LMFDB - Embedded newform 3024.2.cc.d.881.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(881,3024)]

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, 5, 3]))

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

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

chi := DirichletCharacter("3024.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.cc (of order $6$, 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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.15
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.d.2897.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0977451 - 0.169300i) q^{5} +(-0.463555 + 2.60483i) q^{7} +O(q^{10})$	$q+(0.0977451 - 0.169300i) q^{5} +(-0.463555 + 2.60483i) q^{7} +(1.54198 - 0.890263i) q^{11} +(-5.11956 - 2.95578i) q^{13} -0.588306 q^{17} -2.48822i q^{19} +(3.85815 + 2.22750i) q^{23} +(2.48089 + 4.29703i) q^{25} +(-6.28023 + 3.62590i) q^{29} +(3.61605 + 2.08773i) q^{31} +(0.395685 + 0.333089i) q^{35} -2.57069 q^{37} +(-0.311960 + 0.540330i) q^{41} +(-5.08645 - 8.80999i) q^{43} +(3.57762 + 6.19662i) q^{47} +(-6.57023 - 2.41496i) q^{49} +11.2065i q^{53} -0.348075i q^{55} +(-5.75762 + 9.97249i) q^{59} +(-6.57488 + 3.79601i) q^{61} +(-1.00082 + 0.577826i) q^{65} +(-0.927580 + 1.60662i) q^{67} +6.58509i q^{71} -5.66459i q^{73} +(1.60419 + 4.42928i) q^{77} +(-2.92382 - 5.06421i) q^{79} +(0.740392 + 1.28240i) q^{83} +(-0.0575040 + 0.0995999i) q^{85} -9.44670 q^{89} +(10.0725 - 11.9654i) q^{91} +(-0.421255 - 0.243212i) q^{95} +(-0.0722645 + 0.0417220i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{23} - 24 q^{25} + 36 q^{29} - 12 q^{43} + 6 q^{49} - 36 q^{65} + 60 q^{77} + 12 q^{79} + 12 q^{91} - 108 q^{95}+O(q^{100}) $ 48 * q + 12 * q^23 - 24 * q^25 + 36 * q^29 - 12 * q^43 + 6 * q^49 - 36 * q^65 + 60 * q^77 + 12 * q^79 + 12 * q^91 - 108 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.0977451	−	0.169300i	0.0437129	−	0.0757130i	−0.843341	−	0.537379i	$-0.819415\pi$
$5$	0.0977451	−	0.169300i	0.0437129	−	0.0757130i	0.887054	+	0.461666i	$0.152748\pi$
$6$		0			0
$7$	−0.463555	+	2.60483i	−0.175208	+	0.984532i
$7$	−0.463555	+	2.60483i	−0.175208	+	0.984532i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.54198	−	0.890263i	0.464925	−	0.268424i	−0.249188	−	0.968455i	$-0.580164\pi$
$11$	1.54198	−	0.890263i	0.464925	−	0.268424i	0.714113	+	0.700031i	$0.246830\pi$
$12$		0			0
$13$	−5.11956	−	2.95578i	−1.41991	−	0.819786i	−0.423621	−	0.905840i	$-0.639241\pi$
$13$	−5.11956	−	2.95578i	−1.41991	−	0.819786i	−0.996291	+	0.0860533i	$0.972574\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.588306			−0.142685			−0.0713426	−	0.997452i	$-0.522728\pi$
$17$	−0.588306			−0.142685			−0.0713426	+	0.997452i	$0.522728\pi$
$18$		0			0
$19$		−	2.48822i		−	0.570838i	−0.958403	−	0.285419i	$-0.907867\pi$
$19$		−	2.48822i		−	0.570838i	0.958403	−	0.285419i	$-0.0921327\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.85815	+	2.22750i	0.804480	+	0.464466i	0.845035	−	0.534711i	$-0.179579\pi$
$23$	3.85815	+	2.22750i	0.804480	+	0.464466i	−0.0405556	+	0.999177i	$0.512913\pi$
$24$		0			0
$25$	2.48089	+	4.29703i	0.496178	+	0.859406i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.28023	+	3.62590i	−1.16621	+	0.673312i	−0.952784	−	0.303647i	$-0.901796\pi$
$29$	−6.28023	+	3.62590i	−1.16621	+	0.673312i	−0.213426	+	0.976959i	$0.568462\pi$
$30$		0			0
$31$	3.61605	+	2.08773i	0.649462	+	0.374967i	0.788250	−	0.615355i	$-0.210987\pi$
$31$	3.61605	+	2.08773i	0.649462	+	0.374967i	−0.138788	+	0.990322i	$0.544321\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.395685	+	0.333089i	0.0668830	+	0.0563023i
$36$		0			0
$37$	−2.57069			−0.422619			−0.211309	−	0.977419i	$-0.567773\pi$
$37$	−2.57069			−0.422619			−0.211309	+	0.977419i	$0.567773\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.311960	+	0.540330i	−0.0487199	+	0.0843854i	−0.889357	−	0.457214i	$-0.848848\pi$
$41$	−0.311960	+	0.540330i	−0.0487199	+	0.0843854i	0.840637	+	0.541599i	$0.182181\pi$
$42$		0			0
$43$	−5.08645	−	8.80999i	−0.775676	−	1.34351i	−0.934414	−	0.356190i	$-0.884076\pi$
$43$	−5.08645	−	8.80999i	−0.775676	−	1.34351i	0.158737	−	0.987321i	$-0.449258\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.57762	+	6.19662i	0.521849	+	0.903870i	0.999677	+	0.0254159i	$0.00809101\pi$
$47$	3.57762	+	6.19662i	0.521849	+	0.903870i	−0.477828	+	0.878454i	$0.658576\pi$
$48$		0			0
$49$	−6.57023	−	2.41496i	−0.938605	−	0.344995i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			11.2065i			1.53933i	0.638449	+	0.769664i	$0.279576\pi$
$53$			11.2065i			1.53933i	−0.638449	+	0.769664i	$0.720424\pi$
$54$		0			0
$55$		−	0.348075i		−	0.0469345i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.75762	+	9.97249i	−0.749578	+	1.29831i	0.198447	+	0.980112i	$0.436410\pi$
$59$	−5.75762	+	9.97249i	−0.749578	+	1.29831i	−0.948025	+	0.318195i	$0.896923\pi$
$60$		0			0
$61$	−6.57488	+	3.79601i	−0.841828	+	0.486029i	−0.857885	−	0.513842i	$-0.828222\pi$
$61$	−6.57488	+	3.79601i	−0.841828	+	0.486029i	0.0160574	+	0.999871i	$0.494889\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.00082	+	0.577826i	−0.124137	+	0.0716705i
$66$		0			0
$67$	−0.927580	+	1.60662i	−0.113322	+	0.196279i	−0.917108	−	0.398639i	$-0.869482\pi$
$67$	−0.927580	+	1.60662i	−0.113322	+	0.196279i	0.803786	+	0.594919i	$0.202816\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			6.58509i			0.781507i	0.920495	+	0.390753i	$0.127786\pi$
$71$			6.58509i			0.781507i	−0.920495	+	0.390753i	$0.872214\pi$
$72$		0			0
$73$		−	5.66459i		−	0.662991i	−0.943457	−	0.331495i	$-0.892447\pi$
$73$		−	5.66459i		−	0.662991i	0.943457	−	0.331495i	$-0.107553\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.60419	+	4.42928i	0.182814	+	0.504763i
$78$		0			0
$79$	−2.92382	−	5.06421i	−0.328956	−	0.569768i	0.653349	−	0.757057i	$-0.273363\pi$
