LMFDB - Embedded newform 3024.2.cc.d.881.17

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			881.17
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.d.2897.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965651 - 1.67256i) q^{5} +(1.93133 - 1.80831i) q^{7} +O(q^{10})$	$q+(0.965651 - 1.67256i) q^{5} +(1.93133 - 1.80831i) q^{7} +(1.10681 - 0.639015i) q^{11} +(-2.52802 - 1.45955i) q^{13} -0.475237 q^{17} -6.10647i q^{19} +(-6.51132 - 3.75931i) q^{23} +(0.635036 + 1.09991i) q^{25} +(-3.76797 + 2.17544i) q^{29} +(-4.21872 - 2.43568i) q^{31} +(-1.15950 - 4.97645i) q^{35} +1.76145 q^{37} +(-1.16103 + 2.01097i) q^{41} +(-4.63638 - 8.03045i) q^{43} +(4.00447 + 6.93595i) q^{47} +(0.460063 - 6.98487i) q^{49} +10.3345i q^{53} -2.46826i q^{55} +(1.74272 - 3.01848i) q^{59} +(4.26195 - 2.46064i) q^{61} +(-4.88237 + 2.81883i) q^{65} +(-0.602527 + 1.04361i) q^{67} +11.2114i q^{71} +1.84336i q^{73} +(0.982073 - 3.23559i) q^{77} +(-8.54654 - 14.8030i) q^{79} +(0.225217 + 0.390088i) q^{83} +(-0.458913 + 0.794861i) q^{85} -11.2580 q^{89} +(-7.52175 + 1.75255i) q^{91} +(-10.2134 - 5.89672i) q^{95} +(9.22775 - 5.32764i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.965651	−	1.67256i	0.431852	−	0.747990i	−0.565181	−	0.824967i	$-0.691194\pi$
$5$	0.965651	−	1.67256i	0.431852	−	0.747990i	0.997033	+	0.0769771i	$0.0245268\pi$
$6$		0			0
$7$	1.93133	−	1.80831i	0.729974	−	0.683475i
$7$	1.93133	−	1.80831i	0.729974	−	0.683475i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.10681	−	0.639015i	0.333715	−	0.192670i	−0.323774	−	0.946134i	$-0.604952\pi$
$11$	1.10681	−	0.639015i	0.333715	−	0.192670i	0.657489	+	0.753464i	$0.271619\pi$
$12$		0			0
$13$	−2.52802	−	1.45955i	−0.701146	−	0.404807i	0.106628	−	0.994299i	$-0.465995\pi$
$13$	−2.52802	−	1.45955i	−0.701146	−	0.404807i	−0.807774	+	0.589492i	$0.799328\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.475237			−0.115262			−0.0576310	−	0.998338i	$-0.518355\pi$
$17$	−0.475237			−0.115262			−0.0576310	+	0.998338i	$0.518355\pi$
$18$		0			0
$19$		−	6.10647i		−	1.40092i	−0.713691	−	0.700460i	$-0.752978\pi$
$19$		−	6.10647i		−	1.40092i	0.713691	−	0.700460i	$-0.247022\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.51132	−	3.75931i	−1.35770	−	0.783871i	−0.368390	−	0.929671i	$-0.620091\pi$
$23$	−6.51132	−	3.75931i	−1.35770	−	0.783871i	−0.989314	+	0.145801i	$0.953424\pi$
$24$		0			0
$25$	0.635036	+	1.09991i	0.127007	+	0.219983i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.76797	+	2.17544i	−0.699695	+	0.403969i	−0.807234	−	0.590232i	$-0.799036\pi$
$29$	−3.76797	+	2.17544i	−0.699695	+	0.403969i	0.107539	+	0.994201i	$0.465703\pi$
$30$		0			0
$31$	−4.21872	−	2.43568i	−0.757705	−	0.437461i	0.0707660	−	0.997493i	$-0.477456\pi$
$31$	−4.21872	−	2.43568i	−0.757705	−	0.437461i	−0.828471	+	0.560032i	$0.810789\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.15950	−	4.97645i	−0.195992	−	0.841173i
$36$		0			0
$37$	1.76145			0.289580			0.144790	−	0.989462i	$-0.453749\pi$
$37$	1.76145			0.289580			0.144790	+	0.989462i	$0.453749\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.16103	+	2.01097i	−0.181323	+	0.314060i	−0.942331	−	0.334682i	$-0.891371\pi$
$41$	−1.16103	+	2.01097i	−0.181323	+	0.314060i	0.761009	+	0.648742i	$0.224704\pi$
$42$		0			0
$43$	−4.63638	−	8.03045i	−0.707042	−	1.22463i	−0.965950	−	0.258730i	$-0.916696\pi$
$43$	−4.63638	−	8.03045i	−0.707042	−	1.22463i	0.258908	−	0.965902i	$-0.416637\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.00447	+	6.93595i	0.584112	+	1.01171i	0.994985	+	0.100020i	$0.0318906\pi$
$47$	4.00447	+	6.93595i	0.584112	+	1.01171i	−0.410873	+	0.911693i	$0.634776\pi$
$48$		0			0
$49$	0.460063	−	6.98487i	0.0657232	−	0.997838i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			10.3345i			1.41955i	0.704428	+	0.709775i	$0.251204\pi$
$53$			10.3345i			1.41955i	−0.704428	+	0.709775i	$0.748796\pi$
$54$		0			0
$55$		−	2.46826i		−	0.332820i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.74272	−	3.01848i	0.226883	−	0.392973i	−0.730000	−	0.683447i	$-0.760480\pi$
$59$	1.74272	−	3.01848i	0.226883	−	0.392973i	0.956883	+	0.290475i	$0.0938132\pi$
$60$		0			0
$61$	4.26195	−	2.46064i	0.545686	−	0.315052i	−0.201694	−	0.979449i	$-0.564645\pi$
$61$	4.26195	−	2.46064i	0.545686	−	0.315052i	0.747380	+	0.664396i	$0.231311\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.88237	+	2.81883i	−0.605583	+	0.349633i
$66$		0			0
$67$	−0.602527	+	1.04361i	−0.0736104	+	0.127497i	−0.900481	−	0.434895i	$-0.856785\pi$
$67$	−0.602527	+	1.04361i	−0.0736104	+	0.127497i	0.826871	+	0.562392i	$0.190119\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			11.2114i			1.33055i	0.746598	+	0.665275i	$0.231686\pi$
$71$			11.2114i			1.33055i	−0.746598	+	0.665275i	$0.768314\pi$
$72$		0			0
$73$			1.84336i			0.215749i	0.994164	+	0.107875i	$0.0344045\pi$
$73$			1.84336i			0.215749i	−0.994164	+	0.107875i	$0.965595\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.982073	−	3.23559i	0.111918	−	0.368730i
$78$		0			0
$79$	−8.54654	−	14.8030i	−0.961561	−	1.66547i	−0.718584	−	0.695440i	$-0.755209\pi$
$79$	−8.54654	−	14.8030i	−0.961561	−	1.66547i	−0.242977	−	0.970032i	$-0.578124\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.225217	+	0.390088i	0.0247208	+	0.0428177i	0.878121	−	0.478438i	$-0.158797\pi$
$83$	0.225217	+	0.390088i	0.0247208	+	0.0428177i	−0.853400	+	0.521256i	$0.825464\pi$
$84$		0			0
$85$	−0.458913	+	0.794861i	−0.0497761	+	0.0862148i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−11.2580			−1.19335			−0.596675	−	0.802483i	$-0.703512\pi$
$89$	−11.2580			−1.19335			−0.596675	+	0.802483i	$0.703512\pi$
$90$		0			0
$91$	−7.52175	+	1.75255i	−0.788493	+	0.183718i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−10.2134	−	5.89672i	−1.04787	−	0.604991i
$96$		0			0
