LMFDB - Embedded newform 2268.2.bm.i.1025.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2268,2,Mod(593,2268)] 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, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2268.593"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.bm (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:	$\Z[a_1, \ldots, a_{19}]$
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			1025.4
Root			$1.56052 + 0.900969i$ of defining polynomial
Character	$\chi$	$=$	2268.1025
Dual form			2268.2.bm.i.593.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+0.770835 q^{5} +(-0.167563 + 2.64044i) q^{7} -5.40581i q^{11} +(-4.57338 - 2.64044i) q^{13} +(2.85433 - 4.94385i) q^{17} +(0.535344 - 0.309081i) q^{19} +6.74094i q^{23} -4.40581 q^{25} +(-6.99408 + 4.03803i) q^{29} +(-0.502688 + 0.290227i) q^{31} +(-0.129163 + 2.03534i) q^{35} +(-4.53803 - 7.86010i) q^{37} +(-4.29615 + 7.44116i) q^{41} +(-1.70291 - 2.94952i) q^{43} +(-0.385418 + 0.667563i) q^{47} +(-6.94385 - 0.884879i) q^{49} +(6.63798 + 3.83244i) q^{53} -4.16699i q^{55} +(-6.89423 - 11.9412i) q^{59} +(3.57606 + 2.06464i) q^{61} +(-3.52532 - 2.03534i) q^{65} +(-6.77628 - 11.7369i) q^{67} -2.25906i q^{71} +(1.96197 + 1.13274i) q^{73} +(14.2737 + 0.905813i) q^{77} +(4.03534 - 6.98942i) q^{79} +(-1.92709 - 3.33781i) q^{83} +(2.20022 - 3.81089i) q^{85} +(-2.59808 - 4.50000i) q^{89} +(7.73825 - 11.6333i) q^{91} +(0.412662 - 0.238250i) q^{95} +(-12.1468 + 7.01293i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{19} - 24 q^{37} + 6 q^{43} - 18 q^{61} + 54 q^{73} + 24 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 - 18 * q^61 + 54 * q^73 + 24 * q^79 + 6 * q^85 + 42 * q^91 - 36 * q^97

Character values

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

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

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
$5$	0.770835			0.344728			0.172364	−	0.985033i	$-0.444859\pi$
$5$	0.770835			0.344728			0.172364	+	0.985033i	$0.444859\pi$
$6$		0			0
$7$	−0.167563	+	2.64044i	−0.0633328	+	0.997992i
$7$	−0.167563	+	2.64044i	−0.0633328	+	0.997992i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	5.40581i		−	1.62991i	−0.579521	−	0.814957i	$-0.696760\pi$
$11$		−	5.40581i		−	1.62991i	0.579521	−	0.814957i	$-0.303240\pi$
$12$		0			0
$13$	−4.57338	−	2.64044i	−1.26843	−	0.732326i	−0.293736	−	0.955887i	$-0.594899\pi$
$13$	−4.57338	−	2.64044i	−1.26843	−	0.732326i	−0.974690	+	0.223560i	$0.928232\pi$
$14$		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
$23$			6.74094i			1.40558i	0.711396	+	0.702791i	$0.248063\pi$
$23$			6.74094i			1.40558i	−0.711396	+	0.702791i	$0.751937\pi$
$24$		0			0
$25$	−4.40581			−0.881163
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.99408	+	4.03803i	−1.29877	+	0.749844i	−0.980191	−	0.198053i	$-0.936538\pi$
$29$	−6.99408	+	4.03803i	−1.29877	+	0.749844i	−0.318576	+	0.947897i	$0.603205\pi$
$30$		0			0
$31$	−0.502688	+	0.290227i	−0.0902855	+	0.0521264i	−0.544463	−	0.838785i	$-0.683267\pi$
$31$	−0.502688	+	0.290227i	−0.0902855	+	0.0521264i	0.454177	+	0.890911i	$0.349933\pi$
$32$		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	0.306690	+	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
$47$	−0.385418	+	0.667563i	−0.0562189	+	0.0973740i	−0.892765	−	0.450522i	$-0.851238\pi$
$47$	−0.385418	+	0.667563i	−0.0562189	+	0.0973740i	0.836546	+	0.547896i	$0.184571\pi$
$48$		0			0
$49$	−6.94385	−	0.884879i	−0.991978	−	0.126411i
$50$		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
