LMFDB - Embedded newform 539.2.q.f.324.2

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			324.2
Character	$\chi$	$=$	539.324
Dual form			539.2.q.f.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.655108 - 0.139248i) q^{2} +(0.328196 - 3.12257i) q^{3} +(-1.41731 - 0.631029i) q^{4} +(-1.43447 - 1.59314i) q^{5} +(-0.649815 + 1.99992i) q^{6} +(1.92429 + 1.39808i) q^{8} +(-6.70831 - 1.42589i) q^{9} +O(q^{10})$	\(q+(-0.655108 - 0.139248i) q^{2} +(0.328196 - 3.12257i) q^{3} +(-1.41731 - 0.631029i) q^{4} +(-1.43447 - 1.59314i) q^{5} +(-0.649815 + 1.99992i) q^{6} +(1.92429 + 1.39808i) q^{8} +(-6.70831 - 1.42589i) q^{9} +(0.717891 + 1.24342i) q^{10} +(-2.17218 + 2.50631i) q^{11} +(-2.43559 + 4.21857i) q^{12} +(-0.781276 - 2.40452i) q^{13} +(-5.44548 + 3.95637i) q^{15} +(1.01029 + 1.12205i) q^{16} +(-1.75178 + 0.372353i) q^{17} +(4.19612 + 1.86823i) q^{18} +(6.14579 - 2.73628i) q^{19} +(1.02778 + 3.16317i) q^{20} +(1.77201 - 1.33944i) q^{22} +(1.58214 - 2.74035i) q^{23} +(4.99715 - 5.54990i) q^{24} +(0.0422518 - 0.401999i) q^{25} +(0.176997 + 1.68401i) q^{26} +(-3.74337 + 11.5209i) q^{27} +(0.747669 - 0.543213i) q^{29} +(4.11829 - 1.83358i) q^{30} +(-2.00858 + 2.23076i) q^{31} +(-2.88417 - 4.99553i) q^{32} +(7.11325 + 7.60537i) q^{33} +1.19946 q^{34} +(8.60800 + 6.25408i) q^{36} +(0.157543 + 1.49892i) q^{37} +(-4.40718 + 0.936774i) q^{38} +(-7.76470 + 1.65044i) q^{39} +(-0.533001 - 5.07117i) q^{40} +(4.49897 + 3.26870i) q^{41} -8.42985 q^{43} +(4.66022 - 2.18152i) q^{44} +(7.35120 + 12.7327i) q^{45} +(-1.41806 + 1.57492i) q^{46} +(-4.01751 + 1.78871i) q^{47} +(3.83525 - 2.78647i) q^{48} +(-0.0836570 + 0.257470i) q^{50} +(0.587772 + 5.59228i) q^{51} +(-0.410008 + 3.90097i) q^{52} +(0.446592 - 0.495990i) q^{53} +(4.05657 - 7.02619i) q^{54} +(7.10883 - 0.134639i) q^{55} +(-6.52722 - 20.0887i) q^{57} +(-0.565445 + 0.251753i) q^{58} +(0.336514 + 0.149826i) q^{59} +(10.2145 - 2.17117i) q^{60} +(-3.35334 - 3.72426i) q^{61} +(1.62647 - 1.18170i) q^{62} +(0.260682 + 0.802296i) q^{64} +(-2.71002 + 4.69389i) q^{65} +(-3.60092 - 5.97284i) q^{66} +(0.451065 + 0.781267i) q^{67} +(2.71779 + 0.577685i) q^{68} +(-8.03770 - 5.83973i) q^{69} +(-4.59489 + 14.1416i) q^{71} +(-10.9152 - 12.1226i) q^{72} +(-7.34322 - 3.26941i) q^{73} +(0.105514 - 1.00389i) q^{74} +(-1.24141 - 0.263869i) q^{75} -10.4372 q^{76} +5.31654 q^{78} +(-3.96803 - 0.843431i) q^{79} +(0.338339 - 3.21908i) q^{80} +(15.9505 + 7.10164i) q^{81} +(-2.49216 - 2.76782i) q^{82} +(1.25193 - 3.85305i) q^{83} +(3.10609 + 2.25670i) q^{85} +(5.52246 + 1.17384i) q^{86} +(-1.45084 - 2.51293i) q^{87} +(-7.68395 + 1.78600i) q^{88} +(-4.15363 + 7.19431i) q^{89} +(-3.04284 - 9.36491i) q^{90} +(-3.97163 + 2.88556i) q^{92} +(6.30650 + 7.00408i) q^{93} +(2.88097 - 0.612370i) q^{94} +(-13.1752 - 5.86598i) q^{95} +(-16.5455 + 7.36652i) 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 $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.655108	−	0.139248i	−0.463232	−	0.0984629i	−0.0296169	−	0.999561i	$-0.509429\pi$
$2$	−0.655108	−	0.139248i	−0.463232	−	0.0984629i	−0.433615	+	0.901098i	$0.642762\pi$
$3$	0.328196	−	3.12257i	0.189484	−	1.80282i	−0.325419	−	0.945570i	$-0.605505\pi$
$3$	0.328196	−	3.12257i	0.189484	−	1.80282i	0.514903	−	0.857249i	$-0.327828\pi$
$4$	−1.41731	−	0.631029i	−0.708657	−	0.315514i
$5$	−1.43447	−	1.59314i	−0.641514	−	0.712473i	0.331439	−	0.943477i	$-0.392466\pi$
$5$	−1.43447	−	1.59314i	−0.641514	−	0.712473i	−0.972953	+	0.231004i	$0.925799\pi$
$6$	−0.649815	+	1.99992i	−0.265286	+	0.816465i
$7$		0			0
$7$		0			0
$8$	1.92429	+	1.39808i	0.680340	+	0.494296i
$9$	−6.70831	−	1.42589i	−2.23610	−	0.475298i
$10$	0.717891	+	1.24342i	0.227017	+	0.393205i
$11$	−2.17218	+	2.50631i	−0.654938	+	0.755682i
$11$	−2.17218	+	2.50631i	−0.654938	+	0.755682i
$12$	−2.43559	+	4.21857i	−0.703094	+	1.21779i
$13$	−0.781276	−	2.40452i	−0.216687	−	0.666894i	−0.999030	−	0.0440455i	$-0.985975\pi$
$13$	−0.781276	−	2.40452i	−0.216687	−	0.666894i	0.782343	−	0.622848i	$-0.214025\pi$
$14$		0			0
$15$	−5.44548	+	3.95637i	−1.40602	+	1.02153i
$16$	1.01029	+	1.12205i	0.252574	+	0.280512i
$17$	−1.75178	+	0.372353i	−0.424870	+	0.0903089i	−0.415384	−	0.909646i	$-0.636353\pi$
$17$	−1.75178	+	0.372353i	−0.424870	+	0.0903089i	−0.00948587	+	0.999955i	$0.503019\pi$
$18$	4.19612	+	1.86823i	0.989034	+	0.440346i
$19$	6.14579	−	2.73628i	1.40994	−	0.627746i	0.446284	−	0.894891i	$-0.352747\pi$
$19$	6.14579	−	2.73628i	1.40994	−	0.627746i	0.963656	+	0.267146i	$0.0860805\pi$
$20$	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	−0.652592	−	0.757709i	$-0.726318\pi$
$23$	1.58214	−	2.74035i	0.329900	−	0.571403i	0.982492	+	0.186307i	$0.0596518\pi$
$24$	4.99715	−	5.54990i	1.02004	−	1.13287i
$25$	0.0422518	−	0.401999i	0.00845037	−	0.0803999i
$26$	0.176997	+	1.68401i	0.0347119	+	0.330262i
$27$	−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	$0.272653\pi$
$30$	4.11829	−	1.83358i	0.751894	−	0.334765i
$31$	−2.00858	+	2.23076i	−0.360752	+	0.400656i	−0.896011	−	0.444032i	$-0.853548\pi$
$31$	−2.00858	+	2.23076i	−0.360752	+	0.400656i	0.535258	+	0.844688i	$0.320214\pi$
$32$	−2.88417	−	4.99553i	−0.509854	−	0.883092i
$33$	7.11325	+	7.60537i	1.23826	+	1.32392i
$34$	1.19946			0.205705
$35$		0			0
$36$	8.60800	+	6.25408i	1.43467	+	1.04235i
$37$	0.157543	+	1.49892i	0.0258999	+	0.246421i	0.999810	+	0.0194875i	$0.00620346\pi$
$37$	0.157543	+	1.49892i	0.0258999	+	0.246421i	−0.973910	+	0.226934i	$0.927130\pi$
$38$	−4.40718	+	0.936774i	−0.714938	+	0.151965i
$39$	−7.76470	+	1.65044i	−1.24335	+	0.264282i
$40$	−0.533001	−	5.07117i	−0.0842749	−	0.801822i
$41$	4.49897	+	3.26870i	0.702622	+	0.510485i	0.880785	−	0.473516i	$-0.157016\pi$
$41$	4.49897	+	3.26870i	0.702622	+	0.510485i	−0.178163	+	0.984001i	$0.557016\pi$
$42$		0			0
$43$	−8.42985			−1.28554			−0.642770	−	0.766059i	$-0.722215\pi$
$43$	−8.42985			−1.28554			−0.642770	+	0.766059i	$0.722215\pi$
$44$	4.66022	−	2.18152i	0.702555	−	0.328877i
$45$	7.35120	+	12.7327i	1.09585	+	1.89807i
$46$	−1.41806	+	1.57492i	−0.209082	+	0.232209i
$47$	−4.01751	+	1.78871i	−0.586013	+	0.260910i	−0.678255	−	0.734827i	$-0.737263\pi$
$47$	−4.01751	+	1.78871i	−0.586013	+	0.260910i	0.0922416	+	0.995737i	$0.470597\pi$
$48$	3.83525	−	2.78647i	0.553570	−	0.402192i
$49$		0			0
$50$	−0.0836570	+	0.257470i	−0.0118309	+	0.0364117i
$51$	0.587772	+	5.59228i	0.0823046	+	0.783076i
$52$	−0.410008	+	3.90097i	−0.0568579	+	0.540967i
$53$	0.446592	−	0.495990i	0.0613441	−	0.0681295i	−0.711692	−	0.702492i	$-0.752071\pi$
$53$	0.446592	−	0.495990i	0.0613441	−	0.0681295i	0.773036	+	0.634362i	$0.218737\pi$
$54$	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
$58$	−0.565445	+	0.251753i	−0.0742466	+	0.0330567i
$59$	0.336514	+	0.149826i	0.0438104	+	0.0195056i	0.428525	−	0.903530i	$-0.359033\pi$
$59$	0.336514	+	0.149826i	0.0438104	+	0.0195056i	−0.384715	+	0.923036i	$0.625700\pi$
$60$	10.2145	−	2.17117i	1.31869	−	0.280296i
$61$	−3.35334	−	3.72426i	−0.429351	−	0.476843i	0.489185	−	0.872180i	$-0.337294\pi$
$61$	−3.35334	−	3.72426i	−0.429351	−	0.476843i	−0.918536	+	0.395337i	$0.870628\pi$
$62$	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
$66$	−3.60092	−	5.97284i	−0.443243	−	0.735206i
$67$	0.451065	+	0.781267i	0.0551063	+	0.0954469i	0.892263	−	0.451517i	$-0.149117\pi$
$67$	0.451065	+	0.781267i	0.0551063	+	0.0954469i	−0.837156	+	0.546964i	$0.815784\pi$
$68$	2.71779	+	0.577685i	0.329581	+	0.0700546i
$69$	−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	$0.755971\pi$
$72$	−10.9152	−	12.1226i	−1.28637	−	1.42866i
$73$	−7.34322	−	3.26941i	−0.859459	−	0.382656i	−0.0708031	−	0.997490i	$-0.522556\pi$
$73$	−7.34322	−	3.26941i	−0.859459	−	0.382656i	−0.788656	+	0.614834i	$0.789223\pi$
$74$	0.105514	−	1.00389i	0.0122657	−	0.116700i
$75$	−1.24141	−	0.263869i	−0.143345	−	0.0304690i