$79$	−2.92382	−	5.06421i	−0.328956	−	0.569768i	−0.982305	+	0.187289i	$0.940030\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.740392	+	1.28240i	0.0812686	+	0.140761i	0.903795	−	0.427965i	$-0.140770\pi$
$83$	0.740392	+	1.28240i	0.0812686	+	0.140761i	−0.822527	+	0.568727i	$0.807436\pi$
$84$		0			0
$85$	−0.0575040	+	0.0995999i	−0.00623719	+	0.0108031i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−9.44670			−1.00135			−0.500674	−	0.865636i	$-0.666915\pi$
$89$	−9.44670			−1.00135			−0.500674	+	0.865636i	$0.666915\pi$
$90$		0			0
$91$	10.0725	−	11.9654i	1.05588	−	1.25431i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.421255	−	0.243212i	−0.0432199	−	0.0249530i
$96$		0			0
$97$	−0.0722645	+	0.0417220i	−0.00733735	+	0.00423622i	−0.503664	−	0.863900i	$-0.668015\pi$
$97$	−0.0722645	+	0.0417220i	−0.00733735	+	0.00423622i	0.496327	+	0.868136i	$0.334682\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.10012	−	15.7619i	−0.905496	−	1.56837i	−0.820250	−	0.572006i	$-0.806166\pi$
$101$	−9.10012	−	15.7619i	−0.905496	−	1.56837i	−0.0852464	−	0.996360i	$-0.527168\pi$
$102$		0			0
$103$	−8.56917	−	4.94741i	−0.844345	−	0.487483i	0.0143937	−	0.999896i	$-0.495418\pi$
$103$	−8.56917	−	4.94741i	−0.844345	−	0.487483i	−0.858739	+	0.512414i	$0.828752\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			4.02980i			0.389575i	0.980845	+	0.194788i	$0.0624018\pi$
$107$			4.02980i			0.389575i	−0.980845	+	0.194788i	$0.937598\pi$
$108$		0			0
$109$	−17.3582			−1.66262			−0.831308	−	0.555812i	$-0.812407\pi$
$109$	−17.3582			−1.66262			−0.831308	+	0.555812i	$0.812407\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−13.4213	−	7.74881i	−1.26257	−	0.728947i	−0.289001	−	0.957329i	$-0.593323\pi$
$113$	−13.4213	−	7.74881i	−1.26257	−	0.728947i	−0.973572	+	0.228382i	$0.926657\pi$
$114$		0			0
$115$	0.754230	−	0.435455i	0.0703323	−	0.0406064i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.272713	−	1.53243i	0.0249995	−	0.140478i
$120$		0			0
$121$	−3.91486	+	6.78074i	−0.355897	+	0.616431i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.94743			0.174184
$126$		0			0
$127$	4.80452			0.426332			0.213166	−	0.977016i	$-0.431622\pi$
$127$	4.80452			0.426332			0.213166	+	0.977016i	$0.431622\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.38369	−	2.39661i	0.120893	−	0.209393i	−0.799227	−	0.601029i	$-0.794757\pi$
$131$	1.38369	−	2.39661i	0.120893	−	0.209393i	0.920120	+	0.391636i	$0.128091\pi$
$132$		0			0
$133$	6.48139	+	1.15343i	0.562008	+	0.100015i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	14.2630	−	8.23472i	1.21857	−	0.703540i	0.253955	−	0.967216i	$-0.418268\pi$
$137$	14.2630	−	8.23472i	1.21857	−	0.703540i	0.964611	+	0.263676i	$0.0849351\pi$
$138$		0			0
$139$	8.73689	+	5.04425i	0.741054	+	0.427848i	0.822452	−	0.568834i	$-0.192605\pi$
$139$	8.73689	+	5.04425i	0.741054	+	0.427848i	−0.0813986	+	0.996682i	$0.525939\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−10.5257			−0.880202
$144$		0			0
$145$			1.41765i			0.117730i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.54751	+	4.93491i	0.700240	+	0.404284i	0.807437	−	0.589954i	$-0.200854\pi$
$149$	8.54751	+	4.93491i	0.700240	+	0.404284i	−0.107197	+	0.994238i	$0.534188\pi$
$150$		0			0
$151$	6.18320	+	10.7096i	0.503181	+	0.871536i	0.999993	+	0.00367749i	$0.00117058\pi$
$151$	6.18320	+	10.7096i	0.503181	+	0.871536i	−0.496812	+	0.867858i	$0.665496\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.706902	−	0.408130i	0.0567798	−	0.0327818i
$156$		0			0
$157$	−17.3656	−	10.0260i	−1.38592	−	0.800163i	−0.393070	−	0.919508i	$-0.628587\pi$
$157$	−17.3656	−	10.0260i	−1.38592	−	0.800163i	−0.992853	+	0.119345i	$0.961920\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−7.59072	+	9.01723i	−0.598233	+	0.710657i
$162$		0			0
$163$	−18.4297			−1.44353			−0.721765	−	0.692139i	$-0.756669\pi$
$163$	−18.4297			−1.44353			−0.721765	+	0.692139i	$0.756669\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.44968	+	14.6353i	−0.653856	+	1.13251i	0.328323	+	0.944566i	$0.393517\pi$
$167$	−8.44968	+	14.6353i	−0.653856	+	1.13251i	−0.982179	+	0.187947i	$0.939817\pi$
$168$		0			0
$169$	10.9733	+	19.0063i	0.844099	+	1.46202i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.66843	+	11.5501i	0.506992	+	0.878135i	0.999967	+	0.00809224i	$0.00257587\pi$
$173$	6.66843	+	11.5501i	0.506992	+	0.878135i	−0.492976	+	0.870043i	$0.664091\pi$
$174$		0			0
$175$	−12.3430	+	4.47038i	−0.933047	+	0.337929i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			10.5864i			0.791264i	0.918409	+	0.395632i	$0.129474\pi$
$179$			10.5864i			0.791264i	−0.918409	+	0.395632i	$0.870526\pi$
$180$		0			0
$181$			10.1988i			0.758072i	0.925382	+	0.379036i	$0.123744\pi$
$181$			10.1988i			0.758072i	−0.925382	+	0.379036i	$0.876256\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.251272	+	0.435217i	−0.0184739	+	0.0319978i
$186$		0			0
$187$	−0.907156	+	0.523747i	−0.0663379	+	0.0383002i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	14.8714	−	8.58600i	1.07606	−	0.621261i	0.146226	−	0.989251i	$-0.453287\pi$
$191$	14.8714	−	8.58600i	1.07606	−	0.621261i	0.929830	+	0.367990i	$0.119954\pi$
$192$		0			0
$193$	1.34444	−	2.32864i	0.0967748	−	0.167619i	−0.813573	−	0.581463i	$-0.802481\pi$
$193$	1.34444	−	2.32864i	0.0967748	−	0.167619i	0.910348	+	0.413844i	$0.135814\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	0.178302i		−	0.0127035i	−0.999980	−	0.00635174i	$-0.997978\pi$
$197$		−	0.178302i		−	0.0127035i	0.999980	−	0.00635174i	$-0.00202184\pi$
$198$		0			0
$199$			4.76533i			0.337806i	0.985633	+	0.168903i	$0.0540224\pi$
$199$			4.76533i			0.337806i	−0.985633	+	0.168903i	$0.945978\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−6.53359	−	18.0397i	−0.458568	−	1.26614i
$204$		0			0
$205$	0.0609851	+	0.105629i	0.00425938	+	0.00737746i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.21517	−	3.83679i	−0.153227	−	0.265397i
$210$		0			0
$211$	−9.12490	+	15.8048i	−0.628184	+	1.08805i	0.359732	+	0.933056i	$0.382868\pi$
