LMFDB - Embedded newform 729.2.e.k.568.2

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			568.2
Root			$0.0878222i$ of defining polynomial
Character	$\chi$	$=$	729.568
Dual form			729.2.e.k.163.2

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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	$-0.369410\pi$
$2$	0.162544	+	0.0591613i	0.114936	+	0.0418333i	−0.283912	+	0.958850i	$0.591632\pi$
$3$		0			0
$3$		0			0
$4$	−1.50917	−	1.26634i	−0.754584	−	0.633171i
$5$	0.648847	−	3.67980i	0.290173	−	1.64565i	−0.396025	−	0.918240i	$-0.629611\pi$
$5$	0.648847	−	3.67980i	0.290173	−	1.64565i	0.686198	−	0.727415i	$-0.259278\pi$
$6$		0			0
$7$	2.32226	−	1.94861i	0.877733	−	0.736505i	−0.0879791	−	0.996122i	$-0.528041\pi$
$7$	2.32226	−	1.94861i	0.877733	−	0.736505i	0.965712	+	0.259617i	$0.0835964\pi$
$8$	−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	0.977916	+	0.208999i	$0.0670206\pi$
$11$	0.432678	+	2.45384i	0.130457	+	0.739861i	−0.847458	+	0.530862i	$0.821868\pi$
$12$		0			0
$13$	0.718995	−	0.261693i	0.199413	−	0.0725805i	−0.240383	−	0.970678i	$-0.577273\pi$
$13$	0.718995	−	0.261693i	0.199413	−	0.0725805i	0.439796	+	0.898098i	$0.355051\pi$
$14$	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	−0.436850	−	0.899534i	$-0.643906\pi$
$17$	2.31139	−	4.00345i	0.560595	−	0.970979i	0.997445	−	0.0714442i	$-0.0227608\pi$
$18$		0			0
$19$	0.305922	+	0.529872i	0.0701833	+	0.121561i	0.898982	−	0.437987i	$-0.144308\pi$
$19$	0.305922	+	0.529872i	0.0701833	+	0.121561i	−0.828798	+	0.559548i	$0.810975\pi$
$20$	−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	$-0.515891\pi$
$23$	−4.99796	−	4.19379i	−1.04215	−	0.874465i	−0.992246	+	0.124289i	$0.960335\pi$
$24$		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	$-0.597011\pi$
$29$	−6.15583	−	2.24054i	−1.14311	−	0.416057i	−0.843035	+	0.537859i	$0.819233\pi$
$30$		0			0
$31$	5.01792	+	4.21053i	0.901245	+	0.756234i	0.970433	−	0.241370i	$-0.0775966\pi$
$31$	5.01792	+	4.21053i	0.901245	+	0.756234i	−0.0691887	+	0.997604i	$0.522041\pi$
$32$	−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	−0.994630	−	0.103497i	$-0.966997\pi$
$37$	−2.47984	+	4.29522i	−0.407684	+	0.706129i	0.586946	+	0.809626i	$0.300330\pi$
$38$	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	$-0.476376\pi$
$41$	4.94301	−	1.79911i	0.771968	−	0.280973i	0.697819	+	0.716274i	$0.254154\pi$
$42$		0			0
$43$	0.967320	+	5.48594i	0.147515	+	0.836599i	0.965313	+	0.261094i	$0.0840832\pi$
$43$	0.967320	+	5.48594i	0.147515	+	0.836599i	−0.817798	+	0.575505i	$0.804806\pi$
$44$	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	$-0.747964\pi$
$47$	−0.848483	+	0.711962i	−0.123764	+	0.103850i	0.578805	+	0.815466i	$0.303519\pi$
$48$		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	$-0.707766\pi$
$53$	−8.84310			−1.21469			−0.607346	+	0.794437i	$0.707766\pi$
$54$		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	−0.492616	−	0.870247i	$-0.663959\pi$
$59$	2.05804	−	11.6717i	0.267933	−	1.51953i	0.760550	−	0.649280i	$-0.224929\pi$
$60$		0			0
$61$	6.27161	−	5.26250i	0.802997	−	0.673795i	−0.145928	−	0.989295i	$-0.546617\pi$
$61$	6.27161	−	5.26250i	0.802997	−	0.673795i	0.948925	+	0.315500i	$0.102172\pi$
$62$	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	−0.271492	−	0.962441i	$-0.587517\pi$
$67$	1.13923	−	0.414644i	0.139179	−	0.0506568i	0.410670	+	0.911784i	$0.365295\pi$
$68$	−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	$-0.927626\pi$
$71$	−2.45973	+	4.26038i	−0.291916	+	0.505614i	0.682346	+	0.731029i	$0.260960\pi$
