LMFDB - Embedded newform 272.3.x.a.155.6

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			155.6
Character	$\chi$	$=$	272.155
Dual form			272.3.x.a.179.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.95557 + 0.419209i) q^{2} +(4.50783 + 1.86720i) q^{3} +(3.64853 - 1.63959i) q^{4} +(1.59844 - 3.85899i) q^{5} +(-9.59814 - 1.76173i) q^{6} +(1.19737 - 2.89070i) q^{7} +(-6.44763 + 4.73583i) q^{8} +(10.4701 + 10.4701i) q^{9} +(-1.50815 + 8.21661i) q^{10} +(7.41088 - 3.06969i) q^{11} +(19.5084 - 0.578434i) q^{12} +(-2.94048 - 2.94048i) q^{13} +(-1.12973 + 6.15493i) q^{14} +(14.4110 - 14.4110i) q^{15} +(10.6235 - 11.9642i) q^{16} +(15.1590 - 7.69447i) q^{17} +(-24.8643 - 16.0859i) q^{18} +8.13029i q^{19} +(-0.495175 - 16.7004i) q^{20} +(10.7951 - 10.7951i) q^{21} +(-13.2057 + 9.10970i) q^{22} +(-27.9692 - 11.5852i) q^{23} +(-37.9076 + 9.30926i) q^{24} +(5.34092 + 5.34092i) q^{25} +(6.98299 + 4.51764i) q^{26} +(10.8428 + 26.1769i) q^{27} +(-0.370928 - 12.5100i) q^{28} +(-0.808672 - 0.334963i) q^{29} +(-22.1406 + 34.2231i) q^{30} +(0.138688 + 0.334824i) q^{31} +(-15.7596 + 27.8502i) q^{32} +39.1387 q^{33} +(-26.4189 + 21.4019i) q^{34} +(-9.24125 - 9.24125i) q^{35} +(55.3672 + 21.0339i) q^{36} +(25.2739 + 10.4688i) q^{37} +(-3.40829 - 15.8994i) q^{38} +(-7.76470 - 18.7456i) q^{39} +(7.96931 + 32.4513i) q^{40} +(-14.4215 - 5.97357i) q^{41} +(-16.5851 + 25.6359i) q^{42} +34.7101i q^{43} +(22.0058 - 23.3506i) q^{44} +(57.1400 - 23.6682i) q^{45} +(59.5525 + 10.9308i) q^{46} -6.51881 q^{47} +(70.2285 - 34.0961i) q^{48} +(27.7258 + 27.7258i) q^{49} +(-12.6835 - 8.20560i) q^{50} +(82.7013 - 6.38040i) q^{51} +(-15.5496 - 5.90724i) q^{52} -45.8565i q^{53} +(-32.1776 - 46.6455i) q^{54} -33.5052i q^{55} +(5.96968 + 24.3087i) q^{56} +(-15.1809 + 36.6500i) q^{57} +(1.72184 + 0.316042i) q^{58} +17.1725i q^{59} +(28.9509 - 76.2072i) q^{60} +(35.1134 + 84.7712i) q^{61} +(-0.411576 - 0.596632i) q^{62} +(42.8026 - 17.7294i) q^{63} +(19.1439 - 61.0697i) q^{64} +(-16.0474 + 6.64707i) q^{65} +(-76.5386 + 16.4073i) q^{66} +(13.1306 + 13.1306i) q^{67} +(42.6923 - 52.9280i) q^{68} +(-104.449 - 104.449i) q^{69} +(21.9460 + 14.1979i) q^{70} +(-57.4227 + 23.7853i) q^{71} +(-117.092 - 17.9228i) q^{72} +(-115.706 + 47.9268i) q^{73} +(-53.8136 - 9.87744i) q^{74} +(14.1034 + 34.0486i) q^{75} +(13.3303 + 29.6636i) q^{76} -25.0982i q^{77} +(23.0428 + 33.4034i) q^{78} +(-45.4854 + 109.812i) q^{79} +(-29.1884 - 60.1200i) q^{80} +4.98410i q^{81} +(30.7064 + 5.63614i) q^{82} +50.1193i q^{83} +(21.6866 - 57.0856i) q^{84} +(-5.46202 - 70.7975i) q^{85} +(-14.5508 - 67.8782i) q^{86} +(-3.01991 - 3.01991i) q^{87} +(-33.2451 + 54.8889i) q^{88} -105.577 q^{89} +(-101.819 + 70.2384i) q^{90} +(-12.0209 + 4.97921i) q^{91} +(-121.042 + 3.58894i) q^{92} +1.76829i q^{93} +(12.7480 - 2.73275i) q^{94} +(31.3747 + 12.9958i) q^{95} +(-123.044 + 96.1179i) q^{96} +(-68.1316 - 164.484i) q^{97} +(-65.8426 - 42.5968i) q^{98} +(109.733 + 45.4528i) 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 $

$2$	−1.95557	+	0.419209i	−0.977786	+	0.209604i
$2$	−1.95557	+	0.419209i	−0.977786	+	0.209604i
$3$	4.50783	+	1.86720i	1.50261	+	0.622402i	0.974017	−	0.226474i	$-0.0727198\pi$
$3$	4.50783	+	1.86720i	1.50261	+	0.622402i	0.528593	+	0.848875i	$0.322720\pi$
$4$	3.64853	−	1.63959i	0.912132	−	0.409897i
$5$	1.59844	−	3.85899i	0.319689	−	0.771797i	−0.679581	−	0.733600i	$-0.737839\pi$
$5$	1.59844	−	3.85899i	0.319689	−	0.771797i	0.999270	−	0.0381970i	$-0.0121614\pi$
$6$	−9.59814	−	1.76173i	−1.59969	−	0.293622i
$7$	1.19737	−	2.89070i	0.171053	−	0.412958i	−0.814985	−	0.579483i	$-0.803255\pi$
$7$	1.19737	−	2.89070i	0.171053	−	0.412958i	0.986037	+	0.166525i	$0.0532547\pi$
$8$	−6.44763	+	4.73583i	−0.805954	+	0.591978i
$9$	10.4701	+	10.4701i	1.16335	+	1.16335i
$10$	−1.50815	+	8.21661i	−0.150815	+	0.821661i
$11$	7.41088	−	3.06969i	0.673716	−	0.279062i	−0.0194811	−	0.999810i	$-0.506201\pi$
$11$	7.41088	−	3.06969i	0.673716	−	0.279062i	0.693197	+	0.720748i	$0.256201\pi$
$12$	19.5084	−	0.578434i	1.62570	−	0.0482028i
$13$	−2.94048	−	2.94048i	−0.226191	−	0.226191i	0.584909	−	0.811099i	$-0.301130\pi$
$13$	−2.94048	−	2.94048i	−0.226191	−	0.226191i	−0.811099	+	0.584909i	$0.801130\pi$
$14$	−1.12973	+	6.15493i	−0.0806951	+	0.439638i
$15$	14.4110	−	14.4110i	0.960735	−	0.960735i
$16$	10.6235	−	11.9642i	0.663969	−	0.747760i
$17$	15.1590	−	7.69447i	0.891706	−	0.452616i
$17$	15.1590	−	7.69447i	0.891706	−	0.452616i
$18$	−24.8643	−	16.0859i	−1.38135	−	0.893662i
$19$			8.13029i			0.427910i	0.976844	+	0.213955i	$0.0686346\pi$
$19$			8.13029i			0.427910i	−0.976844	+	0.213955i	$0.931365\pi$
$20$	−0.495175	−	16.7004i	−0.0247588	−	0.835020i
$21$	10.7951	−	10.7951i	0.514051	−	0.514051i
$22$	−13.2057	+	9.10970i	−0.600258	+	0.414077i
$23$	−27.9692	−	11.5852i	−1.21605	−	0.503706i	−0.319901	−	0.947451i	$-0.603650\pi$
$23$	−27.9692	−	11.5852i	−1.21605	−	0.503706i	−0.896153	+	0.443745i	$0.853650\pi$
$24$	−37.9076	+	9.30926i	−1.57948	+	0.387886i
$25$	5.34092	+	5.34092i	0.213637	+	0.213637i
$26$	6.98299	+	4.51764i	0.268577	+	0.173755i
$27$	10.8428	+	26.1769i	0.401587	+	0.969516i
$28$	−0.370928	−	12.5100i	−0.0132474	−	0.446786i
$29$	−0.808672	−	0.334963i	−0.0278852	−	0.0115504i	0.368697	−	0.929550i	$-0.379804\pi$
$29$	−0.808672	−	0.334963i	−0.0278852	−	0.0115504i	−0.396582	+	0.917999i	$0.629804\pi$
$30$	−22.1406	+	34.2231i	−0.738019	+	1.14077i
$31$	0.138688	+	0.334824i	0.00447382	+	0.0108008i	0.926101	−	0.377277i	$-0.123139\pi$
$31$	0.138688	+	0.334824i	0.00447382	+	0.0108008i	−0.921627	+	0.388077i	$0.873139\pi$
$32$	−15.7596	+	27.8502i	−0.492486	+	0.870320i
$33$	39.1387			1.18602
$34$	−26.4189	+	21.4019i	−0.777027	+	0.629467i
$35$	−9.24125	−	9.24125i	−0.264036	−	0.264036i
$36$	55.3672	+	21.0339i	1.53798	+	0.584274i
$37$	25.2739	+	10.4688i	0.683078	+	0.282940i	0.697113	−	0.716961i	$-0.254468\pi$
$37$	25.2739	+	10.4688i	0.683078	+	0.282940i	−0.0140347	+	0.999902i	$0.504468\pi$
$38$	−3.40829	−	15.8994i	−0.0896919	−	0.418405i
$39$	−7.76470	−	18.7456i	−0.199095	−	0.480658i
$40$	7.96931	+	32.4513i	0.199233	+	0.811282i
$41$	−14.4215	−	5.97357i	−0.351743	−	0.145697i	0.199814	−	0.979834i	$-0.435966\pi$
$41$	−14.4215	−	5.97357i	−0.351743	−	0.145697i	−0.551557	+	0.834137i	$0.685966\pi$
$42$	−16.5851	+	25.6359i	−0.394884	+	0.610379i
$43$			34.7101i			0.807212i	0.914933	+	0.403606i	$0.132243\pi$
$43$			34.7101i			0.807212i	−0.914933	+	0.403606i	$0.867757\pi$
$44$	22.0058	−	23.3506i	0.500131	−	0.530696i
$45$	57.1400	−	23.6682i	1.26978	−	0.525959i
$46$	59.5525	+	10.9308i	1.29462	+	0.237626i
$47$	−6.51881			−0.138698			−0.0693491	−	0.997592i	$-0.522092\pi$
$47$	−6.51881			−0.138698			−0.0693491	+	0.997592i	$0.522092\pi$
$48$	70.2285	−	34.0961i	1.46309	−	0.710336i
$49$	27.7258	+	27.7258i	0.565832	+	0.565832i
$50$	−12.6835	−	8.20560i	−0.253671	−	0.164112i
$51$	82.7013	−	6.38040i	1.62159	−	0.125106i
$52$	−15.5496	−	5.90724i	−0.299030	−	0.113601i
$53$		−	45.8565i		−	0.865218i	−0.901582	−	0.432609i	$-0.857593\pi$
$53$		−	45.8565i		−	0.865218i	0.901582	−	0.432609i	$-0.142407\pi$
$54$	−32.1776	−	46.6455i	−0.595881	−	0.863805i
$55$		−	33.5052i		−	0.609185i
$56$	5.96968	+	24.3087i	0.106601	+	0.434084i
$57$	−15.1809	+	36.6500i	−0.266332	+	0.642982i
$58$	1.72184	+	0.316042i	0.0296868	+	0.00544899i
$59$			17.1725i			0.291059i	0.989354	+	0.145529i	$0.0464885\pi$
$59$			17.1725i			0.291059i	−0.989354	+	0.145529i	$0.953511\pi$
$60$	28.9509	−	76.2072i	0.482515	−	1.27012i
$61$	35.1134	+	84.7712i	0.575629	+	1.38969i	0.896701	+	0.442637i	$0.145957\pi$
$61$	35.1134	+	84.7712i	0.575629	+	1.38969i	−0.321072	+	0.947055i	$0.604043\pi$
$62$	−0.411576	−	0.596632i	−0.00663833	−	0.00962310i
$63$	42.8026	−	17.7294i	0.679407	−	0.281419i
$64$	19.1439	−	61.0697i	0.299123	−	0.954215i
$65$	−16.0474	+	6.64707i	−0.246884	+	0.102263i
$66$	−76.5386	+	16.4073i	−1.15968	+	0.248596i
$67$	13.1306	+	13.1306i	0.195979	+	0.195979i	0.798274	−	0.602295i	$-0.205747\pi$
$67$	13.1306	+	13.1306i	0.195979	+	0.195979i	−0.602295	+	0.798274i	$0.705747\pi$
$68$	42.6923	−	52.9280i	0.627828	−	0.778352i
$69$	−104.449	−	104.449i	−1.51375	−	1.51375i
$70$	21.9460	+	14.1979i	0.313514	+	0.202828i
$71$	−57.4227	+	23.7853i	−0.808770	+	0.335004i	−0.748463	−	0.663176i	$-0.769208\pi$
$71$	−57.4227	+	23.7853i	−0.808770	+	0.335004i	−0.0603070	+	0.998180i	$0.519208\pi$
$72$	−117.092	−	17.9228i	−1.62628	−	0.248928i
$73$	−115.706	+	47.9268i	−1.58501	+	0.656532i	−0.989197	−	0.146592i	$-0.953169\pi$
$73$	−115.706	+	47.9268i	−1.58501	+	0.656532i	−0.595811	+	0.803124i	$0.703169\pi$
$74$	−53.8136	−	9.87744i	−0.727210	−	0.133479i
$75$	14.1034	+	34.0486i	0.188045	+	0.453981i
$76$	13.3303	+	29.6636i	0.175399	+	0.390310i
$77$		−	25.0982i		−	0.325951i
$78$	23.0428	+	33.4034i	0.295420	+	0.428249i
$79$	−45.4854	+	109.812i	−0.575765	+	1.39002i	0.320817	+	0.947141i	$0.396043\pi$
