LMFDB - Embedded newform 2268.2.w.i.269.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2268,2,Mod(269,2268)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2268, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2268.269"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{9} $
Twist minimal:	no (minimal twist has level 756)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.3
Root			$0.385418 - 0.222521i$ of defining polynomial
Character	$\chi$	$=$	2268.269
Dual form			2268.2.w.i.1349.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.385418 + 0.667563i) q^{5} +(2.37047 - 1.17511i) q^{7} +(-4.68157 + 2.70291i) q^{11} +(4.57338 - 2.64044i) q^{13} +(2.85433 - 4.94385i) q^{17} +(0.535344 - 0.309081i) q^{19} +(-5.83782 - 3.37047i) q^{23} +(2.20291 + 3.81555i) q^{25} +(6.99408 + 4.03803i) q^{29} -0.580455i q^{31} +(-0.129163 + 2.03534i) q^{35} +(-4.53803 - 7.86010i) q^{37} +(-4.29615 - 7.44116i) q^{41} +(-1.70291 + 2.94952i) q^{43} +0.770835 q^{47} +(4.23825 - 5.57111i) q^{49} +(6.63798 + 3.83244i) q^{53} -4.16699i q^{55} +13.7885 q^{59} -4.12928i q^{61} +4.07069i q^{65} +13.5526 q^{67} -2.25906i q^{71} +(1.96197 + 1.13274i) q^{73} +(-7.92132 + 11.9085i) q^{77} -8.07069 q^{79} +(-1.92709 + 3.33781i) q^{83} +(2.20022 + 3.81089i) q^{85} +(-2.59808 - 4.50000i) q^{89} +(7.73825 - 11.6333i) q^{91} +0.476501i q^{95} +(12.1468 + 7.01293i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{19} - 24 q^{37} + 6 q^{43} + 54 q^{73} - 48 q^{79} + 6 q^{85} + 42 q^{91} + 36 q^{97}+O(q^{100}) $ 12 * q - 18 * q^19 - 24 * q^37 + 6 * q^43 + 54 * q^73 - 48 * q^79 + 6 * q^85 + 42 * q^91 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.385418	+	0.667563i	−0.172364	+	0.298543i	−0.939246	−	0.343245i	$-0.888474\pi$
$5$	−0.385418	+	0.667563i	−0.172364	+	0.298543i	0.766882	+	0.641788i	$0.221807\pi$
$6$		0			0
$7$	2.37047	−	1.17511i	0.895953	−	0.444148i
$7$	2.37047	−	1.17511i	0.895953	−	0.444148i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.68157	+	2.70291i	−1.41155	+	0.814957i	−0.995534	−	0.0944018i	$-0.969906\pi$
$11$	−4.68157	+	2.70291i	−1.41155	+	0.814957i	−0.416013	+	0.909359i	$0.636573\pi$
$12$		0			0
$13$	4.57338	−	2.64044i	1.26843	−	0.732326i	0.293736	−	0.955887i	$-0.405101\pi$
$13$	4.57338	−	2.64044i	1.26843	−	0.732326i	0.974690	+	0.223560i	$0.0717680\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.85433	−	4.94385i	0.692277	−	1.19906i	−0.278813	−	0.960345i	$-0.589941\pi$
$17$	2.85433	−	4.94385i	0.692277	−	1.19906i	0.971090	−	0.238713i	$-0.0767256\pi$
$18$		0			0
$19$	0.535344	−	0.309081i	0.122816	−	0.0709080i	−0.437333	−	0.899300i	$-0.644077\pi$
$19$	0.535344	−	0.309081i	0.122816	−	0.0709080i	0.560150	+	0.828391i	$0.310744\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.83782	−	3.37047i	−1.21727	−	0.702791i	−0.252937	−	0.967483i	$-0.581397\pi$
$23$	−5.83782	−	3.37047i	−1.21727	−	0.702791i	−0.964333	+	0.264691i	$0.914730\pi$
$24$		0			0
$25$	2.20291	+	3.81555i	0.440581	+	0.763109i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	6.99408	+	4.03803i	1.29877	+	0.749844i	0.980191	−	0.198053i	$-0.0634620\pi$
$29$	6.99408	+	4.03803i	1.29877	+	0.749844i	0.318576	+	0.947897i	$0.396795\pi$
$30$		0			0
$31$		−	0.580455i		−	0.104253i	−0.998640	−	0.0521264i	$-0.983400\pi$
$31$		−	0.580455i		−	0.104253i	0.998640	−	0.0521264i	$-0.0165999\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.129163	+	2.03534i	−0.0218326	+	0.344036i
$36$		0			0
$37$	−4.53803	−	7.86010i	−0.746048	−	1.29219i	−0.949704	−	0.313150i	$-0.898616\pi$
$37$	−4.53803	−	7.86010i	−0.746048	−	1.29219i	0.203656	−	0.979043i	$-0.434718\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.29615	−	7.44116i	−0.670947	−	1.16211i	−0.977636	−	0.210304i	$-0.932555\pi$
$41$	−4.29615	−	7.44116i	−0.670947	−	1.16211i	0.306690	−	0.951810i	$-0.400779\pi$
$42$		0			0
$43$	−1.70291	+	2.94952i	−0.259691	+	0.449798i	−0.966159	−	0.257947i	$-0.916954\pi$
$43$	−1.70291	+	2.94952i	−0.259691	+	0.449798i	0.706468	+	0.707745i	$0.250287\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.770835			0.112438			0.0562189	−	0.998418i	$-0.482096\pi$
$47$	0.770835			0.112438			0.0562189	+	0.998418i	$0.482096\pi$
$48$		0			0
$49$	4.23825	−	5.57111i	0.605464	−	0.795872i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.63798	+	3.83244i	0.911796	+	0.526426i	0.881009	−	0.473100i	$-0.156865\pi$
$53$	6.63798	+	3.83244i	0.911796	+	0.526426i	0.0307875	+	0.999526i	$0.490198\pi$
$54$		0			0
$55$		−	4.16699i		−	0.561877i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	13.7885			1.79510			0.897552	−	0.440908i	$-0.145343\pi$
$59$	13.7885			1.79510			0.897552	+	0.440908i	$0.145343\pi$
$60$		0			0
$61$		−	4.12928i		−	0.528701i	−0.964427	−	0.264350i	$-0.914842\pi$
$61$		−	4.12928i		−	0.528701i	0.964427	−	0.264350i	$-0.0851575\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			4.07069i			0.504907i
$66$		0			0
$67$	13.5526			1.65571			0.827855	−	0.560943i	$-0.189561\pi$
$67$	13.5526			1.65571			0.827855	+	0.560943i	$0.189561\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	2.25906i		−	0.268101i	−0.990974	−	0.134051i	$-0.957202\pi$
$71$		−	2.25906i		−	0.268101i	0.990974	−	0.134051i	$-0.0427985\pi$
$72$		0			0
$73$	1.96197	+	1.13274i	0.229631	+	0.132577i	0.610402	−	0.792092i	$-0.291008\pi$
$73$	1.96197	+	1.13274i	0.229631	+	0.132577i	−0.380771	+	0.924669i	$0.624341\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.92132	+	11.9085i	−0.902718	+	1.35710i
$78$		0			0
$79$	−8.07069			−0.908023			−0.454012	−	0.890996i	$-0.650008\pi$
$79$	−8.07069			−0.908023			−0.454012	+	0.890996i	$0.650008\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.92709	+	3.33781i	−0.211525	+	0.366373i	−0.952192	−	0.305500i	$-0.901176\pi$
$83$	−1.92709	+	3.33781i	−0.211525	+	0.366373i	0.740667	+	0.671873i	$0.234510\pi$
