LMFDB - Embedded newform 189.2.u.a.130.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(4,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 12]))

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

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

chi := DirichletCharacter("189.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.u (of order $9$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			130.6
Character	$\chi$	$=$	189.130
Dual form			189.2.u.a.16.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65761 - 0.603319i) q^{2} +(-1.50730 - 0.853264i) q^{3} +(0.851575 + 0.714556i) q^{4} +(-3.19083 - 2.67742i) q^{5} +(1.98371 + 2.32376i) q^{6} +(0.729121 - 2.54330i) q^{7} +(0.783518 + 1.35709i) q^{8} +(1.54388 + 2.57224i) q^{9} +O(q^{10})$	\(q+(-1.65761 - 0.603319i) q^{2} +(-1.50730 - 0.853264i) q^{3} +(0.851575 + 0.714556i) q^{4} +(-3.19083 - 2.67742i) q^{5} +(1.98371 + 2.32376i) q^{6} +(0.729121 - 2.54330i) q^{7} +(0.783518 + 1.35709i) q^{8} +(1.54388 + 2.57224i) q^{9} +(3.67380 + 6.36320i) q^{10} +(-1.89226 + 1.58779i) q^{11} +(-0.673870 - 1.80366i) q^{12} +(0.108160 + 0.0907572i) q^{13} +(-2.74302 + 3.77590i) q^{14} +(2.52498 + 6.75829i) q^{15} +(-0.866076 - 4.91176i) q^{16} +(-0.351339 - 0.608536i) q^{17} +(-1.00727 - 5.19522i) q^{18} +(-3.23251 + 5.59887i) q^{19} +(-0.804060 - 4.56005i) q^{20} +(-3.26911 + 3.21138i) q^{21} +(4.09457 - 1.49030i) q^{22} +(5.24538 - 1.90916i) q^{23} +(-0.0230353 - 2.71409i) q^{24} +(2.14455 + 12.1624i) q^{25} +(-0.124532 - 0.215695i) q^{26} +(-0.132287 - 5.19447i) q^{27} +(2.43823 - 1.64481i) q^{28} +(0.100910 - 0.0846735i) q^{29} +(-0.108009 - 12.7259i) q^{30} +(-3.55162 - 2.98016i) q^{31} +(-0.983522 + 5.57783i) q^{32} +(4.20700 - 0.778680i) q^{33} +(0.215239 + 1.22068i) q^{34} +(-9.13599 + 6.16308i) q^{35} +(-0.523280 + 3.29365i) q^{36} +0.775890 q^{37} +(8.73613 - 7.33049i) q^{38} +(-0.0855897 - 0.229087i) q^{39} +(1.13344 - 6.42806i) q^{40} +(-2.52108 - 2.11544i) q^{41} +(7.35638 - 3.35088i) q^{42} +(-5.66175 - 2.06071i) q^{43} -2.74597 q^{44} +(1.96072 - 12.3412i) q^{45} -9.84662 q^{46} +(-4.55973 + 3.82607i) q^{47} +(-2.88560 + 8.14247i) q^{48} +(-5.93677 - 3.70875i) q^{49} +(3.78296 - 21.4542i) q^{50} +(0.0103293 + 1.21703i) q^{51} +(0.0272554 + 0.154573i) q^{52} +(1.85992 - 3.22148i) q^{53} +(-2.91464 + 8.69019i) q^{54} +10.2891 q^{55} +(4.02277 - 1.00324i) q^{56} +(9.64966 - 5.68097i) q^{57} +(-0.218354 + 0.0794744i) q^{58} +(-0.630281 + 3.57450i) q^{59} +(-2.67897 + 7.55942i) q^{60} +(-0.167139 + 0.140247i) q^{61} +(4.08919 + 7.08269i) q^{62} +(7.66766 - 2.05108i) q^{63} +(0.00796973 - 0.0138040i) q^{64} +(-0.102125 - 0.579182i) q^{65} +(-7.44335 - 1.24742i) q^{66} +(-14.4193 + 5.24819i) q^{67} +(0.135642 - 0.769265i) q^{68} +(-9.53537 - 1.59802i) q^{69} +(18.8622 - 4.70403i) q^{70} +(-7.04066 + 12.1948i) q^{71} +(-2.28111 + 4.11059i) q^{72} +12.7274 q^{73} +(-1.28612 - 0.468110i) q^{74} +(7.14522 - 20.1621i) q^{75} +(-6.75343 + 2.45805i) q^{76} +(2.65855 + 5.97028i) q^{77} +(0.00366121 + 0.431374i) q^{78} +(-5.42013 - 1.97277i) q^{79} +(-10.3874 + 17.9914i) q^{80} +(-4.23286 + 7.94248i) q^{81} +(2.90267 + 5.02758i) q^{82} +(-1.84338 + 1.54678i) q^{83} +(-5.07860 + 0.398766i) q^{84} +(-0.508248 + 2.88242i) q^{85} +(8.14168 + 6.83168i) q^{86} +(-0.224350 + 0.0415252i) q^{87} +(-3.63740 - 1.32391i) q^{88} +(-0.452090 + 0.783042i) q^{89} +(-10.6958 + 19.2739i) q^{90} +(0.309685 - 0.208911i) q^{91} +(5.83104 + 2.12233i) q^{92} +(2.81047 + 7.52245i) q^{93} +(9.86659 - 3.59114i) q^{94} +(25.3049 - 9.21024i) q^{95} +(6.24182 - 7.56824i) q^{96} +(-1.73081 - 0.629965i) q^{97} +(7.60326 + 9.72941i) q^{98} +(-7.00562 - 2.41598i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.65761	−	0.603319i	−1.17210	−	0.426611i	−0.318698	−	0.947856i	$-0.603245\pi$
$2$	−1.65761	−	0.603319i	−1.17210	−	0.426611i	−0.853407	+	0.521245i	$0.825468\pi$
$3$	−1.50730	−	0.853264i	−0.870238	−	0.492632i
$3$	−1.50730	−	0.853264i	−0.870238	−	0.492632i
$4$	0.851575	+	0.714556i	0.425787	+	0.357278i
$5$	−3.19083	−	2.67742i	−1.42698	−	1.19738i	−0.947470	−	0.319845i	$-0.896369\pi$
$5$	−3.19083	−	2.67742i	−1.42698	−	1.19738i	−0.479512	−	0.877535i	$-0.659186\pi$
$6$	1.98371	+	2.32376i	0.809847	+	0.948669i
$7$	0.729121	−	2.54330i	0.275582	−	0.961278i
$7$	0.729121	−	2.54330i	0.275582	−	0.961278i
$8$	0.783518	+	1.35709i	0.277015	+	0.479805i
$9$	1.54388	+	2.57224i	0.514627	+	0.857414i
$10$	3.67380	+	6.36320i	1.16176	+	2.01222i
$11$	−1.89226	+	1.58779i	−0.570538	+	0.478738i	−0.881824	−	0.471578i	$-0.843685\pi$
$11$	−1.89226	+	1.58779i	−0.570538	+	0.478738i	0.311287	+	0.950316i	$0.399240\pi$
$12$	−0.673870	−	1.80366i	−0.194530	−	0.520673i
$13$	0.108160	+	0.0907572i	0.0299983	+	0.0251715i	0.657664	−	0.753312i	$-0.271545\pi$
$13$	0.108160	+	0.0907572i	0.0299983	+	0.0251715i	−0.627665	+	0.778483i	$0.715989\pi$
$14$	−2.74302	+	3.77590i	−0.733102	+	1.00915i
$15$	2.52498	+	6.75829i	0.651946	+	1.74498i
$16$	−0.866076	−	4.91176i	−0.216519	−	1.22794i
$17$	−0.351339	−	0.608536i	−0.0852121	−	0.147592i	0.820269	−	0.571977i	$-0.193823\pi$
$17$	−0.351339	−	0.608536i	−0.0852121	−	0.147592i	−0.905482	+	0.424386i	$0.860490\pi$
$18$	−1.00727	−	5.19522i	−0.237415	−	1.22452i
$19$	−3.23251	+	5.59887i	−0.741588	+	1.28447i	0.210183	+	0.977662i	$0.432594\pi$
$19$	−3.23251	+	5.59887i	−0.741588	+	1.28447i	−0.951772	+	0.306807i	$0.900739\pi$
$20$	−0.804060	−	4.56005i	−0.179793	−	1.01966i
$21$	−3.26911	+	3.21138i	−0.713378	+	0.700780i
$22$	4.09457	−	1.49030i	0.872965	−	0.317733i
$23$	5.24538	−	1.90916i	1.09374	−	0.398088i	0.268734	−	0.963214i	$-0.413395\pi$
$23$	5.24538	−	1.90916i	1.09374	−	0.398088i	0.825004	+	0.565126i	$0.191173\pi$
$24$	−0.0230353	−	2.71409i	−0.00470207	−	0.554011i
$25$	2.14455	+	12.1624i	0.428910	+	2.43247i
$26$	−0.124532	−	0.215695i	−0.0244226	−	0.0423012i
$27$	−0.132287	−	5.19447i	−0.0254586	−	0.999676i
$28$	2.43823	−	1.64481i	0.460783	−	0.310841i
$29$	0.100910	−	0.0846735i	0.0187385	−	0.0157235i	−0.633370	−	0.773849i	$-0.718329\pi$
$29$	0.100910	−	0.0846735i	0.0187385	−	0.0157235i	0.652109	+	0.758125i	$0.273885\pi$
$30$	−0.108009	−	12.7259i	−0.0197197	−	2.32343i
$31$	−3.55162	−	2.98016i	−0.637889	−	0.535253i	0.265480	−	0.964116i	$-0.414470\pi$
$31$	−3.55162	−	2.98016i	−0.637889	−	0.535253i	−0.903369	+	0.428864i	$0.858914\pi$
$32$	−0.983522	+	5.57783i	−0.173864	+	0.986030i
$33$	4.20700	−	0.778680i	0.732345	−	0.135551i
$34$	0.215239	+	1.22068i	0.0369132	+	0.209345i
$35$	−9.13599	+	6.16308i	−1.54426	+	1.04175i
$36$	−0.523280	+	3.29365i	−0.0872133	+	0.548941i
$37$	0.775890			0.127556			0.0637778	−	0.997964i	$-0.479685\pi$
$37$	0.775890			0.127556			0.0637778	+	0.997964i	$0.479685\pi$
$38$	8.73613	−	7.33049i	1.41719	−	1.18916i
$39$	−0.0855897	−	0.229087i	−0.0137053	−	0.0366833i
$40$	1.13344	−	6.42806i	0.179213	−	1.01637i
$41$	−2.52108	−	2.11544i	−0.393727	−	0.330376i	0.424336	−	0.905505i	$-0.360507\pi$
$41$	−2.52108	−	2.11544i	−0.393727	−	0.330376i	−0.818063	+	0.575129i	$0.804952\pi$
$42$	7.35638	−	3.35088i	1.13511	−	0.517052i
$43$	−5.66175	−	2.06071i	−0.863409	−	0.314255i	−0.127914	−	0.991785i	$-0.540828\pi$
$43$	−5.66175	−	2.06071i	−0.863409	−	0.314255i	−0.735495	+	0.677530i	$0.763050\pi$
$44$	−2.74597			−0.413970
$45$	1.96072	−	12.3412i	0.292286	−	1.83972i
$46$	−9.84662			−1.45180