$72$		0			0
$73$	−2.14972	−	3.72343i	−0.251606	−	0.435795i	0.712362	−	0.701812i	$-0.247625\pi$
$73$	−2.14972	−	3.72343i	−0.251606	−	0.435795i	−0.963968	+	0.266017i	$0.914292\pi$
$74$	−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	0.879376	−	0.476127i	$-0.157960\pi$
$79$	11.0833	+	4.03399i	1.24697	+	0.453860i	0.367593	+	0.929987i	$0.380182\pi$
$80$	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	$-0.224122\pi$
$83$	8.47234	+	3.08368i	0.929960	+	0.338478i	0.167766	+	0.985827i	$0.446345\pi$
$84$		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	$-0.0358302\pi$
$89$	3.76943	+	6.52884i	0.399558	+	0.692055i	−0.594113	+	0.804382i	$0.702497\pi$
$90$		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	0.975305	−	0.220861i	$-0.0708866\pi$
$97$	−0.164680	−	0.933947i	−0.0167207	−	0.0948279i	−0.992026	+	0.126033i	$0.959776\pi$
$98$	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	$-0.632214\pi$
$101$	4.29610	−	3.60485i	0.427477	−	0.358696i	0.830999	+	0.556274i	$0.187769\pi$
$102$		0			0
$103$	−1.63664	+	9.28183i	−0.161263	+	0.914566i	0.791572	+	0.611076i	$0.209263\pi$
$103$	−1.63664	+	9.28183i	−0.161263	+	0.914566i	−0.952835	+	0.303490i	$0.901848\pi$
$104$	−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	$-0.480320\pi$
$107$	1.27825			0.123573			0.0617864	+	0.998089i	$0.480320\pi$
$108$		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	0.808029	+	0.589143i	$0.200534\pi$
$113$	−1.62395	+	9.20989i	−0.152768	+	0.866393i	−0.960798	+	0.277251i	$0.910577\pi$
$114$		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	−0.795204	−	0.606342i	$-0.792636\pi$
$127$	−10.3984	−	18.0106i	−0.922710	−	1.59818i	−0.127505	−	0.991838i	$-0.540697\pi$
$128$	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	$-0.268657\pi$
$131$	0.502395	+	0.421559i	0.0438944	+	0.0368318i	−0.620577	+	0.784146i	$0.713101\pi$
$132$		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	$-0.269327\pi$
$137$	8.06971	+	2.93713i	0.689442	+	0.250936i	0.0265455	+	0.999648i	$0.491549\pi$
$138$		0			0
$139$	10.3003	+	8.64301i	0.873664	+	0.733091i	0.964866	−	0.262742i	$-0.0846267\pi$
$139$	10.3003	+	8.64301i	0.873664	+	0.733091i	−0.0912026	+	0.995832i	$0.529071\pi$
$140$	−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	$-0.482155\pi$
$149$	9.04179	−	3.29094i	0.740732	−	0.269604i	0.684700	+	0.728825i	$0.259933\pi$
$150$		0			0
$151$	−1.23780	−	7.01991i	−0.100731	−	0.571272i	−0.992840	−	0.119452i	$-0.961886\pi$
$151$	−1.23780	−	7.01991i	−0.100731	−	0.571272i	0.892109	−	0.451820i	$-0.149225\pi$
$152$	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	−0.884090	−	0.467316i	$-0.845221\pi$
$157$	1.33462	−	7.56900i	0.106514	−	0.604072i	0.990605	−	0.136756i	$-0.0436678\pi$
$158$	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	0.875816	+	0.482645i	$0.160324\pi$
$167$	−1.45067	+	8.22716i	−0.112256	+	0.636637i	−0.988072	+	0.153991i	$0.950787\pi$
$168$		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	−0.692833	−	0.721098i	$-0.743638\pi$
$173$	−3.79348	−	21.5139i	−0.288413	−	1.63567i	0.404420	−	0.914573i	$-0.367473\pi$
$174$		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	$-0.943645\pi$
$179$	−4.54433	+	7.87101i	−0.339659	+	0.588307i	0.644709	+	0.764428i	$0.276978\pi$
$180$		0			0
$181$	3.56539	+	6.17543i	0.265013	+	0.459016i	0.967567	−	0.252614i	$-0.0812904\pi$
$181$	3.56539	+	6.17543i	0.265013	+	0.459016i	−0.702554	+	0.711630i	$0.747957\pi$
$182$	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	$-0.246507\pi$
