LMFDB - Embedded newform 162.2.g.b.103.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			103.4
Character	$\chi$	$=$	162.103
Dual form			162.2.g.b.151.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.686242 - 0.727374i) q^{2} +(0.862629 + 1.50196i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-3.71739 + 0.434501i) q^{5} +(0.500511 - 1.65816i) q^{6} +(3.11355 + 1.56368i) q^{7} +(0.766044 - 0.642788i) q^{8} +(-1.51174 + 2.59126i) q^{9} +O(q^{10})$	\(q+(-0.686242 - 0.727374i) q^{2} +(0.862629 + 1.50196i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-3.71739 + 0.434501i) q^{5} +(0.500511 - 1.65816i) q^{6} +(3.11355 + 1.56368i) q^{7} +(0.766044 - 0.642788i) q^{8} +(-1.51174 + 2.59126i) q^{9} +(2.86707 + 2.40576i) q^{10} +(1.94788 + 4.51570i) q^{11} +(-1.54957 + 0.773839i) q^{12} +(-2.77423 - 0.657504i) q^{13} +(-0.999264 - 3.33778i) q^{14} +(-3.85933 - 5.20854i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(-0.261651 + 1.48390i) q^{17} +(2.92224 - 0.678630i) q^{18} +(-0.0992935 - 0.563121i) q^{19} +(-0.217618 - 3.73637i) q^{20} +(0.337255 + 6.02529i) q^{21} +(1.94788 - 4.51570i) q^{22} +(5.45342 - 2.73881i) q^{23} +(1.62625 + 0.596078i) q^{24} +(8.76498 - 2.07734i) q^{25} +(1.42554 + 2.46911i) q^{26} +(-5.19603 - 0.0352723i) q^{27} +(-1.74207 + 3.01736i) q^{28} +(2.50447 - 8.36553i) q^{29} +(-1.14012 + 6.38149i) q^{30} +(-1.77523 - 1.16758i) q^{31} +(0.597159 + 0.802123i) q^{32} +(-5.10209 + 6.82101i) q^{33} +(1.25890 - 0.827995i) q^{34} +(-12.2537 - 4.45998i) q^{35} +(-2.49898 - 1.65985i) q^{36} +(3.89134 - 1.41633i) q^{37} +(-0.341460 + 0.458661i) q^{38} +(-1.40559 - 4.73395i) q^{39} +(-2.56839 + 2.72234i) q^{40} +(0.955468 - 1.01274i) q^{41} +(4.15120 - 4.38011i) q^{42} +(-2.05247 + 2.75694i) q^{43} +(-4.62132 + 1.68202i) q^{44} +(4.49383 - 10.2896i) q^{45} +(-5.73450 - 2.08719i) q^{46} +(4.01010 - 2.63748i) q^{47} +(-0.682430 - 1.59195i) q^{48} +(3.06896 + 4.12233i) q^{49} +(-7.52589 - 4.94986i) q^{50} +(-2.45446 + 0.887065i) q^{51} +(0.817698 - 2.73130i) q^{52} +(-3.41445 + 5.91401i) q^{53} +(3.54008 + 3.80366i) q^{54} +(-9.20312 - 15.9403i) q^{55} +(3.39023 - 0.803499i) q^{56} +(0.760130 - 0.634899i) q^{57} +(-7.80354 + 3.91908i) q^{58} +(1.76994 - 4.10317i) q^{59} +(5.42413 - 3.54995i) q^{60} +(0.555292 + 9.53400i) q^{61} +(0.368964 + 2.09250i) q^{62} +(-8.75879 + 5.70413i) q^{63} +(0.173648 - 0.984808i) q^{64} +(10.5986 + 1.23880i) q^{65} +(8.46269 - 0.969741i) q^{66} +(1.84885 + 6.17560i) q^{67} +(-1.46617 - 0.347490i) q^{68} +(8.81785 + 5.82822i) q^{69} +(5.16492 + 11.9736i) q^{70} +(12.4360 + 10.4350i) q^{71} +(0.507569 + 2.95675i) q^{72} +(4.77797 - 4.00919i) q^{73} +(-3.70061 - 1.85851i) q^{74} +(10.6810 + 11.3726i) q^{75} +(0.567942 - 0.0663829i) q^{76} +(-0.996295 + 17.1057i) q^{77} +(-2.47878 + 4.27102i) q^{78} +(-11.0089 - 11.6688i) q^{79} +3.74270 q^{80} +(-4.42927 - 7.83464i) q^{81} -1.39232 q^{82} +(1.00514 + 1.06539i) q^{83} +(-6.03470 - 0.0136550i) q^{84} +(0.327905 - 5.62992i) q^{85} +(3.41381 - 0.399018i) q^{86} +(14.7251 - 3.45474i) q^{87} +(4.39480 + 2.20715i) q^{88} +(-3.39129 + 2.84563i) q^{89} +(-10.5682 + 3.79245i) q^{90} +(-7.60956 - 6.38518i) q^{91} +(2.41709 + 5.60344i) q^{92} +(0.222299 - 3.67350i) q^{93} +(-4.67033 - 1.10689i) q^{94} +(0.613789 + 2.05020i) q^{95} +(-0.689627 + 1.58884i) q^{96} +(9.47647 + 1.10764i) q^{97} +(0.892426 - 5.06120i) q^{98} +(-14.6461 - 1.77910i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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 $

$2$	−0.686242	−	0.727374i	−0.485246	−	0.514331i
$2$	−0.686242	−	0.727374i	−0.485246	−	0.514331i
$3$	0.862629	+	1.50196i	0.498039	+	0.867155i
$3$	0.862629	+	1.50196i	0.498039	+	0.867155i
$4$	−0.0581448	+	0.998308i	−0.0290724	+	0.499154i
$5$	−3.71739	+	0.434501i	−1.66247	+	0.194315i	−0.894779	−	0.446509i	$-0.852667\pi$
$5$	−3.71739	+	0.434501i	−1.66247	+	0.194315i	−0.767688	+	0.640823i	$0.778593\pi$
$6$	0.500511	−	1.65816i	0.204333	−	0.676940i
$7$	3.11355	+	1.56368i	1.17681	+	0.591016i	0.926186	−	0.377068i	$-0.123068\pi$
$7$	3.11355	+	1.56368i	1.17681	+	0.591016i	0.250625	+	0.968084i	$0.419364\pi$
$8$	0.766044	−	0.642788i	0.270838	−	0.227260i
$9$	−1.51174	+	2.59126i	−0.503914	+	0.863754i
$10$	2.86707	+	2.40576i	0.906648	+	0.760768i
$11$	1.94788	+	4.51570i	0.587309	+	1.36154i	0.909833	+	0.414975i	$0.136210\pi$
$11$	1.94788	+	4.51570i	0.587309	+	1.36154i	−0.322524	+	0.946561i	$0.604531\pi$
$12$	−1.54957	+	0.773839i	−0.447323	+	0.223388i
$13$	−2.77423	−	0.657504i	−0.769432	−	0.182359i	−0.172891	−	0.984941i	$-0.555311\pi$
$13$	−2.77423	−	0.657504i	−0.769432	−	0.182359i	−0.596541	+	0.802582i	$0.703459\pi$
$14$	−0.999264	−	3.33778i	−0.267065	−	0.892058i
$15$	−3.85933	−	5.20854i	−0.996475	−	1.34484i
$16$	−0.993238	−	0.116093i	−0.248310	−	0.0290232i
$17$	−0.261651	+	1.48390i	−0.0634598	+	0.359898i	0.936498	+	0.350674i	$0.114047\pi$
$17$	−0.261651	+	1.48390i	−0.0634598	+	0.359898i	−0.999957	+	0.00922446i	$0.997064\pi$
$18$	2.92224	−	0.678630i	0.688778	−	0.159955i
$19$	−0.0992935	−	0.563121i	−0.0227795	−	0.129189i	0.971297	−	0.237869i	$-0.0764488\pi$
$19$	−0.0992935	−	0.563121i	−0.0227795	−	0.129189i	−0.994077	+	0.108680i	$0.965338\pi$
$20$	−0.217618	−	3.73637i	−0.0486610	−	0.835477i
$21$	0.337255	+	6.02529i	0.0735951	+	1.31483i
$22$	1.94788	−	4.51570i	0.415290	−	0.962751i
$23$	5.45342	−	2.73881i	1.13712	−	0.571081i	0.222311	−	0.974976i	$-0.428640\pi$
$23$	5.45342	−	2.73881i	1.13712	−	0.571081i	0.914806	+	0.403895i	$0.132344\pi$
$24$	1.62625	+	0.596078i	0.331957	+	0.121674i
$25$	8.76498	−	2.07734i	1.75300	−	0.415468i
$26$	1.42554	+	2.46911i	0.279571	+	0.484231i
$27$	−5.19603	−	0.0352723i	−0.999977	−	0.00678815i
$28$	−1.74207	+	3.01736i	−0.329221	+	0.570227i
$29$	2.50447	−	8.36553i	0.465069	−	1.55344i	−0.328224	−	0.944600i	$-0.606450\pi$
$29$	2.50447	−	8.36553i	0.465069	−	1.55344i	0.793294	−	0.608839i	$-0.208365\pi$
$30$	−1.14012	+	6.38149i	−0.208157	+	1.16510i
$31$	−1.77523	−	1.16758i	−0.318840	−	0.209704i	0.379993	−	0.924989i	$-0.375926\pi$
$31$	−1.77523	−	1.16758i	−0.318840	−	0.209704i	−0.698833	+	0.715285i	$0.746297\pi$
$32$	0.597159	+	0.802123i	0.105564	+	0.141797i
$33$	−5.10209	+	6.82101i	−0.888159	+	1.18739i
$34$	1.25890	−	0.827995i	0.215900	−	0.142000i
$35$	−12.2537	−	4.45998i	−2.07125	−	0.753874i
$36$	−2.49898	−	1.65985i	−0.416496	−	0.276642i
$37$	3.89134	−	1.41633i	0.639733	−	0.232844i	−0.00172904	−	0.999999i	$-0.500550\pi$
$37$	3.89134	−	1.41633i	0.639733	−	0.232844i	0.641462	+	0.767155i	$0.278328\pi$
$38$	−0.341460	+	0.458661i	−0.0553922	+	0.0744046i
$39$	−1.40559	−	4.73395i	−0.225074	−	0.758038i
$40$	−2.56839	+	2.72234i	−0.406099	+	0.430440i
$41$	0.955468	−	1.01274i	0.149219	−	0.158163i	−0.648452	−	0.761255i	$-0.724583\pi$
$41$	0.955468	−	1.01274i	0.149219	−	0.158163i	0.797671	+	0.603092i	$0.206065\pi$
$42$	4.15120	−	4.38011i	0.640544	−	0.675866i
$43$	−2.05247	+	2.75694i	−0.312998	+	0.420430i	−0.930587	−	0.366072i	$-0.880702\pi$
$43$	−2.05247	+	2.75694i	−0.312998	+	0.420430i	0.617588	+	0.786502i	$0.288110\pi$
$44$	−4.62132	+	1.68202i	−0.696691	+	0.253575i
$45$	4.49383	−	10.2896i	0.669901	−	1.53388i
$46$	−5.73450	−	2.08719i	−0.845506	−	0.307739i
$47$	4.01010	−	2.63748i	0.584933	−	0.384716i	−0.222275	−	0.974984i	$-0.571348\pi$
$47$	4.01010	−	2.63748i	0.584933	−	0.384716i	0.807208	+	0.590268i	$0.200978\pi$
$48$	−0.682430	−	1.59195i	−0.0985003	−	0.229777i