$79$	−45.4854	+	109.812i	−0.575765	+	1.39002i	−0.896582	+	0.442878i	$0.853957\pi$
$80$	−29.1884	−	60.1200i	−0.364855	−	0.751500i
$81$			4.98410i			0.0615320i
$82$	30.7064	+	5.63614i	0.374468	+	0.0687334i
$83$			50.1193i			0.603847i	0.953332	+	0.301923i	$0.0976287\pi$
$83$			50.1193i			0.603847i	−0.953332	+	0.301923i	$0.902371\pi$
$84$	21.6866	−	57.0856i	0.258174	−	0.679590i
$85$	−5.46202	−	70.7975i	−0.0642590	−	0.832912i
$86$	−14.5508	−	67.8782i	−0.169195	−	0.789281i
$87$	−3.01991	−	3.01991i	−0.0347116	−	0.0347116i
$88$	−33.2451	+	54.8889i	−0.377785	+	0.623737i
$89$	−105.577			−1.18626			−0.593128	−	0.805108i	$-0.702107\pi$
$89$	−105.577			−1.18626			−0.593128	+	0.805108i	$0.702107\pi$
$90$	−101.819	+	70.2384i	−1.13133	+	0.780426i
$91$	−12.0209	+	4.97921i	−0.132098	+	0.0547166i
$92$	−121.042	+	3.58894i	−1.31567	+	0.0390102i
$93$			1.76829i			0.0190138i
$94$	12.7480	−	2.73275i	0.135617	−	0.0290718i
$95$	31.3747	+	12.9958i	0.330260	+	0.136798i
$96$	−123.044	+	96.1179i	−1.28170	+	1.00123i
$97$	−68.1316	−	164.484i	−0.702387	−	1.69571i	−0.718199	−	0.695838i	$-0.755033\pi$
$97$	−68.1316	−	164.484i	−0.702387	−	1.69571i	0.0158113	−	0.999875i	$-0.494967\pi$
$98$	−65.8426	−	42.5968i	−0.671863	−	0.434662i
$99$	109.733	+	45.4528i	1.10841	+	0.459120i
$100$	28.2434	+	10.7296i	0.282434	+	0.107296i
$101$	−119.313	−	119.313i	−1.18132	−	1.18132i	−0.979404	−	0.201912i	$-0.935285\pi$
$101$	−119.313	−	119.313i	−1.18132	−	1.18132i	−0.201912	−	0.979404i	$-0.564715\pi$
$102$	−159.054	+	47.1465i	−1.55935	+	0.462220i
$103$	172.654			1.67625			0.838127	−	0.545476i	$-0.183651\pi$
$103$	172.654			1.67625			0.838127	+	0.545476i	$0.183651\pi$
$104$	32.8847	+	5.03352i	0.316199	+	0.0483992i
$105$	−24.4027	−	58.9133i	−0.232407	−	0.561079i
$106$	19.2235	+	89.6758i	0.181354	+	0.845998i
$107$	−123.137	−	51.0050i	−1.15081	−	0.476682i	−0.276007	−	0.961156i	$-0.589011\pi$
$107$	−123.137	−	51.0050i	−1.15081	−	0.476682i	−0.874806	+	0.484473i	$0.839011\pi$
$108$	82.4798	+	77.7295i	0.763702	+	0.719718i
$109$	−60.0830	−	145.053i	−0.551220	−	1.33076i	−0.916563	−	0.399890i	$-0.869048\pi$
$109$	−60.0830	−	145.053i	−0.551220	−	1.33076i	0.365343	−	0.930873i	$-0.380952\pi$
$110$	14.0457	+	65.5218i	0.127688	+	0.595653i
$111$	94.3831	+	94.3831i	0.850298	+	0.850298i
$112$	−21.8646	−	45.0349i	−0.195219	−	0.402097i
$113$	192.273	+	79.6421i	1.70153	+	0.704798i	0.999970	−	0.00781013i	$-0.00248607\pi$
$113$	192.273	+	79.6421i	1.70153	+	0.704798i	0.701563	+	0.712608i	$0.252486\pi$
$114$	14.3234	−	78.0357i	0.125644	−	0.684523i
$115$	−89.4145	+	89.4145i	−0.777518	+	0.777518i
$116$	−3.49966	+	0.103767i	−0.0301695	+	0.000894541i
$117$		−	61.5743i		−	0.526276i
$118$	−7.19885	−	33.5820i	−0.0610072	−	0.284593i
$119$	−4.09151	−	53.0333i	−0.0343824	−	0.445658i
$120$	−24.6689	+	161.165i	−0.205574	+	1.34304i
$121$	−40.0618	+	40.0618i	−0.331089	+	0.331089i
$122$	−104.204	−	151.056i	−0.854128	−	1.23817i
$123$	−53.8557	−	53.8557i	−0.437851	−	0.437851i
$124$	1.05498	+	0.994221i	0.00850791	+	0.00801791i
$125$	125.622	−	52.0345i	1.00498	−	0.416276i
$126$	−76.2713	+	52.6144i	−0.605328	+	0.417575i
$127$	7.79411	+	7.79411i	0.0613710	+	0.0613710i	0.737126	−	0.675755i	$-0.236182\pi$
$127$	7.79411	+	7.79411i	0.0613710	+	0.0613710i	−0.675755	+	0.737126i	$0.736182\pi$
$128$	−11.8363	+	127.452i	−0.0924709	+	0.995715i
$129$	−64.8109	+	156.467i	−0.502410	+	1.21293i
$130$	28.5954	−	19.7261i	0.219965	−	0.151739i
$131$	11.4707	−	27.6927i	0.0875624	−	0.211394i	−0.874032	−	0.485868i	$-0.838504\pi$
$131$	11.4707	−	27.6927i	0.0875624	−	0.211394i	0.961595	+	0.274474i	$0.0885036\pi$
$132$	142.799	−	64.1714i	1.08181	−	0.486147i
$133$	23.5023	+	9.73495i	0.176709	+	0.0731951i
$134$	−31.1822	−	20.1733i	−0.232703	−	0.150547i
$135$	118.348			0.876653
$136$	−61.3000	+	121.401i	−0.450735	+	0.892658i
$137$		−	164.772i		−	1.20272i	−0.798979	−	0.601359i	$-0.794626\pi$
$137$		−	164.772i		−	1.20272i	0.798979	−	0.601359i	$-0.205374\pi$
$138$	248.043	+	160.471i	1.79741	+	1.16283i
$139$	−93.9293	+	226.765i	−0.675750	+	1.63141i	0.0959250	+	0.995389i	$0.469419\pi$
$139$	−93.9293	+	226.765i	−0.675750	+	1.63141i	−0.771675	+	0.636017i	$0.780581\pi$
$140$	−48.8688	−	18.5651i	−0.349063	−	0.132608i
$141$	−29.3857	−	12.1720i	−0.208409	−	0.0863260i
$142$	102.323	−	70.5859i	0.720586	−	0.497084i
$143$	−30.8179	−	12.7652i	−0.215510	−	0.0892670i
$144$	236.496	−	14.0368i	1.64233	−	0.0974776i
$145$	−2.58523	+	2.58523i	−0.0178292	+	0.0178292i
$146$	206.179	−	142.229i	1.41219	−	0.974173i
$147$	73.2134	+	176.753i	0.498050	+	1.20240i
$148$	109.377	−	3.24308i	0.739034	−	0.0219127i
$149$	−55.7993	+	55.7993i	−0.374492	+	0.374492i	−0.869110	−	0.494618i	$-0.835308\pi$
$149$	−55.7993	+	55.7993i	−0.374492	+	0.374492i	0.494618	+	0.869110i	$0.335308\pi$
$150$	−41.8537	−	60.6722i	−0.279024	−	0.404481i
$151$	−123.648	−	123.648i	−0.818859	−	0.818859i	0.167084	−	0.985943i	$-0.446565\pi$
$151$	−123.648	−	123.648i	−0.818859	−	0.818859i	−0.985943	+	0.167084i	$0.946565\pi$
$152$	−38.5037	−	52.4211i	−0.253313	−	0.344876i
$153$	239.279	+	78.1546i	1.56391	+	0.510814i
$154$	10.5214	+	49.0813i	0.0683207	+	0.318710i
$155$	1.51377			0.00976623
$156$	−59.0648	−	55.6631i	−0.378621	−	0.356815i
$157$	−126.256	−	126.256i	−0.804181	−	0.804181i	0.179565	−	0.983746i	$-0.442531\pi$
$157$	−126.256	−	126.256i	−0.804181	−	0.804181i	−0.983746	+	0.179565i	$0.942531\pi$
$158$	42.9161	−	233.812i	0.271621	−	1.47982i
$159$	85.6235	−	206.714i	0.538513	−	1.30008i
$160$	82.2829	+	105.333i	0.514268	+	0.658331i
$161$	−66.9789	+	66.9789i	−0.416018	+	0.416018i
$162$	−2.08938	−	9.74676i	−0.0128974	−	0.0601652i
$163$	−22.6268	+	9.37232i	−0.138815	+	0.0574989i	−0.451009	−	0.892519i	$-0.648936\pi$
$163$	−22.6268	+	9.37232i	−0.138815	+	0.0574989i	0.312195	+	0.950018i	$0.398936\pi$
$164$	−62.4113	+	1.85053i	−0.380557	+	0.0112837i
$165$	62.5611	−	151.036i	0.379158	−	0.915368i
$166$	−21.0105	−	98.0119i	−0.126569	−	0.590433i
$167$	92.5873	−	38.3509i	0.554415	−	0.229646i	−0.0878437	−	0.996134i	$-0.527998\pi$
$167$	92.5873	−	38.3509i	0.554415	−	0.229646i	0.642258	+	0.766488i	$0.277998\pi$
$168$	−18.4790	+	120.726i	−0.109994	+	0.718608i
$169$		−	151.707i		−	0.897676i
$170$	40.3603	+	136.160i	0.237414	+	0.800941i
$171$	−85.1252	+	85.1252i	−0.497808	+	0.497808i
$172$	56.9103	+	126.641i	0.330874	+	0.736284i
$173$	−10.8066	+	26.0895i	−0.0624660	+	0.150806i	−0.952030	−	0.306004i	$-0.901008\pi$
$173$	−10.8066	+	26.0895i	−0.0624660	+	0.150806i	0.889564	+	0.456810i	$0.151008\pi$
$174$	7.17163	+	4.63968i	0.0412163	+	0.0266648i
$175$	21.8341	−	9.04397i	0.124766	−	0.0516798i
$176$	42.0033	−	121.276i	0.238655	−	0.689067i
$177$	−32.0645	+	77.4106i	−0.181155	+	0.437348i
$178$	206.463	−	44.2587i	1.15990	−	0.248645i
$179$	−113.095			−0.631816			−0.315908	−	0.948790i	$-0.602309\pi$
$179$	−113.095			−0.631816			−0.315908	+	0.948790i	$0.602309\pi$
$180$	169.671	−	180.040i	0.942615	−	1.00022i
$181$	51.9366	+	125.386i	0.286943	+	0.692741i	0.999965	−	0.00840095i	$-0.00267414\pi$
$181$	51.9366	+	125.386i	0.286943	+	0.692741i	−0.713022	+	0.701141i	$0.752674\pi$
$182$	21.4204	−	14.7765i	0.117694	−	0.0811894i
$183$			447.698i			2.44644i
$184$	235.201	−	57.7601i	1.27827	−	0.313914i
$185$	80.7978	−	80.7978i	0.436745	−	0.436745i
$186$	−0.741282	−	3.45802i	−0.00398539	−	0.0185915i
$187$	88.7219	−	103.556i	0.474449	−	0.553776i
$188$	−23.7841	+	10.6882i	−0.126511	+	0.0568519i
$189$	88.6526			0.469062
$190$	−66.8034	−	12.2617i	−0.351597	−	0.0645353i
$191$	66.3178			0.347213			0.173607	−	0.984815i	$-0.444458\pi$
$191$	66.3178			0.347213			0.173607	+	0.984815i	$0.444458\pi$
$192$	200.327	−	239.546i	1.04337	−	1.24764i
$193$	187.295	+	77.5802i	0.970441	+	0.401970i	0.810876	−	0.585217i	$-0.198991\pi$
$193$	187.295	+	77.5802i	0.970441	+	0.401970i	0.159565	+	0.987187i	$0.448991\pi$
$194$	202.189	+	293.099i	1.04221	+	1.51082i
$195$	−84.7506			−0.434618
$196$	146.617	+	55.6994i	0.748046	+	0.284181i
$197$	−133.565	+	55.3246i	−0.677997	+	0.280836i	−0.694989	−	0.719020i	$-0.744591\pi$
$197$	−133.565	+	55.3246i	−0.677997	+	0.280836i	0.0169921	+	0.999856i	$0.494591\pi$
$198$	−233.645	−	42.8853i	−1.18002	−	0.216592i
$199$	139.655	+	337.156i	0.701783	+	1.69425i	0.719578	+	0.694412i	$0.244335\pi$
$199$	139.655	+	337.156i	0.701783	+	1.69425i	−0.0177954	+	0.999842i	$0.505665\pi$
$200$	−59.7300	−	9.14261i	−0.298650	−	0.0457131i
$201$	34.6729	+	83.7079i	0.172502	+	0.416457i
$202$	283.342	+	183.308i	1.40268	+	0.907465i
$203$	−1.93656	+	1.93656i	−0.00953968	+	0.00953968i
$204$	291.277	−	158.875i	1.42783	−	0.778800i
$205$	−46.1038	+	46.1038i	−0.224897	+	0.224897i
$206$	−337.638	+	72.3782i	−1.63902	+	0.351350i
$207$	−171.543	−	414.140i	−0.828708	−	2.00068i
$208$	−66.4185	+	3.94215i	−0.319320	+	0.0189526i
$209$	24.9574	+	60.2526i	0.119414	+	0.288290i
$210$	72.4182	+	104.979i	0.344849	+	0.499902i
$211$	−152.244	+	63.0617i	−0.721537	+	0.298870i	−0.713069	−	0.701094i	$-0.752695\pi$