$47$	−4.55973	+	3.82607i	−0.665106	+	0.558090i	−0.911612	−	0.411051i	$-0.865162\pi$
$47$	−4.55973	+	3.82607i	−0.665106	+	0.558090i	0.246507	+	0.969141i	$0.420717\pi$
$48$	−2.88560	+	8.14247i	−0.416500	+	1.17526i
$49$	−5.93677	−	3.70875i	−0.848109	−	0.529821i
$50$	3.78296	−	21.4542i	0.534992	−	3.03409i
$51$	0.0103293	+	1.21703i	0.00144639	+	0.170418i
$52$	0.0272554	+	0.154573i	0.00377965	+	0.0214354i
$53$	1.85992	−	3.22148i	0.255480	−	0.442504i	−0.709546	−	0.704659i	$-0.751100\pi$
$53$	1.85992	−	3.22148i	0.255480	−	0.442504i	0.965026	+	0.262155i	$0.0844332\pi$
$54$	−2.91464	+	8.69019i	−0.396633	+	1.18259i
$55$	10.2891			1.38738
$56$	4.02277	−	1.00324i	0.537566	−	0.134063i
$57$	9.64966	−	5.68097i	1.27813	−	0.752463i
$58$	−0.218354	+	0.0794744i	−0.0286713	+	0.0104355i
$59$	−0.630281	+	3.57450i	−0.0820555	+	0.465360i	0.915898	+	0.401412i	$0.131480\pi$
$59$	−0.630281	+	3.57450i	−0.0820555	+	0.465360i	−0.997953	+	0.0639483i	$0.979631\pi$
$60$	−2.67897	+	7.55942i	−0.345853	+	0.975917i
$61$	−0.167139	+	0.140247i	−0.0214000	+	0.0179567i	−0.653425	−	0.756991i	$-0.726668\pi$
$61$	−0.167139	+	0.140247i	−0.0214000	+	0.0179567i	0.632025	+	0.774948i	$0.282224\pi$
$62$	4.08919	+	7.08269i	0.519328	+	0.899502i
$63$	7.66766	−	2.05108i	0.966035	−	0.258412i
$64$	0.00796973	−	0.0138040i	0.000996216	−	0.00172550i
$65$	−0.102125	−	0.579182i	−0.0126671	−	0.0718386i
$66$	−7.44335	−	1.24742i	−0.916212	−	0.153547i
$67$	−14.4193	+	5.24819i	−1.76160	+	0.641169i	−0.999977	−	0.00685489i	$-0.997818\pi$
$67$	−14.4193	+	5.24819i	−1.76160	+	0.641169i	−0.761620	+	0.648024i	$0.775596\pi$
$68$	0.135642	−	0.769265i	0.0164490	−	0.0932871i
$69$	−9.53537	−	1.59802i	−1.14792	−	0.192379i
$70$	18.8622	−	4.70403i	2.25446	−	0.562239i
$71$	−7.04066	+	12.1948i	−0.835573	+	1.44725i	0.0579909	+	0.998317i	$0.481531\pi$
$71$	−7.04066	+	12.1948i	−0.835573	+	1.44725i	−0.893563	+	0.448937i	$0.851803\pi$
$72$	−2.28111	+	4.11059i	−0.268831	+	0.484437i
$73$	12.7274			1.48963			0.744815	−	0.667271i	$-0.232538\pi$
$73$	12.7274			1.48963			0.744815	+	0.667271i	$0.232538\pi$
$74$	−1.28612	−	0.468110i	−0.149508	−	0.0544166i
$75$	7.14522	−	20.1621i	0.825059	−	2.32812i
$76$	−6.75343	+	2.45805i	−0.774671	+	0.281957i
$77$	2.65855	+	5.97028i	0.302970	+	0.680377i
$78$	0.00366121	+	0.431374i	0.000414551	+	0.0488435i
$79$	−5.42013	−	1.97277i	−0.609812	−	0.221954i	0.0186088	−	0.999827i	$-0.494076\pi$
$79$	−5.42013	−	1.97277i	−0.609812	−	0.221954i	−0.628421	+	0.777873i	$0.716299\pi$
$80$	−10.3874	+	17.9914i	−1.16134	+	2.01150i
$81$	−4.23286	+	7.94248i	−0.470317	+	0.882497i
$82$	2.90267	+	5.02758i	0.320547	+	0.555203i
$83$	−1.84338	+	1.54678i	−0.202337	+	0.169781i	−0.738326	−	0.674444i	$-0.764383\pi$
$83$	−1.84338	+	1.54678i	−0.202337	+	0.169781i	0.535989	+	0.844225i	$0.319939\pi$
$84$	−5.07860	+	0.398766i	−0.554120	+	0.0435090i
$85$	−0.508248	+	2.88242i	−0.0551272	+	0.312642i
$86$	8.14168	+	6.83168i	0.877940	+	0.736679i
$87$	−0.224350	+	0.0415252i	−0.0240528	+	0.00445197i
$88$	−3.63740	−	1.32391i	−0.387748	−	0.141129i
$89$	−0.452090	+	0.783042i	−0.0479214	+	0.0830023i	−0.888991	−	0.457924i	$-0.848593\pi$
$89$	−0.452090	+	0.783042i	−0.0479214	+	0.0830023i	0.841070	+	0.540927i	$0.181926\pi$
$90$	−10.6958	+	19.2739i	−1.12743	+	2.03165i
$91$	0.309685	−	0.208911i	0.0324638	−	0.0218998i
$92$	5.83104	+	2.12233i	0.607928	+	0.221268i
$93$	2.81047	+	7.52245i	0.291433	+	0.780042i
$94$	9.86659	−	3.59114i	1.01766	−	0.370398i
$95$	25.3049	−	9.21024i	2.59623	−	0.944951i
$96$	6.24182	−	7.56824i	0.637053	−	0.772430i
$97$	−1.73081	−	0.629965i	−0.175737	−	0.0639632i	0.252653	−	0.967557i	$-0.418697\pi$
$97$	−1.73081	−	0.629965i	−0.175737	−	0.0639632i	−0.428390	+	0.903594i	$0.640919\pi$
$98$	7.60326	+	9.72941i	0.768045	+	0.982819i
$99$	−7.00562	−	2.41598i	−0.704091	−	0.242815i
$100$	−6.86444	+	11.8896i	−0.686444	+	1.18896i
$101$	7.64362	+	2.78205i	0.760569	+	0.276824i	0.693046	−	0.720893i	$-0.256268\pi$
$101$	7.64362	+	2.78205i	0.760569	+	0.276824i	0.0675228	+	0.997718i	$0.478490\pi$
$102$	0.717135	−	2.02359i	0.0710069	−	0.200365i
$103$	−4.90711	−	4.11755i	−0.483511	−	0.405714i	0.368183	−	0.929753i	$-0.379980\pi$
$103$	−4.90711	−	4.11755i	−0.483511	−	0.405714i	−0.851694	+	0.524039i	$0.824425\pi$
$104$	−0.0384205	+	0.217893i	−0.00376744	+	0.0213662i
$105$	19.0294	−	1.49417i	1.85708	−	0.145816i
$106$	−5.02660	+	4.21781i	−0.488226	+	0.409670i
$107$	−5.96628	−	10.3339i	−0.576782	−	0.999016i	−0.995846	−	0.0910589i	$-0.970975\pi$
$107$	−5.96628	−	10.3339i	−0.576782	−	0.999016i	0.419063	−	0.907957i	$-0.362358\pi$
$108$	3.59909	−	4.51800i	0.346322	−	0.434745i
$109$	−0.160232	+	0.277531i	−0.0153475	+	0.0265826i	−0.873597	−	0.486650i	$-0.838219\pi$
$109$	−0.160232	+	0.277531i	−0.0153475	+	0.0265826i	0.858250	+	0.513232i	$0.171552\pi$
$110$	−17.0552	−	6.20760i	−1.62615	−	0.591871i
$111$	−1.16950	−	0.662039i	−0.111004	−	0.0628380i
$112$	−13.1236	−	1.37857i	−1.24006	−	0.130263i
$113$	1.98832	−	0.723688i	0.187045	−	0.0680789i	−0.246799	−	0.969067i	$-0.579379\pi$
$113$	1.98832	−	0.723688i	0.187045	−	0.0680789i	0.433845	+	0.900988i	$0.357157\pi$
$114$	−19.4228	+	3.59499i	−1.81911	+	0.336701i
$115$	−21.8488	−	7.95230i	−2.03741	−	0.741556i
$116$	0.146436			0.0135963
$117$	−0.0664629	+	0.418333i	−0.00614449	+	0.0386749i
$118$	3.20132	−	5.54485i	0.294705	−	0.510445i
$119$	−1.80386	+	0.449864i	−0.165360	+	0.0412389i
$120$	−7.19326	+	8.72186i	−0.656652	+	0.796193i
$121$	−0.850574	+	4.82385i	−0.0773249	+	0.438532i
$122$	0.361665	−	0.131635i	0.0327436	−	0.0119177i
$123$	1.99499	+	5.33974i	0.179882	+	0.481468i
$124$	−0.894975	−	5.07566i	−0.0803712	−	0.455807i
$125$	15.3076	−	26.5135i	1.36915	−	2.37144i
$126$	−13.9474	−	1.22616i	−1.24254	−	0.109235i
$127$	−5.21371	−	9.03041i	−0.462642	−	0.801320i	0.536450	−	0.843932i	$-0.319765\pi$
$127$	−5.21371	−	9.03041i	−0.462642	−	0.801320i	−0.999092	+	0.0426127i	$0.986432\pi$
$128$	8.65602	−	7.26327i	0.765092	−	0.641988i
$129$	6.77560	+	7.93706i	0.596559	+	0.698819i
$130$	−0.180148	+	1.02167i	−0.0158000	+	0.0896063i
$131$	−5.67608	+	2.06593i	−0.495922	+	0.180501i	−0.577859	−	0.816137i	$-0.696112\pi$
$131$	−5.67608	+	2.06593i	−0.495922	+	0.180501i	0.0819370	+	0.996638i	$0.473889\pi$
$132$	4.13899	+	2.34303i	0.360253	+	0.203935i
$133$	11.8827	+	12.3035i	1.03036	+	1.06685i
$134$	27.0678			2.33831
$135$	−13.4857	+	16.9288i	−1.16066	+	1.45700i
$136$	0.550560	−	0.953598i	0.0472101	−	0.0817703i
$137$	−0.445164	−	2.52465i	−0.0380329	−	0.215695i	0.959868	−	0.280452i	$-0.0904842\pi$
$137$	−0.445164	−	2.52465i	−0.0380329	−	0.215695i	−0.997901	+	0.0647560i	$0.979373\pi$
$138$	14.8418	+	8.40176i	1.26341	+	0.715205i
$139$	−0.548284	+	3.10947i	−0.0465048	+	0.263742i	−0.999191	−	0.0402133i	$-0.987196\pi$
$139$	−0.548284	+	3.10947i	−0.0465048	+	0.263742i	0.952686	+	0.303955i	$0.0983074\pi$
$140$	−12.1838	−	1.27986i	−1.02972	−	0.108168i
$141$	10.1375	−	1.87637i	0.853733	−	0.158019i
$142$	19.0280	−	15.9664i	1.59679	−	1.33987i
$143$	−0.348771			−0.0291657
$144$	11.2971	−	9.81094i	0.941427	−	0.817578i
$145$	−0.548693			−0.0455665
$146$	−21.0970	−	7.67868i	−1.74600	−	0.635492i
$147$	5.78392	+	10.6558i	0.477050	+	0.878876i
$148$	0.660728	+	0.554417i	0.0543115	+	0.0455728i
$149$	−2.18925	+	12.4159i	−0.179351	+	1.01715i	0.753651	+	0.657275i	$0.228291\pi$
$149$	−2.18925	+	12.4159i	−0.179351	+	1.01715i	−0.933001	+	0.359873i	$0.882820\pi$
$150$	−24.0082	+	29.1100i	−1.96026	+	2.37682i
