LMFDB - Embedded newform 539.2.q.g.214.2

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			214.2
Character	$\chi$	$=$	539.214
Dual form			539.2.q.g.471.2

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.942984	+	1.04729i	−0.666790	+	0.740546i	−0.977726	−	0.209885i	$-0.932691\pi$
$2$	−0.942984	+	1.04729i	−0.666790	+	0.740546i	0.310936	+	0.950431i	$0.399358\pi$
$3$	−1.97635	+	0.879926i	−1.14104	+	0.508026i	−0.888189	−	0.459478i	$-0.848036\pi$
$3$	−1.97635	+	0.879926i	−1.14104	+	0.508026i	−0.252856	+	0.967504i	$0.581370\pi$
$4$	0.00145969	+	0.0138880i	0.000729845	+	0.00694401i
$5$	1.79137	−	0.380767i	0.801123	−	0.170284i	0.210883	−	0.977511i	$-0.432366\pi$
$5$	1.79137	−	0.380767i	0.801123	−	0.170284i	0.590241	+	0.807227i	$0.299033\pi$
$6$	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	−0.926377	−	0.376596i	$-0.877094\pi$
$13$	−1.43602	−	4.41961i	−0.398280	−	1.22578i	0.528097	−	0.849184i	$-0.322906\pi$
$14$		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	$-0.464204\pi$
$17$	−3.66029	−	4.06516i	−0.887750	−	0.985946i	−0.999970	+	0.00773703i	$0.997537\pi$
$18$	0.247511	+	2.35491i	0.0583388	+	0.555057i
$19$	0.606388	−	5.76940i	0.139115	−	1.32359i	−0.672804	−	0.739821i	$-0.734910\pi$
$19$	0.606388	−	5.76940i	0.139115	−	1.32359i	0.811919	−	0.583770i	$-0.198423\pi$
$20$	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	0.901100	−	0.433611i	$-0.142761\pi$
$23$	0.359841	+	0.623263i	0.0750321	+	0.129959i	−0.826068	+	0.563570i	$0.809427\pi$
$24$	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	−0.496221	−	0.868196i	$-0.665280\pi$
$29$	0.948551	−	0.689163i	0.176142	−	0.127974i	0.672363	+	0.740222i	$0.265280\pi$
$30$	0.583635	−	5.55291i	0.106557	−	1.01382i
$31$	1.27929	+	0.271920i	0.229766	+	0.0488384i	0.321356	−	0.946958i	$-0.395861\pi$
$31$	1.27929	+	0.271920i	0.229766	+	0.0488384i	−0.0915895	+	0.995797i	$0.529195\pi$
$32$	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	0.557962	−	0.829867i	$-0.311584\pi$
$37$	1.91364	+	0.852007i	0.314600	+	0.140069i	−0.243362	+	0.969936i	$0.578250\pi$
$38$	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	$-0.277197\pi$
$41$	0.741582	+	0.538791i	0.115816	+	0.0841449i	−0.528370	+	0.849014i	$0.677197\pi$
$42$		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	0.849540	+	0.527524i	$0.176879\pi$
$47$	−0.624645	+	5.94310i	−0.0911138	+	0.866890i	−0.940654	+	0.339367i	$0.889787\pi$
$48$	−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	−0.532394	−	0.846496i	$-0.678708\pi$
$53$	−9.92324	−	2.10925i	−1.36306	−	0.289728i	−0.830668	+	0.556769i	$0.812041\pi$
$54$	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	0.913556	+	0.406713i	$0.133325\pi$
$59$	0.802863	+	7.63873i	0.104524	+	0.994478i	−0.809032	+	0.587765i	$0.800008\pi$
$60$	−0.0370211	−	0.0411161i	−0.00477941	−	0.00530807i
$61$	6.13898	−	1.30488i	0.786015	−	0.167073i	0.202616	−	0.979258i	$-0.435056\pi$
$61$	6.13898	−	1.30488i	0.786015	−	0.167073i	0.583399	+	0.812186i	$0.301722\pi$
$62$	−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	0.188690	−	0.982037i	$-0.439576\pi$
$67$	7.73363	−	13.3950i	0.944814	−	1.63647i	0.756124	−	0.654429i	$-0.227091\pi$
$68$	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	−0.282659	−	0.959221i	$-0.591216\pi$
$71$	4.29593	−	13.2215i	0.509833	−	1.56910i	0.792491	−	0.609883i	$-0.208784\pi$
$72$	−4.66461	+	0.991493i	−0.549730	+	0.116849i
$73$	−0.628699	−	5.98168i	−0.0735837	−	0.700102i	−0.967672	−	0.252212i	$-0.918842\pi$
$73$	−0.628699	−	5.98168i	−0.0735837	−	0.700102i	0.894088	−	0.447891i	$-0.147825\pi$
$74$	−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	−0.235598	+	0.971851i	$0.575705\pi$
$79$	−10.4658	+	11.6235i	−1.17750	+	1.30774i	−0.941900	+	0.335894i	$0.890962\pi$
$80$	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	$-0.977196\pi$
$83$	−1.35217	+	4.16157i	−0.148420	+	0.456791i	0.849015	+	0.528370i	$0.177196\pi$
