LMFDB - Embedded newform 243.2.i.a.106.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(4,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("243.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(162)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.i (of order $81$, degree $54$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			106.23
Character	$\chi$	$=$	243.106
Dual form			243.2.i.a.94.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.793648 - 2.05560i) q^{2} +(-1.07043 + 1.36168i) q^{3} +(-2.11453 - 1.91883i) q^{4} +(2.04843 + 1.46413i) q^{5} +(1.94953 + 3.28107i) q^{6} +(2.10773 + 1.63362i) q^{7} +(-1.68432 + 0.845896i) q^{8} +(-0.708355 - 2.91517i) q^{9} +(4.63539 - 3.04874i) q^{10} +(1.22434 - 1.78513i) q^{11} +(4.87629 - 0.825337i) q^{12} +(-0.702251 + 0.137918i) q^{13} +(5.03086 - 3.03614i) q^{14} +(-4.18637 + 1.22206i) q^{15} +(-0.150793 - 1.55029i) q^{16} +(2.72369 + 6.31422i) q^{17} +(-6.55461 - 0.857526i) q^{18} +(-2.81577 - 3.78224i) q^{19} +(-1.52204 - 7.02652i) q^{20} +(-4.48065 + 1.12139i) q^{21} +(-2.69781 - 3.93351i) q^{22} +(-1.24169 - 0.507285i) q^{23} +(0.651104 - 3.19898i) q^{24} +(0.433712 + 1.26757i) q^{25} +(-0.273837 + 1.55301i) q^{26} +(4.72778 + 2.15594i) q^{27} +(-1.32223 - 7.49871i) q^{28} +(-2.80345 + 1.54688i) q^{29} +(-0.810445 + 9.57540i) q^{30} +(-2.12576 - 4.03566i) q^{31} +(-6.93797 - 1.93132i) q^{32} +(1.12021 + 3.57801i) q^{33} +(15.1412 - 0.587546i) q^{34} +(1.92571 + 6.43233i) q^{35} +(-4.09589 + 7.52342i) q^{36} +(7.28541 + 7.72208i) q^{37} +(-10.0095 + 2.78634i) q^{38} +(0.563912 - 1.10387i) q^{39} +(-4.68870 - 0.733299i) q^{40} +(-6.19752 + 7.68372i) q^{41} +(-1.25093 + 10.1004i) q^{42} +(-4.42888 - 4.34382i) q^{43} +(-6.01424 + 1.42540i) q^{44} +(2.81717 - 7.00864i) q^{45} +(-2.02824 + 2.14981i) q^{46} +(2.01629 - 3.82783i) q^{47} +(2.27241 + 1.45414i) q^{48} +(0.0277496 + 0.107730i) q^{49} +(2.94984 + 0.114467i) q^{50} +(-11.5135 - 3.05014i) q^{51} +(1.74957 + 1.05587i) q^{52} +(-7.34250 - 2.67245i) q^{53} +(8.18394 - 8.00738i) q^{54} +(5.12161 - 1.86411i) q^{55} +(-4.93196 - 0.968606i) q^{56} +(8.16430 + 0.214439i) q^{57} +(0.954809 + 6.99044i) q^{58} +(-0.522197 + 0.0405884i) q^{59} +(11.1971 + 5.44887i) q^{60} +(5.65147 - 5.12843i) q^{61} +(-9.98281 + 1.16682i) q^{62} +(3.26925 - 7.30159i) q^{63} +(-7.61604 + 10.2301i) q^{64} +(-1.64044 - 0.745671i) q^{65} +(8.24401 + 0.536985i) q^{66} +(-8.47876 - 4.67838i) q^{67} +(6.35661 - 18.5779i) q^{68} +(2.01990 - 1.14777i) q^{69} +(14.7506 + 1.14651i) q^{70} +(0.398855 + 6.84808i) q^{71} +(3.65903 + 4.31088i) q^{72} +(-9.13092 - 6.00550i) q^{73} +(21.6556 - 8.84727i) q^{74} +(-2.19029 - 0.766270i) q^{75} +(-1.30345 + 13.4006i) q^{76} +(5.49679 - 1.76247i) q^{77} +(-1.82158 - 2.03526i) q^{78} +(-14.8396 + 2.32087i) q^{79} +(1.96093 - 3.39643i) q^{80} +(-7.99647 + 4.12996i) q^{81} +(10.8760 + 18.8378i) q^{82} +(7.84793 + 9.72991i) q^{83} +(11.6262 + 6.22640i) q^{84} +(-3.66555 + 16.9220i) q^{85} +(-12.4441 + 5.65655i) q^{86} +(0.894542 - 5.47323i) q^{87} +(-0.552140 + 4.04238i) q^{88} +(-0.345828 + 5.93763i) q^{89} +(-12.1711 - 11.3534i) q^{90} +(-1.70546 - 0.856516i) q^{91} +(1.65219 + 3.45526i) q^{92} +(7.77077 + 1.42528i) q^{93} +(-6.26827 - 7.18264i) q^{94} +(-0.230224 - 11.8703i) q^{95} +(10.0565 - 7.37997i) q^{96} +(8.55768 - 6.11666i) q^{97} +(0.243474 + 0.0284580i) q^{98} +(-6.07121 - 2.30465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) $ 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{50}{81}\right)$

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 $

$2$	0.793648	−	2.05560i	0.561194	−	1.45353i	−0.304284	−	0.952581i	$-0.598417\pi$
$2$	0.793648	−	2.05560i	0.561194	−	1.45353i	0.865478	−	0.500947i	$-0.167015\pi$
$3$	−1.07043	+	1.36168i	−0.618014	+	0.786167i
$3$	−1.07043	+	1.36168i	−0.618014	+	0.786167i
$4$	−2.11453	−	1.91883i	−1.05726	−	0.959415i
$5$	2.04843	+	1.46413i	0.916084	+	0.654778i	0.938614	−	0.344969i	$-0.112110\pi$
$5$	2.04843	+	1.46413i	0.916084	+	0.654778i	−0.0225301	+	0.999746i	$0.507172\pi$
$6$	1.94953	+	3.28107i	0.795891	+	1.33949i
$7$	2.10773	+	1.63362i	0.796649	+	0.617449i	0.927445	−	0.373960i	$-0.122000\pi$
$7$	2.10773	+	1.63362i	0.796649	+	0.617449i	−0.130796	+	0.991409i	$0.541753\pi$
$8$	−1.68432	+	0.845896i	−0.595496	+	0.299069i
$9$	−0.708355	−	2.91517i	−0.236118	−	0.971724i
$10$	4.63539	−	3.04874i	1.46584	−	0.964097i
$11$	1.22434	−	1.78513i	0.369151	−	0.538236i	−0.594953	−	0.803761i	$-0.702829\pi$
$11$	1.22434	−	1.78513i	0.369151	−	0.538236i	0.964104	+	0.265525i	$0.0855453\pi$
$12$	4.87629	−	0.825337i	1.40766	−	0.238254i
$13$	−0.702251	+	0.137918i	−0.194769	+	0.0382515i	−0.289146	−	0.957285i	$-0.593371\pi$
$13$	−0.702251	+	0.137918i	−0.194769	+	0.0382515i	0.0943761	+	0.995537i	$0.469914\pi$
$14$	5.03086	−	3.03614i	1.34455	−	0.811443i
$15$	−4.18637	+	1.22206i	−1.08092	+	0.315534i
$16$	−0.150793	−	1.55029i	−0.0376983	−	0.387572i
$17$	2.72369	+	6.31422i	0.660592	+	1.53142i	0.837056	+	0.547117i	$0.184275\pi$
$17$	2.72369	+	6.31422i	0.660592	+	1.53142i	−0.176464	+	0.984307i	$0.556466\pi$
$18$	−6.55461	−	0.857526i	−1.54494	−	0.202121i
$19$	−2.81577	−	3.78224i	−0.645983	−	0.867706i	0.351674	−	0.936123i	$-0.385613\pi$
$19$	−2.81577	−	3.78224i	−0.645983	−	0.867706i	−0.997657	+	0.0684170i	$0.978205\pi$
$20$	−1.52204	−	7.02652i	−0.340339	−	1.57118i
$21$	−4.48065	+	1.12139i	−0.977758	+	0.244707i
$22$	−2.69781	−	3.93351i	−0.575175	−	0.838626i
$23$	−1.24169	−	0.507285i	−0.258910	−	0.105776i	0.245029	−	0.969516i	$-0.421203\pi$
$23$	−1.24169	−	0.507285i	−0.258910	−	0.105776i	−0.503939	+	0.863740i	$0.668116\pi$
$24$	0.651104	−	3.19898i	0.132906	−	0.652988i
$25$	0.433712	+	1.26757i	0.0867425	+	0.253514i
$26$	−0.273837	+	1.55301i	−0.0537038	+	0.304570i
$27$	4.72778	+	2.15594i	0.909862	+	0.414910i
$28$	−1.32223	−	7.49871i	−0.249877	−	1.41712i
$29$	−2.80345	+	1.54688i	−0.520587	+	0.287248i	−0.721563	−	0.692348i	$-0.756576\pi$
$29$	−2.80345	+	1.54688i	−0.520587	+	0.287248i	0.200976	+	0.979596i	$0.435589\pi$
$30$	−0.810445	+	9.57540i	−0.147966	+	1.74822i
$31$	−2.12576	−	4.03566i	−0.381798	−	0.724826i	0.616232	−	0.787565i	$-0.288658\pi$
$31$	−2.12576	−	4.03566i	−0.381798	−	0.724826i	−0.998030	+	0.0627388i	$0.980017\pi$
$32$	−6.93797	−	1.93132i	−1.22647	−	0.341412i
$33$	1.12021	+	3.57801i	0.195003	+	0.622852i
$34$	15.1412	−	0.587546i	2.59669	−	0.100763i
$35$	1.92571	+	6.43233i	0.325505	+	1.08726i
$36$	−4.09589	+	7.52342i	−0.682648	+	1.25390i
$37$	7.28541	+	7.72208i	1.19771	+	1.26950i	0.954052	+	0.299641i	$0.0968671\pi$
$37$	7.28541	+	7.72208i	1.19771	+	1.26950i	0.243661	+	0.969860i	$0.421651\pi$
$38$	−10.0095	+	2.78634i	−1.62376	+	0.452004i
$39$	0.563912	−	1.10387i	0.0902981	−	0.176761i
$40$	−4.68870	−	0.733299i	−0.741348	−	0.115945i
$41$	−6.19752	+	7.68372i	−0.967890	+	1.20000i	0.0118918	+	0.999929i	$0.496215\pi$
$41$	−6.19752	+	7.68372i	−0.967890	+	1.20000i	−0.979782	+	0.200067i	$0.935884\pi$
$42$	−1.25093	+	10.1004i	−0.193023	+	1.55853i
$43$	−4.42888	−	4.34382i	−0.675398	−	0.662426i	0.279231	−	0.960224i	$-0.409921\pi$
$43$	−4.42888	−	4.34382i	−0.675398	−	0.662426i	−0.954629	+	0.297798i	$0.903748\pi$
$44$	−6.01424	+	1.42540i	−0.906681	+	0.214887i
$45$	2.81717	−	7.00864i	0.419959	−	1.04479i
$46$	−2.02824	+	2.14981i	−0.299048	+	0.316972i
$47$	2.01629	−	3.82783i	0.294106	−	0.558347i	−0.692510	−	0.721409i	$-0.743495\pi$
$47$	2.01629	−	3.82783i	0.294106	−	0.558347i	0.986616	+	0.163062i	$0.0521369\pi$
$48$	2.27241	+	1.45414i	0.327995	+	0.209888i
$49$	0.0277496	+	0.107730i	0.00396422	+	0.0153901i
$50$	2.94984	+	0.114467i	0.417170	+	0.0161881i
$51$	−11.5135	−	3.05014i	−1.61221	−	0.427105i
$52$	1.74957	+	1.05587i	0.242622	+	0.146423i
$53$	−7.34250	−	2.67245i	−1.00857	−	0.367090i	−0.215687	−	0.976463i	$-0.569199\pi$
$53$	−7.34250	−	2.67245i	−1.00857	−	0.367090i	−0.792884	+	0.609373i	$0.791421\pi$
$54$	8.18394	−	8.00738i	1.11369	−	1.08967i
$55$	5.12161	−	1.86411i	0.690598	−	0.251357i
$56$	−4.93196	−	0.968606i	−0.659061	−	0.129435i
$57$	8.16430	+	0.214439i	1.08139	+	0.0284032i
$58$	0.954809	+	6.99044i	0.125373	+	0.917890i
$59$	−0.522197	+	0.0405884i	−0.0679843	+	0.00528416i	−0.111440	−	0.993771i	$-0.535546\pi$
$59$	−0.522197	+	0.0405884i	−0.0679843	+	0.00528416i	0.0434552	+	0.999055i	$0.486163\pi$
$60$	11.1971	+	5.44887i	1.44554	+	0.703446i
$61$	5.65147	−	5.12843i	0.723596	−	0.656629i	−0.224550	−	0.974463i	$-0.572091\pi$
$61$	5.65147	−	5.12843i	0.723596	−	0.656629i	0.948146	+	0.317834i	$0.102955\pi$
$62$	−9.98281	+	1.16682i	−1.26782	+	0.148187i
$63$	3.26925	−	7.30159i	0.411887	−	0.919914i
$64$	−7.61604	+	10.2301i	−0.952006	+	1.27877i
$65$	−1.64044	−	0.745671i	−0.203471	−	0.0924891i
$66$	8.24401	+	0.536985i	1.01477	+	0.0660983i
$67$	−8.47876	−	4.67838i	−1.03585	−	0.571555i	−0.128399	−	0.991723i	$-0.540984\pi$
$67$	−8.47876	−	4.67838i	−1.03585	−	0.571555i	−0.907447	+	0.420167i	$0.861971\pi$
$68$	6.35661	−	18.5779i	0.770852	−	2.25290i
$69$	2.01990	−	1.14777i	0.243168	−	0.138175i
$70$	14.7506	+	1.14651i	1.76304	+	0.137034i
$71$	0.398855	+	6.84808i	0.0473354	+	0.812718i	0.935529	+	0.353249i	$0.114923\pi$
$71$	0.398855	+	6.84808i	0.0473354	+	0.812718i	−0.888194	+	0.459469i	$0.848040\pi$
$72$	3.65903	+	4.31088i	0.431221	+	0.508042i
$73$	−9.13092	−	6.00550i	−1.06869	−	0.702891i	−0.111918	−	0.993717i	$-0.535699\pi$
