LMFDB - Embedded newform 756.2.t.e.269.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(269,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("756.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.5
Root			$-1.07992 - 0.623490i$ of defining polynomial
Character	$\chi$	$=$	756.269
Dual form			756.2.t.e.593.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07992 + 1.87047i) q^{5} +(-0.167563 + 2.64044i) q^{7} +O(q^{10})$	$q+(1.07992 + 1.87047i) q^{5} +(-0.167563 + 2.64044i) q^{7} +(1.15625 + 0.667563i) q^{11} -2.35021i q^{13} +(-3.60166 + 6.23825i) q^{17} +(1.03803 - 0.599308i) q^{19} +(-2.08350 + 1.20291i) q^{23} +(0.167563 - 0.290227i) q^{25} +6.14675i q^{29} +(-7.11141 - 4.10577i) q^{31} +(-5.11982 + 2.53803i) q^{35} +(2.57338 + 4.45722i) q^{37} +4.47234 q^{41} -0.664874 q^{43} +(1.07992 + 1.87047i) q^{47} +(-6.94385 - 0.884879i) q^{49} +(11.0340 + 6.37047i) q^{53} +2.88365i q^{55} +(-4.83424 + 8.37316i) q^{59} +(10.6468 - 6.14691i) q^{61} +(4.39600 - 2.53803i) q^{65} +(1.86778 - 3.23509i) q^{67} -11.4058i q^{71} +(9.07338 + 5.23852i) q^{73} +(-1.95640 + 2.94116i) q^{77} +(4.53803 + 7.86010i) q^{79} -10.7992 q^{83} -15.5579 q^{85} +(-2.59808 - 4.50000i) q^{89} +(6.20560 + 0.393808i) q^{91} +(2.24198 + 1.29440i) q^{95} +1.23632i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q - 18 q^{19} - 24 q^{37} - 12 q^{43} + 18 q^{61} + 54 q^{73} + 24 q^{79} - 12 q^{85} + 42 q^{91}+O(q^{100}) $ 12 * q - 18 * q^19 - 24 * q^37 - 12 * q^43 + 18 * q^61 + 54 * q^73 + 24 * q^79 - 12 * q^85 + 42 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.07992	+	1.87047i	0.482953	+	0.836499i	0.999808	−	0.0195734i	$-0.00623081\pi$
$5$	1.07992	+	1.87047i	0.482953	+	0.836499i	−0.516855	+	0.856073i	$0.672897\pi$
$6$		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
$11$	1.15625	+	0.667563i	0.348623	+	0.201278i	0.664079	−	0.747663i	$-0.268824\pi$
$11$	1.15625	+	0.667563i	0.348623	+	0.201278i	−0.315455	+	0.948940i	$0.602157\pi$
$12$		0			0
$13$		−	2.35021i		−	0.651832i	−0.945399	−	0.325916i	$-0.894327\pi$
$13$		−	2.35021i		−	0.651832i	0.945399	−	0.325916i	$-0.105673\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.60166	+	6.23825i	−0.873530	+	1.51300i	−0.0152091	+	0.999884i	$0.504841\pi$
$17$	−3.60166	+	6.23825i	−0.873530	+	1.51300i	−0.858321	+	0.513114i	$0.828492\pi$
$18$		0			0
$19$	1.03803	−	0.599308i	0.238141	−	0.137491i	−0.376181	−	0.926546i	$-0.622763\pi$
$19$	1.03803	−	0.599308i	0.238141	−	0.137491i	0.614322	+	0.789055i	$0.289430\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.08350	+	1.20291i	−0.434439	+	0.250823i	−0.701236	−	0.712929i	$-0.747368\pi$
$23$	−2.08350	+	1.20291i	−0.434439	+	0.250823i	0.266797	+	0.963753i	$0.414035\pi$
$24$		0			0
$25$	0.167563	−	0.290227i	0.0335126	−	0.0580455i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			6.14675i			1.14142i	0.821151	+	0.570712i	$0.193333\pi$
$29$			6.14675i			1.14142i	−0.821151	+	0.570712i	$0.806667\pi$
$30$		0			0
$31$	−7.11141	−	4.10577i	−1.27725	−	0.737419i	−0.300905	−	0.953654i	$-0.597289\pi$
$31$	−7.11141	−	4.10577i	−1.27725	−	0.737419i	−0.976341	+	0.216235i	$0.930622\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.11982	+	2.53803i	−0.865407	+	0.429006i
$36$		0			0
$37$	2.57338	+	4.45722i	0.423060	+	0.732762i	0.996237	−	0.0866697i	$-0.0276225\pi$
$37$	2.57338	+	4.45722i	0.423060	+	0.732762i	−0.573177	+	0.819432i	$0.694289\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.47234			0.698462			0.349231	−	0.937037i	$-0.386443\pi$
$41$	4.47234			0.698462			0.349231	+	0.937037i	$0.386443\pi$
$42$		0			0
$43$	−0.664874			−0.101392			−0.0506962	−	0.998714i	$-0.516144\pi$
$43$	−0.664874			−0.101392			−0.0506962	+	0.998714i	$0.516144\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.07992	+	1.87047i	0.157522	+	0.272836i	0.933974	−	0.357340i	$-0.116316\pi$
$47$	1.07992	+	1.87047i	0.157522	+	0.272836i	−0.776453	+	0.630176i	$0.782983\pi$
$48$		0			0
$49$	−6.94385	−	0.884879i	−0.991978	−	0.126411i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	11.0340	+	6.37047i	1.51563	+	0.875051i	0.999832	+	0.0183431i	$0.00583913\pi$
$53$	11.0340	+	6.37047i	1.51563	+	0.875051i	0.515802	+	0.856708i	$0.327494\pi$
$54$		0			0
$55$			2.88365i			0.388831i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.83424	+	8.37316i	−0.629365	+	1.09009i	0.358314	+	0.933601i	$0.383352\pi$
$59$	−4.83424	+	8.37316i	−0.629365	+	1.09009i	−0.987679	+	0.156491i	$0.949982\pi$
$60$		0			0
$61$	10.6468	−	6.14691i	1.36318	−	0.787031i	0.373131	−	0.927778i	$-0.378284\pi$
$61$	10.6468	−	6.14691i	1.36318	−	0.787031i	0.990045	+	0.140748i	$0.0449507\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.39600	−	2.53803i	0.545257	−	0.314804i
$66$		0			0
$67$	1.86778	−	3.23509i	0.228186	−	0.395229i	−0.729085	−	0.684423i	$-0.760054\pi$
$67$	1.86778	−	3.23509i	0.228186	−	0.395229i	0.957270	+	0.289194i	$0.0933873\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	11.4058i		−	1.35362i	−0.736157	−	0.676810i	$-0.763362\pi$
$71$		−	11.4058i		−	1.35362i	0.736157	−	0.676810i	$-0.236638\pi$
$72$		0			0
$73$	9.07338	+	5.23852i	1.06196	+	0.613122i	0.925973	−	0.377589i	$-0.123247\pi$
$73$	9.07338	+	5.23852i	1.06196	+	0.613122i	0.135985	+	0.990711i	$0.456580\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.95640	+	2.94116i	−0.222953	+	0.335176i
$78$		0			0
$79$	4.53803	+	7.86010i	0.510569	+	0.884331i	0.999925	+	0.0122468i	$0.00389836\pi$
$79$	4.53803	+	7.86010i	0.510569	+	0.884331i	−0.489356	+	0.872084i	$0.662768\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−10.7992			−1.18536			−0.592681	−	0.805437i	$-0.701930\pi$
$83$	−10.7992			−1.18536			−0.592681	+	0.805437i	$0.701930\pi$
$84$		0			0
$85$	−15.5579			−1.68750
$86$		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
