LMFDB - Embedded newform 3024.2.r.m.2017.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(1009,3024)] 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, 2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.1009"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,3,0,-4,0,0,0,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.2091141441.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{6} + 3x^{5} - 15x^{4} + 9x^{3} + 9x^{2} - 27x + 81 $ x^8 - x^7 + x^6 + 3x^5 - 15x^4 + 9x^3 + 9x^2 - 27*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2017.1
Root			$1.65525 + 0.510048i$ of defining polynomial
Character	$\chi$	$=$	3024.2017
Dual form			3024.2.r.m.1009.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15525 - 2.00095i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.655250 + 1.13493i) q^{11} +(1.93281 + 3.34772i) q^{13} +0.326936 q^{17} -3.08232 q^{19} +(-1.81872 - 3.15011i) q^{23} +(-0.169204 + 0.293069i) q^{25} +(4.75152 - 8.22988i) q^{29} +(3.24904 + 5.62751i) q^{31} +2.31050 q^{35} -2.31050 q^{37} +(-4.74904 - 8.22558i) q^{41} +(0.0493786 - 0.0855263i) q^{43} +(-0.108354 + 0.187674i) q^{47} +(-0.500000 - 0.866025i) q^{49} -13.7921 q^{53} +3.02791 q^{55} +(1.22493 + 2.12163i) q^{59} +(7.68433 - 13.3097i) q^{61} +(4.46575 - 7.73490i) q^{65} +(-2.93529 - 5.08407i) q^{67} -1.77182 q^{71} -5.99504 q^{73} +(-0.655250 - 1.13493i) q^{77} +(-7.29594 + 12.6369i) q^{79} +(3.04116 - 5.26744i) q^{83} +(-0.377692 - 0.654183i) q^{85} -5.52224 q^{89} -3.86561 q^{91} +(3.56085 + 6.16757i) q^{95} +(2.99178 - 5.18192i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{5} - 4 q^{7} + 7 q^{11} + 3 q^{13} - 6 q^{17} + 8 q^{19} + 2 q^{23} - 5 q^{25} + 9 q^{29} - 3 q^{31} - 6 q^{35} + 6 q^{37} - 9 q^{41} - 8 q^{43} + 3 q^{47} - 4 q^{49} - 12 q^{53} + 56 q^{55}+ \cdots + 16 q^{97}+O(q^{100}) $ 8 * q + 3 * q^5 - 4 * q^7 + 7 * q^11 + 3 * q^13 - 6 * q^17 + 8 * q^19 + 2 * q^23 - 5 * q^25 + 9 * q^29 - 3 * q^31 - 6 * q^35 + 6 * q^37 - 9 * q^41 - 8 * q^43 + 3 * q^47 - 4 * q^49 - 12 * q^53 + 56 * q^55 + 10 * q^59 + 20 * q^61 - q^65 - 11 * q^67 - 6 * q^71 - 48 * q^73 + 7 * q^77 - 21 * q^79 + 8 * q^83 + 9 * q^85 - 12 * q^89 - 6 * q^91 + 36 * q^95 + 16 * q^97

Character values

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

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.15525	−	2.00095i	−0.516643	−	0.894853i	−0.999813	−	0.0193259i	$-0.993848\pi$
$5$	−1.15525	−	2.00095i	−0.516643	−	0.894853i	0.483170	−	0.875527i	$-0.339485\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.655250	+	1.13493i	−0.197565	+	0.342193i	−0.947738	−	0.319048i	$-0.896637\pi$
$11$	−0.655250	+	1.13493i	−0.197565	+	0.342193i	0.750173	+	0.661241i	$0.229970\pi$
$12$		0			0
$13$	1.93281	+	3.34772i	0.536064	+	0.928490i	0.999111	+	0.0421566i	$0.0134228\pi$
$13$	1.93281	+	3.34772i	0.536064	+	0.928490i	−0.463047	+	0.886334i	$0.653244\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.326936			0.0792936			0.0396468	−	0.999214i	$-0.487377\pi$
$17$	0.326936			0.0792936			0.0396468	+	0.999214i	$0.487377\pi$
$18$		0			0
$19$	−3.08232			−0.707133			−0.353566	−	0.935409i	$-0.615031\pi$
$19$	−3.08232			−0.707133			−0.353566	+	0.935409i	$0.615031\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.81872	−	3.15011i	−0.379229	−	0.656844i	0.611721	−	0.791073i	$-0.290477\pi$
$23$	−1.81872	−	3.15011i	−0.379229	−	0.656844i	−0.990950	+	0.134230i	$0.957144\pi$
$24$		0			0
$25$	−0.169204	+	0.293069i	−0.0338407	+	0.0586139i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.75152	−	8.22988i	0.882336	−	1.52825i	0.0335990	−	0.999435i	$-0.489303\pi$
$29$	4.75152	−	8.22988i	0.882336	−	1.52825i	0.848737	−	0.528815i	$-0.177364\pi$
$30$		0			0
$31$	3.24904	+	5.62751i	0.583545	+	1.01073i	0.995055	+	0.0993246i	$0.0316682\pi$
$31$	3.24904	+	5.62751i	0.583545	+	1.01073i	−0.411510	+	0.911405i	$0.634998\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.31050			0.390546
$36$		0			0
$37$	−2.31050			−0.379844			−0.189922	−	0.981799i	$-0.560823\pi$
$37$	−2.31050			−0.379844			−0.189922	+	0.981799i	$0.560823\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.74904	−	8.22558i	−0.741676	−	1.28462i	−0.951732	−	0.306931i	$-0.900698\pi$
$41$	−4.74904	−	8.22558i	−0.741676	−	1.28462i	0.210056	−	0.977689i	$-0.432635\pi$
$42$		0			0
$43$	0.0493786	−	0.0855263i	0.00753017	−	0.0130426i	−0.862236	−	0.506507i	$-0.830936\pi$
$43$	0.0493786	−	0.0855263i	0.00753017	−	0.0130426i	0.869766	+	0.493465i	$0.164270\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.108354	+	0.187674i	−0.0158050	+	0.0273750i	−0.873820	−	0.486250i	$-0.838364\pi$
$47$	−0.108354	+	0.187674i	−0.0158050	+	0.0273750i	0.858015	+	0.513625i	$0.171698\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−13.7921			−1.89450			−0.947249	−	0.320500i	$-0.896149\pi$
$53$	−13.7921			−1.89450			−0.947249	+	0.320500i	$0.896149\pi$
$54$		0			0
$55$	3.02791			0.408283
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.22493	+	2.12163i	0.159472	+	0.276213i	0.934678	−	0.355495i	$-0.115688\pi$
$59$	1.22493	+	2.12163i	0.159472	+	0.276213i	−0.775207	+	0.631708i	$0.782354\pi$
$60$		0			0
$61$	7.68433	−	13.3097i	0.983878	−	1.70413i	0.337057	−	0.941484i	$-0.390568\pi$
$61$	7.68433	−	13.3097i	0.983878	−	1.70413i	0.646821	−	0.762642i	$-0.276098\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.46575	−	7.73490i	0.553908	−	0.959397i
$66$		0			0
$67$	−2.93529	−	5.08407i	−0.358603	−	0.621118i	0.629125	−	0.777304i	$-0.283413\pi$
$67$	−2.93529	−	5.08407i	−0.358603	−	0.621118i	−0.987728	+	0.156186i	$0.950080\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.77182			−0.210277			−0.105138	−	0.994458i	$-0.533529\pi$
$71$	−1.77182			−0.210277			−0.105138	+	0.994458i	$0.533529\pi$
$72$		0			0
$73$	−5.99504			−0.701666			−0.350833	−	0.936438i	$-0.614101\pi$
