0
$43$	10.8599			1.65613			0.828063	−	0.560635i	$-0.189443\pi$
$43$	10.8599			1.65613			0.828063	+	0.560635i	$0.189443\pi$
$44$		−	1.08988i		−	0.164305i
$45$		0			0
$46$			1.06384i			0.156855i
$47$	−6.38765			−0.931735			−0.465868	−	0.884854i	$-0.654258\pi$
$47$	−6.38765			−0.931735			−0.465868	+	0.884854i	$0.654258\pi$
$48$		0			0
$49$	−1.97480			−0.282114
$50$	1.67114	+	4.71246i	0.236334	+	0.666443i
$51$		0			0
$52$		−	1.37471i		−	0.190638i
$53$			10.0993i			1.38724i	0.720341	+	0.693620i	$0.243985\pi$
$53$			10.0993i			1.38724i	−0.720341	+	0.693620i	$0.756015\pi$
$54$		0			0
$55$	−1.40608	+	1.99050i	−0.189596	+	0.268399i
$56$			2.99580i			0.400330i
$57$		0			0
$58$	−2.49749	−	4.77101i	−0.327937	−	0.626464i
$59$	5.28523			0.688079			0.344039	−	0.938955i	$-0.388205\pi$
$59$	5.28523			0.688079			0.344039	+	0.938955i	$0.388205\pi$
$60$		0			0
$61$		−	3.38530i		−	0.433443i	−0.976233	−	0.216722i	$-0.930464\pi$
$61$		−	3.38530i		−	0.433443i	0.976233	−	0.216722i	$-0.0695364\pi$
$62$			4.22738i			0.536877i
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.77356	+	2.51071i	−0.219983	+	0.311415i
$66$		0			0
$67$			10.2314i			1.24996i	0.780639	+	0.624982i	$0.214894\pi$
$67$			10.2314i			1.24996i	−0.780639	+	0.624982i	$0.785106\pi$
$68$	−0.212256			−0.0257398
$69$		0			0
$70$	3.86496	−	5.47139i	0.461951	−	0.653956i
$71$	5.04538			0.598777			0.299388	−	0.954131i	$-0.403217\pi$
$71$	5.04538			0.598777			0.299388	+	0.954131i	$0.403217\pi$
$72$		0			0
$73$	3.51767			0.411712			0.205856	−	0.978582i	$-0.434002\pi$
$73$	3.51767			0.411712			0.205856	+	0.978582i	$0.434002\pi$
$74$	−5.72993			−0.666090
$75$		0			0
$76$			6.70297i			0.768883i
$77$	3.26505			0.372087
$78$		0			0
$79$		−	8.85669i		−	0.996455i	−0.867046	−	0.498227i	$-0.833984\pi$
$79$		−	8.85669i		−	0.996455i	0.867046	−	0.498227i	$-0.166016\pi$
$80$	−1.82635	−	1.29013i	−0.204193	−	0.144241i
$81$		0			0
$82$			10.3731i			1.14552i
$83$			12.4112i			1.36230i	0.732143	+	0.681151i	$0.238520\pi$
$83$			12.4112i			1.36230i	−0.732143	+	0.681151i	$0.761480\pi$
$84$		0			0
$85$	0.387654	+	0.273837i	0.0420470	+	0.0297018i
$86$	10.8599			1.17106
$87$		0			0
$88$		−	1.08988i		−	0.116181i
$89$			2.95876i			0.313628i	0.987628	+	0.156814i	$0.0501224\pi$
$89$			2.95876i			0.313628i	−0.987628	+	0.156814i	$0.949878\pi$
$90$		0			0
$91$	4.11836			0.431721
$92$			1.06384i			0.110913i
$93$		0			0
$94$	−6.38765			−0.658836
$95$	8.64769	−	12.2420i	0.887234	−	1.25600i
$96$		0			0
$97$	−16.0605			−1.63070			−0.815351	−	0.578968i	$-0.803456\pi$
$97$	−16.0605			−1.63070			−0.815351	+	0.578968i	$0.803456\pi$
$98$	−1.97480			−0.199485
$99$		0			0
$100$	1.67114	+	4.71246i	0.167114	+	0.471246i
$101$			13.7584i			1.36901i	0.729007	+	0.684506i	$0.239982\pi$
$101$			13.7584i			1.36901i	−0.729007	+	0.684506i	$0.760018\pi$
$102$		0			0
$103$			9.16613i			0.903165i	0.892229	+	0.451583i	$0.149140\pi$
$103$			9.16613i			0.903165i	−0.892229	+	0.451583i	$0.850860\pi$
$104$		−	1.37471i		−	0.134802i
$105$		0			0
$106$			10.0993i			0.980927i
$107$			2.34345i			0.226550i	0.993564	+	0.113275i	$0.0361341\pi$
$107$			2.34345i			0.226550i	−0.993564	+	0.113275i	$0.963866\pi$
$108$		0			0
$109$	−1.12260			−0.107526			−0.0537628	−	0.998554i	$-0.517121\pi$
$109$	−1.12260			−0.107526			−0.0537628	+	0.998554i	$0.517121\pi$
$110$	−1.40608	+	1.99050i	−0.134065	+	0.189787i
$111$		0			0
$112$			2.99580i			0.283076i
$113$	−14.7451			−1.38710			−0.693551	−	0.720408i	$-0.743955\pi$
$113$	−14.7451			−1.38710			−0.693551	+	0.720408i	$0.743955\pi$
$114$		0			0
$115$	1.37249	−	1.94295i	0.127986	−	0.181181i
$116$	−2.49749	−	4.77101i	−0.231886	−	0.442977i
$117$		0			0
$118$	5.28523			0.486545
$119$		−	0.635875i		−	0.0582906i
$120$		0			0
$121$	9.81217			0.892015
$122$		−	3.38530i		−	0.306491i
$123$		0			0
$124$			4.22738i			0.379630i
$125$	3.02760	−	10.7626i	0.270796	−	0.962637i
$126$		0			0
$127$	−2.57047			−0.228092			−0.114046	−	0.993475i	$-0.536381\pi$
$127$	−2.57047			−0.228092			−0.114046	+	0.993475i	$0.536381\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−1.77356	+	2.51071i	−0.155551	+	0.220204i
$131$			1.20697i			0.105454i	0.998609	+	0.0527269i	$0.0167913\pi$
$131$			1.20697i			0.105454i	−0.998609	+	0.0527269i	$0.983209\pi$
$132$		0			0
$133$	−20.0807			−1.74122
$134$			10.2314i			0.883858i
$135$		0			0
$136$	−0.212256			−0.0182008
$137$	−5.81534			−0.496838			−0.248419	−	0.968653i	$-0.579911\pi$
$137$	−5.81534			−0.496838			−0.248419	+	0.968653i	$0.579911\pi$
$138$		0			0
$139$	15.0428			1.27591			0.637955	−	0.770074i	$-0.279781\pi$
$139$	15.0428			1.27591			0.637955	+	0.770074i	$0.279781\pi$
$140$	3.86496	−	5.47139i	0.326649	−	0.462416i
$141$		0			0
$142$	5.04538			0.423399
$143$	−1.49827			−0.125292
$144$		0			0
$145$	−1.59392	+	11.9356i	−0.132368	+	0.991201i
$146$	3.51767			0.291125
$147$		0			0
$148$	−5.72993			−0.470997
$149$	−0.968162			−0.0793150			−0.0396575	−	0.999213i	$-0.512627\pi$
$149$	−0.968162			−0.0793150			−0.0396575	+	0.999213i	$0.512627\pi$
$150$		0			0
$151$	−10.3004			−0.838234			−0.419117	−	0.907932i	$-0.637660\pi$
$151$	−10.3004			−0.838234			−0.419117	+	0.907932i	$0.637660\pi$
$152$			6.70297i			0.543682i
$153$		0			0
$154$	3.26505			0.263105
$155$	5.45386	−	7.72069i	0.438065	−	0.620140i
$156$		0			0
$157$	11.5654			0.923023			0.461512	−	0.887134i	$-0.347307\pi$
$157$	11.5654			0.923023			0.461512	+	0.887134i	$0.347307\pi$
$158$		−	8.85669i		−	0.704600i
$159$		0			0
$160$	−1.82635	−	1.29013i	−0.144386	−	0.101994i
$161$	−3.18706			−0.251175
$162$		0			0
