LMFDB - Embedded newform 1944.2.i.n.1297.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1944,2,Mod(649,1944)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1944, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1944.649");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1944 = 2^{3} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1944.i (of order $3$, 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:	$15.5229181529$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1297.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1944.1297
Dual form			1944.2.i.n.649.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 + 0.633975i) q^{5} +(-1.73205 - 3.00000i) q^{7} +O(q^{10})$	$q+(-0.366025 + 0.633975i) q^{5} +(-1.73205 - 3.00000i) q^{7} +(3.09808 + 5.36603i) q^{11} +(1.23205 - 2.13397i) q^{13} -0.732051 q^{17} -4.46410 q^{19} +(4.36603 - 7.56218i) q^{23} +(2.23205 + 3.86603i) q^{25} +(1.26795 + 2.19615i) q^{29} +(-1.23205 + 2.13397i) q^{31} +2.53590 q^{35} +2.53590 q^{37} +(4.73205 - 8.19615i) q^{41} +(2.96410 + 5.13397i) q^{43} +(-3.46410 - 6.00000i) q^{47} +(-2.50000 + 4.33013i) q^{49} +7.66025 q^{53} -4.53590 q^{55} +(0.901924 - 1.56218i) q^{59} +(0.767949 + 1.33013i) q^{61} +(0.901924 + 1.56218i) q^{65} +(1.76795 - 3.06218i) q^{67} +6.19615 q^{71} +11.3923 q^{73} +(10.7321 - 18.5885i) q^{77} +(-6.96410 - 12.0622i) q^{79} +(6.36603 + 11.0263i) q^{83} +(0.267949 - 0.464102i) q^{85} +12.0000 q^{89} -8.53590 q^{91} +(1.63397 - 2.83013i) q^{95} +(-5.96410 - 10.3301i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5}+O(q^{10}) $ 4 * q + 2 * q^5	$ 4 q + 2 q^{5} + 2 q^{11} - 2 q^{13} + 4 q^{17} - 4 q^{19} + 14 q^{23} + 2 q^{25} + 12 q^{29} + 2 q^{31} + 24 q^{35} + 24 q^{37} + 12 q^{41} - 2 q^{43} - 10 q^{49} - 4 q^{53} - 32 q^{55} + 14 q^{59} + 10 q^{61} + 14 q^{65} + 14 q^{67} + 4 q^{71} + 4 q^{73} + 36 q^{77} - 14 q^{79} + 22 q^{83} + 8 q^{85} + 48 q^{89} - 48 q^{91} + 10 q^{95} - 10 q^{97}+O(q^{100}) $ 4 * q + 2 * q^5 + 2 * q^11 - 2 * q^13 + 4 * q^17 - 4 * q^19 + 14 * q^23 + 2 * q^25 + 12 * q^29 + 2 * q^31 + 24 * q^35 + 24 * q^37 + 12 * q^41 - 2 * q^43 - 10 * q^49 - 4 * q^53 - 32 * q^55 + 14 * q^59 + 10 * q^61 + 14 * q^65 + 14 * q^67 + 4 * q^71 + 4 * q^73 + 36 * q^77 - 14 * q^79 + 22 * q^83 + 8 * q^85 + 48 * q^89 - 48 * q^91 + 10 * q^95 - 10 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1944\mathbb{Z}\right)^\times$.

$n$	$487$	$973$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.366025	+	0.633975i	−0.163692	+	0.283522i	−0.936190	−	0.351495i	$-0.885674\pi$
$5$	−0.366025	+	0.633975i	−0.163692	+	0.283522i	0.772498	+	0.635017i	$0.219007\pi$
$6$		0			0
$7$	−1.73205	−	3.00000i	−0.654654	−	1.13389i	−0.981981	−	0.188982i	$-0.939481\pi$
$7$	−1.73205	−	3.00000i	−0.654654	−	1.13389i	0.327327	−	0.944911i	$-0.393852\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.09808	+	5.36603i	0.934105	+	1.61792i	0.776222	+	0.630460i	$0.217134\pi$
$11$	3.09808	+	5.36603i	0.934105	+	1.61792i	0.157883	+	0.987458i	$0.449533\pi$
$12$		0			0
$13$	1.23205	−	2.13397i	0.341709	−	0.591858i	−0.643041	−	0.765832i	$-0.722327\pi$
$13$	1.23205	−	2.13397i	0.341709	−	0.591858i	0.984750	+	0.173974i	$0.0556608\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.732051			−0.177548			−0.0887742	−	0.996052i	$-0.528295\pi$
$17$	−0.732051			−0.177548			−0.0887742	+	0.996052i	$0.528295\pi$
$18$		0			0
$19$	−4.46410			−1.02414			−0.512068	−	0.858945i	$-0.671120\pi$
$19$	−4.46410			−1.02414			−0.512068	+	0.858945i	$0.671120\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.36603	−	7.56218i	0.910379	−	1.57682i	0.0968500	−	0.995299i	$-0.469123\pi$
$23$	4.36603	−	7.56218i	0.910379	−	1.57682i	0.813529	−	0.581524i	$-0.197543\pi$
$24$		0			0
$25$	2.23205	+	3.86603i	0.446410	+	0.773205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.26795	+	2.19615i	0.235452	+	0.407815i	0.959404	−	0.282035i	$-0.0910095\pi$
$29$	1.26795	+	2.19615i	0.235452	+	0.407815i	−0.723952	+	0.689851i	$0.757676\pi$
$30$		0			0
$31$	−1.23205	+	2.13397i	−0.221283	+	0.383273i	−0.955198	−	0.295968i	$-0.904358\pi$
$31$	−1.23205	+	2.13397i	−0.221283	+	0.383273i	0.733915	+	0.679241i	$0.237691\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.53590			0.428645
$36$		0			0
$37$	2.53590			0.416899			0.208450	−	0.978033i	$-0.433158\pi$
$37$	2.53590			0.416899			0.208450	+	0.978033i	$0.433158\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.73205	−	8.19615i	0.739022	−	1.28002i	−0.213914	−	0.976853i	$-0.568621\pi$
$41$	4.73205	−	8.19615i	0.739022	−	1.28002i	0.952936	−	0.303171i	$-0.0980455\pi$
$42$		0			0
$43$	2.96410	+	5.13397i	0.452021	+	0.782924i	0.998511	−	0.0545417i	$-0.0173698\pi$
$43$	2.96410	+	5.13397i	0.452021	+	0.782924i	−0.546490	+	0.837465i	$0.684036\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.46410	−	6.00000i	−0.505291	−	0.875190i	−0.999981	−	0.00612051i	$-0.998052\pi$
$47$	−3.46410	−	6.00000i	−0.505291	−	0.875190i	0.494690	−	0.869069i	$-0.335282\pi$
$48$		0			0
$49$	−2.50000	+	4.33013i	−0.357143	+	0.618590i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	7.66025			1.05222			0.526108	−	0.850418i	$-0.323651\pi$
$53$	7.66025			1.05222			0.526108	+	0.850418i	$0.323651\pi$
$54$		0			0
$55$	−4.53590			−0.611620
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.901924	−	1.56218i	0.117420	−	0.203378i	−0.801324	−	0.598230i	$-0.795871\pi$
$59$	0.901924	−	1.56218i	0.117420	−	0.203378i	0.918745	+	0.394852i	$0.129204\pi$
$60$		0			0
$61$	0.767949	+	1.33013i	0.0983258	+	0.170305i	0.910992	−	0.412424i	$-0.135318\pi$
$61$	0.767949	+	1.33013i	0.0983258	+	0.170305i	−0.812666	+	0.582730i	$0.801985\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.901924	+	1.56218i	0.111870	+	0.193764i
$66$		0			0
$67$	1.76795	−	3.06218i	0.215989	−	0.374105i	−0.737589	−	0.675250i	$-0.764036\pi$
