LMFDB - Embedded newform 189.2.w.a.88.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(25,189)]

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([10, 12]))

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

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

chi := DirichletCharacter("189.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.w (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			88.3
Character	$\chi$	$=$	189.88
Dual form			189.2.w.a.58.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86441 - 1.56443i) q^{2} +(1.55585 - 0.761137i) q^{3} +(0.681303 + 3.86386i) q^{4} +(1.94710 - 1.63381i) q^{5} +(-4.09149 - 1.01494i) q^{6} +(1.59312 + 2.11233i) q^{7} +(2.34068 - 4.05418i) q^{8} +(1.84134 - 2.36843i) q^{9} +O(q^{10})$	\(q+(-1.86441 - 1.56443i) q^{2} +(1.55585 - 0.761137i) q^{3} +(0.681303 + 3.86386i) q^{4} +(1.94710 - 1.63381i) q^{5} +(-4.09149 - 1.01494i) q^{6} +(1.59312 + 2.11233i) q^{7} +(2.34068 - 4.05418i) q^{8} +(1.84134 - 2.36843i) q^{9} -6.18617 q^{10} +(2.75988 + 2.31581i) q^{11} +(4.00093 + 5.49302i) q^{12} +(0.574547 + 0.209118i) q^{13} +(0.334352 - 6.43059i) q^{14} +(1.78584 - 4.02398i) q^{15} +(-3.33276 + 1.21302i) q^{16} -2.17998 q^{17} +(-7.13826 + 1.53509i) q^{18} -6.48741 q^{19} +(7.63938 + 6.41020i) q^{20} +(4.08644 + 2.07389i) q^{21} +(-1.52263 - 8.63526i) q^{22} +(-8.52625 - 3.10330i) q^{23} +(0.555964 - 8.08927i) q^{24} +(0.253619 - 1.43835i) q^{25} +(-0.744042 - 1.28872i) q^{26} +(1.06215 - 5.08644i) q^{27} +(-7.07636 + 7.59475i) q^{28} +(-2.61993 + 0.953577i) q^{29} +(-9.62476 + 4.70853i) q^{30} +(0.599528 + 3.40009i) q^{31} +(-0.686760 - 0.249960i) q^{32} +(6.05661 + 1.50241i) q^{33} +(4.06438 + 3.41042i) q^{34} +(6.55313 + 1.51006i) q^{35} +(10.4058 + 5.50106i) q^{36} +(4.59825 - 7.96441i) q^{37} +(12.0952 + 10.1491i) q^{38} +(1.05308 - 0.111953i) q^{39} +(-2.06622 - 11.7181i) q^{40} +(1.95368 + 0.711080i) q^{41} +(-4.37436 - 10.2595i) q^{42} +(-0.636164 + 3.60787i) q^{43} +(-7.06766 + 12.2415i) q^{44} +(-0.284293 - 7.61997i) q^{45} +(11.0415 + 19.1245i) q^{46} +(-1.15697 + 6.56152i) q^{47} +(-4.26199 + 4.42397i) q^{48} +(-1.92391 + 6.73042i) q^{49} +(-2.72304 + 2.28490i) q^{50} +(-3.39172 + 1.65926i) q^{51} +(-0.416562 + 2.36244i) q^{52} +(1.94162 - 3.36298i) q^{53} +(-9.93765 + 7.82155i) q^{54} +9.15736 q^{55} +(12.2928 - 1.51451i) q^{56} +(-10.0934 + 4.93781i) q^{57} +(6.37644 + 2.32083i) q^{58} +(-4.14711 - 1.50942i) q^{59} +(16.7648 + 4.15870i) q^{60} +(-0.758369 + 4.30092i) q^{61} +(4.20143 - 7.27709i) q^{62} +(7.93640 + 0.116321i) q^{63} +(4.43600 + 7.68339i) q^{64} +(1.46036 - 0.531527i) q^{65} +(-8.94160 - 12.2762i) q^{66} +(7.33069 - 6.15118i) q^{67} +(-1.48523 - 8.42313i) q^{68} +(-15.6276 + 1.66137i) q^{69} +(-9.85535 - 13.0673i) q^{70} +(1.53557 + 2.65969i) q^{71} +(-5.29205 - 13.0089i) q^{72} +(-6.73130 - 11.6590i) q^{73} +(-21.0328 + 7.65530i) q^{74} +(-0.700186 - 2.43089i) q^{75} +(-4.41989 - 25.0664i) q^{76} +(-0.494939 + 9.51916i) q^{77} +(-2.13851 - 1.43874i) q^{78} +(7.81528 + 6.55780i) q^{79} +(-4.50736 + 7.80698i) q^{80} +(-2.21893 - 8.72218i) q^{81} +(-2.53002 - 4.38213i) q^{82} +(-1.25509 + 0.456814i) q^{83} +(-5.22911 + 17.2024i) q^{84} +(-4.24464 + 3.56168i) q^{85} +(6.83031 - 5.73131i) q^{86} +(-3.35042 + 3.47775i) q^{87} +(15.8487 - 5.76846i) q^{88} -16.3622 q^{89} +(-11.3909 + 14.6515i) q^{90} +(0.473598 + 1.54679i) q^{91} +(6.18176 - 35.0585i) q^{92} +(3.52071 + 4.83371i) q^{93} +(12.4221 - 10.4234i) q^{94} +(-12.6316 + 10.5992i) q^{95} +(-1.25875 + 0.133818i) q^{96} +(0.474040 - 2.68841i) q^{97} +(14.1162 - 9.53847i) q^{98} +(10.5667 - 2.27238i) 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} + 3 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 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.86441	−	1.56443i	−1.31834	−	1.10622i	−0.986655	−	0.162827i	$-0.947939\pi$
$2$	−1.86441	−	1.56443i	−1.31834	−	1.10622i	−0.331684	−	0.943391i	$-0.607617\pi$
$3$	1.55585	−	0.761137i	0.898271	−	0.439443i
$3$	1.55585	−	0.761137i	0.898271	−	0.439443i
$4$	0.681303	+	3.86386i	0.340651	+	1.93193i
$5$	1.94710	−	1.63381i	0.870770	−	0.730662i	−0.0934904	−	0.995620i	$-0.529802\pi$
$5$	1.94710	−	1.63381i	0.870770	−	0.730662i	0.964260	+	0.264958i	$0.0853580\pi$
$6$	−4.09149	−	1.01494i	−1.67034	−	0.414348i
$7$	1.59312	+	2.11233i	0.602145	+	0.798387i
$7$	1.59312	+	2.11233i	0.602145	+	0.798387i
$8$	2.34068	−	4.05418i	0.827556	−	1.43337i
$9$	1.84134	−	2.36843i	0.613780	−	0.789477i
$10$	−6.18617			−1.95624
$11$	2.75988	+	2.31581i	0.832135	+	0.698244i	0.955780	−	0.294083i	$-0.0950141\pi$
$11$	2.75988	+	2.31581i	0.832135	+	0.698244i	−0.123645	+	0.992326i	$0.539459\pi$
$12$	4.00093	+	5.49302i	1.15497	+	1.58570i
$13$	0.574547	+	0.209118i	0.159351	+	0.0579989i	0.420464	−	0.907309i	$-0.361867\pi$
$13$	0.574547	+	0.209118i	0.159351	+	0.0579989i	−0.261113	+	0.965308i	$0.584090\pi$
$14$	0.334352	−	6.43059i	0.0893593	−	1.71865i
$15$	1.78584	−	4.02398i	0.461103	−	1.03899i
$16$	−3.33276	+	1.21302i	−0.833189	+	0.303256i
$17$	−2.17998			−0.528723			−0.264361	−	0.964424i	$-0.585161\pi$
$17$	−2.17998			−0.528723			−0.264361	+	0.964424i	$0.585161\pi$
$18$	−7.13826	+	1.53509i	−1.68250	+	0.361823i
$19$	−6.48741			−1.48831			−0.744157	−	0.668005i	$-0.767149\pi$
$19$	−6.48741			−1.48831			−0.744157	+	0.668005i	$0.767149\pi$
$20$	7.63938	+	6.41020i	1.70822	+	1.43336i
$21$	4.08644	+	2.07389i	0.891734	+	0.452560i
$22$	−1.52263	−	8.63526i	−0.324626	−	1.84104i
$23$	−8.52625	−	3.10330i	−1.77785	−	0.647083i	−0.999822	−	0.0188469i	$-0.994000\pi$
$23$	−8.52625	−	3.10330i	−1.77785	−	0.647083i	−0.778023	−	0.628236i	$-0.783777\pi$
$24$	0.555964	−	8.08927i	0.113486	−	1.65122i
$25$	0.253619	−	1.43835i	0.0507239	−	0.287670i
$26$	−0.744042	−	1.28872i	−0.145919	−	0.252739i
$27$	1.06215	−	5.08644i	0.204411	−	0.978885i
$28$	−7.07636	+	7.59475i	−1.33731	+	1.43527i
$29$	−2.61993	+	0.953577i	−0.486509	+	0.177075i	−0.573616	−	0.819124i	$-0.694460\pi$
$29$	−2.61993	+	0.953577i	−0.486509	+	0.177075i	0.0871072	+	0.996199i	$0.472238\pi$
$30$	−9.62476	+	4.70853i	−1.75723	+	0.859655i
$31$	0.599528	+	3.40009i	0.107678	+	0.610675i	0.990117	+	0.140246i	$0.0447895\pi$
$31$	0.599528	+	3.40009i	0.107678	+	0.610675i	−0.882438	+	0.470428i	$0.844099\pi$
$32$	−0.686760	−	0.249960i	−0.121403	−	0.0441871i
$33$	6.05661	+	1.50241i	1.05432	+	0.261536i
$34$	4.06438	+	3.41042i	0.697036	+	0.584882i
$35$	6.55313	+	1.51006i	1.10768	+	0.255247i
$36$	10.4058	+	5.50106i	1.73430	+	0.916844i
$37$	4.59825	−	7.96441i	0.755948	−	1.30934i	−0.188954	−	0.981986i	$-0.560510\pi$
$37$	4.59825	−	7.96441i	0.755948	−	1.30934i	0.944902	−	0.327354i	$-0.106157\pi$
$38$	12.0952	+	10.1491i	1.96210	+	1.64640i
$39$	1.05308	−	0.111953i	0.168627	−	0.0179268i
$40$	−2.06622	−	11.7181i	−0.326698	−	1.85280i
$41$	1.95368	+	0.711080i	0.305113	+	0.111052i	0.490039	−	0.871700i	$-0.336982\pi$
$41$	1.95368	+	0.711080i	0.305113	+	0.111052i	−0.184926	+	0.982752i	$0.559205\pi$
$42$	−4.37436	−	10.2595i	−0.674978	−	1.58308i
$43$	−0.636164	+	3.60787i	−0.0970141	+	0.550194i	0.897097	+	0.441833i	$0.145672\pi$
$43$	−0.636164	+	3.60787i	−0.0970141	+	0.550194i	−0.994112	+	0.108362i	$0.965440\pi$
$44$	−7.06766	+	12.2415i	−1.06549	+	1.84548i
$45$	−0.284293	−	7.61997i	−0.0423799	−	1.13592i
$46$	11.0415	+	19.1245i	1.62799	+	2.81976i
$47$	−1.15697	+	6.56152i	−0.168762	+	0.957096i	0.776339	+	0.630316i	$0.217075\pi$
$47$	−1.15697	+	6.56152i	−0.168762	+	0.957096i	−0.945100	+	0.326780i	$0.894036\pi$
$48$	−4.26199	+	4.42397i	−0.615166	+	0.638545i
$49$	−1.92391	+	6.73042i	−0.274844	+	0.961489i
$50$	−2.72304	+	2.28490i	−0.385096	+	0.323134i
$51$	−3.39172	+	1.65926i	−0.474936	+	0.232343i
$52$	−0.416562	+	2.36244i	−0.0577667	+	0.327612i
$53$	1.94162	−	3.36298i	0.266702	−	0.461941i	−0.701306	−	0.712860i	$-0.747399\pi$
$53$	1.94162	−	3.36298i	0.266702	−	0.461941i	0.968008	+	0.250919i	$0.0807328\pi$
$54$	−9.93765	+	7.82155i	−1.35234	+	1.06438i
$55$	9.15736			1.23478
$56$	12.2928	−	1.51451i	1.64269	−	0.202385i
$57$	−10.0934	+	4.93781i	−1.33691	+	0.654029i
$58$	6.37644	+	2.32083i	0.837267	+	0.304740i
$59$	−4.14711	−	1.50942i	−0.539908	−	0.196510i	0.0576491	−	0.998337i	$-0.481640\pi$
$59$	−4.14711	−	1.50942i	−0.539908	−	0.196510i	−0.597557	+	0.801827i	$0.703862\pi$
$60$	16.7648	+	4.15870i	2.16432	+	0.536886i
$61$	−0.758369	+	4.30092i	−0.0970992	+	0.550677i	0.896985	+	0.442062i	$0.145753\pi$
$61$	−0.758369	+	4.30092i	−0.0970992	+	0.550677i	−0.994084	+	0.108615i	$0.965358\pi$
$62$	4.20143	−	7.27709i	0.533582	−	0.924192i
$63$	7.93640	+	0.116321i	0.999893	+	0.0146551i
$64$	4.43600	+	7.68339i	0.554501	+	0.960423i
$65$	1.46036	−	0.531527i	0.181135	−	0.0659278i
$66$	−8.94160	−	12.2762i	−1.10063	−	1.51110i
$67$	7.33069	−	6.15118i	0.895587	−	0.751486i	−0.0737362	−	0.997278i	$-0.523492\pi$
$67$	7.33069	−	6.15118i	0.895587	−	0.751486i	0.969323	+	0.245791i	$0.0790478\pi$
$68$	−1.48523	−	8.42313i	−0.180110	−	1.02146i
$69$	−15.6276	+	1.66137i	−1.88134	+	0.200006i
$70$	−9.85535	−	13.0673i	−1.17794	−	1.56184i
$71$	1.53557	+	2.65969i	0.182239	+	0.315647i	0.942643	−	0.333804i	$-0.108332\pi$
$71$	1.53557	+	2.65969i	0.182239	+	0.315647i	−0.760404	+	0.649450i	$0.774999\pi$
