LMFDB - Embedded newform 740.2.ce.b.243.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [740,2,Mod(3,740)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(740, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 26]))

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

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

chi := DirichletCharacter("740.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.ce (of order $36$, degree $12$, 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:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{36}]$

Embedding invariants

Embedding label			243.1
Root			$-0.342020 + 0.939693i$ of defining polynomial
Character	$\chi$	$=$	740.243
Dual form			740.2.ce.b.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.597672 + 1.28171i) q^{2} +(-1.28558 + 1.53209i) q^{4} +(-1.33210 - 1.79597i) q^{5} +(-2.73205 - 0.732051i) q^{8} +(1.92836 + 2.29813i) q^{9} +O(q^{10})$	\(q+(0.597672 + 1.28171i) q^{2} +(-1.28558 + 1.53209i) q^{4} +(-1.33210 - 1.79597i) q^{5} +(-2.73205 - 0.732051i) q^{8} +(1.92836 + 2.29813i) q^{9} +(1.50575 - 2.78078i) q^{10} +(-6.80484 + 0.595346i) q^{13} +(-0.694593 - 3.93923i) q^{16} +(-7.67107 - 0.671131i) q^{17} +(-1.79302 + 3.84514i) q^{18} +(4.46410 + 0.267949i) q^{20} +(-1.45100 + 4.78483i) q^{25} +(-4.83013 - 8.36603i) q^{26} +(2.54465 + 4.40746i) q^{29} +(4.63382 - 3.24464i) q^{32} +(-3.72459 - 10.2332i) q^{34} -6.00000 q^{36} +(-3.95348 - 4.62277i) q^{37} +(2.32464 + 5.88184i) q^{40} +(-8.60824 - 7.22317i) q^{41} +(1.55859 - 6.52463i) q^{45} +(-2.39414 + 6.57785i) q^{49} +(-7.00000 + 1.00000i) q^{50} +(7.83601 - 11.1910i) q^{52} +(4.29446 - 6.13313i) q^{53} +(-4.12823 + 5.89572i) q^{58} +(0.0340722 - 0.0406056i) q^{61} +(6.92820 + 4.00000i) q^{64} +(10.1340 + 11.4282i) q^{65} +(10.8900 - 10.8900i) q^{68} +(-3.58603 - 7.69028i) q^{72} +(12.0263 + 12.0263i) q^{73} +(3.56218 - 7.83013i) q^{74} +(-6.14946 + 6.49493i) q^{80} +(-1.56283 + 8.86327i) q^{81} +(4.11312 - 15.3504i) q^{82} +(9.01333 + 14.6710i) q^{85} +(2.43462 + 13.8074i) q^{89} +(9.29423 - 1.90192i) q^{90} +(-9.21335 + 2.46871i) q^{97} +(-9.86182 + 0.862798i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{8}+O(q^{10}) $ 12 * q - 12 * q^8	$ 12 q - 12 q^{8} - 6 q^{17} + 12 q^{20} - 6 q^{26} - 30 q^{34} - 72 q^{36} + 24 q^{41} - 84 q^{50} - 18 q^{58} + 72 q^{61} + 132 q^{65} + 30 q^{73} - 30 q^{74} - 42 q^{85} - 60 q^{89} + 18 q^{90}+O(q^{100}) $ 12 * q - 12 * q^8 - 6 * q^17 + 12 * q^20 - 6 * q^26 - 30 * q^34 - 72 * q^36 + 24 * q^41 - 84 * q^50 - 18 * q^58 + 72 * q^61 + 132 * q^65 + 30 * q^73 - 30 * q^74 - 42 * q^85 - 60 * q^89 + 18 * q^90

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	0.597672	+	1.28171i	0.422618	+	0.906308i
$2$	0.597672	+	1.28171i	0.422618	+	0.906308i
$3$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$3$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$4$	−1.28558	+	1.53209i	−0.642788	+	0.766044i
$5$	−1.33210	−	1.79597i	−0.595735	−	0.803181i
$5$	−1.33210	−	1.79597i	−0.595735	−	0.803181i
$6$		0			0
$7$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$7$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$8$	−2.73205	−	0.732051i	−0.965926	−	0.258819i
$9$	1.92836	+	2.29813i	0.642788	+	0.766044i
$10$	1.50575	−	2.78078i	0.476161	−	0.879358i
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$		0			0
$13$	−6.80484	+	0.595346i	−1.88732	+	0.165119i	−0.971590	−	0.236670i	$-0.923944\pi$
$13$	−6.80484	+	0.595346i	−1.88732	+	0.165119i	−0.915732	+	0.401789i	$0.868389\pi$
$14$		0			0
$15$		0			0
$16$	−0.694593	−	3.93923i	−0.173648	−	0.984808i
$17$	−7.67107	−	0.671131i	−1.86051	−	0.162773i	−0.899071	−	0.437803i	$-0.855757\pi$
$17$	−7.67107	−	0.671131i	−1.86051	−	0.162773i	−0.961436	+	0.275029i	$0.911312\pi$
$18$	−1.79302	+	3.84514i	−0.422618	+	0.906308i
$19$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$19$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$20$	4.46410	+	0.267949i	0.998203	+	0.0599153i
$21$		0			0
$22$		0			0
$23$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$23$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$24$		0			0
$25$	−1.45100	+	4.78483i	−0.290199	+	0.956966i
$26$	−4.83013	−	8.36603i	−0.947266	−	1.64071i
$27$		0			0
$28$		0			0
$29$	2.54465	+	4.40746i	0.472529	+	0.818444i	0.999506	−	0.0314353i	$-0.0100078\pi$
$29$	2.54465	+	4.40746i	0.472529	+	0.818444i	−0.526977	+	0.849880i	$0.676674\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	4.63382	−	3.24464i	0.819152	−	0.573576i
$33$		0			0
$34$	−3.72459	−	10.2332i	−0.638762	−	1.75498i
$35$		0			0
$36$	−6.00000			−1.00000
$37$	−3.95348	−	4.62277i	−0.649948	−	0.759979i
$37$	−3.95348	−	4.62277i	−0.649948	−	0.759979i
$38$		0			0
$39$		0			0
$40$	2.32464	+	5.88184i	0.367557	+	0.930001i
$41$	−8.60824	−	7.22317i	−1.34438	−	1.12807i	−0.980477	−	0.196634i	$-0.936999\pi$
$41$	−8.60824	−	7.22317i	−1.34438	−	1.12807i	−0.363905	−	0.931436i	$-0.618557\pi$
$42$		0			0
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$		0			0
$45$	1.55859	−	6.52463i	0.232341	−	0.972634i
$46$		0			0
$47$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$47$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$48$		0			0
$49$	−2.39414	+	6.57785i	−0.342020	+	0.939693i
$50$	−7.00000	+	1.00000i	−0.989949	+	0.141421i
$51$		0			0
$52$	7.83601	−	11.1910i	1.08666	−	1.55191i
$53$	4.29446	−	6.13313i	0.589890	−	0.842450i	−0.407607	−	0.913157i	$-0.633637\pi$
$53$	4.29446	−	6.13313i	0.589890	−	0.842450i	0.997497	+	0.0707071i	$0.0225256\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−4.12823	+	5.89572i	−0.542063	+	0.774146i
