LMFDB - Embedded newform 27.3.f.a.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,3,Mod(2,27)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			23.2
Character	$\chi$	$=$	27.23
Dual form			27.3.f.a.20.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.524483 + 1.44101i) q^{2} +(-2.15873 + 2.08324i) q^{3} +(1.26276 + 1.05958i) q^{4} +(-0.0496479 - 0.00875427i) q^{5} +(-1.86975 - 4.20337i) q^{6} +(7.55168 - 6.33661i) q^{7} +(-7.50132 + 4.33089i) q^{8} +(0.320214 - 8.99430i) q^{9} +(0.0386545 - 0.0669515i) q^{10} +(12.0681 - 2.12794i) q^{11} +(-4.93332 + 0.343285i) q^{12} +(-11.4873 + 4.18103i) q^{13} +(5.17037 + 14.2055i) q^{14} +(0.125414 - 0.0845305i) q^{15} +(-1.16154 - 6.58743i) q^{16} +(-12.7914 - 7.38513i) q^{17} +(12.7929 + 5.17879i) q^{18} +(6.26584 + 10.8527i) q^{19} +(-0.0534176 - 0.0636606i) q^{20} +(-3.10133 + 29.4110i) q^{21} +(-3.26317 + 18.5063i) q^{22} +(5.93322 - 7.07093i) q^{23} +(7.17102 - 24.9763i) q^{24} +(-23.4899 - 8.54963i) q^{25} -18.7461i q^{26} +(18.0460 + 20.0833i) q^{27} +16.2501 q^{28} +(15.1728 - 41.6870i) q^{29} +(0.0560316 + 0.225057i) q^{30} +(-24.2140 - 20.3180i) q^{31} +(-24.0190 - 4.23520i) q^{32} +(-21.6188 + 29.7345i) q^{33} +(17.3509 - 14.5591i) q^{34} +(-0.430398 + 0.248490i) q^{35} +(9.93456 - 11.0184i) q^{36} +(-7.19801 + 12.4673i) q^{37} +(-18.9252 + 3.33702i) q^{38} +(16.0878 - 32.9565i) q^{39} +(0.410339 - 0.149351i) q^{40} +(23.5871 + 64.8050i) q^{41} +(-40.7548 - 19.8946i) q^{42} +(7.01983 + 39.8114i) q^{43} +(17.4939 + 10.1001i) q^{44} +(-0.0946365 + 0.443745i) q^{45} +(7.07738 + 12.2584i) q^{46} +(1.24938 + 1.48895i) q^{47} +(16.2306 + 11.8007i) q^{48} +(8.36645 - 47.4485i) q^{49} +(24.6402 - 29.3650i) q^{50} +(42.9982 - 10.7051i) q^{51} +(-18.9358 - 6.89208i) q^{52} +47.7390i q^{53} +(-38.4051 + 15.4711i) q^{54} -0.617787 q^{55} +(-29.2044 + 80.2384i) q^{56} +(-36.1351 - 10.3749i) q^{57} +(52.1133 + 43.7282i) q^{58} +(-72.6161 - 12.8042i) q^{59} +(0.247935 + 0.0261442i) q^{60} +(-4.54441 + 3.81321i) q^{61} +(41.9782 - 24.2361i) q^{62} +(-54.5752 - 69.9511i) q^{63} +(32.0786 - 55.5618i) q^{64} +(0.606922 - 0.107017i) q^{65} +(-31.5089 - 46.7481i) q^{66} +(45.8583 - 16.6910i) q^{67} +(-8.32735 - 22.8792i) q^{68} +(1.92225 + 27.6245i) q^{69} +(-0.132340 - 0.750535i) q^{70} +(-8.61519 - 4.97398i) q^{71} +(36.5513 + 68.8559i) q^{72} +(-44.2472 - 76.6383i) q^{73} +(-14.1902 - 16.9113i) q^{74} +(68.5193 - 30.4788i) q^{75} +(-3.58713 + 20.3436i) q^{76} +(77.6508 - 92.5406i) q^{77} +(39.0527 + 40.4678i) q^{78} +(105.233 + 38.3016i) q^{79} +0.337221i q^{80} +(-80.7949 - 5.76021i) q^{81} -105.755 q^{82} +(-6.65732 + 18.2908i) q^{83} +(-35.0796 + 33.8529i) q^{84} +(0.570416 + 0.478636i) q^{85} +(-61.0503 - 10.7648i) q^{86} +(54.0900 + 121.599i) q^{87} +(-81.3111 + 68.2281i) q^{88} +(-33.9430 + 19.5970i) q^{89} +(-0.589805 - 0.369109i) q^{90} +(-60.2547 + 104.364i) q^{91} +(14.9845 - 2.64217i) q^{92} +(94.5988 - 6.58266i) q^{93} +(-2.80086 + 1.01943i) q^{94} +(-0.216078 - 0.593669i) q^{95} +(60.6734 - 40.8947i) q^{96} +(-0.0670785 - 0.380421i) q^{97} +(63.9855 + 36.9420i) q^{98} +(-15.2749 - 109.226i) 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 $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.524483	+	1.44101i	−0.262242	+	0.720503i	0.736774	+	0.676139i	$0.236348\pi$
$2$	−0.524483	+	1.44101i	−0.262242	+	0.720503i	−0.999015	+	0.0443638i	$0.985874\pi$
$3$	−2.15873	+	2.08324i	−0.719576	+	0.694414i
$3$	−2.15873	+	2.08324i	−0.719576	+	0.694414i
$4$	1.26276	+	1.05958i	0.315690	+	0.264896i
$5$	−0.0496479	−	0.00875427i	−0.00992959	−	0.00175085i	0.168681	−	0.985671i	$-0.446049\pi$
$5$	−0.0496479	−	0.00875427i	−0.00992959	−	0.00175085i	−0.178611	+	0.983920i	$0.557160\pi$
$6$	−1.86975	−	4.20337i	−0.311624	−	0.700561i
$7$	7.55168	−	6.33661i	1.07881	−	0.905230i	0.0829894	−	0.996550i	$-0.473553\pi$
$7$	7.55168	−	6.33661i	1.07881	−	0.905230i	0.995822	+	0.0913206i	$0.0291088\pi$
$8$	−7.50132	+	4.33089i	−0.937665	+	0.541361i
$9$	0.320214	−	8.99430i	0.0355794	−	0.999367i
$10$	0.0386545	−	0.0669515i	0.00386545	−	0.00669515i
$11$	12.0681	−	2.12794i	1.09710	−	0.193449i	0.404337	−	0.914610i	$-0.367502\pi$
$11$	12.0681	−	2.12794i	1.09710	−	0.193449i	0.692767	+	0.721161i	$0.256391\pi$
$12$	−4.93332	+	0.343285i	−0.411110	+	0.0286071i
$13$	−11.4873	+	4.18103i	−0.883637	+	0.321618i	−0.743677	−	0.668539i	$-0.766920\pi$
$13$	−11.4873	+	4.18103i	−0.883637	+	0.321618i	−0.139961	+	0.990157i	$0.544698\pi$
$14$	5.17037	+	14.2055i	0.369312	+	1.01468i
$15$	0.125414	−	0.0845305i	0.00836091	−	0.00563537i
$16$	−1.16154	−	6.58743i	−0.0725963	−	0.411714i
$17$	−12.7914	−	7.38513i	−0.752436	−	0.434419i	0.0741373	−	0.997248i	$-0.476380\pi$
$17$	−12.7914	−	7.38513i	−0.752436	−	0.434419i	−0.826574	+	0.562829i	$0.809713\pi$
$18$	12.7929	+	5.17879i	0.710717	+	0.287711i
$19$	6.26584	+	10.8527i	0.329781	+	0.571197i	0.982468	−	0.186430i	$-0.0596918\pi$
$19$	6.26584	+	10.8527i	0.329781	+	0.571197i	−0.652687	+	0.757627i	$0.726358\pi$
$20$	−0.0534176	−	0.0636606i	−0.00267088	−	0.00318303i
$21$	−3.10133	+	29.4110i	−0.147683	+	1.40052i
$22$	−3.26317	+	18.5063i	−0.148326	+	0.841197i
$23$	5.93322	−	7.07093i	0.257966	−	0.307432i	−0.621481	−	0.783430i	$-0.713469\pi$
$23$	5.93322	−	7.07093i	0.257966	−	0.307432i	0.879446	+	0.475998i	$0.157913\pi$
$24$	7.17102	−	24.9763i	0.298793	−	1.04068i
$25$	−23.4899	−	8.54963i	−0.939597	−	0.341985i
$26$		−	18.7461i		−	0.721005i
$27$	18.0460	+	20.0833i	0.668372	+	0.743827i
$28$	16.2501			0.580362
$29$	15.1728	−	41.6870i	0.523200	−	1.43748i	−0.343738	−	0.939066i	$-0.611693\pi$
$29$	15.1728	−	41.6870i	0.523200	−	1.43748i	0.866938	−	0.498416i	$-0.166085\pi$
$30$	0.0560316	+	0.225057i	0.00186772	+	0.00750189i
$31$	−24.2140	−	20.3180i	−0.781098	−	0.655419i	0.162427	−	0.986721i	$-0.448068\pi$
$31$	−24.2140	−	20.3180i	−0.781098	−	0.655419i	−0.943525	+	0.331301i	$0.892512\pi$
$32$	−24.0190	−	4.23520i	−0.750594	−	0.132350i
$33$	−21.6188	+	29.7345i	−0.655116	+	0.901045i
$34$	17.3509	−	14.5591i	0.510321	−	0.428210i
$35$	−0.430398	+	0.248490i	−0.0122971	+	0.00709972i
$36$	9.93456	−	11.0184i	0.275960	−	0.306066i
$37$	−7.19801	+	12.4673i	−0.194541	+	0.336954i	−0.946750	−	0.321970i	$-0.895655\pi$
$37$	−7.19801	+	12.4673i	−0.194541	+	0.336954i	0.752209	+	0.658924i	$0.228988\pi$
$38$	−18.9252	+	3.33702i	−0.498032	+	0.0878164i
$39$	16.0878	−	32.9565i	0.412508	−	0.845038i
$40$	0.410339	−	0.149351i	0.0102585	−	0.00373378i
$41$	23.5871	+	64.8050i	0.575295	+	1.58061i	0.796018	+	0.605273i	$0.206936\pi$
$41$	23.5871	+	64.8050i	0.575295	+	1.58061i	−0.220724	+	0.975336i	$0.570842\pi$
$42$	−40.7548	−	19.8946i	−0.970353	−	0.473681i
$43$	7.01983	+	39.8114i	0.163252	+	0.925847i	0.950849	+	0.309656i	$0.100214\pi$
$43$	7.01983	+	39.8114i	0.163252	+	0.925847i	−0.787597	+	0.616191i	$0.788675\pi$
$44$	17.4939	+	10.1001i	0.397589	+	0.229548i
$45$	−0.0946365	+	0.443745i	−0.00210303	+	0.00986101i
$46$	7.07738	+	12.2584i	0.153856	+	0.266487i
$47$	1.24938	+	1.48895i	0.0265825	+	0.0316797i	0.779172	−	0.626810i	$-0.215640\pi$
$47$	1.24938	+	1.48895i	0.0265825	+	0.0316797i	−0.752589	+	0.658490i	$0.771195\pi$
$48$	16.2306	+	11.8007i	0.338139	+	0.245848i
$49$	8.36645	−	47.4485i	0.170744	−	0.968336i
$50$	24.6402	−	29.3650i	0.492803	−	0.587300i
$51$	42.9982	−	10.7051i	0.843102	−	0.209904i
$52$	−18.9358	−	6.89208i	−0.364151	−	0.132540i
$53$			47.7390i			0.900736i	0.892843	+	0.450368i	$0.148707\pi$
$53$			47.7390i			0.900736i	−0.892843	+	0.450368i	$0.851293\pi$
$54$	−38.4051	+	15.4711i	−0.711205	+	0.286502i
$55$	−0.617787			−0.0112325
$56$	−29.2044	+	80.2384i	−0.521507	+	1.43283i
$57$	−36.1351	−	10.3749i	−0.633950	−	0.182016i
$58$	52.1133	+	43.7282i	0.898505	+	0.753935i
$59$	−72.6161	−	12.8042i	−1.23078	−	0.217020i	−0.479821	−	0.877367i	$-0.659298\pi$
$59$	−72.6161	−	12.8042i	−1.23078	−	0.217020i	−0.750961	+	0.660347i	$0.770409\pi$
$60$	0.247935	+	0.0261442i	0.00413224	+	0.000435737i
$61$	−4.54441	+	3.81321i	−0.0744986	+	0.0625117i	−0.679277	−	0.733882i	$-0.737706\pi$
$61$	−4.54441	+	3.81321i	−0.0744986	+	0.0625117i	0.604778	+	0.796394i	$0.293262\pi$
$62$	41.9782	−	24.2361i	0.677068	−	0.390905i
$63$	−54.5752	−	69.9511i	−0.866273	−	1.11034i
$64$	32.0786	−	55.5618i	0.501228	−	0.868153i
$65$	0.606922	−	0.107017i	0.00933726	−	0.00164641i
$66$	−31.5089	−	46.7481i	−0.477407	−	0.708305i
$67$	45.8583	−	16.6910i	0.684452	−	0.249120i	0.0236939	−	0.999719i	$-0.492457\pi$
$67$	45.8583	−	16.6910i	0.684452	−	0.249120i	0.660758	+	0.750599i	$0.270235\pi$
$68$	−8.32735	−	22.8792i	−0.122461	−	0.336459i
$69$	1.92225	+	27.6245i	0.0278587	+	0.400356i
$70$	−0.132340	−	0.750535i	−0.00189056	−	0.0107219i
$71$	−8.61519	−	4.97398i	−0.121341	−	0.0700561i	0.438101	−	0.898926i	$-0.355651\pi$
$71$	−8.61519	−	4.97398i	−0.121341	−	0.0700561i	−0.559442	+	0.828870i	$0.688984\pi$
$72$	36.5513	+	68.8559i	0.507657	+	0.956332i
$73$	−44.2472	−	76.6383i	−0.606126	−	1.04984i	−0.991873	−	0.127236i	$-0.959390\pi$
$73$	−44.2472	−	76.6383i	−0.606126	−	1.04984i	0.385747	−	0.922605i	$-0.373944\pi$
$74$	−14.1902	−	16.9113i	−0.191760	−	0.228531i
$75$	68.5193	−	30.4788i	0.913591	−	0.406385i
$76$	−3.58713	+	20.3436i	−0.0471990	+	0.267679i
$77$	77.6508	−	92.5406i	1.00845	−	1.20183i
$78$	39.0527	+	40.4678i	0.500676	+	0.518818i
