LMFDB - Embedded newform 27.3.f.a.11.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,3,Mod(2,27)] 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("27.2"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, degree $6$, 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:	$0.735696713773$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	27.11
Dual form			27.3.f.a.5.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.13670 - 2.54642i) q^{2} +(-2.03568 + 2.20363i) q^{3} +(-1.22417 - 6.94260i) q^{4} +(-2.35247 + 6.46335i) q^{5} +(1.26173 + 9.89219i) q^{6} +(1.10811 - 6.28443i) q^{7} +(-8.77937 - 5.06877i) q^{8} +(-0.712002 - 8.97179i) q^{9} +(11.4319 + 19.8006i) q^{10} +(0.425636 + 1.16942i) q^{11} +(17.7910 + 11.4353i) q^{12} +(-4.09039 + 3.43225i) q^{13} +(-13.6351 - 16.2496i) q^{14} +(-9.45398 - 18.3413i) q^{15} +(-5.16785 + 1.88094i) q^{16} +(-13.7418 + 7.93385i) q^{17} +(-24.3672 - 17.3569i) q^{18} +(6.78917 - 11.7592i) q^{19} +(47.7523 + 8.42002i) q^{20} +(11.5928 + 15.2350i) q^{21} +(3.88729 + 1.41486i) q^{22} +(24.4347 - 4.30850i) q^{23} +(29.0417 - 9.02811i) q^{24} +(-17.0897 - 14.3399i) q^{25} +17.7495i q^{26} +(21.2200 + 16.6947i) q^{27} -44.9868 q^{28} +(-19.9186 + 23.7381i) q^{29} +(-66.9048 - 15.1160i) q^{30} +(-2.75731 - 15.6375i) q^{31} +(7.61653 - 20.9262i) q^{32} +(-3.44344 - 1.44263i) q^{33} +(-9.15924 + 51.9446i) q^{34} +(38.0116 + 21.9460i) q^{35} +(-61.4160 + 15.9261i) q^{36} +(26.0365 + 45.0965i) q^{37} +(-15.4374 - 42.4139i) q^{38} +(0.763322 - 16.0007i) q^{39} +(53.4144 - 44.8200i) q^{40} +(-0.694475 - 0.827643i) q^{41} +(63.5649 + 3.03240i) q^{42} +(-45.3904 + 16.5207i) q^{43} +(7.59780 - 4.38659i) q^{44} +(59.6628 + 16.5039i) q^{45} +(41.2384 - 71.4270i) q^{46} +(-56.7291 - 10.0029i) q^{47} +(6.37518 - 15.2170i) q^{48} +(7.77884 + 2.83127i) q^{49} +(-73.0309 + 12.8773i) q^{50} +(10.4907 - 46.4327i) q^{51} +(28.8361 + 24.1963i) q^{52} -13.8414i q^{53} +(87.8523 - 18.3633i) q^{54} -8.55969 q^{55} +(-41.5829 + 49.5566i) q^{56} +(12.0924 + 38.8988i) q^{57} +(17.8870 + 101.442i) q^{58} +(20.6246 - 56.6655i) q^{59} +(-115.763 + 88.0881i) q^{60} +(17.5357 - 99.4497i) q^{61} +(-45.7111 - 26.3913i) q^{62} +(-57.1715 - 5.46725i) q^{63} +(-48.0117 - 83.1587i) q^{64} +(-12.5613 - 34.5119i) q^{65} +(-11.0311 + 5.68597i) q^{66} +(-60.2302 + 50.5391i) q^{67} +(71.9039 + 85.6917i) q^{68} +(-40.2470 + 62.6160i) q^{69} +(137.103 - 49.9014i) q^{70} +(39.7545 - 22.9523i) q^{71} +(-39.2251 + 82.3757i) q^{72} +(-34.4926 + 59.7430i) q^{73} +(170.466 + 30.0578i) q^{74} +(66.3891 - 8.46783i) q^{75} +(-89.9505 - 32.7393i) q^{76} +(7.82081 - 1.37902i) q^{77} +(-39.1134 - 36.1324i) q^{78} +(30.2928 + 25.4187i) q^{79} -37.8265i q^{80} +(-79.9861 + 12.7759i) q^{81} -3.59141 q^{82} +(-27.1277 + 32.3296i) q^{83} +(91.5788 - 99.1344i) q^{84} +(-18.9520 - 107.482i) q^{85} +(-54.9168 + 150.883i) q^{86} +(-11.7621 - 92.2165i) q^{87} +(2.19073 - 12.4243i) q^{88} +(-61.8262 - 35.6954i) q^{89} +(169.507 - 116.662i) q^{90} +(17.0371 + 29.5091i) q^{91} +(-59.8245 - 164.366i) q^{92} +(40.0723 + 25.7569i) q^{93} +(-146.684 + 123.083i) q^{94} +(60.0324 + 71.5439i) q^{95} +(30.6089 + 59.3832i) q^{96} +(-1.06372 + 0.387161i) q^{97} +(23.8306 - 13.7586i) q^{98} +(10.1888 - 4.65135i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8} - 3 q^{10} - 6 q^{11} - 15 q^{12} - 6 q^{13} - 15 q^{14} - 9 q^{15} - 18 q^{16} - 9 q^{17} + 63 q^{18} - 3 q^{19} + 213 q^{20}+ \cdots + 513 q^{99}+O(q^{100}) $ 30 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 15 * q^5 - 18 * q^6 - 6 * q^7 - 9 * q^8 - 3 * q^10 - 6 * q^11 - 15 * q^12 - 6 * q^13 - 15 * q^14 - 9 * q^15 - 18 * q^16 - 9 * q^17 + 63 * q^18 - 3 * q^19 + 213 * q^20 + 132 * q^21 - 42 * q^22 + 120 * q^23 + 144 * q^24 - 15 * q^25 - 90 * q^27 - 12 * q^28 - 168 * q^29 - 243 * q^30 + 39 * q^31 - 360 * q^32 - 207 * q^33 + 54 * q^34 - 252 * q^35 - 360 * q^36 - 3 * q^37 - 84 * q^38 + 15 * q^39 - 33 * q^40 + 228 * q^41 + 486 * q^42 - 96 * q^43 + 639 * q^44 + 477 * q^45 - 3 * q^46 + 399 * q^47 + 453 * q^48 - 78 * q^49 + 303 * q^50 + 36 * q^51 - 9 * q^52 - 54 * q^54 - 12 * q^55 - 393 * q^56 - 192 * q^57 + 129 * q^58 - 474 * q^59 - 846 * q^60 + 138 * q^61 - 900 * q^62 - 585 * q^63 - 51 * q^64 - 411 * q^65 - 423 * q^66 + 354 * q^67 + 99 * q^68 + 99 * q^69 + 489 * q^70 + 315 * q^71 + 720 * q^72 - 66 * q^73 + 321 * q^74 + 255 * q^75 + 258 * q^76 + 201 * q^77 + 180 * q^78 + 30 * q^79 + 36 * q^81 - 12 * q^82 - 33 * q^83 - 588 * q^84 - 261 * q^85 - 258 * q^86 - 279 * q^87 - 642 * q^88 + 72 * q^89 + 288 * q^90 + 96 * q^91 - 3 * q^92 + 591 * q^93 - 861 * q^94 + 681 * q^95 + 270 * q^96 - 582 * q^97 + 882 * q^98 + 513 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	2.13670	−	2.54642i	1.06835	−	1.27321i	0.108076	−	0.994143i	$-0.465531\pi$
$2$	2.13670	−	2.54642i	1.06835	−	1.27321i	0.960272	−	0.279065i	$-0.0900245\pi$
$3$	−2.03568	+	2.20363i	−0.678560	+	0.734545i
$3$	−2.03568	+	2.20363i	−0.678560	+	0.734545i
$4$	−1.22417	−	6.94260i	−0.306042	−	1.73565i
$5$	−2.35247	+	6.46335i	−0.470493	+	1.29267i	0.446863	+	0.894602i	$0.352541\pi$
$5$	−2.35247	+	6.46335i	−0.470493	+	1.29267i	−0.917356	+	0.398067i	$0.869681\pi$
$6$	1.26173	+	9.89219i	0.210289	+	1.64870i
$7$	1.10811	−	6.28443i	0.158302	−	0.897775i	−0.797403	−	0.603448i	$-0.793793\pi$
$7$	1.10811	−	6.28443i	0.158302	−	0.897775i	0.955705	−	0.294328i	$-0.0950957\pi$
$8$	−8.77937	−	5.06877i	−1.09742	−	0.633597i
$9$	−0.712002	−	8.97179i	−0.0791113	−	0.996866i
$10$	11.4319	+	19.8006i	1.14319	+	1.98006i
$11$	0.425636	+	1.16942i	0.0386941	+	0.106311i	0.957535	−	0.288317i	$-0.0930956\pi$
$11$	0.425636	+	1.16942i	0.0386941	+	0.106311i	−0.918841	+	0.394628i	$0.870873\pi$
$12$	17.7910	+	11.4353i	1.48258	+	0.952943i
$13$	−4.09039	+	3.43225i	−0.314646	+	0.264019i	−0.786409	−	0.617706i	$-0.788062\pi$
$13$	−4.09039	+	3.43225i	−0.314646	+	0.264019i	0.471763	+	0.881725i	$0.343618\pi$
$14$	−13.6351	−	16.2496i	−0.973933	−	1.16069i
$15$	−9.45398	−	18.3413i	−0.630265	−	1.22275i
$16$	−5.16785	+	1.88094i	−0.322990	+	0.117559i
$17$	−13.7418	+	7.93385i	−0.808343	+	0.466697i	−0.846380	−	0.532579i	$-0.821223\pi$
$17$	−13.7418	+	7.93385i	−0.808343	+	0.466697i	0.0380373	+	0.999276i	$0.487889\pi$
$18$	−24.3672	−	17.3569i	−1.35374	−	0.964275i
$19$	6.78917	−	11.7592i	0.357325	−	0.618905i	−0.630188	−	0.776442i	$-0.717022\pi$
$19$	6.78917	−	11.7592i	0.357325	−	0.618905i	0.987513	+	0.157538i	$0.0503556\pi$
$20$	47.7523	+	8.42002i	2.38761	+	0.421001i
$21$	11.5928	+	15.2350i	0.552038	+	0.725475i
$22$	3.88729	+	1.41486i	0.176695	+	0.0643118i
$23$	24.4347	−	4.30850i	1.06238	−	0.187326i	0.384968	−	0.922930i	$-0.374213\pi$
$23$	24.4347	−	4.30850i	1.06238	−	0.187326i	0.677412	+	0.735604i	$0.263101\pi$
$24$	29.0417	−	9.02811i	1.21007	−	0.376171i
$25$	−17.0897	−	14.3399i	−0.683587	−	0.573597i
$26$			17.7495i			0.682674i
$27$	21.2200	+	16.6947i	0.785924	+	0.618323i
$28$	−44.9868			−1.60667
$29$	−19.9186	+	23.7381i	−0.686849	+	0.818554i	−0.990971	−	0.134079i	$-0.957192\pi$
$29$	−19.9186	+	23.7381i	−0.686849	+	0.818554i	0.304122	+	0.952633i	$0.401637\pi$
$30$	−66.9048	−	15.1160i	−2.23016	−	0.503867i
$31$	−2.75731	−	15.6375i	−0.0889455	−	0.504435i	−0.996435	−	0.0843610i	$-0.973115\pi$
$31$	−2.75731	−	15.6375i	−0.0889455	−	0.504435i	0.907490	−	0.420074i	$-0.137996\pi$
$32$	7.61653	−	20.9262i	0.238016	−	0.653945i
$33$	−3.44344	−	1.44263i	−0.104347	−	0.0437161i
$34$	−9.15924	+	51.9446i	−0.269389	+	1.52778i
$35$	38.0116	+	21.9460i	1.08605	+	0.627029i
$36$	−61.4160	+	15.9261i	−1.70600	+	0.442392i
$37$	26.0365	+	45.0965i	0.703688	+	1.21882i	0.967163	+	0.254158i	$0.0817982\pi$
$37$	26.0365	+	45.0965i	0.703688	+	1.21882i	−0.263474	+	0.964666i	$0.584868\pi$
$38$	−15.4374	−	42.4139i	−0.406247	−	1.11615i
$39$	0.763322	−	16.0007i	0.0195724	−	0.410274i
$40$	53.4144	−	44.8200i	1.33536	−	1.12050i
$41$	−0.694475	−	0.827643i	−0.0169384	−	0.0201864i	0.757509	−	0.652825i	$-0.226416\pi$
$41$	−0.694475	−	0.827643i	−0.0169384	−	0.0201864i	−0.774447	+	0.632639i	$0.781972\pi$
$42$	63.5649	+	3.03240i	1.51345	+	0.0722000i
$43$	−45.3904	+	16.5207i	−1.05559	+	0.384203i	−0.810770	−	0.585365i	$-0.800951\pi$
$43$	−45.3904	+	16.5207i	−1.05559	+	0.384203i	−0.244820	+	0.969569i	$0.578729\pi$
$44$	7.59780	−	4.38659i	0.172677	−	0.0996953i
$45$	59.6628	+	16.5039i	1.32584	+	0.366754i
$46$	41.2384	−	71.4270i	0.896487	−	1.55276i
$47$	−56.7291	−	10.0029i	−1.20700	−	0.212827i	−0.466279	−	0.884638i	$-0.654406\pi$
$47$	−56.7291	−	10.0029i	−1.20700	−	0.212827i	−0.740723	+	0.671811i	$0.765517\pi$
$48$	6.37518	−	15.2170i	0.132816	−	0.317022i
$49$	7.77884	+	2.83127i	0.158752	+	0.0577809i
$50$	−73.0309	+	12.8773i	−1.46062	+	0.257546i
$51$	10.4907	−	46.4327i	0.205700	−	0.910446i
$52$	28.8361	+	24.1963i	0.554540	+	0.465314i
$53$		−	13.8414i		−	0.261159i	−0.991438	−	0.130579i	$-0.958316\pi$
$53$		−	13.8414i		−	0.261159i	0.991438	−	0.130579i	$-0.0416837\pi$
$54$	87.8523	−	18.3633i	1.62689	−	0.340060i
$55$	−8.55969			−0.155631
$56$	−41.5829	+	49.5566i	−0.742552	+	0.884939i
$57$	12.0924	+	38.8988i	0.212147	+	0.682435i
$58$	17.8870	+	101.442i	0.308396	+	1.74900i
$59$	20.6246	−	56.6655i	0.349569	−	0.960432i	−0.632938	−	0.774203i	$-0.718151\pi$
$59$	20.6246	−	56.6655i	0.349569	−	0.960432i	0.982506	−	0.186229i	$-0.0596268\pi$
$60$	−115.763	+	88.0881i	−1.92938	+	1.46813i
$61$	17.5357	−	99.4497i	0.287470	−	1.63032i	−0.408857	−	0.912598i	$-0.634073\pi$
$61$	17.5357	−	99.4497i	0.287470	−	1.63032i	0.696327	−	0.717725i	$-0.254816\pi$
