LMFDB - Embedded newform 3024.2.cc.d.881.5

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			881.5
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.d.2897.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26858 + 2.19724i) q^{5} +(-0.521158 - 2.59391i) q^{7} +O(q^{10})$	$q+(-1.26858 + 2.19724i) q^{5} +(-0.521158 - 2.59391i) q^{7} +(-5.68321 + 3.28120i) q^{11} +(5.13890 + 2.96694i) q^{13} -3.52698 q^{17} -0.261355i q^{19} +(2.89967 + 1.67412i) q^{23} +(-0.718584 - 1.24462i) q^{25} +(1.00813 - 0.582041i) q^{29} +(-1.69360 - 0.977800i) q^{31} +(6.36059 + 2.14547i) q^{35} -1.16528 q^{37} +(2.85769 - 4.94966i) q^{41} +(-2.67364 - 4.63088i) q^{43} +(-3.79767 - 6.57775i) q^{47} +(-6.45679 + 2.70368i) q^{49} +3.54792i q^{53} -16.6499i q^{55} +(5.47899 - 9.48989i) q^{59} +(-5.53699 + 3.19678i) q^{61} +(-13.0382 + 7.52760i) q^{65} +(-4.54164 + 7.86635i) q^{67} -10.5889i q^{71} -2.72923i q^{73} +(11.4730 + 13.0317i) q^{77} +(0.652687 + 1.13049i) q^{79} +(-4.53241 - 7.85037i) q^{83} +(4.47426 - 7.74964i) q^{85} -14.2599 q^{89} +(5.01782 - 14.8761i) q^{91} +(0.574261 + 0.331550i) q^{95} +(9.95686 - 5.74859i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.26858	+	2.19724i	−0.567326	+	0.982637i	0.429503	+	0.903065i	$0.358689\pi$
$5$	−1.26858	+	2.19724i	−0.567326	+	0.982637i	−0.996829	+	0.0795717i	$0.974645\pi$
$6$		0			0
$7$	−0.521158	−	2.59391i	−0.196979	−	0.980408i
$7$	−0.521158	−	2.59391i	−0.196979	−	0.980408i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−5.68321	+	3.28120i	−1.71355	+	0.989320i	−0.783898	+	0.620889i	$0.786772\pi$
$11$	−5.68321	+	3.28120i	−1.71355	+	0.989320i	−0.929655	+	0.368431i	$0.879895\pi$
$12$		0			0
$13$	5.13890	+	2.96694i	1.42527	+	0.822882i	0.996743	−	0.0806450i	$-0.0256980\pi$
$13$	5.13890	+	2.96694i	1.42527	+	0.822882i	0.428531	+	0.903527i	$0.359031\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.52698			−0.855419			−0.427709	−	0.903916i	$-0.640679\pi$
$17$	−3.52698			−0.855419			−0.427709	+	0.903916i	$0.640679\pi$
$18$		0			0
$19$		−	0.261355i		−	0.0599590i	−0.999551	−	0.0299795i	$-0.990456\pi$
$19$		−	0.261355i		−	0.0599590i	0.999551	−	0.0299795i	$-0.00954420\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.89967	+	1.67412i	0.604622	+	0.349079i	0.770858	−	0.637007i	$-0.219828\pi$
$23$	2.89967	+	1.67412i	0.604622	+	0.349079i	−0.166236	+	0.986086i	$0.553161\pi$
$24$		0			0
$25$	−0.718584	−	1.24462i	−0.143717	−	0.248925i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.00813	−	0.582041i	0.187204	−	0.108082i	−0.403469	−	0.914993i	$-0.632196\pi$
$29$	1.00813	−	0.582041i	0.187204	−	0.108082i	0.590673	+	0.806911i	$0.298862\pi$
$30$		0			0
$31$	−1.69360	−	0.977800i	−0.304179	−	0.175618i	0.340139	−	0.940375i	$-0.389526\pi$
$31$	−1.69360	−	0.977800i	−0.304179	−	0.175618i	−0.644319	+	0.764757i	$0.722859\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	6.36059	+	2.14547i	1.07514	+	0.362651i
$36$		0			0
$37$	−1.16528			−0.191570			−0.0957851	−	0.995402i	$-0.530536\pi$
$37$	−1.16528			−0.191570			−0.0957851	+	0.995402i	$0.530536\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.85769	−	4.94966i	0.446296	−	0.773007i	−0.551846	−	0.833946i	$-0.686076\pi$
$41$	2.85769	−	4.94966i	0.446296	−	0.773007i	0.998141	+	0.0609391i	$0.0194096\pi$
$42$		0			0
$43$	−2.67364	−	4.63088i	−0.407726	−	0.706203i	0.586908	−	0.809654i	$-0.300345\pi$
$43$	−2.67364	−	4.63088i	−0.407726	−	0.706203i	−0.994635	+	0.103451i	$0.967012\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.79767	−	6.57775i	−0.553947	−	0.959464i	−0.997985	−	0.0634560i	$-0.979788\pi$
$47$	−3.79767	−	6.57775i	−0.553947	−	0.959464i	0.444038	−	0.896008i	$-0.353546\pi$
$48$		0			0
$49$	−6.45679	+	2.70368i	−0.922398	+	0.386240i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			3.54792i			0.487344i	0.969858	+	0.243672i	$0.0783521\pi$
$53$			3.54792i			0.487344i	−0.969858	+	0.243672i	$0.921648\pi$
$54$		0			0
$55$		−	16.6499i		−	2.24507i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.47899	−	9.48989i	0.713304	−	1.23548i	−0.250306	−	0.968167i	$-0.580531\pi$
$59$	5.47899	−	9.48989i	0.713304	−	1.23548i	0.963610	−	0.267312i	$-0.0861353\pi$
$60$		0			0
$61$	−5.53699	+	3.19678i	−0.708939	+	0.409306i	−0.810668	−	0.585506i	$-0.800896\pi$
$61$	−5.53699	+	3.19678i	−0.708939	+	0.409306i	0.101729	+	0.994812i	$0.467562\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−13.0382	+	7.52760i	−1.61719	+	0.933684i
$66$		0			0
$67$	−4.54164	+	7.86635i	−0.554850	+	0.961028i	0.443066	+	0.896489i	$0.353891\pi$
$67$	−4.54164	+	7.86635i	−0.554850	+	0.961028i	−0.997915	+	0.0645384i	$0.979442\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	10.5889i		−	1.25667i	−0.777944	−	0.628334i	$-0.783737\pi$
$71$		−	10.5889i		−	1.25667i	0.777944	−	0.628334i	$-0.216263\pi$
$72$		0			0
$73$		−	2.72923i		−	0.319433i	−0.987163	−	0.159716i	$-0.948942\pi$
$73$		−	2.72923i		−	0.319433i	0.987163	−	0.159716i	$-0.0510579\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	11.4730	+	13.0317i	1.30747	+	1.48511i
$78$		0			0
$79$	0.652687	+	1.13049i	0.0734330	+	0.127190i	0.900404	−	0.435055i	$-0.143271\pi$
$79$	0.652687	+	1.13049i	0.0734330	+	0.127190i	−0.826971	+	0.562245i	$0.809938\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.53241	−	7.85037i	−0.497497	−	0.861690i	0.502499	−	0.864578i	$-0.332414\pi$
$83$	−4.53241	−	7.85037i	−0.497497	−	0.861690i	−0.999996	+	0.00288802i	$0.999081\pi$
$84$		0			0
$85$	4.47426	−	7.74964i	0.485301	−	0.840566i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−14.2599			−1.51155			−0.755776	−	0.654830i	$-0.772740\pi$
$89$	−14.2599			−1.51155			−0.755776	+	0.654830i	$0.772740\pi$
$90$		0			0
$91$	5.01782	−	14.8761i	0.526011	−	1.55944i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.574261	+	0.331550i	0.0589180	+	0.0340163i