$49$	3.06896	+	4.12233i	0.438423	+	0.588904i
$50$	−7.52589	−	4.94986i	−1.06432	−	0.700016i
$51$	−2.45446	+	0.887065i	−0.343693	+	0.124214i
$52$	0.817698	−	2.73130i	0.113394	−	0.378764i
$53$	−3.41445	+	5.91401i	−0.469011	+	0.812351i	−0.999372	−	0.0354205i	$-0.988723\pi$
$53$	−3.41445	+	5.91401i	−0.469011	+	0.812351i	0.530361	+	0.847772i	$0.322056\pi$
$54$	3.54008	+	3.80366i	0.481744	+	0.517613i
$55$	−9.20312	−	15.9403i	−1.24095	−	2.14939i
$56$	3.39023	−	0.803499i	0.453039	−	0.107372i
$57$	0.760130	−	0.634899i	0.100682	−	0.0840944i
$58$	−7.80354	+	3.91908i	−1.02465	+	0.514601i
$59$	1.76994	−	4.10317i	0.230426	−	0.534188i	−0.763298	−	0.646047i	$-0.776421\pi$
$59$	1.76994	−	4.10317i	0.230426	−	0.534188i	0.993724	+	0.111859i	$0.0356804\pi$
$60$	5.42413	−	3.54995i	0.700252	−	0.458297i
$61$	0.555292	+	9.53400i	0.0710979	+	1.22070i	0.825543	+	0.564340i	$0.190869\pi$
$61$	0.555292	+	9.53400i	0.0710979	+	1.22070i	−0.754445	+	0.656364i	$0.772094\pi$
$62$	0.368964	+	2.09250i	0.0468584	+	0.265747i
$63$	−8.75879	+	5.70413i	−1.10350	+	0.718653i
$64$	0.173648	−	0.984808i	0.0217060	−	0.123101i
$65$	10.5986	+	1.23880i	1.31459	+	0.153654i
$66$	8.46269	−	0.969741i	1.04169	−	0.119367i
$67$	1.84885	+	6.17560i	0.225873	+	0.754470i	0.993526	+	0.113604i	$0.0362394\pi$
$67$	1.84885	+	6.17560i	0.225873	+	0.754470i	−0.767653	+	0.640866i	$0.778575\pi$
$68$	−1.46617	−	0.347490i	−0.177800	−	0.0421393i
$69$	8.81785	+	5.82822i	1.06154	+	0.701635i
$70$	5.16492	+	11.9736i	0.617326	+	1.43112i
$71$	12.4360	+	10.4350i	1.47588	+	1.23841i	0.910454	+	0.413610i	$0.135732\pi$
$71$	12.4360	+	10.4350i	1.47588	+	1.23841i	0.565425	+	0.824799i	$0.308712\pi$
$72$	0.507569	+	2.95675i	0.0598176	+	0.348456i
$73$	4.77797	−	4.00919i	0.559219	−	0.469241i	−0.318829	−	0.947812i	$-0.603290\pi$
$73$	4.77797	−	4.00919i	0.559219	−	0.469241i	0.878049	+	0.478571i	$0.158845\pi$
$74$	−3.70061	−	1.85851i	−0.430187	−	0.216048i
$75$	10.6810	+	11.3726i	1.23333	+	1.31320i
$76$	0.567942	−	0.0663829i	0.0651474	−	0.00761464i
$77$	−0.996295	+	17.1057i	−0.113538	+	1.94938i
$78$	−2.47878	+	4.27102i	−0.280666	+	0.483598i
$79$	−11.0089	−	11.6688i	−1.23860	−	1.31284i	−0.932644	−	0.360797i	$-0.882505\pi$
$79$	−11.0089	−	11.6688i	−1.23860	−	1.31284i	−0.305958	−	0.952045i	$-0.598977\pi$
$80$	3.74270			0.418446
$81$	−4.42927	−	7.83464i	−0.492141	−	0.870515i
$82$	−1.39232			−0.153756
$83$	1.00514	+	1.06539i	0.110328	+	0.116941i	0.780184	−	0.625550i	$-0.215125\pi$
$83$	1.00514	+	1.06539i	0.110328	+	0.116941i	−0.669856	+	0.742491i	$0.733644\pi$
$84$	−6.03470	−	0.0136550i	−0.658440	−	0.00148988i
$85$	0.327905	−	5.62992i	0.0355663	−	0.610650i
$86$	3.41381	−	0.399018i	0.368121	−	0.0430272i
$87$	14.7251	−	3.45474i	1.57869	−	0.370387i
$88$	4.39480	+	2.20715i	0.468488	+	0.235283i
$89$	−3.39129	+	2.84563i	−0.359476	+	0.301636i	−0.804582	−	0.593842i	$-0.797611\pi$
$89$	−3.39129	+	2.84563i	−0.359476	+	0.301636i	0.445106	+	0.895478i	$0.353166\pi$
$90$	−10.5682	+	3.79245i	−1.11399	+	0.399759i
$91$	−7.60956	−	6.38518i	−0.797698	−	0.669348i
$92$	2.41709	+	5.60344i	0.251999	+	0.584199i
$93$	0.222299	−	3.67350i	0.0230513	−	0.380924i
$94$	−4.67033	−	1.10689i	−0.481708	−	0.114167i
$95$	0.613789	+	2.05020i	0.0629734	+	0.210346i
$96$	−0.689627	+	1.58884i	−0.0703848	+	0.162160i
$97$	9.47647	+	1.10764i	0.962190	+	0.112464i	0.582660	−	0.812716i	$-0.302012\pi$
$97$	9.47647	+	1.10764i	0.962190	+	0.112464i	0.379530	+	0.925180i	$0.376086\pi$
$98$	0.892426	−	5.06120i	0.0901486	−	0.511258i
$99$	−14.6461	−	1.77910i	−1.47199	−	0.178806i
$100$	1.56419	+	8.87093i	0.156419	+	0.887093i
$101$	−0.578273	−	9.92856i	−0.0575403	−	0.987929i	−0.896306	−	0.443436i	$-0.853759\pi$
$101$	−0.578273	−	9.92856i	−0.0575403	−	0.987929i	0.838766	−	0.544493i	$-0.183278\pi$
$102$	2.32958	+	1.17657i	0.230663	+	0.116497i
$103$	0.517847	−	1.20050i	0.0510250	−	0.118289i	−0.890797	−	0.454402i	$-0.849853\pi$
$103$	0.517847	−	1.20050i	0.0510250	−	0.118289i	0.941822	+	0.336113i	$0.109112\pi$
$104$	−2.54782	+	1.27956i	−0.249834	+	0.125471i
$105$	−3.87170	−	22.2518i	−0.377839	−	2.17155i
$106$	6.64483	−	1.57485i	0.645403	−	0.152963i
$107$	2.56010	+	4.43422i	0.247494	+	0.428672i	0.962830	−	0.270109i	$-0.0870596\pi$
$107$	2.56010	+	4.43422i	0.247494	+	0.428672i	−0.715336	+	0.698781i	$0.753726\pi$
$108$	0.337335	−	5.18519i	0.0324601	−	0.498945i
$109$	5.41189	−	9.37367i	0.518365	−	0.897835i	−0.481407	−	0.876497i	$-0.659874\pi$
$109$	5.41189	−	9.37367i	0.518365	−	0.897835i	0.999772	−	0.0213380i	$-0.00679261\pi$
$110$	−5.27897	+	17.6330i	−0.503330	+	1.68124i
$111$	5.48406	+	4.62286i	0.520524	+	0.438782i
$112$	−2.91096	−	1.91457i	−0.275060	−	0.180910i
$113$	5.20852	+	6.99625i	0.489976	+	0.658152i	0.976501	−	0.215515i	$-0.0691430\pi$
$113$	5.20852	+	6.99625i	0.489976	+	0.658152i	−0.486525	+	0.873667i	$0.661736\pi$
$114$	−0.983441	−	0.117204i	−0.0921077	−	0.0109772i
$115$	−19.0825	+	12.5507i	−1.77945	+	1.17036i
$116$	8.20575	+	2.98665i	0.761885	+	0.277303i
$117$	5.89768	−	6.19477i	0.545241	−	0.572707i
$118$	−4.19914	+	1.52836i	−0.386563	+	0.140697i
$119$	−3.13501	+	4.21105i	−0.287386	+	0.386026i
$120$	−6.30441	−	1.50925i	−0.575511	−	0.137775i
$121$	−9.04867	+	9.59103i	−0.822607	+	0.871912i
$122$	6.55371	−	6.94653i	0.593345	−	0.628909i
$123$	2.34530	+	0.561454i	0.211469	+	0.0506246i
$124$	1.26883	−	1.70433i	0.113944	−	0.153054i
$125$	−14.0953	+	5.13027i	−1.26072	+	0.458866i
$126$	10.1597	+	2.45650i	0.905096	+	0.218842i
$127$	7.08214	+	2.57769i	0.628439	+	0.228733i	0.636552	−	0.771234i	$-0.280360\pi$
$127$	7.08214	+	2.57769i	0.628439	+	0.228733i	−0.00811290	+	0.999967i	$0.502582\pi$
$128$	−0.835488	+	0.549509i	−0.0738474	+	0.0485702i
$129$	−5.91132	−	0.704496i	−0.520463	−	0.0620275i
$130$	−6.37211	−	8.55923i	−0.558871	−	0.750694i
$131$	−16.9094	−	11.1215i	−1.47738	−	0.971691i	−0.995430	−	0.0954944i	$-0.969557\pi$
$131$	−16.9094	−	11.1215i	−1.47738	−	0.971691i	−0.481954	−	0.876196i	$-0.660073\pi$
$132$	−6.51281	−	5.49006i	−0.566868	−	0.477848i
$133$	0.571388	−	1.90857i	0.0495456	−	0.165494i
$134$	3.22321	−	5.58276i	0.278443	−	0.482277i
$135$	19.3310	−	2.12656i	1.66375	−	0.183025i
$136$	0.753395	+	1.30492i	0.0646031	+	0.111896i
$137$	−6.00224	+	1.42256i	−0.512806	+	0.121537i	−0.478868	−	0.877887i	$-0.658953\pi$
$137$	−6.00224	+	1.42256i	−0.512806	+	0.121537i	−0.0339376	+	0.999424i	$0.510805\pi$
$138$	−1.81188	−	10.4134i	−0.154238	−	0.886450i
$139$	−1.59450	+	0.800787i	−0.135244	+	0.0679219i	−0.515134	−	0.857110i	$-0.672258\pi$
$139$	−1.59450	+	0.800787i	−0.135244	+	0.0679219i	0.379891	+	0.925031i	$0.375962\pi$
$140$	5.16492	−	11.9736i	0.436516	−	1.01196i
$141$	7.42061	+	3.74782i	0.624928	+	0.315623i
$142$	−0.943924	−	16.2066i	−0.0792124	−	1.36002i
$143$	−2.43478	−	13.8083i	−0.203607	−	1.15471i
$144$	1.80235	−	2.39824i	0.150196	−	0.199853i
$145$	−5.67528	+	32.1861i	−0.471306	+	2.67291i
$146$	−6.19503	−	0.724095i	−0.512704	−	0.0599265i
$147$	−3.54418	+	8.16549i	−0.292319	+	0.673478i
$148$	1.18768	+	3.96711i	0.0976263	+	0.326095i
$149$	−17.8668	−	4.23451i	−1.46371	−	0.346904i	−0.579872	−	0.814707i	$-0.696898\pi$
$149$	−17.8668	−	4.23451i	−1.46371	−	0.346904i	−0.883833	+	0.467803i	$0.845046\pi$
$150$	0.942413	−	15.5734i	0.0769477	−	1.27157i
$151$	−2.27217	−	5.26747i	−0.184906	−	0.428661i	0.800398	−	0.599469i	$-0.204622\pi$
$151$	−2.27217	−	5.26747i	−0.184906	−	0.428661i	−0.985304	+	0.170808i	$0.945362\pi$
$152$	−0.438031	−	0.367551i	−0.0355290	−	0.0298123i