$59$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$59$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$60$		0			0
$61$	0.0340722	−	0.0406056i	0.00436249	−	0.00519902i	−0.763859	−	0.645383i	$-0.776698\pi$
$61$	0.0340722	−	0.0406056i	0.00436249	−	0.00519902i	0.768221	+	0.640184i	$0.221142\pi$
$62$		0			0
$63$		0			0
$64$	6.92820	+	4.00000i	0.866025	+	0.500000i
$65$	10.1340	+	11.4282i	1.25696	+	1.41749i
$66$		0			0
$67$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$67$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$68$	10.8900	−	10.8900i	1.32060	−	1.32060i
$69$		0			0
$70$		0			0
$71$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$71$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$72$	−3.58603	−	7.69028i	−0.422618	−	0.906308i
$73$	12.0263	+	12.0263i	1.40757	+	1.40757i	0.772246	+	0.635323i	$0.219133\pi$
$73$	12.0263	+	12.0263i	1.40757	+	1.40757i	0.635323	+	0.772246i	$0.280867\pi$
$74$	3.56218	−	7.83013i	0.414095	−	0.910234i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$79$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$80$	−6.14946	+	6.49493i	−0.687531	+	0.726155i
$81$	−1.56283	+	8.86327i	−0.173648	+	0.984808i
$82$	4.11312	−	15.3504i	0.454219	−	1.69517i
$83$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$83$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$84$		0			0
$85$	9.01333	+	14.6710i	0.977633	+	1.59129i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.43462	+	13.8074i	0.258070	+	1.46359i	0.788069	+	0.615587i	$0.211081\pi$
$89$	2.43462	+	13.8074i	0.258070	+	1.46359i	−0.529999	+	0.847998i	$0.677808\pi$
$90$	9.29423	−	1.90192i	0.979698	−	0.200480i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−9.21335	+	2.46871i	−0.935474	+	0.250659i	−0.694187	−	0.719794i	$-0.744236\pi$
$97$	−9.21335	+	2.46871i	−0.935474	+	0.250659i	−0.241287	+	0.970454i	$0.577569\pi$
$98$	−9.86182	+	0.862798i	−0.996195	+	0.0871557i
$99$		0			0
$100$	−5.46542	−	8.37432i	−0.546542	−	0.837432i
$101$	7.19392	−	12.4602i	0.715822	−	1.23984i	−0.246820	−	0.969061i	$-0.579386\pi$
$101$	7.19392	−	12.4602i	0.715822	−	1.23984i	0.962642	−	0.270778i	$-0.0872811\pi$
$102$		0			0
$103$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$103$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$104$	19.0270	+	3.35497i	1.86575	+	0.328982i
$105$		0			0
$106$	10.4276	+	1.83867i	1.01282	+	0.178587i
$107$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$107$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$108$		0			0
$109$	−2.28898	−	0.833121i	−0.219245	−	0.0797985i	0.230063	−	0.973176i	$-0.426107\pi$
$109$	−2.28898	−	0.833121i	−0.219245	−	0.0797985i	−0.449307	+	0.893377i	$0.648329\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−16.0091	+	7.46516i	−1.50601	+	0.702263i	−0.988191	−	0.153229i	$-0.951033\pi$
$113$	−16.0091	+	7.46516i	−1.50601	+	0.702263i	−0.517817	+	0.855491i	$0.673255\pi$
$114$		0			0
$115$		0			0
$116$	−10.0240	−	1.76749i	−0.930701	−	0.164108i
$117$	−14.4904	−	14.4904i	−1.33964	−	1.33964i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−5.50000	+	9.52628i	−0.500000	+	0.866025i
$122$	0.0724088	+	0.0194019i	0.00655558	+	0.00175656i
$123$		0			0
$124$		0			0
$125$	10.5263	−	3.76795i	0.941499	−	0.337016i
$126$		0			0
$127$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$127$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$128$	−0.986055	+	11.2707i	−0.0871557	+	0.996195i
$129$		0			0
$130$	−8.59088	+	19.8192i	−0.753470	+	1.73826i
$131$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$131$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	20.4664	+	7.44918i	1.75498	+	0.638762i
$137$	15.9842	+	4.28295i	1.36562	+	0.365917i	0.865878	−	0.500255i	$-0.166761\pi$
$137$	15.9842	+	4.28295i	1.36562	+	0.365917i	0.499745	+	0.866173i	$0.333427\pi$
$138$		0			0
$139$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$139$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	7.71345	−	9.19253i	0.642788	−	0.766044i
$145$	4.52592	−	10.4413i	0.375857	−	0.867102i
$146$	−8.22646	+	22.6020i	−0.680827	+	1.87056i
$147$		0			0
$148$	12.1650	−	0.114163i	0.999956	−	0.00938411i
$149$			6.31529i			0.517369i	0.965962	+	0.258685i	$0.0832890\pi$
$149$			6.31529i			0.517369i	−0.965962	+	0.258685i	$0.916711\pi$
$150$		0			0
$151$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$151$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$152$		0			0
$153$	−13.2503	−	18.9233i	−1.07122	−	1.52986i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−2.17055	+	24.8095i	−0.173229	+	1.98001i	0.0242497	+	0.999706i	$0.492280\pi$
$157$	−2.17055	+	24.8095i	−0.173229	+	1.98001i	−0.197478	+	0.980307i	$0.563275\pi$
$158$		0			0
$159$		0			0
$160$	−12.0000	−	4.00000i	−0.948683	−	0.316228i
$161$		0			0
$162$	−12.2942	+	3.29423i	−0.965926	+	0.258819i
$163$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$163$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$164$	22.1331	−	3.90266i	1.72830	−	0.304747i
$165$		0			0
$166$		0			0
$167$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$167$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$168$		0			0
$169$	33.1489	−	5.84504i	2.54991	−	0.449619i
$170$	−13.4170	+	20.3210i	−1.02904	+	1.55855i
$171$		0			0
$172$		0			0
$173$	−10.6730	−	22.8883i	−0.811453	−	1.74017i	−0.659396	−	0.751796i	$-0.729188\pi$
$173$	−10.6730	−	22.8883i	−0.811453	−	1.74017i	−0.152057	−	0.988372i	$-0.548590\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−16.2421	+	11.3728i	−1.21739	+	0.852429i
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$	7.99262	+	10.7758i	0.595735	+	0.803181i
