LMFDB - Embedded newform 1500.2.i.a.557.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(557,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("1500.557");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			557.3
Character	$\chi$	$=$	1500.557
Dual form			1500.2.i.a.1193.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.51726 + 0.835422i) q^{3} +(1.05575 + 1.05575i) q^{7} +(1.60414 - 2.53510i) q^{9} +O(q^{10})$	$q+(-1.51726 + 0.835422i) q^{3} +(1.05575 + 1.05575i) q^{7} +(1.60414 - 2.53510i) q^{9} -5.36443i q^{11} +(2.50979 - 2.50979i) q^{13} +(-4.79257 + 4.79257i) q^{17} +2.75159i q^{19} +(-2.48384 - 0.719849i) q^{21} +(-3.68934 - 3.68934i) q^{23} +(-0.316015 + 5.18653i) q^{27} -3.14208 q^{29} -9.41986 q^{31} +(4.48157 + 8.13923i) q^{33} +(3.00517 + 3.00517i) q^{37} +(-1.71126 + 5.90473i) q^{39} -10.8360i q^{41} +(-1.30996 + 1.30996i) q^{43} +(3.22241 - 3.22241i) q^{47} -4.77078i q^{49} +(3.26775 - 11.2754i) q^{51} +(0.347725 + 0.347725i) q^{53} +(-2.29874 - 4.17487i) q^{57} -4.13898 q^{59} +3.72055 q^{61} +(4.37001 - 0.982863i) q^{63} +(-8.11379 - 8.11379i) q^{67} +(8.67983 + 2.51552i) q^{69} -6.87034i q^{71} +(-1.19983 + 1.19983i) q^{73} +(5.66351 - 5.66351i) q^{77} -7.55468i q^{79} +(-3.85347 - 8.13331i) q^{81} +(-8.29515 - 8.29515i) q^{83} +(4.76734 - 2.62496i) q^{87} +17.1454 q^{89} +5.29942 q^{91} +(14.2923 - 7.86956i) q^{93} +(7.70248 + 7.70248i) q^{97} +(-13.5994 - 8.60530i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 12 q^{21} - 32 q^{31} + 100 q^{51} + 48 q^{61} + 52 q^{81} + 232 q^{91}+O(q^{100}) $ 32 * q - 12 * q^21 - 32 * q^31 + 100 * q^51 + 48 * q^61 + 52 * q^81 + 232 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.51726	+	0.835422i	−0.875989	+	0.482331i
$3$	−1.51726	+	0.835422i	−0.875989	+	0.482331i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.05575	+	1.05575i	0.399037	+	0.399037i	0.877893	−	0.478857i	$-0.158949\pi$
$7$	1.05575	+	1.05575i	0.399037	+	0.399037i	−0.478857	+	0.877893i	$0.658949\pi$
$8$		0			0
$9$	1.60414	−	2.53510i	0.534713	−	0.845034i
$10$		0			0
$11$		−	5.36443i		−	1.61744i	−0.588196	−	0.808719i	$-0.700161\pi$
$11$		−	5.36443i		−	1.61744i	0.588196	−	0.808719i	$-0.299839\pi$
$12$		0			0
$13$	2.50979	−	2.50979i	0.696090	−	0.696090i	−0.267475	−	0.963565i	$-0.586189\pi$
$13$	2.50979	−	2.50979i	0.696090	−	0.696090i	0.963565	+	0.267475i	$0.0861893\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.79257	+	4.79257i	−1.16237	+	1.16237i	−0.178414	+	0.983955i	$0.557097\pi$
$17$	−4.79257	+	4.79257i	−1.16237	+	1.16237i	−0.983955	+	0.178414i	$0.942903\pi$
$18$		0			0
$19$			2.75159i			0.631258i	0.948883	+	0.315629i	$0.102216\pi$
$19$			2.75159i			0.631258i	−0.948883	+	0.315629i	$0.897784\pi$
$20$		0			0
$21$	−2.48384	−	0.719849i	−0.542019	−	0.157084i
$22$		0			0
$23$	−3.68934	−	3.68934i	−0.769281	−	0.769281i	0.208699	−	0.977980i	$-0.433077\pi$
$23$	−3.68934	−	3.68934i	−0.769281	−	0.769281i	−0.977980	+	0.208699i	$0.933077\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.316015	+	5.18653i	−0.0608170	+	0.998149i
$28$		0			0
$29$	−3.14208			−0.583469			−0.291734	−	0.956499i	$-0.594232\pi$
$29$	−3.14208			−0.583469			−0.291734	+	0.956499i	$0.594232\pi$
$30$		0			0
$31$	−9.41986			−1.69186			−0.845928	−	0.533297i	$-0.820953\pi$
$31$	−9.41986			−1.69186			−0.845928	+	0.533297i	$0.820953\pi$
$32$		0			0
$33$	4.48157	+	8.13923i	0.780140	+	1.41686i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.00517	+	3.00517i	0.494047	+	0.494047i	0.909579	−	0.415532i	$-0.136405\pi$
$37$	3.00517	+	3.00517i	0.494047	+	0.494047i	−0.415532	+	0.909579i	$0.636405\pi$
$38$		0			0
$39$	−1.71126	+	5.90473i	−0.274021	+	0.945513i
$40$		0			0
$41$		−	10.8360i		−	1.69230i	−0.532947	−	0.846148i	$-0.678916\pi$
$41$		−	10.8360i		−	1.69230i	0.532947	−	0.846148i	$-0.321084\pi$
$42$		0			0
$43$	−1.30996	+	1.30996i	−0.199767	+	0.199767i	−0.799900	−	0.600133i	$-0.795114\pi$
$43$	−1.30996	+	1.30996i	−0.199767	+	0.199767i	0.600133	+	0.799900i	$0.295114\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.22241	−	3.22241i	0.470037	−	0.470037i	−0.431890	−	0.901926i	$-0.642153\pi$
$47$	3.22241	−	3.22241i	0.470037	−	0.470037i	0.901926	+	0.431890i	$0.142153\pi$
$48$		0			0
$49$		−	4.77078i		−	0.681540i
$50$		0			0
$51$	3.26775	−	11.2754i	0.457576	−	1.57887i
$52$		0			0
$53$	0.347725	+	0.347725i	0.0477638	+	0.0477638i	0.730585	−	0.682821i	$-0.239247\pi$
$53$	0.347725	+	0.347725i	0.0477638	+	0.0477638i	−0.682821	+	0.730585i	$0.739247\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.29874	−	4.17487i	−0.304475	−	0.552975i
$58$		0			0
$59$	−4.13898			−0.538849			−0.269425	−	0.963021i	$-0.586833\pi$
$59$	−4.13898			−0.538849			−0.269425	+	0.963021i	$0.586833\pi$
$60$		0			0
$61$	3.72055			0.476367			0.238184	−	0.971220i	$-0.423448\pi$
$61$	3.72055			0.476367			0.238184	+	0.971220i	$0.423448\pi$
$62$		0			0
$63$	4.37001	−	0.982863i	0.550569	−	0.123829i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−8.11379	−	8.11379i	−0.991257	−	0.991257i	0.00870492	−	0.999962i	$-0.497229\pi$
$67$	−8.11379	−	8.11379i	−0.991257	−	0.991257i	−0.999962	+	0.00870492i	$0.997229\pi$
$68$		0			0
$69$	8.67983	+	2.51552i	1.04493	+	0.302833i
$70$		0			0
$71$		−	6.87034i		−	0.815359i	−0.913125	−	0.407679i	$-0.866338\pi$
$71$		−	6.87034i		−	0.815359i	0.913125	−	0.407679i	$-0.133662\pi$
$72$		0			0
$73$	−1.19983	+	1.19983i	−0.140429	+	0.140429i	−0.773827	−	0.633397i	$-0.781660\pi$
$73$	−1.19983	+	1.19983i	−0.140429	+	0.140429i	0.633397	+	0.773827i	$0.281660\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.66351	−	5.66351i	0.645417	−	0.645417i
$78$		0			0
$79$		−	7.55468i		−	0.849968i	−0.905201	−	0.424984i	$-0.860280\pi$
$79$		−	7.55468i		−	0.849968i	0.905201	−	0.424984i	$-0.139720\pi$
$80$		0			0
$81$	−3.85347	−	8.13331i	−0.428163	−	0.903701i
$82$		0			0
$83$	−8.29515	−	8.29515i	−0.910511	−	0.910511i	0.0858016	−	0.996312i	$-0.472655\pi$
