LMFDB - Embedded newform 3024.2.t.k.1873.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(289,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))

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

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

chi := DirichletCharacter("3024.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.t (of order $3$, degree $2$, not 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:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1873.6
Character	$\chi$	$=$	3024.1873
Dual form			3024.2.t.k.289.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0619693 q^{5} +(1.63689 + 2.07860i) q^{7} +O(q^{10})$	$q+0.0619693 q^{5} +(1.63689 + 2.07860i) q^{7} -3.18053 q^{11} +(-0.252417 + 0.437198i) q^{13} +(0.554700 - 0.960769i) q^{17} +(-0.933573 - 1.61700i) q^{19} -6.20496 q^{23} -4.99616 q^{25} +(-2.39645 - 4.15077i) q^{29} +(-1.26858 - 2.19724i) q^{31} +(0.101437 + 0.128809i) q^{35} +(-4.26085 - 7.38001i) q^{37} +(4.94516 - 8.56527i) q^{41} +(3.95574 + 6.85154i) q^{43} +(-3.29168 + 5.70136i) q^{47} +(-1.64116 + 6.80489i) q^{49} +(1.58258 - 2.74112i) q^{53} -0.197095 q^{55} +(-4.50652 - 7.80552i) q^{59} +(6.94094 - 12.0221i) q^{61} +(-0.0156421 + 0.0270929i) q^{65} +(1.66642 + 2.88632i) q^{67} +2.25651 q^{71} +(2.07503 - 3.59406i) q^{73} +(-5.20619 - 6.61106i) q^{77} +(-1.48925 + 2.57946i) q^{79} +(2.17289 + 3.76355i) q^{83} +(0.0343744 - 0.0595381i) q^{85} +(4.30077 + 7.44915i) q^{89} +(-1.32194 + 0.190974i) q^{91} +(-0.0578528 - 0.100204i) q^{95} +(-3.27671 - 5.67542i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{5} + q^{7}+O(q^{10}) $ 22 * q + 2 * q^5 + q^7	$ 22 q + 2 q^{5} + q^{7} - 6 q^{11} + 7 q^{13} + q^{17} - 13 q^{19} + 44 q^{25} + 7 q^{29} - 6 q^{31} + 2 q^{35} + 6 q^{37} - 4 q^{41} - 2 q^{43} + 17 q^{47} + 29 q^{49} - q^{53} - 2 q^{55} - 21 q^{59} + 31 q^{61} + 3 q^{65} + 26 q^{67} - 32 q^{71} + 17 q^{73} + 4 q^{77} + 16 q^{79} - 36 q^{83} + 28 q^{85} + 2 q^{89} - 15 q^{91} - 24 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q + 2 * q^5 + q^7 - 6 * q^11 + 7 * q^13 + q^17 - 13 * q^19 + 44 * q^25 + 7 * q^29 - 6 * q^31 + 2 * q^35 + 6 * q^37 - 4 * q^41 - 2 * q^43 + 17 * q^47 + 29 * q^49 - q^53 - 2 * q^55 - 21 * q^59 + 31 * q^61 + 3 * q^65 + 26 * q^67 - 32 * q^71 + 17 * q^73 + 4 * q^77 + 16 * q^79 - 36 * q^83 + 28 * q^85 + 2 * q^89 - 15 * q^91 - 24 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.0619693			0.0277135			0.0138567	−	0.999904i	$-0.495589\pi$
$5$	0.0619693			0.0277135			0.0138567	+	0.999904i	$0.495589\pi$
$6$		0			0
$7$	1.63689	+	2.07860i	0.618688	+	0.785637i
$7$	1.63689	+	2.07860i	0.618688	+	0.785637i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.18053			−0.958967			−0.479483	−	0.877551i	$-0.659176\pi$
$11$	−3.18053			−0.958967			−0.479483	+	0.877551i	$0.659176\pi$
$12$		0			0
$13$	−0.252417	+	0.437198i	−0.0700078	+	0.121257i	−0.898904	−	0.438145i	$-0.855636\pi$
$13$	−0.252417	+	0.437198i	−0.0700078	+	0.121257i	0.828897	+	0.559402i	$0.188969\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.554700	−	0.960769i	0.134535	−	0.233021i	−0.790885	−	0.611965i	$-0.790379\pi$
$17$	0.554700	−	0.960769i	0.134535	−	0.233021i	0.925420	+	0.378944i	$0.123713\pi$
$18$		0			0
$19$	−0.933573	−	1.61700i	−0.214176	−	0.370964i	0.738841	−	0.673880i	$-0.235373\pi$
$19$	−0.933573	−	1.61700i	−0.214176	−	0.370964i	−0.953017	+	0.302915i	$0.902040\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.20496			−1.29382			−0.646912	−	0.762565i	$-0.723940\pi$
$23$	−6.20496			−1.29382			−0.646912	+	0.762565i	$0.723940\pi$
$24$		0			0
$25$	−4.99616			−0.999232
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.39645	−	4.15077i	−0.445010	−	0.770779i	0.553043	−	0.833153i	$-0.313466\pi$
$29$	−2.39645	−	4.15077i	−0.445010	−	0.770779i	−0.998053	+	0.0623731i	$0.980133\pi$
$30$		0			0
$31$	−1.26858	−	2.19724i	−0.227843	−	0.394636i	0.729325	−	0.684167i	$-0.239834\pi$
$31$	−1.26858	−	2.19724i	−0.227843	−	0.394636i	−0.957169	+	0.289531i	$0.906501\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.101437	+	0.128809i	0.0171460	+	0.0217728i
$36$		0			0
$37$	−4.26085	−	7.38001i	−0.700479	−	1.21327i	−0.968298	−	0.249797i	$-0.919636\pi$
$37$	−4.26085	−	7.38001i	−0.700479	−	1.21327i	0.267819	−	0.963469i	$-0.413697\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.94516	−	8.56527i	0.772305	−	1.33767i	−0.163992	−	0.986462i	$-0.552437\pi$
$41$	4.94516	−	8.56527i	0.772305	−	1.33767i	0.936297	−	0.351210i	$-0.114230\pi$
$42$		0			0
$43$	3.95574	+	6.85154i	0.603244	+	1.04485i	0.992326	+	0.123646i	$0.0394589\pi$
$43$	3.95574	+	6.85154i	0.603244	+	1.04485i	−0.389082	+	0.921203i	$0.627208\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.29168	+	5.70136i	−0.480141	+	0.831628i	−0.999740	−	0.0227816i	$-0.992748\pi$
$47$	−3.29168	+	5.70136i	−0.480141	+	0.831628i	0.519600	+	0.854410i	$0.326081\pi$
$48$		0			0
$49$	−1.64116	+	6.80489i	−0.234451	+	0.972128i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.58258	−	2.74112i	0.217385	−	0.376521i	−0.736623	−	0.676304i	$-0.763581\pi$
$53$	1.58258	−	2.74112i	0.217385	−	0.376521i	0.954008	+	0.299782i	$0.0969140\pi$
$54$		0			0
$55$	−0.197095			−0.0265763
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.50652	−	7.80552i	−0.586699	−	1.01619i	−0.994661	−	0.103194i	$-0.967094\pi$
$59$	−4.50652	−	7.80552i	−0.586699	−	1.01619i	0.407962	−	0.912999i	$-0.366240\pi$
$60$		0			0
$61$	6.94094	−	12.0221i	0.888697	−	1.53927i	0.0472794	−	0.998882i	$-0.484945\pi$
$61$	6.94094	−	12.0221i	0.888697	−	1.53927i	0.841417	−	0.540386i	$-0.181722\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.0156421	+	0.0270929i	−0.00194016	+	0.00336046i
$66$		0			0
$67$	1.66642	+	2.88632i	0.203585	+	0.352620i	0.949681	−	0.313219i	$-0.101407\pi$
$67$	1.66642	+	2.88632i	0.203585	+	0.352620i	−0.746096	+	0.665839i	$0.768074\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.25651			0.267798			0.133899	−	0.990995i	$-0.457250\pi$
$71$	2.25651			0.267798			0.133899	+	0.990995i	$0.457250\pi$