$73$	−5.99504			−0.701666			−0.350833	+	0.936438i	$0.614101\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.655250	−	1.13493i	−0.0746726	−	0.129337i
$78$		0			0
$79$	−7.29594	+	12.6369i	−0.820857	+	1.42177i	0.0841876	+	0.996450i	$0.473171\pi$
$79$	−7.29594	+	12.6369i	−0.820857	+	1.42177i	−0.905045	+	0.425316i	$0.860163\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.04116	−	5.26744i	0.333811	−	0.578177i	−0.649445	−	0.760409i	$-0.724999\pi$
$83$	3.04116	−	5.26744i	0.333811	−	0.578177i	0.983256	+	0.182231i	$0.0583320\pi$
$84$		0			0
$85$	−0.377692	−	0.654183i	−0.0409665	−	0.0709561i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.52224			−0.585356			−0.292678	−	0.956211i	$-0.594546\pi$
$89$	−5.52224			−0.585356			−0.292678	+	0.956211i	$0.594546\pi$
$90$		0			0
$91$	−3.86561			−0.405226
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.56085	+	6.16757i	0.365336	+	0.632780i
$96$		0			0
$97$	2.99178	−	5.18192i	0.303769	−	0.526144i	−0.673217	−	0.739445i	$-0.735088\pi$
$97$	2.99178	−	5.18192i	0.303769	−	0.526144i	0.976987	+	0.213301i	$0.0684214\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.85105	+	6.67022i	−0.383194	+	0.663712i	−0.991517	−	0.129978i	$-0.958509\pi$
$101$	−3.85105	+	6.67022i	−0.383194	+	0.663712i	0.608323	+	0.793690i	$0.291843\pi$
$102$		0			0
$103$	2.03046	+	3.51686i	0.200067	+	0.346526i	0.948550	−	0.316628i	$-0.102551\pi$
$103$	2.03046	+	3.51686i	0.200067	+	0.346526i	−0.748483	+	0.663154i	$0.769217\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−14.0774			−1.36091			−0.680455	−	0.732790i	$-0.738218\pi$
$107$	−14.0774			−1.36091			−0.680455	+	0.732790i	$0.738218\pi$
$108$		0			0
$109$	−6.67306			−0.639164			−0.319582	−	0.947559i	$-0.603542\pi$
$109$	−6.67306			−0.639164			−0.319582	+	0.947559i	$0.603542\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.84918	−	6.66697i	−0.362100	−	0.627176i	0.626206	−	0.779658i	$-0.284607\pi$
$113$	−3.84918	−	6.66697i	−0.362100	−	0.627176i	−0.988306	+	0.152482i	$0.951273\pi$
$114$		0			0
$115$	−4.20215	+	7.27833i	−0.391852	+	0.678708i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.163468	+	0.283135i	−0.0149851	+	0.0259549i
$120$		0			0
$121$	4.64130	+	8.03896i	0.421936	+	0.730815i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−10.7706			−0.963352
$126$		0			0
$127$	−14.9847			−1.32968			−0.664838	−	0.746987i	$-0.731500\pi$
$127$	−14.9847			−1.32968			−0.664838	+	0.746987i	$0.731500\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.20788	−	9.02032i	−0.455015	−	0.788109i	0.543674	−	0.839296i	$-0.317033\pi$
$131$	−5.20788	−	9.02032i	−0.455015	−	0.788109i	−0.998689	+	0.0511876i	$0.983699\pi$
$132$		0			0
$133$	1.54116	−	2.66937i	0.133636	−	0.231464i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.13170	−	5.42426i	0.267559	−	0.463426i	−0.700672	−	0.713484i	$-0.747116\pi$
$137$	3.13170	−	5.42426i	0.267559	−	0.463426i	0.968231	+	0.250058i	$0.0804496\pi$
$138$		0			0
$139$	−10.0798	−	17.4588i	−0.854961	−	1.48084i	−0.876681	−	0.481071i	$-0.840248\pi$
$139$	−10.0798	−	17.4588i	−0.854961	−	1.48084i	0.0217207	−	0.999764i	$-0.493086\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−5.06588			−0.423631
$144$		0			0
$145$	−21.9568			−1.82341
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.50878	+	14.7376i	0.697067	+	1.20736i	0.969479	+	0.245174i	$0.0788452\pi$
$149$	8.50878	+	14.7376i	0.697067	+	1.20736i	−0.272412	+	0.962181i	$0.587821\pi$
$150$		0			0
$151$	−8.19641	+	14.1966i	−0.667014	+	1.15530i	0.311721	+	0.950174i	$0.399095\pi$
$151$	−8.19641	+	14.1966i	−0.667014	+	1.15530i	−0.978735	+	0.205129i	$0.934239\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	7.50691	−	13.0023i	0.602969	−	1.04437i
$156$		0			0
$157$	−10.2274	−	17.7144i	−0.816238	−	1.41377i	−0.908435	−	0.418025i	$-0.862722\pi$
$157$	−10.2274	−	17.7144i	−0.816238	−	1.41377i	0.0921971	−	0.995741i	$-0.470611\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	3.63744			0.286670
$162$		0			0
$163$	−16.8810			−1.32222			−0.661110	−	0.750289i	$-0.729914\pi$
$163$	−16.8810			−1.32222			−0.661110	+	0.750289i	$0.729914\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.60587	+	2.78145i	0.124266	+	0.215235i	0.921446	−	0.388507i	$-0.127009\pi$
$167$	1.60587	+	2.78145i	0.124266	+	0.215235i	−0.797180	+	0.603742i	$0.793676\pi$
$168$		0			0
$169$	−0.971485	+	1.68266i	−0.0747296	+	0.129435i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.306072	−	0.530133i	0.0232703	−	0.0403053i	−0.854156	−	0.520017i	$-0.825926\pi$
$173$	0.306072	−	0.530133i	0.0232703	−	0.0403053i	0.877426	+	0.479712i	$0.159259\pi$
$174$		0			0
$175$	−0.169204	−	0.293069i	−0.0127906	−	0.0221540i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.38135			0.327477			0.163739	−	0.986504i	$-0.447645\pi$
$179$	4.38135			0.327477			0.163739	+	0.986504i	$0.447645\pi$
$180$		0			0
$181$	−3.50192			−0.260295			−0.130148	−	0.991495i	$-0.541545\pi$
$181$	−3.50192			−0.260295			−0.130148	+	0.991495i	$0.541545\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.66920	+	4.62320i	0.196244	+	0.339904i
$186$		0			0
$187$	−0.214225	+	0.371048i	−0.0156657	+	0.0271337i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.71533	−	4.70309i	0.196474	−	0.340303i	−0.750909	−	0.660406i	$-0.770384\pi$
$191$	2.71533	−	4.70309i	0.196474	−	0.340303i	0.947383	+	0.320103i	$0.103717\pi$
$192$		0			0
$193$	4.54193	+	7.86686i	0.326935	+	0.566269i	0.981902	−	0.189389i	$-0.0606507\pi$
$193$	4.54193	+	7.86686i	0.326935	+	0.566269i	−0.654967	+	0.755658i	$0.727317\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.58040			0.611329			0.305664	−	0.952139i	$-0.401121\pi$
$197$	8.58040			0.611329			0.305664	+	0.952139i	$0.401121\pi$
$198$		0			0
$199$	25.4905			1.80697			0.903487	−	0.428616i	$-0.140999\pi$
