LMFDB - Embedded newform 135.3.r.a.43.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,3,Mod(7,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([32, 9])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.r (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$408$
Relative dimension:	$34$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			43.8
Character	$\chi$	$=$	135.43
Dual form			135.3.r.a.22.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.49089 + 0.217924i) q^{2} +(2.60172 + 1.49367i) q^{3} +(2.21779 - 0.391056i) q^{4} +(4.54721 + 2.07916i) q^{5} +(-6.80610 - 3.15358i) q^{6} +(-0.867466 - 1.23887i) q^{7} +(4.22177 - 1.13122i) q^{8} +(4.53790 + 7.77222i) q^{9} +(-11.7797 - 4.18799i) q^{10} +(7.38848 - 2.68919i) q^{11} +(6.35418 + 2.29523i) q^{12} +(-18.6824 - 1.63449i) q^{13} +(2.43074 + 2.89684i) q^{14} +(8.72499 + 12.2014i) q^{15} +(-18.7342 + 6.81868i) q^{16} +(19.6038 + 5.25283i) q^{17} +(-12.9971 - 18.3708i) q^{18} +(26.7540 + 15.4465i) q^{19} +(10.8978 + 2.83292i) q^{20} +(-0.406441 - 4.51890i) q^{21} +(-17.8178 + 8.30859i) q^{22} +(-21.7403 + 31.0483i) q^{23} +(12.6735 + 3.36281i) q^{24} +(16.3542 + 18.9087i) q^{25} +46.8918 q^{26} +(0.197204 + 26.9993i) q^{27} +(-2.40833 - 2.40833i) q^{28} +(6.52085 - 7.77124i) q^{29} +(-24.3919 - 28.4909i) q^{30} +(-4.53255 - 25.7054i) q^{31} +(29.3340 - 13.6787i) q^{32} +(23.2395 + 4.03944i) q^{33} +(-49.9756 - 8.81204i) q^{34} +(-1.36875 - 7.43700i) q^{35} +(13.1035 + 15.4626i) q^{36} +(-31.8840 - 8.54330i) q^{37} +(-70.0074 - 32.6450i) q^{38} +(-46.1649 - 32.1578i) q^{39} +(21.5492 + 3.63382i) q^{40} +(31.8883 - 26.7575i) q^{41} +(1.99718 + 11.1675i) q^{42} +(-41.3143 - 19.2652i) q^{43} +(15.3345 - 8.85336i) q^{44} +(4.47510 + 44.7769i) q^{45} +(47.3864 - 82.0756i) q^{46} +(-25.4662 - 36.3695i) q^{47} +(-58.9260 - 10.2424i) q^{48} +(15.9767 - 43.8956i) q^{49} +(-44.8572 - 43.5355i) q^{50} +(43.1577 + 42.9480i) q^{51} +(-42.0727 + 3.68088i) q^{52} +(10.0402 + 10.0402i) q^{53} +(-6.37501 - 67.2091i) q^{54} +(39.1882 + 3.13351i) q^{55} +(-5.06367 - 4.24893i) q^{56} +(46.5346 + 80.1491i) q^{57} +(-14.5491 + 20.7783i) q^{58} +(-4.53496 + 12.4597i) q^{59} +(24.1216 + 23.6482i) q^{60} +(-5.74775 + 32.5971i) q^{61} +(16.8919 + 63.0414i) q^{62} +(5.69230 - 12.3640i) q^{63} +(-1.02459 + 0.591547i) q^{64} +(-81.5542 - 46.2759i) q^{65} +(-58.7673 - 4.99733i) q^{66} +(8.05417 - 92.0596i) q^{67} +(45.5313 + 3.98347i) q^{68} +(-102.938 + 48.3063i) q^{69} +(5.03009 + 18.2264i) q^{70} +(-22.0775 - 38.2394i) q^{71} +(27.9500 + 27.6792i) q^{72} +(49.2915 - 13.2076i) q^{73} +(81.2813 + 14.3321i) q^{74} +(14.3057 + 73.6230i) q^{75} +(65.3753 + 23.7946i) q^{76} +(-9.74081 - 6.82059i) q^{77} +(121.999 + 70.0409i) q^{78} +(20.5814 - 24.5280i) q^{79} +(-99.3653 - 7.94531i) q^{80} +(-39.8150 + 70.5391i) q^{81} +(-73.5991 + 73.5991i) q^{82} +(-3.97363 - 45.4188i) q^{83} +(-2.66855 - 9.86303i) q^{84} +(78.2212 + 64.6451i) q^{85} +(107.108 + 38.9840i) q^{86} +(28.5731 - 10.4786i) q^{87} +(28.1504 - 19.7111i) q^{88} +(26.4081 + 15.2467i) q^{89} +(-20.9049 - 110.559i) q^{90} +(14.1814 + 24.5629i) q^{91} +(-36.0737 + 77.3604i) q^{92} +(26.6029 - 73.6484i) q^{93} +(71.3592 + 85.0426i) q^{94} +(89.5406 + 125.864i) q^{95} +(96.7502 + 8.22724i) q^{96} +(-51.2388 + 109.882i) q^{97} +(-30.2302 + 112.821i) q^{98} +(54.4291 + 45.2217i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 408 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{7} - 6 q^{8} - 6 q^{10} - 60 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 6 q^{17} - 54 q^{18} - 300 q^{20} - 24 q^{21} - 12 q^{22} - 156 q^{23}+ \cdots - 1032 q^{98}+O(q^{100}) $ 408 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^7 - 6 * q^8 - 6 * q^10 - 60 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 6 * q^17 - 54 * q^18 - 300 * q^20 - 24 * q^21 - 12 * q^22 - 156 * q^23 + 6 * q^25 - 48 * q^26 + 180 * q^27 - 24 * q^28 + 276 * q^30 - 24 * q^31 + 72 * q^32 - 78 * q^33 + 156 * q^35 - 312 * q^36 - 6 * q^37 - 252 * q^38 - 108 * q^40 - 384 * q^41 - 528 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 210 * q^47 + 444 * q^48 + 276 * q^50 - 144 * q^51 - 60 * q^52 + 516 * q^53 - 24 * q^55 + 912 * q^56 + 168 * q^57 - 12 * q^58 + 864 * q^60 - 312 * q^61 - 6 * q^62 - 54 * q^63 + 420 * q^65 + 1224 * q^66 - 480 * q^67 - 540 * q^68 - 12 * q^70 - 12 * q^71 - 1548 * q^72 - 6 * q^73 - 852 * q^75 - 216 * q^76 - 876 * q^77 - 1362 * q^78 - 1644 * q^80 - 204 * q^81 - 24 * q^82 - 372 * q^83 - 12 * q^85 + 516 * q^86 + 540 * q^87 + 348 * q^88 - 384 * q^90 - 12 * q^91 + 2082 * q^92 - 1404 * q^93 + 198 * q^95 + 924 * q^96 + 600 * q^97 - 1032 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.49089	+	0.217924i	−1.24544	+	0.108962i	−0.690750	−	0.723093i	$-0.742720\pi$
$2$	−2.49089	+	0.217924i	−1.24544	+	0.108962i	−0.554692	+	0.832055i	$0.687164\pi$
$3$	2.60172	+	1.49367i	0.867240	+	0.497890i
$3$	2.60172	+	1.49367i	0.867240	+	0.497890i
$4$	2.21779	−	0.391056i	0.554447	−	0.0977640i
$5$	4.54721	+	2.07916i	0.909442	+	0.415831i
$5$	4.54721	+	2.07916i	0.909442	+	0.415831i
$6$	−6.80610	−	3.15358i	−1.13435	−	0.525597i
$7$	−0.867466	−	1.23887i	−0.123924	−	0.176981i	0.752396	−	0.658711i	$-0.228898\pi$
$7$	−0.867466	−	1.23887i	−0.123924	−	0.176981i	−0.876320	+	0.481729i	$0.840009\pi$
$8$	4.22177	−	1.13122i	0.527721	−	0.141402i
$9$	4.53790	+	7.77222i	0.504211	+	0.863581i
$10$	−11.7797	−	4.18799i	−1.17797	−	0.418799i
$11$	7.38848	−	2.68919i	0.671680	−	0.244472i	0.0164089	−	0.999865i	$-0.494777\pi$
$11$	7.38848	−	2.68919i	0.671680	−	0.244472i	0.655271	+	0.755394i	$0.272554\pi$
$12$	6.35418	+	2.29523i	0.529515	+	0.191269i
$13$	−18.6824	−	1.63449i	−1.43710	−	0.125730i	−0.658186	−	0.752856i	$-0.728676\pi$
$13$	−18.6824	−	1.63449i	−1.43710	−	0.125730i	−0.778918	+	0.627125i	$0.784231\pi$
$14$	2.43074	+	2.89684i	0.173624	+	0.206917i
$15$	8.72499	+	12.2014i	0.581666	+	0.813428i
$16$	−18.7342	+	6.81868i	−1.17089	+	0.426168i
$17$	19.6038	+	5.25283i	1.15317	+	0.308990i	0.784233	−	0.620466i	$-0.213057\pi$
$17$	19.6038	+	5.25283i	1.15317	+	0.308990i	0.368933	+	0.929456i	$0.379723\pi$
$18$	−12.9971	−	18.3708i	−0.722064	−	1.02060i
$19$	26.7540	+	15.4465i	1.40811	+	0.812971i	0.995206	−	0.0978043i	$-0.0311819\pi$
$19$	26.7540	+	15.4465i	1.40811	+	0.812971i	0.412902	+	0.910776i	$0.364515\pi$
$20$	10.8978	+	2.83292i	0.544891	+	0.141646i
$21$	−0.406441	−	4.51890i	−0.0193543	−	0.215186i
$22$	−17.8178	+	8.30859i	−0.809901	+	0.377663i
$23$	−21.7403	+	31.0483i	−0.945230	+	1.34993i	−0.00846647	+	0.999964i	$0.502695\pi$
$23$	−21.7403	+	31.0483i	−0.945230	+	1.34993i	−0.936763	+	0.349964i	$0.886194\pi$
$24$	12.6735	+	3.36281i	0.528063	+	0.140117i
$25$	16.3542	+	18.9087i	0.654169	+	0.756349i
$26$	46.8918			1.80353
$27$	0.197204	+	26.9993i	0.00730384	+	0.999973i
$28$	−2.40833	−	2.40833i	−0.0860116	−	0.0860116i
$29$	6.52085	−	7.77124i	0.224857	−	0.267974i	−0.641807	−	0.766866i	$-0.721815\pi$
$29$	6.52085	−	7.77124i	0.224857	−	0.267974i	0.866664	+	0.498892i	$0.166260\pi$
$30$	−24.3919	−	28.4909i	−0.813065	−	0.949698i
$31$	−4.53255	−	25.7054i	−0.146211	−	0.829206i	−0.966387	−	0.257094i	$-0.917235\pi$
$31$	−4.53255	−	25.7054i	−0.146211	−	0.829206i	0.820175	−	0.572113i	$-0.193876\pi$
$32$	29.3340	−	13.6787i	0.916686	−	0.427458i
$33$	23.2395	+	4.03944i	0.704228	+	0.122407i
$34$	−49.9756	−	8.81204i	−1.46987	−	0.259178i
$35$	−1.36875	−	7.43700i	−0.0391070	−	0.212486i
$36$	13.1035	+	15.4626i	0.363986	+	0.429516i
$37$	−31.8840	−	8.54330i	−0.861731	−	0.230900i	−0.199222	−	0.979954i	$-0.563842\pi$
$37$	−31.8840	−	8.54330i	−0.861731	−	0.230900i	−0.662509	+	0.749054i	$0.730508\pi$
$38$	−70.0074	−	32.6450i	−1.84230	−	0.859079i
$39$	−46.1649	−	32.1578i	−1.18371	−	0.824558i
$40$	21.5492	+	3.63382i	0.538731	+	0.0908456i
$41$	31.8883	−	26.7575i	0.777764	−	0.652622i	−0.164920	−	0.986307i	$-0.552737\pi$
$41$	31.8883	−	26.7575i	0.777764	−	0.652622i	0.942685	+	0.333685i	$0.108292\pi$
$42$	1.99718	+	11.1675i	0.0475518	+	0.265893i
$43$	−41.3143	−	19.2652i	−0.960798	−	0.448027i	−0.122036	−	0.992526i	$-0.538942\pi$
$43$	−41.3143	−	19.2652i	−0.960798	−	0.448027i	−0.838762	+	0.544498i	$0.816720\pi$
$44$	15.3345	−	8.85336i	0.348511	−	0.201213i
$45$	4.47510	+	44.7769i	0.0994467	+	0.995043i
$46$	47.3864	−	82.0756i	1.03014	−	1.78425i
$47$	−25.4662	−	36.3695i	−0.541834	−	0.773819i	0.451102	−	0.892473i	$-0.351031\pi$
$47$	−25.4662	−	36.3695i	−0.541834	−	0.773819i	−0.992936	+	0.118653i	$0.962142\pi$
$48$	−58.9260	−	10.2424i	−1.22762	−	0.213383i
$49$	15.9767	−	43.8956i	0.326055	−	0.895828i
$50$	−44.8572	−	43.5355i	−0.897143	−	0.870709i
$51$	43.1577	+	42.9480i	0.846229	+	0.842118i
$52$	−42.0727	+	3.68088i	−0.809090	+	0.0707862i
$53$	10.0402	+	10.0402i	0.189438	+	0.189438i	0.795453	−	0.606015i	$-0.207233\pi$
$53$	10.0402	+	10.0402i	0.189438	+	0.189438i	−0.606015	+	0.795453i	$0.707233\pi$
$54$	−6.37501	−	67.2091i	−0.118056	−	1.24461i
$55$	39.1882	+	3.13351i	0.712513	+	0.0569729i
$56$	−5.06367	−	4.24893i	−0.0904227	−	0.0758737i
$57$	46.5346	+	80.1491i	0.816397	+	1.40612i
$58$	−14.5491	+	20.7783i	−0.250847	+	0.358247i
$59$	−4.53496	+	12.4597i	−0.0768638	+	0.211181i	−0.972173	−	0.234263i	$-0.924732\pi$
$59$	−4.53496	+	12.4597i	−0.0768638	+	0.211181i	0.895309	+	0.445445i	$0.146954\pi$
$60$	24.1216	+	23.6482i	0.402027	+	0.394137i
$61$	−5.74775	+	32.5971i	−0.0942254	+	0.534379i	0.900757	+	0.434324i	$0.143013\pi$
$61$	−5.74775	+	32.5971i	−0.0942254	+	0.534379i	−0.994982	+	0.100054i	$0.968098\pi$
$62$	16.8919	+	63.0414i	0.272450	+	1.01680i
$63$	5.69230	−	12.3640i	0.0903540	−	0.196254i