$91$	6.20560	+	0.393808i	0.650523	+	0.0412823i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.24198	+	1.29440i	0.230022	+	0.132803i
$96$		0			0
$97$			1.23632i			0.125530i	0.998028	+	0.0627648i	$0.0199918\pi$
$97$			1.23632i			0.125530i	−0.998028	+	0.0627648i	$0.980008\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.95640	+	3.38859i	−0.194670	+	0.337177i	−0.946792	−	0.321846i	$-0.895697\pi$
$101$	−1.95640	+	3.38859i	−0.194670	+	0.337177i	0.752123	+	0.659023i	$0.229030\pi$
$102$		0			0
$103$	−3.57606	+	2.06464i	−0.352360	+	0.203435i	−0.665724	−	0.746198i	$-0.731877\pi$
$103$	−3.57606	+	2.06464i	−0.352360	+	0.203435i	0.313364	+	0.949633i	$0.398544\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.39823	−	1.96197i	0.328519	−	0.189671i	−0.326664	−	0.945140i	$-0.605925\pi$
$107$	3.39823	−	1.96197i	0.328519	−	0.189671i	0.655183	+	0.755470i	$0.272591\pi$
$108$		0			0
$109$	−0.664874	+	1.15160i	−0.0636834	+	0.110303i	−0.896109	−	0.443834i	$-0.853618\pi$
$109$	−0.664874	+	1.15160i	−0.0636834	+	0.110303i	0.832426	+	0.554137i	$0.186951\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	16.4819i		−	1.55048i	−0.631664	−	0.775242i	$-0.717628\pi$
$113$		−	16.4819i		−	1.55048i	0.631664	−	0.775242i	$-0.282372\pi$
$114$		0			0
$115$	−4.50000	−	2.59808i	−0.419627	−	0.242272i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−15.8682	−	10.5553i	−1.45464	−	0.967599i
$120$		0			0
$121$	−4.60872	−	7.98254i	−0.418975	−	0.725685i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.5230			1.03065
$126$		0			0
$127$	14.8877			1.32107			0.660534	−	0.750796i	$-0.270330\pi$
$127$	14.8877			1.32107			0.660534	+	0.750796i	$0.270330\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.92132	−	13.7201i	−0.692089	−	1.19873i	−0.971152	−	0.238460i	$-0.923357\pi$
$131$	−7.92132	−	13.7201i	−0.692089	−	1.19873i	0.279063	−	0.960273i	$-0.409976\pi$
$132$		0			0
$133$	1.40850	+	2.84128i	0.122133	+	0.246371i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	19.7554	+	11.4058i	1.68782	+	0.974464i	0.956182	+	0.292773i	$0.0945780\pi$
$137$	19.7554	+	11.4058i	1.68782	+	0.974464i	0.731640	+	0.681691i	$0.238755\pi$
$138$		0			0
$139$		−	16.3761i		−	1.38900i	−0.719492	−	0.694500i	$-0.755626\pi$
$139$		−	16.3761i		−	1.38900i	0.719492	−	0.694500i	$-0.244374\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.56891	−	2.71744i	0.131199	−	0.227244i
$144$		0			0
$145$	−11.4973	+	6.63798i	−0.954800	+	0.551254i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.56522	−	4.36778i	0.619767	−	0.357823i	−0.157011	−	0.987597i	$-0.550186\pi$
$149$	7.56522	−	4.36778i	0.619767	−	0.357823i	0.776778	+	0.629774i	$0.216853\pi$
$150$		0			0
$151$	−3.57338	+	6.18927i	−0.290797	+	0.503676i	−0.973998	−	0.226555i	$-0.927254\pi$
$151$	−3.57338	+	6.18927i	−0.290797	+	0.503676i	0.683201	+	0.730230i	$0.260587\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	17.7356i		−	1.42455i
$156$		0			0
$157$	−10.6060	−	6.12340i	−0.846453	−	0.488700i	0.0129992	−	0.999916i	$-0.495862\pi$
$157$	−10.6060	−	6.12340i	−0.846453	−	0.488700i	−0.859453	+	0.511215i	$0.829195\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−2.82709	−	5.70291i	−0.222806	−	0.449452i
$162$		0			0
$163$	−8.03803	−	13.9223i	−0.629587	−	1.09048i	−0.987635	−	0.156774i	$-0.949891\pi$
$163$	−8.03803	−	13.9223i	−0.629587	−	1.09048i	0.358047	−	0.933703i	$-0.383443\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.3703			0.879860			0.439930	−	0.898032i	$-0.355003\pi$
$167$	11.3703			0.879860			0.439930	+	0.898032i	$0.355003\pi$
$168$		0			0
$169$	7.47650			0.575115
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.35241	−	11.0027i	−0.482964	−	0.836519i	0.516844	−	0.856079i	$-0.327107\pi$
$173$	−6.35241	−	11.0027i	−0.482964	−	0.836519i	−0.999809	+	0.0195605i	$0.993773\pi$
$174$		0			0
$175$	0.738250	+	0.491071i	0.0558065	+	0.0371215i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−13.8862	−	8.01722i	−1.03791	−	0.599235i	−0.118666	−	0.992934i	$-0.537862\pi$
$179$	−13.8862	−	8.01722i	−1.03791	−	0.599235i	−0.919239	+	0.393699i	$0.871195\pi$
$180$		0			0
$181$			14.0729i			1.04603i	0.852324	+	0.523015i	$0.175193\pi$
$181$			14.0729i			1.04603i	−0.852324	+	0.523015i	$0.824807\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−5.55806	+	9.62684i	−0.408637	+	0.707780i
$186$		0			0
$187$	−8.32885	+	4.80866i	−0.609066	+	0.351644i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	22.7662	−	13.1441i	1.64730	−	0.951071i	0.669166	−	0.743113i	$-0.266652\pi$
$191$	22.7662	−	13.1441i	1.64730	−	0.951071i	0.978138	−	0.207958i	$-0.0666817\pi$
$192$		0			0
$193$	−1.53803	+	2.66395i	−0.110710	+	0.191755i	−0.916057	−	0.401049i	$-0.868646\pi$
$193$	−1.53803	+	2.66395i	−0.110710	+	0.191755i	0.805347	+	0.592804i	$0.201979\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	9.08144i		−	0.647026i	−0.946224	−	0.323513i	$-0.895136\pi$
$197$		−	9.08144i		−	0.647026i	0.946224	−	0.323513i	$-0.104864\pi$
$198$		0			0
$199$	19.6468	+	11.3431i	1.39272	+	0.804088i	0.993616	−	0.112817i	$-0.0359874\pi$
$199$	19.6468	+	11.3431i	1.39272	+	0.804088i	0.399106	+	0.916905i	$0.369321\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−16.2301	−	1.02997i	−1.13913	−	0.0722895i
$204$		0			0
$205$	4.82975	+	8.36537i	0.337324	+	0.584263i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.60030			0.110695
$210$		0			0
$211$	9.81700			0.675830			0.337915	−	0.941177i	$-0.390278\pi$
$211$	9.81700			0.675830			0.337915	+	0.941177i	$0.390278\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.718009	−	1.24363i	−0.0489678	−	0.0848147i
$216$		0			0
$217$	12.0327	−	18.0893i	0.816830	−	1.22798i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	14.6612	+	8.46466i	0.986220	+	0.569394i
$222$		0			0
$223$		−	7.05064i		−	0.472146i	−0.971735	−	0.236073i	$-0.924140\pi$