$73$	−9.13092	−	6.00550i	−1.06869	−	0.702891i	−0.956776	+	0.290827i	$0.906070\pi$
$74$	21.6556	−	8.84727i	2.51741	−	1.02847i
$75$	−2.19029	−	0.766270i	−0.252913	−	0.0884813i
$76$	−1.30345	+	13.4006i	−0.149516	+	1.53716i
$77$	5.49679	−	1.76247i	0.626417	−	0.200852i
$78$	−1.82158	−	2.03526i	−0.206253	−	0.230448i
$79$	−14.8396	+	2.32087i	−1.66958	+	0.261118i	−0.917437	−	0.397880i	$-0.869746\pi$
$79$	−14.8396	+	2.32087i	−1.66958	+	0.261118i	−0.752145	+	0.658998i	$0.770981\pi$
$80$	1.96093	−	3.39643i	0.219239	−	0.379733i
$81$	−7.99647	+	4.12996i	−0.888496	+	0.458884i
$82$	10.8760	+	18.8378i	1.20105	+	2.08029i
$83$	7.84793	+	9.72991i	0.861423	+	1.06800i	0.997013	+	0.0772314i	$0.0246080\pi$
$83$	7.84793	+	9.72991i	0.861423	+	1.06800i	−0.135591	+	0.990765i	$0.543293\pi$
$84$	11.6262	+	6.22640i	1.26852	+	0.679356i
$85$	−3.66555	+	16.9220i	−0.397584	+	1.83545i
$86$	−12.4441	+	5.65655i	−1.34188	+	0.609961i
$87$	0.894542	−	5.47323i	0.0959050	−	0.586791i
$88$	−0.552140	+	4.04238i	−0.0588583	+	0.430919i
$89$	−0.345828	+	5.93763i	−0.0366577	+	0.629388i	0.929082	+	0.369874i	$0.120599\pi$
$89$	−0.345828	+	5.93763i	−0.0366577	+	0.629388i	−0.965739	+	0.259513i	$0.916438\pi$
$90$	−12.1711	−	11.3534i	−1.28295	−	1.19675i
$91$	−1.70546	−	0.856516i	−0.178781	−	0.0897873i
$92$	1.65219	+	3.45526i	0.172252	+	0.360236i
$93$	7.77077	+	1.42528i	0.805791	+	0.147795i
$94$	−6.26827	−	7.18264i	−0.646523	−	0.740833i
$95$	−0.230224	−	11.8703i	−0.0236205	−	1.21787i
$96$	10.0565	−	7.37997i	1.02638	−	0.753215i
$97$	8.55768	−	6.11666i	0.868901	−	0.621053i	−0.0571861	−	0.998364i	$-0.518213\pi$
$97$	8.55768	−	6.11666i	0.868901	−	0.621053i	0.926087	+	0.377311i	$0.123151\pi$
$98$	0.243474	+	0.0284580i	0.0245946	+	0.00287470i
$99$	−6.07121	−	2.30465i	−0.610180	−	0.231626i
$100$	1.51516	−	3.51254i	0.151516	−	0.351254i
$101$	3.03157	+	0.972035i	0.301653	+	0.0967211i	0.452298	−	0.891867i	$-0.350604\pi$
$101$	3.03157	+	0.972035i	0.301653	+	0.0967211i	−0.150645	+	0.988588i	$0.548135\pi$
$102$	−15.4075	+	21.2464i	−1.52557	+	2.10371i
$103$	−0.0263825	+	0.0551744i	−0.00259955	+	0.00543649i	−0.903463	−	0.428666i	$-0.858984\pi$
$103$	−0.0263825	+	0.0551744i	−0.00259955	+	0.00543649i	0.900864	+	0.434102i	$0.142934\pi$
$104$	1.06615	−	0.826329i	0.104545	−	0.0810282i
$105$	−10.8201	−	4.26316i	−1.05594	−	0.416042i
$106$	−11.3209	+	12.9723i	−1.09958	+	1.25998i
$107$	−12.6338	−	10.6010i	−1.22136	−	1.02484i	−0.998753	−	0.0499323i	$-0.984099\pi$
$107$	−12.6338	−	10.6010i	−1.22136	−	1.02484i	−0.222605	−	0.974909i	$-0.571456\pi$
$108$	−5.86015	−	13.6306i	−0.563893	−	1.31161i
$109$	11.3933	−	9.56012i	1.09128	−	0.915694i	0.0944731	−	0.995527i	$-0.469883\pi$
$109$	11.3933	−	9.56012i	1.09128	−	0.915694i	0.996808	+	0.0798337i	$0.0254389\pi$
$110$	0.232884	−	12.0074i	0.0222046	−	1.14486i
$111$	−18.3135	+	1.65445i	−1.73824	+	0.157034i
$112$	2.21475	−	3.51393i	0.209274	−	0.332035i
$113$	3.22009	−	3.15824i	0.302920	−	0.297102i	−0.532818	−	0.846230i	$-0.678867\pi$
$113$	3.22009	−	3.15824i	0.302920	−	0.297102i	0.835739	+	0.549128i	$0.185040\pi$
$114$	6.92038	−	16.6123i	0.648153	−	1.55589i
$115$	−1.80078	−	2.85713i	−0.167923	−	0.266428i
$116$	8.89616	+	2.10843i	0.825987	+	0.195763i
$117$	0.899497	+	1.94949i	0.0831585	+	0.180230i
$118$	−0.331007	+	1.10564i	−0.0304717	+	0.101783i
$119$	−4.57421	+	17.7582i	−0.419317	+	1.62789i
$120$	6.01745	−	5.59957i	0.549315	−	0.511168i
$121$	2.27428	+	5.89053i	0.206753	+	0.535503i
$122$	−6.05673	−	15.6873i	−0.548351	−	1.42026i
$123$	−3.82877	−	16.6639i	−0.345228	−	1.50254i
$124$	−3.24877	+	12.6125i	−0.291748	+	1.13264i
$125$	2.64322	−	8.82897i	0.236417	−	0.789687i
$126$	−12.4145	−	12.5152i	−1.10597	−	1.11494i
$127$	6.65915	+	1.57825i	0.590904	+	0.140047i	0.515180	−	0.857082i	$-0.327725\pi$
$127$	6.65915	+	1.57825i	0.590904	+	0.140047i	0.0757242	+	0.997129i	$0.475873\pi$
$128$	7.30456	+	11.5895i	0.645638	+	1.02437i
$129$	10.6557	−	1.38097i	0.938183	−	0.121588i
$130$	−2.83473	+	2.78029i	−0.248623	+	0.243847i
$131$	8.21241	−	13.0299i	0.717522	−	1.13843i	−0.267090	−	0.963672i	$-0.586062\pi$
$131$	8.21241	−	13.0299i	0.717522	−	1.13843i	0.984612	−	0.174755i	$-0.0559132\pi$
$132$	4.49689	−	9.71528i	0.391404	−	0.845607i
$133$	0.243831	−	12.5719i	0.0211428	−	1.09012i
$134$	−16.3460	+	13.7160i	−1.41208	+	1.18488i
$135$	6.52795	+	11.3384i	0.561837	+	0.975850i
$136$	−9.92873	−	8.33120i	−0.851382	−	0.714394i
$137$	−1.78531	+	2.04573i	−0.152529	+	0.174779i	−0.824615	−	0.565694i	$-0.808608\pi$
$137$	−1.78531	+	2.04573i	−0.152529	+	0.174779i	0.672086	+	0.740473i	$0.265398\pi$
$138$	−0.756265	−	5.06304i	−0.0643775	−	0.430994i
$139$	−11.2522	+	8.72109i	−0.954396	+	0.739713i	−0.965548	−	0.260225i	$-0.916203\pi$
$139$	−11.2522	+	8.72109i	−0.954396	+	0.739713i	0.0111519	+	0.999938i	$0.496450\pi$
$140$	8.27059	−	17.2965i	0.698992	−	1.46182i
$141$	3.05399	+	6.84298i	0.257193	+	0.576283i
$142$	14.3935	+	4.61508i	1.20787	+	0.387289i
$143$	−0.613591	+	1.42246i	−0.0513111	+	0.118952i
$144$	−4.41254	+	1.53774i	−0.367712	+	0.128145i
$145$	−8.00748	−	0.935940i	−0.664985	−	0.0777256i
$146$	−19.5916	+	14.0033i	−1.62142	+	1.15892i
$147$	−0.176399	−	0.0775319i	−0.0145491	−	0.00639472i
$148$	−0.587823	−	30.3080i	−0.0483188	−	2.49130i
$149$	12.4119	+	14.2225i	1.01682	+	1.16515i	0.986190	+	0.165620i	$0.0529624\pi$
$149$	12.4119	+	14.2225i	1.01682	+	1.16515i	0.0306336	+	0.999531i	$0.490248\pi$
$150$	−3.31346	+	3.89421i	−0.270543	+	0.317961i
$151$	−1.54315	−	3.22721i	−0.125579	−	0.262627i	0.829770	−	0.558105i	$-0.188472\pi$
$151$	−1.54315	−	3.22721i	−0.125579	−	0.262627i	−0.955349	+	0.295478i	$0.904521\pi$
$152$	7.94204	+	3.98864i	0.644184	+	0.323522i
$153$	16.4777	−	12.4127i	1.33214	−	1.00351i
$154$	0.739573	−	12.6980i	0.0595965	−	1.02323i
$155$	1.55425	−	11.3791i	0.124841	−	0.913995i
$156$	−3.31055	+	1.25212i	−0.265056	+	0.100250i
$157$	−8.04023	+	3.65473i	−0.641681	+	0.291680i	−0.708100	−	0.706112i	$-0.750447\pi$
$157$	−8.04023	+	3.65473i	−0.641681	+	0.291680i	0.0664194	+	0.997792i	$0.478842\pi$
$158$	−7.00662	+	32.3462i	−0.557417	+	2.57332i
$159$	11.4987	−	7.13748i	0.911904	−	0.566039i
$160$	−11.3842	−	14.1142i	−0.900002	−	1.11583i
$161$	−1.78844	−	3.09767i	−0.140949	−	0.244130i
$162$	2.14316	+	19.7153i	0.168382	+	1.54898i
$163$	5.65044	−	9.78685i	0.442577	−	0.766565i	−0.555303	−	0.831648i	$-0.687398\pi$
$163$	5.65044	−	9.78685i	0.442577	−	0.766565i	0.997880	+	0.0650829i	$0.0207312\pi$
$164$	27.8486	−	4.35544i	2.17461	−	0.340103i
$165$	−2.94400	+	8.96941i	−0.229190	+	0.698268i
$166$	26.2293	−	8.41009i	2.03579	−	0.652749i
$167$	−1.35234	+	13.9033i	−0.104647	+	1.07587i	0.785085	+	0.619388i	$0.212619\pi$
$167$	−1.35234	+	13.9033i	−0.104647	+	1.07587i	−0.889733	+	0.456482i	$0.849109\pi$
$168$	6.59826	−	5.67894i	0.509067	−	0.438140i
$169$	−11.5603	+	4.72289i	−0.889252	+	0.363299i
$170$	31.8758	+	20.9651i	2.44476	+	1.60795i
$171$	−9.03132	+	10.8876i	−0.690642	+	0.832598i
$172$	1.02994	+	17.6834i	0.0785322	+	1.34835i
$173$	16.1343	+	1.25406i	1.22667	+	0.0953441i	0.674427	−	0.738341i	$-0.264391\pi$
$173$	16.1343	+	1.25406i	1.22667	+	0.0953441i	0.552239	+	0.833686i	$0.313773\pi$
$174$	−10.5408	−	6.18264i	−0.799097	−	0.468705i
$175$	−1.15658	+	3.38023i	−0.0874290	+	0.255521i
$176$	−2.95208	−	1.62889i	−0.222521	−	0.122782i
$177$	0.503708	−	0.754513i	0.0378610	−	0.0567127i
$178$	11.9309	+	5.42327i	0.894261	+	0.406492i
$179$	13.6543	−	18.3409i	1.02057	−	1.37087i	0.0936527	−	0.995605i	$-0.470146\pi$
$179$	13.6543	−	18.3409i	1.02057	−	1.37087i	0.926919	−	0.375261i	$-0.122447\pi$
$180$	−19.4054	+	9.41428i	−1.44639	+	0.701699i
$181$	6.27250	−	0.733150i	0.466231	−	0.0544946i	0.120265	−	0.992742i	$-0.461625\pi$
$181$	6.27250	−	0.733150i	0.466231	−	0.0544946i	0.345966	+	0.938247i	$0.387551\pi$
$182$	−3.11419	+	2.82598i	−0.230839	+	0.209476i
$183$	0.933789	+	13.1851i	0.0690277	+	0.974673i
$184$	2.52051	−	0.195909i	0.185814	−	0.0144426i
$185$	3.61751	+	26.4849i	0.265965	+	1.94721i
$186$	9.09707	−	14.8424i	0.667030	−	1.08830i
$187$	14.6064	+	2.86860i	1.06813	+	0.209773i
$188$	−11.6085	+	4.22514i	−0.846634	+	0.308150i
$189$	6.44293	+	12.2675i	0.468654	+	0.892331i
$190$	−24.5833	−	8.94759i	−1.78346	−	0.649126i
$191$	21.6976	+	13.0946i	1.56998	+	0.947490i	0.991254	+	0.131971i	$0.0421306\pi$
$191$	21.6976	+	13.0946i	1.56998	+	0.947490i	0.578730	+	0.815519i	$0.303548\pi$
$192$	−5.77772	−	21.3213i	−0.416971	−	1.53873i
$193$	0.442267	+	0.0171620i	0.0318351	+	0.00123535i	0.0546880	−	0.998503i	$-0.482584\pi$
$193$	0.442267	+	0.0171620i	0.0318351	+	0.00123535i	−0.0228529	+	0.999739i	$0.507275\pi$
$194$	−5.78162	−	22.4456i	−0.415096	−	1.61150i
$195$	2.77134	−	1.43557i	0.198460	−	0.102803i
$196$	0.148039	−	0.281046i	0.0105742	−	0.0200747i
$197$	6.72502	−	7.12810i	0.479138	−	0.507856i	−0.442042	−	0.896995i	$-0.645746\pi$
$197$	6.72502	−	7.12810i	0.479138	−	0.507856i	0.921179	+	0.389138i	$0.127227\pi$
$198$	−9.55584	+	10.6509i	−0.679104	+	0.756927i
$199$	−4.46570	+	1.05839i	−0.316565	+	0.0750272i	−0.385827	−	0.922571i	$-0.626084\pi$
$199$	−4.46570	+	1.05839i	−0.316565	+	0.0750272i	0.0692619	+	0.997599i	$0.477936\pi$
$200$	−1.80274	−	1.76812i	−0.127473	−	0.125025i
$201$	15.4464	−	6.53749i	1.08950	−	0.461119i
$202$	4.40412	−	5.46025i	0.309873	−	0.384182i
$203$	−8.43592	−	1.31935i	−0.592086	−	0.0926005i
$204$	18.4929	+	28.5420i	1.29476	+	1.99834i
$205$	−23.9451	+	6.66558i	−1.67240	+	0.465544i