$163$	−3.50675			−0.274670			−0.137335	−	0.990525i	$-0.543854\pi$
$163$	−3.50675			−0.274670			−0.137335	+	0.990525i	$0.543854\pi$
$164$			10.3731i			0.810003i
$165$		0			0
$166$			12.4112i			0.963292i
$167$		−	6.80763i		−	0.526791i	−0.964688	−	0.263395i	$-0.915158\pi$
$167$		−	6.80763i		−	0.526791i	0.964688	−	0.263395i	$-0.0848423\pi$
$168$		0			0
$169$	11.1102			0.854628
$170$	0.387654	+	0.273837i	0.0297317	+	0.0210024i
$171$		0			0
$172$	10.8599			0.828063
$173$		−	12.6960i		−	0.965258i	−0.875825	−	0.482629i	$-0.839682\pi$
$173$		−	12.6960i		−	0.965258i	0.875825	−	0.482629i	$-0.160318\pi$
$174$		0			0
$175$	−14.1176	+	5.00638i	−1.06719	+	0.378447i
$176$		−	1.08988i		−	0.0821527i
$177$		0			0
$178$			2.95876i			0.221769i
$179$	3.44971			0.257844			0.128922	−	0.991655i	$-0.458848\pi$
$179$	3.44971			0.257844			0.128922	+	0.991655i	$0.458848\pi$
$180$		0			0
$181$	19.3826			1.44070			0.720350	−	0.693611i	$-0.243981\pi$
$181$	19.3826			1.44070			0.720350	+	0.693611i	$0.243981\pi$
$182$	4.11836			0.305273
$183$		0			0
$184$			1.06384i			0.0784275i
$185$	10.4649	+	7.39234i	0.769393	+	0.543496i
$186$		0			0
$187$			0.231333i			0.0169167i
$188$	−6.38765			−0.465868
$189$		0			0
$190$	8.64769	−	12.2420i	0.627369	−	0.888127i
$191$		−	24.5210i		−	1.77428i	−0.461503	−	0.887139i	$-0.652689\pi$
$191$		−	24.5210i		−	1.77428i	0.461503	−	0.887139i	$-0.347311\pi$
$192$		0			0
$193$	−10.0101			−0.720546			−0.360273	−	0.932847i	$-0.617316\pi$
$193$	−10.0101			−0.720546			−0.360273	+	0.932847i	$0.617316\pi$
$194$	−16.0605			−1.15308
$195$		0			0
$196$	−1.97480			−0.141057
$197$			19.1667i			1.36557i	0.730618	+	0.682786i	$0.239232\pi$
$197$			19.1667i			1.36557i	−0.730618	+	0.682786i	$0.760768\pi$
$198$		0			0
$199$	14.7249			1.04382			0.521910	−	0.853000i	$-0.325219\pi$
$199$	14.7249			1.04382			0.521910	+	0.853000i	$0.325219\pi$
$200$	1.67114	+	4.71246i	0.118167	+	0.333221i
$201$		0			0
$202$			13.7584i			0.968038i
$203$	14.2930	−	7.48197i	1.00317	−	0.525132i
$204$		0			0
$205$	13.3826	−	18.9450i	0.934684	−	1.32317i
$206$			9.16613i			0.638634i
$207$		0			0
$208$		−	1.37471i		−	0.0953192i
$209$	7.30542			0.505326
$210$		0			0
$211$		−	8.19596i		−	0.564233i	−0.959380	−	0.282116i	$-0.908964\pi$
$211$		−	8.19596i		−	0.564233i	0.959380	−	0.282116i	$-0.0910365\pi$
$212$			10.0993i			0.693620i
$213$		0			0
$214$			2.34345i			0.160195i
$215$	−19.8341	−	14.0107i	−1.35267	−	0.955523i
$216$		0			0
$217$	−12.6644			−0.859713
$218$	−1.12260			−0.0760321
$219$		0			0
$220$	−1.40608	+	1.99050i	−0.0947981	+	0.134200i
$221$			0.291791i			0.0196280i
$222$		0			0
$223$		−	6.32850i		−	0.423788i	−0.977293	−	0.211894i	$-0.932037\pi$
$223$		−	6.32850i		−	0.423788i	0.977293	−	0.211894i	$-0.0679631\pi$
$224$			2.99580i			0.200165i
$225$		0			0
$226$	−14.7451			−0.980829
$227$			20.8358i			1.38292i	0.722413	+	0.691461i	$0.243033\pi$
$227$			20.8358i			1.38292i	−0.722413	+	0.691461i	$0.756967\pi$
$228$		0			0
$229$		−	14.2925i		−	0.944473i	−0.881472	−	0.472236i	$-0.843447\pi$
$229$		−	14.2925i		−	0.944473i	0.881472	−	0.472236i	$-0.156553\pi$
$230$	1.37249	−	1.94295i	0.0904995	−	0.128114i
$231$		0			0
$232$	−2.49749	−	4.77101i	−0.163968	−	0.313232i
$233$		−	13.5230i		−	0.885923i	−0.896541	−	0.442961i	$-0.853928\pi$
$233$		−	13.5230i		−	0.885923i	0.896541	−	0.442961i	$-0.146072\pi$
$234$		0			0
$235$	11.6661	+	8.24090i	0.761014	+	0.537577i
$236$	5.28523			0.344039
$237$		0			0
$238$		−	0.635875i		−	0.0412177i
$239$	18.6697			1.20764			0.603822	−	0.797119i	$-0.293644\pi$
$239$	18.6697			1.20764			0.603822	+	0.797119i	$0.293644\pi$
$240$		0			0
$241$	−19.6628			−1.26660			−0.633298	−	0.773908i	$-0.718299\pi$
$241$	−19.6628			−1.26660			−0.633298	+	0.773908i	$0.718299\pi$
$242$	9.81217			0.630750
$243$		0			0
$244$		−	3.38530i		−	0.216722i
$245$	3.60668	+	2.54775i	0.230422	+	0.162769i
$246$		0			0
$247$	9.21465			0.586314
$248$			4.22738i			0.268439i
$249$		0			0
$250$	3.02760	−	10.7626i	0.191482	−	0.680687i
$251$			11.5370i			0.728212i	0.931358	+	0.364106i	$0.118625\pi$
$251$			11.5370i			0.728212i	−0.931358	+	0.364106i	$0.881375\pi$
$252$		0			0
$253$	1.15946			0.0728945
$254$	−2.57047			−0.161286
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	7.27525i		−	0.453817i	−0.973916	−	0.226909i	$-0.927138\pi$
$257$		−	7.27525i		−	0.453817i	0.973916	−	0.226909i	$-0.0728619\pi$
$258$		0			0
$259$		−	17.1657i		−	1.06662i
$260$	−1.77356	+	2.51071i	−0.109991	+	0.155708i
$261$		0			0
$262$			1.20697i			0.0745671i
$263$	−29.7334			−1.83344			−0.916721	−	0.399528i	$-0.869174\pi$
$263$	−29.7334			−1.83344			−0.916721	+	0.399528i	$0.869174\pi$
$264$		0			0
$265$	13.0293	−	18.4448i	0.800387	−	1.13306i
$266$	−20.0807			−1.23123
$267$		0			0
$268$			10.2314i			0.624982i
$269$		−	26.5290i		−	1.61750i	−0.588152	−	0.808750i	$-0.700144\pi$
$269$		−	26.5290i		−	1.61750i	0.588152	−	0.808750i	$-0.299856\pi$
$270$		0			0
$271$			19.2989i			1.17232i	0.810195	+	0.586161i	$0.199361\pi$
$271$			19.2989i			1.17232i	−0.810195	+	0.586161i	$0.800639\pi$
$272$	−0.212256			−0.0128699
$273$		0			0
$274$	−5.81534			−0.351318
$275$	5.13601	−	1.82133i	0.309713	−	0.109831i
$276$		0			0
$277$		−	11.2042i		−	0.673194i	−0.941649	−	0.336597i	$-0.890724\pi$
$277$		−	11.2042i		−	0.673194i	0.941649	−	0.336597i	$-0.109276\pi$
$278$	15.0428			0.902205
$279$		0			0
$280$	3.86496	−	5.47139i	0.230976	−	0.326978i
$281$	7.60493			0.453672			0.226836	−	0.973933i	$-0.427162\pi$
$281$	7.60493			0.453672			0.226836	+	0.973933i	$0.427162\pi$
$282$		0			0