$223$		−	7.05064i		−	0.472146i	0.971735	−	0.236073i	$-0.0758604\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.87772	+	17.1087i	−0.655608	+	1.13555i	0.326134	+	0.945324i	$0.394254\pi$
$227$	−9.87772	+	17.1087i	−0.655608	+	1.13555i	−0.981741	+	0.190222i	$0.939079\pi$
$228$		0			0
$229$	2.88590	−	1.66618i	0.190706	−	0.110104i	−0.401607	−	0.915812i	$-0.631548\pi$
$229$	2.88590	−	1.66618i	0.190706	−	0.110104i	0.592313	+	0.805708i	$0.298215\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.48172	+	3.16487i	−0.359120	+	0.207338i	−0.668695	−	0.743537i	$-0.733147\pi$
$233$	−5.48172	+	3.16487i	−0.359120	+	0.207338i	0.309575	+	0.950875i	$0.399813\pi$
$234$		0			0
$235$	−2.33244	+	4.03990i	−0.152151	+	0.263534i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	27.8877i		−	1.80390i	−0.431836	−	0.901952i	$-0.642134\pi$
$239$		−	27.8877i		−	1.80390i	0.431836	−	0.901952i	$-0.357866\pi$
$240$		0			0
$241$	7.79350	+	4.49958i	0.502024	+	0.289844i	0.729549	−	0.683929i	$-0.239730\pi$
$241$	7.79350	+	4.49958i	0.502024	+	0.289844i	−0.227525	+	0.973772i	$0.573063\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5.84363	−	13.9438i	−0.373336	−	0.890840i
$246$		0			0
$247$	−1.40850	−	2.43960i	−0.0896208	−	0.155228i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−11.5230			−0.727324			−0.363662	−	0.931531i	$-0.618474\pi$
$251$	−11.5230			−0.727324			−0.363662	+	0.931531i	$0.618474\pi$
$252$		0			0
$253$	−3.21206			−0.201941
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.56891	+	2.71744i	0.0978662	+	0.169509i	0.910801	−	0.412845i	$-0.135465\pi$
$257$	1.56891	+	2.71744i	0.0978662	+	0.169509i	−0.812935	+	0.582354i	$0.802132\pi$
$258$		0			0
$259$	−12.2002	+	6.04798i	−0.758085	+	0.375803i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.87772	+	5.70291i	0.609087	+	0.351656i	0.772608	−	0.634884i	$-0.218952\pi$
$263$	9.87772	+	5.70291i	0.609087	+	0.351656i	−0.163521	+	0.986540i	$0.552285\pi$
$264$		0			0
$265$			27.5183i			1.69043i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.6721	+	18.4846i	−0.650688	+	1.12702i	0.332269	+	0.943185i	$0.392186\pi$
$269$	−10.6721	+	18.4846i	−0.650688	+	1.12702i	−0.982956	+	0.183839i	$0.941147\pi$
$270$		0			0
$271$	−15.5434	+	8.97399i	−0.944195	+	0.545131i	−0.891273	−	0.453467i	$-0.850187\pi$
$271$	−15.5434	+	8.97399i	−0.944195	+	0.545131i	−0.0529220	+	0.998599i	$0.516853\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.387490	−	0.223717i	0.0233665	−	0.0134907i
$276$		0			0
$277$	15.8850	−	27.5136i	0.954437	−	1.65313i	0.218787	−	0.975773i	$-0.429790\pi$
$277$	15.8850	−	27.5136i	0.954437	−	1.65313i	0.735651	−	0.677361i	$-0.236877\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			3.55794i			0.212249i	0.994353	+	0.106125i	$0.0338442\pi$
$281$			3.55794i			0.212249i	−0.994353	+	0.106125i	$0.966156\pi$
$282$		0			0
$283$	6.71475	+	3.87676i	0.399151	+	0.230450i	0.686117	−	0.727491i	$-0.259314\pi$
$283$	6.71475	+	3.87676i	0.399151	+	0.230450i	−0.286967	+	0.957941i	$0.592647\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.749397	+	11.8089i	−0.0442355	+	0.697060i
$288$		0			0
$289$	−17.4438	−	30.2136i	−1.02611	−	1.77727i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.04348			0.294643			0.147322	−	0.989089i	$-0.452935\pi$
$293$	5.04348			0.294643			0.147322	+	0.989089i	$0.452935\pi$
$294$		0			0
$295$	−20.8823			−1.21582
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.82709	+	4.89666i	0.163495	+	0.283181i
$300$		0			0
$301$	0.111408	−	1.75556i	0.00642146	−	0.101189i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	22.9952	+	13.2763i	1.31670	+	0.760198i
$306$		0			0
$307$			15.0080i			0.856552i	0.903648	+	0.428276i	$0.140879\pi$
$307$			15.0080i			0.856552i	−0.903648	+	0.428276i	$0.859121\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.04348	+	8.73556i	−0.285989	+	0.495348i	−0.972849	−	0.231442i	$-0.925656\pi$
$311$	−5.04348	+	8.73556i	−0.285989	+	0.495348i	0.686859	+	0.726791i	$0.258989\pi$
$312$		0			0
$313$	15.5761	−	8.99284i	0.880411	−	0.508306i	0.00961724	−	0.999954i	$-0.496939\pi$
$313$	15.5761	−	8.99284i	0.880411	−	0.508306i	0.870794	+	0.491648i	$0.163605\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.09646	+	2.36509i	−0.230080	+	0.132837i	−0.610609	−	0.791932i	$-0.709075\pi$
$317$	−4.09646	+	2.36509i	−0.230080	+	0.132837i	0.380529	+	0.924769i	$0.375742\pi$
$318$		0			0
$319$	−4.10334	+	7.10720i	−0.229743	+	0.397927i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			8.63401i			0.480409i
$324$		0			0
$325$	−0.682096	−	0.393808i	−0.0378359	−	0.0218445i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−5.11982	+	2.53803i	−0.282265	+	0.139926i
$330$		0			0
$331$	1.38859	+	2.40511i	0.0763239	+	0.132197i	0.901661	−	0.432443i	$-0.142348\pi$
$331$	1.38859	+	2.40511i	0.0763239	+	0.132197i	−0.825337	+	0.564640i	$0.809015\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	8.06819			0.440812
$336$		0			0
$337$	−6.99462			−0.381021			−0.190511	−	0.981685i	$-0.561014\pi$
$337$	−6.99462			−0.381021			−0.190511	+	0.981685i	$0.561014\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−5.48172	−	9.49462i	−0.296852	−	0.514163i
$342$		0			0
$343$	3.50000	−	18.1865i	0.188982	−	0.981981i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	17.5840	+	10.1521i	0.943959	+	0.544995i	0.891199	−	0.453612i	$-0.149865\pi$
$347$	17.5840	+	10.1521i	0.943959	+	0.544995i	0.0527597	+	0.998607i	$0.483198\pi$
$348$		0			0
$349$		−	9.77414i		−	0.523198i	−0.965177	−	0.261599i	$-0.915750\pi$
$349$		−	9.77414i		−	0.523198i	0.965177	−	0.261599i	$-0.0842498\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.42874	+	11.1349i	−0.342167	+	0.592651i	−0.984835	−	0.173494i	$-0.944494\pi$
$353$	−6.42874	+	11.1349i	−0.342167	+	0.592651i	0.642668	+	0.766145i	$0.277828\pi$
