LMFDB - Embedded newform 189.2.w.a.25.9

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			25.9
Character	$\chi$	$=$	189.25
Dual form			189.2.w.a.121.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.606828 + 0.220867i) q^{2} +(1.44289 + 0.958162i) q^{3} +(-1.21263 + 1.01752i) q^{4} +(1.46866 + 0.534550i) q^{5} +(-1.08721 - 0.262753i) q^{6} +(1.88474 - 1.85681i) q^{7} +(1.15690 - 2.00380i) q^{8} +(1.16385 + 2.76504i) q^{9} +O(q^{10})$	\(q+(-0.606828 + 0.220867i) q^{2} +(1.44289 + 0.958162i) q^{3} +(-1.21263 + 1.01752i) q^{4} +(1.46866 + 0.534550i) q^{5} +(-1.08721 - 0.262753i) q^{6} +(1.88474 - 1.85681i) q^{7} +(1.15690 - 2.00380i) q^{8} +(1.16385 + 2.76504i) q^{9} -1.00929 q^{10} +(-3.65044 + 1.32865i) q^{11} +(-2.72464 + 0.306267i) q^{12} +(0.906129 + 5.13891i) q^{13} +(-0.733606 + 1.54304i) q^{14} +(1.60693 + 2.17851i) q^{15} +(0.290300 - 1.64637i) q^{16} -3.65214 q^{17} +(-1.31696 - 1.42085i) q^{18} +4.99947 q^{19} +(-2.32486 + 0.846180i) q^{20} +(4.49860 - 0.873281i) q^{21} +(1.92173 - 1.61252i) q^{22} +(-1.04704 - 5.93806i) q^{23} +(3.58924 - 1.78277i) q^{24} +(-1.95899 - 1.64379i) q^{25} +(-1.68488 - 2.91830i) q^{26} +(-0.970052 + 5.10480i) q^{27} +(-0.396158 + 4.16939i) q^{28} +(0.306444 - 1.73793i) q^{29} +(-1.45629 - 0.967064i) q^{30} +(7.06629 - 5.92932i) q^{31} +(0.991039 + 5.62046i) q^{32} +(-6.54023 - 1.58062i) q^{33} +(2.21622 - 0.806639i) q^{34} +(3.76061 - 1.71954i) q^{35} +(-4.22480 - 2.16873i) q^{36} +(-1.10414 + 1.91243i) q^{37} +(-3.03382 + 1.10422i) q^{38} +(-3.61647 + 8.28309i) q^{39} +(2.77022 - 2.32449i) q^{40} +(-0.827927 - 4.69541i) q^{41} +(-2.53700 + 1.52353i) q^{42} +(-0.458222 - 0.384494i) q^{43} +(3.07471 - 5.32555i) q^{44} +(0.231253 + 4.68305i) q^{45} +(1.94690 + 3.37213i) q^{46} +(-6.08797 - 5.10841i) q^{47} +(1.99636 - 2.09738i) q^{48} +(0.104506 - 6.99922i) q^{49} +(1.55183 + 0.564821i) q^{50} +(-5.26963 - 3.49934i) q^{51} +(-6.32774 - 5.30960i) q^{52} +(4.86390 - 8.42452i) q^{53} +(-0.538829 - 3.31199i) q^{54} -6.07149 q^{55} +(-1.54023 - 5.92478i) q^{56} +(7.21367 + 4.79030i) q^{57} +(0.197893 + 1.12231i) q^{58} +(1.36778 + 7.75709i) q^{59} +(-4.16529 - 1.00665i) q^{60} +(-4.58353 - 3.84604i) q^{61} +(-2.97843 + 5.15879i) q^{62} +(7.32772 + 3.05034i) q^{63} +(-0.170996 - 0.296174i) q^{64} +(-1.41621 + 8.03170i) q^{65} +(4.31790 - 0.485361i) q^{66} +(1.70114 + 0.619166i) q^{67} +(4.42870 - 3.71612i) q^{68} +(4.17887 - 9.57119i) q^{69} +(-1.90225 + 1.87406i) q^{70} +(7.39028 + 12.8003i) q^{71} +(6.88705 + 0.866737i) q^{72} +(-3.32613 - 5.76102i) q^{73} +(0.247631 - 1.40438i) q^{74} +(-1.25159 - 4.24884i) q^{75} +(-6.06251 + 5.08705i) q^{76} +(-4.41308 + 9.28233i) q^{77} +(0.365110 - 5.82518i) q^{78} +(-5.09437 + 1.85420i) q^{79} +(1.30642 - 2.26279i) q^{80} +(-6.29090 + 6.43619i) q^{81} +(1.53947 + 2.66644i) q^{82} +(0.752128 - 4.26553i) q^{83} +(-4.56656 + 5.63637i) q^{84} +(-5.36377 - 1.95225i) q^{85} +(0.362984 + 0.132115i) q^{86} +(2.10739 - 2.21402i) q^{87} +(-1.56082 + 8.85185i) q^{88} -7.32849 q^{89} +(-1.17466 - 2.79073i) q^{90} +(11.2498 + 8.00302i) q^{91} +(7.31176 + 6.13530i) q^{92} +(15.8771 - 1.78469i) q^{93} +(4.82263 + 1.75530i) q^{94} +(7.34254 + 2.67246i) q^{95} +(-3.95535 + 9.05927i) q^{96} +(-4.44995 - 3.73395i) q^{97} +(1.48248 + 4.27041i) q^{98} +(-7.92233 - 8.54725i) 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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.606828	+	0.220867i	−0.429092	+	0.156177i	−0.547533	−	0.836784i	$-0.684433\pi$
$2$	−0.606828	+	0.220867i	−0.429092	+	0.156177i	0.118440	+	0.992961i	$0.462211\pi$
$3$	1.44289	+	0.958162i	0.833052	+	0.553195i
$3$	1.44289	+	0.958162i	0.833052	+	0.553195i
$4$	−1.21263	+	1.01752i	−0.606315	+	0.508759i
$5$	1.46866	+	0.534550i	0.656806	+	0.239058i	0.648857	−	0.760911i	$-0.275247\pi$
$5$	1.46866	+	0.534550i	0.656806	+	0.239058i	0.00794934	+	0.999968i	$0.497470\pi$
$6$	−1.08721	−	0.262753i	−0.443852	−	0.107268i
$7$	1.88474	−	1.85681i	0.712366	−	0.701809i
$7$	1.88474	−	1.85681i	0.712366	−	0.701809i
$8$	1.15690	−	2.00380i	0.409024	−	0.708451i
$9$	1.16385	+	2.76504i	0.387950	+	0.921680i
$10$	−1.00929			−0.319166
$11$	−3.65044	+	1.32865i	−1.10065	+	0.400603i	−0.827555	−	0.561385i	$-0.810269\pi$
$11$	−3.65044	+	1.32865i	−1.10065	+	0.400603i	−0.273093	+	0.961988i	$0.588047\pi$
$12$	−2.72464	+	0.306267i	−0.786535	+	0.0884118i
$13$	0.906129	+	5.13891i	0.251315	+	1.42528i	0.805357	+	0.592790i	$0.201973\pi$
$13$	0.906129	+	5.13891i	0.251315	+	1.42528i	−0.554042	+	0.832489i	$0.686915\pi$
$14$	−0.733606	+	1.54304i	−0.196064	+	0.412396i
$15$	1.60693	+	2.17851i	0.414908	+	0.562490i
$16$	0.290300	−	1.64637i	0.0725750	−	0.411593i
$17$	−3.65214			−0.885774			−0.442887	−	0.896577i	$-0.646046\pi$
$17$	−3.65214			−0.885774			−0.442887	+	0.896577i	$0.646046\pi$
$18$	−1.31696	−	1.42085i	−0.310412	−	0.334897i
$19$	4.99947			1.14696			0.573478	−	0.819221i	$-0.305594\pi$
$19$	4.99947			1.14696			0.573478	+	0.819221i	$0.305594\pi$
$20$	−2.32486	+	0.846180i	−0.519855	+	0.189212i
$21$	4.49860	−	0.873281i	0.981674	−	0.190566i
$22$	1.92173	−	1.61252i	0.409715	−	0.343791i
$23$	−1.04704	−	5.93806i	−0.218323	−	1.23817i	−0.875046	−	0.484040i	$-0.839169\pi$
$23$	−1.04704	−	5.93806i	−0.218323	−	1.23817i	0.656723	−	0.754132i	$-0.271942\pi$
$24$	3.58924	−	1.78277i	0.732650	−	0.363906i
$25$	−1.95899	−	1.64379i	−0.391799	−	0.328758i
$26$	−1.68488	−	2.91830i	−0.330433	−	0.572326i
$27$	−0.970052	+	5.10480i	−0.186687	+	0.982420i
$28$	−0.396158	+	4.16939i	−0.0748668	+	0.787940i
$29$	0.306444	−	1.73793i	0.0569053	−	0.322726i	−0.943045	−	0.332664i	$-0.892052\pi$
$29$	0.306444	−	1.73793i	0.0569053	−	0.322726i	0.999951	+	0.00993839i	$0.00316354\pi$
$30$	−1.45629	−	0.967064i	−0.265882	−	0.176561i
$31$	7.06629	−	5.92932i	1.26914	−	1.06494i	0.274498	−	0.961588i	$-0.411488\pi$
$31$	7.06629	−	5.92932i	1.26914	−	1.06494i	0.994645	−	0.103350i	$-0.0329561\pi$
$32$	0.991039	+	5.62046i	0.175193	+	0.993566i
$33$	−6.54023	−	1.58062i	−1.13851	−	0.275150i
$34$	2.21622	−	0.806639i	0.380079	−	0.138337i
$35$	3.76061	−	1.71954i	0.635659	−	0.290656i
$36$	−4.22480	−	2.16873i	−0.704133	−	0.361456i
$37$	−1.10414	+	1.91243i	−0.181520	+	0.314401i	−0.942398	−	0.334493i	$-0.891435\pi$
$37$	−1.10414	+	1.91243i	−0.181520	+	0.314401i	0.760879	+	0.648894i	$0.224768\pi$
$38$	−3.03382	+	1.10422i	−0.492150	+	0.179128i
$39$	−3.61647	+	8.28309i	−0.579099	+	1.32636i
$40$	2.77022	−	2.32449i	0.438010	−	0.367534i
$41$	−0.827927	−	4.69541i	−0.129300	−	0.733300i	−0.978660	−	0.205485i	$-0.934123\pi$
$41$	−0.827927	−	4.69541i	−0.129300	−	0.733300i	0.849360	−	0.527814i	$-0.176988\pi$
$42$	−2.53700	+	1.52353i	−0.391467	+	0.235085i
$43$	−0.458222	−	0.384494i	−0.0698781	−	0.0586347i	0.607180	−	0.794565i	$-0.292301\pi$
$43$	−0.458222	−	0.384494i	−0.0698781	−	0.0586347i	−0.677058	+	0.735930i	$0.736745\pi$
$44$	3.07471	−	5.32555i	0.463529	−	0.802856i
$45$	0.231253	+	4.68305i	0.0344731	+	0.698108i
$46$	1.94690	+	3.37213i	0.287055	+	0.497193i
$47$	−6.08797	−	5.10841i	−0.888022	−	0.745139i	0.0797905	−	0.996812i	$-0.474575\pi$
$47$	−6.08797	−	5.10841i	−0.888022	−	0.745139i	−0.967812	+	0.251673i	$0.919019\pi$
$48$	1.99636	−	2.09738i	0.288150	−	0.302730i
$49$	0.104506	−	6.99922i	0.0149295	−	0.999889i
$50$	1.55183	+	0.564821i	0.219462	+	0.0798777i
$51$	−5.26963	−	3.49934i	−0.737896	−	0.490006i
$52$	−6.32774	−	5.30960i	−0.877499	−	0.736309i
$53$	4.86390	−	8.42452i	0.668108	−	1.15720i	−0.310324	−	0.950631i	$-0.600438\pi$
$53$	4.86390	−	8.42452i	0.668108	−	1.15720i	0.978433	−	0.206567i	$-0.0662290\pi$
$54$	−0.538829	−	3.31199i	−0.0733254	−	0.450705i
$55$	−6.07149			−0.818679
$56$	−1.54023	−	5.92478i	−0.205822	−	0.791733i
$57$	7.21367	+	4.79030i	0.955474	+	0.634491i
$58$	0.197893	+	1.12231i	0.0259847	+	0.147366i
$59$	1.36778	+	7.75709i	0.178070	+	1.00989i	0.934540	+	0.355858i	$0.115811\pi$
$59$	1.36778	+	7.75709i	0.178070	+	1.00989i	−0.756470	+	0.654029i	$0.773078\pi$
$60$	−4.16529	−	1.00665i	−0.537737	−	0.129958i
$61$	−4.58353	−	3.84604i	−0.586861	−	0.492435i	0.300331	−	0.953835i	$-0.402903\pi$
$61$	−4.58353	−	3.84604i	−0.586861	−	0.492435i	−0.887192	+	0.461400i	$0.847347\pi$
$62$	−2.97843	+	5.15879i	−0.378261	+	0.655167i
$63$	7.32772	+	3.05034i	0.923206	+	0.384307i
$64$	−0.170996	−	0.296174i	−0.0213745	−	0.0370217i
$65$	−1.41621	+	8.03170i	−0.175659	+	0.996210i
$66$	4.31790	−	0.485361i	0.531497	−	0.0597438i
$67$	1.70114	+	0.619166i	0.207828	+	0.0756431i	0.443836	−	0.896108i	$-0.353617\pi$
$67$	1.70114	+	0.619166i	0.207828	+	0.0756431i	−0.236009	+	0.971751i	$0.575839\pi$
$68$	4.42870	−	3.71612i	0.537059	−	0.450646i
$69$	4.17887	−	9.57119i	0.503076	−	1.15224i
$70$	−1.90225	+	1.87406i	−0.227363	+	0.223993i
$71$	7.39028	+	12.8003i	0.877065	+	1.51912i	0.854546	+	0.519375i	$0.173835\pi$
$71$	7.39028	+	12.8003i	0.877065	+	1.51912i	0.0225187	+	0.999746i	$0.492831\pi$
$72$	6.88705	+	0.866737i	0.811646	+	0.102146i
$73$	−3.32613	−	5.76102i	−0.389294	−	0.674276i	0.603061	−	0.797695i	$-0.293948\pi$
$73$	−3.32613	−	5.76102i	−0.389294	−	0.674276i	−0.992355	+	0.123419i	$0.960614\pi$
$74$	0.247631	−	1.40438i	0.0287865	−	0.163256i
$75$	−1.25159	−	4.24884i	−0.144521	−	0.490614i
$76$	−6.06251	+	5.08705i	−0.695418	+	0.583525i