$83$	−8.29515	−	8.29515i	−0.910511	−	0.910511i	−0.996312	+	0.0858016i	$0.972655\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	4.76734	−	2.62496i	0.511112	−	0.281425i
$88$		0			0
$89$	17.1454			1.81741			0.908706	−	0.417437i	$-0.137072\pi$
$89$	17.1454			1.81741			0.908706	+	0.417437i	$0.137072\pi$
$90$		0			0
$91$	5.29942			0.555531
$92$		0			0
$93$	14.2923	−	7.86956i	1.48205	−	0.816035i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	7.70248	+	7.70248i	0.782068	+	0.782068i	0.980179	−	0.198112i	$-0.0634808\pi$
$97$	7.70248	+	7.70248i	0.782068	+	0.782068i	−0.198112	+	0.980179i	$0.563481\pi$
$98$		0			0
$99$	−13.5994	−	8.60530i	−1.36679	−	0.864865i
$100$		0			0
$101$		−	10.4893i		−	1.04373i	−0.853029	−	0.521864i	$-0.825237\pi$
$101$		−	10.4893i		−	1.04373i	0.853029	−	0.521864i	$-0.174763\pi$
$102$		0			0
$103$	−9.62286	+	9.62286i	−0.948168	+	0.948168i	−0.998721	−	0.0505529i	$-0.983902\pi$
$103$	−9.62286	+	9.62286i	−0.948168	+	0.948168i	0.0505529	+	0.998721i	$0.483902\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.132819	+	0.132819i	−0.0128401	+	0.0128401i	−0.713498	−	0.700658i	$-0.752890\pi$
$107$	−0.132819	+	0.132819i	−0.0128401	+	0.0128401i	0.700658	+	0.713498i	$0.252890\pi$
$108$		0			0
$109$			8.32624i			0.797509i	0.917058	+	0.398754i	$0.130557\pi$
$109$			8.32624i			0.797509i	−0.917058	+	0.398754i	$0.869443\pi$
$110$		0			0
$111$	−7.07020	−	2.04903i	−0.671074	−	0.194485i
$112$		0			0
$113$	−10.2412	−	10.2412i	−0.963409	−	0.963409i	0.0359451	−	0.999354i	$-0.488556\pi$
$113$	−10.2412	−	10.2412i	−0.963409	−	0.963409i	−0.999354	+	0.0359451i	$0.988556\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.33651	−	10.3886i	−0.216011	−	0.960428i
$118$		0			0
$119$	−10.1195			−0.927656
$120$		0			0
$121$	−17.7771			−1.61610
$122$		0			0
$123$	9.05262	+	16.4410i	0.816247	+	1.48243i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−11.3812	−	11.3812i	−1.00992	−	1.00992i	−0.999950	−	0.00996950i	$-0.996827\pi$
$127$	−11.3812	−	11.3812i	−1.00992	−	1.00992i	−0.00996950	−	0.999950i	$-0.503173\pi$
$128$		0			0
$129$	0.893175	−	3.08191i	0.0786397	−	0.271347i
$130$		0			0
$131$			7.06681i			0.617430i	0.951155	+	0.308715i	$0.0998989\pi$
$131$			7.06681i			0.617430i	−0.951155	+	0.308715i	$0.900101\pi$
$132$		0			0
$133$	−2.90500	+	2.90500i	−0.251895	+	0.251895i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.590772	−	0.590772i	0.0504730	−	0.0504730i	−0.681420	−	0.731893i	$-0.738637\pi$
$137$	0.590772	−	0.590772i	0.0504730	−	0.0504730i	0.731893	+	0.681420i	$0.238637\pi$
$138$		0			0
$139$			13.1515i			1.11549i	0.830011	+	0.557747i	$0.188334\pi$
$139$			13.1515i			1.11549i	−0.830011	+	0.557747i	$0.811666\pi$
$140$		0			0
$141$	−2.19715	+	7.58130i	−0.185034	+	0.638461i
$142$		0			0
$143$	−13.4636	−	13.4636i	−1.12588	−	1.12588i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3.98561	+	7.23850i	0.328728	+	0.597021i
$148$		0			0
$149$	5.57868			0.457023			0.228511	−	0.973541i	$-0.426614\pi$
$149$	5.57868			0.457023			0.228511	+	0.973541i	$0.426614\pi$
$150$		0			0
$151$	−0.114853			−0.00934659			−0.00467330	−	0.999989i	$-0.501488\pi$
$151$	−0.114853			−0.00934659			−0.00467330	+	0.999989i	$0.501488\pi$
$152$		0			0
$153$	4.46170	+	19.8376i	0.360707	+	1.60378i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−10.1232	−	10.1232i	−0.807921	−	0.807921i	0.176398	−	0.984319i	$-0.443555\pi$
$157$	−10.1232	−	10.1232i	−0.807921	−	0.807921i	−0.984319	+	0.176398i	$0.943555\pi$
$158$		0			0
$159$	−0.818086	−	0.237091i	−0.0648785	−	0.0188026i
$160$		0			0
$161$		−	7.79005i		−	0.613942i
$162$		0			0
$163$	10.6706	−	10.6706i	0.835783	−	0.835783i	−0.152518	−	0.988301i	$-0.548738\pi$
$163$	10.6706	−	10.6706i	0.835783	−	0.835783i	0.988301	+	0.152518i	$0.0487382\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10.6490	−	10.6490i	0.824041	−	0.824041i	−0.162644	−	0.986685i	$-0.552002\pi$
$167$	10.6490	−	10.6490i	0.824041	−	0.824041i	0.986685	+	0.162644i	$0.0520022\pi$
$168$		0			0
$169$			0.401935i			0.0309181i
$170$		0			0
$171$	6.97556	+	4.41394i	0.533434	+	0.337542i
$172$		0			0
$173$	0.435013	+	0.435013i	0.0330734	+	0.0330734i	0.723450	−	0.690377i	$-0.242555\pi$
$173$	0.435013	+	0.435013i	0.0330734	+	0.0330734i	−0.690377	+	0.723450i	$0.742555\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	6.27990	−	3.45779i	0.472026	−	0.259904i
$178$		0			0
$179$	−7.58679			−0.567063			−0.283532	−	0.958963i	$-0.591506\pi$
$179$	−7.58679			−0.567063			−0.283532	+	0.958963i	$0.591506\pi$
$180$		0			0
$181$	7.59257			0.564351			0.282176	−	0.959363i	$-0.408944\pi$
$181$	7.59257			0.564351			0.282176	+	0.959363i	$0.408944\pi$
$182$		0			0
$183$	−5.64503	+	3.10823i	−0.417292	+	0.229767i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	25.7094	+	25.7094i	1.88006	+	1.88006i
$188$		0			0
$189$	−5.80932	+	5.14206i	−0.422566	+	0.374030i
$190$		0			0
$191$		−	4.91066i		−	0.355323i	−0.984092	−	0.177661i	$-0.943147\pi$
$191$		−	4.91066i		−	0.355323i	0.984092	−	0.177661i	$-0.0568532\pi$
$192$		0			0
$193$	18.3811	−	18.3811i	1.32310	−	1.32310i	0.411846	−	0.911253i	$-0.364884\pi$
$193$	18.3811	−	18.3811i	1.32310	−	1.32310i	0.911253	−	0.411846i	$-0.135116\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.71657	+	6.71657i	−0.478536	+	0.478536i	−0.904663	−	0.426127i	$-0.859878\pi$
$197$	−6.71657	+	6.71657i	−0.478536	+	0.478536i	0.426127	+	0.904663i	$0.359878\pi$
$198$		0			0
$199$			0.0825425i			0.00585128i	0.999996	+	0.00292564i	$0.000931262\pi$
$199$			0.0825425i			0.00585128i	−0.999996	+	0.00292564i	$0.999069\pi$
$200$		0			0
$201$	19.0891	+	5.53227i	1.34644	+	0.390216i
$202$		0			0
$203$	−3.31725	−	3.31725i	−0.232825	−	0.232825i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−15.2711	+	3.43463i	−1.06141	+	0.238723i
$208$		0			0
$209$	14.7607			1.02102
$210$		0			0
$211$	15.0889			1.03876			0.519382	−	0.854542i	$-0.326162\pi$
$211$	15.0889			1.03876			0.519382	+	0.854542i	$0.326162\pi$