$354$		0			0
$355$	21.3342	−	12.3173i	1.13230	−	0.653735i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	16.7447	−	9.66756i	0.883752	−	0.510234i	0.0118583	−	0.999930i	$-0.496225\pi$
$359$	16.7447	−	9.66756i	0.883752	−	0.510234i	0.871894	+	0.489695i	$0.162892\pi$
$360$		0			0
$361$	−8.78166	+	15.2103i	−0.462193	+	0.800541i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			22.6286i			1.18444i
$366$		0			0
$367$	−23.2881	−	13.4454i	−1.21563	−	0.701845i	−0.251650	−	0.967818i	$-0.580973\pi$
$367$	−23.2881	−	13.4454i	−1.21563	−	0.701845i	−0.963980	+	0.265974i	$0.914307\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−18.6697	+	28.0671i	−0.969284	+	1.45717i
$372$		0			0
$373$	19.2228	+	33.2949i	0.995320	+	1.72394i	0.581350	+	0.813654i	$0.302525\pi$
$373$	19.2228	+	33.2949i	0.995320	+	1.72394i	0.413970	+	0.910291i	$0.364142\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	14.4462			0.744016
$378$		0			0
$379$	3.05993			0.157178			0.0785891	−	0.996907i	$-0.474958\pi$
$379$	3.05993			0.157178			0.0785891	+	0.996907i	$0.474958\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	6.84140	+	11.8497i	0.349579	+	0.605489i	0.986175	−	0.165709i	$-0.0529912\pi$
$383$	6.84140	+	11.8497i	0.349579	+	0.605489i	−0.636595	+	0.771198i	$0.719658\pi$
$384$		0			0
$385$	−7.61410	−	0.483192i	−0.388050	−	0.0246257i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−0.768763	−	0.443845i	−0.0389778	−	0.0225039i	0.480384	−	0.877058i	$-0.340497\pi$
$389$	−0.768763	−	0.443845i	−0.0389778	−	0.0225039i	−0.519362	+	0.854554i	$0.673830\pi$
$390$		0			0
$391$		−	17.3298i		−	0.876407i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−9.80139	+	16.9765i	−0.493161	+	0.854180i
$396$		0			0
$397$	−29.6114	+	17.0962i	−1.48615	+	0.858031i	−0.999876	−	0.0157726i	$-0.994979\pi$
$397$	−29.6114	+	17.0962i	−1.48615	+	0.858031i	−0.486278	+	0.873804i	$0.661646\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−24.1514	+	13.9438i	−1.20607	+	0.696322i	−0.961897	−	0.273410i	$-0.911848\pi$
$401$	−24.1514	+	13.9438i	−1.20607	+	0.696322i	−0.244168	+	0.969733i	$0.578515\pi$
$402$		0			0
$403$	−9.64944	+	16.7133i	−0.480673	+	0.832550i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			6.87156i			0.340611i
$408$		0			0
$409$	11.6848	+	6.74621i	0.577775	+	0.333579i	0.760249	−	0.649632i	$-0.225077\pi$
$409$	11.6848	+	6.74621i	0.577775	+	0.333579i	−0.182473	+	0.983211i	$0.558410\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−21.2988	−	14.1676i	−1.04804	−	0.697140i
$414$		0			0
$415$	−11.6622	−	20.1995i	−0.572474	−	0.991554i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−27.9368			−1.36480			−0.682400	−	0.730979i	$-0.739064\pi$
$419$	−27.9368			−1.36480			−0.682400	+	0.730979i	$0.739064\pi$
$420$		0			0
$421$	12.5472			0.611513			0.305756	−	0.952110i	$-0.401091\pi$
$421$	12.5472			0.611513			0.305756	+	0.952110i	$0.401091\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.20701	+	2.09060i	0.0585484	+	0.101409i
$426$		0			0
$427$	14.4465	+	29.1421i	0.699117	+	1.41029i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	14.9720	+	8.64406i	0.721174	+	0.416370i	0.815185	−	0.579201i	$-0.196635\pi$
$431$	14.9720	+	8.64406i	0.721174	+	0.416370i	−0.0940108	+	0.995571i	$0.529969\pi$
$432$		0			0
$433$		−	27.1920i		−	1.30676i	−0.757028	−	0.653382i	$-0.773349\pi$
$433$		−	27.1920i		−	1.30676i	0.757028	−	0.653382i	$-0.226651\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.44182	+	2.49731i	−0.0689718	+	0.119463i
$438$		0			0
$439$	9.49462	−	5.48172i	0.453154	−	0.261628i	−0.256008	−	0.966675i	$-0.582407\pi$
$439$	9.49462	−	5.48172i	0.453154	−	0.261628i	0.709161	+	0.705046i	$0.249074\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−15.9697	+	9.22013i	−0.758745	+	0.438062i	−0.828845	−	0.559478i	$-0.811001\pi$
$443$	−15.9697	+	9.22013i	−0.758745	+	0.438062i	0.0701001	+	0.997540i	$0.477668\pi$
$444$		0			0
$445$	5.61141	−	9.71924i	0.266006	−	0.460736i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	23.6179i		−	1.11460i	−0.830312	−	0.557298i	$-0.811838\pi$
$449$		−	23.6179i		−	1.11460i	0.830312	−	0.557298i	$-0.188162\pi$
$450$		0			0
$451$	5.17115	+	2.98557i	0.243500	+	0.140585i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	5.96492	+	12.0327i	0.279640	+	0.564100i
$456$		0			0
$457$	14.6141	+	25.3124i	0.683619	+	1.18406i	0.973869	+	0.227111i	$0.0729281\pi$
$457$	14.6141	+	25.3124i	0.683619	+	1.18406i	−0.290250	+	0.956951i	$0.593739\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−5.91997			−0.275720			−0.137860	−	0.990452i	$-0.544022\pi$
$461$	−5.91997			−0.275720			−0.137860	+	0.990452i	$0.544022\pi$
$462$		0			0
$463$	34.4349			1.60032			0.800162	−	0.599784i	$-0.204747\pi$
$463$	34.4349			1.60032			0.800162	+	0.599784i	$0.204747\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.3114	+	33.4483i	0.893625	+	1.54780i	0.835497	+	0.549495i	$0.185180\pi$
$467$	19.3114	+	33.4483i	0.893625	+	1.54780i	0.0581276	+	0.998309i	$0.481487\pi$
$468$		0			0
$469$	8.22909	+	5.47384i	0.379984	+	0.252759i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.768763	−	0.443845i	−0.0353478	−	0.0204080i
$474$		0			0
$475$		−	0.401687i		−	0.0184307i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.51816	−	2.62953i	0.0693665	−	0.120146i	−0.829256	−	0.558869i	$-0.811236\pi$
$479$	1.51816	−	2.62953i	0.0693665	−	0.120146i	0.898623	+	0.438722i	$0.144569\pi$
$480$		0			0
$481$	10.4754	−	6.04798i	0.477638	−	0.275764i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.31251	+	1.33513i	−0.105005	+	0.0606249i
$486$		0			0
$487$	13.3850	−	23.1835i	0.606532	−	1.05054i	−0.385275	−	0.922802i	$-0.625893\pi$
$487$	13.3850	−	23.1835i	0.606532	−	1.05054i	0.991807	−	0.127743i	$-0.0407733\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			10.9584i			0.494545i	0.968946	+	0.247272i	$0.0795342\pi$