$97$	9.22775	−	5.32764i	0.936936	−	0.540940i	0.0479373	−	0.998850i	$-0.484735\pi$
$97$	9.22775	−	5.32764i	0.936936	−	0.540940i	0.888998	+	0.457910i	$0.151402\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.65330	+	11.5239i	0.662028	+	1.14667i	0.980082	+	0.198594i	$0.0636375\pi$
$101$	6.65330	+	11.5239i	0.662028	+	1.14667i	−0.318054	+	0.948073i	$0.603029\pi$
$102$		0			0
$103$	16.4947	+	9.52323i	1.62527	+	0.938352i	0.985478	+	0.169806i	$0.0543141\pi$
$103$	16.4947	+	9.52323i	1.62527	+	0.938352i	0.639795	+	0.768546i	$0.279019\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	16.1392i		−	1.56024i	−0.625630	−	0.780120i	$-0.715158\pi$
$107$		−	16.1392i		−	1.56024i	0.625630	−	0.780120i	$-0.284842\pi$
$108$		0			0
$109$	3.40434			0.326077			0.163038	−	0.986620i	$-0.447871\pi$
$109$	3.40434			0.326077			0.163038	+	0.986620i	$0.447871\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.64150	−	2.10242i	−0.342563	−	0.197779i	0.318842	−	0.947808i	$-0.396706\pi$
$113$	−3.64150	−	2.10242i	−0.342563	−	0.197779i	−0.661405	+	0.750029i	$0.730040\pi$
$114$		0			0
$115$	−12.5753	+	7.26037i	−1.17265	+	0.677033i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.917839	+	0.859374i	−0.0841382	+	0.0787787i
$120$		0			0
$121$	−4.68332	+	8.11175i	−0.425756	+	0.737432i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	12.1094			1.08310
$126$		0			0
$127$	−17.1828			−1.52473			−0.762363	−	0.647150i	$-0.775961\pi$
$127$	−17.1828			−1.52473			−0.762363	+	0.647150i	$0.775961\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.00420	−	6.93548i	0.349848	−	0.605955i	−0.636374	−	0.771381i	$-0.719566\pi$
$131$	4.00420	−	6.93548i	0.349848	−	0.605955i	0.986222	+	0.165425i	$0.0528997\pi$
$132$		0			0
$133$	−11.0424	−	11.7936i	−0.957495	−	1.02264i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.44241	+	4.87423i	−0.721284	+	0.416433i	−0.815225	−	0.579144i	$-0.803387\pi$
$137$	−8.44241	+	4.87423i	−0.721284	+	0.416433i	0.0939411	+	0.995578i	$0.470053\pi$
$138$		0			0
$139$	6.76047	+	3.90316i	0.573416	+	0.331062i	0.758513	−	0.651658i	$-0.225926\pi$
$139$	6.76047	+	3.90316i	0.573416	+	0.331062i	−0.185097	+	0.982720i	$0.559260\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.73070			−0.311977
$144$		0			0
$145$			8.40286i			0.697820i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.62284	−	5.55575i	−0.788333	−	0.455145i	0.0510420	−	0.998697i	$-0.483746\pi$
$149$	−9.62284	−	5.55575i	−0.788333	−	0.455145i	−0.839376	+	0.543552i	$0.817079\pi$
$150$		0			0
$151$	1.88730	+	3.26890i	0.153586	+	0.266020i	0.932543	−	0.361058i	$-0.117584\pi$
$151$	1.88730	+	3.26890i	0.153586	+	0.266020i	−0.778957	+	0.627077i	$0.784251\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−8.14763	+	4.70404i	−0.654433	+	0.377837i
$156$		0			0
$157$	−3.55162	−	2.05053i	−0.283450	−	0.163650i	0.351534	−	0.936175i	$-0.385660\pi$
$157$	−3.55162	−	2.05053i	−0.283450	−	0.163650i	−0.634984	+	0.772525i	$0.718993\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−19.3735	+	4.51399i	−1.52684	+	0.355752i
$162$		0			0
$163$	14.3871			1.12689			0.563443	−	0.826155i	$-0.309477\pi$
$163$	14.3871			1.12689			0.563443	+	0.826155i	$0.309477\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.06975	−	13.9772i	0.624456	−	1.08159i	−0.364190	−	0.931325i	$-0.618654\pi$
$167$	8.06975	−	13.9772i	0.624456	−	1.08159i	0.988646	−	0.150265i	$-0.0480126\pi$
$168$		0			0
$169$	−2.23942	−	3.87879i	−0.172263	−	0.298368i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.695376	−	1.20443i	−0.0528685	−	0.0915709i	0.838380	−	0.545086i	$-0.183503\pi$
$173$	−0.695376	−	1.20443i	−0.0528685	−	0.0915709i	−0.891248	+	0.453515i	$0.850170\pi$
$174$		0			0
$175$	3.21544	+	0.975958i	0.243065	+	0.0737755i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	4.60605i		−	0.344273i	−0.985073	−	0.172136i	$-0.944933\pi$
$179$		−	4.60605i		−	0.344273i	0.985073	−	0.172136i	$-0.0550669\pi$
$180$		0			0
$181$			16.3732i			1.21701i	0.793550	+	0.608505i	$0.208231\pi$
$181$			16.3732i			1.21701i	−0.793550	+	0.608505i	$0.791769\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.70094	−	2.94612i	0.125056	−	0.216603i
$186$		0			0
$187$	−0.525996	+	0.303684i	−0.0384646	+	0.0222075i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−12.7953	+	7.38735i	−0.925833	+	0.534530i	−0.885491	−	0.464656i	$-0.846178\pi$
$191$	−12.7953	+	7.38735i	−0.925833	+	0.534530i	−0.0403419	+	0.999186i	$0.512845\pi$
$192$		0			0
$193$	8.91923	−	15.4486i	0.642020	−	1.11201i	−0.342961	−	0.939350i	$-0.611430\pi$
$193$	8.91923	−	15.4486i	0.642020	−	1.11201i	0.984981	−	0.172662i	$-0.0552369\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	8.00352i		−	0.570227i	−0.958494	−	0.285113i	$-0.907969\pi$
$197$		−	8.00352i		−	0.570227i	0.958494	−	0.285113i	$-0.0920313\pi$
$198$		0			0
$199$		−	16.3034i		−	1.15572i	−0.816137	−	0.577858i	$-0.803889\pi$
$199$		−	16.3034i		−	1.15572i	0.816137	−	0.577858i	$-0.196111\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.34333	+	11.0151i	−0.234656	+	0.773111i
$204$		0			0
$205$	2.24230	+	3.88378i	0.156609	+	0.271255i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.90213	−	6.75868i	−0.269916	−	0.467508i
$210$		0			0
$211$	10.1930	−	17.6548i	0.701717	−	1.21541i	−0.266147	−	0.963933i	$-0.585751\pi$
$211$	10.1930	−	17.6548i	0.701717	−	1.21541i	0.967863	−	0.251476i	$-0.0809161\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−17.9085			−1.22135
$216$		0			0
$217$	−12.5522	+	2.92464i	−0.852099	+	0.198537i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.20141	+	0.693633i	0.0808154	+	0.0466588i
$222$		0			0
$223$	−1.95301	+	1.12757i	−0.130783	+	0.0755078i	−0.563964	−	0.825799i	$-0.690724\pi$
$223$	−1.95301	+	1.12757i	−0.130783	+	0.0755078i	0.433181	+	0.901307i	$0.357391\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.8916	−	18.8648i	−0.722899	−	1.25210i	−0.959833	−	0.280572i	$-0.909476\pi$
