LMFDB - Embedded newform 3024.2.df.e.1601.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(17,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.17"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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			1601.3
Character	$\chi$	$=$	3024.1601
Dual form			3024.2.df.e.17.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-3.53401 q^{5} +(-1.30083 + 2.30388i) q^{7} -1.81827i q^{11} +(2.78280 - 1.60665i) q^{13} +(2.93434 + 5.08242i) q^{17} +(2.09143 + 1.20749i) q^{19} +3.84871i q^{23} +7.48923 q^{25} +(-5.79110 - 3.34349i) q^{29} +(4.21959 + 2.43618i) q^{31} +(4.59714 - 8.14192i) q^{35} +(-0.905385 + 1.56817i) q^{37} +(-5.03152 - 8.71485i) q^{41} +(2.36232 - 4.09166i) q^{43} +(3.96076 + 6.86023i) q^{47} +(-3.61569 - 5.99390i) q^{49} +(-2.26517 + 1.30780i) q^{53} +6.42580i q^{55} +(4.40604 - 7.63149i) q^{59} +(-8.98447 + 5.18718i) q^{61} +(-9.83443 + 5.67791i) q^{65} +(-3.92384 + 6.79630i) q^{67} +7.62952i q^{71} +(-11.7672 + 6.79382i) q^{73} +(4.18907 + 2.36526i) q^{77} +(-0.921268 - 1.59568i) q^{79} +(-5.61748 + 9.72975i) q^{83} +(-10.3700 - 17.9613i) q^{85} +(6.89792 - 11.9475i) q^{89} +(0.0815748 + 8.50119i) q^{91} +(-7.39114 - 4.26728i) q^{95} +(-13.7982 - 7.96638i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{25} - 18 q^{29} - 18 q^{31} + 6 q^{41} + 6 q^{43} + 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} - 6 q^{79} + 18 q^{89} - 6 q^{91} - 54 q^{95}+O(q^{100}) $ 48 * q + 48 * q^25 - 18 * q^29 - 18 * q^31 + 6 * q^41 + 6 * q^43 + 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 - 6 * q^79 + 18 * q^89 - 6 * q^91 - 54 * q^95

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−3.53401			−1.58046			−0.790229	−	0.612812i	$-0.790038\pi$
$5$	−3.53401			−1.58046			−0.790229	+	0.612812i	$0.790038\pi$
$6$		0			0
$7$	−1.30083	+	2.30388i	−0.491667	+	0.870783i
$7$	−1.30083	+	2.30388i	−0.491667	+	0.870783i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	1.81827i		−	0.548230i	−0.961697	−	0.274115i	$-0.911615\pi$
$11$		−	1.81827i		−	0.548230i	0.961697	−	0.274115i	$-0.0883849\pi$
$12$		0			0
$13$	2.78280	−	1.60665i	0.771809	−	0.445604i	−0.0617107	−	0.998094i	$-0.519656\pi$
$13$	2.78280	−	1.60665i	0.771809	−	0.445604i	0.833519	+	0.552490i	$0.186322\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.93434	+	5.08242i	0.711682	+	1.23267i	0.964225	+	0.265083i	$0.0853995\pi$
$17$	2.93434	+	5.08242i	0.711682	+	1.23267i	−0.252544	+	0.967585i	$0.581267\pi$
$18$		0			0
$19$	2.09143	+	1.20749i	0.479807	+	0.277017i	0.720336	−	0.693625i	$-0.243988\pi$
$19$	2.09143	+	1.20749i	0.479807	+	0.277017i	−0.240529	+	0.970642i	$0.577321\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			3.84871i			0.802512i	0.915966	+	0.401256i	$0.131426\pi$
$23$			3.84871i			0.802512i	−0.915966	+	0.401256i	$0.868574\pi$
$24$		0			0
$25$	7.48923			1.49785
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.79110	−	3.34349i	−1.07538	−	0.620871i	−0.145734	−	0.989324i	$-0.546554\pi$
$29$	−5.79110	−	3.34349i	−1.07538	−	0.620871i	−0.929647	+	0.368452i	$0.879888\pi$
$30$		0			0
$31$	4.21959	+	2.43618i	0.757861	+	0.437551i	0.828527	−	0.559949i	$-0.189179\pi$
$31$	4.21959	+	2.43618i	0.757861	+	0.437551i	−0.0706663	+	0.997500i	$0.522513\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.59714	−	8.14192i	0.777059	−	1.37624i
$36$		0			0
$37$	−0.905385	+	1.56817i	−0.148844	+	0.257806i	−0.930801	−	0.365527i	$-0.880889\pi$
$37$	−0.905385	+	1.56817i	−0.148844	+	0.257806i	0.781956	+	0.623333i	$0.214222\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.03152	−	8.71485i	−0.785792	−	1.36103i	−0.928525	−	0.371270i	$-0.878922\pi$
$41$	−5.03152	−	8.71485i	−0.785792	−	1.36103i	0.142733	−	0.989761i	$-0.454411\pi$
$42$		0			0
$43$	2.36232	−	4.09166i	0.360251	−	0.623973i	−0.627751	−	0.778414i	$-0.716024\pi$
$43$	2.36232	−	4.09166i	0.360251	−	0.623973i	0.988002	+	0.154441i	$0.0493577\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.96076	+	6.86023i	0.577736	+	1.00067i	0.995738	+	0.0922218i	$0.0293969\pi$
$47$	3.96076	+	6.86023i	0.577736	+	1.00067i	−0.418003	+	0.908446i	$0.637270\pi$
$48$		0			0
$49$	−3.61569	−	5.99390i	−0.516527	−	0.856271i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.26517	+	1.30780i	−0.311146	+	0.179640i	−0.647439	−	0.762117i	$-0.724160\pi$
$53$	−2.26517	+	1.30780i	−0.311146	+	0.179640i	0.336293	+	0.941757i	$0.390827\pi$
$54$		0			0
$55$			6.42580i			0.866454i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.40604	−	7.63149i	0.573618	−	0.993535i	−0.422573	−	0.906329i	$-0.638873\pi$
$59$	4.40604	−	7.63149i	0.573618	−	0.993535i	0.996190	−	0.0872059i	$-0.0277938\pi$
$60$		0			0
$61$	−8.98447	+	5.18718i	−1.15034	+	0.664151i	−0.948971	−	0.315364i	$-0.897873\pi$
$61$	−8.98447	+	5.18718i	−1.15034	+	0.664151i	−0.201372	+	0.979515i	$0.564540\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.83443	+	5.67791i	−1.21981	+	0.704258i
$66$		0			0
$67$	−3.92384	+	6.79630i	−0.479374	+	0.830300i	−0.999720	−	0.0236554i	$-0.992470\pi$
$67$	−3.92384	+	6.79630i	−0.479374	+	0.830300i	0.520346	+	0.853955i	$0.325803\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			7.62952i			0.905458i	0.891648	+	0.452729i	$0.149549\pi$
$71$			7.62952i			0.905458i	−0.891648	+	0.452729i	$0.850451\pi$
$72$		0			0
$73$	−11.7672	+	6.79382i	−1.37725	+	0.795156i	−0.991828	−	0.127584i	$-0.959278\pi$
$73$	−11.7672	+	6.79382i	−1.37725	+	0.795156i	−0.385423	+	0.922740i	$0.625945\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.18907	+	2.36526i	0.477389	+	0.269547i
$78$		0			0
$79$	−0.921268	−	1.59568i	−0.103651	−	0.179528i	0.809535	−	0.587071i	$-0.199719\pi$
$79$	−0.921268	−	1.59568i	−0.103651	−	0.179528i	−0.913186	+	0.407543i	$0.866386\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−5.61748	+	9.72975i	−0.616598	+	1.06798i	0.373504	+	0.927629i	$0.378156\pi$
