LMFDB - Embedded newform 108.3.j.a.103.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [108,3,Mod(7,108)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(108, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 16])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("108.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.j (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			103.10
Character	$\chi$	$=$	108.103
Dual form			108.3.j.a.43.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22060 + 1.58434i) q^{2} +(1.88167 + 2.33652i) q^{3} +(-1.02026 - 3.86769i) q^{4} +(4.29021 - 1.56151i) q^{5} +(-5.99861 + 0.129252i) q^{6} +(11.3387 - 1.99932i) q^{7} +(7.37308 + 3.10447i) q^{8} +(-1.91862 + 8.79312i) q^{9} +(-2.76268 + 8.70313i) q^{10} +(-2.79665 + 7.68375i) q^{11} +(7.11713 - 9.66160i) q^{12} +(-18.9359 - 15.8891i) q^{13} +(-10.6724 + 20.4047i) q^{14} +(11.7213 + 7.08590i) q^{15} +(-13.9181 + 7.89213i) q^{16} +(-6.56214 + 11.3660i) q^{17} +(-11.5894 - 13.7726i) q^{18} +(8.74492 - 5.04888i) q^{19} +(-10.4166 - 15.0001i) q^{20} +(26.0071 + 22.7310i) q^{21} +(-8.76006 - 13.8096i) q^{22} +(20.3386 + 3.58624i) q^{23} +(6.62006 + 23.0689i) q^{24} +(-3.18352 + 2.67129i) q^{25} +(48.2869 - 10.6066i) q^{26} +(-24.1555 + 12.0629i) q^{27} +(-19.3012 - 41.8148i) q^{28} +(6.33255 - 5.31364i) q^{29} +(-25.5335 + 9.92140i) q^{30} +(-9.50040 - 1.67518i) q^{31} +(4.48468 - 31.6842i) q^{32} +(-23.2156 + 7.92386i) q^{33} +(-9.99778 - 24.2700i) q^{34} +(45.5234 - 26.2830i) q^{35} +(35.9666 - 1.55066i) q^{36} +(21.4626 - 37.1743i) q^{37} +(-2.67492 + 20.0176i) q^{38} +(1.49399 - 74.1421i) q^{39} +(36.4797 + 1.80572i) q^{40} +(-33.7981 - 28.3600i) q^{41} +(-67.7580 + 13.4587i) q^{42} +(-3.42972 + 9.42307i) q^{43} +(32.5717 + 2.97717i) q^{44} +(5.49926 + 40.7203i) q^{45} +(-30.5071 + 27.8458i) q^{46} +(-87.0515 + 15.3495i) q^{47} +(-44.6294 - 17.6695i) q^{48} +(78.5238 - 28.5803i) q^{49} +(-0.346420 - 8.30436i) q^{50} +(-38.9045 + 6.05447i) q^{51} +(-42.1346 + 89.4493i) q^{52} +8.52710 q^{53} +(10.3725 - 52.9944i) q^{54} +37.3319i q^{55} +(89.8079 + 20.4596i) q^{56} +(28.2519 + 10.9323i) q^{57} +(0.689087 + 16.5187i) q^{58} +(-4.23230 - 11.6281i) q^{59} +(15.4473 - 52.5637i) q^{60} +(-5.96660 - 33.8383i) q^{61} +(14.2502 - 13.0071i) q^{62} +(-4.17438 + 103.538i) q^{63} +(44.7245 + 45.7790i) q^{64} +(-106.050 - 38.5990i) q^{65} +(15.7829 - 46.4533i) q^{66} +(38.0852 - 45.3881i) q^{67} +(50.6552 + 13.7841i) q^{68} +(29.8912 + 54.2695i) q^{69} +(-13.9248 + 104.206i) q^{70} +(-22.0271 - 12.7174i) q^{71} +(-41.4441 + 58.8760i) q^{72} +(-9.11022 - 15.7794i) q^{73} +(32.6995 + 79.3791i) q^{74} +(-12.2319 - 2.41185i) q^{75} +(-28.4497 - 28.6715i) q^{76} +(-16.3482 + 92.7151i) q^{77} +(115.643 + 92.8650i) q^{78} +(48.7210 + 58.0634i) q^{79} +(-47.3881 + 55.5922i) q^{80} +(-73.6378 - 33.7413i) q^{81} +(86.1858 - 18.9314i) q^{82} +(20.4415 + 24.3612i) q^{83} +(61.3824 - 123.779i) q^{84} +(-10.4049 + 59.0092i) q^{85} +(-10.7430 - 16.9357i) q^{86} +(24.3312 + 4.79757i) q^{87} +(-44.4739 + 47.9707i) q^{88} +(-13.1160 - 22.7175i) q^{89} +(-71.2271 - 40.9905i) q^{90} +(-246.476 - 142.303i) q^{91} +(-6.88020 - 82.3223i) q^{92} +(-13.9626 - 25.3500i) q^{93} +(81.9364 - 156.655i) q^{94} +(29.6337 - 35.3160i) q^{95} +(82.4693 - 49.1407i) q^{96} +(-29.5430 - 10.7528i) q^{97} +(-50.5654 + 159.294i) q^{98} +(-62.1984 - 39.3335i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25}+ \cdots + 510 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

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 $

$2$	−1.22060	+	1.58434i	−0.610301	+	0.792170i
$2$	−1.22060	+	1.58434i	−0.610301	+	0.792170i
$3$	1.88167	+	2.33652i	0.627224	+	0.778839i
$3$	1.88167	+	2.33652i	0.627224	+	0.778839i
$4$	−1.02026	−	3.86769i	−0.255066	−	0.966924i
$5$	4.29021	−	1.56151i	0.858042	−	0.312302i	0.124727	−	0.992191i	$-0.460194\pi$
$5$	4.29021	−	1.56151i	0.858042	−	0.312302i	0.733315	+	0.679889i	$0.237972\pi$
$6$	−5.99861	+	0.129252i	−0.999768	+	0.0215420i
$7$	11.3387	−	1.99932i	1.61981	−	0.285617i	0.711117	−	0.703074i	$-0.248190\pi$
$7$	11.3387	−	1.99932i	1.61981	−	0.285617i	0.908697	+	0.417457i	$0.137079\pi$
$8$	7.37308	+	3.10447i	0.921634	+	0.388059i
$9$	−1.91862	+	8.79312i	−0.213180	+	0.977013i
$10$	−2.76268	+	8.70313i	−0.276268	+	0.870313i
$11$	−2.79665	+	7.68375i	−0.254241	+	0.698522i	0.745255	+	0.666780i	$0.232328\pi$
$11$	−2.79665	+	7.68375i	−0.254241	+	0.698522i	−0.999496	+	0.0317425i	$0.989894\pi$
$12$	7.11713	−	9.66160i	0.593094	−	0.805133i
$13$	−18.9359	−	15.8891i	−1.45661	−	1.22224i	−0.927575	−	0.373637i	$-0.878111\pi$
$13$	−18.9359	−	15.8891i	−1.45661	−	1.22224i	−0.529032	−	0.848602i	$-0.677445\pi$
$14$	−10.6724	+	20.4047i	−0.762317	+	1.45748i
$15$	11.7213	+	7.08590i	0.781417	+	0.472393i
$16$	−13.9181	+	7.89213i	−0.869883	+	0.493258i
$17$	−6.56214	+	11.3660i	−0.386008	+	0.668586i	−0.991909	−	0.126955i	$-0.959480\pi$
$17$	−6.56214	+	11.3660i	−0.386008	+	0.668586i	0.605900	+	0.795541i	$0.292813\pi$
$18$	−11.5894	−	13.7726i	−0.643856	−	0.765146i
$19$	8.74492	−	5.04888i	0.460259	−	0.265731i	−0.251894	−	0.967755i	$-0.581053\pi$
$19$	8.74492	−	5.04888i	0.460259	−	0.265731i	0.712153	+	0.702024i	$0.247720\pi$
$20$	−10.4166	−	15.0001i	−0.520829	−	0.750004i
$21$	26.0071	+	22.7310i	1.23844	+	1.08243i
$22$	−8.76006	−	13.8096i	−0.398185	−	0.627711i
$23$	20.3386	+	3.58624i	0.884286	+	0.155923i	0.597306	−	0.802013i	$-0.296238\pi$
$23$	20.3386	+	3.58624i	0.884286	+	0.155923i	0.286980	+	0.957937i	$0.407349\pi$
$24$	6.62006	+	23.0689i	0.275836	+	0.961205i
$25$	−3.18352	+	2.67129i	−0.127341	+	0.106852i
$26$	48.2869	−	10.6066i	1.85719	−	0.407947i
$27$	−24.1555	+	12.0629i	−0.894647	+	0.446774i
$28$	−19.3012	−	41.8148i	−0.689328	−	1.49339i
$29$	6.33255	−	5.31364i	0.218364	−	0.183229i	−0.527044	−	0.849838i	$-0.676700\pi$
$29$	6.33255	−	5.31364i	0.218364	−	0.183229i	0.745407	+	0.666609i	$0.232255\pi$
$30$	−25.5335	+	9.92140i	−0.851115	+	0.330713i
$31$	−9.50040	−	1.67518i	−0.306464	−	0.0540379i	0.0183011	−	0.999833i	$-0.494174\pi$
$31$	−9.50040	−	1.67518i	−0.306464	−	0.0540379i	−0.324765	+	0.945795i	$0.605285\pi$
$32$	4.48468	−	31.6842i	0.140146	−	0.990131i
$33$	−23.2156	+	7.92386i	−0.703503	+	0.240117i
$34$	−9.99778	−	24.2700i	−0.294052	−	0.713822i
$35$	45.5234	−	26.2830i	1.30067	−	0.750942i
$36$	35.9666	−	1.55066i	0.999072	−	0.0430739i
$37$	21.4626	−	37.1743i	0.580071	−	1.00471i	−0.415400	−	0.909639i	$-0.636358\pi$
$37$	21.4626	−	37.1743i	0.580071	−	1.00471i	0.995470	−	0.0950729i	$-0.0303084\pi$
$38$	−2.67492	+	20.0176i	−0.0703927	+	0.526779i
$39$	1.49399	−	74.1421i	0.0383076	−	1.90108i
$40$	36.4797	+	1.80572i	0.911993	+	0.0451430i
$41$	−33.7981	−	28.3600i	−0.824344	−	0.691707i	0.129641	−	0.991561i	$-0.458617\pi$
$41$	−33.7981	−	28.3600i	−0.824344	−	0.691707i	−0.953985	+	0.299854i	$0.903062\pi$
$42$	−67.7580	+	13.4587i	−1.61328	+	0.320445i
$43$	−3.42972	+	9.42307i	−0.0797609	+	0.219141i	−0.973163	−	0.230117i	$-0.926089\pi$
$43$	−3.42972	+	9.42307i	−0.0797609	+	0.219141i	0.893402	+	0.449258i	$0.148311\pi$
$44$	32.5717	+	2.97717i	0.740266	+	0.0676630i
$45$	5.49926	+	40.7203i	0.122206	+	0.904895i
$46$	−30.5071	+	27.8458i	−0.663198	+	0.605344i
$47$	−87.0515	+	15.3495i	−1.85216	+	0.326586i	−0.985149	−	0.171703i	$-0.945073\pi$
$47$	−87.0515	+	15.3495i	−1.85216	+	0.326586i	−0.867011	+	0.498288i	$0.833962\pi$
$48$	−44.6294	−	17.6695i	−0.929780	−	0.368115i
$49$	78.5238	−	28.5803i	1.60253	−	0.583272i
$50$	−0.346420	−	8.30436i	−0.00692841	−	0.166087i
$51$	−38.9045	+	6.05447i	−0.762834	+	0.118715i
$52$	−42.1346	+	89.4493i	−0.810281	+	1.72018i
$53$	8.52710			0.160889			0.0804443	−	0.996759i	$-0.474366\pi$
$53$	8.52710			0.160889			0.0804443	+	0.996759i	$0.474366\pi$
$54$	10.3725	−	52.9944i	0.192083	−	0.981379i
$55$			37.3319i			0.678762i
$56$	89.8079	+	20.4596i	1.60371	+	0.365349i
$57$	28.2519	+	10.9323i	0.495647	+	0.191795i
$58$	0.689087	+	16.5187i	0.0118808	+	0.284806i
$59$	−4.23230	−	11.6281i	−0.0717339	−	0.197087i	0.898644	−	0.438678i	$-0.144553\pi$
$59$	−4.23230	−	11.6281i	−0.0717339	−	0.197087i	−0.970378	+	0.241591i	$0.922331\pi$
$60$	15.4473	−	52.5637i	0.257455	−	0.876062i
$61$	−5.96660	−	33.8383i	−0.0978132	−	0.554726i	−0.993849	−	0.110744i	$-0.964677\pi$
$61$	−5.96660	−	33.8383i	−0.0978132	−	0.554726i	0.896036	−	0.443982i	$-0.146435\pi$
$62$	14.2502	−	13.0071i	0.229843	−	0.209792i
$63$	−4.17438	+	103.538i	−0.0662600	+	1.64347i
$64$	44.7245	+	45.7790i	0.698820	+	0.715297i
$65$	−106.050	−	38.5990i	−1.63154	−	0.593831i
$66$	15.7829	−	46.4533i	0.239135	−	0.703837i
$67$	38.0852	−	45.3881i	0.568435	−	0.677435i	−0.402874	−	0.915256i	$-0.631989\pi$
$67$	38.0852	−	45.3881i	0.568435	−	0.677435i	0.971309	+	0.237821i	$0.0764331\pi$
$68$	50.6552	+	13.7841i	0.744929	+	0.202707i
$69$	29.8912	+	54.2695i	0.433206	+	0.786515i
$70$	−13.9248	+	104.206i	−0.198926	+	1.48865i
$71$	−22.0271	−	12.7174i	−0.310241	−	0.179118i	0.336793	−	0.941579i	$-0.390658\pi$
$71$	−22.0271	−	12.7174i	−0.310241	−	0.179118i	−0.647034	+	0.762461i	$0.723991\pi$
$72$	−41.4441	+	58.8760i	−0.575613	+	0.817723i
$73$	−9.11022	−	15.7794i	−0.124797	−	0.216156i	0.796856	−	0.604169i	$-0.206495\pi$
$73$	−9.11022	−	15.7794i	−0.124797	−	0.216156i	−0.921654	+	0.388013i	$0.873161\pi$
