LMFDB - Embedded newform 272.3.x.a.155.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [272,3,Mod(155,272)] 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("272.155"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(272, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 2, 7])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	272.x (of order $8$, degree $4$, 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:	$7.41146319060$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$70$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			155.18
Character	$\chi$	$=$	272.155
Dual form			272.3.x.a.179.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41018 + 1.41824i) q^{2} +(2.02567 + 0.839058i) q^{3} +(-0.0228089 - 3.99993i) q^{4} +(3.32204 - 8.02012i) q^{5} +(-4.04653 + 1.68966i) q^{6} +(-0.771065 + 1.86152i) q^{7} +(5.70503 + 5.60826i) q^{8} +(-2.96466 - 2.96466i) q^{9} +(6.68979 + 16.0212i) q^{10} +(1.63344 - 0.676594i) q^{11} +(3.30997 - 8.12167i) q^{12} +(-10.7609 - 10.7609i) q^{13} +(-1.55274 - 3.71862i) q^{14} +(13.4587 - 13.4587i) q^{15} +(-15.9990 + 0.182469i) q^{16} +(-16.7767 + 2.74613i) q^{17} +(8.38529 - 0.0239076i) q^{18} -26.9860i q^{19} +(-32.1557 - 13.1050i) q^{20} +(-3.12384 + 3.12384i) q^{21} +(-1.34387 + 3.27073i) q^{22} +(10.1286 + 4.19540i) q^{23} +(6.85083 + 16.1473i) q^{24} +(-35.6087 - 35.6087i) q^{25} +(30.4362 - 0.0867779i) q^{26} +(-11.0694 - 26.7239i) q^{27} +(7.46353 + 3.04175i) q^{28} +(-14.6640 - 6.07401i) q^{29} +(0.108534 + 38.0668i) q^{30} +(22.5662 + 54.4797i) q^{31} +(22.3026 - 22.9477i) q^{32} +3.87651 q^{33} +(19.7635 - 27.6660i) q^{34} +(12.3681 + 12.3681i) q^{35} +(-11.7908 + 11.9261i) q^{36} +(55.8530 + 23.1351i) q^{37} +(38.2726 + 38.0550i) q^{38} +(-12.7689 - 30.8269i) q^{39} +(63.9313 - 27.1241i) q^{40} +(46.1214 + 19.1041i) q^{41} +(-0.0251913 - 8.83552i) q^{42} -61.7618i q^{43} +(-2.74359 - 6.51823i) q^{44} +(-33.6256 + 13.9282i) q^{45} +(-20.2332 + 8.44853i) q^{46} -22.1261 q^{47} +(-32.5616 - 13.0544i) q^{48} +(31.7775 + 31.7775i) q^{49} +(100.716 - 0.287156i) q^{50} +(-36.2882 - 8.51390i) q^{51} +(-42.7973 + 43.2882i) q^{52} -59.1788i q^{53} +(53.5107 + 21.9863i) q^{54} -15.3481i q^{55} +(-14.8388 + 6.29567i) q^{56} +(22.6428 - 54.6646i) q^{57} +(29.2932 - 12.2316i) q^{58} -12.7030i q^{59} +(-54.1409 - 53.5269i) q^{60} +(-6.54820 - 15.8088i) q^{61} +(-109.088 - 44.8216i) q^{62} +(7.80470 - 3.23281i) q^{63} +(1.09478 + 63.9906i) q^{64} +(-122.051 + 50.5554i) q^{65} +(-5.46656 + 5.49782i) q^{66} +(64.7763 + 64.7763i) q^{67} +(11.3670 + 67.0432i) q^{68} +(16.9970 + 16.9970i) q^{69} +(-34.9820 + 0.0997387i) q^{70} +(28.2866 - 11.7167i) q^{71} +(-0.286889 - 33.5401i) q^{72} +(80.2017 - 33.2206i) q^{73} +(-111.574 + 46.5884i) q^{74} +(-42.2535 - 102.009i) q^{75} +(-107.942 + 0.615523i) q^{76} +3.56237i q^{77} +(61.7264 + 25.3620i) q^{78} +(-16.7162 + 40.3564i) q^{79} +(-51.6858 + 128.920i) q^{80} -25.6877i q^{81} +(-92.1335 + 38.4711i) q^{82} -66.6246i q^{83} +(12.5664 + 12.4239i) q^{84} +(-33.7087 + 143.674i) q^{85} +(87.5930 + 87.0950i) q^{86} +(-24.6078 - 24.6078i) q^{87} +(13.1134 + 5.30078i) q^{88} -80.4373 q^{89} +(27.6645 - 67.3304i) q^{90} +(28.3288 - 11.7342i) q^{91} +(16.5503 - 40.6094i) q^{92} +129.292i q^{93} +(31.2016 - 31.3801i) q^{94} +(-216.431 - 89.6487i) q^{95} +(64.4320 - 27.7712i) q^{96} +(3.79056 + 9.15123i) q^{97} +(-89.8801 + 0.256261i) q^{98} +(-6.84847 - 2.83673i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 4 q^{2} - 4 q^{3} - 4 q^{5} + 12 q^{6} - 8 q^{7} - 4 q^{8} + 12 q^{10} - 4 q^{11} - 24 q^{12} + 40 q^{14} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 4 q^{20} + 4 q^{22} - 8 q^{23} - 324 q^{24} - 132 q^{26}+ \cdots + 284 q^{99}+O(q^{100}) $ 280 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 + 12 * q^6 - 8 * q^7 - 4 * q^8 + 12 * q^10 - 4 * q^11 - 24 * q^12 + 40 * q^14 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 4 * q^20 + 4 * q^22 - 8 * q^23 - 324 * q^24 - 132 * q^26 - 40 * q^27 + 212 * q^28 - 4 * q^29 - 256 * q^31 - 124 * q^32 - 16 * q^33 - 148 * q^34 - 8 * q^35 - 164 * q^36 - 4 * q^37 + 32 * q^38 - 8 * q^39 - 40 * q^40 + 448 * q^42 - 40 * q^44 - 68 * q^45 - 228 * q^46 - 48 * q^48 - 8 * q^49 - 8 * q^50 - 164 * q^51 - 8 * q^52 - 48 * q^54 + 176 * q^56 + 72 * q^57 - 20 * q^58 - 552 * q^60 - 68 * q^61 + 176 * q^62 - 640 * q^63 + 24 * q^65 + 228 * q^66 - 8 * q^67 - 368 * q^68 - 8 * q^69 + 560 * q^70 + 504 * q^71 + 520 * q^72 - 156 * q^74 + 60 * q^75 + 664 * q^76 + 600 * q^78 + 304 * q^80 + 212 * q^82 - 8 * q^84 - 4 * q^85 + 1136 * q^86 - 8 * q^87 + 408 * q^88 - 200 * q^90 + 384 * q^91 + 60 * q^92 + 584 * q^94 + 200 * q^95 - 112 * q^96 - 8 * q^97 - 624 * q^98 + 284 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−1.41018	+	1.41824i	−0.705088	+	0.709120i
$2$	−1.41018	+	1.41824i	−0.705088	+	0.709120i
$3$	2.02567	+	0.839058i	0.675222	+	0.279686i	0.693828	−	0.720141i	$-0.255923\pi$
$3$	2.02567	+	0.839058i	0.675222	+	0.279686i	−0.0186060	+	0.999827i	$0.505923\pi$
$4$	−0.0228089	−	3.99993i	−0.00570224	−	0.999984i
$5$	3.32204	−	8.02012i	0.664408	−	1.60402i	−0.126414	−	0.991978i	$-0.540347\pi$
$5$	3.32204	−	8.02012i	0.664408	−	1.60402i	0.790822	−	0.612046i	$-0.209653\pi$
$6$	−4.04653	+	1.68966i	−0.674422	+	0.281610i
$7$	−0.771065	+	1.86152i	−0.110152	+	0.265931i	−0.969337	−	0.245734i	$-0.920971\pi$
$7$	−0.771065	+	1.86152i	−0.110152	+	0.265931i	0.859185	+	0.511665i	$0.170971\pi$
$8$	5.70503	+	5.60826i	0.713129	+	0.701033i
$9$	−2.96466	−	2.96466i	−0.329406	−	0.329406i
$10$	6.68979	+	16.0212i	0.668979	+	1.60212i
$11$	1.63344	−	0.676594i	0.148495	−	0.0615085i	−0.307198	−	0.951646i	$-0.599391\pi$
$11$	1.63344	−	0.676594i	0.148495	−	0.0615085i	0.455693	+	0.890137i	$0.349391\pi$
$12$	3.30997	−	8.12167i	0.275831	−	0.676806i
$13$	−10.7609	−	10.7609i	−0.827759	−	0.827759i	0.159447	−	0.987206i	$-0.449029\pi$
$13$	−10.7609	−	10.7609i	−0.827759	−	0.827759i	−0.987206	+	0.159447i	$0.949029\pi$
$14$	−1.55274	−	3.71862i	−0.110910	−	0.265616i
$15$	13.4587	−	13.4587i	0.897246	−	0.897246i
$16$	−15.9990	+	0.182469i	−0.999935	+	0.0114043i
$17$	−16.7767	+	2.74613i	−0.986867	+	0.161537i
$17$	−16.7767	+	2.74613i	−0.986867	+	0.161537i
$18$	8.38529	−	0.0239076i	0.465849	−	0.00132820i
$19$		−	26.9860i		−	1.42032i	−0.704042	−	0.710158i	$-0.748623\pi$
$19$		−	26.9860i		−	1.42032i	0.704042	−	0.710158i	$-0.251377\pi$
$20$	−32.1557	−	13.1050i	−1.60779	−	0.655251i
$21$	−3.12384	+	3.12384i	−0.148754	+	0.148754i
$22$	−1.34387	+	3.27073i	−0.0610849	+	0.148669i
$23$	10.1286	+	4.19540i	0.440374	+	0.182409i	0.591843	−	0.806053i	$-0.298400\pi$
$23$	10.1286	+	4.19540i	0.440374	+	0.182409i	−0.151469	+	0.988462i	$0.548400\pi$
$24$	6.85083	+	16.1473i	0.285451	+	0.672805i
$25$	−35.6087	−	35.6087i	−1.42435	−	1.42435i
$26$	30.4362	−	0.0867779i	1.17062	−	0.00333761i
$27$	−11.0694	−	26.7239i	−0.409978	−	0.989775i
$28$	7.46353	+	3.04175i	0.266555	+	0.108634i
$29$	−14.6640	−	6.07401i	−0.505654	−	0.209449i	0.115248	−	0.993337i	$-0.463234\pi$
$29$	−14.6640	−	6.07401i	−0.505654	−	0.209449i	−0.620902	+	0.783888i	$0.713234\pi$
$30$	0.108534	+	38.0668i	0.00361779	+	1.26889i
$31$	22.5662	+	54.4797i	0.727943	+	1.75741i	0.649334	+	0.760503i	$0.275048\pi$
$31$	22.5662	+	54.4797i	0.727943	+	1.75741i	0.0786083	+	0.996906i	$0.474952\pi$
$32$	22.3026	−	22.9477i	0.696955	−	0.717115i
$33$	3.87651			0.117470
$34$	19.7635	−	27.6660i	0.581278	−	0.813705i
$35$	12.3681	+	12.3681i	0.353373	+	0.353373i
$36$	−11.7908	+	11.9261i	−0.327523	+	0.331279i
$37$	55.8530	+	23.1351i	1.50954	+	0.625272i	0.975463	−	0.220164i	$-0.0706594\pi$
$37$	55.8530	+	23.1351i	1.50954	+	0.625272i	0.534077	+	0.845436i	$0.320659\pi$
$38$	38.2726	+	38.0550i	1.00717	+	1.00145i
$39$	−12.7689	−	30.8269i	−0.327408	−	0.790434i
$40$	63.9313	−	27.1241i	1.59828	−	0.678104i
$41$	46.1214	+	19.1041i	1.12491	+	0.465954i	0.866049	−	0.499960i	$-0.166652\pi$
$41$	46.1214	+	19.1041i	1.12491	+	0.465954i	0.258864	+	0.965914i	$0.416652\pi$
$42$	−0.0251913	−	8.83552i	−0.000599793	−	0.210369i
$43$		−	61.7618i		−	1.43632i	−0.695878	−	0.718160i	$-0.744984\pi$
$43$		−	61.7618i		−	1.43632i	0.695878	−	0.718160i	$-0.255016\pi$
$44$	−2.74359	−	6.51823i	−0.0623543	−	0.148142i
$45$	−33.6256	+	13.9282i	−0.747236	+	0.309515i
$46$	−20.2332	+	8.44853i	−0.439852	+	0.183664i
$47$	−22.1261			−0.470767			−0.235384	−	0.971903i	$-0.575635\pi$
$47$	−22.1261			−0.470767			−0.235384	+	0.971903i	$0.575635\pi$
$48$	−32.5616	−	13.0544i	−0.678368	−	0.271967i
$49$	31.7775	+	31.7775i	0.648521	+	0.648521i
$50$	100.716	−	0.287156i	2.01432	−	0.00574311i
$51$	−36.2882	−	8.51390i	−0.711534	−	0.166939i
$52$	−42.7973	+	43.2882i	−0.823026	+	0.832466i
$53$		−	59.1788i		−	1.11658i	−0.829646	−	0.558290i	$-0.811457\pi$
$53$		−	59.1788i		−	1.11658i	0.829646	−	0.558290i	$-0.188543\pi$
$54$	53.5107	+	21.9863i	0.990940	+	0.407154i
$55$		−	15.3481i		−	0.279056i
$56$	−14.8388	+	6.29567i	−0.264979	+	0.112423i
$57$	22.6428	−	54.6646i	0.397243	−	0.959029i
$58$	29.2932	−	12.2316i	0.505054	−	0.210889i
$59$		−	12.7030i		−	0.215305i	−0.994189	−	0.107652i	$-0.965667\pi$
$59$		−	12.7030i		−	0.215305i	0.994189	−	0.107652i	$-0.0343333\pi$
$60$	−54.1409	−	53.5269i	−0.902348	−	0.892115i
$61$	−6.54820	−	15.8088i	−0.107348	−	0.259160i	0.861073	−	0.508481i	$-0.169793\pi$
