LMFDB - Embedded newform 936.2.m.a.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(181,936)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(936, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("936.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.m (of order $2$, degree $1$, 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	936.181
Dual form			936.2.m.a.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} -2.00000 q^{5} +(2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} -2.00000 q^{5} +(2.00000 + 2.00000i) q^{8} +(2.00000 - 2.00000i) q^{10} -4.00000 q^{11} +(-3.00000 + 2.00000i) q^{13} -4.00000 q^{16} +6.00000 q^{17} +6.00000 q^{19} +4.00000i q^{20} +(4.00000 - 4.00000i) q^{22} -1.00000 q^{25} +(1.00000 - 5.00000i) q^{26} -6.00000i q^{29} +(4.00000 - 4.00000i) q^{32} +(-6.00000 + 6.00000i) q^{34} +6.00000 q^{37} +(-6.00000 + 6.00000i) q^{38} +(-4.00000 - 4.00000i) q^{40} -2.00000i q^{41} -12.0000i q^{43} +8.00000i q^{44} -8.00000i q^{47} +7.00000 q^{49} +(1.00000 - 1.00000i) q^{50} +(4.00000 + 6.00000i) q^{52} -6.00000i q^{53} +8.00000 q^{55} +(6.00000 + 6.00000i) q^{58} +4.00000 q^{59} +8.00000i q^{61} +8.00000i q^{64} +(6.00000 - 4.00000i) q^{65} +6.00000 q^{67} -12.0000i q^{68} -4.00000i q^{71} -12.0000i q^{73} +(-6.00000 + 6.00000i) q^{74} -12.0000i q^{76} +6.00000 q^{79} +8.00000 q^{80} +(2.00000 + 2.00000i) q^{82} +8.00000 q^{83} -12.0000 q^{85} +(12.0000 + 12.0000i) q^{86} +(-8.00000 - 8.00000i) q^{88} +2.00000i q^{89} +(8.00000 + 8.00000i) q^{94} -12.0000 q^{95} +12.0000i q^{97} +(-7.00000 + 7.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{5} + 4 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 - 4 * q^5 + 4 * q^8	$ 2 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 4 q^{10} - 8 q^{11} - 6 q^{13} - 8 q^{16} + 12 q^{17} + 12 q^{19} + 8 q^{22} - 2 q^{25} + 2 q^{26} + 8 q^{32} - 12 q^{34} + 12 q^{37} - 12 q^{38} - 8 q^{40} + 14 q^{49} + 2 q^{50} + 8 q^{52} + 16 q^{55} + 12 q^{58} + 8 q^{59} + 12 q^{65} + 12 q^{67} - 12 q^{74} + 12 q^{79} + 16 q^{80} + 4 q^{82} + 16 q^{83} - 24 q^{85} + 24 q^{86} - 16 q^{88} + 16 q^{94} - 24 q^{95} - 14 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^5 + 4 * q^8 + 4 * q^10 - 8 * q^11 - 6 * q^13 - 8 * q^16 + 12 * q^17 + 12 * q^19 + 8 * q^22 - 2 * q^25 + 2 * q^26 + 8 * q^32 - 12 * q^34 + 12 * q^37 - 12 * q^38 - 8 * q^40 + 14 * q^49 + 2 * q^50 + 8 * q^52 + 16 * q^55 + 12 * q^58 + 8 * q^59 + 12 * q^65 + 12 * q^67 - 12 * q^74 + 12 * q^79 + 16 * q^80 + 4 * q^82 + 16 * q^83 - 24 * q^85 + 24 * q^86 - 16 * q^88 + 16 * q^94 - 24 * q^95 - 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$		0			0
$3$		0			0
$4$		−	2.00000i		−	1.00000i
$5$	−2.00000			−0.894427			−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000			−0.894427			−0.447214	+	0.894427i	$0.647584\pi$
$6$		0			0
$7$		0			0		1.00000			$0$
$7$		0			0		−1.00000			$\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$		0			0
$10$	2.00000	−	2.00000i	0.632456	−	0.632456i
$11$	−4.00000			−1.20605			−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000			−1.20605			−0.603023	+	0.797724i	$0.706037\pi$
$12$		0			0
$13$	−3.00000	+	2.00000i	−0.832050	+	0.554700i
$13$	−3.00000	+	2.00000i	−0.832050	+	0.554700i
$14$		0			0
$15$		0			0
$16$	−4.00000			−1.00000
$17$	6.00000			1.45521			0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000			1.45521			0.727607	+	0.685994i	$0.240633\pi$
$18$		0			0
$19$	6.00000			1.37649			0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000			1.37649			0.688247	+	0.725476i	$0.258380\pi$
$20$			4.00000i			0.894427i
$21$		0			0
$22$	4.00000	−	4.00000i	0.852803	−	0.852803i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	1.00000	−	5.00000i	0.196116	−	0.980581i
$27$		0			0
$28$		0			0
$29$		−	6.00000i		−	1.11417i	−0.830455	−	0.557086i	$-0.811919\pi$
$29$		−	6.00000i		−	1.11417i	0.830455	−	0.557086i	$-0.188081\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$		0			0
$34$	−6.00000	+	6.00000i	−1.02899	+	1.02899i
$35$		0			0
$36$		0			0
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$	−6.00000	+	6.00000i	−0.973329	+	0.973329i
$39$		0			0
$40$	−4.00000	−	4.00000i	−0.632456	−	0.632456i
$41$		−	2.00000i		−	0.312348i	−0.987730	−	0.156174i	$-0.950084\pi$
$41$		−	2.00000i		−	0.312348i	0.987730	−	0.156174i	$-0.0499160\pi$
$42$		0			0
$43$		−	12.0000i		−	1.82998i	−0.403473	−	0.914991i	$-0.632197\pi$
$43$		−	12.0000i		−	1.82998i	0.403473	−	0.914991i	$-0.367803\pi$
$44$			8.00000i			1.20605i
$45$		0			0
$46$		0			0
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$		0			0
$49$	7.00000			1.00000
$50$	1.00000	−	1.00000i	0.141421	−	0.141421i
$51$		0			0
$52$	4.00000	+	6.00000i	0.554700	+	0.832050i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$		0			0
$55$	8.00000			1.07872
$56$		0			0
$57$		0			0
$58$	6.00000	+	6.00000i	0.787839	+	0.787839i
$59$	4.00000			0.520756			0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000			0.520756			0.260378	+	0.965507i	$0.416153\pi$
$60$		0			0
$61$			8.00000i			1.02430i	0.858898	+	0.512148i	$0.171150\pi$
$61$			8.00000i			1.02430i	−0.858898	+	0.512148i	$0.828850\pi$
$62$		0			0
$63$		0			0
$64$			8.00000i			1.00000i
$65$	6.00000	−	4.00000i	0.744208	−	0.496139i
$66$		0			0
$67$	6.00000			0.733017			0.366508	−	0.930415i	$-0.380553\pi$
$67$	6.00000			0.733017			0.366508	+	0.930415i	$0.380553\pi$
$68$		−	12.0000i		−	1.45521i
$69$		0			0
$70$		0			0
$71$		−	4.00000i		−	0.474713i	−0.971423	−	0.237356i	$-0.923719\pi$
$71$		−	4.00000i		−	0.474713i	0.971423	−	0.237356i	$-0.0762809\pi$
$72$		0			0
$73$		−	12.0000i		−	1.40449i	−0.711934	−	0.702247i	$-0.752180\pi$
$73$		−	12.0000i		−	1.40449i	0.711934	−	0.702247i	$-0.247820\pi$
$74$	−6.00000	+	6.00000i	−0.697486	+	0.697486i