$72$		0			0
$73$	2.07503	−	3.59406i	0.242864	−	0.420652i	−0.718665	−	0.695356i	$-0.755247\pi$
$73$	2.07503	−	3.59406i	0.242864	−	0.420652i	0.961529	+	0.274704i	$0.0885799\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.20619	−	6.61106i	−0.593301	−	0.753400i
$78$		0			0
$79$	−1.48925	+	2.57946i	−0.167554	+	0.290211i	−0.937559	−	0.347826i	$-0.886920\pi$
$79$	−1.48925	+	2.57946i	−0.167554	+	0.290211i	0.770006	+	0.638037i	$0.220253\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.17289	+	3.76355i	0.238506	+	0.413104i	0.960286	−	0.279019i	$-0.0900092\pi$
$83$	2.17289	+	3.76355i	0.238506	+	0.413104i	−0.721780	+	0.692122i	$0.756676\pi$
$84$		0			0
$85$	0.0343744	−	0.0595381i	0.00372842	−	0.00645782i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.30077	+	7.44915i	0.455880	+	0.789608i	0.998738	−	0.0502166i	$-0.0159912\pi$
$89$	4.30077	+	7.44915i	0.455880	+	0.789608i	−0.542858	+	0.839824i	$0.682658\pi$
$90$		0			0
$91$	−1.32194	+	0.190974i	−0.138577	+	0.0200195i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.0578528	−	0.100204i	−0.00593558	−	0.0102807i
$96$		0			0
$97$	−3.27671	−	5.67542i	−0.332699	−	0.576252i	0.650341	−	0.759642i	$-0.274626\pi$
$97$	−3.27671	−	5.67542i	−0.332699	−	0.576252i	−0.983040	+	0.183391i	$0.941293\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.51654			−0.648420			−0.324210	−	0.945985i	$-0.605098\pi$
$101$	−6.51654			−0.648420			−0.324210	+	0.945985i	$0.605098\pi$
$102$		0			0
$103$	−17.0196			−1.67699			−0.838494	−	0.544911i	$-0.816563\pi$
$103$	−17.0196			−1.67699			−0.838494	+	0.544911i	$0.816563\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.86075	−	15.3473i	−0.856601	−	1.48368i	−0.875152	−	0.483848i	$-0.839239\pi$
$107$	−8.86075	−	15.3473i	−0.856601	−	1.48368i	0.0185508	−	0.999828i	$-0.494095\pi$
$108$		0			0
$109$	6.62928	−	11.4822i	0.634970	−	1.09980i	−0.351552	−	0.936168i	$-0.614346\pi$
$109$	6.62928	−	11.4822i	0.634970	−	1.09980i	0.986522	−	0.163631i	$-0.0523208\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.10094	+	1.90689i	−0.103568	+	0.179385i	−0.913152	−	0.407619i	$-0.866359\pi$
$113$	−1.10094	+	1.90689i	−0.103568	+	0.179385i	0.809584	+	0.587004i	$0.199693\pi$
$114$		0			0
$115$	−0.384517			−0.0358564
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.90504	−	0.419676i	0.266305	−	0.0384717i
$120$		0			0
$121$	−0.884207			−0.0803825
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.619455			−0.0554057
$126$		0			0
$127$	4.61290			0.409329			0.204664	−	0.978832i	$-0.434390\pi$
$127$	4.61290			0.409329			0.204664	+	0.978832i	$0.434390\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.152139			−0.0132925			−0.00664623	−	0.999978i	$-0.502116\pi$
$131$	−0.152139			−0.0132925			−0.00664623	+	0.999978i	$0.502116\pi$
$132$		0			0
$133$	1.83293	−	4.58738i	0.158935	−	0.397776i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.55540			0.303759			0.151879	−	0.988399i	$-0.451467\pi$
$137$	3.55540			0.303759			0.151879	+	0.988399i	$0.451467\pi$
$138$		0			0
$139$	7.60945	−	13.1800i	0.645425	−	1.11791i	−0.338778	−	0.940866i	$-0.610013\pi$
$139$	7.60945	−	13.1800i	0.645425	−	1.11791i	0.984203	−	0.177043i	$-0.0566532\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.802820	−	1.39052i	0.0671352	−	0.116281i
$144$		0			0
$145$	−0.148506	−	0.257220i	−0.0123328	−	0.0213610i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.366914			−0.0300588			−0.0150294	−	0.999887i	$-0.504784\pi$
$149$	−0.366914			−0.0300588			−0.0150294	+	0.999887i	$0.504784\pi$
$150$		0			0
$151$	12.5832			1.02401			0.512005	−	0.858983i	$-0.328903\pi$
$151$	12.5832			1.02401			0.512005	+	0.858983i	$0.328903\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.0786128	−	0.136161i	−0.00631434	−	0.0109368i
$156$		0			0
$157$	2.72734	+	4.72389i	0.217666	+	0.377008i	0.954094	−	0.299508i	$-0.0968225\pi$
$157$	2.72734	+	4.72389i	0.217666	+	0.377008i	−0.736428	+	0.676516i	$0.763489\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−10.1569	−	12.8976i	−0.800473	−	1.01648i
$162$		0			0
$163$	−3.83559	−	6.64343i	−0.300426	−	0.520354i	0.675806	−	0.737079i	$-0.263796\pi$
$163$	−3.83559	−	6.64343i	−0.300426	−	0.520354i	−0.976233	+	0.216726i	$0.930462\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.47493	+	16.4111i	−0.733192	+	1.26993i	0.222320	+	0.974974i	$0.428637\pi$
$167$	−9.47493	+	16.4111i	−0.733192	+	1.26993i	−0.955512	+	0.294952i	$0.904696\pi$
$168$		0			0
$169$	6.37257	+	11.0376i	0.490198	+	0.849048i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−11.9959	+	20.7776i	−0.912034	+	1.57969i	−0.100846	+	0.994902i	$0.532155\pi$
$173$	−11.9959	+	20.7776i	−0.912034	+	1.57969i	−0.811187	+	0.584787i	$0.801178\pi$
$174$		0			0
$175$	−8.17818	−	10.3850i	−0.618212	−	0.785034i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−4.27901	+	7.41146i	−0.319828	+	0.553959i	−0.980452	−	0.196758i	$-0.936959\pi$
$179$	−4.27901	+	7.41146i	−0.319828	+	0.553959i	0.660624	+	0.750717i	$0.270292\pi$
$180$		0			0
$181$	0.632669			0.0470259			0.0235130	−	0.999724i	$-0.492515\pi$
$181$	0.632669			0.0470259			0.0235130	+	0.999724i	$0.492515\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.264042	−	0.457334i	−0.0194127	−	0.0336238i
$186$		0			0
$187$	−1.76424	+	3.05576i	−0.129014	+	0.223459i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.7915	+	20.4235i	−0.853205	+	1.47780i	0.0250944	+	0.999685i	$0.492011\pi$
$191$	−11.7915	+	20.4235i	−0.853205	+	1.47780i	−0.878300	+	0.478110i	$0.841322\pi$
$192$		0			0
$193$	−12.8030	−	22.1754i	−0.921577	−	1.59622i	−0.796976	−	0.604011i	$-0.793568\pi$
$193$	−12.8030	−	22.1754i	−0.921577	−	1.59622i	−0.124600	−	0.992207i	$-0.539765\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−9.45810			−0.673862			−0.336931	−	0.941529i	$-0.609389\pi$
$197$	−9.45810			−0.673862			−0.336931	+	0.941529i	$0.609389\pi$
$198$		0			0
$199$	−4.15133	+	7.19032i	−0.294280	+	0.509708i	−0.974817	−	0.223005i	$-0.928413\pi$
