LMFDB - Embedded newform 81.2.g.a.7.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(4,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(54))

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("81.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, 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:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			7.5
Character	$\chi$	$=$	81.7
Dual form			81.2.g.a.58.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.120683 - 0.162105i) q^{2} +(1.25647 + 1.19218i) q^{3} +(0.561893 - 1.87685i) q^{4} +(-0.761396 + 0.500778i) q^{5} +(0.0416250 - 0.347556i) q^{6} +(-0.112573 + 0.119321i) q^{7} +(-0.751874 + 0.273660i) q^{8} +(0.157410 + 2.99587i) q^{9} +(0.173067 + 0.0629911i) q^{10} +(-0.670227 + 0.336601i) q^{11} +(2.94355 - 1.68832i) q^{12} +(-1.39965 - 3.24476i) q^{13} +(0.0329282 + 0.00384876i) q^{14} +(-1.55369 - 0.278512i) q^{15} +(-3.13860 - 2.06429i) q^{16} +(-3.09332 + 2.59561i) q^{17} +(0.466650 - 0.387068i) q^{18} +(1.63194 + 1.36936i) q^{19} +(0.512064 + 1.71041i) q^{20} +(-0.283696 + 0.0157146i) q^{21} +(0.135450 + 0.0680255i) q^{22} +(-5.63041 - 5.96789i) q^{23} +(-1.27096 - 0.552526i) q^{24} +(-1.65145 + 3.82850i) q^{25} +(-0.357079 + 0.618479i) q^{26} +(-3.37383 + 3.95187i) q^{27} +(0.160693 + 0.278329i) q^{28} +(6.53664 - 0.764024i) q^{29} +(0.142355 + 0.285473i) q^{30} +(5.44474 - 1.29043i) q^{31} +(0.137190 + 2.35546i) q^{32} +(-1.24341 - 0.376105i) q^{33} +(0.794074 + 0.188199i) q^{34} +(0.0259597 - 0.147225i) q^{35} +(5.71125 + 1.38792i) q^{36} +(0.783915 + 4.44580i) q^{37} +(0.0250334 - 0.429806i) q^{38} +(2.10972 - 5.74556i) q^{39} +(0.435431 - 0.584886i) q^{40} +(6.53505 - 8.77810i) q^{41} +(0.0367848 + 0.0440923i) q^{42} +(0.201195 - 3.45438i) q^{43} +(0.255154 + 1.44705i) q^{44} +(-1.62012 - 2.20221i) q^{45} +(-0.287932 + 1.63294i) q^{46} +(8.68990 + 2.05954i) q^{47} +(-1.48254 - 6.33549i) q^{48} +(0.405449 + 6.96129i) q^{49} +(0.819923 - 0.194325i) q^{50} +(-6.98109 - 0.426511i) q^{51} +(-6.87639 + 0.803734i) q^{52} +(3.06986 + 5.31715i) q^{53} +(1.04778 + 0.0699940i) q^{54} +(0.341746 - 0.591922i) q^{55} +(0.0519877 - 0.120521i) q^{56} +(0.417952 + 3.66613i) q^{57} +(-0.912715 - 0.967421i) q^{58} +(-2.60584 - 1.30870i) q^{59} +(-1.39573 + 2.75955i) q^{60} +(2.02529 + 6.76493i) q^{61} +(-0.866274 - 0.726890i) q^{62} +(-0.375189 - 0.318472i) q^{63} +(-5.39019 + 4.52290i) q^{64} +(2.69059 + 1.76963i) q^{65} +(0.0890894 + 0.246952i) q^{66} +(-8.82173 - 1.03111i) q^{67} +(3.13345 + 7.26416i) q^{68} +(0.0403837 - 14.2109i) q^{69} +(-0.0269988 + 0.0135593i) q^{70} +(-8.94644 - 3.25624i) q^{71} +(-0.938201 - 2.20944i) q^{72} +(8.28233 - 3.01452i) q^{73} +(0.626083 - 0.663610i) q^{74} +(-6.63926 + 2.84155i) q^{75} +(3.48707 - 2.29348i) q^{76} +(0.0352862 - 0.117864i) q^{77} +(-1.18600 + 0.351395i) q^{78} +(-1.92557 - 2.58649i) q^{79} +3.42347 q^{80} +(-8.95044 + 0.943160i) q^{81} -2.21165 q^{82} +(-10.0492 - 13.4985i) q^{83} +(-0.129913 + 0.541286i) q^{84} +(1.05542 - 3.52535i) q^{85} +(-0.584255 + 0.384271i) q^{86} +(9.12392 + 6.83289i) q^{87} +(0.411812 - 0.436496i) q^{88} +(10.7409 - 3.90935i) q^{89} +(-0.161470 + 0.528400i) q^{90} +(0.544730 + 0.198266i) q^{91} +(-14.3645 + 7.21414i) q^{92} +(8.37955 + 4.86974i) q^{93} +(-0.714861 - 1.65723i) q^{94} +(-1.92830 - 0.225386i) q^{95} +(-2.63576 + 3.12311i) q^{96} +(3.78511 + 2.48950i) q^{97} +(1.07953 - 0.905836i) q^{98} +(-1.11391 - 1.95493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{27}\right)$

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 $

$2$	−0.120683	−	0.162105i	−0.0853358	−	0.114626i	0.757405	−	0.652945i	$-0.226467\pi$
$2$	−0.120683	−	0.162105i	−0.0853358	−	0.114626i	−0.842741	+	0.538319i	$0.819059\pi$
$3$	1.25647	+	1.19218i	0.725421	+	0.688306i
$3$	1.25647	+	1.19218i	0.725421	+	0.688306i
$4$	0.561893	−	1.87685i	0.280946	−	0.938426i
$5$	−0.761396	+	0.500778i	−0.340507	+	0.223955i	−0.708232	−	0.705980i	$-0.750507\pi$
$5$	−0.761396	+	0.500778i	−0.340507	+	0.223955i	0.367725	+	0.929934i	$0.380137\pi$
$6$	0.0416250	−	0.347556i	0.0169933	−	0.141889i
$7$	−0.112573	+	0.119321i	−0.0425487	+	0.0450990i	−0.748298	−	0.663362i	$-0.769129\pi$
$7$	−0.112573	+	0.119321i	−0.0425487	+	0.0450990i	0.705750	+	0.708461i	$0.250610\pi$
$8$	−0.751874	+	0.273660i	−0.265828	+	0.0967534i
$9$	0.157410	+	2.99587i	0.0524701	+	0.998622i
$10$	0.173067	+	0.0629911i	0.0547284	+	0.0199195i
$11$	−0.670227	+	0.336601i	−0.202081	+	0.101489i	−0.546962	−	0.837158i	$-0.684216\pi$
$11$	−0.670227	+	0.336601i	−0.202081	+	0.101489i	0.344881	+	0.938647i	$0.387919\pi$
$12$	2.94355	−	1.68832i	0.849728	−	0.487377i
$13$	−1.39965	−	3.24476i	−0.388194	−	0.899934i	−0.994503	−	0.104705i	$-0.966610\pi$
$13$	−1.39965	−	3.24476i	−0.388194	−	0.899934i	0.606310	−	0.795229i	$-0.292649\pi$
$14$	0.0329282	+	0.00384876i	0.00880044	+	0.00102862i
$15$	−1.55369	−	0.278512i	−0.401160	−	0.0719114i
$16$	−3.13860	−	2.06429i	−0.784651	−	0.516073i
$17$	−3.09332	+	2.59561i	−0.750241	+	0.629527i	−0.935567	−	0.353150i	$-0.885110\pi$
$17$	−3.09332	+	2.59561i	−0.750241	+	0.629527i	0.185326	+	0.982677i	$0.440666\pi$
$18$	0.466650	−	0.387068i	0.109990	−	0.0912327i
$19$	1.63194	+	1.36936i	0.374394	+	0.314154i	0.810497	−	0.585743i	$-0.199197\pi$
$19$	1.63194	+	1.36936i	0.374394	+	0.314154i	−0.436103	+	0.899897i	$0.643642\pi$
$20$	0.512064	+	1.71041i	0.114501	+	0.382460i
$21$	−0.283696	+	0.0157146i	−0.0619076	+	0.00342922i
$22$	0.135450	+	0.0680255i	0.0288780	+	0.0145031i
$23$	−5.63041	−	5.96789i	−1.17402	−	1.24439i	−0.963767	−	0.266744i	$-0.914052\pi$
$23$	−5.63041	−	5.96789i	−1.17402	−	1.24439i	−0.210255	−	0.977647i	$-0.567429\pi$
$24$	−1.27096	−	0.552526i	−0.259433	−	0.112784i
$25$	−1.65145	+	3.82850i	−0.330291	+	0.765700i
$26$	−0.357079	+	0.618479i	−0.0700289	+	0.121294i
$27$	−3.37383	+	3.95187i	−0.649295	+	0.760537i
$28$	0.160693	+	0.278329i	0.0303682	+	0.0525992i
$29$	6.53664	−	0.764024i	1.21382	−	0.141876i	0.515013	−	0.857182i	$-0.327787\pi$
$29$	6.53664	−	0.764024i	1.21382	−	0.141876i	0.698811	+	0.715307i	$0.253713\pi$
$30$	0.142355	+	0.285473i	0.0259904	+	0.0521199i
$31$	5.44474	−	1.29043i	0.977905	−	0.231768i	0.289567	−	0.957158i	$-0.406489\pi$
$31$	5.44474	−	1.29043i	0.977905	−	0.231768i	0.688338	+	0.725390i	$0.258341\pi$
$32$	0.137190	+	2.35546i	0.0242520	+	0.416390i
$33$	−1.24341	−	0.376105i	−0.216449	−	0.0654714i
$34$	0.794074	+	0.188199i	0.136183	+	0.0322759i
$35$	0.0259597	−	0.147225i	0.00438799	−	0.0248855i
$36$	5.71125	+	1.38792i	0.951875	+	0.231320i
$37$	0.783915	+	4.44580i	0.128875	+	0.730885i	0.978931	+	0.204193i	$0.0654569\pi$
$37$	0.783915	+	4.44580i	0.128875	+	0.730885i	−0.850056	+	0.526692i	$0.823432\pi$
$38$	0.0250334	−	0.429806i	0.00406095	−	0.0697237i
$39$	2.10972	−	5.74556i	0.337826	−	0.920027i
$40$	0.435431	−	0.584886i	0.0688478	−	0.0924786i
$41$	6.53505	−	8.77810i	1.02060	−	1.37091i	0.0937035	−	0.995600i	$-0.470129\pi$
$41$	6.53505	−	8.77810i	1.02060	−	1.37091i	0.926900	−	0.375308i	$-0.122463\pi$
$42$	0.0367848	+	0.0440923i	0.00567601	+	0.00680358i
$43$	0.201195	−	3.45438i	0.0306819	−	0.526788i	−0.947593	−	0.319479i	$-0.896492\pi$
$43$	0.201195	−	3.45438i	0.0306819	−	0.526788i	0.978275	−	0.207310i	$-0.0664707\pi$
$44$	0.255154	+	1.44705i	0.0384659	+	0.218151i
$45$	−1.62012	−	2.20221i	−0.241513	−	0.328287i
$46$	−0.287932	+	1.63294i	−0.0424533	+	0.240764i
$47$	8.68990	+	2.05954i	1.26755	+	0.300416i	0.808766	−	0.588131i	$-0.200136\pi$
$47$	8.68990	+	2.05954i	1.26755	+	0.300416i	0.458787	+	0.888546i	$0.348284\pi$
$48$	−1.48254	−	6.33549i	−0.213986	−	0.914450i
$49$	0.405449	+	6.96129i	0.0579213	+	0.994470i
$50$	0.819923	−	0.194325i	0.115955	−	0.0274818i
$51$	−6.98109	−	0.426511i	−0.977547	−	0.0597235i
$52$	−6.87639	+	0.803734i	−0.953583	+	0.111458i
$53$	3.06986	+	5.31715i	0.421677	+	0.730366i	0.996104	−	0.0881898i	$-0.0281082\pi$
$53$	3.06986	+	5.31715i	0.421677	+	0.730366i	−0.574426	+	0.818556i	$0.694775\pi$
$54$	1.04778	+	0.0699940i	0.142585	+	0.00952497i
$55$	0.341746	−	0.591922i	0.0460810	−	0.0798147i
$56$	0.0519877	−	0.120521i	0.00694715	−	0.0161053i
$57$	0.417952	+	3.66613i	0.0553591	+	0.485591i
$58$	−0.912715	−	0.967421i	−0.119845	−	0.127029i
$59$	−2.60584	−	1.30870i	−0.339251	−	0.170378i	0.271014	−	0.962575i	$-0.412641\pi$
$59$	−2.60584	−	1.30870i	−0.339251	−	0.170378i	−0.610265	+	0.792197i	$0.708937\pi$
$60$	−1.39573	+	2.75955i	−0.180188	+	0.356256i
$61$	2.02529	+	6.76493i	0.259311	+	0.866160i	0.984165	+	0.177257i	$0.0567223\pi$
$61$	2.02529	+	6.76493i	0.259311	+	0.866160i	−0.724853	+	0.688903i	$0.758093\pi$
$62$	−0.866274	−	0.726890i	−0.110017	−	0.0923151i
$63$	−0.375189	−	0.318472i	−0.0472694	−	0.0401238i
$64$	−5.39019	+	4.52290i	−0.673774	+	0.565363i
$65$	2.69059	+	1.76963i	0.333727	+	0.219496i
$66$	0.0890894	+	0.246952i	0.0109661	+	0.0303977i
$67$	−8.82173	−	1.03111i	−1.07775	−	0.125970i	−0.441351	−	0.897334i	$-0.645501\pi$
$67$	−8.82173	−	1.03111i	−1.07775	−	0.125970i	−0.636394	+	0.771364i	$0.719575\pi$
$68$	3.13345	+	7.26416i	0.379987	+	0.880909i
$69$	0.0403837	−	14.2109i	0.00486162	−	1.71079i
$70$	−0.0269988	+	0.0135593i	−0.00322698	+	0.00162065i
$71$	−8.94644	−	3.25624i	−1.06175	−	0.386444i	−0.248663	−	0.968590i	$-0.579991\pi$
$71$	−8.94644	−	3.25624i	−1.06175	−	0.386444i	−0.813084	+	0.582146i	$0.802213\pi$
$72$	−0.938201	−	2.20944i	−0.110568	−	0.260385i
$73$	8.28233	−	3.01452i	0.969373	−	0.352823i	0.191673	−	0.981459i	$-0.438609\pi$
$73$	8.28233	−	3.01452i	0.969373	−	0.352823i	0.777700	+	0.628636i	$0.216386\pi$