$491$			10.9584i			0.494545i	−0.968946	+	0.247272i	$0.920466\pi$
$492$		0			0
$493$	−38.3450	−	22.1385i	−1.72697	−	0.997067i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	30.1164	+	1.91119i	1.35090	+	0.0857286i
$498$		0			0
$499$	15.0499	+	26.0672i	0.673725	+	1.16693i	0.976840	+	0.213972i	$0.0686401\pi$
$499$	15.0499	+	26.0672i	0.673725	+	1.16693i	−0.303115	+	0.952954i	$0.598027\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	12.0941			0.539250			0.269625	−	0.962965i	$-0.413100\pi$
$503$	12.0941			0.539250			0.269625	+	0.962965i	$0.413100\pi$
$504$		0			0
$505$	−8.45101			−0.376065
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−12.5266	−	21.6966i	−0.555230	−	0.961686i	−0.997886	−	0.0649946i	$-0.979297\pi$
$509$	−12.5266	−	21.6966i	−0.555230	−	0.961686i	0.442656	−	0.896692i	$-0.354036\pi$
$510$		0			0
$511$	−15.3523	+	23.0799i	−0.679148	+	1.02100i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.72370	−	4.45928i	−0.340347	−	0.196499i
$516$		0			0
$517$			2.88365i			0.126823i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−8.35956	+	14.4792i	−0.366239	+	0.634345i	−0.988974	−	0.148088i	$-0.952688\pi$
$521$	−8.35956	+	14.4792i	−0.366239	+	0.634345i	0.622735	+	0.782433i	$0.286021\pi$
$522$		0			0
$523$	−22.5327	+	13.0092i	−0.985284	+	0.568854i	−0.903861	−	0.427826i	$-0.859280\pi$
$523$	−22.5327	+	13.0092i	−0.985284	+	0.568854i	−0.0814229	+	0.996680i	$0.525946\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	51.2257	−	29.5752i	2.23143	−	1.28831i
$528$		0			0
$529$	−8.60603	+	14.9061i	−0.374175	+	0.648091i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	10.5109i		−	0.455280i
$534$		0			0
$535$	7.33960	+	4.23752i	0.317319	+	0.183204i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−7.43813	−	5.65860i	−0.320383	−	0.243733i
$540$		0			0
$541$	−15.4973	−	26.8421i	−0.666281	−	1.15403i	−0.978936	−	0.204167i	$-0.934552\pi$
$541$	−15.4973	−	26.8421i	−0.666281	−	1.15403i	0.312655	−	0.949867i	$-0.398782\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.87203			−0.123024
$546$		0			0
$547$	−36.3696			−1.55505			−0.777525	−	0.628852i	$-0.783525\pi$
$547$	−36.3696			−1.55505			−0.777525	+	0.628852i	$0.783525\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.68380	+	6.38053i	0.156935	+	0.271820i
$552$		0			0
$553$	−21.5145	+	10.6653i	−0.914891	+	0.453536i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	18.6697	+	10.7790i	0.791062	+	0.456720i	0.840336	−	0.542066i	$-0.182358\pi$
$557$	18.6697	+	10.7790i	0.791062	+	0.456720i	−0.0492745	+	0.998785i	$0.515691\pi$
$558$		0			0
$559$			1.56260i			0.0660908i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.356101	+	0.616785i	−0.0150079	+	0.0259944i	−0.873432	−	0.486946i	$-0.838111\pi$
$563$	−0.356101	+	0.616785i	−0.0150079	+	0.0259944i	0.858424	+	0.512941i	$0.171444\pi$
$564$		0			0
$565$	30.8288	−	17.7990i	1.29698	−	0.748811i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−29.7742	+	17.1902i	−1.24820	+	0.720649i	−0.970750	−	0.240091i	$-0.922823\pi$
$569$	−29.7742	+	17.1902i	−1.24820	+	0.720649i	−0.277450	+	0.960740i	$0.589489\pi$
$570$		0			0
$571$	12.7201	−	22.0319i	0.532321	−	0.922007i	−0.466967	−	0.884275i	$-0.654653\pi$
$571$	12.7201	−	22.0319i	0.532321	−	0.922007i	0.999288	−	0.0377320i	$-0.0120133\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			0.806250i			0.0336229i
$576$		0			0
$577$	7.45928	+	4.30662i	0.310534	+	0.179287i	0.647165	−	0.762350i	$-0.275954\pi$
$577$	7.45928	+	4.30662i	0.310534	+	0.179287i	−0.336631	+	0.941636i	$0.609288\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.80954	−	28.5145i	0.0750723	−	1.18298i
$582$		0			0
$583$	8.50538	+	14.7317i	0.352257	+	0.610127i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	31.6853			1.30779			0.653896	−	0.756585i	$-0.273134\pi$
$587$	31.6853			1.30779			0.653896	+	0.756585i	$0.273134\pi$
$588$		0			0
$589$	−9.84249			−0.405553
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−24.1456	−	41.8215i	−0.991543	−	1.71740i	−0.608165	−	0.793811i	$-0.708094\pi$
$593$	−24.1456	−	41.8215i	−0.991543	−	1.71740i	−0.383378	−	0.923592i	$-0.625239\pi$
$594$		0			0
$595$	2.60693	−	41.0798i	0.106874	−	1.68411i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−25.6952	−	14.8351i	−1.04988	−	0.606147i	−0.127262	−	0.991869i	$-0.540619\pi$
$599$	−25.6952	−	14.8351i	−1.04988	−	0.606147i	−0.922615	+	0.385722i	$0.873952\pi$
$600$		0			0
$601$		−	41.0577i		−	1.67478i	−0.546606	−	0.837390i	$-0.684080\pi$
$601$		−	41.0577i		−	1.67478i	0.546606	−	0.837390i	$-0.315920\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.95406	−	17.2409i	0.404690	−	0.700944i
$606$		0			0
$607$	19.8016	−	11.4324i	0.803721	−	0.464028i	−0.0410497	−	0.999157i	$-0.513070\pi$
$607$	19.8016	−	11.4324i	0.803721	−	0.464028i	0.844771	+	0.535129i	$0.179737\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	4.39600	−	2.53803i	0.177843	−	0.102678i
$612$		0			0
$613$	−12.7029	+	22.0021i	−0.513066	+	0.888656i	0.486820	+	0.873503i	$0.338157\pi$
$613$	−12.7029	+	22.0021i	−0.513066	+	0.888656i	−0.999885	+	0.0151531i	$0.995176\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			14.9638i			0.602418i	0.953558	+	0.301209i	$0.0973902\pi$
$617$			14.9638i			0.602418i	−0.953558	+	0.301209i	$0.902610\pi$
$618$		0			0
$619$	−14.6767	−	8.47361i	−0.589907	−	0.340583i	0.175154	−	0.984541i	$-0.443958\pi$
$619$	−14.6767	−	8.47361i	−0.589907	−	0.340583i	−0.765061	+	0.643958i	$0.777291\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	12.3173	−	6.10603i	0.493483	−	0.244633i
$624$		0			0
$625$	11.6060	+	20.1022i	0.464241	+	0.804089i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−37.0737			−1.47822
$630$		0			0
$631$	−21.3534			−0.850067			−0.425033	−	0.905178i	$-0.639738\pi$
