LMFDB - Embedded newform 539.2.q.g.214.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(214,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 12]))

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

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

chi := DirichletCharacter("539.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.q (of order $15$, degree $8$, not 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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			214.3
Character	$\chi$	$=$	539.214
Dual form			539.2.q.g.471.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.448146 - 0.497717i) q^{2} +(2.86833 - 1.27706i) q^{3} +(0.162170 + 1.54294i) q^{4} +(-2.09693 + 0.445717i) q^{5} +(0.649815 - 1.99992i) q^{6} +(1.92429 + 1.39808i) q^{8} +(4.58902 - 5.09662i) q^{9} +O(q^{10})$	\(q+(0.448146 - 0.497717i) q^{2} +(2.86833 - 1.27706i) q^{3} +(0.162170 + 1.54294i) q^{4} +(-2.09693 + 0.445717i) q^{5} +(0.649815 - 1.99992i) q^{6} +(1.92429 + 1.39808i) q^{8} +(4.58902 - 5.09662i) q^{9} +(-0.717891 + 1.24342i) q^{10} +(3.25662 + 0.628009i) q^{11} +(2.43559 + 4.21857i) q^{12} +(0.781276 + 2.40452i) q^{13} +(-5.44548 + 3.95637i) q^{15} +(-1.47687 + 0.313918i) q^{16} +(-1.19836 - 1.33091i) q^{17} +(-0.480122 - 4.56806i) q^{18} +(0.703205 - 6.69055i) q^{19} +(-1.02778 - 3.16317i) q^{20} +(1.77201 - 1.33944i) q^{22} +(1.58214 + 2.74035i) q^{23} +(7.30493 + 1.55271i) q^{24} +(-0.369268 + 0.164409i) q^{25} +(1.54690 + 0.688722i) q^{26} +(3.74337 - 11.5209i) q^{27} +(0.747669 - 0.543213i) q^{29} +(-0.471218 + 4.48334i) q^{30} +(-2.93619 - 0.624106i) q^{31} +(-2.88417 + 4.99553i) q^{32} +(10.1431 - 2.35757i) q^{33} -1.19946 q^{34} +(8.60800 + 6.25408i) q^{36} +(-1.37688 - 0.613025i) q^{37} +(-3.01486 - 3.34834i) q^{38} +(5.31167 + 5.89921i) q^{39} +(-4.65826 - 2.07399i) q^{40} +(-4.49897 - 3.26870i) q^{41} -8.42985 q^{43} +(-0.440857 + 5.12663i) q^{44} +(-7.35120 + 12.7327i) q^{45} +(2.07295 + 0.440619i) q^{46} +(-0.459686 + 4.37362i) q^{47} +(-3.83525 + 2.78647i) q^{48} +(-0.0836570 + 0.257470i) q^{50} +(-5.13694 - 2.28711i) q^{51} +(-3.58334 + 1.59541i) q^{52} +(-0.652836 - 0.138765i) q^{53} +(-4.05657 - 7.02619i) q^{54} +(-7.10883 + 0.134639i) q^{55} +(-6.52722 - 20.0887i) q^{57} +(0.0646986 - 0.615566i) q^{58} +(0.0385041 + 0.366342i) q^{59} +(-6.98755 - 7.76046i) q^{60} +(-4.90197 + 1.04195i) q^{61} +(-1.62647 + 1.18170i) q^{62} +(0.260682 + 0.802296i) q^{64} +(-2.71002 - 4.69389i) q^{65} +(3.37217 - 6.10491i) q^{66} +(0.451065 - 0.781267i) q^{67} +(1.85919 - 2.06484i) q^{68} +(8.03770 + 5.83973i) q^{69} +(-4.59489 + 14.1416i) q^{71} +(15.9561 - 3.39157i) q^{72} +(-0.840216 - 7.99413i) q^{73} +(-0.922155 + 0.410570i) q^{74} +(-0.849220 + 0.943154i) q^{75} +10.4372 q^{76} +5.31654 q^{78} +(2.71445 - 3.01470i) q^{79} +(2.95697 - 1.31653i) q^{80} +(-1.82507 - 17.3644i) q^{81} +(-3.64308 + 0.774361i) q^{82} +(-1.25193 + 3.85305i) q^{83} +(3.10609 + 2.25670i) q^{85} +(-3.77780 + 4.19568i) q^{86} +(1.45084 - 2.51293i) q^{87} +(5.38869 + 5.76150i) q^{88} +(4.15363 + 7.19431i) q^{89} +(3.04284 + 9.36491i) q^{90} +(-3.97163 + 2.88556i) q^{92} +(-9.21896 + 1.95955i) q^{93} +(1.97082 + 2.18881i) q^{94} +(1.50752 + 14.3431i) q^{95} +(-1.89314 + 18.0120i) q^{96} +(2.63154 + 8.09904i) q^{97} +(18.1454 - 13.7158i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9}+O(q^{10}) $ 32 * q + 3 * q^2 + 2 * q^3 + 11 * q^4 + 5 * q^5 + 6 * q^6 - 10 * q^8 + 12 * q^9	$ 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9} - 12 q^{10} + 3 q^{11} - 18 q^{12} - 14 q^{13} - 36 q^{15} - 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + 2 q^{20} - 66 q^{22} - 32 q^{23} + 35 q^{24} - 7 q^{25} + 27 q^{26} + 20 q^{27} + 6 q^{29} + 2 q^{30} + 7 q^{31} - 32 q^{32} + 26 q^{33} - 48 q^{34} + 104 q^{36} - 4 q^{37} + 5 q^{38} - 11 q^{39} + 10 q^{40} - 20 q^{41} - 16 q^{43} + 38 q^{44} - 70 q^{45} + 42 q^{46} + 23 q^{47} - 72 q^{48} + 104 q^{50} + 29 q^{51} - 33 q^{52} - 4 q^{53} - 60 q^{54} - 24 q^{55} - 22 q^{57} - 20 q^{58} - 17 q^{59} + 30 q^{60} + 7 q^{61} + 158 q^{62} + 14 q^{64} + 8 q^{65} - 8 q^{66} + 38 q^{67} + 2 q^{68} + 20 q^{69} - 28 q^{71} + 35 q^{73} + 29 q^{74} - 9 q^{75} + 104 q^{76} - 116 q^{78} - 15 q^{79} + 87 q^{80} + 14 q^{81} - 19 q^{82} + 10 q^{83} + 12 q^{85} + 52 q^{86} + 72 q^{87} - 55 q^{88} - 74 q^{89} - 28 q^{90} - 110 q^{92} - 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 40 q^{97} + 32 q^{99}+O(q^{100}) $ 32 * q + 3 * q^2 + 2 * q^3 + 11 * q^4 + 5 * q^5 + 6 * q^6 - 10 * q^8 + 12 * q^9 - 12 * q^10 + 3 * q^11 - 18 * q^12 - 14 * q^13 - 36 * q^15 - 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + 2 * q^20 - 66 * q^22 - 32 * q^23 + 35 * q^24 - 7 * q^25 + 27 * q^26 + 20 * q^27 + 6 * q^29 + 2 * q^30 + 7 * q^31 - 32 * q^32 + 26 * q^33 - 48 * q^34 + 104 * q^36 - 4 * q^37 + 5 * q^38 - 11 * q^39 + 10 * q^40 - 20 * q^41 - 16 * q^43 + 38 * q^44 - 70 * q^45 + 42 * q^46 + 23 * q^47 - 72 * q^48 + 104 * q^50 + 29 * q^51 - 33 * q^52 - 4 * q^53 - 60 * q^54 - 24 * q^55 - 22 * q^57 - 20 * q^58 - 17 * q^59 + 30 * q^60 + 7 * q^61 + 158 * q^62 + 14 * q^64 + 8 * q^65 - 8 * q^66 + 38 * q^67 + 2 * q^68 + 20 * q^69 - 28 * q^71 + 35 * q^73 + 29 * q^74 - 9 * q^75 + 104 * q^76 - 116 * q^78 - 15 * q^79 + 87 * q^80 + 14 * q^81 - 19 * q^82 + 10 * q^83 + 12 * q^85 + 52 * q^86 + 72 * q^87 - 55 * q^88 - 74 * q^89 - 28 * q^90 - 110 * q^92 - 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 40 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.448146	−	0.497717i	0.316887	−	0.351939i	−0.563567	−	0.826070i	$-0.690571\pi$
$2$	0.448146	−	0.497717i	0.316887	−	0.351939i	0.880454	+	0.474132i	$0.157238\pi$
$3$	2.86833	−	1.27706i	1.65603	−	0.737311i	0.656178	−	0.754606i	$-0.272172\pi$
$3$	2.86833	−	1.27706i	1.65603	−	0.737311i	0.999850	+	0.0172947i	$0.00550534\pi$
$4$	0.162170	+	1.54294i	0.0810850	+	0.771472i
$5$	−2.09693	+	0.445717i	−0.937776	+	0.199331i	−0.651355	−	0.758773i	$-0.725799\pi$
$5$	−2.09693	+	0.445717i	−0.937776	+	0.199331i	−0.286421	+	0.958104i	$0.592466\pi$
$6$	0.649815	−	1.99992i	0.265286	−	0.816465i
$7$		0			0
$7$		0			0
$8$	1.92429	+	1.39808i	0.680340	+	0.494296i
$9$	4.58902	−	5.09662i	1.52967	−	1.69887i
$10$	−0.717891	+	1.24342i	−0.227017	+	0.393205i
$11$	3.25662	+	0.628009i	0.981909	+	0.189352i
$11$	3.25662	+	0.628009i	0.981909	+	0.189352i
$12$	2.43559	+	4.21857i	0.703094	+	1.21779i
$13$	0.781276	+	2.40452i	0.216687	+	0.666894i	0.999030	+	0.0440455i	$0.0140247\pi$
$13$	0.781276	+	2.40452i	0.216687	+	0.666894i	−0.782343	+	0.622848i	$0.785975\pi$
$14$		0			0
$15$	−5.44548	+	3.95637i	−1.40602	+	1.02153i
$16$	−1.47687	+	0.313918i	−0.369217	+	0.0784795i
$17$	−1.19836	−	1.33091i	−0.290645	−	0.322794i	0.580085	−	0.814556i	$-0.303019\pi$
$17$	−1.19836	−	1.33091i	−0.290645	−	0.322794i	−0.870729	+	0.491762i	$0.836353\pi$
$18$	−0.480122	−	4.56806i	−0.113166	−	1.07670i
$19$	0.703205	−	6.69055i	0.161326	−	1.53492i	−0.551857	−	0.833939i	$-0.686080\pi$
$19$	0.703205	−	6.69055i	0.161326	−	1.53492i	0.713183	−	0.700978i	$-0.247253\pi$
$20$	−1.02778	−	3.16317i	−0.229818	−	0.707306i
$21$		0			0
$22$	1.77201	−	1.33944i	0.377795	−	0.285569i
$23$	1.58214	+	2.74035i	0.329900	+	0.571403i	0.982492	−	0.186307i	$-0.0596518\pi$
$23$	1.58214	+	2.74035i	0.329900	+	0.571403i	−0.652592	+	0.757709i	$0.726318\pi$
$24$	7.30493	+	1.55271i	1.49111	+	0.316946i
$25$	−0.369268	+	0.164409i	−0.0738535	+	0.0328817i
$26$	1.54690	+	0.688722i	0.303371	+	0.135070i
$27$	3.74337	−	11.5209i	0.720412	−	2.21720i
$28$		0			0
$29$	0.747669	−	0.543213i	0.138839	−	0.100872i	−0.516198	−	0.856469i	$-0.672653\pi$
$29$	0.747669	−	0.543213i	0.138839	−	0.100872i	0.655037	+	0.755597i	$0.272653\pi$
$30$	−0.471218	+	4.48334i	−0.0860322	+	0.818541i
$31$	−2.93619	−	0.624106i	−0.527355	−	0.112093i	−0.0634623	−	0.997984i	$-0.520214\pi$
$31$	−2.93619	−	0.624106i	−0.527355	−	0.112093i	−0.463892	+	0.885892i	$0.653548\pi$
$32$	−2.88417	+	4.99553i	−0.509854	+	0.883092i
$33$	10.1431	−	2.35757i	1.76568	−	0.410401i
$34$	−1.19946			−0.205705
$35$		0			0
$36$	8.60800	+	6.25408i	1.43467	+	1.04235i
$37$	−1.37688	−	0.613025i	−0.226357	−	0.100781i	0.290425	−	0.956898i	$-0.406203\pi$
$37$	−1.37688	−	0.613025i	−0.226357	−	0.100781i	−0.516782	+	0.856117i	$0.672870\pi$
$38$	−3.01486	−	3.34834i	−0.489075	−	0.543172i
$39$	5.31167	+	5.89921i	0.850548	+	0.944630i
$40$	−4.65826	−	2.07399i	−0.736536	−	0.327927i
$41$	−4.49897	−	3.26870i	−0.702622	−	0.510485i	0.178163	−	0.984001i	$-0.442984\pi$
$41$	−4.49897	−	3.26870i	−0.702622	−	0.510485i	−0.880785	+	0.473516i	$0.842984\pi$
$42$		0			0
$43$	−8.42985			−1.28554			−0.642770	−	0.766059i	$-0.722215\pi$
$43$	−8.42985			−1.28554			−0.642770	+	0.766059i	$0.722215\pi$
$44$	−0.440857	+	5.12663i	−0.0664617	+	0.772869i
$45$	−7.35120	+	12.7327i	−1.09585	+	1.89807i
$46$	2.07295	+	0.440619i	0.305640	+	0.0649657i
$47$	−0.459686	+	4.37362i	−0.0670520	+	0.637957i	0.908454	+	0.417985i	$0.137263\pi$
$47$	−0.459686	+	4.37362i	−0.0670520	+	0.637957i	−0.975506	+	0.219973i	$0.929403\pi$
$48$	−3.83525	+	2.78647i	−0.553570	+	0.402192i
$49$		0			0
$50$	−0.0836570	+	0.257470i	−0.0118309	+	0.0364117i
$51$	−5.13694	−	2.28711i	−0.719316	−	0.320260i
$52$	−3.58334	+	1.59541i	−0.496920	+	0.221243i
$53$	−0.652836	−	0.138765i	−0.0896739	−	0.0190608i	0.162856	−	0.986650i	$-0.447929\pi$