$227$	−10.8916	−	18.8648i	−0.722899	−	1.25210i	0.236934	−	0.971526i	$-0.423858\pi$
$228$		0			0
$229$	−10.4832	−	6.05247i	−0.692748	−	0.399958i	0.111893	−	0.993720i	$-0.464309\pi$
$229$	−10.4832	−	6.05247i	−0.692748	−	0.399958i	−0.804641	+	0.593762i	$0.797642\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	21.9876i		−	1.44046i	−0.693736	−	0.720229i	$-0.744037\pi$
$233$		−	21.9876i		−	1.44046i	0.693736	−	0.720229i	$-0.255963\pi$
$234$		0			0
$235$	15.4677			1.00900
$236$		0			0
$237$		0			0
$238$		0			0
$239$	18.7861	+	10.8462i	1.21517	+	0.701581i	0.963882	−	0.266330i	$-0.0858111\pi$
$239$	18.7861	+	10.8462i	1.21517	+	0.701581i	0.251292	+	0.967911i	$0.419144\pi$
$240$		0			0
$241$	23.1674	−	13.3757i	1.49234	−	0.861604i	0.492380	−	0.870380i	$-0.336127\pi$
$241$	23.1674	−	13.3757i	1.49234	−	0.861604i	0.999961	+	0.00877651i	$0.00279369\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−11.2383	−	7.51442i	−0.717990	−	0.480079i
$246$		0			0
$247$	−8.91271	+	15.4373i	−0.567102	+	0.982250i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.75601			0.110839			0.0554193	−	0.998463i	$-0.482350\pi$
$251$	1.75601			0.110839			0.0554193	+	0.998463i	$0.482350\pi$
$252$		0			0
$253$	−9.60903			−0.604114
$254$		0			0
$255$		0			0
$256$		0			0
$257$	14.9860	−	25.9565i	0.934800	−	1.61912i	0.159809	−	0.987148i	$-0.448912\pi$
$257$	14.9860	−	25.9565i	0.934800	−	1.61912i	0.774991	−	0.631972i	$-0.217754\pi$
$258$		0			0
$259$	3.40193	−	3.18523i	0.211386	−	0.197921i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−13.4273	+	7.75223i	−0.827960	+	0.478023i	−0.853154	−	0.521659i	$-0.825313\pi$
$263$	−13.4273	+	7.75223i	−0.827960	+	0.478023i	0.0251934	+	0.999683i	$0.491980\pi$
$264$		0			0
$265$	17.2850	+	9.97951i	1.06181	+	0.613036i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.412404			0.0251447			0.0125724	−	0.999921i	$-0.495998\pi$
$269$	0.412404			0.0251447			0.0125724	+	0.999921i	$0.495998\pi$
$270$		0			0
$271$		−	0.360056i		−	0.0218718i	−0.999940	−	0.0109359i	$-0.996519\pi$
$271$		−	0.360056i		−	0.0218718i	0.999940	−	0.0109359i	$-0.00348108\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.40572	+	0.811595i	0.0847683	+	0.0489410i
$276$		0			0
$277$	−3.03617	−	5.25881i	−0.182426	−	0.315971i	0.760280	−	0.649595i	$-0.225062\pi$
$277$	−3.03617	−	5.25881i	−0.182426	−	0.315971i	−0.942706	+	0.333624i	$0.891728\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	8.22494	−	4.74867i	0.490659	−	0.283282i	−0.234189	−	0.972191i	$-0.575243\pi$
$281$	8.22494	−	4.74867i	0.490659	−	0.283282i	0.724848	+	0.688909i	$0.241910\pi$
$282$		0			0
$283$	−9.81761	−	5.66820i	−0.583596	−	0.336939i	0.178965	−	0.983855i	$-0.442725\pi$
$283$	−9.81761	−	5.66820i	−0.583596	−	0.336939i	−0.762561	+	0.646916i	$0.776058\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.39411	+	5.98333i	0.0822915	+	0.353185i
$288$		0			0
$289$	−16.7741			−0.986715
$290$		0			0
$291$		0			0
$292$		0			0
$293$	9.22450	−	15.9773i	0.538901	−	0.933404i	−0.460062	−	0.887887i	$-0.652173\pi$
$293$	9.22450	−	15.9773i	0.538901	−	0.933404i	0.998964	−	0.0455177i	$-0.0144937\pi$
$294$		0			0
$295$	−3.36572	−	5.82960i	−0.195960	−	0.339412i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	10.9738	+	19.0072i	0.634632	+	1.09922i
$300$		0			0
$301$	−23.4759	−	7.12545i	−1.35313	−	0.410704i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	9.50447i		−	0.544224i
$306$		0			0
$307$			11.0961i			0.633285i	0.948545	+	0.316643i	$0.102556\pi$
$307$			11.0961i			0.633285i	−0.948545	+	0.316643i	$0.897444\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.06866	+	1.85097i	−0.0605979	+	0.104959i	−0.894733	−	0.446602i	$-0.852634\pi$
$311$	−1.06866	+	1.85097i	−0.0605979	+	0.104959i	0.834135	+	0.551560i	$0.185967\pi$
$312$		0			0
$313$	−22.3161	+	12.8842i	−1.26138	+	0.728259i	−0.973342	−	0.229360i	$-0.926337\pi$
$313$	−22.3161	+	12.8842i	−1.26138	+	0.728259i	−0.288039	+	0.957619i	$0.593003\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.82524	−	3.36320i	0.327178	−	0.188896i	−0.327409	−	0.944883i	$-0.606176\pi$
$317$	5.82524	−	3.36320i	0.327178	−	0.188896i	0.654588	+	0.755986i	$0.272842\pi$
$318$		0			0
$319$	−2.78028	+	4.81558i	−0.155666	+	0.269621i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			2.90202i			0.161473i
$324$		0			0
$325$		−	3.70747i		−	0.205653i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	20.2763	+	6.15429i	1.11787	+	0.339297i
$330$		0			0
$331$	12.0006	+	20.7857i	0.659615	+	1.14249i	0.980715	+	0.195441i	$0.0626139\pi$
$331$	12.0006	+	20.7857i	0.659615	+	1.14249i	−0.321101	+	0.947045i	$0.604053\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.16366	+	2.01552i	0.0635777	+	0.110120i
$336$		0			0
$337$	−1.07839	+	1.86783i	−0.0587438	+	0.101747i	−0.893902	−	0.448263i	$-0.852043\pi$
$337$	−1.07839	+	1.86783i	−0.0587438	+	0.101747i	0.835158	+	0.550010i	$0.185376\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−6.22575			−0.337143
$342$		0			0
$343$	−11.7422	−	14.3220i	−0.634021	−	0.773316i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.31897	+	4.22561i	0.392903	+	0.226843i	0.683417	−	0.730028i	$-0.260493\pi$
$347$	7.31897	+	4.22561i	0.392903	+	0.226843i	−0.290514	+	0.956871i	$0.593826\pi$
$348$		0			0
$349$	11.6656	−	6.73516i	0.624447	−	0.360525i	−0.154151	−	0.988047i	$-0.549264\pi$
$349$	11.6656	−	6.73516i	0.624447	−	0.360525i	0.778598	+	0.627523i	$0.215931\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	14.8956	+	25.7999i	0.792813	+	1.37319i	0.924219	+	0.381863i	$0.124718\pi$
$353$	14.8956	+	25.7999i	0.792813	+	1.37319i	−0.131406	+	0.991329i	$0.541949\pi$
$354$		0			0