$64$	−1.02459	+	0.591547i	−0.0160092	+	0.00924292i
$65$	−81.5542	−	46.2759i	−1.25468	−	0.711937i
$66$	−58.7673	−	4.99733i	−0.890413	−	0.0757171i
$67$	8.05417	−	92.0596i	0.120212	−	1.37402i	−0.661295	−	0.750126i	$-0.729993\pi$
$67$	8.05417	−	92.0596i	0.120212	−	1.37402i	0.781506	−	0.623898i	$-0.214452\pi$
$68$	45.5313	+	3.98347i	0.669578	+	0.0585805i
$69$	−102.938	+	48.3063i	−1.49186	+	0.700091i
$70$	5.03009	+	18.2264i	0.0718585	+	0.260378i
$71$	−22.0775	−	38.2394i	−0.310951	−	0.538583i	0.667618	−	0.744504i	$-0.267314\pi$
$71$	−22.0775	−	38.2394i	−0.310951	−	0.538583i	−0.978568	+	0.205922i	$0.933981\pi$
$72$	27.9500	+	27.6792i	0.388195	+	0.384433i
$73$	49.2915	−	13.2076i	0.675226	−	0.180926i	0.0951183	−	0.995466i	$-0.469677\pi$
$73$	49.2915	−	13.2076i	0.675226	−	0.180926i	0.580108	+	0.814540i	$0.303010\pi$
$74$	81.2813	+	14.3321i	1.09840	+	0.193677i
$75$	14.3057	+	73.6230i	0.190743	+	0.981640i
$76$	65.3753	+	23.7946i	0.860201	+	0.313087i
$77$	−9.74081	−	6.82059i	−0.126504	−	0.0885791i
$78$	121.999	+	70.0409i	1.56409	+	0.897960i
$79$	20.5814	−	24.5280i	0.260525	−	0.310481i	−0.619887	−	0.784691i	$-0.712822\pi$
$79$	20.5814	−	24.5280i	0.260525	−	0.310481i	0.880412	+	0.474210i	$0.157266\pi$
$80$	−99.3653	−	7.94531i	−1.24207	−	0.0993164i
$81$	−39.8150	+	70.5391i	−0.491543	+	0.870854i
$82$	−73.5991	+	73.5991i	−0.897550	+	0.897550i
$83$	−3.97363	−	45.4188i	−0.0478750	−	0.547214i	−0.981822	−	0.189803i	$-0.939215\pi$
$83$	−3.97363	−	45.4188i	−0.0478750	−	0.547214i	0.933947	−	0.357411i	$-0.116340\pi$
$84$	−2.66855	−	9.86303i	−0.0317684	−	0.117417i
$85$	78.2212	+	64.6451i	0.920249	+	0.760531i
$86$	107.108	+	38.9840i	1.24544	+	0.453302i
$87$	28.5731	−	10.4786i	0.328426	−	0.120444i
$88$	28.1504	−	19.7111i	0.319891	−	0.223990i
$89$	26.4081	+	15.2467i	0.296720	+	0.171312i	0.640969	−	0.767567i	$-0.278533\pi$
$89$	26.4081	+	15.2467i	0.296720	+	0.171312i	−0.344248	+	0.938879i	$0.611866\pi$
$90$	−20.9049	−	110.559i	−0.232277	−	1.22843i
$91$	14.1814	+	24.5629i	0.155839	+	0.269922i
$92$	−36.0737	+	77.3604i	−0.392106	+	0.840873i
$93$	26.6029	−	73.6484i	0.286053	−	0.791918i
$94$	71.3592	+	85.0426i	0.759140	+	0.904708i
$95$	89.5406	+	125.864i	0.942533	+	1.32489i
$96$	96.7502	+	8.22724i	1.00781	+	0.0857004i
$97$	−51.2388	+	109.882i	−0.528235	+	1.13280i	0.443402	+	0.896323i	$0.353771\pi$
$97$	−51.2388	+	109.882i	−0.528235	+	1.13280i	−0.971636	+	0.236480i	$0.924006\pi$
$98$	−30.2302	+	112.821i	−0.308471	+	1.15123i
$99$	54.4291	+	45.2217i	0.549789	+	0.456784i
$100$	43.6646	+	35.5401i	0.436646	+	0.355401i
$101$	−2.01063	+	11.4029i	−0.0199072	+	0.112900i	−0.993142	−	0.116913i	$-0.962700\pi$
$101$	−2.01063	+	11.4029i	−0.0199072	+	0.112900i	0.973235	+	0.229812i	$0.0738113\pi$
$102$	−116.860	−	97.5735i	−1.14569	−	0.956603i
$103$	−9.91776	−	21.2687i	−0.0962890	−	0.206492i	0.852263	−	0.523113i	$-0.175229\pi$
$103$	−9.91776	−	21.2687i	−0.0962890	−	0.206492i	−0.948552	+	0.316621i	$0.897452\pi$
$104$	−80.7215	+	14.2334i	−0.776168	+	0.136859i
$105$	7.54733	−	21.3935i	0.0718794	−	0.203747i
$106$	−27.1970	−	22.8210i	−0.256575	−	0.215292i
$107$	71.3346	−	71.3346i	0.666679	−	0.666679i	−0.290267	−	0.956946i	$-0.593744\pi$
$107$	71.3346	−	71.3346i	0.666679	−	0.666679i	0.956946	+	0.290267i	$0.0937441\pi$
$108$	10.9956	+	59.8016i	0.101811	+	0.553719i
$109$		−	117.131i		−	1.07459i	−0.843393	−	0.537297i	$-0.819445\pi$
$109$		−	117.131i		−	1.07459i	0.843393	−	0.537297i	$-0.180555\pi$
$110$	−98.2962	+	0.734841i	−0.893602	+	0.00668037i
$111$	−70.1925	−	69.8515i	−0.632365	−	0.629293i
$112$	24.6987	+	17.2942i	0.220524	+	0.154413i
$113$	−54.3136	−	116.476i	−0.480651	−	1.03076i	−0.985830	−	0.167745i	$-0.946351\pi$
$113$	−54.3136	−	116.476i	−0.480651	−	1.03076i	0.505179	−	0.863014i	$-0.331426\pi$
$114$	−133.379	−	189.501i	−1.16999	−	1.66229i
$115$	−163.412	+	95.9818i	−1.42097	+	0.834625i
$116$	11.4229	−	19.7850i	0.0984731	−	0.170560i
$117$	−72.0750	−	152.621i	−0.616025	−	1.30445i
$118$	8.58080	−	32.0240i	0.0727187	−	0.271390i
$119$	−10.4981	−	28.8432i	−0.0882192	−	0.242380i
$120$	50.6373	+	41.6416i	0.421978	+	0.347014i
$121$	−45.3335	+	38.0393i	−0.374657	+	0.314374i
$122$	7.21329	−	82.4482i	0.0591253	−	0.675805i
$123$	122.931	−	21.9848i	0.999442	−	0.178739i
$124$	−20.1045	−	55.2367i	−0.162133	−	0.445457i
$125$	35.0519	+	119.985i	0.280415	+	0.959879i
$126$	−11.4845	+	32.0378i	−0.0911465	+	0.254269i
$127$	−20.5282	−	76.6121i	−0.161639	−	0.603245i	−0.998445	−	0.0557454i	$-0.982246\pi$
$127$	−20.5282	−	76.6121i	−0.161639	−	0.603245i	0.836806	−	0.547499i	$-0.184420\pi$
$128$	−103.629	+	72.5618i	−0.809601	+	0.566889i
$129$	−78.7124	−	111.833i	−0.610174	−	0.866919i
$130$	213.227	+	97.4954i	1.64021	+	0.749964i
$131$	−30.1965	−	171.253i	−0.230508	−	1.30727i	−0.851871	−	0.523751i	$-0.824532\pi$
$131$	−30.1965	−	171.253i	−0.230508	−	1.30727i	0.621364	−	0.783522i	$-0.286579\pi$
$132$	53.1200	−	0.129328i	0.402424	−	0.000979758i
$133$	−4.07208	−	46.5441i	−0.0306171	−	0.349955i
$134$			231.065i			1.72437i
$135$	−55.2390	+	123.181i	−0.409178	+	0.912455i
$136$	88.7048			0.652241
$137$	−77.6807	+	6.79618i	−0.567012	+	0.0496072i	−0.367058	−	0.930198i	$-0.619635\pi$
$137$	−77.6807	+	6.79618i	−0.567012	+	0.0496072i	−0.199954	+	0.979805i	$0.564079\pi$
$138$	245.880	−	142.758i	1.78174	−	1.03448i
$139$	−45.5336	+	8.02880i	−0.327580	+	0.0577611i	−0.335020	−	0.942211i	$-0.608743\pi$
$139$	−45.5336	+	8.02880i	−0.327580	+	0.0577611i	0.00743985	+	0.999972i	$0.497632\pi$
$140$	−5.94387	−	15.9584i	−0.0424562	−	0.113989i
$141$	−11.9319	−	132.661i	−0.0846233	−	0.940861i
$142$	63.3258	+	90.4387i	0.445957	+	0.636892i
$143$	−142.430	+	38.1639i	−0.996011	+	0.266880i
$144$	−138.010	−	114.664i	−0.958404	−	0.796276i
$145$	45.8093	−	21.7796i	0.315926	−	0.150204i
$146$	−119.901	+	43.6405i	−0.821242	+	0.298907i
$147$	107.132	−	90.3401i	0.728792	−	0.614559i
$148$	−74.0530	−	6.47880i	−0.500358	−	0.0437757i
$149$	157.603	+	187.824i	1.05774	+	1.26056i	0.964264	+	0.264942i	$0.0853528\pi$
$149$	157.603	+	187.824i	1.05774	+	1.26056i	0.0934742	+	0.995622i	$0.470203\pi$
$150$	−51.6781	−	180.269i	−0.344521	−	1.20179i
$151$	−159.561	+	58.0755i	−1.05670	+	0.384606i	−0.811186	−	0.584788i	$-0.801178\pi$
$151$	−159.561	+	58.0755i	−1.05670	+	0.384606i	−0.245511	+	0.969394i	$0.578956\pi$
$152$	130.423	+	34.9466i	0.858044	+	0.229912i
$153$	48.1340	+	176.202i	0.314601	+	1.15165i
$154$	25.7496	+	14.8665i	0.167205	+	0.0965360i
$155$	32.8351	−	126.312i	0.211839	−	0.814914i
$156$	−114.959	−	53.2661i	−0.736919	−	0.341449i
$157$	−23.9104	+	11.1496i	−0.152296	+	0.0710166i	−0.497272	−	0.867595i	$-0.665665\pi$
$157$	−23.9104	+	11.1496i	−0.152296	+	0.0710166i	0.344976	+	0.938611i	$0.387887\pi$
$158$	−45.9208	+	65.5817i	−0.290638	+	0.415074i
$159$	11.1250	+	41.1185i	0.0699688	+	0.258607i
$160$	161.828	−	1.20979i	1.01142	−	0.00756118i
$161$	57.3238			0.356049
$162$	83.8023	−	184.382i	0.517298	−	1.13816i
$163$	−145.013	−	145.013i	−0.889652	−	0.889652i	0.104837	−	0.994489i	$-0.466568\pi$
$163$	−145.013	−	145.013i	−0.889652	−	0.889652i	−0.994489	+	0.104837i	$0.966568\pi$
$164$	60.2579	−	71.8126i	0.367426	−	0.437882i
$165$	97.2763	+	66.6868i	0.589553	+	0.404162i
$166$	19.7957	+	112.267i	0.119251	+	0.676307i
$167$	175.501	−	81.8374i	1.05090	−	0.490044i	0.181111	−	0.983463i	$-0.442031\pi$
$167$	175.501	−	81.8374i	1.05090	−	0.490044i	0.869792	+	0.493419i	$0.164253\pi$
$168$	−6.82777	−	18.6180i	−0.0406415	−	0.110821i
$169$	179.926	+	31.7258i	1.06465	+	0.187727i
$170$	−208.928	−	143.977i	−1.22899	−	0.846925i
$171$	1.35383	+	278.033i	0.00791712	+	1.62592i
$172$	−99.1602	−	26.5699i	−0.576513	−	0.154476i
$173$	245.143	+	114.312i	1.41701	+	0.660762i	0.972047	−	0.234787i	$-0.0754391\pi$
$173$	245.143	+	114.312i	1.41701	+	0.660762i	0.444963	+	0.895549i	$0.353217\pi$
$174$	−68.8888	+	32.3278i	−0.395912	+	0.185792i
$175$	9.23872	−	36.6634i	0.0527927	−	0.209505i
$176$	−120.080	+	100.759i	−0.682275	+	0.572497i
$177$	−30.4094	+	25.6429i	−0.171805	+	0.144875i
$178$	−69.1022	−	32.2229i	−0.388215	−	0.181027i
$179$	−79.5086	+	45.9043i	−0.444182	+	0.256449i	−0.705370	−	0.708839i	$-0.749219\pi$
$179$	−79.5086	+	45.9043i	−0.444182	+	0.256449i	0.261188	+	0.965288i	$0.415886\pi$
$180$	27.4351	+	97.5558i	0.152417	+	0.541977i
$181$	4.51197	−	7.81497i	0.0249280	−	0.0431766i	−0.853292	−	0.521433i	$-0.825398\pi$
$181$	4.51197	−	7.81497i	0.0249280	−	0.0431766i	0.878220	+	0.478256i	$0.158731\pi$
$182$	−40.6771	−	58.0929i	−0.223500	−	0.319192i
$183$	−63.6434	+	76.2233i	−0.347778	+	0.416521i
$184$	−56.6599	+	155.672i	−0.307934	+	0.846043i
$185$	−127.221	−	105.140i	−0.687678	−	0.568325i
$186$	−50.2151	+	189.247i	−0.269974	+	1.01746i
$187$	158.968	−	13.9079i	0.850097	−	0.0743739i
$188$	−70.7012	−	70.7012i	−0.376070	−	0.376070i
$189$	33.2775	−	23.6653i	0.176072	−	0.125213i
$190$	−250.464	−	294.000i	−1.31823	−	1.54737i
$191$	−84.8059	−	71.1606i	−0.444010	−	0.372568i	0.393198	−	0.919454i	$-0.371369\pi$
$191$	−84.8059	−	71.1606i	−0.444010	−	0.372568i	−0.837207	+	0.546886i	$0.815813\pi$
$192$	−3.54927	+	0.00864120i	−0.0184858	+	4.50062e-5i
$193$	−114.757	+	163.890i	−0.594596	+	0.849172i	−0.997824	−	0.0659278i	$-0.978999\pi$
$193$	−114.757	+	163.890i	−0.594596	+	0.849172i	0.403228	+	0.915100i	$0.367888\pi$
$194$	103.684	−	284.869i	0.534453	−	1.46840i
$195$	−143.060	−	242.212i	−0.733642	−	1.24211i
$196$	18.2673	−	103.599i	0.0932004	−	0.528566i
$197$	79.0998	+	295.205i	0.401522	+	1.49850i	0.810381	+	0.585903i	$0.199260\pi$
$197$	79.0998	+	295.205i	0.401522	+	1.49850i	−0.408859	+	0.912597i	$0.634073\pi$
$198$	−145.432	−	100.781i	−0.734503	−	0.508993i
