LMFDB - Embedded newform 740.2.ce.b.447.1

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			447.1
Root			$-0.642788 + 0.766044i$ of defining polynomial
Character	$\chi$	$=$	740.447
Dual form			740.2.ce.b.543.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40883 + 0.123257i) q^{2} +(1.96962 - 0.347296i) q^{4} +(2.22141 + 0.255652i) q^{5} +(-2.73205 + 0.732051i) q^{8} +(-2.95442 - 0.520945i) q^{9} +O(q^{10})$	\(q+(-1.40883 + 0.123257i) q^{2} +(1.96962 - 0.347296i) q^{4} +(2.22141 + 0.255652i) q^{5} +(-2.73205 + 0.732051i) q^{8} +(-2.95442 - 0.520945i) q^{9} +(-3.16110 - 0.0863678i) q^{10} +(3.91800 - 5.59549i) q^{13} +(3.75877 - 1.36808i) q^{16} +(-3.67389 - 5.24685i) q^{17} +(4.22650 + 0.369771i) q^{18} +(4.46410 - 0.267949i) q^{20} +(4.86928 + 1.13581i) q^{25} +(-4.83013 + 8.36603i) q^{26} +(2.83786 - 4.91531i) q^{29} +(-5.12685 + 2.39069i) q^{32} +(5.82260 + 6.93910i) q^{34} -6.00000 q^{36} +(-2.02670 - 5.73520i) q^{37} +(-6.25614 + 0.927726i) q^{40} +(1.89932 + 10.7716i) q^{41} +(-6.42979 - 1.91253i) q^{45} +(-4.49951 + 5.36231i) q^{49} +(-7.00000 - 1.00000i) q^{50} +(5.77367 - 12.3817i) q^{52} +(3.16421 - 6.78568i) q^{53} +(-3.39222 + 7.27463i) q^{58} +(13.3483 - 2.35366i) q^{61} +(6.92820 - 4.00000i) q^{64} +(10.1340 - 11.4282i) q^{65} +(-9.05836 - 9.05836i) q^{68} +(8.45299 - 0.739541i) q^{72} +(12.0263 - 12.0263i) q^{73} +(3.56218 + 7.83013i) q^{74} +(8.69951 - 2.07812i) q^{80} +(8.45723 + 3.07818i) q^{81} +(-4.00349 - 14.9412i) q^{82} +(-6.81982 - 12.5946i) q^{85} +(-3.68792 + 1.34229i) q^{89} +(9.29423 + 1.90192i) q^{90} +(-9.81006 - 2.62860i) q^{97} +(5.67812 - 8.10919i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.40883	+	0.123257i	−0.996195	+	0.0871557i
$2$	−1.40883	+	0.123257i	−0.996195	+	0.0871557i
$3$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$3$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$4$	1.96962	−	0.347296i	0.984808	−	0.173648i
$5$	2.22141	+	0.255652i	0.993443	+	0.114331i
$5$	2.22141	+	0.255652i	0.993443	+	0.114331i
$6$		0			0
$7$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$7$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$8$	−2.73205	+	0.732051i	−0.965926	+	0.258819i
$9$	−2.95442	−	0.520945i	−0.984808	−	0.173648i
$10$	−3.16110	−	0.0863678i	−0.999627	−	0.0273119i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$		0			0
$13$	3.91800	−	5.59549i	1.08666	−	1.55191i	0.280833	−	0.959757i	$-0.409389\pi$
$13$	3.91800	−	5.59549i	1.08666	−	1.55191i	0.805826	−	0.592153i	$-0.201722\pi$
$14$		0			0
$15$		0			0
$16$	3.75877	−	1.36808i	0.939693	−	0.342020i
$17$	−3.67389	−	5.24685i	−0.891048	−	1.27255i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−3.67389	−	5.24685i	−0.891048	−	1.27255i	0.0703875	−	0.997520i	$-0.477576\pi$
$18$	4.22650	+	0.369771i	0.996195	+	0.0871557i
$19$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$19$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$20$	4.46410	−	0.267949i	0.998203	−	0.0599153i
$21$		0			0
$22$		0			0
$23$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$23$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$24$		0			0
$25$	4.86928	+	1.13581i	0.973857	+	0.227163i
$26$	−4.83013	+	8.36603i	−0.947266	+	1.64071i
$27$		0			0
$28$		0			0
$29$	2.83786	−	4.91531i	0.526977	−	0.912750i	−0.472529	−	0.881315i	$-0.656659\pi$
$29$	2.83786	−	4.91531i	0.526977	−	0.912750i	0.999506	−	0.0314353i	$-0.0100078\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−5.12685	+	2.39069i	−0.906308	+	0.422618i
$33$		0			0
$34$	5.82260	+	6.93910i	0.998568	+	1.19005i
$35$		0			0
$36$	−6.00000			−1.00000
$37$	−2.02670	−	5.73520i	−0.333187	−	0.942861i
$37$	−2.02670	−	5.73520i	−0.333187	−	0.942861i
$38$		0			0
$39$		0			0
$40$	−6.25614	+	0.927726i	−0.989183	+	0.146686i
$41$	1.89932	+	10.7716i	0.296624	+	1.68224i	0.660529	+	0.750801i	$0.270332\pi$
$41$	1.89932	+	10.7716i	0.296624	+	1.68224i	−0.363905	+	0.931436i	$0.618557\pi$
$42$		0			0
$43$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$43$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$44$		0			0
$45$	−6.42979	−	1.91253i	−0.958497	−	0.285104i
$46$		0			0
$47$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$47$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$48$		0			0
$49$	−4.49951	+	5.36231i	−0.642788	+	0.766044i
$50$	−7.00000	−	1.00000i	−0.989949	−	0.141421i
$51$		0			0
$52$	5.77367	−	12.3817i	0.800664	−	1.71703i
$53$	3.16421	−	6.78568i	0.434638	−	0.932085i	−0.559983	−	0.828504i	$-0.689192\pi$
$53$	3.16421	−	6.78568i	0.434638	−	0.932085i	0.994621	−	0.103581i	$-0.0330300\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−3.39222	+	7.27463i	−0.445420	+	0.955206i
$59$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$59$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$60$		0			0
$61$	13.3483	−	2.35366i	1.70907	−	0.301355i	0.768221	−	0.640184i	$-0.221142\pi$
$61$	13.3483	−	2.35366i	1.70907	−	0.301355i	0.940848	+	0.338829i	$0.110031\pi$
$62$		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		−0.422618	−	0.906308i	$-0.638889\pi$
$67$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$68$	−9.05836	−	9.05836i	−1.09849	−	1.09849i
$69$		0			0
$70$		0			0
$71$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$71$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$72$	8.45299	−	0.739541i	0.996195	−	0.0871557i