$199$	25.4905			1.80697			0.903487	+	0.428616i	$0.140999\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.75152	+	8.22988i	0.333492	+	0.577624i
$204$		0			0
$205$	−10.9727	+	19.0052i	−0.766364	+	1.32738i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.01969	−	3.49821i	0.139705	−	0.241976i
$210$		0			0
$211$	−8.32066	−	14.4118i	−0.572818	−	0.992150i	−0.996275	−	0.0862336i	$-0.972517\pi$
$211$	−8.32066	−	14.4118i	−0.572818	−	0.992150i	0.423457	−	0.905916i	$-0.360816\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.228179			−0.0155616
$216$		0			0
$217$	−6.49808			−0.441119
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.631904	+	1.09449i	0.0425064	+	0.0736233i
$222$		0			0
$223$	9.28503	−	16.0821i	0.621772	−	1.07694i	−0.367384	−	0.930069i	$-0.619746\pi$
$223$	9.28503	−	16.0821i	0.621772	−	1.07694i	0.989156	−	0.146871i	$-0.0469202\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.84096	−	13.5809i	0.520423	−	0.901399i	−0.479295	−	0.877654i	$-0.659108\pi$
$227$	7.84096	−	13.5809i	0.520423	−	0.901399i	0.999718	−	0.0237449i	$-0.00755895\pi$
$228$		0			0
$229$	−5.57024	−	9.64794i	−0.368092	−	0.637554i	0.621175	−	0.783672i	$-0.286656\pi$
$229$	−5.57024	−	9.64794i	−0.368092	−	0.637554i	−0.989267	+	0.146118i	$0.953322\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	21.6831			1.42050			0.710252	−	0.703948i	$-0.248581\pi$
$233$	21.6831			1.42050			0.710252	+	0.703948i	$0.248581\pi$
$234$		0			0
$235$	0.500702			0.0326622
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.20271	+	10.7434i	0.401220	+	0.694934i	0.993873	−	0.110524i	$-0.0352529\pi$
$239$	6.20271	+	10.7434i	0.401220	+	0.694934i	−0.592653	+	0.805458i	$0.701920\pi$
$240$		0			0
$241$	8.35028	−	14.4631i	0.537889	−	0.931651i	−0.461129	−	0.887333i	$-0.652555\pi$
$241$	8.35028	−	14.4631i	0.537889	−	0.931651i	0.999017	−	0.0443176i	$-0.0141114\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.15525	+	2.00095i	−0.0738062	+	0.127836i
$246$		0			0
$247$	−5.95753	−	10.3187i	−0.379069	−	0.656566i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−27.0215			−1.70558			−0.852790	−	0.522255i	$-0.825091\pi$
$251$	−27.0215			−1.70558			−0.852790	+	0.522255i	$0.825091\pi$
$252$		0			0
$253$	4.76686			0.299690
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.97645	−	17.2797i	−0.622314	−	1.07788i	−0.989054	−	0.147556i	$-0.952859\pi$
$257$	−9.97645	−	17.2797i	−0.622314	−	1.07788i	0.366740	−	0.930324i	$-0.380474\pi$
$258$		0			0
$259$	1.15525	−	2.00095i	0.0717837	−	0.124333i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−7.92841	+	13.7324i	−0.488887	+	0.846776i	−0.999918	−	0.0127855i	$-0.995930\pi$
$263$	−7.92841	+	13.7324i	−0.488887	+	0.846776i	0.511032	+	0.859562i	$0.329263\pi$
$264$		0			0
$265$	15.9334	+	27.5974i	0.978779	+	1.69530i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.694466			−0.0423423			−0.0211712	−	0.999776i	$-0.506739\pi$
$269$	−0.694466			−0.0423423			−0.0211712	+	0.999776i	$0.506739\pi$
$270$		0			0
$271$	9.08883			0.552107			0.276053	−	0.961142i	$-0.410973\pi$
$271$	9.08883			0.552107			0.276053	+	0.961142i	$0.410973\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.221741	−	0.384067i	−0.0133715	−	0.0231601i
$276$		0			0
$277$	−7.20084	+	12.4722i	−0.432656	+	0.749383i	−0.997101	−	0.0760880i	$-0.975757\pi$
$277$	−7.20084	+	12.4722i	−0.432656	+	0.749383i	0.564445	+	0.825471i	$0.309090\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4.68356	+	8.11216i	−0.279398	+	0.483931i	−0.971235	−	0.238122i	$-0.923468\pi$
$281$	−4.68356	+	8.11216i	−0.279398	+	0.483931i	0.691837	+	0.722053i	$0.256801\pi$
$282$		0			0
$283$	−9.54310	−	16.5291i	−0.567279	−	0.982556i	−0.996834	−	0.0795148i	$-0.974663\pi$
$283$	−9.54310	−	16.5291i	−0.567279	−	0.982556i	0.429555	−	0.903041i	$-0.358670\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	9.49808			0.560654
$288$		0			0
$289$	−16.8931			−0.993713
$290$		0			0
$291$		0			0
$292$		0			0
$293$	9.10262	+	15.7662i	0.531781	+	0.921071i	0.999312	+	0.0370944i	$0.0118102\pi$
$293$	9.10262	+	15.7662i	0.531781	+	0.921071i	−0.467531	+	0.883977i	$0.654856\pi$
$294$		0			0
$295$	2.83019	−	4.90203i	0.164780	−	0.285407i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	7.03046	−	12.1771i	0.406582	−	0.704221i
$300$		0			0
$301$	0.0493786	+	0.0855263i	0.00284614	+	0.00492965i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−35.5093			−2.03326
$306$		0			0
$307$	26.8537			1.53262			0.766312	−	0.642469i	$-0.222090\pi$
$307$	26.8537			1.53262			0.766312	+	0.642469i	$0.222090\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.790243	+	1.36874i	0.0448106	+	0.0776142i	0.887561	−	0.460691i	$-0.152398\pi$
$311$	0.790243	+	1.36874i	0.0448106	+	0.0776142i	−0.842750	+	0.538305i	$0.819065\pi$
$312$		0			0
$313$	−10.2617	+	17.7738i	−0.580025	+	1.00463i	0.415451	+	0.909616i	$0.363624\pi$
$313$	−10.2617	+	17.7738i	−0.580025	+	1.00463i	−0.995476	+	0.0950169i	$0.969709\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.9323	−	27.5955i	0.894845	−	1.54992i	0.0608495	−	0.998147i	$-0.480619\pi$
$317$	15.9323	−	27.5955i	0.894845	−	1.54992i	0.833996	−	0.551771i	$-0.186048\pi$
$318$		0			0
$319$	6.22687	+	10.7853i	0.348638	+	0.603858i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.00772			−0.0560711
$324$		0			0
$325$	−1.30815			−0.0725632
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.108354	−	0.187674i	−0.00597372	−	0.0103468i
$330$		0			0
$331$	17.0714	−	29.5686i	0.938330	−	1.62524i	0.169744	−	0.985488i	$-0.445706\pi$
$331$	17.0714	−	29.5686i	0.938330	−	1.62524i	0.768586	−	0.639747i	$-0.220961\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−6.78198	+	11.7467i	−0.370539	+	0.641793i
$336$		0			0
$337$	−0.252833	−	0.437920i	−0.0137727	−	0.0238550i	0.859057	−	0.511880i	$-0.171051\pi$
$337$	−0.252833	−	0.437920i	−0.0137727	−	0.0238550i	−0.872830	+	0.488025i	$0.837717\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−8.51573			−0.461153