$84$		0			0
$85$	2.20022	+	3.81089i	0.238647	+	0.413349i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.59808	−	4.50000i	−0.275396	−	0.476999i	0.694839	−	0.719165i	$-0.255475\pi$
$89$	−2.59808	−	4.50000i	−0.275396	−	0.476999i	−0.970235	+	0.242166i	$0.922142\pi$
$90$		0			0
$91$	7.73825	−	11.6333i	0.811189	−	1.21950i
$92$		0			0
$93$		0			0
$94$		0			0
$95$			0.476501i			0.0488880i
$96$		0			0
$97$	12.1468	+	7.01293i	1.23332	+	0.712055i	0.967720	−	0.252029i	$-0.0810979\pi$
$97$	12.1468	+	7.01293i	1.23332	+	0.712055i	0.265596	+	0.964084i	$0.414431\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.35241	−	11.0027i	−0.632088	−	1.09481i	−0.987124	−	0.159956i	$-0.948865\pi$
$101$	−6.35241	−	11.0027i	−0.632088	−	1.09481i	0.355036	−	0.934853i	$-0.384469\pi$
$102$		0			0
$103$	2.57069	+	1.48419i	0.253297	+	0.146241i	0.621273	−	0.783594i	$-0.286616\pi$
$103$	2.57069	+	1.48419i	0.253297	+	0.146241i	−0.367976	+	0.929835i	$0.619949\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.26891	−	2.46466i	0.412691	−	0.238267i	−0.279254	−	0.960217i	$-0.590087\pi$
$107$	4.26891	−	2.46466i	0.412691	−	0.238267i	0.691945	+	0.721950i	$0.256754\pi$
$108$		0			0
$109$	3.40581	−	5.89904i	0.326218	−	0.565026i	−0.655540	−	0.755160i	$-0.727559\pi$
$109$	3.40581	−	5.89904i	0.326218	−	0.565026i	0.981758	+	0.190134i	$0.0608924\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.48172	+	3.16487i	−0.515677	+	0.297726i	−0.735164	−	0.677889i	$-0.762895\pi$
$113$	−5.48172	+	3.16487i	−0.515677	+	0.297726i	0.219487	+	0.975615i	$0.429562\pi$
$114$		0			0
$115$	4.50000	−	2.59808i	0.419627	−	0.242272i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.956559	−	15.0734i	0.0876876	−	1.38177i
$120$		0			0
$121$	9.11141	−	15.7814i	0.828310	−	1.43467i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−7.25033			−0.648489
$126$		0			0
$127$	−4.41119			−0.391430			−0.195715	−	0.980661i	$-0.562703\pi$
$127$	−4.41119			−0.391430			−0.195715	+	0.980661i	$0.562703\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.39600	−	7.61410i	0.384080	−	0.665247i	−0.607561	−	0.794273i	$-0.707852\pi$
$131$	4.39600	−	7.61410i	0.384080	−	0.665247i	0.991641	+	0.129026i	$0.0411852\pi$
$132$		0			0
$133$	0.905813	−	1.36175i	0.0785440	−	0.118079i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.91281	+	2.25906i	−0.334294	+	0.193005i	−0.657746	−	0.753240i	$-0.728490\pi$
$137$	−3.91281	+	2.25906i	−0.334294	+	0.193005i	0.323452	+	0.946245i	$0.395157\pi$
$138$		0			0
$139$	6.64944	−	3.83906i	0.563998	−	0.325624i	−0.190750	−	0.981639i	$-0.561092\pi$
$139$	6.64944	−	3.83906i	0.563998	−	0.325624i	0.754749	+	0.656014i	$0.227759\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−14.2737	+	24.7228i	−1.19363	+	2.06743i
$144$		0			0
$145$	−5.39128	+	3.11266i	−0.447721	+	0.258492i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.40674	+	4.27628i	0.606784	+	0.350327i	0.771706	−	0.635980i	$-0.219404\pi$
$149$	7.40674	+	4.27628i	0.606784	+	0.350327i	−0.164922	+	0.986307i	$0.552737\pi$
$150$		0			0
$151$	3.53803	+	6.12805i	0.287921	+	0.498694i	0.973313	−	0.229480i	$-0.0737026\pi$
$151$	3.53803	+	6.12805i	0.287921	+	0.498694i	−0.685392	+	0.728174i	$0.740369\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.387490	+	0.223717i	0.0311239	+	0.0179694i
$156$		0			0
$157$		−	10.6465i		−	0.849682i	−0.905268	−	0.424841i	$-0.860330\pi$
$157$		−	10.6465i		−	0.849682i	0.905268	−	0.424841i	$-0.139670\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−17.7990	−	1.12953i	−1.40276	−	0.0890195i
$162$		0			0
$163$	−7.53534	−	13.0516i	−0.590214	−	1.02228i	−0.994203	−	0.107517i	$-0.965710\pi$
$163$	−7.53534	−	13.0516i	−0.590214	−	1.02228i	0.403990	−	0.914764i	$-0.367623\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.69215	+	15.0553i	0.672619	+	1.16501i	0.977159	+	0.212511i	$0.0681641\pi$
$167$	8.69215	+	15.0553i	0.672619	+	1.16501i	−0.304540	+	0.952500i	$0.598503\pi$
$168$		0			0
$169$	7.44385	−	12.8931i	0.572603	−	0.991778i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	19.7554			1.50198			0.750989	−	0.660314i	$-0.229577\pi$
$173$	19.7554			1.50198			0.750989	+	0.660314i	$0.229577\pi$
$174$		0			0
$175$	9.70560	+	6.45599i	0.733674	+	0.488027i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	15.1444	+	8.74363i	1.13195	+	0.653529i	0.944424	−	0.328731i	$-0.106621\pi$
$179$	15.1444	+	8.74363i	1.13195	+	0.653529i	0.187522	+	0.982260i	$0.439954\pi$
$180$		0			0
$181$			4.11997i			0.306235i	0.988208	+	0.153118i	$0.0489313\pi$
$181$			4.11997i			0.306235i	−0.988208	+	0.153118i	$0.951069\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	6.99615			0.514367
$186$		0			0
$187$			30.8600i			2.25670i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	14.3696i		−	1.03975i	−0.854244	−	0.519873i	$-0.825979\pi$
$191$		−	14.3696i		−	1.03975i	0.854244	−	0.519873i	$-0.174021\pi$
$192$		0			0
$193$	2.07069			0.149051			0.0745257	−	0.997219i	$-0.476256\pi$
$193$	2.07069			0.149051			0.0745257	+	0.997219i	$0.476256\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	20.2881i		−	1.44547i	−0.691126	−	0.722735i	$-0.742885\pi$
$197$		−	20.2881i		−	1.44547i	0.691126	−	0.722735i	$-0.257115\pi$
$198$		0			0
$199$	5.42394	+	3.13151i	0.384493	+	0.221987i	0.679771	−	0.733424i	$-0.262079\pi$
$199$	5.42394	+	3.13151i	0.384493	+	0.221987i	−0.295279	+	0.955411i	$0.595412\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	21.3244	+	1.35325i	1.49668	+	0.0949794i
$204$		0			0
$205$	6.62325			0.462588
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.67083	+	2.89397i	−0.115574	+	0.200180i
$210$		0			0
$211$	−1.86778	−	3.23509i	−0.128583	−	0.222713i	0.794545	−	0.607206i	$-0.207710\pi$
$211$	−1.86778	−	3.23509i	−0.128583	−	0.222713i	−0.923128	+	0.384493i	$0.874376\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.31266	−	2.27359i	−0.0895227	−	0.155058i