$96$		0			0
$97$	9.95686	−	5.74859i	1.01097	−	0.583681i	0.0994914	−	0.995038i	$-0.468278\pi$
$97$	9.95686	−	5.74859i	1.01097	−	0.583681i	0.911474	+	0.411357i	$0.134945\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.09191	+	1.89124i	0.108649	+	0.188186i	0.915223	−	0.402947i	$-0.132014\pi$
$101$	1.09191	+	1.89124i	0.108649	+	0.188186i	−0.806574	+	0.591133i	$0.798681\pi$
$102$		0			0
$103$	−9.75576	−	5.63249i	−0.961264	−	0.554986i	−0.0647021	−	0.997905i	$-0.520610\pi$
$103$	−9.75576	−	5.63249i	−0.961264	−	0.554986i	−0.896562	+	0.442919i	$0.853943\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			7.82576i			0.756545i	0.925694	+	0.378272i	$0.123482\pi$
$107$			7.82576i			0.756545i	−0.925694	+	0.378272i	$0.876518\pi$
$108$		0			0
$109$	−17.5453			−1.68053			−0.840266	−	0.542174i	$-0.817601\pi$
$109$	−17.5453			−1.68053			−0.840266	+	0.542174i	$0.817601\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.81112	−	2.20035i	−0.358520	−	0.206992i	0.309911	−	0.950765i	$-0.399701\pi$
$113$	−3.81112	−	2.20035i	−0.358520	−	0.206992i	−0.668431	+	0.743774i	$0.733034\pi$
$114$		0			0
$115$	−7.35691	+	4.24751i	−0.686035	+	0.396083i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.83812	+	9.14869i	0.168500	+	0.838659i
$120$		0			0
$121$	16.0326	−	27.7693i	1.45751	−	2.52448i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.03946			−0.808514
$126$		0			0
$127$	−19.5689			−1.73646			−0.868228	−	0.496165i	$-0.834741\pi$
$127$	−19.5689			−1.73646			−0.868228	+	0.496165i	$0.834741\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.00967786	−	0.0167625i	0.000845559	−	0.00146455i	−0.865602	−	0.500732i	$-0.833064\pi$
$131$	0.00967786	−	0.0167625i	0.000845559	−	0.00146455i	0.866448	+	0.499268i	$0.166398\pi$
$132$		0			0
$133$	−0.677933	+	0.136207i	−0.0587843	+	0.0118107i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.67032	−	2.11906i	0.313577	−	0.181044i	−0.334949	−	0.942236i	$-0.608719\pi$
$137$	3.67032	−	2.11906i	0.313577	−	0.181044i	0.648526	+	0.761193i	$0.275386\pi$
$138$		0			0
$139$	17.6403	+	10.1847i	1.49623	+	0.863851i	0.999991	−	0.00433182i	$-0.00137887\pi$
$139$	17.6403	+	10.1847i	1.49623	+	0.863851i	0.496244	+	0.868183i	$0.334712\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−38.9406			−3.25638
$144$		0			0
$145$			2.95346i			0.245272i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	6.40370	+	3.69718i	0.524611	+	0.302885i	0.738819	−	0.673904i	$-0.235384\pi$
$149$	6.40370	+	3.69718i	0.524611	+	0.302885i	−0.214208	+	0.976788i	$0.568717\pi$
$150$		0			0
$151$	−6.94189	−	12.0237i	−0.564923	−	0.978475i	−0.997057	−	0.0766658i	$-0.975573\pi$
$151$	−6.94189	−	12.0237i	−0.564923	−	0.978475i	0.432134	−	0.901809i	$-0.357761\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.29693	−	2.48083i	0.345138	−	0.199265i
$156$		0			0
$157$	1.86713	+	1.07799i	0.149013	+	0.0860329i	0.572653	−	0.819798i	$-0.305914\pi$
$157$	1.86713	+	1.07799i	0.149013	+	0.0860329i	−0.423639	+	0.905831i	$0.639248\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.83135	−	8.39397i	0.223142	−	0.661538i
$162$		0			0
$163$	17.1866			1.34616			0.673079	−	0.739571i	$-0.264971\pi$
$163$	17.1866			1.34616			0.673079	+	0.739571i	$0.264971\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.40101	−	9.35482i	0.417943	−	0.723898i	−0.577790	−	0.816186i	$-0.696085\pi$
$167$	5.40101	−	9.35482i	0.417943	−	0.723898i	0.995732	+	0.0922879i	$0.0294180\pi$
$168$		0			0
$169$	11.1055	+	19.2353i	0.854270	+	1.47964i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.55489	−	16.5495i	−0.726444	−	1.25824i	−0.958377	−	0.285507i	$-0.907838\pi$
$173$	−9.55489	−	16.5495i	−0.726444	−	1.25824i	0.231932	−	0.972732i	$-0.425495\pi$
$174$		0			0
$175$	−2.85395	+	2.51259i	−0.215739	+	0.189934i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	14.9224i		−	1.11536i	−0.830057	−	0.557678i	$-0.811692\pi$
$179$		−	14.9224i		−	1.11536i	0.830057	−	0.557678i	$-0.188308\pi$
$180$		0			0
$181$		−	18.5179i		−	1.37642i	−0.725511	−	0.688211i	$-0.758396\pi$
$181$		−	18.5179i		−	1.37642i	0.725511	−	0.688211i	$-0.241604\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.47824	−	2.56039i	0.108683	−	0.188244i
$186$		0			0
$187$	20.0446	−	11.5728i	1.46581	−	0.846283i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.08192	+	2.93405i	−0.367715	+	0.212300i	−0.672460	−	0.740134i	$-0.734762\pi$
$191$	−5.08192	+	2.93405i	−0.367715	+	0.212300i	0.304745	+	0.952434i	$0.401429\pi$
$192$		0			0
$193$	−8.19577	+	14.1955i	−0.589945	+	1.02181i	0.404294	+	0.914629i	$0.367517\pi$
$193$	−8.19577	+	14.1955i	−0.589945	+	1.02181i	−0.994239	+	0.107185i	$0.965816\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	6.90103i		−	0.491678i	−0.969311	−	0.245839i	$-0.920936\pi$
$197$		−	6.90103i		−	0.491678i	0.969311	−	0.245839i	$-0.0790635\pi$
$198$		0			0
$199$			10.3555i			0.734078i	0.930205	+	0.367039i	$0.119629\pi$
$199$			10.3555i			0.734078i	−0.930205	+	0.367039i	$0.880371\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.03516	−	2.31166i	−0.142840	−	0.162246i
$204$		0			0
$205$	7.25041	+	12.5581i	0.506390	+	0.877094i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.857560	+	1.48534i	0.0593187	+	0.102743i
$210$		0			0
$211$	−3.43331	+	5.94667i	−0.236359	+	0.409385i	−0.959667	−	0.281140i	$-0.909287\pi$
$211$	−3.43331	+	5.94667i	−0.236359	+	0.409385i	0.723308	+	0.690526i	$0.242621\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	13.5669			0.925255
$216$		0			0
$217$	−1.65370	+	4.90264i	−0.112260	+	0.332813i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−18.1248	−	10.4644i	−1.21921	−	0.703909i
$222$		0			0
$223$	−0.467052	+	0.269653i	−0.0312761	+	0.0180573i	−0.515557	−	0.856856i	$-0.672415\pi$