$83$	−5.61748	+	9.72975i	−0.616598	+	1.06798i	−0.990102	+	0.140351i	$0.955177\pi$
$84$		0			0
$85$	−10.3700	−	17.9613i	−1.12478	−	1.94818i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.89792	−	11.9475i	0.731178	−	1.26644i	−0.225202	−	0.974312i	$-0.572304\pi$
$89$	6.89792	−	11.9475i	0.731178	−	1.26644i	0.956380	−	0.292125i	$-0.0943624\pi$
$90$		0			0
$91$	0.0815748	+	8.50119i	0.00855137	+	0.891167i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−7.39114	−	4.26728i	−0.758315	−	0.437813i
$96$		0			0
$97$	−13.7982	−	7.96638i	−1.40099	−	0.808863i	−0.406497	−	0.913652i	$-0.633250\pi$
$97$	−13.7982	−	7.96638i	−1.40099	−	0.808863i	−0.994494	+	0.104789i	$0.966583\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−11.1250			−1.10698			−0.553489	−	0.832856i	$-0.686704\pi$
$101$	−11.1250			−1.10698			−0.553489	+	0.832856i	$0.686704\pi$
$102$		0			0
$103$		−	0.603028i		−	0.0594181i	−0.999559	−	0.0297091i	$-0.990542\pi$
$103$		−	0.603028i		−	0.0594181i	0.999559	−	0.0297091i	$-0.00945808\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−11.3342	−	6.54381i	−1.09572	−	0.632614i	−0.160627	−	0.987015i	$-0.551351\pi$
$107$	−11.3342	−	6.54381i	−1.09572	−	0.632614i	−0.935094	+	0.354401i	$0.884685\pi$
$108$		0			0
$109$	−1.37061	−	2.37396i	−0.131280	−	0.227384i	0.792890	−	0.609365i	$-0.208575\pi$
$109$	−1.37061	−	2.37396i	−0.131280	−	0.227384i	−0.924170	+	0.381981i	$0.875242\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.65125	+	3.84010i	−0.625697	+	0.361246i	−0.779084	−	0.626920i	$-0.784315\pi$
$113$	−6.65125	+	3.84010i	−0.625697	+	0.361246i	0.153387	+	0.988166i	$0.450982\pi$
$114$		0			0
$115$		−	13.6014i		−	1.26834i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−15.5263	+	0.148986i	−1.42330	+	0.0136575i
$120$		0			0
$121$	7.69388			0.699444
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−8.79697			−0.786825
$126$		0			0
$127$	−17.9246			−1.59055			−0.795277	−	0.606246i	$-0.792675\pi$
$127$	−17.9246			−1.59055			−0.795277	+	0.606246i	$0.792675\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	16.9707			1.48273			0.741367	−	0.671100i	$-0.234178\pi$
$131$	16.9707			1.48273			0.741367	+	0.671100i	$0.234178\pi$
$132$		0			0
$133$	−5.50250	+	3.24766i	−0.477127	+	0.281608i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	5.56139i		−	0.475142i	−0.971370	−	0.237571i	$-0.923649\pi$
$137$		−	5.56139i		−	0.475142i	0.971370	−	0.237571i	$-0.0763512\pi$
$138$		0			0
$139$	12.4503	−	7.18817i	1.05602	−	0.609693i	0.131690	−	0.991291i	$-0.457960\pi$
$139$	12.4503	−	7.18817i	1.05602	−	0.609693i	0.924328	+	0.381598i	$0.124626\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.92132	−	5.05988i	−0.244293	−	0.423129i
$144$		0			0
$145$	20.4658	+	11.8159i	1.69959	+	0.981261i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	6.42112i		−	0.526039i	−0.964791	−	0.263019i	$-0.915282\pi$
$149$		−	6.42112i		−	0.526039i	0.964791	−	0.263019i	$-0.0847184\pi$
$150$		0			0
$151$	−15.9925			−1.30145			−0.650727	−	0.759312i	$-0.725536\pi$
$151$	−15.9925			−1.30145			−0.650727	+	0.759312i	$0.725536\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−14.9121	−	8.60949i	−1.19777	−	0.691531i
$156$		0			0
$157$	−12.0612	−	6.96356i	−0.962592	−	0.555753i	−0.0656219	−	0.997845i	$-0.520903\pi$
$157$	−12.0612	−	6.96356i	−0.962592	−	0.555753i	−0.896970	+	0.442092i	$0.854236\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−8.86696	−	5.00652i	−0.698814	−	0.394569i
$162$		0			0
$163$	−7.79498	+	13.5013i	−0.610550	+	1.05750i	0.380598	+	0.924740i	$0.375718\pi$
$163$	−7.79498	+	13.5013i	−0.610550	+	1.05750i	−0.991148	+	0.132762i	$0.957615\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.58728	−	11.4095i	−0.509739	−	0.882893i	−0.999936	−	0.0112821i	$-0.996409\pi$
$167$	−6.58728	−	11.4095i	−0.509739	−	0.882893i	0.490198	−	0.871611i	$-0.336925\pi$
$168$		0			0
$169$	−1.33736	+	2.31638i	−0.102874	+	0.178183i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.60402	+	9.70645i	0.426066	+	0.737968i	0.996519	−	0.0833623i	$-0.0265659\pi$
$173$	5.60402	+	9.70645i	0.426066	+	0.737968i	−0.570453	+	0.821330i	$0.693233\pi$
$174$		0			0
$175$	−9.74221	+	17.2543i	−0.736442	+	1.30430i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.22783	−	5.32769i	0.689721	−	0.398210i	−0.113787	−	0.993505i	$-0.536298\pi$
$179$	9.22783	−	5.32769i	0.689721	−	0.398210i	0.803507	+	0.595295i	$0.202965\pi$
$180$		0			0
$181$		−	11.8897i		−	0.883754i	−0.897076	−	0.441877i	$-0.854313\pi$
$181$		−	11.8897i		−	0.883754i	0.897076	−	0.441877i	$-0.145687\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.19964	−	5.54194i	0.235242	−	0.407451i
$186$		0			0
$187$	9.24123	−	5.33543i	0.675786	−	0.390165i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.193961	−	0.111983i	0.0140345	−	0.00810283i	−0.492966	−	0.870048i	$-0.664087\pi$
$191$	0.193961	−	0.111983i	0.0140345	−	0.00810283i	0.507001	+	0.861946i	$0.330754\pi$
$192$		0			0
$193$	−13.0373	+	22.5812i	−0.938442	+	1.62543i	−0.170064	+	0.985433i	$0.554398\pi$
$193$	−13.0373	+	22.5812i	−0.938442	+	1.62543i	−0.768378	+	0.639996i	$0.778936\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			1.56289i			0.111352i	0.998449	+	0.0556758i	$0.0177313\pi$
$197$			1.56289i			0.111352i	−0.998449	+	0.0556758i	$0.982269\pi$
$198$		0			0
$199$	−13.4725	+	7.77832i	−0.955037	+	0.551391i	−0.894642	−	0.446784i	$-0.852569\pi$
$199$	−13.4725	+	7.77832i	−0.955037	+	0.551391i	−0.0603949	+	0.998175i	$0.519236\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	15.2362	−	8.99266i	1.06937	−	0.631161i
$204$		0			0
$205$	17.7815	+	30.7984i	1.24191	+	2.15105i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.19554	−	3.80279i	0.151869	−	0.263045i
$210$		0			0
$211$	−6.98216	−	12.0935i	−0.480672	−	0.832548i	0.519082	−	0.854724i	$-0.326274\pi$