$67$	1.76795	−	3.06218i	0.215989	−	0.374105i	0.953578	+	0.301146i	$0.0973690\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.19615			0.735348			0.367674	−	0.929955i	$-0.380154\pi$
$71$	6.19615			0.735348			0.367674	+	0.929955i	$0.380154\pi$
$72$		0			0
$73$	11.3923			1.33337			0.666684	−	0.745340i	$-0.267713\pi$
$73$	11.3923			1.33337			0.666684	+	0.745340i	$0.267713\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	10.7321	−	18.5885i	1.22303	−	2.11835i
$78$		0			0
$79$	−6.96410	−	12.0622i	−0.783523	−	1.35710i	−0.929878	−	0.367869i	$-0.880088\pi$
$79$	−6.96410	−	12.0622i	−0.783523	−	1.35710i	0.146355	−	0.989232i	$-0.453246\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.36603	+	11.0263i	0.698762	+	1.21029i	0.968896	+	0.247469i	$0.0795987\pi$
$83$	6.36603	+	11.0263i	0.698762	+	1.21029i	−0.270134	+	0.962823i	$0.587068\pi$
$84$		0			0
$85$	0.267949	−	0.464102i	0.0290632	−	0.0503389i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	12.0000			1.27200			0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000			1.27200			0.635999	+	0.771690i	$0.280588\pi$
$90$		0			0
$91$	−8.53590			−0.894805
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.63397	−	2.83013i	0.167642	−	0.290365i
$96$		0			0
$97$	−5.96410	−	10.3301i	−0.605563	−	1.04887i	−0.991962	−	0.126534i	$-0.959615\pi$
$97$	−5.96410	−	10.3301i	−0.605563	−	1.04887i	0.386400	−	0.922332i	$-0.373719\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.19615	+	3.80385i	0.218525	+	0.378497i	0.954357	−	0.298667i	$-0.0965420\pi$
$101$	2.19615	+	3.80385i	0.218525	+	0.378497i	−0.735832	+	0.677164i	$0.763209\pi$
$102$		0			0
$103$	9.42820	−	16.3301i	0.928988	−	1.60906i	0.143971	−	0.989582i	$-0.454013\pi$
$103$	9.42820	−	16.3301i	0.928988	−	1.60906i	0.785018	−	0.619473i	$-0.212654\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.46410			−0.914929			−0.457465	−	0.889228i	$-0.651242\pi$
$107$	−9.46410			−0.914929			−0.457465	+	0.889228i	$0.651242\pi$
$108$		0			0
$109$	16.4641			1.57697			0.788487	−	0.615051i	$-0.210865\pi$
$109$	16.4641			1.57697			0.788487	+	0.615051i	$0.210865\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.46410	−	6.00000i	0.325875	−	0.564433i	−0.655814	−	0.754923i	$-0.727674\pi$
$113$	3.46410	−	6.00000i	0.325875	−	0.564433i	0.981689	+	0.190490i	$0.0610077\pi$
$114$		0			0
$115$	3.19615	+	5.53590i	0.298043	+	0.516225i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.26795	+	2.19615i	0.116233	+	0.201321i
$120$		0			0
$121$	−13.6962	+	23.7224i	−1.24510	+	2.15658i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−6.92820			−0.619677
$126$		0			0
$127$	1.92820			0.171100			0.0855502	−	0.996334i	$-0.472735\pi$
$127$	1.92820			0.171100			0.0855502	+	0.996334i	$0.472735\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.63397	−	13.2224i	0.666983	−	1.15525i	−0.311760	−	0.950161i	$-0.600918\pi$
$131$	7.63397	−	13.2224i	0.666983	−	1.15525i	0.978743	−	0.205088i	$-0.0657482\pi$
$132$		0			0
$133$	7.73205	+	13.3923i	0.670454	+	1.16126i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.46410	+	16.3923i	0.808573	+	1.40049i	0.913852	+	0.406046i	$0.133093\pi$
$137$	9.46410	+	16.3923i	0.808573	+	1.40049i	−0.105280	+	0.994443i	$0.533574\pi$
$138$		0			0
$139$	1.73205	−	3.00000i	0.146911	−	0.254457i	−0.783174	−	0.621803i	$-0.786400\pi$
$139$	1.73205	−	3.00000i	0.146911	−	0.254457i	0.930084	+	0.367347i	$0.119734\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	15.2679			1.27677
$144$		0			0
$145$	−1.85641			−0.154166
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.0263	+	17.3660i	−0.821385	+	1.42268i	0.0832663	+	0.996527i	$0.473465\pi$
$149$	−10.0263	+	17.3660i	−0.821385	+	1.42268i	−0.904651	+	0.426153i	$0.859869\pi$
$150$		0			0
$151$	1.76795	+	3.06218i	0.143874	+	0.249196i	0.928952	−	0.370200i	$-0.120711\pi$
$151$	1.76795	+	3.06218i	0.143874	+	0.249196i	−0.785078	+	0.619396i	$0.787377\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.901924	−	1.56218i	−0.0724443	−	0.125477i
$156$		0			0
$157$	−2.69615	+	4.66987i	−0.215176	+	0.372696i	−0.953327	−	0.301939i	$-0.902366\pi$
$157$	−2.69615	+	4.66987i	−0.215176	+	0.372696i	0.738151	+	0.674636i	$0.235699\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−30.2487			−2.38393
$162$		0			0
$163$	−22.3923			−1.75390			−0.876950	−	0.480581i	$-0.840426\pi$
$163$	−22.3923			−1.75390			−0.876950	+	0.480581i	$0.840426\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.19615	−	3.80385i	0.169943	−	0.294351i	−0.768456	−	0.639902i	$-0.778975\pi$
$167$	2.19615	−	3.80385i	0.169943	−	0.294351i	0.938400	+	0.345552i	$0.112308\pi$
$168$		0			0
$169$	3.46410	+	6.00000i	0.266469	+	0.461538i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.46410	+	6.00000i	0.263371	+	0.456172i	0.967135	−	0.254262i	$-0.0818324\pi$
$173$	3.46410	+	6.00000i	0.263371	+	0.456172i	−0.703765	+	0.710433i	$0.748499\pi$
$174$		0			0
$175$	7.73205	−	13.3923i	0.584488	−	1.01236i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2.53590			−0.189542			−0.0947710	−	0.995499i	$-0.530212\pi$
$179$	−2.53590			−0.189542			−0.0947710	+	0.995499i	$0.530212\pi$
$180$		0			0
$181$	−11.3205			−0.841447			−0.420723	−	0.907189i	$-0.638224\pi$
$181$	−11.3205			−0.841447			−0.420723	+	0.907189i	$0.638224\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.928203	+	1.60770i	−0.0682429	+	0.118200i
$186$		0			0
$187$	−2.26795	−	3.92820i	−0.165849	−	0.287259i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.46410	+	16.3923i	0.684798	+	1.18611i	0.973500	+	0.228686i	$0.0734431\pi$
$191$	9.46410	+	16.3923i	0.684798	+	1.18611i	−0.288702	+	0.957419i	$0.593224\pi$
$192$		0			0
$193$	1.42820	−	2.47372i	0.102804	−	0.178062i	−0.810035	−	0.586382i	$-0.800552\pi$
$193$	1.42820	−	2.47372i	0.102804	−	0.178062i	0.912839	+	0.408320i	$0.133885\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	23.3205			1.66152			0.830759	−	0.556633i	$-0.187907\pi$