$74$	0.626083	−	0.663610i	0.0727807	−	0.0771431i
$75$	−6.63926	+	2.84155i	−0.766635	+	0.328113i
$76$	3.48707	−	2.29348i	0.399994	−	0.263080i
$77$	0.0352862	−	0.117864i	0.00402124	−	0.0134319i
$78$	−1.18600	+	0.351395i	−0.134288	+	0.0397876i
$79$	−1.92557	−	2.58649i	−0.216644	−	0.291003i	0.680494	−	0.732754i	$-0.261765\pi$
$79$	−1.92557	−	2.58649i	−0.216644	−	0.291003i	−0.897138	+	0.441750i	$0.854358\pi$
$80$	3.42347			0.382756
$81$	−8.95044	+	0.943160i	−0.994494	+	0.104796i
$82$	−2.21165			−0.244236
$83$	−10.0492	−	13.4985i	−1.10305	−	1.48165i	−0.859061	−	0.511873i	$-0.828952\pi$
$83$	−10.0492	−	13.4985i	−1.10305	−	1.48165i	−0.243987	−	0.969778i	$-0.578456\pi$
$84$	−0.129913	+	0.541286i	−0.0141747	+	0.0590592i
$85$	1.05542	−	3.52535i	0.114477	−	0.382378i
$86$	−0.584255	+	0.384271i	−0.0630018	+	0.0414370i
$87$	9.12392	+	6.83289i	0.978187	+	0.732563i
$88$	0.411812	−	0.436496i	0.0438993	−	0.0465306i
$89$	10.7409	−	3.90935i	1.13853	−	0.414390i	0.297146	−	0.954832i	$-0.403965\pi$
$89$	10.7409	−	3.90935i	1.13853	−	0.414390i	0.841382	+	0.540442i	$0.181743\pi$
$90$	−0.161470	+	0.528400i	−0.0170205	+	0.0556982i
$91$	0.544730	+	0.198266i	0.0571033	+	0.0207839i
$92$	−14.3645	+	7.21414i	−1.49761	+	0.752126i
$93$	8.37955	+	4.86974i	0.868919	+	0.504969i
$94$	−0.714861	−	1.65723i	−0.0737322	−	0.170931i
$95$	−1.92830	−	0.225386i	−0.197840	−	0.0231241i
$96$	−2.63576	+	3.12311i	−0.269011	+	0.318751i
$97$	3.78511	+	2.48950i	0.384319	+	0.252771i	0.726937	−	0.686704i	$-0.240943\pi$
$97$	3.78511	+	2.48950i	0.384319	+	0.252771i	−0.342618	+	0.939475i	$0.611314\pi$
$98$	1.07953	−	0.905836i	0.109049	−	0.0915032i
$99$	−1.11391	−	1.95493i	−0.111952	−	0.196478i
$100$	6.25759	+	5.25074i	0.625759	+	0.525074i
$101$	−0.660124	−	2.20497i	−0.0656848	−	0.219402i	0.918845	−	0.394618i	$-0.129123\pi$
$101$	−0.660124	−	2.20497i	−0.0656848	−	0.219402i	−0.984530	+	0.175215i	$0.943938\pi$
$102$	0.773359	+	1.18314i	0.0765740	+	0.117149i
$103$	2.32565	+	1.16798i	0.229153	+	0.115085i	0.559671	−	0.828715i	$-0.310927\pi$
$103$	2.32565	+	1.16798i	0.229153	+	0.115085i	−0.330519	+	0.943799i	$0.607224\pi$
$104$	1.94032	+	2.05662i	0.190264	+	0.201668i
$105$	0.208136	−	0.154034i	0.0203120	−	0.0150322i
$106$	0.491459	−	1.13933i	0.0477347	−	0.110662i
$107$	−5.97720	+	10.3528i	−0.577837	+	1.00084i	0.417890	+	0.908498i	$0.362770\pi$
$107$	−5.97720	+	10.3528i	−0.577837	+	1.00084i	−0.995727	+	0.0923460i	$0.970563\pi$
$108$	5.52133	+	8.55271i	0.531291	+	0.822985i
$109$	−9.06553	−	15.7020i	−0.868320	−	1.50397i	−0.863712	−	0.503985i	$-0.831867\pi$
$109$	−9.06553	−	15.7020i	−0.868320	−	1.50397i	−0.00460743	−	0.999989i	$-0.501467\pi$
$110$	−0.137197	+	0.0160360i	−0.0130812	+	0.00152897i
$111$	−4.31524	+	6.52056i	−0.409584	+	0.618904i
$112$	0.599636	−	0.142116i	0.0566603	−	0.0134287i
$113$	0.691929	+	11.8800i	0.0650912	+	1.11757i	0.859817	+	0.510603i	$0.170578\pi$
$113$	0.691929	+	11.8800i	0.0650912	+	1.11757i	−0.794725	+	0.606969i	$0.792385\pi$
$114$	0.543860	−	0.510192i	0.0509372	−	0.0477839i
$115$	7.27556	+	1.72434i	0.678450	+	0.160796i
$116$	2.23893	−	12.6976i	0.207880	−	1.17894i
$117$	9.50055	−	4.70393i	0.878326	−	0.434879i
$118$	0.102333	+	0.580358i	0.00942050	+	0.0534263i
$119$	0.0385160	−	0.661294i	0.00353075	−	0.0606207i
$120$	1.24439	−	0.215776i	0.113597	−	0.0196976i
$121$	−6.23284	+	8.37216i	−0.566622	+	0.761105i
$122$	0.852214	−	1.14472i	0.0771558	−	0.103638i
$123$	18.6761	−	3.23841i	1.68397	−	0.291998i
$124$	0.637419	−	10.9441i	0.0572419	−	0.982806i
$125$	−1.45106	−	8.22939i	−0.129787	−	0.736059i
$126$	−0.00634713	+	0.0992545i	−0.000565447	+	0.00884229i
$127$	2.53378	−	14.3698i	0.224837	−	1.27511i	−0.638160	−	0.769903i	$-0.720304\pi$
$127$	2.53378	−	14.3698i	0.224837	−	1.27511i	0.862997	−	0.505209i	$-0.168585\pi$
$128$	5.97539	+	1.41619i	0.528155	+	0.125175i
$129$	4.37104	−	4.10045i	0.384849	−	0.361025i
$130$	−0.0378422	−	0.649725i	−0.00331898	−	0.0569846i
$131$	−6.48742	+	1.53755i	−0.566808	+	0.134336i	−0.504022	−	0.863691i	$-0.668147\pi$
$131$	−6.48742	+	1.53755i	−0.566808	+	0.134336i	−0.0627866	+	0.998027i	$0.519999\pi$
$132$	−1.40455	+	2.12236i	−0.122251	+	0.184728i
$133$	−0.347107	+	0.0405710i	−0.0300980	+	0.00351795i
$134$	0.897484	+	1.55449i	0.0775308	+	0.134287i
$135$	0.589817	−	4.69848i	0.0507634	−	0.404381i
$136$	1.61548	−	2.79809i	0.138526	−	0.239934i
$137$	−5.79364	+	13.4312i	−0.494984	+	1.14750i	0.469397	+	0.882987i	$0.344471\pi$
$137$	−5.79364	+	13.4312i	−0.494984	+	1.14750i	−0.964381	+	0.264516i	$0.914788\pi$
$138$	−2.30854	+	1.70847i	−0.196516	+	0.145435i
$139$	2.27516	+	2.41153i	0.192976	+	0.204543i	0.816636	−	0.577153i	$-0.195836\pi$
$139$	2.27516	+	2.41153i	0.192976	+	0.204543i	−0.623660	+	0.781696i	$0.714355\pi$
$140$	−0.261732	−	0.131447i	−0.0221204	−	0.0111093i
$141$	8.46321	+	12.9477i	0.712731	+	1.09039i
$142$	0.551830	+	1.84324i	0.0463085	+	0.154681i
$143$	2.03027	+	1.70360i	0.169780	+	0.142462i
$144$	5.69030	−	9.72778i	0.474191	−	0.810649i
$145$	−4.59437	+	3.85513i	−0.381542	+	0.320151i
$146$	−1.48821	−	0.978809i	−0.123165	−	0.0810068i
$147$	−7.78969	+	9.22999i	−0.642482	+	0.761277i
$148$	8.78459	+	1.02677i	0.722089	+	0.0844000i
$149$	1.94162	+	4.50117i	0.159063	+	0.368750i	0.979046	−	0.203638i	$-0.0652764\pi$
$149$	1.94162	+	4.50117i	0.159063	+	0.368750i	−0.819983	+	0.572388i	$0.806017\pi$
$150$	1.26188	+	0.733334i	0.103032	+	0.0598764i
$151$	14.4384	−	7.25124i	1.17498	−	0.590098i	0.249309	−	0.968424i	$-0.419797\pi$
$151$	14.4384	−	7.25124i	1.17498	−	0.590098i	0.925672	+	0.378326i	$0.123500\pi$
$152$	−1.60176	−	0.582992i	−0.129920	−	0.0472869i
$153$	−8.26301	−	8.85861i	−0.668025	−	0.716176i
$154$	−0.0233649	+	0.00850413i	−0.00188280	+	0.000685282i
$155$	−3.49939	+	3.70914i	−0.281078	+	0.297925i
$156$	−9.59814	−	7.18803i	−0.768466	−	0.575503i
$157$	−10.3296	+	6.79388i	−0.824391	+	0.542211i	−0.890173	−	0.455623i	$-0.849416\pi$
$157$	−10.3296	+	6.79388i	−0.824391	+	0.542211i	0.0657814	+	0.997834i	$0.479046\pi$
$158$	−0.186901	+	0.624292i	−0.0148690	+	0.0496660i
$159$	−2.48183	+	10.3406i	−0.196822	+	0.820066i
$160$	−1.28402	−	1.72474i	−0.101511	−	0.136352i
$161$	1.34593			0.106074
$162$	1.23306	+	1.33709i	0.0968782	+	0.105052i
$163$	−12.1435			−0.951151			−0.475576	−	0.879675i	$-0.657760\pi$
$163$	−12.1435			−0.951151			−0.475576	+	0.879675i	$0.657760\pi$
$164$	−12.8032	−	17.1977i	−0.999762	−	1.34291i
$165$	1.13507	−	0.336306i	0.0883650	−	0.0261814i
$166$	−0.975404	+	3.25808i	−0.0757061	+	0.252876i
$167$	−2.12309	+	1.39638i	−0.164289	+	0.108055i	−0.628991	−	0.777412i	$-0.716532\pi$
$167$	−2.12309	+	1.39638i	−0.164289	+	0.108055i	0.464702	+	0.885467i	$0.346162\pi$
$168$	0.209004	−	0.0894517i	0.0161250	−	0.00690135i
$169$	0.351711	−	0.372792i	0.0270547	−	0.0286763i
$170$	−0.698851	+	0.254361i	−0.0535994	+	0.0195086i
$171$	−3.84555	+	5.10464i	−0.294076	+	0.390362i
$172$	−6.37031	−	2.31860i	−0.485732	−	0.176792i
$173$	−8.70104	+	4.36982i	−0.661528	+	0.332232i	−0.747689	−	0.664050i	$-0.768836\pi$
$173$	−8.70104	+	4.36982i	−0.661528	+	0.332232i	0.0861609	+	0.996281i	$0.472540\pi$
$174$	0.00654637	−	2.30365i	0.000496279	−	0.174639i
$175$	−0.270910	−	0.628040i	−0.0204789	−	0.0474753i
$176$	2.79842	+	0.327088i	0.210939	+	0.0246552i
$177$	−1.71394	−	4.75096i	−0.128827	−	0.357104i
$178$	−1.92997	−	1.26936i	−0.144657	−	0.0951425i
$179$	−2.85196	+	2.39308i	−0.213165	+	0.178867i	−0.743118	−	0.669160i	$-0.766654\pi$
$179$	−2.85196	+	2.39308i	−0.213165	+	0.178867i	0.529953	+	0.848027i	$0.322210\pi$
$180$	−5.04356	+	1.80331i	−0.375925	+	0.134411i
$181$	−5.59668	−	4.69618i	−0.415998	−	0.349064i	0.410640	−	0.911798i	$-0.365305\pi$
$181$	−5.59668	−	4.69618i	−0.415998	−	0.349064i	−0.826638	+	0.562734i	$0.809750\pi$
$182$	−0.0335998	−	0.112231i	−0.00249058	−	0.00831912i
$183$	−5.52031	+	10.9144i	−0.408073	+	0.806816i
$184$	5.86654	+	2.94628i	0.432487	+	0.217203i
$185$	−2.82323	−	2.99245i	−0.207568	−	0.220009i
$186$	−0.221859	−	1.94607i	−0.0162675	−	0.142693i
$187$	1.19955	−	2.78086i	0.0877195	−	0.203357i
$188$	8.74825	−	15.1524i	0.638032	−	1.10510i
$189$	−0.0917357	−	0.847443i	−0.00667279	−	0.0616424i
$190$	0.196177	+	0.339789i	0.0142322	+	0.0246509i
$191$	20.6359	−	2.41199i	1.49316	−	0.174525i	0.670012	−	0.742351i	$-0.266289\pi$
$191$	20.6359	−	2.41199i	1.49316	−	0.174525i	0.823149	+	0.567825i	$0.192215\pi$
$192$	−12.1647	−	0.743205i	−0.877912	−	0.0536362i
$193$	−3.39877	+	0.805522i	−0.244649	+	0.0579828i	−0.351111	−	0.936334i	$-0.614196\pi$
$193$	−3.39877	+	0.805522i	−0.244649	+	0.0579828i	0.106462	+	0.994317i	$0.466048\pi$
$194$	−0.0532360	−	0.914028i	−0.00382213	−	0.0656234i
$195$	1.27092	+	5.43116i	0.0910123	+	0.388933i
$196$	13.2931	+	3.15053i	0.949510	+	0.225038i
$197$	−0.205736	+	1.16678i	−0.0146580	+	0.0831299i	−0.991259	−	0.131928i	$-0.957883\pi$
$197$	−0.205736	+	1.16678i	−0.0146580	+	0.0831299i	0.976601	+	0.215058i	$0.0689942\pi$
$198$	−0.182474	+	0.416498i	−0.0129679	+	0.0295992i
$199$	−0.191285	−	1.08483i	−0.0135599	−	0.0769018i	0.977277	−	0.211967i	$-0.0679868\pi$
$199$	−0.191285	−	1.08483i	−0.0135599	−	0.0769018i	−0.990837	+	0.135065i	$0.956876\pi$
$200$	0.193979	−	3.33049i	0.0137164	−	0.235501i
$201$	−9.85492	−	11.8127i	−0.695113	−	0.833200i
$202$	−0.277771	+	0.373112i	−0.0195439	+	0.0262521i
$203$	−0.644688	+	0.865966i	−0.0452482	+	0.0607789i
$204$	−4.72312	+	12.8628i	−0.330684	+	0.900577i
$205$	−0.579884	+	9.95622i	−0.0405008	+	0.695373i
$206$	−0.0913296	−	0.517956i	−0.00636324	−	0.0360877i
$207$	16.9927	−	17.8074i	1.18108	−	1.23770i
$208$	−2.30518	+	13.0733i	−0.159835	+	0.906470i