$53$	−0.652836	−	0.138765i	−0.0896739	−	0.0190608i	−0.252530	+	0.967589i	$0.581263\pi$
$54$	−4.05657	−	7.02619i	−0.552029	−	0.956143i
$55$	−7.10883	+	0.134639i	−0.958555	+	0.0181547i
$56$		0			0
$57$	−6.52722	−	20.0887i	−0.864551	−	2.66081i
$58$	0.0646986	−	0.615566i	0.00849535	−	0.0808278i
$59$	0.0385041	+	0.366342i	0.00501281	+	0.0476937i	0.996742	−	0.0806516i	$-0.0257001\pi$
$59$	0.0385041	+	0.366342i	0.00501281	+	0.0476937i	−0.991730	+	0.128345i	$0.959033\pi$
$60$	−6.98755	−	7.76046i	−0.902089	−	1.00187i
$61$	−4.90197	+	1.04195i	−0.627633	+	0.133408i	−0.510738	−	0.859737i	$-0.670628\pi$
$61$	−4.90197	+	1.04195i	−0.627633	+	0.133408i	−0.116896	+	0.993144i	$0.537294\pi$
$62$	−1.62647	+	1.18170i	−0.206562	+	0.150076i
$63$		0			0
$64$	0.260682	+	0.802296i	0.0325852	+	0.100287i
$65$	−2.71002	−	4.69389i	−0.336136	−	0.582205i
$66$	3.37217	−	6.10491i	0.415086	−	0.751463i
$67$	0.451065	−	0.781267i	0.0551063	−	0.0954469i	−0.837156	−	0.546964i	$-0.815784\pi$
$67$	0.451065	−	0.781267i	0.0551063	−	0.0954469i	0.892263	+	0.451517i	$0.149117\pi$
$68$	1.85919	−	2.06484i	0.225459	−	0.250398i
$69$	8.03770	+	5.83973i	0.967625	+	0.703021i
$70$		0			0
$71$	−4.59489	+	14.1416i	−0.545313	+	1.67830i	0.174932	+	0.984580i	$0.444029\pi$
$71$	−4.59489	+	14.1416i	−0.545313	+	1.67830i	−0.720245	+	0.693720i	$0.755971\pi$
$72$	15.9561	−	3.39157i	1.88044	−	0.399701i
$73$	−0.840216	−	7.99413i	−0.0983399	−	0.935642i	−0.926790	−	0.375579i	$-0.877444\pi$
$73$	−0.840216	−	7.99413i	−0.0983399	−	0.935642i	0.828450	−	0.560062i	$-0.189223\pi$
$74$	−0.922155	+	0.410570i	−0.107198	+	0.0477278i
$75$	−0.849220	+	0.943154i	−0.0980595	+	0.108906i
$76$	10.4372			1.19723
$77$		0			0
$78$	5.31654			0.601980
$79$	2.71445	−	3.01470i	0.305399	−	0.339180i	−0.570836	−	0.821064i	$-0.693381\pi$
$79$	2.71445	−	3.01470i	0.305399	−	0.339180i	0.876235	+	0.481884i	$0.160047\pi$
$80$	2.95697	−	1.31653i	0.330600	−	0.147192i
$81$	−1.82507	−	17.3644i	−0.202786	−	1.92938i
$82$	−3.64308	+	0.774361i	−0.402311	+	0.0855139i
$83$	−1.25193	+	3.85305i	−0.137418	+	0.422928i	−0.995958	−	0.0898178i	$-0.971372\pi$
$83$	−1.25193	+	3.85305i	−0.137418	+	0.422928i	0.858541	+	0.512745i	$0.171372\pi$
$84$		0			0
$85$	3.10609	+	2.25670i	0.336902	+	0.244774i
$86$	−3.77780	+	4.19568i	−0.407371	+	0.452431i
$87$	1.45084	−	2.51293i	0.155547	−	0.269415i
$88$	5.38869	+	5.76150i	0.574437	+	0.614178i
$89$	4.15363	+	7.19431i	0.440284	+	0.762595i	0.997710	−	0.0676317i	$-0.0215443\pi$
$89$	4.15363	+	7.19431i	0.440284	+	0.762595i	−0.557426	+	0.830227i	$0.688211\pi$
$90$	3.04284	+	9.36491i	0.320744	+	0.987148i
$91$		0			0
$92$	−3.97163	+	2.88556i	−0.414071	+	0.300840i
$93$	−9.21896	+	1.95955i	−0.955962	+	0.203196i
$94$	1.97082	+	2.18881i	0.203274	+	0.225759i
$95$	1.50752	+	14.3431i	0.154668	+	1.47157i
$96$	−1.89314	+	18.0120i	−0.193218	+	1.83835i
$97$	2.63154	+	8.09904i	0.267192	+	0.822333i	0.991180	+	0.132520i	$0.0423070\pi$
$97$	2.63154	+	8.09904i	0.267192	+	0.822333i	−0.723988	+	0.689812i	$0.757693\pi$
$98$		0			0
$99$	18.1454	−	13.7158i	1.82368	−	1.37849i
$100$	−0.313557	−	0.543097i	−0.0313557	−	0.0543097i
$101$	3.93907	+	0.837275i	0.391952	+	0.0833119i	0.399672	−	0.916658i	$-0.369124\pi$
$101$	3.93907	+	0.837275i	0.391952	+	0.0833119i	−0.00772007	+	0.999970i	$0.502457\pi$
$102$	−3.44043	+	1.53178i	−0.340654	+	0.151669i
$103$	−16.1020	−	7.16907i	−1.58658	−	0.706390i	−0.591576	−	0.806249i	$-0.701494\pi$
$103$	−16.1020	−	7.16907i	−1.58658	−	0.706390i	−0.995002	+	0.0998598i	$0.968161\pi$
$104$	−1.85831	+	5.71929i	−0.182222	+	0.560822i
$105$		0			0
$106$	−0.361631	+	0.262741i	−0.0351248	+	0.0255196i
$107$	1.61013	−	15.3193i	0.155657	−	1.48098i	−0.586062	−	0.810266i	$-0.699323\pi$
$107$	1.61013	−	15.3193i	0.155657	−	1.48098i	0.741719	−	0.670711i	$-0.234011\pi$
$108$	18.3832	+	3.90746i	1.76892	+	0.375996i
$109$	9.46326	−	16.3908i	0.906416	−	1.56996i	0.0874110	−	0.996172i	$-0.472141\pi$
$109$	9.46326	−	16.3908i	0.906416	−	1.56996i	0.819005	−	0.573786i	$-0.194526\pi$
$110$	−3.11878	+	3.59852i	−0.297364	+	0.343106i
$111$	−4.73220			−0.449161
$112$		0			0
$113$	−1.35965	−	0.987844i	−0.127905	−	0.0929286i	0.521993	−	0.852950i	$-0.325189\pi$
$113$	−1.35965	−	0.987844i	−0.127905	−	0.0929286i	−0.649898	+	0.760021i	$0.725189\pi$
$114$	−12.9236	−	5.75397i	−1.21041	−	0.538909i
$115$	−4.53907	−	5.04114i	−0.423270	−	0.470089i
$116$	0.959397	+	1.06552i	0.0890778	+	0.0989309i
$117$	15.8402	+	7.05252i	1.46443	+	0.652005i
$118$	0.199590	+	0.145011i	0.0183738	+	0.0133493i
$119$		0			0
$120$	−16.0100			−1.46151
$121$	10.2112	+	4.09038i	0.928292	+	0.371853i
$122$	−1.67821	+	2.90674i	−0.151938	+	0.263164i
$123$	−17.0788	−	3.63022i	−1.53995	−	0.327326i
$124$	0.486799	−	4.63158i	0.0437158	−	0.415928i
$125$	9.37282	−	6.80975i	0.838330	−	0.609082i
$126$		0			0
$127$	5.42848	−	16.7071i	0.481699	−	1.48252i	−0.355006	−	0.934864i	$-0.615521\pi$
$127$	5.42848	−	16.7071i	0.481699	−	1.48252i	0.836705	−	0.547654i	$-0.184479\pi$
$128$	−10.0231	−	4.46259i	−0.885928	−	0.394441i
$129$	−24.1795	+	10.7654i	−2.12889	+	0.947843i
$130$	−3.55071	−	0.754727i	−0.311418	−	0.0661939i
$131$	−3.36278	−	5.82451i	−0.293808	−	0.508890i	0.680899	−	0.732377i	$-0.261589\pi$
$131$	−3.36278	−	5.82451i	−0.293808	−	0.508890i	−0.974707	+	0.223487i	$0.928256\pi$
$132$	5.28250	+	15.2679i	0.459783	+	1.32890i
$133$		0			0
$134$	−0.186707	−	0.574624i	−0.0161290	−	0.0496400i
$135$	−2.71453	+	25.8270i	−0.233630	+	2.22284i
$136$	−0.445271	−	4.23647i	−0.0381817	−	0.363274i
$137$	9.27925	+	10.3057i	0.792780	+	0.880472i	0.995103	−	0.0988473i	$-0.0315156\pi$
$137$	9.27925	+	10.3057i	0.792780	+	0.880472i	−0.202322	+	0.979319i	$0.564849\pi$
$138$	6.50859	−	1.38344i	0.554048	−	0.117767i
$139$	−11.5453	+	8.38812i	−0.979256	+	0.711471i	−0.957542	−	0.288293i	$-0.906912\pi$
$139$	−11.5453	+	8.38812i	−0.979256	+	0.711471i	−0.0217140	+	0.999764i	$0.506912\pi$
$140$		0			0
$141$	4.26685	+	13.1320i	0.359333	+	1.10591i
$142$	4.97933	+	8.62446i	0.417856	+	0.723749i
$143$	1.03426	+	8.32127i	0.0864893	+	0.695859i
$144$	−5.17745	+	8.96761i	−0.431454	+	0.747300i
$145$	−1.32569	+	1.47233i	−0.110093	+	0.122270i
$146$	−4.35535	−	3.16435i	−0.360451	−	0.261883i
$147$		0			0
$148$	0.722575	−	2.22386i	0.0593953	−	0.182800i
$149$	−2.56560	+	0.545336i	−0.210183	+	0.0446757i	−0.311799	−	0.950148i	$-0.600932\pi$
$149$	−2.56560	+	0.545336i	−0.210183	+	0.0446757i	0.101617	+	0.994824i	$0.467598\pi$
$150$	0.0888490	+	0.845342i	0.00725449	+	0.0690219i
$151$	−2.73113	+	1.21598i	−0.222257	+	0.0989550i	−0.514844	−	0.857284i	$-0.672150\pi$
$151$	−2.73113	+	1.21598i	−0.222257	+	0.0989550i	0.292588	+	0.956239i	$0.405484\pi$
$152$	10.7071	−	11.8914i	0.868460	−	0.964523i
$153$	−12.2824			−0.992977
$154$		0			0
$155$	6.43516			0.516884
$156$	−8.24076	+	9.15229i	−0.659789	+	0.732770i
$157$	10.2817	−	4.57770i	0.820567	−	0.365340i	0.0468741	−	0.998901i	$-0.485074\pi$
$157$	10.2817	−	4.57770i	0.820567	−	0.365340i	0.773693	+	0.633561i	$0.218407\pi$
$158$	−0.283997	−	2.70205i	−0.0225936	−	0.214964i
$159$	−2.04976	+	0.435689i	−0.162556	+	0.0345524i
$160$	3.82131	−	11.7608i	0.302101	−	0.929773i
$161$		0			0
$162$	−9.46045	−	6.87342i	−0.743283	−	0.540027i
$163$	−12.1802	+	13.5274i	−0.954023	+	1.05955i	0.0441434	+	0.999025i	$0.485944\pi$
$163$	−12.1802	+	13.5274i	−0.954023	+	1.05955i	−0.998167	+	0.0605250i	$0.980723\pi$
$164$	4.31382	−	7.47175i	0.336853	−	0.583446i
$165$	−20.2185	+	9.46460i	−1.57401	+	0.736818i
$166$	1.35668	+	2.34984i	0.105299	+	0.182383i
$167$	6.15909	+	18.9557i	0.476605	+	1.46684i	0.843781	+	0.536687i	$0.180325\pi$
$167$	6.15909	+	18.9557i	0.476605	+	1.46684i	−0.367176	+	0.930151i	$0.619675\pi$
$168$		0			0
$169$	5.34590	−	3.88402i	0.411223	−	0.298771i
$170$	2.51518	−	0.534618i	0.192906	−	0.0410033i
$171$	−30.8721	−	34.2870i	−2.36085	−	2.62199i
$172$	−1.36707	−	13.0068i	−0.104238	−	0.991758i
$173$	−0.626134	+	5.95726i	−0.0476041	+	0.452922i	0.944593	+	0.328244i	$0.106457\pi$
$173$	−0.626134	+	5.95726i	−0.0476041	+	0.452922i	−0.992197	+	0.124679i	$0.960210\pi$
$174$	−0.600539	−	1.84827i	−0.0455267	−	0.140117i
$175$		0			0
$176$	−5.00675	+	0.0948260i	−0.377398	+	0.00714778i
$177$	0.578284	+	1.00162i	0.0434665	+	0.0752861i
$178$	5.44216	+	1.15677i	0.407907	+	0.0867034i
$179$	−1.47897	+	0.658482i	−0.110544	+	0.0492172i	−0.461263	−	0.887263i	$-0.652604\pi$
$179$	−1.47897	+	0.658482i	−0.110544	+	0.0492172i	0.350720	+	0.936480i	$0.385937\pi$
$180$	−20.8379	−	9.27764i	−1.55317	−	0.691515i
$181$	0.749929	−	2.30804i	0.0557418	−	0.171556i	−0.919309	−	0.393535i	$-0.871252\pi$
$181$	0.749929	−	2.30804i	0.0557418	−	0.171556i	0.975051	+	0.221980i	$0.0712519\pi$
$182$		0			0
$183$	−12.7298	+	9.24876i	−0.941016	+	0.683688i
$184$	−0.786727	+	7.48520i	−0.0579983	+	0.551817i
$185$	3.16045	+	0.671775i	0.232361	+	0.0493899i
$186$	−3.15614	+	5.46660i	−0.231419	+	0.400830i
$187$	−3.06678	−	5.08686i	−0.224265	−	0.371988i
$188$	−6.82279			−0.497603
$189$		0			0
$190$	7.81436	+	5.67747i	0.566914	+	0.411887i
$191$	11.6029	+	5.16593i	0.839554	+	0.373794i	0.781031	−	0.624492i	$-0.214694\pi$
$191$	11.6029	+	5.16593i	0.839554	+	0.373794i	0.0585233	+	0.998286i	$0.481361\pi$
$192$	1.77230	+	1.96834i	0.127905	+	0.142053i
$193$	−1.17721	−	1.30742i	−0.0847374	−	0.0941104i	0.699285	−	0.714843i	$-0.253502\pi$