$212$		0			0
$213$	5.73963	+	10.4241i	0.393273	+	0.714245i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−9.94503	−	9.94503i	−0.675112	−	0.675112i
$218$		0			0
$219$	0.818086	−	2.82282i	0.0552812	−	0.190748i
$220$		0			0
$221$			24.0567i			1.61823i
$222$		0			0
$223$	3.66264	−	3.66264i	0.245268	−	0.245268i	−0.573757	−	0.819025i	$-0.694515\pi$
$223$	3.66264	−	3.66264i	0.245268	−	0.245268i	0.819025	+	0.573757i	$0.194515\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−16.4232	+	16.4232i	−1.09005	+	1.09005i	−0.0945253	+	0.995522i	$0.530133\pi$
$227$	−16.4232	+	16.4232i	−1.09005	+	1.09005i	−0.995522	+	0.0945253i	$0.969867\pi$
$228$		0			0
$229$		−	26.1344i		−	1.72701i	−0.504339	−	0.863506i	$-0.668264\pi$
$229$		−	26.1344i		−	1.72701i	0.504339	−	0.863506i	$-0.331736\pi$
$230$		0			0
$231$	−3.86158	+	13.3244i	−0.254073	+	0.876682i
$232$		0			0
$233$	−0.407782	−	0.407782i	−0.0267147	−	0.0267147i	0.693623	−	0.720338i	$-0.256013\pi$
$233$	−0.407782	−	0.407782i	−0.0267147	−	0.0267147i	−0.720338	+	0.693623i	$0.756013\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	6.31134	+	11.4624i	0.409966	+	0.744562i
$238$		0			0
$239$	−16.1595			−1.04527			−0.522636	−	0.852556i	$-0.675051\pi$
$239$	−16.1595			−1.04527			−0.522636	+	0.852556i	$0.675051\pi$
$240$		0			0
$241$	0.476850			0.0307166			0.0153583	−	0.999882i	$-0.495111\pi$
$241$	0.476850			0.0307166			0.0153583	+	0.999882i	$0.495111\pi$
$242$		0			0
$243$	12.6415	+	9.12106i	0.810950	+	0.585116i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	6.90591	+	6.90591i	0.439412	+	0.439412i
$248$		0			0
$249$	19.5158	+	5.65592i	1.23676	+	0.358430i
$250$		0			0
$251$			23.9243i			1.51009i	0.655675	+	0.755043i	$0.272384\pi$
$251$			23.9243i			1.51009i	−0.655675	+	0.755043i	$0.727616\pi$
$252$		0			0
$253$	−19.7912	+	19.7912i	−1.24426	+	1.24426i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.0938	+	10.0938i	−0.629636	+	0.629636i	−0.947976	−	0.318341i	$-0.896874\pi$
$257$	−10.0938	+	10.0938i	−0.629636	+	0.629636i	0.318341	+	0.947976i	$0.396874\pi$
$258$		0			0
$259$			6.34542i			0.394286i
$260$		0			0
$261$	−5.04033	+	7.96548i	−0.311989	+	0.493051i
$262$		0			0
$263$	−7.16000	−	7.16000i	−0.441504	−	0.441504i	0.451013	−	0.892517i	$-0.351063\pi$
$263$	−7.16000	−	7.16000i	−0.441504	−	0.441504i	−0.892517	+	0.451013i	$0.851063\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−26.0140	+	14.3237i	−1.59203	+	0.876594i
$268$		0			0
$269$	20.8893			1.27364			0.636822	−	0.771011i	$-0.280249\pi$
$269$	20.8893			1.27364			0.636822	+	0.771011i	$0.280249\pi$
$270$		0			0
$271$	2.08128			0.126429			0.0632143	−	0.998000i	$-0.479865\pi$
$271$	2.08128			0.126429			0.0632143	+	0.998000i	$0.479865\pi$
$272$		0			0
$273$	−8.04059	+	4.42726i	−0.486639	+	0.267950i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	10.1913	+	10.1913i	0.612335	+	0.612335i	0.943554	−	0.331219i	$-0.107460\pi$
$277$	10.1913	+	10.1913i	0.612335	+	0.612335i	−0.331219	+	0.943554i	$0.607460\pi$
$278$		0			0
$279$	−15.1108	+	23.8803i	−0.904658	+	1.42968i
$280$		0			0
$281$			8.85316i			0.528135i	0.964504	+	0.264068i	$0.0850642\pi$
$281$			8.85316i			0.528135i	−0.964504	+	0.264068i	$0.914936\pi$
$282$		0			0
$283$	−7.65052	+	7.65052i	−0.454776	+	0.454776i	−0.896936	−	0.442160i	$-0.854212\pi$
$283$	−7.65052	+	7.65052i	−0.454776	+	0.454776i	0.442160	+	0.896936i	$0.354212\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	11.4401	−	11.4401i	0.675288	−	0.675288i
$288$		0			0
$289$		−	28.9375i		−	1.70221i
$290$		0			0
$291$	−18.1215	−	5.25182i	−1.06230	−	0.307867i
$292$		0			0
$293$	−16.5842	−	16.5842i	−0.968858	−	0.968858i	0.0306711	−	0.999530i	$-0.490236\pi$
$293$	−16.5842	−	16.5842i	−0.968858	−	0.968858i	−0.999530	+	0.0306711i	$0.990236\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	27.8228	+	1.69524i	1.61444	+	0.0983677i
$298$		0			0
$299$	−18.5189			−1.07098
$300$		0			0
$301$	−2.76598			−0.159428
$302$		0			0
$303$	8.76302	+	15.9150i	0.503422	+	0.914294i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−1.09776	−	1.09776i	−0.0626522	−	0.0626522i	0.675086	−	0.737739i	$-0.264106\pi$
$307$	−1.09776	−	1.09776i	−0.0626522	−	0.0626522i	−0.737739	+	0.675086i	$0.764106\pi$
$308$		0			0
$309$	6.56121	−	22.6395i	0.373254	−	1.28792i
$310$		0			0
$311$			27.1988i			1.54230i	0.636654	+	0.771150i	$0.280318\pi$
$311$			27.1988i			1.54230i	−0.636654	+	0.771150i	$0.719682\pi$
$312$		0			0
$313$	17.2574	−	17.2574i	0.975444	−	0.975444i	−0.0242613	−	0.999706i	$-0.507723\pi$
$313$	17.2574	−	17.2574i	0.975444	−	0.975444i	0.999706	+	0.0242613i	$0.00772338\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−19.1703	+	19.1703i	−1.07671	+	1.07671i	−0.0799087	+	0.996802i	$0.525463\pi$
$317$	−19.1703	+	19.1703i	−1.07671	+	1.07671i	−0.996802	+	0.0799087i	$0.974537\pi$
$318$		0			0
$319$			16.8555i			0.943724i
$320$		0			0
$321$	0.0905609	−	0.312481i	0.00505462	−	0.0174410i
$322$		0			0
$323$	−13.1872	−	13.1872i	−0.733755	−	0.733755i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−6.95592	−	12.6330i	−0.384663	−	0.698609i
$328$		0			0
$329$	6.80413			0.375124
$330$		0			0
$331$	−4.87878			−0.268162			−0.134081	−	0.990970i	$-0.542808\pi$
$331$	−4.87878			−0.268162			−0.134081	+	0.990970i	$0.542808\pi$
$332$		0			0
$333$	12.4391	−	2.79769i	0.681660	−	0.153313i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.854739	−	0.854739i	−0.0465606	−	0.0465606i	0.683443	−	0.730004i	$-0.260482\pi$
$337$	−0.854739	−	0.854739i	−0.0465606	−	0.0465606i	−0.730004	+	0.683443i	$0.760482\pi$
$338$		0			0
$339$	24.0942	+	6.98280i	1.30862	+	0.379253i
$340$		0			0
$341$			50.5322i			2.73647i
$342$		0			0
$343$	12.4270	−	12.4270i	0.670996	−	0.670996i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	16.5114	−	16.5114i	0.886380	−	0.886380i	−0.107794	−	0.994173i	$-0.534379\pi$
$347$	16.5114	−	16.5114i	0.886380	−	0.886380i	0.994173	+	0.107794i	$0.0343786\pi$
