LMFDB - Embedded newform 210.3.w.a.173.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(17,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("210.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.w (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			173.2
Character	$\chi$	$=$	210.173
Dual form			210.3.w.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 0.366025i) q^{2} +(-2.72119 + 1.26298i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-2.34013 + 4.41857i) q^{5} +(3.25493 - 2.72129i) q^{6} +(-6.07917 - 3.47039i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(5.80976 - 6.87362i) q^{9} +O(q^{10})$	\(q+(-1.36603 + 0.366025i) q^{2} +(-2.72119 + 1.26298i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-2.34013 + 4.41857i) q^{5} +(3.25493 - 2.72129i) q^{6} +(-6.07917 - 3.47039i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(5.80976 - 6.87362i) q^{9} +(1.57936 - 6.89243i) q^{10} +(-5.23131 + 3.02030i) q^{11} +(-3.45026 + 4.90874i) q^{12} +(-7.33446 + 7.33446i) q^{13} +(9.57456 + 2.51551i) q^{14} +(0.787362 - 14.9793i) q^{15} +(2.00000 - 3.46410i) q^{16} +(22.5211 + 6.03451i) q^{17} +(-5.42036 + 11.5161i) q^{18} +(17.0920 - 29.6042i) q^{19} +(0.365356 + 9.99332i) q^{20} +(20.9256 + 1.76573i) q^{21} +(6.04060 - 6.04060i) q^{22} +(-7.11456 - 26.5519i) q^{23} +(2.91642 - 7.96834i) q^{24} +(-14.0476 - 20.6801i) q^{25} +(7.33446 - 12.7037i) q^{26} +(-7.12823 + 26.0420i) q^{27} +(-13.9998 + 0.0682753i) q^{28} -6.86667 q^{29} +(4.40726 + 20.7503i) q^{30} +(38.9114 - 22.4655i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(10.4208 - 14.8258i) q^{33} -32.9732 q^{34} +(29.5602 - 18.7401i) q^{35} +(3.18919 - 17.7152i) q^{36} +(-9.14352 - 34.1241i) q^{37} +(-12.5122 + 46.6962i) q^{38} +(10.6952 - 29.2218i) q^{39} +(-4.15690 - 13.5174i) q^{40} +18.2221 q^{41} +(-29.2313 + 5.24728i) q^{42} +(17.2571 + 17.2571i) q^{43} +(-6.04060 + 10.4626i) q^{44} +(16.7760 + 41.7560i) q^{45} +(19.4373 + 33.6664i) q^{46} +(-6.24890 - 23.3212i) q^{47} +(-1.06729 + 11.9524i) q^{48} +(24.9127 + 42.1943i) q^{49} +(26.7588 + 23.1077i) q^{50} +(-68.9057 + 12.0226i) q^{51} +(-5.36920 + 20.0381i) q^{52} +(-77.2906 - 20.7100i) q^{53} +(0.205295 - 38.1832i) q^{54} +(-1.10348 - 30.1828i) q^{55} +(19.0991 - 5.21756i) q^{56} +(-9.12106 + 102.145i) q^{57} +(9.38005 - 2.51338i) q^{58} +(-97.9689 + 56.5624i) q^{59} +(-13.6156 - 26.7323i) q^{60} +(16.8856 + 9.74888i) q^{61} +(-44.9310 + 44.9310i) q^{62} +(-59.1727 + 21.6238i) q^{63} -8.00000i q^{64} +(-15.2443 - 49.5715i) q^{65} +(-8.80847 + 24.0668i) q^{66} +(10.9297 + 2.92860i) q^{67} +(45.0422 - 12.0690i) q^{68} +(52.8946 + 63.2672i) q^{69} +(-33.5207 + 36.4193i) q^{70} -80.6556i q^{71} +(2.12771 + 25.3668i) q^{72} +(-1.93873 - 0.519481i) q^{73} +(24.9805 + 43.2676i) q^{74} +(64.3447 + 38.5325i) q^{75} -68.3679i q^{76} +(42.2837 - 0.206212i) q^{77} +(-3.91400 + 43.8324i) q^{78} +(-73.1841 - 42.2528i) q^{79} +(10.6261 + 16.9436i) q^{80} +(-13.4933 - 79.8682i) q^{81} +(-24.8919 + 6.66976i) q^{82} +(-4.56113 - 4.56113i) q^{83} +(38.0100 - 17.8673i) q^{84} +(-79.3662 + 85.3897i) q^{85} +(-29.8902 - 17.2571i) q^{86} +(18.6855 - 8.67247i) q^{87} +(4.42202 - 16.5032i) q^{88} +(-21.5716 - 12.4544i) q^{89} +(-38.2002 - 50.8993i) q^{90} +(70.0410 - 19.1340i) q^{91} +(-38.8747 - 38.8747i) q^{92} +(-77.5118 + 110.277i) q^{93} +(17.0723 + 29.5701i) q^{94} +(90.8109 + 144.800i) q^{95} +(-2.91695 - 16.7180i) q^{96} +(38.4454 + 38.4454i) q^{97} +(-49.4756 - 48.5197i) q^{98} +(-9.63229 + 53.5053i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 32 q^{2} - 6 q^{3} - 12 q^{5} + 4 q^{7} - 128 q^{8} - 16 q^{9}+O(q^{10}) $ 64 * q - 32 * q^2 - 6 * q^3 - 12 * q^5 + 4 * q^7 - 128 * q^8 - 16 * q^9	$ 64 q - 32 q^{2} - 6 q^{3} - 12 q^{5} + 4 q^{7} - 128 q^{8} - 16 q^{9} + 24 q^{10} + 12 q^{12} - 16 q^{14} - 44 q^{15} + 128 q^{16} - 20 q^{18} + 36 q^{21} + 16 q^{22} - 12 q^{23} - 16 q^{25} + 8 q^{28} - 112 q^{29} + 26 q^{30} + 128 q^{32} + 30 q^{33} + 16 q^{36} - 32 q^{37} + 24 q^{38} + 64 q^{39} - 136 q^{42} + 32 q^{43} - 16 q^{44} - 114 q^{45} - 24 q^{46} - 96 q^{47} + 40 q^{50} - 84 q^{51} + 56 q^{53} - 72 q^{54} - 316 q^{57} + 56 q^{58} + 672 q^{59} + 8 q^{60} + 600 q^{61} - 210 q^{63} + 28 q^{65} + 16 q^{67} + 24 q^{72} - 624 q^{73} - 64 q^{74} + 48 q^{75} + 208 q^{77} - 8 q^{78} - 48 q^{80} - 64 q^{81} - 192 q^{82} + 160 q^{84} - 152 q^{85} + 60 q^{87} - 16 q^{88} + 144 q^{89} - 232 q^{91} + 48 q^{92} - 170 q^{93} + 136 q^{95} - 48 q^{96} + 128 q^{98} + 160 q^{99}+O(q^{100}) $ 64 * q - 32 * q^2 - 6 * q^3 - 12 * q^5 + 4 * q^7 - 128 * q^8 - 16 * q^9 + 24 * q^10 + 12 * q^12 - 16 * q^14 - 44 * q^15 + 128 * q^16 - 20 * q^18 + 36 * q^21 + 16 * q^22 - 12 * q^23 - 16 * q^25 + 8 * q^28 - 112 * q^29 + 26 * q^30 + 128 * q^32 + 30 * q^33 + 16 * q^36 - 32 * q^37 + 24 * q^38 + 64 * q^39 - 136 * q^42 + 32 * q^43 - 16 * q^44 - 114 * q^45 - 24 * q^46 - 96 * q^47 + 40 * q^50 - 84 * q^51 + 56 * q^53 - 72 * q^54 - 316 * q^57 + 56 * q^58 + 672 * q^59 + 8 * q^60 + 600 * q^61 - 210 * q^63 + 28 * q^65 + 16 * q^67 + 24 * q^72 - 624 * q^73 - 64 * q^74 + 48 * q^75 + 208 * q^77 - 8 * q^78 - 48 * q^80 - 64 * q^81 - 192 * q^82 + 160 * q^84 - 152 * q^85 + 60 * q^87 - 16 * q^88 + 144 * q^89 - 232 * q^91 + 48 * q^92 - 170 * q^93 + 136 * q^95 - 48 * q^96 + 128 * q^98 + 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−2.72119	+	1.26298i	−0.907064	+	0.420993i
