LMFDB - Embedded newform 864.2.s.a.287.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(287,864)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("864.287");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			287.12
Character	$\chi$	$=$	864.287
Dual form			864.2.s.a.575.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.01113 + 1.73848i) q^{5} +(3.12309 - 1.80312i) q^{7} +O(q^{10})$	$q+(3.01113 + 1.73848i) q^{5} +(3.12309 - 1.80312i) q^{7} +(-1.32430 - 2.29375i) q^{11} +(2.36304 - 4.09290i) q^{13} +1.79223i q^{17} -4.55459i q^{19} +(0.377525 - 0.653893i) q^{23} +(3.54460 + 6.13942i) q^{25} +(-7.19382 + 4.15336i) q^{29} +(-1.94259 - 1.12156i) q^{31} +12.5387 q^{35} -3.98496 q^{37} +(5.57798 + 3.22045i) q^{41} +(-7.60601 + 4.39133i) q^{43} +(1.37819 + 2.38710i) q^{47} +(3.00247 - 5.20044i) q^{49} +4.41211i q^{53} -9.20903i q^{55} +(1.36081 - 2.35700i) q^{59} +(1.19156 + 2.06384i) q^{61} +(14.2308 - 8.21616i) q^{65} +(8.78651 + 5.07289i) q^{67} +0.0730340 q^{71} +13.3207 q^{73} +(-8.27180 - 4.77573i) q^{77} +(-4.51115 + 2.60452i) q^{79} +(0.244846 + 0.424085i) q^{83} +(-3.11576 + 5.39665i) q^{85} -4.41211i q^{89} -17.0433i q^{91} +(7.91805 - 13.7145i) q^{95} +(7.21855 + 12.5029i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 12 q^{25} - 24 q^{29} + 36 q^{41} + 12 q^{49} + 48 q^{65} + 24 q^{73} + 48 q^{77} + 12 q^{97}+O(q^{100}) $ 24 * q + 12 * q^25 - 24 * q^29 + 36 * q^41 + 12 * q^49 + 48 * q^65 + 24 * q^73 + 48 * q^77 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$5$	3.01113	+	1.73848i	1.34662	+	0.777470i	0.987769	−	0.155925i	$-0.0498360\pi$
$5$	3.01113	+	1.73848i	1.34662	+	0.777470i	0.358849	+	0.933396i	$0.383169\pi$
$6$		0			0
$7$	3.12309	−	1.80312i	1.18042	−	0.681515i	0.224307	−	0.974519i	$-0.427988\pi$
$7$	3.12309	−	1.80312i	1.18042	−	0.681515i	0.956111	+	0.293004i	$0.0946548\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.32430	−	2.29375i	−0.399290	−	0.691591i	0.594348	−	0.804208i	$-0.297410\pi$
$11$	−1.32430	−	2.29375i	−0.399290	−	0.691591i	−0.993639	+	0.112617i	$0.964077\pi$
$12$		0			0
$13$	2.36304	−	4.09290i	0.655388	−	1.13517i	−0.326408	−	0.945229i	$-0.605838\pi$
$13$	2.36304	−	4.09290i	0.655388	−	1.13517i	0.981796	−	0.189937i	$-0.0608283\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			1.79223i			0.434681i	0.976096	+	0.217340i	$0.0697381\pi$
$17$			1.79223i			0.434681i	−0.976096	+	0.217340i	$0.930262\pi$
$18$		0			0
$19$		−	4.55459i		−	1.04490i	−0.852671	−	0.522448i	$-0.825019\pi$
$19$		−	4.55459i		−	1.04490i	0.852671	−	0.522448i	$-0.174981\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.377525	−	0.653893i	0.0787195	−	0.136346i	−0.823978	−	0.566621i	$-0.808250\pi$
$23$	0.377525	−	0.653893i	0.0787195	−	0.136346i	0.902698	+	0.430275i	$0.141584\pi$
$24$		0			0
$25$	3.54460	+	6.13942i	0.708920	+	1.22788i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−7.19382	+	4.15336i	−1.33586	+	0.771259i	−0.986191	−	0.165614i	$-0.947039\pi$
$29$	−7.19382	+	4.15336i	−1.33586	+	0.771259i	−0.349669	+	0.936873i	$0.613706\pi$
$30$		0			0
$31$	−1.94259	−	1.12156i	−0.348900	−	0.201437i	0.315301	−	0.948992i	$-0.397895\pi$
$31$	−1.94259	−	1.12156i	−0.348900	−	0.201437i	−0.664201	+	0.747554i	$0.731228\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	12.5387			2.11943
$36$		0			0
$37$	−3.98496			−0.655123			−0.327561	−	0.944830i	$-0.606227\pi$
$37$	−3.98496			−0.655123			−0.327561	+	0.944830i	$0.606227\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.57798	+	3.22045i	0.871134	+	0.502949i	0.867725	−	0.497045i	$-0.165582\pi$
$41$	5.57798	+	3.22045i	0.871134	+	0.502949i	0.00340902	+	0.999994i	$0.498915\pi$
$42$		0			0
$43$	−7.60601	+	4.39133i	−1.15991	+	0.669672i	−0.951281	−	0.308324i	$-0.900232\pi$
$43$	−7.60601	+	4.39133i	−1.15991	+	0.669672i	−0.208624	+	0.977996i	$0.566899\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.37819	+	2.38710i	0.201030	+	0.348194i	0.948861	−	0.315696i	$-0.102238\pi$
$47$	1.37819	+	2.38710i	0.201030	+	0.348194i	−0.747831	+	0.663890i	$0.768904\pi$
$48$		0			0
$49$	3.00247	−	5.20044i	0.428925	−	0.742920i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			4.41211i			0.606050i	0.952983	+	0.303025i	$0.0979966\pi$
$53$			4.41211i			0.606050i	−0.952983	+	0.303025i	$0.902003\pi$
$54$		0			0
$55$		−	9.20903i		−	1.24175i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.36081	−	2.35700i	0.177163	−	0.306855i	−0.763745	−	0.645518i	$-0.776641\pi$
$59$	1.36081	−	2.35700i	0.177163	−	0.306855i	0.940908	+	0.338663i	$0.109975\pi$
$60$		0			0
$61$	1.19156	+	2.06384i	0.152563	+	0.264248i	0.932169	−	0.362023i	$-0.117914\pi$
$61$	1.19156	+	2.06384i	0.152563	+	0.264248i	−0.779606	+	0.626271i	$0.784580\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	14.2308	−	8.21616i	1.76511	−	1.01909i
$66$		0			0
$67$	8.78651	+	5.07289i	1.07344	+	0.619753i	0.929120	−	0.369778i	$-0.120566\pi$
$67$	8.78651	+	5.07289i	1.07344	+	0.619753i	0.144323	+	0.989531i	$0.453900\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.0730340			0.00866754			0.00433377	−	0.999991i	$-0.498621\pi$
$71$	0.0730340			0.00866754			0.00433377	+	0.999991i	$0.498621\pi$
$72$		0			0
$73$	13.3207			1.55907			0.779536	−	0.626358i	$-0.215455\pi$
$73$	13.3207			1.55907			0.779536	+	0.626358i	$0.215455\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−8.27180	−	4.77573i	−0.942659	−	0.544245i
$78$		0			0
$79$	−4.51115	+	2.60452i	−0.507544	+	0.293031i	−0.731824	−	0.681494i	$-0.761331\pi$
$79$	−4.51115	+	2.60452i	−0.507544	+	0.293031i	0.224279	+	0.974525i	$0.427997\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.244846	+	0.424085i	0.0268753	+	0.0465494i	0.879150	−	0.476545i	$-0.158111\pi$
$83$	0.244846	+	0.424085i	0.0268753	+	0.0465494i	−0.852275	+	0.523094i	$0.824778\pi$
$84$		0			0