$84$		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	−0.910602	−	0.413283i	$-0.864382\pi$
$89$	−7.67186	−	13.2880i	−0.813215	−	1.40853i	0.0973874	−	0.995247i	$-0.468951\pi$
$90$	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	$-0.0609370\pi$
$97$	0.745114	+	2.29323i	0.0756549	+	0.232842i	−0.906077	+	0.423114i	$0.860937\pi$
$98$		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	$-0.634932\pi$
$101$	−11.6359	−	2.47329i	−1.15782	−	0.246102i	−0.746497	+	0.665389i	$0.768266\pi$
$102$	−15.2357	+	6.78335i	−1.50855	+	0.671652i
$103$	0.362051	+	0.161195i	0.0356739	+	0.0158830i	0.424496	−	0.905430i	$-0.360451\pi$
$103$	0.362051	+	0.161195i	0.0356739	+	0.0158830i	−0.388822	+	0.921313i	$0.627118\pi$
$104$	−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	−0.965506	−	0.260379i	$-0.916152\pi$
$107$	0.341740	−	3.25144i	0.0330373	−	0.314329i	0.998544	−	0.0539494i	$-0.0171810\pi$
$108$	0.0390001	+	0.00828972i	0.00375278	+	0.000797679i
$109$	1.42319	−	2.46504i	0.136317	−	0.236108i	−0.789783	−	0.613387i	$-0.789807\pi$
$109$	1.42319	−	2.46504i	0.136317	−	0.236108i	0.926100	+	0.377279i	$0.123140\pi$
$110$	−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	−0.124748	−	0.992188i	$-0.539812\pi$
$113$	−11.7668	−	8.54906i	−1.10692	−	0.804228i	−0.982177	+	0.187961i	$0.939812\pi$
$114$	−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	−0.858040	−	0.513583i	$-0.828318\pi$
$127$	1.55524	−	4.78655i	0.138006	−	0.424737i	0.996045	+	0.0888458i	$0.0283178\pi$
$128$	−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	$-0.164163\pi$
$131$	0.0900265	+	0.155930i	0.00786565	+	0.0136237i	−0.862066	+	0.506796i	$0.830830\pi$
$132$	−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	0.932507	−	0.361151i	$-0.117616\pi$
$137$	5.56981	+	6.18590i	0.475861	+	0.528497i	−0.456646	+	0.889648i	$0.650949\pi$
$138$	2.14621	−	0.456191i	0.182697	−	0.0388335i
$139$	5.63172	−	4.09169i	0.477677	−	0.347052i	−0.322749	−	0.946485i	$-0.604607\pi$
$139$	5.63172	−	4.09169i	0.477677	−	0.347052i	0.800425	+	0.599432i	$0.204607\pi$
$140$		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	−0.0773155	−	0.997007i	$-0.524635\pi$
$149$	3.14407	−	0.668293i	0.257572	−	0.0547487i	0.334888	+	0.942258i	$0.391302\pi$
$150$	0.524563	+	4.99088i	0.0428303	+	0.407504i
$151$	20.3419	−	9.05681i	1.65540	−	0.737033i	0.655566	−	0.755138i	$-0.272430\pi$
$151$	20.3419	−	9.05681i	1.65540	−	0.737033i	0.999836	+	0.0181050i	$0.00576330\pi$
$152$	−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	$-0.455929\pi$
$157$	12.1088	−	5.39120i	0.966391	−	0.430265i	0.828380	+	0.560166i	$0.189263\pi$
$158$	−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	−0.267293	−	0.963615i	$-0.586129\pi$
$163$	9.17936	−	10.1947i	0.718983	−	0.798512i	0.986276	+	0.165103i	$0.0527958\pi$
$164$	−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	0.998527	+	0.0542539i	$0.0172780\pi$
$167$	2.87651	+	8.85300i	0.222591	+	0.685066i	−0.775936	+	0.630812i	$0.782722\pi$
$168$		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	0.870024	+	0.493009i	$0.164103\pi$
$173$	−1.09814	+	10.4481i	−0.0834902	+	0.794356i	−0.953514	+	0.301347i	$0.902564\pi$
$174$	−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	−0.670723	−	0.741708i	$-0.734016\pi$
$179$	−7.60372	+	3.38539i	−0.568329	+	0.253036i	0.102395	+	0.994744i	$0.467350\pi$
$180$	0.0392556	+	0.0174777i	0.00292594	+	0.00130271i
$181$	−4.57437	+	14.0785i	−0.340010	+	1.04644i	0.624191	+	0.781272i	$0.285429\pi$
$181$	−4.57437	+	14.0785i	−0.340010	+	1.04644i	−0.964201	+	0.265172i	$0.914571\pi$
$182$		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	0.0638675	−	0.997958i	$-0.479656\pi$
$191$	−8.77621	−	3.90742i	−0.635024	−	0.282731i	−0.698892	+	0.715227i	$0.746323\pi$
$192$	−11.6604	−	12.9502i	−0.841517	−	0.934599i
$193$	−0.995538	−	1.10566i	−0.0716604	−	0.0795869i	0.706248	−	0.707964i	$-0.250386\pi$
$193$	−0.995538	−	1.10566i	−0.0716604	−	0.0795869i	−0.777909	+	0.628377i	$0.783719\pi$