$73$	12.0263	−	12.0263i	1.40757	−	1.40757i	0.635323	−	0.772246i	$-0.280867\pi$
$73$	12.0263	−	12.0263i	1.40757	−	1.40757i	0.772246	−	0.635323i	$-0.219133\pi$
$74$	3.56218	+	7.83013i	0.414095	+	0.910234i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$79$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$80$	8.69951	−	2.07812i	0.972634	−	0.232341i
$81$	8.45723	+	3.07818i	0.939693	+	0.342020i
$82$	−4.00349	−	14.9412i	−0.442112	−	1.64998i
$83$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$83$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$84$		0			0
$85$	−6.81982	−	12.5946i	−0.739713	−	1.36608i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.68792	+	1.34229i	−0.390919	+	0.142283i	−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−3.68792	+	1.34229i	−0.390919	+	0.142283i	0.139080	+	0.990281i	$0.455585\pi$
$90$	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
$97$	−9.81006	−	2.62860i	−0.996061	−	0.266894i	−0.276267	−	0.961081i	$-0.589097\pi$
$97$	−9.81006	−	2.62860i	−0.996061	−	0.266894i	−0.719794	+	0.694187i	$0.755764\pi$
$98$	5.67812	−	8.10919i	0.573576	−	0.819152i
$99$		0			0
$100$	9.98508	+	0.546034i	0.998508	+	0.0546034i
$101$	−9.67443	−	16.7566i	−0.962642	−	1.66734i	−0.715822	−	0.698283i	$-0.753948\pi$
$101$	−9.67443	−	16.7566i	−0.962642	−	1.66734i	−0.246820	−	0.969061i	$-0.579386\pi$
$102$		0			0
$103$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$103$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$104$	−6.60800	+	18.1553i	−0.647968	+	1.78028i
$105$		0			0
$106$	−3.62147	+	9.94990i	−0.351748	+	0.966419i
$107$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$107$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$108$		0			0
$109$	12.8249	+	10.7614i	1.22840	+	1.03075i	0.998341	+	0.0575772i	$0.0183375\pi$
$109$	12.8249	+	10.7614i	1.22840	+	1.03075i	0.230063	+	0.973176i	$0.426107\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.53952	+	17.5968i	0.144826	+	1.65537i	0.626795	+	0.779184i	$0.284366\pi$
$113$	1.53952	+	17.5968i	0.144826	+	1.65537i	−0.481969	+	0.876188i	$0.660078\pi$
$114$		0			0
$115$		0			0
$116$	3.88242	−	10.6669i	0.360473	−	0.990392i
$117$	−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
$122$	−18.5153	+	4.96117i	−1.67630	+	0.449163i
$123$		0			0
$124$		0			0
$125$	10.5263	+	3.76795i	0.941499	+	0.337016i
$126$		0			0
$127$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$127$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$128$	−9.26765	+	6.48928i	−0.819152	+	0.573576i
$129$		0			0
$130$	−12.8685	+	17.3495i	−1.12864	+	1.52165i
$131$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$131$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	13.8782	+	11.6452i	1.19005	+	0.998568i
$137$	−21.8430	+	5.85281i	−1.86617	+	0.500039i	−0.866173	+	0.499745i	$0.833427\pi$
$137$	−21.8430	+	5.85281i	−1.86617	+	0.500039i	−1.00000		0.000294847i	$0.999906\pi$
$138$		0			0
$139$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$139$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−11.8177	+	2.08378i	−0.984808	+	0.173648i
$145$	7.56064	−	10.1934i	0.627877	−	0.846515i
$146$	−15.4607	+	18.4253i	−1.27954	+	1.52489i
$147$		0			0
$148$	−5.98363	−	10.5923i	−0.491851	−	0.870679i
$149$			23.5804i			1.93178i	0.258954	+	0.965890i	$0.416622\pi$
$149$			23.5804i			1.93178i	−0.258954	+	0.965890i	$0.583378\pi$
$150$		0			0
$151$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$151$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$152$		0			0
$153$	8.12090	+	17.4153i	0.656536	+	1.40795i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	12.1786	−	8.52756i	0.971960	−	0.680574i	0.0242497	−	0.999706i	$-0.492280\pi$
$157$	12.1786	−	8.52756i	0.971960	−	0.680574i	0.947710	+	0.319132i	$0.103391\pi$
$158$		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		−0.906308	−	0.422618i	$-0.861111\pi$
$163$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$164$	7.48186	+	20.5562i	0.584235	+	1.60517i
$165$		0			0
$166$		0			0
$167$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$167$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$168$		0			0
$169$	−11.5125	−	31.6303i	−0.885576	−	2.43310i
$170$	11.1604	+	16.9031i	0.855960	+	1.29641i
$171$		0			0
$172$		0			0
$173$	−6.22704	+	0.544796i	−0.473433	+	0.0414200i	−0.321376	−	0.946952i	$-0.604145\pi$
$173$	−6.22704	+	0.544796i	−0.473433	+	0.0414200i	−0.152057	+	0.988372i	$0.548590\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	5.03021	−	2.34563i	0.377031	−	0.175812i
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$	−13.3284	−	1.53391i	−0.993443	−	0.114331i
$181$	0.162022	+	0.918873i	0.0120430	+	0.0682993i	0.990237	−	0.139394i	$-0.0445155\pi$
$181$	0.162022	+	0.918873i	0.0120430	+	0.0682993i	−0.978194	+	0.207693i	$0.933404\pi$
$182$		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
$193$	2.21941	−	0.594690i	0.159757	−	0.0428067i	−0.178054	−	0.984021i	$-0.556980\pi$
$193$	2.21941	−	0.594690i	0.159757	−	0.0428067i	0.337811	+	0.941214i	$0.390314\pi$
$194$	14.1447	+	2.49410i	1.01553	+	0.179066i
$195$		0			0
$196$	−7.00000	+	12.1244i	−0.500000	+	0.866025i
$197$	2.28539	+	26.1221i	0.162827	+	1.86112i	0.437028	+	0.899448i	$0.356031\pi$
$197$	2.28539	+	26.1221i	0.162827	+	1.86112i	−0.274201	+	0.961673i	$0.588413\pi$
$198$		0			0