$199$	−239.148	+	138.072i	−1.20175	+	0.693831i	−0.960944	−	0.276742i	$-0.910745\pi$
$199$	−239.148	+	138.072i	−1.20175	+	0.693831i	−0.240807	+	0.970573i	$0.577412\pi$
$200$	90.4336	+	61.3280i	0.452168	+	0.306640i
$201$	158.461	−	227.483i	0.788365	−	1.13176i
$202$	2.52329	−	28.8414i	0.0124916	−	0.142779i
$203$	−15.2842	−	1.33719i	−0.0752915	−	0.00658715i
$204$	112.510	+	78.3726i	0.551518	+	0.384179i
$205$	200.636	−	55.3710i	0.978712	−	0.270103i
$206$	29.3390	+	50.8166i	0.142422	+	0.246683i
$207$	−339.970	−	28.0761i	−1.64237	−	0.135633i
$208$	361.144	−	96.7681i	1.73627	−	0.465231i
$209$	239.210	+	42.1792i	1.14455	+	0.201814i
$210$	−14.1374	+	54.9334i	−0.0673209	+	0.261588i
$211$	−84.2672	−	30.6708i	−0.399371	−	0.145359i	0.134523	−	0.990910i	$-0.457050\pi$
$211$	−84.2672	−	30.6708i	−0.399371	−	0.145359i	−0.533894	+	0.845551i	$0.679272\pi$
$212$	26.1933	+	18.3408i	0.123553	+	0.0865130i
$213$	−0.322504	−	132.465i	−0.00151410	−	0.621900i
$214$	−162.141	+	193.232i	−0.757668	+	0.902953i
$215$	−147.809	−	173.502i	−0.687486	−	0.806985i
$216$	31.3746	+	113.762i	0.145253	+	0.526674i
$217$	−27.9138	+	27.9138i	−0.128635	+	0.128635i
$218$	25.5256	+	291.759i	0.117090	+	1.33835i
$219$	147.971	+	39.2627i	0.675665	+	0.179282i
$220$	88.1365	−	8.37532i	0.400621	−	0.0380696i
$221$	−357.660	−	130.177i	−1.61837	−	0.589038i
$222$	190.064	+	158.696i	0.856143	+	0.714845i
$223$	312.181	−	218.591i	1.39991	−	0.980230i	0.402001	−	0.915639i	$-0.368315\pi$
$223$	312.181	−	218.591i	1.39991	−	0.980230i	0.997912	−	0.0645906i	$-0.0205741\pi$
$224$	−42.3923	−	24.4752i	−0.189251	−	0.109264i
$225$	−72.7490	+	212.914i	−0.323329	+	0.946287i
$226$	160.672	+	278.292i	0.710937	+	1.23138i
$227$	−4.64435	+	9.95983i	−0.0204597	+	0.0438759i	−0.916272	−	0.400556i	$-0.868817\pi$
$227$	−4.64435	+	9.95983i	−0.0204597	+	0.0438759i	0.895812	+	0.444432i	$0.146595\pi$
$228$	134.547	+	159.556i	0.590118	+	0.699807i
$229$	124.474	+	148.343i	0.543556	+	0.647785i	0.965981	−	0.258613i	$-0.0832655\pi$
$229$	124.474	+	148.343i	0.543556	+	0.647785i	−0.422425	+	0.906398i	$0.638821\pi$
$230$	386.124	−	274.691i	1.67880	−	1.19431i
$231$	−15.1552	−	32.2948i	−0.0656067	−	0.139804i
$232$	18.7385	−	40.1849i	0.0807695	−	0.173211i
$233$	15.3486	−	57.2817i	0.0658737	−	0.245844i	−0.925136	−	0.379637i	$-0.876049\pi$
$233$	15.3486	−	57.2817i	0.0658737	−	0.245844i	0.991009	+	0.133793i	$0.0427156\pi$
$234$	212.790	+	364.454i	0.909360	+	1.55749i
$235$	−40.1822	−	218.328i	−0.170988	−	0.929055i
$236$	−5.18515	+	29.4064i	−0.0219710	+	0.124604i
$237$	90.1839	−	33.0731i	0.380523	−	0.139549i
$238$	32.4352	+	69.5574i	0.136282	+	0.292258i
$239$	−146.929	+	25.9075i	−0.614766	+	0.108400i	−0.472356	−	0.881408i	$-0.656596\pi$
$239$	−146.929	+	25.9075i	−0.614766	+	0.108400i	−0.142410	+	0.989808i	$0.545485\pi$
$240$	−246.653	−	169.090i	−1.02772	−	0.704544i
$241$	−255.936	−	214.756i	−1.06197	−	0.891102i	−0.0676725	−	0.997708i	$-0.521557\pi$
$241$	−255.936	−	214.756i	−1.06197	−	0.891102i	−0.994301	+	0.106606i	$0.966002\pi$
$242$	104.631	−	104.631i	0.432359	−	0.432359i
$243$	−208.950	+	124.053i	−0.859875	+	0.510505i
$244$			74.5412i			0.305497i
$245$	163.915	−	166.384i	0.669041	−	0.679120i
$246$	−301.417	+	81.5515i	−1.22527	+	0.331510i
$247$	−474.581	−	332.305i	−1.92138	−	1.34537i
$248$	−48.2138	−	103.395i	−0.194411	−	0.416915i
$249$	57.5024	−	124.102i	0.230933	−	0.498402i
$250$	−113.458	−	291.230i	−0.453831	−	1.16492i
$251$	115.237	−	199.597i	0.459113	−	0.795207i	−0.539801	−	0.841793i	$-0.681501\pi$
$251$	115.237	−	199.597i	0.459113	−	0.795207i	0.998914	+	0.0465852i	$0.0148339\pi$
$252$	7.78931	−	29.6468i	0.0309100	−	0.117646i
$253$	−77.1328	+	287.864i	−0.304873	+	1.13780i
$254$	67.8289	+	186.358i	0.267043	+	0.733695i
$255$	106.951	+	285.025i	0.419417	+	1.11775i
$256$	245.940	−	206.368i	0.960703	−	0.806126i
$257$	−31.4475	+	359.446i	−0.122364	+	1.39862i	0.648301	+	0.761384i	$0.275480\pi$
$257$	−31.4475	+	359.446i	−0.122364	+	1.39862i	−0.770665	+	0.637240i	$0.780076\pi$
$258$	220.435	+	261.409i	0.854398	+	1.01321i
$259$	17.0743	+	46.9112i	0.0659239	+	0.181124i
$260$	−198.966	−	70.7380i	−0.765256	−	0.272069i
$261$	89.9908	+	15.4164i	0.344792	+	0.0590666i
$262$	112.536	+	419.991i	0.429527	+	1.60302i
$263$	−335.214	+	234.720i	−1.27458	+	0.892470i	−0.997656	−	0.0684226i	$-0.978203\pi$
$263$	−335.214	+	234.720i	−1.27458	+	0.892470i	−0.276922	+	0.960892i	$0.589314\pi$
$264$	102.681	−	9.23541i	0.388944	−	0.0349826i
$265$	24.7797	+	66.5300i	0.0935084	+	0.251057i
$266$	20.2862	+	115.049i	0.0762638	+	0.432513i
$267$	45.9329	+	79.1127i	0.172033	+	0.296302i
$268$	−18.1380	−	207.318i	−0.0676792	−	0.773576i
$269$		−	238.334i		−	0.886001i	−0.896521	−	0.443001i	$-0.853914\pi$
$269$		−	238.334i		−	0.886001i	0.896521	−	0.443001i	$-0.146086\pi$
$270$	110.750	−	318.869i	0.410185	−	1.18100i
$271$	160.306			0.591533			0.295767	−	0.955260i	$-0.404425\pi$
$271$	160.306			0.591533			0.295767	+	0.955260i	$0.404425\pi$
$272$	−403.079	+	35.2648i	−1.48191	+	0.129650i
$273$	0.207159	+	85.0881i	0.000758824	+	0.311678i
$274$	192.013	−	33.8570i	0.700776	−	0.123566i
$275$	171.682	+	95.7271i	0.624298	+	0.348099i
$276$	−209.405	+	147.388i	−0.758712	+	0.534014i
$277$	182.797	+	261.061i	0.659916	+	0.942457i	0.999998	+	0.00206152i	$0.000656204\pi$
$277$	182.797	+	261.061i	0.659916	+	0.942457i	−0.340082	+	0.940396i	$0.610455\pi$
$278$	111.669	−	29.9217i	0.401688	−	0.107632i
$279$	179.220	−	151.876i	0.642365	−	0.544360i
$280$	−14.1914	−	29.8489i	−0.0506836	−	0.106603i
$281$	357.089	−	129.970i	1.27078	−	0.462526i	0.383408	−	0.923579i	$-0.374750\pi$
$281$	357.089	−	129.970i	1.27078	−	0.462526i	0.887373	+	0.461053i	$0.152528\pi$
$282$	58.6311	+	327.844i	0.207912	+	1.16257i
$283$	−119.699	−	10.4723i	−0.422964	−	0.0370046i	−0.126313	−	0.991990i	$-0.540314\pi$
$283$	−119.699	−	10.4723i	−0.422964	−	0.0370046i	−0.296651	+	0.954986i	$0.595870\pi$
$284$	−63.9170	−	76.1733i	−0.225060	−	0.268216i
$285$	44.9602	+	461.207i	0.157755	+	1.61827i
$286$	346.459	−	126.101i	1.21140	−	0.440912i
$287$	−60.8111	−	16.2943i	−0.211885	−	0.0567745i
$288$	239.428	+	165.918i	0.831348	+	0.576103i
$289$	106.436	+	61.4509i	0.368291	+	0.212633i
$290$	−109.359	+	64.2335i	−0.377101	+	0.221495i
$291$	−297.436	+	209.348i	−1.02212	+	0.719409i
$292$	104.153	−	48.5675i	0.356689	−	0.166327i
$293$	68.4927	−	97.8177i	0.233763	−	0.333849i	−0.685082	−	0.728466i	$-0.740234\pi$
$293$	68.4927	−	97.8177i	0.233763	−	0.333849i	0.918846	+	0.394617i	$0.129123\pi$
$294$	−247.167	+	248.374i	−0.840705	+	0.844808i
$295$	−46.5271	+	47.2280i	−0.157719	+	0.160095i
$296$	−144.271			−0.487403
$297$	74.0631	+	198.953i	0.249371	+	0.669876i
$298$	−433.503	−	433.503i	−1.45471	−	1.45471i
$299$	456.908	−	544.522i	1.52812	−	1.82114i
$300$	60.5178	+	157.686i	0.201726	+	0.525620i
$301$	11.9717	+	67.8950i	0.0397731	+	0.225565i
$302$	384.793	−	179.432i	1.27415	−	0.594145i
$303$	−22.2632	+	26.6638i	−0.0734759	+	0.0879994i
$304$	−606.539	−	106.949i	−1.99520	−	0.351807i
$305$	−93.9107	+	136.275i	−0.307904	+	0.446805i
$306$	−158.295	−	428.410i	−0.517304	−	1.40003i
$307$	−285.169	−	76.4108i	−0.928889	−	0.248895i	−0.237508	−	0.971386i	$-0.576331\pi$
$307$	−285.169	−	76.4108i	−0.928889	−	0.248895i	−0.691381	+	0.722490i	$0.742997\pi$
$308$	−24.2703	−	11.3174i	−0.0787997	−	0.0367449i
$309$	5.96519	−	70.1491i	0.0193048	−	0.227020i
$310$	−54.2620	+	321.784i	−0.175039	+	1.03801i
$311$	−178.496	+	149.776i	−0.573942	+	0.481595i	−0.882951	−	0.469464i	$-0.844447\pi$
$311$	−178.496	+	149.776i	−0.573942	+	0.481595i	0.309009	+	0.951059i	$0.400003\pi$
$312$	−231.275	−	83.5400i	−0.741265	−	0.267756i
$313$	18.0288	+	8.40699i	0.0576002	+	0.0268594i	0.451205	−	0.892420i	$-0.350994\pi$
$313$	18.0288	+	8.40699i	0.0576002	+	0.0268594i	−0.393605	+	0.919280i	$0.628772\pi$
$314$	57.1283	−	32.9831i	0.181937	−	0.105042i
$315$	51.5908	−	44.3866i	0.163780	−	0.140910i
$316$	36.0535	−	62.4465i	0.114093	−	0.197615i
$317$	−30.1953	−	43.1234i	−0.0952533	−	0.136036i	0.768697	−	0.639614i	$-0.220906\pi$
$317$	−30.1953	−	43.1234i	−0.0952533	−	0.136036i	−0.863950	+	0.503578i	$0.832017\pi$
$318$	−36.6719	−	99.9971i	−0.115321	−	0.314456i
$319$	27.2808	−	74.9534i	0.0855198	−	0.234964i
$320$	−5.88894	+	0.559606i	−0.0184029	+	0.00174877i
$321$	292.143	−	79.0424i	0.910104	−	0.246238i
$322$	−142.787	+	12.4923i	−0.443438	+	0.0387958i
$323$	443.344	+	443.344i	1.37258	+	1.37258i
$324$	−60.7164	+	172.011i	−0.187396	+	0.530898i
$325$	−274.629	−	379.990i	−0.845012	−	1.16920i
$326$	392.813	+	329.610i	1.20495	+	1.01107i
$327$	174.955	−	304.741i	0.535030	−	0.931931i
$328$	104.356	−	149.037i	0.318160	−	0.454380i
$329$	−22.9660	+	63.0986i	−0.0698056	+	0.191789i
$330$	−256.837	−	144.910i	−0.778293	−	0.439122i
$331$	−94.5778	+	536.377i	−0.285733	+	1.62048i	0.416920	+	0.908943i	$0.363109\pi$
$331$	−94.5778	+	536.377i	−0.285733	+	1.62048i	−0.702654	+	0.711532i	$0.748002\pi$
$332$	−26.5740	−	99.1753i	−0.0800420	−	0.298721i
$333$	−78.2861	−	286.579i	−0.235093	−	0.860596i
$334$	−419.318	+	242.093i	−1.25544	+	0.724831i
$335$	228.030	−	401.868i	0.680687	−	1.19961i
$336$	38.4273	+	81.8865i	0.114367	+	0.243710i
$337$	49.0446	−	560.582i	0.145533	−	1.66345i	−0.475538	−	0.879695i	$-0.657747\pi$
$337$	49.0446	−	560.582i	0.145533	−	1.66345i	0.621071	−	0.783754i	$-0.286698\pi$
$338$	−455.089	−	39.8152i	−1.34642	−	0.117796i
$339$	32.6677	−	384.164i	0.0963650	−	1.13323i
$340$	198.758	+	112.780i	0.584582	+	0.331707i
$341$	−102.615	−	177.735i	−0.300925	−	0.521217i
$342$	−63.9623	−	692.253i	−0.187024	−	2.02413i
$343$	−139.822	+	37.4651i	−0.407644	+	0.109228i
