LMFDB - Embedded newform 2268.2.w.i.1349.3

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			1349.3
Root			$0.385418 + 0.222521i$ of defining polynomial
Character	$\chi$	$=$	2268.1349
Dual form			2268.2.w.i.269.3

$q$-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 $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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	0.766882	−	0.641788i	$-0.221807\pi$
$5$	−0.385418	−	0.667563i	−0.172364	−	0.298543i	−0.939246	+	0.343245i	$0.888474\pi$
$6$		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	−0.416013	−	0.909359i	$-0.636573\pi$
$11$	−4.68157	−	2.70291i	−1.41155	−	0.814957i	−0.995534	+	0.0944018i	$0.969906\pi$
$12$		0			0
$13$	4.57338	+	2.64044i	1.26843	+	0.732326i	0.974690	−	0.223560i	$-0.0717680\pi$
$13$	4.57338	+	2.64044i	1.26843	+	0.732326i	0.293736	+	0.955887i	$0.405101\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.85433	+	4.94385i	0.692277	+	1.19906i	0.971090	+	0.238713i	$0.0767256\pi$
$17$	2.85433	+	4.94385i	0.692277	+	1.19906i	−0.278813	+	0.960345i	$0.589941\pi$
$18$		0			0
$19$	0.535344	+	0.309081i	0.122816	+	0.0709080i	0.560150	−	0.828391i	$-0.310744\pi$
$19$	0.535344	+	0.309081i	0.122816	+	0.0709080i	−0.437333	+	0.899300i	$0.644077\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.83782	+	3.37047i	−1.21727	+	0.702791i	−0.964333	−	0.264691i	$-0.914730\pi$
$23$	−5.83782	+	3.37047i	−1.21727	+	0.702791i	−0.252937	+	0.967483i	$0.581397\pi$
$24$		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	0.318576	−	0.947897i	$-0.396795\pi$
$29$	6.99408	−	4.03803i	1.29877	−	0.749844i	0.980191	+	0.198053i	$0.0634620\pi$
$30$		0			0
$31$			0.580455i			0.104253i	0.998640	+	0.0521264i	$0.0165999\pi$
$31$			0.580455i			0.104253i	−0.998640	+	0.0521264i	$0.983400\pi$
$32$		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	0.203656	+	0.979043i	$0.434718\pi$
$37$	−4.53803	+	7.86010i	−0.746048	+	1.29219i	−0.949704	+	0.313150i	$0.898616\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.29615	+	7.44116i	−0.670947	+	1.16211i	0.306690	+	0.951810i	$0.400779\pi$
$41$	−4.29615	+	7.44116i	−0.670947	+	1.16211i	−0.977636	+	0.210304i	$0.932555\pi$
$42$		0			0
$43$	−1.70291	−	2.94952i	−0.259691	−	0.449798i	0.706468	−	0.707745i	$-0.250287\pi$
$43$	−1.70291	−	2.94952i	−0.259691	−	0.449798i	−0.966159	+	0.257947i	$0.916954\pi$
$44$		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	0.0307875	−	0.999526i	$-0.490198\pi$
$53$	6.63798	−	3.83244i	0.911796	−	0.526426i	0.881009	+	0.473100i	$0.156865\pi$
$54$		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	$0.0851575\pi$
$61$			4.12928i			0.528701i	−0.964427	+	0.264350i	$0.914842\pi$
$62$		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	$0.0427985\pi$
$71$			2.25906i			0.268101i	−0.990974	+	0.134051i	$0.957202\pi$
$72$		0			0
$73$	1.96197	−	1.13274i	0.229631	−	0.132577i	−0.380771	−	0.924669i	$-0.624341\pi$
$73$	1.96197	−	1.13274i	0.229631	−	0.132577i	0.610402	+	0.792092i	$0.291008\pi$
$74$		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	0.740667	−	0.671873i	$-0.234510\pi$
$83$	−1.92709	−	3.33781i	−0.211525	−	0.366373i	−0.952192	+	0.305500i	$0.901176\pi$
$84$		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	−0.970235	−	0.242166i	$-0.922142\pi$
$89$	−2.59808	+	4.50000i	−0.275396	+	0.476999i	0.694839	+	0.719165i	$0.255475\pi$
