LMFDB - Embedded newform 729.2.k.a.4.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(4,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(486))

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

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

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

chi := DirichletCharacter("729.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.k (of order $243$, degree $162$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12960$
Relative dimension:	$80$ over $\Q(\zeta_{243})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{243}]$

Embedding invariants

Embedding label			4.8
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.38931 - 0.0308915i) q^{2} +(0.801520 - 1.53544i) q^{3} +(3.70850 + 0.0959110i) q^{4} +(1.80500 + 0.553120i) q^{5} +(-1.96251 + 3.64387i) q^{6} +(1.52892 - 3.81257i) q^{7} +(-4.08235 - 0.158414i) q^{8} +(-1.71513 - 2.46137i) q^{9} +O(q^{10})$	\(q+(-2.38931 - 0.0308915i) q^{2} +(0.801520 - 1.53544i) q^{3} +(3.70850 + 0.0959110i) q^{4} +(1.80500 + 0.553120i) q^{5} +(-1.96251 + 3.64387i) q^{6} +(1.52892 - 3.81257i) q^{7} +(-4.08235 - 0.158414i) q^{8} +(-1.71513 - 2.46137i) q^{9} +(-4.29561 - 1.37733i) q^{10} +(1.31849 + 0.749911i) q^{11} +(3.11970 - 5.61729i) q^{12} +(-0.594124 - 1.32979i) q^{13} +(-3.77084 + 9.06215i) q^{14} +(2.29603 - 2.32813i) q^{15} +(2.33954 + 0.121094i) q^{16} +(-0.780299 - 0.354689i) q^{17} +(4.02194 + 5.93394i) q^{18} +(-4.68346 - 6.82866i) q^{19} +(6.64079 + 2.22436i) q^{20} +(-4.62849 - 5.40341i) q^{21} +(-3.12712 - 1.83250i) q^{22} +(-0.130173 + 0.397135i) q^{23} +(-3.51532 + 6.14122i) q^{24} +(-1.18948 - 0.804556i) q^{25} +(1.37846 + 3.19564i) q^{26} +(-5.15398 + 0.660642i) q^{27} +(6.03566 - 13.9922i) q^{28} +(1.13257 - 0.724102i) q^{29} +(-5.55783 + 5.49168i) q^{30} +(2.42367 + 8.92970i) q^{31} +(2.56765 + 0.166209i) q^{32} +(2.20824 - 1.42340i) q^{33} +(1.85342 + 0.871566i) q^{34} +(4.86851 - 6.03601i) q^{35} +(-6.12449 - 9.29247i) q^{36} +(9.96350 + 1.95677i) q^{37} +(10.9793 + 16.4604i) q^{38} +(-2.51802 - 0.153617i) q^{39} +(-7.28103 - 2.54397i) q^{40} +(3.34293 - 1.26590i) q^{41} +(10.8920 + 13.0534i) q^{42} +(-3.26513 + 1.43354i) q^{43} +(4.81770 + 2.90750i) q^{44} +(-1.73438 - 5.39144i) q^{45} +(0.323292 - 0.944855i) q^{46} +(-2.56437 + 9.44812i) q^{47} +(2.06112 - 3.49515i) q^{48} +(-7.13760 - 6.82172i) q^{49} +(2.81719 + 1.95908i) q^{50} +(-1.17003 + 0.913809i) q^{51} +(-2.07576 - 4.98852i) q^{52} +(1.39322 - 1.47673i) q^{53} +(12.3349 - 1.41926i) q^{54} +(1.96509 + 2.08288i) q^{55} +(-6.84556 + 15.3220i) q^{56} +(-14.2389 + 1.71786i) q^{57} +(-2.72842 + 1.69511i) q^{58} +(-12.2534 + 2.07903i) q^{59} +(8.73809 - 8.41364i) q^{60} +(5.36764 - 9.87834i) q^{61} +(-5.51503 - 21.4107i) q^{62} +(-12.0064 + 2.77582i) q^{63} +(-10.8010 - 0.839522i) q^{64} +(-0.336858 - 2.72890i) q^{65} +(-5.32013 + 3.33271i) q^{66} +(11.0282 - 5.71828i) q^{67} +(-2.85972 - 1.39020i) q^{68} +(0.505439 + 0.518184i) q^{69} +(-11.8188 + 14.2715i) q^{70} +(-7.00633 - 5.43031i) q^{71} +(6.61186 + 10.3199i) q^{72} +(8.22018 - 2.63569i) q^{73} +(-23.7454 - 4.98310i) q^{74} +(-2.18874 + 1.18151i) q^{75} +(-16.7137 - 25.7732i) q^{76} +(4.87496 - 3.88029i) q^{77} +(6.01157 + 0.444824i) q^{78} +(-1.47018 + 7.75049i) q^{79} +(4.15589 + 1.51262i) q^{80} +(-3.11665 + 8.44313i) q^{81} +(-8.02638 + 2.92136i) q^{82} +(0.229573 + 1.40820i) q^{83} +(-16.6465 - 20.4824i) q^{84} +(-1.21225 - 1.07181i) q^{85} +(7.84568 - 3.32431i) q^{86} +(-0.204036 - 2.31937i) q^{87} +(-5.26376 - 3.27027i) q^{88} +(-5.80531 - 2.37173i) q^{89} +(3.97742 + 12.9354i) q^{90} +(-5.97830 + 0.231985i) q^{91} +(-0.520836 + 1.46029i) q^{92} +(15.6536 + 3.43595i) q^{93} +(6.41894 - 22.4952i) q^{94} +(-4.67659 - 14.9162i) q^{95} +(2.31323 - 3.80924i) q^{96} +(-0.943214 + 4.09759i) q^{97} +(16.8432 + 16.5197i) q^{98} +(-0.415585 - 4.53149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) $ 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{243}\right)$

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 $

$2$	−2.38931	−	0.0308915i	−1.68949	−	0.0218436i	−0.837830	−	0.545931i	$-0.816176\pi$
$2$	−2.38931	−	0.0308915i	−1.68949	−	0.0218436i	−0.851664	+	0.524088i	$0.824406\pi$
$3$	0.801520	−	1.53544i	0.462758	−	0.886485i
$3$	0.801520	−	1.53544i	0.462758	−	0.886485i
$4$	3.70850	+	0.0959110i	1.85425	+	0.0479555i
$5$	1.80500	+	0.553120i	0.807221	+	0.247363i	0.669215	−	0.743069i	$-0.266630\pi$
$5$	1.80500	+	0.553120i	0.807221	+	0.247363i	0.138006	+	0.990431i	$0.455931\pi$
$6$	−1.96251	+	3.64387i	−0.801191	+	1.48760i
$7$	1.52892	−	3.81257i	0.577878	−	1.44101i	−0.296151	−	0.955141i	$-0.595703\pi$
$7$	1.52892	−	3.81257i	0.577878	−	1.44101i	0.874029	−	0.485873i	$-0.161498\pi$
$8$	−4.08235	−	0.158414i	−1.44333	−	0.0560077i
$9$	−1.71513	−	2.46137i	−0.571711	−	0.820455i
$10$	−4.29561	−	1.37733i	−1.35839	−	0.435551i
$11$	1.31849	+	0.749911i	0.397541	+	0.226107i	0.680062	−	0.733154i	$-0.261953\pi$
$11$	1.31849	+	0.749911i	0.397541	+	0.226107i	−0.282521	+	0.959261i	$0.591171\pi$
$12$	3.11970	−	5.61729i	0.900579	−	1.62157i
$13$	−0.594124	−	1.32979i	−0.164780	−	0.368819i	0.811812	−	0.583920i	$-0.198482\pi$
$13$	−0.594124	−	1.32979i	−0.164780	−	0.368819i	−0.976592	+	0.215101i	$0.930992\pi$
$14$	−3.77084	+	9.06215i	−1.00780	+	2.42196i
$15$	2.29603	−	2.32813i	0.592831	−	0.601120i
$16$	2.33954	+	0.121094i	0.584885	+	0.0302734i
$17$	−0.780299	−	0.354689i	−0.189250	−	0.0860248i	0.316944	−	0.948444i	$-0.397343\pi$
$17$	−0.780299	−	0.354689i	−0.189250	−	0.0860248i	−0.506194	+	0.862419i	$0.668948\pi$
$18$	4.02194	+	5.93394i	0.947980	+	1.39864i
$19$	−4.68346	−	6.82866i	−1.07446	−	1.56660i	−0.795163	−	0.606396i	$-0.792615\pi$
$19$	−4.68346	−	6.82866i	−1.07446	−	1.56660i	−0.279297	−	0.960205i	$-0.590102\pi$
$20$	6.64079	+	2.22436i	1.48493	+	0.497383i
$21$	−4.62849	−	5.40341i	−1.01002	−	1.17912i
$22$	−3.12712	−	1.83250i	−0.666704	−	0.390690i
$23$	−0.130173	+	0.397135i	−0.0271430	+	0.0828084i	−0.962923	−	0.269775i	$-0.913051\pi$
$23$	−0.130173	+	0.397135i	−0.0271430	+	0.0828084i	0.935780	+	0.352583i	$0.114697\pi$
$24$	−3.51532	+	6.14122i	−0.717562	+	1.25357i
$25$	−1.18948	−	0.804556i	−0.237897	−	0.160911i
$26$	1.37846	+	3.19564i	0.270339	+	0.626716i
$27$	−5.15398	+	0.660642i	−0.991885	+	0.127141i
$28$	6.03566	−	13.9922i	1.14063	−	2.64429i
$29$	1.13257	−	0.724102i	0.210313	−	0.134462i	−0.429293	−	0.903165i	$-0.641237\pi$
$29$	1.13257	−	0.724102i	0.210313	−	0.134462i	0.639606	+	0.768703i	$0.279097\pi$
$30$	−5.55783	+	5.49168i	−1.01472	+	1.00264i
$31$	2.42367	+	8.92970i	0.435303	+	1.60382i	0.754612	+	0.656171i	$0.227825\pi$
$31$	2.42367	+	8.92970i	0.435303	+	1.60382i	−0.319309	+	0.947651i	$0.603451\pi$
$32$	2.56765	+	0.166209i	0.453901	+	0.0293819i
$33$	2.20824	−	1.42340i	0.384405	−	0.247781i
$34$	1.85342	+	0.871566i	0.317858	+	0.149472i
$35$	4.86851	−	6.03601i	0.822928	−	1.02027i
$36$	−6.12449	−	9.29247i	−1.02075	−	1.54874i
$37$	9.96350	+	1.95677i	1.63799	+	0.321691i	0.925140	−	0.379626i	$-0.123947\pi$
$37$	9.96350	+	1.95677i	1.63799	+	0.321691i	0.712850	+	0.701317i	$0.247404\pi$
$38$	10.9793	+	16.4604i	1.78107	+	2.67023i
$39$	−2.51802	−	0.153617i	−0.403205	−	0.0245984i
$40$	−7.28103	−	2.54397i	−1.15123	−	0.402237i
$41$	3.34293	−	1.26590i	0.522078	−	0.197701i	−0.0790253	−	0.996873i	$-0.525181\pi$
$41$	3.34293	−	1.26590i	0.522078	−	0.197701i	0.601103	+	0.799172i	$0.294728\pi$
$42$	10.8920	+	13.0534i	1.68067	+	2.01418i
$43$	−3.26513	+	1.43354i	−0.497927	+	0.218613i	−0.635825	−	0.771833i	$-0.719340\pi$
$43$	−3.26513	+	1.43354i	−0.497927	+	0.218613i	0.137898	+	0.990446i	$0.455966\pi$
$44$	4.81770	+	2.90750i	0.726296	+	0.438322i
$45$	−1.73438	−	5.39144i	−0.258547	−	0.803709i
$46$	0.323292	−	0.944855i	0.0476668	−	0.139311i
$47$	−2.56437	+	9.44812i	−0.374052	+	1.37815i	0.488668	+	0.872470i	$0.337483\pi$
$47$	−2.56437	+	9.44812i	−0.374052	+	1.37815i	−0.862721	+	0.505681i	$0.831241\pi$
$48$	2.06112	−	3.49515i	0.297497	−	0.504482i
$49$	−7.13760	−	6.82172i	−1.01966	−	0.974531i
$50$	2.81719	+	1.95908i	0.398410	+	0.277055i
$51$	−1.17003	+	0.913809i	−0.163837	+	0.127959i
$52$	−2.07576	−	4.98852i	−0.287857	−	0.691783i
$53$	1.39322	−	1.47673i	0.191374	−	0.202844i	−0.624581	−	0.780960i	$-0.714730\pi$
$53$	1.39322	−	1.47673i	0.191374	−	0.202844i	0.815955	+	0.578116i	$0.196212\pi$
$54$	12.3349	−	1.41926i	1.67856	−	0.193137i
$55$	1.96509	+	2.08288i	0.264973	+	0.280855i
$56$	−6.84556	+	15.3220i	−0.914776	+	2.04749i
$57$	−14.2389	+	1.71786i	−1.88598	+	0.227536i
$58$	−2.72842	+	1.69511i	−0.358260	+	0.222580i
$59$	−12.2534	+	2.07903i	−1.59526	+	0.270667i	−0.895951	−	0.444153i	$-0.853505\pi$
$59$	−12.2534	+	2.07903i	−1.59526	+	0.270667i	−0.699309	+	0.714819i	$0.746509\pi$
$60$	8.73809	−	8.41364i	1.12808	−	1.08620i
$61$	5.36764	−	9.87834i	0.687255	−	1.26479i	−0.266392	−	0.963865i	$-0.585831\pi$
$61$	5.36764	−	9.87834i	0.687255	−	1.26479i	0.953647	−	0.300927i	$-0.0972961\pi$
$62$	−5.51503	−	21.4107i	−0.700409	−	2.71916i
$63$	−12.0064	+	2.77582i	−1.51267	+	0.349720i
$64$	−10.8010	−	0.839522i	−1.35013	−	0.104940i
$65$	−0.336858	−	2.72890i	−0.0417821	−	0.338479i
$66$	−5.32013	+	3.33271i	−0.654863	+	0.410228i
$67$	11.0282	−	5.71828i	1.34731	−	0.698600i	0.373856	−	0.927487i	$-0.378035\pi$
$67$	11.0282	−	5.71828i	1.34731	−	0.698600i	0.973453	+	0.228887i	$0.0735087\pi$
$68$	−2.85972	−	1.39020i	−0.346792	−	0.168587i
$69$	0.505439	+	0.518184i	0.0608477	+	0.0623820i