$283$			4.75740i			0.282798i	0.989953	+	0.141399i	$0.0451601\pi$
$283$			4.75740i			0.282798i	−0.989953	+	0.141399i	$0.954840\pi$
$284$	5.04538			0.299388
$285$		0			0
$286$	−1.49827			−0.0885945
$287$	−31.0757			−1.83434
$288$		0			0
$289$	−16.9549			−0.997350
$290$	−1.59392	+	11.9356i	−0.0935980	+	0.700885i
$291$		0			0
$292$	3.51767			0.205856
$293$	22.2904			1.30222			0.651108	−	0.758985i	$-0.274304\pi$
$293$	22.2904			1.30222			0.651108	+	0.758985i	$0.274304\pi$
$294$		0			0
$295$	−9.65271	−	6.81863i	−0.562002	−	0.396996i
$296$	−5.72993			−0.333045
$297$		0			0
$298$	−0.968162			−0.0560841
$299$	1.46248			0.0845772
$300$		0			0
$301$			32.5342i			1.87524i
$302$	−10.3004			−0.592721
$303$		0			0
$304$			6.70297i			0.384441i
$305$	−4.36747	+	6.18276i	−0.250081	+	0.354024i
$306$		0			0
$307$	−19.9531			−1.13878			−0.569392	−	0.822066i	$-0.692821\pi$
$307$	−19.9531			−1.13878			−0.569392	+	0.822066i	$0.692821\pi$
$308$	3.26505			0.186044
$309$		0			0
$310$	5.45386	−	7.72069i	0.309758	−	0.438506i
$311$		−	15.8156i		−	0.896820i	−0.893828	−	0.448410i	$-0.851990\pi$
$311$		−	15.8156i		−	0.896820i	0.893828	−	0.448410i	$-0.148010\pi$
$312$		0			0
$313$		−	9.71119i		−	0.548909i	−0.961600	−	0.274454i	$-0.911503\pi$
$313$		−	9.71119i		−	0.548909i	0.961600	−	0.274454i	$-0.0884973\pi$
$314$	11.5654			0.652676
$315$		0			0
$316$		−	8.85669i		−	0.498227i
$317$	−31.6058			−1.77516			−0.887580	−	0.460654i	$-0.847615\pi$
$317$	−31.6058			−1.77516			−0.887580	+	0.460654i	$0.847615\pi$
$318$		0			0
$319$	−5.19982	+	2.72196i	−0.291134	+	0.152400i
$320$	−1.82635	−	1.29013i	−0.102096	−	0.0721204i
$321$		0			0
$322$	−3.18706			−0.177608
$323$		−	1.42274i		−	0.0791636i
$324$		0			0
$325$	6.47828	−	2.29733i	0.359350	−	0.127433i
$326$	−3.50675			−0.194221
$327$		0			0
$328$			10.3731i			0.572759i
$329$		−	19.1361i		−	1.05501i
$330$		0			0
$331$		−	18.4649i		−	1.01492i	−0.861674	−	0.507462i	$-0.830584\pi$
$331$		−	18.4649i		−	1.01492i	0.861674	−	0.507462i	$-0.169416\pi$
$332$			12.4112i			0.681151i
$333$		0			0
$334$		−	6.80763i		−	0.372497i
$335$	13.1998	−	18.6862i	0.721183	−	1.02093i
$336$		0			0
$337$	11.7729			0.641311			0.320656	−	0.947196i	$-0.396097\pi$
$337$	11.7729			0.641311			0.320656	+	0.947196i	$0.396097\pi$
$338$	11.1102			0.604313
$339$		0			0
$340$	0.387654	+	0.273837i	0.0210235	+	0.0148509i
$341$	4.60733			0.249501
$342$		0			0
$343$			15.0545i			0.812866i
$344$	10.8599			0.585529
$345$		0			0
$346$		−	12.6960i		−	0.682541i
$347$			12.1497i			0.652232i	0.945330	+	0.326116i	$0.105740\pi$
$347$			12.1497i			0.652232i	−0.945330	+	0.326116i	$0.894260\pi$
$348$		0			0
$349$	−8.13241			−0.435318			−0.217659	−	0.976025i	$-0.569842\pi$
$349$	−8.13241			−0.435318			−0.217659	+	0.976025i	$0.569842\pi$
$350$	−14.1176	+	5.00638i	−0.754616	+	0.267603i
$351$		0			0
$352$		−	1.08988i		−	0.0580907i
$353$		−	17.7354i		−	0.943958i	−0.881610	−	0.471979i	$-0.843540\pi$
$353$		−	17.7354i		−	0.943958i	0.881610	−	0.471979i	$-0.156460\pi$
$354$		0			0
$355$	−9.21465	−	6.50919i	−0.489063	−	0.345472i
$356$			2.95876i			0.156814i
$357$		0			0
$358$	3.44971			0.182323
$359$		−	9.14009i		−	0.482396i	−0.970476	−	0.241198i	$-0.922460\pi$
$359$		−	9.14009i		−	0.482396i	0.970476	−	0.241198i	$-0.0775402\pi$
$360$		0			0
$361$	−25.9297			−1.36472
$362$	19.3826			1.01873
$363$		0			0
$364$	4.11836			0.215861
$365$	−6.42451	−	4.53825i	−0.336274	−	0.237543i
$366$		0			0
$367$	−25.5654			−1.33451			−0.667253	−	0.744831i	$-0.732530\pi$
$367$	−25.5654			−1.33451			−0.667253	+	0.744831i	$0.732530\pi$
$368$			1.06384i			0.0554566i
$369$		0			0
$370$	10.4649	+	7.39234i	0.544043	+	0.384310i
$371$	−30.2553			−1.57078
$372$		0			0
$373$			21.8731i			1.13255i	0.824217	+	0.566273i	$0.191615\pi$
$373$			21.8731i			1.13255i	−0.824217	+	0.566273i	$0.808385\pi$
$374$			0.231333i			0.0119619i
$375$		0			0
$376$	−6.38765			−0.329418
$377$	−6.55877	+	3.43333i	−0.337794	+	0.176826i
$378$		0			0
$379$		−	32.8410i		−	1.68693i	−0.537184	−	0.843465i	$-0.680512\pi$
$379$		−	32.8410i		−	1.68693i	0.537184	−	0.843465i	$-0.319488\pi$
$380$	8.64769	−	12.2420i	0.443617	−	0.628001i
$381$		0			0
$382$		−	24.5210i		−	1.25460i
$383$		−	34.6298i		−	1.76950i	−0.466064	−	0.884751i	$-0.654328\pi$
$383$		−	34.6298i		−	1.76950i	0.466064	−	0.884751i	$-0.345672\pi$
$384$		0			0
$385$	−5.96314	−	4.21234i	−0.303910	−	0.214681i
$386$	−10.0101			−0.509503
$387$		0			0
$388$	−16.0605			−0.815351
$389$		−	12.9103i		−	0.654580i	−0.944924	−	0.327290i	$-0.893865\pi$
$389$		−	12.9103i		−	0.654580i	0.944924	−	0.327290i	$-0.106135\pi$
$390$		0			0
$391$		−	0.225807i		−	0.0114195i
$392$	−1.97480			−0.0997424
$393$		0			0
$394$			19.1667i			0.965605i
$395$	−11.4263	+	16.1754i	−0.574918	+	0.813875i
$396$		0			0
$397$			28.7398i			1.44241i	0.692723	+	0.721204i	$0.256411\pi$
$397$			28.7398i			1.44241i	−0.692723	+	0.721204i	$0.743589\pi$
$398$	14.7249			0.738093
$399$		0			0
$400$	1.67114	+	4.71246i	0.0835568	+	0.235623i
$401$	−24.2030			−1.20864			−0.604320	−	0.796742i	$-0.706555\pi$
$401$	−24.2030			−1.20864			−0.604320	+	0.796742i	$0.706555\pi$
$402$		0			0
$403$	5.81143			0.289488
$404$			13.7584i			0.684506i
$405$		0			0
$406$	14.2930	−	7.48197i	0.709349	−	0.371324i
$407$			6.24492i			0.309549i
$408$		0			0
$409$			17.4820i			0.864431i	0.901770	+	0.432216i	$0.142268\pi$
$409$			17.4820i			0.864431i	−0.901770	+	0.432216i	$0.857732\pi$
$410$	13.3826	−	18.9450i	0.660921	−	0.935624i
$411$		0			0
$412$			9.16613i			0.451583i
$413$			15.8335i			0.779115i
$414$		0			0
$415$	16.0120	−	22.6672i	0.785997	−	1.11269i