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−14.2154	−	24.6217i	−0.763120	−	1.32176i	−0.941235	−	0.337753i	$-0.890333\pi$
$347$	−14.2154	−	24.6217i	−0.763120	−	1.32176i	0.178114	−	0.984010i	$-0.443000\pi$
$348$		0			0
$349$	17.5804	−	30.4502i	0.941057	−	1.62996i	0.177599	−	0.984103i	$-0.443167\pi$
$349$	17.5804	−	30.4502i	0.941057	−	1.62996i	0.763459	−	0.645856i	$-0.223500\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.496139	−	0.859339i	0.0264068	−	0.0457380i	−0.852520	−	0.522695i	$-0.824927\pi$
$353$	0.496139	−	0.859339i	0.0264068	−	0.0457380i	0.878927	+	0.476957i	$0.158260\pi$
$354$		0			0
$355$	2.04690	+	3.54533i	0.108638	+	0.188166i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−23.2914			−1.22928			−0.614638	−	0.788810i	$-0.710698\pi$
$359$	−23.2914			−1.22928			−0.614638	+	0.788810i	$0.710698\pi$
$360$		0			0
$361$	−9.49930			−0.499963
$362$		0			0
$363$		0			0
$364$		0			0
$365$	6.92576	+	11.9958i	0.362511	+	0.627887i
$366$		0			0
$367$	−5.89144	+	10.2043i	−0.307531	+	0.532659i	−0.977822	−	0.209440i	$-0.932836\pi$
$367$	−5.89144	+	10.2043i	−0.307531	+	0.532659i	0.670291	+	0.742099i	$0.266169\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	6.89607	−	11.9443i	0.358026	−	0.620120i
$372$		0			0
$373$	6.91714	+	11.9808i	0.358156	+	0.620344i	0.987653	−	0.156659i	$-0.0500723\pi$
$373$	6.91714	+	11.9808i	0.358156	+	0.620344i	−0.629497	+	0.777003i	$0.716739\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	36.7351			1.89195
$378$		0			0
$379$	21.5877			1.10889			0.554443	−	0.832222i	$-0.312931\pi$
$379$	21.5877			1.10889			0.554443	+	0.832222i	$0.312931\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−8.31989	−	14.4105i	−0.425127	−	0.736341i	0.571306	−	0.820737i	$-0.306437\pi$
$383$	−8.31989	−	14.4105i	−0.425127	−	0.736341i	−0.996432	+	0.0843965i	$0.973104\pi$
$384$		0			0
$385$	−1.51395	+	2.62225i	−0.0771582	+	0.133642i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.46709	+	16.3975i	−0.480000	+	0.831385i	−0.999737	−	0.0229417i	$-0.992697\pi$
$389$	−9.46709	+	16.3975i	−0.480000	+	0.831385i	0.519736	+	0.854327i	$0.326030\pi$
$390$		0			0
$391$	−0.594604	−	1.02988i	−0.0300704	−	0.0520835i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	33.7145			1.69636
$396$		0			0
$397$	16.0746			0.806761			0.403381	−	0.915032i	$-0.367835\pi$
$397$	16.0746			0.806761			0.403381	+	0.915032i	$0.367835\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	19.4409	+	33.6726i	0.970832	+	1.68153i	0.693056	+	0.720884i	$0.256264\pi$
$401$	19.4409	+	33.6726i	0.970832	+	1.68153i	0.277776	+	0.960646i	$0.410403\pi$
$402$		0			0
$403$	−12.5595	+	21.7538i	−0.625635	+	1.08363i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.51395	−	2.62225i	0.0750439	−	0.129980i
$408$		0			0
$409$	−6.39993	−	11.0850i	−0.316456	−	0.548119i	0.663290	−	0.748363i	$-0.269160\pi$
$409$	−6.39993	−	11.0850i	−0.316456	−	0.548119i	−0.979746	+	0.200244i	$0.935826\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.44985			−0.120549
$414$		0			0
$415$	−14.0532			−0.689844
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.597046	−	1.03411i	−0.0291676	−	0.0505197i	0.851073	−	0.525047i	$-0.175952\pi$
$419$	−0.597046	−	1.03411i	−0.0291676	−	0.0505197i	−0.880241	+	0.474527i	$0.842619\pi$
$420$		0			0
$421$	−8.19067	+	14.1867i	−0.399189	+	0.691416i	−0.993626	−	0.112726i	$-0.964042\pi$
$421$	−8.19067	+	14.1867i	−0.399189	+	0.691416i	0.594437	+	0.804142i	$0.297375\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.0553187	+	0.0958149i	−0.00268335	+	0.00464770i
$426$		0			0
$427$	7.68433	+	13.3097i	0.371871	+	0.644099i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−26.3928			−1.27130			−0.635649	−	0.771978i	$-0.719267\pi$
$431$	−26.3928			−1.27130			−0.635649	+	0.771978i	$0.719267\pi$
$432$		0			0
$433$	23.7503			1.14137			0.570684	−	0.821170i	$-0.306678\pi$
$433$	23.7503			1.14137			0.570684	+	0.821170i	$0.306678\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.60587	+	9.70965i	0.268165	+	0.464476i
$438$		0			0
$439$	−10.2431	+	17.7416i	−0.488877	+	0.846759i	−0.999918	−	0.0127969i	$-0.995926\pi$
$439$	−10.2431	+	17.7416i	−0.488877	+	0.846759i	0.511042	+	0.859556i	$0.329260\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.89909	−	6.75343i	0.185252	−	0.320865i	−0.758410	−	0.651778i	$-0.774023\pi$
$443$	3.89909	−	6.75343i	0.185252	−	0.320865i	0.943661	+	0.330913i	$0.107357\pi$
$444$		0			0
$445$	6.37957	+	11.0497i	0.302421	+	0.523808i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−2.35981			−0.111366			−0.0556831	−	0.998448i	$-0.517734\pi$
$449$	−2.35981			−0.111366			−0.0556831	+	0.998448i	$0.517734\pi$
$450$		0			0
$451$	12.4472			0.586117
$452$		0			0
$453$		0			0
$454$		0			0
$455$	4.46575	+	7.73490i	0.209358	+	0.362618i
$456$		0			0
$457$	−10.1012	+	17.4959i	−0.472516	+	0.818422i	−0.999505	−	0.0314501i	$-0.989987\pi$
$457$	−10.1012	+	17.4959i	−0.472516	+	0.818422i	0.526989	+	0.849872i	$0.323321\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.02197	+	10.4304i	−0.280471	+	0.485790i	−0.971501	−	0.237036i	$-0.923824\pi$
$461$	−6.02197	+	10.4304i	−0.280471	+	0.485790i	0.691030	+	0.722826i	$0.257157\pi$
$462$		0			0
$463$	−11.6437	−	20.1675i	−0.541130	−	0.937265i	−0.998839	−	0.0481633i	$-0.984663\pi$
$463$	−11.6437	−	20.1675i	−0.541130	−	0.937265i	0.457709	−	0.889102i	$-0.348670\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	34.0682			1.57649			0.788243	−	0.615364i	$-0.210991\pi$
$467$	34.0682			1.57649			0.788243	+	0.615364i	$0.210991\pi$
$468$		0			0
$469$	5.87058			0.271078
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.0647107	+	0.112082i	0.00297540	+	0.00515354i
$474$		0			0