$211$	−6.98216	−	12.0935i	−0.480672	−	0.832548i	−0.999754	+	0.0221763i	$0.992941\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−8.34848	+	14.4600i	−0.569361	+	0.986163i
$216$		0			0
$217$	−11.1016	+	6.55236i	−0.753628	+	0.444803i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	16.3313	+	9.42890i	1.09856	+	0.634256i
$222$		0			0
$223$	21.4242	+	12.3693i	1.43467	+	0.828307i	0.997472	−	0.0710586i	$-0.0226377\pi$
$223$	21.4242	+	12.3693i	1.43467	+	0.828307i	0.437198	+	0.899366i	$0.355971\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.24153			−0.414265			−0.207132	−	0.978313i	$-0.566413\pi$
$227$	−6.24153			−0.414265			−0.207132	+	0.978313i	$0.566413\pi$
$228$		0			0
$229$		−	15.8574i		−	1.04789i	−0.851753	−	0.523943i	$-0.824460\pi$
$229$		−	15.8574i		−	1.04789i	0.851753	−	0.523943i	$-0.175540\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.94574	−	1.70072i	−0.192982	−	0.111418i	0.400396	−	0.916342i	$-0.368873\pi$
$233$	−2.94574	−	1.70072i	−0.192982	−	0.111418i	−0.593378	+	0.804924i	$0.702206\pi$
$234$		0			0
$235$	−13.9974	−	24.2441i	−0.913087	−	1.58151i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−16.3482	+	9.43864i	−1.05748	+	0.610535i	−0.924733	−	0.380615i	$-0.875712\pi$
$239$	−16.3482	+	9.43864i	−1.05748	+	0.610535i	−0.132744	+	0.991150i	$0.542379\pi$
$240$		0			0
$241$			11.1845i			0.720460i	0.932864	+	0.360230i	$0.117302\pi$
$241$			11.1845i			0.720460i	−0.932864	+	0.360230i	$0.882698\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	12.7779	+	21.1825i	0.816348	+	1.35330i
$246$		0			0
$247$	7.76003			0.493759
$248$		0			0
$249$		0			0
$250$		0			0
$251$	15.4537			0.975431			0.487716	−	0.873003i	$-0.337830\pi$
$251$	15.4537			0.975431			0.487716	+	0.873003i	$0.337830\pi$
$252$		0			0
$253$	6.99801			0.439961
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.6448			0.664002			0.332001	−	0.943279i	$-0.392276\pi$
$257$	10.6448			0.664002			0.332001	+	0.943279i	$0.392276\pi$
$258$		0			0
$259$	−2.43512	−	4.12582i	−0.151311	−	0.256366i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			11.0875i			0.683685i	0.939757	+	0.341842i	$0.111051\pi$
$263$			11.0875i			0.683685i	−0.939757	+	0.341842i	$0.888949\pi$
$264$		0			0
$265$	8.00515	−	4.62178i	0.491753	−	0.283913i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.14147	+	5.44119i	0.191539	+	0.331755i	0.945760	−	0.324865i	$-0.105319\pi$
$269$	3.14147	+	5.44119i	0.191539	+	0.331755i	−0.754221	+	0.656620i	$0.771986\pi$
$270$		0			0
$271$	−0.954533	−	0.551100i	−0.0579838	−	0.0334769i	0.470728	−	0.882278i	$-0.343991\pi$
$271$	−0.954533	−	0.551100i	−0.0579838	−	0.0334769i	−0.528712	+	0.848802i	$0.677325\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	13.6175i		−	0.821164i
$276$		0			0
$277$	−15.3616			−0.922990			−0.461495	−	0.887143i	$-0.652687\pi$
$277$	−15.3616			−0.922990			−0.461495	+	0.887143i	$0.652687\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−18.9133	−	10.9196i	−1.12827	−	0.651407i	−0.184771	−	0.982782i	$-0.559154\pi$
$281$	−18.9133	−	10.9196i	−1.12827	−	0.651407i	−0.943499	+	0.331374i	$0.892488\pi$
$282$		0			0
$283$	9.59426	+	5.53925i	0.570320	+	0.329274i	0.757277	−	0.653094i	$-0.226529\pi$
$283$	9.59426	+	5.53925i	0.570320	+	0.329274i	−0.186957	+	0.982368i	$0.559863\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	26.6231	−	0.255467i	1.57151	−	0.0150797i
$288$		0			0
$289$	−8.72069	+	15.1047i	−0.512982	+	0.888511i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−12.6330	−	21.8810i	−0.738027	−	1.27830i	−0.953382	−	0.301765i	$-0.902424\pi$
$293$	−12.6330	−	21.8810i	−0.738027	−	1.27830i	0.215355	−	0.976536i	$-0.430909\pi$
$294$		0			0
$295$	−15.5710	+	26.9698i	−0.906578	+	1.57024i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.18353	+	10.7102i	0.357603	+	0.619386i
$300$		0			0
$301$	6.35371	+	10.7651i	0.366222	+	0.620488i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	31.7512	−	18.3316i	1.81807	−	1.04966i
$306$		0			0
$307$		−	12.2163i		−	0.697219i	−0.937268	−	0.348610i	$-0.886654\pi$
$307$		−	12.2163i		−	0.697219i	0.937268	−	0.348610i	$-0.113346\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.74484	+	8.21830i	−0.269055	+	0.466017i	−0.968618	−	0.248554i	$-0.920045\pi$
$311$	−4.74484	+	8.21830i	−0.269055	+	0.466017i	0.699563	+	0.714571i	$0.253378\pi$
$312$		0			0
$313$	11.7358	−	6.77564i	0.663344	−	0.382982i	−0.130206	−	0.991487i	$-0.541564\pi$
$313$	11.7358	−	6.77564i	0.663344	−	0.382982i	0.793550	+	0.608505i	$0.208231\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.7559	+	7.94197i	−0.772608	+	0.446065i	−0.833804	−	0.552060i	$-0.813842\pi$
$317$	−13.7559	+	7.94197i	−0.772608	+	0.446065i	0.0611961	+	0.998126i	$0.480508\pi$
$318$		0			0
$319$	−6.07939	+	10.5298i	−0.340380	+	0.589556i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			14.1727i			0.788591i
$324$		0			0
$325$	20.8410	−	12.0326i	1.15605	−	0.667446i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−20.9574	+	0.201101i	−1.15542	+	0.0110870i
$330$		0			0
$331$	5.48697	+	9.50372i	0.301591	+	0.522371i	0.976497	−	0.215533i	$-0.0691489\pi$
$331$	5.48697	+	9.50372i	0.301591	+	0.522371i	−0.674905	+	0.737904i	$0.735816\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	13.8669	−	24.0182i	0.757630	−	1.31225i
$336$		0			0
$337$	2.80751	+	4.86275i	0.152935	+	0.264891i	0.932305	−	0.361673i	$-0.117794\pi$
$337$	2.80751	+	4.86275i	0.152935	+	0.264891i	−0.779370	+	0.626564i	$0.784461\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	4.42964	−	7.67237i	0.239879	−	0.415482i
$342$		0			0
$343$	18.5126	−	0.533054i	0.999586	−	0.0287822i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.18003	−	2.41334i	−0.224396	−	0.129555i	0.383588	−	0.923504i	$-0.374688\pi$
$347$	−4.18003	−	2.41334i	−0.224396	−	0.129555i	−0.607984	+	0.793949i	$0.708022\pi$
$348$		0			0
$349$	22.7167	+	13.1155i	1.21600	+	0.702056i	0.964059	−	0.265688i	$-0.0855991\pi$