$75$		0			0
$76$		−	12.0000i		−	1.37649i
$77$		0			0
$78$		0			0
$79$	6.00000			0.675053			0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000			0.675053			0.337526	+	0.941316i	$0.390410\pi$
$80$	8.00000			0.894427
$81$		0			0
$82$	2.00000	+	2.00000i	0.220863	+	0.220863i
$83$	8.00000			0.878114			0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000			0.878114			0.439057	+	0.898459i	$0.355313\pi$
$84$		0			0
$85$	−12.0000			−1.30158
$86$	12.0000	+	12.0000i	1.29399	+	1.29399i
$87$		0			0
$88$	−8.00000	−	8.00000i	−0.852803	−	0.852803i
$89$			2.00000i			0.212000i	0.994366	+	0.106000i	$0.0338043\pi$
$89$			2.00000i			0.212000i	−0.994366	+	0.106000i	$0.966196\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$	8.00000	+	8.00000i	0.825137	+	0.825137i
$95$	−12.0000			−1.23117
$96$		0			0
$97$			12.0000i			1.21842i	0.793011	+	0.609208i	$0.208512\pi$
$97$			12.0000i			1.21842i	−0.793011	+	0.609208i	$0.791488\pi$
$98$	−7.00000	+	7.00000i	−0.707107	+	0.707107i
$99$		0			0
$100$			2.00000i			0.200000i
$101$			18.0000i			1.79107i	0.444994	+	0.895533i	$0.353206\pi$
$101$			18.0000i			1.79107i	−0.444994	+	0.895533i	$0.646794\pi$
$102$		0			0
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$	−10.0000	−	2.00000i	−0.980581	−	0.196116i
$105$		0			0
$106$	6.00000	+	6.00000i	0.582772	+	0.582772i
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$	−6.00000			−0.574696			−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000			−0.574696			−0.287348	+	0.957826i	$0.592774\pi$
$110$	−8.00000	+	8.00000i	−0.762770	+	0.762770i
$111$		0			0
$112$		0			0
$113$	18.0000			1.69330			0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000			1.69330			0.846649	+	0.532152i	$0.178617\pi$
$114$		0			0
$115$		0			0
$116$	−12.0000			−1.11417
$117$		0			0
$118$	−4.00000	+	4.00000i	−0.368230	+	0.368230i
$119$		0			0
$120$		0			0
$121$	5.00000			0.454545
$122$	−8.00000	−	8.00000i	−0.724286	−	0.724286i
$123$		0			0
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$	−6.00000			−0.532414			−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000			−0.532414			−0.266207	+	0.963916i	$0.585770\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$		0			0
$130$	−2.00000	+	10.0000i	−0.175412	+	0.877058i
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$		0			0
$134$	−6.00000	+	6.00000i	−0.518321	+	0.518321i
$135$		0			0
$136$	12.0000	+	12.0000i	1.02899	+	1.02899i
$137$			2.00000i			0.170872i	0.996344	+	0.0854358i	$0.0272282\pi$
$137$			2.00000i			0.170872i	−0.996344	+	0.0854358i	$0.972772\pi$
$138$		0			0
$139$		−	12.0000i		−	1.01783i	−0.860818	−	0.508913i	$-0.830047\pi$
$139$		−	12.0000i		−	1.01783i	0.860818	−	0.508913i	$-0.169953\pi$
$140$		0			0
$141$		0			0
$142$	4.00000	+	4.00000i	0.335673	+	0.335673i
$143$	12.0000	−	8.00000i	1.00349	−	0.668994i
$144$		0			0
$145$			12.0000i			0.996546i
$146$	12.0000	+	12.0000i	0.993127	+	0.993127i
$147$		0			0
$148$		−	12.0000i		−	0.986394i
$149$	2.00000			0.163846			0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000			0.163846			0.0819232	+	0.996639i	$0.473894\pi$
$150$		0			0
$151$		−	24.0000i		−	1.95309i	−0.215308	−	0.976546i	$-0.569076\pi$
$151$		−	24.0000i		−	1.95309i	0.215308	−	0.976546i	$-0.430924\pi$
$152$	12.0000	+	12.0000i	0.973329	+	0.973329i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		1.00000			$0$
$157$		0			0		−1.00000			$\pi$
$158$	−6.00000	+	6.00000i	−0.477334	+	0.477334i
$159$		0			0
$160$	−8.00000	+	8.00000i	−0.632456	+	0.632456i
$161$		0			0
$162$		0			0
$163$	6.00000			0.469956			0.234978	−	0.972001i	$-0.424498\pi$
$163$	6.00000			0.469956			0.234978	+	0.972001i	$0.424498\pi$
$164$	−4.00000			−0.312348
$165$		0			0
$166$	−8.00000	+	8.00000i	−0.620920	+	0.620920i
$167$		−	20.0000i		−	1.54765i	−0.633402	−	0.773823i	$-0.718342\pi$
$167$		−	20.0000i		−	1.54765i	0.633402	−	0.773823i	$-0.281658\pi$
$168$		0			0
$169$	5.00000	−	12.0000i	0.384615	−	0.923077i
$170$	12.0000	−	12.0000i	0.920358	−	0.920358i
$171$		0			0
$172$	−24.0000			−1.82998
$173$			18.0000i			1.36851i	0.729241	+	0.684257i	$0.239873\pi$
$173$			18.0000i			1.36851i	−0.729241	+	0.684257i	$0.760127\pi$
$174$		0			0
$175$		0			0
$176$	16.0000			1.20605
$177$		0			0
$178$	−2.00000	−	2.00000i	−0.149906	−	0.149906i
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$		0			0
$181$			12.0000i			0.891953i	0.895045	+	0.445976i	$0.147144\pi$
$181$			12.0000i			0.891953i	−0.895045	+	0.445976i	$0.852856\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−12.0000			−0.882258
$186$		0			0
$187$	−24.0000			−1.75505
$188$	−16.0000			−1.16692
$189$		0			0
$190$	12.0000	−	12.0000i	0.870572	−	0.870572i
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$		0			0
$193$		0			0		1.00000			$0$
$193$		0			0		−1.00000			$\pi$
$194$	−12.0000	−	12.0000i	−0.861550	−	0.861550i
$195$		0			0
$196$		−	14.0000i		−	1.00000i
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$		0			0
$199$	−18.0000			−1.27599			−0.637993	−	0.770042i	$-0.720235\pi$
$199$	−18.0000			−1.27599			−0.637993	+	0.770042i	$0.720235\pi$
$200$	−2.00000	−	2.00000i	−0.141421	−	0.141421i
$201$		0			0
$202$	−18.0000	−	18.0000i	−1.26648	−	1.26648i
$203$		0			0
$204$		0			0
$205$			4.00000i			0.279372i
$206$	14.0000	−	14.0000i	0.975426	−	0.975426i
$207$		0			0
$208$	12.0000	−	8.00000i	0.832050	−	0.554700i
$209$	−24.0000			−1.66011
$210$		0			0
$211$		−	4.00000i		−	0.275371i	−0.990476	−	0.137686i	$-0.956034\pi$
$211$		−	4.00000i		−	0.275371i	0.990476	−	0.137686i	$-0.0439664\pi$
$212$	−12.0000			−0.824163
$213$		0			0
$214$		0			0
$215$			24.0000i			1.63679i
$216$		0			0
$217$		0			0
$218$	6.00000	−	6.00000i	0.406371	−	0.406371i
$219$		0			0
$220$		−	16.0000i		−	1.07872i
$221$	−18.0000	+	12.0000i	−1.21081	+	0.807207i