$3$	−2.72119	+	1.26298i	−0.907064	+	0.420993i
$4$	1.73205	−	1.00000i	0.433013	−	0.250000i
$5$	−2.34013	+	4.41857i	−0.468025	+	0.883715i
$5$	−2.34013	+	4.41857i	−0.468025	+	0.883715i
$6$	3.25493	−	2.72129i	0.542489	−	0.453548i
$7$	−6.07917	−	3.47039i	−0.868454	−	0.495771i
$7$	−6.07917	−	3.47039i	−0.868454	−	0.495771i
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	5.80976	−	6.87362i	0.645529	−	0.763736i
$10$	1.57936	−	6.89243i	0.157936	−	0.689243i
$11$	−5.23131	+	3.02030i	−0.475574	+	0.274573i	−0.718570	−	0.695455i	$-0.755203\pi$
$11$	−5.23131	+	3.02030i	−0.475574	+	0.274573i	0.242996	+	0.970027i	$0.421870\pi$
$12$	−3.45026	+	4.90874i	−0.287522	+	0.409061i
$13$	−7.33446	+	7.33446i	−0.564189	+	0.564189i	−0.930495	−	0.366305i	$-0.880623\pi$
$13$	−7.33446	+	7.33446i	−0.564189	+	0.564189i	0.366305	+	0.930495i	$0.380623\pi$
$14$	9.57456	+	2.51551i	0.683897	+	0.179680i
$15$	0.787362	−	14.9793i	0.0524908	−	0.998621i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	22.5211	+	6.03451i	1.32477	+	0.354971i	0.850763	−	0.525549i	$-0.176140\pi$
$17$	22.5211	+	6.03451i	1.32477	+	0.354971i	0.474008	+	0.880520i	$0.342807\pi$
$18$	−5.42036	+	11.5161i	−0.301131	+	0.639781i
$19$	17.0920	−	29.6042i	0.899578	−	1.55811i	0.0715438	−	0.997437i	$-0.477207\pi$
$19$	17.0920	−	29.6042i	0.899578	−	1.55811i	0.828034	−	0.560678i	$-0.189459\pi$
$20$	0.365356	+	9.99332i	0.0182678	+	0.499666i
$21$	20.9256	+	1.76573i	0.996459	+	0.0840824i
$22$	6.04060	−	6.04060i	0.274573	−	0.274573i
$23$	−7.11456	−	26.5519i	−0.309329	−	1.15443i	−0.929155	−	0.369691i	$-0.879464\pi$
$23$	−7.11456	−	26.5519i	−0.309329	−	1.15443i	0.619826	−	0.784739i	$-0.287203\pi$
$24$	2.91642	−	7.96834i	0.121518	−	0.332014i
$25$	−14.0476	−	20.6801i	−0.561904	−	0.827202i
$26$	7.33446	−	12.7037i	0.282095	−	0.488602i
$27$	−7.12823	+	26.0420i	−0.264009	+	0.964520i
$28$	−13.9998	+	0.0682753i	−0.499994	+	0.00243840i
$29$	−6.86667			−0.236782			−0.118391	−	0.992967i	$-0.537774\pi$
$29$	−6.86667			−0.236782			−0.118391	+	0.992967i	$0.537774\pi$
$30$	4.40726	+	20.7503i	0.146909	+	0.691678i
$31$	38.9114	−	22.4655i	1.25520	−	0.724693i	0.283066	−	0.959100i	$-0.408648\pi$
$31$	38.9114	−	22.4655i	1.25520	−	0.724693i	0.972138	+	0.234407i	$0.0753150\pi$
$32$	−1.46410	+	5.46410i	−0.0457532	+	0.170753i
$33$	10.4208	−	14.8258i	0.315782	−	0.449268i
$34$	−32.9732			−0.969800
$35$	29.5602	−	18.7401i	0.844578	−	0.535432i