$77$	−4.41308	+	9.28233i	−0.502917	+	1.05782i
$78$	0.365110	−	5.82518i	0.0413406	−	0.659571i
$79$	−5.09437	+	1.85420i	−0.573161	+	0.208614i	−0.612307	−	0.790620i	$-0.709758\pi$
$79$	−5.09437	+	1.85420i	−0.573161	+	0.208614i	0.0391461	+	0.999233i	$0.487536\pi$
$80$	1.30642	−	2.26279i	0.146062	−	0.252987i
$81$	−6.29090	+	6.43619i	−0.698989	+	0.715132i
$82$	1.53947	+	2.66644i	0.170006	+	0.294459i
$83$	0.752128	−	4.26553i	0.0825567	−	0.468203i	−0.915300	−	0.402772i	$-0.868047\pi$
$83$	0.752128	−	4.26553i	0.0825567	−	0.468203i	0.997857	−	0.0654306i	$-0.0208421\pi$
$84$	−4.56656	+	5.63637i	−0.498252	+	0.614979i
$85$	−5.36377	−	1.95225i	−0.581782	−	0.211751i
$86$	0.362984	+	0.132115i	0.0391416	+	0.0142464i
$87$	2.10739	−	2.21402i	0.225935	−	0.237368i
$88$	−1.56082	+	8.85185i	−0.166384	+	0.943611i
$89$	−7.32849			−0.776818			−0.388409	−	0.921487i	$-0.626975\pi$
$89$	−7.32849			−0.776818			−0.388409	+	0.921487i	$0.626975\pi$
$90$	−1.17466	−	2.79073i	−0.123820	−	0.294169i
$91$	11.2498	+	8.00302i	1.17930	+	0.838944i
$92$	7.31176	+	6.13530i	0.762304	+	0.639649i
$93$	15.8771	−	1.78469i	1.64638	−	0.185064i
$94$	4.82263	+	1.75530i	0.497417	+	0.181045i
$95$	7.34254	+	2.67246i	0.753328	+	0.274189i
$96$	−3.95535	+	9.05927i	−0.403692	+	0.924608i
$97$	−4.44995	−	3.73395i	−0.451824	−	0.379125i	0.388288	−	0.921538i	$-0.373066\pi$
$97$	−4.44995	−	3.73395i	−0.451824	−	0.379125i	−0.840112	+	0.542413i	$0.817511\pi$
$98$	1.48248	+	4.27041i	0.149753	+	0.431376i
$99$	−7.92233	−	8.54725i	−0.796224	−	0.859031i
$100$	4.04812			0.404812
$101$	−0.762165	+	4.32245i	−0.0758382	+	0.430100i	0.923122	+	0.384507i	$0.125629\pi$
$101$	−0.762165	+	4.32245i	−0.0758382	+	0.430100i	−0.998960	+	0.0455926i	$0.985482\pi$
$102$	3.97065	+	0.959611i	0.393153	+	0.0950156i
$103$	8.35540	+	3.04112i	0.823282	+	0.299650i	0.719099	−	0.694908i	$-0.244555\pi$
$103$	8.35540	+	3.04112i	0.823282	+	0.299650i	0.104183	+	0.994558i	$0.466777\pi$
$104$	11.3457	+	4.12948i	1.11253	+	0.404929i
$105$	7.07374	+	1.12217i	0.690326	+	0.109512i
$106$	−1.09085	+	6.18652i	−0.105953	+	0.600888i
$107$	5.88854	+	10.1993i	0.569267	+	0.985999i	0.996639	+	0.0819232i	$0.0261062\pi$
$107$	5.88854	+	10.1993i	0.569267	+	0.985999i	−0.427372	+	0.904076i	$0.640560\pi$
$108$	−4.01791	−	7.17729i	−0.386624	−	0.690635i
$109$	−7.03726	+	12.1889i	−0.674047	+	1.16748i	0.302699	+	0.953086i	$0.402112\pi$
$109$	−7.03726	+	12.1889i	−0.674047	+	1.16748i	−0.976746	+	0.214398i	$0.931221\pi$
$110$	3.68435	−	1.34099i	0.351289	−	0.127859i
$111$	−3.42557	+	1.70147i	−0.325140	+	0.161497i
$112$	−2.50986	−	3.64202i	−0.237160	−	0.344139i
$113$	2.10865	−	1.76937i	0.198366	−	0.166448i	−0.538194	−	0.842821i	$-0.680893\pi$
$113$	2.10865	−	1.76937i	0.198366	−	0.166448i	0.736560	+	0.676372i	$0.236449\pi$
$114$	−5.43548	−	1.31363i	−0.509079	−	0.123032i
$115$	1.63644	−	9.28071i	0.152599	−	0.865431i
$116$	1.39677	+	2.41928i	0.129687	+	0.224625i
$117$	−13.1547	+	8.48641i	−1.21615	+	0.784569i
$118$	−2.54330	−	4.40512i	−0.234130	−	0.405524i
$119$	−6.88335	+	6.78134i	−0.630995	+	0.621644i
$120$	6.22436	−	0.699659i	0.568203	−	0.0638699i
$121$	3.13388	−	2.62964i	0.284898	−	0.239058i
$122$	3.63088	+	1.32153i	0.328725	+	0.119646i
$123$	3.30436	−	7.56824i	0.297944	−	0.682405i
$124$	−2.53561	+	14.3802i	−0.227704	+	1.29138i
$125$	−5.90571	−	10.2290i	−0.528223	−	0.914909i
$126$	−5.12039	−	0.232578i	−0.456160	−	0.0207197i
$127$	−3.40695	+	5.90102i	−0.302318	+	0.523631i	−0.976661	−	0.214788i	$-0.931094\pi$
$127$	−3.40695	+	5.90102i	−0.302318	+	0.523631i	0.674342	+	0.738419i	$0.264427\pi$
$128$	−8.57470	−	7.19503i	−0.757904	−	0.635957i
$129$	−0.292755	−	0.993832i	−0.0257757	−	0.0875020i
$130$	−0.914548	−	5.18666i	−0.0802112	−	0.454900i
$131$	−2.30330	−	13.0627i	−0.201240	−	1.14129i	−0.903247	−	0.429121i	$-0.858823\pi$
$131$	−2.30330	−	13.0627i	−0.201240	−	1.14129i	0.702007	−	0.712170i	$-0.252288\pi$
$132$	9.53919	−	4.73810i	0.830280	−	0.412399i
$133$	9.42271	−	9.28307i	0.817053	−	0.804944i
$134$	−1.16906			−0.100991
$135$	−4.15345	+	6.97869i	−0.357472	+	0.600630i
$136$	−4.22514	+	7.31817i	−0.362303	+	0.627528i
$137$	2.05989	+	1.72845i	0.175988	+	0.147671i	0.726527	−	0.687138i	$-0.241133\pi$
$137$	2.05989	+	1.72845i	0.175988	+	0.147671i	−0.550539	+	0.834810i	$0.685578\pi$
$138$	−0.421888	+	6.73105i	−0.0359135	+	0.572985i
$139$	−1.11028	−	0.404110i	−0.0941731	−	0.0342762i	0.294504	−	0.955650i	$-0.404846\pi$
$139$	−1.11028	−	0.404110i	−0.0941731	−	0.0342762i	−0.388677	+	0.921374i	$0.627068\pi$
$140$	−2.81057	+	5.91166i	−0.237536	+	0.499626i
$141$	−3.88957	−	13.2041i	−0.327561	−	1.11199i
$142$	−7.31181	−	6.13534i	−0.613594	−	0.514866i
$143$	−10.1356	−	17.5553i	−0.847580	−	1.46805i
$144$	4.89015	−	1.11344i	0.407513	−	0.0927867i
$145$	1.37907	−	2.38863i	0.114526	−	0.198365i
$146$	3.29081	+	2.76132i	0.272349	+	0.228528i
$147$	6.85718	−	9.99896i	0.565571	−	0.824700i
$148$	−0.607014	−	3.44255i	−0.0498963	−	0.282976i
$149$	−13.6236	+	11.4316i	−1.11609	+	0.936512i	−0.998400	−	0.0565377i	$-0.981994\pi$
$149$	−13.6236	+	11.4316i	−1.11609	+	0.936512i	−0.117692	+	0.993050i	$0.537549\pi$
$150$	1.69793	+	2.30188i	0.138635	+	0.187948i
$151$	−1.13238	+	0.412151i	−0.0921515	+	0.0335404i	−0.387684	−	0.921792i	$-0.626725\pi$
$151$	−1.13238	+	0.412151i	−0.0921515	+	0.0335404i	0.295533	+	0.955333i	$0.404503\pi$
$152$	5.78386	−	10.0179i	0.469133	−	0.812562i
$153$	−4.25055	−	10.0983i	−0.343636	−	0.816401i
$154$	0.627816	−	6.60748i	0.0505908	−	0.532446i
$155$	13.5475	−	4.93089i	1.08816	−	0.396059i
$156$	−4.04276	−	13.7242i	−0.323679	−	1.09881i
$157$	2.43796	+	13.8264i	0.194570	+	1.10346i	0.913029	+	0.407894i	$0.133737\pi$
$157$	2.43796	+	13.8264i	0.194570	+	1.10346i	−0.718459	+	0.695569i	$0.755152\pi$
$158$	2.68187	−	2.25036i	0.213358	−	0.179029i
$159$	15.0901	−	7.49524i	1.19672	−	0.594411i
$160$	−1.54891	+	8.78432i	−0.122452	+	0.694462i
$161$	−12.9993	−	9.24756i	−1.02449	−	0.728810i
$162$	2.39595	−	5.29512i	0.188244	−	0.416024i
$163$	−5.72878	−	9.92253i	−0.448712	−	0.777193i	0.549590	−	0.835434i	$-0.314784\pi$
$163$	−5.72878	−	9.92253i	−0.448712	−	0.777193i	−0.998303	+	0.0582418i	$0.981451\pi$
$164$	5.78163	+	4.85137i	0.451470	+	0.378828i
$165$	−8.76048	−	5.81747i	−0.682002	−	0.452890i
$166$	0.485704	+	2.75456i	0.0376979	+	0.213796i
$167$	−2.22150	+	1.86406i	−0.171904	+	0.144245i	−0.724681	−	0.689085i	$-0.758013\pi$
$167$	−2.22150	+	1.86406i	−0.171904	+	0.144245i	0.552776	+	0.833330i	$0.313568\pi$
$168$	3.45452	−	10.0246i	0.266522	−	0.773414i
$169$	−13.3714	+	4.86678i	−1.02857	+	0.374367i
$170$	3.68607			0.282709
$171$	5.81863	+	13.8237i	0.444962	+	1.05713i
$172$	0.946883			0.0721991
$173$	−2.36304	+	13.4015i	−0.179658	+	1.01889i	0.752970	+	0.658055i	$0.228621\pi$
$173$	−2.36304	+	13.4015i	−0.179658	+	1.01889i	−0.932628	+	0.360839i	$0.882490\pi$
$174$	−0.789817	+	1.80898i	−0.0598758	+	0.137138i
$175$	−6.74441	+	0.539359i	−0.509829	+	0.0407717i
$176$	1.12773	+	6.39568i	0.0850060	+	0.482093i
$177$	−5.45899	+	12.5032i	−0.410323	+	0.939795i
$178$	4.44713	−	1.61862i	0.333327	−	0.121321i
$179$	17.4650			1.30540			0.652699	−	0.757618i	$-0.273637\pi$
$179$	17.4650			1.30540			0.652699	+	0.757618i	$0.273637\pi$
$180$	−5.04551	−	5.44351i	−0.376070	−	0.405735i
$181$	−3.81801	+	6.61299i	−0.283791	+	0.491540i	−0.972315	−	0.233673i	$-0.924925\pi$
$181$	−3.81801	+	6.61299i	−0.283791	+	0.491540i	0.688525	+	0.725213i	$0.258259\pi$
$182$	−8.59431	−	2.37174i	−0.637052	−	0.175805i
$183$	−2.92839	−	9.94117i	−0.216473	−	0.734873i
$184$	−13.1100	−	4.77165i	−0.966483	−	0.351771i
$185$	−2.64390	+	2.21849i	−0.194383	+	0.163107i
$186$	−9.24050	+	4.58974i	−0.677546	+	0.336536i
$187$	13.3319	−	4.85242i	0.974926	−	0.354844i
$188$	12.5804			0.917517
$189$	7.65035	+	11.4224i	0.556481	+	0.830860i
$190$	−5.04592			−0.366069
$191$	17.4877	−	6.36502i	1.26537	−	0.460557i	0.379802	−	0.925068i	$-0.375992\pi$
$191$	17.4877	−	6.36502i	1.26537	−	0.460557i	0.885567	+	0.464511i	$0.153770\pi$
$192$	0.0370544	−	0.591187i	0.00267417	−	0.0426653i
$193$	9.64772	−	8.09540i	0.694458	−	0.582719i	−0.225733	−	0.974189i	$-0.572478\pi$
$193$	9.64772	−	8.09540i	0.694458	−	0.582719i	0.920191	+	0.391470i	$0.128033\pi$
$194$	3.52506	+	1.28302i	0.253085	+	0.0921153i
$195$	−9.73910	+	10.2319i	−0.697432	+	0.732721i
$196$	6.99511	+	8.59381i	0.499650	+	0.613843i
$197$	−4.48687	+	7.77149i	−0.319676	+	0.553696i	−0.980420	−	0.196915i	$-0.936908\pi$
$197$	−4.48687	+	7.77149i	−0.319676	+	0.553696i	0.660744	+	0.750611i	$0.270241\pi$
$198$	6.69530	+	3.43693i	0.475815	+	0.244252i
$199$	−16.8173			−1.19215			−0.596073	−	0.802930i	$-0.703273\pi$
$199$	−16.8173			−1.19215			−0.596073	+	0.802930i	$0.703273\pi$
$200$	−5.56018	+	2.02374i	−0.393164	+	0.143100i
$201$	1.86130	+	2.52336i	0.131286	+	0.177984i
$202$	−0.492186	−	2.79132i	−0.0346301	−	0.196397i
$203$	−2.64944	−	3.84456i	−0.185954	−	0.269835i
$204$	9.95076	−	1.11853i	0.696693	−	0.0783129i
$205$	1.29398	−	7.33854i	0.0903757	−	0.512546i
$206$	−5.74198			−0.400062
$207$	15.2004	−	9.80613i	1.05650	−	0.681573i
$208$	8.72362			0.604874
$209$	−18.2502	+	6.64254i	−1.26240	+	0.459474i
$210$	−4.54039	+	0.881395i	−0.313317	+	0.0608220i
$211$	−10.2311	+	8.58489i	−0.704336	+	0.591008i	−0.923004	−	0.384791i	$-0.874273\pi$