$222$		0			0
$223$		−	24.0000i		−	1.60716i	−0.595198	−	0.803579i	$-0.702926\pi$
$223$		−	24.0000i		−	1.60716i	0.595198	−	0.803579i	$-0.297074\pi$
$224$		0			0
$225$		0			0
$226$	−18.0000	+	18.0000i	−1.19734	+	1.19734i
$227$	−20.0000			−1.32745			−0.663723	−	0.747978i	$-0.731025\pi$
$227$	−20.0000			−1.32745			−0.663723	+	0.747978i	$0.731025\pi$
$228$		0			0
$229$	−6.00000			−0.396491			−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000			−0.396491			−0.198246	+	0.980152i	$0.563524\pi$
$230$		0			0
$231$		0			0
$232$	12.0000	−	12.0000i	0.787839	−	0.787839i
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$			16.0000i			1.04372i
$236$		−	8.00000i		−	0.520756i
$237$		0			0
$238$		0			0
$239$			8.00000i			0.517477i	0.965947	+	0.258738i	$0.0833068\pi$
$239$			8.00000i			0.517477i	−0.965947	+	0.258738i	$0.916693\pi$
$240$		0			0
$241$			12.0000i			0.772988i	0.922292	+	0.386494i	$0.126314\pi$
$241$			12.0000i			0.772988i	−0.922292	+	0.386494i	$0.873686\pi$
$242$	−5.00000	+	5.00000i	−0.321412	+	0.321412i
$243$		0			0
$244$	16.0000			1.02430
$245$	−14.0000			−0.894427
$246$		0			0
$247$	−18.0000	+	12.0000i	−1.14531	+	0.763542i
$248$		0			0
$249$		0			0
$250$	−12.0000	+	12.0000i	−0.758947	+	0.758947i
$251$		−	24.0000i		−	1.51487i	−0.652913	−	0.757433i	$-0.726453\pi$
$251$		−	24.0000i		−	1.51487i	0.652913	−	0.757433i	$-0.273547\pi$
$252$		0			0
$253$		0			0
$254$	6.00000	−	6.00000i	0.376473	−	0.376473i
$255$		0			0
$256$	16.0000			1.00000
$257$	6.00000			0.374270			0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000			0.374270			0.187135	+	0.982334i	$0.440080\pi$
$258$		0			0
$259$		0			0
$260$	−8.00000	−	12.0000i	−0.496139	−	0.744208i
$261$		0			0
$262$		0			0
$263$	−24.0000			−1.47990			−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000			−1.47990			−0.739952	+	0.672660i	$0.765152\pi$
$264$		0			0
$265$			12.0000i			0.737154i
$266$		0			0
$267$		0			0
$268$		−	12.0000i		−	0.733017i
$269$		−	30.0000i		−	1.82913i	−0.404436	−	0.914566i	$-0.632532\pi$
$269$		−	30.0000i		−	1.82913i	0.404436	−	0.914566i	$-0.367468\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	−24.0000			−1.45521
$273$		0			0
$274$	−2.00000	−	2.00000i	−0.120824	−	0.120824i
$275$	4.00000			0.241209
$276$		0			0
$277$			12.0000i			0.721010i	0.932757	+	0.360505i	$0.117396\pi$
$277$			12.0000i			0.721010i	−0.932757	+	0.360505i	$0.882604\pi$
$278$	12.0000	+	12.0000i	0.719712	+	0.719712i
$279$		0			0
$280$		0			0
$281$			22.0000i			1.31241i	0.754583	+	0.656205i	$0.227839\pi$
$281$			22.0000i			1.31241i	−0.754583	+	0.656205i	$0.772161\pi$
$282$		0			0
$283$			4.00000i			0.237775i	0.992908	+	0.118888i	$0.0379328\pi$
$283$			4.00000i			0.237775i	−0.992908	+	0.118888i	$0.962067\pi$
$284$	−8.00000			−0.474713
$285$		0			0
$286$	−4.00000	+	20.0000i	−0.236525	+	1.18262i
$287$		0			0
$288$		0			0
$289$	19.0000			1.11765
$290$	−12.0000	−	12.0000i	−0.704664	−	0.704664i
$291$		0			0
$292$	−24.0000			−1.40449
$293$	2.00000			0.116841			0.0584206	−	0.998292i	$-0.481394\pi$
$293$	2.00000			0.116841			0.0584206	+	0.998292i	$0.481394\pi$
$294$		0			0
$295$	−8.00000			−0.465778
$296$	12.0000	+	12.0000i	0.697486	+	0.697486i
$297$		0			0
$298$	−2.00000	+	2.00000i	−0.115857	+	0.115857i
$299$		0			0
$300$		0			0
$301$		0			0
$302$	24.0000	+	24.0000i	1.38104	+	1.38104i
$303$		0			0
$304$	−24.0000			−1.37649
$305$		−	16.0000i		−	0.916157i
$306$		0			0
$307$	6.00000			0.342438			0.171219	−	0.985233i	$-0.445229\pi$
$307$	6.00000			0.342438			0.171219	+	0.985233i	$0.445229\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$		0			0
$313$	18.0000			1.01742			0.508710	−	0.860938i	$-0.330123\pi$
$313$	18.0000			1.01742			0.508710	+	0.860938i	$0.330123\pi$
$314$		0			0
$315$		0			0
$316$		−	12.0000i		−	0.675053i
$317$	−26.0000			−1.46031			−0.730153	−	0.683284i	$-0.760551\pi$
$317$	−26.0000			−1.46031			−0.730153	+	0.683284i	$0.760551\pi$
$318$		0			0
$319$			24.0000i			1.34374i
$320$		−	16.0000i		−	0.894427i
$321$		0			0
$322$		0			0
$323$	36.0000			2.00309
$324$		0			0
$325$	3.00000	−	2.00000i	0.166410	−	0.110940i
$326$	−6.00000	+	6.00000i	−0.332309	+	0.332309i
$327$		0			0
$328$	4.00000	−	4.00000i	0.220863	−	0.220863i
$329$		0			0
$330$		0			0
$331$	18.0000			0.989369			0.494685	−	0.869072i	$-0.335284\pi$
$331$	18.0000			0.989369			0.494685	+	0.869072i	$0.335284\pi$
$332$		−	16.0000i		−	0.878114i
$333$		0			0
$334$	20.0000	+	20.0000i	1.09435	+	1.09435i
$335$	−12.0000			−0.655630
$336$		0			0
$337$	−30.0000			−1.63420			−0.817102	−	0.576493i	$-0.804421\pi$
$337$	−30.0000			−1.63420			−0.817102	+	0.576493i	$0.804421\pi$
$338$	7.00000	+	17.0000i	0.380750	+	0.924678i
$339$		0			0
$340$			24.0000i			1.30158i
$341$		0			0
$342$		0			0
$343$		0			0
$344$	24.0000	−	24.0000i	1.29399	−	1.29399i
$345$		0			0
$346$	−18.0000	−	18.0000i	−0.967686	−	0.967686i
$347$		−	24.0000i		−	1.28839i	−0.764862	−	0.644194i	$-0.777193\pi$
$347$		−	24.0000i		−	1.28839i	0.764862	−	0.644194i	$-0.222807\pi$
$348$		0			0
$349$	18.0000			0.963518			0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000			0.963518			0.481759	+	0.876304i	$0.339998\pi$
$350$		0			0
$351$		0			0
$352$	−16.0000	+	16.0000i	−0.852803	+	0.852803i
$353$		−	34.0000i		−	1.80964i	−0.425797	−	0.904819i	$-0.640006\pi$
$353$		−	34.0000i		−	1.80964i	0.425797	−	0.904819i	$-0.359994\pi$
$354$		0			0
$355$			8.00000i			0.424596i
$356$	4.00000			0.212000
$357$		0			0
$358$		0			0
$359$			8.00000i			0.422224i	0.977462	+	0.211112i	$0.0677085\pi$
$359$			8.00000i			0.422224i	−0.977462	+	0.211112i	$0.932292\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$	−12.0000	−	12.0000i	−0.630706	−	0.630706i
$363$		0			0
$364$		0			0
$365$			24.0000i			1.25622i
$366$		0			0