$416$		−	1.37471i		−	0.0674008i
$417$		0			0
$418$	7.30542			0.357320
$419$	−26.2378			−1.28180			−0.640900	−	0.767625i	$-0.721439\pi$
$419$	−26.2378			−1.28180			−0.640900	+	0.767625i	$0.721439\pi$
$420$		0			0
$421$		−	13.6673i		−	0.666105i	−0.942908	−	0.333053i	$-0.891921\pi$
$421$		−	13.6673i		−	0.666105i	0.942908	−	0.333053i	$-0.108079\pi$
$422$		−	8.19596i		−	0.398973i
$423$		0			0
$424$			10.0993i			0.490464i
$425$	−0.354708	−	1.00025i	−0.0172059	−	0.0485191i
$426$		0			0
$427$	10.1417			0.490790
$428$			2.34345i			0.113275i
$429$		0			0
$430$	−19.8341	−	14.0107i	−0.956485	−	0.675657i
$431$	20.1544			0.970805			0.485403	−	0.874291i	$-0.338673\pi$
$431$	20.1544			0.970805			0.485403	+	0.874291i	$0.338673\pi$
$432$		0			0
$433$	9.30542			0.447190			0.223595	−	0.974682i	$-0.428221\pi$
$433$	9.30542			0.447190			0.223595	+	0.974682i	$0.428221\pi$
$434$	−12.6644			−0.607909
$435$		0			0
$436$	−1.12260			−0.0537628
$437$	−7.13090			−0.341117
$438$		0			0
$439$	38.2655			1.82631			0.913156	−	0.407610i	$-0.133638\pi$
$439$	38.2655			1.82631			0.913156	+	0.407610i	$0.133638\pi$
$440$	−1.40608	+	1.99050i	−0.0670324	+	0.0948935i
$441$		0			0
$442$			0.291791i			0.0138791i
$443$	34.1561			1.62281			0.811403	−	0.584488i	$-0.198704\pi$
$443$	34.1561			1.62281			0.811403	+	0.584488i	$0.198704\pi$
$444$		0			0
$445$	3.81719	−	5.40375i	0.180952	−	0.256162i
$446$		−	6.32850i		−	0.299663i
$447$		0			0
$448$			2.99580i			0.141538i
$449$		−	2.90669i		−	0.137175i	−0.997645	−	0.0685876i	$-0.978151\pi$
$449$		−	2.90669i		−	0.137175i	0.997645	−	0.0685876i	$-0.0218493\pi$
$450$		0			0
$451$	11.3054			0.532351
$452$	−14.7451			−0.693551
$453$		0			0
$454$			20.8358i			0.977874i
$455$	−7.52158	−	5.31321i	−0.352617	−	0.249087i
$456$		0			0
$457$			2.65336i			0.124119i	0.998072	+	0.0620596i	$0.0197669\pi$
$457$			2.65336i			0.124119i	−0.998072	+	0.0620596i	$0.980233\pi$
$458$		−	14.2925i		−	0.667843i
$459$		0			0
$460$	1.37249	−	1.94295i	0.0639928	−	0.0905906i
$461$			6.53979i			0.304589i	0.988335	+	0.152294i	$0.0486662\pi$
$461$			6.53979i			0.304589i	−0.988335	+	0.152294i	$0.951334\pi$
$462$		0			0
$463$		−	27.1658i		−	1.26250i	−0.775579	−	0.631250i	$-0.782542\pi$
$463$		−	27.1658i		−	1.26250i	0.775579	−	0.631250i	$-0.217458\pi$
$464$	−2.49749	−	4.77101i	−0.115943	−	0.221489i
$465$		0			0
$466$		−	13.5230i		−	0.626442i
$467$	32.2561			1.49264			0.746318	−	0.665590i	$-0.231820\pi$
$467$	32.2561			1.49264			0.746318	+	0.665590i	$0.231820\pi$
$468$		0			0
$469$	−30.6512			−1.41534
$470$	11.6661	+	8.24090i	0.538118	+	0.380124i
$471$		0			0
$472$	5.28523			0.243273
$473$		−	11.8360i		−	0.544221i
$474$		0			0
$475$	−31.5875	+	11.2016i	−1.44933	+	0.513963i
$476$		−	0.635875i		−	0.0291453i
$477$		0			0
$478$	18.6697			0.853933
$479$			25.8295i			1.18018i	0.807337	+	0.590090i	$0.200908\pi$
$479$			25.8295i			1.18018i	−0.807337	+	0.590090i	$0.799092\pi$
$480$		0			0
$481$			7.87700i			0.359160i
$482$	−19.6628			−0.895618
$483$		0			0
$484$	9.81217			0.446008
$485$	29.3322	+	20.7202i	1.33191	+	0.940854i
$486$		0			0
$487$			1.63351i			0.0740215i	0.999315	+	0.0370107i	$0.0117836\pi$
$487$			1.63351i			0.0740215i	−0.999315	+	0.0370107i	$0.988216\pi$
$488$		−	3.38530i		−	0.153245i
$489$		0			0
$490$	3.60668	+	2.54775i	0.162933	+	0.115095i
$491$			10.3456i			0.466892i	0.972370	+	0.233446i	$0.0750002\pi$
$491$			10.3456i			0.466892i	−0.972370	+	0.233446i	$0.925000\pi$
$492$		0			0
$493$	0.530107	+	1.01267i	0.0238748	+	0.0456086i
$494$	9.21465			0.414587
$495$		0			0
$496$			4.22738i			0.189815i
$497$			15.1149i			0.677998i
$498$		0			0
$499$	0.704726			0.0315479			0.0157739	−	0.999876i	$-0.494979\pi$
$499$	0.704726			0.0315479			0.0157739	+	0.999876i	$0.494979\pi$
$500$	3.02760	−	10.7626i	0.135398	−	0.481318i
$501$		0			0
$502$			11.5370i			0.514924i
$503$	−6.19285			−0.276126			−0.138063	−	0.990423i	$-0.544088\pi$
$503$	−6.19285			−0.276126			−0.138063	+	0.990423i	$0.544088\pi$
$504$		0			0
$505$	17.7501	−	25.1277i	0.789869	−	1.11817i
$506$	1.15946			0.0515442
$507$		0			0
$508$	−2.57047			−0.114046
$509$	14.6292			0.648426			0.324213	−	0.945984i	$-0.394900\pi$
$509$	14.6292			0.648426			0.324213	+	0.945984i	$0.394900\pi$
$510$		0			0
$511$			10.5382i			0.466184i
$512$	1.00000			0.0441942
$513$		0			0
$514$		−	7.27525i		−	0.320897i
$515$	11.8255	−	16.7406i	0.521093	−	0.737679i
$516$		0			0
$517$			6.96176i			0.306178i
$518$		−	17.1657i		−	0.754217i
$519$		0			0
$520$	−1.77356	+	2.51071i	−0.0777756	+	0.110102i
$521$	6.40511			0.280613			0.140306	−	0.990108i	$-0.455191\pi$
$521$	6.40511			0.280613			0.140306	+	0.990108i	$0.455191\pi$
$522$		0			0
$523$		−	16.5805i		−	0.725013i	−0.931981	−	0.362507i	$-0.881921\pi$
$523$		−	16.5805i		−	0.725013i	0.931981	−	0.362507i	$-0.118079\pi$
$524$			1.20697i			0.0527269i
$525$		0			0
$526$	−29.7334			−1.29644
$527$		−	0.897285i		−	0.0390864i
$528$		0			0
$529$	21.8682			0.950793
$530$	13.0293	−	18.4448i	0.565959	−	0.801192i
$531$		0			0
$532$	−20.0807			−0.870610
$533$	14.2600			0.617671
$534$		0			0
$535$	3.02336	−	4.27997i	0.130711	−	0.185039i
$536$			10.2314i			0.441929i
$537$		0			0
$538$		−	26.5290i		−	1.14375i
$539$			2.15229i			0.0927057i
$540$		0			0
$541$			40.5567i			1.74367i	0.489803	+	0.871833i	$0.337069\pi$
$541$			40.5567i			1.74367i	−0.489803	+	0.871833i	$0.662931\pi$
$542$			19.2989i			0.828957i
$543$		0			0
$544$	−0.212256			−0.00910039
$545$	2.05027	+	1.44830i	0.0878238	+	0.0620383i
$546$		0			0
$547$		−	43.0100i		−	1.83897i	−0.393119	−	0.919487i	$-0.628604\pi$
