LMFDB - Embedded newform 729.2.e.t.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			163.1
Root			$0.0878222i$ of defining polynomial
Character	$\chi$	$=$	729.163
Dual form			729.2.e.t.568.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.162544 + 0.0591613i) q^{2} +(-1.50917 + 1.26634i) q^{4} +(-0.648847 - 3.67980i) q^{5} +(2.32226 + 1.94861i) q^{7} +(0.343364 - 0.594724i) q^{8} +O(q^{10})$	\(q+(-0.162544 + 0.0591613i) q^{2} +(-1.50917 + 1.26634i) q^{4} +(-0.648847 - 3.67980i) q^{5} +(2.32226 + 1.94861i) q^{7} +(0.343364 - 0.594724i) q^{8} +(0.323168 + 0.559743i) q^{10} +(-0.432678 + 2.45384i) q^{11} +(0.718995 + 0.261693i) q^{13} +(-0.492752 - 0.179347i) q^{14} +(0.663574 - 3.76332i) q^{16} +(-2.31139 - 4.00345i) q^{17} +(0.305922 - 0.529872i) q^{19} +(5.63910 + 4.73177i) q^{20} +(-0.0748430 - 0.424456i) q^{22} +(4.99796 - 4.19379i) q^{23} +(-8.42143 + 3.06515i) q^{25} -0.132351 q^{26} -5.97229 q^{28} +(6.15583 - 2.24054i) q^{29} +(5.01792 - 4.21053i) q^{31} +(0.353281 + 2.00355i) q^{32} +(0.612552 + 0.513992i) q^{34} +(5.66369 - 9.80980i) q^{35} +(-2.47984 - 4.29522i) q^{37} +(-0.0183779 + 0.104226i) q^{38} +(-2.41125 - 0.877625i) q^{40} +(-4.94301 - 1.79911i) q^{41} +(0.967320 - 5.48594i) q^{43} +(-2.45442 - 4.25118i) q^{44} +(-0.564280 + 0.977362i) q^{46} +(0.848483 + 0.711962i) q^{47} +(0.380286 + 2.15671i) q^{49} +(1.18752 - 0.996445i) q^{50} +(-1.41648 + 0.515556i) q^{52} +8.84310 q^{53} +9.31038 q^{55} +(1.95627 - 0.712023i) q^{56} +(-0.868041 + 0.728373i) q^{58} +(-2.05804 - 11.6717i) q^{59} +(6.27161 + 5.26250i) q^{61} +(-0.566533 + 0.981264i) q^{62} +(3.64541 + 6.31404i) q^{64} +(0.496458 - 2.81555i) q^{65} +(1.13923 + 0.414644i) q^{67} +(8.55801 + 3.11486i) q^{68} +(-0.340240 + 1.92960i) q^{70} +(2.45973 + 4.26038i) q^{71} +(-2.14972 + 3.72343i) q^{73} +(0.657195 + 0.551452i) q^{74} +(0.209312 + 1.18707i) q^{76} +(-5.78637 + 4.85534i) q^{77} +(11.0833 - 4.03399i) q^{79} -14.2788 q^{80} +0.909895 q^{82} +(-8.47234 + 3.08368i) q^{83} +(-13.2321 + 11.1031i) q^{85} +(0.167323 + 0.948936i) q^{86} +(1.31079 + 1.09989i) q^{88} +(-3.76943 + 6.52884i) q^{89} +(1.15976 + 2.00876i) q^{91} +(-2.23199 + 12.6583i) q^{92} +(-0.180037 - 0.0655279i) q^{94} +(-2.14832 - 0.781924i) q^{95} +(-0.164680 + 0.933947i) q^{97} +(-0.189407 - 0.328062i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8} - 6 q^{10} - 15 q^{11} - 3 q^{13} - 21 q^{14} + 9 q^{16} - 9 q^{17} - 12 q^{19} - 3 q^{20} + 33 q^{22} + 15 q^{23} - 12 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} - 12 q^{31} - 27 q^{32} + 27 q^{34} + 30 q^{35} - 3 q^{37} - 39 q^{38} + 24 q^{40} - 39 q^{41} + 24 q^{43} - 33 q^{44} + 3 q^{46} - 42 q^{47} - 30 q^{49} - 15 q^{50} - 45 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} - 30 q^{58} + 15 q^{59} - 3 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} - 3 q^{67} + 36 q^{68} - 75 q^{70} - 12 q^{73} + 60 q^{74} + 30 q^{76} + 33 q^{77} + 33 q^{79} + 42 q^{80} - 42 q^{82} - 33 q^{83} - 18 q^{85} - 30 q^{86} - 42 q^{88} - 9 q^{89} - 18 q^{91} + 33 q^{92} - 66 q^{94} + 12 q^{95} + 15 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8 - 6 * q^10 - 15 * q^11 - 3 * q^13 - 21 * q^14 + 9 * q^16 - 9 * q^17 - 12 * q^19 - 3 * q^20 + 33 * q^22 + 15 * q^23 - 12 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 - 12 * q^31 - 27 * q^32 + 27 * q^34 + 30 * q^35 - 3 * q^37 - 39 * q^38 + 24 * q^40 - 39 * q^41 + 24 * q^43 - 33 * q^44 + 3 * q^46 - 42 * q^47 - 30 * q^49 - 15 * q^50 - 45 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 - 30 * q^58 + 15 * q^59 - 3 * q^61 - 30 * q^62 - 6 * q^64 - 6 * q^65 - 3 * q^67 + 36 * q^68 - 75 * q^70 - 12 * q^73 + 60 * q^74 + 30 * q^76 + 33 * q^77 + 33 * q^79 + 42 * q^80 - 42 * q^82 - 33 * q^83 - 18 * q^85 - 30 * q^86 - 42 * q^88 - 9 * q^89 - 18 * q^91 + 33 * q^92 - 66 * q^94 + 12 * q^95 + 15 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	−0.162544	+	0.0591613i	−0.114936	+	0.0418333i	−0.398848	−	0.917017i	$-0.630590\pi$
$2$	−0.162544	+	0.0591613i	−0.114936	+	0.0418333i	0.283912	+	0.958850i	$0.408368\pi$
$3$		0			0
$3$		0			0
$4$	−1.50917	+	1.26634i	−0.754584	+	0.633171i
$5$	−0.648847	−	3.67980i	−0.290173	−	1.64565i	−0.686198	−	0.727415i	$-0.740722\pi$
$5$	−0.648847	−	3.67980i	−0.290173	−	1.64565i	0.396025	−	0.918240i	$-0.370389\pi$
$6$		0			0
$7$	2.32226	+	1.94861i	0.877733	+	0.736505i	0.965712	−	0.259617i	$-0.0835964\pi$
$7$	2.32226	+	1.94861i	0.877733	+	0.736505i	−0.0879791	+	0.996122i	$0.528041\pi$
$8$	0.343364	−	0.594724i	0.121398	−	0.210267i
$9$		0			0
$10$	0.323168	+	0.559743i	0.102195	+	0.177006i
$11$	−0.432678	+	2.45384i	−0.130457	+	0.739861i	0.847458	+	0.530862i	$0.178132\pi$
$11$	−0.432678	+	2.45384i	−0.130457	+	0.739861i	−0.977916	+	0.208999i	$0.932979\pi$
$12$		0			0
$13$	0.718995	+	0.261693i	0.199413	+	0.0725805i	0.439796	−	0.898098i	$-0.355051\pi$
$13$	0.718995	+	0.261693i	0.199413	+	0.0725805i	−0.240383	+	0.970678i	$0.577273\pi$
$14$	−0.492752	−	0.179347i	−0.131694	−	0.0479326i
$15$		0			0
$16$	0.663574	−	3.76332i	0.165894	−	0.940829i
$17$	−2.31139	−	4.00345i	−0.560595	−	0.970979i	−0.997445	−	0.0714442i	$-0.977239\pi$
$17$	−2.31139	−	4.00345i	−0.560595	−	0.970979i	0.436850	−	0.899534i	$-0.356094\pi$
$18$		0			0
$19$	0.305922	−	0.529872i	0.0701833	−	0.121561i	−0.828798	−	0.559548i	$-0.810975\pi$
$19$	0.305922	−	0.529872i	0.0701833	−	0.121561i	0.898982	+	0.437987i	$0.144308\pi$
$20$	5.63910	+	4.73177i	1.26094	+	1.05806i
$21$		0			0
$22$	−0.0748430	−	0.424456i	−0.0159566	−	0.0904942i
$23$	4.99796	−	4.19379i	1.04215	−	0.874465i	0.0499011	−	0.998754i	$-0.484109\pi$
$23$	4.99796	−	4.19379i	1.04215	−	0.874465i	0.992246	+	0.124289i	$0.0396650\pi$
$24$		0			0
$25$	−8.42143	+	3.06515i	−1.68429	+	0.613030i
$26$	−0.132351			−0.0259561
$27$		0			0
$28$	−5.97229			−1.12866
$29$	6.15583	−	2.24054i	1.14311	−	0.416057i	0.300073	−	0.953916i	$-0.402989\pi$
$29$	6.15583	−	2.24054i	1.14311	−	0.416057i	0.843035	+	0.537859i	$0.180767\pi$
$30$		0			0
$31$	5.01792	−	4.21053i	0.901245	−	0.756234i	−0.0691887	−	0.997604i	$-0.522041\pi$
$31$	5.01792	−	4.21053i	0.901245	−	0.756234i	0.970433	+	0.241370i	$0.0775966\pi$
$32$	0.353281	+	2.00355i	0.0624518	+	0.354182i
$33$		0			0
$34$	0.612552	+	0.513992i	0.105052	+	0.0881490i
$35$	5.66369	−	9.80980i	0.957338	−	1.65816i
$36$		0			0
$37$	−2.47984	−	4.29522i	−0.407684	−	0.706129i	0.586946	−	0.809626i	$-0.300330\pi$
$37$	−2.47984	−	4.29522i	−0.407684	−	0.706129i	−0.994630	+	0.103497i	$0.966997\pi$
$38$	−0.0183779	+	0.104226i	−0.00298129	+	0.0169078i
$39$		0			0
$40$	−2.41125	−	0.877625i	−0.381253	−	0.138765i
$41$	−4.94301	−	1.79911i	−0.771968	−	0.280973i	−0.0741488	−	0.997247i	$-0.523624\pi$
$41$	−4.94301	−	1.79911i	−0.771968	−	0.280973i	−0.697819	+	0.716274i	$0.745846\pi$
$42$		0			0
$43$	0.967320	−	5.48594i	0.147515	−	0.836599i	−0.817798	−	0.575505i	$-0.804806\pi$
$43$	0.967320	−	5.48594i	0.147515	−	0.836599i	0.965313	−	0.261094i	$-0.0840832\pi$
$44$	−2.45442	−	4.25118i	−0.370018	−	0.640889i
$45$		0			0
$46$	−0.564280	+	0.977362i	−0.0831986	+	0.144104i
$47$	0.848483	+	0.711962i	0.123764	+	0.103850i	0.702569	−	0.711616i	$-0.252036\pi$
$47$	0.848483	+	0.711962i	0.123764	+	0.103850i	−0.578805	+	0.815466i	$0.696481\pi$
$48$		0			0
$49$	0.380286	+	2.15671i	0.0543265	+	0.308101i
$50$	1.18752	−	0.996445i	0.167940	−	0.140919i
$51$		0			0
$52$	−1.41648	+	0.515556i	−0.196430	+	0.0714947i
$53$	8.84310			1.21469			0.607346	−	0.794437i	$-0.292234\pi$
$53$	8.84310			1.21469			0.607346	+	0.794437i	$0.292234\pi$
$54$		0			0
$55$	9.31038			1.25541
$56$	1.95627	−	0.712023i	0.261417	−	0.0951480i
$57$		0			0
$58$	−0.868041	+	0.728373i	−0.113979	+	0.0956400i
$59$	−2.05804	−	11.6717i	−0.267933	−	1.51953i	−0.760550	−	0.649280i	$-0.775071\pi$
$59$	−2.05804	−	11.6717i	−0.267933	−	1.51953i	0.492616	−	0.870247i	$-0.336041\pi$
$60$		0			0
$61$	6.27161	+	5.26250i	0.802997	+	0.673795i	0.948925	−	0.315500i	$-0.102172\pi$
$61$	6.27161	+	5.26250i	0.802997	+	0.673795i	−0.145928	+	0.989295i	$0.546617\pi$