$61$	−6.54820	−	15.8088i	−0.107348	−	0.259160i	−0.968421	+	0.249321i	$0.919793\pi$
$62$	−109.088	−	44.8216i	−1.75948	−	0.722929i
$63$	7.80470	−	3.23281i	0.123884	−	0.0513145i
$64$	1.09478	+	63.9906i	0.0171060	+	0.999854i
$65$	−122.051	+	50.5554i	−1.87771	+	0.777775i
$66$	−5.46656	+	5.49782i	−0.0828266	+	0.0833003i
$67$	64.7763	+	64.7763i	0.966811	+	0.966811i	0.999467	−	0.0326560i	$-0.0103966\pi$
$67$	64.7763	+	64.7763i	0.966811	+	0.966811i	−0.0326560	+	0.999467i	$0.510397\pi$
$68$	11.3670	+	67.0432i	0.167162	+	0.985929i
$69$	16.9970	+	16.9970i	0.246333	+	0.246333i
$70$	−34.9820	+	0.0997387i	−0.499743	+	0.00142484i
$71$	28.2866	−	11.7167i	0.398403	−	0.165024i	−0.174481	−	0.984661i	$-0.555825\pi$
$71$	28.2866	−	11.7167i	0.398403	−	0.165024i	0.572884	+	0.819637i	$0.305825\pi$
$72$	−0.286889	−	33.5401i	−0.00398456	−	0.465834i
$73$	80.2017	−	33.2206i	1.09865	−	0.455077i	0.241637	−	0.970367i	$-0.422316\pi$
$73$	80.2017	−	33.2206i	1.09865	−	0.455077i	0.857016	+	0.515290i	$0.172316\pi$
$74$	−111.574	+	46.5884i	−1.50775	+	0.629573i
$75$	−42.2535	−	102.009i	−0.563380	−	1.36012i
$76$	−107.942	+	0.615523i	−1.42029	+	0.00809898i
$77$			3.56237i			0.0462646i
$78$	61.7264	+	25.3620i	0.791364	+	0.325153i
$79$	−16.7162	+	40.3564i	−0.211597	+	0.510840i	−0.993669	−	0.112348i	$-0.964163\pi$
$79$	−16.7162	+	40.3564i	−0.211597	+	0.510840i	0.782072	+	0.623188i	$0.214163\pi$
$80$	−51.6858	+	128.920i	−0.646072	+	1.61150i
$81$		−	25.6877i		−	0.317132i
$82$	−92.1335	+	38.4711i	−1.12358	+	0.469159i
$83$		−	66.6246i		−	0.802706i	−0.915923	−	0.401353i	$-0.868540\pi$
$83$		−	66.6246i		−	0.802706i	0.915923	−	0.401353i	$-0.131460\pi$
$84$	12.5664	+	12.4239i	0.149600	+	0.147904i
$85$	−33.7087	+	143.674i	−0.396573	+	1.69028i
$86$	87.5930	+	87.0950i	1.01852	+	1.01273i
$87$	−24.6078	−	24.6078i	−0.282849	−	0.282849i
$88$	13.1134	+	5.30078i	0.149015	+	0.0602362i
$89$	−80.4373			−0.903790			−0.451895	−	0.892071i	$-0.649252\pi$
$89$	−80.4373			−0.903790			−0.451895	+	0.892071i	$0.649252\pi$
$90$	27.6645	−	67.3304i	0.307384	−	0.748115i
$91$	28.3288	−	11.7342i	0.311306	−	0.128947i
$92$	16.5503	−	40.6094i	0.179895	−	0.441407i
$93$			129.292i			1.39024i
$94$	31.2016	−	31.3801i	0.331932	−	0.333831i
$95$	−216.431	−	89.6487i	−2.27822	−	0.943670i
$96$	64.4320	−	27.7712i	0.671166	−	0.289283i
$97$	3.79056	+	9.15123i	0.0390780	+	0.0943426i	0.942214	−	0.335013i	$-0.108741\pi$
$97$	3.79056	+	9.15123i	0.0390780	+	0.0943426i	−0.903136	+	0.429356i	$0.858741\pi$
$98$	−89.8801	+	0.256261i	−0.917144	+	0.00261491i
$99$	−6.84847	−	2.83673i	−0.0691764	−	0.0286538i
$100$	−141.620	+	143.244i	−1.41620	+	1.43244i
$101$	−8.66029	−	8.66029i	−0.0857455	−	0.0857455i	0.662933	−	0.748679i	$-0.269311\pi$
$101$	−8.66029	−	8.66029i	−0.0857455	−	0.0857455i	−0.748679	+	0.662933i	$0.769311\pi$
$102$	63.2475	−	39.4593i	0.620074	−	0.386856i
$103$	161.381			1.56681			0.783405	−	0.621512i	$-0.213481\pi$
$103$	161.381			1.56681			0.783405	+	0.621512i	$0.213481\pi$
$104$	−1.04132	−	121.741i	−0.0100127	−	1.17059i
$105$	14.6760	+	35.4311i	0.139772	+	0.337439i
$106$	83.9297	+	83.4525i	0.791790	+	0.787288i
$107$	−4.87172	−	2.01793i	−0.0455301	−	0.0188592i	0.359802	−	0.933029i	$-0.382844\pi$
$107$	−4.87172	−	2.01793i	−0.0455301	−	0.0188592i	−0.405332	+	0.914169i	$0.632844\pi$
$108$	−106.641	+	44.8865i	−0.987421	+	0.415615i
$109$	67.4954	+	162.948i	0.619224	+	1.49494i	0.852606	+	0.522554i	$0.175021\pi$
$109$	67.4954	+	162.948i	0.619224	+	1.49494i	−0.233382	+	0.972385i	$0.574979\pi$
$110$	21.7672	+	21.6435i	0.197884	+	0.196759i
$111$	93.7278	+	93.7278i	0.844394	+	0.844394i
$112$	11.9966	−	29.9230i	0.107112	−	0.267170i
$113$	−68.0317	−	28.1796i	−0.602050	−	0.249377i	0.0607751	−	0.998151i	$-0.480643\pi$
$113$	−68.0317	−	28.1796i	−0.602050	−	0.249377i	−0.662825	+	0.748774i	$0.730643\pi$
$114$	45.5972	+	109.200i	0.399975	+	0.957892i
$115$	67.2952	−	67.2952i	0.585176	−	0.585176i
$116$	−23.9612	+	58.7934i	−0.206562	+	0.506840i
$117$			63.8046i			0.545338i
$118$	18.0159	+	17.9134i	0.152677	+	0.151809i
$119$	7.82398	−	33.3476i	0.0657477	−	0.280232i
$120$	152.262	−	1.30239i	1.26885	−	0.0108533i
$121$	−83.3496	+	83.3496i	−0.688839	+	0.688839i
$122$	31.6547	+	13.0062i	0.259465	+	0.106608i
$123$	77.3971	+	77.3971i	0.629245	+	0.629245i
$124$	217.400	−	91.5060i	1.75323	−	0.737952i
$125$	−203.376	+	84.2411i	−1.62701	+	0.673929i
$126$	−6.42109	+	15.6278i	−0.0509611	+	0.124030i
$127$	−63.5997	−	63.5997i	−0.500785	−	0.500785i	0.410897	−	0.911682i	$-0.365216\pi$
$127$	−63.5997	−	63.5997i	−0.500785	−	0.500785i	−0.911682	+	0.410897i	$0.865216\pi$
$128$	−92.2979	−	88.6854i	−0.721077	−	0.692855i
$129$	51.8217	−	125.109i	0.401719	−	0.969835i
$130$	100.414	−	244.390i	0.772418	−	1.87992i
$131$	−59.9457	+	144.722i	−0.457601	+	1.10475i	0.511765	+	0.859126i	$0.328992\pi$
$131$	−59.9457	+	144.722i	−0.457601	+	1.10475i	−0.969366	+	0.245621i	$0.921008\pi$
$132$	−0.0884191	−	15.5058i	−0.000669842	−	0.117468i
$133$	50.2349	+	20.8080i	0.377706	+	0.156451i
$134$	−183.214	+	0.522370i	−1.36727	+	0.00389828i
$135$	−251.102			−1.86001
$136$	−111.113	−	78.4215i	−0.817006	−	0.576629i
$137$		−	205.535i		−	1.50026i	−0.661292	−	0.750128i	$-0.729992\pi$
$137$		−	205.535i		−	1.50026i	0.661292	−	0.750128i	$-0.270008\pi$
$138$	−48.0745	+	0.137067i	−0.348366	+	0.000993240i
$139$	59.4177	−	143.447i	0.427465	−	1.03199i	−0.552623	−	0.833431i	$-0.686373\pi$
$139$	59.4177	−	143.447i	0.427465	−	1.03199i	0.980089	−	0.198561i	$-0.0636268\pi$
$140$	49.1893	−	49.7535i	0.351352	−	0.355382i
$141$	−44.8200	−	18.5651i	−0.317872	−	0.131667i
$142$	−23.2720	+	56.6398i	−0.163887	+	0.398872i
$143$	−24.8580	−	10.2965i	−0.173832	−	0.0720036i
$144$	47.9724	+	46.8905i	0.333142	+	0.325628i
$145$	−97.4285	+	97.4285i	−0.671921	+	0.671921i
$146$	−65.9836	+	160.592i	−0.451943	+	1.09995i
$147$	37.7075	+	91.0339i	0.256513	+	0.619278i
$148$	91.2648	−	223.936i	0.616654	−	1.51308i
$149$	−134.528	+	134.528i	−0.902869	+	0.902869i	−0.995683	−	0.0928142i	$-0.970414\pi$
$149$	−134.528	+	134.528i	−0.902869	+	0.902869i	0.0928142	+	0.995683i	$0.470414\pi$
$150$	204.258	+	83.9250i	1.36172	+	0.559500i
$151$	−17.1725	−	17.1725i	−0.113725	−	0.113725i	0.647954	−	0.761679i	$-0.275625\pi$
$151$	−17.1725	−	17.1725i	−0.113725	−	0.113725i	−0.761679	+	0.647954i	$0.775625\pi$
$152$	151.345	−	153.956i	0.995689	−	1.01287i
$153$	57.8786	+	41.5959i	0.378292	+	0.271869i
$154$	−5.05230	−	5.02357i	−0.0328072	−	0.0326206i
$155$	511.899			3.30258
$156$	−123.014	+	51.7780i	−0.788554	+	0.331910i
$157$	−3.01951	−	3.01951i	−0.0192326	−	0.0192326i	0.697425	−	0.716658i	$-0.254329\pi$
$157$	−3.01951	−	3.01951i	−0.0192326	−	0.0192326i	−0.716658	+	0.697425i	$0.754329\pi$
$158$	−33.6623	−	80.6171i	−0.213053	−	0.510235i
$159$	49.6545	−	119.876i	0.312292	−	0.753940i
$160$	−109.953	−	255.102i	−0.687206	−	1.59439i
$161$	−15.6196	+	15.6196i	−0.0970162	+	0.0970162i
$162$	36.4313	+	36.2241i	0.224884	+	0.223606i
$163$	115.614	−	47.8890i	0.709289	−	0.293797i	0.00127893	−	0.999999i	$-0.499593\pi$
$163$	115.614	−	47.8890i	0.709289	−	0.293797i	0.708011	+	0.706202i	$0.249593\pi$
$164$	75.3632	−	184.918i	0.459532	−	1.12755i
$165$	12.8779	−	31.0901i	0.0780480	−	0.188425i
$166$	94.4897	+	93.9524i	0.569215	+	0.565979i
$167$	−31.6400	+	13.1057i	−0.189461	+	0.0784773i	−0.475397	−	0.879771i	$-0.657696\pi$
$167$	−31.6400	+	13.1057i	−0.189461	+	0.0784773i	0.285936	+	0.958249i	$0.407696\pi$
$168$	−35.3409	+	0.302292i	−0.210363	+	0.00179936i
$169$			62.5926i			0.370370i
$170$	−156.229	−	250.413i	−0.918995	−	1.47302i
$171$	−80.0043	+	80.0043i	−0.467861	+	0.467861i
$172$	−247.043	+	1.40872i	−1.43630	+	0.00819024i
$173$	−33.8257	+	81.6625i	−0.195524	+	0.472037i	−0.990986	−	0.133967i	$-0.957228\pi$
$173$	−33.8257	+	81.6625i	−0.195524	+	0.472037i	0.795462	+	0.606004i	$0.207228\pi$
$174$	69.6012	−	0.198443i	0.400007	−	0.00114048i
$175$	93.7426	−	38.8295i	0.535672	−	0.221883i
$176$	−26.0099	+	11.1228i	−0.147784	+	0.0631980i
$177$	10.6585	−	25.7320i	0.0602177	−	0.145378i
$178$	113.431	−	114.079i	0.637251	−	0.640895i
$179$	204.422			1.14202			0.571012	−	0.820941i	$-0.306551\pi$
$179$	204.422			1.14202			0.571012	+	0.820941i	$0.306551\pi$
$180$	56.4788	+	134.183i	0.313771	+	0.745459i
$181$	2.56101	+	6.18282i	0.0141492	+	0.0341592i	0.930796	−	0.365538i	$-0.119115\pi$
$181$	2.56101	+	6.18282i	0.0141492	+	0.0341592i	−0.916647	+	0.399698i	$0.869115\pi$
$182$	−23.3068	+	56.7244i	−0.128059	+	0.311672i
$183$		−	37.5176i		−	0.205014i
$184$	34.2551	+	80.7387i	0.186169	+	0.438798i
$185$	371.092	−	371.092i	2.00590	−	2.00590i
$186$	−183.367	−	182.324i	−0.985844	−	0.980239i
$187$	−25.5458	+	15.8367i	−0.136609	+	0.0846881i
$188$	0.504672	+	88.5028i	0.00268443	+	0.470760i
$189$	58.2822			0.308372
$190$	432.349	−	180.531i	2.27552	−	0.950162i
$191$	198.208			1.03774			0.518869	−	0.854854i	$-0.326353\pi$
$191$	198.208			1.03774			0.518869	+	0.854854i	$0.326353\pi$
$192$	−51.4742	+	130.542i	−0.268095	+	0.679907i
$193$	90.1268	+	37.3317i	0.466978	+	0.193429i	0.603750	−	0.797174i	$-0.293673\pi$
$193$	90.1268	+	37.3317i	0.466978	+	0.193429i	−0.136772	+	0.990603i	$0.543673\pi$
$194$	−18.3240	−	7.52891i	−0.0944536	−	0.0388088i
$195$	−289.654			−1.48541
$196$	126.383	−	127.833i	0.644813	−	0.652209i
$197$	−202.962	+	84.0696i	−1.03026	+	0.426749i	−0.832808	−	0.553562i	$-0.813268\pi$