$211$	−9.12490	+	15.8048i	−0.628184	+	1.08805i	−0.987916	+	0.154991i	$0.950465\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.98870			−0.135628
$216$		0			0
$217$	−7.11440	+	8.45140i	−0.482957	+	0.573718i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.01187	+	1.73890i	0.202600	+	0.116971i
$222$		0			0
$223$	−22.1757	+	12.8032i	−1.48500	+	0.857364i	−0.999854	−	0.0170708i	$-0.994566\pi$
$223$	−22.1757	+	12.8032i	−1.48500	+	0.857364i	−0.485143	+	0.874435i	$0.661233\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−14.2123	−	24.6164i	−0.943301	−	1.63385i	−0.759117	−	0.650954i	$-0.774369\pi$
$227$	−14.2123	−	24.6164i	−0.943301	−	1.63385i	−0.184184	−	0.982892i	$-0.558964\pi$
$228$		0			0
$229$	3.44409	+	1.98845i	0.227592	+	0.131400i	0.609461	−	0.792816i	$-0.291386\pi$
$229$	3.44409	+	1.98845i	0.227592	+	0.131400i	−0.381869	+	0.924217i	$0.624719\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			4.94057i			0.323667i	0.986818	+	0.161834i	$0.0517408\pi$
$233$			4.94057i			0.323667i	−0.986818	+	0.161834i	$0.948259\pi$
$234$		0			0
$235$	1.39878			0.0912463
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.22599	+	4.17193i	0.467410	+	0.269859i	0.715155	−	0.698966i	$-0.246356\pi$
$239$	7.22599	+	4.17193i	0.467410	+	0.269859i	−0.247745	+	0.968825i	$0.579689\pi$
$240$		0			0
$241$	14.3180	−	8.26652i	0.922306	−	0.532494i	0.0379360	−	0.999280i	$-0.487922\pi$
$241$	14.3180	−	8.26652i	0.922306	−	0.532494i	0.884370	+	0.466787i	$0.154588\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.05106	+	0.876286i	−0.0671498	+	0.0559839i
$246$		0			0
$247$	−7.35465	+	12.7386i	−0.467965	+	0.810539i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	11.7678			0.742775			0.371388	−	0.928478i	$-0.378882\pi$
$251$	11.7678			0.742775			0.371388	+	0.928478i	$0.378882\pi$
$252$		0			0
$253$	7.93225			0.498696
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.5672	+	25.2312i	−0.908680	+	1.57388i	−0.0927800	+	0.995687i	$0.529575\pi$
$257$	−14.5672	+	25.2312i	−0.908680	+	1.57388i	−0.815900	+	0.578193i	$0.803758\pi$
$258$		0			0
$259$	1.19166	−	6.69620i	0.0740460	−	0.416082i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	6.48148	−	3.74208i	0.399665	−	0.230747i	−0.286674	−	0.958028i	$-0.592550\pi$
$263$	6.48148	−	3.74208i	0.399665	−	0.230747i	0.686339	+	0.727281i	$0.259216\pi$
$264$		0			0
$265$	1.89725	+	1.09538i	0.116547	+	0.0672886i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	16.8123			1.02506			0.512531	−	0.858669i	$-0.328708\pi$
$269$	16.8123			1.02506			0.512531	+	0.858669i	$0.328708\pi$
$270$		0			0
$271$		−	10.9153i		−	0.663058i	−0.943445	−	0.331529i	$-0.892436\pi$
$271$		−	10.9153i		−	0.663058i	0.943445	−	0.331529i	$-0.107564\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7.65097	+	4.41729i	0.461371	+	0.266373i
$276$		0			0
$277$	−6.67812	−	11.5668i	−0.401249	−	0.694984i	0.592628	−	0.805476i	$-0.298091\pi$
$277$	−6.67812	−	11.5668i	−0.401249	−	0.694984i	−0.993877	+	0.110492i	$0.964757\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	11.4994	−	6.63918i	0.685997	−	0.396060i	−0.116114	−	0.993236i	$-0.537044\pi$
$281$	11.4994	−	6.63918i	0.685997	−	0.396060i	0.802111	+	0.597175i	$0.203710\pi$
$282$		0			0
$283$	10.1446	+	5.85700i	0.603035	+	0.348163i	0.770235	−	0.637760i	$-0.220139\pi$
$283$	10.1446	+	5.85700i	0.603035	+	0.348163i	−0.167199	+	0.985923i	$0.553472\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.26285	−	1.06307i	−0.0745439	−	0.0627512i
$288$		0			0
$289$	−16.6539			−0.979641
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.29070	+	9.16377i	−0.309086	+	0.535353i	−0.978163	−	0.207840i	$-0.933357\pi$
$293$	−5.29070	+	9.16377i	−0.309086	+	0.535353i	0.669076	+	0.743194i	$0.266690\pi$
$294$		0			0
$295$	1.12556	+	1.94952i	0.0655325	+	0.113506i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−13.1680	−	22.8077i	−0.761526	−	1.31900i
$300$		0			0
$301$	25.3063	−	9.16540i	1.45863	−	0.528285i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			1.48417i			0.0849831i
$306$		0			0
$307$			5.50915i			0.314424i	0.987565	+	0.157212i	$0.0502506\pi$
$307$			5.50915i			0.314424i	−0.987565	+	0.157212i	$0.949749\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−16.8667	+	29.2140i	−0.956424	+	1.65658i	−0.225349	+	0.974278i	$0.572352\pi$
$311$	−16.8667	+	29.2140i	−0.956424	+	1.65658i	−0.731075	+	0.682297i	$0.760981\pi$
$312$		0			0
$313$	13.8096	−	7.97298i	0.780565	−	0.450659i	−0.0560655	−	0.998427i	$-0.517856\pi$
$313$	13.8096	−	7.97298i	0.780565	−	0.450659i	0.836630	+	0.547768i	$0.184522\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	23.3894	−	13.5039i	1.31368	−	0.758454i	0.330977	−	0.943639i	$-0.392622\pi$
$317$	23.3894	−	13.5039i	1.31368	−	0.758454i	0.982704	+	0.185185i	$0.0592883\pi$
$318$		0			0
$319$	−6.45600	+	11.1821i	−0.361467	+	0.626078i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			1.46384i			0.0814501i
$324$		0			0
$325$		−	29.3319i		−	1.62704i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−17.7995	+	6.44660i	−0.981320	+	0.355412i
$330$		0			0
$331$	2.06853	+	3.58279i	0.113697	+	0.196928i	0.917258	−	0.398294i	$-0.130398\pi$
$331$	2.06853	+	3.58279i	0.113697	+	0.196928i	−0.803561	+	0.595222i	$0.797064\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.181333	+	0.314078i	0.00990728	+	0.0171599i
$336$		0			0
$337$	7.47266	−	12.9430i	0.407062	−	0.705052i	−0.587497	−	0.809226i	$-0.699887\pi$
$337$	7.47266	−	12.9430i	0.407062	−	0.705052i	0.994559	+	0.104174i	$0.0332200\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	7.43450			0.402601
$342$		0			0
$343$	9.33622	−	15.9948i	0.504109	−	0.863640i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−26.4882	−	15.2930i	−1.42196	−	0.820969i	−0.425494	−	0.904961i	$-0.639900\pi$
$347$	−26.4882	−	15.2930i	−1.42196	−	0.820969i	−0.996466	+	0.0839919i	$0.973233\pi$
$348$		0			0
$349$	1.29995	−	0.750529i	0.0695850	−	0.0401749i	−0.464804	−	0.885414i	$-0.653875\pi$
