LMFDB - Embedded newform 222.3.l.d.199.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [222,3,Mod(97,222)] 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("222.97"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(222, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 222 = 2 \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	222.l (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,8,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.04906186880$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} + 318 x^{13} + 8876 x^{12} - 14732 x^{11} + 38482 x^{10} + 1520688 x^{9} + \cdots + 4 $ x^16 - 4x^15 + 8x^14 + 318x^13 + 8876x^12 - 14732x^11 + 38482x^10 + 1520688x^9 + 22685392x^8 + 15961410x^7 + 5199688x^6 - 6131200x^5 + 2764889x^4 - 258648x^3 + 12800x^2 - 320*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			199.4
Root			$-5.10315 - 5.10315i$ of defining polynomial
Character	$\chi$	$=$	222.199
Dual form			222.3.l.d.193.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36603 - 0.366025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(1.73205 - 1.00000i) q^{4} +(8.33705 + 2.23391i) q^{5} +(1.73205 - 1.73205i) q^{6} +(-6.46144 - 11.1915i) q^{7} +(2.00000 - 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +12.2063 q^{10} +13.2455i q^{11} +(1.73205 - 3.00000i) q^{12} +(-11.9887 - 3.21235i) q^{13} +(-12.9229 - 12.9229i) q^{14} +(14.4402 - 3.86924i) q^{15} +(2.00000 - 3.46410i) q^{16} +(4.07838 + 15.2207i) q^{17} +(1.09808 - 4.09808i) q^{18} +(4.30012 + 1.15221i) q^{19} +(16.6741 - 4.46781i) q^{20} +(-19.3843 - 11.1915i) q^{21} +(4.84819 + 18.0937i) q^{22} +(-3.26464 + 3.26464i) q^{23} +(1.26795 - 4.73205i) q^{24} +(42.8655 + 24.7484i) q^{25} -17.5526 q^{26} -5.19615i q^{27} +(-22.3831 - 12.9229i) q^{28} +(6.05490 + 6.05490i) q^{29} +(18.3094 - 10.5710i) q^{30} +(-25.8855 - 25.8855i) q^{31} +(1.46410 - 5.46410i) q^{32} +(11.4709 + 19.8682i) q^{33} +(11.1423 + 19.2991i) q^{34} +(-28.8685 - 107.739i) q^{35} -6.00000i q^{36} +(-8.73010 + 35.9553i) q^{37} +6.29582 q^{38} +(-20.7650 + 5.56396i) q^{39} +(21.1419 - 12.2063i) q^{40} +(35.8353 - 20.6895i) q^{41} +(-30.5759 - 8.19277i) q^{42} +(20.0565 - 20.0565i) q^{43} +(13.2455 + 22.9419i) q^{44} +(18.3094 - 18.3094i) q^{45} +(-3.26464 + 5.65452i) q^{46} -53.2450 q^{47} -6.92820i q^{48} +(-59.0003 + 102.192i) q^{49} +(67.6138 + 18.1171i) q^{50} +(19.2991 + 19.2991i) q^{51} +(-23.9773 + 6.42471i) q^{52} +(-18.6282 + 32.2650i) q^{53} +(-1.90192 - 7.09808i) q^{54} +(-29.5892 + 110.428i) q^{55} +(-35.3060 - 9.46020i) q^{56} +(7.44803 - 1.99569i) q^{57} +(10.4874 + 6.05490i) q^{58} +(29.1262 + 108.700i) q^{59} +(21.1419 - 21.1419i) q^{60} +(-16.5497 + 61.7642i) q^{61} +(-44.8349 - 25.8855i) q^{62} -38.7686 q^{63} -8.00000i q^{64} +(-92.7741 - 53.5631i) q^{65} +(22.9419 + 22.9419i) q^{66} +(76.1457 - 43.9628i) q^{67} +(22.2847 + 22.2847i) q^{68} +(-2.06970 + 7.72422i) q^{69} +(-78.8702 - 136.607i) q^{70} +(-13.2247 - 22.9059i) q^{71} +(-2.19615 - 8.19615i) q^{72} -108.076i q^{73} +(1.23503 + 52.3113i) q^{74} +85.7309 q^{75} +(8.60025 - 2.30443i) q^{76} +(148.237 - 85.5849i) q^{77} +(-26.3290 + 15.2010i) q^{78} +(-137.251 - 36.7764i) q^{79} +(24.4126 - 24.4126i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(41.3790 - 41.3790i) q^{82} +(-13.4470 + 23.2908i) q^{83} -44.7662 q^{84} +136.007i q^{85} +(20.0565 - 34.7388i) q^{86} +(14.3261 + 3.83865i) q^{87} +(26.4910 + 26.4910i) q^{88} +(-69.2834 + 18.5644i) q^{89} +(18.3094 - 31.7129i) q^{90} +(41.5129 + 154.928i) q^{91} +(-2.38988 + 8.91916i) q^{92} +(-61.2456 - 16.4107i) q^{93} +(-72.7340 + 19.4890i) q^{94} +(33.2764 + 19.2121i) q^{95} +(-2.53590 - 9.46410i) q^{96} +(-21.0702 + 21.0702i) q^{97} +(-43.1913 + 161.192i) q^{98} +(34.4128 + 19.8682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} + 24 q^{3} + 6 q^{5} - 14 q^{7} + 32 q^{8} + 24 q^{9} + 24 q^{10} - 16 q^{13} - 28 q^{14} + 18 q^{15} + 32 q^{16} - 16 q^{17} - 24 q^{18} + 42 q^{19} + 12 q^{20} - 42 q^{21} + 46 q^{22} - 34 q^{23}+ \cdots + 90 q^{99}+O(q^{100}) $ 16 * q + 8 * q^2 + 24 * q^3 + 6 * q^5 - 14 * q^7 + 32 * q^8 + 24 * q^9 + 24 * q^10 - 16 * q^13 - 28 * q^14 + 18 * q^15 + 32 * q^16 - 16 * q^17 - 24 * q^18 + 42 * q^19 + 12 * q^20 - 42 * q^21 + 46 * q^22 - 34 * q^23 + 48 * q^24 + 12 * q^25 + 8 * q^26 + 74 * q^29 + 36 * q^30 + 26 * q^31 - 32 * q^32 + 30 * q^33 - 10 * q^34 - 18 * q^35 - 62 * q^37 + 60 * q^38 - 12 * q^39 - 150 * q^41 - 42 * q^42 + 4 * q^43 - 32 * q^44 + 36 * q^45 - 34 * q^46 - 20 * q^47 - 278 * q^49 + 100 * q^50 - 42 * q^51 - 32 * q^52 + 154 * q^53 - 72 * q^54 - 24 * q^55 - 28 * q^56 + 72 * q^57 - 90 * q^58 + 12 * q^59 + 38 * q^61 - 66 * q^62 - 84 * q^63 - 282 * q^65 + 60 * q^66 + 132 * q^67 - 20 * q^68 - 72 * q^69 - 30 * q^70 + 34 * q^71 + 48 * q^72 - 42 * q^74 + 24 * q^75 + 84 * q^76 + 258 * q^77 + 12 * q^78 - 46 * q^79 + 48 * q^80 - 72 * q^81 + 188 * q^82 - 136 * q^83 + 4 * q^86 + 66 * q^87 - 64 * q^88 + 152 * q^89 + 36 * q^90 + 192 * q^91 + 76 * q^92 + 6 * q^93 - 232 * q^94 - 1068 * q^95 - 96 * q^96 - 382 * q^97 + 206 * q^98 + 90 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/222\mathbb{Z}\right)^\times$.

$n$	$149$	$187$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	1.36603	−	0.366025i	0.683013	−	0.183013i
$2$	1.36603	−	0.366025i	0.683013	−	0.183013i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$	1.73205	−	1.00000i	0.433013	−	0.250000i
$5$	8.33705	+	2.23391i	1.66741	+	0.446781i	0.964411	−	0.264409i	$-0.0851768\pi$
$5$	8.33705	+	2.23391i	1.66741	+	0.446781i	0.703000	+	0.711190i	$0.251844\pi$
$6$	1.73205	−	1.73205i	0.288675	−	0.288675i
$7$	−6.46144	−	11.1915i	−0.923062	−	1.59879i	−0.794648	−	0.607071i	$-0.792345\pi$
$7$	−6.46144	−	11.1915i	−0.923062	−	1.59879i	−0.128415	−	0.991721i	$-0.540989\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$	12.2063			1.22063
$11$			13.2455i			1.20414i	0.798445	+	0.602068i	$0.205656\pi$
$11$			13.2455i			1.20414i	−0.798445	+	0.602068i	$0.794344\pi$
$12$	1.73205	−	3.00000i	0.144338	−	0.250000i
$13$	−11.9887	−	3.21235i	−0.922206	−	0.247104i	−0.233678	−	0.972314i	$-0.575076\pi$
$13$	−11.9887	−	3.21235i	−0.922206	−	0.247104i	−0.688528	+	0.725210i	$0.741743\pi$
$14$	−12.9229	−	12.9229i	−0.923062	−	0.923062i
$15$	14.4402	−	3.86924i	0.962680	−	0.257949i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	4.07838	+	15.2207i	0.239905	+	0.895337i	0.975876	+	0.218325i	$0.0700591\pi$
$17$	4.07838	+	15.2207i	0.239905	+	0.895337i	−0.735971	+	0.677013i	$0.763274\pi$
$18$	1.09808	−	4.09808i	0.0610042	−	0.227671i
$19$	4.30012	+	1.15221i	0.226322	+	0.0606429i	0.370198	−	0.928953i	$-0.379290\pi$
$19$	4.30012	+	1.15221i	0.226322	+	0.0606429i	−0.143876	+	0.989596i	$0.545957\pi$
$20$	16.6741	−	4.46781i	0.833705	−	0.223391i
$21$	−19.3843	−	11.1915i	−0.923062	−	0.532930i
$22$	4.84819	+	18.0937i	0.220372	+	0.822440i
$23$	−3.26464	+	3.26464i	−0.141941	+	0.141941i	−0.774507	−	0.632566i	$-0.782002\pi$
$23$	−3.26464	+	3.26464i	−0.141941	+	0.141941i	0.632566	+	0.774507i	$0.282002\pi$
$24$	1.26795	−	4.73205i	0.0528312	−	0.197169i
$25$	42.8655	+	24.7484i	1.71462	+	0.989935i
$26$	−17.5526			−0.675101
$27$		−	5.19615i		−	0.192450i
$28$	−22.3831	−	12.9229i	−0.799396	−	0.461531i
$29$	6.05490	+	6.05490i	0.208790	+	0.208790i	0.803753	−	0.594963i	$-0.202833\pi$
$29$	6.05490	+	6.05490i	0.208790	+	0.208790i	−0.594963	+	0.803753i	$0.702833\pi$
$30$	18.3094	−	10.5710i	0.610315	−	0.352365i
$31$	−25.8855	−	25.8855i	−0.835015	−	0.835015i	0.153183	−	0.988198i	$-0.451048\pi$
$31$	−25.8855	−	25.8855i	−0.835015	−	0.835015i	−0.988198	+	0.153183i	$0.951048\pi$
$32$	1.46410	−	5.46410i	0.0457532	−	0.170753i
$33$	11.4709	+	19.8682i	0.347604	+	0.602068i
$34$	11.1423	+	19.2991i	0.327716	+	0.567621i
$35$	−28.8685	−	107.739i	−0.824814	−	3.07825i
$36$		−	6.00000i		−	0.166667i
$37$	−8.73010	+	35.9553i	−0.235949	+	0.971766i
$37$	−8.73010	+	35.9553i	−0.235949	+	0.971766i
$38$	6.29582			0.165679
$39$	−20.7650	+	5.56396i	−0.532436	+	0.142666i
$40$	21.1419	−	12.2063i	0.528548	−	0.305157i
$41$	35.8353	−	20.6895i	0.874032	−	0.504622i	0.00534580	−	0.999986i	$-0.498298\pi$
$41$	35.8353	−	20.6895i	0.874032	−	0.504622i	0.868686	+	0.495363i	$0.164965\pi$
$42$	−30.5759	−	8.19277i	−0.727996	−	0.195066i
$43$	20.0565	−	20.0565i	0.466430	−	0.466430i	−0.434326	−	0.900756i	$-0.643013\pi$
$43$	20.0565	−	20.0565i	0.466430	−	0.466430i	0.900756	+	0.434326i	$0.143013\pi$
$44$	13.2455	+	22.9419i	0.301034	+	0.521406i
$45$	18.3094	−	18.3094i	0.406876	−	0.406876i
$46$	−3.26464	+	5.65452i	−0.0709704	+	0.122924i
$47$	−53.2450			−1.13287			−0.566436	−	0.824106i	$-0.691678\pi$
$47$	−53.2450			−1.13287			−0.566436	+	0.824106i	$0.691678\pi$
$48$		−	6.92820i		−	0.144338i
$49$	−59.0003	+	102.192i	−1.20409	+	2.08554i
$50$	67.6138	+	18.1171i	1.35228	+	0.362341i
$51$	19.2991	+	19.2991i	0.378414	+	0.378414i
$52$	−23.9773	+	6.42471i	−0.461103	+	0.123552i
$53$	−18.6282	+	32.2650i	−0.351476	+	0.608774i	−0.986508	−	0.163712i	$-0.947653\pi$
$53$	−18.6282	+	32.2650i	−0.351476	+	0.608774i	0.635033	+	0.772485i	$0.280987\pi$
$54$	−1.90192	−	7.09808i	−0.0352208	−	0.131446i
$55$	−29.5892	+	110.428i	−0.537985	+	2.00779i
$56$	−35.3060	−	9.46020i	−0.630463	−	0.168932i