$355$	18.7517	+	10.8263i	0.995239	+	0.574601i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			8.88758i			0.469068i	0.972108	+	0.234534i	$0.0753565\pi$
$359$			8.88758i			0.469068i	−0.972108	+	0.234534i	$0.924644\pi$
$360$		0			0
$361$	−18.2890			−0.962579
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.08313	+	1.78005i	0.161378	+	0.0931719i
$366$		0			0
$367$	−32.0068	+	18.4792i	−1.67074	+	0.964604i	−0.703520	+	0.710675i	$0.748390\pi$
$367$	−32.0068	+	18.4792i	−1.67074	+	0.964604i	−0.967223	+	0.253929i	$0.918277\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	18.6879	+	19.9593i	0.970228	+	1.03623i
$372$		0			0
$373$	16.8546	−	29.1931i	0.872700	−	1.51156i	0.0135064	−	0.999909i	$-0.495701\pi$
$373$	16.8546	−	29.1931i	0.872700	−	1.51156i	0.859193	−	0.511651i	$-0.170966\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	12.7007			0.654117
$378$		0			0
$379$	29.7512			1.52821			0.764107	−	0.645089i	$-0.223180\pi$
$379$	29.7512			1.52821			0.764107	+	0.645089i	$0.223180\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.62871	−	13.2133i	0.389809	−	0.675169i	−0.602615	−	0.798032i	$-0.705874\pi$
$383$	7.62871	−	13.2133i	0.389809	−	0.675169i	0.992424	+	0.122863i	$0.0392077\pi$
$384$		0			0
$385$	−4.46337	−	4.76703i	−0.227474	−	0.242950i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.947612	−	0.547104i	0.0480458	−	0.0277393i	−0.475785	−	0.879562i	$-0.657836\pi$
$389$	0.947612	−	0.547104i	0.0480458	−	0.0277393i	0.523831	+	0.851823i	$0.324503\pi$
$390$		0			0
$391$	3.09442	+	1.78656i	0.156492	+	0.0903504i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−33.0119			−1.66101
$396$		0			0
$397$		−	18.2381i		−	0.915345i	−0.889121	−	0.457672i	$-0.848683\pi$
$397$		−	18.2381i		−	0.915345i	0.889121	−	0.457672i	$-0.151317\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−14.3050	−	8.25900i	−0.714358	−	0.412435i	0.0983146	−	0.995155i	$-0.468655\pi$
$401$	−14.3050	−	8.25900i	−0.714358	−	0.412435i	−0.812673	+	0.582721i	$0.801988\pi$
$402$		0			0
$403$	7.11001	+	12.3149i	0.354175	+	0.613448i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.94958	−	1.12559i	0.0966371	−	0.0557934i
$408$		0			0
$409$	12.3657	+	7.13935i	0.611445	+	0.353018i	0.773531	−	0.633759i	$-0.218489\pi$
$409$	12.3657	+	7.13935i	0.611445	+	0.353018i	−0.162086	+	0.986777i	$0.551822\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.09257	−	8.98105i	−0.102969	−	0.441928i
$414$		0			0
$415$	0.869925			0.0427029
$416$		0			0
$417$		0			0
$418$		0			0
$419$	19.2168	−	33.2845i	0.938804	−	1.62606i	0.171098	−	0.985254i	$-0.445268\pi$
$419$	19.2168	−	33.2845i	0.938804	−	1.62606i	0.767706	−	0.640802i	$-0.221398\pi$
$420$		0			0
$421$	−5.90196	−	10.2225i	−0.287644	−	0.498214i	0.685603	−	0.727976i	$-0.259539\pi$
$421$	−5.90196	−	10.2225i	−0.287644	−	0.498214i	−0.973247	+	0.229762i	$0.926205\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.301793	−	0.522720i	−0.0146391	−	0.0253557i
$426$		0			0
$427$	3.78164	−	12.4592i	0.183006	−	0.602943i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			33.9984i			1.63765i	0.574047	+	0.818823i	$0.305373\pi$
$431$			33.9984i			1.63765i	−0.574047	+	0.818823i	$0.694627\pi$
$432$		0			0
$433$			1.24413i			0.0597893i	0.999553	+	0.0298946i	$0.00951718\pi$
$433$			1.24413i			0.0597893i	−0.999553	+	0.0298946i	$0.990483\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−22.9561	+	39.7612i	−1.09814	+	1.90204i
$438$		0			0
$439$	10.3661	−	5.98485i	0.494745	−	0.285641i	−0.231796	−	0.972765i	$-0.574460\pi$
$439$	10.3661	−	5.98485i	0.494745	−	0.285641i	0.726541	+	0.687123i	$0.241127\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.07711	−	2.93127i	0.241221	−	0.139269i	−0.374517	−	0.927220i	$-0.622191\pi$
$443$	5.07711	−	2.93127i	0.241221	−	0.139269i	0.615738	+	0.787951i	$0.288858\pi$
$444$		0			0
$445$	−10.8713	+	18.8297i	−0.515351	+	0.892614i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			13.7990i			0.651215i	0.945505	+	0.325607i	$0.105569\pi$
$449$			13.7990i			0.651215i	−0.945505	+	0.325607i	$0.894431\pi$
$450$		0			0
$451$			2.96767i			0.139742i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−4.33214	+	14.2729i	−0.203094	+	0.669124i
$456$		0			0
$457$	17.6082	+	30.4983i	0.823676	+	1.42665i	0.902927	+	0.429794i	$0.141414\pi$
$457$	17.6082	+	30.4983i	0.823676	+	1.42665i	−0.0792505	+	0.996855i	$0.525253\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	11.6988	+	20.2629i	0.544867	+	0.943736i	0.998615	+	0.0526068i	$0.0167530\pi$
$461$	11.6988	+	20.2629i	0.544867	+	0.943736i	−0.453749	+	0.891130i	$0.649914\pi$
$462$		0			0
$463$	−2.67980	+	4.64155i	−0.124541	+	0.215711i	−0.921553	−	0.388252i	$-0.873079\pi$
$463$	−2.67980	+	4.64155i	−0.124541	+	0.215711i	0.797013	+	0.603963i	$0.206412\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	31.3997			1.45300			0.726502	−	0.687164i	$-0.241145\pi$
$467$	31.3997			1.45300			0.726502	+	0.687164i	$0.241145\pi$
$468$		0			0
$469$	0.723484	+	3.10510i	0.0334074	+	0.143380i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10.2632	−	5.92544i	−0.471901	−	0.272452i
$474$		0			0
$475$	6.71660	−	3.87783i	0.308179	−	0.177927i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−10.7485	−	18.6169i	−0.491109	−	0.850626i	0.508838	−	0.860862i	$-0.330075\pi$
$479$	−10.7485	−	18.6169i	−0.491109	−	0.850626i	−0.999948	+	0.0102359i	$0.996742\pi$
$480$		0			0
$481$	−4.45296	−	2.57092i	−0.203038	−	0.117224i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	20.5786i		−	0.934425i
$486$		0			0
$487$	−2.61173			−0.118349			−0.0591744	−	0.998248i	$-0.518847\pi$
$487$	−2.61173			−0.118349			−0.0591744	+	0.998248i	$0.518847\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−11.1818	−	6.45580i	−0.504626	−	0.291346i	0.225996	−	0.974128i	$-0.427437\pi$
$491$	−11.1818	−	6.45580i	−0.504626	−	0.291346i	−0.730622	+	0.682782i	$0.760770\pi$
$492$		0			0