$74$	32.6995	+	79.3791i	0.441885	+	1.07269i
$75$	−12.2319	−	2.41185i	−0.163091	−	0.0321580i
$76$	−28.4497	−	28.6715i	−0.374338	−	0.377257i
$77$	−16.3482	+	92.7151i	−0.212314	+	1.20409i
$78$	115.643	+	92.8650i	1.48260	+	1.19058i
$79$	48.7210	+	58.0634i	0.616721	+	0.734980i	0.980503	−	0.196505i	$-0.0629591\pi$
$79$	48.7210	+	58.0634i	0.616721	+	0.734980i	−0.363782	+	0.931484i	$0.618515\pi$
$80$	−47.3881	+	55.5922i	−0.592351	+	0.694902i
$81$	−73.6378	−	33.7413i	−0.909109	−	0.416559i
$82$	86.1858	−	18.9314i	1.05105	−	0.230871i
$83$	20.4415	+	24.3612i	0.246283	+	0.293509i	0.874997	−	0.484128i	$-0.160863\pi$
$83$	20.4415	+	24.3612i	0.246283	+	0.293509i	−0.628714	+	0.777636i	$0.716418\pi$
$84$	61.3824	−	123.779i	0.730743	−	1.47356i
$85$	−10.4049	+	59.0092i	−0.122411	+	0.694226i
$86$	−10.7430	−	16.9357i	−0.124919	−	0.196926i
$87$	24.3312	+	4.79757i	0.279669	+	0.0551445i
$88$	−44.4739	+	47.9707i	−0.505386	+	0.545122i
$89$	−13.1160	−	22.7175i	−0.147371	−	0.255253i	0.782884	−	0.622167i	$-0.213748\pi$
$89$	−13.1160	−	22.7175i	−0.147371	−	0.255253i	−0.930255	+	0.366914i	$0.880414\pi$
$90$	−71.2271	−	40.9905i	−0.791412	−	0.455450i
$91$	−246.476	−	142.303i	−2.70852	−	1.56377i
$92$	−6.88020	−	82.3223i	−0.0747848	−	0.894808i
$93$	−13.9626	−	25.3500i	−0.150135	−	0.272580i
$94$	81.9364	−	156.655i	0.871664	−	1.66654i
$95$	29.6337	−	35.3160i	0.311933	−	0.371748i
$96$	82.4693	−	49.1407i	0.859055	−	0.511883i
$97$	−29.5430	−	10.7528i	−0.304567	−	0.110853i	0.185215	−	0.982698i	$-0.440702\pi$
$97$	−29.5430	−	10.7528i	−0.304567	−	0.110853i	−0.489783	+	0.871844i	$0.662924\pi$
$98$	−50.5654	+	159.294i	−0.515973	+	1.62544i
$99$	−62.1984	−	39.3335i	−0.628266	−	0.397308i
$100$	13.5798	+	9.58747i	0.135798	+	0.0958747i
$101$	−7.75907	−	44.0039i	−0.0768225	−	0.435682i	−0.998823	−	0.0484945i	$-0.984558\pi$
$101$	−7.75907	−	44.0039i	−0.0768225	−	0.435682i	0.922001	−	0.387188i	$-0.126553\pi$
$102$	37.8946	−	69.0281i	0.371516	−	0.676746i
$103$	55.3396	+	152.044i	0.537278	+	1.47616i	0.850241	+	0.526393i	$0.176456\pi$
$103$	55.3396	+	152.044i	0.537278	+	1.47616i	−0.312963	+	0.949765i	$0.601322\pi$
$104$	−90.2885	−	175.938i	−0.868159	−	1.69171i
$105$	147.071	+	56.9103i	1.40067	+	0.542003i
$106$	−10.4082	+	13.5098i	−0.0981905	+	0.127451i
$107$		−	130.167i		−	1.21651i	−0.793741	−	0.608256i	$-0.791869\pi$
$107$		−	130.167i		−	1.21651i	0.793741	−	0.608256i	$-0.208131\pi$
$108$	71.3005	+	81.1187i	0.660190	+	0.751099i
$109$	25.8218			0.236897			0.118449	−	0.992960i	$-0.462208\pi$
$109$	25.8218			0.236897			0.118449	+	0.992960i	$0.462208\pi$
$110$	−59.1464	−	45.5674i	−0.537694	−	0.414249i
$111$	127.244	−	19.8022i	1.14634	−	0.178398i
$112$	−142.035	+	117.313i	−1.26817	+	1.04744i
$113$	18.4582	−	6.71825i	0.163347	−	0.0594535i	−0.259052	−	0.965863i	$-0.583410\pi$
$113$	18.4582	−	6.71825i	0.163347	−	0.0594535i	0.422399	+	0.906410i	$0.361188\pi$
$114$	−51.8048	+	31.4166i	−0.454428	+	0.275584i
$115$	92.8567	−	16.3731i	0.807449	−	0.142375i
$116$	−27.0124	−	19.0711i	−0.232865	−	0.164406i
$117$	176.045	−	136.020i	1.50466	−	1.16257i
$118$	23.5889	+	7.48793i	0.199906	+	0.0634571i
$119$	−51.6819	+	141.995i	−0.434302	+	1.19323i
$120$	64.4238	+	88.6332i	0.536865	+	0.738610i
$121$	41.4727	+	34.7997i	0.342750	+	0.287601i
$122$	60.8942	+	31.8500i	0.499133	+	0.261065i
$123$	2.66658	−	132.334i	0.0216795	−	1.07589i
$124$	3.21383	+	38.4538i	0.0259180	+	0.310111i
$125$	−66.5561	+	115.278i	−0.532448	+	0.922228i
$126$	−158.945	−	132.993i	−1.26147	−	1.05550i
$127$	−85.9709	+	49.6353i	−0.676936	+	0.390829i	−0.798700	−	0.601730i	$-0.794478\pi$
$127$	−85.9709	+	49.6353i	−0.676936	+	0.390829i	0.121763	+	0.992559i	$0.461145\pi$
$128$	−127.120	+	14.9808i	−0.993128	+	0.117037i
$129$	−28.4708	+	9.71754i	−0.220704	+	0.0753298i
$130$	190.599	−	120.905i	1.46614	−	0.930039i
$131$	−71.0230	−	12.5233i	−0.542161	−	0.0955976i	−0.104140	−	0.994563i	$-0.533209\pi$
$131$	−71.0230	−	12.5233i	−0.542161	−	0.0955976i	−0.438020	+	0.898965i	$0.644320\pi$
$132$	54.3331	+	81.7064i	0.411614	+	0.618988i
$133$	89.0617	−	74.7316i	0.669637	−	0.561892i
$134$	25.4234	+	115.741i	0.189727	+	0.863736i
$135$	−84.7957	+	89.4713i	−0.628117	+	0.662750i
$136$	−83.6685	+	63.4301i	−0.615209	+	0.466398i
$137$	−78.2241	+	65.6378i	−0.570979	+	0.479108i	−0.881971	−	0.471304i	$-0.843783\pi$
$137$	−78.2241	+	65.6378i	−0.570979	+	0.479108i	0.310992	+	0.950413i	$0.399339\pi$
$138$	−122.467	−	18.8836i	−0.887439	−	0.136838i
$139$	156.260	+	27.5528i	1.12417	+	0.198222i	0.704672	−	0.709533i	$-0.251094\pi$
$139$	156.260	+	27.5528i	1.12417	+	0.198222i	0.419500	+	0.907755i	$0.362205\pi$
$140$	−148.100	−	149.255i	−1.05786	−	1.06611i
$141$	−199.667	−	174.515i	−1.41608	−	1.23769i
$142$	47.0350	−	19.3756i	0.331232	−	0.136448i
$143$	175.045	−	101.062i	1.22409	−	0.706729i
$144$	−42.6928	−	137.526i	−0.296478	−	0.955040i
$145$	18.8707	−	32.6850i	0.130143	−	0.225413i
$146$	36.1198	+	4.82664i	0.247396	+	0.0330592i
$147$	214.534	+	129.693i	1.45942	+	0.882267i
$148$	−165.677	−	45.0833i	−1.11944	−	0.304617i
$149$	−13.9503	−	11.7057i	−0.0936261	−	0.0785616i	0.594773	−	0.803894i	$-0.297242\pi$
$149$	−13.9503	−	11.7057i	−0.0936261	−	0.0785616i	−0.688399	+	0.725332i	$0.741686\pi$
$150$	18.7514	−	16.4355i	0.125009	−	0.109570i
$151$	58.6575	−	161.160i	0.388460	−	1.06729i	−0.579235	−	0.815161i	$-0.696648\pi$
$151$	58.6575	−	161.160i	0.388460	−	1.06729i	0.967695	−	0.252125i	$-0.0811293\pi$
$152$	80.1511	−	10.0774i	0.527310	−	0.0662988i
$153$	−87.3520	−	79.5086i	−0.570928	−	0.519664i
$154$	−126.938	−	139.069i	−0.824270	−	0.903047i
$155$	−43.3745	+	7.64809i	−0.279835	+	0.0493425i
$156$	−288.283	+	69.8661i	−1.84797	+	0.447860i
$157$	−162.347	+	59.0894i	−1.03406	+	0.376365i	−0.802624	−	0.596486i	$-0.796563\pi$
$157$	−162.347	+	59.0894i	−1.03406	+	0.376365i	−0.231432	+	0.972851i	$0.574341\pi$
$158$	−151.461	+	6.31827i	−0.958614	+	0.0399891i
$159$	16.0452	+	19.9237i	0.100913	+	0.125306i
$160$	−30.2349	−	142.935i	−0.188968	−	0.893342i
$161$	237.783			1.47691
$162$	143.340	−	75.4827i	0.884815	−	0.465942i
$163$		−	23.1683i		−	0.142137i	−0.997471	−	0.0710684i	$-0.977359\pi$
$163$		−	23.1683i		−	0.142137i	0.997471	−	0.0710684i	$-0.0226409\pi$
$164$	−75.2048	+	159.655i	−0.458566	+	0.973508i
$165$	−87.2266	+	70.2464i	−0.528646	+	0.425736i
$166$	−63.5474	+	2.65091i	−0.382816	+	0.0159693i
$167$	81.2649	+	223.274i	0.486616	+	1.33697i	0.903726	+	0.428111i	$0.140821\pi$
$167$	81.2649	+	223.274i	0.486616	+	1.33697i	−0.417110	+	0.908856i	$0.636957\pi$
$168$	121.185	+	248.336i	0.721339	+	1.47819i
$169$	76.7580	+	435.316i	0.454189	+	2.57584i
$170$	−80.7903	−	88.5116i	−0.475237	−	0.520657i
$171$	27.6173	+	86.5820i	0.161504	+	0.506327i
$172$	39.9448	+	3.65109i	0.232237	+	0.0212273i
$173$	230.336	+	83.8353i	1.33142	+	0.484597i	0.907100	−	0.420915i	$-0.138291\pi$
$173$	230.336	+	83.8353i	1.33142	+	0.484597i	0.424320	+	0.905512i	$0.360513\pi$
$174$	−37.2997	+	32.6929i	−0.214366	+	0.187890i
$175$	−30.7562	+	36.6538i	−0.175750	+	0.209450i
$176$	−21.7169	−	129.015i	−0.123392	−	0.733039i
$177$	19.2055	−	31.7692i	0.108506	−	0.179487i
$178$	52.0017	+	6.94891i	0.292144	+	0.0390388i
$179$	−51.8077	−	29.9112i	−0.289428	−	0.167102i	0.348256	−	0.937400i	$-0.386774\pi$
$179$	−51.8077	−	29.9112i	−0.289428	−	0.167102i	−0.637684	+	0.770298i	$0.720107\pi$
$180$	151.883	−	62.8148i	0.843794	−	0.348971i
$181$	−33.9126	−	58.7384i	−0.187362	−	0.324521i	0.757008	−	0.653406i	$-0.226661\pi$
$181$	−33.9126	−	58.7384i	−0.187362	−	0.324521i	−0.944370	+	0.328885i	$0.893327\pi$
$182$	526.305	−	216.806i	2.89178	−	1.19124i
$183$	67.8365	−	77.6137i	0.370691	−	0.424118i
$184$	138.824	+	89.5822i	0.754481	+	0.486860i
$185$	34.0311	−	193.000i	0.183952	−	1.04324i
$186$	57.2057	+	8.82078i	0.307557	+	0.0474236i
$187$	−68.9811	−	82.2085i	−0.368883	−	0.439617i
$188$	148.183	+	321.028i	0.788206	+	1.70760i
$189$	−249.774	+	185.072i	−1.32156	+	0.979216i
$190$	19.7817	+	90.0566i	0.104114	+	0.473982i
$191$	−3.10621	−	3.70184i	−0.0162629	−	0.0193814i	0.757852	−	0.652427i	$-0.226249\pi$
$191$	−3.10621	−	3.70184i	−0.0162629	−	0.0193814i	−0.774115	+	0.633045i	$0.781805\pi$
$192$	−22.8066	+	190.641i	−0.118785	+	0.992920i
$193$	−19.2895	+	109.396i	−0.0999455	+	0.566819i	0.893174	+	0.449712i	$0.148473\pi$
$193$	−19.2895	+	109.396i	−0.0999455	+	0.566819i	−0.993119	+	0.117107i	$0.962638\pi$
$194$	53.0964	−	33.6813i	0.273693	−	0.173615i
$195$	−109.364	−	320.418i	−0.560841	−	1.64317i
$196$	−190.655	−	274.547i	−0.972729	−	1.40075i
$197$	−103.487	−	179.244i	−0.525314	−	0.909870i	−0.999565	−	0.0294806i	$-0.990615\pi$
$197$	−103.487	−	179.244i	−0.525314	−	0.909870i	0.474252	−	0.880389i	$-0.342719\pi$
$198$	138.237	−	50.5328i	0.698167	−	0.255216i
$199$	95.4698	+	55.1195i	0.479748	+	0.276982i	0.720311	−	0.693651i	$-0.243999\pi$
$199$	95.4698	+	55.1195i	0.479748	+	0.276982i	−0.240564	+	0.970633i	$0.577332\pi$
$200$	−31.7653	+	9.81247i	−0.158826	+	0.0490624i
$201$	177.714	+	3.58101i	0.884149	+	0.0178160i
$202$	79.1878	+	41.4182i	0.392019	+	0.205041i
$203$	61.1792	−	72.9105i	0.301375	−	0.359165i
$204$	63.1097	+	144.294i	0.309361	+	0.707322i
$205$	−189.285	−	68.8942i	−0.923343	−	0.336069i
$206$	−308.437	−	97.9089i	−1.49727	−	0.475286i