$348$		0			0
$349$			31.2298i			1.67169i	0.548964	+	0.835846i	$0.315023\pi$
$349$			31.2298i			1.67169i	−0.548964	+	0.835846i	$0.684977\pi$
$350$		0			0
$351$	12.2240	+	13.8102i	0.652467	+	0.737135i
$352$		0			0
$353$	−16.2055	−	16.2055i	−0.862529	−	0.862529i	0.129102	−	0.991631i	$-0.458790\pi$
$353$	−16.2055	−	16.2055i	−0.862529	−	0.862529i	−0.991631	+	0.129102i	$0.958790\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	15.3539	−	8.45408i	0.812616	−	0.447437i
$358$		0			0
$359$	−27.5938			−1.45635			−0.728174	−	0.685393i	$-0.759631\pi$
$359$	−27.5938			−1.45635			−0.728174	+	0.685393i	$0.759631\pi$
$360$		0			0
$361$	11.4287			0.601513
$362$		0			0
$363$	26.9725	−	14.8514i	1.41569	−	0.779497i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−19.1487	−	19.1487i	−0.999553	−	0.999553i	0.000446897	−	1.00000i	$-0.499858\pi$
$367$	−19.1487	−	19.1487i	−0.999553	−	0.999553i	−1.00000		0.000446897i	$0.999858\pi$
$368$		0			0
$369$	−27.4703	−	17.3824i	−1.43005	−	0.904894i
$370$		0			0
$371$			0.734223i			0.0381190i
$372$		0			0
$373$	−23.4168	+	23.4168i	−1.21247	+	1.21247i	−0.242264	+	0.970210i	$0.577890\pi$
$373$	−23.4168	+	23.4168i	−1.21247	+	1.21247i	−0.970210	+	0.242264i	$0.922110\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−7.88594	+	7.88594i	−0.406147	+	0.406147i
$378$		0			0
$379$			7.72957i			0.397042i	0.980097	+	0.198521i	$0.0636137\pi$
$379$			7.72957i			0.397042i	−0.980097	+	0.198521i	$0.936386\pi$
$380$		0			0
$381$	26.7764	+	7.76012i	1.37179	+	0.397563i
$382$		0			0
$383$	23.6062	+	23.6062i	1.20622	+	1.20622i	0.972242	+	0.233976i	$0.0751738\pi$
$383$	23.6062	+	23.6062i	1.20622	+	1.20622i	0.233976	+	0.972242i	$0.424826\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.21952	+	5.42223i	0.0619916	+	0.275627i
$388$		0			0
$389$	−8.18514			−0.415003			−0.207502	−	0.978235i	$-0.566533\pi$
$389$	−8.18514			−0.415003			−0.207502	+	0.978235i	$0.566533\pi$
$390$		0			0
$391$	35.3629			1.78838
$392$		0			0
$393$	−5.90377	−	10.7222i	−0.297806	−	0.540862i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	6.88292	+	6.88292i	0.345444	+	0.345444i	0.858409	−	0.512965i	$-0.171453\pi$
$397$	6.88292	+	6.88292i	0.345444	+	0.345444i	−0.512965	+	0.858409i	$0.671453\pi$
$398$		0			0
$399$	1.98073	−	6.83452i	0.0991605	−	0.342154i
$400$		0			0
$401$		−	10.2267i		−	0.510695i	−0.966849	−	0.255347i	$-0.917810\pi$
$401$		−	10.2267i		−	0.510695i	0.966849	−	0.255347i	$-0.0821898\pi$
$402$		0			0
$403$	−23.6418	+	23.6418i	−1.17768	+	1.17768i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	16.1210	−	16.1210i	0.799090	−	0.799090i
$408$		0			0
$409$			29.9396i			1.48042i	0.672378	+	0.740208i	$0.265273\pi$
$409$			29.9396i			1.48042i	−0.672378	+	0.740208i	$0.734727\pi$
$410$		0			0
$411$	−0.402809	+	1.38990i	−0.0198691	+	0.0685585i
$412$		0			0
$413$	−4.36973	−	4.36973i	−0.215021	−	0.215021i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−10.9870	−	19.9542i	−0.538037	−	0.977160i
$418$		0			0
$419$	−4.20518			−0.205437			−0.102718	−	0.994710i	$-0.532754\pi$
$419$	−4.20518			−0.205437			−0.102718	+	0.994710i	$0.532754\pi$
$420$		0			0
$421$	14.0724			0.685846			0.342923	−	0.939364i	$-0.388583\pi$
$421$	14.0724			0.685846			0.342923	+	0.939364i	$0.388583\pi$
$422$		0			0
$423$	−2.99994	−	13.3383i	−0.145862	−	0.648532i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.92797	+	3.92797i	0.190088	+	0.190088i
$428$		0			0
$429$	31.6755	+	9.17995i	1.52931	+	0.443212i
$430$		0			0
$431$		−	19.6714i		−	0.947537i	−0.880649	−	0.473769i	$-0.842893\pi$
$431$		−	19.6714i		−	0.947537i	0.880649	−	0.473769i	$-0.157107\pi$
$432$		0			0
$433$	−18.5624	+	18.5624i	−0.892050	+	0.892050i	−0.994716	−	0.102666i	$-0.967263\pi$
$433$	−18.5624	+	18.5624i	−0.892050	+	0.892050i	0.102666	+	0.994716i	$0.467263\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	10.1516	−	10.1516i	0.485615	−	0.485615i
$438$		0			0
$439$		−	30.8707i		−	1.47338i	−0.676231	−	0.736689i	$-0.736388\pi$
$439$		−	30.8707i		−	1.47338i	0.676231	−	0.736689i	$-0.263612\pi$
$440$		0			0
$441$	−12.0944	−	7.65300i	−0.575924	−	0.364428i
$442$		0			0
$443$	17.2069	+	17.2069i	0.817523	+	0.817523i	0.985749	−	0.168225i	$-0.0538036\pi$
$443$	17.2069	+	17.2069i	0.817523	+	0.817523i	−0.168225	+	0.985749i	$0.553804\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−8.46429	+	4.66055i	−0.400347	+	0.220436i
$448$		0			0
$449$	12.6598			0.597453			0.298726	−	0.954339i	$-0.403438\pi$
$449$	12.6598			0.597453			0.298726	+	0.954339i	$0.403438\pi$
$450$		0			0
$451$	−58.1289			−2.73718
$452$		0			0
$453$	0.174261	−	0.0959506i	0.00818751	−	0.00450815i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−20.9120	−	20.9120i	−0.978220	−	0.978220i	0.0215478	−	0.999768i	$-0.493141\pi$
$457$	−20.9120	−	20.9120i	−0.978220	−	0.978220i	−0.999768	+	0.0215478i	$0.993141\pi$
$458$		0			0
$459$	−23.3423	−	26.3714i	−1.08953	−	1.23091i
$460$		0			0
$461$			22.0486i			1.02690i	0.858118	+	0.513452i	$0.171634\pi$
$461$			22.0486i			1.02690i	−0.858118	+	0.513452i	$0.828366\pi$
$462$		0			0
$463$	11.8425	−	11.8425i	0.550367	−	0.550367i	−0.376180	−	0.926547i	$-0.622762\pi$
$463$	11.8425	−	11.8425i	0.550367	−	0.550367i	0.926547	+	0.376180i	$0.122762\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.82588	+	7.82588i	−0.362139	+	0.362139i	−0.864600	−	0.502461i	$-0.832428\pi$
$467$	−7.82588	+	7.82588i	−0.362139	+	0.362139i	0.502461	+	0.864600i	$0.332428\pi$
$468$		0			0
$469$		−	17.1323i		−	0.791096i
$470$		0			0
$471$	23.8167	+	6.90237i	1.09741	+	0.318044i
$472$		0			0
$473$	7.02718	+	7.02718i	0.323110	+	0.323110i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.43932	−	0.323719i	0.0659019	−	0.0148221i
$478$		0			0
$479$	32.4902			1.48451			0.742257	−	0.670115i	$-0.233755\pi$
$479$	32.4902			1.48451			0.742257	+	0.670115i	$0.233755\pi$
$480$		0			0
$481$	15.0847			0.687802
$482$		0			0