$211$	−10.2311	+	8.58489i	−0.704336	+	0.591008i	0.218668	+	0.975799i	$0.429829\pi$
$212$	2.67399	+	15.1649i	0.183650	+	1.04153i
$213$	−1.60146	+	25.5506i	−0.109730	+	1.75069i
$214$	−5.82602	−	4.88861i	−0.398258	−	0.334178i
$215$	−0.467442	−	0.809634i	−0.0318793	−	0.0552166i
$216$	9.10676	+	7.84951i	0.619636	+	0.534092i
$217$	2.30851	−	24.2960i	0.156712	−	1.64932i
$218$	1.57828	−	8.95086i	0.106895	−	0.606229i
$219$	0.720764	−	11.4995i	0.0487047	−	0.777062i
$220$	7.36248	−	6.17785i	0.496378	−	0.416511i
$221$	−3.30931	−	18.7680i	−0.222608	−	1.26248i
$222$	1.70293	−	1.78910i	0.114293	−	0.120076i
$223$	19.2960	−	7.02318i	1.29216	−	0.470307i	0.397723	−	0.917506i	$-0.369801\pi$
$223$	19.2960	−	7.02318i	1.29216	−	0.470307i	0.894435	+	0.447199i	$0.147578\pi$
$224$	12.3040	+	8.75295i	0.822095	+	0.584831i
$225$	2.26517	−	7.32983i	0.151012	−	0.488655i
$226$	−0.888795	+	1.53944i	−0.0591217	+	0.102402i
$227$	−1.85438	+	0.674940i	−0.123080	+	0.0447974i	−0.402826	−	0.915277i	$-0.631972\pi$
$227$	−1.85438	+	0.674940i	−0.123080	+	0.0447974i	0.279746	+	0.960074i	$0.409750\pi$
$228$	−13.6217	+	1.53117i	−0.902122	+	0.101405i
$229$	0.951693	−	0.798565i	0.0628897	−	0.0527707i	−0.610801	−	0.791784i	$-0.709152\pi$
$229$	0.951693	−	0.798565i	0.0628897	−	0.0527707i	0.673691	+	0.739013i	$0.264708\pi$
$230$	1.05677	+	5.99323i	0.0696813	+	0.395182i
$231$	−15.2616	+	9.16492i	−1.00414	+	0.603007i
$232$	−3.12795	−	2.62466i	−0.205360	−	0.172317i
$233$	−5.65492	+	9.79461i	−0.370466	+	0.641666i	−0.989637	−	0.143590i	$-0.954135\pi$
$233$	−5.65492	+	9.79461i	−0.370466	+	0.641666i	0.619171	+	0.785256i	$0.287469\pi$
$234$	6.10828	−	8.05524i	0.399310	−	0.526588i
$235$	−6.21048	−	10.7569i	−0.405127	−	0.701700i
$236$	−9.55159	−	8.01474i	−0.621756	−	0.521715i
$237$	−9.12722	−	2.20583i	−0.592877	−	0.143284i
$238$	2.67923	−	5.63541i	0.173669	−	0.365290i
$239$	−18.7640	−	6.82953i	−1.21374	−	0.441765i	−0.345741	−	0.938330i	$-0.612372\pi$
$239$	−18.7640	−	6.82953i	−1.21374	−	0.441765i	−0.868000	+	0.496565i	$0.834595\pi$
$240$	4.05314	−	2.01319i	0.261629	−	0.129951i
$241$	−5.29906	−	4.44644i	−0.341342	−	0.286420i	0.455960	−	0.890000i	$-0.349296\pi$
$241$	−5.29906	−	4.44644i	−0.341342	−	0.286420i	−0.797303	+	0.603580i	$0.793740\pi$
$242$	−1.32092	+	2.28791i	−0.0849123	+	0.147072i
$243$	−15.2440	+	3.25899i	−0.977902	+	0.209065i
$244$	9.47155			0.606354
$245$	3.89492	−	10.2236i	0.248837	−	0.653164i
$246$	−0.333600	+	5.32244i	−0.0212696	+	0.339347i
$247$	4.53016	+	25.6918i	0.288247	+	1.63473i
$248$	−3.70622	−	21.0190i	−0.235345	−	1.33471i
$249$	5.17230	−	5.43402i	0.327781	−	0.344367i
$250$	5.84300	+	4.90286i	0.369544	+	0.310084i
$251$	1.70673	−	2.95614i	0.107728	−	0.186590i	−0.807122	−	0.590385i	$-0.798976\pi$
$251$	1.70673	−	2.95614i	0.107728	−	0.186590i	0.914849	+	0.403795i	$0.132309\pi$
$252$	−11.9896	+	3.75715i	−0.755273	+	0.236678i
$253$	11.7118	+	20.2854i	0.736312	+	1.27533i
$254$	0.764094	−	4.33339i	0.0479435	−	0.271901i
$255$	−5.86874	−	7.95624i	−0.367515	−	0.498239i
$256$	7.43525	+	2.70621i	0.464703	+	0.169138i
$257$	10.8256	−	9.08375i	0.675282	−	0.566628i	−0.239342	−	0.970935i	$-0.576932\pi$
$257$	10.8256	−	9.08375i	0.675282	−	0.566628i	0.914623	+	0.404307i	$0.132487\pi$
$258$	0.397157	+	0.538425i	0.0247259	+	0.0335209i
$259$	1.47000	+	5.65461i	0.0913411	+	0.351360i
$260$	−6.45507	−	11.1805i	−0.400326	−	0.693386i
$261$	5.16211	−	1.17536i	0.319526	−	0.0727531i
$262$	4.28283	+	7.41808i	0.264594	+	0.458290i
$263$	−0.297043	+	1.68461i	−0.0183165	+	0.103878i	−0.992595	−	0.121468i	$-0.961240\pi$
$263$	−0.297043	+	1.68461i	−0.0183165	+	0.103878i	0.974279	+	0.225345i	$0.0723511\pi$
$264$	−10.7336	+	11.2767i	−0.660607	+	0.694034i
$265$	11.6468	−	9.77279i	0.715455	−	0.600338i
$266$	−3.66764	+	7.71440i	−0.224877	+	0.473000i
$267$	−10.5742	−	7.02188i	−0.647130	−	0.429732i
$268$	−2.69287	+	0.980125i	−0.164493	+	0.0598707i
$269$	−12.0965	+	20.9517i	−0.737536	+	1.27745i	0.216066	+	0.976379i	$0.430677\pi$
$269$	−12.0965	+	20.9517i	−0.737536	+	1.27745i	−0.953602	+	0.301071i	$0.902656\pi$
$270$	0.979064	−	5.15223i	0.0595840	−	0.313555i
$271$	7.87513	+	13.6401i	0.478380	+	0.828578i	0.999693	−	0.0247874i	$-0.00789090\pi$
$271$	7.87513	+	13.6401i	0.478380	+	0.828578i	−0.521313	+	0.853366i	$0.674558\pi$
$272$	−1.06022	+	6.01279i	−0.0642851	+	0.364579i
$273$	8.56403	+	22.3266i	0.518319	+	1.35127i
$274$	−1.63176	−	0.593910i	−0.0985779	−	0.0358794i
$275$	9.33520	+	3.39774i	0.562934	+	0.204891i
$276$	4.67144	+	15.8584i	0.281188	+	0.954563i
$277$	0.130149	−	0.738114i	0.00781992	−	0.0443490i	−0.980648	−	0.195779i	$-0.937277\pi$
$277$	0.130149	−	0.738114i	0.00781992	−	0.0443490i	0.988468	+	0.151430i	$0.0483877\pi$
$278$	0.763007			0.0457621
$279$	24.6189	+	12.6377i	1.47390	+	0.756601i
$280$	0.905011	−	9.52484i	0.0540848	−	0.569218i
$281$	23.2177	+	19.4820i	1.38505	+	1.16220i	0.967300	+	0.253635i	$0.0816264\pi$
$281$	23.2177	+	19.4820i	1.38505	+	1.16220i	0.417752	+	0.908561i	$0.362818\pi$
$282$	5.27666	+	7.15356i	0.314221	+	0.425988i
$283$	−11.6192	−	4.22905i	−0.690690	−	0.251391i	−0.0272596	−	0.999628i	$-0.508678\pi$
$283$	−11.6192	−	4.22905i	−0.690690	−	0.251391i	−0.663431	+	0.748238i	$0.730900\pi$
$284$	−21.9863	−	8.00235i	−1.30464	−	0.474852i
$285$	8.03380	+	10.8914i	0.475881	+	0.645151i
$286$	10.0280	+	8.41446i	0.592966	+	0.497557i
$287$	−10.2789	−	7.31233i	−0.606745	−	0.431633i
$288$	−14.3874	+	9.28164i	−0.847785	+	0.546926i
$289$	−3.66186			−0.215404
$290$	−0.309291	+	1.75408i	−0.0181622	+	0.103003i
$291$	−2.84305	−	9.65144i	−0.166662	−	0.565777i
$292$	9.89531	+	3.60160i	0.579079	+	0.210768i
$293$	2.71146	+	0.986893i	0.158405	+	0.0576549i	0.420006	−	0.907521i	$-0.362028\pi$
$293$	2.71146	+	0.986893i	0.158405	+	0.0576549i	−0.261600	+	0.965176i	$0.584250\pi$
$294$	−1.95269	+	7.58218i	−0.113883	+	0.442201i
$295$	−2.13773	+	12.1237i	−0.124464	+	0.705869i
$296$	2.55475	+	4.42495i	0.148492	+	0.257195i
$297$	−3.24138	−	19.9236i	−0.188084	−	1.15608i
$298$	5.74234	−	9.94603i	0.332645	−	0.576158i
$299$	29.5664	−	10.7613i	1.70987	−	0.622342i
$300$	5.84099	+	3.87876i	0.337230	+	0.223940i
$301$	−1.57756	+	0.126160i	−0.0909291	+	0.00727172i
$302$	0.596127	−	0.500210i	0.0343033	−	0.0287839i
$303$	−5.24133	+	5.50654i	−0.301106	+	0.316342i
$304$	1.45135	−	8.23099i	0.0832404	−	0.472080i
$305$	−4.67577	−	8.09867i	−0.267734	−	0.463728i
$306$	4.80974	+	5.18914i	0.274955	+	0.296643i
$307$	−7.23176	−	12.5258i	−0.412738	−	0.714884i	0.582450	−	0.812867i	$-0.302094\pi$
$307$	−7.23176	−	12.5258i	−0.412738	−	0.714884i	−0.995188	+	0.0979830i	$0.968761\pi$
$308$	−4.09350	−	15.7464i	−0.233249	−	0.897236i
$309$	9.14202	+	12.3938i	0.520071	+	0.705060i
$310$	−7.13194	+	5.98441i	−0.405067	+	0.339892i
$311$	19.1797	+	6.98083i	1.08758	+	0.395846i	0.822723	−	0.568442i	$-0.192454\pi$
$311$	19.1797	+	6.98083i	1.08758	+	0.395846i	0.264855	+	0.964288i	$0.414676\pi$
$312$	12.4138	+	16.8294i	0.702793	+	0.952775i
$313$	0.953891	−	5.40979i	0.0539171	−	0.305779i	−0.945909	−	0.324432i	$-0.894827\pi$
$313$	0.953891	−	5.40979i	0.0539171	−	0.305779i	0.999826	+	0.0186532i	$0.00593784\pi$
$314$	−4.53321	−	7.85176i	−0.255824	−	0.443100i
$315$	9.13139	+	8.39695i	0.514496	+	0.473115i
$316$	4.29091	−	7.43207i	0.241382	−	0.418087i
$317$	−13.9976	−	11.7454i	−0.786185	−	0.659688i	0.158613	−	0.987341i	$-0.449298\pi$
$317$	−13.9976	−	11.7454i	−0.786185	−	0.659688i	−0.944798	+	0.327653i	$0.893742\pi$
$318$	−7.50166	+	7.88124i	−0.420672	+	0.441958i
$319$	1.19045	+	6.75136i	0.0666523	+	0.378004i
$320$	−0.0928159	−	0.526385i	−0.00518857	−	0.0294258i
$321$	−1.27603	+	20.3586i	−0.0712213	+	1.13630i
$322$	9.93080	+	2.74057i	0.553422	+	0.152726i
$323$	−18.2588			−1.01595
$324$	1.07960	−	14.2058i	0.0599780	−	0.789213i
$325$	6.67220	−	11.5566i	0.370107	−	0.641044i
$326$	5.66795	+	4.75597i	0.313919	+	0.263409i
$327$	−21.8329	+	10.8444i	−1.20736	+	0.599695i
$328$	−10.3665	−	3.77309i	−0.572394	−	0.208334i
$329$	−20.9596	+	1.67617i	−1.15554	+	0.0924101i
$330$	6.60100	+	1.59530i	0.363373	+	0.0878185i
$331$	24.8446	+	20.8471i	1.36558	+	1.14586i	0.974214	+	0.225625i	$0.0724425\pi$
$331$	24.8446	+	20.8471i	1.36558	+	1.14586i	0.391368	+	0.920234i	$0.372002\pi$
$332$	3.42820	+	5.93781i	0.188147	+	0.325880i
$333$	−6.57299	−	0.827214i	−0.360198	−	0.0453310i
$334$	0.936357	−	1.62182i	0.0512352	−	0.0887419i
$335$	2.16743	+	1.81869i	0.118420	+	0.0993658i
$336$	−0.131804	−	7.65988i	−0.00719050	−	0.417881i
$337$	−5.06764	−	28.7400i	−0.276052	−	1.56557i	−0.735601	−	0.677415i	$-0.763100\pi$
$337$	−5.06764	−	28.7400i	−0.276052	−	1.56557i	0.459549	−	0.888152i	$-0.348011\pi$
$338$	7.03921	−	5.90659i	0.382882	−	0.321276i
$339$	4.73790	−	0.532571i	0.257327	−	0.0289253i
$340$	8.49072	−	3.09037i	0.460474	−	0.167599i
$341$	−17.9170	+	31.0332i	−0.970262	+	1.68054i
$342$	−6.58412	−	7.10349i	−0.356029	−	0.384113i
$343$	−12.7993	−	13.3858i	−0.691095	−	0.722764i
$344$	−1.30056	+	0.473366i	−0.0701217	+	0.0255222i
$345$	11.2536	−	11.8231i	0.605875	−	0.636532i
$346$	−1.52599	−	8.65430i	−0.0820376	−	0.465258i
$347$	12.7113	−	10.6661i	0.682380	−	0.572585i	−0.234320	−	0.972159i	$-0.575286\pi$
$347$	12.7113	−	10.6661i	0.682380	−	0.572585i	0.916701	+	0.399574i	$0.130842\pi$