$70$	−11.8188	+	14.2715i	−1.41262	+	1.70577i
$71$	−7.00633	−	5.43031i	−0.831498	−	0.644459i	0.105257	−	0.994445i	$-0.466433\pi$
$71$	−7.00633	−	5.43031i	−0.831498	−	0.644459i	−0.936755	+	0.349986i	$0.886186\pi$
$72$	6.61186	+	10.3199i	0.779215	+	1.21621i
$73$	8.22018	−	2.63569i	0.962099	−	0.308485i	0.217548	−	0.976050i	$-0.430194\pi$
$73$	8.22018	−	2.63569i	0.962099	−	0.308485i	0.744551	+	0.667565i	$0.232663\pi$
$74$	−23.7454	−	4.98310i	−2.76035	−	0.579274i
$75$	−2.18874	+	1.18151i	−0.252734	+	0.136429i
$76$	−16.7137	−	25.7732i	−1.91719	−	2.95639i
$77$	4.87496	−	3.88029i	0.555553	−	0.442200i
$78$	6.01157	+	0.444824i	0.680676	+	0.0503664i
$79$	−1.47018	+	7.75049i	−0.165408	+	0.871998i	0.797735	+	0.603008i	$0.206031\pi$
$79$	−1.47018	+	7.75049i	−0.165408	+	0.871998i	−0.963143	+	0.268990i	$0.913310\pi$
$80$	4.15589	+	1.51262i	0.464643	+	0.169116i
$81$	−3.11665	+	8.44313i	−0.346294	+	0.938126i
$82$	−8.02638	+	2.92136i	−0.886366	+	0.322611i
$83$	0.229573	+	1.40820i	0.0251989	+	0.154570i	0.996539	−	0.0831232i	$-0.0264895\pi$
$83$	0.229573	+	1.40820i	0.0251989	+	0.154570i	−0.971340	+	0.237693i	$0.923609\pi$
$84$	−16.6465	−	20.4824i	−1.81628	−	2.23482i
$85$	−1.21225	−	1.07181i	−0.131487	−	0.116254i
$86$	7.84568	−	3.32431i	0.846021	−	0.358469i
$87$	−0.204036	−	2.31937i	−0.0218750	−	0.248663i
$88$	−5.26376	−	3.27027i	−0.561119	−	0.348612i
$89$	−5.80531	−	2.37173i	−0.615362	−	0.251403i	0.0490181	−	0.998798i	$-0.484391\pi$
$89$	−5.80531	−	2.37173i	−0.615362	−	0.251403i	−0.664380	+	0.747395i	$0.731304\pi$
$90$	3.97742	+	12.9354i	0.419257	+	1.36351i
$91$	−5.97830	+	0.231985i	−0.626696	+	0.0243186i
$92$	−0.520836	+	1.46029i	−0.0543009	+	0.152246i
$93$	15.6536	+	3.43595i	1.62320	+	0.356291i
$94$	6.41894	−	22.4952i	0.662063	−	2.32021i
$95$	−4.67659	−	14.9162i	−0.479808	−	1.53037i
$96$	2.31323	−	3.80924i	0.236093	−	0.388779i
$97$	−0.943214	+	4.09759i	−0.0957688	+	0.416047i	−0.999938	−	0.0111272i	$-0.996458\pi$
$97$	−0.943214	+	4.09759i	−0.0957688	+	0.416047i	0.904169	+	0.427174i	$0.140491\pi$
$98$	16.8432	+	16.5197i	1.70142	+	1.66874i
$99$	−0.415585	−	4.53149i	−0.0417679	−	0.455432i
$100$	−4.33403	−	3.09778i	−0.433403	−	0.309778i
$101$	−1.15440	+	7.70723i	−0.114867	+	0.766898i	0.854172	+	0.519991i	$0.174065\pi$
$101$	−1.15440	+	7.70723i	−0.114867	+	0.766898i	−0.969039	+	0.246907i	$0.920586\pi$
$102$	2.82378	−	2.14722i	0.279596	−	0.212607i
$103$	−1.78032	−	4.99154i	−0.175420	−	0.491831i	0.821504	−	0.570202i	$-0.193135\pi$
$103$	−1.78032	−	4.99154i	−0.175420	−	0.491831i	−0.996924	+	0.0783711i	$0.975028\pi$
$104$	2.21476	+	5.52281i	0.217176	+	0.541556i
$105$	−5.36570	−	12.3133i	−0.523638	−	1.20165i
$106$	−3.37445	+	3.48532i	−0.327755	+	0.338524i
$107$	0.0992235	+	1.70360i	0.00959230	+	0.164693i	0.999702	+	0.0244000i	$0.00776754\pi$
$107$	0.0992235	+	1.70360i	0.00959230	+	0.164693i	−0.990110	+	0.140293i	$0.955195\pi$
$108$	−19.1769	+	1.95567i	−1.84530	+	0.188184i
$109$	0.215547	−	3.70081i	0.0206457	−	0.354473i	−0.972126	−	0.234458i	$-0.924669\pi$
$109$	0.215547	−	3.70081i	0.0206457	−	0.354473i	0.992772	−	0.120015i	$-0.0382944\pi$
$110$	−4.63086	−	5.03733i	−0.441535	−	0.480291i
$111$	10.9904	−	13.7299i	1.04317	−	1.30319i
$112$	4.03865	−	8.73450i	0.381616	−	0.825333i
$113$	13.3275	−	9.78870i	1.25375	−	0.920844i	0.254812	−	0.966991i	$-0.417986\pi$
$113$	13.3275	−	9.78870i	1.25375	−	0.920844i	0.998935	+	0.0461469i	$0.0146942\pi$
$114$	34.0740	−	3.66463i	3.19133	−	0.343224i
$115$	−0.454626	+	0.644827i	−0.0423941	+	0.0601305i
$116$	4.26958	−	2.57670i	0.396421	−	0.239241i
$117$	−2.25411	+	3.74313i	−0.208393	+	0.346052i
$118$	29.3414	−	4.58891i	2.70110	−	0.422444i
$119$	−2.54529	+	2.43265i	−0.233326	+	0.223000i
$120$	−9.74199	+	9.14051i	−0.889318	+	0.834411i
$121$	−4.44664	−	7.47687i	−0.404240	−	0.679716i
$122$	−13.1301	+	23.4366i	−1.18874	+	2.12185i
$123$	0.735707	−	6.14750i	0.0663365	−	0.554302i
$124$	8.13170	+	33.3482i	0.730248	+	2.99476i
$125$	−7.62807	−	9.45733i	−0.682275	−	0.845889i
$126$	28.7728	−	6.26138i	2.56328	−	0.557808i
$127$	0.0488228	+	2.51729i	0.00433232	+	0.223373i	0.995720	+	0.0924167i	$0.0294592\pi$
$127$	0.0488228	+	2.51729i	0.00433232	+	0.223373i	−0.991388	+	0.130957i	$0.958195\pi$
$128$	20.6560	+	1.87446i	1.82575	+	0.165680i
$129$	−0.415951	+	6.16241i	−0.0366224	+	0.542570i
$130$	0.720556	+	6.53059i	0.0631970	+	0.572770i
$131$	4.59060	−	0.416580i	0.401082	−	0.0363968i	0.112017	−	0.993706i	$-0.464269\pi$
$131$	4.59060	−	0.416580i	0.401082	−	0.0363968i	0.289065	+	0.957309i	$0.406656\pi$
$132$	8.32577	−	5.06686i	0.724665	−	0.441014i
$133$	−33.1953	+	7.41553i	−2.87840	+	0.643008i
$134$	−26.5264	+	13.3220i	−2.29153	+	1.15085i
$135$	−9.66836	−	1.65831i	−0.832120	−	0.142725i
$136$	3.12927	+	1.57158i	0.268332	+	0.134762i
$137$	−8.42703	−	2.11267i	−0.719970	−	0.180498i	−0.134176	−	0.990958i	$-0.542839\pi$
$137$	−8.42703	−	2.11267i	−0.719970	−	0.180498i	−0.585794	+	0.810460i	$0.699217\pi$
$138$	−1.19164	−	1.25371i	−0.101439	−	0.106723i
$139$	3.60001	+	0.515444i	0.305349	+	0.0437194i	0.292712	−	0.956201i	$-0.405442\pi$
$139$	3.60001	+	0.515444i	0.305349	+	0.0437194i	0.0126371	+	0.999920i	$0.495977\pi$
$140$	18.6338	−	21.9176i	1.57484	−	1.85237i
$141$	12.4516	+	11.5103i	1.04861	+	0.969341i
$142$	16.5725	+	13.1911i	1.39073	+	1.10697i
$143$	0.213879	−	2.19887i	0.0178854	−	0.183878i
$144$	−3.71456	−	5.96615i	−0.309547	−	0.497179i
$145$	2.44480	−	0.680558i	0.203030	−	0.0565173i
$146$	−19.7219	+	6.04355i	−1.63220	+	0.500167i
$147$	−16.1952	+	5.49158i	−1.33576	+	0.452938i
$148$	36.7619	+	8.21228i	3.02181	+	0.675045i
$149$	10.7905	−	2.70520i	0.883994	−	0.221619i	0.225535	−	0.974235i	$-0.427587\pi$
$149$	10.7905	−	2.70520i	0.883994	−	0.221619i	0.658459	+	0.752616i	$0.271208\pi$
$150$	5.26607	−	2.75537i	0.429973	−	0.224975i
$151$	8.49639	+	9.99369i	0.691426	+	0.813275i	0.989993	−	0.141114i	$-0.0450683\pi$
$151$	8.49639	+	9.99369i	0.691426	+	0.813275i	−0.298567	+	0.954389i	$0.596509\pi$
$152$	18.0378	+	28.6189i	1.46306	+	2.32130i
$153$	0.465295	+	2.52894i	0.0376169	+	0.204453i
$154$	−11.7676	+	9.12060i	−0.948263	+	0.734959i
$155$	−0.564478	+	17.4587i	−0.0453399	+	1.40232i
$156$	−9.32332	−	0.811194i	−0.746463	−	0.0649475i
$157$	−2.39041	+	19.3648i	−0.190776	+	1.54548i	0.527398	+	0.849619i	$0.323168\pi$
$157$	−2.39041	+	19.3648i	−0.190776	+	1.54548i	−0.718173	+	0.695864i	$0.755021\pi$
$158$	3.75213	−	18.4729i	0.298504	−	1.46962i
$159$	−1.15073	−	3.32283i	−0.0912587	−	0.263518i
$160$	4.54268	+	1.72023i	0.359130	+	0.135996i
$161$	1.31508	+	1.10348i	0.103643	+	0.0869665i
$162$	7.70744	−	20.0770i	0.605554	−	1.57739i
$163$	−3.34925	+	2.81035i	−0.262333	+	0.220124i	−0.764462	−	0.644669i	$-0.776995\pi$
$163$	−3.34925	+	2.81035i	−0.262333	+	0.220124i	0.502128	+	0.864793i	$0.332551\pi$
$164$	12.5187	−	4.37398i	0.977542	−	0.341550i
$165$	4.77318	−	1.34781i	0.371592	−	0.104927i
$166$	−0.505018	−	3.37170i	−0.0391970	−	0.261695i
$167$	−2.36141	+	4.62713i	−0.182731	+	0.358058i	−0.963901	−	0.266261i	$-0.914212\pi$
$167$	−2.36141	+	4.62713i	−0.182731	+	0.358058i	0.781170	+	0.624319i	$0.214623\pi$
$168$	18.0392	+	22.7918i	1.39175	+	1.75843i
$169$	7.25832	−	8.10322i	0.558332	−	0.623324i
$170$	2.86334	+	2.59834i	0.219608	+	0.199283i
$171$	−8.77507	+	23.2398i	−0.671046	+	1.77719i
$172$	−12.2462	+	5.00313i	−0.933765	+	0.381485i
$173$	10.4474	+	1.77260i	0.794302	+	0.134769i	0.550257	−	0.834995i	$-0.314530\pi$
$173$	10.4474	+	1.77260i	0.794302	+	0.134769i	0.244045	+	0.969764i	$0.421526\pi$
$174$	0.415856	+	5.54799i	0.0315259	+	0.420592i
$175$	−4.88605	+	3.30488i	−0.369351	+	0.249826i
$176$	2.99386	+	1.91411i	0.225671	+	0.144281i
$177$	−6.62915	+	20.4807i	−0.498277	+	1.53943i
$178$	13.7974	+	5.84613i	1.03416	+	0.438186i
$179$	−11.3149	−	23.6631i	−0.845716	−	1.76867i	−0.601357	−	0.798981i	$-0.705373\pi$
$179$	−11.3149	−	23.6631i	−0.845716	−	1.76867i	−0.244360	−	0.969685i	$-0.578578\pi$
$180$	−5.91485	−	20.1605i	−0.440867	−	1.50267i
$181$	14.5975	+	4.06349i	1.08502	+	0.302037i	0.764119	−	0.645075i	$-0.223174\pi$
$181$	14.5975	+	4.06349i	1.08502	+	0.302037i	0.320904	+	0.947112i	$0.396013\pi$
$182$	14.2911	−	0.369605i	1.05933	−	0.0273969i
$183$	−10.8653	−	16.1594i	−0.803186	−	1.19453i
$184$	0.594324	−	1.60062i	0.0438142	−	0.117999i
$185$	16.9018	+	9.04298i	1.24265	+	0.664853i
$186$	−37.2951	−	8.69309i	−2.73461	−	0.637408i
$187$	−0.762834	−	1.05281i	−0.0557839	−	0.0769891i
$188$	−10.4162	+	34.7924i	−0.759676	+	2.53749i
$189$	−5.36129	+	20.6600i	−0.389977	+	1.50279i
$190$	10.7130	+	35.7839i	0.777203	+	2.59604i
$191$	−1.07596	+	1.40692i	−0.0778535	+	0.101801i	−0.831630	−	0.555330i	$-0.812592\pi$
$191$	−1.07596	+	1.40692i	−0.0778535	+	0.101801i	0.753777	+	0.657131i	$0.228230\pi$
$192$	−9.94626	+	15.9114i	−0.717810	+	1.14831i
$193$	3.30285	−	1.55316i	0.237744	−	0.111799i	−0.302986	−	0.952995i	$-0.597983\pi$
$193$	3.30285	−	1.55316i	0.237744	−	0.111799i	0.540730	+	0.841196i	$0.318148\pi$
$194$	2.38021	−	9.76126i	0.170889	−	0.700817i
$195$	−4.46005	−	1.67005i	−0.319391	−	0.119594i
$196$	−25.8155	−	25.9829i	−1.84396	−	1.85592i
$197$	8.00434	−	1.57200i	0.570285	−	0.112000i	0.100746	−	0.994912i	$-0.467877\pi$
$197$	8.00434	−	1.57200i	0.570285	−	0.112000i	0.469539	+	0.882912i	$0.344420\pi$
$198$	0.852976	+	10.8400i	0.0606184	+	0.770362i
$199$	21.3891	−	11.8020i	1.51623	−	0.836622i	0.516426	−	0.856332i	$-0.327262\pi$
$199$	21.3891	−	11.8020i	1.51623	−	0.836622i	0.999806	+	0.0197101i	$0.00627432\pi$
