LMFDB - Embedded newform 539.2.q.f.471.2

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			471.2
Character	$\chi$	$=$	539.471
Dual form			539.2.q.f.214.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.942984 - 1.04729i) q^{2} +(1.97635 + 0.879926i) q^{3} +(0.00145969 - 0.0138880i) q^{4} +(-1.79137 - 0.380767i) q^{5} +(-0.942126 - 2.89957i) q^{6} +(-2.29616 + 1.66826i) q^{8} +(1.12429 + 1.24865i) q^{9} +O(q^{10})$	\(q+(-0.942984 - 1.04729i) q^{2} +(1.97635 + 0.879926i) q^{3} +(0.00145969 - 0.0138880i) q^{4} +(-1.79137 - 0.380767i) q^{5} +(-0.942126 - 2.89957i) q^{6} +(-2.29616 + 1.66826i) q^{8} +(1.12429 + 1.24865i) q^{9} +(1.29046 + 2.23514i) q^{10} +(3.23218 + 0.743627i) q^{11} +(0.0151053 - 0.0261631i) q^{12} +(1.43602 - 4.41961i) q^{13} +(-3.20531 - 2.32880i) q^{15} +(3.88508 + 0.825799i) q^{16} +(3.66029 - 4.06516i) q^{17} +(0.247511 - 2.35491i) q^{18} +(-0.606388 - 5.76940i) q^{19} +(-0.00790293 + 0.0243227i) q^{20} +(-2.26911 - 4.08626i) q^{22} +(0.359841 - 0.623263i) q^{23} +(-6.00596 + 1.27661i) q^{24} +(-1.50372 - 0.669498i) q^{25} +(-5.98276 + 2.66370i) q^{26} +(-0.882303 - 2.71545i) q^{27} +(0.948551 + 0.689163i) q^{29} +(0.583635 + 5.55291i) q^{30} +(-1.27929 + 0.271920i) q^{31} +(0.0394969 + 0.0684106i) q^{32} +(5.73358 + 4.31375i) q^{33} -7.70900 q^{34} +(0.0189823 - 0.0137915i) q^{36} +(1.91364 - 0.852007i) q^{37} +(-5.47042 + 6.07551i) q^{38} +(6.72701 - 7.47110i) q^{39} +(4.74849 - 2.11416i) q^{40} +(-0.741582 + 0.538791i) q^{41} +8.02379 q^{43} +(0.0150455 - 0.0438032i) q^{44} +(-1.53856 - 2.66487i) q^{45} +(-0.992062 + 0.210869i) q^{46} +(0.624645 + 5.94310i) q^{47} +(6.95163 + 5.05065i) q^{48} +(0.716823 + 2.20615i) q^{50} +(10.8110 - 4.81339i) q^{51} +(-0.0592835 - 0.0263947i) q^{52} +(-9.92324 + 2.10925i) q^{53} +(-2.01186 + 3.48465i) q^{54} +(-5.50688 - 2.56282i) q^{55} +(3.87821 - 11.9359i) q^{57} +(-0.172715 - 1.64328i) q^{58} +(-0.802863 + 7.63873i) q^{59} +(-0.0370211 + 0.0411161i) q^{60} +(-6.13898 - 1.30488i) q^{61} +(1.49113 + 1.08337i) q^{62} +(2.48916 - 7.66083i) q^{64} +(-4.25528 + 7.37036i) q^{65} +(-0.888929 - 10.0725i) q^{66} +(7.73363 + 13.3950i) q^{67} +(-0.0511141 - 0.0567680i) q^{68} +(1.25960 - 0.915151i) q^{69} +(4.29593 + 13.2215i) q^{71} +(-4.66461 - 0.991493i) q^{72} +(0.628699 - 5.98168i) q^{73} +(-2.69683 - 1.20071i) q^{74} +(-2.38276 - 2.64632i) q^{75} -0.0810106 q^{76} -14.1679 q^{78} +(-10.4658 - 11.6235i) q^{79} +(-6.64517 - 2.95862i) q^{80} +(1.17255 - 11.1561i) q^{81} +(1.26357 + 0.268580i) q^{82} +(1.35217 + 4.16157i) q^{83} +(-8.10479 + 5.88848i) q^{85} +(-7.56631 - 8.40324i) q^{86} +(1.26825 + 2.19668i) q^{87} +(-8.66219 + 3.68464i) q^{88} +(7.67186 - 13.2880i) q^{89} +(-1.34005 + 4.12425i) q^{90} +(-0.00813063 - 0.00590725i) q^{92} +(-2.76758 - 0.588268i) q^{93} +(5.63512 - 6.25843i) q^{94} +(-1.11053 + 10.5660i) q^{95} +(0.0178632 + 0.169957i) q^{96} +(-0.745114 + 2.29323i) q^{97} +(2.70537 + 4.87190i) 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 $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.942984	−	1.04729i	−0.666790	−	0.740546i	0.310936	−	0.950431i	$-0.399358\pi$
$2$	−0.942984	−	1.04729i	−0.666790	−	0.740546i	−0.977726	+	0.209885i	$0.932691\pi$
$3$	1.97635	+	0.879926i	1.14104	+	0.508026i	0.888189	−	0.459478i	$-0.151964\pi$
$3$	1.97635	+	0.879926i	1.14104	+	0.508026i	0.252856	+	0.967504i	$0.418630\pi$
$4$	0.00145969	−	0.0138880i	0.000729845	−	0.00694401i
$5$	−1.79137	−	0.380767i	−0.801123	−	0.170284i	−0.210883	−	0.977511i	$-0.567634\pi$
$5$	−1.79137	−	0.380767i	−0.801123	−	0.170284i	−0.590241	+	0.807227i	$0.700967\pi$
$6$	−0.942126	−	2.89957i	−0.384621	−	1.18374i
$7$		0			0
$7$		0			0
$8$	−2.29616	+	1.66826i	−0.811817	+	0.589819i
$9$	1.12429	+	1.24865i	0.374762	+	0.416215i
$10$	1.29046	+	2.23514i	0.408078	+	0.706812i
$11$	3.23218	+	0.743627i	0.974540	+	0.224212i
$11$	3.23218	+	0.743627i	0.974540	+	0.224212i
$12$	0.0151053	−	0.0261631i	0.00436052	−	0.00755264i
$13$	1.43602	−	4.41961i	0.398280	−	1.22578i	−0.528097	−	0.849184i	$-0.677094\pi$
$13$	1.43602	−	4.41961i	0.398280	−	1.22578i	0.926377	−	0.376596i	$-0.122906\pi$
$14$		0			0
$15$	−3.20531	−	2.32880i	−0.827609	−	0.601293i
$16$	3.88508	+	0.825799i	0.971270	+	0.206450i
$17$	3.66029	−	4.06516i	0.887750	−	0.985946i	−0.112220	−	0.993683i	$-0.535796\pi$
$17$	3.66029	−	4.06516i	0.887750	−	0.985946i	0.999970	+	0.00773703i	$0.00246280\pi$
$18$	0.247511	−	2.35491i	0.0583388	−	0.555057i
$19$	−0.606388	−	5.76940i	−0.139115	−	1.32359i	−0.811919	−	0.583770i	$-0.801577\pi$
$19$	−0.606388	−	5.76940i	−0.139115	−	1.32359i	0.672804	−	0.739821i	$-0.265090\pi$
$20$	−0.00790293	+	0.0243227i	−0.00176715	+	0.00543873i
$21$		0			0
$22$	−2.26911	−	4.08626i	−0.483775	−	0.871194i
$23$	0.359841	−	0.623263i	0.0750321	−	0.129959i	−0.826068	−	0.563570i	$-0.809427\pi$
$23$	0.359841	−	0.623263i	0.0750321	−	0.129959i	0.901100	+	0.433611i	$0.142761\pi$
$24$	−6.00596	+	1.27661i	−1.22596	+	0.260586i
$25$	−1.50372	−	0.669498i	−0.300744	−	0.133900i
$26$	−5.98276	+	2.66370i	−1.17332	+	0.522394i
$27$	−0.882303	−	2.71545i	−0.169799	−	0.522588i
$28$		0			0
$29$	0.948551	+	0.689163i	0.176142	+	0.127974i	0.672363	−	0.740222i	$-0.265280\pi$
$29$	0.948551	+	0.689163i	0.176142	+	0.127974i	−0.496221	+	0.868196i	$0.665280\pi$
$30$	0.583635	+	5.55291i	0.106557	+	1.01382i
$31$	−1.27929	+	0.271920i	−0.229766	+	0.0488384i	−0.321356	−	0.946958i	$-0.604139\pi$
$31$	−1.27929	+	0.271920i	−0.229766	+	0.0488384i	0.0915895	+	0.995797i	$0.470805\pi$
$32$	0.0394969	+	0.0684106i	0.00698213	+	0.0120934i
$33$	5.73358	+	4.31375i	0.998088	+	0.750928i
$34$	−7.70900			−1.32208
$35$		0			0
$36$	0.0189823	−	0.0137915i	0.00316372	−	0.00229858i
$37$	1.91364	−	0.852007i	0.314600	−	0.140069i	−0.243362	−	0.969936i	$-0.578250\pi$
$37$	1.91364	−	0.852007i	0.314600	−	0.140069i	0.557962	+	0.829867i	$0.311584\pi$
$38$	−5.47042	+	6.07551i	−0.887419	+	0.985578i
$39$	6.72701	−	7.47110i	1.07718	−	1.19633i
$40$	4.74849	−	2.11416i	0.750802	−	0.334279i
$41$	−0.741582	+	0.538791i	−0.115816	+	0.0841449i	−0.644185	−	0.764869i	$-0.722803\pi$
$41$	−0.741582	+	0.538791i	−0.115816	+	0.0841449i	0.528370	+	0.849014i	$0.322803\pi$
$42$		0			0
$43$	8.02379			1.22362			0.611808	−	0.791006i	$-0.290442\pi$
$43$	8.02379			1.22362			0.611808	+	0.791006i	$0.290442\pi$
$44$	0.0150455	−	0.0438032i	0.00226819	−	0.00660358i
$45$	−1.53856	−	2.66487i	−0.229356	−	0.397256i
$46$	−0.992062	+	0.210869i	−0.146272	+	0.0310910i
$47$	0.624645	+	5.94310i	0.0911138	+	0.866890i	0.940654	+	0.339367i	$0.110213\pi$
$47$	0.624645	+	5.94310i	0.0911138	+	0.866890i	−0.849540	+	0.527524i	$0.823121\pi$
$48$	6.95163	+	5.05065i	1.00338	+	0.728999i
$49$		0			0
$50$	0.716823	+	2.20615i	0.101374	+	0.311997i
$51$	10.8110	−	4.81339i	1.51385	−	0.674009i
$52$	−0.0592835	−	0.0263947i	−0.00822114	−	0.00366029i
$53$	−9.92324	+	2.10925i	−1.36306	+	0.289728i	−0.830668	−	0.556769i	$-0.812041\pi$
$53$	−9.92324	+	2.10925i	−1.36306	+	0.289728i	−0.532394	+	0.846496i	$0.678708\pi$
$54$	−2.01186	+	3.48465i	−0.273780	+	0.474201i
$55$	−5.50688	−	2.56282i	−0.742547	−	0.345570i
$56$		0			0
$57$	3.87821	−	11.9359i	0.513682	−	1.58095i
$58$	−0.172715	−	1.64328i	−0.0226787	−	0.215773i
$59$	−0.802863	+	7.63873i	−0.104524	+	0.994478i	0.809032	+	0.587765i	$0.199992\pi$
$59$	−0.802863	+	7.63873i	−0.104524	+	0.994478i	−0.913556	+	0.406713i	$0.866675\pi$
$60$	−0.0370211	+	0.0411161i	−0.00477941	+	0.00530807i
$61$	−6.13898	−	1.30488i	−0.786015	−	0.167073i	−0.202616	−	0.979258i	$-0.564944\pi$
$61$	−6.13898	−	1.30488i	−0.786015	−	0.167073i	−0.583399	+	0.812186i	$0.698278\pi$
$62$	1.49113	+	1.08337i	0.189373	+	0.137588i
$63$		0			0
$64$	2.48916	−	7.66083i	0.311144	−	0.957604i
$65$	−4.25528	+	7.37036i	−0.527802	+	0.914180i
$66$	−0.888929	−	10.0725i	−0.109420	−	1.23984i
$67$	7.73363	+	13.3950i	0.944814	+	1.63647i	0.756124	+	0.654429i	$0.227091\pi$
$67$	7.73363	+	13.3950i	0.944814	+	1.63647i	0.188690	+	0.982037i	$0.439576\pi$
$68$	−0.0511141	−	0.0567680i	−0.00619850	−	0.00688413i
$69$	1.25960	−	0.915151i	0.151638	−	0.110171i
$70$		0			0
$71$	4.29593	+	13.2215i	0.509833	+	1.56910i	0.792491	+	0.609883i	$0.208784\pi$
$71$	4.29593	+	13.2215i	0.509833	+	1.56910i	−0.282659	+	0.959221i	$0.591216\pi$
$72$	−4.66461	−	0.991493i	−0.549730	−	0.116849i
$73$	0.628699	−	5.98168i	0.0735837	−	0.700102i	−0.894088	−	0.447891i	$-0.852175\pi$
$73$	0.628699	−	5.98168i	0.0735837	−	0.700102i	0.967672	−	0.252212i	$-0.0811579\pi$
$74$	−2.69683	−	1.20071i	−0.313500	−	0.139579i
$75$	−2.38276	−	2.64632i	−0.275137	−	0.305571i
$76$	−0.0810106			−0.00929255
$77$		0			0
$78$	−14.1679			−1.60420
$79$	−10.4658	−	11.6235i	−1.17750	−	1.30774i	−0.941900	−	0.335894i	$-0.890962\pi$
$79$	−10.4658	−	11.6235i	−1.17750	−	1.30774i	−0.235598	−	0.971851i	$-0.575705\pi$
$80$	−6.64517	−	2.95862i	−0.742952	−	0.330784i
$81$	1.17255	−	11.1561i	0.130283	−	1.23956i
$82$	1.26357	+	0.268580i	0.139538	+	0.0296597i
$83$	1.35217	+	4.16157i	0.148420	+	0.456791i	0.997435	−	0.0715783i	$-0.0228036\pi$
$83$	1.35217	+	4.16157i	0.148420	+	0.456791i	−0.849015	+	0.528370i	$0.822804\pi$