$475$	0.521540	−	0.903334i	0.0239299	−	0.0414478i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	9.38477	−	16.2549i	0.428801	−	0.742705i	−0.567966	−	0.823052i	$-0.692270\pi$
$479$	9.38477	−	16.2549i	0.428801	−	0.742705i	0.996767	+	0.0803471i	$0.0256029\pi$
$480$		0			0
$481$	−4.46575	−	7.73490i	−0.203621	−	0.352681i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−13.8250			−0.627762
$486$		0			0
$487$	13.8837			0.629132			0.314566	−	0.949236i	$-0.398141\pi$
$487$	13.8837			0.629132			0.314566	+	0.949236i	$0.398141\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−4.54250	−	7.86784i	−0.205000	−	0.355071i	0.745133	−	0.666916i	$-0.232386\pi$
$491$	−4.54250	−	7.86784i	−0.205000	−	0.355071i	−0.950133	+	0.311846i	$0.899053\pi$
$492$		0			0
$493$	1.55344	−	2.69064i	0.0699636	−	0.121180i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.885911	−	1.53444i	0.0397385	−	0.0688291i
$498$		0			0
$499$	−11.8788	−	20.5747i	−0.531769	−	0.921051i	−0.999312	−	0.0370810i	$-0.988194\pi$
$499$	−11.8788	−	20.5747i	−0.531769	−	0.921051i	0.467543	−	0.883970i	$-0.345139\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−22.5612			−1.00595			−0.502977	−	0.864300i	$-0.667762\pi$
$503$	−22.5612			−1.00595			−0.502977	+	0.864300i	$0.667762\pi$
$504$		0			0
$505$	17.7957			0.791899
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.94814	+	6.83838i	0.174998	+	0.303106i	0.940161	−	0.340732i	$-0.110675\pi$
$509$	3.94814	+	6.83838i	0.174998	+	0.303106i	−0.765162	+	0.643837i	$0.777341\pi$
$510$		0			0
$511$	2.99752	−	5.19185i	0.132602	−	0.229674i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	4.69138	−	8.12570i	0.206727	−	0.358061i
$516$		0			0
$517$	−0.141997	−	0.245946i	−0.00624503	−	0.0108167i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−9.86440			−0.432167			−0.216084	−	0.976375i	$-0.569328\pi$
$521$	−9.86440			−0.432167			−0.216084	+	0.976375i	$0.569328\pi$
$522$		0			0
$523$	−22.9097			−1.00177			−0.500885	−	0.865514i	$-0.666992\pi$
$523$	−22.9097			−1.00177			−0.500885	+	0.865514i	$0.666992\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.06223	+	1.83983i	0.0462714	+	0.0801444i
$528$		0			0
$529$	4.88453	−	8.46026i	0.212371	−	0.367837i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	18.3580	−	31.7969i	0.795172	−	1.37728i
$534$		0			0
$535$	16.2629	+	28.1681i	0.703105	+	1.21781i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.31050			0.0564472
$540$		0			0
$541$	29.7187			1.27771			0.638853	−	0.769329i	$-0.279409\pi$
$541$	29.7187			1.27771			0.638853	+	0.769329i	$0.279409\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	7.70906	+	13.3525i	0.330220	+	0.571957i
$546$		0			0
$547$	−1.30472	+	2.25985i	−0.0557859	+	0.0966240i	−0.892570	−	0.450909i	$-0.851100\pi$
$547$	−1.30472	+	2.25985i	−0.0557859	+	0.0966240i	0.836784	+	0.547533i	$0.184433\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−14.6457	+	25.3671i	−0.623929	+	1.08068i
$552$		0			0
$553$	−7.29594	−	12.6369i	−0.310255	−	0.537377i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−26.0406			−1.10338			−0.551688	−	0.834051i	$-0.686016\pi$
$557$	−26.0406			−1.10338			−0.551688	+	0.834051i	$0.686016\pi$
$558$		0			0
$559$	0.381757			0.0161466
$560$		0			0
$561$		0			0
$562$		0			0
$563$	22.3876	+	38.7765i	0.943525	+	1.63423i	0.758677	+	0.651467i	$0.225846\pi$
$563$	22.3876	+	38.7765i	0.943525	+	1.63423i	0.184848	+	0.982767i	$0.440821\pi$
$564$		0			0
$565$	−8.89352	+	15.4040i	−0.374153	+	0.648052i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.6290	+	25.3382i	−0.613280	+	1.06223i	0.377404	+	0.926049i	$0.376817\pi$
$569$	−14.6290	+	25.3382i	−0.613280	+	1.06223i	−0.990684	+	0.136183i	$0.956516\pi$
$570$		0			0
$571$	18.2628	+	31.6321i	0.764275	+	1.32376i	0.940629	+	0.339437i	$0.110236\pi$
$571$	18.2628	+	31.6321i	0.764275	+	1.32376i	−0.176354	+	0.984327i	$0.556430\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.23093			0.0513335
$576$		0			0
$577$	9.88205			0.411395			0.205698	−	0.978616i	$-0.434054\pi$
$577$	9.88205			0.411395			0.205698	+	0.978616i	$0.434054\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3.04116	+	5.26744i	0.126169	+	0.218530i
$582$		0			0
$583$	9.03730	−	15.6531i	0.374287	−	0.648284i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.05954	−	7.03133i	0.167555	−	0.290214i	−0.770005	−	0.638038i	$-0.779746\pi$
$587$	4.05954	−	7.03133i	0.167555	−	0.290214i	0.937560	+	0.347824i	$0.113079\pi$
$588$		0			0
$589$	−10.0146	−	17.3458i	−0.412644	−	0.714720i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−29.6969			−1.21950			−0.609752	−	0.792592i	$-0.708731\pi$
$593$	−29.6969			−1.21950			−0.609752	+	0.792592i	$0.708731\pi$
$594$		0			0
$595$	0.755385			0.0309678
$596$		0			0
$597$		0			0
$598$		0			0
$599$	8.19531	+	14.1947i	0.334851	+	0.579979i	0.983456	−	0.181146i	$-0.0579806\pi$
$599$	8.19531	+	14.1947i	0.334851	+	0.579979i	−0.648605	+	0.761125i	$0.724647\pi$
$600$		0			0
$601$	24.4424	−	42.3355i	0.997028	−	1.72690i	0.431790	−	0.901974i	$-0.357882\pi$
$601$	24.4424	−	42.3355i	0.997028	−	1.72690i	0.565237	−	0.824928i	$-0.308785\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	10.7237	−	18.5740i	0.435981	−	0.755141i
$606$		0			0
$607$	23.6033	+	40.8820i	0.958027	+	1.65935i	0.727285	+	0.686335i	$0.240782\pi$
$607$	23.6033	+	40.8820i	0.958027	+	1.65935i	0.230741	+	0.973015i	$0.425885\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.837706			−0.0338899
$612$		0			0
$613$	−15.6396			−0.631679			−0.315840	−	0.948813i	$-0.602286\pi$
$613$	−15.6396			−0.631679			−0.315840	+	0.948813i	$0.602286\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	15.7793	+	27.3305i	0.635251	+	1.10029i	0.986462	+	0.163990i	$0.0524365\pi$
$617$	15.7793	+	27.3305i	0.635251	+	1.10029i	−0.351211	+	0.936296i	$0.614230\pi$
$618$		0			0
$619$	7.31619	−	12.6720i	0.294063	−	0.509331i	−0.680704	−	0.732559i	$-0.738326\pi$