$211$	−152.244	+	63.0617i	−0.721537	+	0.298870i	−0.00846789	+	0.999964i	$0.502695\pi$
$212$	−75.1858	−	167.309i	−0.354650	−	0.789193i
$213$	−303.264			−1.42377
$214$	262.185	+	48.1239i	1.22516	+	0.224878i
$215$	133.946	+	55.4822i	0.623004	+	0.258057i
$216$	−193.880	−	117.429i	−0.897593	−	0.543655i
$217$	1.13394			0.00522552
$218$	178.304	+	258.475i	0.817910	+	1.18566i
$219$	−611.071			−2.79028
$220$	−54.9347	−	122.245i	−0.249703	−	0.555657i
$221$	−67.2001	−	21.9493i	−0.304073	−	0.0993180i
$222$	−224.139	−	145.007i	−1.00964	−	0.653184i
$223$	103.947	−	103.947i	0.466132	−	0.466132i	−0.434527	−	0.900659i	$-0.643085\pi$
$223$	103.947	−	103.947i	0.466132	−	0.466132i	0.900659	+	0.434527i	$0.143085\pi$
$224$	61.6368	+	78.9032i	0.275164	+	0.352246i
$225$			111.840i			0.497068i
$226$	−409.391	−	75.1434i	−1.81146	−	0.332493i
$227$	−167.222	−	403.709i	−0.736660	−	1.77845i	−0.618987	−	0.785401i	$-0.712457\pi$
$227$	−167.222	−	403.709i	−0.736660	−	1.77845i	−0.117672	−	0.993052i	$-0.537543\pi$
$228$	4.70283	+	158.609i	0.0206265	+	0.695653i
$229$	−108.529			−0.473925			−0.236962	−	0.971519i	$-0.576152\pi$
$229$	−108.529			−0.473925			−0.236962	+	0.971519i	$0.576152\pi$
$230$	137.373	−	212.340i	0.597275	−	0.923217i
$231$	46.8635	−	113.138i	0.202872	−	0.489777i
$232$	6.80034	−	1.67001i	0.0293118	−	0.00719833i
$233$	−137.295	+	56.8693i	−0.589248	+	0.244074i	−0.657327	−	0.753605i	$-0.728313\pi$
$233$	−137.295	+	56.8693i	−0.589248	+	0.244074i	0.0680792	+	0.997680i	$0.478313\pi$
$234$	25.8125	+	120.413i	0.110310	+	0.514586i
$235$	−10.4200	+	25.1560i	−0.0443403	+	0.107047i
$236$	28.1558	+	62.6542i	0.119304	+	0.265484i
$237$	−410.081	+	410.081i	−1.73030	+	1.73030i
$238$	30.2333	+	101.995i	0.127031	+	0.428551i
$239$			180.305i			0.754413i	0.926129	+	0.377207i	$0.123115\pi$
$239$			180.305i			0.754413i	−0.926129	+	0.377207i	$0.876885\pi$
$240$	−19.3202	−	325.512i	−0.0805006	−	1.35630i
$241$	277.432	−	114.916i	1.15117	−	0.476830i	0.276245	−	0.961087i	$-0.410910\pi$
$241$	277.432	−	114.916i	1.15117	−	0.476830i	0.874926	+	0.484257i	$0.160910\pi$
$242$	61.5494	−	95.1379i	0.254336	−	0.393132i
$243$	88.2793	−	213.125i	0.363289	−	0.877058i
$244$	267.102	+	251.719i	1.09468	+	1.03163i
$245$	151.311	−	62.6752i	0.617597	−	0.255817i
$246$	127.895	+	82.7419i	0.519900	+	0.336349i
$247$	23.9069	−	23.9069i	0.0967892	−	0.0967892i
$248$	−2.47988	−	1.50201i	−0.00999951	−	0.00605651i
$249$	−93.5830	+	225.929i	−0.375835	+	0.907346i
$250$	−223.850	+	154.419i	−0.895401	+	0.617677i
$251$	113.896	+	113.896i	0.453767	+	0.453767i	0.896603	−	0.442836i	$-0.146028\pi$
$251$	113.896	+	113.896i	0.453767	+	0.453767i	−0.442836	+	0.896603i	$0.646028\pi$
$252$	127.098	−	134.865i	0.504356	−	0.535178i
$253$	−242.840			−0.959841
$254$	−18.5093	−	11.9746i	−0.0728713	−	0.0471441i
$255$	107.572	−	329.342i	0.421849	−	1.29154i
$256$	−30.2822	−	254.203i	−0.118290	−	0.992979i
$257$	68.5272	+	68.5272i	0.266643	+	0.266643i	0.827746	−	0.561103i	$-0.189623\pi$
$257$	68.5272	+	68.5272i	0.266643	+	0.266643i	−0.561103	+	0.827746i	$0.689623\pi$
$258$	61.1499	−	333.153i	0.237015	−	1.29129i
$259$	60.5243	−	60.5243i	0.233685	−	0.233685i
$260$	−47.6511	+	50.5632i	−0.183273	+	0.194474i
$261$	−4.95979	−	11.9740i	−0.0190030	−	0.0458774i
$262$	−10.8227	+	58.9636i	−0.0413081	+	0.225052i
$263$	−227.117	+	227.117i	−0.863562	+	0.863562i	−0.991750	−	0.128187i	$-0.959084\pi$
$263$	−227.117	+	227.117i	−0.863562	+	0.863562i	0.128187	+	0.991750i	$0.459084\pi$
$264$	−252.352	+	185.354i	−0.955879	+	0.702099i
$265$	−176.960	−	73.2991i	−0.667772	−	0.276600i
$266$	−50.0413	−	9.18505i	−0.188125	−	0.0345303i
$267$	−475.922	−	197.133i	−1.78248	−	0.738328i
$268$	69.4360	+	26.3785i	0.259089	+	0.0984274i
$269$	28.0671	−	67.7599i	0.104339	−	0.251896i	−0.863085	−	0.505059i	$-0.831471\pi$
$269$	28.0671	−	67.7599i	0.104339	−	0.251896i	0.967424	+	0.253163i	$0.0814709\pi$
$270$	−231.438	+	49.6126i	−0.857179	+	0.183750i
$271$			223.760i			0.825682i	0.910803	+	0.412841i	$0.135463\pi$
$271$			223.760i			0.825682i	−0.910803	+	0.412841i	$0.864537\pi$
$272$	68.9839	−	263.107i	0.253617	−	0.967305i
$273$	−63.4853			−0.232547
$274$	69.0741	+	322.225i	0.252095	+	1.17600i
$275$	55.9759	+	23.1860i	0.203549	+	0.0843127i
$276$	−552.336	−	209.831i	−2.00122	−	0.760257i
$277$	−167.337	+	403.986i	−0.604103	+	1.45843i	0.265219	+	0.964188i	$0.414556\pi$
$277$	−167.337	+	403.986i	−0.604103	+	1.45843i	−0.869322	+	0.494246i	$0.835444\pi$
$278$	88.6235	−	482.832i	0.318789	−	1.73681i
$279$	−2.05356	+	4.95773i	−0.00736043	+	0.0177696i
$280$	103.349	+	15.8192i	0.369104	+	0.0564972i
$281$	259.958	+	259.958i	0.925117	+	0.925117i	0.997385	−	0.0722683i	$-0.0230238\pi$
$281$	259.958	+	259.958i	0.925117	+	0.925117i	−0.0722683	+	0.997385i	$0.523024\pi$
$282$	62.5685	+	11.4844i	0.221874	+	0.0407248i
$283$	144.095	−	59.6860i	0.509169	−	0.210905i	−0.113283	−	0.993563i	$-0.536137\pi$
$283$	144.095	−	59.6860i	0.509169	−	0.210905i	0.622452	+	0.782658i	$0.286137\pi$
$284$	−170.510	+	180.931i	−0.600388	+	0.637080i
$285$	117.166	+	117.166i	0.411108	+	0.411108i
$286$	65.6178	+	12.0441i	0.229433	+	0.0421122i
$287$	−34.5356	+	34.5356i	−0.120333	+	0.120333i
$288$	−456.600	+	126.591i	−1.58542	+	0.439552i
$289$	170.590	−	233.281i	0.590278	−	0.807200i
$290$	3.97186	−	6.13936i	0.0136961	−	0.0211702i
$291$		−	868.682i		−	2.98516i
$292$	−343.575	+	364.572i	−1.17663	+	1.24853i
$293$	163.816	−	163.816i	0.559100	−	0.559100i	−0.369951	−	0.929051i	$-0.620626\pi$
$293$	163.816	−	163.816i	0.559100	−	0.559100i	0.929051	+	0.369951i	$0.120626\pi$
$294$	−217.270	−	314.961i	−0.739015	−	1.07130i
$295$	66.2683	+	27.4492i	0.224638	+	0.0930483i
$296$	−212.535	+	52.1939i	−0.718024	+	0.176331i
$297$	160.710	+	160.710i	0.541111	+	0.541111i
$298$	85.7280	−	132.511i	0.287678	−	0.444668i
$299$	48.1768	+	116.309i	0.161126	+	0.388993i
$300$	107.282	+	101.103i	0.357607	+	0.337012i
$301$	100.337	+	41.5608i	0.333344	+	0.138076i
$302$	293.636	+	189.968i	0.972305	+	0.629032i
$303$	−315.061	−	760.624i	−1.03980	−	2.51031i
$304$	97.2721	+	86.3722i	0.319974	+	0.284119i
$305$	383.258			1.25658
$306$	−500.690	−	52.5292i	−1.63624	−	0.171664i
$307$	−83.2906	−	83.2906i	−0.271305	−	0.271305i	0.558320	−	0.829625i	$-0.311446\pi$
$307$	−83.2906	−	83.2906i	−0.271305	−	0.271305i	−0.829625	+	0.558320i	$0.811446\pi$
$308$	−41.1507	−	91.5715i	−0.133606	−	0.297310i
$309$	778.296	+	322.381i	2.51876	+	1.04330i
$310$	−2.96028	+	0.634584i	−0.00954928	+	0.00204705i
$311$	115.912	+	279.837i	0.372708	+	0.899797i	0.993289	+	0.115655i	$0.0368967\pi$
$311$	115.912	+	279.837i	0.372708	+	0.899797i	−0.620581	+	0.784142i	$0.713103\pi$
$312$	138.840	+	84.0927i	0.445000	+	0.269528i
$313$	291.639	+	120.801i	0.931753	+	0.385945i	0.796343	−	0.604845i	$-0.206765\pi$
$313$	291.639	+	120.801i	0.931753	+	0.385945i	0.135410	+	0.990790i	$0.456765\pi$
$314$	299.832	+	193.976i	0.954877	+	0.617757i
$315$		−	193.514i		−	0.614331i
$316$	14.0907	+	475.228i	0.0445910	+	1.50389i
$317$	173.664	−	71.9342i	0.547837	−	0.226922i	−0.0915581	−	0.995800i	$-0.529185\pi$
$317$	173.664	−	71.9342i	0.547837	−	0.226922i	0.639395	+	0.768878i	$0.279185\pi$
$318$	−80.7869	+	440.137i	−0.254047	+	1.38408i
$319$	−7.02120			−0.0220100
$320$	−205.067	−	171.493i	−0.640834	−	0.535914i
$321$	−459.844	−	459.844i	−1.43254	−	1.43254i
$322$	102.904	−	159.060i	0.319578	−	0.493976i
$323$	62.5582	+	123.247i	0.193679	+	0.381570i
$324$	8.17186	+	18.1846i	0.0252218	+	0.0561253i
$325$		−	31.4097i		−	0.0966453i
$326$	40.3194	−	27.8136i	0.123679	−	0.0853178i
$327$		−	766.063i		−	2.34270i
$328$	121.274	−	29.7822i	0.369738	−	0.0907995i
$329$	−7.80542	+	18.8440i	−0.0237247	+	0.0572765i
$330$	−59.0271	+	321.588i	−0.178870	+	0.974508i
$331$			142.994i			0.432005i	0.976393	+	0.216003i	$0.0693020\pi$
$331$			142.994i			0.432005i	−0.976393	+	0.216003i	$0.930698\pi$
$332$	82.1749	+	182.862i	0.247515	+	0.550788i
$333$	155.011	+	374.230i	0.465499	+	1.12382i
$334$	−164.984	+	113.811i	−0.493964	+	0.340753i
$335$	71.6592	−	29.6822i	0.213908	−	0.0886036i
$336$	−14.4724	−	243.835i	−0.0430726	−	0.725701i
$337$	452.150	−	187.287i	1.34169	−	0.555747i	0.407724	−	0.913105i	$-0.366322\pi$
$337$	452.150	−	187.287i	1.34169	−	0.555747i	0.933967	+	0.357358i	$0.116322\pi$
$338$	63.5970	+	296.674i	0.188157	+	0.877735i
$339$	718.027	+	718.027i	2.11807	+	2.11807i
$340$	−136.007	−	249.351i	−0.400021	−	0.733386i
$341$	2.05561	+	2.05561i	0.00602817	+	0.00602817i
$342$	130.783	−	202.154i	0.382407	−	0.591093i
$343$	254.989	−	105.620i	0.743409	−	0.307930i
$344$	−164.381	−	223.798i	−0.477852	−	0.650576i
$345$	−570.021	+	236.110i	−1.65223	+	0.684378i
$346$	10.1962	−	55.5501i	0.0294687	−	0.160550i
$347$	−71.2348	−	171.976i	−0.205288	−	0.495608i	0.787382	−	0.616465i	$-0.211436\pi$
$347$	−71.2348	−	171.976i	−0.205288	−	0.495608i	−0.992670	+	0.120857i	$0.961436\pi$
$348$	−15.9696	−	6.06682i	−0.0458898	−	0.0174334i