$84$		0			0
$85$	−8.10479	+	5.88848i	−0.879088	+	0.638695i
$86$	−7.56631	−	8.40324i	−0.815896	−	0.906144i
$87$	1.26825	+	2.19668i	0.135971	+	0.235509i
$88$	−8.66219	+	3.68464i	−0.923393	+	0.392784i
$89$	7.67186	−	13.2880i	0.813215	−	1.40853i	−0.0973874	−	0.995247i	$-0.531049\pi$
$89$	7.67186	−	13.2880i	0.813215	−	1.40853i	0.910602	−	0.413283i	$-0.135618\pi$
$90$	−1.34005	+	4.12425i	−0.141254	+	0.434735i
$91$		0			0
$92$	−0.00813063	−	0.00590725i	−0.000847677	−	0.000615873i
$93$	−2.76758	−	0.588268i	−0.286985	−	0.0610005i
$94$	5.63512	−	6.25843i	0.581218	−	0.645508i
$95$	−1.11053	+	10.5660i	−0.113938	+	1.08405i
$96$	0.0178632	+	0.169957i	0.00182316	+	0.0173462i
$97$	−0.745114	+	2.29323i	−0.0756549	+	0.232842i	−0.981731	−	0.190272i	$-0.939063\pi$
$97$	−0.745114	+	2.29323i	−0.0756549	+	0.232842i	0.906077	+	0.423114i	$0.139063\pi$
$98$		0			0
$99$	2.70537	+	4.87190i	0.271900	+	0.489645i
$100$	−0.0114930	+	0.0199064i	−0.00114930	+	0.00199064i
$101$	11.6359	−	2.47329i	1.15782	−	0.246102i	0.411320	−	0.911491i	$-0.365068\pi$
$101$	11.6359	−	2.47329i	1.15782	−	0.246102i	0.746497	+	0.665389i	$0.231734\pi$
$102$	−15.2357	−	6.78335i	−1.50855	−	0.671652i
$103$	−0.362051	+	0.161195i	−0.0356739	+	0.0158830i	−0.424496	−	0.905430i	$-0.639549\pi$
$103$	−0.362051	+	0.161195i	−0.0356739	+	0.0158830i	0.388822	+	0.921313i	$0.372882\pi$
$104$	4.07573	+	12.5438i	0.399658	+	1.23002i
$105$		0			0
$106$	11.5665	+	8.40352i	1.12343	+	0.816222i
$107$	0.341740	+	3.25144i	0.0330373	+	0.314329i	0.998544	+	0.0539494i	$0.0171810\pi$
$107$	0.341740	+	3.25144i	0.0330373	+	0.314329i	−0.965506	+	0.260379i	$0.916152\pi$
$108$	−0.0390001	+	0.00828972i	−0.00375278	+	0.000797679i
$109$	1.42319	+	2.46504i	0.136317	+	0.236108i	0.926100	−	0.377279i	$-0.123140\pi$
$109$	1.42319	+	2.46504i	0.136317	+	0.236108i	−0.789783	+	0.613387i	$0.789807\pi$
$110$	2.50889	+	8.18399i	0.239213	+	0.780313i
$111$	4.53172			0.430132
$112$		0			0
$113$	−11.7668	+	8.54906i	−1.10692	+	0.804228i	−0.982177	−	0.187961i	$-0.939812\pi$
$113$	−11.7668	+	8.54906i	−1.10692	+	0.804228i	−0.124748	+	0.992188i	$0.539812\pi$
$114$	−16.1574	+	7.19376i	−1.51328	+	0.673757i
$115$	−0.881925	+	0.979477i	−0.0822400	+	0.0913367i
$116$	0.0109557	−	0.0121675i	0.00101721	−	0.00112973i
$117$	7.13303	−	3.17583i	0.659448	−	0.293605i
$118$	8.75705	−	6.36237i	0.806152	−	0.585704i
$119$		0			0
$120$	11.2450			1.02652
$121$	9.89404	+	4.80708i	0.899458	+	0.437007i
$122$	4.42237	+	7.65977i	0.400383	+	0.693483i
$123$	−1.93972	+	0.412300i	−0.174899	+	0.0371758i
$124$	0.00190908	+	0.0181637i	0.000171440	+	0.00163114i
$125$	9.84690	+	7.15419i	0.880734	+	0.639890i
$126$		0			0
$127$	1.55524	+	4.78655i	0.138006	+	0.424737i	0.996045	−	0.0888458i	$-0.0283178\pi$
$127$	1.55524	+	4.78655i	0.138006	+	0.424737i	−0.858040	+	0.513583i	$0.828318\pi$
$128$	−10.2260	+	4.55292i	−0.903861	+	0.402425i
$129$	15.8578	+	7.06034i	1.39620	+	0.621629i
$130$	11.7316	−	2.49362i	1.02893	−	0.218705i
$131$	−0.0900265	+	0.155930i	−0.00786565	+	0.0136237i	−0.869931	−	0.493173i	$-0.835837\pi$
$131$	−0.0900265	+	0.155930i	−0.00786565	+	0.0136237i	0.862066	+	0.506796i	$0.169170\pi$
$132$	0.0682787	−	0.0733313i	0.00594290	−	0.00638267i
$133$		0			0
$134$	6.73581	−	20.7307i	0.581885	−	1.79086i
$135$	0.546575	+	5.20031i	0.0470417	+	0.447572i
$136$	−1.62287	+	15.4406i	−0.139160	+	1.32402i
$137$	5.56981	−	6.18590i	0.475861	−	0.528497i	−0.456646	−	0.889648i	$-0.650949\pi$
$137$	5.56981	−	6.18590i	0.475861	−	0.528497i	0.932507	+	0.361151i	$0.117616\pi$
$138$	−2.14621	−	0.456191i	−0.182697	−	0.0388335i
$139$	−5.63172	−	4.09169i	−0.477677	−	0.347052i	0.322749	−	0.946485i	$-0.395393\pi$
$139$	−5.63172	−	4.09169i	−0.477677	−	0.347052i	−0.800425	+	0.599432i	$0.795393\pi$
$140$		0			0
$141$	−3.99497	+	12.2953i	−0.336438	+	1.03545i
$142$	9.79576	−	16.9667i	0.822042	−	1.42382i
$143$	7.92802	−	13.2171i	0.662975	−	1.10527i
$144$	3.33681	+	5.77952i	0.278067	+	0.481627i
$145$	−1.43679	−	1.59572i	−0.119319	−	0.132517i
$146$	−6.85740	+	4.98219i	−0.567523	+	0.412329i
$147$		0			0
$148$	−0.00903937	−	0.0278203i	−0.000743031	−	0.00228682i
$149$	3.14407	+	0.668293i	0.257572	+	0.0547487i	0.334888	−	0.942258i	$-0.391302\pi$
$149$	3.14407	+	0.668293i	0.257572	+	0.0547487i	−0.0773155	+	0.997007i	$0.524635\pi$
$150$	−0.524563	+	4.99088i	−0.0428303	+	0.407504i
$151$	20.3419	+	9.05681i	1.65540	+	0.737033i	0.999836	−	0.0181050i	$-0.00576330\pi$
$151$	20.3419	+	9.05681i	1.65540	+	0.737033i	0.655566	+	0.755138i	$0.272430\pi$
$152$	11.0172	+	12.2359i	0.893615	+	0.992460i
$153$	9.19115			0.743061
$154$		0			0
$155$	2.39521			0.192388
$156$	−0.0939394	−	0.104330i	−0.00752117	−	0.00835311i
$157$	−12.1088	−	5.39120i	−0.966391	−	0.430265i	−0.138010	−	0.990431i	$-0.544071\pi$
$157$	−12.1088	−	5.39120i	−0.966391	−	0.430265i	−0.828380	+	0.560166i	$0.810737\pi$
$158$	−2.30404	+	21.9215i	−0.183300	+	1.74398i
$159$	−21.4678	−	4.56311i	−1.70250	−	0.361878i
$160$	−0.0447049	−	0.137588i	−0.00353423	−	0.0108773i
$161$		0			0
$162$	−12.7893	+	9.29200i	−1.00483	+	0.730048i
$163$	9.17936	+	10.1947i	0.718983	+	0.798512i	0.986276	−	0.165103i	$-0.0527958\pi$
$163$	9.17936	+	10.1947i	0.718983	+	0.798512i	−0.267293	+	0.963615i	$0.586129\pi$
$164$	0.00640025	+	0.0110856i	0.000499776	+	0.000865637i
$165$	−8.62841	−	9.91066i	−0.671721	−	0.771544i
$166$	3.08329	−	5.34041i	0.239310	−	0.414496i
$167$	−2.87651	+	8.85300i	−0.222591	+	0.685066i	0.775936	+	0.630812i	$0.217278\pi$
$167$	−2.87651	+	8.85300i	−0.222591	+	0.685066i	−0.998527	+	0.0542539i	$0.982722\pi$
$168$		0			0
$169$	−6.95361	−	5.05209i	−0.534893	−	0.388623i
$170$	13.8096	+	2.93533i	1.05915	+	0.225129i
$171$	6.52218	−	7.24361i	0.498763	−	0.553933i
$172$	0.0117122	−	0.111435i	0.000893050	−	0.00849680i
$173$	1.09814	+	10.4481i	0.0834902	+	0.794356i	0.953514	+	0.301347i	$0.0974364\pi$
$173$	1.09814	+	10.4481i	0.0834902	+	0.794356i	−0.870024	+	0.493009i	$0.835897\pi$
$174$	1.10462	−	3.39966i	0.0837409	−	0.257728i
$175$		0			0
$176$	11.9432	+	5.55819i	0.900254	+	0.418964i
$177$	−8.30826	+	14.3903i	−0.624487	+	1.08164i
$178$	−21.1509	+	4.49576i	−1.58533	+	0.336971i
$179$	−7.60372	−	3.38539i	−0.568329	−	0.253036i	0.102395	−	0.994744i	$-0.467350\pi$
$179$	−7.60372	−	3.38539i	−0.568329	−	0.253036i	−0.670723	+	0.741708i	$0.734016\pi$
$180$	−0.0392556	+	0.0174777i	−0.00292594	+	0.00130271i
$181$	4.57437	+	14.0785i	0.340010	+	1.04644i	0.964201	+	0.265172i	$0.0854286\pi$
$181$	4.57437	+	14.0785i	0.340010	+	1.04644i	−0.624191	+	0.781272i	$0.714571\pi$
$182$		0			0
$183$	−10.9845	−	7.98074i	−0.812001	−	0.589953i
$184$	0.213511	+	2.03142i	0.0157403	+	0.149759i
$185$	−3.75244	+	0.797607i	−0.275885	+	0.0586412i
$186$	1.99370	+	3.45319i	0.146185	+	0.253200i
$187$	14.8537	−	10.4175i	1.08621	−	0.761800i
$188$	0.0834496			0.00608619
$189$		0			0
$190$	12.1129	−	8.80052i	0.878760	−	0.638457i
$191$	−8.77621	+	3.90742i	−0.635024	+	0.282731i	−0.698892	−	0.715227i	$-0.746323\pi$
$191$	−8.77621	+	3.90742i	−0.635024	+	0.282731i	0.0638675	+	0.997958i	$0.479656\pi$
$192$	11.6604	−	12.9502i	0.841517	−	0.934599i
$193$	−0.995538	+	1.10566i	−0.0716604	+	0.0795869i	−0.777909	−	0.628377i	$-0.783719\pi$
$193$	−0.995538	+	1.10566i	−0.0716604	+	0.0795869i	0.706248	+	0.707964i	$0.250386\pi$
$194$	3.10430	−	1.38212i	0.222876	−	0.0992308i
$195$	−14.8953	+	10.8221i	−1.06667	+	0.774983i
$196$		0			0
$197$	−14.0434			−1.00055			−0.500274	−	0.865867i	$-0.666767\pi$
$197$	−14.0434			−1.00055			−0.500274	+	0.865867i	$0.666767\pi$
$198$	2.55117	−	7.42743i	0.181304	−	0.527845i
$199$	−2.14364	−	3.71290i	−0.151959	−	0.263200i	0.779989	−	0.625794i	$-0.215225\pi$
$199$	−2.14364	−	3.71290i	−0.151959	−	0.263200i	−0.931948	+	0.362593i	$0.881891\pi$
$200$	4.56968	−	0.971316i	0.323125	−	0.0686824i
$201$	3.49769	+	33.2783i	0.246708	+	2.34727i
$202$	−13.5627	−	9.85391i	−0.954271	−	0.693318i
$203$		0			0
$204$	−0.0510676	−	0.157170i	−0.00357545	−	0.0110041i
$205$	1.53360	−	0.682802i	0.107111	−	0.0476889i
$206$	0.510226	+	0.227167i	0.0355492	+	0.0158275i
$207$	1.18280	−	0.251412i	0.0822102	−	0.0174743i
$208$	9.22877	−	15.9847i	0.639900	−	1.10834i
$209$	2.33032	−	19.0987i	0.161192	−	1.32108i
$210$		0			0
$211$	−0.449704	+	1.38405i	−0.0309589	+	0.0952816i	−0.965342	−	0.260988i	$-0.915952\pi$
$211$	−0.449704	+	1.38405i	−0.0309589	+	0.0952816i	0.934383	+	0.356270i	$0.115952\pi$
$212$	0.0148084	+	0.140893i	0.00101705	+	0.00967657i
$213$	−3.14371	+	29.9104i	−0.215403	+	2.04943i
$214$	3.08295	−	3.42396i	0.210746	−	0.234057i
$215$	−14.3735	−	3.05519i	−0.980268	−	0.208362i
$216$	6.55599	+	4.76320i	0.446079	+	0.324095i
$217$		0			0
$218$	1.23957	−	3.81499i	0.0839540	−	0.258384i
$219$	6.50596	−	11.2687i	0.439632	−	0.761465i
$220$	−0.0436308	+	0.0727387i	−0.00294159	+	0.00490404i
$221$	−12.7102	−	22.0147i	−0.854980	−	1.48087i
$222$	−4.27334	−	4.74602i	−0.286808	−	0.318532i
$223$	−3.92893	+	2.85453i	−0.263101	+	0.191154i	−0.711513	−	0.702673i	$-0.751990\pi$
$223$	−3.92893	+	2.85453i	−0.263101	+	0.191154i	0.448412	+	0.893827i	$0.351990\pi$
$224$		0			0
$225$	−0.854642	−	2.63032i	−0.0569761	−	0.175354i