$206$	0.0924780	+	0.0980209i	0.00644325	+	0.00682944i
$207$	−0.599269	+	3.97907i	−0.0416520	+	0.276565i
$208$	0.319707	+	1.06789i	0.0221677	+	0.0740452i
$209$	−10.1992	+	0.395776i	−0.705495	+	0.0273764i
$210$	−17.3507	+	18.8584i	−1.19731	+	1.30136i
$211$	22.5719	+	6.28332i	1.55391	+	0.432562i	0.935510	−	0.353299i	$-0.114940\pi$
$211$	22.5719	+	6.28332i	1.55391	+	0.432562i	0.618404	+	0.785861i	$0.287780\pi$
$212$	10.3979	+	19.7400i	0.714133	+	1.35575i
$213$	−9.75186	−	6.78729i	−0.668186	−	0.465057i
$214$	−31.8183	+	17.5566i	−2.17505	+	1.20014i
$215$	−2.71234	−	15.3824i	−0.184980	−	1.04907i
$216$	−9.78678	+	0.367931i	−0.665906	+	0.0250345i
$217$	2.11218	−	11.9788i	0.143384	−	0.813173i
$218$	−10.6095	−	31.0075i	−0.718567	−	2.10009i
$219$	17.9516	−	6.00493i	1.21306	−	0.405776i
$220$	−14.4067	−	5.88579i	−0.971300	−	0.396820i
$221$	−2.78356	−	4.05853i	−0.187242	−	0.273006i
$222$	−11.1336	+	38.9584i	−0.747239	+	2.61471i
$223$	−0.0521074	−	0.240554i	−0.00348937	−	0.0161087i	0.975556	−	0.219751i	$-0.0705245\pi$
$223$	−0.0521074	−	0.240554i	−0.00348937	−	0.0161087i	−0.979045	+	0.203642i	$0.934722\pi$
$224$	−11.4684	−	15.4047i	−0.766262	−	1.02927i
$225$	3.38797	−	2.16224i	0.225865	−	0.144149i
$226$	−3.93646	−	9.12574i	−0.261849	−	0.607035i
$227$	1.58539	+	16.2992i	0.105226	+	1.08182i	0.888104	+	0.459642i	$0.152022\pi$
$227$	1.58539	+	16.2992i	0.105226	+	1.08182i	−0.782878	+	0.622175i	$0.786249\pi$
$228$	−16.8522	−	16.1193i	−1.11606	−	1.06753i
$229$	−14.3782	+	8.67729i	−0.950138	+	0.573411i	−0.904927	−	0.425566i	$-0.860075\pi$
$229$	−14.3782	+	8.67729i	−0.950138	+	0.573411i	−0.0452106	+	0.998977i	$0.514396\pi$
$230$	−7.30229	+	1.43412i	−0.481499	+	0.0945633i
$231$	−3.48400	+	9.37148i	−0.229230	+	0.616598i
$232$	3.41340	−	4.97685i	0.224100	−	0.326746i
$233$	−0.684539	+	0.450228i	−0.0448456	+	0.0294954i	−0.571734	−	0.820439i	$-0.693729\pi$
$233$	−0.684539	+	0.450228i	−0.0448456	+	0.0294954i	0.526888	+	0.849935i	$0.323359\pi$
$234$	4.72126	−	0.301798i	0.308638	−	0.0197292i
$235$	9.73466	−	4.88893i	0.635019	−	0.318919i
$236$	1.18208	+	0.916183i	0.0769470	+	0.0596384i
$237$	12.7245	−	22.6911i	0.826542	−	1.47395i
$238$	32.8734	+	23.4965i	2.13086	+	1.52305i
$239$	−8.85473	−	8.03524i	−0.572765	−	0.519756i	0.333342	−	0.942806i	$-0.391824\pi$
$239$	−8.85473	−	8.03524i	−0.572765	−	0.519756i	−0.906106	+	0.423050i	$0.860960\pi$
$240$	2.52582	+	6.30581i	0.163041	+	0.407038i
$241$	−4.23792	+	10.9765i	−0.272988	+	0.707058i	0.726807	+	0.686841i	$0.241003\pi$
$241$	−4.23792	+	10.9765i	−0.272988	+	0.707058i	−0.999796	+	0.0202161i	$0.993565\pi$
$242$	13.9136			0.894398
$243$	2.93598	−	15.3095i	0.188343	−	0.982103i
$244$	−21.7908			−1.39501
$245$	−0.100888	+	0.261307i	−0.00644550	+	0.0166943i
$246$	−37.2931	−	5.35490i	−2.37772	−	0.341416i
$247$	2.49902	+	2.26774i	0.159009	+	0.144293i
$248$	6.99421	+	4.99916i	0.444133	+	0.317447i
$249$	−21.6497	+	0.271191i	−1.37199	+	0.0171860i
$250$	−16.0511	−	12.4405i	−1.01516	−	0.786807i
$251$	14.9850	−	7.52577i	0.945847	−	0.475022i	0.0921230	−	0.995748i	$-0.470635\pi$
$251$	14.9850	−	7.52577i	0.945847	−	0.475022i	0.853724	+	0.520725i	$0.174338\pi$
$252$	−20.9234	+	9.16627i	−1.31805	+	0.577420i
$253$	−2.42581	+	1.59548i	−0.152509	+	0.100307i
$254$	8.52927	−	12.4360i	0.535174	−	0.780303i
$255$	−19.1187	−	23.1052i	−1.19726	−	1.44690i
$256$	4.59109	−	0.901661i	0.286943	−	0.0563538i
$257$	−8.11431	+	4.89701i	−0.506157	+	0.305467i	−0.746688	−	0.665174i	$-0.768357\pi$
$257$	−8.11431	+	4.89701i	−0.506157	+	0.305467i	0.240531	+	0.970641i	$0.422678\pi$
$258$	5.61816	−	22.9999i	0.349771	−	1.43191i
$259$	2.74078	+	28.1776i	0.170304	+	1.75087i
$260$	2.03794	+	4.72447i	0.126387	+	0.292999i
$261$	6.49525	+	7.07679i	0.402046	+	0.438043i
$262$	−20.2665	−	27.2226i	−1.25207	−	1.68182i
$263$	2.89031	+	13.3432i	0.178224	+	0.822776i	0.975646	+	0.219353i	$0.0703945\pi$
$263$	2.89031	+	13.3432i	0.178224	+	0.822776i	−0.797421	+	0.603423i	$0.793803\pi$
$264$	−4.91341	−	5.07893i	−0.302399	−	0.312586i
$265$	−11.1278	−	16.2247i	−0.683573	−	0.996674i
$266$	−25.6492	−	10.4788i	−1.57265	−	0.642499i
$267$	−7.71498	−	6.82673i	−0.472149	−	0.417789i
$268$	8.95154	+	26.1619i	0.546803	+	1.59809i
$269$	−0.394828	+	2.23918i	−0.0240731	+	0.136525i	−0.994476	−	0.104968i	$-0.966526\pi$
$269$	−0.394828	+	2.23918i	−0.0240731	+	0.136525i	0.970403	+	0.241493i	$0.0776371\pi$
$270$	28.4880	−	4.42019i	1.73373	−	0.269004i
$271$	−1.44045	−	8.16917i	−0.0875008	−	0.496242i	−0.996789	−	0.0800745i	$-0.974484\pi$
$271$	−1.44045	−	8.16917i	−0.0875008	−	0.496242i	0.909288	−	0.416167i	$-0.136627\pi$
$272$	9.37815	−	5.17464i	0.568634	−	0.313759i
$273$	2.99188	−	1.40546i	0.181077	−	0.0850622i
$274$	2.78831	+	5.29347i	0.168448	+	0.319790i
$275$	2.79379	+	0.777703i	0.168472	+	0.0468973i
$276$	−6.47351	−	1.44886i	−0.389660	−	0.0872112i
$277$	28.2227	−	1.09517i	1.69574	−	0.0658024i	0.827350	−	0.561687i	$-0.189847\pi$
$277$	28.2227	−	1.09517i	1.69574	−	0.0658024i	0.868389	+	0.495884i	$0.165156\pi$
$278$	8.99681	+	30.0514i	0.539593	+	1.80236i
$279$	−10.2589	+	9.05565i	−0.614182	+	0.542147i
$280$	−8.68460	−	9.20514i	−0.519004	−	0.550112i
$281$	−6.86622	+	1.91134i	−0.409604	+	0.114021i	−0.466845	−	0.884339i	$-0.654609\pi$
$281$	−6.86622	+	1.91134i	−0.409604	+	0.114021i	0.0572405	+	0.998360i	$0.481770\pi$
$282$	16.4902	−	0.846869i	0.981979	−	0.0504303i
$283$	−1.63938	−	0.256395i	−0.0974513	−	0.0152411i	0.105605	−	0.994408i	$-0.466322\pi$
$283$	−1.63938	−	0.256395i	−0.0974513	−	0.0152411i	−0.203056	+	0.979167i	$0.565087\pi$
$284$	12.2969	−	15.2458i	0.729688	−	0.904671i
$285$	16.4100	+	12.3928i	0.972045	+	0.734088i
$286$	2.43704	+	2.39023i	0.144105	+	0.141338i
$287$	−25.6150	+	6.07086i	−1.51201	+	0.358352i
$288$	−0.715573	+	21.5934i	−0.0421655	+	1.27241i
$289$	−20.7848	+	22.0306i	−1.22264	+	1.29592i
$290$	−8.27904	+	15.7174i	−0.486162	+	0.922955i
$291$	−0.831457	+	18.2003i	−0.0487409	+	1.06692i
$292$	7.78404	+	30.2195i	0.455526	+	1.76846i
$293$	−13.7093	−	0.531984i	−0.800907	−	0.0310789i	−0.364928	−	0.931036i	$-0.618906\pi$
$293$	−13.7093	−	0.531984i	−0.800907	−	0.0310789i	−0.435979	+	0.899957i	$0.643598\pi$
$294$	−0.299373	+	0.301072i	−0.0174598	+	0.0175589i
$295$	−1.12911	−	0.681421i	−0.0657393	−	0.0396738i
$296$	−18.8030	−	6.84373i	−1.09290	−	0.397784i
$297$	9.63701	−	5.80010i	0.559196	−	0.336556i
$298$	39.0864	−	14.2263i	2.26421	−	0.824107i
$299$	0.941941	+	0.184991i	0.0544738	+	0.0106983i
$300$	3.16108	+	5.82309i	0.182505	+	0.336196i
$301$	−2.23877	−	16.3907i	−0.129041	−	0.944745i
$302$	−7.85858	+	0.610817i	−0.452210	+	0.0351486i
$303$	−4.56869	+	3.08754i	−0.262465	+	0.177375i
$304$	−5.43896	+	4.93560i	−0.311946	+	0.283076i
$305$	19.0853	−	2.23075i	1.09282	−	0.127732i
$306$	−12.4381	−	43.7229i	−0.711040	−	2.49947i
$307$	−5.48455	+	7.36703i	−0.313020	+	0.420458i	−0.930593	−	0.366055i	$-0.880708\pi$
$307$	−5.48455	+	7.36703i	−0.313020	+	0.420458i	0.617574	+	0.786513i	$0.288116\pi$
$308$	−15.0050	−	6.82060i	−0.854989	−	0.388640i
$309$	−0.0468893	−	0.0949849i	−0.00266744	−	0.00540350i
$310$	−22.1574	−	12.2260i	−1.25846	−	0.694388i
$311$	−3.53802	+	10.3402i	−0.200622	+	0.586341i	−0.999893	−	0.0146301i	$-0.995343\pi$
$311$	−3.53802	+	10.3402i	−0.200622	+	0.586341i	0.799270	+	0.600971i	$0.205219\pi$
$312$	−0.0160433	+	2.33628i	−0.000908271	+	0.132266i
$313$	8.40856	+	0.653565i	0.475280	+	0.0369417i	0.312899	−	0.949786i	$-0.398700\pi$
$313$	8.40856	+	0.653565i	0.475280	+	0.0369417i	0.162381	+	0.986728i	$0.448083\pi$
$314$	1.13156	+	19.4281i	0.0638574	+	1.09639i
$315$	17.3873	−	10.1702i	0.979662	−	0.573024i
$316$	35.8320	+	23.5671i	2.01571	+	1.32575i
$317$	−4.53963	+	1.85464i	−0.254971	+	0.104167i	−0.502082	−	0.864820i	$-0.667432\pi$
$317$	−4.53963	+	1.85464i	−0.254971	+	0.104167i	0.247111	+	0.968987i	$0.420519\pi$
$318$	−5.54590	−	29.3013i	−0.310999	−	1.64314i
$319$	−0.670992	+	6.89840i	−0.0375683	+	0.386236i
$320$	−30.5791	+	9.80480i	−1.70942	+	0.548105i
$321$	27.9589	−	5.85557i	1.56051	−	0.326826i
$322$	−7.78695	+	1.21786i	−0.433950	+	0.0678685i
$323$	16.2126	−	28.0811i	0.902094	−	1.56247i
$324$	24.8334	+	6.61096i	1.37963	+	0.367276i
$325$	−0.479396	−	0.830338i	−0.0265921	−	0.0460589i
$326$	−15.6334	−	19.3824i	−0.865853	−	1.07349i
$327$	0.822094	+	25.7475i	0.0454619	+	1.42384i
$328$	3.93896	−	18.1843i	0.217493	−	1.00406i
$329$	10.5030	−	4.77421i	0.579050	−	0.263211i
$330$	16.1010	+	13.1702i	0.886332	+	0.724998i
$331$	−3.59905	+	26.3497i	−0.197822	+	1.44831i	0.577317	+	0.816520i	$0.304100\pi$
$331$	−3.59905	+	26.3497i	−0.197822	+	1.44831i	−0.775139	+	0.631791i	$0.782320\pi$
$332$	2.07539	−	35.6330i	0.113902	−	1.95562i
$333$	17.3505	−	26.7082i	0.950804	−	1.46360i
$334$	27.5063	+	13.8142i	1.50508	+	0.755879i
$335$	−10.5184	−	21.9973i	−0.574680	−	1.20184i
$336$	2.41413	+	6.77720i	0.131701	+	0.369727i
$337$	12.5996	+	14.4375i	0.686342	+	0.786461i	0.985849	−	0.167633i	$-0.0536123\pi$
$337$	12.5996	+	14.4375i	0.686342	+	0.786461i	−0.299507	+	0.954094i	$0.596822\pi$
$338$	0.533587	+	27.5116i	0.0290233	+	1.49643i
$339$	0.853636	+	7.76541i	0.0463631	+	0.421759i
$340$	40.2214	−	28.7486i	2.18131	−	1.55911i
$341$	−9.80681	−	1.14625i	−0.531068	−	0.0620730i
$342$	15.2129	+	27.2057i	0.822622	+	1.47112i
$343$	7.27606	−	16.8678i	0.392870	−	0.910776i
$344$	11.1341	+	3.56999i	0.600308	+	0.192481i
$345$	5.81810	+	0.606272i	0.313236	+	0.0326406i
$346$	15.3828	−	32.1703i	0.826983	−	1.72949i