$199$	−4.15133	+	7.19032i	−0.294280	+	0.509708i	0.680537	+	0.732714i	$0.261747\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.70507	−	11.7756i	0.330231	−	0.826488i
$204$		0			0
$205$	0.306448	−	0.530784i	0.0214033	−	0.0370715i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.96926	+	5.14291i	0.205388	+	0.355742i
$210$		0			0
$211$	10.1164	−	17.5222i	0.696444	−	1.20628i	−0.273247	−	0.961944i	$-0.588098\pi$
$211$	10.1164	−	17.5222i	0.696444	−	1.20628i	0.969691	−	0.244333i	$-0.0785689\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.245134	+	0.424585i	0.0167180	+	0.0289564i
$216$		0			0
$217$	2.49066	−	6.23352i	0.169077	−	0.423159i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.280031	+	0.485028i	0.0188369	+	0.0326265i
$222$		0			0
$223$	2.41918	+	4.19014i	0.162000	+	0.280593i	0.935586	−	0.353099i	$-0.114872\pi$
$223$	2.41918	+	4.19014i	0.162000	+	0.280593i	−0.773586	+	0.633692i	$0.781539\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.672213			0.0446163			0.0223082	−	0.999751i	$-0.492899\pi$
$227$	0.672213			0.0446163			0.0223082	+	0.999751i	$0.492899\pi$
$228$		0			0
$229$	−6.13553			−0.405447			−0.202724	−	0.979236i	$-0.564979\pi$
$229$	−6.13553			−0.405447			−0.202724	+	0.979236i	$0.564979\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.1492	−	21.0431i	−0.795922	−	1.37858i	−0.922252	−	0.386589i	$-0.873653\pi$
$233$	−12.1492	−	21.0431i	−0.795922	−	1.37858i	0.126330	−	0.991988i	$-0.459680\pi$
$234$		0			0
$235$	−0.203983	+	0.353309i	−0.0133064	+	0.0230473i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	13.5978	−	23.5521i	0.879569	−	1.52346i	0.0277545	−	0.999615i	$-0.491164\pi$
$239$	13.5978	−	23.5521i	0.879569	−	1.52346i	0.851815	−	0.523843i	$-0.175502\pi$
$240$		0			0
$241$	−25.8054			−1.66227			−0.831135	−	0.556070i	$-0.812309\pi$
$241$	−25.8054			−1.66227			−0.831135	+	0.556070i	$0.812309\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.101701	+	0.421694i	−0.00649747	+	0.0269411i
$246$		0			0
$247$	0.942598			0.0599760
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−27.0741			−1.70890			−0.854450	−	0.519533i	$-0.826106\pi$
$251$	−27.0741			−1.70890			−0.854450	+	0.519533i	$0.826106\pi$
$252$		0			0
$253$	19.7351			1.24073
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.5215			0.843445			0.421723	−	0.906725i	$-0.361426\pi$
$257$	13.5215			0.843445			0.421723	+	0.906725i	$0.361426\pi$
$258$		0			0
$259$	8.36553	−	20.9369i	0.519809	−	1.30096i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−13.3745			−0.824710			−0.412355	−	0.911023i	$-0.635294\pi$
$263$	−13.3745			−0.824710			−0.412355	+	0.911023i	$0.635294\pi$
$264$		0			0
$265$	0.0980716	−	0.169865i	0.00602449	−	0.0104347i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.91594	+	6.78261i	−0.238759	+	0.413543i	−0.960359	−	0.278768i	$-0.910074\pi$
$269$	−3.91594	+	6.78261i	−0.238759	+	0.413543i	0.721599	+	0.692311i	$0.243407\pi$
$270$		0			0
$271$	−15.1737	−	26.2816i	−0.921735	−	1.59649i	−0.796730	−	0.604335i	$-0.793439\pi$
$271$	−15.1737	−	26.2816i	−0.921735	−	1.59649i	−0.125005	−	0.992156i	$-0.539895\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	15.8905			0.958230
$276$		0			0
$277$	−22.6924			−1.36346			−0.681728	−	0.731606i	$-0.738771\pi$
$277$	−22.6924			−1.36346			−0.681728	+	0.731606i	$0.738771\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	10.0826	+	17.4635i	0.601475	+	1.04179i	0.992598	+	0.121447i	$0.0387536\pi$
$281$	10.0826	+	17.4635i	0.601475	+	1.04179i	−0.391122	+	0.920339i	$0.627913\pi$
$282$		0			0
$283$	−8.45297	−	14.6410i	−0.502477	−	0.870316i	−0.999996	−	0.00286255i	$-0.999089\pi$
$283$	−8.45297	−	14.6410i	−0.502477	−	0.870316i	0.497519	−	0.867453i	$-0.334245\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	25.8985	−	3.74142i	1.52874	−	0.220849i
$288$		0			0
$289$	7.88462	+	13.6566i	0.463801	+	0.803327i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−2.40597	+	4.16727i	−0.140558	+	0.243454i	−0.927707	−	0.373309i	$-0.878223\pi$
$293$	−2.40597	+	4.16727i	−0.140558	+	0.243454i	0.787149	+	0.616763i	$0.211556\pi$
$294$		0			0
$295$	−0.279266	−	0.483703i	−0.0162595	−	0.0281623i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.56624	−	2.71280i	0.0905777	−	0.156885i
$300$		0			0
$301$	−7.76649	+	19.4376i	−0.447653	+	1.12037i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.430125	−	0.744999i	0.0246289	−	0.0426585i
$306$		0			0
$307$	−15.9188			−0.908534			−0.454267	−	0.890866i	$-0.650099\pi$
$307$	−15.9188			−0.908534			−0.454267	+	0.890866i	$0.650099\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.131435	+	0.227651i	0.00745297	+	0.0129089i	0.869728	−	0.493532i	$-0.164294\pi$
$311$	0.131435	+	0.227651i	0.00745297	+	0.0129089i	−0.862275	+	0.506441i	$0.830961\pi$
$312$		0			0
$313$	3.12534	−	5.41325i	0.176655	−	0.305975i	−0.764078	−	0.645124i	$-0.776806\pi$
$313$	3.12534	−	5.41325i	0.176655	−	0.305975i	0.940733	+	0.339149i	$0.110139\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.83961	+	17.0427i	−0.552648	+	0.957214i	0.445435	+	0.895314i	$0.353049\pi$
$317$	−9.83961	+	17.0427i	−0.552648	+	0.957214i	−0.998082	+	0.0618994i	$0.980284\pi$
$318$		0			0
$319$	7.62199	+	13.2017i	0.426750	+	0.739152i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−2.07141			−0.115256
$324$		0			0
$325$	1.26111	−	2.18431i	0.0699540	−	0.121164i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−17.2390	+	2.49043i	−0.950415	+	0.137302i
$330$		0			0
$331$	12.2669	−	21.2469i	0.674249	−	1.16783i	−0.302439	−	0.953169i	$-0.597801\pi$
$331$	12.2669	−	21.2469i	0.674249	−	1.16783i	0.976688	−	0.214665i	$-0.0688659\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.103267	+	0.178863i	0.00564206	+	0.00977233i
$336$		0			0
$337$	−6.89471	+	11.9420i	−0.375579	+	0.650521i	−0.990413	−	0.138135i	$-0.955889\pi$
$337$	−6.89471	+	11.9420i	−0.375579	+	0.650521i	0.614835	+	0.788656i	$0.289223\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	4.03475	+	6.98840i	0.218494	+	0.378443i
$342$		0			0