$151$	12.4271	−	10.4275i	1.01130	−	0.848581i	0.0227902	−	0.999740i	$-0.492745\pi$
$151$	12.4271	−	10.4275i	1.01130	−	0.848581i	0.988509	+	0.151159i	$0.0483006\pi$
$152$	−10.1309			−0.821725
$153$	1.02288	−	1.84324i	0.0826947	−	0.149017i
$154$	−0.804851	−	11.5003i	−0.0648567	−	0.926723i
$155$	3.35345	+	19.0184i	0.269356	+	1.52759i
$156$	0.0908097	−	0.256243i	0.00727059	−	0.0205159i
$157$	1.46311	−	8.29772i	0.116769	−	0.662230i	−0.869090	−	0.494654i	$-0.835295\pi$
$157$	1.46311	−	8.29772i	0.116769	−	0.662230i	0.985859	−	0.167576i	$-0.0535940\pi$
$158$	7.79423	+	6.54014i	0.620076	+	0.520306i
$159$	−5.55222	+	3.26872i	−0.440320	+	0.259226i
$160$	18.0725	−	15.1646i	1.42875	−	1.19887i
$161$	−1.03106	−	14.7326i	−0.0812590	−	1.16109i
$162$	11.8083	−	10.6117i	0.927744	−	0.833736i
$163$	4.06419	+	7.03938i	0.318332	+	0.551367i	0.980140	−	0.198306i	$-0.0635440\pi$
$163$	4.06419	+	7.03938i	0.318332	+	0.551367i	−0.661808	+	0.749673i	$0.730211\pi$
$164$	−0.635290	−	3.60291i	−0.0496078	−	0.281340i
$165$	−15.5087	−	8.77929i	−1.20735	−	0.683467i
$166$	3.98879	−	1.45180i	0.309590	−	0.112682i
$167$	−18.8324	+	6.85444i	−1.45730	+	0.530412i	−0.944619	−	0.328169i	$-0.893568\pi$
$167$	−18.8324	+	6.85444i	−1.45730	+	0.530412i	−0.512677	+	0.858582i	$0.671346\pi$
$168$	−6.91954	−	1.92031i	−0.533854	−	0.148155i
$169$	−2.25396	−	12.7829i	−0.173382	−	0.983298i
$170$	2.58149	−	4.47128i	0.197991	−	0.342931i
$171$	−19.3923	+	0.329200i	−1.48296	+	0.0251746i
$172$	−3.34891	−	5.80048i	−0.255352	−	0.442283i
$173$	−4.49223	−	25.4767i	−0.341538	−	1.93696i	−0.349365	−	0.936987i	$-0.613603\pi$
$173$	−4.49223	−	25.4767i	−0.341538	−	1.93696i	0.00782730	−	0.999969i	$-0.497508\pi$
$174$	0.396937	+	0.0665222i	0.0300917	+	0.00504303i
$175$	32.4962	+	3.41358i	2.45648	+	0.258043i
$176$	9.43771	+	7.91918i	0.711394	+	0.596931i
$177$	4.00001	−	4.85003i	0.300659	−	0.364551i
$178$	1.22181	−	1.02522i	0.0915786	−	0.0768436i
$179$	−9.77341	−	16.9280i	−0.730499	−	1.26526i	−0.956670	−	0.291174i	$-0.905954\pi$
$179$	−9.77341	−	16.9280i	−0.730499	−	1.26526i	0.226171	−	0.974088i	$-0.427379\pi$
$180$	10.4882	−	9.10842i	0.781743	−	0.678901i
$181$	1.41161	+	2.44499i	0.104924	+	0.181734i	0.913707	−	0.406373i	$-0.133207\pi$
$181$	1.41161	+	2.44499i	0.104924	+	0.181734i	−0.808783	+	0.588107i	$0.799873\pi$
$182$	−0.639376	+	0.159454i	−0.0473937	+	0.0118195i
$183$	0.371596	−	0.0687792i	0.0274692	−	0.00508430i
$184$	6.70076	+	5.62261i	0.493987	+	0.414504i
$185$	−2.47573	−	2.07739i	−0.182020	−	0.152733i
$186$	−0.120222	−	14.1649i	−0.00881509	−	1.03862i
$187$	1.63105	+	0.593655i	0.119275	+	0.0434124i
$188$	−6.61690			−0.482587
$189$	−13.3076	−	3.45095i	−0.967982	−	0.251020i
$190$	−47.5023			−3.44618
$191$	7.66448	+	2.78964i	0.554582	+	0.201851i	0.604081	−	0.796923i	$-0.293540\pi$
$191$	7.66448	+	2.78964i	0.554582	+	0.201851i	−0.0494989	+	0.998774i	$0.515762\pi$
$192$	−0.0237912	+	0.0140064i	−0.00171698	+	0.00101082i
$193$	2.27167	+	1.90616i	0.163519	+	0.137208i	0.720875	−	0.693065i	$-0.243740\pi$
$193$	2.27167	+	1.90616i	0.163519	+	0.137208i	−0.557357	+	0.830273i	$0.688184\pi$
$194$	2.48894	+	2.08847i	0.178695	+	0.149943i
$195$	−0.340261	+	0.960138i	−0.0243666	+	0.0687569i
$196$	−2.40549	−	7.40043i	−0.171821	−	0.528602i
$197$	−8.95897	−	15.5174i	−0.638300	−	1.10557i	−0.985806	−	0.167891i	$-0.946304\pi$
$197$	−8.95897	−	15.5174i	−0.638300	−	1.10557i	0.347505	−	0.937678i	$-0.387029\pi$
$198$	10.1549	+	8.23137i	0.721680	+	0.584978i
$199$	−5.88375	−	10.1910i	−0.417088	−	0.722417i	0.578557	−	0.815642i	$-0.303616\pi$
$199$	−5.88375	−	10.1910i	−0.417088	−	0.722417i	−0.995645	+	0.0932243i	$0.970283\pi$
$200$	−14.8251	+	12.4398i	−1.04830	+	0.879625i
$201$	26.2122	+	4.39288i	1.84887	+	0.309850i
$202$	−10.9916	−	9.22309i	−0.773370	−	0.648934i
$203$	−0.141775	−	0.318382i	−0.00995064	−	0.0223460i
$204$	−0.860839	+	1.04377i	−0.0602708	+	0.0730786i
$205$	2.38041	+	13.5000i	0.166255	+	0.942881i
$206$	5.64985	+	9.78583i	0.393644	+	0.681811i
$207$	13.0091	+	10.5449i	0.904194	+	0.732919i
$208$	0.352103	−	0.609860i	0.0244139	−	0.0422862i
$209$	−2.77311	−	15.7271i	−0.191820	−	1.08786i
$210$	−32.4447	−	9.00405i	−2.23889	−	0.621338i
$211$	4.57923	−	1.66670i	0.315247	−	0.114741i	−0.179550	−	0.983749i	$-0.557464\pi$
$211$	4.57923	−	1.66670i	0.315247	−	0.114741i	0.494798	+	0.869008i	$0.335242\pi$
$212$	3.88579	−	1.41431i	0.266877	−	0.0971353i
$213$	21.0177	−	12.3736i	1.44011	−	0.847825i
$214$	3.65510	+	20.7291i	0.249858	+	1.41701i
$215$	12.5483	+	21.7343i	0.855786	+	1.48226i
$216$	6.94572	−	4.24948i	0.472597	−	0.289141i
$217$	−10.1690	+	6.85994i	−0.690317	+	0.465683i
$218$	0.433042	−	0.363365i	0.0293293	−	0.0246102i
$219$	−19.1840	−	10.8598i	−1.29633	−	0.733839i
$220$	8.76191	+	7.35212i	0.590728	+	0.495680i
$221$	0.0172282	−	0.0977060i	0.00115889	−	0.00657241i
$222$	1.53914	+	1.80298i	0.103301	+	0.121008i
$223$	3.39420	+	19.2495i	0.227292	+	1.28904i	0.858254	+	0.513225i	$0.171549\pi$
$223$	3.39420	+	19.2495i	0.227292	+	1.28904i	−0.630962	+	0.775814i	$0.717339\pi$
$224$	13.4690	+	6.56830i	0.899935	+	0.438863i
$225$	−27.9736	+	24.2936i	−1.86491	+	1.61957i
$226$	−3.73246			−0.248280
$227$	−9.43162	+	7.91407i	−0.625999	+	0.525275i	−0.899683	−	0.436544i	$-0.856202\pi$
$227$	−9.43162	+	7.91407i	−0.625999	+	0.525275i	0.273684	+	0.961820i	$0.411758\pi$
$228$	12.2768	+	2.05745i	0.813049	+	0.136258i
$229$	−4.45188	+	25.2478i	−0.294188	+	1.66842i	0.376295	+	0.926500i	$0.377198\pi$
$229$	−4.45188	+	25.2478i	−0.294188	+	1.66842i	−0.670483	+	0.741925i	$0.733913\pi$
$230$	31.4189	+	26.3636i	2.07170	+	1.73836i
$231$	1.08700	−	11.2674i	0.0715190	−	0.741342i
$232$	0.193975	+	0.0706009i	0.0127351	+	0.00463518i
$233$	7.33354			0.480436			0.240218	−	0.970719i	$-0.422781\pi$
$233$	7.33354			0.480436			0.240218	+	0.970719i	$0.422781\pi$
$234$	0.362557	−	0.653333i	0.0237011	−	0.0427097i
$235$	24.7933			1.61734
$236$	−3.09091	+	2.59358i	−0.201201	+	0.168828i
$237$	6.48645	+	7.59834i	0.421340	+	0.493565i
$238$	3.26150	+	0.342606i	0.211412	+	0.0222079i
$239$	2.57748	−	14.6176i	0.166723	−	0.945536i	−0.780546	−	0.625098i	$-0.785059\pi$
$239$	2.57748	−	14.6176i	0.166723	−	0.945536i	0.947270	−	0.320438i	$-0.103830\pi$
$240$	31.0083	−	18.2553i	2.00158	−	1.17837i
$241$	−3.03867	−	17.2332i	−0.195738	−	1.11009i	−0.911364	−	0.411602i	$-0.864970\pi$
$241$	−3.03867	−	17.2332i	−0.195738	−	1.11009i	0.715626	−	0.698484i	$-0.246142\pi$
$242$	4.32024	−	7.48287i	0.277715	−	0.481017i
$243$	13.1572	−	8.35992i	0.844034	−	0.536289i
$244$	−0.242546			−0.0155274
$245$	9.01332	+	27.7292i	0.575840	+	1.77155i
$246$	−0.0853383	−	10.0548i	−0.00544097	−	0.641070i
$247$	−0.857767	+	0.312202i	−0.0545784	+	0.0198649i
$248$	1.26160	−	7.15488i	0.0801116	−	0.454335i
$249$	4.09832	−	0.758564i	0.259721	−	0.0480720i
$250$	−41.3700	+	34.7135i	−2.61647	+	2.19548i
$251$	−6.62373	−	11.4726i	−0.418086	−	0.724147i	0.577661	−	0.816277i	$-0.303966\pi$
$251$	−6.62373	−	11.4726i	−0.418086	−	0.724147i	−0.995747	+	0.0921303i	$0.970632\pi$
$252$	7.99520	+	3.73232i	0.503650	+	0.235114i
$253$	−6.89427	+	11.9412i	−0.433439	+	0.750738i
$254$	3.19406	+	18.1144i	0.200413	+	1.13660i
$255$	3.22554	−	3.91099i	0.201991	−	0.244915i
$256$	−18.7603	+	6.82819i	−1.17252	+	0.426762i
$257$	−3.76921	+	21.3762i	−0.235117	+	1.33341i	0.607251	+	0.794510i	$0.292272\pi$
$257$	−3.76921	+	21.3762i	−0.235117	+	1.33341i	−0.842368	+	0.538903i	$0.818839\pi$