$181$	−18.1973	−	15.2693i	−1.35259	−	1.13496i	−0.978194	−	0.207693i	$-0.933404\pi$
$181$	−18.1973	−	15.2693i	−1.35259	−	1.13496i	−0.374400	−	0.927267i	$-0.622151\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.03590	+	13.2583i	−0.223204	+	0.974772i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		0			0
$193$	−24.2726	−	6.50383i	−1.74718	−	0.468156i	−0.763160	−	0.646210i	$-0.776353\pi$
$193$	−24.2726	−	6.50383i	−1.74718	−	0.468156i	−0.984021	+	0.178054i	$0.943020\pi$
$194$	−8.67074	−	10.3334i	−0.622523	−	0.741894i
$195$		0			0
$196$	−7.00000	−	12.1244i	−0.500000	−	0.866025i
$197$	19.7476	−	9.20847i	1.40696	−	0.656077i	0.437028	−	0.899448i	$-0.356031\pi$
$197$	19.7476	−	9.20847i	1.40696	−	0.656077i	0.969933	+	0.243372i	$0.0782534\pi$
$198$		0			0
$199$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$199$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$200$	7.46694	−	12.0102i	0.527992	−	0.849249i
$201$		0			0
$202$	20.2701	+	1.77340i	1.42620	+	0.124776i
$203$		0			0
$204$		0			0
$205$	−1.50551	+	25.0821i	−0.105149	+	1.75181i
$206$		0			0
$207$		0			0
$208$	7.07180	+	26.3923i	0.490341	+	1.82998i
$209$		0			0
$210$		0			0
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$	3.87564	+	14.4641i	0.266180	+	0.993399i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.300239	−	3.43175i	−0.0203348	−	0.232427i
$219$		0			0
$220$		0			0
$221$	52.5999			3.53825
$222$		0			0
$223$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$223$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$224$		0			0
$225$	−13.7942	+	5.89230i	−0.919615	+	0.392820i
$226$	−19.1364	−	16.0573i	−1.27293	−	1.06812i
$227$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$227$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$228$		0			0
$229$	−15.9730	−	2.81648i	−1.05553	−	0.186118i	−0.381157	−	0.924510i	$-0.624474\pi$
$229$	−15.9730	−	2.81648i	−1.05553	−	0.186118i	−0.674371	+	0.738392i	$0.735585\pi$
$230$		0			0
$231$		0			0
$232$	−3.72562	−	13.9042i	−0.244599	−	0.912856i
$233$	0.909192	−	3.39315i	0.0595632	−	0.222293i	−0.929728	−	0.368246i	$-0.879958\pi$
$233$	0.909192	−	3.39315i	0.0595632	−	0.222293i	0.989291	+	0.145953i	$0.0466250\pi$
$234$	9.91200	−	27.2330i	0.647968	−	1.78028i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$239$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$240$		0			0
$241$	2.76072	+	7.58501i	0.177833	+	0.488593i	0.996298	−	0.0859632i	$-0.0273968\pi$
$241$	2.76072	+	7.58501i	0.177833	+	0.488593i	−0.818465	+	0.574557i	$0.805175\pi$
$242$	−15.4972	−	1.35583i	−0.996195	−	0.0871557i
$243$		0			0
$244$	0.0184091	+	0.104403i	0.00117852	+	0.00668373i
$245$	15.0028	−	4.46258i	0.958497	−	0.285104i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	11.1207	+	11.2397i	0.703335	+	0.710859i
$251$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$251$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−15.0351	+	5.47232i	−0.939693	+	0.342020i
$257$	−2.02070	−	4.33340i	−0.126048	−	0.270310i	0.833150	−	0.553047i	$-0.186535\pi$
$257$	−2.02070	−	4.33340i	−0.126048	−	0.270310i	−0.959197	+	0.282738i	$0.908757\pi$
$258$		0			0
$259$		0			0
$260$	−30.5370	+	0.834335i	−1.89382	+	0.0517433i
$261$	−5.22192	+	14.3471i	−0.323229	+	0.888064i
$262$		0			0
$263$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$263$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$264$		0			0
$265$	−16.7356	+	0.457251i	−1.02806	+	0.0280887i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.74167	−	2.16025i	−0.228134	−	0.131713i	0.381577	−	0.924337i	$-0.375381\pi$
$269$	−3.74167	−	2.16025i	−0.228134	−	0.131713i	−0.609711	+	0.792624i	$0.708714\pi$
$270$		0			0
$271$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$271$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$272$	2.68453	+	30.6843i	0.162773	+	1.86051i
$273$		0			0
$274$	4.06380	+	23.0470i	0.245503	+	1.39232i
$275$		0			0
$276$		0			0
$277$	−29.8934	−	13.9395i	−1.79612	−	0.837545i	−0.954943	−	0.296788i	$-0.904085\pi$
$277$	−29.8934	−	13.9395i	−1.79612	−	0.837545i	−0.841178	−	0.540758i	$-0.818138\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	20.0325	−	3.53228i	1.19504	−	0.210718i	0.459487	−	0.888184i	$-0.348033\pi$
$281$	20.0325	−	3.53228i	1.19504	−	0.210718i	0.735554	+	0.677466i	$0.236922\pi$
$282$		0			0
$283$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$283$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	16.3923	+	4.39230i	0.965926	+	0.258819i
$289$	41.6531	+	7.34457i	2.45018	+	0.432033i
$290$	16.0878	−	0.439551i	0.944706	−	0.0258113i
$291$		0			0
$292$	−33.8860	+	2.96464i	−1.98303	+	0.173493i
$293$	30.3812	+	14.1670i	1.77489	+	0.827645i	0.973218	+	0.229883i	$0.0738342\pi$
$293$	30.3812	+	14.1670i	1.77489	+	0.827645i	0.801673	+	0.597763i	$0.203944\pi$
$294$		0			0
$295$		0			0
$296$	7.41700	+	15.5238i	0.431105	+	0.902302i
$297$		0			0
$298$	−8.09439	+	3.77448i	−0.468896	+	0.218650i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.118314	−	0.00710158i	−0.00677464	−	0.000406635i
$306$	16.3349	−	28.2930i	0.933807	−	1.61740i
$307$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$307$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$311$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$312$		0			0
$313$	1.16973	−	13.3701i	0.0661171	−	0.755722i	−0.888692	−	0.458504i	$-0.848385\pi$
$313$	1.16973	−	13.3701i	0.0661171	−	0.755722i	0.954810	−	0.297218i	$-0.0960589\pi$
$314$	−33.0959	+	12.0459i	−1.86771	+	0.679791i
$315$		0			0
$316$		0			0
$317$	−1.60652	−	1.12490i	−0.0902314	−	0.0631807i	0.527590	−	0.849499i	$-0.323096\pi$
$317$	−1.60652	−	1.12490i	−0.0902314	−	0.0631807i	−0.617822	+	0.786318i	$0.711985\pi$