$90$		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	0.265596	−	0.964084i	$-0.414431\pi$
$97$	12.1468	−	7.01293i	1.23332	−	0.712055i	0.967720	+	0.252029i	$0.0810979\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.35241	+	11.0027i	−0.632088	+	1.09481i	0.355036	+	0.934853i	$0.384469\pi$
$101$	−6.35241	+	11.0027i	−0.632088	+	1.09481i	−0.987124	+	0.159956i	$0.948865\pi$
$102$		0			0
$103$	2.57069	−	1.48419i	0.253297	−	0.146241i	−0.367976	−	0.929835i	$-0.619949\pi$
$103$	2.57069	−	1.48419i	0.253297	−	0.146241i	0.621273	+	0.783594i	$0.286616\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.26891	+	2.46466i	0.412691	+	0.238267i	0.691945	−	0.721950i	$-0.256754\pi$
$107$	4.26891	+	2.46466i	0.412691	+	0.238267i	−0.279254	+	0.960217i	$0.590087\pi$
$108$		0			0
$109$	3.40581	+	5.89904i	0.326218	+	0.565026i	0.981758	−	0.190134i	$-0.0608924\pi$
$109$	3.40581	+	5.89904i	0.326218	+	0.565026i	−0.655540	+	0.755160i	$0.727559\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.48172	−	3.16487i	−0.515677	−	0.297726i	0.219487	−	0.975615i	$-0.429562\pi$
$113$	−5.48172	−	3.16487i	−0.515677	−	0.297726i	−0.735164	+	0.677889i	$0.762895\pi$
$114$		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	0.991641	−	0.129026i	$-0.0411852\pi$
$131$	4.39600	+	7.61410i	0.384080	+	0.665247i	−0.607561	+	0.794273i	$0.707852\pi$
$132$		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	0.323452	−	0.946245i	$-0.395157\pi$
$137$	−3.91281	−	2.25906i	−0.334294	−	0.193005i	−0.657746	+	0.753240i	$0.728490\pi$
$138$		0			0
$139$	6.64944	+	3.83906i	0.563998	+	0.325624i	0.754749	−	0.656014i	$-0.227759\pi$
$139$	6.64944	+	3.83906i	0.563998	+	0.325624i	−0.190750	+	0.981639i	$0.561092\pi$
$140$		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	−0.164922	−	0.986307i	$-0.552737\pi$
$149$	7.40674	−	4.27628i	0.606784	−	0.350327i	0.771706	+	0.635980i	$0.219404\pi$
$150$		0			0
$151$	3.53803	−	6.12805i	0.287921	−	0.498694i	−0.685392	−	0.728174i	$-0.740369\pi$
$151$	3.53803	−	6.12805i	0.287921	−	0.498694i	0.973313	+	0.229480i	$0.0737026\pi$
$152$		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	$0.139670\pi$
$157$			10.6465i			0.849682i	−0.905268	+	0.424841i	$0.860330\pi$
$158$		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	0.403990	+	0.914764i	$0.367623\pi$
$163$	−7.53534	+	13.0516i	−0.590214	+	1.02228i	−0.994203	+	0.107517i	$0.965710\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.69215	−	15.0553i	0.672619	−	1.16501i	−0.304540	−	0.952500i	$-0.598503\pi$
$167$	8.69215	−	15.0553i	0.672619	−	1.16501i	0.977159	−	0.212511i	$-0.0681641\pi$
$168$		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	0.187522	−	0.982260i	$-0.439954\pi$
$179$	15.1444	−	8.74363i	1.13195	−	0.653529i	0.944424	+	0.328731i	$0.106621\pi$
$180$		0			0
$181$		−	4.11997i		−	0.306235i	−0.988208	−	0.153118i	$-0.951069\pi$
$181$		−	4.11997i		−	0.306235i	0.988208	−	0.153118i	$-0.0489313\pi$
$182$		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	$0.174021\pi$
$191$			14.3696i			1.03975i	−0.854244	+	0.519873i	$0.825979\pi$
$192$		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	$0.257115\pi$
$197$			20.2881i			1.44547i	−0.691126	+	0.722735i	$0.742885\pi$
$198$		0			0
$199$	5.42394	−	3.13151i	0.384493	−	0.221987i	−0.295279	−	0.955411i	$-0.595412\pi$
$199$	5.42394	−	3.13151i	0.384493	−	0.221987i	0.679771	+	0.733424i	$0.262079\pi$