$62$	−45.7111	−	26.3913i	−0.737276	−	0.425666i
$63$	−57.1715	−	5.46725i	−0.907485	−	0.0867817i
$64$	−48.0117	−	83.1587i	−0.750183	−	1.29935i
$65$	−12.5613	−	34.5119i	−0.193251	−	0.530952i
$66$	−11.0311	+	5.68597i	−0.167138	+	0.0861510i
$67$	−60.2302	+	50.5391i	−0.898958	+	0.754315i	−0.969986	−	0.243159i	$-0.921816\pi$
$67$	−60.2302	+	50.5391i	−0.898958	+	0.754315i	0.0710284	+	0.997474i	$0.477372\pi$
$68$	71.9039	+	85.6917i	1.05741	+	1.26017i
$69$	−40.2470	+	62.6160i	−0.583290	+	0.907478i
$70$	137.103	−	49.9014i	1.95862	−	0.712878i
$71$	39.7545	−	22.9523i	0.559922	−	0.323271i	−0.193192	−	0.981161i	$-0.561884\pi$
$71$	39.7545	−	22.9523i	0.559922	−	0.323271i	0.753114	+	0.657890i	$0.228551\pi$
$72$	−39.2251	+	82.3757i	−0.544793	+	1.14411i
$73$	−34.4926	+	59.7430i	−0.472502	+	0.818397i	−0.999505	−	0.0314663i	$-0.989982\pi$
$73$	−34.4926	+	59.7430i	−0.472502	+	0.818397i	0.527003	+	0.849863i	$0.323316\pi$
$74$	170.466	+	30.0578i	2.30360	+	0.406187i
$75$	66.3891	−	8.46783i	0.885188	−	0.112904i
$76$	−89.9505	−	32.7393i	−1.18356	−	0.430780i
$77$	7.82081	−	1.37902i	0.101569	−	0.0179094i
$78$	−39.1134	−	36.1324i	−0.501454	−	0.463235i
$79$	30.2928	+	25.4187i	0.383453	+	0.321756i	0.814056	−	0.580786i	$-0.197255\pi$
$79$	30.2928	+	25.4187i	0.383453	+	0.321756i	−0.430603	+	0.902541i	$0.641699\pi$
$80$		−	37.8265i		−	0.472831i
$81$	−79.9861	+	12.7759i	−0.987483	+	0.157727i
$82$	−3.59141			−0.0437976
$83$	−27.1277	+	32.3296i	−0.326840	+	0.389513i	−0.904294	−	0.426910i	$-0.859602\pi$
$83$	−27.1277	+	32.3296i	−0.326840	+	0.389513i	0.577454	+	0.816423i	$0.304046\pi$
$84$	91.5788	−	99.1344i	1.09022	−	1.18017i
$85$	−18.9520	−	107.482i	−0.222965	−	1.26450i
$86$	−54.9168	+	150.883i	−0.638567	+	1.75445i
$87$	−11.7621	−	92.2165i	−0.135196	−	1.05996i
$88$	2.19073	−	12.4243i	0.0248947	−	0.141185i
$89$	−61.8262	−	35.6954i	−0.694676	−	0.401072i	0.110685	−	0.993856i	$-0.464695\pi$
$89$	−61.8262	−	35.6954i	−0.694676	−	0.401072i	−0.805361	+	0.592784i	$0.798029\pi$
$90$	169.507	−	116.662i	1.88341	−	1.29625i
$91$	17.0371	+	29.5091i	0.187221	+	0.324276i
$92$	−59.8245	−	164.366i	−0.650266	−	1.78659i
$93$	40.0723	+	25.7569i	0.430885	+	0.276955i
$94$	−146.684	+	123.083i	−1.56047	+	1.30939i
$95$	60.0324	+	71.5439i	0.631920	+	0.753093i
$96$	30.6089	+	59.3832i	0.318843	+	0.618575i
$97$	−1.06372	+	0.387161i	−0.0109662	+	0.00399135i	−0.347497	−	0.937681i	$-0.612968\pi$
$97$	−1.06372	+	0.387161i	−0.0109662	+	0.00399135i	0.336531	+	0.941672i	$0.390746\pi$
$98$	23.8306	−	13.7586i	0.243169	−	0.140394i
$99$	10.1888	−	4.65135i	0.102917	−	0.0469833i
$100$	−78.6359	+	136.201i	−0.786359	+	1.36201i
$101$	11.1819	+	1.97167i	0.110712	+	0.0195215i	0.228730	−	0.973490i	$-0.426543\pi$
$101$	11.1819	+	1.97167i	0.110712	+	0.0195215i	−0.118018	+	0.993011i	$0.537654\pi$
$102$	−95.8216	−	125.926i	−0.939428	−	1.23457i
$103$	154.650	+	56.2881i	1.50146	+	0.546486i	0.956438	−	0.291937i	$-0.0942997\pi$
$103$	154.650	+	56.2881i	1.50146	+	0.546486i	0.545020	+	0.838423i	$0.316522\pi$
$104$	53.3084	−	9.39971i	0.512581	−	0.0903818i
$105$	−125.741	+	39.0886i	−1.19753	+	0.372272i
$106$	−35.2460	−	29.5749i	−0.332509	−	0.279008i
$107$		−	107.863i		−	1.00807i	−0.863685	−	0.504033i	$-0.831849\pi$
$107$		−	107.863i		−	1.00807i	0.863685	−	0.504033i	$-0.168151\pi$
$108$	89.9280	−	167.759i	0.832667	−	1.55332i
$109$	176.312			1.61754			0.808770	−	0.588125i	$-0.200134\pi$
$109$	176.312			1.61754			0.808770	+	0.588125i	$0.200134\pi$
$110$	−18.2895	+	21.7965i	−0.166268	+	0.198150i
$111$	−152.378	−	34.4273i	−1.37278	−	0.310155i
$112$	6.09408	+	34.5613i	0.0544114	+	0.308583i
$113$	−42.8327	+	117.682i	−0.379050	+	1.04143i	0.592701	+	0.805423i	$0.298062\pi$
$113$	−42.8327	+	117.682i	−0.379050	+	1.04143i	−0.971751	+	0.236009i	$0.924161\pi$
$114$	124.890	+	52.3228i	1.09553	+	0.458972i
$115$	−29.6345	+	168.066i	−0.257692	+	1.46144i
$116$	189.188	+	109.228i	1.63093	+	0.941617i
$117$	33.7058	+	34.2544i	0.288084	+	0.292773i
$118$	−100.226	−	173.596i	−0.849369	−	1.47115i
$119$	34.6322	+	95.1511i	0.291027	+	0.799589i
$120$	−9.96785	+	208.945i	−0.0830654	+	1.74121i
$121$	91.5050	−	76.7818i	0.756240	−	0.634560i
$122$	−215.772	−	257.147i	−1.76862	−	2.10776i
$123$	3.23755	+	0.154449i	0.0263216	+	0.00125569i
$124$	−105.189	+	38.2858i	−0.848302	+	0.308757i
$125$	−16.0295	+	9.25462i	−0.128236	+	0.0740369i
$126$	−136.080	+	133.901i	−1.08000	+	1.06270i
$127$	−0.644295	+	1.11595i	−0.00507319	+	0.00878702i	−0.868551	−	0.495600i	$-0.834948\pi$
$127$	−0.644295	+	1.11595i	−0.00507319	+	0.00878702i	0.863478	+	0.504387i	$0.168282\pi$
$128$	−226.619	−	39.9591i	−1.77046	−	0.312181i
$129$	55.9947	−	133.655i	0.434067	−	1.03608i
$130$	−114.721	−	41.7551i	−0.882472	−	0.321193i
$131$	90.5024	−	15.9580i	0.690858	−	0.121817i	0.182814	−	0.983148i	$-0.441480\pi$
$131$	90.5024	−	15.9580i	0.690858	−	0.121817i	0.508045	+	0.861331i	$0.330368\pi$
$132$	−5.80026	+	25.6725i	−0.0439414	+	0.194488i
$133$	−66.3766	−	55.6966i	−0.499072	−	0.418771i
$134$			261.358i			1.95043i
$135$	−157.823	+	97.8782i	−1.16906	+	0.725024i
$136$	160.860			1.18279
$137$	37.9669	−	45.2471i	0.277130	−	0.330271i	−0.609469	−	0.792810i	$-0.708617\pi$
$137$	37.9669	−	45.2471i	0.277130	−	0.330271i	0.886599	+	0.462539i	$0.153062\pi$
$138$	73.4507	+	236.277i	0.532251	+	1.71215i
$139$	−8.76836	−	49.7279i	−0.0630817	−	0.357754i	−0.999967	−	0.00811749i	$-0.997416\pi$
$139$	−8.76836	−	49.7279i	−0.0630817	−	0.357754i	0.936885	−	0.349637i	$-0.113695\pi$
$140$	105.830	−	290.765i	0.755928	−	2.07690i
$141$	137.525	−	104.647i	0.975355	−	0.742180i
$142$	26.4973	−	150.273i	0.186600	−	1.05826i
$143$	−5.75477	−	3.32252i	−0.0402432	−	0.0232344i
$144$	20.5549	+	45.0256i	0.142743	+	0.312678i
$145$	−106.570	−	184.584i	−0.734963	−	1.27299i
$146$	78.4302	+	215.485i	0.537193	+	1.47593i
$147$	−22.0743	+	11.3782i	−0.150165	+	0.0774024i
$148$	281.214	−	235.967i	1.90009	−	1.59437i
$149$	−46.7223	−	55.6815i	−0.313573	−	0.373701i	0.586121	−	0.810224i	$-0.300654\pi$
$149$	−46.7223	−	55.6815i	−0.313573	−	0.373701i	−0.899693	+	0.436522i	$0.856210\pi$
$150$	120.291	−	187.147i	0.801938	−	1.24765i
$151$	3.18866	−	1.16058i	0.0211170	−	0.00768595i	−0.331440	−	0.943476i	$-0.607534\pi$
$151$	3.18866	−	1.16058i	0.0211170	−	0.00768595i	0.352557	+	0.935790i	$0.385312\pi$
$152$	−119.209	+	68.8255i	−0.784272	+	0.452800i
$153$	80.9650	+	117.640i	0.529183	+	0.768888i
$154$	13.1991	−	22.8616i	0.0857087	−	0.148452i
$155$	107.557	+	18.9652i	0.693917	+	0.122356i
$156$	−112.021	+	14.2881i	−0.718083	+	0.0915904i
$157$	241.142	+	87.7685i	1.53594	+	0.559035i	0.965066	−	0.262005i	$-0.0843838\pi$
$157$	241.142	+	87.7685i	1.53594	+	0.559035i	0.570870	+	0.821040i	$0.306606\pi$
$158$	129.453	−	22.8261i	0.819324	−	0.144469i
$159$	30.5014	+	28.1767i	0.191833	+	0.177212i
$160$	117.336	+	98.4565i	0.733349	+	0.615353i
$161$		−	158.333i		−	0.983433i
$162$	−138.373	+	230.976i	−0.854157	+	1.42578i
$163$	−265.211			−1.62706			−0.813530	−	0.581523i	$-0.802457\pi$
$163$	−265.211			−1.62706			−0.813530	+	0.581523i	$0.802457\pi$
$164$	−4.89584	+	5.83464i	−0.0298527	+	0.0355771i
$165$	17.4248	−	18.8624i	0.105605	−	0.114318i
$166$	24.3608	+	138.157i	0.146752	+	0.832271i
$167$	−1.10732	+	3.04234i	−0.00663066	+	0.0182176i	−0.942964	−	0.332895i	$-0.891974\pi$
$167$	−1.10732	+	3.04234i	−0.00663066	+	0.0182176i	0.936333	+	0.351113i	$0.114197\pi$
$168$	−24.5550	−	192.515i	−0.146161	−	1.14592i
$169$	−24.3955	+	138.354i	−0.144352	+	0.818663i
$170$	−314.189	−	181.397i	−1.84817	−	1.06704i
$171$	−110.335	−	52.5385i	−0.645233	−	0.307242i
$172$	170.262	+	294.903i	0.989898	+	1.71455i
$173$	−65.8301	−	180.867i	−0.380521	−	1.04547i	−0.971138	−	0.238520i	$-0.923338\pi$
$173$	−65.8301	−	180.867i	−0.380521	−	1.04547i	0.590617	−	0.806952i	$-0.298884\pi$
$174$	−259.953	−	167.087i	−1.49399	−	0.960273i
$175$	−109.056	+	91.5085i	−0.623175	+	0.522906i
$176$	−4.39924	−	5.24281i	−0.0249957	−	0.0297887i
$177$	82.8850	+	160.802i	0.468277	+	0.908485i
$178$	−222.999	+	81.1650i	−1.25280	+	0.455983i
$179$	−191.363	+	110.484i	−1.06907	+	0.617228i	−0.927927	−	0.372762i	$-0.878411\pi$
$179$	−191.363	+	110.484i	−1.06907	+	0.617228i	−0.141142	+	0.989989i	$0.545078\pi$
$180$	41.5429	−	434.419i	0.230794	−	2.41344i
$181$	−72.7860	+	126.069i	−0.402133	+	0.696514i	−0.993983	−	0.109534i	$-0.965064\pi$
$181$	−72.7860	+	126.069i	−0.402133	+	0.696514i	0.591851	+	0.806048i	$0.298398\pi$
$182$	111.546	+	19.6685i	0.612887	+	0.108069i
$183$	183.454	+	241.090i	1.00248	+	1.31743i
$184$	−236.361	−	86.0282i	−1.28457	−	0.467545i
$185$	−352.724	+	62.1948i	−1.90662	+	0.336188i
$186$	151.210	−	47.0062i	0.812957	−	0.252721i
$187$	−15.1270	−	12.6931i	−0.0808933	−	0.0678775i
$188$			406.093i			2.16007i
$189$	128.431	−	114.856i	0.679528	−	0.607701i
$190$	310.452			1.63396
$191$	50.2313	−	59.8633i	0.262991	−	0.313420i	−0.618349	−	0.785904i	$-0.712198\pi$
$191$	50.2313	−	59.8633i	0.262991	−	0.313420i	0.881339	+	0.472484i	$0.156642\pi$
$192$	280.988	+	63.4844i	1.46348	+	0.330648i
$193$	−38.8821	−	220.511i	−0.201462	−	1.14255i	−0.902911	−	0.429827i	$-0.858575\pi$
$193$	−38.8821	−	220.511i	−0.201462	−	1.14255i	0.701450	−	0.712719i	$-0.252537\pi$
$194$	−1.28697	+	3.53591i	−0.00663385	+	0.0182263i
$195$	101.622	+	42.5747i	0.521140	+	0.218332i
$196$	10.1337	−	57.4713i	0.0517028	−	0.293221i
$197$	299.369	+	172.841i	1.51964	+	0.877364i	0.999732	+	0.0231411i	$0.00736671\pi$
$197$	299.369	+	172.841i	1.51964	+	0.877364i	0.519907	+	0.854223i	$0.325967\pi$
$198$	9.92606	−	35.8834i	0.0501316	−	0.181229i