$209$	−1.55470	−	0.368471i	−0.107541	−	0.0254877i
$210$	−0.0500882	−	0.0151507i	−0.00345642	−	0.00104549i
$211$	0.871220	+	14.9583i	0.0599773	+	1.02977i	0.885274	+	0.465070i	$0.153971\pi$
$211$	0.871220	+	14.9583i	0.0599773	+	1.02977i	−0.825297	+	0.564700i	$0.808992\pi$
$212$	11.7044	−	2.77400i	0.803864	−	0.190519i
$213$	−7.35887	−	14.7571i	−0.504221	−	1.01114i
$214$	2.39959	−	0.280472i	0.164033	−	0.0191727i
$215$	1.57669	+	2.73091i	0.107529	+	0.186246i
$216$	1.45523	−	3.89459i	0.0990161	−	0.264993i
$217$	−0.458958	+	0.794939i	−0.0311561	+	0.0539640i
$218$	−1.45132	+	3.36453i	−0.0982956	+	0.227875i
$219$	14.0003	+	6.08639i	0.946053	+	0.411280i
$220$	−0.918925	−	0.974003i	−0.0619539	−	0.0656673i
$221$	12.7517	+	6.40414i	0.857772	+	0.430789i
$222$	1.57779	−	0.0873979i	0.105895	−	0.00586577i
$223$	−1.46299	−	4.88672i	−0.0979689	−	0.327239i	0.894929	−	0.446209i	$-0.147226\pi$
$223$	−1.46299	−	4.88672i	−0.0979689	−	0.327239i	−0.992898	+	0.118970i	$0.962041\pi$
$224$	−0.296499	−	0.248792i	−0.0198107	−	0.0166231i
$225$	−11.7296	−	4.34489i	−0.781975	−	0.289659i
$226$	1.84230	−	1.54588i	0.122548	−	0.102830i
$227$	14.0054	+	9.21152i	0.929573	+	0.611390i	0.921416	−	0.388577i	$-0.127033\pi$
$227$	14.0054	+	9.21152i	0.929573	+	0.611390i	0.00815667	+	0.999967i	$0.497404\pi$
$228$	7.11563	+	1.27554i	0.471244	+	0.0844745i
$229$	−16.0140	−	1.87177i	−1.05824	−	0.123690i	−0.430870	−	0.902414i	$-0.641793\pi$
$229$	−16.0140	−	1.87177i	−1.05824	−	0.123690i	−0.627366	+	0.778724i	$0.715867\pi$
$230$	−0.598512	−	1.38751i	−0.0394647	−	0.0914896i
$231$	0.184851	−	0.106025i	0.0121623	−	0.00697592i
$232$	−4.70565	+	2.36327i	−0.308941	+	0.155156i
$233$	9.85526	+	3.58702i	0.645639	+	0.234993i	0.644024	−	0.765005i	$-0.277264\pi$
$233$	9.85526	+	3.58702i	0.645639	+	0.234993i	0.00161517	+	0.999999i	$0.499486\pi$
$234$	−1.90909	−	0.972406i	−0.124801	−	0.0635682i
$235$	−7.64784	+	2.78358i	−0.498890	+	0.181581i
$236$	−3.92044	+	4.15542i	−0.255199	+	0.270495i
$237$	0.664152	−	5.54547i	0.0431413	−	0.360217i
$238$	−0.111848	+	0.0735633i	−0.00725000	+	0.00476840i
$239$	−0.0155911	+	0.0520778i	−0.00100850	+	0.00336863i	−0.958492	−	0.285118i	$-0.907967\pi$
$239$	−0.0155911	+	0.0520778i	−0.00100850	+	0.00336863i	0.957484	+	0.288487i	$0.0931522\pi$
$240$	4.30148	+	4.08140i	0.277659	+	0.263453i
$241$	7.10393	+	9.54223i	0.457604	+	0.614669i	0.969712	−	0.244252i	$-0.0785425\pi$
$241$	7.10393	+	9.54223i	0.457604	+	0.614669i	−0.512108	+	0.858921i	$0.671135\pi$
$242$	2.10937			0.135596
$243$	−12.3703	−	9.48550i	−0.793558	−	0.608495i
$244$	13.8348			0.885680
$245$	−3.79477	−	5.09726i	−0.242439	−	0.325652i
$246$	−2.77886	−	2.63668i	−0.177174	−	0.168109i
$247$	2.15910	−	7.21190i	0.137380	−	0.458882i
$248$	−3.74062	+	2.46025i	−0.237530	+	0.156226i
$249$	3.46610	−	28.9409i	0.219655	−	1.83406i
$250$	−1.15891	+	1.22837i	−0.0732959	+	0.0776891i
$251$	4.18194	−	1.52210i	0.263961	−	0.0960741i	−0.206649	−	0.978415i	$-0.566256\pi$
$251$	4.18194	−	1.52210i	0.263961	−	0.0960741i	0.470611	+	0.882341i	$0.344034\pi$
$252$	−0.808542	+	0.525228i	−0.0509334	+	0.0330862i
$253$	5.78245	+	2.10464i	0.363540	+	0.132318i
$254$	−2.63521	+	1.32345i	−0.165348	+	0.0830407i
$255$	5.52896	−	3.17123i	0.346237	−	0.198590i
$256$	5.08239	+	11.7823i	0.317649	+	0.736394i
$257$	15.3697	+	1.79646i	0.958735	+	0.112060i	0.581045	−	0.813872i	$-0.302644\pi$
$257$	15.3697	+	1.79646i	0.958735	+	0.112060i	0.377691	+	0.925932i	$0.376718\pi$
$258$	−1.19222	−	0.213715i	−0.0742241	−	0.0133053i
$259$	−0.618724	−	0.406941i	−0.0384456	−	0.0252861i
$260$	4.83316	−	4.05550i	0.299740	−	0.251512i
$261$	3.31785	+	19.4626i	0.205370	+	1.20471i
$262$	1.03217	+	0.866090i	0.0637674	+	0.0535072i
$263$	−4.11141	−	13.7331i	−0.253520	−	0.846817i	−0.986102	−	0.166138i	$-0.946870\pi$
$263$	−4.11141	−	13.7331i	−0.253520	−	0.846817i	0.732582	−	0.680679i	$-0.238315\pi$
$264$	1.03781	−	0.0574868i	0.0638728	−	0.00353807i
$265$	−5.00009	−	2.51114i	−0.307153	−	0.154258i
$266$	0.0484667	+	0.0513717i	0.00297168	+	0.00314980i
$267$	18.1562	+	7.89307i	1.11114	+	0.483048i
$268$	−6.89211	+	15.9777i	−0.421003	+	0.975994i
$269$	−0.910225	+	1.57656i	−0.0554974	+	0.0961243i	−0.892439	−	0.451167i	$-0.851008\pi$
$269$	−0.910225	+	1.57656i	−0.0554974	+	0.0961243i	0.836942	+	0.547292i	$0.184341\pi$
$270$	−0.832830	+	0.471414i	−0.0506844	+	0.0286894i
$271$	6.79318	+	11.7661i	0.412656	+	0.714742i	0.995179	−	0.0980726i	$-0.0312677\pi$
$271$	6.79318	+	11.7661i	0.412656	+	0.714742i	−0.582523	+	0.812814i	$0.697934\pi$
$272$	15.0668	−	1.76106i	0.913559	−	0.106780i
$273$	0.448066	+	0.898531i	0.0271182	+	0.0543816i
$274$	2.87646	−	0.681734i	0.173773	−	0.0411851i
$275$	−0.181827	−	3.12184i	−0.0109646	−	0.188254i
$276$	−26.6491	−	8.06080i	−1.60409	−	0.485203i
$277$	−21.2963	−	5.04731i	−1.27957	−	0.303263i	−0.466027	−	0.884770i	$-0.654315\pi$
$277$	−21.2963	−	5.04731i	−1.27957	−	0.303263i	−0.813541	+	0.581507i	$0.802463\pi$
$278$	0.116349	−	0.659846i	0.00697813	−	0.0395749i
$279$	4.72301	+	16.1086i	0.282759	+	0.964397i
$280$	0.0207711	+	0.117799i	0.00124131	+	0.00703981i
$281$	1.46889	−	25.2199i	0.0876268	−	1.50449i	−0.612497	−	0.790473i	$-0.709835\pi$
$281$	1.46889	−	25.2199i	0.0876268	−	1.50449i	0.700124	−	0.714021i	$-0.253128\pi$
$282$	1.07752	−	2.93450i	0.0641656	−	0.174747i
$283$	13.3658	−	17.9534i	0.794516	−	1.06722i	−0.201626	−	0.979463i	$-0.564623\pi$
$283$	13.3658	−	17.9534i	0.794516	−	1.06722i	0.996142	−	0.0877573i	$-0.0279700\pi$
$284$	−11.1384	+	14.9615i	−0.660943	+	0.887801i
$285$	−2.15415	−	2.58208i	−0.127601	−	0.152949i
$286$	0.0311435	−	0.534714i	0.00184156	−	0.0316183i
$287$	0.311737	+	1.76795i	0.0184012	+	0.104359i
$288$	−7.03505	+	0.781776i	−0.414544	+	0.0460666i
$289$	−0.120543	+	0.683633i	−0.00709076	+	0.0402137i
$290$	1.17940	+	0.279523i	0.0692568	+	0.0164142i
$291$	1.78792	+	7.64051i	0.104810	+	0.447894i
$292$	−1.00403	−	17.2385i	−0.0587564	−	1.00881i
$293$	−12.7408	+	3.01963i	−0.744326	+	0.176408i	−0.585244	−	0.810857i	$-0.699001\pi$
$293$	−12.7408	+	3.01963i	−0.744326	+	0.176408i	−0.159081	+	0.987265i	$0.550853\pi$
$294$	2.43632	+	0.148847i	0.142089	+	0.00868095i
$295$	2.63944	−	0.308506i	0.153674	−	0.0179619i
$296$	−1.80604	−	3.12816i	−0.104974	−	0.181820i
$297$	0.931035	−	3.78428i	0.0540241	−	0.219586i
$298$	0.495345	−	0.857962i	0.0286945	−	0.0497004i
$299$	−11.4837	+	26.6223i	−0.664122	+	1.53961i
$300$	1.60261	+	14.0575i	0.0925268	+	0.811613i
$301$	0.389530	+	0.412878i	0.0224522	+	0.0237979i
$302$	−2.91794	−	1.46544i	−0.167908	−	0.0843268i
$303$	1.79930	−	3.55745i	0.103367	−	0.204370i
$304$	−2.29526	−	7.66670i	−0.131642	−	0.439715i
$305$	−4.92977	−	4.13657i	−0.282278	−	0.236859i
$306$	−0.438824	+	2.40856i	−0.0250859	+	0.137688i
$307$	11.2563	−	9.44513i	0.642429	−	0.539062i	−0.262334	−	0.964977i	$-0.584492\pi$
$307$	11.2563	−	9.44513i	0.642429	−	0.539062i	0.904763	+	0.425915i	$0.140048\pi$
$308$	−0.201387	−	0.132454i	−0.0114751	−	0.00754727i
$309$	1.52965	+	4.24012i	0.0870186	+	0.241212i
$310$	1.02359	+	0.119640i	0.0581359	+	0.00679511i
$311$	−13.2219	−	30.6518i	−0.749745	−	1.73810i	−0.671301	−	0.741185i	$-0.734264\pi$
$311$	−13.2219	−	30.6518i	−0.749745	−	1.73810i	−0.0784433	−	0.996919i	$-0.524995\pi$
$312$	−0.0139168	+	4.89729i	−0.000787883	+	0.277254i
$313$	−20.4283	+	10.2595i	−1.15467	+	0.579899i	−0.919901	−	0.392152i	$-0.871731\pi$
$313$	−20.4283	+	10.2595i	−1.15467	+	0.579899i	−0.234773	+	0.972050i	$0.575435\pi$
$314$	2.34793	+	0.854577i	0.132501	+	0.0482266i
$315$	0.445152	+	0.0545971i	0.0250815	+	0.00307620i
$316$	−5.93643	+	2.16069i	−0.333950	+	0.121548i
$317$	−12.8911	+	13.6638i	−0.724039	+	0.767437i	−0.979946	−	0.199265i	$-0.936145\pi$
$317$	−12.8911	+	13.6638i	−0.724039	+	0.767437i	0.255907	+	0.966702i	$0.417626\pi$
$318$	1.97579	−	0.845621i	0.110797	−	0.0474201i
$319$	−4.12386	+	2.71231i	−0.230892	+	0.151860i
$320$	1.83910	−	6.14301i	0.102809	−	0.343405i
$321$	−19.8526	+	5.88205i	−1.10806	+	0.328304i
$322$	−0.162431	−	0.218182i	−0.00905191	−	0.0121588i
$323$	−8.60246			−0.478654
$324$	−3.25902	+	17.3286i	−0.181056	+	0.962701i
$325$	14.7340			0.817296
$326$	1.46551	+	1.96853i	0.0811673	+	0.109027i
$327$	7.32905	−	30.5367i	0.405297	−	1.68868i
$328$	−2.51132	+	8.38841i	−0.138665	+	0.463172i
$329$	−1.22400	+	0.805036i	−0.0674812	+	0.0443831i
$330$	−0.191501	−	0.143415i	−0.0105418	−	0.00789471i
$331$	4.06203	−	4.30550i	0.223270	−	0.236652i	−0.606050	−	0.795427i	$-0.707247\pi$
$331$	4.06203	−	4.30550i	0.223270	−	0.236652i	0.829320	+	0.558775i	$0.188728\pi$
$332$	−30.9813	+	11.2763i	−1.70032	+	0.618865i
$333$	−13.1956	+	3.04832i	−0.723116	+	0.167047i
$334$	0.482581	+	0.175645i	0.0264056	+	0.00961087i
$335$	7.23319	−	3.63264i	0.395191	−	0.198473i
$336$	0.922850	+	0.536310i	0.0503456	+	0.0292581i
$337$	−4.80653	−	11.1428i	−0.261828	−	0.606986i	0.735696	−	0.677312i	$-0.236855\pi$
$337$	−4.80653	−	11.1428i	−0.261828	−	0.606986i	−0.997524	+	0.0703261i	$0.977596\pi$
$338$	−0.102877	−	0.0120246i	−0.00559579	−	0.000654054i
$339$	−13.2937	+	15.7517i	−0.722013	+	0.855513i
$340$	−6.02353	−	3.96174i	−0.326672	−	0.214856i
$341$	−3.21485	+	2.69758i	−0.174094	+	0.146082i
$342$	1.29158	+	0.00734073i	0.0698408	+	0.000396941i
$343$	−1.75592	−	1.47339i	−0.0948108	−	0.0795557i
$344$	0.794052	+	2.65232i	0.0428124	+	0.143004i
$345$	7.08577	+	10.8404i	0.381485	+	0.583625i
$346$	1.75844	+	0.883122i	0.0945343	+	0.0474769i
$347$	1.67386	+	1.77419i	0.0898577	+	0.0952436i	0.770742	−	0.637148i	$-0.219886\pi$
$347$	1.67386	+	1.77419i	0.0898577	+	0.0952436i	−0.680884	+	0.732391i	$0.738404\pi$
$348$	17.9510	−	13.2849i	0.962274	−	0.712145i