$349$	22.7167	+	13.1155i	1.21600	+	0.702056i	0.251937	+	0.967744i	$0.418932\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	34.9914			1.86240			0.931201	−	0.364505i	$-0.118762\pi$
$353$	34.9914			1.86240			0.931201	+	0.364505i	$0.118762\pi$
$354$		0			0
$355$		−	26.9628i		−	1.43104i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−21.6396	−	12.4936i	−1.14209	−	0.659388i	−0.195146	−	0.980774i	$-0.562518\pi$
$359$	−21.6396	−	12.4936i	−1.14209	−	0.659388i	−0.946948	+	0.321386i	$0.895851\pi$
$360$		0			0
$361$	−6.58394	−	11.4037i	−0.346523	−	0.600196i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	41.5855	−	24.0094i	2.17669	−	1.25671i
$366$		0			0
$367$		−	24.6067i		−	1.28446i	−0.766512	−	0.642230i	$-0.778009\pi$
$367$		−	24.6067i		−	1.28446i	0.766512	−	0.642230i	$-0.221991\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.0664013	−	6.91990i	−0.00344738	−	0.359264i
$372$		0			0
$373$	−10.4374			−0.540428			−0.270214	−	0.962800i	$-0.587094\pi$
$373$	−10.4374			−0.540428			−0.270214	+	0.962800i	$0.587094\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−21.4873			−1.10665
$378$		0			0
$379$	−31.8728			−1.63719			−0.818597	−	0.574368i	$-0.805248\pi$
$379$	−31.8728			−1.63719			−0.818597	+	0.574368i	$0.805248\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−24.7719			−1.26579			−0.632893	−	0.774239i	$-0.718133\pi$
$383$	−24.7719			−1.26579			−0.632893	+	0.774239i	$0.718133\pi$
$384$		0			0
$385$	−14.8042	−	8.35886i	−0.754494	−	0.426007i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	23.0227i		−	1.16729i	−0.812007	−	0.583647i	$-0.801625\pi$
$389$		−	23.0227i		−	1.16729i	0.812007	−	0.583647i	$-0.198375\pi$
$390$		0			0
$391$	−19.5608	+	11.2934i	−0.989232	+	0.571133i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	3.25577	+	5.63916i	0.163816	+	0.283737i
$396$		0			0
$397$	23.9247	+	13.8129i	1.20075	+	0.693251i	0.960721	−	0.277515i	$-0.0895109\pi$
$397$	23.9247	+	13.8129i	1.20075	+	0.693251i	0.240025	+	0.970767i	$0.422844\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			5.32384i			0.265860i	0.991125	+	0.132930i	$0.0424385\pi$
$401$			5.32384i			0.265860i	−0.991125	+	0.132930i	$0.957561\pi$
$402$		0			0
$403$	15.6563			0.779898
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.85137	+	1.64624i	0.141337	+	0.0816009i
$408$		0			0
$409$	6.11912	+	3.53288i	0.302571	+	0.174690i	0.643597	−	0.765364i	$-0.277441\pi$
$409$	6.11912	+	3.53288i	0.302571	+	0.174690i	−0.341026	+	0.940054i	$0.610774\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	11.8505	+	20.0782i	0.583124	+	0.987985i
$414$		0			0
$415$	19.8522	−	34.3851i	0.974507	−	1.68790i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.94504	−	3.36891i	−0.0950215	−	0.164582i	0.814596	−	0.580029i	$-0.196959\pi$
$419$	−1.94504	−	3.36891i	−0.0950215	−	0.164582i	−0.909618	+	0.415447i	$0.863625\pi$
$420$		0			0
$421$	−2.18533	+	3.78510i	−0.106506	+	0.184475i	−0.914353	−	0.404919i	$-0.867300\pi$
$421$	−2.18533	+	3.78510i	−0.106506	+	0.184475i	0.807846	+	0.589393i	$0.200633\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	21.9759	+	38.0634i	1.06599	+	1.84635i
$426$		0			0
$427$	−0.263371	−	27.4467i	−0.0127454	−	1.32824i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	10.7505	−	6.20681i	0.517834	−	0.298971i	−0.218214	−	0.975901i	$-0.570023\pi$
$431$	10.7505	−	6.20681i	0.517834	−	0.298971i	0.736048	+	0.676929i	$0.236690\pi$
$432$		0			0
$433$		−	25.2979i		−	1.21574i	−0.794036	−	0.607870i	$-0.792024\pi$
$433$		−	25.2979i		−	1.21574i	0.794036	−	0.607870i	$-0.207976\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.64728	+	8.04932i	−0.222309	+	0.385051i
$438$		0			0
$439$	23.2408	−	13.4181i	1.10922	−	0.640410i	0.170595	−	0.985341i	$-0.445431\pi$
$439$	23.2408	−	13.4181i	1.10922	−	0.640410i	0.938628	+	0.344931i	$0.112098\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−11.3051	+	6.52699i	−0.537120	+	0.310107i	−0.743911	−	0.668279i	$-0.767031\pi$
$443$	−11.3051	+	6.52699i	−0.537120	+	0.310107i	0.206791	+	0.978385i	$0.433698\pi$
$444$		0			0
$445$	−24.3773	+	42.2227i	−1.15560	+	2.00155i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	0.468645i		−	0.0221167i	−0.999939	−	0.0110584i	$-0.996480\pi$
$449$		−	0.468645i		−	0.0221167i	0.999939	−	0.0110584i	$-0.00352006\pi$
$450$		0			0
$451$	−15.8460	+	9.14868i	−0.746158	+	0.430795i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.288286	−	30.0433i	−0.0135151	−	1.40845i
$456$		0			0
$457$	2.06486	+	3.57644i	0.0965901	+	0.167299i	0.910271	−	0.414013i	$-0.135873\pi$
$457$	2.06486	+	3.57644i	0.0965901	+	0.167299i	−0.813681	+	0.581312i	$0.802540\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−12.9115	+	22.3633i	−0.601347	+	1.04156i	0.391271	+	0.920276i	$0.372036\pi$
$461$	−12.9115	+	22.3633i	−0.601347	+	1.04156i	−0.992617	+	0.121288i	$0.961298\pi$
$462$		0			0
$463$	2.56402	+	4.44101i	0.119160	+	0.206391i	0.919435	−	0.393242i	$-0.128647\pi$
$463$	2.56402	+	4.44101i	0.119160	+	0.206391i	−0.800275	+	0.599633i	$0.795313\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.26091	+	2.18396i	−0.0583480	+	0.101062i	−0.893724	−	0.448617i	$-0.851917\pi$
$467$	−1.26091	+	2.18396i	−0.0583480	+	0.101062i	0.835376	+	0.549679i	$0.185250\pi$
$468$		0			0
$469$	−10.5536	−	17.8809i	−0.487319	−	0.825662i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−7.43976	−	4.29535i	−0.342081	−	0.197500i
$474$		0			0
$475$	15.6632	+	9.04316i	0.718677	+	0.414929i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−11.4924			−0.525103			−0.262552	−	0.964918i	$-0.584564\pi$
$479$	−11.4924			−0.525103			−0.262552	+	0.964918i	$0.584564\pi$
$480$		0			0
$481$			5.81854i			0.265303i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	48.7629	+	28.1533i	2.21421	+	1.27837i
$486$		0			0
$487$	10.8463	+	18.7864i	0.491493	+	0.851292i	0.999952	−	0.00979483i	$-0.00311784\pi$