$547$		−	43.0100i		−	1.83897i	0.393119	−	0.919487i	$-0.371396\pi$
$548$	−5.81534			−0.248419
$549$		0			0
$550$	5.13601	−	1.82133i	0.219000	−	0.0776620i
$551$	31.9799	−	16.7406i	1.36239	−	0.713173i
$552$		0			0
$553$	26.5328			1.12829
$554$		−	11.2042i		−	0.476020i
$555$		0			0
$556$	15.0428			0.637955
$557$			35.0002i			1.48301i	0.670949	+	0.741503i	$0.265887\pi$
$557$			35.0002i			1.48301i	−0.670949	+	0.741503i	$0.734113\pi$
$558$		0			0
$559$		−	14.9293i		−	0.631442i
$560$	3.86496	−	5.47139i	0.163325	−	0.231208i
$561$		0			0
$562$	7.60493			0.320795
$563$	−7.82733			−0.329882			−0.164941	−	0.986303i	$-0.552743\pi$
$563$	−7.82733			−0.329882			−0.164941	+	0.986303i	$0.552743\pi$
$564$		0			0
$565$	26.9297	+	19.0231i	1.13294	+	0.800306i
$566$			4.75740i			0.199969i
$567$		0			0
$568$	5.04538			0.211700
$569$			16.3098i			0.683741i	0.939747	+	0.341870i	$0.111060\pi$
$569$			16.3098i			0.683741i	−0.939747	+	0.341870i	$0.888940\pi$
$570$		0			0
$571$	−26.6814			−1.11658			−0.558291	−	0.829645i	$-0.688543\pi$
$571$	−26.6814			−1.11658			−0.558291	+	0.829645i	$0.688543\pi$
$572$	−1.49827			−0.0626458
$573$		0			0
$574$	−31.0757			−1.29707
$575$	−5.01332	+	1.77783i	−0.209070	+	0.0741404i
$576$		0			0
$577$	34.3986			1.43203			0.716016	−	0.698084i	$-0.245964\pi$
$577$	34.3986			1.43203			0.716016	+	0.698084i	$0.245964\pi$
$578$	−16.9549			−0.705233
$579$		0			0
$580$	−1.59392	+	11.9356i	−0.0661838	+	0.495600i
$581$	−37.1813			−1.54254
$582$		0			0
$583$	11.0070			0.455862
$584$	3.51767			0.145562
$585$		0			0
$586$	22.2904			0.920806
$587$		−	25.7402i		−	1.06241i	−0.847243	−	0.531205i	$-0.821739\pi$
$587$		−	25.7402i		−	1.06241i	0.847243	−	0.531205i	$-0.178261\pi$
$588$		0			0
$589$	−28.3360			−1.16756
$590$	−9.65271	−	6.81863i	−0.397396	−	0.280719i
$591$		0			0
$592$	−5.72993			−0.235499
$593$			8.07625i			0.331652i	0.986155	+	0.165826i	$0.0530290\pi$
$593$			8.07625i			0.331652i	−0.986155	+	0.165826i	$0.946971\pi$
$594$		0			0
$595$	−0.820361	+	1.16133i	−0.0336315	+	0.0476100i
$596$	−0.968162			−0.0396575
$597$		0			0
$598$	1.46248			0.0598051
$599$		−	6.48120i		−	0.264815i	−0.991195	−	0.132407i	$-0.957729\pi$
$599$		−	6.48120i		−	0.264815i	0.991195	−	0.132407i	$-0.0422707\pi$
$600$		0			0
$601$		−	9.59123i		−	0.391235i	−0.980680	−	0.195617i	$-0.937329\pi$
$601$		−	9.59123i		−	0.391235i	0.980680	−	0.195617i	$-0.0626710\pi$
$602$			32.5342i			1.32599i
$603$		0			0
$604$	−10.3004			−0.419117
$605$	−17.9205	−	12.6590i	−0.728571	−	0.514660i
$606$		0			0
$607$	28.1680			1.14330			0.571652	−	0.820496i	$-0.306303\pi$
$607$	28.1680			1.14330			0.571652	+	0.820496i	$0.306303\pi$
$608$			6.70297i			0.271841i
$609$		0			0
$610$	−4.36747	+	6.18276i	−0.176834	+	0.250333i
$611$			8.78119i			0.355249i
$612$		0			0
$613$		−	41.3758i		−	1.67115i	−0.549373	−	0.835577i	$-0.685133\pi$
$613$		−	41.3758i		−	1.67115i	0.549373	−	0.835577i	$-0.314867\pi$
$614$	−19.9531			−0.805242
$615$		0			0
$616$	3.26505			0.131553
$617$	9.70399			0.390668			0.195334	−	0.980737i	$-0.437421\pi$
$617$	9.70399			0.390668			0.195334	+	0.980737i	$0.437421\pi$
$618$		0			0
$619$		−	29.7952i		−	1.19757i	−0.800909	−	0.598786i	$-0.795650\pi$
$619$		−	29.7952i		−	1.19757i	0.800909	−	0.598786i	$-0.204350\pi$
$620$	5.45386	−	7.72069i	0.219032	−	0.310070i
$621$		0			0
$622$		−	15.8156i		−	0.634147i
$623$	−8.86386			−0.355123
$624$		0			0
$625$	−19.4146	+	15.7503i	−0.776584	+	0.630013i
$626$		−	9.71119i		−	0.388137i
$627$		0			0
$628$	11.5654			0.461512
$629$	1.21621			0.0484935
$630$		0			0
$631$	−35.9799			−1.43234			−0.716169	−	0.697927i	$-0.754106\pi$
$631$	−35.9799			−1.43234			−0.716169	+	0.697927i	$0.754106\pi$
$632$		−	8.85669i		−	0.352300i
$633$		0			0
$634$	−31.6058			−1.25523
$635$	4.69458	+	3.31623i	0.186299	+	0.131601i
$636$		0			0
$637$			2.71478i			0.107564i
$638$	−5.19982	+	2.72196i	−0.205863	+	0.107763i
$639$		0			0
$640$	−1.82635	−	1.29013i	−0.0721930	−	0.0509968i
$641$		−	7.21413i		−	0.284941i	−0.989799	−	0.142471i	$-0.954495\pi$
$641$		−	7.21413i		−	0.284941i	0.989799	−	0.142471i	$-0.0455046\pi$
$642$		0			0
$643$			16.4543i			0.648895i	0.945904	+	0.324448i	$0.105178\pi$
$643$			16.4543i			0.648895i	−0.945904	+	0.324448i	$0.894822\pi$
$644$	−3.18706			−0.125588
$645$		0			0
$646$		−	1.42274i		−	0.0559771i
$647$			30.8486i			1.21278i	0.795166	+	0.606392i	$0.207384\pi$
$647$			30.8486i			1.21278i	−0.795166	+	0.606392i	$0.792616\pi$
$648$		0			0
$649$		−	5.76026i		−	0.226110i
$650$	6.47828	−	2.29733i	0.254099	−	0.0901088i
$651$		0			0
$652$	−3.50675			−0.137335
$653$	22.3089			0.873014			0.436507	−	0.899701i	$-0.356215\pi$
$653$	22.3089			0.873014			0.436507	+	0.899701i	$0.356215\pi$
$654$		0			0
$655$	1.55715	−	2.20436i	0.0608430	−	0.0861316i
$656$			10.3731i			0.405002i
$657$		0			0
$658$		−	19.1361i		−	0.746003i
$659$			27.0186i			1.05249i	0.850332	+	0.526247i	$0.176401\pi$
$659$			27.0186i			1.05249i	−0.850332	+	0.526247i	$0.823599\pi$
$660$		0			0
$661$	−9.63068			−0.374590			−0.187295	−	0.982304i	$-0.559972\pi$
$661$	−9.63068			−0.374590			−0.187295	+	0.982304i	$0.559972\pi$
$662$		−	18.4649i		−	0.717659i
$663$		0			0
$664$			12.4112i			0.481646i
$665$	36.6745	+	25.9067i	1.42218	+	1.00462i
$666$		0			0
$667$	5.07560	−	2.65694i	0.196528	−	0.102877i
$668$		−	6.80763i		−	0.263395i
$669$		0			0
$670$	13.1998	−	18.6862i	0.509954	−	0.721909i
$671$	−3.68956			−0.142434
$672$		0			0
$673$		−	46.9574i		−	1.81007i	−0.425334	−	0.905037i	$-0.639843\pi$
$673$		−	46.9574i		−	1.81007i	0.425334	−	0.905037i	$-0.360157\pi$
