LMFDB - Embedded newform 1512.2.q.d.793.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(793,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1512.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.q (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:	$12.0733807856$
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			793.6
Character	$\chi$	$=$	1512.793
Dual form			1512.2.q.d.1369.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0309846 - 0.0536670i) q^{5} +(-0.981674 - 2.45689i) q^{7} +O(q^{10})$	$q+(-0.0309846 - 0.0536670i) q^{5} +(-0.981674 - 2.45689i) q^{7} +(-1.59027 + 2.75442i) q^{11} +(-0.252417 + 0.437198i) q^{13} +(0.554700 + 0.960769i) q^{17} +(0.933573 - 1.61700i) q^{19} +(-3.10248 - 5.37365i) q^{23} +(2.49808 - 4.32680i) q^{25} +(-2.39645 - 4.15077i) q^{29} -2.53716 q^{31} +(-0.101437 + 0.128809i) q^{35} +(-4.26085 + 7.38001i) q^{37} +(4.94516 - 8.56527i) q^{41} +(-3.95574 - 6.85154i) q^{43} -6.58336 q^{47} +(-5.07263 + 4.82373i) q^{49} +(1.58258 + 2.74112i) q^{53} +0.197095 q^{55} -9.01304 q^{59} -13.8819 q^{61} +0.0312842 q^{65} +3.33283 q^{67} -2.25651 q^{71} +(2.07503 + 3.59406i) q^{73} +(8.32844 + 1.20317i) q^{77} -2.97850 q^{79} +(-2.17289 - 3.76355i) q^{83} +(0.0343744 - 0.0595381i) q^{85} +(4.30077 - 7.44915i) q^{89} +(1.32194 + 0.190974i) q^{91} -0.115706 q^{95} +(-3.27671 - 5.67542i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{5} + 5 q^{7}+O(q^{10}) $ 22 * q - q^5 + 5 * q^7	$ 22 q - q^{5} + 5 q^{7} - 3 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} - 22 q^{25} + 7 q^{29} - 12 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} + 34 q^{47} - 25 q^{49} - q^{53} + 2 q^{55} - 42 q^{59} - 62 q^{61} - 6 q^{65} + 52 q^{67} + 32 q^{71} + 17 q^{73} + q^{77} + 32 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} - 48 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q - q^5 + 5 * q^7 - 3 * q^11 + 7 * q^13 + q^17 + 13 * q^19 - 22 * q^25 + 7 * q^29 - 12 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 + 34 * q^47 - 25 * q^49 - q^53 + 2 * q^55 - 42 * q^59 - 62 * q^61 - 6 * q^65 + 52 * q^67 + 32 * q^71 + 17 * q^73 + q^77 + 32 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 - 48 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.0309846	−	0.0536670i	−0.0138567	−	0.0240006i	0.859014	−	0.511952i	$-0.171078\pi$
$5$	−0.0309846	−	0.0536670i	−0.0138567	−	0.0240006i	−0.872871	+	0.487952i	$0.837744\pi$
$6$		0			0
$7$	−0.981674	−	2.45689i	−0.371038	−	0.928618i
$7$	−0.981674	−	2.45689i	−0.371038	−	0.928618i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.59027	+	2.75442i	−0.479483	+	0.830490i	−0.999723	−	0.0235306i	$-0.992509\pi$
$11$	−1.59027	+	2.75442i	−0.479483	+	0.830490i	0.520240	+	0.854020i	$0.325843\pi$
$12$		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	0.925420	−	0.378944i	$-0.123713\pi$
$17$	0.554700	+	0.960769i	0.134535	+	0.233021i	−0.790885	+	0.611965i	$0.790379\pi$
$18$		0			0
$19$	0.933573	−	1.61700i	0.214176	−	0.370964i	−0.738841	−	0.673880i	$-0.764627\pi$
$19$	0.933573	−	1.61700i	0.214176	−	0.370964i	0.953017	+	0.302915i	$0.0979599\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.10248	−	5.37365i	−0.646912	−	1.12048i	−0.983856	−	0.178960i	$-0.942727\pi$
$23$	−3.10248	−	5.37365i	−0.646912	−	1.12048i	0.336945	−	0.941525i	$-0.390607\pi$
$24$		0			0
$25$	2.49808	−	4.32680i	0.499616	−	0.865360i
$26$		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
$31$	−2.53716			−0.455687			−0.227843	−	0.973698i	$-0.573167\pi$
$31$	−2.53716			−0.455687			−0.227843	+	0.973698i	$0.573167\pi$
$32$		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	0.267819	+	0.963469i	$0.413697\pi$
$37$	−4.26085	+	7.38001i	−0.700479	+	1.21327i	−0.968298	+	0.249797i	$0.919636\pi$
$38$		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	$-0.960541\pi$
$43$	−3.95574	−	6.85154i	−0.603244	−	1.04485i	0.389082	−	0.921203i	$-0.372792\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.58336			−0.960282			−0.480141	−	0.877191i	$-0.659414\pi$
$47$	−6.58336			−0.960282			−0.480141	+	0.877191i	$0.659414\pi$
$48$		0			0
$49$	−5.07263	+	4.82373i	−0.724662	+	0.689105i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.58258	+	2.74112i	0.217385	+	0.376521i	0.954008	−	0.299782i	$-0.0969140\pi$
$53$	1.58258	+	2.74112i	0.217385	+	0.376521i	−0.736623	+	0.676304i	$0.763581\pi$
$54$		0			0
$55$	0.197095			0.0265763
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−9.01304			−1.17340			−0.586699	−	0.809805i	$-0.699573\pi$
$59$	−9.01304			−1.17340			−0.586699	+	0.809805i	$0.699573\pi$
$60$		0			0
$61$	−13.8819			−1.77739			−0.888697	−	0.458496i	$-0.848388\pi$
$61$	−13.8819			−1.77739			−0.888697	+	0.458496i	$0.848388\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.0312842			0.00388032
$66$		0			0
