LMFDB - Embedded newform 3024.2.df.e.17.15

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			17.15
Character	$\chi$	$=$	3024.17
Dual form			3024.2.df.e.1601.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+1.05582 q^{5} +(-1.79851 - 1.94045i) q^{7} -6.24489i q^{11} +(-0.872074 - 0.503492i) q^{13} +(-3.26821 + 5.66070i) q^{17} +(-1.73329 + 1.00071i) q^{19} +4.40135i q^{23} -3.88524 q^{25} +(-6.12821 + 3.53813i) q^{29} +(2.07210 - 1.19633i) q^{31} +(-1.89890 - 2.04877i) q^{35} +(-3.64197 - 6.30808i) q^{37} +(-1.80119 + 3.11974i) q^{41} +(-1.60595 - 2.78159i) q^{43} +(-1.87024 + 3.23934i) q^{47} +(-0.530720 + 6.97985i) q^{49} +(6.02455 + 3.47827i) q^{53} -6.59348i q^{55} +(6.67084 + 11.5542i) q^{59} +(7.10733 + 4.10342i) q^{61} +(-0.920753 - 0.531597i) q^{65} +(0.0613962 + 0.106341i) q^{67} +5.37678i q^{71} +(14.4429 + 8.33860i) q^{73} +(-12.1179 + 11.2315i) q^{77} +(-4.43136 + 7.67534i) q^{79} +(-1.07668 - 1.86486i) q^{83} +(-3.45064 + 5.97668i) q^{85} +(2.23201 + 3.86595i) q^{89} +(0.591431 + 2.59775i) q^{91} +(-1.83004 + 1.05657i) q^{95} +(0.960756 - 0.554693i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

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

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
$5$	1.05582			0.472177			0.236089	−	0.971732i	$-0.424134\pi$
$5$	1.05582			0.472177			0.236089	+	0.971732i	$0.424134\pi$
$6$		0			0
$7$	−1.79851	−	1.94045i	−0.679773	−	0.733422i
$7$	−1.79851	−	1.94045i	−0.679773	−	0.733422i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	6.24489i		−	1.88291i	−0.337143	−	0.941453i	$-0.609461\pi$
$11$		−	6.24489i		−	1.88291i	0.337143	−	0.941453i	$-0.390539\pi$
$12$		0			0
$13$	−0.872074	−	0.503492i	−0.241870	−	0.139644i	0.374166	−	0.927362i	$-0.377929\pi$
$13$	−0.872074	−	0.503492i	−0.241870	−	0.139644i	−0.616036	+	0.787718i	$0.711262\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.26821	+	5.66070i	−0.792656	+	1.37292i	0.131660	+	0.991295i	$0.457969\pi$
$17$	−3.26821	+	5.66070i	−0.792656	+	1.37292i	−0.924317	+	0.381626i	$0.875364\pi$
$18$		0			0
$19$	−1.73329	+	1.00071i	−0.397643	+	0.229579i	−0.685466	−	0.728104i	$-0.740402\pi$
$19$	−1.73329	+	1.00071i	−0.397643	+	0.229579i	0.287823	+	0.957683i	$0.407068\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			4.40135i			0.917744i	0.888502	+	0.458872i	$0.151746\pi$
$23$			4.40135i			0.917744i	−0.888502	+	0.458872i	$0.848254\pi$
$24$		0			0
$25$	−3.88524			−0.777049
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.12821	+	3.53813i	−1.13798	+	0.657014i	−0.945930	−	0.324371i	$-0.894847\pi$
$29$	−6.12821	+	3.53813i	−1.13798	+	0.657014i	−0.192051	+	0.981385i	$0.561514\pi$
$30$		0			0
$31$	2.07210	−	1.19633i	0.372160	−	0.214867i	−0.302242	−	0.953231i	$-0.597735\pi$
$31$	2.07210	−	1.19633i	0.372160	−	0.214867i	0.674402	+	0.738365i	$0.264402\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.89890	−	2.04877i	−0.320973	−	0.346305i
$36$		0			0
$37$	−3.64197	−	6.30808i	−0.598737	−	1.03704i	−0.993008	−	0.118048i	$-0.962336\pi$
$37$	−3.64197	−	6.30808i	−0.598737	−	1.03704i	0.394271	−	0.918994i	$-0.370997\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.80119	+	3.11974i	−0.281298	+	0.487222i	−0.971705	−	0.236199i	$-0.924098\pi$
$41$	−1.80119	+	3.11974i	−0.281298	+	0.487222i	0.690407	+	0.723421i	$0.257432\pi$
$42$		0			0
$43$	−1.60595	−	2.78159i	−0.244906	−	0.424189i	0.717199	−	0.696868i	$-0.245424\pi$
$43$	−1.60595	−	2.78159i	−0.244906	−	0.424189i	−0.962105	+	0.272679i	$0.912090\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.87024	+	3.23934i	−0.272802	+	0.472507i	−0.969578	−	0.244782i	$-0.921284\pi$
$47$	−1.87024	+	3.23934i	−0.272802	+	0.472507i	0.696776	+	0.717289i	$0.254617\pi$
$48$		0			0
$49$	−0.530720	+	6.97985i	−0.0758171	+	0.997122i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.02455	+	3.47827i	0.827535	+	0.477778i	0.853008	−	0.521898i	$-0.174776\pi$
$53$	6.02455	+	3.47827i	0.827535	+	0.477778i	−0.0254729	+	0.999676i	$0.508109\pi$
$54$		0			0
$55$		−	6.59348i		−	0.889065i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.67084	+	11.5542i	0.868469	+	1.50423i	0.863561	+	0.504244i	$0.168229\pi$
$59$	6.67084	+	11.5542i	0.868469	+	1.50423i	0.00490776	+	0.999988i	$0.498438\pi$
$60$		0			0
$61$	7.10733	+	4.10342i	0.910000	+	0.525389i	0.880431	−	0.474174i	$-0.157253\pi$
$61$	7.10733	+	4.10342i	0.910000	+	0.525389i	0.0295688	+	0.999563i	$0.490587\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.920753	−	0.531597i	−0.114205	−	0.0659365i
$66$		0			0
$67$	0.0613962	+	0.106341i	0.00750074	+	0.0129917i	0.869751	−	0.493490i	$-0.164279\pi$
$67$	0.0613962	+	0.106341i	0.00750074	+	0.0129917i	−0.862251	+	0.506482i	$0.830946\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			5.37678i			0.638107i	0.947737	+	0.319053i	$0.103365\pi$
$71$			5.37678i			0.638107i	−0.947737	+	0.319053i	$0.896635\pi$
$72$		0			0
$73$	14.4429	+	8.33860i	1.69041	+	0.975959i	0.954182	+	0.299225i	$0.0967282\pi$
$73$	14.4429	+	8.33860i	1.69041	+	0.975959i	0.736228	+	0.676734i	$0.236605\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−12.1179	+	11.2315i	−1.38097	+	1.27995i
$78$		0			0
$79$	−4.43136	+	7.67534i	−0.498567	+	0.863544i	−0.999999	−	0.00165372i	$-0.999474\pi$
$79$	−4.43136	+	7.67534i	−0.498567	+	0.863544i	0.501431	+	0.865197i	$0.332807\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.07668	−	1.86486i	−0.118181	−	0.204695i	0.800866	−	0.598844i	$-0.204373\pi$
$83$	−1.07668	−	1.86486i	−0.118181	−	0.204695i	−0.919047	+	0.394149i	$0.871040\pi$
$84$		0			0
$85$	−3.45064	+	5.97668i	−0.374274	+	0.648262i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.23201	+	3.86595i	0.236592	+	0.409790i	0.959734	−	0.280910i	$-0.0906361\pi$
$89$	2.23201	+	3.86595i	0.236592	+	0.409790i	−0.723142	+	0.690699i	$0.757303\pi$