$493$	1.79068	−	1.03385i	0.0806482	−	0.0465622i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	20.2737	+	21.6529i	0.909398	+	0.971267i
$498$		0			0
$499$	−0.117182	+	0.202964i	−0.00524577	+	0.00908593i	−0.868636	−	0.495450i	$-0.835003\pi$
$499$	−0.117182	+	0.202964i	−0.00524577	+	0.00908593i	0.863391	+	0.504536i	$0.168336\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−13.6460			−0.608445			−0.304223	−	0.952601i	$-0.598397\pi$
$503$	−13.6460			−0.608445			−0.304223	+	0.952601i	$0.598397\pi$
$504$		0			0
$505$	25.6991			1.14359
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.71269	+	2.96647i	−0.0759136	+	0.131486i	−0.901483	−	0.432814i	$-0.857521\pi$
$509$	−1.71269	+	2.96647i	−0.0759136	+	0.131486i	0.825570	+	0.564300i	$0.190854\pi$
$510$		0			0
$511$	3.33336	+	3.56014i	0.147459	+	0.157491i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	31.8563	−	18.3922i	1.40376	−	0.810459i
$516$		0			0
$517$	8.86435	+	5.11784i	0.389854	+	0.225082i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−37.3500			−1.63633			−0.818167	−	0.574981i	$-0.805009\pi$
$521$	−37.3500			−1.63633			−0.818167	+	0.574981i	$0.805009\pi$
$522$		0			0
$523$		−	8.99132i		−	0.393163i	−0.980487	−	0.196581i	$-0.937016\pi$
$523$		−	8.99132i		−	0.393163i	0.980487	−	0.196581i	$-0.0629840\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.00489	+	1.15753i	0.0873346	+	0.0504226i
$528$		0			0
$529$	16.7648	+	29.0376i	0.728906	+	1.26250i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	5.87021	−	3.38917i	0.254267	−	0.146801i
$534$		0			0
$535$	−26.9938	−	15.5849i	−1.16704	−	0.673793i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.95423	−	8.02488i	−0.170321	−	0.345656i
$540$		0			0
$541$	7.90934			0.340049			0.170025	−	0.985440i	$-0.445615\pi$
$541$	7.90934			0.340049			0.170025	+	0.985440i	$0.445615\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	3.28741	−	5.69396i	0.140817	−	0.243902i
$546$		0			0
$547$	17.2958	+	29.9573i	0.739516	+	1.28088i	0.952713	+	0.303871i	$0.0982790\pi$
$547$	17.2958	+	29.9573i	0.739516	+	1.28088i	−0.213197	+	0.977009i	$0.568388\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	13.2843	+	23.0090i	0.565928	+	0.980217i
$552$		0			0
$553$	−43.2746	−	13.1348i	−1.84022	−	0.558548i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			2.42861i			0.102903i	0.998675	+	0.0514517i	$0.0163848\pi$
$557$			2.42861i			0.102903i	−0.998675	+	0.0514517i	$0.983615\pi$
$558$		0			0
$559$			27.0682i			1.14486i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−8.53869	+	14.7894i	−0.359863	+	0.623301i	−0.987938	−	0.154852i	$-0.950510\pi$
$563$	−8.53869	+	14.7894i	−0.359863	+	0.623301i	0.628075	+	0.778153i	$0.283843\pi$
$564$		0			0
$565$	−7.03283	+	4.06041i	−0.295873	+	0.170823i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−19.9471	+	11.5165i	−0.836228	+	0.482796i	−0.855980	−	0.517008i	$-0.827046\pi$
$569$	−19.9471	+	11.5165i	−0.836228	+	0.482796i	0.0197523	+	0.999805i	$0.493712\pi$
$570$		0			0
$571$	−4.11356	+	7.12490i	−0.172147	+	0.298168i	−0.939170	−	0.343452i	$-0.888404\pi$
$571$	−4.11356	+	7.12490i	−0.172147	+	0.298168i	0.767023	+	0.641619i	$0.221737\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	9.54919i		−	0.398229i
$576$		0			0
$577$		−	11.3064i		−	0.470691i	−0.971912	−	0.235346i	$-0.924378\pi$
$577$		−	11.3064i		−	0.470691i	0.971912	−	0.235346i	$-0.0756222\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.14037	+	0.346126i	0.0473104	+	0.0143597i
$582$		0			0
$583$	6.60389	+	11.4383i	0.273505	+	0.473725i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	17.2862	+	29.9407i	0.713480	+	1.23578i	0.963543	+	0.267553i	$0.0862152\pi$
$587$	17.2862	+	29.9407i	0.713480	+	1.23578i	−0.250063	+	0.968229i	$0.580451\pi$
$588$		0			0
$589$	−14.8734	+	25.7615i	−0.612849	+	1.06149i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	9.64649			0.396134			0.198067	−	0.980188i	$-0.436534\pi$
$593$	9.64649			0.396134			0.198067	+	0.980188i	$0.436534\pi$
$594$		0			0
$595$	0.551039	+	2.36499i	0.0225904	+	0.0969553i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	5.22049	+	3.01405i	0.213303	+	0.123151i	0.602846	−	0.797858i	$-0.294033\pi$
$599$	5.22049	+	3.01405i	0.213303	+	0.123151i	−0.389542	+	0.921009i	$0.627367\pi$
$600$		0			0
$601$	23.4624	−	13.5460i	0.957052	−	0.552555i	0.0617879	−	0.998089i	$-0.480320\pi$
$601$	23.4624	−	13.5460i	0.957052	−	0.552555i	0.895265	+	0.445535i	$0.146986\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.04491	+	15.6662i	0.367728	+	0.636923i
$606$		0			0
$607$	−16.1410	−	9.31904i	−0.655145	−	0.378248i	0.135280	−	0.990807i	$-0.456807\pi$
$607$	−16.1410	−	9.31904i	−0.655145	−	0.378248i	−0.790425	+	0.612559i	$0.790140\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	23.3789i		−	0.945811i
$612$		0			0
$613$	24.7398			0.999232			0.499616	−	0.866247i	$-0.333474\pi$
$613$	24.7398			0.999232			0.499616	+	0.866247i	$0.333474\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	42.5759	+	24.5812i	1.71404	+	0.989603i	0.928934	+	0.370245i	$0.120726\pi$
$617$	42.5759	+	24.5812i	1.71404	+	0.989603i	0.785109	+	0.619358i	$0.212607\pi$
$618$		0			0
$619$	0.334357	−	0.193041i	0.0134389	−	0.00775898i	−0.493265	−	0.869879i	$-0.664197\pi$
$619$	0.334357	−	0.193041i	0.0134389	−	0.00775898i	0.506704	+	0.862120i	$0.330864\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−21.7430	+	20.3580i	−0.871114	+	0.815625i
$624$		0			0
$625$	8.51828	−	14.7541i	0.340731	−	0.590164i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−0.837104			−0.0333775
$630$		0			0
$631$	−45.6531			−1.81742			−0.908710	−	0.417429i	$-0.862931\pi$
$631$	−45.6531			−1.81742			−0.908710	+	0.417429i	$0.862931\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−16.5926	+	28.7392i	−0.658456	+	1.14048i
$636$		0			0