$258$	−6.44270	−	17.2444i	−0.401105	−	1.07359i
$259$	0.565718	−	1.97332i	0.0351520	−	0.122616i
$260$	0.326890	−	0.566191i	0.0202729	−	0.0351136i
$261$	0.373594	+	0.128839i	0.0231249	+	0.00797493i
$262$	10.6551			0.658276
$263$	−10.1892	−	3.70856i	−0.628292	−	0.228679i	0.00819596	−	0.999966i	$-0.497391\pi$
$263$	−10.1892	−	3.70856i	−0.628292	−	0.228679i	−0.636488	+	0.771287i	$0.719613\pi$
$264$	4.35300	+	5.09918i	0.267909	+	0.313833i
$265$	−14.5599	+	5.29939i	−0.894410	+	0.325539i
$266$	−12.2739	−	27.5634i	−0.752564	−	1.69002i
$267$	1.34957	−	0.794525i	0.0825926	−	0.0486241i
$268$	−16.0292	−	5.83416i	−0.979141	−	0.356378i
$269$	−6.69178	+	11.5905i	−0.408005	+	0.706686i	−0.994666	−	0.103147i	$-0.967109\pi$
$269$	−6.69178	+	11.5905i	−0.408005	+	0.706686i	0.586661	+	0.809833i	$0.300442\pi$
$270$	32.5675	−	19.9252i	1.98199	−	1.21261i
$271$	10.7152	+	18.5593i	0.650904	+	1.12740i	0.982904	+	0.184120i	$0.0589433\pi$
$271$	10.7152	+	18.5593i	0.650904	+	1.12740i	−0.332000	+	0.943279i	$0.607723\pi$
$272$	−2.68470	+	2.25273i	−0.162784	+	0.136592i
$273$	−0.645043	+	0.0506481i	−0.0390398	+	0.00306536i
$274$	−0.785264	+	4.45345i	−0.0474395	+	0.269043i
$275$	−23.3694	−	19.6092i	−1.40923	−	1.18248i
$276$	−6.97820	−	8.17439i	−0.420038	−	0.492040i
$277$	−5.14046	−	1.87098i	−0.308861	−	0.112416i	0.182940	−	0.983124i	$-0.441439\pi$
$277$	−5.14046	−	1.87098i	−0.308861	−	0.112416i	−0.491800	+	0.870708i	$0.663661\pi$
$278$	2.78484	−	4.82349i	0.167024	−	0.289294i
$279$	2.18242	−	13.7366i	0.130658	−	0.822391i
$280$	−15.5221	−	7.56951i	−0.927621	−	0.452365i
$281$	13.4765	+	4.90506i	0.803942	+	0.292611i	0.711119	−	0.703072i	$-0.248189\pi$
$281$	13.4765	+	4.90506i	0.803942	+	0.292611i	0.0928232	+	0.995683i	$0.470411\pi$
$282$	−17.9361	−	3.00588i	−1.06808	−	0.178998i
$283$	7.48499	−	2.72431i	0.444936	−	0.161944i	−0.109829	−	0.993951i	$-0.535030\pi$
$283$	7.48499	−	2.72431i	0.444936	−	0.161944i	0.554765	+	0.832007i	$0.312808\pi$
$284$	−14.7095	+	5.35382i	−0.872848	+	0.317691i
$285$	−46.0008	−	7.70922i	−2.72485	−	0.456655i
$286$	0.578125	+	0.210420i	0.0341853	+	0.0124424i
$287$	−7.21837	+	4.86946i	−0.426087	+	0.287435i
$288$	−15.8660	+	6.08166i	−0.934911	+	0.358365i
$289$	8.25312	−	14.2948i	0.485478	−	0.840872i
$290$	0.909517	+	0.331037i	0.0534087	+	0.0194392i
$291$	2.07132	+	2.42638i	0.121423	+	0.142237i
$292$	10.8383	+	9.09444i	0.634265	+	0.532212i
$293$	3.09426	−	17.5484i	0.180768	−	1.02519i	−0.750504	−	0.660866i	$-0.770189\pi$
$293$	3.09426	−	17.5484i	0.180768	−	1.02519i	0.931273	−	0.364323i	$-0.118700\pi$
$294$	−3.15861	−	21.1527i	−0.184214	−	1.23365i
$295$	11.5816	−	9.71809i	0.674305	−	0.565809i
$296$	0.607924	+	1.05295i	0.0353348	+	0.0612018i
$297$	8.49807	+	9.61924i	0.493108	+	0.558165i
$298$	11.1197	−	19.2598i	0.644144	−	1.11569i
$299$	0.740613	+	0.269561i	0.0428307	+	0.0155891i
$300$	20.4917	−	12.0639i	1.18309	−	0.696510i
$301$	−9.36910	+	12.8970i	−0.540026	+	0.743373i
$302$	−26.8903	+	9.78727i	−1.54736	+	0.563194i
$303$	−9.14738	−	10.7154i	−0.525503	−	0.615584i
$304$	30.2999	+	11.0283i	1.73782	+	0.632515i
$305$	0.908813			0.0520385
$306$	−2.80759	+	2.43824i	−0.160499	+	0.139385i
$307$	−0.753447	+	1.30501i	−0.0430015	+	0.0744808i	−0.886725	−	0.462297i	$-0.847025\pi$
$307$	−0.753447	+	1.30501i	−0.0430015	+	0.0744808i	0.843724	+	0.536778i	$0.180359\pi$
$308$	−2.00214	+	6.98383i	−0.114083	+	0.397940i
$309$	3.88310	+	10.3934i	0.220902	+	0.591261i
$310$	5.91544	−	33.5481i	0.335975	−	1.90541i
$311$	5.51008	−	2.00550i	0.312448	−	0.113722i	−0.181037	−	0.983476i	$-0.557945\pi$
$311$	5.51008	−	2.00550i	0.312448	−	0.113722i	0.493484	+	0.869755i	$0.335723\pi$
$312$	0.243832	−	0.295647i	0.0138042	−	0.0167377i
$313$	−0.324077	−	1.83793i	−0.0183179	−	0.103886i	0.974278	−	0.225350i	$-0.0723524\pi$
$313$	−0.324077	−	1.83793i	−0.0183179	−	0.103886i	−0.992596	+	0.121463i	$0.961241\pi$
$314$	−7.43144	+	12.8716i	−0.419380	+	0.726388i
$315$	−29.9578	−	13.9849i	−1.68793	−	0.787961i
$316$	−3.20599	−	5.55294i	−0.180351	−	0.312378i
$317$	−7.59236	+	6.37075i	−0.426429	+	0.357817i	−0.830603	−	0.556866i	$-0.812004\pi$
$317$	−7.59236	+	6.37075i	−0.426429	+	0.357817i	0.404173	+	0.914683i	$0.367559\pi$
$318$	11.1755	−	2.06848i	0.626690	−	0.115995i
$319$	−0.0565037	+	0.320449i	−0.00316360	+	0.0179417i
$320$	−0.0623891	+	0.0227078i	−0.00348766	+	0.00126940i
$321$	0.175408	+	20.6671i	0.00979031	+	1.15352i
$322$	−7.17937	+	25.0429i	−0.400091	+	1.39559i
$323$	4.54282			0.252769
$324$	−9.27994	+	3.73900i	−0.515552	+	0.207722i
$325$	−0.871867	+	1.51012i	−0.0483625	+	0.0837662i
$326$	−2.48983	−	14.1205i	−0.137899	−	0.782064i
$327$	0.478324	−	0.281600i	0.0264514	−	0.0155725i
$328$	0.895534	−	5.07882i	0.0494476	−	0.280431i
$329$	6.40626	+	14.3864i	0.353188	+	0.793151i
$330$	20.4106	+	23.9093i	1.12356	+	1.31616i
$331$	7.43935	−	6.24236i	0.408904	−	0.343111i	−0.415019	−	0.909813i	$-0.636225\pi$
$331$	7.43935	−	6.24236i	0.408904	−	0.343111i	0.823923	+	0.566702i	$0.191781\pi$
$332$	−2.67503			−0.146811
$333$	1.19788	+	1.99578i	0.0656436	+	0.109368i
$334$	35.3521			1.93438
$335$	60.0611	+	21.8605i	3.28149	+	1.19436i
$336$	18.6048	+	13.2758i	1.01498	+	0.724253i
$337$	−16.7483	−	14.0535i	−0.912339	−	0.765543i	0.0602239	−	0.998185i	$-0.480819\pi$
$337$	−16.7483	−	14.0535i	−0.912339	−	0.765543i	−0.972562	+	0.232642i	$0.925263\pi$
$338$	−3.97597	+	22.5488i	−0.216264	+	1.22649i
$339$	−3.61448	−	0.605747i	−0.196312	−	0.0328996i
$340$	−2.49246	+	2.09142i	−0.135173	+	0.113423i
$341$	11.4525			0.620186
$342$	32.3433	+	11.1540i	1.74893	+	0.603141i
$343$	−13.7611	+	12.3949i	−0.743029	+	0.669260i
$344$	−1.63951	−	9.29812i	−0.0883964	−	0.501321i
$345$	26.1471	+	30.6292i	1.40771	+	1.64902i
$346$	−7.92423	+	44.9405i	−0.426009	+	2.41602i
$347$	7.62044	+	6.39431i	0.409087	+	0.343265i	0.823993	−	0.566599i	$-0.191741\pi$
$347$	7.62044	+	6.39431i	0.409087	+	0.343265i	−0.414907	+	0.909864i	$0.636186\pi$
$348$	−0.220723	−	0.124949i	−0.0118320	−	0.00669796i
$349$	−19.2188	+	16.1265i	−1.02876	+	0.863233i	−0.990703	−	0.136043i	$-0.956562\pi$
$349$	−19.2188	+	16.1265i	−1.02876	+	0.863233i	−0.0380577	+	0.999276i	$0.512117\pi$
$350$	−51.8064	−	25.2639i	−2.76917	−	1.35041i
$351$	0.457127	−	0.573841i	0.0243997	−	0.0306294i
$352$	−6.99537	−	12.1163i	−0.372854	−	0.645803i
$353$	−1.71986	−	9.75380i	−0.0915388	−	0.519142i	−0.995753	−	0.0920634i	$-0.970654\pi$
$353$	−1.71986	−	9.75380i	−0.0915388	−	0.519142i	0.904214	−	0.427079i	$-0.140457\pi$
$354$	−9.55656	+	5.62616i	−0.507925	+	0.299027i
$355$	55.1161	−	20.0606i	2.92526	−	1.06471i
$356$	−0.944515	+	0.343775i	−0.0500592	+	0.0182201i
$357$	3.10280	+	0.861090i	0.164218	+	0.0455737i
$358$	5.98745	+	33.9565i	0.316447	+	1.79466i
$359$	8.26238	−	14.3109i	0.436072	−	0.755298i	−0.561311	−	0.827605i	$-0.689703\pi$
$359$	8.26238	−	14.3109i	0.436072	−	0.755298i	0.997382	+	0.0723067i	$0.0230360\pi$
$360$	18.2844	−	7.00868i	0.963673	−	0.369390i
$361$	−11.3982	−	19.7423i	−0.599907	−	1.03907i
$362$	−0.864792	−	4.90448i	−0.0454525	−	0.257774i
$363$	5.39808	−	6.54520i	0.283326	−	0.343534i
$364$	0.412999	+	0.0433837i	0.0216470	+	0.00227392i
$365$	−40.6109	−	34.0766i	−2.12567	−	1.78365i
$366$	−0.657455	−	0.110182i	−0.0343657	−	0.00575932i
$367$	−24.3072	+	20.3962i	−1.26883	+	1.06467i	−0.274142	+	0.961689i	$0.588394\pi$
$367$	−24.3072	+	20.3962i	−1.26883	+	1.06467i	−0.994683	+	0.102982i	$0.967162\pi$