$347$	−2.50448	+	1.94112i	−0.134447	+	0.104205i	−0.677605	−	0.735426i	$-0.736982\pi$
$347$	−2.50448	+	1.94112i	−0.134447	+	0.104205i	0.543157	+	0.839631i	$0.317229\pi$
$348$	−12.3937	+	9.85681i	−0.664374	+	0.528380i
$349$	18.4689	−	21.1630i	0.988617	−	1.13283i	−0.00252160	−	0.999997i	$-0.500803\pi$
$349$	18.4689	−	21.1630i	0.988617	−	1.13283i	0.991139	−	0.132832i	$-0.0424072\pi$
$350$	6.03048	+	5.06017i	0.322343	+	0.270477i
$351$	−3.61743	−	0.861965i	−0.193084	−	0.0460083i
$352$	−11.9420	+	10.0206i	−0.636513	+	0.534098i
$353$	−0.725164	+	37.3893i	−0.0385966	+	1.99003i	0.0785288	+	0.996912i	$0.474978\pi$
$353$	−0.725164	+	37.3893i	−0.0385966	+	1.99003i	−0.117125	+	0.993117i	$0.537368\pi$
$354$	−1.15121	−	1.63424i	−0.0611862	−	0.0868588i
$355$	−9.20944	+	14.6118i	−0.488786	+	0.775512i
$356$	12.1246	−	11.8917i	0.642601	−	0.630259i
$357$	−19.2846	−	25.2375i	−1.02065	−	1.33571i
$358$	−26.8649	−	42.6241i	−1.41985	−	2.25275i
$359$	−18.4287	−	4.36768i	−0.972629	−	0.230517i	−0.286567	−	0.958060i	$-0.592514\pi$
$359$	−18.4287	−	4.36768i	−0.972629	−	0.230517i	−0.686062	+	0.727543i	$0.740662\pi$
$360$	1.18357	+	14.1878i	0.0623796	+	0.747763i
$361$	−0.927502	+	3.09807i	−0.0488159	+	0.163056i
$362$	3.47109	−	13.4756i	0.182437	−	0.708262i
$363$	−10.4555	−	3.20856i	−0.548771	−	0.168406i
$364$	1.96274	+	5.08362i	0.102875	+	0.266454i
$365$	−9.91120	−	25.6707i	−0.518776	−	1.34366i
$366$	27.8445	+	8.54486i	1.45545	+	0.446647i
$367$	2.80905	−	10.9054i	0.146631	−	0.569256i	−0.852301	−	0.523052i	$-0.824793\pi$
$367$	2.80905	−	10.9054i	0.146631	−	0.569256i	0.998932	−	0.0462048i	$-0.0147127\pi$
$368$	−0.599201	+	2.00147i	−0.0312355	+	0.104334i
$369$	26.7894	+	12.6240i	1.39460	+	0.657182i
$370$	57.3133	+	13.5835i	2.97958	+	0.706173i
$371$	−11.1103	−	17.6277i	−0.576817	−	0.915183i
$372$	−13.6966	−	17.9246i	−0.710137	−	0.929347i
$373$	−14.7694	+	14.4858i	−0.764733	+	0.750044i	−0.973689	−	0.227881i	$-0.926820\pi$
$373$	−14.7694	+	14.4858i	−0.764733	+	0.750044i	0.208957	+	0.977925i	$0.432993\pi$
$374$	17.4890	−	27.7482i	0.904336	−	1.43483i
$375$	9.19287	+	13.0500i	0.474718	+	0.673901i
$376$	−0.158125	+	8.15286i	−0.00815465	+	0.420452i
$377$	1.75538	−	1.47294i	0.0904068	−	0.0758603i
$378$	30.3306	−	3.50800i	1.56004	−	0.180432i
$379$	−17.7735	−	14.9138i	−0.912965	−	0.766069i	0.0597154	−	0.998215i	$-0.480981\pi$
$379$	−17.7735	−	14.9138i	−0.912965	−	0.766069i	−0.972681	+	0.232147i	$0.925425\pi$
$380$	−22.2903	+	25.5418i	−1.14347	+	1.31027i
$381$	−9.27724	+	7.37824i	−0.475287	+	0.377999i
$382$	44.1375	−	34.2091i	2.25827	−	1.75029i
$383$	9.71934	−	20.3263i	0.496635	−	1.03862i	−0.489396	−	0.872062i	$-0.662783\pi$
$383$	9.71934	−	20.3263i	0.496635	−	1.03862i	0.986031	−	0.166562i	$-0.0532667\pi$
$384$	−23.6002	−	2.45924i	−1.20434	−	0.125498i
$385$	13.8402	+	4.43770i	0.705364	+	0.226166i
$386$	0.386282	−	0.895503i	0.0196613	−	0.0455799i
$387$	−9.52575	+	15.9879i	−0.484221	+	0.812712i
$388$	−29.8323	−	3.48689i	−1.51450	−	0.177020i
$389$	−5.19302	+	3.71175i	−0.263296	+	0.188193i	−0.705476	−	0.708733i	$-0.749267\pi$
$389$	−5.19302	+	3.71175i	−0.263296	+	0.188193i	0.442180	+	0.896926i	$0.354205\pi$
$390$	−0.751480	−	6.83611i	−0.0380527	−	0.346160i
$391$	−0.178860	−	9.22198i	−0.00904535	−	0.466376i
$392$	−0.137868	−	0.157979i	−0.00696337	−	0.00797914i
$393$	8.95173	+	25.1303i	0.451555	+	1.26766i
$394$	−9.31523	−	19.4812i	−0.469295	−	0.981446i
$395$	−33.7958	−	16.9729i	−1.70045	−	0.853999i
$396$	8.41551	+	16.5229i	0.422896	+	0.830306i
$397$	0.760522	−	13.0577i	0.0381695	−	0.655345i	−0.923916	−	0.382596i	$-0.875030\pi$
$397$	0.760522	−	13.0577i	0.0381695	−	0.655345i	0.962085	−	0.272749i	$-0.0879329\pi$
$398$	−1.36857	+	10.0197i	−0.0686000	+	0.502241i
$399$	16.8579	+	13.7893i	0.843949	+	0.690330i
$400$	1.89970	−	0.863520i	0.0949851	−	0.0431760i
$401$	0.354015	−	1.63432i	0.0176787	−	0.0816138i	−0.967642	−	0.252326i	$-0.918804\pi$
$401$	0.354015	−	1.63432i	0.0176787	−	0.0816138i	0.985321	+	0.170712i	$0.0546069\pi$
$402$	−1.17946	−	36.9401i	−0.0588262	−	1.84240i
$403$	2.04941	+	2.54087i	0.102088	+	0.126570i
$404$	−4.54517	−	7.87247i	−0.226131	−	0.391670i
$405$	−22.4270	−	3.24793i	−1.11440	−	0.161391i
$406$	−9.40722	+	16.2938i	−0.466872	+	0.808647i
$407$	22.7047	−	3.55094i	1.12543	−	0.176014i
$408$	21.9725	−	4.60181i	1.08780	−	0.227823i
$409$	−5.17720	+	1.66000i	−0.255996	+	0.0820818i	−0.430553	−	0.902565i	$-0.641681\pi$
$409$	−5.17720	+	1.66000i	−0.255996	+	0.0820818i	0.174557	+	0.984647i	$0.444151\pi$
$410$	−5.30223	+	54.5117i	−0.261859	+	2.69214i
$411$	−0.874592	−	4.62084i	−0.0431404	−	0.227929i
$412$	0.161657	−	0.0660441i	0.00796426	−	0.00325376i
$413$	−1.16696	−	0.767521i	−0.0574223	−	0.0377672i
$414$	7.70378	+	4.38984i	0.378620	+	0.215749i
$415$	1.83009	+	31.4214i	0.0898354	+	1.54241i
$416$	5.13856	+	0.399400i	0.251939	+	0.0195822i
$417$	0.169321	−	24.6572i	0.00829168	−	1.20747i
$418$	−7.28104	+	21.2796i	−0.356127	+	1.04082i
$419$	−26.9252	−	14.8567i	−1.31538	−	0.725798i	−0.338784	−	0.940864i	$-0.610016\pi$
$419$	−26.9252	−	14.8567i	−1.31538	−	0.725798i	−0.976599	+	0.215066i	$0.931003\pi$
$420$	14.6992	+	29.7766i	0.717247	+	1.45295i
$421$	−33.8379	−	15.3812i	−1.64916	−	0.749635i	−0.649219	−	0.760601i	$-0.724904\pi$
$421$	−33.8379	−	15.3812i	−1.64916	−	0.749635i	−0.999940	+	0.0109667i	$0.996509\pi$
$422$	30.8301	−	41.4121i	1.50079	−	2.01591i
$423$	−12.5870	−	3.16637i	−0.612003	−	0.153954i
$424$	14.6277	−	1.70974i	0.710385	−	0.0830321i
$425$	−6.82244	+	6.19103i	−0.330937	+	0.300309i
$426$	−21.6915	+	14.6592i	−1.05096	+	0.710241i
$427$	20.2897	−	1.57704i	0.981887	−	0.0763183i
$428$	6.37296	+	46.6583i	0.308049	+	2.25532i
$429$	−1.28014	−	2.35817i	−0.0618056	−	0.113853i
$430$	−33.7728	−	6.63276i	−1.62867	−	0.319860i
$431$	−23.9798	+	8.72793i	−1.15507	+	0.420410i	−0.847332	−	0.531063i	$-0.821793\pi$
$431$	−23.9798	+	8.72793i	−1.15507	+	0.420410i	−0.307734	+	0.951473i	$0.599571\pi$
$432$	2.62941	−	7.65453i	0.126507	−	0.368279i
$433$	1.35338	+	0.492590i	0.0650393	+	0.0236724i	0.374335	−	0.927294i	$-0.377871\pi$
$433$	1.35338	+	0.492590i	0.0650393	+	0.0236724i	−0.309296	+	0.950966i	$0.600093\pi$
$434$	−22.9473	−	13.8487i	−1.10150	−	0.664761i
$435$	9.84590	−	9.90178i	0.472075	−	0.474754i
$436$	−42.4357	−	1.64670i	−2.03230	−	0.0788626i
$437$	1.57764	+	6.12476i	0.0754686	+	0.292987i
$438$	1.90351	−	41.6671i	0.0909532	−	1.99093i
$439$	−6.05152	+	11.4885i	−0.288823	+	0.548318i	−0.985625	−	0.168946i	$-0.945964\pi$
$439$	−6.05152	+	11.4885i	−0.288823	+	0.548318i	0.696802	+	0.717264i	$0.254606\pi$
$440$	−7.04957	+	7.47211i	−0.336075	+	0.356219i
$441$	0.294396	−	0.157206i	0.0140189	−	0.00748601i
$442$	−10.5519	+	2.50084i	−0.501901	+	0.118953i
$443$	−10.7581	−	10.5515i	−0.511135	−	0.501317i	0.398248	−	0.917278i	$-0.369618\pi$
$443$	−10.7581	−	10.5515i	−0.511135	−	0.501317i	−0.909383	+	0.415961i	$0.863445\pi$
$444$	41.8991	+	31.6422i	1.98844	+	1.50167i
$445$	−9.40185	+	11.6565i	−0.445690	+	0.552569i
$446$	−0.535839	−	0.0838036i	−0.0253727	−	0.00396822i
$447$	−32.6526	+	1.67690i	−1.54441	+	0.0793146i
$448$	−32.7647	+	9.12068i	−1.54799	+	0.430911i
$449$	7.70045	+	8.16200i	0.363407	+	0.385188i	0.883116	−	0.469155i	$-0.155441\pi$
$449$	7.70045	+	8.16200i	0.363407	+	0.385188i	−0.519709	+	0.854343i	$0.673960\pi$
$450$	−1.75584	−	8.68037i	−0.0827711	−	0.409197i
$451$	6.12856	+	20.4708i	0.288583	+	0.963933i
$452$	−12.8691	+	0.499379i	−0.605311	+	0.0234888i
$453$	6.04627	+	1.35324i	0.284079	+	0.0635806i
$454$	34.7629	+	9.67692i	1.63150	+	0.454160i
$455$	−2.23947	−	4.25153i	−0.104988	−	0.199315i
$456$	−13.9327	+	6.54496i	−0.652457	+	0.306496i
$457$	35.9536	−	19.8384i	1.68184	−	0.928000i	0.706376	−	0.707837i	$-0.250329\pi$
$457$	35.9536	−	19.8384i	1.68184	−	0.928000i	0.975463	−	0.220162i	$-0.0706588\pi$
$458$	6.42580	+	36.4425i	0.300258	+	1.70285i
$459$	−0.736050	+	35.7244i	−0.0343559	+	1.66747i
$460$	−1.67455	+	9.49685i	−0.0780764	+	0.442793i
$461$	−11.7848	−	34.4423i	−0.548872	−	1.60414i	−0.776313	−	0.630348i	$-0.782912\pi$
$461$	−11.7848	−	34.4423i	−0.548872	−	1.60414i	0.227441	−	0.973792i	$-0.426964\pi$
$462$	16.4989	+	14.5994i	0.767600	+	0.679224i
$463$	24.8809	+	10.1650i	1.15631	+	0.472406i	0.873526	−	0.486777i	$-0.161828\pi$
$463$	24.8809	+	10.1650i	1.15631	+	0.472406i	0.282787	+	0.959183i	$0.408741\pi$
$464$	2.82084	+	4.11289i	0.130954	+	0.190936i
$465$	13.8311	+	14.2970i	0.641400	+	0.663007i
$466$	0.382206	+	1.76446i	0.0177054	+	0.0817371i
$467$	−18.8075	−	25.2628i	−0.870307	−	1.16903i	−0.984468	−	0.175563i	$-0.943825\pi$
$467$	−18.8075	−	25.2628i	−0.870307	−	1.16903i	0.114161	−	0.993462i	$-0.463582\pi$
$468$	1.83873	−	5.84823i	0.0849953	−	0.270335i
$469$	−10.2283	−	23.7118i	−0.472298	−	1.09491i
$470$	−2.32379	−	23.8907i	−0.107188	−	1.10199i
$471$	3.62993	−	14.8604i	0.167258	−	0.684730i
$472$	0.845212	−	0.510088i	0.0389040	−	0.0234787i
$473$	−13.1767	+	2.58782i	−0.605865	+	0.118988i
$474$	−36.5451	−	44.1651i	−1.67857	−	2.02857i
$475$	3.57303	−	5.20960i	0.163942	−	0.239033i
$476$	43.7472	−	28.7730i	2.00515	−	1.31881i
$477$	−2.58956	+	23.2977i	−0.118568	+	1.06673i
$478$	−23.5448	+	11.8246i	−1.07691	+	0.540846i
$479$	1.37387	+	1.06483i	0.0627737	+	0.0486533i	0.643504	−	0.765443i	$-0.277480\pi$
$479$	1.37387	+	1.06483i	0.0627737	+	0.0486533i	−0.580730	+	0.814096i	$0.697233\pi$
$480$	31.4051	−	0.393390i	1.43344	−	0.0179557i