$487$	10.8463	+	18.7864i	0.491493	+	0.851292i	−0.508459	+	0.861086i	$0.669785\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−19.3592	+	11.1771i	−0.873669	+	0.504413i	−0.868566	−	0.495574i	$-0.834958\pi$
$491$	−19.3592	+	11.1771i	−0.873669	+	0.504413i	−0.00510349	+	0.999987i	$0.501624\pi$
$492$		0			0
$493$		−	39.2438i		−	1.76745i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17.5775	−	9.92470i	−0.788457	−	0.445184i
$498$		0			0
$499$	−17.5246			−0.784510			−0.392255	−	0.919857i	$-0.628305\pi$
$499$	−17.5246			−0.784510			−0.392255	+	0.919857i	$0.628305\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−7.60926			−0.339280			−0.169640	−	0.985506i	$-0.554261\pi$
$503$	−7.60926			−0.339280			−0.169640	+	0.985506i	$0.554261\pi$
$504$		0			0
$505$	39.3159			1.74953
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.78746			0.300849			0.150424	−	0.988622i	$-0.451936\pi$
$509$	6.78746			0.300849			0.150424	+	0.988622i	$0.451936\pi$
$510$		0			0
$511$	−0.344945	−	35.9479i	−0.0152595	−	1.59024i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			2.13111i			0.0939078i
$516$		0			0
$517$	12.4738	−	7.20174i	0.548596	−	0.316732i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	13.8435	+	23.9777i	0.606497	+	1.05048i	0.991813	+	0.127698i	$0.0407590\pi$
$521$	13.8435	+	23.9777i	0.606497	+	1.05048i	−0.385316	+	0.922785i	$0.625908\pi$
$522$		0			0
$523$	0.834923	+	0.482043i	0.0365086	+	0.0210783i	0.518143	−	0.855294i	$-0.326623\pi$
$523$	0.834923	+	0.482043i	0.0365086	+	0.0210783i	−0.481635	+	0.876372i	$0.659957\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			28.5943i			1.24559i
$528$		0			0
$529$	8.18740			0.355974
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−28.0034	−	16.1678i	−1.21296	−	0.700304i
$534$		0			0
$535$	40.0552	+	23.1259i	1.73174	+	0.999820i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−10.8985	+	6.57430i	−0.469433	+	0.283175i
$540$		0			0
$541$	2.36867	−	4.10266i	0.101837	−	0.176387i	−0.810604	−	0.585594i	$-0.800861\pi$
$541$	2.36867	−	4.10266i	0.101837	−	0.176387i	0.912442	+	0.409207i	$0.134195\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	4.84374	+	8.38960i	0.207483	+	0.359371i
$546$		0			0
$547$	0.840875	−	1.45644i	0.0359532	−	0.0622728i	−0.847489	−	0.530813i	$-0.821887\pi$
$547$	0.840875	−	1.45644i	0.0359532	−	0.0622728i	0.883442	+	0.468540i	$0.155220\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−8.07446	−	13.9854i	−0.343984	−	0.595797i
$552$		0			0
$553$	4.87467	−	0.0467758i	0.207292	−	0.00198911i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.14983	+	4.70530i	−0.345319	+	0.199370i	−0.662622	−	0.748954i	$-0.730556\pi$
$557$	−8.14983	+	4.70530i	−0.345319	+	0.199370i	0.317303	+	0.948324i	$0.397223\pi$
$558$		0			0
$559$		−	15.1817i		−	0.642117i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−15.5319	+	26.9020i	−0.654591	+	1.13378i	0.327405	+	0.944884i	$0.393826\pi$
$563$	−15.5319	+	26.9020i	−0.654591	+	1.13378i	−0.981996	+	0.188901i	$0.939508\pi$
$564$		0			0
$565$	23.5056	−	13.5710i	0.988888	−	0.570935i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−17.4099	+	10.0516i	−0.729859	+	0.421384i	−0.818371	−	0.574691i	$-0.805122\pi$
$569$	−17.4099	+	10.0516i	−0.729859	+	0.421384i	0.0885114	+	0.996075i	$0.471789\pi$
$570$		0			0
$571$	−3.93707	+	6.81920i	−0.164761	+	0.285375i	−0.936570	−	0.350479i	$-0.886019\pi$
$571$	−3.93707	+	6.81920i	−0.164761	+	0.285375i	0.771809	+	0.635854i	$0.219352\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			28.8239i			1.20204i
$576$		0			0
$577$	−2.77842	+	1.60412i	−0.115667	+	0.0667805i	−0.556717	−	0.830702i	$-0.687939\pi$
$577$	−2.77842	+	1.60412i	−0.115667	+	0.0667805i	0.441050	+	0.897482i	$0.354606\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−15.1088	−	25.5987i	−0.626817	−	1.06201i
$582$		0			0
$583$	2.37794	+	4.11871i	0.0984840	+	0.170579i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.37708	+	4.11722i	−0.0981125	+	0.169936i	−0.910903	−	0.412620i	$-0.864614\pi$
$587$	−2.37708	+	4.11722i	−0.0981125	+	0.169936i	0.812791	+	0.582556i	$0.197947\pi$
$588$		0			0
$589$	5.88332	+	10.1902i	0.242418	+	0.419880i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−13.0354	+	22.5780i	−0.535300	+	0.927166i	0.463849	+	0.885914i	$0.346468\pi$
$593$	−13.0354	+	22.5780i	−0.535300	+	0.927166i	−0.999149	+	0.0412519i	$0.986865\pi$
$594$		0			0
$595$	54.8703	−	0.526519i	2.24946	−	0.0215852i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−23.8178	−	13.7512i	−0.973168	−	0.561859i	−0.0729672	−	0.997334i	$-0.523247\pi$
$599$	−23.8178	−	13.7512i	−0.973168	−	0.561859i	−0.900200	+	0.435476i	$0.856580\pi$
$600$		0			0
$601$	−26.8647	−	15.5104i	−1.09584	−	0.632681i	−0.160712	−	0.987001i	$-0.551379\pi$
$601$	−26.8647	−	15.5104i	−1.09584	−	0.632681i	−0.935124	+	0.354320i	$0.884712\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−27.1903			−1.10544
$606$		0			0
$607$			39.2304i			1.59231i	0.605092	+	0.796156i	$0.293136\pi$
$607$			39.2304i			1.59231i	−0.605092	+	0.796156i	$0.706864\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	22.0440	+	12.7271i	0.891803	+	0.514883i
$612$		0			0
$613$	−11.5364	−	19.9817i	−0.465951	−	0.807051i	0.533293	−	0.845931i	$-0.320954\pi$
$613$	−11.5364	−	19.9817i	−0.465951	−	0.807051i	−0.999244	+	0.0388795i	$0.987621\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.15715	+	2.97748i	−0.207619	+	0.119869i	−0.600204	−	0.799847i	$-0.704914\pi$
$617$	−5.15715	+	2.97748i	−0.207619	+	0.119869i	0.392585	+	0.919716i	$0.371581\pi$
$618$		0			0
$619$		−	32.3650i		−	1.30086i	−0.759567	−	0.650429i	$-0.774589\pi$
$619$		−	32.3650i		−	1.30086i	0.759567	−	0.650429i	$-0.225411\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	18.5526	+	31.4337i	0.743296	+	1.25936i
$624$		0			0
$625$	−6.35758			−0.254303