$197$	23.3205			1.66152			0.830759	+	0.556633i	$0.187907\pi$
$198$		0			0
$199$	−11.0000			−0.779769			−0.389885	−	0.920864i	$-0.627485\pi$
$199$	−11.0000			−0.779769			−0.389885	+	0.920864i	$0.627485\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.39230	−	7.60770i	0.308279	−	0.533956i
$204$		0			0
$205$	3.46410	+	6.00000i	0.241943	+	0.419058i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−13.8301	−	23.9545i	−0.956650	−	1.65697i
$210$		0			0
$211$	−7.42820	+	12.8660i	−0.511379	+	0.885734i	0.488534	+	0.872545i	$0.337532\pi$
$211$	−7.42820	+	12.8660i	−0.511379	+	0.885734i	−0.999913	+	0.0131891i	$0.995802\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.33975			−0.295968
$216$		0			0
$217$	8.53590			0.579455
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.901924	+	1.56218i	−0.0606700	+	0.105083i
$222$		0			0
$223$	−6.96410	−	12.0622i	−0.466351	−	0.807743i	0.532911	−	0.846172i	$-0.321098\pi$
$223$	−6.96410	−	12.0622i	−0.466351	−	0.807743i	−0.999261	+	0.0384284i	$0.987765\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.3923	−	18.0000i	−0.689761	−	1.19470i	−0.971915	−	0.235333i	$-0.924382\pi$
$227$	−10.3923	−	18.0000i	−0.689761	−	1.19470i	0.282153	−	0.959369i	$-0.408951\pi$
$228$		0			0
$229$	8.16025	−	14.1340i	0.539245	−	0.933999i	−0.459700	−	0.888074i	$-0.652043\pi$
$229$	8.16025	−	14.1340i	0.539245	−	0.933999i	0.998945	−	0.0459251i	$-0.0146236\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	17.1244			1.12185			0.560927	−	0.827865i	$-0.310445\pi$
$233$	17.1244			1.12185			0.560927	+	0.827865i	$0.310445\pi$
$234$		0			0
$235$	5.07180			0.330848
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.562178	+	0.973721i	−0.0363643	+	0.0629847i	−0.883635	−	0.468177i	$-0.844911\pi$
$239$	−0.562178	+	0.973721i	−0.0363643	+	0.0629847i	0.847270	+	0.531162i	$0.178244\pi$
$240$		0			0
$241$	−5.66025	−	9.80385i	−0.364609	−	0.631521i	0.624104	−	0.781341i	$-0.285464\pi$
$241$	−5.66025	−	9.80385i	−0.364609	−	0.631521i	−0.988713	+	0.149820i	$0.952131\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.83013	−	3.16987i	−0.116923	−	0.202516i
$246$		0			0
$247$	−5.50000	+	9.52628i	−0.349957	+	0.606143i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	22.5885			1.42577			0.712885	−	0.701281i	$-0.247388\pi$
$251$	22.5885			1.42577			0.712885	+	0.701281i	$0.247388\pi$
$252$		0			0
$253$	54.1051			3.40156
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.16987	+	3.75833i	−0.135353	+	0.234438i	−0.925732	−	0.378180i	$-0.876550\pi$
$257$	−2.16987	+	3.75833i	−0.135353	+	0.234438i	0.790379	+	0.612618i	$0.209884\pi$
$258$		0			0
$259$	−4.39230	−	7.60770i	−0.272925	−	0.472719i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.90192	−	5.02628i	−0.178940	−	0.309934i	0.762578	−	0.646897i	$-0.223934\pi$
$263$	−2.90192	−	5.02628i	−0.178940	−	0.309934i	−0.941518	+	0.336963i	$0.890600\pi$
$264$		0			0
$265$	−2.80385	+	4.85641i	−0.172239	+	0.298327i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−15.2679			−0.930903			−0.465452	−	0.885073i	$-0.654108\pi$
$269$	−15.2679			−0.930903			−0.465452	+	0.885073i	$0.654108\pi$
$270$		0			0
$271$	−10.4641			−0.635649			−0.317824	−	0.948150i	$-0.602952\pi$
$271$	−10.4641			−0.635649			−0.317824	+	0.948150i	$0.602952\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−13.8301	+	23.9545i	−0.833988	+	1.44451i
$276$		0			0
$277$	0.303848	+	0.526279i	0.0182564	+	0.0316211i	0.875009	−	0.484106i	$-0.160855\pi$
$277$	0.303848	+	0.526279i	0.0182564	+	0.0316211i	−0.856753	+	0.515727i	$0.827522\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4.36603	−	7.56218i	−0.260455	−	0.451122i	0.705908	−	0.708304i	$-0.250539\pi$
$281$	−4.36603	−	7.56218i	−0.260455	−	0.451122i	−0.966363	+	0.257182i	$0.917206\pi$
$282$		0			0
$283$	11.2321	−	19.4545i	0.667676	−	1.15645i	−0.310876	−	0.950450i	$-0.600622\pi$
$283$	11.2321	−	19.4545i	0.667676	−	1.15645i	0.978552	−	0.205999i	$-0.0660442\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−32.7846			−1.93521
$288$		0			0
$289$	−16.4641			−0.968477
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.66025	−	9.80385i	0.330676	−	0.572747i	−0.651969	−	0.758246i	$-0.726057\pi$
$293$	5.66025	−	9.80385i	0.330676	−	0.572747i	0.982644	+	0.185499i	$0.0593901\pi$
$294$		0			0
$295$	0.660254	+	1.14359i	0.0384415	+	0.0665826i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−10.7583	−	18.6340i	−0.622170	−	1.07763i
$300$		0			0
$301$	10.2679	−	17.7846i	0.591835	−	1.02509i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.12436			−0.0643804
$306$		0			0
$307$	−20.5359			−1.17205			−0.586023	−	0.810295i	$-0.699307\pi$
$307$	−20.5359			−1.17205			−0.586023	+	0.810295i	$0.699307\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−14.1962	+	24.5885i	−0.804990	+	1.39428i	0.111308	+	0.993786i	$0.464496\pi$
$311$	−14.1962	+	24.5885i	−0.804990	+	1.39428i	−0.916298	+	0.400498i	$0.868837\pi$
$312$		0			0
$313$	−3.80385	−	6.58846i	−0.215006	−	0.372402i	0.738268	−	0.674507i	$-0.235644\pi$
$313$	−3.80385	−	6.58846i	−0.215006	−	0.372402i	−0.953274	+	0.302106i	$0.902310\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.46410	−	16.3923i	−0.531557	−	0.920684i	−0.999322	−	0.0368305i	$-0.988274\pi$
$317$	−9.46410	−	16.3923i	−0.531557	−	0.920684i	0.467765	−	0.883853i	$-0.345059\pi$
$318$		0			0
$319$	−7.85641	+	13.6077i	−0.439874	+	0.761885i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.26795			0.181834
$324$		0			0
$325$	11.0000			0.610170
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−12.0000	+	20.7846i	−0.661581	+	1.14589i
$330$		0			0
$331$	−10.2321	−	17.7224i	−0.562404	−	0.974113i	−0.997286	−	0.0736253i	$-0.976543\pi$
$331$	−10.2321	−	17.7224i	−0.562404	−	0.974113i	0.434882	−	0.900488i	$-0.356790\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.29423	+	2.24167i	0.0707113	+	0.122476i
$336$		0			0
$337$	−16.7321	+	28.9808i	−0.911453	+	1.57868i	−0.0994397	+	0.995044i	$0.531705\pi$