$483$	6.50798	+	11.8195i	0.296123	+	0.537807i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	20.1604	+	20.1604i	0.913553	+	0.913553i	0.996550	−	0.0829964i	$-0.0264490\pi$
$487$	20.1604	+	20.1604i	0.913553	+	0.913553i	−0.0829964	+	0.996550i	$0.526449\pi$
$488$		0			0
$489$	−7.27556	+	25.1044i	−0.329012	+	1.13526i
$490$		0			0
$491$			7.99751i			0.360923i	0.983582	+	0.180461i	$0.0577590\pi$
$491$			7.99751i			0.360923i	−0.983582	+	0.180461i	$0.942241\pi$
$492$		0			0
$493$	15.0586	−	15.0586i	0.678206	−	0.678206i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.25337	−	7.25337i	0.325358	−	0.325358i
$498$		0			0
$499$		−	16.1515i		−	0.723039i	−0.932364	−	0.361520i	$-0.882258\pi$
$499$		−	16.1515i		−	0.723039i	0.932364	−	0.361520i	$-0.117742\pi$
$500$		0			0
$501$	−7.26084	+	25.0536i	−0.324390	+	1.11931i
$502$		0			0
$503$	20.1740	+	20.1740i	0.899516	+	0.899516i	0.995393	−	0.0958769i	$-0.0305655\pi$
$503$	20.1740	+	20.1740i	0.899516	+	0.899516i	−0.0958769	+	0.995393i	$0.530566\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.335785	−	0.609839i	−0.0149127	−	0.0270839i
$508$		0			0
$509$	26.4502			1.17239			0.586193	−	0.810172i	$-0.300626\pi$
$509$	26.4502			1.17239			0.586193	+	0.810172i	$0.300626\pi$
$510$		0			0
$511$	−2.53344			−0.112073
$512$		0			0
$513$	−14.2712	−	0.869543i	−0.630090	−	0.0383912i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−17.2864	−	17.2864i	−0.760255	−	0.760255i
$518$		0			0
$519$	−1.02345	−	0.296607i	−0.0449243	−	0.0130196i
$520$		0			0
$521$		−	28.4508i		−	1.24645i	−0.782041	−	0.623226i	$-0.785821\pi$
$521$		−	28.4508i		−	1.24645i	0.782041	−	0.623226i	$-0.214179\pi$
$522$		0			0
$523$	27.2736	−	27.2736i	1.19259	−	1.19259i	0.216254	−	0.976337i	$-0.430616\pi$
$523$	27.2736	−	27.2736i	1.19259	−	1.19259i	0.976337	−	0.216254i	$-0.0693840\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	45.1454	−	45.1454i	1.96656	−	1.96656i
$528$		0			0
$529$			4.22246i			0.183585i
$530$		0			0
$531$	−6.63950	+	10.4927i	−0.288130	+	0.455346i
$532$		0			0
$533$	−27.1960	−	27.1960i	−1.17799	−	1.17799i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	11.5111	−	6.33817i	0.496741	−	0.273512i
$538$		0			0
$539$	−25.5925			−1.10235
$540$		0			0
$541$	−8.79711			−0.378217			−0.189109	−	0.981956i	$-0.560560\pi$
$541$	−8.79711			−0.378217			−0.189109	+	0.981956i	$0.560560\pi$
$542$		0			0
$543$	−11.5199	+	6.34300i	−0.494365	+	0.272204i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−7.84963	−	7.84963i	−0.335626	−	0.335626i	0.519092	−	0.854718i	$-0.326270\pi$
$547$	−7.84963	−	7.84963i	−0.335626	−	0.335626i	−0.854718	+	0.519092i	$0.826270\pi$
$548$		0			0
$549$	5.96828	−	9.43196i	0.254720	−	0.402546i
$550$		0			0
$551$		−	8.64570i		−	0.368319i
$552$		0			0
$553$	7.97586	−	7.97586i	0.339168	−	0.339168i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−23.0351	+	23.0351i	−0.976029	+	0.976029i	−0.999719	−	0.0236902i	$-0.992458\pi$
$557$	−23.0351	+	23.0351i	−0.976029	+	0.976029i	0.0236902	+	0.999719i	$0.492458\pi$
$558$		0			0
$559$			6.57543i			0.278111i
$560$		0			0
$561$	−60.4861	−	17.5296i	−2.55372	−	0.740100i
$562$		0			0
$563$	−15.4247	−	15.4247i	−0.650072	−	0.650072i	0.302938	−	0.953010i	$-0.402033\pi$
$563$	−15.4247	−	15.4247i	−0.650072	−	0.650072i	−0.953010	+	0.302938i	$0.902033\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	4.51845	−	12.6551i	0.189757	−	0.531463i
$568$		0			0
$569$	−0.584046			−0.0244845			−0.0122422	−	0.999925i	$-0.503897\pi$
$569$	−0.584046			−0.0244845			−0.0122422	+	0.999925i	$0.503897\pi$
$570$		0			0
$571$	5.69247			0.238222			0.119111	−	0.992881i	$-0.461996\pi$
$571$	5.69247			0.238222			0.119111	+	0.992881i	$0.461996\pi$
$572$		0			0
$573$	4.10247	+	7.45073i	0.171383	+	0.311259i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	4.97443	+	4.97443i	0.207088	+	0.207088i	0.803029	−	0.595940i	$-0.203221\pi$
$577$	4.97443	+	4.97443i	0.207088	+	0.207088i	−0.595940	+	0.803029i	$0.703221\pi$
$578$		0			0
$579$	−12.5329	+	43.2448i	−0.520848	+	1.79719i
$580$		0			0
$581$		−	17.5152i		−	0.726654i
$582$		0			0
$583$	1.86535	−	1.86535i	0.0772549	−	0.0772549i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.00375	+	2.00375i	−0.0827036	+	0.0827036i	−0.747248	−	0.664545i	$-0.768625\pi$
$587$	−2.00375	+	2.00375i	−0.0827036	+	0.0827036i	0.664545	+	0.747248i	$0.268625\pi$
$588$		0			0
$589$		−	25.9196i		−	1.06800i
$590$		0			0
$591$	4.57960	−	15.8019i	0.188379	−	0.650005i
$592$		0			0
$593$	2.29289	+	2.29289i	0.0941577	+	0.0941577i	0.752617	−	0.658459i	$-0.228791\pi$
$593$	2.29289	+	2.29289i	0.0941577	+	0.0941577i	−0.658459	+	0.752617i	$0.728791\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.0689578	−	0.125238i	−0.00282226	−	0.00512566i
$598$		0			0
$599$	−3.30110			−0.134879			−0.0674395	−	0.997723i	$-0.521483\pi$
$599$	−3.30110			−0.134879			−0.0674395	+	0.997723i	$0.521483\pi$
$600$		0			0
$601$	−27.1115			−1.10590			−0.552951	−	0.833214i	$-0.686498\pi$
$601$	−27.1115			−1.10590			−0.552951	+	0.833214i	$0.686498\pi$
$602$		0			0
$603$	−33.5849	+	7.55362i	−1.36768	+	0.307607i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−0.725530	−	0.725530i	−0.0294483	−	0.0294483i	0.692229	−	0.721678i	$-0.256629\pi$
$607$	−0.725530	−	0.725530i	−0.0294483	−	0.0294483i	−0.721678	+	0.692229i	$0.756629\pi$
$608$		0			0
$609$	7.80443	+	2.26182i	0.316251	+	0.0916535i
$610$		0			0
$611$		−	16.1751i		−	0.654376i
$612$		0			0
$613$	−2.54878	+	2.54878i	−0.102944	+	0.102944i	−0.756703	−	0.653759i	$-0.773191\pi$
$613$	−2.54878	+	2.54878i	−0.102944	+	0.102944i	0.653759	+	0.756703i	$0.273191\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	13.7733	−	13.7733i	0.554493	−	0.554493i	−0.373241	−	0.927734i	$-0.621754\pi$
$617$	13.7733	−	13.7733i	0.554493	−	0.554493i	0.927734	+	0.373241i	$0.121754\pi$
$618$		0			0
$619$		−	5.31656i		−	0.213691i	−0.994276	−	0.106845i	$-0.965925\pi$
$619$		−	5.31656i		−	0.213691i	0.994276	−	0.106845i	$-0.0340750\pi$