$348$	−0.302678	+	4.82909i	−0.0162252	+	0.258866i
$349$	0.385759	−	2.18775i	0.0206492	−	0.117107i	−0.972741	−	0.231895i	$-0.925508\pi$
$349$	0.385759	−	2.18775i	0.0206492	−	0.117107i	0.993390	+	0.114787i	$0.0366186\pi$
$350$	3.97357	−	1.81692i	0.212396	−	0.0971183i
$351$	−27.1121	−	0.359403i	−1.44714	−	0.0191835i
$352$	−11.0853	−	19.2004i	−0.590851	−	1.02338i
$353$	10.1098	+	8.48315i	0.538092	+	0.451512i	0.870885	−	0.491487i	$-0.163547\pi$
$353$	10.1098	+	8.48315i	0.538092	+	0.451512i	−0.332793	+	0.943000i	$0.607991\pi$
$354$	0.551127	−	8.79299i	0.0292921	−	0.467342i
$355$	4.01142	+	22.7499i	0.212904	+	1.20744i
$356$	8.88675	−	7.45687i	0.470997	−	0.395213i
$357$	−16.4295	+	3.18935i	−0.869542	+	0.168798i
$358$	−10.5983	+	3.85745i	−0.560136	+	0.203873i
$359$	9.29649			0.490650			0.245325	−	0.969441i	$-0.421105\pi$
$359$	9.29649			0.490650			0.245325	+	0.969441i	$0.421105\pi$
$360$	9.65144	+	4.95441i	0.508675	+	0.261121i
$361$	5.99469			0.315510
$362$	0.856283	−	4.85622i	0.0450052	−	0.255237i
$363$	7.04145	−	0.791506i	0.369580	−	0.0415433i
$364$	−21.7851	+	1.74218i	−1.14185	+	0.0913151i
$365$	−1.80541	−	10.2390i	−0.0944994	−	0.535933i
$366$	3.97271	+	5.38580i	0.207657	+	0.281520i
$367$	20.0876	−	7.31129i	1.04857	−	0.381646i	0.240444	−	0.970663i	$-0.422707\pi$
$367$	20.0876	−	7.31129i	1.04857	−	0.381646i	0.808121	+	0.589017i	$0.200485\pi$
$368$	−10.0802			−0.525468
$369$	12.0194	−	7.75401i	0.625706	−	0.403657i
$370$	1.11440	−	1.93019i	0.0579348	−	0.100346i
$371$	−6.47555	−	24.9094i	−0.336194	−	1.29323i
$372$	−17.4371	+	18.3194i	−0.904072	+	0.949818i
$373$	10.1486	+	3.69379i	0.525475	+	0.191257i	0.591117	−	0.806586i	$-0.298687\pi$
$373$	10.1486	+	3.69379i	0.525475	+	0.191257i	−0.0656419	+	0.997843i	$0.520909\pi$
$374$	−7.01844	+	5.88917i	−0.362915	+	0.304522i
$375$	1.27975	−	20.4179i	0.0660862	−	1.05438i
$376$	−17.2794	+	6.28918i	−0.891116	+	0.324340i
$377$	9.20876			0.474275
$378$	−7.16529	−	5.24174i	−0.368543	−	0.269606i
$379$	29.9516			1.53851			0.769254	−	0.638943i	$-0.220628\pi$
$379$	29.9516			1.53851			0.769254	+	0.638943i	$0.220628\pi$
$380$	−11.6231	+	4.23045i	−0.596251	+	0.217018i
$381$	−10.5700	+	5.25009i	−0.541517	+	0.268970i
$382$	−9.20623	+	7.72495i	−0.471032	+	0.395243i
$383$	−14.0313	−	5.10698i	−0.716967	−	0.260955i	−0.0423293	−	0.999104i	$-0.513478\pi$
$383$	−14.0313	−	5.10698i	−0.716967	−	0.260955i	−0.674638	+	0.738149i	$0.735700\pi$
$384$	−5.47833	−	18.5976i	−0.279565	−	0.949054i
$385$	−11.4432	+	11.2736i	−0.583199	+	0.574556i
$386$	−4.06650	+	7.04338i	−0.206979	+	0.358499i
$387$	0.529839	−	1.71449i	0.0269332	−	0.0871527i
$388$	9.19550			0.466831
$389$	10.9865	−	3.99877i	0.557039	−	0.202746i	−0.0481320	−	0.998841i	$-0.515327\pi$
$389$	10.9865	−	3.99877i	0.557039	−	0.202746i	0.605171	+	0.796095i	$0.293105\pi$
$390$	3.65007	−	8.36005i	0.184828	−	0.423328i
$391$	3.82394	+	21.6866i	0.193385	+	1.09674i
$392$	−13.9041	−	8.30677i	−0.702265	−	0.419555i
$393$	9.19276	−	21.0549i	0.463713	−	1.06208i
$394$	1.00629	−	5.70696i	0.0506962	−	0.287513i
$395$	−8.47307			−0.426326
$396$	18.3038	+	2.30355i	0.919803	+	0.115758i
$397$	−16.7910			−0.842714			−0.421357	−	0.906895i	$-0.638446\pi$
$397$	−16.7910			−0.842714			−0.421357	+	0.906895i	$0.638446\pi$
$398$	10.2052	−	3.71439i	0.511541	−	0.186186i
$399$	22.4906	−	4.36594i	1.12594	−	0.218571i
$400$	−3.27499	+	2.74804i	−0.163749	+	0.137402i
$401$	0.288077	+	1.63377i	0.0143859	+	0.0815864i	0.991155	−	0.132706i	$-0.0423666\pi$
$401$	0.288077	+	1.63377i	0.0143859	+	0.0815864i	−0.976770	+	0.214292i	$0.931255\pi$
$402$	−1.68682	−	1.12015i	−0.0841308	−	0.0558678i
$403$	36.8732	+	30.9403i	1.83679	+	1.54125i
$404$	−3.47395	−	6.01706i	−0.172835	−	0.299360i
$405$	−12.6797	+	6.08979i	−0.630058	+	0.302604i
$406$	2.45689	+	1.74781i	0.121934	+	0.0867425i
$407$	1.48965	−	8.44821i	0.0738390	−	0.418762i
$408$	−13.1084	+	6.51092i	−0.648962	+	0.322338i
$409$	−13.3183	+	11.1754i	−0.658548	+	0.552587i	−0.909651	−	0.415373i	$-0.863651\pi$
$409$	−13.3183	+	11.1754i	−0.658548	+	0.552587i	0.251104	+	0.967960i	$0.419207\pi$
$410$	0.835619	+	4.73903i	0.0412683	+	0.234044i
$411$	1.31605	+	4.46766i	0.0649159	+	0.220374i
$412$	−13.2264	+	4.81402i	−0.651618	+	0.237170i
$413$	16.9814	+	12.0804i	0.835598	+	0.594437i
$414$	−7.05817	+	9.30791i	−0.346890	+	0.457459i
$415$	3.38476	−	5.86258i	0.166151	−	0.287782i
$416$	−27.9851	+	10.1857i	−1.37208	+	0.499396i
$417$	−1.21481	−	1.64692i	−0.0594896	−	0.0806499i
$418$	9.60764	−	8.06176i	0.469925	−	0.394314i
$419$	−3.40593	−	19.3160i	−0.166391	−	0.943649i	−0.947619	−	0.319403i	$-0.896518\pi$
$419$	−3.40593	−	19.3160i	−0.166391	−	0.943649i	0.781228	−	0.624246i	$-0.214594\pi$
$420$	−9.71966	+	5.83688i	−0.474271	+	0.284811i
$421$	−20.8334	−	17.4813i	−1.01536	−	0.851985i	−0.0263192	−	0.999654i	$-0.508379\pi$
$421$	−20.8334	−	17.4813i	−1.01536	−	0.851985i	−0.989037	+	0.147669i	$0.952823\pi$
$422$	4.31238	−	7.46926i	0.209923	−	0.363598i
$423$	7.03949	−	22.7789i	0.342272	−	1.10755i
$424$	−11.2540	−	19.4926i	−0.546545	−	0.946643i
$425$	7.15452	+	6.00336i	0.347045	+	0.291206i
$426$	−4.67147	−	15.8585i	−0.226334	−	0.768347i
$427$	−15.7801	+	1.26196i	−0.763655	+	0.0610705i
$428$	−17.5186	−	6.37623i	−0.846791	−	0.308207i
$429$	2.19636	−	35.0419i	0.106041	−	1.69184i
$430$	0.462479	+	0.388066i	0.0223027	+	0.0187142i
$431$	−8.53896	+	14.7899i	−0.411307	+	0.712405i	−0.995033	−	0.0995459i	$-0.968261\pi$
$431$	−8.53896	+	14.7899i	−0.411307	+	0.712405i	0.583726	+	0.811951i	$0.301594\pi$
$432$	8.12280	+	3.07899i	0.390808	+	0.148138i
$433$	−2.60933			−0.125397			−0.0626983	−	0.998033i	$-0.519971\pi$
$433$	−2.60933			−0.125397			−0.0626983	+	0.998033i	$0.519971\pi$
$434$	3.96533	+	15.2534i	0.190342	+	0.732185i
$435$	4.27854	−	2.12514i	0.205140	−	0.101893i
$436$	−3.86882	−	21.9412i	−0.185283	−	1.05079i
$437$	−5.23465	−	29.6872i	−0.250407	−	1.42013i
$438$	2.10248	+	7.13740i	0.100460	+	0.341038i
$439$	−21.9756	−	18.4397i	−1.04884	−	0.880080i	−0.0558676	−	0.998438i	$-0.517792\pi$
$439$	−21.9756	−	18.4397i	−1.04884	−	0.880080i	−0.992971	+	0.118358i	$0.962237\pi$
$440$	−7.02408	+	12.1661i	−0.334860	+	0.579994i
$441$	19.4748	−	7.85708i	0.927370	−	0.374147i
$442$	6.15343	+	10.6581i	0.292689	+	0.506952i
$443$	1.01830	−	5.77506i	0.0483808	−	0.274381i	−0.951015	−	0.309146i	$-0.899957\pi$
$443$	1.01830	−	5.77506i	0.0483808	−	0.274381i	0.999396	+	0.0347643i	$0.0110681\pi$
$444$	2.42267	−	5.54883i	0.114975	−	0.263336i
$445$	−10.7631	−	3.91744i	−0.510219	−	0.185704i
$446$	−10.1582	+	8.52373i	−0.481004	+	0.403610i
$447$	−30.6107	+	3.44085i	−1.44784	+	0.162747i
$448$	−0.872222	−	0.240704i	−0.0412086	−	0.0113722i
$449$	17.7693	+	30.7773i	0.838584	+	1.45247i	0.891078	+	0.453850i	$0.149950\pi$
$449$	17.7693	+	30.7773i	0.838584	+	1.45247i	−0.0524938	+	0.998621i	$0.516717\pi$
$450$	0.244348	+	4.94825i	0.0115187	+	0.233263i
$451$	9.26085	+	16.0403i	0.436076	+	0.755306i
$452$	−0.756652	+	4.29119i	−0.0355899	+	0.201840i
$453$	−2.02880	−	0.490312i	−0.0953213	−	0.0230369i
$454$	0.976220	−	0.819146i	0.0458163	−	0.0384444i
$455$	12.2442	+	17.7673i	0.574016	+	0.832945i
$456$	17.9443	−	8.91289i	0.840318	−	0.417384i
$457$	29.1952	−	10.6262i	1.36570	−	0.497072i	0.447885	−	0.894091i	$-0.352177\pi$
$457$	29.1952	−	10.6262i	1.36570	−	0.497072i	0.917810	+	0.397019i	$0.129955\pi$
$458$	−0.401137	+	0.694790i	−0.0187439	+	0.0324654i
$459$	3.54277	−	18.6435i	0.165362	−	0.870202i
$460$	7.45889	+	12.9192i	0.347773	+	0.602360i
$461$	0.0636647	−	0.361060i	0.00296516	−	0.0168163i	−0.983289	−	0.182050i	$-0.941727\pi$
$461$	0.0636647	−	0.361060i	0.00296516	−	0.0168163i	0.986254	+	0.165234i	$0.0528378\pi$
$462$	7.23691	−	8.93231i	0.336692	−	0.415569i
$463$	−27.1974	−	9.89906i	−1.26397	−	0.460048i	−0.378872	−	0.925449i	$-0.623688\pi$
$463$	−27.1974	−	9.89906i	−1.26397	−	0.460048i	−0.885100	+	0.465401i	$0.845910\pi$
$464$	−2.77232	−	1.00904i	−0.128702	−	0.0468436i
$465$	24.2721	+	5.86599i	1.12559	+	0.272029i
$466$	1.26825	−	7.19263i	0.0587508	−	0.333192i
$467$	24.5125			1.13430			0.567151	−	0.823614i	$-0.308046\pi$
$467$	24.5125			1.13430			0.567151	+	0.823614i	$0.308046\pi$
$468$	7.31673	−	23.6760i	0.338216	−	1.09443i
$469$	4.35589	−	1.99174i	0.201136	−	0.0919698i
$470$	6.14453	+	5.15588i	0.283426	+	0.237823i
$471$	−9.73019	+	22.2858i	−0.448343	+	1.02688i
$472$	17.1260	+	6.23337i	0.788290	+	0.286914i
$473$	2.18357	+	0.794753i	0.100400	+	0.0365428i
$474$	6.02585	−	0.677346i	0.276777	−	0.0311115i
$475$	−9.79393	−	8.21808i	−0.449376	−	0.377071i
$476$	1.44682	−	15.2272i	0.0663151	−	0.697937i
$477$	28.9550	+	3.64400i	1.32576	+	0.166847i
$478$	12.8949			0.589800
$479$	−4.36626	+	24.7623i	−0.199499	+	1.13142i	0.706364	+	0.707848i	$0.250334\pi$
$479$	−4.36626	+	24.7623i	−0.199499	+	1.13142i	−0.905864	+	0.423569i	$0.860777\pi$
$480$	−10.6517	+	11.1907i	−0.486182	+	0.510782i
$481$	−10.8283	−	3.94118i	−0.493728	−	0.179702i
$482$	4.19769	+	1.52784i	0.191200	+	0.0695910i
$483$	−9.89581	−	25.7986i	−0.450275	−	1.17388i
$484$	−1.12454	+	6.37755i	−0.0511152	+	0.289889i
$485$	−4.53949	−	7.86263i	−0.206128	−	0.357024i
$486$	8.53067	−	5.34455i	0.386959	−	0.242434i
$487$	−12.9318	+	22.3985i	−0.585994	+	1.01497i	0.408756	+	0.912643i	$0.365963\pi$