$153$	−3.44962	−	2.92128i	−0.278885	−	0.236171i
$154$	13.1260	−	11.0140i	1.05772	−	0.887532i
$155$	7.10652	+	3.56903i	0.570810	+	0.286671i
$156$	4.80767	−	1.12795i	0.384921	−	0.0903086i
$157$	−12.7563	+	1.49100i	−1.01806	+	0.118994i	−0.608719	−	0.793386i	$-0.708316\pi$
$157$	−12.7563	+	1.49100i	−1.01806	+	0.118994i	−0.409343	+	0.912380i	$0.634242\pi$
$158$	−0.932781	+	16.0152i	−0.0742080	+	1.27410i
$159$	−11.8280	−	0.0267636i	−0.938020	−	0.00212249i
$160$	−2.56839	−	2.72234i	−0.203049	−	0.215220i
$161$	21.2621			1.67569
$162$	−2.65916	+	8.59819i	−0.208923	+	0.675538i
$163$	20.2087			1.58287			0.791434	−	0.611255i	$-0.209335\pi$
$163$	20.2087			1.58287			0.791434	+	0.611255i	$0.209335\pi$
$164$	0.955468	+	1.01274i	0.0746095	+	0.0790814i
$165$	16.0027	−	27.5732i	1.24581	−	2.14657i
$166$	0.0851648	−	1.46222i	0.00661007	−	0.113491i
$167$	1.63900	−	0.191571i	0.126829	−	0.0148242i	−0.0524414	−	0.998624i	$-0.516700\pi$
$167$	1.63900	−	0.191571i	0.126829	−	0.0148242i	0.179271	+	0.983800i	$0.442626\pi$
$168$	4.13133	+	4.39885i	0.318739	+	0.339379i
$169$	−4.35320	−	2.18626i	−0.334862	−	0.168174i
$170$	−4.32008	+	3.62497i	−0.331335	+	0.278023i
$171$	1.60930	+	0.593999i	0.123066	+	0.0454242i
$172$	−2.63294	−	2.20930i	−0.200760	−	0.168457i
$173$	5.52365	+	12.8053i	0.419956	+	0.973566i	0.988542	+	0.150943i	$0.0482311\pi$
$173$	5.52365	+	12.8053i	0.419956	+	0.973566i	−0.568587	+	0.822623i	$0.692510\pi$
$174$	−12.6178	−	8.33985i	−0.956557	−	0.632243i
$175$	30.5385	+	7.23775i	2.30849	+	0.547122i
$176$	−1.41047	−	4.71131i	−0.106318	−	0.355128i
$177$	7.68958	−	0.881151i	0.577984	−	0.0662314i
$178$	4.39708	+	0.513945i	0.329575	+	0.0385218i
$179$	0.782567	−	4.43816i	0.0584918	−	0.331723i	−0.941494	−	0.337029i	$-0.890578\pi$
$179$	0.782567	−	4.43816i	0.0584918	−	0.331723i	0.999986	+	0.00530600i	$0.00168896\pi$
$180$	10.0109	+	5.08451i	0.746167	+	0.378977i
$181$	−3.93735	−	22.3298i	−0.292661	−	1.65976i	−0.676560	−	0.736387i	$-0.736530\pi$
$181$	−3.93735	−	22.3298i	−0.292661	−	1.65976i	0.383899	−	0.923375i	$-0.374581\pi$
$182$	0.577586	+	9.91676i	0.0428135	+	0.735080i
$183$	−13.8406	+	9.05833i	−1.02313	+	0.669611i
$184$	2.41709	−	5.60344i	0.178190	−	0.413091i
$185$	−13.8502	+	6.95586i	−1.01829	+	0.511405i
$186$	−2.82456	+	2.35922i	−0.207107	+	0.172986i
$187$	−7.21051	+	1.70892i	−0.527285	+	0.124969i
$188$	2.39985	+	4.15667i	0.175027	+	0.303156i
$189$	−16.1229	−	8.23476i	−1.17277	−	0.598991i
$190$	1.07005	−	1.85339i	0.0776298	−	0.134459i
$191$	2.55943	−	8.54908i	0.185194	−	0.618590i	−0.814090	−	0.580739i	$-0.802764\pi$
$191$	2.55943	−	8.54908i	0.185194	−	0.618590i	0.999283	−	0.0378507i	$-0.0120511\pi$
$192$	1.62893	−	0.588712i	0.117558	−	0.0424866i
$193$	5.80207	+	3.81608i	0.417642	+	0.274687i	0.740889	−	0.671627i	$-0.234404\pi$
$193$	5.80207	+	3.81608i	0.417642	+	0.274687i	−0.323247	+	0.946314i	$0.604775\pi$
$194$	−5.69748	−	7.65305i	−0.409055	−	0.549457i
$195$	7.28202	+	16.9872i	0.521476	+	1.21648i
$196$	−4.29380	+	2.82408i	−0.306700	+	0.201720i
$197$	0.911676	+	0.331823i	0.0649542	+	0.0236414i	0.374293	−	0.927311i	$-0.377885\pi$
$197$	0.911676	+	0.331823i	0.0649542	+	0.0236414i	−0.309339	+	0.950952i	$0.600108\pi$
$198$	8.75667	+	11.8741i	0.622309	+	0.843853i
$199$	−17.1367	+	6.23725i	−1.21479	+	0.442147i	−0.868362	−	0.495931i	$-0.834827\pi$
$199$	−17.1367	+	6.23725i	−1.21479	+	0.442147i	−0.346426	+	0.938077i	$0.612605\pi$
$200$	5.37908	−	7.22535i	0.380358	−	0.510910i
$201$	−7.68060	+	8.10415i	−0.541748	+	0.571623i
$202$	−6.82494	+	7.23401i	−0.480201	+	0.508983i
$203$	20.8788	−	22.1303i	1.46541	−	1.55324i
$204$	−0.742850	−	2.50188i	−0.0520099	−	0.175167i
$205$	−3.11181	+	4.17989i	−0.217338	+	0.291936i
$206$	−1.22858	+	0.447168i	−0.0855995	+	0.0311557i
$207$	−1.14719	+	18.2716i	−0.0797352	+	1.26996i
$208$	2.67914	+	0.975126i	0.185765	+	0.0676128i
$209$	2.34948	−	1.54527i	0.162517	−	0.106889i
$210$	−13.5285	+	18.0863i	−0.933552	+	1.24807i
$211$	−0.782884	−	1.05160i	−0.0538960	−	0.0723949i	0.774358	−	0.632748i	$-0.218073\pi$
$211$	−0.782884	−	1.05160i	−0.0538960	−	0.0723949i	−0.828254	+	0.560353i	$0.810666\pi$
$212$	−5.70547	−	3.75255i	−0.391853	−	0.257726i
$213$	−4.94531	+	27.6799i	−0.338847	+	1.89659i
$214$	1.46849	−	4.90510i	0.100384	−	0.335305i
$215$	6.43193	−	11.1404i	0.438654	−	0.759771i
$216$	−4.00306	+	3.31293i	−0.272374	+	0.225416i
$217$	−3.70152	−	6.41122i	−0.251275	−	0.435222i
$218$	−10.5320	+	2.49614i	−0.713319	+	0.169060i
$219$	10.1433	+	3.71785i	0.685417	+	0.251229i
$220$	16.4484	−	8.26071i	1.10895	−	0.556937i
$221$	1.70155	−	3.94463i	0.114459	−	0.265345i
$222$	−0.400844	−	7.16136i	−0.0269029	−	0.480639i
$223$	−0.985838	−	16.9262i	−0.0660166	−	1.13346i	−0.854857	−	0.518864i	$-0.826355\pi$
$223$	−0.985838	−	16.9262i	−0.0660166	−	1.13346i	0.788840	−	0.614598i	$-0.210682\pi$
$224$	0.605016	+	3.43121i	0.0404243	+	0.229258i
$225$	−7.86746	+	25.8527i	−0.524497	+	1.72352i
$226$	1.51459	−	8.58966i	0.100749	−	0.571375i
$227$	−1.36267	−	0.159273i	−0.0904437	−	0.0105714i	0.0707507	−	0.997494i	$-0.477461\pi$
$227$	−1.36267	−	0.159273i	−0.0904437	−	0.0105714i	−0.161194	+	0.986923i	$0.551535\pi$
$228$	0.589627	+	0.795760i	0.0390490	+	0.0527005i
$229$	2.85475	+	9.53554i	0.188647	+	0.630126i	0.999022	+	0.0442142i	$0.0140784\pi$
$229$	2.85475	+	9.53554i	0.188647	+	0.630126i	−0.810375	+	0.585912i	$0.800736\pi$
$230$	22.2243	+	5.26725i	1.46542	+	0.347312i
$231$	−26.5515	+	13.2595i	−1.74696	+	0.872412i
$232$	−3.45872	−	8.01821i	−0.227076	−	0.526421i
$233$	−15.2199	−	12.7710i	−0.997087	−	0.836656i	−0.0105090	−	0.999945i	$-0.503345\pi$
$233$	−15.2199	−	12.7710i	−0.997087	−	0.836656i	−0.986578	+	0.163289i	$0.947790\pi$
$234$	−8.55315	−	0.0387072i	−0.559137	−	0.00253037i
$235$	−13.7611	+	11.5469i	−0.897676	+	0.753240i
$236$	3.99332	+	2.00552i	0.259943	+	0.130548i
$237$	8.02938	−	26.6008i	0.521564	−	1.72791i
$238$	5.21438	−	0.609473i	0.337998	−	0.0395063i
$239$	0.200938	−	3.44998i	0.0129976	−	0.223160i	−0.985554	−	0.169361i	$-0.945830\pi$
$239$	0.200938	−	3.44998i	0.0129976	−	0.223160i	0.998552	−	0.0537997i	$-0.0171332\pi$
$240$	3.22856	+	5.62137i	0.208403	+	0.362858i
$241$	6.98615	+	7.40488i	0.450017	+	0.476991i	0.912171	−	0.409809i	$-0.134405\pi$
$241$	6.98615	+	7.40488i	0.450017	+	0.476991i	−0.462154	+	0.886800i	$0.652923\pi$
$242$	13.1858			0.847618
$243$	7.94646	−	13.4110i	0.509766	−	0.860313i
$244$	−9.55015			−0.611386
$245$	−13.1997	−	13.9908i	−0.843297	−	0.893842i
$246$	−1.20106	−	2.09120i	−0.0765765	−	0.133330i
$247$	−0.0947917	+	1.62751i	−0.00603145	+	0.103556i
$248$	−2.11041	+	0.246672i	−0.134011	+	0.0156637i
$249$	−0.733099	+	2.42871i	−0.0464583	+	0.153913i
$250$	13.4044	+	6.73195i	0.847770	+	0.425766i
$251$	−12.7434	+	10.6930i	−0.804355	+	0.674934i	−0.949253	−	0.314512i	$-0.898159\pi$
$251$	−12.7434	+	10.6930i	−0.804355	+	0.674934i	0.144898	+	0.989447i	$0.453715\pi$
$252$	−5.18520	−	9.07564i	−0.326637	−	0.571711i
$253$	22.9903	+	19.2911i	1.44539	+	1.21282i
$254$	−2.98512	−	6.92028i	−0.187303	−	0.434217i
$255$	8.73875	−	4.36403i	0.547242	−	0.273286i
$256$	0.973045	+	0.230616i	0.0608153	+	0.0144135i
$257$	1.43372	+	4.78896i	0.0894330	+	0.298727i	0.990990	−	0.133932i	$-0.0427605\pi$
$257$	1.43372	+	4.78896i	0.0894330	+	0.298727i	−0.901557	+	0.432659i	$0.857575\pi$
$258$	3.54416	+	4.78319i	0.220650	+	0.297789i
$259$	14.3306	+	1.67500i	0.890459	+	0.104080i
$260$	−1.85295	+	10.5086i	−0.114915	+	0.651716i
