LMFDB - Embedded newform 539.2.q.f.361.2

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			361.2
Character	$\chi$	$=$	539.361
Dual form			539.2.q.f.324.2

$q$-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 $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

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

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	−0.433615	−	0.901098i	$-0.642762\pi$
$2$	−0.655108	+	0.139248i	−0.463232	+	0.0984629i	−0.0296169	+	0.999561i	$0.509429\pi$
$3$	0.328196	+	3.12257i	0.189484	+	1.80282i	0.514903	+	0.857249i	$0.327828\pi$
$3$	0.328196	+	3.12257i	0.189484	+	1.80282i	−0.325419	+	0.945570i	$0.605505\pi$
$4$	−1.41731	+	0.631029i	−0.708657	+	0.315514i
$5$	−1.43447	+	1.59314i	−0.641514	+	0.712473i	−0.972953	−	0.231004i	$-0.925799\pi$
$5$	−1.43447	+	1.59314i	−0.641514	+	0.712473i	0.331439	+	0.943477i	$0.392466\pi$
$6$	−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	0.782343	+	0.622848i	$0.214025\pi$
$13$	−0.781276	+	2.40452i	−0.216687	+	0.666894i	−0.999030	+	0.0440455i	$0.985975\pi$
$14$		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	−0.00948587	−	0.999955i	$-0.503019\pi$
$17$	−1.75178	−	0.372353i	−0.424870	−	0.0903089i	−0.415384	+	0.909646i	$0.636353\pi$
$18$	4.19612	−	1.86823i	0.989034	−	0.440346i
$19$	6.14579	+	2.73628i	1.40994	+	0.627746i	0.963656	−	0.267146i	$-0.0860805\pi$
$19$	6.14579	+	2.73628i	1.40994	+	0.627746i	0.446284	+	0.894891i	$0.352747\pi$
$20$	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	$0.726318\pi$
$24$	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	0.655037	−	0.755597i	$-0.272653\pi$
$29$	0.747669	+	0.543213i	0.138839	+	0.100872i	−0.516198	+	0.856469i	$0.672653\pi$
$30$	4.11829	+	1.83358i	0.751894	+	0.334765i
$31$	−2.00858	−	2.23076i	−0.360752	−	0.400656i	0.535258	−	0.844688i	$-0.320214\pi$
$31$	−2.00858	−	2.23076i	−0.360752	−	0.400656i	−0.896011	+	0.444032i	$0.853548\pi$
$32$	−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	−0.973910	−	0.226934i	$-0.927130\pi$
$37$	0.157543	−	1.49892i	0.0258999	−	0.246421i	0.999810	−	0.0194875i	$-0.00620346\pi$
$38$	−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	−0.178163	−	0.984001i	$-0.557016\pi$
$41$	4.49897	−	3.26870i	0.702622	−	0.510485i	0.880785	+	0.473516i	$0.157016\pi$
$42$		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	0.0922416	−	0.995737i	$-0.470597\pi$
$47$	−4.01751	−	1.78871i	−0.586013	−	0.260910i	−0.678255	+	0.734827i	$0.737263\pi$
$48$	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	0.773036	−	0.634362i	$-0.218737\pi$
$53$	0.446592	+	0.495990i	0.0613441	+	0.0681295i	−0.711692	+	0.702492i	$0.752071\pi$
$54$	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	−0.384715	−	0.923036i	$-0.625700\pi$
$59$	0.336514	−	0.149826i	0.0438104	−	0.0195056i	0.428525	+	0.903530i	$0.359033\pi$
$60$	10.2145	+	2.17117i	1.31869	+	0.280296i
$61$	−3.35334	+	3.72426i	−0.429351	+	0.476843i	−0.918536	−	0.395337i	$-0.870628\pi$
$61$	−3.35334	+	3.72426i	−0.429351	+	0.476843i	0.489185	+	0.872180i	$0.337294\pi$
$62$	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	−0.837156	−	0.546964i	$-0.815784\pi$
$67$	0.451065	−	0.781267i	0.0551063	−	0.0954469i	0.892263	+	0.451517i	$0.149117\pi$
$68$	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	−0.720245	−	0.693720i	$-0.755971\pi$
$71$	−4.59489	−	14.1416i	−0.545313	−	1.67830i	0.174932	−	0.984580i	$-0.444029\pi$
$72$	−10.9152	+	12.1226i	−1.28637	+	1.42866i
$73$	−7.34322	+	3.26941i	−0.859459	+	0.382656i	−0.788656	−	0.614834i	$-0.789223\pi$
$73$	−7.34322	+	3.26941i	−0.859459	+	0.382656i	−0.0708031	+	0.997490i	$0.522556\pi$
$74$	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	−0.425645	−	0.904890i	$-0.639953\pi$
$79$	−3.96803	+	0.843431i	−0.446438	+	0.0948934i	−0.0207937	+	0.999784i	$0.506619\pi$
$80$	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	0.995958	−	0.0898178i	$-0.0286285\pi$