$62$	−0.566533	+	0.981264i	−0.0719498	+	0.124621i
$63$		0			0
$64$	3.64541	+	6.31404i	0.455677	+	0.789255i
$65$	0.496458	−	2.81555i	0.0615781	−	0.349227i
$66$		0			0
$67$	1.13923	+	0.414644i	0.139179	+	0.0506568i	0.410670	−	0.911784i	$-0.365295\pi$
$67$	1.13923	+	0.414644i	0.139179	+	0.0506568i	−0.271492	+	0.962441i	$0.587517\pi$
$68$	8.55801	+	3.11486i	1.03781	+	0.377733i
$69$		0			0
$70$	−0.340240	+	1.92960i	−0.0406665	+	0.230631i
$71$	2.45973	+	4.26038i	0.291916	+	0.505614i	0.974263	−	0.225415i	$-0.0723738\pi$
$71$	2.45973	+	4.26038i	0.291916	+	0.505614i	−0.682346	+	0.731029i	$0.739040\pi$
$72$		0			0
$73$	−2.14972	+	3.72343i	−0.251606	+	0.435795i	−0.963968	−	0.266017i	$-0.914292\pi$
$73$	−2.14972	+	3.72343i	−0.251606	+	0.435795i	0.712362	+	0.701812i	$0.247625\pi$
$74$	0.657195	+	0.551452i	0.0763973	+	0.0641050i
$75$		0			0
$76$	0.209312	+	1.18707i	0.0240098	+	0.136166i
$77$	−5.78637	+	4.85534i	−0.659418	+	0.553318i
$78$		0			0
$79$	11.0833	−	4.03399i	1.24697	−	0.453860i	0.367593	−	0.929987i	$-0.380182\pi$
$79$	11.0833	−	4.03399i	1.24697	−	0.453860i	0.879376	+	0.476127i	$0.157960\pi$
$80$	−14.2788			−1.59642
$81$		0			0
$82$	0.909895			0.100481
$83$	−8.47234	+	3.08368i	−0.929960	+	0.338478i	−0.762194	−	0.647349i	$-0.775878\pi$
$83$	−8.47234	+	3.08368i	−0.929960	+	0.338478i	−0.167766	+	0.985827i	$0.553655\pi$
$84$		0			0
$85$	−13.2321	+	11.1031i	−1.43523	+	1.20430i
$86$	0.167323	+	0.948936i	0.0180429	+	0.102326i
$87$		0			0
$88$	1.31079	+	1.09989i	0.139731	+	0.117248i
$89$	−3.76943	+	6.52884i	−0.399558	+	0.692055i	−0.993671	−	0.112326i	$-0.964170\pi$
$89$	−3.76943	+	6.52884i	−0.399558	+	0.692055i	0.594113	+	0.804382i	$0.297503\pi$
$90$		0			0
$91$	1.15976	+	2.00876i	0.121576	+	0.210575i
$92$	−2.23199	+	12.6583i	−0.232701	+	1.31972i
$93$		0			0
$94$	−0.180037	−	0.0655279i	−0.0185694	−	0.00675869i
$95$	−2.14832	−	0.781924i	−0.220413	−	0.0802237i
$96$		0			0
$97$	−0.164680	+	0.933947i	−0.0167207	+	0.0948279i	−0.992026	−	0.126033i	$-0.959776\pi$
$97$	−0.164680	+	0.933947i	−0.0167207	+	0.0948279i	0.975305	+	0.220861i	$0.0708866\pi$
$98$	−0.189407	−	0.328062i	−0.0191330	−	0.0331393i
$99$		0			0
$100$	8.82783	−	15.2902i	0.882783	−	1.52902i
$101$	−4.29610	−	3.60485i	−0.427477	−	0.358696i	0.403521	−	0.914970i	$-0.367786\pi$
$101$	−4.29610	−	3.60485i	−0.427477	−	0.358696i	−0.830999	+	0.556274i	$0.812231\pi$
$102$		0			0
$103$	−1.63664	−	9.28183i	−0.161263	−	0.914566i	−0.952835	−	0.303490i	$-0.901848\pi$
$103$	−1.63664	−	9.28183i	−0.161263	−	0.914566i	0.791572	−	0.611076i	$-0.209263\pi$
$104$	0.402512	−	0.337748i	0.0394696	−	0.0331189i
$105$		0			0
$106$	−1.43739	+	0.523169i	−0.139612	+	0.0508146i
$107$	−1.27825			−0.123573			−0.0617864	−	0.998089i	$-0.519680\pi$
$107$	−1.27825			−0.123573			−0.0617864	+	0.998089i	$0.519680\pi$
$108$		0			0
$109$	−7.40689			−0.709451			−0.354726	−	0.934970i	$-0.615426\pi$
$109$	−7.40689			−0.709451			−0.354726	+	0.934970i	$0.615426\pi$
$110$	−1.51335	+	0.550814i	−0.144292	+	0.0525180i
$111$		0			0
$112$	8.87423	−	7.44636i	0.838535	−	0.703615i
$113$	1.62395	+	9.20989i	0.152768	+	0.866393i	0.960798	+	0.277251i	$0.0894232\pi$
$113$	1.62395	+	9.20989i	0.152768	+	0.866393i	−0.808029	+	0.589143i	$0.799466\pi$
$114$		0			0
$115$	−18.6752	−	15.6704i	−1.74147	−	1.46127i
$116$	−6.45289	+	11.1767i	−0.599136	+	1.03773i
$117$		0			0
$118$	1.02503	+	1.77541i	0.0943621	+	0.163440i
$119$	2.43350	−	13.8011i	0.223078	−	1.26514i
$120$		0			0
$121$	4.50249	+	1.63877i	0.409317	+	0.148979i
$122$	−1.33075	−	0.484353i	−0.120480	−	0.0438513i
$123$		0			0
$124$	−2.24091	+	12.7088i	−0.201239	+	1.14128i
$125$	7.40194	+	12.8205i	0.662050	+	1.14670i
$126$		0			0
$127$	−10.3984	+	18.0106i	−0.922710	+	1.59818i	−0.127505	+	0.991838i	$0.540697\pi$
$127$	−10.3984	+	18.0106i	−0.922710	+	1.59818i	−0.795204	+	0.606342i	$0.792636\pi$
$128$	−4.08306	−	3.42610i	−0.360895	−	0.302827i
$129$		0			0
$130$	0.0858753	+	0.487023i	0.00753176	+	0.0427148i
$131$	−0.502395	+	0.421559i	−0.0438944	+	0.0368318i	−0.664471	−	0.747314i	$-0.731343\pi$
$131$	−0.502395	+	0.421559i	−0.0438944	+	0.0368318i	0.620577	+	0.784146i	$0.286899\pi$
$132$		0			0
$133$	1.74295	−	0.634380i	0.151133	−	0.0550077i
$134$	−0.209705			−0.0181158
$135$		0			0
$136$	−3.17460			−0.272219
$137$	−8.06971	+	2.93713i	−0.689442	+	0.250936i	−0.662896	−	0.748711i	$-0.730673\pi$
$137$	−8.06971	+	2.93713i	−0.689442	+	0.250936i	−0.0265455	+	0.999648i	$0.508451\pi$
$138$		0			0
$139$	10.3003	−	8.64301i	0.873664	−	0.733091i	−0.0912026	−	0.995832i	$-0.529071\pi$
$139$	10.3003	−	8.64301i	0.873664	−	0.733091i	0.964866	+	0.262742i	$0.0846267\pi$
$140$	3.87510	+	21.9768i	0.327506	+	1.85738i
$141$		0			0
$142$	−0.651865	−	0.546979i	−0.0547033	−	0.0459015i
$143$	−0.953247	+	1.65107i	−0.0797145	+	0.138070i
$144$		0			0
$145$	−12.2389	−	21.1984i	−1.01639	−	1.76043i
$146$	0.129142	−	0.732403i	0.0106879	−	0.0606141i
$147$		0			0
$148$	9.18172	+	3.34187i	0.754732	+	0.274700i
$149$	−9.04179	−	3.29094i	−0.740732	−	0.269604i	−0.0560315	−	0.998429i	$-0.517845\pi$
$149$	−9.04179	−	3.29094i	−0.740732	−	0.269604i	−0.684700	+	0.728825i	$0.740067\pi$
$150$		0			0
$151$	−1.23780	+	7.01991i	−0.100731	+	0.571272i	0.892109	+	0.451820i	$0.149225\pi$
$151$	−1.23780	+	7.01991i	−0.100731	+	0.571272i	−0.992840	+	0.119452i	$0.961886\pi$
$152$	−0.210085	−	0.363878i	−0.0170402	−	0.0295144i
$153$		0			0
$154$	0.653293	−	1.13154i	0.0526439	−	0.0911818i
$155$	−18.7498	−	15.7329i	−1.50602	−	1.26370i
$156$		0			0
$157$	1.33462	+	7.56900i	0.106514	+	0.604072i	0.990605	+	0.136756i	$0.0436678\pi$
$157$	1.33462	+	7.56900i	0.106514	+	0.604072i	−0.884090	+	0.467316i	$0.845221\pi$
$158$	−1.56287	+	1.31140i	−0.124335	+	0.104330i
$159$		0			0
$160$	7.14344	−	2.60000i	0.564739	−	0.205548i
$161$	19.7786			1.55877
$162$		0			0
$163$	1.04750			0.0820465			0.0410232	−	0.999158i	$-0.486938\pi$
$163$	1.04750			0.0820465			0.0410232	+	0.999158i	$0.486938\pi$
$164$	9.73812	−	3.54439i	0.760419	−	0.276770i
$165$		0			0
$166$	1.19469	−	1.00247i	0.0927263	−	0.0778066i
$167$	1.45067	+	8.22716i	0.112256	+	0.636637i	0.988072	+	0.153991i	$0.0492128\pi$
$167$	1.45067	+	8.22716i	0.112256	+	0.636637i	−0.875816	+	0.482645i	$0.839676\pi$
$168$		0			0
$169$	−9.51011	−	7.97993i	−0.731547	−	0.613841i
$170$	1.49393	−	2.58757i	0.114580	−	0.198458i
$171$		0			0
$172$	5.48724	+	9.50417i	0.418398	+	0.724686i
$173$	3.79348	−	21.5139i	0.288413	−	1.63567i	−0.404420	−	0.914573i	$-0.632527\pi$
$173$	3.79348	−	21.5139i	0.288413	−	1.63567i	0.692833	−	0.721098i	$-0.256362\pi$
$174$		0			0
$175$	−25.5295	−	9.29200i	−1.92985	−	0.702409i
$176$	8.94747	+	3.25661i	0.674441	+	0.245476i
$177$		0			0
$178$	0.226444	−	1.28423i	0.0169727	−	0.0962570i
$179$	4.54433	+	7.87101i	0.339659	+	0.588307i	0.984369	−	0.176121i	$-0.0563549\pi$
$179$	4.54433	+	7.87101i	0.339659	+	0.588307i	−0.644709	+	0.764428i	$0.723022\pi$
$180$		0			0
$181$	3.56539	−	6.17543i	0.265013	−	0.459016i	−0.702554	−	0.711630i	$-0.747957\pi$
$181$	3.56539	−	6.17543i	0.265013	−	0.459016i	0.967567	+	0.252614i	$0.0812904\pi$
$182$	−0.307353	−	0.257900i	−0.0227825	−	0.0191168i
$183$		0			0
$184$	−0.778026	−	4.41240i	−0.0573568	−	0.325287i
$185$	−14.1965	+	11.9123i	−1.04375	+	0.875807i
$186$		0			0
$187$	10.8239	−	3.93958i	0.791523	−	0.288091i
$188$	−2.18209			−0.159145
$189$		0			0
$190$	0.395456			0.0286894
$191$	−11.2346	+	4.08907i	−0.812908	+	0.295874i	−0.714825	−	0.699304i	$-0.753493\pi$
$191$	−11.2346	+	4.08907i	−0.812908	+	0.295874i	−0.0980836	+	0.995178i	$0.531271\pi$
$192$		0			0
$193$	−6.79760	+	5.70386i	−0.489302	+	0.410573i	−0.853776	−	0.520640i	$-0.825693\pi$
$193$	−6.79760	+	5.70386i	−0.489302	+	0.410573i	0.364474	+	0.931214i	$0.381249\pi$
$194$	−0.0284857	−	0.161550i	−0.00204515	−	0.0115986i
$195$		0			0
$196$	−3.30505	−	2.77326i	−0.236075	−	0.198090i
$197$	−3.69895	+	6.40677i	−0.263539	+	0.456464i	−0.967180	−	0.254093i	$-0.918223\pi$