$344$	−196.212	−	34.5976i	−0.570385	−	0.100574i
$345$	−568.517	+	5.63435i	−1.64788	+	0.0163315i
$346$	−635.534	−	231.315i	−1.83680	−	0.668541i
$347$	249.745	+	174.873i	0.719726	+	0.503957i	0.875127	−	0.483894i	$-0.160778\pi$
$347$	249.745	+	174.873i	0.719726	+	0.503957i	−0.155401	+	0.987851i	$0.549667\pi$
$348$	59.2714	−	34.4130i	0.170320	−	0.0988880i
$349$	−135.744	+	161.774i	−0.388952	+	0.463535i	−0.924618	−	0.380895i	$-0.875616\pi$
$349$	−135.744	+	161.774i	−0.388952	+	0.463535i	0.535666	+	0.844430i	$0.320061\pi$
$350$	−15.0227	+	93.3378i	−0.0429221	+	0.266679i
$351$	40.4459	−	504.732i	0.115231	−	1.43798i
$352$	179.949	−	179.949i	0.511219	−	0.511219i
$353$	34.8659	+	398.519i	0.0987703	+	1.12895i	0.870221	+	0.492661i	$0.163976\pi$
$353$	34.8659	+	398.519i	0.0987703	+	1.12895i	−0.771451	+	0.636289i	$0.780469\pi$
$354$	70.1581	−	70.5006i	0.198187	−	0.199154i
$355$	−20.8854	−	219.785i	−0.0588322	−	0.619113i
$356$	64.5299	+	23.4870i	0.181264	+	0.0659747i
$357$	15.7692	−	90.7227i	0.0441715	−	0.254125i
$358$	188.043	−	131.669i	0.525260	−	0.367791i
$359$	9.76776	+	5.63942i	0.0272082	+	0.0157087i	0.513542	−	0.858064i	$-0.328333\pi$
$359$	9.76776	+	5.63942i	0.0272082	+	0.0157087i	−0.486334	+	0.873773i	$0.661666\pi$
$360$	69.5453	+	183.975i	0.193182	+	0.511043i
$361$	296.686	+	513.875i	0.821844	+	1.42348i
$362$	−9.53574	+	20.4495i	−0.0263418	+	0.0564902i
$363$	−174.763	+	31.2544i	−0.481441	+	0.0861002i
$364$	41.0568	+	48.9296i	0.112793	+	0.134422i
$365$	251.600	+	42.4270i	0.689314	+	0.116238i
$366$	141.917	−	203.733i	0.387753	−	0.556648i
$367$	−66.6419	+	142.914i	−0.181586	+	0.389412i	−0.975939	−	0.218044i	$-0.930032\pi$
$367$	−66.6419	+	142.914i	−0.181586	+	0.389412i	0.794353	+	0.607456i	$0.207810\pi$
$368$	195.578	−	729.905i	0.531461	−	1.98344i
$369$	352.671	+	126.420i	0.955748	+	0.342603i
$370$	339.804	+	234.167i	0.918390	+	0.632885i
$371$	3.72897	−	21.1480i	0.0100511	−	0.0570028i
$372$	30.1991	−	173.740i	0.0811803	−	0.467043i
$373$	−168.873	−	362.150i	−0.452743	−	0.970911i	−0.991700	−	0.128577i	$-0.958959\pi$
$373$	−168.873	−	362.150i	−0.452743	−	0.970911i	0.538956	−	0.842334i	$-0.318819\pi$
$374$	−392.941	+	69.2861i	−1.05064	+	0.185257i
$375$	−88.0227	+	364.523i	−0.234727	+	0.972061i
$376$	−148.654	−	124.736i	−0.395357	−	0.331744i
$377$	−134.527	+	134.527i	−0.356835	+	0.356835i
$378$	−77.7333	+	66.1995i	−0.205644	+	0.175131i
$379$			366.291i			0.966468i	0.875491	+	0.483234i	$0.160538\pi$
$379$			366.291i			0.966468i	−0.875491	+	0.483234i	$0.839462\pi$
$380$	247.802	+	244.125i	0.652111	+	0.642433i
$381$	61.0247	−	229.986i	0.160170	−	0.603637i
$382$	226.749	+	158.772i	0.593585	+	0.415632i
$383$	271.173	+	581.532i	0.708023	+	1.51836i	0.849025	+	0.528352i	$0.177190\pi$
$383$	271.173	+	581.532i	0.708023	+	1.51836i	−0.141002	+	0.990009i	$0.545032\pi$
$384$	−377.997	+	33.9980i	−0.984367	+	0.0885364i
$385$	−30.1124	−	51.2673i	−0.0782141	−	0.133162i
$386$	250.131	−	433.240i	0.648008	−	1.12238i
$387$	−37.7468	−	408.527i	−0.0975371	−	1.05563i
$388$	−70.6668	+	263.732i	−0.182131	+	0.679722i
$389$	−183.702	−	504.717i	−0.472241	−	1.29747i	−0.915947	−	0.401300i	$-0.868559\pi$
$389$	−183.702	−	504.717i	−0.472241	−	1.29747i	0.443705	−	0.896173i	$-0.353664\pi$
$390$	409.131	+	572.146i	1.04905	+	1.46704i
$391$	−589.284	+	494.468i	−1.50712	+	1.26462i
$392$	17.7943	−	203.390i	0.0453937	−	0.518852i
$393$	177.232	−	490.656i	0.450973	−	1.24849i
$394$	−261.361	−	718.083i	−0.663352	−	1.82255i
$395$	144.586	−	68.7420i	0.366040	−	0.174030i
$396$	138.397	+	79.0073i	0.349486	+	0.199513i
$397$	−14.1859	−	52.9425i	−0.0357327	−	0.133356i	0.945755	−	0.324880i	$-0.105324\pi$
$397$	−14.1859	−	52.9425i	−0.0357327	−	0.133356i	−0.981488	+	0.191523i	$0.938657\pi$
$398$	565.602	−	396.039i	1.42111	−	0.995072i
$399$	58.9271	−	127.177i	0.147687	−	0.318739i
$400$	−435.315	−	242.725i	−1.08829	−	0.606813i
$401$	103.149	+	584.989i	0.257230	+	1.45883i	0.790282	+	0.612743i	$0.209934\pi$
$401$	103.149	+	584.989i	0.257230	+	1.45883i	−0.533052	+	0.846083i	$0.678955\pi$
$402$	−345.135	+	601.167i	−0.858545	+	1.49544i
$403$	42.6635	+	487.646i	0.105865	+	1.21004i
$404$			26.0754i			0.0645431i
$405$	−327.709	+	237.975i	−0.809158	+	0.587592i
$406$	38.3626			0.0944890
$407$	−258.549	+	22.6201i	−0.635256	+	0.0555777i
$408$	230.785	+	132.496i	0.565650	+	0.324744i
$409$	329.194	−	58.0457i	0.804875	−	0.141921i	0.243950	−	0.969788i	$-0.421557\pi$
$409$	329.194	−	58.0457i	0.804875	−	0.141921i	0.560925	+	0.827867i	$0.310446\pi$
$410$	−487.694	+	181.646i	−1.18950	+	0.443040i
$411$	−212.255	−	98.3476i	−0.516435	−	0.239288i
$412$	−30.3128	−	43.2911i	−0.0735747	−	0.105076i
$413$	19.3699	−	5.19015i	0.0469005	−	0.0125669i
$414$	852.945	−	4.15325i	2.06025	−	0.0100320i
$415$	76.3638	−	214.790i	0.184009	−	0.517567i
$416$	−570.385	+	207.603i	−1.37112	+	0.499046i
$417$	−130.458	−	47.1235i	−0.312849	−	0.113006i
$418$	−605.037	−	52.9339i	−1.44746	−	0.126636i
$419$	−218.086	−	259.905i	−0.520491	−	0.620297i	0.440206	−	0.897897i	$-0.354906\pi$
$419$	−218.086	−	259.905i	−0.520491	−	0.620297i	−0.960697	+	0.277600i	$0.910461\pi$
$420$	8.37236	−	50.3976i	0.0199342	−	0.119994i
$421$	604.194	−	219.909i	1.43514	−	0.522349i	0.496741	−	0.867899i	$-0.334530\pi$
$421$	604.194	−	219.909i	1.43514	−	0.522349i	0.938400	+	0.345550i	$0.112308\pi$
$422$	216.584	+	58.0335i	0.513232	+	0.137520i
$423$	167.109	−	362.970i	0.395057	−	0.858085i
$424$	53.7450	+	31.0297i	0.126757	+	0.0731833i
$425$	221.281	+	456.589i	0.520661	+	1.07433i
$426$	29.6706	+	329.884i	0.0696493	+	0.774376i
$427$	45.3696	−	21.1562i	0.106252	−	0.0495461i
$428$	130.309	−	186.101i	0.304461	−	0.434816i
$429$	−427.566	−	113.451i	−0.996658	−	0.264455i
$430$	405.987	+	399.962i	0.944155	+	0.930143i
$431$	234.638			0.544404			0.272202	−	0.962240i	$-0.412248\pi$
$431$	234.638			0.544404			0.272202	+	0.962240i	$0.412248\pi$
$432$	−187.794	−	504.465i	−0.434708	−	1.16774i
$433$	588.065	+	588.065i	1.35812	+	1.35812i	0.876236	+	0.481882i	$0.160046\pi$
$433$	588.065	+	588.065i	1.35812	+	1.35812i	0.481882	+	0.876236i	$0.339954\pi$
$434$	63.4470	−	75.6132i	0.146191	−	0.174224i
$435$	151.715	+	11.7595i	0.348769	+	0.0270334i
$436$	−45.8047	−	259.771i	−0.105057	−	0.595806i
$437$	−1061.23	+	494.858i	−2.42844	+	1.13240i
$438$	−377.134	−	65.5526i	−0.861037	−	0.149663i
$439$	255.257	+	45.0087i	0.581451	+	0.102525i	0.456635	−	0.889654i	$-0.349055\pi$
$439$	255.257	+	45.0087i	0.581451	+	0.102525i	0.124816	+	0.992180i	$0.460166\pi$
$440$	168.988	−	31.1015i	0.384064	−	0.0706852i
$441$	413.667	−	75.0193i	0.938020	−	0.170112i
$442$	919.258	+	246.314i	2.07977	+	0.557273i
$443$	−107.986	−	50.3545i	−0.243760	−	0.113667i	0.296899	−	0.954909i	$-0.404047\pi$
$443$	−107.986	−	50.3545i	−0.243760	−	0.113667i	−0.540659	+	0.841242i	$0.681825\pi$
$444$	−182.988	−	127.467i	−0.412135	−	0.287087i
$445$	88.3828	+	124.237i	0.198613	+	0.279183i
$446$	−729.970	+	612.517i	−1.63670	+	1.37336i
$447$	129.492	+	724.073i	0.289691	+	1.61985i
$448$	1.62165	+	0.756187i	0.00361975	+	0.00168792i
$449$	−699.258	+	403.717i	−1.55737	+	0.899146i	−0.559859	+	0.828588i	$0.689145\pi$
$449$	−699.258	+	403.717i	−1.55737	+	0.899146i	−0.997508	+	0.0705578i	$0.977522\pi$
$450$	134.810	−	546.199i	0.299578	−	1.21378i
$451$	163.650	−	283.451i	0.362861	−	0.628494i
$452$	−166.005	−	237.079i	−0.367267	−	0.524511i
$453$	−501.879	−	87.2355i	−1.10790	−	0.192573i
$454$	9.39805	−	25.8209i	0.0207005	−	0.0568743i
$455$	13.4157	+	141.178i	0.0294850	+	0.310281i
$456$	287.124	+	285.730i	0.629659	+	0.626600i
$457$	799.628	−	69.9584i	1.74973	−	0.153082i	0.833182	−	0.552999i	$-0.186517\pi$
$457$	799.628	−	69.9584i	1.74973	−	0.153082i	0.916551	+	0.399918i	$0.130961\pi$
$458$	−342.379	−	342.379i	−0.747552	−	0.747552i
$459$	−137.957	+	530.325i	−0.300559	+	1.15539i
$460$	−324.879	+	276.771i	−0.706259	+	0.601676i
$461$	−424.380	−	356.097i	−0.920564	−	0.772445i	0.0535349	−	0.998566i	$-0.482951\pi$
$461$	−424.380	−	356.097i	−0.920564	−	0.772445i	−0.974099	+	0.226121i	$0.927396\pi$
$462$	44.7876	+	77.1400i	0.0969428	+	0.166970i
$463$	422.629	−	603.577i	0.912806	−	1.30362i	−0.0397349	−	0.999210i	$-0.512651\pi$
$463$	422.629	−	603.577i	0.912806	−	1.30362i	0.952541	−	0.304411i	$-0.0984598\pi$
$464$	−69.1731	+	190.051i	−0.149080	+	0.409594i
$465$	274.096	−	279.583i	0.589453	−	0.601254i
$466$	−25.7485	+	146.027i	−0.0552543	+	0.313362i
$467$	−52.8345	−	197.181i	−0.113136	−	0.422229i	0.886005	−	0.463676i	$-0.153470\pi$
$467$	−52.8345	−	197.181i	−0.113136	−	0.422229i	−0.999141	+	0.0414471i	$0.986803\pi$
$468$	−219.530	−	310.295i	−0.469082	−	0.663024i
$469$	−121.037	+	69.8805i	−0.258074	+	0.148999i
$470$	147.668	+	535.073i	0.314188	+	1.13845i
$471$	−78.8620	−	6.70610i	−0.167435	−	0.0142380i
$472$	−5.05090	+	57.7320i	−0.0107011	+	0.122314i
$473$	−357.058	−	31.2385i	−0.754878	−	0.0660433i
$474$	−217.430	+	102.035i	−0.458714	+	0.215263i
$475$	145.469	+	758.499i	0.306250	+	1.59684i
$476$	−34.5619	−	59.8629i	−0.0726089	−	0.125762i
$477$	−32.4733	+	123.596i	−0.0680781	+	0.259111i
$478$	360.337	−	96.5521i	0.753844	−	0.201992i
$479$	83.7408	+	14.7658i	0.174824	+	0.0308262i	0.260375	−	0.965508i	$-0.416154\pi$
$479$	83.7408	+	14.7658i	0.174824	+	0.0308262i	−0.0855507	+	0.996334i	$0.527265\pi$
$480$	422.837	+	238.570i	0.880911	+	0.497020i
$481$	581.705	+	211.723i	1.20937	+	0.440173i
$482$	684.307	+	479.157i	1.41972	+	0.994102i
$483$	149.141	+	85.6229i	0.308780	+	0.177273i
$484$	−85.6646	+	102.091i	−0.176993	+	0.210932i
$485$	−461.455	+	393.122i	−0.951453	+	0.810562i
$486$	493.435	−	354.536i	1.01530	−	0.729499i