$337$	−16.7321	+	28.9808i	−0.911453	+	1.57868i	−0.812013	+	0.583639i	$0.801628\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−15.2679			−0.826806
$342$		0			0
$343$	−6.92820			−0.374088
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.26795	+	2.19615i	−0.0680671	+	0.117896i	−0.898050	−	0.439893i	$-0.855017\pi$
$347$	−1.26795	+	2.19615i	−0.0680671	+	0.117896i	0.829983	+	0.557788i	$0.188350\pi$
$348$		0			0
$349$	14.1962	+	24.5885i	0.759903	+	1.31619i	0.942900	+	0.333077i	$0.108087\pi$
$349$	14.1962	+	24.5885i	0.759903	+	1.31619i	−0.182997	+	0.983113i	$0.558580\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	9.83013	+	17.0263i	0.523205	+	0.906217i	0.999635	+	0.0270052i	$0.00859708\pi$
$353$	9.83013	+	17.0263i	0.523205	+	0.906217i	−0.476430	+	0.879212i	$0.658070\pi$
$354$		0			0
$355$	−2.26795	+	3.92820i	−0.120370	+	0.208487i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−20.7846			−1.09697			−0.548485	−	0.836160i	$-0.684795\pi$
$359$	−20.7846			−1.09697			−0.548485	+	0.836160i	$0.684795\pi$
$360$		0			0
$361$	0.928203			0.0488528
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.16987	+	7.22243i	−0.218261	+	0.378039i
$366$		0			0
$367$	15.4282	+	26.7224i	0.805346	+	1.39490i	0.916057	+	0.401047i	$0.131354\pi$
$367$	15.4282	+	26.7224i	0.805346	+	1.39490i	−0.110712	+	0.993853i	$0.535313\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−13.2679	−	22.9808i	−0.688838	−	1.19310i
$372$		0			0
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	−0.336557	−	0.941663i	$-0.609263\pi$
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	0.983783	−	0.179364i	$-0.0574041\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.24871			0.321825
$378$		0			0
$379$	16.7846			0.862167			0.431084	−	0.902312i	$-0.358131\pi$
$379$	16.7846			0.862167			0.431084	+	0.902312i	$0.358131\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−14.1962	+	24.5885i	−0.725390	+	1.25641i	0.233424	+	0.972375i	$0.425007\pi$
$383$	−14.1962	+	24.5885i	−0.725390	+	1.25641i	−0.958813	+	0.284036i	$0.908326\pi$
$384$		0			0
$385$	7.85641	+	13.6077i	0.400400	+	0.693512i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	7.83013	+	13.5622i	0.397003	+	0.687630i	0.993355	−	0.115094i	$-0.0367168\pi$
$389$	7.83013	+	13.5622i	0.397003	+	0.687630i	−0.596351	+	0.802723i	$0.703384\pi$
$390$		0			0
$391$	−3.19615	+	5.53590i	−0.161636	+	0.279962i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	10.1962			0.513024
$396$		0			0
$397$	−13.0000			−0.652451			−0.326226	−	0.945292i	$-0.605777\pi$
$397$	−13.0000			−0.652451			−0.326226	+	0.945292i	$0.605777\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	8.19615	−	14.1962i	0.409296	−	0.708922i	−0.585515	−	0.810662i	$-0.699108\pi$
$401$	8.19615	−	14.1962i	0.409296	−	0.708922i	0.994811	+	0.101740i	$0.0324409\pi$
$402$		0			0
$403$	3.03590	+	5.25833i	0.151229	+	0.261936i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.85641	+	13.6077i	0.389428	+	0.674508i
$408$		0			0
$409$	−11.6603	+	20.1962i	−0.576562	+	0.998635i	0.419307	+	0.907844i	$0.362273\pi$
$409$	−11.6603	+	20.1962i	−0.576562	+	0.998635i	−0.995870	+	0.0907912i	$0.971060\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−6.24871			−0.307479
$414$		0			0
$415$	−9.32051			−0.457526
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−15.1244	+	26.1962i	−0.738873	+	1.27977i	0.214130	+	0.976805i	$0.431308\pi$
$419$	−15.1244	+	26.1962i	−0.738873	+	1.27977i	−0.953003	+	0.302961i	$0.902025\pi$
$420$		0			0
$421$	−1.00000	−	1.73205i	−0.0487370	−	0.0844150i	0.840628	−	0.541613i	$-0.182186\pi$
$421$	−1.00000	−	1.73205i	−0.0487370	−	0.0844150i	−0.889365	+	0.457198i	$0.848853\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.63397	−	2.83013i	−0.0792594	−	0.137281i
$426$		0			0
$427$	2.66025	−	4.60770i	0.128739	−	0.222982i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−20.3397			−0.979731			−0.489866	−	0.871798i	$-0.662954\pi$
$431$	−20.3397			−0.979731			−0.489866	+	0.871798i	$0.662954\pi$
$432$		0			0
$433$	−15.3923			−0.739707			−0.369853	−	0.929090i	$-0.620592\pi$
$433$	−15.3923			−0.739707			−0.369853	+	0.929090i	$0.620592\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−19.4904	+	33.7583i	−0.932351	+	1.61488i
$438$		0			0
$439$	11.1962	+	19.3923i	0.534363	+	0.925544i	0.999194	+	0.0401446i	$0.0127819\pi$
$439$	11.1962	+	19.3923i	0.534363	+	0.925544i	−0.464831	+	0.885400i	$0.653885\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14.2224	+	24.6340i	0.675728	+	1.17040i	0.976255	+	0.216622i	$0.0695040\pi$
$443$	14.2224	+	24.6340i	0.675728	+	1.17040i	−0.300527	+	0.953773i	$0.597163\pi$
$444$		0			0
$445$	−4.39230	+	7.60770i	−0.208215	+	0.360639i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−13.8038			−0.651444			−0.325722	−	0.945466i	$-0.605607\pi$
$449$	−13.8038			−0.651444			−0.325722	+	0.945466i	$0.605607\pi$
$450$		0			0
$451$	58.6410			2.76130
$452$		0			0
$453$		0			0
$454$		0			0
$455$	3.12436	−	5.41154i	0.146472	−	0.253697i
$456$		0			0
$457$	−9.42820	−	16.3301i	−0.441033	−	0.763891i	0.556734	−	0.830691i	$-0.312054\pi$
$457$	−9.42820	−	16.3301i	−0.441033	−	0.763891i	−0.997766	+	0.0667999i	$0.978721\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−11.0981	−	19.2224i	−0.516889	−	0.895278i	−0.999808	−	0.0196127i	$-0.993757\pi$
$461$	−11.0981	−	19.2224i	−0.516889	−	0.895278i	0.482919	−	0.875665i	$-0.339577\pi$
$462$		0			0
$463$	−3.30385	+	5.72243i	−0.153543	+	0.265944i	−0.932527	−	0.361099i	$-0.882402\pi$
$463$	−3.30385	+	5.72243i	−0.153543	+	0.265944i	0.778985	+	0.627043i	$0.215735\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.46410			−0.437946			−0.218973	−	0.975731i	$-0.570271\pi$
$467$	−9.46410			−0.437946			−0.218973	+	0.975731i	$0.570271\pi$
$468$		0			0
$469$	−12.2487			−0.565593
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−18.3660	+	31.8109i	−0.844471	+	1.46267i