$197$	−3.69895	+	6.40677i	−0.263539	+	0.456464i	0.703641	+	0.710556i	$0.251557\pi$
$198$		0			0
$199$	5.19187	+	8.99259i	0.368042	+	0.637468i	0.989259	−	0.146171i	$-0.0466948\pi$
$199$	5.19187	+	8.99259i	0.368042	+	0.637468i	−0.621217	+	0.783638i	$0.713362\pi$
$200$	−1.06870	+	6.06089i	−0.0755684	+	0.428570i
$201$		0			0
$202$	0.911573	+	0.331785i	0.0641381	+	0.0233443i
$203$	18.6614	+	6.79218i	1.30977	+	0.476718i
$204$		0			0
$205$	−3.41309	+	19.3566i	−0.238381	+	1.35192i
$206$	0.815151	+	1.41188i	0.0567942	+	0.0983705i
$207$		0			0
$208$	1.46194	−	2.53215i	0.101367	−	0.175573i
$209$	1.16786	+	0.979948i	0.0807824	+	0.0677845i
$210$		0			0
$211$	3.62250	+	20.5442i	0.249383	+	1.41432i	0.810089	+	0.586307i	$0.199419\pi$
$211$	3.62250	+	20.5442i	0.249383	+	1.41432i	−0.560706	+	0.828015i	$0.689470\pi$
$212$	−13.3457	+	11.1984i	−0.916588	+	0.769109i
$213$		0			0
$214$	0.207771	−	0.0756226i	0.0142030	−	0.00516946i
$215$	−20.8148			−1.41956
$216$		0			0
$217$	19.8576			1.34802
$218$	1.20395	−	0.438201i	0.0815416	−	0.0296787i
$219$		0			0
$220$	−14.0509	+	11.7901i	−0.947313	+	0.794890i
$221$	−0.614206	−	3.48333i	−0.0413160	−	0.234314i
$222$		0			0
$223$	18.0622	+	15.1560i	1.20953	+	1.01492i	0.999305	+	0.0372657i	$0.0118648\pi$
$223$	18.0622	+	15.1560i	1.20953	+	1.01492i	0.210227	+	0.977653i	$0.432580\pi$
$224$	−3.08373	+	5.34118i	−0.206041	+	0.356873i
$225$		0			0
$226$	−0.808832	−	1.40094i	−0.0538027	−	0.0931890i
$227$	−1.82055	+	10.3249i	−0.120834	+	0.685285i	0.862861	+	0.505441i	$0.168670\pi$
$227$	−1.82055	+	10.3249i	−0.120834	+	0.685285i	−0.983695	+	0.179843i	$0.942441\pi$
$228$		0			0
$229$	13.0452	+	4.74807i	0.862051	+	0.313761i	0.734944	−	0.678128i	$-0.237208\pi$
$229$	13.0452	+	4.74807i	0.862051	+	0.313761i	0.127107	+	0.991889i	$0.459431\pi$
$230$	3.96262	+	1.44228i	0.261288	+	0.0951009i
$231$		0			0
$232$	0.781188	−	4.43034i	0.0512875	−	0.290866i
$233$	−3.79982	−	6.58149i	−0.248935	−	0.431167i	0.714296	−	0.699844i	$-0.246747\pi$
$233$	−3.79982	−	6.58149i	−0.248935	−	0.431167i	−0.963230	+	0.268676i	$0.913414\pi$
$234$		0			0
$235$	2.06934	−	3.58420i	0.134989	−	0.233807i
$236$	17.8863	+	15.0084i	1.16430	+	0.976963i
$237$		0			0
$238$	0.420937	+	2.38725i	0.0272853	+	0.154742i
$239$	12.6847	−	10.6437i	0.820504	−	0.688485i	−0.132586	−	0.991172i	$-0.542328\pi$
$239$	12.6847	−	10.6437i	0.820504	−	0.688485i	0.953090	+	0.302687i	$0.0978836\pi$
$240$		0			0
$241$	13.6429	−	4.96562i	0.878818	−	0.319863i	0.137085	−	0.990559i	$-0.456227\pi$
$241$	13.6429	−	4.96562i	0.878818	−	0.319863i	0.741732	+	0.670696i	$0.234004\pi$
$242$	−0.828806			−0.0532776
$243$		0			0
$244$	−16.1290			−1.03256
$245$	7.68950	−	2.79875i	0.491264	−	0.178805i
$246$		0			0
$247$	0.358620	−	0.300918i	0.0228185	−	0.0191470i
$248$	−0.781132	−	4.43002i	−0.0496020	−	0.281307i
$249$		0			0
$250$	−1.96162	−	1.64600i	−0.124064	−	0.104102i
$251$	−4.52591	+	7.83910i	−0.285673	+	0.494800i	−0.972772	−	0.231764i	$-0.925550\pi$
$251$	−4.52591	+	7.83910i	−0.285673	+	0.494800i	0.687099	+	0.726563i	$0.258884\pi$
$252$		0			0
$253$	8.12838	+	14.0788i	0.511027	+	0.885125i
$254$	0.624673	−	3.54270i	0.0391955	−	0.222289i
$255$		0			0
$256$	−12.8359	−	4.67189i	−0.802244	−	0.291993i
$257$	−9.11490	−	3.31755i	−0.568572	−	0.206943i	0.0417069	−	0.999130i	$-0.486720\pi$
$257$	−9.11490	−	3.31755i	−0.568572	−	0.206943i	−0.610279	+	0.792187i	$0.708943\pi$
$258$		0			0
$259$	2.61085	−	14.8069i	0.162230	−	0.920054i
$260$	2.81622	+	4.87783i	0.174654	+	0.302510i
$261$		0			0
$262$	0.0567214	−	0.0982443i	0.00350426	−	0.00606955i
$263$	−20.5723	−	17.2622i	−1.26854	−	1.06443i	−0.994717	−	0.102655i	$-0.967266\pi$
$263$	−20.5723	−	17.2622i	−1.26854	−	1.06443i	−0.273826	−	0.961779i	$-0.588289\pi$
$264$		0			0
$265$	−5.73782	−	32.5408i	−0.352471	−	1.99896i
$266$	−0.245775	+	0.206230i	−0.0150694	+	0.0126448i
$267$		0			0
$268$	−2.24436	+	0.816882i	−0.137096	+	0.0498990i
$269$	11.7388			0.715729			0.357865	−	0.933774i	$-0.383505\pi$
$269$	11.7388			0.715729			0.357865	+	0.933774i	$0.383505\pi$
$270$		0			0
$271$	0.144576			0.00878238			0.00439119	−	0.999990i	$-0.498602\pi$
$271$	0.144576			0.00878238			0.00439119	+	0.999990i	$0.498602\pi$
$272$	−16.6000	+	6.04191i	−1.00652	+	0.366345i
$273$		0			0
$274$	1.13792	−	0.954828i	0.0687443	−	0.0576833i
$275$	−3.87762	−	21.9911i	−0.233829	−	1.32611i
$276$		0			0
$277$	−0.777094	−	0.652060i	−0.0466911	−	0.0391785i	0.619144	−	0.785278i	$-0.287480\pi$
$277$	−0.777094	−	0.652060i	−0.0466911	−	0.0391785i	−0.665835	+	0.746099i	$0.731924\pi$
$278$	−1.16293	+	2.01425i	−0.0697479	+	0.120807i
$279$		0			0
$280$	−3.88942	−	6.73667i	−0.232437	−	0.402593i
$281$	−4.78044	+	27.1112i	−0.285177	+	1.61732i	0.419475	+	0.907767i	$0.362214\pi$
$281$	−4.78044	+	27.1112i	−0.285177	+	1.61732i	−0.704652	+	0.709553i	$0.748897\pi$
$282$		0			0
$283$	25.1865	+	9.16713i	1.49718	+	0.544929i	0.955329	−	0.295545i	$-0.0955013\pi$
$283$	25.1865	+	9.16713i	1.49718	+	0.544929i	0.541852	+	0.840474i	$0.317724\pi$
$284$	−9.10725	−	3.31477i	−0.540416	−	0.196695i
$285$		0			0
$286$	0.0572653	−	0.324767i	0.00338617	−	0.0192039i
$287$	−7.97320	−	13.8100i	−0.470643	−	0.815178i
$288$		0			0
$289$	−2.18506	+	3.78464i	−0.128533	+	0.222626i
$290$	3.24349	+	2.72161i	0.190464	+	0.159818i
$291$		0			0
$292$	−1.47084	−	8.34157i	−0.0860747	−	0.488154i
$293$	14.2923	−	11.9927i	0.834964	−	0.700618i	−0.121461	−	0.992596i	$-0.538758\pi$
$293$	14.2923	−	11.9927i	0.834964	−	0.700618i	0.956425	+	0.291978i	$0.0943134\pi$
$294$		0			0
$295$	−41.6141	+	15.1463i	−2.42287	+	0.881852i
$296$	−3.40596			−0.197967
$297$		0			0
$298$	1.66439			0.0964153
$299$	4.69100	−	1.70738i	0.271287	−	0.0987405i
$300$		0			0
$301$	12.9363	−	10.8549i	0.745638	−	0.625664i
$302$	−0.214110	−	1.21428i	−0.0123206	−	0.0698737i
$303$		0			0
$304$	−1.79108	−	1.50289i	−0.102725	−	0.0861967i
$305$	15.2956	−	26.4928i	0.875825	−	1.51697i
$306$		0			0
$307$	−16.8946	−	29.2624i	−0.964227	−	1.67009i	−0.711677	−	0.702507i	$-0.752064\pi$
$307$	−16.8946	−	29.2624i	−0.964227	−	1.67009i	−0.252551	−	0.967584i	$-0.581269\pi$
$308$	2.58408	−	14.6551i	0.147242	−	0.835049i
$309$		0			0
$310$	3.97844	+	1.44804i	0.225960	+	0.0822429i
$311$	−32.5947	−	11.8635i	−1.84828	−	0.672718i	−0.986110	−	0.166093i	$-0.946885\pi$
$311$	−32.5947	−	11.8635i	−1.84828	−	0.672718i	−0.862167	−	0.506625i	$-0.830893\pi$
$312$		0			0
$313$	0.580051	−	3.28963i	0.0327864	−	0.185941i	−0.964016	−	0.265843i	$-0.914350\pi$
$313$	0.580051	−	3.28963i	0.0327864	−	0.185941i	0.996803	+	0.0799021i	$0.0254608\pi$
$314$	−0.664726	−	1.15134i	−0.0375127	−	0.0649739i
$315$		0			0
$316$	−11.6182	+	20.1232i	−0.653572	+	1.13202i
$317$	23.7725	+	19.9475i	1.33520	+	1.12036i	0.982832	+	0.184500i	$0.0590666\pi$
$317$	23.7725	+	19.9475i	1.33520	+	1.12036i	0.352364	+	0.935863i	$0.385378\pi$
$318$		0			0
$319$	2.83443	+	16.0749i	0.158698	+	0.900019i
$320$	20.8691	−	17.5112i	1.16662	−	0.978908i
$321$		0			0
$322$	−3.21490	+	1.17013i	−0.179159	+	0.0652087i
$323$	−2.82842			−0.157378
$324$		0			0
$325$	−6.85710			−0.380363
$326$	−0.170265	+	0.0619714i	−0.00943011	+	0.00343228i
$327$		0			0
$328$	−2.76722	+	2.32198i	−0.152794	+	0.128210i
$329$	0.583065	+	3.30672i	0.0321454	+	0.182306i
$330$		0			0
$331$	2.50625	+	2.10299i	0.137756	+	0.115591i	0.709062	−	0.705146i	$-0.249119\pi$
$331$	2.50625	+	2.10299i	0.137756	+	0.115591i	−0.571306	+	0.820737i	$0.693563\pi$
$332$	8.88119	−	15.3827i	0.487419	−	0.844234i
$333$		0			0
$334$	−0.722527	−	1.25145i	−0.0395349	−	0.0684765i
$335$	0.786622	−	4.46116i	0.0429778	−	0.243739i
$336$		0			0
$337$	−5.98190	−	2.17723i	−0.325855	−	0.118602i	0.173912	−	0.984761i	$-0.444359\pi$
$337$	−5.98190	−	2.17723i	−0.325855	−	0.118602i	−0.499768	+	0.866160i	$0.666581\pi$
$338$	2.01792	+	0.734461i	0.109760	+	0.0399494i
$339$		0			0
$340$	5.90921	−	33.5128i	0.320472	−	1.81749i
$341$	8.16083	+	14.1350i	0.441934	+	0.765452i
$342$		0			0
$343$	7.29078	−	12.6280i	0.393665	−	0.681848i
$344$	−2.93048	−	2.45896i	−0.158001	−	0.132578i