$349$	1.29995	−	0.750529i	0.0695850	−	0.0401749i	0.534389	+	0.845239i	$0.320542\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−10.0433	−	17.3955i	−0.534551	−	0.925870i	−0.999185	−	0.0403668i	$-0.987147\pi$
$353$	−10.0433	−	17.3955i	−0.534551	−	0.925870i	0.464634	−	0.885503i	$-0.346186\pi$
$354$		0			0
$355$	1.11485	+	0.643661i	0.0591703	+	0.0341620i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			18.2135i			0.961273i	0.876920	+	0.480636i	$0.159594\pi$
$359$			18.2135i			0.961273i	−0.876920	+	0.480636i	$0.840406\pi$
$360$		0			0
$361$	12.8087			0.674144
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.959013	−	0.553686i	−0.0501970	−	0.0289813i
$366$		0			0
$367$	−9.83452	+	5.67796i	−0.513358	+	0.296387i	−0.734213	−	0.678919i	$-0.762449\pi$
$367$	−9.83452	+	5.67796i	−0.513358	+	0.296387i	0.220855	+	0.975307i	$0.429115\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−29.1909	−	5.19482i	−1.51552	−	0.269702i
$372$		0			0
$373$	0.278259	−	0.481959i	0.0144077	−	0.0249549i	−0.858732	−	0.512426i	$-0.828747\pi$
$373$	0.278259	−	0.481959i	0.0144077	−	0.0249549i	0.873139	+	0.487471i	$0.162080\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	42.8694			2.20789
$378$		0			0
$379$	19.4513			0.999148			0.499574	−	0.866271i	$-0.333490\pi$
$379$	19.4513			0.999148			0.499574	+	0.866271i	$0.333490\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	13.7288	−	23.7790i	0.701510	−	1.21505i	−0.266426	−	0.963855i	$-0.585843\pi$
$383$	13.7288	−	23.7790i	0.701510	−	1.21505i	0.967936	−	0.251196i	$-0.0808238\pi$
$384$		0			0
$385$	0.906676	+	0.161352i	0.0462085	+	0.00822327i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.43756	+	4.29408i	−0.377099	+	0.217718i	−0.676555	−	0.736392i	$-0.736528\pi$
$389$	−7.43756	+	4.29408i	−0.377099	+	0.217718i	0.299456	+	0.954110i	$0.403195\pi$
$390$		0			0
$391$	−2.26977	−	1.31045i	−0.114787	−	0.0662725i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.14316			−0.0575185
$396$		0			0
$397$			38.9981i			1.95726i	0.205629	+	0.978630i	$0.434076\pi$
$397$			38.9981i			1.95726i	−0.205629	+	0.978630i	$0.565924\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.70569	+	2.13948i	0.185053	+	0.106840i	0.589665	−	0.807648i	$-0.299260\pi$
$401$	3.70569	+	2.13948i	0.185053	+	0.106840i	−0.404612	+	0.914489i	$0.632593\pi$
$402$		0			0
$403$	−12.3417	−	21.3765i	−0.614785	−	1.06484i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.96395	+	2.28859i	−0.196486	+	0.113441i
$408$		0			0
$409$	−10.5734	−	6.10456i	−0.522821	−	0.301851i	0.215267	−	0.976555i	$-0.430938\pi$
$409$	−10.5734	−	6.10456i	−0.522821	−	0.301851i	−0.738088	+	0.674704i	$0.764271\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−23.3076	−	19.6204i	−1.14689	−	0.965456i
$414$		0			0
$415$	0.289479			0.0142100
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.56132	+	2.70429i	−0.0762755	+	0.132113i	−0.901640	−	0.432487i	$-0.857636\pi$
$419$	−1.56132	+	2.70429i	−0.0762755	+	0.132113i	0.825365	+	0.564600i	$0.190970\pi$
$420$		0			0
$421$	1.92965	+	3.34224i	0.0940452	+	0.162891i	0.909210	−	0.416338i	$-0.136687\pi$
$421$	1.92965	+	3.34224i	0.0940452	+	0.162891i	−0.815165	+	0.579229i	$0.803354\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.45952	−	2.52797i	−0.0707973	−	0.122625i
$426$		0			0
$427$	−6.84012	−	18.8861i	−0.331017	−	0.913962i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	6.85535i		−	0.330210i	−0.986276	−	0.165105i	$-0.947204\pi$
$431$		−	6.85535i		−	0.330210i	0.986276	−	0.165105i	$-0.0527964\pi$
$432$		0			0
$433$			15.0114i			0.721404i	0.932681	+	0.360702i	$0.117463\pi$
$433$			15.0114i			0.721404i	−0.932681	+	0.360702i	$0.882537\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.54253	−	9.59994i	0.265135	−	0.459227i
$438$		0			0
$439$	−18.6732	+	10.7810i	−0.891223	+	0.514548i	−0.874342	−	0.485310i	$-0.838707\pi$
$439$	−18.6732	+	10.7810i	−0.891223	+	0.514548i	−0.0168808	+	0.999858i	$0.505374\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.94153	+	1.69830i	−0.139756	+	0.0806884i	−0.568248	−	0.822857i	$-0.692379\pi$
$443$	−2.94153	+	1.69830i	−0.139756	+	0.0806884i	0.428491	+	0.903546i	$0.359045\pi$
$444$		0			0
$445$	−0.923369	+	1.59932i	−0.0437719	+	0.0758151i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			16.9386i			0.799384i	0.916650	+	0.399692i	$0.130883\pi$
$449$			16.9386i			0.799384i	−0.916650	+	0.399692i	$0.869117\pi$
$450$		0			0
$451$			1.11090i			0.0523104i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.04120	−	2.87483i	−0.0488122	−	0.134774i
$456$		0			0
$457$	−16.3383	−	28.2987i	−0.764272	−	1.32376i	−0.940631	−	0.339432i	$-0.889765\pi$
$457$	−16.3383	−	28.2987i	−0.764272	−	1.32376i	0.176359	−	0.984326i	$-0.443568\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	13.7768	+	23.8621i	0.641650	+	1.11137i	0.985064	+	0.172187i	$0.0550833\pi$
$461$	13.7768	+	23.8621i	0.641650	+	1.11137i	−0.343414	+	0.939184i	$0.611583\pi$
$462$		0			0
$463$	1.50753	−	2.61112i	0.0700609	−	0.121349i	−0.828867	−	0.559446i	$-0.811014\pi$
$463$	1.50753	−	2.61112i	0.0700609	−	0.121349i	0.898928	+	0.438097i	$0.144347\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	41.7628			1.93255			0.966275	−	0.257513i	$-0.0829030\pi$
$467$	41.7628			1.93255			0.966275	+	0.257513i	$0.0829030\pi$
$468$		0			0
$469$	−3.75497	−	3.16094i	−0.173388	−	0.145959i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−15.6864	−	9.05656i	−0.721262	−	0.416421i
$474$		0			0
$475$	10.6920	−	6.17302i	0.490582	−	0.283237i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	13.1985	+	22.8604i	0.603053	+	1.04452i	0.992356	+	0.123408i	$0.0393825\pi$
$479$	13.1985	+	22.8604i	0.603053	+	1.04452i	−0.389303	+	0.921110i	$0.627284\pi$
$480$		0			0
$481$	13.1608	+	7.59840i	0.600081	+	0.346457i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			0.0163125i			0.000740711i
$486$		0			0
$487$	−8.64561			−0.391770			−0.195885	−	0.980627i	$-0.562758\pi$