$72$	−5.29205	−	13.0089i	−0.623674	−	1.53311i
$73$	−6.73130	−	11.6590i	−0.787839	−	1.36458i	−0.927288	−	0.374349i	$-0.877866\pi$
$73$	−6.73130	−	11.6590i	−0.787839	−	1.36458i	0.139449	−	0.990229i	$-0.455467\pi$
$74$	−21.0328	+	7.65530i	−2.44501	+	0.889911i
$75$	−0.700186	−	2.43089i	−0.0808505	−	0.280695i
$76$	−4.41989	−	25.0664i	−0.506996	−	2.87532i
$77$	−0.494939	+	9.51916i	−0.0564035	+	1.08481i
$78$	−2.13851	−	1.43874i	−0.242139	−	0.162905i
$79$	7.81528	+	6.55780i	0.879288	+	0.737810i	0.966033	−	0.258421i	$-0.0832020\pi$
$79$	7.81528	+	6.55780i	0.879288	+	0.737810i	−0.0867448	+	0.996231i	$0.527646\pi$
$80$	−4.50736	+	7.80698i	−0.503938	+	0.872846i
$81$	−2.21893	−	8.72218i	−0.246547	−	0.969131i
$82$	−2.53002	−	4.38213i	−0.279394	−	0.483925i
$83$	−1.25509	+	0.456814i	−0.137764	+	0.0501419i	−0.409982	−	0.912094i	$-0.634465\pi$
$83$	−1.25509	+	0.456814i	−0.137764	+	0.0501419i	0.272218	+	0.962236i	$0.412243\pi$
$84$	−5.22911	+	17.2024i	−0.570543	+	1.87693i
$85$	−4.24464	+	3.56168i	−0.460396	+	0.386318i
$86$	6.83031	−	5.73131i	0.736532	−	0.618024i
$87$	−3.35042	+	3.47775i	−0.359203	+	0.372854i
$88$	15.8487	−	5.76846i	1.68948	−	0.614920i
$89$	−16.3622			−1.73439			−0.867194	−	0.497971i	$-0.834079\pi$
$89$	−16.3622			−1.73439			−0.867194	+	0.497971i	$0.834079\pi$
$90$	−11.3909	+	14.6515i	−1.20070	+	1.54441i
$91$	0.473598	+	1.54679i	0.0496466	+	0.162147i
$92$	6.18176	−	35.0585i	0.644493	−	3.65510i
$93$	3.52071	+	4.83371i	0.365081	+	0.501233i
$94$	12.4221	−	10.4234i	1.28124	−	1.07509i
$95$	−12.6316	+	10.5992i	−1.29598	+	1.08746i
$96$	−1.25875	+	0.133818i	−0.128471	+	0.0136577i
$97$	0.474040	−	2.68841i	0.0481314	−	0.272967i	−0.951239	−	0.308456i	$-0.900188\pi$
$97$	0.474040	−	2.68841i	0.0481314	−	0.272967i	0.999370	+	0.0354890i	$0.0112989\pi$
$98$	14.1162	−	9.53847i	1.42595	−	0.963531i
$99$	10.5667	−	2.27238i	1.06200	−	0.228383i
$100$	5.73036			0.573036
$101$	2.78978	−	1.01540i	0.277593	−	0.101036i	−0.199472	−	0.979903i	$-0.563923\pi$
$101$	2.78978	−	1.01540i	0.277593	−	0.101036i	0.477065	+	0.878868i	$0.341701\pi$
$102$	8.91937	+	2.21255i	0.883149	+	0.219075i
$103$	4.87747	−	4.09268i	0.480591	−	0.403264i	−0.370049	−	0.929012i	$-0.620659\pi$
$103$	4.87747	−	4.09268i	0.480591	−	0.403264i	0.850640	+	0.525748i	$0.176215\pi$
$104$	2.19263	−	1.83984i	0.215005	−	0.180411i
$105$	11.3450	−	2.63840i	1.10716	−	0.257481i
$106$	−8.88112	+	3.23246i	−0.862611	+	0.313965i
$107$	7.61176	+	13.1840i	0.735857	+	1.27454i	0.954346	+	0.298702i	$0.0965537\pi$
$107$	7.61176	+	13.1840i	0.735857	+	1.27454i	−0.218490	+	0.975839i	$0.570113\pi$
$108$	20.3769	+	0.638599i	1.96077	+	0.0614492i
$109$	−0.868969	+	1.50510i	−0.0832321	+	0.144162i	−0.904637	−	0.426184i	$-0.859858\pi$
$109$	−0.868969	+	1.50510i	−0.0832321	+	0.144162i	0.821404	+	0.570346i	$0.193191\pi$
$110$	−17.0731	−	14.3260i	−1.62786	−	1.36593i
$111$	1.09219	−	15.8913i	0.103666	−	1.50834i
$112$	−7.87181	−	5.10740i	−0.743816	−	0.482604i
$113$	0.205896	+	1.16770i	0.0193691	+	0.109848i	0.992960	−	0.118454i	$-0.0377938\pi$
$113$	0.205896	+	1.16770i	0.0193691	+	0.109848i	−0.973590	+	0.228302i	$0.926683\pi$
$114$	26.5432	+	6.58435i	2.48600	+	0.616680i
$115$	−21.6717	+	7.88784i	−2.02089	+	0.735545i
$116$	−5.46945	−	9.47337i	−0.507826	−	0.879581i
$117$	1.55322	−	0.975717i	0.143595	−	0.0902051i
$118$	5.37054	+	9.30204i	0.494398	+	0.856322i
$119$	−3.47298	−	4.60485i	−0.318368	−	0.422125i
$120$	−12.1338	−	16.6590i	−1.10766	−	1.52075i
$121$	0.343809	+	1.94984i	0.0312553	+	0.177258i
$122$	8.14240	−	6.83228i	0.737178	−	0.618566i
$123$	3.58086	−	0.380681i	0.322875	−	0.0343249i
$124$	−12.7290	+	4.63298i	−1.14310	+	0.416054i
$125$	4.49823	+	7.79116i	0.402334	+	0.696863i
$126$	−14.6147	−	12.6328i	−1.30199	−	1.12542i
$127$	0.268900	−	0.465748i	0.0238610	−	0.0413284i	−0.853848	−	0.520522i	$-0.825737\pi$
$127$	0.268900	−	0.465748i	0.0238610	−	0.0413284i	0.877709	+	0.479193i	$0.159071\pi$
$128$	3.49574	−	19.8253i	0.308983	−	1.75233i
$129$	1.75630	+	6.09751i	0.154634	+	0.536855i
$130$	−3.55425	−	1.29364i	−0.311728	−	0.113460i
$131$	10.9911	+	4.00044i	0.960299	+	0.349520i	0.774151	−	0.633001i	$-0.218177\pi$
$131$	10.9911	+	4.00044i	0.960299	+	0.349520i	0.186149	+	0.982522i	$0.440399\pi$
$132$	−1.67873	+	24.4255i	−0.146115	+	2.12596i
$133$	−10.3353	−	13.7036i	−0.896180	−	1.18825i
$134$	−23.2905			−2.01199
$135$	−6.24216	−	11.6392i	−0.537240	−	1.00174i
$136$	−5.10264	+	8.83803i	−0.437548	+	0.757855i
$137$	−1.21062	+	6.86578i	−0.103430	+	0.586583i	0.888405	+	0.459060i	$0.151814\pi$
$137$	−1.21062	+	6.86578i	−0.103430	+	0.586583i	−0.991836	+	0.127523i	$0.959297\pi$
$138$	31.7354	+	21.3508i	2.70149	+	1.81750i
$139$	−12.1427	+	10.1889i	−1.02993	+	0.864215i	−0.990843	−	0.135021i	$-0.956890\pi$
$139$	−12.1427	+	10.1889i	−1.02993	+	0.864215i	−0.0390880	+	0.999236i	$0.512445\pi$
$140$	−1.37000	+	26.3492i	−0.115786	+	2.22691i
$141$	3.19414	+	11.0894i	0.268995	+	0.933892i
$142$	1.29795	−	7.36104i	0.108922	−	0.617725i
$143$	1.10140	+	1.90768i	0.0921038	+	0.159528i
$144$	−3.26378	+	10.1270i	−0.271982	+	0.843916i
$145$	−3.54330	+	6.13718i	−0.294255	+	0.509665i
$146$	−5.68967	+	32.2677i	−0.470881	+	2.67050i
$147$	2.12946	+	11.9359i	0.175635	+	0.984455i
$148$	33.9061	+	12.3408i	2.78707	+	1.01441i
$149$	0.329833	+	1.87058i	0.0270210	+	0.153243i	0.995333	−	0.0965001i	$-0.0307648\pi$
$149$	0.329833	+	1.87058i	0.0270210	+	0.153243i	−0.968312	+	0.249744i	$0.919654\pi$
$150$	−2.49752	+	5.62758i	−0.203922	+	0.459490i
$151$	−7.53015	−	6.31855i	−0.612795	−	0.514196i	0.282734	−	0.959198i	$-0.408759\pi$
$151$	−7.53015	−	6.31855i	−0.612795	−	0.514196i	−0.895530	+	0.445002i	$0.853203\pi$
$152$	−15.1850	+	26.3011i	−1.23166	+	2.13330i
$153$	−4.01409	+	5.16313i	−0.324520	+	0.417414i
$154$	15.8148	−	16.9733i	1.27439	−	1.36775i
$155$	6.72245	+	5.64081i	0.539960	+	0.453080i
$156$	1.15003	+	3.99266i	0.0920763	+	0.319669i
$157$	−2.89166	−	1.05248i	−0.230779	−	0.0839968i	0.224042	−	0.974579i	$-0.428075\pi$
$157$	−2.89166	−	1.05248i	−0.230779	−	0.0839968i	−0.454821	+	0.890583i	$0.650297\pi$
$158$	−4.31170	−	24.4529i	−0.343021	−	1.94537i
$159$	0.461178	−	6.71014i	0.0365738	−	0.532148i
$160$	−1.74558	+	0.635338i	−0.138000	+	0.0502279i
$161$	−7.02817	−	22.9542i	−0.553897	−	1.80905i
$162$	−9.50822	+	19.7331i	−0.747036	+	1.55038i
$163$	−4.07453	−	7.05730i	−0.319142	−	0.552770i	0.661167	−	0.750239i	$-0.270061\pi$
$163$	−4.07453	−	7.05730i	−0.319142	−	0.552770i	−0.980309	+	0.197468i	$0.936728\pi$
$164$	−1.41647	+	8.03319i	−0.110608	+	0.627287i
$165$	14.2475	−	6.97000i	1.10916	−	0.542614i
$166$	3.05465	+	1.11180i	0.237087	+	0.0862926i
$167$	−3.47178	−	19.6894i	−0.268654	−	1.52361i	−0.758424	−	0.651762i	$-0.774030\pi$
$167$	−3.47178	−	19.6894i	−0.268654	−	1.52361i	0.489769	−	0.871852i	$-0.337081\pi$
$168$	17.9730	−	11.7128i	1.38664	−	0.903665i
$169$	−9.67220	−	8.11594i	−0.744016	−	0.624303i
$170$	13.4857			1.03431
$171$	−11.9455	+	15.3650i	−0.913498	+	1.17499i
$172$	−14.3737			−1.09598
$173$	8.99507	−	3.27394i	0.683882	−	0.248913i	0.0233688	−	0.999727i	$-0.492561\pi$
$173$	8.99507	−	3.27394i	0.683882	−	0.248913i	0.660514	+	0.750814i	$0.270339\pi$
$174$	11.6873	−	1.24247i	0.886008	−	0.0941916i
$175$	3.44232	−	1.75574i	0.260215	−	0.132721i
$176$	−12.0071	−	4.37024i	−0.905072	−	0.329419i
$177$	−7.60116	+	0.808080i	−0.571338	+	0.0607390i
$178$	30.5058	+	25.5974i	2.28651	+	1.91861i
$179$	16.6077			1.24132			0.620660	−	0.784080i	$-0.286865\pi$
$179$	16.6077			1.24132			0.620660	+	0.784080i	$0.286865\pi$
$180$	29.2488	−	6.28997i	2.18008	−	0.468827i
$181$	9.94849	−	17.2313i	0.739465	−	1.28079i	−0.213271	−	0.976993i	$-0.568412\pi$
$181$	9.94849	−	17.2313i	0.739465	−	1.28079i	0.952736	−	0.303799i	$-0.0982550\pi$
$182$	1.53685	−	3.62476i	0.113919	−	0.268685i
$183$	2.09368	+	7.26882i	0.154770	+	0.537326i
$184$	−32.5385	+	27.3031i	−2.39877	+	2.01281i
$185$	−4.05908	−	23.0202i	−0.298429	−	1.69248i
$186$	0.997934	−	14.5199i	0.0731721	−	1.06465i
$187$	−6.01648	−	5.04843i	−0.439969	−	0.369177i
$188$	−26.1410			−1.90653
$189$	12.4364	−	5.85971i	0.904614	−	0.426231i
$190$	40.1323			2.91150
$191$	17.8858	+	15.0079i	1.29417	+	1.08594i	0.991121	+	0.132961i	$0.0424484\pi$
$191$	17.8858	+	15.0079i	1.29417	+	1.08594i	0.303047	+	0.952976i	$0.401996\pi$
$192$	12.7499	+	8.57779i	0.920143	+	0.619049i
$193$	1.84023	+	10.4365i	0.132463	+	0.751233i	0.976593	+	0.215095i	$0.0690062\pi$
$193$	1.84023	+	10.4365i	0.132463	+	0.751233i	−0.844130	+	0.536138i	$0.819883\pi$
$194$	−5.08963	+	4.27071i	−0.365414	+	0.306619i
$195$	1.86754	−	1.93851i	0.133737	−	0.138820i
$196$	−27.3162	−	2.84825i	−1.95115	−	0.203446i
$197$	3.65213	−	6.32568i	0.260204	−	0.450686i	−0.706092	−	0.708120i	$-0.749544\pi$
$197$	3.65213	−	6.32568i	0.260204	−	0.450686i	0.966296	+	0.257434i	$0.0828770\pi$
$198$	−23.2557	−	12.2942i	−1.65271	−	0.873712i
$199$	6.19397			0.439079			0.219539	−	0.975604i	$-0.429545\pi$
$199$	6.19397			0.439079			0.219539	+	0.975604i	$0.429545\pi$
$200$	−5.23767	−	4.39493i	−0.370360	−	0.310769i
$201$	6.72357	−	15.1500i	0.474244	−	1.06860i
$202$	−6.78980	−	2.47129i	−0.477729	−	0.173879i
$203$	−6.18815	−	4.01500i	−0.434323	−	0.281798i
$204$	−8.72195	−	11.9747i	−0.610659	−	0.838395i
$205$	4.96577	−	1.80739i	0.346825	−	0.126234i