$76$	−10.4372			−1.19723
$77$		0			0
$78$	5.31654			0.601980
$79$	−3.96803	−	0.843431i	−0.446438	−	0.0948934i	−0.0207937	−	0.999784i	$-0.506619\pi$
$79$	−3.96803	−	0.843431i	−0.446438	−	0.0948934i	−0.425645	+	0.904890i	$0.639953\pi$
$80$	0.338339	−	3.21908i	0.0378274	−	0.359904i
$81$	15.9505	+	7.10164i	1.77228	+	0.789071i
$82$	−2.49216	−	2.76782i	−0.275213	−	0.305655i
$83$	1.25193	−	3.85305i	0.137418	−	0.422928i	−0.858541	−	0.512745i	$-0.828628\pi$
$83$	1.25193	−	3.85305i	0.137418	−	0.422928i	0.995958	+	0.0898178i	$0.0286285\pi$
$84$		0			0
$85$	3.10609	+	2.25670i	0.336902	+	0.244774i
$86$	5.52246	+	1.17384i	0.595503	+	0.126578i
$87$	−1.45084	−	2.51293i	−0.155547	−	0.269415i
$88$	−7.68395	+	1.78600i	−0.819112	+	0.190388i
$89$	−4.15363	+	7.19431i	−0.440284	+	0.762595i	−0.997710	−	0.0676317i	$-0.978456\pi$
$89$	−4.15363	+	7.19431i	−0.440284	+	0.762595i	0.557426	+	0.830227i	$0.311789\pi$
$90$	−3.04284	−	9.36491i	−0.320744	−	0.987148i
$91$		0			0
$92$	−3.97163	+	2.88556i	−0.414071	+	0.300840i
$93$	6.30650	+	7.00408i	0.653954	+	0.726289i
$94$	2.88097	−	0.612370i	0.297150	−	0.0631611i
$95$	−13.1752	−	5.86598i	−1.35175	−	0.601837i
$96$	−16.5455	+	7.36652i	−1.68866	+	0.751842i
$97$	−2.63154	−	8.09904i	−0.267192	−	0.822333i	−0.991180	−	0.132520i	$-0.957693\pi$
$97$	−2.63154	−	8.09904i	−0.267192	−	0.822333i	0.723988	−	0.689812i	$-0.242307\pi$
$98$		0			0
$99$	18.1454	−	13.7158i	1.82368	−	1.37849i
$100$	−0.313557	+	0.543097i	−0.0313557	+	0.0543097i
$101$	2.69463	−	2.99269i	0.268126	−	0.297784i	−0.594013	−	0.804455i	$-0.702457\pi$
$101$	2.69463	−	2.99269i	0.268126	−	0.297784i	0.862140	+	0.506671i	$0.169124\pi$
$102$	0.393657	−	3.74539i	0.0389778	−	0.370849i
$103$	−1.84240	−	17.5293i	−0.181537	−	1.72721i	−0.583982	−	0.811767i	$-0.698506\pi$
$103$	−1.84240	−	17.5293i	−0.181537	−	1.72721i	0.402445	−	0.915444i	$-0.368161\pi$
$104$	1.85831	−	5.71929i	0.182222	−	0.560822i
$105$		0			0
$106$	−0.361631	+	0.262741i	−0.0351248	+	0.0255196i
$107$	−14.0720	+	6.26526i	−1.36039	+	0.605685i	−0.951712	−	0.306992i	$-0.900677\pi$
$107$	−14.0720	+	6.26526i	−1.36039	+	0.605685i	−0.408680	+	0.912678i	$0.634011\pi$
$108$	12.5756	−	13.9666i	1.21008	−	1.34393i
$109$	9.46326	+	16.3908i	0.906416	+	1.56996i	0.819005	+	0.573786i	$0.194526\pi$
$109$	9.46326	+	16.3908i	0.906416	+	1.56996i	0.0874110	+	0.996172i	$0.472141\pi$
$110$	−4.67580	−	0.901685i	−0.445821	−	0.0859723i
$111$	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	$0.725189\pi$
$114$	1.47873	+	14.0692i	0.138496	+	1.31770i
$115$	−6.63529	+	1.41037i	−0.618744	+	0.131518i
$116$	−1.40247	+	0.298103i	−0.130216	+	0.0276782i
$117$	1.81245	+	17.2443i	0.167561	+	1.59423i
$118$	−0.199590	−	0.145011i	−0.0183738	−	0.0133493i
$119$		0			0
$120$	−16.0100			−1.46151
$121$	−1.56323	−	10.8884i	−0.142112	−	0.989851i
$122$	1.67821	+	2.90674i	0.151938	+	0.263164i
$123$	11.6833	−	12.9756i	1.05345	−	1.16997i
$124$	4.25447	−	1.89421i	0.382063	−	0.170105i
$125$	−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	$-0.184479\pi$
$128$	1.14685	+	10.9116i	0.101368	+	0.964457i
$129$	−2.76664	+	26.3228i	−0.243589	+	2.31759i
$130$	2.42897	−	2.69764i	0.213035	−	0.236599i
$131$	3.36278	−	5.82451i	0.293808	−	0.508890i	−0.680899	−	0.732377i	$-0.738411\pi$
$131$	3.36278	−	5.82451i	0.293808	−	0.508890i	0.974707	+	0.223487i	$0.0717441\pi$
$132$	−5.28250	−	15.2679i	−0.459783	−	1.32890i
$133$		0			0
$134$	−0.186707	−	0.574624i	−0.0161290	−	0.0496400i
$135$	23.7241	−	10.5627i	2.04185	−	0.909089i
$136$	−3.89153	−	1.73262i	−0.333696	−	0.148571i
$137$	−13.5646	+	2.88324i	−1.15890	+	0.246332i	−0.746954	−	0.664876i	$-0.768484\pi$
$137$	−13.5646	+	2.88324i	−1.15890	+	0.246332i	−0.411947	+	0.911208i	$0.635151\pi$
$138$	4.45239	+	4.94488i	0.379013	+	0.420937i
$139$	11.5453	−	8.38812i	0.979256	−	0.711471i	0.0217140	−	0.999764i	$-0.493088\pi$
$139$	11.5453	−	8.38812i	0.979256	−	0.711471i	0.957542	+	0.288293i	$0.0930877\pi$
$140$		0			0
$141$	4.26685	+	13.1320i	0.359333	+	1.10591i
$142$	4.97933	−	8.62446i	0.417856	−	0.723749i
$143$	7.72356	+	3.26494i	0.645877	+	0.273028i
$144$	−5.17745	−	8.96761i	−0.431454	−	0.747300i
$145$	−1.93792	−	0.411918i	−0.160936	−	0.0342079i
$146$	4.35535	+	3.16435i	0.360451	+	0.261883i
$147$		0			0
$148$	0.722575	−	2.22386i	0.0593953	−	0.182800i
$149$	1.75508	+	1.94921i	0.143782	+	0.159686i	0.810734	−	0.585415i	$-0.199068\pi$
$149$	1.75508	+	1.94921i	0.143782	+	0.159686i	−0.666952	+	0.745100i	$0.732402\pi$
$150$	0.776512	+	0.345725i	0.0634019	+	0.0282284i
$151$	0.312498	−	2.97322i	0.0254307	−	0.241957i	−0.974421	−	0.224731i	$-0.927850\pi$
$151$	0.312498	−	2.97322i	0.0254307	−	0.241957i	0.999852	−	0.0172265i	$-0.00548363\pi$
$152$	15.6518	+	3.32690i	1.26953	+	0.269847i
$153$	12.2824			0.992977
$154$		0			0
$155$	6.43516			0.516884
$156$	12.0465	+	2.56056i	0.964491	+	0.205009i
$157$	1.17644	−	11.1930i	0.0938898	−	0.893302i	−0.841636	−	0.540045i	$-0.818407\pi$
$157$	1.17644	−	11.1930i	0.0938898	−	0.893302i	0.935526	−	0.353257i	$-0.114926\pi$
$158$	2.48204	+	1.10508i	0.197461	+	0.0879152i
$159$	−1.40220	−	1.55730i	−0.111201	−	0.123502i
$160$	−3.82131	+	11.7608i	−0.302101	+	0.929773i
$161$		0			0
$162$	−9.46045	−	6.87342i	−0.743283	−	0.540027i
$163$	17.8052	+	3.78461i	1.39461	+	0.296433i	0.843110	−	0.537742i	$-0.180723\pi$
$163$	17.8052	+	3.78461i	1.39461	+	0.296433i	0.551500	+	0.834175i	$0.314056\pi$
$164$	−4.31382	−	7.47175i	−0.336853	−	0.583446i
$165$	1.91267	−	22.2420i	0.148901	−	1.73154i
$166$	−1.35668	+	2.34984i	−0.105299	+	0.182383i
$167$	−6.15909	−	18.9557i	−0.476605	−	1.46684i	−0.843781	−	0.536687i	$-0.819675\pi$
$167$	−6.15909	−	18.9557i	−0.476605	−	1.46684i	0.367176	−	0.930151i	$-0.380325\pi$
$168$		0			0
$169$	5.34590	−	3.88402i	0.411223	−	0.298771i
$170$	−1.72058	−	1.91090i	−0.131963	−	0.146559i
$171$	−45.1295	+	9.59257i	−3.45114	+	0.733562i
$172$	11.9477	+	5.31948i	0.911007	+	0.405606i
$173$	−5.47221	+	2.43638i	−0.416044	+	0.185235i	−0.604074	−	0.796929i	$-0.706457\pi$
$173$	−5.47221	+	2.43638i	−0.416044	+	0.185235i	0.188029	+	0.982163i	$0.439790\pi$
$174$	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
$178$	3.72287	−	4.13467i	0.279041	−	0.309906i
$179$	0.169225	−	1.61007i	0.0126485	−	0.120342i	−0.986376	−	0.164508i	$-0.947396\pi$
$179$	0.169225	−	1.61007i	0.0126485	−	0.120342i	0.999024	+	0.0441658i	$0.0140630\pi$
$180$	−2.38429	−	22.6850i	−0.177714	−	1.69084i
$181$	−0.749929	+	2.30804i	−0.0557418	+	0.171556i	−0.975051	−	0.221980i	$-0.928748\pi$
$181$	−0.749929	+	2.30804i	−0.0557418	+	0.171556i	0.919309	+	0.393535i	$0.128748\pi$
$182$		0			0
$183$	−12.7298	+	9.24876i	−0.941016	+	0.683688i
$184$	6.87574	−	3.06128i	0.506886	−	0.225680i
$185$	2.16200	−	2.40114i	0.158953	−	0.176536i
$186$	−3.15614	−	5.46660i	−0.231419	−	0.400830i
$187$	2.87196	−	5.19934i	0.210019	−	0.380214i
$188$	6.82279			0.497603
$189$		0			0
$190$	7.81436	+	5.67747i	0.566914	+	0.411887i
$191$	−1.32761	−	12.6313i	−0.0960623	−	0.913972i	−0.931342	−	0.364146i	$-0.881361\pi$
$191$	−1.32761	−	12.6313i	−0.0960623	−	0.913972i	0.835279	−	0.549826i	$-0.185306\pi$
$192$	2.59078	−	0.550688i	0.186974	−	0.0397425i
$193$	1.72087	−	0.365781i	0.123871	−	0.0263295i	−0.145559	−	0.989350i	$-0.546498\pi$
$193$	1.72087	−	0.365781i	0.123871	−	0.0263295i	0.269430	+	0.963020i	$0.413165\pi$
$194$	0.596171	+	5.67218i	0.0428025	+	0.407239i
$195$	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	$0.510242\pi$
$198$	−13.7971	+	6.45865i	−0.980518	+	0.458996i
$199$	−7.81479	−	13.5356i	−0.553976	−	0.959515i	−0.997982	−	0.0634910i	$-0.979777\pi$
$199$	−7.81479	−	13.5356i	−0.553976	−	0.959515i	0.444006	−	0.896024i	$-0.353557\pi$
$200$	0.643333	−	0.714493i	0.0454905	−	0.0505223i
$201$	2.58760	−	1.15207i	0.182515	−	0.0812610i
$202$	−2.18200	+	1.58532i	−0.153525	+	0.111543i