$620$		0			0
$621$	20.3008	−	17.9690i	0.814642	−	0.721071i
$622$		0			0
$623$	18.1013	+	18.1013i	0.725214	+	0.725214i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−22.3958	+	12.3314i	−0.894403	+	0.492470i
$628$		0			0
$629$	−28.8050			−1.14853
$630$		0			0
$631$	14.9595			0.595529			0.297765	−	0.954639i	$-0.403759\pi$
$631$	14.9595			0.595529			0.297765	+	0.954639i	$0.403759\pi$
$632$		0			0
$633$	−22.8938	+	12.6056i	−0.909945	+	0.501028i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−11.9736	−	11.9736i	−0.474413	−	0.474413i
$638$		0			0
$639$	−17.4170	−	11.0210i	−0.689005	−	0.435983i
$640$		0			0
$641$		−	43.0294i		−	1.69956i	−0.527139	−	0.849779i	$-0.676735\pi$
$641$		−	43.0294i		−	1.69956i	0.527139	−	0.849779i	$-0.323265\pi$
$642$		0			0
$643$	4.86447	−	4.86447i	0.191836	−	0.191836i	−0.604653	−	0.796489i	$-0.706688\pi$
$643$	4.86447	−	4.86447i	0.191836	−	0.191836i	0.796489	+	0.604653i	$0.206688\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−30.8140	+	30.8140i	−1.21142	+	1.21142i	−0.240866	+	0.970558i	$0.577431\pi$
$647$	−30.8140	+	30.8140i	−1.21142	+	1.21142i	−0.970558	+	0.240866i	$0.922569\pi$
$648$		0			0
$649$			22.2033i			0.871555i
$650$		0			0
$651$	23.3975	+	6.78087i	0.917019	+	0.265763i
$652$		0			0
$653$	29.4625	+	29.4625i	1.15296	+	1.15296i	0.985957	+	0.167002i	$0.0534086\pi$
$653$	29.4625	+	29.4625i	1.15296	+	1.15296i	0.167002	+	0.985957i	$0.446591\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	1.11699	+	4.96638i	0.0435781	+	0.193757i
$658$		0			0
$659$	21.5130			0.838026			0.419013	−	0.907980i	$-0.362376\pi$
$659$	21.5130			0.838026			0.419013	+	0.907980i	$0.362376\pi$
$660$		0			0
$661$	32.8754			1.27871			0.639353	−	0.768913i	$-0.279202\pi$
$661$	32.8754			1.27871			0.639353	+	0.768913i	$0.279202\pi$
$662$		0			0
$663$	−20.0975	−	36.5002i	−0.780521	−	1.41755i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	11.5922	+	11.5922i	0.448851	+	0.448851i
$668$		0			0
$669$	−2.49732	+	8.61701i	−0.0965518	+	0.333153i
$670$		0			0
$671$		−	19.9586i		−	0.770494i
$672$		0			0
$673$	−20.0746	+	20.0746i	−0.773817	+	0.773817i	−0.978772	−	0.204954i	$-0.934295\pi$
$673$	−20.0746	+	20.0746i	−0.773817	+	0.773817i	0.204954	+	0.978772i	$0.434295\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−23.7207	+	23.7207i	−0.911662	+	0.911662i	−0.996403	−	0.0847414i	$-0.972994\pi$
$677$	−23.7207	+	23.7207i	−0.911662	+	0.911662i	0.0847414	+	0.996403i	$0.472994\pi$
$678$		0			0
$679$			16.2638i			0.624147i
$680$		0			0
$681$	11.1979	−	38.6386i	0.429106	−	1.48063i
$682$		0			0
$683$	−11.5593	−	11.5593i	−0.442305	−	0.442305i	0.450481	−	0.892786i	$-0.351252\pi$
$683$	−11.5593	−	11.5593i	−0.442305	−	0.442305i	−0.892786	+	0.450481i	$0.851252\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	21.8333	+	39.6526i	0.832991	+	1.51284i
$688$		0			0
$689$	1.74543			0.0664957
$690$		0			0
$691$	10.3522			0.393816			0.196908	−	0.980422i	$-0.436910\pi$
$691$	10.3522			0.393816			0.196908	+	0.980422i	$0.436910\pi$
$692$		0			0
$693$	−5.27250	−	23.4426i	−0.200286	−	0.890512i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	51.9323	+	51.9323i	1.96707	+	1.96707i
$698$		0			0
$699$	0.959380	+	0.278040i	0.0362871	+	0.0105164i
$700$		0			0
$701$			17.1863i			0.649119i	0.945865	+	0.324560i	$0.105216\pi$
$701$			17.1863i			0.649119i	−0.945865	+	0.324560i	$0.894784\pi$
$702$		0			0
$703$	−8.26900	+	8.26900i	−0.311871	+	0.311871i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	11.0741	−	11.0741i	0.416486	−	0.416486i
$708$		0			0
$709$			9.73580i			0.365636i	0.983147	+	0.182818i	$0.0585219\pi$
$709$			9.73580i			0.365636i	−0.983147	+	0.182818i	$0.941478\pi$
$710$		0			0
$711$	−19.1519	−	12.1188i	−0.718251	−	0.454489i
$712$		0			0
$713$	34.7531	+	34.7531i	1.30151	+	1.30151i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	24.5181	−	13.5000i	0.915646	−	0.504167i
$718$		0			0
$719$	21.0470			0.784921			0.392461	−	0.919769i	$-0.371624\pi$
$719$	21.0470			0.784921			0.392461	+	0.919769i	$0.371624\pi$
$720$		0			0
$721$	−20.3187			−0.756708
$722$		0			0
$723$	−0.723504	+	0.398371i	−0.0269074	+	0.0148156i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−27.6156	−	27.6156i	−1.02421	−	1.02421i	−0.999700	−	0.0245068i	$-0.992198\pi$
$727$	−27.6156	−	27.6156i	−1.02421	−	1.02421i	−0.0245068	−	0.999700i	$-0.507802\pi$
$728$		0			0
$729$	−26.8003	−	3.27804i	−0.992603	−	0.121409i
$730$		0			0
$731$		−	12.5561i		−	0.464405i
$732$		0			0
$733$	26.4480	−	26.4480i	0.976879	−	0.976879i	−0.0228597	−	0.999739i	$-0.507277\pi$
$733$	26.4480	−	26.4480i	0.976879	−	0.976879i	0.999739	+	0.0228597i	$0.00727710\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−43.5259	+	43.5259i	−1.60330	+	1.60330i
$738$		0			0
$739$			1.90172i			0.0699559i	0.999388	+	0.0349779i	$0.0111361\pi$
$739$			1.90172i			0.0699559i	−0.999388	+	0.0349779i	$0.988864\pi$
$740$		0			0
$741$	−16.2474	−	4.70869i	−0.596863	−	0.172978i
$742$		0			0
$743$	1.31527	+	1.31527i	0.0482527	+	0.0482527i	0.730821	−	0.682569i	$-0.239137\pi$
$743$	1.31527	+	1.31527i	0.0482527	+	0.0482527i	−0.682569	+	0.730821i	$0.739137\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−34.3356	+	7.72245i	−1.25627	+	0.282550i
$748$		0			0
$749$	−0.280448			−0.0102474
$750$		0			0
$751$	−37.0085			−1.35046			−0.675230	−	0.737608i	$-0.735955\pi$
$751$	−37.0085			−1.35046			−0.675230	+	0.737608i	$0.735955\pi$
$752$		0			0
$753$	−19.9869	−	36.2993i	−0.728362	−	1.32282i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	15.0860	+	15.0860i	0.548308	+	0.548308i	0.925951	−	0.377643i	$-0.123265\pi$
$757$	15.0860	+	15.0860i	0.548308	+	0.548308i	−0.377643	+	0.925951i	$0.623265\pi$
$758$		0			0
$759$	13.4944	−	46.5624i	0.489814	−	1.69011i
$760$		0			0
$761$		−	43.9192i		−	1.59207i	−0.605252	−	0.796034i	$-0.706928\pi$
$761$		−	43.9192i		−	1.59207i	0.605252	−	0.796034i	$-0.293072\pi$
$762$		0			0