$674$	11.7729			0.453476
$675$		0			0
$676$	11.1102			0.427314
$677$	28.1645			1.08245			0.541224	−	0.840878i	$-0.317961\pi$
$677$	28.1645			1.08245			0.541224	+	0.840878i	$0.317961\pi$
$678$		0			0
$679$		−	48.1141i		−	1.84645i
$680$	0.387654	+	0.273837i	0.0148659	+	0.0105012i
$681$		0			0
$682$	4.60733			0.176424
$683$			19.8006i			0.757650i	0.925468	+	0.378825i	$0.123672\pi$
$683$			19.8006i			0.757650i	−0.925468	+	0.378825i	$0.876328\pi$
$684$		0			0
$685$	10.6209	+	7.50254i	0.405803	+	0.286657i
$686$			15.0545i			0.574783i
$687$		0			0
$688$	10.8599			0.414031
$689$	13.8836			0.528922
$690$		0			0
$691$	3.64179			0.138540			0.0692701	−	0.997598i	$-0.477933\pi$
$691$	3.64179			0.138540			0.0692701	+	0.997598i	$0.477933\pi$
$692$		−	12.6960i		−	0.482629i
$693$		0			0
$694$			12.1497i			0.461198i
$695$	−27.4734	−	19.4071i	−1.04213	−	0.736153i
$696$		0			0
$697$		−	2.20175i		−	0.0833973i
$698$	−8.13241			−0.307816
$699$		0			0
$700$	−14.1176	+	5.00638i	−0.533594	+	0.189224i
$701$	24.5639			0.927767			0.463883	−	0.885896i	$-0.346456\pi$
$701$	24.5639			0.927767			0.463883	+	0.885896i	$0.346456\pi$
$702$		0			0
$703$		−	38.4075i		−	1.44857i
$704$		−	1.08988i		−	0.0410763i
$705$		0			0
$706$		−	17.7354i		−	0.667479i
$707$	−41.2174			−1.55014
$708$		0			0
$709$	36.5676			1.37333			0.686663	−	0.726976i	$-0.259075\pi$
$709$	36.5676			1.37333			0.686663	+	0.726976i	$0.259075\pi$
$710$	−9.21465	−	6.50919i	−0.345820	−	0.244286i
$711$		0			0
$712$			2.95876i			0.110884i
$713$	−4.49726			−0.168424
$714$		0			0
$715$	2.73637	+	1.93296i	0.102334	+	0.0722886i
$716$	3.44971			0.128922
$717$		0			0
$718$		−	9.14009i		−	0.341105i
$719$	4.40968			0.164453			0.0822267	−	0.996614i	$-0.473797\pi$
$719$	4.40968			0.164453			0.0822267	+	0.996614i	$0.473797\pi$
$720$		0			0
$721$	−27.4599			−1.02266
$722$	−25.9297			−0.965005
$723$		0			0
$724$	19.3826			0.720350
$725$	18.3096	−	19.7423i	0.680000	−	0.733212i
$726$		0			0
$727$	−37.9900			−1.40897			−0.704485	−	0.709719i	$-0.748822\pi$
$727$	−37.9900			−1.40897			−0.704485	+	0.709719i	$0.748822\pi$
$728$	4.11836			0.152637
$729$		0			0
$730$	−6.42451	−	4.53825i	−0.237782	−	0.167968i
$731$	−2.30509			−0.0852567
$732$		0			0
$733$	−6.57895			−0.242999			−0.121500	−	0.992591i	$-0.538770\pi$
$733$	−6.57895			−0.242999			−0.121500	+	0.992591i	$0.538770\pi$
$734$	−25.5654			−0.943638
$735$		0			0
$736$			1.06384i			0.0392137i
$737$	11.1510			0.410752
$738$		0			0
$739$		−	26.6171i		−	0.979127i	−0.871968	−	0.489563i	$-0.837156\pi$
$739$		−	26.6171i		−	0.979127i	0.871968	−	0.489563i	$-0.162844\pi$
$740$	10.4649	+	7.39234i	0.384696	+	0.271748i
$741$		0			0
$742$	−30.2553			−1.11071
$743$	−4.67606			−0.171548			−0.0857741	−	0.996315i	$-0.527336\pi$
$743$	−4.67606			−0.171548			−0.0857741	+	0.996315i	$0.527336\pi$
$744$		0			0
$745$	1.76821	+	1.24905i	0.0647821	+	0.0457618i
$746$			21.8731i			0.800832i
$747$		0			0
$748$			0.231333i			0.00845837i
$749$	−7.02051			−0.256524
$750$		0			0
$751$			12.3371i			0.450187i	0.974337	+	0.225093i	$0.0722687\pi$
$751$			12.3371i			0.450187i	−0.974337	+	0.225093i	$0.927731\pi$
$752$	−6.38765			−0.232934
$753$		0			0
$754$	−6.55877	+	3.43333i	−0.238856	+	0.125035i
$755$	18.8122	+	13.2888i	0.684645	+	0.483630i
$756$		0			0
$757$	−10.2685			−0.373216			−0.186608	−	0.982434i	$-0.559749\pi$
$757$	−10.2685			−0.373216			−0.186608	+	0.982434i	$0.559749\pi$
$758$		−	32.8410i		−	1.19284i
$759$		0			0
$760$	8.64769	−	12.2420i	0.313685	−	0.444064i
$761$	−49.1824			−1.78286			−0.891430	−	0.453159i	$-0.850297\pi$
$761$	−49.1824			−1.78286			−0.891430	+	0.453159i	$0.850297\pi$
$762$		0			0
$763$		−	3.36308i		−	0.121752i
$764$		−	24.5210i		−	0.887139i
$765$		0			0
$766$		−	34.6298i		−	1.25123i
$767$		−	7.26568i		−	0.262348i
$768$		0			0
$769$			36.4972i			1.31612i	0.752964	+	0.658062i	$0.228624\pi$
$769$			36.4972i			1.31612i	−0.752964	+	0.658062i	$0.771376\pi$
$770$	−5.96314	−	4.21234i	−0.214897	−	0.151802i
$771$		0			0
$772$	−10.0101			−0.360273
$773$	−29.4854			−1.06052			−0.530258	−	0.847836i	$-0.677905\pi$
$773$	−29.4854			−1.06052			−0.530258	+	0.847836i	$0.677905\pi$
$774$		0			0
$775$	−19.9214	+	7.06452i	−0.715596	+	0.253765i
$776$	−16.0605			−0.576540
$777$		0			0
$778$		−	12.9103i		−	0.462858i
$779$	−69.5305			−2.49119
$780$		0			0
$781$		−	5.49885i		−	0.196764i
$782$		−	0.225807i		−	0.00807483i
$783$		0			0
$784$	−1.97480			−0.0705285
$785$	−21.1226	−	14.9209i	−0.753898	−	0.532550i
$786$		0			0
$787$			38.4961i			1.37224i	0.727490	+	0.686119i	$0.240687\pi$
$787$			38.4961i			1.37224i	−0.727490	+	0.686119i	$0.759313\pi$
$788$			19.1667i			0.682786i
$789$		0			0
$790$	−11.4263	+	16.1754i	−0.406528	+	0.575496i
$791$		−	44.1733i		−	1.57062i
$792$		0			0
$793$	−4.65382			−0.165262
$794$			28.7398i			1.01994i
$795$		0			0
$796$	14.7249			0.521910
$797$	44.1311			1.56320			0.781602	−	0.623777i	$-0.214403\pi$
$797$	44.1311			1.56320			0.781602	+	0.623777i	$0.214403\pi$
$798$		0			0
$799$	1.35582			0.0479653
$800$	1.67114	+	4.71246i	0.0590836	+	0.166611i
$801$		0			0
$802$	−24.2030			−0.854637
$803$		−	3.83383i		−	0.135293i
$804$		0			0
$805$	5.82069	+	4.11171i	0.205152	+	0.144919i
$806$	5.81143			0.204699
$807$		0			0
$808$			13.7584i			0.484019i
$809$			8.79023i			0.309048i	0.987989	+	0.154524i	$0.0493844\pi$
$809$			8.79023i			0.309048i	−0.987989	+	0.154524i	$0.950616\pi$
$810$		0			0
$811$	−3.91186			−0.137364			−0.0686820	−	0.997639i	$-0.521879\pi$
$811$	−3.91186			−0.137364			−0.0686820	+	0.997639i	$0.521879\pi$