$481$	−6.18120	−	4.41805i	−0.281838	−	0.201446i
$482$	19.1998	+	17.4229i	0.874529	+	0.793593i
$483$	6.13243	+	0.880553i	0.279035	+	0.0400666i
$484$	6.49391	−	16.8197i	0.295178	−	0.764530i
$485$	26.4853			1.20264
$486$	−29.1400	−	18.1855i	−1.32182	−	0.824913i
$487$	10.2449			0.464241			0.232121	−	0.972687i	$-0.425434\pi$
$487$	10.2449			0.464241			0.232121	+	0.972687i	$0.425434\pi$
$488$	−5.18074	+	13.4185i	−0.234521	+	0.607425i
$489$	7.27817	+	18.1702i	0.329130	+	0.821687i
$490$	0.457072	+	0.414771i	0.0206484	+	0.0187375i
$491$	11.9154	+	8.51659i	0.537733	+	0.384348i	0.817685	−	0.575665i	$-0.195257\pi$
$491$	11.9154	+	8.51659i	0.537733	+	0.384348i	−0.279952	+	0.960014i	$0.590319\pi$
$492$	−23.8793	+	42.5831i	−1.07656	+	1.91980i
$493$	−17.4030	−	13.4884i	−0.783794	−	0.607486i
$494$	6.64491	−	3.33720i	0.298968	−	0.150148i
$495$	−9.06214	−	13.6099i	−0.407313	−	0.611721i
$496$	−5.93589	+	3.90409i	−0.266529	+	0.175299i
$497$	−10.3465	+	15.0855i	−0.464102	+	0.676678i
$498$	−16.6248	+	44.7184i	−0.744975	+	2.00388i
$499$	18.3810	−	3.60990i	0.822845	−	0.161602i	0.236468	−	0.971639i	$-0.424010\pi$
$499$	18.3810	−	3.60990i	0.822845	−	0.161602i	0.586378	+	0.810038i	$0.300553\pi$
$500$	−22.5305	+	13.5972i	−1.00759	+	0.608086i
$501$	−17.4843	−	16.7240i	−0.781140	−	0.747172i
$502$	−3.57713	−	36.7761i	−0.159655	−	1.64140i
$503$	11.2452	+	26.0694i	0.501400	+	1.16238i	0.961574	+	0.274547i	$0.0885280\pi$
$503$	11.2452	+	26.0694i	0.501400	+	1.16238i	−0.460173	+	0.887829i	$0.652213\pi$
$504$	0.669927	+	15.0636i	0.0298409	+	0.670988i
$505$	4.78677	+	6.42975i	0.213009	+	0.286120i
$506$	1.35443	+	6.25275i	0.0602118	+	0.277969i
$507$	5.94340	−	20.7969i	0.263956	−	0.923625i
$508$	−11.0526	−	16.1150i	−0.490378	−	0.714989i
$509$	13.9108	+	5.68318i	0.616584	+	0.251902i	0.664903	−	0.746930i	$-0.268473\pi$
$509$	13.9108	+	5.68318i	0.616584	+	0.251902i	−0.0483190	+	0.998832i	$0.515386\pi$
$510$	−62.6686	+	20.9631i	−2.77501	+	0.928261i
$511$	−9.43486	−	27.5744i	−0.417374	−	1.21982i
$512$	−2.96748	+	16.8294i	−0.131145	+	0.743762i
$513$	−5.15810	−	23.9522i	−0.227736	−	1.05752i
$514$	3.62639	+	20.5663i	0.159953	+	0.907140i
$515$	−0.134825	+	0.0743932i	−0.00594110	+	0.00327816i
$516$	−25.1816	−	17.5264i	−1.10856	−	0.771557i
$517$	−4.36455	−	8.28589i	−0.191953	−	0.364413i
$518$	60.0972	+	16.7292i	2.64052	+	0.735039i
$519$	−18.9783	+	20.6274i	−0.833053	+	0.905441i
$520$	3.39378	−	0.131694i	0.148827	−	0.00577517i
$521$	5.92980	+	19.8069i	0.259789	+	0.867757i	0.983999	+	0.178177i	$0.0570198\pi$
$521$	5.92980	+	19.8069i	0.259789	+	0.867757i	−0.724209	+	0.689580i	$0.757795\pi$
$522$	19.7020	−	7.73515i	0.862333	−	0.338558i
$523$	23.6644	+	25.0828i	1.03477	+	1.09679i	0.995228	+	0.0975755i	$0.0311087\pi$
$523$	23.6644	+	25.0828i	1.03477	+	1.09679i	0.0395430	+	0.999218i	$0.487410\pi$
$524$	−42.3675	+	11.7938i	−1.85083	+	0.515215i
$525$	−3.36476	−	5.19319i	−0.146850	−	0.226649i
$526$	29.7221	+	4.64846i	1.29595	+	0.202682i
$527$	19.6921	−	24.4144i	0.857803	−	1.06351i
$528$	5.37803	−	2.27618i	0.234049	−	0.0990581i
$529$	−15.1359	−	14.8452i	−0.658084	−	0.645444i
$530$	−42.1830	+	9.99755i	−1.83231	+	0.434266i
$531$	0.488223	+	1.49354i	0.0211871	+	0.0648143i
$532$	−24.6388	+	26.1157i	−1.06823	+	1.13226i
$533$	3.29250	−	6.25065i	0.142614	−	0.270746i
$534$	−20.1560	+	10.4409i	−0.872236	+	0.451822i
$535$	−10.3582	−	40.2130i	−0.447824	−	1.73856i
$536$	18.2383	+	0.707731i	0.787777	+	0.0305693i
$537$	10.3585	+	38.2255i	0.447003	+	1.64955i
$538$	4.28951	+	2.58873i	0.184934	+	0.111608i
$539$	0.226287	+	0.0823618i	0.00974688	+	0.00354757i
$540$	7.95286	−	36.5013i	0.342236	−	1.57077i
$541$	1.99515	−	0.726174i	0.0857781	−	0.0312207i	−0.298775	−	0.954324i	$-0.596578\pi$
$541$	1.99515	−	0.726174i	0.0857781	−	0.0312207i	0.384553	+	0.923103i	$0.374356\pi$
$542$	−17.9358	−	3.52247i	−0.770407	−	0.151303i
$543$	−5.71596	+	9.32593i	−0.245295	+	0.400214i
$544$	−6.70212	−	49.0682i	−0.287351	−	2.10378i
$545$	37.3356	−	2.90195i	1.59928	−	0.124306i
$546$	−0.514556	−	7.26555i	−0.0220210	−	0.310937i
$547$	6.34869	−	5.76113i	0.271450	−	0.246328i	−0.524900	−	0.851164i	$-0.675897\pi$
$547$	6.34869	−	5.76113i	0.271450	−	0.246328i	0.796350	+	0.604836i	$0.206761\pi$
$548$	7.70049	−	0.900059i	0.328949	−	0.0384486i
$549$	−18.9535	−	12.8423i	−0.808916	−	0.548094i
$550$	3.81593	−	5.12568i	0.162712	−	0.218560i
$551$	13.7445	+	6.24766i	0.585537	+	0.266159i
$552$	−2.43126	+	3.64184i	−0.103481	+	0.155007i
$553$	−35.0693	−	19.3504i	−1.49130	−	0.822863i
$554$	20.1477	−	58.8838i	0.855993	−	2.50173i
$555$	−39.9363	−	23.4243i	−1.69520	−	0.994307i
$556$	40.5273	+	3.15003i	1.71874	+	0.133591i
$557$	−2.00568	−	34.4362i	−0.0849833	−	1.45911i	−0.723939	−	0.689864i	$-0.757670\pi$
$557$	−2.00568	−	34.4362i	−0.0849833	−	1.45911i	0.638956	−	0.769243i	$-0.279367\pi$
$558$	10.4729	+	28.2751i	0.443352	+	1.19698i
$559$	3.70928	+	2.43963i	0.156886	+	0.103185i
$560$	9.68159	−	3.95536i	0.409122	−	0.167145i
$561$	−19.5413	+	16.8186i	−0.825032	+	0.710083i
$562$	−1.52041	+	15.6311i	−0.0641344	+	0.659359i
$563$	4.66543	−	1.49591i	0.196625	−	0.0630451i	−0.205382	−	0.978682i	$-0.565844\pi$
$563$	4.66543	−	1.49591i	0.196625	−	0.0630451i	0.402007	+	0.915637i	$0.368313\pi$
$564$	6.67277	−	20.3298i	0.280974	−	0.856037i
$565$	11.2202	−	1.75480i	0.472036	−	0.0738251i
$566$	−1.82814	+	3.16643i	−0.0768425	+	0.133095i
$567$	−23.6012	−	4.35832i	−0.991157	−	0.183032i
$568$	−6.46456	−	11.1970i	−0.271247	−	0.469814i
$569$	−12.6373	−	15.6678i	−0.529783	−	0.656828i	0.440797	−	0.897607i	$-0.354696\pi$
$569$	−12.6373	−	15.6678i	−0.529783	−	0.656828i	−0.970580	+	0.240779i	$0.922597\pi$
$570$	38.4985	−	23.8969i	1.61252	−	1.00093i
$571$	−1.40074	+	6.46654i	−0.0586192	+	0.270616i	−0.997232	−	0.0743570i	$-0.976310\pi$
$571$	−1.40074	+	6.46654i	−0.0586192	+	0.270616i	0.938612	+	0.344973i	$0.112112\pi$
$572$	4.02692	−	1.83046i	0.168374	−	0.0765354i
$573$	−41.0564	+	15.5284i	−1.71516	+	0.648708i
$574$	−7.85002	+	57.4723i	−0.327653	+	2.39885i
$575$	0.104485	−	1.79395i	0.00435734	−	0.0748127i
$576$	35.2174	+	14.9555i	1.46739	+	0.623147i
$577$	−2.01272	−	1.01083i	−0.0837906	−	0.0420812i	0.406410	−	0.913691i	$-0.366780\pi$
$577$	−2.01272	−	1.01083i	−0.0837906	−	0.0420812i	−0.490201	+	0.871609i	$0.663077\pi$
$578$	28.7903	+	60.2098i	1.19752	+	2.50440i
$579$	−0.496785	+	0.583856i	−0.0206457	+	0.0242642i
$580$	15.1361	+	17.3441i	0.628493	+	0.720173i
$581$	0.646407	+	33.3286i	0.0268175	+	1.38270i
$582$	36.7527	+	16.1538i	1.52345	+	0.669596i
$583$	−13.7604	+	9.83531i	−0.569896	+	0.407337i
$584$	20.4594	+	2.39136i	0.846616	+	0.0989552i
$585$	−1.01175	+	5.31036i	−0.0418306	+	0.219557i
$586$	−11.9739	+	27.7587i	−0.494638	+	1.14670i
$587$	19.1747	+	6.14811i	0.791423	+	0.253760i	0.673426	−	0.739254i	$-0.264822\pi$
$587$	19.1747	+	6.14811i	0.791423	+	0.253760i	0.117997	+	0.993014i	$0.462353\pi$
$588$	0.224229	+	0.502422i	0.00924704	+	0.0207195i
$589$	−9.27818	+	19.4037i	−0.382301	+	0.799514i
$590$	−2.29684	+	1.78019i	−0.0945596	+	0.0732892i
$591$	2.50754	+	16.7875i	0.103146	+	0.690544i
$592$	10.8729	−	12.4589i	0.446872	−	0.512058i
$593$	11.7568	+	9.86514i	0.482794	+	0.405113i	0.851436	−	0.524459i	$-0.175732\pi$
$593$	11.7568	+	9.86514i	0.482794	+	0.405113i	−0.368641	+	0.929572i	$0.620177\pi$
$594$	−4.27428	−	24.4131i	−0.175376	−	1.00168i
$595$	−35.3701	+	29.6791i	−1.45003	+	1.21672i
$596$	1.04520	−	53.8901i	0.0428130	−	2.20743i
$597$	3.33903	−	7.21379i	0.136657	−	0.295241i
$598$	1.12784	−	1.78944i	0.0461207	−	0.0731755i
$599$	3.65666	−	3.58643i	0.149407	−	0.146538i	−0.621670	−	0.783279i	$-0.713545\pi$
$599$	3.65666	−	3.58643i	0.149407	−	0.146538i	0.771077	+	0.636742i	$0.219718\pi$
$600$	4.33733	−	0.562115i	0.177071	−	0.0229482i
$601$	3.50953	+	5.56824i	0.143157	+	0.227133i	0.909907	−	0.414812i	$-0.136152\pi$
$601$	3.50953	+	5.56824i	0.143157	+	0.227133i	−0.766751	+	0.641945i	$0.778128\pi$
$602$	−35.4695	−	8.40643i	−1.44563	−	0.342621i
$603$	−7.63232	+	28.0310i	−0.310812	+	1.14151i
$604$	−2.92946	+	9.78507i	−0.119198	+	0.398149i
$605$	−3.96580	+	15.3962i	−0.161233	+	0.625943i
$606$	2.72082	+	11.8418i	0.110526	+	0.481041i
$607$	1.87597	+	4.85888i	0.0761433	+	0.197216i	0.965729	−	0.259552i	$-0.0835749\pi$
$607$	1.87597	+	4.85888i	0.0761433	+	0.197216i	−0.889586	+	0.456768i	$0.849007\pi$
$608$	12.2311	+	31.6792i	0.496035	+	1.28476i
$609$	10.8266	−	10.0748i	0.438717	−	0.408250i
$610$	10.5615	−	41.0022i	0.427622	−	1.66013i
$611$	−0.888017	+	2.96618i	−0.0359253	+	0.119999i
$612$	−58.6605	−	5.37087i	−2.37121	−	0.217105i
$613$	−1.07299	−	0.254303i	−0.0433376	−	0.0102712i	0.208890	−	0.977939i	$-0.433015\pi$
$613$	−1.07299	−	0.254303i	−0.0433376	−	0.0102712i	−0.252227	+	0.967668i	$0.581163\pi$
$614$	10.7909	+	17.1209i	0.435484	+	0.690942i
$615$	16.5552	−	39.7407i	0.667570	−	1.60250i
$616$	−7.76746	+	7.61827i	−0.312960	+	0.306949i
$617$	12.2160	−	19.3820i	0.491796	−	0.780288i	−0.504755	−	0.863262i	$-0.668417\pi$
$617$	12.2160	−	19.3820i	0.491796	−	0.780288i	0.996552	+	0.0829745i	$0.0264420\pi$
$618$	−0.232465	+	0.0210010i	−0.00935110	+	0.000844782i
$619$	−0.894836	+	46.1375i	−0.0359665	+	1.85442i	0.356054	+	0.934465i	$0.384122\pi$
$619$	−0.894836	+	46.1375i	−0.0359665	+	1.85442i	−0.392020	+	0.919957i	$0.628224\pi$
$620$	−25.1212	+	21.0792i	−1.00889	+	0.846559i
$621$	−4.77676	−	5.07534i	−0.191685	−	0.203666i
$622$	18.4475	+	15.4793i	0.739676	+	0.620662i