$199$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$199$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$200$	−14.1346	+	0.461459i	−0.999467	+	0.0326301i
$201$		0			0
$202$	15.6950	+	22.4148i	1.10430	+	1.57710i
$203$		0			0
$204$		0			0
$205$	1.46538	+	24.4136i	0.102347	+	1.70512i
$206$		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	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$	3.87564	−	14.4641i	0.266180	−	0.993399i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−19.3946	−	13.5802i	−1.31357	−	0.919768i
$219$		0			0
$220$		0			0
$221$	−43.7530			−2.94315
$222$		0			0
$223$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$223$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$224$		0			0
$225$	−13.7942	−	5.89230i	−0.919615	−	0.392820i
$226$	−4.33786	−	24.6012i	−0.288550	−	1.63645i
$227$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$227$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$228$		0			0
$229$	−10.3423	+	28.4152i	−0.683438	+	1.87773i	−0.302281	+	0.953219i	$0.597748\pi$
$229$	−10.3423	+	28.4152i	−0.683438	+	1.87773i	−0.381157	+	0.924510i	$0.624474\pi$
$230$		0			0
$231$		0			0
$232$	−4.15491	+	15.5063i	−0.272783	+	1.01804i
$233$	6.34277	+	23.6715i	0.415528	+	1.55077i	0.783775	+	0.621045i	$0.213292\pi$
$233$	6.34277	+	23.6715i	0.415528	+	1.55077i	−0.368246	+	0.929728i	$0.620042\pi$
$234$	18.6285	−	22.2006i	1.21778	−	1.45130i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$239$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$240$		0			0
$241$	5.18845	+	6.18336i	0.334218	+	0.398305i	0.906813	−	0.421533i	$-0.138508\pi$
$241$	5.18845	+	6.18336i	0.334218	+	0.398305i	−0.572596	+	0.819838i	$0.694063\pi$
$242$	8.92276	+	12.7430i	0.573576	+	0.819152i
$243$		0			0
$244$	25.4735	−	9.27160i	1.63077	−	0.593553i
$245$	−11.3661	+	10.7616i	−0.726155	+	0.687531i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−15.2942	−	4.01097i	−0.967289	−	0.253676i
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	12.2567	−	10.2846i	0.766044	−	0.642788i
$257$	24.9703	−	2.18462i	1.55761	−	0.136273i	0.724457	−	0.689320i	$-0.242091\pi$
$257$	24.9703	−	2.18462i	1.55761	−	0.136273i	0.833150	+	0.553047i	$0.186535\pi$
$258$		0			0
$259$		0			0
$260$	15.9911	−	26.0287i	0.991723	−	1.61423i
$261$	−10.9448	+	13.0435i	−0.677468	+	0.807375i
$262$		0			0
$263$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$263$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$264$		0			0
$265$	8.76378	−	14.2648i	0.538355	−	0.876280i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.74167	+	2.16025i	−0.228134	+	0.131713i	−0.609711	−	0.792624i	$-0.708714\pi$
$269$	−3.74167	+	2.16025i	−0.228134	+	0.131713i	0.381577	+	0.924337i	$0.375381\pi$
$270$		0			0
$271$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$271$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$272$	−20.9874	−	14.6955i	−1.27255	−	0.891048i
$273$		0			0
$274$	30.0517	−	10.9379i	1.81549	−	0.660784i
$275$		0			0
$276$		0			0
$277$	−1.77553	+	20.2943i	−0.106681	+	1.21937i	0.734498	+	0.678611i	$0.237418\pi$
$277$	−1.77553	+	20.2943i	−0.106681	+	1.21937i	−0.841178	+	0.540758i	$0.818138\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4.41506	−	12.1303i	−0.263380	−	0.723631i	−0.998934	−	0.0461646i	$-0.985300\pi$
$281$	−4.41506	−	12.1303i	−0.263380	−	0.723631i	0.735554	−	0.677466i	$-0.236922\pi$
$282$		0			0
$283$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$283$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	16.3923	−	4.39230i	0.965926	−	0.258819i
$289$	−8.21769	+	22.5779i	−0.483394	+	1.32811i
$290$	−9.39527	+	15.2927i	−0.551709	+	0.898017i
$291$		0			0
$292$	19.5105	−	27.8638i	1.14176	−	1.63061i
$293$	1.98525	−	22.6915i	0.115980	−	1.32565i	−0.685693	−	0.727890i	$-0.740501\pi$
$293$	1.98525	−	22.6915i	0.115980	−	1.32565i	0.801673	−	0.597763i	$-0.203944\pi$
$294$		0			0
$295$		0			0
$296$	9.73550	+	14.1852i	0.565864	+	0.824498i
$297$		0			0
$298$	−2.90644	−	33.2208i	−0.168366	−	1.92443i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	30.2536	−	1.81592i	1.73232	−	0.103979i
$306$	−13.5875	−	23.5343i	−0.776748	−	1.34537i
$307$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$307$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$311$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$312$		0			0
$313$	17.7286	−	12.4137i	1.00208	−	0.701664i	0.0472702	−	0.998882i	$-0.484948\pi$
$313$	17.7286	−	12.4137i	1.00208	−	0.701664i	0.954810	+	0.297218i	$0.0960589\pi$
$314$	−16.1066	+	13.5150i	−0.908945	+	0.762696i
$315$		0			0
$316$		0			0
$317$	−28.7953	−	13.4275i	−1.61730	−	0.754161i	−0.617822	−	0.786318i	$-0.711985\pi$
$317$	−28.7953	−	13.4275i	−1.61730	−	0.754161i	−0.999483	+	0.0321569i	$0.989762\pi$
$318$		0			0
$319$		0			0
$320$	16.4130	−	7.11441i	0.917512	−	0.397708i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	17.7265	+	3.12567i	0.984808	+	0.173648i
$325$	25.4333	−	22.7959i	1.41079	−	1.26449i
$326$		0			0
$327$		0			0
$328$	−13.0744	−	28.0381i	−0.721912	−	1.54814i
$329$		0			0
$330$		0			0
$331$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$331$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$332$		0			0
$333$	3.00000	+	18.0000i	0.164399	+	0.986394i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−2.07044	+	2.95690i	−0.112784	+	0.161073i	−0.871576	−	0.490261i	$-0.836901\pi$
$337$	−2.07044	+	2.95690i	−0.112784	+	0.161073i	0.758791	+	0.651334i	$0.225790\pi$