$619$	7.31619	−	12.6720i	0.294063	−	0.509331i	0.974766	+	0.223227i	$0.0716592\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.76112	−	4.78240i	0.110622	−	0.191603i
$624$		0			0
$625$	13.2888	+	23.0168i	0.531550	+	0.920672i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−0.755385			−0.0301192
$630$		0			0
$631$	36.3101			1.44548			0.722742	−	0.691118i	$-0.242881\pi$
$631$	36.3101			1.44548			0.722742	+	0.691118i	$0.242881\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	17.3111	+	29.9836i	0.686969	+	1.18986i
$636$		0			0
$637$	1.93281	−	3.34772i	0.0765806	−	0.132641i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	5.40731	−	9.36574i	0.213576	−	0.369924i	−0.739255	−	0.673425i	$-0.764822\pi$
$641$	5.40731	−	9.36574i	0.213576	−	0.369924i	0.952831	+	0.303501i	$0.0981556\pi$
$642$		0			0
$643$	−6.97535	−	12.0817i	−0.275081	−	0.476454i	0.695075	−	0.718937i	$-0.255371\pi$
$643$	−6.97535	−	12.0817i	−0.275081	−	0.476454i	−0.970155	+	0.242484i	$0.922038\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−34.5634			−1.35883			−0.679414	−	0.733755i	$-0.737766\pi$
$647$	−34.5634			−1.35883			−0.679414	+	0.733755i	$0.737766\pi$
$648$		0			0
$649$	−3.21053			−0.126024
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−13.7927	−	23.8897i	−0.539751	−	0.934875i	−0.998917	−	0.0465252i	$-0.985185\pi$
$653$	−13.7927	−	23.8897i	−0.539751	−	0.934875i	0.459167	−	0.888350i	$-0.348148\pi$
$654$		0			0
$655$	−12.0328	+	20.8414i	−0.470161	+	0.814342i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−10.3059	+	17.8503i	−0.401460	+	0.695348i	−0.993902	−	0.110264i	$-0.964830\pi$
$659$	−10.3059	+	17.8503i	−0.401460	+	0.695348i	0.592443	+	0.805613i	$0.298164\pi$
$660$		0			0
$661$	13.5815	+	23.5239i	0.528259	+	0.914972i	0.999457	+	0.0329446i	$0.0104885\pi$
$661$	13.5815	+	23.5239i	0.528259	+	0.914972i	−0.471198	+	0.882028i	$0.656178\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−7.12170			−0.276168
$666$		0			0
$667$	−34.5667			−1.33843
$668$		0			0
$669$		0			0
$670$		0			0
$671$	10.0703	+	17.4423i	0.388760	+	0.673352i
$672$		0			0
$673$	−9.52644	+	16.5003i	−0.367217	+	0.636039i	−0.989129	−	0.147048i	$-0.953023\pi$
$673$	−9.52644	+	16.5003i	−0.367217	+	0.636039i	0.621912	+	0.783087i	$0.286356\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−10.8695	+	18.8265i	−0.417748	+	0.723560i	−0.995713	−	0.0925013i	$-0.970514\pi$
$677$	−10.8695	+	18.8265i	−0.417748	+	0.723560i	0.577965	+	0.816062i	$0.303847\pi$
$678$		0			0
$679$	2.99178	+	5.18192i	0.114814	+	0.198864i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−41.0808			−1.57191			−0.785957	−	0.618281i	$-0.787829\pi$
$683$	−41.0808			−1.57191			−0.785957	+	0.618281i	$0.787829\pi$
$684$		0			0
$685$	−14.4716			−0.552931
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−26.6576	−	46.1722i	−1.01557	−	1.75902i
$690$		0			0
$691$	9.03599	−	15.6508i	0.343745	−	0.595384i	−0.641380	−	0.767224i	$-0.721638\pi$
$691$	9.03599	−	15.6508i	0.343745	−	0.595384i	0.985125	+	0.171839i	$0.0549710\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−23.2895	+	40.3385i	−0.883420	+	1.53013i
$696$		0			0
$697$	−1.55263	−	2.68924i	−0.0588101	−	0.101862i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	41.5130			1.56793			0.783963	−	0.620808i	$-0.213195\pi$
$701$	41.5130			1.56793			0.783963	+	0.620808i	$0.213195\pi$
$702$		0			0
$703$	7.12170			0.268600
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.85105	−	6.67022i	−0.144834	−	0.250859i
$708$		0			0
$709$	−0.684536	+	1.18565i	−0.0257083	+	0.0445280i	−0.878593	−	0.477571i	$-0.841517\pi$
$709$	−0.684536	+	1.18565i	−0.0257083	+	0.0445280i	0.852885	+	0.522099i	$0.174851\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	11.8182	−	20.4697i	0.442594	−	0.766596i
$714$		0			0
$715$	5.85236	+	10.1366i	0.218866	+	0.379087i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	20.1854			0.752787			0.376394	−	0.926460i	$-0.377164\pi$
$719$	20.1854			0.752787			0.376394	+	0.926460i	$0.377164\pi$
$720$		0			0
$721$	−4.06092			−0.151237
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.60795	+	2.78505i	0.0597178	+	0.103434i
$726$		0			0
$727$	1.69393	−	2.93397i	0.0628243	−	0.108815i	−0.832903	−	0.553420i	$-0.813323\pi$
$727$	1.69393	−	2.93397i	0.0628243	−	0.108815i	0.895727	+	0.444605i	$0.146656\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.0161436	−	0.0279616i	0.000597094	−	0.00103420i
$732$		0			0
$733$	8.90603	+	15.4257i	0.328952	+	0.569761i	0.982304	−	0.187293i	$-0.0599713\pi$
$733$	8.90603	+	15.4257i	0.328952	+	0.569761i	−0.653352	+	0.757054i	$0.726638\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.69339			0.283390
$738$		0			0
$739$	1.15512			0.0424918			0.0212459	−	0.999774i	$-0.493237\pi$
$739$	1.15512			0.0424918			0.0212459	+	0.999774i	$0.493237\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	13.5863	+	23.5322i	0.498435	+	0.863314i	0.999998	−	0.00180657i	$-0.000575048\pi$
$743$	13.5863	+	23.5322i	0.498435	+	0.863314i	−0.501564	+	0.865121i	$0.667242\pi$
$744$		0			0
$745$	19.6595	−	34.0513i	0.720270	−	1.24754i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	7.03868	−	12.1913i	0.257188	−	0.445462i
$750$		0			0
$751$	11.2959	+	19.5651i	0.412195	+	0.713942i	0.995129	−	0.0985769i	$-0.0314290\pi$
$751$	11.2959	+	19.5651i	0.412195	+	0.713942i	−0.582935	+	0.812519i	$0.698096\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	37.8756			1.37843
$756$		0			0
$757$	13.9989			0.508797			0.254399	−	0.967099i	$-0.418122\pi$
$757$	13.9989			0.508797			0.254399	+	0.967099i	$0.418122\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.252336	−	0.437059i	−0.00914718	−	0.0158434i	0.861416	−	0.507901i	$-0.169578\pi$
$761$	−0.252336	−	0.437059i	−0.00914718	−	0.0158434i	−0.870563	+	0.492057i	$0.836245\pi$
$762$		0			0