$216$		0			0
$217$	−0.682096	−	1.37595i	−0.0463037	−	0.0934056i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	30.1468i		−	2.02789i
$222$		0			0
$223$	−13.7201	−	7.92132i	−0.918768	−	0.530451i	−0.0355260	−	0.999369i	$-0.511311\pi$
$223$	−13.7201	−	7.92132i	−0.918768	−	0.530451i	−0.883242	+	0.468918i	$0.844644\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.95640	−	3.38859i	−0.129851	−	0.224909i	0.793768	−	0.608221i	$-0.208117\pi$
$227$	−1.95640	−	3.38859i	−0.129851	−	0.224909i	−0.923619	+	0.383312i	$0.874783\pi$
$228$		0			0
$229$	−4.39397	−	2.53686i	−0.290362	−	0.167640i	0.347743	−	0.937590i	$-0.386948\pi$
$229$	−4.39397	−	2.53686i	−0.290362	−	0.167640i	−0.638105	+	0.769949i	$0.720281\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.56891	−	0.905813i	0.102783	−	0.0593418i	−0.447727	−	0.894170i	$-0.647766\pi$
$233$	1.56891	−	0.905813i	0.102783	−	0.0593418i	0.550510	+	0.834828i	$0.314433\pi$
$234$		0			0
$235$	−0.297093	+	0.514581i	−0.0193802	+	0.0335676i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.43813	+	4.29440i	−0.481132	+	0.277782i	−0.720888	−	0.693051i	$-0.756266\pi$
$239$	−7.43813	+	4.29440i	−0.481132	+	0.277782i	0.239756	+	0.970833i	$0.422933\pi$
$240$		0			0
$241$	20.6521	−	11.9235i	1.33032	−	0.768061i	0.344972	−	0.938613i	$-0.387888\pi$
$241$	20.6521	−	11.9235i	1.33032	−	0.768061i	0.985349	+	0.170552i	$0.0545551\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.08557	+	4.97650i	0.133242	+	0.317937i
$246$		0			0
$247$	1.63222	−	2.82709i	0.103856	−	0.179883i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	7.25033			0.457637			0.228818	−	0.973469i	$-0.426514\pi$
$251$	7.25033			0.457637			0.228818	+	0.973469i	$0.426514\pi$
$252$		0			0
$253$	36.4403			2.29098
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.2737	+	24.7228i	−0.890370	+	1.54217i	−0.0509387	+	0.998702i	$0.516221\pi$
$257$	−14.2737	+	24.7228i	−0.890370	+	1.54217i	−0.839432	+	0.543465i	$0.817112\pi$
$258$		0			0
$259$	−19.9937	−	13.2995i	−1.24235	−	0.826388i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.95640	+	1.12953i	−0.120637	+	0.0696498i	−0.559104	−	0.829097i	$-0.688855\pi$
$263$	−1.95640	+	1.12953i	−0.120637	+	0.0696498i	0.438467	+	0.898747i	$0.355522\pi$
$264$		0			0
$265$	−5.11679	+	2.95418i	−0.314322	+	0.181474i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−8.33605	+	14.4385i	−0.508258	+	0.880329i	0.491696	+	0.870767i	$0.336377\pi$
$269$	−8.33605	+	14.4385i	−0.508258	+	0.880329i	−0.999954	+	0.00956210i	$0.996956\pi$
$270$		0			0
$271$	−27.2528	+	15.7344i	−1.65549	+	0.955797i	−0.680730	+	0.732534i	$0.738337\pi$
$271$	−27.2528	+	15.7344i	−1.65549	+	0.955797i	−0.974758	+	0.223263i	$0.928329\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−20.6261	−	11.9085i	−1.24380	−	0.718110i
$276$		0			0
$277$	−9.51991	−	16.4890i	−0.571996	−	0.990726i	−0.996361	−	0.0852348i	$-0.972836\pi$
$277$	−9.51991	−	16.4890i	−0.571996	−	0.990726i	0.424365	−	0.905491i	$-0.360497\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.58142	+	3.79978i	0.392614	+	0.226676i	0.683292	−	0.730145i	$-0.260547\pi$
$281$	6.58142	+	3.79978i	0.392614	+	0.226676i	−0.290678	+	0.956821i	$0.593881\pi$
$282$		0			0
$283$			30.9824i			1.84171i	0.389903	+	0.920856i	$0.372509\pi$
$283$			30.9824i			1.84171i	−0.389903	+	0.920856i	$0.627491\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−18.9281	−	12.5906i	−1.11729	−	0.743199i
$288$		0			0
$289$	−7.79440	−	13.5003i	−0.458494	−	0.794136i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.46891	+	4.27628i	0.144235	+	0.249823i	0.929087	−	0.369860i	$-0.120594\pi$
$293$	2.46891	+	4.27628i	0.144235	+	0.249823i	−0.784852	+	0.619683i	$0.787261\pi$
$294$		0			0
$295$	−5.31431	+	9.20466i	−0.309411	+	0.535916i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−35.5981			−2.05869
$300$		0			0
$301$	−0.570688	+	8.99284i	−0.0328939	+	0.518339i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.75656	+	1.59150i	0.157840	+	0.0911289i
$306$		0			0
$307$			7.95736i			0.454151i	0.973877	+	0.227075i	$0.0729164\pi$
$307$			7.95736i			0.454151i	−0.973877	+	0.227075i	$0.927084\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.87565			−0.559997			−0.279998	−	0.960000i	$-0.590334\pi$
$311$	−9.87565			−0.559997			−0.279998	+	0.960000i	$0.590334\pi$
$312$		0			0
$313$			16.8248i			0.950993i	0.879718	+	0.475496i	$0.157732\pi$
$313$			16.8248i			0.950993i	−0.879718	+	0.475496i	$0.842268\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			24.7700i			1.39122i	0.718419	+	0.695611i	$0.244866\pi$
$317$			24.7700i			1.39122i	−0.718419	+	0.695611i	$0.755134\pi$
$318$		0			0
$319$	−43.6577			−2.44436
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	3.52888i		−	0.196352i
$324$		0			0
$325$	20.1494	+	11.6333i	1.11769	+	0.645299i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.82724	−	0.905813i	0.100739	−	0.0499391i
$330$		0			0
$331$	−18.0054			−0.989665			−0.494833	−	0.868988i	$-0.664771\pi$
$331$	−18.0054			−0.989665			−0.494833	+	0.868988i	$0.664771\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.22340	+	9.04719i	−0.285385	+	0.494301i
$336$		0			0
$337$	−2.60872	−	4.51844i	−0.142106	−	0.246135i	0.786183	−	0.617993i	$-0.212054\pi$
$337$	−2.60872	−	4.51844i	−0.142106	−	0.246135i	−0.928290	+	0.371858i	$0.878721\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.56891	+	2.71744i	0.0849615	+	0.147158i
$342$		0			0
$343$	3.50000	−	18.1865i	0.188982	−	0.981981i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	16.2828i		−	0.874104i	−0.899436	−	0.437052i	$-0.856023\pi$
$347$		−	16.2828i		−	0.874104i	0.899436	−	0.437052i	$-0.143977\pi$
$348$		0			0
$349$	15.0734	+	8.70262i	0.806859	+	0.465840i	0.845864	−	0.533399i	$-0.179085\pi$