$57$	7.44803	−	1.99569i	0.130667	−	0.0350122i
$58$	10.4874	+	6.05490i	0.180817	+	0.104395i
$59$	29.1262	+	108.700i	0.493664	+	1.84238i	0.537390	+	0.843334i	$0.319410\pi$
$59$	29.1262	+	108.700i	0.493664	+	1.84238i	−0.0437261	+	0.999044i	$0.513923\pi$
$60$	21.1419	−	21.1419i	0.352365	−	0.352365i
$61$	−16.5497	+	61.7642i	−0.271306	+	1.01253i	0.686971	+	0.726685i	$0.258940\pi$
$61$	−16.5497	+	61.7642i	−0.271306	+	1.01253i	−0.958277	+	0.285843i	$0.907727\pi$
$62$	−44.8349	−	25.8855i	−0.723144	−	0.417507i
$63$	−38.7686			−0.615375
$64$		−	8.00000i		−	0.125000i
$65$	−92.7741	−	53.5631i	−1.42729	−	0.824048i
$66$	22.9419	+	22.9419i	0.347604	+	0.347604i
$67$	76.1457	−	43.9628i	1.13650	−	0.656161i	0.190941	−	0.981602i	$-0.438846\pi$
$67$	76.1457	−	43.9628i	1.13650	−	0.656161i	0.945562	+	0.325441i	$0.105513\pi$
$68$	22.2847	+	22.2847i	0.327716	+	0.327716i
$69$	−2.06970	+	7.72422i	−0.0299956	+	0.111945i
$70$	−78.8702	−	136.607i	−1.12672	−	1.95153i
$71$	−13.2247	−	22.9059i	−0.186263	−	0.322618i	0.757738	−	0.652559i	$-0.226304\pi$
$71$	−13.2247	−	22.9059i	−0.186263	−	0.322618i	−0.944002	+	0.329941i	$0.892971\pi$
$72$	−2.19615	−	8.19615i	−0.0305021	−	0.113835i
$73$		−	108.076i		−	1.48049i	−0.672338	−	0.740244i	$-0.734710\pi$
$73$		−	108.076i		−	1.48049i	0.672338	−	0.740244i	$-0.265290\pi$
$74$	1.23503	+	52.3113i	0.0166896	+	0.706910i
$75$	85.7309			1.14308
$76$	8.60025	−	2.30443i	0.113161	−	0.0303214i
$77$	148.237	−	85.5849i	1.92516	−	1.11149i
$78$	−26.3290	+	15.2010i	−0.337551	+	0.194885i
$79$	−137.251	−	36.7764i	−1.73736	−	0.465524i	−0.755502	−	0.655146i	$-0.772607\pi$
$79$	−137.251	−	36.7764i	−1.73736	−	0.465524i	−0.981857	+	0.189622i	$0.939274\pi$
$80$	24.4126	−	24.4126i	0.305157	−	0.305157i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	41.3790	−	41.3790i	0.504622	−	0.504622i
$83$	−13.4470	+	23.2908i	−0.162012	+	0.280612i	−0.935590	−	0.353088i	$-0.885132\pi$
$83$	−13.4470	+	23.2908i	−0.162012	+	0.280612i	0.773578	+	0.633701i	$0.218465\pi$
$84$	−44.7662			−0.532930
$85$			136.007i			1.60008i
$86$	20.0565	−	34.7388i	0.233215	−	0.403940i
$87$	14.3261	+	3.83865i	0.164667	+	0.0441225i
$88$	26.4910	+	26.4910i	0.301034	+	0.301034i
$89$	−69.2834	+	18.5644i	−0.778465	+	0.208589i	−0.626108	−	0.779737i	$-0.715353\pi$
$89$	−69.2834	+	18.5644i	−0.778465	+	0.208589i	−0.152357	+	0.988326i	$0.548686\pi$
$90$	18.3094	−	31.7129i	0.203438	−	0.352365i
$91$	41.5129	+	154.928i	0.456185	+	1.70251i
$92$	−2.38988	+	8.91916i	−0.0259770	+	0.0969474i
$93$	−61.2456	−	16.4107i	−0.658555	−	0.176459i
$94$	−72.7340	+	19.4890i	−0.773765	+	0.207330i
$95$	33.2764	+	19.2121i	0.350278	+	0.202233i
$96$	−2.53590	−	9.46410i	−0.0264156	−	0.0985844i
$97$	−21.0702	+	21.0702i	−0.217219	+	0.217219i	−0.807325	−	0.590106i	$-0.799086\pi$
$97$	−21.0702	+	21.0702i	−0.217219	+	0.217219i	0.590106	+	0.807325i	$0.299086\pi$
$98$	−43.1913	+	161.192i	−0.440727	+	1.64482i
$99$	34.4128	+	19.8682i	0.347604	+	0.200689i
$100$	98.9935			0.989935
$101$		−	136.519i		−	1.35167i	−0.737053	−	0.675835i	$-0.763783\pi$
$101$		−	136.519i		−	1.35167i	0.737053	−	0.675835i	$-0.236217\pi$
$102$	33.4270	+	19.2991i	0.327716	+	0.189207i
$103$	−13.3213	−	13.3213i	−0.129333	−	0.129333i	0.639477	−	0.768810i	$-0.279151\pi$
$103$	−13.3213	−	13.3213i	−0.129333	−	0.129333i	−0.768810	+	0.639477i	$0.779151\pi$
$104$	−30.4021	+	17.5526i	−0.292327	+	0.168775i
$105$	−136.607	−	136.607i	−1.30102	−	1.30102i
$106$	−13.6368	+	50.8932i	−0.128649	+	0.480125i
$107$	−90.1581	−	156.158i	−0.842599	−	1.45942i	−0.887690	−	0.460441i	$-0.847691\pi$
$107$	−90.1581	−	156.158i	−0.842599	−	1.45942i	0.0450918	−	0.998983i	$-0.485642\pi$
$108$	−5.19615	−	9.00000i	−0.0481125	−	0.0833333i
$109$	19.1545	+	71.4855i	0.175729	+	0.655830i	0.996426	+	0.0844669i	$0.0269187\pi$
$109$	19.1545	+	71.4855i	0.175729	+	0.655830i	−0.820697	+	0.571364i	$0.806415\pi$
$110$			161.678i			1.46980i
$111$	18.0431	+	61.4935i	0.162550	+	0.553995i
$112$	−51.6915			−0.461531
$113$	14.2577	−	3.82033i	0.126174	−	0.0338082i	−0.195179	−	0.980768i	$-0.562529\pi$
$113$	14.2577	−	3.82033i	0.126174	−	0.0338082i	0.321353	+	0.946959i	$0.395862\pi$
$114$	9.44373	−	5.45234i	0.0828397	−	0.0478275i
$115$	−34.5104	+	19.9246i	−0.300090	+	0.173257i
$116$	16.5423	+	4.43250i	0.142606	+	0.0382112i
$117$	−26.3290	+	26.3290i	−0.225034	+	0.225034i
$118$	79.5741	+	137.826i	0.674357	+	1.16802i
$119$	143.991	−	143.991i	1.21001	−	1.21001i
$120$	21.1419	−	36.6189i	0.176183	−	0.305157i
$121$	−54.4429			−0.449942
$122$			90.4291i			0.741222i
$123$	35.8353	−	62.0686i	0.291344	−	0.504622i
$124$	−70.7204	−	18.9495i	−0.570326	−	0.152818i
$125$	149.507	+	149.507i	1.19606	+	1.19606i
$126$	−52.9589	+	14.1903i	−0.420309	+	0.112621i
$127$	77.1894	−	133.696i	0.607790	−	1.05272i	−0.383813	−	0.923411i	$-0.625389\pi$
$127$	77.1894	−	133.696i	0.607790	−	1.05272i	0.991604	−	0.129313i	$-0.0412773\pi$
$128$	−2.92820	−	10.9282i	−0.0228766	−	0.0853766i
$129$	12.7153	−	47.4541i	0.0985682	−	0.367862i
$130$	−146.337	−	39.2109i	−1.12567	−	0.301623i
$131$	140.927	−	37.7613i	1.07578	−	0.288254i	0.322913	−	0.946429i	$-0.395338\pi$
$131$	140.927	−	37.7613i	1.07578	−	0.288254i	0.752865	+	0.658175i	$0.228671\pi$
$132$	39.7365	+	22.9419i	0.301034	+	0.173802i
$133$	−14.8899	−	55.5700i	−0.111954	−	0.417819i
$134$	87.9255	−	87.9255i	0.656161	−	0.656161i
$135$	11.6077	−	43.3206i	0.0859831	−	0.320893i
$136$	38.5982	+	22.2847i	0.283811	+	0.163858i
$137$	−94.5607			−0.690224			−0.345112	−	0.938561i	$-0.612159\pi$
$137$	−94.5607			−0.690224			−0.345112	+	0.938561i	$0.612159\pi$
$138$			11.3090i			0.0819496i
$139$	111.198	+	64.2005i	0.799989	+	0.461874i	0.843467	−	0.537180i	$-0.180511\pi$
$139$	111.198	+	64.2005i	0.799989	+	0.461874i	−0.0434783	+	0.999054i	$0.513844\pi$
$140$	−157.740	−	157.740i	−1.12672	−	1.12672i
$141$	−79.8674	+	46.1115i	−0.566436	+	0.327032i
$142$	−26.4494	−	26.4494i	−0.186263	−	0.186263i
$143$	42.5492	−	158.796i	0.297547	−	1.11046i
$144$	−6.00000	−	10.3923i	−0.0416667	−	0.0721688i
$145$	36.9539	+	64.0061i	0.254855	+	0.441421i
$146$	−39.5584	−	147.634i	−0.270948	−	1.01119i
$147$			204.383i			1.39036i
$148$	20.8344	+	71.0065i	0.140773	+	0.479774i
$149$	57.4816			0.385783			0.192891	−	0.981220i	$-0.438214\pi$
$149$	57.4816			0.385783			0.192891	+	0.981220i	$0.438214\pi$
$150$	117.111	−	31.3797i	0.780737	−	0.209198i
$151$	−34.8951	+	20.1467i	−0.231093	+	0.133422i	−0.611076	−	0.791572i	$-0.709263\pi$
$151$	−34.8951	+	20.1467i	−0.231093	+	0.133422i	0.379983	+	0.924993i	$0.375930\pi$
$152$	10.9047	−	6.29582i	0.0717413	−	0.0414199i
$153$	45.6622	+	12.2351i	0.298446	+	0.0799683i
$154$	171.170	−	171.170i	1.11149	−	1.11149i
$155$	−157.983	−	273.634i	−1.01924	−	1.76538i
$156$	−30.4021	+	30.4021i	−0.194885	+	0.194885i
$157$	130.988	−	226.878i	0.834319	−	1.44508i	−0.0602647	−	0.998182i	$-0.519194\pi$
$157$	130.988	−	226.878i	0.834319	−	1.44508i	0.894584	−	0.446900i	$-0.147472\pi$
$158$	−200.950			−1.27184
$159$			64.5300i			0.405849i
$160$	24.4126	−	42.2838i	0.152579	−	0.264274i
$161$	57.6306	+	15.4421i	0.357954	+	0.0959135i
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	68.2662	−	18.2919i	0.418811	−	0.112220i	−0.0432583	−	0.999064i	$-0.513774\pi$
$163$	68.2662	−	18.2919i	0.418811	−	0.112220i	0.462069	+	0.886844i	$0.347107\pi$
$164$	41.3790	−	71.6706i	0.252311	−	0.437016i
$165$	51.2500	+	191.267i	0.310606	+	1.15920i
$166$	−9.84386	+	36.7378i	−0.0593004	+	0.221312i
$167$	−8.35747	−	2.23938i	−0.0500447	−	0.0134094i	0.233710	−	0.972306i	$-0.424913\pi$
$167$	−8.35747	−	2.23938i	−0.0500447	−	0.0134094i	−0.283755	+	0.958897i	$0.591580\pi$
$168$	−61.1517	+	16.3855i	−0.363998	+	0.0975330i
$169$	−12.9493	−	7.47626i	−0.0766229	−	0.0442382i
$170$	49.7819	+	185.789i	0.292835	+	1.09287i
$171$	9.44373	−	9.44373i	0.0552265	−	0.0552265i
$172$	14.6824	−	54.7953i	0.0853626	−	0.318577i
$173$	228.445	+	131.893i	1.32049	+	0.762387i	0.983807	−	0.179229i	$-0.0573604\pi$
$173$	228.445	+	131.893i	1.32049	+	0.762387i	0.336686	+	0.941617i	$0.390694\pi$
$174$	20.9748			0.120545
$175$		−	639.641i		−	3.65509i
$176$	45.8837	+	26.4910i	0.260703	+	0.150517i
$177$	137.826	+	137.826i	0.778680	+	0.778680i
$178$	−87.8478	+	50.7189i	−0.493527	+	0.284938i
$179$	30.4410	+	30.4410i	0.170061	+	0.170061i	0.787006	−	0.616945i	$-0.211630\pi$
$179$	30.4410	+	30.4410i	0.170061	+	0.170061i	−0.616945	+	0.787006i	$0.711630\pi$
$180$	13.4034	−	50.0223i	0.0744635	−	0.277902i
$181$	40.4663	+	70.0896i	0.223571	+	0.387235i	0.955890	−	0.293726i	$-0.0948954\pi$
$181$	40.4663	+	70.0896i	0.223571	+	0.387235i	−0.732319	+	0.680962i	$0.761562\pi$
$182$	113.415	+	196.441i	0.623161	+	1.07935i
$183$	28.6649	+	106.979i	0.156639	+	0.584583i
$184$			13.0586i			0.0709704i
$185$	−153.104	+	280.259i	−0.827590	+	1.51491i
$186$	−89.6699			−0.482096
$187$	−201.606	+	54.0202i	−1.07811	+	0.288878i
$188$	−92.2230	+	53.2450i	−0.490548	+	0.283218i
$189$	−58.1529	+	33.5746i	−0.307687	+	0.177643i
$190$	52.4886	+	14.0643i	0.276256	+	0.0740225i
$191$	−103.726	+	103.726i	−0.543066	+	0.543066i	−0.924427	−	0.381360i	$-0.875456\pi$
$191$	−103.726	+	103.726i	−0.543066	+	0.543066i	0.381360	+	0.924427i	$0.375456\pi$
$192$	−6.92820	−	12.0000i	−0.0360844	−	0.0625000i
$193$	205.840	−	205.840i	1.06653	−	1.06653i	0.0689070	−	0.997623i	$-0.478049\pi$