$194$	−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	$-0.784775\pi$
$199$	2.14364	−	3.71290i	0.151959	−	0.263200i	0.931948	+	0.362593i	$0.118109\pi$
$200$	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	0.934383	−	0.356270i	$-0.115952\pi$
$211$	−0.449704	−	1.38405i	−0.0309589	−	0.0952816i	−0.965342	+	0.260988i	$0.915952\pi$
$212$	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	$-0.248010\pi$
$223$	3.92893	+	2.85453i	0.263101	+	0.191154i	−0.448412	+	0.893827i	$0.648010\pi$
$224$		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	$-0.0375287\pi$
$227$	−0.0415128	−	0.394968i	−0.00275530	−	0.0262150i	−0.995813	+	0.0914119i	$0.970862\pi$
$228$	−0.160105	+	0.0712834i	−0.0106032	+	0.00472086i
$229$	1.46515	−	1.62721i	0.0968199	−	0.107529i	−0.692787	−	0.721142i	$-0.743618\pi$
$229$	1.46515	−	1.62721i	0.0968199	−	0.107529i	0.789607	+	0.613612i	$0.210284\pi$
$230$	−1.85744			−0.122476
$231$		0			0
$232$	−3.32773			−0.218476
$233$	−0.843209	+	0.936478i	−0.0552404	+	0.0613507i	−0.770132	−	0.637885i	$-0.779810\pi$
$233$	−0.843209	+	0.936478i	−0.0552404	+	0.0613507i	0.714891	+	0.699236i	$0.246476\pi$
$234$	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	0.840200	−	0.542277i	$-0.182438\pi$
$239$	9.02997	+	6.56066i	0.584100	+	0.424374i	−0.256100	+	0.966650i	$0.582438\pi$
$240$	−10.5298	+	11.6945i	−0.679695	+	0.754878i
$241$	10.7421	−	18.6059i	0.691962	−	1.19851i	−0.279232	−	0.960224i	$-0.590080\pi$
$241$	10.7421	−	18.6059i	0.691962	−	1.19851i	0.971194	−	0.238290i	$-0.0765869\pi$
$242$	−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	$-0.104258\pi$
$251$	−0.130968	−	0.403077i	−0.00826660	−	0.0254420i	−0.955105	+	0.296268i	$0.904258\pi$
$252$		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	$-0.183598\pi$
$257$	15.9323	+	7.09351i	0.993829	+	0.442481i	0.155612	+	0.987818i	$0.450265\pi$
$258$	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	−0.888438	−	0.458997i	$-0.848209\pi$
$263$	−0.757596	+	1.31219i	−0.0467153	+	0.0809133i	0.841722	+	0.539911i	$0.181542\pi$
$264$	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	$-0.253055\pi$
$269$	−1.35902	−	1.50935i	−0.0828611	−	0.0920266i	−0.783149	+	0.621833i	$0.786388\pi$
$270$	4.93083	+	5.47624i	0.300080	+	0.333273i
$271$	6.94700	+	3.09300i	0.422000	+	0.187887i	0.606739	−	0.794901i	$-0.292477\pi$
$271$	6.94700	+	3.09300i	0.422000	+	0.187887i	−0.184739	+	0.982788i	$0.559144\pi$
$272$	−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	−0.236571	−	0.971614i	$-0.576024\pi$
$277$	−14.1115	−	2.99950i	−0.847881	−	0.180223i	−0.611310	+	0.791392i	$0.709357\pi$
$278$	−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	−0.643232	−	0.765672i	$-0.722407\pi$
$281$	5.48494	−	16.8809i	0.327204	−	1.00703i	0.970436	−	0.241359i	$-0.0775933\pi$
$282$	16.6439	+	7.41035i	0.991130	+	0.441280i
$283$	−28.4443	+	12.6642i	−1.69084	+	0.752809i	−0.691294	+	0.722573i	$0.742959\pi$
$283$	−28.4443	+	12.6642i	−1.69084	+	0.752809i	−0.999543	+	0.0302356i	$0.990374\pi$
$284$	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	$-0.452321\pi$
$293$	19.4409	−	14.1247i	1.13575	−	0.825171i	0.986522	+	0.163632i	$0.0523209\pi$
$294$		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	$-0.549826\pi$
$307$	−5.46298			−0.311789			−0.155894	+	0.987774i	$0.549826\pi$
$308$		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	$-0.504504\pi$
$311$	12.6877	−	5.64894i	0.719454	−	0.320322i	0.733603	+	0.679578i	$0.237837\pi$
$312$	−2.98257	−	28.3773i	−0.168855	−	1.60655i
$313$	−26.8487	+	5.70688i	−1.51758	+	0.322572i	−0.889993	−	0.455974i	$-0.849291\pi$
$313$	−26.8487	+	5.70688i	−1.51758	+	0.322572i	−0.627588	+	0.778546i	$0.715958\pi$
$314$	−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	−0.577923	−	0.816091i	$-0.696137\pi$
$317$	5.23642	−	5.81563i	0.294107	−	0.326638i	0.872030	+	0.489453i	$0.162803\pi$