$631$	−21.3534			−0.850067			−0.425033	+	0.905178i	$0.639738\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	16.0775	+	27.8470i	0.638014	+	1.10507i
$636$		0			0
$637$	−2.07965	+	16.3195i	−0.0823989	+	0.646603i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−38.8064	−	22.4049i	−1.53276	−	0.884941i	−0.999233	−	0.0391594i	$-0.987532\pi$
$641$	−38.8064	−	22.4049i	−1.53276	−	0.884941i	−0.533529	−	0.845781i	$-0.679135\pi$
$642$		0			0
$643$			18.8487i			0.743321i	0.928369	+	0.371660i	$0.121211\pi$
$643$			18.8487i			0.743321i	−0.928369	+	0.371660i	$0.878789\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	19.5404	−	33.8450i	0.768213	−	1.33058i	−0.170319	−	0.985389i	$-0.554480\pi$
$647$	19.5404	−	33.8450i	0.768213	−	1.33058i	0.938531	−	0.345194i	$-0.112187\pi$
$648$		0			0
$649$	−11.1792	+	6.45432i	−0.438823	+	0.253354i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−10.2652	+	5.92662i	−0.401709	+	0.231927i	−0.687221	−	0.726448i	$-0.741170\pi$
$653$	−10.2652	+	5.92662i	−0.401709	+	0.231927i	0.285512	+	0.958375i	$0.407836\pi$
$654$		0			0
$655$	17.1087	−	29.6332i	0.668493	−	1.15786i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	33.3226i		−	1.29806i	−0.760762	−	0.649032i	$-0.775174\pi$
$659$		−	33.3226i		−	1.29806i	0.760762	−	0.649032i	$-0.224826\pi$
$660$		0			0
$661$	−2.69285	−	1.55472i	−0.104740	−	0.0604715i	0.446715	−	0.894676i	$-0.352594\pi$
$661$	−2.69285	−	1.55472i	−0.104740	−	0.0604715i	−0.551455	+	0.834205i	$0.685927\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.79347	+	5.70291i	−0.147104	+	0.221149i
$666$		0			0
$667$	−7.39397	−	12.8067i	−0.286296	−	0.495879i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	16.4138			0.633647
$672$		0			0
$673$	2.68100			0.103345			0.0516726	−	0.998664i	$-0.483545\pi$
$673$	2.68100			0.103345			0.0516726	+	0.998664i	$0.483545\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−14.2737	−	24.7228i	−0.548584	−	0.950175i	−0.998372	−	0.0570397i	$-0.981834\pi$
$677$	−14.2737	−	24.7228i	−0.548584	−	0.950175i	0.449788	−	0.893135i	$-0.351500\pi$
$678$		0			0
$679$	−3.26444	−	0.207162i	−0.125278	−	0.00795014i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−38.0377	−	21.9611i	−1.45547	−	0.840317i	−0.456688	−	0.889627i	$-0.650964\pi$
$683$	−38.0377	−	21.9611i	−1.45547	−	0.840317i	−0.998784	+	0.0493101i	$0.984298\pi$
$684$		0			0
$685$			49.2693i			1.88248i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	14.9720	−	25.9322i	0.570386	−	0.987938i
$690$		0			0
$691$	27.1060	−	15.6497i	1.03116	−	0.595342i	0.113845	−	0.993499i	$-0.463683\pi$
$691$	27.1060	−	15.6497i	1.03116	−	0.595342i	0.917317	+	0.398157i	$0.130350\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	30.6309	−	17.6848i	1.16190	−	0.670822i
$696$		0			0
$697$	−16.1078	+	27.8996i	−0.610127	+	1.05677i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			23.2591i			0.878483i	0.898369	+	0.439241i	$0.144753\pi$
$701$			23.2591i			0.878483i	−0.898369	+	0.439241i	$0.855247\pi$
$702$		0			0
$703$	5.34249	+	3.08449i	0.201496	+	0.116334i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−8.61955	−	5.73357i	−0.324172	−	0.215633i
$708$		0			0
$709$	−10.2962	−	17.8335i	−0.386682	−	0.669752i	0.605319	−	0.795983i	$-0.293045\pi$
$709$	−10.2962	−	17.8335i	−0.386682	−	0.669752i	−0.992001	+	0.126231i	$0.959712\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	19.7554			0.739847
$714$		0			0
$715$	6.77718			0.253452
$716$		0			0
$717$		0			0
$718$		0			0
$719$	3.76014	+	6.51275i	0.140229	+	0.242884i	0.927583	−	0.373617i	$-0.121883\pi$
$719$	3.76014	+	6.51275i	0.140229	+	0.242884i	−0.787354	+	0.616502i	$0.788549\pi$
$720$		0			0
$721$	−4.85235	−	9.78834i	−0.180711	−	0.364537i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.78396	+	1.02997i	0.0662544	+	0.0382520i
$726$		0			0
$727$			33.2949i			1.23484i	0.786634	+	0.617420i	$0.211822\pi$
$727$			33.2949i			1.23484i	−0.786634	+	0.617420i	$0.788178\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.39465	−	4.14765i	0.0885693	−	0.153406i
$732$		0			0
$733$	13.3859	−	7.72835i	0.494420	−	0.285453i	−0.231986	−	0.972719i	$-0.574523\pi$
$733$	13.3859	−	7.72835i	0.494420	−	0.285453i	0.726406	+	0.687266i	$0.241189\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.31925	−	2.49372i	0.159102	−	0.0918574i
$738$		0			0
$739$	−3.10872	+	5.38446i	−0.114356	+	0.198071i	−0.917522	−	0.397685i	$-0.869814\pi$
$739$	−3.10872	+	5.38446i	−0.114356	+	0.198071i	0.803166	+	0.595755i	$0.203147\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	12.0291i		−	0.441304i	−0.975353	−	0.220652i	$-0.929182\pi$
$743$		−	12.0291i		−	0.441304i	0.975353	−	0.220652i	$-0.0708184\pi$
$744$		0			0
$745$	16.3396	+	9.43367i	0.598637	+	0.345623i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	4.61104	+	9.30157i	0.168484	+	0.339872i
$750$		0			0
$751$	16.8877	+	29.2503i	0.616241	+	1.06736i	0.990165	+	0.139901i	$0.0446784\pi$
$751$	16.8877	+	29.2503i	0.616241	+	1.06736i	−0.373925	+	0.927459i	$0.621988\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−15.4358			−0.561766
$756$		0			0
$757$	49.5870			1.80227			0.901135	−	0.433538i	$-0.142735\pi$
$757$	49.5870			1.80227			0.901135	+	0.433538i	$0.142735\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−19.9647	−	34.5798i	−0.723719	−	1.25352i	−0.959499	−	0.281712i	$-0.909098\pi$
$761$	−19.9647	−	34.5798i	−0.723719	−	1.25352i	0.235780	−	0.971806i	$-0.424236\pi$
$762$		0			0
$763$	−2.92931	−	1.94853i	−0.106048	−	0.0705414i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	19.6787	+	11.3615i	0.710557	+	0.410240i
$768$		0			0
$769$		−	15.4693i		−	0.557839i	−0.960315	−	0.278919i	$-0.910024\pi$
$769$		−	15.4693i		−	0.557839i	0.960315	−	0.278919i	$-0.0899762\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	17.3666	−	30.0798i	0.624633	−	1.08190i	−0.363978	−	0.931407i	$-0.618582\pi$