$199$	78.7794	+	136.450i	0.395876	+	0.685678i	0.993213	−	0.116313i	$-0.0371075\pi$
$199$	78.7794	+	136.450i	0.395876	+	0.685678i	−0.597336	+	0.801991i	$0.703774\pi$
$200$	77.3507	+	212.519i	0.386754	+	1.06260i
$201$	11.2398	−	235.607i	0.0559192	−	1.17217i
$202$	28.9130	−	24.2609i	0.143134	−	0.120104i
$203$	127.108	+	151.482i	0.626148	+	0.746214i
$204$	−335.206	−	15.9912i	−1.64317	−	0.0783883i
$205$	6.98308	−	2.54163i	0.0340638	−	0.0123982i
$206$	473.773	−	273.533i	2.29987	−	1.32783i
$207$	−56.0526	−	216.156i	−0.270785	−	1.04423i
$208$	14.6827	−	25.4311i	0.0705897	−	0.122265i
$209$	16.6412	+	2.93429i	0.0796229	+	0.0140397i
$210$	−169.134	+	403.708i	−0.805398	+	1.92242i
$211$	−349.874	−	127.344i	−1.65817	−	0.603524i	−0.668095	−	0.744076i	$-0.732890\pi$
$211$	−349.874	−	127.344i	−1.65817	−	0.603524i	−0.990073	+	0.140552i	$0.955112\pi$
$212$	−96.0954	+	16.9442i	−0.453280	+	0.0799255i
$213$	−30.3491	+	134.328i	−0.142484	+	0.630647i
$214$	−274.664	−	230.470i	−1.28348	−	1.07696i
$215$		−	332.238i		−	1.54529i
$216$	−101.676	−	254.128i	−0.470723	−	1.17652i
$217$	−101.328			−0.466950
$218$	376.725	−	448.963i	1.72810	−	2.05947i
$219$	−61.4356	−	197.627i	−0.280528	−	0.902406i
$220$	10.4785	+	59.4265i	0.0476296	+	0.270121i
$221$	28.9786	−	79.6179i	0.131125	−	0.360262i
$222$	−413.252	+	314.457i	−1.86149	+	1.41647i
$223$	16.2189	−	91.9821i	0.0727306	−	0.412476i	−0.926605	−	0.376036i	$-0.877287\pi$
$223$	16.2189	−	91.9821i	0.0727306	−	0.412476i	0.999336	−	0.0364403i	$-0.0116019\pi$
$224$	−123.069	−	71.0541i	−0.549417	−	0.317206i
$225$	−116.487	+	163.535i	−0.517720	+	0.726822i
$226$	208.146	+	360.520i	0.921001	+	1.59522i
$227$	124.898	+	343.154i	0.550211	+	1.51169i	0.833423	+	0.552636i	$0.186378\pi$
$227$	124.898	+	343.154i	0.550211	+	1.51169i	−0.283211	+	0.959058i	$0.591400\pi$
$228$	255.256	−	131.571i	1.11954	−	0.577066i
$229$	−81.6070	+	68.4764i	−0.356362	+	0.299023i	−0.803339	−	0.595522i	$-0.796945\pi$
$229$	−81.6070	+	68.4764i	−0.356362	+	0.299023i	0.446977	+	0.894546i	$0.352501\pi$
$230$	364.646	+	434.568i	1.58542	+	1.88942i
$231$	−12.8818	+	20.0415i	−0.0557655	+	0.0867595i
$232$	295.196	−	107.443i	1.27240	−	0.463114i
$233$	−206.035	+	118.954i	−0.884270	+	0.510533i	−0.872064	−	0.489392i	$-0.837219\pi$
$233$	−206.035	+	118.954i	−0.884270	+	0.510533i	−0.0122058	+	0.999926i	$0.503885\pi$
$234$	159.245	−	12.6377i	0.680534	−	0.0540072i
$235$	198.105	−	343.128i	0.843001	−	1.46012i
$236$	−418.654	−	73.8200i	−1.77396	−	0.312797i
$237$	−117.680	+	15.0099i	−0.496540	+	0.0633329i
$238$	316.293	+	115.121i	1.32896	+	0.483702i
$239$	84.6278	−	14.9222i	0.354091	−	0.0624358i	0.00622654	−	0.999981i	$-0.498018\pi$
$239$	84.6278	−	14.9222i	0.354091	−	0.0624358i	0.347865	+	0.937545i	$0.386907\pi$
$240$	83.3556	+	77.0026i	0.347315	+	0.320844i
$241$	−22.4930	−	18.8739i	−0.0933319	−	0.0783148i	0.594928	−	0.803779i	$-0.297181\pi$
$241$	−22.4930	−	18.8739i	−0.0933319	−	0.0783148i	−0.688260	+	0.725464i	$0.741625\pi$
$242$		−	397.069i		−	1.64078i
$243$	134.673	−	202.268i	0.554210	−	0.832377i
$244$	−711.906			−2.91765
$245$	−36.5989	+	43.6169i	−0.149383	+	0.178028i
$246$	7.31096	−	7.91414i	0.0297193	−	0.0321713i
$247$	12.5901	+	71.4018i	0.0509719	+	0.289076i
$248$	−55.0555	+	151.264i	−0.221998	+	0.609934i
$249$	−16.0191	−	125.592i	−0.0643338	−	0.504387i
$250$	−10.6840	+	60.5920i	−0.0427360	+	0.242368i
$251$	−108.333	−	62.5458i	−0.431604	−	0.249186i	0.268426	−	0.963300i	$-0.413497\pi$
$251$	−108.333	−	62.5458i	−0.431604	−	0.249186i	−0.700030	+	0.714114i	$0.746830\pi$
$252$	32.0307	+	403.612i	0.127106	+	1.60164i
$253$	15.4388	+	26.7407i	0.0610228	+	0.105695i
$254$	1.46501	+	4.02509i	0.00576777	+	0.0158468i
$255$	275.432	+	177.036i	1.08013	+	0.694261i
$256$	−291.737	+	244.796i	−1.13960	+	0.956234i
$257$	−150.115	−	178.900i	−0.584104	−	0.696108i	0.390357	−	0.920663i	$-0.372352\pi$
$257$	−150.115	−	178.900i	−0.584104	−	0.696108i	−0.974461	+	0.224555i	$0.927907\pi$
$258$	−220.697	−	428.165i	−0.855414	−	1.65956i
$259$	312.257	−	113.652i	1.20563	−	0.438812i
$260$	−224.225	+	129.456i	−0.862405	+	0.497910i
$261$	227.155	+	161.804i	0.870326	+	0.619939i
$262$	152.740	−	264.554i	0.582979	−	1.00975i
$263$	−121.603	−	21.4418i	−0.462368	−	0.0815279i	−0.0623882	−	0.998052i	$-0.519872\pi$
$263$	−121.603	−	21.4418i	−0.462368	−	0.0815279i	−0.399980	+	0.916524i	$0.630983\pi$
$264$	22.9189	+	30.1194i	0.0868140	+	0.114089i
$265$	89.4618	+	32.5614i	0.337592	+	0.122873i
$266$	−283.653	+	50.0157i	−1.06637	+	0.188029i
$267$	204.518	−	63.5779i	0.765985	−	0.238119i
$268$	424.605	+	356.286i	1.58435	+	1.32942i
$269$			509.553i			1.89425i	0.320867	+	0.947124i	$0.396026\pi$
$269$			509.553i			1.89425i	−0.320867	+	0.947124i	$0.603974\pi$
$270$	−87.9814	+	611.019i	−0.325857	+	2.26303i
$271$	49.6722			0.183292			0.0916461	−	0.995792i	$-0.470787\pi$
$271$	49.6722			0.183292			0.0916461	+	0.995792i	$0.470787\pi$
$272$	56.0925	−	66.8485i	0.206223	−	0.245766i
$273$	−99.7093	−	22.5276i	−0.365236	−	0.0825188i
$274$	−34.0944	−	193.359i	−0.124432	−	0.705689i
$275$	9.49550	−	26.0887i	0.0345291	−	0.0948679i
$276$	483.987	+	202.766i	1.75358	+	0.734661i
$277$	19.8143	−	112.372i	0.0715316	−	0.405676i	−0.927927	−	0.372763i	$-0.878410\pi$
$277$	19.8143	−	112.372i	0.0715316	−	0.405676i	0.999458	−	0.0329130i	$-0.0104784\pi$
$278$	−145.363	−	83.9254i	−0.522889	−	0.301890i
$279$	−138.333	+	35.8720i	−0.495818	+	0.128573i
$280$	−222.479	−	385.345i	−0.794568	−	1.37623i
$281$	−8.86037	−	24.3437i	−0.0315316	−	0.0866323i	0.922928	−	0.384973i	$-0.125789\pi$
$281$	−8.86037	−	24.3437i	−0.0315316	−	0.0866323i	−0.954460	+	0.298340i	$0.903567\pi$
$282$	27.3733	−	573.796i	0.0970683	−	2.03474i
$283$	−120.665	+	101.250i	−0.426380	+	0.357775i	−0.830584	−	0.556894i	$-0.811993\pi$
$283$	−120.665	+	101.250i	−0.426380	+	0.357775i	0.404204	+	0.914669i	$0.367549\pi$
$284$	−208.015	−	247.902i	−0.732446	−	0.872895i
$285$	−279.863	−	13.3510i	−0.981977	−	0.0468458i
$286$	−20.7567	+	7.55483i	−0.0725759	+	0.0264155i
$287$	−5.97082	+	3.44725i	−0.0208042	+	0.0120113i
$288$	−193.169	−	53.4344i	−0.670725	−	0.185536i
$289$	−18.6082	+	32.2303i	−0.0643881	+	0.111523i
$290$	−697.734	−	123.029i	−2.40598	−	0.424239i
$291$	1.31223	−	3.13218i	0.00450937	−	0.0107635i
$292$	456.997	+	166.333i	1.56506	+	0.569634i
$293$	413.555	−	72.9209i	1.41145	−	0.248877i	0.584611	−	0.811314i	$-0.301247\pi$
$293$	413.555	−	72.9209i	1.41145	−	0.248877i	0.826840	+	0.562437i	$0.190136\pi$
$294$	−18.1926	+	80.5220i	−0.0618796	+	0.273884i
$295$	317.730	+	266.607i	1.07705	+	0.903754i
$296$		−	527.892i		−	1.78342i
$297$	−10.4912	+	31.9210i	−0.0353241	+	0.107478i
$298$	−241.620			−0.810804
$299$	−85.1599	+	101.490i	−0.284816	+	0.339430i
$300$	−140.060	−	450.547i	−0.466867	−	1.50182i
$301$	53.5257	+	303.559i	0.177826	+	1.00850i
$302$	3.85789	−	10.5995i	0.0127745	−	0.0350976i
$303$	−27.1076	+	20.6271i	−0.0894642	+	0.0680763i
$304$	−12.9670	+	73.5397i	−0.0426547	+	0.241907i
$305$	601.526	+	347.291i	1.97222	+	1.13866i
$306$	472.558	+	45.1901i	1.54431	+	0.147680i
$307$	−101.037	−	175.001i	−0.329110	−	0.570035i	0.653225	−	0.757163i	$-0.273415\pi$
$307$	−101.037	−	175.001i	−0.329110	−	0.570035i	−0.982336	+	0.187128i	$0.940082\pi$
$308$	−19.1480	−	52.6087i	−0.0621688	−	0.170807i
$309$	−438.857	+	226.208i	−1.42025	+	0.732064i
$310$	278.110	−	233.362i	0.897129	−	0.752781i
$311$	−170.488	−	203.179i	−0.548192	−	0.653310i	0.418811	−	0.908073i	$-0.362447\pi$
$311$	−170.488	−	203.179i	−0.548192	−	0.653310i	−0.967003	+	0.254763i	$0.918002\pi$
$312$	−87.8054	+	136.607i	−0.281428	+	0.437843i
$313$	−259.112	+	94.3092i	−0.827835	+	0.301307i	−0.720970	−	0.692966i	$-0.756304\pi$
$313$	−259.112	+	94.3092i	−0.827835	+	0.301307i	−0.106865	+	0.994274i	$0.534081\pi$
$314$	738.742	−	426.513i	2.35268	−	1.35832i
$315$	169.831	−	356.658i	0.539146	−	1.13225i
$316$	139.388	−	241.428i	0.441102	−	0.764012i
$317$	34.4742	+	6.07873i	0.108751	+	0.0191758i	0.227759	−	0.973718i	$-0.426860\pi$
$317$	34.4742	+	6.07873i	0.108751	+	0.0191758i	−0.119008	+	0.992893i	$0.537971\pi$
$318$	136.922	−	17.4642i	0.430571	−	0.0549187i
$319$	−36.2379	−	13.1895i	−0.113599	−	0.0413465i
$320$	650.430	−	114.688i	2.03259	−	0.358401i
$321$	237.690	+	219.575i	0.740469	+	0.684033i
$322$	−403.181	−	338.309i	−1.25211	−	1.05065i
$323$			215.457i			0.667049i
$324$	186.614	+	539.672i	0.575970	+	1.66565i
$325$	119.122			0.366528
$326$	−566.675	+	675.337i	−1.73827	+	2.07159i
$327$	−358.915	+	388.527i	−1.09760	+	1.18816i
$328$	1.90192	+	10.7863i	0.00579854	+	0.0328851i
$329$	−125.725	+	345.425i	−0.382142	+	1.04993i
$330$	−10.8000	−	84.6741i	−0.0327274	−	0.256588i
$331$	36.6162	−	207.661i	0.110623	−	0.627373i	−0.878202	−	0.478290i	$-0.841257\pi$
$331$	36.6162	−	207.661i	0.110623	−	0.627373i	0.988825	−	0.149083i	$-0.0476322\pi$
$332$	257.660	+	148.760i	0.776086	+	0.448073i
$333$	386.058	−	265.703i	1.15933	−	0.797906i
$334$	5.38105	+	9.32025i	0.0161109	+	0.0279049i
$335$	−184.963	−	508.180i	−0.552127	−	1.51696i
$336$	−88.5659	−	56.9266i	−0.263589	−	0.169424i
$337$	118.176	−	99.1618i	0.350672	−	0.294249i	−0.450388	−	0.892833i	$-0.648714\pi$
$337$	118.176	−	99.1618i	0.350672	−	0.294249i	0.801060	+	0.598584i	$0.204270\pi$
$338$	300.181	+	357.742i	0.888109	+	1.05841i
$339$	−172.134	−	333.950i	−0.507769	−	0.985104i
$340$	−723.007	+	263.153i	−2.12649	+	0.773979i
$341$	17.1133	−	9.88034i	0.0501855	−	0.0289746i
$342$	−369.537	+	168.700i	−1.08052	+	0.493274i
$343$	182.756	−	316.543i	0.532817	−	0.922867i
$344$	482.239	+	85.0317i	1.40186	+	0.247185i
$345$	−310.029	−	407.432i	−0.898635	−	1.18096i