$193$	205.840	−	205.840i	1.06653	−	1.06653i	0.997623	−	0.0689070i	$-0.0219512\pi$
$194$	−21.0702	+	36.4947i	−0.108609	+	0.188117i
$195$	−185.548			−0.951529
$196$			236.001i			1.20409i
$197$	−79.4814	+	137.666i	−0.403459	+	0.698812i	−0.994141	−	0.108093i	$-0.965526\pi$
$197$	−79.4814	+	137.666i	−0.403459	+	0.698812i	0.590682	+	0.806905i	$0.298859\pi$
$198$	54.2810	+	14.5446i	0.274147	+	0.0734573i
$199$	−213.808	−	213.808i	−1.07441	−	1.07441i	−0.996999	−	0.0774127i	$-0.975334\pi$
$199$	−213.808	−	213.808i	−1.07441	−	1.07441i	−0.0774127	−	0.996999i	$-0.524666\pi$
$200$	135.228	−	36.2341i	0.676138	−	0.181171i
$201$	76.1457	−	131.888i	0.378834	−	0.656161i
$202$	−49.9693	−	186.488i	−0.247373	−	0.923207i
$203$	28.6403	−	106.887i	0.141085	−	0.526537i
$204$	52.7262	+	14.1279i	0.258462	+	0.0692546i
$205$	344.979	−	92.4369i	1.68283	−	0.450912i
$206$	−23.0731	−	13.3213i	−0.112005	−	0.0646663i
$207$	3.58482	+	13.3787i	0.0173180	+	0.0646316i
$208$	−35.1053	+	35.1053i	−0.168775	+	0.168775i
$209$	−15.2616	+	56.9572i	−0.0730222	+	0.272523i
$210$	−236.611	−	136.607i	−1.12672	−	0.650510i
$211$	397.448			1.88364			0.941820	−	0.336118i	$-0.109114\pi$
$211$	397.448			1.88364			0.941820	+	0.336118i	$0.109114\pi$
$212$			74.5129i			0.351476i
$213$	−39.6741	−	22.9059i	−0.186263	−	0.107539i
$214$	−180.316	−	180.316i	−0.842599	−	0.842599i
$215$	212.016	−	122.408i	0.986122	−	0.569338i
$216$	−10.3923	−	10.3923i	−0.0481125	−	0.0481125i
$217$	−122.441	+	456.955i	−0.564243	+	2.10578i
$218$	52.3310	+	90.6400i	0.240051	+	0.415780i
$219$	−93.5963	−	162.113i	−0.427380	−	0.740244i
$220$	59.1784	+	220.857i	0.268993	+	1.00389i
$221$		−	195.578i		−	0.884966i
$222$	47.1555	+	77.3974i	0.212412	+	0.348637i
$223$	5.38998			0.0241703			0.0120852	−	0.999927i	$-0.496153\pi$
$223$	5.38998			0.0241703			0.0120852	+	0.999927i	$0.496153\pi$
$224$	−70.6119	+	18.9204i	−0.315232	+	0.0844661i
$225$	128.596	−	74.2452i	0.571539	−	0.329978i
$226$	18.0780	−	10.4373i	0.0799912	−	0.0461829i
$227$	−214.518	−	57.4800i	−0.945014	−	0.253216i	−0.246769	−	0.969074i	$-0.579369\pi$
$227$	−214.518	−	57.4800i	−0.945014	−	0.253216i	−0.698245	+	0.715859i	$0.746036\pi$
$228$	10.9047	−	10.9047i	0.0478275	−	0.0478275i
$229$	−106.678	−	184.772i	−0.465842	−	0.806862i	0.533397	−	0.845865i	$-0.320915\pi$
$229$	−106.678	−	184.772i	−0.465842	−	0.806862i	−0.999239	+	0.0390026i	$0.987582\pi$
$230$	−39.8492	+	39.8492i	−0.173257	+	0.173257i
$231$	148.237	−	256.755i	0.641720	−	1.11149i
$232$	24.2196			0.104395
$233$		−	188.995i		−	0.811139i	−0.914064	−	0.405569i	$-0.867073\pi$
$233$		−	188.995i		−	0.811139i	0.914064	−	0.405569i	$-0.132927\pi$
$234$	−26.3290	+	45.6031i	−0.112517	+	0.194885i
$235$	−443.906	−	118.944i	−1.88896	−	0.506146i
$236$	159.148	+	159.148i	0.674357	+	0.674357i
$237$	−237.726	+	63.6986i	−1.00306	+	0.268770i
$238$	143.991	−	249.400i	0.605005	−	1.04790i
$239$	63.7008	+	237.735i	0.266531	+	0.994706i	0.961307	+	0.275480i	$0.0888368\pi$
$239$	63.7008	+	237.735i	0.266531	+	0.994706i	−0.694776	+	0.719226i	$0.744497\pi$
$240$	15.4770	−	57.7608i	0.0644873	−	0.240670i
$241$	133.251	+	35.7046i	0.552911	+	0.148152i	0.524447	−	0.851443i	$-0.324272\pi$
$241$	133.251	+	35.7046i	0.552911	+	0.148152i	0.0284633	+	0.999595i	$0.490939\pi$
$242$	−74.3704	+	19.9275i	−0.307316	+	0.0823450i
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$	33.0993	+	123.528i	0.135653	+	0.506264i
$245$	−720.175	+	720.175i	−2.93949	+	2.93949i
$246$	26.2333	−	97.9039i	0.106639	−	0.397983i
$247$	−47.8515	−	27.6270i	−0.193731	−	0.111850i
$248$	−103.542			−0.417507
$249$			46.5817i			0.187075i
$250$	258.954	+	149.507i	1.03582	+	0.598029i
$251$	43.6282	+	43.6282i	0.173818	+	0.173818i	0.788654	−	0.614837i	$-0.210778\pi$
$251$	43.6282	+	43.6282i	0.173818	+	0.173818i	−0.614837	+	0.788654i	$0.710778\pi$
$252$	−67.1492	+	38.7686i	−0.266465	+	0.153844i
$253$	−43.2418	−	43.2418i	−0.170916	−	0.170916i
$254$	56.5066	−	210.885i	0.222467	−	0.830257i
$255$	117.785	+	204.010i	0.461903	+	0.800040i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	84.6679	+	315.985i	0.329447	+	1.22951i	0.909765	+	0.415123i	$0.136262\pi$
$257$	84.6679	+	315.985i	0.329447	+	1.22951i	−0.580318	+	0.814390i	$0.697072\pi$
$258$		−	69.4777i		−	0.269293i
$259$	458.804	−	134.620i	1.77145	−	0.519768i
$260$	−214.253			−0.824048
$261$	24.8135	−	6.64874i	0.0950707	−	0.0254741i
$262$	178.688	−	103.166i	0.682016	−	0.393762i
$263$	311.134	−	179.633i	1.18302	−	0.683015i	0.226307	−	0.974056i	$-0.427335\pi$
$263$	311.134	−	179.633i	1.18302	−	0.683015i	0.956711	+	0.291041i	$0.0940015\pi$
$264$	62.6783	+	16.7946i	0.237418	+	0.0636159i
$265$	−227.381	+	227.381i	−0.858043	+	0.858043i
$266$	−40.6800	−	70.4599i	−0.152932	−	0.264887i
$267$	−87.8478	+	87.8478i	−0.329018	+	0.329018i
$268$	87.9255	−	152.291i	0.328080	−	0.568252i
$269$	−462.224			−1.71830			−0.859152	−	0.511721i	$-0.829008\pi$
$269$	−462.224			−1.71830			−0.859152	+	0.511721i	$0.829008\pi$
$270$		−	63.4257i		−	0.234910i
$271$	−41.2912	+	71.5184i	−0.152366	+	0.263906i	−0.932097	−	0.362209i	$-0.882023\pi$
$271$	−41.2912	+	71.5184i	−0.152366	+	0.263906i	0.779731	+	0.626115i	$0.215356\pi$
$272$	60.8829	+	16.3135i	0.223834	+	0.0599762i
$273$	196.441	+	196.441i	0.719564	+	0.719564i
$274$	−129.172	+	34.6116i	−0.471432	+	0.126320i
$275$	−327.804	+	567.774i	−1.19202	+	2.06463i
$276$	4.13940	+	15.4484i	0.0149978	+	0.0559726i
$277$	−1.69193	+	6.31439i	−0.00610807	+	0.0227956i	−0.968913	−	0.247403i	$-0.920423\pi$
$277$	−1.69193	+	6.31439i	−0.00610807	+	0.0227956i	0.962805	+	0.270199i	$0.0870894\pi$
$278$	175.399	+	46.9980i	0.630932	+	0.169058i
$279$	−106.081	+	28.4242i	−0.380217	+	0.101879i
$280$	−273.214	−	157.740i	−0.975765	−	0.563358i
$281$	−71.3610	−	266.323i	−0.253954	−	0.947768i	−0.968670	−	0.248353i	$-0.920111\pi$
$281$	−71.3610	−	266.323i	−0.253954	−	0.947768i	0.714716	−	0.699415i	$-0.246556\pi$
$282$	−92.2230	+	92.2230i	−0.327032	+	0.327032i
$283$	−87.7544	+	327.504i	−0.310086	+	1.15726i	0.618392	+	0.785870i	$0.287785\pi$
$283$	−87.7544	+	327.504i	−0.310086	+	1.15726i	−0.928478	+	0.371388i	$0.878882\pi$
$284$	−45.8117	−	26.4494i	−0.161309	−	0.0931317i
$285$	66.5528			0.233519
$286$		−	232.493i		−	0.812913i
$287$	−463.095	−	267.368i	−1.61357	−	0.931596i
$288$	−12.0000	−	12.0000i	−0.0416667	−	0.0416667i
$289$	35.2439	−	20.3481i	0.121951	−	0.0704085i
$290$	73.9079	+	73.9079i	0.254855	+	0.254855i
$291$	−13.3580	+	49.8527i	−0.0459038	+	0.171315i
$292$	−108.076	−	187.193i	−0.370122	−	0.641070i
$293$	−25.2608	−	43.7530i	−0.0862144	−	0.149328i	0.819694	−	0.572802i	$-0.194144\pi$
$293$	−25.2608	−	43.7530i	−0.0862144	−	0.149328i	−0.905908	+	0.423474i	$0.860810\pi$
$294$	74.8094	+	279.193i	0.254454	+	0.949635i
$295$			971.305i			3.29256i
$296$	54.4505	+	89.3708i	0.183954	+	0.301929i
$297$	68.8256			0.231736
$298$	78.5214	−	21.0397i	0.263494	−	0.0706031i
$299$	49.6259	−	28.6515i	0.165973	−	0.0958245i
$300$	148.490	−	85.7309i	0.494968	−	0.285770i
$301$	−354.057	−	94.8692i	−1.17627	−	0.315180i
$302$	−40.2934	+	40.2934i	−0.133422	+	0.133422i
$303$	−118.229	−	204.778i	−0.390193	−	0.675835i
$304$	12.5916	−	12.5916i	0.0414199	−	0.0414199i
$305$	−275.951	+	477.961i	−0.904757	+	1.56709i
$306$	66.8541			0.218477
$307$		−	282.699i		−	0.920843i	−0.887701	−	0.460421i	$-0.847698\pi$
$307$		−	282.699i		−	0.920843i	0.887701	−	0.460421i	$-0.152302\pi$
$308$	171.170	−	296.475i	0.555746	−	0.962580i
$309$	−31.5184	−	8.44534i	−0.102001	−	0.0273312i
$310$	−315.965	−	315.965i	−1.01924	−	1.01924i
$311$	286.637	−	76.8042i	0.921663	−	0.246959i	0.233367	−	0.972389i	$-0.425026\pi$
$311$	286.637	−	76.8042i	0.921663	−	0.246959i	0.688296	+	0.725430i	$0.258359\pi$
$312$	−30.4021	+	52.6579i	−0.0974425	+	0.168775i
$313$	−79.3492	−	296.135i	−0.253512	−	0.946119i	−0.968912	−	0.247404i	$-0.920422\pi$
$313$	−79.3492	−	296.135i	−0.253512	−	0.946119i	0.715401	−	0.698715i	$-0.246244\pi$
$314$	95.8899	−	357.866i	0.305382	−	1.13970i
$315$	−323.216	−	86.6055i	−1.02608	−	0.274938i
$316$	−274.503	+	73.5528i	−0.868680	+	0.232762i
$317$	357.471	+	206.386i	1.12767	+	0.651060i	0.943347	−	0.331807i	$-0.107658\pi$
$317$	357.471	+	206.386i	1.12767	+	0.651060i	0.184321	+	0.982866i	$0.440991\pi$
$318$	23.6196	+	88.1497i	0.0742756	+	0.277200i
$319$	−80.2001	+	80.2001i	−0.251411	+	0.251411i
$320$	17.8713	−	66.6964i	0.0558477	−	0.208426i
$321$	−270.474	−	156.158i	−0.842599	−	0.486475i
$322$	84.3771			0.262041
$323$			70.1502i			0.217183i
$324$	−15.5885	−	9.00000i	−0.0481125	−	0.0277778i
$325$	−434.399	−	434.399i	−1.33661	−	1.33661i
$326$	86.5580	−	49.9743i	0.265515	−	0.153295i
$327$	90.6400	+	90.6400i	0.277187	+	0.277187i
$328$	30.2916	−	113.050i	0.0923523	−	0.344664i
$329$	344.039	+	595.893i	1.04571	+	1.81122i
$330$	140.017	+	242.517i	0.424295	+	0.734901i
$331$	87.6889	+	327.259i	0.264921	+	0.988699i	0.962299	+	0.271995i	$0.0876834\pi$
$331$	87.6889	+	327.259i	0.264921	+	0.988699i	−0.697378	+	0.716704i	$0.745650\pi$
$332$			53.7879i			0.162012i
$333$	80.3195	+	76.6144i	0.241200	+	0.230073i
$334$	−12.2362			−0.0366353
$335$	733.040	−	196.417i	2.18818	−	0.586320i
$336$	−77.5372	+	44.7662i	−0.230766	+	0.133233i
$337$	−450.823	+	260.283i	−1.33775	+	0.772352i	−0.986474	−	0.163919i	$-0.947586\pi$
