LMFDB - Embedded newform 3024.2.q.l.2305.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2305,3024)]

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, 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("3024.2305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.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:	$24.1467615712$
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			2305.6
Character	$\chi$	$=$	3024.2305
Dual form			3024.2.q.l.2881.6

$q$-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 $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

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

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
$5$	−0.0309846	−	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	−0.520240	−	0.854020i	$-0.674157\pi$
$11$	1.59027	−	2.75442i	0.479483	−	0.830490i	0.999723	+	0.0235306i	$0.00749072\pi$
$12$		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	−0.953017	−	0.302915i	$-0.902040\pi$
$19$	−0.933573	+	1.61700i	−0.214176	+	0.370964i	0.738841	+	0.673880i	$0.235373\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.10248	+	5.37365i	0.646912	+	1.12048i	0.983856	+	0.178960i	$0.0572732\pi$
$23$	3.10248	+	5.37365i	0.646912	+	1.12048i	−0.336945	+	0.941525i	$0.609393\pi$
$24$		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	$-0.426833\pi$
$31$	2.53716			0.455687			0.227843	+	0.973698i	$0.426833\pi$
$32$		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	$0.0394589\pi$
$43$	3.95574	+	6.85154i	0.603244	+	1.04485i	−0.389082	+	0.921203i	$0.627208\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.58336			0.960282			0.480141	−	0.877191i	$-0.340586\pi$
$47$	6.58336			0.960282			0.480141	+	0.877191i	$0.340586\pi$
$48$		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	$-0.300427\pi$
$59$	9.01304			1.17340			0.586699	+	0.809805i	$0.300427\pi$
$60$		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	$-0.565259\pi$
$67$	−3.33283			−0.407170			−0.203585	+	0.979057i	$0.565259\pi$
$68$		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	0.961529	−	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	$-0.446413\pi$
$79$	2.97850			0.335107			0.167554	+	0.985863i	$0.446413\pi$
$80$		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	−0.542858	−	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	$0.149897\pi$
$103$	8.50978	+	14.7394i	0.838494	+	1.45231i	−0.0526599	+	0.998613i	$0.516770\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.86075	+	15.3473i	−0.856601	+	1.48368i	0.0185508	+	0.999828i	$0.494095\pi$
$107$	−8.86075	+	15.3473i	−0.856601	+	1.48368i	−0.875152	+	0.483848i	$0.839239\pi$
$108$		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	$-0.434390\pi$
$127$	4.61290			0.409329			0.204664	+	0.978832i	$0.434390\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.0760695	+	0.131756i	0.00664623	+	0.0115116i	0.869329	−	0.494233i	$-0.164551\pi$
$131$	0.0760695	+	0.131756i	0.00664623	+	0.0115116i	−0.862683	+	0.505745i	$0.831218\pi$
$132$		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	$-0.610013\pi$
$139$	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
$149$	0.183457	+	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	$0.337764\pi$
$151$	−6.29162	+	10.8974i	−0.512005	+	0.886818i	−0.999903	+	0.0139176i	$0.995570\pi$
$152$		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	−0.976233	−	0.216726i	$-0.930462\pi$
$163$	−3.83559	+	6.64343i	−0.300426	+	0.520354i	0.675806	+	0.737079i	$0.263796\pi$
$164$		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
$173$	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	0.660624	−	0.750717i	$-0.270292\pi$
$179$	−4.27901	−	7.41146i	−0.319828	−	0.553959i	−0.980452	+	0.196758i	$0.936959\pi$
$180$		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	$-0.174655\pi$
$191$	23.5831			1.70641			0.853205	+	0.521575i	$0.174655\pi$
$192$		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	0.680537	−	0.732714i	$-0.261747\pi$
$199$	−4.15133	−	7.19032i	−0.294280	−	0.509708i	−0.974817	+	0.223005i	$0.928413\pi$
$200$		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	$-0.588098\pi$
$211$	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
$221$	−0.560062			−0.0376739
$222$		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
$227$	−0.336106	+	0.582153i	−0.0223082	+	0.0386389i	−0.876964	−	0.480556i	$-0.840435\pi$
$227$	−0.336106	+	0.582153i	−0.0223082	+	0.0386389i	0.854656	+	0.519195i	$0.173768\pi$
$228$		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	$-0.491164\pi$
$239$	13.5978	−	23.5521i	0.879569	−	1.52346i	0.851815	−	0.523843i	$-0.175502\pi$
$240$		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	$-0.826106\pi$
$251$	−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