$763$	−8.79044	+	8.79044i	−0.318235	+	0.318235i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−10.3880	+	10.3880i	−0.375087	+	0.375087i
$768$		0			0
$769$		−	13.7444i		−	0.495637i	−0.968806	−	0.247819i	$-0.920286\pi$
$769$		−	13.7444i		−	0.495637i	0.968806	−	0.247819i	$-0.0797137\pi$
$770$		0			0
$771$	6.88233	−	23.7475i	0.247861	−	0.855247i
$772$		0			0
$773$	12.2220	+	12.2220i	0.439594	+	0.439594i	0.891875	−	0.452281i	$-0.149390\pi$
$773$	12.2220	+	12.2220i	0.439594	+	0.439594i	−0.452281	+	0.891875i	$0.649390\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−5.30111	−	9.62764i	−0.190176	−	0.345390i
$778$		0			0
$779$	29.8162			1.06828
$780$		0			0
$781$	−36.8555			−1.31879
$782$		0			0
$783$	0.992941	−	16.2965i	0.0354848	−	0.582389i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	6.67770	+	6.67770i	0.238034	+	0.238034i	0.816036	−	0.578001i	$-0.196167\pi$
$787$	6.67770	+	6.67770i	0.238034	+	0.238034i	−0.578001	+	0.816036i	$0.696167\pi$
$788$		0			0
$789$	16.8452	+	4.88194i	0.599704	+	0.173802i
$790$		0			0
$791$		−	21.6243i		−	0.768871i
$792$		0			0
$793$	9.33778	−	9.33778i	0.331594	−	0.331594i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	13.9958	−	13.9958i	0.495756	−	0.495756i	−0.414358	−	0.910114i	$-0.635994\pi$
$797$	13.9958	−	13.9958i	0.495756	−	0.495756i	0.910114	+	0.414358i	$0.135994\pi$
$798$		0			0
$799$			30.8873i			1.09271i
$800$		0			0
$801$	27.5037	−	43.4654i	0.971794	−	1.53577i
$802$		0			0
$803$	6.43641	+	6.43641i	0.227136	+	0.227136i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−31.6945	+	17.4514i	−1.11570	+	0.614318i
$808$		0			0
$809$	−48.9116			−1.71964			−0.859821	−	0.510596i	$-0.829425\pi$
$809$	−48.9116			−1.71964			−0.859821	+	0.510596i	$0.829425\pi$
$810$		0			0
$811$	9.91061			0.348009			0.174004	−	0.984745i	$-0.444329\pi$
$811$	9.91061			0.348009			0.174004	+	0.984745i	$0.444329\pi$
$812$		0			0
$813$	−3.15783	+	1.73874i	−0.110750	+	0.0609804i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−3.60447	−	3.60447i	−0.126104	−	0.126104i
$818$		0			0
$819$	8.50102	−	13.4346i	0.297050	−	0.469442i
$820$		0			0
$821$			31.3930i			1.09562i	0.836602	+	0.547811i	$0.184539\pi$
$821$			31.3930i			1.09562i	−0.836602	+	0.547811i	$0.815461\pi$
$822$		0			0
$823$	−14.4174	+	14.4174i	−0.502560	+	0.502560i	−0.912233	−	0.409673i	$-0.865643\pi$
$823$	−14.4174	+	14.4174i	−0.502560	+	0.502560i	0.409673	+	0.912233i	$0.365643\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−2.76302	+	2.76302i	−0.0960795	+	0.0960795i	−0.753513	−	0.657433i	$-0.771642\pi$
$827$	−2.76302	+	2.76302i	−0.0960795	+	0.0960795i	0.657433	+	0.753513i	$0.271642\pi$
$828$		0			0
$829$		−	31.5824i		−	1.09690i	−0.836183	−	0.548450i	$-0.815218\pi$
$829$		−	31.5824i		−	1.09690i	0.836183	−	0.548450i	$-0.184782\pi$
$830$		0			0
$831$	−23.9768	−	6.94878i	−0.831747	−	0.241050i
$832$		0			0
$833$	22.8643	+	22.8643i	0.792201	+	0.792201i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.97681	−	48.8564i	0.102894	−	1.68872i
$838$		0			0
$839$	12.0505			0.416028			0.208014	−	0.978126i	$-0.433300\pi$
$839$	12.0505			0.416028			0.208014	+	0.978126i	$0.433300\pi$
$840$		0			0
$841$	−19.1274			−0.659564
$842$		0			0
$843$	−7.39613	−	13.4325i	−0.254736	−	0.462641i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−18.7682	−	18.7682i	−0.644884	−	0.644884i
$848$		0			0
$849$	5.21639	−	17.9992i	0.179026	−	0.617732i
$850$		0			0
$851$		−	22.1742i		−	0.760121i
$852$		0			0
$853$	23.5979	−	23.5979i	0.807978	−	0.807978i	−0.176350	−	0.984328i	$-0.556429\pi$
$853$	23.5979	−	23.5979i	0.807978	−	0.807978i	0.984328	+	0.176350i	$0.0564290\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2.51855	+	2.51855i	−0.0860319	+	0.0860319i	−0.748813	−	0.662781i	$-0.769376\pi$
$857$	−2.51855	+	2.51855i	−0.0860319	+	0.0860319i	0.662781	+	0.748813i	$0.269376\pi$
$858$		0			0
$859$			18.2203i			0.621668i	0.950464	+	0.310834i	$0.100608\pi$
$859$			18.2203i			0.621668i	−0.950464	+	0.310834i	$0.899392\pi$
$860$		0			0
$861$	−7.80027	+	26.9149i	−0.265833	+	0.917258i
$862$		0			0
$863$	22.0844	+	22.0844i	0.751763	+	0.751763i	0.974808	−	0.223045i	$-0.0715998\pi$
$863$	22.0844	+	22.0844i	0.751763	+	0.751763i	−0.223045	+	0.974808i	$0.571600\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	24.1750	+	43.9057i	0.821027	+	1.49111i
$868$		0			0
$869$	−40.5266			−1.37477
$870$		0			0
$871$	−40.7278			−1.38001
$872$		0			0
$873$	31.8824	−	7.17070i	1.07906	−	0.242691i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	26.8814	+	26.8814i	0.907719	+	0.907719i	0.996088	−	0.0883686i	$-0.0281653\pi$
$877$	26.8814	+	26.8814i	0.907719	+	0.907719i	−0.0883686	+	0.996088i	$0.528165\pi$
$878$		0			0
$879$	39.0173	+	11.3077i	1.31602	+	0.381399i
$880$		0			0
$881$		−	21.6378i		−	0.728998i	−0.931204	−	0.364499i	$-0.881240\pi$
$881$		−	21.6378i		−	0.728998i	0.931204	−	0.364499i	$-0.118760\pi$
$882$		0			0
$883$	−12.7073	+	12.7073i	−0.427634	+	0.427634i	−0.887822	−	0.460188i	$-0.847782\pi$
$883$	−12.7073	+	12.7073i	−0.427634	+	0.427634i	0.460188	+	0.887822i	$0.347782\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	36.7681	−	36.7681i	1.23455	−	1.23455i	0.272356	−	0.962197i	$-0.412197\pi$
$887$	36.7681	−	36.7681i	1.23455	−	1.23455i	0.962197	−	0.272356i	$-0.0878028\pi$
$888$		0			0
$889$		−	24.0315i		−	0.805990i
$890$		0			0
$891$	−43.6306	+	20.6717i	−1.46168	+	0.692527i
$892$		0			0
$893$	8.86676	+	8.86676i	0.296715	+	0.296715i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	28.0980	−	15.4711i	0.938164	−	0.516565i
$898$		0			0
$899$	29.5979			0.987145
$900$		0			0
$901$	−3.33300			−0.111038
$902$		0			0
$903$	4.19670	−	2.31076i	0.139658	−	0.0768973i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−1.52831	−	1.52831i	−0.0507468	−	0.0507468i	0.681278	−	0.732025i	$-0.261424\pi$
$907$	−1.52831	−	1.52831i	−0.0507468	−	0.0507468i	−0.732025	+	0.681278i	$0.761424\pi$
$908$		0			0