$338$	20.1178	+	43.1428i	1.09426	+	2.34666i
$339$		0			0
$340$	−17.8065	−	22.4381i	−0.965693	−	1.21688i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	8.70571	−	1.53505i	0.468022	−	0.0825248i
$347$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$347$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$348$		0			0
$349$	5.50632	+	15.1285i	0.294747	+	0.809810i	0.995356	+	0.0962646i	$0.0306895\pi$
$349$	5.50632	+	15.1285i	0.294747	+	0.809810i	−0.700609	+	0.713545i	$0.747088\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−26.7109	+	18.7032i	−1.42168	+	0.995471i	−0.425797	+	0.904819i	$0.640006\pi$
$353$	−26.7109	+	18.7032i	−1.42168	+	0.995471i	−0.995883	+	0.0906521i	$0.971105\pi$
$354$		0			0
$355$		0			0
$356$	−6.79761	+	3.92460i	−0.360273	+	0.208004i
$357$		0			0
$358$		0			0
$359$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$359$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$360$	18.9666	+	0.518207i	0.999627	+	0.0273119i
$361$	3.29932	−	18.7113i	0.173648	−	0.984808i
$362$	−0.341519	−	1.27457i	−0.0179499	−	0.0669898i
$363$		0			0
$364$		0			0
$365$	29.7898	−	23.6407i	1.55927	−	1.23741i
$366$		0			0
$367$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$367$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$368$		0			0
$369$		−	32.8132i		−	1.70819i
$370$	5.91125	+	18.3046i	0.307311	+	0.951609i
$371$		0			0
$372$		0			0
$373$	−3.35931	+	38.3971i	−0.173938	+	1.98812i	−0.0218237	+	0.999762i	$0.506947\pi$
$373$	−3.35931	+	38.3971i	−0.173938	+	1.98812i	−0.152115	+	0.988363i	$0.548608\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−16.3848	−	35.1374i	−0.843862	−	1.80967i
$378$		0			0
$379$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$379$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$383$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$384$		0			0
$385$		0			0
$386$	−3.05348	+	1.11138i	−0.155418	+	0.0565676i
$387$		0			0
$388$	−20.2350	−	1.77033i	−1.02727	−	0.0898749i
$389$	28.4782	−	23.8961i	1.44390	−	1.21158i	0.507020	−	0.861934i	$-0.330747\pi$
$389$	28.4782	−	23.8961i	1.44390	−	1.21158i	0.936883	−	0.349644i	$-0.113697\pi$
$390$		0			0
$391$		0			0
$392$	8.36741	−	17.9440i	0.422618	−	0.906308i
$393$		0			0
$394$	−6.43945	−	36.5199i	−0.324415	−	1.83985i
$395$		0			0
$396$		0			0
$397$	−3.95120	+	14.7461i	−0.198305	+	0.740084i	0.793082	+	0.609115i	$0.208475\pi$
$397$	−3.95120	+	14.7461i	−0.198305	+	0.740084i	−0.991387	+	0.130969i	$0.958191\pi$
$398$		0			0
$399$		0			0
$400$	19.8564	−	2.39230i	0.992820	−	0.119615i
$401$			21.7321i			1.08525i	0.839976	+	0.542623i	$0.182569\pi$
$401$			21.7321i			1.08525i	−0.839976	+	0.542623i	$0.817431\pi$
$402$		0			0
$403$		0			0
$404$	−24.8744	−	29.6442i	−1.23755	−	1.47485i
$405$	18.0000	+	9.00000i	0.894427	+	0.447214i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−20.5185	−	17.2171i	−1.01458	−	0.851331i	−0.0256402	−	0.999671i	$-0.508162\pi$
$409$	−20.5185	−	17.2171i	−1.01458	−	0.851331i	−0.988936	+	0.148340i	$0.952607\pi$
$410$	−5.07362	−	34.2140i	−0.250568	−	1.68971i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−6.70994	+	38.0540i	−0.328982	+	1.86575i
$417$		0			0
$418$		0			0
$419$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$419$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$420$		0			0
$421$	−32.7075	+	18.8837i	−1.59406	+	0.920334i	−0.601466	+	0.798899i	$0.705416\pi$
$421$	−32.7075	+	18.8837i	−1.59406	+	0.920334i	−0.992599	+	0.121435i	$0.961250\pi$
$422$		0			0
$423$		0			0
$424$	−3.67733	+	20.8552i	−0.178587	+	1.01282i
$425$	−11.9297	−	29.7213i	−0.578677	−	1.44169i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$431$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$432$		0			0
$433$	5.35021	+	19.9673i	0.257115	+	0.959565i	0.966902	+	0.255149i	$0.0821245\pi$
$433$	5.35021	+	19.9673i	0.257115	+	0.959565i	−0.709787	+	0.704416i	$0.751209\pi$
$434$		0			0
$435$		0			0
$436$	28.9975	+	16.7417i	1.38873	+	0.801784i
$437$		0			0
$438$		0			0
$439$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$439$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$440$		0			0
$441$	16.0869	−	13.4985i	0.766044	−	0.642788i
$442$	61.6407	−	5.39286i	2.93195	−	0.256512i
$443$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$443$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$444$		0			0
$445$	−8.53553	+	2.03895i	−0.404623	+	0.0966556i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	30.1870	+	10.9872i	1.42461	+	0.518517i	0.935383	−	0.353637i	$-0.115055\pi$
$449$	30.1870	+	10.9872i	1.42461	+	0.518517i	0.489231	+	0.872154i	$0.337278\pi$
$450$	20.1600	+	6.60103i	0.950352	+	0.311176i
$451$		0			0
$452$	9.14359	+	34.1244i	0.430078	+	1.60507i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	8.60069	+	6.02227i	0.402323	+	0.281710i	0.757174	−	0.653213i	$-0.226579\pi$
$457$	8.60069	+	6.02227i	0.402323	+	0.281710i	−0.354851	+	0.934923i	$0.615468\pi$
$458$	11.0682	−	41.3070i	0.517182	−	1.93015i
$459$		0			0
$460$		0			0
$461$	42.2571	+	7.45106i	1.96811	+	0.347031i	0.990846	+	0.134999i	$0.0431030\pi$
$461$	42.2571	+	7.45106i	1.96811	+	0.347031i	0.977263	+	0.212032i	$0.0680081\pi$
$462$		0			0
$463$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$463$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$464$	3.94231	−	22.3579i	0.183017	−	1.03794i
$465$		0			0