$59$	−6.89423	−	11.9412i	−0.897552	−	1.55461i	−0.830614	−	0.556849i	$-0.812010\pi$
$59$	−6.89423	−	11.9412i	−0.897552	−	1.55461i	−0.0669387	−	0.997757i	$-0.521323\pi$
$60$		0			0
$61$	3.57606	+	2.06464i	0.457868	+	0.264350i	0.711147	−	0.703043i	$-0.248176\pi$
$61$	3.57606	+	2.06464i	0.457868	+	0.264350i	−0.253279	+	0.967393i	$0.581509\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.52532	−	2.03534i	−0.437262	−	0.252453i
$66$		0			0
$67$	−6.77628	−	11.7369i	−0.827855	−	1.43389i	−0.899718	−	0.436472i	$-0.856228\pi$
$67$	−6.77628	−	11.7369i	−0.827855	−	1.43389i	0.0718632	−	0.997414i	$-0.477105\pi$
$68$		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
$77$	14.2737	+	0.905813i	1.62664	+	0.103227i
$78$		0			0
$79$	4.03534	−	6.98942i	0.454012	−	0.786371i	−0.544619	−	0.838683i	$-0.683326\pi$
$79$	4.03534	−	6.98942i	0.454012	−	0.786371i	0.998631	+	0.0523123i	$0.0166591\pi$
$80$		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	0.694839	−	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
$95$	0.412662	−	0.238250i	0.0423382	−	0.0244440i
$96$		0			0
$97$	−12.1468	+	7.01293i	−1.23332	+	0.712055i	−0.967720	−	0.252029i	$-0.918902\pi$
$97$	−12.1468	+	7.01293i	−1.23332	+	0.712055i	−0.265596	+	0.964084i	$0.585569\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	12.7048			1.26418			0.632088	−	0.774897i	$-0.282198\pi$
$101$	12.7048			1.26418			0.632088	+	0.774897i	$0.282198\pi$
$102$		0			0
$103$		−	2.96837i		−	0.292483i	−0.989249	−	0.146241i	$-0.953282\pi$
$103$		−	2.96837i		−	0.292483i	0.989249	−	0.146241i	$-0.0467176\pi$
$104$		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	$-0.237105\pi$
$113$	5.48172	+	3.16487i	0.515677	+	0.297726i	−0.219487	+	0.975615i	$0.570438\pi$
$114$		0			0
$115$			5.19615i			0.484544i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	12.5756	+	8.36509i	1.15281	+	0.766827i
$120$		0			0
$121$	−18.2228			−1.65662
$122$		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
$131$	−8.79200			−0.768161			−0.384080	−	0.923300i	$-0.625481\pi$
$131$	−8.79200			−0.768161			−0.384080	+	0.923300i	$0.625481\pi$
$132$		0			0
$133$	0.726406	+	1.46533i	0.0629874	+	0.127061i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	4.51812i		−	0.386009i	−0.981198	−	0.193005i	$-0.938177\pi$
$137$		−	4.51812i		−	0.386009i	0.981198	−	0.193005i	$-0.0618232\pi$
$138$		0			0
$139$	−6.64944	−	3.83906i	−0.563998	−	0.325624i	0.190750	−	0.981639i	$-0.438908\pi$
$139$	−6.64944	−	3.83906i	−0.563998	−	0.325624i	−0.754749	+	0.656014i	$0.772241\pi$
$140$		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
$149$		−	8.55257i		−	0.700653i	−0.936628	−	0.350327i	$-0.886071\pi$
$149$		−	8.55257i		−	0.700653i	0.936628	−	0.350327i	$-0.113929\pi$
$150$		0			0
$151$	−7.07606			−0.575842			−0.287921	−	0.957654i	$-0.592964\pi$
$151$	−7.07606			−0.575842			−0.287921	+	0.957654i	$0.592964\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.387490	+	0.223717i	−0.0311239	+	0.0179694i
$156$		0			0
$157$	−9.22013	+	5.32324i	−0.735846	+	0.424841i	−0.820557	−	0.571565i	$-0.806337\pi$
$157$	−9.22013	+	5.32324i	−0.735846	+	0.424841i	0.0847108	+	0.996406i	$0.473003\pi$
$158$		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	−0.304540	−	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
$173$	−9.87772	+	17.1087i	−0.750989	+	1.30075i	0.196354	+	0.980533i	$0.437090\pi$
$173$	−9.87772	+	17.1087i	−0.750989	+	1.30075i	−0.947344	+	0.320219i	$0.896244\pi$
$174$		0			0
$175$	0.738250	−	11.6333i	0.0558065	−	0.879394i