$85$	−3.11576	+	5.39665i	−0.337951	+	0.585349i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	4.41211i		−	0.467683i	−0.972275	−	0.233841i	$-0.924870\pi$
$89$		−	4.41211i		−	0.467683i	0.972275	−	0.233841i	$-0.0751297\pi$
$90$		0			0
$91$		−	17.0433i		−	1.78663i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.91805	−	13.7145i	0.812375	−	1.40708i
$96$		0			0
$97$	7.21855	+	12.5029i	0.732933	+	1.26948i	0.955624	+	0.294588i	$0.0951823\pi$
$97$	7.21855	+	12.5029i	0.732933	+	1.26948i	−0.222692	+	0.974889i	$0.571484\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.88785	+	1.08995i	−0.187848	+	0.108454i	−0.590975	−	0.806690i	$-0.701257\pi$
$101$	−1.88785	+	1.08995i	−0.187848	+	0.108454i	0.403127	+	0.915144i	$0.367923\pi$
$102$		0			0
$103$	3.33065	+	1.92295i	0.328179	+	0.189474i	0.655032	−	0.755601i	$-0.272655\pi$
$103$	3.33065	+	1.92295i	0.328179	+	0.189474i	−0.326853	+	0.945075i	$0.605988\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−19.4071			−1.87615			−0.938077	−	0.346426i	$-0.887395\pi$
$107$	−19.4071			−1.87615			−0.938077	+	0.346426i	$0.887395\pi$
$108$		0			0
$109$	−13.0941			−1.25419			−0.627096	−	0.778942i	$-0.715757\pi$
$109$	−13.0941			−1.25419			−0.627096	+	0.778942i	$0.715757\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.23482	+	0.712921i	0.116162	+	0.0670660i	0.556955	−	0.830543i	$-0.311970\pi$
$113$	1.23482	+	0.712921i	0.116162	+	0.0670660i	−0.440793	+	0.897609i	$0.645303\pi$
$114$		0			0
$115$	2.27355	−	1.31264i	0.212010	−	0.122404i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.23161	+	5.59731i	0.296241	+	0.513105i
$120$		0			0
$121$	1.99248	−	3.45107i	0.181134	−	0.313734i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			7.26404i			0.649715i
$126$		0			0
$127$			13.5554i			1.20285i	0.798929	+	0.601425i	$0.205400\pi$
$127$			13.5554i			1.20285i	−0.798929	+	0.601425i	$0.794600\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.88176	+	13.6516i	−0.688632	+	1.19275i	0.283648	+	0.958928i	$0.408455\pi$
$131$	−7.88176	+	13.6516i	−0.688632	+	1.19275i	−0.972280	+	0.233818i	$0.924878\pi$
$132$		0			0
$133$	−8.21247	−	14.2244i	−0.712112	−	1.23341i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.70126	+	3.86897i	−0.572527	+	0.330549i	−0.758158	−	0.652071i	$-0.773900\pi$
$137$	−6.70126	+	3.86897i	−0.572527	+	0.330549i	0.185631	+	0.982620i	$0.440567\pi$
$138$		0			0
$139$	0.490339	+	0.283097i	0.0415900	+	0.0240120i	0.520651	−	0.853770i	$-0.325689\pi$
$139$	0.490339	+	0.283097i	0.0415900	+	0.0240120i	−0.479061	+	0.877782i	$0.659023\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−12.5174			−1.04676
$144$		0			0
$145$	−28.8820			−2.39852
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8.19013	−	4.72857i	−0.670961	−	0.387380i	0.125479	−	0.992096i	$-0.459953\pi$
$149$	−8.19013	−	4.72857i	−0.670961	−	0.387380i	−0.796441	+	0.604716i	$0.793286\pi$
$150$		0			0
$151$	−16.5260	+	9.54127i	−1.34486	+	0.776458i	−0.987517	−	0.157514i	$-0.949652\pi$
$151$	−16.5260	+	9.54127i	−1.34486	+	0.776458i	−0.357347	+	0.933972i	$0.616319\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.89960	−	6.75430i	−0.313223	−	0.542519i
$156$		0			0
$157$	10.5680	−	18.3043i	0.843417	−	1.46084i	−0.0435713	−	0.999050i	$-0.513874\pi$
$157$	10.5680	−	18.3043i	0.843417	−	1.46084i	0.886989	−	0.461791i	$-0.152793\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	2.72289i		−	0.214594i
$162$		0			0
$163$			22.6646i			1.77523i	0.460586	+	0.887615i	$0.347639\pi$
$163$			22.6646i			1.77523i	−0.460586	+	0.887615i	$0.652361\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.92712	+	5.06992i	−0.226507	+	0.392322i	−0.956771	−	0.290844i	$-0.906064\pi$
$167$	−2.92712	+	5.06992i	−0.226507	+	0.392322i	0.730263	+	0.683166i	$0.239397\pi$
$168$		0			0
$169$	−4.66788	−	8.08500i	−0.359067	−	0.621923i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.11907	−	2.95549i	0.389195	−	0.224702i	−0.292616	−	0.956230i	$-0.594526\pi$
$173$	5.11907	−	2.95549i	0.389195	−	0.224702i	0.681811	+	0.731528i	$0.261192\pi$
$174$		0			0
$175$	22.1402	+	12.7827i	1.67364	+	0.966279i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.8823			0.962871			0.481436	−	0.876481i	$-0.340116\pi$
$179$	12.8823			0.962871			0.481436	+	0.876481i	$0.340116\pi$
$180$		0			0
$181$	−10.1934			−0.757672			−0.378836	−	0.925464i	$-0.623676\pi$
$181$	−10.1934			−0.757672			−0.378836	+	0.925464i	$0.623676\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−11.9992	−	6.92775i	−0.882200	−	0.509338i
$186$		0			0
$187$	4.11093	−	2.37345i	0.300621	−	0.173564i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.2960	+	19.5653i	0.817353	+	1.41570i	0.907626	+	0.419779i	$0.137893\pi$
$191$	11.2960	+	19.5653i	0.817353	+	1.41570i	−0.0902735	+	0.995917i	$0.528774\pi$
$192$		0			0
$193$	−1.12935	+	1.95610i	−0.0812926	+	0.140803i	−0.903805	−	0.427944i	$-0.859238\pi$
$193$	−1.12935	+	1.95610i	−0.0812926	+	0.140803i	0.822513	+	0.568747i	$0.192571\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	5.65685i		−	0.403034i	−0.979485	−	0.201517i	$-0.935413\pi$
$197$		−	5.65685i		−	0.403034i	0.979485	−	0.201517i	$-0.0645872\pi$
$198$		0			0
$199$		−	13.8193i		−	0.979621i	−0.871829	−	0.489811i	$-0.837066\pi$
$199$		−	13.8193i		−	0.979621i	0.871829	−	0.489811i	$-0.162934\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−14.9780	+	25.9426i	−1.05125	+	1.82082i
$204$		0			0
$205$	11.1973	+	19.3944i	0.782056	+	1.35456i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−10.4471	+	6.03163i	−0.722641	+	0.417217i
$210$		0			0
$211$	5.52413	+	3.18936i	0.380297	+	0.219565i	0.677947	−	0.735110i	$-0.262870\pi$
$211$	5.52413	+	3.18936i	0.380297	+	0.219565i	−0.297651	+	0.954675i	$0.596203\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−30.5369			−2.08260
$216$		0			0
$217$	−8.08920			−0.549130
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.33543	+	4.23511i	0.493435	+	0.284885i