$261$	17.8911	+	19.1363i	1.10743	+	1.18451i
$262$	3.51446	+	19.9315i	0.217124	+	1.23137i
$263$	−0.760577	−	13.0586i	−0.0468992	−	0.805228i	−0.936971	−	0.349407i	$-0.886383\pi$
$263$	−0.760577	−	13.0586i	−0.0468992	−	0.805228i	0.890072	−	0.455820i	$-0.150654\pi$
$264$	0.476039	+	8.50476i	0.0292982	+	0.523432i
$265$	10.1232	−	23.4683i	0.621864	−	1.44164i
$266$	−1.78035	+	0.894126i	−0.109160	+	0.0548224i
$267$	−7.19944	−	2.63884i	−0.440598	−	0.161495i
$268$	−6.27265	+	1.48665i	−0.383163	+	0.0908114i
$269$	−13.8342	−	23.9615i	−0.843485	−	1.46096i	−0.886930	−	0.461904i	$-0.847167\pi$
$269$	−13.8342	−	23.9615i	−0.843485	−	1.46096i	0.0434449	−	0.999056i	$-0.486167\pi$
$270$	−14.8125	−	12.6015i	−0.901463	−	0.766905i
$271$	−1.18001	+	2.04383i	−0.0716803	+	0.124154i	−0.899638	−	0.436637i	$-0.856169\pi$
$271$	−1.18001	+	2.04383i	−0.0716803	+	0.124154i	0.827958	+	0.560791i	$0.189503\pi$
$272$	0.432152	−	1.44349i	0.0262031	−	0.0875244i
$273$	3.02603	−	16.9373i	0.183143	−	1.02509i
$274$	5.15372	+	3.38965i	0.311347	+	0.204776i
$275$	26.4538	+	35.5336i	1.59522	+	2.14276i
$276$	−6.33107	+	8.46405i	−0.381085	+	0.509476i
$277$	−25.3011	+	16.6408i	−1.52020	+	0.999850i	−0.531987	+	0.846753i	$0.678554\pi$
$277$	−25.3011	+	16.6408i	−1.52020	+	0.999850i	−0.988211	+	0.153097i	$0.951075\pi$
$278$	1.67668	+	0.610263i	0.100561	+	0.0366011i
$279$	5.70920	−	2.83499i	0.341801	−	0.169726i
$280$	−12.2537	+	4.45998i	−0.732298	+	0.266535i
$281$	−9.81810	+	13.1880i	−0.585699	+	0.786730i	−0.991896	−	0.127056i	$-0.959447\pi$
$281$	−9.81810	+	13.1880i	−0.585699	+	0.786730i	0.406197	+	0.913786i	$0.366855\pi$
$282$	−2.36627	−	7.96947i	−0.140909	−	0.474575i
$283$	8.06942	−	8.55308i	0.479677	−	0.508428i	−0.441665	−	0.897180i	$-0.645612\pi$
$283$	8.06942	−	8.55308i	0.479677	−	0.508428i	0.921343	+	0.388752i	$0.127094\pi$
$284$	−11.1405	+	11.8082i	−0.661065	+	0.700688i
$285$	−2.54983	+	2.69044i	−0.151039	+	0.159368i
$286$	−8.37297	+	11.2468i	−0.495104	+	0.665040i
$287$	4.55849	−	1.65916i	0.269079	−	0.0979368i
$288$	−2.98126	+	0.334791i	−0.175672	+	0.0197277i
$289$	13.8413	+	5.03781i	0.814193	+	0.296342i
$290$	27.3060	−	17.9594i	1.60346	−	1.05461i
$291$	6.51105	+	15.1887i	0.381685	+	0.890379i
$292$	3.72460	+	5.00300i	0.217966	+	0.292779i
$293$	19.4629	+	12.8010i	1.13704	+	0.747841i	0.971189	−	0.238310i	$-0.0765935\pi$
$293$	19.4629	+	12.8010i	1.13704	+	0.747841i	0.165848	+	0.986151i	$0.446964\pi$
$294$	8.37153	−	3.02555i	0.488237	−	0.176454i
$295$	−4.79671	+	16.0221i	−0.279275	+	0.932845i
$296$	2.07054	−	3.58628i	0.120348	−	0.208448i
$297$	−9.96199	−	23.5325i	−0.578053	−	1.36549i
$298$	9.18087	+	15.9017i	0.531834	+	0.921163i
$299$	−16.9298	+	4.01243i	−0.979075	+	0.232045i
$300$	−11.9744	+	10.0017i	−0.691345	+	0.577446i
$301$	−10.7014	+	5.37446i	−0.616820	+	0.309779i
$302$	−2.27217	+	5.26747i	−0.130749	+	0.303109i
$303$	14.4134	−	9.43321i	0.828030	−	0.541924i
$304$	0.0332477	+	0.570841i	0.00190689	+	0.0327400i
$305$	−6.20677	−	35.2003i	−0.355398	−	2.01556i
$306$	0.242411	+	4.51387i	0.0138577	+	0.258040i
$307$	2.46697	−	13.9909i	0.140797	−	0.798502i	−0.829848	−	0.557989i	$-0.811573\pi$
$307$	2.46697	−	13.9909i	0.140797	−	0.798502i	0.970646	−	0.240513i	$-0.0773157\pi$
$308$	−17.0189	−	1.98922i	−0.969739	−	0.113346i
$309$	2.24981	−	0.257807i	0.127987	−	0.0146661i
$310$	−2.28077	−	7.61831i	−0.129539	−	0.432691i
$311$	−7.22174	−	1.71158i	−0.409507	−	0.0970550i	0.0206988	−	0.999786i	$-0.493411\pi$
$311$	−7.22174	−	1.71158i	−0.409507	−	0.0970550i	−0.430206	+	0.902731i	$0.641559\pi$
$312$	−4.11966	−	2.72292i	−0.233230	−	0.154155i
$313$	−2.93500	−	6.80410i	−0.165896	−	0.384591i	0.814907	−	0.579592i	$-0.196788\pi$
$313$	−2.93500	−	6.80410i	−0.165896	−	0.384591i	−0.980803	+	0.195001i	$0.937529\pi$
$314$	9.83840	+	8.25540i	0.555213	+	0.465879i
$315$	30.0814	−	25.0102i	1.69489	−	1.40916i
$316$	12.2892	−	10.3118i	0.691320	−	0.580086i
$317$	−14.3836	−	7.22372i	−0.807864	−	0.405725i	−0.00359761	−	0.999994i	$-0.501145\pi$
$317$	−14.3836	−	7.22372i	−0.807864	−	0.405725i	−0.804266	+	0.594269i	$0.797441\pi$
$318$	8.09739	+	8.62173i	0.454079	+	0.483483i
$319$	42.6547	−	4.98562i	2.38820	−	0.279141i
$320$	−0.217618	+	3.73637i	−0.0121652	+	0.208869i
$321$	−4.45159	+	7.67024i	−0.248463	+	0.428111i
$322$	−14.5909	−	15.4655i	−0.813121	−	0.861858i
$323$	0.861595			0.0479404
$324$	8.07892	−	3.96623i	0.448829	−	0.220346i
$325$	−25.6819			−1.42457
$326$	−13.8680	−	14.6993i	−0.768080	−	0.814117i
$327$	18.7473	+	0.0424202i	1.03673	+	0.00234584i
$328$	0.0809562	−	1.38996i	0.00447006	−	0.0767479i
$329$	16.6098	−	1.94141i	0.915729	−	0.107033i
$330$	−31.0378	+	7.28195i	−1.70857	+	0.400858i
$331$	9.29091	+	4.66607i	0.510675	+	0.256470i	0.685426	−	0.728142i	$-0.259616\pi$
$331$	9.29091	+	4.66607i	0.510675	+	0.256470i	−0.174752	+	0.984613i	$0.555912\pi$
$332$	−1.12203	+	0.941492i	−0.0615792	+	0.0516711i
$333$	−2.21262	+	12.2246i	−0.121251	+	0.669905i
$334$	−1.26409	−	1.06070i	−0.0691680	−	0.0580388i
$335$	−9.55621	−	22.1538i	−0.522112	−	1.21039i
$336$	0.364519	−	6.02370i	0.0198861	−	0.328620i
$337$	−3.47624	−	0.823883i	−0.189363	−	0.0448798i	0.134840	−	0.990867i	$-0.456948\pi$
$337$	−3.47624	−	0.823883i	−0.189363	−	0.0448798i	−0.324203	+	0.945988i	$0.605096\pi$
$338$	1.39712	+	4.66671i	0.0759934	+	0.253835i
$339$	−6.01504	+	13.8581i	−0.326692	+	0.752670i
$340$	5.60133	+	0.654701i	0.303775	+	0.0355062i
$341$	1.81453	−	10.2907i	0.0982623	−	0.557273i
$342$	−0.672310	−	1.57819i	−0.0363544	−	0.0853387i
$343$	−1.12577	−	6.38455i	−0.0607858	−	0.344733i
$344$	0.199847	+	3.43124i	0.0107750	+	0.185000i
$345$	−35.3117	−	17.8344i	−1.90112	−	0.960171i
$346$	5.52365	−	12.8053i	0.296953	−	0.688415i
$347$	7.83141	−	3.93308i	0.420412	−	0.211139i	−0.226000	−	0.974127i	$-0.572565\pi$
$347$	7.83141	−	3.93308i	0.420412	−	0.211139i	0.646412	+	0.762988i	$0.276269\pi$
$348$	2.59270	+	14.9010i	0.138984	+	0.798780i
$349$	27.7033	−	6.56580i	1.48292	−	0.351459i	0.592120	−	0.805850i	$-0.298291\pi$
$349$	27.7033	−	6.56580i	1.48292	−	0.351459i	0.890802	+	0.454391i	$0.150143\pi$
$350$	−15.6922	−	27.1797i	−0.838784	−	1.45282i
$351$	14.3918	+	3.51426i	0.768176	+	0.187578i
$352$	−2.45895	+	4.25903i	−0.131063	+	0.227007i
$353$	−1.42302	+	4.75323i	−0.0757399	+	0.252989i	−0.987471	−	0.157798i	$-0.949561\pi$
$353$	−1.42302	+	4.75323i	−0.0757399	+	0.252989i	0.911732	+	0.410787i	$0.134746\pi$
$354$	−5.91784	−	4.98852i	−0.314530	−	0.265137i
$355$	−50.7634	−	33.3876i	−2.69424	−	1.77203i
$356$	−2.64363	−	3.55101i	−0.140112	−	0.188203i
$357$	−9.02916	−	1.07607i	−0.477874	−	0.0569518i
$358$	−3.76523	+	2.47643i	−0.198998	+	0.130883i
$359$	−0.851975	−	0.310094i	−0.0449655	−	0.0163661i	0.319439	−	0.947607i	$-0.396505\pi$
$359$	−0.851975	−	0.310094i	−0.0449655	−	0.0163661i	−0.364405	+	0.931241i	$0.618728\pi$
$360$	−3.17154	−	10.7709i	−0.167155	−	0.567674i
$361$	17.5469	−	6.38655i	0.923522	−	0.336134i
$362$	−13.5401	+	18.1876i	−0.711654	+	0.955918i
$363$	−22.2110	−	5.31720i	−1.16577	−	0.279081i
$364$	6.81683	−	7.22542i	0.357299	−	0.378715i
$365$	−16.0196	+	16.9798i	−0.838504	+	0.888762i
$366$	16.0868	+	3.85111i	0.840871	+	0.201301i
$367$	−4.04248	+	5.43000i	−0.211016	+	0.283444i	−0.895012	−	0.446042i	$-0.852833\pi$
$367$	−4.04248	+	5.43000i	−0.211016	+	0.283444i	0.683996	+	0.729486i	$0.260241\pi$
$368$	−5.73450	+	2.08719i	−0.298931	+	0.108802i
$369$	1.17984	+	4.00686i	0.0614203	+	0.208589i
$370$	14.5641	+	5.30091i	0.757153	+	0.275581i