$349$	9.10243	−	21.1018i	0.487242	−	1.12955i	−0.480360	−	0.877071i	$-0.659494\pi$
$349$	9.10243	−	21.1018i	0.487242	−	1.12955i	0.967602	−	0.252482i	$-0.0812468\pi$
$350$	−0.0691144	+	0.119710i	−0.00369432	+	0.00639875i
$351$	17.5450	+	5.41604i	0.936485	+	0.289087i
$352$	−0.884797	−	1.53251i	−0.0471598	−	0.0816833i
$353$	22.9990	−	2.68819i	1.22411	−	0.143078i	0.520625	−	0.853786i	$-0.325699\pi$
$353$	22.9990	−	2.68819i	1.22411	−	0.143078i	0.703488	+	0.710708i	$0.251625\pi$
$354$	−0.563314	+	0.851199i	−0.0299398	+	0.0452407i
$355$	8.44244	−	2.00089i	0.448078	−	0.106196i
$356$	−1.30207	−	22.3556i	−0.0690094	−	1.18485i
$357$	0.836776	−	0.784975i	0.0442869	−	0.0415453i
$358$	0.732114	+	0.173514i	0.0386934	+	0.00917051i
$359$	−5.43706	+	30.8351i	−0.286957	+	1.62741i	0.411254	+	0.911521i	$0.365091\pi$
$359$	−5.43706	+	30.8351i	−0.286957	+	1.62741i	−0.698211	+	0.715892i	$0.746020\pi$
$360$	1.82078	+	1.21243i	0.0959636	+	0.0639006i
$361$	−2.51123	−	14.2419i	−0.132170	−	0.749574i
$362$	−0.0858508	+	1.47400i	−0.00451222	+	0.0774718i
$363$	−17.8125	+	3.08865i	−0.934912	+	0.162112i
$364$	0.678195	−	0.910975i	0.0355471	−	0.0477480i
$365$	−4.79653	+	6.44285i	−0.251062	+	0.337234i
$366$	2.43549	−	0.422310i	0.127305	−	0.0220745i
$367$	−0.446242	+	7.66168i	−0.0232937	+	0.399937i	0.966429	+	0.256935i	$0.0827125\pi$
$367$	−0.446242	+	7.66168i	−0.0232937	+	0.399937i	−0.989722	+	0.143002i	$0.954324\pi$
$368$	5.35217	+	30.3537i	0.279001	+	1.58229i
$369$	27.3267	+	18.1964i	1.42257	+	0.947266i
$370$	−0.144376	+	0.818799i	−0.00750577	+	0.0425673i
$371$	−0.980030	−	0.232271i	−0.0508806	−	0.0120589i
$372$	13.8482	−	12.9909i	0.717995	−	0.673548i
$373$	−1.50909	−	25.9100i	−0.0781376	−	1.34157i	−0.778438	−	0.627722i	$-0.783988\pi$
$373$	−1.50909	−	25.9100i	−0.0781376	−	1.34157i	0.700300	−	0.713849i	$-0.253050\pi$
$374$	−0.595558	+	0.141150i	−0.0307955	+	0.00729868i
$375$	7.98771	−	12.0699i	0.412483	−	0.623286i
$376$	−7.09733	+	0.829559i	−0.366017	+	0.0427812i
$377$	−11.6281	−	20.1405i	−0.598878	−	1.03729i
$378$	−0.126304	+	0.117143i	−0.00649639	+	0.00602518i
$379$	−13.2851	+	23.0104i	−0.682408	+	1.18197i	0.291835	+	0.956469i	$0.405734\pi$
$379$	−13.2851	+	23.0104i	−0.682408	+	1.18197i	−0.974244	+	0.225497i	$0.927599\pi$
$380$	−1.50652	+	3.49250i	−0.0772827	+	0.179161i
$381$	20.3150	−	15.0344i	1.04077	−	0.770236i
$382$	−2.88140	−	3.05411i	−0.147425	−	0.156262i
$383$	−2.40889	−	1.20979i	−0.123089	−	0.0618175i	0.386189	−	0.922420i	$-0.373791\pi$
$383$	−2.40889	−	1.20979i	−0.123089	−	0.0618175i	−0.509278	+	0.860602i	$0.670087\pi$
$384$	5.81952	+	8.90315i	0.296976	+	0.454337i
$385$	0.0321570	+	0.107412i	0.00163887	+	0.00547422i
$386$	0.540753	+	0.453746i	0.0275236	+	0.0230951i
$387$	10.3805	+	0.0589980i	0.527673	+	0.00299904i
$388$	6.79926	−	5.70525i	0.345180	−	0.289640i
$389$	19.7963	+	13.0202i	1.00371	+	0.660152i	0.941185	−	0.337892i	$-0.109714\pi$
$389$	19.7963	+	13.0202i	1.00371	+	0.660152i	0.0625269	+	0.998043i	$0.480084\pi$
$390$	0.727042	−	0.861471i	0.0368152	−	0.0436223i
$391$	32.9070	+	3.84627i	1.66418	+	0.194514i
$392$	−2.20987	−	5.12306i	−0.111615	−	0.258754i
$393$	−9.98425	−	5.80230i	−0.503639	−	0.292687i
$394$	0.213971	−	0.107460i	0.0107797	−	0.00541377i
$395$	2.76138	+	1.00506i	0.138940	+	0.0505702i
$396$	−4.29501	+	0.992188i	−0.215832	+	0.0498593i
$397$	−0.102939	+	0.0374669i	−0.00516638	+	0.00188041i	−0.344602	−	0.938749i	$-0.611986\pi$
$397$	−0.102939	+	0.0374669i	−0.00516638	+	0.00188041i	0.339436	+	0.940629i	$0.389764\pi$
$398$	−0.152773	+	0.161929i	−0.00765780	+	0.00811679i
$399$	−0.484496	−	0.362838i	−0.0242551	−	0.0181646i
$400$	13.0864	−	8.60706i	0.654320	−	0.430353i
$401$	2.42258	−	8.09197i	0.120978	−	0.404094i	−0.875952	−	0.482399i	$-0.839766\pi$
$401$	2.42258	−	8.09197i	0.120978	−	0.404094i	0.996929	+	0.0783050i	$0.0249508\pi$
$402$	−0.725573	+	3.02312i	−0.0361883	+	0.150780i
$403$	−11.8079	−	15.8607i	−0.588192	−	0.790079i
$404$	−4.50932			−0.224347
$405$	6.34252	−	5.20031i	0.315162	−	0.258405i
$406$	0.218181			0.0108281
$407$	−2.02186	−	2.71583i	−0.100220	−	0.134619i
$408$	5.36562	−	1.58976i	0.265638	−	0.0787049i
$409$	1.44994	−	4.84314i	0.0716949	−	0.239478i	−0.914630	−	0.404293i	$-0.867518\pi$
$409$	1.44994	−	4.84314i	0.0716949	−	0.239478i	0.986324	+	0.164815i	$0.0527028\pi$
$410$	1.68394	−	1.10755i	0.0831639	−	0.0546978i
$411$	−23.2919	+	9.96874i	−1.14890	+	0.491722i
$412$	3.49890	−	3.70861i	0.172378	−	0.182710i
$413$	0.449503	−	0.163606i	0.0221186	−	0.00805050i
$414$	−4.93741	−	0.605564i	−0.242660	−	0.0297619i
$415$	14.4112	+	5.24525i	0.707418	+	0.257479i
$416$	7.45088	−	3.74197i	0.365309	−	0.183465i
$417$	−0.0163184	+	5.74240i	−0.000799114	+	0.281206i
$418$	0.127895	+	0.296494i	0.00625555	+	0.0145020i
$419$	−12.6886	−	1.48309i	−0.619879	−	0.0724534i	−0.199644	−	0.979869i	$-0.563978\pi$
$419$	−12.6886	−	1.48309i	−0.619879	−	0.0724534i	−0.420235	+	0.907415i	$0.638052\pi$
$420$	−0.172149	−	0.477191i	−0.00840002	−	0.0232845i
$421$	15.2120	+	10.0051i	0.741388	+	0.487618i	0.863154	−	0.504940i	$-0.168486\pi$
$421$	15.2120	+	10.0051i	0.741388	+	0.487618i	−0.121767	+	0.992559i	$0.538856\pi$
$422$	2.31968	−	1.94644i	0.112920	−	0.0947512i
$423$	−4.80224	+	26.3580i	−0.233493	+	1.28157i
$424$	−3.76324	−	3.15773i	−0.182759	−	0.153353i
$425$	−4.82880	−	16.1293i	−0.234231	−	0.782386i
$426$	−1.50412	+	2.97385i	−0.0728749	+	0.144083i
$427$	−1.03519	−	0.519892i	−0.0500963	−	0.0251593i
$428$	16.0721	+	17.0355i	0.776877	+	0.823441i
$429$	0.519967	+	4.56097i	0.0251042	+	0.220206i
$430$	0.252415	−	0.585164i	0.0121725	−	0.0282191i
$431$	−11.5675	+	20.0355i	−0.557188	+	0.965077i	0.440542	+	0.897732i	$0.354786\pi$
$431$	−11.5675	+	20.0355i	−0.557188	+	0.965077i	−0.997730	+	0.0673455i	$0.978547\pi$
$432$	18.7469	−	5.43876i	0.901962	−	0.261672i
$433$	16.7531	+	29.0173i	0.805104	+	1.39448i	0.916221	+	0.400674i	$0.131224\pi$
$433$	16.7531	+	29.0173i	0.805104	+	1.39448i	−0.111116	+	0.993807i	$0.535443\pi$
$434$	0.184252	−	0.0215360i	0.00884440	−	0.00103376i
$435$	−10.3687	−	0.633477i	−0.497140	−	0.0303729i
$436$	−34.5641	+	8.19184i	−1.65532	+	0.392318i
$437$	−1.01631	−	17.4493i	−0.0486166	−	0.834715i
$438$	−0.702963	−	3.00405i	−0.0335889	−	0.143539i
$439$	−30.8003	−	7.29981i	−1.47002	−	0.348401i	−0.583888	−	0.811834i	$-0.698469\pi$
$439$	−30.8003	−	7.29981i	−1.47002	−	0.348401i	−0.886132	+	0.463433i	$0.846617\pi$
$440$	−0.0949649	+	0.538573i	−0.00452727	+	0.0256755i
$441$	−20.7913	+	2.31045i	−0.990061	+	0.110021i
$442$	−0.500767	−	2.83999i	−0.0238191	−	0.135085i
$443$	1.31468	−	22.5722i	0.0624623	−	1.07244i	−0.810843	−	0.585263i	$-0.800991\pi$
$443$	1.31468	−	22.5722i	0.0624623	−	1.07244i	0.873306	−	0.487173i	$-0.161972\pi$
$444$	9.81343	+	11.7629i	0.465725	+	0.558243i
$445$	−6.22033	+	8.35535i	−0.294872	+	0.396082i
$446$	−0.615606	+	0.826902i	−0.0291498	+	0.0391550i
$447$	−2.92664	+	7.97032i	−0.138425	+	0.376983i
$448$	0.0671150	−	1.15232i	0.00317088	−	0.0544420i
$449$	−3.12921	−	17.7466i	−0.147677	−	0.837515i	−0.965179	−	0.261590i	$-0.915753\pi$
$449$	−3.12921	−	17.7466i	−0.147677	−	0.837515i	0.817503	−	0.575925i	$-0.195358\pi$
$450$	0.711237	+	2.42579i	0.0335281	+	0.114353i
$451$	−1.42525	+	8.08302i	−0.0671126	+	0.380615i
$452$	22.6857	+	5.37661i	1.06705	+	0.252895i
$453$	26.7862	+	8.10226i	1.25852	+	0.380677i
$454$	−0.196981	−	3.38203i	−0.00924477	−	0.158727i
$455$	−0.514043	+	0.121830i	−0.0240987	+	0.00571150i
$456$	−1.31752	−	2.64209i	−0.0616985	−	0.123727i
$457$	23.4000	−	2.73507i	1.09461	−	0.127941i	0.450426	−	0.892814i	$-0.351272\pi$
$457$	23.4000	−	2.73507i	1.09461	−	0.127941i	0.644181	+	0.764873i	$0.277198\pi$
$458$	1.62920	+	2.82185i	0.0761274	+	0.131856i
$459$	0.178876	−	20.9815i	0.00834921	−	0.979335i
$460$	7.32442	−	12.6863i	0.341503	−	0.591500i
$461$	−15.9112	+	36.8862i	−0.741056	+	1.71796i	−0.0460709	+	0.998938i	$0.514670\pi$
$461$	−15.9112	+	36.8862i	−0.741056	+	1.71796i	−0.694985	+	0.719024i	$0.744589\pi$
$462$	−0.0394956	−	0.0171700i	−0.00183750	−	0.000798822i
$463$	7.53656	+	7.98829i	0.350254	+	0.371247i	0.878416	−	0.477896i	$-0.158600\pi$
$463$	7.53656	+	7.98829i	0.350254	+	0.371247i	−0.528163	+	0.849143i	$0.677119\pi$
$464$	−22.0931	−	11.0956i	−1.02565	−	0.515099i
$465$	−8.81882	+	0.488496i	−0.408963	+	0.0226535i
$466$	−0.607887	−	2.03048i	−0.0281598	−	0.0940603i
$467$	−1.29116	−	1.08341i	−0.0597479	−	0.0501344i	0.612425	−	0.790529i	$-0.290194\pi$
$467$	−1.29116	−	1.08341i	−0.0597479	−	0.0501344i	−0.672173	+	0.740395i	$0.734639\pi$
$468$	−3.49029	−	20.4742i	−0.161339	−	0.946421i
$469$	1.11612	−	0.936540i	0.0515378	−	0.0432454i
$470$	1.37420	+	0.903825i	0.0633871	+	0.0416903i
$471$	−21.0783	−	3.77847i	−0.971237	−	0.174103i
$472$	2.31740	+	0.270865i	0.106667	+	0.0124676i
$473$	1.02790	+	2.38294i	0.0472629	+	0.109568i
$474$	−0.979104	+	0.561582i	−0.0449717	+	0.0257943i
$475$	−7.93769	+	3.98646i	−0.364206	+	0.182911i
$476$	−1.21951	−	0.443865i	−0.0558961	−	0.0203445i
$477$	−15.4462	+	10.0339i	−0.707235	+	0.459419i
$478$	0.0103237	−	0.00375751i	0.000472194	−	0.000171864i
$479$	13.6490	−	14.4671i	0.623640	−	0.661020i	−0.336127	−	0.941817i	$-0.609117\pi$
$479$	13.6490	−	14.4671i	0.623640	−	0.661020i	0.959767	+	0.280797i	$0.0905987\pi$
$480$	0.442872	−	3.69785i	0.0202143	−	0.168783i
$481$	13.3283	−	8.76619i	0.607720	−	0.399704i
$482$	0.689524	−	2.30317i	0.0314070	−	0.104907i
$483$	1.69111	+	1.60459i	0.0769482	+	0.0730113i
$484$	12.2111	+	16.4024i	0.555051	+	0.745562i
$485$	−4.12866			−0.187473
$486$	−0.0447608	+	3.15004i	−0.00203039	+	0.142889i