$343$	−16.8311	+	7.72757i	−0.908792	+	0.417250i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.84786	+	17.0570i	0.528661	+	0.915667i	0.999441	+	0.0334170i	$0.0106389\pi$
$347$	9.84786	+	17.0570i	0.528661	+	0.915667i	−0.470781	+	0.882250i	$0.656028\pi$
$348$		0			0
$349$	5.34712	+	9.26149i	0.286225	+	0.495756i	0.972905	−	0.231203i	$-0.0742662\pi$
$349$	5.34712	+	9.26149i	0.286225	+	0.495756i	−0.686681	+	0.726959i	$0.740933\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	11.6615			0.620677			0.310338	−	0.950626i	$-0.399558\pi$
$353$	11.6615			0.620677			0.310338	+	0.950626i	$0.399558\pi$
$354$		0			0
$355$	0.139834			0.00742162
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.82159	−	15.2794i	−0.465586	−	0.806418i	0.533642	−	0.845710i	$-0.320823\pi$
$359$	−8.82159	−	15.2794i	−0.465586	−	0.806418i	−0.999228	+	0.0392925i	$0.987490\pi$
$360$		0			0
$361$	7.75688	−	13.4353i	0.408257	−	0.707122i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.128588	−	0.222721i	0.00673061	−	0.0116578i
$366$		0			0
$367$	−3.38292			−0.176587			−0.0882934	−	0.996095i	$-0.528141\pi$
$367$	−3.38292			−0.176587			−0.0882934	+	0.996095i	$0.528141\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	8.28821	−	1.19736i	0.430302	−	0.0621636i
$372$		0			0
$373$	13.3902			0.693320			0.346660	−	0.937991i	$-0.387316\pi$
$373$	13.3902			0.693320			0.346660	+	0.937991i	$0.387316\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.41962			0.124617
$378$		0			0
$379$	27.6131			1.41839			0.709194	−	0.705013i	$-0.249059\pi$
$379$	27.6131			1.41839			0.709194	+	0.705013i	$0.249059\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	25.0040			1.27764			0.638822	−	0.769354i	$-0.279422\pi$
$383$	25.0040			1.27764			0.638822	+	0.769354i	$0.279422\pi$
$384$		0			0
$385$	−0.322624	−	0.409682i	−0.0164424	−	0.0208793i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.136646			0.00692821			0.00346411	−	0.999994i	$-0.498897\pi$
$389$	0.136646			0.00692821			0.00346411	+	0.999994i	$0.498897\pi$
$390$		0			0
$391$	−3.44189	+	5.96153i	−0.174064	+	0.301488i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.0922877	+	0.159847i	−0.00464350	+	0.00804277i
$396$		0			0
$397$	7.91030	+	13.7010i	0.397006	+	0.687635i	0.993355	−	0.115090i	$-0.0367157\pi$
$397$	7.91030	+	13.7010i	0.397006	+	0.687635i	−0.596349	+	0.802726i	$0.703382\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.0549			0.552055			0.276028	−	0.961150i	$-0.410982\pi$
$401$	11.0549			0.552055			0.276028	+	0.961150i	$0.410982\pi$
$402$		0			0
$403$	1.28084			0.0638032
$404$		0			0
$405$		0			0
$406$		0			0
$407$	13.5518	+	23.4724i	0.671737	+	1.16348i
$408$		0			0
$409$	18.0064	+	31.1880i	0.890358	+	1.54215i	0.839446	+	0.543443i	$0.182880\pi$
$409$	18.0064	+	31.1880i	0.890358	+	1.54215i	0.0509122	+	0.998703i	$0.483787\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	8.84787	−	22.1441i	0.435375	−	1.08964i
$414$		0			0
$415$	0.134652	+	0.233225i	0.00660982	+	0.0114485i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	16.4877	−	28.5576i	0.805477	−	1.39513i	−0.110491	−	0.993877i	$-0.535242\pi$
$419$	16.4877	−	28.5576i	0.805477	−	1.39513i	0.915968	−	0.401251i	$-0.131424\pi$
$420$		0			0
$421$	14.9800	+	25.9461i	0.730080	+	1.26454i	0.956849	+	0.290587i	$0.0938505\pi$
$421$	14.9800	+	25.9461i	0.730080	+	1.26454i	−0.226769	+	0.973949i	$0.572816\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.77137	+	4.80016i	−0.134431	+	0.232842i
$426$		0			0
$427$	36.3507	−	5.25139i	1.75913	−	0.254133i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−12.4021	+	21.4811i	−0.597389	+	1.03471i	0.395816	+	0.918330i	$0.370462\pi$
$431$	−12.4021	+	21.4811i	−0.597389	+	1.03471i	−0.993205	+	0.116379i	$0.962871\pi$
$432$		0			0
$433$	−5.00906			−0.240720			−0.120360	−	0.992730i	$-0.538405\pi$
$433$	−5.00906			−0.240720			−0.120360	+	0.992730i	$0.538405\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.79278	+	10.0334i	0.277106	+	0.479962i
$438$		0			0
$439$	−20.2918	+	35.1464i	−0.968475	+	1.67745i	−0.268502	+	0.963279i	$0.586529\pi$
$439$	−20.2918	+	35.1464i	−0.968475	+	1.67745i	−0.699973	+	0.714169i	$0.746805\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14.1332	−	24.4795i	0.671490	−	1.16305i	−0.305992	−	0.952034i	$-0.598988\pi$
$443$	14.1332	−	24.4795i	0.671490	−	1.16305i	0.977482	−	0.211021i	$-0.0676787\pi$
$444$		0			0
$445$	0.266515	+	0.461618i	0.0126340	+	0.0218828i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−36.6443			−1.72935			−0.864676	−	0.502329i	$-0.832477\pi$
$449$	−36.6443			−1.72935			−0.864676	+	0.502329i	$0.832477\pi$
$450$		0			0
$451$	−15.7283	+	27.2421i	−0.740615	+	1.28278i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.0819197	+	0.0118345i	−0.00384045	+	0.000554811i
$456$		0			0
$457$	3.19154	−	5.52791i	0.149294	−	0.258585i	−0.781673	−	0.623689i	$-0.785633\pi$
$457$	3.19154	−	5.52791i	0.149294	−	0.258585i	0.930967	+	0.365104i	$0.118967\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.24366	−	12.5464i	−0.337371	−	0.584343i	0.646567	−	0.762858i	$-0.276204\pi$
$461$	−7.24366	−	12.5464i	−0.337371	−	0.584343i	−0.983937	+	0.178514i	$0.942871\pi$
$462$		0			0
$463$	−13.2527	+	22.9544i	−0.615907	+	1.06678i	0.374317	+	0.927301i	$0.377877\pi$
$463$	−13.2527	+	22.9544i	−0.615907	+	1.06678i	−0.990225	+	0.139482i	$0.955456\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−11.6879	−	20.2440i	−0.540851	−	0.936782i	−0.998855	−	0.0478318i	$-0.984769\pi$
$467$	−11.6879	−	20.2440i	−0.540851	−	0.936782i	0.458004	−	0.888950i	$-0.348564\pi$
$468$		0			0
$469$	−3.27176	+	8.18841i	−0.151076	+	0.378106i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−12.5814	−	21.7915i	−0.578491	−	1.00198i
$474$		0			0
$475$	4.66428	+	8.07877i	0.214012	+	0.370679i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	9.29606			0.424748			0.212374	−	0.977188i	$-0.431881\pi$
$479$	9.29606			0.424748			0.212374	+	0.977188i	$0.431881\pi$
$480$		0			0
$481$	4.30204			0.196156