$349$	15.0734	+	8.70262i	0.806859	+	0.465840i	−0.0390047	+	0.999239i	$0.512419\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.9447	−	25.8850i	−0.795427	−	1.37772i	−0.922568	−	0.385835i	$-0.873913\pi$
$353$	−14.9447	−	25.8850i	−0.795427	−	1.37772i	0.127141	−	0.991885i	$-0.459420\pi$
$354$		0			0
$355$	1.50807	+	0.870682i	0.0800398	+	0.0462110i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	20.2700	−	11.7029i	1.06981	−	0.617656i	0.141681	−	0.989912i	$-0.454749\pi$
$359$	20.2700	−	11.7029i	1.06981	−	0.617656i	0.928130	+	0.372257i	$0.121416\pi$
$360$		0			0
$361$	−9.30894	+	16.1236i	−0.489944	+	0.848608i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.51235	+	0.873158i	−0.0791602	+	0.0457032i
$366$		0			0
$367$	−17.3696	+	10.0283i	−0.906684	+	0.523474i	−0.879363	−	0.476152i	$-0.842031\pi$
$367$	−17.3696	+	10.0283i	−0.906684	+	0.523474i	−0.0273213	+	0.999627i	$0.508698\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	20.2386	+	1.28435i	1.05074	+	0.0666800i
$372$		0			0
$373$	3.99462	−	6.91889i	0.206834	−	0.358247i	−0.743882	−	0.668311i	$-0.767017\pi$
$373$	3.99462	−	6.91889i	0.206834	−	0.358247i	0.950715	+	0.310065i	$0.100351\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	42.6487			2.19652
$378$		0			0
$379$	−34.5816			−1.77634			−0.888170	−	0.459516i	$-0.848023\pi$
$379$	−34.5816			−1.77634			−0.888170	+	0.459516i	$0.848023\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−4.01058	+	6.94653i	−0.204931	+	0.354951i	−0.950111	−	0.311913i	$-0.899030\pi$
$383$	−4.01058	+	6.94653i	−0.204931	+	0.354951i	0.745180	+	0.666864i	$0.232364\pi$
$384$		0			0
$385$	−4.89666	−	9.87772i	−0.249557	−	0.503415i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−15.9446	+	9.20560i	−0.808421	+	0.466742i	−0.846407	−	0.532536i	$-0.821239\pi$
$389$	−15.9446	+	9.20560i	−0.808421	+	0.466742i	0.0379861	+	0.999278i	$0.487906\pi$
$390$		0			0
$391$	−33.3262	+	19.2409i	−1.68538	+	0.973052i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	3.11058	−	5.38769i	0.156511	−	0.271084i
$396$		0			0
$397$	−21.9973	+	12.7002i	−1.10401	+	0.637402i	−0.937272	−	0.348598i	$-0.886658\pi$
$397$	−21.9973	+	12.7002i	−1.10401	+	0.637402i	−0.166741	+	0.986001i	$0.553324\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.43813	+	4.29440i	0.371442	+	0.214452i	0.674088	−	0.738651i	$-0.264537\pi$
$401$	7.43813	+	4.29440i	0.371442	+	0.214452i	−0.302646	+	0.953103i	$0.597870\pi$
$402$		0			0
$403$	−1.53266	−	2.65464i	−0.0763470	−	0.132237i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	42.4902	+	24.5318i	2.10616	+	1.21599i
$408$		0			0
$409$			3.51112i			0.173614i	0.996225	+	0.0868069i	$0.0276663\pi$
$409$			3.51112i			0.173614i	−0.996225	+	0.0868069i	$0.972334\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	32.6851	−	16.2029i	1.60833	−	0.797293i
$414$		0			0
$415$	−1.48547	−	2.57290i	−0.0729187	−	0.126299i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−14.7862	−	25.6105i	−0.722355	−	1.25116i	−0.960054	−	0.279816i	$-0.909726\pi$
$419$	−14.7862	−	25.6105i	−0.722355	−	1.25116i	0.237699	−	0.971339i	$-0.423607\pi$
$420$		0			0
$421$	11.5172	−	19.9484i	0.561315	−	0.972226i	−0.436067	−	0.899914i	$-0.643629\pi$
$421$	11.5172	−	19.9484i	0.561315	−	0.972226i	0.997382	−	0.0723120i	$-0.0230377\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	25.1513			1.22002
$426$		0			0
$427$	−4.85235	−	9.78834i	−0.234822	−	0.473691i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−20.2386	−	11.6848i	−0.974861	−	0.562836i	−0.0741463	−	0.997247i	$-0.523623\pi$
$431$	−20.2386	−	11.6848i	−0.974861	−	0.562836i	−0.900715	+	0.434411i	$0.856957\pi$
$432$		0			0
$433$			37.9199i			1.82231i	0.412059	+	0.911157i	$0.364810\pi$
$433$			37.9199i			1.82231i	−0.412059	+	0.911157i	$0.635190\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.16699			−0.199334
$438$		0			0
$439$		−	3.13783i		−	0.149760i	−0.997193	−	0.0748802i	$-0.976143\pi$
$439$		−	3.13783i		−	0.149760i	0.997193	−	0.0748802i	$-0.0238574\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			24.2282i			1.15112i	0.817761	+	0.575558i	$0.195215\pi$
$443$			24.2282i			1.15112i	−0.817761	+	0.575558i	$0.804785\pi$
$444$		0			0
$445$	4.00538			0.189873
$446$		0			0
$447$		0			0
$448$		0			0
$449$			25.1812i			1.18837i	0.804327	+	0.594187i	$0.202526\pi$
$449$			25.1812i			1.18837i	−0.804327	+	0.594187i	$0.797474\pi$
$450$		0			0
$451$	40.2255	+	23.2242i	1.89415	+	1.09359i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	4.78349	+	9.64944i	0.224253	+	0.452373i
$456$		0			0
$457$	−26.2121			−1.22615			−0.613074	−	0.790025i	$-0.710067\pi$
$457$	−26.2121			−1.22615			−0.613074	+	0.790025i	$0.710067\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.899998	−	1.55884i	0.0419171	−	0.0726026i	−0.844306	−	0.535862i	$-0.819987\pi$
$461$	0.899998	−	1.55884i	0.0419171	−	0.0726026i	0.886223	+	0.463259i	$0.153320\pi$
$462$		0			0
$463$	10.2228	+	17.7064i	0.475095	+	0.822888i	0.999593	−	0.0285234i	$-0.00908051\pi$
$463$	10.2228	+	17.7064i	0.475095	+	0.822888i	−0.524499	+	0.851411i	$0.675747\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.25271	+	9.09797i	0.243067	+	0.421004i	0.961586	−	0.274503i	$-0.0885133\pi$
$467$	5.25271	+	9.09797i	0.243067	+	0.421004i	−0.718520	+	0.695507i	$0.755180\pi$
$468$		0			0
$469$	32.1259	−	15.9257i	1.48344	−	0.735381i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	18.4112i		−	0.846547i
$474$		0			0
$475$	2.35862	+	1.36175i	0.108221	+	0.0624815i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.98349	+	5.16756i	0.136319	+	0.236112i	0.926101	−	0.377276i	$-0.123139\pi$
$479$	2.98349	+	5.16756i	0.136319	+	0.236112i	−0.789781	+	0.613388i	$0.789806\pi$
$480$		0			0
$481$	−41.5083	−	23.9648i	−1.89261	−	1.09270i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−9.36314	+	5.40581i	−0.425158	+	0.245465i