$346$	−601.220	−	218.826i	−1.73763	−	0.632446i
$347$	−288.832	+	50.9288i	−0.832368	+	0.146769i	−0.573564	−	0.819161i	$-0.694440\pi$
$347$	−288.832	+	50.9288i	−0.832368	+	0.146769i	−0.258804	+	0.965930i	$0.583328\pi$
$348$	−625.824	+	194.548i	−1.79834	+	0.559046i
$349$	−313.333	−	262.918i	−0.897803	−	0.753346i	0.0719569	−	0.997408i	$-0.477076\pi$
$349$	−313.333	−	262.918i	−0.897803	−	0.753346i	−0.969760	+	0.244062i	$0.921520\pi$
$350$			473.227i			1.35208i
$351$	−144.098	+	4.54415i	−0.410537	+	0.0129463i
$352$	27.7135			0.0787316
$353$	321.434	−	383.070i	0.910577	−	1.08518i	−0.0854686	−	0.996341i	$-0.527239\pi$
$353$	321.434	−	383.070i	0.910577	−	1.08518i	0.996046	−	0.0888426i	$-0.0283168\pi$
$354$	586.568	+	132.525i	1.65697	+	0.374365i
$355$	54.8274	+	310.941i	0.154443	+	0.875892i
$356$	−172.133	+	472.932i	−0.483520	+	1.32846i
$357$	−280.178	−	117.381i	−0.784813	−	0.328798i
$358$	−127.548	+	723.361i	−0.356280	+	2.02056i
$359$	−216.295	−	124.878i	−0.602492	−	0.347849i	0.167529	−	0.985867i	$-0.446421\pi$
$359$	−216.295	−	124.878i	−0.602492	−	0.347849i	−0.770021	+	0.638018i	$0.779754\pi$
$360$	−440.147	−	447.311i	−1.22263	−	1.24253i
$361$	88.3143	+	152.965i	0.244638	+	0.423725i
$362$	165.503	+	454.715i	0.457189	+	1.25612i
$363$	−17.0761	+	357.947i	−0.0470415	+	0.986079i
$364$	184.014	−	154.406i	0.505532	−	0.424192i
$365$	−304.997	−	363.481i	−0.835608	−	0.995839i
$366$	1005.90	+	47.9871i	2.74836	+	0.131112i
$367$	300.825	−	109.491i	0.819686	−	0.298341i	0.102068	−	0.994777i	$-0.467454\pi$
$367$	300.825	−	109.491i	0.819686	−	0.298341i	0.717619	+	0.696436i	$0.245232\pi$
$368$	−118.171	+	68.2260i	−0.321117	+	0.185397i
$369$	−6.93097	+	6.81997i	−0.0187831	+	0.0184823i
$370$	−595.291	+	1031.07i	−1.60889	+	2.78669i
$371$	−86.9853	−	15.3379i	−0.234462	−	0.0413419i
$372$	129.764	−	309.737i	0.348829	−	0.832626i
$373$	−185.784	−	67.6197i	−0.498079	−	0.181286i	0.0807505	−	0.996734i	$-0.474268\pi$
$373$	−185.784	−	67.6197i	−0.498079	−	0.181286i	−0.578830	+	0.815448i	$0.696491\pi$
$374$	−64.6438	+	11.3984i	−0.172844	+	0.0304771i
$375$	12.2371	−	54.1625i	0.0326323	−	0.144433i
$376$	447.344	+	375.366i	1.18974	+	0.998313i
$377$		−	165.464i		−	0.438896i
$378$	−18.0522	−	572.450i	−0.0477572	−	1.51442i
$379$	364.905			0.962811			0.481405	−	0.876498i	$-0.340127\pi$
$379$	364.905			0.962811			0.481405	+	0.876498i	$0.340127\pi$
$380$	423.211	−	504.363i	1.11371	−	1.32727i
$381$	−1.14757	−	3.69151i	−0.00301199	−	0.00968901i
$382$	−45.1079	−	255.819i	−0.118083	−	0.669684i
$383$	221.375	−	608.221i	0.578001	−	1.58805i	−0.213543	−	0.976934i	$-0.568500\pi$
$383$	221.375	−	608.221i	0.578001	−	1.58805i	0.791544	−	0.611112i	$-0.209277\pi$
$384$	549.380	−	418.042i	1.43068	−	1.08865i
$385$	−9.48511	+	53.7927i	−0.0246367	+	0.139721i
$386$	−644.593	−	372.156i	−1.66993	−	0.964134i
$387$	180.539	+	395.470i	0.466508	+	1.02189i
$388$	3.99007	+	6.91101i	0.0102837	+	0.0178119i
$389$	19.3516	+	53.1682i	0.0497471	+	0.136679i	0.962078	−	0.272775i	$-0.0879414\pi$
$389$	19.3516	+	53.1682i	0.0497471	+	0.136679i	−0.912331	+	0.409454i	$0.865719\pi$
$390$	325.549	−	167.804i	0.834741	−	0.430266i
$391$	−301.595	+	253.068i	−0.771343	+	0.647233i
$392$	−53.9423	−	64.2859i	−0.137608	−	0.163995i
$393$	−149.069	+	231.920i	−0.379309	+	0.590126i
$394$	1079.78	−	393.010i	2.74057	−	0.997486i
$395$	−235.553	+	135.996i	−0.596336	+	0.344295i
$396$	−44.7652	−	65.0426i	−0.113044	−	0.164249i
$397$	−327.487	+	567.224i	−0.824905	+	1.42878i	0.0770876	+	0.997024i	$0.475438\pi$
$397$	−327.487	+	567.224i	−0.824905	+	1.42878i	−0.901992	+	0.431752i	$0.857895\pi$
$398$	515.786	+	90.9470i	1.29594	+	0.228510i
$399$	257.856	−	32.8892i	0.646257	−	0.0824291i
$400$	115.289	+	41.9619i	0.288223	+	0.104905i
$401$	124.761	−	21.9988i	0.311125	−	0.0548598i	−0.0159053	−	0.999874i	$-0.505063\pi$
$401$	124.761	−	21.9988i	0.311125	−	0.0548598i	0.327031	+	0.945014i	$0.393952\pi$
$402$	−575.937	−	532.041i	−1.43268	−	1.32349i
$403$	64.9502	+	54.4997i	0.161167	+	0.135235i
$404$		−	80.0452i		−	0.198132i
$405$	105.590	−	547.033i	0.260716	−	1.35070i
$406$	657.326			1.61903
$407$	−41.6549	+	49.6424i	−0.102346	+	0.121971i
$408$	−327.459	+	354.475i	−0.802595	+	0.868812i
$409$	94.5803	+	536.391i	0.231248	+	1.31147i	0.850374	+	0.526179i	$0.176376\pi$
$409$	94.5803	+	536.391i	0.231248	+	1.31147i	−0.619126	+	0.785291i	$0.712513\pi$
$410$	8.44866	−	23.2125i	0.0206065	−	0.0566159i
$411$	22.4197	+	175.774i	0.0545491	+	0.427673i
$412$	201.468	−	1142.58i	0.489000	−	2.77325i
$413$	−333.256	−	192.405i	−0.806915	−	0.465873i
$414$	−670.190	−	319.126i	−1.61882	−	0.770836i
$415$	−145.140	−	251.390i	−0.349736	−	0.605760i
$416$	40.6694	+	111.738i	0.0977631	+	0.268602i
$417$	127.432	+	81.9078i	0.305591	+	0.196422i
$418$	43.0291	−	36.1057i	0.102940	−	0.0863773i
$419$	429.462	+	511.813i	1.02497	+	1.22151i	0.974872	+	0.222765i	$0.0715083\pi$
$419$	429.462	+	511.813i	1.02497	+	1.22151i	0.0500962	+	0.998744i	$0.484047\pi$
$420$	425.304	+	825.116i	1.01263	+	1.96456i
$421$	−213.714	+	77.7856i	−0.507635	+	0.184764i	−0.583125	−	0.812383i	$-0.698170\pi$
$421$	−213.714	+	77.7856i	−0.507635	+	0.184764i	0.0754901	+	0.997147i	$0.475948\pi$
$422$	−1071.84	+	618.829i	−2.53991	+	1.46642i
$423$	−49.3524	+	516.084i	−0.116672	+	1.22006i
$424$	−70.1589	+	121.519i	−0.165469	+	0.286601i
$425$	348.614	+	61.4701i	0.820269	+	0.144635i
$426$	277.208	+	364.299i	0.650722	+	0.855162i
$427$	−605.553	−	220.403i	−1.41816	−	0.516167i
$428$	−748.850	+	132.042i	−1.74965	+	0.308510i
$429$	19.0365	−	5.91782i	0.0443741	−	0.0137944i
$430$	−846.017	−	709.892i	−1.96748	−	1.65091i
$431$		−	429.608i		−	0.996769i	−0.866956	−	0.498385i	$-0.833927\pi$
$431$		−	429.608i		−	0.996769i	0.866956	−	0.498385i	$-0.166073\pi$
$432$	−141.063	−	46.3623i	−0.326535	−	0.107320i
$433$	−11.9987			−0.0277106			−0.0138553	−	0.999904i	$-0.504410\pi$
$433$	−11.9987			−0.0277106			−0.0138553	+	0.999904i	$0.504410\pi$
$434$	−216.507	+	258.023i	−0.498865	+	0.594524i
$435$	623.697	+	140.914i	1.43379	+	0.323940i
$436$	−215.835	−	1224.06i	−0.495035	−	2.80749i
$437$	115.227	−	316.584i	0.263678	−	0.724448i
$438$	−634.509	−	265.828i	−1.44865	−	0.606913i
$439$	−13.0874	+	74.2226i	−0.0298119	+	0.169072i	−0.996079	−	0.0884713i	$-0.971802\pi$
$439$	−13.0874	+	74.2226i	−0.0298119	+	0.169072i	0.966267	+	0.257543i	$0.0829130\pi$
$440$	75.1487	+	43.3871i	0.170793	+	0.0986071i
$441$	19.8630	−	71.8060i	0.0450408	−	0.162825i
$442$	−140.822	−	243.911i	−0.318602	−	0.551834i
$443$	84.8156	+	233.029i	0.191457	+	0.526024i	0.997863	−	0.0653379i	$-0.0208125\pi$
$443$	84.8156	+	233.029i	0.191457	+	0.526024i	−0.806406	+	0.591362i	$0.798590\pi$
$444$	−52.4783	+	1100.05i	−0.118194	+	2.47758i
$445$	376.156	−	315.632i	0.845294	−	0.709286i
$446$	−199.570	−	237.838i	−0.447466	−	0.533269i
$447$	217.813	+	10.3909i	0.487278	+	0.0232459i
$448$	−575.807	+	209.577i	−1.28528	+	0.467805i
$449$	178.012	−	102.775i	0.396462	−	0.228898i	−0.288494	−	0.957482i	$-0.593155\pi$
$449$	178.012	−	102.775i	0.396462	−	0.228898i	0.684956	+	0.728584i	$0.259821\pi$
$450$	167.531	+	646.049i	0.372290	+	1.43566i
$451$	0.672273	−	1.16441i	0.00149063	−	0.00258184i
$452$	869.452	+	153.308i	1.92357	+	0.339177i
$453$	−3.93361	+	9.38921i	−0.00868347	+	0.0207267i
$454$	1140.68	+	415.175i	2.51252	+	0.914482i
$455$	−230.807	+	40.6975i	−0.507268	+	0.0894450i
$456$	91.0060	−	402.801i	0.199575	−	0.883335i
$457$	489.550	+	410.781i	1.07122	+	0.898864i	0.995163	−	0.0982390i	$-0.0313210\pi$
$457$	489.550	+	410.781i	1.07122	+	0.898864i	0.0760617	+	0.997103i	$0.475765\pi$
$458$			354.118i			0.773184i
$459$	−424.054	−	61.0601i	−0.923865	−	0.133029i
$460$	1203.09			2.61542
$461$	91.0478	−	108.507i	0.197501	−	0.235372i	−0.658200	−	0.752843i	$-0.728682\pi$
$461$	91.0478	−	108.507i	0.197501	−	0.235372i	0.855701	+	0.517471i	$0.173126\pi$
$462$	23.5093	+	75.6250i	0.0508860	+	0.163690i
$463$	−48.9254	−	277.470i	−0.105670	−	0.599287i	−0.990950	−	0.134229i	$-0.957144\pi$
$463$	−48.9254	−	277.470i	−0.105670	−	0.599287i	0.885280	−	0.465059i	$-0.153967\pi$
$464$	58.2864	−	160.140i	0.125617	−	0.345130i
$465$	−260.744	+	198.409i	−0.560740	+	0.426687i
$466$	−137.327	+	778.819i	−0.294693	+	1.67129i
$467$	462.423	+	266.980i	0.990199	+	0.571692i	0.905334	−	0.424700i	$-0.139621\pi$
$467$	462.423	+	266.980i	0.990199	+	0.571692i	0.0848656	+	0.996392i	$0.472954\pi$
$468$	196.553	−	275.939i	0.419985	−	0.589613i
$469$	250.868	+	434.515i	0.534899	+	0.926472i
$470$	−450.457	−	1237.62i	−0.958419	−	2.63323i
$471$	−684.298	+	352.720i	−1.45286	+	0.748875i
$472$	−468.295	+	392.947i	−0.992151	+	0.832514i
$473$	−38.6395	−	46.0488i	−0.0816903	−	0.0973547i
$474$	−213.225	+	331.734i	−0.449842	+	0.699860i
$475$	−284.651	+	103.604i	−0.599265	+	0.218114i
$476$	618.201	−	356.918i	1.29874	−	0.749828i
$477$	−124.182	+	9.85510i	−0.260340	+	0.0206606i
$478$	142.826	−	247.382i	0.298799	−	0.517535i
$479$	−167.090	−	29.4625i	−0.348831	−	0.0615084i	−0.00351250	−	0.999994i	$-0.501118\pi$
$479$	−167.090	−	29.4625i	−0.348831	−	0.0615084i	−0.345319	+	0.938485i	$0.612229\pi$
$480$	−455.821	+	58.1392i	−0.949626	+	0.121123i
$481$	−261.282	−	95.0988i	−0.543205	−	0.197711i
$482$	−96.1214	+	16.9488i	−0.199422	+	0.0351635i
$483$	348.907	+	322.315i	0.722375	+	0.667319i
$484$	−645.083	−	541.289i	−1.33282	−	1.11837i
$485$		−	7.78596i		−	0.0160535i
$486$	−227.302	−	775.118i	−0.467700	−	1.59489i
$487$	20.8058			0.0427223			0.0213612	−	0.999772i	$-0.493200\pi$
$487$	20.8058			0.0427223			0.0213612	+	0.999772i	$0.493200\pi$