$83$	1.25193	+	3.85305i	0.137418	+	0.422928i	−0.858541	+	0.512745i	$0.828628\pi$
$84$		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	0.557426	−	0.830227i	$-0.311789\pi$
$89$	−4.15363	−	7.19431i	−0.440284	−	0.762595i	−0.997710	+	0.0676317i	$0.978456\pi$
$90$	−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	0.723988	+	0.689812i	$0.242307\pi$
$97$	−2.63154	+	8.09904i	−0.267192	+	0.822333i	−0.991180	+	0.132520i	$0.957693\pi$
$98$		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	0.862140	−	0.506671i	$-0.169124\pi$
$101$	2.69463	+	2.99269i	0.268126	+	0.297784i	−0.594013	+	0.804455i	$0.702457\pi$
$102$	0.393657	+	3.74539i	0.0389778	+	0.370849i
$103$	−1.84240	+	17.5293i	−0.181537	+	1.72721i	0.402445	+	0.915444i	$0.368161\pi$
$103$	−1.84240	+	17.5293i	−0.181537	+	1.72721i	−0.583982	+	0.811767i	$0.698506\pi$
$104$	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	−0.408680	−	0.912678i	$-0.634011\pi$
$107$	−14.0720	−	6.26526i	−1.36039	−	0.605685i	−0.951712	+	0.306992i	$0.900677\pi$
$108$	12.5756	+	13.9666i	1.21008	+	1.34393i
$109$	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	$-0.194526\pi$
$110$	−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	−0.649898	−	0.760021i	$-0.725189\pi$
$113$	−1.35965	+	0.987844i	−0.127905	+	0.0929286i	0.521993	+	0.852950i	$0.325189\pi$
$114$	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	0.836705	+	0.547654i	$0.184479\pi$
$127$	5.42848	+	16.7071i	0.481699	+	1.48252i	−0.355006	+	0.934864i	$0.615521\pi$
$128$	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	0.974707	−	0.223487i	$-0.0717441\pi$
$131$	3.36278	+	5.82451i	0.293808	+	0.508890i	−0.680899	+	0.732377i	$0.738411\pi$
$132$	−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	−0.411947	−	0.911208i	$-0.635151\pi$
$137$	−13.5646	−	2.88324i	−1.15890	−	0.246332i	−0.746954	+	0.664876i	$0.768484\pi$
$138$	4.45239	−	4.94488i	0.379013	−	0.420937i
$139$	11.5453	+	8.38812i	0.979256	+	0.711471i	0.957542	−	0.288293i	$-0.0930877\pi$
$139$	11.5453	+	8.38812i	0.979256	+	0.711471i	0.0217140	+	0.999764i	$0.493088\pi$
$140$		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	−0.666952	−	0.745100i	$-0.732402\pi$
$149$	1.75508	−	1.94921i	0.143782	−	0.159686i	0.810734	+	0.585415i	$0.199068\pi$
$150$	0.776512	−	0.345725i	0.0634019	−	0.0282284i
$151$	0.312498	+	2.97322i	0.0254307	+	0.241957i	0.999852	+	0.0172265i	$0.00548363\pi$
$151$	0.312498	+	2.97322i	0.0254307	+	0.241957i	−0.974421	+	0.224731i	$0.927850\pi$
$152$	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	0.935526	+	0.353257i	$0.114926\pi$
$157$	1.17644	+	11.1930i	0.0938898	+	0.893302i	−0.841636	+	0.540045i	$0.818407\pi$
$158$	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	0.551500	−	0.834175i	$-0.314056\pi$
$163$	17.8052	−	3.78461i	1.39461	−	0.296433i	0.843110	+	0.537742i	$0.180723\pi$
$164$	−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	0.367176	+	0.930151i	$0.380325\pi$
$167$	−6.15909	+	18.9557i	−0.476605	+	1.46684i	−0.843781	+	0.536687i	$0.819675\pi$
$168$		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	0.188029	−	0.982163i	$-0.439790\pi$
$173$	−5.47221	−	2.43638i	−0.416044	−	0.185235i	−0.604074	+	0.796929i	$0.706457\pi$
$174$	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	0.999024	−	0.0441658i	$-0.0140630\pi$
$179$	0.169225	+	1.61007i	0.0126485	+	0.120342i	−0.986376	+	0.164508i	$0.947396\pi$
$180$	−2.38429	+	22.6850i	−0.177714	+	1.69084i
$181$	−0.749929	−	2.30804i	−0.0557418	−	0.171556i	0.919309	−	0.393535i	$-0.128748\pi$
$181$	−0.749929	−	2.30804i	−0.0557418	−	0.171556i	−0.975051	+	0.221980i	$0.928748\pi$
$182$		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	0.835279	+	0.549826i	$0.185306\pi$
$191$	−1.32761	+	12.6313i	−0.0960623	+	0.913972i	−0.931342	+	0.364146i	$0.881361\pi$
$192$	2.59078	+	0.550688i	0.186974	+	0.0397425i