$368$	−13.9203	−	24.1106i	−0.725644	−	1.25685i
$369$	1.54917	−	9.75082i	0.0806464	−	0.507607i
$370$	2.85046	+	4.93715i	0.148188	+	0.256670i
$371$	−6.83708	−	7.07919i	−0.354964	−	0.367533i
$372$	−2.98188	+	8.41417i	−0.154603	+	0.436254i
$373$	−18.3549	−	15.4016i	−0.950381	−	0.797465i	0.0289804	−	0.999580i	$-0.490774\pi$
$373$	−18.3549	−	15.4016i	−0.950381	−	0.797465i	−0.979362	+	0.202115i	$0.935218\pi$
$374$	−2.34548	−	1.96809i	−0.121282	−	0.101768i
$375$	−45.6960	+	26.9023i	−2.35973	+	1.38923i
$376$	−8.76496	−	3.19019i	−0.452019	−	0.164521i
$377$	0.0185992			0.000957907
$378$	19.9767	+	13.7490i	1.02749	+	0.707173i
$379$	18.5458			0.952632			0.476316	−	0.879274i	$-0.341972\pi$
$379$	18.5458			0.952632			0.476316	+	0.879274i	$0.341972\pi$
$380$	28.1303	+	10.2386i	1.44305	+	0.525228i
$381$	0.153283	+	18.0602i	0.00785290	+	0.925251i
$382$	−11.0216	−	9.24826i	−0.563916	−	0.473182i
$383$	−17.3412	−	14.5510i	−0.886096	−	0.743523i	0.0813271	−	0.996687i	$-0.474084\pi$
$383$	−17.3412	−	14.5510i	−0.886096	−	0.743523i	−0.967423	+	0.253164i	$0.918529\pi$
$384$	−19.2447	+	3.56202i	−0.982075	+	0.181774i
$385$	7.50198	−	26.1682i	0.382336	−	1.33366i
$386$	−2.61552	−	4.53021i	−0.133126	−	0.230581i
$387$	−3.44043	−	17.7449i	−0.174887	−	0.902023i
$388$	−1.02377	−	1.77322i	−0.0519741	−	0.0900218i
$389$	7.05404	−	5.91904i	0.357654	−	0.300107i	−0.446201	−	0.894933i	$-0.647223\pi$
$389$	7.05404	−	5.91904i	0.357654	−	0.300107i	0.803855	+	0.594826i	$0.202779\pi$
$390$	1.14329	−	1.38624i	0.0578927	−	0.0701952i
$391$	−3.00470	−	2.52124i	−0.151954	−	0.127505i
$392$	0.381551	−	10.9626i	0.0192713	−	0.553695i
$393$	10.3183	+	1.72924i	0.520490	+	0.0872284i
$394$	5.48850	+	31.1268i	0.276507	+	1.56815i
$395$	12.0128	+	20.8067i	0.604429	+	1.04690i
$396$	−4.23945	−	7.06329i	−0.213040	−	0.354944i
$397$	8.17669	−	14.1624i	0.410376	−	0.710793i	−0.584554	−	0.811355i	$-0.698731\pi$
$397$	8.17669	−	14.1624i	0.410376	−	0.710793i	0.994931	+	0.100562i	$0.0320640\pi$
$398$	3.60454	+	20.4424i	0.180679	+	1.02468i
$399$	−7.41266	−	28.6841i	−0.371097	−	1.43600i
$400$	57.8813	−	21.0671i	2.89406	−	1.05335i
$401$	−34.4552	+	12.5407i	−1.72061	+	0.626251i	−0.997892	−	0.0648916i	$-0.979330\pi$
$401$	−34.4552	+	12.5407i	−1.72061	+	0.626251i	−0.722718	+	0.691143i	$0.757108\pi$
$402$	−40.7992	−	23.0960i	−2.03488	−	1.15192i
$403$	−0.113673	−	0.644670i	−0.00566244	−	0.0321133i
$404$	4.52118	+	7.83092i	0.224937	+	0.389603i
$405$	34.7717	−	14.0099i	1.72782	−	0.696159i
$406$	0.0429209	+	0.613287i	0.00213013	+	0.0304369i
$407$	−1.46819	+	1.23195i	−0.0727753	+	0.0610657i
$408$	−1.64353	+	0.967581i	−0.0813667	+	0.0479024i
$409$	1.23796	+	1.03877i	0.0612132	+	0.0513640i	0.672881	−	0.739751i	$-0.265057\pi$
$409$	1.23796	+	1.03877i	0.0612132	+	0.0513640i	−0.611668	+	0.791115i	$0.709501\pi$
$410$	4.19902	−	23.8138i	0.207375	−	1.17608i
$411$	−1.48320	+	4.18524i	−0.0731608	+	0.206443i
$412$	−1.23655	−	7.01280i	−0.0609203	−	0.345496i
$413$	8.63148	+	4.20923i	0.424727	+	0.207123i
$414$	−15.2020	−	25.3279i	−0.747138	−	1.24480i
$415$	10.0233			0.492023
$416$	−0.612606	+	0.514038i	−0.0300355	+	0.0252028i
$417$	3.47963	−	4.21906i	0.170398	−	0.206608i
$418$	−4.89173	+	27.7424i	−0.239262	+	1.35692i
$419$	11.2741	+	9.46013i	0.550778	+	0.462158i	0.875204	−	0.483753i	$-0.160727\pi$
$419$	11.2741	+	9.46013i	0.550778	+	0.462158i	−0.324426	+	0.945911i	$0.605171\pi$
$420$	17.2726	+	12.3252i	0.842816	+	0.601406i
$421$	12.7240	+	4.63116i	0.620130	+	0.225709i	0.632930	−	0.774209i	$-0.281852\pi$
$421$	12.7240	+	4.63116i	0.620130	+	0.225709i	−0.0127998	+	0.999918i	$0.504074\pi$
$422$	−8.59612			−0.418452
$423$	−16.8813	−	5.82174i	−0.820796	−	0.283062i
$424$	5.82912			0.283087
$425$	6.64777	−	5.57814i	0.322464	−	0.270580i
$426$	−42.3043	+	7.83016i	−2.04965	+	0.379373i
$427$	0.234825	+	0.527343i	0.0113640	+	0.0255199i
$428$	2.30342	−	13.0633i	0.111340	−	0.631440i
$429$	0.525701	+	0.297594i	0.0253811	+	0.0143680i
$430$	−7.68741	−	43.5975i	−0.370720	−	2.10246i
$431$	−10.9091	+	18.8951i	−0.525472	+	0.910145i	0.474088	+	0.880478i	$0.342778\pi$
$431$	−10.9091	+	18.8951i	−0.525472	+	0.910145i	−0.999560	+	0.0296670i	$0.990555\pi$
$432$	−25.3994	+	5.14857i	−1.22203	+	0.247711i
$433$	10.1358			0.487096			0.243548	−	0.969889i	$-0.421689\pi$
$433$	10.1358			0.487096			0.243548	+	0.969889i	$0.421689\pi$
$434$	20.9949	−	5.23592i	1.00779	−	0.251332i
$435$	0.827043	+	0.468180i	0.0396537	+	0.0224475i
$436$	−0.334761	+	0.121843i	−0.0160321	+	0.00583522i
$437$	−6.26659	+	35.5396i	−0.299772	+	1.70009i
$438$	25.2475	+	29.5754i	1.20637	+	1.41317i
$439$	2.18007	−	1.82930i	0.104049	−	0.0873077i	−0.589279	−	0.807930i	$-0.700588\pi$
$439$	2.18007	−	1.82930i	0.104049	−	0.0873077i	0.693328	+	0.720622i	$0.256144\pi$
$440$	8.06167	+	13.9632i	0.384325	+	0.665671i
$441$	0.374127	−	20.9967i	0.0178156	−	0.999841i
$442$	−0.0875055	+	0.151564i	−0.00416221	+	0.00720916i
$443$	−1.10720	−	6.27927i	−0.0526049	−	0.298337i	0.947142	−	0.320813i	$-0.103956\pi$
$443$	−1.10720	−	6.27927i	−0.0526049	−	0.298337i	−0.999747	+	0.0224760i	$0.992845\pi$
$444$	−0.522849	−	1.39945i	−0.0248133	−	0.0664148i
$445$	3.53908	−	1.28812i	0.167768	−	0.0610627i
$446$	5.98733	−	33.9558i	0.283508	−	1.60785i
$447$	13.8939	−	16.8464i	0.657157	−	0.796807i
$448$	−0.0292968	−	0.0303342i	−0.00138414	−	0.00143316i
$449$	−2.33757	+	4.04880i	−0.110317	+	0.191074i	−0.915898	−	0.401411i	$-0.868520\pi$
$449$	−2.33757	+	4.04880i	−0.110317	+	0.191074i	0.805581	+	0.592485i	$0.201853\pi$
$450$	61.0260	−	23.3921i	2.87679	−	1.10272i
$451$	8.12942			0.382799
$452$	2.21032	+	0.804489i	0.103965	+	0.0378400i
$453$	−27.6287	+	5.11383i	−1.29811	+	0.240269i
$454$	20.4086	−	7.42813i	0.957824	−	0.348620i
$455$	−1.54750	−	0.162558i	−0.0725477	−	0.00762082i
$456$	15.2703	+	8.64434i	0.715096	+	0.404808i
$457$	−18.0410	−	6.56637i	−0.843921	−	0.307162i	−0.116361	−	0.993207i	$-0.537123\pi$
$457$	−18.0410	−	6.56637i	−0.843921	−	0.307162i	−0.727559	+	0.686045i	$0.759345\pi$
$458$	22.6120	−	39.1651i	1.05659	−	1.83006i
$459$	−3.11455	+	1.90552i	−0.145375	+	0.0889420i
$460$	−12.9235	−	22.3841i	−0.602561	−	1.04367i
$461$	−1.41824	+	1.19004i	−0.0660540	+	0.0554259i	−0.675217	−	0.737619i	$-0.735950\pi$
$461$	−1.41824	+	1.19004i	−0.0660540	+	0.0554259i	0.609163	+	0.793045i	$0.291506\pi$
$462$	−8.59967	+	18.0212i	−0.400093	+	0.838420i
$463$	−2.62612	+	14.8935i	−0.122046	+	0.692158i	0.860972	+	0.508652i	$0.169856\pi$
$463$	−2.62612	+	14.8935i	−0.122046	+	0.692158i	−0.983019	+	0.183506i	$0.941255\pi$
$464$	−0.503292	−	0.422312i	−0.0233647	−	0.0196053i
$465$	11.1730	−	31.5277i	0.518137	−	1.46206i
$466$	−12.1561	−	4.42447i	−0.563122	−	0.204960i
$467$	12.3675	−	21.4212i	0.572300	−	0.991253i	−0.424029	−	0.905649i	$-0.639385\pi$
$467$	12.3675	−	21.4212i	0.572300	−	0.991253i	0.996329	−	0.0856044i	$-0.0272821\pi$
$468$	−0.355520	+	0.308750i	−0.0164339	+	0.0142720i
$469$	2.83434	+	40.4992i	0.130877	+	1.87008i
$470$	−41.0976	−	14.9583i	−1.89569	−	0.689975i
$471$	−9.28549	+	11.2587i	−0.427853	+	0.518773i
$472$	−5.34476	+	1.94533i	−0.246013	+	0.0895413i
$473$	13.9855	−	5.09030i	0.643053	−	0.234052i
$474$	−6.16775	−	16.5085i	−0.283294	−	0.758259i
$475$	−75.0277	−	27.3079i	−3.44251	−	1.25297i
$476$	−1.85757	−	0.905866i	−0.0851418	−	0.0415203i
$477$	11.1579	−	0.189415i	0.510886	−	0.00867273i
$478$	−13.0915	+	22.6752i	−0.598793	+	1.03714i