$176$		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
$185$	−3.49807	−	6.05884i	−0.257184	−	0.445455i
$186$		0			0
$187$	−26.7255	−	15.4300i	−1.95436	−	1.12835i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.4444	+	7.18478i	0.900446	+	0.519873i	0.877345	−	0.479860i	$-0.159313\pi$
$191$	12.4444	+	7.18478i	0.900446	+	0.519873i	0.0231011	+	0.999733i	$0.492646\pi$
$192$		0			0
$193$	−1.03534	−	1.79327i	−0.0745257	−	0.129082i	0.826354	−	0.563151i	$-0.190411\pi$
$193$	−1.03534	−	1.79327i	−0.0745257	−	0.129082i	−0.900880	+	0.434068i	$0.857078\pi$
$194$		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
$203$	−9.49023	−	19.1441i	−0.666084	−	1.34365i
$204$		0			0
$205$	−3.31163	+	5.73591i	−0.231294	+	0.400613i
$206$		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
$221$	−26.1079	+	15.0734i	−1.75620	+	1.01394i
$222$		0			0
$223$	13.7201	−	7.92132i	0.918768	−	0.530451i	0.0355260	−	0.999369i	$-0.488689\pi$
$223$	13.7201	−	7.92132i	0.918768	−	0.530451i	0.883242	+	0.468918i	$0.155356\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.91281			0.259702			0.129851	−	0.991534i	$-0.458550\pi$
$227$	3.91281			0.259702			0.129851	+	0.991534i	$0.458550\pi$
$228$		0			0
$229$			5.07372i			0.335281i	0.985848	+	0.167640i	$0.0536147\pi$
$229$			5.07372i			0.335281i	−0.985848	+	0.167640i	$0.946385\pi$
$230$		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	$-0.243734\pi$
$239$	7.43813	+	4.29440i	0.481132	+	0.277782i	−0.239756	+	0.970833i	$0.577067\pi$
$240$		0			0
$241$			23.8470i			1.53612i	0.640377	+	0.768061i	$0.278778\pi$
$241$			23.8470i			1.53612i	−0.640377	+	0.768061i	$0.721222\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5.35256	−	0.682096i	−0.341963	−	0.0435775i
$246$		0			0
$247$	−3.26444			−0.207711
$248$		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
$257$	28.5474			1.78074			0.890370	−	0.455237i	$-0.150445\pi$
$257$	28.5474			1.78074			0.890370	+	0.455237i	$0.150445\pi$
$258$		0			0
$259$	21.5145	−	10.6653i	1.33685	−	0.662712i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	2.25906i		−	0.139300i	−0.997572	−	0.0696498i	$-0.977812\pi$
$263$		−	2.25906i		−	0.139300i	0.997572	−	0.0696498i	$-0.0221882\pi$
$264$		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
$275$			23.8170i			1.43622i
$276$		0			0
$277$	19.0398			1.14399			0.571996	−	0.820256i	$-0.306169\pi$
$277$	19.0398			1.14399			0.571996	+	0.820256i	$0.306169\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.58142	+	3.79978i	−0.392614	+	0.226676i	−0.683292	−	0.730145i	$-0.739453\pi$
$281$	−6.58142	+	3.79978i	−0.392614	+	0.226676i	0.290678	+	0.956821i	$0.406119\pi$
$282$		0			0
$283$	26.8315	−	15.4912i	1.59497	−	0.920856i	0.602533	−	0.798094i	$-0.294158\pi$
$283$	26.8315	−	15.4912i	1.59497	−	0.920856i	0.992436	−	0.122762i	$-0.0391752\pi$
$284$		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
$299$	17.7990	−	30.8288i	1.02935	−	1.78288i
$300$		0			0
$301$	8.07338	−	4.00219i	0.465342	−	0.230683i
$302$		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
$311$	4.93783	+	8.55257i	0.279998	+	0.484971i	0.971384	−	0.237514i	$-0.0763327\pi$
$311$	4.93783	+	8.55257i	0.279998	+	0.484971i	−0.691386	+	0.722486i	$0.742999\pi$
$312$		0			0
$313$	−14.5707	−	8.41239i	−0.823584	−	0.475496i	0.0280668	−	0.999606i	$-0.491065\pi$
$313$	−14.5707	−	8.41239i	−0.823584	−	0.475496i	−0.851651	+	0.524110i	$0.824398\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−21.4515	−	12.3850i	−1.20483	−	0.695611i	−0.243208	−	0.969974i	$-0.578200\pi$