$193$	1.72087	+	0.365781i	0.123871	+	0.0263295i	0.269430	−	0.963020i	$-0.413165\pi$
$193$	1.72087	+	0.365781i	0.123871	+	0.0263295i	−0.145559	+	0.989350i	$0.546498\pi$
$194$	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	0.444006	+	0.896024i	$0.353557\pi$
$199$	−7.81479	+	13.5356i	−0.553976	+	0.959515i	−0.997982	+	0.0634910i	$0.979777\pi$
$200$	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	−0.661905	−	0.749587i	$-0.730252\pi$
$211$	4.56378	−	14.0459i	0.314184	−	0.966958i	0.976089	−	0.217371i	$-0.0697480\pi$
$212$	−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	−0.636649	−	0.771153i	$-0.719680\pi$
$223$	−1.49293	+	1.08468i	−0.0999743	+	0.0726356i	0.536675	+	0.843789i	$0.319680\pi$
$224$		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	0.386349	−	0.922352i	$-0.373736\pi$
$227$	20.0431	−	8.92378i	1.33031	−	0.592292i	0.943960	+	0.330061i	$0.107069\pi$
$228$	−3.42544	−	32.5909i	−0.226855	−	2.15838i
$229$	−19.8092	+	4.21058i	−1.30903	+	0.278243i	−0.809023	−	0.587777i	$-0.800003\pi$
$229$	−19.8092	+	4.21058i	−1.30903	+	0.278243i	−0.500009	+	0.866020i	$0.666670\pi$
$230$	4.54323			0.299571
$231$		0			0
$232$	2.19819			0.144318
$233$	−20.6023	+	4.37916i	−1.34970	+	0.286888i	−0.825354	−	0.564616i	$-0.809024\pi$
$233$	−20.6023	+	4.37916i	−1.34970	+	0.286888i	−0.524349	+	0.851504i	$0.675691\pi$
$234$	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	−0.914105	−	0.405477i	$-0.867106\pi$
$239$	−12.5370	+	9.10863i	−0.810948	+	0.589188i	0.103157	+	0.994665i	$0.467106\pi$
$240$	−9.94077	+	2.11297i	−0.641674	+	0.136392i
$241$	7.04241	−	12.1978i	0.453641	−	0.785730i	−0.544967	−	0.838457i	$-0.683458\pi$
$241$	7.04241	−	12.1978i	0.453641	−	0.785730i	0.998609	+	0.0527271i	$0.0167913\pi$
$242$	−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	−0.940001	−	0.341173i	$-0.889176\pi$
$251$	0.332894	−	1.02454i	0.0210121	−	0.0646686i	0.961013	+	0.276504i	$0.0891759\pi$
$252$		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	−0.865341	−	0.501184i	$-0.832898\pi$
$257$	1.36734	−	13.0094i	0.0852922	−	0.811501i	0.950633	−	0.310317i	$-0.100435\pi$
$258$	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	−0.679891	−	0.733313i	$-0.737973\pi$
$263$	4.78608	−	8.28973i	0.295122	−	0.511167i	0.975013	+	0.222146i	$0.0713062\pi$
$264$	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	0.0635085	−	0.997981i	$-0.479771\pi$
$269$	−4.66433	−	0.991434i	−0.284389	−	0.0604488i	−0.347898	+	0.937533i	$0.613104\pi$
$270$	−17.0127	−	3.61616i	−1.03536	−	0.220073i
$271$	−2.09603	+	19.9424i	−0.127325	+	1.21142i	0.725128	+	0.688614i	$0.241780\pi$
$271$	−2.09603	+	19.9424i	−0.127325	+	1.21142i	−0.852453	+	0.522803i	$0.824886\pi$
$272$	−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	0.463306	−	0.886199i	$-0.346663\pi$
$277$	−7.76355	−	8.62230i	−0.466467	−	0.518064i	−0.929772	+	0.368135i	$0.879997\pi$
$278$	−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	0.998520	+	0.0543830i	$0.0173192\pi$
$281$	3.73256	+	11.4876i	0.222666	+	0.685295i	−0.775854	+	0.630912i	$0.782681\pi$
$282$	−0.966647	+	9.19703i	−0.0575630	+	0.547675i
$283$	2.29892	+	21.8727i	0.136656	+	1.30020i	0.820953	+	0.570996i	$0.193443\pi$
$283$	2.29892	+	21.8727i	0.136656	+	1.30020i	−0.684297	+	0.729204i	$0.739891\pi$
$284$	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	0.620772	−	0.783991i	$-0.286819\pi$
$293$	1.14654	+	0.833014i	0.0669819	+	0.0486652i	−0.553790	+	0.832656i	$0.686819\pi$
$294$		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	0.723600	+	0.690219i	$0.242486\pi$
$311$	2.80959	+	26.7314i	0.159317	+	1.51580i	−0.564283	+	0.825581i	$0.690847\pi$
$312$	−17.2490	+	7.67975i	−0.976533	+	0.434780i
$313$	3.00620	−	3.33873i	0.169921	−	0.188716i	−0.652170	−	0.758073i	$-0.726141\pi$
$313$	3.00620	−	3.33873i	0.169921	−	0.188716i	0.822090	+	0.569357i	$0.192808\pi$