$90$		0			0
$91$	0.591431	+	2.59775i	0.0619988	+	0.272319i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.83004	+	1.05657i	−0.187758	+	0.108402i
$96$		0			0
$97$	0.960756	−	0.554693i	0.0975500	−	0.0563205i	−0.450431	−	0.892811i	$-0.648730\pi$
$97$	0.960756	−	0.554693i	0.0975500	−	0.0563205i	0.547981	+	0.836491i	$0.315396\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.78892			−0.576019			−0.288009	−	0.957628i	$-0.592993\pi$
$101$	−5.78892			−0.576019			−0.288009	+	0.957628i	$0.592993\pi$
$102$		0			0
$103$		−	19.7693i		−	1.94793i	−0.226696	−	0.973966i	$-0.572792\pi$
$103$		−	19.7693i		−	1.94793i	0.226696	−	0.973966i	$-0.427208\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.50275	−	3.17701i	0.531971	−	0.307133i	−0.209848	−	0.977734i	$-0.567297\pi$
$107$	5.50275	−	3.17701i	0.531971	−	0.307133i	0.741819	+	0.670601i	$0.233964\pi$
$108$		0			0
$109$	−1.03951	+	1.80048i	−0.0995669	+	0.172455i	−0.911505	−	0.411288i	$-0.865079\pi$
$109$	−1.03951	+	1.80048i	−0.0995669	+	0.172455i	0.811939	+	0.583743i	$0.198412\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	12.9040	+	7.45015i	1.21391	+	0.700851i	0.963609	−	0.267317i	$-0.0861371\pi$
$113$	12.9040	+	7.45015i	1.21391	+	0.700851i	0.250301	+	0.968168i	$0.419470\pi$
$114$		0			0
$115$			4.64703i			0.433338i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	16.8622	−	3.83903i	1.54576	−	0.351923i
$120$		0			0
$121$	−27.9987			−2.54534
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.38122			−0.839082
$126$		0			0
$127$	−18.6841			−1.65794			−0.828971	−	0.559292i	$-0.811073\pi$
$127$	−18.6841			−1.65794			−0.828971	+	0.559292i	$0.811073\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.54126			−0.746253			−0.373126	−	0.927780i	$-0.621714\pi$
$131$	−8.54126			−0.746253			−0.373126	+	0.927780i	$0.621714\pi$
$132$		0			0
$133$	5.05917	+	1.56357i	0.438686	+	0.135578i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	12.3980i		−	1.05923i	−0.848238	−	0.529616i	$-0.822336\pi$
$137$		−	12.3980i		−	1.05923i	0.848238	−	0.529616i	$-0.177664\pi$
$138$		0			0
$139$	−15.4789	−	8.93676i	−1.31291	−	0.758006i	−0.330329	−	0.943866i	$-0.607160\pi$
$139$	−15.4789	−	8.93676i	−1.31291	−	0.758006i	−0.982576	+	0.185860i	$0.940493\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.14425	+	5.44601i	−0.262936	+	0.455418i
$144$		0			0
$145$	−6.47029	+	3.73562i	−0.537328	+	0.310227i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			7.38513i			0.605014i	0.953147	+	0.302507i	$0.0978235\pi$
$149$			7.38513i			0.605014i	−0.953147	+	0.302507i	$0.902176\pi$
$150$		0			0
$151$	−10.2797			−0.836548			−0.418274	−	0.908321i	$-0.637365\pi$
$151$	−10.2797			−0.836548			−0.418274	+	0.908321i	$0.637365\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.18776	−	1.26311i	0.175725	−	0.101455i
$156$		0			0
$157$	−13.4562	+	7.76894i	−1.07392	+	0.620029i	−0.929250	−	0.369451i	$-0.879546\pi$
$157$	−13.4562	+	7.76894i	−1.07392	+	0.620029i	−0.144672	+	0.989480i	$0.546213\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	8.54061	−	7.91587i	0.673094	−	0.623858i
$162$		0			0
$163$	−1.98761	−	3.44264i	−0.155682	−	0.269649i	0.777625	−	0.628728i	$-0.216424\pi$
$163$	−1.98761	−	3.44264i	−0.155682	−	0.269649i	−0.933307	+	0.359079i	$0.883091\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.65088	+	6.32351i	−0.282513	+	0.489328i	−0.972003	−	0.234968i	$-0.924502\pi$
$167$	−3.65088	+	6.32351i	−0.282513	+	0.489328i	0.689490	+	0.724295i	$0.257835\pi$
$168$		0			0
$169$	−5.99299	−	10.3802i	−0.460999	−	0.798474i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.22713	−	7.32160i	0.321383	−	0.556651i	−0.659391	−	0.751800i	$-0.729186\pi$
$173$	4.22713	−	7.32160i	0.321383	−	0.556651i	0.980774	+	0.195149i	$0.0625191\pi$
$174$		0			0
$175$	6.98765	+	7.53914i	0.528217	+	0.569905i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.0439783	−	0.0253909i	−0.00328709	−	0.00189780i	0.498356	−	0.866973i	$-0.333937\pi$
$179$	−0.0439783	−	0.0253909i	−0.00328709	−	0.00189780i	−0.501643	+	0.865075i	$0.667271\pi$
$180$		0			0
$181$			2.64284i			0.196440i	0.995165	+	0.0982202i	$0.0313149\pi$
$181$			2.64284i			0.196440i	−0.995165	+	0.0982202i	$0.968685\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.84527	−	6.66020i	−0.282710	−	0.489668i
$186$		0			0
$187$	35.3505	+	20.4096i	2.58508	+	1.49250i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−21.0319	−	12.1428i	−1.52181	−	0.878619i	−0.999668	−	0.0257624i	$-0.991799\pi$
$191$	−21.0319	−	12.1428i	−1.52181	−	0.878619i	−0.522145	−	0.852857i	$-0.674868\pi$
$192$		0			0
$193$	2.98935	+	5.17771i	0.215178	+	0.372699i	0.953328	−	0.301938i	$-0.0976335\pi$
$193$	2.98935	+	5.17771i	0.215178	+	0.372699i	−0.738150	+	0.674637i	$0.764300\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	0.110985i		−	0.00790737i	−0.999992	−	0.00395369i	$-0.998741\pi$
$197$		−	0.110985i		−	0.00790737i	0.999992	−	0.00395369i	$-0.00125850\pi$
$198$		0			0
$199$	−7.95580	−	4.59329i	−0.563972	−	0.325609i	0.190766	−	0.981636i	$-0.438903\pi$
$199$	−7.95580	−	4.59329i	−0.563972	−	0.325609i	−0.754738	+	0.656026i	$0.772236\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	17.8872	+	5.52816i	1.25544	+	0.388001i
$204$		0			0
$205$	−1.90173	+	3.29389i	−0.132822	+	0.230055i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.24935	+	10.8242i	0.432276	+	0.748725i
$210$		0			0
$211$	−7.95208	+	13.7734i	−0.547443	+	0.948200i	0.451005	+	0.892521i	$0.351066\pi$
$211$	−7.95208	+	13.7734i	−0.547443	+	0.948200i	−0.998449	+	0.0556786i	$0.982268\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.69560	−	2.93686i	−0.115639	−	0.200292i
$216$		0			0
$217$	−6.04811	−	1.86921i	−0.410573	−	0.126890i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	5.70023	−	3.29103i	0.383439	−	0.221379i