$318$		0			0
$319$		0			0
$320$	−2.04522	−	17.7712i	−0.114331	−	0.993443i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−11.5702	−	13.7888i	−0.642788	−	0.766044i
$325$	7.02517	−	33.4238i	0.389686	−	1.85402i
$326$		0			0
$327$		0			0
$328$	18.2304	+	26.0357i	1.00661	+	1.43758i
$329$		0			0
$330$		0			0
$331$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$331$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$332$		0			0
$333$	3.00000	−	18.0000i	0.164399	−	0.986394i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−33.3198	+	2.91510i	−1.81504	+	0.158796i	−0.943467	−	0.331466i	$-0.892457\pi$
$337$	−33.3198	+	2.91510i	−1.81504	+	0.158796i	−0.871576	+	0.490261i	$0.836901\pi$
$338$	27.3038	+	38.9939i	1.48513	+	2.12099i
$339$		0			0
$340$	−34.0646	−	5.05145i	−1.84741	−	0.273954i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	22.9573	−	27.3594i	1.23419	−	1.47085i
$347$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$347$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$348$		0			0
$349$	−20.8284	+	3.67261i	−1.11492	+	0.196590i	−0.700609	−	0.713545i	$-0.747088\pi$
$349$	−20.8284	+	3.67261i	−1.11492	+	0.196590i	−0.414310	+	0.910136i	$0.635977\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.83048	−	32.3525i	0.150651	−	1.72195i	−0.425797	−	0.904819i	$-0.640006\pi$
$353$	2.83048	−	32.3525i	0.150651	−	1.72195i	0.576448	−	0.817134i	$-0.304438\pi$
$354$		0			0
$355$		0			0
$356$	−24.2841	−	14.0204i	−1.28706	−	0.743082i
$357$		0			0
$358$		0			0
$359$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$	−9.03451	+	16.6847i	−0.476161	+	0.879358i
$361$	14.5548	−	12.2130i	0.766044	−	0.642788i
$362$	8.69489	−	32.4498i	0.456993	−	1.70552i
$363$		0			0
$364$		0			0
$365$	5.57855	−	37.6191i	0.291995	−	1.96907i
$366$		0			0
$367$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$367$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$368$		0			0
$369$		−	33.7118i		−	1.75497i
$370$	−18.8078	+	4.03299i	−0.977773	+	0.209665i
$371$		0			0
$372$		0			0
$373$	−19.4488	−	9.06914i	−1.00702	−	0.469582i	−0.152115	−	0.988363i	$-0.548608\pi$
$373$	−19.4488	−	9.06914i	−1.00702	−	0.469582i	−0.854907	+	0.518781i	$0.826386\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−19.9399	−	28.4771i	−1.02696	−	1.46664i
$378$		0			0
$379$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$379$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$383$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$384$		0			0
$385$		0			0
$386$	−6.17103	−	34.9977i	−0.314097	−	1.78133i
$387$		0			0
$388$	8.06217	−	17.2894i	0.409295	−	0.877735i
$389$	6.73306	−	2.45063i	0.341379	−	0.124252i	−0.165641	−	0.986186i	$-0.552969\pi$
$389$	6.73306	−	2.45063i	0.341379	−	0.124252i	0.507020	+	0.861934i	$0.330747\pi$
$390$		0			0
$391$		0			0
$392$	11.3562	−	16.2184i	0.573576	−	0.819152i
$393$		0			0
$394$	23.6052	+	19.8071i	1.18921	+	0.997870i
$395$		0			0
$396$		0			0
$397$	10.2262	+	38.1648i	0.513240	+	1.91544i	0.382271	+	0.924050i	$0.375142\pi$
$397$	10.2262	+	38.1648i	0.513240	+	1.91544i	0.130969	+	0.991387i	$0.458191\pi$
$398$		0			0
$399$		0			0
$400$	19.8564	+	2.39230i	0.992820	+	0.119615i
$401$		−	21.7321i		−	1.08525i	−0.839976	−	0.542623i	$-0.817431\pi$
$401$		−	21.7321i		−	1.08525i	0.839976	−	0.542623i	$-0.182569\pi$
$402$		0			0
$403$		0			0
$404$	9.84186	+	27.0403i	0.489651	+	1.34531i
$405$	18.0000	−	9.00000i	0.894427	−	0.447214i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−37.2493	−	13.5576i	−1.84186	−	0.670381i	−0.988936	−	0.148340i	$-0.952607\pi$
$409$	−37.2493	−	13.5576i	−1.84186	−	0.670381i	−0.852921	−	0.522041i	$-0.825171\pi$
$410$	−33.0479	+	13.0613i	−1.63212	+	0.645051i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−29.6007	+	24.8380i	−1.45130	+	1.21778i
$417$		0			0
$418$		0			0
$419$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$419$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$420$		0			0
$421$	28.3918	+	16.3920i	1.38373	+	0.798899i	0.992599	−	0.121435i	$-0.0387496\pi$
$421$	28.3918	+	16.3920i	1.38373	+	0.798899i	0.391134	+	0.920334i	$0.372083\pi$
$422$		0			0
$423$		0			0
$424$	−16.2225	+	13.6123i	−0.787832	+	0.661070i
$425$	14.3419	−	35.7309i	0.695687	−	1.73321i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$431$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$432$		0			0
$433$	−10.7713	+	40.1989i	−0.517634	+	1.93184i	−0.255149	+	0.966902i	$0.582124\pi$
$433$	−10.7713	+	40.1989i	−0.517634	+	1.93184i	−0.262485	+	0.964936i	$0.584542\pi$
$434$		0			0
$435$		0			0
$436$	4.21907	−	2.43588i	0.202057	−	0.116658i
$437$		0			0
$438$		0			0
$439$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$439$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$440$		0			0
$441$	−19.7335	+	7.18242i	−0.939693	+	0.342020i
$442$	31.4375	+	67.4180i	1.49533	+	3.20675i
$443$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$443$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$444$		0			0
$445$	21.5545	−	22.7655i	1.02178	−	1.07919i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−5.57834	+	31.6363i	−0.263258	+	1.49301i	0.510692	+	0.859764i	$0.329389\pi$
$449$	−5.57834	+	31.6363i	−0.263258	+	1.49301i	−0.773950	+	0.633246i	$0.781722\pi$
$450$	−15.7967	−	14.1586i	−0.744662	−	0.667441i
$451$		0			0
$452$	9.14359	−	34.1244i	0.430078	−	1.60507i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	2.67075	+	30.5268i	0.124932	+	1.42798i	0.757174	+	0.653213i	$0.226579\pi$
$457$	2.67075	+	30.5268i	0.124932	+	1.42798i	−0.632242	+	0.774771i	$0.717865\pi$
$458$	−5.93673	−	22.1562i	−0.277405	−	1.03529i
$459$		0			0