$206$	−15.4963			−1.07968
$207$	−23.0497	+	14.4796i	−1.60206	+	1.00640i
$208$	−2.16849			−0.150358
$209$	−17.9045	−	15.0236i	−1.23848	−	1.03921i
$210$	−25.2794	−	12.8294i	−1.74445	−	0.885315i
$211$	4.53736	+	25.7326i	0.312365	+	1.77151i	0.586631	+	0.809855i	$0.300454\pi$
$211$	4.53736	+	25.7326i	0.312365	+	1.77151i	−0.274266	+	0.961654i	$0.588435\pi$
$212$	14.3169	+	5.21093i	0.983290	+	0.357888i
$213$	4.41350	+	2.96929i	0.302408	+	0.203453i
$214$	6.43389	−	36.4884i	0.439811	−	2.49429i
$215$	4.65589	+	8.06425i	0.317529	+	0.549977i
$216$	−18.1352	−	16.2119i	−1.23394	−	1.10308i
$217$	−6.22701	+	6.68318i	−0.422717	+	0.453684i
$218$	3.97473	−	1.44668i	0.269203	−	0.0979818i
$219$	−19.3470	−	13.0162i	−1.30735	−	0.879550i
$220$	6.23893	+	35.3827i	0.420629	+	2.38550i
$221$	−1.25250	−	0.455873i	−0.0842523	−	0.0306653i
$222$	−26.8971	+	27.9193i	−1.80522	+	1.87382i
$223$	11.5176	+	9.66439i	0.771273	+	0.647175i	0.941035	−	0.338310i	$-0.109855\pi$
$223$	11.5176	+	9.66439i	0.771273	+	0.647175i	−0.169761	+	0.985485i	$0.554300\pi$
$224$	−0.566095	−	1.84888i	−0.0378238	−	0.123534i
$225$	−2.93963	−	3.24917i	−0.195975	−	0.216611i
$226$	1.44290	−	2.49918i	0.0959804	−	0.166243i
$227$	−9.50428	−	7.97504i	−0.630821	−	0.529322i	0.270363	−	0.962758i	$-0.412856\pi$
$227$	−9.50428	−	7.97504i	−0.630821	−	0.529322i	−0.901184	+	0.433437i	$0.857301\pi$
$228$	−25.9557	−	35.6355i	−1.71896	−	2.36002i
$229$	−2.53686	−	14.3873i	−0.167641	−	0.950737i	−0.946300	−	0.323290i	$-0.895211\pi$
$229$	−2.53686	−	14.3873i	−0.167641	−	0.950737i	0.778659	−	0.627447i	$-0.215900\pi$
$230$	52.7449	+	19.1976i	3.47789	+	1.26585i
$231$	6.47534	+	15.1871i	0.426046	+	0.999238i
$232$	−2.26645	+	12.8537i	−0.148800	+	0.843886i
$233$	−3.87772	+	6.71641i	−0.254038	+	0.440006i	−0.964634	−	0.263594i	$-0.915092\pi$
$233$	−3.87772	+	6.71641i	−0.254038	+	0.440006i	0.710596	+	0.703600i	$0.248425\pi$
$234$	−4.42228	−	0.610758i	−0.289093	−	0.0399265i
$235$	8.46754	+	14.6662i	0.552361	+	0.956718i
$236$	3.00677	−	17.0522i	0.195724	−	1.11001i
$237$	17.1508	+	4.25446i	1.11406	+	0.276357i
$238$	−0.728880	+	14.0186i	−0.0472463	+	0.908688i
$239$	11.8099	−	9.90971i	0.763921	−	0.641006i	−0.175223	−	0.984529i	$-0.556065\pi$
$239$	11.8099	−	9.90971i	0.763921	−	0.641006i	0.939144	+	0.343523i	$0.111620\pi$
$240$	−1.07060	+	15.5772i	−0.0691069	+	1.00550i
$241$	1.45496	−	8.25146i	0.0937219	−	0.531524i	−0.901410	−	0.432967i	$-0.857466\pi$
$241$	1.45496	−	8.25146i	0.0937219	−	0.531524i	0.995131	−	0.0985561i	$-0.0314224\pi$
$242$	2.40937	−	4.17316i	0.154880	−	0.268261i
$243$	−10.0911	−	11.8815i	−0.647344	−	0.762198i
$244$	−17.1348			−1.09695
$245$	7.25020	+	16.2481i	0.463198	+	1.03805i
$246$	−7.27174	−	4.89224i	−0.463629	−	0.311918i
$247$	−3.72732	−	1.35663i	−0.237164	−	0.0863205i
$248$	15.1879	+	5.52794i	0.964432	+	0.351024i
$249$	−1.60503	+	1.66603i	−0.101715	+	0.105580i
$250$	3.80216	−	21.5631i	0.240469	−	1.36377i
$251$	−5.15077	+	8.92139i	−0.325114	+	0.563113i	−0.981535	−	0.191281i	$-0.938736\pi$
$251$	−5.15077	+	8.92139i	−0.325114	+	0.563113i	0.656422	+	0.754394i	$0.272069\pi$
$252$	4.95764	+	30.7444i	0.312302	+	1.93671i
$253$	−16.3447	−	28.3099i	−1.02758	−	1.77983i
$254$	−1.22997	+	0.447672i	−0.0771750	+	0.0280894i
$255$	−3.89310	+	8.77219i	−0.243795	+	0.549336i
$256$	−23.9401	+	20.0881i	−1.49626	+	1.25551i
$257$	−0.251706	−	1.42750i	−0.0157010	−	0.0890448i	0.975950	−	0.217993i	$-0.0699510\pi$
$257$	−0.251706	−	1.42750i	−0.0157010	−	0.0890448i	−0.991651	+	0.128948i	$0.958840\pi$
$258$	6.26463	−	14.1159i	0.390019	−	0.878816i
$259$	24.1491	−	2.97525i	1.50055	−	0.184873i
$260$	3.04869	+	5.28049i	0.189072	+	0.327482i
$261$	−2.56571	+	7.96099i	−0.158813	+	0.492773i
$262$	−14.2336	−	24.6533i	−0.879354	−	1.52309i
$263$	11.5948	−	4.22015i	0.714965	−	0.260226i	0.0411780	−	0.999152i	$-0.486889\pi$
$263$	11.5948	−	4.22015i	0.714965	−	0.260226i	0.673787	+	0.738926i	$0.264667\pi$
$264$	20.2676	−	21.0379i	1.24739	−	1.29479i
$265$	−1.71395	−	9.72030i	−0.105287	−	0.597113i
$266$	−2.16908	+	41.7179i	−0.132995	+	2.55789i
$267$	−25.4571	+	12.4539i	−1.55795	+	0.762164i
$268$	28.7617	+	24.1339i	1.75690	+	1.47422i
$269$	−1.92905	+	3.34120i	−0.117616	+	0.203717i	−0.918822	−	0.394671i	$-0.870859\pi$
$269$	−1.92905	+	3.34120i	−0.117616	+	0.203717i	0.801206	+	0.598388i	$0.204192\pi$
$270$	−6.57065	+	31.4656i	−0.399877	+	1.91493i
$271$	−7.34960	−	12.7299i	−0.446456	−	0.773285i	0.551696	−	0.834045i	$-0.313981\pi$
$271$	−7.34960	−	12.7299i	−0.446456	−	0.773285i	−0.998152	+	0.0607603i	$0.980647\pi$
$272$	7.26534	−	2.64437i	0.440526	−	0.160338i
$273$	1.91416	+	2.04609i	0.115850	+	0.123835i
$274$	12.9981	−	10.9067i	0.785245	−	0.658899i
$275$	4.03090	−	3.38233i	0.243073	−	0.203962i
$276$	−17.0664	−	59.2509i	−1.02728	−	3.56649i
$277$	5.54965	−	2.01991i	0.333446	−	0.121365i	−0.169871	−	0.985466i	$-0.554335\pi$
$277$	5.54965	−	2.01991i	0.333446	−	0.121365i	0.503317	+	0.864102i	$0.332113\pi$
$278$	38.5789			2.31381
$279$	9.15682	+	4.84079i	0.548205	+	0.289811i
$280$	21.4608	−	23.0330i	1.28253	−	1.37648i
$281$	−2.69676	+	15.2941i	−0.160875	+	0.912367i	0.792341	+	0.610078i	$0.208862\pi$
$281$	−2.69676	+	15.2941i	−0.160875	+	0.912367i	−0.953216	+	0.302289i	$0.902249\pi$
$282$	11.3933	−	25.6721i	0.678461	−	1.52875i
$283$	−16.5451	+	13.8830i	−0.983505	+	0.825259i	−0.984614	−	0.174741i	$-0.944091\pi$
$283$	−16.5451	+	13.8830i	−0.983505	+	0.825259i	0.00110955	+	0.999999i	$0.499647\pi$
$284$	−9.23046	+	7.74528i	−0.547727	+	0.459598i
$285$	−11.5855	+	26.1052i	−0.686265	+	1.54634i
$286$	0.930966	−	5.27977i	0.0550492	−	0.312199i
$287$	1.61041	+	5.25965i	0.0950596	+	0.310468i
$288$	−1.85657	+	1.16628i	−0.109400	+	0.0687238i
$289$	−12.2477			−0.720452
$290$	16.2074	−	5.89900i	0.951729	−	0.346401i
$291$	−1.30872	−	4.54358i	−0.0767183	−	0.266349i
$292$	40.4625	−	33.9521i	2.36789	−	1.98690i
$293$	−8.59601	+	7.21291i	−0.502184	+	0.421383i	−0.858369	−	0.513033i	$-0.828522\pi$
$293$	−8.59601	+	7.21291i	−0.502184	+	0.421383i	0.356185	+	0.934416i	$0.384077\pi$
$294$	14.7026	−	25.5848i	0.857475	−	1.49214i
$295$	−10.5410	+	3.83659i	−0.613718	+	0.223375i
$296$	−21.5261	−	37.2843i	−1.25118	−	2.16710i
$297$	14.7106	−	11.5782i	0.853598	−	0.671835i
$298$	2.31143	−	4.00352i	0.133898	−	0.231918i
$299$	−4.24977	−	3.56598i	−0.245771	−	0.206226i
$300$	8.91559	−	4.36159i	0.514742	−	0.251817i
$301$	−8.63450	+	4.40399i	−0.497684	+	0.253842i
$302$	4.15440	+	23.5608i	0.239059	+	1.35577i
$303$	3.56762	−	3.70320i	0.204954	−	0.212744i
$304$	21.6210	−	7.86939i	1.24005	−	0.451340i
$305$	5.55028	+	9.61336i	0.317808	+	0.550459i
$306$	15.5613	−	3.34646i	0.889578	−	0.191304i
$307$	−5.09131	−	8.81840i	−0.290576	−	0.503293i	0.683370	−	0.730072i	$-0.260514\pi$
$307$	−5.09131	−	8.81840i	−0.290576	−	0.503293i	−0.973946	+	0.226780i	$0.927180\pi$
$308$	−37.1179	+	4.57305i	−2.11499	+	0.260574i
$309$	4.47352	−	10.0800i	0.254490	−	0.573432i
$310$	−3.70879	−	21.0336i	−0.210645	−	1.19463i
$311$	7.23875	−	6.07403i	0.410472	−	0.344427i	−0.414053	−	0.910253i	$-0.635887\pi$
$311$	7.23875	−	6.07403i	0.410472	−	0.344427i	0.824525	+	0.565826i	$0.191443\pi$
$312$	2.01104	−	4.53140i	0.113853	−	0.256540i
$313$	23.5051	−	8.55515i	1.32859	−	0.483566i	0.422386	−	0.906416i	$-0.361193\pi$
$313$	23.5051	−	8.55515i	1.32859	−	0.483566i	0.906199	+	0.422850i	$0.138970\pi$
$314$	3.74471	+	6.48604i	0.211326	+	0.366028i
$315$	15.6430	−	12.7401i	0.881384	−	0.717823i
$316$	−20.0138	+	34.6650i	−1.12587	+	1.95006i
$317$	−0.794760	+	4.50731i	−0.0446382	+	0.253156i	−0.998958	−	0.0456301i	$-0.985470\pi$
$317$	−0.794760	+	4.50731i	−0.0446382	+	0.253156i	0.954320	+	0.298786i	$0.0965816\pi$
$318$	−11.3573	+	11.7890i	−0.636888	+	0.661093i
$319$	−9.43900	−	3.43551i	−0.528483	−	0.192352i
$320$	21.1905	+	7.71273i	1.18459	+	0.431155i
$321$	21.8776	+	14.7187i	1.22109	+	0.821516i
$322$	−22.8068	+	53.7912i	−1.27097	+	2.99767i
$323$	14.1424			0.786906
$324$	32.1895	−	14.5161i	1.78831	−	0.806448i
$325$	0.446501	−	0.773362i	0.0247674	−	0.0428984i
$326$	−3.44402	+	19.5320i	−0.190747	+	1.08178i
$327$	−0.206400	+	3.00311i	−0.0114139	+	0.166073i
$328$	7.45578	−	6.25614i	0.411676	−	0.345437i
$329$	−15.7033	+	8.00941i	−0.865752	+	0.441573i
$330$	−37.4672	−	9.29419i	−2.06250	−	0.511628i
$331$	−4.44554	+	25.2119i	−0.244349	+	1.38577i	0.577651	+	0.816284i	$0.303969\pi$
$331$	−4.44554	+	25.2119i	−0.244349	+	1.38577i	−0.822000	+	0.569488i	$0.807142\pi$
$332$	−2.62016	−	4.53825i	−0.143800	−	0.249069i
$333$	−10.3962	−	25.5558i	−0.569708	−	1.40045i
$334$	−24.3299	+	42.1406i	−1.33127	+	2.30583i
$335$	4.22372	−	23.9539i	0.230767	−	1.30874i
$336$	−16.1348	−	1.95482i	−0.880225	−	0.106644i
$337$	2.83251	+	1.03095i	0.154297	+	0.0561594i	0.418014	−	0.908441i	$-0.362726\pi$
$337$	2.83251	+	1.03095i	0.154297	+	0.0561594i	−0.263717	+	0.964600i	$0.584949\pi$
$338$	5.33617	+	30.2629i	0.290249	+	1.64609i
$339$	1.20912	+	1.66005i	0.0656705	+	0.0901613i
$340$	−16.6537	−	13.9741i	−0.903173	−	0.757852i
$341$	−6.21935	+	10.7722i	−0.336797	+	0.583349i
$342$	46.3088	−	9.95873i	2.50409	−	0.538507i
$343$	−17.2819	+	6.65847i	−0.933136	+	0.359524i
$344$	13.1379	+	11.0240i	0.708346	+	0.594373i
$345$	−27.7141	+	28.7674i	−1.49208	+	1.54878i