$349$		−	650.550i		−	1.86404i	−0.362406	−	0.932020i	$-0.618045\pi$
$349$		−	650.550i		−	1.86404i	0.362406	−	0.932020i	$-0.381955\pi$
$350$	−38.9068	+	26.8392i	−0.111162	+	0.0766834i
$351$	45.0896	−	108.856i	0.128460	−	0.310131i
$352$	−31.3006	+	254.772i	−0.0889223	+	0.723783i
$353$			37.6483i			0.106652i	0.998577	+	0.0533262i	$0.0169823\pi$
$353$			37.6483i			0.106652i	−0.998577	+	0.0533262i	$0.983018\pi$
$354$	30.2533	−	164.824i	0.0854612	−	0.465604i
$355$			259.613i			0.731304i
$356$	−385.200	+	173.102i	−1.08202	+	0.486243i
$357$	80.5801	−	246.705i	0.225715	−	0.691050i
$358$	221.166	−	47.4105i	0.617781	−	0.132431i
$359$	24.7473	+	24.7473i	0.0689340	+	0.0689340i	0.740733	−	0.671799i	$-0.234478\pi$
$359$	24.7473	+	24.7473i	0.0689340	+	0.0689340i	−0.671799	+	0.740733i	$0.734478\pi$
$360$	−256.329	+	423.209i	−0.712025	+	1.17558i
$361$	294.898			0.816893
$362$	−154.129	−	223.429i	−0.425770	−	0.617208i
$363$	−255.395	+	105.788i	−0.703568	+	0.291427i
$364$	−35.6947	+	37.8761i	−0.0980622	+	0.104055i
$365$			523.115i			1.43319i
$366$	−187.679	−	875.506i	−0.512784	−	2.39209i
$367$	−456.821	−	189.222i	−1.24474	−	0.515590i	−0.339550	−	0.940588i	$-0.610275\pi$
$367$	−456.821	−	189.222i	−1.24474	−	0.515590i	−0.905194	+	0.424998i	$0.860275\pi$
$368$	−435.739	+	211.552i	−1.18407	+	0.574871i
$369$	−88.4506	−	213.539i	−0.239704	−	0.578696i
$370$	−124.135	+	191.877i	−0.335500	+	0.518587i
$371$	−132.558	−	54.9072i	−0.357298	−	0.147998i
$372$	2.89926	+	6.45165i	0.00779372	+	0.0173431i
$373$	−174.765	−	174.765i	−0.468538	−	0.468538i	0.432903	−	0.901441i	$-0.357489\pi$
$373$	−174.765	−	174.765i	−0.468538	−	0.468538i	−0.901441	+	0.432903i	$0.857489\pi$
$374$	−130.090	+	239.705i	−0.347835	+	0.640921i
$375$	663.443			1.76918
$376$	42.0309	−	30.8720i	0.111784	−	0.0821063i
$377$	1.39293	+	3.36283i	0.00369477	+	0.00891998i
$378$	−173.367	+	37.1640i	−0.458642	+	0.0983174i
$379$	90.7878	+	37.6055i	0.239546	+	0.0992231i	0.499227	−	0.866471i	$-0.333617\pi$
$379$	90.7878	+	37.6055i	0.239546	+	0.0992231i	−0.259681	+	0.965694i	$0.583617\pi$
$380$	135.779	−	4.02592i	0.357314	−	0.0105945i
$381$	20.5813	+	49.6878i	0.0540193	+	0.130414i
$382$	−129.689	+	27.8010i	−0.339501	+	0.0727775i
$383$	357.517	+	357.517i	0.933464	+	0.933464i	0.997921	−	0.0644567i	$-0.0205314\pi$
$383$	357.517	+	357.517i	0.933464	+	0.933464i	−0.0644567	+	0.997921i	$0.520531\pi$
$384$	−291.334	+	552.429i	−0.758682	+	1.43862i
$385$	−96.8536	−	40.1181i	−0.251568	−	0.104203i
$386$	−398.792	−	73.1979i	−1.03314	−	0.189632i
$387$	−363.419	+	363.419i	−0.939068	+	0.939068i
$388$	−518.266	−	488.417i	−1.33574	−	1.25881i
$389$			31.0839i			0.0799071i	0.999202	+	0.0399536i	$0.0127210\pi$
$389$			31.0839i			0.0799071i	−0.999202	+	0.0399536i	$0.987279\pi$
$390$	165.736	−	35.5282i	0.424964	−	0.0910980i
$391$	−513.128	+	39.5877i	−1.31235	+	0.101247i
$392$	−310.070	−	47.4611i	−0.790995	−	0.121074i
$393$	103.416	−	103.416i	0.263144	−	0.263144i
$394$	238.004	−	164.183i	0.604072	−	0.416709i
$395$	351.055	+	351.055i	0.888747	+	0.888747i
$396$	474.887	−	14.0806i	1.19921	−	0.0355572i
$397$	−421.146	+	174.444i	−1.06082	+	0.439407i	−0.843743	−	0.536747i	$-0.819653\pi$
$397$	−421.146	+	174.444i	−1.06082	+	0.439407i	−0.217079	+	0.976154i	$0.569653\pi$
$398$	−414.444	−	600.789i	−1.04132	−	1.50952i
$399$	87.7670	+	87.7670i	0.219968	+	0.219968i
$400$	120.639	−	7.16031i	0.301598	−	0.0179008i
$401$	−149.264	+	360.355i	−0.372229	+	0.898640i	0.621143	+	0.783697i	$0.286668\pi$
$401$	−149.264	+	360.355i	−0.372229	+	0.898640i	−0.993372	+	0.114943i	$0.963332\pi$
$402$	−102.897	−	149.162i	−0.255961	−	0.371049i
$403$	0.576731	−	1.39235i	0.00143109	−	0.00345497i
$404$	−630.940	−	239.692i	−1.56173	−	0.593298i
$405$	19.2336	+	7.96680i	0.0474903	+	0.0196711i
$406$	2.97525	−	4.59890i	0.00732821	−	0.0113273i
$407$	219.438			0.539159
$408$	−503.011	+	432.798i	−1.23287	+	1.06078i
$409$		−	272.952i		−	0.667365i	−0.942685	−	0.333683i	$-0.891709\pi$
$409$		−	272.952i		−	0.667365i	0.942685	−	0.333683i	$-0.108291\pi$
$410$	70.8323	−	109.487i	0.172762	−	0.267040i
$411$	307.664	−	742.766i	0.748574	−	1.80722i
$412$	629.933	−	283.081i	1.52896	−	0.687091i
$413$	49.6405	+	20.5618i	0.120195	+	0.0497864i
$414$	509.075	+	737.969i	1.22965	+	1.78253i
$415$	193.410	+	80.1129i	0.466047	+	0.193043i
$416$	128.234	−	35.5524i	0.308254	−	0.0854625i
$417$	−846.835	+	846.835i	−2.03078	+	2.03078i
$418$	−74.0645	−	107.366i	−0.177188	−	0.256856i
$419$	188.420	+	454.887i	0.449690	+	1.08565i	0.972438	+	0.233161i	$0.0749069\pi$
$419$	188.420	+	454.887i	0.449690	+	1.08565i	−0.522748	+	0.852487i	$0.675093\pi$
$420$	−185.627	−	174.937i	−0.441970	−	0.416516i
$421$	406.160	−	406.160i	0.964750	−	0.964750i	−0.0346498	−	0.999400i	$-0.511032\pi$
$421$	406.160	−	406.160i	0.964750	−	0.964750i	0.999400	+	0.0346498i	$0.0110316\pi$
$422$	271.289	−	187.144i	0.642864	−	0.443469i
$423$	−68.2528	−	68.2528i	−0.161354	−	0.161354i
$424$	217.169	+	295.666i	0.512190	+	0.697325i
$425$	122.059	+	39.8675i	0.287197	+	0.0938059i
$426$	593.054	−	127.131i	1.39215	−	0.298429i
$427$	287.092			0.672347
$428$	−532.896	+	15.8006i	−1.24508	+	0.0369174i
$429$	−115.087	−	115.087i	−0.268267	−	0.268267i
$430$	−285.200	−	52.3482i	−0.663255	−	0.121740i
$431$	−51.2641	+	123.762i	−0.118942	+	0.287152i	−0.972126	−	0.234458i	$-0.924668\pi$
$431$	−51.2641	+	123.762i	−0.118942	+	0.287152i	0.853184	+	0.521610i	$0.174668\pi$
$432$	428.374	+	148.365i	0.991607	+	0.343439i
$433$	98.5965	−	98.5965i	0.227706	−	0.227706i	−0.584028	−	0.811734i	$-0.698524\pi$
$433$	98.5965	−	98.5965i	0.227706	−	0.227706i	0.811734	+	0.584028i	$0.198524\pi$
$434$	−2.21750	+	0.475356i	−0.00510944	+	0.00109529i
$435$	−16.4810	+	6.82663i	−0.0378872	+	0.0156934i
$436$	−457.042	−	430.719i	−1.04826	−	0.987888i
$437$	94.1913	−	227.398i	0.215541	−	0.520362i
$438$	1194.99	−	256.166i	2.72829	−	0.584855i
$439$	−469.979	+	194.672i	−1.07057	+	0.443443i	−0.847191	−	0.531289i	$-0.821708\pi$
$439$	−469.979	+	194.672i	−1.07057	+	0.443443i	−0.223376	+	0.974732i	$0.571708\pi$
$440$	158.675	+	216.029i	0.360625	+	0.490975i
$441$			580.584i			1.31652i
$442$	140.616	+	14.7525i	0.318136	+	0.0333768i
$443$	−70.7661	+	70.7661i	−0.159743	+	0.159743i	−0.782453	−	0.622710i	$-0.786032\pi$
$443$	−70.7661	+	70.7661i	−0.159743	+	0.159743i	0.622710	+	0.782453i	$0.286032\pi$
$444$	499.109	+	189.610i	1.12412	+	0.427050i
$445$	−168.759	+	407.419i	−0.379233	+	0.915549i
$446$	−159.701	+	246.852i	−0.358074	+	0.553480i
$447$	−355.722	+	147.345i	−0.795799	+	0.329631i
$448$	−153.612	−	128.462i	−0.342884	−	0.286746i
$449$	94.3559	−	227.795i	0.210147	−	0.507339i	−0.783299	−	0.621645i	$-0.786465\pi$
$449$	94.3559	−	227.795i	0.210147	−	0.507339i	0.993446	+	0.114306i	$0.0364645\pi$
$450$	−46.8845	−	218.712i	−0.104188	−	0.486026i
$451$	−125.213			−0.277634
$452$	832.094	−	24.6720i	1.84092	−	0.0545841i
$453$	−326.507	−	788.258i	−0.720766	−	1.74008i
$454$	496.253	+	719.381i	1.09307	+	1.58454i
$455$			54.3474i			0.119445i
$456$	−75.6870	−	308.200i	−0.165980	−	0.675877i
$457$	464.493	−	464.493i	1.01640	−	1.01640i	0.0165336	−	0.999863i	$-0.494737\pi$
$457$	464.493	−	464.493i	1.01640	−	1.01640i	0.999863	−	0.0165336i	$-0.00526304\pi$
$458$	212.236	−	45.4962i	0.463397	−	0.0993367i
$459$	365.784	+	313.386i	0.796915	+	0.682759i
$460$	−179.628	+	472.834i	−0.390497	+	1.02790i
$461$	−3.65468			−0.00792772			−0.00396386	−	0.999992i	$-0.501262\pi$
$461$	−3.65468			−0.00792772			−0.00396386	+	0.999992i	$0.501262\pi$
$462$	−44.2163	+	240.896i	−0.0957062	+	0.521420i
$463$	351.436			0.759041			0.379520	−	0.925183i	$-0.376089\pi$
$463$	351.436			0.759041			0.379520	+	0.925183i	$0.376089\pi$
$464$	−12.5985	+	6.11660i	−0.0271519	+	0.0131823i
$465$	6.82380	+	2.82651i	0.0146748	+	0.00607852i
$466$	244.650	−	168.767i	0.524999	−	0.362162i
$467$	−404.461			−0.866083			−0.433041	−	0.901374i	$-0.642560\pi$
$467$	−404.461			−0.866083			−0.433041	+	0.901374i	$0.642560\pi$
$468$	−100.956	−	224.656i	−0.215719	−	0.480033i
$469$	53.6787	−	22.2344i	0.114454	−	0.0474082i
$470$	9.83136	−	53.5625i	0.0209178	−	0.113963i
$471$	−333.396	−	804.889i	−0.707847	−	1.70889i
$472$	−81.3259	−	110.722i	−0.172301	−	0.234580i
$473$	106.549	+	257.233i	0.225263	+	0.543832i
$474$	630.034	−	973.853i	1.32919	−	2.05454i
$475$	−43.4233	+	43.4233i	−0.0914174	+	0.0914174i
$476$	−101.881	−	186.785i	−0.214035	−	0.392405i
$477$	480.124	−	480.124i	1.00655	−	1.00655i
$478$	−75.5854	−	352.599i	−0.158128	−	0.737655i
$479$	202.510	+	488.902i	0.422776	+	1.02067i	0.981525	+	0.191335i	$0.0612818\pi$
$479$	202.510	+	488.902i	0.422776	+	1.02067i	−0.558748	+	0.829337i	$0.688718\pi$
$480$	174.239	+	628.462i	0.362999	+	1.30930i
$481$	−43.5341	−	105.101i	−0.0905074	−	0.218504i
$482$	−494.365	+	341.029i	−1.02565	+	0.707529i
$483$	−426.993	+	176.866i	−0.884044	+	0.366183i
$484$	−80.4817	+	211.851i	−0.166284	+	0.437709i
$485$	−743.647			−1.53329