$460$		0			0
$461$	−27.5814	−	32.8702i	−1.28459	−	1.53092i	−0.672256	−	0.740318i	$-0.734675\pi$
$461$	−27.5814	−	32.8702i	−1.28459	−	1.53092i	−0.612335	−	0.790598i	$-0.709770\pi$
$462$		0			0
$463$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$463$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$464$	15.5945	−	13.0853i	0.723957	−	0.607472i
$465$		0			0
$466$	4.89245	−	0.862670i	0.226638	−	0.0399624i
$467$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$467$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$468$	40.8290	−	3.57208i	1.88732	−	0.165119i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	22.3760	−	1.95765i	1.02453	−	0.0896346i
$478$		0			0
$479$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$479$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$480$		0			0
$481$	29.6549	+	29.1035i	1.35215	+	1.32701i
$482$	−8.07180	+	8.07180i	−0.367660	+	0.367660i
$483$		0			0
$484$	−7.52444	−	20.6732i	−0.342020	−	0.939693i
$485$	16.7069	+	13.2583i	0.758620	+	0.602028i
$486$		0			0
$487$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$487$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$488$	−0.122812	+	0.0859941i	−0.00555945	+	0.00389277i
$489$		0			0
$490$	14.6865	+	16.5622i	0.663470	+	0.748203i
$491$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$491$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$492$		0			0
$493$	−16.5622	−	35.5177i	−0.745923	−	1.59964i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$499$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$500$	−7.75949	+	20.9712i	−0.347015	+	0.937860i
$501$		0			0
$502$		0			0
$503$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$503$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$504$		0			0
$505$	−31.9612	+	3.67829i	−1.42226	+	0.163682i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−24.3785	−	29.0532i	−1.08056	−	1.28776i	−0.955300	−	0.295637i	$-0.904468\pi$
$509$	−24.3785	−	29.0532i	−1.08056	−	1.28776i	−0.125259	−	0.992124i	$-0.539976\pi$
$510$		0			0
$511$		0			0
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$		0			0
$514$	4.34645	−	5.17990i	0.191714	−	0.228476i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−19.3205	−	38.6410i	−0.847260	−	1.69452i
$521$	−42.8885	+	15.6101i	−1.87898	+	0.683893i	−0.932392	+	0.361449i	$0.882282\pi$
$521$	−42.8885	+	15.6101i	−1.87898	+	0.683893i	−0.946589	+	0.322444i	$0.895496\pi$
$522$	−21.5099	+	1.88187i	−0.941462	+	0.0823672i
$523$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$523$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−19.9186	+	11.5000i	−0.866025	+	0.500000i
$530$	−10.5885	−	21.1769i	−0.459933	−	0.919866i
$531$		0			0
$532$		0			0
$533$	62.8780	+	44.0276i	2.72355	+	1.90705i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	0.532532	−	6.08687i	0.0229591	−	0.262424i
$539$		0			0
$540$		0			0
$541$	−38.8282	−	22.4174i	−1.66935	−	0.963801i	−0.967987	−	0.250999i	$-0.919241\pi$
$541$	−38.8282	−	22.4174i	−1.66935	−	0.963801i	−0.701365	−	0.712802i	$-0.747426\pi$
$542$		0			0
$543$		0			0
$544$	−37.7240	+	21.7799i	−1.61740	+	0.933807i
$545$	1.55290	+	5.22074i	0.0665191	+	0.223632i
$546$		0			0
$547$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$547$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$548$	−27.1108	+	18.9832i	−1.15811	+	0.810920i
$549$	0.159021			0.00678684
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		−	46.6461i		−	1.98180i
$555$		0			0
$556$		0			0
$557$	0.481934	+	1.03351i	0.0204202	+	0.0437912i	0.916253	−	0.400599i	$-0.131198\pi$
$557$	0.481934	+	1.03351i	0.0204202	+	0.0437912i	−0.895833	+	0.444391i	$0.853420\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	16.5003	+	23.5648i	0.696021	+	0.994022i
$563$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$563$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$564$		0			0
$565$	34.7329	+	18.8074i	1.46123	+	0.791234i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−23.6771	+	41.0100i	−0.992597	+	1.71923i	−0.391115	+	0.920342i	$0.627910\pi$
$569$	−23.6771	+	41.0100i	−0.992597	+	1.71923i	−0.601482	+	0.798886i	$0.705423\pi$
$570$		0			0
$571$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$571$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	4.16756	+	23.6354i	0.173648	+	0.984808i
$577$	−26.8905	+	38.4035i	−1.11946	+	1.59876i	−0.380844	+	0.924639i	$0.624366\pi$
$577$	−26.8905	+	38.4035i	−1.11946	+	1.59876i	−0.738621	+	0.674121i	$0.764523\pi$
$578$	15.4813	+	57.7770i	0.643937	+	2.40321i
$579$		0			0
$580$	10.1786	+	20.3572i	0.422643	+	0.845286i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−24.0526	−	41.6603i	−0.995302	−	1.72391i
$585$	−6.72155	+	45.3269i	−0.277902	+	1.87404i
$586$			47.4073i			1.95838i
$587$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$587$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−15.4641	+	18.7846i	−0.635571	+	0.772043i
$593$	−31.4171	−	31.4171i	−1.29014	−	1.29014i	−0.934696	−	0.355449i	$-0.884328\pi$
$593$	−31.4171	−	31.4171i	−1.29014	−	1.29014i	−0.355449	−	0.934696i	$-0.615672\pi$
$594$		0			0
$595$		0			0
$596$	−9.67559	−	8.11879i	−0.396328	−	0.332558i
$597$		0			0
$598$		0			0
$599$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$599$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$600$		0			0
$601$	33.0916	−	27.7671i	1.34983	−	1.13265i	0.370854	−	0.928691i	$-0.379065\pi$
$601$	33.0916	−	27.7671i	1.34983	−	1.13265i	0.978980	−	0.203954i	$-0.0653794\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	24.4355	−	2.81218i	0.993443	−	0.114331i
$606$		0			0