$337$	−450.823	+	260.283i	−1.33775	+	0.772352i	−0.351279	+	0.936271i	$0.614253\pi$
$338$	−20.4255	−	5.47300i	−0.0604305	−	0.0161923i
$339$	18.0780	−	18.0780i	0.0533274	−	0.0533274i
$340$	136.007	+	235.571i	0.400020	+	0.692855i
$341$	342.866	−	342.866i	1.00547	−	1.00547i
$342$	9.44373	−	16.3570i	0.0276132	−	0.0478275i
$343$	891.687			2.59967
$344$		−	80.2259i		−	0.233215i
$345$	−34.5104	+	59.7737i	−0.100030	+	0.173257i
$346$	360.338	+	96.5524i	1.04144	+	0.279053i
$347$	−366.677	−	366.677i	−1.05671	−	1.05671i	−0.998292	−	0.0584143i	$-0.981396\pi$
$347$	−366.677	−	366.677i	−1.05671	−	1.05671i	−0.0584143	−	0.998292i	$-0.518604\pi$
$348$	28.6521	−	7.67731i	0.0823336	−	0.0220612i
$349$	−117.841	+	204.106i	−0.337653	+	0.584832i	−0.983991	−	0.178220i	$-0.942966\pi$
$349$	−117.841	+	204.106i	−0.337653	+	0.584832i	0.646338	+	0.763051i	$0.276300\pi$
$350$	−234.125	−	873.765i	−0.668928	−	2.49647i
$351$	−16.6919	+	62.2950i	−0.0475552	+	0.177479i
$352$	72.3747	+	19.3927i	0.205610	+	0.0550930i
$353$	236.057	−	63.2512i	0.668716	−	0.179182i	0.0915394	−	0.995801i	$-0.470821\pi$
$353$	236.057	−	63.2512i	0.668716	−	0.179182i	0.577176	+	0.816620i	$0.304155\pi$
$354$	238.722	+	137.826i	0.674357	+	0.389340i
$355$	−59.0855	−	220.510i	−0.166438	−	0.621155i
$356$	−101.438	+	101.438i	−0.284938	+	0.284938i
$357$	91.2868	−	340.687i	0.255705	−	0.954305i
$358$	52.7253	+	30.4410i	0.147277	+	0.0850307i
$359$	−318.760			−0.887911			−0.443955	−	0.896049i	$-0.646425\pi$
$359$	−318.760			−0.887911			−0.443955	+	0.896049i	$0.646425\pi$
$360$		−	73.2377i		−	0.203438i
$361$	−295.472	−	170.591i	−0.818481	−	0.472550i
$362$	80.9325	+	80.9325i	0.223571	+	0.223571i
$363$	−81.6644	+	47.1490i	−0.224971	+	0.129887i
$364$	226.830	+	226.830i	0.623161	+	0.623161i
$365$	241.431	−	901.032i	0.661454	−	2.46858i
$366$	78.3139	+	135.644i	0.213972	+	0.370611i
$367$	−37.3197	−	64.6397i	−0.101689	−	0.176130i	0.810692	−	0.585473i	$-0.199091\pi$
$367$	−37.3197	−	64.6397i	−0.101689	−	0.176130i	−0.912380	+	0.409343i	$0.865758\pi$
$368$	4.77977	+	17.8383i	0.0129885	+	0.0484737i
$369$		−	124.137i		−	0.336415i
$370$	−106.562	+	438.881i	−0.288006	+	1.18617i
$371$	481.460			1.29774
$372$	−122.491	+	32.8214i	−0.329278	+	0.0882297i
$373$	−293.775	+	169.611i	−0.787601	+	0.454722i	−0.839117	−	0.543950i	$-0.816928\pi$
$373$	−293.775	+	169.611i	−0.787601	+	0.454722i	0.0515163	+	0.998672i	$0.483595\pi$
$374$	−255.626	+	147.586i	−0.683492	+	0.394615i
$375$	353.738	+	94.7839i	0.943302	+	0.252757i
$376$	−106.490	+	106.490i	−0.283218	+	0.283218i
$377$	−53.1397	−	92.0407i	−0.140954	−	0.244140i
$378$	−67.1492	+	67.1492i	−0.177643	+	0.177643i
$379$	−191.809	+	332.223i	−0.506093	+	0.876578i	0.493882	+	0.869529i	$0.335577\pi$
$379$	−191.809	+	332.223i	−0.506093	+	0.876578i	−0.999975	+	0.00704971i	$0.997756\pi$
$380$	76.8486			0.202233
$381$		−	267.392i		−	0.701816i
$382$	−103.726	+	179.658i	−0.271533	+	0.470309i
$383$	−45.5100	−	12.1944i	−0.118825	−	0.0318391i	0.198916	−	0.980016i	$-0.436258\pi$
$383$	−45.5100	−	12.1944i	−0.118825	−	0.0318391i	−0.317742	+	0.948177i	$0.602924\pi$
$384$	−13.8564	−	13.8564i	−0.0360844	−	0.0360844i
$385$	1427.05	−	382.377i	3.70663	−	0.993188i
$386$	205.840	−	356.526i	0.533265	−	0.923642i
$387$	−22.0235	−	82.1930i	−0.0569084	−	0.212385i
$388$	−15.4245	+	57.5650i	−0.0397538	+	0.148363i
$389$	403.816	+	108.202i	1.03809	+	0.278155i	0.737321	−	0.675543i	$-0.236091\pi$
$389$	403.816	+	108.202i	1.03809	+	0.278155i	0.300767	+	0.953698i	$0.402757\pi$
$390$	−253.463	+	67.9153i	−0.649906	+	0.174142i
$391$	−63.0047	−	36.3758i	−0.161137	−	0.0930326i
$392$	86.3825	+	322.384i	0.220364	+	0.822408i
$393$	178.688	−	178.688i	0.454677	−	0.454677i
$394$	−58.1845	+	217.147i	−0.147676	+	0.551135i
$395$	−1062.12	−	613.214i	−2.68890	−	1.55244i
$396$	79.4729			0.200689
$397$		−	392.565i		−	0.988828i	−0.869227	−	0.494414i	$-0.835383\pi$
$397$		−	392.565i		−	0.988828i	0.869227	−	0.494414i	$-0.164617\pi$
$398$	−370.326	−	213.808i	−0.930468	−	0.537206i
$399$	−70.4599	−	70.4599i	−0.176591	−	0.176591i
$400$	171.462	−	98.9935i	0.428655	−	0.247484i
$401$	487.920	+	487.920i	1.21676	+	1.21676i	0.968761	+	0.247998i	$0.0797725\pi$
$401$	487.920	+	487.920i	1.21676	+	1.21676i	0.247998	+	0.968761i	$0.420227\pi$
$402$	55.7425	−	208.034i	0.138663	−	0.517497i
$403$	227.179	+	393.486i	0.563720	+	0.976391i
$404$	−136.519	−	236.457i	−0.337917	−	0.585290i
$405$	−20.1052	−	75.0335i	−0.0496424	−	0.185268i
$406$		−	156.493i		−	0.385452i
$407$	−476.246	−	115.634i	−1.17014	−	0.284114i
$408$	77.1965			0.189207
$409$	34.5191	−	9.24937i	0.0843988	−	0.0226146i	−0.216373	−	0.976311i	$-0.569423\pi$
$409$	34.5191	−	9.24937i	0.0843988	−	0.0226146i	0.300771	+	0.953696i	$0.402756\pi$
$410$	437.416	−	252.542i	1.06687	−	0.615957i
$411$	−141.841	+	81.8920i	−0.345112	+	0.199251i
$412$	−36.3943	−	9.75183i	−0.0883358	−	0.0236695i
$413$	1028.33	−	1028.33i	2.48989	−	2.48989i
$414$	9.79392	+	16.9636i	0.0236568	+	0.0409748i
$415$	−164.138	+	164.138i	−0.395512	+	0.395512i
$416$	−35.1053	+	60.8041i	−0.0843877	+	0.146164i
$417$	222.397			0.533326
$418$			83.3912i			0.199500i
$419$	158.171	−	273.961i	0.377498	−	0.653845i	−0.613200	−	0.789928i	$-0.710118\pi$
$419$	158.171	−	273.961i	0.377498	−	0.653845i	0.990697	+	0.136083i	$0.0434513\pi$
$420$	−373.218	−	100.003i	−0.888614	−	0.238103i
$421$	−108.805	−	108.805i	−0.258443	−	0.258443i	0.565977	−	0.824421i	$-0.308499\pi$
$421$	−108.805	−	108.805i	−0.258443	−	0.258443i	−0.824421	+	0.565977i	$0.808499\pi$
$422$	542.924	−	145.476i	1.28655	−	0.344730i
$423$	−79.8674	+	138.334i	−0.188812	+	0.327032i
$424$	27.2736	+	101.786i	0.0643245	+	0.240062i
$425$	−201.867	+	753.377i	−0.474981	+	1.77265i
$426$	−62.5800	−	16.7683i	−0.146901	−	0.0393621i
$427$	798.171	−	213.869i	1.86925	−	0.500865i
$428$	−312.317	−	180.316i	−0.729712	−	0.421299i
$429$	−73.6974	−	275.042i	−0.171789	−	0.641124i
$430$	244.815	−	244.815i	0.569338	−	0.569338i
$431$	−139.505	+	520.639i	−0.323677	+	1.20798i	0.591959	+	0.805968i	$0.298355\pi$
$431$	−139.505	+	520.639i	−0.323677	+	1.20798i	−0.915635	+	0.402010i	$0.868312\pi$
$432$	−18.0000	−	10.3923i	−0.0416667	−	0.0240563i
$433$	358.433			0.827791			0.413895	−	0.910324i	$-0.364168\pi$
$433$	358.433			0.827791			0.413895	+	0.910324i	$0.364168\pi$
$434$			669.029i			1.54154i
$435$	110.862	+	64.0061i	0.254855	+	0.147140i
$436$	104.662	+	104.662i	0.240051	+	0.240051i
$437$	−17.7999	+	10.2768i	−0.0407321	+	0.0235167i
$438$	−187.193	−	187.193i	−0.427380	−	0.427380i
$439$	−26.5492	+	99.0828i	−0.0604764	+	0.225701i	−0.989549	−	0.144196i	$-0.953940\pi$
$439$	−26.5492	+	99.0828i	−0.0604764	+	0.225701i	0.929073	+	0.369897i	$0.120607\pi$
$440$	161.678	+	280.035i	0.367451	+	0.636443i
$441$	177.001	+	306.575i	0.401363	+	0.695181i
$442$	−71.5864	−	267.164i	−0.161960	−	0.604443i
$443$			342.682i			0.773549i	0.922174	+	0.386774i	$0.126411\pi$
$443$			342.682i			0.773549i	−0.922174	+	0.386774i	$0.873589\pi$
$444$	92.7450	+	88.4667i	0.208885	+	0.199249i
$445$	−619.090			−1.39121
$446$	7.36285	−	1.97287i	0.0165086	−	0.00442348i
$447$	86.2224	−	49.7805i	0.192891	−	0.111366i
$448$	−89.5323	+	51.6915i	−0.199849	+	0.115383i
$449$	−245.503	−	65.7825i	−0.546778	−	0.146509i	−0.0251532	−	0.999684i	$-0.508007\pi$
$449$	−245.503	−	65.7825i	−0.546778	−	0.146509i	−0.521625	+	0.853175i	$0.674674\pi$
$450$	148.490	−	148.490i	0.329978	−	0.329978i
$451$	274.043	+	474.656i	0.607634	+	1.05245i
$452$	20.8747	−	20.8747i	0.0461829	−	0.0461829i
$453$	−34.8951	+	60.4401i	−0.0770311	+	0.133422i
$454$	−314.077			−0.691799
$455$			1384.38i			3.04259i
$456$	10.9047	−	18.8875i	0.0239138	−	0.0414199i
$457$	21.5568	+	5.77614i	0.0471703	+	0.0126392i	0.282327	−	0.959318i	$-0.408894\pi$
$457$	21.5568	+	5.77614i	0.0471703	+	0.0126392i	−0.235157	+	0.971957i	$0.575560\pi$
$458$	−213.356	−	213.356i	−0.465842	−	0.465842i
$459$	79.0892	−	21.1919i	0.172308	−	0.0461697i
$460$	−39.8492	+	69.0208i	−0.0866286	+	0.150045i
$461$	−56.5725	−	211.132i	−0.122717	−	0.457986i	0.877031	−	0.480434i	$-0.159521\pi$
$461$	−56.5725	−	211.132i	−0.122717	−	0.457986i	−0.999748	+	0.0224476i	$0.992854\pi$
$462$	108.517	−	404.992i	0.234886	−	0.876606i
$463$	−116.780	−	31.2911i	−0.252225	−	0.0675834i	0.130491	−	0.991449i	$-0.458345\pi$
$463$	−116.780	−	31.2911i	−0.252225	−	0.0675834i	−0.382716	+	0.923866i	$0.625011\pi$
$464$	33.0846	−	8.86499i	0.0713030	−	0.0191056i
$465$	−473.948	−	273.634i	−1.01924	−	0.588460i
$466$	−69.1771	−	258.172i	−0.148449	−	0.554018i
$467$	−112.257	+	112.257i	−0.240380	+	0.240380i	−0.817007	−	0.576628i	$-0.804368\pi$
$467$	−112.257	+	112.257i	−0.240380	+	0.240380i	0.576628	+	0.817007i	$0.304368\pi$
$468$	−19.2741	+	71.9320i	−0.0411840	+	0.153701i
$469$	−984.022	−	568.125i	−2.09813	−	1.21135i
$470$	−649.923			−1.38282
$471$		−	453.756i		−	0.963389i
$472$	275.653	+	159.148i	0.584010	+	0.337179i
$473$	265.658	+	265.658i	0.561644	+	0.561644i
$474$	−301.425	+	174.028i	−0.635918	+	0.367147i
$475$	155.811	+	155.811i	0.328024	+	0.328024i
$476$	105.409	−	393.391i	0.221447	−	0.826452i
$477$	55.8846	+	96.7950i	0.117159	+	0.202925i
$478$	174.034	+	301.436i	0.364088	+	0.630618i
$479$	−180.423	−	673.350i	−0.376667	−	1.40574i	−0.850894	−	0.525338i	$-0.823939\pi$