$318$	−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	0.935619	+	0.353012i	$0.114843\pi$
$331$	14.0731	+	24.3753i	0.773527	+	1.33979i	−0.162092	+	0.986776i	$0.551824\pi$
$332$	−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	0.119628	−	0.992819i	$-0.461830\pi$
$337$	20.2084	−	14.6823i	1.10082	−	0.799793i	0.981194	+	0.193025i	$0.0618300\pi$
$338$	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	0.989423	−	0.145058i	$-0.0463368\pi$
$347$	13.8170	+	15.3454i	0.741737	+	0.823782i	−0.247686	+	0.968840i	$0.579670\pi$
$348$	−0.0323588	−	0.0144071i	−0.00173461	−	0.000772299i
$349$	4.85185	+	3.52507i	0.259713	+	0.188693i	0.710021	−	0.704181i	$-0.248686\pi$
$349$	4.85185	+	3.52507i	0.259713	+	0.188693i	−0.450307	+	0.892874i	$0.648686\pi$
$350$		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	0.345784	+	0.938314i	$0.387613\pi$
$353$	−12.0191	+	20.8177i	−0.639712	+	1.10801i	−0.985496	+	0.169699i	$0.945720\pi$
$354$	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	0.125405	−	0.992106i	$-0.459977\pi$
$359$	−10.0034	−	4.45382i	−0.527961	−	0.235063i	−0.653366	+	0.757042i	$0.726644\pi$
$360$	−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	−0.984538	−	0.175169i	$-0.943953\pi$
$367$	−1.10986	−	10.5596i	−0.0579341	−	0.551206i	0.926604	−	0.376038i	$-0.122714\pi$
$368$	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	−0.750395	−	0.660989i	$-0.770137\pi$
$373$	−18.3018	−	31.6996i	−0.947631	−	1.64135i	−0.197236	−	0.980356i	$-0.563196\pi$
$374$	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	0.798938	+	0.601414i	$0.205396\pi$
$379$	−3.91147	+	12.0383i	−0.200919	+	0.618364i	−0.999856	+	0.0169501i	$0.994604\pi$
$380$	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	$-0.895987\pi$
$383$	−10.3500	+	11.4949i	−0.528862	+	0.587361i	0.418223	+	0.908345i	$0.362653\pi$
$384$	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	0.975145	+	0.221570i	$0.0711180\pi$
$389$	1.32887	+	12.6433i	0.0673762	+	0.641041i	−0.907768	+	0.419472i	$0.862215\pi$
$390$	−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	$-0.00885338\pi$
$397$	9.47870	+	16.4176i	0.475722	+	0.823975i	−0.523891	+	0.851785i	$0.675520\pi$
$398$	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	0.00907651	−	0.999959i	$-0.497111\pi$
$401$	8.49236	−	1.80511i	0.424088	−	0.0901427i	0.415012	+	0.909816i	$0.363777\pi$
$402$	−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	$-0.478452\pi$
$409$	−5.58920	−	1.18802i	−0.276368	−	0.0587438i	−0.344011	+	0.938966i	$0.611786\pi$
$410$	−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	$-0.731220\pi$
$419$	−27.1909			−1.32836			−0.664181	+	0.747571i	$0.731220\pi$
$420$		0			0
$421$	19.3881	+	14.0863i	0.944921	+	0.686525i	0.949600	−	0.313464i	$-0.101490\pi$
$421$	19.3881	+	14.0863i	0.944921	+	0.686525i	−0.00467947	+	0.999989i	$0.501490\pi$
$422$	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	−0.197224	−	0.980358i	$-0.563193\pi$
$431$	−16.1132	−	3.42496i	−0.776145	−	0.164975i	−0.578921	+	0.815384i	$0.696526\pi$
$432$	1.18540	−	11.2783i	0.0570327	−	0.542629i
$433$	−16.2539	+	11.8092i	−0.781113	+	0.567512i	−0.905313	−	0.424745i	$-0.860364\pi$
$433$	−16.2539	+	11.8092i	−0.781113	+	0.567512i	0.124200	+	0.992257i	$0.460364\pi$
$434$		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	−0.985699	−	0.168515i	$-0.946103\pi$
$439$	−13.3841	−	23.1819i	−0.638788	−	1.10641i	0.346912	−	0.937898i	$-0.387230\pi$
$440$	−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	0.713027	+	0.701137i	$0.247324\pi$
$443$	−2.74025	+	26.0717i	−0.130193	+	1.23870i	−0.843220	+	0.537568i	$0.819343\pi$
$444$	−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	0.996634	−	0.0819851i	$-0.0261260\pi$
$449$	3.01211	+	9.27033i	0.142150	+	0.437494i	−0.854483	+	0.519479i	$0.826126\pi$
$450$	−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	−0.471628	−	0.881798i	$-0.656333\pi$
$457$	−11.6256	+	2.47109i	−0.543822	+	0.115593i	−0.0721940	+	0.997391i	$0.523000\pi$