$222$		0			0
$223$	−2.25361	+	1.30112i	−0.150913	+	0.0871296i	−0.573555	−	0.819167i	$-0.694436\pi$
$223$	−2.25361	+	1.30112i	−0.150913	+	0.0871296i	0.422642	+	0.906297i	$0.361103\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.7192	−	18.5663i	−0.711461	−	1.23229i	−0.964309	−	0.264780i	$-0.914701\pi$
$227$	−10.7192	−	18.5663i	−0.711461	−	1.23229i	0.252848	−	0.967506i	$-0.418633\pi$
$228$		0			0
$229$	−0.370558	+	0.641825i	−0.0244872	+	0.0424130i	−0.878009	−	0.478644i	$-0.841129\pi$
$229$	−0.370558	+	0.641825i	−0.0244872	+	0.0424130i	0.853522	+	0.521057i	$0.174462\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	20.3832i		−	1.33535i	−0.744454	−	0.667673i	$-0.767290\pi$
$233$		−	20.3832i		−	1.33535i	0.744454	−	0.667673i	$-0.232710\pi$
$234$		0			0
$235$			9.58381i			0.625179i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	4.78964	−	8.29589i	0.309816	−	0.536617i	−0.668506	−	0.743707i	$-0.733066\pi$
$239$	4.78964	−	8.29589i	0.309816	−	0.536617i	0.978322	+	0.207090i	$0.0663993\pi$
$240$		0			0
$241$	3.17787	+	5.50424i	0.204705	+	0.354559i	0.950039	−	0.312132i	$-0.101043\pi$
$241$	3.17787	+	5.50424i	0.204705	+	0.354559i	−0.745334	+	0.666691i	$0.767710\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	18.0817	−	10.4395i	1.15520	−	0.666953i
$246$		0			0
$247$	−18.6415	−	10.7627i	−1.18613	−	0.684812i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	27.0938			1.71014			0.855072	−	0.518509i	$-0.173513\pi$
$251$	27.0938			1.71014			0.855072	+	0.518509i	$0.173513\pi$
$252$		0			0
$253$	−1.99982			−0.125728
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.31700	+	1.91507i	0.206909	+	0.119459i	0.599874	−	0.800095i	$-0.295217\pi$
$257$	3.31700	+	1.91507i	0.206909	+	0.119459i	−0.392965	+	0.919553i	$0.628551\pi$
$258$		0			0
$259$	−12.4454	+	7.18535i	−0.773319	+	0.446476i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−16.0988	−	27.8840i	−0.992697	−	1.71940i	−0.600819	−	0.799385i	$-0.705159\pi$
$263$	−16.0988	−	27.8840i	−0.992697	−	1.71940i	−0.391878	−	0.920017i	$-0.628174\pi$
$264$		0			0
$265$	−7.67035	+	13.2854i	−0.471186	+	0.816118i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	27.2601i		−	1.66208i	−0.556214	−	0.831039i	$-0.687747\pi$
$269$		−	27.2601i		−	1.66208i	0.556214	−	0.831039i	$-0.312253\pi$
$270$		0			0
$271$		−	8.48623i		−	0.515501i	−0.966211	−	0.257751i	$-0.917019\pi$
$271$		−	8.48623i		−	0.515501i	0.966211	−	0.257751i	$-0.0829813\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	9.38820	−	16.2608i	0.566130	−	0.980565i
$276$		0			0
$277$	3.90516	+	6.76394i	0.234638	+	0.406405i	0.959168	−	0.282839i	$-0.0912761\pi$
$277$	3.90516	+	6.76394i	0.234638	+	0.406405i	−0.724529	+	0.689244i	$0.757943\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.05260	+	3.49447i	−0.361068	+	0.208462i	−0.669549	−	0.742768i	$-0.733513\pi$
$281$	−6.05260	+	3.49447i	−0.361068	+	0.208462i	0.308481	+	0.951230i	$0.400179\pi$
$282$		0			0
$283$	−24.3037	−	14.0318i	−1.44471	−	0.834101i	−0.446547	−	0.894760i	$-0.647346\pi$
$283$	−24.3037	−	14.0318i	−1.44471	−	0.834101i	−0.998159	+	0.0606590i	$0.980680\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	23.2274			1.37107
$288$		0			0
$289$	13.7879			0.811053
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7.54841	−	4.35808i	−0.440983	−	0.254602i	0.263031	−	0.964787i	$-0.415278\pi$
$293$	−7.54841	−	4.35808i	−0.440983	−	0.254602i	−0.704015	+	0.710186i	$0.748611\pi$
$294$		0			0
$295$	8.19517	−	4.73148i	0.477141	−	0.275478i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.78421	−	3.09035i	−0.103184	−	0.178719i
$300$		0			0
$301$	−15.8362	+	27.4291i	−0.912782	+	1.58099i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			8.28599i			0.474454i
$306$		0			0
$307$			9.62380i			0.549259i	0.961550	+	0.274630i	$0.0885552\pi$
$307$			9.62380i			0.549259i	−0.961550	+	0.274630i	$0.911445\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−8.31685	+	14.4052i	−0.471606	+	0.816845i	−0.999472	−	0.0324824i	$-0.989659\pi$
$311$	−8.31685	+	14.4052i	−0.471606	+	0.816845i	0.527867	+	0.849327i	$0.322992\pi$
$312$		0			0
$313$	−12.3153	−	21.3307i	−0.696100	−	1.20568i	−0.969808	−	0.243868i	$-0.921584\pi$
$313$	−12.3153	−	21.3307i	−0.696100	−	1.20568i	0.273708	−	0.961813i	$-0.411750\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−20.8576	+	12.0421i	−1.17148	+	0.676354i	−0.954028	−	0.299717i	$-0.903108\pi$
$317$	−20.8576	+	12.0421i	−1.17148	+	0.676354i	−0.217452	+	0.976071i	$0.569774\pi$
$318$		0			0
$319$	19.0535	+	11.0005i	1.06679	+	0.615913i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	8.16290			0.454196
$324$		0			0
$325$	33.5041			1.85847
$326$		0			0
$327$		0			0
$328$		0			0
$329$	8.60844	+	4.97009i	0.474599	+	0.274010i
$330$		0			0
$331$	11.1084	−	6.41343i	0.610573	−	0.352514i	−0.162617	−	0.986689i	$-0.551993\pi$
$331$	11.1084	−	6.41343i	0.610573	−	0.352514i	0.773189	+	0.634175i	$0.218660\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	17.6382	+	30.5503i	0.963678	+	1.66914i
$336$		0			0
$337$	10.0754	−	17.4511i	0.548843	−	0.950624i	−0.449511	−	0.893275i	$-0.648402\pi$
$337$	10.0754	−	17.4511i	0.548843	−	0.950624i	0.998354	−	0.0573495i	$-0.0182649\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			5.94109i			0.321728i
$342$		0			0
$343$			3.58839i			0.193755i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.50392	−	6.06897i	0.188100	−	0.325800i	−0.756516	−	0.653975i	$-0.773100\pi$
$347$	3.50392	−	6.06897i	0.188100	−	0.325800i	0.944617	+	0.328175i	$0.106434\pi$
$348$		0			0
$349$	−2.47879	−	4.29339i	−0.132687	−	0.229820i	0.792025	−	0.610489i	$-0.209027\pi$
$349$	−2.47879	−	4.29339i	−0.132687	−	0.229820i	−0.924711	+	0.380669i	$0.875694\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	3.05985	−	1.76661i	0.162859	−	0.0940270i	−0.416355	−	0.909202i	$-0.636693\pi$