$200$		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	−0.923128	−	0.384493i	$-0.874376\pi$
$211$	−1.86778	+	3.23509i	−0.128583	+	0.222713i	0.794545	+	0.607206i	$0.207710\pi$
$212$		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	−0.883242	−	0.468918i	$-0.844644\pi$
$223$	−13.7201	+	7.92132i	−0.918768	+	0.530451i	−0.0355260	+	0.999369i	$0.511311\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.95640	+	3.38859i	−0.129851	+	0.224909i	−0.923619	−	0.383312i	$-0.874783\pi$
$227$	−1.95640	+	3.38859i	−0.129851	+	0.224909i	0.793768	+	0.608221i	$0.208117\pi$
$228$		0			0
$229$	−4.39397	+	2.53686i	−0.290362	+	0.167640i	−0.638105	−	0.769949i	$-0.720281\pi$
$229$	−4.39397	+	2.53686i	−0.290362	+	0.167640i	0.347743	+	0.937590i	$0.386948\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.56891	+	0.905813i	0.102783	+	0.0593418i	0.550510	−	0.834828i	$-0.314433\pi$
$233$	1.56891	+	0.905813i	0.102783	+	0.0593418i	−0.447727	+	0.894170i	$0.647766\pi$
$234$		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	0.239756	−	0.970833i	$-0.422933\pi$
$239$	−7.43813	−	4.29440i	−0.481132	−	0.277782i	−0.720888	+	0.693051i	$0.756266\pi$
$240$		0			0
$241$	20.6521	+	11.9235i	1.33032	+	0.768061i	0.985349	−	0.170552i	$-0.0545551\pi$
$241$	20.6521	+	11.9235i	1.33032	+	0.768061i	0.344972	+	0.938613i	$0.387888\pi$
$242$		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	−0.839432	−	0.543465i	$-0.817112\pi$
$257$	−14.2737	−	24.7228i	−0.890370	−	1.54217i	−0.0509387	−	0.998702i	$-0.516221\pi$
$258$		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	0.438467	−	0.898747i	$-0.355522\pi$
$263$	−1.95640	−	1.12953i	−0.120637	−	0.0696498i	−0.559104	+	0.829097i	$0.688855\pi$
$264$		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	−0.999954	−	0.00956210i	$-0.996956\pi$
$269$	−8.33605	−	14.4385i	−0.508258	−	0.880329i	0.491696	−	0.870767i	$-0.336377\pi$
$270$		0			0
$271$	−27.2528	−	15.7344i	−1.65549	−	0.955797i	−0.974758	−	0.223263i	$-0.928329\pi$
$271$	−27.2528	−	15.7344i	−1.65549	−	0.955797i	−0.680730	−	0.732534i	$-0.738337\pi$
$272$		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	0.424365	+	0.905491i	$0.360497\pi$
$277$	−9.51991	+	16.4890i	−0.571996	+	0.990726i	−0.996361	+	0.0852348i	$0.972836\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.58142	−	3.79978i	0.392614	−	0.226676i	−0.290678	−	0.956821i	$-0.593881\pi$
$281$	6.58142	−	3.79978i	0.392614	−	0.226676i	0.683292	+	0.730145i	$0.260547\pi$
$282$		0			0
$283$		−	30.9824i		−	1.84171i	−0.389903	−	0.920856i	$-0.627491\pi$
$283$		−	30.9824i		−	1.84171i	0.389903	−	0.920856i	$-0.372509\pi$
$284$		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	−0.784852	−	0.619683i	$-0.787261\pi$
$293$	2.46891	−	4.27628i	0.144235	−	0.249823i	0.929087	+	0.369860i	$0.120594\pi$
$294$		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	$-0.927084\pi$
$307$		−	7.95736i		−	0.454151i	0.973877	−	0.227075i	$-0.0729164\pi$
$308$		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	$-0.842268\pi$
$313$		−	16.8248i		−	0.950993i	0.879718	−	0.475496i	$-0.157732\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	24.7700i		−	1.39122i	−0.718419	−	0.695611i	$-0.755134\pi$
$317$		−	24.7700i		−	1.39122i	0.718419	−	0.695611i	$-0.244866\pi$
$318$		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	−0.928290	−	0.371858i	$-0.878721\pi$