$486$		0			0
$487$	−12.0199	+	20.8191i	−0.544674	+	0.943403i	0.453953	+	0.891026i	$0.350013\pi$
$487$	−12.0199	+	20.8191i	−0.544674	+	0.943403i	−0.998627	+	0.0523777i	$0.983320\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−18.6697	+	10.7790i	−0.842553	+	0.486448i	−0.858131	−	0.513430i	$-0.828374\pi$
$491$	−18.6697	+	10.7790i	−0.842553	+	0.486448i	0.0155783	+	0.999879i	$0.495041\pi$
$492$		0			0
$493$	39.9268	−	23.0518i	1.79821	−	1.03820i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.65464	−	5.35504i	−0.119077	−	0.240206i
$498$		0			0
$499$	−14.4257	+	24.9861i	−0.645784	+	1.11853i	0.338336	+	0.941025i	$0.390136\pi$
$499$	−14.4257	+	24.9861i	−0.645784	+	1.11853i	−0.984120	+	0.177505i	$0.943197\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−20.7805			−0.926555			−0.463278	−	0.886213i	$-0.653327\pi$
$503$	−20.7805			−0.926555			−0.463278	+	0.886213i	$0.653327\pi$
$504$		0			0
$505$	9.79331			0.435797
$506$		0			0
$507$		0			0
$508$		0			0
$509$	12.7027	−	22.0018i	0.563039	−	0.975212i	−0.434190	−	0.900821i	$-0.642965\pi$
$509$	12.7027	−	22.0018i	0.563039	−	0.975212i	0.997229	−	0.0743909i	$-0.0237012\pi$
$510$		0			0
$511$	5.98188	+	0.379611i	0.264623	+	0.0167930i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.98158	+	1.14406i	−0.0873187	+	0.0504135i
$516$		0			0
$517$	−3.60872	+	2.08350i	−0.158711	+	0.0916320i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.02709	−	1.77897i	0.0449976	−	0.0779381i	−0.842649	−	0.538463i	$-0.819005\pi$
$521$	1.02709	−	1.77897i	0.0449976	−	0.0779381i	0.887647	+	0.460524i	$0.152339\pi$
$522$		0			0
$523$	−9.81790	+	5.66837i	−0.429307	+	0.247860i	−0.699051	−	0.715071i	$-0.746394\pi$
$523$	−9.81790	+	5.66837i	−0.429307	+	0.247860i	0.269744	+	0.962932i	$0.413061\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.86968	−	1.65681i	−0.125005	−	0.0721717i
$528$		0			0
$529$	11.2201	+	19.4338i	0.487832	+	0.844949i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−39.2959	−	22.6875i	−1.70209	−	0.982704i
$534$		0			0
$535$			3.79969i			0.164275i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−4.78349	+	37.5371i	−0.206040	+	1.61684i
$540$		0			0
$541$	−9.39128	−	16.2662i	−0.403763	−	0.699337i	0.590414	−	0.807101i	$-0.298965\pi$
$541$	−9.39128	−	16.2662i	−0.403763	−	0.699337i	−0.994177	+	0.107763i	$0.965631\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2.62532	+	4.54719i	0.112456	+	0.194780i
$546$		0			0
$547$	3.45928	−	5.99165i	0.147908	−	0.256184i	−0.782546	−	0.622593i	$-0.786079\pi$
$547$	3.45928	−	5.99165i	0.147908	−	0.256184i	0.930454	+	0.366408i	$0.119413\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.99231			0.212680
$552$		0			0
$553$	−19.1313	+	9.48392i	−0.813546	+	0.403297i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.00704	+	5.20022i	0.381641	+	0.220340i	0.678532	−	0.734571i	$-0.262617\pi$
$557$	9.00704	+	5.20022i	0.381641	+	0.220340i	−0.296891	+	0.954911i	$0.595950\pi$
$558$		0			0
$559$			17.9857i			0.760714i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	6.02148			0.253775			0.126887	−	0.991917i	$-0.459501\pi$
$563$	6.02148			0.253775			0.126887	+	0.991917i	$0.459501\pi$
$564$		0			0
$565$		−	4.87919i		−	0.205269i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	29.3534i		−	1.23056i	−0.788309	−	0.615280i	$-0.789043\pi$
$569$		−	29.3534i		−	1.23056i	0.788309	−	0.615280i	$-0.210957\pi$
$570$		0			0
$571$	17.2282			0.720977			0.360489	−	0.932764i	$-0.382610\pi$
$571$	17.2282			0.720977			0.360489	+	0.932764i	$0.382610\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	29.6993i		−	1.23855i
$576$		0			0
$577$	1.85594	+	1.07153i	0.0772636	+	0.0446082i	0.538134	−	0.842859i	$-0.319129\pi$
$577$	1.85594	+	1.07153i	0.0772636	+	0.0446082i	−0.460870	+	0.887467i	$0.652463\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.645816	+	10.1767i	−0.0267930	+	0.422201i
$582$		0			0
$583$	−41.4349			−1.71606
$584$		0			0
$585$		0			0
$586$		0			0
$587$	8.79200	−	15.2282i	0.362885	−	0.628535i	−0.625550	−	0.780184i	$-0.715125\pi$
$587$	8.79200	−	15.2282i	0.362885	−	0.628535i	0.988434	+	0.151650i	$0.0484585\pi$
$588$		0			0
$589$	−0.179407	−	0.310743i	−0.00739235	−	0.0128039i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−12.1469	−	21.0391i	−0.498815	−	0.863973i	0.501184	−	0.865341i	$-0.332898\pi$
$593$	−12.1469	−	21.0391i	−0.498815	−	0.863973i	−0.999999	+	0.00136757i	$0.999565\pi$
$594$		0			0
$595$	9.69375	+	6.44811i	0.397405	+	0.264347i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			37.8116i			1.54494i	0.635051	+	0.772471i	$0.280979\pi$
$599$			37.8116i			1.54494i	−0.635051	+	0.772471i	$0.719021\pi$
$600$		0			0
$601$	−2.51344	−	1.45114i	−0.102525	−	0.0591931i	0.447861	−	0.894103i	$-0.352186\pi$
$601$	−2.51344	−	1.45114i	−0.102525	−	0.0591931i	−0.550386	+	0.834910i	$0.685519\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7.02339	+	12.1649i	0.285542	+	0.494572i
$606$		0			0
$607$	−9.67403	−	5.58530i	−0.392657	−	0.226701i	0.290654	−	0.956828i	$-0.406127\pi$
$607$	−9.67403	−	5.58530i	−0.392657	−	0.226701i	−0.683311	+	0.730128i	$0.739461\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.52532	−	2.03534i	0.142619	−	0.0823412i
$612$		0			0
$613$	−8.12953	+	14.0808i	−0.328349	+	0.568717i	−0.982184	−	0.187920i	$-0.939825\pi$
$613$	−8.12953	+	14.0808i	−0.328349	+	0.568717i	0.653836	+	0.756637i	$0.273159\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4.62501	+	2.67025i	−0.186196	+	0.107500i	−0.590200	−	0.807257i	$-0.700951\pi$
$617$	−4.62501	+	2.67025i	−0.186196	+	0.107500i	0.404005	+	0.914757i	$0.367618\pi$
$618$		0			0
$619$	−18.3669	+	10.6041i	−0.738227	+	0.426216i	−0.821424	−	0.570317i	$-0.806820\pi$
$619$	−18.3669	+	10.6041i	−0.738227	+	0.426216i	0.0831972	+	0.996533i	$0.473487\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−11.4466	−	7.61410i	−0.458600	−	0.305052i