$67$	3.33283			0.407170			0.203585	−	0.979057i	$-0.434741\pi$
$67$	3.33283			0.407170			0.203585	+	0.979057i	$0.434741\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.25651			−0.267798			−0.133899	−	0.990995i	$-0.542750\pi$
$71$	−2.25651			−0.267798			−0.133899	+	0.990995i	$0.542750\pi$
$72$		0			0
$73$	2.07503	+	3.59406i	0.242864	+	0.420652i	0.961529	−	0.274704i	$-0.0885799\pi$
$73$	2.07503	+	3.59406i	0.242864	+	0.420652i	−0.718665	+	0.695356i	$0.755247\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.32844	+	1.20317i	0.949114	+	0.137114i
$78$		0			0
$79$	−2.97850			−0.335107			−0.167554	−	0.985863i	$-0.553587\pi$
$79$	−2.97850			−0.335107			−0.167554	+	0.985863i	$0.553587\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.17289	−	3.76355i	−0.238506	−	0.413104i	0.721780	−	0.692122i	$-0.243324\pi$
$83$	−2.17289	−	3.76355i	−0.238506	−	0.413104i	−0.960286	+	0.279019i	$0.909991\pi$
$84$		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	−0.542858	−	0.839824i	$-0.682658\pi$
$89$	4.30077	−	7.44915i	0.455880	−	0.789608i	0.998738	+	0.0502166i	$0.0159912\pi$
$90$		0			0
$91$	1.32194	+	0.190974i	0.138577	+	0.0200195i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.115706			−0.0118712
$96$		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
$101$	3.25827	−	5.64349i	0.324210	−	0.561548i	−0.657142	−	0.753767i	$-0.728235\pi$
$101$	3.25827	−	5.64349i	0.324210	−	0.561548i	0.981352	+	0.192219i	$0.0615683\pi$
$102$		0			0
$103$	−8.50978	−	14.7394i	−0.838494	−	1.45231i	−0.891154	−	0.453701i	$-0.850103\pi$
$103$	−8.50978	−	14.7394i	−0.838494	−	1.45231i	0.0526599	−	0.998613i	$-0.483230\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.86075	−	15.3473i	0.856601	−	1.48368i	−0.0185508	−	0.999828i	$-0.505905\pi$
$107$	8.86075	−	15.3473i	0.856601	−	1.48368i	0.875152	−	0.483848i	$-0.160761\pi$
$108$		0			0
$109$	6.62928	+	11.4822i	0.634970	+	1.09980i	0.986522	+	0.163631i	$0.0523208\pi$
$109$	6.62928	+	11.4822i	0.634970	+	1.09980i	−0.351552	+	0.936168i	$0.614346\pi$
$110$		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
$115$	−0.192258	+	0.333001i	−0.0179282	+	0.0310525i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.81597	−	2.30600i	0.166470	−	0.211391i
$120$		0			0
$121$	0.442104	+	0.765746i	0.0401912	+	0.0696133i
$122$		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	$-0.565610\pi$
$127$	−4.61290			−0.409329			−0.204664	+	0.978832i	$0.565610\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.0760695	−	0.131756i	−0.00664623	−	0.0115116i	0.862683	−	0.505745i	$-0.168782\pi$
$131$	−0.0760695	−	0.131756i	−0.00664623	−	0.0115116i	−0.869329	+	0.494233i	$0.835449\pi$
$132$		0			0
$133$	−4.88925	−	0.706325i	−0.423952	−	0.0612461i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.77770	+	3.07907i	−0.151879	+	0.263063i	−0.931918	−	0.362668i	$-0.881866\pi$
$137$	−1.77770	+	3.07907i	−0.151879	+	0.263063i	0.780039	+	0.625731i	$0.215199\pi$
$138$		0			0
$139$	−7.60945	+	13.1800i	−0.645425	+	1.11791i	0.338778	+	0.940866i	$0.389987\pi$
$139$	−7.60945	+	13.1800i	−0.645425	+	1.11791i	−0.984203	+	0.177043i	$0.943347\pi$
$140$		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
$149$	0.183457	+	0.317757i	0.0150294	+	0.0260317i	0.873442	−	0.486928i	$-0.161882\pi$
$149$	0.183457	+	0.317757i	0.0150294	+	0.0260317i	−0.858413	+	0.512959i	$0.828549\pi$
$150$		0			0
$151$	6.29162	−	10.8974i	0.512005	−	0.886818i	−0.487899	−	0.872900i	$-0.662236\pi$
$151$	6.29162	−	10.8974i	0.512005	−	0.886818i	0.999903	−	0.0139176i	$-0.00443024\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.0786128	+	0.136161i	0.00631434	+	0.0109368i
$156$		0			0
$157$	−5.45468			−0.435331			−0.217666	−	0.976023i	$-0.569844\pi$
$157$	−5.45468			−0.435331			−0.217666	+	0.976023i	$0.569844\pi$
$158$		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	$-0.736204\pi$
$163$	3.83559	−	6.64343i	0.300426	−	0.520354i	0.976233	+	0.216726i	$0.0695377\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.47493	−	16.4111i	0.733192	−	1.26993i	−0.222320	−	0.974974i	$-0.571363\pi$
$167$	9.47493	−	16.4111i	0.733192	−	1.26993i	0.955512	−	0.294952i	$-0.0953037\pi$
$168$		0			0
$169$	6.37257	+	11.0376i	0.490198	+	0.849048i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	23.9919			1.82407			0.912034	−	0.410115i	$-0.134512\pi$
$173$	23.9919			1.82407			0.912034	+	0.410115i	$0.134512\pi$
$174$		0			0
$175$	−13.0828	−	1.89000i	−0.988965	−	0.142871i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.27901	+	7.41146i	0.319828	+	0.553959i	0.980452	−	0.196758i	$-0.0630415\pi$
$179$	4.27901	+	7.41146i	0.319828	+	0.553959i	−0.660624	+	0.750717i	$0.729708\pi$
$180$		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
$185$	0.528083			0.0388255
$186$		0			0
$187$	−3.52849			−0.258028