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.203055	−	0.351702i	−0.00922026	−	0.0159700i
$486$		0			0
$487$	−2.04947	+	3.54979i	−0.0928704	+	0.160856i	−0.908718	−	0.417411i	$-0.862938\pi$
$487$	−2.04947	+	3.54979i	−0.0928704	+	0.160856i	0.815847	+	0.578267i	$0.196271\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	4.98703	−	8.63778i	0.225061	−	0.389818i	−0.731277	−	0.682081i	$-0.761075\pi$
$491$	4.98703	−	8.63778i	0.225061	−	0.389818i	0.956338	+	0.292264i	$0.0944084\pi$
$492$		0			0
$493$	−5.31725			−0.239477
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.69366	+	4.69037i	0.165683	+	0.210392i
$498$		0			0
$499$	11.2083			0.501752			0.250876	−	0.968019i	$-0.419281\pi$
$499$	11.2083			0.501752			0.250876	+	0.968019i	$0.419281\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−1.69350			−0.0755094			−0.0377547	−	0.999287i	$-0.512021\pi$
$503$	−1.69350			−0.0755094			−0.0377547	+	0.999287i	$0.512021\pi$
$504$		0			0
$505$	−0.403825			−0.0179700
$506$		0			0
$507$		0			0
$508$		0			0
$509$	40.9555			1.81532			0.907659	−	0.419707i	$-0.137867\pi$
$509$	40.9555			1.81532			0.907659	+	0.419707i	$0.137867\pi$
$510$		0			0
$511$	10.8672	−	1.56993i	0.480737	−	0.0694496i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.05469			−0.0464752
$516$		0			0
$517$	10.4693	−	18.1334i	0.460439	−	0.797504i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−15.5075	+	26.8598i	−0.679396	+	1.17675i	0.295767	+	0.955260i	$0.404425\pi$
$521$	−15.5075	+	26.8598i	−0.679396	+	1.17675i	−0.975163	+	0.221488i	$0.928909\pi$
$522$		0			0
$523$	3.67840	+	6.37117i	0.160845	+	0.278592i	0.935172	−	0.354194i	$-0.115245\pi$
$523$	3.67840	+	6.37117i	0.160845	+	0.278592i	−0.774327	+	0.632786i	$0.781911\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.81472			−0.122611
$528$		0			0
$529$	15.5015			0.673980
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2.49648	+	4.32404i	0.108135	+	0.187295i
$534$		0			0
$535$	−0.549094	−	0.951059i	−0.0237394	−	0.0411179i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.21976	−	21.6432i	0.224831	−	0.932238i
$540$		0			0
$541$	−14.4735	−	25.0688i	−0.622262	−	1.07779i	−0.989063	−	0.147491i	$-0.952880\pi$
$541$	−14.4735	−	25.0688i	−0.622262	−	1.07779i	0.366801	−	0.930299i	$-0.380453\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.410812	−	0.711546i	0.0175972	−	0.0304793i
$546$		0			0
$547$	−9.34891	−	16.1928i	−0.399731	−	0.692354i	0.593962	−	0.804493i	$-0.297563\pi$
$547$	−9.34891	−	16.1928i	−0.399731	−	0.692354i	−0.993692	+	0.112140i	$0.964230\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−4.47452	+	7.75010i	−0.190621	+	0.330165i
$552$		0			0
$553$	−7.79940	+	1.12674i	−0.331664	+	0.0479138i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	17.1787	−	29.7544i	0.727886	−	1.26074i	−0.229889	−	0.973217i	$-0.573836\pi$
$557$	17.1787	−	29.7544i	0.727886	−	1.26074i	0.957775	−	0.287519i	$-0.0928303\pi$
$558$		0			0
$559$	−3.99397			−0.168927
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.37355	+	12.7714i	0.310758	+	0.538249i	0.978527	−	0.206120i	$-0.0660838\pi$
$563$	7.37355	+	12.7714i	0.310758	+	0.538249i	−0.667769	+	0.744369i	$0.732750\pi$
$564$		0			0
$565$	−0.0682247	+	0.118169i	−0.00287024	+	0.00497139i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.66821	−	2.88942i	0.0699349	−	0.121131i	−0.828938	−	0.559341i	$-0.811054\pi$
$569$	1.66821	−	2.88942i	0.0699349	−	0.121131i	0.898872	+	0.438210i	$0.144387\pi$
$570$		0			0
$571$	9.40360	+	16.2875i	0.393528	+	0.681611i	0.992912	−	0.118851i	$-0.0379210\pi$
$571$	9.40360	+	16.2875i	0.393528	+	0.681611i	−0.599384	+	0.800462i	$0.704588\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	31.0010			1.29283
$576$		0			0
$577$	−17.6961	+	30.6505i	−0.736697	+	1.27600i	0.217277	+	0.976110i	$0.430282\pi$
$577$	−17.6961	+	30.6505i	−0.736697	+	1.27600i	−0.953975	+	0.299887i	$0.903051\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−4.26614	+	10.6771i	−0.176989	+	0.442961i
$582$		0			0
$583$	−5.03346	+	8.71821i	−0.208465	+	0.361072i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−17.2921	−	29.9508i	−0.713722	−	1.23620i	−0.963450	−	0.267887i	$-0.913674\pi$
$587$	−17.2921	−	29.9508i	−0.713722	−	1.23620i	0.249728	−	0.968316i	$-0.419659\pi$
$588$		0			0
$589$	−2.36862	+	4.10257i	−0.0975973	+	0.169043i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	15.9787	+	27.6759i	0.656166	+	1.13651i	0.981600	+	0.190949i	$0.0611564\pi$
$593$	15.9787	+	27.6759i	0.656166	+	1.13651i	−0.325434	+	0.945565i	$0.605510\pi$
$594$		0			0
$595$	0.180023	−	0.0260070i	0.00738023	−	0.00106618i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	4.92476	+	8.52993i	0.201220	+	0.348524i	0.948922	−	0.315511i	$-0.102176\pi$
$599$	4.92476	+	8.52993i	0.201220	+	0.348524i	−0.747702	+	0.664035i	$0.768843\pi$
$600$		0			0
$601$	−3.77340	−	6.53572i	−0.153920	−	0.266598i	0.778745	−	0.627340i	$-0.215857\pi$
$601$	−3.77340	−	6.53572i	−0.153920	−	0.266598i	−0.932665	+	0.360743i	$0.882523\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.0547937			−0.00222768
$606$		0			0
$607$	−10.8584			−0.440730			−0.220365	−	0.975417i	$-0.570725\pi$
$607$	−10.8584			−0.440730			−0.220365	+	0.975417i	$0.570725\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.66175	−	2.87823i	−0.0672272	−	0.116441i
$612$		0			0
$613$	−23.8823	+	41.3653i	−0.964596	+	1.67073i	−0.253899	+	0.967231i	$0.581713\pi$
$613$	−23.8823	+	41.3653i	−0.964596	+	1.67073i	−0.710697	+	0.703499i	$0.751620\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	18.7769	−	32.5225i	0.755929	−	1.30931i	−0.188982	−	0.981980i	$-0.560519\pi$
$617$	18.7769	−	32.5225i	0.755929	−	1.30931i	0.944911	−	0.327327i	$-0.106148\pi$
$618$		0			0
$619$	−35.9657			−1.44558			−0.722792	−	0.691065i	$-0.757142\pi$
$619$	−35.9657			−1.44558			−0.722792	+	0.691065i	$0.757142\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−8.44390	+	21.1330i	−0.338298	+	0.846677i
$624$		0			0
$625$	24.9424			0.997696
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−9.45398			−0.376955