$345$		0			0
$346$	0.656181	+	3.72139i	0.0352765	+	0.200063i
$347$	6.73538	−	5.65165i	0.361574	−	0.303397i	−0.443844	−	0.896104i	$-0.646385\pi$
$347$	6.73538	−	5.65165i	0.361574	−	0.303397i	0.805418	+	0.592708i	$0.201941\pi$
$348$		0			0
$349$	−13.5318	+	4.92517i	−0.724340	+	0.263638i	−0.677767	−	0.735277i	$-0.737052\pi$
$349$	−13.5318	+	4.92517i	−0.724340	+	0.263638i	−0.0465728	+	0.998915i	$0.514830\pi$
$350$	4.69941			0.251194
$351$		0			0
$352$	−5.06926			−0.270192
$353$	31.1982	−	11.3552i	1.66051	−	0.604378i	0.670071	−	0.742297i	$-0.266263\pi$
$353$	31.1982	−	11.3552i	1.66051	−	0.604378i	0.990444	+	0.137919i	$0.0440413\pi$
$354$		0			0
$355$	14.0813	−	11.8156i	0.747360	−	0.627109i
$356$	−2.57905	−	14.6265i	−0.136689	−	0.775203i
$357$		0			0
$358$	−1.20431	−	1.01054i	−0.0636500	−	0.0534087i
$359$	2.47257	−	4.28262i	0.130497	−	0.226028i	−0.793371	−	0.608738i	$-0.791676\pi$
$359$	2.47257	−	4.28262i	0.130497	−	0.226028i	0.923868	+	0.382710i	$0.125009\pi$
$360$		0			0
$361$	9.31282	+	16.1303i	0.490149	+	0.848962i
$362$	−0.214187	+	1.21471i	−0.0112574	+	0.0638439i
$363$		0			0
$364$	−4.29405	−	1.56291i	−0.225069	−	0.0819185i
$365$	15.0963	+	5.49461i	0.790177	+	0.287601i
$366$		0			0
$367$	−0.432810	+	2.45459i	−0.0225925	+	0.128128i	−0.994018	−	0.109216i	$-0.965166\pi$
$367$	−0.432810	+	2.45459i	−0.0225925	+	0.128128i	0.971426	+	0.237345i	$0.0762770\pi$
$368$	−12.4660	−	21.5918i	−0.649837	−	1.12555i
$369$		0			0
$370$	1.60281	−	2.77615i	0.0833262	−	0.144325i
$371$	20.5360	+	17.2317i	1.06618	+	0.894627i
$372$		0			0
$373$	−4.87041	−	27.6215i	−0.252180	−	1.43019i	−0.803208	−	0.595699i	$-0.796875\pi$
$373$	−4.87041	−	27.6215i	−0.252180	−	1.43019i	0.551028	−	0.834487i	$-0.314236\pi$
$374$	−1.52629	+	1.28071i	−0.0789228	+	0.0662241i
$375$		0			0
$376$	0.714759	−	0.260151i	0.0368609	−	0.0134163i
$377$	5.01234			0.258149
$378$		0			0
$379$	5.13991			0.264019			0.132010	−	0.991248i	$-0.457857\pi$
$379$	5.13991			0.264019			0.132010	+	0.991248i	$0.457857\pi$
$380$	4.23236	−	1.54045i	0.217115	−	0.0790235i
$381$		0			0
$382$	1.58421	−	1.32931i	0.0810551	−	0.0680133i
$383$	0.00775737	+	0.0439942i	0.000396383	+	0.00224800i	0.985005	−	0.172524i	$-0.0551923\pi$
$383$	0.00775737	+	0.0439942i	0.000396383	+	0.00224800i	−0.984609	+	0.174772i	$0.944081\pi$
$384$		0			0
$385$	21.6211	+	18.1423i	1.10192	+	0.924617i
$386$	0.767463	−	1.32928i	0.0390628	−	0.0676588i
$387$		0			0
$388$	−0.934167	−	1.61802i	−0.0474251	−	0.0821427i
$389$	−3.64353	+	20.6635i	−0.184734	+	1.04768i	0.741562	+	0.670885i	$0.234085\pi$
$389$	−3.64353	+	20.6635i	−0.184734	+	1.04768i	−0.926296	+	0.376796i	$0.877026\pi$
$390$		0			0
$391$	−28.3419	−	10.3156i	−1.43331	−	0.521682i
$392$	1.41322	+	0.514371i	0.0713785	+	0.0259797i
$393$		0			0
$394$	0.222210	−	1.26022i	0.0111948	−	0.0634889i
$395$	−22.0356	−	38.1668i	−1.10873	−	1.92038i
$396$		0			0
$397$	0.00122821	−	0.00212731i	6.16419e−5	−	0.000106767i	−0.865995	−	0.500053i	$-0.833314\pi$
$397$	0.00122821	−	0.00212731i	6.16419e−5	−	0.000106767i	0.866056	+	0.499947i	$0.166647\pi$
$398$	−1.37592	−	1.15454i	−0.0689687	−	0.0578716i
$399$		0			0
$400$	5.94688	+	33.7265i	0.297344	+	1.68632i
$401$	−19.3475	+	16.2345i	−0.966166	+	0.810710i	−0.981945	−	0.189166i	$-0.939422\pi$
$401$	−19.3475	+	16.2345i	−0.966166	+	0.810710i	0.0157788	+	0.999876i	$0.494977\pi$
$402$		0			0
$403$	4.70972	−	1.71420i	0.234608	−	0.0853904i
$404$	11.0485			0.549684
$405$		0			0
$406$	−3.43513			−0.170483
$407$	11.6128	−	4.22670i	0.575623	−	0.209510i
$408$		0			0
$409$	−17.8401	+	14.9696i	−0.882134	+	0.740198i	−0.966617	−	0.256227i	$-0.917521\pi$
$409$	−17.8401	+	14.9696i	−0.882134	+	0.740198i	0.0844827	+	0.996425i	$0.473076\pi$
$410$	−0.590383	−	3.34823i	−0.0291569	−	0.165357i
$411$		0			0
$412$	14.2239	+	11.9353i	0.700763	+	0.588010i
$413$	17.9643	−	31.1151i	0.883965	−	1.53107i
$414$		0			0
$415$	16.8446	+	29.1756i	0.826867	+	1.43218i
$416$	−0.270309	+	1.53300i	−0.0132530	+	0.0751613i
$417$		0			0
$418$	−0.247803	−	0.0901931i	−0.0121205	−	0.00441149i
$419$	29.4014	+	10.7013i	1.43635	+	0.522790i	0.938746	−	0.344611i	$-0.111989\pi$
$419$	29.4014	+	10.7013i	1.43635	+	0.522790i	0.497609	+	0.867401i	$0.334211\pi$
$420$		0			0
$421$	5.30141	−	30.0658i	0.258375	−	1.46532i	−0.528885	−	0.848694i	$-0.677390\pi$
$421$	5.30141	−	30.0658i	0.258375	−	1.46532i	0.787259	−	0.616622i	$-0.211499\pi$
$422$	−1.80424	−	3.12503i	−0.0878289	−	0.152124i
$423$		0			0
$424$	3.03640	−	5.25920i	0.147461	−	0.255409i
$425$	31.7364	+	26.6300i	1.53944	+	1.29174i
$426$		0			0
$427$	4.30975	+	24.4418i	0.208564	+	1.18282i
$428$	1.92909	−	1.61870i	0.0932460	−	0.0782427i
$429$		0			0
$430$	3.38332	−	1.23143i	0.163158	−	0.0593848i
$431$	−12.4246			−0.598474			−0.299237	−	0.954179i	$-0.596732\pi$
$431$	−12.4246			−0.598474			−0.299237	+	0.954179i	$0.596732\pi$
$432$		0			0
$433$	−0.760649			−0.0365545			−0.0182772	−	0.999833i	$-0.505818\pi$
$433$	−0.760649			−0.0365545			−0.0182772	+	0.999833i	$0.505818\pi$
$434$	−3.22774	+	1.17480i	−0.154936	+	0.0563922i
$435$		0			0
$436$	11.1782	−	9.37966i	0.535341	−	0.449204i
$437$	−0.693186	−	3.93125i	−0.0331596	−	0.188057i
$438$		0			0
$439$	23.0651	+	19.3539i	1.10084	+	0.923712i	0.997481	−	0.0709321i	$-0.0225974\pi$
$439$	23.0651	+	19.3539i	1.10084	+	0.923712i	0.103356	+	0.994644i	$0.467042\pi$
$440$	3.19685	−	5.53711i	0.152404	−	0.263971i
$441$		0			0
$442$	0.305914	+	0.529859i	0.0145508	+	0.0252028i
$443$	2.37231	−	13.4540i	0.112712	−	0.639220i	−0.875146	−	0.483859i	$-0.839235\pi$
$443$	2.37231	−	13.4540i	0.112712	−	0.639220i	0.987858	−	0.155361i	$-0.0496541\pi$
$444$		0			0
$445$	26.4706	+	9.63450i	1.25483	+	0.456719i
$446$	−3.83255	−	1.39493i	−0.181476	−	0.0660520i
$447$		0			0
$448$	−3.83800	+	21.7664i	−0.181328	+	1.02836i
$449$	10.9995	+	19.0516i	0.519097	+	0.899102i	0.999754	+	0.0221934i	$0.00706496\pi$
$449$	10.9995	+	19.0516i	0.519097	+	0.899102i	−0.480657	+	0.876909i	$0.659602\pi$
$450$		0			0
$451$	6.55346	−	11.3509i	0.308590	−	0.534494i
$452$	−14.1137	−	11.8428i	−0.663852	−	0.557038i
$453$		0			0
$454$	−0.314911	−	1.78595i	−0.0147795	−	0.0838188i
$455$	6.63932	−	5.57105i	0.311256	−	0.261175i
$456$		0			0
$457$	1.39904	−	0.509209i	0.0654443	−	0.0238198i	−0.309091	−	0.951033i	$-0.600025\pi$
$457$	1.39904	−	0.509209i	0.0654443	−	0.0238198i	0.374535	+	0.927213i	$0.377802\pi$
$458$	−2.40132			−0.112206
$459$		0			0
$460$	48.0281			2.23932
$461$	6.68435	−	2.43290i	0.311321	−	0.113312i	−0.181634	−	0.983366i	$-0.558139\pi$
$461$	6.68435	−	2.43290i	0.311321	−	0.113312i	0.492956	+	0.870054i	$0.335917\pi$
$462$		0			0
$463$	−20.3314	+	17.0601i	−0.944879	+	0.792848i	−0.978428	−	0.206589i	$-0.933764\pi$
$463$	−20.3314	+	17.0601i	−0.944879	+	0.792848i	0.0335484	+	0.999437i	$0.489319\pi$
$464$	−4.34700	−	24.6531i	−0.201805	−	1.14449i
$465$		0			0
$466$	1.00701	+	0.844980i	0.0466487	+	0.0391429i
$467$	−13.0760	+	22.6482i	−0.605084	+	1.04804i	0.386955	+	0.922099i	$0.373527\pi$
$467$	−13.0760	+	22.6482i	−0.605084	+	1.04804i	−0.992038	+	0.125937i	$0.959806\pi$
$468$		0			0
$469$	1.83760	+	3.18282i	0.0848525	+	0.146969i
$470$	−0.124313	+	0.705015i	−0.00573414	+	0.0325199i
$471$		0			0
$472$	−7.64810	−	2.78368i	−0.352032	−	0.128129i
$473$	13.0431	+	4.74730i	0.599722	+	0.218281i
$474$		0			0
$475$	−0.952162	+	5.39998i	−0.0436882	+	0.247768i
$476$	13.8043	+	23.9098i	0.632719	+	1.09590i
$477$		0			0
$478$	−1.43213	+	2.48052i	−0.0655040	+	0.113456i
$479$	−7.97188	−	6.68920i	−0.364244	−	0.305637i	0.442235	−	0.896899i	$-0.354186\pi$
$479$	−7.97188	−	6.68920i	−0.364244	−	0.305637i	−0.806480	+	0.591262i	$0.798630\pi$
$480$		0			0
$481$	−0.658969	−	3.73720i	−0.0300464	−	0.170402i
$482$	−1.92381	+	1.61426i	−0.0876269	+	0.0735277i
$483$		0			0
$484$	−8.87026	+	3.22851i	−0.403194	+	0.146751i
$485$	3.54358			0.160906
$486$		0			0
$487$	−18.4664			−0.836791			−0.418396	−	0.908265i	$-0.637407\pi$
$487$	−18.4664			−0.836791			−0.418396	+	0.908265i	$0.637407\pi$