$624$		0			0
$625$	−8.22013	+	14.2377i	−0.328805	+	0.569507i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−51.8122			−2.06589
$630$		0			0
$631$	44.7338			1.78082			0.890411	−	0.455157i	$-0.150417\pi$
$631$	44.7338			1.78082			0.890411	+	0.455157i	$0.150417\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.70015	−	2.94475i	0.0674684	−	0.116859i
$636$		0			0
$637$	4.67294	−	36.6696i	0.185149	−	1.45290i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−23.6508	+	13.6548i	−0.934152	+	0.539333i	−0.888122	−	0.459607i	$-0.847990\pi$
$641$	−23.6508	+	13.6548i	−0.934152	+	0.539333i	−0.0460296	+	0.998940i	$0.514657\pi$
$642$		0			0
$643$	−30.9429	+	17.8649i	−1.22027	+	0.704524i	−0.964976	−	0.262340i	$-0.915506\pi$
$643$	−30.9429	+	17.8649i	−1.22027	+	0.704524i	−0.255295	+	0.966863i	$0.582173\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	20.4537	−	35.4268i	0.804117	−	1.39277i	−0.112768	−	0.993621i	$-0.535972\pi$
$647$	20.4537	−	35.4268i	0.804117	−	1.39277i	0.916885	−	0.399150i	$-0.130695\pi$
$648$		0			0
$649$	−64.5517	+	37.2689i	−2.53387	+	1.46293i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	22.5825	+	13.0380i	0.883723	+	0.510218i	0.871884	−	0.489712i	$-0.162898\pi$
$653$	22.5825	+	13.0380i	0.883723	+	0.510218i	0.0118388	+	0.999930i	$0.496232\pi$
$654$		0			0
$655$	3.38859	+	5.86921i	0.132403	+	0.229329i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−35.3830	−	20.4284i	−1.37833	−	0.795778i	−0.386370	−	0.922344i	$-0.626271\pi$
$659$	−35.3830	−	20.4284i	−1.37833	−	0.795778i	−0.991958	+	0.126566i	$0.959604\pi$
$660$		0			0
$661$			7.25780i			0.282296i	0.989989	+	0.141148i	$0.0450793\pi$
$661$			7.25780i			0.282296i	−0.989989	+	0.141148i	$0.954921\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.559939	+	1.12953i	0.0217135	+	0.0438013i
$666$		0			0
$667$	−27.2201	−	47.1466i	−1.05397	−	1.82553i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	11.1611	+	19.3315i	0.430868	+	0.746286i
$672$		0			0
$673$	−17.6233	+	30.5244i	−0.679326	+	1.17663i	0.295858	+	0.955232i	$0.404395\pi$
$673$	−17.6233	+	30.5244i	−0.679326	+	1.17663i	−0.975184	+	0.221396i	$0.928939\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	10.9634			0.421359			0.210680	−	0.977555i	$-0.432432\pi$
$677$	10.9634			0.421359			0.210680	+	0.977555i	$0.432432\pi$
$678$		0			0
$679$	37.0344	+	2.35021i	1.42125	+	0.0901929i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	7.70628	+	4.44922i	0.294873	+	0.170245i	0.640137	−	0.768261i	$-0.278877\pi$
$683$	7.70628	+	4.44922i	0.294873	+	0.170245i	−0.345265	+	0.938505i	$0.612211\pi$
$684$		0			0
$685$		−	3.48273i		−	0.133068i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	40.4773			1.54206
$690$		0			0
$691$			8.40607i			0.319782i	0.987135	+	0.159891i	$0.0511143\pi$
$691$			8.40607i			0.319782i	−0.987135	+	0.159891i	$0.948886\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			5.91856i			0.224504i
$696$		0			0
$697$	−49.0506			−1.85792
$698$		0			0
$699$		0			0
$700$		0			0
$701$			28.3351i			1.07020i	0.844788	+	0.535101i	$0.179727\pi$
$701$			28.3351i			1.07020i	−0.844788	+	0.535101i	$0.820273\pi$
$702$		0			0
$703$	−4.85881	−	2.80524i	−0.183254	−	0.105802i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−27.9875	−	18.6168i	−1.05258	−	0.700156i
$708$		0			0
$709$	−24.0868			−0.904599			−0.452300	−	0.891866i	$-0.649396\pi$
$709$	−24.0868			−0.904599			−0.452300	+	0.891866i	$0.649396\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.95640	+	3.38859i	−0.0732679	+	0.126904i
$714$		0			0
$715$	−11.0027	−	19.0572i	−0.411477	−	0.712699i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	2.57083	+	4.45281i	0.0958759	+	0.166062i	0.909974	−	0.414666i	$-0.136101\pi$
$719$	2.57083	+	4.45281i	0.0958759	+	0.166062i	−0.814098	+	0.580728i	$0.802768\pi$
$720$		0			0
$721$	7.83781	+	0.497389i	0.291895	+	0.0185237i
$722$		0			0
$723$		0			0
$724$		0			0
$725$			35.5816i			1.32147i
$726$		0			0
$727$	−5.99193	−	3.45945i	−0.222229	−	0.128304i	0.384753	−	0.923019i	$-0.374287\pi$
$727$	−5.99193	−	3.45945i	−0.222229	−	0.128304i	−0.606982	+	0.794716i	$0.707620\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	9.72132	+	16.8378i	0.359556	+	0.622769i
$732$		0			0
$733$	−14.8940	−	8.59904i	−0.550121	−	0.317613i	0.199050	−	0.979989i	$-0.436215\pi$
$733$	−14.8940	−	8.59904i	−0.550121	−	0.317613i	−0.749171	+	0.662377i	$0.769548\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−63.4473	+	36.6313i	−2.33711	+	1.34933i
$738$		0			0
$739$	10.6114	−	18.3795i	0.390347	−	0.676101i	−0.602148	−	0.798384i	$-0.705688\pi$
$739$	10.6114	−	18.3795i	0.390347	−	0.676101i	0.992495	+	0.122284i	$0.0390217\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	29.1891	−	16.8523i	1.07085	−	0.618253i	0.142433	−	0.989804i	$-0.454508\pi$
$743$	29.1891	−	16.8523i	1.07085	−	0.618253i	0.928412	+	0.371552i	$0.121174\pi$
$744$		0			0
$745$	−5.70937	+	3.29631i	−0.209175	+	0.120767i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	7.22309	−	10.8588i	0.263926	−	0.396772i
$750$		0			0
$751$	−2.41119	+	4.17630i	−0.0879856	+	0.152395i	−0.906660	−	0.421863i	$-0.861376\pi$
$751$	−2.41119	+	4.17630i	−0.0879856	+	0.152395i	0.818674	+	0.574259i	$0.194710\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−5.45448			−0.198509
$756$		0			0
$757$	−7.30426			−0.265478			−0.132739	−	0.991151i	$-0.542377\pi$
$757$	−7.30426			−0.265478			−0.132739	+	0.991151i	$0.542377\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	7.91925	−	13.7165i	0.287072	−	0.497224i	−0.686037	−	0.727566i	$-0.740651\pi$
$761$	7.91925	−	13.7165i	0.287072	−	0.497224i	0.973110	+	0.230342i	$0.0739846\pi$
$762$		0			0
$763$	1.14138	−	17.9857i	0.0413206	−	0.651126i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	63.0598	−	36.4076i	2.27696	−	1.31460i