$773$	17.3666	−	30.0798i	0.624633	−	1.08190i	0.988612	−	0.150489i	$-0.0480849\pi$
$774$		0			0
$775$	−2.38321	+	1.37595i	−0.0856076	+	0.0494256i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.64243	−	2.68031i	0.166332	−	0.0960320i
$780$		0			0
$781$	7.61410	−	13.1880i	0.272454	−	0.471904i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	26.4510i		−	0.944077i
$786$		0			0
$787$	−22.5814	−	13.0374i	−0.804941	−	0.464733i	0.0402547	−	0.999189i	$-0.487183\pi$
$787$	−22.5814	−	13.0374i	−0.804941	−	0.464733i	−0.845196	+	0.534456i	$0.820516\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	43.5194	+	2.76175i	1.54737	+	0.0981965i
$792$		0			0
$793$	−14.4465	−	25.0221i	−0.513011	−	0.888562i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−14.1013			−0.499493			−0.249746	−	0.968311i	$-0.580347\pi$
$797$	−14.1013			−0.499493			−0.249746	+	0.968311i	$0.580347\pi$
$798$		0			0
$799$	−15.5579			−0.550400
$800$		0			0
$801$		0			0
$802$		0			0
$803$	6.99408	+	12.1141i	0.246816	+	0.427497i
$804$		0			0
$805$	7.61410	−	11.4466i	0.268362	−	0.403441i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−27.4791	−	15.8651i	−0.966115	−	0.557787i	−0.0680656	−	0.997681i	$-0.521683\pi$
$809$	−27.4791	−	15.8651i	−0.966115	−	0.557787i	−0.898050	+	0.439894i	$0.855016\pi$
$810$		0			0
$811$			18.3590i			0.644671i	0.946625	+	0.322336i	$0.104468\pi$
$811$			18.3590i			0.644671i	−0.946625	+	0.322336i	$0.895532\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	17.3608	−	30.0698i	0.608122	−	1.05330i
$816$		0			0
$817$	−0.690161	+	0.398465i	−0.0241457	+	0.0139405i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−16.8858	+	9.74900i	−0.589317	+	0.340243i	−0.764828	−	0.644235i	$-0.777176\pi$
$821$	−16.8858	+	9.74900i	−0.589317	+	0.340243i	0.175510	+	0.984478i	$0.443843\pi$
$822$		0			0
$823$	−0.317904	+	0.550626i	−0.0110814	+	0.0191936i	−0.871513	−	0.490372i	$-0.836861\pi$
$823$	−0.317904	+	0.550626i	−0.0110814	+	0.0191936i	0.860432	+	0.509566i	$0.170194\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			28.6939i			0.997786i	0.866664	+	0.498893i	$0.166260\pi$
$827$			28.6939i			0.997786i	−0.866664	+	0.498893i	$0.833740\pi$
$828$		0			0
$829$	29.5461	+	17.0584i	1.02618	+	0.592464i	0.915888	−	0.401435i	$-0.131488\pi$
$829$	29.5461	+	17.0584i	1.02618	+	0.592464i	0.110291	+	0.993899i	$0.464822\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	30.5294	−	40.1304i	1.05778	−	1.39044i
$834$		0			0
$835$	12.2790	+	21.2678i	0.424931	+	0.736003i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−14.6105			−0.504409			−0.252205	−	0.967674i	$-0.581156\pi$
$839$	−14.6105			−0.504409			−0.252205	+	0.967674i	$0.581156\pi$
$840$		0			0
$841$	−8.78256			−0.302847
$842$		0			0
$843$		0			0
$844$		0			0
$845$	8.07399	+	13.9846i	0.277754	+	0.481084i
$846$		0			0
$847$	21.8497	−	10.8315i	0.750763	−	0.372174i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−10.7232	−	6.19106i	−0.367588	−	0.212227i
$852$		0			0
$853$		−	27.1794i		−	0.930604i	−0.885152	−	0.465302i	$-0.845946\pi$
$853$		−	27.1794i		−	0.930604i	0.885152	−	0.465302i	$-0.154054\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.30893	−	2.26713i	0.0447121	−	0.0774436i	−0.842803	−	0.538222i	$-0.819096\pi$
$857$	1.30893	−	2.26713i	0.0447121	−	0.0774436i	0.887515	+	0.460778i	$0.152430\pi$
$858$		0			0
$859$	−38.9783	+	22.5041i	−1.32992	+	0.767831i	−0.985287	−	0.170906i	$-0.945331\pi$
$859$	−38.9783	+	22.5041i	−1.32992	+	0.767831i	−0.344635	+	0.938737i	$0.611997\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−25.8475	+	14.9230i	−0.879858	+	0.507986i	−0.870611	−	0.491971i	$-0.836277\pi$
$863$	−25.8475	+	14.9230i	−0.879858	+	0.507986i	−0.00924613	+	0.999957i	$0.502943\pi$
$864$		0			0
$865$	13.7201	−	23.7640i	0.466498	−	0.807999i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			12.1177i			0.411064i
$870$		0			0
$871$	−7.60315	−	4.38968i	−0.257623	−	0.148739i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.93082	+	30.4257i	−0.0652737	+	1.02858i
$876$		0			0
$877$	−20.3642	−	35.2718i	−0.687650	−	1.19104i	−0.972596	−	0.232501i	$-0.925309\pi$
$877$	−20.3642	−	35.2718i	−0.687650	−	1.19104i	0.284946	−	0.958543i	$-0.408024\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.774980			0.0261097			0.0130549	−	0.999915i	$-0.495844\pi$
$881$	0.774980			0.0261097			0.0130549	+	0.999915i	$0.495844\pi$
$882$		0			0
$883$	7.22819			0.243248			0.121624	−	0.992576i	$-0.461190\pi$
$883$	7.22819			0.243248			0.121624	+	0.992576i	$0.461190\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	26.9588	+	46.6939i	0.905187	+	1.56783i	0.820667	+	0.571407i	$0.193602\pi$
$887$	26.9588	+	46.6939i	0.905187	+	1.56783i	0.0845199	+	0.996422i	$0.473064\pi$
$888$		0			0
$889$	−2.49462	+	39.3101i	−0.0836670	+	1.31842i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	2.24198	+	1.29440i	0.0750248	+	0.0433156i
$894$		0			0
$895$		−	34.6317i		−	1.15761i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	25.2372	−	43.7121i	0.841707	−	1.45788i
$900$		0			0
$901$	−79.4812	+	45.8885i	−2.64790	+	1.52877i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−26.3229	+	15.1975i	−0.875003	+	0.505183i
$906$		0			0
$907$	−17.1468	+	29.6990i	−0.569349	+	0.986141i	0.427282	+	0.904118i	$0.359471\pi$
$907$	−17.1468	+	29.6990i	−0.569349	+	0.986141i	−0.996631	+	0.0820222i	$0.973862\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	3.55794i		−	0.117880i	−0.998262	−	0.0589399i	$-0.981228\pi$
$911$		−	3.55794i		−	0.117880i	0.998262	−	0.0589399i	$-0.0187720\pi$
$912$		0			0
$913$	−12.4866	−	7.20912i	−0.413245	−	0.238587i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	37.5545	−	18.6168i	1.24016	−	0.614780i
$918$		0			0