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−23.5831			−1.70641			−0.853205	−	0.521575i	$-0.825345\pi$
$191$	−23.5831			−1.70641			−0.853205	+	0.521575i	$0.825345\pi$
$192$		0			0
$193$	25.6059			1.84315			0.921577	−	0.388196i	$-0.126902\pi$
$193$	25.6059			1.84315			0.921577	+	0.388196i	$0.126902\pi$
$194$		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	$-0.0715868\pi$
$199$	4.15133	+	7.19032i	0.294280	+	0.509708i	−0.680537	+	0.732714i	$0.738253\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−7.84547	+	9.96253i	−0.550644	+	0.699232i
$204$		0			0
$205$	−0.612896			−0.0428065
$206$		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	$0.411902\pi$
$211$	−10.1164	+	17.5222i	−0.696444	+	1.20628i	−0.969691	+	0.244333i	$0.921431\pi$
$212$		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
$221$	−0.560062			−0.0376739
$222$		0			0
$223$	−2.41918	−	4.19014i	−0.162000	−	0.280593i	0.773586	−	0.633692i	$-0.218461\pi$
$223$	−2.41918	−	4.19014i	−0.162000	−	0.280593i	−0.935586	+	0.353099i	$0.885128\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.336106	−	0.582153i	0.0223082	−	0.0386389i	−0.854656	−	0.519195i	$-0.826232\pi$
$227$	0.336106	−	0.582153i	0.0223082	−	0.0386389i	0.876964	+	0.480556i	$0.159565\pi$
$228$		0			0
$229$	3.06776	+	5.31352i	0.202724	+	0.351128i	0.949405	−	0.314054i	$-0.101687\pi$
$229$	3.06776	+	5.31352i	0.202724	+	0.351128i	−0.746681	+	0.665182i	$0.768354\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.1492	+	21.0431i	−0.795922	+	1.37858i	0.126330	+	0.991988i	$0.459680\pi$
$233$	−12.1492	+	21.0431i	−0.795922	+	1.37858i	−0.922252	+	0.386589i	$0.873653\pi$
$234$		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	$0.508836\pi$
$239$	−13.5978	+	23.5521i	−0.879569	+	1.52346i	−0.851815	+	0.523843i	$0.824498\pi$
$240$		0			0
$241$	12.9027	−	22.3481i	0.831135	−	1.43957i	−0.0660031	−	0.997819i	$-0.521025\pi$
$241$	12.9027	−	22.3481i	0.831135	−	1.43957i	0.897139	−	0.441749i	$-0.145642\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.416049	+	0.122771i	0.0265804	+	0.00784356i
$246$		0			0
$247$	0.471299	+	0.816313i	0.0299880	+	0.0519408i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	27.0741			1.70890			0.854450	−	0.519533i	$-0.173894\pi$
$251$	27.0741			1.70890			0.854450	+	0.519533i	$0.173894\pi$
$252$		0			0
$253$	19.7351			1.24073
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.76073	−	11.7099i	−0.421723	−	0.730445i	0.574385	−	0.818585i	$-0.305241\pi$
$257$	−6.76073	−	11.7099i	−0.421723	−	0.730445i	−0.996108	+	0.0881399i	$0.971908\pi$
$258$		0			0
$259$	22.3146	+	3.22368i	1.38656	+	0.200310i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.68727	+	11.5827i	−0.412355	+	0.714220i	−0.995147	−	0.0984018i	$-0.968627\pi$
$263$	−6.68727	+	11.5827i	−0.412355	+	0.714220i	0.582792	+	0.812621i	$0.301960\pi$
$264$		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	0.721599	−	0.692311i	$-0.243407\pi$
$269$	−3.91594	−	6.78261i	−0.238759	−	0.413543i	−0.960359	+	0.278768i	$0.910074\pi$
$270$		0			0
$271$	15.1737	−	26.2816i	0.921735	−	1.59649i	0.125005	−	0.992156i	$-0.460105\pi$
$271$	15.1737	−	26.2816i	0.921735	−	1.59649i	0.796730	−	0.604335i	$-0.206561\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7.94523	+	13.7615i	0.479115	+	0.829852i
$276$		0			0
$277$	11.3462	−	19.6522i	0.681728	−	1.18079i	−0.292725	−	0.956197i	$-0.594562\pi$
$277$	11.3462	−	19.6522i	0.681728	−	1.18079i	0.974453	−	0.224591i	$-0.0721046\pi$
$278$		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
$283$	−16.9059			−1.00495			−0.502477	−	0.864591i	$-0.667578\pi$
$283$	−16.9059			−1.00495			−0.502477	+	0.864591i	$0.667578\pi$
$284$		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
$299$	3.13247			0.181155
$300$		0			0
$301$	−12.9502	+	16.4448i	−0.746439	+	0.947862i
$302$		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	$-0.349901\pi$
$307$	15.9188			0.908534			0.454267	+	0.890866i	$0.349901\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.262869			0.0149059			0.00745297	−	0.999972i	$-0.497628\pi$
$311$	0.262869			0.0149059			0.00745297	+	0.999972i	$0.497628\pi$
$312$		0			0
$313$	−6.25068			−0.353309			−0.176655	−	0.984273i	$-0.556528\pi$
$313$	−6.25068			−0.353309			−0.176655	+	0.984273i	$0.556528\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	19.6792			1.10530			0.552648	−	0.833415i	$-0.313618\pi$
$317$	19.6792			1.10530			0.552648	+	0.833415i	$0.313618\pi$
$318$		0			0
$319$	15.2440			0.853499
$320$		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
$329$	6.46271	+	16.1746i	0.356301	+	0.891734i
$330$		0			0
$331$	24.5338			1.34850			0.674249	−	0.738504i	$-0.264467\pi$
$331$	24.5338			1.34850			0.674249	+	0.738504i	$0.264467\pi$
$332$		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
$347$	19.6957			1.05732			0.528661	−	0.848833i	$-0.322694\pi$
