LMFDB - Embedded newform 507.2.s.a.5.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(5,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(52))

chi = DirichletCharacter(H, H._module([26, 3]))

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

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

chi := DirichletCharacter("507.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$507 = 3 \cdot 13^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	507.s (of order $52$ , degree $24$ , 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$1392$
Relative dimension:	$58$ over $\Q(\zeta_{52})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label			5.13
Character	$\chi$	$=$	507.5
Dual form			507.2.s.a.203.13

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.315367 + 1.72090i) q^{2} +(1.06756 - 1.36393i) q^{3} +(-0.992015 - 0.376222i) q^{4} +(3.73990 + 0.226222i) q^{5} +(2.01052 + 2.26731i) q^{6} +(2.39720 + 1.44916i) q^{7} +(-0.849938 + 1.40597i) q^{8} +(-0.720612 - 2.91217i) q^{9} +(-1.56875 + 6.36465i) q^{10} +(0.260858 + 1.42346i) q^{11} +(-1.57218 + 0.951398i) q^{12} +(0.121358 - 3.60351i) q^{13} +(-3.24986 + 3.66833i) q^{14} +(4.30113 - 4.85945i) q^{15} +(-3.73977 - 3.31315i) q^{16} +(-7.89137 + 1.94505i) q^{17} +(5.23881 - 0.321700i) q^{18} +(3.41908 - 3.41908i) q^{19} +(-3.62492 - 1.63145i) q^{20} +(4.53572 - 1.72254i) q^{21} -2.53189 q^{22} -4.72662 q^{23} +(1.01028 + 2.66022i) q^{24} +(8.97210 + 1.08941i) q^{25} +(6.16301 + 1.34527i) q^{26} +(-4.74129 - 2.12606i) q^{27} +(-1.83285 - 2.33947i) q^{28} +(1.84858 - 1.27598i) q^{29} +(7.00620 + 8.93434i) q^{30} +(-4.32331 - 3.38710i) q^{31} +(4.29447 - 3.36450i) q^{32} +(2.21998 + 1.16384i) q^{33} +(-0.858559 - 14.1937i) q^{34} +(8.63745 + 5.96200i) q^{35} +(-0.380763 + 3.16002i) q^{36} +(-7.17389 + 9.15679i) q^{37} +(4.80564 + 6.96217i) q^{38} +(-4.78538 - 4.01250i) q^{39} +(-3.49674 + 5.06590i) q^{40} +(1.12563 + 3.61227i) q^{41} +(1.53391 + 8.34876i) q^{42} +(4.10862 + 0.498877i) q^{43} +(0.276760 - 1.51023i) q^{44} +(-2.03622 - 11.0542i) q^{45} +(1.49062 - 8.13406i) q^{46} +(4.04344 + 1.81980i) q^{47} +(-8.51135 + 1.56379i) q^{48} +(0.393449 + 0.749654i) q^{49} +(-4.70427 + 15.0965i) q^{50} +(-5.77163 + 12.8397i) q^{51} +(-1.47611 + 3.52908i) q^{52} +(-0.799081 - 3.24200i) q^{53} +(5.15399 - 7.48881i) q^{54} +(0.653565 + 5.38259i) q^{55} +(-4.07494 + 2.13869i) q^{56} +(-1.01330 - 8.31348i) q^{57} +(1.61286 + 3.58362i) q^{58} +(-0.323629 + 5.35022i) q^{59} +(-6.09502 + 3.20247i) q^{60} +(1.67812 + 0.413618i) q^{61} +(7.19229 - 6.37181i) q^{62} +(2.49274 - 8.02533i) q^{63} +(-0.208135 - 0.396569i) q^{64} +(1.26906 - 13.4493i) q^{65} +(-2.70296 + 3.45333i) q^{66} +(-10.6143 - 4.77710i) q^{67} +(8.56012 + 1.03939i) q^{68} +(-5.04598 + 6.44678i) q^{69} +(-12.9840 + 12.9840i) q^{70} +(0.375728 + 1.20575i) q^{71} +(4.70689 + 1.46200i) q^{72} +(6.83304 - 1.25220i) q^{73} +(-13.4955 - 15.2333i) q^{74} +(11.0642 - 11.0743i) q^{75} +(-4.67812 + 2.10545i) q^{76} +(-1.43748 + 3.79033i) q^{77} +(8.41427 - 6.96975i) q^{78} +(2.44702 + 6.45225i) q^{79} +(-13.2369 - 13.2369i) q^{80} +(-7.96144 + 4.19708i) q^{81} +(-6.57134 + 0.797905i) q^{82} +(0.218247 + 0.0680085i) q^{83} +(-5.14756 + 0.00235472i) q^{84} +(-29.9529 + 5.48907i) q^{85} +(-2.15424 + 6.91320i) q^{86} +(0.233127 - 3.88352i) q^{87} +(-2.22305 - 0.843091i) q^{88} +(0.769106 - 0.769106i) q^{89} +(19.6654 - 0.0179916i) q^{90} +(5.51297 - 8.46247i) q^{91} +(4.68888 + 1.77826i) q^{92} +(-9.23517 + 2.28075i) q^{93} +(-4.40687 + 6.38446i) q^{94} +(13.5605 - 12.0135i) q^{95} +(-0.00432247 - 9.44918i) q^{96} +(4.07212 - 0.246318i) q^{97} +(-1.41416 + 0.440671i) q^{98} +(3.95737 - 1.78542i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27}+ \cdots - 58 q^{99}+O(q^{100})$ 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$ .

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{3}{52}\right)$

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

)

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

$2$	−0.315367	+	1.72090i	−0.222998	+	1.21686i	0.661366	+	0.750063i	$0.269977\pi$
$2$	−0.315367	+	1.72090i	−0.222998	+	1.21686i	−0.884364	+	0.466798i	$0.845408\pi$
$3$	1.06756	−	1.36393i	0.616359	−	0.787466i
$3$	1.06756	−	1.36393i	0.616359	−	0.787466i
$4$	−0.992015	−	0.376222i	−0.496007	−	0.188111i
$5$	3.73990	+	0.226222i	1.67253	+	0.101170i	0.869232	−	0.494405i	$-0.164614\pi$
$5$	3.73990	+	0.226222i	1.67253	+	0.101170i	0.803300	+	0.595574i	$0.203075\pi$
$6$	2.01052	+	2.26731i	0.820790	+	0.925627i
$7$	2.39720	+	1.44916i	0.906057	+	0.547730i	0.891932	−	0.452170i	$-0.149350\pi$
$7$	2.39720	+	1.44916i	0.906057	+	0.547730i	0.0141248	+	0.999900i	$0.495504\pi$
$8$	−0.849938	+	1.40597i	−0.300498	+	0.497085i
$9$	−0.720612	−	2.91217i	−0.240204	−	0.970722i
$10$	−1.56875	+	6.36465i	−0.496081	+	2.01268i
$11$	0.260858	+	1.42346i	0.0786517	+	0.429188i	0.999252	+	0.0386812i	$0.0123157\pi$
$11$	0.260858	+	1.42346i	0.0786517	+	0.429188i	−0.920600	+	0.390507i	$0.872300\pi$
$12$	−1.57218	+	0.951398i	−0.453849	+	0.274645i
$13$	0.121358	−	3.60351i	0.0336587	−	0.999433i
$13$	0.121358	−	3.60351i	0.0336587	−	0.999433i
$14$	−3.24986	+	3.66833i	−0.868561	+	0.980403i
$15$	4.30113	−	4.85945i	1.11055	−	1.25470i
$16$	−3.73977	−	3.31315i	−0.934943	−	0.828287i
$17$	−7.89137	+	1.94505i	−1.91394	+	0.471743i	−0.916514	+	0.400003i	$0.869009\pi$
$17$	−7.89137	+	1.94505i	−1.91394	+	0.471743i	−0.997423	+	0.0717403i	$0.977145\pi$
$18$	5.23881	−	0.321700i	1.23480	−	0.0758255i
$19$	3.41908	−	3.41908i	0.784392	−	0.784392i	−0.196177	−	0.980569i	$-0.562853\pi$
$19$	3.41908	−	3.41908i	0.784392	−	0.784392i	0.980569	+	0.196177i	$0.0628527\pi$
$20$	−3.62492	−	1.63145i	−0.810557	−	0.364802i
$21$	4.53572	−	1.72254i	0.989775	−	0.375890i
$22$	−2.53189			−0.539802
$23$	−4.72662			−0.985569			−0.492785	−	0.870151i	$-0.664021\pi$
$23$	−4.72662			−0.985569			−0.492785	+	0.870151i	$0.664021\pi$
$24$	1.01028	+	2.66022i	0.206223	+	0.543015i
$25$	8.97210	+	1.08941i	1.79442	+	0.217882i
$26$	6.16301	+	1.34527i	1.20867	+	0.263830i
$27$	−4.74129	−	2.12606i	−0.912462	−	0.409161i
$28$	−1.83285	−	2.33947i	−0.346377	−	0.442117i
$29$	1.84858	−	1.27598i	0.343272	−	0.236943i	−0.383938	−	0.923359i	$-0.625432\pi$
$29$	1.84858	−	1.27598i	0.343272	−	0.236943i	0.727210	+	0.686416i	$0.240817\pi$
$30$	7.00620	+	8.93434i	1.27915	+	1.63118i
$31$	−4.32331	−	3.38710i	−0.776489	−	0.608340i	0.148247	−	0.988950i	$-0.452637\pi$
$31$	−4.32331	−	3.38710i	−0.776489	−	0.608340i	−0.924736	+	0.380610i	$0.875714\pi$
$32$	4.29447	−	3.36450i	0.759162	−	0.594765i
$33$	2.21998	+	1.16384i	0.386449	+	0.202598i
$34$	−0.858559	−	14.1937i	−0.147242	−	2.43419i
$35$	8.63745	+	5.96200i	1.46000	+	1.00776i
$36$	−0.380763	+	3.16002i	−0.0634605	+	0.526671i
$37$	−7.17389	+	9.15679i	−1.17938	+	1.50537i	−0.359202	+	0.933260i	$0.616951\pi$
$37$	−7.17389	+	9.15679i	−1.17938	+	1.50537i	−0.820179	+	0.572108i	$0.806126\pi$
$38$	4.80564	+	6.96217i	0.779578	+	1.12941i
$39$	−4.78538	−	4.01250i	−0.766273	−	0.642515i
$40$	−3.49674	+	5.06590i	−0.552883	+	0.800989i
$41$	1.12563	+	3.61227i	0.175794	+	0.564141i	0.999998	−	0.00215155i	$-0.000684859\pi$
$41$	1.12563	+	3.61227i	0.175794	+	0.564141i	−0.824204	+	0.566293i	$0.808377\pi$
$42$	1.53391	+	8.34876i	0.236688	+	1.28824i
$43$	4.10862	+	0.498877i	0.626558	+	0.0760780i	0.427656	−	0.903941i	$-0.359339\pi$
$43$	4.10862	+	0.498877i	0.626558	+	0.0760780i	0.198902	+	0.980019i	$0.436262\pi$
$44$	0.276760	−	1.51023i	0.0417231	−	0.227676i
$45$	−2.03622	−	11.0542i	−0.303541	−	1.64787i
$46$	1.49062	−	8.13406i	0.219780	−	1.19930i
$47$	4.04344	+	1.81980i	0.589796	+	0.265446i	0.683258	−	0.730177i	$-0.260562\pi$
$47$	4.04344	+	1.81980i	0.589796	+	0.265446i	−0.0934616	+	0.995623i	$0.529793\pi$
$48$	−8.51135	+	1.56379i	−1.22851	+	0.225713i
$49$	0.393449	+	0.749654i	0.0562070	+	0.107093i
$50$	−4.70427	+	15.0965i	−0.665284	+	2.13497i
$51$	−5.77163	+	12.8397i	−0.808190	+	1.79792i
$52$	−1.47611	+	3.52908i	−0.204699	+	0.489395i
$53$	−0.799081	−	3.24200i	−0.109762	−	0.445323i	0.890185	−	0.455599i	$-0.150575\pi$
$53$	−0.799081	−	3.24200i	−0.109762	−	0.445323i	−0.999947	+	0.0102766i	$0.996729\pi$
$54$	5.15399	−	7.48881i	0.701370	−	1.01910i
$55$	0.653565	+	5.38259i	0.0881266	+	0.725788i
$56$	−4.07494	+	2.13869i	−0.544537	+	0.285795i
$57$	−1.01330	−	8.31348i	−0.134215	−	1.10115i
$58$	1.61286	+	3.58362i	0.211778	+	0.470552i
$59$	−0.323629	+	5.35022i	−0.0421329	+	0.696540i	0.914381	+	0.404854i	$0.132678\pi$
$59$	−0.323629	+	5.35022i	−0.0421329	+	0.696540i	−0.956514	+	0.291686i	$0.905784\pi$
$60$	−6.09502	+	3.20247i	−0.786863	+	0.413437i
$61$	1.67812	+	0.413618i	0.214861	+	0.0529584i	0.345277	−	0.938501i	$-0.387785\pi$
$61$	1.67812	+	0.413618i	0.214861	+	0.0529584i	−0.130416	+	0.991459i	$0.541631\pi$
$62$	7.19229	−	6.37181i	0.913421	−	0.809221i
$63$	2.49274	−	8.02533i	0.314056	−	1.01110i
$64$	−0.208135	−	0.396569i	−0.0260169	−	0.0495711i
$65$	1.26906	−	13.4493i	0.157408	−	1.66818i