$203$		0			0
$204$	2.69583	−	8.29691i	0.188746	−	0.580900i
$205$	−1.24615	−	11.8563i	−0.0870349	−	0.828082i
$206$	−1.23394	+	11.7401i	−0.0859725	+	0.817973i
$207$	−14.5210	+	16.1272i	−1.00928	+	1.12091i
$208$	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	$0.730252\pi$
$212$	−0.945945	+	0.421162i	−0.0649678	+	0.0289255i
$213$	42.6502	+	18.9891i	2.92234	+	1.30111i
$214$	10.0911	−	2.14493i	0.689814	−	0.146624i
$215$	12.0923	+	13.4299i	0.824691	+	0.915912i
$216$	−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
$220$	−10.1604	−	4.29505i	−0.685015	−	0.289572i
$221$	2.26396	+	3.92129i	0.152290	+	0.263774i
$222$	−3.10010	−	0.658948i	−0.208065	−	0.0442257i
$223$	−1.49293	−	1.08468i	−0.0999743	−	0.0726356i	0.536675	−	0.843789i	$-0.319680\pi$
$223$	−1.49293	−	1.08468i	−0.0999743	−	0.0726356i	−0.636649	+	0.771153i	$0.719680\pi$
$224$		0			0
$225$	−0.856647	+	2.63649i	−0.0571098	+	0.175766i
$226$	0.753164	+	0.836473i	0.0500997	+	0.0556414i
$227$	20.0431	+	8.92378i	1.33031	+	0.592292i	0.943960	−	0.330061i	$-0.107069\pi$
$227$	20.0431	+	8.92378i	1.33031	+	0.592292i	0.386349	+	0.922352i	$0.373736\pi$
$228$	−3.42544	+	32.5909i	−0.226855	+	2.15838i
$229$	−19.8092	−	4.21058i	−1.30903	−	0.278243i	−0.500009	−	0.866020i	$-0.666670\pi$
$229$	−19.8092	−	4.21058i	−1.30903	−	0.278243i	−0.809023	+	0.587777i	$0.800003\pi$
$230$	4.54323			0.299571
$231$		0			0
$232$	2.19819			0.144318
$233$	−20.6023	−	4.37916i	−1.34970	−	0.286888i	−0.524349	−	0.851504i	$-0.675691\pi$
$233$	−20.6023	−	4.37916i	−1.34970	−	0.286888i	−0.825354	+	0.564616i	$0.809024\pi$
$234$	1.21388	−	11.5493i	0.0793535	−	0.754998i
$235$	8.61264	+	3.83459i	0.561827	+	0.250141i
$236$	−0.382401	−	0.424700i	−0.0248922	−	0.0276456i
$237$	−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	$0.867106\pi$
$240$	−9.94077	−	2.11297i	−0.641674	−	0.136392i
$241$	7.04241	+	12.1978i	0.453641	+	0.785730i	0.998609	−	0.0527271i	$-0.0167913\pi$
$241$	7.04241	+	12.1978i	0.453641	+	0.785730i	−0.544967	+	0.838457i	$0.683458\pi$
$242$	−0.492093	+	7.35073i	−0.0316329	+	0.472523i
$243$	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
$247$	−11.3810	−	12.6399i	−0.724156	−	0.804256i
$248$	−6.98389	+	1.48447i	−0.443477	+	0.0942640i
$249$	−11.6206	−	5.17381i	−0.736423	−	0.327877i
$250$	7.08845	−	3.15598i	0.448313	−	0.199602i
$251$	0.332894	+	1.02454i	0.0210121	+	0.0646686i	0.961013	−	0.276504i	$-0.0891759\pi$
$251$	0.332894	+	1.02454i	0.0210121	+	0.0646686i	−0.940001	+	0.341173i	$0.889176\pi$
$252$		0			0
$253$	3.43148	+	9.91790i	0.215735	+	0.623533i
$254$	−5.88267	+	10.1891i	−0.369111	+	0.639320i
$255$	8.06613	−	8.95834i	0.505121	−	0.560993i
$256$	0.944455	−	8.98589i	0.0590284	−	0.561618i
$257$	1.36734	+	13.0094i	0.0852922	+	0.811501i	0.950633	+	0.310317i	$0.100435\pi$
$257$	1.36734	+	13.0094i	0.0852922	+	0.811501i	−0.865341	+	0.501184i	$0.832898\pi$
$258$	5.47784	−	16.8591i	0.341035	−	1.04960i
$259$		0			0
$260$	6.80292	−	4.94261i	0.421899	−	0.306528i
$261$	−5.79016	+	2.57795i	−0.358402	+	0.159571i
$262$	−3.01404	+	3.34743i	−0.186208	+	0.206805i
$263$	4.78608	+	8.28973i	0.295122	+	0.511167i	0.975013	−	0.222146i	$-0.0713062\pi$
$263$	4.78608	+	8.28973i	0.295122	+	0.511167i	−0.679891	+	0.733313i	$0.737973\pi$
$264$	3.05506	+	24.5799i	0.188026	+	1.51279i
$265$	−1.43080			−0.0878935
$266$		0			0
$267$	21.1015	+	15.3312i	1.29139	+	0.938252i
$268$	−0.146298	−	1.39193i	−0.00893659	−	0.0850260i
$269$	−4.66433	+	0.991434i	−0.284389	+	0.0604488i	−0.347898	−	0.937533i	$-0.613104\pi$
$269$	−4.66433	+	0.991434i	−0.284389	+	0.0604488i	0.0635085	+	0.997981i	$0.479771\pi$
$270$	−17.0127	+	3.61616i	−1.03536	+	0.220073i
$271$	−2.09603	−	19.9424i	−0.127325	−	1.21142i	−0.852453	−	0.522803i	$-0.824886\pi$
$271$	−2.09603	−	19.9424i	−0.127325	−	1.21142i	0.725128	−	0.688614i	$-0.241780\pi$
$272$	−2.18762	−	1.58940i	−0.132644	−	0.0963713i
$273$		0			0
$274$	9.28776			0.561094
$275$	0.915758	+	0.979113i	0.0552223	+	0.0590427i
$276$	7.70690	+	13.3487i	0.463901	+	0.803500i
$277$	−7.76355	+	8.62230i	−0.466467	+	0.518064i	−0.929772	−	0.368135i	$-0.879997\pi$
$277$	−7.76355	+	8.62230i	−0.466467	+	0.518064i	0.463306	+	0.886199i	$0.346663\pi$
$278$	−8.73142	+	3.88748i	−0.523676	+	0.233156i
$279$	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	$-0.0173192\pi$
$282$	−0.966647	−	9.19703i	−0.0575630	−	0.547675i
$283$	2.29892	−	21.8727i	0.136656	−	1.30020i	−0.684297	−	0.729204i	$-0.739891\pi$
$283$	2.29892	−	21.8727i	0.136656	−	1.30020i	0.820953	−	0.570996i	$-0.193443\pi$
$284$	15.4362	−	17.1436i	0.915968	−	1.01729i
$285$	−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
$289$	−12.6002	+	5.60996i	−0.741187	+	0.329998i
$290$	1.21219	+	0.539702i	0.0711822	+	0.0316924i
$291$	−26.1535	+	5.55910i	−1.53315	+	0.325880i
$292$	8.34456	+	9.26757i	0.488328	+	0.542344i
$293$	1.14654	−	0.833014i	0.0669819	−	0.0486652i	−0.553790	−	0.832656i	$-0.686819\pi$
$293$	1.14654	−	0.833014i	0.0669819	−	0.0486652i	0.620772	+	0.783991i	$0.286819\pi$
$294$		0			0
$295$	−0.244025	−	0.751033i	−0.0142077	−	0.0437268i
$296$	−1.79246	+	3.10463i	−0.104184	+	0.180453i
$297$	−20.7437	−	34.4076i	−1.20367	−	1.99653i
$298$	−0.878343	−	1.52133i	−0.0508810	−	0.0881286i
$299$	−7.82532	−	1.66332i	−0.452550	−	0.0961925i
$300$	1.59295	+	1.15735i	0.0919691	+	0.0668195i
$301$		0			0
$302$	−0.618734	+	1.90427i	−0.0356041	+	0.109578i
$303$	−8.46054	−	9.39638i	−0.486045	−	0.539808i
$304$	9.27929	+	4.13141i	0.532204	+	0.236952i
$305$	−1.12300	+	10.6847i	−0.0643030	+	0.611802i
$306$	−8.04633	−	1.71030i	−0.459978	−	0.0977714i
$307$	−29.4646			−1.68163			−0.840817	−	0.541319i	$-0.817925\pi$
$307$	−29.4646			−1.68163			−0.840817	+	0.541319i	$0.817925\pi$
$308$		0			0
$309$	−55.3411			−3.14825
$310$	−4.21573	−	0.896080i	−0.239437	−	0.0508939i
$311$	2.80959	−	26.7314i	0.159317	−	1.51580i	−0.564283	−	0.825581i	$-0.690847\pi$
$311$	2.80959	−	26.7314i	0.159317	−	1.51580i	0.723600	−	0.690219i	$-0.242486\pi$
$312$	−17.2490	−	7.67975i	−0.976533	−	0.434780i
$313$	3.00620	+	3.33873i	0.169921	+	0.188716i	0.822090	−	0.569357i	$-0.192808\pi$
$313$	3.00620	+	3.33873i	0.169921	+	0.188716i	−0.652170	+	0.758073i	$0.726141\pi$
$314$	−2.32930	+	7.16884i	−0.131450	+	0.404561i
$315$		0			0
$316$	5.09172	+	3.69935i	0.286431	+	0.208105i
$317$	10.7108	+	2.27665i	0.601577	+	0.127869i	0.498626	−	0.866817i	$-0.333838\pi$
$317$	10.7108	+	2.27665i	0.601577	+	0.127869i	0.102951	+	0.994686i	$0.467171\pi$
$318$	0.701741	+	1.21545i	0.0393517	+	0.0681591i
$319$	−0.262611	+	3.05385i	−0.0147034	+	0.170983i
$320$	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
$324$	−18.1256	−	20.1305i	−1.00698	−	1.11836i
$325$	−0.999626	+	0.212477i	−0.0554493	+	0.0117861i
$326$	−11.1373	−	4.95866i	−0.616839	−	0.274635i
$327$	54.2874	−	24.1703i	3.00210	−	1.33662i
$328$	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	−0.998635	−	0.0522322i	$-0.983366\pi$
$331$	−8.26132	+	14.3090i	−0.454083	+	0.786495i	0.544552	+	0.838727i	$0.316700\pi$
$332$	−4.20577	+	4.67098i	−0.230822	+	0.256353i
$333$	1.08046	−	10.2799i	0.0592088	−	0.563334i
$334$	1.39533	+	13.2757i	0.0763492	+	0.726414i
$335$	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	$0.192908\pi$
$338$	−4.04298	+	1.80005i	−0.219909	+	0.0979099i
$339$	−3.53085	+	3.92140i	−0.191769	+	0.212981i
$340$	−2.97826	−	5.15849i	−0.161519	−	0.279758i
$341$	−1.22797	−	9.87977i	−0.0664983	−	0.535019i
$342$	30.9004			1.67090
$343$		0			0
$344$	−16.2215	−	11.7856i	−0.874605	−	0.635437i
$345$	2.22632	+	21.1821i	0.119861	+	1.14040i
$346$	3.92415	−	0.834104i	0.210964	−	0.0448417i
$347$	23.7544	−	5.04916i	1.27521	−	0.271053i	0.479933	−	0.877305i	$-0.340661\pi$
$347$	23.7544	−	5.04916i	1.27521	−	0.271053i	0.795273	+	0.606252i	$0.207328\pi$
$348$	0.470566	+	4.47714i	0.0252250	+	0.240000i