$79$	105.233	+	38.3016i	1.33206	+	0.484831i	0.907304	−	0.420476i	$-0.138137\pi$
$79$	105.233	+	38.3016i	1.33206	+	0.484831i	0.424758	+	0.905307i	$0.360359\pi$
$80$			0.337221i			0.00421526i
$81$	−80.7949	−	5.76021i	−0.997468	−	0.0711137i
$82$	−105.755			−1.28970
$83$	−6.65732	+	18.2908i	−0.0802087	+	0.220371i	−0.973315	−	0.229475i	$-0.926299\pi$
$83$	−6.65732	+	18.2908i	−0.0802087	+	0.220371i	0.893106	+	0.449846i	$0.148521\pi$
$84$	−35.0796	+	33.8529i	−0.417614	+	0.403011i
$85$	0.570416	+	0.478636i	0.00671078	+	0.00563101i
$86$	−61.0503	−	10.7648i	−0.709888	−	0.125172i
$87$	54.0900	+	121.599i	0.621724	+	1.39769i
$88$	−81.3111	+	68.2281i	−0.923990	+	0.775319i
$89$	−33.9430	+	19.5970i	−0.381382	+	0.220191i	−0.678419	−	0.734675i	$-0.737335\pi$
$89$	−33.9430	+	19.5970i	−0.381382	+	0.220191i	0.297037	+	0.954866i	$0.404001\pi$
$90$	−0.589805	−	0.369109i	−0.00655338	−	0.00410121i
$91$	−60.2547	+	104.364i	−0.662140	+	1.14686i
$92$	14.9845	−	2.64217i	0.162875	−	0.0287192i
$93$	94.5988	−	6.58266i	1.01719	−	0.0707813i
$94$	−2.80086	+	1.01943i	−0.0297964	+	0.0108450i
$95$	−0.216078	−	0.593669i	−0.00227451	−	0.00624915i
$96$	60.6734	−	40.8947i	0.632015	−	0.425987i
$97$	−0.0670785	−	0.380421i	−0.000691531	−	0.00392187i	0.984460	−	0.175609i	$-0.0561894\pi$
$97$	−0.0670785	−	0.380421i	−0.000691531	−	0.00392187i	−0.985152	+	0.171687i	$0.945078\pi$
$98$	63.9855	+	36.9420i	0.652913	+	0.376960i
$99$	−15.2749	−	109.226i	−0.154292	−	1.10329i
$100$	−20.6031	−	35.6857i	−0.206031	−	0.356857i
$101$	30.6686	+	36.5494i	0.303649	+	0.361875i	0.896194	−	0.443662i	$-0.146321\pi$
$101$	30.6686	+	36.5494i	0.303649	+	0.361875i	−0.592545	+	0.805538i	$0.701877\pi$
$102$	−7.12569	+	67.5753i	−0.0698597	+	0.662503i
$103$	−3.18310	+	18.0523i	−0.0309039	+	0.175265i	−0.996353	−	0.0853269i	$-0.972807\pi$
$103$	−3.18310	+	18.0523i	−0.0309039	+	0.175265i	0.965449	+	0.260592i	$0.0839176\pi$
$104$	68.0622	−	81.1134i	0.654444	−	0.779936i
$105$	0.411447	−	1.43304i	0.00391854	−	0.0136480i
$106$	−68.7922	−	25.0383i	−0.648983	−	0.236211i
$107$		−	68.8842i		−	0.643778i	−0.946777	−	0.321889i	$-0.895682\pi$
$107$		−	68.8842i		−	0.643778i	0.946777	−	0.321889i	$-0.104318\pi$
$108$	1.50789	+	44.4817i	0.0139619	+	0.411868i
$109$	9.57392			0.0878341			0.0439171	−	0.999035i	$-0.486016\pi$
$109$	9.57392			0.0878341			0.0439171	+	0.999035i	$0.486016\pi$
$110$	0.324019	−	0.890235i	0.00294563	−	0.00809305i
$111$	−10.4339	−	41.9087i	−0.0939989	−	0.377556i
$112$	−50.5135	−	42.3859i	−0.451014	−	0.378445i
$113$	0.497499	+	0.0877225i	0.00440265	+	0.000776306i	0.175849	−	0.984417i	$-0.443733\pi$
$113$	0.497499	+	0.0877225i	0.00440265	+	0.000776306i	−0.171446	+	0.985193i	$0.554844\pi$
$114$	33.9026	−	46.6295i	0.297391	−	0.409031i
$115$	−0.356473	+	0.299116i	−0.00309976	+	0.00260101i
$116$	63.3304	−	36.5638i	0.545952	−	0.315205i
$117$	33.9270	+	104.659i	0.289975	+	0.894521i
$118$	56.5369	−	97.9247i	0.479126	−	0.829870i
$119$	−143.393	+	25.2841i	−1.20499	+	0.212472i
$120$	−0.574675	+	1.17724i	−0.00478896	+	0.00981036i
$121$	27.4091	−	9.97611i	0.226522	−	0.0824472i
$122$	−3.11140	−	8.54849i	−0.0255033	−	0.0700696i
$123$	−185.922	−	90.7587i	−1.51156	−	0.737876i
$124$	−9.04796	−	51.3136i	−0.0729674	−	0.413819i
$125$	2.18287	+	1.26028i	0.0174630	+	0.0100823i
$126$	129.424	−	41.9550i	1.02717	−	0.332976i
$127$	52.2761	+	90.5449i	0.411623	+	0.712952i	0.995067	−	0.0992011i	$-0.0316287\pi$
$127$	52.2761	+	90.5449i	0.411623	+	0.712952i	−0.583444	+	0.812153i	$0.698295\pi$
$128$	0.531037	+	0.632865i	0.00414872	+	0.00494426i
$129$	−98.0907	−	71.3181i	−0.760393	−	0.552853i
$130$	−0.164109	+	0.930707i	−0.00126237	+	0.00715928i
$131$	−129.652	+	154.513i	−0.989709	+	1.17949i	−0.00595223	+	0.999982i	$0.501895\pi$
$131$	−129.652	+	154.513i	−0.989709	+	1.17949i	−0.983757	+	0.179507i	$0.942550\pi$
$132$	−58.8056	+	14.6406i	−0.445497	+	0.110914i
$133$	116.087	+	42.2523i	0.872836	+	0.317686i
$134$			74.8362i			0.558479i
$135$	−0.720134	−	1.15508i	−0.00533432	−	0.00855612i
$136$	127.937			0.940710
$137$	66.3180	−	182.207i	0.484073	−	1.32998i	−0.421899	−	0.906643i	$-0.638636\pi$
$137$	66.3180	−	182.207i	0.484073	−	1.32998i	0.905972	−	0.423338i	$-0.139142\pi$
$138$	−40.8153	−	11.7186i	−0.295763	−	0.0849176i
$139$	22.0112	+	18.4696i	0.158354	+	0.132875i	0.718522	−	0.695504i	$-0.244819\pi$
$139$	22.0112	+	18.4696i	0.158354	+	0.132875i	−0.560168	+	0.828379i	$0.689263\pi$
$140$	−0.806785	−	0.142258i	−0.00576275	−	0.00101613i
$141$	−5.79890	−	0.611483i	−0.0411269	−	0.00433676i
$142$	11.6861	−	9.80577i	0.0822962	−	0.0690547i
$143$	−129.733	+	74.9015i	−0.907225	+	0.523787i
$144$	−59.6213	+	8.33786i	−0.414036	+	0.0579018i
$145$	−1.11824	+	1.93684i	−0.00771199	+	0.0133575i
$146$	133.643	−	23.5649i	0.915365	−	0.161403i
$147$	80.7857	+	119.858i	0.549563	+	0.815358i
$148$	−22.2995	+	8.11636i	−0.150672	+	0.0548403i
$149$	85.1055	+	233.825i	0.571178	+	1.56930i	0.802646	+	0.596455i	$0.203425\pi$
$149$	85.1055	+	233.825i	0.571178	+	1.56930i	−0.231469	+	0.972842i	$0.574353\pi$
$150$	7.98296	+	114.722i	0.0532197	+	0.764816i
$151$	−25.3887	−	143.986i	−0.168137	−	0.953552i	−0.945771	−	0.324835i	$-0.894691\pi$
$151$	−25.3887	−	143.986i	−0.168137	−	0.953552i	0.777634	−	0.628717i	$-0.216420\pi$
$152$	−94.0041	−	54.2733i	−0.618448	−	0.357061i
$153$	−70.5201	+	112.685i	−0.460915	+	0.736503i
$154$	92.6251	+	160.431i	0.601461	+	1.04176i
$155$	1.02431	+	1.22072i	0.00660844	+	0.00787563i
$156$	55.2352	−	24.5698i	0.354072	−	0.157499i
$157$	18.0884	−	102.584i	0.115213	−	0.653403i	−0.871432	−	0.490516i	$-0.836808\pi$
$157$	18.0884	−	102.584i	0.115213	−	0.653403i	0.986645	−	0.162887i	$-0.0520805\pi$
$158$	−110.386	+	131.553i	−0.698644	+	0.832612i
$159$	−99.4519	−	103.056i	−0.625484	−	0.648148i
$160$	1.15542	+	0.420538i	0.00722136	+	0.00262836i
$161$		−	90.9939i		−	0.565179i
$162$	50.6761	−	113.405i	0.312815	−	0.700030i
$163$	126.261			0.774609			0.387304	−	0.921952i	$-0.373406\pi$
$163$	126.261			0.774609			0.387304	+	0.921952i	$0.373406\pi$
$164$	−38.8814	+	106.826i	−0.237081	+	0.651376i
$165$	1.33363	−	1.28700i	0.00808263	−	0.00779999i
$166$	−22.8656	−	19.1865i	−0.137744	−	0.115581i
$167$	240.870	+	42.4718i	1.44233	+	0.254322i	0.839420	−	0.543484i	$-0.182895\pi$
$167$	240.870	+	42.4718i	1.44233	+	0.254322i	0.602914	+	0.797806i	$0.294006\pi$
$168$	−104.112	−	234.053i	−0.619712	−	1.39317i
$169$	−14.9848	+	12.5738i	−0.0886676	+	0.0744010i
$170$	−0.988891	+	0.570937i	−0.00581701	+	0.00335845i
$171$	99.6193	−	52.8816i	0.582569	−	0.309249i
$172$	−33.3191	+	57.7104i	−0.193716	+	0.335526i
$173$	90.5467	−	15.9658i	0.523391	−	0.0922880i	0.0942906	−	0.995545i	$-0.469942\pi$
$173$	90.5467	−	15.9658i	0.523391	−	0.0922880i	0.429101	+	0.903257i	$0.358831\pi$
$174$	−203.595	+	14.1672i	−1.17009	+	0.0814204i
$175$	−231.564	+	84.2824i	−1.32322	+	0.481614i
$176$	−28.0353	−	77.0263i	−0.159291	−	0.437650i
$177$	183.433	−	123.636i	1.03634	−	0.698509i
$178$	−10.4369	−	59.1904i	−0.0586341	−	0.332530i
$179$	−54.8413	−	31.6626i	−0.306376	−	0.176886i	0.338928	−	0.940812i	$-0.389936\pi$
$179$	−54.8413	−	31.6626i	−0.306376	−	0.176886i	−0.645304	+	0.763926i	$0.723269\pi$
$180$	−0.589688	+	0.460069i	−0.00327604	+	0.00255594i
$181$	−77.4956	−	134.226i	−0.428153	−	0.741582i	0.568556	−	0.822644i	$-0.307502\pi$
$181$	−77.4956	−	134.226i	−0.428153	−	0.741582i	−0.996709	+	0.0810622i	$0.974169\pi$
$182$	−118.787	−	141.565i	−0.652675	−	0.777828i
$183$	1.86631	−	17.6988i	0.0101984	−	0.0967147i
$184$	−13.8835	+	78.7374i	−0.0754540	+	0.427921i
$185$	0.466509	−	0.555963i	0.00252167	−	0.00300521i
$186$	−40.1299	+	139.770i	−0.215752	+	0.751452i
$187$	−170.084	−	61.9054i	−0.909539	−	0.331045i
$188$			3.20400i			0.0170426i
$189$	263.538	+	37.3122i	1.39438	+	0.197419i
$190$	0.968811			0.00509900
$191$	19.6000	−	53.8506i	0.102618	−	0.281940i	−0.877750	−	0.479120i	$-0.840956\pi$
$191$	19.6000	−	53.8506i	0.102618	−	0.281940i	0.980367	+	0.197179i	$0.0631782\pi$
$192$	46.4996	+	186.770i	0.242185	+	0.972762i
$193$	−7.03809	−	5.90566i	−0.0364668	−	0.0305993i	0.624372	−	0.781127i	$-0.285355\pi$
$193$	−7.03809	−	5.90566i	−0.0364668	−	0.0305993i	−0.660839	+	0.750528i	$0.729799\pi$
$194$	0.583371	+	0.102864i	0.00300707	+	0.000530227i
$195$	−1.08724	+	1.49538i	−0.00557558	+	0.00766864i
$196$	60.8404	−	51.0511i	0.310410	−	0.260465i
$197$	71.8373	−	41.4753i	0.364657	−	0.210535i	−0.306465	−	0.951882i	$-0.599146\pi$
$197$	71.8373	−	41.4753i	0.364657	−	0.210535i	0.671121	+	0.741347i	$0.265813\pi$
$198$	165.407	+	35.2759i	0.835387	+	0.178161i
$199$	−18.3108	+	31.7153i	−0.0920141	+	0.159373i	−0.908359	−	0.418192i	$-0.862664\pi$
$199$	−18.3108	+	31.7153i	−0.0920141	+	0.159373i	0.816344	+	0.577565i	$0.195997\pi$
$200$	213.233	−	37.5987i	1.06616	−	0.187994i
$201$	−64.2241	+	131.565i	−0.319523	+	0.654553i
$202$	−68.7531	+	25.0241i	−0.340362	+	0.123882i
$203$	−149.574	−	410.951i	−0.736817	−	2.02439i
$204$	65.6394	+	32.0421i	0.321762	+	0.157069i
$205$	−0.603730	−	3.42392i	−0.00294502	−	0.0167021i
$206$	−24.3440	−	14.0550i	−0.118175	−	0.0682281i
$207$	−61.6982	−	55.6294i	−0.298059	−	0.268741i
$208$	40.8852	+	70.8152i	0.196563	+	0.340458i
$209$	98.7110	+	117.639i	0.472301	+	0.562867i
$210$	1.84923	+	1.34451i	0.00880585	+	0.00640241i
$211$	−53.6264	+	304.130i	−0.254154	+	1.44138i	0.544083	+	0.839032i	$0.316878\pi$