$66$	−2.70296	+	3.45333i	−0.332712	+	0.425075i
$67$	−10.6143	−	4.77710i	−1.29674	−	0.583615i	−0.359775	−	0.933039i	$-0.617147\pi$
$67$	−10.6143	−	4.77710i	−1.29674	−	0.583615i	−0.936965	+	0.349423i	$0.886377\pi$
$68$	8.56012	+	1.03939i	1.03807	+	0.126044i
$69$	−5.04598	+	6.44678i	−0.607464	+	0.776102i
$70$	−12.9840	+	12.9840i	−1.55188	+	1.55188i
$71$	0.375728	+	1.20575i	0.0445907	+	0.143097i	0.974331	−	0.225118i	$-0.0722768\pi$
$71$	0.375728	+	1.20575i	0.0445907	+	0.143097i	−0.929741	+	0.368215i	$0.879969\pi$
$72$	4.70689	+	1.46200i	0.554712	+	0.172299i
$73$	6.83304	−	1.25220i	0.799747	−	0.146559i	0.235186	−	0.971950i	$-0.424430\pi$
$73$	6.83304	−	1.25220i	0.799747	−	0.146559i	0.564561	+	0.825391i	$0.309045\pi$
$74$	−13.4955	−	15.2333i	−1.56882	−	1.77084i
$75$	11.0642	−	11.0743i	1.27758	−	1.27875i
$76$	−4.67812	+	2.10545i	−0.536617	+	0.241512i
$77$	−1.43748	+	3.79033i	−0.163817	+	0.431949i
$78$	8.41427	−	6.96975i	0.952729	−	0.789169i
$79$	2.44702	+	6.45225i	0.275311	+	0.725935i	0.999346	+	0.0361715i	$0.0115163\pi$
$79$	2.44702	+	6.45225i	0.275311	+	0.725935i	−0.724035	+	0.689763i	$0.757715\pi$
$80$	−13.2369	−	13.2369i	−1.47992	−	1.47992i
$81$	−7.96144	+	4.19708i	−0.884604	+	0.466343i
$82$	−6.57134	+	0.797905i	−0.725683	+	0.0881139i
$83$	0.218247	+	0.0680085i	0.0239557	+	0.00746490i	0.309457	−	0.950913i	$-0.399853\pi$
$83$	0.218247	+	0.0680085i	0.0239557	+	0.00746490i	−0.285502	+	0.958378i	$0.592160\pi$
$84$	−5.14756	+	0.00235472i	−0.561645	+	0.000256921i
$85$	−29.9529	+	5.48907i	−3.24885	+	0.595373i
$86$	−2.15424	+	6.91320i	−0.232298	+	0.745470i
$87$	0.233127	−	3.88352i	0.0249938	−	0.416357i
$88$	−2.22305	−	0.843091i	−0.236978	−	0.0898738i
$89$	0.769106	−	0.769106i	0.0815250	−	0.0815250i	−0.665168	−	0.746693i	$-0.731640\pi$
$89$	0.769106	−	0.769106i	0.0815250	−	0.0815250i	0.746693	+	0.665168i	$0.231640\pi$
$90$	19.6654	−	0.0179916i	2.07291	−	0.00189648i
$91$	5.51297	−	8.46247i	0.577917	−	0.887107i
$92$	4.68888	+	1.77826i	0.488850	+	0.185396i
$93$	−9.23517	+	2.28075i	−0.957643	+	0.236502i
$94$	−4.40687	+	6.38446i	−0.454534	+	0.658507i
$95$	13.5605	−	12.0135i	1.39128	−	1.23256i
$96$	−0.00432247	−	9.44918i	−0.000441160	−	0.964403i
$97$	4.07212	−	0.246318i	0.413461	−	0.0250098i	0.147661	−	0.989038i	$-0.452826\pi$
$97$	4.07212	−	0.246318i	0.413461	−	0.0250098i	0.265800	+	0.964028i	$0.414364\pi$
$98$	−1.41416	+	0.440671i	−0.142852	+	0.0445145i
$99$	3.95737	−	1.78542i	0.397730	−	0.179442i
$100$	−8.49060	−	4.45621i	−0.849060	−	0.445621i
$101$	−0.661505	+	5.44798i	−0.0658222	+	0.542095i	0.922078	+	0.387004i	$0.126490\pi$
$101$	−0.661505	+	5.44798i	−0.0658222	+	0.542095i	−0.987900	+	0.155091i	$0.950433\pi$
$102$	−20.2757	−	13.9816i	−2.00760	−	1.38439i
$103$	5.94248	−	11.3224i	0.585530	−	1.11563i	−0.394892	−	0.918727i	$-0.629218\pi$
$103$	5.94248	−	11.3224i	0.585530	−	1.11563i	0.980422	−	0.196907i	$-0.0630896\pi$
$104$	4.96327	+	3.23338i	0.486689	+	0.317059i
$105$	17.3528	−	5.41606i	1.69346	−	0.528553i
$106$	5.83116	−	0.352720i	0.566373	−	0.0342592i
$107$	−7.07166	−	7.98225i	−0.683643	−	0.771673i	0.299582	−	0.954071i	$-0.403153\pi$
$107$	−7.07166	−	7.98225i	−0.683643	−	0.771673i	−0.983225	+	0.182397i	$0.941614\pi$
$108$	3.90356	+	3.89286i	0.375620	+	0.374591i
$109$	11.1140	+	14.1859i	1.06452	+	1.35876i	0.929877	+	0.367870i	$0.119913\pi$
$109$	11.1140	+	14.1859i	1.06452	+	1.35876i	0.134646	+	0.990894i	$0.457010\pi$
$110$	−9.46902	−	0.572770i	−0.902836	−	0.0546115i
$111$	4.83064	+	19.5602i	0.458504	+	1.85657i
$112$	−4.16371	−	13.3618i	−0.393433	−	1.26257i
$113$	3.01770	+	5.74976i	0.283882	+	0.540891i	0.985085	−	0.172070i	$-0.0550456\pi$
$113$	3.01770	+	5.74976i	0.283882	+	0.540891i	−0.701203	+	0.712962i	$0.747353\pi$
$114$	14.6263	+	0.878010i	1.36987	+	0.0822332i
$115$	−17.6771	−	1.06927i	−1.64840	−	0.0997096i
$116$	−2.31387	+	0.570317i	−0.214837	+	0.0529526i
$117$	−10.5815	+	2.24331i	−0.978257	+	0.207394i
$118$	−9.10515	−	2.24422i	−0.838197	−	0.206597i
$119$	−21.7359	−	6.77317i	−1.99252	−	0.620895i
$120$	3.17654	+	10.1775i	0.289977	+	0.929073i
$121$	8.32700	−	3.15801i	0.757000	−	0.287092i
$122$	−1.24102	+	2.75743i	−0.112357	+	0.249646i
$123$	6.12856	+	2.32105i	0.552594	+	0.209282i
$124$	3.01449	+	4.98657i	0.270709	+	0.447807i
$125$	14.8815	+	2.72713i	1.33104	+	0.243922i
$126$	13.0247	+	6.82069i	1.16033	+	0.607635i
$127$	3.28009	−	1.24398i	0.291061	−	0.110385i	−0.204753	−	0.978814i	$-0.565639\pi$
$127$	3.28009	−	1.24398i	0.291061	−	0.110385i	0.495814	+	0.868429i	$0.334870\pi$
$128$	11.1650	−	3.47916i	0.986858	−	0.307517i
$129$	5.06665	−	5.07129i	0.446094	−	0.446502i
$130$	22.7447	+	6.42539i	1.99484	+	0.563544i
$131$	10.7746	−	7.43714i	0.941377	−	0.649786i	0.00470347	−	0.999989i	$-0.498503\pi$
$131$	10.7746	−	7.43714i	0.941377	−	0.649786i	0.936674	+	0.350203i	$0.113887\pi$
$132$	−1.76439	−	1.98975i	−0.153570	−	0.173185i
$133$	13.1510	−	3.24144i	1.14034	−	0.281068i
$134$	11.5683	−	16.7596i	0.999350	−	1.44781i
$135$	−17.2510	−	9.02384i	−1.48473	−	0.776648i
$136$	3.97249	−	12.7482i	0.340639	−	1.09315i
$137$	−1.08931	−	1.39041i	−0.0930663	−	0.118790i	0.738406	−	0.674356i	$-0.235579\pi$
$137$	−1.08931	−	1.39041i	−0.0930663	−	0.118790i	−0.831473	+	0.555566i	$0.812502\pi$
$138$	−9.50295	−	10.7167i	−0.808945	−	0.912269i
$139$	−7.04246	−	6.23907i	−0.597334	−	0.529191i	0.309380	−	0.950939i	$-0.399879\pi$
$139$	−7.04246	−	6.23907i	−0.597334	−	0.529191i	−0.906713	+	0.421747i	$0.861417\pi$
$140$	−6.32544	−	9.16399i	−0.534598	−	0.774498i
$141$	6.79872	−	3.57221i	0.572556	−	0.300834i
$142$	−2.19348	+	0.266336i	−0.184072	+	0.0223504i
$143$	5.16109	−	0.767256i	0.431592	−	0.0641612i
$144$	−6.95352	+	13.2783i	−0.579460	+	1.10653i
$145$	7.20213	−	4.35384i	0.598105	−	0.361567i
$146$			12.1539i			1.00586i
$147$	1.44251	+	0.263667i	0.118976	+	0.0217469i
$148$	10.5616	−	6.38470i	0.868157	−	0.524819i
$149$	3.42528	−	7.61067i	0.280610	−	0.623490i	−0.716652	−	0.697430i	$-0.754327\pi$
$149$	3.42528	−	7.61067i	0.280610	−	0.623490i	0.997263	+	0.0739401i	$0.0235574\pi$
$150$	15.5685	+	22.5328i	1.27116	+	1.83980i
$151$	4.44377	−	1.99998i	0.361629	−	0.162756i	−0.221450	−	0.975172i	$-0.571079\pi$
$151$	4.44377	−	1.99998i	0.361629	−	0.162756i	0.583078	+	0.812416i	$0.301848\pi$
$152$	1.90112	+	7.71313i	0.154201	+	0.625618i
$153$	11.3509	+	21.5794i	0.917667	+	1.74459i
$154$	−6.06946	−	3.66912i	−0.489091	−	0.295666i
$155$	−15.4025	−	13.6454i	−1.23716	−	1.09603i
$156$	3.23757	+	5.78082i	0.259213	+	0.462836i
$157$	−16.3842	+	14.5151i	−1.30760	+	1.15843i	−0.330938	+	0.943653i	$0.607365\pi$
$157$	−16.3842	+	14.5151i	−1.30760	+	1.15843i	−0.976662	+	0.214780i	$0.931097\pi$
$158$	−11.8754	+	2.17625i	−0.944756	+	0.173133i
$159$	−5.27493	−	2.37115i	−0.418329	−	0.188045i
$160$	16.8220	−	11.6114i	1.32989	−	0.917960i
$161$	−11.3307	−	6.84963i	−0.892981	−	0.539826i
$162$	−4.71199	−	15.0245i	−0.370209	−	1.18043i
$163$	3.71138	−	4.73723i	0.290698	−	0.371048i	−0.619660	−	0.784870i	$-0.712729\pi$
$163$	3.71138	−	4.73723i	0.290698	−	0.371048i	0.910358	+	0.413822i	$0.135806\pi$
$164$	0.242373	−	4.00691i	0.0189262	−	0.312887i
$165$	8.03920	+	4.85485i	0.625851	+	0.377949i
$166$	−0.185864	+	0.354134i	−0.0144258	+	0.0274861i
$167$	−22.2516	−	4.07775i	−1.72188	−	0.315546i	−0.773764	−	0.633474i	$-0.781628\pi$
$167$	−22.2516	−	4.07775i	−1.72188	−	0.315546i	−0.948115	+	0.317929i	$0.897013\pi$
$168$	−1.43323	+	7.84113i	−0.110576	+	0.604956i
$169$	−12.9705	−	0.874631i	−0.997734	−	0.0672793i
$170$		−	53.2771i		−	4.08616i
$171$	−12.4208	−	7.49311i	−0.949840	−	0.573013i
$172$	−3.88812	−	2.04064i	−0.296467	−	0.155598i
$173$	−6.05776	+	15.9730i	−0.460563	+	1.21440i	0.480747	+	0.876859i	$0.340366\pi$
$173$	−6.05776	+	15.9730i	−0.460563	+	1.21440i	−0.941310	+	0.337545i	$0.890404\pi$
$174$	6.60963	+	1.62592i	0.501075	+	0.123261i
$175$	19.9292	+	15.6135i	1.50651	+	1.18027i
$176$	3.74057	−	6.18766i	0.281956	−	0.466413i
$177$	6.95184	+	6.15311i	0.522532	+	0.462496i
$178$	1.08100	+	1.56611i	0.0810247	+	0.117385i
$179$	−10.1320	−	2.49731i	−0.757299	−	0.186658i	−0.158282	−	0.987394i	$-0.550596\pi$
$179$	−10.1320	−	2.49731i	−0.757299	−	0.186658i	−0.599017	+	0.800736i	$0.704442\pi$
$180$	−2.13888	+	11.7320i	−0.159423	+	0.874453i
$181$	7.24544	+	8.17841i	0.538549	+	0.607896i	0.953295	−	0.302041i	$-0.0976680\pi$
$181$	7.24544	+	8.17841i	0.538549	+	0.607896i	−0.414746	+	0.909937i	$0.636130\pi$
$182$	12.8245	+	12.1561i	0.950612	+	0.901068i
$183$	2.35564	−	1.84727i	0.174134	−	0.136554i
$184$	4.01734	−	6.64548i	0.296162	−	0.489912i
$185$	−28.9011	+	32.6226i	−2.12485	+	2.39846i
$186$	−1.01247	−	16.6121i	−0.0742382	−	1.21806i
$187$	−4.82721	−	10.7256i	−0.353001	−	0.784336i
$188$	−3.32650	−	3.32650i	−0.242610	−	0.242610i
$189$	−8.28483	−	11.9675i	−0.602633	−	0.870506i
$190$	16.3976	+	27.1249i	1.18961	+	1.96785i
$191$		−	25.3939i		−	1.83744i	−0.394908	−	0.918721i	$-0.629224\pi$
$191$		−	25.3939i		−	1.83744i	0.394908	−	0.918721i	$-0.370776\pi$
$192$	−0.763090	−	0.139481i	−0.0550713	−	0.0100661i