$191$	11.2346	+	4.08907i	0.812908	+	0.295874i	0.0980836	+	0.995178i	$0.468729\pi$
$192$		0			0
$193$	−6.79760	−	5.70386i	−0.489302	−	0.410573i	0.364474	−	0.931214i	$-0.381249\pi$
$193$	−6.79760	−	5.70386i	−0.489302	−	0.410573i	−0.853776	+	0.520640i	$0.825693\pi$
$194$	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	$-0.0817768\pi$
$197$	3.69895	+	6.40677i	0.263539	+	0.456464i	−0.703641	+	0.710556i	$0.748443\pi$
$198$		0			0
$199$	5.19187	−	8.99259i	0.368042	−	0.637468i	−0.621217	−	0.783638i	$-0.713362\pi$
$199$	5.19187	−	8.99259i	0.368042	−	0.637468i	0.989259	+	0.146171i	$0.0466948\pi$
$200$	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	−0.560706	−	0.828015i	$-0.689470\pi$
$211$	3.62250	−	20.5442i	0.249383	−	1.41432i	0.810089	−	0.586307i	$-0.199419\pi$
$212$	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	0.210227	−	0.977653i	$-0.432580\pi$
$223$	18.0622	−	15.1560i	1.20953	−	1.01492i	0.999305	−	0.0372657i	$-0.0118648\pi$
$224$	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	0.983695	+	0.179843i	$0.0575591\pi$
$227$	1.82055	+	10.3249i	0.120834	+	0.685285i	−0.862861	+	0.505441i	$0.831330\pi$
$228$		0			0
$229$	13.0452	−	4.74807i	0.862051	−	0.313761i	0.127107	−	0.991889i	$-0.459431\pi$
$229$	13.0452	−	4.74807i	0.862051	−	0.313761i	0.734944	+	0.678128i	$0.237208\pi$
$230$	−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	$-0.753253\pi$
$233$	3.79982	−	6.58149i	0.248935	−	0.431167i	0.963230	+	0.268676i	$0.0865862\pi$
$234$		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	$-0.457672\pi$
$239$	−12.6847	−	10.6437i	−0.820504	−	0.688485i	−0.953090	+	0.302687i	$0.902116\pi$
$240$		0			0
$241$	13.6429	+	4.96562i	0.878818	+	0.319863i	0.741732	−	0.670696i	$-0.234004\pi$
$241$	13.6429	+	4.96562i	0.878818	+	0.319863i	0.137085	+	0.990559i	$0.456227\pi$
$242$	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	$-0.0744497\pi$
$251$	4.52591	+	7.83910i	0.285673	+	0.494800i	−0.687099	+	0.726563i	$0.741116\pi$
$252$		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	$-0.513280\pi$
$257$	9.11490	−	3.31755i	0.568572	−	0.206943i	0.610279	+	0.792187i	$0.291057\pi$
$258$		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	0.273826	−	0.961779i	$-0.411711\pi$
$263$	20.5723	−	17.2622i	1.26854	−	1.06443i	0.994717	−	0.102655i	$-0.0327336\pi$
$264$		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	$-0.616495\pi$
$269$	−11.7388			−0.715729			−0.357865	+	0.933774i	$0.616495\pi$
$270$		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	−0.665835	−	0.746099i	$-0.731924\pi$
$277$	−0.777094	+	0.652060i	−0.0466911	+	0.0391785i	0.619144	+	0.785278i	$0.287480\pi$
$278$	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	0.704652	+	0.709553i	$0.251103\pi$
$281$	4.78044	+	27.1112i	0.285177	+	1.61732i	−0.419475	+	0.907767i	$0.637786\pi$
$282$		0			0
$283$	25.1865	−	9.16713i	1.49718	−	0.544929i	0.541852	−	0.840474i	$-0.317724\pi$
$283$	25.1865	−	9.16713i	1.49718	−	0.544929i	0.955329	+	0.295545i	$0.0955013\pi$
$284$	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	$-0.461242\pi$
$293$	−14.2923	−	11.9927i	−0.834964	−	0.700618i	−0.956425	+	0.291978i	$0.905687\pi$
$294$		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	−0.252551	+	0.967584i	$0.581269\pi$
$307$	−16.8946	+	29.2624i	−0.964227	+	1.67009i	−0.711677	+	0.702507i	$0.752064\pi$
$308$	−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	0.862167	−	0.506625i	$-0.169107\pi$
$311$	32.5947	−	11.8635i	1.84828	−	0.672718i	0.986110	−	0.166093i	$-0.0531152\pi$