$207$	−70.5561	+	171.959i	−0.340851	+	0.830719i
$208$	388.951	+	71.7021i	1.86996	+	0.344722i
$209$	14.3378	+	81.3137i	0.0686019	+	0.389061i
$210$	−269.680	+	163.545i	−1.28419	+	0.778787i
$211$	61.7185	+	169.570i	0.292505	+	0.803651i	0.995699	+	0.0926522i	$0.0295345\pi$
$211$	61.7185	+	169.570i	0.292505	+	0.803651i	−0.703194	+	0.710998i	$0.748243\pi$
$212$	−8.69988	−	32.9802i	−0.0410372	−	0.155567i
$213$	−11.7335	−	75.3966i	−0.0550868	−	0.353975i
$214$	206.229	+	158.882i	0.963685	+	0.742439i
$215$			45.7825i			0.212942i
$216$	−215.549	+	13.9506i	−0.997912	+	0.0645859i
$217$	−111.071			−0.511849
$218$	−31.5181	+	40.9105i	−0.144578	+	0.187663i
$219$	19.7263	−	50.9778i	0.0900744	−	0.232775i
$220$	144.388	−	38.0883i	0.656311	−	0.173129i
$221$	304.855	−	110.958i	1.37943	−	0.502073i
$222$	−123.941	+	225.768i	−0.558293	+	1.01697i
$223$	−8.13269	+	1.43401i	−0.0364695	+	0.00643055i	−0.191853	−	0.981424i	$-0.561450\pi$
$223$	−8.13269	+	1.43401i	−0.0364695	+	0.00643055i	0.155384	+	0.987854i	$0.450339\pi$
$224$	−12.4963	−	368.224i	−0.0557870	−	1.64386i
$225$	−17.3810	−	33.1183i	−0.0772490	−	0.147192i
$226$	−11.8862	+	37.4444i	−0.0525937	+	0.165683i
$227$	−45.2829	+	124.414i	−0.199484	+	0.548079i	−0.998588	−	0.0531140i	$-0.983085\pi$
$227$	−45.2829	+	124.414i	−0.199484	+	0.548079i	0.799104	+	0.601193i	$0.205308\pi$
$228$	13.4585	−	120.423i	0.0590285	−	0.528173i
$229$	−286.648	−	240.527i	−1.25174	−	1.05033i	−0.996512	−	0.0834533i	$-0.973405\pi$
$229$	−286.648	−	240.527i	−1.25174	−	1.05033i	−0.255228	−	0.966881i	$-0.582150\pi$
$230$	−87.4004	+	167.102i	−0.380002	+	0.726529i
$231$	−247.392	+	136.262i	−1.07096	+	0.589877i
$232$	63.1864	−	19.5186i	0.272355	−	0.0841320i
$233$	−48.4626	+	83.9396i	−0.207994	+	0.360256i	−0.951082	−	0.308937i	$-0.900027\pi$
$233$	−48.4626	+	83.9396i	−0.207994	+	0.360256i	0.743089	+	0.669193i	$0.233360\pi$
$234$	0.621113	+	444.943i	0.00265433	+	1.90146i
$235$	−349.501	+	201.784i	−1.48724	+	0.858657i
$236$	−40.6560	+	28.2330i	−0.172271	+	0.119631i
$237$	−43.9892	+	223.094i	−0.185608	+	0.941323i
$238$	−161.885	−	255.201i	−0.680189	−	1.07227i
$239$	461.201	+	81.3223i	1.92971	+	0.340261i	0.999633	−	0.0270953i	$-0.00862575\pi$
$239$	461.201	+	81.3223i	1.92971	+	0.340261i	0.930080	+	0.367356i	$0.119737\pi$
$240$	−219.061	−	6.11675i	−0.912753	−	0.0254864i
$241$	110.780	−	92.9556i	0.459669	−	0.385708i	−0.383341	−	0.923607i	$-0.625226\pi$
$241$	110.780	−	92.9556i	0.459669	−	0.385708i	0.843009	+	0.537899i	$0.180782\pi$
$242$	−105.756	+	23.2302i	−0.437009	+	0.0959926i
$243$	−59.7253	−	235.546i	−0.245783	−	0.969325i
$244$	−124.789	+	57.6009i	−0.511429	+	0.236069i
$245$	292.255	−	245.231i	1.19288	−	1.00094i
$246$	206.407	+	165.752i	0.839053	+	0.673788i
$247$	−245.815	−	43.3438i	−0.995203	−	0.175481i
$248$	−64.8466	−	41.8449i	−0.261478	−	0.168730i
$249$	−18.4562	+	93.6018i	−0.0741213	+	0.375911i
$250$	−101.402	−	246.156i	−0.405607	−	0.984626i
$251$	−246.323	+	142.215i	−0.981366	+	0.566592i	−0.902682	−	0.430308i	$-0.858405\pi$
$251$	−246.323	+	142.215i	−0.981366	+	0.566592i	−0.0786839	+	0.996900i	$0.525072\pi$
$252$	404.714	−	89.4911i	1.60601	−	0.355123i
$253$	−84.4357	+	146.247i	−0.333738	+	0.578051i
$254$	26.2970	−	196.792i	0.103532	−	0.774772i
$255$	−157.455	+	86.7247i	−0.617469	+	0.340097i
$256$	131.429	−	219.687i	0.513393	−	0.858154i
$257$	164.184	+	137.767i	0.638848	+	0.536057i	0.903664	−	0.428242i	$-0.140867\pi$
$257$	164.184	+	137.767i	0.638848	+	0.536057i	−0.264816	+	0.964299i	$0.585311\pi$
$258$	19.3556	−	56.9686i	0.0750216	−	0.220809i
$259$	169.035	−	464.419i	0.652644	−	1.79312i
$260$	−41.0905	+	449.550i	−0.158040	+	1.72904i
$261$	34.5737	+	65.8777i	0.132466	+	0.252405i
$262$	106.532	−	97.2387i	0.406611	−	0.371140i
$263$	−121.818	+	21.4798i	−0.463187	+	0.0816723i	−0.400372	−	0.916353i	$-0.631119\pi$
$263$	−121.818	+	21.4798i	−0.463187	+	0.0816723i	−0.0628152	+	0.998025i	$0.520008\pi$
$264$	−195.770	−	13.6489i	−0.741552	−	0.0517005i
$265$	36.5830	−	13.3151i	0.138049	−	0.0502458i
$266$	9.69140	+	232.321i	0.0364338	+	0.873389i
$267$	28.3999	−	73.3927i	0.106367	−	0.274879i
$268$	−214.404	−	100.994i	−0.800016	−	0.376843i
$269$	395.510			1.47030			0.735150	−	0.677905i	$-0.237112\pi$
$269$	395.510			1.47030			0.735150	+	0.677905i	$0.237112\pi$
$270$	−38.2511	−	243.554i	−0.141671	−	0.902052i
$271$		−	462.522i		−	1.70672i	−0.521320	−	0.853361i	$-0.674560\pi$
$271$		−	462.522i		−	1.70672i	0.521320	−	0.853361i	$-0.325440\pi$
$272$	1.63110	−	209.982i	0.00599670	−	0.771993i
$273$	−131.294	−	843.662i	−0.480929	−	3.09034i
$274$	−8.51209	−	204.051i	−0.0310660	−	0.744712i
$275$	−11.6223	−	31.9320i	−0.0422630	−	0.116117i
$276$	179.401	−	170.979i	0.650004	−	0.619490i
$277$	−6.18174	−	35.0584i	−0.0223168	−	0.126565i	0.971614	−	0.236572i	$-0.0760238\pi$
$277$	−6.18174	−	35.0584i	−0.0223168	−	0.126565i	−0.993931	+	0.110007i	$0.964913\pi$
$278$	−234.384	+	213.938i	−0.843109	+	0.769560i
$279$	32.9576	−	80.3241i	0.118128	−	0.287900i
$280$	417.242	−	52.4600i	1.49015	−	0.187357i
$281$	−58.6385	−	21.3427i	−0.208678	−	0.0759525i	0.235566	−	0.971858i	$-0.424306\pi$
$281$	−58.6385	−	21.3427i	−0.208678	−	0.0759525i	−0.444244	+	0.895906i	$0.646528\pi$
$282$	520.204	−	103.327i	1.84470	−	0.366409i
$283$	−177.070	+	211.024i	−0.625690	+	0.745668i	−0.982038	−	0.188685i	$-0.939577\pi$
$283$	−177.070	+	211.024i	−0.625690	+	0.745668i	0.356348	+	0.934353i	$0.384022\pi$
$284$	−26.7134	+	98.1692i	−0.0940614	+	0.345666i
$285$	138.277	+	2.78635i	0.485184	+	0.00977665i
$286$	−53.5433	+	400.688i	−0.187214	+	1.40101i
$287$	−439.927	−	253.992i	−1.53285	−	0.884989i
$288$	269.998	+	100.224i	0.937494	+	0.348001i
$289$	58.3767	+	101.111i	0.201995	+	0.349866i
$290$	28.7505	+	69.7928i	0.0991396	+	0.240665i
$291$	−30.4663	−	89.2610i	−0.104695	−	0.306739i
$292$	−51.7349	+	51.3346i	−0.177174	+	0.175804i
$293$	−89.3427	+	506.688i	−0.304924	+	1.72931i	0.318938	+	0.947776i	$0.396674\pi$
$293$	−89.3427	+	506.688i	−0.304924	+	1.72931i	−0.623862	+	0.781534i	$0.714437\pi$
$294$	−467.339	+	181.591i	−1.58959	+	0.617658i
$295$	−36.3149	−	43.2784i	−0.123101	−	0.146706i
$296$	273.652	−	207.459i	0.924501	−	0.700875i
$297$	−25.1336	−	219.340i	−0.0846251	−	0.738519i
$298$	35.5735	−	7.81401i	0.119374	−	0.0262215i
$299$	−328.147	−	391.070i	−1.09748	−	1.30793i
$300$	3.15139	+	49.7698i	0.0105046	+	0.165899i
$301$	−20.0488	+	113.702i	−0.0666073	+	0.377749i
$302$	183.735	+	289.646i	0.608394	+	0.959092i
$303$	88.2158	−	100.930i	0.291141	−	0.333103i
$304$	−81.8665	+	139.287i	−0.269298	+	0.458181i
$305$	−78.4368	−	135.856i	−0.257170	−	0.445431i
$306$	232.591	−	41.3468i	0.760100	−	0.135120i
$307$	369.715	+	213.455i	1.20428	+	0.695294i	0.961505	−	0.274787i	$-0.0886075\pi$
$307$	369.715	+	213.455i	1.20428	+	0.695294i	0.242780	+	0.970081i	$0.421941\pi$
$308$	375.273	−	31.3640i	1.21842	−	0.101831i
$309$	−251.123	+	415.400i	−0.812696	+	1.34434i
$310$	40.8258	−	78.0552i	0.131696	−	0.251791i
$311$	−303.936	+	362.217i	−0.977287	+	1.16468i	0.00905262	+	0.999959i	$0.497118\pi$
$311$	−303.936	+	362.217i	−0.977287	+	1.16468i	−0.986339	+	0.164726i	$0.947326\pi$
$312$	241.188	−	542.017i	0.773037	−	1.73724i
$313$	−271.635	−	98.8672i	−0.867845	−	0.315870i	−0.130551	−	0.991442i	$-0.541675\pi$
$313$	−271.635	−	98.8672i	−0.867845	−	0.315870i	−0.737294	+	0.675572i	$0.763897\pi$
$314$	104.543	−	329.337i	0.332940	−	1.04884i
$315$	143.767	+	450.720i	0.456404	+	1.43086i
$316$	174.863	−	247.678i	0.553365	−	0.783790i
$317$	−45.4577	−	257.803i	−0.143400	−	0.813260i	−0.968638	−	0.248476i	$-0.920070\pi$
$317$	−45.4577	−	257.803i	−0.143400	−	0.813260i	0.825238	−	0.564784i	$-0.191041\pi$
$318$	−51.1507	+	1.10214i	−0.160851	+	0.00346586i
$319$	23.1187	+	63.5181i	0.0724724	+	0.199116i
$320$	263.362	+	126.564i	0.823006	+	0.395512i
$321$	304.137	−	244.931i	0.947467	−	0.763026i
$322$	−290.238	+	376.729i	−0.901361	+	1.16997i
$323$			132.526i			0.410297i
$324$	−55.3710	+	319.234i	−0.170898	+	0.985289i
$325$	102.727			0.316084
$326$	36.7065	+	28.2793i	0.112597	+	0.0867463i
$327$	48.5881	+	60.3330i	0.148588	+	0.184505i
$328$	−161.153	−	314.025i	−0.491321	−	0.957395i
$329$	−956.362	+	348.087i	−2.90688	+	1.05802i
$330$	−4.82521	−	223.939i	−0.0146219	−	0.678604i
$331$	63.1721	−	11.1389i	0.190852	−	0.0336524i	−0.0774050	−	0.997000i	$-0.524663\pi$
$331$	63.1721	−	11.1389i	0.190852	−	0.0336524i	0.268257	+	0.963347i	$0.413552\pi$
$332$	73.3661	−	103.916i	0.220982	−	0.313001i
$333$	285.700	+	260.047i	0.857957	+	0.780921i
$334$	−452.933	−	143.777i	−1.35609	−	0.430470i
$335$	92.5194	−	254.195i	0.276177	−	0.758791i
$336$	−541.367	−	111.121i	−1.61121	−	0.330717i
$337$	274.967	+	230.725i	0.815926	+	0.684644i	0.952014	−	0.306053i	$-0.0990086\pi$
$337$	274.967	+	230.725i	0.815926	+	0.684644i	−0.136088	+	0.990697i	$0.543453\pi$
$338$	−783.380	−	409.737i	−2.31769	−	1.21224i
$339$	50.4296	+	30.4864i	0.148760	+	0.0899304i
$340$	238.845	−	19.9618i	0.702486	−	0.0587113i
$341$	39.4410	−	68.3137i	0.115663	−	0.200334i
$342$	−170.885	−	61.9270i	−0.499664	−	0.181073i
$343$	344.633	−	198.974i	1.00476	−	0.580099i
$344$	−54.5412	+	58.8295i	−0.158550	+	0.171016i
$345$	212.982	+	186.152i	0.617339	+	0.539572i
$346$	−413.972	+	262.600i	−1.19645	+	0.758960i
$347$	468.627	+	82.6316i	1.35051	+	0.238131i	0.801655	−	0.597787i	$-0.203953\pi$