$630$		0			0
$631$	31.8848			1.26931			0.634656	−	0.772794i	$-0.281142\pi$
$631$	31.8848			1.26931			0.634656	+	0.772794i	$0.281142\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.285858			0.0113439
$636$		0			0
$637$	−2.56083	−	2.43518i	−0.101464	−	0.0964854i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−16.6788			−0.658772			−0.329386	−	0.944195i	$-0.606842\pi$
$641$	−16.6788			−0.658772			−0.329386	+	0.944195i	$0.606842\pi$
$642$		0			0
$643$	−23.5295	+	40.7544i	−0.927915	+	1.60720i	−0.141109	+	0.989994i	$0.545067\pi$
$643$	−23.5295	+	40.7544i	−0.927915	+	1.60720i	−0.786805	+	0.617201i	$0.788266\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.2324	+	21.1872i	−0.480906	+	0.832954i	−0.999760	−	0.0219091i	$-0.993026\pi$
$647$	−12.2324	+	21.1872i	−0.480906	+	0.832954i	0.518854	+	0.854863i	$0.326359\pi$
$648$		0			0
$649$	14.3331	+	24.8257i	0.562625	+	0.974495i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	11.8261			0.462792			0.231396	−	0.972860i	$-0.425671\pi$
$653$	11.8261			0.462792			0.231396	+	0.972860i	$0.425671\pi$
$654$		0			0
$655$	−0.00942795			−0.000368380
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.51539	+	6.08883i	0.136940	+	0.237187i	0.926337	−	0.376696i	$-0.122940\pi$
$659$	3.51539	+	6.08883i	0.136940	+	0.237187i	−0.789397	+	0.613883i	$0.789607\pi$
$660$		0			0
$661$	−7.43024	−	12.8696i	−0.289003	−	0.500568i	0.684569	−	0.728948i	$-0.259990\pi$
$661$	−7.43024	−	12.8696i	−0.289003	−	0.500568i	−0.973572	+	0.228380i	$0.926657\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.113585	−	0.284276i	0.00440465	−	0.0110238i
$666$		0			0
$667$	14.8699	+	25.7554i	0.575764	+	0.997253i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−22.0759	+	38.2366i	−0.852231	+	1.47611i
$672$		0			0
$673$	7.81679	+	13.5391i	0.301315	+	0.521893i	0.976434	−	0.215816i	$-0.0692411\pi$
$673$	7.81679	+	13.5391i	0.301315	+	0.521893i	−0.675119	+	0.737709i	$0.735908\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	12.3561	−	21.4014i	0.474883	−	0.822522i	−0.524703	−	0.851285i	$-0.675824\pi$
$677$	12.3561	−	21.4014i	0.474883	−	0.822522i	0.999586	+	0.0287634i	$0.00915694\pi$
$678$		0			0
$679$	6.43332	−	16.1010i	0.246888	−	0.617901i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−16.7467	+	29.0061i	−0.640794	+	1.10989i	0.344462	+	0.938800i	$0.388061\pi$
$683$	−16.7467	+	29.0061i	−0.640794	+	1.10989i	−0.985256	+	0.171087i	$0.945272\pi$
$684$		0			0
$685$	0.220326			0.00841821
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.798941	+	1.38381i	0.0304372	+	0.0527189i
$690$		0			0
$691$	−1.33836	+	2.31811i	−0.0509137	+	0.0881851i	−0.890359	−	0.455259i	$-0.849547\pi$
$691$	−1.33836	+	2.31811i	−0.0509137	+	0.0881851i	0.839445	+	0.543444i	$0.182880\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.471552	−	0.816752i	0.0178870	−	0.0309812i
$696$		0			0
$697$	−5.48617	−	9.50232i	−0.207803	−	0.359926i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	36.3715			1.37373			0.686866	−	0.726784i	$-0.258986\pi$
$701$	36.3715			1.37373			0.686866	+	0.726784i	$0.258986\pi$
$702$		0			0
$703$	−7.95563	+	13.7796i	−0.300052	+	0.519706i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−10.6669	−	13.5453i	−0.401169	−	0.509423i
$708$		0			0
$709$	5.95369	−	10.3121i	0.223596	−	0.387279i	−0.732302	−	0.680980i	$-0.761554\pi$
$709$	5.95369	−	10.3121i	0.223596	−	0.387279i	0.955897	+	0.293702i	$0.0948872\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	7.87148	+	13.6338i	0.294789	+	0.510590i
$714$		0			0
$715$	0.0497501	−	0.0861698i	0.00186055	−	0.00322257i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	8.44050	+	14.6194i	0.314778	+	0.545211i	0.979390	−	0.201977i	$-0.0647367\pi$
$719$	8.44050	+	14.6194i	0.314778	+	0.545211i	−0.664613	+	0.747188i	$0.731403\pi$
$720$		0			0
$721$	−27.8592	−	35.3769i	−1.03753	−	1.31750i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	11.9731	+	20.7379i	0.444668	+	0.770187i
$726$		0			0
$727$	−1.24570	−	2.15762i	−0.0462006	−	0.0800218i	0.842000	−	0.539477i	$-0.181378\pi$
$727$	−1.24570	−	2.15762i	−0.0462006	−	0.0800218i	−0.888201	+	0.459455i	$0.848045\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	8.77699			0.324629
$732$		0			0
$733$	−12.5131			−0.462181			−0.231090	−	0.972932i	$-0.574229\pi$
$733$	−12.5131			−0.462181			−0.231090	+	0.972932i	$0.574229\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.30009	−	9.18003i	−0.195231	−	0.338151i
$738$		0			0
$739$	10.0051	−	17.3294i	0.368044	−	0.637472i	−0.621215	−	0.783640i	$-0.713361\pi$
$739$	10.0051	−	17.3294i	0.368044	−	0.637472i	0.989260	+	0.146168i	$0.0466941\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5.49879	−	9.52419i	0.201731	−	0.349408i	−0.747355	−	0.664425i	$-0.768677\pi$
$743$	5.49879	−	9.52419i	0.201731	−	0.349408i	0.949086	+	0.315016i	$0.102010\pi$
$744$		0			0
$745$	−0.0227374			−0.000833034
$746$		0			0
$747$		0			0
$748$		0			0
$749$	17.3967	−	43.5398i	0.635663	−	1.59091i
$750$		0			0
$751$	−28.8670			−1.05337			−0.526686	−	0.850060i	$-0.676566\pi$
$751$	−28.8670			−1.05337			−0.526686	+	0.850060i	$0.676566\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.779774			0.0283789
$756$		0			0
$757$	−17.3626			−0.631053			−0.315527	−	0.948917i	$-0.602181\pi$
$757$	−17.3626			−0.631053			−0.315527	+	0.948917i	$0.602181\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	52.0039			1.88514			0.942571	−	0.334006i	$-0.108401\pi$
$761$	52.0039			1.88514			0.942571	+	0.334006i	$0.108401\pi$
$762$		0			0
$763$	34.7184	−	5.01559i	1.25689	−	0.181577i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.55008			0.164294
$768$		0			0
$769$	13.5839	−	23.5280i	0.489849	−	0.848443i	−0.510083	−	0.860125i	$-0.670385\pi$
$769$	13.5839	−	23.5280i	0.489849	−	0.848443i	0.999932	+	0.0116822i	$0.00371865\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−12.2452	+	21.2093i	−0.440428	+	0.762845i	−0.997721	−	0.0674716i	$-0.978507\pi$
$773$	−12.2452	+	21.2093i	−0.440428	+	0.762845i	0.557293	+	0.830316i	$0.311840\pi$