$371$	−19.8787	+	13.0744i	−1.03205	+	0.678790i
$372$	3.65436	+	0.435518i	0.189470	+	0.0225805i
$373$	10.3052	+	13.8423i	0.533583	+	0.716727i	0.984411	−	0.175884i	$-0.0562785\pi$
$373$	10.3052	+	13.8423i	0.533583	+	0.716727i	−0.450828	+	0.892611i	$0.648871\pi$
$374$	6.19118	+	4.07200i	0.320138	+	0.210558i
$375$	−19.8645	−	16.7450i	−1.02580	−	0.864709i
$376$	1.37657	−	4.59807i	0.0709913	−	0.237127i
$377$	−12.4483	+	21.5612i	−0.641122	+	1.11046i
$378$	5.07448	+	17.3784i	0.261003	+	0.893850i
$379$	5.41713	+	9.38275i	0.278259	+	0.481959i	0.970952	−	0.239273i	$-0.0769092\pi$
$379$	5.41713	+	9.38275i	0.278259	+	0.481959i	−0.692693	+	0.721233i	$0.743576\pi$
$380$	−2.08242	+	0.493542i	−0.106826	+	0.0253182i
$381$	2.23769	+	12.8607i	0.114640	+	0.658871i
$382$	−7.97476	+	4.00507i	−0.408024	+	0.204917i
$383$	−9.79155	+	22.6994i	−0.500325	+	1.15988i	0.461728	+	0.887021i	$0.347229\pi$
$383$	−9.79155	+	22.6994i	−0.500325	+	1.15988i	−0.962053	+	0.272862i	$0.912030\pi$
$384$	−1.54605	−	0.780843i	−0.0788968	−	0.0398472i
$385$	−3.72883	−	64.0216i	−0.190039	−	3.26284i
$386$	−1.20590	−	6.83902i	−0.0613789	−	0.348097i
$387$	−4.04116	−	9.48626i	−0.205423	−	0.482214i
$388$	−1.65677	+	9.39604i	−0.0841100	+	0.477012i
$389$	24.3320	+	2.84400i	1.23368	+	0.144197i	0.707831	−	0.706381i	$-0.249674\pi$
$389$	24.3320	+	2.84400i	1.23368	+	0.144197i	0.525849	+	0.850578i	$0.323748\pi$
$390$	7.35882	−	16.9541i	0.372628	−	0.858503i
$391$	2.63722	+	8.80893i	0.133370	+	0.445487i
$392$	5.00074	+	1.18520i	0.252576	+	0.0598615i
$393$	2.11745	−	34.9910i	0.106811	−	1.76506i
$394$	−0.384271	−	0.890840i	−0.0193593	−	0.0448799i
$395$	45.9946	+	38.5941i	2.31424	+	1.94188i
$396$	2.62769	−	14.5178i	0.132046	−	0.729549i
$397$	−21.4666	+	18.0126i	−1.07738	+	0.904026i	−0.995700	−	0.0926332i	$-0.970472\pi$
$397$	−21.4666	+	18.0126i	−1.07738	+	0.904026i	−0.0816756	+	0.996659i	$0.526027\pi$
$398$	16.2967	+	8.18452i	0.816881	+	0.410253i
$399$	3.35948	−	0.788187i	0.168184	−	0.0394587i
$400$	−8.94688	+	1.04574i	−0.447344	+	0.0522870i
$401$	1.50608	−	25.8583i	0.0752098	−	1.29130i	−0.723810	−	0.689999i	$-0.757611\pi$
$401$	1.50608	−	25.8583i	0.0752098	−	1.29130i	0.799020	−	0.601304i	$-0.205352\pi$
$402$	11.1655	+	0.0252646i	0.556884	+	0.00126008i
$403$	4.15719	+	4.40636i	0.207084	+	0.219496i
$404$	9.94539			0.494802
$405$	19.8695	+	27.1999i	0.987323	+	1.35157i
$406$	−30.4249			−1.50996
$407$	13.9756	+	14.8133i	0.692746	+	0.734268i
$408$	−1.31003	+	2.25723i	−0.0648561	+	0.111749i
$409$	0.583604	−	10.0201i	0.0288574	−	0.495462i	−0.952654	−	0.304057i	$-0.901659\pi$
$409$	0.583604	−	10.0201i	0.0288574	−	0.495462i	0.981511	−	0.191405i	$-0.0613043\pi$
$410$	5.17580	−	0.604964i	0.255614	−	0.0298770i
$411$	−7.31432	−	7.78796i	−0.360789	−	0.384152i
$412$	1.16836	+	0.586774i	0.0575611	+	0.0289083i
$413$	11.9268	−	10.0078i	0.586881	−	0.492452i
$414$	14.0775	−	11.7043i	0.691873	−	0.575235i
$415$	−4.19941	−	3.52372i	−0.206141	−	0.172973i
$416$	−1.12925	−	2.61791i	−0.0553662	−	0.128353i
$417$	−2.57821	−	1.70408i	−0.126255	−	0.0834494i
$418$	−2.73630	−	0.648515i	−0.133837	−	0.0317199i
$419$	−7.22973	−	24.1490i	−0.353196	−	1.17976i	−0.931441	−	0.363893i	$-0.881448\pi$
$419$	−7.22973	−	24.1490i	−0.353196	−	1.17976i	0.578245	−	0.815863i	$-0.303738\pi$
$420$	22.4393	−	2.57132i	1.09492	−	0.125468i
$421$	−0.760746	−	0.0889184i	−0.0370765	−	0.00433362i	0.0975345	−	0.995232i	$-0.468904\pi$
$421$	−0.760746	−	0.0889184i	−0.0370765	−	0.00433362i	−0.134611	+	0.990899i	$0.542978\pi$
$422$	−0.227656	+	1.29110i	−0.0110821	+	0.0628497i
$423$	0.772174	+	14.3784i	0.0375444	+	0.699102i
$424$	1.18583	+	6.72516i	0.0575889	+	0.326603i
$425$	0.789190	+	13.5499i	0.0382813	+	0.657265i
$426$	23.5273	−	15.3980i	1.13990	−	0.746034i
$427$	−13.1792	+	30.5528i	−0.637787	+	1.47856i
$428$	−4.57558	+	2.29794i	−0.221169	+	0.111075i
$429$	18.6392	−	15.5684i	0.899908	−	0.751649i
$430$	−12.5171	+	2.96661i	−0.603629	+	0.143063i
$431$	8.29510	+	14.3675i	0.399561	+	0.692060i	0.993672	−	0.112323i	$-0.0358293\pi$
$431$	8.29510	+	14.3675i	0.399561	+	0.692060i	−0.594111	+	0.804383i	$0.702496\pi$
$432$	5.15680	+	0.638256i	0.248107	+	0.0307081i
$433$	1.71941	−	2.97811i	0.0826296	−	0.143119i	−0.821749	−	0.569850i	$-0.807001\pi$
$433$	1.71941	−	2.97811i	0.0826296	−	0.143119i	0.904379	+	0.426731i	$0.140335\pi$
$434$	−2.12321	+	7.09203i	−0.101918	+	0.340428i
$435$	−53.2378	+	19.2407i	−2.55256	+	0.922519i
$436$	9.04314	+	5.94777i	0.433088	+	0.284846i
$437$	−2.08377	−	2.79899i	−0.0996802	−	0.133894i
$438$	−4.25645	−	9.92928i	−0.203381	−	0.474439i
$439$	−20.0945	+	13.2163i	−0.959057	+	0.630781i	−0.929516	−	0.368782i	$-0.879775\pi$
$439$	−20.0945	+	13.2163i	−0.959057	+	0.630781i	−0.0295408	+	0.999564i	$0.509404\pi$
$440$	−17.2962	−	6.29531i	−0.824565	−	0.300117i
$441$	−15.3215	+	1.72058i	−0.729596	+	0.0819324i
$442$	−4.03690	+	1.46931i	−0.192016	+	0.0698879i
$443$	2.06941	−	2.77970i	0.0983206	−	0.132067i	−0.750240	−	0.661165i	$-0.770062\pi$
$443$	2.06941	−	2.77970i	0.0983206	−	0.132067i	0.848561	+	0.529098i	$0.177470\pi$
$444$	−4.93391	+	5.20598i	−0.234153	+	0.247065i
$445$	11.3703	−	12.0518i	0.539005	−	0.571312i
$446$	−11.6351	+	12.3325i	−0.550940	+	0.583962i
$447$	−9.05237	−	30.4880i	−0.428163	−	1.44203i
$448$	2.08059	−	2.79471i	0.0982985	−	0.132038i
$449$	−3.38732	+	1.23288i	−0.159858	+	0.0581834i	−0.420709	−	0.907195i	$-0.638219\pi$
$449$	−3.38732	+	1.23288i	−0.159858	+	0.0581834i	0.260852	+	0.965379i	$0.415997\pi$
$450$	24.2036	−	12.0186i	1.14097	−	0.566564i
$451$	6.43436	+	2.34192i	0.302982	+	0.110276i
$452$	−7.28726	+	4.79291i	−0.342764	+	0.225439i
$453$	5.95148	−	7.95657i	0.279625	−	0.373832i
$454$	0.819271	+	1.10047i	0.0384503	+	0.0516477i
$455$	31.0621	+	20.4298i	1.45621	+	0.957766i
$456$	0.174188	−	0.974963i	0.00815709	−	0.0456568i
$457$	5.53319	−	18.4821i	0.258832	−	0.864558i	−0.725499	−	0.688224i	$-0.758391\pi$
$457$	5.53319	−	18.4821i	0.258832	−	0.864558i	0.984330	−	0.176334i	$-0.0564240\pi$
$458$	4.97685	−	8.62016i	0.232553	−	0.402793i
$459$	1.41189	−	7.70116i	0.0659013	−	0.359459i
$460$	−11.4200	−	19.7799i	−0.532458	−	0.922245i
$461$	17.4374	−	4.13275i	0.812142	−	0.192481i	0.196497	−	0.980505i	$-0.437044\pi$
$461$	17.4374	−	4.13275i	0.812142	−	0.192481i	0.615645	+	0.788023i	$0.288895\pi$
$462$	27.8653	+	10.2136i	1.29641	+	0.475181i
$463$	−17.7274	+	8.90303i	−0.823861	+	0.413759i	−0.810204	−	0.586148i	$-0.800644\pi$
$463$	−17.7274	+	8.90303i	−0.823861	+	0.413759i	−0.0136574	+	0.999907i	$0.504347\pi$
$464$	−3.45872	+	8.01821i	−0.160567	+	0.372236i
$465$	0.769768	+	13.7524i	0.0356971	+	0.637754i
$466$	1.15523	+	19.8345i	0.0535150	+	0.918817i
$467$	3.06252	+	17.3684i	0.141716	+	0.803713i	0.969945	+	0.243323i	$0.0782376\pi$
$467$	3.06252	+	17.3684i	0.141716	+	0.803713i	−0.828229	+	0.560390i	$0.810651\pi$
$468$	5.84137	+	6.24789i	0.270017	+	0.288809i
$469$	−3.90018	+	22.1190i	−0.180094	+	1.02136i
$470$	17.8424	+	2.08548i	0.823008	+	0.0961959i
$471$	−13.2434	−	17.8732i	−0.610221	−	0.823553i
$472$	−1.28162	−	4.28091i	−0.0589913	−	0.197045i
$473$	−16.4475	−	3.89813i	−0.756257	−	0.179236i
$474$	−24.8588	+	12.4142i	−1.14180	+	0.570203i
$475$	−2.04010	−	4.72948i	−0.0936061	−	0.217003i
$476$	−4.02164	−	3.37456i	−0.184331	−	0.154672i
$477$	−10.1630	−	17.7882i	−0.465330	−	0.814465i
$478$	−2.64731	+	2.22136i	−0.121085	+	0.101603i
$479$	−29.4010	−	14.7657i	−1.34336	−	0.674663i	−0.375661	−	0.926757i	$-0.622584\pi$