$226$	20.0492	+	4.26159i	1.33365	+	0.283477i
$227$	0.0415128	−	0.394968i	0.00275530	−	0.0262150i	−0.993058	−	0.117627i	$-0.962471\pi$
$227$	0.0415128	−	0.394968i	0.00275530	−	0.0262150i	0.995813	+	0.0914119i	$0.0291380\pi$
$228$	−0.160105	−	0.0712834i	−0.0106032	−	0.00472086i
$229$	−1.46515	−	1.62721i	−0.0968199	−	0.107529i	0.692787	−	0.721142i	$-0.256382\pi$
$229$	−1.46515	−	1.62721i	−0.0968199	−	0.107529i	−0.789607	+	0.613612i	$0.789716\pi$
$230$	1.85744			0.122476
$231$		0			0
$232$	−3.32773			−0.218476
$233$	−0.843209	−	0.936478i	−0.0552404	−	0.0613507i	0.714891	−	0.699236i	$-0.246476\pi$
$233$	−0.843209	−	0.936478i	−0.0552404	−	0.0613507i	−0.770132	+	0.637885i	$0.779810\pi$
$234$	−10.0523	−	4.47559i	−0.657142	−	0.292579i
$235$	1.14397	−	10.8841i	0.0746241	−	0.710001i
$236$	0.104915	+	0.0223003i	0.00682938	+	0.00145163i
$237$	−10.4563	−	32.1812i	−0.679210	−	2.09039i
$238$		0			0
$239$	9.02997	−	6.56066i	0.584100	−	0.424374i	−0.256100	−	0.966650i	$-0.582438\pi$
$239$	9.02997	−	6.56066i	0.584100	−	0.424374i	0.840200	+	0.542277i	$0.182438\pi$
$240$	−10.5298	−	11.6945i	−0.679695	−	0.754878i
$241$	−10.7421	−	18.6059i	−0.691962	−	1.19851i	−0.971194	−	0.238290i	$-0.923413\pi$
$241$	−10.7421	−	18.6059i	−0.691962	−	1.19851i	0.279232	−	0.960224i	$-0.409920\pi$
$242$	−4.29551	−	14.8949i	−0.276126	−	0.957482i
$243$	7.85110	−	13.5985i	0.503648	−	0.872344i
$244$	−0.0270832	+	0.0833535i	−0.00173382	+	0.00533616i
$245$		0			0
$246$	2.26092	+	1.64266i	0.144151	+	0.104732i
$247$	−26.3693	−	5.60496i	−1.67784	−	0.356635i
$248$	2.48381	−	2.75856i	0.157722	−	0.175168i
$249$	−0.989505	+	9.41451i	−0.0627073	+	0.596621i
$250$	−1.79296	−	17.0588i	−0.113397	−	1.07890i
$251$	0.130968	−	0.403077i	0.00826660	−	0.0254420i	−0.946838	−	0.321710i	$-0.895742\pi$
$251$	0.130968	−	0.403077i	0.00826660	−	0.0254420i	0.955105	+	0.296268i	$0.0957423\pi$
$252$		0			0
$253$	1.62655	−	1.74691i	0.102260	−	0.109828i
$254$	3.54633	−	6.14243i	0.222517	−	0.385410i
$255$	−21.1993	+	4.50605i	−1.32755	+	0.282180i
$256$	−0.306158	−	0.136310i	−0.0191349	−	0.00851940i
$257$	−15.9323	+	7.09351i	−0.993829	+	0.442481i	−0.838217	−	0.545337i	$-0.816402\pi$
$257$	−15.9323	+	7.09351i	−0.993829	+	0.442481i	−0.155612	+	0.987818i	$0.549735\pi$
$258$	−7.55942	−	23.2655i	−0.470629	−	1.44845i
$259$		0			0
$260$	0.0961483	+	0.0698558i	0.00596286	+	0.00433227i
$261$	0.205922	+	1.95922i	0.0127463	+	0.121273i
$262$	0.248198	−	0.0527561i	0.0153337	−	0.00325928i
$263$	−0.757596	−	1.31219i	−0.0467153	−	0.0809133i	0.841722	−	0.539911i	$-0.181542\pi$
$263$	−0.757596	−	1.31219i	−0.0467153	−	0.0809133i	−0.888438	+	0.458997i	$0.848209\pi$
$264$	−20.3617	−	0.339968i	−1.25318	−	0.0209236i
$265$	18.5793			1.14132
$266$		0			0
$267$	26.8548	−	19.5111i	1.64348	−	1.19406i
$268$	0.197319	−	0.0878522i	0.0120532	−	0.00536643i
$269$	1.35902	−	1.50935i	0.0828611	−	0.0920266i	−0.700288	−	0.713860i	$-0.746945\pi$
$269$	1.35902	−	1.50935i	0.0828611	−	0.0920266i	0.783149	+	0.621833i	$0.213612\pi$
$270$	4.93083	−	5.47624i	0.300080	−	0.333273i
$271$	−6.94700	+	3.09300i	−0.422000	+	0.187887i	−0.606739	−	0.794901i	$-0.707523\pi$
$271$	−6.94700	+	3.09300i	−0.422000	+	0.187887i	0.184739	+	0.982788i	$0.440856\pi$
$272$	17.5775	−	12.7708i	1.06579	−	0.774344i
$273$		0			0
$274$	−11.7307			−0.708676
$275$	−4.36244	−	3.28215i	−0.263065	−	0.197921i
$276$	−0.0108710	−	0.0188291i	−0.000654358	−	0.00113338i
$277$	−14.1115	+	2.99950i	−0.847881	+	0.180223i	−0.611310	−	0.791392i	$-0.709357\pi$
$277$	−14.1115	+	2.99950i	−0.847881	+	0.180223i	−0.236571	+	0.971614i	$0.576024\pi$
$278$	1.02544	+	9.75644i	0.0615020	+	0.585153i
$279$	−1.77781	−	1.29166i	−0.106435	−	0.0773295i
$280$		0			0
$281$	5.48494	+	16.8809i	0.327204	+	1.00703i	0.970436	+	0.241359i	$0.0775933\pi$
$281$	5.48494	+	16.8809i	0.327204	+	1.00703i	−0.643232	+	0.765672i	$0.722407\pi$
$282$	16.6439	−	7.41035i	0.991130	−	0.441280i
$283$	28.4443	+	12.6642i	1.69084	+	0.752809i	0.999543	+	0.0302356i	$0.00962577\pi$
$283$	28.4443	+	12.6642i	1.69084	+	0.752809i	0.691294	+	0.722573i	$0.257041\pi$
$284$	0.189891	−	0.0403626i	0.0112680	−	0.00239508i
$285$	−11.4921	+	19.9049i	−0.680733	+	1.17906i
$286$	−21.3182	+	4.16062i	−1.26057	+	0.246022i
$287$		0			0
$288$	−0.0410148	+	0.126231i	−0.00241682	+	0.00743821i
$289$	−1.35085	−	12.8524i	−0.0794615	−	0.756026i
$290$	−0.316309	+	3.00948i	−0.0185743	+	0.176723i
$291$	−3.49047	+	3.87656i	−0.204615	+	0.227248i
$292$	−0.0821559	−	0.0174628i	−0.00480781	−	0.00102193i
$293$	−19.4409	−	14.1247i	−1.13575	−	0.825171i	−0.149229	−	0.988803i	$-0.547679\pi$
$293$	−19.4409	−	14.1247i	−1.13575	−	0.825171i	−0.986522	+	0.163632i	$0.947679\pi$
$294$		0			0
$295$	4.34679	−	13.3781i	0.253080	−	0.778901i
$296$	−2.97266	+	5.14880i	−0.172782	+	0.299268i
$297$	−0.832484	−	9.43294i	−0.0483056	−	0.547354i
$298$	−2.26491	−	3.92295i	−0.131203	−	0.227250i
$299$	−2.23784	−	2.48538i	−0.129418	−	0.143733i
$300$	−0.0402302	+	0.0292290i	−0.00232269	+	0.00168754i
$301$		0			0
$302$	−9.69701	−	29.8443i	−0.558000	−	1.71735i
$303$	25.1729	+	5.35067i	1.44615	+	0.307388i
$304$	2.40850	−	22.9153i	0.138137	−	1.31428i
$305$	10.5003	+	4.67503i	0.601245	+	0.267692i
$306$	−8.66711	−	9.62580i	−0.495466	−	0.550270i
$307$	5.46298			0.311789			0.155894	−	0.987774i	$-0.450174\pi$
$307$	5.46298			0.311789			0.155894	+	0.987774i	$0.450174\pi$
$308$		0			0
$309$	−0.857378			−0.0487745
$310$	−2.25864	−	2.50848i	−0.128282	−	0.142472i
$311$	−12.6877	−	5.64894i	−0.719454	−	0.320322i	0.0141487	−	0.999900i	$-0.495496\pi$
$311$	−12.6877	−	5.64894i	−0.719454	−	0.320322i	−0.733603	+	0.679578i	$0.762163\pi$
$312$	−2.98257	+	28.3773i	−0.168855	+	1.60655i
$313$	26.8487	+	5.70688i	1.51758	+	0.322572i	0.889993	−	0.455974i	$-0.150709\pi$
$313$	26.8487	+	5.70688i	1.51758	+	0.322572i	0.627588	+	0.778546i	$0.284042\pi$
$314$	5.77229	+	17.7653i	0.325749	+	1.00255i
$315$		0			0
$316$	−0.176704	+	0.128383i	−0.00994038	+	0.00722211i
$317$	5.23642	+	5.81563i	0.294107	+	0.326638i	0.872030	−	0.489453i	$-0.162803\pi$
$317$	5.23642	+	5.81563i	0.294107	+	0.326638i	−0.577923	+	0.816091i	$0.696137\pi$
$318$	15.4648	+	26.7859i	0.867226	+	1.50208i
$319$	2.55341	+	2.93287i	0.142964	+	0.164209i
$320$	−7.37598	+	12.7756i	−0.412330	+	0.714176i
$321$	−2.18563	+	6.72669i	−0.121990	+	0.375447i
$322$		0			0
$323$	−25.6731	−	18.6526i	−1.42849	−	1.03786i
$324$	−0.153224	−	0.0325688i	−0.00851245	−	0.00180938i
$325$	−5.11829	+	5.68444i	−0.283912	+	0.315316i
$326$	2.02083	−	19.2269i	0.111923	−	1.06488i
$327$	0.643667	+	6.12408i	0.0355949	+	0.338663i
$328$	0.803950	−	2.47430i	0.0443907	−	0.136621i
$329$		0			0
$330$	−2.24288	+	18.3820i	−0.123467	+	1.01190i
$331$	14.0731	−	24.3753i	0.773527	−	1.33979i	−0.162092	−	0.986776i	$-0.551824\pi$
$331$	14.0731	−	24.3753i	0.773527	−	1.33979i	0.935619	−	0.353012i	$-0.114843\pi$
$332$	0.0597696	−	0.0127044i	0.00328029	−	0.000697246i
$333$	3.21533	+	1.43156i	0.176199	+	0.0784489i
$334$	11.9842	−	5.33569i	0.655744	−	0.291956i
$335$	−8.75338	−	26.9401i	−0.478248	−	1.47190i
$336$		0			0
$337$	20.2084	+	14.6823i	1.10082	+	0.799793i	0.981194	−	0.193025i	$-0.0618300\pi$
$337$	20.2084	+	14.6823i	1.10082	+	0.799793i	0.119628	+	0.992819i	$0.461830\pi$
$338$	1.26614	+	12.0465i	0.0688688	+	0.655243i
$339$	−30.7778	+	6.54201i	−1.67162	+	0.355313i
$340$	0.0699488	+	0.121155i	0.00379350	+	0.00657054i
$341$	−4.33709	−	0.0724141i	−0.234867	−	0.00392144i
$342$	−13.7365			−0.742783
$343$		0			0
$344$	−18.4239	+	13.3858i	−0.993352	+	0.721713i
$345$	−2.60486	+	1.15976i	−0.140241	+	0.0624393i
$346$	9.90669	−	11.0025i	0.532587	−	0.591498i
$347$	13.8170	−	15.3454i	0.741737	−	0.823782i	−0.247686	−	0.968840i	$-0.579670\pi$
$347$	13.8170	−	15.3454i	0.741737	−	0.823782i	0.989423	+	0.145058i	$0.0463368\pi$
$348$	0.0323588	−	0.0144071i	0.00173461	−	0.000772299i
$349$	−4.85185	+	3.52507i	−0.259713	+	0.188693i	−0.710021	−	0.704181i	$-0.751314\pi$
$349$	−4.85185	+	3.52507i	−0.259713	+	0.188693i	0.450307	+	0.892874i	$0.351314\pi$
$350$		0			0
$351$	−13.2682			−0.708206
$352$	0.0767892	+	0.250487i	0.00409288	+	0.0133510i
$353$	12.0191	+	20.8177i	0.639712	+	1.10801i	0.985496	+	0.169699i	$0.0542796\pi$
$353$	12.0191	+	20.8177i	0.639712	+	1.10801i	−0.345784	+	0.938314i	$0.612387\pi$
$354$	22.9054	−	4.86869i	1.21741	−	0.258768i
$355$	−2.66127	−	25.3203i	−0.141246	−	1.34386i
$356$	−0.173346	−	0.125943i	−0.00918732	−	0.00667498i
$357$		0			0
$358$	3.62470	+	11.1557i	0.191571	+	0.589596i
$359$	−10.0034	+	4.45382i	−0.527961	+	0.235063i	−0.653366	−	0.757042i	$-0.726644\pi$
$359$	−10.0034	+	4.45382i	−0.527961	+	0.235063i	0.125405	+	0.992106i	$0.459977\pi$
$360$	7.97850	+	3.55226i	0.420504	+	0.187220i
$361$	−14.3334	+	3.04666i	−0.754391	+	0.160351i
$362$	10.4307	−	18.0664i	0.548224	−	0.949551i
$363$	15.3242	+	18.2065i	0.804311	+	0.955593i
$364$		0			0
$365$	−3.40385	+	10.4760i	−0.178166	+	0.548338i
$366$	2.00010	+	19.0297i	0.104547	+	0.994699i
$367$	1.10986	−	10.5596i	0.0579341	−	0.551206i	−0.926604	−	0.376038i	$-0.877286\pi$
$367$	1.10986	−	10.5596i	0.0579341	−	0.551206i	0.984538	−	0.175169i	$-0.0560470\pi$