$193$	−9.86192	−	16.3136i	−0.709876	−	1.17428i	−0.977537	−	0.210765i	$-0.932404\pi$
$193$	−9.86192	−	16.3136i	−0.709876	−	1.17428i	0.267660	−	0.963513i	$-0.413749\pi$
$194$	−0.860322	+	7.08539i	−0.0617675	+	0.508702i
$195$	−16.9891	−	16.0889i	−1.21661	−	1.15215i
$196$	−0.108271	−	0.891692i	−0.00773365	−	0.0636923i
$197$	−0.183656	+	0.143885i	−0.0130849	+	0.0102514i	−0.623240	−	0.782031i	$-0.714184\pi$
$197$	−0.183656	+	0.143885i	−0.0130849	+	0.0102514i	0.610155	+	0.792282i	$0.291107\pi$
$198$	1.82451	+	7.37330i	0.129662	+	0.523998i
$199$	−11.2851	+	12.7383i	−0.799983	+	0.902994i	−0.997000	−	0.0774062i	$-0.975336\pi$
$199$	−11.2851	+	12.7383i	−0.799983	+	0.902994i	0.197017	+	0.980400i	$0.436875\pi$
$200$	−9.15740	+	11.6886i	−0.647526	+	0.826506i
$201$	−17.8471	+	9.37727i	−1.25883	+	0.661422i
$202$	−9.16683	−	2.85650i	−0.644976	−	0.200983i
$203$	6.28050	−	0.379900i	0.440805	−	0.0266638i
$204$	10.5561	−	10.5658i	0.739077	−	0.739754i
$205$	3.39256	+	13.7641i	0.236946	+	0.961329i
$206$	17.6108	+	13.7972i	1.22700	+	0.961293i
$207$	3.40606	+	13.7647i	0.236738	+	0.956714i
$208$	−12.3928	+	13.0742i	−0.859287	+	0.906534i
$209$	5.75881	+	3.97502i	0.398345	+	0.274958i
$210$	3.84801	+	31.5705i	0.265538	+	2.17857i
$211$	−1.87985	−	4.95677i	−0.129414	−	0.341238i	0.854610	−	0.519270i	$-0.173796\pi$
$211$	−1.87985	−	4.95677i	−0.129414	−	0.341238i	−0.984025	+	0.178032i	$0.943027\pi$
$212$	−0.427010	+	3.51674i	−0.0293271	+	0.241531i
$213$	2.04568	+	0.774753i	0.140167	+	0.0530852i
$214$	15.9668	−	9.65229i	1.09147	−	0.659817i
$215$	15.2529	+	2.79521i	1.04024	+	0.190631i
$216$	7.01898	−	4.85909i	0.477581	−	0.330619i
$217$	−5.45540	−	14.3847i	−0.370337	−	0.976497i
$218$	−27.9175	+	14.6523i	−1.89081	+	0.992376i
$219$	5.58680	−	10.6566i	0.377521	−	0.720106i
$220$	1.37670	−	5.58549i	0.0928171	−	0.376574i
$221$	6.05131	+	28.6726i	0.407055	+	1.92873i
$222$	−35.1845	+	2.14443i	−2.36143	+	0.143924i
$223$	−0.280400	+	4.63557i	−0.0187770	+	0.310421i	0.976646	+	0.214854i	$0.0689277\pi$
$223$	−0.280400	+	4.63557i	−0.0187770	+	0.310421i	−0.995423	+	0.0955662i	$0.969534\pi$
$224$	15.1704	−	1.84202i	1.01361	−	0.123075i
$225$	−3.29285	−	26.9133i	−0.219524	−	1.79422i
$226$	−10.8464	+	3.37989i	−0.721495	+	0.224827i
$227$	15.5486	−	6.99787i	1.03200	−	0.464465i	0.177611	−	0.984101i	$-0.443163\pi$
$227$	15.5486	−	6.99787i	1.03200	−	0.464465i	0.854388	+	0.519636i	$0.173932\pi$
$228$	−2.12251	+	8.62833i	−0.140566	+	0.571425i
$229$	5.47688	−	4.29086i	0.361923	−	0.283548i	−0.419241	−	0.907875i	$-0.637704\pi$
$229$	5.47688	−	4.29086i	0.361923	−	0.283548i	0.781163	+	0.624327i	$0.214627\pi$
$230$	7.41487	−	30.0833i	0.488922	−	1.98363i
$231$	3.63514	+	6.00706i	0.239175	+	0.395235i
$232$	0.222813	+	3.68354i	0.0146284	+	0.241836i
$233$	22.6796	−	11.9032i	1.48579	−	0.779802i	0.490021	−	0.871710i	$-0.336989\pi$
$233$	22.6796	−	11.9032i	1.48579	−	0.779802i	0.995767	+	0.0919082i	$0.0292966\pi$
$234$	−0.523477	−	18.9171i	−0.0342208	−	1.23665i
$235$	14.7104	+	7.72059i	0.959598	+	0.503636i
$236$	2.33391	−	5.18574i	0.151925	−	0.337563i
$237$	11.4128	+	3.55064i	0.741339	+	0.230639i
$238$	18.5107	−	35.2693i	1.19987	−	2.28617i
$239$	−1.77462	−	1.77462i	−0.114790	−	0.114790i	0.647378	−	0.762169i	$-0.275865\pi$
$239$	−1.77462	−	1.77462i	−0.114790	−	0.114790i	−0.762169	+	0.647378i	$0.775865\pi$
$240$	−32.1853	+	3.92295i	−2.07755	+	0.253225i
$241$	0.850814	+	14.0656i	0.0548058	+	0.906047i	0.916854	+	0.399222i	$0.130720\pi$
$241$	0.850814	+	14.0656i	0.0548058	+	0.906047i	−0.862049	+	0.506826i	$0.830819\pi$
$242$	2.80857	+	15.3259i	0.180542	+	0.985185i
$243$	−2.77482	+	15.3395i	−0.178005	+	0.984030i
$244$	−1.50910	−	1.04166i	−0.0966105	−	0.0666854i
$245$	1.30187	+	2.89264i	0.0831734	+	0.184804i
$246$	−5.92704	+	9.81467i	−0.377895	+	0.625760i
$247$	−11.9058	−	12.7356i	−0.757546	−	0.810349i
$248$	8.43669	−	3.19962i	0.535730	−	0.203176i
$249$	0.325752	−	0.225070i	0.0206437	−	0.0142632i
$250$	−9.38625	+	24.7495i	−0.593638	+	1.56530i
$251$	−0.482727	−	3.97561i	−0.0304694	−	0.250938i	−0.999983	−	0.00589919i	$-0.998122\pi$
$251$	−0.482727	−	3.97561i	−0.0304694	−	0.250938i	0.969513	−	0.245039i	$-0.0788009\pi$
$252$	−5.49214	+	7.02342i	−0.345972	+	0.442434i
$253$	−1.23298	−	6.72814i	−0.0775166	−	0.422995i
$254$	1.10633	+	6.03703i	0.0694171	+	0.378797i
$255$	−24.4899	+	46.7136i	−1.53362	+	2.92532i
$256$	2.35825	+	19.4219i	0.147391	+	1.21387i
$257$	−1.53688	+	4.05241i	−0.0958677	+	0.252782i	−0.974368	−	0.224959i	$-0.927775\pi$
$257$	−1.53688	+	4.05241i	−0.0958677	+	0.252782i	0.878501	+	0.477741i	$0.158544\pi$
$258$	7.12933	+	10.3185i	0.443853	+	0.642403i
$259$	−30.4669	+	11.5546i	−1.89312	+	0.717966i
$260$	−6.31884	+	12.8644i	−0.391878	+	0.797819i
$261$	−5.04797	−	4.46388i	−0.312462	−	0.276307i
$262$	9.40065	+	20.8874i	0.580774	+	1.29043i
$263$	8.88811	+	6.13502i	0.548064	+	0.378301i	0.809681	−	0.586871i	$-0.199640\pi$
$263$	8.88811	+	6.13502i	0.548064	+	0.378301i	−0.261617	+	0.965172i	$0.584256\pi$
$264$	−3.52316	+	2.13203i	−0.216836	+	0.131217i
$265$	−2.25507	−	12.3055i	−0.138528	−	0.755921i
$266$	1.43080	+	23.6539i	0.0877277	+	1.45031i
$267$	−0.227936	−	1.87008i	−0.0139495	−	0.114447i
$268$	8.73227	+	8.73227i	0.533409	+	0.533409i
$269$	1.08808	−	2.07316i	0.0663412	−	0.126403i	−0.850027	−	0.526739i	$-0.823414\pi$
$269$	1.08808	−	2.07316i	0.0663412	−	0.126403i	0.916368	+	0.400337i	$0.131107\pi$
$270$	20.9695	−	26.8414i	1.27616	−	1.63352i
$271$	−3.39401	+	7.54118i	−0.206171	+	0.458094i	−0.985751	−	0.168209i	$-0.946202\pi$
$271$	−3.39401	+	7.54118i	−0.206171	+	0.458094i	0.779580	+	0.626303i	$0.215433\pi$
$272$	35.9561	+	18.8712i	2.18016	+	1.14424i
$273$	−5.65676	−	16.5535i	−0.342362	−	1.00187i
$274$	2.73629	−	1.43611i	0.165305	−	0.0867588i
$275$	0.789717	+	13.0556i	0.0476217	+	0.787281i
$276$	7.43110	−	4.49690i	0.447300	−	0.270682i
$277$	−2.73688	+	11.1039i	−0.164443	+	0.667172i	0.829617	+	0.558334i	$0.188559\pi$
$277$	−2.73688	+	11.1039i	−0.164443	+	0.667172i	−0.994060	+	0.108838i	$0.965287\pi$
$278$	12.9578	−	10.1518i	0.777157	−	0.608864i
$279$	−6.74836	+	15.0310i	−0.404014	+	0.899881i
$280$	−15.7237	+	7.07665i	−0.939670	+	0.422911i
$281$	3.50527	−	1.09229i	0.209107	−	0.0651604i	−0.191160	−	0.981559i	$-0.561225\pi$
$281$	3.50527	−	1.09229i	0.209107	−	0.0651604i	0.400267	+	0.916398i	$0.368917\pi$
$282$	4.00333	+	12.8265i	0.238395	+	0.763806i
$283$	0.738599	−	0.0896821i	0.0439051	−	0.00533105i	−0.0985546	−	0.995132i	$-0.531422\pi$
$283$	0.738599	−	0.0896821i	0.0439051	−	0.00533105i	0.142460	+	0.989801i	$0.454499\pi$
$284$	0.0809028	−	1.33748i	0.00480070	−	0.0793650i
$285$	−1.90894	−	31.3208i	−0.113076	−	1.85528i
$286$	−0.307266	+	9.12370i	−0.0181690	+	0.539496i
$287$	−2.53639	+	10.2905i	−0.149718	+	0.607431i
$288$	−12.8926	−	10.0817i	−0.759706	−	0.594071i
$289$	43.4377	−	22.7979i	2.55516	−	1.34105i
$290$	5.22122	+	13.7672i	0.306601	+	0.808439i
$291$	4.01129	−	5.81704i	0.235146	−	0.341001i
$292$	−7.24958	−	1.32854i	−0.424250	−	0.0777467i
$293$	−28.0870	+	16.9792i	−1.64086	+	0.991934i	−0.673272	+	0.739395i	$0.735112\pi$
$293$	−28.0870	+	16.9792i	−1.64086	+	0.991934i	−0.967587	+	0.252538i	$0.918735\pi$
$294$	−0.908665	+	2.39926i	−0.0529944	+	0.139928i
$295$	−2.42068	+	19.9361i	−0.140937	+	1.16072i
$296$	−6.77681	−	17.8690i	−0.393894	−	1.03861i
$297$	1.78955	−	7.30362i	0.103840	−	0.423799i
$298$	12.0170	+	8.29473i	0.696126	+	0.480501i
$299$	−0.573615	+	17.0324i	−0.0331730	+	0.985011i
$300$	−15.1422	+	6.82329i	−0.874236	+	0.393943i
$301$	9.12623	+	7.14995i	0.526027	+	0.412116i
$302$	2.04035	+	8.27802i	0.117409	+	0.476346i
$303$	6.72447	+	6.71832i	0.386311	+	0.385957i
$304$	−24.1145	+	1.45866i	−1.38306	+	0.0836599i
$305$	6.18241	+	1.92652i	0.354004	+	0.110312i
$306$	−40.7157	+	12.7284i	−2.32756	+	0.727634i
$307$	−11.3080	+	14.4336i	−0.645383	+	0.823771i	−0.993518	−	0.113674i	$-0.963738\pi$
$307$	−11.3080	+	14.4336i	−0.645383	+	0.823771i	0.348135	+	0.937444i	$0.386815\pi$
$308$	2.85201	−	3.21926i	0.162508	−	0.183434i
$309$	−9.09905	−	20.1926i	−0.517627	−	1.14872i
$310$	28.3398	−	22.2029i	1.60960	−	1.26104i
$311$	−1.93014	−	15.8962i	−0.109448	−	0.901389i	−0.939227	−	0.343296i	$-0.888456\pi$
$311$	−1.93014	−	15.8962i	−0.109448	−	0.901389i	0.829779	−	0.558093i	$-0.188467\pi$
$312$	9.70872	−	3.31771i	0.549648	−	0.187828i
$313$	−1.99055	+	16.3937i	−0.112513	+	0.926624i	0.821703	+	0.569916i	$0.193024\pi$
$313$	−1.99055	+	16.3937i	−0.112513	+	0.926624i	−0.934216	+	0.356708i	$0.883899\pi$
$314$	−19.8121	−	32.7732i	−1.11806	−	1.84950i
$315$	11.1381	−	29.4500i	0.627561	−	1.65932i
$316$		−	7.32135i		−	0.411858i
$317$	10.3137	+	17.0609i	0.579275	+	0.958237i	0.998726	+	0.0504596i	$0.0160686\pi$
$317$	10.3137	+	17.0609i	0.579275	+	0.958237i	−0.419451	+	0.907778i	$0.637778\pi$
$318$	5.74406	−	8.32985i	0.322111	−	0.467115i
$319$	2.29852	+	2.29852i	0.128692	+	0.128692i
$320$	−0.688692	−	1.53021i	−0.0384990	−	0.0855413i
$321$	−18.4367	+	1.12368i	−1.02904	+	0.0627176i
$322$	15.3609	−	17.3388i	0.856027	−	0.966255i