$367$	10.0000			0.521996			0.260998	−	0.965339i	$-0.415948\pi$
$367$	10.0000			0.521996			0.260998	+	0.965339i	$0.415948\pi$
$368$		0			0
$369$		0			0
$370$	12.0000	−	12.0000i	0.623850	−	0.623850i
$371$		0			0
$372$		0			0
$373$		−	32.0000i		−	1.65690i	−0.560065	−	0.828449i	$-0.689224\pi$
$373$		−	32.0000i		−	1.65690i	0.560065	−	0.828449i	$-0.310776\pi$
$374$	24.0000	−	24.0000i	1.24101	−	1.24101i
$375$		0			0
$376$	16.0000	−	16.0000i	0.825137	−	0.825137i
$377$	12.0000	+	18.0000i	0.618031	+	0.927047i
$378$		0			0
$379$	18.0000			0.924598			0.462299	−	0.886724i	$-0.347025\pi$
$379$	18.0000			0.924598			0.462299	+	0.886724i	$0.347025\pi$
$380$			24.0000i			1.23117i
$381$		0			0
$382$	−12.0000	+	12.0000i	−0.613973	+	0.613973i
$383$			20.0000i			1.02195i	0.859595	+	0.510976i	$0.170716\pi$
$383$			20.0000i			1.02195i	−0.859595	+	0.510976i	$0.829284\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$	24.0000			1.21842
$389$		−	6.00000i		−	0.304212i	−0.988364	−	0.152106i	$-0.951394\pi$
$389$		−	6.00000i		−	0.304212i	0.988364	−	0.152106i	$-0.0486055\pi$
$390$		0			0
$391$		0			0
$392$	14.0000	+	14.0000i	0.707107	+	0.707107i
$393$		0			0
$394$	−2.00000	+	2.00000i	−0.100759	+	0.100759i
$395$	−12.0000			−0.603786
$396$		0			0
$397$	−18.0000			−0.903394			−0.451697	−	0.892171i	$-0.649181\pi$
$397$	−18.0000			−0.903394			−0.451697	+	0.892171i	$0.649181\pi$
$398$	18.0000	−	18.0000i	0.902258	−	0.902258i
$399$		0			0
$400$	4.00000			0.200000
$401$			10.0000i			0.499376i	0.968326	+	0.249688i	$0.0803281\pi$
$401$			10.0000i			0.499376i	−0.968326	+	0.249688i	$0.919672\pi$
$402$		0			0
$403$		0			0
$404$	36.0000			1.79107
$405$		0			0
$406$		0			0
$407$	−24.0000			−1.18964
$408$		0			0
$409$			36.0000i			1.78009i	0.455877	+	0.890043i	$0.349326\pi$
$409$			36.0000i			1.78009i	−0.455877	+	0.890043i	$0.650674\pi$
$410$	−4.00000	−	4.00000i	−0.197546	−	0.197546i
$411$		0			0
$412$			28.0000i			1.37946i
$413$		0			0
$414$		0			0
$415$	−16.0000			−0.785409
$416$	−4.00000	+	20.0000i	−0.196116	+	0.980581i
$417$		0			0
$418$	24.0000	−	24.0000i	1.17388	−	1.17388i
$419$		−	12.0000i		−	0.586238i	−0.956076	−	0.293119i	$-0.905307\pi$
$419$		−	12.0000i		−	0.586238i	0.956076	−	0.293119i	$-0.0946933\pi$
$420$		0			0
$421$	30.0000			1.46211			0.731055	−	0.682318i	$-0.239028\pi$
$421$	30.0000			1.46211			0.731055	+	0.682318i	$0.239028\pi$
$422$	4.00000	+	4.00000i	0.194717	+	0.194717i
$423$		0			0
$424$	12.0000	−	12.0000i	0.582772	−	0.582772i
$425$	−6.00000			−0.291043
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$	−24.0000	−	24.0000i	−1.15738	−	1.15738i
$431$			32.0000i			1.54139i	0.637207	+	0.770693i	$0.280090\pi$
$431$			32.0000i			1.54139i	−0.637207	+	0.770693i	$0.719910\pi$
$432$		0			0
$433$	−6.00000			−0.288342			−0.144171	−	0.989553i	$-0.546051\pi$
$433$	−6.00000			−0.288342			−0.144171	+	0.989553i	$0.546051\pi$
$434$		0			0
$435$		0			0
$436$			12.0000i			0.574696i
$437$		0			0
$438$		0			0
$439$	26.0000			1.24091			0.620456	−	0.784241i	$-0.286947\pi$
$439$	26.0000			1.24091			0.620456	+	0.784241i	$0.286947\pi$
$440$	16.0000	+	16.0000i	0.762770	+	0.762770i
$441$		0			0
$442$	6.00000	−	30.0000i	0.285391	−	1.42695i
$443$			36.0000i			1.71041i	0.518289	+	0.855206i	$0.326569\pi$
$443$			36.0000i			1.71041i	−0.518289	+	0.855206i	$0.673431\pi$
$444$		0			0
$445$		−	4.00000i		−	0.189618i
$446$	24.0000	+	24.0000i	1.13643	+	1.13643i
$447$		0			0
$448$		0			0
$449$			10.0000i			0.471929i	0.971762	+	0.235965i	$0.0758249\pi$
$449$			10.0000i			0.471929i	−0.971762	+	0.235965i	$0.924175\pi$
$450$		0			0
$451$			8.00000i			0.376705i
$452$		−	36.0000i		−	1.69330i
$453$		0			0
$454$	20.0000	−	20.0000i	0.938647	−	0.938647i
$455$		0			0
$456$		0			0
$457$		−	36.0000i		−	1.68401i	−0.539471	−	0.842004i	$-0.681376\pi$
$457$		−	36.0000i		−	1.68401i	0.539471	−	0.842004i	$-0.318624\pi$
$458$	6.00000	−	6.00000i	0.280362	−	0.280362i
$459$		0			0
$460$		0			0
$461$	34.0000			1.58354			0.791769	−	0.610821i	$-0.209160\pi$
$461$	34.0000			1.58354			0.791769	+	0.610821i	$0.209160\pi$
$462$		0			0
$463$			24.0000i			1.11537i	0.830051	+	0.557687i	$0.188311\pi$
$463$			24.0000i			1.11537i	−0.830051	+	0.557687i	$0.811689\pi$
$464$			24.0000i			1.11417i
$465$		0			0
$466$	6.00000	−	6.00000i	0.277945	−	0.277945i
$467$			24.0000i			1.11059i	0.831654	+	0.555294i	$0.187394\pi$
$467$			24.0000i			1.11059i	−0.831654	+	0.555294i	$0.812606\pi$
$468$		0			0
$469$		0			0
$470$	−16.0000	−	16.0000i	−0.738025	−	0.738025i
$471$		0			0
$472$	8.00000	+	8.00000i	0.368230	+	0.368230i
$473$			48.0000i			2.20704i
$474$		0			0
$475$	−6.00000			−0.275299
$476$		0			0
$477$		0			0
$478$	−8.00000	−	8.00000i	−0.365911	−	0.365911i
$479$			4.00000i			0.182765i	0.995816	+	0.0913823i	$0.0291285\pi$
$479$			4.00000i			0.182765i	−0.995816	+	0.0913823i	$0.970871\pi$
$480$		0			0
$481$	−18.0000	+	12.0000i	−0.820729	+	0.547153i
$482$	−12.0000	−	12.0000i	−0.546585	−	0.546585i
$483$		0			0
$484$		−	10.0000i		−	0.454545i
$485$		−	24.0000i		−	1.08978i
$486$		0			0
$487$		−	24.0000i		−	1.08754i	−0.839233	−	0.543772i	$-0.816996\pi$
$487$		−	24.0000i		−	1.08754i	0.839233	−	0.543772i	$-0.183004\pi$
$488$	−16.0000	+	16.0000i	−0.724286	+	0.724286i
$489$		0			0
$490$	14.0000	−	14.0000i	0.632456	−	0.632456i
$491$			12.0000i			0.541552i	0.962642	+	0.270776i	$0.0872803\pi$
$491$			12.0000i			0.541552i	−0.962642	+	0.270776i	$0.912720\pi$
$492$		0			0
$493$		−	36.0000i		−	1.62136i
$494$	6.00000	−	30.0000i	0.269953	−	1.34976i
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−18.0000			−0.805791			−0.402895	−	0.915246i	$-0.631996\pi$
$499$	−18.0000			−0.805791			−0.402895	+	0.915246i	$0.631996\pi$
$500$		−	24.0000i		−	1.07331i
$501$		0			0
$502$	24.0000	+	24.0000i	1.07117	+	1.07117i