$368$	1.91270	−	2.12427i	0.0997065	−	0.110735i
$369$	−1.50651	−	0.320218i	−0.0784257	−	0.0166699i
$370$	4.37382	+	3.17777i	0.227384	+	0.165204i
$371$		0			0
$372$	−0.0122097	+	0.0375775i	−0.000633042	+	0.00194830i
$373$	−18.3018	+	31.6996i	−0.947631	+	1.64135i	−0.197236	+	0.980356i	$0.563196\pi$
$373$	−18.3018	+	31.6996i	−0.947631	+	1.64135i	−0.750395	+	0.660989i	$0.770137\pi$
$374$	−24.9169	−	5.73262i	−1.28842	−	0.296427i
$375$	13.1657	+	22.8037i	0.679875	+	1.17758i
$376$	−11.3489	−	12.6043i	−0.585276	−	0.650015i
$377$	4.40797	−	3.20258i	0.227022	−	0.164941i
$378$		0			0
$379$	−3.91147	−	12.0383i	−0.200919	−	0.618364i	−0.999856	−	0.0169501i	$-0.994604\pi$
$379$	−3.91147	−	12.0383i	−0.200919	−	0.618364i	0.798938	−	0.601414i	$-0.205396\pi$
$380$	0.145120	+	0.0308461i	0.00744448	+	0.00158237i
$381$	−1.13811	+	10.8284i	−0.0583071	+	0.554755i
$382$	12.3680	+	5.50660i	0.632804	+	0.281742i
$383$	10.3500	+	11.4949i	0.528862	+	0.587361i	0.947085	−	0.320984i	$-0.104013\pi$
$383$	10.3500	+	11.4949i	0.528862	+	0.587361i	−0.418223	+	0.908345i	$0.637347\pi$
$384$	−24.2164			−1.23579
$385$		0			0
$386$	2.09672			0.106720
$387$	9.02103	+	10.0189i	0.458565	+	0.509288i
$388$	0.0307607	+	0.0136956i	0.00156164	+	0.000695286i
$389$	1.32887	−	12.6433i	0.0673762	−	0.641041i	−0.907768	−	0.419472i	$-0.862215\pi$
$389$	1.32887	−	12.6433i	0.0673762	−	0.641041i	0.975145	−	0.221570i	$-0.0711180\pi$
$390$	25.3798	+	5.39465i	1.28516	+	0.273169i
$391$	−1.21654	−	3.74414i	−0.0615232	−	0.189349i
$392$		0			0
$393$	−0.315131	+	0.228956i	−0.0158963	+	0.0115493i
$394$	13.2427	+	14.7075i	0.667156	+	0.740952i
$395$	14.3223	+	24.8070i	0.720633	+	1.24817i
$396$	0.0716100	−	0.0304608i	0.00359854	−	0.00153071i
$397$	−9.47870	+	16.4176i	−0.475722	+	0.823975i	−0.999613	−	0.0278101i	$-0.991147\pi$
$397$	−9.47870	+	16.4176i	−0.475722	+	0.823975i	0.523891	+	0.851785i	$0.324480\pi$
$398$	−1.86706	+	5.74622i	−0.0935873	+	0.288032i
$399$		0			0
$400$	−5.28919	−	3.84282i	−0.264460	−	0.192141i
$401$	8.49236	+	1.80511i	0.424088	+	0.0901427i	0.415012	−	0.909816i	$-0.363777\pi$
$401$	8.49236	+	1.80511i	0.424088	+	0.0901427i	0.00907651	+	0.999959i	$0.497111\pi$
$402$	31.5538	−	35.0440i	1.57376	−	1.74784i
$403$	−0.635295	+	6.04443i	−0.0316463	+	0.301094i
$404$	−0.0173643	−	0.165210i	−0.000863905	−	0.00821951i
$405$	−6.34833	+	19.5381i	−0.315451	+	0.970858i
$406$		0			0
$407$	6.81881	−	1.33081i	0.337996	−	0.0659658i
$408$	−16.7939	+	29.0880i	−0.831424	+	1.44007i
$409$	5.58920	−	1.18802i	0.276368	−	0.0587438i	−0.0676425	−	0.997710i	$-0.521548\pi$
$409$	5.58920	−	1.18802i	0.276368	−	0.0587438i	0.344011	+	0.938966i	$0.388214\pi$
$410$	−2.16125	−	0.962250i	−0.106737	−	0.0475222i
$411$	16.4510	−	7.32447i	0.811469	−	0.361289i
$412$	0.00171020	+	0.00526346i	8.42556e−5	+	0.000259312i
$413$		0			0
$414$	−1.37866	−	1.00166i	−0.0677575	−	0.0492287i
$415$	−0.837655	−	7.96975i	−0.0411189	−	0.391220i
$416$	0.359067	−	0.0763220i	0.0176047	−	0.00374199i
$417$	−7.52986	−	13.0421i	−0.368739	−	0.638674i
$418$	−22.1993	+	15.5692i	−1.08580	+	0.761516i
$419$	27.1909			1.32836			0.664181	−	0.747571i	$-0.268780\pi$
$419$	27.1909			1.32836			0.664181	+	0.747571i	$0.268780\pi$
$420$		0			0
$421$	19.3881	−	14.0863i	0.944921	−	0.686525i	−0.00467947	−	0.999989i	$-0.501490\pi$
$421$	19.3881	−	14.0863i	0.944921	−	0.686525i	0.949600	+	0.313464i	$0.101490\pi$
$422$	1.87356	−	0.834163i	0.0912035	−	0.0406064i
$423$	−6.71854	+	7.46170i	−0.326667	+	0.362800i
$424$	19.2666	−	21.3977i	0.935669	−	1.03917i
$425$	−8.22566	+	3.66230i	−0.399003	+	0.177648i
$426$	34.2893	−	24.9126i	1.66132	−	1.20702i
$427$		0			0
$428$	0.0456549			0.00220681
$429$	27.2986	−	19.1456i	1.31799	−	0.924358i
$430$	10.3544	+	17.9343i	0.499331	+	0.864867i
$431$	−16.1132	+	3.42496i	−0.776145	+	0.164975i	−0.578921	−	0.815384i	$-0.696526\pi$
$431$	−16.1132	+	3.42496i	−0.776145	+	0.164975i	−0.197224	+	0.980358i	$0.563193\pi$
$432$	−1.18540	−	11.2783i	−0.0570327	−	0.542629i
$433$	16.2539	+	11.8092i	0.781113	+	0.567512i	0.905313	−	0.424745i	$-0.139636\pi$
$433$	16.2539	+	11.8092i	0.781113	+	0.567512i	−0.124200	+	0.992257i	$0.539636\pi$
$434$		0			0
$435$	−1.43548	−	4.41797i	−0.0688262	−	0.211825i
$436$	0.0363120	−	0.0161671i	0.00173903	−	0.000774265i
$437$	−3.81406	−	1.69813i	−0.182451	−	0.0812324i
$438$	−17.9366	+	3.81254i	−0.857043	+	0.182170i
$439$	13.3841	−	23.1819i	0.638788	−	1.10641i	−0.346912	−	0.937898i	$-0.612770\pi$
$439$	13.3841	−	23.1819i	0.638788	−	1.10641i	0.985699	−	0.168515i	$-0.0538970\pi$
$440$	16.9201	−	3.30226i	0.806636	−	0.157429i
$441$		0			0
$442$	−11.0703	+	34.0708i	−0.526559	+	1.62058i
$443$	−2.74025	−	26.0717i	−0.130193	−	1.23870i	−0.843220	−	0.537568i	$-0.819343\pi$
$443$	−2.74025	−	26.0717i	−0.130193	−	1.23870i	0.713027	−	0.701137i	$-0.247324\pi$
$444$	0.00661490	−	0.0629366i	0.000313929	−	0.00298684i
$445$	−18.8027	+	20.8826i	−0.891336	+	0.989929i
$446$	6.69444	+	1.42295i	0.316991	+	0.0673785i
$447$	5.62573	+	4.08733i	0.266088	+	0.193324i
$448$		0			0
$449$	3.01211	−	9.27033i	0.142150	−	0.437494i	−0.854483	−	0.519479i	$-0.826126\pi$
$449$	3.01211	−	9.27033i	0.142150	−	0.437494i	0.996634	+	0.0819851i	$0.0261260\pi$
$450$	−1.94879	+	3.37541i	−0.0918669	+	0.159118i
$451$	−2.79759	+	1.19001i	−0.131733	+	0.0560354i
$452$	0.101554	+	0.175896i	0.00477668	+	0.00827345i
$453$	32.2334	+	35.7988i	1.51446	+	1.68197i
$454$	−0.452792	+	0.328973i	−0.0212506	+	0.0154395i
$455$		0			0
$456$	11.0072	+	33.8767i	0.515459	+	1.58642i
$457$	−11.6256	−	2.47109i	−0.543822	−	0.115593i	−0.0721940	−	0.997391i	$-0.523000\pi$
$457$	−11.6256	−	2.47109i	−0.543822	−	0.115593i	−0.471628	+	0.881798i	$0.656333\pi$
$458$	−0.322552	+	3.06887i	−0.0150719	+	0.143399i
$459$	−14.2682	−	6.35262i	−0.665983	−	0.296515i
$460$	0.0123157	+	0.0136779i	0.000574221	+	0.000637736i
$461$	−9.14737			−0.426035			−0.213018	−	0.977048i	$-0.568329\pi$
$461$	−9.14737			−0.426035			−0.213018	+	0.977048i	$0.568329\pi$
$462$		0			0
$463$	38.9342			1.80943			0.904713	−	0.426021i	$-0.140085\pi$
$463$	38.9342			1.80943			0.904713	+	0.426021i	$0.140085\pi$
$464$	3.11609	+	3.46077i	0.144661	+	0.160662i
$465$	4.73376	+	2.10761i	0.219523	+	0.0977379i
$466$	−0.185632	+	1.76617i	−0.00859922	+	0.0818162i
$467$	−20.3293	−	4.32112i	−0.940726	−	0.199957i	−0.288068	−	0.957610i	$-0.593013\pi$
$467$	−20.3293	−	4.32112i	−0.940726	−	0.199957i	−0.652658	+	0.757653i	$0.726346\pi$
$468$	−0.0336939	−	0.103699i	−0.00155750	−	0.00479350i
$469$		0			0
$470$	−12.4776	+	9.06548i	−0.575547	+	0.418159i
$471$	−19.1874	−	21.3098i	−0.884109	−	0.981903i
$472$	−10.8999	−	18.8792i	−0.501708	−	0.868984i
$473$	25.9344	+	5.96671i	1.19246	+	0.274350i
$474$	−23.8429	+	41.2971i	−1.09514	+	1.89684i
$475$	−2.95076	+	9.08152i	−0.135390	+	0.416689i
$476$		0			0
$477$	−13.7903	−	10.0192i	−0.631413	−	0.458748i
$478$	−15.3860	−	3.27040i	−0.703740	−	0.149585i
$479$	16.4180	−	18.2340i	0.750157	−	0.833134i	−0.240337	−	0.970690i	$-0.577258\pi$
$479$	16.4180	−	18.2340i	0.750157	−	0.833134i	0.990494	+	0.137556i	$0.0439246\pi$
$480$	0.0327145	−	0.311258i	0.00149321	−	0.0142069i
$481$	−1.01752	−	9.68104i	−0.0463949	−	0.441418i
$482$	−9.35614	+	28.7952i	−0.426161	+	1.31159i
$483$		0			0
$484$	0.0812030	−	0.130392i	0.00369105	−	0.00592690i
$485$	2.20796	−	3.82429i	0.100258	−	0.173652i
$486$	−21.6450	+	4.60080i	−0.981839	+	0.208696i
$487$	−11.3018	−	5.03187i	−0.512132	−	0.228016i	0.134366	−	0.990932i	$-0.457100\pi$
$487$	−11.3018	−	5.03187i	−0.512132	−	0.228016i	−0.646497	+	0.762916i	$0.723767\pi$
$488$	16.2730	−	7.24520i	0.736643	−	0.327975i
$489$	9.17101	+	28.2255i	0.414727	+	1.27640i
$490$		0			0
$491$	−13.3691	−	9.71320i	−0.603338	−	0.438350i	0.243724	−	0.969845i	$-0.421631\pi$
$491$	−13.3691	−	9.71320i	−0.603338	−	0.438350i	−0.847062	+	0.531494i	$0.821631\pi$
$492$	0.00289464	+	0.0275407i	0.000130500	+	0.00124163i
$493$	6.27353	−	1.33348i	0.282546	−	0.0600569i
$494$	18.9958	+	32.9017i	0.854661	+	1.48032i
$495$	−2.99125	−	9.75747i	−0.134447	−	0.438566i
$496$	−5.19468			−0.233248
$497$		0			0
$498$	10.7928	−	7.84144i	0.483638	−	0.351383i
$499$	−12.5530	+	5.58895i	−0.561949	+	0.250196i	−0.667995	−	0.744165i	$-0.732847\pi$
$499$	−12.5530	+	5.58895i	−0.561949	+	0.250196i	0.106047	+	0.994361i	$0.466181\pi$
$500$	0.113731	−	0.126311i	0.00508620	−	0.00564880i
$501$	−13.4750	+	14.9655i	−0.602018	+	0.668608i
$502$	−0.545638	+	0.242934i	−0.0243530	+	0.0108427i
$503$	−18.2812	+	13.2820i	−0.815117	+	0.592217i	−0.915310	−	0.402751i	$-0.868054\pi$
$503$	−18.2812	+	13.2820i	−0.815117	+	0.592217i	0.100193	+	0.994968i	$0.468054\pi$
$504$		0			0
$505$	−21.7859			−0.969461
$506$	−3.36334	−	0.0561558i	−0.149519	−	0.00249643i
$507$	−9.29728	−	16.1034i	−0.412907	−	0.715175i
$508$	0.0687458	−	0.0146124i	0.00305010	−	0.000648319i
$509$	−2.24356	−	21.3460i	−0.0994440	−	0.946146i	−0.924522	−	0.381128i	$-0.875536\pi$
$509$	−2.24356	−	21.3460i	−0.0994440	−	0.946146i	0.825078	−	0.565018i	$-0.191131\pi$
$510$	24.7098	+	17.9527i	1.09417	+	0.794958i
$511$		0			0
$512$	7.06408	+	21.7410i	0.312191	+	0.960825i