$637$	−11.3578	+	16.9864i	−0.450013	+	0.673025i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	34.2119	−	19.7523i	1.35129	−	0.780167i	0.362859	−	0.931844i	$-0.381801\pi$
$641$	34.2119	−	19.7523i	1.35129	−	0.780167i	0.988430	+	0.151677i	$0.0484674\pi$
$642$		0			0
$643$	23.1404	+	13.3601i	0.912570	+	0.526873i	0.881257	−	0.472637i	$-0.156698\pi$
$643$	23.1404	+	13.3601i	0.912570	+	0.526873i	0.0313129	+	0.999510i	$0.490031\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−40.2634			−1.58292			−0.791459	−	0.611222i	$-0.790678\pi$
$647$	−40.2634			−1.58292			−0.791459	+	0.611222i	$0.790678\pi$
$648$		0			0
$649$		−	4.45450i		−	0.174854i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	36.6920	+	21.1841i	1.43587	+	0.828998i	0.997559	−	0.0698266i	$-0.0222446\pi$
$653$	36.6920	+	21.1841i	1.43587	+	0.828998i	0.438308	+	0.898825i	$0.355578\pi$
$654$		0			0
$655$	−7.73332	−	13.3945i	−0.302166	−	0.523366i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	33.3031	−	19.2276i	1.29731	−	0.749000i	0.317368	−	0.948302i	$-0.397201\pi$
$659$	33.3031	−	19.2276i	1.29731	−	0.749000i	0.979938	+	0.199302i	$0.0638676\pi$
$660$		0			0
$661$	14.2400	+	8.22149i	0.553874	+	0.319779i	0.750683	−	0.660663i	$-0.229725\pi$
$661$	14.2400	+	8.22149i	0.553874	+	0.319779i	−0.196809	+	0.980442i	$0.563058\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−30.3885	+	7.08048i	−1.17842	+	0.274569i
$666$		0			0
$667$	32.7126			1.26664
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.14477	−	5.44690i	0.121402	−	0.210275i
$672$		0			0
$673$	−16.8254	−	29.1424i	−0.648570	−	1.12336i	−0.983465	−	0.181100i	$-0.942034\pi$
$673$	−16.8254	−	29.1424i	−0.648570	−	1.12336i	0.334895	−	0.942255i	$-0.391299\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.0119	−	36.3938i	−0.807555	−	1.39873i	−0.914553	−	0.404466i	$-0.867457\pi$
$677$	−21.0119	−	36.3938i	−0.807555	−	1.39873i	0.106998	−	0.994259i	$-0.465876\pi$
$678$		0			0
$679$	8.18781	−	26.9760i	0.314219	−	1.03524i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	28.0238i		−	1.07230i	−0.844122	−	0.536151i	$-0.819878\pi$
$683$		−	28.0238i		−	1.07230i	0.844122	−	0.536151i	$-0.180122\pi$
$684$		0			0
$685$			18.8272i			0.719351i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	15.0837	−	26.1258i	0.574644	−	0.995312i
$690$		0			0
$691$	−4.58578	+	2.64760i	−0.174451	+	0.100720i	−0.584683	−	0.811262i	$-0.698781\pi$
$691$	−4.58578	+	2.64760i	−0.174451	+	0.100720i	0.410232	+	0.911981i	$0.365448\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	13.0565	−	7.53818i	0.495262	−	0.285940i
$696$		0			0
$697$	0.551765	−	0.955685i	0.0208996	−	0.0361992i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			38.6055i			1.45811i	0.684455	+	0.729055i	$0.260040\pi$
$701$			38.6055i			1.45811i	−0.684455	+	0.729055i	$0.739960\pi$
$702$		0			0
$703$		−	10.7562i		−	0.405678i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	33.6884	+	10.2252i	1.26698	+	0.384557i
$708$		0			0
$709$	21.9037	+	37.9383i	0.822610	+	1.42480i	0.903732	+	0.428098i	$0.140816\pi$
$709$	21.9037	+	37.9383i	0.822610	+	1.42480i	−0.0811228	+	0.996704i	$0.525851\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	18.3130	+	31.7190i	0.685826	+	1.18789i
$714$		0			0
$715$	−3.60256	+	6.23981i	−0.134728	+	0.233356i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	21.2855			0.793813			0.396907	−	0.917859i	$-0.370084\pi$
$719$	21.2855			0.793813			0.396907	+	0.917859i	$0.370084\pi$
$720$		0			0
$721$	49.0776	−	11.4350i	1.82775	−	0.425862i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4.78559	−	2.76296i	−0.177733	−	0.102614i
$726$		0			0
$727$	36.2267	−	20.9155i	1.34358	−	0.775713i	0.356245	−	0.934393i	$-0.384057\pi$
$727$	36.2267	−	20.9155i	1.34358	−	0.775713i	0.987330	+	0.158679i	$0.0507236\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.20338	+	3.81637i	0.0814950	+	0.141154i
$732$		0			0
$733$	36.6457	+	21.1574i	1.35354	+	0.781466i	0.988743	−	0.149622i	$-0.0478057\pi$
$733$	36.6457	+	21.1574i	1.35354	+	0.781466i	0.364795	+	0.931088i	$0.381139\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			1.54010i			0.0567302i
$738$		0			0
$739$	−20.4280			−0.751456			−0.375728	−	0.926730i	$-0.622607\pi$
$739$	−20.4280			−0.751456			−0.375728	+	0.926730i	$0.622607\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−7.44740	−	4.29976i	−0.273219	−	0.157743i	0.357131	−	0.934054i	$-0.383755\pi$
$743$	−7.44740	−	4.29976i	−0.273219	−	0.157743i	−0.630349	+	0.776312i	$0.717088\pi$
$744$		0			0
$745$	−18.5846	+	10.7298i	−0.680887	+	0.393110i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−29.1847	−	31.1702i	−1.06639	−	1.13893i
$750$		0			0
$751$	−20.0359	+	34.7032i	−0.731120	+	1.26634i	0.225285	+	0.974293i	$0.427669\pi$
$751$	−20.0359	+	34.7032i	−0.731120	+	1.26634i	−0.956405	+	0.292043i	$0.905665\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	7.28990			0.265307
$756$		0			0
$757$	10.6186			0.385941			0.192970	−	0.981205i	$-0.438188\pi$
$757$	10.6186			0.385941			0.192970	+	0.981205i	$0.438188\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.36550	+	2.36512i	−0.0494993	+	0.0857354i	−0.889713	−	0.456519i	$-0.849096\pi$
$761$	−1.36550	+	2.36512i	−0.0494993	+	0.0857354i	0.840214	+	0.542255i	$0.182429\pi$
$762$		0			0
$763$	6.57490	−	6.15609i	0.238028	−	0.222865i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−8.81125	+	5.08718i	−0.318156	+	0.183687i
$768$		0			0
$769$	5.44566	+	3.14405i	0.196376	+	0.113377i	0.594964	−	0.803753i	$-0.297166\pi$
$769$	5.44566	+	3.14405i	0.196376	+	0.113377i	−0.398588	+	0.917130i	$0.630500\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	15.6236			0.561942			0.280971	−	0.959716i	$-0.409344\pi$
$773$	15.6236			0.561942			0.280971	+	0.959716i	$0.409344\pi$
$774$		0			0