$812$	14.2930	−	7.48197i	0.501585	−	0.262566i
$813$		0			0
$814$			6.24492i			0.218884i
$815$	6.40457	+	4.52416i	0.224342	+	0.158474i
$816$		0			0
$817$			72.7938i			2.54673i
$818$			17.4820i			0.611245i
$819$		0			0
$820$	13.3826	−	18.9450i	0.467342	−	0.661586i
$821$	8.59729			0.300047			0.150024	−	0.988682i	$-0.452065\pi$
$821$	8.59729			0.300047			0.150024	+	0.988682i	$0.452065\pi$
$822$		0			0
$823$	2.31892			0.0808323			0.0404162	−	0.999183i	$-0.487132\pi$
$823$	2.31892			0.0808323			0.0404162	+	0.999183i	$0.487132\pi$
$824$			9.16613i			0.319317i
$825$		0			0
$826$			15.8335i			0.550918i
$827$	−13.5864			−0.472446			−0.236223	−	0.971699i	$-0.575910\pi$
$827$	−13.5864			−0.472446			−0.236223	+	0.971699i	$0.575910\pi$
$828$		0			0
$829$			24.1451i			0.838594i	0.907849	+	0.419297i	$0.137723\pi$
$829$			24.1451i			0.838594i	−0.907849	+	0.419297i	$0.862277\pi$
$830$	16.0120	−	22.6672i	0.555784	−	0.786789i
$831$		0			0
$832$		−	1.37471i		−	0.0476596i
$833$	0.419163			0.0145231
$834$		0			0
$835$	−8.78272	+	12.4331i	−0.303939	+	0.430267i
$836$	7.30542			0.252663
$837$		0			0
$838$	−26.2378			−0.906369
$839$		−	19.9698i		−	0.689434i	−0.938707	−	0.344717i	$-0.887975\pi$
$839$		−	19.9698i		−	0.689434i	0.938707	−	0.344717i	$-0.112025\pi$
$840$		0			0
$841$	−16.5251	+	23.8311i	−0.569831	+	0.821762i
$842$		−	13.6673i		−	0.471008i
$843$		0			0
$844$		−	8.19596i		−	0.282116i
$845$	−20.2911	−	14.3335i	−0.698035	−	0.493089i
$846$		0			0
$847$			29.3953i			1.01003i
$848$			10.0993i			0.346810i
$849$		0			0
$850$	−0.354708	−	1.00025i	−0.0121664	−	0.0343082i
$851$		−	6.09574i		−	0.208959i
$852$		0			0
$853$	36.0840			1.23549			0.617746	−	0.786378i	$-0.288046\pi$
$853$	36.0840			1.23549			0.617746	+	0.786378i	$0.288046\pi$
$854$	10.1417			0.347041
$855$		0			0
$856$			2.34345i			0.0800976i
$857$			19.0491i			0.650705i	0.945593	+	0.325352i	$0.105483\pi$
$857$			19.0491i			0.650705i	−0.945593	+	0.325352i	$0.894517\pi$
$858$		0			0
$859$			43.1051i			1.47073i	0.677673	+	0.735364i	$0.262989\pi$
$859$			43.1051i			1.47073i	−0.677673	+	0.735364i	$0.737011\pi$
$860$	−19.8341	−	14.0107i	−0.676337	−	0.477762i
$861$		0			0
$862$	20.1544			0.686463
$863$		−	25.9382i		−	0.882947i	−0.897274	−	0.441474i	$-0.854456\pi$
$863$		−	25.9382i		−	0.882947i	0.897274	−	0.441474i	$-0.145544\pi$
$864$		0			0
$865$	−16.3795	+	23.1874i	−0.556918	+	0.788394i
$866$	9.30542			0.316211
$867$		0			0
$868$	−12.6644			−0.429857
$869$	−9.65271			−0.327446
$870$		0			0
$871$	14.0652			0.476582
$872$	−1.12260			−0.0380161
$873$		0			0
$874$	−7.13090			−0.241206
$875$	32.2426	+	9.07007i	1.09000	+	0.306624i
$876$		0			0
$877$		−	43.0492i		−	1.45367i	−0.686812	−	0.726835i	$-0.740991\pi$
$877$		−	43.0492i		−	1.45367i	0.686812	−	0.726835i	$-0.259009\pi$
$878$	38.2655			1.29140
$879$		0			0
$880$	−1.40608	+	1.99050i	−0.0473990	+	0.0670998i
$881$			49.8210i			1.67851i	0.543736	+	0.839256i	$0.317009\pi$
$881$			49.8210i			1.67851i	−0.543736	+	0.839256i	$0.682991\pi$
$882$		0			0
$883$		−	9.29618i		−	0.312841i	−0.987691	−	0.156421i	$-0.950004\pi$
$883$		−	9.29618i		−	0.312841i	0.987691	−	0.156421i	$-0.0499955\pi$
$884$			0.291791i			0.00981398i
$885$		0			0
$886$	34.1561			1.14750
$887$	−1.49827			−0.0503070			−0.0251535	−	0.999684i	$-0.508007\pi$
$887$	−1.49827			−0.0503070			−0.0251535	+	0.999684i	$0.508007\pi$
$888$		0			0
$889$		−	7.70060i		−	0.258270i
$890$	3.81719	−	5.40375i	0.127952	−	0.181134i
$891$		0			0
$892$		−	6.32850i		−	0.211894i
$893$		−	42.8162i		−	1.43279i
$894$		0			0
$895$	−6.30040	−	4.45057i	−0.210599	−	0.148766i
$896$			2.99580i			0.100083i
$897$		0			0
$898$		−	2.90669i		−	0.0969976i
$899$	20.1689	−	10.5578i	0.672669	−	0.352123i
$900$		0			0
$901$		−	2.14363i		−	0.0714146i
$902$	11.3054			0.376429
$903$		0			0
$904$	−14.7451			−0.490414
$905$	−35.3995	−	25.0061i	−1.17672	−	0.831231i
$906$		0			0
$907$	32.7075			1.08603			0.543017	−	0.839722i	$-0.317282\pi$
$907$	32.7075			1.08603			0.543017	+	0.839722i	$0.317282\pi$
$908$			20.8358i			0.691461i
$909$		0			0
$910$	−7.52158	−	5.31321i	−0.249338	−	0.176131i
$911$		−	38.5452i		−	1.27706i	−0.769598	−	0.638529i	$-0.779543\pi$
$911$		−	38.5452i		−	1.27706i	0.769598	−	0.638529i	$-0.220457\pi$
$912$		0			0
$913$	13.5266			0.447667
$914$			2.65336i			0.0877655i
$915$		0			0
$916$		−	14.2925i		−	0.472236i
$917$	−3.61585			−0.119406
$918$		0			0
$919$	−36.8375			−1.21516			−0.607579	−	0.794259i	$-0.707859\pi$
$919$	−36.8375			−1.21516			−0.607579	+	0.794259i	$0.707859\pi$
$920$	1.37249	−	1.94295i	0.0452498	−	0.0640572i
$921$		0			0
$922$			6.53979i			0.215377i
$923$		−	6.93595i		−	0.228300i
$924$		0			0
$925$	−9.57549	−	27.0021i	−0.314840	−	0.887822i
$926$		−	27.1658i		−	0.892722i
$927$		0			0
$928$	−2.49749	−	4.77101i	−0.0819841	−	0.156616i
$929$	−29.3787			−0.963885			−0.481942	−	0.876203i	$-0.660069\pi$
$929$	−29.3787			−0.963885			−0.481942	+	0.876203i	$0.660069\pi$
$930$		0			0
$931$		−	13.2370i		−	0.433826i
$932$		−	13.5230i		−	0.442961i
$933$		0			0
$934$	32.2561			1.05545
$935$	0.298449	−	0.422496i	0.00976033	−	0.0138171i
$936$		0			0
$937$			29.1188i			0.951270i	0.879643	+	0.475635i	$0.157782\pi$
$937$			29.1188i			0.951270i	−0.879643	+	0.475635i	$0.842218\pi$
$938$	−30.6512			−1.00080
$939$		0			0
$940$	11.6661	+	8.24090i	0.380507	+	0.268788i
$941$	34.4784			1.12396			0.561982	−	0.827149i	$-0.310039\pi$
$941$	34.4784			1.12396			0.561982	+	0.827149i	$0.310039\pi$
$942$		0			0
$943$	−11.0353			−0.359360
$944$	5.28523			0.172020
$945$		0			0
$946$		−	11.8360i		−	0.384822i