$223$	−0.467052	+	0.269653i	−0.0312761	+	0.0180573i	0.484280	+	0.874913i	$0.339081\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.610518	−	1.05745i	−0.0405215	−	0.0701852i	0.845053	−	0.534682i	$-0.179569\pi$
$227$	−0.610518	−	1.05745i	−0.0405215	−	0.0701852i	−0.885575	+	0.464497i	$0.846235\pi$
$228$		0			0
$229$	−10.4049	−	6.00725i	−0.687573	−	0.396970i	0.115129	−	0.993351i	$-0.463272\pi$
$229$	−10.4049	−	6.00725i	−0.687573	−	0.396970i	−0.802702	+	0.596380i	$0.796605\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	5.13142i		−	0.336171i	−0.985772	−	0.168085i	$-0.946242\pi$
$233$		−	5.13142i		−	0.336171i	0.985772	−	0.168085i	$-0.0537584\pi$
$234$		0			0
$235$	19.2706			1.25707
$236$		0			0
$237$		0			0
$238$		0			0
$239$	10.5981	+	6.11881i	0.685533	+	0.395793i	0.801937	−	0.597409i	$-0.203803\pi$
$239$	10.5981	+	6.11881i	0.685533	+	0.395793i	−0.116403	+	0.993202i	$0.537137\pi$
$240$		0			0
$241$	24.9320	−	14.3945i	1.60601	−	0.927231i	0.615761	−	0.787933i	$-0.288849\pi$
$241$	24.9320	−	14.3945i	1.60601	−	0.927231i	0.990251	−	0.139298i	$-0.0444846\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.25030	−	17.6170i	0.143767	−	1.12551i
$246$		0			0
$247$	0.775427	−	1.34308i	0.0493392	−	0.0854580i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	4.82335			0.304447			0.152223	−	0.988346i	$-0.451357\pi$
$251$	4.82335			0.304447			0.152223	+	0.988346i	$0.451357\pi$
$252$		0			0
$253$	−21.9726			−1.38140
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.15022	−	3.72430i	0.134127	−	0.232315i	−0.791136	−	0.611640i	$-0.790510\pi$
$257$	2.15022	−	3.72430i	0.134127	−	0.232315i	0.925264	+	0.379324i	$0.123844\pi$
$258$		0			0
$259$	0.607293	+	3.02263i	0.0377354	+	0.187817i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−19.2444	+	11.1107i	−1.18666	+	0.685118i	−0.957546	−	0.288282i	$-0.906916\pi$
$263$	−19.2444	+	11.1107i	−1.18666	+	0.685118i	−0.229113	+	0.973400i	$0.573583\pi$
$264$		0			0
$265$	−7.79564	−	4.50082i	−0.478883	−	0.276483i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	21.6564			1.32042			0.660208	−	0.751083i	$-0.270468\pi$
$269$	21.6564			1.32042			0.660208	+	0.751083i	$0.270468\pi$
$270$		0			0
$271$		−	17.0808i		−	1.03758i	−0.854901	−	0.518792i	$-0.826382\pi$
$271$		−	17.0808i		−	1.03758i	0.854901	−	0.518792i	$-0.173618\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.16774	+	4.71565i	0.492533	+	0.284364i
$276$		0			0
$277$	−1.60480	−	2.77959i	−0.0964230	−	0.167009i	0.813779	−	0.581175i	$-0.197407\pi$
$277$	−1.60480	−	2.77959i	−0.0964230	−	0.167009i	−0.910202	+	0.414165i	$0.864073\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−18.0599	+	10.4269i	−1.07736	+	0.622016i	−0.930184	−	0.367094i	$-0.880353\pi$
$281$	−18.0599	+	10.4269i	−1.07736	+	0.622016i	−0.147179	+	0.989110i	$0.547019\pi$
$282$		0			0
$283$	−9.99941	−	5.77316i	−0.594403	−	0.343179i	0.172433	−	0.985021i	$-0.444837\pi$
$283$	−9.99941	−	5.77316i	−0.594403	−	0.343179i	−0.766837	+	0.641842i	$0.778170\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−14.3283	−	4.83304i	−0.845773	−	0.285286i
$288$		0			0
$289$	−4.56040			−0.268259
$290$		0			0
$291$		0			0
$292$		0			0
$293$	14.1600	−	24.5259i	0.827238	−	1.43282i	−0.0729596	−	0.997335i	$-0.523244\pi$
$293$	14.1600	−	24.5259i	0.827238	−	1.43282i	0.900197	−	0.435483i	$-0.143422\pi$
$294$		0			0
$295$	13.9011	+	24.0773i	0.809351	+	1.40184i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	9.93406	+	17.2063i	0.574501	+	0.995066i
$300$		0			0
$301$	−10.6187	+	9.34862i	−0.612053	+	0.538845i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	16.2215i		−	0.928839i
$306$		0			0
$307$			24.2818i			1.38584i	0.721016	+	0.692918i	$0.243675\pi$
$307$			24.2818i			1.38584i	−0.721016	+	0.692918i	$0.756325\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−16.3119	+	28.2531i	−0.924964	+	1.60209i	−0.133346	+	0.991070i	$0.542572\pi$
$311$	−16.3119	+	28.2531i	−0.924964	+	1.60209i	−0.791619	+	0.611016i	$0.790761\pi$
$312$		0			0
$313$	12.5650	−	7.25443i	0.710218	−	0.410045i	−0.100924	−	0.994894i	$-0.532180\pi$
$313$	12.5650	−	7.25443i	0.710218	−	0.410045i	0.811142	+	0.584850i	$0.198846\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−14.0182	+	8.09338i	−0.787338	+	0.454570i	−0.839024	−	0.544094i	$-0.816874\pi$
$317$	−14.0182	+	8.09338i	−0.787338	+	0.454570i	0.0516867	+	0.998663i	$0.483540\pi$
$318$		0			0
$319$	−3.81959	+	6.61573i	−0.213856	+	0.370410i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			0.921796i			0.0512901i
$324$		0			0
$325$		−	8.52800i		−	0.473048i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−15.0829	+	13.2789i	−0.831550	+	0.732088i
$330$		0			0
$331$	−14.6054	−	25.2973i	−0.802787	−	1.39047i	−0.917775	−	0.397100i	$-0.870016\pi$
$331$	−14.6054	−	25.2973i	−0.802787	−	1.39047i	0.114989	−	0.993367i	$-0.463317\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−11.5229	−	19.9582i	−0.629561	−	1.09043i
$336$		0			0
$337$	−8.46812	+	14.6672i	−0.461288	+	0.798974i	−0.999025	−	0.0441385i	$-0.985946\pi$
$337$	−8.46812	+	14.6672i	−0.461288	+	0.798974i	0.537738	+	0.843112i	$0.319279\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	12.8334			0.694970
$342$		0			0
$343$	10.3781	+	15.3393i	0.560366	+	0.828245i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−17.7384	−	10.2413i	−0.952247	−	0.549780i	−0.0584689	−	0.998289i	$-0.518622\pi$
$347$	−17.7384	−	10.2413i	−0.952247	−	0.549780i	−0.893778	+	0.448509i	$0.851955\pi$
$348$		0			0
$349$	5.98087	−	3.45306i	0.320149	−	0.184838i	−0.331310	−	0.943522i	$-0.607491\pi$
$349$	5.98087	−	3.45306i	0.320149	−	0.184838i	0.651459	+	0.758684i	$0.274157\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	10.5025	+	18.1908i	0.558990	+	0.968198i	0.997581	+	0.0695118i	$0.0221441\pi$
$353$	10.5025	+	18.1908i	0.558990	+	0.968198i	−0.438592	+	0.898686i	$0.644523\pi$
$354$		0			0