$503$	36.0000			1.60516			0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000			1.60516			0.802580	+	0.596544i	$0.203460\pi$
$504$		0			0
$505$		−	36.0000i		−	1.60198i
$506$		0			0
$507$		0			0
$508$			12.0000i			0.532414i
$509$	14.0000			0.620539			0.310270	−	0.950649i	$-0.399581\pi$
$509$	14.0000			0.620539			0.310270	+	0.950649i	$0.399581\pi$
$510$		0			0
$511$		0			0
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$		0			0
$514$	−6.00000	+	6.00000i	−0.264649	+	0.264649i
$515$	28.0000			1.23383
$516$		0			0
$517$			32.0000i			1.40736i
$518$		0			0
$519$		0			0
$520$	20.0000	+	4.00000i	0.877058	+	0.175412i
$521$	−30.0000			−1.31432			−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000			−1.31432			−0.657162	+	0.753749i	$0.728243\pi$
$522$		0			0
$523$		−	36.0000i		−	1.57417i	−0.616844	−	0.787085i	$-0.711589\pi$
$523$		−	36.0000i		−	1.57417i	0.616844	−	0.787085i	$-0.288411\pi$
$524$		0			0
$525$		0			0
$526$	24.0000	−	24.0000i	1.04645	−	1.04645i
$527$		0			0
$528$		0			0
$529$	−23.0000			−1.00000
$530$	−12.0000	−	12.0000i	−0.521247	−	0.521247i
$531$		0			0
$532$		0			0
$533$	4.00000	+	6.00000i	0.173259	+	0.259889i
$534$		0			0
$535$		0			0
$536$	12.0000	+	12.0000i	0.518321	+	0.518321i
$537$		0			0
$538$	30.0000	+	30.0000i	1.29339	+	1.29339i
$539$	−28.0000			−1.20605
$540$		0			0
$541$	30.0000			1.28980			0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000			1.28980			0.644900	+	0.764267i	$0.276899\pi$
$542$		0			0
$543$		0			0
$544$	24.0000	−	24.0000i	1.02899	−	1.02899i
$545$	12.0000			0.514024
$546$		0			0
$547$		−	12.0000i		−	0.513083i	−0.966533	−	0.256541i	$-0.917417\pi$
$547$		−	12.0000i		−	0.513083i	0.966533	−	0.256541i	$-0.0825830\pi$
$548$	4.00000			0.170872
$549$		0			0
$550$	−4.00000	+	4.00000i	−0.170561	+	0.170561i
$551$		−	36.0000i		−	1.53365i
$552$		0			0
$553$		0			0
$554$	−12.0000	−	12.0000i	−0.509831	−	0.509831i
$555$		0			0
$556$	−24.0000			−1.01783
$557$	2.00000			0.0847427			0.0423714	−	0.999102i	$-0.486509\pi$
$557$	2.00000			0.0847427			0.0423714	+	0.999102i	$0.486509\pi$
$558$		0			0
$559$	24.0000	+	36.0000i	1.01509	+	1.52264i
$560$		0			0
$561$		0			0
$562$	−22.0000	−	22.0000i	−0.928014	−	0.928014i
$563$		−	12.0000i		−	0.505740i	−0.967500	−	0.252870i	$-0.918626\pi$
$563$		−	12.0000i		−	0.505740i	0.967500	−	0.252870i	$-0.0813744\pi$
$564$		0			0
$565$	−36.0000			−1.51453
$566$	−4.00000	−	4.00000i	−0.168133	−	0.168133i
$567$		0			0
$568$	8.00000	−	8.00000i	0.335673	−	0.335673i
$569$	6.00000			0.251533			0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000			0.251533			0.125767	+	0.992060i	$0.459861\pi$
$570$		0			0
$571$			4.00000i			0.167395i	0.996491	+	0.0836974i	$0.0266729\pi$
$571$			4.00000i			0.167395i	−0.996491	+	0.0836974i	$0.973327\pi$
$572$	−16.0000	−	24.0000i	−0.668994	−	1.00349i
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$			24.0000i			0.999133i	0.866276	+	0.499567i	$0.166507\pi$
$577$			24.0000i			0.999133i	−0.866276	+	0.499567i	$0.833493\pi$
$578$	−19.0000	+	19.0000i	−0.790296	+	0.790296i
$579$		0			0
$580$	24.0000			0.996546
$581$		0			0
$582$		0			0
$583$			24.0000i			0.993978i
$584$	24.0000	−	24.0000i	0.993127	−	0.993127i
$585$		0			0
$586$	−2.00000	+	2.00000i	−0.0826192	+	0.0826192i
$587$	−20.0000			−0.825488			−0.412744	−	0.910847i	$-0.635430\pi$
$587$	−20.0000			−0.825488			−0.412744	+	0.910847i	$0.635430\pi$
$588$		0			0
$589$		0			0
$590$	8.00000	−	8.00000i	0.329355	−	0.329355i
$591$		0			0
$592$	−24.0000			−0.986394
$593$		−	34.0000i		−	1.39621i	−0.715994	−	0.698106i	$-0.754026\pi$
$593$		−	34.0000i		−	1.39621i	0.715994	−	0.698106i	$-0.245974\pi$
$594$		0			0
$595$		0			0
$596$		−	4.00000i		−	0.163846i
$597$		0			0
$598$		0			0
$599$	−36.0000			−1.47092			−0.735460	−	0.677568i	$-0.763034\pi$
$599$	−36.0000			−1.47092			−0.735460	+	0.677568i	$0.763034\pi$
$600$		0			0
$601$	30.0000			1.22373			0.611863	−	0.790964i	$-0.290420\pi$
$601$	30.0000			1.22373			0.611863	+	0.790964i	$0.290420\pi$
$602$		0			0
$603$		0			0
$604$	−48.0000			−1.95309
$605$	−10.0000			−0.406558
$606$		0			0
$607$	14.0000			0.568242			0.284121	−	0.958788i	$-0.408298\pi$
$607$	14.0000			0.568242			0.284121	+	0.958788i	$0.408298\pi$
$608$	24.0000	−	24.0000i	0.973329	−	0.973329i
$609$		0			0
$610$	16.0000	+	16.0000i	0.647821	+	0.647821i
$611$	16.0000	+	24.0000i	0.647291	+	0.970936i
$612$		0			0
$613$	−42.0000			−1.69636			−0.848182	−	0.529705i	$-0.822303\pi$
$613$	−42.0000			−1.69636			−0.848182	+	0.529705i	$0.822303\pi$
$614$	−6.00000	+	6.00000i	−0.242140	+	0.242140i
$615$		0			0
$616$		0			0
$617$			10.0000i			0.402585i	0.979531	+	0.201292i	$0.0645141\pi$
$617$			10.0000i			0.402585i	−0.979531	+	0.201292i	$0.935486\pi$
$618$		0			0
$619$	−6.00000			−0.241160			−0.120580	−	0.992704i	$-0.538475\pi$
$619$	−6.00000			−0.241160			−0.120580	+	0.992704i	$0.538475\pi$
$620$		0			0
$621$		0			0
$622$	−12.0000	+	12.0000i	−0.481156	+	0.481156i
$623$		0			0
$624$		0			0
$625$	−19.0000			−0.760000
$626$	−18.0000	+	18.0000i	−0.719425	+	0.719425i
$627$		0			0
$628$		0			0
$629$	36.0000			1.43541
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$	12.0000	+	12.0000i	0.477334	+	0.477334i
$633$		0			0
$634$	26.0000	−	26.0000i	1.03259	−	1.03259i
$635$	12.0000			0.476205
$636$		0			0
$637$	−21.0000	+	14.0000i	−0.832050	+	0.554700i
$638$	−24.0000	−	24.0000i	−0.950169	−	0.950169i
$639$		0			0
$640$	16.0000	+	16.0000i	0.632456	+	0.632456i
$641$	6.00000			0.236986			0.118493	−	0.992955i	$-0.462194\pi$
$641$	6.00000			0.236986			0.118493	+	0.992955i	$0.462194\pi$
$642$		0			0
$643$	−30.0000			−1.18308			−0.591542	−	0.806274i	$-0.701481\pi$
$643$	−30.0000			−1.18308			−0.591542	+	0.806274i	$0.701481\pi$
$644$		0			0
$645$		0			0
$646$	−36.0000	+	36.0000i	−1.41640	+	1.41640i