$466$	−11.8536	−	32.5674i	−0.549106	−	1.50866i
$467$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$467$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$468$	−23.5080	+	33.5729i	−1.08666	+	1.55191i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−12.8834	+	18.3994i	−0.589890	+	0.842450i
$478$		0			0
$479$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$479$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$480$		0			0
$481$	−40.0318	−	11.1302i	−1.82530	−	0.507492i
$482$	−8.07180	−	8.07180i	−0.367660	−	0.367660i
$483$		0			0
$484$	−14.1413	−	16.8530i	−0.642788	−	0.766044i
$485$	−21.1201	−	8.34715i	−0.959015	−	0.379025i
$486$		0			0
$487$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$487$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$488$	−34.7451	+	16.2019i	−1.57284	+	0.733426i
$489$		0			0
$490$	14.6865	−	16.5622i	0.663470	−	0.748203i
$491$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$491$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$492$		0			0
$493$	−36.2159	+	3.16848i	−1.63108	+	0.142701i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$499$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$500$	22.0413	+	3.76567i	0.985718	+	0.168406i
$501$		0			0
$502$		0			0
$503$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$503$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$504$		0			0
$505$	−17.2070	−	39.6965i	−0.765700	−	1.76647i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−39.5241	−	6.96917i	−1.75188	−	0.308903i	−0.796575	−	0.604540i	$-0.793357\pi$
$509$	−39.5241	−	6.96917i	−1.75188	−	0.308903i	−0.955300	+	0.295637i	$0.904468\pi$
$510$		0			0
$511$		0			0
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$		0			0
$514$	−34.9097	+	6.15553i	−1.53980	+	0.271509i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−19.3205	+	38.6410i	−0.847260	+	1.69452i
$521$	34.9630	−	29.3375i	1.53176	−	1.28530i	0.752539	−	0.658548i	$-0.228829\pi$
$521$	34.9630	−	29.3375i	1.53176	−	1.28530i	0.779220	−	0.626751i	$-0.215616\pi$
$522$	13.8117	−	19.7252i	0.604523	−	0.863348i
$523$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$523$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$524$		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
$533$	67.7138	+	31.5754i	2.93301	+	1.36768i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	5.00512	−	3.50462i	0.215786	−	0.151095i
$539$		0			0
$540$		0			0
$541$	28.7163	−	16.5793i	1.23461	−	0.712802i	0.266622	−	0.963801i	$-0.414093\pi$
$541$	28.7163	−	16.5793i	1.23461	−	0.712802i	0.967987	+	0.250999i	$0.0807592\pi$
$542$		0			0
$543$		0			0
$544$	31.3791	+	18.1167i	1.34537	+	0.776748i
$545$	25.7382	+	27.1841i	1.10250	+	1.16444i
$546$		0			0
$547$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$547$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$548$	−40.9896	+	19.1138i	−1.75099	+	0.816500i
$549$	−40.6625			−1.73543
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		−	28.8102i		−	1.22403i
$555$		0			0
$556$		0			0
$557$	41.2784	−	3.61140i	1.74902	−	0.153020i	0.832770	−	0.553619i	$-0.186754\pi$
$557$	41.2784	−	3.61140i	1.74902	−	0.153020i	0.916253	+	0.400599i	$0.131198\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	7.71521	+	16.5453i	0.325446	+	0.697922i
$563$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$563$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$564$		0			0
$565$	−1.07877	+	39.4833i	−0.0453841	+	1.66108i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.32954	+	16.1592i	0.391115	+	0.677430i	0.992597	−	0.121456i	$-0.0387563\pi$
$569$	9.32954	+	16.1592i	0.391115	+	0.677430i	−0.601482	+	0.798886i	$0.705423\pi$
$570$		0			0
$571$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$571$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−22.5526	+	8.20848i	−0.939693	+	0.342020i
$577$	−19.8132	+	42.4896i	−0.824835	+	1.76886i	−0.214496	+	0.976725i	$0.568811\pi$
$577$	−19.8132	+	42.4896i	−0.824835	+	1.76886i	−0.610340	+	0.792140i	$0.708967\pi$
$578$	8.79446	−	32.8214i	0.365801	−	1.36519i
$579$		0			0
$580$	11.3514	−	22.7029i	0.471342	−	0.942685i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−24.0526	+	41.6603i	−0.995302	+	1.72391i
$585$	−35.8935	+	28.4845i	−1.48401	+	1.17769i
$586$			32.2132i			1.33072i
$587$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$587$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−15.4641	−	18.7846i	−0.635571	−	0.772043i
$593$	27.9243	−	27.9243i	1.14671	−	1.14671i	0.159520	−	0.987195i	$-0.449006\pi$
$593$	27.9243	−	27.9243i	1.14671	−	1.14671i	0.987195	−	0.159520i	$-0.0509945\pi$
$594$		0			0
$595$		0			0
$596$	8.18938	+	46.4443i	0.335450	+	1.90243i
$597$		0			0
$598$		0			0
$599$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$599$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$600$		0			0
$601$	−0.262724	+	1.48998i	−0.0107167	+	0.0607775i	−0.989697	−	0.143177i	$-0.954268\pi$
$601$	−0.262724	+	1.48998i	−0.0107167	+	0.0607775i	0.978980	+	0.203954i	$0.0653794\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−9.78231	−	22.5678i	−0.397708	−	0.917512i
$606$		0			0
$607$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$607$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$608$		0			0
$609$		0			0
$610$	−42.3984	+	6.28728i	−1.71666	+	0.254565i
$611$		0			0
$612$	22.0433	+	31.4811i	0.891048	+	1.27255i