$479$	−29.4010	−	14.7657i	−1.34336	−	0.674663i	−0.967703	+	0.252094i	$0.918881\pi$
$480$	1.87326	−	6.20598i	0.0855023	−	0.283263i
$481$	−11.7267	+	1.37066i	−0.534692	+	0.0624966i
$482$	0.591932	−	10.1631i	0.0269618	−	0.462916i
$483$	18.3413	+	31.9347i	0.834558	+	1.45308i
$484$	−9.04867	−	9.59103i	−0.411303	−	0.435956i
$485$	−35.7090			−1.62146
$486$	−15.2080	+	3.42311i	−0.689847	+	0.155275i
$487$	−22.3905			−1.01461			−0.507305	−	0.861767i	$-0.669358\pi$
$487$	−22.3905			−1.01461			−0.507305	+	0.861767i	$0.669358\pi$
$488$	6.55371	+	6.94653i	0.296673	+	0.314455i
$489$	17.4326	+	30.3526i	0.788330	+	1.37259i
$490$	−1.11840	+	19.2022i	−0.0505242	+	0.867467i
$491$	7.75544	−	0.906480i	0.349998	−	0.0409089i	0.0607222	−	0.998155i	$-0.480660\pi$
$491$	7.75544	−	0.906480i	0.349998	−	0.0409089i	0.289276	+	0.957246i	$0.406586\pi$
$492$	−0.696871	+	2.30869i	−0.0314174	+	0.104084i
$493$	11.7583	+	5.90524i	0.529567	+	0.265958i
$494$	1.24886	−	1.04792i	0.0561888	−	0.0471480i
$495$	55.2182	+	0.249890i	2.48187	+	0.0112317i
$496$	1.62767	+	1.36578i	0.0730847	+	0.0613253i
$497$	22.4029	+	51.9359i	1.00491	+	2.32964i
$498$	2.26966	−	1.13344i	0.101706	−	0.0507908i
$499$	−10.3322	−	2.44878i	−0.462534	−	0.109623i	−0.00725938	−	0.999974i	$-0.502311\pi$
$499$	−10.3322	−	2.44878i	−0.462534	−	0.109623i	−0.455275	+	0.890351i	$0.650459\pi$
$500$	−4.30203	−	14.3698i	−0.192392	−	0.642635i
$501$	1.70158	+	2.29645i	0.0760209	+	0.102598i
$502$	16.5228	+	1.93124i	0.737450	+	0.0861955i
$503$	1.07716	−	6.10888i	0.0480282	−	0.272381i	−0.951331	−	0.308170i	$-0.900283\pi$
$503$	1.07716	−	6.10888i	0.0480282	−	0.272381i	0.999359	+	0.0357890i	$0.0113944\pi$
$504$	−3.04308	+	9.99966i	−0.135549	+	0.445420i
$505$	6.46363	+	36.6571i	0.287628	+	1.63122i
$506$	−1.74502	−	29.9609i	−0.0775758	−	1.33192i
$507$	−0.471533	−	8.42425i	−0.0209415	−	0.374134i
$508$	−2.98512	+	6.92028i	−0.132443	+	0.307038i
$509$	0.0126805	−	0.00636840i	0.000562055	−	0.000282275i	−0.448518	−	0.893774i	$-0.648048\pi$
$509$	0.0126805	−	0.00636840i	0.000562055	−	0.000282275i	0.449080	+	0.893491i	$0.351752\pi$
$510$	−9.17117	−	3.36155i	−0.406106	−	0.148852i
$511$	21.1455	−	5.01159i	0.935424	−	0.221700i
$512$	−0.500000	−	0.866025i	−0.0220971	−	0.0382733i
$513$	0.496069	+	2.92950i	0.0219020	+	0.129341i
$514$	2.49948	−	4.32923i	0.110248	−	0.190954i
$515$	−1.40342	+	4.68775i	−0.0618421	+	0.206567i
$516$	1.04702	−	5.86036i	0.0460924	−	0.257988i
$517$	19.7213	+	12.9709i	0.867342	+	0.570460i
$518$	−8.61589	−	11.5731i	−0.378560	−	0.508495i
$519$	−14.4681	+	19.3425i	−0.635078	+	0.849041i
$520$	8.91526	−	5.86366i	0.390960	−	0.257138i
$521$	34.8531	+	12.6855i	1.52694	+	0.555761i	0.962870	−	0.269964i	$-0.0870119\pi$
$521$	34.8531	+	12.6855i	1.52694	+	0.555761i	0.564072	+	0.825726i	$0.309234\pi$
$522$	1.64157	−	26.1456i	0.0718494	−	1.14436i
$523$	2.32654	−	0.846793i	0.101733	−	0.0370277i	−0.290652	−	0.956829i	$-0.593872\pi$
$523$	2.32654	−	0.846793i	0.101733	−	0.0370277i	0.392385	+	0.919801i	$0.371650\pi$
$524$	12.0859	−	16.2342i	0.527975	−	0.709193i
$525$	15.4726	+	52.1109i	0.675279	+	2.27431i
$526$	−8.97654	+	9.51458i	−0.391396	+	0.414855i
$527$	2.19707	−	2.32875i	0.0957057	−	0.101442i
$528$	5.85946	−	6.18258i	0.255000	−	0.269062i
$529$	8.50404	−	11.4229i	0.369741	−	0.496648i
$530$	−24.0172	+	8.74153i	−1.04324	+	0.379708i
$531$	7.95671	+	10.7893i	0.345292	+	0.468216i
$532$	1.87212	+	0.681394i	0.0811665	+	0.0295422i
$533$	−3.31656	+	2.18134i	−0.143656	+	0.0944842i
$534$	3.02113	+	7.04757i	0.130737	+	0.304978i
$535$	−11.4436	−	15.3714i	−0.494748	−	0.664562i
$536$	5.38590	+	3.54236i	0.232636	+	0.153007i
$537$	7.34098	−	2.65310i	0.316787	−	0.114490i
$538$	−7.93538	+	26.5060i	−0.342118	+	1.14276i
$539$	−12.6372	+	21.8883i	−0.544325	+	0.942798i
$540$	0.998963	+	19.4220i	0.0429885	+	0.835788i
$541$	18.7360	+	32.4517i	0.805524	+	1.39521i	0.915937	+	0.401323i	$0.131449\pi$
$541$	18.7360	+	32.4517i	0.805524	+	1.39521i	−0.110412	+	0.993886i	$0.535217\pi$
$542$	2.29640	−	0.544257i	0.0986388	−	0.0233778i
$543$	30.1419	−	25.1761i	1.29351	−	1.08041i
$544$	−1.34652	+	0.676246i	−0.0577314	+	0.0289938i
$545$	−16.0453	+	37.1971i	−0.687303	+	1.59335i
$546$	−14.3963	+	9.42200i	−0.616105	+	0.403224i
$547$	1.05989	+	18.1976i	0.0453176	+	0.778074i	0.942044	+	0.335489i	$0.108901\pi$
$547$	1.05989	+	18.1976i	0.0453176	+	0.778074i	−0.896727	+	0.442585i	$0.854061\pi$
$548$	−1.07115	−	6.07480i	−0.0457573	−	0.259503i
$549$	−25.5445	−	12.9740i	−1.09021	−	0.553718i
$550$	7.69252	−	43.6265i	0.328010	−	1.86024i
$551$	−4.95948	−	0.579680i	−0.211281	−	0.0246952i
$552$	10.5012	−	1.20333i	0.446959	−	0.0512172i
$553$	−16.0306	−	53.5458i	−0.681689	−	2.27700i
$554$	29.4668	+	6.98376i	1.25192	+	0.296711i
$555$	−22.3950	−	14.8021i	−0.950616	−	0.628316i
$556$	−0.706721	−	1.63836i	−0.0299716	−	0.0694821i
$557$	1.32660	+	1.11315i	0.0562100	+	0.0471658i	0.670460	−	0.741946i	$-0.266097\pi$
$557$	1.32660	+	1.11315i	0.0562100	+	0.0471658i	−0.614250	+	0.789112i	$0.710541\pi$
$558$	−5.97998	−	2.20723i	−0.253153	−	0.0934397i
$559$	7.50671	−	6.29887i	0.317500	−	0.266414i
$560$	11.6531	+	5.85239i	0.492432	+	0.247309i
$561$	−8.78672	−	9.35570i	−0.370976	−	0.394998i
$562$	16.3302	−	1.90873i	0.688847	−	0.0805147i
$563$	1.55451	−	26.6900i	0.0655149	−	1.12485i	−0.792045	−	0.610463i	$-0.790983\pi$
$563$	1.55451	−	26.6900i	0.0655149	−	1.12485i	0.857560	−	0.514385i	$-0.171980\pi$
$564$	−4.17295	+	7.19014i	−0.175713	+	0.302760i
$565$	−22.4020	−	23.7447i	−0.942458	−	0.998947i
$566$	−11.7589			−0.494262
$567$	−1.53986	−	31.3195i	−0.0646681	−	1.31529i
$568$	16.2340			0.681164
$569$	−11.6240	−	12.3208i	−0.487305	−	0.516513i	0.436330	−	0.899787i	$-0.356278\pi$
$569$	−11.6240	−	12.3208i	−0.487305	−	0.516513i	−0.923635	+	0.383274i	$0.874797\pi$
$570$	3.70676	+	0.00838743i	0.155259	+	0.000351311i
$571$	1.50497	−	25.8393i	0.0629810	−	1.08134i	−0.807731	−	0.589551i	$-0.799305\pi$
$571$	1.50497	−	25.8393i	0.0629810	−	1.08134i	0.870713	−	0.491792i	$-0.163658\pi$
$572$	13.9265	−	1.62778i	0.582298	−	0.0680608i
$573$	15.0482	−	3.53054i	0.628646	−	0.147490i
$574$	−4.33505	−	2.17715i	−0.180942	−	0.0908723i
$575$	42.1097	−	35.3342i	1.75609	−	1.47354i
$576$	2.28938	+	1.93874i	0.0953910	+	0.0807810i
$577$	−22.7143	−	19.0596i	−0.945609	−	0.793460i	0.0329440	−	0.999457i	$-0.489512\pi$
$577$	−22.7143	−	19.0596i	−0.945609	−	0.793460i	−0.978553	+	0.205997i	$0.933956\pi$
$578$	−5.83409	−	13.5249i	−0.242666	−	0.562563i
$579$	−0.726551	+	12.0063i	−0.0301944	+	0.498965i
$580$	−31.8017	−	7.53714i	−1.32049	−	0.312963i
$581$	1.46362	+	4.88885i	0.0607214	+	0.202824i
$582$	6.57972	−	15.1591i	0.272738	−	0.628365i
$583$	−33.3569	−	3.89886i	−1.38150	−	0.161474i
$584$	1.08308	−	6.14244i	0.0448181	−	0.254176i
$585$	−19.2323	+	25.5909i	−0.795160	+	1.05805i
$586$	−4.04519	−	22.9414i	−0.167105	−	0.947700i
$587$	1.68775	+	28.9776i	0.0696610	+	1.19603i	0.834202	+	0.551459i	$0.185929\pi$
$587$	1.68775	+	28.9776i	0.0696610	+	1.19603i	−0.764541	+	0.644575i	$0.777034\pi$
$588$	−7.94560	−	4.01297i	−0.327671	−	0.165492i
$589$	−0.481223	+	1.11560i	−0.0198285	+	0.0459675i
$590$	14.9458	−	7.50605i	0.615308	−	0.309019i
$591$	0.288055	+	1.65554i	0.0118490	+	0.0680997i
$592$	−4.02946	+	0.954999i	−0.165610	+	0.0392502i
$593$	12.9366	+	22.4069i	0.531244	+	0.920142i	0.999335	+	0.0364615i	$0.0116086\pi$
$593$	12.9366	+	22.4069i	0.531244	+	0.920142i	−0.468091	+	0.883680i	$0.655058\pi$
$594$	−10.2806	+	23.3950i	−0.421816	+	0.959910i