$458$	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	$-0.431671\pi$
$461$	9.14737			0.426035			0.213018	+	0.977048i	$0.431671\pi$
$462$		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	$-0.406987\pi$
$467$	20.3293	−	4.32112i	0.940726	−	0.199957i	0.652658	+	0.757653i	$0.273654\pi$
$468$	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	$-0.422742\pi$
$479$	−16.4180	−	18.2340i	−0.750157	−	0.833134i	−0.990494	+	0.137556i	$0.956075\pi$
$480$	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	−0.646497	−	0.762916i	$-0.723767\pi$
$487$	−11.3018	+	5.03187i	−0.512132	+	0.228016i	0.134366	+	0.990932i	$0.457100\pi$
$488$	−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	−0.847062	−	0.531494i	$-0.821631\pi$
$491$	−13.3691	+	9.71320i	−0.603338	+	0.438350i	0.243724	+	0.969845i	$0.421631\pi$
$492$	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	0.106047	−	0.994361i	$-0.466181\pi$
$499$	−12.5530	−	5.58895i	−0.561949	−	0.250196i	−0.667995	+	0.744165i	$0.732847\pi$
$500$	−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	$-0.131946\pi$
$503$	18.2812	+	13.2820i	0.815117	+	0.592217i	−0.100193	+	0.994968i	$0.531946\pi$
$504$		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	−0.825078	−	0.565018i	$-0.808869\pi$
$509$	2.24356	−	21.3460i	0.0994440	−	0.946146i	0.924522	−	0.381128i	$-0.124464\pi$
$510$	−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	−0.725412	−	0.688315i	$-0.758351\pi$
$521$	−3.62835	−	34.5214i	−0.158961	−	1.51241i	0.566451	−	0.824095i	$-0.308316\pi$
$522$	1.85769	+	2.06317i	0.0813089	+	0.0903027i
$523$	−19.2970	+	4.10171i	−0.843800	+	0.179355i	−0.609477	−	0.792803i	$-0.708621\pi$
$523$	−19.2970	+	4.10171i	−0.843800	+	0.179355i	−0.234323	+	0.972159i	$0.575287\pi$
$524$	−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	−0.817661	−	0.575699i	$-0.804730\pi$
$541$	−3.71329	+	4.12403i	−0.159647	+	0.177306i	0.658015	+	0.753005i	$0.271397\pi$
$542$	−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	0.724213	−	0.689576i	$-0.242203\pi$
$547$	6.83353	+	4.96485i	0.292181	+	0.212282i	−0.432032	+	0.901858i	$0.642203\pi$
$548$	−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	0.987802	+	0.155715i	$0.0497682\pi$
$557$	1.27352	+	12.1167i	0.0539608	+	0.513403i	−0.933841	+	0.357688i	$0.883565\pi$
$558$	−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	$-0.237788\pi$
$563$	26.7558	+	5.68712i	1.12762	+	0.239683i	0.393913	+	0.919148i	$0.371121\pi$
$564$	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	0.967702	+	0.252096i	$0.0811198\pi$
$569$	−0.745836	+	7.09615i	−0.0312671	+	0.297486i	−0.998969	+	0.0453903i	$0.985547\pi$
$570$	−31.6830	−	6.73444i	−1.32706	−	0.282075i
$571$	−16.2420	+	28.1319i	−0.679705	+	1.17728i	0.295365	+	0.955385i	$0.404559\pi$
$571$	−16.2420	+	28.1319i	−0.679705	+	1.17728i	−0.975070	+	0.221899i	$0.928775\pi$
$572$	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	0.997072	+	0.0764628i	$0.0243627\pi$
$577$	23.2736	+	25.8480i	0.968894	+	1.07607i	−0.0281785	+	0.999603i	$0.508971\pi$
$578$	−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	$-0.603440\pi$
$587$	11.7105	−	8.50816i	0.483343	−	0.351169i	0.802618	+	0.596493i	$0.203440\pi$
$588$		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	$-0.0668114\pi$
$593$	7.51453	+	13.0155i	0.308585	+	0.534484i	−0.669468	+	0.742841i	$0.733478\pi$
$594$	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	0.766729	−	0.641970i	$-0.221883\pi$
$599$	1.17797	+	1.30827i	0.0481307	+	0.0534545i	−0.718599	+	0.695425i	$0.755216\pi$
$600$	−9.88596	+	2.10133i	−0.403593	+	0.0857863i
$601$	−18.9605	+	13.7756i	−0.773415	+	0.561919i	−0.902995	−	0.429650i	$-0.858637\pi$
$601$	−18.9605	+	13.7756i	−0.773415	+	0.561919i	0.129581	+	0.991569i	$0.458637\pi$
$602$		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	$-0.938137\pi$
$607$	−16.9146	+	18.7856i	−0.686544	+	0.762484i	0.294630	+	0.955611i	$0.404804\pi$