$487$	−8.64561			−0.391770			−0.195885	+	0.980627i	$0.562758\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−35.3591	−	20.4146i	−1.59573	−	0.921296i	−0.992297	−	0.123884i	$-0.960465\pi$
$491$	−35.3591	−	20.4146i	−1.59573	−	0.921296i	−0.603435	−	0.797412i	$-0.706202\pi$
$492$		0			0
$493$	3.69470	−	2.13314i	0.166401	−	0.0960716i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17.1530	−	3.05256i	−0.769418	−	0.136926i
$498$		0			0
$499$	13.4024	−	23.2137i	0.599975	−	1.03919i	−0.392849	−	0.919603i	$-0.628511\pi$
$499$	13.4024	−	23.2137i	0.599975	−	1.03919i	0.992824	−	0.119584i	$-0.0381560\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	30.0026			1.33775			0.668874	−	0.743376i	$-0.266776\pi$
$503$	30.0026			1.33775			0.668874	+	0.743376i	$0.266776\pi$
$504$		0			0
$505$	−3.55797			−0.158328
$506$		0			0
$507$		0			0
$508$		0			0
$509$	11.5930	−	20.0797i	0.513852	−	0.890018i	−0.486019	−	0.873948i	$-0.661551\pi$
$509$	11.5930	−	20.0797i	0.513852	−	0.890018i	0.999871	−	0.0160697i	$-0.00511536\pi$
$510$		0			0
$511$	14.7553	+	2.62585i	0.652735	+	0.116161i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.67519	+	0.967171i	−0.0738176	+	0.0426186i
$516$		0			0
$517$	11.0332	+	6.37004i	0.485241	+	0.280154i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	34.1532			1.49628			0.748139	−	0.663542i	$-0.230948\pi$
$521$	34.1532			1.49628			0.748139	+	0.663542i	$0.230948\pi$
$522$		0			0
$523$		−	26.9547i		−	1.17865i	−0.807897	−	0.589323i	$-0.799394\pi$
$523$		−	26.9547i		−	1.17865i	0.807897	−	0.589323i	$-0.200606\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.12734	−	1.22822i	−0.0926685	−	0.0535022i
$528$		0			0
$529$	−1.57646	−	2.73051i	−0.0685418	−	0.118718i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3.19419	−	1.84417i	0.138356	−	0.0798798i
$534$		0			0
$535$	0.682243	+	0.393893i	0.0294959	+	0.0170295i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−12.2811	+	2.12541i	−0.528985	+	0.0915479i
$540$		0			0
$541$	26.5112			1.13981			0.569903	−	0.821712i	$-0.306981\pi$
$541$	26.5112			1.13981			0.569903	+	0.821712i	$0.306981\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.69668	+	2.93874i	−0.0726779	+	0.125882i
$546$		0			0
$547$	−2.17119	−	3.76061i	−0.0928334	−	0.160792i	0.815869	−	0.578237i	$-0.196259\pi$
$547$	−2.17119	−	3.76061i	−0.0928334	−	0.160792i	−0.908702	+	0.417445i	$0.862926\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9.02204	+	15.6266i	0.384352	+	0.665717i
$552$		0			0
$553$	14.5467	−	5.26851i	0.618590	−	0.224040i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			6.66124i			0.282246i	0.989992	+	0.141123i	$0.0450712\pi$
$557$			6.66124i			0.282246i	−0.989992	+	0.141123i	$0.954929\pi$
$558$		0			0
$559$			60.1377i			2.54356i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.63853	−	4.57007i	0.111201	−	0.192606i	−0.805054	−	0.593202i	$-0.797864\pi$
$563$	2.63853	−	4.57007i	0.111201	−	0.192606i	0.916255	+	0.400596i	$0.131197\pi$
$564$		0			0
$565$	−2.62374	+	1.51482i	−0.110382	+	0.0637288i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.11994	−	2.95600i	0.214639	−	0.123922i	−0.388826	−	0.921311i	$-0.627119\pi$
$569$	5.11994	−	2.95600i	0.214639	−	0.123922i	0.603466	+	0.797389i	$0.293786\pi$
$570$		0			0
$571$	17.7272	−	30.7044i	0.741859	−	1.28494i	−0.209789	−	0.977747i	$-0.567278\pi$
$571$	17.7272	−	30.7044i	0.741859	−	1.28494i	0.951648	−	0.307191i	$-0.0993891\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			22.1048i			0.921833i
$576$		0			0
$577$		−	32.1696i		−	1.33924i	−0.742705	−	0.669619i	$-0.766457\pi$
$577$		−	32.1696i		−	1.33924i	0.742705	−	0.669619i	$-0.233543\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.68363	+	1.33413i	−0.152823	+	0.0553490i
$582$		0			0
$583$	9.97671	+	17.2802i	0.413193	+	0.715671i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	14.3802	+	24.9072i	0.593534	+	1.02803i	0.993752	+	0.111611i	$0.0356011\pi$
$587$	14.3802	+	24.9072i	0.593534	+	1.02803i	−0.400218	+	0.916420i	$0.631066\pi$
$588$		0			0
$589$	5.19473	−	8.99754i	0.214045	−	0.370737i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−4.01776			−0.164989			−0.0824947	−	0.996592i	$-0.526289\pi$
$593$	−4.01776			−0.164989			−0.0824947	+	0.996592i	$0.526289\pi$
$594$		0			0
$595$	−0.232784	−	0.195958i	−0.00954322	−	0.00803350i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	17.7948	+	10.2738i	0.727075	+	0.419777i	0.817351	−	0.576140i	$-0.195442\pi$
$599$	17.7948	+	10.2738i	0.727075	+	0.419777i	−0.0902760	+	0.995917i	$0.528775\pi$
$600$		0			0
$601$	−33.6081	+	19.4037i	−1.37090	+	0.791492i	−0.991042	−	0.133551i	$-0.957362\pi$
$601$	−33.6081	+	19.4037i	−1.37090	+	0.791492i	−0.379862	+	0.925043i	$0.624029\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.765318	+	1.32557i	0.0311146	+	0.0538921i
$606$		0			0
$607$	2.93293	+	1.69333i	0.119044	+	0.0687302i	0.558340	−	0.829612i	$-0.311439\pi$
$607$	2.93293	+	1.69333i	0.119044	+	0.0687302i	−0.439296	+	0.898343i	$0.644772\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	42.2986i		−	1.71122i
$612$		0			0
$613$	15.1087			0.610234			0.305117	−	0.952315i	$-0.401304\pi$
$613$	15.1087			0.610234			0.305117	+	0.952315i	$0.401304\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−7.46339	−	4.30899i	−0.300465	−	0.173473i	0.342187	−	0.939632i	$-0.388832\pi$
$617$	−7.46339	−	4.30899i	−0.300465	−	0.173473i	−0.642652	+	0.766158i	$0.722166\pi$
$618$		0			0
$619$	21.9554	−	12.6760i	0.882462	−	0.509489i	0.0109924	−	0.999940i	$-0.496501\pi$
$619$	21.9554	−	12.6760i	0.882462	−	0.509489i	0.871469	+	0.490450i	$0.163168\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.37907	−	24.6070i	0.175444	−	0.985859i
$624$		0			0
$625$	−12.2141	+	21.1555i	−0.488564	+	0.846218i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.51235			0.0603015
$630$		0			0
$631$	43.5736			1.73464			0.867319	−	0.497752i	$-0.165841\pi$