$479$	−180.423	−	673.350i	−0.376667	−	1.40574i	0.474227	−	0.880403i	$-0.342728\pi$
$480$		−	84.5677i		−	0.176183i
$481$	220.164	−	403.012i	0.457720	−	0.837864i
$482$	195.094			0.404759
$483$	99.8192	−	26.7465i	0.206665	−	0.0553757i
$484$	−94.2980	+	54.4429i	−0.194830	+	0.112485i
$485$	−222.733	+	128.595i	−0.459242	+	0.265144i
$486$	−21.2942	−	5.70577i	−0.0438153	−	0.0117403i
$487$	−363.592	+	363.592i	−0.746596	+	0.746596i	−0.973838	−	0.227242i	$-0.927029\pi$
$487$	−363.592	+	363.592i	−0.746596	+	0.746596i	0.227242	+	0.973838i	$0.427029\pi$
$488$	90.4291	+	156.628i	0.185305	+	0.320959i
$489$	86.5580	−	86.5580i	0.177010	−	0.177010i
$490$	−720.175	+	1247.38i	−1.46975	+	2.54567i
$491$	224.922			0.458090			0.229045	−	0.973416i	$-0.426440\pi$
$491$	224.922			0.458090			0.229045	+	0.973416i	$0.426440\pi$
$492$		−	143.341i		−	0.291344i
$493$	−67.4658	+	116.854i	−0.136848	+	0.237027i
$494$	−75.4785	−	20.2244i	−0.152790	−	0.0409401i
$495$	242.517	+	242.517i	0.489934	+	0.489934i
$496$	−141.441	+	37.8989i	−0.285163	+	0.0764092i
$497$	−170.901	+	296.010i	−0.343866	+	0.595593i
$498$	17.0501	+	63.6317i	0.0342371	+	0.127775i
$499$	−96.7698	+	361.150i	−0.193927	+	0.723747i	0.798614	+	0.601843i	$0.205567\pi$
$499$	−96.7698	+	361.150i	−0.193927	+	0.723747i	−0.992542	+	0.121904i	$0.961100\pi$
$500$	408.462	+	109.447i	0.816923	+	0.218894i
$501$	−14.4756	+	3.87872i	−0.0288933	+	0.00774195i
$502$	75.5663	+	43.6282i	0.150530	+	0.0869088i
$503$	4.47789	+	16.7117i	0.00890236	+	0.0332241i	0.970234	−	0.242169i	$-0.0778588\pi$
$503$	4.47789	+	16.7117i	0.00890236	+	0.0332241i	−0.961332	+	0.275393i	$0.911192\pi$
$504$	−77.5372	+	77.5372i	−0.153844	+	0.153844i
$505$	304.970	−	1138.16i	0.603901	−	2.25379i
$506$	−74.8969	−	43.2418i	−0.148018	−	0.0854580i
$507$	−25.8985			−0.0510819
$508$		−	308.758i		−	0.607790i
$509$	−14.6995	−	8.48678i	−0.0288792	−	0.0166734i	0.485491	−	0.874242i	$-0.338641\pi$
$509$	−14.6995	−	8.48678i	−0.0288792	−	0.0166734i	−0.514370	+	0.857568i	$0.671974\pi$
$510$	235.571	+	235.571i	0.461903	+	0.461903i
$511$	−1209.53	+	698.324i	−2.36699	+	1.36658i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	5.98708	−	22.3441i	0.0116707	−	0.0435557i
$514$	231.317	+	400.653i	0.450033	+	0.779480i
$515$	−81.3015	−	140.818i	−0.157867	−	0.273434i
$516$	−25.4306	−	94.9083i	−0.0492841	−	0.183931i
$517$		−	705.255i		−	1.36413i
$518$	577.464	−	351.828i	1.11480	−	0.679205i
$519$	456.891			0.880329
$520$	−292.674	+	78.4219i	−0.562835	+	0.150811i
$521$	154.105	−	88.9727i	0.295787	−	0.170773i	−0.344762	−	0.938690i	$-0.612040\pi$
$521$	154.105	−	88.9727i	0.295787	−	0.170773i	0.640549	+	0.767917i	$0.278707\pi$
$522$	31.4622	−	18.1647i	0.0602724	−	0.0347983i
$523$	−98.0174	−	26.2637i	−0.187414	−	0.0502174i	0.163891	−	0.986478i	$-0.447595\pi$
$523$	−98.0174	−	26.2637i	−0.187414	−	0.0502174i	−0.351305	+	0.936261i	$0.614262\pi$
$524$	206.331	−	206.331i	0.393762	−	0.393762i
$525$	−553.945	−	959.461i	−1.05513	−	1.82754i
$526$	359.266	−	359.266i	0.683015	−	0.683015i
$527$	288.425	−	499.566i	0.547296	−	0.947944i
$528$	91.7674			0.173802
$529$			507.684i			0.959706i
$530$	−227.381	+	393.836i	−0.429021	+	0.743087i
$531$	326.101	+	87.3785i	0.614126	+	0.164555i
$532$	−81.3601	−	81.3601i	−0.152932	−	0.152932i
$533$	−496.080	+	132.924i	−0.930731	+	0.249389i
$534$	−87.8478	+	152.157i	−0.164509	+	0.284938i
$535$	−402.809	−	1503.30i	−0.752915	−	2.80992i
$536$	64.3659	−	240.217i	0.120086	−	0.448166i
$537$	72.0241	+	19.2988i	0.134123	+	0.0359382i
$538$	−631.409	+	169.186i	−1.17362	+	0.314471i
$539$	−1353.58	−	781.488i	−2.51128	−	1.44989i
$540$	−23.2154	−	86.6412i	−0.0429915	−	0.160447i
$541$	123.584	−	123.584i	0.228437	−	0.228437i	−0.583603	−	0.812039i	$-0.698357\pi$
$541$	123.584	−	123.584i	0.228437	−	0.228437i	0.812039	+	0.583603i	$0.198357\pi$
$542$	−30.2272	+	112.810i	−0.0557698	+	0.208136i
$543$	121.399	+	70.0896i	0.223571	+	0.129078i
$544$	89.1388			0.163858
$545$			638.768i			1.17205i
$546$	340.246	+	196.441i	0.623161	+	0.359782i
$547$	582.996	+	582.996i	1.06581	+	1.06581i	0.997677	+	0.0681290i	$0.0217029\pi$
$547$	582.996	+	582.996i	1.06581	+	1.06581i	0.0681290	+	0.997677i	$0.478297\pi$
$548$	−163.784	+	94.5607i	−0.298876	+	0.172556i
$549$	135.644	+	135.644i	0.247074	+	0.247074i
$550$	−239.969	+	895.578i	−0.436308	+	1.62832i
$551$	19.0603	+	33.0134i	0.0345922	+	0.0599154i
$552$	11.3090	+	19.5878i	0.0204874	+	0.0354852i
$553$	475.257	+	1773.68i	0.859416	+	3.20738i
$554$			9.24490i			0.0166876i
$555$	13.0555	+	552.981i	0.0235234	+	0.996362i
$556$	256.802			0.461874
$557$	87.0469	−	23.3241i	0.156278	−	0.0418746i	−0.179832	−	0.983697i	$-0.557555\pi$
$557$	87.0469	−	23.3241i	0.156278	−	0.0418746i	0.336110	+	0.941823i	$0.390889\pi$
$558$	−134.505	+	77.6564i	−0.241048	+	0.139169i
$559$	−304.879	+	176.022i	−0.545401	+	0.314887i
$560$	−430.955	−	115.474i	−0.769562	−	0.206204i
$561$	−255.626	+	255.626i	−0.455662	+	0.455662i
$562$	−194.962	−	337.684i	−0.346907	−	0.600861i
$563$	115.035	−	115.035i	0.204326	−	0.204326i	−0.597525	−	0.801850i	$-0.703849\pi$
$563$	115.035	−	115.035i	0.204326	−	0.204326i	0.801850	+	0.597525i	$0.203849\pi$
$564$	−92.2230	+	159.735i	−0.163516	+	0.283218i
$565$	127.401			0.225489
$566$			479.499i			0.847172i
$567$	−58.1529	+	100.724i	−0.102562	+	0.177643i
$568$	−72.2611	−	19.3623i	−0.127220	−	0.0340886i
$569$	−257.854	−	257.854i	−0.453170	−	0.453170i	0.443235	−	0.896405i	$-0.353831\pi$
$569$	−257.854	−	257.854i	−0.453170	−	0.453170i	−0.896405	+	0.443235i	$0.853831\pi$
$570$	90.9129	−	24.3600i	0.159496	−	0.0427369i
$571$	−482.525	+	835.758i	−0.845053	+	1.46368i	0.0405217	+	0.999179i	$0.487098\pi$
$571$	−482.525	+	835.758i	−0.845053	+	1.46368i	−0.885575	+	0.464496i	$0.846235\pi$
$572$	−85.0984	−	317.592i	−0.148773	−	0.555230i
$573$	−65.7594	+	245.418i	−0.114763	+	0.428303i
$574$	−730.463	−	195.727i	−1.27258	−	0.340988i
$575$	−220.735	+	59.1457i	−0.383887	+	0.102862i
$576$	−20.7846	−	12.0000i	−0.0360844	−	0.0208333i
$577$	−43.7233	−	163.178i	−0.0757770	−	0.282803i	0.917631	−	0.397433i	$-0.130099\pi$
$577$	−43.7233	−	163.178i	−0.0757770	−	0.282803i	−0.993408	+	0.114629i	$0.963432\pi$
$578$	40.6961	−	40.6961i	0.0704085	−	0.0704085i
$579$	130.498	−	487.023i	0.225384	−	0.841146i
$580$	128.012	+	73.9079i	0.220711	+	0.127427i
$581$	347.547			0.598187
$582$			72.9894i			0.125411i
$583$	−427.366	−	246.740i	−0.733046	−	0.423224i
$584$	−216.151	−	216.151i	−0.370122	−	0.370122i
$585$	−278.322	+	160.689i	−0.475765	+	0.274683i
$586$	−50.5216	−	50.5216i	−0.0862144	−	0.0862144i
$587$	−2.92172	+	10.9040i	−0.00497737	+	0.0185758i	−0.968370	−	0.249519i	$-0.919727\pi$
$587$	−2.92172	+	10.9040i	−0.00497737	+	0.0185758i	0.963392	+	0.268095i	$0.0863941\pi$
$588$	204.383	+	354.002i	0.347590	+	0.602044i
$589$	−81.4851	−	141.136i	−0.138345	−	0.239620i
$590$	355.522	+	1326.83i	0.602580	+	2.24886i
$591$			275.332i			0.465874i
$592$	107.093	+	102.153i	0.180900	+	0.172555i
$593$	596.119			1.00526			0.502630	−	0.864502i	$-0.332366\pi$
$593$	596.119			1.00526			0.502630	+	0.864502i	$0.332366\pi$
$594$	94.0175	−	25.1919i	0.158279	−	0.0424106i
$595$	1522.12	−	878.799i	2.55819	−	1.47697i
$596$	99.5611	−	57.4816i	0.167049	−	0.0964457i
$597$	−505.875	−	135.549i	−0.847362	−	0.227050i
$598$	57.3030	−	57.3030i	0.0958245	−	0.0958245i
$599$	272.940	+	472.745i	0.455659	+	0.789224i	0.998726	−	0.0504652i	$-0.0160704\pi$
$599$	272.940	+	472.745i	0.455659	+	0.789224i	−0.543067	+	0.839689i	$0.682737\pi$
$600$	171.462	−	171.462i	0.285770	−	0.285770i
$601$	−121.877	+	211.098i	−0.202791	+	0.351244i	−0.949427	−	0.313989i	$-0.898335\pi$
$601$	−121.877	+	211.098i	−0.202791	+	0.351244i	0.746636	+	0.665233i	$0.231668\pi$
$602$	−518.375			−0.861088
$603$		−	263.777i		−	0.437440i
$604$	−40.2934	+	69.7902i	−0.0667109	+	0.115547i
$605$	−453.894	−	121.620i	−0.750237	−	0.201026i
$606$	−236.457	−	236.457i	−0.390193	−	0.390193i
$607$	−760.511	+	203.778i	−1.25290	+	0.335714i	−0.823456	−	0.567379i	$-0.807957\pi$
$607$	−760.511	+	203.778i	−1.25290	+	0.335714i	−0.429444	+	0.903093i	$0.641291\pi$
$608$	12.5916	−	21.8094i	0.0207099	−	0.0358706i
$609$	−49.6064	−	185.134i	−0.0814556	−	0.303996i
$610$	−202.010	+	753.912i	−0.331164	+	1.23592i
$611$	638.336	+	171.042i	1.04474	+	0.279937i
$612$	91.3244	−	24.4703i	0.149223	−	0.0399841i
$613$	692.435	+	399.778i	1.12958	+	0.652166i	0.943830	−	0.330431i	$-0.107194\pi$
$613$	692.435	+	399.778i	1.12958	+	0.652166i	0.185754	+	0.982596i	$0.440527\pi$
$614$	−103.475	−	386.174i	−0.168526	−	0.628947i
$615$	437.416	−	437.416i	0.711246	−	0.711246i
$616$	125.305	−	467.645i	0.203417	−	0.759163i
$617$	728.315	+	420.493i	1.18041	+	0.681512i	0.956110	−	0.293008i	$-0.0946563\pi$
$617$	728.315	+	420.493i	1.18041	+	0.681512i	0.224303	+	0.974520i	$0.427990\pi$
$618$	−46.1462			−0.0746702
$619$		−	115.168i		−	0.186056i	−0.995664	−	0.0930278i	$-0.970345\pi$
$619$		−	115.168i		−	0.186056i	0.995664	−	0.0930278i	$-0.0296545\pi$
$620$	−547.268	−	315.965i	−0.882691	−	0.509622i
$621$	16.9636	+	16.9636i	0.0273165	+	0.0273165i
$622$	363.441	−	209.833i	0.584311	−	0.337352i
$623$	655.434	+	655.434i	1.05206	+	1.05206i
$624$	−22.2558	+	83.0600i	−0.0356664	+	0.133109i
$625$	293.755	+	508.799i	0.470009	+	0.814079i