$222$		0			0
$223$	−2.79336	+	1.61275i	−0.187057	+	0.107998i	−0.590604	−	0.806961i	$-0.701111\pi$
$223$	−2.79336	+	1.61275i	−0.187057	+	0.107998i	0.403547	+	0.914959i	$0.367777\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.19265			−0.411021			−0.205510	−	0.978655i	$-0.565885\pi$
$227$	−6.19265			−0.411021			−0.205510	+	0.978655i	$0.565885\pi$
$228$		0			0
$229$		−	19.1873i		−	1.26793i	−0.773361	−	0.633965i	$-0.781426\pi$
$229$		−	19.1873i		−	1.26793i	0.773361	−	0.633965i	$-0.218574\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.45069	+	1.99225i	−0.226062	+	0.130517i	−0.608754	−	0.793359i	$-0.708330\pi$
$233$	−3.45069	+	1.99225i	−0.226062	+	0.130517i	0.382692	+	0.923876i	$0.374997\pi$
$234$		0			0
$235$	−1.97463	+	3.42016i	−0.128811	+	0.223107i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−13.2139	−	7.62905i	−0.854736	−	0.493482i	0.00750987	−	0.999972i	$-0.497610\pi$
$239$	−13.2139	−	7.62905i	−0.854736	−	0.493482i	−0.862246	+	0.506490i	$0.830943\pi$
$240$		0			0
$241$		−	8.79681i		−	0.566653i	−0.959024	−	0.283326i	$-0.908562\pi$
$241$		−	8.79681i		−	0.566653i	0.959024	−	0.283326i	$-0.0914379\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.560344	+	7.36947i	−0.0357991	+	0.470818i
$246$		0			0
$247$	2.01540			0.128237
$248$		0			0
$249$		0			0
$250$		0			0
$251$	9.38549			0.592407			0.296204	−	0.955125i	$-0.404279\pi$
$251$	9.38549			0.592407			0.296204	+	0.955125i	$0.404279\pi$
$252$		0			0
$253$	27.4860			1.72803
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.65183			−0.290173			−0.145087	−	0.989419i	$-0.546346\pi$
$257$	−4.65183			−0.290173			−0.145087	+	0.989419i	$0.546346\pi$
$258$		0			0
$259$	−5.69042	+	18.4122i	−0.353585	+	1.14408i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			21.1175i			1.30216i	0.759010	+	0.651079i	$0.225683\pi$
$263$			21.1175i			1.30216i	−0.759010	+	0.651079i	$0.774317\pi$
$264$		0			0
$265$	6.36084	+	3.67243i	0.390743	+	0.225596i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	5.87450	−	10.1749i	0.358175	−	0.620377i	−0.629481	−	0.777016i	$-0.716733\pi$
$269$	5.87450	−	10.1749i	0.358175	−	0.620377i	0.987656	+	0.156639i	$0.0500659\pi$
$270$		0			0
$271$	−6.24601	+	3.60613i	−0.379418	+	0.219057i	−0.677565	−	0.735463i	$-0.736965\pi$
$271$	−6.24601	+	3.60613i	−0.379418	+	0.219057i	0.298147	+	0.954520i	$0.403631\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			24.2629i			1.46311i
$276$		0			0
$277$	0.275860			0.0165749			0.00828743	−	0.999966i	$-0.497362\pi$
$277$	0.275860			0.0165749			0.00828743	+	0.999966i	$0.497362\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	14.7254	−	8.50170i	0.878442	−	0.507169i	0.00829763	−	0.999966i	$-0.497359\pi$
$281$	14.7254	−	8.50170i	0.878442	−	0.507169i	0.870144	+	0.492797i	$0.164025\pi$
$282$		0			0
$283$	4.14236	−	2.39159i	0.246238	−	0.142165i	−0.371803	−	0.928312i	$-0.621260\pi$
$283$	4.14236	−	2.39159i	0.246238	−	0.142165i	0.618040	+	0.786146i	$0.287927\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	9.29317	−	2.11578i	0.548558	−	0.124890i
$288$		0			0
$289$	−12.8623	−	22.2782i	−0.756608	−	1.31048i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−11.8580	+	20.5386i	−0.692750	+	1.19988i	0.278184	+	0.960528i	$0.410268\pi$
$293$	−11.8580	+	20.5386i	−0.692750	+	1.19988i	−0.970933	+	0.239350i	$0.923066\pi$
$294$		0			0
$295$	7.04320	+	12.1992i	0.410071	+	0.710264i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.21604	−	3.83830i	0.128157	−	0.221975i
$300$		0			0
$301$	−2.50923	+	8.11901i	−0.144630	+	0.467972i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	7.50406	+	4.33247i	0.429681	+	0.248076i
$306$		0			0
$307$		−	8.38070i		−	0.478312i	−0.970981	−	0.239156i	$-0.923129\pi$
$307$		−	8.38070i		−	0.478312i	0.970981	−	0.239156i	$-0.0768707\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−8.39585	−	14.5420i	−0.476085	−	0.824603i	0.523540	−	0.852001i	$-0.324611\pi$
$311$	−8.39585	−	14.5420i	−0.476085	−	0.824603i	−0.999625	+	0.0273979i	$0.991278\pi$
$312$		0			0
$313$	−10.8945	−	6.28994i	−0.615793	−	0.355528i	0.159436	−	0.987208i	$-0.449032\pi$
$313$	−10.8945	−	6.28994i	−0.615793	−	0.355528i	−0.775229	+	0.631680i	$0.782366\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.61807	−	5.55300i	−0.540205	−	0.311887i	0.204957	−	0.978771i	$-0.434294\pi$
$317$	−9.61807	−	5.55300i	−0.540205	−	0.311887i	−0.745162	+	0.666884i	$0.767628\pi$
$318$		0			0
$319$	22.0952	+	38.2701i	1.23710	+	2.14271i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	13.0821i		−	0.727910i
$324$		0			0
$325$	3.38822	+	1.95619i	0.187945	+	0.108510i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	9.64943	−	2.19689i	0.531991	−	0.121118i
$330$		0			0
$331$	−2.07127	+	3.58754i	−0.113847	+	0.197189i	−0.917318	−	0.398154i	$-0.869651\pi$
$331$	−2.07127	+	3.58754i	−0.113847	+	0.197189i	0.803471	+	0.595344i	$0.202984\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.0648233	+	0.112277i	0.00354168	+	0.00613437i
$336$		0			0
$337$	14.7897	−	25.6166i	0.805649	−	1.39542i	−0.110204	−	0.993909i	$-0.535150\pi$
$337$	14.7897	−	25.6166i	0.805649	−	1.39542i	0.915852	−	0.401515i	$-0.131516\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−7.47094	−	12.9400i	−0.404574	−	0.700743i
$342$		0			0
$343$	14.4986	−	11.5235i	0.782850	−	0.622211i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.42191	+	0.820940i	−0.0763321	+	0.0440704i	−0.537680	−	0.843149i	$-0.680699\pi$
$347$	−1.42191	+	0.820940i	−0.0763321	+	0.0440704i	0.461348	+	0.887219i	$0.347366\pi$
$348$		0			0
$349$	−17.5869	+	10.1538i	−0.941405	+	0.543520i	−0.890400	−	0.455178i	$-0.849576\pi$
$349$	−17.5869	+	10.1538i	−0.941405	+	0.543520i	−0.0510046	+	0.998698i	$0.516242\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−17.7337			−0.943872			−0.471936	−	0.881633i	$-0.656445\pi$