$337$	−2.60872	+	4.51844i	−0.142106	+	0.246135i	0.786183	+	0.617993i	$0.212054\pi$
$338$		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	$0.143977\pi$
$347$			16.2828i			0.874104i	−0.899436	+	0.437052i	$0.856023\pi$
$348$		0			0
$349$	15.0734	−	8.70262i	0.806859	−	0.465840i	−0.0390047	−	0.999239i	$-0.512419\pi$
$349$	15.0734	−	8.70262i	0.806859	−	0.465840i	0.845864	+	0.533399i	$0.179085\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.9447	+	25.8850i	−0.795427	+	1.37772i	0.127141	+	0.991885i	$0.459420\pi$
$353$	−14.9447	+	25.8850i	−0.795427	+	1.37772i	−0.922568	+	0.385835i	$0.873913\pi$
$354$		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	0.928130	−	0.372257i	$-0.121416\pi$
$359$	20.2700	+	11.7029i	1.06981	+	0.617656i	0.141681	+	0.989912i	$0.454749\pi$
$360$		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	−0.0273213	−	0.999627i	$-0.508698\pi$
$367$	−17.3696	−	10.0283i	−0.906684	−	0.523474i	−0.879363	+	0.476152i	$0.842031\pi$
$368$		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	0.950715	−	0.310065i	$-0.100351\pi$
$373$	3.99462	+	6.91889i	0.206834	+	0.358247i	−0.743882	+	0.668311i	$0.767017\pi$
$374$		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	0.745180	−	0.666864i	$-0.232364\pi$
$383$	−4.01058	−	6.94653i	−0.204931	−	0.354951i	−0.950111	+	0.311913i	$0.899030\pi$
$384$		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	0.0379861	−	0.999278i	$-0.487906\pi$
$389$	−15.9446	−	9.20560i	−0.808421	−	0.466742i	−0.846407	+	0.532536i	$0.821239\pi$
$390$		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	−0.166741	−	0.986001i	$-0.553324\pi$
$397$	−21.9973	−	12.7002i	−1.10401	−	0.637402i	−0.937272	+	0.348598i	$0.886658\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.43813	−	4.29440i	0.371442	−	0.214452i	−0.302646	−	0.953103i	$-0.597870\pi$
$401$	7.43813	−	4.29440i	0.371442	−	0.214452i	0.674088	+	0.738651i	$0.264537\pi$
$402$		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	$-0.972334\pi$
$409$		−	3.51112i		−	0.173614i	0.996225	−	0.0868069i	$-0.0276663\pi$
$410$		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	0.237699	+	0.971339i	$0.423607\pi$
$419$	−14.7862	+	25.6105i	−0.722355	+	1.25116i	−0.960054	+	0.279816i	$0.909726\pi$
$420$		0			0
$421$	11.5172	+	19.9484i	0.561315	+	0.972226i	0.997382	+	0.0723120i	$0.0230377\pi$
$421$	11.5172	+	19.9484i	0.561315	+	0.972226i	−0.436067	+	0.899914i	$0.643629\pi$
$422$		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	−0.900715	−	0.434411i	$-0.856957\pi$
$431$	−20.2386	+	11.6848i	−0.974861	+	0.562836i	−0.0741463	+	0.997247i	$0.523623\pi$
$432$		0			0
$433$		−	37.9199i		−	1.82231i	−0.412059	−	0.911157i	$-0.635190\pi$
$433$		−	37.9199i		−	1.82231i	0.412059	−	0.911157i	$-0.364810\pi$
$434$		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	$0.0238574\pi$
$439$			3.13783i			0.149760i	−0.997193	+	0.0748802i	$0.976143\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	24.2282i		−	1.15112i	−0.817761	−	0.575558i	$-0.804785\pi$
$443$		−	24.2282i		−	1.15112i	0.817761	−	0.575558i	$-0.195215\pi$
$444$		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	$-0.797474\pi$
$449$		−	25.1812i		−	1.18837i	0.804327	−	0.594187i	$-0.202526\pi$
$450$		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	0.886223	−	0.463259i	$-0.153320\pi$