$487$	−12.9318	+	22.3985i	−0.585994	+	1.01497i	−0.994751	+	0.102328i	$0.967371\pi$
$488$	−13.0094	+	4.73502i	−0.588906	+	0.214344i
$489$	1.24141	−	19.8062i	0.0561386	−	0.895667i
$490$	−0.105477	+	7.06425i	−0.00476497	+	0.319130i
$491$	6.43769	−	5.40186i	0.290529	−	0.243783i	−0.485860	−	0.874037i	$-0.661494\pi$
$491$	6.43769	−	5.40186i	0.290529	−	0.243783i	0.776389	+	0.630254i	$0.217049\pi$
$492$	3.69385	+	12.5397i	0.166532	+	0.565334i
$493$	−1.11918	+	6.34717i	−0.0504052	+	0.285862i
$494$	−8.42352	−	14.5900i	−0.378992	−	0.656434i
$495$	−7.06631	−	16.7879i	−0.317607	−	0.754561i
$496$	−7.71053	−	13.3550i	−0.346213	−	0.599658i
$497$	37.6966	+	10.4030i	1.69092	+	0.466638i
$498$	−1.93850	+	4.43991i	−0.0868664	+	0.198957i
$499$	−19.5520	+	16.4061i	−0.875269	+	0.734438i	−0.965201	−	0.261510i	$-0.915780\pi$
$499$	−19.5520	+	16.4061i	−0.875269	+	0.734438i	0.0899316	+	0.995948i	$0.471335\pi$
$500$	17.5696	+	6.39482i	0.785738	+	0.285985i
$501$	−4.99144	+	0.561071i	−0.223001	+	0.0250668i
$502$	−0.382776	+	2.17083i	−0.0170841	+	0.0968888i
$503$	7.84102	+	13.5810i	0.349614	+	0.605549i	0.986181	−	0.165673i	$-0.0529795\pi$
$503$	7.84102	+	13.5810i	0.349614	+	0.605549i	−0.636567	+	0.771221i	$0.719646\pi$
$504$	14.5897	−	11.1544i	0.649876	−	0.496855i
$505$	−3.42993	+	5.94081i	−0.152630	+	0.264363i
$506$	−11.5874	−	9.72299i	−0.515123	−	0.432239i
$507$	−23.9565	−	5.78972i	−1.06395	−	0.257130i
$508$	−1.87301	−	10.6224i	−0.0831016	−	0.471293i
$509$	−4.38431	−	24.8647i	−0.194331	−	1.10211i	−0.913368	−	0.407135i	$-0.866528\pi$
$509$	−4.38431	−	24.8647i	−0.194331	−	1.10211i	0.719037	−	0.694972i	$-0.244583\pi$
$510$	5.31859	+	3.53186i	0.235511	+	0.156393i
$511$	−16.9660	−	4.68205i	−0.750532	−	0.207122i
$512$	17.2773			0.763557
$513$	−4.84974	+	25.5213i	−0.214121	+	1.12679i
$514$	−4.56297	+	7.90329i	−0.201264	+	0.348599i
$515$	10.6456	+	8.93275i	0.469103	+	0.393624i
$516$	1.36625	+	0.907267i	0.0601456	+	0.0399402i
$517$	29.0110	+	10.5592i	1.27590	+	0.464391i
$518$	−2.14095	−	3.10670i	−0.0940681	−	0.136501i
$519$	−16.2504	+	17.0726i	−0.713312	+	0.749405i
$520$	14.4555	+	12.1296i	0.633917	+	0.531920i
$521$	−0.778135	−	1.34777i	−0.0340907	−	0.0590468i	0.848477	−	0.529233i	$-0.177520\pi$
$521$	−0.778135	−	1.34777i	−0.0340907	−	0.0590468i	−0.882567	+	0.470186i	$0.844187\pi$
$522$	−2.87291	+	1.85338i	−0.125744	+	0.0811204i
$523$	1.49945	−	2.59712i	0.0655663	−	0.113564i	−0.831379	−	0.555706i	$-0.812448\pi$
$523$	1.49945	−	2.59712i	0.0655663	−	0.113564i	0.896945	+	0.442142i	$0.145781\pi$
$524$	16.0846	+	13.4966i	0.702658	+	0.589600i
$525$	−10.2482	−	5.68400i	−0.447269	−	0.248070i
$526$	−0.191822	−	1.08788i	−0.00836385	−	0.0474338i
$527$	−25.8071	+	21.6547i	−1.12417	+	0.943294i
$528$	−4.50091	+	10.3088i	−0.195877	+	0.448633i
$529$	−12.5514	+	4.56833i	−0.545712	+	0.198623i
$530$	−4.90909	+	8.50280i	−0.213237	+	0.369338i
$531$	−19.8568	+	12.8101i	−0.861710	+	0.555910i
$532$	−1.98058	+	20.8447i	−0.0858690	+	0.903733i
$533$	23.3791	−	8.50929i	1.01266	−	0.368578i
$534$	7.96762	+	1.92558i	0.344793	+	0.0833281i
$535$	3.19628	+	18.1270i	0.138187	+	0.783698i
$536$	3.20873	−	2.69244i	0.138596	−	0.116296i
$537$	25.2001	+	16.7343i	1.08746	+	0.722139i
$538$	2.71294	−	15.3858i	0.116963	−	0.663330i
$539$	8.91802	+	25.6891i	0.384126	+	1.10651i
$540$	−2.06435	−	12.6888i	−0.0888353	−	0.546039i
$541$	−9.55593	−	16.5514i	−0.410842	−	0.711598i	0.584140	−	0.811653i	$-0.301432\pi$
$541$	−9.55593	−	16.5514i	−0.410842	−	0.711598i	−0.994982	+	0.100054i	$0.968098\pi$
$542$	−7.79151	−	6.53785i	−0.334674	−	0.280825i
$543$	−11.8453	+	5.88353i	−0.508330	+	0.252486i
$544$	−3.61941	−	20.5267i	−0.155181	−	0.880076i
$545$	−16.8509	+	14.1396i	−0.721815	+	0.605674i
$546$	−10.1281	−	11.6569i	−0.433443	−	0.498869i
$547$	−3.22747	+	1.17470i	−0.137997	+	0.0502266i	−0.410095	−	0.912043i	$-0.634505\pi$
$547$	−3.22747	+	1.17470i	−0.137997	+	0.0502266i	0.272099	+	0.962269i	$0.412282\pi$
$548$	−4.25661			−0.181833
$549$	5.29991	−	17.1499i	0.226195	−	0.731939i
$550$	−6.41531			−0.273550
$551$	1.53206	−	8.68874i	0.0652679	−	0.370153i
$552$	−14.3443	−	19.4465i	−0.610532	−	0.827697i
$553$	−6.15867	+	12.9540i	−0.261893	+	0.550859i
$554$	0.0840469	+	0.476654i	0.00357081	+	0.0202511i
$555$	−5.94052	+	0.667755i	−0.252161	+	0.0283446i
$556$	1.75755	−	0.639698i	0.0745369	−	0.0271292i
$557$	15.1957			0.643861			0.321931	−	0.946763i	$-0.395668\pi$
$557$	15.1957			0.643861			0.321931	+	0.946763i	$0.395668\pi$
$558$	−17.7307	−	2.23142i	−0.750601	−	0.0944634i
$559$	1.56067	−	2.70316i	0.0660094	−	0.114332i
$560$	−1.73930	−	6.69055i	−0.0734989	−	0.282727i
$561$	23.8858	+	5.77263i	1.00846	+	0.243721i
$562$	−18.3921	−	6.69417i	−0.775823	−	0.282377i
$563$	17.7643	−	14.9060i	0.748676	−	0.628214i	−0.186476	−	0.982460i	$-0.559707\pi$
$563$	17.7643	−	14.9060i	0.748676	−	0.628214i	0.935153	+	0.354245i	$0.115262\pi$
$564$	18.1521	+	12.0540i	0.764339	+	0.507566i
$565$	4.04272	−	1.47143i	0.170079	−	0.0619035i
$566$	7.98492			0.335631
$567$	0.0940551	+	23.8116i	0.00394994	+	0.999992i
$568$	34.1991			1.43496
$569$	0.215396	−	0.0783976i	0.00902985	−	0.00328660i	−0.337501	−	0.941325i	$-0.609582\pi$
$569$	0.215396	−	0.0783976i	0.00902985	−	0.00328660i	0.346531	+	0.938038i	$0.387360\pi$
$570$	−7.28069	−	4.83481i	−0.304955	−	0.202508i
$571$	−7.79350	+	6.53953i	−0.326148	+	0.273671i	−0.791128	−	0.611650i	$-0.790506\pi$
$571$	−7.79350	+	6.53953i	−0.326148	+	0.273671i	0.464980	+	0.885321i	$0.346061\pi$
$572$	30.1536	+	10.9750i	1.26079	+	0.458888i
$573$	31.3316	+	7.57209i	1.30890	+	0.316329i
$574$	7.85259	+	2.16705i	0.327761	+	0.0904509i
$575$	−7.70979	+	13.3537i	−0.321520	+	0.556890i
$576$	0.619918	−	0.817513i	0.0258299	−	0.0340630i
$577$	−29.5660			−1.23085			−0.615424	−	0.788196i	$-0.711015\pi$
$577$	−29.5660			−1.23085			−0.615424	+	0.788196i	$0.711015\pi$
$578$	2.22212	−	0.808786i	0.0924280	−	0.0336411i
$579$	21.6773	−	2.43667i	0.900877	−	0.101265i
$580$	0.758163	+	4.29976i	0.0314810	+	0.178538i
$581$	−6.50271	−	9.43598i	−0.269778	−	0.391470i
$582$	3.85693	+	5.22883i	0.159875	+	0.216742i
$583$	−6.56211	+	37.2156i	−0.271775	+	1.54131i
$584$	−15.3919			−0.636922
$585$	−23.8562	+	5.43184i	−0.986334	+	0.224579i
$586$	−1.86337			−0.0769749
$587$	−9.65370	+	3.51366i	−0.398451	+	0.145024i	−0.533470	−	0.845819i	$-0.679112\pi$
$587$	−9.65370	+	3.51366i	−0.398451	+	0.145024i	0.135020	+	0.990843i	$0.456890\pi$
$588$	1.85889	+	19.1023i	0.0766594	+	0.787767i
$589$	35.3277	−	29.6435i	1.45565	−	1.22144i
$590$	−1.38049	−	7.82916i	−0.0568339	−	0.322321i
$591$	−13.9204	+	6.91424i	−0.572609	+	0.284414i
$592$	2.82804	+	2.37300i	0.116232	+	0.0975299i
$593$	−5.67774	−	9.83413i	−0.233157	−	0.403839i	0.725579	−	0.688139i	$-0.241572\pi$
$593$	−5.67774	−	9.83413i	−0.233157	−	0.403839i	−0.958735	+	0.284300i	$0.908239\pi$
$594$	6.36744	+	11.3743i	0.261259	+	0.466693i
$595$	−13.7343	+	6.28001i	−0.563051	+	0.257455i
$596$	4.88860	−	27.7246i	0.200245	−	1.13564i
$597$	−24.2655	−	16.1137i	−0.993119	−	0.659490i
$598$	−15.5649	+	13.0605i	−0.636497	+	0.534085i
$599$	5.88663	+	33.3847i	0.240521	+	1.36406i	0.830668	+	0.556768i	$0.187959\pi$
$599$	5.88663	+	33.3847i	0.240521	+	1.36406i	−0.590147	+	0.807296i	$0.700930\pi$
$600$	−9.96179	−	2.40752i	−0.406688	−	0.0982868i
$601$	−22.9226	+	8.34314i	−0.935031	+	0.340324i	−0.764202	−	0.644977i	$-0.776867\pi$
$601$	−22.9226	+	8.34314i	−0.935031	+	0.340324i	−0.170829	+	0.985301i	$0.554645\pi$
$602$	0.929444	−	0.424989i	0.0378813	−	0.0173213i
$603$	0.267859	+	5.42435i	0.0109080	+	0.220897i
$604$	0.953783	−	1.65200i	0.0388089	−	0.0672190i
$605$	6.00828	−	2.18684i	0.244271	−	0.0889075i
$606$	1.96437	−	4.49916i	0.0797971	−	0.182766i
$607$	−7.53409	+	6.32185i	−0.305799	+	0.256596i	−0.782753	−	0.622332i	$-0.786185\pi$
$607$	−7.53409	+	6.32185i	−0.305799	+	0.256596i	0.476954	+	0.878928i	$0.341741\pi$
$608$	4.95467	+	28.0993i	0.200938	+	1.13958i
$609$	−0.139134	−	8.08587i	−0.00563799	−	0.327656i
$610$	4.62612	+	3.88177i	0.187306	+	0.157168i
$611$	20.7352	−	35.9144i	0.838857	−	1.45294i
$612$	15.4296	+	7.92053i	0.623703	+	0.320168i
$613$	19.3354	+	33.4899i	0.780951	+	1.35265i	0.931388	+	0.364027i	$0.118598\pi$
$613$	19.3354	+	33.4899i	0.780951	+	1.35265i	−0.150438	+	0.988619i	$0.548068\pi$
$614$	7.15497	+	6.00373i	0.288751	+	0.242291i
$615$	8.89858	−	9.34885i	0.358826	−	0.376982i
$616$	13.4945	+	19.5816i	0.543708	+	0.788966i
$617$	−4.43231	−	1.61323i	−0.178438	−	0.0649461i	0.251256	−	0.967921i	$-0.419156\pi$
$617$	−4.43231	−	1.61323i	−0.178438	−	0.0649461i	−0.429694	+	0.902975i	$0.641379\pi$
$618$	−8.28503	−	5.50174i	−0.333273	−	0.221313i
$619$	−33.0892	−	27.7652i	−1.32997	−	1.11598i	−0.984085	−	0.177699i	$-0.943135\pi$
$619$	−33.0892	−	27.7652i	−1.32997	−	1.11598i	−0.345884	−	0.938277i	$-0.612421\pi$
$620$	−11.4109	+	19.7642i	−0.458271	+	0.793749i
$621$	31.3283	+	0.415294i	1.25716	+	0.0166652i
$622$	−13.1806			−0.528494
$623$	−13.8123	+	13.6076i	−0.553378	+	0.545178i
$624$	12.5872	+	8.35864i	0.503891	+	0.334613i
$625$	−0.985257	−	5.58767i	−0.0394103	−	0.223507i
$626$	0.615997	+	3.49349i	0.0246202	+	0.139628i
$627$	−32.6977	−	7.90224i	−1.30582	−	0.315585i
$628$	−17.0249	−	14.2856i	−0.679368	−	0.570057i
$629$	4.03248	−	6.98445i	0.160785	−	0.278488i