$323$	−20.3310	+	33.6315i	−1.13124	+	1.87131i
$324$	9.47690	−	1.16830i	0.526494	−	0.0649058i
$325$	5.01454	−	32.1988i	0.278156	−	1.78607i
$326$	6.98186	+	7.88089i	0.386689	+	0.436482i
$327$	31.2135	−	0.0142784i	1.72611	−	0.000789598i
$328$	−6.03545	−	1.48760i	−0.333252	−	0.0821392i
$329$	7.05575	+	10.2220i	0.388996	+	0.563558i
$330$	−10.8900	+	12.3036i	−0.599475	+	0.677292i
$331$	−6.81379	+	11.2714i	−0.374520	+	0.619531i	−0.985011	−	0.172492i	$-0.944818\pi$
$331$	−6.81379	+	11.2714i	−0.374520	+	0.619531i	0.610491	+	0.792023i	$0.290972\pi$
$332$	−0.190918	−	0.149575i	−0.0104780	−	0.00820898i
$333$	31.8357	+	14.2931i	1.74459	+	0.783256i
$334$	14.0348	−	37.0068i	0.767951	−	2.02492i
$335$	−38.6156	−	20.2670i	−2.10980	−	1.10731i
$336$	−22.6696	−	8.58558i	−1.23673	−	0.468382i
$337$			9.75372i			0.531319i	0.964067	+	0.265660i	$0.0855897\pi$
$337$			9.75372i			0.531319i	−0.964067	+	0.265660i	$0.914410\pi$
$338$	5.59564	−	22.0452i	0.304363	−	1.19910i
$339$	11.0639	+	2.02230i	0.600906	+	0.109836i
$340$	31.7788	+	5.82369i	1.72345	+	0.315834i
$341$	3.69361	−	7.03759i	0.200020	−	0.381107i
$342$	16.8120	−	19.0119i	0.909090	−	1.02804i
$343$	1.04073	−	17.2053i	0.0561940	−	0.928997i
$344$	−4.19347	+	5.35258i	−0.226097	+	0.288592i
$345$	−20.3298	+	22.9688i	−1.09452	+	1.23660i
$346$	−25.5775	−	15.4622i	−1.37506	−	0.831251i
$347$	23.1493	−	15.9788i	1.24272	−	0.857788i	0.248871	−	0.968537i	$-0.419940\pi$
$347$	23.1493	−	15.9788i	1.24272	−	0.857788i	0.993848	+	0.110749i	$0.0353249\pi$
$348$	−1.69233	+	3.76480i	−0.0907183	+	0.201815i
$349$	18.5805	−	3.40501i	0.994593	−	0.182266i	0.341776	−	0.939782i	$-0.388972\pi$
$349$	18.5805	−	3.40501i	0.994593	−	0.182266i	0.652817	+	0.757516i	$0.273587\pi$
$350$	−33.1544	+	29.3722i	−1.77217	+	1.57001i
$351$	−8.23668	+	16.8273i	−0.439641	+	0.898173i
$352$	5.90947	+	5.23533i	0.314976	+	0.279044i
$353$	17.0396	+	10.3008i	0.906927	+	0.548256i	0.892203	−	0.451635i	$-0.149159\pi$
$353$	17.0396	+	10.3008i	0.906927	+	0.548256i	0.0147241	+	0.999892i	$0.495313\pi$
$354$	−12.7813	+	10.0229i	−0.679318	+	0.532713i
$355$	1.13242	+	4.59439i	0.0601024	+	0.243845i
$356$	−1.05232	+	0.473610i	−0.0557728	+	0.0251013i
$357$	−32.4426	+	22.4154i	−1.71704	+	1.18635i
$358$	7.49291	−	16.6486i	0.396013	−	0.879904i
$359$	26.9007	−	16.2620i	1.41976	−	0.858278i	0.420956	−	0.907081i	$-0.361695\pi$
$359$	26.9007	−	16.2620i	1.41976	−	0.858278i	0.998808	+	0.0488034i	$0.0155408\pi$
$360$	17.2725	+	6.53254i	0.910343	+	0.344295i
$361$		−	4.38027i		−	0.230540i
$362$	−16.3592	+	9.88949i	−0.859821	+	0.519780i
$363$	4.58230	−	14.7288i	0.240508	−	0.773063i
$364$	−8.65272	+	6.32079i	−0.453526	+	0.331299i
$365$	25.8381	−	3.13732i	1.35243	−	0.164215i
$366$	2.43608	+	4.63640i	0.127336	+	0.242349i
$367$	19.5730	+	28.3564i	1.02170	+	1.48019i	0.870795	+	0.491646i	$0.163605\pi$
$367$	19.5730	+	28.3564i	1.02170	+	1.48019i	0.150909	+	0.988548i	$0.451780\pi$
$368$	17.6765	+	15.6600i	0.921451	+	0.816334i
$369$	9.70838	−	5.88106i	0.505398	−	0.306156i
$370$	−47.0258	−	60.0240i	−2.44475	−	3.12050i
$371$	2.78261	−	8.92971i	0.144466	−	0.463608i
$372$	10.0195	+	1.21194i	0.519487	+	0.0628360i
$373$	1.51851	−	2.19994i	0.0786255	−	0.113909i	−0.781698	−	0.623657i	$-0.785646\pi$
$373$	1.51851	−	2.19994i	0.0786255	−	0.113909i	0.860323	+	0.509748i	$0.170262\pi$
$374$	19.9801	−	4.92465i	1.03315	−	0.254648i
$375$	19.6065	−	17.3859i	1.01248	−	0.897804i
$376$	−5.99526	+	4.13823i	−0.309182	+	0.213413i
$377$	−4.37366	−	6.81621i	−0.225255	−	0.351053i
$378$	23.2076	−	10.4832i	1.19367	−	0.539199i
$379$	12.9856	−	4.04648i	0.667026	−	0.207854i	0.0547526	−	0.998500i	$-0.482563\pi$
$379$	12.9856	−	4.04648i	0.667026	−	0.207854i	0.612273	+	0.790646i	$0.290255\pi$
$380$	−17.9720	+	6.81587i	−0.921942	+	0.349647i
$381$	1.80502	−	5.80185i	0.0924738	−	0.297238i
$382$	43.7005	+	8.00841i	2.23591	+	0.409746i
$383$	−15.7108	−	25.9888i	−0.802784	−	1.32797i	−0.941288	−	0.337604i	$-0.890383\pi$
$383$	−15.7108	−	25.9888i	−0.802784	−	1.32797i	0.138505	−	0.990362i	$-0.455770\pi$
$384$	7.17405	−	18.9425i	0.366099	−	0.966658i
$385$	−6.23350	+	13.8503i	−0.317688	+	0.705875i
$386$	31.1842	−	11.8266i	1.58724	−	0.601959i
$387$	−1.50791	−	12.3245i	−0.0766512	−	0.626489i
$388$	−4.13227	−	1.28767i	−0.209784	−	0.0653714i
$389$	−4.97862	−	1.22712i	−0.252426	−	0.0622174i	0.111072	−	0.993812i	$-0.464572\pi$
$389$	−4.97862	−	1.22712i	−0.252426	−	0.0622174i	−0.363498	+	0.931595i	$0.618418\pi$
$390$	33.0452	−	24.1627i	1.67331	−	1.22352i
$391$	37.2995	−	9.19350i	1.88632	−	0.464935i
$392$	−1.38840	−	0.0839826i	−0.0701247	−	0.00424176i
$393$	1.35880	−	22.6354i	0.0685422	−	1.14180i
$394$	−0.189693	−	0.361430i	−0.00955660	−	0.0182086i
$395$	7.69194	+	24.6843i	0.387024	+	1.24200i
$396$	−4.59748	+	0.282318i	−0.231032	+	0.0141870i
$397$	14.5769	+	0.881742i	0.731595	+	0.0442534i	0.421976	−	0.906607i	$-0.361337\pi$
$397$	14.5769	+	0.881742i	0.731595	+	0.0442534i	0.309619	+	0.950861i	$0.399798\pi$
$398$	−18.3624	−	23.4379i	−0.920424	−	1.17483i
$399$	9.61847	−	21.3975i	0.481526	−	1.07122i
$400$	−29.9442	−	33.8000i	−1.49721	−	1.69000i
$401$	−20.3468	+	1.23076i	−1.01607	+	0.0614611i	−0.560009	−	0.828486i	$-0.689202\pi$
$401$	−20.3468	+	1.23076i	−1.01607	+	0.0614611i	−0.456063	+	0.889947i	$0.650741\pi$
$402$	−10.5090	−	33.6703i	−0.524141	−	1.67932i
$403$	−12.7301	+	15.1680i	−0.634131	+	0.755573i
$404$	2.70587	−	5.15561i	0.134622	−	0.256501i
$405$	−30.7244	+	13.8956i	−1.52671	+	0.690478i
$406$	−1.32689	+	10.9279i	−0.0658525	+	0.542344i
$407$	−14.9057	−	7.82309i	−0.738846	−	0.387776i
$408$	−13.1467	−	19.0277i	−0.650860	−	0.942012i
$409$	17.7890	−	5.54327i	0.879608	−	0.274097i	0.175747	−	0.984435i	$-0.443766\pi$
$409$	17.7890	−	5.54327i	0.879608	−	0.274097i	0.703860	+	0.710338i	$0.251458\pi$
$410$	−24.7566	+	1.49750i	−1.22264	+	0.0739563i
$411$	−3.05933	+	0.00139947i	−0.150906	+	6.90309e-5i
$412$	−10.1548	+	8.99635i	−0.500290	+	0.443218i
$413$	−8.52912	+	12.3566i	−0.419691	+	0.608027i
$414$	−24.7619	+	1.52056i	−1.21698	+	0.0747313i
$415$	0.800836	+	0.303717i	0.0393115	+	0.0149089i
$416$	−11.6028	−	15.8835i	−0.568876	−	0.778751i
$417$	−16.0279	+	2.94481i	−0.784892	+	0.144208i
$418$	−8.65676	+	8.65676i	−0.423416	+	0.423416i
$419$	2.03842	+	0.773072i	0.0995835	+	0.0377670i	0.403893	−	0.914806i	$-0.367657\pi$
$419$	2.03842	+	0.773072i	0.0995835	+	0.0377670i	−0.304310	+	0.952573i	$0.598426\pi$
$420$	−19.2519	−	1.15568i	−0.939395	−	0.0563916i
$421$	5.83914	−	18.7385i	0.284582	−	0.913257i	−0.696149	−	0.717897i	$-0.745105\pi$
$421$	5.83914	−	18.7385i	0.284582	−	0.913257i	0.980732	−	0.195360i	$-0.0625874\pi$
$422$	9.12296	−	1.67184i	0.444099	−	0.0813841i
$423$	2.38583	−	13.0865i	0.116003	−	0.636290i
$424$	5.23732	+	1.63201i	0.254347	+	0.0792576i
$425$	−72.9211	+	8.85422i	−3.53719	+	0.429493i
$426$	−1.97841	+	3.27608i	−0.0958544	+	0.158727i
$427$	3.42338	+	3.42338i	0.165669	+	0.165669i
$428$	4.01209	+	10.5790i	0.193932	+	0.511356i
$429$	4.46332	−	7.85847i	0.215491	−	0.379410i
$430$	−9.62055	+	25.3673i	−0.463944	+	1.22332i
$431$	3.67351	−	1.65331i	0.176947	−	0.0796373i	−0.320003	−	0.947416i	$-0.603684\pi$
$431$	3.67351	−	1.65331i	0.176947	−	0.0796373i	0.496950	+	0.867779i	$0.334453\pi$
$432$	10.6874	+	23.6596i	0.514197	+	1.13832i
$433$	13.3098	+	15.0236i	0.639627	+	0.721990i	0.975520	−	0.219910i	$-0.0705764\pi$
$433$	13.3098	+	15.0236i	0.639627	+	0.721990i	−0.335893	+	0.941900i	$0.609038\pi$
$434$	26.4751	−	4.85175i	1.27085	−	0.232891i
$435$	1.75041	−	14.4712i	0.0839256	−	0.693842i
$436$	−5.68816	−	18.2539i	−0.272413	−	0.874205i
$437$	−16.1607	+	16.1607i	−0.773072	+	0.773072i
$438$	16.5771	+	12.9751i	0.792083	+	0.619973i
$439$	12.2561	+	1.48816i	0.584953	+	0.0710262i	0.407663	−	0.913132i	$-0.366344\pi$
$439$	12.2561	+	1.48816i	0.584953	+	0.0710262i	0.177290	+	0.984159i	$0.443267\pi$
$440$	−8.12324	−	3.65597i	−0.387260	−	0.174292i
$441$	1.89959	−	1.68600i	0.0904569	−	0.0802856i
$442$	−51.2512	+	1.37130i	−2.43777	+	0.0652263i
$443$	−4.14961	−	7.90642i	−0.197154	−	0.375645i	0.766729	−	0.641970i	$-0.221883\pi$
$443$	−4.14961	−	7.90642i	−0.197154	−	0.375645i	−0.963883	+	0.266325i	$0.914191\pi$
$444$	2.56689	−	21.2214i	0.121819	−	1.00712i
$445$	3.05036	−	2.70239i	0.144601	−	0.128105i
$446$	−7.88893	−	1.94445i	−0.373552	−	0.0920722i
$447$	−6.72371	−	12.7967i	−0.318021	−	0.605265i
$448$	0.0757487	−	1.25228i	0.00357879	−	0.0591645i
$449$	−7.97130	−	17.7115i	−0.376189	−	0.835857i	−0.998586	−	0.0531558i	$-0.983072\pi$
$449$	−7.97130	−	17.7115i	−0.376189	−	0.835857i	0.622397	−	0.782701i	$-0.286159\pi$
$450$	47.3536	+	2.82089i	2.23227	+	0.132978i
$451$	−4.84827	+	2.54457i	−0.228296	+	0.119819i
$452$	−0.830425	−	6.83917i	−0.0390599	−	0.321687i
$453$	2.01618	−	8.19610i	0.0947284	−	0.385086i
$454$	7.13912	+	28.9646i	0.335056	+	1.35937i
$455$	22.5323	−	30.4016i	1.05633	−	1.42525i
$456$	12.5497	+	5.64128i	0.587695	+	0.264177i
$457$	−8.00959	+	25.7037i	−0.374673	+	1.20237i	0.554331	+	0.832296i	$0.312974\pi$