$626$	−216.786	−	375.484i	−0.346304	−	0.599815i
$627$	26.4339	+	98.6528i	0.0421594	+	0.157341i
$628$		−	523.952i		−	0.834319i
$629$	−582.871	+	13.7611i	−0.926663	+	0.0218778i
$630$	−473.221			−0.751145
$631$	411.795	−	110.340i	0.652607	−	0.174866i	0.0826998	−	0.996575i	$-0.473646\pi$
$631$	411.795	−	110.340i	0.652607	−	0.174866i	0.569907	+	0.821709i	$0.306979\pi$
$632$	−348.056	+	200.950i	−0.550721	+	0.317959i
$633$	596.172	−	344.200i	0.941820	−	0.543760i
$634$	563.857	+	151.085i	0.889364	+	0.238304i
$635$	942.196	−	942.196i	1.48377	−	1.48377i
$636$	64.5300	+	111.769i	0.101462	+	0.175738i
$637$	1035.61	−	1035.61i	1.62576	−	1.62576i
$638$	−80.2001	+	138.911i	−0.125706	+	0.217728i
$639$	−79.3482			−0.124176
$640$		−	97.6503i		−	0.152579i
$641$	−277.571	+	480.767i	−0.433028	+	0.750027i	−0.997132	−	0.0756766i	$-0.975888\pi$
$641$	−277.571	+	480.767i	−0.433028	+	0.750027i	0.564104	+	0.825704i	$0.309222\pi$
$642$	−426.632	−	114.316i	−0.664537	−	0.178062i
$643$	129.409	+	129.409i	0.201258	+	0.201258i	0.800539	−	0.599281i	$-0.204547\pi$
$643$	129.409	+	129.409i	0.201258	+	0.201258i	−0.599281	+	0.800539i	$0.704547\pi$
$644$	115.261	−	30.8842i	0.178977	−	0.0479568i
$645$	212.016	−	367.223i	0.328707	−	0.569338i
$646$	25.6768	+	95.8270i	0.0397473	+	0.148339i
$647$	231.442	−	863.753i	0.357715	−	1.33501i	−0.519317	−	0.854581i	$-0.673814\pi$
$647$	231.442	−	863.753i	0.357715	−	1.33501i	0.877033	−	0.480430i	$-0.159520\pi$
$648$	−24.5885	−	6.58846i	−0.0379452	−	0.0101674i
$649$	−1439.79	+	385.790i	−2.21847	+	0.594438i
$650$	−752.402	−	434.399i	−1.15754	−	0.668307i
$651$	212.074	+	791.470i	0.325766	+	1.21578i
$652$	99.9486	−	99.9486i	0.153295	−	0.153295i
$653$	150.712	−	562.463i	0.230799	−	0.861353i	−0.749199	−	0.662345i	$-0.769561\pi$
$653$	150.712	−	562.463i	0.230799	−	0.861353i	0.979998	−	0.199008i	$-0.0637720\pi$
$654$	156.993	+	90.6400i	0.240051	+	0.138593i
$655$	1259.27			1.92255
$656$		−	165.516i		−	0.252311i
$657$	−280.789	−	162.113i	−0.427380	−	0.246748i
$658$	688.078	+	688.078i	1.04571	+	1.04571i
$659$	−996.667	+	575.426i	−1.51239	+	0.873181i	−0.512499	+	0.858688i	$0.671280\pi$
$659$	−996.667	+	575.426i	−1.51239	+	0.873181i	−0.999895	+	0.0144927i	$0.995387\pi$
$660$	280.035	+	280.035i	0.424295	+	0.424295i
$661$	123.143	−	459.576i	0.186298	−	0.695274i	−0.808051	−	0.589113i	$-0.799477\pi$
$661$	123.143	−	459.576i	0.186298	−	0.695274i	0.994349	−	0.106161i	$-0.0338560\pi$
$662$	239.570	+	414.948i	0.361889	+	0.626810i
$663$	−169.375	−	293.366i	−0.255468	−	0.442483i
$664$	19.6877	+	73.4756i	0.0296502	+	0.110656i
$665$		−	496.552i		−	0.746695i
$666$	137.761	+	75.2583i	0.206849	+	0.113000i
$667$	−39.5342			−0.0592716
$668$	−16.7149	+	4.47876i	−0.0250224	+	0.00670472i
$669$	8.08498	−	4.66786i	0.0120852	−	0.00697737i
$670$	929.457	−	536.622i	1.38725	−	0.800929i
$671$	−818.097	−	219.208i	−1.21922	−	0.326689i
$672$	−89.5323	+	89.5323i	−0.133233	+	0.133233i
$673$	−636.394	−	1102.27i	−0.945608	−	1.63784i	−0.754529	−	0.656267i	$-0.772135\pi$
$673$	−636.394	−	1102.27i	−0.945608	−	1.63784i	−0.191079	−	0.981575i	$-0.561199\pi$
$674$	−520.565	+	520.565i	−0.772352	+	0.772352i
$675$	128.596	−	222.735i	0.190513	−	0.329978i
$676$	−29.9050			−0.0442382
$677$		−	24.4441i		−	0.0361065i	−0.999837	−	0.0180533i	$-0.994253\pi$
$677$		−	24.4441i		−	0.0361065i	0.999837	−	0.0180533i	$-0.00574685\pi$
$678$	18.0780	−	31.3120i	0.0266637	−	0.0461829i
$679$	371.952	+	99.6643i	0.547794	+	0.146781i
$680$	272.014	+	272.014i	0.400020	+	0.400020i
$681$	−371.557	+	99.5583i	−0.545604	+	0.146194i
$682$	342.866	−	593.860i	0.502735	−	0.870763i
$683$	107.529	+	401.305i	0.157437	+	0.587562i	0.998884	+	0.0472235i	$0.0150373\pi$
$683$	107.529	+	401.305i	0.157437	+	0.587562i	−0.841447	+	0.540339i	$0.818296\pi$
$684$	6.91329	−	25.8007i	0.0101071	−	0.0377204i
$685$	−788.358	−	211.240i	−1.15089	−	0.308379i
$686$	1218.07	−	326.380i	1.77561	−	0.475773i
$687$	−320.034	−	184.772i	−0.465842	−	0.268954i
$688$	−29.3647	−	109.591i	−0.0426813	−	0.159289i
$689$	326.974	−	326.974i	0.474563	−	0.474563i
$690$	−25.2634	+	94.2841i	−0.0366136	+	0.136644i
$691$	−994.065	−	573.924i	−1.43859	−	0.830570i	−0.440838	−	0.897587i	$-0.645319\pi$
$691$	−994.065	−	573.924i	−1.43859	−	0.830570i	−0.997752	+	0.0670169i	$0.978652\pi$
$692$	527.572			0.762387
$693$		−	513.509i		−	0.740995i
$694$	−635.104	−	366.677i	−0.915135	−	0.528353i
$695$	783.650	+	783.650i	1.12755	+	1.12755i
$696$	36.3294	−	20.9748i	0.0521974	−	0.0301362i
$697$	461.060	+	461.060i	0.661492	+	0.661492i
$698$	−86.2655	+	321.947i	−0.123589	+	0.461242i
$699$	−163.675	−	283.493i	−0.234156	−	0.405569i
$700$	−639.641	−	1107.89i	−0.913772	−	1.58270i
$701$	−259.404	−	968.109i	−0.370049	−	1.38104i	−0.860446	−	0.509541i	$-0.829815\pi$
$701$	−259.404	−	968.109i	−0.370049	−	1.38104i	0.490398	−	0.871499i	$-0.336852\pi$
$702$			91.2062i			0.129923i
$703$	−78.9687	+	144.553i	−0.112331	+	0.205624i
$704$	105.964			0.150517
$705$	−768.868	+	206.017i	−1.09059	+	0.292223i
$706$	299.308	−	172.805i	0.423949	−	0.244767i
$707$	−1527.85	+	882.107i	−2.16104	+	1.24768i
$708$	376.549	+	100.896i	0.531849	+	0.142508i
$709$	−482.069	+	482.069i	−0.679928	+	0.679928i	−0.959984	−	0.280055i	$-0.909647\pi$
$709$	−482.069	+	482.069i	−0.679928	+	0.679928i	0.280055	+	0.959984i	$0.409647\pi$
$710$	−161.425	−	279.596i	−0.227359	−	0.393797i
$711$	−301.425	+	301.425i	−0.423945	+	0.423945i
$712$	−101.438	+	175.696i	−0.142469	+	0.246763i
$713$	169.013			0.237045
$714$		−	498.800i		−	0.698600i
$715$	709.470	−	1228.84i	0.992266	−	1.71865i
$716$	83.1663	+	22.2843i	0.116154	+	0.0311234i
$717$	301.436	+	301.436i	0.420412	+	0.420412i
$718$	−435.434	+	116.674i	−0.606454	+	0.162499i
$719$	−17.6334	+	30.5419i	−0.0245249	+	0.0424783i	−0.878027	−	0.478610i	$-0.841141\pi$
$719$	−17.6334	+	30.5419i	−0.0245249	+	0.0424783i	0.853502	+	0.521089i	$0.174474\pi$
$720$	−26.8069	−	100.045i	−0.0372318	−	0.138951i
$721$	−63.0109	+	235.160i	−0.0873937	+	0.326158i
$722$	−466.062	−	124.881i	−0.645516	−	0.172965i
$723$	230.798	−	61.8422i	0.319223	−	0.0855356i
$724$	140.179	+	80.9325i	0.193618	+	0.111785i
$725$	109.697	+	409.395i	0.151306	+	0.564683i
$726$	−94.2980	+	94.2980i	−0.129887	+	0.129887i
$727$	−193.703	+	722.911i	−0.266442	+	0.994376i	0.694919	+	0.719088i	$0.255440\pi$
$727$	−193.703	+	722.911i	−0.266442	+	0.994376i	−0.961362	+	0.275288i	$0.911227\pi$
$728$	392.882	+	226.830i	0.539673	+	0.311580i
$729$	−27.0000			−0.0370370
$730$		−	1319.20i		−	1.80713i
$731$	387.072	+	223.476i	0.529511	+	0.305713i
$732$	156.628	+	156.628i	0.213972	+	0.213972i
$733$	160.212	−	92.4983i	0.218570	−	0.126191i	−0.386718	−	0.922198i	$-0.626391\pi$
$733$	160.212	−	92.4983i	0.218570	−	0.126191i	0.605288	+	0.796007i	$0.293058\pi$
$734$	−74.6395	−	74.6395i	−0.101689	−	0.101689i
$735$	−456.573	+	1703.95i	−0.621188	+	2.31830i
$736$	13.0586	+	22.6181i	0.0177426	+	0.0307311i
$737$	582.308	+	1008.59i	0.790106	+	1.36850i
$738$	−45.4373	−	169.574i	−0.0615682	−	0.229776i
$739$			1105.39i			1.49580i	0.663813	+	0.747898i	$0.268937\pi$
$739$			1105.39i			1.49580i	−0.663813	+	0.747898i	$0.731063\pi$
$740$	15.0751	+	638.527i	0.0203718	+	0.862875i
$741$	−95.7029			−0.129154
$742$	657.687	−	176.227i	0.886370	−	0.237502i
$743$	−349.037	+	201.516i	−0.469766	+	0.271220i	−0.716142	−	0.697955i	$-0.754094\pi$
$743$	−349.037	+	201.516i	−0.469766	+	0.271220i	0.246375	+	0.969174i	$0.420760\pi$
$744$	−155.313	+	89.6699i	−0.208754	+	0.120524i
$745$	479.227	+	128.409i	0.643258	+	0.172360i
$746$	−339.222	+	339.222i	−0.454722	+	0.454722i
$747$	40.3409	+	69.8725i	0.0540039	+	0.0935375i
$748$	−295.172	+	295.172i	−0.394615	+	0.394615i
$749$	−1165.10	+	2018.01i	−1.55554	+	2.69428i
$750$	517.909			0.690545
$751$			502.543i			0.669165i	0.942366	+	0.334583i	$0.108595\pi$
$751$			502.543i			0.669165i	−0.942366	+	0.334583i	$0.891405\pi$
$752$	−106.490	+	184.446i	−0.141609	+	0.245274i
$753$	103.225	+	27.6592i	0.137086	+	0.0367320i
$754$	−106.279	−	106.279i	−0.140954	−	0.140954i
$755$	−335.928	+	90.0117i	−0.444938	+	0.119221i
$756$	−67.1492	+	116.306i	−0.0888217	+	0.153844i
$757$	272.129	+	1015.60i	0.359484	+	1.34161i	0.874747	+	0.484581i	$0.161028\pi$
$757$	272.129	+	1015.60i	0.359484	+	1.34161i	−0.515263	+	0.857032i	$0.672306\pi$
$758$	−140.414	+	524.032i	−0.185243	+	0.691336i
$759$	−102.311	−	27.4142i	−0.134797	−	0.0361188i
$760$	104.977	−	28.1285i	0.138128	−	0.0370112i
$761$	−865.105	−	499.469i	−1.13680	−	0.656332i	−0.191164	−	0.981558i	$-0.561226\pi$
$761$	−865.105	−	499.469i	−1.13680	−	0.656332i	−0.945636	+	0.325226i	$0.894560\pi$
$762$	−97.8722	−	365.264i	−0.128441	−	0.479349i
$763$	676.267	−	676.267i	0.886327	−	0.886327i
$764$	−75.9325	+	283.384i	−0.0993880	+	0.370921i
$765$	353.356	+	204.010i	0.461903	+	0.266680i
$766$	−66.6313			−0.0869860
$767$		−	1396.74i		−	1.82104i
$768$	−24.0000	−	13.8564i	−0.0312500	−	0.0180422i
$769$	−366.269	−	366.269i	−0.476293	−	0.476293i	0.427651	−	0.903944i	$-0.359341\pi$
$769$	−366.269	−	366.269i	−0.476293	−	0.476293i	−0.903944	+	0.427651i	$0.859341\pi$
$770$	1809.43	−	1044.67i	2.34991	−	1.35672i
$771$	400.653	+	400.653i	0.519654	+	0.519654i
$772$	150.686	−	562.366i	0.195189	−	0.728454i
$773$	284.671	+	493.065i	0.368268	+	0.637858i	0.989295	−	0.145931i	$-0.0466176\pi$