$487$	−16.9386			−0.767563			−0.383782	−	0.923424i	$-0.625378\pi$
$487$	−16.9386			−0.767563			−0.383782	+	0.923424i	$0.625378\pi$
$488$	−3.37405	−	4.53213i	−0.152736	−	0.205160i
$489$	−15.2579	−	14.4772i	−0.689985	−	0.654683i
$490$	−0.368330	+	1.23031i	−0.0166394	+	0.0555796i
$491$	28.7372	−	18.9008i	1.29689	−	0.852980i	0.301941	−	0.953327i	$-0.402365\pi$
$491$	28.7372	−	18.9008i	1.29689	−	0.852980i	0.994953	+	0.100346i	$0.0319951\pi$
$492$	4.41597	−	36.8720i	0.199087	−	1.66232i
$493$	−18.2368	+	19.3299i	−0.821346	+	0.870576i
$494$	−1.42965	+	0.520352i	−0.0643232	+	0.0234117i
$495$	1.82711	+	0.930651i	0.0821226	+	0.0418297i
$496$	−19.7527	−	7.18940i	−0.886923	−	0.322814i
$497$	1.39567	−	0.700930i	0.0626042	−	0.0314410i
$498$	−5.10978	+	2.93080i	−0.228975	+	0.131332i
$499$	6.96828	+	16.1543i	0.311943	+	0.723165i	0.999997	−	0.00249447i	$-0.000794016\pi$
$499$	6.96828	+	16.1543i	0.311943	+	0.723165i	−0.688054	+	0.725660i	$0.741535\pi$
$500$	−16.2607	−	1.90060i	−0.727200	−	0.0849975i
$501$	−4.33232	−	0.776605i	−0.193554	−	0.0346961i
$502$	−0.751430	−	0.494223i	−0.0335379	−	0.0220583i
$503$	17.6438	−	14.8049i	0.786697	−	0.660117i	−0.158229	−	0.987402i	$-0.550578\pi$
$503$	17.6438	−	14.8049i	0.786697	−	0.660117i	0.944925	+	0.327286i	$0.106134\pi$
$504$	0.369248	+	0.136777i	0.0164476	+	0.00609253i
$505$	1.60682	+	1.34828i	0.0715023	+	0.0599976i
$506$	−0.356670	−	1.19136i	−0.0158559	−	0.0529625i
$507$	0.886349	−	0.0490971i	0.0393641	−	0.00218048i
$508$	−25.5463	−	12.8298i	−1.13343	−	0.569231i
$509$	21.9775	+	23.2948i	0.974134	+	1.03252i	0.999461	+	0.0328429i	$0.0104561\pi$
$509$	21.9775	+	23.2948i	0.974134	+	1.03252i	−0.0253261	+	0.999679i	$0.508062\pi$
$510$	−1.18133	−	0.513561i	−0.0523100	−	0.0227409i
$511$	−0.572674	+	1.32761i	−0.0253336	+	0.0587299i
$512$	7.43754	−	12.8822i	0.328696	−	0.569318i
$513$	−10.9174	+	1.82922i	−0.482017	+	0.0807618i
$514$	−1.56365	−	2.70831i	−0.0689695	−	0.119459i
$515$	−2.35564	+	0.275335i	−0.103802	+	0.0121327i
$516$	−5.23988	−	10.5078i	−0.230673	−	0.462581i
$517$	−6.51745	+	1.54466i	−0.286637	+	0.0679343i
$518$	0.00870211	+	0.149409i	0.000382349	+	0.00656468i
$519$	−16.1422	−	4.88267i	−0.708563	−	0.214326i
$520$	−2.50727	−	0.594233i	−0.109951	−	0.0260588i
$521$	0.436835	−	2.47742i	0.0191381	−	0.108538i	−0.973742	−	0.227653i	$-0.926895\pi$
$521$	0.436835	−	2.47742i	0.0191381	−	0.108538i	0.992880	+	0.119116i	$0.0380059\pi$
$522$	2.75459	−	2.88665i	0.120565	−	0.126345i
$523$	4.83329	+	27.4110i	0.211345	+	1.19860i	0.887137	+	0.461506i	$0.152691\pi$
$523$	4.83329	+	27.4110i	0.211345	+	1.19860i	−0.675792	+	0.737092i	$0.736198\pi$
$524$	−0.759485	+	13.0399i	−0.0331783	+	0.569649i
$525$	0.408348	−	1.11208i	0.0178218	−	0.0485353i
$526$	−1.73003	+	2.32383i	−0.0754328	+	0.101324i
$527$	−13.4929	+	18.1241i	−0.587760	+	0.789499i
$528$	3.12617	+	3.74720i	0.136049	+	0.163076i
$529$	−2.57682	+	44.2423i	−0.112036	+	1.92358i
$530$	0.196357	+	1.11359i	0.00852919	+	0.0483714i
$531$	3.51051	−	8.01274i	0.152343	−	0.347723i
$532$	−0.118891	+	0.674265i	−0.00515458	+	0.0292331i
$533$	−37.6296	−	8.91838i	−1.62992	−	0.386298i
$534$	−0.911631	−	3.89577i	−0.0394501	−	0.168587i
$535$	−0.633446	−	10.8758i	−0.0273862	−	0.470204i
$536$	6.91500	−	1.63889i	0.298683	−	0.0707891i
$537$	−6.43637	−	0.393231i	−0.277750	−	0.0169692i
$538$	0.365417	−	0.0427112i	0.0157543	−	0.00184141i
$539$	−2.61492	−	4.52917i	−0.112633	−	0.195085i
$540$	−8.48694	−	3.74704i	−0.365220	−	0.161247i
$541$	3.23851	−	5.60926i	0.139234	−	0.241161i	−0.787973	−	0.615710i	$-0.788869\pi$
$541$	3.23851	−	5.60926i	0.139234	−	0.241161i	0.927207	+	0.374549i	$0.122203\pi$
$542$	1.08753	−	2.52118i	0.0467135	−	0.108294i
$543$	−1.43335	−	12.5728i	−0.0615109	−	0.539552i
$544$	−6.53822	−	6.93010i	−0.280324	−	0.297126i
$545$	14.7657	+	7.41559i	0.632491	+	0.317649i
$546$	0.0915828	−	0.181072i	0.00391938	−	0.00774915i
$547$	−4.41664	−	14.7526i	−0.188842	−	0.630776i	−0.999006	−	0.0445731i	$-0.985807\pi$
$547$	−4.41664	−	14.7526i	−0.188842	−	0.630776i	0.810164	−	0.586203i	$-0.199378\pi$
$548$	21.9529	+	18.4207i	0.937783	+	0.786893i
$549$	−19.9480	+	7.13236i	−0.851361	+	0.304402i
$550$	−0.484125	+	0.406229i	−0.0206431	+	0.0173217i
$551$	11.7137	+	7.70419i	0.499019	+	0.328210i
$552$	3.85859	+	10.6959i	0.164233	+	0.455247i
$553$	0.525391	+	0.0614094i	0.0223419	+	0.00261139i
$554$	1.75190	+	4.06137i	0.0744312	+	0.172551i
$555$	0.0202494	−	7.12571i	0.000859538	−	0.302469i
$556$	5.80447	−	2.91512i	0.246165	−	0.123628i
$557$	21.2492	+	7.73409i	0.900359	+	0.327704i	0.750397	−	0.660988i	$-0.229862\pi$
$557$	21.2492	+	7.73409i	0.900359	+	0.327704i	0.149963	+	0.988692i	$0.452085\pi$
$558$	2.04131	−	2.70966i	0.0864154	−	0.114709i
$559$	−11.4902	+	4.18210i	−0.485985	+	0.176884i
$560$	−0.385392	+	0.408491i	−0.0162858	+	0.0172619i
$561$	4.82248	−	2.06398i	0.203605	−	0.0871412i
$562$	−4.26556	+	2.80550i	−0.179932	+	0.118343i
$563$	−6.80463	+	22.7291i	−0.286781	+	0.957916i	0.686274	+	0.727343i	$0.259245\pi$
$563$	−6.80463	+	22.7291i	−0.286781	+	0.957916i	−0.973055	+	0.230573i	$0.925940\pi$
$564$	29.0563	−	8.60899i	1.22349	−	0.362504i
$565$	−6.47606	−	8.69885i	−0.272450	−	0.365963i
$566$	−4.52338			−0.190132
$567$	0.895043	−	1.17415i	0.0375883	−	0.0493096i
$568$	7.61770			0.319632
$569$	−0.377798	−	0.507471i	−0.0158381	−	0.0212743i	0.794134	−	0.607743i	$-0.207925\pi$
$569$	−0.377798	−	0.507471i	−0.0158381	−	0.0212743i	−0.809972	+	0.586469i	$0.800518\pi$
$570$	−0.158600	+	0.660812i	−0.00664302	+	0.0276784i
$571$	−11.4987	+	38.4084i	−0.481207	+	1.60734i	0.280795	+	0.959768i	$0.409402\pi$
$571$	−11.4987	+	38.4084i	−0.481207	+	1.60734i	−0.762002	+	0.647575i	$0.775783\pi$
$572$	4.33820	−	2.85328i	0.181389	−	0.119302i
$573$	28.8038	+	21.5711i	1.20330	+	0.901147i
$574$	0.248973	−	0.263895i	0.0103919	−	0.0110148i
$575$	32.1464	−	11.7003i	1.34060	−	0.487938i
$576$	−14.3985	−	15.4363i	−0.599937	−	0.643181i
$577$	15.7332	+	5.72640i	0.654980	+	0.238393i	0.648068	−	0.761583i	$-0.275577\pi$
$577$	15.7332	+	5.72640i	0.654980	+	0.238393i	0.00691246	+	0.999976i	$0.497800\pi$
$578$	0.125368	−	0.0629622i	0.00521463	−	0.00261888i
$579$	−5.23076	−	3.03983i	−0.217383	−	0.126331i
$580$	4.65397	+	10.7891i	0.193246	+	0.447994i
$581$	2.74193	+	0.320485i	0.113754	+	0.0132960i
$582$	1.02280	−	1.21191i	0.0423963	−	0.0502353i
$583$	−3.84726	−	2.53038i	−0.159337	−	0.104798i
$584$	−5.40231	+	4.53308i	−0.223549	+	0.187580i
$585$	−4.87805	+	8.33922i	−0.201683	+	0.344784i
$586$	2.02710	+	1.70094i	0.0837386	+	0.0702650i
$587$	−4.72396	−	15.7791i	−0.194979	−	0.651274i	−0.998436	−	0.0559115i	$-0.982194\pi$
$587$	−4.72396	−	15.7791i	−0.194979	−	0.651274i	0.803457	−	0.595363i	$-0.202992\pi$
$588$	12.9464	+	19.8064i	0.533899	+	0.816800i
$589$	10.6526	+	5.34993i	0.438932	+	0.220440i
$590$	−0.368547	−	0.390636i	−0.0151728	−	0.0160823i
$591$	−1.64952	+	1.22075i	−0.0678521	+	0.0502149i
$592$	6.71703	−	15.5718i	0.276068	−	0.639998i
$593$	20.1750	−	34.9441i	0.828487	−	1.43498i	−0.0707373	−	0.997495i	$-0.522535\pi$
$593$	20.1750	−	34.9441i	0.828487	−	1.43498i	0.899225	−	0.437487i	$-0.144131\pi$
$594$	−0.725813	+	0.305773i	−0.0297805	+	0.0125460i
$595$	0.301836	+	0.522795i	0.0123741	+	0.0214325i
$596$	9.53902	−	1.11495i	0.390733	−	0.0456702i
$597$	1.05297	−	1.59110i	0.0430954	−	0.0651195i
$598$	5.70151	−	1.35128i	0.233152	−	0.0552581i
$599$	−0.327503	−	5.62300i	−0.0133814	−	0.229750i	−0.998368	−	0.0571162i	$-0.981809\pi$
$599$	−0.327503	−	5.62300i	−0.0133814	−	0.229750i	0.984986	−	0.172633i	$-0.0552276\pi$
$600$	4.21427	−	3.95338i	0.172047	−	0.161396i
$601$	16.6314	+	3.94172i	0.678410	+	0.160786i	0.555355	−	0.831614i	$-0.312582\pi$
$601$	16.6314	+	3.94172i	0.678410	+	0.160786i	0.123056	+	0.992400i	$0.460731\pi$
$602$	0.0199201	−	0.112972i	0.000811882	−	0.00460441i
$603$	1.70044	−	26.5910i	0.0692475	−	1.08287i
$604$	−5.49667	−	31.1732i	−0.223656	−	1.26842i
$605$	0.553067	−	9.49580i	0.0224854	−	0.386059i
$606$	−0.793827	+	0.137648i	−0.0322470	+	0.00559158i
$607$	10.8231	−	14.5380i	0.439297	−	0.590079i	−0.526242	−	0.850335i	$-0.676400\pi$
$607$	10.8231	−	14.5380i	0.439297	−	0.590079i	0.965540	+	0.260256i	$0.0838069\pi$
$608$	−3.00159	+	4.03184i	−0.121731	+	0.163513i
$609$	−1.84242	+	0.319472i	−0.0746584	+	0.0129457i
$610$	−0.0756207	+	1.29836i	−0.00306179	+	0.0525689i
$611$	−5.48012	−	31.0793i	−0.221702	−	1.25733i
$612$	−21.2692	+	10.5309i	−0.859758	+	0.425685i
$613$	3.85172	−	21.8442i	0.155570	−	0.882279i	−0.802694	−	0.596392i	$-0.796601\pi$
$613$	3.85172	−	21.8442i	0.155570	−	0.882279i	0.958263	−	0.285887i	$-0.0922883\pi$
$614$	−2.88955	−	0.684836i	−0.116613	−	0.0276377i
$615$	−12.5982	+	11.8183i	−0.508009	+	0.476561i
$616$	0.00572390	+	0.0982755i	0.000230622	+	0.00395963i
$617$	9.76840	−	2.31515i	0.393261	−	0.0932046i	−0.0292277	−	0.999573i	$-0.509305\pi$
$617$	9.76840	−	2.31515i	0.393261	−	0.0932046i	0.422489	+	0.906368i	$0.361157\pi$
$618$	0.502745	−	0.759675i	0.0202234	−	0.0305586i
$619$	19.8020	−	2.31452i	0.795910	−	0.0930285i	0.291588	−	0.956544i	$-0.405817\pi$
$619$	19.8020	−	2.31452i	0.795910	−	0.0930285i	0.504322	+	0.863516i	$0.331742\pi$
$620$	4.99522	+	8.65197i	0.200613	+	0.347472i
$621$	42.5804	−	2.11596i	1.70869	−	0.0849105i
$622$	−3.37316	+	5.84249i	−0.135252	+	0.234263i
$623$	−0.742667	+	1.72169i	−0.0297543	+	0.0689783i
$624$	−18.4821	+	13.6780i	−0.739877	+	0.547557i
$625$	−9.08048	−	9.62475i	−0.363219	−	0.384990i
$626$	4.12846	+	2.07339i	0.165006	+	0.0828693i
$627$	−1.51414	−	2.31646i	−0.0604691	−	0.0925103i
$628$	6.94699	+	23.2046i	0.277215	+	0.925962i