$314$	−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	0.102951	−	0.994686i	$-0.467171\pi$
$317$	10.7108	−	2.27665i	0.601577	−	0.127869i	0.498626	+	0.866817i	$0.333838\pi$
$318$	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	0.544552	−	0.838727i	$-0.316700\pi$
$331$	−8.26132	−	14.3090i	−0.454083	−	0.786495i	−0.998635	+	0.0522322i	$0.983366\pi$
$332$	−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	0.821912	−	0.569615i	$-0.192908\pi$
$337$	9.80588	+	7.12439i	0.534160	+	0.388090i	−0.287751	+	0.957705i	$0.592908\pi$
$338$	−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	0.795273	−	0.606252i	$-0.207328\pi$
$347$	23.7544	+	5.04916i	1.27521	+	0.271053i	0.479933	+	0.877305i	$0.340661\pi$
$348$	0.470566	−	4.47714i	0.0252250	−	0.240000i
$349$	−2.68497	+	1.95074i	−0.143723	+	0.104421i	−0.657323	−	0.753609i	$-0.728311\pi$
$349$	−2.68497	+	1.95074i	−0.143723	+	0.104421i	0.513600	+	0.858030i	$0.328311\pi$
$350$		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	−0.457894	−	0.889007i	$-0.651396\pi$
$353$	10.1636	−	17.6039i	0.540955	−	0.936962i	0.998849	−	0.0479552i	$-0.0152705\pi$
$354$	−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	0.558774	+	0.829320i	$0.311272\pi$
$359$	−3.03564	+	28.8821i	−0.160215	+	1.52434i	−0.718989	+	0.695021i	$0.755395\pi$
$360$	−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	0.215440	−	0.976517i	$-0.430881\pi$
$367$	20.7912	−	9.25683i	1.08529	−	0.483203i	0.869851	+	0.493314i	$0.164215\pi$
$368$	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	0.995954	+	0.0898652i	$0.0286436\pi$
$373$	11.1206	+	19.2614i	0.575802	+	0.997319i	−0.420151	+	0.907454i	$0.638023\pi$
$374$	−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	0.751543	+	0.659685i	$0.229310\pi$
$379$	10.3430	+	31.8325i	0.531285	+	1.63513i	−0.220258	+	0.975442i	$0.570690\pi$
$380$	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	−0.358922	−	0.933367i	$-0.616856\pi$
$383$	−6.01162	+	1.27781i	−0.307179	+	0.0652930i	0.0517429	+	0.998660i	$0.483522\pi$
$384$	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	−0.228045	−	0.973651i	$-0.573233\pi$
$389$	6.76357	−	3.01133i	0.342926	−	0.152681i	0.570971	+	0.820970i	$0.306567\pi$
$390$	−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	0.998181	−	0.0602921i	$-0.0192032\pi$
$397$	8.90394	+	15.4221i	0.446876	+	0.774012i	−0.551305	+	0.834304i	$0.685870\pi$
$398$	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	−0.141261	−	0.989972i	$-0.545116\pi$
$401$	17.1825	−	19.0831i	0.858054	−	0.952965i	0.999315	+	0.0370073i	$0.0117825\pi$
$402$	−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	0.720611	−	0.693339i	$-0.243861\pi$
$409$	−0.894992	−	0.993990i	−0.0442545	−	0.0491496i	−0.764866	+	0.644190i	$0.777195\pi$
$410$	−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	−0.738623	−	0.674118i	$-0.764524\pi$
$421$	−6.68374	+	4.85602i	−0.325746	+	0.236668i	0.412878	+	0.910787i	$0.364524\pi$
$422$	−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	0.985229	+	0.171239i	$0.0547772\pi$
$431$	21.8514	+	24.2685i	1.05255	+	1.16897i	0.0673168	+	0.997732i	$0.478556\pi$
$432$	−16.7089	−	7.43928i	−0.803907	−	0.357922i
$433$	12.7786	+	9.28422i	0.614102	+	0.446171i	0.850856	−	0.525398i	$-0.176084\pi$
$433$	12.7786	+	9.28422i	0.614102	+	0.446171i	−0.236754	+	0.971570i	$0.576084\pi$
$434$		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	0.506136	−	0.862454i	$-0.331073\pi$
$439$	−10.3471	−	17.9217i	−0.493839	−	0.855354i	−0.999975	+	0.00709942i	$0.997740\pi$
$440$	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	0.937514	−	0.347947i	$-0.113121\pi$
$443$	27.4936	+	12.2409i	1.30626	+	0.581584i	0.368745	+	0.929531i	$0.379788\pi$
$444$	−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	−0.221892	−	0.975071i	$-0.571223\pi$
$449$	11.2465	−	34.6132i	0.530755	−	1.63350i	0.752647	−	0.658424i	$-0.228777\pi$