$768$		0			0
$769$	40.9810	−	23.6604i	1.47781	−	0.853215i	0.478126	−	0.878291i	$-0.341316\pi$
$769$	40.9810	−	23.6604i	1.47781	−	0.853215i	0.999686	+	0.0250761i	$0.00798279\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−10.5173	+	18.2165i	−0.378282	+	0.655203i	−0.990812	−	0.135244i	$-0.956818\pi$
$773$	−10.5173	+	18.2165i	−0.378282	+	0.655203i	0.612531	+	0.790447i	$0.290152\pi$
$774$		0			0
$775$	2.21475	−	1.27869i	0.0795562	−	0.0459318i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.59984	−	2.65572i	−0.164806	−	0.0951510i
$780$		0			0
$781$	6.10603	+	10.5760i	0.218491	+	0.378437i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	7.10720	+	4.10334i	0.253667	+	0.146455i
$786$		0			0
$787$			39.0152i			1.39074i	0.718652	+	0.695370i	$0.244760\pi$
$787$			39.0152i			1.39074i	−0.718652	+	0.695370i	$0.755240\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−9.27519	+	13.9438i	−0.329788	+	0.495786i
$792$		0			0
$793$	−10.9031	−	18.8848i	−0.387181	−	0.670618i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−15.8426	−	27.4403i	−0.561175	−	0.971984i	−0.997394	−	0.0721433i	$-0.977016\pi$
$797$	−15.8426	−	27.4403i	−0.561175	−	0.971984i	0.436219	−	0.899840i	$-0.356317\pi$
$798$		0			0
$799$	2.20022	−	3.81089i	0.0778381	−	0.134820i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−12.2468			−0.432180
$804$		0			0
$805$	7.61410	−	11.4466i	0.268362	−	0.403441i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.93123	−	1.11500i	−0.0678985	−	0.0392012i	0.465666	−	0.884960i	$-0.345815\pi$
$809$	−1.93123	−	1.11500i	−0.0678985	−	0.0392012i	−0.533565	+	0.845759i	$0.679148\pi$
$810$		0			0
$811$			55.3535i			1.94373i	0.235548	+	0.971863i	$0.424312\pi$
$811$			55.3535i			1.94373i	−0.235548	+	0.971863i	$0.575688\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	11.6170			0.406926
$816$		0			0
$817$			2.10534i			0.0736566i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	45.9821i		−	1.60479i	−0.596797	−	0.802393i	$-0.703560\pi$
$821$		−	45.9821i		−	1.60479i	0.596797	−	0.802393i	$-0.296440\pi$
$822$		0			0
$823$	42.2989			1.47445			0.737223	−	0.675649i	$-0.236137\pi$
$823$	42.2989			1.47445			0.737223	+	0.675649i	$0.236137\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	21.1105i		−	0.734084i	−0.930204	−	0.367042i	$-0.880370\pi$
$827$		−	21.1105i		−	0.734084i	0.930204	−	0.367042i	$-0.119630\pi$
$828$		0			0
$829$	47.3615	+	27.3442i	1.64493	+	0.949703i	0.979043	+	0.203652i	$0.0652812\pi$
$829$	47.3615	+	27.3442i	1.64493	+	0.949703i	0.665890	+	0.746050i	$0.268052\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−15.4453	−	36.8550i	−0.535149	−	1.27695i
$834$		0			0
$835$	−13.4004			−0.463741
$836$		0			0
$837$		0			0
$838$		0			0
$839$	21.6825	−	37.5553i	0.748564	−	1.29655i	−0.199947	−	0.979807i	$-0.564077\pi$
$839$	21.6825	−	37.5553i	0.748564	−	1.29655i	0.948511	−	0.316745i	$-0.102590\pi$
$840$		0			0
$841$	18.1114	+	31.3699i	0.624531	+	1.08172i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.73798	+	9.93847i	0.197392	+	0.341894i
$846$		0			0
$847$	3.05347	−	48.1163i	0.104918	−	1.65329i
$848$		0			0
$849$		0			0
$850$		0			0
$851$			61.1812i			2.09726i
$852$		0			0
$853$	23.0353	+	13.2995i	0.788715	+	0.455365i	0.839510	−	0.543344i	$-0.182842\pi$
$853$	23.0353	+	13.2995i	0.788715	+	0.455365i	−0.0507949	+	0.998709i	$0.516175\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	14.8155	+	25.6613i	0.506090	+	0.876573i	0.999975	+	0.00704593i	$0.00224281\pi$
$857$	14.8155	+	25.6613i	0.506090	+	0.876573i	−0.493886	+	0.869527i	$0.664424\pi$
$858$		0			0
$859$	−4.19285	−	2.42074i	−0.143058	−	0.0825947i	0.426763	−	0.904364i	$-0.359654\pi$
$859$	−4.19285	−	2.42074i	−0.143058	−	0.0825947i	−0.569821	+	0.821769i	$0.692987\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	19.0258	−	10.9846i	0.647647	−	0.373919i	−0.139907	−	0.990165i	$-0.544680\pi$
$863$	19.0258	−	10.9846i	0.647647	−	0.373919i	0.787554	+	0.616246i	$0.211347\pi$
$864$		0			0
$865$	−7.61410	+	13.1880i	−0.258887	+	0.448406i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	37.7835	−	21.8143i	1.28172	−	0.740000i
$870$		0			0
$871$	61.9810	−	35.7847i	2.10015	−	1.21252i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−17.1867	+	8.51991i	−0.581016	+	0.288026i
$876$		0			0
$877$	21.2989	−	36.8907i	0.719212	−	1.24571i	−0.242100	−	0.970251i	$-0.577836\pi$
$877$	21.2989	−	36.8907i	0.719212	−	1.24571i	0.961312	−	0.275461i	$-0.0888304\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	41.2523			1.38982			0.694912	−	0.719095i	$-0.255443\pi$
$881$	41.2523			1.38982			0.694912	+	0.719095i	$0.255443\pi$
$882$		0			0
$883$	4.21206			0.141747			0.0708736	−	0.997485i	$-0.477421\pi$
$883$	4.21206			0.141747			0.0708736	+	0.997485i	$0.477421\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.79585	+	3.11051i	−0.0602988	+	0.104441i	−0.894599	−	0.446870i	$-0.852539\pi$
$887$	−1.79585	+	3.11051i	−0.0602988	+	0.104441i	0.834300	+	0.551310i	$0.185872\pi$
$888$		0			0
$889$	−10.4566	+	5.18362i	−0.350703	+	0.173853i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.412662	−	0.238250i	0.0138092	−	0.00797275i
$894$		0			0
$895$	−11.6738	+	6.73989i	−0.390213	+	0.225290i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.34389	−	4.05974i	0.0781733	−	0.135400i
$900$		0			0
$901$	37.8940	−	21.8781i	1.26243	−	0.728865i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.75034	−	1.58791i	−0.0914244	−	0.0527839i
$906$		0			0
$907$	−2.92394	−	5.06440i	−0.0970877	−	0.168161i	0.813390	−	0.581718i	$-0.197619\pi$
$907$	−2.92394	−	5.06440i	−0.0970877	−	0.168161i	−0.910478	+	0.413558i	$0.864286\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−6.58142	−	3.79978i	−0.218052	−	0.125892i	0.386996	−	0.922081i	$-0.373513\pi$