$608$	−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	−0.385207	−	0.922830i	$-0.625870\pi$
$613$	1.06057	−	0.472198i	0.0428362	−	0.0190719i	0.428043	+	0.903758i	$0.359203\pi$
$614$	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	0.681553	−	0.731768i	$-0.261305\pi$
$619$	41.8330	−	18.6253i	1.68141	−	0.748613i	0.999858	−	0.0168441i	$-0.00536191\pi$
$620$	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	−0.365703	−	0.930732i	$-0.619171\pi$
$631$	10.2103	−	7.41824i	0.406467	−	0.295316i	0.772170	+	0.635416i	$0.219171\pi$
$632$	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	0.165255	−	0.986251i	$-0.447155\pi$
$641$	25.5397	−	11.3710i	1.00876	−	0.449129i	0.843504	+	0.537122i	$0.180489\pi$
$642$	−9.10581	−	4.05417i	−0.359378	−	0.160005i
$643$	−15.3575	+	47.2657i	−0.605642	+	1.86398i	−0.113330	+	0.993557i	$0.536152\pi$
$643$	−15.3575	+	47.2657i	−0.605642	+	1.86398i	−0.492313	+	0.870418i	$0.663848\pi$
$644$		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	$-0.363915\pi$
$647$	10.7662	+	2.28842i	0.423262	+	0.0899671i	0.00864379	+	0.999963i	$0.497249\pi$
$648$	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	0.852500	−	0.522728i	$-0.175086\pi$
$653$	26.4347	+	11.7695i	1.03447	+	0.460576i	0.181971	+	0.983304i	$0.441752\pi$
$654$	−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	$-0.962815\pi$
$661$	−10.1722	+	17.6187i	−0.395652	+	0.685290i	0.597532	+	0.801845i	$0.296148\pi$
$662$	−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	0.852986	−	0.521934i	$-0.174789\pi$
$673$	−3.73255	−	11.4876i	−0.143879	−	0.442815i	−0.996865	+	0.0791188i	$0.974789\pi$
$674$	−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	$-0.587456\pi$
$677$	−3.32208	+	0.706130i	−0.127678	+	0.0271388i	0.143629	+	0.989632i	$0.454123\pi$
$678$	−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	−0.816932	−	0.576734i	$-0.804327\pi$
$683$	2.37821	−	4.11919i	0.0909999	−	0.157616i	0.907932	+	0.419117i	$0.137660\pi$
$684$	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	$-0.726394\pi$
$691$	4.43893	−	4.92994i	0.168865	−	0.187544i	0.821637	+	0.570010i	$0.193061\pi$
$692$	−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	0.540529	−	0.841325i	$-0.318224\pi$
$701$	−2.45134	−	1.78101i	−0.0925860	−	0.0672677i	−0.633115	+	0.774058i	$0.718224\pi$
$702$	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	0.0498880	−	0.998755i	$-0.484114\pi$
$709$	13.3586	−	2.83946i	0.501693	−	0.106638i	0.451805	+	0.892117i	$0.350780\pi$
$710$	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	$-0.377948\pi$
$719$	−1.73600	−	0.772918i	−0.0647419	−	0.0288250i	−0.438852	+	0.898559i	$0.644615\pi$
$720$	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	$-0.582503\pi$
$727$	−13.8211			−0.512595			−0.256298	+	0.966598i	$0.582503\pi$
$728$		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	$-0.0149981\pi$
$733$	44.1922	+	19.6756i	1.63228	+	0.726736i	0.633385	+	0.773837i	$0.281665\pi$
$734$	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	−0.229516	−	0.973305i	$-0.573714\pi$
$739$	−22.7009	−	4.82523i	−0.835068	−	0.177499i	−0.605552	+	0.795806i	$0.707048\pi$
$740$	−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	0.287019	+	0.957925i	$0.407336\pi$
$743$	−13.8536	+	42.6369i	−0.508238	+	1.56420i	−0.795257	+	0.606272i	$0.792664\pi$
$744$	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	−0.577638	−	0.816293i	$-0.696025\pi$
$751$	4.30507	−	40.9600i	0.157094	−	1.49465i	0.734732	−	0.678358i	$-0.237308\pi$
$752$	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	−0.995497	−	0.0947948i	$-0.969781\pi$
$757$	−6.76401	−	20.8175i	−0.245842	−	0.756624i	0.749655	−	0.661829i	$-0.230219\pi$
$758$	−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	$-0.990785\pi$
$761$	−23.8982	+	26.5417i	−0.866310	+	0.962135i	0.133271	+	0.991080i	$0.457452\pi$
$762$	−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	$-0.469521\pi$