$36$	3.18919	−	17.7152i	0.0885885	−	0.492090i
$37$	−9.14352	−	34.1241i	−0.247122	−	0.922272i	−0.972305	−	0.233716i	$-0.924911\pi$
$37$	−9.14352	−	34.1241i	−0.247122	−	0.922272i	0.725183	−	0.688556i	$-0.241755\pi$
$38$	−12.5122	+	46.6962i	−0.329268	+	1.22885i
$39$	10.6952	−	29.2218i	0.274236	−	0.749276i
$40$	−4.15690	−	13.5174i	−0.103922	−	0.337935i
$41$	18.2221			0.444442			0.222221	−	0.974996i	$-0.428669\pi$
$41$	18.2221			0.444442			0.222221	+	0.974996i	$0.428669\pi$
$42$	−29.2313	+	5.24728i	−0.695982	+	0.124935i
$43$	17.2571	+	17.2571i	0.401329	+	0.401329i	0.878701	−	0.477372i	$-0.158411\pi$
$43$	17.2571	+	17.2571i	0.401329	+	0.401329i	−0.477372	+	0.878701i	$0.658411\pi$
$44$	−6.04060	+	10.4626i	−0.137286	+	0.237787i
$45$	16.7760	+	41.7560i	0.372800	+	0.927912i
$46$	19.4373	+	33.6664i	0.422551	+	0.731879i
$47$	−6.24890	−	23.3212i	−0.132955	−	0.496196i	0.867043	−	0.498234i	$-0.166018\pi$
$47$	−6.24890	−	23.3212i	−0.132955	−	0.496196i	−0.999998	+	0.00203792i	$0.999351\pi$
$48$	−1.06729	+	11.9524i	−0.0222352	+	0.249009i
$49$	24.9127	+	42.1943i	0.508423	+	0.861107i
$50$	26.7588	+	23.1077i	0.535176	+	0.462154i
$51$	−68.9057	+	12.0226i	−1.35109	+	0.235738i
$52$	−5.36920	+	20.0381i	−0.103254	+	0.385349i
$53$	−77.2906	−	20.7100i	−1.45831	−	0.390754i	−0.559407	−	0.828893i	$-0.688971\pi$
$53$	−77.2906	−	20.7100i	−1.45831	−	0.390754i	−0.898907	+	0.438139i	$0.855638\pi$
$54$	0.205295	−	38.1832i	0.00380176	−	0.707097i
$55$	−1.10348	−	30.1828i	−0.0200633	−	0.548779i
$56$	19.0991	−	5.21756i	0.341056	−	0.0931707i
$57$	−9.12106	+	102.145i	−0.160019	+	1.79203i
$58$	9.38005	−	2.51338i	0.161725	−	0.0433341i
$59$	−97.9689	+	56.5624i	−1.66049	+	0.958684i	−0.688009	+	0.725702i	$0.741515\pi$
$59$	−97.9689	+	56.5624i	−1.66049	+	0.958684i	−0.972481	+	0.232982i	$0.925152\pi$
$60$	−13.6156	−	26.7323i	−0.226926	−	0.445538i
$61$	16.8856	+	9.74888i	0.276812	+	0.159818i	0.631979	−	0.774985i	$-0.282243\pi$
$61$	16.8856	+	9.74888i	0.276812	+	0.159818i	−0.355167	+	0.934803i	$0.615576\pi$
$62$	−44.9310	+	44.9310i	−0.724693	+	0.724693i
$63$	−59.1727	+	21.6238i	−0.939250	+	0.343234i
$64$		−	8.00000i		−	0.125000i
$65$	−15.2443	−	49.5715i	−0.234528	−	0.762638i
$66$	−8.80847	+	24.0668i	−0.133462	+	0.364648i
$67$	10.9297	+	2.92860i	0.163130	+	0.0437104i	0.339459	−	0.940621i	$-0.389756\pi$
$67$	10.9297	+	2.92860i	0.163130	+	0.0437104i	−0.176330	+	0.984331i	$0.556423\pi$
$68$	45.0422	−	12.0690i	0.662386	−	0.177486i
$69$	52.8946	+	63.2672i	0.766588	+	0.916916i
$70$	−33.5207	+	36.4193i	−0.478867	+	0.520275i
$71$		−	80.6556i		−	1.13599i	−0.823030	−	0.567997i	$-0.807718\pi$