$346$	−21.8924	−	7.96816i	−1.17694	−	0.428371i
$347$	−4.00821	−	22.7317i	−0.215172	−	1.22030i	−0.880608	−	0.473845i	$-0.842866\pi$
$347$	−4.00821	−	22.7317i	−0.215172	−	1.22030i	0.665436	−	0.746454i	$-0.268245\pi$
$348$	−15.7202	−	10.5761i	−0.842690	−	0.566941i
$349$	9.45461	−	3.44120i	0.506094	−	0.184203i	−0.0763390	−	0.997082i	$-0.524323\pi$
$349$	9.45461	−	3.44120i	0.506094	−	0.184203i	0.582433	+	0.812879i	$0.302101\pi$
$350$	−9.16462	−	2.11184i	−0.489870	−	0.112882i
$351$	1.67392	−	2.70028i	0.0893473	−	0.144130i
$352$	−1.31651	−	2.28027i	−0.0701703	−	0.121539i
$353$	1.98637	−	11.2653i	0.105724	−	0.599589i	−0.885205	−	0.465201i	$-0.845982\pi$
$353$	1.98637	−	11.2653i	0.105724	−	0.599589i	0.990929	−	0.134388i	$-0.0429069\pi$
$354$	15.4359	+	10.3849i	0.820408	+	0.551950i
$355$	7.33533	+	2.66984i	0.389319	+	0.141701i
$356$	−11.1476	−	63.2211i	−0.590821	−	3.35071i
$357$	−8.90836	−	4.52104i	−0.471480	−	0.239279i
$358$	−30.9637	−	25.9816i	−1.63648	−	1.37317i
$359$	10.9462			0.577716			0.288858	−	0.957372i	$-0.406724\pi$
$359$	10.9462			0.577716			0.288858	+	0.957372i	$0.406724\pi$
$360$	−31.5582	−	16.6834i	−1.66326	−	0.879290i
$361$	23.0865			1.21508
$362$	−45.5052	+	16.5625i	−2.39170	+	0.870507i
$363$	2.01901	+	2.77197i	0.105970	+	0.145491i
$364$	−5.65390	+	2.88374i	−0.296345	+	0.151149i
$365$	−32.1551	−	11.7035i	−1.68307	−	0.612588i
$366$	7.46805	−	16.8275i	0.390361	−	0.879587i
$367$	−11.4852	−	9.63724i	−0.599524	−	0.503060i	0.291769	−	0.956489i	$-0.405756\pi$
$367$	−11.4852	−	9.63724i	−0.599524	−	0.503060i	−0.891292	+	0.453429i	$0.850201\pi$
$368$	32.1803			1.67751
$369$	5.28153	−	3.31781i	0.274945	−	0.172718i
$370$	−28.4456	+	49.2692i	−1.47882	+	2.56138i
$371$	10.1970	−	1.25630i	0.529401	−	0.0652240i
$372$	−16.2781	+	16.8968i	−0.843981	+	0.876056i
$373$	8.13285	−	6.82427i	0.421103	−	0.353347i	−0.407480	−	0.913214i	$-0.633592\pi$
$373$	8.13285	−	6.82427i	0.421103	−	0.353347i	0.828582	+	0.559867i	$0.189148\pi$
$374$	3.31930	+	18.8247i	0.171637	+	0.973401i
$375$	12.9287	+	8.69812i	0.667636	+	0.449169i
$376$	23.8935	+	20.0490i	1.23221	+	1.03395i
$377$	−1.70468			−0.0877957
$378$	−32.3536	−	8.53091i	−1.66409	−	0.438783i
$379$	4.75796			0.244400			0.122200	−	0.992505i	$-0.461005\pi$
$379$	4.75796			0.244400			0.122200	+	0.992505i	$0.461005\pi$
$380$	−49.5598	−	41.5856i	−2.54236	−	2.13330i
$381$	0.0638697	−	0.929303i	0.00327214	−	0.0476096i
$382$	−9.86760	−	55.9620i	−0.504870	−	2.86326i
$383$	−13.3480	+	11.2003i	−0.682050	+	0.572308i	−0.916604	−	0.399795i	$-0.869081\pi$
$383$	−13.3480	+	11.2003i	−0.682050	+	0.572308i	0.234555	+	0.972103i	$0.424637\pi$
$384$	−9.65095	−	33.5060i	−0.492498	−	1.70985i
$385$	14.5888	+	19.3434i	0.743515	+	0.985831i
$386$	12.8961	−	22.3368i	0.656396	−	1.13691i
$387$	7.37358	+	8.15002i	0.374820	+	0.414289i
$388$	10.7106			0.543749
$389$	16.3280	+	13.7008i	0.827864	+	0.694661i	0.954800	−	0.297250i	$-0.0960696\pi$
$389$	16.3280	+	13.7008i	0.827864	+	0.694661i	−0.126935	+	0.991911i	$0.540514\pi$
$390$	−6.51451	+	0.692558i	−0.329875	+	0.0350691i
$391$	18.5870	+	6.76513i	0.939987	+	0.342127i
$392$	22.7831	+	23.5536i	1.15072	+	1.18964i
$393$	20.1454	−	2.14166i	1.01620	−	0.108033i
$394$	−16.7051	+	6.08017i	−0.841593	+	0.306315i
$395$	25.9313			1.30475
$396$	15.9793	+	39.2801i	0.802989	+	1.97390i
$397$	27.5520			1.38280			0.691399	−	0.722474i	$-0.256995\pi$
$397$	27.5520			1.38280			0.691399	+	0.722474i	$0.256995\pi$
$398$	−11.5481	−	9.69001i	−0.578854	−	0.485716i
$399$	−26.5104	−	13.4542i	−1.32718	−	0.673551i
$400$	0.899499	+	5.10131i	0.0449749	+	0.255066i
$401$	−7.73240	−	2.81436i	−0.386138	−	0.140543i	0.141655	−	0.989916i	$-0.454758\pi$
$401$	−7.73240	−	2.81436i	−0.386138	−	0.140543i	−0.527792	+	0.849374i	$0.676980\pi$
$402$	−36.2365	+	17.7273i	−1.80731	+	0.884156i
$403$	−0.366564	+	2.07889i	−0.0182598	+	0.103557i
$404$	5.82402	+	10.0875i	0.289756	+	0.501872i
$405$	−18.5709	−	13.3576i	−0.922793	−	0.663747i
$406$	5.25608	+	17.1665i	0.260855	+	0.851961i
$407$	31.1347	−	11.3321i	1.54329	−	0.561711i
$408$	−1.21199	+	17.6345i	−0.0600025	+	0.873035i
$409$	−3.05378	−	17.3188i	−0.151000	−	0.856361i	−0.962352	−	0.271805i	$-0.912380\pi$
$409$	−3.05378	−	17.3188i	−0.151000	−	0.856361i	0.811353	−	0.584557i	$-0.198732\pi$
$410$	−12.0858	−	4.39886i	−0.596874	−	0.217244i
$411$	3.34225	+	11.6036i	0.164861	+	0.572362i
$412$	19.1366	+	16.0575i	0.942791	+	0.791096i
$413$	−3.41846	−	11.1648i	−0.168211	−	0.549383i
$414$	65.6264	+	9.06363i	3.22536	+	0.445453i
$415$	−1.69743	+	2.94004i	−0.0833236	+	0.144321i
$416$	−0.342304	−	0.287228i	−0.0167829	−	0.0140825i
$417$	−11.1371	+	25.0947i	−0.545384	+	1.22889i
$418$	9.87792	+	56.0205i	0.483145	+	2.74005i
$419$	−27.2312	−	9.91134i	−1.33033	−	0.484201i	−0.423576	−	0.905860i	$-0.639225\pi$
$419$	−27.2312	−	9.91134i	−1.33033	−	0.484201i	−0.906754	+	0.421660i	$0.861448\pi$
$420$	17.9238	+	42.0381i	0.874592	+	2.05125i
$421$	1.96282	−	11.1317i	0.0956621	−	0.542527i	−0.898880	−	0.438194i	$-0.855618\pi$
$421$	1.96282	−	11.1317i	0.0956621	−	0.542527i	0.994542	−	0.104333i	$-0.0332706\pi$
$422$	31.7974	−	55.0746i	1.54787	−	2.68099i
$423$	13.4101	+	14.8222i	0.652022	+	0.720680i
$424$	−9.08942	−	15.7433i	−0.441421	−	0.764564i
$425$	−0.552885	+	3.13557i	−0.0268189	+	0.152097i
$426$	−3.58334	−	12.4406i	−0.173614	−	0.602749i
$427$	−10.2932	+	5.24998i	−0.498121	+	0.254064i
$428$	−45.7550	+	38.3930i	−2.21165	+	1.85580i
$429$	3.16562	+	2.12975i	0.152838	+	0.102825i
$430$	3.93542	−	22.3189i	0.189783	−	1.07631i
$431$	14.3539	−	24.8616i	0.691402	−	1.19754i	−0.279977	−	0.960007i	$-0.590327\pi$
$431$	14.3539	−	24.8616i	0.691402	−	1.19754i	0.971379	−	0.237536i	$-0.0763399\pi$
$432$	2.63008	+	18.2403i	0.126540	+	0.877586i
$433$	6.39115			0.307139			0.153569	−	0.988138i	$-0.450923\pi$
$433$	6.39115			0.307139			0.153569	+	0.988138i	$0.450923\pi$
$434$	22.0651	−	2.71849i	1.05916	−	0.130492i
$435$	−0.841614	+	12.2455i	−0.0403523	+	0.587126i
$436$	−6.40752	−	2.33215i	−0.306864	−	0.111690i
$437$	55.3133	+	20.1324i	2.64599	+	0.963062i
$438$	15.7079	+	54.5344i	0.750552	+	2.60575i
$439$	−4.20771	+	23.8631i	−0.200823	+	1.13892i	0.703055	+	0.711135i	$0.251819\pi$
$439$	−4.20771	+	23.8631i	−0.200823	+	1.13892i	−0.903878	+	0.427789i	$0.859292\pi$
$440$	21.4345	−	37.1256i	1.02185	−	1.76989i
$441$	12.3980	+	16.9496i	0.590379	+	0.807126i
$442$	1.62200	+	2.80938i	0.0771505	+	0.133629i
$443$	−20.9303	+	7.61799i	−0.994427	+	0.361942i	−0.787433	−	0.616401i	$-0.788590\pi$
$443$	−20.9303	+	7.61799i	−0.994427	+	0.361942i	−0.206994	+	0.978342i	$0.566368\pi$
$444$	62.1459	−	6.60674i	2.94932	−	0.313542i
$445$	−31.8588	+	26.7327i	−1.51025	+	1.26725i
$446$	−6.35426	−	36.0368i	−0.300883	−	1.70639i
$447$	1.93693	+	2.65929i	0.0916139	+	0.125780i
$448$	−9.16277	+	21.6109i	−0.432900	+	1.02102i
$449$	0.443176	+	0.767604i	0.0209148	+	0.0362255i	0.876293	−	0.481778i	$-0.160009\pi$
$449$	0.443176	+	0.767604i	0.0209148	+	0.0362255i	−0.855379	+	0.518003i	$0.826675\pi$
$450$	0.397587	+	10.6566i	0.0187424	+	0.502358i
$451$	3.74518	+	6.48684i	0.176354	+	0.305453i
$452$	−4.37154	+	1.59111i	−0.205620	+	0.0748395i
$453$	−16.5251	−	4.09924i	−0.776416	−	0.192599i
$454$	5.24352	+	29.7375i	0.246091	+	1.39565i
$455$	3.44930	+	2.23798i	0.161706	+	0.104918i
$456$	−3.60677	+	52.4784i	−0.168902	+	2.45753i
$457$	−2.68851	−	2.25593i	−0.125763	−	0.105528i	0.577737	−	0.816223i	$-0.303936\pi$
$457$	−2.68851	−	2.25593i	−0.125763	−	0.105528i	−0.703500	+	0.710695i	$0.748380\pi$
$458$	−17.7781	+	30.7925i	−0.830715	+	1.43884i
$459$	−2.31547	+	11.0883i	−0.108077	+	0.517559i
$460$	−45.2425	−	78.3622i	−2.10944	−	3.65366i
$461$	−16.8870	+	6.14638i	−0.786508	+	0.286266i	−0.703884	−	0.710315i	$-0.748552\pi$
$461$	−16.8870	+	6.14638i	−0.786508	+	0.286266i	−0.0826244	+	0.996581i	$0.526330\pi$
$462$	11.6864	−	38.4452i	0.543702	−	1.78863i
$463$	21.3499	−	17.9147i	0.992212	−	0.832565i	0.00632577	−	0.999980i	$-0.497986\pi$
$463$	21.3499	−	17.9147i	0.992212	−	0.832565i	0.985887	+	0.167415i	$0.0535420\pi$
$464$	7.57489	−	6.35608i	0.351655	−	0.295074i
$465$	14.7526	+	3.65954i	0.684133	+	0.169707i
$466$	17.7370	−	6.45574i	0.821650	−	0.299056i
$467$	−18.8374			−0.871691			−0.435845	−	0.900022i	$-0.643551\pi$
$467$	−18.8374			−0.871691			−0.435845	+	0.900022i	$0.643551\pi$
$468$	4.82824	+	5.33666i	0.223186	+	0.246687i
$469$	24.6721	+	5.68527i	1.13925	+	0.262521i
$470$	7.15724	−	40.5907i	0.330139	−	1.87231i
$471$	−5.30006	+	0.563450i	−0.244214	+	0.0259624i
$472$	−15.8265	+	13.2800i	−0.728475	+	0.611263i
$473$	−10.1109	+	8.48403i	−0.464898	+	0.390096i
$474$	−25.3204	−	34.7632i	−1.16300	−	1.59673i
$475$	−1.64533	+	9.33115i	−0.0754931	+	0.428143i
$476$	15.4263	−	16.5564i	0.707064	−	0.758861i
$477$	−4.38981	−	10.7910i	−0.200996	−	0.494085i
$478$	−37.5216			−1.71620
$479$	7.39543	−	2.69172i	0.337906	−	0.122988i	−0.167494	−	0.985873i	$-0.553567\pi$
$479$	7.39543	−	2.69172i	0.337906	−	0.122988i	0.505399	+	0.862886i	$0.331345\pi$
$480$	−2.23228	+	2.31711i	−0.101889	+	0.105761i
$481$	4.30741	−	3.61435i	0.196401	−	0.164800i
$482$	−15.6215	+	13.1080i	−0.711538	+	0.597051i
$483$	−28.4061	−	30.3639i	−1.29252	−	1.38161i
$484$	−7.29965	+	2.65686i	−0.331802	+	0.120766i
$485$	−3.46936	−	6.00910i	−0.157535	−	0.272859i