$347$	19.6957			1.05732			0.528661	+	0.848833i	$0.322694\pi$
$348$		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
$353$	−5.83073	+	10.0991i	−0.310338	+	0.537522i	−0.978436	−	0.206552i	$-0.933776\pi$
$353$	−5.83073	+	10.0991i	−0.310338	+	0.537522i	0.668097	+	0.744074i	$0.267109\pi$
$354$		0			0
$355$	0.0699170	+	0.121100i	0.00371081	+	0.00642731i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.82159	−	15.2794i	0.465586	−	0.806418i	−0.533642	−	0.845710i	$-0.679177\pi$
$359$	8.82159	−	15.2794i	0.465586	−	0.806418i	0.999228	+	0.0392925i	$0.0125104\pi$
$360$		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
$367$	−1.69146	+	2.92969i	−0.0882934	+	0.152929i	−0.906790	−	0.421583i	$-0.861475\pi$
$367$	−1.69146	+	2.92969i	−0.0882934	+	0.152929i	0.818496	+	0.574512i	$0.194808\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	5.18104	−	6.57912i	0.268986	−	0.341571i
$372$		0			0
$373$	−6.69511	−	11.5963i	−0.346660	−	0.600433i	0.638994	−	0.769212i	$-0.279351\pi$
$373$	−6.69511	−	11.5963i	−0.346660	−	0.600433i	−0.985654	+	0.168779i	$0.946018\pi$
$374$		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	$-0.750941\pi$
$379$	−27.6131			−1.41839			−0.709194	+	0.705013i	$0.750941\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	12.5020	+	21.6541i	0.638822	+	1.10647i	0.985692	+	0.168559i	$0.0539114\pi$
$383$	12.5020	+	21.6541i	0.638822	+	1.10647i	−0.346869	+	0.937913i	$0.612755\pi$
$384$		0			0
$385$	−0.193483	−	0.484242i	−0.00986083	−	0.0246792i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−0.0683229	+	0.118339i	−0.00346411	+	0.00600001i	−0.867752	−	0.496997i	$-0.834436\pi$
$389$	−0.0683229	+	0.118339i	−0.00346411	+	0.00600001i	0.864288	+	0.502997i	$0.167769\pi$
$390$		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	−0.596349	−	0.802726i	$-0.703382\pi$
$397$	7.91030	−	13.7010i	0.397006	−	0.687635i	0.993355	+	0.115090i	$0.0367157\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.52745	−	9.57383i	−0.276028	−	0.478094i	0.694366	−	0.719622i	$-0.255685\pi$
$401$	−5.52745	−	9.57383i	−0.276028	−	0.478094i	−0.970394	+	0.241528i	$0.922352\pi$
$402$		0			0
$403$	0.640420	−	1.10924i	0.0319016	−	0.0552552i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−13.5518	−	23.4724i	−0.671737	−	1.16348i
$408$		0			0
$409$	−36.0128			−1.78072			−0.890358	−	0.455260i	$-0.849546\pi$
$409$	−36.0128			−1.78072			−0.890358	+	0.455260i	$0.849546\pi$
$410$		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	$0.464758\pi$
$419$	−16.4877	+	28.5576i	−0.805477	+	1.39513i	−0.915968	+	0.401251i	$0.868576\pi$
$420$		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
$425$	5.54274			0.268862
$426$		0			0
$427$	13.6275	+	34.1063i	0.659480	+	1.65052i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	12.4021	+	21.4811i	0.597389	+	1.03471i	0.993205	+	0.116379i	$0.0371286\pi$
$431$	12.4021	+	21.4811i	0.597389	+	1.03471i	−0.395816	+	0.918330i	$0.629538\pi$
$432$		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
$437$	−11.5856			−0.554213
$438$		0			0
$439$	−40.5836			−1.93695			−0.968475	−	0.249110i	$-0.919862\pi$
$439$	−40.5836			−1.93695			−0.968475	+	0.249110i	$0.919862\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	28.2665			1.34298			0.671490	−	0.741014i	$-0.265655\pi$
$443$	28.2665			1.34298			0.671490	+	0.741014i	$0.265655\pi$
$444$		0			0
$445$	−0.533031			−0.0252681
$446$		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
$455$	−0.0307108	−	0.0768618i	−0.00143975	−	0.00360334i
$456$		0			0
$457$	−6.38308			−0.298588			−0.149294	−	0.988793i	$-0.547700\pi$
$457$	−6.38308			−0.298588			−0.149294	+	0.988793i	$0.547700\pi$
$458$		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	$-0.622123\pi$
$463$	13.2527	−	22.9544i	0.615907	−	1.06678i	0.990225	−	0.139482i	$-0.0445438\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	11.6879	−	20.2440i	0.540851	−	0.936782i	−0.458004	−	0.888950i	$-0.651436\pi$
$467$	11.6879	−	20.2440i	0.540851	−	0.936782i	0.998855	−	0.0478318i	$-0.0152311\pi$
$468$		0			0
$469$	−3.27176	−	8.18841i	−0.151076	−	0.378106i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	25.1627			1.15698
$474$		0			0
$475$	−4.66428	−	8.07877i	−0.214012	−	0.370679i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.64803	−	8.05063i	0.212374	−	0.367842i	−0.740083	−	0.672515i	$-0.765214\pi$
$479$	4.64803	−	8.05063i	0.212374	−	0.367842i	0.952457	+	0.304673i	$0.0985472\pi$
$480$		0			0
$481$	−2.15102	−	3.72567i	−0.0980780	−	0.169876i
$482$		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	$-0.137062\pi$
$487$	2.04947	+	3.54979i	0.0928704	+	0.160856i	−0.815847	+	0.578267i	$0.803729\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−4.98703	+	8.63778i	−0.225061	+	0.389818i	−0.956338	−	0.292264i	$-0.905592\pi$