$630$	−7.39580	−	3.07868i	−0.294656	−	0.122658i
$631$	−8.12350	−	14.0703i	−0.323391	−	0.560130i	0.657794	−	0.753198i	$-0.271490\pi$
$631$	−8.12350	−	14.0703i	−0.323391	−	0.560130i	−0.981185	+	0.193068i	$0.938156\pi$
$632$	−2.17820	+	12.3532i	−0.0866443	+	0.491384i
$633$	−22.9880	+	2.58400i	−0.913691	+	0.102705i
$634$	11.0883	+	4.03582i	0.440374	+	0.160283i
$635$	−8.15806	+	6.84542i	−0.323743	+	0.271652i
$636$	−10.6722	+	24.4434i	−0.423181	+	0.969245i
$637$	36.0631	−	5.80515i	1.42887	−	0.230008i
$638$	−2.21355	−	3.83399i	−0.0876354	−	0.151789i
$639$	−26.7923	+	35.3321i	−1.05989	+	1.39772i
$640$	−8.74725	−	15.1507i	−0.345765	−	0.598883i
$641$	−2.91125	+	16.5105i	−0.114987	+	0.652125i	0.871769	+	0.489917i	$0.162973\pi$
$641$	−2.91125	+	16.5105i	−0.114987	+	0.652125i	−0.986756	+	0.162209i	$0.948138\pi$
$642$	−3.72221	−	12.6360i	−0.146904	−	0.498702i
$643$	−7.19938	+	6.04100i	−0.283916	+	0.238234i	−0.773612	−	0.633659i	$-0.781552\pi$
$643$	−7.19938	+	6.04100i	−0.283916	+	0.238234i	0.489696	+	0.871893i	$0.337108\pi$
$644$	25.1729	−	2.01311i	0.991950	−	0.0793275i
$645$	0.101294	−	1.61610i	0.00398843	−	0.0636337i
$646$	11.0799	−	4.03277i	0.435934	−	0.158667i
$647$	20.6797	−	35.8183i	0.813003	−	1.40816i	−0.0977500	−	0.995211i	$-0.531165\pi$
$647$	20.6797	−	35.8183i	0.813003	−	1.40816i	0.910753	−	0.412952i	$-0.135502\pi$
$648$	5.61893	+	20.0517i	0.220732	+	0.787706i
$649$	−15.2995	−	26.4994i	−0.600556	−	1.04019i
$650$	−1.49640	+	8.48653i	−0.0586938	+	0.332869i
$651$	26.6104	−	32.8445i	1.04294	−	1.28728i
$652$	17.0432	+	6.20323i	0.667465	+	0.242937i
$653$	40.2772	+	14.6597i	1.57617	+	0.573679i	0.974367	−	0.224965i	$-0.0722268\pi$
$653$	40.2772	+	14.6597i	1.57617	+	0.573679i	0.601803	+	0.798644i	$0.294449\pi$
$654$	10.8537	−	11.4028i	0.424412	−	0.445887i
$655$	3.59987	−	20.4159i	0.140659	−	0.797715i
$656$	−7.97074			−0.311205
$657$	12.0583	−	15.9018i	0.470441	−	0.620390i
$658$	12.3487	−	5.64644i	0.481401	−	0.220121i
$659$	−32.2237	−	27.0389i	−1.25526	−	1.05328i	−0.996171	−	0.0874302i	$-0.972135\pi$
$659$	−32.2237	−	27.0389i	−1.25526	−	1.05328i	−0.259085	−	0.965854i	$-0.583421\pi$
$660$	16.5426	−	1.85950i	0.643920	−	0.0723809i
$661$	36.4064	+	13.2509i	1.41605	+	0.515399i	0.932898	−	0.360140i	$-0.117271\pi$
$661$	36.4064	+	13.2509i	1.41605	+	0.515399i	0.483148	+	0.875539i	$0.339493\pi$
$662$	−19.6808	−	7.16324i	−0.764918	−	0.278407i
$663$	13.2079	−	30.2510i	0.512951	−	1.17485i
$664$	−7.67714	−	6.44188i	−0.297931	−	0.249994i
$665$	18.8010	−	8.59679i	0.729073	−	0.333369i
$666$	4.17138	−	0.949783i	0.161638	−	0.0368034i
$667$	−10.6408			−0.412014
$668$	0.797143	−	4.52082i	0.0308424	−	0.174916i
$669$	34.5713	+	8.35506i	1.33661	+	0.323025i
$670$	−1.71695	−	0.624918i	−0.0663315	−	0.0241427i
$671$	21.8419	+	7.94981i	0.843198	+	0.306899i
$672$	9.36653	+	24.4187i	0.361322	+	0.941973i
$673$	−6.33835	+	35.9466i	−0.244325	+	1.38564i	0.577729	+	0.816229i	$0.303939\pi$
$673$	−6.33835	+	35.9466i	−0.244325	+	1.38564i	−0.822054	+	0.569409i	$0.807172\pi$
$674$	9.42291	+	16.3210i	0.362957	+	0.628660i
$675$	10.2916	−	8.40571i	0.396122	−	0.323536i
$676$	11.2625	−	19.5072i	0.433173	−	0.750277i
$677$	−20.2879	+	7.38418i	−0.779726	+	0.283797i	−0.701058	−	0.713104i	$-0.747289\pi$
$677$	−20.2879	+	7.38418i	−0.779726	+	0.283797i	−0.0786677	+	0.996901i	$0.525067\pi$
$678$	−2.75746	+	1.36963i	−0.105900	+	0.0526002i
$679$	−15.3202	+	1.22518i	−0.587937	+	0.0470181i
$680$	−10.1172	+	8.48937i	−0.387978	+	0.325553i
$681$	−3.32237	−	0.802937i	−0.127313	−	0.0307686i
$682$	4.01834	−	22.7891i	0.153870	−	0.872641i
$683$	−21.5556	−	37.3353i	−0.824801	−	1.42860i	−0.902071	−	0.431587i	$-0.857954\pi$
$683$	−21.5556	−	37.3353i	−0.824801	−	1.42860i	0.0772703	−	0.997010i	$-0.475380\pi$
$684$	−21.1218	−	10.8425i	−0.807611	−	0.414574i
$685$	2.10134	+	3.63962i	0.0802880	+	0.139063i
$686$	10.7234	+	5.29593i	0.409423	+	0.202199i
$687$	2.13834	−	0.240364i	0.0815828	−	0.00917046i
$688$	−0.766042	+	0.642785i	−0.0292051	+	0.0245060i
$689$	47.7002	+	17.3615i	1.81723	+	0.661419i
$690$	−4.21769	+	9.66012i	−0.160565	+	0.367754i
$691$	3.60542	−	20.4473i	0.137157	−	0.777853i	−0.836177	−	0.548459i	$-0.815215\pi$
$691$	3.60542	−	20.4473i	0.137157	−	0.777853i	0.973334	−	0.229394i	$-0.0736744\pi$
$692$	−10.7707	−	18.6555i	−0.409442	−	0.709174i
$693$	−30.8022	−	1.39910i	−1.17008	−	0.0531472i
$694$	−5.35781	+	9.28000i	−0.203380	+	0.352264i
$695$	−1.41462	−	1.18700i	−0.0536595	−	0.0450256i
$696$	−1.99843	−	6.78417i	−0.0757502	−	0.257153i
$697$	3.02371	+	17.1483i	0.114531	+	0.649538i
$698$	0.249113	+	1.41279i	0.00942906	+	0.0534748i
$699$	−17.5442	+	8.71419i	−0.663584	+	0.329601i
$700$	7.62967	−	7.51660i	0.288374	−	0.284101i
$701$	−30.2790			−1.14362			−0.571811	−	0.820385i	$-0.693759\pi$
$701$	−30.2790			−1.14362			−0.571811	+	0.820385i	$0.693759\pi$
$702$	16.5318	−	5.77009i	0.623952	−	0.217778i
$703$	−5.52011	+	9.56112i	−0.208195	+	0.360604i
$704$	1.01772	+	0.853969i	0.0383568	+	0.0321852i
$705$	1.34580	−	21.4716i	0.0506856	−	0.808667i
$706$	−8.00858	−	2.91488i	−0.301407	−	0.109703i
$707$	6.58949	+	9.56190i	0.247823	+	0.359612i
$708$	−6.10246	−	20.7163i	−0.229344	−	0.778568i
$709$	7.66586	+	6.43242i	0.287898	+	0.241575i	0.775286	−	0.631611i	$-0.217606\pi$
$709$	7.66586	+	6.43242i	0.287898	+	0.241575i	−0.487388	+	0.873185i	$0.662050\pi$
$710$	−7.45894	−	12.9193i	−0.279929	−	0.484852i
$711$	−11.0560	−	11.9281i	−0.414633	−	0.447340i
$712$	−8.47829	+	14.6848i	−0.317737	+	0.550337i
$713$	−42.6074	−	35.7518i	−1.59566	−	1.33892i
$714$	9.26547	−	5.56413i	0.346752	−	0.208232i
$715$	−5.50155	−	31.2009i	−0.205746	−	1.16685i
$716$	−21.1786	+	17.7710i	−0.791482	+	0.664133i
$717$	−20.5305	−	27.8332i	−0.766726	−	1.03945i
$718$	−5.64137	+	2.05329i	−0.210534	+	0.0766282i
$719$	−15.1427	+	26.2279i	−0.564727	+	0.978136i	0.432348	+	0.901707i	$0.357685\pi$
$719$	−15.1427	+	26.2279i	−0.564727	+	0.978136i	−0.997075	+	0.0764295i	$0.975648\pi$
$720$	7.77718	+	0.978761i	0.289838	+	0.0364763i
$721$	21.3946	−	9.78268i	0.796775	−	0.364326i
$722$	−3.63775	+	1.32403i	−0.135383	+	0.0492753i
$723$	−3.38554	−	11.4931i	−0.125910	−	0.427432i
$724$	−2.09900	−	11.9040i	−0.0780087	−	0.442409i
$725$	−3.45712	+	2.90087i	−0.128394	+	0.107736i
$726$	−4.09813	+	2.03554i	−0.152096	+	0.0755458i
$727$	1.58573	−	8.99314i	0.0588116	−	0.333537i	−0.941179	−	0.337909i	$-0.890280\pi$
$727$	1.58573	−	8.99314i	0.0588116	−	0.333537i	0.999990	+	0.00437166i	$0.00139155\pi$
$728$	29.0513	−	13.2837i	1.07671	−	0.492328i
$729$	−25.1180	−	9.90384i	−0.930296	−	0.366809i
$730$	3.35703	+	5.81455i	0.124249	+	0.215206i
$731$	1.67349	+	1.40423i	0.0618963	+	0.0519371i
$732$	13.6664	+	9.07528i	0.505124	+	0.335432i
$733$	−6.02255	−	34.1556i	−0.222448	−	1.26156i	−0.867504	−	0.497430i	$-0.834277\pi$
$733$	−6.02255	−	34.1556i	−0.222448	−	1.26156i	0.645057	−	0.764135i	$-0.276834\pi$
$734$	−10.5749	+	8.87340i	−0.390327	+	0.327523i
$735$	15.4158	−	11.0196i	0.568621	−	0.406464i
$736$	32.3370	−	11.7697i	1.19196	−	0.433837i
$737$	−7.03257			−0.259048
$738$	−5.58111	+	7.36005i	−0.205444	+	0.270927i
$739$	−45.3929			−1.66980			−0.834902	−	0.550399i	$-0.814476\pi$
$739$	−45.3929			−1.66980			−0.834902	+	0.550399i	$0.814476\pi$
$740$	0.948714	−	5.38043i	0.0348754	−	0.197788i
$741$	−18.0804	+	41.4111i	−0.664201	+	1.52127i
$742$	9.43122	+	13.6855i	0.346231	+	0.502410i
$743$	−4.09123	−	23.2025i	−0.150093	−	0.851219i	−0.963136	−	0.269015i	$-0.913302\pi$
$743$	−4.09123	−	23.2025i	−0.150093	−	0.851219i	0.813043	−	0.582204i	$-0.197809\pi$
$744$	14.7920	−	33.8793i	0.542300	−	1.24207i
$745$	−26.1193	+	9.50665i	−0.956937	+	0.348297i
$746$	−6.97430			−0.255347
$747$	12.6697	−	2.88477i	0.463561	−	0.105548i
$748$	−11.2293	+	19.4496i	−0.410582	+	0.711150i
$749$	30.0365	+	8.28906i	1.09751	+	0.302876i
$750$	3.73306	+	12.6728i	0.136312	+	0.462746i
$751$	−1.26690	−	0.461113i	−0.0462298	−	0.0168263i	0.318802	−	0.947821i	$-0.396720\pi$
$751$	−1.26690	−	0.461113i	−0.0462298	−	0.0168263i	−0.365032	+	0.930995i	$0.618942\pi$
$752$	−10.1777	+	8.54010i	−0.371142	+	0.311425i
$753$	5.29507	−	2.63005i	0.192963	−	0.0958445i
$754$	−5.58813	+	2.03391i	−0.203508	+	0.0740708i
$755$	−1.88339			−0.0685438
$756$	−20.8996	−	6.06683i	−0.760111	−	0.220648i
$757$	4.51470			0.164089			0.0820447	−	0.996629i	$-0.473855\pi$
$757$	4.51470			0.164089			0.0820447	+	0.996629i	$0.473855\pi$
$758$	−18.1755	+	6.61532i	−0.660162	+	0.240279i
$759$	−2.53791	+	40.4913i	−0.0921204	+	1.46974i
$760$	13.8496	−	11.6212i	0.502379	−	0.421546i
$761$	−10.3614	−	3.77123i	−0.375599	−	0.136707i	0.147321	−	0.989089i	$-0.452935\pi$
$761$	−10.3614	−	3.77123i	−0.375599	−	0.136707i	−0.522920	+	0.852382i	$0.675157\pi$
$762$	5.25459	−	5.52047i	0.190354	−	0.199986i
$763$	9.36905	+	36.0398i	0.339182	+	1.30473i
$764$	−14.7297	+	25.5125i	−0.532900	+	0.923010i
$765$	−0.844568	−	17.1032i	−0.0305354	−	0.618366i
$766$	9.64257			0.348400
$767$	−38.6236	+	14.0578i	−1.39462	+	0.507599i
$768$	8.13525	+	11.0289i	0.293555	+	0.397973i
$769$	−5.27491	−	29.9155i	−0.190218	−	1.07878i	−0.919066	−	0.394105i	$-0.871055\pi$
$769$	−5.27491	−	29.9155i	−0.190218	−	1.07878i	0.728847	−	0.684676i	$-0.240056\pi$
$770$	4.45408	−	9.36857i	0.160514	−	0.337620i
$771$	24.3238	−	2.73416i	0.876001	−	0.0984683i