$457$	−8.00959	+	25.7037i	−0.374673	+	1.20237i	−0.929004	+	0.370070i	$0.879334\pi$
$458$	5.65693	+	10.7784i	0.264331	+	0.503640i
$459$	41.5506	+	7.55550i	1.93941	+	0.352661i
$460$	17.1336	+	7.71123i	0.798860	+	0.359538i
$461$	0.330066	−	1.80111i	0.0153727	−	0.0838862i	−0.975039	−	0.222034i	$-0.928730\pi$
$461$	0.330066	−	1.80111i	0.0153727	−	0.0838862i	0.990412	+	0.138148i	$0.0441150\pi$
$462$	−11.4840	+	4.36130i	−0.534282	+	0.202906i
$463$	4.82161	−	26.3107i	0.224079	−	1.22276i	−0.658494	−	0.752586i	$-0.728806\pi$
$463$	4.82161	−	26.3107i	0.224079	−	1.22276i	0.882573	−	0.470175i	$-0.155809\pi$
$464$	−11.1408	−	1.35273i	−0.517197	−	0.0627991i
$465$	−35.0545	+	6.44056i	−1.62562	+	0.298674i
$466$	13.3318	+	42.7832i	0.617583	+	1.98189i
$467$	−13.8016	+	19.9951i	−0.638662	+	0.925261i	−0.999974	−	0.00718352i	$-0.997713\pi$
$467$	−13.8016	+	19.9951i	−0.638662	+	0.925261i	0.361312	+	0.932445i	$0.382329\pi$
$468$	11.3410	+	1.75558i	0.524236	+	0.0811516i
$469$	−18.5218	−	26.8334i	−0.855256	−	1.23905i
$470$	−17.9255	+	22.8803i	−0.826844	+	1.05539i
$471$	2.30644	+	37.8427i	0.106275	+	1.74370i
$472$	−7.24718	−	5.00237i	−0.333579	−	0.230253i
$473$	0.361637	+	5.97857i	0.0166281	+	0.274895i
$474$	−9.70951	+	18.5205i	−0.445972	+	0.850675i
$475$	34.4011	−	26.9516i	1.57843	−	1.23662i
$476$	19.0141	+	14.8966i	0.871509	+	0.682784i
$477$	−8.86541	+	4.66328i	−0.405919	+	0.213517i
$478$	3.61360	−	2.49428i	0.165282	−	0.114086i
$479$	16.6721	+	21.2804i	0.761767	+	0.972324i	0.999999	+	0.00111595i	$0.000355217\pi$
$479$	16.6721	+	21.2804i	0.761767	+	0.972324i	−0.238232	+	0.971208i	$0.576568\pi$
$480$	2.12145	−	35.3399i	0.0968303	−	1.61304i
$481$	32.1260	+	26.9624i	1.46482	+	1.22938i
$482$	−24.4739	−	2.97167i	−1.11476	−	0.135356i
$483$	−21.4386	+	8.14182i	−0.975491	+	0.370466i
$484$	−9.44862			−0.429483
$485$	15.2850			0.694057
$486$	−25.5227	−	9.61277i	−1.15773	−	0.436044i
$487$	0.459998	+	0.207028i	0.0208445	+	0.00938134i	0.420808	−	0.907150i	$-0.361747\pi$
$487$	0.459998	+	0.207028i	0.0208445	+	0.00938134i	−0.399964	+	0.916531i	$0.630977\pi$
$488$	−2.00783	+	2.00783i	−0.0908901	+	0.0908901i
$489$	−2.49911	−	10.1194i	−0.113014	−	0.457613i
$490$	−5.38851	+	1.32815i	−0.243428	+	0.0599996i
$491$	−7.27297	−	6.44329i	−0.328224	−	0.290781i	0.482876	−	0.875689i	$-0.339592\pi$
$491$	−7.27297	−	6.44329i	−0.328224	−	0.290781i	−0.811100	+	0.584908i	$0.801131\pi$
$492$	−5.20639	−	4.60821i	−0.234722	−	0.207754i
$493$	−12.1059	+	13.6648i	−0.545224	+	0.615431i
$494$	25.6715	−	16.4723i	1.15501	−	0.741122i
$495$	15.2040	−	5.78205i	0.683371	−	0.259884i
$496$	4.94623	+	26.9907i	0.222092	+	1.21192i
$497$	−0.846632	+	3.43492i	−0.0379766	+	0.154077i
$498$	0.284592	+	0.631566i	0.0127529	+	0.0283012i
$499$	−2.87959	+	4.76342i	−0.128908	+	0.213240i	−0.913568	−	0.406687i	$-0.866684\pi$
$499$	−2.87959	+	4.76342i	−0.128908	+	0.213240i	0.784659	+	0.619927i	$0.212838\pi$
$500$	−13.7366	−	8.30408i	−0.614321	−	0.371370i
$501$	−29.3168	+	25.9963i	−1.30978	+	1.16143i
$502$	6.99388	+	0.423052i	0.312152	+	0.0188817i
$503$	17.8109	+	6.75480i	0.794151	+	0.301182i	0.718116	−	0.695923i	$-0.245005\pi$
$503$	17.8109	+	6.75480i	0.794151	+	0.301182i	0.0760350	+	0.997105i	$0.475774\pi$
$504$	9.16469	+	10.3257i	0.408228	+	0.459945i
$505$	−3.70641	+	20.2252i	−0.164933	+	0.900012i
$506$	11.9673			0.532012
$507$	−15.0398	+	16.7572i	−0.667942	+	0.744213i
$508$	−3.72191			−0.165133
$509$	3.83456	−	20.9245i	0.169964	−	0.927464i	−0.782463	−	0.622697i	$-0.786037\pi$
$509$	3.83456	−	20.9245i	0.169964	−	0.927464i	0.952427	−	0.304767i	$-0.0985785\pi$
$510$	−72.6662	−	56.8767i	−3.21771	−	2.51854i
$511$	18.1948	+	6.90038i	0.804891	+	0.305255i
$512$	−10.8205	−	0.654521i	−0.478204	−	0.0289260i
$513$	−23.4801	+	8.94169i	−1.03667	+	0.394785i
$514$	−6.48912	−	3.92281i	−0.286223	−	0.173028i
$515$	24.7856	−	41.0005i	1.09219	−	1.80670i
$516$	−6.93412	+	3.12461i	−0.305258	+	0.137553i
$517$	−1.53565	+	6.23037i	−0.0675377	+	0.274011i
$518$	−10.2760	−	56.0745i	−0.451503	−	2.46377i
$519$	15.3190	+	25.3146i	0.672429	+	1.11119i
$520$	17.8307	+	13.2153i	0.781926	+	0.579530i
$521$	−12.1473	+	13.7115i	−0.532183	+	0.600710i	−0.951697	−	0.307039i	$-0.900662\pi$
$521$	−12.1473	+	13.7115i	−0.532183	+	0.600710i	0.419514	+	0.907749i	$0.362200\pi$
$522$	9.27386	−	7.27930i	0.405906	−	0.318606i
$523$	−30.3065	−	26.8492i	−1.32521	−	1.17403i	−0.971058	−	0.238846i	$-0.923231\pi$
$523$	−30.3065	−	26.8492i	−1.32521	−	1.17403i	−0.354152	−	0.935188i	$-0.615231\pi$
$524$	−13.4865	+	3.32413i	−0.589162	+	0.145215i
$525$	42.5715	−	10.5136i	1.85797	−	0.458850i
$526$	−13.3608	+	13.3608i	−0.582558	+	0.582558i
$527$	40.7049	+	18.3198i	1.77313	+	0.798022i
$528$	−4.44624	−	11.7076i	−0.193498	−	0.509508i
$529$	−0.659033			−0.0286536
$530$	21.8877			0.950742
$531$	15.8140	−	2.91297i	0.686267	−	0.126412i
$532$	−14.2655	−	1.73215i	−0.618488	−	0.0750981i
$533$	13.1534	−	3.61783i	0.569739	−	0.156706i
$534$	3.29010	+	0.197504i	0.142377	+	0.00854683i
$535$	−24.6415	−	31.4526i	−1.06535	−	1.35981i
$536$	15.7379	−	10.8631i	0.679775	−	0.469215i
$537$	−14.2227	+	11.1533i	−0.613754	+	0.481299i
$538$	3.22456	+	2.52628i	0.139020	+	0.108916i
$539$	−0.964466	+	0.755611i	−0.0415425	+	0.0325465i
$540$	13.7183	+	15.4420i	0.590340	+	0.664517i
$541$	0.901624	+	14.9056i	0.0387639	+	0.640843i	0.964731	+	0.263238i	$0.0847906\pi$
$541$	0.901624	+	14.9056i	0.0387639	+	0.640843i	−0.925967	+	0.377605i	$0.876748\pi$
$542$	−11.9073	−	8.21899i	−0.511461	−	0.353036i
$543$	18.8898	−	1.15129i	0.810637	−	0.0494067i
$544$	−27.3451	+	34.9034i	−1.17241	+	1.49647i
$545$	38.3559	+	55.5680i	1.64298	+	2.38027i
$546$	30.2710	−	4.51428i	1.29548	−	0.193193i
$547$	13.9698	−	20.2388i	0.597306	−	0.865347i	−0.401416	−	0.915896i	$-0.631482\pi$
$547$	13.9698	−	20.2388i	0.597306	−	0.865347i	0.998722	+	0.0505488i	$0.0160970\pi$
$548$	0.557514	+	1.78913i	0.0238158	+	0.0764277i
$549$	−0.00474371	−	5.18501i	−0.000202457	−	0.221291i
$550$	−22.7164	−	2.75827i	−0.968631	−	0.117613i
$551$	1.95775	−	10.6831i	0.0834031	−	0.455116i
$552$	−4.77521	−	12.5738i	−0.203247	−	0.535179i
$553$	−3.48434	+	19.0135i	−0.148169	+	0.808534i
$554$	−18.2457	−	8.21172i	−0.775185	−	0.348882i
$555$	13.6411	+	74.2457i	0.579034	+	3.15156i
$556$	4.63895	+	8.83878i	0.196735	+	0.374848i
$557$	2.65677	−	8.52588i	0.112571	−	0.361253i	−0.881193	−	0.472757i	$-0.843259\pi$
$557$	2.65677	−	8.52588i	0.112571	−	0.361253i	0.993764	+	0.111504i	$0.0355667\pi$
$558$	−23.7386	−	16.3535i	−1.00494	−	0.692301i
$559$	2.29632	−	14.7449i	0.0971240	−	0.623643i
$560$	−12.5491	−	50.9137i	−0.530296	−	2.15150i
$561$	−19.7824	−	4.86632i	−0.835213	−	0.205456i
$562$	0.774272	+	6.37670i	0.0326607	+	0.268985i
$563$	−16.2791	+	8.54392i	−0.686081	+	0.360083i	−0.771471	−	0.636264i	$-0.780479\pi$
$563$	−16.2791	+	8.54392i	−0.686081	+	0.360083i	0.0853898	+	0.996348i	$0.472786\pi$
$564$	−8.08837	+	0.985861i	−0.340582	+	0.0415122i
$565$	9.98518	+	22.1862i	0.420080	+	0.933379i
$566$	−0.0785955	+	1.29934i	−0.00330362	+	0.0546153i
$567$	−25.1674	−	1.47613i	−1.05693	−	0.0619918i
$568$	−2.01460	−	0.496553i	−0.0845306	−	0.0208349i
$569$	−26.8911	+	23.8235i	−1.12733	+	0.998731i	−0.127358	+	0.991857i	$0.540650\pi$
$569$	−26.8911	+	23.8235i	−1.12733	+	0.998731i	−0.999976	+	0.00687439i	$0.997812\pi$
$570$	54.5020	+	6.59245i	2.28284	+	0.276127i
$571$	0.469592	+	0.894733i	0.0196518	+	0.0374434i	0.895084	−	0.445898i	$-0.147115\pi$
$571$	0.469592	+	0.894733i	0.0196518	+	0.0374434i	−0.875432	+	0.483341i	$0.839423\pi$
$572$	−5.40854	−	1.18059i	−0.226142	−	0.0493628i
$573$	−34.6356	−	27.1097i	−1.44692	−	1.13252i
$574$	−16.9091	−	7.61018i	−0.705773	−	0.317643i
$575$	−42.4077	−	5.14923i	−1.76852	−	0.214738i
$576$	−1.00489	+	0.891897i	−0.0418704	+	0.0371624i
$577$	3.82213	−	3.82213i	0.159118	−	0.159118i	−0.623058	−	0.782176i	$-0.714110\pi$
$577$	3.82213	−	3.82213i	0.159118	−	0.159118i	0.782176	+	0.623058i	$0.214110\pi$
$578$	25.5341	+	81.9417i	1.06208	+	3.40833i
$579$	−32.7788	−	3.96486i	−1.36224	−	0.164774i
$580$	−8.78263	+	1.60948i	−0.364679	+	0.0668299i
$581$	0.424627	+	0.479304i	0.0176165	+	0.0198849i
$582$	8.74553	+	8.73753i	0.362514	+	0.362182i
$583$	4.40639	−	1.98316i	0.182494	−	0.0821340i
$584$	−4.04710	+	10.6713i	−0.167470	+	0.441583i
$585$	−40.0811	+	5.99600i	−1.65715	+	0.247904i
$586$	−20.3618	−	53.6896i	−0.841137	−	2.21790i
$587$	8.05926	+	8.05926i	0.332641	+	0.332641i	0.853589	−	0.520947i	$-0.174421\pi$
$587$	8.05926	+	8.05926i	0.332641	+	0.332641i	−0.520947	+	0.853589i	$0.674421\pi$
$588$	−1.33179	−	0.804265i	−0.0549222	−	0.0331673i
$589$	−26.3625	+	3.20099i	−1.08625	+	0.131894i
$590$	−33.5446	−	10.4529i	−1.38101	−	0.430340i
$591$	0.000184853		0.404100i	7.60384e−6		0.0166224i
$592$	57.1665	−	10.4762i	2.34953	−	0.430567i
$593$	−4.90753	+	15.7488i	−0.201528	+	0.646726i	0.797528	+	0.603282i	$0.206141\pi$
$593$	−4.90753	+	15.7488i	−0.201528	+	0.646726i	−0.999056	+	0.0434442i	$0.986167\pi$
$594$	12.0045	+	5.38297i	0.492549	+	0.220866i
$595$	−79.7576	−	30.2481i	−3.26974	−	1.24005i