$631$	43.5736			1.73464			0.867319	+	0.497752i	$0.165841\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.469618	−	0.813403i	0.0186362	−	0.0322789i
$636$		0			0
$637$	26.4986	+	31.7837i	1.04991	+	1.25932i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	17.9475	−	10.3620i	0.708885	−	0.409275i	−0.101763	−	0.994809i	$-0.532448\pi$
$641$	17.9475	−	10.3620i	0.708885	−	0.409275i	0.810648	+	0.585534i	$0.199115\pi$
$642$		0			0
$643$	23.3328	+	13.4712i	0.920155	+	0.531252i	0.883684	−	0.468083i	$-0.155055\pi$
$643$	23.3328	+	13.4712i	0.920155	+	0.531252i	0.0364703	+	0.999335i	$0.488389\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.9848			−0.549799			−0.274900	−	0.961473i	$-0.588645\pi$
$647$	−13.9848			−0.549799			−0.274900	+	0.961473i	$0.588645\pi$
$648$		0			0
$649$			20.5032i			0.804820i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−10.2211	−	5.90117i	−0.399984	−	0.230931i	0.286493	−	0.958082i	$-0.407510\pi$
$653$	−10.2211	−	5.90117i	−0.399984	−	0.230931i	−0.686477	+	0.727152i	$0.740844\pi$
$654$		0			0
$655$	−0.270497	−	0.468515i	−0.0105692	−	0.0183064i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	27.9203	−	16.1198i	1.08762	−	0.627939i	0.154679	−	0.987965i	$-0.450566\pi$
$659$	27.9203	−	16.1198i	1.08762	−	0.627939i	0.932942	+	0.360026i	$0.117232\pi$
$660$		0			0
$661$	−20.7314	−	11.9693i	−0.806359	−	0.465552i	0.0393306	−	0.999226i	$-0.487477\pi$
$661$	−20.7314	−	11.9693i	−0.806359	−	0.465552i	−0.845690	+	0.533674i	$0.820811\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.828799	−	0.984554i	0.0321395	−	0.0381794i
$666$		0			0
$667$	−32.3068			−1.25092
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−6.75890	+	11.7068i	−0.260924	+	0.451934i
$672$		0			0
$673$	−7.07953	−	12.2621i	−0.272896	−	0.472670i	0.696706	−	0.717357i	$-0.254648\pi$
$673$	−7.07953	−	12.2621i	−0.272896	−	0.472670i	−0.969602	+	0.244687i	$0.921315\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.15370	−	1.99826i	−0.0443401	−	0.0767993i	0.843004	−	0.537908i	$-0.180785\pi$
$677$	−1.15370	−	1.99826i	−0.0443401	−	0.0767993i	−0.887344	+	0.461109i	$0.847452\pi$
$678$		0			0
$679$	−0.0751798	−	0.207577i	−0.00288514	−	0.00796607i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			45.9967i			1.76002i	0.474959	+	0.880008i	$0.342463\pi$
$683$			45.9967i			1.76002i	−0.474959	+	0.880008i	$0.657537\pi$
$684$		0			0
$685$		−	3.21961i		−	0.123015i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	33.1239	−	57.3723i	1.26192	−	2.18571i
$690$		0			0
$691$	25.2462	−	14.5759i	0.960412	−	0.554494i	0.0641119	−	0.997943i	$-0.479579\pi$
$691$	25.2462	−	14.5759i	0.960412	−	0.554494i	0.896300	+	0.443449i	$0.146245\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.70798	−	0.986101i	0.0647873	−	0.0374050i
$696$		0			0
$697$	0.183528	−	0.317879i	0.00695161	−	0.0120405i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	3.43609i		−	0.129779i	−0.997892	−	0.0648897i	$-0.979330\pi$
$701$		−	3.43609i		−	0.129779i	0.997892	−	0.0648897i	$-0.0206696\pi$
$702$		0			0
$703$			6.39646i			0.241247i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	45.2754	−	16.3977i	1.70275	−	0.616700i
$708$		0			0
$709$	−12.2430	−	21.2056i	−0.459797	−	0.796392i	0.539153	−	0.842208i	$-0.318745\pi$
$709$	−12.2430	−	21.2056i	−0.459797	−	0.796392i	−0.998950	+	0.0458160i	$0.985411\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	9.30084	+	16.1095i	0.348319	+	0.603306i
$714$		0			0
$715$	−1.02883	+	1.78199i	−0.0384762	+	0.0666428i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−4.32284			−0.161215			−0.0806073	−	0.996746i	$-0.525686\pi$
$719$	−4.32284			−0.161215			−0.0806073	+	0.996746i	$0.525686\pi$
$720$		0			0
$721$	16.8594	−	20.0278i	0.627878	−	0.745874i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−31.1612	−	17.9909i	−1.15730	−	0.668166i
$726$		0			0
$727$	4.31470	−	2.49109i	0.160023	−	0.0923895i	−0.417850	−	0.908516i	$-0.637216\pi$
$727$	4.31470	−	2.49109i	0.160023	−	0.0923895i	0.577873	+	0.816127i	$0.303883\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.99239	+	5.18297i	0.110678	+	0.191699i
$732$		0			0
$733$	24.0538	+	13.8874i	0.888446	+	0.512944i	0.873434	−	0.486943i	$-0.161888\pi$
$733$	24.0538	+	13.8874i	0.888446	+	0.512944i	0.0150118	+	0.999887i	$0.495221\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			3.30316i			0.121674i
$738$		0			0
$739$	−2.70031			−0.0993324			−0.0496662	−	0.998766i	$-0.515816\pi$
$739$	−2.70031			−0.0993324			−0.0496662	+	0.998766i	$0.515816\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−35.5112	−	20.5024i	−1.30278	−	0.752161i	−0.321901	−	0.946773i	$-0.604322\pi$
$743$	−35.5112	−	20.5024i	−1.30278	−	0.752161i	−0.980880	+	0.194612i	$0.937655\pi$
$744$		0			0
$745$	1.67096	−	0.964727i	0.0612191	−	0.0353449i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−10.4969	−	1.86804i	−0.383549	−	0.0682565i
$750$		0			0
$751$	23.0762	−	39.9691i	0.842062	−	1.45849i	−0.0460870	−	0.998937i	$-0.514675\pi$
$751$	23.0762	−	39.9691i	0.842062	−	1.45849i	0.888149	−	0.459556i	$-0.151992\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.41751			0.0879822
$756$		0			0
$757$	−25.7424			−0.935622			−0.467811	−	0.883829i	$-0.654957\pi$
$757$	−25.7424			−0.935622			−0.467811	+	0.883829i	$0.654957\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−23.4514	+	40.6191i	−0.850114	+	1.47244i	0.0309915	+	0.999520i	$0.490134\pi$
$761$	−23.4514	+	40.6191i	−0.850114	+	1.47244i	−0.881105	+	0.472920i	$0.843200\pi$
$762$		0			0
$763$	8.04650	−	45.2151i	0.291303	−	1.63690i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	58.9530	−	34.0365i	2.12867	−	1.22899i
$768$		0			0
$769$	3.83927	+	2.21660i	0.138447	+	0.0799327i	0.567624	−	0.823288i	$-0.307863\pi$
$769$	3.83927	+	2.21660i	0.138447	+	0.0799327i	−0.429176	+	0.903221i	$0.641196\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−50.3141			−1.80967			−0.904836	−	0.425759i	$-0.860007\pi$
$773$	−50.3141			−1.80967			−0.904836	+	0.425759i	$0.860007\pi$