$775$		−	6.18698i		−	0.222243i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.2799	+	7.08981i	0.439973	+	0.254019i
$780$		0			0
$781$	7.16426	+	12.4089i	0.256358	+	0.444024i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−6.85925	+	3.96019i	−0.244817	+	0.141345i
$786$		0			0
$787$	−39.7379	−	22.9427i	−1.41650	−	0.817819i	−0.420514	−	0.907286i	$-0.638150\pi$
$787$	−39.7379	−	22.9427i	−1.41650	−	0.817819i	−0.995990	+	0.0894671i	$0.971484\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−10.8347	+	2.52448i	−0.385239	+	0.0897600i
$792$		0			0
$793$	−14.3657			−0.510141
$794$		0			0
$795$		0			0
$796$		0			0
$797$	14.8057	−	25.6442i	0.524444	−	0.908364i	−0.475151	−	0.879904i	$-0.657606\pi$
$797$	14.8057	−	25.6442i	0.524444	−	0.908364i	0.999595	−	0.0284597i	$-0.00906022\pi$
$798$		0			0
$799$	−1.90307	−	3.29622i	−0.0673259	−	0.116612i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.17794	+	2.04025i	0.0415685	+	0.0719987i
$804$		0			0
$805$	−11.1581	+	36.7622i	−0.393272	+	1.29570i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			27.7761i			0.976556i	0.872688	+	0.488278i	$0.162375\pi$
$809$			27.7761i			0.976556i	−0.872688	+	0.488278i	$0.837625\pi$
$810$		0			0
$811$		−	17.8221i		−	0.625820i	−0.949783	−	0.312910i	$-0.898696\pi$
$811$		−	17.8221i		−	0.625820i	0.949783	−	0.312910i	$-0.101304\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	13.8929	−	24.0633i	0.486648	−	0.842899i
$816$		0			0
$817$	−49.0377	+	28.3119i	−1.71561	+	0.990510i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.242236	+	0.139855i	−0.00845409	+	0.00488097i	−0.504221	−	0.863575i	$-0.668220\pi$
$821$	−0.242236	+	0.139855i	−0.00845409	+	0.00488097i	0.495767	+	0.868456i	$0.334887\pi$
$822$		0			0
$823$	5.56224	−	9.63408i	0.193887	−	0.335823i	−0.752648	−	0.658423i	$-0.771224\pi$
$823$	5.56224	−	9.63408i	0.193887	−	0.335823i	0.946535	+	0.322600i	$0.104557\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	22.9832i		−	0.799205i	−0.916688	−	0.399603i	$-0.869148\pi$
$827$		−	22.9832i		−	0.799205i	0.916688	−	0.399603i	$-0.130852\pi$
$828$		0			0
$829$		−	6.30082i		−	0.218837i	−0.993996	−	0.109418i	$-0.965101\pi$
$829$		−	6.30082i		−	0.218837i	0.993996	−	0.109418i	$-0.0348988\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.218639	+	3.31947i	−0.00757539	+	0.115013i
$834$		0			0
$835$	−15.5851	−	26.9942i	−0.539345	−	0.934174i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−11.7701	−	20.3864i	−0.406349	−	0.703816i	0.588129	−	0.808767i	$-0.299865\pi$
$839$	−11.7701	−	20.3864i	−0.406349	−	0.703816i	−0.994477	+	0.104951i	$0.966531\pi$
$840$		0			0
$841$	−5.03493	+	8.72075i	−0.173618	+	0.300716i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−8.64999			−0.297569
$846$		0			0
$847$	5.62349	+	24.1353i	0.193225	+	0.829300i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−11.4693	−	6.62182i	−0.393164	−	0.226993i
$852$		0			0
$853$	1.56621	−	0.904252i	0.0536260	−	0.0309610i	−0.472947	−	0.881091i	$-0.656810\pi$
$853$	1.56621	−	0.904252i	0.0536260	−	0.0309610i	0.526573	+	0.850130i	$0.323477\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.704571	+	1.22035i	0.0240677	+	0.0416865i	0.877808	−	0.479012i	$-0.159005\pi$
$857$	0.704571	+	1.22035i	0.0240677	+	0.0416865i	−0.853741	+	0.520698i	$0.825672\pi$
$858$		0			0
$859$	35.4862	+	20.4879i	1.21077	+	0.699040i	0.962928	−	0.269760i	$-0.0869444\pi$
$859$	35.4862	+	20.4879i	1.21077	+	0.699040i	0.247845	+	0.968800i	$0.420278\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	7.34316i		−	0.249964i	−0.992159	−	0.124982i	$-0.960113\pi$
$863$		−	7.34316i		−	0.249964i	0.992159	−	0.124982i	$-0.0398873\pi$
$864$		0			0
$865$	−2.68596			−0.0913255
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−18.9187	−	10.9227i	−0.641774	−	0.370528i
$870$		0			0
$871$	3.04640	−	1.75884i	0.103223	−	0.0595960i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	23.3872	−	21.8975i	0.790633	−	0.740271i
$876$		0			0
$877$	1.80443	−	3.12536i	0.0609312	−	0.105536i	−0.833951	−	0.551839i	$-0.813926\pi$
$877$	1.80443	−	3.12536i	0.0609312	−	0.105536i	0.894882	+	0.446303i	$0.147260\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	12.6937			0.427660			0.213830	−	0.976871i	$-0.431406\pi$
$881$	12.6937			0.427660			0.213830	+	0.976871i	$0.431406\pi$
$882$		0			0
$883$	8.55621			0.287939			0.143970	−	0.989582i	$-0.454013\pi$
$883$	8.55621			0.287939			0.143970	+	0.989582i	$0.454013\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	7.45990	−	12.9209i	0.250479	−	0.433842i	−0.713179	−	0.700982i	$-0.752745\pi$
$887$	7.45990	−	12.9209i	0.250479	−	0.433842i	0.963658	+	0.267140i	$0.0860785\pi$
$888$		0			0
$889$	−33.1856	+	31.0717i	−1.11301	+	1.04211i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	42.3542	−	24.4532i	1.41733	−	0.818295i
$894$		0			0
$895$	−7.70388	−	4.44784i	−0.257512	−	0.148675i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	21.1947			0.706883
$900$		0			0
$901$		−	4.91133i		−	0.163620i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	27.3851	+	15.8108i	0.910312	+	0.525569i
$906$		0			0
$907$	−16.1506	−	27.9737i	−0.536273	−	0.928852i	−0.999101	−	0.0424034i	$-0.986499\pi$
$907$	−16.1506	−	27.9737i	−0.536273	−	0.928852i	0.462828	−	0.886448i	$-0.346835\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	13.3778	−	7.72366i	0.443225	−	0.255896i	−0.261740	−	0.965139i	$-0.584296\pi$
$911$	13.3778	−	7.72366i	0.443225	−	0.255896i	0.704965	+	0.709242i	$0.250963\pi$
$912$		0			0
$913$	0.498544	+	0.287834i	0.0164994	+	0.00952593i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4.80803	−	20.6355i	−0.158775	−	0.681444i
$918$		0			0
$919$	1.01879			0.0336069			0.0168034	−	0.999859i	$-0.494651\pi$
$919$	1.01879			0.0336069			0.0168034	+	0.999859i	$0.494651\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	16.3636	−	28.3427i	0.538616	−	0.932910i