$487$	−133.297	+	133.297i	−0.273711	+	0.273711i	−0.830592	−	0.556881i	$-0.811998\pi$
$487$	−133.297	+	133.297i	−0.273711	+	0.273711i	0.556881	+	0.830592i	$0.311998\pi$
$488$	12.6088	+	144.119i	0.0258377	+	0.295326i
$489$	−160.682	−	593.886i	−0.328593	−	1.21449i
$490$	−372.035	+	450.165i	−0.759254	+	0.918705i
$491$	194.091	+	70.6434i	0.395297	+	0.143877i	0.532018	−	0.846733i	$-0.321434\pi$
$491$	194.091	+	70.6434i	0.395297	+	0.143877i	−0.136720	+	0.990610i	$0.543656\pi$
$492$	264.039	−	96.8308i	0.536664	−	0.196811i
$493$	168.654	−	118.093i	0.342098	−	0.239540i
$494$	1254.55	+	724.312i	2.53957	+	1.46622i
$495$	153.478	+	318.799i	0.310056	+	0.644038i
$496$	260.191	+	450.663i	0.524578	+	0.908595i
$497$	−28.2221	+	60.5225i	−0.0567850	+	0.121776i
$498$	−116.187	+	321.656i	−0.233307	+	0.645895i
$499$	182.688	+	217.719i	0.366108	+	0.436311i	0.917379	−	0.398016i	$-0.130301\pi$
$499$	182.688	+	217.719i	0.366108	+	0.436311i	−0.551270	+	0.834327i	$0.685857\pi$
$500$	124.658	+	252.394i	0.249317	+	0.504788i
$501$	578.842	+	49.2224i	1.15537	+	0.0982482i
$502$	−243.546	+	522.286i	−0.485152	+	1.04041i
$503$	117.764	−	439.500i	0.234122	−	0.873757i	−0.744420	−	0.667712i	$-0.767274\pi$
$503$	117.764	−	439.500i	0.234122	−	0.873757i	0.978543	−	0.206045i	$-0.0660594\pi$
$504$	10.0452	−	58.6372i	0.0199309	−	0.116344i
$505$	−32.8511	+	47.6708i	−0.0650517	+	0.0943975i
$506$	129.397	−	733.845i	0.255725	−	1.45029i
$507$	420.730	+	351.292i	0.829842	+	0.692884i
$508$	−75.4867	−	161.882i	−0.148596	−	0.318665i
$509$	−258.517	+	45.5835i	−0.507892	+	0.0895550i	−0.421722	−	0.906725i	$-0.638574\pi$
$509$	−258.517	+	45.5835i	−0.507892	+	0.0895550i	−0.0861703	+	0.996280i	$0.527463\pi$
$510$	−328.517	−	686.658i	−0.644151	−	1.34639i
$511$	−59.1213	−	49.6086i	−0.115697	−	0.0970815i
$512$	−209.819	+	209.819i	−0.409802	+	0.409802i
$513$	−411.767	+	725.386i	−0.802665	+	1.41401i
$514$		−	902.193i		−	1.75524i
$515$	−0.877162	−	117.334i	−0.00170323	−	0.227833i
$516$	−218.300	−	217.240i	−0.423063	−	0.421008i
$517$	−285.961	−	200.232i	−0.553116	−	0.387296i
$518$	−52.7532	−	113.130i	−0.101840	−	0.218397i
$519$	467.048	+	663.570i	0.899901	+	1.27855i
$520$	−396.651	−	103.110i	−0.762790	−	0.198289i
$521$	279.823	−	484.668i	0.537089	−	0.930265i	−0.461971	−	0.886895i	$-0.652857\pi$
$521$	279.823	−	484.668i	0.537089	−	0.930265i	0.999059	−	0.0433694i	$-0.0138092\pi$
$522$	−227.516	−	18.7893i	−0.435855	−	0.0359947i
$523$	−66.7883	+	249.257i	−0.127702	+	0.476591i	−0.999922	−	0.0125237i	$-0.996013\pi$
$523$	−66.7883	+	249.257i	−0.127702	+	0.476591i	0.872219	+	0.489115i	$0.162680\pi$
$524$	−133.939	−	367.994i	−0.255609	−	0.702279i
$525$	78.7996	−	81.5884i	0.150095	−	0.155406i
$526$	783.829	−	657.711i	1.49017	−	1.25040i
$527$	46.1706	−	527.733i	0.0876103	−	1.00139i
$528$	−462.917	+	82.7873i	−0.876736	+	0.156794i
$529$	−310.431	−	852.902i	−0.586826	−	1.61229i
$530$	−76.2220	−	160.319i	−0.143815	−	0.302488i
$531$	−117.419	+	21.2941i	−0.221128	+	0.0401020i
$532$	−27.2324	−	101.633i	−0.0511886	−	0.191039i
$533$	−639.484	+	447.771i	−1.19978	+	0.840096i
$534$	−131.654	−	187.051i	−0.246544	−	0.350282i
$535$	472.689	−	176.058i	0.883532	−	0.329080i
$536$	−70.1367	−	397.765i	−0.130852	−	0.742099i
$537$	−275.425	+	0.670561i	−0.512896	+	0.00124872i
$538$	51.9388	+	593.664i	0.0965406	+	1.10346i
$539$		−	367.286i		−	0.681421i
$540$	−74.3376	+	294.792i	−0.137662	+	0.545911i
$541$	−424.251			−0.784198			−0.392099	−	0.919923i	$-0.628251\pi$
$541$	−424.251			−0.784198			−0.392099	+	0.919923i	$0.628251\pi$
$542$	−399.303	+	34.9345i	−0.736721	+	0.0644547i
$543$	23.4119	−	13.5930i	0.0431158	−	0.0250331i
$544$	646.909	−	114.068i	1.18917	−	0.209683i
$545$	243.533	−	532.618i	0.446850	−	0.977281i
$546$	−19.0588	−	211.899i	−0.0349062	−	0.388094i
$547$	−367.227	−	524.455i	−0.671348	−	0.958785i	−0.999898	−	0.0142979i	$-0.995449\pi$
$547$	−367.227	−	524.455i	−0.671348	−	0.958785i	0.328550	−	0.944487i	$-0.393440\pi$
$548$	−169.622	+	45.4500i	−0.309529	+	0.0829380i
$549$	−279.435	+	103.250i	−0.508989	+	0.188068i
$550$	−448.501	−	201.032i	−0.815457	−	0.365512i
$551$	294.497	−	107.188i	0.534478	−	0.194534i
$552$	−379.936	+	320.383i	−0.688289	+	0.580405i
$553$	−48.2407	−	4.22052i	−0.0872346	−	0.00763204i
$554$	−512.217	−	610.436i	−0.924579	−	1.10187i
$555$	−173.948	−	463.571i	−0.313419	−	0.835262i
$556$	−97.8442	+	35.6124i	−0.175979	+	0.0640510i
$557$	−351.487	−	94.1808i	−0.631037	−	0.169086i	−0.0708966	−	0.997484i	$-0.522586\pi$
$557$	−351.487	−	94.1808i	−0.631037	−	0.169086i	−0.560140	+	0.828398i	$0.689253\pi$
$558$	−413.318	+	417.363i	−0.740714	+	0.747963i
$559$	740.360	+	427.447i	1.32444	+	0.764663i
$560$	76.3529	+	129.993i	0.136344	+	0.232130i
$561$	434.365	+	201.262i	0.774269	+	0.358755i
$562$	−861.145	+	401.559i	−1.53229	+	0.714517i
$563$	435.033	−	621.291i	0.772705	−	1.10354i	−0.219091	−	0.975704i	$-0.570309\pi$
$563$	435.033	−	621.291i	0.772705	−	1.10354i	0.991796	−	0.127832i	$-0.0408019\pi$
$564$	−78.3405	−	289.549i	−0.138902	−	0.513385i
$565$	−4.80369	−	642.566i	−0.00850210	−	1.13729i
$566$	300.438			0.530810
$567$	121.927	−	11.8648i	0.215039	−	0.0209255i
$568$	−136.463	−	136.463i	−0.240252	−	0.240252i
$569$	−333.693	+	397.680i	−0.586455	+	0.698910i	−0.974920	−	0.222553i	$-0.928561\pi$
$569$	−333.693	+	397.680i	−0.586455	+	0.698910i	0.388465	+	0.921463i	$0.373005\pi$
$570$	−212.499	−	1139.02i	−0.372805	−	1.99828i
$571$	−51.8056	−	293.804i	−0.0907279	−	0.514543i	−0.995973	−	0.0896537i	$-0.971424\pi$
$571$	−51.8056	−	293.804i	−0.0907279	−	0.514543i	0.905245	−	0.424890i	$-0.139687\pi$
$572$	−300.955	+	140.337i	−0.526145	+	0.245345i
$573$	−114.351	−	311.812i	−0.199565	−	0.544174i
$574$	155.024	+	27.3350i	0.270077	+	0.0476219i
$575$	−942.630	+	96.6905i	−1.63936	+	0.168157i
$576$	−9.24712	−	5.27896i	−0.0160540	−	0.00916486i
$577$	89.1903	+	23.8985i	0.154576	+	0.0414185i	0.335277	−	0.942120i	$-0.391170\pi$
$577$	89.1903	+	23.8985i	0.154576	+	0.0414185i	−0.180701	+	0.983538i	$0.557837\pi$
$578$	−278.512	−	129.872i	−0.481854	−	0.224692i
$579$	−543.364	+	254.987i	−0.938452	+	0.440392i
$580$	93.0783	−	66.2166i	0.160480	−	0.114167i
$581$	−52.8210	+	44.3221i	−0.0909139	+	0.0762858i
$582$	695.257	−	586.281i	1.19460	−	1.00736i
$583$	101.182	+	47.1818i	0.173554	+	0.0809294i
$584$	193.157	−	111.519i	0.330747	−	0.190957i
$585$	−10.4178	−	843.853i	−0.0178082	−	1.44248i
$586$	−149.291	+	258.579i	−0.254762	+	0.441261i
$587$	216.926	+	309.803i	0.369551	+	0.527773i	0.960258	−	0.279113i	$-0.0900403\pi$
$587$	216.926	+	309.803i	0.369551	+	0.527773i	−0.590708	+	0.806886i	$0.701151\pi$
$588$	202.269	−	242.250i	0.343995	−	0.411990i
$589$	275.793	−	757.735i	0.468239	−	1.28648i
$590$	105.602	−	127.779i	0.178986	−	0.216574i
$591$	−235.143	+	886.189i	−0.397872	+	1.49947i
$592$	655.575	−	57.3554i	1.10739	−	0.0968841i
$593$	−450.055	−	450.055i	−0.758945	−	0.758945i	0.217185	−	0.976130i	$-0.430312\pi$
$593$	−450.055	−	450.055i	−0.758945	−	0.758945i	−0.976130	+	0.217185i	$0.930312\pi$
$594$	−227.840	−	479.430i	−0.383568	−	0.807121i
$595$	12.2326	−	152.983i	0.0205591	−	0.257115i
$596$	422.980	+	354.922i	0.709698	+	0.595507i
$597$	−828.432	+	2.01693i	−1.38766	+	0.00337845i
$598$	−1019.44	+	1455.91i	−1.70475	+	2.43464i
$599$	−291.283	+	800.294i	−0.486282	+	1.33605i	0.417741	+	0.908566i	$0.362822\pi$
$599$	−291.283	+	800.294i	−0.486282	+	1.33605i	−0.904023	+	0.427483i	$0.859400\pi$
$600$	143.679	+	294.636i	0.239465	+	0.491060i
$601$	40.3813	−	229.014i	0.0671902	−	0.381055i	−0.932607	−	0.360895i	$-0.882471\pi$
$601$	40.3813	−	229.014i	0.0671902	−	0.381055i	0.999797	−	0.0201599i	$-0.00641754\pi$
$602$	−44.6161	−	166.510i	−0.0741132	−	0.276594i
$603$	752.057	−	355.158i	1.24719	−	0.588986i
$604$	−331.162	+	191.197i	−0.548282	+	0.316551i
$605$	−285.230	+	78.7173i	−0.471455	+	0.130111i
$606$	49.6444	−	71.2682i	0.0819215	−	0.117604i
$607$	0.359400	−	4.10796i	0.000592092	−	0.00676764i	−0.995893	−	0.0905391i	$-0.971141\pi$
$607$	0.359400	−	4.10796i	0.000592092	−	0.00676764i	0.996485	+	0.0837714i	$0.0266966\pi$
$608$	996.089	+	87.1465i	1.63830	+	0.143333i
$609$	−37.7678	−	26.3085i	−0.0620162	−	0.0431995i
$610$	204.223	−	359.912i	0.334792	−	0.590019i
$611$	416.323	+	721.092i	0.681379	+	1.18018i
$612$	175.656	+	371.956i	0.287019	+	0.607771i
$613$	−214.180	+	57.3893i	−0.349396	+	0.0936203i	−0.429249	−	0.903186i	$-0.641222\pi$
$613$	−214.180	+	57.3893i	−0.349396	+	0.0936203i	0.0798529	+	0.996807i	$0.474555\pi$
$614$	726.975	+	128.185i	1.18400	+	0.208771i
$615$	604.705	+	155.624i	0.983259	+	0.253047i
$616$	−48.8390	−	17.7759i	−0.0792841	−	0.0288571i
$617$	136.438	+	95.5350i	0.221131	+	0.154838i	0.678893	−	0.734237i	$-0.262460\pi$
$617$	136.438	+	95.5350i	0.221131	+	0.154838i	−0.457762	+	0.889075i	$0.651349\pi$
$618$	0.428578	+	176.033i	0.000693492	+	0.284844i
$619$	281.498	−	335.476i	0.454762	−	0.541965i	−0.489133	−	0.872209i	$-0.662687\pi$
$619$	281.498	−	335.476i	0.454762	−	0.541965i	0.943895	+	0.330245i	$0.107131\pi$
$620$	23.4263	−	292.973i	0.0377843	−	0.472537i
$621$	−842.570	−	580.849i	−1.35680	−	0.935345i
$622$	411.973	−	411.973i	0.662337	−	0.662337i
$623$	−4.01943	−	45.9422i	−0.00645173	−	0.0737436i
$624$	1084.13	+	287.666i	1.73739	+	0.461003i
$625$	−90.0792	+	618.475i	−0.144127	+	0.989559i
$626$	−46.7399	−	17.0119i	−0.0746644	−	0.0271756i
$627$	559.356	+	467.039i	0.892115	+	0.744879i
$628$	−48.6681	+	34.0778i	−0.0774970	+	0.0542640i
$629$	−580.172	−	334.963i	−0.922373	−	0.532532i
$630$	−118.834	+	121.805i	−0.188625	+	0.193341i
$631$	−262.915	−	455.382i	−0.416664	−	0.721683i	0.578938	−	0.815372i	$-0.303467\pi$