$774$		0			0
$775$			20.7177i			0.744202i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.34446	+	0.776226i	0.0481704	+	0.0278112i
$780$		0			0
$781$	5.86246	+	10.1541i	0.209775	+	0.363342i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.39480	+	1.95999i	−0.121166	+	0.0699550i
$786$		0			0
$787$	17.1506	+	9.90189i	0.611352	+	0.352964i	0.773494	−	0.633803i	$-0.218507\pi$
$787$	17.1506	+	9.90189i	0.611352	+	0.352964i	−0.162142	+	0.986767i	$0.551840\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	26.4058	−	31.3682i	0.938884	−	1.11533i
$792$		0			0
$793$	44.8807			1.59376
$794$		0			0
$795$		0			0
$796$		0			0
$797$	20.2555	−	35.0836i	0.717487	−	1.24272i	−0.244506	−	0.969648i	$-0.578626\pi$
$797$	20.2555	−	35.0836i	0.717487	−	1.24272i	0.961993	−	0.273076i	$-0.0880410\pi$
$798$		0			0
$799$	−2.10473	−	3.64551i	−0.0744602	−	0.128969i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.04298	−	8.73469i	−0.177963	−	0.308241i
$804$		0			0
$805$	0.784657	+	2.16650i	0.0276555	+	0.0763590i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			12.0795i			0.424693i	0.977194	+	0.212346i	$0.0681105\pi$
$809$			12.0795i			0.424693i	−0.977194	+	0.212346i	$0.931889\pi$
$810$		0			0
$811$			44.6716i			1.56863i	0.620362	+	0.784316i	$0.286986\pi$
$811$			44.6716i			1.56863i	−0.620362	+	0.784316i	$0.713014\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.80142	+	3.12015i	−0.0631009	+	0.109294i
$816$		0			0
$817$	−21.9212	+	12.6562i	−0.766927	+	0.442785i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−48.2449	+	27.8542i	−1.68376	+	0.972118i	−0.724634	+	0.689134i	$0.757991\pi$
$821$	−48.2449	+	27.8542i	−1.68376	+	0.972118i	−0.959125	+	0.282984i	$0.908676\pi$
$822$		0			0
$823$	−7.77809	+	13.4721i	−0.271127	+	0.469606i	−0.969151	−	0.246469i	$-0.920730\pi$
$823$	−7.77809	+	13.4721i	−0.271127	+	0.469606i	0.698023	+	0.716075i	$0.254063\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	40.2570i		−	1.39987i	−0.714205	−	0.699937i	$-0.753212\pi$
$827$		−	40.2570i		−	1.39987i	0.714205	−	0.699937i	$-0.246788\pi$
$828$		0			0
$829$		−	33.1447i		−	1.15116i	−0.817744	−	0.575582i	$-0.804775\pi$
$829$		−	33.1447i		−	1.15116i	0.817744	−	0.575582i	$-0.195225\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	3.86531	+	1.42074i	0.133925	+	0.0492256i
$834$		0			0
$835$	1.65183	+	2.86106i	0.0571640	+	0.0990109i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	18.7660	+	32.5036i	0.647873	+	1.12215i	0.983630	+	0.180201i	$0.0576748\pi$
$839$	18.7660	+	32.5036i	0.647873	+	1.12215i	−0.335756	+	0.941949i	$0.608992\pi$
$840$		0			0
$841$	11.7942	−	20.4282i	0.406698	−	0.704421i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.29034			0.147592
$846$		0			0
$847$	−15.8479	−	13.3408i	−0.544540	−	0.458395i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−9.91811	−	5.72622i	−0.339988	−	0.196292i
$852$		0			0
$853$	−1.29530	+	0.747840i	−0.0443501	+	0.0256056i	−0.522011	−	0.852939i	$-0.674818\pi$
$853$	−1.29530	+	0.747840i	−0.0443501	+	0.0256056i	0.477661	+	0.878544i	$0.341485\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−18.7804	−	32.5286i	−0.641526	−	1.11116i	−0.985092	−	0.172027i	$-0.944968\pi$
$857$	−18.7804	−	32.5286i	−0.641526	−	1.11116i	0.343566	−	0.939129i	$-0.388365\pi$
$858$		0			0
$859$	18.1235	+	10.4636i	0.618367	+	0.357014i	0.776233	−	0.630446i	$-0.217128\pi$
$859$	18.1235	+	10.4636i	0.618367	+	0.357014i	−0.157866	+	0.987461i	$0.550461\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	16.2006i		−	0.551476i	−0.961233	−	0.275738i	$-0.911078\pi$
$863$		−	16.2006i		−	0.551476i	0.961233	−	0.275738i	$-0.0889221\pi$
$864$		0			0
$865$	2.60723			0.0886484
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−9.01696	−	5.20594i	−0.305879	−	0.176599i
$870$		0			0
$871$	9.49761	−	5.48345i	0.321814	−	0.185800i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.902743	+	5.07272i	−0.0305183	+	0.171489i
$876$		0			0
$877$	−22.9486	+	39.7482i	−0.774920	+	1.34220i	0.159919	+	0.987130i	$0.448877\pi$
$877$	−22.9486	+	39.7482i	−0.774920	+	1.34220i	−0.934839	+	0.355071i	$0.884457\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	34.4250			1.15981			0.579905	−	0.814684i	$-0.303090\pi$
$881$	34.4250			1.15981			0.579905	+	0.814684i	$0.303090\pi$
$882$		0			0
$883$	−32.5432			−1.09517			−0.547583	−	0.836751i	$-0.684452\pi$
$883$	−32.5432			−1.09517			−0.547583	+	0.836751i	$0.684452\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−15.6638	+	27.1305i	−0.525938	+	0.910952i	0.473605	+	0.880737i	$0.342952\pi$
$887$	−15.6638	+	27.1305i	−0.525938	+	0.910952i	−0.999543	+	0.0302145i	$0.990381\pi$
$888$		0			0
$889$	−2.22716	+	12.5149i	−0.0746966	+	0.419737i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	15.4186	−	8.90192i	0.515963	−	0.297891i
$894$		0			0
$895$	1.79227	+	1.03477i	0.0599090	+	0.0345885i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−30.2795			−1.00988
$900$		0			0
$901$		−	6.59284i		−	0.219639i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.72665	+	0.996884i	0.0573959	+	0.0331375i
$906$		0			0
$907$	11.7024	+	20.2691i	0.388570	+	0.673023i	0.992257	−	0.124198i	$-0.0396358\pi$
$907$	11.7024	+	20.2691i	0.388570	+	0.673023i	−0.603687	+	0.797221i	$0.706302\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−27.8823	+	16.0979i	−0.923783	+	0.533346i	−0.884840	−	0.465895i	$-0.845732\pi$
$911$	−27.8823	+	16.0979i	−0.923783	+	0.533346i	−0.0389427	+	0.999241i	$0.512399\pi$
$912$		0			0
$913$	2.28334	+	1.31829i	0.0755675	+	0.0436289i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.60135	+	4.71522i	0.184973	+	0.155710i
$918$		0			0
$919$	−10.6796			−0.352289			−0.176144	−	0.984364i	$-0.556363\pi$
$919$	−10.6796			−0.352289			−0.176144	+	0.984364i	$0.556363\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	19.4641	−	33.7128i	0.640669	−	1.10967i
$924$		0			0
$925$	−6.37760	−	11.0463i	−0.209694	−	0.363201i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−11.2032	−	19.4045i	−0.367565	−	0.636642i	0.621619	−	0.783320i	$-0.286475\pi$