$613$	15.6404	−	33.5408i	0.631708	−	1.35470i	−0.286300	−	0.958140i	$-0.592425\pi$
$613$	15.6404	−	33.5408i	0.631708	−	1.35470i	0.918008	−	0.396562i	$-0.129797\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−2.47723	−	28.3148i	−0.0997293	−	1.13991i	−0.866905	−	0.498474i	$-0.833894\pi$
$617$	−2.47723	−	28.3148i	−0.0997293	−	1.13991i	0.767175	−	0.641437i	$-0.221662\pi$
$618$		0			0
$619$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$619$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	22.4198	+	11.0612i	0.896794	+	0.442448i
$626$	−23.4465	+	19.6740i	−0.937112	+	0.786331i
$627$		0			0
$628$	21.0256	−	21.0256i	0.839013	−	0.839013i
$629$	−22.6459	+	31.7043i	−0.902951	+	1.26413i
$630$		0			0
$631$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$631$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$632$		0			0
$633$		0			0
$634$	42.2227	+	15.3678i	1.67688	+	0.610334i
$635$		0			0
$636$		0			0
$637$	12.3756	+	46.1865i	0.490341	+	1.82998i
$638$		0			0
$639$		0			0
$640$	−22.2462	+	12.0460i	−0.879358	+	0.476161i
$641$	−19.9256	−	16.7196i	−0.787014	−	0.660383i	0.157991	−	0.987441i	$-0.449498\pi$
$641$	−19.9256	−	16.7196i	−0.787014	−	0.660383i	−0.945004	+	0.327058i	$0.893943\pi$
$642$		0			0
$643$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$643$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$647$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$648$	−25.3590	−	2.21862i	−0.996195	−	0.0871557i
$649$		0			0
$650$	−33.0215	+	35.2504i	−1.29521	+	1.38264i
$651$		0			0
$652$		0			0
$653$	−2.84999	+	4.07020i	−0.111529	+	0.159279i	−0.871036	−	0.491220i	$-0.836551\pi$
$653$	−2.84999	+	4.07020i	−0.111529	+	0.159279i	0.759507	+	0.650499i	$0.225440\pi$
$654$		0			0
$655$		0			0
$656$	21.8755	+	37.8895i	0.854094	+	1.47933i
$657$	−41.7957	+	29.2657i	−1.63061	+	1.14176i
$658$		0			0
$659$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$659$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$660$		0			0
$661$	10.4620	−	28.7440i	0.406924	−	1.11801i	−0.551875	−	0.833927i	$-0.686087\pi$
$661$	10.4620	−	28.7440i	0.406924	−	1.11801i	0.958799	−	0.284087i	$-0.0916904\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−6.44512	−	24.9892i	−0.249743	−	0.968312i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−34.6399	+	16.1529i	−1.33527	+	0.622647i	−0.953439	−	0.301585i	$-0.902484\pi$
$673$	−34.6399	+	16.1529i	−1.33527	+	0.622647i	−0.381832	+	0.924232i	$0.624707\pi$
$674$	2.55245	−	4.42097i	0.0983167	−	0.170290i
$675$		0			0
$676$	−33.6603	−	58.3013i	−1.29463	−	2.24236i
$677$	30.3922	−	8.14355i	1.16807	−	0.312982i	0.377883	−	0.925853i	$-0.376652\pi$
$677$	30.3922	−	8.14355i	1.16807	−	0.312982i	0.790183	+	0.612871i	$0.209986\pi$
$678$		0			0
$679$		0			0
$680$	27.8520	+	29.4167i	1.06808	+	1.12808i
$681$		0			0
$682$		0			0
$683$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$683$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$684$		0			0
$685$	−50.0184	+	7.41726i	−1.91111	+	0.283399i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−25.5718	−	44.2917i	−0.974208	−	1.68738i
$690$		0			0
$691$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$691$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$692$	−12.0757	+	3.23567i	−0.459048	+	0.123002i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	49.5390	−	49.5390i	1.87642	−	1.87642i
$698$	−9.62218	−	20.6348i	−0.364205	−	0.781040i
$699$		0			0
$700$		0			0
$701$	−25.7329	+	30.6673i	−0.971919	+	1.15829i	0.0154547	+	0.999881i	$0.495080\pi$
$701$	−25.7329	+	30.6673i	−0.971919	+	1.15829i	−0.987374	+	0.158407i	$0.949364\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	35.3259	−	29.6420i	1.32951	−	1.11559i
$707$		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
$712$	9.09296	−	6.36696i	0.340773	−	0.238612i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$719$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$720$	−26.7846	+	1.60770i	−0.998203	+	0.0599153i
$721$		0			0
$722$	−2.34188	+	26.7678i	−0.0871557	+	0.996195i
$723$		0			0
$724$	0.638242	+	1.75356i	0.0237201	+	0.0651704i
$725$	19.4012	−	20.7108i	0.720543	−	0.769179i
$726$		0			0
$727$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$727$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$728$		0			0
$729$	−23.3827	−	13.5000i	−0.866025	−	0.500000i
$730$	−39.0549	+	36.9776i	−1.44549	+	1.36860i
$731$		0			0
$732$		0			0
$733$	−48.2113	+	22.4813i	−1.78072	+	0.830365i	−0.811435	+	0.584442i	$0.801313\pi$
$733$	−48.2113	+	22.4813i	−1.78072	+	0.830365i	−0.969289	+	0.245923i	$0.920909\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	4.04445	+	46.2283i	0.148878	+	1.70169i
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$	−10.5841	−	25.0595i	−0.389080	−	0.921204i
$741$		0			0
$742$		0			0
$743$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$743$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$744$		0			0
$745$	−6.02838	+	52.3816i	−0.220863	+	1.91911i
$746$		−	54.5091i		−	1.99572i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$		0			0
$753$		0			0
$754$	27.4144	+	47.4832i	0.998374	+	1.72923i
$755$		0			0
$756$		0			0
$757$	30.3538	+	43.3498i	1.10323	+	1.57557i	0.776118	+	0.630588i	$0.217186\pi$
$757$	30.3538	+	43.3498i	1.10323	+	1.57557i	0.327111	+	0.944986i	$0.393925\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	51.5151	−	18.7500i	1.86742	−	0.679685i	0.895177	−	0.445710i	$-0.147049\pi$