$773$	284.671	+	493.065i	0.368268	+	0.637858i	−0.621027	+	0.783789i	$0.713284\pi$
$774$	−60.1694	−	104.217i	−0.0777383	−	0.134647i
$775$	−468.969	−	1750.22i	−0.605121	−	2.25834i
$776$			84.2809i			0.108609i
$777$	571.622	−	599.266i	0.735679	−	0.771256i
$778$	591.228			0.759933
$779$	177.935	−	47.6775i	0.228415	−	0.0612035i
$780$	−321.379	+	185.548i	−0.412024	+	0.237882i
$781$	303.399	−	175.168i	0.388475	−	0.224286i
$782$	−99.3804	−	26.6289i	−0.127085	−	0.0340523i
$783$	31.4622	−	31.4622i	0.0401816	−	0.0401816i
$784$	236.001	+	408.766i	0.301022	+	0.521386i
$785$	1598.88	−	1598.88i	2.03679	−	2.03679i
$786$	178.688	−	309.497i	0.227339	−	0.393762i
$787$	−1045.99			−1.32908			−0.664541	−	0.747252i	$-0.731373\pi$
$787$	−1045.99			−1.32908			−0.664541	+	0.747252i	$0.731373\pi$
$788$			317.926i			0.403459i
$789$	311.134	−	538.899i	0.394339	−	0.683015i
$790$	−1675.33	−	448.903i	−2.12067	−	0.568232i
$791$	−134.880	−	134.880i	−0.170519	−	0.170519i
$792$	108.562	−	29.0891i	0.137073	−	0.0367287i
$793$	396.817	−	687.307i	0.500400	−	0.866718i
$794$	−143.689	−	536.253i	−0.180968	−	0.675382i
$795$	−144.154	+	537.990i	−0.181326	+	0.676717i
$796$	−584.134	−	156.518i	−0.733837	−	0.196631i
$797$	−1429.45	+	383.019i	−1.79353	+	0.480576i	−0.992939	−	0.118629i	$-0.962150\pi$
$797$	−1429.45	+	383.019i	−1.79353	+	0.480576i	−0.800596	+	0.599205i	$0.795483\pi$
$798$	−122.040	−	70.4599i	−0.152932	−	0.0882956i
$799$	−217.153	−	810.427i	−0.271781	−	1.01430i
$800$	197.987	−	197.987i	0.247484	−	0.247484i
$801$	−55.6933	+	207.850i	−0.0695297	+	0.259488i
$802$	845.102	+	487.920i	1.05374	+	0.608379i
$803$	1431.51			1.78271
$804$		−	304.583i		−	0.378834i
$805$	445.973	+	257.483i	0.554004	+	0.319854i
$806$	454.358	+	454.358i	0.563720	+	0.563720i
$807$	−693.335	+	400.297i	−0.859152	+	0.496031i
$808$	−273.037	−	273.037i	−0.337917	−	0.337917i
$809$	−14.8368	+	55.3716i	−0.0183397	+	0.0684446i	−0.974489	−	0.224434i	$-0.927947\pi$
$809$	−14.8368	+	55.3716i	−0.0183397	+	0.0684446i	0.956150	+	0.292879i	$0.0946133\pi$
$810$	−54.9283	−	95.1386i	−0.0678127	−	0.117455i
$811$	−393.872	−	682.206i	−0.485662	−	0.841192i	0.514202	−	0.857669i	$-0.328088\pi$
$811$	−393.872	−	682.206i	−0.485662	−	0.841192i	−0.999864	+	0.0164775i	$0.994755\pi$
$812$	−57.2806	−	213.774i	−0.0705426	−	0.263269i
$813$			143.037i			0.175937i
$814$	−692.889	+	16.3586i	−0.851215	+	0.0200965i
$815$	610.001			0.748467
$816$	105.452	−	28.2559i	0.129231	−	0.0346273i
$817$	109.355	−	63.1360i	0.133849	−	0.0772778i
$818$	43.7685	−	25.2697i	0.0535067	−	0.0308921i
$819$	464.784	+	124.539i	0.567502	+	0.152062i
$820$	505.085	−	505.085i	0.615957	−	0.615957i
$821$	148.781	+	257.696i	0.181219	+	0.313880i	0.942296	−	0.334781i	$-0.108662\pi$
$821$	148.781	+	257.696i	0.181219	+	0.313880i	−0.761077	+	0.648662i	$0.775329\pi$
$822$	−163.784	+	163.784i	−0.199251	+	0.199251i
$823$	5.37236	−	9.30520i	0.00652778	−	0.0113064i	−0.862743	−	0.505643i	$-0.831255\pi$
$823$	5.37236	−	9.30520i	0.00652778	−	0.0113064i	0.869271	+	0.494336i	$0.164589\pi$
$824$	−53.2850			−0.0646663
$825$			1135.55i			1.37642i
$826$	1028.33	−	1781.11i	1.24495	−	2.15631i
$827$	126.628	+	33.9300i	0.153118	+	0.0410278i	0.334564	−	0.942373i	$-0.391411\pi$
$827$	126.628	+	33.9300i	0.153118	+	0.0410278i	−0.181446	+	0.983401i	$0.558078\pi$
$828$	19.5878	+	19.5878i	0.0236568	+	0.0236568i
$829$	839.753	−	225.011i	1.01297	−	0.271425i	0.286101	−	0.958200i	$-0.407641\pi$
$829$	839.753	−	225.011i	1.01297	−	0.271425i	0.726870	+	0.686775i	$0.240974\pi$
$830$	−164.138	+	284.295i	−0.197756	+	0.342524i
$831$	2.93052	+	10.9368i	0.00352649	+	0.0131611i
$832$	−25.6988	+	95.9094i	−0.0308880	+	0.115276i
$833$	−1796.06	−	481.252i	−2.15613	−	0.577734i
$834$	303.800	−	81.4029i	0.364268	−	0.0976054i
$835$	−64.6741	−	37.3396i	−0.0774540	−	0.0447181i
$836$	30.5233	+	113.914i	0.0365111	+	0.136261i
$837$	−134.505	+	134.505i	−0.160699	+	0.160699i
$838$	115.790	−	432.133i	0.138174	−	0.515671i
$839$	283.276	+	163.550i	0.337636	+	0.194934i	0.659226	−	0.751945i	$-0.270884\pi$
$839$	283.276	+	163.550i	0.337636	+	0.194934i	−0.321590	+	0.946879i	$0.604217\pi$
$840$	−546.429			−0.650510
$841$		−	767.676i		−	0.912814i
$842$	−188.455	−	108.805i	−0.223819	−	0.129222i
$843$	−337.684	−	337.684i	−0.400574	−	0.400574i
$844$	688.400	−	397.448i	0.815640	−	0.470910i
$845$	−91.2574	−	91.2574i	−0.107997	−	0.107997i
$846$	−58.4670	+	218.202i	−0.0691099	+	0.257922i
$847$	351.780	+	609.300i	0.415324	+	0.719363i
$848$	74.5129	+	129.060i	0.0878689	+	0.152193i
$849$	151.995	+	567.254i	0.179028	+	0.668143i
$850$			1103.02i			1.29767i
$851$	−88.8806	−	145.882i	−0.104443	−	0.171424i
$852$	−91.6234			−0.107539
$853$	1137.18	−	304.706i	1.33315	−	0.357217i	0.479263	−	0.877671i	$-0.340904\pi$
$853$	1137.18	−	304.706i	1.33315	−	0.357217i	0.853890	+	0.520454i	$0.174237\pi$
$854$	1012.04	−	584.302i	1.18506	−	0.684194i
$855$	99.8292	−	57.6364i	0.116759	−	0.0674110i
$856$	−492.633	−	132.001i	−0.575506	−	0.154206i
$857$	344.846	−	344.846i	0.402387	−	0.402387i	−0.476686	−	0.879073i	$-0.658162\pi$
$857$	344.846	−	344.846i	0.402387	−	0.402387i	0.879073	+	0.476686i	$0.158162\pi$
$858$	−201.345	−	348.740i	−0.234668	−	0.406457i
$859$	−284.680	+	284.680i	−0.331408	+	0.331408i	−0.853121	−	0.521713i	$-0.825293\pi$
$859$	−284.680	+	284.680i	−0.331408	+	0.331408i	0.521713	+	0.853121i	$0.325293\pi$
$860$	244.815	−	424.032i	0.284669	−	0.493061i
$861$	−926.190			−1.07571
$862$			762.268i			0.884301i
$863$	130.236	−	225.575i	0.150911	−	0.261385i	−0.780652	−	0.624966i	$-0.785113\pi$
$863$	130.236	−	225.575i	0.150911	−	0.261385i	0.931563	+	0.363581i	$0.118446\pi$
$864$	−28.3923	−	7.60770i	−0.0328615	−	0.00880520i
$865$	1609.92	+	1609.92i	1.86118	+	1.86118i
$866$	489.629	−	131.196i	0.565392	−	0.151496i
$867$	35.2439	−	61.0442i	0.0406504	−	0.0704085i
$868$	244.882	+	913.911i	0.282122	+	1.05289i
$869$	487.121	−	1817.96i	0.560554	−	2.09202i
$870$	174.868	+	46.8557i	0.200998	+	0.0538572i
$871$	−1054.11	+	282.448i	−1.21023	+	0.324280i
$872$	181.280	+	104.662i	0.207890	+	0.120025i
$873$	23.1367	+	86.3474i	0.0265025	+	0.0989089i
$874$	−20.5536	+	20.5536i	−0.0235167	+	0.0235167i
$875$	707.185	−	2639.25i	0.808211	−	3.01629i
$876$	−324.227	−	187.193i	−0.370122	−	0.213690i
$877$	578.074			0.659149			0.329574	−	0.944130i	$-0.393095\pi$
$877$	578.074			0.659149			0.329574	+	0.944130i	$0.393095\pi$
$878$			145.067i			0.165225i
$879$	−75.7825	−	43.7530i	−0.0862144	−	0.0497759i
$880$	323.357	+	323.357i	0.367451	+	0.367451i
$881$	1164.41	−	672.274i	1.32169	−	0.763081i	0.337696	−	0.941255i	$-0.390352\pi$
$881$	1164.41	−	672.274i	1.32169	−	0.763081i	0.983999	+	0.178174i	$0.0570191\pi$
$882$	354.002	+	354.002i	0.401363	+	0.401363i
$883$	80.0049	−	298.582i	0.0906058	−	0.338146i	−0.905711	−	0.423896i	$-0.860662\pi$
$883$	80.0049	−	298.582i	0.0906058	−	0.338146i	0.996317	+	0.0857506i	$0.0273288\pi$
$884$	−195.578	−	338.750i	−0.221242	−	0.383202i
$885$	841.175	+	1456.96i	0.950480	+	1.64628i
$886$	125.430	+	468.112i	0.141569	+	0.528344i
$887$			1645.51i			1.85515i	0.373642	+	0.927573i	$0.378109\pi$
$887$			1645.51i			1.85515i	−0.373642	+	0.927573i	$0.621891\pi$
$888$	159.073	+	86.9008i	0.179136	+	0.0978612i
$889$	−1995.02			−2.24411
$890$	−845.693	+	226.603i	−0.950217	+	0.254610i
$891$	103.238	−	59.6047i	0.115868	−	0.0668964i
$892$	9.33573	−	5.38998i	0.0104661	−	0.00604258i
$893$	−228.960	−	61.3496i	−0.256394	−	0.0687006i
$894$	99.5611	−	99.5611i	0.111366	−	0.111366i
$895$	185.786	+	321.790i	0.207582	+	0.359542i
$896$	−103.383	+	103.383i	−0.115383	+	0.115383i
$897$	49.6259	−	85.9546i	0.0553243	−	0.0958245i
$898$	−359.442			−0.400270
$899$		−	313.468i		−	0.348685i
$900$	148.490	−	257.193i	0.164989	−	0.285770i
$901$	−567.070	−	151.946i	−0.629379	−	0.168641i
$902$	548.086	+	548.086i	0.607634	+	0.607634i
$903$	−613.244	+	164.318i	−0.679118	+	0.181969i
$904$	20.8747	−	36.1560i	0.0230915	−	0.0399956i
$905$	180.796	+	674.739i	0.199774	+	0.745568i
$906$	−25.5450	+	95.3352i	−0.0281953	+	0.105226i
$907$	878.702	+	235.447i	0.968800	+	0.259589i	0.708321	−	0.705890i	$-0.249453\pi$
$907$	878.702	+	235.447i	0.968800	+	0.259589i	0.260479	+	0.965480i	$0.416120\pi$
$908$	−429.037	+	114.960i	−0.472507	+	0.126608i
$909$	−354.686	−	204.778i	−0.390193	−	0.225278i
$910$	506.718	+	1891.10i	0.556833	+	2.07813i
$911$	−476.404	+	476.404i	−0.522946	+	0.522946i	−0.918460	−	0.395514i	$-0.870567\pi$
$911$	−476.404	+	476.404i	−0.522946	+	0.522946i	0.395514	+	0.918460i	$0.370567\pi$
$912$	7.98278	−	29.7921i	0.00875305	−	0.0326668i
$913$	−308.498	−	178.112i	−0.337895	−	0.195084i
$914$	31.5614			0.0345311
$915$			955.922i			1.04472i
$916$	−369.543	−	213.356i	−0.403431	−	0.232921i
$917$	−1333.20	−	1333.20i	−1.45387	−	1.45387i
$918$	100.281	−	57.8973i	0.109239	−	0.0630690i
$919$	778.050	+	778.050i	0.846626	+	0.846626i	0.989711	−	0.143084i	$-0.0457019\pi$
$919$	778.050	+	778.050i	0.846626	+	0.846626i	−0.143084	+	0.989711i	$0.545702\pi$
$920$	−29.1716	+	108.870i	−0.0317083	+	0.118337i
$921$	−244.824	−	424.048i	−0.265824	−	0.460421i
$922$	−154.559	−	267.704i	−0.167635	−	0.290352i
$923$	84.9649	+	317.093i	0.0920530	+	0.343546i
$924$		−	592.950i		−	0.641720i