$197$	−202.962	+	84.0696i	−1.03026	+	0.426749i	−0.197456	+	0.980312i	$0.563268\pi$
$198$	13.6807	−	5.71248i	0.0690944	−	0.0288509i
$199$	59.0114	+	142.466i	0.296540	+	0.715911i	0.999987	+	0.00516267i	$0.00164333\pi$
$199$	59.0114	+	142.466i	0.296540	+	0.715911i	−0.703447	+	0.710748i	$0.748357\pi$
$200$	−3.44583	−	402.851i	−0.0172292	−	2.01426i
$201$	76.8641	+	185.566i	0.382408	+	0.923215i
$202$	24.4949	−	0.0698385i	0.121262	−	0.000345735i
$203$	22.6137	−	22.6137i	0.111398	−	0.111398i
$204$	−33.2274	+	145.345i	−0.162879	+	0.712474i
$205$	306.434	−	306.434i	1.49480	−	1.49480i
$206$	−227.576	+	228.878i	−1.10474	+	1.11106i
$207$	−17.5899	−	42.4658i	−0.0849753	−	0.205149i
$208$	174.126	+	170.199i	0.837145	+	0.818265i
$209$	−18.2586	−	44.0801i	−0.0873616	−	0.210910i
$210$	−70.9456	−	29.1499i	−0.337836	−	0.138809i
$211$	142.205	−	58.9033i	0.673958	−	0.279163i	−0.0193405	−	0.999813i	$-0.506157\pi$
$211$	142.205	−	58.9033i	0.673958	−	0.279163i	0.693299	+	0.720650i	$0.256157\pi$
$212$	−236.711	+	1.34981i	−1.11656	+	0.00636701i
$213$	67.1303			0.315166
$214$	9.73190	−	4.06363i	0.0454762	−	0.0189889i
$215$	−495.337	−	205.175i	−2.30389	−	0.954303i
$216$	86.7234	−	214.541i	0.401497	−	0.993245i
$217$	−118.815			−0.547533
$218$	−326.280	−	134.061i	−1.49670	−	0.614959i
$219$	190.336			0.869113
$220$	−61.3913	+	0.350073i	−0.279051	+	0.00159124i
$221$	210.083	+	150.981i	0.950602	+	0.683174i
$222$	−265.101	+	0.755841i	−1.19415	+	0.00340469i
$223$	−19.6369	+	19.6369i	−0.0880580	+	0.0880580i	−0.749764	−	0.661706i	$-0.769833\pi$
$223$	−19.6369	+	19.6369i	−0.0880580	+	0.0880580i	0.661706	+	0.749764i	$0.269833\pi$
$224$	25.5207	+	59.2107i	0.113932	+	0.264333i
$225$			211.135i			0.938378i
$226$	135.902	−	56.7470i	0.601337	−	0.251093i
$227$	58.8922	+	142.178i	0.259437	+	0.626336i	0.998901	−	0.0468593i	$-0.0149212\pi$
$227$	58.8922	+	142.178i	0.259437	+	0.626336i	−0.739465	+	0.673195i	$0.764921\pi$
$228$	−219.171	−	89.3230i	−0.961278	−	0.391768i
$229$	179.865			0.785438			0.392719	−	0.919659i	$-0.371535\pi$
$229$	179.865			0.785438			0.392719	+	0.919659i	$0.371535\pi$
$230$	0.542683	+	190.339i	0.00235949	+	0.827561i
$231$	−2.98904	+	7.21618i	−0.0129396	+	0.0312389i
$232$	−49.5937	−	116.892i	−0.213766	−	0.503844i
$233$	41.7529	−	17.2946i	0.179197	−	0.0742258i	−0.291281	−	0.956638i	$-0.594081\pi$
$233$	41.7529	−	17.2946i	0.179197	−	0.0742258i	0.470478	+	0.882412i	$0.344081\pi$
$234$	−90.4902	−	89.9757i	−0.386710	−	0.384511i
$235$	−73.5037	+	177.454i	−0.312782	+	0.755122i
$236$	−50.8111	+	0.289741i	−0.215301	+	0.00122772i
$237$	−67.7227	+	67.7227i	−0.285750	+	0.285750i
$238$	36.2617	+	58.1222i	0.152360	+	0.244211i
$239$			462.847i			1.93660i	0.249794	+	0.968299i	$0.419637\pi$
$239$			462.847i			1.93660i	−0.249794	+	0.968299i	$0.580363\pi$
$240$	−212.869	+	217.781i	−0.886955	+	0.907420i
$241$	−347.757	+	144.046i	−1.44298	+	0.597700i	−0.960518	−	0.278219i	$-0.910256\pi$
$241$	−347.757	+	144.046i	−1.44298	+	0.597700i	−0.482458	+	0.875919i	$0.660256\pi$
$242$	−0.672149	−	235.747i	−0.00277747	−	0.974162i
$243$	−78.0712	+	188.481i	−0.321281	+	0.775641i
$244$	−63.0847	+	26.5530i	−0.258544	+	0.108824i
$245$	360.426	−	149.293i	1.47113	−	0.609360i
$246$	−218.911	+	0.624147i	−0.889883	+	0.00253718i
$247$	−290.393	+	290.393i	−1.17568	+	1.17568i
$248$	−176.795	+	437.366i	−0.712884	+	1.76357i
$249$	55.9019	−	134.959i	0.224506	−	0.542005i
$250$	167.322	−	407.231i	0.669287	−	1.62892i
$251$	−94.6078	−	94.6078i	−0.376923	−	0.376923i	0.493068	−	0.869991i	$-0.335876\pi$
$251$	−94.6078	−	94.6078i	−0.376923	−	0.376923i	−0.869991	+	0.493068i	$0.835876\pi$
$252$	−13.1091	−	31.1446i	−0.0520201	−	0.123590i
$253$	19.3831			0.0766129
$254$	179.887	−	0.512882i	0.708215	−	0.00201922i
$255$	−188.833	+	262.752i	−0.740523	+	1.03040i
$256$	255.933	−	5.83862i	0.999740	−	0.0228071i
$257$	−139.291	−	139.291i	−0.541987	−	0.541987i	0.382124	−	0.924111i	$-0.375193\pi$
$257$	−139.291	−	139.291i	−0.541987	−	0.541987i	−0.924111	+	0.382124i	$0.875193\pi$
$258$	104.356	+	249.921i	0.404482	+	0.968686i
$259$	−86.1325	+	86.1325i	−0.332558	+	0.332558i
$260$	205.002	+	487.045i	0.788470	+	1.87325i
$261$	25.4663	+	61.4810i	0.0975719	+	0.235559i
$262$	−120.716	−	289.101i	−0.460749	−	1.10344i
$263$	−64.8955	+	64.8955i	−0.246751	+	0.246751i	−0.819636	−	0.572885i	$-0.805824\pi$
$263$	−64.8955	+	64.8955i	−0.246751	+	0.246751i	0.572885	+	0.819636i	$0.305824\pi$
$264$	22.1156	+	21.7405i	0.0837712	+	0.0823503i
$265$	−474.621	−	196.594i	−1.79102	−	0.741866i
$266$	−100.351	+	41.9022i	−0.377258	+	0.157527i
$267$	−162.939	−	67.4916i	−0.610259	−	0.252777i
$268$	257.624	−	260.579i	0.961282	−	0.972308i
$269$	−57.4557	+	138.710i	−0.213590	+	0.515652i	−0.993970	−	0.109654i	$-0.965026\pi$
$269$	−57.4557	+	138.710i	−0.213590	+	0.515652i	0.780380	+	0.625306i	$0.215026\pi$
$270$	354.098	−	356.123i	1.31147	−	1.31897i
$271$		−	24.4080i		−	0.0900665i	−0.998985	−	0.0450333i	$-0.985661\pi$
$271$		−	24.4080i		−	0.0900665i	0.998985	−	0.0450333i	$-0.0143394\pi$
$272$	267.909	−	46.9965i	0.984960	−	0.172781i
$273$	67.2304			0.246265
$274$	291.498	+	289.841i	1.06386	+	1.05781i
$275$	−82.2572	−	34.0721i	−0.299117	−	0.123898i
$276$	67.5991	−	68.3744i	0.244924	−	0.247734i
$277$	7.46638	−	18.0254i	0.0269545	−	0.0650738i	−0.909829	−	0.414983i	$-0.863788\pi$
$277$	7.46638	−	18.0254i	0.0269545	−	0.0650738i	0.936784	+	0.349909i	$0.113788\pi$
$278$	119.653	+	286.554i	0.430406	+	1.03077i
$279$	94.6125	−	228.415i	0.339113	−	0.818691i
$280$	1.19685	+	139.924i	0.00427447	+	0.499727i
$281$	−80.0241	−	80.0241i	−0.284783	−	0.284783i	0.550230	−	0.835013i	$-0.314540\pi$
$281$	−80.0241	−	80.0241i	−0.284783	−	0.284783i	−0.835013	+	0.550230i	$0.814540\pi$
$282$	89.5338	−	37.3855i	0.317496	−	0.132573i
$283$	−52.9583	+	21.9361i	−0.187132	+	0.0775126i	−0.474282	−	0.880373i	$-0.657292\pi$
$283$	−52.9583	+	21.9361i	−0.187132	+	0.0775126i	0.287150	+	0.957886i	$0.407292\pi$
$284$	−47.5113	−	112.877i	−0.167293	−	0.397456i
$285$	−363.196	−	363.196i	−1.27437	−	1.27437i
$286$	49.6571	−	20.7347i	0.173626	−	0.0724989i
$287$	−71.1252	+	71.1252i	−0.247823	+	0.247823i
$288$	−134.151	+	1.91255i	−0.465804	+	0.00664079i
$289$	273.917	−	92.1423i	0.947811	−	0.318832i
$290$	−0.785685	−	275.568i	−0.00270926	−	0.950236i
$291$			21.7178i			0.0746317i
$292$	−134.710	−	320.044i	−0.461334	−	1.09604i
$293$	313.832	−	313.832i	1.07110	−	1.07110i	0.0738281	−	0.997271i	$-0.476478\pi$
$293$	313.832	−	313.832i	1.07110	−	1.07110i	0.997271	−	0.0738281i	$-0.0235216\pi$
$294$	−182.282	−	74.8955i	−0.620007	−	0.254747i
$295$	−101.879	−	42.1998i	−0.345354	−	0.143050i
$296$	188.895	+	445.224i	0.638160	+	1.50414i
$297$	−36.1625	−	36.1625i	−0.121759	−	0.121759i
$298$	−1.08486	−	380.500i	−0.00364046	−	1.27684i
$299$	−63.8463	−	154.139i	−0.213533	−	0.515514i
$300$	−407.065	+	171.338i	−1.35688	+	0.571126i
$301$	114.971	+	47.6224i	0.381962	+	0.158214i
$302$	48.5711	−	0.138483i	0.160831	−	0.000458553i
$303$	−10.2764	−	24.8094i	−0.0339154	−	0.0818791i
$304$	4.92410	+	431.748i	0.0161977	+	1.42022i
$305$	−148.542			−0.487021
$306$	−140.612	+	23.4282i	−0.459516	+	0.0765628i
$307$	−49.0134	−	49.0134i	−0.159653	−	0.159653i	0.622760	−	0.782413i	$-0.286011\pi$
$307$	−49.0134	−	49.0134i	−0.159653	−	0.159653i	−0.782413	+	0.622760i	$0.786011\pi$
$308$	14.2493	−	0.0812540i	0.0462639	−	0.000263812i
$309$	326.905	+	135.408i	1.05794	+	0.438215i
$310$	−721.868	+	725.996i	−2.32861	+	2.34192i
$311$	−83.7018	−	202.074i	−0.269138	−	0.649755i	0.730306	−	0.683120i	$-0.239378\pi$
$311$	−83.7018	−	202.074i	−0.269138	−	0.649755i	−0.999443	+	0.0333650i	$0.989378\pi$
$312$	100.038	−	247.480i	0.320636	−	0.793205i
$313$	−316.760	−	131.206i	−1.01201	−	0.419190i	−0.185824	−	0.982583i	$-0.559496\pi$
$313$	−316.760	−	131.206i	−1.01201	−	0.419190i	−0.826189	+	0.563393i	$0.809496\pi$
$314$	8.54044	−	0.0243500i	0.0271989	−	7.75478e-5i
$315$		−	73.3341i		−	0.232807i
$316$	161.804	+	65.9431i	0.512038	+	0.208681i
$317$	145.935	−	60.4481i	0.460361	−	0.190688i	−0.140435	−	0.990090i	$-0.544850\pi$
$317$	145.935	−	60.4481i	0.460361	−	0.190688i	0.600797	+	0.799402i	$0.294850\pi$
$318$	99.9921	+	239.469i	0.314440	+	0.753046i
$319$	−28.0624			−0.0879698
$320$	516.849	+	203.799i	1.61515	+	0.636873i
$321$	−8.17532	−	8.17532i	−0.0254683	−	0.0254683i
$322$	−0.125960	−	44.1788i	−0.000391180	−	0.137201i
$323$	74.1072	+	452.737i	0.229434	+	1.40166i
$324$	−102.749	+	0.585909i	−0.317127	+	0.00180836i
$325$			766.360i			2.35803i
$326$	−95.1183	+	231.501i	−0.291774	+	0.710124i
$327$			386.711i			1.18260i
$328$	155.983	+	367.650i	0.475559	+	1.12089i
$329$	17.0606	−	41.1880i	0.0518560	−	0.125192i
$330$	25.9330	+	62.1064i	0.0785849	+	0.188201i
$331$		−	661.061i		−	1.99716i	−0.0532374	−	0.998582i	$-0.516954\pi$
$331$		−	661.061i		−	1.99716i	0.0532374	−	0.998582i	$-0.483046\pi$
$332$	−266.494	+	1.51964i	−0.802693	+	0.00457722i
$333$	−96.9974	−	234.172i	−0.291284	−	0.703221i
$334$	26.0309	−	63.3544i	0.0779368	−	0.189684i
$335$	734.703	−	304.324i	2.19314	−	0.908430i
$336$	49.4082	−	50.5482i	0.147048	−	0.150441i
$337$	393.629	−	163.047i	1.16804	−	0.483818i	0.287495	−	0.957782i	$-0.407178\pi$
$337$	393.629	−	163.047i	1.16804	−	0.483818i	0.880544	+	0.473965i	$0.157178\pi$
$338$	−88.7713	−	88.2665i	−0.262637	−	0.261144i