$200$	4.72844	+	3.47291i	0.334351	+	0.245572i
$201$	0.0592570	−	21.5164i	0.00417967	−	1.51765i
$202$	2.99630	−	18.3793i	0.210819	−	1.29316i
$203$	−1.02908	−	5.42509i	−0.0722271	−	0.380767i
$204$	−4.42669	+	3.27664i	−0.309930	+	0.229411i
$205$	6.73419	−	0.435917i	0.470336	−	0.0304458i
$206$	4.09952	+	11.9813i	0.285627	+	0.834777i
$207$	1.20076	−	0.360735i	0.0834585	−	0.0250728i
$208$	−1.22895	−	3.18305i	−0.0852121	−	0.220705i
$209$	−1.05423	−	12.5157i	−0.0729228	−	0.865730i
$210$	12.4399	+	29.5859i	0.858436	+	2.04162i
$211$	3.74920	−	5.62091i	0.258106	−	0.386959i	−0.680054	−	0.733162i	$-0.738044\pi$
$211$	3.74920	−	5.62091i	0.258106	−	0.386959i	0.938160	+	0.346203i	$0.112529\pi$
$212$	5.30839	−	5.34281i	0.364582	−	0.366946i
$213$	−13.9536	+	6.40527i	−0.956086	+	0.438882i
$214$	−0.184448	−	4.07349i	−0.0126086	−	0.278458i
$215$	−6.68648	+	0.781538i	−0.456014	+	0.0533004i
$216$	21.1450	−	1.88051i	1.43874	−	0.127953i
$217$	37.7507	+	4.41242i	2.56268	+	0.299535i
$218$	−0.629332	+	8.83570i	−0.0426238	+	0.598429i
$219$	2.54169	−	14.7341i	0.171752	−	0.995640i
$220$	7.08776	+	7.91281i	0.477857	+	0.533481i
$221$	−0.00806978	+	1.24837i	−0.000542832	+	0.0839742i
$222$	−26.6837	+	32.4655i	−1.79089	+	2.17894i
$223$	−4.83198	+	4.27219i	−0.323573	+	0.286087i	−0.808535	−	0.588448i	$-0.799739\pi$
$223$	−4.83198	+	4.27219i	−0.323573	+	0.286087i	0.484961	+	0.874536i	$0.338834\pi$
$224$	4.55942	−	9.53521i	0.304639	−	0.637098i
$225$	0.0598137	+	4.30768i	0.00398758	+	0.287178i
$226$	−32.1459	+	22.9765i	−2.13831	+	1.52837i
$227$	8.23892	+	16.1440i	0.546836	+	1.07151i	0.984990	+	0.172614i	$0.0552212\pi$
$227$	8.23892	+	16.1440i	0.546836	+	1.07151i	−0.438153	+	0.898900i	$0.644367\pi$
$228$	−52.9695	+	5.00500i	−3.50799	+	0.331465i
$229$	0.764490	+	0.999644i	0.0505189	+	0.0660583i	0.818909	−	0.573924i	$-0.194580\pi$
$229$	0.764490	+	0.999644i	0.0505189	+	0.0660583i	−0.768390	+	0.639982i	$0.778942\pi$
$230$	1.10616	−	1.52665i	0.0729381	−	0.100664i
$231$	−2.05056	−	10.5953i	−0.134917	−	0.697121i
$232$	−4.73826	+	2.77663i	−0.311082	+	0.182294i
$233$	4.33368	+	20.0065i	0.283909	+	1.31067i	0.867019	+	0.498275i	$0.166033\pi$
$233$	4.33368	+	20.0065i	0.283909	+	1.31067i	−0.583111	+	0.812393i	$0.698165\pi$
$234$	5.50139	−	8.87385i	0.359637	−	0.580101i
$235$	−9.85465	+	15.6355i	−0.642846	+	1.01994i
$236$	−45.6412	+	6.53484i	−2.97099	+	0.425382i
$237$	10.7220	+	8.46954i	0.696469	+	0.550156i
$238$	6.15663	−	5.73371i	0.399075	−	0.371661i
$239$	1.64468	+	3.02678i	0.106385	+	0.195786i	0.926385	−	0.376577i	$-0.122899\pi$
$239$	1.64468	+	3.02678i	0.106385	+	0.195786i	−0.820000	+	0.572364i	$0.806027\pi$
$240$	5.65356	−	5.16871i	0.364936	−	0.333639i
$241$	−1.50798	+	2.53561i	−0.0971373	+	0.163333i	−0.904169	−	0.427175i	$-0.859509\pi$
$241$	−1.50798	+	2.53561i	−0.0971373	+	0.163333i	0.807032	+	0.590508i	$0.201073\pi$
$242$	10.3934	+	18.0019i	0.668113	+	1.15721i
$243$	10.4658	+	11.5528i	0.671384	+	0.741109i
$244$	20.8533	−	36.1190i	1.33500	−	2.31228i
$245$	−9.11014	−	16.2612i	−0.582025	−	1.03889i
$246$	−1.94774	+	14.6655i	−0.124183	+	0.935040i
$247$	−6.29815	+	10.2851i	−0.400742	+	0.654426i
$248$	−8.47967	−	36.8381i	−0.538460	−	2.33922i
$249$	2.34620	+	0.776202i	0.148685	+	0.0491898i
$250$	17.9336	+	22.8321i	1.13422	+	1.44403i
$251$	−0.507427	−	0.963327i	−0.0320285	−	0.0608047i	0.868225	−	0.496171i	$-0.165261\pi$
$251$	−0.507427	−	0.963327i	−0.0320285	−	0.0608047i	−0.900254	+	0.435366i	$0.856619\pi$
$252$	−44.7920	+	9.14256i	−2.82163	+	0.575927i
$253$	−0.469448	+	0.426002i	−0.0295140	+	0.0267825i
$254$	−0.0388896	−	6.01608i	−0.00244015	−	0.377483i
$255$	−2.61735	+	1.00226i	−0.163905	+	0.0627639i
$256$	−27.7442	−	2.87977i	−1.73401	−	0.179986i
$257$	15.9476	−	2.07333i	0.994784	−	0.129331i	0.385859	−	0.922558i	$-0.373905\pi$
$257$	15.9476	−	2.07333i	0.994784	−	0.129331i	0.608926	+	0.793227i	$0.291601\pi$
$258$	1.18420	−	14.7110i	0.0737251	−	0.915869i
$259$	22.6937	−	34.9948i	1.41012	−	2.17447i
$260$	−0.987504	−	10.1524i	−0.0612424	−	0.629627i
$261$	−3.72479	−	1.54574i	−0.230559	−	0.0956788i
$262$	−10.9812	+	0.853527i	−0.678421	+	0.0527311i
$263$	−3.94223	−	19.4088i	−0.243088	−	1.19680i	−0.897623	−	0.440764i	$-0.854708\pi$
$263$	−3.94223	−	19.4088i	−0.243088	−	1.19680i	0.654535	−	0.756032i	$-0.272865\pi$
$264$	−9.24030	+	5.46098i	−0.568701	+	0.336100i
$265$	3.33157	−	1.89488i	0.204657	−	0.116401i
$266$	79.5429	−	16.6925i	4.87709	−	1.02348i
$267$	−8.29472	+	7.01270i	−0.507628	+	0.429170i
$268$	41.4465	−	20.1485i	2.53175	−	1.23077i
$269$	−13.3323	+	17.9084i	−0.812886	+	1.09190i	0.181216	+	0.983443i	$0.441997\pi$
$269$	−13.3323	+	17.9084i	−0.812886	+	1.09190i	−0.994102	+	0.108452i	$0.965411\pi$
$270$	23.0494	+	4.26089i	1.40274	+	0.259309i
$271$	3.93229	+	5.28198i	0.238870	+	0.320857i	0.905351	−	0.424664i	$-0.139608\pi$
$271$	3.93229	+	5.28198i	0.238870	+	0.320857i	−0.666481	+	0.745522i	$0.732200\pi$
$272$	−1.78259	−	0.924299i	−0.108085	−	0.0560438i
$273$	−4.43552	+	9.36524i	−0.268450	+	0.566810i
$274$	20.0695	+	5.30814i	1.21244	+	0.320676i
$275$	−0.964982	−	1.95281i	−0.0581906	−	0.117759i
$276$	1.82472	+	1.97016i	0.109835	+	0.118590i
$277$	−6.30152	+	4.38209i	−0.378622	+	0.263294i	−0.744851	−	0.667230i	$-0.767480\pi$
$277$	−6.30152	+	4.38209i	−0.378622	+	0.263294i	0.366230	+	0.930524i	$0.380648\pi$
$278$	−8.58560	−	1.34276i	−0.514930	−	0.0805336i
$279$	17.8224	−	21.2811i	1.06700	−	1.27407i
$280$	−20.8312	+	23.8699i	−1.24490	+	1.42650i
$281$	13.3501	−	27.0163i	0.796402	−	1.61166i	0.00529052	−	0.999986i	$-0.498316\pi$
$281$	13.3501	−	27.0163i	0.796402	−	1.61166i	0.791111	−	0.611672i	$-0.209503\pi$
$282$	−29.3951	−	27.8863i	−1.75045	−	1.66060i
$283$	−11.1010	+	9.56208i	−0.659884	+	0.568407i	−0.917449	−	0.397854i	$-0.869755\pi$
$283$	−11.1010	+	9.56208i	−0.659884	+	0.568407i	0.257565	+	0.966261i	$0.417080\pi$
$284$	−25.4621	−	20.8103i	−1.51090	−	1.23486i
$285$	−26.6513	−	4.77507i	−1.57869	−	0.282850i
$286$	−0.578948	+	5.24715i	−0.0342339	+	0.310271i
$287$	0.284730	−	14.6806i	0.0168071	−	0.866568i
$288$	−3.99476	−	6.60500i	−0.235393	−	0.389203i
$289$	−10.6948	−	12.2549i	−0.629106	−	0.720875i
$290$	−5.86241	+	1.55054i	−0.344253	+	0.0910507i
$291$	5.53559	+	4.73254i	0.324502	+	0.277427i
$292$	30.7373	−	8.98606i	1.79876	−	0.525869i
$293$	2.37592	−	28.2066i	0.138803	−	1.64785i	−0.491051	−	0.871131i	$-0.663387\pi$
$293$	2.37592	−	28.2066i	0.138803	−	1.64785i	0.629853	−	0.776714i	$-0.283115\pi$
$294$	38.8650	−	12.6208i	2.26665	−	0.736059i
$295$	−23.2674	−	3.02497i	−1.35468	−	0.176120i
$296$	−40.3645	−	9.56657i	−2.34614	−	0.556046i
$297$	−7.29092	−	2.99398i	−0.423062	−	0.173728i
$298$	−25.8654	+	6.13022i	−1.49834	+	0.355114i
$299$	0.605447	−	0.0628437i	0.0350139	−	0.00363435i
$300$	−8.23026	+	4.17170i	−0.475174	+	0.240853i
$301$	0.473352	+	14.6403i	0.0272836	+	0.843852i
$302$	−19.9918	−	24.1404i	−1.15040	−	1.38913i
$303$	10.9087	+	7.95001i	0.626688	+	0.456716i
$304$	−10.1302	−	16.5430i	−0.581009	−	0.948808i
$305$	15.1525	−	14.8615i	0.867629	−	0.850965i
$306$	−1.03361	−	6.05678i	−0.0590875	−	0.346243i
$307$	10.9421	−	15.9539i	0.624497	−	0.910539i	−0.375370	−	0.926875i	$-0.622484\pi$
$307$	10.9421	−	15.9539i	0.624497	−	0.910539i	0.999867	+	0.0163364i	$0.00520027\pi$
$308$	18.4509	−	13.9225i	1.05134	−	0.793307i
$309$	−9.09115	−	1.26725i	−0.517178	−	0.0720916i
$310$	1.88804	−	41.6967i	0.107233	−	2.36821i
$311$	1.88337	+	26.4421i	0.106796	+	1.49940i	0.711353	+	0.702835i	$0.248083\pi$
$311$	1.88337	+	26.4421i	0.106796	+	1.49940i	−0.604557	+	0.796562i	$0.706650\pi$
$312$	10.2551	+	1.02601i	0.580580	+	0.0580863i
$313$	8.25875	+	22.2423i	0.466812	+	1.25721i	0.928885	+	0.370368i	$0.120768\pi$
$313$	8.25875	+	22.2423i	0.466812	+	1.25721i	−0.462073	+	0.886842i	$0.652894\pi$
$314$	6.30963	−	46.1947i	0.356073	−	2.60692i
$315$	−23.2070	−	1.63064i	−1.30756	−	0.0918762i
$316$	−6.19551	+	28.6017i	−0.348525	+	1.60897i
$317$	−3.43804	−	10.4888i	−0.193100	−	0.589112i	0.806899	−	0.590689i	$-0.201144\pi$
$317$	−3.43804	−	10.4888i	−0.193100	−	0.589112i	−0.999999	+	0.00157731i	$0.999498\pi$
$318$	2.64679	+	7.97480i	0.148425	+	0.447205i
$319$	2.03630	−	0.105398i	0.114011	−	0.00590116i
$320$	−19.0315	−	7.48960i	−1.06389	−	0.418681i
$321$	2.69530	+	1.21312i	0.150437	+	0.0677097i
$322$	−3.10804	−	2.67718i	−0.173204	−	0.149193i
$323$	1.23245	+	6.98957i	0.0685753	+	0.388910i
$324$	−12.3679	+	31.0124i	−0.687103	+	1.72291i
$325$	−0.363194	+	2.05977i	−0.0201464	+	0.114256i
$326$	8.08920	−	6.61133i	0.448019	−	0.366168i
$327$	−5.50959	−	3.29723i	−0.304681	−	0.182337i
$328$	−13.8475	+	4.63830i	−0.764603	+	0.256107i
$329$	32.1009	+	24.2223i	1.76978	+	1.33542i
$330$	−11.4462	+	3.07287i	−0.630094	+	0.169156i
$331$	−18.8294	+	10.0743i	−1.03496	+	0.553734i	−0.899442	−	0.437041i	$-0.856026\pi$
$331$	−18.8294	+	10.0743i	−1.03496	+	0.553734i	−0.135516	+	0.990775i	$0.543269\pi$
$332$	0.716309	+	5.24431i	0.0393125	+	0.287819i
$333$	−12.2724	−	27.8799i	−0.672523	−	1.52781i
$334$	5.78506	−	10.9827i	0.316545	−	0.600945i
$335$	23.0688	−	4.22159i	1.26038	−	0.230650i
$336$	−10.1742	−	13.2020i	−0.555049	−	0.720226i
$337$	−7.67546	−	7.92764i	−0.418109	−	0.431846i	0.476172	−	0.879352i	$-0.342024\pi$
$337$	−7.67546	−	7.92764i	−0.418109	−	0.431846i	−0.894281	+	0.447506i	$0.852312\pi$
$338$	−17.5927	+	19.1368i	−0.956915	+	1.04091i
$339$	−4.34767	−	28.3094i	−0.236133	−	1.53755i
$340$	−4.39284	−	4.09108i	−0.238235	−	0.221870i
$341$	−3.50089	+	13.5913i	−0.189584	+	0.736010i