$772$	−3.46191	+	19.6335i	−0.124597	+	0.706624i
$773$	14.7603			0.530889			0.265445	−	0.964126i	$-0.414481\pi$
$773$	14.7603			0.530889			0.265445	+	0.964126i	$0.414481\pi$
$774$	0.0571547	+	1.15743i	0.00205438	+	0.0416029i
$775$	−23.5894			−0.847356
$776$	−12.6302	+	4.59702i	−0.453398	+	0.165023i
$777$	−3.29700	+	9.56746i	−0.118279	+	0.343231i
$778$	−5.78374	+	4.85313i	−0.207357	+	0.173993i
$779$	−4.13920	−	23.4745i	−0.148302	−	0.841063i
$780$	1.39880	−	22.3172i	0.0500850	−	0.799085i
$781$	−43.9849	−	36.9077i	−1.57390	−	1.32066i
$782$	−7.11035	−	12.3155i	−0.254266	−	0.440401i
$783$	8.57453	+	3.25022i	0.306429	+	0.116153i
$784$	−11.4930	−	2.20393i	−0.410464	−	0.0787118i
$785$	−3.81033	+	21.6095i	−0.135997	+	0.771275i
$786$	−0.928079	+	14.8071i	−0.0331035	+	0.528152i
$787$	38.1223	−	31.9884i	1.35891	−	1.14026i	0.382596	−	0.923916i	$-0.375030\pi$
$787$	38.1223	−	31.9884i	1.35891	−	1.14026i	0.976316	−	0.216348i	$-0.0694145\pi$
$788$	−2.46671	−	13.9894i	−0.0878730	−	0.498353i
$789$	−2.04273	+	2.14609i	−0.0727232	+	0.0764030i
$790$	5.14170	−	1.87143i	0.182933	−	0.0665823i
$791$	0.688882	−	7.25018i	0.0244938	−	0.257787i
$792$	−26.2923	+	5.98650i	−0.934256	+	0.212721i
$793$	15.6112	−	27.0394i	0.554370	−	0.960197i
$794$	10.1892	−	3.70857i	0.361602	−	0.131612i
$795$	26.1689	−	2.94156i	0.928115	−	0.104326i
$796$	20.3932	−	17.1119i	0.722817	−	0.606515i
$797$	−7.86822	−	44.6229i	−0.278707	−	1.58062i	−0.726935	−	0.686706i	$-0.759056\pi$
$797$	−7.86822	−	44.6229i	−0.278707	−	1.58062i	0.448229	−	0.893919i	$-0.352055\pi$
$798$	−12.6836	+	7.61682i	−0.448996	+	0.269632i
$799$	22.2341	+	18.6567i	0.786587	+	0.660025i
$800$	7.29742	−	12.6395i	0.258003	−	0.446874i
$801$	−8.52926	−	20.2636i	−0.301367	−	0.715978i
$802$	−0.535659	−	0.927789i	−0.0189148	−	0.0327614i
$803$	19.7962	+	16.6110i	0.698592	+	0.586189i
$804$	−4.82463	−	1.16600i	−0.170152	−	0.0411216i
$805$	−14.1483	−	20.5303i	−0.498661	−	0.723598i
$806$	−29.2094	−	10.6314i	−1.02886	−	0.374474i
$807$	−37.5290	+	18.6406i	−1.32108	+	0.656180i
$808$	7.77959	+	6.52785i	0.273685	+	0.229649i
$809$	−12.9947	+	22.5074i	−0.456868	+	0.791319i	−0.998794	−	0.0491074i	$-0.984362\pi$
$809$	−12.9947	+	22.5074i	−0.456868	+	0.791319i	0.541925	+	0.840427i	$0.317696\pi$
$810$	6.34935	−	6.49599i	0.223093	−	0.228246i
$811$	37.8470			1.32899			0.664494	−	0.747293i	$-0.268647\pi$
$811$	37.8470			1.32899			0.664494	+	0.747293i	$0.268647\pi$
$812$	7.12471	+	1.96618i	0.250028	+	0.0689994i
$813$	−1.70652	+	27.2268i	−0.0598503	+	0.954886i
$814$	0.961974	+	5.45562i	0.0337172	+	0.191220i
$815$	−3.10956	−	17.6352i	−0.108923	−	0.617733i
$816$	−7.29100	+	7.65992i	−0.255236	+	0.268151i
$817$	−2.29086	−	1.92226i	−0.0801472	−	0.0672515i
$818$	5.61364	−	9.72311i	0.196276	−	0.339961i
$819$	−9.03557	+	40.4205i	−0.315728	+	1.41241i
$820$	5.89798	+	10.2156i	0.205966	+	0.356744i
$821$	5.27240	−	29.9013i	0.184008	−	1.04356i	−0.743215	−	0.669053i	$-0.766700\pi$
$821$	5.27240	−	29.9013i	0.184008	−	1.04356i	0.927223	−	0.374510i	$-0.122189\pi$
$822$	−1.78538	−	2.42043i	−0.0622722	−	0.0844223i
$823$	38.0151	+	13.8364i	1.32512	+	0.482306i	0.905097	−	0.425206i	$-0.139798\pi$
$823$	38.0151	+	13.8364i	1.32512	+	0.482306i	0.420027	+	0.907512i	$0.362021\pi$
$824$	15.7601	−	13.2243i	0.549030	−	0.460690i
$825$	10.2141	+	13.8472i	0.355608	+	0.482097i
$826$	−12.9729	−	3.58009i	−0.451386	−	0.124567i
$827$	−4.78968	−	8.29596i	−0.166553	−	0.288479i	0.770652	−	0.637256i	$-0.219930\pi$
$827$	−4.78968	−	8.29596i	−0.166553	−	0.288479i	−0.937206	+	0.348777i	$0.886597\pi$
$828$	−8.45455	+	27.3579i	−0.293816	+	0.950752i
$829$	14.9886	+	25.9609i	0.520574	+	0.901661i	0.999714	+	0.0239223i	$0.00761542\pi$
$829$	14.9886	+	25.9609i	0.520574	+	0.901661i	−0.479140	+	0.877739i	$0.659051\pi$
$830$	−0.759116	+	4.30516i	−0.0263493	+	0.149434i
$831$	0.895023	−	0.940311i	0.0310480	−	0.0326190i
$832$	1.36707	−	1.14710i	0.0473945	−	0.0397687i
$833$	−0.381671	+	25.5621i	−0.0132241	+	0.885676i
$834$	1.10093	+	0.731084i	0.0381222	+	0.0253154i
$835$	−4.25906	+	1.55017i	−0.147391	+	0.0536459i
$836$	15.3719	−	26.6249i	0.531648	−	0.920841i
$837$	23.4133	+	41.8238i	0.809283	+	1.44564i
$838$	6.33309	+	10.9692i	0.218773	+	0.378926i
$839$	5.87222	−	33.3030i	0.202731	−	1.14975i	−0.698238	−	0.715865i	$-0.746032\pi$
$839$	5.87222	−	33.3030i	0.202731	−	1.14975i	0.900970	−	0.433882i	$-0.142856\pi$
$840$	10.4322	−	12.8761i	0.359944	−	0.444269i
$841$	24.3246	+	8.85343i	0.838779	+	0.305291i
$842$	16.5033	+	6.00672i	0.568742	+	0.207005i
$843$	14.8337	+	50.3566i	0.510898	+	1.73437i
$844$	3.67123	−	20.8206i	0.126369	−	0.716675i
$845$	−22.2396			−0.765064
$846$	0.759362	+	15.3777i	0.0261074	+	0.528696i
$847$	1.02382	−	10.7752i	0.0351787	−	0.370240i
$848$	−12.4579	−	10.4534i	−0.427807	−	0.358972i
$849$	−12.7131	−	17.2351i	−0.436313	−	0.591508i
$850$	−5.66751	−	2.06281i	−0.194394	−	0.0707537i
$851$	12.5122	+	4.55407i	0.428912	+	0.156111i
$852$	−24.0562	−	32.6129i	−0.824151	−	1.11730i
$853$	22.9539	+	19.2606i	0.785927	+	0.659471i	0.944734	−	0.327838i	$-0.106320\pi$
$853$	22.9539	+	19.2606i	0.785927	+	0.659471i	−0.158807	+	0.987310i	$0.550765\pi$
$854$	9.29711	−	4.25111i	0.318141	−	0.145470i
$855$	1.15614	+	23.4128i	0.0395392	+	0.800700i
$856$	27.2497			0.931376
$857$	1.12732	−	6.39335i	0.0385085	−	0.218393i	−0.959481	−	0.281774i	$-0.909077\pi$
$857$	1.12732	−	6.39335i	0.0385085	−	0.218393i	0.997989	+	0.0633811i	$0.0201884\pi$
$858$	6.40681	+	21.7495i	0.218725	+	0.742517i
$859$	6.58220	+	2.39572i	0.224582	+	0.0817410i	0.451860	−	0.892089i	$-0.350761\pi$
$859$	6.58220	+	2.39572i	0.224582	+	0.0817410i	−0.227279	+	0.973830i	$0.572983\pi$
$860$	1.39065	+	0.506156i	0.0474208	+	0.0172598i
$861$	−7.82492	−	20.3997i	−0.266673	−	0.695221i
$862$	1.91507	−	10.8609i	0.0652276	−	0.369924i
$863$	−24.8999	−	43.1279i	−0.847603	−	1.46809i	−0.883341	−	0.468730i	$-0.844712\pi$
$863$	−24.8999	−	43.1279i	−0.847603	−	1.46809i	0.0357383	−	0.999361i	$-0.488622\pi$
$864$	−29.6527	−	0.393081i	−1.00881	−	0.0133729i
$865$	−10.6343	+	18.4191i	−0.361575	+	0.626267i
$866$	1.58342	−	0.576317i	0.0538067	−	0.0195840i
$867$	−5.28365	−	3.50866i	−0.179442	−	0.119160i
$868$	21.9223	+	31.8110i	0.744090	+	1.07974i
$869$	16.1331	−	13.5373i	0.547277	−	0.459220i
$870$	−2.12696	+	2.23459i	−0.0721109	+	0.0757596i
$871$	−1.64038	+	9.30308i	−0.0555823	+	0.315223i
$872$	16.2827	+	28.2025i	0.551403	+	0.955058i
$873$	5.14545	−	16.6500i	0.174147	−	0.563519i
$874$	9.73346	+	16.8588i	0.329239	+	0.570259i
$875$	−30.1240	−	8.31322i	−1.01838	−	0.281038i
$876$	10.8269	+	14.6780i	0.365807	+	0.495924i
$877$	−5.32821	+	4.47090i	−0.179921	+	0.150972i	−0.728300	−	0.685258i	$-0.759689\pi$
$877$	−5.32821	+	4.47090i	−0.179921	+	0.150972i	0.548379	+	0.836230i	$0.315245\pi$
$878$	17.4082	+	6.33605i	0.587497	+	0.213831i
$879$	2.96674	+	4.02200i	0.100066	+	0.135659i
$880$	−1.76255	+	9.99594i	−0.0594157	+	0.336963i
$881$	−2.42562	−	4.20129i	−0.0817211	−	0.141545i	0.822268	−	0.569100i	$-0.192708\pi$
$881$	−2.42562	−	4.20129i	−0.0817211	−	0.141545i	−0.903989	+	0.427555i	$0.859375\pi$
$882$	−10.0825	+	9.06924i	−0.339494	+	0.305377i
$883$	9.67442	−	16.7566i	0.325570	−	0.563904i	−0.656057	−	0.754711i	$-0.727777\pi$
$883$	9.67442	−	16.7566i	0.325570	−	0.563904i	0.981628	+	0.190807i	$0.0611104\pi$
$884$	23.1098	+	19.3914i	0.777266	+	0.652204i
$885$	−14.7010	+	15.4448i	−0.494168	+	0.519173i
$886$	0.657590	+	3.72938i	0.0220922	+	0.125291i
$887$	8.74908	+	49.6185i	0.293766	+	1.66603i	0.672178	+	0.740390i	$0.265359\pi$
$887$	8.74908	+	49.6185i	0.293766	+	1.66603i	−0.378412	+	0.925637i	$0.623530\pi$
$888$	−0.553608	+	8.83258i	−0.0185779	+	0.296402i
$889$	4.53584	+	17.4480i	0.152127	+	0.585186i
$890$	7.39658			0.247934
$891$	14.4131	−	31.8533i	0.482857	−	1.06713i
$892$	−16.2527	+	28.1506i	−0.544182	+	0.942551i
$893$	−30.4366	−	25.5394i	−1.01852	−	0.854642i
$894$	17.8155	−	8.84891i	0.595838	−	0.295952i
$895$	25.6502	+	9.33592i	0.857393	+	0.312065i
$896$	−29.5209	+	2.36083i	−0.986225	+	0.0788697i
$897$	52.9721	+	12.8021i	1.76869	+	0.427449i
$898$	−17.5806	−	14.7519i	−0.586672	−	0.492277i
$899$	−8.13933	−	14.0977i	−0.271462	−	0.470186i
$900$	4.71141	+	11.1932i	0.157047	+	0.373108i
$901$	−17.7637	+	30.7676i	−0.591793	+	1.02502i
$902$	−9.16251	−	7.68826i	−0.305078	−	0.255991i
$903$	−2.39713	−	1.32953i	−0.0797713	−	0.0442438i
$904$	−1.10598	−	6.27230i	−0.0367842	−	0.208614i
$905$	−9.14234	+	7.67134i	−0.303902	+	0.255004i
$906$	1.33943	−	0.150561i	0.0444995	−	0.00500204i
$907$	−21.0336	+	7.65560i	−0.698409	+	0.254200i	−0.666731	−	0.745298i	$-0.732307\pi$
$907$	−21.0336	+	7.65560i	−0.698409	+	0.254200i	−0.0316774	+	0.999498i	$0.510085\pi$
$908$	1.56192	−	2.70532i	0.0518341	−	0.0897793i
$909$	−12.8388	+	2.92327i	−0.425836	+	0.0969588i
$910$	−11.3543	−	8.07737i	−0.376392	−	0.267762i
$911$	29.4404	−	10.7154i	0.975405	−	0.355018i	0.195353	−	0.980733i	$-0.437415\pi$
$911$	29.4404	−	10.7154i	0.975405	−	0.355018i	0.780052	+	0.625715i	$0.215193\pi$
$912$	9.98075	−	10.4858i	0.330496	−	0.347219i
$913$	2.92180	+	16.5703i	0.0966975	+	0.548398i
$914$	−15.3695	+	12.8965i	−0.508378	+	0.426580i
$915$	1.01323	−	16.1656i	0.0334963	−	0.534419i
$916$	−0.341498	+	1.93673i	−0.0112834	+	0.0639914i