$349$	−2.68497	−	1.95074i	−0.143723	−	0.104421i	0.513600	−	0.858030i	$-0.328311\pi$
$349$	−2.68497	−	1.95074i	−0.143723	−	0.104421i	−0.657323	+	0.753609i	$0.728311\pi$
$350$		0			0
$351$	30.6269			1.63474
$352$	18.7853	+	3.62257i	1.00126	+	0.193084i
$353$	10.1636	+	17.6039i	0.540955	+	0.936962i	0.998849	+	0.0479552i	$0.0152705\pi$
$353$	10.1636	+	17.6039i	0.540955	+	0.936962i	−0.457894	+	0.889007i	$0.651396\pi$
$354$	−0.518311	+	0.575643i	−0.0275479	+	0.0305951i
$355$	29.1208	−	12.9654i	1.54557	−	0.688132i
$356$	10.4268	−	7.57553i	0.552620	−	0.401502i
$357$		0			0
$358$	−0.335059	+	1.03121i	−0.0177084	+	0.0545009i
$359$	−3.03564	−	28.8821i	−0.160215	−	1.52434i	−0.718989	−	0.695021i	$-0.755395\pi$
$359$	−3.03564	−	28.8821i	−0.160215	−	1.52434i	0.558774	−	0.829320i	$-0.311272\pi$
$360$	−3.65542	+	34.7790i	−0.192657	+	1.83301i
$361$	17.5700	−	19.5134i	0.924736	−	1.02702i
$362$	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
$366$	9.62728	−	4.28634i	0.503226	−	0.224051i
$367$	20.7912	+	9.25683i	1.08529	+	0.483203i	0.869851	−	0.493314i	$-0.164215\pi$
$367$	20.7912	+	9.25683i	1.08529	+	0.483203i	0.215440	+	0.976517i	$0.430881\pi$
$368$	4.67323	−	0.993326i	0.243609	−	0.0517807i
$369$	−25.5197	−	28.3425i	−1.32850	−	1.47545i
$370$	−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	−0.420151	−	0.907454i	$-0.638023\pi$
$373$	11.1206	−	19.2614i	0.575802	−	0.997319i	0.995954	−	0.0898652i	$-0.0286436\pi$
$374$	−2.60544	+	3.00622i	−0.134724	+	0.155448i
$375$	18.1878	+	31.5022i	0.939215	+	1.62677i
$376$	−10.2316	−	2.17480i	−0.527655	−	0.112157i
$377$	−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	$-0.229310\pi$
$380$	14.9718	+	16.6279i	0.768037	+	0.852992i
$381$	−50.3876	−	22.4340i	−2.58144	−	1.14933i
$382$	−0.889157	+	8.45977i	−0.0454932	+	0.432839i
$383$	−6.01162	−	1.27781i	−0.307179	−	0.0652930i	0.0517429	−	0.998660i	$-0.483522\pi$
$383$	−6.01162	−	1.27781i	−0.307179	−	0.0652930i	−0.358922	+	0.933367i	$0.616856\pi$
$384$	34.4486			1.75795
$385$		0			0
$386$	−1.17829			−0.0599733
$387$	56.5500	+	12.0201i	2.87460	+	0.611015i
$388$	−1.38101	+	13.1395i	−0.0701103	+	0.667055i
$389$	6.76357	+	3.01133i	0.342926	+	0.152681i	0.570971	−	0.820970i	$-0.306567\pi$
$389$	6.76357	+	3.01133i	0.342926	+	0.152681i	−0.228045	+	0.973651i	$0.573233\pi$
$390$	−7.62641	−	8.46998i	−0.386178	−	0.428894i
$391$	−1.75119	+	5.38962i	−0.0885617	+	0.272565i
$392$		0			0
$393$	−17.0838	−	12.4121i	−0.861765	−	0.626109i
$394$	0.591598	+	0.125748i	0.0298043	+	0.00633509i
$395$	4.34831	+	7.53150i	0.218787	+	0.378951i
$396$	−34.3728	+	7.98935i	−1.72730	+	0.401480i
$397$	8.90394	−	15.4221i	0.446876	−	0.774012i	−0.551305	−	0.834304i	$-0.685870\pi$
$397$	8.90394	−	15.4221i	0.446876	−	0.774012i	0.998181	+	0.0602921i	$0.0192032\pi$
$398$	3.23473	+	9.95549i	0.162143	+	0.499024i
$399$		0			0
$400$	0.493749	−	0.358729i	0.0246874	−	0.0179365i
$401$	17.1825	+	19.0831i	0.858054	+	0.952965i	0.999315	−	0.0370073i	$-0.0117825\pi$
$401$	17.1825	+	19.0831i	0.858054	+	0.952965i	−0.141261	+	0.989972i	$0.545116\pi$
$402$	−1.85558	+	0.394416i	−0.0925480	+	0.0196717i
$403$	6.93317	+	3.08684i	0.345366	+	0.153767i
$404$	−5.70762	+	2.54120i	−0.283965	+	0.126429i
$405$	−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
$409$	−0.894992	+	0.993990i	−0.0442545	+	0.0491496i	−0.764866	−	0.644190i	$-0.777195\pi$
$409$	−0.894992	+	0.993990i	−0.0442545	+	0.0491496i	0.720611	+	0.693339i	$0.243861\pi$
$410$	−0.834601	+	7.94070i	−0.0412180	+	0.392163i
$411$	4.55130	+	43.3027i	0.224499	+	2.13596i
$412$	−8.45022	+	26.0071i	−0.416312	+	1.28128i
$413$		0			0
$414$	11.7585	−	8.54303i	0.577897	−	0.419867i
$415$	−7.93431	+	3.53258i	−0.389480	+	0.173408i
$416$	−9.75851	+	10.8379i	−0.478450	+	0.531373i
$417$	−22.4034	−	38.8039i	−1.09710	−	1.90023i
$418$	7.22535	−	13.0806i	0.353403	−	0.639794i
$419$	−37.4618			−1.83013			−0.915064	−	0.403310i	$-0.867860\pi$
$419$	−37.4618			−1.83013			−0.915064	+	0.403310i	$0.867860\pi$
$420$		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	$0.764524\pi$
$422$	−1.03392	−	9.83707i	−0.0503303	−	0.478861i
$423$	29.5012	−	6.27067i	1.43440	−	0.304890i
$424$	1.55281	−	0.330060i	0.0754110	−	0.0160291i
$425$	0.0756696	+	0.719949i	0.00367052	+	0.0349226i
$426$	−25.2963	−	18.3788i	−1.22561	−	0.890458i
$427$		0			0
$428$	23.8980			1.15515
$429$	12.7298	−	23.0458i	0.614603	−	1.11266i
$430$	−6.05171	−	10.4819i	−0.291840	−	0.505481i
$431$	21.8514	−	24.2685i	1.05255	−	1.16897i	0.0673168	−	0.997732i	$-0.478556\pi$
$431$	21.8514	−	24.2685i	1.05255	−	1.16897i	0.985229	−	0.171239i	$-0.0547772\pi$
$432$	−16.7089	+	7.43928i	−0.803907	+	0.357922i
$433$	12.7786	−	9.28422i	0.614102	−	0.446171i	−0.236754	−	0.971570i	$-0.576084\pi$
$433$	12.7786	−	9.28422i	0.614102	−	0.446171i	0.850856	+	0.525398i	$0.176084\pi$
$434$		0			0
$435$	−1.92226	+	5.91611i	−0.0921654	+	0.283656i
$436$	−3.06931	−	29.2026i	−0.146993	−	1.39855i
$437$	2.22514	−	21.1708i	0.106443	−	1.01274i
$438$	11.3103	−	12.5614i	0.540428	−	0.600206i
$439$	−10.3471	+	17.9217i	−0.493839	+	0.855354i	−0.999975	−	0.00709942i	$-0.997740\pi$
$439$	−10.3471	+	17.9217i	−0.493839	+	0.855354i	0.506136	+	0.862454i	$0.331073\pi$
$440$	13.8677	+	9.67964i	0.661118	+	0.461459i
$441$		0			0
$442$	−0.937107	−	2.88412i	−0.0445737	−	0.137184i
$443$	27.4936	−	12.2409i	1.30626	−	0.581584i	0.368745	−	0.929531i	$-0.379788\pi$
$443$	27.4936	−	12.2409i	1.30626	−	0.581584i	0.937514	+	0.347947i	$0.113121\pi$
$444$	−6.70701	−	2.98616i	−0.318301	−	0.141717i
$445$	17.4198	−	3.70269i	0.825777	−	0.175524i
$446$	0.826995	+	0.918470i	0.0391593	+	0.0434908i
$447$	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
$451$	−17.9650	+	4.17564i	−0.845938	+	0.196623i
$452$	1.30369	+	2.25806i	0.0613206	+	0.106210i
$453$	−9.18154	−	1.95160i	−0.431386	−	0.0916940i
$454$	−11.8878	−	8.63700i	−0.557922	−	0.405354i
$455$		0			0
$456$	15.5254	−	47.7821i	0.727041	−	2.23760i
$457$	−6.55347	−	7.27837i	−0.306559	−	0.340468i	0.570105	−	0.821572i	$-0.306903\pi$
$457$	−6.55347	−	7.27837i	−0.306559	−	0.340468i	−0.876663	+	0.481104i	$0.840236\pi$
$458$	12.3909	+	5.51678i	0.578988	+	0.257782i
$459$	2.26773	−	21.5760i	0.105848	−	1.00708i
$460$	10.2943	+	2.18812i	0.479973	+	0.102021i
$461$	21.8596			1.01810			0.509052	−	0.860736i	$-0.329996\pi$
$461$	21.8596			1.01810			0.509052	+	0.860736i	$0.329996\pi$
$462$		0			0
$463$	6.75889			0.314112			0.157056	−	0.987590i	$-0.449800\pi$
$463$	6.75889			0.314112			0.157056	+	0.987590i	$0.449800\pi$
$464$	1.36488	+	0.290114i	0.0633628	+	0.0134682i
$465$	2.11199	−	20.0943i	0.0979412	−	0.931849i
$466$	12.8870	+	5.73765i	0.596977	+	0.265791i
$467$	20.0894	+	22.3116i	0.929628	+	1.03246i	0.999391	+	0.0348933i	$0.0111091\pi$
$467$	20.0894	+	22.3116i	0.929628	+	1.03246i	−0.0697626	+	0.997564i	$0.522224\pi$
$468$	8.31283	−	25.5843i	0.384261	−	1.18263i
$469$		0			0
$470$	−5.10826	−	3.71136i	−0.235626	−	0.171192i
$471$	−34.5650	−	7.34701i	−1.59267	−	0.338533i
$472$	0.438083	+	0.758782i	0.0201644	+	0.0349258i
$473$	18.3112	−	21.1279i	0.841949	−	0.971460i
$474$	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
$478$	6.94471	+	7.71288i	0.317644	+	0.352779i
$479$	−5.87234	+	1.24820i	−0.268314	+	0.0570319i	−0.340104	−	0.940388i	$-0.610462\pi$
$479$	−5.87234	+	1.24820i	−0.268314	+	0.0570319i	0.0717898	+	0.997420i	$0.477129\pi$
$480$	35.4698	+	15.7922i	1.61897	+	0.720811i
$481$	3.48111	−	1.54989i	0.158725	−	0.0706688i
$482$	−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
$486$	−8.28138	+	9.19741i	−0.375651	+	0.417203i
$487$	−0.665556	+	6.33235i	−0.0301592	+	0.286946i	0.969039	+	0.246908i	$0.0794146\pi$
$487$	−0.665556	+	6.33235i	−0.0301592	+	0.286946i	−0.999198	+	0.0400380i	$0.987252\pi$
$488$	−1.24599	−	11.8548i	−0.0564033	−	0.536642i
$489$	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	$0.390096\pi$