$488$	−658.040	+	784.222i	−1.34844	+	1.60701i
$489$	539.885	−	584.428i	1.10406	−	1.19515i
$490$	32.8660	+	186.392i	0.0670734	+	0.380392i
$491$	51.6877	−	142.011i	0.105270	−	0.289228i	−0.875863	−	0.482560i	$-0.839707\pi$
$491$	51.6877	−	142.011i	0.105270	−	0.289228i	0.981133	+	0.193332i	$0.0619294\pi$
$492$	−2.89103	−	22.6661i	−0.00587607	−	0.0460693i
$493$	85.3838	−	484.236i	0.173192	−	0.982222i
$494$	208.720	+	120.504i	0.422510	+	0.243936i
$495$	6.09451	+	76.7958i	0.0123122	+	0.155143i
$496$	43.6626	+	75.6258i	0.0880294	+	0.152471i
$497$	−100.189	−	275.268i	−0.201588	−	0.553859i
$498$	−354.038	−	227.561i	−0.710920	−	0.456951i
$499$	626.300	−	525.528i	1.25511	−	1.05316i	0.258925	−	0.965897i	$-0.416632\pi$
$499$	626.300	−	525.528i	1.25511	−	1.05316i	0.996185	−	0.0872648i	$-0.0278126\pi$
$500$	83.8739	+	99.9570i	0.167748	+	0.199914i
$501$	−4.45004	−	8.63335i	−0.00888232	−	0.0172322i
$502$	−390.741	+	142.218i	−0.778369	+	0.283303i
$503$	−201.176	+	116.149i	−0.399953	+	0.230913i	−0.686464	−	0.727164i	$-0.740838\pi$
$503$	−201.176	+	116.149i	−0.399953	+	0.230913i	0.286511	+	0.958077i	$0.407505\pi$
$504$	474.218	+	337.789i	0.940909	+	0.670216i
$505$	−39.0487	+	67.6343i	−0.0773241	+	0.133929i
$506$	101.081	+	17.8233i	0.199765	+	0.0352239i
$507$	−255.220	−	335.404i	−0.503392	−	0.661545i
$508$	8.53634	+	3.10697i	0.0168038	+	0.00611609i
$509$	−318.833	+	56.2189i	−0.626392	+	0.110450i	−0.477828	−	0.878453i	$-0.658576\pi$
$509$	−318.833	+	56.2189i	−0.626392	+	0.110450i	−0.148563	+	0.988903i	$0.547465\pi$
$510$	1039.32	−	323.091i	2.03789	−	0.633512i
$511$	337.229	+	282.968i	0.659939	+	0.553754i
$512$			345.476i			0.674758i
$513$	340.382	−	136.186i	0.663513	−	0.265470i
$514$	−776.303			−1.51032
$515$	−727.619	+	867.142i	−1.41285	+	1.68377i
$516$	−996.458	−	225.133i	−1.93112	−	0.436304i
$517$	−12.4483	−	70.5979i	−0.0240780	−	0.136553i
$518$	377.792	−	1037.98i	0.729329	−	2.00382i
$519$	532.573	+	223.121i	1.02615	+	0.429906i
$520$	−64.6526	+	366.663i	−0.124332	+	0.705122i
$521$	480.156	+	277.218i	0.921604	+	0.532088i	0.884146	−	0.467210i	$-0.154741\pi$
$521$	480.156	+	277.218i	0.921604	+	0.532088i	0.0374577	+	0.999298i	$0.488074\pi$
$522$	897.382	−	232.705i	1.71912	−	0.445795i
$523$	−472.881	−	819.053i	−0.904170	−	1.56607i	−0.822028	−	0.569447i	$-0.807157\pi$
$523$	−472.881	−	819.053i	−0.904170	−	1.56607i	−0.0821414	−	0.996621i	$-0.526176\pi$
$524$	−221.580	−	608.787i	−0.422863	−	1.16181i
$525$	20.3512	−	426.601i	0.0387643	−	0.812573i
$526$	−314.428	+	263.836i	−0.597772	+	0.501590i
$527$	161.956	+	193.012i	0.307317	+	0.366246i
$528$	20.5087	+	0.978378i	0.0388422	+	0.00185299i
$529$	81.3960	−	29.6257i	0.153868	−	0.0560033i
$530$	274.068	−	158.233i	0.517109	−	0.298553i
$531$	−523.076	−	144.693i	−0.985077	−	0.272492i
$532$	−305.423	+	529.008i	−0.574103	+	0.994376i
$533$	5.68135	+	1.00178i	0.0106592	+	0.00187950i
$534$	275.097	−	656.634i	0.515163	−	1.22965i
$535$	697.156	+	253.744i	1.30310	+	0.474288i
$536$	784.955	−	138.409i	1.46447	−	0.258225i
$537$	146.089	−	646.605i	0.272047	−	1.20411i
$538$	1297.53	+	1088.76i	2.41177	+	2.02372i
$539$			10.3019i			0.0191129i
$540$	872.731	+	975.883i	1.61617	+	1.80719i
$541$	−390.158			−0.721179			−0.360590	−	0.932725i	$-0.617425\pi$
$541$	−390.158			−0.721179			−0.360590	+	0.932725i	$0.617425\pi$
$542$	106.134	−	126.486i	0.195820	−	0.233369i
$543$	−129.641	−	417.030i	−0.238749	−	0.768011i
$544$	61.3605	+	347.993i	0.112795	+	0.639693i
$545$	−414.768	+	1139.57i	−0.761042	+	2.09095i
$546$	−270.413	+	205.767i	−0.495262	+	0.376862i
$547$	−80.6120	+	457.174i	−0.147371	+	0.835784i	0.818061	+	0.575131i	$0.195049\pi$
$547$	−80.6120	+	457.174i	−0.147371	+	0.835784i	−0.965433	+	0.260653i	$0.916062\pi$
$548$	−360.611	−	208.199i	−0.658049	−	0.379925i
$549$	−904.727	−	86.5180i	−1.64796	−	0.157592i
$550$	−46.1436	−	79.9230i	−0.0838974	−	0.145315i
$551$	143.910	+	395.388i	0.261179	+	0.717583i
$552$	670.730	−	345.726i	1.21509	−	0.626315i
$553$	193.310	−	162.206i	0.349566	−	0.293320i
$554$	−243.809	−	290.561i	−0.440089	−	0.524478i
$555$	580.980	−	903.884i	1.04681	−	1.62862i
$556$	−334.507	+	121.751i	−0.601631	+	0.218976i
$557$	−203.531	+	117.509i	−0.365406	+	0.210967i	−0.671450	−	0.741050i	$-0.734328\pi$
$557$	−203.531	+	117.509i	−0.365406	+	0.210967i	0.306043	+	0.952018i	$0.400995\pi$
$558$	−204.231	+	428.901i	−0.366005	+	0.768640i
$559$	128.961	−	223.367i	0.230700	−	0.399584i
$560$	−237.718	−	41.9160i	−0.424496	−	0.0748500i
$561$	58.7648	−	7.49536i	0.104750	−	0.0133607i
$562$	−80.9210	−	29.4528i	−0.143988	−	0.0524072i
$563$	−82.3270	+	14.5165i	−0.146229	+	0.0257842i	−0.246284	−	0.969198i	$-0.579209\pi$
$563$	−82.3270	+	14.5165i	−0.146229	+	0.0257842i	0.100054	+	0.994982i	$0.468098\pi$
$564$	−894.879	−	826.675i	−1.58667	−	1.46574i
$565$	−659.856	−	553.685i	−1.16789	−	0.979973i
$566$			523.606i			0.925099i
$567$	−8.34476	+	516.824i	−0.0147174	+	0.911506i
$568$	−465.359			−0.819295
$569$	592.627	−	706.266i	1.04152	−	1.24124i	0.0717022	−	0.997426i	$-0.477157\pi$
$569$	592.627	−	706.266i	1.04152	−	1.24124i	0.969822	−	0.243814i	$-0.0783987\pi$
$570$	−631.980	+	684.121i	−1.10874	+	1.20021i
$571$	69.2165	+	392.546i	0.121220	+	0.687471i	0.983482	+	0.181008i	$0.0579361\pi$
$571$	69.2165	+	392.546i	0.121220	+	0.687471i	−0.862262	+	0.506463i	$0.830953\pi$
$572$	−16.0221	+	44.0204i	−0.0280107	+	0.0769588i
$573$	29.6619	+	232.554i	0.0517660	+	0.405853i
$574$	−3.97969	+	22.5699i	−0.00693325	+	0.0393204i
$575$	−479.365	−	276.762i	−0.833679	−	0.481325i
$576$	−711.898	+	489.960i	−1.23593	+	0.850625i
$577$	8.33213	+	14.4317i	0.0144404	+	0.0250116i	0.873155	−	0.487442i	$-0.162070\pi$
$577$	8.33213	+	14.4317i	0.0144404	+	0.0250116i	−0.858715	+	0.512454i	$0.828737\pi$
$578$	42.3117	+	116.250i	0.0732036	+	0.201125i
$579$	565.078	+	363.209i	0.975955	+	0.627304i
$580$	−1151.03	+	965.832i	−1.98454	+	1.66523i
$581$	173.112	+	206.307i	0.297956	+	0.355090i
$582$	−5.17200	−	10.0340i	−0.00888659	−	0.0172405i
$583$	16.1865	−	5.89139i	0.0277641	−	0.0101053i
$584$	605.648	−	349.671i	1.03707	−	0.598751i
$585$	−300.690	+	137.270i	−0.514000	+	0.234649i
$586$	697.955	−	1208.89i	1.19105	−	2.06296i
$587$	183.618	+	32.3769i	0.312808	+	0.0551565i	0.327848	−	0.944730i	$-0.393677\pi$
$587$	183.618	+	32.3769i	0.312808	+	0.0551565i	−0.0150403	+	0.999887i	$0.504788\pi$
$588$	106.017	+	139.324i	0.180300	+	0.236946i
$589$	−202.604	−	73.7419i	−0.343980	−	0.125198i
$590$	1357.79	−	239.414i	2.30133	−	0.405787i
$591$	−990.297	+	307.851i	−1.67563	+	0.520898i
$592$	−219.376	−	184.079i	−0.370568	−	0.310944i
$593$		−	373.725i		−	0.630228i	−0.949054	−	0.315114i	$-0.897957\pi$
$593$		−	373.725i		−	0.630228i	0.949054	−	0.315114i	$-0.102043\pi$
$594$	58.8675	+	94.9205i	0.0991036	+	0.159799i
$595$	−696.466			−1.17053
$596$	−329.378	+	392.538i	−0.552648	+	0.658621i
$597$	−461.055	−	104.168i	−0.772287	−	0.174485i
$598$	76.4739	+	433.705i	0.127883	+	0.725259i
$599$	5.06227	−	13.9085i	0.00845120	−	0.0232195i	−0.935395	−	0.353604i	$-0.884956\pi$
$599$	5.06227	−	13.9085i	0.00845120	−	0.0232195i	0.943846	+	0.330384i	$0.107178\pi$
$600$	−625.776	−	262.169i	−1.04296	−	0.436948i
$601$	−33.7445	+	191.375i	−0.0561473	+	0.318427i	−0.999926	−	0.0121504i	$-0.996132\pi$
$601$	−33.7445	+	191.375i	−0.0561473	+	0.318427i	0.943779	+	0.330577i	$0.107243\pi$
$602$	887.356	+	512.315i	1.47401	+	0.851022i
$603$	496.311	+	504.389i	0.823069	+	0.836466i
$604$	−11.9609	−	20.7169i	−0.0198028	−	0.0342995i
$605$	281.005	+	772.055i	0.464471	+	1.27612i
$606$	−5.39556	+	113.101i	−0.00890356	+	0.186636i
$607$	444.453	−	372.941i	0.732213	−	0.614400i	−0.198521	−	0.980097i	$-0.563614\pi$
$607$	444.453	−	372.941i	0.732213	−	0.614400i	0.930734	+	0.365697i	$0.119169\pi$
$608$	−194.366	−	231.636i	−0.319680	−	0.380980i
$609$	−592.561	−	28.2685i	−0.973007	−	0.0464179i
$610$	2169.63	−	789.679i	3.55676	−	1.29456i
$611$	266.377	−	153.793i	0.435968	−	0.251706i
$612$	717.612	−	706.119i	1.17257	−	1.15379i
$613$	80.1803	−	138.876i	0.130800	−	0.226552i	−0.793185	−	0.608980i	$-0.791579\pi$
$613$	80.1803	−	138.876i	0.130800	−	0.226552i	0.923985	+	0.382428i	$0.124912\pi$
$614$	−661.510	−	116.642i	−1.07738	−	0.189971i
$615$	−8.61449	+	20.5621i	−0.0140073	+	0.0334343i
$616$	−75.6518	−	27.5350i	−0.122811	−	0.0446997i
$617$	409.534	−	72.2118i	0.663750	−	0.117037i	0.168384	−	0.985721i	$-0.446145\pi$
$617$	409.534	−	72.2118i	0.663750	−	0.117037i	0.495366	+	0.868685i	$0.335034\pi$
$618$	−361.685	+	1600.85i	−0.585250	+	2.59037i
$619$	−502.301	−	421.481i	−0.811472	−	0.680906i	0.139486	−	0.990224i	$-0.455455\pi$
$619$	−502.301	−	421.481i	−0.811472	−	0.680906i	−0.950959	+	0.309318i	$0.899899\pi$
$620$		−	769.943i		−	1.24184i
$621$	590.433	+	316.505i	0.950778	+	0.509670i
$622$	−881.659			−1.41746
$623$	−292.835	+	348.988i	−0.470041	+	0.560173i
$624$	26.1516	+	84.1249i	0.0419097	+	0.134816i
$625$	−118.955	−	674.627i	−0.190328	−	1.07940i
$626$	−313.494	+	861.318i	−0.500789	+	1.37591i
$627$	−40.3423	+	30.6978i	−0.0643417	+	0.0489598i
$628$	314.144	−	1781.60i	0.500229	−	2.83694i
$629$	−715.577	−	413.139i	−1.13764	−	0.656818i
$630$	−545.323	−	1194.53i	−0.865592	−	1.89608i
$631$	321.500	+	556.855i	0.509509	+	0.882496i	0.999939	+	0.0110155i	$0.00350642\pi$
$631$	321.500	+	556.855i	0.509509	+	0.882496i	−0.490430	+	0.871481i	$0.663160\pi$
$632$	−137.110	−	376.708i	−0.216947	−	0.596057i
$633$	992.850	−	511.762i	1.56848	−	0.808471i
$634$	89.1398	−	74.7972i	0.140599	−	0.117977i
$635$	−5.69710	−	6.78954i	−0.00897182	−	0.0106922i