$909$	−26.5915	−	16.8264i	−0.881985	−	0.558095i
$910$		0			0
$911$		−	14.7675i		−	0.489269i	−0.969615	−	0.244635i	$-0.921332\pi$
$911$		−	14.7675i		−	0.489269i	0.969615	−	0.244635i	$-0.0786680\pi$
$912$		0			0
$913$	−44.4988	+	44.4988i	−1.47269	+	1.47269i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−7.46080	+	7.46080i	−0.246377	+	0.246377i
$918$		0			0
$919$			41.7950i			1.37869i	0.724433	+	0.689345i	$0.242102\pi$
$919$			41.7950i			1.37869i	−0.724433	+	0.689345i	$0.757898\pi$
$920$		0			0
$921$	2.58267	+	0.748488i	0.0851017	+	0.0246635i
$922$		0			0
$923$	−17.2431	−	17.2431i	−0.567563	−	0.567563i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	8.95850	+	39.8313i	0.294236	+	1.30823i
$928$		0			0
$929$	0.468082			0.0153573			0.00767863	−	0.999971i	$-0.497556\pi$
$929$	0.468082			0.0153573			0.00767863	+	0.999971i	$0.497556\pi$
$930$		0			0
$931$	13.1272			0.430227
$932$		0			0
$933$	−22.7224	−	41.2675i	−0.743899	−	1.35104i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−29.4650	−	29.4650i	−0.962578	−	0.962578i	0.0367464	−	0.999325i	$-0.488301\pi$
$937$	−29.4650	−	29.4650i	−0.962578	−	0.962578i	−0.999325	+	0.0367464i	$0.988301\pi$
$938$		0			0
$939$	−11.7667	+	40.6011i	−0.383991	+	1.32497i
$940$		0			0
$941$		−	7.77228i		−	0.253369i	−0.991943	−	0.126685i	$-0.959566\pi$
$941$		−	7.77228i		−	0.253369i	0.991943	−	0.126685i	$-0.0404336\pi$
$942$		0			0
$943$	−39.9776	+	39.9776i	−1.30185	+	1.30185i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	22.7465	−	22.7465i	0.739163	−	0.739163i	−0.233253	−	0.972416i	$-0.574937\pi$
$947$	22.7465	−	22.7465i	0.739163	−	0.739163i	0.972416	+	0.233253i	$0.0749370\pi$
$948$		0			0
$949$			6.02264i			0.195503i
$950$		0			0
$951$	13.0710	−	45.1016i	0.423856	−	1.46252i
$952$		0			0
$953$	2.75462	+	2.75462i	0.0892309	+	0.0892309i	0.750313	−	0.661082i	$-0.229903\pi$
$953$	2.75462	+	2.75462i	0.0892309	+	0.0892309i	−0.661082	+	0.750313i	$0.729903\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−14.0814	−	25.5741i	−0.455188	−	0.826692i
$958$		0			0
$959$	1.24742			0.0402812
$960$		0			0
$961$	57.7337			1.86238
$962$		0			0
$963$	0.123650	+	0.549771i	0.00398455	+	0.0177161i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	13.1302	+	13.1302i	0.422240	+	0.422240i	0.885974	−	0.463735i	$-0.153491\pi$
$967$	13.1302	+	13.1302i	0.422240	+	0.422240i	−0.463735	+	0.885974i	$0.653491\pi$
$968$		0			0
$969$	31.0253	+	8.99150i	0.996675	+	0.288849i
$970$		0			0
$971$		−	47.3723i		−	1.52025i	−0.649776	−	0.760125i	$-0.725137\pi$
$971$		−	47.3723i		−	1.52025i	0.649776	−	0.760125i	$-0.274863\pi$
$972$		0			0
$973$	−13.8847	+	13.8847i	−0.445123	+	0.445123i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.897303	−	0.897303i	0.0287073	−	0.0287073i	−0.692607	−	0.721315i	$-0.743538\pi$
$977$	0.897303	−	0.897303i	0.0287073	−	0.0287073i	0.721315	+	0.692607i	$0.243538\pi$
$978$		0			0
$979$		−	91.9755i		−	2.93955i
$980$		0			0
$981$	21.1079	+	13.3565i	0.673922	+	0.426439i
$982$		0			0
$983$	29.0539	+	29.0539i	0.926676	+	0.926676i	0.997490	−	0.0708140i	$-0.0225597\pi$
$983$	29.0539	+	29.0539i	0.926676	+	0.926676i	−0.0708140	+	0.997490i	$0.522560\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−10.3236	+	5.68432i	−0.328604	+	0.180934i
$988$		0			0
$989$	9.66576			0.307353
$990$		0			0
$991$	56.3697			1.79064			0.895321	−	0.445421i	$-0.146946\pi$
$991$	56.3697			1.79064			0.895321	+	0.445421i	$0.146946\pi$
$992$		0			0
$993$	7.40237	−	4.07584i	0.234907	−	0.129343i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−17.9840	−	17.9840i	−0.569560	−	0.569560i	0.362445	−	0.932005i	$-0.381942\pi$
$997$	−17.9840	−	17.9840i	−0.569560	−	0.569560i	−0.932005	+	0.362445i	$0.881942\pi$
$998$		0			0
$999$	−16.5361	+	14.6367i	−0.523179	+	0.463086i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.i.a.557.3	✓	32
3.2	odd	2	inner	1500.2.i.a.557.6	yes	32
5.2	odd	4	inner	1500.2.i.a.1193.11	yes	32
5.3	odd	4	inner	1500.2.i.a.1193.6	yes	32
5.4	even	2	inner	1500.2.i.a.557.14	yes	32
15.2	even	4	inner	1500.2.i.a.1193.14	yes	32
15.8	even	4	inner	1500.2.i.a.1193.3	yes	32
15.14	odd	2	inner	1500.2.i.a.557.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1500.2.i.a.557.3	✓	32	1.1	even	1	trivial
1500.2.i.a.557.6	yes	32	3.2	odd	2	inner
1500.2.i.a.557.11	yes	32	15.14	odd	2	inner
1500.2.i.a.557.14	yes	32	5.4	even	2	inner
1500.2.i.a.1193.3	yes	32	15.8	even	4	inner
1500.2.i.a.1193.6	yes	32	5.3	odd	4	inner
1500.2.i.a.1193.11	yes	32	5.2	odd	4	inner
1500.2.i.a.1193.14	yes	32	15.2	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.51726 + 0.835422i) q^{3} +(1.05575 + 1.05575i) q^{7} +(1.60414 - 2.53510i) q^{9} +O(q^{10})\)	\(q+(-1.51726 + 0.835422i) q^{3} +(1.05575 + 1.05575i) q^{7} +(1.60414 - 2.53510i) q^{9} -5.36443i q^{11} +(2.50979 - 2.50979i) q^{13} +(-4.79257 + 4.79257i) q^{17} +2.75159i q^{19} +(-2.48384 - 0.719849i) q^{21} +(-3.68934 - 3.68934i) q^{23} +(-0.316015 + 5.18653i) q^{27} -3.14208 q^{29} -9.41986 q^{31} +(4.48157 + 8.13923i) q^{33} +(3.00517 + 3.00517i) q^{37} +(-1.71126 + 5.90473i) q^{39} -10.8360i q^{41} +(-1.30996 + 1.30996i) q^{43} +(3.22241 - 3.22241i) q^{47} -4.77078i q^{49} +(3.26775 - 11.2754i) q^{51} +(0.347725 + 0.347725i) q^{53} +(-2.29874 - 4.17487i) q^{57} -4.13898 q^{59} +3.72055 q^{61} +(4.37001 - 0.982863i) q^{63} +(-8.11379 - 8.11379i) q^{67} +(8.67983 + 2.51552i) q^{69} -6.87034i q^{71} +(-1.19983 + 1.19983i) q^{73} +(5.66351 - 5.66351i) q^{77} -7.55468i q^{79} +(-3.85347 - 8.13331i) q^{81} +(-8.29515 - 8.29515i) q^{83} +(4.76734 - 2.62496i) q^{87} +17.1454 q^{89} +5.29942 q^{91} +(14.2923 - 7.86956i) q^{93} +(7.70248 + 7.70248i) q^{97} +(-13.5994 - 8.60530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 12 q^{21} - 32 q^{31} + 100 q^{51} + 48 q^{61} + 52 q^{81} + 232 q^{91}+O(q^{100}) \) 32 * q - 12 * q^21 - 32 * q^31 + 100 * q^51 + 48 * q^61 + 52 * q^81 + 232 * q^91

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