$257$	−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	−0.582792	−	0.812621i	$-0.698040\pi$
$263$	6.68727	−	11.5827i	0.412355	−	0.714220i	0.995147	+	0.0984018i	$0.0313730\pi$
$264$		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	$0.539895\pi$
$271$	−15.1737	+	26.2816i	−0.921735	+	1.59649i	−0.796730	+	0.604335i	$0.793439\pi$
$272$		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	$-0.332422\pi$
$283$	16.9059			1.00495			0.502477	+	0.864591i	$0.332422\pi$
$284$		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	$-0.650099\pi$
$307$	−15.9188			−0.908534			−0.454267	+	0.890866i	$0.650099\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.262869			−0.0149059			−0.00745297	−	0.999972i	$-0.502372\pi$
$311$	−0.262869			−0.0149059			−0.00745297	+	0.999972i	$0.502372\pi$
$312$		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	$-0.735533\pi$
$331$	−24.5338			−1.34850			−0.674249	+	0.738504i	$0.735533\pi$
$332$		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	$-0.677306\pi$
$347$	−19.6957			−1.05732			−0.528661	+	0.848833i	$0.677306\pi$
$348$		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	−0.999228	−	0.0392925i	$-0.987490\pi$
$359$	−8.82159	+	15.2794i	−0.465586	+	0.806418i	0.533642	+	0.845710i	$0.320823\pi$
$360$		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	−0.818496	−	0.574512i	$-0.805192\pi$
$367$	1.69146	−	2.92969i	0.0882934	−	0.152929i	0.906790	+	0.421583i	$0.138525\pi$
$368$		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	$-0.249059\pi$
$379$	27.6131			1.41839			0.709194	+	0.705013i	$0.249059\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−12.5020	−	21.6541i	−0.638822	−	1.10647i	−0.985692	−	0.168559i	$-0.946089\pi$
$383$	−12.5020	−	21.6541i	−0.638822	−	1.10647i	0.346869	−	0.937913i	$-0.387245\pi$
$384$		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	$-0.535242\pi$
$419$	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
$425$	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	$-0.962871\pi$
$431$	−12.4021	−	21.4811i	−0.597389	−	1.03471i	0.395816	−	0.918330i	$-0.370462\pi$
$432$		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	$-0.0801381\pi$
$439$	40.5836			1.93695			0.968475	+	0.249110i	$0.0801381\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−28.2665			−1.34298			−0.671490	−	0.741014i	$-0.734345\pi$
$443$	−28.2665			−1.34298			−0.671490	+	0.741014i	$0.734345\pi$
$444$		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	$0.377877\pi$
$463$	−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	0.458004	+	0.888950i	$0.348564\pi$
$467$	−11.6879	+	20.2440i	−0.540851	+	0.936782i	−0.998855	+	0.0478318i	$0.984769\pi$
$468$		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	−0.952457	−	0.304673i	$-0.901453\pi$
$479$	−4.64803	+	8.05063i	−0.212374	+	0.367842i	0.740083	+	0.672515i	$0.234786\pi$
$480$		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	0.815847	−	0.578267i	$-0.196271\pi$
$487$	−2.04947	−	3.54979i	−0.0928704	−	0.160856i	−0.908718	+	0.417411i	$0.862938\pi$
$488$		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
$493$	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	0.712891	−	0.701275i	$-0.247385\pi$
$499$	−5.60415	−	9.70667i	−0.250876	−	0.434530i	−0.963767	+	0.266744i	$0.914052\pi$
$500$		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
$509$	−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	−0.774327	−	0.632786i	$-0.781911\pi$
$523$	3.67840	−	6.37117i	0.160845	−	0.278592i	0.935172	+	0.354194i	$0.115245\pi$
$524$		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	0.593962	−	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
$551$	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	$-0.600583\pi$
$563$	−14.7471			−0.621516			−0.310758	+	0.950489i	$0.600583\pi$
$564$		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	$-0.628746\pi$
$571$	−18.8072			−0.787057			−0.393528	+	0.919313i	$0.628746\pi$
$572$		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	$-0.913674\pi$
$587$	−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	−0.325434	−	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	$-0.564491\pi$
$599$	−9.84952			−0.402440			−0.201220	+	0.979546i	$0.564491\pi$
$600$		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	0.954919	−	0.296867i	$-0.0959418\pi$
$607$	5.42922	+	9.40368i	0.220365	+	0.381683i	−0.734554	+	0.678550i	$0.762608\pi$
$608$		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	$-0.576192\pi$
$619$	17.9829	−	31.1472i	0.722792	−	1.25191i	0.959876	−	0.280424i	$-0.0904750\pi$
$620$		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	$-0.281142\pi$
$631$	31.8848			1.26931			0.634656	+	0.772794i	$0.281142\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.142929	−	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	$0.545067\pi$