$347$	468.627	+	82.6316i	1.35051	+	0.238131i	0.548854	+	0.835918i	$0.315064\pi$
$348$	−6.26864	−	99.0004i	−0.0180133	−	0.284484i
$349$	369.888	−	310.373i	1.05985	−	0.889320i	0.0657560	−	0.997836i	$-0.479054\pi$
$349$	369.888	−	310.373i	1.05985	−	0.889320i	0.994095	+	0.108515i	$0.0346097\pi$
$350$	−20.5310	−	93.4680i	−0.0586600	−	0.267051i
$351$	649.074	+	155.387i	1.84921	+	0.442699i
$352$	230.911	+	123.069i	0.655998	+	0.349628i
$353$	−314.600	+	263.981i	−0.891219	+	0.747822i	−0.968454	−	0.249191i	$-0.919835\pi$
$353$	−314.600	+	263.981i	−0.891219	+	0.747822i	0.0772349	+	0.997013i	$0.475391\pi$
$354$	26.8908	+	69.2056i	0.0759628	+	0.195496i
$355$	−114.359	−	20.1646i	−0.322139	−	0.0568017i
$356$	−74.4828	+	73.9065i	−0.209221	+	0.207602i
$357$	−429.022	+	146.432i	−1.20174	+	0.410174i
$358$	110.626	−	45.5713i	0.309011	−	0.127294i
$359$	560.800	−	323.778i	1.56212	−	0.901889i	0.565074	−	0.825040i	$-0.308848\pi$
$359$	560.800	−	323.778i	1.56212	−	0.901889i	0.997043	−	0.0768487i	$-0.0244858\pi$
$360$	−85.8685	+	317.306i	−0.238524	+	0.881405i
$361$	−129.518	+	224.331i	−0.358774	+	0.621416i
$362$	134.455	+	17.9671i	0.371423	+	0.0496328i
$363$	−3.27209	+	162.383i	−0.00901403	+	0.447337i
$364$	−298.914	+	1098.48i	−0.821192	+	3.01780i
$365$	−63.7244	−	53.4711i	−0.174587	−	0.146496i
$366$	40.1650	+	202.211i	0.109740	+	0.552490i
$367$	−147.995	+	406.613i	−0.403256	+	1.10794i	0.557412	+	0.830236i	$0.311794\pi$
$367$	−147.995	+	406.613i	−0.403256	+	1.10794i	−0.960668	+	0.277700i	$0.910428\pi$
$368$	−311.378	+	110.601i	−0.846136	+	0.300546i
$369$	314.218	−	242.779i	0.851540	−	0.657937i
$370$	264.239	+	289.493i	0.714159	+	0.782413i
$371$	96.6862	−	17.0484i	0.260610	−	0.0459525i
$372$	−83.8005	+	79.8665i	−0.225270	+	0.214695i
$373$	442.492	−	161.054i	1.18630	−	0.431779i	0.327880	−	0.944719i	$-0.393666\pi$
$373$	442.492	−	161.054i	1.18630	−	0.431779i	0.858424	+	0.512940i	$0.171444\pi$
$374$	214.445	−	8.94566i	0.573381	−	0.0239189i
$375$	−394.587	+	61.4070i	−1.05223	+	0.163752i
$376$	−689.490	−	157.076i	−1.83375	−	0.417755i
$377$	−204.341			−0.542020
$378$	11.6579	−	621.626i	0.0308411	−	1.64451i
$379$			387.390i			1.02214i	0.859540	+	0.511068i	$0.170750\pi$
$379$			387.390i			1.02214i	−0.859540	+	0.511068i	$0.829250\pi$
$380$	−166.826	−	78.5824i	−0.439015	−	0.206796i
$381$	−277.743	−	107.475i	−0.728984	−	0.282087i
$382$	9.65643	−	0.402823i	0.0252786	−	0.00105451i
$383$	97.0070	+	266.524i	0.253282	+	0.695886i	0.999543	+	0.0302328i	$0.00962487\pi$
$383$	97.0070	+	266.524i	0.253282	+	0.695886i	−0.746261	+	0.665653i	$0.768153\pi$
$384$	−274.202	−	268.830i	−0.714067	−	0.700077i
$385$	74.6383	+	423.295i	0.193866	+	1.09947i
$386$	−149.776	−	164.090i	−0.388020	−	0.425104i
$387$	−76.2778	−	48.2372i	−0.197100	−	0.124644i
$388$	−11.4468	+	125.234i	−0.0295022	+	0.322768i
$389$	−67.3782	−	24.5237i	−0.173209	−	0.0630428i	0.253960	−	0.967215i	$-0.418267\pi$
$389$	−67.3782	−	24.5237i	−0.173209	−	0.0630428i	−0.427169	+	0.904172i	$0.640489\pi$
$390$	641.141	+	217.833i	1.64395	+	0.558547i
$391$	−174.226	+	207.634i	−0.445590	+	0.531033i
$392$	667.689	+	33.0502i	1.70329	+	0.0843116i
$393$	−104.381	−	189.511i	−0.265601	−	0.482217i
$394$	410.300	+	54.8278i	1.04137	+	0.139157i
$395$	299.690	+	173.026i	0.758708	+	0.438040i
$396$	−88.6712	+	280.695i	−0.223917	+	0.708825i
$397$	66.7682	+	115.646i	0.168182	+	0.291300i	0.937781	−	0.347228i	$-0.112877\pi$
$397$	66.7682	+	115.646i	0.168182	+	0.291300i	−0.769599	+	0.638528i	$0.779544\pi$
$398$	−203.859	+	83.9776i	−0.512207	+	0.210999i
$399$	342.197	+	67.4736i	0.857635	+	0.169107i
$400$	23.2265	−	62.3041i	0.0580662	−	0.155760i
$401$	95.0909	−	539.287i	0.237134	−	1.34486i	−0.600937	−	0.799296i	$-0.705206\pi$
$401$	95.0909	−	539.287i	0.237134	−	1.34486i	0.838072	−	0.545560i	$-0.183683\pi$
$402$	−222.591	+	277.188i	−0.553710	+	0.689523i
$403$	153.281	+	182.674i	0.380351	+	0.453285i
$404$	−162.277	+	74.9053i	−0.401677	+	0.185409i
$405$	−368.609	−	29.7710i	−0.910146	−	0.0735085i
$406$	40.8396	+	185.923i	0.100590	+	0.457939i
$407$	225.615	+	268.877i	0.554336	+	0.660632i
$408$	−305.642	−	76.1381i	−0.749123	−	0.186613i
$409$	105.910	−	600.648i	0.258950	−	1.46858i	−0.526778	−	0.850003i	$-0.676600\pi$
$409$	105.910	−	600.648i	0.258950	−	1.46858i	0.785727	−	0.618573i	$-0.212289\pi$
$410$	340.194	−	215.800i	0.829741	−	0.526341i
$411$	−300.556	−	59.2630i	−0.731280	−	0.144192i
$412$	531.600	−	369.162i	1.29029	−	0.896024i
$413$	−71.2371	−	123.386i	−0.172487	−	0.298756i
$414$	−186.320	−	321.678i	−0.450049	−	0.777000i
$415$	125.739	+	72.5952i	0.302985	+	0.174928i
$416$	−588.355	+	528.711i	−1.41431	+	1.27094i
$417$	229.652	+	416.949i	0.550725	+	0.999878i
$418$	−146.329	−	76.5357i	−0.350070	−	0.183100i
$419$	271.624	−	323.708i	0.648267	−	0.772574i	−0.337385	−	0.941367i	$-0.609542\pi$
$419$	271.624	−	323.708i	0.648267	−	0.772574i	0.985652	+	0.168793i	$0.0539869\pi$
$420$	70.0609	−	626.888i	0.166812	−	1.49259i
$421$	−158.812	−	57.8029i	−0.377226	−	0.137299i	0.146447	−	0.989219i	$-0.453216\pi$
$421$	−158.812	−	57.8029i	−0.377226	−	0.137299i	−0.523673	+	0.851920i	$0.675438\pi$
$422$	−343.991	−	109.195i	−0.815144	−	0.258755i
$423$	32.0483	−	794.904i	0.0757643	−	1.87921i
$424$	62.8709	+	26.4721i	0.148281	+	0.0624343i
$425$	−9.47107	−	53.7131i	−0.0222849	−	0.126384i
$426$	133.776	+	73.4394i	0.314028	+	0.172393i
$427$	−135.307	−	371.753i	−0.316878	−	0.870616i
$428$	−503.446	+	132.804i	−1.17628	+	0.310291i
$429$	565.511	+	218.829i	1.31821	+	0.510092i
$430$	−72.5350	−	55.8822i	−0.168686	−	0.129959i
$431$		−	132.068i		−	0.306422i	−0.988193	−	0.153211i	$-0.951039\pi$
$431$		−	132.068i		−	0.306422i	0.988193	−	0.153211i	$-0.0489614\pi$
$432$	240.997	−	358.531i	0.557864	−	0.829933i
$433$	303.878			0.701797			0.350898	−	0.936414i	$-0.385876\pi$
$433$	303.878			0.701797			0.350898	+	0.936414i	$0.385876\pi$
$434$	135.574	−	175.975i	0.312382	−	0.405472i
$435$	111.877	−	17.4108i	0.257189	−	0.0400247i
$436$	−26.3450	−	99.8708i	−0.0604243	−	0.229061i
$437$	195.966	−	71.3257i	0.448434	−	0.163217i
$438$	56.6881	+	93.4767i	0.129425	+	0.213417i
$439$	−419.874	+	74.0352i	−0.956433	+	0.168645i	−0.630017	−	0.776581i	$-0.716952\pi$
$439$	−419.874	+	74.0352i	−0.956433	+	0.168645i	−0.326416	+	0.945226i	$0.605841\pi$
$440$	−115.896	+	275.251i	−0.263400	+	0.625570i
$441$	100.653	+	745.304i	0.228238	+	1.69003i
$442$	−196.311	+	618.429i	−0.444143	+	1.39916i
$443$	101.688	−	279.386i	0.229544	−	0.630667i	−0.770432	−	0.637522i	$-0.779960\pi$
$443$	101.688	−	279.386i	0.229544	−	0.630667i	0.999977	+	0.00685446i	$0.00218186\pi$
$444$	−206.411	−	471.938i	−0.464890	−	1.06292i
$445$	−91.7440	−	76.9823i	−0.206166	−	0.172994i
$446$	7.65481	−	14.6353i	0.0171633	−	0.0328146i
$447$	1.10064	−	54.6213i	0.00246229	−	0.122195i
$448$	598.644	+	429.656i	1.33626	+	0.959054i
$449$	−344.212	+	596.193i	−0.766620	+	1.32782i	0.172766	+	0.984963i	$0.444729\pi$
$449$	−344.212	+	596.193i	−0.766620	+	1.32782i	−0.939386	+	0.342861i	$0.888604\pi$
$450$	73.6858	+	12.8868i	0.163746	+	0.0286373i
$451$	312.432	−	180.383i	0.692755	−	0.399962i
$452$	−44.8164	−	64.5364i	−0.0991513	−	0.142780i
$453$	486.927	−	166.196i	1.07490	−	0.366879i
$454$	−141.841	−	223.603i	−0.312426	−	0.492518i
$455$	−1279.64	−	225.635i	−2.81239	−	0.495901i
$456$	174.364	+	168.312i	0.382377	+	0.369105i
$457$	426.489	−	357.867i	0.933237	−	0.783079i	−0.0431589	−	0.999068i	$-0.513742\pi$
$457$	426.489	−	357.867i	0.933237	−	0.783079i	0.976396	+	0.215990i	$0.0692977\pi$
$458$	730.959	−	160.561i	1.59598	−	0.350570i
$459$	21.4053	−	353.708i	0.0466346	−	0.770607i
$460$	−158.064	−	342.436i	−0.343618	−	0.744427i
$461$	−263.908	+	221.445i	−0.572469	+	0.480358i	−0.882464	−	0.470380i	$-0.844117\pi$
$461$	−263.908	+	221.445i	−0.572469	+	0.480358i	0.309995	+	0.950738i	$0.399672\pi$
$462$	86.0826	−	558.274i	0.186326	−	1.20839i
$463$	613.691	+	108.210i	1.32547	+	0.233715i	0.791177	−	0.611587i	$-0.209468\pi$
$463$	613.691	+	108.210i	1.32547	+	0.233715i	0.534289	+	0.845302i	$0.320580\pi$
$464$	−46.2013	+	123.933i	−0.0995718	+	0.267097i
$465$	−99.4865	−	86.9540i	−0.213949	−	0.186998i
$466$	−73.8354	−	179.238i	−0.158445	−	0.384631i
$467$	−513.973	+	296.742i	−1.10058	+	0.635422i	−0.936374	−	0.351003i	$-0.885841\pi$
$467$	−513.973	+	296.742i	−1.10058	+	0.635422i	−0.164210	+	0.986425i	$0.552507\pi$
$468$	−705.698	−	542.114i	−1.50790	−	1.15836i
$469$	341.091	−	590.787i	0.727272	−	1.25967i
$470$	106.906	−	800.026i	0.227460	−	1.70218i
$471$	−443.547	−	268.139i	−0.941713	−	0.569297i
$472$	4.89421	−	98.8742i	0.0103691	−	0.209479i
$473$	−62.8127	−	52.7062i	−0.132797	−	0.111429i
$474$	−299.763	−	342.002i	−0.632411	−	0.721524i
$475$	−14.3526	+	39.4334i	−0.0302160	+	0.0830178i
$476$	601.922	+	55.0178i	1.26454	+	0.115584i
$477$	−16.3602	+	74.9798i	−0.0342982	+	0.157190i
$478$	−691.785	+	631.438i	−1.44725	+	1.32100i
$479$	539.671	−	95.1586i	1.12666	−	0.198661i	0.420898	−	0.907108i	$-0.361715\pi$
$479$	539.671	−	95.1586i	1.12666	−	0.198661i	0.705764	+	0.708447i	$0.250604\pi$
$480$	277.077	−	339.601i	0.577244	−	0.707501i
$481$	−997.081	+	362.908i	−2.07293	+	0.754486i
$482$	12.0547	+	288.975i	0.0250098	+	0.599533i
$483$	447.430	+	555.584i	0.926355	+	1.15028i