$917$	−28.5961	−	20.3430i	−0.944325	−	0.671784i
$918$	1.96788	+	12.0959i	0.0649498	+	0.399223i
$919$	22.1981	+	38.4482i	0.732247	+	1.26829i	0.955921	+	0.293625i	$0.0948618\pi$
$919$	22.1981	+	38.4482i	0.732247	+	1.26829i	−0.223673	+	0.974664i	$0.571805\pi$
$920$	−16.7035	−	14.0159i	−0.550698	−	0.462091i
$921$	1.56711	−	25.0025i	0.0516379	−	0.823860i
$922$	0.0411129	+	0.233163i	0.00135398	+	0.00767882i
$923$	−59.0833	+	49.5768i	−1.94475	+	1.63184i
$924$	9.18116	−	26.6426i	0.302038	−	0.876476i
$925$	5.30663	−	1.93146i	0.174481	−	0.0635059i
$926$	18.6906			0.614210
$927$	1.31562	+	26.6424i	0.0432108	+	0.875052i
$928$	10.0717			0.330619
$929$	−7.47918	+	42.4165i	−0.245384	+	1.39164i	0.574216	+	0.818704i	$0.305307\pi$
$929$	−7.47918	+	42.4165i	−0.245384	+	1.39164i	−0.819600	+	0.572937i	$0.805804\pi$
$930$	−16.0246	+	1.80128i	−0.525468	+	0.0590661i
$931$	0.522475	−	34.9924i	0.0171234	−	1.14683i
$932$	−3.10886	−	17.6312i	−0.101834	−	0.577530i
$933$	20.9853	+	28.4498i	0.687029	+	0.931404i
$934$	−14.8749	+	5.41400i	−0.486720	+	0.177152i
$935$	22.1739			0.725165
$936$	1.78646	+	36.1773i	0.0583924	+	1.18249i
$937$	8.03273	−	13.9131i	0.262418	−	0.454521i	−0.704466	−	0.709738i	$-0.748813\pi$
$937$	8.03273	−	13.9131i	0.262418	−	0.454521i	0.966884	+	0.255217i	$0.0821468\pi$
$938$	−2.20337	+	2.17072i	−0.0719425	+	0.0708764i
$939$	6.55981	−	6.89173i	0.214071	−	0.224903i
$940$	18.4763	+	6.72483i	0.602631	+	0.219340i
$941$	−22.6766	+	19.0279i	−0.739235	+	0.620292i	−0.932632	−	0.360829i	$-0.882494\pi$
$941$	−22.6766	+	19.0279i	−0.739235	+	0.620292i	0.193397	+	0.981121i	$0.438049\pi$
$942$	0.982337	−	15.6728i	0.0320063	−	0.510646i
$943$	−27.0148	+	9.83257i	−0.879722	+	0.320192i
$944$	13.1681			0.428586
$945$	5.12993	+	20.8652i	0.166877	+	0.678745i
$946$	−1.50058			−0.0487882
$947$	−47.2531	+	17.1987i	−1.53552	+	0.558883i	−0.964965	−	0.262377i	$-0.915494\pi$
$947$	−47.2531	+	17.1987i	−1.53552	+	0.558883i	−0.570554	+	0.821260i	$0.693271\pi$
$948$	13.3124	−	6.61226i	0.432367	−	0.214756i
$949$	26.5915	−	22.3129i	0.863196	−	0.724308i
$950$	7.75834	+	2.82380i	0.251714	+	0.0916163i
$951$	−8.94301	−	30.3593i	−0.289997	−	0.984468i
$952$	5.62514	+	21.6382i	0.182312	+	0.701296i
$953$	−0.592625	+	1.02646i	−0.0191970	+	0.0332502i	−0.875464	−	0.483283i	$-0.839444\pi$
$953$	−0.592625	+	1.02646i	−0.0191970	+	0.0332502i	0.856267	+	0.516533i	$0.172778\pi$
$954$	−18.3756	+	4.18394i	−0.594931	+	0.135460i
$955$	29.0860			0.941202
$956$	29.7029	−	10.8110i	0.960662	−	0.349652i
$957$	−4.75122	+	10.8821i	−0.153585	+	0.351768i
$958$	−2.81961	−	15.9908i	−0.0910975	−	0.516640i
$959$	7.09176	−	0.567137i	0.229005	−	0.0183138i
$960$	0.370439	−	0.848447i	0.0119559	−	0.0273835i
$961$	9.39250	−	53.2675i	0.302984	−	1.71831i
$962$	7.44139			0.239920
$963$	−21.3480	+	28.1525i	−0.687929	+	0.907201i
$964$	10.9501			0.352680
$965$	18.4966	−	6.73223i	0.595428	−	0.216718i
$966$	11.7031	+	13.4697i	0.376542	+	0.433379i
$967$	39.8193	−	33.4124i	1.28050	−	1.07447i	0.287329	−	0.957832i	$-0.407233\pi$
$967$	39.8193	−	33.4124i	1.28050	−	1.07447i	0.993175	−	0.116638i	$-0.0372117\pi$
$968$	−1.64370	−	9.32188i	−0.0528305	−	0.299617i
$969$	−26.3454	−	17.4949i	−0.846335	−	0.562016i
$970$	4.49129	+	3.76864i	0.144207	+	0.121004i
$971$	12.6805	+	21.9632i	0.406935	+	0.704832i	0.994545	−	0.104312i	$-0.0332641\pi$
$971$	12.6805	+	21.9632i	0.406935	+	0.704832i	−0.587609	+	0.809145i	$0.699931\pi$
$972$	15.1692	−	19.4630i	0.486554	−	0.624275i
$973$	−2.84296	+	1.29994i	−0.0911410	+	0.0416743i
$974$	2.90027	−	16.4482i	0.0929305	−	0.527035i
$975$	20.7003	−	10.2818i	0.662941	−	0.329281i
$976$	−7.66262	+	6.42970i	−0.245274	+	0.205810i
$977$	6.09877	+	34.5879i	0.195117	+	1.10656i	0.912252	+	0.409629i	$0.134342\pi$
$977$	6.09877	+	34.5879i	0.195117	+	1.10656i	−0.717135	+	0.696934i	$0.754547\pi$
$978$	3.62122	+	12.2931i	0.115794	+	0.393091i
$979$	26.7522	−	9.73699i	0.855003	−	0.311196i
$980$	5.67964	+	16.3606i	0.181429	+	0.522621i
$981$	−41.8931	−	5.27226i	−1.33754	−	0.168330i
$982$	−2.71348	+	4.69988i	−0.0865905	+	0.149979i
$983$	16.9439	−	6.16707i	0.540426	−	0.196699i	−0.0573617	−	0.998353i	$-0.518269\pi$
$983$	16.9439	−	6.16707i	0.540426	−	0.196699i	0.597788	+	0.801655i	$0.296047\pi$
$984$	−11.3424	−	15.3769i	−0.361584	−	0.490199i
$985$	−10.7440	+	9.01525i	−0.342331	+	0.287250i
$986$	−0.722735	−	4.09883i	−0.0230166	−	0.130533i
$987$	−31.8484	−	17.6642i	−1.01375	−	0.562257i
$988$	−31.6353	−	26.5452i	−1.00645	−	0.844515i
$989$	−1.80337	+	3.12353i	−0.0573438	+	0.0993225i
$990$	7.99594	+	8.62666i	0.254128	+	0.274173i
$991$	−8.35016	−	14.4629i	−0.265251	−	0.459429i	0.702378	−	0.711804i	$-0.252122\pi$
$991$	−8.35016	−	14.4629i	−0.265251	−	0.459429i	−0.967629	+	0.252375i	$0.918788\pi$
$992$	40.3285	+	33.8396i	1.28043	+	1.07441i
$993$	15.8731	+	53.8852i	0.503717	+	1.70999i
$994$	−25.1730	+	2.01312i	−0.798440	+	0.0638523i
$995$	−24.6989	−	8.98968i	−0.783009	−	0.284992i
$996$	−0.742883	+	11.8524i	−0.0235391	+	0.375557i
$997$	−1.52210	−	1.27719i	−0.0482054	−	0.0404492i	0.618367	−	0.785890i	$-0.287795\pi$
$997$	−1.52210	−	1.27719i	−0.0482054	−	0.0404492i	−0.666572	+	0.745441i	$0.732239\pi$
$998$	8.24115	−	14.2741i	0.260869	−	0.451839i
$999$	−8.69149	−	7.49157i	−0.274986	−	0.237023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.25.9	yes	132
3.2	odd	2		567.2.w.a.235.14		132
7.2	even	3		189.2.u.a.79.14	yes	132
21.2	odd	6		567.2.u.a.478.9		132
27.13	even	9		189.2.u.a.67.14	✓	132
27.14	odd	18		567.2.u.a.172.9		132
189.121	even	9	inner	189.2.w.a.121.9	yes	132
189.149	odd	18		567.2.w.a.415.14		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.14	✓	132	27.13	even	9
189.2.u.a.79.14	yes	132	7.2	even	3
189.2.w.a.25.9	yes	132	1.1	even	1	trivial
189.2.w.a.121.9	yes	132	189.121	even	9	inner
567.2.u.a.172.9		132	27.14	odd	18
567.2.u.a.478.9		132	21.2	odd	6
567.2.w.a.235.14		132	3.2	odd	2
567.2.w.a.415.14		132	189.149	odd	18

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)

\(f(q)\)	\(=\)	\(q+(-0.606828 + 0.220867i) q^{2} +(1.44289 + 0.958162i) q^{3} +(-1.21263 + 1.01752i) q^{4} +(1.46866 + 0.534550i) q^{5} +(-1.08721 - 0.262753i) q^{6} +(1.88474 - 1.85681i) q^{7} +(1.15690 - 2.00380i) q^{8} +(1.16385 + 2.76504i) q^{9} +O(q^{10})\)	\(q+(-0.606828 + 0.220867i) q^{2} +(1.44289 + 0.958162i) q^{3} +(-1.21263 + 1.01752i) q^{4} +(1.46866 + 0.534550i) q^{5} +(-1.08721 - 0.262753i) q^{6} +(1.88474 - 1.85681i) q^{7} +(1.15690 - 2.00380i) q^{8} +(1.16385 + 2.76504i) q^{9} -1.00929 q^{10} +(-3.65044 + 1.32865i) q^{11} +(-2.72464 + 0.306267i) q^{12} +(0.906129 + 5.13891i) q^{13} +(-0.733606 + 1.54304i) q^{14} +(1.60693 + 2.17851i) q^{15} +(0.290300 - 1.64637i) q^{16} -3.65214 q^{17} +(-1.31696 - 1.42085i) q^{18} +4.99947 q^{19} +(-2.32486 + 0.846180i) q^{20} +(4.49860 - 0.873281i) q^{21} +(1.92173 - 1.61252i) q^{22} +(-1.04704 - 5.93806i) q^{23} +(3.58924 - 1.78277i) q^{24} +(-1.95899 - 1.64379i) q^{25} +(-1.68488 - 2.91830i) q^{26} +(-0.970052 + 5.10480i) q^{27} +(-0.396158 + 4.16939i) q^{28} +(0.306444 - 1.73793i) q^{29} +(-1.45629 - 0.967064i) q^{30} +(7.06629 - 5.92932i) q^{31} +(0.991039 + 5.62046i) q^{32} +(-6.54023 - 1.58062i) q^{33} +(2.21622 - 0.806639i) q^{34} +(3.76061 - 1.71954i) q^{35} +(-4.22480 - 2.16873i) q^{36} +(-1.10414 + 1.91243i) q^{37} +(-3.03382 + 1.10422i) q^{38} +(-3.61647 + 8.28309i) q^{39} +(2.77022 - 2.32449i) q^{40} +(-0.827927 - 4.69541i) q^{41} +(-2.53700 + 1.52353i) q^{42} +(-0.458222 - 0.384494i) q^{43} +(3.07471 - 5.32555i) q^{44} +(0.231253 + 4.68305i) q^{45} +(1.94690 + 3.37213i) q^{46} +(-6.08797 - 5.10841i) q^{47} +(1.99636 - 2.09738i) q^{48} +(0.104506 - 6.99922i) q^{49} +(1.55183 + 0.564821i) q^{50} +(-5.26963 - 3.49934i) q^{51} +(-6.32774 - 5.30960i) q^{52} +(4.86390 - 8.42452i) q^{53} +(-0.538829 - 3.31199i) q^{54} -6.07149 q^{55} +(-1.54023 - 5.92478i) q^{56} +(7.21367 + 4.79030i) q^{57} +(0.197893 + 1.12231i) q^{58} +(1.36778 + 7.75709i) q^{59} +(-4.16529 - 1.00665i) q^{60} +(-4.58353 - 3.84604i) q^{61} +(-2.97843 + 5.15879i) q^{62} +(7.32772 + 3.05034i) q^{63} +(-0.170996 - 0.296174i) q^{64} +(-1.41621 + 8.03170i) q^{65} +(4.31790 - 0.485361i) q^{66} +(1.70114 + 0.619166i) q^{67} +(4.42870 - 3.71612i) q^{68} +(4.17887 - 9.57119i) q^{69} +(-1.90225 + 1.87406i) q^{70} +(7.39028 + 12.8003i) q^{71} +(6.88705 + 0.866737i) q^{72} +(-3.32613 - 5.76102i) q^{73} +(0.247631 - 1.40438i) q^{74} +(-1.25159 - 4.24884i) q^{75} +(-6.06251 + 5.08705i) q^{76} +(-4.41308 + 9.28233i) q^{77} +(0.365110 - 5.82518i) q^{78} +(-5.09437 + 1.85420i) q^{79} +(1.30642 - 2.26279i) q^{80} +(-6.29090 + 6.43619i) q^{81} +(1.53947 + 2.66644i) q^{82} +(0.752128 - 4.26553i) q^{83} +(-4.56656 + 5.63637i) q^{84} +(-5.36377 - 1.95225i) q^{85} +(0.362984 + 0.132115i) q^{86} +(2.10739 - 2.21402i) q^{87} +(-1.56082 + 8.85185i) q^{88} -7.32849 q^{89} +(-1.17466 - 2.79073i) q^{90} +(11.2498 + 8.00302i) q^{91} +(7.31176 + 6.13530i) q^{92} +(15.8771 - 1.78469i) q^{93} +(4.82263 + 1.75530i) q^{94} +(7.34254 + 2.67246i) q^{95} +(-3.95535 + 9.05927i) q^{96} +(-4.44995 - 3.73395i) q^{97} +(1.48248 + 4.27041i) q^{98} +(-7.92233 - 8.54725i) 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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