$211$	−53.6264	+	304.130i	−0.254154	+	1.44138i	−0.798236	+	0.602345i	$0.794233\pi$
$212$	−50.5834	+	60.2830i	−0.238601	+	0.284354i
$213$	28.9599	−	7.21004i	0.135962	−	0.0338500i
$214$	99.2626	+	36.1286i	0.463844	+	0.168825i
$215$		−	2.03801i		−	0.00947911i
$216$	−222.348	−	72.4961i	−1.02939	−	0.335630i
$217$	−311.604			−1.43596
$218$	−5.02136	+	13.7961i	−0.0230338	+	0.0632848i
$219$	255.174	+	73.2638i	1.16518	+	0.334538i
$220$	−0.780117	−	0.654596i	−0.00354599	−	0.00297544i
$221$	177.816	+	31.3538i	0.804598	+	0.141872i
$222$	65.8631	+	6.94515i	0.296681	+	0.0312845i
$223$	237.313	−	199.130i	1.06419	−	0.892958i	0.0696724	−	0.997570i	$-0.477805\pi$
$223$	237.313	−	199.130i	1.06419	−	0.892958i	0.994513	+	0.104612i	$0.0333601\pi$
$224$	−208.221	+	120.216i	−0.929556	+	0.536679i
$225$	−84.4198	+	208.538i	−0.375199	+	0.926835i
$226$	−0.387339	+	0.670891i	−0.00171389	+	0.00296854i
$227$	−164.338	+	28.9773i	−0.723957	+	0.127653i	−0.523471	−	0.852044i	$-0.675363\pi$
$227$	−164.338	+	28.9773i	−0.723957	+	0.127653i	−0.200486	+	0.979697i	$0.564252\pi$
$228$	−34.6370	−	51.3891i	−0.151917	−	0.225391i
$229$	218.452	−	79.5101i	0.953939	−	0.347206i	0.182284	−	0.983246i	$-0.441651\pi$
$229$	218.452	−	79.5101i	0.953939	−	0.347206i	0.771656	+	0.636040i	$0.219429\pi$
$230$	−0.244064	−	0.670561i	−0.00106115	−	0.00291548i
$231$	25.1574	+	361.535i	0.108907	+	1.56509i
$232$	66.7255	+	378.419i	0.287610	+	1.63112i
$233$	−98.2315	−	56.7140i	−0.421594	−	0.243408i	0.274165	−	0.961683i	$-0.411599\pi$
$233$	−98.2315	−	56.7140i	−0.421594	−	0.243408i	−0.695759	+	0.718275i	$0.744932\pi$
$234$	−168.608	−	6.00278i	−0.720549	−	0.0256529i
$235$	−0.0489943	−	0.0848606i	−0.000208486	−	0.000361109i
$236$	−78.1297	−	93.1114i	−0.331058	−	0.394540i
$237$	−306.961	+	136.543i	−1.29519	+	0.576129i
$238$	38.7729	−	219.892i	0.162911	−	0.923915i
$239$	−22.6159	+	26.9525i	−0.0946270	+	0.112772i	−0.811280	−	0.584658i	$-0.801229\pi$
$239$	−22.6159	+	26.9525i	−0.0946270	+	0.112772i	0.716653	+	0.697430i	$0.245673\pi$
$240$	−0.702512	−	0.727968i	−0.00292713	−	0.00303320i
$241$	−240.771	−	87.6335i	−0.999050	−	0.363624i	−0.209832	−	0.977737i	$-0.567292\pi$
$241$	−240.771	−	87.6335i	−0.999050	−	0.363624i	−0.789218	+	0.614113i	$0.789514\pi$
$242$			44.7290i			0.184831i
$243$	186.414	−	155.881i	0.767137	−	0.641484i
$244$	−9.77892			−0.0400775
$245$	−0.830753	+	2.28248i	−0.00339083	+	0.00931623i
$246$	228.297	−	220.314i	0.928037	−	0.895585i
$247$	−117.353	−	98.4709i	−0.475114	−	0.398668i
$248$	269.632	+	47.5434i	1.08723	+	0.191707i
$249$	−23.7329	−	53.3537i	−0.0953127	−	0.214272i
$250$	−2.96095	+	2.48454i	−0.0118438	+	0.00993814i
$251$	339.228	−	195.854i	1.35151	−	0.780293i	0.363046	−	0.931771i	$-0.381737\pi$
$251$	339.228	−	195.854i	1.35151	−	0.780293i	0.988461	+	0.151478i	$0.0484033\pi$
$252$	5.20353	−	146.159i	0.0206489	−	0.579994i
$253$	56.5564	−	97.9585i	0.223543	−	0.387188i
$254$	−157.894	+	27.8409i	−0.621629	+	0.109610i
$255$	−2.22849	+	0.155069i	−0.00873916	+	0.000608115i
$256$	239.962	−	87.3390i	0.937351	−	0.341168i
$257$	−97.6997	−	268.428i	−0.380155	−	1.04447i	−0.971291	−	0.237895i	$-0.923543\pi$
$257$	−97.6997	−	268.428i	−0.380155	−	1.04447i	0.591136	−	0.806572i	$-0.298680\pi$
$258$	154.217	−	103.944i	0.597739	−	0.402885i
$259$	24.6435	+	139.760i	0.0951486	+	0.539614i
$260$	0.879790	+	0.507947i	0.00338381	+	0.00195364i
$261$	−370.087	−	149.818i	−1.41796	−	0.574014i
$262$	−154.654	−	267.869i	−0.590283	−	1.02240i
$263$	290.740	+	346.490i	1.10547	+	1.31745i	0.943766	+	0.330615i	$0.107256\pi$
$263$	290.740	+	346.490i	1.10547	+	1.31745i	0.161709	+	0.986838i	$0.448299\pi$
$264$	33.3930	−	316.677i	0.126488	−	1.19953i
$265$	0.417920	−	2.37014i	0.00157706	−	0.00894394i
$266$	−121.772	+	145.122i	−0.457788	+	0.545571i
$267$	32.4484	−	113.016i	0.121530	−	0.423281i
$268$	75.5936	+	27.5138i	0.282066	+	0.102663i
$269$			277.616i			1.03203i	0.856580	+	0.516014i	$0.172585\pi$
$269$			277.616i			1.03203i	−0.856580	+	0.516014i	$0.827415\pi$
$270$	2.04217	−	0.431899i	0.00756359	−	0.00159963i
$271$	310.311			1.14506			0.572530	−	0.819884i	$-0.305962\pi$
$271$	310.311			1.14506			0.572530	+	0.819884i	$0.305962\pi$
$272$	−33.7912	+	92.8407i	−0.124232	+	0.341326i
$273$	−87.3423	−	350.819i	−0.319935	−	1.28505i
$274$	227.779	+	191.129i	0.831311	+	0.697553i
$275$	−301.673	−	53.1931i	−1.09699	−	0.193429i
$276$	−26.8431	+	36.9200i	−0.0972577	+	0.133768i
$277$	−263.622	+	221.206i	−0.951706	+	0.798576i	−0.979584	−	0.201035i	$-0.935569\pi$
$277$	−263.622	+	221.206i	−0.951706	+	0.798576i	0.0278782	+	0.999611i	$0.491125\pi$
$278$	−38.1593	+	22.0313i	−0.137264	+	0.0792493i
$279$	−190.500	+	211.282i	−0.682795	+	0.757284i
$280$	2.15237	−	3.72801i	0.00768702	−	0.0133143i
$281$	−433.676	+	76.4687i	−1.54333	+	0.272131i	−0.879553	−	0.475801i	$-0.842158\pi$
$281$	−433.676	+	76.4687i	−1.54333	+	0.272131i	−0.663776	+	0.747931i	$0.731047\pi$
$282$	3.92258	−	8.03554i	0.0139098	−	0.0284948i
$283$	−14.0232	+	5.10404i	−0.0495521	+	0.0180355i	−0.366677	−	0.930348i	$-0.619505\pi$
$283$	−14.0232	+	5.10404i	−0.0495521	+	0.0180355i	0.317125	+	0.948384i	$0.397282\pi$
$284$	−5.60858	−	15.4095i	−0.0197485	−	0.0542587i
$285$	1.70321	+	0.831428i	0.00597618	+	0.00291729i
$286$	−39.8906	−	226.231i	−0.139478	−	0.791017i
$287$	588.766	+	339.924i	2.05145	+	1.18440i
$288$	−45.7839	+	214.678i	−0.158972	+	0.745410i
$289$	−35.4198	−	61.3489i	−0.122560	−	0.212280i
$290$	−2.20451	−	2.62723i	−0.00760175	−	0.00905942i
$291$	0.937313	+	0.681485i	0.00322101	+	0.00234187i
$292$	25.3310	−	143.659i	0.0867501	−	0.491984i
$293$	−104.147	+	124.118i	−0.355451	+	0.423610i	−0.913907	−	0.405924i	$-0.866950\pi$
$293$	−104.147	+	124.118i	−0.355451	+	0.423610i	0.558456	+	0.829534i	$0.311394\pi$
$294$	−215.086	+	53.5494i	−0.731586	+	0.182141i
$295$	3.49315	+	1.27140i	0.0118412	+	0.00430984i
$296$		−	124.695i		−	0.421267i
$297$	260.518	+	203.968i	0.877166	+	0.686760i
$298$	−381.580			−1.28047
$299$	−38.5928	+	106.033i	−0.129073	+	0.354625i
$300$	118.818	+	34.1144i	0.396061	+	0.113715i
$301$	305.281	+	256.161i	1.01422	+	0.851034i
$302$	220.801	+	38.9332i	0.731130	+	0.128918i
$303$	−142.346	−	15.0102i	−0.469790	−	0.0495385i
$304$	64.2137	−	53.8817i	0.211229	−	0.177242i
$305$	0.259003	−	0.149535i	0.000849189	−	0.000490279i
$306$	−125.393	−	160.721i	−0.409782	−	0.525233i
$307$	69.5247	−	120.420i	0.226465	−	0.392248i	−0.730293	−	0.683134i	$-0.760617\pi$
$307$	69.5247	−	120.420i	0.226465	−	0.392248i	0.956758	+	0.290886i	$0.0939499\pi$
$308$	196.109	−	34.5793i	0.636717	−	0.112270i
$309$	−30.7358	−	45.6011i	−0.0994686	−	0.147576i
$310$	−2.29630	+	0.835786i	−0.00740743	+	0.00269608i
$311$	−61.7283	−	169.597i	−0.198483	−	0.545328i	0.800023	−	0.599970i	$-0.204821\pi$
$311$	−61.7283	−	169.597i	−0.198483	−	0.545328i	−0.998506	+	0.0546413i	$0.982598\pi$
$312$	22.0509	+	316.892i	0.0706760	+	1.01568i
$313$	100.622	+	570.654i	0.321475	+	1.82317i	0.533370	+	0.845882i	$0.320925\pi$
$313$	100.622	+	570.654i	0.321475	+	1.82317i	−0.211895	+	0.977292i	$0.567963\pi$
$314$	138.337	+	79.8692i	0.440565	+	0.254360i
$315$	2.09718	+	3.95070i	0.00665770	+	0.0125419i
$316$	92.3003	+	159.869i	0.292089	+	0.505914i
$317$	−324.996	−	387.315i	−1.02522	−	1.22181i	−0.974799	−	0.223085i	$-0.928387\pi$
$317$	−324.996	−	387.315i	−1.02522	−	1.22181i	−0.0504239	−	0.998728i	$-0.516057\pi$
$318$	200.665	−	89.2599i	0.631021	−	0.280691i
$319$	94.4004	−	535.371i	0.295926	−	1.67828i
$320$	−2.07904	+	2.47770i	−0.00649700	+	0.00774282i
$321$	143.502	+	148.702i	0.447048	+	0.463247i
$322$	131.123	+	47.7248i	0.407214	+	0.148214i
$323$		−	185.096i		−	0.573053i
$324$	−95.9213	−	92.8827i	−0.296053	−	0.286675i
$325$	305.582			0.940251
$326$	−66.2219	+	181.943i	−0.203135	+	0.558108i
$327$	−20.6675	+	19.9448i	−0.0632033	+	0.0609932i
$328$	−457.597	−	383.970i	−1.39511	−	1.17064i
$329$	18.8698	+	3.32725i	0.0573549	+	0.0101132i
$330$	1.15510	+	2.59678i	0.00350032	+	0.00786905i
$331$	−173.811	+	145.845i	−0.525108	+	0.440618i	−0.866408	−	0.499336i	$-0.833577\pi$
$331$	−173.811	+	145.845i	−0.525108	+	0.440618i	0.341300	+	0.939954i	$0.389133\pi$
$332$	−27.7872	+	16.0430i	−0.0836965	+	0.0483222i
$333$	109.830	+	68.7333i	0.329820	+	0.206406i
$334$	−187.534	+	324.819i	−0.561480	+	0.972512i
$335$	−2.42289	+	0.427220i	−0.00723250	+	0.00127528i
$336$	197.345	−	13.7323i	0.587336	−	0.0408698i
$337$	90.1787	−	32.8224i	0.267593	−	0.0973957i	−0.204739	−	0.978817i	$-0.565635\pi$
$337$	90.1787	−	32.8224i	0.267593	−	0.0973957i	0.472332	+	0.881421i	$0.343412\pi$
$338$	−10.2596	−	28.1880i	−0.0303538	−	0.0833964i
$339$	−1.25671	+	0.847042i	−0.00370712	+	0.00249865i
$340$	0.213145	+	1.20881i	0.000626897	+	0.00355531i
$341$	−335.454	−	193.674i	−0.983736	−	0.567960i
$342$	23.9541	+	171.288i	0.0700412	+	0.500841i
$343$	4.03963	+	6.99685i	0.0117774	+	0.0203990i
$344$	−225.077	−	268.236i	−0.654293	−	0.779756i
$345$	0.146397	−	1.38833i	0.000424339	−	0.00402414i
$346$	−24.4834	+	138.852i	−0.0707612	+	0.401307i
$347$	166.349	−	198.247i	0.479393	−	0.571318i	−0.471094	−	0.882083i	$-0.656141\pi$
$347$	166.349	−	198.247i	0.479393	−	0.571318i	0.950487	+	0.310765i	$0.100585\pi$
$348$	−60.5419	+	210.864i	−0.173971	+	0.605931i
$349$	−258.307	−	94.0161i	−0.740135	−	0.269387i	−0.0556864	−	0.998448i	$-0.517735\pi$