$353$	−17.7337			−0.943872			−0.471936	+	0.881633i	$0.656445\pi$
$354$		0			0
$355$			5.67691i			0.301299i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−23.6573	+	13.6585i	−1.24858	+	0.720871i	−0.970827	−	0.239781i	$-0.922924\pi$
$359$	−23.6573	+	13.6585i	−1.24858	+	0.720871i	−0.277757	+	0.960651i	$0.589591\pi$
$360$		0			0
$361$	−7.49715	+	12.9854i	−0.394587	+	0.683444i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	15.2491	+	8.80406i	0.798173	+	0.460825i
$366$		0			0
$367$			1.88999i			0.0986565i	0.998783	+	0.0493283i	$0.0157080\pi$
$367$			1.88999i			0.0986565i	−0.998783	+	0.0493283i	$0.984292\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.08578	−	17.9461i	−0.212123	−	0.931713i
$372$		0			0
$373$	18.1173			0.938080			0.469040	−	0.883177i	$-0.344600\pi$
$373$	18.1173			0.938080			0.469040	+	0.883177i	$0.344600\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	7.12567			0.366991
$378$		0			0
$379$	3.05133			0.156736			0.0783682	−	0.996924i	$-0.475029\pi$
$379$	3.05133			0.156736			0.0783682	+	0.996924i	$0.475029\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−17.7393			−0.906438			−0.453219	−	0.891399i	$-0.649725\pi$
$383$	−17.7393			−0.906438			−0.453219	+	0.891399i	$0.649725\pi$
$384$		0			0
$385$	−12.7943	+	11.8585i	−0.652060	+	0.604363i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	21.0907i		−	1.06934i	−0.845061	−	0.534670i	$-0.820436\pi$
$389$		−	21.0907i		−	1.06934i	0.845061	−	0.534670i	$-0.179564\pi$
$390$		0			0
$391$	−24.9147	−	14.3845i	−1.25999	−	0.727456i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.67872	+	8.10378i	−0.235412	+	0.407745i
$396$		0			0
$397$	19.7684	−	11.4133i	0.992147	−	0.572816i	0.0862315	−	0.996275i	$-0.472518\pi$
$397$	19.7684	−	11.4133i	0.992147	−	0.572816i	0.905915	+	0.423459i	$0.139184\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	1.61190i		−	0.0804944i	−0.999190	−	0.0402472i	$-0.987185\pi$
$401$		−	1.61190i		−	0.0804944i	0.999190	−	0.0402472i	$-0.0128145\pi$
$402$		0			0
$403$	−2.40937			−0.120019
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−39.3933	+	22.7437i	−1.95265	+	1.12737i
$408$		0			0
$409$	−19.9023	+	11.4906i	−0.984103	+	0.568172i	−0.903506	−	0.428575i	$-0.859016\pi$
$409$	−19.9023	+	11.4906i	−0.984103	+	0.568172i	−0.0805967	+	0.996747i	$0.525683\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.4229	−	33.7248i	0.512876	−	1.65949i
$414$		0			0
$415$	−1.13678	−	1.96896i	−0.0558022	−	0.0966522i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	9.46660	−	16.3966i	0.462474	−	0.801028i	−0.536610	−	0.843830i	$-0.680295\pi$
$419$	9.46660	−	16.3966i	0.462474	−	0.801028i	0.999084	+	0.0428027i	$0.0136287\pi$
$420$		0			0
$421$	−9.69784	−	16.7971i	−0.472644	−	0.818643i	0.526866	−	0.849948i	$-0.323367\pi$
$421$	−9.69784	−	16.7971i	−0.472644	−	0.818643i	−0.999510	+	0.0313053i	$0.990034\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.6978	−	21.9932i	0.615933	−	1.06683i
$426$		0			0
$427$	−4.82011	−	21.1715i	−0.233262	−	1.02456i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	21.5507	+	12.4423i	1.03806	+	0.599323i	0.919283	−	0.393598i	$-0.128770\pi$
$431$	21.5507	+	12.4423i	1.03806	+	0.599323i	0.118776	+	0.992921i	$0.462103\pi$
$432$		0			0
$433$			26.4665i			1.27190i	0.771731	+	0.635949i	$0.219391\pi$
$433$			26.4665i			1.27190i	−0.771731	+	0.635949i	$0.780609\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.40449	−	7.62879i	−0.210695	−	0.364935i
$438$		0			0
$439$	−23.7117	−	13.6900i	−1.13170	−	0.653386i	−0.187336	−	0.982296i	$-0.559985\pi$
$439$	−23.7117	−	13.6900i	−1.13170	−	0.653386i	−0.944361	+	0.328910i	$0.893319\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	25.6713	+	14.8213i	1.21968	+	0.704183i	0.964850	−	0.262802i	$-0.0846467\pi$
$443$	25.6713	+	14.8213i	1.21968	+	0.704183i	0.254831	+	0.966985i	$0.417980\pi$
$444$		0			0
$445$	2.35660	+	4.08175i	0.111713	+	0.193493i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			18.2726i			0.862339i	0.902271	+	0.431170i	$0.141899\pi$
$449$			18.2726i			0.862339i	−0.902271	+	0.431170i	$0.858101\pi$
$450$		0			0
$451$	19.4825	+	11.2482i	0.917394	+	0.529658i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.624445	+	2.74276i	0.0292744	+	0.128583i
$456$		0			0
$457$	8.98232	−	15.5578i	0.420175	−	0.727765i	−0.575781	−	0.817604i	$-0.695302\pi$
$457$	8.98232	−	15.5578i	0.420175	−	0.727765i	0.995956	+	0.0898389i	$0.0286352\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6.51625	+	11.2865i	0.303492	+	0.525664i	0.976924	−	0.213585i	$-0.0685140\pi$
$461$	6.51625	+	11.2865i	0.303492	+	0.525664i	−0.673432	+	0.739249i	$0.735181\pi$
$462$		0			0
$463$	4.24422	−	7.35121i	0.197246	−	0.341640i	−0.750389	−	0.660997i	$-0.770134\pi$
$463$	4.24422	−	7.35121i	0.197246	−	0.341640i	0.947634	+	0.319357i	$0.103467\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.895025	+	1.55023i	0.0414168	+	0.0717360i	0.885991	−	0.463703i	$-0.153480\pi$
$467$	0.895025	+	1.55023i	0.0414168	+	0.0717360i	−0.844574	+	0.535439i	$0.820146\pi$
$468$		0			0
$469$	0.0959287	−	0.310393i	0.00442958	−	0.0143326i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−17.3708	+	10.0290i	−0.798709	+	0.461135i
$474$		0			0
$475$	6.73424	−	3.88801i	0.308988	−	0.178394i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−24.6379			−1.12573			−0.562867	−	0.826547i	$-0.690302\pi$
$479$	−24.6379			−1.12573			−0.562867	+	0.826547i	$0.690302\pi$
$480$		0			0
$481$			7.33482i			0.334439i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.01439	−	0.585656i	0.0460609	−	0.0265933i
$486$		0			0
$487$	−13.1846	+	22.8364i	−0.597450	+	1.03481i	0.395746	+	0.918360i	$0.370486\pi$
$487$	−13.1846	+	22.8364i	−0.597450	+	1.03481i	−0.993196	+	0.116454i	$0.962847\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	21.0365	+	12.1454i	0.949365	+	0.548116i	0.892884	−	0.450288i	$-0.148679\pi$