$71$		−	80.6556i		−	1.13599i	0.823030	−	0.567997i	$-0.192282\pi$
$72$	2.12771	+	25.3668i	0.0295516	+	0.352316i
$73$	−1.93873	−	0.519481i	−0.0265579	−	0.00711618i	0.245516	−	0.969393i	$-0.421043\pi$
$73$	−1.93873	−	0.519481i	−0.0265579	−	0.00711618i	−0.272074	+	0.962276i	$0.587709\pi$
$74$	24.9805	+	43.2676i	0.337575	+	0.584697i
$75$	64.3447	+	38.5325i	0.857930	+	0.513767i
$76$		−	68.3679i		−	0.899578i
$77$	42.2837	−	0.206212i	0.549139	−	0.00267807i
$78$	−3.91400	+	43.8324i	−0.0501796	+	0.561954i
$79$	−73.1841	−	42.2528i	−0.926381	−	0.534846i	−0.0407156	−	0.999171i	$-0.512964\pi$
$79$	−73.1841	−	42.2528i	−0.926381	−	0.534846i	−0.885665	+	0.464325i	$0.846297\pi$
$80$	10.6261	+	16.9436i	0.132827	+	0.211795i
$81$	−13.4933	−	79.8682i	−0.166584	−	0.986027i
$82$	−24.8919	+	6.66976i	−0.303559	+	0.0813385i
$83$	−4.56113	−	4.56113i	−0.0549533	−	0.0549533i	0.679096	−	0.734049i	$-0.262372\pi$
$83$	−4.56113	−	4.56113i	−0.0549533	−	0.0549533i	−0.734049	+	0.679096i	$0.762372\pi$
$84$	38.0100	−	17.8673i	0.452500	−	0.212706i
$85$	−79.3662	+	85.3897i	−0.933720	+	1.00458i
$86$	−29.8902	−	17.2571i	−0.347561	−	0.200664i
$87$	18.6855	−	8.67247i	0.214776	−	0.0996835i
$88$	4.42202	−	16.5032i	0.0502503	−	0.187537i
$89$	−21.5716	−	12.4544i	−0.242377	−	0.139937i	0.373892	−	0.927472i	$-0.378023\pi$
$89$	−21.5716	−	12.4544i	−0.242377	−	0.139937i	−0.616269	+	0.787536i	$0.711357\pi$
$90$	−38.2002	−	50.8993i	−0.424447	−	0.565548i
$91$	70.0410	−	19.1340i	0.769681	−	0.210264i
$92$	−38.8747	−	38.8747i	−0.422551	−	0.422551i
$93$	−77.5118	+	110.277i	−0.833460	+	1.18578i
$94$	17.0723	+	29.5701i	0.181620	+	0.314576i
$95$	90.8109	+	144.800i	0.955904	+	1.52421i
$96$	−2.91695	−	16.7180i	−0.0303849	−	0.174146i
$97$	38.4454	+	38.4454i	0.396345	+	0.396345i	0.876942	−	0.480597i	$-0.159580\pi$
$97$	38.4454	+	38.4454i	0.396345	+	0.396345i	−0.480597	+	0.876942i	$0.659580\pi$
$98$	−49.4756	−	48.5197i	−0.504853	−	0.495099i
$99$	−9.63229	+	53.5053i	−0.0972959	+	0.540457i
$100$	−45.0112	−	21.7713i	−0.450112	−	0.217713i
$101$	−11.7303	−	20.3175i	−0.116142	−	0.201163i	0.802094	−	0.597198i	$-0.203719\pi$
$101$	−11.7303	−	20.3175i	−0.116142	−	0.201163i	−0.918235	+	0.396035i	$0.870386\pi$
$102$	89.7264	−	41.6445i	0.879670	−	0.408279i
$103$	−48.6683	−	181.632i	−0.472507	−	1.76342i	−0.630714	−	0.776015i	$-0.717238\pi$
$103$	−48.6683	−	181.632i	−0.472507	−	1.76342i	0.158207	−	0.987406i	$-0.449429\pi$
$104$		−	29.3379i		−	0.282095i
$105$	−56.7707	+	88.3295i	−0.540673	+	0.841233i
$106$	113.161			1.06756
$107$	80.3041	−	21.5174i	0.750506	−	0.201097i	0.136763	−	0.990604i	$-0.456330\pi$