$774$		0			0
$775$	6.33802	+	10.9778i	0.227668	+	0.394333i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−18.4667			−0.661638
$780$		0			0
$781$	−7.17689			−0.256809
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.169011	+	0.292736i	0.00603227	+	0.0104482i
$786$		0			0
$787$	0.939312	+	1.62694i	0.0334828	+	0.0579940i	0.882281	−	0.470723i	$-0.156007\pi$
$787$	0.939312	+	1.62694i	0.0334828	+	0.0579940i	−0.848798	+	0.528717i	$0.822673\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−5.76579	+	0.832955i	−0.205008	+	0.0296165i
$792$		0			0
$793$	3.50402	+	6.06914i	0.124431	+	0.215521i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−17.6067	+	30.4957i	−0.623662	+	1.08021i	0.365137	+	0.930954i	$0.381022\pi$
$797$	−17.6067	+	30.4957i	−0.623662	+	1.08021i	−0.988798	+	0.149259i	$0.952311\pi$
$798$		0			0
$799$	3.65179	+	6.32509i	0.129191	+	0.223765i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6.59970	+	11.4310i	−0.232898	+	0.403392i
$804$		0			0
$805$	−0.629413	−	0.799257i	−0.0221839	−	0.0281701i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.53614	+	2.66067i	−0.0540077	+	0.0935441i	−0.891765	−	0.452498i	$-0.850533\pi$
$809$	−1.53614	+	2.66067i	−0.0540077	+	0.0935441i	0.837758	+	0.546042i	$0.183866\pi$
$810$		0			0
$811$	14.8034			0.519818			0.259909	−	0.965633i	$-0.416307\pi$
$811$	14.8034			0.519818			0.259909	+	0.965633i	$0.416307\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.237688	−	0.411689i	−0.00832586	−	0.0144208i
$816$		0			0
$817$	7.38594	−	12.7928i	0.258401	−	0.447564i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	12.5061	−	21.6612i	0.436467	−	0.755982i	−0.560947	−	0.827851i	$-0.689563\pi$
$821$	12.5061	−	21.6612i	0.436467	−	0.755982i	0.997414	+	0.0718690i	$0.0228963\pi$
$822$		0			0
$823$	19.7480	+	34.2046i	0.688374	+	1.19230i	0.972364	+	0.233471i	$0.0750084\pi$
$823$	19.7480	+	34.2046i	0.688374	+	1.19230i	−0.283990	+	0.958827i	$0.591658\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	12.4528			0.433026			0.216513	−	0.976280i	$-0.430532\pi$
$827$	12.4528			0.433026			0.216513	+	0.976280i	$0.430532\pi$
$828$		0			0
$829$	−14.2995	+	24.7675i	−0.496643	+	0.860211i	−0.999993	−	0.00387209i	$-0.998767\pi$
$829$	−14.2995	+	24.7675i	−0.496643	+	0.860211i	0.503350	+	0.864083i	$0.332101\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	5.62758	+	5.35145i	0.194984	+	0.185417i
$834$		0			0
$835$	−0.587154	+	1.01698i	−0.0203193	+	0.0351941i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	21.0794	+	36.5107i	0.727743	+	1.26049i	0.957835	+	0.287319i	$0.0927641\pi$
$839$	21.0794	+	36.5107i	0.727743	+	1.26049i	−0.230092	+	0.973169i	$0.573903\pi$
$840$		0			0
$841$	3.01405	−	5.22048i	0.103933	−	0.180017i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.394904	+	0.683993i	0.0135851	+	0.0235301i
$846$		0			0
$847$	−1.44735	−	1.83791i	−0.0497316	−	0.0631514i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	26.4384	+	45.7927i	0.906297	+	1.56975i
$852$		0			0
$853$	−25.6206	−	44.3761i	−0.877232	−	1.51941i	−0.854366	−	0.519671i	$-0.826054\pi$
$853$	−25.6206	−	44.3761i	−0.877232	−	1.51941i	−0.0228654	−	0.999739i	$-0.507279\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	37.8058			1.29142			0.645710	−	0.763582i	$-0.276561\pi$
$857$	37.8058			1.29142			0.645710	+	0.763582i	$0.276561\pi$
$858$		0			0
$859$	44.6224			1.52250			0.761249	−	0.648460i	$-0.224587\pi$
$859$	44.6224			1.52250			0.761249	+	0.648460i	$0.224587\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−15.4848	−	26.8205i	−0.527109	−	0.912980i	−0.999501	−	0.0315912i	$-0.989943\pi$
$863$	−15.4848	−	26.8205i	−0.527109	−	0.912980i	0.472392	−	0.881389i	$-0.343391\pi$
$864$		0			0
$865$	−0.743379	+	1.28757i	−0.0252756	+	0.0437787i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.73661	−	8.20405i	0.160678	−	0.278303i
$870$		0			0
$871$	−1.68253			−0.0570102
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.01398	−	1.28760i	−0.0342788	−	0.0435288i
$876$		0			0
$877$	23.1686			0.782347			0.391174	−	0.920317i	$-0.372069\pi$
$877$	23.1686			0.782347			0.391174	+	0.920317i	$0.372069\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−14.0143			−0.472155			−0.236077	−	0.971734i	$-0.575862\pi$
$881$	−14.0143			−0.472155			−0.236077	+	0.971734i	$0.575862\pi$
$882$		0			0
$883$	39.9269			1.34365			0.671824	−	0.740711i	$-0.265511\pi$
$883$	39.9269			1.34365			0.671824	+	0.740711i	$0.265511\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−26.8441			−0.901338			−0.450669	−	0.892691i	$-0.648814\pi$
$887$	−26.8441			−0.901338			−0.450669	+	0.892691i	$0.648814\pi$
$888$		0			0
$889$	7.55082	+	9.58837i	0.253246	+	0.321584i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	12.2921			0.411339
$894$		0			0
$895$	−0.265167	+	0.459283i	−0.00886356	+	0.0153521i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.08017	+	10.5312i	−0.202785	+	0.351234i
$900$		0			0
$901$	−1.75572	−	3.04100i	−0.0584915	−	0.101310i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.0392060			0.00130325
$906$		0			0
$907$	−37.7617			−1.25386			−0.626928	−	0.779077i	$-0.715688\pi$
$907$	−37.7617			−1.25386			−0.626928	+	0.779077i	$0.715688\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	7.93650	+	13.7464i	0.262948	+	0.455439i	0.967024	−	0.254685i	$-0.0819719\pi$
$911$	7.93650	+	13.7464i	0.262948	+	0.455439i	−0.704076	+	0.710125i	$0.748639\pi$
$912$		0			0
$913$	−6.91094	−	11.9701i	−0.228719	−	0.396153i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.249035	−	0.316236i	−0.00822388	−	0.0104430i
$918$		0			0
$919$	−5.22203	−	9.04482i	−0.172259	−	0.298361i	0.766950	−	0.641706i	$-0.221773\pi$
$919$	−5.22203	−	9.04482i	−0.172259	−	0.298361i	−0.939209	+	0.343345i	$0.888440\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.569580	+	0.986541i	−0.0187479	+	0.0324724i
$924$		0			0
$925$	21.2879	+	36.8717i	0.699941	+	1.21233i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−9.58169	+	16.5960i	−0.314365	+	0.544496i	−0.979302	−	0.202403i	$-0.935125\pi$