$193$	−1.17721	−	1.30742i	−0.0847374	−	0.0941104i	−0.784022	+	0.620733i	$0.786835\pi$
$194$	5.21034	+	2.31979i	0.374081	+	0.166551i
$195$	−13.7676	−	10.0027i	−0.985918	−	0.716311i
$196$		0			0
$197$	−0.903053			−0.0643399			−0.0321699	−	0.999482i	$-0.510242\pi$
$197$	−0.903053			−0.0643399			−0.0321699	+	0.999482i	$0.510242\pi$
$198$	1.30521	−	15.1780i	0.0927569	−	1.07865i
$199$	7.81479	−	13.5356i	0.553976	−	0.959515i	−0.444006	−	0.896024i	$-0.646443\pi$
$199$	7.81479	−	13.5356i	0.553976	−	0.959515i	0.997982	−	0.0634910i	$-0.0202234\pi$
$200$	−0.940435	−	0.199896i	−0.0664988	−	0.0141348i
$201$	0.296075	−	2.81696i	0.0208835	−	0.198693i
$202$	2.18200	−	1.58532i	0.153525	−	0.111543i
$203$		0			0
$204$	2.69583	−	8.29691i	0.188746	−	0.580900i
$205$	10.8910	+	4.84897i	0.760657	+	0.338666i
$206$	−10.7842	+	4.80144i	−0.751372	+	0.334532i
$207$	21.2270	+	4.51194i	1.47538	+	0.313601i
$208$	−1.90866	−	3.30590i	−0.132342	−	0.229223i
$209$	6.49180	−	21.3470i	0.449047	−	1.47660i
$210$		0			0
$211$	4.56378	+	14.0459i	0.314184	+	0.966958i	0.976089	+	0.217371i	$0.0697480\pi$
$211$	4.56378	+	14.0459i	0.314184	+	0.966958i	−0.661905	+	0.749587i	$0.730252\pi$
$212$	0.108236	−	1.02979i	0.00743365	−	0.0707265i
$213$	4.88006	+	46.4307i	0.334376	+	3.18138i
$214$	−6.90312	−	7.66669i	−0.471888	−	0.524084i
$215$	17.6768	−	3.75732i	1.20555	−	0.256247i
$216$	23.3105	−	16.9361i	1.58608	−	1.15235i
$217$		0			0
$218$	−3.91708	−	12.0555i	−0.265298	−	0.816503i
$219$	−12.6190	−	21.8567i	−0.852713	−	1.47694i
$220$	−1.36058	−	10.9467i	−0.0917302	−	0.738026i
$221$	2.26396	−	3.92129i	0.152290	−	0.263774i
$222$	−2.12072	+	2.35530i	−0.142333	+	0.158077i
$223$	1.49293	+	1.08468i	0.0999743	+	0.0726356i	0.636649	−	0.771153i	$-0.280320\pi$
$223$	1.49293	+	1.08468i	0.0999743	+	0.0726356i	−0.536675	+	0.843789i	$0.680320\pi$
$224$		0			0
$225$	−0.856647	+	2.63649i	−0.0571098	+	0.175766i
$226$	−1.10099	+	0.234022i	−0.0732367	+	0.0155669i
$227$	2.29335	+	21.8197i	0.152215	+	1.44823i	0.757821	+	0.652463i	$0.226264\pi$
$227$	2.29335	+	21.8197i	0.152215	+	1.44823i	−0.605606	+	0.795765i	$0.707069\pi$
$228$	29.9372	−	13.3289i	1.98264	−	0.882729i
$229$	−13.5511	+	15.0500i	−0.895482	+	0.994533i	0.104518	+	0.994523i	$0.466670\pi$
$229$	−13.5511	+	15.0500i	−0.895482	+	0.994533i	−1.00000		1.01247e-5i	$0.999997\pi$
$230$	−4.54323			−0.299571
$231$		0			0
$232$	2.19819			0.144318
$233$	14.0936	−	15.6525i	0.923304	−	1.02543i	−0.0762945	−	0.997085i	$-0.524309\pi$
$233$	14.0936	−	15.6525i	0.923304	−	1.02543i	0.999598	−	0.0283473i	$-0.00902442\pi$
$234$	10.6089	−	4.72338i	0.693524	−	0.308777i
$235$	−0.985464	−	9.37606i	−0.0642846	−	0.611627i
$236$	−0.559001	+	0.118819i	−0.0363879	+	0.00773449i
$237$	3.93597	−	12.1137i	0.255668	−	0.786867i
$238$		0			0
$239$	−12.5370	−	9.10863i	−0.810948	−	0.589188i	0.103157	−	0.994665i	$-0.467106\pi$
$239$	−12.5370	−	9.10863i	−0.810948	−	0.589188i	−0.914105	+	0.405477i	$0.867106\pi$
$240$	6.80027	−	7.55247i	0.438956	−	0.487510i
$241$	−7.04241	+	12.1978i	−0.453641	+	0.785730i	−0.998609	−	0.0527271i	$-0.983209\pi$
$241$	−7.04241	+	12.1978i	−0.453641	+	0.785730i	0.544967	+	0.838457i	$0.316542\pi$
$242$	6.61197	−	3.24920i	0.425033	−	0.208866i
$243$	−9.23960	−	16.0035i	−0.592721	−	1.02662i
$244$	−2.40262	−	7.39450i	−0.153812	−	0.473384i
$245$		0			0
$246$	−9.46064	+	6.87356i	−0.603188	+	0.438242i
$247$	16.6370	−	3.53629i	1.05858	−	0.225009i
$248$	−4.77753	−	5.30599i	−0.303374	−	0.336931i
$249$	1.32963	+	12.6506i	0.0842620	+	0.801700i
$250$	0.811065	−	7.71677i	0.0512963	−	0.488051i
$251$	−0.332894	−	1.02454i	−0.0210121	−	0.0646686i	0.940001	−	0.341173i	$-0.110824\pi$
$251$	−0.332894	−	1.02454i	−0.0210121	−	0.0646686i	−0.961013	+	0.276504i	$0.910824\pi$
$252$		0			0
$253$	3.43148	+	9.91790i	0.215735	+	0.623533i
$254$	−5.88267	−	10.1891i	−0.369111	−	0.639320i
$255$	11.7912	+	2.50630i	0.738395	+	0.156951i
$256$	−8.25424	+	3.67502i	−0.515890	+	0.229689i
$257$	11.9501	+	5.32053i	0.745427	+	0.331885i	0.744059	−	0.668114i	$-0.232898\pi$
$257$	11.9501	+	5.32053i	0.745427	+	0.331885i	0.00136767	+	0.999999i	$0.499565\pi$
$258$	−5.47784	+	16.8591i	−0.341035	+	1.04960i
$259$		0			0
$260$	6.80292	−	4.94261i	0.421899	−	0.306528i
$261$	0.662514	−	6.30340i	0.0410086	−	0.390171i
$262$	−4.40598	−	0.936519i	−0.272202	−	0.0578584i
$263$	4.78608	−	8.28973i	0.295122	−	0.511167i	−0.679891	−	0.733313i	$-0.737973\pi$
$263$	4.78608	−	8.28973i	0.295122	−	0.511167i	0.975013	+	0.222146i	$0.0713062\pi$
$264$	22.8143	+	9.64417i	1.40412	+	0.593557i
$265$	1.43080			0.0878935
$266$		0			0
$267$	21.1015	+	15.3312i	1.29139	+	0.938252i
$268$	1.27860	+	0.569269i	0.0781029	+	0.0347737i
$269$	−3.19077	−	3.54371i	−0.194545	−	0.216064i	0.637978	−	0.770054i	$-0.279771\pi$
$269$	−3.19077	−	3.54371i	−0.194545	−	0.216064i	−0.832523	+	0.553991i	$0.813104\pi$
$270$	11.6380	+	12.9254i	0.708269	+	0.786612i
$271$	−18.3187	−	8.15600i	−1.11278	−	0.495442i	−0.233793	−	0.972286i	$-0.575114\pi$
$271$	−18.3187	−	8.15600i	−1.11278	−	0.495442i	−0.878988	+	0.476845i	$0.841780\pi$
$272$	2.18762	+	1.58940i	0.132644	+	0.0963713i
$273$		0			0
$274$	9.28776			0.561094
$275$	−1.30582	+	0.303513i	−0.0787437	+	0.0183025i
$276$	−7.70690	+	13.3487i	−0.463901	+	0.803500i
$277$	11.3489	+	2.41228i	0.681890	+	0.144940i	0.535818	−	0.844334i	$-0.320003\pi$
$277$	11.3489	+	2.41228i	0.681890	+	0.144940i	0.146072	+	0.989274i	$0.453337\pi$
$278$	−0.999055	+	9.50537i	−0.0599193	+	0.570094i
$279$	−16.6550	+	12.1006i	−0.997111	+	0.724443i
$280$		0			0
$281$	3.73256	−	11.4876i	0.222666	−	0.685295i	−0.775854	−	0.630912i	$-0.782681\pi$
$281$	3.73256	−	11.4876i	0.222666	−	0.685295i	0.998520	−	0.0543830i	$-0.0173192\pi$
$282$	8.44819	+	3.76137i	0.503082	+	0.223987i
$283$	20.0918	−	8.94545i	1.19433	−	0.531752i	0.289361	−	0.957220i	$-0.406557\pi$
$283$	20.0918	−	8.94545i	1.19433	−	0.531752i	0.904973	+	0.425469i	$0.139891\pi$
$284$	−22.5649	−	4.79631i	−1.33898	−	0.284609i
$285$	22.6410	+	39.2154i	1.34114	+	2.32292i
$286$	4.60513	+	3.21438i	0.272307	+	0.190070i
$287$		0			0
$288$	12.2248	+	37.6240i	0.720353	+	2.21702i
$289$	1.44172	−	13.7170i	0.0848071	−	0.806885i
$290$	0.138700	+	1.31964i	0.00814472	+	0.0774918i
$291$	17.8911	+	19.8700i	1.04879	+	1.16480i
$292$	12.1982	−	2.59281i	0.713848	−	0.151733i
$293$	−1.14654	+	0.833014i	−0.0669819	+	0.0486652i	−0.620772	−	0.783991i	$-0.713181\pi$
$293$	−1.14654	+	0.833014i	−0.0669819	+	0.0486652i	0.553790	+	0.832656i	$0.313181\pi$
$294$		0			0
$295$	−0.244025	−	0.751033i	−0.0142077	−	0.0437268i
$296$	−1.79246	−	3.10463i	−0.104184	−	0.180453i
$297$	19.4260	−	35.1684i	1.12721	−	2.04068i
$298$	−0.878343	+	1.52133i	−0.0508810	+	0.0881286i
$299$	−5.35314	+	5.94527i	−0.309580	+	0.343824i
$300$	−1.59295	−	1.15735i	−0.0919691	−	0.0668195i
$301$		0			0
$302$	−0.618734	+	1.90427i	−0.0356041	+	0.109578i
$303$	12.3678	−	2.62885i	0.710510	−	0.151024i
$304$	1.06174	+	10.1018i	0.0608951	+	0.579378i
$305$	9.81469	−	4.36978i	0.561988	−	0.250213i
$306$	−5.50433	+	6.11318i	−0.314662	+	0.349467i
$307$	29.4646			1.68163			0.840817	−	0.541319i	$-0.182075\pi$
$307$	29.4646			1.68163			0.840817	+	0.541319i	$0.182075\pi$
$308$		0			0
$309$	−55.3411			−3.14825
$310$	2.88389	−	3.20289i	0.163794	−	0.181912i
$311$	24.5549	−	10.9325i	1.39238	−	0.619928i	0.432833	−	0.901474i	$-0.357514\pi$
$311$	24.5549	−	10.9325i	1.39238	−	0.619928i	0.959548	+	0.281546i	$0.0908473\pi$
$312$	1.97364	+	18.7780i	0.111736	+	1.06309i
$313$	4.39452	−	0.934085i	0.248393	−	0.0527976i	−0.0820323	−	0.996630i	$-0.526141\pi$
$313$	4.39452	−	0.934085i	0.248393	−	0.0527976i	0.330426	+	0.943832i	$0.392808\pi$
$314$	2.32930	−	7.16884i	0.131450	−	0.404561i
$315$		0			0
$316$	5.09172	+	3.69935i	0.286431	+	0.208105i
$317$	−7.32702	+	8.13748i	−0.411527	+	0.457046i	−0.912899	−	0.408185i	$-0.866162\pi$
$317$	−7.32702	+	8.13748i	−0.411527	+	0.457046i	0.501373	+	0.865231i	$0.332829\pi$
$318$	−0.701741	+	1.21545i	−0.0393517	+	0.0681591i
$319$	2.77602	−	1.29950i	0.155427	−	0.0727580i
$320$	−0.904228	−	1.56617i	−0.0505479	−	0.0875515i
$321$	−14.9454	−	45.9971i	−0.834169	−	2.56731i
$322$		0			0
$323$	−9.74723	+	7.08177i	−0.542350	+	0.394040i
$324$	26.4963	−	5.63197i	1.47202	−	0.312887i
$325$	−0.683823	−	0.759463i	−0.0379317	−	0.0421274i
$326$	1.27434	+	12.1245i	0.0705791	+	0.671516i
$327$	6.21160	−	59.0995i	0.343502	−	3.26821i
$328$	−4.08744	−	12.5799i	−0.225691	−	0.694607i
$329$		0			0
$330$	−4.35016	+	14.3046i	−0.239468	+	0.787443i
$331$	−8.26132	−	14.3090i	−0.454083	−	0.786495i	0.544552	−	0.838727i	$-0.316700\pi$
$331$	−8.26132	−	14.3090i	−0.454083	−	0.786495i	−0.998635	+	0.0522322i	$0.983366\pi$
$332$	−6.14807	−	1.30681i	−0.337419	−	0.0717207i
$333$	−9.44286	+	4.20423i	−0.517466	+	0.230391i
$334$	12.1948	+	5.42946i	0.667268	+	0.297087i
$335$	−0.597628	+	1.83931i	−0.0326519	+	0.100492i
$336$		0			0
$337$	9.80588	−	7.12439i	0.534160	−	0.388090i	−0.287751	−	0.957705i	$-0.592908\pi$
$337$	9.80588	−	7.12439i	0.534160	−	0.388090i	0.821912	+	0.569615i	$0.192908\pi$
$338$	0.462601	−	4.40135i	0.0251622	−	0.239402i
$339$	−5.16146	−	1.09710i	−0.280332	−	0.0595864i
$340$	−2.97826	+	5.15849i	−0.161519	+	0.279758i
$341$	−9.17011	−	3.87643i	−0.496590	−	0.209921i
$342$	−30.9004			−1.67090
$343$		0			0
$344$	−16.2215	−	11.7856i	−0.874605	−	0.635437i