$491$	21.0365	+	12.1454i	0.949365	+	0.548116i	0.0564812	+	0.998404i	$0.482012\pi$
$492$		0			0
$493$		−	46.2533i		−	2.08314i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	10.4334	−	9.67020i	0.468002	−	0.433768i
$498$		0			0
$499$	33.0439			1.47925			0.739625	−	0.673020i	$-0.235003\pi$
$499$	33.0439			1.47925			0.739625	+	0.673020i	$0.235003\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	31.5400			1.40630			0.703149	−	0.711043i	$-0.251777\pi$
$503$	31.5400			1.40630			0.703149	+	0.711043i	$0.251777\pi$
$504$		0			0
$505$	−6.11205			−0.271983
$506$		0			0
$507$		0			0
$508$		0			0
$509$	10.7247			0.475365			0.237683	−	0.971343i	$-0.423612\pi$
$509$	10.7247			0.475365			0.237683	+	0.971343i	$0.423612\pi$
$510$		0			0
$511$	−9.79500	−	43.0228i	−0.433305	−	1.90322i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	20.8729i		−	0.919768i
$516$		0			0
$517$	20.2294	+	11.6794i	0.889686	+	0.513661i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−7.64350	+	13.2389i	−0.334868	+	0.580008i	−0.983459	−	0.181128i	$-0.942025\pi$
$521$	−7.64350	+	13.2389i	−0.334868	+	0.580008i	0.648591	+	0.761137i	$0.275358\pi$
$522$		0			0
$523$	28.6654	−	16.5500i	1.25345	−	0.723681i	0.281659	−	0.959515i	$-0.409115\pi$
$523$	28.6654	−	16.5500i	1.25345	−	0.723681i	0.971793	+	0.235834i	$0.0757820\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			15.6394i			0.681262i
$528$		0			0
$529$	3.62814			0.157745
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3.14153	−	1.81376i	0.136075	−	0.0785629i
$534$		0			0
$535$	5.80991	−	3.35435i	0.251184	−	0.145021i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	43.5884	+	3.31429i	1.87749	+	0.142756i
$540$		0			0
$541$	−16.2012	−	28.0613i	−0.696543	−	1.20645i	−0.969658	−	0.244466i	$-0.921387\pi$
$541$	−16.2012	−	28.0613i	−0.696543	−	1.20645i	0.273115	−	0.961981i	$-0.411946\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.09753	+	1.90099i	−0.0470132	+	0.0814293i
$546$		0			0
$547$	4.77988	+	8.27900i	0.204373	+	0.353984i	0.949933	−	0.312454i	$-0.101151\pi$
$547$	4.77988	+	8.27900i	0.204373	+	0.353984i	−0.745560	+	0.666439i	$0.767818\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.08130	−	12.2652i	0.301673	−	0.522514i
$552$		0			0
$553$	22.8635	−	5.20534i	0.972255	−	0.221353i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	16.6963	+	9.63963i	0.707446	+	0.408444i	0.810115	−	0.586271i	$-0.199405\pi$
$557$	16.6963	+	9.63963i	0.707446	+	0.408444i	−0.102669	+	0.994716i	$0.532738\pi$
$558$		0			0
$559$			3.23434i			0.136798i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.71960	+	2.97844i	0.0724725	+	0.125526i	0.899984	−	0.435922i	$-0.143578\pi$
$563$	1.71960	+	2.97844i	0.0724725	+	0.125526i	−0.827512	+	0.561448i	$0.810244\pi$
$564$		0			0
$565$	13.6243	+	7.86602i	0.573180	+	0.330926i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−29.9406	−	17.2862i	−1.25518	−	0.724677i	−0.283044	−	0.959107i	$-0.591344\pi$
$569$	−29.9406	−	17.2862i	−1.25518	−	0.724677i	−0.972133	+	0.234430i	$0.924678\pi$
$570$		0			0
$571$	23.7474	+	41.1317i	0.993797	+	1.72131i	0.593205	+	0.805051i	$0.297862\pi$
$571$	23.7474	+	41.1317i	0.993797	+	1.72131i	0.400592	+	0.916256i	$0.368804\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	17.1003i		−	0.713132i
$576$		0			0
$577$	16.6404	+	9.60732i	0.692748	+	0.399958i	0.804641	−	0.593762i	$-0.202358\pi$
$577$	16.6404	+	9.60732i	0.692748	+	0.399958i	−0.111893	+	0.993720i	$0.535691\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.68226	+	5.44321i	−0.0697918	+	0.225822i
$582$		0			0
$583$	21.7215	−	37.6227i	0.899611	−	1.55817i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.1279	−	21.0061i	−0.500570	−	0.867013i	−1.00000		0.000658772i	$-0.999790\pi$
$587$	−12.1279	−	21.0061i	−0.500570	−	0.867013i	0.499429	−	0.866355i	$-0.333543\pi$
$588$		0			0
$589$	−2.39436	+	4.14716i	−0.0986579	+	0.170881i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.31832	+	2.28340i	0.0541371	+	0.0937681i	0.891824	−	0.452383i	$-0.149426\pi$
$593$	1.31832	+	2.28340i	0.0541371	+	0.0937681i	−0.837687	+	0.546151i	$0.816093\pi$
$594$		0			0
$595$	17.8035	−	4.05332i	0.729871	−	0.166170i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−32.8545	+	18.9686i	−1.34240	+	0.775034i	−0.987159	−	0.159741i	$-0.948934\pi$
$599$	−32.8545	+	18.9686i	−1.34240	+	0.775034i	−0.355240	+	0.934775i	$0.615601\pi$
$600$		0			0
$601$	26.3440	−	15.2097i	1.07459	−	0.620417i	0.145161	−	0.989408i	$-0.453630\pi$
$601$	26.3440	−	15.2097i	1.07459	−	0.620417i	0.929433	+	0.368991i	$0.120297\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−29.5616			−1.20185
$606$		0			0
$607$		−	44.4970i		−	1.80608i	−0.429557	−	0.903040i	$-0.641330\pi$
$607$		−	44.4970i		−	1.80608i	0.429557	−	0.903040i	$-0.358670\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.26197	−	1.88330i	0.131965	−	0.0761901i
$612$		0			0
$613$	−23.2533	+	40.2759i	−0.939192	+	1.62673i	−0.172210	+	0.985060i	$0.555091\pi$
$613$	−23.2533	+	40.2759i	−0.939192	+	1.62673i	−0.766982	+	0.641668i	$0.778243\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−18.9058	−	10.9153i	−0.761118	−	0.439432i	0.0685792	−	0.997646i	$-0.478153\pi$
$617$	−18.9058	−	10.9153i	−0.761118	−	0.439432i	−0.829697	+	0.558214i	$0.811487\pi$
$618$		0			0
$619$		−	7.27326i		−	0.292337i	−0.989260	−	0.146169i	$-0.953306\pi$
$619$		−	7.27326i		−	0.292337i	0.989260	−	0.146169i	$-0.0466942\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.48741	−	11.2841i	0.139720	−	0.452086i
$624$		0			0
$625$	9.52135			0.380854
$626$		0			0
$627$		0			0
$628$		0			0
$629$	47.6109			1.89837
$630$		0			0
$631$	−39.2496			−1.56250			−0.781252	−	0.624216i	$-0.785418\pi$