$491$	−4.98703	+	8.63778i	−0.225061	+	0.389818i	0.731277	+	0.682081i	$0.238925\pi$
$492$		0			0
$493$	2.65862	−	4.60487i	0.119738	−	0.207393i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.21515	+	5.54399i	0.0993632	+	0.248682i
$498$		0			0
$499$	5.60415	+	9.70667i	0.250876	+	0.434530i	0.963767	−	0.266744i	$-0.0859480\pi$
$499$	5.60415	+	9.70667i	0.250876	+	0.434530i	−0.712891	+	0.701275i	$0.752615\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.69350			0.0755094			0.0377547	−	0.999287i	$-0.487979\pi$
$503$	1.69350			0.0755094			0.0377547	+	0.999287i	$0.487979\pi$
$504$		0			0
$505$	−0.403825			−0.0179700
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−20.4777	−	35.4685i	−0.907659	−	1.57211i	−0.817307	−	0.576202i	$-0.804534\pi$
$509$	−20.4777	−	35.4685i	−0.907659	−	1.57211i	−0.0903524	−	0.995910i	$-0.528799\pi$
$510$		0			0
$511$	6.79320	−	8.62631i	0.300514	−	0.381606i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.527345	+	0.913388i	−0.0232376	+	0.0402487i
$516$		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	−0.975163	−	0.221488i	$-0.928909\pi$
$521$	−15.5075	−	26.8598i	−0.679396	−	1.17675i	0.295767	−	0.955260i	$-0.404425\pi$
$522$		0			0
$523$	−3.67840	+	6.37117i	−0.160845	+	0.278592i	−0.935172	−	0.354194i	$-0.884755\pi$
$523$	−3.67840	+	6.37117i	−0.160845	+	0.278592i	0.774327	+	0.632786i	$0.218089\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.40736	−	2.43762i	−0.0613056	−	0.106184i
$528$		0			0
$529$	−7.75077	+	13.4247i	−0.336990	+	0.583684i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2.49648	+	4.32404i	0.108135	+	0.187295i
$534$		0			0
$535$	−1.09819			−0.0474788
$536$		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	0.366801	+	0.930299i	$0.380453\pi$
$541$	−14.4735	+	25.0688i	−0.622262	+	1.07779i	−0.989063	+	0.147491i	$0.952880\pi$
$542$		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	0.993692	−	0.112140i	$-0.0357704\pi$
$547$	9.34891	+	16.1928i	0.399731	+	0.692354i	−0.593962	+	0.804493i	$0.702437\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−8.94905			−0.381242
$552$		0			0
$553$	2.92392	+	7.31785i	0.124338	+	0.311187i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	17.1787	+	29.7544i	0.727886	+	1.26074i	0.957775	+	0.287519i	$0.0928303\pi$
$557$	17.1787	+	29.7544i	0.727886	+	1.26074i	−0.229889	+	0.973217i	$0.573836\pi$
$558$		0			0
$559$	3.99397			0.168927
$560$		0			0
$561$		0			0
$562$		0			0
$563$	14.7471			0.621516			0.310758	−	0.950489i	$-0.399417\pi$
$563$	14.7471			0.621516			0.310758	+	0.950489i	$0.399417\pi$
$564$		0			0
$565$	0.136449			0.00574047
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3.33642			−0.139870			−0.0699349	−	0.997552i	$-0.522279\pi$
$569$	−3.33642			−0.139870			−0.0699349	+	0.997552i	$0.522279\pi$
$570$		0			0
$571$	18.8072			0.787057			0.393528	−	0.919313i	$-0.371254\pi$
$571$	18.8072			0.787057			0.393528	+	0.919313i	$0.371254\pi$
$572$		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	−0.953975	−	0.299887i	$-0.903051\pi$
$577$	−17.6961	−	30.6505i	−0.736697	−	1.27600i	0.217277	−	0.976110i	$-0.430282\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−7.11357	+	9.03313i	−0.295121	+	0.374758i
$582$		0			0
$583$	−10.0669			−0.416930
$584$		0			0
$585$		0			0
$586$		0			0
$587$	17.2921	+	29.9508i	0.713722	+	1.23620i	0.963450	+	0.267887i	$0.0863256\pi$
$587$	17.2921	+	29.9508i	0.713722	+	1.23620i	−0.249728	+	0.968316i	$0.580341\pi$
$588$		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	−0.325434	−	0.945565i	$-0.605510\pi$
$593$	15.9787	−	27.6759i	0.656166	−	1.13651i	0.981600	−	0.190949i	$-0.0611564\pi$
$594$		0			0
$595$	−0.180023	−	0.0260070i	−0.00738023	−	0.00106618i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	9.84952			0.402440			0.201220	−	0.979546i	$-0.435509\pi$
$599$	9.84952			0.402440			0.201220	+	0.979546i	$0.435509\pi$
$600$		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
$605$	0.0273968	−	0.0474527i	0.00111384	−	0.00192923i
$606$		0			0
$607$	−5.42922	−	9.40368i	−0.220365	−	0.381683i	0.734554	−	0.678550i	$-0.237392\pi$
$607$	−5.42922	−	9.40368i	−0.220365	−	0.381683i	−0.954919	+	0.296867i	$0.904058\pi$
$608$		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	−0.710697	−	0.703499i	$-0.751620\pi$
$613$	−23.8823	−	41.3653i	−0.964596	−	1.67073i	−0.253899	−	0.967231i	$-0.581713\pi$
$614$		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
$619$	−17.9829	+	31.1472i	−0.722792	+	1.25191i	0.237084	+	0.971489i	$0.423808\pi$
$619$	−17.9829	+	31.1472i	−0.722792	+	1.25191i	−0.959876	+	0.280424i	$0.909525\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−22.5237	−	3.25388i	−0.902393	−	0.130364i
$624$		0			0
$625$	−12.4712	−	21.6008i	−0.498848	−	0.864030i
$626$		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	$-0.718858\pi$