$317$	−21.4515	−	12.3850i	−1.20483	−	0.695611i	−0.961626	+	0.274363i	$0.911533\pi$
$318$		0			0
$319$	21.8288	+	37.8087i	1.22218	+	2.11688i
$320$		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
$329$	−1.69808	−	1.12953i	−0.0936181	−	0.0622730i
$330$		0			0
$331$	9.00269	−	15.5931i	0.494833	−	0.857075i	−0.505150	−	0.863032i	$-0.668563\pi$
$331$	9.00269	−	15.5931i	0.494833	−	0.857075i	0.999982	+	0.00595666i	$0.00189608\pi$
$332$		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
$347$	−14.1013	+	8.14138i	−0.756996	+	0.437052i	−0.828216	−	0.560409i	$-0.810644\pi$
$347$	−14.1013	+	8.14138i	−0.756996	+	0.437052i	0.0712201	+	0.997461i	$0.477311\pi$
$348$		0			0
$349$	−15.0734	+	8.70262i	−0.806859	+	0.465840i	−0.845864	−	0.533399i	$-0.820915\pi$
$349$	−15.0734	+	8.70262i	−0.806859	+	0.465840i	0.0390047	+	0.999239i	$0.487581\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	29.8894			1.59085			0.795427	−	0.606050i	$-0.207247\pi$
$353$	29.8894			1.59085			0.795427	+	0.606050i	$0.207247\pi$
$354$		0			0
$355$		−	1.74136i		−	0.0924220i
$356$		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
$367$		−	20.0567i		−	1.04695i	−0.852041	−	0.523474i	$-0.824636\pi$
$367$		−	20.0567i		−	1.04695i	0.852041	−	0.523474i	$-0.175364\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−11.2316	+	16.8850i	−0.583116	+	0.876626i
$372$		0			0
$373$	−7.98925			−0.413667			−0.206834	−	0.978376i	$-0.566316\pi$
$373$	−7.98925			−0.413667			−0.206834	+	0.978376i	$0.566316\pi$
$374$		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
$383$	8.02117			0.409862			0.204931	−	0.978776i	$-0.434303\pi$
$383$	8.02117			0.409862			0.204931	+	0.978776i	$0.434303\pi$
$384$		0			0
$385$	11.0027	+	0.698233i	0.560749	+	0.0355852i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	18.4112i		−	0.933484i	−0.884393	−	0.466742i	$-0.845428\pi$
$389$		−	18.4112i		−	0.933484i	0.884393	−	0.466742i	$-0.154572\pi$
$390$		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
$401$		−	8.58881i		−	0.428905i	−0.976734	−	0.214452i	$-0.931203\pi$
$401$		−	8.58881i		−	0.428905i	0.976734	−	0.214452i	$-0.0687967\pi$
$402$		0			0
$403$	3.06531			0.152694
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−42.4902	+	24.5318i	−2.10616	+	1.21599i
$408$		0			0
$409$	3.04072	−	1.75556i	0.150354	−	0.0868069i	−0.422936	−	0.906160i	$-0.639000\pi$
$409$	3.04072	−	1.75556i	0.150354	−	0.0868069i	0.573290	+	0.819353i	$0.305667\pi$
$410$		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
$425$	−12.5756	+	21.7817i	−0.610008	+	1.05657i
$426$		0			0
$427$	−6.05078	+	9.09643i	−0.292818	+	0.440207i
$428$		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
$437$	2.08350	+	3.60872i	0.0996671	+	0.172628i
$438$		0			0
$439$	2.71744	+	1.56891i	0.129696	+	0.0748802i	0.563444	−	0.826154i	$-0.309476\pi$
$439$	2.71744	+	1.56891i	0.129696	+	0.0748802i	−0.433748	+	0.901034i	$0.642809\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−20.9822	−	12.1141i	−0.996896	−	0.575558i	−0.0895675	−	0.995981i	$-0.528548\pi$
$443$	−20.9822	−	12.1141i	−0.996896	−	0.575558i	−0.907328	+	0.420423i	$0.861882\pi$
$444$		0			0
$445$	−2.00269	−	3.46876i	−0.0949365	−	0.164435i
$446$		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
$455$	5.96492	−	8.96734i	0.279640	−	0.420396i
$456$		0			0
$457$	13.1060	−	22.7003i	0.613074	−	1.06188i	−0.377645	−	0.925951i	$-0.623266\pi$
$457$	13.1060	−	22.7003i	0.613074	−	1.06188i	0.990719	−	0.135925i	$-0.0434007\pi$