$595$	9.82435	−	17.0163i	0.402759	−	0.697599i
$596$	5.26621	−	17.5904i	0.215712	−	0.720529i
$597$	−24.1507	−	20.3581i	−0.988421	−	0.833203i
$598$	14.5365	+	9.56079i	0.594440	+	0.390970i
$599$	−24.8120	−	33.3284i	−1.01379	−	1.36176i	−0.930929	−	0.365199i	$-0.881001\pi$
$599$	−24.8120	−	33.3284i	−1.01379	−	1.36176i	−0.0828632	−	0.996561i	$-0.526406\pi$
$600$	15.4923	+	1.84633i	0.632471	+	0.0753763i
$601$	−40.2891	+	26.4986i	−1.64343	+	1.08090i	−0.722345	+	0.691532i	$0.756936\pi$
$601$	−40.2891	+	26.4986i	−1.64343	+	1.08090i	−0.921083	+	0.389367i	$0.872694\pi$
$602$	11.2530	+	4.09576i	0.458638	+	0.166931i
$603$	−18.7976	−	4.54505i	−0.765497	−	0.185089i
$604$	5.39068	−	1.96205i	0.219344	−	0.0798345i
$605$	29.4701	−	39.5853i	1.19813	−	1.60937i
$606$	−16.7526	−	4.01049i	−0.680526	−	0.162915i
$607$	28.3412	−	30.0400i	1.15034	−	1.21928i	0.178420	−	0.983954i	$-0.442902\pi$
$607$	28.3412	−	30.0400i	1.15034	−	1.21928i	0.971916	−	0.235330i	$-0.0756170\pi$
$608$	0.392399	−	0.415918i	0.0159139	−	0.0168677i
$609$	51.2493	+	12.2689i	2.07673	+	0.497159i
$610$	−21.3444	+	28.6706i	−0.864211	+	1.16084i
$611$	−12.8591	+	4.68032i	−0.520223	+	0.189346i
$612$	3.11691	−	3.27393i	0.125994	−	0.132341i
$613$	−21.2292	−	7.72678i	−0.857438	−	0.312082i	−0.124369	−	0.992236i	$-0.539691\pi$
$613$	−21.2292	−	7.72678i	−0.857438	−	0.312082i	−0.733069	+	0.680154i	$0.761913\pi$
$614$	−11.8695	+	7.80672i	−0.479016	+	0.315053i
$615$	−8.96235	−	1.06811i	−0.361397	−	0.0430704i
$616$	10.2321	+	13.7442i	0.412265	+	0.553768i
$617$	8.00594	+	5.26559i	0.322307	+	0.211985i	0.700343	−	0.713806i	$-0.253030\pi$
$617$	8.00594	+	5.26559i	0.322307	+	0.211985i	−0.378036	+	0.925791i	$0.623401\pi$
$618$	−1.73144	−	1.45954i	−0.0696486	−	0.0587112i
$619$	−8.30865	+	27.7528i	−0.333953	+	1.11548i	0.611914	+	0.790924i	$0.290400\pi$
$619$	−8.30865	+	27.7528i	−0.333953	+	1.11548i	−0.945867	+	0.324556i	$0.894785\pi$
$620$	−3.97620	+	6.88698i	−0.159688	+	0.276588i
$621$	−28.4327	+	14.0386i	−1.14097	+	0.563349i
$622$	3.71090	+	6.42746i	0.148793	+	0.257718i
$623$	−15.0086	+	3.55710i	−0.601307	+	0.142512i
$624$	0.846505	+	4.86512i	0.0338873	+	0.194761i
$625$	9.92043	−	4.98223i	0.396817	−	0.199289i
$626$	−2.93500	+	6.80410i	−0.117306	+	0.271947i
$627$	4.34766	+	2.19581i	0.173629	+	0.0876922i
$628$	−0.746761	−	12.8214i	−0.0297990	−	0.511629i
$629$	1.08352	+	6.14495i	0.0432028	+	0.245015i
$630$	−38.8348	−	4.71738i	−1.54722	−	0.187945i
$631$	5.30053	−	30.0608i	0.211011	−	1.19670i	−0.676685	−	0.736272i	$-0.736584\pi$
$631$	5.30053	−	30.0608i	0.211011	−	1.19670i	0.887696	−	0.460430i	$-0.152305\pi$
$632$	−15.9339	−	1.86240i	−0.633816	−	0.0740825i
$633$	0.904112	−	2.08300i	0.0359352	−	0.0827916i
$634$	4.61629	+	15.4195i	0.183336	+	0.612386i
$635$	−27.4471	−	6.50508i	−1.08921	−	0.258146i
$636$	0.714454	−	11.8064i	0.0283300	−	0.468155i
$637$	−5.80355	−	13.4541i	−0.229945	−	0.533072i
$638$	−32.8978	−	27.6045i	−1.30244	−	1.09287i
$639$	−45.8399	+	16.4498i	−1.81340	+	0.650744i
$640$	2.86707	−	2.40576i	0.113331	−	0.0950960i
$641$	25.6267	+	12.8702i	1.01219	+	0.508343i	0.875986	−	0.482337i	$-0.160212\pi$
$641$	25.6267	+	12.8702i	1.01219	+	0.508343i	0.136209	+	0.990680i	$0.456508\pi$
$642$	8.63400	−	2.02567i	0.340757	−	0.0799469i
$643$	−13.6666	+	1.59740i	−0.538959	+	0.0629953i	−0.381218	−	0.924485i	$-0.624495\pi$
$643$	−13.6666	+	1.59740i	−0.538959	+	0.0629953i	−0.157741	+	0.987480i	$0.550421\pi$
$644$	−1.23628	+	21.2261i	−0.0487163	+	0.836427i
$645$	22.2808	+	0.0504156i	0.877305	+	0.00198511i
$646$	−0.591262	−	0.626701i	−0.0232629	−	0.0246572i
$647$	10.7886			0.424143			0.212072	−	0.977254i	$-0.431979\pi$
$647$	10.7886			0.424143			0.212072	+	0.977254i	$0.431979\pi$
$648$	−8.42903	−	3.15460i	−0.331123	−	0.123924i
$649$	21.9763			0.862647
$650$	17.6240	+	18.6803i	0.691269	+	0.732703i
$651$	6.43633	−	11.0900i	0.252259	−	0.434652i
$652$	−1.17503	+	20.1745i	−0.0460178	+	0.790095i
$653$	−4.66348	+	0.545083i	−0.182496	+	0.0213307i	−0.206850	−	0.978373i	$-0.566321\pi$
$653$	−4.66348	+	0.545083i	−0.182496	+	0.0213307i	0.0243539	+	0.999703i	$0.492247\pi$
$654$	−12.8343	−	13.6654i	−0.501862	−	0.534360i
$655$	67.6913	+	33.9958i	2.64492	+	1.32833i
$656$	−1.06658	+	0.894966i	−0.0416429	+	0.0349425i
$657$	3.16581	+	18.4418i	0.123510	+	0.719485i
$658$	−12.8105	−	10.7493i	−0.499404	−	0.419050i
$659$	−18.0813	−	41.9172i	−0.704348	−	1.63286i	−0.772367	−	0.635177i	$-0.780927\pi$
$659$	−18.0813	−	41.9172i	−0.704348	−	1.63286i	0.0680190	−	0.997684i	$-0.478332\pi$
$660$	26.5961	+	17.5789i	1.03525	+	0.684257i
$661$	−1.13586	−	0.269203i	−0.0441797	−	0.0104708i	0.208467	−	0.978029i	$-0.433153\pi$
$661$	−1.13586	−	0.269203i	−0.0441797	−	0.0104708i	−0.252646	+	0.967559i	$0.581301\pi$
$662$	−2.98183	−	9.96001i	−0.115892	−	0.387107i
$663$	7.39247	−	0.847105i	0.287100	−	0.0328988i
$664$	1.45480	+	0.170042i	0.0564571	+	0.00659889i
$665$	−1.29480	+	7.34316i	−0.0502101	+	0.284755i
$666$	10.4103	−	6.77964i	0.403389	−	0.262706i
$667$	−9.25364	−	52.4800i	−0.358302	−	2.03203i
$668$	0.0959479	+	1.64736i	0.00371234	+	0.0637384i
$669$	24.5720	−	16.0817i	0.950008	−	0.621755i
$670$	−9.55621	+	22.1538i	−0.369189	+	0.855876i
$671$	−41.9711	+	21.0787i	−1.62028	+	0.813733i
$672$	−4.63163	+	3.86857i	−0.178669	+	0.149233i
$673$	31.2740	−	7.41207i	1.20552	−	0.285714i	0.421721	−	0.906725i	$-0.361426\pi$
$673$	31.2740	−	7.41207i	1.20552	−	0.285714i	0.783802	+	0.621011i	$0.213278\pi$
$674$	1.78627	+	3.09391i	0.0688045	+	0.119173i
$675$	−45.6164	+	10.4848i	−1.75578	+	0.403558i
$676$	2.43568	−	4.21872i	0.0936799	−	0.162258i
$677$	−0.272489	+	0.910178i	−0.0104726	+	0.0349810i	−0.963066	−	0.269265i	$-0.913219\pi$
$677$	−0.272489	+	0.910178i	−0.0104726	+	0.0349810i	0.952594	+	0.304246i	$0.0984045\pi$
$678$	14.2078	−	5.13484i	0.545648	−	0.197202i
$679$	27.7734	+	18.2669i	1.06585	+	0.701019i
$680$	−3.36765	−	4.52354i	−0.129144	−	0.173470i
$681$	−0.936258	−	2.18407i	−0.0358775	−	0.0836936i
$682$	−8.73040	+	5.74207i	−0.334304	+	0.219875i
$683$	−37.1229	−	13.5116i	−1.42047	−	0.517009i	−0.486286	−	0.873800i	$-0.661649\pi$
$683$	−37.1229	−	13.5116i	−1.42047	−	0.517009i	−0.934184	+	0.356791i	$0.883871\pi$
$684$	−0.686566	+	1.57204i	−0.0262515	+	0.0601084i
$685$	21.6946	−	7.89618i	0.828907	−	0.301697i
$686$	−3.87140	+	5.20020i	−0.147811	+	0.198544i
$687$	−11.8594	+	12.5133i	−0.452463	+	0.477414i
$688$	2.35865	−	2.50002i	0.0899227	−	0.0953125i
$689$	13.3609	−	14.1618i	0.509012	−	0.539521i
$690$	11.2601	+	37.9235i	0.428666	+	1.44372i
$691$	17.0712	−	22.9306i	0.649418	−	0.872320i	−0.348467	−	0.937321i	$-0.613298\pi$
$691$	17.0712	−	22.9306i	0.649418	−	0.872320i	0.997885	+	0.0650013i	$0.0207052\pi$
$692$	−13.1048	+	4.76975i	−0.498169	+	0.181319i
$693$	−42.8193	−	28.4411i	−1.62657	−	1.08039i
$694$	−8.23506	−	2.99732i	−0.312598	−	0.113777i
$695$	5.57943	−	3.66965i	0.211640	−	0.139198i
$696$	9.05940	−	12.1116i	0.343396	−	0.459088i
$697$	1.25280	+	1.68280i	0.0474531	+	0.0637406i
$698$	−23.7869	−	15.6449i	−0.900348	−	0.592168i
$699$	6.05236	−	33.8762i	0.228921	−	1.28132i
$700$	−9.00116	+	30.0660i	−0.340212	+	1.13639i
$701$	20.1828	−	34.9576i	0.762293	−	1.32033i	−0.179372	−	0.983781i	$-0.557407\pi$
$701$	20.1828	−	34.9576i	0.762293	−	1.32033i	0.941666	−	0.336550i	$-0.109260\pi$
$702$	−7.32006	−	12.8798i	−0.276278	−	0.486118i
$703$	−1.18395	−	2.05067i	−0.0446536	−	0.0773423i
$704$	4.78535	−	1.13415i	0.180355	−	0.0427448i