$607$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$607$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$608$		0			0
$609$		0			0
$610$	−0.0616109	−	0.155889i	−0.00249455	−	0.00631176i
$611$		0			0
$612$	46.0264	+	4.02679i	1.86051	+	0.162773i
$613$	−26.9559	+	38.4970i	−1.08874	+	1.55488i	−0.286300	+	0.958140i	$0.592425\pi$
$613$	−26.9559	+	38.4970i	−1.08874	+	1.55488i	−0.802437	+	0.596737i	$0.796463\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	25.7600	−	12.0121i	1.03706	−	0.483588i	0.171913	−	0.985112i	$-0.445005\pi$
$617$	25.7600	−	12.0121i	1.03706	−	0.483588i	0.865143	+	0.501524i	$0.167227\pi$
$618$		0			0
$619$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$619$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−20.7892	−	13.8856i	−0.831569	−	0.555422i
$626$	17.8357	−	6.49168i	0.712859	−	0.259460i
$627$		0			0
$628$	−35.2199	−	35.2199i	−1.40543	−	1.40543i
$629$	27.2249	+	38.1149i	1.08553	+	1.51974i
$630$		0			0
$631$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$631$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$632$		0			0
$633$		0			0
$634$	0.481624	−	2.73143i	0.0191277	−	0.108479i
$635$		0			0
$636$		0			0
$637$	12.3756	−	46.1865i	0.490341	−	1.82998i
$638$		0			0
$639$		0			0
$640$	21.5553	−	13.2428i	0.852046	−	0.523466i
$641$	23.1339	+	8.42004i	0.913733	+	0.332572i	0.755742	−	0.654869i	$-0.227276\pi$
$641$	23.1339	+	8.42004i	0.913733	+	0.332572i	0.157991	+	0.987441i	$0.449498\pi$
$642$		0			0
$643$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$643$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$647$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$648$	10.7581	−	23.0708i	0.422618	−	0.906308i
$649$		0			0
$650$	47.0385	−	10.9723i	1.84500	−	0.430367i
$651$		0			0
$652$		0			0
$653$	−46.3582	+	4.05582i	−1.81414	+	0.158717i	−0.943102	−	0.332503i	$-0.892107\pi$
$653$	−46.3582	+	4.05582i	−1.81414	+	0.158717i	−0.871036	+	0.491220i	$0.836551\pi$
$654$		0			0
$655$		0			0
$656$	−22.4745	+	38.9270i	−0.877483	+	1.51984i
$657$	−4.44696	+	50.8290i	−0.173493	+	1.98303i
$658$		0			0
$659$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$659$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$660$		0			0
$661$	50.3127	+	8.87149i	1.95694	+	0.345061i	0.998139	+	0.0609742i	$0.0194207\pi$
$661$	50.3127	+	8.87149i	1.95694	+	0.345061i	0.958799	+	0.284087i	$0.0916904\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	24.8638	−	6.91297i	0.963455	−	0.267872i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	31.3088	−	21.9226i	1.20686	−	0.845055i	0.215540	−	0.976495i	$-0.430849\pi$
$673$	31.3088	−	21.9226i	1.20686	−	0.845055i	0.991324	+	0.131440i	$0.0419601\pi$
$674$	−23.6506	−	40.9641i	−0.910988	−	1.57788i
$675$		0			0
$676$	−33.6603	+	58.3013i	−1.29463	+	2.24236i
$677$	−49.8686	−	13.3623i	−1.91661	−	0.513553i	−0.990754	−	0.135671i	$-0.956681\pi$
$677$	−49.8686	−	13.3623i	−1.91661	−	0.513553i	−0.925853	−	0.377883i	$-0.876652\pi$
$678$		0			0
$679$		0			0
$680$	−13.8850	−	46.6801i	−0.532464	−	1.79010i
$681$		0			0
$682$		0			0
$683$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$683$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$684$		0			0
$685$	−13.6006	−	34.4124i	−0.519651	−	1.31483i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−25.5718	+	44.2917i	−0.974208	+	1.68738i
$690$		0			0
$691$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$691$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$692$	48.7879	+	13.0727i	1.85464	+	0.496949i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	61.1867	+	61.1867i	2.31761	+	2.31761i
$698$	−17.1558	−	24.5010i	−0.649357	−	0.927377i
$699$		0			0
$700$		0			0
$701$	−13.6922	+	37.6190i	−0.517147	+	1.42085i	0.356502	+	0.934295i	$0.383969\pi$
$701$	−13.6922	+	37.6190i	−0.517147	+	1.42085i	−0.873649	+	0.486556i	$0.838253\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	43.1584	−	15.7084i	1.62429	−	0.591192i
$707$		0			0
$708$		0			0
$709$	30.0000			1.12667			0.563337	−	0.826227i	$-0.309517\pi$
$709$	30.0000			1.12667			0.563337	+	0.826227i	$0.309517\pi$
$710$		0			0
$711$		0			0
$712$	3.45623	−	39.5049i	0.129528	−	1.48051i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$719$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$720$	−26.7846	−	1.60770i	−0.998203	−	0.0599153i
$721$		0			0
$722$	24.3525	+	11.3558i	0.906308	+	0.422618i
$723$		0			0
$724$	46.7880	−	8.24998i	1.73886	−	0.306608i
$725$	−24.7812	+	5.78050i	−0.920351	+	0.214682i
$726$		0			0
$727$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$727$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$728$		0			0
$729$	−23.3827	+	13.5000i	−0.866025	+	0.500000i
$730$	51.5510	−	15.3338i	1.90799	−	0.567529i
$731$		0			0
$732$		0			0
$733$	43.5750	−	30.5116i	1.60948	−	1.12697i	0.697620	−	0.716468i	$-0.254242\pi$
$733$	43.5750	−	30.5116i	1.60948	−	1.12697i	0.911860	−	0.410502i	$-0.134647\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	43.2088	−	20.1486i	1.59054	−	0.741681i
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$	−16.4101	−	21.6958i	−0.603246	−	0.797555i
$741$		0			0
$742$		0			0
$743$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$743$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$744$		0			0
$745$	11.3421	−	8.41263i	0.415541	−	0.308215i
$746$		−	30.3482i		−	1.11113i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$		0			0
$753$		0			0
$754$	24.5819	−	42.5772i	0.895221	−	1.55057i
$755$		0			0
$756$		0			0
$757$	13.3484	+	1.16784i	0.485156	+	0.0424457i	0.327111	−	0.944986i	$-0.393925\pi$