$486$	0.226213	+	37.9388i	0.0102612	+	1.72094i
$487$	−7.08994	+	12.2801i	−0.321276	+	0.556466i	−0.980752	−	0.195260i	$-0.937445\pi$
$487$	−7.08994	+	12.2801i	−0.321276	+	0.556466i	0.659476	+	0.751726i	$0.270778\pi$
$488$	15.6616	+	13.1417i	0.708968	+	0.594895i
$489$	−11.7109	−	7.87882i	−0.529587	−	0.356293i
$490$	11.9016	−	41.6356i	0.537661	−	1.88090i
$491$	2.15381	+	12.2149i	0.0972002	+	0.551250i	0.994051	+	0.108916i	$0.0347381\pi$
$491$	2.15381	+	12.2149i	0.0972002	+	0.551250i	−0.896851	+	0.442333i	$0.854151\pi$
$492$	3.91054	+	13.5766i	0.176301	+	0.612079i
$493$	5.71140	−	2.07878i	0.257229	−	0.0936235i
$494$	4.82691	+	8.36045i	0.217173	+	0.376154i
$495$	16.8618	−	21.6886i	0.757882	−	0.974829i
$496$	−6.12248	−	10.6044i	−0.274907	−	0.476154i
$497$	−3.17179	+	7.48085i	−0.142274	+	0.335562i
$498$	5.59881	−	0.595210i	0.250889	−	0.0266720i
$499$	−6.25641	−	35.4818i	−0.280075	−	1.58839i	−0.722364	−	0.691513i	$-0.756945\pi$
$499$	−6.25641	−	35.4818i	−0.280075	−	1.58839i	0.442289	−	0.896873i	$-0.354167\pi$
$500$	−27.0393	+	22.6887i	−1.20923	+	1.01467i
$501$	−20.3879	−	27.9913i	−0.910865	−	1.25056i
$502$	23.5600	−	8.57515i	1.05154	−	0.382728i
$503$	−16.3462	−	28.3124i	−0.728841	−	1.26239i	−0.957373	−	0.288853i	$-0.906726\pi$
$503$	−16.3462	−	28.3124i	−0.728841	−	1.26239i	0.228532	−	0.973536i	$-0.426607\pi$
$504$	19.0482	−	31.9033i	0.848473	−	1.42109i
$505$	3.77301	−	6.53504i	0.167897	−	0.290806i
$506$	−13.8155	+	78.3515i	−0.614173	+	3.48315i
$507$	−21.2258	−	5.26532i	−0.942673	−	0.233841i
$508$	1.98278	+	0.721675i	0.0879719	+	0.0320191i
$509$	7.72478	+	2.81159i	0.342395	+	0.124622i	0.507494	−	0.861656i	$-0.330572\pi$
$509$	7.72478	+	2.81159i	0.342395	+	0.124622i	−0.165099	+	0.986277i	$0.552794\pi$
$510$	20.9818	−	10.2645i	0.929089	−	0.454519i
$511$	13.9038	−	32.7929i	0.615068	−	1.45067i
$512$	35.7983			1.58208
$513$	−6.89061	+	32.9978i	−0.304228	+	1.45689i
$514$	−1.76393	+	3.05522i	−0.0778036	+	0.134760i
$515$	2.81025	−	15.9377i	0.123834	−	0.702300i
$516$	−22.3633	+	10.9404i	−0.984491	+	0.481622i
$517$	−18.3884	+	15.4297i	−0.808719	+	0.678596i
$518$	−49.6784	−	32.2324i	−2.18274	−	1.41621i
$519$	11.5031	−	11.9402i	0.504929	−	0.524118i
$520$	1.26333	−	7.16469i	0.0554006	−	0.314193i
$521$	−2.83582	−	4.91179i	−0.124240	−	0.215189i	0.797196	−	0.603721i	$-0.206316\pi$
$521$	−2.83582	−	4.91179i	−0.124240	−	0.215189i	−0.921435	+	0.388531i	$0.872983\pi$
$522$	17.2379	−	10.8287i	0.754483	−	0.473959i
$523$	−3.45346	+	5.98157i	−0.151009	+	0.261556i	−0.931599	−	0.363488i	$-0.881586\pi$
$523$	−3.45346	+	5.98157i	−0.151009	+	0.261556i	0.780589	+	0.625044i	$0.214919\pi$
$524$	−7.96887	+	45.1937i	−0.348121	+	1.97430i
$525$	4.01937	−	5.35174i	0.175420	−	0.233569i
$526$	−28.2196	−	10.2711i	−1.23043	−	0.447840i
$527$	−1.30696	−	7.41214i	−0.0569321	−	0.322878i
$528$	−22.0077	+	2.33964i	−0.957761	+	0.101820i
$529$	45.4474	+	38.1349i	1.97597	+	1.65804i
$530$	−12.0112	+	20.8040i	−0.521733	+	0.903668i
$531$	−11.2112	+	7.04278i	−0.486525	+	0.305631i
$532$	45.9072	−	49.2702i	1.99033	−	2.13614i
$533$	0.973779	+	0.817097i	0.0421790	+	0.0353924i
$534$	66.9457	+	16.6067i	2.89702	+	0.718641i
$535$	36.3610	+	13.2343i	1.57202	+	0.572169i
$536$	−7.77917	−	44.1179i	−0.336009	−	1.90560i
$537$	25.8391	−	12.6408i	1.11504	−	0.545489i
$538$	8.82361	−	3.21153i	0.380413	−	0.138459i
$539$	−20.8961	+	14.1197i	−0.900061	+	0.608180i
$540$	40.7192	−	32.0486i	1.75228	−	1.37915i
$541$	9.42354	+	16.3220i	0.405150	+	0.701740i	0.994339	−	0.106255i	$-0.0338861\pi$
$541$	9.42354	+	16.3220i	0.405150	+	0.701740i	−0.589189	+	0.807995i	$0.700553\pi$
$542$	−6.21229	+	35.2316i	−0.266841	+	1.51333i
$543$	2.36299	−	34.3815i	0.101406	−	1.47545i
$544$	1.49712	+	0.544908i	0.0641886	+	0.0233627i
$545$	0.767077	+	4.35031i	0.0328580	+	0.186347i
$546$	−0.367823	−	6.80933i	−0.0157414	−	0.291412i
$547$	−4.28734	−	3.59751i	−0.183313	−	0.153818i	0.546513	−	0.837450i	$-0.315955\pi$
$547$	−4.28734	−	3.59751i	−0.183313	−	0.153818i	−0.729827	+	0.683632i	$0.760399\pi$
$548$	−27.3532			−1.16847
$549$	8.79003	+	9.71561i	0.375149	+	0.414652i
$550$	−12.8067			−0.546078
$551$	16.9966	−	6.18625i	0.724078	−	0.263543i
$552$	−29.8437	+	67.2458i	−1.27023	+	2.86217i
$553$	−1.40154	+	26.9559i	−0.0595997	+	1.14628i
$554$	−13.5068	−	4.91609i	−0.573851	−	0.208865i
$555$	−23.8368	−	32.7264i	−1.01182	−	1.38916i
$556$	−47.6415	−	39.9759i	−2.02045	−	1.69536i
$557$	−24.1009			−1.02119			−0.510593	−	0.859822i	$-0.670574\pi$
$557$	−24.1009			−1.02119			−0.510593	+	0.859822i	$0.670574\pi$
$558$	−9.49902	−	23.3504i	−0.402126	−	0.988502i
$559$	−1.11998	+	1.93985i	−0.0473699	+	0.0820471i
$560$	−23.6717	+	2.91644i	−1.00031	+	0.123242i
$561$	−13.2033	−	3.27523i	−0.557443	−	0.138280i
$562$	28.9543	−	24.2956i	1.22136	−	1.02485i
$563$	−1.12211	−	6.36380i	−0.0472913	−	0.268202i	0.951989	−	0.306132i	$-0.0990349\pi$
$563$	−1.12211	−	6.36380i	−0.0472913	−	0.268202i	−0.999280	+	0.0379296i	$0.987924\pi$
$564$	−40.6715	+	19.8969i	−1.71258	+	0.837811i
$565$	2.30870	+	1.93723i	0.0971276	+	0.0814997i
$566$	52.5659			2.20951
$567$	14.8891	−	18.5826i	0.625284	−	0.780397i
$568$	14.3771			0.603250
$569$	−25.9231	−	21.7521i	−1.08675	−	0.911894i	−0.0902890	−	0.995916i	$-0.528779\pi$
$569$	−25.9231	−	21.7521i	−1.08675	−	0.911894i	−0.996464	+	0.0840216i	$0.973224\pi$
$570$	62.4398	−	30.5461i	2.61531	−	1.27944i
$571$	−5.70890	−	32.3768i	−0.238910	−	1.35493i	−0.834221	−	0.551431i	$-0.814082\pi$
$571$	−5.70890	−	32.3768i	−0.238910	−	1.35493i	0.595311	−	0.803496i	$-0.297029\pi$
$572$	−6.62063	+	5.55537i	−0.276822	+	0.232282i
$573$	39.2507	+	9.73659i	1.63972	+	0.406752i
$574$	5.22588	−	12.3255i	0.218124	−	0.514458i
$575$	−6.62605	+	11.4766i	−0.276325	+	0.478609i
$576$	26.3658	+	3.64136i	1.09857	+	0.151723i
$577$	−35.4912			−1.47752			−0.738758	−	0.673970i	$-0.764588\pi$
$577$	−35.4912			−1.47752			−0.738758	+	0.673970i	$0.764588\pi$
$578$	22.8347	+	19.1606i	0.949800	+	0.796977i
$579$	10.8067	+	14.8369i	0.449111	+	0.616601i
$580$	−26.1273	−	9.50955i	−1.08488	−	0.394863i
$581$	−2.96445	−	1.92340i	−0.122986	−	0.0797961i
$582$	−4.66811	+	10.5185i	−0.193499	+	0.436005i
$583$	13.1467	−	4.78500i	0.544479	−	0.198174i
$584$	−63.0233			−2.60792
$585$	1.43013	−	4.43748i	0.0591288	−	0.183467i
$586$	27.3106			1.12819
$587$	−16.8088	−	14.1043i	−0.693775	−	0.582146i	0.226220	−	0.974076i	$-0.427363\pi$
$587$	−16.8088	−	14.1043i	−0.693775	−	0.582146i	−0.919995	+	0.391930i	$0.871808\pi$
$588$	−44.6678	+	16.3599i	−1.84207	+	0.674670i
$589$	−3.88939	−	22.0578i	−0.160259	−	0.908876i
$590$	25.6548	+	9.33757i	1.05619	+	0.384421i
$591$	0.867463	−	12.6216i	0.0356827	−	0.519182i
$592$	−5.66384	+	32.1212i	−0.232782	+	1.32017i
$593$	6.03316	+	10.4497i	0.247752	+	0.429119i	0.962902	−	0.269852i	$-0.0869748\pi$
$593$	6.03316	+	10.4497i	0.247752	+	0.429119i	−0.715150	+	0.698971i	$0.753642\pi$
$594$	−45.5399	−	1.42719i	−1.86853	−	0.0585584i
$595$	−14.2857	−	3.29190i	−0.585656	−	0.134955i
$596$	−7.00292	+	2.54885i	−0.286851	+	0.104405i
$597$	9.63689	−	4.71446i	0.394411	−	0.192950i
$598$	2.34461	+	13.2969i	0.0958781	+	0.543752i
$599$	39.3957	+	14.3388i	1.60966	+	0.585869i	0.981373	−	0.192110i	$-0.0615332\pi$
$599$	39.3957	+	14.3388i	1.60966	+	0.585869i	0.628289	+	0.777980i	$0.283755\pi$
$600$	−11.4942	−	2.85127i	−0.469248	−	0.116402i
$601$	4.41327	+	3.70317i	0.180021	+	0.151055i	0.728345	−	0.685210i	$-0.240290\pi$
$601$	4.41327	+	3.70317i	0.180021	+	0.151055i	−0.548324	+	0.836266i	$0.684734\pi$
$602$	22.9880	+	5.29720i	0.936921	+	0.215898i
$603$	−1.07034	−	28.6887i	−0.0435877	−	1.16829i
$604$	19.2837	−	33.4003i	0.784641	−	1.35904i
$605$	3.85509	+	3.23481i	0.156732	+	0.131514i
$606$	−12.4449	+	1.32302i	−0.505540	+	0.0537440i
$607$	−5.07219	−	28.7658i	−0.205874	−	1.16757i	−0.896059	−	0.443936i	$-0.853582\pi$
$607$	−5.07219	−	28.7658i	−0.205874	−	1.16757i	0.690185	−	0.723633i	$-0.257529\pi$
$608$	4.45529	+	1.62159i	0.180686	+	0.0657643i
$609$	−12.6838	−	1.53671i	−0.513974	−	0.0622707i
$610$	4.69140	−	26.6063i	0.189949	−	1.07726i
$611$	−2.03687	+	3.52796i	−0.0824028	+	0.142726i
$612$	−22.6844	−	11.9922i	−0.916963	−	0.484756i
$613$	−5.96690	−	10.3350i	−0.241001	−	0.417426i	0.719999	−	0.693975i	$-0.244142\pi$
$613$	−5.96690	−	10.3350i	−0.241001	−	0.417426i	−0.961000	+	0.276550i	$0.910809\pi$
$614$	−4.30346	+	24.4061i	−0.173673	+	0.984950i
$615$	6.35033	−	6.59167i	0.256070	−	0.265802i
$616$	37.4339	+	24.2879i	1.50825	+	0.978587i
$617$	−0.736782	+	0.618233i	−0.0296617	+	0.0248891i	−0.657498	−	0.753456i	$-0.728385\pi$
$617$	−0.736782	+	0.618233i	−0.0296617	+	0.0248891i	0.627836	+	0.778345i	$0.283941\pi$
$618$	−24.1099	+	11.7948i	−0.969844	+	0.474457i
$619$	0.624219	−	3.54012i	0.0250895	−	0.142290i	−0.969690	−	0.244339i	$-0.921429\pi$
$619$	0.624219	−	3.54012i	0.0250895	−	0.142290i	0.994779	+	0.102050i	$0.0325401\pi$
$620$	−17.2153	+	29.8177i	−0.691381	+	1.19751i
$621$	−24.8409	+	40.0720i	−0.996831	+	1.60804i
$622$	−22.9984			−0.922152
$623$	−26.0670	−	34.5624i	−1.04435	−	1.38471i
$624$	−3.37385	+	1.65052i	−0.135062	+	0.0660736i
$625$	28.3501	+	10.3186i	1.13400	+	0.412743i
$626$	−57.2071	−	20.8217i	−2.28645	−	0.832201i
$627$	−39.2917	−	9.74677i	−1.56916	−	0.389248i