$631$	−262.915	−	455.382i	−0.416664	−	0.721683i	−0.995602	+	0.0936889i	$0.970134\pi$
$632$	59.1435	−	126.834i	0.0935815	−	0.200686i
$633$	−173.428	−	205.664i	−0.273978	−	0.324904i
$634$	84.6107	+	100.835i	0.133455	+	0.159046i
$635$	65.9428	−	391.052i	0.103847	−	0.615831i
$636$	40.7526	+	86.8417i	0.0640765	+	0.136544i
$637$	−370.229	+	793.959i	−0.581207	+	1.24640i
$638$	−51.6192	+	192.646i	−0.0809079	+	0.301952i
$639$	197.019	−	345.118i	0.308325	−	0.540090i
$640$	−622.090	+	114.493i	−0.972015	+	0.178895i
$641$	−42.8495	+	243.011i	−0.0668478	+	0.379113i	0.932969	+	0.359958i	$0.117209\pi$
$641$	−42.8495	+	243.011i	−0.0668478	+	0.379113i	−0.999817	+	0.0191554i	$0.993902\pi$
$642$	−710.470	+	260.551i	−1.10665	+	0.405842i
$643$	334.068	+	716.410i	0.519545	+	1.11417i	0.974651	+	0.223731i	$0.0718237\pi$
$643$	334.068	+	716.410i	0.519545	+	1.11417i	−0.455106	+	0.890437i	$0.650398\pi$
$644$	127.132	−	22.4168i	0.197410	−	0.0348088i
$645$	−125.405	−	672.181i	−0.194426	−	1.04214i
$646$	−1200.93	−	1007.70i	−1.85903	−	1.55991i
$647$	519.013	−	519.013i	0.802184	−	0.802184i	−0.181253	−	0.983437i	$-0.558015\pi$
$647$	519.013	−	519.013i	0.802184	−	0.802184i	0.983437	+	0.181253i	$0.0580151\pi$
$648$	−88.2942	+	342.839i	−0.136256	+	0.529073i
$649$			104.254i			0.160637i
$650$	766.879	+	886.664i	1.17981	+	1.36410i
$651$	−114.318	+	30.9299i	−0.175604	+	0.0475114i
$652$	−378.317	−	264.901i	−0.580241	−	0.406289i
$653$	−147.025	−	315.296i	−0.225153	−	0.482843i	0.760985	−	0.648770i	$-0.224716\pi$
$653$	−147.025	−	315.296i	−0.225153	−	0.482843i	−0.986138	+	0.165927i	$0.946938\pi$
$654$	−369.382	+	797.203i	−0.564804	+	1.21896i
$655$	218.752	−	841.506i	0.333972	−	1.28474i
$656$	−414.951	+	718.716i	−0.632547	+	1.09560i
$657$	326.333	+	323.170i	0.496701	+	0.491887i
$658$	43.4550	−	162.176i	0.0660411	−	0.246469i
$659$	244.610	+	672.060i	0.371184	+	1.01982i	0.974905	+	0.222623i	$0.0714619\pi$
$659$	244.610	+	672.060i	0.371184	+	1.01982i	−0.603721	+	0.797196i	$0.706316\pi$
$660$	241.817	+	109.857i	0.366389	+	0.166450i
$661$	−374.311	+	314.084i	−0.566280	+	0.475165i	−0.880409	−	0.474215i	$-0.842732\pi$
$661$	−374.311	+	314.084i	−0.566280	+	0.475165i	0.314129	+	0.949380i	$0.398288\pi$
$662$	118.693	−	1356.67i	0.179294	−	2.04934i
$663$	−736.088	−	872.911i	−1.11024	−	1.31661i
$664$	−68.1543	−	187.252i	−0.102642	−	0.282007i
$665$	78.2558	−	220.112i	0.117678	−	0.330996i
$666$	257.454	+	696.774i	0.386568	+	1.04621i
$667$	99.5192	+	371.411i	0.149204	+	0.556837i
$668$	357.221	−	250.129i	0.534762	−	0.374444i
$669$	1138.71	−	102.418i	1.70211	−	0.153092i
$670$	−480.421	+	1050.70i	−0.717046	+	1.56821i
$671$	45.1926	+	256.300i	0.0673511	+	0.381967i
$672$	−73.7350	−	126.998i	−0.109725	−	0.188985i
$673$	32.9157	+	376.228i	0.0489089	+	0.559031i	0.980632	+	0.195861i	$0.0627500\pi$
$673$	32.9157	+	376.228i	0.0489089	+	0.559031i	−0.931723	+	0.363170i	$0.881694\pi$
$674$			1407.03i			2.08759i
$675$	−507.297	+	445.281i	−0.751551	+	0.659675i
$676$	411.445			0.608646
$677$	714.801	−	62.5370i	1.05584	−	0.0923737i	0.454007	−	0.890998i	$-0.349994\pi$
$677$	714.801	−	62.5370i	1.05584	−	0.0923737i	0.601829	+	0.798625i	$0.294439\pi$
$678$	2.34706	+	964.028i	0.00346174	+	1.42187i
$679$	180.577	−	31.8406i	0.265946	−	0.0468934i
$680$	403.359	+	184.431i	0.593176	+	0.271222i
$681$	−26.9600	+	18.9756i	−0.0395888	+	0.0278643i
$682$	294.336	+	420.355i	0.431577	+	0.616356i
$683$	−209.365	+	56.0992i	−0.306537	+	0.0821365i	−0.408809	−	0.912620i	$-0.634056\pi$
$683$	−209.365	+	56.0992i	−0.306537	+	0.0821365i	0.102271	+	0.994757i	$0.467389\pi$
$684$	111.729	+	616.089i	0.163346	+	0.900715i
$685$	−367.361	−	130.607i	−0.536293	−	0.190667i
$686$	340.115	−	123.792i	0.495795	−	0.180455i
$687$	102.272	+	571.870i	0.148868	+	0.832416i
$688$	905.353	+	79.2081i	1.31592	+	0.115128i
$689$	−171.164	−	203.985i	−0.248424	−	0.296060i
$690$	1414.88	−	137.928i	2.05056	−	0.199896i
$691$	−229.279	+	83.4506i	−0.331807	+	0.120768i	−0.502551	−	0.864547i	$-0.667605\pi$
$691$	−229.279	+	83.4506i	−0.331807	+	0.120768i	0.170744	+	0.985315i	$0.445383\pi$
$692$	588.377	+	157.655i	0.850256	+	0.227825i
$693$	8.80834	−	106.659i	0.0127104	−	0.153909i
$694$	−660.195	−	381.164i	−0.951289	−	0.549227i
$695$	−223.744	−	58.1628i	−0.321934	−	0.0836875i
$696$	108.775	−	76.5607i	0.156286	−	0.110001i
$697$	765.685	−	357.045i	1.09854	−	0.512260i
$698$	302.869	−	432.542i	0.433910	−	0.619688i
$699$	125.493	−	126.105i	0.179532	−	0.180408i
$700$	6.15207	−	84.9246i	0.00878867	−	0.121321i
$701$	287.312			0.409861			0.204930	−	0.978777i	$-0.434303\pi$
$701$	287.312			0.409861			0.204930	+	0.978777i	$0.434303\pi$
$702$	9.24724	+	1266.04i	0.0131727	+	1.80348i
$703$	−721.063	−	721.063i	−1.02569	−	1.02569i
$704$	−5.97938	+	7.12595i	−0.00849344	+	0.0101221i
$705$	221.567	−	628.047i	0.314279	−	0.890847i
$706$	−173.694	−	985.068i	−0.246026	−	1.39528i
$707$	15.8708	−	7.40068i	0.0224481	−	0.0104677i
$708$	−57.4138	+	68.7624i	−0.0810930	+	0.0971221i
$709$	876.568	+	154.563i	1.23634	+	0.218001i	0.753348	−	0.657622i	$-0.228437\pi$
$709$	876.568	+	154.563i	1.23634	+	0.218001i	0.482996	+	0.875623i	$0.339549\pi$
$710$	99.9197	+	542.908i	0.140732	+	0.764659i
$711$	284.034	+	48.6580i	0.399485	+	0.0684360i
$712$	128.736	+	34.4948i	0.180809	+	0.0484477i
$713$	896.649	+	418.114i	1.25757	+	0.586415i
$714$	−19.5086	+	229.416i	−0.0273230	+	0.321311i
$715$	−727.006	−	122.594i	−1.01679	−	0.171460i
$716$	−158.382	+	132.898i	−0.221204	+	0.185612i
$717$	−420.965	−	152.059i	−0.587121	−	0.212077i
$718$	−25.5593	−	11.9185i	−0.0355980	−	0.0165996i
$719$	−746.732	+	431.126i	−1.03857	+	0.599619i	−0.919428	−	0.393259i	$-0.871348\pi$
$719$	−746.732	+	431.126i	−1.03857	+	0.599619i	−0.119142	+	0.992877i	$0.538014\pi$
$720$	−389.157	−	808.345i	−0.540496	−	1.12270i
$721$	−17.7459	+	30.7367i	−0.0246128	+	0.0426307i
$722$	−850.996	−	1215.35i	−1.17867	−	1.68331i
$723$	−345.099	−	941.017i	−0.477316	−	1.30155i
$724$	6.95051	−	19.0964i	0.00960016	−	0.0263762i
$725$	253.588	−	3.79174i	0.349776	−	0.00522999i
$726$	428.504	−	115.936i	0.590226	−	0.159692i
$727$	−1227.45	+	107.388i	−1.68837	+	0.147714i	−0.890462	−	0.455058i	$-0.849618\pi$
$727$	−1227.45	+	107.388i	−1.68837	+	0.147714i	−0.797913	+	0.602772i	$0.794063\pi$
$728$	87.6565	+	87.6565i	0.120407	+	0.120407i
$729$	−728.922	+	10.6487i	−0.999893	+	0.0146073i
$730$	−635.952	−	50.8511i	−0.871166	−	0.0696590i
$731$	−708.721	−	594.688i	−0.969523	−	0.813526i
$732$	−111.340	+	193.935i	−0.152104	+	0.264939i
$733$	−127.296	+	181.798i	−0.173664	+	0.248019i	−0.896543	−	0.442956i	$-0.853930\pi$
$733$	−127.296	+	181.798i	−0.173664	+	0.248019i	0.722879	+	0.690975i	$0.242819\pi$
$734$	134.853	−	370.506i	0.183723	−	0.504776i
$735$	674.985	−	188.050i	0.918346	−	0.255851i
$736$	−213.029	+	1208.15i	−0.289442	+	1.64151i
$737$	−188.057	−	701.840i	−0.255166	−	0.952293i
$738$	−906.014	−	238.043i	−1.22766	−	0.322552i
$739$	−862.244	+	497.817i	−1.16677	+	0.673635i	−0.952917	−	0.303230i	$-0.901935\pi$
$739$	−862.244	+	497.817i	−1.16677	+	0.673635i	−0.213854	+	0.976866i	$0.568602\pi$
$740$	−323.264	−	183.428i	−0.436843	−	0.247876i
$741$	−738.373	−	1573.43i	−0.996455	−	2.12339i
$742$	−4.67977	+	53.4900i	−0.00630696	+	0.0720889i
$743$	270.935	+	23.7038i	0.364650	+	0.0319028i	0.268009	−	0.963416i	$-0.413634\pi$
$743$	270.935	+	23.7038i	0.364650	+	0.0319028i	0.0966417	+	0.995319i	$0.469190\pi$
$744$	28.9989	−	341.020i	0.0389771	−	0.458360i
$745$	326.139	+	1181.76i	0.437770	+	1.58625i
$746$	499.565	+	865.272i	0.669658	+	1.15988i
$747$	334.973	−	236.990i	0.448424	−	0.317255i
$748$	347.119	−	93.0103i	0.464063	−	0.124345i
$749$	−150.255	−	26.4940i	−0.200607	−	0.0353725i
$750$	139.816	−	927.167i	0.186421	−	1.23622i
$751$	−67.0427	−	24.4015i	−0.0892712	−	0.0324921i	0.296998	−	0.954878i	$-0.404014\pi$
$751$	−67.0427	−	24.4015i	−0.0892712	−	0.0324921i	−0.386270	+	0.922386i	$0.626237\pi$
$752$	725.080	+	507.707i	0.964203	+	0.675142i
$753$	597.948	−	347.169i	0.794087	−	0.461048i
$754$	305.774	−	364.408i	0.405536	−	0.483299i
$755$	−846.306	−	67.6711i	−1.12094	−	0.0896307i
$756$	64.5481	−	65.4980i	0.0853811	−	0.0866376i
$757$	449.679	−	449.679i	0.594028	−	0.594028i	−0.344689	−	0.938717i	$-0.612016\pi$
$757$	449.679	−	449.679i	0.594028	−	0.594028i	0.938717	+	0.344689i	$0.112016\pi$
$758$	−79.8238	−	912.390i	−0.105308	−	1.20368i
$759$	−630.652	+	633.730i	−0.830898	+	0.834954i
$760$	520.399	+	430.079i	0.684736	+	0.565893i
$761$	1091.88	+	397.413i	1.43480	+	0.522224i	0.938303	−	0.345814i	$-0.112397\pi$
$761$	1091.88	+	397.413i	1.43480	+	0.522224i	0.496497	+	0.868039i	$0.334619\pi$
$762$	−101.886	+	586.166i	−0.133709	+	0.769247i
$763$	−145.110	+	101.607i	−0.190183	+	0.133168i
$764$	−215.909	−	124.655i	−0.282604	−	0.163161i
$765$	−147.476	+	901.306i	−0.192780	+	1.17818i
$766$	−802.191	−	1389.44i	−1.04725	−	1.81388i
$767$	105.089	−	225.364i	0.137013	−	0.293826i
$768$	948.113	−	169.559i	1.23452	−	0.220780i
$769$	−129.235	−	154.017i	−0.168056	−	0.200282i	0.675443	−	0.737412i	$-0.263953\pi$
$769$	−129.235	−	154.017i	−0.168056	−	0.200282i	−0.843499	+	0.537131i	$0.819508\pi$
$770$	86.1790	+	121.139i	0.111921	+	0.157323i
$771$	−618.712	+	888.207i	−0.802480	+	1.15202i
$772$	−190.417	+	408.350i	−0.246654	+	0.528951i
$773$	−205.852	+	768.252i	−0.266303	+	0.993858i	0.695144	+	0.718870i	$0.255340\pi$
$773$	−205.852	+	768.252i	−0.266303	+	0.993858i	−0.961448	+	0.274988i	$0.911326\pi$
$774$	183.051	+	1009.37i	0.236500	+	1.30409i
$775$	411.930	−	506.096i	0.531522	−	0.653028i
$776$	−92.0176	+	521.858i	−0.118579	+	0.672497i
$777$	−25.6474	+	147.553i	−0.0330082	+	0.189901i
$778$	567.570	+	1217.16i	0.729525	+	1.56447i