$355$	23.2663	+	13.4328i	1.23485	+	0.712939i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			2.61864i			0.138206i	0.997610	+	0.0691032i	$0.0220138\pi$
$359$			2.61864i			0.138206i	−0.997610	+	0.0691032i	$0.977986\pi$
$360$		0			0
$361$	18.9317			0.996405
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5.99679	+	3.46225i	0.313886	+	0.181222i
$366$		0			0
$367$	−23.8455	+	13.7672i	−1.24472	+	0.718641i	−0.970052	−	0.242897i	$-0.921902\pi$
$367$	−23.8455	+	13.7672i	−1.24472	+	0.718641i	−0.274671	+	0.961538i	$0.588569\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	9.20300	−	1.84903i	0.477796	−	0.0959967i
$372$		0			0
$373$	−2.67768	+	4.63788i	−0.138645	+	0.240140i	−0.926984	−	0.375101i	$-0.877608\pi$
$373$	−2.67768	+	4.63788i	−0.138645	+	0.240140i	0.788339	+	0.615241i	$0.210941\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.90754			0.355756
$378$		0			0
$379$	−21.5330			−1.10608			−0.553038	−	0.833156i	$-0.686532\pi$
$379$	−21.5330			−1.10608			−0.553038	+	0.833156i	$0.686532\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.85948	+	3.22071i	−0.0950149	+	0.164571i	−0.909615	−	0.415453i	$-0.863623\pi$
$383$	−1.85948	+	3.22071i	−0.0950149	+	0.164571i	0.814600	+	0.580023i	$0.196957\pi$
$384$		0			0
$385$	−43.1883	+	8.67721i	−2.20108	+	0.442232i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.72516	+	4.46012i	−0.391681	+	0.226137i	−0.682888	−	0.730523i	$-0.739276\pi$
$389$	−7.72516	+	4.46012i	−0.391681	+	0.226137i	0.291207	+	0.956660i	$0.405943\pi$
$390$		0			0
$391$	−10.2271	−	5.90460i	−0.517205	−	0.298609i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.31194			−0.166642
$396$		0			0
$397$			13.3591i			0.670476i	0.942134	+	0.335238i	$0.108817\pi$
$397$			13.3591i			0.670476i	−0.942134	+	0.335238i	$0.891183\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	18.6966	+	10.7945i	0.933663	+	0.539051i	0.887968	−	0.459905i	$-0.152116\pi$
$401$	18.6966	+	10.7945i	0.933663	+	0.539051i	0.0456950	+	0.998955i	$0.485450\pi$
$402$		0			0
$403$	−5.80216	−	10.0496i	−0.289026	−	0.500608i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.62251	−	3.82351i	0.328266	−	0.189524i
$408$		0			0
$409$	−25.8784	−	14.9409i	−1.27960	−	0.738779i	−0.302827	−	0.953045i	$-0.597931\pi$
$409$	−25.8784	−	14.9409i	−1.27960	−	0.738779i	−0.976775	+	0.214266i	$0.931264\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−27.4714	−	9.26630i	−1.35178	−	0.455965i
$414$		0			0
$415$	22.9989			1.12897
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−9.30438	+	16.1157i	−0.454549	+	0.787302i	−0.998662	−	0.0517100i	$-0.983533\pi$
$419$	−9.30438	+	16.1157i	−0.454549	+	0.787302i	0.544113	+	0.839012i	$0.316866\pi$
$420$		0			0
$421$	−9.79010	−	16.9570i	−0.477140	−	0.826431i	0.522516	−	0.852629i	$-0.324993\pi$
$421$	−9.79010	−	16.9570i	−0.477140	−	0.826431i	−0.999657	+	0.0261979i	$0.991660\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.53443	+	4.38977i	0.122938	+	0.212935i
$426$		0			0
$427$	11.1778	+	12.6965i	0.540933	+	0.614424i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			13.3632i			0.643683i	0.946794	+	0.321842i	$0.104302\pi$
$431$			13.3632i			0.643683i	−0.946794	+	0.321842i	$0.895698\pi$
$432$		0			0
$433$		−	3.05246i		−	0.146692i	−0.997307	−	0.0733458i	$-0.976632\pi$
$433$		−	3.05246i		−	0.146692i	0.997307	−	0.0733458i	$-0.0233677\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.437541	−	0.757843i	0.0209304	−	0.0362526i
$438$		0			0
$439$	16.8139	−	9.70754i	0.802486	−	0.463316i	−0.0418537	−	0.999124i	$-0.513326\pi$
$439$	16.8139	−	9.70754i	0.802486	−	0.463316i	0.844340	+	0.535808i	$0.179993\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−28.5753	+	16.4979i	−1.35765	+	0.783841i	−0.989307	−	0.145848i	$-0.953409\pi$
$443$	−28.5753	+	16.4979i	−1.35765	+	0.783841i	−0.368345	+	0.929689i	$0.620076\pi$
$444$		0			0
$445$	18.0899	−	31.3326i	0.857542	−	1.48531i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	9.72985i		−	0.459180i	−0.973287	−	0.229590i	$-0.926262\pi$
$449$		−	9.72985i		−	0.459180i	0.973287	−	0.229590i	$-0.0737385\pi$
$450$		0			0
$451$			37.5066i			1.76612i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	26.3209	+	29.8969i	1.23394	+	1.40159i
$456$		0			0
$457$	7.14815	+	12.3810i	0.334376	+	0.579157i	0.983365	−	0.181641i	$-0.0581410\pi$
$457$	7.14815	+	12.3810i	0.334376	+	0.579157i	−0.648989	+	0.760798i	$0.724808\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.95893	+	6.85706i	0.184386	+	0.319365i	0.943369	−	0.331744i	$-0.107637\pi$
$461$	3.95893	+	6.85706i	0.184386	+	0.319365i	−0.758984	+	0.651110i	$0.774304\pi$
$462$		0			0
$463$	−8.81566	+	15.2692i	−0.409698	+	0.709618i	−0.994856	−	0.101301i	$-0.967699\pi$
$463$	−8.81566	+	15.2692i	−0.409698	+	0.709618i	0.585157	+	0.810920i	$0.301033\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	25.1745			1.16494			0.582469	−	0.812853i	$-0.302087\pi$
$467$	25.1745			1.16494			0.582469	+	0.812853i	$0.302087\pi$
$468$		0			0
$469$	22.7716	+	7.68101i	1.05149	+	0.354676i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	30.3897	+	17.5455i	1.39732	+	0.806744i
$474$		0			0
$475$	−0.325289	+	0.187806i	−0.0149253	+	0.00861712i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	11.3258	+	19.6168i	0.517488	+	0.896316i	0.999794	+	0.0203125i	$0.00646613\pi$
$479$	11.3258	+	19.6168i	0.517488	+	0.896316i	−0.482306	+	0.876003i	$0.660201\pi$
$480$		0			0
$481$	−5.98823	−	3.45731i	−0.273040	−	0.157640i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			29.1702i			1.32455i
$486$		0			0
$487$	6.17391			0.279767			0.139883	−	0.990168i	$-0.455327\pi$
$487$	6.17391			0.279767			0.139883	+	0.990168i	$0.455327\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	20.8632	+	12.0454i	0.941544	+	0.543601i	0.890444	−	0.455093i	$-0.150394\pi$
$491$	20.8632	+	12.0454i	0.941544	+	0.543601i	0.0511002	+	0.998694i	$0.483727\pi$