$631$	−39.2496			−1.56250			−0.781252	+	0.624216i	$0.785418\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−19.7270			−0.782842
$636$		0			0
$637$	3.97713	−	5.81973i	0.157579	−	0.230586i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			34.5008i			1.36270i	0.731957	+	0.681351i	$0.238607\pi$
$641$			34.5008i			1.36270i	−0.731957	+	0.681351i	$0.761393\pi$
$642$		0			0
$643$	5.08992	+	2.93867i	0.200727	+	0.115890i	0.596994	−	0.802245i	$-0.296361\pi$
$643$	5.08992	+	2.93867i	0.200727	+	0.115890i	−0.396268	+	0.918135i	$0.629695\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	14.6539	−	25.3814i	0.576106	−	0.997844i	−0.419815	−	0.907610i	$-0.637905\pi$
$647$	14.6539	−	25.3814i	0.576106	−	0.997844i	0.995921	−	0.0902346i	$-0.0287617\pi$
$648$		0			0
$649$	72.1549	−	41.6587i	2.83233	−	1.63525i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	42.6083i		−	1.66739i	−0.552224	−	0.833696i	$-0.686221\pi$
$653$		−	42.6083i		−	1.66739i	0.552224	−	0.833696i	$-0.313779\pi$
$654$		0			0
$655$	−9.01803			−0.352363
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−19.0891	+	11.0211i	−0.743608	+	0.429322i	−0.823380	−	0.567491i	$-0.807914\pi$
$659$	−19.0891	+	11.0211i	−0.743608	+	0.429322i	0.0797719	+	0.996813i	$0.474581\pi$
$660$		0			0
$661$	12.7181	−	7.34280i	0.494677	−	0.285602i	−0.231836	−	0.972755i	$-0.574473\pi$
$661$	12.7181	−	7.34280i	0.494677	−	0.285602i	0.726513	+	0.687153i	$0.241140\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	5.34157	+	1.65085i	0.207137	+	0.0640170i
$666$		0			0
$667$	−15.5725	−	26.9724i	−0.602971	−	1.04438i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	25.6254	−	44.3845i	0.989258	−	1.71344i
$672$		0			0
$673$	18.8645	+	32.6743i	0.727173	+	1.25950i	0.958073	+	0.286524i	$0.0924997\pi$
$673$	18.8645	+	32.6743i	0.727173	+	1.25950i	−0.230900	+	0.972978i	$0.574167\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−10.7985	+	18.7036i	−0.415021	+	0.718838i	−0.995431	−	0.0954871i	$-0.969559\pi$
$677$	−10.7985	+	18.7036i	−0.415021	+	0.718838i	0.580410	+	0.814325i	$0.302892\pi$
$678$		0			0
$679$	−2.80429	−	0.866682i	−0.107619	−	0.0332602i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−15.8213	−	9.13444i	−0.605386	−	0.349520i	0.165772	−	0.986164i	$-0.446989\pi$
$683$	−15.8213	−	9.13444i	−0.605386	−	0.349520i	−0.771157	+	0.636645i	$0.780322\pi$
$684$		0			0
$685$		−	13.0900i		−	0.500145i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−3.50257	−	6.06662i	−0.133437	−	0.231120i
$690$		0			0
$691$	8.58995	+	4.95941i	0.326777	+	0.188665i	0.654409	−	0.756140i	$-0.272917\pi$
$691$	8.58995	+	4.95941i	0.326777	+	0.188665i	−0.327632	+	0.944805i	$0.606251\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−16.3430	−	9.43561i	−0.619924	−	0.357913i
$696$		0			0
$697$	−11.7733	−	20.3919i	−0.445945	−	0.772400i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			4.41270i			0.166665i	0.996522	+	0.0833327i	$0.0265564\pi$
$701$			4.41270i			0.166665i	−0.996522	+	0.0833327i	$0.973444\pi$
$702$		0			0
$703$	12.6252	+	7.28914i	0.476167	+	0.274915i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	10.4114	+	11.2331i	0.391562	+	0.422465i
$708$		0			0
$709$	−16.7513	+	29.0141i	−0.629108	+	1.08965i	0.358623	+	0.933482i	$0.383246\pi$
$709$	−16.7513	+	29.0141i	−0.629108	+	1.08965i	−0.987731	+	0.156165i	$0.950087\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	5.26545	+	9.12003i	0.197193	+	0.341548i
$714$		0			0
$715$	−3.31977	+	5.75000i	−0.124152	+	0.215038i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	3.57296	+	6.18855i	0.133249	+	0.230794i	0.924927	−	0.380144i	$-0.124126\pi$
$719$	3.57296	+	6.18855i	0.133249	+	0.230794i	−0.791678	+	0.610938i	$0.790792\pi$
$720$		0			0
$721$	−38.3615	+	35.5554i	−1.42866	+	1.32415i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	23.8096	−	13.7465i	0.884267	−	0.510532i
$726$		0			0
$727$	8.71161	−	5.02965i	0.323096	−	0.186539i	−0.329676	−	0.944094i	$-0.606939\pi$
$727$	8.71161	−	5.02965i	0.323096	−	0.186539i	0.652772	+	0.757555i	$0.273606\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	20.9944			0.776504
$732$		0			0
$733$		−	25.2511i		−	0.932671i	−0.884608	−	0.466335i	$-0.845574\pi$
$733$		−	25.2511i		−	0.932671i	0.884608	−	0.466335i	$-0.154426\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.664091	−	0.383413i	0.0244621	−	0.0141232i
$738$		0			0
$739$	−7.29244	+	12.6309i	−0.268257	+	0.464634i	−0.968412	−	0.249357i	$-0.919781\pi$
$739$	−7.29244	+	12.6309i	−0.268257	+	0.464634i	0.700155	+	0.713991i	$0.253114\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−26.0383	−	15.0332i	−0.955251	−	0.551515i	−0.0605431	−	0.998166i	$-0.519283\pi$
$743$	−26.0383	−	15.0332i	−0.955251	−	0.551515i	−0.894708	+	0.446651i	$0.852617\pi$
$744$		0			0
$745$			7.79737i			0.285674i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−16.0616	−	4.96394i	−0.586878	−	0.181378i
$750$		0			0
$751$	−5.52772			−0.201709			−0.100855	−	0.994901i	$-0.532158\pi$
$751$	−5.52772			−0.201709			−0.100855	+	0.994901i	$0.532158\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−10.8535			−0.394999
$756$		0			0
$757$	−22.2176			−0.807512			−0.403756	−	0.914867i	$-0.632296\pi$
$757$	−22.2176			−0.807512			−0.403756	+	0.914867i	$0.632296\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−39.5470			−1.43358			−0.716789	−	0.697290i	$-0.754389\pi$
$761$	−39.5470			−1.43358			−0.716789	+	0.697290i	$0.754389\pi$
$762$		0			0
$763$	5.36332	−	1.22107i	0.194165	−	0.0442056i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	13.4348i		−	0.485104i
$768$		0			0
$769$	27.1448	+	15.6720i	0.978865	+	0.565148i	0.901927	−	0.431888i	$-0.142152\pi$
$769$	27.1448	+	15.6720i	0.978865	+	0.565148i	0.0769379	+	0.997036i	$0.475486\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	5.11009	−	8.85093i	0.183797	−	0.318346i	−0.759373	−	0.650655i	$-0.774494\pi$