$349$	−258.307	−	94.0161i	−0.740135	−	0.269387i	−0.684448	+	0.729061i	$0.739957\pi$
$350$		−	377.890i		−	1.07969i
$351$	−291.269	−	155.252i	−0.829826	−	0.442313i
$352$	−298.877			−0.849082
$353$	90.5211	−	248.705i	0.256434	−	0.704545i	−0.742947	−	0.669350i	$-0.766573\pi$
$353$	90.5211	−	248.705i	0.256434	−	0.704545i	0.999380	−	0.0351951i	$-0.0112053\pi$
$354$	81.9530	+	329.173i	0.231506	+	0.929866i
$355$	0.384183	+	0.322368i	0.00108221	+	0.000908078i
$356$	−63.6266	−	11.2191i	−0.178726	−	0.0315143i
$357$	256.874	−	353.304i	0.719536	−	0.989648i
$358$	74.3894	−	62.4202i	0.207792	−	0.174358i
$359$	183.469	−	105.926i	0.511055	−	0.295058i	−0.222212	−	0.974998i	$-0.571328\pi$
$359$	183.469	−	105.926i	0.511055	−	0.295058i	0.733267	+	0.679941i	$0.237994\pi$
$360$	−1.21191	−	3.73853i	−0.00336642	−	0.0103848i
$361$	101.979	−	176.632i	0.282489	−	0.489286i
$362$	234.066	−	41.2722i	0.646592	−	0.114012i
$363$	−38.3862	+	78.6355i	−0.105747	+	0.216627i
$364$	−186.670	+	67.9422i	−0.512829	+	0.186655i
$365$	1.52587	+	4.19229i	0.00418046	+	0.0114857i
$366$	24.5252	+	11.9721i	0.0670088	+	0.0327106i
$367$	−112.035	−	635.384i	−0.305273	−	1.73129i	−0.622216	−	0.782846i	$-0.713767\pi$
$367$	−112.035	−	635.384i	−0.305273	−	1.73129i	0.316943	−	0.948445i	$-0.397344\pi$
$368$	−53.4709	−	30.8715i	−0.145301	−	0.0838898i
$369$	590.428	−	191.398i	1.60008	−	0.518693i
$370$	0.556471	+	0.963835i	0.00150397	+	0.00260496i
$371$	302.504	+	360.510i	0.815373	+	0.971724i
$372$	126.431	+	91.9229i	0.339867	+	0.247105i
$373$	−122.107	+	692.506i	−0.327366	+	1.85658i	0.165133	+	0.986271i	$0.447195\pi$
$373$	−122.107	+	692.506i	−0.327366	+	1.85658i	−0.492499	+	0.870313i	$0.663917\pi$
$374$	178.412	−	212.623i	0.477038	−	0.568512i
$375$	−7.33770	+	1.82684i	−0.0195672	+	0.00487158i
$376$	−15.8204	−	5.75816i	−0.0420756	−	0.0153143i
$377$			542.308i			1.43848i
$378$	−191.988	+	360.191i	−0.507906	+	0.952885i
$379$	−352.196			−0.929278			−0.464639	−	0.885500i	$-0.653816\pi$
$379$	−352.196			−0.929278			−0.464639	+	0.885500i	$0.653816\pi$
$380$	0.356187	−	0.978615i	0.000937334	−	0.00257530i
$381$	−301.477	−	86.5581i	−0.791278	−	0.227187i
$382$	67.3192	+	56.4875i	0.176228	+	0.147873i
$383$	−266.149	−	46.9293i	−0.694906	−	0.122531i	−0.184972	−	0.982744i	$-0.559219\pi$
$383$	−266.149	−	46.9293i	−0.694906	−	0.122531i	−0.509935	+	0.860213i	$0.670330\pi$
$384$	−2.46477	−	0.259906i	−0.00641868	−	0.000676838i
$385$	−4.66533	+	3.91467i	−0.0121177	+	0.0101680i
$386$	12.2015	−	7.04451i	0.0316100	−	0.0182500i
$387$	360.324	−	50.3903i	0.931070	−	0.130207i
$388$	0.318383	−	0.551456i	0.000820576	−	0.00142128i
$389$	216.727	−	38.2149i	0.557140	−	0.0982388i	0.112014	−	0.993707i	$-0.464270\pi$
$389$	216.727	−	38.2149i	0.557140	−	0.0982388i	0.445126	+	0.895468i	$0.353159\pi$
$390$	−1.58462	−	2.35102i	−0.00406313	−	0.00602826i
$391$	−128.114	+	46.6297i	−0.327657	+	0.119257i
$392$	142.735	+	392.160i	0.364119	+	1.00041i
$393$	−42.0048	−	603.648i	−0.106883	−	1.53600i
$394$	22.0887	+	125.271i	0.0560627	+	0.317947i
$395$	−4.88929	−	2.82283i	−0.0123780	−	0.00714642i
$396$	96.4453	−	154.111i	0.243549	−	0.389170i
$397$	58.0173	+	100.489i	0.146139	+	0.253121i	0.929797	−	0.368072i	$-0.119982\pi$
$397$	58.0173	+	100.489i	0.146139	+	0.253121i	−0.783658	+	0.621192i	$0.786649\pi$
$398$	−36.0982	−	43.0201i	−0.0906989	−	0.108091i
$399$	−338.622	+	150.626i	−0.848678	+	0.377510i
$400$	−29.0356	+	164.669i	−0.0725889	+	0.411672i
$401$	−122.249	+	145.690i	−0.304860	+	0.363317i	−0.896623	−	0.442794i	$-0.853987\pi$
$401$	−122.249	+	145.690i	−0.304860	+	0.363317i	0.591764	+	0.806111i	$0.298432\pi$
$402$	−155.902	−	161.551i	−0.387816	−	0.401868i
$403$	363.104	+	132.159i	0.901002	+	0.327938i
$404$			78.6491i			0.194676i
$405$	3.96088	+	0.993283i	0.00977994	+	0.00245255i
$406$	670.631			1.65180
$407$	−60.3369	+	165.774i	−0.148248	+	0.407308i
$408$	−276.180	+	266.523i	−0.676913	+	0.653242i
$409$	−18.2230	−	15.2909i	−0.0445550	−	0.0373861i	0.620238	−	0.784413i	$-0.287036\pi$
$409$	−18.2230	−	15.2909i	−0.0445550	−	0.0373861i	−0.664793	+	0.747027i	$0.731480\pi$
$410$	5.25054	+	0.925812i	0.0128062	+	0.00225808i
$411$	236.419	+	531.493i	0.575229	+	1.29317i
$412$	−23.1474	+	19.4230i	−0.0561829	+	0.0471431i
$413$	−629.508	+	363.447i	−1.52423	+	0.880017i
$414$	112.522	−	59.7308i	0.271792	−	0.144277i
$415$	0.490645	−	0.849822i	0.00118228	−	0.00204776i
$416$	293.621	−	51.7732i	0.705819	−	0.124455i
$417$	−85.9929	+	5.98381i	−0.206218	+	0.0143497i
$418$	−221.291	+	80.5434i	−0.529405	+	0.192688i
$419$	117.310	+	322.307i	0.279977	+	0.769230i	0.997364	+	0.0725558i	$0.0231155\pi$
$419$	117.310	+	322.307i	0.279977	+	0.769230i	−0.717387	+	0.696674i	$0.754662\pi$
$420$	2.03799	−	1.37363i	0.00485235	−	0.00327055i
$421$	−85.7847	−	486.509i	−0.203764	−	1.15560i	−0.899372	−	0.437183i	$-0.855976\pi$
$421$	−85.7847	−	486.509i	−0.203764	−	1.15560i	0.695608	−	0.718421i	$-0.255135\pi$
$422$	−410.128	−	236.787i	−0.971867	−	0.561107i
$423$	13.7921	−	10.7605i	0.0326055	−	0.0254385i
$424$	−206.752	−	358.106i	−0.487623	−	0.844589i
$425$	237.329	+	282.838i	0.558422	+	0.665501i
$426$	−4.79925	+	45.5129i	−0.0112658	+	0.106838i
$427$	−10.1551	+	57.5923i	−0.0237824	+	0.134877i
$428$	72.9885	−	86.9843i	0.170534	−	0.203234i
$429$	124.021	−	431.957i	0.289093	−	1.00689i
$430$	2.93678	+	1.06890i	0.00682973	+	0.00248582i
$431$		−	519.074i		−	1.20435i	−0.798365	−	0.602174i	$-0.794301\pi$
$431$		−	519.074i		−	1.20435i	0.798365	−	0.602174i	$-0.205699\pi$
$432$	111.336	−	142.205i	0.257723	−	0.329177i
$433$	290.297			0.670433			0.335216	−	0.942141i	$-0.391191\pi$
$433$	290.297			0.670433			0.335216	+	0.942141i	$0.391191\pi$
$434$	163.431	−	449.023i	0.376569	−	1.03462i
$435$	−1.62094	−	6.51068i	−0.00372631	−	0.0149671i
$436$	12.0896	+	10.1444i	0.0277284	+	0.0232669i
$437$	113.916	+	20.0864i	0.260676	+	0.0459643i
$438$	−239.408	+	329.281i	−0.546594	+	0.751784i
$439$	255.941	−	214.760i	0.583009	−	0.489203i	−0.302925	−	0.953015i	$-0.597963\pi$
$439$	255.941	−	214.760i	0.583009	−	0.489203i	0.885934	+	0.463812i	$0.153519\pi$
$440$	4.63422	−	2.67557i	0.0105323	−	0.00608083i
$441$	−424.087	−	90.4440i	−0.961648	−	0.205088i
$442$	−138.443	+	239.790i	−0.313218	+	0.542510i
$443$	−327.502	+	57.7474i	−0.739282	+	0.130355i	−0.530593	−	0.847627i	$-0.678031\pi$
$443$	−327.502	+	57.7474i	−0.739282	+	0.130355i	−0.208689	+	0.977982i	$0.566920\pi$
$444$	31.2303	−	63.9763i	0.0703384	−	0.144091i
$445$	1.85676	−	0.675805i	0.00417249	−	0.00151866i
$446$	162.480	+	446.410i	0.364305	+	1.00092i
$447$	−670.834	−	327.470i	−1.50075	−	0.732596i
$448$	−109.826	−	622.854i	−0.245147	−	1.39030i
$449$	−291.154	−	168.098i	−0.648449	−	0.374382i	0.139413	−	0.990234i	$-0.455479\pi$
$449$	−291.154	−	168.098i	−0.648449	−	0.374382i	−0.787862	+	0.615852i	$0.788812\pi$
$450$	−256.227	−	231.024i	−0.569394	−	0.513387i
$451$	422.553	+	731.884i	0.936925	+	1.62280i
$452$	0.535273	+	0.637914i	0.00118423	+	0.00141131i
$453$	354.765	+	257.937i	0.783147	+	0.569396i
$454$	44.4362	−	252.010i	0.0978772	−	0.555089i
$455$	3.90515	−	4.65398i	0.00858276	−	0.0102285i
$456$	315.994	−	78.6719i	0.692968	−	0.172526i
$457$	746.228	+	271.605i	1.63288	+	0.594321i	0.985774	−	0.168076i	$-0.0537553\pi$
$457$	746.228	+	271.605i	1.63288	+	0.594321i	0.647110	+	0.762397i	$0.275977\pi$
$458$			356.493i			0.778368i
$459$	−82.5164	−	390.167i	−0.179774	−	0.850036i
$460$	−0.767078			−0.00166756
$461$	97.6760	−	268.363i	0.211878	−	0.582131i	−0.787539	−	0.616265i	$-0.788645\pi$
$461$	97.6760	−	268.363i	0.211878	−	0.582131i	0.999417	+	0.0341338i	$0.0108672\pi$
$462$	−534.169	−	153.367i	−1.15621	−	0.331964i
$463$	−102.894	−	86.3380i	−0.222232	−	0.186475i	0.524873	−	0.851180i	$-0.324113\pi$
$463$	−102.894	−	86.3380i	−0.222232	−	0.186475i	−0.747106	+	0.664705i	$0.768557\pi$
$464$	−292.234	−	51.5287i	−0.629814	−	0.111053i
$465$	−4.75426	−	0.501328i	−0.0102242	−	0.00107813i
$466$	133.246	−	111.807i	0.285935	−	0.239928i
$467$	−232.832	+	134.426i	−0.498570	+	0.287849i	−0.728123	−	0.685447i	$-0.759607\pi$
$467$	−232.832	+	134.426i	−0.498570	+	0.287849i	0.229553	+	0.973296i	$0.426274\pi$
$468$	−68.0530	+	168.108i	−0.145412	+	0.359205i
$469$	240.542	−	416.631i	0.512883	−	0.888339i
$470$	0.147981	−	0.0260931i	0.000314854	−	5.55172e-5i
$471$	174.660	+	259.134i	0.370828	+	0.550178i
$472$	600.170	−	218.444i	1.27155	−	0.462805i
$473$	169.433	+	465.512i	0.358209	+	0.984170i
$474$	−35.7630	−	513.947i	−0.0754493	−	1.08428i
$475$	−54.3970	−	308.501i	−0.114520	−	0.649476i
$476$	−207.862	−	120.009i	−0.436685	−	0.252120i
$477$	429.379	+	15.2867i	0.900166	+	0.0320477i
$478$	−26.9771	−	46.7257i	−0.0564375	−	0.0977526i
$479$	61.2759	+	73.0257i	0.127925	+	0.152455i	0.826205	−	0.563370i	$-0.190495\pi$
$479$	61.2759	+	73.0257i	0.127925	+	0.152455i	−0.698280	+	0.715825i	$0.746051\pi$
$480$	−3.37031	+	1.49919i	−0.00702149	+	0.00312331i
$481$	30.5593	−	173.311i	0.0635330	−	0.360313i
$482$	252.561	−	300.990i	0.523985	−	0.624461i
$483$	189.562	+	196.431i	0.392468	+	0.406689i
$484$	45.1817	+	16.4448i	0.0933506	+	0.0339768i
$485$			0.0194743i			4.01533e-5i
$486$	126.854	+	350.381i	0.261016	+	0.720948i
$487$	−210.939			−0.433139			−0.216569	−	0.976267i	$-0.569487\pi$
$487$	−210.939			−0.433139			−0.216569	+	0.976267i	$0.569487\pi$
$488$	17.5745	−	48.2855i	0.0360133	−	0.0989456i