$474$		0			0
$475$	−9.96410	−	17.2583i	−0.457184	−	0.791866i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.83013	−	13.5622i	−0.357768	−	0.619672i	0.629820	−	0.776741i	$-0.283129\pi$
$479$	−7.83013	−	13.5622i	−0.357768	−	0.619672i	−0.987588	+	0.157069i	$0.949795\pi$
$480$		0			0
$481$	3.12436	−	5.41154i	0.142458	−	0.246745i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	8.73205			0.396502
$486$		0			0
$487$	−4.07180			−0.184511			−0.0922554	−	0.995735i	$-0.529408\pi$
$487$	−4.07180			−0.184511			−0.0922554	+	0.995735i	$0.529408\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.928203	−	1.60770i	0.0418892	−	0.0725543i	−0.844321	−	0.535838i	$-0.819996\pi$
$491$	0.928203	−	1.60770i	0.0418892	−	0.0725543i	0.886210	+	0.463284i	$0.153329\pi$
$492$		0			0
$493$	−0.928203	−	1.60770i	−0.0418042	−	0.0724069i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−10.7321	−	18.5885i	−0.481398	−	0.833806i
$498$		0			0
$499$	14.6603	−	25.3923i	0.656283	−	1.13672i	−0.325287	−	0.945615i	$-0.605461\pi$
$499$	14.6603	−	25.3923i	0.656283	−	1.13672i	0.981570	−	0.191100i	$-0.0612056\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	21.4641			0.957037			0.478518	−	0.878077i	$-0.341174\pi$
$503$	21.4641			0.957037			0.478518	+	0.878077i	$0.341174\pi$
$504$		0			0
$505$	−3.21539			−0.143083
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.3923	+	28.3923i	−0.726576	+	1.25847i	0.231746	+	0.972776i	$0.425556\pi$
$509$	−16.3923	+	28.3923i	−0.726576	+	1.25847i	−0.958322	+	0.285690i	$0.907777\pi$
$510$		0			0
$511$	−19.7321	−	34.1769i	−0.872895	−	1.51190i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	6.90192	+	11.9545i	0.304135	+	0.526777i
$516$		0			0
$517$	21.4641	−	37.1769i	0.943990	−	1.63504i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−17.8038			−0.780001			−0.390000	−	0.920815i	$-0.627525\pi$
$521$	−17.8038			−0.780001			−0.390000	+	0.920815i	$0.627525\pi$
$522$		0			0
$523$	−12.8564			−0.562171			−0.281086	−	0.959683i	$-0.590695\pi$
$523$	−12.8564			−0.562171			−0.281086	+	0.959683i	$0.590695\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.901924	−	1.56218i	0.0392884	−	0.0680495i
$528$		0			0
$529$	−26.6244	−	46.1147i	−1.15758	−	2.00499i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−11.6603	−	20.1962i	−0.505062	−	0.874792i
$534$		0			0
$535$	3.46410	−	6.00000i	0.149766	−	0.259403i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−30.9808			−1.33444
$540$		0			0
$541$	−4.39230			−0.188840			−0.0944200	−	0.995532i	$-0.530100\pi$
$541$	−4.39230			−0.188840			−0.0944200	+	0.995532i	$0.530100\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−6.02628	+	10.4378i	−0.258137	+	0.447107i
$546$		0			0
$547$	3.83975	+	6.65064i	0.164176	+	0.284361i	0.936362	−	0.351035i	$-0.114170\pi$
$547$	3.83975	+	6.65064i	0.164176	+	0.284361i	−0.772187	+	0.635396i	$0.780837\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−5.66025	−	9.80385i	−0.241135	−	0.417658i
$552$		0			0
$553$	−24.1244	+	41.7846i	−1.02587	+	1.77686i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6.19615			−0.262539			−0.131270	−	0.991347i	$-0.541905\pi$
$557$	−6.19615			−0.262539			−0.131270	+	0.991347i	$0.541905\pi$
$558$		0			0
$559$	14.6077			0.617840
$560$		0			0
$561$		0			0
$562$		0			0
$563$	6.56218	−	11.3660i	0.276563	−	0.479021i	−0.693965	−	0.720008i	$-0.744138\pi$
$563$	6.56218	−	11.3660i	0.276563	−	0.479021i	0.970528	+	0.240987i	$0.0774713\pi$
$564$		0			0
$565$	2.53590	+	4.39230i	0.106686	+	0.184786i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13.2942	−	23.0263i	−0.557323	−	0.965312i	−0.997719	−	0.0675081i	$-0.978495\pi$
$569$	−13.2942	−	23.0263i	−0.557323	−	0.965312i	0.440396	−	0.897804i	$-0.354838\pi$
$570$		0			0
$571$	1.73205	−	3.00000i	0.0724841	−	0.125546i	−0.827505	−	0.561458i	$-0.810241\pi$
$571$	1.73205	−	3.00000i	0.0724841	−	0.125546i	0.899989	+	0.435912i	$0.143574\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	38.9808			1.62561
$576$		0			0
$577$	−14.8564			−0.618480			−0.309240	−	0.950984i	$-0.600075\pi$
$577$	−14.8564			−0.618480			−0.309240	+	0.950984i	$0.600075\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	22.0526	−	38.1962i	0.914894	−	1.58464i
$582$		0			0
$583$	23.7321	+	41.1051i	0.982881	+	1.70240i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.90192	−	5.02628i	−0.119775	−	0.207457i	0.799903	−	0.600129i	$-0.204884\pi$
$587$	−2.90192	−	5.02628i	−0.119775	−	0.207457i	−0.919679	+	0.392672i	$0.871551\pi$
$588$		0			0
$589$	5.50000	−	9.52628i	0.226624	−	0.392524i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	26.5885			1.09186			0.545929	−	0.837832i	$-0.316177\pi$
$593$	26.5885			1.09186			0.545929	+	0.837832i	$0.316177\pi$
$594$		0			0
$595$	−1.85641			−0.0761052
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7.85641	−	13.6077i	0.321004	−	0.555995i	−0.659691	−	0.751537i	$-0.729313\pi$
$599$	7.85641	−	13.6077i	0.321004	−	0.555995i	0.980695	+	0.195541i	$0.0626463\pi$
$600$		0			0
$601$	−6.16025	−	10.6699i	−0.251282	−	0.435233i	0.712597	−	0.701574i	$-0.247519\pi$
$601$	−6.16025	−	10.6699i	−0.251282	−	0.435233i	−0.963879	+	0.266340i	$0.914185\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−10.0263	−	17.3660i	−0.407626	−	0.706029i
$606$		0			0
$607$	6.39230	−	11.0718i	0.259456	−	0.449390i	−0.706641	−	0.707573i	$-0.749790\pi$
$607$	6.39230	−	11.0718i	0.259456	−	0.449390i	0.966096	+	0.258182i	$0.0831235\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−17.0718			−0.690651
$612$		0			0
$613$	−19.9282			−0.804893			−0.402446	−	0.915444i	$-0.631840\pi$
$613$	−19.9282			−0.804893			−0.402446	+	0.915444i	$0.631840\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4.73205	+	8.19615i	−0.190505	+	0.329965i	−0.945418	−	0.325861i	$-0.894346\pi$
$617$	−4.73205	+	8.19615i	−0.190505	+	0.329965i	0.754913	+	0.655825i	$0.227679\pi$