$488$	5.28318	−	1.92292i	0.239158	−	0.0870466i
$489$		0			0
$490$	−1.08431	+	0.909841i	−0.0489839	+	0.0411024i
$491$	−2.94749	−	16.7160i	−0.133018	−	0.754383i	−0.976219	−	0.216785i	$-0.930443\pi$
$491$	−2.94749	−	16.7160i	−0.133018	−	0.754383i	0.843201	−	0.537598i	$-0.180668\pi$
$492$		0			0
$493$	−23.1984	−	19.4658i	−1.04480	−	0.876694i
$494$	−0.0404890	+	0.0701289i	−0.00182168	+	0.00315525i
$495$		0			0
$496$	−12.5158	−	21.6780i	−0.561976	−	0.973371i
$497$	−2.58967	+	14.6868i	−0.116163	+	0.658792i
$498$		0			0
$499$	−23.1598	−	8.42949i	−1.03678	−	0.377356i	−0.233119	−	0.972448i	$-0.574893\pi$
$499$	−23.1598	−	8.42949i	−1.03678	−	0.377356i	−0.803657	+	0.595093i	$0.797115\pi$
$500$	−27.4060	−	9.97496i	−1.22563	−	0.446094i
$501$		0			0
$502$	0.271889	−	1.54196i	0.0121350	−	0.0688210i
$503$	−20.0569	−	34.7395i	−0.894291	−	1.54896i	−0.834679	−	0.550736i	$-0.814347\pi$
$503$	−20.0569	−	34.7395i	−0.894291	−	1.54896i	−0.0596120	−	0.998222i	$-0.518986\pi$
$504$		0			0
$505$	−10.4776	+	18.1478i	−0.466248	+	0.807564i
$506$	−2.15414	−	1.80754i	−0.0957632	−	0.0803548i
$507$		0			0
$508$	−7.11461	−	40.3489i	−0.315660	−	1.79019i
$509$	3.79079	−	3.18085i	0.168024	−	0.140989i	−0.554899	−	0.831918i	$-0.687243\pi$
$509$	3.79079	−	3.18085i	0.168024	−	0.140989i	0.722922	+	0.690929i	$0.242798\pi$
$510$		0			0
$511$	−12.2477	+	4.45781i	−0.541808	+	0.197202i
$512$	13.0229			0.575537
$513$		0			0
$514$	1.67785			0.0740066
$515$	−33.0933	+	12.0450i	−1.45827	+	0.530765i
$516$		0			0
$517$	−2.11416	+	1.77399i	−0.0929807	+	0.0780201i
$518$	0.451614	+	2.56123i	0.0198428	+	0.112534i
$519$		0			0
$520$	−1.50401	−	1.26202i	−0.0659553	−	0.0553431i
$521$	−3.86979	+	6.70267i	−0.169539	+	0.293649i	−0.938258	−	0.345937i	$-0.887561\pi$
$521$	−3.86979	+	6.70267i	−0.169539	+	0.293649i	0.768719	+	0.639586i	$0.220894\pi$
$522$		0			0
$523$	−18.0070	−	31.1891i	−0.787391	−	1.36380i	−0.927560	−	0.373674i	$-0.878098\pi$
$523$	−18.0070	−	31.1891i	−0.787391	−	1.36380i	0.140169	−	0.990128i	$-0.455236\pi$
$524$	0.224360	−	1.27241i	0.00980120	−	0.0555854i
$525$		0			0
$526$	4.36516	+	1.58879i	0.190330	+	0.0692745i
$527$	−28.4550	−	10.3568i	−1.23952	−	0.451148i
$528$		0			0
$529$	3.39786	−	19.2702i	0.147733	−	0.837835i
$530$	2.85780	+	4.94986i	0.124135	+	0.215008i
$531$		0			0
$532$	−1.82705	+	3.16455i	−0.0792129	+	0.137201i
$533$	−3.08319	−	2.58710i	−0.133548	−	0.112060i
$534$		0			0
$535$	0.829386	+	4.70368i	0.0358575	+	0.203358i
$536$	0.637768	−	0.535151i	0.0275474	−	0.0231150i
$537$		0			0
$538$	−1.90808	+	0.694484i	−0.0822631	+	0.0299413i
$539$	−5.45676			−0.235039
$540$		0			0
$541$	−24.4147			−1.04967			−0.524834	−	0.851204i	$-0.675873\pi$
$541$	−24.4147			−1.04967			−0.524834	+	0.851204i	$0.675873\pi$
$542$	−0.0235000	+	0.00855331i	−0.00100941	+	0.000367396i
$543$		0			0
$544$	7.20455	−	6.04534i	0.308893	−	0.259192i
$545$	4.80594	+	27.2558i	0.205864	+	1.16751i
$546$		0			0
$547$	−21.7264	−	18.2306i	−0.928953	−	0.779484i	0.0466761	−	0.998910i	$-0.485137\pi$
$547$	−21.7264	−	18.2306i	−0.928953	−	0.779484i	−0.975629	+	0.219426i	$0.929582\pi$
$548$	8.45913	−	14.6516i	0.361356	−	0.625887i
$549$		0			0
$550$	1.93130	+	3.34512i	0.0823511	+	0.142636i
$551$	0.696003	−	3.94723i	0.0296507	−	0.168158i
$552$		0			0
$553$	33.5990	+	12.2290i	1.42878	+	0.520032i
$554$	0.164889	+	0.0600146i	0.00700546	+	0.00254978i
$555$		0			0
$556$	−4.59993	+	26.0875i	−0.195081	+	1.10636i
$557$	18.4687	+	31.9887i	0.782542	+	1.35540i	0.930456	+	0.366403i	$0.119411\pi$
$557$	18.4687	+	31.9887i	0.782542	+	1.35540i	−0.147914	+	0.989000i	$0.547256\pi$
$558$		0			0
$559$	2.13113	−	3.69123i	0.0901372	−	0.156122i
$560$	−33.1591	−	27.8238i	−1.40123	−	1.17577i
$561$		0			0
$562$	−0.826901	−	4.68959i	−0.0348807	−	0.197818i
$563$	17.4470	−	14.6398i	0.735303	−	0.616992i	−0.196269	−	0.980550i	$-0.562883\pi$
$563$	17.4470	−	14.6398i	0.735303	−	0.616992i	0.931572	+	0.363558i	$0.118438\pi$
$564$		0			0
$565$	32.8368	−	11.9516i	1.38145	−	0.502808i
$566$	−4.63625			−0.194876
$567$		0			0
$568$	3.37833			0.141752
$569$	−29.0071	+	10.5577i	−1.21604	+	0.442603i	−0.868796	−	0.495170i	$-0.835106\pi$
$569$	−29.0071	+	10.5577i	−1.21604	+	0.442603i	−0.347247	+	0.937774i	$0.612883\pi$
$570$		0			0
$571$	9.82107	−	8.24085i	0.410999	−	0.344869i	−0.413728	−	0.910401i	$-0.635773\pi$
$571$	9.82107	−	8.24085i	0.410999	−	0.344869i	0.824727	+	0.565532i	$0.191329\pi$
$572$	−0.652213	−	3.69888i	−0.0272704	−	0.154658i
$573$		0			0
$574$	2.11301	+	1.77303i	0.0881955	+	0.0740048i
$575$	−29.2354	+	50.6372i	−1.21920	+	2.11172i
$576$		0			0
$577$	11.7632	+	20.3745i	0.489708	+	0.848200i	0.999930	−	0.0118433i	$-0.00376992\pi$
$577$	11.7632	+	20.3745i	0.489708	+	0.848200i	−0.510222	+	0.860043i	$0.670437\pi$
$578$	0.131265	−	0.744442i	0.00545991	−	0.0309647i
$579$		0			0
$580$	45.3150	+	16.4933i	1.88160	+	0.684848i
$581$	−25.6839	−	9.34816i	−1.06555	−	0.387827i
$582$		0			0
$583$	−3.82622	+	21.6996i	−0.158466	+	0.898704i
$584$	1.47628	+	2.55699i	0.0610888	+	0.105809i
$585$		0			0
$586$	−1.61363	+	2.79489i	−0.0666584	+	0.115456i
$587$	8.72329	+	7.31971i	0.360049	+	0.302117i	0.804810	−	0.593532i	$-0.202267\pi$
$587$	8.72329	+	7.31971i	0.360049	+	0.302117i	−0.444762	+	0.895649i	$0.646712\pi$
$588$		0			0
$589$	−0.695954	−	3.94695i	−0.0286763	−	0.162631i
$590$	5.86806	−	4.92389i	0.241584	−	0.202713i
$591$		0			0
$592$	−17.8098	+	6.48224i	−0.731979	+	0.266419i
$593$	−37.7324			−1.54948			−0.774742	−	0.632277i	$-0.782120\pi$
$593$	−37.7324			−1.54948			−0.774742	+	0.632277i	$0.782120\pi$
$594$		0			0
$595$	−52.3640			−2.14672
$596$	17.8130	−	6.48341i	0.729650	−	0.265571i
$597$		0			0
$598$	−0.661483	+	0.555050i	−0.0270501	+	0.0226977i
$599$	8.22366	+	46.6387i	0.336010	+	1.90561i	0.417028	+	0.908894i	$0.363072\pi$
$599$	8.22366	+	46.6387i	0.336010	+	1.90561i	−0.0810181	+	0.996713i	$0.525817\pi$
$600$		0			0
$601$	−23.8297	−	19.9955i	−0.972033	−	0.815632i	0.0108354	−	0.999941i	$-0.496551\pi$
$601$	−23.8297	−	19.9955i	−0.972033	−	0.815632i	−0.982868	+	0.184309i	$0.940995\pi$
$602$	−1.46054	+	2.52973i	−0.0595271	+	0.103104i
$603$		0			0
$604$	−7.02156	−	12.1617i	−0.285703	−	0.494853i
$605$	3.10892	−	17.6316i	0.126396	−	0.716825i
$606$		0			0
$607$	−27.7082	−	10.0850i	−1.12464	−	0.409336i	−0.288297	−	0.957541i	$-0.593089\pi$
$607$	−27.7082	−	10.0850i	−1.12464	−	0.409336i	−0.836344	+	0.548205i	$0.815311\pi$
$608$	1.16970	+	0.425737i	0.0474378	+	0.0172659i
$609$		0			0
$610$	−0.918868	+	5.21116i	−0.0372039	+	0.210994i
$611$	0.423740	+	0.733939i	0.0171427	+	0.0296920i
$612$		0			0
$613$	3.05214	−	5.28646i	0.123275	−	0.213518i	−0.797782	−	0.602945i	$-0.793994\pi$
$613$	3.05214	−	5.28646i	0.123275	−	0.213518i	0.921057	+	0.389427i	$0.127327\pi$
$614$	4.47732	+	3.75692i	0.180690	+	0.151617i
$615$		0			0
$616$	0.900757	+	5.10844i	0.0362925	+	0.205825i
$617$	−14.6469	+	12.2902i	−0.589660	+	0.494784i	−0.888103	−	0.459644i	$-0.847977\pi$
$617$	−14.6469	+	12.2902i	−0.589660	+	0.494784i	0.298443	+	0.954427i	$0.403533\pi$
$618$		0			0
$619$	6.34655	−	2.30995i	0.255089	−	0.0928449i	−0.211310	−	0.977419i	$-0.567773\pi$
$619$	6.34655	−	2.30995i	0.255089	−	0.0928449i	0.466400	+	0.884574i	$0.345551\pi$
$620$	48.2198			1.93655
$621$		0			0
$622$	5.99994			0.240576
$623$	−21.4757	+	7.81653i	−0.860408	+	0.313163i
$624$		0			0
$625$	8.04818	−	6.75322i	0.321927	−	0.270129i
$626$	0.100335	+	0.569027i	0.00401019	+	0.0227429i
$627$		0			0
$628$	−11.5991	−	9.73282i	−0.462855	−	0.388382i
$629$	−11.4638	+	19.8559i	−0.457091	+	0.791705i
$630$		0			0
$631$	0.228453	+	0.395693i	0.00909458	+	0.0157523i	0.870537	−	0.492103i	$-0.163772\pi$
$631$	0.228453	+	0.395693i	0.00909458	+	0.0157523i	−0.861442	+	0.507855i	$0.830438\pi$
$632$	1.40650	−	7.97663i	0.0559474	−	0.317294i
$633$		0			0
$634$	−5.04420	−	1.83594i	−0.200331	−	0.0729145i
$635$	73.0222	+	26.5779i	2.89780	+	1.05471i
$636$		0			0
$637$	−0.290971	+	1.65018i	−0.0115287	+	0.0653825i
$638$	−1.41173	−	2.44519i	−0.0558909	−	0.0968058i
$639$		0			0