$312$		0			0
$313$	0.580051	+	3.28963i	0.0327864	+	0.185941i	0.996803	−	0.0799021i	$-0.0254608\pi$
$313$	0.580051	+	3.28963i	0.0327864	+	0.185941i	−0.964016	+	0.265843i	$0.914350\pi$
$314$	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	−0.352364	+	0.935863i	$0.614622\pi$
$317$	−23.7725	+	19.9475i	−1.33520	+	1.12036i	−0.982832	+	0.184500i	$0.940933\pi$
$318$		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	−0.571306	−	0.820737i	$-0.693563\pi$
$331$	2.50625	−	2.10299i	0.137756	−	0.115591i	0.709062	+	0.705146i	$0.249119\pi$
$332$	−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	−0.499768	−	0.866160i	$-0.666581\pi$
$337$	−5.98190	+	2.17723i	−0.325855	+	0.118602i	0.173912	+	0.984761i	$0.444359\pi$
$338$	−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	$-0.353615\pi$
$347$	−6.73538	−	5.65165i	−0.361574	−	0.303397i	−0.805418	+	0.592708i	$0.798059\pi$
$348$		0			0
$349$	−13.5318	−	4.92517i	−0.724340	−	0.263638i	−0.0465728	−	0.998915i	$-0.514830\pi$
$349$	−13.5318	−	4.92517i	−0.724340	−	0.263638i	−0.677767	+	0.735277i	$0.737052\pi$
$350$	−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	$-0.733737\pi$
$353$	−31.1982	−	11.3552i	−1.66051	−	0.604378i	−0.990444	+	0.137919i	$0.955959\pi$
$354$		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	$-0.208324\pi$
$359$	−2.47257	−	4.28262i	−0.130497	−	0.226028i	−0.923868	+	0.382710i	$0.874991\pi$
$360$		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	0.971426	−	0.237345i	$-0.0762770\pi$
$367$	−0.432810	−	2.45459i	−0.0225925	−	0.128128i	−0.994018	+	0.109216i	$0.965166\pi$
$368$	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	0.551028	+	0.834487i	$0.314236\pi$
$373$	−4.87041	+	27.6215i	−0.252180	+	1.43019i	−0.803208	+	0.595699i	$0.796875\pi$
$374$	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	$-0.944808\pi$
$383$	−0.00775737	+	0.0439942i	−0.000396383	+	0.00224800i	0.984609	+	0.174772i	$0.0559189\pi$
$384$		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	0.926296	+	0.376796i	$0.122974\pi$
$389$	3.64353	+	20.6635i	0.184734	+	1.04768i	−0.741562	+	0.670885i	$0.765915\pi$
$390$		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	0.866056	−	0.499947i	$-0.166647\pi$
$397$	0.00122821	+	0.00212731i	6.16419e−5	+	0.000106767i	−0.865995	+	0.500053i	$0.833314\pi$
$398$	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	$-0.0605783\pi$
$401$	19.3475	+	16.2345i	0.966166	+	0.810710i	−0.0157788	+	0.999876i	$0.505023\pi$
$402$		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	0.0844827	−	0.996425i	$-0.473076\pi$
$409$	−17.8401	−	14.9696i	−0.882134	−	0.740198i	−0.966617	+	0.256227i	$0.917521\pi$
$410$	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	$-0.888011\pi$
$419$	−29.4014	+	10.7013i	−1.43635	+	0.522790i	−0.497609	+	0.867401i	$0.665789\pi$
$420$		0			0
$421$	5.30141	+	30.0658i	0.258375	+	1.46532i	0.787259	+	0.616622i	$0.211499\pi$
$421$	5.30141	+	30.0658i	0.258375	+	1.46532i	−0.528885	+	0.848694i	$0.677390\pi$
$422$	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	$-0.403268\pi$
$431$	12.4246			0.598474			0.299237	+	0.954179i	$0.403268\pi$
$432$		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	0.103356	−	0.994644i	$-0.467042\pi$
$439$	23.0651	−	19.3539i	1.10084	−	0.923712i	0.997481	+	0.0709321i	$0.0225974\pi$
$440$	−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	−0.987858	−	0.155361i	$-0.950346\pi$
$443$	−2.37231	−	13.4540i	−0.112712	−	0.639220i	0.875146	−	0.483859i	$-0.160765\pi$