$779$	1266.45	−	223.309i	1.62574	−	0.286661i
$780$	−411.996	−	481.231i	−0.528200	−	0.616963i
$781$	−265.952	−	223.160i	−0.340528	−	0.285737i
$782$	1360.08	−	1360.08i	1.73924	−	1.73924i
$783$	211.104	+	174.526i	0.269609	+	0.222894i
$784$			931.288i			1.18787i
$785$	−131.907	+	0.986111i	−0.168035	+	0.00125619i
$786$	−334.540	+	1260.79i	−0.425623	+	1.60406i
$787$	−261.788	−	183.306i	−0.332640	−	0.232917i	0.395309	−	0.918548i	$-0.370637\pi$
$787$	−261.788	−	183.306i	−0.332640	−	0.232917i	−0.727949	+	0.685631i	$0.759526\pi$
$788$	290.868	+	623.769i	0.369122	+	0.791585i
$789$	−1222.73	+	109.975i	−1.54972	+	0.139385i
$790$	−345.166	+	202.737i	−0.436919	+	0.256629i
$791$	−97.1832	+	168.326i	−0.122861	+	0.212802i
$792$	280.943	+	129.344i	0.354726	+	0.163313i
$793$	160.661	−	599.596i	0.202599	−	0.756111i
$794$	46.8729	+	128.782i	0.0590339	+	0.162194i
$795$	−34.9040	+	210.105i	−0.0439043	+	0.264283i
$796$	−476.387	+	399.736i	−0.598476	+	0.502181i
$797$	−53.0660	+	606.547i	−0.0665821	+	0.761037i	0.887366	+	0.461066i	$0.152533\pi$
$797$	−53.0660	+	606.547i	−0.0665821	+	0.761037i	−0.953948	+	0.299972i	$0.903023\pi$
$798$	−119.066	+	329.625i	−0.149205	+	0.413064i
$799$	−308.192	−	846.751i	−0.385722	−	1.05976i
$800$	738.380	+	330.964i	0.922975	+	0.413705i
$801$	1.33632	+	274.438i	0.00166832	+	0.342619i
$802$	−384.417	−	1434.66i	−0.479322	−	1.78886i
$803$	328.672	−	230.138i	0.409305	−	0.286598i
$804$	262.475	−	566.477i	0.326462	−	0.704573i
$805$	260.663	+	119.185i	0.323806	+	0.148056i
$806$	−212.540	−	1205.37i	−0.263697	−	1.49550i
$807$	355.993	−	620.079i	0.441131	−	0.768376i
$808$	4.41071	+	50.4147i	0.00545880	+	0.0623944i
$809$			610.430i			0.754549i	0.926102	+	0.377274i	$0.123139\pi$
$809$			610.430i			0.754549i	−0.926102	+	0.377274i	$0.876861\pi$
$810$	764.425	−	664.183i	0.943734	−	0.819980i
$811$	−1157.70			−1.42749			−0.713746	−	0.700404i	$-0.753003\pi$
$811$	−1157.70			−1.42749			−0.713746	+	0.700404i	$0.753003\pi$
$812$	−34.4200	+	3.01136i	−0.0423892	+	0.00370857i
$813$	417.070	+	239.444i	0.513001	+	0.294519i
$814$	639.087	−	112.688i	0.785119	−	0.138438i
$815$	−357.900	−	960.911i	−0.439142	−	1.17903i
$816$	−1101.37	−	510.317i	−1.34972	−	0.625389i
$817$	−807.746	−	1153.58i	−0.988673	−	1.41197i
$818$	−807.334	+	216.325i	−0.986961	+	0.264456i
$819$	−126.555	+	221.685i	−0.154523	+	0.270677i
$820$	423.315	−	201.261i	0.516238	−	0.245440i
$821$	−431.833	+	157.175i	−0.525985	+	0.191443i	−0.591345	−	0.806419i	$-0.701403\pi$
$821$	−431.833	+	157.175i	−0.525985	+	0.191443i	0.0653599	+	0.997862i	$0.479180\pi$
$822$	550.134	+	198.717i	0.669263	+	0.241748i
$823$	1418.50	+	124.102i	1.72357	+	0.150793i	0.905504	−	0.424337i	$-0.139493\pi$
$823$	1418.50	+	124.102i	1.72357	+	0.150793i	0.818062	+	0.575129i	$0.195048\pi$
$824$	−65.9300	−	78.5724i	−0.0800122	−	0.0953548i
$825$	303.683	+	505.491i	0.368101	+	0.612717i
$826$	−47.1171	+	17.1492i	−0.0570425	+	0.0207618i
$827$	−552.049	−	147.921i	−0.667532	−	0.178865i	−0.0908891	−	0.995861i	$-0.528971\pi$
$827$	−552.049	−	147.921i	−0.667532	−	0.178865i	−0.576643	+	0.816996i	$0.695638\pi$
$828$	−764.961	+	70.6804i	−0.923866	+	0.0853627i
$829$	−265.795	−	153.457i	−0.320621	−	0.185111i	0.331048	−	0.943614i	$-0.392598\pi$
$829$	−265.795	−	153.457i	−0.320621	−	0.185111i	−0.651669	+	0.758503i	$0.725931\pi$
$830$	−143.405	+	551.660i	−0.172778	+	0.664650i
$831$	85.6472	+	952.245i	0.103065	+	1.14590i
$832$	20.1086	−	9.37680i	0.0241690	−	0.0112702i
$833$	543.780	−	776.598i	0.652797	−	0.932291i
$834$	335.225	+	88.9492i	0.401949	+	0.106654i
$835$	968.191	−	7.23799i	1.15951	−	0.00866825i
$836$	547.012			0.654321
$837$	693.133	−	127.445i	0.828116	−	0.152264i
$838$	599.866	+	599.866i	0.715831	+	0.715831i
$839$	116.028	−	138.277i	0.138293	−	0.164811i	−0.692453	−	0.721463i	$-0.743470\pi$
$839$	116.028	−	138.277i	0.138293	−	0.164811i	0.830746	+	0.556652i	$0.187914\pi$
$840$	7.66240	−	98.8558i	0.00912190	−	0.117686i
$841$	128.167	+	726.873i	0.152399	+	0.864296i
$842$	−1457.06	+	679.436i	−1.73047	+	0.806931i
$843$	1123.18	+	195.228i	1.33236	+	0.231588i
$844$	−198.881	−	35.0681i	−0.235641	−	0.0415499i
$845$	752.199	+	518.359i	0.890176	+	0.613442i
$846$	−337.149	+	940.534i	−0.398522	+	1.11174i
$847$	86.4510	+	23.1645i	0.102067	+	0.0273489i
$848$	−256.556	−	119.634i	−0.302542	−	0.141078i
$849$	−295.781	−	206.037i	−0.348387	−	0.242682i
$850$	−650.687	−	1089.09i	−0.765514	−	1.28128i
$851$	958.423	−	804.213i	1.12623	−	0.945021i
$852$	−52.5164	−	293.653i	−0.0616389	−	0.344663i
$853$	−183.227	−	85.4401i	−0.214803	−	0.100164i	0.312239	−	0.950004i	$-0.398921\pi$
$853$	−183.227	−	85.4401i	−0.214803	−	0.100164i	−0.527042	+	0.849839i	$0.676699\pi$
$854$	−108.400	+	62.5847i	−0.126932	+	0.0732842i
$855$	−571.918	+	1267.09i	−0.668910	+	1.48197i
$856$	220.463	−	381.853i	0.257550	−	0.446090i
$857$	514.009	+	734.080i	0.599777	+	0.856570i	0.998159	−	0.0606495i	$-0.0193172\pi$
$857$	514.009	+	734.080i	0.599777	+	0.856570i	−0.398382	+	0.917219i	$0.630428\pi$
$858$	1089.74	+	189.417i	1.27010	+	0.220765i
$859$	−168.173	+	462.051i	−0.195777	+	0.537894i	−0.998272	−	0.0587657i	$-0.981284\pi$
$859$	−168.173	+	462.051i	−0.195777	+	0.537894i	0.802494	+	0.596660i	$0.203506\pi$
$860$	−395.659	−	326.988i	−0.460069	−	0.380219i
$861$	−133.875	−	133.225i	−0.155488	−	0.154733i
$862$	−584.457	+	51.1334i	−0.678024	+	0.0593194i
$863$	535.726	+	535.726i	0.620771	+	0.620771i	0.945729	−	0.324957i	$-0.105350\pi$
$863$	535.726	+	535.726i	0.620771	+	0.620771i	−0.324957	+	0.945729i	$0.605350\pi$
$864$	375.098	+	789.298i	0.434142	+	0.913540i
$865$	877.043	+	1029.49i	1.01392	+	1.19016i
$866$	−1592.96	−	1336.65i	−1.83944	−	1.54347i
$867$	185.130	+	318.858i	0.213529	+	0.367772i
$868$	−50.9911	+	72.8228i	−0.0587455	+	0.0838973i
$869$	86.1052	−	236.572i	0.0990854	−	0.272235i
$870$	−380.466	+	3.77065i	−0.437317	+	0.00433408i
$871$	−300.942	+	1706.73i	−0.345513	+	1.95950i
$872$	−132.501	−	494.499i	−0.151950	−	0.567086i
$873$	−1086.54	+	100.394i	−1.24461	+	0.114998i
$874$	2535.55	−	1463.90i	2.90109	−	1.67495i
$875$	118.239	−	147.508i	0.135131	−	0.168580i
$876$	343.522	+	29.2117i	0.392148	+	0.0333466i
$877$	−24.0676	+	275.094i	−0.0274431	+	0.313676i	0.970050	+	0.242907i	$0.0781010\pi$
$877$	−24.0676	+	275.094i	−0.0274431	+	0.313676i	−0.997493	+	0.0707694i	$0.977455\pi$
$878$	−645.624	−	56.4848i	−0.735335	−	0.0643335i
$879$	324.306	−	152.189i	0.368949	−	0.173139i
$880$	−755.525	+	208.508i	−0.858551	+	0.236941i
$881$	−300.344	−	520.212i	−0.340913	−	0.590478i	0.643690	−	0.765287i	$-0.277403\pi$
$881$	−300.344	−	520.212i	−0.340913	−	0.590478i	−0.984603	+	0.174808i	$0.944069\pi$
$882$	−1014.05	+	277.013i	−1.14971	+	0.314073i
$883$	−964.073	+	258.323i	−1.09182	+	0.292551i	−0.759428	−	0.650592i	$-0.774521\pi$
$883$	−964.073	+	258.323i	−1.09182	+	0.292551i	−0.332388	+	0.943143i	$0.607854\pi$
$884$	−844.121	−	148.841i	−0.954887	−	0.168372i
$885$	−191.594	+	53.3779i	−0.216490	+	0.0603140i
$886$	279.953	+	101.895i	0.315974	+	0.115005i
$887$	181.226	+	126.896i	0.204313	+	0.143061i	0.671255	−	0.741226i	$-0.265756\pi$
$887$	181.226	+	126.896i	0.204313	+	0.143061i	−0.466942	+	0.884288i	$0.654644\pi$
$888$	−375.354	−	215.494i	−0.422695	−	0.242673i
$889$	−77.1050	+	91.8901i	−0.0867323	+	0.103363i
$890$	−247.226	−	290.198i	−0.277782	−	0.326066i
$891$	−104.479	+	628.247i	−0.117260	+	0.705103i
$892$	606.869	−	606.869i	0.680347	−	0.680347i
$893$	−119.544	−	1366.39i	−0.133868	−	1.53012i
$894$	−480.343	−	1775.36i	−0.537296	−	1.98586i
$895$	−456.984	+	43.4257i	−0.510597	+	0.0485203i
$896$	179.789	+	65.4379i	0.200658	+	0.0730334i
$897$	2002.08	−	734.223i	2.23198	−	0.818532i
$898$	1653.79	−	1158.00i	1.84164	−	1.28953i
$899$	−229.319	−	132.397i	−0.255082	−	0.147272i
$900$	−78.0805	+	500.648i	−0.0867561	+	0.556276i
$901$	144.087	+	249.566i	0.159919	+	0.276987i
$902$	−345.864	+	741.707i	−0.383441	+	0.822291i
$903$	−70.2656	+	194.526i	−0.0778135	+	0.215421i
$904$	−361.059	−	430.293i	−0.399401	−	0.475988i
$905$	36.7654	−	26.1552i	0.0406248	−	0.0289008i
$906$	1269.13	+	107.922i	1.40081	+	0.119119i
$907$	476.303	−	1021.43i	0.525141	−	1.12617i	−0.447591	−	0.894238i	$-0.647718\pi$
$907$	476.303	−	1021.43i	0.525141	−	1.12617i	0.972732	−	0.231930i	$-0.0745042\pi$
$908$	−6.40533	+	23.9050i	−0.00705433	+	0.0263271i
$909$	−97.7496	+	36.1179i	−0.107535	+	0.0397337i
$910$	−64.1829	−	348.734i	−0.0705307	−	0.383225i
$911$	−40.7800	+	231.275i	−0.0447639	+	0.253869i	−0.998975	−	0.0452652i	$-0.985587\pi$
$911$	−40.7800	+	231.275i	−0.0447639	+	0.253869i	0.954211	+	0.299134i	$0.0966978\pi$
$912$	−1418.30	−	1184.22i	−1.55515	−	1.29849i
$913$	−151.499	−	324.890i	−0.165935	−	0.355849i
$914$	−1976.54	+	348.517i	−2.16251	+	0.381309i
$915$	−447.880	+	214.279i	−0.489486	+	0.234185i
$916$	334.068	+	280.316i	0.364703	+	0.306022i
$917$	−185.966	+	185.966i	−0.202798	+	0.202798i
$918$	228.063	−	1351.04i	0.248435	−	1.47172i
$919$			1188.19i			1.29291i	0.762951	+	0.646456i	$0.223750\pi$
$919$			1188.19i			1.29291i	−0.762951	+	0.646456i	$0.776250\pi$
$920$	−581.311	+	590.068i	−0.631859	+	0.641378i
$921$	−627.797	−	624.748i	−0.681648	−	0.678337i
$922$	1134.68	+	794.515i	1.23068	+	0.861730i
$923$	349.958	+	750.487i	0.379152	+	0.813095i
$924$	−46.2400	−	65.6966i	−0.0500433	−	0.0711002i
$925$	−359.896	−	742.605i	−0.389076	−	0.802816i
$926$	−921.187	+	1595.54i	−0.994802	+	1.72305i
$927$	120.299	−	173.598i	0.129773	−	0.187269i
$928$	84.9822	−	317.158i	0.0915756	−	0.341765i
$929$	−67.6920	−	185.982i	−0.0728654	−	0.200196i	0.897913	−	0.440172i	$-0.145083\pi$