$596$	−6.26123	+	6.26123i	−0.256470	+	0.256470i
$597$	5.32653	+	28.9911i	0.218000	+	1.18653i
$598$	−29.1302	−	6.35860i	−1.19122	−	0.260023i
$599$	−13.0318	−	4.94231i	−0.532465	−	0.201937i	0.0736938	−	0.997281i	$-0.476521\pi$
$599$	−13.0318	−	4.94231i	−0.532465	−	0.201937i	−0.606159	+	0.795344i	$0.707290\pi$
$600$	6.16626	+	24.9683i	0.251737	+	1.01933i
$601$	20.8025	−	30.1377i	0.848554	−	1.22934i	−0.122973	−	0.992410i	$-0.539243\pi$
$601$	20.8025	−	30.1377i	0.848554	−	1.22934i	0.971526	−	0.236932i	$-0.0761419\pi$
$602$	−15.1825	+	13.4505i	−0.618791	+	0.548201i
$603$	−6.26294	+	34.3530i	−0.255047	+	1.39896i
$604$	−5.16072	+	0.312166i	−0.209987	+	0.0127019i
$605$	31.8565	−	9.92689i	1.29515	−	0.403586i
$606$	−13.6822	+	9.45342i	−0.555803	+	0.384019i
$607$	1.44364	+	0.757683i	0.0585957	+	0.0307534i	0.493767	−	0.869594i	$-0.335620\pi$
$607$	1.44364	+	0.757683i	0.0585957	+	0.0307534i	−0.435171	+	0.900348i	$0.643312\pi$
$608$	3.17964	−	26.1867i	0.128951	−	1.06201i
$609$	6.18668	−	8.97174i	0.250697	−	0.363553i
$610$	−5.26507	+	10.0318i	−0.213177	+	0.406174i
$611$	7.04839	−	14.3497i	0.285147	−	0.580528i
$612$	−3.14165	−	25.6775i	−0.126994	−	1.03795i
$613$	−2.37828	+	0.143859i	−0.0960578	+	0.00581043i	−0.108337	−	0.994114i	$-0.534553\pi$
$613$	−2.37828	+	0.143859i	−0.0960578	+	0.00581043i	0.0122797	+	0.999925i	$0.496091\pi$
$614$	−21.2727	−	24.0119i	−0.858496	−	0.969041i
$615$	22.3951	+	10.0669i	0.903058	+	0.405937i
$616$	−4.10732	−	5.24261i	−0.165489	−	0.211231i
$617$	−4.09430	−	0.247659i	−0.164830	−	0.00997039i	−0.0222427	−	0.999753i	$-0.507081\pi$
$617$	−4.09430	−	0.247659i	−0.164830	−	0.00997039i	−0.142587	+	0.989782i	$0.545542\pi$
$618$	37.6190	−	9.29050i	1.51326	−	0.373719i
$619$	−9.25460	−	29.6991i	−0.371974	−	1.19371i	−0.931144	−	0.364653i	$-0.881188\pi$
$619$	−9.25460	−	29.6991i	−0.371974	−	1.19371i	0.559170	−	0.829053i	$-0.311120\pi$
$620$	10.1458	+	19.3312i	0.407465	+	0.776360i
$621$	22.4103	+	10.0491i	0.899295	+	0.403256i
$622$	27.9645	+	1.69154i	1.12127	+	0.0678245i
$623$	2.95826	−	0.729145i	0.118520	−	0.0292126i
$624$	4.60220	+	30.8605i	0.184235	+	1.23541i
$625$	11.1614	+	2.75103i	0.446454	+	0.110041i
$626$	−27.5841	−	8.59556i	−1.10248	−	0.343548i
$627$	11.5696	−	3.61103i	0.462043	−	0.144210i
$628$	21.7143	−	8.23513i	0.866493	−	0.328618i
$629$	38.8014	−	86.2132i	1.54711	−	3.43754i
$630$	47.1679	+	28.4551i	1.87922	+	1.13368i
$631$	−11.9992	−	19.8490i	−0.477679	−	0.790178i	0.520283	−	0.853994i	$-0.325827\pi$
$631$	−11.9992	−	19.8490i	−0.477679	−	0.790178i	−0.997962	+	0.0638165i	$0.979673\pi$
$632$	−11.1515	−	2.04358i	−0.443582	−	0.0812894i
$633$	−8.76755	−	2.72768i	−0.348479	−	0.108416i
$634$	−32.6128	+	12.3684i	−1.29522	+	0.491212i
$635$	12.5486	−	3.91031i	0.497977	−	0.155176i
$636$	4.34073	+	4.33676i	0.172121	+	0.171964i
$637$	2.74913	−	1.32682i	0.108925	−	0.0525705i
$638$	−4.68040	+	3.23065i	−0.185299	+	0.127902i
$639$	3.24060	−	1.96306i	0.128196	−	0.0776575i
$640$	42.5431	−	10.4859i	1.68166	−	0.414493i
$641$	−4.97622	+	7.20929i	−0.196549	+	0.284750i	−0.908849	−	0.417125i	$-0.863038\pi$
$641$	−4.97622	+	7.20929i	−0.196549	+	0.284750i	0.712301	+	0.701875i	$0.247653\pi$
$642$	3.88058	−	32.0821i	0.153154	−	1.26618i
$643$	−12.3158	+	39.5227i	−0.485687	+	1.55862i	0.308669	+	0.951170i	$0.400117\pi$
$643$	−12.3158	+	39.5227i	−0.485687	+	1.55862i	−0.794355	+	0.607453i	$0.792191\pi$
$644$	8.66321	+	11.0578i	0.341378	+	0.435737i
$645$	20.0960	−	17.8199i	0.791278	−	0.701658i
$646$	−51.4648	−	45.5939i	−2.02486	−	1.79387i
$647$	11.7166	+	16.9745i	0.460629	+	0.667336i	0.982623	−	0.185613i	$-0.0594272\pi$
$647$	11.7166	+	16.9745i	0.460629	+	0.667336i	−0.521994	+	0.852949i	$0.674812\pi$
$648$	0.865759	−	14.7608i	0.0340102	−	0.579859i
$649$	−7.70023	+	0.934977i	−0.302260	+	0.0367011i
$650$	53.8296	+	18.7840i	2.11137	+	0.736768i
$651$	−25.4437	−	7.91582i	−0.997218	−	0.310245i
$652$	−5.46399	+	3.30310i	−0.213986	+	0.129359i
$653$			4.11117i			0.160882i	0.996759	+	0.0804412i	$0.0256329\pi$
$653$			4.11117i			0.160882i	−0.996759	+	0.0804412i	$0.974367\pi$
$654$	−9.81912	+	53.7198i	−0.383958	+	2.10061i
$655$	41.9782	−	25.3767i	1.64022	−	0.991549i
$656$	7.75839	−	17.2384i	0.302914	−	0.673047i
$657$	−8.57059	−	18.9966i	−0.334371	−	0.741128i
$658$	−19.8162	+	8.91857i	−0.772518	+	0.347682i
$659$	8.75013	+	35.5007i	0.340857	+	1.38291i	0.852058	+	0.523448i	$0.175355\pi$
$659$	8.75013	+	35.5007i	0.340857	+	1.38291i	−0.511201	+	0.859461i	$0.670799\pi$
$660$	−6.14851	−	7.84060i	−0.239330	−	0.305195i
$661$	−4.25996	−	2.57523i	−0.165693	−	0.100165i	0.432061	−	0.901844i	$-0.357786\pi$
$661$	−4.25996	−	2.57523i	−0.165693	−	0.100165i	−0.597754	+	0.801679i	$0.703940\pi$
$662$	−17.2481	−	15.2805i	−0.670367	−	0.593893i
$663$	45.5677	+	22.3563i	1.76970	+	0.868248i
$664$	−0.281114	+	0.249045i	−0.0109093	+	0.00966483i
$665$	49.9167	−	9.14758i	1.93569	−	0.354728i
$666$	−34.6369	+	50.2786i	−1.34215	+	1.94825i
$667$	−8.73752	+	6.03107i	−0.338318	+	0.233524i
$668$	20.5398	+	12.4167i	0.794707	+	0.480417i
$669$	6.02325	+	5.33121i	0.232872	+	0.206117i
$670$	47.0557	−	60.0621i	1.81792	−	2.32040i
$671$	−0.151018	+	2.49662i	−0.00582997	+	0.0963810i
$672$	13.6830	−	22.6578i	0.527833	−	0.874045i
$673$	−4.54071	+	8.65159i	−0.175031	+	0.333494i	−0.957129	−	0.289661i	$-0.906457\pi$
$673$	−4.54071	+	8.65159i	−0.175031	+	0.333494i	0.782098	+	0.623156i	$0.214150\pi$
$674$	−16.7852	−	3.07600i	−0.646542	−	0.118483i
$675$	−40.2232	−	24.2405i	−1.54819	−	0.933016i
$676$	12.5379	+	5.74745i	0.482228	+	0.221056i
$677$		−	22.6340i		−	0.869894i	−0.900456	−	0.434947i	$-0.856767\pi$
$677$		−	22.6340i		−	0.869894i	0.900456	−	0.434947i	$-0.143233\pi$
$678$	−6.96935	+	18.4021i	−0.267656	+	0.706727i
$679$	10.1186	+	5.31067i	0.388317	+	0.203805i
$680$	17.7406	−	46.7782i	0.680322	−	1.79386i
$681$	7.05456	−	28.6779i	0.270331	−	1.09894i
$682$	10.9462	+	8.57577i	0.419150	+	0.328383i
$683$	−15.9420	+	26.3713i	−0.610003	+	1.00907i	0.386234	+	0.922401i	$0.373776\pi$
$683$	−15.9420	+	26.3713i	−0.610003	+	1.00907i	−0.996237	+	0.0866681i	$0.972378\pi$
$684$	9.50252	+	12.1062i	0.363338	+	0.462894i
$685$	−3.75938	−	5.44640i	−0.143638	−	0.208096i
$686$	29.2804	+	7.21696i	1.11793	+	0.275545i
$687$	−0.00551259	−	12.0509i	−0.000210319	−	0.459769i
$688$	−13.7124	−	15.4782i	−0.522782	−	0.590099i
$689$	−11.7795	+	2.48605i	−0.448765	+	0.0947110i
$690$	−33.1157	−	42.2292i	−1.26069	−	1.60764i
$691$	18.3158	−	30.2980i	0.696766	−	1.15259i	−0.284266	−	0.958746i	$-0.591750\pi$
$691$	18.3158	−	30.2980i	0.696766	−	1.15259i	0.981032	−	0.193846i	$-0.0620964\pi$
$692$	12.0188	−	13.5664i	0.456885	−	0.515717i
$693$	12.0740	+	1.45484i	0.458652	+	0.0552646i
$694$	20.1974	+	44.8769i	0.766684	+	1.70350i
$695$	−24.9266	−	24.9266i	−0.945522	−	0.945522i
$696$	5.26196	+	3.62852i	0.199454	+	0.137539i
$697$	−15.9088	−	26.3163i	−0.602587	−	0.996801i
$698$			33.0491i			1.25093i
$699$	7.97684	−	43.6408i	0.301712	−	1.65065i
$700$	−13.8959	−	22.9866i	−0.525216	−	0.868813i
$701$	−0.0671068	+	0.552674i	−0.00253459	+	0.0208742i	−0.993921	−	0.110093i	$-0.964885\pi$
$701$	−0.0671068	+	0.552674i	−0.00253459	+	0.0208742i	0.991387	+	0.130967i	$0.0418082\pi$
$702$	−26.3605	−	19.4813i	−0.994913	−	0.735274i
$703$	6.77971	+	55.8360i	0.255702	+	2.10589i
$704$	0.510204	−	0.399719i	0.0192290	−	0.0150650i
$705$	26.2346	−	11.8217i	0.988053	−	0.445230i
$706$	−23.1004	+	26.0750i	−0.869395	+	0.981344i
$707$	−9.48075	+	12.1013i	−0.356560	+	0.455116i
$708$	−4.58139	−	8.71941i	−0.172179	−	0.327696i
$709$	16.8108	+	5.23845i	0.631341	+	0.196734i	0.596441	−	0.802657i	$-0.296581\pi$
$709$	16.8108	+	5.23845i	0.631341	+	0.196734i	0.0349004	+	0.999391i	$0.488889\pi$
$710$	−8.26362	+	0.499857i	−0.310128	+	0.0187593i
$711$	17.0267	−	11.7757i	0.638551	−	0.441623i
$712$	0.427647	+	1.73503i	0.0160267	+	0.0650230i
$713$	20.4346	+	16.0095i	0.765284	+	0.599561i
$714$	−28.3434	−	62.8996i	−1.06073	−	2.35396i
$715$	19.4755	−	1.70190i	0.728343	−	0.0636476i
$716$	9.11153	+	6.28924i	0.340514	+	0.235040i
$717$	−4.31497	+	0.525935i	−0.161145	+	0.0196414i
$718$	19.5018	+	51.4220i	0.727800	+	1.91905i
$719$	−2.10540	+	17.3396i	−0.0785183	+	0.646656i	0.899320	+	0.437292i	$0.144062\pi$
$719$	−2.10540	+	17.3396i	−0.0785183	+	0.646656i	−0.977838	+	0.209364i	$0.932861\pi$
$720$	−29.0093	+	48.0866i	−1.08111	+	1.79208i
$721$	30.6533	−	18.5306i	1.14159	−	0.690115i
$722$	7.53801	+	1.38139i	0.280536	+	0.0514101i
$723$	20.0928	+	13.8555i	0.747261	+	0.515293i
$724$	−4.11069	−	10.8390i	−0.152773	−	0.402828i
$725$	17.9757	−	9.43436i	0.667599	−	0.350383i
$726$	23.9018	+	12.5307i	0.887078	+	0.465057i
$727$	−0.0570645	+	0.231520i	−0.00211641	+	0.00858660i	−0.971991	−	0.235020i	$-0.924484\pi$
$727$	−0.0570645	+	0.231520i	−0.00211641	+	0.00858660i	0.969874	+	0.243607i	$0.0783306\pi$
$728$	7.21228	+	14.9436i	0.267305	+	0.553848i
$729$	17.9597	+	20.1606i	0.665175	+	0.746688i
$730$	−2.74948	+	45.4543i	−0.101763	+	1.68234i
$731$	−33.3929	+	4.05464i	−1.23508	+	0.149966i
$732$	−3.03182	+	0.946274i	−0.112059	+	0.0349753i