$461$	0.899998	+	1.55884i	0.0419171	+	0.0726026i	−0.844306	+	0.535862i	$0.819987\pi$
$462$		0			0
$463$	10.2228	−	17.7064i	0.475095	−	0.822888i	−0.524499	−	0.851411i	$-0.675747\pi$
$463$	10.2228	−	17.7064i	0.475095	−	0.822888i	0.999593	+	0.0285234i	$0.00908051\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.25271	−	9.09797i	0.243067	−	0.421004i	−0.718520	−	0.695507i	$-0.755180\pi$
$467$	5.25271	−	9.09797i	0.243067	−	0.421004i	0.961586	+	0.274503i	$0.0885133\pi$
$468$		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	−0.789781	−	0.613388i	$-0.789806\pi$
$479$	2.98349	−	5.16756i	0.136319	−	0.236112i	0.926101	+	0.377276i	$0.123139\pi$
$480$		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	−0.998627	−	0.0523777i	$-0.983320\pi$
$487$	−12.0199	−	20.8191i	−0.544674	−	0.943403i	0.453953	−	0.891026i	$-0.350013\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−18.6697	−	10.7790i	−0.842553	−	0.486448i	0.0155783	−	0.999879i	$-0.495041\pi$
$491$	−18.6697	−	10.7790i	−0.842553	−	0.486448i	−0.858131	+	0.513430i	$0.828374\pi$
$492$		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	−0.984120	−	0.177505i	$-0.943197\pi$
$499$	−14.4257	−	24.9861i	−0.645784	−	1.11853i	0.338336	−	0.941025i	$-0.390136\pi$
$500$		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	0.997229	+	0.0743909i	$0.0237012\pi$
$509$	12.7027	+	22.0018i	0.563039	+	0.975212i	−0.434190	+	0.900821i	$0.642965\pi$
$510$		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	0.887647	−	0.460524i	$-0.152339\pi$
$521$	1.02709	+	1.77897i	0.0449976	+	0.0779381i	−0.842649	+	0.538463i	$0.819005\pi$
$522$		0			0
$523$	−9.81790	−	5.66837i	−0.429307	−	0.247860i	0.269744	−	0.962932i	$-0.413061\pi$
$523$	−9.81790	−	5.66837i	−0.429307	−	0.247860i	−0.699051	+	0.715071i	$0.746394\pi$
$524$		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	−0.994177	−	0.107763i	$-0.965631\pi$
$541$	−9.39128	+	16.2662i	−0.403763	+	0.699337i	0.590414	+	0.807101i	$0.298965\pi$
$542$		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	0.930454	−	0.366408i	$-0.119413\pi$
$547$	3.45928	+	5.99165i	0.147908	+	0.256184i	−0.782546	+	0.622593i	$0.786079\pi$
$548$		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	−0.296891	−	0.954911i	$-0.595950\pi$
$557$	9.00704	−	5.20022i	0.381641	−	0.220340i	0.678532	+	0.734571i	$0.262617\pi$
$558$		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	$0.210957\pi$
$569$			29.3534i			1.23056i	−0.788309	+	0.615280i	$0.789043\pi$
$570$		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	−0.460870	−	0.887467i	$-0.652463\pi$
$577$	1.85594	−	1.07153i	0.0772636	−	0.0446082i	0.538134	+	0.842859i	$0.319129\pi$
$578$		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	0.988434	−	0.151650i	$-0.0484585\pi$
$587$	8.79200	+	15.2282i	0.362885	+	0.628535i	−0.625550	+	0.780184i	$0.715125\pi$
$588$		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	−0.999999	−	0.00136757i	$-0.999565\pi$
$593$	−12.1469	+	21.0391i	−0.498815	+	0.863973i	0.501184	+	0.865341i	$0.332898\pi$
$594$		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	$-0.719021\pi$
$599$		−	37.8116i		−	1.54494i	0.635051	−	0.772471i	$-0.280979\pi$
$600$		0			0
$601$	−2.51344	+	1.45114i	−0.102525	+	0.0591931i	−0.550386	−	0.834910i	$-0.685519\pi$
$601$	−2.51344	+	1.45114i	−0.102525	+	0.0591931i	0.447861	+	0.894103i	$0.352186\pi$