$513$	−15.1315	+	6.73697i	−0.668071	+	0.297444i
$514$	22.4529	+	9.99666i	0.990354	+	0.440934i
$515$	0.709943	−	0.150903i	0.0312838	−	0.00664958i
$516$	0.121202	−	0.209927i	0.00533560	−	0.00924154i
$517$	−2.40048	+	19.6737i	−0.105573	+	0.865248i
$518$		0			0
$519$	−7.02327	+	21.6154i	−0.308287	+	0.948811i
$520$	−2.52486	−	24.0225i	−0.110723	−	1.05345i
$521$	3.62835	−	34.5214i	0.158961	−	1.51241i	−0.566451	−	0.824095i	$-0.691684\pi$
$521$	3.62835	−	34.5214i	0.158961	−	1.51241i	0.725412	−	0.688315i	$-0.241649\pi$
$522$	1.85769	−	2.06317i	0.0813089	−	0.0903027i
$523$	19.2970	+	4.10171i	0.843800	+	0.179355i	0.609477	−	0.792803i	$-0.291379\pi$
$523$	19.2970	+	4.10171i	0.843800	+	0.179355i	0.234323	+	0.972159i	$0.424713\pi$
$524$	0.00203415	+	0.00147790i	8.88624e−5	+	6.45623e-5i
$525$		0			0
$526$	−0.659847	+	2.03080i	−0.0287707	+	0.0885471i
$527$	−3.57715	+	6.19581i	−0.155823	+	0.269894i
$528$	18.7131	+	21.4941i	0.814385	+	0.935409i
$529$	11.2410	+	19.4700i	0.488740	+	0.846523i
$530$	−17.5200	−	19.4579i	−0.761019	−	0.845197i
$531$	−10.4407	+	7.58562i	−0.453088	+	0.329188i
$532$		0			0
$533$	1.31632	+	4.05122i	0.0570162	+	0.175478i
$534$	−45.7574	−	9.72604i	−1.98012	−	0.420887i
$535$	0.625859	−	5.95465i	0.0270582	−	0.257442i
$536$	−40.1041	−	17.8555i	−1.73223	−	0.771241i
$537$	−12.0487	−	13.3814i	−0.519939	−	0.577451i
$538$	−2.86226			−0.123401
$539$		0			0
$540$	0.0730199			0.00314227
$541$	−3.71329	−	4.12403i	−0.159647	−	0.177306i	0.658015	−	0.753005i	$-0.271397\pi$
$541$	−3.71329	−	4.12403i	−0.159647	−	0.177306i	−0.817661	+	0.575699i	$0.804730\pi$
$542$	9.79018	+	4.35887i	0.420524	+	0.187230i
$543$	−3.34747	+	31.8490i	−0.143654	+	1.36677i
$544$	0.422670	+	0.0898413i	0.0181218	+	0.00385191i
$545$	−1.61085	−	4.95770i	−0.0690014	−	0.212364i
$546$		0			0
$547$	6.83353	−	4.96485i	0.292181	−	0.212282i	−0.432032	−	0.901858i	$-0.642203\pi$
$547$	6.83353	−	4.96485i	0.292181	−	0.212282i	0.724213	+	0.689576i	$0.242203\pi$
$548$	−0.0777797	−	0.0863831i	−0.00332259	−	0.00369010i
$549$	−5.27263	−	9.13246i	−0.225030	−	0.389764i
$550$	0.676348	+	7.66375i	0.0288396	+	0.326783i
$551$	3.40086	−	5.89047i	0.144882	−	0.250942i
$552$	−1.36553	+	4.20267i	−0.0581209	+	0.178878i
$553$		0			0
$554$	16.4483	+	11.9504i	0.698822	+	0.507724i
$555$	−8.11797	−	1.72553i	−0.344589	−	0.0732445i
$556$	−0.0650460	+	0.0722409i	−0.00275856	+	0.00306370i
$557$	1.27352	−	12.1167i	0.0539608	−	0.513403i	−0.933841	−	0.357688i	$-0.883565\pi$
$557$	1.27352	−	12.1167i	0.0539608	−	0.513403i	0.987802	−	0.155715i	$-0.0497682\pi$
$558$	0.323710	+	3.07990i	0.0137038	+	0.130383i
$559$	11.5223	−	35.4620i	0.487342	−	1.49988i
$560$		0			0
$561$	38.5226	−	7.51837i	1.62643	−	0.317426i
$562$	12.5070	−	21.6628i	0.527576	−	0.913789i
$563$	−26.7558	+	5.68712i	−1.12762	+	0.239683i	−0.733709	−	0.679464i	$-0.762212\pi$
$563$	−26.7558	+	5.68712i	−1.12762	+	0.239683i	−0.393913	+	0.919148i	$0.628879\pi$
$564$	0.164925	+	0.0734295i	0.00694461	+	0.00309194i
$565$	24.3338	−	10.8341i	1.02373	−	0.455794i
$566$	−13.5594	−	41.7316i	−0.569944	−	1.75411i
$567$		0			0
$568$	−31.9211	−	23.1920i	−1.33938	−	0.973115i
$569$	−0.745836	−	7.09615i	−0.0312671	−	0.297486i	−0.998969	−	0.0453903i	$-0.985547\pi$
$569$	−0.745836	−	7.09615i	−0.0312671	−	0.297486i	0.967702	−	0.252096i	$-0.0811198\pi$
$570$	31.6830	−	6.73444i	1.32706	−	0.282075i
$571$	−16.2420	−	28.1319i	−0.679705	−	1.17728i	−0.975070	−	0.221899i	$-0.928775\pi$
$571$	−16.2420	−	28.1319i	−0.679705	−	1.17728i	0.295365	−	0.955385i	$-0.404559\pi$
$572$	−0.171987	−	0.129397i	−0.00719116	−	0.00541038i
$573$	−20.7831			−0.868226
$574$		0			0
$575$	−0.958373	+	0.696299i	−0.0399669	+	0.0290377i
$576$	12.3642	−	5.50489i	0.515174	−	0.229370i
$577$	−23.2736	+	25.8480i	−0.968894	+	1.07607i	0.0281785	+	0.999603i	$0.491029\pi$
$577$	−23.2736	+	25.8480i	−0.968894	+	1.07607i	−0.997072	+	0.0764628i	$0.975637\pi$
$578$	−12.1864	+	13.5344i	−0.506888	+	0.562956i
$579$	−2.94043	+	1.30916i	−0.122200	+	0.0544069i
$580$	−0.0242587	+	0.0176249i	−0.00100729	+	0.000731836i
$581$		0			0
$582$	7.35135			0.304723
$583$	−33.6422	−	0.561706i	−1.39332	−	0.0232635i
$584$	8.53540	+	14.7837i	0.353197	+	0.611756i
$585$	−13.9871	+	2.97305i	−0.578296	+	0.122921i
$586$	3.53987	+	33.6796i	0.146231	+	1.39129i
$587$	−11.7105	−	8.50816i	−0.483343	−	0.351169i	0.319276	−	0.947662i	$-0.396560\pi$
$587$	−11.7105	−	8.50816i	−0.483343	−	0.351169i	−0.802618	+	0.596493i	$0.796560\pi$
$588$		0			0
$589$	2.34456	+	7.21581i	0.0966059	+	0.297322i
$590$	−18.1097	+	8.06294i	−0.745563	+	0.331946i
$591$	−27.7546	−	12.3571i	−1.14167	−	0.508304i
$592$	8.13823	−	1.72983i	0.334479	−	0.0710957i
$593$	−7.51453	+	13.0155i	−0.308585	+	0.534484i	−0.978053	−	0.208356i	$-0.933189\pi$
$593$	−7.51453	+	13.0155i	−0.308585	+	0.534484i	0.669468	+	0.742841i	$0.266522\pi$
$594$	−9.09400	+	9.76696i	−0.373131	+	0.400743i
$595$		0			0
$596$	0.0138706	−	0.0426894i	0.000568163	−	0.00174863i
$597$	−0.969505	−	9.22422i	−0.0396792	−	0.377522i
$598$	−0.492660	+	4.68734i	−0.0201463	+	0.191680i
$599$	1.17797	−	1.30827i	0.0481307	−	0.0534545i	−0.718599	−	0.695425i	$-0.755216\pi$
$599$	1.17797	−	1.30827i	0.0481307	−	0.0534545i	0.766729	+	0.641970i	$0.221883\pi$
$600$	9.88596	+	2.10133i	0.403593	+	0.0857863i
$601$	18.9605	+	13.7756i	0.773415	+	0.561919i	0.902995	−	0.429650i	$-0.141363\pi$
$601$	18.9605	+	13.7756i	0.773415	+	0.561919i	−0.129581	+	0.991569i	$0.541363\pi$
$602$		0			0
$603$	−8.03085	+	24.7164i	−0.327042	+	1.00653i
$604$	0.155474	−	0.269289i	0.00632615	−	0.0109572i
$605$	−15.8935	−	12.3786i	−0.646161	−	0.503260i
$606$	−18.1340	−	31.4089i	−0.736642	−	1.27590i
$607$	16.9146	+	18.7856i	0.686544	+	0.762484i	0.981174	−	0.193127i	$-0.0618631\pi$
$607$	16.9146	+	18.7856i	0.686544	+	0.762484i	−0.294630	+	0.955611i	$0.595196\pi$
$608$	0.370738	−	0.269357i	0.0150354	−	0.0109239i
$609$		0			0
$610$	−5.00550	−	15.4053i	−0.202667	−	0.623744i
$611$	27.1632	+	5.77372i	1.09891	+	0.233580i
$612$	0.0134162	−	0.127647i	0.000542319	−	0.00515982i
$613$	1.06057	+	0.472198i	0.0428362	+	0.0190719i	0.428043	−	0.903758i	$-0.359203\pi$
$613$	1.06057	+	0.472198i	0.0428362	+	0.0190719i	−0.385207	+	0.922830i	$0.625870\pi$
$614$	−5.15150	−	5.72132i	−0.207898	−	0.230894i
$615$	3.63174			0.146446
$616$		0			0
$617$	12.9711			0.522197			0.261098	−	0.965312i	$-0.415915\pi$
$617$	12.9711			0.522197			0.261098	+	0.965312i	$0.415915\pi$
$618$	0.808494	+	0.897923i	0.0325224	+	0.0361198i
$619$	−41.8330	−	18.6253i	−1.68141	−	0.748613i	−0.999858	−	0.0168441i	$-0.994638\pi$
$619$	−41.8330	−	18.6253i	−1.68141	−	0.748613i	−0.681553	−	0.731768i	$-0.738695\pi$
$620$	0.00349626	−	0.0332647i	0.000140413	−	0.00133594i
$621$	−2.00993	−	0.427223i	−0.0806556	−	0.0171439i
$622$	6.04824	+	18.6146i	0.242512	+	0.746377i
$623$		0			0
$624$	32.3046	−	23.4707i	1.29322	−	0.939578i
$625$	−9.40830	−	10.4490i	−0.376332	−	0.417959i
$626$	−19.3412	−	33.4999i	−0.773029	−	1.33893i
$627$	21.4110	−	35.6951i	0.855071	−	1.42553i
$628$	−0.0925483	+	0.160298i	−0.00369308	+	0.00639660i
$629$	3.54092	−	10.8978i	0.141186	−	0.434525i
$630$		0			0
$631$	10.2103	+	7.41824i	0.406467	+	0.295316i	0.772170	−	0.635416i	$-0.219171\pi$
$631$	10.2103	+	7.41824i	0.406467	+	0.295316i	−0.365703	+	0.930732i	$0.619171\pi$
$632$	43.4223	+	9.22969i	1.72725	+	0.367137i
$633$	−2.10663	+	2.33965i	−0.0837310	+	0.0929927i
$634$	1.15279	−	10.9681i	0.0457833	−	0.435599i
$635$	−0.963453	−	9.16664i	−0.0382335	−	0.363767i
$636$	−0.0947088	+	0.291484i	−0.00375545	+	0.0115581i
$637$		0			0
$638$	0.663738	−	5.43981i	0.0262776	−	0.215364i
$639$	−11.6791	+	20.2288i	−0.462019	+	0.800240i
$640$	20.0521	−	4.26221i	0.792630	−	0.168479i
$641$	25.5397	+	11.3710i	1.00876	+	0.449129i	0.843504	−	0.537122i	$-0.180489\pi$
$641$	25.5397	+	11.3710i	1.00876	+	0.449129i	0.165255	+	0.986251i	$0.447155\pi$
$642$	9.10581	−	4.05417i	0.359378	−	0.160005i
$643$	15.3575	+	47.2657i	0.605642	+	1.86398i	0.492313	+	0.870418i	$0.336152\pi$
$643$	15.3575	+	47.2657i	0.605642	+	1.86398i	0.113330	+	0.993557i	$0.463848\pi$
$644$		0			0
$645$	−25.7188	−	18.6858i	−1.01268	−	0.735752i
$646$	4.67464	+	44.4763i	0.183921	+	1.74989i
$647$	−10.7662	+	2.28842i	−0.423262	+	0.0899671i	−0.414618	−	0.909996i	$-0.636085\pi$
$647$	−10.7662	+	2.28842i	−0.423262	+	0.0899671i	−0.00864379	+	0.999963i	$0.502751\pi$
$648$	15.9189	+	27.5723i	0.625352	+	1.08314i
$649$	−8.27537	+	24.0928i	−0.324837	+	0.945723i
$650$	10.7797			0.422816
$651$		0			0
$652$	0.154983	−	0.112602i	0.00606962	−	0.00440984i
$653$	26.4347	−	11.7695i	1.03447	−	0.460576i	0.181971	−	0.983304i	$-0.441752\pi$
$653$	26.4347	−	11.7695i	1.03447	−	0.460576i	0.852500	+	0.522728i	$0.175086\pi$
$654$	5.80672	−	6.44902i	0.227061	−	0.252177i
$655$	0.220644	−	0.245049i	0.00862126	−	0.00957487i
$656$	−3.32604	+	1.48085i	−0.129860	+	0.0578174i
$657$	8.17583	−	5.94009i	0.318969	−	0.231745i
$658$		0			0
$659$	10.8405			0.422288			0.211144	−	0.977455i	$-0.432281\pi$
$659$	10.8405			0.422288			0.211144	+	0.977455i	$0.432281\pi$
$660$	−0.150234	+	0.105365i	−0.00584786	+	0.00410133i