$479$	−29.7795	−	10.8389i	−1.36066	−	0.495240i	−0.444403	−	0.895827i	$-0.646584\pi$
$479$	−29.7795	−	10.8389i	−1.36066	−	0.495240i	−0.916259	+	0.400586i	$0.868806\pi$
$480$	−40.1799	+	7.43696i	−1.83396	+	0.339449i
$481$	0.0839205	+	0.0704177i	0.00382645	+	0.00321077i
$482$	−5.36018	+	30.3991i	−0.244149	+	1.38464i
$483$	−11.0167	+	23.0862i	−0.501276	+	1.05046i
$484$	−4.17124	+	3.50008i	−0.189602	+	0.159095i
$485$	3.83605	+	6.64423i	0.174186	+	0.301699i
$486$	−26.8531	+	5.91947i	−1.21808	+	0.268512i
$487$	15.0234	−	26.0213i	0.680775	−	1.17914i	−0.293969	−	0.955815i	$-0.594976\pi$
$487$	15.0234	−	26.0213i	0.680775	−	1.17914i	0.974745	−	0.223323i	$-0.0716904\pi$
$488$	−0.321284	−	0.116938i	−0.0145439	−	0.00529353i
$489$	−0.119487	−	14.0783i	−0.00540337	−	0.636641i
$490$	1.78904	−	51.4020i	0.0808204	−	2.32211i
$491$	29.0255	−	10.5644i	1.30990	−	0.476766i	0.409695	−	0.912223i	$-0.365635\pi$
$491$	29.0255	−	10.5644i	1.30990	−	0.476766i	0.900210	+	0.435456i	$0.143413\pi$
$492$	−2.11666	+	5.97272i	−0.0954264	+	0.269271i
$493$	−0.0869805	−	0.0316583i	−0.00391740	−	0.00142582i
$494$	1.61020			0.0724462
$495$	15.8851	+	26.4660i	0.713983	+	1.18956i
$496$	−11.5619	+	20.0257i	−0.519143	+	0.899182i
$497$	25.8815	+	26.7980i	1.16094	+	1.20205i
$498$	−7.25106	−	1.21520i	−0.324928	−	0.0544543i
$499$	2.68427	−	15.2233i	0.120164	−	0.681486i	−0.863899	−	0.503666i	$-0.831984\pi$
$499$	2.68427	−	15.2233i	0.120164	−	0.681486i	0.984063	−	0.177820i	$-0.0569046\pi$
$500$	31.9809	−	11.6401i	1.43023	−	0.520561i
$501$	34.2347	+	5.73735i	1.52949	+	0.256326i
$502$	4.05787	+	23.0133i	0.181112	+	1.02714i
$503$	−12.4023	+	21.4813i	−0.552989	+	0.957806i	0.445067	+	0.895497i	$0.353180\pi$
$503$	−12.4023	+	21.4813i	−0.552989	+	0.957806i	−0.998057	+	0.0623088i	$0.980154\pi$
$504$	8.79126	+	8.79867i	0.391594	+	0.391924i
$505$	−16.9408	−	29.3423i	−0.753854	−	1.30571i
$506$	18.6324	−	15.6344i	0.828309	−	0.695034i
$507$	−7.50977	+	21.1908i	−0.333520	+	0.941116i
$508$	2.01287	−	11.4156i	0.0893067	−	0.506484i
$509$	−1.28303	+	0.466983i	−0.0568691	+	0.0206987i	−0.370298	−	0.928913i	$-0.620744\pi$
$509$	−1.28303	+	0.466983i	−0.0568691	+	0.0206987i	0.313429	+	0.949612i	$0.398522\pi$
$510$	−7.70625	+	4.53684i	−0.341239	+	0.200895i
$511$	9.27981	−	32.3696i	0.410515	−	1.43195i
$512$	12.6175			0.557620
$513$	29.5108	+	16.0505i	1.30293	+	0.708647i
$514$	19.1446	−	33.1594i	0.844430	−	1.46260i
$515$	4.63331	+	26.2768i	0.204168	+	1.15789i
$516$	0.0984576	+	11.6005i	0.00433435	+	0.510686i
$517$	2.55319	−	14.4798i	0.112289	−	0.636823i
$518$	−2.12828	+	2.92968i	−0.0935113	+	0.128723i
$519$	−14.9672	+	42.2339i	−0.656988	+	1.85386i
$520$	0.705986	−	0.592392i	0.0309595	−	0.0259781i
$521$	−26.5548			−1.16339			−0.581693	−	0.813408i	$-0.697610\pi$
$521$	−26.5548			−1.16339			−0.581693	+	0.813408i	$0.697610\pi$
$522$	−0.541540	−	0.438960i	−0.0237026	−	0.0192128i
$523$	−34.0011			−1.48676			−0.743381	−	0.668868i	$-0.766779\pi$
$523$	−34.0011			−1.48676			−0.743381	+	0.668868i	$0.766779\pi$
$524$	−6.30983	−	2.29659i	−0.275646	−	0.100327i
$525$	−46.0687	−	32.8731i	−2.01060	−	1.43470i
$526$	14.6522	+	12.2947i	0.638866	+	0.536072i
$527$	−0.565716	+	3.20833i	−0.0246430	+	0.139757i
$528$	−7.46827	−	19.9894i	−0.325015	−	0.869927i
$529$	6.25013	−	5.24448i	0.271745	−	0.228021i
$530$	27.3319			1.18722
$531$	−10.1676	+	3.89737i	−0.441234	+	0.169131i
$532$	1.32749	+	18.9682i	0.0575540	+	0.822377i
$533$	−0.0806895	−	0.457613i	−0.00349505	−	0.0198214i
$534$	−2.71641	+	0.502785i	−0.117551	+	0.0217576i
$535$	−8.63085	+	48.9480i	−0.373144	+	2.11620i
$536$	−18.4201	−	15.4563i	−0.795625	−	0.667609i
$537$	0.287337	+	33.8549i	0.0123995	+	1.46095i
$538$	18.0851	−	15.1752i	0.779705	−	0.654250i
$539$	17.1226	−	2.40845i	0.737524	−	0.103739i
$540$	−23.5807	+	4.77990i	−1.01475	+	0.205694i
$541$	−1.17215	−	2.03023i	−0.0503948	−	0.0872863i	0.839728	−	0.543008i	$-0.182715\pi$
$541$	−1.17215	−	2.03023i	−0.0503948	−	0.0872863i	−0.890122	+	0.455722i	$0.849381\pi$
$542$	−6.56444	−	37.2288i	−0.281967	−	1.59911i
$543$	−0.0415013	−	4.88980i	−0.00178099	−	0.209841i
$544$	3.73986	−	1.36120i	0.160345	−	0.0583609i
$545$	1.25434	−	0.456543i	0.0537300	−	0.0195561i
$546$	1.09978	+	0.305212i	0.0470664	+	0.0130619i
$547$	3.75899	+	21.3183i	0.160723	+	0.911504i	0.953366	+	0.301818i	$0.0975934\pi$
$547$	3.75899	+	21.3183i	0.160723	+	0.911504i	−0.792643	+	0.609686i	$0.791296\pi$
$548$	1.42491	−	2.46802i	0.0608693	−	0.105429i
$549$	−0.618792	−	0.213399i	−0.0264094	−	0.00910764i
$550$	26.9066	+	46.6036i	1.14730	+	1.98718i
$551$	0.147884	+	0.838690i	0.00630005	+	0.0357294i
$552$	−5.30247	−	14.1925i	−0.225688	−	0.604071i
$553$	−8.96927	+	12.3466i	−0.381412	+	0.525033i
$554$	7.39207	+	6.20268i	0.314059	+	0.263527i
$555$	1.95910	+	5.24369i	0.0831593	+	0.222582i
$556$	−2.68880	+	2.25617i	−0.114030	+	0.0956828i
$557$	4.57436	+	7.92303i	0.193822	+	0.335709i	0.946514	−	0.322664i	$-0.104578\pi$
$557$	4.57436	+	7.92303i	0.193822	+	0.335709i	−0.752692	+	0.658373i	$0.771245\pi$
$558$	−11.9052	+	21.4532i	−0.503986	+	0.908188i
$559$	−0.425352	−	0.736731i	−0.0179905	−	0.0311604i
$560$	38.1840	+	39.5361i	1.61357	+	1.67071i
$561$	−1.95194	−	2.28653i	−0.0824109	−	0.0965375i
$562$	−19.3795	−	16.2613i	−0.817473	−	0.685941i
$563$	25.9935	+	21.8111i	1.09549	+	0.919229i	0.997114	−	0.0759200i	$-0.0241894\pi$
$563$	25.9935	+	21.8111i	1.09549	+	0.919229i	0.0983804	+	0.995149i	$0.468634\pi$
$564$	9.97362	+	5.64596i	0.419965	+	0.237738i
$565$	−8.28200	−	3.01440i	−0.348426	−	0.126817i
$566$	−14.0508			−0.590599
$567$	17.1139	+	16.5565i	0.718714	+	0.695306i
$568$	−22.0659			−0.925866
$569$	−17.5317	−	6.38100i	−0.734965	−	0.267506i	−0.0527002	−	0.998610i	$-0.516783\pi$
$569$	−17.5317	−	6.38100i	−0.734965	−	0.267506i	−0.682265	+	0.731105i	$0.739005\pi$
$570$	71.6000	+	40.5320i	2.99900	+	1.69770i
$571$	3.01139	+	2.52686i	0.126023	+	0.105746i	0.703621	−	0.710576i	$-0.251565\pi$
$571$	3.01139	+	2.52686i	0.126023	+	0.105746i	−0.577598	+	0.816321i	$0.696010\pi$
$572$	−0.297005	−	0.249216i	−0.0124184	−	0.0104203i
$573$	−9.17234	−	10.7446i	−0.383180	−	0.448864i
$574$	14.9031	−	3.71666i	0.622041	−	0.155131i
$575$	34.4689	+	59.7019i	1.43745	+	2.48974i
$576$	0.0478115		0.000811641i	0.00199214		3.38184e-5i
$577$	−3.97502	−	6.88494i	−0.165482	−	0.286624i	0.771344	−	0.636418i	$-0.219585\pi$
$577$	−3.97502	−	6.88494i	−0.165482	−	0.286624i	−0.936826	+	0.349794i	$0.886251\pi$
$578$	−22.3048	+	18.7159i	−0.927756	+	0.778480i
$579$	−1.79763	−	4.81148i	−0.0747068	−	0.199958i
$580$	−0.467253	−	0.392072i	−0.0194016	−	0.0162799i
$581$	2.58987	+	5.81605i	0.107446	+	0.241290i
$582$	−1.96955	−	5.27166i	−0.0816406	−	0.218517i
$583$	1.59559	+	9.04904i	0.0660826	+	0.374773i
$584$	9.97214	+	17.2723i	0.412650	+	0.714731i
$585$	1.33213	−	1.15688i	0.0550766	−	0.0478311i
$586$	−15.7164	+	27.2215i	−0.649236	+	1.12451i
$587$	−3.92585	−	22.2646i	−0.162037	−	0.918958i	−0.952067	−	0.305890i	$-0.901046\pi$
$587$	−3.92585	−	22.2646i	−0.162037	−	0.918958i	0.790030	−	0.613068i	$-0.210065\pi$
$588$	−2.68873	+	13.2072i	−0.110881	+	0.544654i
$589$	28.1662	−	10.2516i	1.16057	−	0.422412i
$590$	−25.0608	+	9.12138i	−1.03174	+	0.375521i
$591$	0.263393	+	31.0337i	0.0108345	+	1.27655i
$592$	−0.671980	−	3.81099i	−0.0276182	−	0.156631i
$593$	−11.6835	−	20.2365i	−0.479785	−	0.831011i	0.519946	−	0.854199i	$-0.325952\pi$