$486$	−83.2926	+	453.789i	−0.171384	+	0.933722i
$487$	−700.113	−	289.996i	−1.43760	−	0.595475i	−0.478387	−	0.878149i	$-0.658778\pi$
$487$	−700.113	−	289.996i	−1.43760	−	0.595475i	−0.959216	+	0.282675i	$0.908778\pi$
$488$	−627.860	−	380.282i	−1.28660	−	0.779267i
$489$	−119.498			−0.244372
$490$	−269.626	+	185.997i	−0.550258	+	0.379586i
$491$	567.109			1.15501			0.577504	−	0.816388i	$-0.304027\pi$
$491$	567.109			1.15501			0.577504	+	0.816388i	$0.304027\pi$
$492$	−284.795	−	108.193i	−0.578852	−	0.219904i
$493$	−14.8360	+	1.14460i	−0.0300933	+	0.00232170i
$494$	−36.7297	+	56.7737i	−0.0743517	+	0.114927i
$495$	350.804	−	350.804i	0.708694	−	0.708694i
$496$	5.47924	+	1.89771i	0.0110469	+	0.00382603i
$497$			194.472i			0.391291i
$498$	88.2967	−	481.052i	0.177303	−	0.965968i
$499$	−46.3352	−	111.863i	−0.0928561	−	0.224174i	0.870627	−	0.491944i	$-0.163713\pi$
$499$	−46.3352	−	111.863i	−0.0928561	−	0.224174i	−0.963483	+	0.267769i	$0.913713\pi$
$500$	373.022	−	395.818i	0.746043	−	0.791636i
$501$	488.977			0.976001
$502$	−270.477	−	174.985i	−0.538799	−	0.348575i
$503$	151.482	−	365.709i	0.301156	−	0.727055i	−0.698775	−	0.715341i	$-0.746271\pi$
$503$	151.482	−	365.709i	0.301156	−	0.727055i	0.999931	−	0.0117140i	$-0.00372877\pi$
$504$	−192.012	+	317.019i	−0.380976	+	0.629005i
$505$	−651.142	+	269.712i	−1.28939	+	0.534083i
$506$	474.891	−	101.801i	0.938519	−	0.201187i
$507$	283.268	−	683.870i	0.558715	−	1.34886i
$508$	41.2162	+	15.6579i	0.0811342	+	0.0308227i
$509$	221.764	−	221.764i	0.435685	−	0.435685i	−0.454872	−	0.890557i	$-0.650315\pi$
$509$	221.764	−	221.764i	0.435685	−	0.435685i	0.890557	+	0.454872i	$0.150315\pi$
$510$	−72.3010	+	689.147i	−0.141767	+	1.35127i
$511$			391.857i			0.766843i
$512$	165.783	+	484.417i	0.323795	+	0.946127i
$513$	−212.826	+	88.1555i	−0.414866	+	0.171843i
$514$	−162.737	−	105.283i	−0.316609	−	0.204830i
$515$	275.978	−	666.270i	0.535880	−	1.29373i
$516$	20.0775	+	677.139i	0.0389099	+	1.31228i
$517$	−48.3102	+	20.0107i	−0.0934432	+	0.0387055i
$518$	−92.9874	+	143.732i	−0.179512	+	0.277475i
$519$	−97.4288	+	97.4288i	−0.187724	+	0.187724i
$520$	71.9886	−	118.856i	0.138440	−	0.228569i
$521$	130.385	−	314.777i	0.250259	−	0.604178i	−0.747966	−	0.663737i	$-0.768969\pi$
$521$	130.385	−	314.777i	0.250259	−	0.604178i	0.998225	+	0.0595588i	$0.0189694\pi$
$522$	14.7188	+	21.3368i	0.0281970	+	0.0408752i
$523$	−62.6046	−	62.6046i	−0.119703	−	0.119703i	0.644718	−	0.764421i	$-0.276975\pi$
$523$	−62.6046	−	62.6046i	−0.119703	−	0.119703i	−0.764421	+	0.644718i	$0.776975\pi$
$524$	−3.55345	−	119.845i	−0.00678140	−	0.228711i
$525$	115.311			0.219641
$526$	348.934	−	539.353i	0.663373	−	1.02539i
$527$	4.67867	+	4.00846i	0.00887793	+	0.00760618i
$528$	415.791	−	468.262i	0.787482	−	0.886860i
$529$	274.001	+	274.001i	0.517960	+	0.517960i
$530$	376.785	+	69.1586i	0.710915	+	0.130488i
$531$	−179.798	+	179.798i	−0.338602	+	0.338602i
$532$	101.710	−	3.01575i	0.191184	−	0.00566870i
$533$	24.8409	+	59.9712i	0.0466057	+	0.112516i
$534$	1013.34	+	185.998i	1.89764	+	0.348311i
$535$	−393.655	+	393.655i	−0.735804	+	0.735804i
$536$	−146.845	−	22.4770i	−0.273965	−	0.0419346i
$537$	−509.813	−	211.172i	−0.949373	−	0.393243i
$538$	−26.4816	+	144.275i	−0.0492224	+	0.268170i
$539$	290.582	+	120.363i	0.539113	+	0.223308i
$540$	431.796	−	194.042i	0.799623	−	0.359337i
$541$	173.807	−	419.607i	0.321270	−	0.775614i	−0.677911	−	0.735144i	$-0.737115\pi$
$541$	173.807	−	419.607i	0.321270	−	0.775614i	0.999181	−	0.0404697i	$-0.0128854\pi$
$542$	−93.8021	−	437.579i	−0.173067	−	0.807341i
$543$			662.195i			1.21951i
$544$	−24.6063	+	543.443i	−0.0452322	+	0.998976i
$545$	−655.798			−1.20330
$546$	124.150	−	26.6136i	0.227381	−	0.0487429i
$547$	281.038	+	116.410i	0.513781	+	0.212815i	0.624483	−	0.781039i	$-0.285310\pi$
$547$	281.038	+	116.410i	0.513781	+	0.212815i	−0.110702	+	0.993854i	$0.535310\pi$
$548$	−270.159	−	601.177i	−0.492991	−	1.09704i
$549$	−519.924	+	1255.21i	−0.947037	+	2.28635i
$550$	−119.185	−	21.8763i	−0.216700	−	0.0397750i
$551$	2.72334	−	6.57474i	0.00494255	−	0.0119324i
$552$	1168.10	+	178.795i	2.11612	+	0.323905i
$553$	262.970	+	262.970i	0.475533	+	0.475533i
$554$	157.884	−	860.174i	0.284990	−	1.55266i
$555$	515.089	−	213.357i	0.928088	−	0.384427i
$556$	29.0980	+	981.365i	0.0523345	+	1.76504i
$557$	556.957	+	556.957i	0.999924	+	0.999924i	1.00000		7.63823e-5i	$-2.43132e-5\pi$
$557$	556.957	+	556.957i	0.999924	+	0.999924i	−7.63823e−5		1.00000i	$0.500024\pi$
$558$	1.93756	−	10.5561i	0.00347233	−	0.0189177i
$559$	102.064	−	102.064i	0.182584	−	0.182584i
$560$	−208.738	+	12.3893i	−0.372747	+	0.0221237i
$561$	593.304	−	301.152i	1.05758	−	0.536812i
$562$	−617.343	−	399.390i	−1.09848	−	0.710658i
$563$		−	967.345i		−	1.71820i	−0.511810	−	0.859098i	$-0.671025\pi$
$563$		−	967.345i		−	1.71820i	0.511810	−	0.859098i	$-0.328975\pi$
$564$	−127.172	+	3.77070i	−0.225482	+	0.00668564i
$565$	614.676	−	614.676i	1.08792	−	1.08792i
$566$	−256.767	+	177.126i	−0.453652	+	0.312944i
$567$	14.4075	+	5.96780i	0.0254101	+	0.0105252i
$568$	257.597	−	425.303i	0.453517	−	0.748772i
$569$	196.834	+	196.834i	0.345929	+	0.345929i	0.858591	−	0.512662i	$-0.171341\pi$
$569$	196.834	+	196.834i	0.345929	+	0.345929i	−0.512662	+	0.858591i	$0.671341\pi$
$570$	−278.243	−	180.009i	−0.488146	−	0.315806i
$571$	306.126	+	739.053i	0.536122	+	1.29431i	0.927410	+	0.374046i	$0.122030\pi$
$571$	306.126	+	739.053i	0.536122	+	1.29431i	−0.391288	+	0.920268i	$0.627970\pi$
$572$	−133.369	+	3.95447i	−0.233163	+	0.00691341i
$573$	298.949	+	123.829i	0.521727	+	0.216106i
$574$	53.0593	−	82.0146i	0.0924378	−	0.142883i
$575$	−87.5057	−	211.257i	−0.152184	−	0.367404i
$576$	839.847	−	438.969i	1.45807	−	0.762099i
$577$	−250.264			−0.433733			−0.216867	−	0.976201i	$-0.569584\pi$
$577$	−250.264			−0.433733			−0.216867	+	0.976201i	$0.569584\pi$
$578$	−235.809	+	527.710i	−0.407973	+	0.912994i
$579$	699.437	+	699.437i	1.20801	+	1.20801i
$580$	−5.19358	+	13.6710i	−0.00895445	+	0.0235707i
$581$	144.880	+	60.0112i	0.249363	+	0.103290i
$582$	364.159	+	1698.77i	0.625704	+	2.91885i
$583$	−140.765	−	339.837i	−0.241450	−	0.582911i
$584$	519.054	−	856.976i	0.888791	−	1.46743i
$585$	−237.614	−	98.4231i	−0.406178	−	0.168245i
$586$	−251.681	+	389.028i	−0.429490	+	0.663870i
$587$		−	902.640i		−	1.53772i	−0.639418	−	0.768859i	$-0.720825\pi$
$587$		−	902.640i		−	1.53772i	0.639418	−	0.768859i	$-0.279175\pi$
$588$	556.922	+	524.847i	0.947147	+	0.892598i
$589$	−2.72221	+	1.12758i	−0.00462175	+	0.00191439i
$590$	−141.099	−	25.8987i	−0.239152	−	0.0438961i
$591$	−705.393			−1.19356
$592$	393.748	−	191.166i	0.665114	−	0.322915i
$593$	403.515	+	403.515i	0.680464	+	0.680464i	0.960105	−	0.279641i	$-0.0902154\pi$
$593$	403.515	+	403.515i	0.680464	+	0.680464i	−0.279641	+	0.960105i	$0.590215\pi$
$594$	−381.651	−	246.909i	−0.642510	−	0.415672i
$595$	−211.195	−	68.9816i	−0.354949	−	0.115936i
$596$	−112.097	+	295.073i	−0.188083	+	0.495089i
$597$			1780.61i			2.98259i
$598$	−142.971	−	207.255i	−0.239082	−	0.346580i
$599$		−	248.744i		−	0.415265i	−0.978207	−	0.207632i	$-0.933424\pi$
$599$		−	248.744i		−	0.415265i	0.978207	−	0.207632i	$-0.0665758\pi$
$600$	−252.182	−	152.741i	−0.420303	−	0.254569i
$601$	45.2324	−	109.201i	0.0752618	−	0.181698i	−0.881771	−	0.471678i	$-0.843649\pi$
$601$	45.2324	−	109.201i	0.0752618	−	0.181698i	0.957033	+	0.289980i	$0.0936485\pi$
$602$	−213.638	−	39.2131i	−0.354881	−	0.0651381i
$603$			274.957i			0.455982i
$604$	−653.863	−	248.401i	−1.08255	−	0.411260i
$605$	90.5613	+	218.634i	0.149688	+	0.361379i
$606$	934.984	+	1355.38i	1.54288	+	2.23660i
$607$	−830.851	+	344.150i	−1.36878	+	0.566968i	−0.941458	−	0.337130i	$-0.890544\pi$
$607$	−830.851	+	344.150i	−1.36878	+	0.566968i	−0.427324	+	0.904098i	$0.640544\pi$
$608$	−226.431	−	128.130i	−0.372419	−	0.210740i
$609$	−12.3456	+	5.11372i	−0.0202719	+	0.00839691i
$610$	−749.488	+	160.665i	−1.22867	+	0.263385i
$611$	19.1684	+	19.1684i	0.0313722	+	0.0313722i
$612$	1001.16	−	107.169i	1.63588	−	0.175113i
$613$	−363.124	−	363.124i	−0.592373	−	0.592373i	0.345899	−	0.938272i	$-0.387574\pi$
$613$	−363.124	−	363.124i	−0.592373	−	0.592373i	−0.938272	+	0.345899i	$0.887574\pi$
$614$	197.797	+	127.965i	0.322145	+	0.208411i
$615$	−293.914	+	121.743i	−0.477908	+	0.197956i
$616$	118.861	+	161.824i	0.192956	+	0.262701i
$617$	−1009.69	+	418.229i	−1.63646	+	0.677842i	−0.995933	−	0.0900966i	$-0.971282\pi$
$617$	−1009.69	+	418.229i	−1.63646	+	0.677842i	−0.640523	+	0.767939i	$0.721282\pi$
$618$	−1657.16	−	304.170i	−2.68149	−	0.492185i
$619$	−75.9590	−	183.381i	−0.122712	−	0.296254i	0.850571	−	0.525860i	$-0.176256\pi$
$619$	−75.9590	−	183.381i	−0.122712	−	0.296254i	−0.973284	+	0.229606i	$0.926256\pi$
$620$	5.52301	−	2.48195i	0.00890809	−	0.00400315i
$621$		−	857.766i		−	1.38127i
$622$	−343.985	−	498.650i	−0.553030	−	0.801688i
$623$	−126.414	+	305.191i	−0.202912	+	0.489873i