$339$	−114.165	−	114.165i	−0.336770	−	0.336770i
$340$	575.456	+	131.555i	1.69252	+	0.386928i
$341$	73.7212	+	73.7212i	0.216191	+	0.216191i
$342$	−0.645172	−	226.285i	−0.00188647	−	0.661653i
$343$	−174.871	+	72.4340i	−0.509828	+	0.211178i
$344$	346.376	−	352.353i	1.00691	−	1.02428i
$345$	192.782	−	79.8530i	0.558789	−	0.231458i
$346$	−68.1168	−	163.131i	−0.196869	−	0.471478i
$347$	40.6442	+	98.1238i	0.117130	+	0.282778i	0.971562	−	0.236787i	$-0.0760943\pi$
$347$	40.6442	+	98.1238i	0.117130	+	0.282778i	−0.854431	+	0.519564i	$0.826094\pi$
$348$	−97.8684	+	98.9910i	−0.281231	+	0.284457i
$349$		−	136.881i		−	0.392210i	−0.980583	−	0.196105i	$-0.937171\pi$
$349$		−	136.881i		−	0.392210i	0.980583	−	0.196105i	$-0.0628293\pi$
$350$	−77.1241	+	187.706i	−0.220354	+	0.536303i
$351$	−168.456	+	406.689i	−0.479932	+	1.15866i
$352$	20.9037	−	52.5735i	0.0593855	−	0.149356i
$353$		−	46.2853i		−	0.131120i	−0.997849	−	0.0655599i	$-0.979117\pi$
$353$		−	46.2853i		−	0.131120i	0.997849	−	0.0655599i	$-0.0208833\pi$
$354$	21.4637	+	51.4030i	0.0606319	+	0.145206i
$355$		−	265.785i		−	0.748691i
$356$	1.83469	+	321.744i	0.00515362	+	0.903775i
$357$	43.8293	−	60.9863i	0.122771	−	0.170830i
$358$	−288.272	+	289.920i	−0.805228	+	0.809833i
$359$	204.919	+	204.919i	0.570805	+	0.570805i	0.932353	−	0.361548i	$-0.117752\pi$
$359$	204.919	+	204.919i	0.570805	+	0.570805i	−0.361548	+	0.932353i	$0.617752\pi$
$360$	−269.948	−	109.121i	−0.749856	−	0.303113i
$361$	−367.245			−1.01730
$362$	−12.3802	−	5.08674i	−0.0341994	−	0.0140518i
$363$	−238.773	+	98.9032i	−0.657778	+	0.272461i
$364$	−47.5822	−	113.046i	−0.130720	−	0.310566i
$365$		−	753.587i		−	2.06462i
$366$	53.2089	+	52.9064i	0.145380	+	0.144553i
$367$	149.849	+	62.0694i	0.408307	+	0.169126i	0.577377	−	0.816478i	$-0.304076\pi$
$367$	149.849	+	62.0694i	0.408307	+	0.169126i	−0.169070	+	0.985604i	$0.554076\pi$
$368$	−162.813	−	65.2739i	−0.442425	−	0.177375i
$369$	−80.0970	−	193.371i	−0.217065	−	0.524042i
$370$	2.99256	+	1049.60i	0.00808801	+	2.83676i
$371$	110.162	+	45.6307i	0.296933	+	0.122994i
$372$	517.159	−	2.94901i	1.39021	−	0.00792746i
$373$	−383.824	−	383.824i	−1.02902	−	1.02902i	−0.999566	−	0.0294515i	$-0.990624\pi$
$373$	−383.824	−	383.824i	−1.02902	−	1.02902i	−0.0294515	−	0.999566i	$-0.509376\pi$
$374$	13.5638	−	58.5626i	0.0362670	−	0.156584i
$375$	−482.655			−1.28708
$376$	−126.230	−	124.089i	−0.335718	−	0.330023i
$377$	92.4353	+	223.159i	0.245186	+	0.591932i
$378$	−82.1882	+	82.6582i	−0.217429	+	0.218672i
$379$	448.564	+	185.801i	1.18355	+	0.490241i	0.885648	−	0.464357i	$-0.153715\pi$
$379$	448.564	+	185.801i	1.18355	+	0.490241i	0.297898	+	0.954598i	$0.403715\pi$
$380$	−353.652	+	867.755i	−0.930664	+	2.28357i
$381$	−75.4679	−	182.196i	−0.198079	−	0.478204i
$382$	−279.508	+	281.106i	−0.731696	+	0.735881i
$383$	−34.6565	−	34.6565i	−0.0904870	−	0.0904870i	0.660414	−	0.750901i	$-0.270381\pi$
$383$	−34.6565	−	34.6565i	−0.0904870	−	0.0904870i	−0.750901	+	0.660414i	$0.770381\pi$
$384$	−112.553	−	257.090i	−0.293106	−	0.669506i
$385$	28.5707	+	11.8344i	0.0742095	+	0.0307386i
$386$	−180.040	+	75.1771i	−0.466425	+	0.194759i
$387$	−183.103	+	183.103i	−0.473133	+	0.473133i
$388$	36.5179	−	15.3707i	0.0941182	−	0.0396153i
$389$			235.502i			0.605404i	0.953085	+	0.302702i	$0.0978886\pi$
$389$			235.502i			0.605404i	−0.953085	+	0.302702i	$0.902111\pi$
$390$	408.464	−	410.799i	1.04734	−	1.05333i
$391$	−181.446	−	42.5707i	−0.464056	−	0.108876i
$392$	3.07510	+	359.509i	0.00784463	+	0.917114i
$393$	−242.860	+	242.860i	−0.617964	+	0.617964i
$394$	166.981	−	406.402i	0.423810	−	1.03148i
$395$	268.131	+	268.131i	0.678813	+	0.678813i
$396$	−11.1905	+	27.4581i	−0.0282589	+	0.0693387i
$397$	−153.143	+	63.4340i	−0.385751	+	0.159783i	−0.567127	−	0.823631i	$-0.691945\pi$
$397$	−153.143	+	63.4340i	−0.385751	+	0.159783i	0.181376	+	0.983414i	$0.441945\pi$
$398$	−285.268	−	117.210i	−0.716753	−	0.294498i
$399$	84.3000	+	84.3000i	0.211278	+	0.211278i
$400$	576.199	+	563.204i	1.44050	+	1.40801i
$401$	196.269	−	473.834i	0.489448	−	1.18163i	−0.465551	−	0.885021i	$-0.654144\pi$
$401$	196.269	−	473.834i	0.489448	−	1.18163i	0.954999	−	0.296610i	$-0.0958562\pi$
$402$	−371.569	−	152.669i	−0.924302	−	0.379774i
$403$	343.416	−	829.081i	0.852150	−	2.05727i
$404$	−34.4431	+	34.8381i	−0.0852552	+	0.0862330i
$405$	−206.018	−	85.3355i	−0.508687	−	0.210705i
$406$	0.182362	+	63.9610i	0.000449167	+	0.157539i
$407$	106.886			0.262618
$408$	−159.277	−	252.086i	−0.390385	−	0.617858i
$409$		−	212.549i		−	0.519681i	−0.965652	−	0.259840i	$-0.916330\pi$
$409$		−	212.549i		−	0.519681i	0.965652	−	0.259840i	$-0.0836699\pi$
$410$	2.47115	+	866.724i	0.00602720	+	2.11396i
$411$	172.456	−	416.346i	0.419601	−	1.01301i
$412$	−3.68094	−	645.515i	−0.00893432	−	1.56678i
$413$	23.6468	+	9.79481i	0.0572561	+	0.0237163i
$414$	85.0315	+	34.9375i	0.205390	+	0.0843901i
$415$	−534.337	−	221.330i	−1.28756	−	0.533325i
$416$	−486.932	+	6.94201i	−1.17051	+	0.0166875i
$417$	240.721	−	240.721i	0.577268	−	0.577268i
$418$	88.2639	+	36.2656i	0.211158	+	0.0867599i
$419$	28.1811	+	68.0351i	0.0672580	+	0.162375i	0.953934	−	0.300015i	$-0.0969918\pi$
$419$	28.1811	+	68.0351i	0.0672580	+	0.162375i	−0.886676	+	0.462390i	$0.846992\pi$
$420$	141.387	−	59.5113i	0.336636	−	0.141694i
$421$	93.4487	−	93.4487i	0.221968	−	0.221968i	−0.587359	−	0.809327i	$-0.699832\pi$
$421$	93.4487	−	93.4487i	0.221968	−	0.221968i	0.809327	+	0.587359i	$0.199832\pi$
$422$	−116.995	+	284.745i	−0.277240	+	0.674751i
$423$	65.5962	+	65.5962i	0.155074	+	0.155074i
$424$	331.890	−	337.617i	0.782760	−	0.796266i
$425$	695.183	+	499.611i	1.63572	+	1.17555i
$426$	−94.6655	+	95.2068i	−0.222219	+	0.223490i
$427$	34.4773			0.0807432
$428$	−7.96049	+	19.5326i	−0.0185993	+	0.0456369i
$429$	−41.7146	−	41.7146i	−0.0972368	−	0.0972368i
$430$	989.500	−	413.173i	2.30116	−	0.960868i
$431$	215.565	−	520.420i	0.500151	−	1.20747i	−0.449251	−	0.893406i	$-0.648309\pi$
$431$	215.565	−	520.420i	0.500151	−	1.20747i	0.949401	−	0.314065i	$-0.101691\pi$
$432$	181.975	+	425.535i	0.421239	+	0.985035i
$433$	−476.972	+	476.972i	−1.10155	+	1.10155i	−0.107328	+	0.994224i	$0.534229\pi$
$433$	−476.972	+	476.972i	−1.10155	+	1.10155i	−0.994224	+	0.107328i	$0.965771\pi$
$434$	167.550	−	168.508i	0.386059	−	0.388267i
$435$	−279.106	+	115.609i	−0.641623	+	0.265769i
$436$	650.243	−	273.694i	1.49138	−	0.627738i
$437$	113.217	−	273.331i	0.259078	−	0.625470i
$438$	−268.407	+	269.942i	−0.612801	+	0.616306i
$439$	654.816	−	271.234i	1.49161	−	0.617845i	0.519943	−	0.854201i	$-0.325953\pi$
$439$	654.816	−	271.234i	1.49161	−	0.617845i	0.971666	+	0.236356i	$0.0759532\pi$
$440$	86.0760	−	87.5612i	0.195627	−	0.199003i
$441$		−	188.419i		−	0.427254i
$442$	−510.382	+	85.0378i	−1.15471	+	0.192393i
$443$	−424.632	+	424.632i	−0.958537	+	0.958537i	−0.999174	−	0.0406374i	$-0.987061\pi$
$443$	−424.632	+	424.632i	−0.958537	+	0.958537i	0.0406374	+	0.999174i	$0.487061\pi$
$444$	372.767	−	377.043i	0.839566	−	0.849196i
$445$	−267.216	+	645.117i	−0.600485	+	1.44970i
$446$	−0.158356	−	55.5414i	−0.000355059	−	0.124532i
$447$	−385.384	+	159.631i	−0.862157	+	0.357117i
$448$	−119.964	−	47.3030i	−0.267776	−	0.105587i
$449$	26.4054	−	63.7484i	0.0588094	−	0.141979i	−0.891743	−	0.452541i	$-0.850518\pi$
$449$	26.4054	−	63.7484i	0.0588094	−	0.141979i	0.950553	+	0.310563i	$0.100518\pi$
$450$	−299.440	−	297.737i	−0.665422	−	0.661639i
$451$	88.2623			0.195704
$452$	−111.165	+	272.765i	−0.245940	+	0.603462i
$453$	−20.3771	−	49.1946i	−0.0449825	−	0.108597i
$454$	−284.691	−	116.973i	−0.627073	−	0.257650i
$455$		−	266.182i		−	0.585016i
$456$	435.752	−	184.877i	0.955596	−	0.405431i
$457$	−40.6882	+	40.6882i	−0.0890334	+	0.0890334i	−0.750221	−	0.661187i	$-0.770053\pi$
$457$	−40.6882	+	40.6882i	−0.0890334	+	0.0890334i	0.661187	+	0.750221i	$0.270053\pi$
$458$	−253.642	+	255.092i	−0.553803	+	0.556970i
$459$	259.096	+	417.942i	0.564479	+	0.910549i
$460$	−270.712	−	267.642i	−0.588503	−	0.581830i
$461$	−673.932			−1.46189			−0.730946	−	0.682436i	$-0.760921\pi$
$461$	−673.932			−1.46189			−0.730946	+	0.682436i	$0.760921\pi$
$462$	−6.01920	−	14.4153i	−0.0130286	−	0.0312019i
$463$	675.131			1.45817			0.729083	−	0.684425i	$-0.239947\pi$
$463$	675.131			1.45817			0.729083	+	0.684425i	$0.239947\pi$
$464$	235.716	+	94.5021i	0.508009	+	0.203668i
$465$	1036.94	+	429.513i	2.22997	+	0.923684i
$466$	−34.3510	+	83.6041i	−0.0737146	+	0.179408i
$467$	−743.894			−1.59292			−0.796460	−	0.604691i	$-0.793297\pi$
$467$	−743.894			−1.59292			−0.796460	+	0.604691i	$0.793297\pi$
$468$	255.214	−	1.45532i	0.545330	−	0.00310965i
$469$	−170.529	+	70.6354i	−0.363601	+	0.150608i
$470$	−148.019	−	354.487i	−0.314933	−	0.754227i
$471$	−3.58298	−	8.65008i	−0.00760717	−	0.0183653i
$472$	71.2416	−	72.4709i	0.150936	−	0.153540i
$473$	−41.7876	−	100.884i	−0.0883460	−	0.213286i
$474$	−0.546130	−	191.548i	−0.00115217	−	0.404110i
$475$	−960.936	+	960.936i	−2.02302	+	2.02302i
$476$	−133.567	−	30.5348i	−0.280602	−	0.0641487i
$477$	−175.445	+	175.445i	−0.367809	+	0.367809i
$478$	−656.428	−	652.696i	−1.37328	−	1.36547i
$479$	−64.4321	−	155.553i	−0.134514	−	0.324745i	0.842242	−	0.539099i	$-0.181235\pi$
$479$	−64.4321	−	155.553i	−0.134514	−	0.324745i	−0.976756	+	0.214354i	$0.931235\pi$
$480$	−8.68242	−	609.009i	−0.0180884	−	1.26877i