$929$	−11.2032	−	19.4045i	−0.367565	−	0.636642i	−0.989184	+	0.146678i	$0.953142\pi$
$930$		0			0
$931$	−6.00897	+	16.3482i	−0.196936	+	0.535791i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			0.204775i			0.00669685i
$936$		0			0
$937$			45.3689i			1.48214i	0.671429	+	0.741069i	$0.265681\pi$
$937$			45.3689i			1.48214i	−0.671429	+	0.741069i	$0.734319\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−6.96149	+	12.0577i	−0.226938	+	0.393068i	−0.956899	−	0.290420i	$-0.906205\pi$
$941$	−6.96149	+	12.0577i	−0.226938	+	0.393068i	0.729961	+	0.683489i	$0.239538\pi$
$942$		0			0
$943$	−2.40717	+	1.38978i	−0.0783883	+	0.0452575i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−19.7813	+	11.4207i	−0.642805	+	0.371124i	−0.785694	−	0.618615i	$-0.787694\pi$
$947$	−19.7813	+	11.4207i	−0.642805	+	0.371124i	0.142889	+	0.989739i	$0.454361\pi$
$948$		0			0
$949$	−16.7433	+	29.0003i	−0.543511	+	0.941388i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			11.3331i			0.367115i	0.983009	+	0.183557i	$0.0587613\pi$
$953$			11.3331i			0.367115i	−0.983009	+	0.183557i	$0.941239\pi$
$954$		0			0
$955$		−	3.35696i		−	0.108629i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	14.8383	+	40.9698i	0.479155	+	1.32298i
$960$		0			0
$961$	−6.78279	−	11.7481i	−0.218800	−	0.378972i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.262825	−	0.455226i	−0.00846063	−	0.0146542i
$966$		0			0
$967$	20.4384	−	35.4004i	0.657256	−	1.13840i	−0.324068	−	0.946034i	$-0.605051\pi$
$967$	20.4384	−	35.4004i	0.657256	−	1.13840i	0.981323	−	0.192366i	$-0.0616161\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	37.5881			1.20626			0.603129	−	0.797644i	$-0.293920\pi$
$971$	37.5881			1.20626			0.603129	+	0.797644i	$0.293920\pi$
$972$		0			0
$973$	−17.1894	+	20.4198i	−0.551068	+	0.654629i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−18.9539	−	10.9430i	−0.606388	−	0.350098i	0.165163	−	0.986266i	$-0.447185\pi$
$977$	−18.9539	−	10.9430i	−0.606388	−	0.350098i	−0.771550	+	0.636168i	$0.780518\pi$
$978$		0			0
$979$	−14.5666	+	8.41005i	−0.465552	+	0.268786i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−23.8731	−	41.3494i	−0.761433	−	1.31884i	−0.942112	−	0.335298i	$-0.891163\pi$
$983$	−23.8731	−	41.3494i	−0.761433	−	1.31884i	0.180680	−	0.983542i	$-0.442170\pi$
$984$		0			0
$985$	−0.0301864	−	0.0174281i	−0.000961819	−	0.000555307i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	45.3203i		−	1.44110i
$990$		0			0
$991$	−15.4393			−0.490445			−0.245222	−	0.969467i	$-0.578861\pi$
$991$	−15.4393			−0.490445			−0.245222	+	0.969467i	$0.578861\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.806769	+	0.465788i	0.0255763	+	0.0147665i
$996$		0			0
$997$	−3.47738	+	2.00767i	−0.110130	+	0.0635834i	−0.554053	−	0.832481i	$-0.686920\pi$
$997$	−3.47738	+	2.00767i	−0.110130	+	0.0635834i	0.443923	+	0.896065i	$0.353586\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cc.d.881.15		48
3.2	odd	2		1008.2.cc.d.545.3		48
4.3	odd	2		1512.2.bu.a.881.15		48
7.6	odd	2	inner	3024.2.cc.d.881.10		48
9.2	odd	6	inner	3024.2.cc.d.2897.10		48
9.7	even	3		1008.2.cc.d.209.22		48
12.11	even	2		504.2.bu.a.41.22	yes	48
21.20	even	2		1008.2.cc.d.545.22		48
28.27	even	2		1512.2.bu.a.881.10		48
36.7	odd	6		504.2.bu.a.209.3	yes	48
36.11	even	6		1512.2.bu.a.1385.10		48
36.23	even	6		4536.2.k.a.3401.30		48
36.31	odd	6		4536.2.k.a.3401.19		48
63.20	even	6	inner	3024.2.cc.d.2897.15		48
63.34	odd	6		1008.2.cc.d.209.3		48
84.83	odd	2		504.2.bu.a.41.3	✓	48
252.83	odd	6		1512.2.bu.a.1385.15		48
252.139	even	6		4536.2.k.a.3401.29		48
252.167	odd	6		4536.2.k.a.3401.20		48
252.223	even	6		504.2.bu.a.209.22	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bu.a.41.3	✓	48	84.83	odd	2
504.2.bu.a.41.22	yes	48	12.11	even	2
504.2.bu.a.209.3	yes	48	36.7	odd	6
504.2.bu.a.209.22	yes	48	252.223	even	6
1008.2.cc.d.209.3		48	63.34	odd	6
1008.2.cc.d.209.22		48	9.7	even	3
1008.2.cc.d.545.3		48	3.2	odd	2
1008.2.cc.d.545.22		48	21.20	even	2
1512.2.bu.a.881.10		48	28.27	even	2
1512.2.bu.a.881.15		48	4.3	odd	2
1512.2.bu.a.1385.10		48	36.11	even	6
1512.2.bu.a.1385.15		48	252.83	odd	6
3024.2.cc.d.881.10		48	7.6	odd	2	inner
3024.2.cc.d.881.15		48	1.1	even	1	trivial
3024.2.cc.d.2897.10		48	9.2	odd	6	inner
3024.2.cc.d.2897.15		48	63.20	even	6	inner
4536.2.k.a.3401.19		48	36.31	odd	6
4536.2.k.a.3401.20		48	252.167	odd	6
4536.2.k.a.3401.29		48	252.139	even	6
4536.2.k.a.3401.30		48	36.23	even	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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0977451 - 0.169300i) q^{5} +(-0.463555 + 2.60483i) q^{7} +O(q^{10})\)	\(q+(0.0977451 - 0.169300i) q^{5} +(-0.463555 + 2.60483i) q^{7} +(1.54198 - 0.890263i) q^{11} +(-5.11956 - 2.95578i) q^{13} -0.588306 q^{17} -2.48822i q^{19} +(3.85815 + 2.22750i) q^{23} +(2.48089 + 4.29703i) q^{25} +(-6.28023 + 3.62590i) q^{29} +(3.61605 + 2.08773i) q^{31} +(0.395685 + 0.333089i) q^{35} -2.57069 q^{37} +(-0.311960 + 0.540330i) q^{41} +(-5.08645 - 8.80999i) q^{43} +(3.57762 + 6.19662i) q^{47} +(-6.57023 - 2.41496i) q^{49} +11.2065i q^{53} -0.348075i q^{55} +(-5.75762 + 9.97249i) q^{59} +(-6.57488 + 3.79601i) q^{61} +(-1.00082 + 0.577826i) q^{65} +(-0.927580 + 1.60662i) q^{67} +6.58509i q^{71} -5.66459i q^{73} +(1.60419 + 4.42928i) q^{77} +(-2.92382 - 5.06421i) q^{79} +(0.740392 + 1.28240i) q^{83} +(-0.0575040 + 0.0995999i) q^{85} -9.44670 q^{89} +(10.0725 - 11.9654i) q^{91} +(-0.421255 - 0.243212i) q^{95} +(-0.0722645 + 0.0417220i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{23} - 24 q^{25} + 36 q^{29} - 12 q^{43} + 6 q^{49} - 36 q^{65} + 60 q^{77} + 12 q^{79} + 12 q^{91} - 108 q^{95}+O(q^{100}) \) 48 * q + 12 * q^23 - 24 * q^25 + 36 * q^29 - 12 * q^43 + 6 * q^49 - 36 * q^65 + 60 * q^77 + 12 * q^79 + 12 * q^91 - 108 * q^95

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