$643$	−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	0.518854	−	0.854863i	$-0.326359\pi$
$647$	−12.2324	−	21.1872i	−0.480906	−	0.832954i	−0.999760	+	0.0219091i	$0.993026\pi$
$648$		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	0.926337	−	0.376696i	$-0.122940\pi$
$659$	3.51539	+	6.08883i	0.136940	+	0.237187i	−0.789397	+	0.613883i	$0.789607\pi$
$660$		0			0
$661$	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	$-0.945272\pi$
$683$	−16.7467	−	29.0061i	−0.640794	−	1.10989i	0.344462	−	0.938800i	$-0.388061\pi$
$684$		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	$-0.483787\pi$
$691$	2.67672			0.101827			0.0509137	+	0.998703i	$0.483787\pi$
$692$		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	−0.664613	−	0.747188i	$-0.731403\pi$
$719$	8.44050	−	14.6194i	0.314778	−	0.545211i	0.979390	+	0.201977i	$0.0647367\pi$
$720$		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	0.842000	−	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
$731$	−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	0.989260	−	0.146168i	$-0.0466941\pi$
$739$	10.0051	+	17.3294i	0.368044	+	0.637472i	−0.621215	+	0.783640i	$0.713361\pi$
$740$		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
$745$	0.0113687	−	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	$0.00989905\pi$
$751$	14.4335	+	24.9996i	0.526686	+	0.912247i	−0.472830	+	0.881154i	$0.656768\pi$
$752$		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	$-0.510660\pi$
$787$	−1.87862			−0.0669657			−0.0334828	+	0.999439i	$0.510660\pi$
$788$		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	$-0.416307\pi$
$811$	14.8034			0.519818			0.259909	+	0.965633i	$0.416307\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.475377			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	$-0.741675\pi$
$823$	−39.4961			−1.37675			−0.688374	+	0.725356i	$0.741675\pi$
$824$		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	0.503350	−	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	$0.0927641\pi$
$839$	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
$851$	−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	$-0.891253\pi$
$859$	−22.3112	−	38.6442i	−0.761249	−	1.31852i	0.180958	−	0.983491i	$-0.442080\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−15.4848	+	26.8205i	−0.527109	+	0.912980i	0.472392	+	0.881389i	$0.343391\pi$
$863$	−15.4848	+	26.8205i	−0.527109	+	0.912980i	−0.999501	+	0.0315912i	$0.989943\pi$
$864$		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	$-0.265511\pi$
$883$	39.9269			1.34365			0.671824	+	0.740711i	$0.265511\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	13.4221	+	23.2477i	0.450669	+	0.780581i	0.998428	−	0.0560549i	$-0.0178522\pi$
$887$	13.4221	+	23.2477i	0.450669	+	0.780581i	−0.547759	+	0.836636i	$0.684519\pi$
$888$		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	$-0.617645\pi$
$907$	18.8808	−	32.7026i	0.626928	−	1.08587i	0.988165	−	0.153397i	$-0.0490212\pi$
$908$		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
$913$	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	−0.939209	−	0.343345i	$-0.888440\pi$
$919$	−5.22203	+	9.04482i	−0.172259	+	0.298361i	0.766950	+	0.641706i	$0.221773\pi$
$920$		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	$-0.494748\pi$
$947$	1.01549			0.0329991			0.0164995	+	0.999864i	$0.494748\pi$
$948$		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	−0.955163	−	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	0.275187	+	0.961391i	$0.411260\pi$
$971$	−21.6567	+	37.5104i	−0.694995	+	1.20377i	−0.970182	+	0.242376i	$0.922073\pi$
$972$		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	−0.969686	−	0.244353i	$-0.921424\pi$
$983$	−8.56644	+	14.8375i	−0.273227	+	0.473243i	0.696459	+	0.717596i	$0.254758\pi$
$984$		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	0.747821	−	0.663901i	$-0.231100\pi$
$991$	−6.32891	−	10.9620i	−0.201044	−	0.348219i	−0.948865	+	0.315682i	$0.897767\pi$
$992$		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	3024.2.q.l.2305.6		22
3.2	odd	2		1008.2.q.l.625.1		22
4.3	odd	2		1512.2.q.d.793.6		22
7.4	even	3		3024.2.t.k.1873.6		22
9.2	odd	6		1008.2.t.l.961.8		22
9.7	even	3		3024.2.t.k.289.6		22
12.11	even	2		504.2.q.c.121.11	yes	22
21.11	odd	6		1008.2.t.l.193.8		22
28.11	odd	6		1512.2.t.c.361.6		22
36.7	odd	6		1512.2.t.c.289.6		22
36.11	even	6		504.2.t.c.457.4	yes	22
63.11	odd	6		1008.2.q.l.529.1		22
63.25	even	3	inner	3024.2.q.l.2881.6		22
84.11	even	6		504.2.t.c.193.4	yes	22
252.11	even	6		504.2.q.c.25.11	✓	22
252.151	odd	6		1512.2.q.d.1369.6		22

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

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.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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