$342$	21.6842	−	55.2558i	1.17255	−	2.98789i
$343$	−10.7445	+	4.88399i	−0.580151	+	0.263711i
$344$	13.5565	−	5.33499i	0.730917	−	0.287643i
$345$	0.625700	+	1.21489i	0.0336865	+	0.0654076i
$346$	−24.9073	−	4.55803i	−1.33902	−	0.245041i
$347$	−1.92085	+	2.44552i	−0.103117	+	0.131282i	−0.835230	−	0.549900i	$-0.814666\pi$
$347$	−1.92085	+	2.44552i	−0.103117	+	0.131282i	0.732113	+	0.681183i	$0.238534\pi$
$348$	−0.534214	−	8.62095i	−0.0286369	−	0.462131i
$349$	1.68412	+	5.90201i	0.0901488	+	0.315927i	0.993629	−	0.112703i	$-0.0359510\pi$
$349$	1.68412	+	5.90201i	0.0901488	+	0.315927i	−0.903480	+	0.428630i	$0.858996\pi$
$350$	11.7764	−	7.74544i	0.629473	−	0.414011i
$351$	3.94062	+	6.46124i	0.210335	+	0.344875i
$352$	3.26079	+	2.14465i	0.173801	+	0.114310i
$353$	−5.12177	+	16.3362i	−0.272604	+	0.869487i	0.713109	+	0.701053i	$0.247287\pi$
$353$	−5.12177	+	16.3362i	−0.272604	+	0.869487i	−0.985713	+	0.168434i	$0.946129\pi$
$354$	16.4717	−	48.7300i	0.875463	−	2.58997i
$355$	−9.64281	−	13.6771i	−0.511787	−	0.725903i
$356$	−21.3015	−	9.35235i	−1.12898	−	0.495674i
$357$	1.69508	+	5.85795i	0.0897129	+	0.310036i
$358$	26.3038	+	56.8880i	1.39020	+	3.00662i
$359$	10.9698	+	6.05286i	0.578962	+	0.319458i	0.745424	−	0.666590i	$-0.232247\pi$
$359$	10.9698	+	6.05286i	0.578962	+	0.319458i	−0.166463	+	0.986048i	$0.553235\pi$
$360$	6.22628	+	22.2845i	0.328154	+	1.17450i
$361$	−17.8523	+	46.2387i	−0.939597	+	2.43362i
$362$	−34.7523	−	10.1599i	−1.82654	−	0.533990i
$363$	−15.0443	+	0.834666i	−0.789623	+	0.0438086i
$364$	−22.1927	+	0.286932i	−1.16322	+	0.0150393i
$365$	16.2953	−	0.210683i	0.852934	−	0.0110277i
$366$	25.4613	+	38.9453i	1.33089	+	2.03570i
$367$	11.0237	+	3.22278i	0.575433	+	0.168228i	0.555417	−	0.831572i	$-0.312559\pi$
$367$	11.0237	+	3.22278i	0.575433	+	0.168228i	0.0200153	+	0.999800i	$0.493628\pi$
$368$	−0.352636	+	0.913349i	−0.0183824	+	0.0476116i
$369$	−8.84942	−	6.05698i	−0.460682	−	0.315314i
$370$	−40.1042	−	22.1286i	−2.08492	−	1.15041i
$371$	−3.50000	−	7.56955i	−0.181711	−	0.392991i
$372$	57.7218	+	14.2435i	2.99274	+	0.738493i
$373$	6.59075	+	2.89364i	0.341256	+	0.149827i	0.565593	−	0.824684i	$-0.308647\pi$
$373$	6.59075	+	2.89364i	0.341256	+	0.149827i	−0.224337	+	0.974512i	$0.572022\pi$
$374$	1.79012	+	2.53905i	0.0925649	+	0.131291i
$375$	−20.6352	+	4.13219i	−1.06560	+	0.213385i
$376$	11.9654	−	38.1643i	0.617068	−	1.96817i
$377$	−1.63579	−	1.07588i	−0.0842477	−	0.0554106i
$378$	13.4480	−	49.1974i	0.691690	−	2.53044i
$379$	31.7671	−	20.8936i	1.63177	−	1.07323i	0.697544	−	0.716542i	$-0.254276\pi$
$379$	31.7671	−	20.8936i	1.63177	−	1.07323i	0.934223	−	0.356689i	$-0.116094\pi$
$380$	−15.9125	−	55.7654i	−0.816292	−	2.86070i
$381$	3.90427	+	1.94269i	0.200022	+	0.0995272i
$382$	2.61425	−	3.32832i	0.133757	−	0.170291i
$383$	−6.24872	−	1.14351i	−0.319295	−	0.0584309i	0.0179766	−	0.999838i	$-0.494278\pi$
$383$	−6.24872	−	1.14351i	−0.319295	−	0.0584309i	−0.337271	+	0.941408i	$0.609504\pi$
$384$	19.4343	−	30.2136i	0.991753	−	1.54183i
$385$	10.9456	−	4.30749i	0.557838	−	0.219530i
$386$	−7.93949	+	3.60894i	−0.404110	+	0.183690i
$387$	9.12860	+	5.57796i	0.464033	+	0.283544i
$388$	−3.89091	+	15.1054i	−0.197531	+	0.766862i
$389$	15.9718	+	14.8746i	0.809800	+	0.754173i	0.972600	−	0.232486i	$-0.0746861\pi$
$389$	15.9718	+	14.8746i	0.809800	+	0.754173i	−0.162799	+	0.986659i	$0.552052\pi$
$390$	10.6048	+	4.12803i	0.536997	+	0.209031i
$391$	0.242433	−	0.263713i	0.0122604	−	0.0133365i
$392$	28.0575	+	28.9793i	1.41712	+	1.46368i
$393$	3.03982	−	7.38247i	0.153339	−	0.372396i
$394$	−19.1734	+	3.50872i	−0.965940	+	0.176767i
$395$	−6.94063	+	13.1765i	−0.349221	+	0.662979i
$396$	−1.10658	−	16.8449i	−0.0556076	−	0.846487i
$397$	−3.30193	−	24.1744i	−0.165719	−	1.21328i	−0.866233	−	0.499640i	$-0.833465\pi$
$397$	−3.30193	−	24.1744i	−0.165719	−	1.21328i	0.700514	−	0.713639i	$-0.252954\pi$
$398$	−51.4696	+	27.5378i	−2.57994	+	1.38035i
$399$	−15.2206	+	56.9130i	−0.761985	+	2.84922i
$400$	−2.68542	−	2.02633i	−0.134271	−	0.101316i
$401$	−29.0795	+	9.74031i	−1.45216	+	0.486408i	−0.930356	−	0.366658i	$-0.880502\pi$
$401$	−29.0795	+	9.74031i	−1.45216	+	0.486408i	−0.521804	+	0.853065i	$0.674741\pi$
$402$	−0.806258	+	51.4075i	−0.0402125	+	2.56397i
$403$	10.4347	−	8.52833i	0.519790	−	0.424826i
$404$	−5.02030	+	28.4715i	−0.249769	+	1.41651i
$405$	−10.2956	+	13.5160i	−0.511593	+	0.671615i
$406$	2.29119	+	12.9940i	0.113710	+	0.644881i
$407$	11.6694	+	10.0517i	0.578431	+	0.498246i
$408$	4.92123	−	3.54514i	0.243637	−	0.175511i
$409$	−28.4776	−	11.2070i	−1.40813	−	0.554150i	−0.464622	−	0.885509i	$-0.653810\pi$
$409$	−28.4776	−	11.2070i	−1.40813	−	0.554150i	−0.943505	+	0.331359i	$0.892493\pi$
$410$	−16.1035	+	0.833511i	−0.795295	+	0.0411642i
$411$	−9.99830	+	11.2458i	−0.493180	+	0.554715i
$412$	−6.12355	−	18.6819i	−0.301686	−	0.920389i
$413$	−10.8081	+	49.8957i	−0.531831	+	2.45521i
$414$	−2.88012	+	0.824813i	−0.141550	+	0.0405373i
$415$	−0.364522	+	2.66878i	−0.0178937	+	0.131005i
$416$	−1.30448	−	3.51320i	−0.0639573	−	0.172249i
$417$	3.67691	−	5.11445i	0.180059	−	0.250455i
$418$	2.13226	+	29.9364i	0.104292	+	1.46424i
$419$	−1.25712	+	27.7631i	−0.0614142	+	1.35632i	0.702816	+	0.711372i	$0.251926\pi$
$419$	−1.25712	+	27.7631i	−0.0614142	+	1.35632i	−0.764230	+	0.644944i	$0.776881\pi$
$420$	−18.7177	−	46.1783i	−0.913330	−	2.25327i
$421$	3.73727	−	2.82003i	0.182143	−	0.137440i	−0.507326	−	0.861754i	$-0.669366\pi$
$421$	3.73727	−	2.82003i	0.182143	−	0.137440i	0.689470	+	0.724314i	$0.257844\pi$
$422$	−9.13163	+	13.3142i	−0.444521	+	0.648127i
$423$	27.6535	−	9.89291i	1.34456	−	0.481010i
$424$	−5.92155	+	5.80782i	−0.287576	+	0.282053i
$425$	0.642785	+	1.04969i	0.0311797	+	0.0509175i
$426$	33.5373	−	14.8731i	1.62489	−	0.720604i
$427$	−29.4551	−	35.5677i	−1.42543	−	1.72124i
$428$	0.204576	+	6.32732i	0.00988855	+	0.305842i
$429$	−3.20479	−	2.09083i	−0.154729	−	0.100946i
$430$	16.0002	−	1.66078i	0.771598	−	0.0800898i
$431$	13.4705	−	3.19256i	0.648850	−	0.153780i	0.107004	−	0.994259i	$-0.465874\pi$
$431$	13.4705	−	3.19256i	0.648850	−	0.153780i	0.541845	+	0.840478i	$0.317726\pi$
$432$	−12.1379	+	0.921484i	−0.583987	+	0.0443349i
$433$	27.8624	+	6.60350i	1.33898	+	0.317344i	0.836843	−	0.547443i	$-0.184399\pi$
$433$	27.8624	+	6.60350i	1.33898	+	0.317344i	0.502138	+	0.864788i	$0.332547\pi$
$434$	−90.0616	−	11.7088i	−4.32309	−	0.562040i
$435$	0.914606	−	4.29932i	0.0438520	−	0.206137i
$436$	1.15430	−	13.7038i	0.0552812	−	0.656291i
$437$	3.32156	−	0.971059i	0.158892	−	0.0464520i
$438$	−6.52805	+	35.1258i	−0.311922	+	1.67838i
$439$	1.77361	−	0.469098i	0.0846496	−	0.0223888i	−0.213126	−	0.977025i	$-0.568364\pi$
$439$	1.77361	−	0.469098i	0.0846496	−	0.0223888i	0.297775	+	0.954636i	$0.403755\pi$
$440$	−7.69224	−	8.81433i	−0.366713	−	0.420207i
$441$	−4.54883	+	29.2684i	−0.216611	+	1.39373i
$442$	0.0578451	−	2.98248i	0.00275141	−	0.141862i
$443$	−0.0384768	+	0.348725i	−0.00182809	+	0.0165684i	−0.994848	−	0.101382i	$-0.967674\pi$
$443$	−0.0384768	+	0.348725i	−0.00182809	+	0.0165684i	0.993019	+	0.117950i	$0.0376324\pi$
$444$	42.0748	−	49.8633i	1.99678	−	2.36641i
$445$	−9.16674	−	7.49201i	−0.434545	−	0.355155i
$446$	11.6771	−	10.0583i	0.552924	−	0.476274i
$447$	4.49515	−	18.7364i	0.212613	−	0.886203i
$448$	−19.7146	+	39.8960i	−0.931429	+	1.88491i
$449$	27.2031	−	31.1712i	1.28379	−	1.47106i	0.478617	−	0.878024i	$-0.341138\pi$
$449$	27.2031	−	31.1712i	1.28379	−	1.47106i	0.805175	−	0.593038i	$-0.202072\pi$
$450$	−0.00984254	−	10.2942i	−0.000463982	−	0.485273i
$451$	5.35695	+	0.837811i	0.252249	+	0.0394510i
$452$	50.3639	−	35.0231i	2.36892	−	1.64735i
$453$	22.1547	−	5.03553i	1.04092	−	0.236590i
$454$	−19.1866	−	38.8274i	−0.900471	−	1.82226i
$455$	−10.9191	−	2.88798i	−0.511897	−	0.135391i
$456$	58.4001	−	4.75727i	2.73484	−	0.222779i
$457$	21.9851	+	11.3996i	1.02842	+	0.533250i	0.889443	−	0.457046i	$-0.151092\pi$
$457$	21.9851	+	11.3996i	1.02842	+	0.533250i	0.138975	+	0.990296i	$0.455619\pi$
$458$	−1.79572	−	2.41207i	−0.0839085	−	0.112709i
$459$	4.25597	+	1.31256i	0.198652	+	0.0612653i
$460$	−1.74782	+	2.34774i	−0.0814928	+	0.109464i
$461$	−13.2833	+	6.45747i	−0.618667	+	0.300754i	−0.719867	−	0.694112i	$-0.755797\pi$
$461$	−13.2833	+	6.45747i	−0.618667	+	0.300754i	0.101201	+	0.994866i	$0.467732\pi$
$462$	4.57212	+	25.3788i	0.212714	+	1.18073i
$463$	−32.9696	+	6.91885i	−1.53223	+	0.321546i	−0.893917	−	0.448233i	$-0.852054\pi$
$463$	−32.9696	+	6.91885i	−1.53223	+	0.321546i	−0.638310	+	0.769779i	$0.720366\pi$
$464$	2.73737	−	1.55692i	0.127079	−	0.0722781i
$465$	26.3543	+	14.8602i	1.22215	+	0.689126i
$466$	−9.73644	−	47.9355i	−0.451032	−	2.22057i
$467$	31.4167	−	2.44190i	1.45379	−	0.112998i	0.673858	−	0.738860i	$-0.264636\pi$
$467$	31.4167	−	2.44190i	1.45379	−	0.112998i	0.779933	+	0.625863i	$0.215253\pi$
$468$	−8.71837	+	13.6652i	−0.403007	+	0.631673i
$469$	−4.94009	−	50.7885i	−0.228112	−	2.34520i
$470$	24.0288	−	37.0535i	1.10836	−	1.70915i
$471$	27.8175	+	19.1916i	1.28176	+	0.884304i
$472$	50.3521	−	6.54622i	2.31765	−	0.301314i
$473$	−5.38008	−	0.558438i	−0.247376	−	0.0256770i
$474$	−25.3565	−	20.5675i	−1.16466	−	0.944698i
$475$	0.0768646	+	11.8907i	0.00352679	+	0.545582i
$476$	−9.67252	+	8.77734i	−0.443339	+	0.402309i
$477$	−6.02433	−	0.896444i	−0.275835	−	0.0410453i
$478$	−3.83613	−	7.28272i	−0.175461	−	0.333104i
$479$	−22.6189	−	28.7971i	−1.03348	−	1.31577i	−0.947598	−	0.319466i	$-0.896497\pi$