$769$	5.30246			0.191212			0.0956058	+	0.995419i	$0.469521\pi$
$770$		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	$-0.987758\pi$
$773$	−45.5779	+	20.2926i	−1.63932	+	0.729874i	−0.640062	+	0.768323i	$0.721091\pi$
$774$	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	$-0.0126481\pi$
$787$	23.9930	+	26.6469i	0.855258	+	0.949860i	−0.143953	+	0.989585i	$0.545981\pi$
$788$	−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	$-0.815921\pi$
$797$	4.55530	−	14.0198i	0.161357	−	0.496606i	0.998749	+	0.0499962i	$0.0159209\pi$
$798$		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	0.336965	−	0.941517i	$-0.390600\pi$
$809$	−18.0504	−	20.0470i	−0.634617	−	0.704814i	−0.971582	+	0.236704i	$0.923933\pi$
$810$	−26.4485	−	11.7756i	−0.929305	−	0.413753i
$811$	−1.18472	−	0.860750i	−0.0416012	−	0.0302250i	0.566790	−	0.823862i	$-0.308185\pi$
$811$	−1.18472	−	0.860750i	−0.0416012	−	0.0302250i	−0.608392	+	0.793637i	$0.708185\pi$
$812$		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	0.832034	−	0.554725i	$-0.187176\pi$
$821$	27.9807	+	12.4578i	0.976533	+	0.434780i	0.144499	+	0.989505i	$0.453843\pi$
$822$	23.1839	−	10.3221i	0.808631	−	0.360026i
$823$	23.9977	+	5.10087i	0.836507	+	0.177805i	0.606199	−	0.795313i	$-0.292693\pi$
$823$	23.9977	+	5.10087i	0.836507	+	0.177805i	0.230308	+	0.973118i	$0.426027\pi$
$824$	−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	0.909555	−	0.415584i	$-0.136423\pi$
$827$	−2.02927	−	6.24545i	−0.0705646	−	0.217176i	−0.980119	+	0.198408i	$0.936423\pi$
$828$	−0.00176509	+	0.0167937i	−6.13411e−5	+	0.000583622i
$829$	2.07429	+	19.7355i	0.0720430	+	0.685443i	0.969625	+	0.244596i	$0.0786554\pi$
$829$	2.07429	+	19.7355i	0.0720430	+	0.685443i	−0.897582	+	0.440847i	$0.854678\pi$
$830$	−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	$-0.256121\pi$
$839$	6.44019	+	4.67907i	0.222340	+	0.161539i	−0.471039	+	0.882112i	$0.656121\pi$
$840$		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	−0.592231	−	0.805768i	$-0.701753\pi$
$853$	10.5292	−	32.4055i	0.360513	−	1.10954i	0.952744	−	0.303776i	$-0.0982473\pi$
$854$		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	$-0.972882\pi$
$857$	−12.4269	+	21.5241i	−0.424496	+	0.735249i	0.571877	+	0.820339i	$0.306215\pi$
$858$	−45.7932	+	10.5356i	−1.56335	+	0.359680i
$859$	−1.02827	−	1.78102i	−0.0350841	−	0.0607675i	0.847950	−	0.530076i	$-0.177837\pi$
$859$	−1.02827	−	1.78102i	−0.0350841	−	0.0607675i	−0.883034	+	0.469308i	$0.844503\pi$
$860$	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	−0.203590	−	0.979056i	$-0.565261\pi$
$863$	0.253805	−	0.0539480i	0.00863964	−	0.00183641i	0.212229	+	0.977220i	$0.431928\pi$
$864$	−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	0.911435	+	0.411445i	$0.134976\pi$
$877$	−1.94350	+	18.4911i	−0.0656272	+	0.624401i	−0.977062	+	0.212956i	$0.931691\pi$
$878$	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	$-0.465330\pi$
$881$	6.45292			0.217404			0.108702	+	0.994074i	$0.465330\pi$
$882$		0			0
$883$	0.225301	+	0.163691i	0.00758198	+	0.00550863i	0.591570	−	0.806254i	$-0.298508\pi$
$883$	0.225301	+	0.163691i	0.00758198	+	0.00550863i	−0.583988	+	0.811762i	$0.698508\pi$
$884$	−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	$-0.195200\pi$
$887$	27.9152	+	12.4286i	0.937300	+	0.417313i	0.119512	+	0.992833i	$0.461867\pi$
$888$	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	0.984863	−	0.173337i	$-0.0554551\pi$
$907$	21.3685	+	23.7321i	0.709529	+	0.788011i	−0.275334	+	0.961349i	$0.588788\pi$
$908$	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	0.964368	−	0.264564i	$-0.0852280\pi$
$911$	0.865378	+	2.66336i	0.0286713	+	0.0882411i	−0.935697	+	0.352805i	$0.885228\pi$
$912$	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	0.0547522	−	0.998500i	$-0.482563\pi$
$919$	15.4879	−	3.29205i	0.510897	−	0.108595i	0.456145	+	0.889905i	$0.349230\pi$