$489$	−272.564	+	263.033i	−0.557390	+	0.537899i
$490$	−2.85335	−	2.39424i	−0.00582316	−	0.00488621i
$491$	−588.397	−	103.750i	−1.19837	−	0.211304i	−0.461373	−	0.887206i	$-0.652643\pi$
$491$	−588.397	−	103.750i	−1.19837	−	0.211304i	−0.736992	+	0.675902i	$0.763754\pi$
$492$	−138.609	−	311.607i	−0.281726	−	0.633347i
$493$	−501.945	+	421.182i	−1.01814	+	0.854325i
$494$	203.447	−	117.460i	0.411836	−	0.237774i
$495$	−0.197824	+	5.55656i	−0.000399645	+	0.0112254i
$496$	−105.718	+	183.108i	−0.213141	+	0.369170i
$497$	−96.5773	+	17.0292i	−0.194321	+	0.0342640i
$498$	89.3306	−	6.21607i	0.179379	−	0.0124821i
$499$	−865.738	+	315.103i	−1.73495	+	0.631469i	−0.998963	−	0.0455319i	$-0.985502\pi$
$499$	−865.738	+	315.103i	−1.73495	+	0.631469i	−0.735983	+	0.677000i	$0.763280\pi$
$500$	1.42107	+	3.90437i	0.00284215	+	0.00780874i
$501$	−608.451	+	410.105i	−1.21447	+	0.818572i
$502$	104.307	+	591.552i	0.207782	+	1.17839i
$503$	797.759	+	460.587i	1.58600	+	0.915679i	0.993956	+	0.109775i	$0.0350131\pi$
$503$	797.759	+	460.587i	1.58600	+	0.915679i	0.592046	+	0.805904i	$0.298320\pi$
$504$	712.337	+	288.367i	1.41337	+	0.572156i
$505$	−1.20267	−	2.08308i	−0.00238152	−	0.00412492i
$506$	111.496	+	132.876i	0.220348	+	0.262600i
$507$	6.15399	−	58.3604i	0.0121381	−	0.115109i
$508$	−29.9275	+	169.727i	−0.0589125	+	0.334109i
$509$	266.365	−	317.442i	0.523311	−	0.623658i	−0.438049	−	0.898951i	$-0.644331\pi$
$509$	266.365	−	317.442i	0.523311	−	0.623658i	0.961360	+	0.275293i	$0.0887750\pi$
$510$	0.945349	−	3.29260i	0.00185362	−	0.00645607i
$511$	−819.767	−	298.371i	−1.60424	−	0.583896i
$512$			394.899i			0.771287i
$513$	−104.886	+	321.688i	−0.204456	+	0.627072i
$514$	438.048			0.852234
$515$	0.316069	−	0.868393i	0.000613726	−	0.00168620i
$516$	−48.2978	−	193.993i	−0.0936003	−	0.375955i
$517$	18.2460	+	15.3102i	0.0352921	+	0.0296136i
$518$	−214.320	−	37.7905i	−0.413746	−	0.0729545i
$519$	−162.205	+	223.096i	−0.312534	+	0.429858i
$520$	−4.08924	+	3.43128i	−0.00786391	+	0.00659861i
$521$	700.211	−	404.267i	1.34397	−	0.775944i	0.356586	−	0.934262i	$-0.383941\pi$
$521$	700.211	−	404.267i	1.34397	−	0.775944i	0.987388	+	0.158318i	$0.0506073\pi$
$522$	409.992	−	454.720i	0.785426	−	0.871112i
$523$	−75.3714	+	130.547i	−0.144114	+	0.249612i	−0.929042	−	0.369975i	$-0.879366\pi$
$523$	−75.3714	+	130.547i	−0.144114	+	0.249612i	0.784928	+	0.619587i	$0.212700\pi$
$524$	−327.439	+	57.7363i	−0.624883	+	0.110184i
$525$	324.303	−	664.346i	0.617720	−	1.26542i
$526$	−651.783	+	237.230i	−1.23913	+	0.451007i
$527$	159.681	+	438.720i	0.303000	+	0.832485i
$528$	220.985	+	107.875i	0.418532	+	0.204308i
$529$	77.0649	+	437.057i	0.145680	+	0.826194i
$530$	3.19620	+	1.84533i	0.00603057	+	0.00348175i
$531$	−138.417	+	649.031i	−0.260673	+	1.22228i
$532$	101.821	+	176.358i	0.191392	+	0.331501i
$533$	−541.903	−	645.815i	−1.01670	−	1.21166i
$534$	145.838	+	106.033i	0.273105	+	0.198565i
$535$	−0.603031	+	3.41996i	−0.00112716	+	0.00639245i
$536$	−271.710	+	323.812i	−0.506922	+	0.604126i
$537$	184.348	−	45.8966i	0.343293	−	0.0854686i
$538$	−400.046	−	145.605i	−0.743579	−	0.270641i
$539$		−	590.418i		−	1.09540i
$540$	0.314541	−	2.22163i	0.000582484	−	0.00411412i
$541$	−764.505			−1.41313			−0.706567	−	0.707646i	$-0.749757\pi$
$541$	−764.505			−1.41313			−0.706567	+	0.707646i	$0.749757\pi$
$542$	−162.753	+	447.160i	−0.300282	+	0.825019i
$543$	446.918	+	128.316i	0.823053	+	0.236310i
$544$	275.960	+	231.558i	0.507279	+	0.425657i
$545$	−0.475325	−	0.0838127i	−0.000872157	−	0.000153785i
$546$	551.342	+	58.1380i	1.00978	+	0.106480i
$547$	222.538	−	186.732i	0.406834	−	0.341374i	−0.416294	−	0.909230i	$-0.636671\pi$
$547$	222.538	−	186.732i	0.406834	−	0.341374i	0.823128	+	0.567856i	$0.192227\pi$
$548$	276.808	−	159.815i	0.505123	−	0.291633i
$549$	32.8420	+	42.0949i	0.0598215	+	0.0766755i
$550$	234.874	−	406.814i	0.427044	−	0.739661i
$551$	547.488	−	96.5370i	0.993627	−	0.175203i
$552$	−134.058	−	198.895i	−0.242859	−	0.360318i
$553$	1037.39	−	377.578i	1.87593	−	0.682781i
$554$	−180.493	−	495.900i	−0.325800	−	0.895127i
$555$	0.151140	+	2.17202i	0.000272325	+	0.00391356i
$556$	8.22484	+	46.6454i	0.0147929	+	0.0838946i
$557$	−490.922	−	283.434i	−0.881368	−	0.508858i	−0.0102587	−	0.999947i	$-0.503266\pi$
$557$	−490.922	−	283.434i	−0.881368	−	0.508858i	−0.871109	+	0.491089i	$0.836599\pi$
$558$	−204.545	−	385.326i	−0.366568	−	0.690548i
$559$	−247.092	−	427.975i	−0.442024	−	0.765609i
$560$	2.13684	+	2.54658i	0.00381578	+	0.00454747i
$561$	496.128	−	220.688i	0.884364	−	0.393384i
$562$	117.264	−	665.036i	0.208654	−	1.18334i
$563$	647.051	−	771.125i	1.14929	−	1.36967i	0.231390	−	0.972861i	$-0.425673\pi$
$563$	647.051	−	771.125i	1.14929	−	1.36967i	0.917901	−	0.396810i	$-0.129883\pi$
$564$	−6.67471	−	6.91657i	−0.0118346	−	0.0122634i
$565$	−0.0239319	−	0.00871049i	−4.23573e−5	−	1.54168e-5i
$566$		−	22.8846i		−	0.0404321i
$567$	−646.637	+	468.467i	−1.14045	+	0.826220i
$568$	86.1670			0.151703
$569$	47.4246	−	130.298i	0.0833472	−	0.228995i	−0.891017	−	0.453969i	$-0.850008\pi$
$569$	47.4246	−	130.298i	0.0833472	−	0.228995i	0.974365	+	0.224974i	$0.0722299\pi$
$570$	−2.09140	+	2.01827i	−0.00366912	+	0.00354082i
$571$	−401.032	−	336.506i	−0.702333	−	0.589327i	0.220103	−	0.975477i	$-0.429361\pi$
$571$	−401.032	−	336.506i	−0.702333	−	0.589327i	−0.922436	+	0.386149i	$0.873805\pi$
$572$	−243.186	−	42.8803i	−0.425151	−	0.0749656i
$573$	69.8727	+	157.080i	0.121942	+	0.274137i
$574$	−798.631	+	670.131i	−1.39134	+	1.16748i
$575$	−199.825	+	115.369i	−0.347521	+	0.200641i
$576$	−489.467	−	306.316i	−0.849770	−	0.531799i
$577$	−477.478	+	827.016i	−0.827518	+	1.43330i	0.0724610	+	0.997371i	$0.476915\pi$
$577$	−477.478	+	827.016i	−0.827518	+	1.43330i	−0.899979	+	0.435933i	$0.856419\pi$
$578$	106.981	−	18.8637i	0.185089	−	0.0326361i
$579$	27.4962	−	1.91333i	0.0474892	−	0.00330454i
$580$	−3.46431	+	1.26091i	−0.00597296	+	0.00217398i
$581$	65.6279	+	180.311i	0.112957	+	0.310346i
$582$	−1.47363	+	0.993247i	−0.00253201	+	0.00170661i
$583$	101.586	+	576.121i	0.174247	+	0.988201i
$584$	663.824	+	383.259i	1.13668	+	0.656265i
$585$	−0.768195	−	5.49311i	−0.00131315	−	0.00938993i
$586$	−124.231	−	215.174i	−0.211998	−	0.367192i
$587$	−480.945	−	573.168i	−0.819327	−	0.976435i	0.180648	−	0.983548i	$-0.442180\pi$
$587$	−480.945	−	573.168i	−0.819327	−	0.976435i	−0.999975	+	0.00711237i	$0.997736\pi$
$588$	−24.9860	+	236.951i	−0.0424932	+	0.402977i
$589$	68.7848	−	390.098i	0.116782	−	0.662306i
$590$	−3.66420	+	4.36682i	−0.00621050	+	0.00740139i
$591$	−68.6742	+	239.188i	−0.116200	+	0.404718i
$592$	90.4883	+	32.9351i	0.152852	+	0.0556335i
$593$		−	164.211i		−	0.276916i	−0.990368	−	0.138458i	$-0.955785\pi$
$593$		−	164.211i		−	0.276916i	0.990368	−	0.138458i	$-0.0442145\pi$
$594$	−430.556	+	268.431i	−0.724842	+	0.451904i
$595$	7.34053			0.0123370
$596$	−140.289	+	385.442i	−0.235385	+	0.646715i
$597$	−26.5425	−	106.610i	−0.0444597	−	0.178577i
$598$	−132.553	−	111.225i	−0.221660	−	0.185995i
$599$	152.697	+	26.9245i	0.254919	+	0.0449491i	0.299647	−	0.954050i	$-0.403131\pi$
$599$	152.697	+	26.9245i	0.254919	+	0.0449491i	−0.0447281	+	0.998999i	$0.514242\pi$
$600$	−381.985	+	525.381i	−0.636641	+	0.875635i
$601$	568.060	−	476.659i	0.945191	−	0.793110i	−0.0332899	−	0.999446i	$-0.510598\pi$
$601$	568.060	−	476.659i	0.945191	−	0.793110i	0.978481	+	0.206336i	$0.0661540\pi$
$602$	−529.245	+	305.560i	−0.879144	+	0.507574i
$603$	−135.440	−	417.808i	−0.224610	−	0.692882i
$604$	120.506	−	208.722i	0.199512	−	0.345566i
$605$	−1.44814	+	0.255346i	−0.00239362	+	0.000422060i
$606$	96.2881	−	197.249i	0.158891	−	0.325494i
$607$	781.335	−	284.383i	1.28721	−	0.468505i	0.394398	−	0.918940i	$-0.370953\pi$
$607$	781.335	−	284.383i	1.28721	−	0.468505i	0.892810	+	0.450434i	$0.148731\pi$
$608$	−104.536	−	287.209i	−0.171934	−	0.472384i
$609$	1179.00	+	575.532i	1.93596	+	0.945045i
$610$	0.0796386	+	0.451653i	0.000130555	+	0.000740415i
$611$	−20.5773	−	11.8803i	−0.0336780	−	0.0194440i
$612$	−208.449	+	67.5725i	−0.340603	+	0.110413i
$613$	−197.308	−	341.747i	−0.321873	−	0.557500i	0.659002	−	0.752141i	$-0.270979\pi$
$613$	−197.308	−	341.747i	−0.321873	−	0.557500i	−0.980874	+	0.194642i	$0.937646\pi$
$614$	137.062	+	163.344i	0.223228	+	0.266032i
$615$	8.43614	+	6.13360i	0.0137173	+	0.00997333i
$616$	−181.700	+	1030.47i	−0.294968	+	1.67285i
$617$	4.31265	−	5.13962i	0.00698971	−	0.00833001i	−0.762538	−	0.646943i	$-0.776047\pi$
$617$	4.31265	−	5.13962i	0.00698971	−	0.00833001i	0.769528	+	0.638613i	$0.220492\pi$
$618$	81.8319	−	20.3734i	0.132414	−	0.0329667i
$619$	338.641	+	123.255i	0.547078	+	0.199120i	0.600748	−	0.799439i	$-0.294870\pi$
$619$	338.641	+	123.255i	0.547078	+	0.199120i	−0.0536699	+	0.998559i	$0.517092\pi$
$620$			2.62682i			0.00423681i
$621$	249.079	−	8.44355i	0.401093	−	0.0135967i
$622$	276.766			0.444961
$623$	−132.148	+	363.074i	−0.212116	+	0.582783i
$624$	−235.785	−	67.6971i	−0.377861	−	0.108489i
$625$	478.632	+	401.620i	0.765811	+	0.642592i
$626$	−875.090	−	154.302i	−1.39791	−	0.246489i
$627$	−458.161	−	48.3122i	−0.730719	−	0.0770530i
$628$	131.538	−	110.373i	0.209455	−	0.175754i
$629$	184.145	−	106.316i	0.292759	−	0.169025i
$630$	−6.79291	+	0.949969i	−0.0107824	+	0.00150789i
$631$	394.087	−	682.578i	0.624543	−	1.08174i	−0.364086	−	0.931365i	$-0.618619\pi$