$640$	−9.95805	+	17.2479i	−0.393627	+	0.681781i
$641$	2.19934	+	1.84546i	0.0868686	+	0.0728914i	0.685188	−	0.728366i	$-0.259720\pi$
$641$	2.19934	+	1.84546i	0.0868686	+	0.0728914i	−0.598319	+	0.801258i	$0.704165\pi$
$642$		0			0
$643$	−0.295696	−	1.67697i	−0.0116611	−	0.0661334i	0.978422	−	0.206617i	$-0.0662454\pi$
$643$	−0.295696	−	1.67697i	−0.0116611	−	0.0661334i	−0.990083	+	0.140484i	$0.955134\pi$
$644$	−29.8493	+	25.0465i	−1.17623	+	0.986971i
$645$		0			0
$646$	0.459744	−	0.167333i	0.0180884	−	0.00658363i
$647$	−36.1004			−1.41925			−0.709626	−	0.704579i	$-0.751136\pi$
$647$	−36.1004			−1.41925			−0.709626	+	0.704579i	$0.751136\pi$
$648$		0			0
$649$	29.5310			1.15919
$650$	1.11458	−	0.405674i	0.0437175	−	0.0159119i
$651$		0			0
$652$	−1.58085	+	1.32649i	−0.0619110	+	0.0519495i
$653$	7.56550	+	42.9061i	0.296061	+	1.67904i	0.662859	+	0.748744i	$0.269343\pi$
$653$	7.56550	+	42.9061i	0.296061	+	1.67904i	−0.366798	+	0.930301i	$0.619546\pi$
$654$		0			0
$655$	1.87723	+	1.57518i	0.0733494	+	0.0615475i
$656$	−10.0507	+	17.4083i	−0.392412	+	0.679678i
$657$		0			0
$658$	−0.290404	−	0.502994i	−0.0113211	−	0.0196087i
$659$	−4.42473	+	25.0939i	−0.172363	+	0.977518i	0.768781	+	0.639512i	$0.220864\pi$
$659$	−4.42473	+	25.0939i	−0.172363	+	0.977518i	−0.941144	+	0.338006i	$0.890248\pi$
$660$		0			0
$661$	−32.1067	−	11.6859i	−1.24880	−	0.454528i	−0.368807	−	0.929506i	$-0.620234\pi$
$661$	−32.1067	−	11.6859i	−1.24880	−	0.454528i	−0.879998	+	0.474978i	$0.842456\pi$
$662$	−0.531792	−	0.193557i	−0.0206687	−	0.00752279i
$663$		0			0
$664$	−1.07516	+	6.09753i	−0.0417242	+	0.236630i
$665$	−3.46529	−	6.00207i	−0.134378	−	0.232750i
$666$		0			0
$667$	21.3702	−	37.0143i	0.827459	−	1.43320i
$668$	−12.6077	−	10.5791i	−0.487807	−	0.409319i
$669$		0			0
$670$	0.136067	+	0.771673i	0.00525672	+	0.0298123i
$671$	−15.6269	+	13.1126i	−0.603271	+	0.506205i
$672$		0			0
$673$	27.7620	−	10.1045i	1.07015	−	0.389502i	0.253916	−	0.967226i	$-0.418281\pi$
$673$	27.7620	−	10.1045i	1.07015	−	0.389502i	0.816232	+	0.577725i	$0.196059\pi$
$674$	1.10113			0.0424140
$675$		0			0
$676$	24.4577			0.940680
$677$	38.3209	−	13.9477i	1.47279	−	0.536052i	0.523935	−	0.851759i	$-0.324464\pi$
$677$	38.3209	−	13.9477i	1.47279	−	0.536052i	0.948857	+	0.315706i	$0.102241\pi$
$678$		0			0
$679$	−2.20233	+	1.84797i	−0.0845176	+	0.0709186i
$680$	2.05983	+	11.6819i	0.0789908	+	0.447979i
$681$		0			0
$682$	−2.16274	−	1.81475i	−0.0828156	−	0.0694905i
$683$	15.8213	−	27.4033i	0.605384	−	1.04856i	−0.386606	−	0.922245i	$-0.626353\pi$
$683$	15.8213	−	27.4033i	0.605384	−	1.04856i	0.991991	−	0.126312i	$-0.0403139\pi$
$684$		0			0
$685$	16.0441	+	27.7891i	0.613012	+	1.06177i
$686$	−0.437986	+	2.48394i	−0.0167224	+	0.0948373i
$687$		0			0
$688$	−20.0035	−	7.28066i	−0.762624	−	0.277573i
$689$	6.35814	+	2.31418i	0.242226	+	0.0881631i
$690$		0			0
$691$	−4.96369	+	28.1505i	−0.188828	+	1.07090i	0.732110	+	0.681186i	$0.238536\pi$
$691$	−4.96369	+	28.1505i	−0.188828	+	1.07090i	−0.920938	+	0.389709i	$0.872576\pi$
$692$	21.5190	+	37.2719i	0.818028	+	1.41687i
$693$		0			0
$694$	−0.760438	+	1.31712i	−0.0288658	+	0.0499971i
$695$	−38.4879	−	32.2952i	−1.45993	−	1.22503i
$696$		0			0
$697$	4.22259	+	23.9475i	0.159942	+	0.907077i
$698$	1.90813	−	1.60111i	0.0722239	−	0.0606031i
$699$		0			0
$700$	50.2952	−	18.3060i	1.90098	−	0.691901i
$701$	7.52982			0.284397			0.142199	−	0.989838i	$-0.454583\pi$
$701$	7.52982			0.284397			0.142199	+	0.989838i	$0.454583\pi$
$702$		0			0
$703$	−3.03455			−0.114450
$704$	−17.0710	+	6.21332i	−0.643386	+	0.234173i
$705$		0			0
$706$	−4.39930	+	3.69145i	−0.165570	+	0.138930i
$707$	−2.95221	−	16.7428i	−0.111029	−	0.629679i
$708$		0			0
$709$	6.13907	+	5.15129i	0.230558	+	0.193461i	0.750746	−	0.660590i	$-0.229694\pi$
$709$	6.13907	+	5.15129i	0.230558	+	0.193461i	−0.520189	+	0.854051i	$0.674138\pi$
$710$	−1.58981	+	2.75363i	−0.0596646	+	0.103342i
$711$		0			0
$712$	2.58857	+	4.48354i	0.0970108	+	0.168028i
$713$	7.42128	−	42.0882i	0.277929	−	1.57621i
$714$		0			0
$715$	6.69412	+	2.43646i	0.250346	+	0.0911184i
$716$	−16.8256	−	6.12400i	−0.628801	−	0.228865i
$717$		0			0
$718$	−0.148537	+	0.842396i	−0.00554335	+	0.0314379i
$719$	13.4913	+	23.3676i	0.503140	+	0.871464i	0.999993	+	0.00362928i	$0.00115524\pi$
$719$	13.4913	+	23.3676i	0.503140	+	0.871464i	−0.496854	+	0.867834i	$0.665511\pi$
$720$		0			0
$721$	14.2860	−	24.7440i	0.532037	−	0.921515i
$722$	−2.46803	−	2.07093i	−0.0918507	−	0.0770719i
$723$		0			0
$724$	2.43944	+	13.8348i	0.0906611	+	0.514165i
$725$	−44.9733	+	37.7371i	−1.67027	+	1.40152i
$726$		0			0
$727$	13.8082	−	5.02576i	0.512116	−	0.186395i	−0.0730194	−	0.997331i	$-0.523263\pi$
$727$	13.8082	−	5.02576i	0.512116	−	0.186395i	0.585136	+	0.810935i	$0.301041\pi$
$728$	1.59288			0.0590360
$729$		0			0
$730$	−2.77889			−0.102851
$731$	−24.1985	+	8.80755i	−0.895015	+	0.325759i
$732$		0			0
$733$	−24.0107	+	20.1474i	−0.886856	+	0.744161i	−0.967577	−	0.252576i	$-0.918722\pi$
$733$	−24.0107	+	20.1474i	−0.886856	+	0.744161i	0.0807207	+	0.996737i	$0.474278\pi$
$734$	−0.0748657	−	0.424584i	−0.00276334	−	0.0156717i
$735$		0			0
$736$	10.1682	+	8.53210i	0.374803	+	0.314497i
$737$	−1.51039	+	2.61607i	−0.0556359	+	0.0963642i
$738$		0			0
$739$	−0.241454	−	0.418211i	−0.00888205	−	0.0153842i	0.861550	−	0.507672i	$-0.169494\pi$
$739$	−0.241454	−	0.418211i	−0.00888205	−	0.0153842i	−0.870432	+	0.492288i	$0.836161\pi$
$740$	6.33987	−	35.9552i	0.233058	−	1.32174i
$741$		0			0
$742$	−4.35746	−	1.58598i	−0.159967	−	0.0582233i
$743$	40.4545	+	14.7242i	1.48413	+	0.540179i	0.951897	−	0.306418i	$-0.0991307\pi$
$743$	40.4545	+	14.7242i	1.48413	+	0.540179i	0.532233	+	0.846598i	$0.321353\pi$
$744$		0			0
$745$	−6.24325	+	35.4072i	−0.228735	+	1.29722i
$746$	2.42578	+	4.20157i	0.0888140	+	0.153830i
$747$		0			0
$748$	−11.3462	+	19.6523i	−0.414860	+	0.718558i
$749$	−2.96842	−	2.49080i	−0.108464	−	0.0910119i
$750$		0			0
$751$	7.62691	+	43.2543i	0.278310	+	1.57837i	0.728248	+	0.685314i	$0.240335\pi$
$751$	7.62691	+	43.2543i	0.278310	+	1.57837i	−0.449938	+	0.893060i	$0.648554\pi$
$752$	3.24237	−	2.72067i	0.118237	−	0.0992126i
$753$		0			0
$754$	−0.814727	+	0.296536i	−0.0296706	+	0.0107992i
$755$	26.6350			0.969346
$756$		0			0
$757$	22.4143			0.814661			0.407331	−	0.913281i	$-0.366460\pi$
$757$	22.4143			0.814661			0.407331	+	0.913281i	$0.366460\pi$
$758$	−0.835463	+	0.304084i	−0.0303454	+	0.0110448i
$759$		0			0
$760$	−1.20268	+	1.00917i	−0.0436260	+	0.0366065i
$761$	1.73592	+	9.84487i	0.0629269	+	0.356876i	0.999971	+	0.00766415i	$0.00243960\pi$
$761$	1.73592	+	9.84487i	0.0629269	+	0.356876i	−0.937044	+	0.349212i	$0.886449\pi$
$762$		0			0
$763$	−17.2007	−	14.4331i	−0.622708	−	0.522514i
$764$	11.7768	−	20.3980i	0.426069	−	0.737972i
$765$		0			0
$766$	−0.00386367	−	0.00669207i	−0.000139600	−	0.000241794i
$767$	1.57468	−	8.93047i	0.0568585	−	0.322461i
$768$		0			0
$769$	7.04412	+	2.56385i	0.254017	+	0.0924547i	0.465890	−	0.884842i	$-0.345734\pi$
$769$	7.04412	+	2.56385i	0.254017	+	0.0924547i	−0.211873	+	0.977297i	$0.567956\pi$
$770$	−4.58771	−	1.66979i	−0.165330	−	0.0601751i
$771$		0			0
$772$	3.03568	−	17.2162i	0.109256	−	0.619624i
$773$	−9.91954	−	17.1812i	−0.356781	−	0.617963i	0.630640	−	0.776076i	$-0.282793\pi$
$773$	−9.91954	−	17.1812i	−0.356781	−	0.617963i	−0.987421	+	0.158112i	$0.949459\pi$
$774$		0			0
$775$	−29.3521	+	50.8394i	−1.05436	+	1.82620i
$776$	0.498895	+	0.418623i	0.0179093	+	0.0150277i
$777$		0			0
$778$	−0.630243	−	3.57429i	−0.0225953	−	0.128144i
$779$	−2.46547	+	2.06878i	−0.0883347	+	0.0741216i
$780$		0			0
$781$	−11.5186	+	4.19242i	−0.412167	+	0.150016i
$782$	5.21709			0.186563
$783$		0			0
$784$	8.36872			0.298883
$785$	26.9864	−	9.82226i	0.963187	−	0.350571i
$786$		0			0
$787$	30.4336	−	25.5368i	1.08484	−	0.910290i	0.0885273	−	0.996074i	$-0.471784\pi$
$787$	30.4336	−	25.5368i	1.08484	−	0.910290i	0.996314	+	0.0857841i	$0.0273395\pi$
$788$	−2.53083	−	14.3530i	−0.0901570	−	0.511306i