$647$	12.0000			0.471769			0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000			0.471769			0.235884	+	0.971781i	$0.424201\pi$
$648$		0			0
$649$	−16.0000			−0.628055
$650$	−1.00000	+	5.00000i	−0.0392232	+	0.196116i
$651$		0			0
$652$		−	12.0000i		−	0.469956i
$653$		−	18.0000i		−	0.704394i	−0.935926	−	0.352197i	$-0.885435\pi$
$653$		−	18.0000i		−	0.704394i	0.935926	−	0.352197i	$-0.114565\pi$
$654$		0			0
$655$		0			0
$656$			8.00000i			0.312348i
$657$		0			0
$658$		0			0
$659$			12.0000i			0.467454i	0.972302	+	0.233727i	$0.0750921\pi$
$659$			12.0000i			0.467454i	−0.972302	+	0.233727i	$0.924908\pi$
$660$		0			0
$661$	42.0000			1.63361			0.816805	−	0.576913i	$-0.195743\pi$
$661$	42.0000			1.63361			0.816805	+	0.576913i	$0.195743\pi$
$662$	−18.0000	+	18.0000i	−0.699590	+	0.699590i
$663$		0			0
$664$	16.0000	+	16.0000i	0.620920	+	0.620920i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−40.0000			−1.54765
$669$		0			0
$670$	12.0000	−	12.0000i	0.463600	−	0.463600i
$671$		−	32.0000i		−	1.23535i
$672$		0			0
$673$	−26.0000			−1.00223			−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000			−1.00223			−0.501113	+	0.865382i	$0.667076\pi$
$674$	30.0000	−	30.0000i	1.15556	−	1.15556i
$675$		0			0
$676$	−24.0000	−	10.0000i	−0.923077	−	0.384615i
$677$		−	18.0000i		−	0.691796i	−0.938272	−	0.345898i	$-0.887574\pi$
$677$		−	18.0000i		−	0.691796i	0.938272	−	0.345898i	$-0.112426\pi$
$678$		0			0
$679$		0			0
$680$	−24.0000	−	24.0000i	−0.920358	−	0.920358i
$681$		0			0
$682$		0			0
$683$	−44.0000			−1.68361			−0.841807	−	0.539779i	$-0.818508\pi$
$683$	−44.0000			−1.68361			−0.841807	+	0.539779i	$0.818508\pi$
$684$		0			0
$685$		−	4.00000i		−	0.152832i
$686$		0			0
$687$		0			0
$688$			48.0000i			1.82998i
$689$	12.0000	+	18.0000i	0.457164	+	0.685745i
$690$		0			0
$691$	18.0000			0.684752			0.342376	−	0.939563i	$-0.388768\pi$
$691$	18.0000			0.684752			0.342376	+	0.939563i	$0.388768\pi$
$692$	36.0000			1.36851
$693$		0			0
$694$	24.0000	+	24.0000i	0.911028	+	0.911028i
$695$			24.0000i			0.910372i
$696$		0			0
$697$		−	12.0000i		−	0.454532i
$698$	−18.0000	+	18.0000i	−0.681310	+	0.681310i
$699$		0			0
$700$		0			0
$701$		−	6.00000i		−	0.226617i	−0.993560	−	0.113308i	$-0.963855\pi$
$701$		−	6.00000i		−	0.226617i	0.993560	−	0.113308i	$-0.0361448\pi$
$702$		0			0
$703$	36.0000			1.35777
$704$		−	32.0000i		−	1.20605i
$705$		0			0
$706$	34.0000	+	34.0000i	1.27961	+	1.27961i
$707$		0			0
$708$		0			0
$709$	−18.0000			−0.676004			−0.338002	−	0.941145i	$-0.609751\pi$
$709$	−18.0000			−0.676004			−0.338002	+	0.941145i	$0.609751\pi$
$710$	−8.00000	−	8.00000i	−0.300235	−	0.300235i
$711$		0			0
$712$	−4.00000	+	4.00000i	−0.149906	+	0.149906i
$713$		0			0
$714$		0			0
$715$	−24.0000	+	16.0000i	−0.897549	+	0.598366i
$716$		0			0
$717$		0			0
$718$	−8.00000	−	8.00000i	−0.298557	−	0.298557i
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$		0			0
$721$		0			0
$722$	−17.0000	+	17.0000i	−0.632674	+	0.632674i
$723$		0			0
$724$	24.0000			0.891953
$725$			6.00000i			0.222834i
$726$		0			0
$727$	42.0000			1.55769			0.778847	−	0.627214i	$-0.215805\pi$
$727$	42.0000			1.55769			0.778847	+	0.627214i	$0.215805\pi$
$728$		0			0
$729$		0			0
$730$	−24.0000	−	24.0000i	−0.888280	−	0.888280i
$731$		−	72.0000i		−	2.66302i
$732$		0			0
$733$	6.00000			0.221615			0.110808	−	0.993842i	$-0.464656\pi$
$733$	6.00000			0.221615			0.110808	+	0.993842i	$0.464656\pi$
$734$	−10.0000	+	10.0000i	−0.369107	+	0.369107i
$735$		0			0
$736$		0			0
$737$	−24.0000			−0.884051
$738$		0			0
$739$	6.00000			0.220714			0.110357	−	0.993892i	$-0.464801\pi$
$739$	6.00000			0.220714			0.110357	+	0.993892i	$0.464801\pi$
$740$			24.0000i			0.882258i
$741$		0			0
$742$		0			0
$743$		−	8.00000i		−	0.293492i	−0.989174	−	0.146746i	$-0.953120\pi$
$743$		−	8.00000i		−	0.293492i	0.989174	−	0.146746i	$-0.0468799\pi$
$744$		0			0
$745$	−4.00000			−0.146549
$746$	32.0000	+	32.0000i	1.17160	+	1.17160i
$747$		0			0
$748$			48.0000i			1.75505i
$749$		0			0
$750$		0			0
$751$	−14.0000			−0.510867			−0.255434	−	0.966827i	$-0.582218\pi$
$751$	−14.0000			−0.510867			−0.255434	+	0.966827i	$0.582218\pi$
$752$			32.0000i			1.16692i
$753$		0			0
$754$	−30.0000	−	6.00000i	−1.09254	−	0.218507i
$755$			48.0000i			1.74690i
$756$		0			0
$757$		−	20.0000i		−	0.726912i	−0.931611	−	0.363456i	$-0.881597\pi$
$757$		−	20.0000i		−	0.726912i	0.931611	−	0.363456i	$-0.118403\pi$
$758$	−18.0000	+	18.0000i	−0.653789	+	0.653789i
$759$		0			0
$760$	−24.0000	−	24.0000i	−0.870572	−	0.870572i
$761$		−	46.0000i		−	1.66750i	−0.552143	−	0.833749i	$-0.686190\pi$
$761$		−	46.0000i		−	1.66750i	0.552143	−	0.833749i	$-0.313810\pi$
$762$		0			0
$763$		0			0
$764$		−	24.0000i		−	0.868290i
$765$		0			0
$766$	−20.0000	−	20.0000i	−0.722629	−	0.722629i
$767$	−12.0000	+	8.00000i	−0.433295	+	0.288863i
$768$		0			0
$769$			24.0000i			0.865462i	0.901523	+	0.432731i	$0.142450\pi$
$769$			24.0000i			0.865462i	−0.901523	+	0.432731i	$0.857550\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	22.0000			0.791285			0.395643	−	0.918405i	$-0.370522\pi$
$773$	22.0000			0.791285			0.395643	+	0.918405i	$0.370522\pi$
$774$		0			0
$775$		0			0
$776$	−24.0000	+	24.0000i	−0.861550	+	0.861550i
$777$		0			0
$778$	6.00000	+	6.00000i	0.215110	+	0.215110i
$779$		−	12.0000i		−	0.429945i
$780$		0			0
$781$			16.0000i			0.572525i
$782$		0			0
$783$		0			0
$784$	−28.0000			−1.00000
$785$		0			0
$786$		0			0
$787$	42.0000			1.49714			0.748569	−	0.663057i	$-0.230741\pi$
$787$	42.0000			1.49714			0.748569	+	0.663057i	$0.230741\pi$
$788$		−	4.00000i		−	0.142494i
$789$		0			0
$790$	12.0000	−	12.0000i	0.426941	−	0.426941i
$791$		0			0
$792$		0			0
$793$	−16.0000	−	24.0000i	−0.568177	−	0.852265i
$794$	18.0000	−	18.0000i	0.638796	−	0.638796i