$479$	−22.6189	−	28.7971i	−1.03348	−	1.31577i	−0.0858850	−	0.996305i	$-0.527372\pi$
$480$	6.28235	−	5.59620i	0.286749	−	0.255430i
$481$	−3.31745	−	14.4120i	−0.151263	−	0.657129i
$482$	3.68134	−	6.01177i	0.167681	−	0.273829i
$483$	2.74839	−	1.13476i	0.125056	−	0.0516332i
$484$	−15.7732	−	28.1544i	−0.716965	−	1.27975i
$485$	−3.96896	+	6.87444i	−0.180221	+	0.312152i
$486$	−24.6492	−	27.9264i	−1.11811	−	1.26677i
$487$	12.7342	+	22.0563i	0.577043	+	0.999468i	0.995816	+	0.0913772i	$0.0291269\pi$
$487$	12.7342	+	22.0563i	0.577043	+	0.999468i	−0.418773	+	0.908091i	$0.637540\pi$
$488$	−23.4774	+	39.4766i	−1.06277	+	1.78702i
$489$	1.63063	+	7.39512i	0.0737397	+	0.334419i
$490$	21.2646	+	39.1343i	0.960635	+	1.76791i
$491$	−26.4752	+	24.6566i	−1.19481	+	1.11274i	−0.203791	+	0.979014i	$0.565326\pi$
$491$	−26.4752	+	24.6566i	−1.19481	+	1.11274i	−0.991019	+	0.133721i	$0.957307\pi$
$492$	3.31798	−	22.7274i	0.149586	−	1.02463i
$493$	−1.14057	+	0.163306i	−0.0513689	+	0.00735492i
$494$	15.3659	−	24.3797i	0.691346	−	1.09689i
$495$	1.75633	−	8.40922i	0.0789411	−	0.377966i
$496$	4.58893	+	21.1849i	0.206049	+	0.951229i
$497$	−31.4155	+	18.4096i	−1.40918	+	0.825781i
$498$	−5.58182	−	1.92706i	−0.250127	−	0.0863537i
$499$	−16.2458	+	22.4213i	−0.727261	+	1.00372i	0.271882	+	0.962331i	$0.412354\pi$
$499$	−16.2458	+	22.4213i	−0.727261	+	1.00372i	−0.999143	+	0.0413847i	$0.986823\pi$
$500$	−27.3816	−	35.8041i	−1.22454	−	1.60121i
$501$	5.21194	+	7.33453i	0.232853	+	0.327682i
$502$	1.18264	+	2.31736i	0.0527838	+	0.103429i
$503$	14.9782	−	10.7058i	0.667846	−	0.477348i	−0.196330	−	0.980538i	$-0.562902\pi$
$503$	14.9782	−	10.7058i	0.667846	−	0.477348i	0.864176	+	0.503190i	$0.167841\pi$
$504$	49.4542	−	9.42988i	2.20286	−	0.420040i
$505$	−6.34672	+	13.2730i	−0.282425	+	0.590642i
$506$	1.13482	−	1.00335i	0.0504487	−	0.0446042i
$507$	−6.62429	−	17.6396i	−0.294195	−	0.783401i
$508$	−0.0603766	+	9.34004i	−0.00267878	+	0.414397i
$509$	29.3612	+	32.7790i	1.30141	+	1.45290i	0.815336	+	0.578989i	$0.196553\pi$
$509$	29.3612	+	32.7790i	1.30141	+	1.45290i	0.486078	+	0.873915i	$0.338427\pi$
$510$	6.28460	−	2.31385i	0.278287	−	0.102459i
$511$	2.51925	−	35.3697i	0.111445	−	1.56466i
$512$	24.9992	+	2.92198i	1.10482	+	0.129135i
$513$	28.6498	+	32.1007i	1.26492	+	1.41728i
$514$	−38.1678	+	4.46117i	−1.68351	+	0.196774i
$515$	−0.452551	−	9.99446i	−0.0199418	−	0.440409i
$516$	−2.13360	+	22.8134i	−0.0939263	+	1.00430i
$517$	−10.4664	+	10.5342i	−0.460310	+	0.463295i
$518$	−55.3033	+	82.9121i	−2.42989	+	3.64295i
$519$	11.0955	−	14.6206i	0.487040	−	0.641771i
$520$	0.942876	+	11.1937i	0.0413478	+	0.490876i
$521$	−1.44477	−	3.74204i	−0.0632963	−	0.163942i	0.897627	−	0.440755i	$-0.145289\pi$
$521$	−1.44477	−	3.74204i	−0.0632963	−	0.163942i	−0.960924	+	0.276814i	$0.910721\pi$
$522$	8.85191	+	3.80831i	0.387437	+	0.166685i
$523$	2.08202	+	6.08493i	0.0910404	+	0.266076i	0.982268	−	0.187480i	$-0.0600320\pi$
$523$	2.08202	+	6.08493i	0.0910404	+	0.266076i	−0.891228	+	0.453555i	$0.850155\pi$
$524$	17.0642	−	1.10460i	0.745451	−	0.0482546i
$525$	1.15817	+	10.1511i	0.0505467	+	0.443033i
$526$	8.81962	+	46.4953i	0.384554	+	2.02729i
$527$	1.27609	−	7.82748i	0.0555871	−	0.340971i
$528$	5.33863	−	3.06268i	0.232334	−	0.133286i
$529$	18.3965	+	13.5117i	0.799846	+	0.587466i
$530$	−8.01868	+	4.42452i	−0.348309	+	0.192189i
$531$	26.1335	+	26.5944i	1.13410	+	1.15410i
$532$	−123.816	+	24.3167i	−5.36811	+	1.05426i
$533$	−3.66951	−	3.69330i	−0.158944	−	0.159975i
$534$	20.0352	−	16.4993i	0.867010	−	0.713992i
$535$	−0.763198	+	3.12988i	−0.0329959	+	0.135317i
$536$	−45.9268	+	21.5970i	−1.98374	+	0.932849i
$537$	−45.4024	−	1.59314i	−1.95926	−	0.0687490i
$538$	32.4082	−	42.3768i	1.39722	−	1.82699i
$539$	−4.29520	−	14.3470i	−0.185007	−	0.617967i
$540$	−35.6960	−	7.07715i	−1.53611	−	0.304552i
$541$	−2.38081	+	7.95245i	−0.102359	+	0.341902i	−0.993793	−	0.111249i	$-0.964515\pi$
$541$	−2.38081	+	7.95245i	−0.102359	+	0.341902i	0.891434	+	0.453151i	$0.149700\pi$
$542$	−9.23227	−	12.7417i	−0.396560	−	0.547305i
$543$	17.9394	−	19.1566i	0.769854	−	0.822087i
$544$	−1.94458	−	1.04041i	−0.0833733	−	0.0446073i
$545$	2.43605	−	6.56073i	0.104349	−	0.281031i
$546$	10.8871	−	22.2394i	0.465926	−	0.951758i
$547$	9.53958	−	0.246717i	0.407883	−	0.0105489i	0.178631	−	0.983916i	$-0.442833\pi$
$547$	9.53958	−	0.246717i	0.407883	−	0.0105489i	0.229252	+	0.973367i	$0.426372\pi$
$548$	−31.0490	−	8.64307i	−1.32635	−	0.369214i
$549$	−33.5204	+	3.73094i	−1.43062	+	0.159233i
$550$	2.24531	+	4.69567i	0.0957404	+	0.200224i
$551$	−10.2490	−	4.34262i	−0.436622	−	0.185002i
$552$	−1.98129	−	2.19548i	−0.0843294	−	0.0934458i
$553$	27.3015	+	17.4550i	1.16098	+	0.742264i
$554$	15.1916	−	10.2755i	0.645430	−	0.436563i
$555$	27.4321	−	18.7035i	1.16443	−	0.793920i
$556$	13.3012	+	2.25680i	0.564096	+	0.0957097i
$557$	−18.1956	+	7.43373i	−0.770974	+	0.314977i	−0.729336	−	0.684155i	$-0.760171\pi$
$557$	−18.1956	+	7.43373i	−0.770974	+	0.314977i	−0.0416375	+	0.999133i	$0.513257\pi$
$558$	−43.2405	+	50.2966i	−1.83051	+	2.12922i
$559$	3.84621	+	3.49025i	0.162677	+	0.147622i
$560$	12.1210	−	13.5319i	0.512205	−	0.571828i
$561$	−2.22795	+	0.327435i	−0.0940641	+	0.0138243i
$562$	−32.7321	+	64.1378i	−1.38072	+	2.70549i
$563$	−0.328497	−	2.19317i	−0.0138445	−	0.0924313i	0.980965	−	0.194183i	$-0.0622055\pi$
$563$	−0.328497	−	2.19317i	−0.0138445	−	0.0924313i	−0.994810	+	0.101752i	$0.967555\pi$
$564$	45.0727	+	43.8801i	1.89790	+	1.84769i
$565$	29.4705	−	10.2969i	1.23983	−	0.433194i
$566$	26.8190	−	22.5038i	1.12729	−	0.945905i
$567$	27.4249	+	24.7913i	1.15174	+	1.04114i
$568$	27.7420	+	23.2783i	1.16403	+	0.976737i
$569$	−6.56594	−	2.48640i	−0.275258	−	0.104235i	0.212655	−	0.977127i	$-0.431789\pi$
$569$	−6.56594	−	2.48640i	−0.275258	−	0.104235i	−0.487913	+	0.872892i	$0.662242\pi$
$570$	63.5307	+	12.2324i	2.66101	+	0.512359i
$571$	−2.12922	+	10.4828i	−0.0891050	+	0.438691i	0.910574	+	0.413347i	$0.135640\pi$
$571$	−2.12922	+	10.4828i	−0.0891050	+	0.438691i	−0.999679	+	0.0253442i	$0.991932\pi$
$572$	1.00406	−	8.13397i	0.0419820	−	0.340098i
$573$	1.29783	+	2.77974i	0.0542176	+	0.116125i
$574$	−1.13381	+	35.0676i	−0.0473244	+	1.46370i
$575$	0.474356	−	0.367654i	0.0197820	−	0.0153322i
$576$	16.4588	+	28.0252i	0.685783	+	1.16771i
$577$	−8.19791	−	13.0069i	−0.341284	−	0.541483i	0.630852	−	0.775903i	$-0.282706\pi$
$577$	−8.19791	−	13.0069i	−0.341284	−	0.541483i	−0.972135	+	0.234420i	$0.924681\pi$
$578$	25.1746	+	29.6110i	1.04712	+	1.23166i
$579$	0.262521	−	6.31620i	0.0109100	−	0.262492i
$580$	9.13182	−	2.28936i	0.379178	−	0.0950606i
$581$	5.71984	+	1.27776i	0.237299	+	0.0530104i
$582$	−13.0800	−	11.4785i	−0.542184	−	0.475799i
$583$	2.94437	−	0.902265i	0.121943	−	0.0373680i
$584$	−33.9752	+	9.45764i	−1.40590	+	0.391360i
$585$	−6.13907	+	5.50956i	−0.253819	+	0.227792i
$586$	−6.54813	+	67.3207i	−0.270501	+	2.78099i
$587$	0.287488	+	0.228830i	0.0118659	+	0.00944482i	0.628683	−	0.777662i	$-0.283594\pi$
$587$	0.287488	+	0.228830i	0.0118659	+	0.00944482i	−0.616817	+	0.787107i	$0.711578\pi$
$588$	−60.5867	+	18.8122i	−2.49855	+	0.775803i
$589$	49.6267	−	58.3723i	2.04483	−	2.40519i
$590$	55.4995	+	7.94634i	2.28488	+	0.327145i
$591$	4.00193	−	13.5501i	0.164617	−	0.557378i
$592$	23.0730	+	5.78445i	0.948296	+	0.237739i
$593$	−3.79345	−	1.90514i	−0.155778	−	0.0782348i	0.369202	−	0.929349i	$-0.379631\pi$
$593$	−3.79345	−	1.90514i	−0.155778	−	0.0782348i	−0.524980	+	0.851114i	$0.675927\pi$
$594$	17.3277	+	7.37875i	0.710966	+	0.302754i
$595$	−5.93980	+	2.98308i	−0.243508	+	0.122294i
$596$	40.2761	−	8.99730i	1.64977	−	0.368544i
$597$	−0.977444	−	42.3011i	−0.0400041	−	1.73127i
$598$	−1.44854	+	0.131450i	−0.0592352	+	0.00537538i
$599$	−1.55831	−	14.1234i	−0.0636708	−	0.577065i	−0.983004	−	0.183585i	$-0.941230\pi$
$599$	−1.55831	−	14.1234i	−0.0636708	−	0.577065i	0.919333	−	0.393480i	$-0.128729\pi$
$600$	9.12238	−	4.47661i	0.372419	−	0.182757i
$601$	6.81288	+	0.618245i	0.277903	+	0.0252187i	0.228443	−	0.973557i	$-0.426637\pi$
$601$	6.81288	+	0.618245i	0.277903	+	0.0252187i	0.0494605	+	0.998776i	$0.484250\pi$
$602$	−0.678722	−	34.9948i	−0.0276627	−	1.42628i
$603$	−32.9896	−	17.3368i	−1.34344	−	0.706010i
$604$	30.5503	+	37.8765i	1.24307	+	1.54117i
$605$	−3.89057	−	15.9553i	−0.158174	−	0.648675i
$606$	−25.8186	−	19.3320i	−1.04881	−	0.785308i
$607$	9.78907	−	17.4730i	0.397326	−	0.709208i	−0.598436	−	0.801170i	$-0.704211\pi$
$607$	9.78907	−	17.4730i	0.397326	−	0.709208i	0.995762	+	0.0919623i	$0.0293139\pi$
$608$	−10.8905	−	18.3120i	−0.441668	−	0.742651i
$609$	−9.15471	−	2.76824i	−0.370968	−	0.112175i
$610$	−36.6630	+	35.0405i	−1.48444	+	1.41875i
$611$	14.0876	−	2.20326i	0.569924	−	0.0891345i
$612$	1.48299	+	9.42319i	0.0599464	+	0.380910i
$613$	11.7424	−	7.08655i	0.474269	−	0.286223i	−0.259350	−	0.965783i	$-0.583508\pi$
$613$	11.7424	−	7.08655i	0.474269	−	0.286223i	0.733620	+	0.679560i	$0.237829\pi$
$614$	−26.6368	+	37.7808i	−1.07497	+	1.52471i
$615$	4.72826	−	10.6893i	0.190662	−	0.431035i
$616$	−20.5160	+	15.0684i	−0.826612	+	0.607125i
$617$	−14.3557	+	31.0474i	−0.577937	+	1.24992i	0.369277	+	0.929319i	$0.379605\pi$
$617$	−14.3557	+	31.0474i	−0.577937	+	1.24992i	−0.947214	+	0.320602i	$0.896115\pi$
$618$	21.6824	+	3.30870i	0.872194	+	0.133095i
$619$	10.9668	+	11.9294i	0.440792	+	0.479483i	0.916451	−	0.400148i	$-0.131041\pi$
$619$	10.9668	+	11.9294i	0.440792	+	0.479483i	−0.475658	+	0.879630i	$0.657790\pi$
$620$	−3.76784	+	64.6914i	−0.151320	+	2.59807i