$458$		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	0.961586	−	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
$473$	−15.9446	+	9.20560i	−0.733132	+	0.423274i
$474$		0			0
$475$	−2.35862	+	1.36175i	−0.108221	+	0.0624815i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5.96699			−0.272639			−0.136319	−	0.990665i	$-0.543527\pi$
$479$	−5.96699			−0.272639			−0.136319	+	0.990665i	$0.543527\pi$
$480$		0			0
$481$			47.9296i			2.18540i
$482$		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	$-0.171626\pi$
$491$	18.6697	+	10.7790i	0.842553	+	0.486448i	−0.0155783	+	0.999879i	$0.504959\pi$
$492$		0			0
$493$			46.1035i			2.07640i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	5.96492	+	0.378535i	0.267563	+	0.0169796i
$498$		0			0
$499$	28.8514			1.29157			0.645784	−	0.763520i	$-0.276531\pi$
$499$	28.8514			1.29157			0.645784	+	0.763520i	$0.276531\pi$
$500$		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
$509$	−25.4055			−1.12608			−0.563039	−	0.826430i	$-0.690368\pi$
$509$	−25.4055			−1.12608			−0.563039	+	0.826430i	$0.690368\pi$
$510$		0			0
$511$	−3.31969	+	4.99065i	−0.146855	+	0.220773i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	2.28813i		−	0.100827i
$516$		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
$527$			3.31362i			0.144343i
$528$		0			0
$529$	−22.4403			−0.975663
$530$		0			0
$531$		0			0
$532$		0			0
$533$	39.2959	−	22.6875i	1.70209	−	0.982704i
$534$		0			0
$535$	3.29063	−	1.89984i	0.142266	−	0.0821374i
$536$		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	0.930454	−	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
$551$	−2.49616	+	4.32347i	−0.106340	+	0.184186i
$552$		0			0
$553$	17.7790	+	11.8262i	0.756039	+	0.502903i
$554$		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
$563$	−3.01074	−	5.21475i	−0.126887	−	0.219776i	0.795582	−	0.605846i	$-0.207165\pi$
$563$	−3.01074	−	5.21475i	−0.126887	−	0.219776i	−0.922469	+	0.386071i	$0.873832\pi$
$564$		0			0
$565$	4.22550	+	2.43960i	0.177768	+	0.102635i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	25.4208	+	14.6767i	1.06570	+	0.615280i	0.927002	−	0.375055i	$-0.122376\pi$
$569$	25.4208	+	14.6767i	1.06570	+	0.615280i	0.138694	+	0.990335i	$0.455710\pi$
$570$		0			0
$571$	−8.61410	−	14.9201i	−0.360489	−	0.624385i	0.627553	−	0.778574i	$-0.284057\pi$
$571$	−8.61410	−	14.9201i	−0.360489	−	0.624385i	−0.988041	+	0.154189i	$0.950723\pi$
$572$		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
$581$	9.13621	−	4.52907i	0.379034	−	0.187897i
$582$		0			0
$583$	20.7174	−	35.8837i	0.858029	−	1.48615i
$584$		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	0.501184	−	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
$599$	32.7458	−	18.9058i	1.33796	−	0.772471i	0.351454	−	0.936205i	$-0.385687\pi$
$599$	32.7458	−	18.9058i	1.33796	−	0.772471i	0.986504	+	0.163735i	$0.0523541\pi$
$600$		0			0
$601$	2.51344	−	1.45114i	0.102525	−	0.0591931i	−0.447861	−	0.894103i	$-0.647814\pi$
$601$	2.51344	−	1.45114i	0.102525	−	0.0591931i	0.550386	+	0.834910i	$0.314481\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−14.0468			−0.571083
$606$		0			0
$607$			11.1706i			0.453401i	0.973965	+	0.226701i	$0.0727939\pi$
$607$			11.1706i			0.453401i	−0.973965	+	0.226701i	$0.927206\pi$
$608$		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	$-0.299049\pi$
$617$	4.62501	+	2.67025i	0.186196	+	0.107500i	−0.404005	+	0.914757i	$0.632382\pi$
$618$		0			0
$619$		−	21.2082i		−	0.852431i	−0.904622	−	0.426216i	$-0.859846\pi$