$602$		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	−0.683311	−	0.730128i	$-0.739461\pi$
$607$	−9.67403	+	5.58530i	−0.392657	+	0.226701i	0.290654	+	0.956828i	$0.406127\pi$
$608$		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	0.653836	−	0.756637i	$-0.273159\pi$
$613$	−8.12953	−	14.0808i	−0.328349	−	0.568717i	−0.982184	+	0.187920i	$0.939825\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4.62501	−	2.67025i	−0.186196	−	0.107500i	0.404005	−	0.914757i	$-0.367618\pi$
$617$	−4.62501	−	2.67025i	−0.186196	−	0.107500i	−0.590200	+	0.807257i	$0.700951\pi$
$618$		0			0
$619$	−18.3669	−	10.6041i	−0.738227	−	0.426216i	0.0831972	−	0.996533i	$-0.473487\pi$
$619$	−18.3669	−	10.6041i	−0.738227	−	0.426216i	−0.821424	+	0.570317i	$0.806820\pi$
$620$		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	−0.0460296	−	0.998940i	$-0.514657\pi$
$641$	−23.6508	−	13.6548i	−0.934152	−	0.539333i	−0.888122	+	0.459607i	$0.847990\pi$
$642$		0			0
$643$	−30.9429	−	17.8649i	−1.22027	−	0.704524i	−0.255295	−	0.966863i	$-0.582173\pi$
$643$	−30.9429	−	17.8649i	−1.22027	−	0.704524i	−0.964976	+	0.262340i	$0.915506\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	20.4537	+	35.4268i	0.804117	+	1.39277i	0.916885	+	0.399150i	$0.130695\pi$
$647$	20.4537	+	35.4268i	0.804117	+	1.39277i	−0.112768	+	0.993621i	$0.535972\pi$
$648$		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	0.0118388	−	0.999930i	$-0.496232\pi$
$653$	22.5825	−	13.0380i	0.883723	−	0.510218i	0.871884	+	0.489712i	$0.162898\pi$
$654$		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	−0.991958	−	0.126566i	$-0.959604\pi$
$659$	−35.3830	+	20.4284i	−1.37833	+	0.795778i	−0.386370	+	0.922344i	$0.626271\pi$
$660$		0			0
$661$		−	7.25780i		−	0.282296i	−0.989989	−	0.141148i	$-0.954921\pi$
$661$		−	7.25780i		−	0.282296i	0.989989	−	0.141148i	$-0.0450793\pi$
$662$		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	−0.975184	−	0.221396i	$-0.928939\pi$
$673$	−17.6233	−	30.5244i	−0.679326	−	1.17663i	0.295858	−	0.955232i	$-0.404395\pi$
$674$		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	−0.345265	−	0.938505i	$-0.612211\pi$
$683$	7.70628	−	4.44922i	0.294873	−	0.170245i	0.640137	+	0.768261i	$0.278877\pi$
$684$		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	$-0.948886\pi$
$691$		−	8.40607i		−	0.319782i	0.987135	−	0.159891i	$-0.0511143\pi$
$692$		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	$-0.820273\pi$
$701$		−	28.3351i		−	1.07020i	0.844788	−	0.535101i	$-0.179727\pi$
$702$		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	−0.814098	−	0.580728i	$-0.802768\pi$
$719$	2.57083	−	4.45281i	0.0958759	−	0.166062i	0.909974	+	0.414666i	$0.136101\pi$
$720$		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	−0.606982	−	0.794716i	$-0.707620\pi$
$727$	−5.99193	+	3.45945i	−0.222229	+	0.128304i	0.384753	+	0.923019i	$0.374287\pi$
$728$		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	−0.749171	−	0.662377i	$-0.769548\pi$
$733$	−14.8940	+	8.59904i	−0.550121	+	0.317613i	0.199050	+	0.979989i	$0.436215\pi$
$734$		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	0.992495	−	0.122284i	$-0.0390217\pi$
$739$	10.6114	+	18.3795i	0.390347	+	0.676101i	−0.602148	+	0.798384i	$0.705688\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	29.1891	+	16.8523i	1.07085	+	0.618253i	0.928412	−	0.371552i	$-0.121174\pi$