$631$	394.087	−	682.578i	0.624543	−	1.08174i	0.988629	−	0.150375i	$-0.0480480\pi$
$632$	−955.265	+	168.439i	−1.51150	+	0.266517i
$633$	−517.812	−	768.252i	−0.818029	−	1.21367i
$634$	728.578	−	265.181i	1.14918	−	0.418266i
$635$	−1.80275	−	4.95301i	−0.00283897	−	0.00780001i
$636$	−16.3881	−	235.512i	−0.0257675	−	0.370302i
$637$	102.276	+	580.034i	0.160558	+	0.910572i
$638$	721.962	+	416.825i	1.13160	+	0.653330i
$639$	−47.4962	+	75.8949i	−0.0743290	+	0.118771i
$640$	−0.0208246	−	0.0360693i	−3.25385e−5	−	5.63583e-5i
$641$	750.028	+	893.849i	1.17009	+	1.39446i	0.902369	+	0.430964i	$0.141826\pi$
$641$	750.028	+	893.849i	1.17009	+	1.39446i	0.267722	+	0.963496i	$0.413729\pi$
$642$	−289.546	+	128.796i	−0.451006	+	0.200617i
$643$	−50.6737	+	287.385i	−0.0788083	+	0.446944i	0.919713	+	0.392590i	$0.128421\pi$
$643$	−50.6737	+	287.385i	−0.0788083	+	0.446944i	−0.998522	+	0.0543538i	$0.982690\pi$
$644$	96.4155	−	114.904i	0.149714	−	0.178422i
$645$	4.24566	+	4.39951i	0.00658243	+	0.00682094i
$646$	266.725	+	97.0798i	0.412886	+	0.150278i
$647$			547.391i			0.846045i	0.906119	+	0.423023i	$0.139031\pi$
$647$			547.391i			0.846045i	−0.906119	+	0.423023i	$0.860969\pi$
$648$	631.015	−	306.705i	0.973789	−	0.473310i
$649$	−903.588			−1.39228
$650$	−160.273	+	440.345i	−0.246573	+	0.677454i
$651$	672.668	−	649.146i	1.03328	−	0.997152i
$652$	159.438	+	133.784i	0.244537	+	0.205191i
$653$	430.668	+	75.9385i	0.659523	+	0.116292i	0.493385	−	0.869811i	$-0.335759\pi$
$653$	430.668	+	75.9385i	0.659523	+	0.116292i	0.166138	+	0.986103i	$0.446870\pi$
$654$	−17.9008	−	40.2427i	−0.0273713	−	0.0615332i
$655$	7.78960	−	6.53625i	0.0118925	−	0.00997901i
$656$	399.501	−	230.652i	0.608995	−	0.351603i
$657$	−703.477	+	373.432i	−1.07074	+	0.568389i
$658$	−14.6915	+	25.4464i	−0.0223274	+	0.0386723i
$659$	−7.11079	+	1.25382i	−0.0107903	+	0.00190262i	−0.179041	−	0.983842i	$-0.557299\pi$
$659$	−7.11079	+	1.25382i	−0.0107903	+	0.00190262i	0.168250	+	0.985744i	$0.446188\pi$
$660$	3.04774	−	0.212077i	0.00461779	−	0.000321329i
$661$	−830.669	+	302.339i	−1.25669	+	0.457396i	−0.882656	−	0.470020i	$-0.844247\pi$
$661$	−830.669	+	302.339i	−1.25669	+	0.457396i	−0.374030	+	0.927416i	$0.622024\pi$
$662$	−119.002	−	326.956i	−0.179761	−	0.493891i
$663$	−449.174	+	302.749i	−0.677487	+	0.456636i
$664$	−29.2769	−	166.037i	−0.0440917	−	0.250056i
$665$	−5.39360	−	3.11400i	−0.00811068	−	0.00468270i
$666$	−156.649	+	122.216i	−0.235209	+	0.183508i
$667$	−204.742	−	354.624i	−0.306960	−	0.531670i
$668$	259.159	+	308.853i	0.387962	+	0.462355i
$669$	−97.4602	+	924.248i	−0.145680	+	1.38154i
$670$	0.655137	−	3.71546i	0.000977816	−	0.00554547i
$671$	−46.7283	+	55.6886i	−0.0696398	+	0.0829935i
$672$	199.052	−	693.287i	0.296209	−	1.03168i
$673$	−445.775	−	162.249i	−0.662370	−	0.241083i	−0.0111109	−	0.999938i	$-0.503537\pi$
$673$	−445.775	−	162.249i	−0.662370	−	0.241083i	−0.651259	+	0.758855i	$0.725759\pi$
$674$			147.163i			0.218343i
$675$	−252.195	−	626.043i	−0.373622	−	0.927471i
$676$	−32.2452			−0.0477000
$677$	−109.514	+	300.887i	−0.161763	+	0.444441i	−0.993921	−	0.110098i	$-0.964883\pi$
$677$	−109.514	+	300.887i	−0.161763	+	0.444441i	0.832157	+	0.554540i	$0.187106\pi$
$678$	−0.561467	−	2.25519i	−0.000828123	−	0.00332624i
$679$	−2.91714	−	2.44777i	−0.00429622	−	0.00360496i
$680$	−6.35179	−	1.11999i	−0.00934087	−	0.00164705i
$681$	294.395	−	404.910i	0.432298	−	0.594581i
$682$	455.026	−	381.812i	0.667194	−	0.559842i
$683$	−812.276	+	468.967i	−1.18928	+	0.686629i	−0.958142	−	0.286293i	$-0.907577\pi$
$683$	−812.276	+	468.967i	−1.18928	+	0.686629i	−0.231134	+	0.972922i	$0.574244\pi$
$684$	181.828	+	38.7780i	0.265830	+	0.0566930i
$685$	−4.88765	+	8.46565i	−0.00713525	+	0.0123586i
$686$	−12.2012	+	2.15141i	−0.0177860	+	0.00313616i
$687$	−305.940	+	626.729i	−0.445328	+	0.912269i
$688$	254.101	−	92.4853i	0.369333	−	0.134426i
$689$	−199.598	−	548.392i	−0.289693	−	0.795924i
$690$	1.92381	+	0.939114i	0.00278813	+	0.00136104i
$691$	−10.2172	−	57.9445i	−0.0147861	−	0.0838560i	0.976522	−	0.215419i	$-0.0691116\pi$
$691$	−10.2172	−	57.9445i	−0.0147861	−	0.0838560i	−0.991308	+	0.131563i	$0.958001\pi$
$692$	131.256	+	75.7806i	0.189676	+	0.109510i
$693$	−807.473	−	728.048i	−1.16519	−	1.05057i
$694$	198.428	+	343.688i	0.285920	+	0.495228i
$695$	−0.931124	−	1.10967i	−0.00133975	−	0.00159665i
$696$	−932.380	−	677.898i	−1.33963	−	0.973992i
$697$	176.881	−	1003.14i	0.253774	−	1.43923i
$698$	270.956	−	322.912i	0.388188	−	0.462625i
$699$	330.204	−	82.2098i	0.472395	−	0.117611i
$700$	−381.714	−	138.933i	−0.545306	−	0.198475i
$701$			591.380i			0.843623i	0.906683	+	0.421812i	$0.138606\pi$
$701$			591.380i			0.843623i	−0.906683	+	0.421812i	$0.861394\pi$
$702$	376.485	−	338.293i	0.536303	−	0.481899i
$703$	−180.406			−0.256623
$704$	268.897	−	738.789i	0.381956	−	1.04942i
$705$	0.282550	+	0.0811240i	0.000400781	+	0.000115070i
$706$	310.908	+	260.883i	0.440380	+	0.369522i
$707$	463.199	+	81.6744i	0.655161	+	0.115523i
$708$	362.634	+	38.2391i	0.512195	+	0.0540100i
$709$	337.105	−	282.865i	0.475465	−	0.398963i	−0.373318	−	0.927703i	$-0.621780\pi$
$709$	337.105	−	282.865i	0.475465	−	0.398963i	0.848783	+	0.528741i	$0.177336\pi$
$710$	−0.666031	+	0.384533i	−0.000938073	+	0.000541596i
$711$	378.194	−	934.232i	0.531918	−	1.31397i
$712$	169.745	−	294.007i	0.238406	−	0.412931i
$713$	−287.334	+	50.6648i	−0.402993	+	0.0710586i
$714$	374.387	+	555.460i	0.524352	+	0.777955i
$715$	7.09669	−	2.58299i	0.00992545	−	0.00361257i
$716$	−35.7023	−	98.0913i	−0.0498635	−	0.136999i
$717$	−7.32712	−	105.297i	−0.0102191	−	0.146858i
$718$	56.4133	+	319.936i	0.0785701	+	0.445593i
$719$	−499.498	−	288.385i	−0.694712	−	0.401092i	0.110663	−	0.993858i	$-0.464703\pi$
$719$	−499.498	−	288.385i	−0.694712	−	0.401092i	−0.805375	+	0.592766i	$0.798036\pi$
$720$	3.03306	+	0.107983i	0.00421259	+	0.000149976i
$721$	90.3525	+	156.495i	0.125315	+	0.217053i
$722$	201.042	+	239.592i	0.278451	+	0.331845i
$723$	702.321	−	312.407i	0.971398	−	0.432098i
$724$	44.3654	−	251.609i	0.0612782	−	0.347526i
$725$	−712.817	+	849.502i	−0.983195	+	1.17173i
$726$	−93.1814	−	96.5578i	−0.128349	−	0.133000i
$727$	562.999	+	204.915i	0.774414	+	0.281863i	0.698841	−	0.715277i	$-0.253699\pi$
$727$	562.999	+	204.915i	0.774414	+	0.281863i	0.0755723	+	0.997140i	$0.475922\pi$
$728$		−	1043.83i		−	1.43383i
$729$	−77.6808	+	724.849i	−0.106558	+	0.994306i
$730$	−6.84140			−0.00937179
$731$	204.219	−	561.087i	0.279369	−	0.767561i
$732$	21.1100	−	20.3719i	0.0288388	−	0.0278304i
$733$	−424.519	−	356.213i	−0.579152	−	0.485966i	0.305516	−	0.952187i	$-0.401171\pi$
$733$	−424.519	−	356.213i	−0.579152	−	0.485966i	−0.884669	+	0.466220i	$0.845615\pi$
$734$	974.352	+	171.805i	1.32746	+	0.234066i
$735$	−2.96158	−	6.65791i	−0.00402936	−	0.00905838i
$736$	−172.457	+	144.708i	−0.234316	+	0.196615i
$737$	517.906	−	299.013i	0.702723	−	0.405717i
$738$	−33.8644	+	951.196i	−0.0458867	+	1.28888i
$739$	−708.201	+	1226.64i	−0.958324	+	1.65987i	−0.231752	+	0.972775i	$0.574446\pi$
$739$	−708.201	+	1226.64i	−0.958324	+	1.65987i	−0.726572	+	0.687090i	$0.758888\pi$
$740$	1.17818	−	0.207745i	0.00159213	−	0.000280736i
$741$	458.472	−	31.9028i	0.618721	−	0.0430537i
$742$	−678.155	+	246.828i	−0.913955	+	0.332653i
$743$	103.170	+	283.457i	0.138856	+	0.381504i	0.989556	−	0.144147i	$-0.0460440\pi$
$743$	103.170	+	283.457i	0.138856	+	0.381504i	−0.850700	+	0.525651i	$0.823822\pi$
$744$	−681.107	+	459.075i	−0.915466	+	0.617037i
$745$	−2.17834	−	12.3540i	−0.00292395	−	0.0165825i
$746$	−933.862	−	539.166i	−1.25183	−	0.722742i
$747$	162.381	+	65.7349i	0.217378	+	0.0879986i
$748$	−149.181	−	258.389i	−0.199440	−	0.345441i
$749$	−436.492	−	520.191i	−0.582767	−	0.694514i
$750$	1.21601	−	11.5318i	0.00162135	−	0.0153758i
$751$	−86.3699	+	489.828i	−0.115007	+	0.652235i	0.871740	+	0.489968i	$0.162992\pi$
$751$	−86.3699	+	489.828i	−0.115007	+	0.652235i	−0.986747	+	0.162267i	$0.948120\pi$
$752$	8.35713	−	9.95964i	0.0111132	−	0.0132442i
$753$	−324.292	+	1129.49i	−0.430666	+	1.49998i
$754$	−781.469	−	284.432i	−1.03643	−	0.377230i
$755$			7.37088i			0.00976276i
$756$	293.250	+	326.357i	0.387897	+	0.431689i
$757$	1028.94			1.35924			0.679620	−	0.733565i	$-0.262145\pi$
$757$	1028.94			1.35924			0.679620	+	0.733565i	$0.262145\pi$
$758$	184.721	−	507.517i	0.243696	−	0.669548i
$759$	81.9814	+	329.286i	0.108012	+	0.433842i
$760$	4.19198	+	3.51749i	0.00551577	+	0.00462828i
$761$	−37.0662	−	6.53577i	−0.0487073	−	0.00858840i	0.149241	−	0.988801i	$-0.452317\pi$
$761$	−37.0662	−	6.53577i	−0.0487073	−	0.00858840i	−0.197949	+	0.980212i	$0.563428\pi$
$762$	282.850	−	389.032i	0.371195	−	0.510540i
$763$	72.2991	−	60.6662i	0.0947564	−	0.0795101i
$764$	81.8093	−	47.2326i	0.107080	−	0.0618228i
$765$	4.48765	−	4.97723i	0.00586621	−	0.00650618i
$766$	207.216	−	358.909i	0.270517	−	0.468550i
$767$	887.696	−	156.525i	1.15736	−	0.204074i
$768$	−336.064	+	688.439i	−0.437584	+	0.896405i
$769$	−1065.80	+	387.921i	−1.38596	+	0.504449i	−0.923980	−	0.382441i	$-0.875084\pi$
$769$	−1065.80	+	387.921i	−1.38596	+	0.504449i	−0.461981	+	0.886890i	$0.652861\pi$
$770$	−3.19418	−	8.77595i	−0.00414829	−	0.0113973i
$771$	770.107	+	375.931i	0.998842	+	0.487588i
$772$	−2.62990	−	14.9149i	−0.00340660	−	0.0193198i
$773$	−441.262	−	254.763i	−0.570843	−	0.329577i	0.186643	−	0.982428i	$-0.440239\pi$