$623$	−10.4287	+	11.9500i	−0.417818	+	0.478767i
$624$	−1.79636	−	0.707769i	−0.0719118	−	0.0283334i
$625$	23.6357	−	18.3191i	0.945428	−	0.732762i
$626$	8.01690	−	16.7659i	0.320420	−	0.670101i
$627$	10.3786	−	14.3118i	0.414483	−	0.571556i
$628$	24.0141	+	7.69981i	0.958267	+	0.307256i
$629$	−28.9157	+	67.0342i	−1.15295	+	2.67283i
$630$	−7.10642	−	43.8128i	−0.283127	−	1.74554i
$631$	−6.56642	−	0.767505i	−0.261405	−	0.0305539i	−0.0156192	−	0.999878i	$-0.504972\pi$
$631$	−6.56642	−	0.767505i	−0.261405	−	0.0305539i	−0.245786	+	0.969324i	$0.579046\pi$
$632$	23.0313	−	16.4618i	0.916137	−	0.654816i
$633$	−32.7175	+	24.0099i	−1.30041	+	0.954308i
$634$	0.209535	+	10.8036i	0.00832172	+	0.429065i
$635$	11.3300	+	12.9828i	0.449619	+	0.515206i
$636$	−38.0099	−	6.97162i	−1.50719	−	0.276443i
$637$	−0.0343451	−	0.0718267i	−0.00136080	−	0.00284588i
$638$	13.6478	+	6.85419i	0.540322	+	0.271360i
$639$	19.6808	−	6.01361i	0.778561	−	0.237895i
$640$	−2.00561	+	34.4350i	−0.0792787	+	1.36116i
$641$	−1.75504	+	12.8492i	−0.0693199	+	0.507511i	0.923094	+	0.384573i	$0.125651\pi$
$641$	−1.75504	+	12.8492i	−0.0693199	+	0.507511i	−0.992414	+	0.122938i	$0.960768\pi$
$642$	10.1528	−	62.1195i	0.400699	−	2.45166i
$643$	−7.73685	+	3.51683i	−0.305112	+	0.138690i	−0.560515	−	0.828144i	$-0.689397\pi$
$643$	−7.73685	+	3.51683i	−0.305112	+	0.138690i	0.255403	+	0.966835i	$0.417792\pi$
$644$	−2.16220	+	9.98181i	−0.0852024	+	0.393338i
$645$	23.8494	+	12.7725i	0.939067	+	0.502916i
$646$	−44.8563	−	55.6131i	−1.76485	−	2.18807i
$647$	5.57532	+	9.65674i	0.219188	+	0.379646i	0.954560	−	0.298019i	$-0.0963257\pi$
$647$	5.57532	+	9.65674i	0.219188	+	0.379646i	−0.735372	+	0.677664i	$0.762992\pi$
$648$	9.97507	−	13.7203i	0.391858	−	0.538986i
$649$	−0.566889	+	0.981881i	−0.0222524	+	0.0385422i
$650$	−2.08731	+	0.326450i	−0.0818712	+	0.0128044i
$651$	14.0503	+	15.6986i	0.550676	+	0.615276i
$652$	−30.7273	+	9.85231i	−1.20337	+	0.385846i
$653$	−0.419633	+	4.31421i	−0.0164215	+	0.168828i	−0.999927	−	0.0120480i	$-0.996165\pi$
$653$	−0.419633	+	4.31421i	−0.0164215	+	0.168828i	0.983506	+	0.180876i	$0.0578933\pi$
$654$	53.5791	+	18.7446i	2.09511	+	0.732971i
$655$	35.8999	−	14.6667i	1.40273	−	0.573077i
$656$	12.8465	+	8.44929i	0.501573	+	0.329890i
$657$	−11.0391	+	30.8722i	−0.430678	+	1.20444i
$658$	−1.47816	−	25.3791i	−0.0576247	−	0.989378i
$659$	20.4685	+	1.59094i	0.797340	+	0.0619742i	0.469697	−	0.882827i	$-0.344363\pi$
$659$	20.4685	+	1.59094i	0.797340	+	0.0619742i	0.327643	+	0.944802i	$0.393746\pi$
$660$	23.4360	−	13.3170i	0.912243	−	0.518364i
$661$	8.93816	−	26.1228i	0.347654	−	1.01606i	−0.624360	−	0.781137i	$-0.714640\pi$
$661$	8.93816	−	26.1228i	0.347654	−	1.01606i	0.972014	−	0.234921i	$-0.0754832\pi$
$662$	51.3081	+	28.3106i	1.99414	+	1.10032i
$663$	8.50603	+	0.554052i	0.330347	+	0.0215176i
$664$	−21.4489	−	9.74972i	−0.832379	−	0.378363i
$665$	18.9063	−	25.3955i	0.733153	−	0.984796i
$666$	−41.1311	−	56.8627i	−1.59380	−	2.20338i
$667$	4.26571	−	0.498590i	0.165169	−	0.0193055i
$668$	29.5376	−	26.8040i	1.14285	−	1.03708i
$669$	0.383336	+	0.186543i	0.0148206	+	0.00721218i
$670$	−53.5656	+	4.16344i	−2.06942	+	0.160848i
$671$	−2.23560	−	16.3675i	−0.0863045	−	0.631860i
$672$	33.2524	+	0.873389i	1.28274	+	0.0336917i
$673$	19.9228	+	3.91271i	0.767967	+	0.150824i	0.561328	−	0.827593i	$-0.310291\pi$
$673$	19.9228	+	3.91271i	0.767967	+	0.150824i	0.206639	+	0.978417i	$0.433747\pi$
$674$	39.6774	−	14.4414i	1.52832	−	0.556261i
$675$	−0.682308	+	6.92786i	−0.0262620	+	0.266654i
$676$	33.5069	+	12.1955i	1.28873	+	0.469059i
$677$	−5.26153	−	3.17535i	−0.202217	−	0.122039i	0.411975	−	0.911195i	$-0.364839\pi$
$677$	−5.26153	−	3.17535i	−0.202217	−	0.122039i	−0.614192	+	0.789156i	$0.710518\pi$
$678$	16.6401	+	4.40827i	0.639058	+	0.169299i
$679$	28.0296	+	1.08768i	1.07568	+	0.0417412i
$680$	−8.14035	−	31.6028i	−0.312168	−	1.21191i
$681$	−23.8914	−	15.2884i	−0.915520	−	0.585852i
$682$	−10.1394	+	19.2492i	−0.388257	+	0.737088i
$683$	−23.9372	+	25.3719i	−0.915931	+	0.970831i	−0.999671	−	0.0256571i	$-0.991832\pi$
$683$	−23.9372	+	25.3719i	−0.915931	+	0.970831i	0.0837394	+	0.996488i	$0.473314\pi$
$684$	39.9885	−	5.69263i	1.52900	−	0.217663i
$685$	−6.65228	+	1.57662i	−0.254171	+	0.0602396i
$686$	−28.8988	−	28.3438i	−1.10336	−	1.08217i
$687$	3.57516	−	28.8670i	0.136401	−	1.10134i
$688$	−6.06632	+	7.52106i	−0.231276	+	0.286738i
$689$	5.52486	+	0.864073i	0.210480	+	0.0329185i
$690$	5.86378	−	11.4785i	0.223230	−	0.436980i
$691$	−5.48349	+	1.52643i	−0.208602	+	0.0580683i	−0.370897	−	0.928674i	$-0.620950\pi$
$691$	−5.48349	+	1.52643i	−0.208602	+	0.0580683i	0.162295	+	0.986742i	$0.448110\pi$
$692$	−31.7100	−	33.6107i	−1.20543	−	1.27769i
$693$	−9.03159	−	14.7756i	−0.343082	−	0.561280i
$694$	2.00248	+	6.68876i	0.0760133	+	0.253902i
$695$	−35.8180	+	1.38990i	−1.35865	+	0.0527220i
$696$	3.12309	+	9.97534i	0.118380	+	0.378114i
$697$	−65.3969	−	18.2045i	−2.47708	−	0.689543i
$698$	−28.8449	−	54.7606i	−1.09179	−	2.07272i
$699$	0.119684	−	1.41406i	0.00452686	−	0.0534848i
$700$	8.93169	−	4.92830i	0.337586	−	0.186272i
$701$	−3.03177	−	17.1940i	−0.114508	−	0.649408i	−0.986993	−	0.160766i	$-0.948604\pi$
$701$	−3.03177	−	17.1940i	−0.114508	−	0.649408i	0.872484	−	0.488642i	$-0.162508\pi$
$702$	−4.64282	+	6.75190i	−0.175232	+	0.254834i
$703$	8.69271	−	49.2988i	0.327852	−	1.85934i
$704$	8.93746	+	26.1207i	0.336843	+	0.984461i
$705$	−3.76311	+	18.4888i	−0.141727	+	0.696327i
$706$	76.2818	+	31.1646i	2.87090	+	1.17289i
$707$	4.80182	+	7.00122i	0.180591	+	0.263308i
$708$	−2.51289	+	0.628909i	−0.0944401	+	0.0236359i
$709$	−3.90662	−	18.0350i	−0.146716	−	0.677317i	−0.990141	−	0.140071i	$-0.955267\pi$
$709$	−3.90662	−	18.0350i	−0.146716	−	0.677317i	0.843425	−	0.537246i	$-0.180536\pi$
$710$	22.7269	+	30.5275i	0.852925	+	1.14568i
$711$	17.2774	+	41.6159i	0.647954	+	1.56072i
$712$	−4.44013	−	10.2934i	−0.166401	−	0.385761i
$713$	0.592302	+	6.08940i	0.0221819	+	0.228050i
$714$	−67.1834	+	19.6117i	−2.51428	+	0.733950i
$715$	−3.33956	+	2.01544i	−0.124893	+	0.0753731i
$716$	−64.0656	+	12.5821i	−2.39424	+	0.470214i
$717$	20.4198	−	3.45616i	0.762592	−	0.129073i
$718$	−23.6041	+	34.4156i	−0.880897	+	1.28438i
$719$	13.3264	−	8.76490i	0.496990	−	0.326876i	−0.276146	−	0.961116i	$-0.589057\pi$
$719$	13.3264	−	8.76490i	0.496990	−	0.326876i	0.773136	+	0.634240i	$0.218687\pi$
$720$	−11.2902	−	3.31057i	−0.420762	−	0.123378i
$721$	−0.145741	+	0.0731939i	−0.00542768	+	0.00272588i
$722$	5.63229	+	4.36535i	0.209612	+	0.162462i
$723$	−10.4101	−	17.5203i	−0.387155	−	0.651586i
$724$	−14.6702	−	10.4856i	−0.545212	−	0.389694i
$725$	−3.17667	−	2.88267i	−0.117978	−	0.107060i
$726$	−14.8935	+	18.9458i	−0.552750	+	0.703146i
$727$	0.111817	−	0.289613i	0.00414707	−	0.0107412i	−0.930795	−	0.365542i	$-0.880884\pi$
$727$	0.111817	−	0.289613i	0.00414707	−	0.0107412i	0.934942	+	0.354801i	$0.115451\pi$
$728$	3.59706			0.133316
$729$	17.7039	+	20.3856i	0.655699	+	0.755022i
$730$	−60.6346			−2.24419
$731$	15.3649	−	39.7962i	0.568292	−	1.47191i
$732$	23.3255	−	29.6721i	0.862136	−	1.09671i
$733$	16.6882	+	15.1437i	0.616392	+	0.559346i	0.919242	−	0.393692i	$-0.128802\pi$
$733$	16.6882	+	15.1437i	0.616392	+	0.559346i	−0.302850	+	0.953038i	$0.597938\pi$
$734$	−20.1877	−	14.4293i	−0.745142	−	0.532596i
$735$	−0.247823	−	0.417088i	−0.00914109	−	0.0153845i
$736$	7.63506	+	5.91762i	0.281432	+	0.218126i
$737$	−18.7324	+	9.40774i	−0.690015	+	0.346539i
$738$	47.2114	−	45.0493i	1.73787	−	1.65829i
$739$	33.3162	−	21.9124i	1.22556	−	0.806061i	0.239245	−	0.970959i	$-0.423100\pi$
$739$	33.3162	−	21.9124i	1.22556	−	0.806061i	0.986311	+	0.164899i	$0.0527297\pi$
$740$	43.1707	−	62.9444i	1.58698	−	2.31388i
$741$	−5.76297	+	0.975411i	−0.211708	+	0.0358326i
$742$	−45.0531	+	8.84814i	−1.65395	+	0.324825i
$743$	−32.3459	+	19.5208i	−1.18665	+	0.716150i	−0.965833	−	0.259164i	$-0.916553\pi$
$743$	−32.3459	+	19.5208i	−1.18665	+	0.716150i	−0.220821	+	0.975314i	$0.570874\pi$
$744$	−14.2941	+	4.17263i	−0.524046	+	0.152976i
$745$	4.60138	+	47.3063i	0.168581	+	1.73317i
$746$	18.0552	+	41.8567i	0.661048	+	1.53248i
$747$	22.8052	−	29.7703i	0.834400	−	1.08924i
$748$	−25.3812	−	34.0929i	−0.928030	−	1.24656i
$749$	−9.31070	−	42.9830i	−0.340206	−	1.57056i
$750$	34.1216	−	8.53973i	1.24594	−	0.311827i
$751$	−9.60076	−	13.9983i	−0.350337	−	0.510803i	0.608961	−	0.793200i	$-0.291587\pi$
$751$	−9.60076	−	13.9983i	−0.350337	−	0.510803i	−0.959298	+	0.282397i	$0.908871\pi$
$752$	−6.23829	−	2.54862i	−0.227487	−	0.0929387i
$753$	−5.79275	+	28.4607i	−0.211099	+	1.03716i
$754$	−1.63462	−	4.77736i	−0.0595294	−	0.173981i
$755$	1.56403	−	8.87007i	0.0569210	−	0.322815i
$756$	9.91555	−	38.3029i	0.360625	−	1.39306i
$757$	−5.38910	−	30.5631i	−0.195870	−	1.11084i	−0.911174	−	0.412022i	$-0.864823\pi$
$757$	−5.38910	−	30.5631i	−0.195870	−	1.11084i	0.715304	−	0.698814i	$-0.246288\pi$
$758$	−44.7627	+	24.6990i	−1.62585	+	0.897108i
$759$	0.424126	−	5.01104i	0.0153948	−	0.181889i
$760$	10.4288	+	19.7986i	0.378292	+	0.718170i
$761$	0.879111	+	0.244717i	0.0318677	+	0.00887099i	0.284070	−	0.958804i	$-0.408315\pi$
$761$	0.879111	+	0.244717i	0.0318677	+	0.00887099i	−0.252202	+	0.967675i	$0.581155\pi$
$762$	7.80386	+	24.9260i	0.282704	+	0.902974i
$763$	39.6316	−	1.53789i	1.43476	−	0.0556753i
$764$	−20.7539	−	69.3229i	−0.750850	−	2.50801i
$765$	51.9272	−	1.30112i	1.87743	−	0.0470420i