$353$	3.05985	−	1.76661i	0.162859	−	0.0940270i	0.579215	+	0.815175i	$0.303359\pi$
$354$		0			0
$355$	0.219915	+	0.126968i	0.0116719	+	0.00673875i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−15.2054			−0.802511			−0.401255	−	0.915966i	$-0.631426\pi$
$359$	−15.2054			−0.802511			−0.401255	+	0.915966i	$0.631426\pi$
$360$		0			0
$361$	−1.74433			−0.0918070
$362$		0			0
$363$		0			0
$364$		0			0
$365$	40.1104	+	23.1577i	2.09947	+	1.21213i
$366$		0			0
$367$	3.23512	−	1.86780i	0.168872	−	0.0974983i	−0.413182	−	0.910649i	$-0.635583\pi$
$367$	3.23512	−	1.86780i	0.168872	−	0.0974983i	0.582054	+	0.813150i	$0.302249\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	7.95556	+	13.7794i	0.413032	+	0.715393i
$372$		0			0
$373$	0.760243	−	1.31678i	0.0393639	−	0.0681802i	−0.845672	−	0.533703i	$-0.820800\pi$
$373$	0.760243	−	1.31678i	0.0393639	−	0.0681802i	0.885036	+	0.465522i	$0.154134\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			39.2581i			2.02190i
$378$		0			0
$379$		−	23.7948i		−	1.22226i	−0.791531	−	0.611129i	$-0.790716\pi$
$379$		−	23.7948i		−	1.22226i	0.791531	−	0.611129i	$-0.209284\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.48499	−	2.57208i	0.0758796	−	0.131427i	−0.825589	−	0.564272i	$-0.809157\pi$
$383$	1.48499	−	2.57208i	0.0758796	−	0.131427i	0.901468	+	0.432845i	$0.142490\pi$
$384$		0			0
$385$	−16.6050	−	28.7607i	−0.846268	−	1.46578i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.55562	−	2.05284i	0.180277	−	0.104083i	−0.407146	−	0.913363i	$-0.633476\pi$
$389$	3.55562	−	2.05284i	0.180277	−	0.104083i	0.587423	+	0.809280i	$0.300143\pi$
$390$		0			0
$391$	1.17193	+	0.676614i	0.0592670	+	0.0342178i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−18.1116			−0.911291
$396$		0			0
$397$	16.4643			0.826319			0.413160	−	0.910659i	$-0.364425\pi$
$397$	16.4643			0.826319			0.413160	+	0.910659i	$0.364425\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−26.8460	−	15.4996i	−1.34063	−	0.774012i	−0.353728	−	0.935348i	$-0.615086\pi$
$401$	−26.8460	−	15.4996i	−1.34063	−	0.774012i	−0.986899	+	0.161337i	$0.948419\pi$
$402$		0			0
$403$	−9.18083	+	5.30056i	−0.457330	+	0.264039i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	5.27726	+	9.14049i	0.261584	+	0.453077i
$408$		0			0
$409$	2.24112	−	3.88173i	0.110816	−	0.191939i	−0.805283	−	0.592890i	$-0.797987\pi$
$409$	2.24112	−	3.88173i	0.110816	−	0.191939i	0.916100	+	0.400951i	$0.131320\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	9.81483i		−	0.482956i
$414$		0			0
$415$			1.70263i			0.0835791i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.48571	+	11.2336i	−0.316848	+	0.548796i	−0.979829	−	0.199840i	$-0.935958\pi$
$419$	−6.48571	+	11.2336i	−0.316848	+	0.548796i	0.662981	+	0.748636i	$0.269291\pi$
$420$		0			0
$421$	9.21256	+	15.9566i	0.448993	+	0.777679i	0.998321	−	0.0579284i	$-0.0184495\pi$
$421$	9.21256	+	15.9566i	0.448993	+	0.777679i	−0.549328	+	0.835607i	$0.685116\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−11.0033	+	6.35275i	−0.533738	+	0.308154i
$426$		0			0
$427$	7.44270	+	4.29704i	0.360177	+	0.207949i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	22.3743			1.07773			0.538867	−	0.842391i	$-0.318852\pi$
$431$	22.3743			1.07773			0.538867	+	0.842391i	$0.318852\pi$
$432$		0			0
$433$	0.857684			0.0412177			0.0206088	−	0.999788i	$-0.493440\pi$
$433$	0.857684			0.0412177			0.0206088	+	0.999788i	$0.493440\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.97822	−	1.71947i	−0.142467	−	0.0822536i
$438$		0			0
$439$	10.3089	−	5.95187i	0.492019	−	0.284067i	−0.233393	−	0.972383i	$-0.574983\pi$
$439$	10.3089	−	5.95187i	0.492019	−	0.284067i	0.725412	+	0.688315i	$0.241649\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−8.99773	−	15.5845i	−0.427495	−	0.740443i	0.569155	−	0.822230i	$-0.307270\pi$
$443$	−8.99773	−	15.5845i	−0.427495	−	0.740443i	−0.996650	+	0.0817875i	$0.973937\pi$
$444$		0			0
$445$	7.67035	−	13.2854i	0.363610	−	0.629790i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			37.0489i			1.74845i	0.485524	+	0.874223i	$0.338629\pi$
$449$			37.0489i			1.74845i	−0.485524	+	0.874223i	$0.661371\pi$
$450$		0			0
$451$		−	17.0593i		−	0.803291i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	29.6294	−	51.3197i	1.38905	−	2.40590i
$456$		0			0
$457$	4.16540	+	7.21469i	0.194849	+	0.337489i	0.946851	−	0.321672i	$-0.104245\pi$
$457$	4.16540	+	7.21469i	0.194849	+	0.337489i	−0.752002	+	0.659161i	$0.770912\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	20.2118	−	11.6693i	0.941356	−	0.543492i	0.0509708	−	0.998700i	$-0.483768\pi$
$461$	20.2118	−	11.6693i	0.941356	−	0.543492i	0.890385	+	0.455208i	$0.150435\pi$
$462$		0			0
$463$	−29.9990	−	17.3199i	−1.39417	−	0.804926i	−0.400399	−	0.916341i	$-0.631128\pi$
$463$	−29.9990	−	17.3199i	−1.39417	−	0.804926i	−0.993774	+	0.111415i	$0.964462\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	17.1281			0.792595			0.396298	−	0.918122i	$-0.370295\pi$
$467$	17.1281			0.792595			0.396298	+	0.918122i	$0.370295\pi$
$468$		0			0
$469$	36.5881			1.68948
$470$		0			0
$471$		0			0
$472$		0			0
$473$	20.1452	+	11.6308i	0.926278	+	0.534787i
$474$		0			0
$475$	27.9626	−	16.1442i	1.28301	−	0.740747i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−18.1500	−	31.4366i	−0.829293	−	1.43638i	−0.898594	−	0.438781i	$-0.855410\pi$
$479$	−18.1500	−	31.4366i	−0.829293	−	1.43638i	0.0693014	−	0.997596i	$-0.477923\pi$
$480$		0			0
$481$	−9.41659	+	16.3100i	−0.429360	+	0.743673i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			50.1971i			2.27933i
$486$		0			0
$487$			1.00757i			0.0456575i	0.999739	+	0.0228287i	$0.00726724\pi$
$487$			1.00757i			0.0456575i	−0.999739	+	0.0228287i	$0.992733\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	5.20416	−	9.01387i	0.234860	−	0.406790i	−0.724372	−	0.689410i	$-0.757870\pi$