$444$		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	0.480657	+	0.876909i	$0.340398\pi$
$449$	−10.9995	+	19.0516i	−0.519097	+	0.899102i	−0.999754	+	0.0221934i	$0.992935\pi$
$450$		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	0.374535	−	0.927213i	$-0.377802\pi$
$457$	1.39904	+	0.509209i	0.0654443	+	0.0238198i	−0.309091	+	0.951033i	$0.600025\pi$
$458$	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	$-0.441861\pi$
$461$	−6.68435	−	2.43290i	−0.311321	−	0.113312i	−0.492956	+	0.870054i	$0.664083\pi$
$462$		0			0
$463$	−20.3314	−	17.0601i	−0.944879	−	0.792848i	0.0335484	−	0.999437i	$-0.489319\pi$
$463$	−20.3314	−	17.0601i	−0.944879	−	0.792848i	−0.978428	+	0.206589i	$0.933764\pi$
$464$	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	0.992038	+	0.125937i	$0.0401937\pi$
$467$	13.0760	+	22.6482i	0.605084	+	1.04804i	−0.386955	+	0.922099i	$0.626473\pi$
$468$		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	$-0.645814\pi$
$479$	7.97188	−	6.68920i	0.364244	−	0.305637i	0.806480	+	0.591262i	$0.201370\pi$
$480$		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	−0.843201	−	0.537598i	$-0.819332\pi$
$491$	2.94749	−	16.7160i	0.133018	−	0.754383i	0.976219	−	0.216785i	$-0.0695572\pi$
$492$		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	−0.803657	−	0.595093i	$-0.797115\pi$
$499$	−23.1598	+	8.42949i	−1.03678	+	0.377356i	−0.233119	+	0.972448i	$0.574893\pi$
$500$	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	0.0596120	−	0.998222i	$-0.481014\pi$
$503$	20.0569	−	34.7395i	0.894291	−	1.54896i	0.834679	−	0.550736i	$-0.185653\pi$
$504$		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	$-0.312757\pi$
$509$	−3.79079	−	3.18085i	−0.168024	−	0.140989i	−0.722922	+	0.690929i	$0.757202\pi$
$510$		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	$-0.112439\pi$
$521$	3.86979	+	6.70267i	0.169539	+	0.293649i	−0.768719	+	0.639586i	$0.779106\pi$
$522$		0			0
$523$	−18.0070	+	31.1891i	−0.787391	+	1.36380i	0.140169	+	0.990128i	$0.455236\pi$
$523$	−18.0070	+	31.1891i	−0.787391	+	1.36380i	−0.927560	+	0.373674i	$0.878098\pi$
$524$	−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	−0.975629	−	0.219426i	$-0.929582\pi$
$547$	−21.7264	+	18.2306i	−0.928953	+	0.779484i	0.0466761	+	0.998910i	$0.485137\pi$
$548$	−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	0.147914	+	0.989000i	$0.452744\pi$
$557$	−18.4687	+	31.9887i	−0.782542	+	1.35540i	−0.930456	+	0.366403i	$0.880589\pi$
$558$		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	$-0.437117\pi$
$563$	−17.4470	−	14.6398i	−0.735303	−	0.616992i	−0.931572	+	0.363558i	$0.881562\pi$
$564$		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	$-0.164894\pi$
$569$	29.0071	+	10.5577i	1.21604	+	0.442603i	0.347247	+	0.937774i	$0.387117\pi$
$570$		0			0
$571$	9.82107	+	8.24085i	0.410999	+	0.344869i	0.824727	−	0.565532i	$-0.191329\pi$
$571$	9.82107	+	8.24085i	0.410999	+	0.344869i	−0.413728	+	0.910401i	$0.635773\pi$
$572$	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	−0.510222	−	0.860043i	$-0.670437\pi$
$577$	11.7632	−	20.3745i	0.489708	−	0.848200i	0.999930	+	0.0118433i	$0.00376992\pi$
$578$	−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	$-0.797733\pi$
$587$	−8.72329	+	7.31971i	−0.360049	+	0.302117i	0.444762	+	0.895649i	$0.353288\pi$
$588$		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	$-0.217880\pi$
$593$	37.7324			1.54948			0.774742	+	0.632277i	$0.217880\pi$
$594$		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	0.0810181	+	0.996713i	$0.474183\pi$