$492$		0			0
$493$	−3.55564	+	2.05285i	−0.160138	+	0.0924557i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−27.4666	+	5.51847i	−1.23205	+	0.247537i
$498$		0			0
$499$	7.18584	−	12.4462i	0.321682	−	0.557170i	−0.659153	−	0.752009i	$-0.729085\pi$
$499$	7.18584	−	12.4462i	0.321682	−	0.557170i	0.980835	+	0.194839i	$0.0624184\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−18.4937			−0.824593			−0.412296	−	0.911050i	$-0.635273\pi$
$503$	−18.4937			−0.824593			−0.412296	+	0.911050i	$0.635273\pi$
$504$		0			0
$505$	−5.54069			−0.246557
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.48887	−	12.9711i	0.331938	−	0.574934i	−0.650954	−	0.759118i	$-0.725631\pi$
$509$	7.48887	−	12.9711i	0.331938	−	0.574934i	0.982892	+	0.184184i	$0.0589641\pi$
$510$		0			0
$511$	−7.07940	+	1.42236i	−0.313174	+	0.0629216i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	24.7519	−	14.2905i	1.09070	−	0.629716i
$516$		0			0
$517$	43.1659	+	24.9219i	1.89843	+	1.09606i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	15.4043			0.674873			0.337436	−	0.941348i	$-0.390440\pi$
$521$	15.4043			0.674873			0.337436	+	0.941348i	$0.390440\pi$
$522$		0			0
$523$			16.9319i			0.740381i	0.928956	+	0.370191i	$0.120708\pi$
$523$			16.9319i			0.740381i	−0.928956	+	0.370191i	$0.879292\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.97329	+	3.44868i	0.260201	+	0.150227i
$528$		0			0
$529$	−5.89462	−	10.2098i	−0.256288	−	0.443904i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	29.3707	−	16.9572i	1.27219	−	0.734498i
$534$		0			0
$535$	−17.1951	−	9.92760i	−0.743409	−	0.429207i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	27.8240	−	36.5516i	1.19846	−	1.57439i
$540$		0			0
$541$	6.44265			0.276991			0.138496	−	0.990363i	$-0.455773\pi$
$541$	6.44265			0.276991			0.138496	+	0.990363i	$0.455773\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	22.2576	−	38.5512i	0.953409	−	1.65135i
$546$		0			0
$547$	2.89191	+	5.00893i	0.123649	+	0.214166i	0.921204	−	0.389080i	$-0.127207\pi$
$547$	2.89191	+	5.00893i	0.123649	+	0.214166i	−0.797555	+	0.603246i	$0.793874\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.152120	−	0.263479i	−0.00648051	−	0.0112246i
$552$		0			0
$553$	2.59223	−	2.28218i	0.110233	−	0.0970480i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			3.86933i			0.163949i	0.996634	+	0.0819745i	$0.0261226\pi$
$557$			3.86933i			0.163949i	−0.996634	+	0.0819745i	$0.973877\pi$
$558$		0			0
$559$		−	31.7302i		−	1.34204i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12.2712	−	21.2544i	0.517171	−	0.895766i	−0.482630	−	0.875824i	$-0.660319\pi$
$563$	12.2712	−	21.2544i	0.517171	−	0.895766i	0.999801	−	0.0199420i	$-0.00634815\pi$
$564$		0			0
$565$	9.66941	−	5.58264i	0.406795	−	0.234863i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	12.0119	−	6.93510i	0.503567	−	0.290735i	−0.226618	−	0.973984i	$-0.572767\pi$
$569$	12.0119	−	6.93510i	0.503567	−	0.290735i	0.730185	+	0.683249i	$0.239434\pi$
$570$		0			0
$571$	3.32890	−	5.76582i	0.139310	−	0.241292i	−0.787926	−	0.615770i	$-0.788845\pi$
$571$	3.32890	−	5.76582i	0.139310	−	0.241292i	0.927236	+	0.374478i	$0.122178\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	4.81200i		−	0.200674i
$576$		0			0
$577$		−	20.4063i		−	0.849525i	−0.905305	−	0.424763i	$-0.860358\pi$
$577$		−	20.4063i		−	0.849525i	0.905305	−	0.424763i	$-0.139642\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−18.0011	+	15.8480i	−0.746811	+	0.657485i
$582$		0			0
$583$	−11.6415	−	20.1636i	−0.482140	−	0.835090i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.43838	−	5.95544i	−0.141917	−	0.245807i	0.786302	−	0.617843i	$-0.211993\pi$
$587$	−3.43838	−	5.95544i	−0.141917	−	0.245807i	−0.928218	+	0.372036i	$0.878660\pi$
$588$		0			0
$589$	−0.255553	+	0.442631i	−0.0105299	+	0.0182383i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−13.7068			−0.562871			−0.281435	−	0.959580i	$-0.590811\pi$
$593$	−13.7068			−0.562871			−0.281435	+	0.959580i	$0.590811\pi$
$594$		0			0
$595$	−22.4337	−	7.56705i	−0.919692	−	0.310219i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	15.3640	+	8.87044i	0.627758	+	0.362436i	0.779883	−	0.625925i	$-0.215278\pi$
$599$	15.3640	+	8.87044i	0.627758	+	0.362436i	−0.152125	+	0.988361i	$0.548612\pi$
$600$		0			0
$601$	−6.31369	+	3.64521i	−0.257541	+	0.148691i	−0.623212	−	0.782053i	$-0.714173\pi$
$601$	−6.31369	+	3.64521i	−0.257541	+	0.148691i	0.365671	+	0.930744i	$0.380839\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	40.6773	+	70.4551i	1.65377	+	2.86441i
$606$		0			0
$607$	−6.00042	−	3.46434i	−0.243550	−	0.140613i	0.373258	−	0.927728i	$-0.378241\pi$
$607$	−6.00042	−	3.46434i	−0.243550	−	0.140613i	−0.616807	+	0.787114i	$0.711574\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	45.0699i		−	1.82333i
$612$		0			0
$613$	−4.60656			−0.186057			−0.0930287	−	0.995663i	$-0.529655\pi$
$613$	−4.60656			−0.186057			−0.0930287	+	0.995663i	$0.529655\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	25.4618	+	14.7004i	1.02505	+	0.591816i	0.915564	−	0.402172i	$-0.131745\pi$
$617$	25.4618	+	14.7004i	1.02505	+	0.591816i	0.109491	+	0.993988i	$0.465078\pi$
$618$		0			0
$619$	−28.9537	+	16.7165i	−1.16375	+	0.671891i	−0.952200	−	0.305476i	$-0.901184\pi$
$619$	−28.9537	+	16.7165i	−1.16375	+	0.671891i	−0.211550	+	0.977367i	$0.567851\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	7.43169	+	36.9891i	0.297744	+	1.48194i
$624$		0			0
$625$	15.0602	−	26.0850i	0.602408	−	1.04340i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	4.10991			0.163873
$630$		0			0
$631$	26.3381			1.04850			0.524251	−	0.851564i	$-0.324345\pi$
$631$	26.3381			1.04850			0.524251	+	0.851564i	$0.324345\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	24.8247	−	42.9976i	0.985136	−	1.70631i