$631$	−31.8848			−1.26931			−0.634656	+	0.772794i	$0.718858\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.142929	+	0.247560i	0.00567196	+	0.00982413i
$636$		0			0
$637$	−0.828512	−	3.43534i	−0.0328268	−	0.136113i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	8.33939	−	14.4442i	0.329386	−	0.570513i	−0.653004	−	0.757354i	$-0.726492\pi$
$641$	8.33939	−	14.4442i	0.329386	−	0.570513i	0.982390	+	0.186841i	$0.0598249\pi$
$642$		0			0
$643$	23.5295	−	40.7544i	0.927915	−	1.60720i	0.141109	−	0.989994i	$-0.454933\pi$
$643$	23.5295	−	40.7544i	0.927915	−	1.60720i	0.786805	−	0.617201i	$-0.211734\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	12.2324	+	21.1872i	0.480906	+	0.832954i	0.999760	−	0.0219091i	$-0.00697444\pi$
$647$	12.2324	+	21.1872i	0.480906	+	0.832954i	−0.518854	+	0.854863i	$0.673641\pi$
$648$		0			0
$649$	14.3331	−	24.8257i	0.562625	−	0.974495i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.91306	−	10.2417i	−0.231396	−	0.400789i	0.726823	−	0.686824i	$-0.240996\pi$
$653$	−5.91306	−	10.2417i	−0.231396	−	0.400789i	−0.958219	+	0.286035i	$0.907663\pi$
$654$		0			0
$655$	−0.00471397	+	0.00816484i	−0.000184190	+	0.000319027i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−3.51539	−	6.08883i	−0.136940	−	0.237187i	0.789397	−	0.613883i	$-0.210393\pi$
$659$	−3.51539	−	6.08883i	−0.136940	−	0.237187i	−0.926337	+	0.376696i	$0.877060\pi$
$660$		0			0
$661$	14.8605			0.578006			0.289003	−	0.957328i	$-0.406676\pi$
$661$	14.8605			0.578006			0.289003	+	0.957328i	$0.406676\pi$
$662$		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
$677$	−24.7122			−0.949767			−0.474883	−	0.880049i	$-0.657510\pi$
$677$	−24.7122			−0.949767			−0.474883	+	0.880049i	$0.657510\pi$
$678$		0			0
$679$	−10.7272	+	13.6219i	−0.411674	+	0.522762i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16.7467	+	29.0061i	0.640794	+	1.10989i	0.985256	+	0.171087i	$0.0547279\pi$
$683$	16.7467	+	29.0061i	0.640794	+	1.10989i	−0.344462	+	0.938800i	$0.611939\pi$
$684$		0			0
$685$	0.220326			0.00841821
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.59788			−0.0608745
$690$		0			0
$691$	−2.67672			−0.101827			−0.0509137	−	0.998703i	$-0.516213\pi$
$691$	−2.67672			−0.101827			−0.0509137	+	0.998703i	$0.516213\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.943104			0.0357740
$696$		0			0
$697$	10.9723			0.415607
$698$		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
$707$	−17.0640	−	2.46515i	−0.641758	−	0.0927114i
$708$		0			0
$709$	−11.9074			−0.447191			−0.223596	−	0.974682i	$-0.571779\pi$
$709$	−11.9074			−0.447191			−0.223596	+	0.974682i	$0.571779\pi$
$710$		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	$-0.935263\pi$
$719$	−8.44050	+	14.6194i	−0.314778	+	0.545211i	0.664613	+	0.747188i	$0.268597\pi$
$720$		0			0
$721$	−27.8592	+	35.3769i	−1.03753	+	1.31750i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−23.9461			−0.889336
$726$		0			0
$727$	1.24570	+	2.15762i	0.0462006	+	0.0800218i	0.888201	−	0.459455i	$-0.151955\pi$
$727$	1.24570	+	2.15762i	0.0462006	+	0.0800218i	−0.842000	+	0.539477i	$0.818622\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.38850	−	7.60110i	0.162314	−	0.281137i
$732$		0			0
$733$	6.25653	+	10.8366i	0.231090	+	0.400260i	0.958129	−	0.286336i	$-0.0924374\pi$
$733$	6.25653	+	10.8366i	0.231090	+	0.400260i	−0.727039	+	0.686596i	$0.759104\pi$
$734$		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	$-0.286639\pi$
$739$	−10.0051	−	17.3294i	−0.368044	−	0.637472i	−0.989260	+	0.146168i	$0.953306\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−5.49879	+	9.52419i	−0.201731	+	0.349408i	−0.949086	−	0.315016i	$-0.897990\pi$
$743$	−5.49879	+	9.52419i	−0.201731	+	0.349408i	0.747355	+	0.664425i	$0.231323\pi$
$744$		0			0
$745$	0.0113687	−	0.0196912i	0.000416517	−	0.000721428i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−46.4049	−	6.70388i	−1.69560	−	0.244955i
$750$		0			0
$751$	−14.4335	−	24.9996i	−0.526686	−	0.912247i	−0.999516	−	0.0310938i	$-0.990101\pi$
$751$	−14.4335	−	24.9996i	−0.526686	−	0.912247i	0.472830	−	0.881154i	$-0.343232\pi$
$752$		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
$761$	−26.0020	−	45.0367i	−0.942571	−	1.63258i	−0.760543	−	0.649287i	$-0.775067\pi$
$761$	−26.0020	−	45.0367i	−0.942571	−	1.63258i	−0.182027	−	0.983293i	$-0.558266\pi$
$762$		0			0
$763$	21.7028	−	27.5592i	0.785696	−	0.997712i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.27504	−	3.94049i	0.0821470	−	0.142283i
$768$		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	0.557293	−	0.830316i	$-0.311840\pi$
$773$	−12.2452	−	21.2093i	−0.440428	−	0.762845i	−0.997721	+	0.0674716i	$0.978507\pi$
$774$		0			0
$775$	−6.33802	+	10.9778i	−0.227668	+	0.394333i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−9.23334	−	15.9926i	−0.330819	−	0.572995i