$757$	13.3484	+	1.16784i	0.485156	+	0.0424457i	0.158046	+	0.987432i	$0.449481\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	3.82504	+	21.6929i	0.138658	+	0.786366i	0.972243	+	0.233975i	$0.0751733\pi$
$761$	3.82504	+	21.6929i	0.138658	+	0.786366i	−0.833585	+	0.552391i	$0.813716\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−16.3349	+	49.0048i	−0.590591	+	1.77177i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.825518	+	0.564376i	$0.190883\pi$
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.0760054	+	0.997107i	$0.475783\pi$
$770$		0			0
$771$		0			0
$772$	41.1687	−	28.8266i	1.48169	−	1.03749i
$773$	2.61779	+	29.9215i	0.0941553	+	1.07620i	0.885440	+	0.464753i	$0.153857\pi$
$773$	2.61779	+	29.9215i	0.0941553	+	1.07620i	−0.791285	+	0.611448i	$0.790588\pi$
$774$		0			0
$775$		0			0
$776$	26.9786			0.968474
$777$		0			0
$778$	7.16517	+	7.16517i	0.256884	+	0.256884i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	27.5746	+	4.86215i	0.984808	+	0.173648i
$785$	47.4484	−	29.1506i	1.69351	−	1.04043i
$786$		0			0
$787$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$787$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$788$	−11.2789	+	42.0933i	−0.401793	+	1.49951i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−0.207681	+	0.296599i	−0.00737497	+	0.0105326i
$794$	−42.8044	+	35.9171i	−1.51907	+	1.27465i
$795$		0			0
$796$		0			0
$797$	52.1268	+	4.56050i	1.84643	+	0.161541i	0.955958	−	0.293505i	$-0.0948217\pi$
$797$	52.1268	+	4.56050i	1.84643	+	0.161541i	0.890468	+	0.455046i	$0.150377\pi$
$798$		0			0
$799$		0			0
$800$	8.80138	+	26.8800i	0.311176	+	0.950352i
$801$	−27.0365	+	32.2208i	−0.955288	+	1.13847i
$802$	27.8542	−	12.9886i	0.983568	−	0.458645i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−28.7757	+	28.7757i	−1.01232	+	1.01232i
$809$	9.28973	−	52.6847i	0.326610	−	1.85229i	−0.171505	−	0.985183i	$-0.554863\pi$
$809$	9.28973	−	52.6847i	0.326610	−	1.85229i	0.498114	−	0.867111i	$-0.334026\pi$
$810$	22.2935	+	17.6918i	0.783314	+	0.621626i
$811$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$811$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−4.88588	−	55.8459i	−0.170831	−	1.95260i
$819$		0			0
$820$	−36.4926	−	34.5516i	−1.27438	−	1.20659i
$821$	−5.08811	+	28.8561i	−0.177576	+	1.00709i	0.757552	+	0.652775i	$0.226395\pi$
$821$	−5.08811	+	28.8561i	−0.177576	+	1.00709i	−0.935128	+	0.354310i	$0.884716\pi$
$822$		0			0
$823$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$823$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$827$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$828$		0			0
$829$	−3.47296	−	19.6962i	−0.120621	−	0.684076i	−0.983813	−	0.179200i	$-0.942649\pi$
$829$	−3.47296	−	19.6962i	−0.120621	−	0.684076i	0.863192	−	0.504876i	$-0.168462\pi$
$830$		0			0
$831$		0			0
$832$	−49.5267	−	23.0947i	−1.71703	−	0.800664i
$833$	22.7802	−	48.8523i	0.789288	−	1.69263i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$839$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$840$		0			0
$841$	1.54954	−	2.68389i	0.0534325	−	0.0925479i
$842$	−4.04086	+	46.1872i	−0.139257	+	1.59172i
$843$		0			0
$844$		0			0
$845$	−54.6553	−	51.7481i	−1.88020	−	1.78019i
$846$		0			0
$847$		0			0
$848$	−27.1427	−	12.6569i	−0.932085	−	0.434638i
$849$		0			0
$850$	54.3686	−	2.97315i	1.86483	−	0.101978i
$851$		0			0
$852$		0			0
$853$	15.4365	−	7.19814i	0.528534	−	0.246460i	−0.139986	−	0.990153i	$-0.544706\pi$
$853$	15.4365	−	7.19814i	0.528534	−	0.246460i	0.668520	+	0.743694i	$0.266928\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−22.4594	−	22.4594i	−0.767197	−	0.767197i	0.210415	−	0.977612i	$-0.432518\pi$
$857$	−22.4594	−	22.4594i	−0.767197	−	0.767197i	−0.977612	+	0.210415i	$0.932518\pi$
$858$		0			0
$859$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$859$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$863$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$864$		0			0
$865$	−26.8891	+	49.6580i	−0.914258	+	1.68842i
$866$	−57.9612	+	10.2201i	−1.96960	+	0.347294i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	5.64373	+	3.95178i	0.191121	+	0.133824i
$873$	−23.4401	−	16.4129i	−0.793327	−	0.555494i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−56.8207	−	15.2251i	−1.91870	−	0.514114i	−0.989499	−	0.144540i	$-0.953830\pi$
$877$	−56.8207	−	15.2251i	−1.91870	−	0.514114i	−0.929201	−	0.369574i	$-0.879504\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.32423	−	7.51010i	0.0446146	−	0.253022i	−0.954341	−	0.298720i	$-0.903440\pi$
$881$	1.32423	−	7.51010i	0.0446146	−	0.253022i	0.998955	+	0.0456985i	$0.0145514\pi$
$882$	−21.0000	−	21.0000i	−0.707107	−	0.707107i
$883$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$883$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$884$	−67.6212	+	80.5878i	−2.27435	+	2.71046i
$885$		0			0
$886$		0			0
$887$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$887$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$888$		0			0
$889$		0			0
$890$	42.0613	+	14.0204i	1.40990	+	0.469966i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−43.8827	+	11.7583i	−1.46438	+	0.392381i
$899$		0			0
$900$	8.70598	−	28.7090i	0.290199	−	0.956966i
$901$	−37.0593	+	44.1655i	−1.23462	+	1.47137i
$902$		0			0
$903$		0			0
$904$	49.2025	−	8.67573i	1.63645	−	0.288550i
$905$	−3.18255	+	53.0221i	−0.105792	+	1.76251i
$906$		0			0
$907$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$907$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$908$		0			0
$909$	42.5078	−	7.49527i	1.40989	−	0.248602i
$910$		0			0
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$		0			0
$913$		0			0
$914$	−37.5304	+	21.6682i	−1.24139	+	0.716720i
$915$		0			0