$450$	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	−0.876663	−	0.481104i	$-0.840236\pi$
$457$	−6.55347	+	7.27837i	−0.306559	+	0.340468i	0.570105	+	0.821572i	$0.306903\pi$
$458$	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	−0.0697626	−	0.997564i	$-0.522224\pi$
$467$	20.0894	−	22.3116i	0.929628	−	1.03246i	0.999391	−	0.0348933i	$-0.0111091\pi$
$468$	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	0.0717898	−	0.997420i	$-0.477129\pi$
$479$	−5.87234	−	1.24820i	−0.268314	−	0.0570319i	−0.340104	+	0.940388i	$0.610462\pi$
$480$	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	−0.999198	−	0.0400380i	$-0.987252\pi$
$487$	−0.665556	−	6.33235i	−0.0301592	−	0.286946i	0.969039	−	0.246908i	$-0.0794146\pi$
$488$	−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	0.338454	−	0.940983i	$-0.390096\pi$
$491$	−10.0131	−	7.27496i	−0.451886	−	0.328314i	−0.790340	+	0.612669i	$0.790096\pi$
$492$	−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	−0.908945	−	0.416917i	$-0.863111\pi$
$499$	1.49263	−	14.2014i	0.0668193	−	0.635743i	0.975764	−	0.218826i	$-0.0702228\pi$
$500$	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	−0.475756	−	0.879577i	$-0.657826\pi$
$503$	4.79402	−	3.48306i	0.213755	−	0.155302i	0.689511	+	0.724275i	$0.257826\pi$
$504$		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	−0.328445	−	0.944523i	$-0.606525\pi$
$509$	−28.2043	−	12.5574i	−1.25014	−	0.556596i	−0.921690	+	0.387927i	$0.873191\pi$
$510$	−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	−0.748251	−	0.663415i	$-0.769106\pi$
$521$	−17.2541	+	7.68202i	−0.755916	+	0.336555i	−0.00766428	+	0.999971i	$0.502440\pi$
$522$	4.15216	+	0.882568i	0.181735	+	0.0386289i
$523$	5.31429	−	5.90212i	0.232378	−	0.258082i	−0.615667	−	0.788007i	$-0.711113\pi$
$523$	5.31429	−	5.90212i	0.232378	−	0.258082i	0.848045	+	0.529925i	$0.177780\pi$
$524$	−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	−0.364956	−	0.931025i	$-0.618916\pi$
$541$	−7.43554	+	1.58047i	−0.319679	+	0.0679498i	0.0452777	+	0.998974i	$0.485583\pi$
$542$	−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	−0.896010	−	0.444035i	$-0.853547\pi$
$547$	−17.5548	+	12.7543i	−0.750590	+	0.545335i	0.145420	+	0.989370i	$0.453547\pi$
$548$	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	−0.993300	−	0.115562i	$-0.963133\pi$
$557$	−37.1022	+	16.5189i	−1.57207	+	0.699930i	−0.578769	+	0.815492i	$0.696467\pi$
$558$	−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	0.976616	−	0.214993i	$-0.0689728\pi$
$563$	15.6772	+	17.4113i	0.660717	+	0.733800i	−0.315899	+	0.948793i	$0.602306\pi$
$564$	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	0.182060	−	0.983287i	$-0.441723\pi$
$569$	−10.1818	−	4.53322i	−0.426842	−	0.190043i	−0.608903	+	0.793245i	$0.708390\pi$
$570$	20.2929	+	22.5376i	0.849978	+	0.943996i
$571$	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	$0.125534\pi$
$572$	−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	−0.0966659	−	0.995317i	$-0.530818\pi$
$577$	−14.1676	−	3.01142i	−0.589807	−	0.125367i	−0.493141	+	0.869950i	$0.664151\pi$
$578$	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	0.820167	−	0.572124i	$-0.193880\pi$
$587$	12.8285	+	9.32048i	0.529491	+	0.384698i	−0.290676	+	0.956821i	$0.593880\pi$
$588$		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	0.999441	−	0.0334179i	$-0.0106392\pi$
$593$	11.4642	+	19.8566i	0.470780	+	0.815415i	−0.528662	+	0.848833i	$0.677306\pi$
$594$	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	−0.0625335	−	0.998043i	$-0.519918\pi$
$599$	−12.8638	−	2.73429i	−0.525601	−	0.111720i	−0.463068	+	0.886323i	$0.653251\pi$
$600$	−2.01992	+	2.24335i	−0.0824628	+	0.0915842i
$601$	22.1286	+	16.0774i	0.902645	+	0.655810i	0.939144	−	0.343524i	$-0.111621\pi$
$601$	22.1286	+	16.0774i	0.902645	+	0.655810i	−0.0364993	+	0.999334i	$0.511621\pi$