$481$	−352.073	−	849.980i	−0.731961	−	1.76711i
$482$	286.107	−	696.333i	0.593584	−	1.44467i
$483$	−44.7459	+	18.5343i	−0.0926416	+	0.0383734i
$484$	335.294	+	331.492i	0.692756	+	0.684900i
$485$	85.9864			0.177291
$486$	−157.217	−	376.515i	−0.323491	−	0.774721i
$487$	674.334	+	279.318i	1.38467	+	0.573548i	0.945726	−	0.324967i	$-0.105353\pi$
$487$	674.334	+	279.318i	1.38467	+	0.573548i	0.438943	+	0.898515i	$0.355353\pi$
$488$	51.3020	−	126.914i	0.105127	−	0.260069i
$489$	274.377			0.561099
$490$	−296.530	+	721.700i	−0.605163	+	1.47286i
$491$	−794.079			−1.61727			−0.808634	−	0.588312i	$-0.799793\pi$
$491$	−794.079			−1.61727			−0.808634	+	0.588312i	$0.799793\pi$
$492$	307.818	−	311.349i	0.625646	−	0.632822i
$493$	262.693	+	61.6328i	0.532847	+	0.125016i
$494$	−2.34179	−	821.352i	−0.00474047	−	1.66266i
$495$	−45.5018	+	45.5018i	−0.0919228	+	0.0919228i
$496$	−370.977	−	867.500i	−0.747937	−	1.74899i
$497$			61.6903i			0.124125i
$498$	112.573	+	269.599i	0.226050	+	0.541363i
$499$	201.862	+	487.339i	0.404534	+	0.976631i	0.986551	+	0.163454i	$0.0522636\pi$
$499$	201.862	+	487.339i	0.404534	+	0.976631i	−0.582017	+	0.813177i	$0.697736\pi$
$500$	341.598	+	811.569i	0.683195	+	1.62314i
$501$	−75.0884			−0.149877
$502$	267.590	−	0.762937i	0.533048	−	0.00151980i
$503$	294.810	−	711.734i	0.586103	−	1.41498i	−0.301096	−	0.953594i	$-0.597353\pi$
$503$	294.810	−	711.734i	0.586103	−	1.41498i	0.887200	−	0.461385i	$-0.152647\pi$
$504$	62.6565	+	25.3275i	0.124319	+	0.0502530i
$505$	−98.2264	+	40.6867i	−0.194508	+	0.0805678i
$506$	−27.3335	+	27.4898i	−0.0540188	+	0.0543277i
$507$	−52.5188	+	126.792i	−0.103587	+	0.250082i
$508$	−252.944	+	255.845i	−0.497922	+	0.503633i
$509$	−43.1937	+	43.1937i	−0.0848599	+	0.0848599i	−0.748263	−	0.663403i	$-0.769112\pi$
$509$	−43.1937	+	43.1937i	−0.0848599	+	0.0848599i	0.663403	+	0.748263i	$0.269112\pi$
$510$	−106.357	−	638.338i	−0.208544	−	1.25164i
$511$			174.912i			0.342293i
$512$	−352.631	+	371.208i	−0.688731	+	0.725017i
$513$	−721.172	+	298.719i	−1.40579	+	0.582299i
$514$	393.972	−	1.12327i	0.766482	−	0.00218535i
$515$	536.116	−	1294.30i	1.04100	−	2.51320i
$516$	−501.609	−	204.430i	−0.972110	−	0.396182i
$517$	−36.1416	+	14.9704i	−0.0699065	+	0.0289562i
$518$	−0.694591	−	243.619i	−0.00134091	−	0.470306i
$519$	−137.039	+	137.039i	−0.264045	+	0.264045i
$520$	−979.835	−	396.077i	−1.88430	−	0.761686i
$521$	252.532	−	609.666i	0.484706	−	1.17018i	−0.472644	−	0.881254i	$-0.656700\pi$
$521$	252.532	−	609.666i	0.484706	−	1.17018i	0.957350	−	0.288931i	$-0.0932998\pi$
$522$	−123.107	−	50.5817i	−0.235837	−	0.0968999i
$523$	73.6180	+	73.6180i	0.140761	+	0.140761i	0.773976	−	0.633215i	$-0.218265\pi$
$523$	73.6180	+	73.6180i	0.140761	+	0.140761i	−0.633215	+	0.773976i	$0.718265\pi$
$524$	580.245	+	236.478i	1.10734	+	0.451294i
$525$	222.471			0.423755
$526$	−0.523331	−	183.551i	−0.000994926	−	0.348957i
$527$	−528.196	−	852.021i	−1.00227	−	1.61674i
$528$	−62.0201	+	0.707341i	−0.117462	+	0.00133966i
$529$	−289.072	−	289.072i	−0.546451	−	0.546451i
$530$	948.117	−	395.894i	1.78890	−	0.746969i
$531$	−37.6600	+	37.6600i	−0.0709227	+	0.0709227i
$532$	82.0847	−	201.411i	0.154295	−	0.378592i
$533$	−290.730	−	701.883i	−0.545459	−	1.31685i
$534$	325.492	−	135.912i	0.609536	−	0.254516i
$535$	−32.3681	+	32.3681i	−0.0605012	+	0.0605012i
$536$	6.26837	+	732.834i	0.0116947	+	1.36723i
$537$	414.092	+	171.522i	0.771120	+	0.319408i
$538$	−115.702	−	277.092i	−0.215059	−	0.515041i
$539$	73.4072	+	30.4063i	0.136192	+	0.0564124i
$540$	5.72737	+	1004.39i	0.0106062	+	1.85998i
$541$	−126.508	+	305.417i	−0.233841	+	0.564542i	−0.996623	−	0.0821135i	$-0.973833\pi$
$541$	−126.508	+	305.417i	−0.233841	+	0.564542i	0.762782	+	0.646656i	$0.223833\pi$
$542$	34.6164	+	34.4196i	0.0638680	+	0.0635048i
$543$			14.6732i			0.0270224i
$544$	−311.147	+	446.233i	−0.571961	+	0.820281i
$545$	1531.09			2.80933
$546$	−94.8067	+	95.3489i	−0.173639	+	0.174632i
$547$	−143.249	−	59.3358i	−0.261881	−	0.108475i	0.247880	−	0.968791i	$-0.420266\pi$
$547$	−143.249	−	59.3358i	−0.261881	−	0.108475i	−0.509761	+	0.860316i	$0.670266\pi$
$548$	−822.127	+	4.68804i	−1.50023	+	0.00855482i
$549$	−27.4544	+	66.2808i	−0.0500080	+	0.120730i
$550$	164.320	−	68.6129i	0.298763	−	0.124751i
$551$	−163.913	+	395.722i	−0.297483	+	0.718188i
$552$	1.64479	+	192.292i	0.00297969	+	0.348355i
$553$	−62.2348	−	62.2348i	−0.112540	−	0.112540i
$554$	15.0355	+	36.0082i	0.0271399	+	0.0649967i
$555$	1063.08	−	440.340i	1.91545	−	0.793406i
$556$	−575.134	−	234.395i	−1.03441	−	0.421574i
$557$	443.757	+	443.757i	0.796692	+	0.796692i	0.982572	−	0.185881i	$-0.0595138\pi$
$557$	443.757	+	443.757i	0.796692	+	0.796692i	−0.185881	+	0.982572i	$0.559514\pi$
$558$	190.527	+	456.288i	0.341446	+	0.817721i
$559$	−664.611	+	664.611i	−1.18893	+	1.18893i
$560$	−200.133	−	195.619i	−0.357380	−	0.349320i
$561$	−65.0351	+	10.6454i	−0.115927	+	0.0189758i
$562$	226.341	−	0.645331i	0.402742	−	0.00114828i
$563$		−	523.007i		−	0.928965i	−0.885582	−	0.464482i	$-0.846240\pi$
$563$		−	523.007i		−	0.928965i	0.885582	−	0.464482i	$-0.153760\pi$
$564$	−73.2367	+	179.701i	−0.129852	+	0.318618i
$565$	−452.008	+	452.008i	−0.800014	+	0.800014i
$566$	43.5699	−	106.041i	0.0769787	−	0.187352i
$567$	47.8180	+	19.8069i	0.0843351	+	0.0349327i
$568$	227.087	+	91.7947i	0.399800	+	0.161610i
$569$	29.0867	+	29.0867i	0.0511191	+	0.0511191i	0.732204	−	0.681085i	$-0.238492\pi$
$569$	29.0867	+	29.0867i	0.0511191	+	0.0511191i	−0.681085	+	0.732204i	$0.738492\pi$
$570$	1027.27	−	2.92889i	1.80223	−	0.00513841i
$571$	427.541	+	1032.17i	0.748758	+	1.80766i	0.565803	+	0.824540i	$0.308566\pi$
$571$	427.541	+	1032.17i	0.748758	+	1.80766i	0.182955	+	0.983121i	$0.441434\pi$
$572$	−40.6184	+	99.6652i	−0.0710112	+	0.174240i
$573$	401.503	+	166.308i	0.700703	+	0.290241i
$574$	−0.573569	−	201.172i	−0.000999249	−	0.350473i
$575$	−211.273	−	510.058i	−0.367431	−	0.887058i
$576$	186.465	−	192.956i	0.323723	−	0.334993i
$577$	72.2471			0.125212			0.0626058	−	0.998038i	$-0.480059\pi$
$577$	72.2471			0.125212			0.0626058	+	0.998038i	$0.480059\pi$
$578$	−255.592	+	518.418i	−0.442200	+	0.896916i
$579$	151.243	+	151.243i	0.261214	+	0.261214i
$580$	391.930	+	387.486i	0.675742	+	0.668079i
$581$	124.023	+	51.3719i	0.213464	+	0.0884198i
$582$	−30.8011	−	30.6260i	−0.0529229	−	0.0526219i
$583$	−40.0400	−	96.6651i	−0.0686792	−	0.165806i
$584$	643.863	+	260.267i	1.10251	+	0.445663i
$585$	511.720	+	211.961i	0.874736	+	0.362327i
$586$	2.53081	+	887.647i	0.00431879	+	1.51476i
$587$		−	292.718i		−	0.498667i	−0.968418	−	0.249334i	$-0.919788\pi$
$587$		−	292.718i		−	0.498667i	0.968418	−	0.249334i	$-0.0802116\pi$
$588$	363.269	−	152.904i	0.617805	−	0.260040i
$589$	1470.19	−	608.972i	2.49608	−	1.03391i
$590$	203.517	−	84.9802i	0.344944	−	0.144034i
$591$	−481.673			−0.815013
$592$	−897.811	−	359.945i	−1.51657	−	0.608016i
$593$	−123.417	−	123.417i	−0.208123	−	0.208123i	0.595346	−	0.803469i	$-0.297015\pi$
$593$	−123.417	−	123.417i	−0.208123	−	0.208123i	−0.803469	+	0.595346i	$0.797015\pi$
$594$	102.283	−	0.291622i	0.172193	−	0.000490946i
$595$	−241.460	−	173.531i	−0.405815	−	0.291649i
$596$	541.170	+	535.033i	0.908003	+	0.897706i
$597$			338.103i			0.566337i
$598$	308.640	+	126.813i	0.516121	+	0.212062i
$599$			803.581i			1.34154i	0.741666	+	0.670769i	$0.234036\pi$
$599$			803.581i			1.34154i	−0.741666	+	0.670769i	$0.765964\pi$
$600$	331.035	−	818.933i	0.551726	−	1.36489i
$601$	−373.039	+	900.595i	−0.620697	+	1.49849i	0.230191	+	0.973146i	$0.426065\pi$
$601$	−373.039	+	900.595i	−0.620697	+	1.49849i	−0.850887	+	0.525348i	$0.823935\pi$
$602$	−229.669	+	95.8999i	−0.381509	+	0.159302i
$603$		−	384.079i		−	0.636947i
$604$	−68.2974	+	69.0807i	−0.113075	+	0.114372i
$605$	391.583	+	945.364i	0.647244	+	1.56259i
$606$	49.6771	+	20.4112i	0.0819754	+	0.0336818i
$607$	−353.725	+	146.518i	−0.582742	+	0.241380i	−0.654525	−	0.756040i	$-0.727131\pi$
$607$	−353.725	+	146.518i	−0.582742	+	0.241380i	0.0717824	+	0.997420i	$0.477131\pi$
$608$	−619.266	−	601.857i	−1.01853	−	0.989897i
$609$	64.7821	−	26.8336i	0.106375	−	0.0440618i
$610$	209.470	−	210.667i	0.343393	−	0.345357i
$611$	238.096	+	238.096i	0.389682	+	0.389682i
$612$	165.061	−	232.460i	0.269707	−	0.379836i
$613$	27.5706	+	27.5706i	0.0449766	+	0.0449766i	0.729237	−	0.684261i	$-0.239875\pi$
$613$	27.5706	+	27.5706i	0.0449766	+	0.0449766i	−0.684261	+	0.729237i	$0.739875\pi$
$614$	138.630	−	0.395255i	0.225782	−	0.000643737i
$615$	877.850	−	363.617i	1.42740	−	0.591248i
$616$	−19.9787	+	20.3235i	−0.0324330	+	0.0329926i
$617$	−509.792	+	211.163i	−0.826243	+	0.342241i	−0.755414	−	0.655247i	$-0.772564\pi$
$617$	−509.792	+	211.163i	−0.826243	+	0.342241i	−0.0708286	+	0.997489i	$0.522564\pi$
$618$	−653.035	+	272.680i	−1.05669	+	0.441229i
$619$	−450.601	−	1087.85i	−0.727950	−	1.75743i	−0.649310	−	0.760524i	$-0.724942\pi$
$619$	−450.601	−	1087.85i	−0.727950	−	1.75743i	−0.0786403	−	0.996903i	$-0.525058\pi$
$620$	−11.6759	−	2047.56i	−0.0188321	−	3.30252i
$621$		−	317.116i		−	0.510655i
$622$	404.624	+	166.251i	0.650520	+	0.267284i
$623$	62.0224	−	149.735i	0.0995544	−	0.240346i
$624$	209.914	+	490.869i	0.336401	+	0.786648i
$625$			651.996i			1.04319i
$626$	632.769	−	264.218i	1.01081	−	0.422073i
$627$		−	104.612i		−	0.166845i