$593$	−11.6835	−	20.2365i	−0.479785	−	0.831011i	−0.999731	+	0.0231874i	$0.992619\pi$
$594$	−8.28298	−	21.0720i	−0.339855	−	0.864593i
$595$	6.96028	+	3.39426i	0.285344	+	0.139151i
$596$	−10.7361	+	9.00870i	−0.439770	+	0.369011i
$597$	0.172982	+	20.3812i	0.00707966	+	0.834146i
$598$	−1.06501	−	0.893652i	−0.0435516	−	0.0365441i
$599$	−5.69406	+	32.2926i	−0.232653	+	1.31944i	0.614847	+	0.788646i	$0.289218\pi$
$599$	−5.69406	+	32.2926i	−0.232653	+	1.31944i	−0.847500	+	0.530795i	$0.821893\pi$
$600$	32.9603	−	6.10066i	1.34560	−	0.249059i
$601$	6.43928	+	36.5190i	0.262664	+	1.48964i	0.775606	+	0.631217i	$0.217444\pi$
$601$	6.43928	+	36.5190i	0.262664	+	1.48964i	−0.512943	+	0.858423i	$0.671445\pi$
$602$	23.3113	−	15.7256i	0.950098	−	0.640929i
$603$	−35.7613	−	28.9873i	−1.45631	−	1.18045i
$604$	18.0336			0.733778
$605$	15.6295	−	13.1147i	0.635430	−	0.533189i
$606$	8.69794	+	23.2807i	0.353330	+	0.945714i
$607$	2.60941	−	14.7987i	0.105913	−	0.600661i	−0.884939	−	0.465707i	$-0.845800\pi$
$607$	2.60941	−	14.7987i	0.105913	−	0.600661i	0.990852	−	0.134954i	$-0.0430887\pi$
$608$	−28.0503	−	23.5370i	−1.13759	−	0.954551i
$609$	−0.0579670	+	0.600867i	−0.00234894	+	0.0243483i
$610$	−1.50645	−	0.548304i	−0.0609945	−	0.0222002i
$611$	−0.840426			−0.0340000
$612$	2.18815	−	0.838750i	0.0884508	−	0.0339045i
$613$	−28.1322			−1.13625			−0.568125	−	0.822942i	$-0.692331\pi$
$613$	−28.1322			−1.13625			−0.568125	+	0.822942i	$0.692331\pi$
$614$	2.03626	−	1.70862i	0.0821766	−	0.0689544i
$615$	7.93107	−	22.3796i	0.319812	−	0.902433i
$616$	−6.01920	+	8.28572i	−0.242520	+	0.333841i
$617$	0.135031	−	0.765797i	0.00543613	−	0.0308298i	−0.981969	−	0.189042i	$-0.939462\pi$
$617$	0.135031	−	0.765797i	0.00543613	−	0.0308298i	0.987405	+	0.158212i	$0.0505729\pi$
$618$	−0.166105	−	19.5709i	−0.00668172	−	0.787259i
$619$	−1.90778	−	10.8196i	−0.0766802	−	0.434875i	−0.998844	−	0.0480749i	$-0.984691\pi$
$619$	−1.90778	−	10.8196i	−0.0766802	−	0.434875i	0.922163	−	0.386800i	$-0.126420\pi$
$620$	−10.7340	+	18.5918i	−0.431087	+	0.746664i
$621$	−10.6110	−	26.9944i	−0.425804	−	1.08325i
$622$	−10.3435			−0.414737
$623$	1.66188	+	1.72073i	0.0665820	+	0.0689397i
$624$	−1.05109	+	0.618803i	−0.0420775	+	0.0247719i
$625$	−61.8056	+	22.4954i	−2.47222	+	0.899816i
$626$	−0.571668	+	3.24209i	−0.0228484	+	0.129580i
$627$	−9.23945	+	26.0715i	−0.368988	+	1.04120i
$628$	7.17513	−	6.02065i	0.286319	−	0.240250i
$629$	−0.272600	−	0.472157i	−0.0108693	−	0.0188262i
$630$	41.2209	+	41.2556i	1.64228	+	1.64366i
$631$	21.9799	−	38.0704i	0.875008	−	1.51556i	0.0182532	−	0.999833i	$-0.494190\pi$
$631$	21.9799	−	38.0704i	0.875008	−	1.51556i	0.856755	−	0.515724i	$-0.172477\pi$
$632$	−1.56954	−	8.90132i	−0.0624330	−	0.354075i
$633$	−8.32440	−	1.39508i	−0.330865	−	0.0554493i
$634$	16.4287	−	5.97957i	0.652469	−	0.237479i
$635$	−7.54218	+	42.7738i	−0.299302	+	1.69743i
$636$	−7.06381	−	1.18382i	−0.280098	−	0.0469414i
$637$	−0.305527	−	0.939944i	−0.0121054	−	0.0372419i
$638$	0.286994	−	0.497088i	0.0113622	−	0.0196799i
$639$	−42.2379	+	0.717024i	−1.67090	+	0.0283650i
$640$	−47.0667			−1.86048
$641$	30.7822	+	11.2038i	1.21582	+	0.442524i	0.868720	−	0.495303i	$-0.164943\pi$
$641$	30.7822	+	11.2038i	1.21582	+	0.442524i	0.347104	+	0.937827i	$0.387165\pi$
$642$	12.1781	−	34.3637i	0.480630	−	1.35623i
$643$	15.9951	−	5.82174i	0.630785	−	0.229587i	−0.00678774	−	0.999977i	$-0.502161\pi$
$643$	15.9951	−	5.82174i	0.630785	−	0.229587i	0.637573	+	0.770390i	$0.279938\pi$
$644$	9.64925	−	13.2827i	0.380234	−	0.523410i
$645$	−0.368918	−	43.4670i	−0.0145261	−	1.71151i
$646$	−7.53021	−	2.74077i	−0.296272	−	0.107834i
$647$	14.6339	−	25.3466i	0.575317	−	0.996479i	−0.420690	−	0.907205i	$-0.638212\pi$
$647$	14.6339	−	25.3466i	0.575317	−	0.996479i	0.996007	−	0.0892745i	$-0.0284548\pi$
$648$	−14.0952	+	0.478694i	−0.553711	+	0.0188049i
$649$	−4.48291	−	7.76464i	−0.175970	−	0.304789i
$650$	2.35629	−	1.97717i	0.0924215	−	0.0775508i
$651$	21.1810	−	1.66311i	0.830150	−	0.0651825i
$652$	−1.56907	+	8.89865i	−0.0614496	+	0.348498i
$653$	17.4521	+	14.6441i	0.682954	+	0.573066i	0.916868	−	0.399191i	$-0.130709\pi$
$653$	17.4521	+	14.6441i	0.682954	+	0.573066i	−0.233914	+	0.972257i	$0.575153\pi$
$654$	−0.962768	+	0.178200i	−0.0376472	+	0.00696817i
$655$	23.6428	+	8.60527i	0.923800	+	0.336236i
$656$	−8.20708	+	14.2151i	−0.320433	+	0.555006i
$657$	19.6496	+	32.7379i	0.766604	+	1.27723i
$658$	−1.93943	−	27.7121i	−0.0756069	−	1.08033i
$659$	−1.59882	−	0.581922i	−0.0622810	−	0.0226684i	0.310692	−	0.950511i	$-0.399439\pi$
$659$	−1.59882	−	0.581922i	−0.0622810	−	0.0226684i	−0.372973	+	0.927842i	$0.621662\pi$
$660$	−6.93350	−	18.5580i	−0.269886	−	0.722371i
$661$	14.6772	−	5.34207i	0.570877	−	0.207782i	−0.0404209	−	0.999183i	$-0.512870\pi$
$661$	14.6772	−	5.34207i	0.570877	−	0.207782i	0.611298	+	0.791400i	$0.290648\pi$
$662$	−16.0977	+	5.85907i	−0.625653	+	0.227719i
$663$	−0.109337	+	0.132572i	−0.00424630	+	0.00514865i
$664$	−3.54344	−	1.28971i	−0.137512	−	0.0500503i
$665$	−4.97408	−	71.0734i	−0.192886	−	2.75611i
$666$	−0.781527	−	4.03092i	−0.0302836	−	0.156195i
$667$	0.367656	−	0.636799i	0.0142357	−	0.0246569i
$668$	−20.9351	−	7.61975i	−0.810003	−	0.294817i
$669$	11.3088	−	31.9108i	0.437224	−	1.23374i
$670$	−86.3688	−	72.4721i	−3.33672	−	2.79984i
$671$	0.0935884	−	0.530766i	0.00361294	−	0.0204900i
$672$	−14.6973	−	21.3930i	−0.566960	−	0.825252i
$673$	−27.8478	+	23.3671i	−1.07346	+	0.900736i	−0.995361	−	0.0962102i	$-0.969328\pi$
$673$	−27.8478	+	23.3671i	−1.07346	+	0.900736i	−0.0780940	+	0.996946i	$0.524883\pi$
$674$	19.2834	+	33.3997i	0.742767	+	1.28651i
$675$	62.8933	−	12.7487i	2.42076	−	0.490699i
$676$	7.21466	−	12.4961i	0.277487	−	0.480621i
$677$	30.0579	+	10.9402i	1.15522	+	0.420466i	0.847388	−	0.530975i	$-0.178174\pi$
$677$	30.0579	+	10.9402i	1.15522	+	0.420466i	0.307833	+	0.951440i	$0.400396\pi$
$678$	5.62592	+	3.18477i	0.216062	+	0.122311i
$679$	−2.86416	+	3.94266i	−0.109916	+	0.151305i
$680$	−4.30993	+	1.56869i	−0.165278	+	0.0601563i
$681$	20.9690	−	3.88119i	0.803535	−	0.148727i
$682$	−18.9837	−	6.90949i	−0.726922	−	0.264578i
$683$	−1.48087			−0.0566638			−0.0283319	−	0.999599i	$-0.509020\pi$
$683$	−1.48087			−0.0566638			−0.0283319	+	0.999599i	$0.509020\pi$
$684$	−16.7492	−	13.5765i	−0.640421	−	0.519111i
$685$	−5.33912	+	9.24762i	−0.203997	+	0.353333i
$686$	30.2885	−	12.2435i	1.15642	−	0.467458i
$687$	28.2534	−	34.2574i	1.07793	−	1.30700i
$688$	−5.21820	+	29.5939i	−0.198942	+	1.12826i
$689$	0.493542	−	0.179635i	0.0188024	−	0.00684353i
$690$	−24.8625	−	66.5463i	−0.946498	−	2.53337i
$691$	1.52814	+	8.66651i	0.0581332	+	0.329689i	0.999980	−	0.00635346i	$-0.00202238\pi$
$691$	1.52814	+	8.66651i	0.0581332	+	0.329689i	−0.941847	+	0.336043i	$0.890911\pi$
$692$	14.3790	−	24.9052i	0.546609	−	0.946755i
$693$	−11.2525	+	16.0559i	−0.427448	+	0.609911i
$694$	−8.77388	−	15.1968i	−0.333052	−	0.576863i
$695$	10.0749	−	8.45380i	0.382161	−	0.320671i
$696$	−0.232136	−	0.271928i	−0.00879908	−	0.0103074i
$697$	−0.401568	+	2.27740i	−0.0152105	+	0.0862628i
$698$	41.5867	−	15.1363i	1.57408	−	0.572918i
$699$	−11.0538	−	6.25745i	−0.418094	−	0.236678i
$700$	25.2337	+	26.1273i	0.953745	+	0.987518i
$701$	1.01529			0.0383469			0.0191734	−	0.999816i	$-0.493897\pi$
$701$	1.01529			0.0383469			0.0191734	+	0.999816i	$0.493897\pi$
$702$	−1.10395	+	0.675409i	−0.0416658	+	0.0254917i