$636$		0			0
$637$	−41.2024	−	5.26300i	−1.63250	−	0.208528i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−11.6878	+	6.74797i	−0.461641	+	0.266529i	−0.712734	−	0.701434i	$-0.752543\pi$
$641$	−11.6878	+	6.74797i	−0.461641	+	0.266529i	0.251093	+	0.967963i	$0.419210\pi$
$642$		0			0
$643$	19.2270	+	11.1007i	0.758239	+	0.437769i	0.828663	−	0.559748i	$-0.189102\pi$
$643$	19.2270	+	11.1007i	0.758239	+	0.437769i	−0.0704244	+	0.997517i	$0.522435\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−11.6716			−0.458856			−0.229428	−	0.973326i	$-0.573686\pi$
$647$	−11.6716			−0.458856			−0.229428	+	0.973326i	$0.573686\pi$
$648$		0			0
$649$			71.9107i			2.82274i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−20.3964	−	11.7759i	−0.798174	−	0.460826i	0.0446586	−	0.999002i	$-0.485780\pi$
$653$	−20.3964	−	11.7759i	−0.798174	−	0.460826i	−0.842832	+	0.538177i	$0.819113\pi$
$654$		0			0
$655$	0.0245543	+	0.0425292i	0.000959414	+	0.00166175i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−9.47020	+	5.46763i	−0.368907	+	0.212988i	−0.672981	−	0.739660i	$-0.734986\pi$
$659$	−9.47020	+	5.46763i	−0.368907	+	0.212988i	0.304074	+	0.952648i	$0.401653\pi$
$660$		0			0
$661$	−9.96651	−	5.75417i	−0.387652	−	0.223811i	0.293490	−	0.955962i	$-0.405183\pi$
$661$	−9.96651	−	5.75417i	−0.387652	−	0.223811i	−0.681142	+	0.732151i	$0.738517\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.560731	−	1.66237i	0.0217442	−	0.0644641i
$666$		0			0
$667$	3.89764			0.150917
$668$		0			0
$669$		0			0
$670$		0			0
$671$	20.9786	−	36.3360i	0.809870	−	1.40274i
$672$		0			0
$673$	−14.5621	−	25.2224i	−0.561329	−	0.972251i	−0.997381	−	0.0723293i	$-0.976957\pi$
$673$	−14.5621	−	25.2224i	−0.561329	−	0.972251i	0.436051	−	0.899922i	$-0.356377\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	4.60972	+	7.98426i	0.177166	+	0.306860i	0.940909	−	0.338660i	$-0.109974\pi$
$677$	4.60972	+	7.98426i	0.177166	+	0.306860i	−0.763743	+	0.645521i	$0.776640\pi$
$678$		0			0
$679$	−20.1005	−	22.8313i	−0.771385	−	0.876185i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			17.2370i			0.659554i	0.944059	+	0.329777i	$0.106974\pi$
$683$			17.2370i			0.659554i	−0.944059	+	0.329777i	$0.893026\pi$
$684$		0			0
$685$			10.7528i			0.410843i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−10.5265	+	18.2324i	−0.401027	+	0.694599i
$690$		0			0
$691$	13.2875	−	7.67157i	0.505482	−	0.291840i	−0.225492	−	0.974245i	$-0.572399\pi$
$691$	13.2875	−	7.67157i	0.505482	−	0.291840i	0.730975	+	0.682405i	$0.239066\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−44.7563	+	25.8401i	−1.69770	+	0.980170i
$696$		0			0
$697$	−10.0790	+	17.4574i	−0.381770	+	0.661245i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	13.1791i		−	0.497767i	−0.968533	−	0.248883i	$-0.919936\pi$
$701$		−	13.1791i		−	0.497767i	0.968533	−	0.248883i	$-0.0800636\pi$
$702$		0			0
$703$			0.304551i			0.0114864i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.33666	−	3.81795i	0.163097	−	0.143589i
$708$		0			0
$709$	8.23396	+	14.2616i	0.309233	+	0.535607i	0.978195	−	0.207690i	$-0.0665944\pi$
$709$	8.23396	+	14.2616i	0.309233	+	0.535607i	−0.668962	+	0.743297i	$0.733261\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.27392	−	5.67059i	−0.122609	−	0.212365i
$714$		0			0
$715$	49.3992	−	85.5620i	1.84743	−	3.19984i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	13.3816			0.499048			0.249524	−	0.968369i	$-0.419726\pi$
$719$	13.3816			0.499048			0.249524	+	0.968369i	$0.419726\pi$
$720$		0			0
$721$	−9.52591	+	28.2410i	−0.354763	+	1.05175i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.44885	−	0.836492i	−0.0538088	−	0.0310665i
$726$		0			0
$727$	7.16036	−	4.13403i	0.265563	−	0.153323i	−0.361307	−	0.932447i	$-0.617669\pi$
$727$	7.16036	−	4.13403i	0.265563	−	0.153323i	0.626870	+	0.779124i	$0.284336\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	9.42988	+	16.3330i	0.348777	+	0.604099i
$732$		0			0
$733$	−12.1773	−	7.03056i	−0.449778	−	0.259679i	0.257958	−	0.966156i	$-0.416950\pi$
$733$	−12.1773	−	7.03056i	−0.449778	−	0.259679i	−0.707736	+	0.706477i	$0.750284\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	59.6082i		−	2.19570i
$738$		0			0
$739$	−25.8860			−0.952231			−0.476115	−	0.879383i	$-0.657956\pi$
$739$	−25.8860			−0.952231			−0.476115	+	0.879383i	$0.657956\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−36.5554	−	21.1053i	−1.34109	−	0.774277i	−0.354120	−	0.935200i	$-0.615220\pi$
$743$	−36.5554	−	21.1053i	−1.34109	−	0.774277i	−0.986967	+	0.160923i	$0.948553\pi$
$744$		0			0
$745$	−16.2472	+	9.38032i	−0.595251	+	0.343668i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	20.2994	−	4.07846i	0.741723	−	0.149024i
$750$		0			0
$751$	−21.3157	+	36.9198i	−0.777820	+	1.34722i	0.155375	+	0.987856i	$0.450341\pi$
$751$	−21.3157	+	36.9198i	−0.777820	+	1.34722i	−0.933196	+	0.359369i	$0.882992\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	35.2253			1.28198
$756$		0			0
$757$	51.5092			1.87213			0.936067	−	0.351823i	$-0.114438\pi$
$757$	51.5092			1.87213			0.936067	+	0.351823i	$0.114438\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−15.4845	+	26.8199i	−0.561313	+	0.972222i	0.436070	+	0.899913i	$0.356370\pi$
$761$	−15.4845	+	26.8199i	−0.561313	+	0.972222i	−0.997382	+	0.0723091i	$0.976963\pi$
$762$		0			0
$763$	9.14386	+	45.5110i	0.331030	+	1.64761i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	56.3119	−	32.5117i	2.03331	−	1.17393i
$768$		0			0
$769$	41.2004	+	23.7871i	1.48572	+	0.857783i	0.999868	−	0.0162553i	$-0.00517444\pi$
$769$	41.2004	+	23.7871i	1.48572	+	0.857783i	0.485856	+	0.874039i	$0.338508\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	27.9971			1.00699			0.503493	−	0.864000i	$-0.332048\pi$
$773$	27.9971			1.00699			0.503493	+	0.864000i	$0.332048\pi$