$763$	3.33653	−	5.77904i	0.120791	−	0.209215i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.73509	+	8.20141i	−0.170974	+	0.296136i
$768$		0			0
$769$	4.89218	+	8.47351i	0.176417	+	0.305563i	0.940651	−	0.339376i	$-0.110216\pi$
$769$	4.89218	+	8.47351i	0.176417	+	0.305563i	−0.764234	+	0.644939i	$0.776883\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−26.5907			−0.956403			−0.478201	−	0.878250i	$-0.658711\pi$
$773$	−26.5907			−0.956403			−0.478201	+	0.878250i	$0.658711\pi$
$774$		0			0
$775$	−2.19900			−0.0789904
$776$		0			0
$777$		0			0
$778$		0			0
$779$	14.6381	+	25.3539i	0.524463	+	0.908397i
$780$		0			0
$781$	1.16099	−	2.01089i	0.0415433	−	0.0719551i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−23.6305	+	40.9292i	−0.843408	+	1.46083i
$786$		0			0
$787$	−19.1108	−	33.1009i	−0.681227	−	1.17992i	−0.974607	−	0.223924i	$-0.928113\pi$
$787$	−19.1108	−	33.1009i	−0.681227	−	1.17992i	0.293379	−	0.955996i	$-0.405220\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	7.69835			0.273722
$792$		0			0
$793$	59.4093			2.10969
$794$		0			0
$795$		0			0
$796$		0			0
$797$	11.1866	+	19.3758i	0.396250	+	0.686325i	0.993260	−	0.115909i	$-0.0369780\pi$
$797$	11.1866	+	19.3758i	0.396250	+	0.686325i	−0.597010	+	0.802234i	$0.703645\pi$
$798$		0			0
$799$	−0.0354246	+	0.0613573i	−0.00125323	+	0.00217066i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.92824	−	6.80392i	0.138625	−	0.240105i
$804$		0			0
$805$	−4.20215	−	7.27833i	−0.148106	−	0.256527i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−5.50319			−0.193482			−0.0967409	−	0.995310i	$-0.530842\pi$
$809$	−5.50319			−0.193482			−0.0967409	+	0.995310i	$0.530842\pi$
$810$		0			0
$811$	12.3713			0.434414			0.217207	−	0.976126i	$-0.430305\pi$
$811$	12.3713			0.434414			0.217207	+	0.976126i	$0.430305\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	19.5017	+	33.7780i	0.683116	+	1.18319i
$816$		0			0
$817$	−0.152201	+	0.263619i	−0.00532483	+	0.00922288i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	21.2767	−	36.8524i	0.742564	−	1.28616i	−0.208761	−	0.977967i	$-0.566943\pi$
$821$	21.2767	−	36.8524i	0.742564	−	1.28616i	0.951324	−	0.308191i	$-0.0997236\pi$
$822$		0			0
$823$	−8.11754	−	14.0600i	−0.282960	−	0.490101i	0.689153	−	0.724616i	$-0.257983\pi$
$823$	−8.11754	−	14.0600i	−0.282960	−	0.490101i	−0.972112	+	0.234516i	$0.924650\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	34.0199			1.18299			0.591494	−	0.806309i	$-0.298538\pi$
$827$	34.0199			1.18299			0.591494	+	0.806309i	$0.298538\pi$
$828$		0			0
$829$	38.6394			1.34200			0.671000	−	0.741457i	$-0.265865\pi$
$829$	38.6394			1.34200			0.671000	+	0.741457i	$0.265865\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.163468	−	0.283135i	−0.00566383	−	0.00981004i
$834$		0			0
$835$	3.71036	−	6.42654i	0.128402	−	0.222400i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	3.88612	−	6.73095i	0.134164	−	0.232378i	−0.791114	−	0.611669i	$-0.790499\pi$
$839$	3.88612	−	6.73095i	0.134164	−	0.232378i	0.925278	+	0.379291i	$0.123832\pi$
$840$		0			0
$841$	−30.6540	−	53.0942i	−1.05703	−	1.83084i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.48923			0.154434
$846$		0			0
$847$	−9.28259			−0.318954
$848$		0			0
$849$		0			0
$850$		0			0
$851$	4.20215	+	7.27833i	0.144048	+	0.249498i
$852$		0			0
$853$	−10.0272	+	17.3676i	−0.343324	+	0.594654i	−0.985048	−	0.172282i	$-0.944886\pi$
$853$	−10.0272	+	17.3676i	−0.343324	+	0.594654i	0.641724	+	0.766936i	$0.278219\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.837910	−	1.45130i	0.0286225	−	0.0495756i	−0.851359	−	0.524583i	$-0.824221\pi$
$857$	0.837910	−	1.45130i	0.0286225	−	0.0495756i	0.879982	+	0.475007i	$0.157555\pi$
$858$		0			0
$859$	18.7256	+	32.4336i	0.638908	+	1.10662i	0.985673	+	0.168669i	$0.0539468\pi$
$859$	18.7256	+	32.4336i	0.638908	+	1.10662i	−0.346765	+	0.937952i	$0.612720\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−30.0265			−1.02211			−0.511057	−	0.859547i	$-0.670746\pi$
$863$	−30.0265			−1.02211			−0.511057	+	0.859547i	$0.670746\pi$
$864$		0			0
$865$	−1.41436			−0.0480897
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−9.56132	−	16.5607i	−0.324346	−	0.561783i
$870$		0			0
$871$	11.3467	−	19.6531i	0.384468	−	0.665918i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	5.38530	−	9.32762i	0.182056	−	0.315331i
$876$		0			0
$877$	−11.3517	−	19.6617i	−0.383318	−	0.663927i	0.608216	−	0.793772i	$-0.291885\pi$
$877$	−11.3517	−	19.6617i	−0.383318	−	0.663927i	−0.991534	+	0.129845i	$0.958552\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	36.0266			1.21377			0.606883	−	0.794791i	$-0.292420\pi$
$881$	36.0266			1.21377			0.606883	+	0.794791i	$0.292420\pi$
$882$		0			0
$883$	−47.7159			−1.60577			−0.802884	−	0.596135i	$-0.796702\pi$
$883$	−47.7159			−1.60577			−0.802884	+	0.596135i	$0.796702\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.70962	+	9.88935i	0.191710	+	0.332052i	0.945817	−	0.324700i	$-0.105263\pi$
$887$	5.70962	+	9.88935i	0.191710	+	0.332052i	−0.754107	+	0.656752i	$0.771930\pi$
$888$		0			0
$889$	7.49235	−	12.9771i	0.251285	−	0.435239i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.333980	−	0.578471i	0.0111762	−	0.0193578i
$894$		0			0
$895$	−5.06155	−	8.76686i	−0.169189	−	0.293044i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	61.7516			2.05953
$900$		0			0
$901$	−4.50915			−0.150221
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.04559	+	7.00716i	0.134480	+	0.232926i
$906$		0			0
$907$	1.81546	−	3.14448i	0.0602815	−	0.104411i	−0.834310	−	0.551296i	$-0.814133\pi$
$907$	1.81546	−	3.14448i	0.0602815	−	0.104411i	0.894591	+	0.446885i	$0.147467\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.24848	+	2.16242i	−0.0413638	+	0.0716443i	−0.885966	−	0.463750i	$-0.846504\pi$
$911$	−1.24848	+	2.16242i	−0.0413638	+	0.0716443i	0.844602	+	0.535394i	$0.179837\pi$