$733$	−38.6137	+	12.0325i	−1.42623	+	0.444431i	−0.910924	−	0.412575i	$-0.864629\pi$
$733$	−38.6137	+	12.0325i	−1.42623	+	0.444431i	−0.515306	+	0.857006i	$0.672322\pi$
$734$	−54.9713	+	24.7406i	−2.02903	+	0.913192i
$735$	5.33518	+	1.31242i	0.196791	+	0.0484092i
$736$	−20.2983	+	15.9027i	−0.748206	+	0.586182i
$737$	4.03117	−	16.3551i	0.148490	−	0.602448i
$738$	7.05902	+	18.5619i	0.259846	+	0.683272i
$739$	1.61001	+	26.6166i	0.0592251	+	0.979108i	0.899493	+	0.436936i	$0.143936\pi$
$739$	1.61001	+	26.6166i	0.0592251	+	0.979108i	−0.840267	+	0.542172i	$0.817602\pi$
$740$	40.9436	−	21.4889i	1.50512	−	0.789946i
$741$	−30.0807	+	2.64252i	−1.10504	+	0.0970754i
$742$	14.4896	+	7.60474i	0.531931	+	0.279179i
$743$	15.7423	−	34.9779i	0.577529	−	1.28322i	−0.359233	−	0.933248i	$-0.616962\pi$
$743$	15.7423	−	34.9779i	0.577529	−	1.28322i	0.936762	−	0.349968i	$-0.113808\pi$
$744$	4.64266	−	14.9229i	0.170208	−	0.547098i
$745$	14.5319	−	27.6882i	0.532408	−	1.01442i
$746$	3.30700	+	3.30700i	0.121078	+	0.121078i
$747$	0.0407808	−	0.684579i	0.00149209	−	0.0250474i
$748$	0.753455	+	12.4561i	0.0275490	+	0.455440i
$749$	−5.38464	−	29.3830i	−0.196750	−	1.07363i
$750$	23.7362	+	39.2239i	0.866722	+	1.43225i
$751$	5.10477	+	3.52357i	0.186276	+	0.128577i	0.657553	−	0.753408i	$-0.271592\pi$
$751$	5.10477	+	3.52357i	0.186276	+	0.128577i	−0.471277	+	0.881985i	$0.656207\pi$
$752$	−9.09226	−	20.2022i	−0.331561	−	0.736697i
$753$	−5.93780	−	3.58582i	−0.216385	−	0.130674i
$754$	13.1093	−	5.37704i	0.477414	−	0.195820i
$755$	17.0717	−	6.47443i	0.621302	−	0.235629i
$756$	3.71625	+	14.9889i	0.135159	+	0.545139i
$757$	−2.19456	+	5.78657i	−0.0797625	+	0.210317i	−0.968965	−	0.247197i	$-0.920491\pi$
$757$	−2.19456	+	5.78657i	−0.0797625	+	0.210317i	0.889203	+	0.457513i	$0.151260\pi$
$758$	2.86836	+	23.6231i	0.104184	+	0.858029i
$759$	−10.4930	−	5.50103i	−0.380872	−	0.199675i
$760$	5.36510	+	29.2764i	0.194613	+	1.06197i
$761$	−8.60383	−	46.9496i	−0.311888	−	1.70192i	−0.649275	−	0.760554i	$-0.724927\pi$
$761$	−8.60383	−	46.9496i	−0.311888	−	1.70192i	0.337386	−	0.941366i	$-0.390457\pi$
$762$	9.41516	+	4.93597i	0.341075	+	0.178811i
$763$	6.08474	+	50.1124i	0.220282	+	1.81419i
$764$	−9.55375	+	25.1912i	−0.345643	+	0.911385i
$765$	37.5695	+	83.2724i	1.35833	+	3.01072i
$766$	49.6789	−	18.8407i	1.79497	−	0.680742i
$767$	19.2403	+	1.81549i	0.694727	+	0.0655537i
$768$	29.0077	+	17.5177i	1.04673	+	0.632114i
$769$	16.0164	+	35.5870i	0.577566	+	1.28330i	0.936739	+	0.350028i	$0.113828\pi$
$769$	16.0164	+	35.5870i	0.577566	+	1.28330i	−0.359173	+	0.933271i	$0.616941\pi$
$770$	−21.8691	−	15.0952i	−0.788108	−	0.543992i
$771$	3.88649	+	6.42240i	0.139968	+	0.231297i
$772$	3.64564	+	19.8936i	0.131209	+	0.715986i
$773$	0.552840	+	9.13954i	0.0198843	+	0.328726i	0.994492	+	0.104809i	$0.0334231\pi$
$773$	0.552840	+	9.13954i	0.0198843	+	0.328726i	−0.974608	+	0.223917i	$0.928115\pi$
$774$	21.6848	+	1.29178i	0.779443	+	0.0464319i
$775$	−35.0992	−	35.0992i	−1.26080	−	1.26080i
$776$	−3.11473	+	5.93462i	−0.111812	+	0.213040i
$777$	−16.7658	+	53.8900i	−0.601468	+	1.93329i
$778$	3.68185	−	8.18073i	0.132001	−	0.293293i
$779$	16.1993	+	8.50203i	0.580399	+	0.304617i
$780$	10.8004	+	22.3521i	0.386718	+	0.800333i
$781$	−1.61833	+	0.849363i	−0.0579082	+	0.0303926i
$782$	4.05808	+	67.0881i	0.145117	+	2.39907i
$783$	−11.4774	+	2.11960i	−0.410171	+	0.0757485i
$784$	1.01231	−	4.10709i	0.0361538	−	0.146682i
$785$	−64.5588	+	50.5786i	−2.30420	+	1.80523i
$786$	38.5247	+	9.47680i	1.37413	+	0.338026i
$787$	3.98154	−	1.79195i	0.141927	−	0.0638760i	−0.338205	−	0.941072i	$-0.609820\pi$
$787$	3.98154	−	1.79195i	0.141927	−	0.0638760i	0.480131	+	0.877197i	$0.340589\pi$
$788$	0.236322	−	0.0736408i	0.00841861	−	0.00262335i
$789$	17.8564	−	5.57323i	0.635703	−	0.198412i
$790$	−44.9051	+	5.45246i	−1.59765	+	0.193990i
$791$	−1.09826	+	18.1564i	−0.0390497	+	0.645569i
$792$	−0.853268	+	7.08143i	−0.0303195	+	0.251628i
$793$	1.69413	−	5.99691i	0.0601604	−	0.212956i
$794$	−6.11447	+	24.8074i	−0.216995	+	0.880381i
$795$	−19.1913	−	10.0612i	−0.680644	−	0.356833i
$796$	15.9875	−	8.39086i	0.566660	−	0.297406i
$797$	7.93960	+	20.9350i	0.281235	+	0.741556i	0.998976	+	0.0452456i	$0.0144070\pi$
$797$	7.93960	+	20.9350i	0.281235	+	0.741556i	−0.717741	+	0.696310i	$0.754824\pi$
$798$	33.7897	+	23.3005i	1.19614	+	0.824830i
$799$	−35.4479	−	6.49606i	−1.25406	−	0.229814i
$800$	42.1957	−	25.5082i	1.49184	−	0.901851i
$801$	−2.79399	−	1.68554i	−0.0987208	−	0.0595555i
$802$	4.29871	−	35.4030i	0.151793	−	1.25013i
$803$	3.56491	+	9.39989i	0.125803	+	0.331715i
$804$	21.2325	−	2.58795i	0.748812	−	0.0912698i
$805$	−40.8260	−	28.1801i	−1.43893	−	0.993219i
$806$	−22.0880	−	26.6907i	−0.778018	−	0.940141i
$807$	−1.66605	−	3.69729i	−0.0586477	−	0.130151i
$808$	−7.09746	−	5.56050i	−0.249688	−	0.195618i
$809$	−9.91628	−	40.2319i	−0.348638	−	1.41448i	−0.839556	−	0.543274i	$-0.817185\pi$
$809$	−9.91628	−	40.2319i	−0.348638	−	1.41448i	0.490918	−	0.871206i	$-0.336662\pi$
$810$	−14.2235	−	57.2559i	−0.499763	−	2.01177i
$811$	16.7126	−	1.01093i	0.586860	−	0.0354985i	0.235719	−	0.971821i	$-0.424255\pi$
$811$	16.7126	−	1.01093i	0.586860	−	0.0354985i	0.351141	+	0.936323i	$0.385794\pi$
$812$	−6.37328	−	1.98599i	−0.223658	−	0.0696947i
$813$	6.66232	+	12.6799i	0.233658	+	0.444703i
$814$	18.1635	−	23.1840i	0.636631	−	0.812600i
$815$	14.9518	−	16.8771i	0.523740	−	0.591181i
$816$	64.1246	−	28.8954i	2.24481	−	1.01154i
$817$	15.7534	−	12.3420i	0.551142	−	0.431792i
$818$	3.92936	+	32.3612i	0.137387	+	1.13148i
$819$	−28.6168	−	9.95655i	−0.999953	−	0.347910i
$820$	1.81290	−	14.9306i	0.0633093	−	0.521399i
$821$	−16.7623	−	27.7282i	−0.585008	−	0.967722i	−0.998365	−	0.0571531i	$-0.981798\pi$
$821$	−16.7623	−	27.7282i	−0.585008	−	0.967722i	0.413357	−	0.910569i	$-0.364356\pi$
$822$	0.962403	−	5.26525i	0.0335677	−	0.183647i
$823$			37.3112i			1.30059i	0.759684	+	0.650293i	$0.225354\pi$
$823$			37.3112i			1.30059i	−0.759684	+	0.650293i	$0.774646\pi$
$824$	10.8683	+	17.9783i	0.378614	+	0.626304i
$825$	18.6500	+	12.8605i	0.649308	+	0.447747i
$826$	−18.5746	−	18.5746i	−0.646294	−	0.646294i
$827$	−6.19846	−	13.7724i	−0.215541	−	0.478913i	0.772128	−	0.635467i	$-0.219192\pi$
$827$	−6.19846	−	13.7724i	−0.215541	−	0.478913i	−0.987669	+	0.156554i	$0.949962\pi$
$828$	1.79972	−	14.9362i	0.0625447	−	0.519070i
$829$	−18.3018	+	20.6585i	−0.635649	+	0.717499i	−0.974762	−	0.223246i	$-0.928335\pi$
$829$	−18.3018	+	20.6585i	−0.635649	+	0.717499i	0.339113	+	0.940746i	$0.389873\pi$
$830$	−0.775224	+	1.28238i	−0.0269084	+	0.0445120i
$831$	12.2232	+	15.5871i	0.424019	+	0.540710i
$832$	−1.45430	+	0.701890i	−0.0504187	+	0.0243337i
$833$	−4.56296	−	5.15052i	−0.158097	−	0.178455i
$834$	−0.0130423	−	28.5112i	−0.000451617	−	0.987263i
$835$	−82.2961	−	20.2842i	−2.84797	−	0.701962i
$836$	−4.21734	−	6.10987i	−0.145860	−	0.211314i
$837$	13.2969	+	25.2508i	0.459608	+	0.872796i
$838$	−1.97323	+	3.26412i	−0.0681642	+	0.112757i
$839$	2.79973	+	2.19344i	0.0966572	+	0.0757261i	0.663884	−	0.747835i	$-0.268907\pi$
$839$	2.79973	+	2.19344i	0.0966572	+	0.0757261i	−0.567227	+	0.823562i	$0.691984\pi$
$840$	−7.13398	+	29.0008i	−0.246146	+	1.00062i
$841$	−8.49443	+	22.3980i	−0.292912	+	0.772344i
$842$	30.4056	+	15.9581i	1.04785	+	0.549952i
$843$	2.25230	−	5.94704i	0.0775734	−	0.204827i
$844$			5.62443i			0.193601i
$845$	−48.3106	−	6.20525i	−1.66194	−	0.213467i
$846$	21.7683	+	8.23284i	0.748408	+	0.283051i
$847$	24.5379	+	4.49675i	0.843134	+	0.154510i
$848$	−7.75284	+	14.7718i	−0.266234	+	0.507266i
$849$	0.666182	−	1.10314i	0.0228633	−	0.0378596i
$850$	7.75965	−	128.282i	0.266154	−	4.40005i
$851$	33.9083	−	43.2807i	1.16236	−	1.48364i
$852$	−1.73786	−	1.53819i	−0.0595382	−	0.0526977i
$853$	−29.3761	−	17.7585i	−1.00582	−	0.608038i	−0.0843266	−	0.996438i	$-0.526874\pi$
$853$	−29.3761	−	17.7585i	−1.00582	−	0.608038i	−0.921491	+	0.388400i	$0.873028\pi$
$854$	−6.97093	+	4.81168i	−0.238540	+	0.164652i
$855$	−44.7573	−	30.8333i	−1.53067	−	1.05448i
$856$	17.2333	−	3.15811i	0.589021	−	0.107942i
$857$	1.61550	−	1.43121i	0.0551846	−	0.0488893i	−0.635080	−	0.772447i	$-0.719033\pi$
$857$	1.61550	−	1.43121i	0.0551846	−	0.0488893i	0.690264	+	0.723557i	$0.257494\pi$
$858$	12.1161	+	10.1592i	0.413636	+	0.346830i
$859$	−13.3741	−	11.8485i	−0.456320	−	0.404264i	0.403405	−	0.915022i	$-0.367827\pi$
$859$	−13.3741	−	11.8485i	−0.456320	−	0.404264i	−0.859725	+	0.510757i	$0.829365\pi$
$860$	−14.0795	−	8.51138i	−0.480108	−	0.290236i
$861$	11.3278	+	14.4453i	0.386051	+	0.492294i
$862$	1.68669	+	6.84315i	0.0574487	+	0.233079i
$863$	−9.29458	+	4.18315i	−0.316391	+	0.142396i	−0.562386	−	0.826875i	$-0.690116\pi$
$863$	−9.29458	+	4.18315i	−0.316391	+	0.142396i	0.245994	+	0.969271i	$0.420886\pi$
$864$	−27.5145	+	6.82177i	−0.936061	+	0.232081i
$865$	−26.2688	+	58.3669i	−0.893167	+	1.98453i
$866$	−30.0517	+	18.1669i	−1.02120	+	0.617336i
$867$	15.2779	−	83.5842i	0.518863	−	2.83867i
$868$			16.3223i			0.554014i