$774$		0			0
$775$			2.81053i			0.100957i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.29362	−	0.746872i	−0.0463488	−	0.0267595i
$780$		0			0
$781$	34.7442	+	60.1788i	1.24325	+	2.15337i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−4.73721	+	2.73503i	−0.169078	+	0.0976174i
$786$		0			0
$787$	−8.86189	−	5.11642i	−0.315892	−	0.182381i	0.333668	−	0.942691i	$-0.391714\pi$
$787$	−8.86189	−	5.11642i	−0.315892	−	0.182381i	−0.649560	+	0.760310i	$0.725047\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−3.72133	+	11.0324i	−0.132315	+	0.392269i
$792$		0			0
$793$	−37.9387			−1.34724
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−17.7557	+	30.7538i	−0.628940	+	1.08936i	0.358825	+	0.933405i	$0.383177\pi$
$797$	−17.7557	+	30.7538i	−0.628940	+	1.08936i	−0.987765	+	0.155951i	$0.950156\pi$
$798$		0			0
$799$	13.3943	+	23.1996i	0.473857	+	0.820744i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	8.95517	+	15.5108i	0.316021	+	0.547365i
$804$		0			0
$805$	14.8518	+	16.8696i	0.523457	+	0.594574i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			18.4932i			0.650188i	0.945682	+	0.325094i	$0.105396\pi$
$809$			18.4932i			0.650188i	−0.945682	+	0.325094i	$0.894604\pi$
$810$		0			0
$811$			35.6320i			1.25121i	0.780140	+	0.625605i	$0.215148\pi$
$811$			35.6320i			1.25121i	−0.780140	+	0.625605i	$0.784852\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−21.8026	+	37.7631i	−0.763710	+	1.32278i
$816$		0			0
$817$	−1.21031	+	0.698770i	−0.0423432	+	0.0244469i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−17.1389	+	9.89514i	−0.598151	+	0.345343i	−0.768314	−	0.640073i	$-0.778904\pi$
$821$	−17.1389	+	9.89514i	−0.598151	+	0.345343i	0.170163	+	0.985416i	$0.445571\pi$
$822$		0			0
$823$	3.47939	−	6.02647i	0.121284	−	0.210070i	−0.798990	−	0.601344i	$-0.794632\pi$
$823$	3.47939	−	6.02647i	0.121284	−	0.210070i	0.920274	+	0.391274i	$0.127966\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			4.92505i			0.171261i	0.996327	+	0.0856304i	$0.0272904\pi$
$827$			4.92505i			0.171261i	−0.996327	+	0.0856304i	$0.972710\pi$
$828$		0			0
$829$			42.9274i			1.49093i	0.666544	+	0.745466i	$0.267773\pi$
$829$			42.9274i			1.49093i	−0.666544	+	0.745466i	$0.732227\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	22.7730	−	9.53583i	0.789037	−	0.330397i
$834$		0			0
$835$	13.7032	+	23.7347i	0.474219	+	0.821372i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.84639	+	15.3224i	0.305411	+	0.528988i	0.977353	−	0.211616i	$-0.0678727\pi$
$839$	8.84639	+	15.3224i	0.305411	+	0.528988i	−0.671941	+	0.740604i	$0.734539\pi$
$840$		0			0
$841$	−13.8225	+	23.9412i	−0.476636	+	0.825558i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−56.3529			−1.93860
$846$		0			0
$847$	−80.3867	−	27.1150i	−2.76212	−	0.931683i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.37891	−	1.95082i	−0.115828	−	0.0668731i
$852$		0			0
$853$	23.5730	−	13.6099i	0.807123	−	0.465993i	−0.0388328	−	0.999246i	$-0.512364\pi$
$853$	23.5730	−	13.6099i	0.807123	−	0.465993i	0.845956	+	0.533253i	$0.179031\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−12.8303	−	22.2227i	−0.438274	−	0.759113i	0.559282	−	0.828977i	$-0.311077\pi$
$857$	−12.8303	−	22.2227i	−0.438274	−	0.759113i	−0.997557	+	0.0698641i	$0.977743\pi$
$858$		0			0
$859$	−16.8087	−	9.70452i	−0.573506	−	0.331114i	0.185042	−	0.982731i	$-0.440758\pi$
$859$	−16.8087	−	9.70452i	−0.573506	−	0.331114i	−0.758549	+	0.651617i	$0.774091\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	22.6418i		−	0.770737i	−0.922763	−	0.385368i	$-0.874074\pi$
$863$		−	22.6418i		−	0.770737i	0.922763	−	0.385368i	$-0.125926\pi$
$864$		0			0
$865$	48.4845			1.64852
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−7.41871	−	4.28320i	−0.251663	−	0.145298i
$870$		0			0
$871$	−46.6780	+	26.9496i	−1.58162	+	0.913152i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	4.71099	+	23.4476i	0.159261	+	0.792674i
$876$		0			0
$877$	−17.6395	+	30.5525i	−0.595644	+	1.03169i	0.397812	+	0.917467i	$0.369770\pi$
$877$	−17.6395	+	30.5525i	−0.595644	+	1.03169i	−0.993456	+	0.114219i	$0.963564\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.975907			0.0328791			0.0164396	−	0.999865i	$-0.494767\pi$
$881$	0.975907			0.0328791			0.0164396	+	0.999865i	$0.494767\pi$
$882$		0			0
$883$	−3.26917			−0.110016			−0.0550082	−	0.998486i	$-0.517519\pi$
$883$	−3.26917			−0.110016			−0.0550082	+	0.998486i	$0.517519\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.1653	+	21.0709i	−0.408470	+	0.707490i	−0.994718	−	0.102641i	$-0.967271\pi$
$887$	−12.1653	+	21.0709i	−0.408470	+	0.707490i	0.586249	+	0.810131i	$0.300604\pi$
$888$		0			0
$889$	10.1985	+	50.7600i	0.342046	+	1.70244i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.71913	+	0.992541i	−0.0575285	+	0.0332141i
$894$		0			0
$895$	32.7882	+	18.9303i	1.09599	+	0.632770i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.27648			−0.0759249
$900$		0			0
$901$		−	12.5135i		−	0.416884i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	40.6882	+	23.4914i	1.35252	+	0.780880i
$906$		0			0
$907$	22.0508	+	38.1932i	0.732186	+	1.26818i	0.955947	+	0.293539i	$0.0948330\pi$
$907$	22.0508	+	38.1932i	0.732186	+	1.26818i	−0.223761	+	0.974644i	$0.571834\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−20.1215	+	11.6171i	−0.666654	+	0.384893i	−0.794807	−	0.606862i	$-0.792428\pi$
$911$	−20.1215	+	11.6171i	−0.666654	+	0.384893i	0.128154	+	0.991754i	$0.459095\pi$
$912$		0			0
$913$	51.5173	+	29.7435i	1.70497	+	0.984368i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.0485243	−	0.0163676i	−0.00160241	−	0.000540506i
$918$		0			0
$919$	−2.91416			−0.0961291			−0.0480646	−	0.998844i	$-0.515305\pi$
$919$	−2.91416			−0.0961291			−0.0480646	+	0.998844i	$0.515305\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	31.4166	−	54.4151i	1.03409	−	1.79109i