$345$	−19.4574	−	8.66298i	−1.04755	−	0.466399i
$346$	2.68443	+	2.98136i	0.144316	+	0.160279i
$347$	−16.2499	−	18.0474i	−0.872342	−	0.968833i	0.127393	−	0.991852i	$-0.459339\pi$
$347$	−16.2499	−	18.0474i	−0.872342	−	0.968833i	−0.999735	+	0.0230188i	$0.992672\pi$
$348$	4.11260	+	1.83105i	0.220458	+	0.0981544i
$349$	2.68497	+	1.95074i	0.143723	+	0.104421i	0.657323	−	0.753609i	$-0.271689\pi$
$349$	2.68497	+	1.95074i	0.143723	+	0.104421i	−0.513600	+	0.858030i	$0.671689\pi$
$350$		0			0
$351$	30.6269			1.63474
$352$	−12.5299	+	14.4573i	−0.667845	+	0.770575i
$353$	−10.1636	+	17.6039i	−0.540955	+	0.936962i	0.457894	+	0.889007i	$0.348604\pi$
$353$	−10.1636	+	17.6039i	−0.540955	+	0.936962i	−0.998849	+	0.0479552i	$0.984730\pi$
$354$	0.757677	+	0.161049i	0.0402701	+	0.00855967i
$355$	3.33202	−	31.7020i	0.176845	−	1.68257i
$356$	−10.4268	+	7.57553i	−0.552620	+	0.401502i
$357$		0			0
$358$	−0.335059	+	1.03121i	−0.0177084	+	0.0545009i
$359$	26.5305	+	11.8121i	1.40023	+	0.623421i	0.961401	−	0.275152i	$-0.0887282\pi$
$359$	26.5305	+	11.8121i	1.40023	+	0.623421i	0.438825	+	0.898573i	$0.355395\pi$
$360$	−31.9472	+	14.2238i	−1.68376	+	0.749660i
$361$	−25.6841	−	5.45933i	−1.35180	−	0.287333i
$362$	−0.812674	−	1.40759i	−0.0427132	−	0.0739814i
$363$	34.5127	−	1.30779i	1.81145	−	0.0686410i
$364$		0			0
$365$	5.32499	+	16.3886i	0.278723	+	0.857821i
$366$	−1.10156	+	10.4806i	−0.0575795	+	0.547832i
$367$	2.37894	+	22.6341i	0.124180	+	1.18149i	0.862148	+	0.506656i	$0.169119\pi$
$367$	2.37894	+	22.6341i	0.124180	+	1.18149i	−0.737969	+	0.674835i	$0.764215\pi$
$368$	−3.19686	−	3.55047i	−0.166648	−	0.185081i
$369$	−37.3052	+	7.92946i	−1.94203	+	0.412791i
$370$	1.75070	−	1.27196i	0.0910145	−	0.0661259i
$371$		0			0
$372$	−4.51852	−	13.9066i	−0.234274	−	0.721022i
$373$	11.1206	+	19.2614i	0.575802	+	0.997319i	0.995954	+	0.0898652i	$0.0286436\pi$
$373$	11.1206	+	19.2614i	0.575802	+	0.997319i	−0.420151	+	0.907454i	$0.638023\pi$
$374$	−3.90618	−	0.753271i	−0.201984	−	0.0389507i
$375$	18.1878	−	31.5022i	0.939215	−	1.62677i
$376$	−6.99924	+	7.77344i	−0.360958	+	0.400885i
$377$	1.89030	+	1.37339i	0.0973556	+	0.0707330i
$378$		0			0
$379$	10.3430	−	31.8325i	0.531285	−	1.63513i	−0.220258	−	0.975442i	$-0.570690\pi$
$379$	10.3430	−	31.8325i	0.531285	−	1.63513i	0.751543	−	0.659685i	$-0.229310\pi$
$380$	−21.8861	+	4.65202i	−1.12273	+	0.238644i
$381$	−5.76539	−	54.8540i	−0.295370	−	2.81025i
$382$	7.77095	−	3.45985i	0.397596	−	0.177021i
$383$	−4.11243	+	4.56731i	−0.210135	+	0.233379i	−0.838994	−	0.544141i	$-0.816856\pi$
$383$	−4.11243	+	4.56731i	−0.210135	+	0.233379i	0.628859	+	0.777520i	$0.283522\pi$
$384$	−34.4486			−1.75795
$385$		0			0
$386$	−1.17829			−0.0599733
$387$	−38.6847	+	42.9637i	−1.96645	+	2.18397i
$388$	−12.0696	+	5.37374i	−0.612742	+	0.272810i
$389$	−0.773892	−	7.36309i	−0.0392379	−	0.373323i	−0.996467	−	0.0839908i	$-0.973233\pi$
$389$	−0.773892	−	7.36309i	−0.0392379	−	0.373323i	0.957229	−	0.289332i	$-0.0934333\pi$
$390$	−11.1484	+	2.36967i	−0.564522	+	0.119993i
$391$	1.75119	−	5.38962i	0.0885617	−	0.272565i
$392$		0			0
$393$	−17.0838	−	12.4121i	−0.861765	−	0.626109i
$394$	−0.404700	+	0.449465i	−0.0203885	+	0.0226437i
$395$	−4.34831	+	7.53150i	−0.218787	+	0.378951i
$396$	24.1054	+	25.7731i	1.21134	+	1.29515i
$397$	−8.90394	−	15.4221i	−0.446876	−	0.774012i	0.551305	−	0.834304i	$-0.314130\pi$
$397$	−8.90394	−	15.4221i	−0.446876	−	0.774012i	−0.998181	+	0.0602921i	$0.980797\pi$
$398$	−3.23473	−	9.95549i	−0.162143	−	0.499024i
$399$		0			0
$400$	0.493749	−	0.358729i	0.0246874	−	0.0179365i
$401$	−25.1177	+	5.33893i	−1.25432	+	0.266614i	−0.786710	−	0.617322i	$-0.788218\pi$
$401$	−25.1177	+	5.33893i	−1.25432	+	0.266614i	−0.467608	+	0.883936i	$0.654884\pi$
$402$	−1.26937	−	1.40977i	−0.0633102	−	0.0703131i
$403$	−0.793297	−	7.54772i	−0.0395170	−	0.375979i
$404$	−0.653070	+	6.21354i	−0.0324914	+	0.309135i
$405$	11.5667	+	35.5985i	0.574752	+	1.76890i
$406$		0			0
$407$	−4.09899	−	2.86108i	−0.203179	−	0.141819i
$408$	−6.68741	−	11.5829i	−0.331076	−	0.573441i
$409$	−1.30832	−	0.278091i	−0.0646921	−	0.0137507i	0.175452	−	0.984488i	$-0.443861\pi$
$409$	−1.30832	−	0.278091i	−0.0646921	−	0.0137507i	−0.240144	+	0.970737i	$0.577195\pi$
$410$	7.29415	−	3.24757i	0.360232	−	0.160386i
$411$	39.7769	+	17.7098i	1.96205	+	0.873560i
$412$	8.45022	−	26.0071i	0.416312	−	1.28128i
$413$		0			0
$414$	11.7585	−	8.54303i	0.577897	−	0.419867i
$415$	0.907848	−	8.63760i	0.0445645	−	0.424003i
$416$	−14.2652	−	3.03216i	−0.699408	−	0.148664i
$417$	−22.4034	+	38.8039i	−1.09710	+	1.90023i
$418$	−7.71547	−	12.7976i	−0.377376	−	0.625953i
$419$	37.4618			1.83013			0.915064	−	0.403310i	$-0.132140\pi$
$419$	37.4618			1.83013			0.915064	+	0.403310i	$0.132140\pi$
$420$		0			0
$421$	−6.68374	−	4.85602i	−0.325746	−	0.236668i	0.412878	−	0.910787i	$-0.364524\pi$
$421$	−6.68374	−	4.85602i	−0.325746	−	0.236668i	−0.738623	+	0.674118i	$0.764524\pi$
$422$	9.03611	+	4.02313i	0.439871	+	0.195843i
$423$	20.1811	+	22.4134i	0.981241	+	1.08978i
$424$	−1.06224	−	1.17974i	−0.0515871	−	0.0572933i
$425$	0.661329	+	0.294442i	0.0320791	+	0.0142826i
$426$	25.2963	+	18.3788i	1.22561	+	0.890458i
$427$		0			0
$428$	23.8980			1.15515
$429$	13.5934	+	22.5473i	0.656294	+	1.08859i
$430$	6.05171	−	10.4819i	0.291840	−	0.505481i
$431$	−31.9428	−	6.78966i	−1.53863	−	0.327046i	−0.640912	−	0.767614i	$-0.721444\pi$
$431$	−31.9428	−	6.78966i	−1.53863	−	0.327046i	−0.897719	+	0.440568i	$0.854777\pi$
$432$	−1.91184	+	18.1900i	−0.0919836	+	0.875165i
$433$	−12.7786	+	9.28422i	−0.614102	+	0.446171i	−0.850856	−	0.525398i	$-0.823916\pi$
$433$	−12.7786	+	9.28422i	−0.614102	+	0.446171i	0.236754	+	0.971570i	$0.423916\pi$
$434$		0			0
$435$	−1.92226	+	5.91611i	−0.0921654	+	0.283656i
$436$	26.8248	+	11.9432i	1.28468	+	0.571975i
$437$	19.4470	−	8.65837i	0.930277	−	0.414186i
$438$	−16.5336	−	3.51433i	−0.790007	−	0.167921i
$439$	10.3471	+	17.9217i	0.493839	+	0.855354i	0.999975	−	0.00709942i	$-0.00225984\pi$
$439$	10.3471	+	17.9217i	0.493839	+	0.855354i	−0.506136	+	0.862454i	$0.668927\pi$
$440$	−13.8677	−	9.67964i	−0.661118	−	0.461459i
$441$		0			0
$442$	−0.937107	−	2.88412i	−0.0445737	−	0.137184i
$443$	−3.14583	+	29.9306i	−0.149463	+	1.42205i	0.620625	+	0.784108i	$0.286879\pi$
$443$	−3.14583	+	29.9306i	−0.149463	+	1.42205i	−0.770088	+	0.637938i	$0.779788\pi$
$444$	−0.767421	−	7.30152i	−0.0364202	−	0.346515i
$445$	−11.9165	−	13.2346i	−0.564897	−	0.627381i
$446$	1.20892	−	0.256963i	0.0572438	−	0.0121676i
$447$	−6.66256	+	4.84063i	−0.315128	+	0.228954i
$448$		0			0
$449$	11.2465	+	34.6132i	0.530755	+	1.63350i	0.752647	+	0.658424i	$0.228777\pi$
$449$	11.2465	+	34.6132i	0.530755	+	1.63350i	−0.221892	+	0.975071i	$0.571223\pi$
$450$	0.928321	+	1.60790i	0.0437615	+	0.0757971i
$451$	−12.5987	−	13.4703i	−0.593250	−	0.634292i
$452$	1.30369	−	2.25806i	0.0613206	−	0.106210i
$453$	−6.28090	+	6.97565i	−0.295103	+	0.327745i
$454$	11.8878	+	8.63700i	0.557922	+	0.405354i
$455$		0			0
$456$	15.5254	−	47.7821i	0.727041	−	2.23760i
$457$	9.57999	−	2.03629i	0.448133	−	0.0952536i	0.0216834	−	0.999765i	$-0.493097\pi$
$457$	9.57999	−	2.03629i	0.448133	−	0.0952536i	0.426450	+	0.904511i	$0.359764\pi$
$458$	1.41777	+	13.4892i	0.0662482	+	0.630310i
$459$	−19.8192	+	8.82409i	−0.925082	+	0.411873i
$460$	7.04210	−	7.82105i	0.328340	−	0.364658i
$461$	−21.8596			−1.01810			−0.509052	−	0.860736i	$-0.670004\pi$
$461$	−21.8596			−1.01810			−0.509052	+	0.860736i	$0.670004\pi$
$462$		0			0
$463$	6.75889			0.314112			0.157056	−	0.987590i	$-0.449800\pi$
$463$	6.75889			0.314112			0.157056	+	0.987590i	$0.449800\pi$
$464$	−0.933684	+	1.03696i	−0.0433452	+	0.0481397i
$465$	18.4581	−	8.21809i	0.855975	−	0.381105i
$466$	−1.47453	−	14.0293i	−0.0683065	−	0.649893i
$467$	29.3671	−	6.24217i	1.35895	−	0.288853i	0.529914	−	0.848051i	$-0.322224\pi$
$467$	29.3671	−	6.24217i	1.35895	−	0.288853i	0.829034	+	0.559198i	$0.188891\pi$
$468$	−8.31283	+	25.5843i	−0.384261	+	1.18263i
$469$		0			0
$470$	−5.10826	−	3.71136i	−0.235626	−	0.171192i
$471$	23.6452	−	26.2606i	1.08951	−	1.21003i
$472$	−0.438083	+	0.758782i	−0.0201644	+	0.0349258i
$473$	−27.4529	−	5.29402i	−1.26228	−	0.243419i
$474$	−4.26528	−	7.38768i	−0.195911	−	0.339328i
$475$	0.840312	+	2.58622i	0.0385562	+	0.118664i
$476$		0			0
$477$	−3.70311	+	2.69046i	−0.169554	+	0.123188i
$478$	−10.1519	+	2.15785i	−0.464337	+	0.0986980i
$479$	−4.01715	−	4.46149i	−0.183548	−	0.203851i	0.644348	−	0.764733i	$-0.277129\pi$
$479$	−4.01715	−	4.46149i	−0.183548	−	0.203851i	−0.827896	+	0.560882i	$0.810462\pi$
$480$	−4.05848	−	38.6138i	−0.185243	−	1.76247i
$481$	0.398310	−	3.78967i	0.0181614	−	0.172794i
$482$	2.91503	+	8.97153i	0.132776	+	0.408642i
$483$		0			0
$484$	−4.65528	+	16.4187i	−0.211604	+	0.746303i
$485$	−9.12803	−	15.8102i	−0.414483	−	0.717905i
$486$	−12.1059	−	2.57318i	−0.549134	−	0.116722i
$487$	5.81675	−	2.58978i	0.263582	−	0.117354i	−0.270691	−	0.962666i	$-0.587252\pi$
$487$	5.81675	−	2.58978i	0.263582	−	0.117354i	0.534273	+	0.845312i	$0.320585\pi$
$488$	−10.8896	−	4.84834i	−0.492947	−	0.219474i
$489$	−17.6613	+	54.3559i	−0.798671	+	2.45806i
$490$		0			0
$491$	−10.0131	+	7.27496i	−0.451886	+	0.328314i	−0.790340	−	0.612669i	$-0.790096\pi$
$491$	−10.0131	+	7.27496i	−0.451886	+	0.328314i	0.338454	+	0.940983i	$0.390096\pi$