$492$	−24.7469	+	11.0180i	−1.11567	+	0.496730i
$493$	−1.10749	+	1.22999i	−0.0498787	+	0.0553959i
$494$	5.69571	+	9.86527i	0.256262	+	0.443859i
$495$	−47.8802	−	9.23325i	−2.15206	−	0.415004i
$496$	−4.53228			−0.203505
$497$		0			0
$498$	6.89229	+	5.00754i	0.308851	+	0.224393i
$499$	1.49263	+	14.2014i	0.0668193	+	0.635743i	0.975764	+	0.218826i	$0.0702228\pi$
$499$	1.49263	+	14.2014i	0.0668193	+	0.635743i	−0.908945	+	0.416917i	$0.863111\pi$
$500$	17.5814	−	3.73704i	0.786263	−	0.167125i
$501$	−61.2121	+	13.0110i	−2.73475	+	0.581290i
$502$	−0.0754167	−	0.717542i	−0.00336601	−	0.0320255i
$503$	4.79402	+	3.48306i	0.213755	+	0.155302i	0.689511	−	0.724275i	$-0.257826\pi$
$503$	4.79402	+	3.48306i	0.213755	+	0.155302i	−0.475756	+	0.879577i	$0.657826\pi$
$504$		0			0
$505$	−8.63314			−0.384170
$506$	−0.866947	−	6.97512i	−0.0385405	−	0.310082i
$507$	−10.3736	−	17.9677i	−0.460709	−	0.797972i
$508$	−18.2365	+	20.2537i	−0.809115	+	0.898614i
$509$	−28.2043	+	12.5574i	−1.25014	+	0.556596i	−0.921690	−	0.387927i	$-0.873191\pi$
$509$	−28.2043	+	12.5574i	−1.25014	+	0.556596i	−0.328445	+	0.944523i	$0.606525\pi$
$510$	−6.53162	+	4.74550i	−0.289225	+	0.210134i
$511$		0			0
$512$	4.91089	−	15.1142i	0.217033	−	0.667958i
$513$	8.51848	+	81.0479i	0.376100	+	3.57835i
$514$	0.915767	−	8.71294i	0.0403927	−	0.384311i
$515$	−25.2837	+	28.0804i	−1.11413	+	1.23737i
$516$	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
$520$	−11.7773	+	5.24359i	−0.516469	+	0.229947i
$521$	−17.2541	−	7.68202i	−0.755916	−	0.336555i	−0.00766428	−	0.999971i	$-0.502440\pi$
$521$	−17.2541	−	7.68202i	−0.755916	−	0.336555i	−0.748251	+	0.663415i	$0.769106\pi$
$522$	4.15216	−	0.882568i	0.181735	−	0.0386289i
$523$	5.31429	+	5.90212i	0.232378	+	0.258082i	0.848045	−	0.529925i	$-0.177780\pi$
$523$	5.31429	+	5.90212i	0.232378	+	0.258082i	−0.615667	+	0.788007i	$0.711113\pi$
$524$	−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
$528$	−1.34709	+	15.6651i	−0.0586246	+	0.681734i
$529$	6.49365	+	11.2473i	0.282333	+	0.489014i
$530$	0.937331	+	0.199236i	0.0407150	+	0.00865425i
$531$	−2.04380	−	1.48491i	−0.0886935	−	0.0644396i
$532$		0			0
$533$	4.34471	−	13.3716i	0.188190	−	0.579190i
$534$	−11.6890	−	12.9819i	−0.505831	−	0.561782i
$535$	30.1673	+	13.4313i	1.30424	+	0.580687i
$536$	−0.224294	+	2.13401i	−0.00968801	+	0.0921752i
$537$	−4.97202	−	1.05684i	−0.214559	−	0.0456058i
$538$	3.19370			0.137690
$539$		0			0
$540$	−40.2899			−1.73380
$541$	−7.43554	−	1.58047i	−0.319679	−	0.0679498i	0.0452777	−	0.998974i	$-0.485583\pi$
$541$	−7.43554	−	1.58047i	−0.319679	−	0.0679498i	−0.364956	+	0.931025i	$0.618916\pi$
$542$	−1.40381	+	13.3563i	−0.0602986	+	0.573703i
$543$	6.96091	+	3.09920i	0.298721	+	0.132999i
$544$	6.91254	+	7.67715i	0.296373	+	0.329155i
$545$	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	$0.853547\pi$
$548$	21.0447	+	4.47319i	0.898984	+	0.191085i
$549$	17.1848	+	29.7650i	0.733431	+	1.27034i
$550$	−0.463582	−	0.768942i	−0.0197672	−	0.0327878i
$551$	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
$555$	−6.78819	−	7.53905i	−0.288143	−	0.320015i
$556$	−21.6564	+	4.60321i	−0.918436	+	0.195220i
$557$	−37.1022	−	16.5189i	−1.57207	−	0.699930i	−0.578769	−	0.815492i	$-0.696467\pi$
$557$	−37.1022	−	16.5189i	−1.57207	−	0.699930i	−0.993300	+	0.115562i	$0.963133\pi$
$558$	−12.5958	+	5.60803i	−0.533224	+	0.237407i
$559$	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
$563$	15.6772	−	17.4113i	0.660717	−	0.733800i	−0.315899	−	0.948793i	$-0.602306\pi$
$563$	15.6772	−	17.4113i	0.660717	−	0.733800i	0.976616	+	0.214993i	$0.0689728\pi$
$564$	2.23921	−	21.3047i	0.0942878	−	0.897088i
$565$	0.376603	+	3.58314i	0.0158438	+	0.150744i
$566$	−4.55177	+	14.0089i	−0.191325	+	0.588838i
$567$		0			0
$568$	−28.6130	+	20.7886i	−1.20058	+	0.872269i
$569$	−10.1818	+	4.53322i	−0.426842	+	0.190043i	−0.608903	−	0.793245i	$-0.708390\pi$
$569$	−10.1818	+	4.53322i	−0.426842	+	0.190043i	0.182060	+	0.983287i	$0.441723\pi$
$570$	20.2929	−	22.5376i	0.849978	−	0.943996i
$571$	3.07923	+	5.33338i	0.128862	+	0.223195i	0.923236	−	0.384234i	$-0.125534\pi$
$571$	3.07923	+	5.33338i	0.128862	+	0.223195i	−0.794374	+	0.607429i	$0.792201\pi$
$572$	−8.88644	−	9.50123i	−0.371561	−	0.397266i
$573$	−39.8780			−1.66593
$574$		0			0
$575$	−1.03477	−	0.751805i	−0.0431529	−	0.0313524i
$576$	−0.604744	−	5.75375i	−0.0251977	−	0.239740i
$577$	−14.1676	+	3.01142i	−0.589807	+	0.125367i	−0.493141	−	0.869950i	$-0.664151\pi$
$577$	−14.1676	+	3.01142i	−0.589807	+	0.125367i	−0.0966659	+	0.995317i	$0.530818\pi$
$578$	9.03565	−	1.92059i	0.375834	−	0.0798859i
$579$	−0.577398	−	5.49358i	−0.0239959	−	0.228305i
$580$	2.48671	+	1.80670i	0.103255	+	0.0750192i
$581$		0			0
$582$	17.9075			0.742288
$583$	0.273028	+	2.19668i	0.0113077	+	0.0909773i
$584$	−9.55961	−	16.5577i	−0.395580	−	0.685164i
$585$	24.8726	−	27.6238i	1.02836	−	1.14211i
$586$	−0.867106	+	0.386061i	−0.0358198	+	0.0159480i
$587$	12.8285	−	9.32048i	0.529491	−	0.384698i	−0.290676	−	0.956821i	$-0.593880\pi$
$587$	12.8285	−	9.32048i	0.529491	−	0.384698i	0.820167	+	0.572124i	$0.193880\pi$
$588$		0			0
$589$	−6.24035	+	19.2058i	−0.257129	+	0.791362i
$590$	0.0552836	+	0.525988i	0.00227599	+	0.0216546i
$591$	−0.296378	+	2.81985i	−0.0121914	+	0.115993i
$592$	−1.52270	+	1.69112i	−0.0625824	+	0.0695048i
$593$	11.4642	−	19.8566i	0.470780	−	0.815415i	−0.528662	−	0.848833i	$-0.677306\pi$
$593$	11.4642	−	19.8566i	0.470780	−	0.815415i	0.999441	+	0.0334179i	$0.0106392\pi$
$594$	8.79822	+	25.4292i	0.360995	+	1.04337i
$595$		0			0
$596$	−1.25749	−	3.87015i	−0.0515087	−	0.158527i
$597$	−44.8307	+	19.9599i	−1.83480	+	0.816906i
$598$	4.89482	+	2.17931i	0.200164	+	0.0891188i
$599$	−12.8638	+	2.73429i	−0.525601	+	0.111720i	−0.463068	−	0.886323i	$-0.653251\pi$
$599$	−12.8638	+	2.73429i	−0.525601	+	0.111720i	−0.0625335	+	0.998043i	$0.519918\pi$
$600$	−2.01992	−	2.24335i	−0.0824628	−	0.0915842i
$601$	22.1286	−	16.0774i	0.902645	−	0.655810i	−0.0364993	−	0.999334i	$-0.511621\pi$
$601$	22.1286	−	16.0774i	0.902645	−	0.655810i	0.939144	+	0.343524i	$0.111621\pi$
$602$		0			0
$603$	−1.91188	−	5.88415i	−0.0778576	−	0.239621i
$604$	−2.31910	+	4.01679i	−0.0943627	+	0.163441i
$605$	−15.1043	+	18.1094i	−0.614075	+	0.736253i
$606$	4.23415	+	7.33376i	0.172001	+	0.297914i
$607$	−45.8500	−	9.74572i	−1.86099	−	0.395567i	−0.866395	−	0.499359i	$-0.833569\pi$
$607$	−45.8500	−	9.74572i	−1.86099	−	0.395567i	−0.994599	+	0.103792i	$0.966902\pi$
$608$	−31.3946	−	22.8095i	−1.27322	−	0.925049i
$609$		0			0
$610$	2.22350	−	6.84324i	0.0900270	−	0.277075i
$611$	7.43977	+	8.26270i	0.300981	+	0.334273i
$612$	−17.4081	−	7.75057i	−0.703680	−	0.313298i
$613$	2.13964	−	20.3573i	0.0864192	−	0.822223i	−0.862363	−	0.506291i	$-0.831016\pi$
$613$	2.13964	−	20.3573i	0.0864192	−	0.822223i	0.948782	−	0.315932i	$-0.102317\pi$
$614$	19.3025	+	4.10288i	0.778986	+	0.165579i
$615$	−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	$0.151338\pi$
$618$	36.2544	+	7.70612i	1.45837	+	0.309986i
$619$	0.0712449	−	0.677850i	0.00286357	−	0.0272451i	−0.992997	−	0.118141i	$-0.962306\pi$
$619$	0.0712449	−	0.677850i	0.00286357	−	0.0272451i	0.995860	+	0.0908961i	$0.0289731\pi$
$620$	−9.12064	−	4.06077i	−0.366294	−	0.163084i
$621$	25.6488	+	28.4859i	1.02925	+	1.14310i
$622$	−5.56287	+	17.1208i	−0.223051	+	0.686480i
$623$		0			0
$624$	−9.69651	−	7.04492i	−0.388171	−	0.282023i
$625$	22.3170	+	4.74362i	0.892679	+	0.189745i
$626$	−1.50448	−	2.60584i	−0.0601311	−	0.104150i
$627$	64.5269	+	27.2771i	2.57696	+	1.08934i
$628$	−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	$0.0376880\pi$
$632$	−6.45647	−	7.17064i	−0.256825	−	0.285233i
$633$	45.3571	−	9.64095i	1.80278	−	0.383193i
$634$	−6.69970	−	2.98290i	−0.266079	−	0.118466i
$635$	−34.4037	+	15.3175i	−1.36527	+	0.607858i