$628$	2.09653	−	11.8900i	0.0836606	−	0.474463i
$629$	−10.0241	+	17.3622i	−0.399687	+	0.692278i
$630$	−49.0960	−	0.719582i	−1.95603	−	0.0286688i
$631$	−3.22485	−	5.58561i	−0.128379	−	0.222360i	0.794669	−	0.607042i	$-0.207644\pi$
$631$	−3.22485	−	5.58561i	−0.128379	−	0.222360i	−0.923049	+	0.384683i	$0.874311\pi$
$632$	44.8796	−	16.3348i	1.78521	−	0.649764i
$633$	26.6455	+	36.5826i	1.05906	+	1.45403i
$634$	8.53311	−	7.16013i	0.338893	−	0.284365i
$635$	−0.237369	−	1.34619i	−0.00941971	−	0.0534219i
$636$	26.2412	−	2.78971i	1.04053	−	0.110619i
$637$	−2.51283	+	3.46462i	−0.0995618	+	0.137273i
$638$	12.2236	+	21.1718i	0.483936	+	0.838201i
$639$	9.12679	+	1.26050i	0.361050	+	0.0498645i
$640$	−25.5843	−	44.3133i	−1.01131	−	1.75164i
$641$	−4.60968	+	1.67779i	−0.182071	+	0.0662686i	−0.431447	−	0.902138i	$-0.641997\pi$
$641$	−4.60968	+	1.67779i	−0.182071	+	0.0662686i	0.249376	+	0.968407i	$0.419775\pi$
$642$	−17.7625	−	61.6675i	−0.701030	−	2.43382i
$643$	8.27088	+	46.9065i	0.326172	+	1.84981i	0.501311	+	0.865267i	$0.332851\pi$
$643$	8.27088	+	46.9065i	0.326172	+	1.84981i	−0.175140	+	0.984544i	$0.556038\pi$
$644$	83.9036	−	42.7946i	3.30626	−	1.68634i
$645$	13.3819	+	9.00299i	0.526911	+	0.354492i
$646$	−26.3673	−	22.1248i	−1.03741	−	0.870488i
$647$	−9.63930	+	16.6958i	−0.378960	+	0.656378i	−0.990911	−	0.134518i	$-0.957052\pi$
$647$	−9.63930	+	16.6958i	−0.378960	+	0.656378i	0.611951	+	0.790895i	$0.290385\pi$
$648$	−40.5551	−	11.4199i	−1.59315	−	0.448616i
$649$	−7.94997	−	13.7698i	−0.312064	−	0.540510i
$650$	−2.04233	+	0.743347i	−0.0801067	+	0.0291565i
$651$	−4.60148	+	15.1376i	−0.180346	+	0.593290i
$652$	24.4924	−	20.5516i	0.959197	−	0.804862i
$653$	18.3936	−	15.4340i	0.719795	−	0.603980i	−0.207533	−	0.978228i	$-0.566544\pi$
$653$	18.3936	−	15.4340i	0.719795	−	0.603980i	0.927329	+	0.374248i	$0.122099\pi$
$654$	5.08297	−	5.27614i	0.198760	−	0.206313i
$655$	27.9368	−	10.1682i	1.09158	−	0.397303i
$656$	−7.37369			−0.287894
$657$	−40.0081	−	5.52549i	−1.56086	−	0.215570i
$658$	41.8076	+	9.63387i	1.62983	+	0.375567i
$659$	1.89295	−	10.7354i	0.0737387	−	0.418193i	−0.925485	−	0.378785i	$-0.876342\pi$
$659$	1.89295	−	10.7354i	0.0737387	−	0.418193i	0.999223	−	0.0394075i	$-0.0125471\pi$
$660$	36.6380	+	50.3016i	1.42613	+	1.95799i
$661$	1.32958	−	1.11565i	0.0517148	−	0.0433939i	−0.616564	−	0.787305i	$-0.711476\pi$
$661$	1.32958	−	1.11565i	0.0517148	−	0.0433939i	0.668279	+	0.743911i	$0.267031\pi$
$662$	47.7305	−	40.0507i	1.85510	−	1.55661i
$663$	−2.29569	+	0.244054i	−0.0891570	+	0.00947829i
$664$	−1.08575	+	6.15760i	−0.0421353	+	0.238961i
$665$	−42.5128	−	9.79638i	−1.64858	−	0.379887i
$666$	−20.5975	+	63.9107i	−0.798135	+	2.47649i
$667$	25.2974			0.979520
$668$	73.7118	−	26.8289i	2.85200	−	1.03804i
$669$	25.2755	+	6.26989i	0.977209	+	0.242408i
$670$	−45.3489	+	38.0523i	−1.75198	+	1.47009i
$671$	−12.0531	+	10.1138i	−0.465306	+	0.390438i
$672$	−2.28801	−	2.44571i	−0.0882620	−	0.0943453i
$673$	9.44702	−	3.43844i	0.364156	−	0.132542i	−0.153460	−	0.988155i	$-0.549042\pi$
$673$	9.44702	−	3.43844i	0.364156	−	0.132542i	0.517616	+	0.855613i	$0.326819\pi$
$674$	−3.66812	−	6.35338i	−0.141291	−	0.244723i
$675$	−7.04668	−	2.81776i	−0.271227	−	0.108456i
$676$	24.7692	−	42.9014i	0.952660	−	1.65006i
$677$	−0.130533	−	0.109530i	−0.00501680	−	0.00420959i	0.640276	−	0.768145i	$-0.278820\pi$
$677$	−0.130533	−	0.109530i	−0.00501680	−	0.00420959i	−0.645293	+	0.763936i	$0.723265\pi$
$678$	0.342721	−	4.98659i	0.0131621	−	0.191509i
$679$	6.43403	−	3.28165i	0.246915	−	0.125938i
$680$	4.50432	+	25.5453i	0.172733	+	0.979616i
$681$	−20.8573	−	5.17390i	−0.799255	−	0.198264i
$682$	28.4478	−	10.3542i	1.08932	−	0.396481i
$683$	2.45760	+	4.25669i	0.0940376	+	0.162878i	0.909207	−	0.416345i	$-0.136689\pi$
$683$	2.45760	+	4.25669i	0.0940376	+	0.162878i	−0.815169	+	0.579223i	$0.803356\pi$
$684$	−67.5066	−	35.6877i	−2.58118	−	1.36455i
$685$	8.86018	+	15.3463i	0.338530	+	0.586352i
$686$	42.6373	+	14.6222i	1.62790	+	0.558277i
$687$	−14.8977	−	20.4535i	−0.568381	−	0.780351i
$688$	−2.25625	−	12.7958i	−0.0860187	−	0.487836i
$689$	1.81881	−	1.52616i	0.0692912	−	0.0581422i
$690$	96.6751	−	10.2775i	3.68036	−	0.391259i
$691$	−13.9385	+	5.07319i	−0.530244	+	0.192993i	−0.593247	−	0.805020i	$-0.702154\pi$
$691$	−13.9385	+	5.07319i	−0.530244	+	0.192993i	0.0630031	+	0.998013i	$0.479932\pi$
$692$	18.7784	+	32.5251i	0.713847	+	1.23642i
$693$	21.6341	+	18.7003i	0.821812	+	0.710364i
$694$	−28.0891	+	48.6517i	−1.06625	+	1.84679i
$695$	−6.99626	+	39.6778i	−0.265383	+	1.50506i
$696$	6.25716	+	21.7235i	0.237177	+	0.823427i
$697$	−4.25897	−	1.55014i	−0.161320	−	0.0587157i
$698$	−23.0108	−	8.37525i	−0.870972	−	0.317008i
$699$	−0.921045	+	13.4012i	−0.0348371	+	0.506880i
$700$	9.12918	+	12.1044i	0.345051	+	0.457505i
$701$	−45.2847			−1.71038			−0.855189	−	0.518316i	$-0.826559\pi$
$701$	−45.2847			−1.71038			−0.855189	+	0.518316i	$0.826559\pi$
$702$	−7.34527	+	2.41571i	−0.277229	+	0.0911751i
$703$	−29.8308	+	51.6684i	−1.12509	+	1.94871i
$704$	−5.55045	+	31.4782i	−0.209190	+	1.18638i
$705$	24.3372	+	16.3735i	0.916593	+	0.616660i
$706$	−21.3271	+	17.8956i	−0.802656	+	0.673508i
$707$	6.58931	+	4.27529i	0.247817	+	0.160789i
$708$	−8.30100	−	28.8193i	−0.311971	−	1.08309i
$709$	−6.82513	+	38.7072i	−0.256323	+	1.45368i	0.536330	+	0.844008i	$0.319810\pi$
$709$	−6.82513	+	38.7072i	−0.256323	+	1.45368i	−0.792653	+	0.609673i	$0.791301\pi$
$710$	−9.49931	−	16.4533i	−0.356503	−	0.617481i
$711$	29.9223	−	6.43481i	1.12217	−	0.241324i
$712$	−38.2986	+	66.3352i	−1.43530	+	2.48602i
$713$	5.43978	−	30.8506i	0.203722	−	1.15536i
$714$	9.53601	+	22.3655i	0.356876	+	0.837010i
$715$	5.26133	+	1.91497i	0.196763	+	0.0716157i
$716$	11.3149	+	64.1699i	0.422857	+	2.39814i
$717$	10.8318	−	24.4070i	0.404523	−	0.911496i
$718$	−20.4081	−	17.1245i	−0.761625	−	0.639079i
$719$	7.63163	−	13.2184i	0.284612	−	0.492962i	−0.687903	−	0.725803i	$-0.741469\pi$
$719$	7.63163	−	13.2184i	0.284612	−	0.492962i	0.972515	+	0.232840i	$0.0748020\pi$
$720$	10.1907	+	25.0507i	0.379785	+	0.933583i
$721$	16.4155	+	3.78269i	0.611346	+	0.140875i
$722$	−43.0427	−	36.1171i	−1.60188	−	1.34414i
$723$	−4.01680	−	13.9455i	−0.149386	−	0.518637i
$724$	73.3572	+	26.6998i	2.72630	+	0.992292i
$725$	0.707110	+	4.01022i	0.0262614	+	0.148936i
$726$	0.572281	−	8.32668i	0.0212393	−	0.309032i
$727$	−21.4105	+	7.79278i	−0.794071	+	0.289018i	−0.707027	−	0.707186i	$-0.749964\pi$
$727$	−21.4105	+	7.79278i	−0.794071	+	0.289018i	−0.0870436	+	0.996205i	$0.527742\pi$
$728$	7.37948	+	1.70048i	0.273502	+	0.0630240i
$729$	−24.7437	−	10.8051i	−0.916432	−	0.400190i
$730$	41.6410	+	72.1244i	1.54120	+	2.66944i
$731$	1.38682	−	7.86507i	0.0512936	−	0.290900i
$732$	−26.6593	+	13.0420i	−0.985354	+	0.482045i
$733$	−25.1348	−	9.14831i	−0.928375	−	0.337901i	−0.166809	−	0.985989i	$-0.553346\pi$
$733$	−25.1348	−	9.14831i	−0.928375	−	0.337901i	−0.761565	+	0.648088i	$0.775569\pi$
$734$	6.33641	+	35.9356i	0.233881	+	1.32641i
$735$	23.6473	+	19.7612i	0.872242	+	0.728904i
$736$	5.07978	+	4.26244i	0.187243	+	0.157116i
$737$	34.4768			1.26997
$738$	−15.0374	−	2.07681i	−0.553535	−	0.0764484i
$739$	−40.9019			−1.50460			−0.752300	−	0.658820i	$-0.771056\pi$
$739$	−40.9019			−1.50460			−0.752300	+	0.658820i	$0.771056\pi$
$740$	86.1812	−	31.3674i	3.16809	−	1.15309i
$741$	−6.83174	+	0.726283i	−0.250970	+	0.0266807i
$742$	−20.9768	−	13.6102i	−0.770081	−	0.499645i
$743$	41.0686	+	14.9477i	1.50666	+	0.548379i	0.957775	−	0.287519i	$-0.0928303\pi$
$743$	41.0686	+	14.9477i	1.50666	+	0.548379i	0.548885	+	0.835898i	$0.315053\pi$
$744$	27.8376	−	2.95942i	1.02058	−	0.108497i
$745$	3.69838	+	3.10331i	0.135498	+	0.113697i
$746$	−25.8390			−0.946035
$747$	−1.22911	+	3.81374i	−0.0449708	+	0.139537i
$748$	15.4074	−	26.6863i	0.563349	−	0.975749i
$749$	−15.7224	+	37.0823i	−0.574485	+	1.35496i
$750$	−10.4969	−	36.4429i	−0.383292	−	1.33071i
$751$	19.9179	−	16.7131i	0.726814	−	0.609869i	−0.202447	−	0.979293i	$-0.564889\pi$
$751$	19.9179	−	16.7131i	0.726814	−	0.609869i	0.929261	+	0.369424i	$0.120445\pi$
$752$	−4.10337	−	23.2714i	−0.149635	−	0.848620i
$753$	−1.22342	+	17.8008i	−0.0445840	+	0.648697i
$754$	3.17823	+	2.66685i	0.115744	+	0.0971211i
$755$	−24.9853			−0.909307
$756$	31.1140	+	44.0602i	1.13161	+	1.60245i
$757$	12.7481			0.463337			0.231669	−	0.972795i	$-0.425582\pi$
$757$	12.7481			0.463337			0.231669	+	0.972795i	$0.425582\pi$
$758$	−8.87080	−	7.44349i	−0.322202	−	0.270360i
$759$	−46.9777	−	31.6054i	−1.70518	−	1.14720i
$760$	13.4044	+	76.0202i	0.486229	+	2.75754i
$761$	3.36934	−	2.82721i	0.122139	−	0.102486i	−0.579673	−	0.814850i	$-0.696820\pi$
$761$	3.36934	−	2.82721i	0.122139	−	0.102486i	0.701811	+	0.712363i	$0.252375\pi$
$762$	−1.57291	+	1.63268i	−0.0569804	+	0.0591459i
$763$	−4.56365	+	0.562257i	−0.165215	+	0.0203551i
$764$	−45.8029	+	79.3330i	−1.65709	+	2.87017i
$765$	0.619753	+	16.6114i	0.0224072	+	0.600586i
$766$	42.4081			1.53227
$767$	−2.06706	−	1.73447i	−0.0746373	−	0.0626281i
$768$	−21.9574	+	49.4758i	−0.792319	+	1.78531i
$769$	36.3969	+	13.2474i	1.31251	+	0.477713i	0.901050	−	0.433716i	$-0.142798\pi$
$769$	36.3969	+	13.2474i	1.31251	+	0.477713i	0.411457	+	0.911429i	$0.365020\pi$
$770$	3.06178	−	58.8872i	0.110339	−	2.12215i