$789$		0			0
$790$	5.83976	+	4.90014i	0.207769	+	0.174339i
$791$	−14.1752	+	24.5522i	−0.504013	+	0.872976i
$792$		0			0
$793$	3.13210	+	5.42495i	0.111224	+	0.192646i
$794$	−7.37831e−5	0	0.000418445i	−2.61846e−6	0	1.48500e-5i
$795$		0			0
$796$	−19.2231	−	6.99664i	−0.681345	−	0.247989i
$797$	−8.55680	−	3.11442i	−0.303097	−	0.110318i	0.185994	−	0.982551i	$-0.440449\pi$
$797$	−8.55680	−	3.11442i	−0.303097	−	0.110318i	−0.489092	+	0.872232i	$0.662672\pi$
$798$		0			0
$799$	0.889125	−	5.04248i	0.0314550	−	0.178390i
$800$	−9.11632	−	15.7899i	−0.322311	−	0.558258i
$801$		0			0
$802$	2.18437	−	3.78344i	0.0771327	−	0.133598i
$803$	−8.20657	−	6.88613i	−0.289604	−	0.243006i
$804$		0			0
$805$	−12.8333	−	72.7813i	−0.452315	−	2.56520i
$806$	−0.664124	+	0.557266i	−0.0233928	+	0.0196289i
$807$		0			0
$808$	−3.61902	+	1.31721i	−0.127317	+	0.0463394i
$809$	−3.01910			−0.106146			−0.0530730	−	0.998591i	$-0.516902\pi$
$809$	−3.01910			−0.106146			−0.0530730	+	0.998591i	$0.516902\pi$
$810$		0			0
$811$	33.1722			1.16483			0.582416	−	0.812891i	$-0.302107\pi$
$811$	33.1722			1.16483			0.582416	+	0.812891i	$0.302107\pi$
$812$	−36.7644	+	13.3811i	−1.29018	+	0.469586i
$813$		0			0
$814$	−1.63753	+	1.37405i	−0.0573954	+	0.0481604i
$815$	−0.679667	−	3.85458i	−0.0238077	−	0.135020i
$816$		0			0
$817$	−2.61093	−	2.19083i	−0.0913447	−	0.0766473i
$818$	2.01418	−	3.48866i	0.0704241	−	0.121978i
$819$		0			0
$820$	−19.3612	−	33.5345i	−0.676121	−	1.17108i
$821$	−7.42554	+	42.1123i	−0.259153	+	1.46973i	0.526030	+	0.850466i	$0.323680\pi$
$821$	−7.42554	+	42.1123i	−0.259153	+	1.46973i	−0.785183	+	0.619264i	$0.787431\pi$
$822$		0			0
$823$	33.1043	+	12.0490i	1.15394	+	0.420001i	0.846930	−	0.531704i	$-0.178448\pi$
$823$	33.1043	+	12.0490i	1.15394	+	0.420001i	0.307013	+	0.951705i	$0.400670\pi$
$824$	−6.08209	−	2.21370i	−0.211880	−	0.0771179i
$825$		0			0
$826$	−1.07918	+	6.12036i	−0.0375496	+	0.212955i
$827$	13.0190	+	22.5495i	0.452714	+	0.784125i	0.998554	−	0.0537655i	$-0.0171223\pi$
$827$	13.0190	+	22.5495i	0.452714	+	0.784125i	−0.545839	+	0.837890i	$0.683789\pi$
$828$		0			0
$829$	3.95134	−	6.84392i	0.137236	−	0.237699i	−0.789214	−	0.614119i	$-0.789512\pi$
$829$	3.95134	−	6.84392i	0.137236	−	0.237699i	0.926449	+	0.376420i	$0.122845\pi$
$830$	−4.46405	−	3.74578i	−0.154950	−	0.130018i
$831$		0			0
$832$	0.968696	+	5.49375i	0.0335835	+	0.190461i
$833$	7.75528	−	6.50745i	0.268704	−	0.225470i
$834$		0			0
$835$	29.3330	−	10.6763i	1.01511	−	0.369470i
$836$	−3.00344			−0.103876
$837$		0			0
$838$	−5.41213			−0.186959
$839$	4.83791	−	1.76085i	0.167023	−	0.0607914i	−0.257155	−	0.966370i	$-0.582785\pi$
$839$	4.83791	−	1.76085i	0.167023	−	0.0607914i	0.424178	+	0.905579i	$0.360563\pi$
$840$		0			0
$841$	10.6589	−	8.94387i	0.367548	−	0.308409i
$842$	0.917016	+	5.20065i	0.0316024	+	0.179226i
$843$		0			0
$844$	−31.4830	−	26.4174i	−1.08369	−	0.909323i
$845$	−23.1939	+	40.1730i	−0.797894	+	1.38199i
$846$		0			0
$847$	7.26264	+	12.5793i	0.249547	+	0.432228i
$848$	5.86805	−	33.2794i	0.201510	−	1.14282i
$849$		0			0
$850$	−6.73403	−	2.45099i	−0.230975	−	0.0840681i
$851$	−30.4074	−	11.0674i	−1.04235	−	0.379385i
$852$		0			0
$853$	4.51320	−	25.5956i	0.154529	−	0.876377i	−0.804686	−	0.593700i	$-0.797667\pi$
$853$	4.51320	−	25.5956i	0.154529	−	0.876377i	0.959215	−	0.282677i	$-0.0912223\pi$
$854$	−2.14653	−	3.71791i	−0.0734529	−	0.127224i
$855$		0			0
$856$	−0.438904	+	0.760204i	−0.0150014	+	0.0259832i
$857$	3.15544	+	2.64773i	0.107788	+	0.0904447i	0.695089	−	0.718924i	$-0.255365\pi$
$857$	3.15544	+	2.64773i	0.107788	+	0.0904447i	−0.587301	+	0.809369i	$0.699810\pi$
$858$		0			0
$859$	−1.11646	−	6.33175i	−0.0380931	−	0.216036i	0.959819	−	0.280619i	$-0.0905396\pi$
$859$	−1.11646	−	6.33175i	−0.0380931	−	0.216036i	−0.997912	+	0.0645822i	$0.979429\pi$
$860$	31.4130	−	26.3587i	1.07118	−	0.898823i
$861$		0			0
$862$	2.01955	−	0.735058i	0.0687863	−	0.0250362i
$863$	−29.6195			−1.00826			−0.504129	−	0.863628i	$-0.668187\pi$
$863$	−29.6195			−1.00826			−0.504129	+	0.863628i	$0.668187\pi$
$864$		0			0
$865$	−81.6282			−2.77544
$866$	0.123639	−	0.0450010i	0.00420143	−	0.00152920i
$867$		0			0
$868$	−29.9685	+	25.1465i	−1.01720	+	0.853529i
$869$	5.10327	+	28.9421i	0.173117	+	0.981793i
$870$		0			0
$871$	0.710588	+	0.596254i	0.0240774	+	0.0202033i
$872$	−2.54326	+	4.40505i	−0.0861256	+	0.149174i
$873$		0			0
$874$	0.345251	+	0.597993i	0.0116783	+	0.0202274i
$875$	−7.79297	+	44.1961i	−0.263451	+	1.49410i
$876$		0			0
$877$	29.9458	+	10.8994i	1.01120	+	0.368046i	0.793893	−	0.608057i	$-0.208051\pi$
$877$	29.9458	+	10.8994i	1.01120	+	0.368046i	0.217306	+	0.976104i	$0.430273\pi$
$878$	−4.89410	−	1.78131i	−0.165168	−	0.0601162i
$879$		0			0
$880$	6.17813	−	35.0379i	0.208265	−	1.18113i
$881$	17.3932	+	30.1259i	0.585991	+	1.01497i	0.994751	+	0.102325i	$0.0326280\pi$
$881$	17.3932	+	30.1259i	0.585991	+	1.01497i	−0.408760	+	0.912642i	$0.634039\pi$
$882$		0			0
$883$	15.1882	−	26.3067i	0.511124	−	0.885292i	−0.488793	−	0.872400i	$-0.662563\pi$
$883$	15.1882	−	26.3067i	0.511124	−	0.885292i	0.999917	−	0.0128924i	$-0.00410388\pi$
$884$	5.33803	+	4.47914i	0.179538	+	0.150650i
$885$		0			0
$886$	0.410352	+	2.32722i	0.0137861	+	0.0781846i
$887$	38.3234	−	32.1571i	1.28677	−	1.07973i	0.294502	−	0.955651i	$-0.404846\pi$
$887$	38.3234	−	32.1571i	1.28677	−	1.07973i	0.992272	−	0.124080i	$-0.0395981\pi$
$888$		0			0
$889$	−59.2434	+	21.5628i	−1.98696	+	0.723194i
$890$	−4.87263			−0.163331
$891$		0			0
$892$	−46.4515			−1.55531
$893$	0.636818	−	0.231783i	0.0213103	−	0.00775632i
$894$		0			0
$895$	26.0151	−	21.8293i	0.869590	−	0.729673i
$896$	−2.80582	−	15.9126i	−0.0937358	−	0.531602i
$897$		0			0
$898$	−2.91502	−	2.44599i	−0.0972754	−	0.0816238i
$899$	21.4556	−	37.1621i	0.715583	−	1.23943i
$900$		0			0
$901$	−20.4399	−	35.4029i	−0.680950	−	1.17944i
$902$	−0.393692	+	2.23274i	−0.0131085	+	0.0743420i
$903$		0			0
$904$	6.03495	+	2.19654i	0.200719	+	0.0730559i
$905$	−25.0377	−	9.11298i	−0.832282	−	0.302926i
$906$		0			0
$907$	−7.65169	+	43.3949i	−0.254070	+	1.44090i	0.544378	+	0.838840i	$0.316766\pi$
$907$	−7.65169	+	43.3949i	−0.254070	+	1.44090i	−0.798448	+	0.602063i	$0.794345\pi$
$908$	−10.3273	−	17.8874i	−0.342723	−	0.593614i
$909$		0			0
$910$	−0.749593	+	1.29833i	−0.0248488	+	0.0430393i
$911$	28.4802	+	23.8977i	0.943591	+	0.791767i	0.978207	−	0.207634i	$-0.0665762\pi$
$911$	28.4802	+	23.8977i	0.943591	+	0.791767i	−0.0346154	+	0.999401i	$0.511021\pi$
$912$		0			0
$913$	−3.90106	−	22.1240i	−0.129106	−	0.732198i
$914$	−0.197280	+	0.165538i	−0.00652546	+	0.00547551i
$915$		0			0
$916$	−25.7001	+	9.35407i	−0.849155	+	0.309067i
$917$	−1.98815			−0.0656544
$918$		0			0
$919$	12.3976			0.408958			0.204479	−	0.978871i	$-0.434450\pi$
$919$	12.3976			0.408958			0.204479	+	0.978871i	$0.434450\pi$
$920$	−15.7319	+	5.72595i	−0.518666	+	0.188779i
$921$		0			0
$922$	−0.942569	+	0.790909i	−0.0310418	+	0.0260472i
$923$	0.653624	+	3.70689i	0.0215143	+	0.122014i
$924$		0			0
$925$	34.0493	+	28.5708i	1.11953	+	0.939401i
$926$	2.29545	−	3.97584i	0.0754333	−	0.130654i
$927$		0			0
$928$	6.66377	+	11.5420i	0.218749	+	0.378884i
$929$	−5.79780	+	32.8810i	−0.190220	+	1.07879i	0.728844	+	0.684680i	$0.240058\pi$
$929$	−5.79780	+	32.8810i	−0.190220	+	1.07879i	−0.919064	+	0.394109i	$0.871053\pi$
$930$		0			0
$931$	1.25912	+	0.458281i	0.0412659	+	0.0150196i
$932$	14.0690	+	5.12069i	0.460845	+	0.167734i
$933$		0			0
$934$	0.785525	−	4.45493i	0.0257031	−	0.145770i
$935$	−21.5199	−	37.2736i	−0.703777	−	1.21898i
$936$		0			0
$937$	12.4220	−	21.5156i	0.405810	−	0.702884i	−0.588605	−	0.808421i	$-0.700323\pi$
$937$	12.4220	−	21.5156i	0.405810	−	0.702884i	0.994415	+	0.105537i	$0.0336561\pi$
$938$	−0.486991	−	0.408634i	−0.0159008	−	0.0133424i
$939$		0			0
$940$	1.41584	+	8.02965i	0.0461797	+	0.261898i
$941$	−19.4804	+	16.3460i	−0.635044	+	0.532865i	−0.902492	−	0.430707i	$-0.858264\pi$
$941$	−19.4804	+	16.3460i	−0.635044	+	0.532865i	0.267448	+	0.963572i	$0.413820\pi$