$773$	5.11009	−	8.85093i	0.183797	−	0.318346i	0.943171	+	0.332309i	$0.107828\pi$
$774$		0			0
$775$	−8.05062	+	4.64803i	−0.289187	+	0.166962i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	7.20988i		−	0.258321i
$780$		0			0
$781$	33.5774			1.20150
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−14.2073	+	8.20260i	−0.507081	+	0.292763i
$786$		0			0
$787$	41.4304	−	23.9198i	1.47683	−	0.852650i	0.477176	−	0.878808i	$-0.341661\pi$
$787$	41.4304	−	23.9198i	1.47683	−	0.852650i	0.999658	+	0.0261578i	$0.00832724\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−8.75138	−	38.4389i	−0.311163	−	1.36673i
$792$		0			0
$793$	−4.13207	−	7.15696i	−0.146734	−	0.254151i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−18.7811	+	32.5297i	−0.665259	+	1.15226i	0.313956	+	0.949438i	$0.398346\pi$
$797$	−18.7811	+	32.5297i	−0.665259	+	1.15226i	−0.979215	+	0.202825i	$0.934988\pi$
$798$		0			0
$799$	−12.2246	−	21.1737i	−0.432476	−	0.749071i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	52.0737	−	90.1942i	1.83764	−	3.18289i
$804$		0			0
$805$	9.01735	−	8.35773i	0.317820	−	0.294571i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−4.88303	−	2.81922i	−0.171678	−	0.0991184i	0.411699	−	0.911320i	$-0.364936\pi$
$809$	−4.88303	−	2.81922i	−0.171678	−	0.0991184i	−0.583377	+	0.812202i	$0.698269\pi$
$810$		0			0
$811$			29.2693i			1.02778i	0.857855	+	0.513892i	$0.171797\pi$
$811$			29.2693i			1.02778i	−0.857855	+	0.513892i	$0.828203\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.09856	−	3.63481i	−0.0735093	−	0.127322i
$816$		0			0
$817$	5.56716	+	3.21420i	0.194770	+	0.112451i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−41.3052	−	23.8476i	−1.44156	−	0.832286i	−0.443608	−	0.896221i	$-0.646302\pi$
$821$	−41.3052	−	23.8476i	−1.44156	−	0.832286i	−0.997954	+	0.0639351i	$0.979635\pi$
$822$		0			0
$823$	−19.7712	−	34.2447i	−0.689180	−	1.19369i	−0.972104	−	0.234552i	$-0.924638\pi$
$823$	−19.7712	−	34.2447i	−0.689180	−	1.19369i	0.282924	−	0.959142i	$-0.408696\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	27.9149i		−	0.970696i	−0.874321	−	0.485348i	$-0.838693\pi$
$827$		−	27.9149i		−	0.970696i	0.874321	−	0.485348i	$-0.161307\pi$
$828$		0			0
$829$	−19.5489	−	11.2866i	−0.678962	−	0.391999i	0.120502	−	0.992713i	$-0.461550\pi$
$829$	−19.5489	−	11.2866i	−0.678962	−	0.391999i	−0.799464	+	0.600714i	$0.794883\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−37.7763	−	25.8158i	−1.30887	−	0.894466i
$834$		0			0
$835$	−3.85467	+	6.67648i	−0.133396	+	0.231049i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	25.2760	+	43.7794i	0.872625	+	1.51143i	0.859271	+	0.511520i	$0.170918\pi$
$839$	25.2760	+	43.7794i	0.872625	+	1.51143i	0.0133541	+	0.999911i	$0.495749\pi$
$840$		0			0
$841$	10.5367	−	18.2501i	0.363334	−	0.629312i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.32752	−	10.9596i	−0.217673	−	0.377021i
$846$		0			0
$847$	50.3560	+	54.3302i	1.73025	+	1.86681i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	27.7641	−	16.0296i	0.951740	−	0.549487i
$852$		0			0
$853$	−31.0102	+	17.9037i	−1.06177	+	0.613013i	−0.925921	−	0.377717i	$-0.876709\pi$
$853$	−31.0102	+	17.9037i	−1.06177	+	0.613013i	−0.135848	+	0.990730i	$0.543376\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	27.6398			0.944157			0.472079	−	0.881556i	$-0.343504\pi$
$857$	27.6398			0.944157			0.472079	+	0.881556i	$0.343504\pi$
$858$		0			0
$859$			32.3990i			1.10544i	0.833367	+	0.552721i	$0.186410\pi$
$859$			32.3990i			1.10544i	−0.833367	+	0.552721i	$0.813590\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−14.5080	+	8.37622i	−0.493859	+	0.285130i	−0.726174	−	0.687511i	$-0.758703\pi$
$863$	−14.5080	+	8.37622i	−0.493859	+	0.285130i	0.232315	+	0.972641i	$0.425370\pi$
$864$		0			0
$865$	4.46309	−	7.73029i	0.151749	−	0.262838i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	47.9317	+	27.6734i	1.62597	+	0.938755i
$870$		0			0
$871$		−	0.123650i		−	0.00418972i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	16.8722	+	18.2038i	0.570385	+	0.615401i
$876$		0			0
$877$	−26.0180			−0.878565			−0.439282	−	0.898349i	$-0.644767\pi$
$877$	−26.0180			−0.878565			−0.439282	+	0.898349i	$0.644767\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	8.83562			0.297680			0.148840	−	0.988861i	$-0.452446\pi$
$881$	8.83562			0.297680			0.148840	+	0.988861i	$0.452446\pi$
$882$		0			0
$883$	12.1308			0.408234			0.204117	−	0.978946i	$-0.434568\pi$
$883$	12.1308			0.408234			0.204117	+	0.978946i	$0.434568\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	20.5105			0.688676			0.344338	−	0.938846i	$-0.388103\pi$
$887$	20.5105			0.688676			0.344338	+	0.938846i	$0.388103\pi$
$888$		0			0
$889$	33.6035	+	36.2555i	1.12702	+	1.21597i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	7.48628i		−	0.250519i
$894$		0			0
$895$	−0.0464332	−	0.0268082i	−0.00155209	−	0.000896100i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−8.46552	+	14.6627i	−0.282341	+	0.489029i
$900$		0			0
$901$	−39.3789	+	22.7354i	−1.31190	+	0.757427i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			2.79036i			0.0927546i
$906$		0			0
$907$	−42.4131			−1.40830			−0.704152	−	0.710049i	$-0.748673\pi$
$907$	−42.4131			−1.40830			−0.704152	+	0.710049i	$0.748673\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−6.19281	+	3.57542i	−0.205177	+	0.118459i	−0.599068	−	0.800698i	$-0.704462\pi$
$911$	−6.19281	+	3.57542i	−0.205177	+	0.118459i	0.393891	+	0.919157i	$0.371129\pi$
$912$		0			0
$913$	−11.6459	+	6.72373i	−0.385421	+	0.222523i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	15.3615	+	16.5739i	0.507283	+	0.547319i
$918$		0			0
$919$	−3.31427	−	5.74049i	−0.109328	−	0.189361i	0.806170	−	0.591683i	$-0.201536\pi$