$107$	80.3041	−	21.5174i	0.750506	−	0.201097i	0.613742	+	0.789506i	$0.289663\pi$
$108$	13.6956	+	52.2344i	0.126811	+	0.483652i
$109$	28.9994	−	16.7428i	0.266049	−	0.153604i	−0.361042	−	0.932550i	$-0.617579\pi$
$109$	28.9994	−	16.7428i	0.266049	−	0.153604i	0.627091	+	0.778946i	$0.284245\pi$
$110$	12.5551	+	40.8266i	0.114137	+	0.371151i
$111$	67.9793	+	81.3100i	0.612426	+	0.732523i
$112$	−24.1801	+	14.1181i	−0.215894	+	0.126054i
$113$	12.6123	−	12.6123i	0.111613	−	0.111613i	−0.649095	−	0.760708i	$-0.724852\pi$
$113$	12.6123	−	12.6123i	0.111613	−	0.111613i	0.760708	+	0.649095i	$0.224852\pi$
$114$	−24.9282	−	142.872i	−0.218669	−	1.25326i
$115$	133.970	+	30.6986i	1.16496	+	0.266944i
$116$	−11.8934	+	6.86667i	−0.102530	+	0.0591954i
$117$	7.80282	+	93.0258i	0.0666908	+	0.795092i
$118$	113.125	−	113.125i	0.958684	−	0.958684i
$119$	−115.968	−	114.842i	−0.974518	−	0.965059i
$120$	28.3839	+	31.5334i	0.236533	+	0.262778i
$121$	−42.2556	+	73.1888i	−0.349220	+	0.604866i
$122$	−26.6344	−	7.13668i	−0.218315	−	0.0584973i
$123$	−49.5859	+	23.0142i	−0.403137	+	0.187107i
$124$	44.9310	−	77.8227i	0.362346	−	0.627602i
$125$	124.250	−	13.6764i	0.993997	−	0.109412i
$126$	72.9166	−	51.1973i	0.578703	−	0.406328i
$127$	147.938	−	147.938i	1.16486	−	1.16486i	0.181467	−	0.983397i	$-0.441915\pi$
$127$	147.938	−	147.938i	1.16486	−	1.16486i	0.983397	−	0.181467i	$-0.0580847\pi$
$128$	2.92820	+	10.9282i	0.0228766	+	0.0853766i
$129$	−68.7554	−	25.1645i	−0.532987	−	0.195074i
$130$	38.9685	+	62.1361i	0.299758	+	0.477970i
$131$	74.8356	−	129.619i	0.571264	−	0.989459i	−0.425172	−	0.905113i	$-0.639786\pi$
$131$	74.8356	−	129.619i	0.571264	−	0.989459i	0.996436	−	0.0843465i	$-0.0268803\pi$
$132$	3.22354	−	36.0999i	0.0244207	−	0.273484i
$133$	−206.643	+	120.653i	−1.55371	+	0.907166i
$134$	−16.0022			−0.119419
$135$	−98.3878	−	92.4383i	−0.728798	−	0.684728i
$136$	−57.1113	+	32.9732i	−0.419936	+	0.242450i
$137$	6.54134	−	24.4126i	0.0477470	−	0.178194i	−0.937934	−	0.346813i	$-0.887264\pi$
$137$	6.54134	−	24.4126i	0.0477470	−	0.178194i	0.985681	+	0.168619i	$0.0539306\pi$
$138$	−95.4127	−	67.0639i	−0.691397	−	0.485970i
$139$	−237.437			−1.70818			−0.854090	−	0.520125i	$-0.825885\pi$
$139$	−237.437			−1.70818			−0.854090	+	0.520125i	$0.825885\pi$
$140$	32.4597	−	62.0191i	0.231855	−	0.442993i
$141$	46.4587	+	55.5693i	0.329494	+	0.394108i
$142$	29.5220	+	110.178i	0.207901	+	0.775899i
$143$	16.2166	−	60.5211i	0.113403	−	0.423225i
$144$	−12.1914	−	33.8729i	−0.0846624	−	0.235228i
$145$	16.0689	−	30.3409i	0.110820	−	0.209248i
$146$	2.83850			0.0194418