$599$	−8.22366	+	46.6387i	−0.336010	+	1.90561i	−0.417028	+	0.908894i	$0.636928\pi$
$600$		0			0
$601$	−23.8297	+	19.9955i	−0.972033	+	0.815632i	−0.982868	−	0.184309i	$-0.940995\pi$
$601$	−23.8297	+	19.9955i	−0.972033	+	0.815632i	0.0108354	+	0.999941i	$0.496551\pi$
$602$	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	−0.836344	−	0.548205i	$-0.815311\pi$
$607$	−27.7082	+	10.0850i	−1.12464	+	0.409336i	−0.288297	+	0.957541i	$0.593089\pi$
$608$	−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	0.921057	−	0.389427i	$-0.127327\pi$
$613$	3.05214	+	5.28646i	0.123275	+	0.213518i	−0.797782	+	0.602945i	$0.793994\pi$
$614$	−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	$-0.152023\pi$
$617$	14.6469	+	12.2902i	0.589660	+	0.494784i	−0.298443	+	0.954427i	$0.596467\pi$
$618$		0			0
$619$	6.34655	+	2.30995i	0.255089	+	0.0928449i	0.466400	−	0.884574i	$-0.345551\pi$
$619$	6.34655	+	2.30995i	0.255089	+	0.0928449i	−0.211310	+	0.977419i	$0.567773\pi$
$620$	−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	−0.861442	−	0.507855i	$-0.830438\pi$
$631$	0.228453	−	0.395693i	0.00909458	−	0.0157523i	0.870537	+	0.492103i	$0.163772\pi$
$632$	−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	$-0.740280\pi$
$641$	−2.19934	+	1.84546i	−0.0868686	+	0.0728914i	0.598319	+	0.801258i	$0.295835\pi$
$642$		0			0
$643$	−0.295696	+	1.67697i	−0.0116611	+	0.0661334i	−0.990083	−	0.140484i	$-0.955134\pi$
$643$	−0.295696	+	1.67697i	−0.0116611	+	0.0661334i	0.978422	+	0.206617i	$0.0662454\pi$
$644$	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	$-0.248864\pi$
$647$	36.1004			1.41925			0.709626	+	0.704579i	$0.248864\pi$
$648$		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	0.366798	+	0.930301i	$0.380454\pi$
$653$	−7.56550	+	42.9061i	−0.296061	+	1.67904i	−0.662859	+	0.748744i	$0.730657\pi$
$654$		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	0.941144	+	0.338006i	$0.109752\pi$
$659$	4.42473	+	25.0939i	0.172363	+	0.977518i	−0.768781	+	0.639512i	$0.779136\pi$
$660$		0			0
$661$	−32.1067	+	11.6859i	−1.24880	+	0.454528i	−0.879998	−	0.474978i	$-0.842456\pi$
$661$	−32.1067	+	11.6859i	−1.24880	+	0.454528i	−0.368807	+	0.929506i	$0.620234\pi$
$662$	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	0.816232	−	0.577725i	$-0.196059\pi$
$673$	27.7620	+	10.1045i	1.07015	+	0.389502i	0.253916	+	0.967226i	$0.418281\pi$
$674$	−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	$-0.675536\pi$
$677$	−38.3209	−	13.9477i	−1.47279	−	0.536052i	−0.948857	+	0.315706i	$0.897759\pi$
$678$		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	−0.991991	−	0.126312i	$-0.959686\pi$
$683$	−15.8213	−	27.4033i	−0.605384	−	1.04856i	0.386606	−	0.922245i	$-0.373647\pi$
$684$		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	−0.920938	−	0.389709i	$-0.872576\pi$
$691$	−4.96369	−	28.1505i	−0.188828	−	1.07090i	0.732110	−	0.681186i	$-0.238536\pi$
$692$	−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	$-0.545417\pi$
$701$	−7.52982			−0.284397			−0.142199	+	0.989838i	$0.545417\pi$
$702$		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	−0.520189	−	0.854051i	$-0.674138\pi$
$709$	6.13907	−	5.15129i	0.230558	−	0.193461i	0.750746	+	0.660590i	$0.229694\pi$
$710$	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	0.496854	+	0.867834i	$0.334489\pi$
$719$	−13.4913	+	23.3676i	−0.503140	+	0.871464i	−0.999993	+	0.00362928i	$0.998845\pi$
$720$		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	0.585136	−	0.810935i	$-0.301041\pi$
$727$	13.8082	+	5.02576i	0.512116	+	0.186395i	−0.0730194	+	0.997331i	$0.523263\pi$