$618$		0			0
$619$	−0.500000	−	0.866025i	−0.0200967	−	0.0348085i	0.855802	−	0.517303i	$-0.173064\pi$
$619$	−0.500000	−	0.866025i	−0.0200967	−	0.0348085i	−0.875899	+	0.482495i	$0.839731\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−20.7846	−	36.0000i	−0.832718	−	1.44231i
$624$		0			0
$625$	−8.62436	+	14.9378i	−0.344974	+	0.597513i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1.85641			−0.0740198
$630$		0			0
$631$	28.0000			1.11466			0.557331	−	0.830290i	$-0.311825\pi$
$631$	28.0000			1.11466			0.557331	+	0.830290i	$0.311825\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.705771	+	1.22243i	−0.0280077	+	0.0485107i
$636$		0			0
$637$	6.16025	+	10.6699i	0.244078	+	0.422756i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	15.0981	+	26.1506i	0.596338	+	1.03289i	0.993357	+	0.115077i	$0.0367116\pi$
$641$	15.0981	+	26.1506i	0.596338	+	1.03289i	−0.397018	+	0.917811i	$0.629955\pi$
$642$		0			0
$643$	−12.8038	+	22.1769i	−0.504934	+	0.874572i	0.495049	+	0.868865i	$0.335150\pi$
$643$	−12.8038	+	22.1769i	−0.504934	+	0.874572i	−0.999984	+	0.00570722i	$0.998183\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	25.1244			0.987740			0.493870	−	0.869536i	$-0.335582\pi$
$647$	25.1244			0.987740			0.493870	+	0.869536i	$0.335582\pi$
$648$		0			0
$649$	11.1769			0.438732
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.39230	−	7.60770i	0.171884	−	0.297712i	−0.767194	−	0.641415i	$-0.778348\pi$
$653$	4.39230	−	7.60770i	0.171884	−	0.297712i	0.939079	+	0.343703i	$0.111681\pi$
$654$		0			0
$655$	5.58846	+	9.67949i	0.218359	+	0.378209i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	0.725175	−	0.688565i	$-0.241759\pi$
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	−0.958902	+	0.283738i	$0.908425\pi$
$660$		0			0
$661$	14.3564	−	24.8660i	0.558399	−	0.967176i	−0.439231	−	0.898374i	$-0.644749\pi$
$661$	14.3564	−	24.8660i	0.558399	−	0.967176i	0.997630	−	0.0688021i	$-0.0219177\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−11.3205			−0.438990
$666$		0			0
$667$	22.1436			0.857403
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.75833	+	8.24167i	−0.183693	+	0.318166i
$672$		0			0
$673$	8.62436	+	14.9378i	0.332444	+	0.575811i	0.982991	−	0.183656i	$-0.0587933\pi$
$673$	8.62436	+	14.9378i	0.332444	+	0.575811i	−0.650546	+	0.759467i	$0.725460\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	22.9545	+	39.7583i	0.882212	+	1.52804i	0.848876	+	0.528593i	$0.177280\pi$
$677$	22.9545	+	39.7583i	0.882212	+	1.52804i	0.0333368	+	0.999444i	$0.489387\pi$
$678$		0			0
$679$	−20.6603	+	35.7846i	−0.792868	+	1.37329i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.0525589			0.00201111			0.00100555	−	0.999999i	$-0.499680\pi$
$683$	0.0525589			0.00201111			0.00100555	+	0.999999i	$0.499680\pi$
$684$		0			0
$685$	−13.8564			−0.529426
$686$		0			0
$687$		0			0
$688$		0			0
$689$	9.43782	−	16.3468i	0.359552	−	0.622763i
$690$		0			0
$691$	16.0885	+	27.8660i	0.612034	+	1.06007i	0.990897	+	0.134621i	$0.0429817\pi$
$691$	16.0885	+	27.8660i	0.612034	+	1.06007i	−0.378863	+	0.925453i	$0.623685\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.26795	+	2.19615i	0.0480961	+	0.0833048i
$696$		0			0
$697$	−3.46410	+	6.00000i	−0.131212	+	0.227266i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−23.3205			−0.880803			−0.440402	−	0.897801i	$-0.645164\pi$
$701$	−23.3205			−0.880803			−0.440402	+	0.897801i	$0.645164\pi$
$702$		0			0
$703$	−11.3205			−0.426961
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7.60770	−	13.1769i	0.286117	−	0.495569i
$708$		0			0
$709$	0.0358984	+	0.0621778i	0.00134819	+	0.00233514i	0.866699	−	0.498832i	$-0.166238\pi$
$709$	0.0358984	+	0.0621778i	0.00134819	+	0.00233514i	−0.865351	+	0.501167i	$0.832904\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	10.7583	+	18.6340i	0.402903	+	0.697848i
$714$		0			0
$715$	−5.58846	+	9.67949i	−0.208996	+	0.361992i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	12.7321			0.474825			0.237413	−	0.971409i	$-0.423701\pi$
$719$	12.7321			0.474825			0.237413	+	0.971409i	$0.423701\pi$
$720$		0			0
$721$	−65.3205			−2.43266
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−5.66025	+	9.80385i	−0.210217	+	0.364106i
$726$		0			0
$727$	11.1962	+	19.3923i	0.415242	+	0.719221i	0.995454	−	0.0952450i	$-0.0303635\pi$
$727$	11.1962	+	19.3923i	0.415242	+	0.719221i	−0.580212	+	0.814466i	$0.697030\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.16987	−	3.75833i	−0.0802557	−	0.139007i
$732$		0			0
$733$	18.9641	−	32.8468i	0.700455	−	1.21322i	−0.267852	−	0.963460i	$-0.586314\pi$
$733$	18.9641	−	32.8468i	0.700455	−	1.21322i	0.968307	−	0.249764i	$-0.0803529\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	21.9090			0.807027
$738$		0			0
$739$	−14.6077			−0.537353			−0.268676	−	0.963231i	$-0.586586\pi$
$739$	−14.6077			−0.537353			−0.268676	+	0.963231i	$0.586586\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−6.02628	+	10.4378i	−0.221083	+	0.382927i	−0.955137	−	0.296164i	$-0.904292\pi$
$743$	−6.02628	+	10.4378i	−0.221083	+	0.382927i	0.734054	+	0.679091i	$0.237626\pi$
$744$		0			0
$745$	−7.33975	−	12.7128i	−0.268907	−	0.465761i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	16.3923	+	28.3923i	0.598962	+	1.03743i
$750$		0			0
$751$	10.2679	−	17.7846i	0.374683	−	0.648970i	−0.615597	−	0.788061i	$-0.711085\pi$
$751$	10.2679	−	17.7846i	0.374683	−	0.648970i	0.990280	+	0.139092i	$0.0444183\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.58846			−0.0942036
$756$		0			0
$757$	−0.0717968			−0.00260950			−0.00130475	−	0.999999i	$-0.500415\pi$
$757$	−0.0717968			−0.00260950			−0.00130475	+	0.999999i	$0.500415\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	17.0981	−	29.6147i	0.619805	−	1.07353i	−0.369716	−	0.929145i	$-0.620545\pi$
$761$	17.0981	−	29.6147i	0.619805	−	1.07353i	0.989521	−	0.144389i	$-0.0461216\pi$