$484$	92.2817	−	195.909i	0.190665	−	0.404770i
$485$	−143.536			−0.295951
$486$	446.085	+	192.883i	0.917871	+	0.396878i
$487$			190.678i			0.391536i	0.980650	+	0.195768i	$0.0627199\pi$
$487$			190.678i			0.391536i	−0.980650	+	0.195768i	$0.937280\pi$
$488$	61.0579	−	268.015i	0.125119	−	0.549212i
$489$	54.1331	−	43.5952i	0.110702	−	0.0891517i
$490$	31.8023	+	762.361i	0.0649026	+	1.55584i
$491$	−117.631	−	323.189i	−0.239575	−	0.658226i	−0.999962	−	0.00875596i	$-0.997213\pi$
$491$	−117.631	−	323.189i	−0.239575	−	0.658226i	0.760387	−	0.649470i	$-0.225009\pi$
$492$	−514.548	+	124.702i	−1.04583	+	0.253459i
$493$	18.8395	+	106.844i	0.0382141	+	0.216723i
$494$	368.714	−	336.549i	0.746384	−	0.681273i
$495$	−328.264	−	71.6256i	−0.663159	−	0.144698i
$496$	145.448	−	51.6630i	0.293243	−	0.104159i
$497$	−275.185	−	100.159i	−0.553692	−	0.201527i
$498$	−125.769	−	143.491i	−0.252549	−	0.288135i
$499$	286.634	−	341.597i	0.574417	−	0.684563i	−0.398114	−	0.917336i	$-0.630335\pi$
$499$	286.634	−	341.597i	0.574417	−	0.684563i	0.972531	+	0.232772i	$0.0747797\pi$
$500$	513.767	+	139.804i	1.02753	+	0.279608i
$501$	−368.768	+	610.004i	−0.736064	+	1.21757i
$502$	75.3460	−	563.847i	0.150092	−	1.12320i
$503$	−756.960	−	437.031i	−1.50489	−	0.868849i	−0.999984	−	0.00567418i	$-0.998194\pi$
$503$	−756.960	−	437.031i	−1.50489	−	0.868849i	−0.504906	−	0.863174i	$-0.668473\pi$
$504$	−352.210	+	750.437i	−0.698830	+	1.48896i
$505$	−102.001	−	176.670i	−0.201981	−	0.349842i
$506$	−128.642	−	312.284i	−0.254234	−	0.617162i
$507$	−872.690	+	998.469i	−1.72128	+	1.96937i
$508$	279.687	+	281.868i	0.550565	+	0.554859i
$509$	121.243	−	687.602i	0.238198	−	1.35089i	−0.597575	−	0.801813i	$-0.703869\pi$
$509$	121.243	−	687.602i	0.238198	−	1.35089i	0.835773	−	0.549075i	$-0.185020\pi$
$510$	54.7879	−	355.318i	0.107427	−	0.696701i
$511$	−134.846	−	160.703i	−0.263886	−	0.314488i
$512$	187.637	+	476.378i	0.366479	+	0.930426i
$513$	−150.334	+	227.447i	−0.293048	+	0.443367i
$514$	−418.672	+	91.9648i	−0.814538	+	0.178920i
$515$	474.837	+	565.889i	0.922014	+	1.09881i
$516$	66.6321	+	100.202i	0.129132	+	0.194189i
$517$	125.511	−	711.809i	0.242768	−	1.37681i
$518$	529.473	+	834.679i	1.02215	+	1.61135i
$519$	237.534	+	695.933i	0.457676	+	1.34091i
$520$	−662.085	−	613.823i	−1.27324	−	1.18043i
$521$	−198.852	−	344.421i	−0.381673	−	0.661077i	0.609629	−	0.792687i	$-0.291319\pi$
$521$	−198.852	−	344.421i	−0.381673	−	0.661077i	−0.991302	+	0.131610i	$0.957985\pi$
$522$	−146.573	−	25.6339i	−0.280792	−	0.0491071i
$523$	−732.018	−	422.631i	−1.39965	−	0.808089i	−0.405296	−	0.914186i	$-0.632831\pi$
$523$	−732.018	−	422.631i	−1.39965	−	0.808089i	−0.994356	+	0.106096i	$0.966165\pi$
$524$	24.0259	+	287.473i	0.0458510	+	0.548612i
$525$	−143.515	−	2.89189i	−0.273363	−	0.00550837i
$526$	114.660	−	219.220i	0.217985	−	0.416767i
$527$	81.3829	−	96.9884i	0.154427	−	0.184039i
$528$	260.581	−	293.506i	0.493525	−	0.555882i
$529$	−96.3010	−	35.0507i	−0.182044	−	0.0662584i
$530$	−23.5576	+	74.2124i	−0.0444484	+	0.140023i
$531$	110.368	−	14.9051i	0.207849	−	0.0280699i
$532$	−379.905	−	268.218i	−0.714108	−	0.504168i
$533$	189.383	+	1074.04i	0.355315	+	2.01509i
$534$	81.6139	+	134.578i	0.152835	+	0.252019i
$535$	−203.257	−	558.443i	−0.379919	−	1.04382i
$536$	421.711	−	216.416i	0.786774	−	0.403761i
$537$	−27.5971	−	177.333i	−0.0513913	−	0.330228i
$538$	−482.761	+	626.623i	−0.897325	+	1.16473i
$539$			683.286i			1.26769i
$540$	432.562	+	236.680i	0.801040	+	0.438296i
$541$	−419.088			−0.774654			−0.387327	−	0.921942i	$-0.626602\pi$
$541$	−419.088			−0.774654			−0.387327	+	0.921942i	$0.626602\pi$
$542$	732.791	+	564.555i	1.35201	+	1.04161i
$543$	73.4307	−	189.764i	0.135232	−	0.349473i
$544$	330.692	+	258.889i	0.607890	+	0.475898i
$545$	110.781	−	40.3209i	0.203268	−	0.0739834i
$546$	1496.90	+	821.761i	2.74158	+	1.50506i
$547$	−360.585	+	63.5809i	−0.659205	+	0.116236i	−0.493236	−	0.869895i	$-0.664186\pi$
$547$	−360.585	+	63.5809i	−0.659205	+	0.116236i	−0.165969	+	0.986131i	$0.553075\pi$
$548$	333.676	+	235.579i	0.608898	+	0.429889i
$549$	308.992	+	12.4577i	0.562826	+	0.0226916i
$550$	64.7774	+	20.5626i	0.117777	+	0.0373866i
$551$	28.5497	−	78.4396i	0.0518143	−	0.142359i
$552$	51.9119	+	492.930i	0.0940434	+	0.892989i
$553$	668.519	+	560.954i	1.20890	+	1.01438i
$554$	63.0899	+	32.9984i	0.113881	+	0.0595638i
$555$	514.982	−	283.648i	0.927896	−	0.511078i
$556$	−52.8602	−	632.477i	−0.0950722	−	1.13755i
$557$	96.4150	−	166.996i	0.173097	−	0.299813i	−0.766404	−	0.642359i	$-0.777956\pi$
$557$	96.4150	−	166.996i	0.173097	−	0.299813i	0.939501	+	0.342546i	$0.111289\pi$
$558$	87.0324	+	150.260i	0.155972	+	0.269283i
$559$	214.669	−	123.939i	0.384023	−	0.221716i
$560$	−426.172	+	725.086i	−0.761022	+	1.29480i
$561$	62.2816	−	315.865i	0.111019	−	0.563039i
$562$	105.388	−	66.8524i	0.187524	−	0.118954i
$563$	−413.192	−	72.8569i	−0.733912	−	0.129408i	−0.205813	−	0.978591i	$-0.565984\pi$
$563$	−413.192	−	72.8569i	−0.733912	−	0.129408i	−0.528099	+	0.849183i	$0.677095\pi$
$564$	−471.256	+	950.301i	−0.835561	+	1.68493i
$565$	68.6991	−	57.6454i	0.121591	−	0.102027i
$566$	−118.202	−	538.116i	−0.208837	−	0.950735i
$567$	−902.416	−	235.356i	−1.59156	−	0.415091i
$568$	−122.927	−	162.149i	−0.216421	−	0.285473i
$569$	787.303	−	660.626i	1.38366	−	1.16103i	0.415825	−	0.909445i	$-0.363493\pi$
$569$	787.303	−	660.626i	1.38366	−	1.16103i	0.967835	−	0.251584i	$-0.0809516\pi$
$570$	−173.196	+	215.677i	−0.303853	+	0.378381i
$571$	99.4864	+	17.5421i	0.174232	+	0.0307218i	0.260083	−	0.965586i	$-0.416250\pi$
$571$	99.4864	+	17.5421i	0.174232	+	0.0307218i	−0.0858515	+	0.996308i	$0.527361\pi$
$572$	−569.470	−	573.911i	−0.995577	−	1.00334i
$573$	2.80454	−	14.2234i	0.00489448	−	0.0248226i
$574$	939.385	−	386.970i	1.63656	−	0.674165i
$575$	−74.3281	+	42.9134i	−0.129266	+	0.0746319i
$576$	−488.350	+	305.435i	−0.847829	+	0.530269i
$577$	93.5986	−	162.118i	0.162216	−	0.280966i	−0.773447	−	0.633861i	$-0.781469\pi$
$577$	93.5986	−	162.118i	0.162216	−	0.280966i	0.935663	+	0.352894i	$0.114803\pi$
$578$	−231.449	−	30.9283i	−0.400431	−	0.0535091i
$579$	−291.902	+	160.777i	−0.504149	+	0.277681i
$580$	−145.668	−	39.6387i	−0.251153	−	0.0683427i
$581$	280.486	+	235.356i	0.482764	+	0.405087i
$582$	178.607	+	60.6833i	0.306885	+	0.104267i
$583$	−23.8473	+	65.5201i	−0.0409045	+	0.112384i
$584$	−18.1837	−	144.625i	−0.0311365	−	0.247645i
$585$	542.875	−	858.453i	0.927991	−	1.46744i
$586$	−693.714	−	760.013i	−1.18381	−	1.29695i
$587$	−408.972	+	72.1129i	−0.696716	+	0.122850i	−0.510779	−	0.859712i	$-0.670643\pi$
$587$	−408.972	+	72.1129i	−0.696716	+	0.122850i	−0.185937	+	0.982562i	$0.559532\pi$
$588$	282.733	−	962.075i	0.480838	−	1.63618i
$589$	−91.5380	+	33.3171i	−0.155413	+	0.0565655i
$590$	112.894	−	4.70942i	0.191345	−	0.00798206i
$591$	224.079	−	579.078i	0.379153	−	0.979827i
$592$	−5.33480	+	686.783i	−0.00901149	+	1.16011i
$593$	−598.860			−1.00988			−0.504941	−	0.863154i	$-0.668486\pi$
$593$	−598.860			−1.00988			−0.504941	+	0.863154i	$0.668486\pi$
$594$	378.188	+	227.907i	0.636679	+	0.383682i
$595$			689.890i			1.15948i
$596$	−31.0411	+	65.8983i	−0.0520823	+	0.110568i
$597$	50.8552	+	326.784i	0.0851846	+	0.547376i
$598$	1020.12	−	42.5550i	1.70589	−	0.0711622i
$599$	−346.568	−	952.189i	−0.578578	−	1.58963i	−0.790578	−	0.612361i	$-0.790220\pi$
$599$	−346.568	−	952.189i	−0.578578	−	1.58963i	0.212000	−	0.977270i	$-0.432002\pi$
$600$	−82.6989	−	55.7562i	−0.137831	−	0.0929271i
$601$	68.1551	+	386.527i	0.113403	+	0.643140i	0.987529	+	0.157440i	$0.0503241\pi$
$601$	68.1551	+	386.527i	0.113403	+	0.643140i	−0.874126	+	0.485700i	$0.838565\pi$
$602$	−155.672	−	170.549i	−0.258591	−	0.283305i
$603$	326.032	+	421.970i	0.540684	+	0.699784i
$604$	−683.164	−	62.4436i	−1.13107	−	0.103384i
$605$	232.267	+	84.5381i	0.383912	+	0.139732i
$606$	52.2312	+	262.959i	0.0861901	+	0.433926i
$607$	121.947	−	145.331i	0.200901	−	0.239424i	−0.656182	−	0.754602i	$-0.727830\pi$
$607$	121.947	−	145.331i	0.200901	−	0.239424i	0.857083	+	0.515178i	$0.172274\pi$
$608$	−120.752	−	299.718i	−0.198604	−	0.492958i
$609$	285.476	+	5.75245i	0.468761	+	0.00944574i
$610$	310.983	+	41.5562i	0.509808	+	0.0681249i
$611$	1892.29	+	1092.51i	3.09704	+	1.78807i
$612$	−218.393	+	418.970i	−0.356851	+	0.684592i
$613$	−373.608	−	647.108i	−0.609474	−	1.05564i	−0.991327	−	0.131418i	$-0.958047\pi$
$613$	−373.608	−	647.108i	−0.609474	−	1.05564i	0.381853	−	0.924223i	$-0.375286\pi$
$614$	−789.461	+	325.211i	−1.28577	+	0.529659i
$615$	−195.200	−	571.904i	−0.317399	−	0.929926i
$616$	−408.368	+	632.843i	−0.662935	+	1.02734i
$617$	−117.557	+	666.700i	−0.190530	+	1.08055i	0.728111	+	0.685459i	$0.240399\pi$
$617$	−117.557	+	666.700i	−0.190530	+	1.08055i	−0.918641	+	0.395092i	$0.870713\pi$
$618$	−351.613	−	904.902i	−0.568953	−	1.46424i
$619$	639.472	+	762.093i	1.03307	+	1.23117i	0.972475	+	0.233006i	$0.0748560\pi$
$619$	639.472	+	762.093i	1.03307	+	1.23117i	0.0605971	+	0.998162i	$0.480700\pi$
$620$	73.8339	+	159.956i	0.119087	+	0.257994i
$621$	−534.548	+	158.715i	−0.860786	+	0.255579i
$622$	−202.890	−	923.661i	−0.326189	−	1.48499i
$623$	−194.138	−	231.364i	−0.311618	−	0.371371i
$624$	564.345	+	1043.71i	0.904400	+	1.67261i
$625$	−87.4900	+	496.180i	−0.139984	+	0.793888i