$773$	−441.262	−	254.763i	−0.570843	−	0.329577i	−0.757486	+	0.652851i	$0.773573\pi$
$774$	−116.371	+	545.658i	−0.150350	+	0.704984i
$775$	395.075	+	684.289i	0.509774	+	0.882954i
$776$	2.15074	+	2.56315i	0.00277157	+	0.00330303i
$777$	−344.353	−	250.366i	−0.443182	−	0.322221i
$778$	−58.6021	+	332.349i	−0.0753240	+	0.427184i
$779$	−555.519	+	662.042i	−0.713118	+	0.849861i
$780$	−2.95740	+	0.736295i	−0.00379154	+	0.000943968i
$781$	−114.554	−	41.6941i	−0.146676	−	0.0533856i
$782$		−	209.070i		−	0.267352i
$783$	1111.02	−	447.564i	1.41893	−	0.571601i
$784$	−322.281			−0.411073
$785$	−1.79610	+	4.93474i	−0.00228803	+	0.00628630i
$786$	891.891	+	256.074i	1.13472	+	0.325794i
$787$	203.516	+	170.770i	0.258597	+	0.216988i	0.762864	−	0.646560i	$-0.223793\pi$
$787$	203.516	+	170.770i	0.258597	+	0.216988i	−0.504267	+	0.863548i	$0.668237\pi$
$788$	134.660	+	23.7442i	0.170888	+	0.0301322i
$789$	−1349.45	−	142.297i	−1.71033	−	0.180351i
$790$	6.63208	−	5.56497i	0.00839503	−	0.00704427i
$791$	4.31282	−	2.49001i	0.00545236	−	0.00314792i
$792$	587.627	+	753.184i	0.741954	+	0.950990i
$793$	36.2598	−	62.8038i	0.0457248	−	0.0791977i
$794$	−175.234	+	30.8985i	−0.220698	+	0.0389150i
$795$	4.03541	+	5.98713i	0.00507598	+	0.00753098i
$796$	−56.7271	+	20.6470i	−0.0712652	+	0.0259384i
$797$	−153.358	−	421.349i	−0.192420	−	0.528668i	0.805538	−	0.592544i	$-0.201876\pi$
$797$	−153.358	−	421.349i	−0.192420	−	0.528668i	−0.997958	+	0.0638752i	$0.979654\pi$
$798$	−39.4518	−	566.958i	−0.0494383	−	0.710474i
$799$	−4.98521	−	28.2725i	−0.00623932	−	0.0353849i
$800$	527.995	+	304.838i	0.659994	+	0.381048i
$801$	165.392	+	311.569i	0.206482	+	0.388975i
$802$	−145.823	−	252.573i	−0.181825	−	0.314929i
$803$	−697.063	−	830.727i	−0.868073	−	1.03453i
$804$	−220.504	+	98.0848i	−0.274259	+	0.121996i
$805$	−0.796585	+	4.51766i	−0.000989547	+	0.00561200i
$806$	−380.884	+	453.920i	−0.472561	+	0.563176i
$807$	−578.340	−	599.296i	−0.716654	−	0.742623i
$808$	−388.346	−	141.346i	−0.480627	−	0.174934i
$809$			357.505i			0.441910i	0.975284	+	0.220955i	$0.0709174\pi$
$809$			357.505i			0.441910i	−0.975284	+	0.220955i	$0.929083\pi$
$810$	−3.50874	+	5.18669i	−0.00433178	+	0.00640332i
$811$	1269.44			1.56528			0.782638	−	0.622477i	$-0.213874\pi$
$811$	1269.44			1.56528			0.782638	+	0.622477i	$0.213874\pi$
$812$	246.560	−	677.418i	0.303645	−	0.834259i
$813$	−669.878	+	646.453i	−0.823958	+	0.795145i
$814$	−207.236	−	173.892i	−0.254590	−	0.213626i
$815$	−6.26861	−	1.10533i	−0.00769155	−	0.00135623i
$816$	−120.463	−	270.813i	−0.147627	−	0.331879i
$817$	−388.078	+	325.636i	−0.475004	+	0.398576i
$818$	31.5920	−	18.2396i	0.0386210	−	0.0222978i
$819$	919.389	+	575.368i	1.12257	+	0.702525i
$820$	2.86556	−	4.96330i	0.00349459	−	0.00605280i
$821$	1142.82	−	201.510i	1.39199	−	0.245445i	0.573140	−	0.819458i	$-0.305725\pi$
$821$	1142.82	−	201.510i	1.39199	−	0.245445i	0.818846	+	0.574013i	$0.194614\pi$
$822$	−889.882	+	61.9225i	−1.08258	+	0.0753314i
$823$	776.798	−	282.731i	0.943862	−	0.343538i	0.176172	−	0.984359i	$-0.443629\pi$
$823$	776.798	−	282.731i	0.943862	−	0.343538i	0.767690	+	0.640822i	$0.221406\pi$
$824$	−54.3049	−	149.202i	−0.0659040	−	0.181070i
$825$	762.044	−	513.628i	0.923689	−	0.622579i
$826$	−193.563	−	1097.75i	−0.234337	−	1.32899i
$827$	74.5639	+	43.0495i	0.0901619	+	0.0520550i	0.544403	−	0.838824i	$-0.316756\pi$
$827$	74.5639	+	43.0495i	0.0901619	+	0.0520550i	−0.454241	+	0.890879i	$0.650090\pi$
$828$	−18.9662	−	135.621i	−0.0229060	−	0.163793i
$829$	316.737	+	548.604i	0.382071	+	0.661766i	0.991358	−	0.131184i	$-0.0418778\pi$
$829$	316.737	+	548.604i	0.382071	+	0.661766i	−0.609287	+	0.792949i	$0.708544\pi$
$830$	0.967264	+	1.15274i	0.00116538	+	0.00138884i
$831$	108.265	−	1026.71i	0.130283	−	1.23551i
$832$	−136.191	+	772.376i	−0.163691	+	0.928336i
$833$	−457.432	+	545.146i	−0.549138	+	0.654437i
$834$	36.4791	−	127.055i	0.0437400	−	0.152344i
$835$	−11.5869	−	4.21728i	−0.0138765	−	0.00505063i
$836$			253.143i			0.302802i
$837$	−28.9145	−	852.958i	−0.0345454	−	1.01907i
$838$	−525.974			−0.627654
$839$	−251.928	+	692.167i	−0.300272	+	0.824990i	0.694180	+	0.719801i	$0.255767\pi$
$839$	−251.928	+	692.167i	−0.300272	+	0.824990i	−0.994452	+	0.105189i	$0.966455\pi$
$840$	3.11996	+	12.5317i	0.00371424	+	0.0149186i
$841$	−863.345	−	724.433i	−1.02657	−	0.861394i
$842$	746.056	+	131.550i	0.886052	+	0.156235i
$843$	776.885	−	1068.53i	0.921572	−	1.26753i
$844$	−389.969	+	327.222i	−0.462048	+	0.387704i
$845$	0.854040	−	0.493080i	0.00101070	−	0.000583527i
$846$	8.27218	+	25.5182i	0.00977799	+	0.0301634i
$847$	143.770	−	249.017i	0.169741	−	0.293999i
$848$	314.477	−	55.4508i	0.370846	−	0.0653901i
$849$	19.6394	−	40.2320i	0.0231324	−	0.0473876i
$850$	−532.047	+	193.649i	−0.625937	+	0.227823i
$851$	45.4482	+	124.868i	0.0534056	+	0.146731i
$852$	44.2090	+	21.5808i	0.0518885	+	0.0253296i
$853$	−284.876	−	1615.61i	−0.333970	−	1.89404i	−0.437174	−	0.899377i	$-0.644020\pi$
$853$	−284.876	−	1615.61i	−0.333970	−	1.89404i	0.103204	−	0.994660i	$-0.467091\pi$
$854$	−77.6647	−	44.8398i	−0.0909423	−	0.0525056i
$855$	−5.40883	+	1.75337i	−0.00632612	+	0.00205072i
$856$	298.330	+	516.722i	0.348516	+	0.603647i
$857$	−219.660	−	261.780i	−0.256312	−	0.305461i	0.622509	−	0.782613i	$-0.286114\pi$
$857$	−219.660	−	261.780i	−0.256312	−	0.305461i	−0.878821	+	0.477152i	$0.841669\pi$
$858$	557.407	+	405.269i	0.649658	+	0.472342i
$859$	53.2766	−	302.146i	0.0620216	−	0.351742i	−0.937966	−	0.346728i	$-0.887293\pi$
$859$	53.2766	−	302.146i	0.0620216	−	0.351742i	0.999987	−	0.00501434i	$-0.00159612\pi$
$860$	2.15944	−	2.57352i	0.00251098	−	0.00299246i
$861$	−1979.13	+	492.737i	−2.29864	+	0.572285i
$862$	747.989	+	272.246i	0.867737	+	0.315830i
$863$		−	1546.03i		−	1.79146i	−0.444596	−	0.895731i	$-0.646653\pi$
$863$		−	1546.03i		−	1.79146i	0.444596	−	0.895731i	$-0.353347\pi$
$864$	−348.391	−	558.810i	−0.403230	−	0.646771i
$865$	−4.63522			−0.00535864
$866$	−152.256	+	418.320i	−0.175815	+	0.483049i
$867$	204.266	+	58.6476i	0.235601	+	0.0676443i
$868$	−393.481	−	330.170i	−0.453319	−	0.380380i
$869$	1351.47	+	238.300i	1.55520	+	0.274224i
$870$	10.2321	+	1.07896i	0.0117610	+	0.00124018i
$871$	−457.001	+	383.469i	−0.524686	+	0.440263i
$872$	−71.8170	+	41.4636i	−0.0823589	+	0.0475500i
$873$	−3.44310	+	0.481508i	−0.00394399	+	0.000551556i
$874$	−88.6915	+	153.618i	−0.101478	+	0.175764i
$875$	24.4703	−	4.31477i	0.0279660	−	0.00493116i
$876$	244.594	+	362.892i	0.279217	+	0.414261i
$877$	254.149	−	92.5028i	0.289794	−	0.105476i	−0.193033	−	0.981192i	$-0.561832\pi$
$877$	254.149	−	92.5028i	0.289794	−	0.105476i	0.482827	+	0.875716i	$0.339610\pi$
$878$	175.234	+	481.451i	0.199583	+	0.548349i
$879$	−33.7418	−	484.900i	−0.0383865	−	0.551650i
$880$	0.717585	+	4.06963i	0.000815437	+	0.00462458i
$881$	−240.352	−	138.767i	−0.272817	−	0.157511i	0.357350	−	0.933970i	$-0.383680\pi$
$881$	−240.352	−	138.767i	−0.272817	−	0.157511i	−0.630167	+	0.776460i	$0.717014\pi$
$882$	352.757	−	563.675i	0.399951	−	0.639088i
$883$	334.464	+	579.308i	0.378781	+	0.656068i	0.990885	−	0.134709i	$-0.0430101\pi$
$883$	334.464	+	579.308i	0.378781	+	0.656068i	−0.612104	+	0.790777i	$0.709677\pi$
$884$	191.317	+	228.003i	0.216422	+	0.257922i
$885$	−10.1894	+	4.53246i	−0.0115134	+	0.00512142i
$886$	88.5549	−	502.220i	0.0999491	−	0.566840i
$887$	−707.659	+	843.355i	−0.797811	+	0.950795i	−0.999590	−	0.0286367i	$-0.990883\pi$
$887$	−707.659	+	843.355i	−0.797811	+	0.950795i	0.201779	+	0.979431i	$0.435328\pi$
$888$	259.770	+	269.183i	0.292534	+	0.303134i
$889$	968.520	+	352.512i	1.08945	+	0.396527i
$890$			3.03005i			0.00340455i
$891$	−987.302	+	102.412i	−1.10808	+	0.114940i
$892$	510.664			0.572494
$893$	−8.33079	+	22.8887i	−0.00932899	+	0.0256312i
$894$	823.728	−	794.924i	0.921396	−	0.889176i
$895$	2.44557	+	2.05208i	0.00273249	+	0.00229283i
$896$	8.02044	+	1.41422i	0.00895138	+	0.00157837i
$897$	−137.580	−	309.294i	−0.153378	−	0.344809i
$898$	394.935	−	331.390i	0.439794	−	0.369031i
$899$	−1214.39	+	701.129i	−1.35082	+	0.779899i
$900$	−327.565	+	173.884i	−0.363961	+	0.193204i
$901$	352.559	−	610.650i	0.391297	−	0.677747i
$902$	−1276.27	+	225.041i	−1.41494	+	0.249491i
$903$	−1192.66	+	82.9915i	−1.32078	+	0.0919065i
$904$	−4.11182	+	1.49658i	−0.00454847	+	0.00165551i
$905$	2.67244	+	7.34248i	0.00295298	+	0.00811324i
$906$	−557.757	+	375.936i	−0.615626	+	0.414940i
$907$	159.627	+	905.289i	0.175994	+	0.998114i	0.936990	+	0.349357i	$0.113600\pi$
$907$	159.627	+	905.289i	0.175994	+	0.998114i	−0.760995	+	0.648757i	$0.775289\pi$
$908$	−238.224	−	137.538i	−0.262361	−	0.151474i
$909$	338.557	−	264.139i	0.372450	−	0.290582i
$910$	4.65823	+	8.06829i	0.00511893	+	0.00886625i
$911$	109.112	+	130.035i	0.119772	+	0.142739i	0.822599	−	0.568623i	$-0.192524\pi$
$911$	109.112	+	130.035i	0.119772	+	0.142739i	−0.702827	+	0.711361i	$0.748079\pi$
$912$	−26.3714	+	250.088i	−0.0289160	+	0.274220i
$913$	−41.4197	+	234.903i	−0.0453666	+	0.257287i
$914$	−782.768	+	932.867i	−0.856421	+	1.02064i
$915$	−0.247598	+	0.862371i	−0.000270599	+	0.000942482i
$916$	360.100	+	131.066i	0.393123	+	0.143085i
$917$			1988.39i			2.16836i
$918$	605.511	+	85.7292i	0.659598	+	0.0933870i
$919$	120.333			0.130939			0.0654697	−	0.997855i	$-0.479145\pi$
$919$	120.333			0.130939			0.0654697	+	0.997855i	$0.479145\pi$