$780$		0			0
$781$	3.58845	−	6.21537i	0.128405	−	0.222403i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.169011	+	0.292736i	0.00603227	+	0.0104482i
$786$		0			0
$787$	1.87862			0.0669657			0.0334828	−	0.999439i	$-0.489340\pi$
$787$	1.87862			0.0669657			0.0334828	+	0.999439i	$0.489340\pi$
$788$		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
$803$	−13.1994			−0.465797
$804$		0			0
$805$	1.00688	+	0.145459i	0.0354880	+	0.00512677i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.53614	−	2.66067i	−0.0540077	−	0.0935441i	0.837758	−	0.546042i	$-0.183866\pi$
$809$	−1.53614	−	2.66067i	−0.0540077	−	0.0935441i	−0.891765	+	0.452498i	$0.850533\pi$
$810$		0			0
$811$	−14.8034			−0.519818			−0.259909	−	0.965633i	$-0.583693\pi$
$811$	−14.8034			−0.519818			−0.259909	+	0.965633i	$0.583693\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.475377			−0.0166517
$816$		0			0
$817$	−14.7719			−0.516802
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−25.0122			−0.872933			−0.436467	−	0.899720i	$-0.643770\pi$
$821$	−25.0122			−0.872933			−0.436467	+	0.899720i	$0.643770\pi$
$822$		0			0
$823$	39.4961			1.37675			0.688374	−	0.725356i	$-0.258325\pi$
$823$	39.4961			1.37675			0.688374	+	0.725356i	$0.258325\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.4528			−0.433026			−0.216513	−	0.976280i	$-0.569468\pi$
$827$	−12.4528			−0.433026			−0.216513	+	0.976280i	$0.569468\pi$
$828$		0			0
$829$	−14.2995	−	24.7675i	−0.496643	−	0.860211i	0.503350	−	0.864083i	$-0.332101\pi$
$829$	−14.2995	−	24.7675i	−0.496643	−	0.860211i	−0.999993	+	0.00387209i	$0.998767\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−7.44828	−	2.19790i	−0.258068	−	0.0761528i
$834$		0			0
$835$	−1.17431			−0.0406386
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−21.0794	−	36.5107i	−0.727743	−	1.26049i	−0.957835	−	0.287319i	$-0.907236\pi$
$839$	−21.0794	−	36.5107i	−0.727743	−	1.26049i	0.230092	−	0.973169i	$-0.426097\pi$
$840$		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
$851$	52.8768			1.81259
$852$		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
$857$	−18.9029	+	32.7408i	−0.645710	+	1.11840i	0.338427	+	0.940993i	$0.390105\pi$
$857$	−18.9029	+	32.7408i	−0.645710	+	1.11840i	−0.984137	+	0.177410i	$0.943228\pi$
$858$		0			0
$859$	22.3112	+	38.6442i	0.761249	+	1.31852i	0.942207	+	0.335031i	$0.108747\pi$
$859$	22.3112	+	38.6442i	0.761249	+	1.31852i	−0.180958	+	0.983491i	$0.557920\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	15.4848	−	26.8205i	0.527109	−	0.912980i	−0.472392	−	0.881389i	$-0.656609\pi$
$863$	15.4848	−	26.8205i	0.527109	−	0.912980i	0.999501	−	0.0315912i	$-0.0100575\pi$
$864$		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
$871$	−0.841263	+	1.45711i	−0.0285051	+	0.0493723i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.608103	+	1.52193i	0.0205576	+	0.0514507i
$876$		0			0
$877$	−11.5843	−	20.0646i	−0.391174	−	0.677533i	0.601431	−	0.798925i	$-0.294597\pi$
$877$	−11.5843	−	20.0646i	−0.391174	−	0.677533i	−0.992605	+	0.121392i	$0.961264\pi$
$878$		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	$-0.734489\pi$
$883$	−39.9269			−1.34365			−0.671824	+	0.740711i	$0.734489\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−13.4221	−	23.2477i	−0.450669	−	0.780581i	0.547759	−	0.836636i	$-0.315481\pi$
$887$	−13.4221	−	23.2477i	−0.450669	−	0.780581i	−0.998428	+	0.0560549i	$0.982148\pi$
$888$		0			0
$889$	4.52836	+	11.3334i	0.151876	+	0.380110i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−6.14605	+	10.6453i	−0.205670	+	0.356230i
$894$		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
$905$	−0.0196030	−	0.0339534i	−0.000651626	−	0.00112865i
$906$		0			0
$907$	−18.8808	+	32.7026i	−0.626928	+	1.08587i	0.361237	+	0.932474i	$0.382355\pi$
$907$	−18.8808	+	32.7026i	−0.626928	+	1.08587i	−0.988165	+	0.153397i	$0.950979\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−7.93650	−	13.7464i	−0.262948	−	0.455439i	0.704076	−	0.710125i	$-0.251361\pi$
$911$	−7.93650	−	13.7464i	−0.262948	−	0.455439i	−0.967024	+	0.254685i	$0.918028\pi$
$912$		0			0
$913$	13.8219			0.457438
$914$		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	$-0.778227\pi$
$919$	5.22203	−	9.04482i	0.172259	−	0.298361i	0.939209	+	0.343345i	$0.111560\pi$
$920$		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
$929$	19.1634			0.628730			0.314365	−	0.949302i	$-0.398208\pi$
$929$	19.1634			0.628730			0.314365	+	0.949302i	$0.398208\pi$
$930$		0			0
$931$	3.06428	+	12.7057i	0.100428	+	0.416414i
$932$		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
$941$	−15.3113			−0.499133			−0.249567	−	0.968358i	$-0.580288\pi$
$941$	−15.3113			−0.499133			−0.249567	+	0.968358i	$0.580288\pi$
$942$		0			0
$943$	−61.3691			−1.99845