$491$	5.20416	−	9.01387i	0.234860	−	0.406790i	0.959232	+	0.282620i	$0.0912034\pi$
$492$		0			0
$493$	−7.44379	−	12.8930i	−0.335251	−	0.580672i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.228092	−	0.131689i	0.0102313	−	0.00590705i
$498$		0			0
$499$	3.25233	+	1.87773i	0.145594	+	0.0840590i	0.571028	−	0.820931i	$-0.306545\pi$
$499$	3.25233	+	1.87773i	0.145594	+	0.0840590i	−0.425433	+	0.904990i	$0.639878\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−20.5980			−0.918417			−0.459209	−	0.888328i	$-0.651867\pi$
$503$	−20.5980			−0.918417			−0.459209	+	0.888328i	$0.651867\pi$
$504$		0			0
$505$	−7.57942			−0.337280
$506$		0			0
$507$		0			0
$508$		0			0
$509$	10.7984	+	6.23445i	0.478630	+	0.276337i	0.719845	−	0.694135i	$-0.244213\pi$
$509$	10.7984	+	6.23445i	0.478630	+	0.276337i	−0.241216	+	0.970472i	$0.577546\pi$
$510$		0			0
$511$	41.6018	−	24.0188i	1.84036	−	1.06253i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	6.68602	+	11.5805i	0.294621	+	0.510299i
$516$		0			0
$517$	3.65027	−	6.32245i	0.160539	−	0.278061i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	15.9193i		−	0.697438i	−0.937227	−	0.348719i	$-0.886617\pi$
$521$		−	15.9193i		−	0.697438i	0.937227	−	0.348719i	$-0.113383\pi$
$522$		0			0
$523$		−	3.71297i		−	0.162357i	−0.996700	−	0.0811784i	$-0.974132\pi$
$523$		−	3.71297i		−	0.162357i	0.996700	−	0.0811784i	$-0.0258683\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.01009	−	3.48158i	0.0875610	−	0.151660i
$528$		0			0
$529$	11.2149	+	19.4249i	0.487606	+	0.844559i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	26.3619	−	15.2201i	1.14186	−	0.659254i
$534$		0			0
$535$	−58.4373	−	33.7388i	−2.52646	−	1.45865i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−15.9047			−0.685062
$540$		0			0
$541$	19.1191			0.821994			0.410997	−	0.911637i	$-0.365181\pi$
$541$	19.1191			0.821994			0.410997	+	0.911637i	$0.365181\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−39.4282	−	22.7639i	−1.68892	−	0.975097i
$546$		0			0
$547$	22.8869	−	13.2137i	0.978571	−	0.564978i	0.0767328	−	0.997052i	$-0.475551\pi$
$547$	22.8869	−	13.2137i	0.978571	−	0.564978i	0.901839	+	0.432073i	$0.142218\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	18.9169	+	32.7650i	0.805885	+	1.39583i
$552$		0			0
$553$	−9.39250	+	16.2683i	−0.399410	+	0.691798i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	24.9370i		−	1.05662i	−0.849053	−	0.528308i	$-0.822827\pi$
$557$		−	24.9370i		−	1.05662i	0.849053	−	0.528308i	$-0.177173\pi$
$558$		0			0
$559$			41.5075i			1.75558i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	15.2599	−	26.4309i	0.643127	−	1.11393i	−0.341604	−	0.939844i	$-0.610970\pi$
$563$	15.2599	−	26.4309i	0.643127	−	1.11393i	0.984731	−	0.174084i	$-0.0556964\pi$
$564$		0			0
$565$	2.47879	+	4.29339i	0.104284	+	0.180624i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.93936	−	5.16114i	0.374758	−	0.216366i	−0.300777	−	0.953694i	$-0.597246\pi$
$569$	8.93936	−	5.16114i	0.374758	−	0.216366i	0.675535	+	0.737328i	$0.263913\pi$
$570$		0			0
$571$	−7.55903	−	4.36421i	−0.316335	−	0.182636i	0.333423	−	0.942777i	$-0.391796\pi$
$571$	−7.55903	−	4.36421i	−0.316335	−	0.182636i	−0.649758	+	0.760141i	$0.725130\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	5.35270			0.223223
$576$		0			0
$577$	34.4398			1.43375			0.716874	−	0.697203i	$-0.245572\pi$
$577$	34.4398			1.43375			0.716874	+	0.697203i	$0.245572\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.52935	+	0.882972i	0.0634483	+	0.0366319i
$582$		0			0
$583$	10.1203	−	5.84294i	0.419139	−	0.241990i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.31697	−	4.01312i	−0.0956318	−	0.165639i	0.814240	−	0.580528i	$-0.197154\pi$
$587$	−2.31697	−	4.01312i	−0.0956318	−	0.165639i	−0.909872	+	0.414889i	$0.863820\pi$
$588$		0			0
$589$	−5.10823	+	8.84772i	−0.210481	+	0.364564i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	1.49543i		−	0.0614098i	−0.999528	−	0.0307049i	$-0.990225\pi$
$593$		−	1.49543i		−	0.0614098i	0.999528	−	0.0307049i	$-0.00977521\pi$
$594$		0			0
$595$			22.4723i			0.921275i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−15.8095	+	27.3828i	−0.645957	+	1.11883i	0.338123	+	0.941102i	$0.390208\pi$
$599$	−15.8095	+	27.3828i	−0.645957	+	1.11883i	−0.984080	+	0.177728i	$0.943125\pi$
$600$		0			0
$601$	7.08294	+	12.2680i	0.288919	+	0.500423i	0.973552	−	0.228465i	$-0.0733707\pi$
$601$	7.08294	+	12.2680i	0.288919	+	0.500423i	−0.684633	+	0.728888i	$0.740037\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	11.9992	−	6.92775i	0.487837	−	0.281653i
$606$		0			0
$607$	−7.26079	−	4.19202i	−0.294706	−	0.170149i	0.345356	−	0.938472i	$-0.387758\pi$
$607$	−7.26079	−	4.19202i	−0.294706	−	0.170149i	−0.640062	+	0.768323i	$0.721092\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	13.0269			0.527011
$612$		0			0
$613$	−20.9574			−0.846462			−0.423231	−	0.906022i	$-0.639104\pi$
$613$	−20.9574			−0.846462			−0.423231	+	0.906022i	$0.639104\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	25.5516	+	14.7522i	1.02867	+	0.593903i	0.916603	−	0.399798i	$-0.130920\pi$
$617$	25.5516	+	14.7522i	1.02867	+	0.593903i	0.112066	+	0.993701i	$0.464253\pi$
$618$		0			0
$619$	−32.7743	+	18.9222i	−1.31731	+	0.760549i	−0.983295	−	0.182019i	$-0.941737\pi$
$619$	−32.7743	+	18.9222i	−1.31731	+	0.760549i	−0.334015	+	0.942568i	$0.608404\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−7.95556	−	13.7794i	−0.318733	−	0.552061i
$624$		0			0
$625$	5.09464	−	8.82417i	0.203786	−	0.352967i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	7.14197i		−	0.284769i
$630$		0			0
$631$			15.9867i			0.636420i	0.948020	+	0.318210i	$0.103082\pi$
$631$			15.9867i			0.636420i	−0.948020	+	0.318210i	$0.896918\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−23.5658	+	40.8171i	−0.935180	+	1.61978i
$636$		0			0