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−10.6268			−0.423719
$630$		0			0
$631$	35.6689			1.41996			0.709978	−	0.704224i	$-0.248705\pi$
$631$	35.6689			1.41996			0.709978	+	0.704224i	$0.248705\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	63.3459			2.51380
$636$		0			0
$637$	−19.6918	−	10.8707i	−0.780218	−	0.430711i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	24.8536i		−	0.981659i	−0.871256	−	0.490829i	$-0.836694\pi$
$641$		−	24.8536i		−	0.981659i	0.871256	−	0.490829i	$-0.163306\pi$
$642$		0			0
$643$	−14.8270	+	8.56038i	−0.584720	+	0.337588i	−0.763007	−	0.646390i	$-0.776278\pi$
$643$	−14.8270	+	8.56038i	−0.584720	+	0.337588i	0.178287	+	0.983979i	$0.442944\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.7208	+	28.9613i	0.657363	+	1.13859i	0.981296	+	0.192506i	$0.0616614\pi$
$647$	16.7208	+	28.9613i	0.657363	+	1.13859i	−0.323933	+	0.946080i	$0.605005\pi$
$648$		0			0
$649$	−13.8761	−	8.01138i	−0.544686	−	0.314474i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			26.4238i			1.03404i	0.855972	+	0.517022i	$0.172959\pi$
$653$			26.4238i			1.03404i	−0.855972	+	0.517022i	$0.827041\pi$
$654$		0			0
$655$	−59.9745			−2.34340
$656$		0			0
$657$		0			0
$658$		0			0
$659$	25.8862	+	14.9454i	1.00838	+	0.582191i	0.910718	−	0.413029i	$-0.135529\pi$
$659$	25.8862	+	14.9454i	1.00838	+	0.582191i	0.0976658	+	0.995219i	$0.468862\pi$
$660$		0			0
$661$	−3.92629	−	2.26684i	−0.152715	−	0.0881699i	0.421695	−	0.906738i	$-0.361435\pi$
$661$	−3.92629	−	2.26684i	−0.152715	−	0.0881699i	−0.574410	+	0.818568i	$0.694769\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	19.4459	−	11.4773i	0.754079	−	0.445069i
$666$		0			0
$667$	12.8682	−	22.2883i	0.498257	−	0.863006i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	9.43172	+	16.3362i	0.364107	+	0.630652i
$672$		0			0
$673$	4.12239	−	7.14019i	0.158907	−	0.275234i	−0.775568	−	0.631264i	$-0.782536\pi$
$673$	4.12239	−	7.14019i	0.158907	−	0.275234i	0.934475	+	0.356030i	$0.115870\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.75631	−	4.77407i	−0.105934	−	0.183483i	0.808186	−	0.588928i	$-0.200450\pi$
$677$	−2.75631	−	4.77407i	−0.105934	−	0.183483i	−0.914119	+	0.405445i	$0.867116\pi$
$678$		0			0
$679$	36.3026	−	21.4264i	1.39317	−	0.822268i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	24.0097	−	13.8620i	0.918706	−	0.530415i	0.0354840	−	0.999370i	$-0.488703\pi$
$683$	24.0097	−	13.8620i	0.918706	−	0.530415i	0.883222	+	0.468955i	$0.155369\pi$
$684$		0			0
$685$			19.6540i			0.750942i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−4.20235	+	7.27868i	−0.160097	+	0.277296i
$690$		0			0
$691$	−36.5312	+	21.0913i	−1.38971	+	0.802351i	−0.993283	−	0.115714i	$-0.963084\pi$
$691$	−36.5312	+	21.0913i	−1.38971	+	0.802351i	−0.396430	+	0.918065i	$0.629751\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−43.9994	+	25.4031i	−1.66899	+	0.963593i
$696$		0			0
$697$	29.5284	−	51.1447i	1.11847	−	1.93724i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			1.07738i			0.0406922i	0.999793	+	0.0203461i	$0.00647681\pi$
$701$			1.07738i			0.0406922i	−0.999793	+	0.0203461i	$0.993523\pi$
$702$		0			0
$703$	−3.78710	+	2.18648i	−0.142833	+	0.0824648i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	14.4717	−	25.6306i	0.544265	−	0.963938i
$708$		0			0
$709$	10.9806	+	19.0189i	0.412385	+	0.714271i	0.995150	−	0.0983694i	$-0.0313627\pi$
$709$	10.9806	+	19.0189i	0.412385	+	0.714271i	−0.582765	+	0.812640i	$0.698029\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−9.37617	+	16.2400i	−0.351140	+	0.608193i
$714$		0			0
$715$	10.3240	+	17.8817i	0.386095	+	0.668737i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−5.89267	+	10.2064i	−0.219760	+	0.380635i	−0.954734	−	0.297460i	$-0.903861\pi$
$719$	−5.89267	+	10.2064i	−0.219760	+	0.380635i	0.734975	+	0.678094i	$0.237194\pi$
$720$		0			0
$721$	1.38930	+	0.784436i	0.0517403	+	0.0292139i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−43.3709	−	25.0402i	−1.61075	−	0.929970i
$726$		0			0
$727$	10.1963	+	5.88682i	0.378159	+	0.218330i	0.677017	−	0.735967i	$-0.263272\pi$
$727$	10.1963	+	5.88682i	0.378159	+	0.218330i	−0.298858	+	0.954298i	$0.596606\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	27.7274			1.02554
$732$		0			0
$733$		−	43.7655i		−	1.61652i	−0.588829	−	0.808258i	$-0.700411\pi$
$733$		−	43.7655i		−	1.61652i	0.588829	−	0.808258i	$-0.299589\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	12.3575	+	7.13462i	0.455195	+	0.262807i
$738$		0			0
$739$	−13.9728	−	24.2016i	−0.513998	−	0.890270i	−0.999868	−	0.0162393i	$-0.994831\pi$
$739$	−13.9728	−	24.2016i	−0.513998	−	0.890270i	0.485870	−	0.874031i	$-0.338503\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	31.0951	−	17.9528i	1.14077	−	0.658623i	0.194147	−	0.980972i	$-0.437806\pi$
$743$	31.0951	−	17.9528i	1.14077	−	0.658623i	0.946621	+	0.322350i	$0.104473\pi$
$744$		0			0
$745$			22.6923i			0.831382i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	29.8200	−	17.6002i	1.08960	−	0.643099i
$750$		0			0
$751$	2.35031			0.0857642			0.0428821	−	0.999080i	$-0.486346\pi$
$751$	2.35031			0.0857642			0.0428821	+	0.999080i	$0.486346\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	56.5178			2.05689
$756$		0			0
$757$	8.88061			0.322771			0.161386	−	0.986891i	$-0.448404\pi$
$757$	8.88061			0.322771			0.161386	+	0.986891i	$0.448404\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−26.9766			−0.977902			−0.488951	−	0.872311i	$-0.662620\pi$
$761$	−26.9766			−0.977902			−0.488951	+	0.872311i	$0.662620\pi$
$762$		0			0
$763$	7.25223	−	0.0695902i	0.262548	−	0.00251933i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	28.3158i		−	1.02243i
$768$		0			0
$769$	7.88232	−	4.55086i	0.284244	−	0.164108i	−0.351099	−	0.936338i	$-0.614192\pi$