$602$		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	−0.994599	−	0.103792i	$-0.966902\pi$
$607$	−45.8500	+	9.74572i	−1.86099	+	0.395567i	−0.866395	+	0.499359i	$0.833569\pi$
$608$	−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	0.948782	+	0.315932i	$0.102317\pi$
$613$	2.13964	+	20.3573i	0.0864192	+	0.822223i	−0.862363	+	0.506291i	$0.831016\pi$
$614$	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	0.995860	−	0.0908961i	$-0.0289731\pi$
$619$	0.0712449	+	0.677850i	0.00286357	+	0.0272451i	−0.992997	+	0.118141i	$0.962306\pi$
$620$	−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	0.992999	−	0.118124i	$-0.0376880\pi$
$631$	29.8299	+	21.6727i	1.18751	+	0.862776i	0.194511	+	0.980900i	$0.437688\pi$
$632$	−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	0.951608	+	0.307314i	$0.0994301\pi$
$641$	2.14415	+	20.4003i	0.0846890	+	0.805762i	−0.866919	+	0.498449i	$0.833903\pi$
$642$	−3.38585	+	32.2142i	−0.133629	+	1.27139i
$643$	2.35984	+	7.26283i	0.0930629	+	0.286418i	0.986744	−	0.162284i	$-0.0518862\pi$
$643$	2.35984	+	7.26283i	0.0930629	+	0.286418i	−0.893681	+	0.448703i	$0.851886\pi$
$644$		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	0.518394	−	0.855142i	$-0.326530\pi$
$647$	−9.82473	−	10.9115i	−0.386250	−	0.428974i	−0.904644	+	0.426168i	$0.859863\pi$
$648$	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	−0.996585	−	0.0825717i	$-0.973687\pi$
$653$	−0.117807	+	1.12086i	−0.00461015	+	0.0438627i	0.991975	+	0.126434i	$0.0403533\pi$
$654$	−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	−0.671444	−	0.741055i	$-0.734326\pi$
$661$	7.86853	−	13.6287i	0.306050	−	0.530095i	0.977495	+	0.210960i	$0.0676591\pi$
$662$	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	−0.557797	−	0.829977i	$-0.688353\pi$
$673$	9.89226	−	30.4452i	0.381319	−	1.17358i	0.939116	−	0.343601i	$-0.111647\pi$
$674$	−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	−0.512874	−	0.858464i	$-0.671419\pi$
$677$	10.2645	−	11.3999i	0.394496	−	0.438133i	0.907371	+	0.420331i	$0.138086\pi$
$678$	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	−0.875873	−	0.482541i	$-0.839714\pi$
$683$	−0.523820	+	0.907282i	−0.0200434	+	0.0347162i	0.855830	+	0.517258i	$0.173047\pi$
$684$	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	0.370131	−	0.928980i	$-0.379313\pi$
$691$	28.5505	−	6.06859i	1.08611	−	0.230860i	0.715981	+	0.698120i	$0.245980\pi$
$692$	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	−0.765644	−	0.643264i	$-0.777580\pi$
$701$	−10.3380	+	7.51100i	−0.390461	+	0.283687i	0.375183	+	0.926951i	$0.377580\pi$
$702$	−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	−0.0412760	−	0.999148i	$-0.513142\pi$
$709$	25.4744	−	28.2922i	0.956713	−	1.06254i	0.997989	−	0.0633895i	$-0.0201910\pi$
$710$	−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	0.600764	+	0.799426i	$0.294863\pi$
$719$	−4.10477	+	39.0542i	−0.153082	+	1.45648i	−0.753846	+	0.657051i	$0.771804\pi$
$720$	−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	−0.998780	−	0.0493902i	$-0.984272\pi$
$733$	−0.312892	+	2.97697i	−0.0115569	+	0.109957i	0.987223	+	0.159347i	$0.0509389\pi$
$734$	−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	−0.891589	−	0.452846i	$-0.850409\pi$
$739$	−33.9469	−	37.7019i	−1.24876	−	1.38689i	−0.357169	−	0.934040i	$-0.616258\pi$
$740$	−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	0.948857	−	0.315706i	$-0.102241\pi$
$743$	−0.118625	−	0.365089i	−0.00435191	−	0.0133938i	−0.953209	+	0.302312i	$0.902241\pi$
$744$	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	−0.372923	−	0.927862i	$-0.621645\pi$
$751$	−35.9544	−	16.0079i	−1.31199	−	0.584137i	−0.939070	+	0.343725i	$0.888311\pi$
$752$	−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	−0.866528	−	0.499129i	$-0.833653\pi$
$757$	3.51868	−	10.8294i	0.127889	−	0.393600i	0.994416	+	0.105528i	$0.0336534\pi$