$492$	2.83155	−	26.9404i	0.127656	−	1.21457i
$493$	−1.61895	−	0.344118i	−0.0729137	−	0.0154983i
$494$	5.69571	−	9.86527i	0.256262	−	0.443859i
$495$	−31.9363	+	36.8489i	−1.43543	+	1.65623i
$496$	4.53228			0.203505
$497$		0			0
$498$	6.89229	+	5.00754i	0.308851	+	0.224393i
$499$	−13.0451	−	5.80806i	−0.583979	−	0.260004i	0.0934116	−	0.995628i	$-0.470223\pi$
$499$	−13.0451	−	5.80806i	−0.583979	−	0.260004i	−0.677391	+	0.735623i	$0.736889\pi$
$500$	12.0271	+	13.3574i	0.537866	+	0.597361i
$501$	41.8739	+	46.5057i	1.87079	+	2.07772i
$502$	−0.659118	−	0.293458i	−0.0294179	−	0.0130977i
$503$	−4.79402	−	3.48306i	−0.213755	−	0.155302i	0.475756	−	0.879577i	$-0.342174\pi$
$503$	−4.79402	−	3.48306i	−0.213755	−	0.155302i	−0.689511	+	0.724275i	$0.742174\pi$
$504$		0			0
$505$	−8.63314			−0.384170
$506$	6.47411	+	2.73676i	0.287809	+	0.121664i
$507$	10.3736	−	17.9677i	0.460709	−	0.797972i
$508$	26.6585	+	5.66644i	1.18278	+	0.251408i
$509$	−3.22716	+	30.7044i	−0.143041	+	1.36095i	0.653758	+	0.756703i	$0.273191\pi$
$509$	−3.22716	+	30.7044i	−0.143041	+	1.36095i	−0.796800	+	0.604244i	$0.793475\pi$
$510$	6.53162	−	4.74550i	0.289225	−	0.210134i
$511$		0			0
$512$	4.91089	−	15.1142i	0.217033	−	0.667958i
$513$	−74.4488	−	33.1467i	−3.28700	−	1.46346i
$514$	8.00351	−	3.56339i	0.353020	−	0.157174i
$515$	36.9602	+	7.85613i	1.62866	+	0.346182i
$516$	−20.5317	−	35.5619i	−0.903856	−	1.56552i
$517$	−4.24370	+	13.9545i	−0.186637	+	0.613720i
$518$		0			0
$519$	5.81183	+	17.8870i	0.255111	+	0.785151i
$520$	1.34757	−	12.8212i	0.0590947	−	0.562249i
$521$	−1.97422	−	18.7835i	−0.0864924	−	0.822920i	−0.948660	−	0.316297i	$-0.897560\pi$
$521$	−1.97422	−	18.7835i	−0.0864924	−	0.822920i	0.862168	−	0.506623i	$-0.169106\pi$
$522$	−2.84040	−	3.15459i	−0.124321	−	0.138073i
$523$	7.76853	−	1.65125i	0.339694	−	0.0722043i	−0.0349061	−	0.999391i	$-0.511113\pi$
$523$	7.76853	−	1.65125i	0.339694	−	0.0722043i	0.374600	+	0.927186i	$0.377780\pi$
$524$	8.44156	−	6.13315i	0.368771	−	0.267928i
$525$		0			0
$526$	−1.98108	−	6.09712i	−0.0863790	−	0.265847i
$527$	2.68798	+	4.65571i	0.117090	+	0.202806i
$528$	−14.2399	+	6.66591i	−0.619711	+	0.290097i
$529$	6.49365	−	11.2473i	0.282333	−	0.489014i
$530$	0.641209	−	0.712134i	0.0278523	−	0.0309331i
$531$	2.04380	+	1.48491i	0.0886935	+	0.0644396i
$532$		0			0
$533$	4.34471	−	13.3716i	0.188190	−	0.579190i
$534$	17.0872	−	3.63199i	0.739434	−	0.157171i
$535$	3.45176	+	32.8413i	0.149232	+	1.41985i
$536$	1.96025	−	0.872762i	0.0846701	−	0.0376976i
$537$	−3.40126	+	3.77748i	−0.146775	+	0.163010i
$538$	−3.19370			−0.137690
$539$		0			0
$540$	−40.2899			−1.73380
$541$	5.08650	−	5.64913i	0.218686	−	0.242875i	−0.623813	−	0.781574i	$-0.714417\pi$
$541$	5.08650	−	5.64913i	0.218686	−	0.242875i	0.842498	+	0.538699i	$0.181084\pi$
$542$	−12.2688	+	5.46243i	−0.526991	+	0.234631i
$543$	−0.796472	−	7.57792i	−0.0341799	−	0.325200i
$544$	10.1049	−	2.14786i	0.433243	−	0.0920886i
$545$	−12.5381	+	38.5884i	−0.537075	+	1.65295i
$546$		0			0
$547$	−17.5548	−	12.7543i	−0.750590	−	0.545335i	0.145420	−	0.989370i	$-0.453547\pi$
$547$	−17.5548	−	12.7543i	−0.750590	−	0.545335i	−0.896010	+	0.444035i	$0.853547\pi$
$548$	−14.3962	+	15.9886i	−0.614977	+	0.683001i
$549$	−17.1848	+	29.7650i	−0.733431	+	1.27034i
$550$	−0.434133	+	0.785945i	−0.0185115	+	0.0335128i
$551$	−3.10863	−	5.38431i	−0.132432	−	0.229379i
$552$	7.30247	+	22.4747i	0.310814	+	0.956587i
$553$		0			0
$554$	6.28660	−	4.56749i	0.267092	−	0.194054i
$555$	9.92310	−	2.10922i	0.421212	−	0.0895314i
$556$	−14.8147	−	16.4534i	−0.628283	−	0.697779i
$557$	4.24525	+	40.3909i	0.179877	+	1.71142i	0.596729	+	0.802443i	$0.296467\pi$
$557$	4.24525	+	40.3909i	0.179877	+	1.71142i	−0.416852	+	0.908974i	$0.636867\pi$
$558$	−1.44122	+	13.7123i	−0.0610118	+	0.580489i
$559$	−6.58604	−	20.2697i	−0.278560	−	0.857319i
$560$		0			0
$561$	−15.2928	−	10.6743i	−0.645661	−	0.450670i
$562$	−4.04486	−	7.00590i	−0.170622	−	0.295526i
$563$	22.9173	+	4.87122i	0.965848	+	0.205297i	0.663729	−	0.747973i	$-0.268973\pi$
$563$	22.9173	+	4.87122i	0.965848	+	0.205297i	0.302119	+	0.953270i	$0.402306\pi$
$564$	−19.5700	+	8.71312i	−0.824045	+	0.366889i
$565$	3.29139	+	1.46542i	0.138470	+	0.0616508i
$566$	4.55177	−	14.0089i	0.191325	−	0.588838i
$567$		0			0
$568$	−28.6130	+	20.7886i	−1.20058	+	0.872269i
$569$	1.16501	−	11.0843i	0.0488396	−	0.464678i	−0.942582	−	0.333975i	$-0.891610\pi$
$569$	1.16501	−	11.0843i	0.0488396	−	0.464678i	0.991422	−	0.130703i	$-0.0417234\pi$
$570$	29.6646	+	6.30541i	1.24251	+	0.264104i
$571$	3.07923	−	5.33338i	0.128862	−	0.223195i	−0.794374	−	0.607429i	$-0.792201\pi$
$571$	3.07923	−	5.33338i	0.128862	−	0.223195i	0.923236	+	0.384234i	$0.125534\pi$
$572$	−12.6715	+	2.94527i	−0.529823	+	0.123148i
$573$	39.8780			1.66593
$574$		0			0
$575$	−1.03477	−	0.751805i	−0.0431529	−	0.0313524i
$576$	5.28527	+	2.35315i	0.220219	+	0.0980480i
$577$	−9.69179	−	10.7638i	−0.403474	−	0.448104i	0.506828	−	0.862047i	$-0.330818\pi$
$577$	−9.69179	−	10.7638i	−0.403474	−	0.448104i	−0.910303	+	0.413943i	$0.864151\pi$
$578$	−6.18110	−	6.86481i	−0.257100	−	0.285538i
$579$	−5.04628	−	2.24675i	−0.209716	−	0.0933716i
$580$	−2.48671	−	1.80670i	−0.103255	−	0.0750192i
$581$		0			0
$582$	17.9075			0.742288
$583$	−2.03890	−	0.861892i	−0.0844425	−	0.0356959i
$584$	9.55961	−	16.5577i	0.395580	−	0.685164i
$585$	−36.3593	−	7.72840i	−1.50327	−	0.319530i
$586$	−0.0992149	+	0.943966i	−0.00409853	+	0.0389949i
$587$	−12.8285	+	9.32048i	−0.529491	+	0.384698i	−0.820167	−	0.572124i	$-0.806120\pi$
$587$	−12.8285	+	9.32048i	−0.529491	+	0.384698i	0.290676	+	0.956821i	$0.406120\pi$
$588$		0			0
$589$	−6.24035	+	19.2058i	−0.257129	+	0.791362i
$590$	−0.483161	−	0.215117i	−0.0198914	−	0.00885623i
$591$	−2.59025	+	1.15325i	−0.106549	+	0.0474385i
$592$	2.22590	+	0.473131i	0.0914841	+	0.0194456i
$593$	−11.4642	−	19.8566i	−0.470780	−	0.815415i	0.528662	−	0.848833i	$-0.322694\pi$
$593$	−11.4642	−	19.8566i	−0.470780	−	0.815415i	−0.999441	+	0.0334179i	$0.989361\pi$
$594$	−8.79822	−	25.4292i	−0.360995	−	1.04337i
$595$		0			0
$596$	−1.25749	−	3.87015i	−0.0515087	−	0.158527i
$597$	5.12956	−	48.8045i	0.209939	−	1.99744i
$598$	0.560068	+	5.32870i	0.0229029	+	0.217907i
$599$	8.79987	+	9.77325i	0.359553	+	0.399324i	0.895597	−	0.444866i	$-0.146749\pi$
$599$	8.79987	+	9.77325i	0.359553	+	0.399324i	−0.536044	+	0.844190i	$0.680082\pi$
$600$	−2.95275	+	0.627627i	−0.120546	+	0.0256228i
$601$	−22.1286	+	16.0774i	−0.902645	+	0.655810i	−0.939144	−	0.343524i	$-0.888379\pi$
$601$	−22.1286	+	16.0774i	−0.902645	+	0.655810i	0.0364993	+	0.999334i	$0.488379\pi$
$602$		0			0
$603$	−1.91188	−	5.88415i	−0.0778576	−	0.239621i
$604$	−2.31910	−	4.01679i	−0.0943627	−	0.163441i
$605$	−23.2354	−	4.02595i	−0.944652	−	0.163678i
$606$	4.23415	−	7.33376i	0.172001	−	0.297914i
$607$	−31.3650	+	34.8344i	−1.27307	+	1.41389i	−0.407413	+	0.913244i	$0.633569\pi$
$607$	−31.3650	+	34.8344i	−1.27307	+	1.41389i	−0.865655	+	0.500641i	$0.833098\pi$
$608$	31.3946	+	22.8095i	1.27322	+	0.925049i
$609$		0			0
$610$	2.22350	−	6.84324i	0.0900270	−	0.277075i
$611$	−10.8756	+	2.31168i	−0.439979	+	0.0935205i
$612$	−1.99184	−	18.9511i	−0.0805155	−	0.766054i
$613$	−18.6998	+	8.32567i	−0.755276	+	0.336270i	−0.747996	−	0.663703i	$-0.768984\pi$
$613$	−18.6998	+	8.32567i	−0.755276	+	0.336270i	−0.00727967	+	0.999974i	$0.502317\pi$
$614$	13.2045	−	14.6650i	0.532888	−	0.591832i
$615$	37.4312			1.50937
$616$		0			0
$617$	44.1691			1.77818			0.889090	−	0.457733i	$-0.151338\pi$
$617$	44.1691			1.77818			0.889090	+	0.457733i	$0.151338\pi$
$618$	−24.8009	+	27.5442i	−0.997639	+	1.10799i
$619$	0.622658	−	0.277225i	0.0250267	−	0.0111426i	−0.394185	−	0.919031i	$-0.628973\pi$
$619$	0.622658	−	0.277225i	0.0250267	−	0.0111426i	0.419212	+	0.907888i	$0.362306\pi$
$620$	1.04359	+	9.92909i	0.0419116	+	0.398762i
$621$	37.4939	−	7.96957i	1.50458	−	0.319808i
$622$	5.56287	−	17.1208i	0.223051	−	0.686480i
$623$		0			0
$624$	−9.69651	−	7.04492i	−0.388171	−	0.282023i
$625$	−15.2666	+	16.9553i	−0.610663	+	0.678210i
$626$	1.50448	−	2.60584i	0.0601311	−	0.104150i
$627$	−8.64080	−	69.5205i	−0.345080	−	2.77638i
$628$	8.73051	+	15.1217i	0.348385	+	0.603421i
$629$	0.834110	+	2.56713i	0.0332582	+	0.102358i
$630$		0			0
$631$	29.8299	−	21.6727i	1.18751	−	0.862776i	0.194511	−	0.980900i	$-0.437688\pi$
$631$	29.8299	−	21.6727i	1.18751	−	0.862776i	0.992999	+	0.118124i	$0.0376880\pi$
$632$	9.43819	−	2.00615i	0.375431	−	0.0798003i
$633$	31.0278	+	34.4599i	1.23325	+	1.36966i
$634$	0.766584	+	7.29356i	0.0304449	+	0.289664i
$635$	−3.93650	+	37.4533i	−0.156215	+	1.48629i
$636$	−1.00465	−	3.09201i	−0.0398371	−	0.122606i
$637$		0			0
$638$	0.597281	−	1.96404i	0.0236466	−	0.0777570i
$639$	50.9884	+	88.3144i	2.01707	+	3.49367i
$640$	23.0069	+	4.89026i	0.909427	+	0.193305i
$641$	−18.7392	+	8.34324i	−0.740155	+	0.329538i	−0.741946	−	0.670460i	$-0.766097\pi$
$641$	−18.7392	+	8.34324i	−0.740155	+	0.329538i	0.00179052	+	0.999998i	$0.499430\pi$
$642$	−29.5912	−	13.1749i	−1.16787	−	0.519970i
$643$	−2.35984	+	7.26283i	−0.0930629	+	0.286418i	−0.986744	−	0.162284i	$-0.948114\pi$
$643$	−2.35984	+	7.26283i	−0.0930629	+	0.286418i	0.893681	+	0.448703i	$0.148114\pi$
$644$		0			0
$645$	45.9045	−	33.3516i	1.80749	−	1.31322i
$646$	−0.843464	+	8.02503i	−0.0331857	+	0.315741i