$636$	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
$640$	15.7385	−	17.4794i	0.622120	−	0.690934i
$641$	2.14415	−	20.4003i	0.0846890	−	0.805762i	−0.866919	−	0.498449i	$-0.833903\pi$
$641$	2.14415	−	20.4003i	0.0846890	−	0.805762i	0.951608	−	0.307314i	$-0.0994301\pi$
$642$	−3.38585	−	32.2142i	−0.133629	−	1.27139i
$643$	2.35984	−	7.26283i	0.0930629	−	0.286418i	−0.893681	−	0.448703i	$-0.851886\pi$
$643$	2.35984	−	7.26283i	0.0930629	−	0.286418i	0.986744	+	0.162284i	$0.0518862\pi$
$644$		0			0
$645$	45.9045	−	33.3516i	1.80749	−	1.31322i
$646$	7.37161	−	3.28205i	0.290032	−	0.129131i
$647$	−9.82473	+	10.9115i	−0.386250	+	0.428974i	−0.904644	−	0.426168i	$-0.859863\pi$
$647$	−9.82473	+	10.9115i	−0.386250	+	0.428974i	0.518394	+	0.855142i	$0.326530\pi$
$648$	20.7649	+	35.9658i	0.815721	+	1.41287i
$649$	−1.10648	+	0.517961i	−0.0434331	+	0.0203317i
$650$	0.684450			0.0268463
$651$		0			0
$652$	−22.8473	−	16.5996i	−0.894770	−	0.650089i
$653$	−0.117807	−	1.12086i	−0.00461015	−	0.0438627i	0.991975	−	0.126434i	$-0.0403533\pi$
$653$	−0.117807	−	1.12086i	−0.00461015	−	0.0438627i	−0.996585	+	0.0825717i	$0.973687\pi$
$654$	−38.9298	+	8.27479i	−1.52228	+	0.323570i
$655$	−14.1031	+	2.99770i	−0.551052	+	0.117130i
$656$	0.877663	+	8.35040i	0.0342670	+	0.326028i
$657$	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	$0.437467\pi$
$660$	−16.7462	+	30.3170i	−0.651846	+	1.18009i
$661$	7.86853	+	13.6287i	0.306050	+	0.530095i	0.977495	−	0.210960i	$-0.0676591\pi$
$661$	7.86853	+	13.6287i	0.306050	+	0.530095i	−0.671444	+	0.741055i	$0.734326\pi$
$662$	7.40456	−	8.22359i	0.287786	−	0.319619i
$663$	12.9875	−	5.78242i	0.504394	−	0.224571i
$664$	7.79597	−	5.66410i	0.302542	−	0.219810i
$665$		0			0
$666$	−2.13927	+	6.58398i	−0.0828949	+	0.255124i
$667$	−0.305676	−	2.90832i	−0.0118358	−	0.112611i
$668$	−3.23225	+	30.7528i	−0.125059	+	1.18986i
$669$	−3.87697	+	4.30581i	−0.149892	+	0.166472i
$670$	−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	$0.688353\pi$
$674$	−7.41597	+	3.30180i	−0.285652	+	0.127181i
$675$	4.47323	+	1.99161i	0.172175	+	0.0766572i
$676$	−10.0277	+	2.13146i	−0.385682	+	0.0819793i
$677$	10.2645	+	11.3999i	0.394496	+	0.438133i	0.907371	−	0.420331i	$-0.138086\pi$
$677$	10.2645	+	11.3999i	0.394496	+	0.438133i	−0.512874	+	0.858464i	$0.671419\pi$
$678$	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
$682$	−0.571281	+	6.64331i	−0.0218755	+	0.254385i
$683$	−0.523820	−	0.907282i	−0.0200434	−	0.0347162i	0.855830	−	0.517258i	$-0.173047\pi$
$683$	−0.523820	−	0.907282i	−0.0200434	−	0.0347162i	−0.875873	+	0.482541i	$0.839714\pi$
$684$	70.0158	+	14.8823i	2.67712	+	0.569040i
$685$	24.0514	+	17.4743i	0.918955	+	0.667660i
$686$		0			0
$687$	−19.6492	+	60.4739i	−0.749663	+	2.30722i
$688$	−8.51663	−	9.45868i	−0.324694	−	0.360609i
$689$	−1.54153	−	0.686334i	−0.0587276	−	0.0261472i
$690$	1.49107	−	14.1866i	0.0567640	−	0.540073i
$691$	28.5505	+	6.06859i	1.08611	+	0.230860i	0.715981	−	0.698120i	$-0.245980\pi$
$691$	28.5505	+	6.06859i	1.08611	+	0.230860i	0.370131	+	0.928980i	$0.379313\pi$
$692$	9.29326			0.353277
$693$		0			0
$694$	−16.2648			−0.617404
$695$	−29.9247	−	6.36070i	−1.13511	−	0.241275i
$696$	0.721437	−	6.86401i	0.0273460	−	0.260180i
$697$	−9.09834	−	4.05084i	−0.344624	−	0.153437i
$698$	1.48731	+	1.65182i	0.0562955	+	0.0625224i
$699$	−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	$0.777580\pi$
$702$	−20.0639	−	4.26472i	−0.757263	−	0.160961i
$703$	5.06970	+	8.78098i	0.191207	+	0.331181i
$704$	−2.57705	−	1.08938i	−0.0971264	−	0.0410577i
$705$	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
$709$	25.4744	+	28.2922i	0.956713	+	1.06254i	0.997989	+	0.0633895i	$0.0201910\pi$
$709$	25.4744	+	28.2922i	0.956713	+	1.06254i	−0.0412760	+	0.999148i	$0.513142\pi$
$710$	−20.8826	+	4.43874i	−0.783712	+	0.166583i
$711$	25.4161	+	11.3160i	0.953179	+	0.424383i
$712$	−18.0510	+	8.03684i	−0.676491	+	0.301193i
$713$	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
$717$	−32.5569	+	36.1581i	−1.21586	+	1.35035i
$718$	−2.03310	+	19.3436i	−0.0758746	+	0.721898i
$719$	−4.10477	−	39.0542i	−0.153082	−	1.45648i	−0.753846	−	0.657051i	$-0.771804\pi$
$719$	−4.10477	−	39.0542i	−0.153082	−	1.45648i	0.600764	−	0.799426i	$-0.294863\pi$
$720$	−6.85975	+	21.1121i	−0.255648	+	0.786803i
$721$		0			0
$722$	−14.2274	+	10.3368i	−0.529491	+	0.384697i
$723$	40.3998	−	17.9872i	1.50249	−	0.668950i
$724$	2.51933	−	2.79800i	0.0936300	−	0.103987i
$725$	−0.186781	−	0.323514i	−0.00693687	−	0.0120150i
$726$	22.7917	+	3.94907i	0.845879	+	0.146564i
$727$	28.4699			1.05589			0.527946	−	0.849278i	$-0.322963\pi$
$727$	28.4699			1.05589			0.527946	+	0.849278i	$0.322963\pi$
$728$		0			0
$729$	−4.56314	−	3.31531i	−0.169005	−	0.122789i
$730$	−1.20637	−	11.4778i	−0.0446497	−	0.424813i
$731$	14.7673	−	3.13888i	0.546187	−	0.116096i
$732$	23.8784	−	5.07551i	0.882571	−	0.187596i
$733$	−0.312892	−	2.97697i	−0.0115569	−	0.109957i	0.987223	−	0.159347i	$-0.0509389\pi$
$733$	−0.312892	−	2.97697i	−0.0115569	−	0.109957i	−0.998780	+	0.0493902i	$0.984272\pi$
$734$	−12.3315	−	8.95935i	−0.455163	−	0.330696i
$735$		0			0
$736$	−18.2527			−0.672802
$737$	−2.93790	−	0.566546i	−0.108219	−	0.0208690i
$738$	12.7715	+	22.1210i	0.470127	+	0.814284i
$739$	−33.9469	+	37.7019i	−1.24876	+	1.38689i	−0.357169	+	0.934040i	$0.616258\pi$
$739$	−33.9469	+	37.7019i	−1.24876	+	1.38689i	−0.891589	+	0.452846i	$0.850409\pi$
$740$	−4.57942	+	2.03889i	−0.168343	+	0.0749511i
$741$	−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	$0.102241\pi$
$744$	2.34329	+	22.2949i	0.0859091	+	0.817371i
$745$	0.587760	−	5.59216i	0.0215339	−	0.204881i
$746$	−9.96730	+	11.0698i	−0.364929	+	0.405295i
$747$	−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
$751$	−35.9544	+	16.0079i	−1.31199	+	0.584137i	−0.939070	−	0.343725i	$-0.888311\pi$
$751$	−35.9544	+	16.0079i	−1.31199	+	0.584137i	−0.372923	+	0.927862i	$0.621645\pi$
$752$	−6.06588	−	2.70070i	−0.221200	−	0.0984845i
$753$	3.30847	−	0.703236i	0.120567	−	0.0256274i
$754$	1.04711	+	1.16294i	0.0381336	+	0.0423517i
$755$	−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
$759$	32.0956	−	7.46003i	1.16499	−	0.270782i
$760$	−17.1518	−	29.7079i	−0.622163	−	1.07762i
$761$	−7.31816	−	1.55552i	−0.265283	−	0.0563876i	0.0733498	−	0.997306i	$-0.476631\pi$
$761$	−7.31816	−	1.55552i	−0.265283	−	0.0563876i	−0.338633	+	0.940919i	$0.609964\pi$
$762$	29.8855	+	21.7131i	1.08264	+	0.786582i
$763$		0			0
$764$	−6.08911	+	18.7403i	−0.220296	+	0.678002i
$765$	−17.6188	−	19.5676i	−0.637008	−	0.707469i
$766$	3.76033	+	1.67421i	0.135866	+	0.0604916i
$767$	0.0973485	−	0.926209i	0.00351505	−	0.0334435i
$768$	−27.7491	−	5.89826i	−1.00131	−	0.212835i
$769$	26.8378			0.967798			0.483899	−	0.875124i	$-0.339220\pi$
$769$	26.8378			0.967798			0.483899	+	0.875124i	$0.339220\pi$
$770$		0			0
$771$	41.0714			1.47915
$772$	−2.66983	−	0.567489i	−0.0960891	−	0.0204244i
$773$	0.467013	−	4.44333i	0.0167973	−	0.159816i	−0.982908	−	0.184098i	$-0.941064\pi$
$773$	0.467013	−	4.44333i	0.0167973	−	0.159816i	0.999705	+	0.0242827i	$0.00773020\pi$
$774$	−35.3726	−	15.7489i	−1.27144	−	0.566083i
$775$	0.811897	+	0.901703i	0.0291642	+	0.0323901i
$776$	6.25926	−	19.2640i	0.224694	−	0.691538i
$777$		0			0
$778$	−4.01155	−	2.91456i	−0.143821	−	0.104492i
$779$	36.5938	+	7.77825i	1.31111	+	0.278685i
$780$	−13.2010	−	22.8648i	−0.472671	−	0.818690i
$781$	−25.4624	−	42.2344i	−0.911116	−	1.51127i
$782$	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
$786$	9.46340	+	10.5102i	0.337548	+	0.374885i
$787$	−13.1912	+	2.80388i	−0.470217	+	0.0999476i	−0.436925	−	0.899498i	$-0.643932\pi$
$787$	−13.1912	+	2.80388i	−0.470217	+	0.0999476i	−0.0332918	+	0.999446i	$0.510599\pi$
$788$	1.27991	+	0.569853i	0.0455949	+	0.0203002i
$789$	27.4561	−	12.2242i	0.977462	−	0.435194i