$925$	−1264.06	+	1325.19i	−1.36655	+	1.43263i
$926$	−170.978			−0.184641
$927$	−54.5915	+	14.6278i	−0.0588905	+	0.0157797i
$928$	41.9496	−	24.2196i	0.0452043	−	0.0260987i
$929$	−814.847	+	470.452i	−0.877123	+	0.506407i	−0.869709	−	0.493565i	$-0.835693\pi$
$929$	−814.847	+	470.452i	−0.877123	+	0.506407i	−0.00741430	+	0.999973i	$0.502360\pi$
$930$	−747.582	−	200.314i	−0.803852	−	0.215391i
$931$	−371.455	+	371.455i	−0.398985	+	0.398985i
$932$	−188.995	−	327.349i	−0.202785	−	0.351233i
$933$	363.441	−	363.441i	0.389541	−	0.389541i
$934$	−112.257	+	194.435i	−0.120190	+	0.208175i
$935$	−1801.48			−1.92671
$936$			105.316i			0.112517i
$937$	370.454	−	641.644i	0.395361	−	0.684786i	−0.597786	−	0.801656i	$-0.703953\pi$
$937$	370.454	−	641.644i	0.395361	−	0.684786i	0.993147	+	0.116870i	$0.0372860\pi$
$938$	−1552.15	−	415.897i	−1.65474	−	0.443386i
$939$	−375.484	−	375.484i	−0.399877	−	0.399877i
$940$	−887.812	+	237.888i	−0.944481	+	0.253073i
$941$	−313.412	+	542.846i	−0.333063	+	0.576882i	−0.983111	−	0.183011i	$-0.941415\pi$
$941$	−313.412	+	542.846i	−0.333063	+	0.576882i	0.650048	+	0.759893i	$0.274749\pi$
$942$	−166.086	−	619.842i	−0.176312	−	0.658007i
$943$	−49.4455	+	184.533i	−0.0524343	+	0.195687i
$944$	434.801	+	116.505i	0.460594	+	0.123416i
$945$	−559.827	+	150.005i	−0.592409	+	0.158736i
$946$	460.133	+	265.658i	0.486398	+	0.280822i
$947$	425.514	+	1588.04i	0.449329	+	1.67692i	0.704247	+	0.709955i	$0.251285\pi$
$947$	425.514	+	1588.04i	0.449329	+	1.67692i	−0.254918	+	0.966963i	$0.582049\pi$
$948$	−348.056	+	348.056i	−0.367147	+	0.367147i
$949$	−347.177	+	1295.68i	−0.365835	+	1.36531i
$950$	269.873	+	155.811i	0.284077	+	0.164012i
$951$	714.942			0.751779
$952$		−	575.965i		−	0.605005i
$953$	−419.556	−	242.231i	−0.440248	−	0.254177i	0.263455	−	0.964672i	$-0.415138\pi$
$953$	−419.556	−	242.231i	−0.440248	−	0.254177i	−0.703703	+	0.710494i	$0.748471\pi$
$954$	111.769	+	111.769i	0.117159	+	0.117159i
$955$	−1096.48	+	633.053i	−1.14815	+	0.662883i
$956$	348.068	+	348.068i	0.364088	+	0.364088i
$957$	−50.8448	+	189.756i	−0.0531294	+	0.198282i
$958$	−492.926	−	853.773i	−0.514537	−	0.891204i
$959$	610.998	+	1058.28i	0.637120	+	1.10352i
$960$	−30.9539	−	115.522i	−0.0322437	−	0.120335i
$961$			379.114i			0.394499i
$962$	153.236	−	631.111i	0.159289	−	0.656040i
$963$	−540.948			−0.561732
$964$	266.503	−	71.4092i	0.276455	−	0.0740760i
$965$	2175.93	−	1256.27i	2.25485	−	1.30184i
$966$	126.566	−	73.0727i	0.131020	−	0.0756446i
$967$	130.367	+	34.9317i	0.134816	+	0.0361237i	0.325596	−	0.945509i	$-0.394435\pi$
$967$	130.367	+	34.9317i	0.134816	+	0.0361237i	−0.190780	+	0.981633i	$0.561102\pi$
$968$	−108.886	+	108.886i	−0.112485	+	0.112485i
$969$	60.7519	+	105.225i	0.0626954	+	0.108592i
$970$	−257.189	+	257.189i	−0.265144	+	0.265144i
$971$	−49.0286	+	84.9200i	−0.0504929	+	0.0874562i	−0.890167	−	0.455634i	$-0.849413\pi$
$971$	−49.0286	+	84.9200i	−0.0504929	+	0.0874562i	0.839674	+	0.543090i	$0.182746\pi$
$972$	−31.1769			−0.0320750
$973$		−	1659.31i		−	1.70535i
$974$	−363.592	+	629.760i	−0.373298	+	0.646571i
$975$	−1027.80	−	275.398i	−1.05415	−	0.282460i
$976$	180.858	+	180.858i	0.185305	+	0.185305i
$977$	269.262	−	72.1486i	0.275601	−	0.0738471i	−0.118371	−	0.992969i	$-0.537767\pi$
$977$	269.262	−	72.1486i	0.275601	−	0.0738471i	0.393972	+	0.919122i	$0.371101\pi$
$978$	86.5580	−	149.923i	0.0885051	−	0.153295i
$979$	−245.895	−	917.692i	−0.251169	−	0.937377i
$980$	−527.205	+	1967.56i	−0.537964	+	2.00771i
$981$	214.457	+	57.4635i	0.218610	+	0.0585764i
$982$	307.250	−	82.3273i	0.312882	−	0.0838364i
$983$	178.468	+	103.039i	0.181555	+	0.104821i	0.588023	−	0.808844i	$-0.299906\pi$
$983$	178.468	+	103.039i	0.181555	+	0.104821i	−0.406468	+	0.913665i	$0.633240\pi$
$984$	−52.4665	−	195.808i	−0.0533196	−	0.198992i
$985$	−970.174	+	970.174i	−0.984948	+	0.984948i
$986$	−49.3884	+	184.320i	−0.0500897	+	0.186937i
$987$	1032.12	+	595.893i	1.04571	+	0.603742i
$988$	−110.508			−0.111850
$989$			130.954i			0.132411i
$990$	420.052	+	242.517i	0.424295	+	0.244967i
$991$	−804.959	−	804.959i	−0.812269	−	0.812269i	0.172704	−	0.984974i	$-0.444749\pi$
$991$	−804.959	−	804.959i	−0.812269	−	0.812269i	−0.984974	+	0.172704i	$0.944749\pi$
$992$	−179.340	+	103.542i	−0.180786	+	0.104377i
$993$	414.948	+	414.948i	0.417873	+	0.417873i
$994$	−125.108	+	466.911i	−0.125864	+	0.469729i
$995$	−1304.90	−	2260.15i	−1.31146	−	2.27151i
$996$	46.5817	+	80.6818i	0.0467687	+	0.0810058i
$997$	−423.960	−	1582.24i	−0.425236	−	1.58700i	−0.763408	−	0.645917i	$-0.776475\pi$
$997$	−423.960	−	1582.24i	−0.425236	−	1.58700i	0.338173	−	0.941084i	$-0.390191\pi$
$998$			528.760i			0.529820i
$999$	186.829	+	45.3629i	0.187016	+	0.0454083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	222.3.l.d.199.4	yes	16
37.8	odd	12	inner	222.3.l.d.193.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
222.3.l.d.193.4	✓	16	37.8	odd	12	inner
222.3.l.d.199.4	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 222 = 2 \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	222.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 0.366025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(1.73205 - 1.00000i) q^{4} +(8.33705 + 2.23391i) q^{5} +(1.73205 - 1.73205i) q^{6} +(-6.46144 - 11.1915i) q^{7} +(2.00000 - 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +12.2063 q^{10} +13.2455i q^{11} +(1.73205 - 3.00000i) q^{12} +(-11.9887 - 3.21235i) q^{13} +(-12.9229 - 12.9229i) q^{14} +(14.4402 - 3.86924i) q^{15} +(2.00000 - 3.46410i) q^{16} +(4.07838 + 15.2207i) q^{17} +(1.09808 - 4.09808i) q^{18} +(4.30012 + 1.15221i) q^{19} +(16.6741 - 4.46781i) q^{20} +(-19.3843 - 11.1915i) q^{21} +(4.84819 + 18.0937i) q^{22} +(-3.26464 + 3.26464i) q^{23} +(1.26795 - 4.73205i) q^{24} +(42.8655 + 24.7484i) q^{25} -17.5526 q^{26} -5.19615i q^{27} +(-22.3831 - 12.9229i) q^{28} +(6.05490 + 6.05490i) q^{29} +(18.3094 - 10.5710i) q^{30} +(-25.8855 - 25.8855i) q^{31} +(1.46410 - 5.46410i) q^{32} +(11.4709 + 19.8682i) q^{33} +(11.1423 + 19.2991i) q^{34} +(-28.8685 - 107.739i) q^{35} -6.00000i q^{36} +(-8.73010 + 35.9553i) q^{37} +6.29582 q^{38} +(-20.7650 + 5.56396i) q^{39} +(21.1419 - 12.2063i) q^{40} +(35.8353 - 20.6895i) q^{41} +(-30.5759 - 8.19277i) q^{42} +(20.0565 - 20.0565i) q^{43} +(13.2455 + 22.9419i) q^{44} +(18.3094 - 18.3094i) q^{45} +(-3.26464 + 5.65452i) q^{46} -53.2450 q^{47} -6.92820i q^{48} +(-59.0003 + 102.192i) q^{49} +(67.6138 + 18.1171i) q^{50} +(19.2991 + 19.2991i) q^{51} +(-23.9773 + 6.42471i) q^{52} +(-18.6282 + 32.2650i) q^{53} +(-1.90192 - 7.09808i) q^{54} +(-29.5892 + 110.428i) q^{55} +(-35.3060 - 9.46020i) q^{56} +(7.44803 - 1.99569i) q^{57} +(10.4874 + 6.05490i) q^{58} +(29.1262 + 108.700i) q^{59} +(21.1419 - 21.1419i) q^{60} +(-16.5497 + 61.7642i) q^{61} +(-44.8349 - 25.8855i) q^{62} -38.7686 q^{63} -8.00000i q^{64} +(-92.7741 - 53.5631i) q^{65} +(22.9419 + 22.9419i) q^{66} +(76.1457 - 43.9628i) q^{67} +(22.2847 + 22.2847i) q^{68} +(-2.06970 + 7.72422i) q^{69} +(-78.8702 - 136.607i) q^{70} +(-13.2247 - 22.9059i) q^{71} +(-2.19615 - 8.19615i) q^{72} -108.076i q^{73} +(1.23503 + 52.3113i) q^{74} +85.7309 q^{75} +(8.60025 - 2.30443i) q^{76} +(148.237 - 85.5849i) q^{77} +(-26.3290 + 15.2010i) q^{78} +(-137.251 - 36.7764i) q^{79} +(24.4126 - 24.4126i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(41.3790 - 41.3790i) q^{82} +(-13.4470 + 23.2908i) q^{83} -44.7662 q^{84} +136.007i q^{85} +(20.0565 - 34.7388i) q^{86} +(14.3261 + 3.83865i) q^{87} +(26.4910 + 26.4910i) q^{88} +(-69.2834 + 18.5644i) q^{89} +(18.3094 - 31.7129i) q^{90} +(41.5129 + 154.928i) q^{91} +(-2.38988 + 8.91916i) q^{92} +(-61.2456 - 16.4107i) q^{93} +(-72.7340 + 19.4890i) q^{94} +(33.2764 + 19.2121i) q^{95} +(-2.53590 - 9.46410i) q^{96} +(-21.0702 + 21.0702i) q^{97} +(-43.1913 + 161.192i) q^{98} +(34.4128 + 19.8682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} + 24 q^{3} + 6 q^{5} - 14 q^{7} + 32 q^{8} + 24 q^{9} + 24 q^{10} - 16 q^{13} - 28 q^{14} + 18 q^{15} + 32 q^{16} - 16 q^{17} - 24 q^{18} + 42 q^{19} + 12 q^{20} - 42 q^{21} + 46 q^{22} - 34 q^{23}+ \cdots + 90 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 + 24 * q^3 + 6 * q^5 - 14 * q^7 + 32 * q^8 + 24 * q^9 + 24 * q^10 - 16 * q^13 - 28 * q^14 + 18 * q^15 + 32 * q^16 - 16 * q^17 - 24 * q^18 + 42 * q^19 + 12 * q^20 - 42 * q^21 + 46 * q^22 - 34 * q^23 + 48 * q^24 + 12 * q^25 + 8 * q^26 + 74 * q^29 + 36 * q^30 + 26 * q^31 - 32 * q^32 + 30 * q^33 - 10 * q^34 - 18 * q^35 - 62 * q^37 + 60 * q^38 - 12 * q^39 - 150 * q^41 - 42 * q^42 + 4 * q^43 - 32 * q^44 + 36 * q^45 - 34 * q^46 - 20 * q^47 - 278 * q^49 + 100 * q^50 - 42 * q^51 - 32 * q^52 + 154 * q^53 - 72 * q^54 - 24 * q^55 - 28 * q^56 + 72 * q^57 - 90 * q^58 + 12 * q^59 + 38 * q^61 - 66 * q^62 - 84 * q^63 - 282 * q^65 + 60 * q^66 + 132 * q^67 - 20 * q^68 - 72 * q^69 - 30 * q^70 + 34 * q^71 + 48 * q^72 - 42 * q^74 + 24 * q^75 + 84 * q^76 + 258 * q^77 + 12 * q^78 - 46 * q^79 + 48 * q^80 - 72 * q^81 + 188 * q^82 - 136 * q^83 + 4 * q^86 + 66 * q^87 - 64 * q^88 + 152 * q^89 + 36 * q^90 + 192 * q^91 + 76 * q^92 + 6 * q^93 - 232 * q^94 - 1068 * q^95 - 96 * q^96 - 382 * q^97 + 206 * q^98 + 90 * q^99

Introduction

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