$621$	0.408546	−	2.13282i	0.0163944	−	0.0855873i
$622$	−3.68311	−	63.2365i	−0.147679	−	2.53555i
$623$	−17.9182	+	18.5069i	−0.717879	+	0.741465i
$624$	−5.87240	−	0.664309i	−0.235084	−	0.0265936i
$625$	−5.86513	−	14.6255i	−0.234605	−	0.585019i
$626$	−19.0456	−	53.3988i	−0.761215	−	2.13425i
$627$	−20.0621	−	8.41289i	−0.801202	−	0.335978i
$628$	−10.7221	+	71.5852i	−0.427860	+	2.85656i
$629$	−7.08046	−	5.06081i	−0.282317	−	0.201788i
$630$	55.3981	+	4.61300i	2.20711	+	0.183786i
$631$	−0.494127	−	0.484637i	−0.0196709	−	0.0192931i	0.690315	−	0.723509i	$-0.257472\pi$
$631$	−0.494127	−	0.484637i	−0.0196709	−	0.0192931i	−0.709986	+	0.704215i	$0.751299\pi$
$632$	7.22957	−	31.4073i	0.287577	−	1.24932i
$633$	−5.62548	−	10.2619i	−0.223593	−	0.407875i
$634$	7.89051	+	25.1672i	0.313372	+	0.999519i
$635$	−1.30424	+	4.57072i	−0.0517571	+	0.181383i
$636$	−3.94877	−	12.4331i	−0.156579	−	0.493003i
$637$	−4.83087	+	13.5445i	−0.191406	+	0.536652i
$638$	−4.86860	+	0.188924i	−0.192750	+	0.00747956i
$639$	−1.34921	+	26.5588i	−0.0533741	+	1.05065i
$640$	36.2473	+	14.8087i	1.43280	+	0.585364i
$641$	39.9694	+	24.8322i	1.57870	+	0.980812i	0.984272	+	0.176661i	$0.0565297\pi$
$641$	39.9694	+	24.8322i	1.57870	+	0.980812i	0.594425	+	0.804151i	$0.297380\pi$
$642$	−6.40243	−	2.98177i	−0.252684	−	0.117681i
$643$	−14.3837	+	6.09453i	−0.567236	+	0.240345i	−0.654785	−	0.755815i	$-0.727241\pi$
$643$	−14.3837	+	6.09453i	−0.567236	+	0.240345i	0.0875485	+	0.996160i	$0.472097\pi$
$644$	4.77113	+	4.21839i	0.188009	+	0.166228i
$645$	−4.15935	+	10.8931i	−0.163774	+	0.428915i
$646$	−2.72878	−	16.7383i	−0.107362	−	0.658559i
$647$	33.6011	−	12.2298i	1.32099	−	0.480803i	0.417218	−	0.908807i	$-0.363005\pi$
$647$	33.6011	−	12.2298i	1.32099	−	0.480803i	0.903777	+	0.428004i	$0.140783\pi$
$648$	14.0608	−	33.9741i	0.552359	−	1.33463i
$649$	−17.7152	−	6.44779i	−0.695381	−	0.253098i
$650$	0.931411	−	4.91021i	0.0365329	−	0.192594i
$651$	37.0329	−	54.4271i	1.45143	−	2.13317i
$652$	−12.6902	+	10.1010i	−0.496987	+	0.395584i
$653$	−1.89758	−	2.92615i	−0.0742580	−	0.114509i	0.799938	−	0.600083i	$-0.204866\pi$
$653$	−1.89758	−	2.92615i	−0.0742580	−	0.114509i	−0.874196	+	0.485574i	$0.838611\pi$
$654$	13.0622	+	8.04829i	0.510774	+	0.314713i
$655$	8.51645	+	1.78722i	0.332765	+	0.0698326i
$656$	7.97420	−	2.55683i	0.311340	−	0.0998273i
$657$	−20.5861	−	15.7123i	−0.803140	−	0.612995i
$658$	−75.9505	−	58.8661i	−2.96086	−	2.29484i
$659$	−15.4711	+	18.6816i	−0.602667	+	0.727733i	−0.980144	−	0.198286i	$-0.936463\pi$
$659$	−15.4711	+	18.6816i	−0.602667	+	0.727733i	0.377477	+	0.926019i	$0.376792\pi$
$660$	17.8306	−	4.54054i	0.694055	−	0.176740i
$661$	−11.6313	−	5.65435i	−0.452405	−	0.219929i	0.196952	−	0.980413i	$-0.436896\pi$
$661$	−11.6313	−	5.65435i	−0.452405	−	0.219929i	−0.649356	+	0.760484i	$0.724962\pi$
$662$	45.3004	−	23.4889i	1.76065	−	0.912923i
$663$	1.91032	+	1.01298i	0.0741906	+	0.0393409i
$664$	−0.714119	−	5.78512i	−0.0277132	−	0.224506i
$665$	−64.0193	−	4.97597i	−2.48256	−	0.192960i
$666$	28.4613	+	66.9928i	1.10285	+	2.59592i
$667$	0.140136	+	0.544042i	0.00542609	+	0.0210654i
$668$	−9.20106	+	16.9332i	−0.356000	+	0.655165i
$669$	2.68675	+	10.8434i	0.103876	+	0.419232i
$670$	−55.2488	+	9.37403i	−2.13445	+	0.362150i
$671$	14.4851	−	8.99928i	0.559190	−	0.347413i
$672$	−10.9863	−	14.6434i	−0.423804	−	0.564880i
$673$	−4.61635	+	10.3325i	−0.177947	+	0.398290i	−0.980009	−	0.198951i	$-0.936247\pi$
$673$	−4.61635	+	10.3325i	−0.177947	+	0.398290i	0.802062	+	0.597241i	$0.203736\pi$
$674$	18.0941	+	19.1787i	0.696960	+	0.738734i
$675$	6.66211	+	3.36085i	0.256425	+	0.129359i
$676$	27.6946	−	29.3546i	1.06518	−	1.12902i
$677$	13.9617	+	33.5532i	0.536594	+	1.28955i	0.929108	+	0.369808i	$0.120576\pi$
$677$	13.9617	+	33.5532i	0.536594	+	1.28955i	−0.392515	+	0.919746i	$0.628395\pi$
$678$	9.51339	+	67.7741i	0.365360	+	2.60285i
$679$	14.1802	+	9.86095i	0.544187	+	0.378429i
$680$	4.77906	+	4.56756i	0.183268	+	0.175158i
$681$	31.3917	+	0.289384i	1.20293	+	0.0110892i
$682$	8.78455	−	32.3656i	0.336378	−	1.23934i
$683$	−7.99236	+	23.3586i	−0.305819	+	0.893790i	0.681045	+	0.732241i	$0.261526\pi$
$683$	−7.99236	+	23.3586i	−0.305819	+	0.893790i	−0.986865	+	0.161549i	$0.948351\pi$
$684$	−34.7712	+	85.3429i	−1.32951	+	3.26317i
$685$	−14.0422	−	8.47453i	−0.536526	−	0.323795i
$686$	25.8229	−	11.3374i	0.985922	−	0.432865i
$687$	2.14764	−	0.372592i	0.0819377	−	0.0142153i
$688$	−7.81249	+	2.95844i	−0.297848	+	0.112790i
$689$	−2.79149	−	0.975338i	−0.106347	−	0.0371574i
$690$	−1.45746	−	2.92208i	−0.0554845	−	0.111242i
$691$	1.77329	+	2.65856i	0.0674590	+	0.101136i	0.864109	−	0.503304i	$-0.167882\pi$
$691$	1.77329	+	2.65856i	0.0674590	+	0.101136i	−0.796650	+	0.604440i	$0.793397\pi$
$692$	38.5742	+	7.57572i	1.46637	+	0.287986i
$693$	−17.9120	−	5.34385i	−0.680421	−	0.202996i
$694$	4.66505	−	5.78376i	0.177083	−	0.219549i
$695$	6.21291	+	2.92161i	0.235669	+	0.110823i
$696$	0.465526	+	9.50081i	0.0176457	+	0.360127i
$697$	−3.05749	−	0.197917i	−0.115811	−	0.00749665i
$698$	−3.84155	−	14.1537i	−0.145405	−	0.535726i
$699$	34.1922	+	9.38150i	1.29327	+	0.354841i
$700$	−18.4369	+	11.7875i	−0.696848	+	0.445526i
$701$	−7.76594	+	18.0035i	−0.293315	+	0.679982i	−0.999610	−	0.0279367i	$-0.991106\pi$
$701$	−7.76594	+	18.0035i	−0.293315	+	0.679982i	0.706294	+	0.707918i	$0.250366\pi$
$702$	−9.21576	−	15.5596i	−0.347826	−	0.587259i
$703$	−33.3016	−	77.2018i	−1.25599	−	2.91172i
$704$	−13.6115	−	9.20671i	−0.513003	−	0.346991i
$705$	16.1086	+	27.6633i	0.606684	+	1.04186i
$706$	12.7421	−	38.8739i	0.479556	−	1.46304i
$707$	27.6193	+	16.1850i	1.03873	+	0.608698i
$708$	−26.5485	+	75.3170i	−0.997753	+	2.83058i
$709$	−30.0696	−	10.0720i	−1.12929	−	0.378260i	−0.309484	−	0.950905i	$-0.600156\pi$
$709$	−30.0696	−	10.0720i	−1.12929	−	0.378260i	−0.819804	+	0.572644i	$0.805918\pi$
$710$	22.6171	+	32.9766i	0.848805	+	1.23759i
$711$	21.5983	−	9.67446i	0.810001	−	0.362821i
$712$	23.3236	+	10.6019i	0.874089	+	0.397322i
$713$	−3.86179	−	0.199885i	−0.144625	−	0.00748575i
$714$	−3.86909	−	14.0488i	−0.144797	−	0.525763i
$715$	1.60229	−	3.85065i	0.0599222	−	0.144006i
$716$	−39.6918	−	88.8399i	−1.48335	−	3.32010i
$717$	5.96567	−	0.0992691i	0.222792	−	0.00370727i
$718$	−26.0231	−	14.8010i	−0.971174	−	0.552368i
$719$	−10.1615	−	3.25814i	−0.378959	−	0.121508i	0.109741	−	0.993960i	$-0.464998\pi$
$719$	−10.1615	−	3.25814i	−0.378959	−	0.121508i	−0.488700	+	0.872452i	$0.662529\pi$
$720$	−3.40479	−	12.8235i	−0.126889	−	0.477904i
$721$	−21.7525	−	0.844097i	−0.810107	−	0.0314358i
$722$	44.0831	−	109.927i	1.64060	−	4.09106i
$723$	2.68460	+	4.34774i	0.0998413	+	0.161694i
$724$	53.7450	+	16.4695i	1.99742	+	0.612084i
$725$	−1.92975	−	0.0499083i	−0.0716693	−	0.00185355i
$726$	35.9713	−	1.52953i	1.33502	−	0.0567662i
$727$	−12.2485	−	0.158362i	−0.454273	−	0.00587333i	−0.214546	−	0.976714i	$-0.568827\pi$
$727$	−12.2485	−	0.158362i	−0.454273	−	0.00587333i	−0.239726	+	0.970840i	$0.577058\pi$
$728$	24.4423			0.905890
$729$	26.1271	−	6.80988i	0.967670	−	0.252218i
$730$	−38.9409			−1.44127
$731$	3.05624	+	0.0395144i	0.113039	+	0.00146149i
$732$	−38.7441	−	60.9690i	−1.43202	−	2.25348i
$733$	26.4494	+	0.684048i	0.976931	+	0.0252659i	0.511023	−	0.859567i	$-0.329267\pi$
$733$	26.4494	+	0.684048i	0.976931	+	0.0252659i	0.465908	+	0.884833i	$0.345728\pi$
$734$	−26.2394	−	8.04075i	−0.968516	−	0.296790i
$735$	−32.2699	+	0.954399i	−1.19029	+	0.0352036i
$736$	−0.400247	+	0.998068i	−0.0147533	+	0.0367893i
$737$	18.8288	+	0.730644i	0.693568	+	0.0269136i
$738$	20.9569	+	14.7453i	0.771432	+	0.542784i
$739$	10.5533	+	3.38379i	0.388211	+	0.124475i	0.493021	−	0.870018i	$-0.335893\pi$
$739$	10.5533	+	3.38379i	0.388211	+	0.124475i	−0.104810	+	0.994492i	$0.533424\pi$
$740$	61.8129	+	35.1569i	2.27229	+	1.29239i
$741$	10.7440	+	17.9141i	0.394692	+	0.658092i
$742$	8.12873	+	18.1941i	0.298415	+	0.667926i
$743$	4.48777	−	10.7851i	0.164640	−	0.395667i	−0.819495	−	0.573086i	$-0.805746\pi$
$743$	4.48777	−	10.7851i	0.164640	−	0.395667i	0.984135	+	0.177419i	$0.0567748\pi$
$744$	−63.3592	−	16.5065i	−2.32286	−	0.605157i
$745$	20.9732	+	1.08556i	0.768399	+	0.0397720i
$746$	−15.6579	−	7.11740i	−0.573277	−	0.260586i
$747$	3.07234	−	2.98030i	0.112411	−	0.109044i
$748$	−2.72799	−	3.97751i	−0.0997452	−	0.145432i
$749$	6.64680	+	2.22638i	0.242869	+	0.0813500i
$750$	49.4314	−	9.23561i	1.80498	−	0.337237i
$751$	28.2948	+	16.5808i	1.03249	+	0.605042i	0.921339	−	0.388761i	$-0.127097\pi$
$751$	28.2948	+	16.5808i	1.03249	+	0.605042i	0.111154	+	0.993803i	$0.464545\pi$
$752$	−7.14356	+	21.7937i	−0.260499	+	0.794735i
$753$	−1.88584	+	0.00699679i	−0.0687238	+	0.000254977i
$754$	3.87518	+	2.62113i	0.141126	+	0.0954561i
$755$	9.80828	+	22.7381i	0.356960	+	0.827526i
$756$	−21.8638	+	76.1032i	−0.795181	+	2.76785i
$757$	4.75528	−	11.0240i	0.172834	−	0.400673i	−0.809678	−	0.586874i	$-0.800358\pi$
$757$	4.75528	−	11.0240i	0.172834	−	0.400673i	0.982512	+	0.186201i	$0.0596175\pi$
$758$	−76.5468	+	48.9398i	−2.78031	+	1.77757i
$759$	0.277826	+	1.06226i	0.0100845	+	0.0385575i
$760$	16.7285	+	61.6342i	0.606808	+	2.23571i
$761$	−51.4216	−	3.32862i	−1.86403	−	0.120663i	−0.908931	−	0.416946i	$-0.863101\pi$
$761$	−51.4216	−	3.32862i	−1.86403	−	0.120663i	−0.955100	+	0.296283i	$0.904253\pi$
$762$	−9.26849	−	4.76230i	−0.335762	−	0.172520i
$763$	−13.7800	−	6.48003i	−0.498870	−	0.234593i
$764$	−4.12512	+	5.11435i	−0.149242	+	0.185031i
$765$	−0.558950	+	4.82210i	−0.0202089	+	0.174343i