$636$	158.281	−	246.252i	0.248869	−	0.387189i
$637$	−41.5361	+	15.1179i	−0.0652058	+	0.0237330i
$638$	−111.016	+	64.0948i	−0.174006	+	0.100462i
$639$	−234.228	−	340.327i	−0.366554	−	0.532593i
$640$	791.384	−	1370.72i	1.23654	−	2.14175i
$641$	−115.857	−	20.4287i	−0.180744	−	0.0318700i	0.0825436	−	0.996587i	$-0.473696\pi$
$641$	−115.857	−	20.4287i	−0.180744	−	0.0318700i	−0.263287	+	0.964717i	$0.584807\pi$
$642$	1067.00	−	136.094i	1.66199	−	0.211985i
$643$	−407.907	−	148.466i	−0.634382	−	0.230896i	0.00475561	−	0.999989i	$-0.498486\pi$
$643$	−407.907	−	148.466i	−0.634382	−	0.230896i	−0.639137	+	0.769093i	$0.720708\pi$
$644$	−1099.24	+	193.826i	−1.70690	+	0.300972i
$645$	732.131	+	676.331i	1.13509	+	1.04858i
$646$	548.643	+	460.366i	0.849292	+	0.712641i
$647$		−	202.797i		−	0.313443i	−0.987643	−	0.156721i	$-0.949908\pi$
$647$		−	202.797i		−	0.313443i	0.987643	−	0.156721i	$-0.0500924\pi$
$648$	766.986	+	293.267i	1.18362	+	0.452573i
$649$	75.0446			0.115631
$650$	254.527	−	303.333i	0.391580	−	0.466667i
$651$	206.272	−	223.290i	0.316854	−	0.342995i
$652$	324.663	+	1841.25i	0.497949	+	2.82401i
$653$	−306.142	+	841.119i	−0.468824	+	1.28808i	0.449862	+	0.893098i	$0.351473\pi$
$653$	−306.142	+	841.119i	−0.468824	+	1.28808i	−0.918687	+	0.394987i	$0.870749\pi$
$654$	222.459	+	1744.11i	0.340151	+	2.66684i
$655$	−109.762	+	622.490i	−0.167575	+	0.950366i
$656$	5.14569	+	2.97087i	0.00784404	+	0.00452876i
$657$	560.561	+	266.924i	0.853212	+	0.406276i
$658$	610.961	+	1058.22i	0.928513	+	1.60823i
$659$	−287.917	−	791.045i	−0.436899	−	1.20037i	−0.941498	−	0.337017i	$-0.890582\pi$
$659$	−287.917	−	791.045i	−0.436899	−	1.20037i	0.504599	−	0.863354i	$-0.331640\pi$
$660$	−152.285	−	97.8827i	−0.230735	−	0.148307i
$661$	173.104	−	145.252i	0.261882	−	0.219745i	−0.502386	−	0.864643i	$-0.667545\pi$
$661$	173.104	−	145.252i	0.261882	−	0.219745i	0.764269	+	0.644898i	$0.223100\pi$
$662$	−450.552	−	536.947i	−0.680593	−	0.811099i
$663$	116.458	+	225.935i	0.175652	+	0.340776i
$664$	402.036	−	146.329i	0.605476	−	0.220375i
$665$	516.135	−	297.991i	0.776143	−	0.448106i
$666$	148.300	−	1550.79i	0.222673	−	2.32851i
$667$	−384.430	+	665.853i	−0.576357	+	0.998280i
$668$	22.4773	+	3.96335i	0.0336486	+	0.00593316i
$669$	169.678	+	222.987i	0.253630	+	0.333314i
$670$	−1689.25	−	614.836i	−2.52126	−	0.917665i
$671$	123.763	−	21.8227i	0.184445	−	0.0325227i
$672$	407.107	−	126.556i	0.605815	−	0.188328i
$673$	−84.6901	−	71.0634i	−0.125840	−	0.105592i	0.577696	−	0.816252i	$-0.303952\pi$
$673$	−84.6901	−	71.0634i	−0.125840	−	0.105592i	−0.703536	+	0.710660i	$0.748396\pi$
$674$		−	512.805i		−	0.760838i
$675$	−123.241	−	589.600i	−0.182579	−	0.873482i
$676$	990.401			1.46509
$677$	1.83780	−	2.19020i	0.00271462	−	0.00323516i	−0.764685	−	0.644404i	$-0.777106\pi$
$677$	1.83780	−	2.19020i	0.00271462	−	0.00323516i	0.767400	+	0.641169i	$0.221550\pi$
$678$	−1218.17	−	275.226i	−1.79672	−	0.405938i
$679$	1.25437	+	7.11387i	0.00184737	+	0.0104770i
$680$	−378.417	+	1039.69i	−0.556495	+	1.52896i
$681$	−1010.44	−	423.324i	−1.48376	−	0.621621i
$682$	11.4064	−	64.6887i	0.0167249	−	0.0948515i
$683$	−843.279	−	486.868i	−1.23467	−	0.712837i	−0.266670	−	0.963788i	$-0.585923\pi$
$683$	−843.279	−	486.868i	−1.23467	−	0.712837i	−0.968000	+	0.250951i	$0.919257\pi$
$684$	−229.685	+	830.327i	−0.335797	+	1.21393i
$685$	203.132	+	351.835i	0.296543	+	0.513628i
$686$	−415.556	−	1141.73i	−0.605767	−	1.66433i
$687$	15.2290	−	319.228i	0.0221673	−	0.464669i
$688$	203.496	−	170.753i	0.295779	−	0.248188i
$689$	47.5071	+	56.6168i	0.0689508	+	0.0821724i
$690$	−1699.93	−	81.0961i	−2.46367	−	0.117531i
$691$	−614.590	+	223.693i	−0.889421	+	0.323723i	−0.746006	−	0.665940i	$-0.768031\pi$
$691$	−614.590	+	223.693i	−0.889421	+	0.323723i	−0.143416	+	0.989663i	$0.545809\pi$
$692$	−1175.10	+	678.443i	−1.69812	+	0.980409i
$693$	−17.9407	−	69.1848i	−0.0258885	−	0.0998338i
$694$	−487.460	+	844.305i	−0.702391	+	1.21658i
$695$	342.036	+	60.3101i	0.492138	+	0.0867772i
$696$	−364.161	+	869.222i	−0.523220	+	1.24888i
$697$	16.1097	+	5.86347i	0.0231130	+	0.00841244i
$698$	−1339.00	+	236.101i	−1.91833	+	0.338254i
$699$	157.290	−	696.178i	0.225021	−	0.995963i
$700$	768.810	+	645.108i	1.09830	+	0.921583i
$701$			41.7083i			0.0594983i	0.999557	+	0.0297492i	$0.00947085\pi$
$701$			41.7083i			0.0594983i	−0.999557	+	0.0297492i	$0.990529\pi$
$702$	−296.323	+	376.644i	−0.422113	+	0.536530i
$703$	707.064			1.00578
$704$	76.8123	−	91.5413i	0.109108	−	0.130030i
$705$	352.850	+	1135.05i	0.500497	+	1.61000i
$706$	−288.649	−	1637.01i	−0.408851	−	2.31871i
$707$	24.7817	−	68.0870i	0.0350518	−	0.0963042i
$708$	1014.92	−	772.286i	1.43350	−	1.09080i
$709$	−86.0416	+	487.966i	−0.121356	+	0.688246i	0.862049	+	0.506825i	$0.169181\pi$
$709$	−86.0416	+	487.966i	−0.121356	+	0.688246i	−0.983406	+	0.181421i	$0.941930\pi$
$710$	908.936	+	524.774i	1.28019	+	0.739119i
$711$	206.483	−	289.879i	0.290412	−	0.407706i
$712$	361.863	+	626.766i	0.508235	+	0.880289i
$713$	−134.748	−	370.218i	−0.188988	−	0.519240i
$714$	−897.556	+	462.643i	−1.25708	+	0.647960i
$715$	35.0125	−	29.3790i	0.0489685	−	0.0410895i
$716$	1001.31	+	1193.31i	1.39847	+	1.66663i
$717$	−139.392	+	216.865i	−0.194410	+	0.302462i
$718$	−780.147	+	283.950i	−1.08656	+	0.395474i
$719$	124.160	−	71.6839i	0.172684	−	0.0996994i	−0.411167	−	0.911560i	$-0.634879\pi$
$719$	124.160	−	71.6839i	0.172684	−	0.0996994i	0.583851	+	0.811861i	$0.301545\pi$
$720$	−339.371	+	26.9325i	−0.471349	+	0.0374062i
$721$	525.108	−	909.514i	0.728305	−	1.26146i
$722$	578.213	+	101.955i	0.800849	+	0.141211i
$723$	87.3796	−	11.1451i	0.120857	−	0.0154151i
$724$	964.350	+	350.995i	1.33197	+	0.484799i
$725$	680.805	−	120.044i	0.939041	−	0.165578i
$726$	874.995	+	808.306i	1.20523	+	1.11337i
$727$	−252.723	−	212.060i	−0.347624	−	0.291692i	0.452211	−	0.891911i	$-0.350635\pi$
$727$	−252.723	−	212.060i	−0.347624	−	0.291692i	−0.799835	+	0.600220i	$0.795080\pi$
$728$		−	345.429i		−	0.474490i
$729$	171.573	+	708.522i	0.235353	+	0.971910i
$730$	−1577.26			−2.16063
$731$	492.673	−	587.145i	0.673972	−	0.803208i
$732$	1449.21	−	1568.78i	1.97980	−	2.14314i
$733$	32.0098	+	181.537i	0.0436696	+	0.247663i	0.998826	−	0.0484385i	$-0.0154245\pi$
$733$	32.0098	+	181.537i	0.0436696	+	0.247663i	−0.955157	+	0.296101i	$0.904313\pi$
$734$	363.961	−	999.975i	0.495860	−	1.36236i
$735$	−21.6119	−	169.441i	−0.0294040	−	0.230532i
$736$	95.9471	−	544.143i	0.130363	−	0.739325i
$737$	−84.7378	−	48.9234i	−0.114977	−	0.0663818i
$738$	2.55709	+	32.2213i	0.00346489	+	0.0436604i
$739$	225.818	+	391.128i	0.305572	+	0.529267i	0.977389	−	0.211451i	$-0.0678189\pi$
$739$	225.818	+	391.128i	0.305572	+	0.529267i	−0.671816	+	0.740718i	$0.734486\pi$
$740$	863.588	+	2372.69i	1.16701	+	3.20633i
$741$	−182.973	−	117.607i	−0.246927	−	0.158715i
$742$	−224.918	+	188.728i	−0.303124	+	0.254351i
$743$	384.245	+	457.925i	0.517153	+	0.616319i	0.959905	−	0.280325i	$-0.0904422\pi$
$743$	384.245	+	457.925i	0.517153	+	0.616319i	−0.442752	+	0.896644i	$0.645998\pi$
$744$	−221.254	−	429.247i	−0.297385	−	0.576944i
$745$	469.802	−	170.994i	0.630606	−	0.229522i
$746$	−569.151	+	328.600i	−0.762937	+	0.440482i
$747$	309.369	+	220.366i	0.414149	+	0.295001i
$748$	−69.6051	+	120.560i	−0.0930549	+	0.161176i
$749$	−677.857	−	119.524i	−0.905016	−	0.159579i
$750$	−111.773	−	146.890i	−0.149031	−	0.195853i
$751$	585.524	+	213.113i	0.779659	+	0.283773i	0.701030	−	0.713131i	$-0.252724\pi$
$751$	585.524	+	213.113i	0.779659	+	0.283773i	0.0786285	+	0.996904i	$0.474946\pi$
$752$	311.982	−	55.0108i	0.414870	−	0.0731527i
$753$	358.358	−	111.402i	0.475908	−	0.147944i
$754$	−421.339	−	353.546i	−0.558805	−	0.468893i
$755$			23.3397i			0.0309135i
$756$	−954.618	−	751.042i	−1.26272	−	0.993442i
$757$	−1029.21			−1.35960			−0.679798	−	0.733399i	$-0.737933\pi$
$757$	−1029.21			−1.35960			−0.679798	+	0.733399i	$0.737933\pi$
$758$	779.692	−	929.200i	1.02862	−	1.22586i
$759$	−90.3552	−	20.4142i	−0.119045	−	0.0268962i
$760$	−164.408	−	932.401i	−0.216326	−	1.22684i
$761$	213.042	−	585.329i	0.279951	−	0.769158i	−0.717417	−	0.696644i	$-0.754676\pi$
$761$	213.042	−	585.329i	0.279951	−	0.769158i	0.997367	−	0.0725138i	$-0.0231021\pi$
$762$	−11.8521	−	4.96545i	−0.0155540	−	0.00651634i
$763$	195.374	−	1108.02i	0.256060	−	1.45219i
$764$	−477.099	−	275.453i	−0.624475	−	0.360541i
$765$	−950.815	+	246.561i	−1.24290	+	0.322302i
$766$	−1075.77	−	1863.30i	−1.40441	−	2.43250i
$767$	110.128	+	302.573i	0.143582	+	0.394489i
$768$	54.4419	−	1141.21i	0.0708880	−	1.48595i
$769$	−803.159	+	673.931i	−1.04442	+	0.876373i	−0.992496	−	0.122278i	$-0.960980\pi$
$769$	−803.159	+	673.931i	−1.04442	+	0.876373i	−0.0519247	+	0.998651i	$0.516536\pi$
$770$	116.712	+	139.092i	0.151574	+	0.180639i
$771$	699.815	+	33.3851i	0.907672	+	0.0433010i
$772$	−1483.32	+	539.886i	−1.92141	+	0.699334i
$773$	719.632	−	415.480i	0.930960	−	0.537490i	0.0438447	−	0.999038i	$-0.486039\pi$
$773$	719.632	−	415.480i	0.930960	−	0.537490i	0.887115	+	0.461549i	$0.152706\pi$
$774$	1392.79	+	385.273i	1.79947	+	0.497769i
$775$	−177.119	+	306.779i	−0.228541	+	0.395844i
$776$	11.3012	+	1.99271i	0.0145634	+	0.00256792i
$777$	−385.208	+	919.460i	−0.495763	+	1.18335i
$778$	176.737	+	64.3269i	0.227168	+	0.0826824i
$779$	−14.4473	+	2.54745i	−0.0185460	+	0.00327016i
$780$	171.176	−	757.642i	0.219457	−	0.971336i
$781$	43.7619	+	36.7206i	0.0560331	+	0.0470174i
$782$			1308.72i			1.67355i
$783$	−818.972	+	171.185i	−1.04594	+	0.218627i
$784$	−45.5253			−0.0580680
$785$	−1134.56	+	1352.11i	−1.44530	+	1.72244i