$728$	−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	0.0807207	−	0.996737i	$-0.474278\pi$
$733$	−24.0107	−	20.1474i	−0.886856	−	0.744161i	−0.967577	+	0.252576i	$0.918722\pi$
$734$	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	−0.870432	−	0.492288i	$-0.836161\pi$
$739$	−0.241454	+	0.418211i	−0.00888205	+	0.0153842i	0.861550	+	0.507672i	$0.169494\pi$
$740$	−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	$-0.900869\pi$
$743$	−40.4545	+	14.7242i	−1.48413	+	0.540179i	−0.532233	+	0.846598i	$0.678647\pi$
$744$		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	−0.449938	−	0.893060i	$-0.648554\pi$
$751$	7.62691	−	43.2543i	0.278310	−	1.57837i	0.728248	−	0.685314i	$-0.240335\pi$
$752$	−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	0.937044	+	0.349212i	$0.113551\pi$
$761$	−1.73592	+	9.84487i	−0.0629269	+	0.356876i	−0.999971	+	0.00766415i	$0.997560\pi$
$762$		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	−0.211873	−	0.977297i	$-0.567956\pi$
$769$	7.04412	−	2.56385i	0.254017	−	0.0924547i	0.465890	+	0.884842i	$0.345734\pi$
$770$	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	$-0.717207\pi$
$773$	9.91954	−	17.1812i	0.356781	−	0.617963i	0.987421	+	0.158112i	$0.0505408\pi$
$774$		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	0.996314	−	0.0857841i	$-0.0273395\pi$
$787$	30.4336	+	25.5368i	1.08484	+	0.910290i	0.0885273	+	0.996074i	$0.471784\pi$
$788$	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	$-0.559551\pi$
$797$	8.55680	−	3.11442i	0.303097	−	0.110318i	0.489092	+	0.872232i	$0.337328\pi$
$798$		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	$-0.483098\pi$
$809$	3.01910			0.106146			0.0530730	+	0.998591i	$0.483098\pi$
$810$		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	0.785183	+	0.619264i	$0.212569\pi$
$821$	7.42554	+	42.1123i	0.259153	+	1.46973i	−0.526030	+	0.850466i	$0.676320\pi$
$822$		0			0
$823$	33.1043	−	12.0490i	1.15394	−	0.420001i	0.307013	−	0.951705i	$-0.400670\pi$
$823$	33.1043	−	12.0490i	1.15394	−	0.420001i	0.846930	+	0.531704i	$0.178448\pi$
$824$	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	$-0.982878\pi$
$827$	−13.0190	+	22.5495i	−0.452714	+	0.784125i	0.545839	+	0.837890i	$0.316211\pi$
$828$		0			0
$829$	3.95134	+	6.84392i	0.137236	+	0.237699i	0.926449	−	0.376420i	$-0.122845\pi$
$829$	3.95134	+	6.84392i	0.137236	+	0.237699i	−0.789214	+	0.614119i	$0.789512\pi$
$830$	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	$-0.417215\pi$
$839$	−4.83791	−	1.76085i	−0.167023	−	0.0607914i	−0.424178	+	0.905579i	$0.639437\pi$
$840$		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	0.959215	+	0.282677i	$0.0912223\pi$
$853$	4.51320	+	25.5956i	0.154529	+	0.876377i	−0.804686	+	0.593700i	$0.797667\pi$
$854$	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	$-0.744635\pi$
$857$	−3.15544	+	2.64773i	−0.107788	+	0.0904447i	0.587301	+	0.809369i	$0.300190\pi$
$858$		0			0
$859$	−1.11646	+	6.33175i	−0.0380931	+	0.216036i	−0.997912	−	0.0645822i	$-0.979429\pi$
$859$	−1.11646	+	6.33175i	−0.0380931	+	0.216036i	0.959819	+	0.280619i	$0.0905396\pi$
$860$	−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	$-0.331813\pi$
$863$	29.6195			1.00826			0.504129	+	0.863628i	$0.331813\pi$
$864$		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	0.217306	−	0.976104i	$-0.430273\pi$
$877$	29.9458	−	10.8994i	1.01120	−	0.368046i	0.793893	+	0.608057i	$0.208051\pi$
$878$	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	0.408760	+	0.912642i	$0.365961\pi$