$758$	−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	−0.338633	−	0.940919i	$-0.609964\pi$
$761$	−7.31816	+	1.55552i	−0.265283	+	0.0563876i	0.0733498	+	0.997306i	$0.476631\pi$
$762$	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	0.999705	−	0.0242827i	$-0.00773020\pi$
$773$	0.467013	+	4.44333i	0.0167973	+	0.159816i	−0.982908	+	0.184098i	$0.941064\pi$
$774$	−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	−0.0332918	−	0.999446i	$-0.510599\pi$
$787$	−13.1912	−	2.80388i	−0.470217	−	0.0999476i	−0.436925	+	0.899498i	$0.643932\pi$
$788$	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	−0.637134	−	0.770753i	$-0.719880\pi$
$797$	−16.2250	−	49.9354i	−0.574719	−	1.76880i	0.0624156	−	0.998050i	$-0.480120\pi$
$798$		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	0.230037	−	0.973182i	$-0.426115\pi$
$809$	1.26166	+	0.268173i	0.0443575	+	0.00942847i	−0.185680	+	0.982610i	$0.559449\pi$
$810$	2.62041	−	24.9315i	0.0920717	−	0.876004i
$811$	−27.6585	+	20.0951i	−0.971220	+	0.705633i	−0.955729	−	0.294247i	$-0.904931\pi$
$811$	−27.6585	+	20.0951i	−0.971220	+	0.705633i	−0.0154910	+	0.999880i	$0.504931\pi$
$812$		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	0.645534	+	0.763731i	$0.276635\pi$
$821$	−4.14559	+	39.4427i	−0.144682	+	1.37656i	−0.790217	+	0.612828i	$0.790032\pi$
$822$	3.04820	+	29.0017i	0.106318	+	1.01155i
$823$	−6.17416	−	6.85710i	−0.215218	−	0.239024i	0.625863	−	0.779933i	$-0.284747\pi$
$823$	−6.17416	−	6.85710i	−0.215218	−	0.239024i	−0.841081	+	0.540909i	$0.818080\pi$
$824$	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	0.712806	+	0.701361i	$0.247424\pi$
$827$	−7.94043	+	24.4381i	−0.276116	+	0.849797i	−0.988922	+	0.148436i	$0.952576\pi$
$828$	30.7574	+	13.6941i	1.06890	+	0.475903i
$829$	−9.99284	+	4.44910i	−0.347066	+	0.154524i	−0.572864	−	0.819651i	$-0.694168\pi$
$829$	−9.99284	+	4.44910i	−0.347066	+	0.154524i	0.225798	+	0.974174i	$0.427501\pi$
$830$	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	−0.955503	−	0.294980i	$-0.904687\pi$
$839$	−28.1031	+	20.4181i	−0.970228	+	0.704912i	−0.0147243	+	0.999892i	$0.504687\pi$
$840$		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	0.998894	+	0.0470143i	$0.0149706\pi$
$853$	6.37880	+	19.6319i	0.218406	+	0.672185i	−0.780488	+	0.625171i	$0.785029\pi$
$854$		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	0.411795	+	0.911276i	$0.364902\pi$
$857$	−17.0756	+	29.5758i	−0.583291	+	1.01029i	−0.995086	+	0.0990131i	$0.968431\pi$
$858$	−11.5485	−	13.3249i	−0.394260	−	0.454905i
$859$	−16.7246	−	28.9679i	−0.570637	−	0.988373i	−0.996501	−	0.0835852i	$-0.973363\pi$
$859$	−16.7246	−	28.9679i	−0.570637	−	0.988373i	0.425863	−	0.904787i	$-0.359970\pi$
$860$	−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	−0.993371	−	0.114956i	$-0.963327\pi$
$863$	−22.7732	+	25.2922i	−0.775208	+	0.860956i	0.218162	+	0.975913i	$0.429994\pi$
$864$	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	0.524475	−	0.851426i	$-0.324262\pi$
$877$	7.18692	+	3.19982i	0.242685	+	0.108050i	−0.281790	+	0.959476i	$0.590928\pi$
$878$	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	−0.330153	−	0.943927i	$-0.607100\pi$
$883$	13.8340	−	10.0510i	0.465552	−	0.338243i	0.795705	+	0.605684i	$0.207100\pi$
$884$	−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	0.843989	+	0.536361i	$0.180201\pi$
$887$	−2.77193	+	26.3732i	−0.0930724	+	0.885525i	−0.937061	+	0.349165i	$0.886465\pi$
$888$	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	0.0618934	−	0.998083i	$-0.480286\pi$
$907$	−8.65911	−	1.84055i	−0.287521	−	0.0611145i	−0.349414	+	0.936968i	$0.613619\pi$
$908$	−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	0.0728381	+	0.997344i	$0.476794\pi$
$911$	−17.2740	+	53.1639i	−0.572313	+	1.76140i	−0.645151	+	0.764055i	$0.723206\pi$
$912$	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	0.0859639	−	0.996298i	$-0.472603\pi$