$628$	−12.0090	+	12.1467i	−0.0191226	+	0.0193419i
$629$	−1000.56	−	234.751i	−1.59072	−	0.373213i
$630$	104.005	+	103.414i	0.165088	+	0.164149i
$631$	668.512	+	668.512i	1.05945	+	1.05945i	0.998117	+	0.0613318i	$0.0195348\pi$
$631$	668.512	+	668.512i	1.05945	+	1.05945i	0.0613318	+	0.998117i	$0.480465\pi$
$632$	−321.695	+	136.486i	−0.509012	+	0.215959i
$633$	337.483			0.533149
$634$	−120.063	+	292.213i	−0.189375	+	0.460903i
$635$	−721.358	+	298.796i	−1.13600	+	0.470546i
$636$	−480.631	−	195.880i	−0.755708	−	0.307988i
$637$		−	683.908i		−	1.07364i
$638$	39.5729	−	39.7992i	0.0620264	−	0.0623811i
$639$	−118.596	−	49.1242i	−0.185597	−	0.0768766i
$640$	−1017.88	+	445.624i	−1.59044	+	0.696287i
$641$	379.689	+	916.650i	0.592338	+	1.43003i	0.881239	+	0.472672i	$0.156710\pi$
$641$	379.689	+	916.650i	0.592338	+	1.43003i	−0.288900	+	0.957359i	$0.593290\pi$
$642$	23.1232	−	0.0659275i	0.0360174	−	0.000102691i
$643$	663.343	+	274.766i	1.03164	+	0.427318i	0.833303	−	0.552816i	$-0.186447\pi$
$643$	663.343	+	274.766i	1.03164	+	0.427318i	0.198334	+	0.980134i	$0.436447\pi$
$644$	62.8337	+	62.1212i	0.0975679	+	0.0964614i
$645$	−831.233	−	831.233i	−1.28873	−	1.28873i
$646$	−746.594	−	533.337i	−1.15572	−	0.825599i
$647$	580.473			0.897176			0.448588	−	0.893739i	$-0.351927\pi$
$647$	580.473			0.897176			0.448588	+	0.893739i	$0.351927\pi$
$648$	144.063	−	146.549i	0.222320	−	0.226156i
$649$	−8.59475	−	20.7496i	−0.0132431	−	0.0319716i
$650$	−1086.88	−	1080.70i	−1.67213	−	1.66262i
$651$	−240.679	−	99.6925i	−0.369707	−	0.153137i
$652$	−194.190	−	461.357i	−0.297837	−	0.707603i
$653$	30.7350	+	74.2009i	0.0470674	+	0.113631i	0.945665	−	0.325144i	$-0.105413\pi$
$653$	30.7350	+	74.2009i	0.0470674	+	0.113631i	−0.898597	+	0.438774i	$0.855413\pi$
$654$	−548.450	−	545.331i	−0.838608	−	0.833840i
$655$	961.544	+	961.544i	1.46801	+	1.46801i
$656$	−741.380	−	297.230i	−1.13015	−	0.453095i
$657$	−336.258	−	139.283i	−0.511809	−	0.211998i
$658$	34.3560	+	82.2784i	0.0522127	+	0.125043i
$659$	10.4899	−	10.4899i	0.0159180	−	0.0159180i	−0.699103	−	0.715021i	$-0.746417\pi$
$659$	10.4899	−	10.4899i	0.0159180	−	0.0159180i	0.715021	+	0.699103i	$0.246417\pi$
$660$	−124.652	−	50.8017i	−0.188867	−	0.0769723i
$661$		−	150.444i		−	0.227601i	−0.993504	−	0.113800i	$-0.963698\pi$
$661$		−	150.444i		−	0.227601i	0.993504	−	0.113800i	$-0.0363025\pi$
$662$	937.543	+	932.212i	1.41623	+	1.40818i
$663$	298.876	+	482.110i	0.450793	+	0.727164i
$664$	373.648	−	380.096i	0.562724	−	0.572433i
$665$	333.765	−	333.765i	0.501902	−	0.501902i
$666$	468.896	+	192.659i	0.704048	+	0.289277i
$667$	−123.042	−	123.042i	−0.184471	−	0.184471i
$668$	53.1436	+	126.259i	0.0795563	+	0.189010i
$669$	−56.2544	+	23.3013i	−0.0840873	+	0.0348301i
$670$	−604.456	+	1471.14i	−0.902173	+	2.19573i
$671$	−21.3922	−	21.3922i	−0.0318811	−	0.0318811i
$672$	2.01524	+	141.354i	0.00299887	+	0.210349i
$673$	58.8508	−	142.079i	0.0874455	−	0.211112i	−0.874107	−	0.485734i	$-0.838553\pi$
$673$	58.8508	−	142.079i	0.0874455	−	0.211112i	0.961552	+	0.274621i	$0.0885525\pi$
$674$	−323.847	+	788.185i	−0.480485	+	1.16941i
$675$	−557.436	+	1345.77i	−0.825831	+	1.99373i
$676$	250.366	−	1.42767i	0.370364	−	0.00211194i
$677$	−352.413	−	145.974i	−0.520552	−	0.215620i	0.106908	−	0.994269i	$-0.465905\pi$
$677$	−352.413	−	145.974i	−0.520552	−	0.215620i	−0.627459	+	0.778649i	$0.715905\pi$
$678$	322.906	−	0.920651i	0.476263	−	0.00135789i
$679$	−19.9579			−0.0293931
$680$	−998.071	+	630.618i	−1.46775	+	0.927380i
$681$			337.420i			0.495477i
$682$	−208.514	+	0.594504i	−0.305739	+	0.000871706i
$683$	−356.543	+	860.771i	−0.522025	+	1.26028i	0.414618	+	0.909995i	$0.363915\pi$
$683$	−356.543	+	860.771i	−0.522025	+	1.26028i	−0.936643	+	0.350284i	$0.886085\pi$
$684$	321.837	+	318.187i	0.470522	+	0.465186i
$685$	−1648.42	−	682.796i	−2.40645	−	0.996783i
$686$	143.870	−	350.154i	0.209723	−	0.510428i
$687$	364.347	+	150.917i	0.530345	+	0.219676i
$688$	11.2696	+	988.124i	0.0163802	+	1.43623i
$689$	−636.815	+	636.815i	−0.924260	+	0.924260i
$690$	−158.606	+	386.018i	−0.229864	+	0.559447i
$691$	−193.910	−	468.139i	−0.280622	−	0.677481i	0.719229	−	0.694773i	$-0.244495\pi$
$691$	−193.910	−	468.139i	−0.280622	−	0.677481i	−0.999850	+	0.0172927i	$0.994495\pi$
$692$	327.416	+	133.438i	0.473145	+	0.192829i
$693$	10.5612	−	10.5612i	0.0152399	−	0.0152399i
$694$	−196.479	−	80.7286i	−0.283110	−	0.116324i
$695$	−953.073	−	953.073i	−1.37133	−	1.37133i
$696$	−2.38129	−	278.396i	−0.00342139	−	0.399994i
$697$	−826.229	−	193.849i	−1.18541	−	0.278119i
$698$	194.130	+	193.026i	0.278124	+	0.276542i
$699$	99.0886			0.141758
$700$	−157.454	−	374.079i	−0.224934	−	0.534398i
$701$	−70.3709	−	70.3709i	−0.100387	−	0.100387i	0.655130	−	0.755516i	$-0.272614\pi$
$701$	−70.3709	−	70.3709i	−0.100387	−	0.100387i	−0.755516	+	0.655130i	$0.772614\pi$
$702$	−339.230	−	812.414i	−0.483233	−	1.15729i
$703$	624.323	−	1507.25i	0.888084	−	2.14402i
$704$	45.0839	+	103.784i	0.0640397	+	0.147421i
$705$	−297.788	+	297.788i	−0.422394	+	0.422394i
$706$	65.6437	+	65.2704i	0.0929797	+	0.0924510i
$707$	22.7989	−	9.44362i	0.0322474	−	0.0133573i
$708$	−103.169	−	42.0465i	−0.145719	−	0.0593877i
$709$	364.147	−	879.128i	0.513606	−	1.23996i	−0.428165	−	0.903701i	$-0.640840\pi$
$709$	364.147	−	879.128i	0.513606	−	1.23996i	0.941771	−	0.336254i	$-0.109160\pi$
$710$	376.948	+	374.804i	0.530912	+	0.527893i
$711$	169.201	−	70.0852i	0.237975	−	0.0985727i
$712$	−458.897	−	451.114i	−0.644519	−	0.633586i
$713$			646.477i			0.906700i
$714$	24.6861	+	148.162i	0.0345744	+	0.207510i
$715$	−165.159	+	165.159i	−0.230991	+	0.230991i
$716$	−4.66266	−	817.677i	−0.00651210	−	1.14201i
$717$	−388.356	+	937.573i	−0.541640	+	1.30763i
$718$	−579.596	+	1.65251i	−0.807237	+	0.00230155i
$719$	141.715	−	58.7003i	0.197100	−	0.0816416i	−0.281950	−	0.959429i	$-0.590981\pi$
$719$	141.715	−	58.7003i	0.197100	−	0.0816416i	0.479050	+	0.877788i	$0.340981\pi$
$720$	535.434	−	228.972i	0.743658	−	0.318017i
$721$	−124.436	+	300.414i	−0.172587	+	0.416663i
$722$	517.880	−	520.842i	0.717285	−	0.721387i
$723$	−825.303			−1.14150
$724$	24.6725	−	10.3849i	0.0340780	−	0.0143438i
$725$	305.876	+	738.451i	0.421899	+	1.01855i
$726$	196.444	−	478.109i	0.270584	−	0.658552i
$727$			1057.96i			1.45524i	0.685981	+	0.727620i	$0.259374\pi$
$727$			1057.96i			1.45524i	−0.685981	+	0.727620i	$0.740626\pi$
$728$	227.425	+	91.9317i	0.312398	+	0.126280i
$729$	−479.768	+	479.768i	−0.658118	+	0.658118i
$730$	1068.77	+	1062.69i	1.46406	+	1.45574i
$731$	169.606	+	1036.16i	0.232019	+	1.41746i
$732$	−150.068	+	0.855737i	−0.205011	+	0.00116904i
$733$	−501.771			−0.684544			−0.342272	−	0.939601i	$-0.611196\pi$
$733$	−501.771			−0.684544			−0.342272	+	0.939601i	$0.611196\pi$
$734$	−299.342	+	124.993i	−0.407823	+	0.170290i
$735$	855.368			1.16377
$736$	322.168	−	138.860i	0.437729	−	0.188668i
$737$	149.636	+	61.9811i	0.203033	+	0.0840992i
$738$	387.198	+	159.091i	0.524658	+	0.215570i
$739$	373.267			0.505098			0.252549	−	0.967584i	$-0.418731\pi$
$739$	373.267			0.505098			0.252549	+	0.967584i	$0.418731\pi$
$740$	−1492.81	−	1475.88i	−2.01731	−	1.99443i
$741$	−831.896	+	344.582i	−1.12267	+	0.465024i
$742$	−220.063	+	91.8892i	−0.296581	+	0.123840i
$743$	75.6291	+	182.585i	0.101789	+	0.245740i	0.966567	−	0.256414i	$-0.0825410\pi$
$743$	75.6291	+	182.585i	0.101789	+	0.245740i	−0.864778	+	0.502154i	$0.832541\pi$
$744$	−725.103	+	737.615i	−0.974601	+	0.991418i
$745$	632.020	+	1525.83i	0.848350	+	2.04810i
$746$	1085.61	−	3.09524i	1.45524	−	0.00414911i
$747$	−197.519	+	197.519i	−0.264417	+	0.264417i
$748$	63.9284	+	101.820i	0.0854657	+	0.136123i
$749$	7.51283	−	7.51283i	0.0100305	−	0.0100305i
$750$	680.628	−	684.521i	0.907505	−	0.912694i
$751$	429.559	+	1037.05i	0.571983	+	1.38089i	0.899864	+	0.436170i	$0.143665\pi$
$751$	429.559	+	1037.05i	0.571983	+	1.38089i	−0.327881	+	0.944719i	$0.606335\pi$
$752$	353.994	−	4.03731i	0.470737	−	0.00536877i
$753$	−112.262	−	271.025i	−0.149087	−	0.359927i
$754$	−446.842	−	183.597i	−0.592629	−	0.243498i
$755$	−194.774	+	80.6779i	−0.257978	+	0.106858i
$756$	−1.32936	−	233.125i	−0.00175841	−	0.308366i
$757$	598.817			0.791039			0.395520	−	0.918457i	$-0.370565\pi$
$757$	598.817			0.791039			0.395520	+	0.918457i	$0.370565\pi$
$758$	−896.065	+	374.159i	−1.18214	+	0.493613i
$759$	39.2636	+	16.2635i	0.0517307	+	0.0214276i
$760$	−731.973	−	1725.25i	−0.963122	−	2.27007i
$761$	−1245.20			−1.63627			−0.818134	−	0.575027i	$-0.804991\pi$
$761$	−1245.20			−1.63627			−0.818134	+	0.575027i	$0.804991\pi$
$762$	364.820	+	149.896i	0.478767	+	0.196714i
$763$	−355.374			−0.465759
$764$	−4.52091	−	792.819i	−0.00591743	−	1.03772i
$765$	525.879	−	326.010i	0.687424	−	0.426157i
$766$	98.0230	−	0.279477i	0.127967	−	0.000364853i
$767$	−136.695	+	136.695i	−0.178220	+	0.178220i
$768$	523.334	+	202.916i	0.681425	+	0.264213i
$769$			586.971i			0.763291i	0.924309	+	0.381645i	$0.124642\pi$
$769$			586.971i			0.763291i	−0.924309	+	0.381645i	$0.875358\pi$
$770$	−57.0736	+	23.8315i	−0.0741216	+	0.0309500i
$771$	−165.283	−	399.029i	−0.214375	−	0.517547i
$772$	147.269	−	361.353i	0.190763	−	0.468073i
$773$	755.605			0.977497			0.488748	−	0.872425i	$-0.337454\pi$
$773$	755.605			0.977497			0.488748	+	0.872425i	$0.337454\pi$
$774$	−1.47658	−	517.890i	−0.00190772	−	0.669109i
$775$	1136.39	−	2743.50i	1.46632	−	3.54000i