$147$	−121.083	−	83.3544i	−0.823693	−	0.567037i
$148$	−49.9611	−	49.9611i	−0.337575	−	0.337575i
$149$	19.6566	−	34.0462i	0.131924	−	0.228498i	−0.792494	−	0.609879i	$-0.791218\pi$
$149$	19.6566	−	34.0462i	0.131924	−	0.228498i	0.924418	+	0.381381i	$0.124551\pi$
$150$	−102.000	−	29.0846i	−0.680003	−	0.193897i
$151$	−19.0601	−	33.0130i	−0.126226	−	0.218629i	0.795986	−	0.605315i	$-0.206953\pi$
$151$	−19.0601	−	33.0130i	−0.126226	−	0.218629i	−0.922211	+	0.386686i	$0.873620\pi$
$152$	25.0244	+	93.3923i	0.164634	+	0.614423i
$153$	172.321	−	119.742i	1.12628	−	0.782631i
$154$	−57.6851	+	15.7586i	−0.374579	+	0.102329i
$155$	8.20789	+	224.505i	0.0529541	+	1.44842i
$156$	−10.6971	−	61.3088i	−0.0685714	−	0.393005i
$157$	15.5225	−	57.9306i	0.0988692	−	0.368985i	−0.898708	−	0.438547i	$-0.855493\pi$
$157$	15.5225	−	57.9306i	0.0988692	−	0.368985i	0.997578	+	0.0695618i	$0.0221601\pi$
$158$	115.437	+	30.9312i	0.730613	+	0.195767i
$159$	236.479	−	41.2608i	1.48729	−	0.259502i
$160$	−20.7174	−	19.2559i	−0.129483	−	0.120350i
$161$	−48.8949	+	186.104i	−0.303695	+	1.15592i
$162$	47.6660	+	104.163i	0.294234	+	0.642982i
$163$	5.64718	−	1.51316i	0.0346453	−	0.00928317i	−0.241455	−	0.970412i	$-0.577625\pi$
$163$	5.64718	−	1.51316i	0.0346453	−	0.00928317i	0.276100	+	0.961129i	$0.410958\pi$
$164$	31.5616	−	18.2221i	0.192449	−	0.111110i
$165$	41.1231	+	80.7395i	0.249231	+	0.489331i
$166$	7.90010	+	4.56113i	0.0475910	+	0.0274767i
$167$	−6.13829	+	6.13829i	−0.0367562	+	0.0367562i	−0.725246	−	0.688490i	$-0.758274\pi$
$167$	−6.13829	+	6.13829i	−0.0367562	+	0.0367562i	0.688490	+	0.725246i	$0.258274\pi$
$168$	−45.3827	+	38.3198i	−0.270135	+	0.228094i
$169$			61.4113i			0.363381i
$170$	77.1615	−	145.695i	0.453891	−	0.857027i
$171$	−104.188	−	289.477i	−0.609284	−	1.69285i
$172$	47.1474	+	12.6331i	0.274113	+	0.0734483i
$173$	194.574	−	52.1359i	1.12470	−	0.301363i	0.351918	−	0.936031i	$-0.385530\pi$
$173$	194.574	−	52.1359i	1.12470	−	0.301363i	0.772785	+	0.634668i	$0.218863\pi$
$174$	−22.3506	+	18.6862i	−0.128451	+	0.107392i
$175$	13.6299	+	174.468i	0.0778852	+	0.996962i
$176$			24.1624i			0.137286i
$177$	195.155	−	277.650i	1.10257	−	1.56864i
$178$	34.0259	+	9.11722i	0.191157	+	0.0512203i
$179$	−17.6436	−	30.5596i	−0.0985676	−	0.170724i	0.812524	−	0.582927i	$-0.198093\pi$
$179$	−17.6436	−	30.5596i	−0.0985676	−	0.170724i	−0.911092	+	0.412203i	$0.864759\pi$
$180$	70.8129	+	55.5475i	0.393405	+	0.308597i
$181$			194.579i			1.07502i	0.843258	+	0.537510i	$0.180635\pi$
$181$			194.579i			1.07502i	−0.843258	+	0.537510i	$0.819365\pi$
$182$	−88.6742	+	51.7743i	−0.487221	+	0.284474i