$637$	−14.1899	−	24.5776i	−0.562225	−	0.973802i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−28.3907	+	16.3914i	−1.12136	+	0.647420i	−0.941749	−	0.336317i	$-0.890819\pi$
$641$	−28.3907	+	16.3914i	−1.12136	+	0.647420i	−0.179616	+	0.983737i	$0.557485\pi$
$642$		0			0
$643$	4.53896	+	2.62057i	0.178999	+	0.103345i	0.586822	−	0.809716i	$-0.300379\pi$
$643$	4.53896	+	2.62057i	0.178999	+	0.103345i	−0.407823	+	0.913061i	$0.633712\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	30.4906			1.19871			0.599354	−	0.800484i	$-0.295424\pi$
$647$	30.4906			1.19871			0.599354	+	0.800484i	$0.295424\pi$
$648$		0			0
$649$	−7.20848			−0.282958
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−21.9758	−	12.6877i	−0.859980	−	0.496510i	0.00402567	−	0.999992i	$-0.498719\pi$
$653$	−21.9758	−	12.6877i	−0.859980	−	0.496510i	−0.864006	+	0.503482i	$0.832052\pi$
$654$		0			0
$655$	−47.4660	+	27.4045i	−1.85465	+	1.07078i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	16.6127	+	28.7740i	0.647137	+	1.12087i	0.983803	+	0.179250i	$0.0573672\pi$
$659$	16.6127	+	28.7740i	0.647137	+	1.12087i	−0.336666	+	0.941624i	$0.609299\pi$
$660$		0			0
$661$	−15.9993	+	27.7116i	−0.622301	+	1.07786i	0.366755	+	0.930317i	$0.380469\pi$
$661$	−15.9993	+	27.7116i	−0.622301	+	1.07786i	−0.989056	+	0.147539i	$0.952865\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	57.1088i		−	2.21458i
$666$		0			0
$667$			6.27199i			0.242852i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.15595	−	5.46627i	0.121834	−	0.211023i
$672$		0			0
$673$	−25.1871	−	43.6253i	−0.970891	−	1.68163i	−0.692878	−	0.721055i	$-0.743658\pi$
$673$	−25.1871	−	43.6253i	−0.970891	−	1.68163i	−0.278013	−	0.960577i	$-0.589676\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−29.1301	+	16.8183i	−1.11956	+	0.646379i	−0.941289	−	0.337603i	$-0.890384\pi$
$677$	−29.1301	+	16.8183i	−1.11956	+	0.646379i	−0.178272	+	0.983981i	$0.557051\pi$
$678$		0			0
$679$	45.0884	+	26.0318i	1.73033	+	0.999009i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	12.2382			0.468280			0.234140	−	0.972203i	$-0.424773\pi$
$683$	12.2382			0.468280			0.234140	+	0.972203i	$0.424773\pi$
$684$		0			0
$685$	−26.9045			−1.02797
$686$		0			0
$687$		0			0
$688$		0			0
$689$	18.0583	+	10.4260i	0.687967	+	0.397198i
$690$		0			0
$691$	29.2860	−	16.9083i	1.11409	−	0.643222i	0.174207	−	0.984709i	$-0.444264\pi$
$691$	29.2860	−	16.9083i	1.11409	−	0.643222i	0.939886	+	0.341487i	$0.110931\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.984316	+	1.70488i	0.0373372	+	0.0646700i
$696$		0			0
$697$	−5.77180	+	9.99704i	−0.218622	+	0.378665i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			40.9032i			1.54489i	0.635079	+	0.772447i	$0.280967\pi$
$701$			40.9032i			1.54489i	−0.635079	+	0.772447i	$0.719033\pi$
$702$		0			0
$703$			18.1499i			0.684535i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.93062	+	6.80804i	−0.147826	+	0.256043i
$708$		0			0
$709$	0.286310	+	0.495903i	0.0107526	+	0.0186240i	0.871352	−	0.490659i	$-0.163244\pi$
$709$	0.286310	+	0.495903i	0.0107526	+	0.0186240i	−0.860599	+	0.509283i	$0.829911\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.46676	+	0.846832i	−0.0549304	+	0.0317141i
$714$		0			0
$715$	−37.6916	−	21.7613i	−1.40959	−	0.813825i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.517752			0.0193089			0.00965445	−	0.999953i	$-0.496927\pi$
$719$	0.517752			0.0193089			0.00965445	+	0.999953i	$0.496927\pi$
$720$		0			0
$721$	13.8692			0.516518
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−50.9984	−	29.4440i	−1.89403	−	1.09352i
$726$		0			0
$727$	7.28291	−	4.20479i	0.270108	−	0.155947i	−0.358829	−	0.933403i	$-0.616824\pi$
$727$	7.28291	−	4.20479i	0.270108	−	0.155947i	0.628937	+	0.777456i	$0.283490\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−7.87029	−	13.6318i	−0.291093	−	0.504188i
$732$		0			0
$733$	−6.55945	+	11.3613i	−0.242279	+	0.419639i	−0.961363	−	0.275284i	$-0.911228\pi$
$733$	−6.55945	+	11.3613i	−0.242279	+	0.419639i	0.719084	+	0.694923i	$0.244562\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	26.8721i		−	0.989845i
$738$		0			0
$739$			9.78098i			0.359799i	0.983685	+	0.179900i	$0.0575773\pi$
$739$			9.78098i			0.359799i	−0.983685	+	0.179900i	$0.942423\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.703207	−	1.21799i	0.0257982	−	0.0446838i	−0.852838	−	0.522175i	$-0.825121\pi$
$743$	0.703207	−	1.21799i	0.0257982	−	0.0446838i	0.878636	+	0.477492i	$0.158454\pi$
$744$		0			0
$745$	−16.4410	−	28.4767i	−0.602352	−	1.04330i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−60.6102	+	34.9933i	−2.21465	+	1.27863i
$750$		0			0
$751$	−6.49013	−	3.74708i	−0.236828	−	0.136733i	0.376890	−	0.926258i	$-0.376993\pi$
$751$	−6.49013	−	3.74708i	−0.236828	−	0.136733i	−0.613718	+	0.789525i	$0.710327\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−66.3491			−2.41469
$756$		0			0
$757$	−36.6513			−1.33211			−0.666057	−	0.745901i	$-0.732019\pi$
$757$	−36.6513			−1.33211			−0.666057	+	0.745901i	$0.732019\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	30.5513	+	17.6388i	1.10749	+	0.639407i	0.938177	−	0.346156i	$-0.112513\pi$
$761$	30.5513	+	17.6388i	1.10749	+	0.639407i	0.169308	+	0.985563i	$0.445847\pi$
$762$		0			0
$763$	−40.8942	+	23.6103i	−1.48047	+	0.854750i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.43130	−	11.1393i	−0.232221	−	0.402218i
$768$		0			0
$769$	−19.4694	+	33.7219i	−0.702083	+	1.21604i	0.265650	+	0.964069i	$0.414413\pi$
$769$	−19.4694	+	33.7219i	−0.702083	+	1.21604i	−0.967734	+	0.251975i	$0.918920\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	47.4524i		−	1.70674i	−0.521303	−	0.853372i	$-0.674554\pi$
$773$		−	47.4524i		−	1.70674i	0.521303	−	0.853372i	$-0.325446\pi$
$774$		0			0
$775$		−	15.9019i		−	0.571212i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	14.6678	−	25.4054i	0.525530	−	0.910244i
$780$		0			0