$766$	14.8948	+	2.92524i	0.538170	+	0.105693i
$767$	10.0447	+	15.0593i	0.362694	+	0.543761i
$768$	−26.6593	+	40.2913i	−0.961983	+	1.45389i
$769$	−10.8732	−	3.79906i	−0.392098	−	0.136998i	0.126603	−	0.991953i	$-0.459592\pi$
$769$	−10.8732	−	3.79906i	−0.392098	−	0.136998i	−0.518701	+	0.854956i	$0.673584\pi$
$770$	−26.2854	+	9.95378i	−0.947259	+	0.358709i
$771$	9.59886	−	26.1484i	0.345694	−	0.941710i
$772$	12.3976	−	5.44311i	0.446198	−	0.195902i
$773$	24.2814	+	14.6539i	0.873342	+	0.527064i	0.881113	−	0.472905i	$-0.156795\pi$
$773$	24.2814	+	14.6539i	0.873342	+	0.527064i	−0.00777143	+	0.999970i	$0.502474\pi$
$774$	−21.6387	−	13.6095i	−0.777787	−	0.489182i
$775$	4.30154	−	12.5717i	0.154516	−	0.451589i
$776$	4.49964	−	16.5784i	0.161528	−	0.595129i
$777$	−35.5428	−	62.8938i	−1.27509	−	2.25630i
$778$	−37.7019	−	36.0334i	−1.35168	−	1.29186i
$779$	−24.3009	−	16.8989i	−0.870670	−	0.605466i
$780$	−16.3799	−	6.62112i	−0.586495	−	0.237074i
$781$	−5.16555	−	12.4140i	−0.184838	−	0.444206i
$782$	−0.587394	+	0.622601i	−0.0210052	+	0.0222642i
$783$	−5.35887	+	4.48024i	−0.191511	+	0.160111i
$784$	−15.8726	−	16.8240i	−0.566879	−	0.600857i
$785$	−15.0258	+	33.6314i	−0.536293	+	1.20036i
$786$	−7.49112	+	17.5451i	−0.267199	+	0.625812i
$787$	10.2802	−	6.38689i	0.366450	−	0.227668i	−0.332076	−	0.943253i	$-0.607749\pi$
$787$	10.2802	−	6.38689i	0.366450	−	0.227668i	0.698526	+	0.715585i	$0.253840\pi$
$788$	29.8348	−	5.06205i	1.06282	−	0.180328i
$789$	−32.9607	−	9.50348i	−1.17343	−	0.338333i
$790$	16.9903	−	31.2682i	0.604488	−	1.11247i
$791$	−16.9434	−	65.7782i	−0.602436	−	2.33880i
$792$	0.978715	+	18.5650i	0.0347771	+	0.659678i
$793$	−16.3252	−	1.26890i	−0.579725	−	0.0450598i
$794$	7.14254	+	57.8621i	0.253479	+	2.05345i
$795$	−0.239141	−	6.63420i	−0.00848145	−	0.235291i
$796$	80.4533	−	41.7162i	2.85159	−	1.47859i
$797$	40.2396	+	19.5618i	1.42536	+	0.692915i	0.979361	−	0.202117i	$-0.0647823\pi$
$797$	40.2396	+	19.5618i	1.42536	+	0.692915i	0.446000	+	0.895033i	$0.352848\pi$
$798$	38.1249	−	135.512i	1.34961	−	4.79709i
$799$	5.35213	−	6.46280i	0.189345	−	0.228637i
$800$	−2.92045	−	2.26352i	−0.103254	−	0.0800276i
$801$	4.11918	+	18.3568i	0.145544	+	0.648607i
$802$	69.7807	−	22.3743i	2.46404	−	0.790063i
$803$	12.8148	+	2.68925i	0.452224	+	0.0949017i
$804$	2.28341	−	79.7879i	0.0805298	−	2.81390i
$805$	1.76336	+	2.71918i	0.0621502	+	0.0958386i
$806$	−25.1952	+	20.0544i	−0.887462	+	0.706387i
$807$	16.8111	+	34.8249i	0.591779	+	1.22589i
$808$	5.93360	−	31.2807i	0.208743	−	1.10045i
$809$	−31.8951	−	11.6089i	−1.12137	−	0.408146i	−0.286219	−	0.958164i	$-0.592398\pi$
$809$	−31.8951	−	11.6089i	−1.12137	−	0.408146i	−0.835152	+	0.550019i	$0.814621\pi$
$810$	25.0169	−	31.9758i	0.879004	−	1.12351i
$811$	−7.18153	+	2.61386i	−0.252178	+	0.0917852i	−0.465016	−	0.885302i	$-0.653951\pi$
$811$	−7.18153	+	2.61386i	−0.252178	+	0.0917852i	0.212838	+	0.977087i	$0.431729\pi$
$812$	−3.29600	−	20.2176i	−0.115667	−	0.709500i
$813$	11.2620	−	1.80417i	0.394974	−	0.0632749i
$814$	−27.5713	−	24.3771i	−0.966373	−	0.854418i
$815$	−7.59986	+	3.22015i	−0.266212	+	0.112797i
$816$	−2.84798	+	1.99621i	−0.0996993	+	0.0698813i
$817$	25.0813	+	15.5825i	0.877483	+	0.545162i
$818$	67.6955	+	27.6567i	2.36692	+	0.966992i
$819$	10.8246	+	14.3169i	0.378241	+	0.500273i
$820$	25.0155	−	0.970716i	0.873580	−	0.0338989i
$821$	−1.87042	+	5.24418i	−0.0652783	+	0.183023i	−0.970067	−	0.242838i	$-0.921922\pi$
$821$	−1.87042	+	5.24418i	−0.0652783	+	0.183023i	0.904789	+	0.425861i	$0.140029\pi$
$822$	24.2364	−	26.5608i	0.845341	−	0.926416i
$823$	1.61081	−	5.64510i	0.0561493	−	0.196776i	−0.928496	−	0.371342i	$-0.878898\pi$
$823$	1.61081	−	5.64510i	0.0561493	−	0.196776i	0.984645	+	0.174567i	$0.0558524\pi$
$824$	6.47715	+	20.6592i	0.225642	+	0.719699i
$825$	−3.77187	−	0.0835476i	−0.131320	−	0.00290875i
$826$	27.3652	−	118.882i	0.952156	−	4.13644i
$827$	−35.9120	−	35.2223i	−1.24878	−	1.22480i	−0.963909	−	0.266234i	$-0.914221\pi$
$827$	−35.9120	−	35.2223i	−1.24878	−	1.22480i	−0.284875	−	0.958565i	$-0.591952\pi$
$828$	4.48761	−	1.22262i	0.155955	−	0.0424889i
$829$	26.1879	+	18.7180i	0.909543	+	0.650103i	0.936928	−	0.349522i	$-0.113656\pi$
$829$	26.1879	+	18.7180i	0.909543	+	0.650103i	−0.0273846	+	0.999625i	$0.508718\pi$
$830$	0.953398	−	6.36526i	0.0330929	−	0.220941i
$831$	1.67762	+	13.1879i	0.0581961	+	0.457484i
$832$	5.30075	+	14.8619i	0.183770	+	0.515244i
$833$	3.14987	+	7.85461i	0.109136	+	0.272146i
$834$	−8.94325	+	12.1064i	−0.309680	+	0.419210i
$835$	−6.82170	+	7.04582i	−0.236075	+	0.243831i
$836$	−2.70923	−	46.5156i	−0.0937005	−	1.60878i
$837$	−18.3909	−	44.4224i	−0.635682	−	1.53546i
$838$	3.86128	−	66.2957i	0.133386	−	2.29015i
$839$	−32.2430	−	35.0731i	−1.11315	−	1.21086i	−0.975412	−	0.220388i	$-0.929268\pi$
$839$	−32.2430	−	35.0731i	−1.11315	−	1.21086i	−0.137738	−	0.990469i	$-0.543983\pi$
$840$	19.9541	+	51.1171i	0.688481	+	1.76371i
$841$	−11.4125	+	24.6822i	−0.393535	+	0.851111i
$842$	−9.01660	+	6.62245i	−0.310733	+	0.228225i
$843$	−30.7815	−	42.1524i	−1.06017	−	1.45181i
$844$	14.4430	−	20.4855i	0.497149	−	0.705141i
$845$	17.5833	−	10.6116i	0.604885	−	0.365050i
$846$	−66.3783	+	22.7829i	−2.28213	+	0.783293i
$847$	−35.3046	+	5.52154i	−1.21308	+	0.189722i
$848$	3.43832	−	3.28615i	0.118072	−	0.112847i
$849$	5.78432	+	24.7090i	0.198517	+	0.848012i
$850$	−1.50338	−	2.52789i	−0.0515656	−	0.0867059i
$851$	−2.07408	+	3.70214i	−0.0710986	+	0.126908i
$852$	−52.3612	+	22.4156i	−1.79387	+	0.767946i
$853$	−9.18371	−	37.6625i	−0.314444	−	1.28954i	−0.883961	−	0.467560i	$-0.845133\pi$
$853$	−9.18371	−	37.6625i	−0.314444	−	1.28954i	0.569517	−	0.821979i	$-0.307130\pi$
$854$	69.2786	+	85.8919i	2.37066	+	2.93916i
$855$	−28.6934	+	37.0941i	−0.981293	+	1.26859i
$856$	−0.135191	−	6.97042i	−0.00462074	−	0.238244i
$857$	36.5747	+	3.31903i	1.24937	+	0.113376i	0.695070	−	0.718942i	$-0.255373\pi$
$857$	36.5747	+	3.31903i	1.24937	+	0.113376i	0.554299	+	0.832318i	$0.312986\pi$
$858$	7.59264	+	5.09464i	0.259208	+	0.173928i
$859$	−1.28070	−	11.6073i	−0.0436969	−	0.396036i	−0.995892	−	0.0905465i	$-0.971139\pi$
$859$	−1.28070	−	11.6073i	−0.0436969	−	0.396036i	0.952195	−	0.305490i	$-0.0988202\pi$
$860$	−24.8717	+	2.25702i	−0.848120	+	0.0769638i
$861$	−22.3129	−	12.2040i	−0.760422	−	0.415910i
$862$	−32.2837	+	7.21188i	−1.09959	+	0.245638i
$863$	−25.8890	+	13.0019i	−0.881271	+	0.442591i	−0.831083	−	0.556149i	$-0.812278\pi$
$863$	−25.8890	+	13.0019i	−0.881271	+	0.442591i	−0.0501882	+	0.998740i	$0.515982\pi$
$864$	−13.3434	+	0.839659i	−0.453953	+	0.0285658i
$865$	17.8771	+	8.97822i	0.607840	+	0.305269i
$866$	−66.3677	−	16.6385i	−2.25527	−	0.565399i
$867$	−27.3887	+	6.59866i	−0.930169	+	0.224102i
$868$	139.575	+	19.9841i	4.73748	+	0.678306i
$869$	−7.75060	+	9.11647i	−0.262921	+	0.309255i
$870$	−2.31809	+	10.2441i	−0.0785905	+	0.347309i
$871$	−14.1563	−	11.2679i	−0.479666	−	0.381797i
$872$	−1.46620	+	15.0738i	−0.0496518	+	0.510465i
$873$	11.7034	−	4.70631i	0.396100	−	0.159285i
$874$	−7.96622	+	2.21755i	−0.269461	+	0.0750097i
$875$	−47.7194	+	14.6230i	−1.61321	+	0.494348i
$876$	10.8390	−	54.3977i	0.366217	−	1.83793i
$877$	−23.2029	−	5.18331i	−0.783506	−	0.175028i	−0.192071	−	0.981381i	$-0.561521\pi$
$877$	−23.2029	−	5.18331i	−0.783506	−	0.175028i	−0.591435	+	0.806353i	$0.701438\pi$
$878$	−4.25218	+	1.06603i	−0.143504	+	0.0359767i
$879$	−41.4051	−	26.2562i	−1.39656	−	0.885599i
$880$	4.34518	+	5.11093i	0.146476	+	0.172289i
$881$	−16.6013	−	26.3397i	−0.559312	−	0.887408i	0.440635	−	0.897686i	$-0.354753\pi$
$881$	−16.6013	−	26.3397i	−0.559312	−	0.887408i	−0.999947	+	0.0102777i	$0.996728\pi$
$882$	11.7727	−	69.7906i	0.396407	−	2.34997i
$883$	−24.3981	+	18.9100i	−0.821063	+	0.636372i	−0.934017	−	0.357228i	$-0.883722\pi$
$883$	−24.3981	+	18.9100i	−0.821063	+	0.636372i	0.112954	+	0.993600i	$0.463969\pi$
$884$	−0.149659	+	4.62879i	−0.00503357	+	0.155683i
$885$	−23.2939	+	33.3010i	−0.783017	+	1.11940i
$886$	0.102705	−	0.832022i	0.00345046	−	0.0279523i
$887$	−5.36764	+	26.4265i	−0.180228	+	0.887315i	0.783698	+	0.621142i	$0.213331\pi$
$887$	−5.36764	+	26.4265i	−0.180228	+	0.887315i	−0.963925	+	0.266172i	$0.914241\pi$
$888$	−47.0418	+	54.3094i	−1.57862	+	1.82250i
$889$	9.67198	+	3.66260i	0.324388	+	0.122840i
$890$	21.6707	+	18.1839i	0.726404	+	0.609525i
$891$	−10.4409	+	8.79501i	−0.349783	+	0.294644i
$892$	−18.3291	+	15.3800i	−0.613705	+	0.514959i
$893$	76.5281	−	26.7387i	2.56092	−	0.894776i
$894$	−11.3191	+	44.6282i	−0.378567	+	1.49259i
$895$	−7.33487	−	48.9705i	−0.245178	−	1.63690i
$896$	38.7279	−	75.8865i	1.29381	−	2.53519i
$897$	0.388785	−	0.979996i	0.0129812	−	0.0327211i
$898$	−65.9593	+	73.6373i	−2.20109	+	2.45731i
$899$	9.21099	+	8.35853i	0.307204	+	0.278772i
$900$	−0.191334	+	15.9807i	−0.00637781	+	0.532691i
$901$	−1.61091	+	0.658128i	−0.0536671	+	0.0219254i
$902$	−12.7735	−	2.16727i	−0.425311	−	0.0721622i
$903$	22.8586	+	11.0077i	0.760688	+	0.366313i
$904$	−55.9582	+	37.8497i	−1.86114	+	1.25886i
$905$	24.1009	+	15.4088i	0.801141	+	0.512205i
$906$	−53.0899	+	11.3470i	−1.76379	+	0.376979i
$907$	−16.6742	−	7.06506i	−0.553658	−	0.234592i	0.0952568	−	0.995453i	$-0.469633\pi$
$907$	−16.6742	−	7.06506i	−0.553658	−	0.234592i	−0.648915	+	0.760861i	$0.724777\pi$
$908$	29.0056	+	60.6601i	0.962585	+	2.01308i
$909$	20.9503	−	10.3775i	0.694876	−	0.344200i
$910$	26.0000	+	7.23758i	0.861890	+	0.239924i
$911$	−4.11167	+	0.106338i	−0.136226	+	0.00352313i	−0.0939066	−	0.995581i	$-0.529935\pi$