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.01549			−0.0329991			−0.0164995	−	0.999864i	$-0.505252\pi$
$947$	−1.01549			−0.0329991			−0.0164995	+	0.999864i	$0.505252\pi$
$948$		0			0
$949$	−2.09509			−0.0680094
$950$		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
$959$	9.31006	+	1.34498i	0.300638	+	0.0434316i
$960$		0			0
$961$	−24.5628			−0.792350
$962$		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	−0.733994	−	0.679156i	$-0.762346\pi$
$967$	6.87762	−	11.9124i	0.221169	−	0.383077i	0.955163	+	0.296079i	$0.0956793\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	21.6567	−	37.5104i	0.694995	−	1.20377i	−0.275187	−	0.961391i	$-0.588740\pi$
$971$	21.6567	−	37.5104i	0.694995	−	1.20377i	0.970182	−	0.242376i	$-0.0779269\pi$
$972$		0			0
$973$	39.8517	+	5.75718i	1.27759	+	0.184567i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	9.56840			0.306120			0.153060	−	0.988217i	$-0.451087\pi$
$977$	9.56840			0.306120			0.153060	+	0.988217i	$0.451087\pi$
$978$		0			0
$979$	13.6787	+	23.6923i	0.437174	+	0.757208i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	8.56644	−	14.8375i	0.273227	−	0.473243i	−0.696459	−	0.717596i	$-0.745242\pi$
$983$	8.56644	−	14.8375i	0.273227	−	0.473243i	0.969686	+	0.244353i	$0.0785757\pi$
$984$		0			0
$985$	0.293056	+	0.507587i	0.00933753	+	0.0161731i
$986$		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	$-0.102233\pi$
$991$	6.32891	+	10.9620i	0.201044	+	0.348219i	−0.747821	+	0.663901i	$0.768900\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.257255	−	0.445579i	0.00815553	−	0.0141258i
$996$		0			0
$997$	12.8352	−	22.2312i	0.406495	−	0.704069i	−0.588000	−	0.808861i	$-0.700084\pi$
$997$	12.8352	−	22.2312i	0.406495	−	0.704069i	0.994494	+	0.104792i	$0.0334177\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.q.d.793.6		22
3.2	odd	2		504.2.q.c.121.11	yes	22
4.3	odd	2		3024.2.q.l.2305.6		22
7.4	even	3		1512.2.t.c.361.6		22
9.2	odd	6		504.2.t.c.457.4	yes	22
9.7	even	3		1512.2.t.c.289.6		22
12.11	even	2		1008.2.q.l.625.1		22
21.11	odd	6		504.2.t.c.193.4	yes	22
28.11	odd	6		3024.2.t.k.1873.6		22
36.7	odd	6		3024.2.t.k.289.6		22
36.11	even	6		1008.2.t.l.961.8		22
63.11	odd	6		504.2.q.c.25.11	✓	22
63.25	even	3	inner	1512.2.q.d.1369.6		22
84.11	even	6		1008.2.t.l.193.8		22
252.11	even	6		1008.2.q.l.529.1		22
252.151	odd	6		3024.2.q.l.2881.6		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.11	✓	22	63.11	odd	6
504.2.q.c.121.11	yes	22	3.2	odd	2
504.2.t.c.193.4	yes	22	21.11	odd	6
504.2.t.c.457.4	yes	22	9.2	odd	6
1008.2.q.l.529.1		22	252.11	even	6
1008.2.q.l.625.1		22	12.11	even	2
1008.2.t.l.193.8		22	84.11	even	6
1008.2.t.l.961.8		22	36.11	even	6
1512.2.q.d.793.6		22	1.1	even	1	trivial
1512.2.q.d.1369.6		22	63.25	even	3	inner
1512.2.t.c.289.6		22	9.7	even	3
1512.2.t.c.361.6		22	7.4	even	3
3024.2.q.l.2305.6		22	4.3	odd	2
3024.2.q.l.2881.6		22	252.151	odd	6
3024.2.t.k.289.6		22	36.7	odd	6
3024.2.t.k.1873.6		22	28.11	odd	6

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0309846 - 0.0536670i) q^{5} +(-0.981674 - 2.45689i) q^{7} +O(q^{10})\)	\(q+(-0.0309846 - 0.0536670i) q^{5} +(-0.981674 - 2.45689i) q^{7} +(-1.59027 + 2.75442i) q^{11} +(-0.252417 + 0.437198i) q^{13} +(0.554700 + 0.960769i) q^{17} +(0.933573 - 1.61700i) q^{19} +(-3.10248 - 5.37365i) q^{23} +(2.49808 - 4.32680i) q^{25} +(-2.39645 - 4.15077i) q^{29} -2.53716 q^{31} +(-0.101437 + 0.128809i) q^{35} +(-4.26085 + 7.38001i) q^{37} +(4.94516 - 8.56527i) q^{41} +(-3.95574 - 6.85154i) q^{43} -6.58336 q^{47} +(-5.07263 + 4.82373i) q^{49} +(1.58258 + 2.74112i) q^{53} +0.197095 q^{55} -9.01304 q^{59} -13.8819 q^{61} +0.0312842 q^{65} +3.33283 q^{67} -2.25651 q^{71} +(2.07503 + 3.59406i) q^{73} +(8.32844 + 1.20317i) q^{77} -2.97850 q^{79} +(-2.17289 - 3.76355i) q^{83} +(0.0343744 - 0.0595381i) q^{85} +(4.30077 - 7.44915i) q^{89} +(1.32194 + 0.190974i) q^{91} -0.115706 q^{95} +(-3.27671 - 5.67542i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{5} + 5 q^{7}+O(q^{10}) \) 22 * q - q^5 + 5 * q^7	\( 22 q - q^{5} + 5 q^{7} - 3 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} - 22 q^{25} + 7 q^{29} - 12 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} + 34 q^{47} - 25 q^{49} - q^{53} + 2 q^{55} - 42 q^{59} - 62 q^{61} - 6 q^{65} + 52 q^{67} + 32 q^{71} + 17 q^{73} + q^{77} + 32 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} - 48 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q - q^5 + 5 * q^7 - 3 * q^11 + 7 * q^13 + q^17 + 13 * q^19 - 22 * q^25 + 7 * q^29 - 12 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 + 34 * q^47 - 25 * q^49 - q^53 + 2 * q^55 - 42 * q^59 - 62 * q^61 - 6 * q^65 + 52 * q^67 + 32 * q^71 + 17 * q^73 + q^77 + 32 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 - 48 * q^95 + 19 * q^97

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