$790$	−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
$794$	−7.98053	+	8.86328i	−0.283218	+	0.314546i
$795$	−0.469583	+	4.46779i	−0.0166544	+	0.158456i
$796$	2.53465	+	24.1156i	0.0898383	+	0.854754i
$797$	−16.2250	+	49.9354i	−0.574719	+	1.76880i	0.0624156	+	0.998050i	$0.480120\pi$
$797$	−16.2250	+	49.9354i	−0.574719	+	1.76880i	−0.637134	+	0.770753i	$0.719880\pi$
$798$		0			0
$799$	6.37177	−	4.62936i	0.225417	−	0.163775i
$800$	−2.13006	+	0.948363i	−0.0753090	+	0.0335297i
$801$	38.1222	−	42.3390i	1.34698	−	1.49597i
$802$	−8.59913	−	14.8941i	−0.303646	−	0.525930i
$803$	24.1450	−	11.3027i	0.852059	−	0.398862i
$804$	−4.39443			−0.154980
$805$		0			0
$806$	−4.11214	−	2.98764i	−0.144844	−	0.105235i
$807$	1.56501	+	14.8901i	0.0550910	+	0.524156i
$808$	9.36930	−	1.99151i	0.329611	−	0.0700609i
$809$	1.26166	−	0.268173i	0.0443575	−	0.00942847i	−0.185680	−	0.982610i	$-0.559449\pi$
$809$	1.26166	−	0.268173i	0.0443575	−	0.00942847i	0.230037	+	0.973182i	$0.426115\pi$
$810$	2.62041	+	24.9315i	0.0920717	+	0.876004i
$811$	−27.6585	−	20.0951i	−0.971220	−	0.705633i	−0.0154910	−	0.999880i	$-0.504931\pi$
$811$	−27.6585	−	20.0951i	−0.971220	−	0.705633i	−0.955729	+	0.294247i	$0.904931\pi$
$812$		0			0
$813$	−62.9596			−2.20809
$814$	2.28688	+	2.44509i	0.0801551	+	0.0857005i
$815$	−19.5116	−	33.7950i	−0.683460	−	1.18379i
$816$	−5.68097	+	6.30936i	−0.198874	+	0.220872i
$817$	−51.8080	+	23.0664i	−1.81253	+	0.806992i
$818$	0.724728	−	0.526545i	0.0253395	−	0.0184102i
$819$		0			0
$820$	−5.71550	+	17.5905i	−0.199594	+	0.614287i
$821$	−4.14559	−	39.4427i	−0.144682	−	1.37656i	−0.790217	−	0.612828i	$-0.790032\pi$
$821$	−4.14559	−	39.4427i	−0.144682	−	1.37656i	0.645534	−	0.763731i	$-0.276635\pi$
$822$	3.04820	−	29.0017i	0.106318	−	1.01155i
$823$	−6.17416	+	6.85710i	−0.215218	+	0.239024i	−0.841081	−	0.540909i	$-0.818080\pi$
$823$	−6.17416	+	6.85710i	−0.215218	+	0.239024i	0.625863	+	0.779933i	$0.284747\pi$
$824$	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	$-0.247424\pi$
$828$	30.7574	−	13.6941i	1.06890	−	0.475903i
$829$	−9.99284	−	4.44910i	−0.347066	−	0.154524i	0.225798	−	0.974174i	$-0.427501\pi$
$829$	−9.99284	−	4.44910i	−0.347066	−	0.154524i	−0.572864	+	0.819651i	$0.694168\pi$
$830$	5.68973	−	1.20939i	0.197494	−	0.0419785i
$831$	24.3758	+	27.0721i	0.845587	+	0.939120i
$832$	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
$836$	22.6715	−	26.1589i	0.784110	−	0.904723i
$837$	−18.1815	−	31.4913i	−0.628444	−	1.08850i
$838$	24.5415	+	5.21646i	0.847773	+	0.180200i
$839$	−28.1031	−	20.4181i	−0.970228	−	0.704912i	−0.0147243	−	0.999892i	$-0.504687\pi$
$839$	−28.1031	−	20.4181i	−0.970228	−	0.704912i	−0.955503	+	0.294980i	$0.904687\pi$
$840$		0			0
$841$	−8.69756	+	26.7684i	−0.299916	+	0.923047i
$842$	3.70239	+	4.11192i	0.127593	+	0.141706i
$843$	−34.6460	−	15.4254i	−1.19327	−	0.531279i
$844$	2.39504	−	22.7873i	0.0824407	−	0.784371i
$845$	−13.8563	−	2.94525i	−0.476671	−	0.101320i
$846$	−20.1996			−0.694478
$847$		0			0
$848$	1.00771			0.0346050
$849$	−67.5447	−	14.3571i	−2.31813	−	0.492733i
$850$	0.0506793	−	0.482181i	0.00173828	−	0.0165387i
$851$	4.35683	+	1.93979i	0.149350	+	0.0664950i
$852$	−48.4660	−	53.8270i	−1.66042	−	1.84408i
$853$	6.37880	−	19.6319i	0.218406	−	0.672185i	−0.780488	−	0.625171i	$-0.785029\pi$
$853$	6.37880	−	19.6319i	0.218406	−	0.672185i	0.998894	−	0.0470143i	$-0.0149706\pi$
$854$		0			0
$855$	80.0191	+	58.1373i	2.73659	+	1.98825i
$856$	−35.8380	−	7.61760i	−1.22492	−	0.260364i
$857$	−17.0756	−	29.5758i	−0.583291	−	1.01029i	−0.995086	−	0.0990131i	$-0.968431\pi$
$857$	−17.0756	−	29.5758i	−0.583291	−	1.01029i	0.411795	−	0.911276i	$-0.364902\pi$
$858$	−11.5485	+	13.3249i	−0.394260	+	0.454905i
$859$	−16.7246	+	28.9679i	−0.570637	+	0.988373i	0.425863	+	0.904787i	$0.359970\pi$
$859$	−16.7246	+	28.9679i	−0.570637	+	0.988373i	−0.996501	+	0.0835852i	$0.973363\pi$
$860$	−8.66399	−	26.6650i	−0.295440	−	0.909269i
$861$		0			0
$862$	−17.6944	+	12.8557i	−0.602673	+	0.437868i
$863$	−22.7732	−	25.2922i	−0.775208	−	0.860956i	0.218162	−	0.975913i	$-0.429994\pi$
$863$	−22.7732	−	25.2922i	−0.775208	−	0.860956i	−0.993371	+	0.114956i	$0.963327\pi$
$864$	68.3495	−	14.5281i	2.32530	−	0.494257i
$865$	11.7312	+	5.22307i	0.398873	+	0.177590i
$866$	−9.66420	+	4.30278i	−0.328403	+	0.146214i
$867$	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
$871$	1.52617	−	1.69498i	0.0517122	−	0.0574322i
$872$	−4.70564	+	44.7712i	−0.159353	+	1.51614i
$873$	6.10478	+	58.0831i	0.206616	+	1.96582i
$874$	−4.40569	+	13.5593i	−0.149025	+	0.458651i
$875$		0			0
$876$	31.6773	−	23.0149i	1.07028	−	0.777602i
$877$	7.18692	−	3.19982i	0.242685	−	0.108050i	−0.281790	−	0.959476i	$-0.590928\pi$
$877$	7.18692	−	3.19982i	0.242685	−	0.108050i	0.524475	+	0.851426i	$0.324262\pi$
$878$	9.27401	−	10.2998i	0.312983	−	0.347602i
$879$	−2.22485	−	3.85356i	−0.0750425	−	0.129977i
$880$	7.33309	+	7.84041i	0.247198	+	0.264300i
$881$	−13.3289			−0.449063			−0.224531	−	0.974467i	$-0.572085\pi$
$881$	−13.3289			−0.449063			−0.224531	+	0.974467i	$0.572085\pi$
$882$		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	$0.607100\pi$
$884$	−0.734292	−	6.98632i	−0.0246969	−	0.234975i
$885$	−2.42524	+	0.515501i	−0.0815237	+	0.0173284i
$886$	−19.7158	+	4.19072i	−0.662365	+	0.140790i
$887$	−2.77193	−	26.3732i	−0.0930724	−	0.885525i	−0.937061	−	0.349165i	$-0.886465\pi$
$887$	−2.77193	−	26.3732i	−0.0930724	−	0.885525i	0.843989	−	0.536361i	$-0.180201\pi$
$888$	9.10614	+	6.61600i	0.305582	+	0.222018i
$889$		0			0
$890$	−11.9274			−0.399808
$891$	−52.4465	+	24.5510i	−1.75702	+	0.822490i
$892$	1.43149	+	2.47942i	0.0479299	+	0.0830170i
$893$	−19.7963	+	21.9860i	−0.662459	+	0.735735i
$894$	−5.03875	+	2.24339i	−0.168521	+	0.0750303i
$895$	−2.80781	+	2.03999i	−0.0938548	+	0.0681895i
$896$		0			0
$897$	−7.76209	+	23.8892i	−0.259168	+	0.797639i
$898$	−2.54788	−	24.2414i	−0.0850237	−	0.808946i
$899$	−0.289978	+	2.75896i	−0.00967132	+	0.0920165i
$900$	2.87784	−	3.19616i	0.0959279	−	0.106539i
$901$	−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
$905$	4.75278	−	2.11607i	0.157988	−	0.0703407i
$906$	5.74315	+	2.55702i	0.190803	+	0.0849511i
$907$	−8.65911	+	1.84055i	−0.287521	+	0.0611145i	−0.349414	−	0.936968i	$-0.613619\pi$
$907$	−8.65911	+	1.84055i	−0.287521	+	0.0611145i	0.0618934	+	0.998083i	$0.480286\pi$
$908$	−22.7762	−	25.2956i	−0.755856	−	0.839463i
$909$	−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
$913$	6.93754	+	11.5073i	0.229599	+	0.380836i
$914$	3.27974	+	5.68068i	0.108484	+	0.187900i
$915$	32.9951	+	7.01332i	1.09078	+	0.231853i
$916$	25.4189	+	18.4679i	0.839865	+	0.610197i
$917$		0			0
$918$	−4.49001	+	13.8188i	−0.148192	+	0.456090i
$919$	32.3709	+	35.9516i	1.06782	+	1.18593i	0.981855	+	0.189634i	$0.0607303\pi$
$919$	32.3709	+	35.9516i	1.06782	+	1.18593i	0.0859639	+	0.996298i	$0.472603\pi$
$920$	−14.7401	−	6.56270i	−0.485966	−	0.216366i
$921$	−9.67016	+	92.0054i	−0.318643	+	3.03168i
$922$	−14.3204	−	3.04390i	−0.471618	−	0.100246i
$923$	37.5937			1.23741
$924$		0			0
$925$	0.609223			0.0200311
$926$	−4.42781	−	0.941159i	−0.145507	−	0.0309284i
$927$	−12.6355	+	120.219i	−0.415005	+	3.94851i
$928$	−4.87004	−	2.16828i	−0.159867	−	0.0711773i
$929$	−0.578326	−	0.642296i	−0.0189743	−	0.0210731i	0.733583	−	0.679600i	$-0.237847\pi$
$929$	−0.578326	−	0.642296i	−0.0189743	−	0.0210731i	−0.752557	+	0.658527i	$0.771180\pi$
$930$	−4.18166	+	12.8698i	−0.137122	+	0.422018i
$931$		0			0
$932$	26.4366	+	19.2073i	0.865959	+	0.629156i
$933$	−82.5488	−	17.5463i	−2.70253	−	0.574440i
$934$	−10.0539	−	17.4139i	−0.328975	−	0.569801i
$935$	−12.4030	+	2.88285i	−0.405622	+	0.0942794i
$936$	−20.6212	+	35.7170i	−0.674026	+	1.16745i
$937$	−16.5194	−	50.8416i	−0.539667	−	1.66092i	−0.733344	−	0.679858i	$-0.762042\pi$
$937$	−16.5194	−	50.8416i	−0.539667	−	1.66092i	0.193678	−	0.981065i	$-0.437958\pi$