$661$	10.1722	+	17.6187i	0.395652	+	0.685290i	0.993184	−	0.116555i	$-0.0371852\pi$
$661$	10.1722	+	17.6187i	0.395652	+	0.685290i	−0.597532	+	0.801845i	$0.703852\pi$
$662$	−38.7987	+	8.24692i	−1.50795	+	0.320526i
$663$	−5.74844	−	54.6927i	−0.223251	−	2.12409i
$664$	−10.0474	−	7.29986i	−0.389915	−	0.283289i
$665$		0			0
$666$	−1.53275	−	4.71732i	−0.0593929	−	0.182792i
$667$	0.770858	−	0.343208i	0.0298477	−	0.0132891i
$668$	0.118752	+	0.0528717i	0.00459464	+	0.00204567i
$669$	−10.2767	+	2.18438i	−0.397321	+	0.0844531i
$670$	−19.9598	+	34.5715i	−0.771116	+	1.33561i
$671$	−18.8720	−	8.78272i	−0.728544	−	0.339053i
$672$		0			0
$673$	−3.73255	+	11.4876i	−0.143879	+	0.442815i	−0.996865	−	0.0791188i	$-0.974789\pi$
$673$	−3.73255	+	11.4876i	−0.143879	+	0.442815i	0.852986	+	0.521934i	$0.174789\pi$
$674$	−3.67961	−	35.0092i	−0.141733	−	1.34850i
$675$	−0.491254	+	4.67397i	−0.0189084	+	0.179901i
$676$	−0.0803137	+	0.0891974i	−0.00308899	+	0.00343067i
$677$	3.32208	+	0.706130i	0.127678	+	0.0271388i	0.271307	−	0.962493i	$-0.412544\pi$
$677$	3.32208	+	0.706130i	0.127678	+	0.0271388i	−0.143629	+	0.989632i	$0.545877\pi$
$678$	35.8743	+	26.0642i	1.37775	+	1.00099i
$679$		0			0
$680$	8.78642	−	27.0418i	0.336944	−	1.03701i
$681$	0.429587	−	0.744066i	0.0164618	−	0.0285127i
$682$	4.01397	+	4.61048i	0.153703	+	0.176544i
$683$	2.37821	+	4.11919i	0.0909999	+	0.157616i	0.907932	−	0.419117i	$-0.137660\pi$
$683$	2.37821	+	4.11919i	0.0909999	+	0.157616i	−0.816932	+	0.576734i	$0.804327\pi$
$684$	−0.0910790	−	0.101154i	−0.00348249	−	0.00386770i
$685$	−12.3330	+	8.96042i	−0.471218	+	0.342360i
$686$		0			0
$687$	−1.46382	−	4.50516i	−0.0558481	−	0.171883i
$688$	31.1731	+	6.62604i	1.18846	+	0.252615i
$689$	−4.92790	+	46.8858i	−0.187738	+	1.78621i
$690$	3.67094	+	1.63441i	0.139750	+	0.0622209i
$691$	−4.43893	−	4.92994i	−0.168865	−	0.187544i	0.652772	−	0.757554i	$-0.273606\pi$
$691$	−4.43893	−	4.92994i	−0.168865	−	0.187544i	−0.821637	+	0.570010i	$0.806939\pi$
$692$	0.146707			0.00557695
$693$		0			0
$694$	−29.1003			−1.10463
$695$	8.53050	+	9.47408i	0.323580	+	0.359372i
$696$	−6.57676	−	2.92816i	−0.249291	−	0.110992i
$697$	−0.524131	+	4.98678i	−0.0198529	+	0.188888i
$698$	8.26699	+	1.75720i	0.312910	+	0.0665111i
$699$	−0.842441	−	2.59277i	−0.0318641	−	0.0980675i
$700$		0			0
$701$	−2.45134	+	1.78101i	−0.0925860	+	0.0672677i	−0.633115	−	0.774058i	$-0.718224\pi$
$701$	−2.45134	+	1.78101i	−0.0925860	+	0.0672677i	0.540529	+	0.841325i	$0.318224\pi$
$702$	12.5117	+	13.8957i	0.472225	+	0.524459i
$703$	−6.07597	−	10.5239i	−0.229160	−	0.396916i
$704$	13.7422	−	22.9102i	0.517929	−	0.863461i
$705$	11.8381	−	20.5042i	0.445848	−	0.772232i
$706$	10.4683	−	32.2182i	0.393981	−	1.21255i
$707$		0			0
$708$	0.187726	+	0.136391i	0.00705516	+	0.00512587i
$709$	13.3586	+	2.83946i	0.501693	+	0.106638i	0.451805	−	0.892117i	$-0.350780\pi$
$709$	13.3586	+	2.83946i	0.501693	+	0.106638i	0.0498880	+	0.998755i	$0.484114\pi$
$710$	−24.0082	+	26.6638i	−0.901010	+	1.00067i
$711$	2.74703	−	26.1362i	0.103022	−	0.980185i
$712$	4.55208	+	43.3102i	0.170597	+	1.62312i
$713$	−0.290862	+	0.895180i	−0.0108928	+	0.0335247i
$714$		0			0
$715$	−19.2346	+	20.6580i	−0.719335	+	0.772566i
$716$	−0.0581155	+	0.100659i	−0.00217188	+	0.00376180i
$717$	23.6192	−	5.02043i	0.882077	−	0.187491i
$718$	14.0975	+	6.27662i	0.526115	+	0.234241i
$719$	1.73600	−	0.772918i	0.0647419	−	0.0288250i	−0.374110	−	0.927384i	$-0.622052\pi$
$719$	1.73600	−	0.772918i	0.0647419	−	0.0288250i	0.438852	+	0.898559i	$0.355385\pi$
$720$	−3.77680	−	11.6238i	−0.140753	−	0.433193i
$721$		0			0
$722$	16.7069	+	12.1383i	0.621768	+	0.451741i
$723$	−4.85835	−	46.2241i	−0.180684	−	1.71909i
$724$	0.202199	−	0.0429787i	0.00751466	−	0.00159729i
$725$	−0.964960	−	1.67136i	−0.0358377	−	0.0620727i
$726$	4.61702	−	33.2173i	0.171354	−	1.23281i
$727$	13.8211			0.512595			0.256298	−	0.966598i	$-0.417497\pi$
$727$	13.8211			0.512595			0.256298	+	0.966598i	$0.417497\pi$
$728$		0			0
$729$	0.256684	−	0.186492i	0.00950682	−	0.00690711i
$730$	14.1812	−	6.31386i	0.524869	−	0.233687i
$731$	29.3694	−	32.6180i	1.08627	−	1.20642i
$732$	−0.126871	+	0.140904i	−0.00468928	+	0.00520797i
$733$	−44.1922	+	19.6756i	−1.63228	+	0.726736i	−0.998890	−	0.0471006i	$-0.985002\pi$
$733$	−44.1922	+	19.6756i	−1.63228	+	0.726736i	−0.633385	+	0.773837i	$0.718335\pi$
$734$	−12.1055	+	8.79519i	−0.446824	+	0.324636i
$735$		0			0
$736$	0.0568504			0.00209553
$737$	15.0356	+	49.0462i	0.553844	+	1.80664i
$738$	1.08525	+	1.87971i	0.0399487	+	0.0691931i
$739$	−22.7009	+	4.82523i	−0.835068	+	0.177499i	−0.605552	−	0.795806i	$-0.707048\pi$
$739$	−22.7009	+	4.82523i	−0.835068	+	0.177499i	−0.229516	+	0.973305i	$0.573714\pi$
$740$	0.00559977	+	0.0532783i	0.000205852	+	0.00195855i
$741$	−47.1829	−	34.2804i	−1.73331	−	1.25932i
$742$		0			0
$743$	−13.8536	−	42.6369i	−0.508238	−	1.56420i	−0.795257	−	0.606272i	$-0.792664\pi$
$743$	−13.8536	−	42.6369i	−0.508238	−	1.56420i	0.287019	−	0.957925i	$-0.407336\pi$
$744$	7.33621	−	3.26629i	0.268958	−	0.119748i
$745$	−5.37772	−	2.39432i	−0.197024	−	0.0877209i
$746$	50.4570	−	10.7250i	1.84736	−	0.392669i
$747$	−3.67609	+	6.36717i	−0.134501	+	0.232963i
$748$	−0.122996	−	0.221495i	−0.00449718	−	0.00809864i
$749$		0			0
$750$	11.4670	−	35.2919i	0.418717	−	1.28868i
$751$	4.30507	+	40.9600i	0.157094	+	1.49465i	0.734732	+	0.678358i	$0.237308\pi$
$751$	4.30507	+	40.9600i	0.157094	+	1.49465i	−0.577638	+	0.816293i	$0.696025\pi$
$752$	−2.48101	+	23.6053i	−0.0904732	+	0.860795i
$753$	0.613515	−	0.681377i	0.0223577	−	0.0248308i
$754$	−7.51068	−	1.59644i	−0.273523	−	0.0581390i
$755$	−32.9913	−	23.9696i	−1.20068	−	0.872343i
$756$		0			0
$757$	−6.76401	+	20.8175i	−0.245842	+	0.756624i	0.749655	+	0.661829i	$0.230219\pi$
$757$	−6.76401	+	20.8175i	−0.245842	+	0.756624i	−0.995497	+	0.0947948i	$0.969781\pi$
$758$	−8.91910	+	15.4483i	−0.323956	+	0.561109i
$759$	4.75178	−	2.02127i	0.172479	−	0.0733673i
$760$	−15.0769	−	26.1139i	−0.546896	−	0.947251i
$761$	23.8982	+	26.5417i	0.866310	+	0.962135i	0.999581	−	0.0289445i	$-0.00921461\pi$
$761$	23.8982	+	26.5417i	0.866310	+	0.962135i	−0.133271	+	0.991080i	$0.542548\pi$
$762$	12.4137	−	9.01906i	0.449700	−	0.326726i
$763$		0			0
$764$	0.0414558	+	0.127588i	0.00149982	+	0.00461596i
$765$	−16.4647	−	3.49968i	−0.595283	−	0.126531i
$766$	2.27855	−	21.6790i	0.0823274	−	0.783293i
$767$	32.6073	+	14.5177i	1.17738	+	0.524204i
$768$	−0.485132	−	0.538794i	−0.0175057	−	0.0194420i
$769$	−5.30246			−0.191212			−0.0956058	−	0.995419i	$-0.530479\pi$
$769$	−5.30246			−0.191212			−0.0956058	+	0.995419i	$0.530479\pi$
$770$		0			0
$771$	−37.7295			−1.35880
$772$	0.0139022	+	0.0154400i	0.000500351	+	0.000555696i
$773$	45.5779	+	20.2926i	1.63932	+	0.729874i	0.999261	−	0.0384496i	$-0.0122419\pi$
$773$	45.5779	+	20.2926i	1.63932	+	0.729874i	0.640062	+	0.768323i	$0.278909\pi$
$774$	1.98597	−	18.8953i	0.0713843	−	0.679176i
$775$	2.10573	+	0.447588i	0.0756402	+	0.0160778i
$776$	−2.11479	−	6.50867i	−0.0759167	−	0.233648i
$777$		0			0
$778$	−14.4943	+	10.5307i	−0.519646	+	0.377545i
$779$	3.55818	+	3.95176i	0.127485	+	0.141587i
$780$	0.128554	+	0.222663i	0.00460298	+	0.00797260i
$781$	4.05336	+	45.9289i	0.145041	+	1.64347i
$782$	−2.77401	+	4.80473i	−0.0991986	+	0.171817i
$783$	1.03448	−	3.18379i	0.0369692	−	0.113779i
$784$		0			0
$785$	19.6386	+	14.2683i	0.700931	+	0.509256i
$786$	0.536947	+	0.114132i	0.0191523	+	0.00407094i
$787$	−23.9930	+	26.6469i	−0.855258	+	0.949860i	−0.999211	−	0.0397248i	$-0.987352\pi$
$787$	−23.9930	+	26.6469i	−0.855258	+	0.949860i	0.143953	+	0.989585i	$0.454019\pi$
$788$	−0.0204990	+	0.195035i	−0.000730245	+	0.00694782i
$789$	−0.342638	−	3.25998i	−0.0121982	−	0.116058i
$790$	12.4744	−	38.3922i	0.443818	−	1.36593i
$791$		0			0
$792$	−14.3396	−	6.67342i	−0.509535	−	0.237130i
$793$	−14.5828	+	25.2581i	−0.517849	+	0.896940i
$794$	26.1322	−	5.55458i	0.927399	−	0.197125i
$795$	36.7191	+	16.3484i	1.30229	+	0.579818i
$796$	−0.0546938	+	0.0243513i	−0.00193857	+	0.000863108i
$797$	−4.55530	−	14.0198i	−0.161357	−	0.496606i	0.837392	−	0.546602i	$-0.184079\pi$
$797$	−4.55530	−	14.0198i	−0.161357	−	0.496606i	−0.998749	+	0.0499962i	$0.984079\pi$
$798$		0			0
$799$	26.4460	+	19.2142i	0.935593	+	0.679748i
$800$	−0.0135914	−	0.129313i	−0.000480528	−	0.00457192i
$801$	25.2174	−	5.36013i	0.891013	−	0.189391i
$802$	−6.11769	−	10.5962i	−0.216023	−	0.374163i
$803$	6.48021	−	18.8664i	0.228682	−	0.665779i
$804$	0.467275			0.0164795
$805$		0			0
$806$	6.92934	−	5.03446i	0.244076	−	0.177331i
$807$	4.01402	−	1.78715i	0.141300	−	0.0629108i
$808$	−22.5919	+	25.0908i	−0.794780	+	0.882692i
$809$	−18.0504	+	20.0470i	−0.634617	+	0.704814i	−0.971582	−	0.236704i	$-0.923933\pi$
$809$	−18.0504	+	20.0470i	−0.634617	+	0.704814i	0.336965	+	0.941517i	$0.390600\pi$
$810$	26.4485	−	11.7756i	0.929305	−	0.413753i
$811$	1.18472	−	0.860750i	0.0416012	−	0.0302250i	−0.566790	−	0.823862i	$-0.691815\pi$
$811$	1.18472	−	0.860750i	0.0416012	−	0.0302250i	0.608392	+	0.793637i	$0.291815\pi$
$812$		0			0
$813$	−16.4513			−0.576972
$814$	−7.82377	−	5.88634i	−0.274223	−	0.206316i