$629$	−13.9644	−	11.7176i	−0.556799	−	0.467210i
$630$	−0.0448718	−	0.0787505i	−0.00178774	−	0.00313750i
$631$	1.55588	−	1.30554i	0.0619385	−	0.0519726i	−0.611293	−	0.791404i	$-0.709350\pi$
$631$	1.55588	−	1.30554i	0.0619385	−	0.0519726i	0.673231	+	0.739432i	$0.264906\pi$
$632$	2.15561	+	1.41777i	0.0857455	+	0.0563957i
$633$	−16.7383	+	19.8332i	−0.665288	+	0.788299i
$634$	3.77072	+	0.440734i	0.149755	+	0.0175038i
$635$	5.26686	+	12.2100i	0.209009	+	0.484538i
$636$	18.0133	+	10.4684i	0.714275	+	0.415098i
$637$	22.0202	−	11.0590i	0.872473	−	0.438172i
$638$	0.937360	+	0.341171i	0.0371105	+	0.0135071i
$639$	8.34700	−	27.3149i	0.330202	−	1.08056i
$640$	−5.25884	+	1.91406i	−0.207874	+	0.0756599i
$641$	−18.3587	+	19.4590i	−0.725123	+	0.768586i	−0.980131	−	0.198354i	$-0.936441\pi$
$641$	−18.3587	+	19.4590i	−0.725123	+	0.768586i	0.255007	+	0.966939i	$0.417922\pi$
$642$	3.34938	+	2.50835i	0.132189	+	0.0989965i
$643$	7.31393	−	4.81045i	0.288433	−	0.189706i	−0.397044	−	0.917800i	$-0.629964\pi$
$643$	7.31393	−	4.81045i	0.288433	−	0.189706i	0.685477	+	0.728094i	$0.259594\pi$
$644$	0.756267	−	2.52611i	0.0298011	−	0.0995426i
$645$	−1.27468	+	5.31099i	−0.0501904	+	0.209120i
$646$	1.03817	+	1.39451i	0.0408463	+	0.0548661i
$647$	1.73387			0.0681653			0.0340827	−	0.999419i	$-0.489149\pi$
$647$	1.73387			0.0681653			0.0340827	+	0.999419i	$0.489149\pi$
$648$	6.47150	−	3.15852i	0.254225	−	0.124078i
$649$	2.18701			0.0858477
$650$	−1.77815	−	2.38846i	−0.0697446	−	0.0936833i
$651$	−1.52438	+	0.451652i	−0.0597450	+	0.0177016i
$652$	−6.82333	+	22.7915i	−0.267222	+	0.892585i
$653$	−21.6103	+	14.2133i	−0.845678	+	0.556211i	−0.896777	−	0.442482i	$-0.854098\pi$
$653$	−21.6103	+	14.2133i	−0.845678	+	0.556211i	0.0510991	+	0.998694i	$0.483728\pi$
$654$	−5.83466	+	2.49718i	−0.228153	+	0.0976476i
$655$	4.16953	−	4.41944i	0.162917	−	0.172682i
$656$	−38.6315	+	14.0607i	−1.50831	+	0.548979i
$657$	10.3348	+	24.3382i	0.403200	+	0.949525i
$658$	0.278217	+	0.101263i	0.0108460	+	0.00394763i
$659$	−6.95554	+	3.49320i	−0.270949	+	0.136076i	−0.579087	−	0.815266i	$-0.696591\pi$
$659$	−6.95554	+	3.49320i	−0.270949	+	0.136076i	0.308137	+	0.951342i	$0.400294\pi$
$660$	0.00659091	−	2.31933i	0.000256551	−	0.0902796i
$661$	3.09964	+	7.18577i	0.120562	+	0.279494i	0.967800	−	0.251719i	$-0.0809958\pi$
$661$	3.09964	+	7.18577i	0.120562	+	0.279494i	−0.847239	+	0.531213i	$0.821737\pi$
$662$	−1.18816	−	0.138877i	−0.0461793	−	0.00539759i
$663$	8.38717	+	23.2489i	0.325731	+	0.902912i
$664$	11.2498	+	7.39909i	0.436576	+	0.287140i
$665$	0.243969	−	0.204714i	0.00946070	−	0.00793847i
$666$	2.08664	+	1.77120i	0.0808556	+	0.0686328i
$667$	−41.3636	−	34.7082i	−1.60161	−	1.34391i
$668$	1.42784	+	4.76933i	0.0552450	+	0.184531i
$669$	3.98766	−	7.88414i	0.154172	−	0.304818i
$670$	−1.46180	−	0.734141i	−0.0564741	−	0.0283623i
$671$	−3.63448	−	3.85232i	−0.140308	−	0.148717i
$672$	−0.0759354	−	0.666079i	−0.00292927	−	0.0256946i
$673$	2.50537	−	5.80809i	0.0965748	−	0.223886i	−0.863079	−	0.505068i	$-0.831467\pi$
$673$	2.50537	−	5.80809i	0.0965748	−	0.223886i	0.959654	+	0.281183i	$0.0907266\pi$
$674$	−1.22624	+	2.12391i	−0.0472330	+	0.0818099i
$675$	−9.55798	−	19.4430i	−0.367887	−	0.748363i
$676$	−0.502052	−	0.869580i	−0.0193097	−	0.0334454i
$677$	−24.4993	+	2.86355i	−0.941583	+	0.110055i	−0.573015	−	0.819545i	$-0.694226\pi$
$677$	−24.4993	+	2.86355i	−0.941583	+	0.110055i	−0.368569	+	0.929600i	$0.620152\pi$
$678$	4.15775	+	0.254019i	0.159677	+	0.00975553i
$679$	−0.723152	+	0.171390i	−0.0277520	+	0.00657735i
$680$	0.171203	+	2.93945i	0.00656535	+	0.112723i
$681$	6.61554	+	28.2710i	0.253508	+	1.08335i
$682$	0.825272	+	0.195593i	0.0316013	+	0.00748964i
$683$	−3.77494	+	21.4087i	−0.144444	+	0.819183i	0.823368	+	0.567508i	$0.192092\pi$
$683$	−3.77494	+	21.4087i	−0.144444	+	0.819183i	−0.967812	+	0.251675i	$0.919019\pi$
$684$	7.41987	+	10.0858i	0.283706	+	0.385640i
$685$	−2.31478	−	13.1278i	−0.0884433	−	0.501587i
$686$	−0.0269351	+	0.462458i	−0.00102839	+	0.0176567i
$687$	−17.8896	−	21.4434i	−0.682530	−	0.818117i
$688$	−7.76232	+	10.4266i	−0.295936	+	0.397511i
$689$	12.9561	−	17.4031i	0.493589	−	0.663005i
$690$	0.902150	−	2.45689i	0.0343443	−	0.0935322i
$691$	2.82508	−	48.5047i	0.107471	−	1.84520i	−0.327609	−	0.944813i	$-0.606243\pi$
$691$	2.82508	−	48.5047i	0.107471	−	1.84520i	0.435080	−	0.900392i	$-0.356720\pi$
$692$	3.31247	+	18.7859i	0.125921	+	0.714134i
$693$	0.358660	+	0.0871598i	0.0136244	+	0.00331093i
$694$	0.0855992	−	0.485457i	0.00324930	−	0.0184277i
$695$	−2.93994	−	0.696778i	−0.111518	−	0.0264303i
$696$	−8.72993	−	2.64062i	−0.330907	−	0.100093i
$697$	2.56946	+	44.1159i	0.0973252	+	1.67101i
$698$	−4.51923	+	1.07108i	−0.171055	+	0.0405408i
$699$	8.10641	+	16.2562i	0.306613	+	0.614866i
$700$	−1.33096	+	0.155567i	−0.0503055	+	0.00587988i
$701$	−12.9938	−	22.5060i	−0.490770	−	0.850039i	0.509174	−	0.860664i	$-0.329951\pi$
$701$	−12.9938	−	22.5060i	−0.490770	−	0.850039i	−0.999944	+	0.0106253i	$0.996618\pi$
$702$	−1.23942	−	3.49777i	−0.0467789	−	0.132015i
$703$	−4.80861	+	8.32876i	−0.181360	+	0.314125i
$704$	2.09024	−	4.84571i	0.0787788	−	0.182630i
$705$	−12.9278	−	5.62012i	−0.486888	−	0.211666i
$706$	−3.21136	−	3.40384i	−0.120861	−	0.128105i
$707$	0.337411	+	0.169454i	0.0126896	+	0.00637297i
$708$	−9.87990	+	0.547272i	−0.371309	+	0.0205677i
$709$	−10.4008	−	34.7411i	−0.390610	−	1.30473i	−0.896849	−	0.442336i	$-0.854150\pi$
$709$	−10.4008	−	34.7411i	−0.390610	−	1.30473i	0.506239	−	0.862393i	$-0.331035\pi$
$710$	−1.34322	−	1.12709i	−0.0504100	−	0.0422990i
$711$	7.44569	−	6.17590i	0.279235	−	0.231615i
$712$	−7.00594	+	5.87868i	−0.262559	+	0.220313i
$713$	−38.3573	−	25.2280i	−1.43649	−	0.944795i
$714$	−0.228233	−	0.0409128i	−0.00854142	−	0.00153112i
$715$	−2.39897	−	0.280399i	−0.0897163	−	0.0104863i
$716$	2.88896	+	6.69736i	0.107965	+	0.250292i
$717$	−0.0816757	+	0.0468465i	−0.00305024	+	0.00174952i
$718$	5.65470	−	2.83990i	0.211031	−	0.105984i
$719$	0.547249	+	0.199183i	0.0204090	+	0.00742825i	0.352204	−	0.935923i	$-0.385432\pi$
$719$	0.547249	+	0.199183i	0.0204090	+	0.00742825i	−0.331795	+	0.943351i	$0.607654\pi$
$720$	0.538890	+	10.2563i	0.0200832	+	0.382229i
$721$	−0.401170	+	0.146014i	−0.0149404	+	0.00543785i
$722$	−2.00563	+	2.12584i	−0.0746417	+	0.0791156i
$723$	−2.45022	+	20.4586i	−0.0911248	+	0.760865i
$724$	−11.9588	+	7.86540i	−0.444444	+	0.292315i
$725$	−7.86990	+	26.2873i	−0.292281	+	0.976285i
$726$	2.65035	+	2.51475i	0.0983638	+	0.0933312i
$727$	11.9433	+	16.0426i	0.442951	+	0.594986i	0.966391	−	0.257076i	$-0.0827591\pi$
$727$	11.9433	+	16.0426i	0.442951	+	0.594986i	−0.523440	+	0.852062i	$0.675352\pi$
$728$	−0.463826			−0.0171905
$729$	−4.23448	−	26.6659i	−0.156832	−	0.987625i
$730$	1.62328			0.0600803
$731$	8.34385	+	11.2077i	0.308609	+	0.414533i
$732$	17.3829	+	16.4935i	0.642490	+	0.609618i
$733$	12.2974	−	41.0761i	0.454214	−	1.51718i	−0.357944	−	0.933743i	$-0.616522\pi$
$733$	12.2974	−	41.0761i	0.454214	−	1.51718i	0.812158	−	0.583438i	$-0.198293\pi$
$734$	1.29585	−	0.852297i	0.0478309	−	0.0314589i
$735$	1.30886	−	10.9286i	0.0482780	−	0.403107i
$736$	13.2847	−	14.0809i	0.489680	−	0.519030i
$737$	6.25963	−	2.27832i	0.230577	−	0.0839230i
$738$	−0.348136	−	6.62580i	−0.0128151	−	0.243899i
$739$	−30.4321	−	11.0764i	−1.11946	−	0.407452i	−0.285008	−	0.958525i	$-0.591996\pi$
$739$	−30.4321	−	11.0764i	−1.11946	−	0.407452i	−0.834457	+	0.551074i	$0.814218\pi$
$740$	−7.20274	+	3.61735i	−0.264778	+	0.132976i
$741$	11.3107	−	6.48746i	0.415510	−	0.238323i
$742$	0.0806206	+	0.186899i	0.00295967	+	0.00686130i
$743$	−12.4511	−	1.45532i	−0.456786	−	0.0533906i	−0.115411	−	0.993318i	$-0.536818\pi$
$743$	−12.4511	−	1.45532i	−0.456786	−	0.0533906i	−0.341375	+	0.939927i	$0.610893\pi$
$744$	−7.63302	−	1.36828i	−0.279840	−	0.0501638i
$745$	−3.73243	−	2.45486i	−0.136746	−	0.0899390i
$746$	−4.01804	+	3.37153i	−0.147111	+	0.123441i
$747$	38.8578	−	32.2310i	1.42173	−	1.17927i
$748$	−4.54525	−	3.81392i	−0.166191	−	0.139451i
$749$	−0.562432	−	1.87865i	−0.0205508	−	0.0686445i
$750$	−2.92057	+	0.161778i	−0.106644	+	0.00590729i
$751$	−21.8955	−	10.9963i	−0.798977	−	0.401261i	0.00196900	−	0.999998i	$-0.499373\pi$
$751$	−21.8955	−	10.9963i	−0.798977	−	0.401261i	−0.800946	+	0.598737i	$0.795670\pi$
$752$	−23.0227	−	24.4026i	−0.839550	−	0.889871i
$753$	7.06908	+	3.07316i	0.257611	+	0.111992i
$754$	−1.86156	+	4.31559i	−0.0677942	+	0.157165i
$755$	−7.36209	+	12.7515i	−0.267934	+	0.464075i
$756$	−1.64207	−	0.303998i	−0.0597215	−	0.0110563i
$757$	−10.7313	−	18.5872i	−0.390037	−	0.675564i	0.602417	−	0.798182i	$-0.294205\pi$
$757$	−10.7313	−	18.5872i	−0.390037	−	0.675564i	−0.992454	+	0.122617i	$0.960871\pi$
$758$	5.33340	−	0.623385i	0.193718	−	0.0226424i
$759$	4.75634	+	9.53813i	0.172644	+	0.346212i
$760$	1.51152	−	0.358237i	0.0548286	−	0.0129946i
$761$	2.07041	+	35.5475i	0.0750522	+	1.28860i	0.800087	+	0.599884i	$0.204787\pi$
$761$	2.07041	+	35.5475i	0.0750522	+	1.28860i	−0.725035	+	0.688712i	$0.758176\pi$
$762$	−4.88884	−	1.47877i	−0.177104	−	0.0535703i
$763$	2.89411	+	0.685916i	0.104774	+	0.0248318i
$764$	7.06821	−	40.0858i	0.255719	−	1.45025i
$765$	10.7276	+	2.60698i	0.387858	+	0.0942554i
$766$	0.0945988	+	0.536496i	0.00341799	+	0.0193844i
$767$	−0.599151	+	10.2870i	−0.0216341	+	0.371443i
$768$	−7.66079	+	20.8632i	−0.276435	+	0.752835i
$769$	−9.90767	+	13.3083i	−0.357280	+	0.479910i	−0.944031	−	0.329857i	$-0.892999\pi$
$769$	−9.90767	+	13.3083i	−0.357280	+	0.479910i	0.586751	+	0.809767i	$0.300407\pi$
$770$	0.0135313	−	0.0181756i	0.000487633	−	0.000655005i