$624$	−306.764	−	106.246i	−0.491609	−	0.170267i
$625$		−	379.119i		−	0.606590i
$626$	−620.961	−	113.977i	−0.991951	−	0.182072i
$627$			318.209i			0.507511i
$628$	−667.659	−	253.642i	−1.06315	−	0.403888i
$629$	463.679	−	35.7727i	0.737168	−	0.0568724i
$630$	81.1229	+	378.431i	0.128766	+	0.600684i
$631$	563.845	+	563.845i	0.893574	+	0.893574i	0.994858	−	0.101283i	$-0.0322949\pi$
$631$	563.845	+	563.845i	0.893574	+	0.893574i	−0.101283	+	0.994858i	$0.532295\pi$
$632$	−226.775	−	923.435i	−0.358822	−	1.46113i
$633$	−804.041			−1.27021
$634$	−309.458	+	213.474i	−0.488104	+	0.336710i
$635$	42.5358	−	17.6189i	0.0669856	−	0.0277463i
$636$	−26.5250	−	894.587i	−0.0417059	−	1.40658i
$637$		−	163.054i		−	0.255972i
$638$	13.7305	−	2.94335i	0.0215211	−	0.00461340i
$639$	−850.257	−	352.188i	−1.33061	−	0.551155i
$640$	472.914	+	249.400i	0.738928	+	0.389688i
$641$	131.959	+	318.576i	0.205864	+	0.496999i	0.992764	−	0.120081i	$-0.0383155\pi$
$641$	131.959	+	318.576i	0.205864	+	0.496999i	−0.786900	+	0.617080i	$0.788316\pi$
$642$	1092.03	+	706.488i	1.70098	+	1.10045i
$643$	−988.936	−	409.631i	−1.53800	−	0.637062i	−0.556906	−	0.830576i	$-0.688011\pi$
$643$	−988.936	−	409.631i	−1.53800	−	0.637062i	−0.981097	+	0.193514i	$0.938011\pi$
$644$	−134.557	+	354.192i	−0.208939	+	0.549988i
$645$	500.209	+	500.209i	0.775518	+	0.775518i
$646$	−174.003	−	214.794i	−0.269355	−	0.332498i
$647$	623.489			0.963662			0.481831	−	0.876264i	$-0.339972\pi$
$647$	623.489			0.963662			0.481831	+	0.876264i	$0.339972\pi$
$648$	−23.6038	−	32.1356i	−0.0364256	−	0.0495920i
$649$	52.7141	+	127.263i	0.0812236	+	0.196091i
$650$	13.1672	+	61.4240i	0.0202573	+	0.0944985i
$651$	5.11160	+	2.11729i	0.00785191	+	0.00325237i
$652$	−67.1877	+	71.2938i	−0.103049	+	0.109346i
$653$	−354.903	−	856.812i	−0.543496	−	1.31212i	−0.922241	−	0.386615i	$-0.873644\pi$
$653$	−354.903	−	856.812i	−0.543496	−	1.31212i	0.378745	−	0.925501i	$-0.376356\pi$
$654$	321.140	+	1498.09i	0.491040	+	2.29066i
$655$	−88.5303	−	88.5303i	−0.135161	−	0.135161i
$656$	−224.675	+	109.081i	−0.342493	+	0.166281i
$657$	−1713.25	−	709.652i	−2.60769	−	1.08014i
$658$	7.36451	−	40.1228i	0.0111923	−	0.0609769i
$659$	316.243	−	316.243i	0.479883	−	0.479883i	−0.425211	−	0.905094i	$-0.639800\pi$
$659$	316.243	−	316.243i	0.479883	−	0.479883i	0.905094	+	0.425211i	$0.139800\pi$
$660$	−19.3805	−	653.633i	−0.0293644	−	0.990352i
$661$			719.855i			1.08904i	0.838748	+	0.544520i	$0.183288\pi$
$661$			719.855i			1.08904i	−0.838748	+	0.544520i	$0.816712\pi$
$662$	−59.9443	−	279.635i	−0.0905503	−	0.422409i
$663$	−261.943	−	224.420i	−0.395087	−	0.338492i
$664$	−237.356	−	323.151i	−0.357464	−	0.486673i
$665$	75.1341	−	75.1341i	0.112984	−	0.112984i
$666$	−460.017	−	666.853i	−0.690716	−	1.00128i
$667$	18.7373	+	18.7373i	0.0280919	+	0.0280919i
$668$	274.928	−	291.729i	0.411568	−	0.436720i
$669$	662.668	−	274.486i	0.990535	−	0.410293i
$670$	−127.692	+	88.0859i	−0.190585	+	0.131471i
$671$	520.442	+	520.442i	0.775622	+	0.775622i
$672$	130.520	+	470.771i	0.194226	+	0.700552i
$673$	355.691	−	858.715i	0.528516	−	1.27595i	−0.403979	−	0.914768i	$-0.632373\pi$
$673$	355.691	−	858.715i	0.528516	−	1.27595i	0.932495	−	0.361182i	$-0.117627\pi$
$674$	−805.700	+	555.798i	−1.19540	+	0.824626i
$675$	−81.8982	+	197.720i	−0.121331	+	0.292918i
$676$	−248.737	−	553.508i	−0.367954	−	0.818799i
$677$	−516.651	−	214.004i	−0.763148	−	0.316106i	−0.0330546	−	0.999454i	$-0.510524\pi$
$677$	−516.651	−	214.004i	−0.763148	−	0.316106i	−0.730094	+	0.683347i	$0.760524\pi$
$678$	−1705.16	−	1103.15i	−2.51498	−	1.62706i
$679$	−557.053			−0.820403
$680$	370.502	+	430.609i	0.544856	+	0.633249i
$681$		−	2132.09i		−	3.13082i
$682$	−4.88162	−	3.15816i	−0.00715780	−	0.00463073i
$683$	7.51546	−	18.1439i	0.0110036	−	0.0265651i	−0.918282	−	0.395926i	$-0.870424\pi$
$683$	7.51546	−	18.1439i	0.0110036	−	0.0265651i	0.929286	+	0.369361i	$0.120424\pi$
$684$	−171.011	+	450.152i	−0.250017	+	0.658116i
$685$	−635.855	−	263.380i	−0.928255	−	0.384496i
$686$	−454.373	+	313.441i	−0.662352	+	0.456912i
$687$	−489.229	−	202.645i	−0.712124	−	0.294971i
$688$	415.278	+	368.743i	0.603601	+	0.535964i
$689$	−134.840	+	134.840i	−0.195704	+	0.195704i
$690$	1015.74	−	700.689i	1.47208	−	1.01549i
$691$	−73.6858	−	177.893i	−0.106636	−	0.257443i	0.861550	−	0.507672i	$-0.169494\pi$
$691$	−73.6858	−	177.893i	−0.106636	−	0.257443i	−0.968187	+	0.250229i	$0.919494\pi$
$692$	3.34774	+	112.907i	0.00483777	+	0.163160i
$693$	262.781	−	262.781i	0.379194	−	0.379194i
$694$	211.399	+	306.449i	0.304609	+	0.441569i
$695$	724.943	+	724.943i	1.04308	+	1.04308i
$696$	33.7731	+	5.16949i	0.0485245	+	0.00742744i
$697$	−264.579	+	20.4122i	−0.379596	+	0.0292858i
$698$	272.717	+	1272.20i	0.390711	+	1.82263i
$699$	−725.088			−1.03732
$700$	64.8339	−	68.7961i	0.0926198	−	0.0982801i
$701$	130.417	+	130.417i	0.186045	+	0.186045i	0.793984	−	0.607939i	$-0.208003\pi$
$701$	130.417	+	130.417i	0.186045	+	0.186045i	−0.607939	+	0.793984i	$0.708003\pi$
$702$	−42.5426	+	231.777i	−0.0606019	+	0.330167i
$703$	−85.1143	+	205.484i	−0.121073	+	0.292296i
$704$	−45.5919	−	511.346i	−0.0647613	−	0.726344i
$705$	−93.9428	+	93.9428i	−0.133252	+	0.133252i
$706$	−15.7825	−	73.6240i	−0.0223548	−	0.104283i
$707$	−487.760	+	202.037i	−0.689900	+	0.285766i
$708$	9.93313	+	335.007i	0.0140299	+	0.473174i
$709$	97.7424	−	235.971i	0.137860	−	0.332822i	−0.839839	−	0.542836i	$-0.817351\pi$
$709$	97.7424	−	235.971i	0.137860	−	0.332822i	0.977699	+	0.210013i	$0.0673507\pi$
$710$	−108.832	−	507.692i	−0.153285	−	0.715059i
$711$	−1625.98	+	673.502i	−2.28689	+	0.947261i
$712$	680.720	−	499.993i	0.956068	−	0.702238i
$713$		−	10.9715i		−	0.0153878i
$714$	−54.1595	+	516.229i	−0.0758536	+	0.723010i
$715$	−98.5213	+	98.5213i	−0.137792	+	0.137792i
$716$	−412.630	+	185.429i	−0.576299	+	0.258979i
$717$	−336.666	+	812.784i	−0.469548	+	1.13359i
$718$	−58.7694	−	38.0209i	−0.0818516	−	0.0529538i
$719$	265.890	−	110.135i	0.369806	−	0.153179i	−0.190038	−	0.981777i	$-0.560861\pi$
$719$	265.890	−	110.135i	0.369806	−	0.153179i	0.559844	+	0.828598i	$0.310861\pi$
$720$	323.857	−	935.070i	0.449802	−	1.29871i
$721$	206.731	−	499.092i	0.286728	−	0.692222i
$722$	−576.695	+	123.624i	−0.798747	+	0.171224i
$723$	1465.19			2.02654
$724$	395.073	+	372.320i	0.545682	+	0.514254i
$725$	−2.53004	−	6.10807i	−0.00348972	−	0.00842492i
$726$	455.096	−	313.940i	0.626855	−	0.432425i
$727$		−	550.834i		−	0.757681i	−0.925462	−	0.378840i	$-0.876323\pi$
$727$		−	550.834i		−	0.757681i	0.925462	−	0.378840i	$-0.123677\pi$
$728$	53.9255	−	89.0329i	0.0740735	−	0.122298i
$729$	827.615	−	827.615i	1.13527	−	1.13527i
$730$	−219.294	−	1022.99i	−0.300403	−	1.40135i
$731$	267.076	+	526.171i	0.365357	+	0.719796i
$732$	734.040	+	1633.44i	1.00279	+	2.23147i
$733$	−490.988			−0.669833			−0.334917	−	0.942248i	$-0.608708\pi$
$733$	−490.988			−0.669833			−0.334917	+	0.942248i	$0.608708\pi$
$734$	972.670	+	178.533i	1.32516	+	0.243233i
$735$	799.114			1.08723
$736$	763.434	−	596.372i	1.03728	−	0.810288i
$737$	137.616	+	57.0023i	0.186724	+	0.0773437i
$738$	262.489	+	380.511i	0.355676	+	0.515598i
$739$	−216.153			−0.292494			−0.146247	−	0.989248i	$-0.546719\pi$
$739$	−216.153			−0.292494			−0.146247	+	0.989248i	$0.546719\pi$
$740$	162.318	−	427.268i	0.219349	−	0.577390i
$741$	152.408	−	63.1293i	0.205678	−	0.0851947i
$742$	282.244	+	51.8056i	0.380382	+	0.0698189i
$743$	38.2393	+	92.3179i	0.0514661	+	0.124250i	0.947521	−	0.319692i	$-0.103580\pi$
$743$	38.2393	+	92.3179i	0.0514661	+	0.124250i	−0.896055	+	0.443942i	$0.853580\pi$
$744$	−8.37431	−	11.4013i	−0.0112558	−	0.0153243i
$745$	126.137	+	304.521i	0.169311	+	0.408753i
$746$	415.028	+	268.502i	0.556337	+	0.359922i
$747$	−524.755	+	524.755i	−0.702483	+	0.702483i
$748$	153.915	−	523.295i	0.205769	−	0.699592i
$749$	−294.881	+	294.881i	−0.393699	+	0.393699i
$750$	−1297.41	+	278.121i	−1.72988	+	0.370829i
$751$	236.146	+	570.107i	0.314442	+	0.759131i	0.999530	+	0.0306697i	$0.00976400\pi$
$751$	236.146	+	570.107i	0.314442	+	0.759131i	−0.685087	+	0.728461i	$0.740236\pi$
$752$	−69.2527	+	77.9921i	−0.0920913	+	0.103713i
$753$	300.755	+	726.088i	0.399410	+	0.964260i
$754$	−4.13370	−	5.99233i	−0.00548237	−	0.00794739i
$755$	−674.798	+	279.511i	−0.893773	+	0.370213i
$756$	323.452	−	145.354i	0.427846	−	0.192267i
$757$	316.523			0.418129			0.209064	−	0.977902i	$-0.432958\pi$
$757$	316.523			0.418129			0.209064	+	0.977902i	$0.432958\pi$
$758$	−193.307	−	35.4813i	−0.255022	−	0.0468091i
$759$	−1094.68	−	453.431i	−1.44227	−	0.597406i
$760$	−263.838	+	64.7928i	−0.347156	+	0.0852537i
$761$	1096.84			1.44131			0.720657	−	0.693292i	$-0.243840\pi$
$761$	1096.84			1.44131			0.720657	+	0.693292i	$0.243840\pi$
$762$	−61.0779	−	88.5401i	−0.0801547	−	0.116194i
$763$	−491.247			−0.643836
$764$	241.962	−	108.734i	0.316704	−	0.142322i
$765$	684.071	−	798.447i	0.894210	−	1.04372i
$766$	−849.024	−	549.276i	−1.10839	−	0.717070i