$912$		0			0
$913$	3.98544	+	6.90298i	0.131899	+	0.228455i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	10.4158			0.343959
$918$		0			0
$919$	−0.454816			−0.0150030			−0.00750149	−	0.999972i	$-0.502388\pi$
$919$	−0.454816			−0.0150030			−0.00750149	+	0.999972i	$0.502388\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−3.42459	−	5.93156i	−0.112722	−	0.195240i
$924$		0			0
$925$	0.390945	−	0.677137i	0.0128542	−	0.0222641i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−16.6846	+	28.8985i	−0.547403	+	0.948129i	0.451049	+	0.892499i	$0.351050\pi$
$929$	−16.6846	+	28.8985i	−0.547403	+	0.948129i	−0.998451	+	0.0556301i	$0.982283\pi$
$930$		0			0
$931$	1.54116	+	2.66937i	0.0505095	+	0.0874850i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.989932			0.0323742
$936$		0			0
$937$	−5.28675			−0.172711			−0.0863553	−	0.996264i	$-0.527522\pi$
$937$	−5.28675			−0.172711			−0.0863553	+	0.996264i	$0.527522\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	22.3084	+	38.6393i	0.727234	+	1.25961i	0.958048	+	0.286608i	$0.0925277\pi$
$941$	22.3084	+	38.6393i	0.727234	+	1.25961i	−0.230814	+	0.972998i	$0.574139\pi$
$942$		0			0
$943$	−17.2743	+	29.9200i	−0.562530	+	0.974330i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.3695	−	24.8887i	0.466945	−	0.808773i	−0.532342	−	0.846530i	$-0.678688\pi$
$947$	14.3695	−	24.8887i	0.466945	−	0.808773i	0.999287	+	0.0377568i	$0.0120212\pi$
$948$		0			0
$949$	−11.5872	−	20.0697i	−0.376138	−	0.651490i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	52.6957			1.70698			0.853491	−	0.521107i	$-0.174481\pi$
$953$	52.6957			1.70698			0.853491	+	0.521107i	$0.174481\pi$
$954$		0			0
$955$	−12.5475			−0.406029
$956$		0			0
$957$		0			0
$958$		0			0
$959$	3.13170	+	5.42426i	0.101128	+	0.175159i
$960$		0			0
$961$	−5.61255	+	9.72122i	−0.181050	+	0.313588i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	10.4941	−	18.1764i	0.337818	−	0.585118i
$966$		0			0
$967$	22.1564	+	38.3759i	0.712500	+	1.23409i	0.963916	+	0.266207i	$0.0857706\pi$
$967$	22.1564	+	38.3759i	0.712500	+	1.23409i	−0.251415	+	0.967879i	$0.580896\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−49.8993			−1.60134			−0.800672	−	0.599103i	$-0.795524\pi$
$971$	−49.8993			−1.60134			−0.800672	+	0.599103i	$0.795524\pi$
$972$		0			0
$973$	20.1597			0.646290
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−16.0981	−	27.8827i	−0.515022	−	0.892045i	−0.999848	−	0.0174342i	$-0.994450\pi$
$977$	−16.0981	−	27.8827i	−0.515022	−	0.892045i	0.484826	−	0.874611i	$-0.338883\pi$
$978$		0			0
$979$	3.61845	−	6.26733i	0.115646	−	0.200305i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	6.17356	−	10.6929i	0.196906	−	0.341051i	−0.750618	−	0.660737i	$-0.770244\pi$
$983$	6.17356	−	10.6929i	0.196906	−	0.341051i	0.947524	+	0.319686i	$0.103577\pi$
$984$		0			0
$985$	−9.91251	−	17.1690i	−0.315839	−	0.547049i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.359223			−0.0114226
$990$		0			0
$991$	−6.80483			−0.216163			−0.108081	−	0.994142i	$-0.534471\pi$
$991$	−6.80483			−0.216163			−0.108081	+	0.994142i	$0.534471\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−29.4479	−	51.0052i	−0.933561	−	1.61698i
$996$		0			0
$997$	−0.812415	+	1.40714i	−0.0257295	+	0.0445647i	−0.878603	−	0.477552i	$-0.841524\pi$
$997$	−0.812415	+	1.40714i	−0.0257295	+	0.0445647i	0.852874	+	0.522117i	$0.174858\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.r.m.2017.1		8
3.2	odd	2		1008.2.r.l.673.2		8
4.3	odd	2		1512.2.r.e.505.1		8
9.2	odd	6		9072.2.a.cj.1.1		4
9.4	even	3	inner	3024.2.r.m.1009.1		8
9.5	odd	6		1008.2.r.l.337.2		8
9.7	even	3		9072.2.a.cg.1.4		4
12.11	even	2		504.2.r.e.169.3	✓	8
36.7	odd	6		4536.2.a.y.1.4		4
36.11	even	6		4536.2.a.z.1.1		4
36.23	even	6		504.2.r.e.337.3	yes	8
36.31	odd	6		1512.2.r.e.1009.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.e.169.3	✓	8	12.11	even	2
504.2.r.e.337.3	yes	8	36.23	even	6
1008.2.r.l.337.2		8	9.5	odd	6
1008.2.r.l.673.2		8	3.2	odd	2
1512.2.r.e.505.1		8	4.3	odd	2
1512.2.r.e.1009.1		8	36.31	odd	6
3024.2.r.m.1009.1		8	9.4	even	3	inner
3024.2.r.m.2017.1		8	1.1	even	1	trivial
4536.2.a.y.1.4		4	36.7	odd	6
4536.2.a.z.1.1		4	36.11	even	6
9072.2.a.cg.1.4		4	9.7	even	3
9072.2.a.cj.1.1		4	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.15525 - 2.00095i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.655250 + 1.13493i) q^{11} +(1.93281 + 3.34772i) q^{13} +0.326936 q^{17} -3.08232 q^{19} +(-1.81872 - 3.15011i) q^{23} +(-0.169204 + 0.293069i) q^{25} +(4.75152 - 8.22988i) q^{29} +(3.24904 + 5.62751i) q^{31} +2.31050 q^{35} -2.31050 q^{37} +(-4.74904 - 8.22558i) q^{41} +(0.0493786 - 0.0855263i) q^{43} +(-0.108354 + 0.187674i) q^{47} +(-0.500000 - 0.866025i) q^{49} -13.7921 q^{53} +3.02791 q^{55} +(1.22493 + 2.12163i) q^{59} +(7.68433 - 13.3097i) q^{61} +(4.46575 - 7.73490i) q^{65} +(-2.93529 - 5.08407i) q^{67} -1.77182 q^{71} -5.99504 q^{73} +(-0.655250 - 1.13493i) q^{77} +(-7.29594 + 12.6369i) q^{79} +(3.04116 - 5.26744i) q^{83} +(-0.377692 - 0.654183i) q^{85} -5.52224 q^{89} -3.86561 q^{91} +(3.56085 + 6.16757i) q^{95} +(2.99178 - 5.18192i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{5} - 4 q^{7} + 7 q^{11} + 3 q^{13} - 6 q^{17} + 8 q^{19} + 2 q^{23} - 5 q^{25} + 9 q^{29} - 3 q^{31} - 6 q^{35} + 6 q^{37} - 9 q^{41} - 8 q^{43} + 3 q^{47} - 4 q^{49} - 12 q^{53} + 56 q^{55}+ \cdots + 16 q^{97}+O(q^{100}) \) 8 * q + 3 * q^5 - 4 * q^7 + 7 * q^11 + 3 * q^13 - 6 * q^17 + 8 * q^19 + 2 * q^23 - 5 * q^25 + 9 * q^29 - 3 * q^31 - 6 * q^35 + 6 * q^37 - 9 * q^41 - 8 * q^43 + 3 * q^47 - 4 * q^49 - 12 * q^53 + 56 * q^55 + 10 * q^59 + 20 * q^61 - q^65 - 11 * q^67 - 6 * q^71 - 48 * q^73 + 7 * q^77 - 21 * q^79 + 8 * q^83 + 9 * q^85 - 12 * q^89 - 6 * q^91 + 36 * q^95 + 16 * q^97

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