$881$	−17.3932	+	30.1259i	−0.585991	+	1.01497i	−0.994751	+	0.102325i	$0.967372\pi$
$882$		0			0
$883$	15.1882	+	26.3067i	0.511124	+	0.885292i	0.999917	+	0.0128924i	$0.00410388\pi$
$883$	15.1882	+	26.3067i	0.511124	+	0.885292i	−0.488793	+	0.872400i	$0.662563\pi$
$884$	−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	−0.992272	−	0.124080i	$-0.960402\pi$
$887$	−38.3234	−	32.1571i	−1.28677	−	1.07973i	−0.294502	−	0.955651i	$-0.595154\pi$
$888$		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	−0.798448	−	0.602063i	$-0.794345\pi$
$907$	−7.65169	−	43.3949i	−0.254070	−	1.44090i	0.544378	−	0.838840i	$-0.316766\pi$
$908$	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	$-0.933424\pi$
$911$	−28.4802	+	23.8977i	−0.943591	+	0.791767i	0.0346154	+	0.999401i	$0.488979\pi$
$912$		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	0.919064	+	0.394109i	$0.128947\pi$
$929$	5.79780	+	32.8810i	0.190220	+	1.07879i	−0.728844	+	0.684680i	$0.759942\pi$
$930$		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	0.994415	−	0.105537i	$-0.0336561\pi$
$937$	12.4220	+	21.5156i	0.405810	+	0.702884i	−0.588605	+	0.808421i	$0.700323\pi$
$938$	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	$-0.141736\pi$
$941$	19.4804	+	16.3460i	0.635044	+	0.532865i	−0.267448	+	0.963572i	$0.586180\pi$
$942$		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	$-0.475980\pi$
$947$	−15.6272	−	5.68785i	−0.507817	−	0.184830i	−0.583206	+	0.812324i	$0.698202\pi$
$948$		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	$-0.240892\pi$
$953$	−7.13357	−	12.3557i	−0.231079	−	0.400240i	−0.958126	+	0.286347i	$0.907559\pi$
$954$		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	0.656913	+	0.753967i	$0.271862\pi$
$967$	−6.78700	+	38.4910i	−0.218255	+	1.23779i	−0.875168	+	0.483819i	$0.839249\pi$
$968$	−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	$-0.522511\pi$
$971$	−4.40370			−0.141321			−0.0706607	+	0.997500i	$0.522511\pi$
$972$		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	−0.610605	−	0.791936i	$-0.709074\pi$
$977$	7.31520	−	41.4866i	0.234034	−	1.32727i	0.844639	−	0.535337i	$-0.179815\pi$
$978$		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	−0.987659	−	0.156621i	$-0.949940\pi$
$983$	−3.54696	−	20.1158i	−0.113131	−	0.641595i	0.874528	−	0.484974i	$-0.161171\pi$
$984$		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	0.865484	−	0.500936i	$-0.167011\pi$
$991$	−0.0340356	−	0.0589514i	−0.00108118	−	0.00187265i	−0.866565	+	0.499063i	$0.833677\pi$
$992$	−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	0.178709	−	0.983902i	$-0.442808\pi$
$997$	−10.0041	−	3.64118i	−0.316832	−	0.115317i	−0.495541	+	0.868585i	$0.665030\pi$
$998$	−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.k.568.2		12
3.2	odd	2		729.2.e.t.568.1		12
9.2	odd	6		729.2.e.s.82.2		12
9.4	even	3		729.2.e.u.325.1		12
9.5	odd	6		729.2.e.j.325.2		12
9.7	even	3		729.2.e.l.82.1		12
27.2	odd	18		729.2.e.j.406.2		12
27.4	even	9		729.2.c.a.244.4		12
27.5	odd	18		729.2.c.d.487.3		12
27.7	even	9	inner	729.2.e.k.163.2		12
27.11	odd	18		729.2.e.s.649.2		12
27.13	even	9		729.2.a.e.1.3	yes	6
27.14	odd	18		729.2.a.b.1.4	✓	6
27.16	even	9		729.2.e.l.649.1		12
27.20	odd	18		729.2.e.t.163.1		12
27.22	even	9		729.2.c.a.487.4		12
27.23	odd	18		729.2.c.d.244.3		12
27.25	even	9		729.2.e.u.406.1		12

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

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

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