$647$	−14.3620	−	3.05273i	−0.564627	−	0.120015i	−0.0832499	−	0.996529i	$-0.526530\pi$
$647$	−14.3620	−	3.05273i	−0.564627	−	0.120015i	−0.481377	+	0.876513i	$0.659863\pi$
$648$	20.7649	−	35.9658i	0.815721	−	1.41287i
$649$	−0.104673	+	1.21722i	−0.00410877	+	0.0477801i
$650$	−0.684450			−0.0268463
$651$		0			0
$652$	−22.8473	−	16.5996i	−0.894770	−	0.650089i
$653$	1.02960	+	0.458406i	0.0402913	+	0.0179388i	0.426783	−	0.904354i	$-0.359647\pi$
$653$	1.02960	+	0.458406i	0.0402913	+	0.0179388i	−0.386492	+	0.922293i	$0.626313\pi$
$654$	−26.6311	−	29.5768i	−1.04136	−	1.15654i
$655$	9.64761	+	10.7148i	0.376963	+	0.418660i
$656$	7.67049	+	3.41512i	0.299482	+	0.133338i
$657$	−44.5988	−	32.4029i	−1.73996	−	1.26416i
$658$		0			0
$659$	10.0215			0.390384			0.195192	−	0.980765i	$-0.437467\pi$
$659$	10.0215			0.390384			0.195192	+	0.980765i	$0.437467\pi$
$660$	−17.8822	−	29.6612i	−0.696063	−	1.15456i
$661$	−7.86853	+	13.6287i	−0.306050	+	0.530095i	−0.977495	−	0.210960i	$-0.932341\pi$
$661$	−7.86853	+	13.6287i	−0.306050	+	0.530095i	0.671444	+	0.741055i	$0.265674\pi$
$662$	−10.8241	−	2.30074i	−0.420691	−	0.0894207i
$663$	1.48604	−	14.1387i	0.0577131	−	0.549103i
$664$	−7.79597	+	5.66410i	−0.302542	+	0.219810i
$665$		0			0
$666$	−2.13927	+	6.58398i	−0.0828949	+	0.255124i
$667$	2.67152	+	1.18944i	0.103441	+	0.0460551i
$668$	−28.2488	+	12.5772i	−1.09298	+	0.486626i
$669$	5.66742	+	1.20465i	0.219115	+	0.0465744i
$670$	0.647631	+	1.12173i	0.0250202	+	0.0433362i
$671$	−16.6182	+	0.314744i	−0.641540	+	0.0121505i
$672$		0			0
$673$	9.89226	+	30.4452i	0.381319	+	1.17358i	0.939116	+	0.343601i	$0.111647\pi$
$673$	9.89226	+	30.4452i	0.381319	+	1.17358i	−0.557797	+	0.829977i	$0.688353\pi$
$674$	0.848540	−	8.07332i	0.0326845	−	0.310973i
$675$	0.511830	+	4.86974i	0.0197004	+	0.187436i
$676$	6.85977	+	7.61855i	0.263837	+	0.293021i
$677$	15.0048	−	3.18937i	0.576682	−	0.122578i	0.0896681	−	0.995972i	$-0.471419\pi$
$677$	15.0048	−	3.18937i	0.576682	−	0.122578i	0.487014	+	0.873394i	$0.338086\pi$
$678$	−2.85913	+	2.07728i	−0.109804	+	0.0797775i
$679$		0			0
$680$	2.82197	+	8.68512i	0.108218	+	0.333059i
$681$	34.4432	+	59.6574i	1.31987	+	2.28608i
$682$	−6.03892	+	2.82691i	−0.231242	+	0.108248i
$683$	−0.523820	+	0.907282i	−0.0200434	+	0.0347162i	−0.875873	−	0.482541i	$-0.839714\pi$
$683$	−0.523820	+	0.907282i	−0.0200434	+	0.0347162i	0.855830	+	0.517258i	$0.173047\pi$
$684$	47.8964	−	53.1943i	1.83136	−	2.03394i
$685$	−24.0514	−	17.4743i	−0.918955	−	0.667660i
$686$		0			0
$687$	−19.6492	+	60.4739i	−0.749663	+	2.30722i
$688$	12.4498	−	2.64628i	0.474643	−	0.100889i
$689$	−0.176383	−	1.67817i	−0.00671965	−	0.0639332i
$690$	−13.0315	+	5.80198i	−0.496099	+	0.220877i
$691$	19.5308	−	21.6911i	0.742987	−	0.825170i	−0.246599	−	0.969118i	$-0.579313\pi$
$691$	19.5308	−	21.6911i	0.742987	−	0.825170i	0.989585	+	0.143947i	$0.0459796\pi$
$692$	−9.29326			−0.353277
$693$		0			0
$694$	−16.2648			−0.617404
$695$	20.4709	−	22.7352i	0.776505	−	0.862397i
$696$	6.30513	−	2.80722i	0.238995	−	0.106408i
$697$	1.04104	+	9.90481i	0.0394321	+	0.375172i
$698$	2.17418	−	0.462135i	0.0822937	−	0.0174921i
$699$	20.4358	−	62.8950i	0.772954	−	2.37891i
$700$		0			0
$701$	−10.3380	−	7.51100i	−0.390461	−	0.283687i	0.375183	−	0.926951i	$-0.377580\pi$
$701$	−10.3380	−	7.51100i	−0.390461	−	0.283687i	−0.765644	+	0.643264i	$0.777580\pi$
$702$	13.7253	−	15.2435i	0.518028	−	0.575329i
$703$	−5.06970	+	8.78098i	−0.191207	+	0.331181i
$704$	0.345093	+	2.77649i	0.0130062	+	0.104643i
$705$	−14.8004	−	25.6351i	−0.557417	−	0.965474i
$706$	4.20697	+	12.9477i	0.158332	+	0.487294i
$707$		0			0
$708$	−1.45166	+	1.05469i	−0.0545567	+	0.0396377i
$709$	−37.2390	+	7.91540i	−1.39854	+	0.297269i	−0.844649	−	0.535320i	$-0.820191\pi$
$709$	−37.2390	+	7.91540i	−1.39854	+	0.297269i	−0.553891	+	0.832589i	$0.686858\pi$
$710$	−14.2854	−	15.8655i	−0.536121	−	0.595423i
$711$	−2.90813	−	27.6690i	−0.109063	−	1.03767i
$712$	−2.06541	+	19.6511i	−0.0774046	+	0.736455i
$713$	−2.93520	−	9.03361i	−0.109924	−	0.338311i
$714$		0			0
$715$	−5.87770	−	16.9881i	−0.219814	−	0.635321i
$716$	−1.25585	−	2.17519i	−0.0469332	−	0.0812906i
$717$	−47.5923	−	10.1161i	−1.77737	−	0.377791i
$718$	17.7686	−	7.91110i	0.663119	−	0.295240i
$719$	−35.8743	−	15.9723i	−1.33789	−	0.595666i	−0.391941	−	0.919990i	$-0.628196\pi$
$719$	−35.8743	−	15.9723i	−1.33789	−	0.595666i	−0.945946	+	0.324325i	$0.894863\pi$
$720$	6.85975	−	21.1121i	0.255648	−	0.786803i
$721$		0			0
$722$	−14.2274	+	10.3368i	−0.529491	+	0.384697i
$723$	−4.62258	+	43.9809i	−0.171915	+	1.63567i
$724$	3.68280	+	0.782803i	0.136870	+	0.0290926i
$725$	−0.186781	+	0.323514i	−0.00693687	+	0.0120150i
$726$	14.8158	−	17.7636i	0.549867	−	0.659271i
$727$	−28.4699			−1.05589			−0.527946	−	0.849278i	$-0.677037\pi$
$727$	−28.4699			−1.05589			−0.527946	+	0.849278i	$0.677037\pi$
$728$		0			0
$729$	−4.56314	−	3.31531i	−0.169005	−	0.122789i
$730$	10.5433	+	4.69417i	0.390224	+	0.173739i
$731$	10.1020	+	11.2194i	0.373635	+	0.414964i
$732$	−16.3347	−	18.1415i	−0.603748	−	0.670531i
$733$	−2.73458	−	1.21751i	−0.101004	−	0.0449698i	0.355613	−	0.934633i	$-0.384272\pi$
$733$	−2.73458	−	1.21751i	−0.101004	−	0.0449698i	−0.456617	+	0.889664i	$0.650939\pi$
$734$	12.3315	+	8.95935i	0.455163	+	0.330696i
$735$		0			0
$736$	−18.2527			−0.672802
$737$	1.95959	−	2.26102i	0.0721825	−	0.0832857i
$738$	−12.7715	+	22.1210i	−0.470127	+	0.814284i
$739$	49.6242	+	10.5480i	1.82546	+	0.388013i	0.987487	−	0.157702i	$-0.0504087\pi$
$739$	49.6242	+	10.5480i	1.82546	+	0.388013i	0.837971	+	0.545715i	$0.183742\pi$
$740$	−0.523981	+	4.98534i	−0.0192619	+	0.183265i
$741$	43.2041	−	31.3896i	1.58714	−	1.15313i
$742$		0			0
$743$	−0.118625	+	0.365089i	−0.00435191	+	0.0133938i	−0.953209	−	0.302312i	$-0.902241\pi$
$743$	−0.118625	+	0.365089i	−0.00435191	+	0.0133938i	0.948857	+	0.315706i	$0.102241\pi$
$744$	−20.4796	−	9.11810i	−0.750818	−	0.334286i
$745$	5.13683	−	2.28707i	0.188199	−	0.0837916i
$746$	14.5704	+	3.09703i	0.533460	+	0.113390i
$747$	13.8924	+	24.0624i	0.508297	+	0.880395i
$748$	7.35141	−	5.55681i	0.268794	−	0.203177i
$749$		0			0
$750$	−7.52839	−	23.1700i	−0.274898	−	0.846048i
$751$	4.11392	−	39.1414i	0.150119	−	1.42829i	−0.617091	−	0.786892i	$-0.711689\pi$
$751$	4.11392	−	39.1414i	0.150119	−	1.42829i	0.767210	−	0.641396i	$-0.221645\pi$
$752$	−0.694062	−	6.60356i	−0.0253098	−	0.240807i
$753$	−2.26325	−	2.51360i	−0.0824775	−	0.0916006i
$754$	1.53069	−	0.325358i	0.0557444	−	0.0118488i
$755$	5.18502	−	3.76714i	0.188702	−	0.137100i
$756$		0			0
$757$	3.51868	+	10.8294i	0.127889	+	0.393600i	0.994416	−	0.105528i	$-0.0336534\pi$
$757$	3.51868	+	10.8294i	0.127889	+	0.393600i	−0.866528	+	0.499129i	$0.833653\pi$
$758$	−11.2084	−	19.4135i	−0.407107	−	0.705130i
$759$	22.5084	+	24.0656i	0.817002	+	0.873524i
$760$	−17.1518	+	29.7079i	−0.622163	+	1.07762i
$761$	−5.00620	+	5.55995i	−0.181475	+	0.201548i	−0.827018	−	0.562176i	$-0.809964\pi$
$761$	−5.00620	+	5.55995i	−0.181475	+	0.201548i	0.645543	+	0.763724i	$0.276631\pi$
$762$	−29.8855	−	21.7131i	−1.08264	−	0.786582i
$763$		0			0
$764$	−6.08911	+	18.7403i	−0.220296	+	0.678002i
$765$	25.7554	−	5.47449i	0.931190	−	0.197931i
$766$	0.430260	+	4.09365i	0.0155459	+	0.147909i
$767$	−0.850795	+	0.378798i	−0.0307204	+	0.0136776i
$768$	−18.9826	+	21.0823i	−0.684976	+	0.760743i
$769$	−26.8378			−0.967798			−0.483899	−	0.875124i	$-0.660780\pi$
$769$	−26.8378			−0.967798			−0.483899	+	0.875124i	$0.660780\pi$
$770$		0			0
$771$	41.0714			1.47915
$772$	1.82637	−	2.02839i	0.0657326	−	0.0730034i
$773$	4.08154	−	1.81722i	0.146803	−	0.0653609i	−0.332020	−	0.943272i	$-0.607730\pi$
$773$	4.08154	−	1.81722i	0.146803	−	0.0653609i	0.478823	+	0.877911i	$0.341064\pi$
$774$	4.04736	+	38.5080i	0.145479	+	1.38414i
$775$	1.18685	−	0.252272i	0.0426328	−	0.00906188i
$776$	−6.25926	+	19.2640i	−0.224694	+	0.691538i
$777$		0			0
$778$	−4.01155	−	2.91456i	−0.143821	−	0.104492i
$779$	−25.0331	+	27.8020i	−0.896903	+	0.996111i
$780$	13.2010	−	22.8648i	0.472671	−	0.818690i
$781$	−23.8449	+	43.1683i	−0.853237	+	1.54468i
$782$	−1.89771	−	3.28694i	−0.0678621	−	0.117541i
$783$	−3.45951	−	10.6473i	−0.123633	−	0.380503i
$784$		0			0
$785$	−19.5196	+	14.1818i	−0.696685	+	0.506171i
$786$	−13.8338	+	2.94046i	−0.493434	+	0.104883i
$787$	−9.02385	−	10.0220i	−0.321665	−	0.357246i	0.560526	−	0.828137i	$-0.310599\pi$
$787$	−9.02385	−	10.0220i	−0.321665	−	0.357246i	−0.882191	+	0.470891i	$0.843932\pi$
$788$	−0.146448	−	1.39336i	−0.00521700	−	0.0496364i
$789$	3.14154	−	29.8898i	0.111842	−	1.06410i
$790$	1.79987	+	5.53944i	0.0640366	+	0.197084i
$791$		0			0
$792$	54.0930	−	1.02450i	1.92211	−	0.0364041i
$793$	−6.33518	−	10.9728i	−0.224969	−	0.389657i
$794$	−11.6661	−	2.47970i	−0.414014	−	0.0880014i
$795$	4.10401	−	1.82722i	0.145554	−	0.0648049i
$796$	22.1520	+	9.86272i	0.785158	+	0.349575i
$797$	16.2250	−	49.9354i	0.574719	−	1.76880i	−0.0624156	−	0.998050i	$-0.519880\pi$
$797$	16.2250	−	49.9354i	0.574719	−	1.76880i	0.637134	−	0.770753i	$-0.280120\pi$
$798$		0			0
$799$	6.37177	−	4.62936i	0.225417	−	0.163775i
$800$	0.243723	−	2.31887i	0.00861690	−	0.0819843i
$801$	55.7277	+	11.8453i	1.96904	+	0.418533i
$802$	−8.59913	+	14.8941i	−0.303646	+	0.525930i
$803$	2.28412	−	26.5615i	0.0806047	−	0.937336i
$804$	4.39443			0.154980
$805$		0			0