$919$	−3.31427	−	5.74049i	−0.109328	−	0.189361i	−0.915498	+	0.402322i	$0.868203\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.70717	−	4.68895i	0.0891075	−	0.154339i
$924$		0			0
$925$	14.1500	+	24.5084i	0.465248	+	0.805833i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	6.48279	−	11.2285i	0.212693	−	0.368396i	−0.739863	−	0.672757i	$-0.765110\pi$
$929$	6.48279	−	11.2285i	0.212693	−	0.368396i	0.952557	+	0.304362i	$0.0984431\pi$
$930$		0			0
$931$	−6.06494	−	12.6292i	−0.198770	−	0.413905i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	37.3237	+	21.5489i	1.22062	+	0.704723i
$936$		0			0
$937$		−	29.9409i		−	0.978127i	−0.872248	−	0.489063i	$-0.837339\pi$
$937$		−	29.9409i		−	0.978127i	0.872248	−	0.489063i	$-0.162661\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	27.4460	+	47.5379i	0.894715	+	1.54969i	0.834157	+	0.551527i	$0.185955\pi$
$941$	27.4460	+	47.5379i	0.894715	+	1.54969i	0.0605579	+	0.998165i	$0.480712\pi$
$942$		0			0
$943$	−13.7311	−	7.92764i	−0.447145	−	0.258160i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.56505	−	1.48093i	−0.0833530	−	0.0481239i	0.457744	−	0.889084i	$-0.348658\pi$
$947$	−2.56505	−	1.48093i	−0.0833530	−	0.0481239i	−0.541097	+	0.840960i	$0.681991\pi$
$948$		0			0
$949$	−8.39683	−	14.5437i	−0.272573	−	0.472110i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	25.3530i		−	0.821264i	−0.911801	−	0.410632i	$-0.865308\pi$
$953$		−	25.3530i		−	0.821264i	0.911801	−	0.410632i	$-0.134692\pi$
$954$		0			0
$955$	−22.2059	−	12.8206i	−0.718565	−	0.414864i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−24.0577	+	22.2979i	−0.776864	+	0.720037i
$960$		0			0
$961$	−12.6376	+	21.8890i	−0.407665	+	0.706096i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	3.15621	+	5.46672i	0.101602	+	0.175980i
$966$		0			0
$967$	−10.3196	+	17.8741i	−0.331857	+	0.574794i	−0.982876	−	0.184268i	$-0.941009\pi$
$967$	−10.3196	+	17.8741i	−0.331857	+	0.574794i	0.651019	+	0.759062i	$0.274342\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−15.1851	−	26.3013i	−0.487312	−	0.844050i	0.512581	−	0.858639i	$-0.328689\pi$
$971$	−15.1851	−	26.3013i	−0.487312	−	0.844050i	−0.999894	+	0.0145888i	$0.995356\pi$
$972$		0			0
$973$	10.4976	+	46.1090i	0.336539	+	1.47819i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	4.43133	−	2.55843i	0.141771	−	0.0818514i	−0.427437	−	0.904045i	$-0.640583\pi$
$977$	4.43133	−	2.55843i	0.141771	−	0.0818514i	0.569208	+	0.822194i	$0.307250\pi$
$978$		0			0
$979$	24.1425	−	13.9387i	0.771596	−	0.445481i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	3.89768			0.124317			0.0621584	−	0.998066i	$-0.480202\pi$
$983$	3.89768			0.124317			0.0621584	+	0.998066i	$0.480202\pi$
$984$		0			0
$985$		−	0.117180i		−	0.00373368i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	12.2428	−	7.06836i	0.389297	−	0.224761i
$990$		0			0
$991$	7.39964	−	12.8166i	0.235057	−	0.407131i	−0.724232	−	0.689556i	$-0.757806\pi$
$991$	7.39964	−	12.8166i	0.235057	−	0.407131i	0.959289	+	0.282425i	$0.0911389\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−8.39990	−	4.84968i	−0.266295	−	0.153745i
$996$		0			0
$997$			31.4855i			0.997156i	0.866845	+	0.498578i	$0.166144\pi$
$997$			31.4855i			0.997156i	−0.866845	+	0.498578i	$0.833856\pi$
$998$		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.17.15		48
3.2	odd	2		1008.2.df.e.689.10		48
4.3	odd	2		1512.2.cx.a.17.15		48
7.5	odd	6		3024.2.ca.e.2609.15		48
9.2	odd	6		3024.2.ca.e.2033.15		48
9.7	even	3		1008.2.ca.e.353.18		48
12.11	even	2		504.2.cx.a.185.15	yes	48
21.5	even	6		1008.2.ca.e.257.18		48
28.19	even	6		1512.2.bs.a.1097.15		48
36.7	odd	6		504.2.bs.a.353.7	yes	48
36.11	even	6		1512.2.bs.a.521.15		48
63.47	even	6	inner	3024.2.df.e.1601.15		48
63.61	odd	6		1008.2.df.e.929.10		48
84.47	odd	6		504.2.bs.a.257.7	✓	48
252.47	odd	6		1512.2.cx.a.89.15		48
252.187	even	6		504.2.cx.a.425.15	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.7	✓	48	84.47	odd	6
504.2.bs.a.353.7	yes	48	36.7	odd	6
504.2.cx.a.185.15	yes	48	12.11	even	2
504.2.cx.a.425.15	yes	48	252.187	even	6
1008.2.ca.e.257.18		48	21.5	even	6
1008.2.ca.e.353.18		48	9.7	even	3
1008.2.df.e.689.10		48	3.2	odd	2
1008.2.df.e.929.10		48	63.61	odd	6
1512.2.bs.a.521.15		48	36.11	even	6
1512.2.bs.a.1097.15		48	28.19	even	6
1512.2.cx.a.17.15		48	4.3	odd	2
1512.2.cx.a.89.15		48	252.47	odd	6
3024.2.ca.e.2033.15		48	9.2	odd	6
3024.2.ca.e.2609.15		48	7.5	odd	6
3024.2.df.e.17.15		48	1.1	even	1	trivial
3024.2.df.e.1601.15		48	63.47	even	6	inner

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)

\(f(q)\)	\(=\)	\(q+1.05582 q^{5} +(-1.79851 - 1.94045i) q^{7} -6.24489i q^{11} +(-0.872074 - 0.503492i) q^{13} +(-3.26821 + 5.66070i) q^{17} +(-1.73329 + 1.00071i) q^{19} +4.40135i q^{23} -3.88524 q^{25} +(-6.12821 + 3.53813i) q^{29} +(2.07210 - 1.19633i) q^{31} +(-1.89890 - 2.04877i) q^{35} +(-3.64197 - 6.30808i) q^{37} +(-1.80119 + 3.11974i) q^{41} +(-1.60595 - 2.78159i) q^{43} +(-1.87024 + 3.23934i) q^{47} +(-0.530720 + 6.97985i) q^{49} +(6.02455 + 3.47827i) q^{53} -6.59348i q^{55} +(6.67084 + 11.5542i) q^{59} +(7.10733 + 4.10342i) q^{61} +(-0.920753 - 0.531597i) q^{65} +(0.0613962 + 0.106341i) q^{67} +5.37678i q^{71} +(14.4429 + 8.33860i) q^{73} +(-12.1179 + 11.2315i) q^{77} +(-4.43136 + 7.67534i) q^{79} +(-1.07668 - 1.86486i) q^{83} +(-3.45064 + 5.97668i) q^{85} +(2.23201 + 3.86595i) q^{89} +(0.591431 + 2.59775i) q^{91} +(-1.83004 + 1.05657i) q^{95} +(0.960756 - 0.554693i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{25} - 18 q^{29} - 18 q^{31} + 6 q^{41} + 6 q^{43} + 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} - 6 q^{79} + 18 q^{89} - 6 q^{91} - 54 q^{95}+O(q^{100}) \) 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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