$920$	1.37858	−	3.78761i	0.00149845	−	0.00411697i
$921$	100.780	+	404.791i	0.109424	+	0.439513i
$922$	335.483	+	281.503i	0.363864	+	0.305318i
$923$	119.762	+	21.1172i	0.129752	+	0.0228789i
$924$	−351.309	+	483.189i	−0.380204	+	0.522932i
$925$	275.672	−	231.316i	0.298023	−	0.250071i
$926$	178.380	−	102.987i	0.192635	−	0.111218i
$927$	161.348	+	34.4104i	0.174054	+	0.0371202i
$928$	−540.988	+	937.019i	−0.582962	+	1.00972i
$929$	989.307	−	174.442i	1.06492	−	0.187773i	0.386379	−	0.922340i	$-0.373726\pi$
$929$	989.307	−	174.442i	1.06492	−	0.187773i	0.678537	+	0.734566i	$0.262614\pi$
$930$	3.21595	−	6.58798i	0.00345801	−	0.00708385i
$931$	567.369	−	206.505i	0.609419	−	0.221810i
$932$	−63.9498	−	175.700i	−0.0686156	−	0.188520i
$933$	486.566	+	237.519i	0.521507	+	0.254576i
$934$	−71.5917	−	406.016i	−0.0766506	−	0.434707i
$935$	7.90237	+	4.56244i	0.00845173	+	0.00487961i
$936$	−707.764	−	638.146i	−0.756158	−	0.681779i
$937$	−374.211	−	648.153i	−0.399372	−	0.691732i	0.594277	−	0.804261i	$-0.297438\pi$
$937$	−374.211	−	648.153i	−0.399372	−	0.691732i	−0.993649	+	0.112528i	$0.964105\pi$
$938$	474.208	+	565.139i	0.505552	+	0.602494i
$939$	−1406.02	−	1022.27i	−1.49736	−	1.08868i
$940$	0.0280487	−	0.159072i	2.98390e−5	−	0.000169226i
$941$	952.151	−	1134.73i	1.01185	−	1.20588i	0.0333896	−	0.999442i	$-0.489370\pi$
$941$	952.151	−	1134.73i	1.01185	−	1.20588i	0.978461	−	0.206434i	$-0.0661858\pi$
$942$	−465.020	+	115.774i	−0.493652	+	0.122903i
$943$	598.179	+	217.719i	0.634336	+	0.230879i
$944$			493.226i			0.522485i
$945$	−12.7575	−	4.15956i	−0.0135000	−	0.00440165i
$946$	−759.671			−0.803035
$947$	160.976	−	442.278i	0.169985	−	0.467030i	−0.825223	−	0.564807i	$-0.808951\pi$
$947$	160.976	−	442.278i	0.169985	−	0.467030i	0.995208	+	0.0977764i	$0.0311730\pi$
$948$	−532.296	−	152.829i	−0.561494	−	0.161213i
$949$	828.707	+	695.368i	0.873242	+	0.732737i
$950$	473.082	+	83.4171i	0.497981	+	0.0878075i
$951$	1508.45	+	159.063i	1.58617	+	0.167259i
$952$	966.136	−	810.684i	1.01485	−	0.851559i
$953$	733.980	−	423.764i	0.770179	−	0.444663i	−0.0627596	−	0.998029i	$-0.519990\pi$
$953$	733.980	−	423.764i	0.770179	−	0.444663i	0.832938	+	0.553366i	$0.186657\pi$
$954$	−247.231	+	610.721i	−0.259152	+	0.640168i
$955$	−1.44452	+	2.50199i	−0.00151259	+	0.00261988i
$956$	−57.1168	+	10.0712i	−0.0597457	+	0.0105348i
$957$	911.522	+	1352.38i	0.952479	+	1.41314i
$958$	−137.369	+	49.9981i	−0.143391	+	0.0521901i
$959$	−653.764	−	1796.20i	−0.681715	−	1.87300i
$960$	−0.673571	−	9.67983i	−0.000701636	−	0.0100832i
$961$	6.62309	+	37.5614i	0.00689187	+	0.0390857i
$962$	233.714	+	134.935i	0.242946	+	0.140265i
$963$	−619.565	−	22.0577i	−0.643370	−	0.0229052i
$964$	−211.181	−	365.777i	−0.219068	−	0.379437i
$965$	0.297727	+	0.354817i	0.000308525	+	0.000367686i
$966$	−382.481	+	170.135i	−0.395943	+	0.176124i
$967$	−17.9690	+	101.907i	−0.0185822	+	0.105385i	−0.992688	−	0.120707i	$-0.961484\pi$
$967$	−17.9690	+	101.907i	−0.0185822	+	0.105385i	0.974106	+	0.226092i	$0.0725950\pi$
$968$	−162.399	+	193.540i	−0.167768	+	0.199938i
$969$	385.600	+	399.572i	0.397936	+	0.412355i
$970$	−0.0280627	−	0.0102140i	−2.89306e−5	−	1.05299e-5i
$971$			171.424i			0.176543i	0.996096	+	0.0882717i	$0.0281344\pi$
$971$			171.424i			0.176543i	−0.996096	+	0.0882717i	$0.971866\pi$
$972$	400.565	+	0.681276i	0.412104	+	0.000700901i
$973$	283.256			0.291116
$974$	110.634	−	303.964i	0.113587	−	0.312078i
$975$	−659.668	+	636.600i	−0.676582	+	0.652923i
$976$	30.3978	+	25.5068i	0.0311453	+	0.0261340i
$977$	−1695.45	−	298.954i	−1.73536	−	0.305991i	−0.785548	−	0.618801i	$-0.787619\pi$
$977$	−1695.45	−	298.954i	−1.73536	−	0.305991i	−0.949816	+	0.312809i	$0.898730\pi$
$978$	−236.077	−	530.722i	−0.241387	−	0.542661i
$979$	−367.928	+	308.728i	−0.375820	+	0.315350i
$980$	−3.46752	+	2.00197i	−0.00353828	+	0.00204283i
$981$	3.06571	−	86.1107i	0.00312508	−	0.0877785i
$982$	458.109	−	793.469i	0.466507	−	0.808013i
$983$	−1292.07	+	227.827i	−1.31442	+	0.231767i	−0.786532	−	0.617550i	$-0.788126\pi$
$983$	−1292.07	+	227.827i	−1.31442	+	0.231767i	−0.527884	+	0.849317i	$0.677014\pi$
$984$	1787.73	−	124.399i	1.81680	−	0.126422i
$985$	−3.92966	+	1.43028i	−0.00398950	+	0.00145206i
$986$	−343.664	−	944.209i	−0.348544	−	0.957616i
$987$	−47.6661	+	32.1276i	−0.0482940	+	0.0325508i
$988$	−43.8509	−	248.691i	−0.0443835	−	0.251711i
$989$	323.154	+	186.573i	0.326748	+	0.188648i
$990$	−7.90329	−	3.19939i	−0.00798312	−	0.00323171i
$991$	−964.265	−	1670.16i	−0.973022	−	1.68532i	−0.686314	−	0.727305i	$-0.740773\pi$
$991$	−964.265	−	1670.16i	−0.973022	−	1.68532i	−0.286707	−	0.958018i	$-0.592561\pi$
$992$	495.546	+	590.569i	0.499543	+	0.595332i
$993$	71.3809	−	676.929i	0.0718841	−	0.681700i
$994$	26.1140	−	148.100i	0.0262717	−	0.148994i
$995$	1.18674	−	1.41430i	0.00119270	−	0.00142141i
$996$	26.5637	−	92.5199i	0.0266704	−	0.0928915i
$997$	−1167.31	−	424.866i	−1.17082	−	0.426144i	−0.317870	−	0.948134i	$-0.602968\pi$
$997$	−1167.31	−	424.866i	−1.17082	−	0.426144i	−0.852952	+	0.521990i	$0.825190\pi$
$998$		−	1412.80i		−	1.41563i
$999$	−380.281	+	80.4257i	−0.380662	+	0.0805062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.3.f.a.23.2	yes	30
3.2	odd	2		81.3.f.a.17.4		30
4.3	odd	2		432.3.bc.a.401.4		30
9.2	odd	6		243.3.f.a.215.2		30
9.4	even	3		243.3.f.c.134.2		30
9.5	odd	6		243.3.f.b.134.4		30
9.7	even	3		243.3.f.d.215.4		30
27.2	odd	18		243.3.f.c.107.2		30
27.7	even	9		81.3.f.a.62.4		30
27.11	odd	18		243.3.f.d.26.4		30
27.13	even	9		729.3.b.a.728.10		30
27.14	odd	18		729.3.b.a.728.21		30
27.16	even	9		243.3.f.a.26.2		30
27.20	odd	18	inner	27.3.f.a.20.2	✓	30
27.25	even	9		243.3.f.b.107.4		30
108.47	even	18		432.3.bc.a.209.4		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.20.2	✓	30	27.20	odd	18	inner
27.3.f.a.23.2	yes	30	1.1	even	1	trivial
81.3.f.a.17.4		30	3.2	odd	2
81.3.f.a.62.4		30	27.7	even	9
243.3.f.a.26.2		30	27.16	even	9
243.3.f.a.215.2		30	9.2	odd	6
243.3.f.b.107.4		30	27.25	even	9
243.3.f.b.134.4		30	9.5	odd	6
243.3.f.c.107.2		30	27.2	odd	18
243.3.f.c.134.2		30	9.4	even	3
243.3.f.d.26.4		30	27.11	odd	18
243.3.f.d.215.4		30	9.7	even	3
432.3.bc.a.209.4		30	108.47	even	18
432.3.bc.a.401.4		30	4.3	odd	2
729.3.b.a.728.10		30	27.13	even	9
729.3.b.a.728.21		30	27.14	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.524483 + 1.44101i) q^{2} +(-2.15873 + 2.08324i) q^{3} +(1.26276 + 1.05958i) q^{4} +(-0.0496479 - 0.00875427i) q^{5} +(-1.86975 - 4.20337i) q^{6} +(7.55168 - 6.33661i) q^{7} +(-7.50132 + 4.33089i) q^{8} +(0.320214 - 8.99430i) q^{9} +(0.0386545 - 0.0669515i) q^{10} +(12.0681 - 2.12794i) q^{11} +(-4.93332 + 0.343285i) q^{12} +(-11.4873 + 4.18103i) q^{13} +(5.17037 + 14.2055i) q^{14} +(0.125414 - 0.0845305i) q^{15} +(-1.16154 - 6.58743i) q^{16} +(-12.7914 - 7.38513i) q^{17} +(12.7929 + 5.17879i) q^{18} +(6.26584 + 10.8527i) q^{19} +(-0.0534176 - 0.0636606i) q^{20} +(-3.10133 + 29.4110i) q^{21} +(-3.26317 + 18.5063i) q^{22} +(5.93322 - 7.07093i) q^{23} +(7.17102 - 24.9763i) q^{24} +(-23.4899 - 8.54963i) q^{25} -18.7461i q^{26} +(18.0460 + 20.0833i) q^{27} +16.2501 q^{28} +(15.1728 - 41.6870i) q^{29} +(0.0560316 + 0.225057i) q^{30} +(-24.2140 - 20.3180i) q^{31} +(-24.0190 - 4.23520i) q^{32} +(-21.6188 + 29.7345i) q^{33} +(17.3509 - 14.5591i) q^{34} +(-0.430398 + 0.248490i) q^{35} +(9.93456 - 11.0184i) q^{36} +(-7.19801 + 12.4673i) q^{37} +(-18.9252 + 3.33702i) q^{38} +(16.0878 - 32.9565i) q^{39} +(0.410339 - 0.149351i) q^{40} +(23.5871 + 64.8050i) q^{41} +(-40.7548 - 19.8946i) q^{42} +(7.01983 + 39.8114i) q^{43} +(17.4939 + 10.1001i) q^{44} +(-0.0946365 + 0.443745i) q^{45} +(7.07738 + 12.2584i) q^{46} +(1.24938 + 1.48895i) q^{47} +(16.2306 + 11.8007i) q^{48} +(8.36645 - 47.4485i) q^{49} +(24.6402 - 29.3650i) q^{50} +(42.9982 - 10.7051i) q^{51} +(-18.9358 - 6.89208i) q^{52} +47.7390i q^{53} +(-38.4051 + 15.4711i) q^{54} -0.617787 q^{55} +(-29.2044 + 80.2384i) q^{56} +(-36.1351 - 10.3749i) q^{57} +(52.1133 + 43.7282i) q^{58} +(-72.6161 - 12.8042i) q^{59} +(0.247935 + 0.0261442i) q^{60} +(-4.54441 + 3.81321i) q^{61} +(41.9782 - 24.2361i) q^{62} +(-54.5752 - 69.9511i) q^{63} +(32.0786 - 55.5618i) q^{64} +(0.606922 - 0.107017i) q^{65} +(-31.5089 - 46.7481i) q^{66} +(45.8583 - 16.6910i) q^{67} +(-8.32735 - 22.8792i) q^{68} +(1.92225 + 27.6245i) q^{69} +(-0.132340 - 0.750535i) q^{70} +(-8.61519 - 4.97398i) q^{71} +(36.5513 + 68.8559i) q^{72} +(-44.2472 - 76.6383i) q^{73} +(-14.1902 - 16.9113i) q^{74} +(68.5193 - 30.4788i) q^{75} +(-3.58713 + 20.3436i) q^{76} +(77.6508 - 92.5406i) q^{77} +(39.0527 + 40.4678i) q^{78} +(105.233 + 38.3016i) q^{79} +0.337221i q^{80} +(-80.7949 - 5.76021i) q^{81} -105.755 q^{82} +(-6.65732 + 18.2908i) q^{83} +(-35.0796 + 33.8529i) q^{84} +(0.570416 + 0.478636i) q^{85} +(-61.0503 - 10.7648i) q^{86} +(54.0900 + 121.599i) q^{87} +(-81.3111 + 68.2281i) q^{88} +(-33.9430 + 19.5970i) q^{89} +(-0.589805 - 0.369109i) q^{90} +(-60.2547 + 104.364i) q^{91} +(14.9845 - 2.64217i) q^{92} +(94.5988 - 6.58266i) q^{93} +(-2.80086 + 1.01943i) q^{94} +(-0.216078 - 0.593669i) q^{95} +(60.6734 - 40.8947i) q^{96} +(-0.0670785 - 0.380421i) q^{97} +(63.9855 + 36.9420i) q^{98} +(-15.2749 - 109.226i) 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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