$920$	−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	$-0.417788\pi$
$929$	26.8828	−	5.71411i	0.881995	−	0.187474i	0.626580	+	0.779357i	$0.284454\pi$
$930$	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	$-0.164436\pi$
$937$	−3.80357	−	11.7062i	−0.124257	−	0.382425i	−0.993765	+	0.111495i	$0.964436\pi$
$938$		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	$-0.225757\pi$
$941$	0.977023	+	1.08509i	0.0318500	+	0.0353731i	−0.727009	+	0.686628i	$0.759090\pi$
$942$	−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	0.761956	−	0.647629i	$-0.224239\pi$
$947$	−5.53568	−	9.58807i	−0.179885	−	0.311571i	−0.941841	+	0.336059i	$0.890906\pi$
$948$	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	−0.376358	−	0.926474i	$-0.622824\pi$
$953$	11.9924	−	8.71296i	0.388471	−	0.282240i	0.764828	+	0.644234i	$0.222824\pi$
$954$	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	0.683355	+	0.730086i	$0.260520\pi$
$971$	−4.26469	+	40.5758i	−0.136860	+	1.30214i	−0.820216	+	0.572054i	$0.806147\pi$
$972$	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	−0.639860	−	0.768492i	$-0.721008\pi$
$977$	−48.0412	−	10.2115i	−1.53697	−	0.326694i	−0.897115	+	0.441798i	$0.854341\pi$
$978$	−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	$-0.0389520\pi$
$983$	−0.115691	−	1.10073i	−0.00368997	−	0.0351077i	−0.996212	+	0.0869583i	$0.972285\pi$
$984$	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	0.315969	+	0.948769i	$0.397670\pi$
$991$	−20.8926	+	36.1870i	−0.663674	+	1.14952i	−0.979643	+	0.200747i	$0.935663\pi$
$992$	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	−0.783551	−	0.621327i	$-0.786594\pi$
$997$	−4.61958	−	43.9524i	−0.146304	−	1.39199i	0.637248	−	0.770659i	$-0.280073\pi$
$998$	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.g.214.2		32
7.2	even	3	inner	539.2.q.g.324.3		32
7.3	odd	6		539.2.f.e.148.2		16
7.4	even	3		77.2.f.b.71.2	yes	16
7.5	odd	6		539.2.q.f.324.3		32
7.6	odd	2		539.2.q.f.214.2		32
11.9	even	5	inner	539.2.q.g.361.3		32
21.11	odd	6		693.2.m.i.379.3		16
77.3	odd	30		5929.2.a.bt.1.3		8
77.4	even	15		847.2.f.w.729.3		16
77.9	even	15	inner	539.2.q.g.471.2		32
77.18	odd	30		847.2.f.v.729.2		16
77.20	odd	10		539.2.q.f.361.3		32
77.25	even	15		847.2.a.p.1.3		8
77.31	odd	30		539.2.f.e.295.2		16
77.32	odd	6		847.2.f.x.148.3		16
77.39	odd	30		847.2.f.v.323.2		16
77.46	odd	30		847.2.f.x.372.3		16
77.52	even	30		5929.2.a.bs.1.6		8
77.53	even	15		77.2.f.b.64.2	✓	16
77.60	even	15		847.2.f.w.323.3		16
77.74	odd	30		847.2.a.o.1.6		8
77.75	odd	30		539.2.q.f.471.2		32
231.53	odd	30		693.2.m.i.64.3		16
231.74	even	30		7623.2.a.cw.1.3		8
231.179	odd	30		7623.2.a.ct.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.2	✓	16	77.53	even	15
77.2.f.b.71.2	yes	16	7.4	even	3
539.2.f.e.148.2		16	7.3	odd	6
539.2.f.e.295.2		16	77.31	odd	30
539.2.q.f.214.2		32	7.6	odd	2
539.2.q.f.324.3		32	7.5	odd	6
539.2.q.f.361.3		32	77.20	odd	10
539.2.q.f.471.2		32	77.75	odd	30
539.2.q.g.214.2		32	1.1	even	1	trivial
539.2.q.g.324.3		32	7.2	even	3	inner
539.2.q.g.361.3		32	11.9	even	5	inner
539.2.q.g.471.2		32	77.9	even	15	inner
693.2.m.i.64.3		16	231.53	odd	30
693.2.m.i.379.3		16	21.11	odd	6
847.2.a.o.1.6		8	77.74	odd	30
847.2.a.p.1.3		8	77.25	even	15
847.2.f.v.323.2		16	77.39	odd	30
847.2.f.v.729.2		16	77.18	odd	30
847.2.f.w.323.3		16	77.60	even	15
847.2.f.w.729.3		16	77.4	even	15
847.2.f.x.148.3		16	77.32	odd	6
847.2.f.x.372.3		16	77.46	odd	30
5929.2.a.bs.1.6		8	77.52	even	30
5929.2.a.bt.1.3		8	77.3	odd	30
7623.2.a.ct.1.6		8	231.179	odd	30
7623.2.a.cw.1.3		8	231.74	even	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.942984 + 1.04729i) q^{2} +(-1.97635 + 0.879926i) q^{3} +(0.00145969 + 0.0138880i) q^{4} +(1.79137 - 0.380767i) q^{5} +(0.942126 - 2.89957i) q^{6} +(-2.29616 - 1.66826i) q^{8} +(1.12429 - 1.24865i) q^{9} +O(q^{10})\)	\(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

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