$626$	488.198	−	309.685i	0.779869	−	0.494705i
$627$	−163.012	+	186.506i	−0.259987	+	0.297458i
$628$	394.176	+	567.621i	0.627669	+	0.903855i
$629$	281.681	+	487.886i	0.447824	+	0.775654i
$630$	−889.576	−	322.373i	−1.41202	−	0.511704i
$631$	301.563	+	174.107i	0.477913	+	0.275923i	0.719546	−	0.694445i	$-0.244350\pi$
$631$	301.563	+	174.107i	0.477913	+	0.275923i	−0.241634	+	0.970368i	$0.577683\pi$
$632$	178.967	+	579.359i	0.283176	+	0.916707i
$633$	−280.070	+	463.282i	−0.442448	+	0.731883i
$634$	463.934	+	242.655i	0.731757	+	0.382737i
$635$	−291.327	+	347.190i	−0.458783	+	0.546756i
$636$	60.6885	−	82.3854i	0.0954221	−	0.129537i
$637$	−1941.03	−	706.479i	−3.04715	−	1.10907i
$638$	−128.853	−	40.9024i	−0.201964	−	0.0641104i
$639$	154.087	−	169.287i	0.241138	−	0.264925i
$640$	−521.980	+	262.770i	−0.815594	+	0.410578i
$641$	−34.7159	−	196.884i	−0.0541589	−	0.307151i	0.945680	−	0.325099i	$-0.105398\pi$
$641$	−34.7159	−	196.884i	−0.0541589	−	0.307151i	−0.999839	+	0.0179485i	$0.994287\pi$
$642$	16.8243	+	780.820i	0.0262061	+	1.21623i
$643$	−255.040	−	700.717i	−0.396641	−	1.08976i	−0.963910	−	0.266230i	$-0.914222\pi$
$643$	−255.040	−	700.717i	−0.396641	−	1.08976i	0.567269	−	0.823533i	$-0.308000\pi$
$644$	−242.601	−	919.672i	−0.376710	−	1.42806i
$645$	−106.972	+	86.1476i	−0.165847	+	0.133562i
$646$	−209.966	−	161.761i	−0.325025	−	0.250405i
$647$			654.355i			1.01137i	0.862719	+	0.505684i	$0.168760\pi$
$647$			654.355i			1.01137i	−0.862719	+	0.505684i	$0.831240\pi$
$648$	−438.188	−	477.383i	−0.676217	−	0.736703i
$649$	101.184			0.155907
$650$	−125.389	+	162.755i	−0.192906	+	0.250392i
$651$	−209.000	−	259.520i	−0.321044	−	0.398648i
$652$	−89.6080	+	23.6378i	−0.137436	+	0.0362542i
$653$	621.236	−	226.111i	0.951357	−	0.346266i	0.180716	−	0.983535i	$-0.442158\pi$
$653$	621.236	−	226.111i	0.951357	−	0.346266i	0.770641	+	0.637270i	$0.219936\pi$
$654$	−154.895	+	3.33751i	−0.236842	+	0.00510323i
$655$	−324.259	+	57.1756i	−0.495052	+	0.0872910i
$656$	694.227	+	127.979i	1.05827	+	0.195090i
$657$	156.229	−	49.8327i	0.237791	−	0.0758488i
$658$	615.849	−	1940.08i	0.935940	−	2.94845i
$659$	125.066	−	343.616i	0.189782	−	0.521421i	−0.807912	−	0.589304i	$-0.799402\pi$
$659$	125.066	−	343.616i	0.189782	−	0.521421i	0.997693	+	0.0678827i	$0.0216244\pi$
$660$	360.686	+	265.696i	0.546493	+	0.402570i
$661$	90.6624	+	76.0748i	0.137159	+	0.115090i	0.708786	−	0.705423i	$-0.249243\pi$
$661$	90.6624	+	76.0748i	0.137159	+	0.115090i	−0.571627	+	0.820514i	$0.693687\pi$
$662$	−59.4601	+	113.682i	−0.0898188	+	0.171725i
$663$	832.892	+	503.512i	1.25625	+	0.759444i
$664$	75.0879	+	243.077i	0.113084	+	0.366080i
$665$	265.399	−	459.685i	0.399097	−	0.691255i
$666$	−760.728	+	135.232i	−1.14223	+	0.203051i
$667$	147.851	−	85.3618i	0.221666	−	0.127979i
$668$	780.642	−	542.105i	1.16863	−	0.811535i
$669$	−18.6537	−	16.3038i	−0.0278829	−	0.0243704i
$670$	289.802	+	456.853i	0.432540	+	0.681870i
$671$	276.691	+	48.7882i	0.412357	+	0.0727096i
$672$	836.847	−	722.074i	1.24531	−	1.07451i
$673$	594.886	−	499.169i	0.883932	−	0.741707i	−0.0830516	−	0.996545i	$-0.526467\pi$
$673$	594.886	−	499.169i	0.883932	−	0.741707i	0.966984	+	0.254838i	$0.0820222\pi$
$674$	−701.172	+	154.018i	−1.04031	+	0.228514i
$675$	44.6760	−	102.929i	0.0661866	−	0.152487i
$676$	1605.36	−	741.014i	2.37479	−	1.09617i
$677$	−149.055	+	125.072i	−0.220170	+	0.184745i	−0.746201	−	0.665721i	$-0.768124\pi$
$677$	−149.055	+	125.072i	−0.220170	+	0.184745i	0.526031	+	0.850466i	$0.323680\pi$
$678$	−109.855	+	42.6859i	−0.162029	+	0.0629585i
$679$	−356.478	−	62.8567i	−0.525004	−	0.0925724i
$680$	−259.909	+	402.777i	−0.382219	+	0.592320i
$681$	−375.903	+	128.302i	−0.551986	+	0.188402i
$682$	60.0904	+	145.872i	0.0881092	+	0.213888i
$683$	−420.466	+	242.756i	−0.615617	+	0.355427i	−0.775161	−	0.631764i	$-0.782331\pi$
$683$	−420.466	+	242.756i	−0.615617	+	0.355427i	0.159544	+	0.987191i	$0.448998\pi$
$684$	306.696	−	195.151i	0.448386	−	0.285309i
$685$	−233.104	+	403.748i	−0.340297	+	0.589413i
$686$	−105.417	+	788.884i	−0.153670	+	1.14998i
$687$	22.6158	−	1122.35i	0.0329197	−	1.63370i
$688$	−26.6328	−	158.219i	−0.0387105	−	0.229970i
$689$	−161.468	−	135.488i	−0.234352	−	0.196644i
$690$	−554.895	+	110.218i	−0.804195	+	0.159736i
$691$	−373.852	+	1027.15i	−0.541030	+	1.48647i	0.304485	+	0.952517i	$0.401516\pi$
$691$	−373.852	+	1027.15i	−0.541030	+	1.48647i	−0.845515	+	0.533951i	$0.820707\pi$
$692$	89.2466	−	976.402i	0.128969	−	1.41099i
$693$	−783.888	−	321.636i	−1.13115	−	0.464121i
$694$	−702.923	+	641.604i	−1.01286	+	0.924501i
$695$	713.412	−	125.794i	1.02649	−	0.180998i
$696$	164.502	+	110.908i	0.236353	+	0.159351i
$697$	544.126	−	198.046i	0.780669	−	0.284140i
$698$	40.2500	+	964.870i	0.0576648	+	1.38233i
$699$	−287.317	+	44.7133i	−0.411040	+	0.0639675i
$700$	173.145	+	81.5591i	0.247350	+	0.116513i
$701$	933.794			1.33209			0.666044	−	0.745912i	$-0.267986\pi$
$701$	933.794			1.33209			0.666044	+	0.745912i	$0.267986\pi$
$702$	−1038.45	+	838.687i	−1.47927	+	1.19471i
$703$		−	433.449i		−	0.616570i
$704$	−476.833	+	215.623i	−0.677320	+	0.306283i
$705$	−1129.12	−	436.922i	−1.60159	−	0.619748i
$706$	−34.2338	−	820.650i	−0.0484898	−	1.16239i
$707$	−175.956	−	483.434i	−0.248876	−	0.683782i
$708$	−142.468	−	41.8683i	−0.201226	−	0.0591360i
$709$	212.090	+	1202.82i	0.299139	+	1.69650i	0.649886	+	0.760032i	$0.274817\pi$
$709$	212.090	+	1202.82i	0.299139	+	1.69650i	−0.350746	+	0.936470i	$0.614072\pi$
$710$	171.535	−	156.571i	0.241598	−	0.220522i
$711$	−604.035	+	317.008i	−0.849557	+	0.445862i
$712$	−26.1791	−	208.216i	−0.0367684	−	0.292439i
$713$	−187.217	−	68.1414i	−0.262576	−	0.0955700i
$714$	291.666	−	858.452i	0.408496	−	1.20231i
$715$	593.170	−	706.913i	0.829609	−	0.988689i
$716$	−62.8299	+	230.894i	−0.0877512	+	0.322477i
$717$	677.819	+	1230.63i	0.945355	+	1.71636i
$718$	−171.539	+	1283.70i	−0.238913	+	1.78789i
$719$	392.348	+	226.522i	0.545685	+	0.315052i	0.747380	−	0.664397i	$-0.231311\pi$
$719$	392.348	+	226.522i	0.545685	+	0.315052i	−0.201695	+	0.979448i	$0.564645\pi$
$720$	−397.909	−	523.349i	−0.552651	−	0.726873i
$721$	931.464	+	1613.34i	1.29191	+	2.23765i
$722$	−197.327	−	479.019i	−0.273306	−	0.663461i
$723$	425.644	+	83.9276i	0.588719	+	0.116082i
$724$	−192.582	+	191.092i	−0.265998	+	0.263939i
$725$	−5.96552	+	33.8321i	−0.00822830	+	0.0466650i
$726$	−253.276	−	203.389i	−0.348866	−	0.280151i
$727$	−183.034	−	218.131i	−0.251766	−	0.300043i	0.625328	−	0.780362i	$-0.284965\pi$
$727$	−183.034	−	218.131i	−0.251766	−	0.300043i	−0.877094	+	0.480319i	$0.840521\pi$
$728$	−1375.51	−	1814.39i	−1.88944	−	2.49229i
$729$	437.974	−	582.769i	0.600787	−	0.799409i
$730$	162.498	−	35.6941i	0.222601	−	0.0488960i
$731$	−84.5959	−	100.818i	−0.115726	−	0.137917i
$732$	−369.397	−	183.185i	−0.504641	−	0.250252i
$733$	−127.118	+	720.924i	−0.173422	+	0.983525i	0.766528	+	0.642211i	$0.221983\pi$
$733$	−127.118	+	720.924i	−0.173422	+	0.983525i	−0.939950	+	0.341313i	$0.889128\pi$
$734$	−463.570	−	730.786i	−0.631566	−	0.995622i
$735$	1122.92	+	221.414i	1.52778	+	0.301244i
$736$	204.839	−	628.328i	0.278314	−	0.853706i
$737$	242.240	+	419.572i	0.328684	+	0.569297i
$738$	1.10860	+	794.164i	0.00150217	+	1.07610i
$739$	266.611	+	153.928i	0.360772	+	0.208292i	0.669419	−	0.742885i	$-0.266543\pi$
$739$	266.611	+	153.928i	0.360772	+	0.208292i	−0.308647	+	0.951177i	$0.599876\pi$
$740$	−781.185	+	65.2886i	−1.05566	+	0.0882279i
$741$	−361.270	−	655.910i	−0.487544	−	0.885169i
$742$	−91.0049	+	173.993i	−0.122648	+	0.234492i
$743$	−39.9815	+	47.6481i	−0.0538109	+	0.0641294i	−0.792279	−	0.610160i	$-0.791105\pi$
$743$	−39.9815	+	47.6481i	−0.0538109	+	0.0641294i	0.738468	+	0.674289i	$0.235550\pi$
$744$	−24.2487	−	230.254i	−0.0325923	−	0.309481i
$745$	−78.1282	−	28.4363i	−0.104870	−	0.0381696i
$746$	−284.942	+	897.639i	−0.381960	+	1.20327i
$747$	−253.431	+	133.005i	−0.339264	+	0.178052i
$748$	−247.578	+	350.672i	−0.330987	+	0.468813i
$749$	−260.245	−	1475.92i	−0.347457	−	1.97052i
$750$	384.344	−	700.113i	0.512458	−	0.933484i
$751$	81.5013	+	223.923i	0.108524	+	0.298167i	0.982053	−	0.188605i	$-0.0603966\pi$
$751$	81.5013	+	223.923i	0.108524	+	0.298167i	−0.873529	+	0.486772i	$0.838174\pi$
$752$	1090.45	−	900.659i	1.45007	−	1.19768i
$753$	−795.786	−	307.936i	−1.05682	−	0.408946i
$754$	249.419	−	323.746i	0.330795	−	0.429372i
$755$		−	783.005i		−	1.03709i
$756$	970.636	+	777.228i	1.28391	+	1.02808i
$757$	−1178.31			−1.55655			−0.778276	−	0.627923i	$-0.783905\pi$
$757$	−1178.31			−1.55655			−0.778276	+	0.627923i	$0.783905\pi$
$758$	−613.757	−	472.849i	−0.809706	−	0.623811i
$759$	−500.589	+	77.9034i	−0.659537	+	0.102640i
$760$	328.129	−	168.391i	0.431749	−	0.221567i
$761$	1203.80	−	438.148i	1.58187	−	0.575753i	0.606260	−	0.795267i	$-0.292669\pi$
$761$	1203.80	−	438.148i	1.58187	−	0.575753i	0.975610	+	0.219513i	$0.0704469\pi$
$762$	509.290	−	308.855i	0.668360	−	0.405321i
$763$	292.785	−	51.6259i	0.383729	−	0.0676618i
$764$	−11.1484	+	15.7907i	−0.0145922	+	0.0206685i
$765$	−498.912	−	204.708i	−0.652172	−	0.267592i
$766$	−540.672	−	171.628i	−0.705838	−	0.224058i
$767$	−104.618	+	287.437i	−0.136399	+	0.374754i
$768$	760.609	−	106.294i	0.990376	−	0.138404i
$769$	−143.704	−	120.582i	−0.186871	−	0.156803i	0.544553	−	0.838726i	$-0.316699\pi$