$795$		0			0
$796$			36.0000i			1.27599i
$797$		−	18.0000i		−	0.637593i	−0.947823	−	0.318796i	$-0.896721\pi$
$797$		−	18.0000i		−	0.637593i	0.947823	−	0.318796i	$-0.103279\pi$
$798$		0			0
$799$		−	48.0000i		−	1.69812i
$800$	−4.00000	+	4.00000i	−0.141421	+	0.141421i
$801$		0			0
$802$	−10.0000	−	10.0000i	−0.353112	−	0.353112i
$803$			48.0000i			1.69388i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−36.0000	+	36.0000i	−1.26648	+	1.26648i
$809$	−6.00000			−0.210949			−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000			−0.210949			−0.105474	+	0.994422i	$0.533636\pi$
$810$		0			0
$811$	−54.0000			−1.89620			−0.948098	−	0.317978i	$-0.896996\pi$
$811$	−54.0000			−1.89620			−0.948098	+	0.317978i	$0.896996\pi$
$812$		0			0
$813$		0			0
$814$	24.0000	−	24.0000i	0.841200	−	0.841200i
$815$	−12.0000			−0.420342
$816$		0			0
$817$		−	72.0000i		−	2.51896i
$818$	−36.0000	−	36.0000i	−1.25871	−	1.25871i
$819$		0			0
$820$	8.00000			0.279372
$821$	−10.0000			−0.349002			−0.174501	−	0.984657i	$-0.555831\pi$
$821$	−10.0000			−0.349002			−0.174501	+	0.984657i	$0.555831\pi$
$822$		0			0
$823$	14.0000			0.488009			0.244005	−	0.969774i	$-0.421539\pi$
$823$	14.0000			0.488009			0.244005	+	0.969774i	$0.421539\pi$
$824$	−28.0000	−	28.0000i	−0.975426	−	0.975426i
$825$		0			0
$826$		0			0
$827$	−56.0000			−1.94731			−0.973655	−	0.228024i	$-0.926773\pi$
$827$	−56.0000			−1.94731			−0.973655	+	0.228024i	$0.926773\pi$
$828$		0			0
$829$		−	20.0000i		−	0.694629i	−0.937749	−	0.347314i	$-0.887094\pi$
$829$		−	20.0000i		−	0.694629i	0.937749	−	0.347314i	$-0.112906\pi$
$830$	16.0000	−	16.0000i	0.555368	−	0.555368i
$831$		0			0
$832$	−16.0000	−	24.0000i	−0.554700	−	0.832050i
$833$	42.0000			1.45521
$834$		0			0
$835$			40.0000i			1.38426i
$836$			48.0000i			1.66011i
$837$		0			0
$838$	12.0000	+	12.0000i	0.414533	+	0.414533i
$839$		−	20.0000i		−	0.690477i	−0.938515	−	0.345238i	$-0.887798\pi$
$839$		−	20.0000i		−	0.690477i	0.938515	−	0.345238i	$-0.112202\pi$
$840$		0			0
$841$	−7.00000			−0.241379
$842$	−30.0000	+	30.0000i	−1.03387	+	1.03387i
$843$		0			0
$844$	−8.00000			−0.275371
$845$	−10.0000	+	24.0000i	−0.344010	+	0.825625i
$846$		0			0
$847$		0			0
$848$			24.0000i			0.824163i
$849$		0			0
$850$	6.00000	−	6.00000i	0.205798	−	0.205798i
$851$		0			0
$852$		0			0
$853$	42.0000			1.43805			0.719026	−	0.694983i	$-0.244588\pi$
$853$	42.0000			1.43805			0.719026	+	0.694983i	$0.244588\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	6.00000			0.204956			0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000			0.204956			0.102478	+	0.994735i	$0.467323\pi$
$858$		0			0
$859$		−	4.00000i		−	0.136478i	−0.997669	−	0.0682391i	$-0.978262\pi$
$859$		−	4.00000i		−	0.136478i	0.997669	−	0.0682391i	$-0.0217381\pi$
$860$	48.0000			1.63679
$861$		0			0
$862$	−32.0000	−	32.0000i	−1.08992	−	1.08992i
$863$		−	20.0000i		−	0.680808i	−0.940279	−	0.340404i	$-0.889436\pi$
$863$		−	20.0000i		−	0.680808i	0.940279	−	0.340404i	$-0.110564\pi$
$864$		0			0
$865$		−	36.0000i		−	1.22404i
$866$	6.00000	−	6.00000i	0.203888	−	0.203888i
$867$		0			0
$868$		0			0
$869$	−24.0000			−0.814144
$870$		0			0
$871$	−18.0000	+	12.0000i	−0.609907	+	0.406604i
$872$	−12.0000	−	12.0000i	−0.406371	−	0.406371i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	30.0000			1.01303			0.506514	−	0.862232i	$-0.330934\pi$
$877$	30.0000			1.01303			0.506514	+	0.862232i	$0.330934\pi$
$878$	−26.0000	+	26.0000i	−0.877457	+	0.877457i
$879$		0			0
$880$	−32.0000			−1.07872
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$			20.0000i			0.673054i	0.941674	+	0.336527i	$0.109252\pi$
$883$			20.0000i			0.673054i	−0.941674	+	0.336527i	$0.890748\pi$
$884$	24.0000	+	36.0000i	0.807207	+	1.21081i
$885$		0			0
$886$	−36.0000	−	36.0000i	−1.20944	−	1.20944i
$887$	−12.0000			−0.402921			−0.201460	−	0.979497i	$-0.564569\pi$
$887$	−12.0000			−0.402921			−0.201460	+	0.979497i	$0.564569\pi$
$888$		0			0
$889$		0			0
$890$	4.00000	+	4.00000i	0.134080	+	0.134080i
$891$		0			0
$892$	−48.0000			−1.60716
$893$		−	48.0000i		−	1.60626i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−10.0000	−	10.0000i	−0.333704	−	0.333704i
$899$		0			0
$900$		0			0
$901$		−	36.0000i		−	1.19933i
$902$	−8.00000	−	8.00000i	−0.266371	−	0.266371i
$903$		0			0
$904$	36.0000	+	36.0000i	1.19734	+	1.19734i
$905$		−	24.0000i		−	0.797787i
$906$		0			0
$907$			44.0000i			1.46100i	0.682915	+	0.730498i	$0.260712\pi$
$907$			44.0000i			1.46100i	−0.682915	+	0.730498i	$0.739288\pi$
$908$			40.0000i			1.32745i
$909$		0			0
$910$		0			0
$911$	36.0000			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$912$		0			0
$913$	−32.0000			−1.05905
$914$	36.0000	+	36.0000i	1.19077	+	1.19077i
$915$		0			0
$916$			12.0000i			0.396491i
$917$		0			0
$918$		0			0
$919$	−6.00000			−0.197922			−0.0989609	−	0.995091i	$-0.531552\pi$
$919$	−6.00000			−0.197922			−0.0989609	+	0.995091i	$0.531552\pi$
$920$		0			0
$921$		0			0
$922$	−34.0000	+	34.0000i	−1.11973	+	1.11973i
$923$	8.00000	+	12.0000i	0.263323	+	0.394985i
$924$		0			0
$925$	−6.00000			−0.197279
$926$	−24.0000	−	24.0000i	−0.788689	−	0.788689i
$927$		0			0
$928$	−24.0000	−	24.0000i	−0.787839	−	0.787839i
$929$			2.00000i			0.0656179i	0.999462	+	0.0328089i	$0.0104453\pi$
$929$			2.00000i			0.0656179i	−0.999462	+	0.0328089i	$0.989555\pi$
$930$		0			0
$931$	42.0000			1.37649
$932$			12.0000i			0.393073i
$933$		0			0
$934$	−24.0000	−	24.0000i	−0.785304	−	0.785304i
$935$	48.0000			1.56977
$936$		0			0
$937$	−30.0000			−0.980057			−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000			−0.980057			−0.490029	+	0.871706i	$0.663014\pi$
$938$		0			0
$939$		0			0
$940$	32.0000			1.04372
$941$	−10.0000			−0.325991			−0.162995	−	0.986627i	$-0.552116\pi$