$806$	−4.11214	−	2.98764i	−0.144844	−	0.105235i
$807$	−13.6777	−	6.08971i	−0.481478	−	0.214368i
$808$	6.40934	+	7.11830i	0.225480	+	0.250421i
$809$	−0.863073	−	0.958540i	−0.0303440	−	0.0337005i	0.727782	−	0.685809i	$-0.240551\pi$
$809$	−0.863073	−	0.958540i	−0.0303440	−	0.0337005i	−0.758126	+	0.652108i	$0.773885\pi$
$810$	22.9015	+	10.1964i	0.804677	+	0.358265i
$811$	27.6585	+	20.0951i	0.971220	+	0.705633i	0.955729	−	0.294247i	$-0.0950689\pi$
$811$	27.6585	+	20.0951i	0.971220	+	0.705633i	0.0154910	+	0.999880i	$0.495069\pi$
$812$		0			0
$813$	−62.9596			−2.20809
$814$	−3.26095	+	0.757950i	−0.114296	+	0.0265661i
$815$	19.5116	−	33.7950i	0.683460	−	1.18379i
$816$	8.30455	+	1.76519i	0.290717	+	0.0617939i
$817$	−5.92791	+	56.4003i	−0.207391	+	1.97320i
$818$	−0.724728	+	0.526545i	−0.0253395	+	0.0184102i
$819$		0			0
$820$	−5.71550	+	17.5905i	−0.199594	+	0.614287i
$821$	36.2312	+	16.1311i	1.26448	+	0.562981i	0.925833	−	0.377934i	$-0.123365\pi$
$821$	36.2312	+	16.1311i	1.26448	+	0.562981i	0.338643	+	0.940915i	$0.390032\pi$
$822$	26.6403	−	11.8610i	0.929188	−	0.413701i
$823$	9.02551	+	1.91843i	0.314609	+	0.0668723i	0.362510	−	0.931980i	$-0.381920\pi$
$823$	9.02551	+	1.91843i	0.314609	+	0.0668723i	−0.0479008	+	0.998852i	$0.515253\pi$
$824$	−20.9620	−	36.3073i	−0.730247	−	1.26482i
$825$	−3.35790	+	2.53818i	−0.116907	+	0.0883681i
$826$		0			0
$827$	−7.94043	−	24.4381i	−0.276116	−	0.849797i	−0.988922	−	0.148436i	$-0.952576\pi$
$827$	−7.94043	−	24.4381i	−0.276116	−	0.849797i	0.712806	−	0.701361i	$-0.247424\pi$
$828$	−3.51929	+	33.4838i	−0.122304	+	1.16364i
$829$	−1.14339	−	10.8786i	−0.0397115	−	0.377829i	−0.996270	−	0.0862894i	$-0.972499\pi$
$829$	−1.14339	−	10.8786i	−0.0397115	−	0.377829i	0.956559	−	0.291540i	$-0.0941676\pi$
$830$	−3.89223	−	4.32276i	−0.135101	−	0.150045i
$831$	35.6330	−	7.57403i	1.23609	−	0.262740i
$832$	−1.72547	+	1.25363i	−0.0598200	+	0.0434618i
$833$		0			0
$834$	9.27333	+	28.5404i	0.321109	+	0.988272i
$835$	−21.3641	−	37.0037i	−0.739334	−	1.28056i
$836$	33.9900	+	6.55465i	1.17557	+	0.226697i
$837$	−18.1815	+	31.4913i	−0.628444	+	1.08850i
$838$	16.7883	−	18.6453i	0.579944	−	0.644093i
$839$	28.1031	+	20.4181i	0.970228	+	0.704912i	0.955503	−	0.294980i	$-0.0953129\pi$
$839$	28.1031	+	20.4181i	0.970228	+	0.704912i	0.0147243	+	0.999892i	$0.495313\pi$
$840$		0			0
$841$	−8.69756	+	26.7684i	−0.299916	+	0.923047i
$842$	−5.41222	+	1.15040i	−0.186517	+	0.0396455i
$843$	−3.96422	−	37.7170i	−0.136535	−	1.29904i
$844$	−20.9319	+	9.31948i	−0.720505	+	0.320790i
$845$	−9.47881	+	10.5273i	−0.326081	+	0.362149i
$846$	20.1996			0.694478
$847$		0			0
$848$	1.00771			0.0346050
$849$	46.2060	−	51.3169i	1.58578	−	1.76119i
$850$	0.442921	−	0.197201i	0.0151921	−	0.00676394i
$851$	−0.498511	−	4.74302i	−0.0170888	−	0.162589i
$852$	−70.8486	+	15.0593i	−2.42723	+	0.515924i
$853$	−6.37880	+	19.6319i	−0.218406	+	0.672185i	0.780488	+	0.625171i	$0.214971\pi$
$853$	−6.37880	+	19.6319i	−0.218406	+	0.672185i	−0.998894	+	0.0470143i	$0.985029\pi$
$854$		0			0
$855$	80.0191	+	58.1373i	2.73659	+	1.98825i
$856$	24.5160	−	27.2278i	0.837941	−	0.930628i
$857$	17.0756	−	29.5758i	0.583291	−	1.01029i	−0.411795	−	0.911276i	$-0.635098\pi$
$857$	17.0756	−	29.5758i	0.583291	−	1.01029i	0.995086	−	0.0990131i	$-0.0315686\pi$
$858$	17.3140	+	3.33884i	0.591089	+	0.113986i
$859$	16.7246	+	28.9679i	0.570637	+	0.988373i	0.996501	+	0.0835852i	$0.0266371\pi$
$859$	16.7246	+	28.9679i	0.570637	+	0.988373i	−0.425863	+	0.904787i	$0.640030\pi$
$860$	8.66399	+	26.6650i	0.295440	+	0.909269i
$861$		0			0
$862$	−17.6944	+	12.8557i	−0.602673	+	0.437868i
$863$	33.2903	−	7.07607i	1.13321	−	0.240872i	0.397130	−	0.917762i	$-0.370006\pi$
$863$	33.2903	−	7.07607i	1.13321	−	0.240872i	0.736084	+	0.676890i	$0.236673\pi$
$864$	46.7565	+	51.9283i	1.59069	+	1.76664i
$865$	−1.34229	−	12.7711i	−0.0456393	−	0.434229i
$866$	−1.10578	+	10.5208i	−0.0375761	+	0.357512i
$867$	−13.3822	−	41.1861i	−0.454483	−	1.39875i
$868$		0			0
$869$	10.7332	−	8.11305i	0.364099	−	0.275216i
$870$	2.08309	+	3.60802i	0.0706235	+	0.122323i
$871$	2.23098	+	0.474209i	0.0755938	+	0.0160680i
$872$	41.1258	−	18.3104i	1.39270	−	0.620068i
$873$	53.3539	+	23.7547i	1.80575	+	0.803974i
$874$	4.40569	−	13.5593i	0.149025	−	0.458651i
$875$		0			0
$876$	31.6773	−	23.0149i	1.07028	−	0.777602i
$877$	−0.822332	+	7.82396i	−0.0277682	+	0.264196i	0.971826	+	0.235701i	$0.0757384\pi$
$877$	−0.822332	+	7.82396i	−0.0277682	+	0.264196i	−0.999594	+	0.0284960i	$0.990928\pi$
$878$	13.5569	+	2.88161i	0.457524	+	0.0972497i
$879$	−2.22485	+	3.85356i	−0.0750425	+	0.129977i
$880$	10.4565	−	2.43043i	0.352490	−	0.0819299i
$881$	13.3289			0.449063			0.224531	−	0.974467i	$-0.427915\pi$
$881$	13.3289			0.449063			0.224531	+	0.974467i	$0.427915\pi$
$882$		0			0
$883$	13.8340	+	10.0510i	0.465552	+	0.338243i	0.795705	−	0.605684i	$-0.207100\pi$
$883$	13.8340	+	10.0510i	0.465552	+	0.338243i	−0.330153	+	0.943927i	$0.607100\pi$
$884$	6.41748	+	2.85724i	0.215843	+	0.0960995i
$885$	−1.65906	−	1.84257i	−0.0557687	−	0.0619374i
$886$	13.4872	+	14.9790i	0.453110	+	0.503230i
$887$	−24.2258	−	10.7860i	−0.813424	−	0.362159i	−0.0425074	−	0.999096i	$-0.513535\pi$
$887$	−24.2258	−	10.7860i	−0.813424	−	0.362159i	−0.770916	+	0.636937i	$0.780201\pi$
$888$	−9.10614	−	6.61600i	−0.305582	−	0.222018i
$889$		0			0
$890$	−11.9274			−0.399808
$891$	4.96143	−	57.6955i	0.166214	−	1.93287i
$892$	−1.43149	+	2.47942i	−0.0479299	+	0.0830170i
$893$	28.9386	+	6.15110i	0.968394	+	0.205839i
$894$	−0.576537	+	5.48538i	−0.0192823	+	0.183459i
$895$	2.80781	−	2.03999i	0.0938548	−	0.0681895i
$896$		0			0
$897$	−7.76209	+	23.8892i	−0.259168	+	0.797639i
$898$	22.2676	+	9.91418i	0.743080	+	0.330841i
$899$	−2.53432	+	1.12835i	−0.0845243	+	0.0376326i
$900$	−4.20688	−	0.894199i	−0.140229	−	0.0298066i
$901$	0.597649	+	1.03516i	0.0199106	+	0.0344861i
$902$	−12.3505	+	0.233913i	−0.411225	+	0.00778846i
$903$		0			0
$904$	−1.23528	−	3.80180i	−0.0410848	−	0.126446i
$905$	−0.543816	+	5.17407i	−0.0180771	+	0.171992i
$906$	0.657135	+	6.25222i	0.0218318	+	0.207716i
$907$	5.92352	+	6.57873i	0.196687	+	0.218443i	0.833418	−	0.552643i	$-0.186381\pi$
$907$	5.92352	+	6.57873i	0.196687	+	0.218443i	−0.636731	+	0.771086i	$0.719714\pi$
$908$	−33.2947	+	7.07702i	−1.10492	+	0.234859i
$909$	22.3437	−	16.2337i	0.741094	−	0.538436i
$910$		0			0
$911$	−17.2740	−	53.1639i	−0.572313	−	1.76140i	−0.645151	−	0.764055i	$-0.723206\pi$
$911$	−17.2740	−	53.1639i	−0.572313	−	1.76140i	0.0728381	−	0.997344i	$-0.476794\pi$
$912$	15.9460	+	27.6194i	0.528026	+	0.914568i
$913$	−6.49683	+	11.7617i	−0.215014	+	0.389256i
$914$	3.27974	−	5.68068i	0.108484	−	0.187900i
$915$	22.5713	−	25.0679i	0.746183	−	0.828720i
$916$	−25.4189	−	18.4679i	−0.839865	−	0.610197i
$917$		0			0
$918$	−4.49001	+	13.8188i	−0.148192	+	0.456090i
$919$	−47.3204	+	10.0583i	−1.56096	+	0.331792i	−0.905802	−	0.423702i	$-0.860730\pi$
$919$	−47.3204	+	10.0583i	−1.56096	+	0.331792i	−0.655156	+	0.755494i	$0.727397\pi$
$920$	−1.68657	−	16.0466i	−0.0556045	−	0.529041i
$921$	84.5141	−	37.6281i	2.78483	−	1.23989i
$922$	−9.79631	+	10.8799i	−0.322624	+	0.358311i
$923$	−37.5937			−1.23741
$924$		0			0
$925$	0.609223			0.0200311
$926$	3.02897	−	3.36401i	0.0995382	−	0.110548i
$927$	−110.430	+	49.1668i	−3.62701	+	1.61485i
$928$	0.557233	+	5.30172i	0.0182921	+	0.174037i
$929$	−0.845408	+	0.179697i	−0.0277369	+	0.00589567i	−0.221759	−	0.975101i	$-0.571180\pi$
$929$	−0.845408	+	0.179697i	−0.0277369	+	0.00589567i	0.194022	+	0.980997i	$0.437847\pi$
$930$	4.18166	−	12.8698i	0.137122	−	0.422018i
$931$		0			0
$932$	26.4366	+	19.2073i	0.865959	+	0.629156i
$933$	56.4699	−	62.7162i	1.84874	−	2.05324i
$934$	10.0539	−	17.4139i	0.328975	−	0.569801i
$935$	8.69813	+	9.29989i	0.284459	+	0.304139i
$936$	20.6212	+	35.7170i	0.674026	+	1.16745i
$937$	16.5194	+	50.8416i	0.539667	+	1.66092i	0.733344	+	0.679858i	$0.237958\pi$
$937$	16.5194	+	50.8416i	0.539667	+	1.66092i	−0.193678	+	0.981065i	$0.562042\pi$
$938$		0			0
$939$	11.4120	−	8.29134i	0.372418	−	0.270578i
$940$	14.3069	−	3.04103i	0.466641	−	0.0991875i
$941$	9.16709	+	10.1811i	0.298838	+	0.331894i	0.873799	−	0.486287i	$-0.161649\pi$
$941$	9.16709	+	10.1811i	0.298838	+	0.331894i	−0.574960	+	0.818181i	$0.694983\pi$
$942$	−2.47386	−	23.5372i	−0.0806027	−	0.766884i
$943$	1.83936	−	17.5003i	0.0598977	−	0.569889i
$944$	−0.171867	−	0.528952i	−0.00559379	−	0.0172159i
$945$		0			0
$946$	−14.9378	+	11.2912i	−0.485670	+	0.367110i
$947$	−15.8222	−	27.4049i	−0.514152	−	0.890538i	−0.999865	−	0.0164197i	$-0.994773\pi$
$947$	−15.8222	−	27.4049i	−0.514152	−	0.890538i	0.485713	−	0.874119i	$-0.338560\pi$
$948$	19.3290	+	4.10850i	0.627776	+	0.133438i
$949$	18.5656	−	8.26594i	0.602665	−	0.268324i
$950$	1.66379	+	0.740765i	0.0539803	+	0.0240336i
$951$	−10.6242	+	32.6980i	−0.344514	+	1.06031i
$952$		0			0
$953$	−26.4856	+	19.2429i	−0.857951	+	0.623338i	−0.927327	−	0.374253i	$-0.877899\pi$
$953$	−26.4856	+	19.2429i	−0.857951	+	0.623338i	0.0693755	+	0.997591i	$0.477899\pi$
$954$	−0.320444	+	3.04882i	−0.0103747	+	0.0987091i
$955$	−26.6330	−	5.66101i	−0.861823	−	0.183186i
$956$	12.0210	−	20.8210i	0.388787	−	0.673398i
$957$	6.30299	−	7.27253i	0.203747	−	0.235088i
$958$	−4.02083			−0.129907
$959$		0			0
$960$	−4.59371	−	3.33753i	−0.148261	−	0.107718i