$947$	16.7368			0.543873			0.271936	−	0.962315i	$-0.412336\pi$
$947$	16.7368			0.543873			0.271936	+	0.962315i	$0.412336\pi$
$948$		0			0
$949$		−	4.83579i		−	0.156976i
$950$	−31.5875	+	11.2016i	−1.02483	+	0.363427i
$951$		0			0
$952$		−	0.635875i		−	0.0206088i
$953$			49.5247i			1.60426i	0.597149	+	0.802131i	$0.296300\pi$
$953$			49.5247i			1.60426i	−0.597149	+	0.802131i	$0.703700\pi$
$954$		0			0
$955$	−31.6353	+	44.7840i	−1.02369	+	1.44918i
$956$	18.6697			0.603822
$957$		0			0
$958$			25.8295i			0.834514i
$959$		−	17.4216i		−	0.562572i
$960$		0			0
$961$	13.1293			0.423525
$962$			7.87700i			0.253965i
$963$		0			0
$964$	−19.6628			−0.633298
$965$	18.2821	+	12.9144i	0.588520	+	0.415728i
$966$		0			0
$967$	−28.3924			−0.913040			−0.456520	−	0.889713i	$-0.650904\pi$
$967$	−28.3924			−0.913040			−0.456520	+	0.889713i	$0.650904\pi$
$968$	9.81217			0.315375
$969$		0			0
$970$	29.3322	+	20.7202i	0.941801	+	0.665284i
$971$			4.86155i			0.156014i	0.996953	+	0.0780072i	$0.0248557\pi$
$971$			4.86155i			0.156014i	−0.996953	+	0.0780072i	$0.975144\pi$
$972$		0			0
$973$			45.0650i			1.44472i
$974$			1.63351i			0.0523411i
$975$		0			0
$976$		−	3.38530i		−	0.108361i
$977$			34.0078i			1.08801i	0.839083	+	0.544003i	$0.183092\pi$
$977$			34.0078i			1.08801i	−0.839083	+	0.544003i	$0.816908\pi$
$978$		0			0
$979$	3.22469			0.103062
$980$	3.60668	+	2.54775i	0.115211	+	0.0813847i
$981$		0			0
$982$			10.3456i			0.330142i
$983$	38.6176			1.23171			0.615855	−	0.787860i	$-0.288811\pi$
$983$	38.6176			1.23171			0.615855	+	0.787860i	$0.288811\pi$
$984$		0			0
$985$	24.7275	−	35.0052i	0.787885	−	1.11536i
$986$	0.530107	+	1.01267i	0.0168820	+	0.0322501i
$987$		0			0
$988$	9.21465			0.293157
$989$			11.5533i			0.367372i
$990$		0			0
$991$	26.3189			0.836048			0.418024	−	0.908436i	$-0.362723\pi$
$991$	26.3189			0.836048			0.418024	+	0.908436i	$0.362723\pi$
$992$			4.22738i			0.134219i
$993$		0			0
$994$			15.1149i			0.479417i
$995$	−26.8929	−	18.9970i	−0.852562	−	0.602246i
$996$		0			0
$997$	34.2096			1.08343			0.541715	−	0.840562i	$-0.317775\pi$
$997$	34.2096			1.08343			0.541715	+	0.840562i	$0.317775\pi$
$998$	0.704726			0.0223077
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2610.2.b.f.289.1		8
3.2	odd	2		290.2.d.a.289.4	yes	8
5.4	even	2		2610.2.b.d.289.2		8
12.11	even	2		2320.2.j.d.289.6		8
15.2	even	4		1450.2.c.g.1101.5		16
15.8	even	4		1450.2.c.g.1101.12		16
15.14	odd	2		290.2.d.b.289.5	yes	8
29.28	even	2		2610.2.b.d.289.1		8
60.59	even	2		2320.2.j.e.289.3		8
87.86	odd	2		290.2.d.b.289.6	yes	8
145.144	even	2	inner	2610.2.b.f.289.2		8
348.347	even	2		2320.2.j.e.289.4		8
435.173	even	4		1450.2.c.g.1101.6		16
435.347	even	4		1450.2.c.g.1101.11		16
435.434	odd	2		290.2.d.a.289.3	✓	8
1740.1739	even	2		2320.2.j.d.289.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.d.a.289.3	✓	8	435.434	odd	2
290.2.d.a.289.4	yes	8	3.2	odd	2
290.2.d.b.289.5	yes	8	15.14	odd	2
290.2.d.b.289.6	yes	8	87.86	odd	2
1450.2.c.g.1101.5		16	15.2	even	4
1450.2.c.g.1101.6		16	435.173	even	4
1450.2.c.g.1101.11		16	435.347	even	4
1450.2.c.g.1101.12		16	15.8	even	4
2320.2.j.d.289.5		8	1740.1739	even	2
2320.2.j.d.289.6		8	12.11	even	2
2320.2.j.e.289.3		8	60.59	even	2
2320.2.j.e.289.4		8	348.347	even	2
2610.2.b.d.289.1		8	29.28	even	2
2610.2.b.d.289.2		8	5.4	even	2
2610.2.b.f.289.1		8	1.1	even	1	trivial
2610.2.b.f.289.2		8	145.144	even	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2610 = 2 \cdot 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2610.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.82635 - 1.29013i) q^{5} +2.99580i q^{7} +1.00000 q^{8} +(-1.82635 - 1.29013i) q^{10} -1.08988i q^{11} -1.37471i q^{13} +2.99580i q^{14} +1.00000 q^{16} -0.212256 q^{17} +6.70297i q^{19} +(-1.82635 - 1.29013i) q^{20} -1.08988i q^{22} +1.06384i q^{23} +(1.67114 + 4.71246i) q^{25} -1.37471i q^{26} +2.99580i q^{28} +(-2.49749 - 4.77101i) q^{29} +4.22738i q^{31} +1.00000 q^{32} -0.212256 q^{34} +(3.86496 - 5.47139i) q^{35} -5.72993 q^{37} +6.70297i q^{38} +(-1.82635 - 1.29013i) q^{40} +10.3731i q^{41} +10.8599 q^{43} -1.08988i q^{44} +1.06384i q^{46} -6.38765 q^{47} -1.97480 q^{49} +(1.67114 + 4.71246i) q^{50} -1.37471i q^{52} +10.0993i q^{53} +(-1.40608 + 1.99050i) q^{55} +2.99580i q^{56} +(-2.49749 - 4.77101i) q^{58} +5.28523 q^{59} -3.38530i q^{61} +4.22738i q^{62} +1.00000 q^{64} +(-1.77356 + 2.51071i) q^{65} +10.2314i q^{67} -0.212256 q^{68} +(3.86496 - 5.47139i) q^{70} +5.04538 q^{71} +3.51767 q^{73} -5.72993 q^{74} +6.70297i q^{76} +3.26505 q^{77} -8.85669i q^{79} +(-1.82635 - 1.29013i) q^{80} +10.3731i q^{82} +12.4112i q^{83} +(0.387654 + 0.273837i) q^{85} +10.8599 q^{86} -1.08988i q^{88} +2.95876i q^{89} +4.11836 q^{91} +1.06384i q^{92} -6.38765 q^{94} +(8.64769 - 12.2420i) q^{95} -16.0605 q^{97} -1.97480 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} + q^{5} + 8 q^{8} + q^{10} + 8 q^{16} - 2 q^{17} + q^{20} + 5 q^{25} + 4 q^{29} + 8 q^{32} - 2 q^{34} + 16 q^{37} + q^{40} + 8 q^{43} - 6 q^{47} - 6 q^{49} + 5 q^{50} + 11 q^{55}+ \cdots - 6 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^4 + q^5 + 8 * q^8 + q^10 + 8 * q^16 - 2 * q^17 + q^20 + 5 * q^25 + 4 * q^29 + 8 * q^32 - 2 * q^34 + 16 * q^37 + q^40 + 8 * q^43 - 6 * q^47 - 6 * q^49 + 5 * q^50 + 11 * q^55 + 4 * q^58 + 18 * q^59 + 8 * q^64 + 15 * q^65 - 2 * q^68 + 12 * q^71 - 34 * q^73 + 16 * q^74 + 40 * q^77 + q^80 - 42 * q^85 + 8 * q^86 - 20 * q^91 - 6 * q^94 - 10 * q^95 - 14 * q^97 - 6 * q^98

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