$815$	−12.5618	−	21.7577i	−0.440021	−	0.762138i
$816$	45.9767	−	9.77264i	1.60950	−	0.342111i
$817$	−4.86553	−	46.2924i	−0.170223	−	1.61957i
$818$	−6.51473	−	4.73323i	−0.227782	−	0.165493i
$819$		0			0
$820$	−0.00724418	−	0.0222953i	−0.000252978	−	0.000778586i
$821$	27.9807	−	12.4578i	0.976533	−	0.434780i	0.144499	−	0.989505i	$-0.453843\pi$
$821$	27.9807	−	12.4578i	0.976533	−	0.434780i	0.832034	+	0.554725i	$0.187176\pi$
$822$	−23.1839	−	10.3221i	−0.808631	−	0.360026i
$823$	23.9977	−	5.10087i	0.836507	−	0.177805i	0.230308	−	0.973118i	$-0.426027\pi$
$823$	23.9977	−	5.10087i	0.836507	−	0.177805i	0.606199	+	0.795313i	$0.292693\pi$
$824$	0.562412	−	0.974126i	0.0195925	−	0.0339353i
$825$	−5.73364	−	10.3253i	−0.199620	−	0.359480i
$826$		0			0
$827$	−2.02927	+	6.24545i	−0.0705646	+	0.217176i	−0.980119	−	0.198408i	$-0.936423\pi$
$827$	−2.02927	+	6.24545i	−0.0705646	+	0.217176i	0.909555	+	0.415584i	$0.136423\pi$
$828$	−0.00176509	−	0.0167937i	−6.13411e−5	−	0.000583622i
$829$	−2.07429	+	19.7355i	−0.0720430	+	0.685443i	0.897582	+	0.440847i	$0.145322\pi$
$829$	−2.07429	+	19.7355i	−0.0720430	+	0.685443i	−0.969625	+	0.244596i	$0.921345\pi$
$830$	−7.55675	+	8.39262i	−0.262299	+	0.291312i
$831$	−30.5287	−	6.48907i	−1.05903	−	0.225103i
$832$	−30.2834	−	22.0022i	−1.04989	−	0.762789i
$833$		0			0
$834$	−6.55832	+	20.1844i	−0.227096	+	0.698930i
$835$	8.52382	−	14.7637i	0.294979	−	0.510918i
$836$	−0.261841	−	0.0602417i	−0.00905597	−	0.00208350i
$837$	1.86710	+	3.23392i	0.0645365	+	0.111781i
$838$	−25.6406	−	28.4768i	−0.885740	−	0.983714i
$839$	−6.44019	+	4.67907i	−0.222340	+	0.161539i	−0.693379	−	0.720573i	$-0.743879\pi$
$839$	−6.44019	+	4.67907i	−0.222340	+	0.161539i	0.471039	+	0.882112i	$0.343879\pi$
$840$		0			0
$841$	−8.53669	−	26.2732i	−0.294369	−	0.905973i
$842$	−33.0352	−	7.02184i	−1.13847	−	0.241989i
$843$	−4.01381	+	38.1889i	−0.138243	+	1.31530i
$844$	0.0185652	+	0.00826577i	0.000639041	+	0.000284519i
$845$	10.5328	+	11.6979i	0.362339	+	0.402418i
$846$	14.1500			0.486489
$847$		0			0
$848$	−40.2944			−1.38372
$849$	45.0722	+	50.0577i	1.54687	+	1.71798i
$850$	11.5922	+	5.16116i	0.397608	+	0.177026i
$851$	0.157582	−	1.49929i	0.00540183	−	0.0513949i
$852$	0.410807	+	0.0873197i	0.0140740	+	0.00299152i
$853$	−10.5292	−	32.4055i	−0.360513	−	1.10954i	−0.952744	−	0.303776i	$-0.901753\pi$
$853$	−10.5292	−	32.4055i	−0.360513	−	1.10954i	0.592231	−	0.805768i	$-0.298247\pi$
$854$		0			0
$855$	−14.4417	+	10.4925i	−0.493897	+	0.358837i
$856$	−6.20895	−	6.89574i	−0.212217	−	0.235691i
$857$	12.4269	+	21.5241i	0.424496	+	0.735249i	0.996373	−	0.0850904i	$-0.0271179\pi$
$857$	12.4269	+	21.5241i	0.424496	+	0.735249i	−0.571877	+	0.820339i	$0.693785\pi$
$858$	−45.7932	−	10.5356i	−1.56335	−	0.359680i
$859$	1.02827	−	1.78102i	0.0350841	−	0.0607675i	−0.847950	−	0.530076i	$-0.822163\pi$
$859$	1.02827	−	1.78102i	0.0350841	−	0.0607675i	0.883034	+	0.469308i	$0.155497\pi$
$860$	−0.0634115	+	0.195160i	−0.00216231	+	0.00665491i
$861$		0			0
$862$	18.7814	+	13.6455i	0.639697	+	0.464767i
$863$	0.253805	+	0.0539480i	0.00863964	+	0.00183641i	0.212229	−	0.977220i	$-0.431928\pi$
$863$	0.253805	+	0.0539480i	0.00863964	+	0.00183641i	−0.203590	+	0.979056i	$0.565261\pi$
$864$	0.150917	−	0.167611i	0.00513431	−	0.00570223i
$865$	2.01112	−	19.1346i	0.0683802	−	0.650595i
$866$	−2.95957	−	28.1584i	−0.100570	−	0.956862i
$867$	8.63946	−	26.5895i	0.293412	−	0.903028i
$868$		0			0
$869$	−25.1840	−	45.3519i	−0.854307	−	1.53846i
$870$	−3.27325	+	5.66944i	−0.110974	+	0.192212i
$871$	70.3066	−	14.9441i	2.38225	−	0.506362i
$872$	−7.38022	−	3.28588i	−0.249926	−	0.111274i
$873$	−3.70115	+	1.64786i	−0.125265	+	0.0557715i
$874$	1.81816	+	5.59573i	0.0615003	+	0.189278i
$875$		0			0
$876$	−0.147003	−	0.106804i	−0.00496676	−	0.00360856i
$877$	−1.94350	−	18.4911i	−0.0656272	−	0.624401i	−0.977062	−	0.212956i	$-0.931691\pi$
$877$	−1.94350	−	18.4911i	−0.0656272	−	0.624401i	0.911435	−	0.411445i	$-0.134976\pi$
$878$	−36.8992	+	7.84316i	−1.24529	+	0.264694i
$879$	−25.9933	−	45.0218i	−0.876734	−	1.51855i
$880$	−19.2783	−	14.5043i	−0.649871	−	0.488941i
$881$	−6.45292			−0.217404			−0.108702	−	0.994074i	$-0.534670\pi$
$881$	−6.45292			−0.217404			−0.108702	+	0.994074i	$0.534670\pi$
$882$		0			0
$883$	0.225301	−	0.163691i	0.00758198	−	0.00550863i	−0.583988	−	0.811762i	$-0.698508\pi$
$883$	0.225301	−	0.163691i	0.00758198	−	0.00550863i	0.591570	+	0.806254i	$0.298508\pi$
$884$	−0.324293	+	0.144385i	−0.0109072	+	0.00485619i
$885$	20.3625	−	22.6148i	0.684477	−	0.760189i
$886$	−24.7206	+	27.4551i	−0.830506	+	0.922371i
$887$	−27.9152	+	12.4286i	−0.937300	+	0.417313i	−0.817788	−	0.575520i	$-0.804800\pi$
$887$	−27.9152	+	12.4286i	−0.937300	+	0.417313i	−0.119512	+	0.992833i	$0.538133\pi$
$888$	−10.4056	+	7.56009i	−0.349188	+	0.253700i
$889$		0			0
$890$	39.6008			1.32742
$891$	12.0859	−	35.1865i	0.404891	−	1.17879i
$892$	0.0339088	+	0.0587318i	0.00113535	+	0.00196649i
$893$	33.9093	−	7.20765i	1.13473	−	0.241195i
$894$	−1.02435	−	9.74606i	−0.0342595	−	0.325957i
$895$	12.3320	+	8.95972i	0.412213	+	0.299491i
$896$		0			0
$897$	−2.23581	−	6.88111i	−0.0746514	−	0.229753i
$898$	−12.5491	+	5.58722i	−0.418769	+	0.186448i
$899$	−1.40087	−	0.623705i	−0.0467215	−	0.0208017i
$900$	−0.0377774	+	0.00802983i	−0.00125925	+	0.000267661i
$901$	−27.7475	+	48.0600i	−0.924402	+	1.60111i
$902$	3.88437	+	1.80773i	0.129335	+	0.0601907i
$903$		0			0
$904$	12.7564	−	39.2601i	0.424271	−	1.30577i
$905$	−2.83376	−	26.9614i	−0.0941974	−	0.896228i
$906$	7.09615	−	67.5154i	0.235754	−	2.24305i
$907$	21.3685	−	23.7321i	0.709529	−	0.788011i	−0.275334	−	0.961349i	$-0.588788\pi$
$907$	21.3685	−	23.7321i	0.709529	−	0.788011i	0.984863	+	0.173337i	$0.0554551\pi$
$908$	−0.00542473	−	0.00115306i	−0.000180026	−	3.82657e-5i
$909$	16.1704	+	11.7484i	0.536337	+	0.389671i
$910$		0			0
$911$	0.865378	−	2.66336i	0.0286713	−	0.0882411i	−0.935697	−	0.352805i	$-0.885228\pi$
$911$	0.865378	−	2.66336i	0.0286713	−	0.0882411i	0.964368	+	0.264564i	$0.0852280\pi$
$912$	24.9238	−	43.1693i	0.825310	−	1.42948i
$913$	1.27583	+	14.4565i	0.0422236	+	0.478439i
$914$	8.37479	+	14.5056i	0.277013	+	0.479801i
$915$	16.6385	+	18.4790i	0.550053	+	0.610896i
$916$	−0.0247374	+	0.0179728i	−0.000817348	+	0.000593838i
$917$		0			0
$918$	6.80167	+	20.9334i	0.224488	+	0.690904i
$919$	15.4879	+	3.29205i	0.510897	+	0.108595i	0.456145	−	0.889905i	$-0.349230\pi$
$919$	15.4879	+	3.29205i	0.510897	+	0.108595i	0.0547522	+	0.998500i	$0.482563\pi$
$920$	0.391022	−	3.72032i	0.0128916	−	0.122655i
$921$	10.7967	+	4.80702i	0.355765	+	0.158397i
$922$	8.62582	+	9.57994i	0.284076	+	0.315499i
$923$	64.6030			2.12643
$924$		0			0
$925$	−3.44799			−0.113369
$926$	−36.7144	−	40.7754i	−1.20651	−	1.33996i
$927$	−0.608324	−	0.270843i	−0.0199800	−	0.00889566i
$928$	−0.00968123	+	0.0921108i	−0.000317802	+	0.00302368i
$929$	−26.8828	−	5.71411i	−0.881995	−	0.187474i	−0.255416	−	0.966831i	$-0.582212\pi$
$929$	−26.8828	−	5.71411i	−0.881995	−	0.187474i	−0.626580	+	0.779357i	$0.715546\pi$
$930$	−2.25659	−	6.94506i	−0.0739964	−	0.227737i
$931$		0			0
$932$	−0.0142366	+	0.0103435i	−0.000466337	+	0.000338814i
$933$	−20.1047	−	22.3285i	−0.658198	−	0.731003i
$934$	14.6447	+	25.3654i	0.479189	+	0.829980i
$935$	−30.5750	+	13.0057i	−0.999910	+	0.425332i
$936$	−11.0805	+	19.1920i	−0.362177	+	0.627309i
$937$	3.80357	−	11.7062i	0.124257	−	0.382425i	−0.869508	−	0.493919i	$-0.835564\pi$
$937$	3.80357	−	11.7062i	0.124257	−	0.382425i	0.993765	+	0.111495i	$0.0355638\pi$
$938$		0			0
$939$	48.0408	+	34.9037i	1.56775	+	1.13904i
$940$	−0.149489	−	0.0317748i	−0.00487579	−	0.00103638i
$941$	−0.977023	+	1.08509i	−0.0318500	+	0.0353731i	−0.758859	−	0.651255i	$-0.774243\pi$
$941$	−0.977023	+	1.08509i	−0.0318500	+	0.0353731i	0.727009	+	0.686628i	$0.240910\pi$
$942$	−4.22409	+	40.1896i	−0.137628	+	1.30945i
$943$	0.0689567	+	0.656080i	0.00224554	+	0.0213649i
$944$	−9.42725	+	29.0141i	−0.306831	+	0.944328i
$945$		0			0
$946$	−18.2068	−	32.7873i	−0.591955	−	1.06601i
$947$	−5.53568	+	9.58807i	−0.179885	+	0.311571i	−0.941841	−	0.336059i	$-0.890906\pi$
$947$	−5.53568	+	9.58807i	−0.179885	+	0.311571i	0.761956	+	0.647629i	$0.224239\pi$
$948$	−0.462196	+	0.0982428i	−0.0150114	+	0.00319078i
$949$	−25.5339	−	11.3684i	−0.828864	−	0.369034i
$950$	12.2935	−	5.47342i	0.398854	−	0.177581i
$951$	5.23165	+	16.1014i	0.169648	+	0.522123i
$952$		0			0
$953$	11.9924	+	8.71296i	0.388471	+	0.282240i	0.764828	−	0.644234i	$-0.222824\pi$
$953$	11.9924	+	8.71296i	0.388471	+	0.282240i	−0.376358	+	0.926474i	$0.622824\pi$
$954$	2.51098	+	23.8904i	0.0812959	+	0.773479i
$955$	17.2092	−	3.65793i	0.556877	−	0.118368i
$956$	−0.0779335	−	0.134985i	−0.00252055	−	0.00436572i
$957$	2.46572	+	8.04318i	0.0797054	+	0.259999i
$958$	−34.5782			−1.11717
$959$		0			0
$960$	−25.8191	+	18.7586i	−0.833306	+	0.605432i
$961$	−26.7573	+	11.9131i	−0.863138	+	0.384294i
$962$	−9.17936	+	10.1947i	−0.295954	+	0.328691i
$963$	−3.67569	+	4.08226i	−0.118447	+	0.131549i
$964$	−0.274080	+	0.122028i	−0.00882751	+	0.00393026i
$965$	2.20437	−	1.60157i	0.0709612	−	0.0515563i
$966$		0			0