$911$	−4.11167	+	0.106338i	−0.136226	+	0.00352313i	−0.0423190	+	0.999104i	$0.513475\pi$
$912$	−33.5204	+	2.29476i	−1.10997	+	0.0759871i
$913$	−0.753331	+	2.02886i	−0.0249316	+	0.0671454i
$914$	−52.1769	−	27.9162i	−1.72586	−	0.923387i
$915$	−10.6738	−	35.1775i	−0.352865	−	1.16293i
$916$	2.73923	+	3.78050i	0.0905068	+	0.124911i
$917$	5.43042	−	18.1389i	0.179328	−	0.598998i
$918$	−10.1283	−	3.26759i	−0.334283	−	0.107847i
$919$	−2.81548	−	9.40436i	−0.0928741	−	0.310221i	0.898912	−	0.438129i	$-0.144359\pi$
$919$	−2.81548	−	9.40436i	−0.0928741	−	0.310221i	−0.991786	+	0.127908i	$0.959174\pi$
$920$	1.95809	−	2.56039i	0.0645564	−	0.0844137i
$921$	−15.7260	−	29.5882i	−0.518188	−	0.974966i
$922$	31.9374	−	15.0185i	1.05180	−	0.494609i
$923$	−3.05857	+	12.5432i	−0.100674	+	0.412866i
$924$	−6.58830	−	39.4894i	−0.216739	−	1.29910i
$925$	−10.2771	−	10.3437i	−0.337909	−	0.340100i
$926$	78.9882	−	15.5128i	2.59571	−	0.509781i
$927$	−9.23253	+	12.9432i	−0.303236	+	0.425109i
$928$	3.02840	−	1.67100i	0.0994120	−	0.0548532i
$929$	9.09534	+	6.68029i	0.298408	+	0.219173i	0.730933	−	0.682449i	$-0.239085\pi$
$929$	9.09534	+	6.68029i	0.298408	+	0.219173i	−0.432525	+	0.901622i	$0.642377\pi$
$930$	−62.5094	−	36.3197i	−2.04976	−	1.19097i
$931$	−13.1545	+	80.6894i	−0.431121	+	2.64449i
$932$	14.1526	+	74.6096i	0.463583	+	2.44392i
$933$	42.1098	+	18.3021i	1.37861	+	0.599184i
$934$	−75.1395	+	4.86393i	−2.45864	+	0.159153i
$935$	−0.794585	−	2.32226i	−0.0259857	−	0.0759461i
$936$	9.79503	−	14.9237i	0.320161	−	0.487796i
$937$	17.3373	+	44.9047i	0.566384	+	1.46697i	0.859621	+	0.510932i	$0.170699\pi$
$937$	17.3373	+	44.9047i	0.566384	+	1.46697i	−0.293238	+	0.956040i	$0.594733\pi$
$938$	10.2344	+	121.502i	0.334166	+	3.96718i
$939$	40.7712	+	5.14687i	1.33052	+	0.167962i
$940$	−38.0455	+	57.0389i	−1.24091	+	1.86040i
$941$	−40.2298	+	40.4907i	−1.31145	+	1.31996i	−0.395611	+	0.918418i	$0.629467\pi$
$941$	−40.2298	+	40.4907i	−1.31145	+	1.31996i	−0.915842	+	0.401539i	$0.868475\pi$
$942$	−65.8717	−	46.7140i	−2.14622	−	1.52202i
$943$	0.0675753	+	1.49238i	0.00220055	+	0.0485986i
$944$	−28.9191	+	3.38016i	−0.941237	+	0.110015i
$945$	−21.1046	+	34.3258i	−0.686532	+	1.11662i
$946$	12.8374	+	1.50048i	0.417380	+	0.0487847i
$947$	−0.0544594	+	0.764599i	−0.00176969	+	0.0248461i	−0.998281	−	0.0586175i	$-0.981331\pi$
$947$	−0.0544594	+	0.764599i	−0.00176969	+	0.0248461i	0.996511	+	0.0834637i	$0.0265982\pi$
$948$	38.9502	+	32.4376i	1.26504	+	1.05352i
$949$	−8.38873	−	9.36522i	−0.272310	−	0.304008i
$950$	0.183668	−	28.4129i	0.00595899	−	0.921835i
$951$	−18.8606	−	3.12812i	−0.611597	−	0.101436i
$952$	10.7761	−	9.52771i	0.349257	−	0.308795i
$953$	4.81651	−	10.0729i	0.156022	−	0.326292i	−0.809282	−	0.587420i	$-0.800144\pi$
$953$	4.81651	−	10.0729i	0.156022	−	0.326292i	0.965304	+	0.261128i	$0.0840943\pi$
$954$	14.3663	+	2.32798i	0.465125	+	0.0753711i
$955$	−2.72030	+	1.94435i	−0.0880268	+	0.0629178i
$956$	5.80897	+	11.3826i	0.187876	+	0.368138i
$957$	1.47030	−	3.21109i	0.0475281	−	0.103800i
$958$	53.1538	+	69.5037i	1.71732	+	2.24556i
$959$	−20.9389	+	28.8985i	−0.676154	+	0.933181i
$960$	−26.7539	+	23.2186i	−0.863479	+	0.749377i
$961$	−47.1194	+	27.6120i	−1.51998	+	0.890710i
$962$	7.48120	+	34.5371i	0.241204	+	1.11352i
$963$	4.02301	−	3.16613i	0.129640	−	0.102027i
$964$	−5.83552	+	9.25867i	−0.187949	+	0.298202i
$965$	6.82073	−	0.976582i	0.219567	−	0.0314373i
$966$	−6.60179	+	2.62638i	−0.212409	+	0.0845024i
$967$	−44.3989	+	41.3490i	−1.42777	+	1.32969i	−0.564035	+	0.825751i	$0.690752\pi$
$967$	−44.3989	+	41.3490i	−1.42777	+	1.32969i	−0.863737	+	0.503943i	$0.831882\pi$
$968$	16.9683	+	31.2276i	0.545382	+	1.00369i
$969$	11.7199	+	3.70993i	0.376496	+	0.119180i
$970$	9.69542	−	16.3025i	0.311301	−	0.523443i
$971$	15.0702	+	26.1023i	0.483625	+	0.837664i	0.999823	−	0.0188056i	$-0.00598637\pi$
$971$	15.0702	+	26.1023i	0.483625	+	0.837664i	−0.516198	+	0.856469i	$0.672653\pi$
$972$	37.7045	+	43.8471i	1.20937	+	1.40640i
$973$	7.46929	−	12.9372i	0.239454	−	0.414747i
$974$	−29.7446	−	53.0927i	−0.953079	−	1.70120i
$975$	2.87155	+	2.20861i	0.0919631	+	0.0707322i
$976$	13.7540	−	22.4608i	0.440255	−	0.718952i
$977$	−8.76785	−	38.0900i	−0.280508	−	1.21861i	−0.900799	−	0.434236i	$-0.857018\pi$
$977$	−8.76785	−	38.0900i	−0.280508	−	1.21861i	0.620291	−	0.784372i	$-0.287015\pi$
$978$	−3.66763	−	17.7196i	−0.117278	−	0.566609i
$979$	−5.87568	−	7.48058i	−0.187788	−	0.239080i
$980$	−32.2253	−	61.1782i	−1.02940	−	1.95427i
$981$	−9.47873	+	5.81683i	−0.302633	+	0.185717i
$982$	64.0191	−	58.0942i	2.04293	−	1.85386i
$983$	−0.330263	−	51.0905i	−0.0105338	−	1.62953i	−0.585020	−	0.811019i	$-0.698913\pi$
$983$	−0.330263	−	51.0905i	−0.0105338	−	1.62953i	0.574486	−	0.818515i	$-0.305202\pi$
$984$	−3.97727	+	24.9797i	−0.126791	+	0.796324i
$985$	15.3173	+	1.58990i	0.488051	+	0.0506584i
$986$	2.73023	−	0.354953i	0.0869481	−	0.0113040i
$987$	62.9212	−	29.8742i	2.00281	−	0.950906i
$988$	−24.3431	+	37.5382i	−0.774458	+	1.19425i
$989$	−0.144278	−	1.48331i	−0.00458777	−	0.0471664i
$990$	−4.45618	+	20.0379i	−0.141627	+	0.636847i
$991$	−60.8599	+	4.73040i	−1.93328	+	0.150266i	−0.985615	−	0.169008i	$-0.945944\pi$
$991$	−60.8599	+	4.73040i	−1.93328	+	0.150266i	−0.947662	+	0.319274i	$0.896561\pi$
$992$	4.73893	+	23.3312i	0.150461	+	0.740766i
$993$	0.376322	+	36.9861i	0.0119422	+	1.17372i
$994$	75.6300	−	43.0156i	2.39884	−	1.36437i
$995$	45.1352	−	9.47188i	1.43088	−	0.300279i
$996$	8.62644	+	3.10357i	0.273339	+	0.0983404i
$997$	20.8193	−	10.1209i	0.659353	−	0.320534i	−0.0770985	−	0.997023i	$-0.524566\pi$
$997$	20.8193	−	10.1209i	0.659353	−	0.320534i	0.736452	+	0.676490i	$0.236500\pi$
$998$	39.5088	−	53.0695i	1.25063	−	1.67989i
$999$	−52.6445	−	3.50284i	−1.66560	−	0.110825i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.k.a.4.8	✓	12960
729.547	even	243	inner	729.2.k.a.547.8	yes	12960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.k.a.4.8	✓	12960	1.1	even	1	trivial
729.2.k.a.547.8	yes	12960	729.547	even	243	inner

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.k (of order \(243\), degree \(162\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.38931 - 0.0308915i) q^{2} +(0.801520 - 1.53544i) q^{3} +(3.70850 + 0.0959110i) q^{4} +(1.80500 + 0.553120i) q^{5} +(-1.96251 + 3.64387i) q^{6} +(1.52892 - 3.81257i) q^{7} +(-4.08235 - 0.158414i) q^{8} +(-1.71513 - 2.46137i) q^{9} +O(q^{10})\)	\(q+(-2.38931 - 0.0308915i) q^{2} +(0.801520 - 1.53544i) q^{3} +(3.70850 + 0.0959110i) q^{4} +(1.80500 + 0.553120i) q^{5} +(-1.96251 + 3.64387i) q^{6} +(1.52892 - 3.81257i) q^{7} +(-4.08235 - 0.158414i) q^{8} +(-1.71513 - 2.46137i) q^{9} +(-4.29561 - 1.37733i) q^{10} +(1.31849 + 0.749911i) q^{11} +(3.11970 - 5.61729i) q^{12} +(-0.594124 - 1.32979i) q^{13} +(-3.77084 + 9.06215i) q^{14} +(2.29603 - 2.32813i) q^{15} +(2.33954 + 0.121094i) q^{16} +(-0.780299 - 0.354689i) q^{17} +(4.02194 + 5.93394i) q^{18} +(-4.68346 - 6.82866i) q^{19} +(6.64079 + 2.22436i) q^{20} +(-4.62849 - 5.40341i) q^{21} +(-3.12712 - 1.83250i) q^{22} +(-0.130173 + 0.397135i) q^{23} +(-3.51532 + 6.14122i) q^{24} +(-1.18948 - 0.804556i) q^{25} +(1.37846 + 3.19564i) q^{26} +(-5.15398 + 0.660642i) q^{27} +(6.03566 - 13.9922i) q^{28} +(1.13257 - 0.724102i) q^{29} +(-5.55783 + 5.49168i) q^{30} +(2.42367 + 8.92970i) q^{31} +(2.56765 + 0.166209i) q^{32} +(2.20824 - 1.42340i) q^{33} +(1.85342 + 0.871566i) q^{34} +(4.86851 - 6.03601i) q^{35} +(-6.12449 - 9.29247i) q^{36} +(9.96350 + 1.95677i) q^{37} +(10.9793 + 16.4604i) q^{38} +(-2.51802 - 0.153617i) q^{39} +(-7.28103 - 2.54397i) q^{40} +(3.34293 - 1.26590i) q^{41} +(10.8920 + 13.0534i) q^{42} +(-3.26513 + 1.43354i) q^{43} +(4.81770 + 2.90750i) q^{44} +(-1.73438 - 5.39144i) q^{45} +(0.323292 - 0.944855i) q^{46} +(-2.56437 + 9.44812i) q^{47} +(2.06112 - 3.49515i) q^{48} +(-7.13760 - 6.82172i) q^{49} +(2.81719 + 1.95908i) q^{50} +(-1.17003 + 0.913809i) q^{51} +(-2.07576 - 4.98852i) q^{52} +(1.39322 - 1.47673i) q^{53} +(12.3349 - 1.41926i) q^{54} +(1.96509 + 2.08288i) q^{55} +(-6.84556 + 15.3220i) q^{56} +(-14.2389 + 1.71786i) q^{57} +(-2.72842 + 1.69511i) q^{58} +(-12.2534 + 2.07903i) q^{59} +(8.73809 - 8.41364i) q^{60} +(5.36764 - 9.87834i) q^{61} +(-5.51503 - 21.4107i) q^{62} +(-12.0064 + 2.77582i) q^{63} +(-10.8010 - 0.839522i) q^{64} +(-0.336858 - 2.72890i) q^{65} +(-5.32013 + 3.33271i) q^{66} +(11.0282 - 5.71828i) q^{67} +(-2.85972 - 1.39020i) q^{68} +(0.505439 + 0.518184i) q^{69} +(-11.8188 + 14.2715i) q^{70} +(-7.00633 - 5.43031i) q^{71} +(6.61186 + 10.3199i) q^{72} +(8.22018 - 2.63569i) q^{73} +(-23.7454 - 4.98310i) q^{74} +(-2.18874 + 1.18151i) q^{75} +(-16.7137 - 25.7732i) q^{76} +(4.87496 - 3.88029i) q^{77} +(6.01157 + 0.444824i) q^{78} +(-1.47018 + 7.75049i) q^{79} +(4.15589 + 1.51262i) q^{80} +(-3.11665 + 8.44313i) q^{81} +(-8.02638 + 2.92136i) q^{82} +(0.229573 + 1.40820i) q^{83} +(-16.6465 - 20.4824i) q^{84} +(-1.21225 - 1.07181i) q^{85} +(7.84568 - 3.32431i) q^{86} +(-0.204036 - 2.31937i) q^{87} +(-5.26376 - 3.27027i) q^{88} +(-5.80531 - 2.37173i) q^{89} +(3.97742 + 12.9354i) q^{90} +(-5.97830 + 0.231985i) q^{91} +(-0.520836 + 1.46029i) q^{92} +(15.6536 + 3.43595i) q^{93} +(6.41894 - 22.4952i) q^{94} +(-4.67659 - 14.9162i) q^{95} +(2.31323 - 3.80924i) q^{96} +(-0.943214 + 4.09759i) q^{97} +(16.8432 + 16.5197i) q^{98} +(-0.415585 - 4.53149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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