$786$	272.050	+	875.132i	0.346119	+	1.11340i
$787$	32.2419	+	182.853i	0.0409682	+	0.232342i	0.998416	−	0.0562647i	$-0.0179191\pi$
$787$	32.2419	+	182.853i	0.0409682	+	0.232342i	−0.957448	+	0.288607i	$0.906808\pi$
$788$	833.487	−	2289.99i	1.05772	−	2.90607i
$789$	294.794	−	224.319i	0.373630	−	0.284308i
$790$	−157.001	+	890.398i	−0.198736	+	1.12709i
$791$	692.099	+	399.584i	0.874967	+	0.505162i
$792$	−113.028	−	10.8087i	−0.142712	−	0.0136474i
$793$	269.608	+	466.975i	0.339985	+	0.588872i
$794$	744.648	+	2045.90i	0.937844	+	2.57671i
$795$	−253.869	+	130.856i	−0.319332	+	0.164599i
$796$	850.878	−	713.972i	1.06894	−	0.896950i
$797$	−949.323	−	1131.36i	−1.19112	−	1.41952i	−0.883768	−	0.467926i	$-0.845001\pi$
$797$	−949.323	−	1131.36i	−1.19112	−	1.41952i	−0.307352	−	0.951596i	$-0.599443\pi$
$798$	467.211	−	726.884i	0.585478	−	0.910882i
$799$	858.922	−	312.622i	1.07500	−	0.391267i
$800$	−430.245	+	248.402i	−0.537806	+	0.310502i
$801$	−276.231	+	580.107i	−0.344858	+	0.724228i
$802$	210.559	−	364.699i	0.262542	−	0.454737i
$803$	−84.5462	−	14.9078i	−0.105288	−	0.0185651i
$804$	−1649.48	+	210.389i	−2.05160	+	0.261678i
$805$	1023.36	+	372.472i	1.27125	+	0.462698i
$806$	277.558	−	48.9410i	0.344365	−	0.0607208i
$807$	−1122.87	−	1037.29i	−1.39141	−	1.28536i
$808$	−88.1762	−	73.9886i	−0.109129	−	0.0915701i
$809$			1487.78i			1.83903i	0.393055	+	0.919515i	$0.371418\pi$
$809$			1487.78i			1.83903i	−0.393055	+	0.919515i	$0.628582\pi$
$810$	−1167.36	−	1437.72i	−1.44118	−	1.77496i
$811$	391.709			0.482995			0.241497	−	0.970401i	$-0.422361\pi$
$811$	391.709			0.482995			0.241497	+	0.970401i	$0.422361\pi$
$812$	896.074	−	1067.90i	1.10354	−	1.31515i
$813$	−101.117	+	109.459i	−0.124375	+	0.134636i
$814$	37.4062	+	212.141i	0.0459536	+	0.260616i
$815$	623.900	−	1714.15i	0.765521	−	2.10325i
$816$	33.1230	+	259.690i	0.0405919	+	0.318247i
$817$	−113.892	+	645.916i	−0.139403	+	0.790595i
$818$	1567.96	+	905.265i	1.91683	+	1.10668i
$819$	252.619	−	173.864i	0.308448	−	0.212288i
$820$	−26.1940	−	45.3693i	−0.0319439	−	0.0553285i
$821$	1.02976	+	2.82925i	0.00125428	+	0.00344610i	0.940318	−	0.340297i	$-0.110527\pi$
$821$	1.02976	+	2.82925i	0.00125428	+	0.00344610i	−0.939064	+	0.343743i	$0.888305\pi$
$822$	495.497	+	318.485i	0.602795	+	0.387452i
$823$	−1037.37	+	870.460i	−1.26048	+	1.05767i	−0.264847	+	0.964290i	$0.585322\pi$
$823$	−1037.37	+	870.460i	−1.26048	+	1.05767i	−0.995631	+	0.0933764i	$0.970234\pi$
$824$	−1072.42	−	1278.06i	−1.30148	−	1.55104i
$825$	38.1600	+	74.0328i	0.0462546	+	0.0897367i
$826$	−1202.01	+	437.496i	−1.45522	+	0.529656i
$827$	1186.03	−	684.755i	1.43414	−	0.827999i	0.436703	−	0.899606i	$-0.356146\pi$
$827$	1186.03	−	684.755i	1.43414	−	0.827999i	0.997433	+	0.0716069i	$0.0228127\pi$
$828$	−1432.07	+	653.762i	−1.72955	+	0.789567i
$829$	−39.8034	+	68.9416i	−0.0480138	+	0.0831623i	−0.889033	−	0.457842i	$-0.848622\pi$
$829$	−39.8034	+	68.9416i	−0.0480138	+	0.0831623i	0.841020	+	0.541005i	$0.181956\pi$
$830$	−950.265	−	167.557i	−1.14490	−	0.201876i
$831$	207.292	+	272.417i	0.249449	+	0.327819i
$832$	481.808	+	175.364i	0.579096	+	0.210774i
$833$	−129.358	+	22.8094i	−0.155292	+	0.0273822i
$834$	480.854	−	149.482i	0.576563	−	0.179234i
$835$	−17.0587	−	14.3140i	−0.0204296	−	0.0171425i
$836$		−	119.125i		−	0.142494i
$837$	202.554	−	377.859i	0.241999	−	0.451445i
$838$	2220.92			2.65026
$839$	646.328	−	770.264i	0.770355	−	0.918074i	−0.228100	−	0.973638i	$-0.573251\pi$
$839$	646.328	−	770.264i	0.770355	−	0.918074i	0.998455	+	0.0555640i	$0.0176957\pi$
$840$	1302.06	+	294.177i	1.55007	+	0.350211i
$841$	−20.7070	−	117.435i	−0.0246219	−	0.139638i
$842$	−258.568	+	710.409i	−0.307088	+	0.843716i
$843$	71.6814	+	30.0309i	0.0850313	+	0.0356239i
$844$	−455.792	+	2584.92i	−0.540037	+	3.06270i
$845$	−836.841	−	483.150i	−0.990344	−	0.571775i
$846$	1208.71	+	1228.39i	1.42874	+	1.45199i
$847$	−381.132	−	660.139i	−0.449978	−	0.779385i
$848$	26.0349	+	71.5302i	0.0307015	+	0.0843517i
$849$	22.5178	−	472.016i	0.0265227	−	0.555967i
$850$	901.411	−	756.374i	1.06048	−	0.889851i
$851$	830.493	+	989.743i	0.975902	+	1.16304i
$852$	969.737	+	46.2619i	1.13819	+	0.0542980i
$853$	−331.253	+	120.566i	−0.388339	+	0.141344i	−0.528808	−	0.848741i	$-0.677361\pi$
$853$	−331.253	+	120.566i	−0.388339	+	0.141344i	0.140470	+	0.990085i	$0.455139\pi$
$854$	−1855.12	+	1071.05i	−2.17227	+	1.25416i
$855$	599.134	−	589.538i	0.700741	−	0.689518i
$856$	−546.733	+	946.969i	−0.638707	+	1.10627i
$857$	−1186.99	−	209.299i	−1.38506	−	0.244223i	−0.569068	−	0.822290i	$-0.692696\pi$
$857$	−1186.99	−	209.299i	−1.38506	−	0.244223i	−0.815989	+	0.578067i	$0.803807\pi$
$858$	25.6060	−	61.1194i	0.0298438	−	0.0712347i
$859$	−594.390	−	216.340i	−0.691956	−	0.251851i	−0.0279836	−	0.999608i	$-0.508909\pi$
$859$	−594.390	−	216.340i	−0.691956	−	0.251851i	−0.663973	+	0.747757i	$0.731131\pi$
$860$	−2306.60	+	406.716i	−2.68209	+	0.472925i
$861$	4.55820	−	20.1750i	0.00529408	−	0.0234321i
$862$	−1093.96	−	917.941i	−1.26909	−	1.06490i
$863$			1076.50i			1.24739i	0.781668	+	0.623695i	$0.214369\pi$
$863$			1076.50i			1.24739i	−0.781668	+	0.623695i	$0.785631\pi$
$864$	510.980	−	316.898i	0.591412	−	0.366780i
$865$	1323.87			1.53048
$866$	−25.6375	+	30.5536i	−0.0296045	+	0.0352813i
$867$	−33.1434	−	106.616i	−0.0382277	−	0.122971i
$868$	124.043	+	703.481i	0.142906	+	0.810462i
$869$	−16.8315	+	46.2443i	−0.0193689	+	0.0532155i
$870$	1691.48	−	1287.10i	1.94423	−	1.47943i
$871$	72.9024	−	413.450i	0.0836996	−	0.474684i
$872$	−1547.91	−	893.685i	−1.77512	−	1.02487i
$873$	4.23090	+	9.26779i	0.00484639	+	0.0106160i
$874$	−559.949	−	969.860i	−0.640674	−	1.10968i
$875$	40.3975	+	110.991i	0.0461686	+	0.126847i
$876$	−1296.84	+	668.452i	−1.48041	+	0.763073i
$877$	981.482	−	823.562i	1.11914	−	0.939067i	0.120576	−	0.992704i	$-0.461526\pi$
$877$	981.482	−	823.562i	1.11914	−	0.939067i	0.998560	+	0.0536374i	$0.0170815\pi$
$878$	161.038	+	191.917i	0.183414	+	0.218584i
$879$	−681.175	+	1059.77i	−0.774943	+	1.20565i
$880$	44.2352	−	16.1003i	0.0502672	−	0.0182958i
$881$	−787.917	+	454.904i	−0.894344	+	0.516350i	−0.875361	−	0.483470i	$-0.839376\pi$
$881$	−787.917	+	454.904i	−0.894344	+	0.516350i	−0.0189831	+	0.999820i	$0.506043\pi$
$882$	−140.407	−	204.007i	−0.159191	−	0.231300i
$883$	−817.068	+	1415.20i	−0.925332	+	1.60272i	−0.134305	+	0.990940i	$0.542880\pi$
$883$	−817.068	+	1415.20i	−0.925332	+	1.60272i	−0.791027	+	0.611782i	$0.790453\pi$
$884$	−588.230	−	103.721i	−0.665419	−	0.117331i
$885$	−1234.30	+	157.433i	−1.39469	+	0.177891i
$886$	774.613	+	281.936i	0.874281	+	0.318212i
$887$	−585.651	+	103.266i	−0.660260	+	0.116422i	−0.493731	−	0.869615i	$-0.664367\pi$
$887$	−585.651	+	103.266i	−0.660260	+	0.116422i	−0.166529	+	0.986037i	$0.553256\pi$
$888$	1163.28	+	1074.62i	1.31000	+	1.21016i
$889$	6.29916	+	5.28563i	0.00708567	+	0.00594559i
$890$		−	1632.26i		−	1.83400i
$891$	−48.9853	−	88.0998i	−0.0549779	−	0.0988775i
$892$	−658.450			−0.738173
$893$	−502.769	+	599.177i	−0.563011	+	0.670971i
$894$	491.861	−	532.441i	0.550180	−	0.595572i
$895$	−263.919	−	1496.76i	−0.294881	−	1.67236i
$896$	−502.240	+	1379.89i	−0.560536	+	1.54006i
$897$	−50.2875	−	394.262i	−0.0560618	−	0.439534i
$898$	118.649	−	672.891i	0.132126	−	0.749321i
$899$	426.126	+	246.024i	0.474000	+	0.273664i
$900$	1277.96	+	608.529i	1.41995	+	0.676143i
$901$	109.816	+	190.206i	0.121882	+	0.211106i
$902$	−1.52863	−	4.19988i	−0.00169471	−	0.00465618i
$903$	−777.895	−	499.999i	−0.861456	−	0.553709i
$904$	972.546	−	816.063i	1.07583	−	0.902725i
$905$	−643.602	−	767.014i	−0.711162	−	0.847530i
$906$	15.5039	+	30.0785i	0.0171125	+	0.0331992i
$907$	−276.952	+	100.802i	−0.305349	+	0.111138i	−0.490150	−	0.871638i	$-0.663058\pi$
$907$	−276.952	+	100.802i	−0.305349	+	0.111138i	0.184801	+	0.982776i	$0.440836\pi$
$908$	2229.49	−	1287.20i	2.45538	−	1.41762i
$909$	9.72789	−	101.726i	0.0107018	−	0.111909i
$910$	−389.531	+	674.688i	−0.428056	+	0.741416i
$911$	−820.799	−	144.729i	−0.900986	−	0.158868i	−0.296078	−	0.955164i	$-0.595679\pi$
$911$	−820.799	−	144.729i	−0.900986	−	0.158868i	−0.604908	+	0.796295i	$0.706790\pi$
$912$	−135.658	−	178.278i	−0.148748	−	0.195480i
$913$	−49.3535	−	17.9632i	−0.0540565	−	0.0196749i
$914$	2092.04	−	368.883i	2.28888	−	0.403592i
$915$	−1989.82	+	618.569i	−2.17466	+	0.676031i
$916$	575.305	+	482.738i	0.628062	+	0.527007i
$917$		−	586.439i		−	0.639519i
$918$	−1061.56	+	949.351i	−1.15638	+	1.03415i
$919$	1687.49			1.83623			0.918114	−	0.396315i	$-0.129711\pi$
$919$	1687.49			1.83623			0.918114	+	0.396315i	$0.129711\pi$
$920$	1112.06	−	1325.30i	1.20876	−	1.44055i
$921$	591.316	+	133.598i	0.642037	+	0.145057i
$922$	−81.7612	−	463.691i	−0.0886781	−	0.502919i
$923$	−83.8336	+	230.331i	−0.0908273	+	0.249546i
$924$	154.909	+	64.8993i	0.167651	+	0.0702374i
$925$	201.726	−	1144.05i	0.218082	−	1.23681i
$926$	−811.093	−	468.285i	−0.875910	−	0.505707i
$927$	394.894	−	1427.57i	0.425991	−	1.53999i
$928$	345.038	+	597.623i	0.371808	+	0.643990i
$929$	−354.196	−	973.147i	−0.381266	−	1.04752i	−0.970824	−	0.239794i	$-0.922920\pi$
$929$	−354.196	−	973.147i	−0.381266	−	1.04752i	0.589557	−	0.807726i	$-0.299302\pi$
$930$	−51.8991	+	1087.90i	−0.0558055	+	1.16979i
$931$	86.1053	−	72.2509i	0.0924869	−	0.0776057i
$932$	1078.07	+	1284.80i	1.15673	+	1.37854i
$933$	794.791	+	37.9160i	0.851867	+	0.0406388i
$934$	1667.90	−	607.066i	1.78576	−	0.649964i
$935$	117.626	−	67.9113i	0.125803	−	0.0726324i
$936$	−122.288	−	471.579i	−0.130649	−	0.503824i
$937$	687.817	−	1191.33i	0.734063	−	1.27143i	−0.221071	−	0.975258i	$-0.570955\pi$