$781$	−0.0967186	−	0.167522i	−0.00346086	−	0.00599439i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	63.6432	−	36.7444i	2.27152	−	1.31146i
$786$		0			0
$787$	19.0786	+	11.0150i	0.680078	+	0.392643i	0.799884	−	0.600154i	$-0.204894\pi$
$787$	19.0786	+	11.0150i	0.680078	+	0.392643i	−0.119806	+	0.992797i	$0.538227\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	5.14192			0.182826
$792$		0			0
$793$	11.2628			0.399953
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−7.74174	−	4.46970i	−0.274227	−	0.158325i	0.356580	−	0.934265i	$-0.383943\pi$
$797$	−7.74174	−	4.46970i	−0.274227	−	0.158325i	−0.630807	+	0.775940i	$0.717276\pi$
$798$		0			0
$799$	−4.27824	+	2.47004i	−0.151353	+	0.0873838i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−17.6406	−	30.5544i	−0.622522	−	1.07824i
$804$		0			0
$805$	4.73368	−	8.19898i	0.166840	−	0.288976i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			8.93421i			0.314110i	0.987590	+	0.157055i	$0.0502000\pi$
$809$			8.93421i			0.314110i	−0.987590	+	0.157055i	$0.949800\pi$
$810$		0			0
$811$			22.1717i			0.778552i	0.921121	+	0.389276i	$0.127275\pi$
$811$			22.1717i			0.778552i	−0.921121	+	0.389276i	$0.872725\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−39.4019	+	68.2461i	−1.38019	+	2.39056i
$816$		0			0
$817$	20.0007	+	34.6423i	0.699737	+	1.21198i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.83428	+	1.05902i	−0.0640167	+	0.0369601i	−0.531667	−	0.846954i	$-0.678434\pi$
$821$	−1.83428	+	1.05902i	−0.0640167	+	0.0369601i	0.467650	+	0.883914i	$0.345101\pi$
$822$		0			0
$823$	20.3807	+	11.7668i	0.710428	+	0.410166i	0.811219	−	0.584742i	$-0.198804\pi$
$823$	20.3807	+	11.7668i	0.710428	+	0.410166i	−0.100792	+	0.994908i	$0.532138\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−15.3293			−0.533051			−0.266526	−	0.963828i	$-0.585876\pi$
$827$	−15.3293			−0.533051			−0.266526	+	0.963828i	$0.585876\pi$
$828$		0			0
$829$	−6.88566			−0.239149			−0.119574	−	0.992825i	$-0.538153\pi$
$829$	−6.88566			−0.239149			−0.119574	+	0.992825i	$0.538153\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	9.32040	+	5.38114i	0.322933	+	0.186445i
$834$		0			0
$835$	−17.6279	+	10.1775i	−0.610038	+	0.352205i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−17.1856	−	29.7663i	−0.593312	−	1.02765i	−0.993783	−	0.111337i	$-0.964487\pi$
$839$	−17.1856	−	29.7663i	−0.593312	−	1.02765i	0.400470	−	0.916310i	$-0.368847\pi$
$840$		0			0
$841$	20.0007	−	34.6423i	0.689681	−	1.19456i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	32.4600i		−	1.11666i
$846$		0			0
$847$		−	14.3707i		−	0.493783i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.50442	+	2.60574i	−0.0515709	+	0.0893234i
$852$		0			0
$853$	−28.4800	−	49.3288i	−0.975136	−	1.68898i	−0.679486	−	0.733688i	$-0.737797\pi$
$853$	−28.4800	−	49.3288i	−0.975136	−	1.68898i	−0.295650	−	0.955296i	$-0.595536\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−12.9801	+	7.49405i	−0.443391	+	0.255992i	−0.705035	−	0.709172i	$-0.749069\pi$
$857$	−12.9801	+	7.49405i	−0.443391	+	0.255992i	0.261644	+	0.965164i	$0.415735\pi$
$858$		0			0
$859$	37.3920	+	21.5883i	1.27580	+	0.736583i	0.976073	−	0.217443i	$-0.0697716\pi$
$859$	37.3920	+	21.5883i	1.27580	+	0.736583i	0.299725	+	0.954025i	$0.403105\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−48.9439			−1.66607			−0.833035	−	0.553220i	$-0.813399\pi$
$863$	−48.9439			−1.66607			−0.833035	+	0.553220i	$0.813399\pi$
$864$		0			0
$865$	20.5522			0.698797
$866$		0			0
$867$		0			0
$868$		0			0
$869$	11.9482	+	6.89830i	0.405315	+	0.234009i
$870$		0			0
$871$	41.5257	−	23.9749i	1.40704	−	0.812357i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	13.0979	+	22.6863i	0.442791	+	0.766936i
$876$		0			0
$877$	−14.4280	+	24.9901i	−0.487200	+	0.843854i	−0.999892	−	0.0147181i	$-0.995315\pi$
$877$	−14.4280	+	24.9901i	−0.487200	+	0.843854i	0.512692	+	0.858573i	$0.328648\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			10.9613i			0.369294i	0.982805	+	0.184647i	$0.0591143\pi$
$881$			10.9613i			0.369294i	−0.982805	+	0.184647i	$0.940886\pi$
$882$		0			0
$883$		−	23.8707i		−	0.803313i	−0.915790	−	0.401657i	$-0.868435\pi$
$883$		−	23.8707i		−	0.803313i	0.915790	−	0.401657i	$-0.131565\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−27.2765	+	47.2442i	−0.915854	+	1.58631i	−0.110207	+	0.993909i	$0.535151\pi$
$887$	−27.2765	+	47.2442i	−0.915854	+	1.58631i	−0.805647	+	0.592397i	$0.798182\pi$
$888$		0			0
$889$	24.4420	+	42.3349i	0.819760	+	1.41987i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	10.8723	−	6.27711i	0.363826	−	0.210055i
$894$		0			0
$895$	38.7904	+	22.3956i	1.29662	+	0.748604i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	18.6329			0.621442
$900$		0			0
$901$	−7.90754			−0.263438
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−30.6938	−	17.7210i	−1.02029	−	0.589068i
$906$		0			0
$907$	44.9556	−	25.9552i	1.49273	−	0.861827i	0.492762	−	0.870164i	$-0.335987\pi$
$907$	44.9556	−	25.9552i	1.49273	−	0.861827i	0.999965	+	0.00833717i	$0.00265384\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−27.0141	−	46.7897i	−0.895016	−	1.55021i	−0.833785	−	0.552089i	$-0.813831\pi$
$911$	−27.0141	−	46.7897i	−0.895016	−	1.55021i	−0.0612304	−	0.998124i	$-0.519502\pi$
$912$		0			0
$913$	0.648497	−	1.12323i	0.0214621	−	0.0371735i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			56.8470i			1.87725i
$918$		0			0
$919$		−	26.0348i		−	0.858808i	−0.903113	−	0.429404i	$-0.858724\pi$
$919$		−	26.0348i		−	0.858808i	0.903113	−	0.429404i	$-0.141276\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.172582	−	0.298921i	0.00568060	−	0.00983909i
$924$		0			0
$925$	−14.1251	−	24.4653i	−0.464429	−	0.804415i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	33.1077	−	19.1148i	1.08623	−	0.627135i	0.153659	−	0.988124i	$-0.450894\pi$