$619$		−	21.2082i		−	0.852431i	0.904622	−	0.426216i	$-0.140154\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	12.3173	−	6.10603i	0.493483	−	0.244633i
$624$		0			0
$625$	16.4403			0.657610
$626$		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
$635$	−3.40030			−0.134937
$636$		0			0
$637$	29.4203	+	22.3817i	1.16568	+	0.886795i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	27.3096i		−	1.07867i	−0.842093	−	0.539333i	$-0.818676\pi$
$641$		−	27.3096i		−	1.07867i	0.842093	−	0.539333i	$-0.181324\pi$
$642$		0			0
$643$	30.9429	+	17.8649i	1.22027	+	0.704524i	0.964976	−	0.262340i	$-0.0844941\pi$
$643$	30.9429	+	17.8649i	1.22027	+	0.704524i	0.255295	+	0.966863i	$0.417827\pi$
$644$		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
$653$		−	26.0761i		−	1.02044i	−0.860045	−	0.510218i	$-0.829565\pi$
$653$		−	26.0761i		−	1.02044i	0.860045	−	0.510218i	$-0.170435\pi$
$654$		0			0
$655$	−6.77718			−0.264806
$656$		0			0
$657$		0			0
$658$		0			0
$659$	35.3830	−	20.4284i	1.37833	−	0.795778i	0.386370	−	0.922344i	$-0.373729\pi$
$659$	35.3830	−	20.4284i	1.37833	−	0.795778i	0.991958	+	0.126566i	$0.0403956\pi$
$660$		0			0
$661$	6.28544	−	3.62890i	0.244475	−	0.141148i	−0.372757	−	0.927929i	$-0.621587\pi$
$661$	6.28544	−	3.62890i	0.244475	−	0.141148i	0.617232	+	0.786781i	$0.288254\pi$
$662$		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
$677$	−5.48172	+	9.49462i	−0.210680	+	0.364908i	−0.951927	−	0.306324i	$-0.900901\pi$
$677$	−5.48172	+	9.49462i	−0.210680	+	0.364908i	0.741248	+	0.671232i	$0.234234\pi$
$678$		0			0
$679$	−16.4819	−	33.2479i	−0.632516	−	1.27594i
$680$		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
$689$	−20.2386	−	35.0544i	−0.771031	−	1.33546i
$690$		0			0
$691$	−7.27987	−	4.20304i	−0.276939	−	0.159891i	0.355098	−	0.934829i	$-0.384448\pi$
$691$	−7.27987	−	4.20304i	−0.276939	−	0.159891i	−0.632037	+	0.774938i	$0.717781\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−5.12562	−	2.95928i	−0.194426	−	0.112252i
$696$		0			0
$697$	24.5253	+	42.4790i	0.928961	+	1.60901i
$698$		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
$707$	−2.12885	+	33.5463i	−0.0800638	+	1.26164i
$708$		0			0
$709$	12.0434	−	20.8598i	0.452300	−	0.783406i	−0.546229	−	0.837636i	$-0.683937\pi$
$709$	12.0434	−	20.8598i	0.452300	−	0.783406i	0.998528	+	0.0542300i	$0.0172704\pi$
$710$		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
$725$	30.8146	−	17.7908i	1.14443	−	0.660734i
$726$		0			0
$727$	5.99193	−	3.45945i	0.222229	−	0.128304i	−0.384753	−	0.923019i	$-0.625713\pi$
$727$	5.99193	−	3.45945i	0.222229	−	0.128304i	0.606982	+	0.794716i	$0.292380\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−19.4426			−0.719112
$732$		0			0
$733$			17.1981i			0.635225i	0.948221	+	0.317613i	$0.102881\pi$
$733$			17.1981i			0.635225i	−0.948221	+	0.317613i	$0.897119\pi$
$734$		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	$-0.545492\pi$
$743$	−29.1891	−	16.8523i	−1.07085	−	0.618253i	−0.928412	+	0.371552i	$0.878826\pi$
$744$		0			0
$745$		−	6.59262i		−	0.241535i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	5.79247	+	11.6848i	0.211652	+	0.426953i
$750$		0			0
$751$	4.82238			0.175971			0.0879856	−	0.996122i	$-0.471957\pi$
$751$	4.82238			0.175971			0.0879856	+	0.996122i	$0.471957\pi$
$752$		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
$761$	−15.8385			−0.574145			−0.287072	−	0.957909i	$-0.592682\pi$
$761$	−15.8385			−0.574145			−0.287072	+	0.957909i	$0.592682\pi$
$762$		0			0
$763$	15.0054	+	9.98130i	0.543231	+	0.361347i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			72.8152i			2.62920i