$942$		0			0
$943$	−32.2500	+	11.7381i	−1.05021	+	0.382244i
$944$	−45.2900			−1.47406
$945$		0			0
$946$	−2.40094			−0.0780612
$947$	15.6272	−	5.68785i	0.507817	−	0.184830i	−0.0753897	−	0.997154i	$-0.524020\pi$
$947$	15.6272	−	5.68785i	0.507817	−	0.184830i	0.583206	+	0.812324i	$0.301798\pi$
$948$		0			0
$949$	−2.52004	+	2.11456i	−0.0818039	+	0.0686416i
$950$	−0.164701	−	0.934067i	−0.00534361	−	0.0303051i
$951$		0			0
$952$	−7.37224	−	6.18605i	−0.238936	−	0.200491i
$953$	7.13357	−	12.3557i	0.231079	−	0.400240i	−0.727047	−	0.686588i	$-0.759108\pi$
$953$	7.13357	−	12.3557i	0.231079	−	0.400240i	0.958126	+	0.286347i	$0.0924411\pi$
$954$		0			0
$955$	22.3365	+	38.6879i	0.722791	+	1.25191i
$956$	−5.66474	+	32.1263i	−0.183211	+	1.03904i
$957$		0			0
$958$	1.69152	+	0.615664i	0.0546507	+	0.0198912i
$959$	−24.4633	−	8.90391i	−0.789961	−	0.287522i
$960$		0			0
$961$	2.06782	−	11.7272i	0.0667037	−	0.378296i
$962$	0.328209	+	0.568474i	0.0105819	+	0.0183283i
$963$		0			0
$964$	−14.3013	+	24.7706i	−0.460613	+	0.797806i
$965$	25.3997	+	21.3128i	0.817644	+	0.686085i
$966$		0			0
$967$	−6.78700	−	38.4910i	−0.218255	−	1.23779i	−0.875168	−	0.483819i	$-0.839249\pi$
$967$	−6.78700	−	38.4910i	−0.218255	−	1.23779i	0.656913	−	0.753967i	$-0.271862\pi$
$968$	2.52061	−	2.11504i	0.0810155	−	0.0679801i
$969$		0			0
$970$	−0.575989	+	0.209643i	−0.0184939	+	0.00673123i
$971$	4.40370			0.141321			0.0706607	−	0.997500i	$-0.477489\pi$
$971$	4.40370			0.141321			0.0706607	+	0.997500i	$0.477489\pi$
$972$		0			0
$973$	40.7619			1.30677
$974$	3.00160	−	1.09249i	0.0961775	−	0.0350058i
$975$		0			0
$976$	23.9661	−	20.1100i	0.767138	−	0.643705i
$977$	−7.31520	−	41.4866i	−0.234034	−	1.32727i	−0.844639	−	0.535337i	$-0.820185\pi$
$977$	−7.31520	−	41.4866i	−0.234034	−	1.32727i	0.610605	−	0.791936i	$-0.290926\pi$
$978$		0			0
$979$	−14.3898	−	12.0745i	−0.459899	−	0.385901i
$980$	−8.06057	+	13.9613i	−0.257486	+	0.445978i
$981$		0			0
$982$	1.46804	+	2.54272i	0.0468470	+	0.0811413i
$983$	3.54696	−	20.1158i	0.113131	−	0.641595i	−0.874528	−	0.484974i	$-0.838829\pi$
$983$	3.54696	−	20.1158i	0.113131	−	0.641595i	0.987659	−	0.156621i	$-0.0500600\pi$
$984$		0			0
$985$	25.9757	+	9.45437i	0.827654	+	0.301241i
$986$	4.92238	+	1.79160i	0.156761	+	0.0570562i
$987$		0			0
$988$	−0.160153	+	0.908272i	−0.00509514	+	0.0288960i
$989$	−18.1723	−	31.4753i	−0.577844	−	1.00086i
$990$		0			0
$991$	−0.0340356	+	0.0589514i	−0.00108118	+	0.00187265i	−0.866565	−	0.499063i	$-0.833677\pi$
$991$	−0.0340356	+	0.0589514i	−0.00108118	+	0.00187265i	0.865484	+	0.500936i	$0.167011\pi$
$992$	10.2088	+	8.56617i	0.324128	+	0.271976i
$993$		0			0
$994$	−0.447951	−	2.54046i	−0.0142082	−	0.0805784i
$995$	29.7222	−	24.9399i	0.942256	−	0.790647i
$996$		0			0
$997$	−10.0041	+	3.64118i	−0.316832	+	0.115317i	−0.495541	−	0.868585i	$-0.665030\pi$
$997$	−10.0041	+	3.64118i	−0.316832	+	0.115317i	0.178709	+	0.983902i	$0.442808\pi$
$998$	4.26319			0.134949
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.t.163.1		12
3.2	odd	2		729.2.e.k.163.2		12
9.2	odd	6		729.2.e.u.406.1		12
9.4	even	3		729.2.e.s.649.2		12
9.5	odd	6		729.2.e.l.649.1		12
9.7	even	3		729.2.e.j.406.2		12
27.2	odd	18		729.2.a.e.1.3	yes	6
27.4	even	9	inner	729.2.e.t.568.1		12
27.5	odd	18		729.2.e.l.82.1		12
27.7	even	9		729.2.c.d.487.3		12
27.11	odd	18		729.2.c.a.244.4		12
27.13	even	9		729.2.e.j.325.2		12
27.14	odd	18		729.2.e.u.325.1		12
27.16	even	9		729.2.c.d.244.3		12
27.20	odd	18		729.2.c.a.487.4		12
27.22	even	9		729.2.e.s.82.2		12
27.23	odd	18		729.2.e.k.568.2		12
27.25	even	9		729.2.a.b.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.b.1.4	✓	6	27.25	even	9
729.2.a.e.1.3	yes	6	27.2	odd	18
729.2.c.a.244.4		12	27.11	odd	18
729.2.c.a.487.4		12	27.20	odd	18
729.2.c.d.244.3		12	27.16	even	9
729.2.c.d.487.3		12	27.7	even	9
729.2.e.j.325.2		12	27.13	even	9
729.2.e.j.406.2		12	9.7	even	3
729.2.e.k.163.2		12	3.2	odd	2
729.2.e.k.568.2		12	27.23	odd	18
729.2.e.l.82.1		12	27.5	odd	18
729.2.e.l.649.1		12	9.5	odd	6
729.2.e.s.82.2		12	27.22	even	9
729.2.e.s.649.2		12	9.4	even	3
729.2.e.t.163.1		12	1.1	even	1	trivial
729.2.e.t.568.1		12	27.4	even	9	inner
729.2.e.u.325.1		12	27.14	odd	18
729.2.e.u.406.1		12	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.162544 + 0.0591613i) q^{2} +(-1.50917 + 1.26634i) q^{4} +(-0.648847 - 3.67980i) q^{5} +(2.32226 + 1.94861i) q^{7} +(0.343364 - 0.594724i) q^{8} +O(q^{10})\)	\(q+(-0.162544 + 0.0591613i) q^{2} +(-1.50917 + 1.26634i) q^{4} +(-0.648847 - 3.67980i) q^{5} +(2.32226 + 1.94861i) q^{7} +(0.343364 - 0.594724i) q^{8} +(0.323168 + 0.559743i) q^{10} +(-0.432678 + 2.45384i) q^{11} +(0.718995 + 0.261693i) q^{13} +(-0.492752 - 0.179347i) q^{14} +(0.663574 - 3.76332i) q^{16} +(-2.31139 - 4.00345i) q^{17} +(0.305922 - 0.529872i) q^{19} +(5.63910 + 4.73177i) q^{20} +(-0.0748430 - 0.424456i) q^{22} +(4.99796 - 4.19379i) q^{23} +(-8.42143 + 3.06515i) q^{25} -0.132351 q^{26} -5.97229 q^{28} +(6.15583 - 2.24054i) q^{29} +(5.01792 - 4.21053i) q^{31} +(0.353281 + 2.00355i) q^{32} +(0.612552 + 0.513992i) q^{34} +(5.66369 - 9.80980i) q^{35} +(-2.47984 - 4.29522i) q^{37} +(-0.0183779 + 0.104226i) q^{38} +(-2.41125 - 0.877625i) q^{40} +(-4.94301 - 1.79911i) q^{41} +(0.967320 - 5.48594i) q^{43} +(-2.45442 - 4.25118i) q^{44} +(-0.564280 + 0.977362i) q^{46} +(0.848483 + 0.711962i) q^{47} +(0.380286 + 2.15671i) q^{49} +(1.18752 - 0.996445i) q^{50} +(-1.41648 + 0.515556i) q^{52} +8.84310 q^{53} +9.31038 q^{55} +(1.95627 - 0.712023i) q^{56} +(-0.868041 + 0.728373i) q^{58} +(-2.05804 - 11.6717i) q^{59} +(6.27161 + 5.26250i) q^{61} +(-0.566533 + 0.981264i) q^{62} +(3.64541 + 6.31404i) q^{64} +(0.496458 - 2.81555i) q^{65} +(1.13923 + 0.414644i) q^{67} +(8.55801 + 3.11486i) q^{68} +(-0.340240 + 1.92960i) q^{70} +(2.45973 + 4.26038i) q^{71} +(-2.14972 + 3.72343i) q^{73} +(0.657195 + 0.551452i) q^{74} +(0.209312 + 1.18707i) q^{76} +(-5.78637 + 4.85534i) q^{77} +(11.0833 - 4.03399i) q^{79} -14.2788 q^{80} +0.909895 q^{82} +(-8.47234 + 3.08368i) q^{83} +(-13.2321 + 11.1031i) q^{85} +(0.167323 + 0.948936i) q^{86} +(1.31079 + 1.09989i) q^{88} +(-3.76943 + 6.52884i) q^{89} +(1.15976 + 2.00876i) q^{91} +(-2.23199 + 12.6583i) q^{92} +(-0.180037 - 0.0655279i) q^{94} +(-2.14832 - 0.781924i) q^{95} +(-0.164680 + 0.933947i) q^{97} +(-0.189407 - 0.328062i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8} - 6 q^{10} - 15 q^{11} - 3 q^{13} - 21 q^{14} + 9 q^{16} - 9 q^{17} - 12 q^{19} - 3 q^{20} + 33 q^{22} + 15 q^{23} - 12 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} - 12 q^{31} - 27 q^{32} + 27 q^{34} + 30 q^{35} - 3 q^{37} - 39 q^{38} + 24 q^{40} - 39 q^{41} + 24 q^{43} - 33 q^{44} + 3 q^{46} - 42 q^{47} - 30 q^{49} - 15 q^{50} - 45 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} - 30 q^{58} + 15 q^{59} - 3 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} - 3 q^{67} + 36 q^{68} - 75 q^{70} - 12 q^{73} + 60 q^{74} + 30 q^{76} + 33 q^{77} + 33 q^{79} + 42 q^{80} - 42 q^{82} - 33 q^{83} - 18 q^{85} - 30 q^{86} - 42 q^{88} - 9 q^{89} - 18 q^{91} + 33 q^{92} - 66 q^{94} + 12 q^{95} + 15 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8 - 6 * q^10 - 15 * q^11 - 3 * q^13 - 21 * q^14 + 9 * q^16 - 9 * q^17 - 12 * q^19 - 3 * q^20 + 33 * q^22 + 15 * q^23 - 12 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 - 12 * q^31 - 27 * q^32 + 27 * q^34 + 30 * q^35 - 3 * q^37 - 39 * q^38 + 24 * q^40 - 39 * q^41 + 24 * q^43 - 33 * q^44 + 3 * q^46 - 42 * q^47 - 30 * q^49 - 15 * q^50 - 45 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 - 30 * q^58 + 15 * q^59 - 3 * q^61 - 30 * q^62 - 6 * q^64 - 6 * q^65 - 3 * q^67 + 36 * q^68 - 75 * q^70 - 12 * q^73 + 60 * q^74 + 30 * q^76 + 33 * q^77 + 33 * q^79 + 42 * q^80 - 42 * q^82 - 33 * q^83 - 18 * q^85 - 30 * q^86 - 42 * q^88 - 9 * q^89 - 18 * q^91 + 33 * q^92 - 66 * q^94 + 12 * q^95 + 15 * q^97 + 18 * q^98

Introduction

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