$762$		0			0
$763$	−28.5167	−	49.3923i	−1.03237	−	1.78812i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.22243	−	3.84936i	−0.0802474	−	0.138993i
$768$		0			0
$769$	15.2846	−	26.4737i	0.551177	−	0.954667i	−0.447013	−	0.894528i	$-0.647512\pi$
$769$	15.2846	−	26.4737i	0.551177	−	0.954667i	0.998190	−	0.0601393i	$-0.0191545\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	33.4641			1.20362			0.601810	−	0.798639i	$-0.294446\pi$
$773$	33.4641			1.20362			0.601810	+	0.798639i	$0.294446\pi$
$774$		0			0
$775$	−11.0000			−0.395132
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−21.1244	+	36.5885i	−0.756859	+	1.31092i
$780$		0			0
$781$	19.1962	+	33.2487i	0.686892	+	1.18973i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.97372	−	3.41858i	−0.0704451	−	0.122015i
$786$		0			0
$787$	−23.8205	+	41.2583i	−0.849109	+	1.47070i	0.0328946	+	0.999459i	$0.489527\pi$
$787$	−23.8205	+	41.2583i	−0.849109	+	1.47070i	−0.882004	+	0.471242i	$0.843806\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−24.0000			−0.853342
$792$		0			0
$793$	3.78461			0.134395
$794$		0			0
$795$		0			0
$796$		0			0
$797$	4.36603	−	7.56218i	0.154653	−	0.267866i	−0.778280	−	0.627918i	$-0.783908\pi$
$797$	4.36603	−	7.56218i	0.154653	−	0.267866i	0.932932	+	0.360051i	$0.117241\pi$
$798$		0			0
$799$	2.53590	+	4.39230i	0.0897136	+	0.155389i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	35.2942	+	61.1314i	1.24551	+	2.15728i
$804$		0			0
$805$	11.0718	−	19.1769i	0.390230	−	0.675897i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	4.33975			0.152577			0.0762887	−	0.997086i	$-0.475693\pi$
$809$	4.33975			0.152577			0.0762887	+	0.997086i	$0.475693\pi$
$810$		0			0
$811$	45.7846			1.60772			0.803858	−	0.594822i	$-0.202777\pi$
$811$	45.7846			1.60772			0.803858	+	0.594822i	$0.202777\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	8.19615	−	14.1962i	0.287099	−	0.497270i
$816$		0			0
$817$	−13.2321	−	22.9186i	−0.462931	−	0.801820i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−12.9282	−	22.3923i	−0.451197	−	0.781497i	0.547263	−	0.836960i	$-0.315670\pi$
$821$	−12.9282	−	22.3923i	−0.451197	−	0.781497i	−0.998461	+	0.0554637i	$0.982336\pi$
$822$		0			0
$823$	−21.0885	+	36.5263i	−0.735097	+	1.27323i	0.219583	+	0.975594i	$0.429530\pi$
$823$	−21.0885	+	36.5263i	−0.735097	+	1.27323i	−0.954681	+	0.297632i	$0.903803\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−21.5167			−0.748208			−0.374104	−	0.927387i	$-0.622050\pi$
$827$	−21.5167			−0.748208			−0.374104	+	0.927387i	$0.622050\pi$
$828$		0			0
$829$	13.2487			0.460147			0.230073	−	0.973173i	$-0.426103\pi$
$829$	13.2487			0.460147			0.230073	+	0.973173i	$0.426103\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.83013	−	3.16987i	0.0634101	−	0.109830i
$834$		0			0
$835$	1.60770	+	2.78461i	0.0556366	+	0.0963654i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	5.66025	+	9.80385i	0.195414	+	0.338466i	0.947036	−	0.321127i	$-0.104062\pi$
$839$	5.66025	+	9.80385i	0.195414	+	0.338466i	−0.751622	+	0.659594i	$0.770728\pi$
$840$		0			0
$841$	11.2846	−	19.5455i	0.389124	−	0.673983i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−5.07180			−0.174475
$846$		0			0
$847$	94.8897			3.26045
$848$		0			0
$849$		0			0
$850$		0			0
$851$	11.0718	−	19.1769i	0.379536	−	0.657376i
$852$		0			0
$853$	−15.8923	−	27.5263i	−0.544142	−	0.942482i	−0.998660	−	0.0517444i	$-0.983522\pi$
$853$	−15.8923	−	27.5263i	−0.544142	−	0.942482i	0.454518	−	0.890737i	$-0.349811\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	6.58846	+	11.4115i	0.225057	+	0.389811i	0.956337	−	0.292267i	$-0.0944097\pi$
$857$	6.58846	+	11.4115i	0.225057	+	0.389811i	−0.731279	+	0.682078i	$0.761076\pi$
$858$		0			0
$859$	−16.2679	+	28.1769i	−0.555055	+	0.961384i	0.442844	+	0.896599i	$0.353970\pi$
$859$	−16.2679	+	28.1769i	−0.555055	+	0.961384i	−0.997899	+	0.0647852i	$0.979364\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	15.9474			0.542857			0.271429	−	0.962459i	$-0.412504\pi$
$863$	15.9474			0.542857			0.271429	+	0.962459i	$0.412504\pi$
$864$		0			0
$865$	−5.07180			−0.172446
$866$		0			0
$867$		0			0
$868$		0			0
$869$	43.1506	−	74.7391i	1.46379	−	2.53535i
$870$		0			0
$871$	−4.35641	−	7.54552i	−0.147611	−	0.255670i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	12.0000	+	20.7846i	0.405674	+	0.702648i
$876$		0			0
$877$	22.7321	−	39.3731i	0.767607	−	1.32953i	−0.171250	−	0.985228i	$-0.554781\pi$
$877$	22.7321	−	39.3731i	0.767607	−	1.32953i	0.938857	−	0.344306i	$-0.111886\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	15.6603			0.527607			0.263804	−	0.964576i	$-0.415023\pi$
$881$	15.6603			0.527607			0.263804	+	0.964576i	$0.415023\pi$
$882$		0			0
$883$	11.6795			0.393046			0.196523	−	0.980499i	$-0.437035\pi$
$883$	11.6795			0.393046			0.196523	+	0.980499i	$0.437035\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.5622	−	25.2224i	0.488950	−	0.846886i	−0.510969	−	0.859599i	$-0.670713\pi$
$887$	14.5622	−	25.2224i	0.488950	−	0.846886i	0.999919	+	0.0127127i	$0.00404669\pi$
$888$		0			0
$889$	−3.33975	−	5.78461i	−0.112011	−	0.194010i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	15.4641	+	26.7846i	0.517486	+	0.896313i
$894$		0			0
$895$	0.928203	−	1.60770i	0.0310264	−	0.0537393i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.24871			−0.208406
$900$		0			0
$901$	−5.60770			−0.186819
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.14359	−	7.17691i	0.137738	−	0.238569i
$906$		0			0
$907$	−3.50000	−	6.06218i	−0.116216	−	0.201291i	0.802049	−	0.597258i	$-0.203743\pi$
$907$	−3.50000	−	6.06218i	−0.116216	−	0.201291i	−0.918265	+	0.395966i	$0.870410\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	6.90192	+	11.9545i	0.228671	+	0.396070i	0.957414	−	0.288717i	$-0.0932287\pi$
$911$	6.90192	+	11.9545i	0.228671	+	0.396070i	−0.728744	+	0.684787i	$0.759895\pi$
$912$		0			0