$768$		0			0
$769$	−40.9810	−	23.6604i	−1.47781	−	0.853215i	−0.478126	−	0.878291i	$-0.658684\pi$
$769$	−40.9810	−	23.6604i	−1.47781	−	0.853215i	−0.999686	+	0.0250761i	$0.992017\pi$
$770$		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
$779$			5.31144i			0.190302i
$780$		0			0
$781$	−12.2121			−0.436982
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−7.10720	+	4.10334i	−0.253667	+	0.146455i
$786$		0			0
$787$	33.7881	−	19.5076i	1.20442	−	0.695370i	0.242883	−	0.970056i	$-0.421907\pi$
$787$	33.7881	−	19.5076i	1.20442	−	0.695370i	0.961534	+	0.274685i	$0.0885737\pi$
$788$		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
$803$	6.12340	−	10.6060i	0.216090	−	0.374279i
$804$		0			0
$805$	−13.7201	−	0.870682i	−0.483571	−	0.0306875i
$806$		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
$815$	−5.80851	−	10.0606i	−0.203463	−	0.352409i
$816$		0			0
$817$	−1.82328	−	1.05267i	−0.0637885	−	0.0368283i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	39.8216	+	22.9910i	1.38978	+	0.802393i	0.993291	−	0.115645i	$-0.0368934\pi$
$821$	39.8216	+	22.9910i	1.38978	+	0.802393i	0.396494	+	0.918037i	$0.370227\pi$
$822$		0			0
$823$	−21.1494	−	36.6319i	−0.737223	−	1.27691i	−0.953741	−	0.300629i	$-0.902803\pi$
$823$	−21.1494	−	36.6319i	−0.737223	−	1.27691i	0.216518	−	0.976279i	$-0.430530\pi$
$824$		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
$833$	−24.1947	+	31.8036i	−0.838298	+	1.10193i
$834$		0			0
$835$	6.70022	−	11.6051i	0.231871	−	0.401612i
$836$		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
$851$	52.9845	−	30.5906i	1.81628	−	1.04863i
$852$		0			0
$853$	−23.0353	+	13.2995i	−0.788715	+	0.455365i	−0.839510	−	0.543344i	$-0.817158\pi$
$853$	−23.0353	+	13.2995i	−0.788715	+	0.455365i	0.0507949	+	0.998709i	$0.483825\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−29.6311			−1.01218			−0.506090	−	0.862481i	$-0.668909\pi$
$857$	−29.6311			−1.01218			−0.506090	+	0.862481i	$0.668909\pi$
$858$		0			0
$859$			4.84149i			0.165189i	0.996583	+	0.0825947i	$0.0263207\pi$
$859$			4.84149i			0.165189i	−0.996583	+	0.0825947i	$0.973679\pi$
$860$		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
$871$			71.5695i			2.42504i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.21489	−	19.1441i	0.0410706	−	0.647187i
$876$		0			0
$877$	−42.5978			−1.43842			−0.719212	−	0.694791i	$-0.755497\pi$
$877$	−42.5978			−1.43842			−0.719212	+	0.694791i	$0.755497\pi$
$878$		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
$887$	3.59170			0.120598			0.0602988	−	0.998180i	$-0.480795\pi$
$887$	3.59170			0.120598			0.0602988	+	0.998180i	$0.480795\pi$
$888$		0			0
$889$	0.739151	−	11.6475i	0.0247903	−	0.390644i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			0.476501i			0.0159455i
$894$		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
$905$			3.17582i			0.105568i
$906$		0			0
$907$	5.84787			0.194175			0.0970877	−	0.995276i	$-0.469047\pi$
$907$	5.84787			0.194175			0.0970877	+	0.995276i	$0.469047\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	6.58142	−	3.79978i	0.218052	−	0.125892i	−0.386996	−	0.922081i	$-0.626487\pi$
$911$	6.58142	−	3.79978i	0.218052	−	0.125892i	0.605048	+	0.796189i	$0.293154\pi$
$912$		0			0
$913$	−18.0436	+	10.4175i	−0.597156	+	0.344768i
$914$		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
$929$	26.2056	−	45.3895i	0.859779	−	1.48918i	−0.0123610	−	0.999924i	$-0.503935\pi$
$929$	26.2056	−	45.3895i	0.859779	−	1.48918i	0.872140	−	0.489257i	$-0.162732\pi$