$941$	−10.0000			−0.325991			−0.162995	+	0.986627i	$0.552116\pi$
$942$		0			0
$943$		0			0
$944$	−16.0000			−0.520756
$945$		0			0
$946$	−48.0000	−	48.0000i	−1.56061	−	1.56061i
$947$	28.0000			0.909878			0.454939	−	0.890523i	$-0.349661\pi$
$947$	28.0000			0.909878			0.454939	+	0.890523i	$0.349661\pi$
$948$		0			0
$949$	24.0000	+	36.0000i	0.779073	+	1.16861i
$950$	6.00000	−	6.00000i	0.194666	−	0.194666i
$951$		0			0
$952$		0			0
$953$	−18.0000			−0.583077			−0.291539	−	0.956559i	$-0.594167\pi$
$953$	−18.0000			−0.583077			−0.291539	+	0.956559i	$0.594167\pi$
$954$		0			0
$955$	−24.0000			−0.776622
$956$	16.0000			0.517477
$957$		0			0
$958$	−4.00000	−	4.00000i	−0.129234	−	0.129234i
$959$		0			0
$960$		0			0
$961$	31.0000			1.00000
$962$	6.00000	−	30.0000i	0.193448	−	0.967239i
$963$		0			0
$964$	24.0000			0.772988
$965$		0			0
$966$		0			0
$967$			48.0000i			1.54358i	0.635880	+	0.771788i	$0.280637\pi$
$967$			48.0000i			1.54358i	−0.635880	+	0.771788i	$0.719363\pi$
$968$	10.0000	+	10.0000i	0.321412	+	0.321412i
$969$		0			0
$970$	24.0000	+	24.0000i	0.770594	+	0.770594i
$971$		−	24.0000i		−	0.770197i	−0.922876	−	0.385098i	$-0.874168\pi$
$971$		−	24.0000i		−	0.770197i	0.922876	−	0.385098i	$-0.125832\pi$
$972$		0			0
$973$		0			0
$974$	24.0000	+	24.0000i	0.769010	+	0.769010i
$975$		0			0
$976$		−	32.0000i		−	1.02430i
$977$		−	34.0000i		−	1.08776i	−0.839164	−	0.543878i	$-0.816955\pi$
$977$		−	34.0000i		−	1.08776i	0.839164	−	0.543878i	$-0.183045\pi$
$978$		0			0
$979$		−	8.00000i		−	0.255681i
$980$			28.0000i			0.894427i
$981$		0			0
$982$	−12.0000	−	12.0000i	−0.382935	−	0.382935i
$983$			16.0000i			0.510321i	0.966899	+	0.255160i	$0.0821283\pi$
$983$			16.0000i			0.510321i	−0.966899	+	0.255160i	$0.917872\pi$
$984$		0			0
$985$	−4.00000			−0.127451
$986$	36.0000	+	36.0000i	1.14647	+	1.14647i
$987$		0			0
$988$	24.0000	+	36.0000i	0.763542	+	1.14531i
$989$		0			0
$990$		0			0
$991$	−38.0000			−1.20711			−0.603555	−	0.797321i	$-0.706250\pi$
$991$	−38.0000			−1.20711			−0.603555	+	0.797321i	$0.706250\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	36.0000			1.14128
$996$		0			0
$997$		−	48.0000i		−	1.52018i	−0.649821	−	0.760088i	$-0.725156\pi$
$997$		−	48.0000i		−	1.52018i	0.649821	−	0.760088i	$-0.274844\pi$
$998$	18.0000	−	18.0000i	0.569780	−	0.569780i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.m.a.181.2		2
3.2	odd	2		312.2.m.b.181.1	yes	2
4.3	odd	2		3744.2.m.a.1585.2		2
8.3	odd	2		3744.2.m.d.1585.1		2
8.5	even	2		936.2.m.d.181.2		2
12.11	even	2		1248.2.m.b.337.2		2
13.12	even	2		936.2.m.d.181.1		2
24.5	odd	2		312.2.m.a.181.1	✓	2
24.11	even	2		1248.2.m.a.337.1		2
39.38	odd	2		312.2.m.a.181.2	yes	2
52.51	odd	2		3744.2.m.d.1585.2		2
104.51	odd	2		3744.2.m.a.1585.1		2
104.77	even	2	inner	936.2.m.a.181.1		2
156.155	even	2		1248.2.m.a.337.2		2
312.77	odd	2		312.2.m.b.181.2	yes	2
312.155	even	2		1248.2.m.b.337.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.m.a.181.1	✓	2	24.5	odd	2
312.2.m.a.181.2	yes	2	39.38	odd	2
312.2.m.b.181.1	yes	2	3.2	odd	2
312.2.m.b.181.2	yes	2	312.77	odd	2
936.2.m.a.181.1		2	104.77	even	2	inner
936.2.m.a.181.2		2	1.1	even	1	trivial
936.2.m.d.181.1		2	13.12	even	2
936.2.m.d.181.2		2	8.5	even	2
1248.2.m.a.337.1		2	24.11	even	2
1248.2.m.a.337.2		2	156.155	even	2
1248.2.m.b.337.1		2	312.155	even	2
1248.2.m.b.337.2		2	12.11	even	2
3744.2.m.a.1585.1		2	104.51	odd	2
3744.2.m.a.1585.2		2	4.3	odd	2
3744.2.m.d.1585.1		2	8.3	odd	2
3744.2.m.d.1585.2		2	52.51	odd	2

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} -2.00000 q^{5} +(2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} -2.00000 q^{5} +(2.00000 + 2.00000i) q^{8} +(2.00000 - 2.00000i) q^{10} -4.00000 q^{11} +(-3.00000 + 2.00000i) q^{13} -4.00000 q^{16} +6.00000 q^{17} +6.00000 q^{19} +4.00000i q^{20} +(4.00000 - 4.00000i) q^{22} -1.00000 q^{25} +(1.00000 - 5.00000i) q^{26} -6.00000i q^{29} +(4.00000 - 4.00000i) q^{32} +(-6.00000 + 6.00000i) q^{34} +6.00000 q^{37} +(-6.00000 + 6.00000i) q^{38} +(-4.00000 - 4.00000i) q^{40} -2.00000i q^{41} -12.0000i q^{43} +8.00000i q^{44} -8.00000i q^{47} +7.00000 q^{49} +(1.00000 - 1.00000i) q^{50} +(4.00000 + 6.00000i) q^{52} -6.00000i q^{53} +8.00000 q^{55} +(6.00000 + 6.00000i) q^{58} +4.00000 q^{59} +8.00000i q^{61} +8.00000i q^{64} +(6.00000 - 4.00000i) q^{65} +6.00000 q^{67} -12.0000i q^{68} -4.00000i q^{71} -12.0000i q^{73} +(-6.00000 + 6.00000i) q^{74} -12.0000i q^{76} +6.00000 q^{79} +8.00000 q^{80} +(2.00000 + 2.00000i) q^{82} +8.00000 q^{83} -12.0000 q^{85} +(12.0000 + 12.0000i) q^{86} +(-8.00000 - 8.00000i) q^{88} +2.00000i q^{89} +(8.00000 + 8.00000i) q^{94} -12.0000 q^{95} +12.0000i q^{97} +(-7.00000 + 7.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{5} + 4 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 - 4 * q^5 + 4 * q^8	\( 2 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 4 q^{10} - 8 q^{11} - 6 q^{13} - 8 q^{16} + 12 q^{17} + 12 q^{19} + 8 q^{22} - 2 q^{25} + 2 q^{26} + 8 q^{32} - 12 q^{34} + 12 q^{37} - 12 q^{38} - 8 q^{40} + 14 q^{49} + 2 q^{50} + 8 q^{52} + 16 q^{55} + 12 q^{58} + 8 q^{59} + 12 q^{65} + 12 q^{67} - 12 q^{74} + 12 q^{79} + 16 q^{80} + 4 q^{82} + 16 q^{83} - 24 q^{85} + 24 q^{86} - 16 q^{88} + 16 q^{94} - 24 q^{95} - 14 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^5 + 4 * q^8 + 4 * q^10 - 8 * q^11 - 6 * q^13 - 8 * q^16 + 12 * q^17 + 12 * q^19 + 8 * q^22 - 2 * q^25 + 2 * q^26 + 8 * q^32 - 12 * q^34 + 12 * q^37 - 12 * q^38 - 8 * q^40 + 14 * q^49 + 2 * q^50 + 8 * q^52 + 16 * q^55 + 12 * q^58 + 8 * q^59 + 12 * q^65 + 12 * q^67 - 12 * q^74 + 12 * q^79 + 16 * q^80 + 4 * q^82 + 16 * q^83 - 24 * q^85 + 24 * q^86 - 16 * q^88 + 16 * q^94 - 24 * q^95 - 14 * q^98

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