$743$	29.1891	+	16.8523i	1.07085	+	0.618253i	0.142433	+	0.989804i	$0.454508\pi$
$744$		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	0.818674	−	0.574259i	$-0.194710\pi$
$751$	−2.41119	−	4.17630i	−0.0879856	−	0.152395i	−0.906660	+	0.421863i	$0.861376\pi$
$752$		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	0.973110	−	0.230342i	$-0.0739846\pi$
$761$	7.91925	+	13.7165i	0.287072	+	0.497224i	−0.686037	+	0.727566i	$0.740651\pi$
$762$		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	0.999686	−	0.0250761i	$-0.00798279\pi$
$769$	40.9810	+	23.6604i	1.47781	+	0.853215i	0.478126	+	0.878291i	$0.341316\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−10.5173	−	18.2165i	−0.378282	−	0.655203i	0.612531	−	0.790447i	$-0.290152\pi$
$773$	−10.5173	−	18.2165i	−0.378282	−	0.655203i	−0.990812	+	0.135244i	$0.956818\pi$
$774$		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	$-0.755240\pi$
$787$		−	39.0152i		−	1.39074i	0.718652	−	0.695370i	$-0.244760\pi$
$788$		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	0.436219	+	0.899840i	$0.356317\pi$
$797$	−15.8426	+	27.4403i	−0.561175	+	0.971984i	−0.997394	+	0.0721433i	$0.977016\pi$
$798$		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	−0.533565	−	0.845759i	$-0.679148\pi$
$809$	−1.93123	+	1.11500i	−0.0678985	+	0.0392012i	0.465666	+	0.884960i	$0.345815\pi$
$810$		0			0
$811$		−	55.3535i		−	1.94373i	−0.235548	−	0.971863i	$-0.575688\pi$
$811$		−	55.3535i		−	1.94373i	0.235548	−	0.971863i	$-0.424312\pi$
$812$		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	$0.296440\pi$
$821$			45.9821i			1.60479i	−0.596797	+	0.802393i	$0.703560\pi$
$822$		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	$0.119630\pi$
$827$			21.1105i			0.734084i	−0.930204	+	0.367042i	$0.880370\pi$
$828$		0			0
$829$	47.3615	−	27.3442i	1.64493	−	0.949703i	0.665890	−	0.746050i	$-0.268052\pi$
$829$	47.3615	−	27.3442i	1.64493	−	0.949703i	0.979043	−	0.203652i	$-0.0652812\pi$
$830$		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	0.948511	+	0.316745i	$0.102590\pi$
$839$	21.6825	+	37.5553i	0.748564	+	1.29655i	−0.199947	+	0.979807i	$0.564077\pi$
$840$		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	−0.0507949	−	0.998709i	$-0.516175\pi$
$853$	23.0353	−	13.2995i	0.788715	−	0.455365i	0.839510	+	0.543344i	$0.182842\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	14.8155	−	25.6613i	0.506090	−	0.876573i	−0.493886	−	0.869527i	$-0.664424\pi$
$857$	14.8155	−	25.6613i	0.506090	−	0.876573i	0.999975	−	0.00704593i	$-0.00224281\pi$
$858$		0			0
$859$	−4.19285	+	2.42074i	−0.143058	+	0.0825947i	−0.569821	−	0.821769i	$-0.692987\pi$
$859$	−4.19285	+	2.42074i	−0.143058	+	0.0825947i	0.426763	+	0.904364i	$0.359654\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	19.0258	+	10.9846i	0.647647	+	0.373919i	0.787554	−	0.616246i	$-0.211347\pi$
$863$	19.0258	+	10.9846i	0.647647	+	0.373919i	−0.139907	+	0.990165i	$0.544680\pi$
$864$		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	0.961312	+	0.275461i	$0.0888304\pi$
$877$	21.2989	+	36.8907i	0.719212	+	1.24571i	−0.242100	+	0.970251i	$0.577836\pi$
$878$		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	0.834300	−	0.551310i	$-0.185872\pi$
$887$	−1.79585	−	3.11051i	−0.0602988	−	0.104441i	−0.894599	+	0.446870i	$0.852539\pi$
$888$		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	−0.910478	−	0.413558i	$-0.864286\pi$