$769$	7.88232	−	4.55086i	0.284244	−	0.164108i	0.635343	+	0.772230i	$0.280859\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	6.46864	+	11.2040i	0.232661	+	0.402980i	0.958590	−	0.284789i	$-0.0919235\pi$
$773$	6.46864	+	11.2040i	0.232661	+	0.402980i	−0.725929	+	0.687769i	$0.758590\pi$
$774$		0			0
$775$	31.6015	+	18.2451i	1.13516	+	0.655384i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	24.3020i		−	0.870710i
$780$		0			0
$781$	13.8726			0.496399
$782$		0			0
$783$		0			0
$784$		0			0
$785$	42.6245	+	24.6093i	1.52134	+	0.878343i
$786$		0			0
$787$	−21.5265	−	12.4283i	−0.767336	−	0.443022i	0.0645875	−	0.997912i	$-0.479427\pi$
$787$	−21.5265	−	12.4283i	−0.767336	−	0.443022i	−0.831923	+	0.554890i	$0.812760\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−0.194975	−	20.3190i	−0.00693250	−	0.722460i
$792$		0			0
$793$	−16.6680	+	28.8697i	−0.591896	+	1.02519i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.71671	−	11.6337i	−0.237918	−	0.412086i	0.722199	−	0.691686i	$-0.243132\pi$
$797$	−6.71671	−	11.6337i	−0.237918	−	0.412086i	−0.960117	+	0.279600i	$0.909798\pi$
$798$		0			0
$799$	−23.2444	+	40.2605i	−0.822328	+	1.42431i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	12.3530	+	21.3961i	0.435928	+	0.755050i
$804$		0			0
$805$	31.3359	+	17.6931i	1.10445	+	0.623600i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	9.38524	−	5.41857i	0.329967	−	0.190507i	−0.325859	−	0.945418i	$-0.605654\pi$
$809$	9.38524	−	5.41857i	0.329967	−	0.190507i	0.655827	+	0.754912i	$0.272320\pi$
$810$		0			0
$811$			35.3334i			1.24072i	0.784316	+	0.620361i	$0.213014\pi$
$811$			35.3334i			1.24072i	−0.784316	+	0.620361i	$0.786986\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	27.5475	−	47.7137i	0.964948	−	1.67134i
$816$		0			0
$817$	9.88127	−	5.70496i	0.345702	−	0.199591i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	16.6412	−	9.60782i	0.580783	−	0.335315i	−0.180661	−	0.983545i	$-0.557824\pi$
$821$	16.6412	−	9.60782i	0.580783	−	0.335315i	0.761445	+	0.648230i	$0.224490\pi$
$822$		0			0
$823$	14.9074	−	25.8204i	0.519639	−	0.900041i	−0.480100	−	0.877214i	$-0.659400\pi$
$823$	14.9074	−	25.8204i	0.519639	−	0.900041i	0.999739	−	0.0228278i	$-0.00726695\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			0.356137i			0.0123841i	0.999981	+	0.00619205i	$0.00197100\pi$
$827$			0.356137i			0.0123841i	−0.999981	+	0.00619205i	$0.998029\pi$
$828$		0			0
$829$	−17.5571	+	10.1366i	−0.609783	+	0.352058i	−0.772880	−	0.634552i	$-0.781185\pi$
$829$	−17.5571	+	10.1366i	−0.609783	+	0.352058i	0.163098	+	0.986610i	$0.447851\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	19.8539	−	35.9646i	0.687896	−	1.24610i
$834$		0			0
$835$	23.2795	+	40.3213i	0.805620	+	1.39538i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.662663	+	1.14777i	−0.0228777	+	0.0396253i	−0.877238	−	0.480056i	$-0.840616\pi$
$839$	−0.662663	+	1.14777i	−0.0228777	+	0.0396253i	0.854360	+	0.519682i	$0.173949\pi$
$840$		0			0
$841$	7.85791	+	13.6103i	0.270962	+	0.469321i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.72626	−	8.18612i	0.162588	−	0.281611i
$846$		0			0
$847$	−10.0084	+	17.7258i	−0.343894	+	0.609064i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−6.03545	−	3.48457i	−0.206893	−	0.119449i
$852$		0			0
$853$	−41.7558	−	24.1077i	−1.42969	−	0.825432i	−0.432594	−	0.901589i	$-0.642402\pi$
$853$	−41.7558	−	24.1077i	−1.42969	−	0.825432i	−0.997096	+	0.0761571i	$0.975735\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	20.8773			0.713155			0.356578	−	0.934266i	$-0.383944\pi$
$857$	20.8773			0.713155			0.356578	+	0.934266i	$0.383944\pi$
$858$		0			0
$859$		−	13.7094i		−	0.467758i	−0.972266	−	0.233879i	$-0.924858\pi$
$859$		−	13.7094i		−	0.467758i	0.972266	−	0.233879i	$-0.0751419\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	28.1125	+	16.2307i	0.956959	+	0.552501i	0.895236	−	0.445593i	$-0.147007\pi$
$863$	28.1125	+	16.2307i	0.956959	+	0.552501i	0.0617233	+	0.998093i	$0.480340\pi$
$864$		0			0
$865$	−19.8047	−	34.3027i	−0.673379	−	1.16633i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.90139	+	1.67512i	−0.0984228	+	0.0568244i
$870$		0			0
$871$			25.2169i			0.854444i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	11.4434	−	20.2671i	0.386856	−	0.685154i
$876$		0			0
$877$	21.9338			0.740653			0.370326	−	0.928902i	$-0.379246\pi$
$877$	21.9338			0.740653			0.370326	+	0.928902i	$0.379246\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−21.8019			−0.734526			−0.367263	−	0.930117i	$-0.619705\pi$
$881$	−21.8019			−0.734526			−0.367263	+	0.930117i	$0.619705\pi$
$882$		0			0
$883$	24.4085			0.821411			0.410705	−	0.911768i	$-0.365283\pi$
$883$	24.4085			0.821411			0.410705	+	0.911768i	$0.365283\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−33.7444			−1.13303			−0.566513	−	0.824053i	$-0.691708\pi$
$887$	−33.7444			−1.13303			−0.566513	+	0.824053i	$0.691708\pi$
$888$		0			0
$889$	23.3169	−	41.2961i	0.782024	−	1.38503i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			19.1303i			0.640170i
$894$		0			0
$895$	−32.6113	+	18.8281i	−1.09007	+	0.629355i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−16.2907	−	28.2164i	−0.543326	−	0.941068i
$900$		0			0
$901$	−13.2936	−	7.67505i	−0.442873	−	0.255693i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			42.0183i			1.39674i
$906$		0			0
$907$	−15.0566			−0.499948			−0.249974	−	0.968253i	$-0.580422\pi$
$907$	−15.0566			−0.499948			−0.249974	+	0.968253i	$0.580422\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−21.5047	−	12.4157i	−0.712481	−	0.411351i	0.0994977	−	0.995038i	$-0.468276\pi$
$911$	−21.5047	−	12.4157i	−0.712481	−	0.411351i	−0.811979	+	0.583686i	$0.801610\pi$
$912$		0			0
$913$	17.6913	+	10.2141i	0.585498	+	0.338038i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−22.0759	+	39.0983i	−0.729012	+	1.29114i
$918$		0			0
$919$	12.0689	−	20.9039i	0.398115	−	0.689555i	−0.595378	−	0.803445i	$-0.702998\pi$