$766$	−34.0689	−	36.1110i	−1.23096	−	1.30474i
$767$	0.361116	−	0.100523i	0.0130391	−	0.00362969i
$768$	−3.68667	+	7.21678i	−0.133031	+	0.260413i
$769$	23.3532	+	3.65238i	0.842138	+	0.131708i	0.560852	−	0.827916i	$-0.310474\pi$
$769$	23.3532	+	3.65238i	0.842138	+	0.131708i	0.281286	+	0.959624i	$0.409239\pi$
$770$	20.1064	−	24.9280i	0.724585	−	0.898344i
$771$	2.01764	−	16.2910i	0.0726634	−	0.586707i
$772$	−0.902254	−	0.884925i	−0.0324728	−	0.0318491i
$773$	−12.9466	+	3.06840i	−0.465657	+	0.110363i	−0.456745	−	0.889598i	$-0.650985\pi$
$773$	−12.9466	+	3.06840i	−0.465657	+	0.110363i	−0.00891158	+	0.999960i	$0.502837\pi$
$774$	25.3047	+	32.2699i	0.909558	+	1.15992i
$775$	4.19352	−	4.44487i	0.150636	−	0.159665i
$776$	−9.23979	+	17.5413i	−0.331689	+	0.629696i
$777$	−41.3028	−	26.4302i	−1.48173	−	0.948177i
$778$	3.50844	+	13.6206i	0.125784	+	0.488322i
$779$	46.5125	+	1.80490i	1.66648	+	0.0646672i
$780$	−8.61469	−	2.28219i	−0.308455	−	0.0817157i
$781$	12.7130	+	7.67235i	0.454908	+	0.274538i
$782$	−19.0987	−	6.95134i	−0.682967	−	0.248580i
$783$	−16.5891	+	1.26924i	−0.592844	+	0.0453590i
$784$	0.162829	−	0.0592648i	0.00581531	−	0.00211660i
$785$	−21.8208	−	4.28547i	−0.778819	−	0.152955i
$786$	58.7623	+	1.54342i	2.09598	+	0.0550520i
$787$	3.11209	+	22.7845i	0.110934	+	0.812181i	0.959224	+	0.282649i	$0.0912130\pi$
$787$	3.11209	+	22.7845i	0.110934	+	0.812181i	−0.848289	+	0.529533i	$0.822367\pi$
$788$	−27.8979	+	2.16839i	−0.993820	+	0.0772458i
$789$	−21.2630	−	10.3473i	−0.756984	−	0.368372i
$790$	−61.7115	+	56.0002i	−2.19560	+	1.99240i
$791$	11.9464	−	1.39634i	0.424766	−	0.0496481i
$792$	12.1753	−	1.25386i	0.432632	−	0.0445538i
$793$	−3.26145	+	4.38089i	−0.115817	+	0.155570i
$794$	−26.2377	−	11.9265i	−0.931143	−	0.423256i
$795$	34.0044	+	2.21492i	1.20601	+	0.0785552i
$796$	11.4737	+	6.33092i	0.406675	+	0.224394i
$797$	−12.8986	+	37.6975i	−0.456891	+	1.33532i	0.441949	+	0.897040i	$0.354287\pi$
$797$	−12.8986	+	37.6975i	−0.456891	+	1.33532i	−0.898841	+	0.438275i	$0.855589\pi$
$798$	41.7245	−	23.7092i	1.47703	−	0.839295i
$799$	29.6615	+	2.30548i	1.04935	+	0.0815619i
$800$	−0.561001	−	9.63201i	−0.0198344	−	0.340543i
$801$	17.5542	−	3.19780i	0.620247	−	0.112989i
$802$	−3.07853	−	2.02478i	−0.108707	−	0.0714976i
$803$	−21.8999	+	8.94709i	−0.772830	+	0.315736i
$804$	−45.2062	−	15.8153i	−1.59430	−	0.557764i
$805$	0.871893	−	8.96384i	0.0307302	−	0.315934i
$806$	6.84952	−	2.19621i	0.241264	−	0.0773582i
$807$	−2.62642	−	2.93452i	−0.0924542	−	0.103300i
$808$	−5.92837	+	0.927180i	−0.208559	+	0.0326181i
$809$	−20.0019	+	34.6443i	−0.703230	+	1.21803i	0.264097	+	0.964496i	$0.414926\pi$
$809$	−20.0019	+	34.6443i	−0.703230	+	1.21803i	−0.967327	+	0.253533i	$0.918407\pi$
$810$	−24.4756	+	43.5231i	−0.859984	+	1.52925i
$811$	14.8520	+	25.7245i	0.521525	+	0.903308i	0.999687	+	0.0250358i	$0.00796997\pi$
$811$	14.8520	+	25.7245i	0.521525	+	0.903308i	−0.478162	+	0.878272i	$0.658697\pi$
$812$	15.3064	+	18.9769i	0.537148	+	0.665959i
$813$	12.6657	+	6.78310i	0.444206	+	0.237894i
$814$	10.7202	−	49.4899i	0.375742	−	1.73462i
$815$	25.9037	−	11.7747i	0.907367	−	0.412449i
$816$	−2.99244	+	18.3092i	−0.104756	+	0.640949i
$817$	−3.95863	+	28.9823i	−0.138495	+	1.01396i
$818$	−0.696573	+	11.9597i	−0.0243551	+	0.418161i
$819$	−1.28882	+	5.57844i	−0.0450350	+	0.194926i
$820$	63.4227	+	31.8521i	2.21482	+	1.11232i
$821$	−15.8567	−	33.1615i	−0.553403	−	1.15734i	−0.968832	−	0.247719i	$-0.920319\pi$
$821$	−15.8567	−	33.1615i	−0.553403	−	1.15734i	0.415429	−	0.909626i	$-0.363632\pi$
$822$	−10.1927	−	1.86951i	−0.355512	−	0.0652065i
$823$	1.33501	+	1.52975i	0.0465355	+	0.0533238i	0.776232	−	0.630448i	$-0.217129\pi$
$823$	1.33501	+	1.52975i	0.0465355	+	0.0533238i	−0.729696	+	0.683771i	$0.760339\pi$
$824$	−0.00223523	−	0.115248i	−7.78680e−5	−	0.00401485i
$825$	−4.04954	+	2.97177i	−0.140987	+	0.103464i
$826$	−2.50387	+	1.78966i	−0.0871208	+	0.0622702i
$827$	−0.283950	−	0.0331890i	−0.00987391	−	0.00115409i	0.111155	−	0.993803i	$-0.464545\pi$
$827$	−0.283950	−	0.0331890i	−0.00987391	−	0.00115409i	−0.121028	+	0.992649i	$0.538619\pi$
$828$	8.90234	−	7.26396i	0.309378	−	0.252440i
$829$	12.3531	−	28.6377i	0.429041	−	0.994629i	−0.557359	−	0.830271i	$-0.688185\pi$
$829$	12.3531	−	28.6377i	0.429041	−	0.994629i	0.986401	−	0.164358i	$-0.0525553\pi$
$830$	66.0422	+	21.1756i	2.29236	+	0.735015i
$831$	−28.7192	+	39.6027i	−0.996258	+	1.37380i
$832$	3.93746	−	8.23450i	0.136507	−	0.285480i
$833$	−0.604653	+	0.468641i	−0.0209500	+	0.0162375i
$834$	−50.5509	−	19.9172i	−1.75044	−	0.689676i
$835$	−23.1264	+	26.4999i	−0.800321	+	0.917066i
$836$	22.3260	+	18.7337i	0.772160	+	0.647919i
$837$	−1.34952	−	23.6627i	−0.0466461	−	0.817904i
$838$	−51.9086	+	43.5565i	−1.79315	+	1.50463i
$839$	0.0389356	−	2.00751i	0.00134421	−	0.0693070i	−0.998539	−	0.0540332i	$-0.982792\pi$
$839$	0.0389356	−	2.00751i	0.00134421	−	0.0693070i	0.999883	−	0.0152738i	$-0.00486200\pi$
$840$	21.8307	−	1.97220i	0.753232	−	0.0680473i
$841$	−9.99644	+	15.8604i	−0.344705	+	0.546912i
$842$	−58.4730	+	57.3499i	−2.01511	+	1.97641i
$843$	4.74717	−	11.3956i	0.163501	−	0.392484i
$844$	−35.6723	−	56.5979i	−1.22789	−	1.94818i
$845$	−30.5953	−	7.25122i	−1.05251	−	0.249449i
$846$	−16.4985	+	23.3610i	−0.567229	+	0.803166i
$847$	−4.82930	+	16.1310i	−0.165937	+	0.554267i
$848$	−3.03587	+	11.7860i	−0.104252	+	0.404732i
$849$	2.10398	−	1.95787i	0.0722083	−	0.0671938i
$850$	7.31167	+	18.9377i	0.250788	+	0.649558i
$851$	−5.12890	−	13.2842i	−0.175817	−	0.455376i
$852$	7.59691	+	33.0641i	0.260266	+	1.13276i
$853$	3.26133	−	12.6613i	0.111666	−	0.433513i	−0.887987	−	0.459869i	$-0.847896\pi$
$853$	3.26133	−	12.6613i	0.111666	−	0.433513i	0.999653	+	0.0263555i	$0.00839020\pi$
$854$	12.8611	−	42.9591i	0.440098	−	1.47003i
$855$	−34.4409	+	9.07953i	−1.17785	+	0.310513i
$856$	30.2467	+	7.16861i	1.03381	+	0.245018i
$857$	1.25661	+	1.99374i	0.0429249	+	0.0681050i	0.866763	−	0.498720i	$-0.166196\pi$
$857$	1.25661	+	1.99374i	0.0429249	+	0.0681050i	−0.823838	+	0.566825i	$0.808172\pi$
$858$	−5.86342	+	0.759896i	−0.200174	+	0.0259424i
$859$	5.64199	−	5.53363i	0.192502	−	0.188805i	−0.597573	−	0.801814i	$-0.703868\pi$
$859$	5.64199	−	5.53363i	0.192502	−	0.188805i	0.790076	+	0.613009i	$0.210041\pi$
$860$	−23.7810	+	37.7311i	−0.810924	+	1.28662i
$861$	19.1525	−	41.3779i	0.652715	−	1.41016i
$862$	−1.09038	+	56.2198i	−0.0371385	+	1.91485i
$863$	32.1636	−	26.9885i	1.09486	−	0.918699i	0.0977940	−	0.995207i	$-0.468821\pi$
$863$	32.1636	−	26.9885i	1.09486	−	0.918699i	0.997069	+	0.0765075i	$0.0243769\pi$
$864$	−28.6374	−	24.0887i	−0.974265	−	0.819513i
$865$	31.2138	+	26.1915i	1.06130	+	0.890537i
$866$	2.08668	−	2.39107i	0.0709082	−	0.0812517i
$867$	−7.74998	−	51.8846i	−0.263203	−	1.76209i
$868$	−27.4515	+	21.2765i	−0.931765	+	0.722173i
$869$	−14.0256	+	29.3320i	−0.475785	+	0.995020i
$870$	−12.5399	−	28.0978i	−0.425143	−	0.952604i
$871$	6.59945	+	2.11603i	0.223614	+	0.0716989i
$872$	−11.1031	+	25.7398i	−0.375998	+	0.871661i
$873$	−23.8930	−	20.6143i	−0.808656	−	0.697690i
$874$	13.8422	+	1.61792i	0.468218	+	0.0547268i
$875$	19.9944	−	14.2911i	0.675933	−	0.483128i
$876$	−49.4816	−	21.7485i	−1.67183	−	0.734813i
$877$	0.989896	+	51.0388i	0.0334264	+	1.72346i	0.523711	+	0.851896i	$0.324547\pi$
$877$	0.989896	+	51.0388i	0.0334264	+	1.72346i	−0.490285	+	0.871562i	$0.663107\pi$
$878$	18.8131	+	21.5574i	0.634910	+	0.727526i
$879$	15.3993	−	18.0983i	0.519405	−	0.610440i
$880$	−3.66222	−	7.65888i	−0.123453	−	0.258181i
$881$	6.96527	+	3.49809i	0.234666	+	0.117854i	0.562247	−	0.826969i	$-0.309937\pi$
$881$	6.96527	+	3.49809i	0.234666	+	0.117854i	−0.327581	+	0.944823i	$0.606233\pi$
$882$	−0.0895060	−	0.729927i	−0.00301382	−	0.0245779i
$883$	1.33937	−	22.9960i	0.0450733	−	0.773878i	−0.897734	−	0.440539i	$-0.854787\pi$
$883$	1.33937	−	22.9960i	0.0450733	−	0.773878i	0.942807	−	0.333339i	$-0.108176\pi$
$884$	−1.90172	+	13.9230i	−0.0639617	+	0.468282i
$885$	2.13651	−	0.808073i	0.0718180	−	0.0271631i
$886$	−30.2279	+	13.7402i	−1.01552	+	0.461613i
$887$	2.77847	−	12.8268i	0.0932918	−	0.430683i	−0.906669	−	0.421843i	$-0.861384\pi$
$887$	2.77847	−	12.8268i	0.0932918	−	0.430683i	0.999961	−	0.00884037i	$-0.00281401\pi$
$888$	29.4463	−	18.2780i	0.988153	−	0.613368i
$889$	11.4575	+	14.2050i	0.384271	+	0.476422i
$890$	16.4993	+	28.5776i	0.553057	+	0.957922i
$891$	−2.41787	+	19.3311i	−0.0810018	+	0.647618i
$892$	−0.351401	+	0.608644i	−0.0117658	+	0.0203789i
$893$	−20.1552	+	3.15222i	−0.674468	+	0.105485i
$894$	−22.4676	+	68.4515i	−0.751430	+	2.28936i
$895$	54.8233	−	17.5784i	1.83254	−	0.587581i
$896$	−3.53669	+	36.3604i	−0.118153	+	1.21471i
$897$	−1.26018	+	1.08460i	−0.0420762	+	0.0362139i
$898$	22.8892	−	9.35129i	0.763824	−	0.312056i
$899$	12.2021	+	8.02547i	0.406964	+	0.267664i
$900$	−11.3129	−	1.92883i	−0.377097	−	0.0642944i
$901$	−3.12424	−	53.6411i	−0.104084	−	1.78705i
$902$	46.9437	+	3.64876i	1.56306	+	0.121490i
$903$	24.7154	+	14.4966i	0.822476	+	0.482417i
$904$	−2.75211	+	8.04333i	−0.0915337	+	0.267517i
$905$	13.9222	+	7.68193i	0.462789	+	0.255356i
$906$	7.58033	−	11.3547i	0.251839	−	0.377235i
$907$	−8.48593	−	3.85733i	−0.281771	−	0.128081i	0.267940	−	0.963436i	$-0.413657\pi$
$907$	−8.48593	−	3.85733i	−0.281771	−	0.128081i	−0.549711	+	0.835355i	$0.685262\pi$
$908$	27.9231	−	37.5072i	0.926660	−	1.24472i
$909$	0.686219	−	9.52611i	0.0227605	−	0.315961i