$911$	−6.58142	−	3.79978i	−0.218052	−	0.125892i	−0.605048	+	0.796189i	$0.706846\pi$
$912$		0			0
$913$		−	20.8350i		−	0.689536i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.47321	−	23.2148i	0.0486498	−	0.766619i
$918$		0			0
$919$	−13.3062	−	23.0471i	−0.438933	−	0.760254i	0.558675	−	0.829387i	$-0.311310\pi$
$919$	−13.3062	−	23.0471i	−0.438933	−	0.760254i	−0.997607	+	0.0691331i	$0.977977\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−5.96492	−	10.3315i	−0.196338	−	0.340067i
$924$		0			0
$925$	19.9937	−	34.6301i	0.657390	−	1.13863i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−52.4113			−1.71956			−0.859779	−	0.510667i	$-0.829399\pi$
$929$	−52.4113			−1.71956			−0.859779	+	0.510667i	$0.829399\pi$
$930$		0			0
$931$	0.546998	−	4.29242i	0.0179271	−	0.140678i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−20.6010	−	11.8940i	−0.673723	−	0.388974i
$936$		0			0
$937$		−	49.0719i		−	1.60311i	−0.597922	−	0.801554i	$-0.704007\pi$
$937$		−	49.0719i		−	1.60311i	0.597922	−	0.801554i	$-0.295993\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−27.4638			−0.895294			−0.447647	−	0.894210i	$-0.647738\pi$
$941$	−27.4638			−0.895294			−0.447647	+	0.894210i	$0.647738\pi$
$942$		0			0
$943$			57.9202i			1.88614i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			58.9512i			1.91566i	0.287341	+	0.957828i	$0.407229\pi$
$947$			58.9512i			1.91566i	−0.287341	+	0.957828i	$0.592771\pi$
$948$		0			0
$949$	11.9638			0.388360
$950$		0			0
$951$		0			0
$952$		0			0
$953$			16.6649i			0.539828i	0.962884	+	0.269914i	$0.0869953\pi$
$953$			16.6649i			0.539828i	−0.962884	+	0.269914i	$0.913005\pi$
$954$		0			0
$955$	9.59259	+	5.53828i	0.310409	+	0.179215i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−6.62056	+	9.95300i	−0.213789	+	0.321399i
$960$		0			0
$961$	30.6631			0.989131
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.798079	+	1.38231i	−0.0256911	+	0.0444983i
$966$		0			0
$967$	−11.6729	−	20.2181i	−0.375376	−	0.650171i	0.615007	−	0.788522i	$-0.289153\pi$
$967$	−11.6729	−	20.2181i	−0.375376	−	0.650171i	−0.990383	+	0.138351i	$0.955820\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	7.66507	+	13.2763i	0.245984	+	0.426056i	0.962408	−	0.271609i	$-0.0875557\pi$
$971$	7.66507	+	13.2763i	0.245984	+	0.426056i	−0.716424	+	0.697665i	$0.754222\pi$
$972$		0			0
$973$	11.2510	−	16.9142i	0.360690	−	0.542243i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			19.7463i			0.631741i	0.948802	+	0.315870i	$0.102296\pi$
$977$			19.7463i			0.631741i	−0.948802	+	0.315870i	$0.897704\pi$
$978$		0			0
$979$	24.3262	+	14.0447i	0.777467	+	0.448871i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	11.4194	+	19.7790i	0.364222	+	0.630851i	0.988651	−	0.150230i	$-0.0480016\pi$
$983$	11.4194	+	19.7790i	0.364222	+	0.630851i	−0.624429	+	0.781082i	$0.714668\pi$
$984$		0			0
$985$	13.5436	+	7.81940i	0.431535	+	0.249147i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	19.8825	−	11.4792i	0.632228	−	0.365017i
$990$		0			0
$991$	−3.92125	+	6.79180i	−0.124563	+	0.215749i	−0.921562	−	0.388232i	$-0.873086\pi$
$991$	−3.92125	+	6.79180i	−0.124563	+	0.215749i	0.796999	+	0.603980i	$0.206419\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−4.18096	+	2.41388i	−0.132545	+	0.0765251i
$996$		0			0
$997$	−0.608720	+	0.351445i	−0.0192783	+	0.0111304i	−0.509608	−	0.860407i	$-0.670210\pi$
$997$	−0.608720	+	0.351445i	−0.0192783	+	0.0111304i	0.490330	+	0.871537i	$0.336876\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.w.i.269.3		12
3.2	odd	2	inner	2268.2.w.i.269.4		12
7.5	odd	6		2268.2.bm.i.593.3		12
9.2	odd	6		756.2.t.e.269.4	yes	12
9.4	even	3		2268.2.bm.i.1025.4		12
9.5	odd	6		2268.2.bm.i.1025.3		12
9.7	even	3		756.2.t.e.269.3	✓	12
21.5	even	6		2268.2.bm.i.593.4		12
63.5	even	6	inner	2268.2.w.i.1349.3		12
63.11	odd	6		5292.2.f.e.2645.6		12
63.25	even	3		5292.2.f.e.2645.7		12
63.38	even	6		5292.2.f.e.2645.8		12
63.40	odd	6	inner	2268.2.w.i.1349.4		12
63.47	even	6		756.2.t.e.593.3	yes	12
63.52	odd	6		5292.2.f.e.2645.5		12
63.61	odd	6		756.2.t.e.593.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.t.e.269.3	✓	12	9.7	even	3
756.2.t.e.269.4	yes	12	9.2	odd	6
756.2.t.e.593.3	yes	12	63.47	even	6
756.2.t.e.593.4	yes	12	63.61	odd	6
2268.2.w.i.269.3		12	1.1	even	1	trivial
2268.2.w.i.269.4		12	3.2	odd	2	inner
2268.2.w.i.1349.3		12	63.5	even	6	inner
2268.2.w.i.1349.4		12	63.40	odd	6	inner
2268.2.bm.i.593.3		12	7.5	odd	6
2268.2.bm.i.593.4		12	21.5	even	6
2268.2.bm.i.1025.3		12	9.5	odd	6
2268.2.bm.i.1025.4		12	9.4	even	3
5292.2.f.e.2645.5		12	63.52	odd	6
5292.2.f.e.2645.6		12	63.11	odd	6
5292.2.f.e.2645.7		12	63.25	even	3
5292.2.f.e.2645.8		12	63.38	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.385418 + 0.667563i) q^{5} +(2.37047 - 1.17511i) q^{7} +(-4.68157 + 2.70291i) q^{11} +(4.57338 - 2.64044i) q^{13} +(2.85433 - 4.94385i) q^{17} +(0.535344 - 0.309081i) q^{19} +(-5.83782 - 3.37047i) q^{23} +(2.20291 + 3.81555i) q^{25} +(6.99408 + 4.03803i) q^{29} -0.580455i q^{31} +(-0.129163 + 2.03534i) q^{35} +(-4.53803 - 7.86010i) q^{37} +(-4.29615 - 7.44116i) q^{41} +(-1.70291 + 2.94952i) q^{43} +0.770835 q^{47} +(4.23825 - 5.57111i) q^{49} +(6.63798 + 3.83244i) q^{53} -4.16699i q^{55} +13.7885 q^{59} -4.12928i q^{61} +4.07069i q^{65} +13.5526 q^{67} -2.25906i q^{71} +(1.96197 + 1.13274i) q^{73} +(-7.92132 + 11.9085i) q^{77} -8.07069 q^{79} +(-1.92709 + 3.33781i) q^{83} +(2.20022 + 3.81089i) q^{85} +(-2.59808 - 4.50000i) q^{89} +(7.73825 - 11.6333i) q^{91} +0.476501i q^{95} +(12.1468 + 7.01293i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{19} - 24 q^{37} + 6 q^{43} + 54 q^{73} - 48 q^{79} + 6 q^{85} + 42 q^{91} + 36 q^{97}+O(q^{100}) \) 12 * q - 18 * q^19 - 24 * q^37 + 6 * q^43 + 54 * q^73 - 48 * q^79 + 6 * q^85 + 42 * q^91 + 36 * q^97

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