$924$		0			0
$925$	1.11858	+	1.93744i	0.0367787	+	0.0637026i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	17.5872	+	30.4619i	0.577016	+	0.999421i	0.995819	+	0.0913443i	$0.0291164\pi$
$929$	17.5872	+	30.4619i	0.577016	+	0.999421i	−0.418803	+	0.908077i	$0.637550\pi$
$930$		0			0
$931$	−42.6529	−	2.80936i	−1.39789	−	0.0920731i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			1.17301i			0.0383615i
$936$		0			0
$937$			19.5780i			0.639586i	0.947487	+	0.319793i	$0.103613\pi$
$937$			19.5780i			0.639586i	−0.947487	+	0.319793i	$0.896387\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−23.2160	+	40.2113i	−0.756820	+	1.31085i	0.187645	+	0.982237i	$0.439915\pi$
$941$	−23.2160	+	40.2113i	−0.756820	+	1.31085i	−0.944464	+	0.328614i	$0.893419\pi$
$942$		0			0
$943$	15.1197	−	8.72936i	0.492365	−	0.284267i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−32.1063	+	18.5366i	−1.04331	+	0.602358i	−0.920770	−	0.390105i	$-0.872439\pi$
$947$	−32.1063	+	18.5366i	−1.04331	+	0.602358i	−0.122544	+	0.992463i	$0.539105\pi$
$948$		0			0
$949$	2.69048	−	4.66006i	0.0873368	−	0.151272i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			2.73116i			0.0884709i	0.999021	+	0.0442354i	$0.0140852\pi$
$953$			2.73116i			0.0884709i	−0.999021	+	0.0442354i	$0.985915\pi$
$954$		0			0
$955$			28.5344i			0.923352i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−7.49098	+	24.6802i	−0.241896	+	0.796965i
$960$		0			0
$961$	−3.63491	−	6.29585i	−0.117255	−	0.203092i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−17.2257	−	29.8358i	−0.554516	−	0.960450i
$966$		0			0
$967$	−14.6811	+	25.4285i	−0.472113	+	0.817724i	−0.999491	−	0.0319070i	$-0.989842\pi$
$967$	−14.6811	+	25.4285i	−0.472113	+	0.817724i	0.527378	+	0.849631i	$0.323175\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−17.1103			−0.549094			−0.274547	−	0.961574i	$-0.588528\pi$
$971$	−17.1103			−0.549094			−0.274547	+	0.961574i	$0.588528\pi$
$972$		0			0
$973$	20.1148	−	4.68671i	0.644851	−	0.150249i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−36.4251	−	21.0301i	−1.16534	−	0.672812i	−0.212765	−	0.977103i	$-0.568247\pi$
$977$	−36.4251	−	21.0301i	−1.16534	−	0.672812i	−0.952579	+	0.304292i	$0.901580\pi$
$978$		0			0
$979$	−12.4605	+	7.19406i	−0.398238	+	0.229923i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	3.87731	+	6.71569i	0.123667	+	0.214197i	0.921211	−	0.389063i	$-0.127201\pi$
$983$	3.87731	+	6.71569i	0.123667	+	0.214197i	−0.797544	+	0.603261i	$0.793868\pi$
$984$		0			0
$985$	−13.3863	−	7.72860i	−0.426524	−	0.246254i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			69.7184i			2.21692i
$990$		0			0
$991$	11.5135			0.365738			0.182869	−	0.983137i	$-0.441462\pi$
$991$	11.5135			0.365738			0.182869	+	0.983137i	$0.441462\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−27.2683	−	15.7434i	−0.864464	−	0.499099i
$996$		0			0
$997$	−15.0836	+	8.70850i	−0.477701	+	0.275801i	−0.719458	−	0.694536i	$-0.755610\pi$
$997$	−15.0836	+	8.70850i	−0.477701	+	0.275801i	0.241757	+	0.970337i	$0.422276\pi$
$998$		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.881.17		48
3.2	odd	2		1008.2.cc.d.545.5		48
4.3	odd	2		1512.2.bu.a.881.17		48
7.6	odd	2	inner	3024.2.cc.d.881.8		48
9.2	odd	6	inner	3024.2.cc.d.2897.8		48
9.7	even	3		1008.2.cc.d.209.20		48
12.11	even	2		504.2.bu.a.41.20	yes	48
21.20	even	2		1008.2.cc.d.545.20		48
28.27	even	2		1512.2.bu.a.881.8		48
36.7	odd	6		504.2.bu.a.209.5	yes	48
36.11	even	6		1512.2.bu.a.1385.8		48
36.23	even	6		4536.2.k.a.3401.34		48
36.31	odd	6		4536.2.k.a.3401.15		48
63.20	even	6	inner	3024.2.cc.d.2897.17		48
63.34	odd	6		1008.2.cc.d.209.5		48
84.83	odd	2		504.2.bu.a.41.5	✓	48
252.83	odd	6		1512.2.bu.a.1385.17		48
252.139	even	6		4536.2.k.a.3401.33		48
252.167	odd	6		4536.2.k.a.3401.16		48
252.223	even	6		504.2.bu.a.209.20	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bu.a.41.5	✓	48	84.83	odd	2
504.2.bu.a.41.20	yes	48	12.11	even	2
504.2.bu.a.209.5	yes	48	36.7	odd	6
504.2.bu.a.209.20	yes	48	252.223	even	6
1008.2.cc.d.209.5		48	63.34	odd	6
1008.2.cc.d.209.20		48	9.7	even	3
1008.2.cc.d.545.5		48	3.2	odd	2
1008.2.cc.d.545.20		48	21.20	even	2
1512.2.bu.a.881.8		48	28.27	even	2
1512.2.bu.a.881.17		48	4.3	odd	2
1512.2.bu.a.1385.8		48	36.11	even	6
1512.2.bu.a.1385.17		48	252.83	odd	6
3024.2.cc.d.881.8		48	7.6	odd	2	inner
3024.2.cc.d.881.17		48	1.1	even	1	trivial
3024.2.cc.d.2897.8		48	9.2	odd	6	inner
3024.2.cc.d.2897.17		48	63.20	even	6	inner
4536.2.k.a.3401.15		48	36.31	odd	6
4536.2.k.a.3401.16		48	252.167	odd	6
4536.2.k.a.3401.33		48	252.139	even	6
4536.2.k.a.3401.34		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)

\(f(q)\)	\(=\)	\(q+(0.965651 - 1.67256i) q^{5} +(1.93133 - 1.80831i) q^{7} +O(q^{10})\)	\(q+(0.965651 - 1.67256i) q^{5} +(1.93133 - 1.80831i) q^{7} +(1.10681 - 0.639015i) q^{11} +(-2.52802 - 1.45955i) q^{13} -0.475237 q^{17} -6.10647i q^{19} +(-6.51132 - 3.75931i) q^{23} +(0.635036 + 1.09991i) q^{25} +(-3.76797 + 2.17544i) q^{29} +(-4.21872 - 2.43568i) q^{31} +(-1.15950 - 4.97645i) q^{35} +1.76145 q^{37} +(-1.16103 + 2.01097i) q^{41} +(-4.63638 - 8.03045i) q^{43} +(4.00447 + 6.93595i) q^{47} +(0.460063 - 6.98487i) q^{49} +10.3345i q^{53} -2.46826i q^{55} +(1.74272 - 3.01848i) q^{59} +(4.26195 - 2.46064i) q^{61} +(-4.88237 + 2.81883i) q^{65} +(-0.602527 + 1.04361i) q^{67} +11.2114i q^{71} +1.84336i q^{73} +(0.982073 - 3.23559i) q^{77} +(-8.54654 - 14.8030i) q^{79} +(0.225217 + 0.390088i) q^{83} +(-0.458913 + 0.794861i) q^{85} -11.2580 q^{89} +(-7.52175 + 1.75255i) q^{91} +(-10.2134 - 5.89672i) q^{95} +(9.22775 - 5.32764i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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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