$767$	50.4953	−	50.4953i	0.0658347	−	0.0658347i
$768$	338.142	−	1202.45i	0.440288	−	1.56568i
$769$		−	309.454i		−	0.402411i	−0.979549	−	0.201206i	$-0.935514\pi$
$769$		−	309.454i		−	0.402411i	0.979549	−	0.201206i	$-0.0644859\pi$
$770$	206.222	+	37.8519i	0.267821	+	0.0491583i
$771$	180.955	+	436.863i	0.234701	+	0.566619i
$772$	810.551	−	24.0333i	1.04994	−	0.0311312i
$773$	−941.575			−1.21808			−0.609040	−	0.793140i	$-0.708445\pi$
$773$	−941.575			−1.21808			−0.609040	+	0.793140i	$0.708445\pi$
$774$	558.344	−	863.042i	0.721375	−	1.11504i
$775$	−1.04754	+	2.52899i	−0.00135167	+	0.00326322i
$776$	1218.26	+	737.874i	1.56992	+	0.950868i
$777$	385.845	−	159.822i	0.496583	−	0.205691i
$778$	−13.0306	−	60.7867i	−0.0167489	−	0.0781321i
$779$	48.5669	−	117.251i	0.0623451	−	0.150514i
$780$	−309.215	+	138.956i	−0.396429	+	0.178149i
$781$	−352.539	+	352.539i	−0.451395	+	0.451395i
$782$	986.863	−	292.524i	1.26197	−	0.374072i
$783$		−	24.8005i		−	0.0316737i
$784$	626.260	−	37.1705i	0.798801	−	0.0474114i
$785$	−689.036	+	285.408i	−0.877753	+	0.363577i
$786$	−158.884	+	245.590i	−0.202143	+	0.312455i
$787$	308.104	−	743.829i	0.391492	−	0.945145i	−0.598123	−	0.801404i	$-0.704087\pi$
$787$	308.104	−	743.829i	0.391492	−	0.945145i	0.989615	−	0.143741i	$-0.0459133\pi$
$788$	−396.608	+	420.846i	−0.503309	+	0.534068i
$789$	−1447.88	+	599.731i	−1.83508	+	0.760115i
$790$	−833.679	−	539.348i	−1.05529	−	0.682719i
$791$	460.444	−	460.444i	0.582103	−	0.582103i
$792$	−922.774	+	226.613i	−1.16512	+	0.286127i
$793$	146.018	−	352.518i	0.184133	−	0.444537i
$794$	750.453	−	517.687i	0.945155	−	0.651999i
$795$	−660.840	−	660.840i	−0.831245	−	0.831245i
$796$	1062.33	+	1001.15i	1.33459	+	1.25772i
$797$	298.282			0.374256			0.187128	−	0.982336i	$-0.440082\pi$
$797$	298.282			0.374256			0.187128	+	0.982336i	$0.440082\pi$
$798$	−208.428	−	134.842i	−0.261187	−	0.168975i
$799$	−98.8187	+	50.1588i	−0.123678	+	0.0627770i
$800$	−232.917	+	64.5755i	−0.291146	+	0.0807193i
$801$	−1105.40	−	1105.40i	−1.38003	−	1.38003i
$802$	140.832	−	767.272i	0.175601	−	0.956699i
$803$	−710.360	+	710.360i	−0.884633	+	0.884633i
$804$	263.751	+	248.561i	0.328049	+	0.309156i
$805$	151.409	+	365.533i	0.188085	+	0.454078i
$806$	−0.544153	+	2.96461i	−0.000675127	+	0.00367818i
$807$	253.043	−	253.043i	0.313561	−	0.313561i
$808$	1334.33	+	204.240i	1.65140	+	0.252773i
$809$	−976.488	−	404.474i	−1.20703	−	0.499968i	−0.313766	−	0.949500i	$-0.601591\pi$
$809$	−976.488	−	404.474i	−1.20703	−	0.499968i	−0.893264	+	0.449532i	$0.851591\pi$
$810$	−40.9524	−	7.51677i	−0.0505585	−	0.00927997i
$811$	467.852	+	193.790i	0.576882	+	0.238952i	0.651996	−	0.758223i	$-0.273932\pi$
$811$	467.852	+	193.790i	0.576882	+	0.238952i	−0.0751136	+	0.997175i	$0.523932\pi$
$812$	−3.89043	+	10.2407i	−0.00479116	+	0.0126117i
$813$	−417.805	+	1008.67i	−0.513906	+	1.24068i
$814$	−429.126	+	91.9903i	−0.527182	+	0.113010i
$815$			102.298i			0.125518i
$816$	802.242	−	1057.23i	0.983140	−	1.29563i
$817$	−282.203			−0.345414
$818$	114.424	+	533.778i	0.139883	+	0.652541i
$819$	−177.993	−	73.7271i	−0.217330	−	0.0900209i
$820$	−92.6199	+	243.802i	−0.112951	+	0.297320i
$821$	−531.424	+	1282.97i	−0.647289	+	1.56269i	0.169356	+	0.985555i	$0.445831\pi$
$821$	−531.424	+	1282.97i	−0.647289	+	1.56269i	−0.816645	+	0.577140i	$0.804169\pi$
$822$	−290.285	+	1581.51i	−0.353144	+	1.92398i
$823$	−428.812	+	1035.24i	−0.521035	+	1.25789i	0.416227	+	0.909261i	$0.363352\pi$
$823$	−428.812	+	1035.24i	−0.521035	+	1.25789i	−0.937261	+	0.348628i	$0.886648\pi$
$824$	−1113.21	+	817.660i	−1.35098	+	0.992306i
$825$	209.037	+	209.037i	0.253378	+	0.253378i
$826$	−105.695	−	19.4003i	−0.127960	−	0.0234870i
$827$	743.335	−	307.900i	0.898833	−	0.372309i	0.115062	−	0.993358i	$-0.463293\pi$
$827$	743.335	−	307.900i	0.898833	−	0.372309i	0.783772	+	0.621049i	$0.213293\pi$
$828$	−1304.90	−	1229.74i	−1.57596	−	1.48520i
$829$	240.705	+	240.705i	0.290356	+	0.290356i	0.837221	−	0.546865i	$-0.184179\pi$
$829$	240.705	+	240.705i	0.290356	+	0.290356i	−0.546865	+	0.837221i	$0.684179\pi$
$830$	−411.811	−	75.5875i	−0.496157	−	0.0910693i
$831$	−1508.65	+	1508.65i	−1.81546	+	1.81546i
$832$	−235.866	+	123.282i	−0.283493	+	0.148175i
$833$	633.630	+	206.960i	0.760660	+	0.248451i
$834$	1301.05	−	2011.05i	1.56001	−	2.41133i
$835$		−	418.595i		−	0.501311i
$836$	189.847	+	178.913i	0.227090	+	0.214011i
$837$	−7.26088	+	7.26088i	−0.00867489	+	0.00867489i
$838$	−559.162	−	810.576i	−0.667258	−	0.967275i
$839$	24.9938	+	10.3528i	0.0297900	+	0.0123394i	0.397529	−	0.917590i	$-0.369868\pi$
$839$	24.9938	+	10.3528i	0.0297900	+	0.0123394i	−0.367739	+	0.929929i	$0.619868\pi$
$840$	436.343	+	264.284i	0.519456	+	0.314624i
$841$	−594.135	−	594.135i	−0.706463	−	0.706463i
$842$	−624.009	+	964.540i	−0.741103	+	1.14553i
$843$	686.452	+	1657.24i	0.814296	+	1.96588i
$844$	−452.072	+	479.700i	−0.535631	+	0.568365i
$845$	−585.436	−	242.495i	−0.692823	−	0.286977i
$846$	162.085	+	104.861i	0.191590	+	0.123949i
$847$	67.8380	+	163.775i	0.0800920	+	0.193359i
$848$	−548.635	−	487.157i	−0.646975	−	0.574478i
$849$	761.001			0.896350
$850$	−255.407	−	26.7957i	−0.300479	−	0.0315244i
$851$	−585.608	−	585.608i	−0.688141	−	0.688141i
$852$	−1106.47	+	497.227i	−1.29867	+	0.583600i
$853$	−111.073	−	46.0078i	−0.130214	−	0.0539365i	0.316625	−	0.948551i	$-0.397450\pi$
$853$	−111.073	−	46.0078i	−0.130214	−	0.0539365i	−0.446839	+	0.894614i	$0.647450\pi$
$854$	−561.429	+	120.352i	−0.657411	+	0.140927i
$855$	192.429	+	464.565i	0.225063	+	0.543350i
$856$	1035.49	−	254.294i	1.20969	−	0.297073i
$857$	915.120	+	379.055i	1.06782	+	0.442304i	0.846220	−	0.532834i	$-0.178873\pi$
$857$	915.120	+	379.055i	1.06782	+	0.442304i	0.221597	+	0.975138i	$0.428873\pi$
$858$	273.305	+	176.815i	0.318538	+	0.206078i
$859$		−	805.381i		−	0.937579i	−0.883310	−	0.468790i	$-0.844690\pi$
$859$		−	805.381i		−	0.937579i	0.883310	−	0.468790i	$-0.155310\pi$
$860$	579.673	−	17.1876i	0.674039	−	0.0199856i
$861$	−220.166	+	91.1957i	−0.255710	+	0.105918i
$862$	48.3683	−	263.517i	0.0561117	−	0.305704i
$863$	908.957			1.05325			0.526627	−	0.850097i	$-0.323457\pi$
$863$	908.957			1.05325			0.526627	+	0.850097i	$0.323457\pi$
$864$	−899.913	−	110.561i	−1.04157	−	0.127964i
$865$	83.4052	+	83.4052i	0.0964222	+	0.0964222i
$866$	−151.480	+	234.145i	−0.174919	+	0.270376i
$867$	1204.58	−	733.063i	1.38936	−	0.845517i
$868$	4.13720	−	1.85919i	0.00476636	−	0.00214192i
$869$			953.426i			1.09715i
$870$	29.3679	−	20.2589i	0.0337562	−	0.0232861i
$871$		−	77.2203i		−	0.0886570i
$872$	1074.34	+	650.707i	1.23204	+	0.746223i
$873$	1008.82	−	2435.52i	1.15558	−	2.78982i
$874$	−88.8707	+	484.179i	−0.101683	+	0.553981i
$875$		−	425.441i		−	0.486219i
$876$	−2229.51	+	1001.90i	−2.54510	+	1.14373i
$877$	182.177	+	439.814i	0.207727	+	0.501499i	0.993065	−	0.117570i	$-0.0375104\pi$
$877$	182.177	+	439.814i	0.207727	+	0.501499i	−0.785337	+	0.619068i	$0.787510\pi$
$878$	837.470	−	577.714i	0.953838	−	0.657989i
$879$	1044.33	−	432.578i	1.18809	−	0.492125i
$880$	−400.862	−	355.943i	−0.455524	−	0.404480i
$881$	96.6929	−	40.0515i	0.109754	−	0.0454614i	−0.327131	−	0.944979i	$-0.606082\pi$
$881$	96.6929	−	40.0515i	0.109754	−	0.0454614i	0.436885	+	0.899518i	$0.356082\pi$
$882$	−243.386	−	1135.37i	−0.275948	−	1.28727i
$883$	956.784	+	956.784i	1.08356	+	1.08356i	0.996174	+	0.0873867i	$0.0278516\pi$
$883$	956.784	+	956.784i	1.08356	+	1.08356i	0.0873867	+	0.996174i	$0.472148\pi$
$884$	−281.169	+	30.0978i	−0.318065	+	0.0340473i
$885$	247.473	+	247.473i	0.279631	+	0.279631i
$886$	108.722	−	168.054i	0.122711	−	0.189677i
$887$	1370.33	−	567.608i	1.54490	−	0.639919i	0.562517	−	0.826786i	$-0.309833\pi$
$887$	1370.33	−	567.608i	1.54490	−	0.639919i	0.982385	+	0.186867i	$0.0598333\pi$
$888$	−1055.53	−	161.565i	−1.18866	−	0.181943i
$889$	31.8629	−	13.1980i	0.0358413	−	0.0148459i
$890$	159.226	−	867.483i	0.178905	−	0.974700i
$891$	15.2996	+	36.9365i	0.0171713	+	0.0414551i
$892$	208.824	−	549.685i	0.234108	−	0.616239i
$893$		−	52.9999i		−	0.0593503i
$894$	633.873	−	437.266i	0.709030	−	0.489112i
$895$	−180.776	+	436.432i	−0.201984	+	0.487634i
$896$	354.252	+	186.822i	0.395371	+	0.208506i
$897$			614.257i			0.684791i
$898$	−89.0259	+	485.025i	−0.0991380	+	0.540117i
$899$		−	0.317218i		−	0.000352856i
$900$	183.372	+	408.052i	0.203747	+	0.453392i
$901$	−352.842	−	695.139i	−0.391611	−	0.771520i
$902$	244.863	−	52.4903i	0.271466	−	0.0581933i
$903$	374.698	+	374.698i	0.414948	+	0.414948i
$904$	−1616.88	+	397.069i	−1.78858	+	0.439236i
$905$	566.881			0.626387
$906$	968.953	+	1404.62i	1.06948	+	1.55035i
$907$	−147.613	+	61.1434i	−0.162749	+	0.0674128i	−0.462571	−	0.886582i	$-0.653073\pi$
$907$	−147.613	+	61.1434i	−0.162749	+	0.0674128i	0.299822	+	0.953995i	$0.403073\pi$
$908$	−1272.03	−	1198.77i	−1.40091	−	1.32023i
$909$		−	2498.44i		−	2.74856i
$910$	−22.7829	−	106.280i	−0.0250362	−	0.116791i