$929$	−67.6920	−	185.982i	−0.0728654	−	0.200196i	−0.970779	+	0.239976i	$0.922860\pi$
$930$	−621.813	+	756.141i	−0.668616	+	0.813055i
$931$	1105.47	−	927.601i	1.18740	−	0.996349i
$932$	11.6396	−	133.041i	0.0124888	−	0.142748i
$933$	−688.113	+	123.061i	−0.737527	+	0.131898i
$934$	174.575	+	479.641i	0.186911	+	0.513535i
$935$	751.778	+	267.278i	0.804041	+	0.285858i
$936$	−476.931	−	562.796i	−0.509542	−	0.601278i
$937$	−81.9174	−	305.720i	−0.0874252	−	0.326275i	0.908337	−	0.418239i	$-0.137352\pi$
$937$	−81.9174	−	305.720i	−0.0874252	−	0.326275i	−0.995762	+	0.0919634i	$0.970686\pi$
$938$	286.260	−	200.441i	0.305181	−	0.213690i
$939$	34.3488	+	48.8018i	0.0365801	+	0.0519721i
$940$	−174.494	−	468.492i	−0.185632	−	0.498396i
$941$	66.2170	+	375.536i	0.0703688	+	0.399081i	0.999565	+	0.0294943i	$0.00938970\pi$
$941$	66.2170	+	375.536i	0.0703688	+	0.399081i	−0.929196	+	0.369587i	$0.879499\pi$
$942$	197.898	−	0.481810i	0.210083	−	0.000511475i
$943$	137.514	+	1571.79i	0.145826	+	1.66680i
$944$		−	264.345i		−	0.280026i
$945$	200.524	−	38.4217i	0.212194	−	0.0406579i
$946$	896.197			0.947354
$947$	−213.893	+	18.7132i	−0.225864	+	0.0197605i	−0.199526	−	0.979893i	$-0.563940\pi$
$947$	−213.893	+	18.7132i	−0.225864	+	0.0197605i	−0.0263379	+	0.999653i	$0.508385\pi$
$948$	187.076	−	108.616i	0.197337	−	0.114574i
$949$	−942.469	+	166.183i	−0.993118	+	0.175114i
$950$	−527.642	−	1857.63i	−0.555412	−	1.95540i
$951$	−14.1477	−	157.297i	−0.0148766	−	0.165401i
$952$	−76.9485	−	109.894i	−0.0808282	−	0.115435i
$953$	820.738	−	219.916i	0.861215	−	0.230762i	0.198930	−	0.980014i	$-0.436253\pi$
$953$	820.738	−	219.916i	0.861215	−	0.230762i	0.662285	+	0.749252i	$0.269587\pi$
$954$	53.9526	−	314.940i	0.0565541	−	0.330126i
$955$	−237.676	−	499.907i	−0.248875	−	0.523462i
$956$	−315.726	+	114.915i	−0.330258	+	0.120204i
$957$	182.933	−	154.259i	0.191152	−	0.161191i
$958$	−211.807	−	18.5307i	−0.221093	−	0.0193431i
$959$	75.8050	+	90.3408i	0.0790459	+	0.0942032i
$960$	−16.1572	−	7.34020i	−0.0168305	−	0.00764604i
$961$	262.821	−	95.6592i	0.273487	−	0.0995413i
$962$	−1495.10	−	400.611i	−1.55416	−	0.416435i
$963$	878.138	+	230.719i	0.911878	+	0.239584i
$964$	−651.593	−	376.197i	−0.675926	−	0.390246i
$965$	−862.578	+	506.645i	−0.893863	+	0.525020i
$966$	−390.151	−	180.776i	−0.403884	−	0.187138i
$967$	1270.58	−	592.483i	1.31394	−	0.612702i	0.365845	−	0.930676i	$-0.380780\pi$
$967$	1270.58	−	592.483i	1.31394	−	0.612702i	0.948100	+	0.317974i	$0.103002\pi$
$968$	−148.357	+	211.875i	−0.153261	+	0.218879i
$969$	491.247	+	1815.67i	0.506963	+	1.87375i
$970$	1063.76	−	1079.79i	1.09666	−	1.11318i
$971$	−1406.37			−1.44838			−0.724188	−	0.689603i	$-0.757785\pi$
$971$	−1406.37			−1.44838			−0.724188	+	0.689603i	$0.757785\pi$
$972$	−414.895	+	356.834i	−0.426846	+	0.367113i
$973$	49.4455	+	49.4455i	0.0508176	+	0.0508176i
$974$	302.980	−	361.077i	0.311067	−	0.370716i
$975$	−146.928	−	1398.83i	−0.150695	−	1.43470i
$976$	−114.590	−	649.872i	−0.117408	−	0.665852i
$977$	−618.440	+	288.383i	−0.632999	+	0.295172i	−0.712510	−	0.701662i	$-0.752442\pi$
$977$	−618.440	+	288.383i	−0.632999	+	0.295172i	0.0795115	+	0.996834i	$0.474664\pi$
$978$	529.663	+	1444.29i	0.541577	+	1.47677i
$979$	236.117	+	41.6338i	0.241182	+	0.0425269i
$980$	298.464	−	433.105i	0.304555	−	0.441944i
$981$	910.366	−	531.527i	0.927998	−	0.541822i
$982$	−498.853	−	133.667i	−0.507997	−	0.136118i
$983$	196.808	+	91.7729i	0.200211	+	0.0933601i	0.520138	−	0.854082i	$-0.325881\pi$
$983$	196.808	+	91.7729i	0.200211	+	0.0933601i	−0.319927	+	0.947442i	$0.603658\pi$
$984$	494.118	−	231.877i	0.502152	−	0.235648i
$985$	−254.093	+	1506.82i	−0.257962	+	1.52976i
$986$	−394.364	+	330.910i	−0.399963	+	0.335609i
$987$	−154.000	+	129.861i	−0.156028	+	0.131572i
$988$	−1182.47	−	551.395i	−1.19683	−	0.558093i
$989$	1496.34	−	863.910i	1.51298	−	0.873519i
$990$	−451.769	−	760.645i	−0.456333	−	0.768329i
$991$	−386.026	+	668.617i	−0.389532	+	0.674689i	−0.992387	−	0.123162i	$-0.960697\pi$
$991$	−386.026	+	668.617i	−0.389532	+	0.674689i	0.602855	+	0.797851i	$0.294030\pi$
$992$	−484.573	−	692.042i	−0.488481	−	0.697623i
$993$	−1047.24	+	1254.24i	−1.05462	+	1.26308i
$994$	57.1087	−	156.905i	0.0574535	−	0.157852i
$995$	−1374.53	+	130.617i	−1.38144	+	0.131273i
$996$	78.9972	−	297.719i	0.0793145	−	0.298915i
$997$	566.670	−	49.5772i	0.568375	−	0.0497264i	0.200654	−	0.979662i	$-0.435693\pi$
$997$	566.670	−	49.5772i	0.568375	−	0.0497264i	0.367722	+	0.929936i	$0.380138\pi$
$998$	−502.501	−	502.501i	−0.503508	−	0.503508i
$999$	224.375	−	862.531i	0.224600	−	0.863394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.r.a.43.8	yes	408
3.2	odd	2		405.3.s.a.208.27		408
5.2	odd	4	inner	135.3.r.a.97.8	yes	408
15.2	even	4		405.3.s.a.127.27		408
27.5	odd	18		405.3.s.a.118.27		408
27.22	even	9	inner	135.3.r.a.103.8	yes	408
135.22	odd	36	inner	135.3.r.a.22.8	✓	408
135.32	even	36		405.3.s.a.37.27		408

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.r.a.22.8	✓	408	135.22	odd	36	inner
135.3.r.a.43.8	yes	408	1.1	even	1	trivial
135.3.r.a.97.8	yes	408	5.2	odd	4	inner
135.3.r.a.103.8	yes	408	27.22	even	9	inner
405.3.s.a.37.27		408	135.32	even	36
405.3.s.a.118.27		408	27.5	odd	18
405.3.s.a.127.27		408	15.2	even	4
405.3.s.a.208.27		408	3.2	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.r (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.49089 + 0.217924i) q^{2} +(2.60172 + 1.49367i) q^{3} +(2.21779 - 0.391056i) q^{4} +(4.54721 + 2.07916i) q^{5} +(-6.80610 - 3.15358i) q^{6} +(-0.867466 - 1.23887i) q^{7} +(4.22177 - 1.13122i) q^{8} +(4.53790 + 7.77222i) q^{9} +(-11.7797 - 4.18799i) q^{10} +(7.38848 - 2.68919i) q^{11} +(6.35418 + 2.29523i) q^{12} +(-18.6824 - 1.63449i) q^{13} +(2.43074 + 2.89684i) q^{14} +(8.72499 + 12.2014i) q^{15} +(-18.7342 + 6.81868i) q^{16} +(19.6038 + 5.25283i) q^{17} +(-12.9971 - 18.3708i) q^{18} +(26.7540 + 15.4465i) q^{19} +(10.8978 + 2.83292i) q^{20} +(-0.406441 - 4.51890i) q^{21} +(-17.8178 + 8.30859i) q^{22} +(-21.7403 + 31.0483i) q^{23} +(12.6735 + 3.36281i) q^{24} +(16.3542 + 18.9087i) q^{25} +46.8918 q^{26} +(0.197204 + 26.9993i) q^{27} +(-2.40833 - 2.40833i) q^{28} +(6.52085 - 7.77124i) q^{29} +(-24.3919 - 28.4909i) q^{30} +(-4.53255 - 25.7054i) q^{31} +(29.3340 - 13.6787i) q^{32} +(23.2395 + 4.03944i) q^{33} +(-49.9756 - 8.81204i) q^{34} +(-1.36875 - 7.43700i) q^{35} +(13.1035 + 15.4626i) q^{36} +(-31.8840 - 8.54330i) q^{37} +(-70.0074 - 32.6450i) q^{38} +(-46.1649 - 32.1578i) q^{39} +(21.5492 + 3.63382i) q^{40} +(31.8883 - 26.7575i) q^{41} +(1.99718 + 11.1675i) q^{42} +(-41.3143 - 19.2652i) q^{43} +(15.3345 - 8.85336i) q^{44} +(4.47510 + 44.7769i) q^{45} +(47.3864 - 82.0756i) q^{46} +(-25.4662 - 36.3695i) q^{47} +(-58.9260 - 10.2424i) q^{48} +(15.9767 - 43.8956i) q^{49} +(-44.8572 - 43.5355i) q^{50} +(43.1577 + 42.9480i) q^{51} +(-42.0727 + 3.68088i) q^{52} +(10.0402 + 10.0402i) q^{53} +(-6.37501 - 67.2091i) q^{54} +(39.1882 + 3.13351i) q^{55} +(-5.06367 - 4.24893i) q^{56} +(46.5346 + 80.1491i) q^{57} +(-14.5491 + 20.7783i) q^{58} +(-4.53496 + 12.4597i) q^{59} +(24.1216 + 23.6482i) q^{60} +(-5.74775 + 32.5971i) q^{61} +(16.8919 + 63.0414i) q^{62} +(5.69230 - 12.3640i) q^{63} +(-1.02459 + 0.591547i) q^{64} +(-81.5542 - 46.2759i) q^{65} +(-58.7673 - 4.99733i) q^{66} +(8.05417 - 92.0596i) q^{67} +(45.5313 + 3.98347i) q^{68} +(-102.938 + 48.3063i) q^{69} +(5.03009 + 18.2264i) q^{70} +(-22.0775 - 38.2394i) q^{71} +(27.9500 + 27.6792i) q^{72} +(49.2915 - 13.2076i) q^{73} +(81.2813 + 14.3321i) q^{74} +(14.3057 + 73.6230i) q^{75} +(65.3753 + 23.7946i) q^{76} +(-9.74081 - 6.82059i) q^{77} +(121.999 + 70.0409i) q^{78} +(20.5814 - 24.5280i) q^{79} +(-99.3653 - 7.94531i) q^{80} +(-39.8150 + 70.5391i) q^{81} +(-73.5991 + 73.5991i) q^{82} +(-3.97363 - 45.4188i) q^{83} +(-2.66855 - 9.86303i) q^{84} +(78.2212 + 64.6451i) q^{85} +(107.108 + 38.9840i) q^{86} +(28.5731 - 10.4786i) q^{87} +(28.1504 - 19.7111i) q^{88} +(26.4081 + 15.2467i) q^{89} +(-20.9049 - 110.559i) q^{90} +(14.1814 + 24.5629i) q^{91} +(-36.0737 + 77.3604i) q^{92} +(26.6029 - 73.6484i) q^{93} +(71.3592 + 85.0426i) q^{94} +(89.5406 + 125.864i) q^{95} +(96.7502 + 8.22724i) q^{96} +(-51.2388 + 109.882i) q^{97} +(-30.2302 + 112.821i) q^{98} +(54.4291 + 45.2217i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 408 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{7} - 6 q^{8} - 6 q^{10} - 60 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 6 q^{17} - 54 q^{18} - 300 q^{20} - 24 q^{21} - 12 q^{22} - 156 q^{23}+ \cdots - 1032 q^{98}+O(q^{100}) \) 408 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^7 - 6 * q^8 - 6 * q^10 - 60 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 6 * q^17 - 54 * q^18 - 300 * q^20 - 24 * q^21 - 12 * q^22 - 156 * q^23 + 6 * q^25 - 48 * q^26 + 180 * q^27 - 24 * q^28 + 276 * q^30 - 24 * q^31 + 72 * q^32 - 78 * q^33 + 156 * q^35 - 312 * q^36 - 6 * q^37 - 252 * q^38 - 108 * q^40 - 384 * q^41 - 528 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 210 * q^47 + 444 * q^48 + 276 * q^50 - 144 * q^51 - 60 * q^52 + 516 * q^53 - 24 * q^55 + 912 * q^56 + 168 * q^57 - 12 * q^58 + 864 * q^60 - 312 * q^61 - 6 * q^62 - 54 * q^63 + 420 * q^65 + 1224 * q^66 - 480 * q^67 - 540 * q^68 - 12 * q^70 - 12 * q^71 - 1548 * q^72 - 6 * q^73 - 852 * q^75 - 216 * q^76 - 876 * q^77 - 1362 * q^78 - 1644 * q^80 - 204 * q^81 - 24 * q^82 - 372 * q^83 - 12 * q^85 + 516 * q^86 + 540 * q^87 + 348 * q^88 - 384 * q^90 - 12 * q^91 + 2082 * q^92 - 1404 * q^93 + 198 * q^95 + 924 * q^96 + 600 * q^97 - 1032 * q^98

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