$930$		0			0
$931$	−3.99084	+	1.67250i	−0.130795	+	0.0548138i
$932$		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
$941$	13.7319	+	23.7843i	0.447647	+	0.775348i	0.998232	−	0.0594314i	$-0.0189287\pi$
$941$	13.7319	+	23.7843i	0.447647	+	0.775348i	−0.550585	+	0.834779i	$0.685595\pi$
$942$		0			0
$943$	−50.1604	−	28.9601i	−1.63345	−	0.943071i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−51.0532	−	29.4756i	−1.65901	−	0.957828i	−0.973174	−	0.230069i	$-0.926105\pi$
$947$	−51.0532	−	29.4756i	−1.65901	−	0.957828i	−0.685833	−	0.727759i	$-0.740562\pi$
$948$		0			0
$949$	−5.98188	−	10.3609i	−0.194180	−	0.336330i
$950$		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
$959$	11.9298	+	0.757069i	0.385234	+	0.0244470i
$960$		0			0
$961$	−15.3315	+	26.5550i	−0.494566	+	0.856613i
$962$		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	0.962408	−	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
$977$	17.1008	−	9.87316i	0.547103	−	0.315870i	−0.200849	−	0.979622i	$-0.564370\pi$
$977$	17.1008	−	9.87316i	0.547103	−	0.315870i	0.747953	+	0.663752i	$0.231037\pi$
$978$		0			0
$979$	−24.3262	+	14.0447i	−0.777467	+	0.448871i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−22.8388			−0.728444			−0.364222	−	0.931312i	$-0.618665\pi$
$983$	−22.8388			−0.728444			−0.364222	+	0.931312i	$0.618665\pi$
$984$		0			0
$985$		−	15.6388i		−	0.498294i
$986$		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
$997$		−	0.702889i		−	0.0222607i	−0.999938	−	0.0111304i	$-0.996457\pi$
$997$		−	0.702889i		−	0.0222607i	0.999938	−	0.0111304i	$-0.00354298\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.t.e.269.3	✓	12	9.4	even	3
756.2.t.e.269.4	yes	12	9.5	odd	6
756.2.t.e.593.3	yes	12	63.5	even	6
756.2.t.e.593.4	yes	12	63.40	odd	6
2268.2.w.i.269.3		12	9.7	even	3
2268.2.w.i.269.4		12	9.2	odd	6
2268.2.w.i.1349.3		12	21.5	even	6
2268.2.w.i.1349.4		12	7.5	odd	6
2268.2.bm.i.593.3		12	63.61	odd	6	inner
2268.2.bm.i.593.4		12	63.47	even	6	inner
2268.2.bm.i.1025.3		12	3.2	odd	2	inner
2268.2.bm.i.1025.4		12	1.1	even	1	trivial
5292.2.f.e.2645.5		12	63.31	odd	6
5292.2.f.e.2645.6		12	63.32	odd	6
5292.2.f.e.2645.7		12	63.4	even	3
5292.2.f.e.2645.8		12	63.59	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.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.770835 q^{5} +(-0.167563 + 2.64044i) q^{7} -5.40581i q^{11} +(-4.57338 - 2.64044i) q^{13} +(2.85433 - 4.94385i) q^{17} +(0.535344 - 0.309081i) q^{19} +6.74094i q^{23} -4.40581 q^{25} +(-6.99408 + 4.03803i) q^{29} +(-0.502688 + 0.290227i) q^{31} +(-0.129163 + 2.03534i) q^{35} +(-4.53803 - 7.86010i) q^{37} +(-4.29615 + 7.44116i) q^{41} +(-1.70291 - 2.94952i) q^{43} +(-0.385418 + 0.667563i) q^{47} +(-6.94385 - 0.884879i) q^{49} +(6.63798 + 3.83244i) q^{53} -4.16699i q^{55} +(-6.89423 - 11.9412i) q^{59} +(3.57606 + 2.06464i) q^{61} +(-3.52532 - 2.03534i) q^{65} +(-6.77628 - 11.7369i) q^{67} -2.25906i q^{71} +(1.96197 + 1.13274i) q^{73} +(14.2737 + 0.905813i) q^{77} +(4.03534 - 6.98942i) q^{79} +(-1.92709 - 3.33781i) q^{83} +(2.20022 - 3.81089i) q^{85} +(-2.59808 - 4.50000i) q^{89} +(7.73825 - 11.6333i) q^{91} +(0.412662 - 0.238250i) q^{95} +(-12.1468 + 7.01293i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{19} - 24 q^{37} + 6 q^{43} - 18 q^{61} + 54 q^{73} + 24 q^{79} + 6 q^{85} + 42 q^{91} - 36 q^{97}+O(q^{100}) \) 12 * q - 18 * q^19 - 24 * q^37 + 6 * q^43 - 18 * q^61 + 54 * q^73 + 24 * q^79 + 6 * q^85 + 42 * q^91 - 36 * q^97

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