$776$	−29.6972	+	73.4665i	−0.0382696	+	0.0946734i
$777$	−246.746	+	102.205i	−0.317562	+	0.131539i
$778$	−333.998	−	332.099i	−0.429304	−	0.426863i
$779$	515.544	−	1244.63i	0.661802	−	1.59773i
$780$	6.60671	+	1158.60i	0.00847014	+	1.48538i
$781$	38.2771	−	38.2771i	0.0490104	−	0.0490104i
$782$	316.246	−	197.302i	0.404407	−	0.252304i
$783$			459.114i			0.586353i
$784$	−514.206	−	502.609i	−0.655875	−	0.641083i
$785$	−34.2478	+	14.1859i	−0.0436278	+	0.0180712i
$786$	−1.95848	−	686.909i	−0.00249170	−	0.873930i
$787$	−217.792	+	525.798i	−0.276738	+	0.668104i	−0.999741	−	0.0227404i	$-0.992761\pi$
$787$	−217.792	+	525.798i	−0.276738	+	0.668104i	0.723004	+	0.690844i	$0.242761\pi$
$788$	340.902	+	809.918i	0.432617	+	1.02781i
$789$	−185.908	+	77.0054i	−0.235624	+	0.0975988i
$790$	−758.386	+	2.16227i	−0.959983	+	0.00273705i
$791$	104.914	−	104.914i	0.132634	−	0.132634i
$792$	−23.1616	−	54.5916i	−0.0292445	−	0.0689288i
$793$	−99.6516	+	240.580i	−0.125664	+	0.303380i
$794$	125.994	−	306.647i	0.158683	−	0.386205i
$795$	−796.469	−	796.469i	−1.00185	−	1.00185i
$796$	568.510	−	239.291i	0.714208	−	0.300617i
$797$	595.190			0.746788			0.373394	−	0.927673i	$-0.378194\pi$
$797$	595.190			0.746788			0.373394	+	0.927673i	$0.378194\pi$
$798$	−238.435	+	0.679813i	−0.298791	+	0.000851896i
$799$	371.203	−	60.7611i	0.464585	−	0.0760465i
$800$	−1611.30	+	22.9717i	−2.01412	+	0.0287146i
$801$	238.469	+	238.469i	0.297714	+	0.297714i
$802$	395.237	+	946.545i	0.492815	+	1.18023i
$803$	108.528	−	108.528i	0.135153	−	0.135153i
$804$	740.500	−	311.684i	0.921020	−	0.387666i
$805$	73.3821	+	177.160i	0.0911579	+	0.220075i
$806$	691.558	+	1656.20i	0.858012	+	2.05483i
$807$	−232.772	+	232.772i	−0.288441	+	0.288441i
$808$	−0.838052	−	97.9765i	−0.00103719	−	0.121258i
$809$	113.659	+	47.0790i	0.140493	+	0.0581941i	0.451822	−	0.892108i	$-0.350774\pi$
$809$	113.659	+	47.0790i	0.140493	+	0.0581941i	−0.311329	+	0.950302i	$0.600774\pi$
$810$	411.548	−	171.845i	0.508084	−	0.212154i
$811$	196.737	+	81.4911i	0.242586	+	0.100482i	0.500664	−	0.865642i	$-0.333089\pi$
$811$	196.737	+	81.4911i	0.242586	+	0.100482i	−0.258078	+	0.966124i	$0.583089\pi$
$812$	−90.9692	−	89.9376i	−0.112031	−	0.110761i
$813$	20.4798	−	49.4425i	0.0251904	−	0.0608149i
$814$	−150.727	+	151.589i	−0.185169	+	0.186228i
$815$		−	1086.33i		−	1.33292i
$816$	582.127	+	129.592i	0.713391	+	0.158814i
$817$	−1666.70			−2.04003
$818$	301.446	+	299.732i	0.368516	+	0.366421i
$819$	−118.773	−	49.1975i	−0.145022	−	0.0600702i
$820$	−1232.71	−	1218.73i	−1.50330	−	1.48625i
$821$	315.826	−	762.473i	0.384685	−	0.928712i	−0.606361	−	0.795190i	$-0.707371\pi$
$821$	315.826	−	762.473i	0.384685	−	0.928712i	0.991046	−	0.133522i	$-0.0426288\pi$
$822$	347.285	+	831.704i	0.422487	+	1.01181i
$823$	−111.574	+	269.363i	−0.135570	+	0.327294i	−0.977055	−	0.212985i	$-0.931681\pi$
$823$	−111.574	+	269.363i	−0.135570	+	0.327294i	0.841486	+	0.540279i	$0.181681\pi$
$824$	920.686	+	905.069i	1.11734	+	1.09839i
$825$	−138.037	−	138.037i	−0.167318	−	0.167318i
$826$	−47.2375	+	19.7244i	−0.0571883	+	0.0238794i
$827$	945.100	−	391.473i	1.14281	−	0.473366i	0.270691	−	0.962666i	$-0.412748\pi$
$827$	945.100	−	391.473i	1.14281	−	0.473366i	0.872115	+	0.489301i	$0.162748\pi$
$828$	−169.459	+	71.3270i	−0.204661	+	0.0861438i
$829$	1028.17	+	1028.17i	1.24025	+	1.24025i	0.959895	+	0.280359i	$0.0904535\pi$
$829$	1028.17	+	1028.17i	1.24025	+	1.24025i	0.280359	+	0.959895i	$0.409547\pi$
$830$	1067.41	−	445.705i	1.28603	−	0.536994i
$831$	30.2488	−	30.2488i	0.0364005	−	0.0364005i
$832$	676.814	−	700.376i	0.813478	−	0.841798i
$833$	−620.389	−	445.858i	−0.744764	−	0.535243i
$834$	1.94122	+	680.858i	0.00232760	+	0.816376i
$835$			297.294i			0.356041i
$836$	−175.901	+	74.0385i	−0.210408	+	0.0885628i
$837$	1206.12	−	1206.12i	1.44100	−	1.44100i
$838$	−136.230	−	55.9740i	−0.162566	−	0.0667947i
$839$	855.893	+	354.522i	1.02013	+	0.422554i	0.829142	−	0.559038i	$-0.188829\pi$
$839$	855.893	+	354.522i	1.02013	+	0.422554i	0.190993	+	0.981591i	$0.438829\pi$
$840$	−114.980	+	284.443i	−0.136880	+	0.338622i
$841$	−416.539	−	416.539i	−0.495290	−	0.495290i
$842$	0.753590	+	264.312i	0.000895000	+	0.313909i
$843$	−94.9571	−	229.247i	−0.112642	−	0.271942i
$844$	−238.853	−	567.468i	−0.283001	−	0.672355i
$845$	502.000	+	207.935i	0.594082	+	0.246077i
$846$	−185.533	+	0.528982i	−0.219307	+	0.000625274i
$847$	−90.8886	−	219.424i	−0.107306	−	0.259061i
$848$	10.7983	+	946.799i	0.0127338	+	1.11651i
$849$	−125.681			−0.148035
$850$	−1688.90	+	281.397i	−1.98694	+	0.331056i
$851$	468.651	+	468.651i	0.550707	+	0.550707i
$852$	−1.53117	−	268.517i	−0.00179715	−	0.315160i
$853$	−1029.16	−	426.291i	−1.20651	−	0.499755i	−0.313416	−	0.949616i	$-0.601473\pi$
$853$	−1029.16	−	426.291i	−1.20651	−	0.499755i	−0.893098	+	0.449861i	$0.851473\pi$
$854$	−48.6191	+	48.8971i	−0.0569310	+	0.0572566i
$855$	375.866	+	907.422i	0.439610	+	1.06131i
$856$	−16.4762	−	38.8343i	−0.0192479	−	0.0453672i
$857$	1301.46	+	539.082i	1.51862	+	0.629034i	0.977315	−	0.211790i	$-0.0679293\pi$
$857$	1301.46	+	539.082i	1.51862	+	0.629034i	0.541308	+	0.840824i	$0.317929\pi$
$858$	117.986	−	0.336395i	0.137513	−	0.000392069i
$859$		−	219.944i		−	0.256047i	−0.991771	−	0.128023i	$-0.959137\pi$
$859$		−	219.944i		−	0.256047i	0.991771	−	0.128023i	$-0.0408632\pi$
$860$	−809.389	+	1985.99i	−0.941151	+	2.30930i
$861$	−203.754	+	84.3977i	−0.236648	+	0.0980229i
$862$	434.096	+	1039.61i	0.503591	+	1.20604i
$863$	−995.486			−1.15352			−0.576759	−	0.816914i	$-0.695683\pi$
$863$	−995.486			−1.15352			−0.576759	+	0.816914i	$0.695683\pi$
$864$	−860.128	−	341.995i	−0.995518	−	0.395827i
$865$	542.572	+	542.572i	0.627251	+	0.627251i
$866$	−3.84640	−	1349.07i	−0.00444157	−	1.55782i
$867$	632.178	+	43.1832i	0.729156	+	0.0498076i
$868$	2.71004	+	475.251i	0.00312217	+	0.547525i
$869$			77.2298i			0.0888721i
$870$	229.626	−	558.869i	0.263938	−	0.642378i
$871$		−	1394.10i		−	1.60057i
$872$	−528.794	+	1308.16i	−0.606415	+	1.50018i
$873$	15.8925	−	38.3680i	0.0182045	−	0.0439496i
$874$	227.992	+	546.013i	0.260861	+	0.624729i
$875$		−	443.543i		−	0.506906i
$876$	−4.34136	−	761.331i	−0.00495589	−	0.869099i
$877$	239.212	+	577.509i	0.272762	+	0.658506i	0.999599	−	0.0283040i	$-0.00901065\pi$
$877$	239.212	+	577.509i	0.272762	+	0.658506i	−0.726837	+	0.686810i	$0.759011\pi$
$878$	−538.732	+	1311.17i	−0.613590	+	1.49336i
$879$	899.042	−	372.395i	1.02280	−	0.423658i
$880$	2.80054	+	245.553i	0.00318243	+	0.279038i
$881$	367.147	−	152.077i	0.416739	−	0.172619i	−0.164454	−	0.986385i	$-0.552586\pi$
$881$	367.147	−	152.077i	0.416739	−	0.172619i	0.581193	+	0.813766i	$0.302586\pi$
$882$	267.223	+	265.704i	0.302974	+	0.301252i
$883$	−463.477	−	463.477i	−0.524890	−	0.524890i	0.394155	−	0.919044i	$-0.371037\pi$
$883$	−463.477	−	463.477i	−0.524890	−	0.524890i	−0.919044	+	0.394155i	$0.871037\pi$
$884$	599.124	−	843.762i	0.677742	−	0.954482i
$885$	−170.965	−	170.965i	−0.193181	−	0.193181i
$886$	−3.42432	−	1201.03i	−0.00386492	−	1.35557i
$887$	−1080.90	+	447.724i	−1.21860	+	0.504762i	−0.896965	−	0.442101i	$-0.854233\pi$
$887$	−1080.90	+	447.724i	−1.21860	+	0.504762i	−0.321637	+	0.946863i	$0.604233\pi$
$888$	9.06999	+	1060.37i	0.0102140	+	1.19411i
$889$	167.431	−	69.3524i	0.188337	−	0.0780117i
$890$	−538.109	−	1288.70i	−0.604616	−	1.44798i
$891$	−17.3801	−	41.9593i	−0.0195063	−	0.0470924i
$892$	78.9943	+	78.0985i	0.0885587	+	0.0875544i
$893$			597.094i			0.668639i
$894$	317.064	−	771.675i	0.354658	−	0.863172i
$895$	679.100	−	1639.49i	0.758771	−	1.83183i
$896$	236.257	−	103.432i	0.263680	−	0.115437i
$897$		−	365.804i		−	0.407809i
$898$	53.1742	+	127.346i	0.0592140	+	0.141810i
$899$		−	935.955i		−	1.04111i
$900$	844.526	−	4.81577i	0.938362	−	0.00535085i
$901$	162.513	+	992.827i	0.180369	+	1.10192i
$902$	−124.465	+	125.177i	−0.137988	+	0.138777i
$903$	192.934	+	192.934i	0.213659	+	0.213659i
$904$	−230.084	−	542.305i	−0.254518	−	0.599895i
$905$	58.0947			0.0641931
$906$	98.5050	+	40.4734i	0.108725	+	0.0446727i
$907$	−610.966	+	253.070i	−0.673612	+	0.279019i	−0.693154	−	0.720790i	$-0.743779\pi$
$907$	−610.966	+	253.070i	−0.673612	+	0.279019i	0.0195419	+	0.999809i	$0.493779\pi$
$908$	567.361	−	238.808i	0.624847	−	0.263004i
$909$			51.3496i			0.0564902i
$910$	377.510	+	375.364i	0.414846	+	0.412487i
$911$	−1599.16	−	662.393i	−1.75539	−	0.727105i	−0.997176	−	0.0750950i	$-0.976074\pi$
$911$	−1599.16	−	662.393i	−1.75539	−	0.727105i	−0.758210	−	0.652010i	$-0.773926\pi$
$912$	−352.287	+	878.709i	−0.386280	+	0.963497i
$913$	−45.0778	−	108.827i	−0.0493733	−	0.119198i
$914$	−0.328119	−	115.083i	−0.000358992	−	0.125912i
$915$	−300.895	−	124.635i	−0.328847	−	0.136213i
$916$	−4.10254	−	719.449i	−0.00447875	−	0.785425i
$917$	−223.180	−	223.180i	−0.243380	−	0.243380i
$918$	−958.113	−	221.911i	−1.04370	−	0.241733i
$919$	−78.0223			−0.0848991			−0.0424495	−	0.999099i	$-0.513516\pi$
$919$	−78.0223			−0.0848991			−0.0424495	+	0.999099i	$0.513516\pi$
$920$	761.331	−	6.51213i	0.827534	−	0.00707840i
$921$	−58.1597	−	140.410i	−0.0631484	−	0.152454i
$922$	950.362	−	955.797i	1.03076	−	1.03666i
$923$	−430.471	−	178.307i	−0.466382	−	0.193182i
$924$	28.9324	+	11.7914i	0.0313122	+	0.0127612i
$925$	−1165.04	−	2812.66i	−1.25950	−	3.04071i
$926$	−952.053	+	957.498i	−1.02814	+	1.03401i