$869$	−8.54617	+	5.16634i	−0.289909	+	0.175256i
$870$	24.3515	+	7.57602i	0.825594	+	0.256851i
$871$	−18.5024	+	37.6689i	−0.626931	+	1.27636i
$872$	−29.3911	+	3.56873i	−0.995309	+	0.120852i
$873$	−3.65173	−	11.6812i	−0.123592	−	0.395348i
$874$	−22.7145	−	32.9076i	−0.768328	−	1.11312i
$875$	31.7218	+	28.1031i	1.07239	+	0.950057i
$876$	−9.55143	+	8.46963i	−0.322713	+	0.286162i
$877$	−13.6394	−	17.4094i	−0.460571	−	0.587875i	0.499960	−	0.866048i	$-0.333348\pi$
$877$	−13.6394	−	17.4094i	−0.460571	−	0.587875i	−0.960531	+	0.278173i	$0.910271\pi$
$878$	−6.42616	+	20.6223i	−0.216873	+	0.695968i
$879$	−6.82626	+	56.4350i	−0.230244	+	1.90351i
$880$	15.3891	−	22.2950i	0.518768	−	0.751565i
$881$	−25.2445	+	6.22221i	−0.850509	+	0.209632i	−0.640395	−	0.768045i	$-0.721229\pi$
$881$	−25.2445	+	6.22221i	−0.850509	+	0.209632i	−0.210113	+	0.977677i	$0.567383\pi$
$882$	2.30237	+	3.80072i	0.0775248	+	0.127977i
$883$	10.8863	−	7.51427i	0.366353	−	0.252875i	−0.370639	−	0.928777i	$-0.620861\pi$
$883$	10.8863	−	7.51427i	0.366353	−	0.252875i	0.736992	+	0.675902i	$0.236246\pi$
$884$	4.78428	−	30.7203i	0.160913	−	1.03324i
$885$	24.6072	+	24.5847i	0.827161	+	0.826405i
$886$	14.9148	−	4.64765i	0.501073	−	0.156141i
$887$	7.65492	−	2.90313i	0.257027	−	0.0974775i	−0.222726	−	0.974881i	$-0.571495\pi$
$887$	7.65492	−	2.90313i	0.257027	−	0.0974775i	0.479753	+	0.877404i	$0.340726\pi$
$888$	−31.6067	−	9.83319i	−1.06065	−	0.329980i
$889$	9.66576	+	1.77132i	0.324179	+	0.0594081i
$890$	3.68856	+	6.10162i	0.123641	+	0.204527i
$891$	−8.05117	−	10.2379i	−0.269724	−	0.342983i
$892$	2.02216	−	4.49306i	0.0677070	−	0.150439i
$893$	20.0469	−	7.60280i	0.670845	−	0.254418i
$894$	24.1424	−	7.53518i	0.807441	−	0.252014i
$895$	−37.3276	−	11.6317i	−1.24772	−	0.388806i
$896$	31.8067	+	7.83964i	1.06259	+	0.261904i
$897$	22.6187	+	18.9656i	0.755215	+	0.633242i
$898$	32.9936	−	8.13220i	1.10101	−	0.271375i
$899$	−12.3138	−	0.744849i	−0.410689	−	0.0248421i
$900$	−6.85880	+	27.9372i	−0.228627	+	0.931241i
$901$	12.6117	+	24.0295i	0.420156	+	0.800540i
$902$	−2.84997	−	9.14588i	−0.0948936	−	0.304524i
$903$	19.4949	−	4.81451i	0.648749	−	0.160217i
$904$	−10.6488	−	0.644136i	−0.354175	−	0.0214236i
$905$	25.2470	+	32.2255i	0.839240	+	1.07121i
$906$	13.4688	+	6.05443i	0.447472	+	0.201145i
$907$	9.30820	+	10.5068i	0.309074	+	0.348872i	0.882438	−	0.470428i	$-0.155901\pi$
$907$	9.30820	+	10.5068i	0.309074	+	0.348872i	−0.573365	+	0.819300i	$0.694362\pi$
$908$	−18.0572	+	1.09226i	−0.599250	+	0.0362479i
$909$	16.3421	−	1.99947i	0.542034	−	0.0663181i
$910$	45.2122	+	48.3636i	1.49877	+	1.60324i
$911$	−11.0182	+	20.9934i	−0.365048	+	0.695542i	−0.996826	−	0.0796078i	$-0.974633\pi$
$911$	−11.0182	+	20.9934i	−0.365048	+	0.695542i	0.631778	+	0.775150i	$0.282326\pi$
$912$	−23.7543	+	34.4477i	−0.786584	+	1.14068i
$913$	−0.0398756	+	0.328405i	−0.00131969	+	0.0108686i
$914$	−41.7075	−	21.8898i	−1.37956	−	0.724050i
$915$	9.22776	−	6.37569i	0.305060	−	0.210774i
$916$	−7.04746	+	2.19608i	−0.232855	+	0.0725605i
$917$	36.6064	−	2.21428i	1.20885	−	0.0731219i
$918$	−26.1060	+	69.1217i	−0.861625	+	2.28136i
$919$	17.4044	−	15.4190i	0.574119	−	0.508625i	−0.325359	−	0.945590i	$-0.605485\pi$
$919$	17.4044	−	15.4190i	0.574119	−	0.508625i	0.899478	+	0.436965i	$0.143947\pi$
$920$	16.5278	−	23.9446i	0.544904	−	0.789430i
$921$	7.61442	+	30.8322i	0.250904	+	1.01596i
$922$	2.99545	+	1.13602i	0.0986498	+	0.0374129i
$923$	4.39054	−	1.20761i	0.144516	−	0.0397490i
$924$	−1.34613	−	7.32671i	−0.0442845	−	0.241031i
$925$	−74.3403	+	74.3403i	−2.44430	+	2.44430i
$926$	43.7575	+	16.5950i	1.43796	+	0.545347i
$927$	−37.2551	−	9.14641i	−1.22362	−	0.300407i
$928$	3.64561	−	11.6992i	0.119673	−	0.384045i
$929$	55.9276	−	10.2491i	1.83492	−	0.336262i	0.852471	−	0.522774i	$-0.175103\pi$
$929$	55.9276	−	10.2491i	1.83492	−	0.336262i	0.982453	+	0.186512i	$0.0597183\pi$
$930$	−0.0285246	−	62.3566i	−0.000935360	−	2.04475i
$931$	3.90837	+	1.21790i	0.128092	+	0.0399149i
$932$	−26.9767	+	3.27557i	−0.883652	+	0.107295i
$933$	−23.7418	−	14.3376i	−0.777272	−	0.469392i
$934$	−30.0570	−	30.0570i	−0.983494	−	0.983494i
$935$	−15.6269	−	41.2048i	−0.511054	−	1.34754i
$936$	5.83956	−	16.7839i	0.190872	−	0.548599i
$937$	−10.8036	+	28.4867i	−0.352938	+	0.930621i	0.634544	+	0.772887i	$0.281188\pi$
$937$	−10.8036	+	28.4867i	−0.352938	+	0.930621i	−0.987482	+	0.157734i	$0.949581\pi$
$938$	52.0189	−	23.4118i	1.69848	−	0.764422i
$939$	20.2348	+	20.2163i	0.660336	+	0.659733i
$940$	−11.6882	−	13.1933i	−0.381229	−	0.430318i
$941$	4.01447	−	0.735678i	0.130868	−	0.0239824i	−0.114422	−	0.993432i	$-0.536502\pi$
$941$	4.01447	−	0.735678i	0.130868	−	0.0239824i	0.245290	+	0.969450i	$0.421117\pi$
$942$	−65.8510	−	7.96519i	−2.14554	−	0.259520i
$943$	−5.32042	−	17.0738i	−0.173257	−	0.556000i
$944$	18.9364	−	18.9364i	0.616327	−	0.616327i
$945$	−28.2771	−	46.6313i	−0.919854	−	1.51692i
$946$	−10.4026	−	1.26310i	−0.338217	−	0.0410670i
$947$	24.6393	+	11.0892i	0.800668	+	0.360352i	0.769082	−	0.639150i	$-0.220714\pi$
$947$	24.6393	+	11.0892i	0.800668	+	0.360352i	0.0315857	+	0.999501i	$0.489944\pi$
$948$	−9.98581	−	7.81601i	−0.324324	−	0.253852i
$949$	−3.68307	−	24.7749i	−0.119558	−	0.804227i
$950$	35.5320	+	67.7006i	1.15281	+	2.19650i
$951$	34.2805	+	4.14649i	1.11162	+	0.134459i
$952$	27.9970	−	24.8032i	0.907388	−	0.803876i
$953$	−40.8350	−	10.0649i	−1.32278	−	0.326035i	−0.486181	−	0.873858i	$-0.661610\pi$
$953$	−40.8350	−	10.0649i	−1.32278	−	0.326035i	−0.836594	+	0.547823i	$0.815457\pi$
$954$	−5.22918	−	16.7271i	−0.169301	−	0.541561i
$955$	5.74467	−	94.9707i	0.185893	−	3.07318i
$956$	1.09280	+	2.42809i	0.0353436	+	0.0785302i
$957$	5.58883	−	0.681201i	0.180661	−	0.0220201i
$958$	−41.8792	+	21.9799i	−1.35306	+	0.710139i
$959$	−0.596385	−	4.91167i	−0.0192583	−	0.158606i
$960$	−2.82232	−	0.694271i	−0.0910901	−	0.0224075i
$961$	−0.200211	−	0.812288i	−0.00645842	−	0.0262029i
$962$	−56.5312	+	46.7826i	−1.82264	+	1.50833i
$963$	−18.1497	+	26.3460i	−0.584867	+	0.848987i
$964$	4.44778	−	14.2734i	0.143253	−	0.459716i
$965$	−33.1920	−	63.2422i	−1.06849	−	2.03584i
$966$	−7.25024	−	39.4614i	−0.233273	−	1.26965i
$967$	27.6419	+	12.4406i	0.888904	+	0.400063i	0.802818	−	0.596225i	$-0.203333\pi$
$967$	27.6419	+	12.4406i	0.888904	+	0.400063i	0.0860860	+	0.996288i	$0.472564\pi$
$968$	−2.63736	+	14.3916i	−0.0847680	+	0.462564i
$969$	24.1664	+	63.6338i	0.776338	+	2.04421i
$970$	−4.82039	+	26.3040i	−0.154773	+	0.844571i
$971$	−29.6037	−	3.59454i	−0.950028	−	0.115354i	−0.369172	−	0.929361i	$-0.620359\pi$
$971$	−29.6037	−	3.59454i	−0.950028	−	0.115354i	−0.580855	+	0.814007i	$0.697282\pi$
$972$	8.52372	−	14.1731i	0.273398	−	0.454601i
$973$	−7.84078	−	25.1620i	−0.251364	−	0.806655i
$974$	−0.501343	+	0.726321i	−0.0160641	+	0.0232728i
$975$	−38.5636	−	41.2138i	−1.23502	−	1.31990i
$976$	−4.90539	−	7.10669i	−0.157018	−	0.227480i
$977$	10.7138	−	13.6751i	0.342764	−	0.437506i	−0.584796	−	0.811181i	$-0.698825\pi$
$977$	10.7138	−	13.6751i	0.342764	−	0.437506i	0.927560	+	0.373674i	$0.121902\pi$
$978$	18.2026	−	1.10941i	0.582054	−	0.0354750i
$979$	1.29542	+	0.894161i	0.0414017	+	0.0285775i
$980$	−0.203202	−	3.35933i	−0.00649105	−	0.107310i
$981$	33.3029	−	42.5882i	1.06328	−	1.35974i
$982$	13.3819	−	10.4841i	0.427034	−	0.334560i
$983$	−24.9714	−	19.5638i	−0.796463	−	0.623989i	0.133747	−	0.991015i	$-0.457299\pi$
$983$	−24.9714	−	19.5638i	−0.796463	−	0.623989i	−0.930211	+	0.367026i	$0.880376\pi$
$984$	−8.47222	+	6.64381i	−0.270084	+	0.211797i
$985$	−0.719403	+	0.496568i	−0.0229221	+	0.0158220i
$986$	−19.6979	−	25.1426i	−0.627310	−	0.800702i
$987$	21.4746	+	1.28911i	0.683544	+	0.0410330i
$988$	7.01927	+	17.1131i	0.223313	+	0.544442i
$989$	−19.4199	−	2.35800i	−0.617517	−	0.0749801i
$990$	5.15548	+	27.9881i	0.163852	+	0.889521i
$991$	−43.4566			−1.38045			−0.690223	−	0.723597i	$-0.742487\pi$
$991$	−43.4566			−1.38045			−0.690223	+	0.723597i	$0.742487\pi$
$992$	−29.9622			−0.951300
$993$	8.09922	+	21.3265i	0.257021	+	0.676775i
$994$	−5.64416	−	2.54023i	−0.179022	−	0.0805713i
$995$	−45.0869	+	45.0869i	−1.42935	+	1.42935i
$996$	−0.407827	+	0.100718i	−0.0129225	+	0.00319138i
$997$	49.6715	−	12.2429i	1.57311	−	0.387737i	0.646246	−	0.763129i	$-0.276338\pi$
$997$	49.6715	−	12.2429i	1.57311	−	0.387737i	0.926866	+	0.375392i	$0.122492\pi$
$998$	−7.28926	−	6.45772i	−0.230737	−	0.204415i
$999$	53.4814	−	28.1629i	1.69208	−	0.891035i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.s.a.5.13	✓	1392
3.2	odd	2	inner	507.2.s.a.5.46	yes	1392
169.34	odd	52	inner	507.2.s.a.203.46	yes	1392
507.203	even	52	inner	507.2.s.a.203.13	yes	1392

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.s.a.5.13	✓	1392	1.1	even	1	trivial
507.2.s.a.5.46	yes	1392	3.2	odd	2	inner
507.2.s.a.203.13	yes	1392	507.203	even	52	inner
507.2.s.a.203.46	yes	1392	169.34	odd	52	inner

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	507.2.s.a.5.13

Level	$507$
Weight	$2$
Character	507.5
Analytic conductor	$4.048$
Analytic rank	$0$
Dimension	$1392$
Inner twists	$4$