$769$	−143.704	−	120.582i	−0.186871	−	0.156803i	−0.731424	+	0.681923i	$0.761144\pi$
$770$	−761.746	−	398.422i	−0.989281	−	0.517431i
$771$	−12.9537	+	642.850i	−0.0168012	+	0.833787i
$772$	442.791	−	37.0069i	0.573563	−	0.0479364i
$773$	226.649	−	392.567i	0.293207	−	0.507849i	−0.681359	−	0.731949i	$-0.738611\pi$
$773$	226.649	−	392.567i	0.293207	−	0.507849i	0.974566	+	0.224100i	$0.0719442\pi$
$774$	169.529	−	61.9716i	0.219030	−	0.0800667i
$775$	34.7196	−	20.0454i	0.0447995	−	0.0258650i
$776$	−184.441	−	170.997i	−0.237682	−	0.220357i
$777$	1403.19	−	478.932i	1.80591	−	0.616386i
$778$	121.096	−	76.8163i	0.155650	−	0.0987356i
$779$	−438.748	−	77.3631i	−0.563219	−	0.0993107i
$780$	−1127.70	+	749.897i	−1.44577	+	0.961407i
$781$	159.319	−	133.685i	0.203994	−	0.171171i
$782$	−116.303	−	529.471i	−0.148725	−	0.677073i
$783$	−88.8679	+	204.742i	−0.113497	+	0.261484i
$784$	−867.345	+	1017.50i	−1.10631	+	1.29784i
$785$	−604.233	+	507.012i	−0.769724	+	0.645875i
$786$	427.658	+	65.9424i	0.544094	+	0.0838962i
$787$	−817.303	−	144.113i	−1.03850	−	0.183116i	−0.371703	−	0.928352i	$-0.621226\pi$
$787$	−817.303	−	144.113i	−1.03850	−	0.183116i	−0.666802	+	0.745235i	$0.732337\pi$
$788$	−587.679	+	583.132i	−0.745785	+	0.740015i
$789$	−279.410	−	244.212i	−0.354132	−	0.309521i
$790$	−639.934	+	263.614i	−0.810042	+	0.333689i
$791$	195.860	−	113.080i	0.247611	−	0.142958i
$792$	−336.484	−	483.102i	−0.424853	−	0.609977i
$793$	−424.677	+	735.562i	−0.535532	+	0.927569i
$794$	−264.720	−	35.3741i	−0.333400	−	0.0445518i
$795$	99.9483	+	60.4221i	0.125721	+	0.0760027i
$796$	115.781	−	425.484i	0.145454	−	0.534528i
$797$	−418.325	−	351.017i	−0.524875	−	0.440422i	0.341452	−	0.939899i	$-0.389081\pi$
$797$	−418.325	−	351.017i	−0.524875	−	0.440422i	−0.866327	+	0.499477i	$0.833526\pi$
$798$	−524.587	+	459.797i	−0.657377	+	0.576187i
$799$	396.782	−	1090.15i	0.496598	−	1.36439i
$800$	70.3606	+	112.847i	0.0879507	+	0.141059i
$801$	224.923	−	71.7441i	0.280802	−	0.0895682i
$802$	738.346	+	808.912i	0.920631	+	1.00862i
$803$	146.723	−	25.8712i	0.182718	−	0.0322182i
$804$	−167.465	−	690.997i	−0.208289	−	0.859449i
$805$	1020.14	−	371.300i	1.26725	−	0.461242i
$806$	−476.513	+	19.8780i	−0.591207	+	0.0246625i
$807$	744.221	+	924.117i	0.922207	+	1.14513i
$808$	79.4007	−	348.532i	0.0982682	−	0.431351i
$809$	−1048.73			−1.29633			−0.648167	−	0.761499i	$-0.724464\pi$
$809$	−1048.73			−1.29633			−0.648167	+	0.761499i	$0.724464\pi$
$810$	497.092	−	547.663i	0.613694	−	0.676127i
$811$			28.9928i			0.0357495i	0.999840	+	0.0178747i	$0.00569001\pi$
$811$			28.9928i			0.0357495i	−0.999840	+	0.0178747i	$0.994310\pi$
$812$	−344.414	−	162.235i	−0.424156	−	0.199796i
$813$	1080.69	−	870.314i	1.32926	−	1.07050i
$814$	−701.378	+	29.2583i	−0.861644	+	0.0359439i
$815$	−36.1775	−	99.3969i	−0.0443896	−	0.121959i
$816$	493.696	−	391.306i	0.605019	−	0.479542i
$817$	17.5834	+	99.7202i	0.0215219	+	0.122057i
$818$	822.355	+	900.950i	1.00532	+	1.10141i
$819$	1724.18	−	1894.27i	2.10522	−	2.31290i
$820$	−73.3411	+	802.388i	−0.0894404	+	0.978522i
$821$	687.233	+	250.132i	0.837069	+	0.304668i	0.724757	−	0.689005i	$-0.241952\pi$
$821$	687.233	+	250.132i	0.837069	+	0.304668i	0.112312	+	0.993673i	$0.464174\pi$
$822$	460.752	−	403.846i	0.560525	−	0.491297i
$823$	−337.483	+	402.197i	−0.410065	+	0.488696i	−0.931061	−	0.364863i	$-0.881116\pi$
$823$	−337.483	+	402.197i	−0.410065	+	0.488696i	0.520997	+	0.853559i	$0.325560\pi$
$824$	−63.9945	+	1292.83i	−0.0776632	+	1.56897i
$825$	52.7403	−	87.2414i	0.0639277	−	0.105747i
$826$	282.438	+	37.7418i	0.341934	+	0.0456922i
$827$	−437.915	−	252.830i	−0.529522	−	0.305720i	0.211300	−	0.977421i	$-0.432230\pi$
$827$	−437.915	−	252.830i	−0.529522	−	0.305720i	−0.740822	+	0.671702i	$0.765564\pi$
$828$	737.070	+	97.4465i	0.890181	+	0.117689i
$829$	−334.899	−	580.062i	−0.403979	−	0.699712i	0.590223	−	0.807240i	$-0.299040\pi$
$829$	−334.899	−	580.062i	−0.403979	−	0.699712i	−0.994202	+	0.107528i	$0.965706\pi$
$830$	−268.492	+	110.603i	−0.323485	+	0.133256i
$831$	70.2825	−	80.4122i	0.0845758	−	0.0967656i
$832$	−119.510	−	1577.50i	−0.143642	−	1.89603i
$833$	−190.441	+	1080.05i	−0.228621	+	1.29657i
$834$	−940.903	−	145.082i	−1.12818	−	0.173959i
$835$	697.287	+	830.994i	0.835074	+	0.995203i
$836$	299.868	−	138.416i	0.358694	−	0.165569i
$837$	249.694	−	74.1375i	0.298320	−	0.0885753i
$838$	181.320	+	825.463i	0.216372	+	0.985040i
$839$	402.854	+	480.103i	0.480160	+	0.572233i	0.950687	−	0.310153i	$-0.100380\pi$
$839$	402.854	+	480.103i	0.480160	+	0.572233i	−0.470526	+	0.882386i	$0.655936\pi$
$840$	907.687	+	876.181i	1.08058	+	1.04307i
$841$	−134.172	+	760.926i	−0.159538	+	0.904787i
$842$	285.426	−	181.058i	0.338985	−	0.215033i
$843$	−60.4709	−	177.170i	−0.0717330	−	0.210166i
$844$	592.877	−	411.715i	0.702461	−	0.487814i
$845$	1009.06	+	1747.74i	1.19415	+	2.06833i
$846$	1220.28	+	1021.04i	1.44241	+	1.20690i
$847$	539.822	+	311.666i	0.637334	+	0.367965i
$848$	−118.681	+	67.2969i	−0.139954	+	0.0793596i
$849$	−826.250	−	16.6493i	−0.973203	−	0.0196105i
$850$	96.6602	+	50.5570i	0.113718	+	0.0594788i
$851$	569.835	−	679.103i	0.669606	−	0.798006i
$852$	−279.640	+	122.306i	−0.328216	+	0.143552i
$853$	774.167	+	281.774i	0.907582	+	0.330333i	0.753287	−	0.657692i	$-0.228467\pi$
$853$	774.167	+	281.774i	0.907582	+	0.330333i	0.154295	+	0.988025i	$0.450689\pi$
$854$	754.139	+	239.390i	0.883067	+	0.280316i
$855$	253.682	+	328.330i	0.296705	+	0.384012i
$856$	404.100	−	959.730i	0.472079	−	1.12118i
$857$	131.996	+	748.584i	0.154020	+	0.873494i	0.959676	+	0.281109i	$0.0907023\pi$
$857$	131.996	+	748.584i	0.154020	+	0.873494i	−0.805655	+	0.592385i	$0.798187\pi$
$858$	−1036.96	+	628.858i	−1.20858	+	0.732935i
$859$	−48.7050	−	133.816i	−0.0566997	−	0.155781i	0.908109	−	0.418734i	$-0.137526\pi$
$859$	−48.7050	−	133.816i	−0.0566997	−	0.155781i	−0.964809	+	0.262953i	$0.915304\pi$
$860$	177.073	−	46.7101i	0.205898	−	0.0543141i
$861$	−234.342	−	1505.83i	−0.272174	−	1.74893i
$862$	209.240	+	161.202i	0.242738	+	0.187010i
$863$			507.425i			0.587978i	0.955809	+	0.293989i	$0.0949830\pi$
$863$			507.425i			0.587978i	−0.955809	+	0.293989i	$0.905017\pi$
$864$	273.873	+	819.445i	0.316983	+	0.948431i
$865$	1119.10			1.29375
$866$	−370.914	+	481.446i	−0.428307	+	0.555942i
$867$	−126.403	+	326.657i	−0.145793	+	0.376766i
$868$	113.322	+	429.590i	0.130555	+	0.494919i
$869$	−582.400	+	211.976i	−0.670196	+	0.243931i
$870$	−108.973	+	198.503i	−0.125256	+	0.228165i
$871$	−1442.35	+	254.326i	−1.65597	+	0.291993i
$872$	190.386	+	80.1630i	0.218332	+	0.0919301i
$873$	151.232	−	239.145i	0.173233	−	0.273935i
$874$	−126.192	+	397.536i	−0.144384	+	0.454847i
$875$	−524.180	+	1440.17i	−0.599063	+	1.64591i
$876$	−217.292	−	24.2846i	−0.248051	−	0.0277221i
$877$	−855.706	−	718.023i	−0.975720	−	0.818726i	0.00771826	−	0.999970i	$-0.497543\pi$
$877$	−855.706	−	718.023i	−0.975720	−	0.818726i	−0.983438	+	0.181244i	$0.941988\pi$
$878$	395.202	−	755.591i	0.450117	−	0.860582i
$879$	−1352.00	+	744.670i	−1.53811	+	0.847178i
$880$	−294.628	−	519.590i	−0.334805	−	0.590443i
$881$	220.266	−	381.511i	0.250018	−	0.433044i	−0.713513	−	0.700642i	$-0.752897\pi$
$881$	220.266	−	381.511i	0.250018	−	0.433044i	0.963530	+	0.267599i	$0.0862302\pi$
$882$	−1303.67	−	750.250i	−1.47809	−	0.850624i
$883$	−513.152	+	296.269i	−0.581146	+	0.335525i	−0.761589	−	0.648060i	$-0.775580\pi$
$883$	−513.152	+	296.269i	−0.581146	+	0.335525i	0.180442	+	0.983586i	$0.442247\pi$
$884$	−740.184	−	1065.88i	−0.837312	−	1.20575i
$885$	32.7880	−	166.286i	0.0370485	−	0.187894i
$886$	318.521	+	502.127i	0.359504	+	0.566735i
$887$	−447.779	−	78.9555i	−0.504824	−	0.0890140i	−0.0845643	−	0.996418i	$-0.526950\pi$
$887$	−447.779	−	78.9555i	−0.504824	−	0.0890140i	−0.420259	+	0.907404i	$0.638061\pi$
$888$	999.656	+	249.023i	1.12574	+	0.280431i
$889$	−875.561	+	734.683i	−0.984883	+	0.826415i
$890$	233.949	−	51.3888i	0.262864	−	0.0577402i
$891$	465.199	−	471.452i	0.522109	−	0.529126i
$892$	13.8438	+	29.9917i	0.0155200	+	0.0336230i
$893$	−683.761	+	573.743i	−0.765689	+	0.642490i
$894$	85.1953	+	68.4147i	0.0952967	+	0.0765265i
$895$	−268.972	−	47.4271i	−0.300528	−	0.0529912i
$896$	−1411.43	+	424.017i	−1.57525	+	0.473233i
$897$	296.277	−	1502.59i	0.330298	−	1.67512i
$898$	−524.426	−	1273.06i	−0.583993	−	1.41767i
$899$	−69.0630	+	39.8735i	−0.0768220	+	0.0443532i
$900$	−110.358	+	101.014i	−0.122620	+	0.112238i
$901$	−55.9560	+	96.9186i	−0.0621043	+	0.107568i
$902$	−95.5678	+	715.175i	−0.105951	+	0.792877i
$903$	−303.393	+	167.106i	−0.335983	+	0.185057i
$904$	156.951	+	7.76895i	0.173618	+	0.00859397i
$905$	−237.213	−	199.045i	−0.262113	−	0.219939i
$906$	−331.033	+	974.318i	−0.365379	+	1.07541i
$907$	−509.329	+	1399.37i	−0.561554	+	1.54286i	0.255806	+	0.966728i	$0.417659\pi$
$907$	−509.329	+	1399.37i	−0.561554	+	1.54286i	−0.817360	+	0.576128i	$0.804563\pi$
$908$	527.395	+	48.2058i	0.580832	+	0.0530901i
$909$	401.818	+	16.2002i	0.442044	+	0.0178220i
$910$	1919.41	−	1751.97i	2.10924	−	1.92525i
$911$	372.965	−	65.7638i	0.409402	−	0.0721886i	0.0348454	−	0.999393i	$-0.488906\pi$
$911$	372.965	−	65.7638i	0.409402	−	0.0721886i	0.374556	+	0.927204i	$0.377795\pi$
$912$	−479.492	+	70.8101i	−0.525759	+	0.0776427i