$911$	−970.168	−	401.857i	−1.06495	−	0.441116i	−0.219743	−	0.975558i	$-0.570522\pi$
$911$	−970.168	−	401.857i	−1.06495	−	0.441116i	−0.845205	+	0.534442i	$0.820522\pi$
$912$	277.211	+	570.978i	0.303960	+	0.626073i
$913$	153.851	+	371.428i	0.168511	+	0.406821i
$914$	−713.631	+	1103.07i	−0.780778	+	1.20686i
$915$	1727.66	+	715.620i	1.88815	+	0.782099i
$916$	−395.970	+	177.942i	−0.432282	+	0.194260i
$917$	−66.3166	−	66.3166i	−0.0723191	−	0.0723191i
$918$	−846.692	−	459.510i	−0.922322	−	0.500555i
$919$	808.077			0.879300			0.439650	−	0.898169i	$-0.355103\pi$
$919$	808.077			0.879300			0.439650	+	0.898169i	$0.355103\pi$
$920$	153.060	−	999.963i	0.166370	−	1.08692i
$921$	−219.939	−	530.981i	−0.238805	−	0.576526i
$922$	7.14699	−	1.53207i	0.00775161	−	0.00166169i
$923$	238.790	+	98.9101i	0.258711	+	0.107162i
$924$	−14.5176	−	489.625i	−0.0157117	−	0.529898i
$925$	79.0730	+	190.899i	0.0854843	+	0.206377i
$926$	−687.258	+	147.325i	−0.742179	+	0.159098i
$927$	1807.71	+	1807.71i	1.95006	+	1.95006i
$928$	22.0731	−	17.2428i	0.0237857	−	0.0185806i
$929$	−1180.53	−	488.992i	−1.27076	−	0.526364i	−0.357562	−	0.933889i	$-0.616392\pi$
$929$	−1180.53	−	488.992i	−1.27076	−	0.526364i	−0.913194	+	0.407525i	$0.866392\pi$
$930$	−14.5293	−	2.66685i	−0.0156229	−	0.00286758i
$931$	−225.418	+	225.418i	−0.242125	+	0.242125i
$932$	−407.681	+	432.596i	−0.437426	+	0.464159i
$933$			1477.89i			1.58402i
$934$	790.952	−	169.554i	0.846844	−	0.181535i
$935$	−257.805	−	507.905i	−0.275727	−	0.543214i
$936$	291.605	+	397.008i	0.311544	+	0.424154i
$937$	1273.07	−	1273.07i	1.35867	−	1.35867i	0.483113	−	0.875558i	$-0.339506\pi$
$937$	1273.07	−	1273.07i	1.35867	−	1.35867i	0.875558	−	0.483113i	$-0.160494\pi$
$938$	−95.6517	+	65.9837i	−0.101974	+	0.0703451i
$939$	1089.10	+	1089.10i	1.15985	+	1.15985i
$940$	3.22796	+	108.867i	0.00343400	+	0.115816i
$941$	−590.365	+	244.537i	−0.627380	+	0.259869i	−0.673640	−	0.739060i	$-0.735270\pi$
$941$	−590.365	+	244.537i	−0.627380	+	0.259869i	0.0462593	+	0.998929i	$0.485270\pi$
$942$	989.397	+	1434.26i	1.05032	+	1.52257i
$943$	334.152	+	334.152i	0.354350	+	0.354350i
$944$	205.454	+	182.432i	0.217642	+	0.193254i
$945$	141.706	−	342.109i	0.149954	−	0.362020i
$946$	−316.199	−	458.371i	−0.334248	−	0.484536i
$947$	29.2296	−	70.5665i	0.0308655	−	0.0745158i	−0.907695	−	0.419630i	$-0.862160\pi$
$947$	29.2296	−	70.5665i	0.0308655	−	0.0745158i	0.938561	+	0.345114i	$0.112160\pi$
$948$	−823.829	+	2168.56i	−0.869018	+	2.28751i
$949$	481.157	+	199.302i	0.507015	+	0.210013i
$950$	66.7139	−	103.121i	0.0702252	−	0.108548i
$951$	917.166			0.964422
$952$	277.537	+	322.562i	0.291530	+	0.338826i
$953$		−	1419.10i		−	1.48909i	−0.667574	−	0.744544i	$-0.732667\pi$
$953$		−	1419.10i		−	1.48909i	0.667574	−	0.744544i	$-0.267333\pi$
$954$	−737.644	+	1140.19i	−0.773212	+	1.19517i
$955$	106.005	−	255.919i	0.111000	−	0.267978i
$956$	295.625	+	657.847i	0.309232	+	0.688125i
$957$	−31.6504	−	13.1100i	−0.0330725	−	0.0136991i
$958$	−600.975	−	871.190i	−0.627323	−	0.909384i
$959$	−476.308	−	197.293i	−0.496672	−	0.205728i
$960$	−604.195	−	1155.96i	−0.629369	−	1.20413i
$961$	679.437	−	679.437i	0.707010	−	0.707010i
$962$	129.193	+	187.282i	0.134296	+	0.194680i
$963$	−755.231	−	1823.29i	−0.784248	−	1.89334i
$964$	823.804	−	874.149i	0.854568	−	0.906793i
$965$	598.762	−	598.762i	0.620479	−	0.620479i
$966$	760.872	−	524.874i	0.787652	−	0.543348i
$967$	1163.68	+	1163.68i	1.20339	+	1.20339i	0.973127	+	0.230267i	$0.0739601\pi$
$967$	1163.68	+	1163.68i	1.20339	+	1.20339i	0.230267	+	0.973127i	$0.426040\pi$
$968$	68.5779	−	448.029i	0.0708449	−	0.462840i
$969$	51.8745	+	672.386i	0.0535340	+	0.693897i
$970$	1454.25	−	311.743i	1.49923	−	0.321385i
$971$	−1411.20			−1.45335			−0.726676	−	0.686980i	$-0.758936\pi$
$971$	−1411.20			−1.45335			−0.726676	+	0.686980i	$0.758936\pi$
$972$	−27.3477	−	922.334i	−0.0281355	−	0.948903i
$973$	543.043	+	543.043i	0.558112	+	0.558112i
$974$	1490.69	+	273.615i	1.53048	+	0.280919i
$975$	58.6484	−	141.590i	0.0601522	−	0.145220i
$976$	1387.24	+	480.465i	1.42136	+	0.492280i
$977$	−240.302	+	240.302i	−0.245959	+	0.245959i	−0.819310	−	0.573351i	$-0.805643\pi$
$977$	−240.302	+	240.302i	−0.245959	+	0.245959i	0.573351	+	0.819310i	$0.305643\pi$
$978$	233.687	−	50.0945i	0.238943	−	0.0512214i
$979$	−782.417	+	324.088i	−0.799200	+	0.331040i
$980$	449.302	−	476.760i	0.458472	−	0.486490i
$981$	889.649	−	2147.80i	0.906879	−	2.18940i
$982$	−1109.02	+	237.737i	−1.12935	+	0.242095i
$983$	401.020	−	166.108i	0.407955	−	0.168980i	−0.169262	−	0.985571i	$-0.554139\pi$
$983$	401.020	−	166.108i	0.407955	−	0.168980i	0.577217	+	0.816591i	$0.304139\pi$
$984$	602.293	+	92.1904i	0.612086	+	0.0936894i
$985$			603.861i			0.613056i
$986$	28.5331	−	8.45773i	0.0289382	−	0.00857782i
$987$	−70.3710	+	70.3710i	−0.0712979	+	0.0712979i
$988$	48.0276	−	126.423i	0.0486109	−	0.127958i
$989$	402.125	−	970.816i	0.406598	−	0.981614i
$990$	−538.962	+	833.082i	−0.544406	+	0.841497i
$991$	434.560	−	180.000i	0.438506	−	0.181635i	−0.152498	−	0.988304i	$-0.548732\pi$
$991$	434.560	−	180.000i	0.438506	−	0.181635i	0.591004	+	0.806669i	$0.298732\pi$
$992$	−11.5106	−	1.41416i	−0.0116034	−	0.00142557i
$993$	−266.999	+	644.592i	−0.268881	+	0.649136i
$994$	−81.5243	−	380.303i	−0.0820164	−	0.382599i
$995$	1524.31			1.53197
$996$	28.9907	+	977.747i	0.0291071	+	0.981673i
$997$	−439.236	−	1060.41i	−0.440558	−	1.06360i	−0.975753	−	0.218872i	$-0.929762\pi$
$997$	−439.236	−	1060.41i	−0.440558	−	1.06360i	0.535196	−	0.844728i	$-0.320238\pi$
$998$	137.506	+	199.332i	0.137781	+	0.199732i
$999$			775.105i			0.775881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.3.x.a.155.6	✓	280
16.3	odd	4		272.3.z.a.19.41	yes	280
17.9	even	8		272.3.z.a.43.41	yes	280
272.179	odd	8	inner	272.3.x.a.179.6	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.3.x.a.155.6	✓	280	1.1	even	1	trivial
272.3.x.a.179.6	yes	280	272.179	odd	8	inner
272.3.z.a.19.41	yes	280	16.3	odd	4
272.3.z.a.43.41	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+(-1.95557 + 0.419209i) q^{2} +(4.50783 + 1.86720i) q^{3} +(3.64853 - 1.63959i) q^{4} +(1.59844 - 3.85899i) q^{5} +(-9.59814 - 1.76173i) q^{6} +(1.19737 - 2.89070i) q^{7} +(-6.44763 + 4.73583i) q^{8} +(10.4701 + 10.4701i) q^{9} +(-1.50815 + 8.21661i) q^{10} +(7.41088 - 3.06969i) q^{11} +(19.5084 - 0.578434i) q^{12} +(-2.94048 - 2.94048i) q^{13} +(-1.12973 + 6.15493i) q^{14} +(14.4110 - 14.4110i) q^{15} +(10.6235 - 11.9642i) q^{16} +(15.1590 - 7.69447i) q^{17} +(-24.8643 - 16.0859i) q^{18} +8.13029i q^{19} +(-0.495175 - 16.7004i) q^{20} +(10.7951 - 10.7951i) q^{21} +(-13.2057 + 9.10970i) q^{22} +(-27.9692 - 11.5852i) q^{23} +(-37.9076 + 9.30926i) q^{24} +(5.34092 + 5.34092i) q^{25} +(6.98299 + 4.51764i) q^{26} +(10.8428 + 26.1769i) q^{27} +(-0.370928 - 12.5100i) q^{28} +(-0.808672 - 0.334963i) q^{29} +(-22.1406 + 34.2231i) q^{30} +(0.138688 + 0.334824i) q^{31} +(-15.7596 + 27.8502i) q^{32} +39.1387 q^{33} +(-26.4189 + 21.4019i) q^{34} +(-9.24125 - 9.24125i) q^{35} +(55.3672 + 21.0339i) q^{36} +(25.2739 + 10.4688i) q^{37} +(-3.40829 - 15.8994i) q^{38} +(-7.76470 - 18.7456i) q^{39} +(7.96931 + 32.4513i) q^{40} +(-14.4215 - 5.97357i) q^{41} +(-16.5851 + 25.6359i) q^{42} +34.7101i q^{43} +(22.0058 - 23.3506i) q^{44} +(57.1400 - 23.6682i) q^{45} +(59.5525 + 10.9308i) q^{46} -6.51881 q^{47} +(70.2285 - 34.0961i) q^{48} +(27.7258 + 27.7258i) q^{49} +(-12.6835 - 8.20560i) q^{50} +(82.7013 - 6.38040i) q^{51} +(-15.5496 - 5.90724i) q^{52} -45.8565i q^{53} +(-32.1776 - 46.6455i) q^{54} -33.5052i q^{55} +(5.96968 + 24.3087i) q^{56} +(-15.1809 + 36.6500i) q^{57} +(1.72184 + 0.316042i) q^{58} +17.1725i q^{59} +(28.9509 - 76.2072i) q^{60} +(35.1134 + 84.7712i) q^{61} +(-0.411576 - 0.596632i) q^{62} +(42.8026 - 17.7294i) q^{63} +(19.1439 - 61.0697i) q^{64} +(-16.0474 + 6.64707i) q^{65} +(-76.5386 + 16.4073i) q^{66} +(13.1306 + 13.1306i) q^{67} +(42.6923 - 52.9280i) q^{68} +(-104.449 - 104.449i) q^{69} +(21.9460 + 14.1979i) q^{70} +(-57.4227 + 23.7853i) q^{71} +(-117.092 - 17.9228i) q^{72} +(-115.706 + 47.9268i) q^{73} +(-53.8136 - 9.87744i) q^{74} +(14.1034 + 34.0486i) q^{75} +(13.3303 + 29.6636i) q^{76} -25.0982i q^{77} +(23.0428 + 33.4034i) q^{78} +(-45.4854 + 109.812i) q^{79} +(-29.1884 - 60.1200i) q^{80} +4.98410i q^{81} +(30.7064 + 5.63614i) q^{82} +50.1193i q^{83} +(21.6866 - 57.0856i) q^{84} +(-5.46202 - 70.7975i) q^{85} +(-14.5508 - 67.8782i) q^{86} +(-3.01991 - 3.01991i) q^{87} +(-33.2451 + 54.8889i) q^{88} -105.577 q^{89} +(-101.819 + 70.2384i) q^{90} +(-12.0209 + 4.97921i) q^{91} +(-121.042 + 3.58894i) q^{92} +1.76829i q^{93} +(12.7480 - 2.73275i) q^{94} +(31.3747 + 12.9958i) q^{95} +(-123.044 + 96.1179i) q^{96} +(-68.1316 - 164.484i) q^{97} +(-65.8426 - 42.5968i) q^{98} +(109.733 + 45.4528i) 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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