$907$	−2.92394	+	5.06440i	−0.0970877	+	0.168161i	0.813390	+	0.581718i	$0.197619\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−6.58142	+	3.79978i	−0.218052	+	0.125892i	−0.605048	−	0.796189i	$-0.706846\pi$
$911$	−6.58142	+	3.79978i	−0.218052	+	0.125892i	0.386996	+	0.922081i	$0.373513\pi$
$912$		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	−0.997607	−	0.0691331i	$-0.977977\pi$
$919$	−13.3062	+	23.0471i	−0.438933	+	0.760254i	0.558675	+	0.829387i	$0.311310\pi$
$920$		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	$0.295993\pi$
$937$			49.0719i			1.60311i	−0.597922	+	0.801554i	$0.704007\pi$
$938$		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	$-0.592771\pi$
$947$		−	58.9512i		−	1.91566i	0.287341	−	0.957828i	$-0.407229\pi$
$948$		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	$-0.913005\pi$
$953$		−	16.6649i		−	0.539828i	0.962884	−	0.269914i	$-0.0869953\pi$
$954$		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	−0.990383	−	0.138351i	$-0.955820\pi$
$967$	−11.6729	+	20.2181i	−0.375376	+	0.650171i	0.615007	+	0.788522i	$0.289153\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	7.66507	−	13.2763i	0.245984	−	0.426056i	−0.716424	−	0.697665i	$-0.754222\pi$
$971$	7.66507	−	13.2763i	0.245984	−	0.426056i	0.962408	+	0.271609i	$0.0875557\pi$
$972$		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	$-0.897704\pi$
$977$		−	19.7463i		−	0.631741i	0.948802	−	0.315870i	$-0.102296\pi$
$978$		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	−0.624429	−	0.781082i	$-0.714668\pi$
$983$	11.4194	−	19.7790i	0.364222	−	0.630851i	0.988651	+	0.150230i	$0.0480016\pi$
$984$		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	0.796999	−	0.603980i	$-0.206419\pi$
$991$	−3.92125	−	6.79180i	−0.124563	−	0.215749i	−0.921562	+	0.388232i	$0.873086\pi$
$992$		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	0.490330	−	0.871537i	$-0.336876\pi$
$997$	−0.608720	−	0.351445i	−0.0192783	−	0.0111304i	−0.509608	+	0.860407i	$0.670210\pi$
$998$		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.1349.3		12
3.2	odd	2	inner	2268.2.w.i.1349.4		12
7.3	odd	6		2268.2.bm.i.1025.3		12
9.2	odd	6		2268.2.bm.i.593.3		12
9.4	even	3		756.2.t.e.593.3	yes	12
9.5	odd	6		756.2.t.e.593.4	yes	12
9.7	even	3		2268.2.bm.i.593.4		12
21.17	even	6		2268.2.bm.i.1025.4		12
63.5	even	6		5292.2.f.e.2645.7		12
63.23	odd	6		5292.2.f.e.2645.5		12
63.31	odd	6		756.2.t.e.269.4	yes	12
63.38	even	6	inner	2268.2.w.i.269.3		12
63.40	odd	6		5292.2.f.e.2645.6		12
63.52	odd	6	inner	2268.2.w.i.269.4		12
63.58	even	3		5292.2.f.e.2645.8		12
63.59	even	6		756.2.t.e.269.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.t.e.269.3	✓	12	63.59	even	6
756.2.t.e.269.4	yes	12	63.31	odd	6
756.2.t.e.593.3	yes	12	9.4	even	3
756.2.t.e.593.4	yes	12	9.5	odd	6
2268.2.w.i.269.3		12	63.38	even	6	inner
2268.2.w.i.269.4		12	63.52	odd	6	inner
2268.2.w.i.1349.3		12	1.1	even	1	trivial
2268.2.w.i.1349.4		12	3.2	odd	2	inner
2268.2.bm.i.593.3		12	9.2	odd	6
2268.2.bm.i.593.4		12	9.7	even	3
2268.2.bm.i.1025.3		12	7.3	odd	6
2268.2.bm.i.1025.4		12	21.17	even	6
5292.2.f.e.2645.5		12	63.23	odd	6
5292.2.f.e.2645.6		12	63.40	odd	6
5292.2.f.e.2645.7		12	63.5	even	6
5292.2.f.e.2645.8		12	63.58	even	3

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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