$927$	−478.441	−	478.441i	−0.516117	−	0.516117i
$928$	−466.428	+	201.038i	−0.502617	+	0.216636i
$929$	1041.60	+	431.446i	1.12121	+	0.464420i	0.864784	−	0.502145i	$-0.167456\pi$
$929$	1041.60	+	431.446i	1.12121	+	0.464420i	0.256424	+	0.966564i	$0.417456\pi$
$930$	−2071.42	+	864.936i	−2.22733	+	0.930039i
$931$	857.549	−	857.549i	0.921105	−	0.921105i
$932$	−70.1297	−	166.614i	−0.0752464	−	0.178771i
$933$		−	479.565i		−	0.514003i
$934$	1049.02	−	1055.02i	1.12315	−	1.12957i
$935$	42.1479	+	257.490i	0.0450779	+	0.275391i
$936$	−357.833	+	364.007i	−0.382300	+	0.388897i
$937$	449.792	−	449.792i	0.480034	−	0.480034i	−0.425109	−	0.905142i	$-0.639764\pi$
$937$	449.792	−	449.792i	0.480034	−	0.480034i	0.905142	+	0.425109i	$0.139764\pi$
$938$	140.298	−	341.459i	0.149571	−	0.364029i
$939$	−531.560	−	531.560i	−0.566092	−	0.566092i
$940$	711.480	+	289.962i	0.756893	+	0.308471i
$941$	214.961	−	89.0396i	0.228439	−	0.0946223i	−0.265528	−	0.964103i	$-0.585546\pi$
$941$	214.961	−	89.0396i	0.228439	−	0.0946223i	0.493967	+	0.869481i	$0.335546\pi$
$942$	17.3205	+	7.11660i	0.0183870	+	0.00755478i
$943$	386.996	+	386.996i	0.410388	+	0.410388i
$944$	2.31789	+	203.234i	0.00245540	+	0.215291i
$945$	193.616	−	467.430i	0.204885	−	0.494635i
$946$	202.006	+	82.9997i	0.213537	+	0.0877375i
$947$	−511.400	+	1234.63i	−0.540021	+	1.30373i	0.384687	+	0.923047i	$0.374309\pi$
$947$	−511.400	+	1234.63i	−0.540021	+	1.30373i	−0.924708	+	0.380678i	$0.875691\pi$
$948$	272.431	+	269.342i	0.287375	+	0.284116i
$949$	−1220.52	−	505.557i	−1.28611	−	0.532726i
$950$	−7.74919	−	2717.93i	−0.00815704	−	2.86097i
$951$	346.334			0.364179
$952$	231.658	−	146.370i	0.243338	−	0.153750i
$953$		−	1286.22i		−	1.34965i	−0.737977	−	0.674826i	$-0.764219\pi$
$953$		−	1286.22i		−	1.34965i	0.737977	−	0.674826i	$-0.235781\pi$
$954$	−1.41482	−	496.231i	−0.00148305	−	0.520158i
$955$	658.455	−	1589.65i	0.689482	−	1.66456i
$956$	1851.36	−	10.5571i	1.93657	−	0.0110429i
$957$	−56.8450	−	23.5460i	−0.0593991	−	0.0246039i
$958$	311.472	+	127.977i	0.325127	+	0.133587i
$959$	382.607	+	158.481i	0.398964	+	0.165256i
$960$	875.964	+	846.496i	0.912463	+	0.881766i
$961$	−1779.27	+	1779.27i	−1.85148	+	1.85148i
$962$	1701.96	+	699.296i	1.76919	+	0.726919i
$963$	8.46051	+	20.4255i	0.00878558	+	0.0212103i
$964$	584.106	+	1387.72i	0.605919	+	1.43954i
$965$	598.810	−	598.810i	0.620528	−	0.620528i
$966$	36.8134	−	89.5971i	0.0381091	−	0.0927506i
$967$	−539.901	−	539.901i	−0.558325	−	0.558325i	0.370505	−	0.928830i	$-0.379185\pi$
$967$	−539.901	−	539.901i	−0.558325	−	0.558325i	−0.928830	+	0.370505i	$0.879185\pi$
$968$	−942.958	+	8.06570i	−0.974130	+	0.00833233i
$969$	−229.756	+	979.274i	−0.237107	+	1.01060i
$970$	−121.256	+	121.949i	−0.125006	+	0.125721i
$971$	680.017			0.700327			0.350163	−	0.936689i	$-0.386126\pi$
$971$	680.017			0.700327			0.350163	+	0.936689i	$0.386126\pi$
$972$	755.691	+	307.981i	0.777460	+	0.316853i
$973$	221.214	+	221.214i	0.227352	+	0.227352i
$974$	−1347.07	+	562.479i	−1.38303	+	0.577494i
$975$	−643.021	+	1552.39i	−0.659508	+	1.59219i
$976$	107.649	+	251.729i	0.110296	+	0.257919i
$977$	1291.84	−	1291.84i	1.32226	−	1.32226i	0.410310	−	0.911946i	$-0.365421\pi$
$977$	1291.84	−	1291.84i	1.32226	−	1.32226i	0.911946	−	0.410310i	$-0.134579\pi$
$978$	−386.920	+	389.133i	−0.395624	+	0.397886i
$979$	−131.390	+	54.4234i	−0.134208	+	0.0555908i
$980$	−605.384	−	1438.27i	−0.617739	−	1.46763i
$981$	282.985	−	683.187i	0.288466	−	0.696419i
$982$	1119.79	−	1126.19i	1.14032	−	1.14684i
$983$	570.386	−	236.262i	0.580251	−	0.240348i	−0.0731993	−	0.997317i	$-0.523321\pi$
$983$	570.386	−	236.262i	0.580251	−	0.240348i	0.653450	+	0.756970i	$0.273321\pi$
$984$	7.48968	+	875.616i	0.00761146	+	0.889854i
$985$			1907.06i			1.93610i
$986$	−457.854	+	285.649i	−0.464355	+	0.289705i
$987$	69.1183	−	69.1183i	0.0700286	−	0.0700286i
$988$	1168.18	+	1154.93i	1.18236	+	1.16896i
$989$	259.116	−	625.560i	0.261998	−	0.632518i
$990$	−0.366936	−	128.698i	−0.000370642	−	0.129998i
$991$	568.597	−	235.521i	0.573761	−	0.237660i	−0.0768859	−	0.997040i	$-0.524498\pi$
$991$	568.597	−	235.521i	0.573761	−	0.237660i	0.650647	+	0.759380i	$0.274498\pi$
$992$	1753.47	+	697.194i	1.76761	+	0.702816i
$993$	554.669	−	1339.09i	0.558579	−	1.34853i
$994$	−87.4917	−	86.9942i	−0.0880198	−	0.0875193i
$995$	1338.63			1.34536
$996$	−541.103	−	220.526i	−0.543276	−	0.221412i
$997$	60.8514	+	146.908i	0.0610345	+	0.147350i	0.951454	−	0.307790i	$-0.0995893\pi$
$997$	60.8514	+	146.908i	0.0610345	+	0.147350i	−0.890420	+	0.455140i	$0.849589\pi$
$998$	−975.825	−	400.944i	−0.977780	−	0.401748i
$999$		−	1748.70i		−	1.75045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.3.x.a.155.18	✓	280
16.3	odd	4		272.3.z.a.19.53	yes	280
17.9	even	8		272.3.z.a.43.53	yes	280
272.179	odd	8	inner	272.3.x.a.179.18	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.3.x.a.155.18	✓	280	1.1	even	1	trivial
272.3.x.a.179.18	yes	280	272.179	odd	8	inner
272.3.z.a.19.53	yes	280	16.3	odd	4
272.3.z.a.43.53	yes	280	17.9	even	8

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:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	272.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41018 + 1.41824i) q^{2} +(2.02567 + 0.839058i) q^{3} +(-0.0228089 - 3.99993i) q^{4} +(3.32204 - 8.02012i) q^{5} +(-4.04653 + 1.68966i) q^{6} +(-0.771065 + 1.86152i) q^{7} +(5.70503 + 5.60826i) q^{8} +(-2.96466 - 2.96466i) q^{9} +(6.68979 + 16.0212i) q^{10} +(1.63344 - 0.676594i) q^{11} +(3.30997 - 8.12167i) q^{12} +(-10.7609 - 10.7609i) q^{13} +(-1.55274 - 3.71862i) q^{14} +(13.4587 - 13.4587i) q^{15} +(-15.9990 + 0.182469i) q^{16} +(-16.7767 + 2.74613i) q^{17} +(8.38529 - 0.0239076i) q^{18} -26.9860i q^{19} +(-32.1557 - 13.1050i) q^{20} +(-3.12384 + 3.12384i) q^{21} +(-1.34387 + 3.27073i) q^{22} +(10.1286 + 4.19540i) q^{23} +(6.85083 + 16.1473i) q^{24} +(-35.6087 - 35.6087i) q^{25} +(30.4362 - 0.0867779i) q^{26} +(-11.0694 - 26.7239i) q^{27} +(7.46353 + 3.04175i) q^{28} +(-14.6640 - 6.07401i) q^{29} +(0.108534 + 38.0668i) q^{30} +(22.5662 + 54.4797i) q^{31} +(22.3026 - 22.9477i) q^{32} +3.87651 q^{33} +(19.7635 - 27.6660i) q^{34} +(12.3681 + 12.3681i) q^{35} +(-11.7908 + 11.9261i) q^{36} +(55.8530 + 23.1351i) q^{37} +(38.2726 + 38.0550i) q^{38} +(-12.7689 - 30.8269i) q^{39} +(63.9313 - 27.1241i) q^{40} +(46.1214 + 19.1041i) q^{41} +(-0.0251913 - 8.83552i) q^{42} -61.7618i q^{43} +(-2.74359 - 6.51823i) q^{44} +(-33.6256 + 13.9282i) q^{45} +(-20.2332 + 8.44853i) q^{46} -22.1261 q^{47} +(-32.5616 - 13.0544i) q^{48} +(31.7775 + 31.7775i) q^{49} +(100.716 - 0.287156i) q^{50} +(-36.2882 - 8.51390i) q^{51} +(-42.7973 + 43.2882i) q^{52} -59.1788i q^{53} +(53.5107 + 21.9863i) q^{54} -15.3481i q^{55} +(-14.8388 + 6.29567i) q^{56} +(22.6428 - 54.6646i) q^{57} +(29.2932 - 12.2316i) q^{58} -12.7030i q^{59} +(-54.1409 - 53.5269i) q^{60} +(-6.54820 - 15.8088i) q^{61} +(-109.088 - 44.8216i) q^{62} +(7.80470 - 3.23281i) q^{63} +(1.09478 + 63.9906i) q^{64} +(-122.051 + 50.5554i) q^{65} +(-5.46656 + 5.49782i) q^{66} +(64.7763 + 64.7763i) q^{67} +(11.3670 + 67.0432i) q^{68} +(16.9970 + 16.9970i) q^{69} +(-34.9820 + 0.0997387i) q^{70} +(28.2866 - 11.7167i) q^{71} +(-0.286889 - 33.5401i) q^{72} +(80.2017 - 33.2206i) q^{73} +(-111.574 + 46.5884i) q^{74} +(-42.2535 - 102.009i) q^{75} +(-107.942 + 0.615523i) q^{76} +3.56237i q^{77} +(61.7264 + 25.3620i) q^{78} +(-16.7162 + 40.3564i) q^{79} +(-51.6858 + 128.920i) q^{80} -25.6877i q^{81} +(-92.1335 + 38.4711i) q^{82} -66.6246i q^{83} +(12.5664 + 12.4239i) q^{84} +(-33.7087 + 143.674i) q^{85} +(87.5930 + 87.0950i) q^{86} +(-24.6078 - 24.6078i) q^{87} +(13.1134 + 5.30078i) q^{88} -80.4373 q^{89} +(27.6645 - 67.3304i) q^{90} +(28.3288 - 11.7342i) q^{91} +(16.5503 - 40.6094i) q^{92} +129.292i q^{93} +(31.2016 - 31.3801i) q^{94} +(-216.431 - 89.6487i) q^{95} +(64.4320 - 27.7712i) q^{96} +(3.79056 + 9.15123i) q^{97} +(-89.8801 + 0.256261i) q^{98} +(-6.84847 - 2.83673i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 4 q^{2} - 4 q^{3} - 4 q^{5} + 12 q^{6} - 8 q^{7} - 4 q^{8} + 12 q^{10} - 4 q^{11} - 24 q^{12} + 40 q^{14} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 4 q^{20} + 4 q^{22} - 8 q^{23} - 324 q^{24} - 132 q^{26}+ \cdots + 284 q^{99}+O(q^{100}) \) 280 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 + 12 * q^6 - 8 * q^7 - 4 * q^8 + 12 * q^10 - 4 * q^11 - 24 * q^12 + 40 * q^14 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 4 * q^20 + 4 * q^22 - 8 * q^23 - 324 * q^24 - 132 * q^26 - 40 * q^27 + 212 * q^28 - 4 * q^29 - 256 * q^31 - 124 * q^32 - 16 * q^33 - 148 * q^34 - 8 * q^35 - 164 * q^36 - 4 * q^37 + 32 * q^38 - 8 * q^39 - 40 * q^40 + 448 * q^42 - 40 * q^44 - 68 * q^45 - 228 * q^46 - 48 * q^48 - 8 * q^49 - 8 * q^50 - 164 * q^51 - 8 * q^52 - 48 * q^54 + 176 * q^56 + 72 * q^57 - 20 * q^58 - 552 * q^60 - 68 * q^61 + 176 * q^62 - 640 * q^63 + 24 * q^65 + 228 * q^66 - 8 * q^67 - 368 * q^68 - 8 * q^69 + 560 * q^70 + 504 * q^71 + 520 * q^72 - 156 * q^74 + 60 * q^75 + 664 * q^76 + 600 * q^78 + 304 * q^80 + 212 * q^82 - 8 * q^84 - 4 * q^85 + 1136 * q^86 - 8 * q^87 + 408 * q^88 - 200 * q^90 + 384 * q^91 + 60 * q^92 + 584 * q^94 + 200 * q^95 - 112 * q^96 - 8 * q^97 - 624 * q^98 + 284 * q^99

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