$961$	−20.0882	−	8.94385i	−0.648007	−	0.288511i
$962$	−1.70768	−	1.89657i	−0.0550578	−	0.0611479i
$963$	−70.6879	−	78.5069i	−2.27789	−	2.52985i
$964$	−19.9626	−	8.88793i	−0.642952	−	0.286261i
$965$	3.05127	+	2.21688i	0.0982238	+	0.0713637i
$966$		0			0
$967$	−32.3487			−1.04026			−0.520132	−	0.854086i	$-0.674117\pi$
$967$	−32.3487			−1.04026			−0.520132	+	0.854086i	$0.674117\pi$
$968$	13.9307	+	22.1472i	0.447749	+	0.711838i
$969$	−18.9144	+	32.7606i	−0.607617	+	1.05242i
$970$	−11.9597	−	2.54211i	−0.384003	−	0.0816223i
$971$	3.07596	−	29.2658i	0.0987122	−	0.939184i	−0.827318	−	0.561734i	$-0.810134\pi$
$971$	3.07596	−	29.2658i	0.0987122	−	0.939184i	0.926030	−	0.377450i	$-0.123199\pi$
$972$	23.1941	−	16.8515i	0.743950	−	0.540511i
$973$		0			0
$974$	1.31778	−	4.05570i	0.0422243	−	0.129953i
$975$	−2.93131	−	1.30510i	−0.0938770	−	0.0417967i
$976$	6.91248	−	3.07763i	0.221263	−	0.0985127i
$977$	−13.3952	−	2.84723i	−0.428550	−	0.0910911i	−0.0114132	−	0.999935i	$-0.503633\pi$
$977$	−13.3952	−	2.84723i	−0.428550	−	0.0910911i	−0.417137	+	0.908844i	$0.636966\pi$
$978$	19.1390	+	33.1497i	0.611997	+	1.06001i
$979$	9.00874	+	26.0377i	0.287920	+	0.832168i
$980$		0			0
$981$	−40.1108	−	123.448i	−1.28064	−	3.94141i
$982$	−0.866473	+	8.24394i	−0.0276503	+	0.263075i
$983$	−1.78032	−	16.9386i	−0.0567835	−	0.540259i	−0.985525	−	0.169531i	$-0.945775\pi$
$983$	−1.78032	−	16.9386i	−0.0567835	−	0.540259i	0.928741	−	0.370728i	$-0.120892\pi$
$984$	−27.7894	−	30.8632i	−0.885893	−	0.983884i
$985$	1.89364	−	0.402506i	0.0603364	−	0.0128249i
$986$	−0.896797	+	0.651561i	−0.0285598	+	0.0207499i
$987$		0			0
$988$	8.15432	+	25.0964i	0.259423	+	0.798423i
$989$	−13.3372	−	23.1007i	−0.424099	−	0.734561i
$990$	4.02815	+	32.4089i	0.128023	+	1.03002i
$991$	−11.6101	+	20.1093i	−0.368807	+	0.638792i	−0.989379	−	0.145357i	$-0.953567\pi$
$991$	−11.6101	+	20.1093i	−0.368807	+	0.638792i	0.620572	+	0.784149i	$0.286900\pi$
$992$	11.5862	−	12.8678i	0.367862	−	0.408552i
$993$	−41.9696	−	30.4927i	−1.33187	−	0.967657i
$994$		0			0
$995$	−10.3540	+	31.8665i	−0.328245	+	1.01023i
$996$	−19.3036	+	4.10310i	−0.611657	+	0.130012i
$997$	1.92098	+	18.2769i	0.0608381	+	0.578836i	0.981897	+	0.189414i	$0.0606587\pi$
$997$	1.92098	+	18.2769i	0.0608381	+	0.578836i	−0.921059	+	0.389422i	$0.872675\pi$
$998$	−8.73688	+	3.88991i	−0.276561	+	0.123133i
$999$	−12.2168	+	13.5681i	−0.386521	+	0.429275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.g.214.3		32
7.2	even	3	inner	539.2.q.g.324.2		32
7.3	odd	6		539.2.f.e.148.3		16
7.4	even	3		77.2.f.b.71.3	yes	16
7.5	odd	6		539.2.q.f.324.2		32
7.6	odd	2		539.2.q.f.214.3		32
11.9	even	5	inner	539.2.q.g.361.2		32
21.11	odd	6		693.2.m.i.379.2		16
77.3	odd	30		5929.2.a.bt.1.5		8
77.4	even	15		847.2.f.w.729.2		16
77.9	even	15	inner	539.2.q.g.471.3		32
77.18	odd	30		847.2.f.v.729.3		16
77.20	odd	10		539.2.q.f.361.2		32
77.25	even	15		847.2.a.p.1.5		8
77.31	odd	30		539.2.f.e.295.3		16
77.32	odd	6		847.2.f.x.148.2		16
77.39	odd	30		847.2.f.v.323.3		16
77.46	odd	30		847.2.f.x.372.2		16
77.52	even	30		5929.2.a.bs.1.4		8
77.53	even	15		77.2.f.b.64.3	✓	16
77.60	even	15		847.2.f.w.323.2		16
77.74	odd	30		847.2.a.o.1.4		8
77.75	odd	30		539.2.q.f.471.3		32
231.53	odd	30		693.2.m.i.64.2		16
231.74	even	30		7623.2.a.cw.1.5		8
231.179	odd	30		7623.2.a.ct.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.3	✓	16	77.53	even	15
77.2.f.b.71.3	yes	16	7.4	even	3
539.2.f.e.148.3		16	7.3	odd	6
539.2.f.e.295.3		16	77.31	odd	30
539.2.q.f.214.3		32	7.6	odd	2
539.2.q.f.324.2		32	7.5	odd	6
539.2.q.f.361.2		32	77.20	odd	10
539.2.q.f.471.3		32	77.75	odd	30
539.2.q.g.214.3		32	1.1	even	1	trivial
539.2.q.g.324.2		32	7.2	even	3	inner
539.2.q.g.361.2		32	11.9	even	5	inner
539.2.q.g.471.3		32	77.9	even	15	inner
693.2.m.i.64.2		16	231.53	odd	30
693.2.m.i.379.2		16	21.11	odd	6
847.2.a.o.1.4		8	77.74	odd	30
847.2.a.p.1.5		8	77.25	even	15
847.2.f.v.323.3		16	77.39	odd	30
847.2.f.v.729.3		16	77.18	odd	30
847.2.f.w.323.2		16	77.60	even	15
847.2.f.w.729.2		16	77.4	even	15
847.2.f.x.148.2		16	77.32	odd	6
847.2.f.x.372.2		16	77.46	odd	30
5929.2.a.bs.1.4		8	77.52	even	30
5929.2.a.bt.1.5		8	77.3	odd	30
7623.2.a.ct.1.4		8	231.179	odd	30
7623.2.a.cw.1.5		8	231.74	even	30

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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.q (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.448146 - 0.497717i) q^{2} +(2.86833 - 1.27706i) q^{3} +(0.162170 + 1.54294i) q^{4} +(-2.09693 + 0.445717i) q^{5} +(0.649815 - 1.99992i) q^{6} +(1.92429 + 1.39808i) q^{8} +(4.58902 - 5.09662i) q^{9} +O(q^{10})\)	\(q+(0.448146 - 0.497717i) q^{2} +(2.86833 - 1.27706i) q^{3} +(0.162170 + 1.54294i) q^{4} +(-2.09693 + 0.445717i) q^{5} +(0.649815 - 1.99992i) q^{6} +(1.92429 + 1.39808i) q^{8} +(4.58902 - 5.09662i) q^{9} +(-0.717891 + 1.24342i) q^{10} +(3.25662 + 0.628009i) q^{11} +(2.43559 + 4.21857i) q^{12} +(0.781276 + 2.40452i) q^{13} +(-5.44548 + 3.95637i) q^{15} +(-1.47687 + 0.313918i) q^{16} +(-1.19836 - 1.33091i) q^{17} +(-0.480122 - 4.56806i) q^{18} +(0.703205 - 6.69055i) q^{19} +(-1.02778 - 3.16317i) q^{20} +(1.77201 - 1.33944i) q^{22} +(1.58214 + 2.74035i) q^{23} +(7.30493 + 1.55271i) q^{24} +(-0.369268 + 0.164409i) q^{25} +(1.54690 + 0.688722i) q^{26} +(3.74337 - 11.5209i) q^{27} +(0.747669 - 0.543213i) q^{29} +(-0.471218 + 4.48334i) q^{30} +(-2.93619 - 0.624106i) q^{31} +(-2.88417 + 4.99553i) q^{32} +(10.1431 - 2.35757i) q^{33} -1.19946 q^{34} +(8.60800 + 6.25408i) q^{36} +(-1.37688 - 0.613025i) q^{37} +(-3.01486 - 3.34834i) q^{38} +(5.31167 + 5.89921i) q^{39} +(-4.65826 - 2.07399i) q^{40} +(-4.49897 - 3.26870i) q^{41} -8.42985 q^{43} +(-0.440857 + 5.12663i) q^{44} +(-7.35120 + 12.7327i) q^{45} +(2.07295 + 0.440619i) q^{46} +(-0.459686 + 4.37362i) q^{47} +(-3.83525 + 2.78647i) q^{48} +(-0.0836570 + 0.257470i) q^{50} +(-5.13694 - 2.28711i) q^{51} +(-3.58334 + 1.59541i) q^{52} +(-0.652836 - 0.138765i) q^{53} +(-4.05657 - 7.02619i) q^{54} +(-7.10883 + 0.134639i) q^{55} +(-6.52722 - 20.0887i) q^{57} +(0.0646986 - 0.615566i) q^{58} +(0.0385041 + 0.366342i) q^{59} +(-6.98755 - 7.76046i) q^{60} +(-4.90197 + 1.04195i) q^{61} +(-1.62647 + 1.18170i) q^{62} +(0.260682 + 0.802296i) q^{64} +(-2.71002 - 4.69389i) q^{65} +(3.37217 - 6.10491i) q^{66} +(0.451065 - 0.781267i) q^{67} +(1.85919 - 2.06484i) q^{68} +(8.03770 + 5.83973i) q^{69} +(-4.59489 + 14.1416i) q^{71} +(15.9561 - 3.39157i) q^{72} +(-0.840216 - 7.99413i) q^{73} +(-0.922155 + 0.410570i) q^{74} +(-0.849220 + 0.943154i) q^{75} +10.4372 q^{76} +5.31654 q^{78} +(2.71445 - 3.01470i) q^{79} +(2.95697 - 1.31653i) q^{80} +(-1.82507 - 17.3644i) q^{81} +(-3.64308 + 0.774361i) q^{82} +(-1.25193 + 3.85305i) q^{83} +(3.10609 + 2.25670i) q^{85} +(-3.77780 + 4.19568i) q^{86} +(1.45084 - 2.51293i) q^{87} +(5.38869 + 5.76150i) q^{88} +(4.15363 + 7.19431i) q^{89} +(3.04284 + 9.36491i) q^{90} +(-3.97163 + 2.88556i) q^{92} +(-9.21896 + 1.95955i) q^{93} +(1.97082 + 2.18881i) q^{94} +(1.50752 + 14.3431i) q^{95} +(-1.89314 + 18.0120i) q^{96} +(2.63154 + 8.09904i) q^{97} +(18.1454 - 13.7158i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9}+O(q^{10}) \) 32 * q + 3 * q^2 + 2 * q^3 + 11 * q^4 + 5 * q^5 + 6 * q^6 - 10 * q^8 + 12 * q^9	\( 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9} - 12 q^{10} + 3 q^{11} - 18 q^{12} - 14 q^{13} - 36 q^{15} - 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + 2 q^{20} - 66 q^{22} - 32 q^{23} + 35 q^{24} - 7 q^{25} + 27 q^{26} + 20 q^{27} + 6 q^{29} + 2 q^{30} + 7 q^{31} - 32 q^{32} + 26 q^{33} - 48 q^{34} + 104 q^{36} - 4 q^{37} + 5 q^{38} - 11 q^{39} + 10 q^{40} - 20 q^{41} - 16 q^{43} + 38 q^{44} - 70 q^{45} + 42 q^{46} + 23 q^{47} - 72 q^{48} + 104 q^{50} + 29 q^{51} - 33 q^{52} - 4 q^{53} - 60 q^{54} - 24 q^{55} - 22 q^{57} - 20 q^{58} - 17 q^{59} + 30 q^{60} + 7 q^{61} + 158 q^{62} + 14 q^{64} + 8 q^{65} - 8 q^{66} + 38 q^{67} + 2 q^{68} + 20 q^{69} - 28 q^{71} + 35 q^{73} + 29 q^{74} - 9 q^{75} + 104 q^{76} - 116 q^{78} - 15 q^{79} + 87 q^{80} + 14 q^{81} - 19 q^{82} + 10 q^{83} + 12 q^{85} + 52 q^{86} + 72 q^{87} - 55 q^{88} - 74 q^{89} - 28 q^{90} - 110 q^{92} - 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 40 q^{97} + 32 q^{99}+O(q^{100}) \) 32 * q + 3 * q^2 + 2 * q^3 + 11 * q^4 + 5 * q^5 + 6 * q^6 - 10 * q^8 + 12 * q^9 - 12 * q^10 + 3 * q^11 - 18 * q^12 - 14 * q^13 - 36 * q^15 - 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + 2 * q^20 - 66 * q^22 - 32 * q^23 + 35 * q^24 - 7 * q^25 + 27 * q^26 + 20 * q^27 + 6 * q^29 + 2 * q^30 + 7 * q^31 - 32 * q^32 + 26 * q^33 - 48 * q^34 + 104 * q^36 - 4 * q^37 + 5 * q^38 - 11 * q^39 + 10 * q^40 - 20 * q^41 - 16 * q^43 + 38 * q^44 - 70 * q^45 + 42 * q^46 + 23 * q^47 - 72 * q^48 + 104 * q^50 + 29 * q^51 - 33 * q^52 - 4 * q^53 - 60 * q^54 - 24 * q^55 - 22 * q^57 - 20 * q^58 - 17 * q^59 + 30 * q^60 + 7 * q^61 + 158 * q^62 + 14 * q^64 + 8 * q^65 - 8 * q^66 + 38 * q^67 + 2 * q^68 + 20 * q^69 - 28 * q^71 + 35 * q^73 + 29 * q^74 - 9 * q^75 + 104 * q^76 - 116 * q^78 - 15 * q^79 + 87 * q^80 + 14 * q^81 - 19 * q^82 + 10 * q^83 + 12 * q^85 + 52 * q^86 + 72 * q^87 - 55 * q^88 - 74 * q^89 - 28 * q^90 - 110 * q^92 - 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 40 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more