$937$	687.817	−	1191.33i	0.734063	−	1.27143i	0.955133	−	0.296176i	$-0.0957115\pi$
$938$	1642.48	+	289.614i	1.75105	+	0.308757i
$939$	319.647	−	762.972i	0.340413	−	0.812537i
$940$	−2624.72	−	955.319i	−2.79225	−	1.01630i
$941$	1678.41	−	295.949i	1.78365	−	0.314505i	0.818166	−	0.574983i	$-0.194991\pi$
$941$	1678.41	−	295.949i	1.78365	−	0.314505i	0.965480	+	0.260478i	$0.0838800\pi$
$942$	−563.966	+	2496.16i	−0.598690	+	2.64985i
$943$	−20.5352	−	17.2311i	−0.0217765	−	0.0182726i
$944$			331.632i			0.351305i
$945$	440.222	+	1100.29i	0.465844	+	1.16433i
$946$	−199.820			−0.211226
$947$	−14.5188	+	17.3028i	−0.0153314	+	0.0182712i	−0.773656	−	0.633606i	$-0.781574\pi$
$947$	−14.5188	+	17.3028i	−0.0153314	+	0.0182712i	0.758324	+	0.651878i	$0.226018\pi$
$948$	248.268	+	798.631i	0.261886	+	0.842438i
$949$	−63.9643	−	362.760i	−0.0674018	−	0.382255i
$950$	−344.392	+	946.210i	−0.362518	+	0.996011i
$951$	−83.5737	+	63.5941i	−0.0878798	+	0.0668707i
$952$	178.251	−	1010.91i	0.187238	−	1.06188i
$953$	877.360	+	506.544i	0.920630	+	0.531526i	0.883836	−	0.467797i	$-0.154952\pi$
$953$	877.360	+	506.544i	0.920630	+	0.531526i	0.0367941	+	0.999323i	$0.488285\pi$
$954$	−240.244	+	337.277i	−0.251829	+	0.353540i
$955$	268.750	+	465.489i	0.281414	+	0.487423i
$956$	−207.197	−	569.270i	−0.216734	−	0.595470i
$957$	102.834	−	53.0055i	0.107454	−	0.0553871i
$958$	−432.045	+	362.529i	−0.450986	+	0.378422i
$959$	−242.281	−	288.739i	−0.252639	−	0.301083i
$960$	−1071.34	+	1666.78i	−1.11598	+	1.73623i
$961$	666.116	−	242.446i	0.693149	−	0.252286i
$962$	−800.441	+	462.135i	−0.832059	+	0.480390i
$963$	−967.724	+	76.7986i	−1.00491	+	0.0797493i
$964$	−103.499	+	179.265i	−0.107364	+	0.185959i
$965$	1516.71	+	267.437i	1.57172	+	0.277137i
$966$	1566.26	−	199.774i	1.62138	−	0.206805i
$967$	−92.8853	−	33.8075i	−0.0960551	−	0.0349612i	0.293546	−	0.955945i	$-0.405165\pi$
$967$	−92.8853	−	33.8075i	−0.0960551	−	0.0349612i	−0.389601	+	0.920984i	$0.627387\pi$
$968$	−1192.55	+	210.278i	−1.23197	+	0.217229i
$969$	−474.788	−	438.602i	−0.489977	−	0.452633i
$970$	−19.8263	−	16.6362i	−0.0204395	−	0.0171507i
$971$			415.261i			0.427664i	0.976871	+	0.213832i	$0.0685944\pi$
$971$			415.261i			0.427664i	−0.976871	+	0.213832i	$0.931406\pi$
$972$	−1569.13	−	687.371i	−1.61433	−	0.707172i
$973$	−322.227			−0.331169
$974$	44.4556	−	52.9802i	0.0456423	−	0.0543944i
$975$	−242.494	+	262.501i	−0.248712	+	0.269231i
$976$	96.4375	+	546.924i	0.0988089	+	0.560373i
$977$	−107.877	+	296.389i	−0.110416	+	0.303366i	−0.982578	−	0.185852i	$-0.940496\pi$
$977$	−107.877	+	296.389i	−0.110416	+	0.303366i	0.872161	+	0.489218i	$0.162718\pi$
$978$	−334.625	−	2623.52i	−0.342153	−	2.68253i
$979$	15.4276	−	87.4943i	0.0157585	−	0.0893711i
$980$	347.618	+	200.697i	0.354712	+	0.204793i
$981$	−125.534	−	1581.83i	−0.127966	−	1.61247i
$982$	−251.177	−	435.052i	−0.255781	−	0.443027i
$983$	219.236	+	602.345i	0.223027	+	0.612762i	0.999856	−	0.0169496i	$-0.00539547\pi$
$983$	219.236	+	602.345i	0.223027	+	0.612762i	−0.776829	+	0.629711i	$0.783173\pi$
$984$	−27.6408	−	17.7664i	−0.0280903	−	0.0180553i
$985$	−1821.39	+	1528.32i	−1.84912	+	1.55160i
$986$	−1050.63	−	1252.09i	−1.06554	−	1.26987i
$987$	−505.256	−	980.227i	−0.511911	−	0.993138i
$988$	480.302	−	174.816i	0.486136	−	0.176939i
$989$	−1037.92	+	599.245i	−1.04947	+	0.605910i
$990$	208.576	+	148.570i	0.210683	+	0.150071i
$991$	−464.001	+	803.674i	−0.468215	+	0.810973i	−0.999340	−	0.0363209i	$-0.988436\pi$
$991$	−464.001	+	803.674i	−0.468215	+	0.810973i	0.531125	+	0.847294i	$0.321769\pi$
$992$	−348.235	−	61.4032i	−0.351043	−	0.0618984i
$993$	383.069	+	503.419i	0.385769	+	0.506968i
$994$	−915.020	−	333.040i	−0.920544	−	0.335050i
$995$	−1067.25	+	188.185i	−1.07261	+	0.189131i
$996$	−852.328	+	264.961i	−0.855751	+	0.266025i
$997$	872.811	+	732.376i	0.875438	+	0.734579i	0.965236	−	0.261381i	$-0.0841778\pi$
$997$	872.811	+	732.376i	0.875438	+	0.734579i	−0.0897982	+	0.995960i	$0.528622\pi$
$998$		−	2717.71i		−	2.72316i
$999$	−200.381	+	1391.62i	−0.200581	+	1.39301i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.3.f.a.11.5	yes	30
3.2	odd	2		81.3.f.a.35.1		30
4.3	odd	2		432.3.bc.a.65.4		30
9.2	odd	6		243.3.f.b.26.5		30
9.4	even	3		243.3.f.d.188.5		30
9.5	odd	6		243.3.f.a.188.1		30
9.7	even	3		243.3.f.c.26.1		30
27.4	even	9		243.3.f.b.215.5		30
27.5	odd	18	inner	27.3.f.a.5.5	✓	30
27.7	even	9		729.3.b.a.728.4		30
27.13	even	9		243.3.f.a.53.1		30
27.14	odd	18		243.3.f.d.53.5		30
27.20	odd	18		729.3.b.a.728.27		30
27.22	even	9		81.3.f.a.44.1		30
27.23	odd	18		243.3.f.c.215.1		30
108.59	even	18		432.3.bc.a.113.4		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.5.5	✓	30	27.5	odd	18	inner
27.3.f.a.11.5	yes	30	1.1	even	1	trivial
81.3.f.a.35.1		30	3.2	odd	2
81.3.f.a.44.1		30	27.22	even	9
243.3.f.a.53.1		30	27.13	even	9
243.3.f.a.188.1		30	9.5	odd	6
243.3.f.b.26.5		30	9.2	odd	6
243.3.f.b.215.5		30	27.4	even	9
243.3.f.c.26.1		30	9.7	even	3
243.3.f.c.215.1		30	27.23	odd	18
243.3.f.d.53.5		30	27.14	odd	18
243.3.f.d.188.5		30	9.4	even	3
432.3.bc.a.65.4		30	4.3	odd	2
432.3.bc.a.113.4		30	108.59	even	18
729.3.b.a.728.4		30	27.7	even	9
729.3.b.a.728.27		30	27.20	odd	18

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.13670 - 2.54642i) q^{2} +(-2.03568 + 2.20363i) q^{3} +(-1.22417 - 6.94260i) q^{4} +(-2.35247 + 6.46335i) q^{5} +(1.26173 + 9.89219i) q^{6} +(1.10811 - 6.28443i) q^{7} +(-8.77937 - 5.06877i) q^{8} +(-0.712002 - 8.97179i) q^{9} +(11.4319 + 19.8006i) q^{10} +(0.425636 + 1.16942i) q^{11} +(17.7910 + 11.4353i) q^{12} +(-4.09039 + 3.43225i) q^{13} +(-13.6351 - 16.2496i) q^{14} +(-9.45398 - 18.3413i) q^{15} +(-5.16785 + 1.88094i) q^{16} +(-13.7418 + 7.93385i) q^{17} +(-24.3672 - 17.3569i) q^{18} +(6.78917 - 11.7592i) q^{19} +(47.7523 + 8.42002i) q^{20} +(11.5928 + 15.2350i) q^{21} +(3.88729 + 1.41486i) q^{22} +(24.4347 - 4.30850i) q^{23} +(29.0417 - 9.02811i) q^{24} +(-17.0897 - 14.3399i) q^{25} +17.7495i q^{26} +(21.2200 + 16.6947i) q^{27} -44.9868 q^{28} +(-19.9186 + 23.7381i) q^{29} +(-66.9048 - 15.1160i) q^{30} +(-2.75731 - 15.6375i) q^{31} +(7.61653 - 20.9262i) q^{32} +(-3.44344 - 1.44263i) q^{33} +(-9.15924 + 51.9446i) q^{34} +(38.0116 + 21.9460i) q^{35} +(-61.4160 + 15.9261i) q^{36} +(26.0365 + 45.0965i) q^{37} +(-15.4374 - 42.4139i) q^{38} +(0.763322 - 16.0007i) q^{39} +(53.4144 - 44.8200i) q^{40} +(-0.694475 - 0.827643i) q^{41} +(63.5649 + 3.03240i) q^{42} +(-45.3904 + 16.5207i) q^{43} +(7.59780 - 4.38659i) q^{44} +(59.6628 + 16.5039i) q^{45} +(41.2384 - 71.4270i) q^{46} +(-56.7291 - 10.0029i) q^{47} +(6.37518 - 15.2170i) q^{48} +(7.77884 + 2.83127i) q^{49} +(-73.0309 + 12.8773i) q^{50} +(10.4907 - 46.4327i) q^{51} +(28.8361 + 24.1963i) q^{52} -13.8414i q^{53} +(87.8523 - 18.3633i) q^{54} -8.55969 q^{55} +(-41.5829 + 49.5566i) q^{56} +(12.0924 + 38.8988i) q^{57} +(17.8870 + 101.442i) q^{58} +(20.6246 - 56.6655i) q^{59} +(-115.763 + 88.0881i) q^{60} +(17.5357 - 99.4497i) q^{61} +(-45.7111 - 26.3913i) q^{62} +(-57.1715 - 5.46725i) q^{63} +(-48.0117 - 83.1587i) q^{64} +(-12.5613 - 34.5119i) q^{65} +(-11.0311 + 5.68597i) q^{66} +(-60.2302 + 50.5391i) q^{67} +(71.9039 + 85.6917i) q^{68} +(-40.2470 + 62.6160i) q^{69} +(137.103 - 49.9014i) q^{70} +(39.7545 - 22.9523i) q^{71} +(-39.2251 + 82.3757i) q^{72} +(-34.4926 + 59.7430i) q^{73} +(170.466 + 30.0578i) q^{74} +(66.3891 - 8.46783i) q^{75} +(-89.9505 - 32.7393i) q^{76} +(7.82081 - 1.37902i) q^{77} +(-39.1134 - 36.1324i) q^{78} +(30.2928 + 25.4187i) q^{79} -37.8265i q^{80} +(-79.9861 + 12.7759i) q^{81} -3.59141 q^{82} +(-27.1277 + 32.3296i) q^{83} +(91.5788 - 99.1344i) q^{84} +(-18.9520 - 107.482i) q^{85} +(-54.9168 + 150.883i) q^{86} +(-11.7621 - 92.2165i) q^{87} +(2.19073 - 12.4243i) q^{88} +(-61.8262 - 35.6954i) q^{89} +(169.507 - 116.662i) q^{90} +(17.0371 + 29.5091i) q^{91} +(-59.8245 - 164.366i) q^{92} +(40.0723 + 25.7569i) q^{93} +(-146.684 + 123.083i) q^{94} +(60.0324 + 71.5439i) q^{95} +(30.6089 + 59.3832i) q^{96} +(-1.06372 + 0.387161i) q^{97} +(23.8306 - 13.7586i) q^{98} +(10.1888 - 4.65135i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8} - 3 q^{10} - 6 q^{11} - 15 q^{12} - 6 q^{13} - 15 q^{14} - 9 q^{15} - 18 q^{16} - 9 q^{17} + 63 q^{18} - 3 q^{19} + 213 q^{20}+ \cdots + 513 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 15 * q^5 - 18 * q^6 - 6 * q^7 - 9 * q^8 - 3 * q^10 - 6 * q^11 - 15 * q^12 - 6 * q^13 - 15 * q^14 - 9 * q^15 - 18 * q^16 - 9 * q^17 + 63 * q^18 - 3 * q^19 + 213 * q^20 + 132 * q^21 - 42 * q^22 + 120 * q^23 + 144 * q^24 - 15 * q^25 - 90 * q^27 - 12 * q^28 - 168 * q^29 - 243 * q^30 + 39 * q^31 - 360 * q^32 - 207 * q^33 + 54 * q^34 - 252 * q^35 - 360 * q^36 - 3 * q^37 - 84 * q^38 + 15 * q^39 - 33 * q^40 + 228 * q^41 + 486 * q^42 - 96 * q^43 + 639 * q^44 + 477 * q^45 - 3 * q^46 + 399 * q^47 + 453 * q^48 - 78 * q^49 + 303 * q^50 + 36 * q^51 - 9 * q^52 - 54 * q^54 - 12 * q^55 - 393 * q^56 - 192 * q^57 + 129 * q^58 - 474 * q^59 - 846 * q^60 + 138 * q^61 - 900 * q^62 - 585 * q^63 - 51 * q^64 - 411 * q^65 - 423 * q^66 + 354 * q^67 + 99 * q^68 + 99 * q^69 + 489 * q^70 + 315 * q^71 + 720 * q^72 - 66 * q^73 + 321 * q^74 + 255 * q^75 + 258 * q^76 + 201 * q^77 + 180 * q^78 + 30 * q^79 + 36 * q^81 - 12 * q^82 - 33 * q^83 - 588 * q^84 - 261 * q^85 - 258 * q^86 - 279 * q^87 - 642 * q^88 + 72 * q^89 + 288 * q^90 + 96 * q^91 - 3 * q^92 + 591 * q^93 - 861 * q^94 + 681 * q^95 + 270 * q^96 - 582 * q^97 + 882 * q^98 + 513 * q^99

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