$761$	51.5151	−	18.7500i	1.86742	−	0.679685i	0.972243	−	0.233975i	$-0.0751733\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	13.5875	+	40.7626i	0.491258	+	1.47378i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	25.0000	−	43.3013i	0.901523	−	1.56148i	0.0760054	−	0.997107i	$-0.475783\pi$
$769$	25.0000	−	43.3013i	0.901523	−	1.56148i	0.825518	−	0.564376i	$-0.190883\pi$
$770$		0			0
$771$		0			0
$772$	4.16486	−	1.94210i	0.149896	−	0.0698979i
$773$	−45.4992	−	31.8589i	−1.63649	−	1.14588i	−0.845208	−	0.534437i	$-0.820524\pi$
$773$	−45.4992	−	31.8589i	−1.63649	−	1.14588i	−0.791285	−	0.611448i	$-0.790588\pi$
$774$		0			0
$775$		0			0
$776$	28.7259			1.03120
$777$		0			0
$778$	−37.1757	+	37.1757i	−1.33281	+	1.33281i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−9.57656	+	26.3114i	−0.342020	+	0.939693i
$785$	29.2337	−	15.8297i	1.04340	−	0.564986i
$786$		0			0
$787$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$787$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$788$	13.5734	+	50.6567i	0.483533	+	1.80457i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	39.1287	−	83.9117i	1.38950	−	2.97979i
$794$	3.74902	−	21.2617i	0.133048	−	0.754551i
$795$		0			0
$796$		0			0
$797$	−30.0129	−	42.8629i	−1.06311	−	1.51828i	−0.839315	−	0.543645i	$-0.817044\pi$
$797$	−30.0129	−	42.8629i	−1.06311	−	1.51828i	−0.223796	−	0.974636i	$-0.571845\pi$
$798$		0			0
$799$		0			0
$800$	−27.6795	+	5.81779i	−0.978617	+	0.205690i
$801$	11.5949	−	2.04450i	0.409687	−	0.0722389i
$802$	−2.67862	−	30.6168i	−0.0945855	−	1.08112i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	38.6977	+	38.6977i	1.36138	+	1.36138i
$809$	−50.2711	−	18.2972i	−1.76744	−	0.643295i	−0.999998	−	0.00217593i	$-0.999307\pi$
$809$	−50.2711	−	18.2972i	−1.76744	−	0.643295i	−0.767441	−	0.641119i	$-0.778470\pi$
$810$	−26.4683	−	10.4609i	−0.930001	−	0.367557i
$811$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$811$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	31.0293	+	21.7270i	1.08491	+	0.759665i
$819$		0			0
$820$	11.3650	+	47.5765i	0.396883	+	1.66144i
$821$	27.5342	+	10.0216i	0.960950	+	0.349757i	0.774406	−	0.632689i	$-0.218049\pi$
$821$	27.5342	+	10.0216i	0.960950	+	0.349757i	0.186544	+	0.982447i	$0.440271\pi$
$822$		0			0
$823$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$823$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$827$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$828$		0			0
$829$	18.7939	−	6.84040i	0.652737	−	0.237577i	0.00563977	−	0.999984i	$-0.498205\pi$
$829$	18.7939	−	6.84040i	0.652737	−	0.237577i	0.647098	+	0.762407i	$0.275983\pi$
$830$		0			0
$831$		0			0
$832$	4.76277	−	54.4387i	0.165119	−	1.88732i
$833$	44.6660	+	3.90777i	1.54758	+	0.135396i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$839$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$840$		0			0
$841$	−1.60686	−	2.78316i	−0.0554089	−	0.0959710i
$842$	43.7518	−	30.6353i	1.50779	−	1.05576i
$843$		0			0
$844$		0			0
$845$	−17.4875	−	73.2069i	−0.601590	−	2.51839i
$846$		0			0
$847$		0			0
$848$	2.61020	−	29.8347i	0.0896346	−	1.02453i
$849$		0			0
$850$	20.4704	+	40.4019i	0.702127	+	1.38577i
$851$		0			0
$852$		0			0
$853$	4.95955	+	56.6879i	0.169812	+	1.94096i	0.309798	+	0.950802i	$0.399739\pi$
$853$	4.95955	+	56.6879i	0.169812	+	1.94096i	−0.139986	+	0.990153i	$0.544706\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	41.3492	−	41.3492i	1.41246	−	1.41246i	0.671031	−	0.741429i	$-0.265852\pi$
$857$	41.3492	−	41.3492i	1.41246	−	1.41246i	0.741429	−	0.671031i	$-0.234148\pi$
$858$		0			0
$859$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$859$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$863$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$864$		0			0
$865$	−13.9721	−	0.381746i	−0.475064	−	0.0129798i
$866$	−9.99865	−	27.4711i	−0.339768	−	0.933505i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−42.9162	−	20.0121i	−1.45333	−	0.677697i
$873$	27.6137	+	12.8765i	0.934583	+	0.435803i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	22.6390	−	6.06610i	0.764464	−	0.204838i	0.144540	−	0.989499i	$-0.453830\pi$
$877$	22.6390	−	6.06610i	0.764464	−	0.204838i	0.619925	+	0.784661i	$0.287163\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	51.4925	+	18.7417i	1.73482	+	0.631425i	0.998955	−	0.0456985i	$-0.0145514\pi$
$881$	51.4925	+	18.7417i	1.73482	+	0.631425i	0.735870	+	0.677123i	$0.236774\pi$
$882$	−21.0000	+	21.0000i	−0.707107	+	0.707107i
$883$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$883$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$884$	−86.1766	+	15.1953i	−2.89843	+	0.511072i
$885$		0			0
$886$		0			0
$887$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$887$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$888$		0			0
$889$		0			0
$890$	11.7738	−	3.92460i	0.394659	−	0.131553i
$891$		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
$900$	−29.2157	−	6.81489i	−0.973857	−	0.227163i
$901$	−47.2284	+	8.32765i	−1.57341	+	0.277434i
$902$		0			0
$903$		0			0
$904$	−17.0878	−	46.9485i	−0.568333	−	1.56148i
$905$	0.125005	+	2.08261i	0.00415530	+	0.0692283i
$906$		0			0
$907$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$907$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$908$		0			0