$705$	−29.2137	−	10.7079i	−1.10025	−	0.403281i
$706$	4.43391	−	2.22679i	0.166873	−	0.0838065i
$707$	13.7246	−	31.8173i	0.516168	−	1.19661i
$708$	0.432551	+	7.72781i	0.0162562	+	0.290429i
$709$	−0.861427	−	14.7901i	−0.0323516	−	0.555455i	−0.975074	−	0.221878i	$-0.928781\pi$
$709$	−0.861427	−	14.7901i	−0.0323516	−	0.555455i	0.942723	−	0.333577i	$-0.108256\pi$
$710$	10.5507	+	59.8360i	0.395960	+	2.24560i
$711$	46.8796	−	10.8868i	1.75812	−	0.408288i
$712$	−0.768743	+	4.35976i	−0.0288099	+	0.163389i
$713$	−12.8788	−	1.50532i	−0.482316	−	0.0563747i
$714$	5.41348	+	7.30602i	0.202594	+	0.273421i
$715$	15.0508	+	50.2730i	0.562866	+	1.88010i
$716$	4.38514	+	1.03930i	0.163881	+	0.0388404i
$717$	5.35505	−	2.67425i	0.199988	−	0.0998717i
$718$	0.359107	+	0.832503i	0.0134018	+	0.0310688i
$719$	−12.7932	−	10.7348i	−0.477107	−	0.400340i	0.372272	−	0.928124i	$-0.378579\pi$
$719$	−12.7932	−	10.7348i	−0.477107	−	0.400340i	−0.849379	+	0.527784i	$0.823023\pi$
$720$	−5.65799	+	9.69831i	−0.210861	+	0.361435i
$721$	3.48955	−	2.92808i	0.129958	−	0.109047i
$722$	−16.6868	−	8.38044i	−0.621020	−	0.311888i
$723$	−5.09535	+	16.8806i	−0.189498	+	0.627795i
$724$	22.5210	−	2.63232i	0.836985	−	0.0978296i
$725$	4.57364	−	78.5263i	0.169861	−	2.91639i
$726$	11.3745	+	19.8045i	0.422147	+	0.735016i
$727$	6.49001	+	6.87901i	0.240701	+	0.255128i	0.836451	−	0.548042i	$-0.184626\pi$
$727$	6.49001	+	6.87901i	0.240701	+	0.255128i	−0.595750	+	0.803170i	$0.703145\pi$
$728$	−9.93357			−0.368163
$729$	26.9975	+	0.366552i	0.999908	+	0.0135760i
$730$	23.3440			0.863998
$731$	−3.55399	−	3.76701i	−0.131449	−	0.139328i
$732$	−8.23824	−	14.3439i	−0.304494	−	0.530166i
$733$	−1.89210	+	32.4861i	−0.0698864	+	1.19990i	0.762978	+	0.646425i	$0.223737\pi$
$733$	−1.89210	+	32.4861i	−0.0698864	+	1.19990i	−0.832864	+	0.553478i	$0.813300\pi$
$734$	6.72376	−	0.785895i	0.248178	−	0.0290079i
$735$	9.62720	−	31.8943i	0.355105	−	1.17644i
$736$	5.45342	+	2.73881i	0.201016	+	0.100954i
$737$	−24.2858	+	20.3782i	−0.894580	+	0.750642i
$738$	2.10483	−	3.60786i	0.0774798	−	0.132807i
$739$	29.2558	+	24.5485i	1.07619	+	0.903032i	0.995599	−	0.0937154i	$-0.0298744\pi$
$739$	29.2558	+	24.5485i	1.07619	+	0.903032i	0.0805923	+	0.996747i	$0.474319\pi$
$740$	−6.13877	−	14.2313i	−0.225666	−	0.523152i
$741$	−2.52622	+	1.26157i	−0.0928030	+	0.0463448i
$742$	23.1516	+	5.48702i	0.849921	+	0.201435i
$743$	0.451286	+	1.50740i	0.0165561	+	0.0553012i	0.965868	−	0.259033i	$-0.0834039\pi$
$743$	0.451286	+	1.50740i	0.0165561	+	0.0553012i	−0.949312	+	0.314334i	$0.898219\pi$
$744$	−2.19099	−	2.95696i	−0.0803256	−	0.108407i
$745$	68.2578	+	7.97819i	2.50077	+	0.292298i
$746$	2.99666	−	16.9949i	0.109715	−	0.622227i
$747$	−4.28020	+	0.993991i	−0.156604	+	0.0363682i
$748$	−1.28678	−	7.29768i	−0.0470492	−	0.266830i
$749$	1.03728	+	17.8093i	0.0379012	+	0.650739i
$750$	1.45195	+	25.9400i	0.0530176	+	0.947196i
$751$	−20.6097	+	47.7787i	−0.752059	+	1.74347i	−0.0875854	+	0.996157i	$0.527915\pi$
$751$	−20.6097	+	47.7787i	−0.752059	+	1.74347i	−0.664474	+	0.747312i	$0.731344\pi$
$752$	−4.28918	+	2.15411i	−0.156410	+	0.0785522i
$753$	−27.0532	−	9.91594i	−0.985873	−	0.361357i
$754$	24.2256	−	5.74157i	0.882244	−	0.209096i
$755$	10.7353	+	18.5940i	0.390696	+	0.676705i
$756$	9.15830	−	15.6168i	0.333084	−	0.567979i
$757$	−18.7664	+	32.5044i	−0.682078	+	1.18139i	0.292267	+	0.956337i	$0.405590\pi$
$757$	−18.7664	+	32.5044i	−0.682078	+	1.18139i	−0.974345	+	0.225057i	$0.927743\pi$
$758$	3.10730	−	10.3791i	0.112862	−	0.376986i
$759$	−9.14235	+	51.1715i	−0.331846	+	1.85741i
$760$	1.78803	+	1.17601i	0.0648587	+	0.0426583i
$761$	−6.13854	−	8.24549i	−0.222522	−	0.298899i	0.676817	−	0.736152i	$-0.263359\pi$
$761$	−6.13854	−	8.24549i	−0.222522	−	0.298899i	−0.899339	+	0.437253i	$0.855952\pi$
$762$	7.81891	−	10.4532i	0.283249	−	0.378678i
$763$	31.5076	−	20.7229i	1.14065	−	0.750219i
$764$	8.38580	+	3.05218i	0.303388	+	0.110424i
$765$	14.0929	+	9.36067i	0.509529	+	0.338436i
$766$	23.2303	−	8.45513i	0.839344	−	0.305496i
$767$	−7.60806	+	10.2194i	−0.274711	+	0.369001i

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.686242 - 0.727374i) q^{2} +(0.862629 + 1.50196i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-3.71739 + 0.434501i) q^{5} +(0.500511 - 1.65816i) q^{6} +(3.11355 + 1.56368i) q^{7} +(0.766044 - 0.642788i) q^{8} +(-1.51174 + 2.59126i) q^{9} +O(q^{10})\)	\(q+(-0.686242 - 0.727374i) q^{2} +(0.862629 + 1.50196i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-3.71739 + 0.434501i) q^{5} +(0.500511 - 1.65816i) q^{6} +(3.11355 + 1.56368i) q^{7} +(0.766044 - 0.642788i) q^{8} +(-1.51174 + 2.59126i) q^{9} +(2.86707 + 2.40576i) q^{10} +(1.94788 + 4.51570i) q^{11} +(-1.54957 + 0.773839i) q^{12} +(-2.77423 - 0.657504i) q^{13} +(-0.999264 - 3.33778i) q^{14} +(-3.85933 - 5.20854i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(-0.261651 + 1.48390i) q^{17} +(2.92224 - 0.678630i) q^{18} +(-0.0992935 - 0.563121i) q^{19} +(-0.217618 - 3.73637i) q^{20} +(0.337255 + 6.02529i) q^{21} +(1.94788 - 4.51570i) q^{22} +(5.45342 - 2.73881i) q^{23} +(1.62625 + 0.596078i) q^{24} +(8.76498 - 2.07734i) q^{25} +(1.42554 + 2.46911i) q^{26} +(-5.19603 - 0.0352723i) q^{27} +(-1.74207 + 3.01736i) q^{28} +(2.50447 - 8.36553i) q^{29} +(-1.14012 + 6.38149i) q^{30} +(-1.77523 - 1.16758i) q^{31} +(0.597159 + 0.802123i) q^{32} +(-5.10209 + 6.82101i) q^{33} +(1.25890 - 0.827995i) q^{34} +(-12.2537 - 4.45998i) q^{35} +(-2.49898 - 1.65985i) q^{36} +(3.89134 - 1.41633i) q^{37} +(-0.341460 + 0.458661i) q^{38} +(-1.40559 - 4.73395i) q^{39} +(-2.56839 + 2.72234i) q^{40} +(0.955468 - 1.01274i) q^{41} +(4.15120 - 4.38011i) q^{42} +(-2.05247 + 2.75694i) q^{43} +(-4.62132 + 1.68202i) q^{44} +(4.49383 - 10.2896i) q^{45} +(-5.73450 - 2.08719i) q^{46} +(4.01010 - 2.63748i) q^{47} +(-0.682430 - 1.59195i) q^{48} +(3.06896 + 4.12233i) q^{49} +(-7.52589 - 4.94986i) q^{50} +(-2.45446 + 0.887065i) q^{51} +(0.817698 - 2.73130i) q^{52} +(-3.41445 + 5.91401i) q^{53} +(3.54008 + 3.80366i) q^{54} +(-9.20312 - 15.9403i) q^{55} +(3.39023 - 0.803499i) q^{56} +(0.760130 - 0.634899i) q^{57} +(-7.80354 + 3.91908i) q^{58} +(1.76994 - 4.10317i) q^{59} +(5.42413 - 3.54995i) q^{60} +(0.555292 + 9.53400i) q^{61} +(0.368964 + 2.09250i) q^{62} +(-8.75879 + 5.70413i) q^{63} +(0.173648 - 0.984808i) q^{64} +(10.5986 + 1.23880i) q^{65} +(8.46269 - 0.969741i) q^{66} +(1.84885 + 6.17560i) q^{67} +(-1.46617 - 0.347490i) q^{68} +(8.81785 + 5.82822i) q^{69} +(5.16492 + 11.9736i) q^{70} +(12.4360 + 10.4350i) q^{71} +(0.507569 + 2.95675i) q^{72} +(4.77797 - 4.00919i) q^{73} +(-3.70061 - 1.85851i) q^{74} +(10.6810 + 11.3726i) q^{75} +(0.567942 - 0.0663829i) q^{76} +(-0.996295 + 17.1057i) q^{77} +(-2.47878 + 4.27102i) q^{78} +(-11.0089 - 11.6688i) q^{79} +3.74270 q^{80} +(-4.42927 - 7.83464i) q^{81} -1.39232 q^{82} +(1.00514 + 1.06539i) q^{83} +(-6.03470 - 0.0136550i) q^{84} +(0.327905 - 5.62992i) q^{85} +(3.41381 - 0.399018i) q^{86} +(14.7251 - 3.45474i) q^{87} +(4.39480 + 2.20715i) q^{88} +(-3.39129 + 2.84563i) q^{89} +(-10.5682 + 3.79245i) q^{90} +(-7.60956 - 6.38518i) q^{91} +(2.41709 + 5.60344i) q^{92} +(0.222299 - 3.67350i) q^{93} +(-4.67033 - 1.10689i) q^{94} +(0.613789 + 2.05020i) q^{95} +(-0.689627 + 1.58884i) q^{96} +(9.47647 + 1.10764i) q^{97} +(0.892426 - 5.06120i) q^{98} +(-14.6461 - 1.77910i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

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