$771$	17.1698	+	20.5806i	0.618355	+	0.741194i
$772$	−0.397895	+	6.83160i	−0.0143206	+	0.245875i
$773$	1.97712	+	11.2128i	0.0711121	+	0.403297i	0.999498	+	0.0316795i	$0.0100856\pi$
$773$	1.97712	+	11.2128i	0.0711121	+	0.403297i	−0.928386	+	0.371617i	$0.878803\pi$
$774$	−1.24319	−	1.68986i	−0.0446856	−	0.0607409i
$775$	−4.05134	+	22.9763i	−0.145528	+	0.825332i
$776$	−3.52720	−	0.835962i	−0.126619	−	0.0300093i
$777$	−0.292258	−	1.24894i	−0.0104847	−	0.0448054i
$778$	−0.278427	−	4.78041i	−0.00998210	−	0.171386i
$779$	22.6852	−	5.37650i	0.812783	−	0.192633i
$780$	10.9076	+	0.666402i	0.390555	+	0.0238610i
$781$	7.09220	−	0.828959i	0.253779	−	0.0296625i
$782$	−3.34781	−	5.79858i	−0.119718	−	0.207357i
$783$	−19.0342	+	28.4096i	−0.680228	+	1.01528i
$784$	13.0976	−	22.6857i	0.467771	−	0.810204i
$785$	4.46269	−	10.3457i	0.159280	−	0.369253i
$786$	0.264345	+	2.31874i	0.00942887	+	0.0827068i
$787$	29.5496	+	31.3207i	1.05333	+	1.11646i	0.992980	+	0.118285i	$0.0377396\pi$
$787$	29.5496	+	31.3207i	1.05333	+	1.11646i	0.0603481	+	0.998177i	$0.480779\pi$
$788$	2.07428	+	1.04174i	0.0738932	+	0.0371105i
$789$	11.2064	−	22.1567i	0.398960	−	0.788798i
$790$	−0.170326	−	0.568930i	−0.00605994	−	0.0202416i
$791$	−1.49542	−	1.25480i	−0.0531709	−	0.0446157i
$792$	1.37251	+	1.16503i	0.0487699	+	0.0413974i
$793$	19.1159	−	16.0401i	0.678824	−	0.569601i
$794$	0.0184966	+	0.0121654i	0.000656421	+	0.000431735i
$795$	−3.28871	−	9.11617i	−0.116638	−	0.323317i
$796$	−2.14355	−	0.250546i	−0.0759763	−	0.00888035i
$797$	12.9510	+	30.0238i	0.458748	+	1.06350i	0.977949	+	0.208845i	$0.0669704\pi$
$797$	12.9510	+	30.0238i	0.458748	+	1.06350i	−0.519201	+	0.854652i	$0.673770\pi$
$798$	−0.000347623		0.122328i	−1.23057e−5		0.00433036i
$799$	−32.2264	+	16.1847i	−1.14009	+	0.572575i
$800$	−9.24443	−	3.36470i	−0.326840	−	0.118960i
$801$	13.4026	+	31.5628i	0.473558	+	1.11522i
$802$	−1.60412	+	0.583851i	−0.0566433	+	0.0206165i
$803$	−4.53635	+	4.80825i	−0.160084	+	0.169679i
$804$	−27.7080	+	11.8588i	−0.977186	+	0.418227i
$805$	−1.02478	+	0.674011i	−0.0361189	+	0.0237558i
$806$	−1.14610	+	3.82824i	−0.0403697	+	0.134844i
$807$	−3.02321	+	0.895736i	−0.106422	+	0.0315314i
$808$	1.09974	+	1.47721i	0.0386888	+	0.0519680i
$809$	25.5159			0.897092			0.448546	−	0.893760i	$-0.351942\pi$
$809$	25.5159			0.897092			0.448546	+	0.893760i	$0.351942\pi$
$810$	−1.60843	−	0.400569i	−0.0565146	−	0.0140745i
$811$	−8.80464			−0.309173			−0.154586	−	0.987979i	$-0.549404\pi$
$811$	−8.80464			−0.309173			−0.154586	+	0.987979i	$0.549404\pi$
$812$	1.26304	+	1.69656i	0.0443242	+	0.0595377i
$813$	−5.49196	+	22.8824i	−0.192611	+	0.802522i
$814$	−0.196247	+	0.655509i	−0.00687844	+	0.0229756i
$815$	9.24600	−	6.08119i	0.323873	−	0.213015i
$816$	21.0304	+	15.7496i	0.736212	+	0.551348i
$817$	5.05864	−	5.36185i	0.176980	−	0.187587i
$818$	−0.960082	+	0.349441i	−0.0335685	+	0.0122179i
$819$	−0.508232	+	1.66315i	−0.0177590	+	0.0581151i
$820$	18.3605	+	6.68268i	0.641177	+	0.233369i
$821$	5.26569	−	2.64453i	0.183774	−	0.0922947i	−0.354533	−	0.935043i	$-0.615360\pi$
$821$	5.26569	−	2.64453i	0.183774	−	0.0922947i	0.538307	+	0.842749i	$0.319064\pi$
$822$	4.42693	+	2.57269i	0.154407	+	0.0897328i
$823$	−17.9055	−	41.5096i	−0.624146	−	1.44693i	−0.877509	−	0.479561i	$-0.840796\pi$
$823$	−17.9055	−	41.5096i	−0.624146	−	1.44693i	0.253363	−	0.967371i	$-0.418463\pi$
$824$	−2.06822	−	0.241741i	−0.0720500	−	0.00842144i
$825$	3.49334	−	4.13926i	0.121623	−	0.144110i
$826$	−0.0807687	−	0.0531224i	−0.00281030	−	0.00184837i
$827$	−3.29612	+	2.76578i	−0.114617	+	0.0961755i	−0.698295	−	0.715810i	$-0.746058\pi$
$827$	−3.29612	+	2.76578i	−0.114617	+	0.0961755i	0.583678	+	0.811986i	$0.301613\pi$
$828$	−23.8737	−	41.8987i	−0.829670	−	1.45608i
$829$	39.1908	+	32.8850i	1.36115	+	1.14214i	0.975624	+	0.219448i	$0.0704255\pi$
$829$	39.1908	+	32.8850i	1.36115	+	1.14214i	0.385529	+	0.922696i	$0.374019\pi$
$830$	−0.888905	−	2.96915i	−0.0308543	−	0.103061i
$831$	−20.7407	−	31.7308i	−0.719487	−	1.10073i
$832$	22.2201	+	11.1594i	0.770344	+	0.386881i
$833$	−19.3230	−	20.4811i	−0.669501	−	0.709629i
$834$	0.932844	−	0.690365i	0.0323017	−	0.0239054i
$835$	0.917236	−	2.12639i	0.0317422	−	0.0735868i
$836$	−1.56514	+	2.71090i	−0.0541315	+	0.0937586i
$837$	−13.2701	+	25.8706i	−0.458681	+	0.894218i
$838$	1.29088	+	2.23588i	0.0445928	+	0.0772370i
$839$	−22.1161	+	2.58500i	−0.763532	+	0.0892441i	−0.488941	−	0.872317i	$-0.662617\pi$
$839$	−22.1161	+	2.58500i	−0.763532	+	0.0892441i	−0.274591	+	0.961561i	$0.588542\pi$
$840$	−0.114339	+	0.172773i	−0.00394507	+	0.00596122i
$841$	13.9257	−	3.30044i	0.480195	−	0.113808i
$842$	−0.213951	−	3.67339i	−0.00737323	−	0.126594i
$843$	31.9123	−	29.9368i	1.09912	−	1.03108i
$844$	28.5640	+	6.76979i	0.983213	+	0.233026i
$845$	−0.0811055	+	0.459972i	−0.00279011	+	0.0158235i
$846$	4.85232	−	2.40249i	0.166826	−	0.0825994i
$847$	−0.297321	−	1.68619i	−0.0102161	−	0.0579381i
$848$	1.34108	−	23.0255i	0.0460530	−	0.790699i
$849$	38.1974	−	6.62337i	1.31093	−	0.227313i
$850$	−2.03190	+	2.72931i	−0.0696934	+	0.0936145i
$851$	22.1183	−	29.7100i	0.758205	−	1.01845i
$852$	−31.8318	+	5.51959i	−1.09054	+	0.189098i
$853$	0.388118	−	6.66373i	0.0132889	−	0.228162i	−0.985124	−	0.171845i	$-0.945027\pi$
$853$	0.388118	−	6.66373i	0.0132889	−	0.228162i	0.998413	−	0.0563169i	$-0.0179357\pi$
$854$	0.0406525	+	0.230552i	0.00139110	+	0.00788933i
$855$	0.371693	−	5.81242i	0.0127116	−	0.198781i
$856$	1.66095	−	9.41973i	0.0567702	−	0.321960i
$857$	−3.14898	−	0.746322i	−0.107567	−	0.0254939i	0.176480	−	0.984304i	$-0.443529\pi$
$857$	−3.14898	−	0.746322i	−0.107567	−	0.0254939i	−0.284047	+	0.958810i	$0.591677\pi$
$858$	0.676607	−	0.634721i	0.0230990	−	0.0216690i
$859$	0.520474	+	8.93620i	0.0177584	+	0.304899i	0.995479	+	0.0949867i	$0.0302809\pi$
$859$	0.520474	+	8.93620i	0.0177584	+	0.304899i	−0.977720	+	0.209912i	$0.932682\pi$
$860$	6.01144	−	1.42474i	0.204988	−	0.0485831i
$861$	−1.71603	+	2.59301i	−0.0584820	+	0.0883696i
$862$	4.64387	−	0.542791i	0.158171	−	0.0184875i
$863$	8.30305	+	14.3813i	0.282639	+	0.489546i	0.972034	−	0.234840i	$-0.0754567\pi$
$863$	8.30305	+	14.3813i	0.282639	+	0.489546i	−0.689395	+	0.724386i	$0.742123\pi$
$864$	−9.77131	−	7.40477i	−0.332427	−	0.251915i
$865$	4.43662	−	7.68446i	0.150850	−	0.261279i
$866$	2.68204	−	6.21767i	0.0911395	−	0.211285i
$867$	−0.966472	+	0.715252i	−0.0328231	+	0.0242912i
$868$	1.23410	+	1.30807i	0.0418880	+	0.0443987i
$869$	2.16119	+	1.08539i	0.0733133	+	0.0368193i
$870$	1.14863	+	1.75727i	0.0389423	+	0.0595770i
$871$	9.00164	+	30.0676i	0.305009	+	1.01880i
$872$	11.1131	+	9.32502i	0.376338	+	0.315785i
$873$	−6.86241	+	11.7316i	−0.232257	+	0.397053i
$874$	−2.70598	+	2.27059i	−0.0915312	+	0.0768038i
$875$	1.14529	+	0.753268i	0.0387178	+	0.0254651i
$876$	19.2899	−	22.8566i	0.651746	−	0.772253i
$877$	−5.55689	−	0.649507i	−0.187643	−	0.0219323i	0.0217525	−	0.999763i	$-0.493075\pi$
$877$	−5.55689	−	0.649507i	−0.187643	−	0.0219323i	−0.209395	+	0.977831i	$0.567150\pi$
$878$	2.53374	+	5.87387i	0.0855096	+	0.198233i
$879$	−19.6083	−	11.3953i	−0.661372	−	0.384353i
$880$	−2.29450	+	1.15234i	−0.0773477	+	0.0388455i
$881$	−8.40136	−	3.05784i	−0.283049	−	0.103021i	0.196595	−	0.980485i	$-0.437012\pi$
$881$	−8.40136	−	3.05784i	−0.283049	−	0.103021i	−0.479643	+	0.877464i	$0.659234\pi$
$882$	2.88369	+	3.09155i	0.0970990	+	0.104098i
$883$	13.8259	−	5.03222i	0.465279	−	0.169348i	−0.0987335	−	0.995114i	$-0.531479\pi$
$883$	13.8259	−	5.03222i	0.465279	−	0.169348i	0.564013	+	0.825766i	$0.309257\pi$
$884$	19.1847	−	20.3346i	0.645252	−	0.683927i
$885$	3.68416	+	2.75906i	0.123842	+	0.0927449i
$886$	−3.81773	+	2.51096i	−0.128259	+	0.0843574i
$887$	−1.26449	+	4.22369i	−0.0424574	+	0.141818i	−0.976590	−	0.215108i	$-0.930990\pi$
$887$	−1.26449	+	4.22369i	−0.0424574	+	0.141818i	0.934133	+	0.356925i	$0.116175\pi$
$888$	1.46010	−	6.08355i	0.0489977	−	0.204151i
$889$	1.42938	+	1.91999i	0.0479398	+	0.0643943i
$890$	2.10514			0.0705643
$891$	5.68136	−	3.64486i	0.190333	−	0.122107i
$892$	−9.99369			−0.334614
$893$	11.3612	+	15.2607i	0.380187	+	0.510680i
$894$	1.64523	−	0.487459i	0.0550247	−	0.0163031i
$895$	0.973070	−	3.25028i	0.0325261	−	0.108645i
$896$	−0.841651	+	0.553563i	−0.0281176	+	0.0184932i
$897$	−46.1675	+	19.7593i	−1.54149	+	0.659744i
$898$	−2.49918	+	2.64898i	−0.0833988	+	0.0883976i
$899$	34.6044	−	12.5950i	1.15412	−	0.420066i
$900$	−14.7455	+	19.5734i	−0.491517	+	0.652447i
$901$	−23.2973	−	8.47952i	−0.776145	−	0.282494i
$902$	1.48231	−	0.744442i	0.0493554	−	0.0247872i
$903$	−0.00279387	+	0.983157i	−9.29743e−5	+	0.0327174i
$904$	−3.77131	−	8.74288i	−0.125432	−	0.290784i
$905$	6.61304	+	0.772953i	0.219825	+	0.0256938i
$906$	−1.91921	−	5.31999i	−0.0637616	−	0.176745i
$907$	−2.73796	−	1.80079i	−0.0909126	−	0.0597941i	0.503239	−	0.864147i	$-0.332142\pi$
$907$	−2.73796	−	1.80079i	−0.0909126	−	0.0597941i	−0.594151	+	0.804353i	$0.702512\pi$
$908$	25.1582	−	21.1102i	0.834904	−	0.700568i
$909$	6.50188	−	2.32473i	0.215654	−	0.0771064i
$910$	0.0817857	+	0.0686263i	0.00271117	+	0.00227494i
$911$	12.0728	+	40.3259i	0.399989	+	1.33606i	0.886640	+	0.462460i	$0.153033\pi$
$911$	12.0728	+	40.3259i	0.399989	+	1.33606i	−0.486651	+	0.873596i	$0.661782\pi$
$912$	6.25618	−	12.3693i	0.207163	−	0.409589i
$913$	11.2789	+	5.66446i	0.373276	+	0.187466i
$914$	−3.26736	−	3.46320i	−0.108075	−	0.114552i
$915$	−1.26255	−	11.0746i	−0.0417386	−	0.366116i
$916$	−12.5112	+	29.0042i	−0.413382	+	0.958326i
$917$	0.546849	−	0.947170i	0.0180585	−	0.0312783i
$918$	−3.42281	+	2.50312i	−0.112970	+	0.0826153i