$919$	12.0689	−	20.9039i	0.398115	−	0.689555i	0.993493	+	0.113890i	$0.0363312\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	12.2580	+	21.2314i	0.403476	+	0.698840i
$924$		0			0
$925$	−6.78064	+	11.7444i	−0.222946	+	0.386154i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	13.3310	+	23.0900i	0.437376	+	0.757558i	0.997486	−	0.0708606i	$-0.0225745\pi$
$929$	13.3310	+	23.0900i	0.437376	+	0.757558i	−0.560110	+	0.828418i	$0.689241\pi$
$930$		0			0
$931$	−0.324397	−	16.9017i	−0.0106317	−	0.553932i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−32.6586	+	18.8555i	−1.06805	+	0.616640i
$936$		0			0
$937$		−	8.17165i		−	0.266956i	−0.991052	−	0.133478i	$-0.957385\pi$
$937$		−	8.17165i		−	0.266956i	0.991052	−	0.133478i	$-0.0426146\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−16.0136	+	27.7363i	−0.522028	+	0.904179i	0.477644	+	0.878554i	$0.341491\pi$
$941$	−16.0136	+	27.7363i	−0.522028	+	0.904179i	−0.999672	+	0.0256254i	$0.991842\pi$
$942$		0			0
$943$	33.5410	−	19.3649i	1.09224	−	0.630608i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15.5020	+	8.95009i	−0.503748	+	0.290839i	−0.730260	−	0.683169i	$-0.760601\pi$
$947$	−15.5020	+	8.95009i	−0.503748	+	0.290839i	0.226512	+	0.974008i	$0.427268\pi$
$948$		0			0
$949$	−21.8305	+	37.8116i	−0.708650	+	1.22742i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	11.2737i		−	0.365191i	−0.983188	−	0.182596i	$-0.941550\pi$
$953$		−	11.2737i		−	0.365191i	0.983188	−	0.182596i	$-0.0584499\pi$
$954$		0			0
$955$	−0.685459	+	0.395750i	−0.0221809	+	0.0128062i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	12.8128	+	7.23442i	0.413746	+	0.233612i
$960$		0			0
$961$	−3.63003	−	6.28740i	−0.117098	−	0.202819i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	46.0738	−	79.8022i	1.48317	−	2.56892i
$966$		0			0
$967$	−15.3313	−	26.5546i	−0.493022	−	0.853939i	0.506946	−	0.861978i	$-0.330774\pi$
$967$	−15.3313	−	26.5546i	−0.493022	−	0.853939i	−0.999968	+	0.00803913i	$0.997441\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	19.0807	−	33.0488i	0.612330	−	1.06059i	−0.378517	−	0.925595i	$-0.623566\pi$
$971$	19.0807	−	33.0488i	0.612330	−	1.06059i	0.990847	−	0.134992i	$-0.0431010\pi$
$972$		0			0
$973$	0.364967	+	38.0345i	0.0117003	+	1.21933i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−26.5862	−	15.3496i	−0.850568	−	0.491076i	0.0102745	−	0.999947i	$-0.496729\pi$
$977$	−26.5862	−	15.3496i	−0.850568	−	0.491076i	−0.860842	+	0.508872i	$0.830063\pi$
$978$		0			0
$979$	−21.7239	−	12.5423i	−0.694299	−	0.400854i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	25.8057			0.823073			0.411536	−	0.911393i	$-0.364992\pi$
$983$	25.8057			0.823073			0.411536	+	0.911393i	$0.364992\pi$
$984$		0			0
$985$		−	5.52328i		−	0.175986i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	15.7476	+	9.09191i	0.500746	+	0.289106i
$990$		0			0
$991$	11.4388	+	19.8126i	0.363366	+	0.629369i	0.988513	−	0.151139i	$-0.0482940\pi$
$991$	11.4388	+	19.8126i	0.363366	+	0.629369i	−0.625146	+	0.780508i	$0.714961\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	47.6118	−	27.4887i	1.50940	−	0.871450i
$996$		0			0
$997$			41.5407i			1.31561i	0.753189	+	0.657804i	$0.228514\pi$
$997$			41.5407i			1.31561i	−0.753189	+	0.657804i	$0.771486\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.df.e.1601.3		48
3.2	odd	2		1008.2.df.e.929.18		48
4.3	odd	2		1512.2.cx.a.89.3		48
7.3	odd	6		3024.2.ca.e.2033.3		48
9.4	even	3		1008.2.ca.e.257.24		48
9.5	odd	6		3024.2.ca.e.2609.3		48
12.11	even	2		504.2.cx.a.425.7	yes	48
21.17	even	6		1008.2.ca.e.353.24		48
28.3	even	6		1512.2.bs.a.521.3		48
36.23	even	6		1512.2.bs.a.1097.3		48
36.31	odd	6		504.2.bs.a.257.1	✓	48
63.31	odd	6		1008.2.df.e.689.18		48
63.59	even	6	inner	3024.2.df.e.17.3		48
84.59	odd	6		504.2.bs.a.353.1	yes	48
252.31	even	6		504.2.cx.a.185.7	yes	48
252.59	odd	6		1512.2.cx.a.17.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.1	✓	48	36.31	odd	6
504.2.bs.a.353.1	yes	48	84.59	odd	6
504.2.cx.a.185.7	yes	48	252.31	even	6
504.2.cx.a.425.7	yes	48	12.11	even	2
1008.2.ca.e.257.24		48	9.4	even	3
1008.2.ca.e.353.24		48	21.17	even	6
1008.2.df.e.689.18		48	63.31	odd	6
1008.2.df.e.929.18		48	3.2	odd	2
1512.2.bs.a.521.3		48	28.3	even	6
1512.2.bs.a.1097.3		48	36.23	even	6
1512.2.cx.a.17.3		48	252.59	odd	6
1512.2.cx.a.89.3		48	4.3	odd	2
3024.2.ca.e.2033.3		48	7.3	odd	6
3024.2.ca.e.2609.3		48	9.5	odd	6
3024.2.df.e.17.3		48	63.59	even	6	inner
3024.2.df.e.1601.3		48	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-3.53401 q^{5} +(-1.30083 + 2.30388i) q^{7} -1.81827i q^{11} +(2.78280 - 1.60665i) q^{13} +(2.93434 + 5.08242i) q^{17} +(2.09143 + 1.20749i) q^{19} +3.84871i q^{23} +7.48923 q^{25} +(-5.79110 - 3.34349i) q^{29} +(4.21959 + 2.43618i) q^{31} +(4.59714 - 8.14192i) q^{35} +(-0.905385 + 1.56817i) q^{37} +(-5.03152 - 8.71485i) q^{41} +(2.36232 - 4.09166i) q^{43} +(3.96076 + 6.86023i) q^{47} +(-3.61569 - 5.99390i) q^{49} +(-2.26517 + 1.30780i) q^{53} +6.42580i q^{55} +(4.40604 - 7.63149i) q^{59} +(-8.98447 + 5.18718i) q^{61} +(-9.83443 + 5.67791i) q^{65} +(-3.92384 + 6.79630i) q^{67} +7.62952i q^{71} +(-11.7672 + 6.79382i) q^{73} +(4.18907 + 2.36526i) q^{77} +(-0.921268 - 1.59568i) q^{79} +(-5.61748 + 9.72975i) q^{83} +(-10.3700 - 17.9613i) q^{85} +(6.89792 - 11.9475i) q^{89} +(0.0815748 + 8.50119i) q^{91} +(-7.39114 - 4.26728i) q^{95} +(-13.7982 - 7.96638i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{25} - 18 q^{29} - 18 q^{31} + 6 q^{41} + 6 q^{43} + 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} - 6 q^{79} + 18 q^{89} - 6 q^{91} - 54 q^{95}+O(q^{100}) \) 48 * q + 48 * q^25 - 18 * q^29 - 18 * q^31 + 6 * q^41 + 6 * q^43 + 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 - 6 * q^79 + 18 * q^89 - 6 * q^91 - 54 * q^95

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