$919$	32.3709	−	35.9516i	1.06782	−	1.18593i	0.981855	−	0.189634i	$-0.0607303\pi$
$920$	−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	−0.752557	−	0.658527i	$-0.771180\pi$
$929$	−0.578326	+	0.642296i	−0.0189743	+	0.0210731i	0.733583	+	0.679600i	$0.237847\pi$
$930$	−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	0.193678	+	0.981065i	$0.437958\pi$
$937$	−16.5194	+	50.8416i	−0.539667	+	1.66092i	−0.733344	+	0.679858i	$0.762042\pi$
$938$		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	0.421086	−	0.907021i	$-0.361649\pi$
$941$	13.4006	+	2.84839i	0.436848	+	0.0928548i	0.0157621	+	0.999876i	$0.494983\pi$
$942$	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	−0.999865	−	0.0164197i	$-0.994773\pi$
$947$	−15.8222	−	27.4049i	−0.514152	−	0.890538i	0.485713	−	0.874119i	$-0.338560\pi$
$948$	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	0.0693755	−	0.997591i	$-0.477899\pi$
$953$	−26.4856	−	19.2429i	−0.857951	−	0.623338i	−0.927327	+	0.374253i	$0.877899\pi$
$954$	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	0.789896	−	0.613240i	$-0.210134\pi$
$971$	26.8829	+	11.9690i	0.862714	+	0.384105i	0.0728173	+	0.997345i	$0.476801\pi$
$972$	−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	0.871676	−	0.490083i	$-0.163034\pi$
$977$	9.16337	+	10.1770i	0.293162	+	0.325590i	−0.578513	+	0.815673i	$0.696367\pi$
$978$	−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	−0.639580	−	0.768724i	$-0.720892\pi$
$983$	−15.5595	+	6.92751i	−0.496269	+	0.220953i	0.143311	+	0.989678i	$0.454225\pi$
$984$	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	−0.989379	−	0.145357i	$-0.953567\pi$
$991$	−11.6101	+	20.1093i	−0.368807	+	0.638792i	0.620572	+	0.784149i	$0.286900\pi$
$992$	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	−0.123280	−	0.992372i	$-0.539341\pi$
$997$	16.7888	−	7.47485i	0.531706	−	0.236731i	0.654986	+	0.755641i	$0.272675\pi$
$998$	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.361.2		32
7.2	even	3	inner	539.2.q.f.471.3		32
7.3	odd	6		77.2.f.b.64.3	✓	16
7.4	even	3		539.2.f.e.295.3		16
7.5	odd	6		539.2.q.g.471.3		32
7.6	odd	2		539.2.q.g.361.2		32
11.5	even	5	inner	539.2.q.f.214.3		32
21.17	even	6		693.2.m.i.64.2		16
77.3	odd	30		847.2.f.w.323.2		16
77.4	even	15		5929.2.a.bt.1.5		8
77.5	odd	30		539.2.q.g.324.2		32
77.10	even	6		847.2.f.x.372.2		16
77.16	even	15	inner	539.2.q.f.324.2		32
77.17	even	30		847.2.f.x.148.2		16
77.18	odd	30		5929.2.a.bs.1.4		8
77.24	even	30		847.2.f.v.729.3		16
77.27	odd	10		539.2.q.g.214.3		32
77.31	odd	30		847.2.f.w.729.2		16
77.38	odd	30		77.2.f.b.71.3	yes	16
77.52	even	30		847.2.f.v.323.3		16
77.59	odd	30		847.2.a.p.1.5		8
77.60	even	15		539.2.f.e.148.3		16
77.73	even	30		847.2.a.o.1.4		8
231.38	even	30		693.2.m.i.379.2		16
231.59	even	30		7623.2.a.ct.1.4		8
231.227	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	7.3	odd	6
77.2.f.b.71.3	yes	16	77.38	odd	30
539.2.f.e.148.3		16	77.60	even	15
539.2.f.e.295.3		16	7.4	even	3
539.2.q.f.214.3		32	11.5	even	5	inner
539.2.q.f.324.2		32	77.16	even	15	inner
539.2.q.f.361.2		32	1.1	even	1	trivial
539.2.q.f.471.3		32	7.2	even	3	inner
539.2.q.g.214.3		32	77.27	odd	10
539.2.q.g.324.2		32	77.5	odd	30
539.2.q.g.361.2		32	7.6	odd	2
539.2.q.g.471.3		32	7.5	odd	6
693.2.m.i.64.2		16	21.17	even	6
693.2.m.i.379.2		16	231.38	even	30
847.2.a.o.1.4		8	77.73	even	30
847.2.a.p.1.5		8	77.59	odd	30
847.2.f.v.323.3		16	77.52	even	30
847.2.f.v.729.3		16	77.24	even	30
847.2.f.w.323.2		16	77.3	odd	30
847.2.f.w.729.2		16	77.31	odd	30
847.2.f.x.148.2		16	77.17	even	30
847.2.f.x.372.2		16	77.10	even	6
5929.2.a.bs.1.4		8	77.18	odd	30
5929.2.a.bt.1.5		8	77.4	even	15
7623.2.a.ct.1.4		8	231.59	even	30
7623.2.a.cw.1.5		8	231.227	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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