$910$	−10.5168	+	1.22924i	−0.348628	+	0.0407488i
$911$	12.0980	−	10.9783i	0.400823	−	0.363728i	−0.446520	−	0.894774i	$-0.647337\pi$
$911$	12.0980	−	10.9783i	0.400823	−	0.363728i	0.847343	+	0.531046i	$0.178201\pi$
$912$	−0.898677	−	12.6894i	−0.0297582	−	0.420186i
$913$	26.9776	−	2.09687i	0.892829	−	0.0693961i
$914$	−12.2452	−	89.6509i	−0.405036	−	2.96539i
$915$	−17.3919	+	28.3760i	−0.574959	+	0.938080i
$916$	47.0533	+	9.24097i	1.55469	+	0.305330i
$917$	38.5954	−	14.0476i	1.27453	−	0.463892i
$918$	72.8509	+	29.8656i	2.40444	+	0.985712i
$919$	29.1018	+	10.5922i	0.959980	+	0.349404i	0.774026	−	0.633154i	$-0.218240\pi$
$919$	29.1018	+	10.5922i	0.959980	+	0.349404i	0.185954	+	0.982558i	$0.440462\pi$
$920$	5.44991	+	3.28904i	0.179678	+	0.108436i
$921$	−4.16072	−	15.3541i	−0.137100	−	0.505935i
$922$	−80.1527	−	3.11029i	−2.63969	−	0.102432i
$923$	−1.22457	−	4.75407i	−0.0403072	−	0.156482i
$924$	25.3493	−	13.1310i	0.833931	−	0.431979i
$925$	−6.62852	+	12.5839i	−0.217944	+	0.413757i
$926$	40.6418	−	43.0778i	1.33557	−	1.41562i
$927$	0.179531	+	0.0378266i	0.00589657	+	0.00124239i
$928$	22.4377	−	5.31784i	0.736555	−	0.174567i
$929$	15.7371	+	15.4348i	0.516317	+	0.506400i	0.910994	−	0.412420i	$-0.135316\pi$
$929$	15.7371	+	15.4348i	0.516317	+	0.506400i	−0.394677	+	0.918820i	$0.629143\pi$
$930$	40.3659	−	17.0843i	1.32365	−	0.560218i
$931$	0.329326	−	0.408300i	0.0107932	−	0.0133815i
$932$	2.31139	+	0.361495i	0.0757120	+	0.0118411i
$933$	−10.2929	−	15.8862i	−0.336975	−	0.520090i
$934$	−66.8568	+	18.6109i	−2.18762	+	0.608966i
$935$	25.7201	+	27.2617i	0.841138	+	0.891554i
$936$	−3.16410	−	2.52268i	−0.103422	−	0.0824563i
$937$	−13.3304	−	44.5265i	−0.435484	−	1.45462i	−0.841253	−	0.540642i	$-0.818181\pi$
$937$	−13.3304	−	44.5265i	−0.435484	−	1.45462i	0.405768	−	0.913976i	$-0.367004\pi$
$938$	−56.8597	+	2.20642i	−1.85654	+	0.0720420i
$939$	−9.89073	+	10.7502i	−0.322772	+	0.350819i
$940$	−29.9652	−	8.34139i	−0.977358	−	0.272066i
$941$	−16.6386	−	31.5876i	−0.542402	−	1.02973i	−0.990729	−	0.135855i	$-0.956622\pi$
$941$	−16.6386	−	31.5876i	−0.542402	−	1.02973i	0.448326	−	0.893870i	$-0.352020\pi$
$942$	−27.6661	−	19.2556i	−0.901411	−	0.627381i
$943$	11.5932	−	6.39687i	0.377528	−	0.208311i
$944$	0.141667	+	0.803436i	0.00461088	+	0.0261496i
$945$	−4.76335	+	34.5624i	−0.154952	+	1.12432i
$946$	−5.13814	+	29.1398i	−0.167055	+	0.947418i
$947$	8.11034	+	23.7034i	0.263551	+	0.770256i	0.995993	+	0.0894270i	$0.0285036\pi$
$947$	8.11034	+	23.7034i	0.263551	+	0.770256i	−0.732443	+	0.680829i	$0.761620\pi$
$948$	−70.4466	+	23.5649i	−2.28800	+	0.765351i
$949$	7.24047	+	2.95806i	0.235035	+	0.0960225i
$950$	−7.87313	−	11.4793i	−0.255438	−	0.372438i
$951$	2.33393	−	8.16680i	0.0756827	−	0.264826i
$952$	−7.31714	−	33.7797i	−0.237150	−	1.09481i
$953$	−8.47152	−	11.3792i	−0.274420	−	0.368609i	0.643452	−	0.765486i	$-0.277501\pi$
$953$	−8.47152	−	11.3792i	−0.274420	−	0.368609i	−0.917872	+	0.396877i	$0.870094\pi$
$954$	45.8356	+	23.8133i	1.48398	+	0.770984i
$955$	25.2738	+	58.5913i	0.817842	+	1.89597i
$956$	3.30530	+	33.9814i	0.106901	+	1.09904i
$957$	−8.67518	−	8.29794i	−0.280429	−	0.268234i
$958$	3.27923	−	1.97903i	0.105947	−	0.0639395i
$959$	−7.10490	+	1.39536i	−0.229429	+	0.0450584i
$960$	19.3818	−	52.1344i	0.625545	−	1.68263i
$961$	5.76612	−	8.40721i	0.186004	−	0.271200i
$962$	−13.9874	+	9.19969i	−0.450973	+	0.296610i
$963$	−21.9546	+	44.3391i	−0.707478	+	1.42881i
$964$	30.0232	−	15.0782i	0.966982	−	0.485637i
$965$	0.880824	+	0.682690i	0.0283547	+	0.0219766i
$966$	6.67706	−	11.9070i	0.214831	−	0.383101i
$967$	−26.7486	−	19.1188i	−0.860178	−	0.614818i	0.0635026	−	0.997982i	$-0.479773\pi$
$967$	−26.7486	−	19.1188i	−0.860178	−	0.614818i	−0.923681	+	0.383163i	$0.874835\pi$
$968$	−8.81339	−	7.99772i	−0.283273	−	0.257057i
$969$	20.8830	+	52.1353i	0.670859	+	1.67483i
$970$	21.0200	−	54.4433i	0.674913	−	1.74807i
$971$	−15.6152			−0.501116			−0.250558	−	0.968102i	$-0.580614\pi$
$971$	−15.6152			−0.501116			−0.250558	+	0.968102i	$0.580614\pi$
$972$	−35.5845	+	26.7386i	−1.14137	+	0.857643i
$973$	−37.9635			−1.21705
$974$	8.13085	−	21.0594i	0.260529	−	0.674788i
$975$	1.64382	+	0.236035i	0.0526442	+	0.00755916i
$976$	−8.80275	−	7.98807i	−0.281769	−	0.255692i
$977$	−15.5874	−	11.1412i	−0.498685	−	0.356439i	0.304165	−	0.952619i	$-0.401622\pi$
$977$	−15.5874	−	11.1412i	−0.498685	−	0.356439i	−0.802850	+	0.596181i	$0.796684\pi$
$978$	43.1271	−	0.540223i	1.37905	−	0.0172744i
$979$	10.1760	+	7.88700i	0.325227	+	0.252070i
$980$	0.714734	−	0.358953i	0.0228313	−	0.0114663i
$981$	−35.9399	−	26.4415i	−1.14747	−	0.844212i
$982$	26.9633	−	17.7341i	0.860434	−	0.565916i
$983$	−17.3087	+	25.2367i	−0.552062	+	0.804926i	−0.995831	−	0.0912148i	$-0.970925\pi$
$983$	−17.3087	+	25.2367i	−0.552062	+	0.804926i	0.443769	+	0.896141i	$0.353641\pi$
$984$	20.5448	+	24.8286i	0.654945	+	0.791508i
$985$	24.2122	−	4.75511i	0.771463	−	0.151510i
$986$	−41.5386	+	25.0687i	−1.32286	+	0.798349i
$987$	−4.74180	+	19.4122i	−0.150933	+	0.617898i
$988$	−0.932836	−	9.59039i	−0.0296775	−	0.305111i
$989$	3.29573	+	7.64037i	0.104798	+	0.242950i
$990$	−35.1687	+	7.82663i	−1.11774	+	0.248747i
$991$	−2.36847	−	3.18141i	−0.0752370	−	0.101061i	0.762911	−	0.646503i	$-0.223769\pi$
$991$	−2.36847	−	3.18141i	−0.0752370	−	0.101061i	−0.838149	+	0.545442i	$0.816362\pi$
$992$	6.95434	+	32.1048i	0.220801	+	1.01933i
$993$	−32.0274	−	33.1063i	−1.01636	−	1.05060i
$994$	22.7983	+	33.2408i	0.723119	+	1.05433i
$995$	−10.6973	−	4.37031i	−0.339126	−	0.138548i
$996$	46.2993	+	40.9687i	1.46705	+	1.29814i
$997$	17.7840	+	51.9757i	0.563225	+	1.64609i	0.748299	+	0.663361i	$0.230871\pi$
$997$	17.7840	+	51.9757i	0.563225	+	1.64609i	−0.185075	+	0.982724i	$0.559253\pi$
$998$	7.16750	−	40.6489i	0.226883	−	1.28672i
$999$	17.7955	+	52.2152i	0.563025	+	1.65202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.i.a.106.23	yes	1404
3.2	odd	2		729.2.i.a.559.4		1404
243.94	even	81	inner	243.2.i.a.94.23	✓	1404
243.149	odd	162		729.2.i.a.253.4		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.94.23	✓	1404	243.94	even	81	inner
243.2.i.a.106.23	yes	1404	1.1	even	1	trivial
729.2.i.a.253.4		1404	243.149	odd	162
729.2.i.a.559.4		1404	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.i (of order \(81\), degree \(54\), minimal)

\(f(q)\)	\(=\)	\(q+(0.793648 - 2.05560i) q^{2} +(-1.07043 + 1.36168i) q^{3} +(-2.11453 - 1.91883i) q^{4} +(2.04843 + 1.46413i) q^{5} +(1.94953 + 3.28107i) q^{6} +(2.10773 + 1.63362i) q^{7} +(-1.68432 + 0.845896i) q^{8} +(-0.708355 - 2.91517i) q^{9} +(4.63539 - 3.04874i) q^{10} +(1.22434 - 1.78513i) q^{11} +(4.87629 - 0.825337i) q^{12} +(-0.702251 + 0.137918i) q^{13} +(5.03086 - 3.03614i) q^{14} +(-4.18637 + 1.22206i) q^{15} +(-0.150793 - 1.55029i) q^{16} +(2.72369 + 6.31422i) q^{17} +(-6.55461 - 0.857526i) q^{18} +(-2.81577 - 3.78224i) q^{19} +(-1.52204 - 7.02652i) q^{20} +(-4.48065 + 1.12139i) q^{21} +(-2.69781 - 3.93351i) q^{22} +(-1.24169 - 0.507285i) q^{23} +(0.651104 - 3.19898i) q^{24} +(0.433712 + 1.26757i) q^{25} +(-0.273837 + 1.55301i) q^{26} +(4.72778 + 2.15594i) q^{27} +(-1.32223 - 7.49871i) q^{28} +(-2.80345 + 1.54688i) q^{29} +(-0.810445 + 9.57540i) q^{30} +(-2.12576 - 4.03566i) q^{31} +(-6.93797 - 1.93132i) q^{32} +(1.12021 + 3.57801i) q^{33} +(15.1412 - 0.587546i) q^{34} +(1.92571 + 6.43233i) q^{35} +(-4.09589 + 7.52342i) q^{36} +(7.28541 + 7.72208i) q^{37} +(-10.0095 + 2.78634i) q^{38} +(0.563912 - 1.10387i) q^{39} +(-4.68870 - 0.733299i) q^{40} +(-6.19752 + 7.68372i) q^{41} +(-1.25093 + 10.1004i) q^{42} +(-4.42888 - 4.34382i) q^{43} +(-6.01424 + 1.42540i) q^{44} +(2.81717 - 7.00864i) q^{45} +(-2.02824 + 2.14981i) q^{46} +(2.01629 - 3.82783i) q^{47} +(2.27241 + 1.45414i) q^{48} +(0.0277496 + 0.107730i) q^{49} +(2.94984 + 0.114467i) q^{50} +(-11.5135 - 3.05014i) q^{51} +(1.74957 + 1.05587i) q^{52} +(-7.34250 - 2.67245i) q^{53} +(8.18394 - 8.00738i) q^{54} +(5.12161 - 1.86411i) q^{55} +(-4.93196 - 0.968606i) q^{56} +(8.16430 + 0.214439i) q^{57} +(0.954809 + 6.99044i) q^{58} +(-0.522197 + 0.0405884i) q^{59} +(11.1971 + 5.44887i) q^{60} +(5.65147 - 5.12843i) q^{61} +(-9.98281 + 1.16682i) q^{62} +(3.26925 - 7.30159i) q^{63} +(-7.61604 + 10.2301i) q^{64} +(-1.64044 - 0.745671i) q^{65} +(8.24401 + 0.536985i) q^{66} +(-8.47876 - 4.67838i) q^{67} +(6.35661 - 18.5779i) q^{68} +(2.01990 - 1.14777i) q^{69} +(14.7506 + 1.14651i) q^{70} +(0.398855 + 6.84808i) q^{71} +(3.65903 + 4.31088i) q^{72} +(-9.13092 - 6.00550i) q^{73} +(21.6556 - 8.84727i) q^{74} +(-2.19029 - 0.766270i) q^{75} +(-1.30345 + 13.4006i) q^{76} +(5.49679 - 1.76247i) q^{77} +(-1.82158 - 2.03526i) q^{78} +(-14.8396 + 2.32087i) q^{79} +(1.96093 - 3.39643i) q^{80} +(-7.99647 + 4.12996i) q^{81} +(10.8760 + 18.8378i) q^{82} +(7.84793 + 9.72991i) q^{83} +(11.6262 + 6.22640i) q^{84} +(-3.66555 + 16.9220i) q^{85} +(-12.4441 + 5.65655i) q^{86} +(0.894542 - 5.47323i) q^{87} +(-0.552140 + 4.04238i) q^{88} +(-0.345828 + 5.93763i) q^{89} +(-12.1711 - 11.3534i) q^{90} +(-1.70546 - 0.856516i) q^{91} +(1.65219 + 3.45526i) q^{92} +(7.77077 + 1.42528i) q^{93} +(-6.26827 - 7.18264i) q^{94} +(-0.230224 - 11.8703i) q^{95} +(10.0565 - 7.37997i) q^{96} +(8.55768 - 6.11666i) q^{97} +(0.243474 + 0.0284580i) q^{98} +(-6.07121 - 2.30465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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