$771$	−1.47814	−	2.02939i	−0.0532338	−	0.0730866i
$772$	−39.0713	+	14.2208i	−1.40621	+	0.511817i
$773$	8.12596			0.292270			0.146135	−	0.989265i	$-0.453317\pi$
$773$	8.12596			0.292270			0.146135	+	0.989265i	$0.453317\pi$
$774$	−0.997283	−	26.7304i	−0.0358466	−	0.960805i
$775$	5.04257			0.181134
$776$	−9.78973	−	8.21456i	−0.351431	−	0.294885i
$777$	35.3078	−	23.0098i	1.26666	−	0.825472i
$778$	−9.00820	−	51.0880i	−0.322960	−	1.83160i
$779$	−12.6743	−	4.61307i	−0.454104	−	0.165280i
$780$	8.76249	+	5.89518i	0.313747	+	0.211081i
$781$	−1.92135	+	10.8965i	−0.0687512	+	0.389907i
$782$	−24.0704	−	41.6911i	−0.860754	−	1.49087i
$783$	2.06755	+	14.3390i	0.0738881	+	0.512433i
$784$	−1.75225	−	24.7646i	−0.0625804	−	0.884450i
$785$	−7.34989	+	2.67514i	−0.262329	+	0.0954799i
$786$	−40.9099	−	27.5231i	−1.45921	−	0.981718i
$787$	−0.614588	−	3.48550i	−0.0219077	−	0.124245i	0.971893	−	0.235425i	$-0.0756481\pi$
$787$	−0.614588	−	3.48550i	−0.0219077	−	0.124245i	−0.993800	+	0.111180i	$0.964537\pi$
$788$	26.9297	+	9.80162i	0.959332	+	0.349168i
$789$	14.8276	−	15.3911i	0.527877	−	0.547939i
$790$	−48.3467	−	40.5677i	−1.72010	−	1.44333i
$791$	−2.13855	+	2.29521i	−0.0760380	+	0.0816082i
$792$	15.5207	−	48.1583i	0.551503	−	1.71123i
$793$	−1.33512	+	2.31249i	−0.0474115	+	0.0821191i
$794$	−51.3683	−	43.1032i	−1.82299	−	1.52967i
$795$	−10.0651	−	13.8188i	−0.356973	−	0.490102i
$796$	4.21996	+	23.9326i	0.149573	+	0.848269i
$797$	36.7547	+	13.3776i	1.30192	+	0.473859i	0.897621	−	0.440768i	$-0.145294\pi$
$797$	36.7547	+	13.3776i	1.30192	+	0.473859i	0.404297	+	0.914628i	$0.367516\pi$
$798$	28.3782	+	66.5577i	1.00458	+	2.35612i
$799$	2.52218	−	14.3040i	0.0892282	−	0.506038i
$800$	−0.533705	+	0.924404i	−0.0188693	+	0.0326826i
$801$	−30.1284	+	38.7527i	−1.06453	+	1.36926i
$802$	10.0135	+	17.3439i	0.353589	+	0.612435i
$803$	8.42239	−	47.7657i	0.297220	−	1.68562i
$804$	63.1182	+	15.6572i	2.22601	+	0.552187i
$805$	−51.1874	−	33.2115i	−1.80412	−	1.17055i
$806$	3.93569	−	3.30244i	0.138629	−	0.116323i
$807$	−0.458192	+	6.66668i	−0.0161291	+	0.234678i
$808$	2.41338	−	13.6870i	0.0849024	−	0.481506i
$809$	7.03190	−	12.1796i	0.247229	−	0.428212i	−0.715527	−	0.698585i	$-0.753813\pi$
$809$	7.03190	−	12.1796i	0.247229	−	0.428212i	0.962756	+	0.270372i	$0.0871468\pi$
$810$	13.7267	+	53.9569i	0.482306	+	1.89585i
$811$	32.7098			1.14860			0.574299	−	0.818646i	$-0.305275\pi$
$811$	32.7098			1.14860			0.574299	+	0.818646i	$0.305275\pi$
$812$	11.2974	−	26.6456i	0.396461	−	0.935076i
$813$	−21.1241	−	14.2117i	−0.740853	−	0.498427i
$814$	−75.7761	−	27.5803i	−2.65595	−	0.966688i
$815$	−19.4638	−	7.08425i	−0.681788	−	0.248150i
$816$	9.29106	−	9.64417i	0.325252	−	0.337613i
$817$	4.12706	−	23.4057i	0.144387	−	0.818862i
$818$	−21.4006	+	37.0669i	−0.748253	+	1.29601i
$819$	4.53551	+	1.72648i	0.158484	+	0.0603279i
$820$	10.3667	+	17.9557i	0.362021	+	0.627039i
$821$	−7.28033	+	2.64982i	−0.254085	+	0.0924794i	−0.465923	−	0.884825i	$-0.654277\pi$
$821$	−7.28033	+	2.64982i	−0.254085	+	0.0924794i	0.211837	+	0.977305i	$0.432055\pi$
$822$	11.9216	−	26.8626i	0.415814	−	0.936939i
$823$	−38.0898	+	31.9611i	−1.32773	+	1.11409i	−0.343123	+	0.939290i	$0.611485\pi$
$823$	−38.0898	+	31.9611i	−1.32773	+	1.11409i	−0.984603	+	0.174804i	$0.944071\pi$
$824$	−5.17586	−	29.3538i	−0.180310	−	1.02259i
$825$	3.69707	−	8.33047i	0.128715	−	0.290030i
$826$	−11.0931	+	26.1637i	−0.385978	+	0.910351i
$827$	14.3373	+	24.8329i	0.498555	+	0.863523i	0.999999	−	0.00166744i	$-0.000530764\pi$
$827$	14.3373	+	24.8329i	0.498555	+	0.863523i	−0.501443	+	0.865190i	$0.667197\pi$
$828$	−71.6509	−	79.1957i	−2.49004	−	2.75224i
$829$	−6.32412	−	10.9537i	−0.219646	−	0.380437i	0.735054	−	0.678009i	$-0.237157\pi$
$829$	−6.32412	−	10.9537i	−0.219646	−	0.380437i	−0.954700	+	0.297571i	$0.903823\pi$
$830$	7.76418	−	2.82593i	0.269499	−	0.0980895i
$831$	7.09700	−	7.36672i	0.246192	−	0.255549i
$832$	0.941959	+	5.34211i	0.0326565	+	0.185204i
$833$	4.19408	−	14.6722i	0.145316	−	0.508361i
$834$	60.0229	−	29.3638i	2.07842	−	1.01679i
$835$	−38.9287	−	32.6651i	−1.34718	−	1.13042i
$836$	45.8508	−	79.4159i	1.58578	−	2.74666i
$837$	17.9311	+	0.561950i	0.619791	+	0.0194238i
$838$	35.2646	+	61.0800i	1.21819	+	2.10997i
$839$	46.3085	−	16.8549i	1.59875	−	0.581897i	0.619578	−	0.784935i	$-0.287304\pi$
$839$	46.3085	−	16.8549i	1.59875	−	0.581897i	0.979171	+	0.203038i	$0.0650816\pi$
$840$	15.8586	−	52.1705i	0.547173	−	1.80005i
$841$	−16.2606	+	13.6442i	−0.560709	+	0.470491i
$842$	−21.0743	+	17.6834i	−0.726267	+	0.609411i
$843$	7.44513	+	25.8479i	0.256424	+	0.890248i
$844$	−96.3360	+	35.0634i	−3.31602	+	1.20693i
$845$	−32.0927			−1.10402
$846$	−1.81373	−	48.6138i	−0.0623573	−	1.67138i
$847$	−3.57097	+	3.83257i	−0.122700	+	0.131689i
$848$	−2.39156	+	13.5632i	−0.0821267	+	0.465763i
$849$	−15.1749	+	34.1930i	−0.520800	+	1.17350i
$850$	5.93618	−	4.98104i	0.203609	−	0.170848i
$851$	−63.9218	+	53.6367i	−2.19121	+	1.83864i
$852$	−8.46600	+	19.0761i	−0.290040	+	0.653538i
$853$	2.96955	−	16.8411i	0.101675	−	0.576630i	−0.890821	−	0.454355i	$-0.849870\pi$
$853$	2.96955	−	16.8411i	0.101675	−	0.576630i	0.992496	−	0.122275i	$-0.0390190\pi$
$854$	27.4039	+	6.31478i	0.937743	+	0.216087i
$855$	1.84432	+	49.4339i	0.0630745	+	1.69060i
$856$	71.2668			2.43585
$857$	−12.6420	+	4.60131i	−0.431843	+	0.157178i	−0.548790	−	0.835960i	$-0.684911\pi$
$857$	−12.6420	+	4.60131i	−0.431843	+	0.157178i	0.116947	+	0.993138i	$0.462689\pi$
$858$	−2.57018	−	8.92312i	−0.0877446	−	0.304630i
$859$	−38.5090	+	32.3129i	−1.31391	+	1.10250i	−0.326353	+	0.945248i	$0.605820\pi$
$859$	−38.5090	+	32.3129i	−1.31391	+	1.10250i	−0.987558	+	0.157254i	$0.949736\pi$
$860$	−27.9870	+	23.4839i	−0.954350	+	0.800795i
$861$	6.50888	+	6.95749i	0.221822	+	0.237111i
$862$	−65.6558	+	23.8967i	−2.23624	+	0.813926i
$863$	−5.56310	−	9.63557i	−0.189370	−	0.327999i	0.755670	−	0.654952i	$-0.227311\pi$
$863$	−5.56310	−	9.63557i	−0.189370	−	0.327999i	−0.945040	+	0.326954i	$0.893978\pi$
$864$	−2.00085	+	3.22766i	−0.0680703	+	0.109807i
$865$	12.1653	−	21.0709i	0.413633	−	0.716433i
$866$	−11.9157	−	9.99848i	−0.404913	−	0.339762i
$867$	−19.0556	+	9.32217i	−0.647161	+	0.316597i
$868$	−30.0653	−	19.5070i	−1.02048	−	0.662111i
$869$	6.38259	+	36.1975i	0.216514	+	1.22791i
$870$	20.7263	−	21.5140i	0.702687	−	0.729392i
$871$	5.49815	−	2.00116i	0.186298	−	0.0678068i
$872$	4.06796	+	7.04591i	0.137758	+	0.238605i
$873$	−5.49445	−	6.07302i	−0.185959	−	0.205540i
$874$	−71.6311	−	124.069i	−2.42296	−	4.19668i
$875$	−9.29130	+	21.9141i	−0.314103	+	0.740830i
$876$	37.1114	−	83.6219i	1.25388	−	2.82532i
$877$	4.16868	+	23.6418i	0.140766	+	0.798326i	0.970669	+	0.240418i	$0.0772845\pi$
$877$	4.16868	+	23.6418i	0.140766	+	0.798326i	−0.829903	+	0.557908i	$0.811604\pi$
$878$	45.1770	−	37.9080i	1.52465	−	1.27933i
$879$	−7.88409	+	17.7649i	−0.265924	+	0.599197i
$880$	−30.5193	+	11.1081i	−1.02880	+	0.374454i
$881$	18.4848	+	32.0165i	0.622767	+	1.07866i	0.988968	+	0.148129i	$0.0473251\pi$
$881$	18.4848	+	32.0165i	0.622767	+	1.07866i	−0.366201	+	0.930536i	$0.619342\pi$
$882$	3.40156	−	50.9968i	0.114537	−	1.71715i
$883$	−23.9003	+	41.3965i	−0.804309	+	1.39310i	0.112448	+	0.993658i	$0.464131\pi$
$883$	−23.9003	+	41.3965i	−0.804309	+	1.39310i	−0.916757	+	0.399446i	$0.869203\pi$
$884$	0.908097	−	5.15007i	0.0305426	−	0.173216i
$885$	−13.4800	+	13.9923i	−0.453124	+	0.470345i
$886$	50.9404	+	18.5408i	1.71138	+	0.622890i
$887$	0.00265206		0.000965270i	8.90474e−5		3.24106e-5i	0.342065	−	0.939676i	$-0.388874\pi$
$887$	0.00265206		0.000965270i	8.90474e−5		3.24106e-5i	−0.341976	+	0.939709i	$0.611096\pi$
$888$	−61.8698	−	41.6244i	−2.07621	−	1.39682i
$889$	1.41220	−	0.173989i	0.0473638	−	0.00583539i
$890$	101.219			3.39288
$891$	14.0750	−	29.2108i	0.471529	−	0.978597i
$892$	−29.4949	+	51.0866i	−0.987561	+	1.71051i
$893$	7.50576	−	42.5673i	0.251171	−	1.42446i
$894$	0.549018	−	7.98820i	0.0183619	−	0.267165i
$895$	32.3369	−	27.1339i	1.08090	−	0.906986i
$896$	47.4469	−	24.2001i	1.58509	−	0.808467i
$897$	−9.32621	−	2.31348i	−0.311393	−	0.0772447i
$898$	0.374597	−	2.12445i	0.0125005	−	0.0708937i
$899$	−4.81298	−	8.33632i	−0.160522	−	0.278032i
$900$	10.5516	−	13.5720i	0.351718	−	0.452399i
$901$	−4.23269	+	7.33123i	−0.141011	+	0.244239i
$902$	3.16563	−	17.9532i	0.105404	−	0.597776i
$903$	−10.0820	+	13.4240i	−0.335507	+	0.446722i
$904$	5.21599	+	1.89846i	0.173481	+	0.0631420i
$905$	−8.78196	−	49.8050i	−0.291922	−	1.65557i
$906$	24.3966	+	33.4949i	0.810522	+	1.11280i
$907$	14.4949	+	12.1626i	0.481294	+	0.403854i	0.850894	−	0.525337i	$-0.176061\pi$
$907$	14.4949	+	12.1626i	0.481294	+	0.403854i	−0.369600	+	0.929191i	$0.620505\pi$
$908$	24.3391	−	42.1566i	0.807722	−	1.39902i
$909$	2.73203	−	8.47708i	0.0906159	−	0.281167i
$910$	−2.92976	−	9.56869i	−0.0971206	−	0.317199i
$911$	−17.4724	−	14.6610i	−0.578885	−	0.485742i	0.305696	−	0.952129i	$-0.401111\pi$
$911$	−17.4724	−	14.6610i	−0.578885	−	0.485742i	−0.884581	+	0.466387i	$0.845555\pi$
$912$	27.6493	−	28.7001i	0.915560	−	0.950355i
$913$	−4.52178	−	1.64579i	−0.149649	−	0.0544678i
$914$	1.48325	+	8.41196i	0.0490617	+	0.278243i
$915$	15.9525	+	10.7324i	0.527373	+	0.354803i
$916$	53.8620	−	19.6042i	1.77965	−	0.647740i