$703$	−2.50807	+	4.34411i	−0.0945937	+	0.163841i
$704$	0.00683708	+	0.0387750i	0.000257682	+	0.00146139i
$705$	−37.3709	−	21.1553i	−1.40747	−	0.796753i
$706$	−3.03381	+	17.2056i	−0.114179	+	0.647540i
$707$	12.6487	−	17.4116i	0.475704	−	0.654830i
$708$	6.87193	−	1.27193i	0.258263	−	0.0478022i
$709$	34.2643	−	28.7511i	1.28682	−	1.07977i	0.294557	−	0.955634i	$-0.404828\pi$
$709$	34.2643	−	28.7511i	1.28682	−	1.07977i	0.992265	−	0.124138i	$-0.0396166\pi$
$710$	−103.464			−3.88293
$711$	−3.29361	−	16.9876i	−0.123520	−	0.637085i
$712$	−1.41688			−0.0530998
$713$	−24.3192	−	8.85147i	−0.910762	−	0.331490i
$714$	−4.62371	−	3.29933i	−0.173038	−	0.123474i
$715$	1.11287	+	0.933808i	0.0416189	+	0.0349224i
$716$	3.77325	−	21.3991i	0.141013	−	0.799723i
$717$	−16.3577	+	19.8338i	−0.610890	+	0.740708i
$718$	−22.3298	+	18.7369i	−0.833340	+	0.699256i
$719$	5.26881			0.196493			0.0982467	−	0.995162i	$-0.468677\pi$
$719$	5.26881			0.196493			0.0982467	+	0.995162i	$0.468677\pi$
$720$	−62.3152	+	1.05785i	−2.32235	+	0.0394239i
$721$	−14.0500	+	9.47806i	−0.523251	+	0.352981i
$722$	6.98286	+	39.6017i	0.259875	+	1.47382i
$723$	−10.1243	+	28.5683i	−0.376525	+	1.06246i
$724$	−0.544985	+	3.09077i	−0.0202542	+	0.114867i
$725$	1.24624	+	1.04572i	0.0462841	+	0.0388369i
$726$	−12.8967	+	7.59260i	−0.478643	+	0.281788i
$727$	31.0047	−	26.0161i	1.14990	−	0.964882i	0.150185	−	0.988658i	$-0.452013\pi$
$727$	31.0047	−	26.0161i	1.14990	−	0.964882i	0.999717	+	0.0237758i	$0.00756878\pi$
$728$	0.526155	+	0.256585i	0.0195006	+	0.00950969i
$729$	−26.9650	+	1.37432i	−0.998704	+	0.0509007i
$730$	46.7579	+	80.9870i	1.73059	+	2.99746i
$731$	0.735175	+	4.16939i	0.0271914	+	0.154210i
$732$	0.365588	+	0.206955i	0.0135125	+	0.00764929i
$733$	23.1085	−	8.41079i	0.853530	−	0.310660i	0.122052	−	0.992524i	$-0.461053\pi$
$733$	23.1085	−	8.41079i	0.853530	−	0.310660i	0.731479	+	0.681864i	$0.238830\pi$
$734$	52.5972	−	19.1438i	1.94140	−	0.706610i
$735$	10.0746	−	49.4869i	0.371607	−	1.82535i
$736$	5.49004	+	31.1356i	0.202366	+	1.14767i
$737$	18.9520	−	32.8258i	0.698106	−	1.20915i
$738$	−8.45076	+	15.2284i	−0.311077	+	0.560564i
$739$	−20.6453	−	35.7586i	−0.759448	−	1.31540i	−0.943132	−	0.332417i	$-0.892136\pi$
$739$	−20.6453	−	35.7586i	−0.759448	−	1.31540i	0.183684	−	0.982985i	$-0.441198\pi$
$740$	−0.623862	−	3.53810i	−0.0229336	−	0.130063i
$741$	1.55930	+	0.261321i	0.0572823	+	0.00959987i
$742$	7.06218	+	15.8594i	0.259261	+	0.582219i
$743$	−8.19507	−	6.87648i	−0.300648	−	0.252274i	0.479966	−	0.877287i	$-0.340649\pi$
$743$	−8.19507	−	6.87648i	−0.300648	−	0.252274i	−0.780614	+	0.625013i	$0.785093\pi$
$744$	−8.00660	+	9.70804i	−0.293536	+	0.355914i
$745$	40.2281	−	33.7554i	1.47384	−	1.23670i
$746$	21.1331	+	36.6037i	0.773739	+	1.34015i
$747$	−6.82464	−	2.35357i	−0.249700	−	0.0861126i
$748$	0.964765	+	1.67102i	0.0352753	+	0.0610986i
$749$	−30.6324	+	7.63939i	−1.11928	+	0.279137i
$750$	91.9766	−	17.0241i	3.35851	−	0.621631i
$751$	9.92649	+	8.32931i	0.362223	+	0.303941i	0.805676	−	0.592357i	$-0.201802\pi$
$751$	9.92649	+	8.32931i	0.362223	+	0.303941i	−0.443453	+	0.896298i	$0.646247\pi$
$752$	22.7418	+	19.0827i	0.829309	+	0.695873i
$753$	0.194737	+	22.9445i	0.00709661	+	0.836142i
$754$	−0.0308301	−	0.0112212i	−0.00112277	−	0.000408654i
$755$	−67.5716			−2.45918
$756$	−8.86648	−	12.4477i	−0.322471	−	0.452720i
$757$	28.7036			1.04325			0.521625	−	0.853175i	$-0.325326\pi$
$757$	28.7036			1.04325			0.521625	+	0.853175i	$0.325326\pi$
$758$	−30.7416	−	11.1890i	−1.11658	−	0.406403i
$759$	20.5807	−	12.1163i	0.747033	−	0.439795i
$760$	32.3260	+	27.1247i	1.17259	+	0.983918i
$761$	−28.7049	−	24.0862i	−1.04055	−	0.873125i	−0.0484819	−	0.998824i	$-0.515438\pi$
$761$	−28.7049	−	24.0862i	−1.04055	−	0.873125i	−0.992068	+	0.125699i	$0.959883\pi$
$762$	10.6420	−	30.0291i	0.385518	−	1.08784i
$763$	0.589015	+	0.609872i	0.0213238	+	0.0220789i
$764$	4.53352	+	7.85229i	0.164017	+	0.284086i
$765$	−8.19895	+	3.14278i	−0.296434	+	0.113627i
$766$	19.9660	+	34.5822i	0.721402	+	1.24951i
$767$	−0.392583	+	0.329416i	−0.0141753	+

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65761 - 0.603319i) q^{2} +(-1.50730 - 0.853264i) q^{3} +(0.851575 + 0.714556i) q^{4} +(-3.19083 - 2.67742i) q^{5} +(1.98371 + 2.32376i) q^{6} +(0.729121 - 2.54330i) q^{7} +(0.783518 + 1.35709i) q^{8} +(1.54388 + 2.57224i) q^{9} +O(q^{10})\)	\(q+(-1.65761 - 0.603319i) q^{2} +(-1.50730 - 0.853264i) q^{3} +(0.851575 + 0.714556i) q^{4} +(-3.19083 - 2.67742i) q^{5} +(1.98371 + 2.32376i) q^{6} +(0.729121 - 2.54330i) q^{7} +(0.783518 + 1.35709i) q^{8} +(1.54388 + 2.57224i) q^{9} +(3.67380 + 6.36320i) q^{10} +(-1.89226 + 1.58779i) q^{11} +(-0.673870 - 1.80366i) q^{12} +(0.108160 + 0.0907572i) q^{13} +(-2.74302 + 3.77590i) q^{14} +(2.52498 + 6.75829i) q^{15} +(-0.866076 - 4.91176i) q^{16} +(-0.351339 - 0.608536i) q^{17} +(-1.00727 - 5.19522i) q^{18} +(-3.23251 + 5.59887i) q^{19} +(-0.804060 - 4.56005i) q^{20} +(-3.26911 + 3.21138i) q^{21} +(4.09457 - 1.49030i) q^{22} +(5.24538 - 1.90916i) q^{23} +(-0.0230353 - 2.71409i) q^{24} +(2.14455 + 12.1624i) q^{25} +(-0.124532 - 0.215695i) q^{26} +(-0.132287 - 5.19447i) q^{27} +(2.43823 - 1.64481i) q^{28} +(0.100910 - 0.0846735i) q^{29} +(-0.108009 - 12.7259i) q^{30} +(-3.55162 - 2.98016i) q^{31} +(-0.983522 + 5.57783i) q^{32} +(4.20700 - 0.778680i) q^{33} +(0.215239 + 1.22068i) q^{34} +(-9.13599 + 6.16308i) q^{35} +(-0.523280 + 3.29365i) q^{36} +0.775890 q^{37} +(8.73613 - 7.33049i) q^{38} +(-0.0855897 - 0.229087i) q^{39} +(1.13344 - 6.42806i) q^{40} +(-2.52108 - 2.11544i) q^{41} +(7.35638 - 3.35088i) q^{42} +(-5.66175 - 2.06071i) q^{43} -2.74597 q^{44} +(1.96072 - 12.3412i) q^{45} -9.84662 q^{46} +(-4.55973 + 3.82607i) q^{47} +(-2.88560 + 8.14247i) q^{48} +(-5.93677 - 3.70875i) q^{49} +(3.78296 - 21.4542i) q^{50} +(0.0103293 + 1.21703i) q^{51} +(0.0272554 + 0.154573i) q^{52} +(1.85992 - 3.22148i) q^{53} +(-2.91464 + 8.69019i) q^{54} +10.2891 q^{55} +(4.02277 - 1.00324i) q^{56} +(9.64966 - 5.68097i) q^{57} +(-0.218354 + 0.0794744i) q^{58} +(-0.630281 + 3.57450i) q^{59} +(-2.67897 + 7.55942i) q^{60} +(-0.167139 + 0.140247i) q^{61} +(4.08919 + 7.08269i) q^{62} +(7.66766 - 2.05108i) q^{63} +(0.00796973 - 0.0138040i) q^{64} +(-0.102125 - 0.579182i) q^{65} +(-7.44335 - 1.24742i) q^{66} +(-14.4193 + 5.24819i) q^{67} +(0.135642 - 0.769265i) q^{68} +(-9.53537 - 1.59802i) q^{69} +(18.8622 - 4.70403i) q^{70} +(-7.04066 + 12.1948i) q^{71} +(-2.28111 + 4.11059i) q^{72} +12.7274 q^{73} +(-1.28612 - 0.468110i) q^{74} +(7.14522 - 20.1621i) q^{75} +(-6.75343 + 2.45805i) q^{76} +(2.65855 + 5.97028i) q^{77} +(0.00366121 + 0.431374i) q^{78} +(-5.42013 - 1.97277i) q^{79} +(-10.3874 + 17.9914i) q^{80} +(-4.23286 + 7.94248i) q^{81} +(2.90267 + 5.02758i) q^{82} +(-1.84338 + 1.54678i) q^{83} +(-5.07860 + 0.398766i) q^{84} +(-0.508248 + 2.88242i) q^{85} +(8.14168 + 6.83168i) q^{86} +(-0.224350 + 0.0415252i) q^{87} +(-3.63740 - 1.32391i) q^{88} +(-0.452090 + 0.783042i) q^{89} +(-10.6958 + 19.2739i) q^{90} +(0.309685 - 0.208911i) q^{91} +(5.83104 + 2.12233i) q^{92} +(2.81047 + 7.52245i) q^{93} +(9.86659 - 3.59114i) q^{94} +(25.3049 - 9.21024i) q^{95} +(6.24182 - 7.56824i) q^{96} +(-1.73081 - 0.629965i) q^{97} +(7.60326 + 9.72941i) q^{98} +(-7.00562 - 2.41598i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

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