$909$	19.8531	+	54.5459i	0.658486	+	1.80917i
$910$		0			0
$911$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$911$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$912$		0			0
$913$		0			0
$914$	−12.8592	−	7.42427i	−0.425345	−	0.245573i
$915$		0			0
$916$	−10.5018	+	59.5589i	−0.346990	+	1.96788i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	−60.4515	−	5.28882i	−1.99086	−	0.174178i
$923$		0			0
$924$		0			0
$925$	−3.35444	−	30.2283i	−0.110293	−	0.993899i
$926$		0			0
$927$		0			0
$928$	−2.79828	+	31.9845i	−0.0918581	+	1.04994i
$929$	−9.38181	+	1.65427i	−0.307807	+	0.0542747i	−0.325418	−	0.945570i	$-0.605505\pi$
$929$	−9.38181	+	1.65427i	−0.307807	+	0.0542747i	0.0176110	+	0.999845i	$0.494394\pi$
$930$		0			0
$931$		0			0
$932$	20.7138	+	44.4210i	0.678505	+	1.45506i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	28.9808	−	50.1962i	0.947266	−	1.64071i
$937$	5.32654	+	60.8826i	0.174011	+	1.98895i	0.145522	+	0.989355i	$0.453514\pi$
$937$	5.32654	+	60.8826i	0.174011	+	1.98895i	0.0284889	+	0.999594i	$0.490930\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	44.7874	−	16.3013i	1.46003	−	0.531407i	0.514655	−	0.857397i	$-0.327920\pi$
$941$	44.7874	−	16.3013i	1.46003	−	0.531407i	0.945373	+	0.325991i	$0.105698\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$947$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$948$		0			0
$949$	−20.1739	−	114.412i	−0.654873	−	3.71397i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−22.7182	−	32.4449i	−0.735914	−	1.05099i	−0.996338	−	0.0854999i	$-0.972751\pi$
$953$	−22.7182	−	32.4449i	−0.735914	−	1.05099i	0.260424	−	0.965494i	$-0.416138\pi$
$954$	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
$962$	57.7700	+	10.7463i	1.86258	+	0.346476i
$963$		0			0
$964$	12.3667	+	10.3769i	0.398305	+	0.334218i
$965$	5.08225	−	0.753649i	0.163603	−	0.0242608i
$966$		0			0
$967$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$967$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$968$	22.0000	+	22.0000i	0.707107	+	0.707107i
$969$		0			0
$970$	30.7835	+	9.15653i	0.988400	+	0.293999i
$971$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$971$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	46.9530	−	27.1083i	1.50293	−	0.867717i
$977$	10.0474	−	21.5467i	0.321445	−	0.689341i	−0.677488	−	0.735534i	$-0.736931\pi$
$977$	10.0474	−	21.5467i	0.321445	−	0.689341i	0.998933	+	0.0461933i	$0.0147090\pi$
$978$		0			0
$979$		0			0
$980$	−18.6495	+	25.1435i	−0.595735	+	0.803181i
$981$	−32.2841	−	38.4747i	−1.03075	−	1.22840i
$982$		0			0
$983$		0			0		0.422618	−	0.906308i	$-0.361111\pi$
$983$		0			0		−0.422618	+	0.906308i	$0.638889\pi$
$984$		0			0
$985$	−1.60140	+	58.6120i	−0.0510249	+	1.86753i
$986$	50.6316	−	8.92771i	1.61244	−	0.284316i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$991$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−52.1268	+	4.56050i	−1.65087	+	0.144433i	−0.874231	−	0.485511i	$-0.838634\pi$
$997$	−52.1268	+	4.56050i	−1.65087	+	0.144433i	−0.776641	+	0.629943i	$0.783078\pi$
$998$		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.447.1	yes	12
4.3	odd	2	CM	740.2.ce.b.447.1	yes	12
5.3	odd	4		740.2.ce.a.3.1	✓	12
20.3	even	4		740.2.ce.a.3.1	✓	12
37.25	even	18		740.2.ce.a.247.1	yes	12
148.99	odd	18		740.2.ce.a.247.1	yes	12
185.173	odd	36	inner	740.2.ce.b.543.1	yes	12
740.543	even	36	inner	740.2.ce.b.543.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.ce.a.3.1	✓	12	5.3	odd	4
740.2.ce.a.3.1	✓	12	20.3	even	4
740.2.ce.a.247.1	yes	12	37.25	even	18
740.2.ce.a.247.1	yes	12	148.99	odd	18
740.2.ce.b.447.1	yes	12	1.1	even	1	trivial
740.2.ce.b.447.1	yes	12	4.3	odd	2	CM
740.2.ce.b.543.1	yes	12	185.173	odd	36	inner
740.2.ce.b.543.1	yes	12	740.543	even	36	inner

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)

\(f(q)\)	\(=\)	\(q+(-1.40883 + 0.123257i) q^{2} +(1.96962 - 0.347296i) q^{4} +(2.22141 + 0.255652i) q^{5} +(-2.73205 + 0.732051i) q^{8} +(-2.95442 - 0.520945i) q^{9} +O(q^{10})\)	\(q+(-1.40883 + 0.123257i) q^{2} +(1.96962 - 0.347296i) q^{4} +(2.22141 + 0.255652i) q^{5} +(-2.73205 + 0.732051i) q^{8} +(-2.95442 - 0.520945i) q^{9} +(-3.16110 - 0.0863678i) q^{10} +(3.91800 - 5.59549i) q^{13} +(3.75877 - 1.36808i) q^{16} +(-3.67389 - 5.24685i) q^{17} +(4.22650 + 0.369771i) q^{18} +(4.46410 - 0.267949i) q^{20} +(4.86928 + 1.13581i) q^{25} +(-4.83013 + 8.36603i) q^{26} +(2.83786 - 4.91531i) q^{29} +(-5.12685 + 2.39069i) q^{32} +(5.82260 + 6.93910i) q^{34} -6.00000 q^{36} +(-2.02670 - 5.73520i) q^{37} +(-6.25614 + 0.927726i) q^{40} +(1.89932 + 10.7716i) q^{41} +(-6.42979 - 1.91253i) q^{45} +(-4.49951 + 5.36231i) q^{49} +(-7.00000 - 1.00000i) q^{50} +(5.77367 - 12.3817i) q^{52} +(3.16421 - 6.78568i) q^{53} +(-3.39222 + 7.27463i) q^{58} +(13.3483 - 2.35366i) q^{61} +(6.92820 - 4.00000i) q^{64} +(10.1340 - 11.4282i) q^{65} +(-9.05836 - 9.05836i) q^{68} +(8.45299 - 0.739541i) q^{72} +(12.0263 - 12.0263i) q^{73} +(3.56218 + 7.83013i) q^{74} +(8.69951 - 2.07812i) q^{80} +(8.45723 + 3.07818i) q^{81} +(-4.00349 - 14.9412i) q^{82} +(-6.81982 - 12.5946i) q^{85} +(-3.68792 + 1.34229i) q^{89} +(9.29423 + 1.90192i) q^{90} +(-9.81006 - 2.62860i) q^{97} +(5.67812 - 8.10919i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{8}+O(q^{10}) \) 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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