$929$	33.1077	−	19.1148i	1.08623	−	0.627135i	0.932570	+	0.360989i	$0.117561\pi$
$930$		0			0
$931$	−23.6859	−	13.6751i	−0.776274	−	0.448182i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	16.5047			0.539763
$936$		0			0
$937$	−19.6872			−0.643154			−0.321577	−	0.946883i	$-0.604213\pi$
$937$	−19.6872			−0.643154			−0.321577	+	0.946883i	$0.604213\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	26.5374	+	15.3214i	0.865094	+	0.499462i	0.865715	−	0.500537i	$-0.166864\pi$
$941$	26.5374	+	15.3214i	0.865094	+	0.499462i	−0.000620548		1.00000i	$0.500198\pi$
$942$		0			0
$943$	4.21166	−	2.43160i	0.137150	−	0.0791838i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	16.8490	+	29.1833i	0.547519	+	0.948331i	0.998444	+	0.0557689i	$0.0177610\pi$
$947$	16.8490	+	29.1833i	0.547519	+	0.948331i	−0.450925	+	0.892562i	$0.648906\pi$
$948$		0			0
$949$	31.4773	−	54.5203i	1.02180	−	1.76980i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	58.8965i		−	1.90784i	−0.300054	−	0.953922i	$-0.597005\pi$
$953$		−	58.8965i		−	1.90784i	0.300054	−	0.953922i	$-0.402995\pi$
$954$		0			0
$955$			78.5516i			2.54187i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−13.9524	+	24.1663i	−0.450548	+	0.780371i
$960$		0			0
$961$	−12.9842	−	22.4893i	−0.418846	−	0.725462i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−6.80126	+	3.92671i	−0.218940	+	0.126405i
$966$		0			0
$967$	−0.153116	−	0.0884018i	−0.00492389	−	0.00284281i	0.497536	−	0.867443i	$-0.334238\pi$
$967$	−0.153116	−	0.0884018i	−0.00492389	−	0.00284281i	−0.502460	+	0.864600i	$0.667572\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	8.94370			0.287017			0.143509	−	0.989649i	$-0.454162\pi$
$971$	8.94370			0.287017			0.143509	+	0.989649i	$0.454162\pi$
$972$		0			0
$973$	2.04183			0.0654581
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.61238	−	0.930909i	−0.0515847	−	0.0297824i	0.473986	−	0.880532i	$-0.342815\pi$
$977$	−1.61238	−	0.930909i	−0.0515847	−	0.0297824i	−0.525571	+	0.850750i	$0.676148\pi$
$978$		0			0
$979$	−10.1203	+	5.84294i	−0.323445	+	0.186741i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	8.41816	+	14.5807i	0.268498	+	0.465052i	0.968474	−	0.249114i	$-0.0801395\pi$
$983$	8.41816	+	14.5807i	0.268498	+	0.465052i	−0.699976	+	0.714166i	$0.746806\pi$
$984$		0			0
$985$	9.83431	−	17.0335i	0.313347	−	0.542733i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			6.63136i			0.210865i
$990$		0			0
$991$		−	15.9182i		−	0.505658i	−0.967511	−	0.252829i	$-0.918639\pi$
$991$		−	15.9182i		−	0.505658i	0.967511	−	0.252829i	$-0.0813609\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	24.0245	−	41.6116i	0.761626	−	1.31918i
$996$		0			0
$997$	−3.40192	−	5.89230i	−0.107740	−	0.186611i	0.807114	−	0.590395i	$-0.201028\pi$
$997$	−3.40192	−	5.89230i	−0.107740	−	0.186611i	−0.914854	+	0.403784i	$0.867695\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.s.a.287.12		24
3.2	odd	2		288.2.s.a.95.4	✓	24
4.3	odd	2	inner	864.2.s.a.287.11		24
8.3	odd	2		1728.2.s.g.1151.1		24
8.5	even	2		1728.2.s.g.1151.2		24
9.2	odd	6	inner	864.2.s.a.575.11		24
9.4	even	3		2592.2.c.c.2591.4		24
9.5	odd	6		2592.2.c.c.2591.22		24
9.7	even	3		288.2.s.a.191.9	yes	24
12.11	even	2		288.2.s.a.95.9	yes	24
24.5	odd	2		576.2.s.g.383.9		24
24.11	even	2		576.2.s.g.383.4		24
36.7	odd	6		288.2.s.a.191.4	yes	24
36.11	even	6	inner	864.2.s.a.575.12		24
36.23	even	6		2592.2.c.c.2591.21		24
36.31	odd	6		2592.2.c.c.2591.3		24
72.5	odd	6		5184.2.c.m.5183.4		24
72.11	even	6		1728.2.s.g.575.2		24
72.13	even	6		5184.2.c.m.5183.22		24
72.29	odd	6		1728.2.s.g.575.1		24
72.43	odd	6		576.2.s.g.191.9		24
72.59	even	6		5184.2.c.m.5183.3		24
72.61	even	6		576.2.s.g.191.4		24
72.67	odd	6		5184.2.c.m.5183.21		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.s.a.95.4	✓	24	3.2	odd	2
288.2.s.a.95.9	yes	24	12.11	even	2
288.2.s.a.191.4	yes	24	36.7	odd	6
288.2.s.a.191.9	yes	24	9.7	even	3
576.2.s.g.191.4		24	72.61	even	6
576.2.s.g.191.9		24	72.43	odd	6
576.2.s.g.383.4		24	24.11	even	2
576.2.s.g.383.9		24	24.5	odd	2
864.2.s.a.287.11		24	4.3	odd	2	inner
864.2.s.a.287.12		24	1.1	even	1	trivial
864.2.s.a.575.11		24	9.2	odd	6	inner
864.2.s.a.575.12		24	36.11	even	6	inner
1728.2.s.g.575.1		24	72.29	odd	6
1728.2.s.g.575.2		24	72.11	even	6
1728.2.s.g.1151.1		24	8.3	odd	2
1728.2.s.g.1151.2		24	8.5	even	2
2592.2.c.c.2591.3		24	36.31	odd	6
2592.2.c.c.2591.4		24	9.4	even	3
2592.2.c.c.2591.21		24	36.23	even	6
2592.2.c.c.2591.22		24	9.5	odd	6
5184.2.c.m.5183.3		24	72.59	even	6
5184.2.c.m.5183.4		24	72.5	odd	6
5184.2.c.m.5183.21		24	72.67	odd	6
5184.2.c.m.5183.22		24	72.13	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.01113 + 1.73848i) q^{5} +(3.12309 - 1.80312i) q^{7} +O(q^{10})\)	\(q+(3.01113 + 1.73848i) q^{5} +(3.12309 - 1.80312i) q^{7} +(-1.32430 - 2.29375i) q^{11} +(2.36304 - 4.09290i) q^{13} +1.79223i q^{17} -4.55459i q^{19} +(0.377525 - 0.653893i) q^{23} +(3.54460 + 6.13942i) q^{25} +(-7.19382 + 4.15336i) q^{29} +(-1.94259 - 1.12156i) q^{31} +12.5387 q^{35} -3.98496 q^{37} +(5.57798 + 3.22045i) q^{41} +(-7.60601 + 4.39133i) q^{43} +(1.37819 + 2.38710i) q^{47} +(3.00247 - 5.20044i) q^{49} +4.41211i q^{53} -9.20903i q^{55} +(1.36081 - 2.35700i) q^{59} +(1.19156 + 2.06384i) q^{61} +(14.2308 - 8.21616i) q^{65} +(8.78651 + 5.07289i) q^{67} +0.0730340 q^{71} +13.3207 q^{73} +(-8.27180 - 4.77573i) q^{77} +(-4.51115 + 2.60452i) q^{79} +(0.244846 + 0.424085i) q^{83} +(-3.11576 + 5.39665i) q^{85} -4.41211i q^{89} -17.0433i q^{91} +(7.91805 - 13.7145i) q^{95} +(7.21855 + 12.5029i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 12 q^{25} - 24 q^{29} + 36 q^{41} + 12 q^{49} + 48 q^{65} + 24 q^{73} + 48 q^{77} + 12 q^{97}+O(q^{100}) \) 24 * q + 12 * q^25 - 24 * q^29 + 36 * q^41 + 12 * q^49 + 48 * q^65 + 24 * q^73 + 48 * q^77 + 12 * q^97

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