$924$		0			0
$925$	0.837349	+	1.45033i	0.0275319	+	0.0476866i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−8.34767	−	14.4586i	−0.273878	−	0.474371i	0.695973	−	0.718068i	$-0.254973\pi$
$929$	−8.34767	−	14.4586i	−0.273878	−	0.474371i	−0.969852	+	0.243697i	$0.921640\pi$
$930$		0			0
$931$	0.706621	+	1.68752i	0.0231586	+	0.0553061i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			58.7238i			1.92047i
$936$		0			0
$937$		−	40.4272i		−	1.32070i	−0.750959	−	0.660349i	$-0.770408\pi$
$937$		−	40.4272i		−	1.32070i	0.750959	−	0.660349i	$-0.229592\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−27.9889	+	48.4782i	−0.912411	+	1.58034i	−0.101764	+	0.994809i	$0.532449\pi$
$941$	−27.9889	+	48.4782i	−0.912411	+	1.58034i	−0.810648	+	0.585534i	$0.800885\pi$
$942$		0			0
$943$	16.5727	−	9.56824i	0.539681	−	0.311585i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	17.8498	−	10.3056i	0.580041	−	0.334887i	−0.181109	−	0.983463i	$-0.557969\pi$
$947$	17.8498	−	10.3056i	0.580041	−	0.334887i	0.761150	+	0.648576i	$0.224635\pi$
$948$		0			0
$949$	8.09748	−	14.0253i	0.262855	−	0.455279i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	17.3803i		−	0.563005i	−0.959561	−	0.281502i	$-0.909167\pi$
$953$		−	17.3803i		−	0.563005i	0.959561	−	0.281502i	$-0.0908327\pi$
$954$		0			0
$955$		−	14.8883i		−	0.481773i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−7.40949	−	8.41614i	−0.239265	−	0.271771i
$960$		0			0
$961$	−13.5878	−	23.5348i	−0.438317	−	0.759187i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−20.7940	−	36.0162i	−0.669381	−	1.15940i
$966$		0			0
$967$	−1.32992	+	2.30349i	−0.0427674	+	0.0740753i	−0.886617	−	0.462505i	$-0.846951\pi$
$967$	−1.32992	+	2.30349i	−0.0427674	+	0.0740753i	0.843849	+	0.536580i	$0.180284\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−34.9474			−1.12151			−0.560757	−	0.827980i	$-0.689490\pi$
$971$	−34.9474			−1.12151			−0.560757	+	0.827980i	$0.689490\pi$
$972$		0			0
$973$	17.2247	−	51.0654i	0.552199	−	1.63708i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−13.6938	−	7.90614i	−0.438105	−	0.252940i	0.264689	−	0.964334i	$-0.414731\pi$
$977$	−13.6938	−	7.90614i	−0.438105	−	0.252940i	−0.702793	+	0.711394i	$0.748064\pi$
$978$		0			0
$979$	81.0423	−	46.7898i	2.59012	−	1.49541i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−30.2832	−	52.4521i	−0.965885	−	1.67296i	−0.707219	−	0.706994i	$-0.750051\pi$
$983$	−30.2832	−	52.4521i	−0.965885	−	1.67296i	−0.258666	−	0.965967i	$-0.583283\pi$
$984$		0			0
$985$	15.1632	+	8.75451i	0.483141	+	0.278942i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	17.9040i		−	0.569315i
$990$		0			0
$991$	−8.00131			−0.254170			−0.127085	−	0.991892i	$-0.540562\pi$
$991$	−8.00131			−0.254170			−0.127085	+	0.991892i	$0.540562\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−22.7534	−	13.1367i	−0.721333	−	0.416462i
$996$		0			0
$997$	−37.8349	+	21.8440i	−1.19824	+	0.691805i	−0.960163	−	0.279440i	$-0.909851\pi$
$997$	−37.8349	+	21.8440i	−1.19824	+	0.691805i	−0.238079	+	0.971246i	$0.576518\pi$
$998$		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.881.5		48
3.2	odd	2		1008.2.cc.d.545.12		48
4.3	odd	2		1512.2.bu.a.881.5		48
7.6	odd	2	inner	3024.2.cc.d.881.20		48
9.2	odd	6	inner	3024.2.cc.d.2897.20		48
9.7	even	3		1008.2.cc.d.209.13		48
12.11	even	2		504.2.bu.a.41.13	yes	48
21.20	even	2		1008.2.cc.d.545.13		48
28.27	even	2		1512.2.bu.a.881.20		48
36.7	odd	6		504.2.bu.a.209.12	yes	48
36.11	even	6		1512.2.bu.a.1385.20		48
36.23	even	6		4536.2.k.a.3401.10		48
36.31	odd	6		4536.2.k.a.3401.39		48
63.20	even	6	inner	3024.2.cc.d.2897.5		48
63.34	odd	6		1008.2.cc.d.209.12		48
84.83	odd	2		504.2.bu.a.41.12	✓	48
252.83	odd	6		1512.2.bu.a.1385.5		48
252.139	even	6		4536.2.k.a.3401.9		48
252.167	odd	6		4536.2.k.a.3401.40		48
252.223	even	6		504.2.bu.a.209.13	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bu.a.41.12	✓	48	84.83	odd	2
504.2.bu.a.41.13	yes	48	12.11	even	2
504.2.bu.a.209.12	yes	48	36.7	odd	6
504.2.bu.a.209.13	yes	48	252.223	even	6
1008.2.cc.d.209.12		48	63.34	odd	6
1008.2.cc.d.209.13		48	9.7	even	3
1008.2.cc.d.545.12		48	3.2	odd	2
1008.2.cc.d.545.13		48	21.20	even	2
1512.2.bu.a.881.5		48	4.3	odd	2
1512.2.bu.a.881.20		48	28.27	even	2
1512.2.bu.a.1385.5		48	252.83	odd	6
1512.2.bu.a.1385.20		48	36.11	even	6
3024.2.cc.d.881.5		48	1.1	even	1	trivial
3024.2.cc.d.881.20		48	7.6	odd	2	inner
3024.2.cc.d.2897.5		48	63.20	even	6	inner
3024.2.cc.d.2897.20		48	9.2	odd	6	inner
4536.2.k.a.3401.9		48	252.139	even	6
4536.2.k.a.3401.10		48	36.23	even	6
4536.2.k.a.3401.39		48	36.31	odd	6
4536.2.k.a.3401.40		48	252.167	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.26858 + 2.19724i) q^{5} +(-0.521158 - 2.59391i) q^{7} +O(q^{10})\)	\(q+(-1.26858 + 2.19724i) q^{5} +(-0.521158 - 2.59391i) q^{7} +(-5.68321 + 3.28120i) q^{11} +(5.13890 + 2.96694i) q^{13} -3.52698 q^{17} -0.261355i q^{19} +(2.89967 + 1.67412i) q^{23} +(-0.718584 - 1.24462i) q^{25} +(1.00813 - 0.582041i) q^{29} +(-1.69360 - 0.977800i) q^{31} +(6.36059 + 2.14547i) q^{35} -1.16528 q^{37} +(2.85769 - 4.94966i) q^{41} +(-2.67364 - 4.63088i) q^{43} +(-3.79767 - 6.57775i) q^{47} +(-6.45679 + 2.70368i) q^{49} +3.54792i q^{53} -16.6499i q^{55} +(5.47899 - 9.48989i) q^{59} +(-5.53699 + 3.19678i) q^{61} +(-13.0382 + 7.52760i) q^{65} +(-4.54164 + 7.86635i) q^{67} -10.5889i q^{71} -2.72923i q^{73} +(11.4730 + 13.0317i) q^{77} +(0.652687 + 1.13049i) q^{79} +(-4.53241 - 7.85037i) q^{83} +(4.47426 - 7.74964i) q^{85} -14.2599 q^{89} +(5.01782 - 14.8761i) q^{91} +(0.574261 + 0.331550i) q^{95} +(9.95686 - 5.74859i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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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