$913$	−39.4449	+	68.3205i	−1.30543	+	2.26108i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−52.8897			−1.74657
$918$		0			0
$919$	4.00000			0.131948			0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000			0.131948			0.0659739	+	0.997821i	$0.478985\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	7.63397	−	13.2224i	0.251275	−	0.435222i
$924$		0			0
$925$	5.66025	+	9.80385i	0.186108	+	0.322349i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	25.2942	+	43.8109i	0.829877	+	1.43739i	0.898134	+	0.439721i	$0.144923\pi$
$929$	25.2942	+	43.8109i	0.829877	+	1.43739i	−0.0682577	+	0.997668i	$0.521744\pi$
$930$		0			0
$931$	11.1603	−	19.3301i	0.365763	−	0.633519i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	3.32051			0.108592
$936$		0			0
$937$	−16.3923			−0.535513			−0.267757	−	0.963487i	$-0.586282\pi$
$937$	−16.3923			−0.535513			−0.267757	+	0.963487i	$0.586282\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3.46410	+	6.00000i	−0.112926	+	0.195594i	−0.916949	−	0.399004i	$-0.869356\pi$
$941$	−3.46410	+	6.00000i	−0.112926	+	0.195594i	0.804022	+	0.594599i	$0.202689\pi$
$942$		0			0
$943$	−41.3205	−	71.5692i	−1.34558	−	2.33061i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.12436	+	15.8038i	0.296502	+	0.513556i	0.975333	−	0.220738i	$-0.0708466\pi$
$947$	9.12436	+	15.8038i	0.296502	+	0.513556i	−0.678831	+	0.734294i	$0.737513\pi$
$948$		0			0
$949$	14.0359	−	24.3109i	0.455625	−	0.789165i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	3.21539			0.104157			0.0520784	−	0.998643i	$-0.483415\pi$
$953$	3.21539			0.104157			0.0520784	+	0.998643i	$0.483415\pi$
$954$		0			0
$955$	−13.8564			−0.448383
$956$		0			0
$957$		0			0
$958$		0			0
$959$	32.7846	−	56.7846i	1.05867	−	1.83367i
$960$		0			0
$961$	12.4641	+	21.5885i	0.402068	+	0.696402i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.04552	+	1.81089i	0.0336564	+	0.0582946i
$966$		0			0
$967$	21.6244	−	37.4545i	0.695392	−	1.20445i	−0.274656	−	0.961543i	$-0.588564\pi$
$967$	21.6244	−	37.4545i	0.695392	−	1.20445i	0.970048	−	0.242912i	$-0.0781027\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	46.6410			1.49678			0.748391	−	0.663258i	$-0.230827\pi$
$971$	46.6410			1.49678			0.748391	+	0.663258i	$0.230827\pi$
$972$		0			0
$973$	−12.0000			−0.384702
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−5.66025	+	9.80385i	−0.181088	+	0.313653i	−0.942251	−	0.334907i	$-0.891295\pi$
$977$	−5.66025	+	9.80385i	−0.181088	+	0.313653i	0.761164	+	0.648560i	$0.224628\pi$
$978$		0			0
$979$	37.1769	+	64.3923i	1.18818	+	2.05799i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−20.1962	−	34.9808i	−0.644157	−	1.11571i	−0.984495	−	0.175410i	$-0.943875\pi$
$983$	−20.1962	−	34.9808i	−0.644157	−	1.11571i	0.340338	−	0.940303i	$-0.389458\pi$
$984$		0			0
$985$	−8.53590	+	14.7846i	−0.271976	+	0.471077i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	51.7654			1.64604
$990$		0			0
$991$	13.9282			0.442444			0.221222	−	0.975223i	$-0.428995\pi$
$991$	13.9282			0.442444			0.221222	+	0.975223i	$0.428995\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	4.02628	−	6.97372i	0.127642	−	0.221082i
$996$		0			0
$997$	−5.00000	−	8.66025i	−0.158352	−	0.274273i	0.775923	−	0.630828i	$-0.217285\pi$
$997$	−5.00000	−	8.66025i	−0.158352	−	0.274273i	−0.934274	+	0.356555i	$0.883951\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1944.2.i.n.1297.1		4
3.2	odd	2		1944.2.i.k.1297.2		4
9.2	odd	6		1944.2.i.k.649.2		4
9.4	even	3		1944.2.a.k.1.2	✓	2
9.5	odd	6		1944.2.a.n.1.1	yes	2
9.7	even	3	inner	1944.2.i.n.649.1		4
36.23	even	6		3888.2.a.bc.1.1		2
36.31	odd	6		3888.2.a.w.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1944.2.a.k.1.2	✓	2	9.4	even	3
1944.2.a.n.1.1	yes	2	9.5	odd	6
1944.2.i.k.649.2		4	9.2	odd	6
1944.2.i.k.1297.2		4	3.2	odd	2
1944.2.i.n.649.1		4	9.7	even	3	inner
1944.2.i.n.1297.1		4	1.1	even	1	trivial
3888.2.a.w.1.2		2	36.31	odd	6
3888.2.a.bc.1.1		2	36.23	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:	\( N \)	\(=\)	\( 1944 = 2^{3} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1944.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 + 0.633975i) q^{5} +(-1.73205 - 3.00000i) q^{7} +O(q^{10})\)	\(q+(-0.366025 + 0.633975i) q^{5} +(-1.73205 - 3.00000i) q^{7} +(3.09808 + 5.36603i) q^{11} +(1.23205 - 2.13397i) q^{13} -0.732051 q^{17} -4.46410 q^{19} +(4.36603 - 7.56218i) q^{23} +(2.23205 + 3.86603i) q^{25} +(1.26795 + 2.19615i) q^{29} +(-1.23205 + 2.13397i) q^{31} +2.53590 q^{35} +2.53590 q^{37} +(4.73205 - 8.19615i) q^{41} +(2.96410 + 5.13397i) q^{43} +(-3.46410 - 6.00000i) q^{47} +(-2.50000 + 4.33013i) q^{49} +7.66025 q^{53} -4.53590 q^{55} +(0.901924 - 1.56218i) q^{59} +(0.767949 + 1.33013i) q^{61} +(0.901924 + 1.56218i) q^{65} +(1.76795 - 3.06218i) q^{67} +6.19615 q^{71} +11.3923 q^{73} +(10.7321 - 18.5885i) q^{77} +(-6.96410 - 12.0622i) q^{79} +(6.36603 + 11.0263i) q^{83} +(0.267949 - 0.464102i) q^{85} +12.0000 q^{89} -8.53590 q^{91} +(1.63397 - 2.83013i) q^{95} +(-5.96410 - 10.3301i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5}+O(q^{10}) \) 4 * q + 2 * q^5	\( 4 q + 2 q^{5} + 2 q^{11} - 2 q^{13} + 4 q^{17} - 4 q^{19} + 14 q^{23} + 2 q^{25} + 12 q^{29} + 2 q^{31} + 24 q^{35} + 24 q^{37} + 12 q^{41} - 2 q^{43} - 10 q^{49} - 4 q^{53} - 32 q^{55} + 14 q^{59} + 10 q^{61} + 14 q^{65} + 14 q^{67} + 4 q^{71} + 4 q^{73} + 36 q^{77} - 14 q^{79} + 22 q^{83} + 8 q^{85} + 48 q^{89} - 48 q^{91} + 10 q^{95} - 10 q^{97}+O(q^{100}) \) 4 * q + 2 * q^5 + 2 * q^11 - 2 * q^13 + 4 * q^17 - 4 * q^19 + 14 * q^23 + 2 * q^25 + 12 * q^29 + 2 * q^31 + 24 * q^35 + 24 * q^37 + 12 * q^41 - 2 * q^43 - 10 * q^49 - 4 * q^53 - 32 * q^55 + 14 * q^59 + 10 * q^61 + 14 * q^65 + 14 * q^67 + 4 * q^71 + 4 * q^73 + 36 * q^77 - 14 * q^79 + 22 * q^83 + 8 * q^85 + 48 * q^89 - 48 * q^91 + 10 * q^95 - 10 * q^97

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