$916$	24.8496	−	20.8513i	0.821055	−	0.688947i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	25.6455	−	54.9970i	0.844590	−	1.81123i
$923$		0			0
$924$		0			0
$925$	27.8557	−	12.2091i	0.915888	−	0.401433i
$926$		0			0
$927$		0			0
$928$	26.0921	+	12.1669i	0.856514	+	0.399399i
$929$	−36.5789	+	43.5930i	−1.20011	+	1.43024i	−0.325418	+	0.945570i	$0.605505\pi$
$929$	−36.5789	+	43.5930i	−1.20011	+	1.43024i	−0.874697	+	0.484671i	$0.838939\pi$
$930$		0			0
$931$		0			0
$932$	4.02978	+	5.75512i	0.132000	+	0.188515i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	28.9808	+	50.1962i	0.947266	+	1.64071i
$937$	30.5171	−	14.2304i	0.996951	−	0.464886i	0.145522	−	0.989355i	$-0.453514\pi$
$937$	30.5171	−	14.2304i	0.996951	−	0.464886i	0.851429	+	0.524469i	$0.175736\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.67129	−	9.47834i	−0.0544824	−	0.308985i	0.945373	−	0.325991i	$-0.105698\pi$
$941$	−1.67129	−	9.47834i	−0.0544824	−	0.308985i	−0.999855	+	0.0170056i	$0.994587\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$947$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$948$		0			0
$949$	−88.9967	−	74.6771i	−2.88895	−	2.42412i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	39.4572	+	3.45206i	1.27814	+	0.111823i	0.705931	−	0.708281i	$-0.250529\pi$
$953$	39.4572	+	3.45206i	1.27814	+	0.111823i	0.572214	+	0.820104i	$0.306085\pi$
$954$	15.8827	+	27.5096i	0.514221	+	0.890657i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−31.0000			−1.00000
$962$	−19.5784	+	55.4035i	−0.631233	+	1.78628i
$963$		0			0
$964$	−15.1700	−	5.52143i	−0.488593	−	0.177833i
$965$	20.6530	+	52.2566i	0.664843	+	1.68220i
$966$		0			0
$967$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$967$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$968$	22.0000	−	22.0000i	0.707107	−	0.707107i
$969$		0			0
$970$	−7.00810	+	29.3375i	−0.225016	+	0.941971i
$971$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$971$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.183621	−	0.106014i	−0.00587757	−	0.00339342i
$977$	13.6363	−	19.4747i	0.436264	−	0.623050i	−0.539471	−	0.842004i	$-0.681376\pi$
$977$	13.6363	−	19.4747i	0.436264	−	0.623050i	0.975735	+	0.218954i	$0.0702646\pi$
$978$		0			0
$979$		0			0
$980$	−12.4502	+	28.7227i	−0.397708	+	0.917512i
$981$	−2.49936	−	6.86694i	−0.0797985	−	0.219245i
$982$		0			0
$983$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$983$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$984$		0			0
$985$	−42.8440	−	23.1995i	−1.36512	−	0.739196i
$986$	35.6247	−	42.4559i	1.13452	−	1.35207i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$991$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	22.1139	+	47.4234i	0.700354	+	1.50191i	0.857580	+	0.514351i	$0.171967\pi$
$997$	22.1139	+	47.4234i	0.700354	+	1.50191i	−0.157226	+	0.987563i	$0.550255\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.ce.b.243.1	yes	12
4.3	odd	2	CM	740.2.ce.b.243.1	yes	12
5.2	odd	4		740.2.ce.a.687.1	yes	12
20.7	even	4		740.2.ce.a.687.1	yes	12
37.30	even	18		740.2.ce.a.363.1	✓	12
148.67	odd	18		740.2.ce.a.363.1	✓	12
185.67	odd	36	inner	740.2.ce.b.67.1	yes	12
740.67	even	36	inner	740.2.ce.b.67.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.ce.a.363.1	✓	12	37.30	even	18
740.2.ce.a.363.1	✓	12	148.67	odd	18
740.2.ce.a.687.1	yes	12	5.2	odd	4
740.2.ce.a.687.1	yes	12	20.7	even	4
740.2.ce.b.67.1	yes	12	185.67	odd	36	inner
740.2.ce.b.67.1	yes	12	740.67	even	36	inner
740.2.ce.b.243.1	yes	12	1.1	even	1	trivial
740.2.ce.b.243.1	yes	12	4.3	odd	2	CM

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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.ce (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.597672 + 1.28171i) q^{2} +(-1.28558 + 1.53209i) q^{4} +(-1.33210 - 1.79597i) q^{5} +(-2.73205 - 0.732051i) q^{8} +(1.92836 + 2.29813i) q^{9} +O(q^{10})\)	\(q+(0.597672 + 1.28171i) q^{2} +(-1.28558 + 1.53209i) q^{4} +(-1.33210 - 1.79597i) q^{5} +(-2.73205 - 0.732051i) q^{8} +(1.92836 + 2.29813i) q^{9} +(1.50575 - 2.78078i) q^{10} +(-6.80484 + 0.595346i) q^{13} +(-0.694593 - 3.93923i) q^{16} +(-7.67107 - 0.671131i) q^{17} +(-1.79302 + 3.84514i) q^{18} +(4.46410 + 0.267949i) q^{20} +(-1.45100 + 4.78483i) q^{25} +(-4.83013 - 8.36603i) q^{26} +(2.54465 + 4.40746i) q^{29} +(4.63382 - 3.24464i) q^{32} +(-3.72459 - 10.2332i) q^{34} -6.00000 q^{36} +(-3.95348 - 4.62277i) q^{37} +(2.32464 + 5.88184i) q^{40} +(-8.60824 - 7.22317i) q^{41} +(1.55859 - 6.52463i) q^{45} +(-2.39414 + 6.57785i) q^{49} +(-7.00000 + 1.00000i) q^{50} +(7.83601 - 11.1910i) q^{52} +(4.29446 - 6.13313i) q^{53} +(-4.12823 + 5.89572i) q^{58} +(0.0340722 - 0.0406056i) q^{61} +(6.92820 + 4.00000i) q^{64} +(10.1340 + 11.4282i) q^{65} +(10.8900 - 10.8900i) q^{68} +(-3.58603 - 7.69028i) q^{72} +(12.0263 + 12.0263i) q^{73} +(3.56218 - 7.83013i) q^{74} +(-6.14946 + 6.49493i) q^{80} +(-1.56283 + 8.86327i) q^{81} +(4.11312 - 15.3504i) q^{82} +(9.01333 + 14.6710i) q^{85} +(2.43462 + 13.8074i) q^{89} +(9.29423 - 1.90192i) q^{90} +(-9.21335 + 2.46871i) q^{97} +(-9.86182 + 0.862798i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{8}+O(q^{10}) \) 12 * q - 12 * q^8	\( 12 q - 12 q^{8} - 6 q^{17} + 12 q^{20} - 6 q^{26} - 30 q^{34} - 72 q^{36} + 24 q^{41} - 84 q^{50} - 18 q^{58} + 72 q^{61} + 132 q^{65} + 30 q^{73} - 30 q^{74} - 42 q^{85} - 60 q^{89} + 18 q^{90}+O(q^{100}) \) 12 * q - 12 * q^8 - 6 * q^17 + 12 * q^20 - 6 * q^26 - 30 * q^34 - 72 * q^36 + 24 * q^41 - 84 * q^50 - 18 * q^58 + 72 * q^61 + 132 * q^65 + 30 * q^73 - 30 * q^74 - 42 * q^85 - 60 * q^89 + 18 * q^90

Introduction

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