$938$		0			0
$939$	11.4120	−	8.29134i	0.372418	−	0.270578i
$940$	−9.78708	−	10.8696i	−0.319219	−	0.354529i
$941$	13.4006	−	2.84839i	0.436848	−	0.0928548i	0.0157621	−	0.999876i	$-0.494983\pi$
$941$	13.4006	−	2.84839i	0.436848	−	0.0928548i	0.421086	+	0.907021i	$0.361649\pi$
$942$	21.6208	+	9.62618i	0.704442	+	0.313638i
$943$	16.0754	−	7.15723i	0.523487	−	0.233071i
$944$	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	0.485713	+	0.874119i	$0.338560\pi$
$947$	−15.8222	+	27.4049i	−0.514152	+	0.890538i	−0.999865	+	0.0164197i	$0.994773\pi$
$948$	13.2226	−	14.6851i	0.429449	−	0.476951i
$949$	−2.12429	+	20.2112i	−0.0689573	+	0.656085i
$950$	0.190371	+	1.81126i	0.00617646	+	0.0587651i
$951$	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	$0.477899\pi$
$954$	2.80058	−	1.24690i	0.0906720	−	0.0403698i
$955$	−18.2191	+	20.2343i	−0.589555	+	0.654767i
$956$	12.0210	+	20.8210i	0.388787	+	0.673398i
$957$	9.44970	+	1.82228i	0.305465	+	0.0589061i
$958$	4.02083			0.129907
$959$		0			0
$960$	−4.59371	−	3.33753i	−0.148261	−	0.107718i
$961$	2.29851	+	21.8688i	0.0741454	+	0.705446i
$962$	−2.49632	+	0.530609i	−0.0804846	+	0.0171075i
$963$	103.333	−	21.9641i	3.32986	−	0.707783i
$964$	−2.28413	−	21.7321i	−0.0735670	−	0.699943i
$965$	−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	$0.674117\pi$
$968$	12.2147	−	23.1379i	0.392595	−	0.743681i
$969$	18.9144	+	32.7606i	0.607617	+	1.05242i
$970$	8.18138	−	9.08635i	0.262688	−	0.291745i
$971$	26.8829	−	11.9690i	0.862714	−	0.384105i	0.0728173	−	0.997345i	$-0.476801\pi$
$971$	26.8829	−	11.9690i	0.862714	−	0.384105i	0.789896	+	0.613240i	$0.210134\pi$
$972$	−23.1941	+	16.8515i	−0.743950	+	0.540511i
$973$		0			0
$974$	1.31778	−	4.05570i	0.0422243	−	0.129953i
$975$	0.335402	+	3.19114i	0.0107415	+	0.102198i
$976$	0.790931	−	7.52520i	0.0253171	−	0.240876i
$977$	9.16337	−	10.1770i	0.293162	−	0.325590i	−0.578513	−	0.815673i	$-0.696367\pi$
$977$	9.16337	−	10.1770i	0.293162	−	0.325590i	0.871676	+	0.490083i	$0.163034\pi$
$978$	−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
$982$	7.57270	−	3.37158i	0.241654	−	0.107592i
$983$	−15.5595	−	6.92751i	−0.496269	−	0.220953i	0.143311	−	0.989678i	$-0.454225\pi$
$983$	−15.5595	−	6.92751i	−0.496269	−	0.220953i	−0.639580	+	0.768724i	$0.720892\pi$
$984$	40.6230	−	8.63469i	1.29501	−	0.275264i
$985$	1.29540	+	1.43869i	0.0412749	+	0.0458404i
$986$	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
$990$	30.0810	+	12.7160i	0.956038	+	0.404141i
$991$	−11.6101	−	20.1093i	−0.368807	−	0.638792i	0.620572	−	0.784149i	$-0.286900\pi$
$991$	−11.6101	−	20.1093i	−0.368807	−	0.638792i	−0.989379	+	0.145357i	$0.953567\pi$
$992$	16.9369	+	3.60005i	0.537747	+	0.114302i
$993$	41.9696	+	30.4927i	1.33187	+	0.967657i
$994$		0			0
$995$	−10.3540	+	31.8665i	−0.328245	+	1.01023i
$996$	13.2052	+	14.6658i	0.418422	+	0.464704i
$997$	16.7888	+	7.47485i	0.531706	+	0.236731i	0.654986	−	0.755641i	$-0.272675\pi$
$997$	16.7888	+	7.47485i	0.531706	+	0.236731i	−0.123280	+	0.992372i	$0.539341\pi$
$998$	0.999680	−	9.51132i	0.0316443	−	0.301076i
$999$	−17.8587	−	3.79598i	−0.565024	−	0.120100i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.f.324.2		32
7.2	even	3		539.2.f.e.148.3		16
7.3	odd	6		539.2.q.g.214.3		32
7.4	even	3	inner	539.2.q.f.214.3		32
7.5	odd	6		77.2.f.b.71.3	yes	16
7.6	odd	2		539.2.q.g.324.2		32
11.9	even	5	inner	539.2.q.f.471.3		32
21.5	even	6		693.2.m.i.379.2		16
77.5	odd	30		847.2.f.w.323.2		16
77.9	even	15		539.2.f.e.295.3		16
77.19	even	30		847.2.a.o.1.4		8
77.20	odd	10		539.2.q.g.471.3		32
77.26	odd	30		847.2.f.w.729.2		16
77.30	odd	30		5929.2.a.bs.1.4		8
77.31	odd	30		539.2.q.g.361.2		32
77.40	even	30		847.2.f.v.729.3		16
77.47	odd	30		847.2.a.p.1.5		8
77.53	even	15	inner	539.2.q.f.361.2		32
77.54	even	6		847.2.f.x.148.2		16
77.58	even	15		5929.2.a.bt.1.5		8
77.61	even	30		847.2.f.v.323.3		16
77.68	even	30		847.2.f.x.372.2		16
77.75	odd	30		77.2.f.b.64.3	✓	16
231.47	even	30		7623.2.a.ct.1.4		8
231.152	even	30		693.2.m.i.64.2		16
231.173	odd	30		7623.2.a.cw.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.3	✓	16	77.75	odd	30
77.2.f.b.71.3	yes	16	7.5	odd	6
539.2.f.e.148.3		16	7.2	even	3
539.2.f.e.295.3		16	77.9	even	15
539.2.q.f.214.3		32	7.4	even	3	inner
539.2.q.f.324.2		32	1.1	even	1	trivial
539.2.q.f.361.2		32	77.53	even	15	inner
539.2.q.f.471.3		32	11.9	even	5	inner
539.2.q.g.214.3		32	7.3	odd	6
539.2.q.g.324.2		32	7.6	odd	2
539.2.q.g.361.2		32	77.31	odd	30
539.2.q.g.471.3		32	77.20	odd	10
693.2.m.i.64.2		16	231.152	even	30
693.2.m.i.379.2		16	21.5	even	6
847.2.a.o.1.4		8	77.19	even	30
847.2.a.p.1.5		8	77.47	odd	30
847.2.f.v.323.3		16	77.61	even	30
847.2.f.v.729.3		16	77.40	even	30
847.2.f.w.323.2		16	77.5	odd	30
847.2.f.w.729.2		16	77.26	odd	30
847.2.f.x.148.2		16	77.54	even	6
847.2.f.x.372.2		16	77.68	even	30
5929.2.a.bs.1.4		8	77.30	odd	30
5929.2.a.bt.1.5		8	77.58	even	15
7623.2.a.ct.1.4		8	231.47	even	30
7623.2.a.cw.1.5		8	231.173	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.655108 - 0.139248i) q^{2} +(0.328196 - 3.12257i) q^{3} +(-1.41731 - 0.631029i) q^{4} +(-1.43447 - 1.59314i) q^{5} +(-0.649815 + 1.99992i) q^{6} +(1.92429 + 1.39808i) q^{8} +(-6.70831 - 1.42589i) q^{9} +O(q^{10})\)	\(q+(-0.655108 - 0.139248i) q^{2} +(0.328196 - 3.12257i) q^{3} +(-1.41731 - 0.631029i) q^{4} +(-1.43447 - 1.59314i) q^{5} +(-0.649815 + 1.99992i) q^{6} +(1.92429 + 1.39808i) q^{8} +(-6.70831 - 1.42589i) q^{9} +(0.717891 + 1.24342i) q^{10} +(-2.17218 + 2.50631i) q^{11} +(-2.43559 + 4.21857i) q^{12} +(-0.781276 - 2.40452i) q^{13} +(-5.44548 + 3.95637i) q^{15} +(1.01029 + 1.12205i) q^{16} +(-1.75178 + 0.372353i) q^{17} +(4.19612 + 1.86823i) q^{18} +(6.14579 - 2.73628i) q^{19} +(1.02778 + 3.16317i) q^{20} +(1.77201 - 1.33944i) q^{22} +(1.58214 - 2.74035i) q^{23} +(4.99715 - 5.54990i) q^{24} +(0.0422518 - 0.401999i) q^{25} +(0.176997 + 1.68401i) q^{26} +(-3.74337 + 11.5209i) q^{27} +(0.747669 - 0.543213i) q^{29} +(4.11829 - 1.83358i) q^{30} +(-2.00858 + 2.23076i) q^{31} +(-2.88417 - 4.99553i) q^{32} +(7.11325 + 7.60537i) q^{33} +1.19946 q^{34} +(8.60800 + 6.25408i) q^{36} +(0.157543 + 1.49892i) q^{37} +(-4.40718 + 0.936774i) q^{38} +(-7.76470 + 1.65044i) q^{39} +(-0.533001 - 5.07117i) q^{40} +(4.49897 + 3.26870i) q^{41} -8.42985 q^{43} +(4.66022 - 2.18152i) q^{44} +(7.35120 + 12.7327i) q^{45} +(-1.41806 + 1.57492i) q^{46} +(-4.01751 + 1.78871i) q^{47} +(3.83525 - 2.78647i) q^{48} +(-0.0836570 + 0.257470i) q^{50} +(0.587772 + 5.59228i) q^{51} +(-0.410008 + 3.90097i) q^{52} +(0.446592 - 0.495990i) q^{53} +(4.05657 - 7.02619i) q^{54} +(7.10883 - 0.134639i) q^{55} +(-6.52722 - 20.0887i) q^{57} +(-0.565445 + 0.251753i) q^{58} +(0.336514 + 0.149826i) q^{59} +(10.2145 - 2.17117i) q^{60} +(-3.35334 - 3.72426i) q^{61} +(1.62647 - 1.18170i) q^{62} +(0.260682 + 0.802296i) q^{64} +(-2.71002 + 4.69389i) q^{65} +(-3.60092 - 5.97284i) q^{66} +(0.451065 + 0.781267i) q^{67} +(2.71779 + 0.577685i) q^{68} +(-8.03770 - 5.83973i) q^{69} +(-4.59489 + 14.1416i) q^{71} +(-10.9152 - 12.1226i) q^{72} +(-7.34322 - 3.26941i) q^{73} +(0.105514 - 1.00389i) q^{74} +(-1.24141 - 0.263869i) q^{75} -10.4372 q^{76} +5.31654 q^{78} +(-3.96803 - 0.843431i) q^{79} +(0.338339 - 3.21908i) q^{80} +(15.9505 + 7.10164i) q^{81} +(-2.49216 - 2.76782i) q^{82} +(1.25193 - 3.85305i) q^{83} +(3.10609 + 2.25670i) q^{85} +(5.52246 + 1.17384i) q^{86} +(-1.45084 - 2.51293i) q^{87} +(-7.68395 + 1.78600i) q^{88} +(-4.15363 + 7.19431i) q^{89} +(-3.04284 - 9.36491i) q^{90} +(-3.97163 + 2.88556i) q^{92} +(6.30650 + 7.00408i) q^{93} +(2.88097 - 0.612370i) q^{94} +(-13.1752 - 5.86598i) q^{95} +(-16.5455 + 7.36652i) 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

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