$919$	−20.3931	−	35.3218i	−0.672705	−	1.16516i	−0.977134	−	0.212625i	$-0.931799\pi$
$919$	−20.3931	−	35.3218i	−0.672705	−	1.16516i	0.304429	−	0.952535i	$-0.401534\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−26.8061			−0.882333
$924$		0			0
$925$	1.72481			0.0567114
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−11.9356	−	20.6731i	−0.391596	−	0.678263i	0.601065	−	0.799200i	$-0.294743\pi$
$929$	−11.9356	−	20.6731i	−0.391596	−	0.678263i	−0.992660	+	0.120937i	$0.961410\pi$
$930$		0			0
$931$	−7.73825	+	3.24297i	−0.253611	+	0.106284i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−17.9889	−	10.3859i	−0.588300	−	0.339655i
$936$		0			0
$937$		−	48.4063i		−	1.58136i	−0.612228	−	0.790682i	$-0.709726\pi$
$937$		−	48.4063i		−	1.58136i	0.612228	−	0.790682i	$-0.290274\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−4.44676	+	7.70201i	−0.144960	+	0.251078i	−0.929358	−	0.369180i	$-0.879639\pi$
$941$	−4.44676	+	7.70201i	−0.144960	+	0.251078i	0.784398	+	0.620258i	$0.212972\pi$
$942$		0			0
$943$	−9.31809	+	5.37980i	−0.303439	+	0.175191i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−16.7559	+	9.67403i	−0.544494	+	0.314364i	−0.746898	−	0.664938i	$-0.768458\pi$
$947$	−16.7559	+	9.67403i	−0.544494	+	0.314364i	0.202404	+	0.979302i	$0.435124\pi$
$948$		0			0
$949$	12.3116	−	21.3244i	0.399652	−	0.692218i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			21.7409i			0.704258i	0.935951	+	0.352129i	$0.114542\pi$
$953$			21.7409i			0.704258i	−0.935951	+	0.352129i	$0.885458\pi$
$954$		0			0
$955$	49.1711	+	28.3890i	1.59114	+	0.918645i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−33.4266	+	50.2519i	−1.07940	+	1.62272i
$960$		0			0
$961$	18.2148	+	31.5489i	0.587573	+	1.01771i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−6.64378			−0.213871
$966$		0			0
$967$	−12.1866			−0.391894			−0.195947	−	0.980615i	$-0.562778\pi$
$967$	−12.1866			−0.391894			−0.195947	+	0.980615i	$0.562778\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	2.67441	+	4.63222i	0.0858260	+	0.148655i	0.905743	−	0.423828i	$-0.139314\pi$
$971$	2.67441	+	4.63222i	0.0858260	+	0.148655i	−0.819917	+	0.572483i	$0.805980\pi$
$972$		0			0
$973$	43.2400	+	2.74402i	1.38621	+	0.0879693i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	4.00851	+	2.31431i	0.128244	+	0.0740415i	0.562749	−	0.826628i	$-0.309744\pi$
$977$	4.00851	+	2.31431i	0.128244	+	0.0740415i	−0.434506	+	0.900669i	$0.643077\pi$
$978$		0			0
$979$		−	6.93752i		−	0.221724i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	2.03274	−	3.52081i	0.0648344	−	0.112296i	−0.831786	−	0.555096i	$-0.812681\pi$
$983$	2.03274	−	3.52081i	0.0648344	−	0.112296i	0.896621	+	0.442800i	$0.146015\pi$
$984$		0			0
$985$	16.9866	−	9.80719i	0.541237	−	0.312483i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.38526	−	0.799782i	0.0440488	−	0.0254316i
$990$		0			0
$991$	−25.7582	+	44.6144i	−0.818235	+	1.41722i	0.0887467	+	0.996054i	$0.471714\pi$
$991$	−25.7582	+	44.6144i	−0.818235	+	1.41722i	−0.906982	+	0.421170i	$0.861619\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			48.9982i			1.55335i
$996$		0			0
$997$	−5.49731	−	3.17387i	−0.174102	−	0.100518i	0.410417	−	0.911898i	$-0.365383\pi$
$997$	−5.49731	−	3.17387i	−0.174102	−	0.100518i	−0.584518	+	0.811380i	$0.698717\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.t.e.269.5	yes	12
3.2	odd	2	inner	756.2.t.e.269.2	✓	12
7.3	odd	6		5292.2.f.e.2645.9		12
7.4	even	3		5292.2.f.e.2645.3		12
7.5	odd	6	inner	756.2.t.e.593.2	yes	12
9.2	odd	6		2268.2.bm.i.1025.5		12
9.4	even	3		2268.2.w.i.269.5		12
9.5	odd	6		2268.2.w.i.269.2		12
9.7	even	3		2268.2.bm.i.1025.2		12
21.5	even	6	inner	756.2.t.e.593.5	yes	12
21.11	odd	6		5292.2.f.e.2645.10		12
21.17	even	6		5292.2.f.e.2645.4		12
63.5	even	6		2268.2.bm.i.593.2		12
63.40	odd	6		2268.2.bm.i.593.5		12
63.47	even	6		2268.2.w.i.1349.5		12
63.61	odd	6		2268.2.w.i.1349.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.t.e.269.2	✓	12	3.2	odd	2	inner
756.2.t.e.269.5	yes	12	1.1	even	1	trivial
756.2.t.e.593.2	yes	12	7.5	odd	6	inner
756.2.t.e.593.5	yes	12	21.5	even	6	inner
2268.2.w.i.269.2		12	9.5	odd	6
2268.2.w.i.269.5		12	9.4	even	3
2268.2.w.i.1349.2		12	63.61	odd	6
2268.2.w.i.1349.5		12	63.47	even	6
2268.2.bm.i.593.2		12	63.5	even	6
2268.2.bm.i.593.5		12	63.40	odd	6
2268.2.bm.i.1025.2		12	9.7	even	3
2268.2.bm.i.1025.5		12	9.2	odd	6
5292.2.f.e.2645.3		12	7.4	even	3
5292.2.f.e.2645.4		12	21.17	even	6
5292.2.f.e.2645.9		12	7.3	odd	6
5292.2.f.e.2645.10		12	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.07992 + 1.87047i) q^{5} +(-0.167563 + 2.64044i) q^{7} +O(q^{10})\)	\(q+(1.07992 + 1.87047i) q^{5} +(-0.167563 + 2.64044i) q^{7} +(1.15625 + 0.667563i) q^{11} -2.35021i q^{13} +(-3.60166 + 6.23825i) q^{17} +(1.03803 - 0.599308i) q^{19} +(-2.08350 + 1.20291i) q^{23} +(0.167563 - 0.290227i) q^{25} +6.14675i q^{29} +(-7.11141 - 4.10577i) q^{31} +(-5.11982 + 2.53803i) q^{35} +(2.57338 + 4.45722i) q^{37} +4.47234 q^{41} -0.664874 q^{43} +(1.07992 + 1.87047i) q^{47} +(-6.94385 - 0.884879i) q^{49} +(11.0340 + 6.37047i) q^{53} +2.88365i q^{55} +(-4.83424 + 8.37316i) q^{59} +(10.6468 - 6.14691i) q^{61} +(4.39600 - 2.53803i) q^{65} +(1.86778 - 3.23509i) q^{67} -11.4058i q^{71} +(9.07338 + 5.23852i) q^{73} +(-1.95640 + 2.94116i) q^{77} +(4.53803 + 7.86010i) q^{79} -10.7992 q^{83} -15.5579 q^{85} +(-2.59808 - 4.50000i) q^{89} +(6.20560 + 0.393808i) q^{91} +(2.24198 + 1.29440i) q^{95} +1.23632i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q - 18 q^{19} - 24 q^{37} - 12 q^{43} + 18 q^{61} + 54 q^{73} + 24 q^{79} - 12 q^{85} + 42 q^{91}+O(q^{100}) \) 12 * q - 18 * q^19 - 24 * q^37 - 12 * q^43 + 18 * q^61 + 54 * q^73 + 24 * q^79 - 12 * q^85 + 42 * q^91

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