$913$	−244.353	+	88.9373i	−0.267638	+	0.0974122i
$914$	46.4092	+	1112.52i	0.0507759	+	1.21720i
$915$	169.839	−	438.906i	0.185616	−	0.479679i
$916$	−637.827	+	1354.07i	−0.696317	+	1.47824i
$917$	−830.347			−0.905503
$918$	534.267	+	465.650i	0.581990	+	0.507244i
$919$		−	235.053i		−	0.255771i	−0.991789	−	0.127885i	$-0.959181\pi$
$919$		−	235.053i		−	0.255771i	0.991789	−	0.127885i	$-0.0408190\pi$
$920$	735.469	+	167.551i	0.799423	+	0.182120i
$921$	196.942	+	1265.50i	0.213834	+	1.37405i
$922$	−28.7176	−	688.416i	−0.0311471	−	0.746655i
$923$	215.036	+	590.806i	0.232975	+	0.640093i
$924$	779.423	+	817.815i	0.843532	+	0.885081i
$925$	30.9768	+	175.678i	0.0334884	+	0.189922i
$926$	−920.514	+	840.213i	−0.994075	+	0.907357i
$927$	−1443.12	+	194.893i	−1.55676	+	0.210240i
$928$	−139.959	−	224.472i	−0.150818	−	0.241887i
$929$	227.048	+	82.6386i	0.244400	+	0.0889543i	0.461316	−	0.887236i	$-0.347378\pi$
$929$	227.048	+	82.6386i	0.244400	+	0.0889543i	−0.216916	+	0.976190i	$0.569600\pi$
$930$	259.198	−	51.4841i	0.278708	−	0.0553593i
$931$	542.386	−	646.390i	0.582584	−	0.694297i
$932$	374.097	+	101.798i	0.401392	+	0.109225i
$933$	−1418.23	−	28.5780i	−1.52008	−	0.0306302i
$934$	157.216	−	1176.51i	0.168325	−	1.25965i
$935$	−424.313	−	244.977i	−0.453810	−	0.262007i
$936$	1720.27	−	456.361i	1.83789	−	0.487565i
$937$	−244.489	−	423.467i	−0.260927	−	0.451939i	0.705561	−	0.708649i	$-0.250695\pi$
$937$	−244.489	−	423.467i	−0.260927	−	0.451939i	−0.966489	+	0.256710i	$0.917362\pi$
$938$	519.670	+	1261.52i	0.554020	+	1.34490i
$939$	−280.124	−	820.716i	−0.298322	−	0.874032i
$940$	1137.02	+	1145.89i	1.20960	+	1.21903i
$941$	181.612	−	1029.97i	0.192999	−	1.09455i	−0.722242	−	0.691641i	$-0.756888\pi$
$941$	181.612	−	1029.97i	0.192999	−	1.09455i	0.915240	−	0.402909i	$-0.132001\pi$
$942$	966.217	−	375.438i	1.02571	−	0.398554i
$943$	−585.699	−	698.009i	−0.621102	−	0.740201i
$944$	150.676	+	128.440i	0.159615	+	0.136059i
$945$	−782.591	+	1184.02i	−0.828139	+	1.25293i
$946$	160.174	−	35.1835i	0.169317	−	0.0371918i
$947$	−1167.17	−	1390.98i	−1.23250	−	1.46883i	−0.834097	−	0.551618i	$-0.814011\pi$
$947$	−1167.17	−	1390.98i	−1.23250	−	1.46883i	−0.398399	−	0.917212i	$-0.630434\pi$
$948$	907.739	−	57.4774i	0.957530	−	0.0606302i
$949$	−78.2097	+	443.550i	−0.0824128	+	0.467386i
$950$	−44.9571	−	70.8719i	−0.0473233	−	0.0746020i
$951$	516.825	−	591.314i	0.543455	−	0.621782i
$952$	−821.874	+	886.494i	−0.863313	+	0.931191i
$953$	−541.513	−	937.929i	−0.568220	−	0.984185i	−0.996742	−	0.0806543i	$-0.974299\pi$
$953$	−541.513	−	937.929i	−0.568220	−	0.984185i	0.428522	−	0.903531i	$-0.359034\pi$
$954$	−98.8241	−	117.441i	−0.103589	−	0.123103i
$955$	−19.1068	−	11.0313i	−0.0200071	−	0.0115511i
$956$	−156.017	−	1866.76i	−0.163198	−	1.95267i
$957$	−104.909	+	173.537i	−0.109623	+	0.181335i
$958$	−507.960	+	971.173i	−0.530230	+	1.01375i
$959$	−755.728	+	900.642i	−0.788038	+	0.939147i
$960$	199.842	+	853.501i	0.208169	+	0.889064i
$961$	−815.593	−	296.852i	−0.848692	−	0.308899i
$962$	642.070	−	2022.68i	0.667432	−	2.10258i
$963$	1144.57	+	249.740i	1.18855	+	0.259336i
$964$	−472.549	−	333.625i	−0.490196	−	0.346084i
$965$	88.0670	+	499.453i	0.0912611	+	0.517568i
$966$	−1426.37	+	30.7339i	−1.47657	+	0.0318156i
$967$	93.2391	+	256.172i	0.0964210	+	0.264915i	0.978521	−	0.206148i	$-0.0660928\pi$
$967$	93.2391	+	256.172i	0.0964210	+	0.264915i	−0.882100	+	0.471063i	$0.843871\pi$
$968$	197.747	+	385.332i	0.204284	+	0.398070i
$969$	−309.649	+	249.370i	−0.319555	+	0.257348i
$970$	175.201	−	227.410i	0.180619	−	0.234444i
$971$		−	1287.81i		−	1.32627i	−0.748498	−	0.663137i	$-0.769225\pi$
$971$		−	1287.81i		−	1.32627i	0.748498	−	0.663137i	$-0.230775\pi$
$972$	−850.084	+	471.318i	−0.874572	+	0.484895i
$973$	1826.87			1.87756
$974$	−302.099	−	232.742i	−0.310163	−	0.238955i
$975$	193.299	+	240.024i	0.198255	+	0.246178i
$976$	350.100	+	423.877i	0.358709	+	0.434300i
$977$	−286.009	+	104.099i	−0.292742	+	0.106549i	−0.484216	−	0.874948i	$-0.660895\pi$
$977$	−286.009	+	104.099i	−0.292742	+	0.106549i	0.191475	+	0.981498i	$0.438673\pi$
$978$	2.99455	+	138.978i	0.00306191	+	0.142104i
$979$	211.237	−	37.2467i	0.215768	−	0.0380457i
$980$	−1246.66	−	880.154i	−1.27210	−	0.898116i
$981$	−49.5421	+	227.054i	−0.0505016	+	0.231452i
$982$	655.622	+	208.117i	0.667640	+	0.211932i
$983$	368.108	−	1011.37i	0.374474	−	1.02886i	−0.599138	−	0.800646i	$-0.704490\pi$
$983$	368.108	−	1011.37i	0.374474	−	1.02886i	0.973611	−	0.228212i	$-0.0732880\pi$
$984$	430.488	−	967.430i	0.437488	−	0.983161i
$985$	−723.872	−	607.400i	−0.734895	−	0.616650i
$986$	−192.273	−	100.566i	−0.195003	−	0.101994i
$987$	−2612.87	−	1579.57i	−2.64729	−	1.60037i
$988$	83.1552	+	994.960i	0.0841652	+	1.00704i
$989$	−103.549	+	179.352i	−0.104701	+	0.181347i
$990$	514.158	−	432.655i	0.519352	−	0.437025i
$991$	616.046	−	355.674i	0.621641	−	0.358904i	−0.155867	−	0.987778i	$-0.549817\pi$
$991$	616.046	−	355.674i	0.621641	−	0.358904i	0.777508	+	0.628874i	$0.216484\pi$
$992$	−95.6829	+	293.500i	−0.0964545	+	0.295867i
$993$	144.895	+	126.643i	0.145917	+	0.127535i
$994$	494.577	−	313.732i	0.497563	−	0.315626i
$995$	495.655	+	87.3973i	0.498146	+	0.0878365i
$996$	380.853	−	24.1154i	0.382383	−	0.0242122i
$997$	−128.599	+	107.907i	−0.128985	+	0.108232i	−0.704998	−	0.709209i	$-0.749052\pi$
$997$	−128.599	+	107.907i	−0.128985	+	0.108232i	0.576013	+	0.817441i	$0.304608\pi$
$998$	191.340	+	871.080i	0.191723	+	0.872825i
$999$	−70.0097	+	1156.86i	−0.0700798	+	1.15802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.j.a.103.10	yes	204
3.2	odd	2		324.3.j.a.199.25		204
4.3	odd	2	inner	108.3.j.a.103.6	yes	204
12.11	even	2		324.3.j.a.199.29		204
27.11	odd	18		324.3.j.a.127.29		204
27.16	even	9	inner	108.3.j.a.43.6	✓	204
108.11	even	18		324.3.j.a.127.25		204
108.43	odd	18	inner	108.3.j.a.43.10	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.6	✓	204	27.16	even	9	inner
108.3.j.a.43.10	yes	204	108.43	odd	18	inner
108.3.j.a.103.6	yes	204	4.3	odd	2	inner
108.3.j.a.103.10	yes	204	1.1	even	1	trivial
324.3.j.a.127.25		204	108.11	even	18
324.3.j.a.127.29		204	27.11	odd	18
324.3.j.a.199.25		204	3.2	odd	2
324.3.j.a.199.29		204	12.11	even	2

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22060 + 1.58434i) q^{2} +(1.88167 + 2.33652i) q^{3} +(-1.02026 - 3.86769i) q^{4} +(4.29021 - 1.56151i) q^{5} +(-5.99861 + 0.129252i) q^{6} +(11.3387 - 1.99932i) q^{7} +(7.37308 + 3.10447i) q^{8} +(-1.91862 + 8.79312i) q^{9} +(-2.76268 + 8.70313i) q^{10} +(-2.79665 + 7.68375i) q^{11} +(7.11713 - 9.66160i) q^{12} +(-18.9359 - 15.8891i) q^{13} +(-10.6724 + 20.4047i) q^{14} +(11.7213 + 7.08590i) q^{15} +(-13.9181 + 7.89213i) q^{16} +(-6.56214 + 11.3660i) q^{17} +(-11.5894 - 13.7726i) q^{18} +(8.74492 - 5.04888i) q^{19} +(-10.4166 - 15.0001i) q^{20} +(26.0071 + 22.7310i) q^{21} +(-8.76006 - 13.8096i) q^{22} +(20.3386 + 3.58624i) q^{23} +(6.62006 + 23.0689i) q^{24} +(-3.18352 + 2.67129i) q^{25} +(48.2869 - 10.6066i) q^{26} +(-24.1555 + 12.0629i) q^{27} +(-19.3012 - 41.8148i) q^{28} +(6.33255 - 5.31364i) q^{29} +(-25.5335 + 9.92140i) q^{30} +(-9.50040 - 1.67518i) q^{31} +(4.48468 - 31.6842i) q^{32} +(-23.2156 + 7.92386i) q^{33} +(-9.99778 - 24.2700i) q^{34} +(45.5234 - 26.2830i) q^{35} +(35.9666 - 1.55066i) q^{36} +(21.4626 - 37.1743i) q^{37} +(-2.67492 + 20.0176i) q^{38} +(1.49399 - 74.1421i) q^{39} +(36.4797 + 1.80572i) q^{40} +(-33.7981 - 28.3600i) q^{41} +(-67.7580 + 13.4587i) q^{42} +(-3.42972 + 9.42307i) q^{43} +(32.5717 + 2.97717i) q^{44} +(5.49926 + 40.7203i) q^{45} +(-30.5071 + 27.8458i) q^{46} +(-87.0515 + 15.3495i) q^{47} +(-44.6294 - 17.6695i) q^{48} +(78.5238 - 28.5803i) q^{49} +(-0.346420 - 8.30436i) q^{50} +(-38.9045 + 6.05447i) q^{51} +(-42.1346 + 89.4493i) q^{52} +8.52710 q^{53} +(10.3725 - 52.9944i) q^{54} +37.3319i q^{55} +(89.8079 + 20.4596i) q^{56} +(28.2519 + 10.9323i) q^{57} +(0.689087 + 16.5187i) q^{58} +(-4.23230 - 11.6281i) q^{59} +(15.4473 - 52.5637i) q^{60} +(-5.96660 - 33.8383i) q^{61} +(14.2502 - 13.0071i) q^{62} +(-4.17438 + 103.538i) q^{63} +(44.7245 + 45.7790i) q^{64} +(-106.050 - 38.5990i) q^{65} +(15.7829 - 46.4533i) q^{66} +(38.0852 - 45.3881i) q^{67} +(50.6552 + 13.7841i) q^{68} +(29.8912 + 54.2695i) q^{69} +(-13.9248 + 104.206i) q^{70} +(-22.0271 - 12.7174i) q^{71} +(-41.4441 + 58.8760i) q^{72} +(-9.11022 - 15.7794i) q^{73} +(32.6995 + 79.3791i) q^{74} +(-12.2319 - 2.41185i) q^{75} +(-28.4497 - 28.6715i) q^{76} +(-16.3482 + 92.7151i) q^{77} +(115.643 + 92.8650i) q^{78} +(48.7210 + 58.0634i) q^{79} +(-47.3881 + 55.5922i) q^{80} +(-73.6378 - 33.7413i) q^{81} +(86.1858 - 18.9314i) q^{82} +(20.4415 + 24.3612i) q^{83} +(61.3824 - 123.779i) q^{84} +(-10.4049 + 59.0092i) q^{85} +(-10.7430 - 16.9357i) q^{86} +(24.3312 + 4.79757i) q^{87} +(-44.4739 + 47.9707i) q^{88} +(-13.1160 - 22.7175i) q^{89} +(-71.2271 - 40.9905i) q^{90} +(-246.476 - 142.303i) q^{91} +(-6.88020 - 82.3223i) q^{92} +(-13.9626 - 25.3500i) q^{93} +(81.9364 - 156.655i) q^{94} +(29.6337 - 35.3160i) q^{95} +(82.4693 - 49.1407i) q^{96} +(-29.5430 - 10.7528i) q^{97} +(-50.5654 + 159.294i) q^{98} +(-62.1984 - 39.3335i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25}+ \cdots + 510 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more