$919$	15.0654	+	26.0940i	0.496962	+	0.860763i	0.999994	−	0.00350463i	$-0.00111556\pi$
$919$	15.0654	+	26.0940i	0.496962	+	0.860763i	−0.503032	+	0.864268i	$0.667782\pi$
$920$	−5.94219	+	0.694543i	−0.195908	+	0.0228984i
$921$	25.4034	+	1.55203i	0.837071	+	0.0511410i
$922$	7.89966	−	1.87225i	0.260162	−	0.0616594i
$923$	1.95620	+	33.5866i	0.0643891	+	1.10552i
$924$	−0.0951262	−	0.406513i	−0.00312942	−	0.0133733i
$925$	−18.3153	−	4.34082i	−0.602205	−	0.142725i
$926$	0.385410	−	2.18577i	0.0126654	−	0.0718288i
$927$	−3.13304	+	7.15118i	−0.102903	+	0.234876i
$928$	2.69639	+	15.2920i	0.0885133	+	0.501984i
$929$	−2.07372	+	35.6043i	−0.0680364	+	1.16814i	0.775600	+	0.631225i	$0.217448\pi$
$929$	−2.07372	+	35.6043i	−0.0680364	+	1.16814i	−0.843636	+	0.536915i	$0.819589\pi$
$930$	1.14347	+	1.37063i	0.0374959	+	0.0449446i
$931$	−8.87087	+	11.9156i	−0.290731	+	0.390519i
$932$	12.2699	−	16.4813i	0.401914	−	0.539864i
$933$	19.9296	−	54.2758i	0.652466	−	1.77691i
$934$	−0.0198059	+	0.340054i	−0.000648069	+	0.0111269i
$935$	0.479264	+	2.71804i	0.0156736	+	0.0888895i
$936$	−5.85594	+	6.13668i	−0.191407	+	0.200584i
$937$	−2.81383	+	15.9580i	−0.0919239	+	0.521326i	0.903723	+	0.428118i	$0.140823\pi$
$937$	−2.81383	+	15.9580i	−0.0919239	+	0.521326i	−0.995647	+	0.0932080i	$0.970288\pi$
$938$	−0.286516	−	0.0679054i	−0.00935506	−	0.00221719i
$939$	−37.8985	−	11.4635i	−1.23677	−	0.374098i
$940$	0.927114	+	15.9179i	0.0302391	+	0.519186i
$941$	−15.2035	+	3.60329i	−0.495619	+	0.117464i	−0.470821	−	0.882229i	$-0.656042\pi$
$941$	−15.2035	+	3.60329i	−0.495619	+	0.117464i	−0.0247977	+	0.999692i	$0.507894\pi$
$942$	1.93128	+	3.87291i	0.0629247	+	0.126186i
$943$	−89.1818	+	10.4239i	−2.90416	+	0.339447i
$944$	5.47715	+	9.48670i	0.178266	+	0.308766i
$945$	0.494228	+	0.599301i	0.0160772	+	0.0194953i
$946$	0.262238	−	0.454209i	0.00852609	−	0.0147676i
$947$	20.1940	−	46.8149i	0.656216	−	1.52128i	−0.186234	−	0.982505i	$-0.559628\pi$
$947$	20.1940	−	46.8149i	0.656216	−	1.52128i	0.842450	−	0.538774i	$-0.181113\pi$
$948$	−10.0349	−	4.36248i	−0.325917	−	0.141687i
$949$	−21.3738	−	22.6549i	−0.693822	−	0.735408i
$950$	1.60417	+	0.805645i	0.0520462	+	0.0261386i
$951$	−32.4870	+	1.79954i	−1.05346	+	0.0583540i
$952$	0.152010	+	0.507750i	0.00492668	+	0.0164563i
$953$	−30.4826	−	25.5779i	−0.987428	−	0.828550i	−0.00223469	−	0.999998i	$-0.500711\pi$
$953$	−30.4826	−	25.5779i	−0.987428	−	0.828550i	−0.985193	+	0.171447i	$0.945156\pi$
$954$	3.49064	+	1.29300i	0.113014	+	0.0418626i
$955$	−14.5042	+	12.1705i	−0.469346	+	0.393828i
$956$	0.0889818	+	0.0585242i	0.00287788	+	0.00189281i
$957$	−8.41505	−	1.50847i	−0.272020	−	0.0487619i
$958$	−3.99241	−	0.466645i	−0.128989	−	0.0150766i
$959$	−0.950408	−	2.20329i	−0.0306903	−	0.0711481i
$960$	9.63434	−	5.52595i	0.310947	−	0.178349i
$961$	0.277414	−	0.139323i	0.00894885	−	0.00449428i
$962$	−3.02955	−	1.10267i	−0.0976767	−	0.0355514i
$963$	−31.9565	−	16.2773i	−1.02978	−	0.524527i
$964$	21.9010	−	7.97131i	0.705384	−	0.256739i
$965$	2.18442	−	2.31535i	0.0703190	−	0.0745338i
$966$	0.0560242	−	0.467785i	0.00180255	−	0.0150507i
$967$	−18.8634	+	12.4066i	−0.606605	+	0.398970i	−0.815324	−	0.579006i	$-0.803441\pi$
$967$	−18.8634	+	12.4066i	−0.606605	+	0.398970i	0.208719	+	0.977976i	$0.433071\pi$
$968$	2.39519	−	8.00049i	0.0769843	−	0.257145i
$969$	−10.8087	−	10.2557i	−0.347225	−	0.329460i
$970$	0.498259	+	0.669278i	0.0159981	+	0.0214892i
$971$	7.94868			0.255085			0.127543	−	0.991833i	$-0.459291\pi$
$971$	7.94868			0.255085			0.127543	+	0.991833i	$0.459291\pi$
$972$	−24.7537	+	17.8875i	−0.793975	+	0.573741i
$973$	−0.543867			−0.0174356
$974$	2.04421	+	2.74585i	0.0655007	+	0.0879826i
$975$	18.5128	+	17.5656i	0.592883	+	0.562550i
$976$	7.60821	−	25.4132i	0.243533	−	0.813457i
$977$	−32.3908	+	21.3038i	−1.03628	+	0.681569i	−0.949213	−	0.314634i	$-0.898118\pi$
$977$	−32.3908	+	21.3038i	−1.03628	+	0.681569i	−0.0870620	+	0.996203i	$0.527748\pi$
$978$	−0.505472	+	4.22054i	−0.0161632	+	0.134958i
$979$	−5.88292	+	6.23553i	−0.188019	+	0.199288i
$980$	−11.6991	+	4.25811i	−0.373713	+	0.136020i
$981$	45.6140	−	29.6308i	1.45634	−	0.946037i
$982$	−6.53202	−	2.37746i	−0.208445	−	0.0758678i
$983$	15.0544	−	7.56062i	0.480162	−	0.241146i	−0.192219	−	0.981352i	$-0.561568\pi$
$983$	15.0544	−	7.56062i	0.480162	−	0.241146i	0.672380	+	0.740206i	$0.265272\pi$
$984$	−13.1559	+	7.54579i	−0.419394	+	0.240551i
$985$	−0.427654	−	0.991413i	−0.0136262	−	0.0315890i
$986$	5.33437	+	0.623498i	0.169881	+	0.0198562i
$987$	−2.49766	−	0.447727i	−0.0795014	−	0.0142513i
$988$	−12.3225	−	8.10462i	−0.392030	−	0.257842i
$989$	−21.7482	+	18.2489i	−0.691552	+	0.580281i
$990$	−0.0696379	−	0.408499i	−0.00221324	−	0.0129829i
$991$	−5.22377	−	4.38327i	−0.165939	−	0.139239i	0.556037	−	0.831158i	$-0.312321\pi$
$991$	−5.22377	−	4.38327i	−0.165939	−	0.139239i	−0.721976	+	0.691919i	$0.756766\pi$
$992$	3.78651	+	12.6478i	0.120222	+	0.401569i
$993$	10.2367	−	0.567039i	0.324853	−	0.0179944i
$994$	−0.282058	−	0.141655i	−0.00894634	−	0.00449302i
$995$	0.688905	+	0.730197i	0.0218398	+	0.0231488i
$996$	−52.3702	−	22.7670i	−1.65941	−	0.721401i
$997$	−4.68352	+	10.8576i	−0.148329	+	0.343864i	−0.976140	−	0.217142i	$-0.930326\pi$
$997$	−4.68352	+	10.8576i	−0.148329	+	0.343864i	0.827811	+	0.561007i	$0.189586\pi$
$998$	1.77775	−	3.07914i	0.0562735	−	0.0974686i
$999$	−20.2140	−	11.9015i	−0.639543	−	0.376546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.7.5	✓	144
3.2	odd	2		243.2.g.a.100.4		144
9.2	odd	6		729.2.g.b.55.4		144
9.4	even	3		729.2.g.d.298.4		144
9.5	odd	6		729.2.g.a.298.5		144
9.7	even	3		729.2.g.c.55.5		144
81.4	even	27		729.2.g.c.676.5		144
81.23	odd	54		243.2.g.a.226.4		144
81.25	even	27		6561.2.a.c.1.36		72
81.31	even	27		729.2.g.d.433.4		144
81.50	odd	54		729.2.g.a.433.5		144
81.56	odd	54		6561.2.a.d.1.37		72
81.58	even	27	inner	81.2.g.a.58.5	yes	144
81.77	odd	54		729.2.g.b.676.4		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.7.5	✓	144	1.1	even	1	trivial
81.2.g.a.58.5	yes	144	81.58	even	27	inner
243.2.g.a.100.4		144	3.2	odd	2
243.2.g.a.226.4		144	81.23	odd	54
729.2.g.a.298.5		144	9.5	odd	6
729.2.g.a.433.5		144	81.50	odd	54
729.2.g.b.55.4		144	9.2	odd	6
729.2.g.b.676.4		144	81.77	odd	54
729.2.g.c.55.5		144	9.7	even	3
729.2.g.c.676.5		144	81.4	even	27
729.2.g.d.298.4		144	9.4	even	3
729.2.g.d.433.4		144	81.31	even	27
6561.2.a.c.1.36		72	81.25	even	27
6561.2.a.d.1.37		72	81.56	odd	54

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.120683 - 0.162105i) q^{2} +(1.25647 + 1.19218i) q^{3} +(0.561893 - 1.87685i) q^{4} +(-0.761396 + 0.500778i) q^{5} +(0.0416250 - 0.347556i) q^{6} +(-0.112573 + 0.119321i) q^{7} +(-0.751874 + 0.273660i) q^{8} +(0.157410 + 2.99587i) q^{9} +(0.173067 + 0.0629911i) q^{10} +(-0.670227 + 0.336601i) q^{11} +(2.94355 - 1.68832i) q^{12} +(-1.39965 - 3.24476i) q^{13} +(0.0329282 + 0.00384876i) q^{14} +(-1.55369 - 0.278512i) q^{15} +(-3.13860 - 2.06429i) q^{16} +(-3.09332 + 2.59561i) q^{17} +(0.466650 - 0.387068i) q^{18} +(1.63194 + 1.36936i) q^{19} +(0.512064 + 1.71041i) q^{20} +(-0.283696 + 0.0157146i) q^{21} +(0.135450 + 0.0680255i) q^{22} +(-5.63041 - 5.96789i) q^{23} +(-1.27096 - 0.552526i) q^{24} +(-1.65145 + 3.82850i) q^{25} +(-0.357079 + 0.618479i) q^{26} +(-3.37383 + 3.95187i) q^{27} +(0.160693 + 0.278329i) q^{28} +(6.53664 - 0.764024i) q^{29} +(0.142355 + 0.285473i) q^{30} +(5.44474 - 1.29043i) q^{31} +(0.137190 + 2.35546i) q^{32} +(-1.24341 - 0.376105i) q^{33} +(0.794074 + 0.188199i) q^{34} +(0.0259597 - 0.147225i) q^{35} +(5.71125 + 1.38792i) q^{36} +(0.783915 + 4.44580i) q^{37} +(0.0250334 - 0.429806i) q^{38} +(2.10972 - 5.74556i) q^{39} +(0.435431 - 0.584886i) q^{40} +(6.53505 - 8.77810i) q^{41} +(0.0367848 + 0.0440923i) q^{42} +(0.201195 - 3.45438i) q^{43} +(0.255154 + 1.44705i) q^{44} +(-1.62012 - 2.20221i) q^{45} +(-0.287932 + 1.63294i) q^{46} +(8.68990 + 2.05954i) q^{47} +(-1.48254 - 6.33549i) q^{48} +(0.405449 + 6.96129i) q^{49} +(0.819923 - 0.194325i) q^{50} +(-6.98109 - 0.426511i) q^{51} +(-6.87639 + 0.803734i) q^{52} +(3.06986 + 5.31715i) q^{53} +(1.04778 + 0.0699940i) q^{54} +(0.341746 - 0.591922i) q^{55} +(0.0519877 - 0.120521i) q^{56} +(0.417952 + 3.66613i) q^{57} +(-0.912715 - 0.967421i) q^{58} +(-2.60584 - 1.30870i) q^{59} +(-1.39573 + 2.75955i) q^{60} +(2.02529 + 6.76493i) q^{61} +(-0.866274 - 0.726890i) q^{62} +(-0.375189 - 0.318472i) q^{63} +(-5.39019 + 4.52290i) q^{64} +(2.69059 + 1.76963i) q^{65} +(0.0890894 + 0.246952i) q^{66} +(-8.82173 - 1.03111i) q^{67} +(3.13345 + 7.26416i) q^{68} +(0.0403837 - 14.2109i) q^{69} +(-0.0269988 + 0.0135593i) q^{70} +(-8.94644 - 3.25624i) q^{71} +(-0.938201 - 2.20944i) q^{72} +(8.28233 - 3.01452i) q^{73} +(0.626083 - 0.663610i) q^{74} +(-6.63926 + 2.84155i) q^{75} +(3.48707 - 2.29348i) q^{76} +(0.0352862 - 0.117864i) q^{77} +(-1.18600 + 0.351395i) q^{78} +(-1.92557 - 2.58649i) q^{79} +3.42347 q^{80} +(-8.95044 + 0.943160i) q^{81} -2.21165 q^{82} +(-10.0492 - 13.4985i) q^{83} +(-0.129913 + 0.541286i) q^{84} +(1.05542 - 3.52535i) q^{85} +(-0.584255 + 0.384271i) q^{86} +(9.12392 + 6.83289i) q^{87} +(0.411812 - 0.436496i) q^{88} +(10.7409 - 3.90935i) q^{89} +(-0.161470 + 0.528400i) q^{90} +(0.544730 + 0.198266i) q^{91} +(-14.3645 + 7.21414i) q^{92} +(8.37955 + 4.86974i) q^{93} +(-0.714861 - 1.65723i) q^{94} +(-1.92830 - 0.225386i) q^{95} +(-2.63576 + 3.12311i) q^{96} +(3.78511 + 2.48950i) q^{97} +(1.07953 - 0.905836i) q^{98} +(-1.11391 - 1.95493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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