$967$	16.5193			0.531224			0.265612	−	0.964080i	$-0.414426\pi$
$967$	16.5193			0.531224			0.265612	+	0.964080i	$0.414426\pi$
$968$	−30.7378	+	5.46799i	−0.987950	+	0.175748i
$969$	−34.3260	−	59.4544i	−1.10271	−	1.90995i
$970$	−6.08721	+	1.29388i	−0.195449	+	0.0415439i
$971$	4.26469	+	40.5758i	0.136860	+	1.30214i	0.820216	+	0.572054i	$0.193853\pi$
$971$	4.26469	+	40.5758i	0.136860	+	1.30214i	−0.683355	+	0.730086i	$0.739480\pi$
$972$	−0.177396	−	0.128886i	−0.00568998	−	0.00413401i
$973$		0			0
$974$	5.38755	+	16.5812i	0.172628	+	0.531296i
$975$	−15.1174	+	6.73070i	−0.484144	+	0.215555i
$976$	−22.7728	−	10.1391i	−0.728941	−	0.324546i
$977$	−48.0412	+	10.2115i	−1.53697	+	0.326694i	−0.897115	−	0.441798i	$-0.854341\pi$
$977$	−48.0412	+	10.2115i	−1.53697	+	0.326694i	−0.639860	+	0.768492i	$0.721008\pi$
$978$	20.9121	−	36.2209i	0.668696	−	1.15822i
$979$	34.6782	−	37.2444i	1.10832	−	1.19034i
$980$		0			0
$981$	−1.47789	+	4.54847i	−0.0471853	+	0.145222i
$982$	2.43429	+	23.1607i	0.0776812	+	0.739087i
$983$	0.115691	−	1.10073i	0.00368997	−	0.0351077i	−0.992522	−	0.122066i	$-0.961048\pi$
$983$	0.115691	−	1.10073i	0.00368997	−	0.0351077i	0.996212	+	0.0869583i	$0.0277147\pi$
$984$	3.76609	−	4.18267i	0.120059	−	0.133338i
$985$	25.1568	+	5.34725i	0.801563	+	0.170377i
$986$	−7.31238	−	5.31275i	−0.232874	−	0.169193i
$987$		0			0
$988$	−0.116333	+	0.358036i	−0.00370104	+	0.0113906i
$989$	2.88729	−	5.00093i	0.0918105	−	0.159020i
$990$	−7.39820	+	12.3339i	−0.235130	+	0.391996i
$991$	−20.8926	−	36.1870i	−0.663674	−	1.14952i	−0.979643	−	0.200747i	$-0.935663\pi$
$991$	−20.8926	−	36.1870i	−0.663674	−	1.14952i	0.315969	−	0.948769i	$-0.397670\pi$
$992$	−0.0691300	−	0.0767767i	−0.00219488	−	0.00243766i
$993$	49.2618	−	35.7908i	1.56328	−	1.13579i
$994$		0			0
$995$	2.42630	+	7.46739i	0.0769189	+	0.236732i
$996$	0.129305	+	0.0274845i	0.00409717	+	0.000870881i
$997$	4.61958	−	43.9524i	0.146304	−	1.39199i	−0.637248	−	0.770659i	$-0.719927\pi$
$997$	4.61958	−	43.9524i	0.146304	−	1.39199i	0.783551	−	0.621327i	$-0.213406\pi$
$998$	17.6905	+	7.87632i	0.559983	+	0.249321i
$999$	−4.00199	−	4.44466i	−0.126617	−	0.140623i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.f.471.2		32
7.2	even	3		539.2.f.e.295.2		16
7.3	odd	6		539.2.q.g.361.3		32
7.4	even	3	inner	539.2.q.f.361.3		32
7.5	odd	6		77.2.f.b.64.2	✓	16
7.6	odd	2		539.2.q.g.471.2		32
11.5	even	5	inner	539.2.q.f.324.3		32
21.5	even	6		693.2.m.i.64.3		16
77.5	odd	30		77.2.f.b.71.2	yes	16
77.16	even	15		539.2.f.e.148.2		16
77.19	even	30		847.2.f.v.323.2		16
77.26	odd	30		847.2.a.p.1.3		8
77.27	odd	10		539.2.q.g.324.3		32
77.37	even	15		5929.2.a.bt.1.3		8
77.38	odd	30		539.2.q.g.214.2		32
77.40	even	30		847.2.a.o.1.6		8
77.47	odd	30		847.2.f.w.323.3		16
77.51	odd	30		5929.2.a.bs.1.6		8
77.54	even	6		847.2.f.x.372.3		16
77.60	even	15	inner	539.2.q.f.214.2		32
77.61	even	30		847.2.f.x.148.3		16
77.68	even	30		847.2.f.v.729.2		16
77.75	odd	30		847.2.f.w.729.3		16
231.5	even	30		693.2.m.i.379.3		16
231.26	even	30		7623.2.a.ct.1.6		8
231.194	odd	30		7623.2.a.cw.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.2	✓	16	7.5	odd	6
77.2.f.b.71.2	yes	16	77.5	odd	30
539.2.f.e.148.2		16	77.16	even	15
539.2.f.e.295.2		16	7.2	even	3
539.2.q.f.214.2		32	77.60	even	15	inner
539.2.q.f.324.3		32	11.5	even	5	inner
539.2.q.f.361.3		32	7.4	even	3	inner
539.2.q.f.471.2		32	1.1	even	1	trivial
539.2.q.g.214.2		32	77.38	odd	30
539.2.q.g.324.3		32	77.27	odd	10
539.2.q.g.361.3		32	7.3	odd	6
539.2.q.g.471.2		32	7.6	odd	2
693.2.m.i.64.3		16	21.5	even	6
693.2.m.i.379.3		16	231.5	even	30
847.2.a.o.1.6		8	77.40	even	30
847.2.a.p.1.3		8	77.26	odd	30
847.2.f.v.323.2		16	77.19	even	30
847.2.f.v.729.2		16	77.68	even	30
847.2.f.w.323.3		16	77.47	odd	30
847.2.f.w.729.3		16	77.75	odd	30
847.2.f.x.148.3		16	77.61	even	30
847.2.f.x.372.3		16	77.54	even	6
5929.2.a.bs.1.6		8	77.51	odd	30
5929.2.a.bt.1.3		8	77.37	even	15
7623.2.a.ct.1.6		8	231.26	even	30
7623.2.a.cw.1.3		8	231.194	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)

\(f(q)\)	\(=\)	\(q+(-0.942984 - 1.04729i) q^{2} +(1.97635 + 0.879926i) q^{3} +(0.00145969 - 0.0138880i) q^{4} +(-1.79137 - 0.380767i) q^{5} +(-0.942126 - 2.89957i) q^{6} +(-2.29616 + 1.66826i) q^{8} +(1.12429 + 1.24865i) q^{9} +O(q^{10})\)	\(q+(-0.942984 - 1.04729i) q^{2} +(1.97635 + 0.879926i) q^{3} +(0.00145969 - 0.0138880i) q^{4} +(-1.79137 - 0.380767i) q^{5} +(-0.942126 - 2.89957i) q^{6} +(-2.29616 + 1.66826i) q^{8} +(1.12429 + 1.24865i) q^{9} +(1.29046 + 2.23514i) q^{10} +(3.23218 + 0.743627i) q^{11} +(0.0151053 - 0.0261631i) q^{12} +(1.43602 - 4.41961i) q^{13} +(-3.20531 - 2.32880i) q^{15} +(3.88508 + 0.825799i) q^{16} +(3.66029 - 4.06516i) q^{17} +(0.247511 - 2.35491i) q^{18} +(-0.606388 - 5.76940i) q^{19} +(-0.00790293 + 0.0243227i) q^{20} +(-2.26911 - 4.08626i) q^{22} +(0.359841 - 0.623263i) q^{23} +(-6.00596 + 1.27661i) q^{24} +(-1.50372 - 0.669498i) q^{25} +(-5.98276 + 2.66370i) q^{26} +(-0.882303 - 2.71545i) q^{27} +(0.948551 + 0.689163i) q^{29} +(0.583635 + 5.55291i) q^{30} +(-1.27929 + 0.271920i) q^{31} +(0.0394969 + 0.0684106i) q^{32} +(5.73358 + 4.31375i) q^{33} -7.70900 q^{34} +(0.0189823 - 0.0137915i) q^{36} +(1.91364 - 0.852007i) q^{37} +(-5.47042 + 6.07551i) q^{38} +(6.72701 - 7.47110i) q^{39} +(4.74849 - 2.11416i) q^{40} +(-0.741582 + 0.538791i) q^{41} +8.02379 q^{43} +(0.0150455 - 0.0438032i) q^{44} +(-1.53856 - 2.66487i) q^{45} +(-0.992062 + 0.210869i) q^{46} +(0.624645 + 5.94310i) q^{47} +(6.95163 + 5.05065i) q^{48} +(0.716823 + 2.20615i) q^{50} +(10.8110 - 4.81339i) q^{51} +(-0.0592835 - 0.0263947i) q^{52} +(-9.92324 + 2.10925i) q^{53} +(-2.01186 + 3.48465i) q^{54} +(-5.50688 - 2.56282i) q^{55} +(3.87821 - 11.9359i) q^{57} +(-0.172715 - 1.64328i) q^{58} +(-0.802863 + 7.63873i) q^{59} +(-0.0370211 + 0.0411161i) q^{60} +(-6.13898 - 1.30488i) q^{61} +(1.49113 + 1.08337i) q^{62} +(2.48916 - 7.66083i) q^{64} +(-4.25528 + 7.37036i) q^{65} +(-0.888929 - 10.0725i) q^{66} +(7.73363 + 13.3950i) q^{67} +(-0.0511141 - 0.0567680i) q^{68} +(1.25960 - 0.915151i) q^{69} +(4.29593 + 13.2215i) q^{71} +(-4.66461 - 0.991493i) q^{72} +(0.628699 - 5.98168i) q^{73} +(-2.69683 - 1.20071i) q^{74} +(-2.38276 - 2.64632i) q^{75} -0.0810106 q^{76} -14.1679 q^{78} +(-10.4658 - 11.6235i) q^{79} +(-6.64517 - 2.95862i) q^{80} +(1.17255 - 11.1561i) q^{81} +(1.26357 + 0.268580i) q^{82} +(1.35217 + 4.16157i) q^{83} +(-8.10479 + 5.88848i) q^{85} +(-7.56631 - 8.40324i) q^{86} +(1.26825 + 2.19668i) q^{87} +(-8.66219 + 3.68464i) q^{88} +(7.67186 - 13.2880i) q^{89} +(-1.34005 + 4.12425i) q^{90} +(-0.00813063 - 0.00590725i) q^{92} +(-2.76758 - 0.588268i) q^{93} +(5.63512 - 6.25843i) q^{94} +(-1.11053 + 10.5660i) q^{95} +(0.0178632 + 0.169957i) q^{96} +(-0.745114 + 2.29323i) q^{97} +(2.70537 + 4.87190i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 3 q^{2} - 2 q^{3} + 11 q^{4} - 5 q^{5} - 6 q^{6} - 10 q^{8} + 12 q^{9}+O(q^{10}) \) 32 * q + 3 * q^2 - 2 * q^3 + 11 * q^4 - 5 * q^5 - 6 * q^6 - 10 * q^8 + 12 * q^9	\( 32 q + 3 q^{2} - 2 q^{3} + 11 q^{4} - 5 q^{5} - 6 q^{6} - 10 q^{8} + 12 q^{9} + 12 q^{10} + 3 q^{11} + 18 q^{12} + 14 q^{13} - 36 q^{15} - 17 q^{16} - 5 q^{17} - 11 q^{18} + 19 q^{19} - 2 q^{20} - 66 q^{22} - 32 q^{23} - 35 q^{24} - 7 q^{25} - 27 q^{26} - 20 q^{27} + 6 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 26 q^{33} + 48 q^{34} + 104 q^{36} - 4 q^{37} - 5 q^{38} - 11 q^{39} - 10 q^{40} + 20 q^{41} - 16 q^{43} + 38 q^{44} + 70 q^{45} + 42 q^{46} - 23 q^{47} + 72 q^{48} + 104 q^{50} + 29 q^{51} + 33 q^{52} - 4 q^{53} + 60 q^{54} + 24 q^{55} - 22 q^{57} - 20 q^{58} + 17 q^{59} + 30 q^{60} - 7 q^{61} - 158 q^{62} + 14 q^{64} + 8 q^{65} + 8 q^{66} + 38 q^{67} - 2 q^{68} - 20 q^{69} - 28 q^{71} - 35 q^{73} + 29 q^{74} + 9 q^{75} - 104 q^{76} - 116 q^{78} - 15 q^{79} - 87 q^{80} + 14 q^{81} + 19 q^{82} - 10 q^{83} + 12 q^{85} + 52 q^{86} - 72 q^{87} - 55 q^{88} + 74 q^{89} + 28 q^{90} - 110 q^{92} - 32 q^{93} - 24 q^{94} - 32 q^{95} - 42 q^{96} - 40 q^{97} + 32 q^{99}+O(q^{100}) \) 32 * q + 3 * q^2 - 2 * q^3 + 11 * q^4 - 5 * q^5 - 6 * q^6 - 10 * q^8 + 12 * q^9 + 12 * q^10 + 3 * q^11 + 18 * q^12 + 14 * q^13 - 36 * q^15 - 17 * q^16 - 5 * q^17 - 11 * q^18 + 19 * q^19 - 2 * q^20 - 66 * q^22 - 32 * q^23 - 35 * q^24 - 7 * q^25 - 27 * q^26 - 20 * q^27 + 6 * q^29 + 2 * q^30 - 7 * q^31 - 32 * q^32 - 26 * q^33 + 48 * q^34 + 104 * q^36 - 4 * q^37 - 5 * q^38 - 11 * q^39 - 10 * q^40 + 20 * q^41 - 16 * q^43 + 38 * q^44 + 70 * q^45 + 42 * q^46 - 23 * q^47 + 72 * q^48 + 104 * q^50 + 29 * q^51 + 33 * q^52 - 4 * q^53 + 60 * q^54 + 24 * q^55 - 22 * q^57 - 20 * q^58 + 17 * q^59 + 30 * q^60 - 7 * q^61 - 158 * q^62 + 14 * q^64 + 8 * q^65 + 8 * q^66 + 38 * q^67 - 2 * q^68 - 20 * q^69 - 28 * q^71 - 35 * q^73 + 29 * q^74 + 9 * q^75 - 104 * q^76 - 116 * q^78 - 15 * q^79 - 87 * q^80 + 14 * q^81 + 19 * q^82 - 10 * q^83 + 12 * q^85 + 52 * q^86 - 72 * q^87 - 55 * q^88 + 74 * q^89 + 28 * q^90 - 110 * q^92 - 32 * q^93 - 24 * q^94 - 32 * q^95 - 42 * q^96 - 40 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more