$917$	9.05997	+	29.5901i	0.299186	+	0.977152i
$918$	21.6639	−	17.0508i	0.715014	−	0.562761i
$919$	−9.55283	−	16.5460i	−0.315119	−	0.545802i	0.664344	−	0.747427i	$-0.268711\pi$
$919$	−9.55283	−	16.5460i	−0.315119	−	0.545802i	−0.979463	+	0.201625i	$0.935378\pi$
$920$	−18.7477	+	106.324i	−0.618094	+	3.50539i
$921$	−14.6333	−	9.84493i	−0.482184	−	0.324401i
$922$	41.1000	+	14.9592i	1.35356	+	0.492654i
$923$	0.326069	+	1.84923i	0.0107327	+	0.0608681i
$924$	−54.2692	+	35.3668i	−1.78532	+	1.16348i
$925$	−10.2894	−	8.63381i	−0.338313	−	0.283878i
$926$	−67.8311			−2.22907
$927$	−0.712151	−	19.0880i	−0.0233901	−	0.626931i
$928$	2.03762			0.0668882
$929$	31.4659	−	11.4526i	1.03236	−	0.375749i	0.230382	−	0.973100i	$-0.426003\pi$
$929$	31.4659	−	11.4526i	1.03236	−	0.375749i	0.801979	+	0.597352i	$0.203780\pi$
$930$	−21.7797	−	29.9022i	−0.714186	−	0.980532i
$931$	12.4812	−	43.6630i	0.409054	−	1.43100i
$932$	−28.5931	−	10.4071i	−0.936599	−	0.340894i
$933$	6.63924	−	14.9600i	0.217359	−	0.489767i
$934$	35.1207	+	29.4697i	1.14918	+	0.964279i
$935$	−19.9629			−0.652855
$936$	−0.320142	−	8.58086i	−0.0104642	−	0.280474i
$937$	−0.156340	+	0.270788i	−0.00510739	+	0.00884627i	−0.868568	−	0.495570i	$-0.834959\pi$
$937$	−0.156340	+	0.270788i	−0.00510739	+	0.00884627i	0.863460	+	0.504417i	$0.168292\pi$
$938$	−37.1047	−	49.1973i	−1.21151	−	1.60635i
$939$	30.0587	−	31.2011i	0.980930	−	1.01821i
$940$	−50.8992	+	42.7095i	−1.66015	+	1.39303i
$941$	−0.364115	−	2.06500i	−0.0118698	−	0.0673170i	0.978297	−	0.207205i	$-0.0664368\pi$
$941$	−0.364115	−	2.06500i	−0.0118698	−	0.0673170i	−0.990167	+	0.139888i	$0.955326\pi$
$942$	10.7630	+	7.24106i	0.350677	+	0.235927i
$943$	−14.4508	−	12.1257i	−0.470584	−	0.394867i
$944$	15.6523			0.509438
$945$	14.6412	−	31.7282i	0.476279	−	1.03212i
$946$	32.1235			1.04442
$947$	16.4991	+	13.8444i	0.536148	+	0.449881i	0.870218	−	0.492667i	$-0.163978\pi$
$947$	16.4991	+	13.8444i	0.536148	+	0.449881i	−0.334070	+	0.942548i	$0.608422\pi$
$948$	−4.75374	+	69.1668i	−0.154394	+	2.24643i
$949$	−1.42935	−	8.10625i	−0.0463987	−	0.263140i
$950$	17.6655	−	14.8231i	0.573144	−	0.480925i
$951$	2.19415	+	7.61762i	0.0711502	+	0.247018i
$952$	−26.7980	+	3.30161i	−0.868528	+	0.107006i
$953$	24.0435	−	41.6445i	0.778844	−	1.34900i	−0.153764	−	0.988108i	$-0.549140\pi$
$953$	24.0435	−	41.6445i	0.778844	−	1.34900i	0.932608	−	0.360890i	$-0.117527\pi$
$954$	−8.69730	+	26.9864i	−0.281586	+	0.873716i
$955$	59.3455			1.92038
$956$	46.3359	+	38.8804i	1.49861	+	1.25748i
$957$	−17.3006	+	1.83922i	−0.559248	+	0.0594537i
$958$	−17.9991	−	6.55114i	−0.581525	−	0.211658i
$959$	−16.4315	+	8.38081i	−0.530601	+	0.270630i
$960$	38.8398	−	4.12906i	1.25355	−	0.133265i
$961$	17.9293	−	6.52572i	0.578364	−	0.210507i
$962$	−13.6852			−0.441228
$963$	45.2411	+	6.24823i	1.45788	+	0.201346i
$964$	32.8738			1.05879
$965$	20.6343	+	17.3142i	0.664242	+	0.557365i
$966$	5.45848	+	101.050i	0.175624	+	3.25124i
$967$	6.05338	+	34.3304i	0.194663	+	1.10399i	0.912897	+	0.408189i	$0.133840\pi$
$967$	6.05338	+	34.3304i	0.194663	+	1.10399i	−0.718234	+	0.695802i	$0.755049\pi$
$968$	8.70973	+	3.17008i	0.279941	+	0.101890i
$969$	22.0035	−	10.7643i	0.706854	−	0.345800i
$970$	−2.93249	+	16.6310i	−0.0941567	+	0.533989i
$971$	27.4357	+	47.5200i	0.880453	+	1.52499i	0.850839	+	0.525427i	$0.176094\pi$
$971$	27.4357	+	47.5200i	0.880453	+	1.52499i	0.0296139	+	0.999561i	$0.490572\pi$
$972$	39.0333	−	47.0854i	1.25199	−	1.51027i
$973$	−40.8673	−	9.41719i	−1.31014	−	0.301901i
$974$	32.4299	−	11.8035i	1.03912	−	0.378210i
$975$	0.106054	−	1.54308i	0.00339644	−	0.0494182i
$976$	−2.68967	−	15.2539i	−0.0860941	−	0.488264i
$977$	12.0554	+	4.38780i	0.385686	+	0.140378i	0.527583	−	0.849503i	$-0.323098\pi$
$977$	12.0554	+	4.38780i	0.385686	+	0.140378i	−0.141898	+	0.989881i	$0.545320\pi$
$978$	9.50816	+	33.0103i	0.304038	+	1.05555i
$979$	−45.1576	−	37.8917i	−1.44324	−	1.21103i
$980$	−57.8408	+	39.0836i	−1.84766	+	1.24848i
$981$	1.96465	+	4.82949i	0.0627265	+	0.154194i
$982$	15.0937	−	26.1430i	0.481659	−	0.834258i
$983$	−22.8196	−	19.1479i	−0.727833	−	0.610725i	0.201707	−	0.979446i	$-0.435351\pi$
$983$	−22.8196	−	19.1479i	−0.727833	−	0.610725i	−0.929540	+	0.368721i	$0.879796\pi$
$984$	6.83829	−	15.4085i	0.217997	−	0.491204i
$985$	−3.22390	−	18.2836i	−0.102722	−	0.582565i
$986$	−13.9005	−	5.05937i	−0.442682	−	0.161123i
$987$	−18.3358	+	24.4138i	−0.583634	+	0.777100i
$988$	2.70241	−	15.3261i	0.0859751	−	0.487589i
$989$	16.6204	−	28.7873i	0.528497	−	0.915384i
$990$	−65.3676	+	14.0573i	−2.07752	+	0.446771i
$991$	27.8463	+	48.2312i	0.884567	+	1.53211i	0.846209	+	0.532850i	$0.178879\pi$
$991$	27.8463	+	48.2312i	0.884567	+	1.53211i	0.0383573	+	0.999264i	$0.487788\pi$
$992$	0.438156	−	2.48491i	0.0139115	−	0.0788958i
$993$	12.2731	+	42.6096i	0.389476	+	1.35218i
$994$	17.6168	−	8.98535i	0.558770	−	0.284998i
$995$	12.0603	−	10.1198i	0.382336	−	0.320818i
$996$	−7.53080	−	5.06654i	−0.238623	−	0.160539i
$997$	−7.48486	+	42.4487i	−0.237048	+	1.34437i	0.601210	+	0.799091i	$0.294686\pi$
$997$	−7.48486	+	42.4487i	−0.237048	+	1.34437i	−0.838258	+	0.545274i	$0.816426\pi$
$998$	−43.8442	+	75.9405i	−1.38787	+	2.40385i
$999$	−35.6264	−	31.8481i	−1.12717	−	1.00763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.88.3	yes	132
3.2	odd	2		567.2.w.a.424.20		132
7.2	even	3		189.2.u.a.142.3	yes	132
21.2	odd	6		567.2.u.a.100.20		132
27.4	even	9		189.2.u.a.4.3	✓	132
27.23	odd	18		567.2.u.a.550.20		132
189.23	odd	18		567.2.w.a.226.20		132
189.58	even	9	inner	189.2.w.a.58.3	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.4.3	✓	132	27.4	even	9
189.2.u.a.142.3	yes	132	7.2	even	3
189.2.w.a.58.3	yes	132	189.58	even	9	inner
189.2.w.a.88.3	yes	132	1.1	even	1	trivial
567.2.u.a.100.20		132	21.2	odd	6
567.2.u.a.550.20		132	27.23	odd	18
567.2.w.a.226.20		132	189.23	odd	18
567.2.w.a.424.20		132	3.2	odd	2

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.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.86441 - 1.56443i) q^{2} +(1.55585 - 0.761137i) q^{3} +(0.681303 + 3.86386i) q^{4} +(1.94710 - 1.63381i) q^{5} +(-4.09149 - 1.01494i) q^{6} +(1.59312 + 2.11233i) q^{7} +(2.34068 - 4.05418i) q^{8} +(1.84134 - 2.36843i) q^{9} +O(q^{10})\)	\(q+(-1.86441 - 1.56443i) q^{2} +(1.55585 - 0.761137i) q^{3} +(0.681303 + 3.86386i) q^{4} +(1.94710 - 1.63381i) q^{5} +(-4.09149 - 1.01494i) q^{6} +(1.59312 + 2.11233i) q^{7} +(2.34068 - 4.05418i) q^{8} +(1.84134 - 2.36843i) q^{9} -6.18617 q^{10} +(2.75988 + 2.31581i) q^{11} +(4.00093 + 5.49302i) q^{12} +(0.574547 + 0.209118i) q^{13} +(0.334352 - 6.43059i) q^{14} +(1.78584 - 4.02398i) q^{15} +(-3.33276 + 1.21302i) q^{16} -2.17998 q^{17} +(-7.13826 + 1.53509i) q^{18} -6.48741 q^{19} +(7.63938 + 6.41020i) q^{20} +(4.08644 + 2.07389i) q^{21} +(-1.52263 - 8.63526i) q^{22} +(-8.52625 - 3.10330i) q^{23} +(0.555964 - 8.08927i) q^{24} +(0.253619 - 1.43835i) q^{25} +(-0.744042 - 1.28872i) q^{26} +(1.06215 - 5.08644i) q^{27} +(-7.07636 + 7.59475i) q^{28} +(-2.61993 + 0.953577i) q^{29} +(-9.62476 + 4.70853i) q^{30} +(0.599528 + 3.40009i) q^{31} +(-0.686760 - 0.249960i) q^{32} +(6.05661 + 1.50241i) q^{33} +(4.06438 + 3.41042i) q^{34} +(6.55313 + 1.51006i) q^{35} +(10.4058 + 5.50106i) q^{36} +(4.59825 - 7.96441i) q^{37} +(12.0952 + 10.1491i) q^{38} +(1.05308 - 0.111953i) q^{39} +(-2.06622 - 11.7181i) q^{40} +(1.95368 + 0.711080i) q^{41} +(-4.37436 - 10.2595i) q^{42} +(-0.636164 + 3.60787i) q^{43} +(-7.06766 + 12.2415i) q^{44} +(-0.284293 - 7.61997i) q^{45} +(11.0415 + 19.1245i) q^{46} +(-1.15697 + 6.56152i) q^{47} +(-4.26199 + 4.42397i) q^{48} +(-1.92391 + 6.73042i) q^{49} +(-2.72304 + 2.28490i) q^{50} +(-3.39172 + 1.65926i) q^{51} +(-0.416562 + 2.36244i) q^{52} +(1.94162 - 3.36298i) q^{53} +(-9.93765 + 7.82155i) q^{54} +9.15736 q^{55} +(12.2928 - 1.51451i) q^{56} +(-10.0934 + 4.93781i) q^{57} +(6.37644 + 2.32083i) q^{58} +(-4.14711 - 1.50942i) q^{59} +(16.7648 + 4.15870i) q^{60} +(-0.758369 + 4.30092i) q^{61} +(4.20143 - 7.27709i) q^{62} +(7.93640 + 0.116321i) q^{63} +(4.43600 + 7.68339i) q^{64} +(1.46036 - 0.531527i) q^{65} +(-8.94160 - 12.2762i) q^{66} +(7.33069 - 6.15118i) q^{67} +(-1.48523 - 8.42313i) q^{68} +(-15.6276 + 1.66137i) q^{69} +(-9.85535 - 13.0673i) q^{70} +(1.53557 + 2.65969i) q^{71} +(-5.29205 - 13.0089i) q^{72} +(-6.73130 - 11.6590i) q^{73} +(-21.0328 + 7.65530i) q^{74} +(-0.700186 - 2.43089i) q^{75} +(-4.41989 - 25.0664i) q^{76} +(-0.494939 + 9.51916i) q^{77} +(-2.13851 - 1.43874i) q^{78} +(7.81528 + 6.55780i) q^{79} +(-4.50736 + 7.80698i) q^{80} +(-2.21893 - 8.72218i) q^{81} +(-2.53002 - 4.38213i) q^{82} +(-1.25509 + 0.456814i) q^{83} +(-5.22911 + 17.2024i) q^{84} +(-4.24464 + 3.56168i) q^{85} +(6.83031 - 5.73131i) q^{86} +(-3.35042 + 3.47775i) q^{87} +(15.8487 - 5.76846i) q^{88} -16.3622 q^{89} +(-11.3909 + 14.6515i) q^{90} +(0.473598 + 1.54679i) q^{91} +(6.18176 - 35.0585i) q^{92} +(3.52071 + 4.83371i) q^{93} +(12.4221 - 10.4234i) q^{94} +(-12.6316 + 10.5992i) q^{95} +(-1.25875 + 0.133818i) q^{96} +(0.474040 - 2.68841i) q^{97} +(14.1162 - 9.53847i) q^{98} +(10.5667 - 2.27238i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Introduction

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