$929$	−9.58169	+	16.5960i	−0.314365	+	0.544496i	0.664937	+	0.746899i	$0.268458\pi$
$930$		0			0
$931$	12.5356	−	3.69912i	0.410839	−	0.121234i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.109329	+	0.189363i	−0.00357543	+	0.00619283i
$936$		0			0
$937$	3.09451			0.101093			0.0505467	−	0.998722i	$-0.483904\pi$
$937$	3.09451			0.101093			0.0505467	+	0.998722i	$0.483904\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	7.65564	+	13.2600i	0.249567	+	0.432262i	0.963406	−	0.268048i	$-0.0863785\pi$
$941$	7.65564	+	13.2600i	0.249567	+	0.432262i	−0.713839	+	0.700310i	$0.753045\pi$
$942$		0			0
$943$	−30.6845	+	53.1472i	−0.999226	+	1.73071i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.507747	+	0.879443i	−0.0164995	+	0.0285781i	−0.874157	−	0.485643i	$-0.838586\pi$
$947$	−0.507747	+	0.879443i	−0.0164995	+	0.0285781i	0.857658	+	0.514221i	$0.171919\pi$
$948$		0			0
$949$	1.04754	+	1.81440i	0.0340047	+	0.0588979i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	35.4930			1.14973			0.574865	−	0.818248i	$-0.305055\pi$
$953$	35.4930			1.14973			0.574865	+	0.818248i	$0.305055\pi$
$954$		0			0
$955$	−0.730713	+	1.26563i	−0.0236453	+	0.0409549i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	5.81982	+	7.39026i	0.187932	+	0.238644i
$960$		0			0
$961$	12.2814	−	21.2720i	0.396175	−	0.686195i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.793390	−	1.37419i	−0.0255401	−	0.0442368i
$966$		0			0
$967$	−6.87762	+	11.9124i	−0.221169	+	0.383077i	−0.955163	−	0.296079i	$-0.904321\pi$
$967$	−6.87762	+	11.9124i	−0.221169	+	0.383077i	0.733994	+	0.679156i	$0.237654\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−21.6567	−	37.5104i	−0.694995	−	1.20377i	−0.970182	−	0.242376i	$-0.922073\pi$
$971$	−21.6567	−	37.5104i	−0.694995	−	1.20377i	0.275187	−	0.961391i	$-0.411260\pi$
$972$		0			0
$973$	39.8517	−	5.75718i	1.27759	−	0.184567i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−4.78420	−	8.28648i	−0.153060	−	0.265108i	0.779291	−	0.626662i	$-0.215579\pi$
$977$	−4.78420	−	8.28648i	−0.153060	−	0.265108i	−0.932351	+	0.361554i	$0.882246\pi$
$978$		0			0
$979$	−13.6787	−	23.6923i	−0.437174	−	0.757208i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	17.1329			0.546454			0.273227	−	0.961950i	$-0.411909\pi$
$983$	17.1329			0.546454			0.273227	+	0.961950i	$0.411909\pi$
$984$		0			0
$985$	−0.586111			−0.0186751
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−24.5452	−	42.5135i	−0.780492	−	1.35185i
$990$		0			0
$991$	−6.32891	+	10.9620i	−0.201044	+	0.348219i	−0.948865	−	0.315682i	$-0.897767\pi$
$991$	−6.32891	+	10.9620i	−0.201044	+	0.348219i	0.747821	+	0.663901i	$0.231100\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.257255	+	0.445579i	−0.00815553	+	0.0141258i
$996$		0			0
$997$	−25.6704			−0.812989			−0.406495	−	0.913653i	$-0.633249\pi$
$997$	−25.6704			−0.812989			−0.406495	+	0.913653i	$0.633249\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.t.k.1873.6		22
3.2	odd	2		1008.2.t.l.193.8		22
4.3	odd	2		1512.2.t.c.361.6		22
7.2	even	3		3024.2.q.l.2305.6		22
9.2	odd	6		1008.2.q.l.529.1		22
9.7	even	3		3024.2.q.l.2881.6		22
12.11	even	2		504.2.t.c.193.4	yes	22
21.2	odd	6		1008.2.q.l.625.1		22
28.23	odd	6		1512.2.q.d.793.6		22
36.7	odd	6		1512.2.q.d.1369.6		22
36.11	even	6		504.2.q.c.25.11	✓	22
63.2	odd	6		1008.2.t.l.961.8		22
63.16	even	3	inner	3024.2.t.k.289.6		22
84.23	even	6		504.2.q.c.121.11	yes	22
252.79	odd	6		1512.2.t.c.289.6		22
252.191	even	6		504.2.t.c.457.4	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.11	✓	22	36.11	even	6
504.2.q.c.121.11	yes	22	84.23	even	6
504.2.t.c.193.4	yes	22	12.11	even	2
504.2.t.c.457.4	yes	22	252.191	even	6
1008.2.q.l.529.1		22	9.2	odd	6
1008.2.q.l.625.1		22	21.2	odd	6
1008.2.t.l.193.8		22	3.2	odd	2
1008.2.t.l.961.8		22	63.2	odd	6
1512.2.q.d.793.6		22	28.23	odd	6
1512.2.q.d.1369.6		22	36.7	odd	6
1512.2.t.c.289.6		22	252.79	odd	6
1512.2.t.c.361.6		22	4.3	odd	2
3024.2.q.l.2305.6		22	7.2	even	3
3024.2.q.l.2881.6		22	9.7	even	3
3024.2.t.k.289.6		22	63.16	even	3	inner
3024.2.t.k.1873.6		22	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.0619693 q^{5} +(1.63689 + 2.07860i) q^{7} +O(q^{10})\)	\(q+0.0619693 q^{5} +(1.63689 + 2.07860i) q^{7} -3.18053 q^{11} +(-0.252417 + 0.437198i) q^{13} +(0.554700 - 0.960769i) q^{17} +(-0.933573 - 1.61700i) q^{19} -6.20496 q^{23} -4.99616 q^{25} +(-2.39645 - 4.15077i) q^{29} +(-1.26858 - 2.19724i) q^{31} +(0.101437 + 0.128809i) q^{35} +(-4.26085 - 7.38001i) q^{37} +(4.94516 - 8.56527i) q^{41} +(3.95574 + 6.85154i) q^{43} +(-3.29168 + 5.70136i) q^{47} +(-1.64116 + 6.80489i) q^{49} +(1.58258 - 2.74112i) q^{53} -0.197095 q^{55} +(-4.50652 - 7.80552i) q^{59} +(6.94094 - 12.0221i) q^{61} +(-0.0156421 + 0.0270929i) q^{65} +(1.66642 + 2.88632i) q^{67} +2.25651 q^{71} +(2.07503 - 3.59406i) q^{73} +(-5.20619 - 6.61106i) q^{77} +(-1.48925 + 2.57946i) q^{79} +(2.17289 + 3.76355i) q^{83} +(0.0343744 - 0.0595381i) q^{85} +(4.30077 + 7.44915i) q^{89} +(-1.32194 + 0.190974i) q^{91} +(-0.0578528 - 0.100204i) q^{95} +(-3.27671 - 5.67542i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{5} + q^{7}+O(q^{10}) \) 22 * q + 2 * q^5 + q^7	\( 22 q + 2 q^{5} + q^{7} - 6 q^{11} + 7 q^{13} + q^{17} - 13 q^{19} + 44 q^{25} + 7 q^{29} - 6 q^{31} + 2 q^{35} + 6 q^{37} - 4 q^{41} - 2 q^{43} + 17 q^{47} + 29 q^{49} - q^{53} - 2 q^{55} - 21 q^{59} + 31 q^{61} + 3 q^{65} + 26 q^{67} - 32 q^{71} + 17 q^{73} + 4 q^{77} + 16 q^{79} - 36 q^{83} + 28 q^{85} + 2 q^{89} - 15 q^{91} - 24 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q + 2 * q^5 + q^7 - 6 * q^11 + 7 * q^13 + q^17 - 13 * q^19 + 44 * q^25 + 7 * q^29 - 6 * q^31 + 2 * q^35 + 6 * q^37 - 4 * q^41 - 2 * q^43 + 17 * q^47 + 29 * q^49 - q^53 - 2 * q^55 - 21 * q^59 + 31 * q^61 + 3 * q^65 + 26 * q^67 - 32 * q^71 + 17 * q^73 + 4 * q^77 + 16 * q^79 - 36 * q^83 + 28 * q^85 + 2 * q^89 - 15 * q^91 - 24 * q^95 + 19 * q^97

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