$183$	−58.2615	−	5.20245i	−0.318369	−	0.0284287i
$184$	67.3329	+	38.8747i	0.365940	+	0.211275i
$185$	172.177	+	39.4533i	0.930685	+	0.213261i
$186$	65.5188	−	179.013i	0.352252	−	0.962434i
$187$	−136.041	+	36.4521i	−0.727492	+	0.194931i
$188$	−34.1446	−	34.1446i	−0.181620	−	0.181620i
$189$	133.710	−	133.576i	0.707460	−	0.706753i
$190$	−177.050	−	164.561i	−0.931844	−	0.866111i
$191$	−114.428	−	66.0651i	−0.599100	−	0.345890i	0.169588	−	0.985515i	$-0.445756\pi$
$191$	−114.428	−	66.0651i	−0.599100	−	0.345890i	−0.768687	+	0.639625i	$0.779090\pi$
$192$	10.1038	+	21.7695i	0.0526242	+	0.113383i
$193$	54.3985	−	203.018i	0.281858	−	1.05191i	−0.669248	−	0.743039i	$-0.733383\pi$
$193$	54.3985	−	203.018i	0.281858	−	1.05191i	0.951105	−	0.308867i	$-0.0999498\pi$
$194$	−66.5894	−	38.4454i	−0.343244	−	0.198172i
$195$	104.090	+	115.640i	0.533797	+	0.593026i
$196$	85.3444	+	48.1699i	0.435430	+	0.245765i
$197$	−94.5121	−	94.5121i	−0.479757	−	0.479757i	0.425297	−	0.905054i	$-0.360170\pi$
$197$	−94.5121	−	94.5121i	−0.479757	−	0.479757i	−0.905054	+	0.425297i	$0.860170\pi$
$198$	−6.42633	−	76.6152i	−0.0324562	−	0.386945i
$199$	182.775	+	316.575i	0.918465	+	1.59083i	0.801748	+	0.597663i	$0.203904\pi$
$199$	182.775	+	316.575i	0.918465	+	1.59083i	0.116717	+	0.993165i	$0.462763\pi$
$200$	69.4553	+	13.2649i	0.347277	+	0.0663245i
$201$	−33.4405	+	5.83469i	−0.166371	+	0.0290283i
$202$	23.4606	+	23.4606i	0.116142	+	0.116142i
$203$	41.7437	+	23.8301i	0.205634	+	0.117389i
$204$	−107.326	+	89.7296i	−0.526106	+	0.439851i
$205$	−42.6421	+	80.5158i	−0.208010	+	0.392760i
$206$	132.964	+	230.301i	0.645457	+	1.11796i
$207$	−223.841	−	105.357i	−1.08136	−	0.508973i
$208$	10.7384	+	40.0763i	0.0516269	+	0.192674i
$209$			206.492i			0.987998i
$210$	45.2193	−	141.440i	0.215330	−	0.673523i
$211$	49.4419			0.234322			0.117161	−	0.993113i	$-0.462621\pi$
$211$	49.4419			0.234322			0.117161	+	0.993113i	$0.462621\pi$
$212$	−154.581	+	41.4199i	−0.729157	+	0.195377i
$213$	101.866	+	219.479i	0.478246	+	1.03042i
$214$	−101.822	+	58.7867i	−0.475801	+	0.274704i
$215$	−116.636	+	35.8681i	−0.542492	+	0.166828i
$216$	−37.8276	−	66.3406i	−0.175128	−	0.307132i
$217$	−314.513	+	1.53384i	−1.44937	+	0.00706837i
$218$	−33.4856	+	33.4856i	−0.153604	+	0.153604i
$219$	5.93175	−	1.03497i	0.0270856	−	0.00472589i
$220$	−32.0941	−	51.1747i	−0.145882	−	0.232612i
$221$	−209.440	+	120.920i	−0.947693	+	0.547151i
$222$	−122.623	−	86.1894i	−0.552356	−	0.388241i
$223$	−147.669	+	147.669i	−0.662195	+	0.662195i	−0.955897	−	0.293702i	$-0.905113\pi$
$223$	−147.669	+	147.669i	−0.662195	+	0.662195i	0.293702	+	0.955897i	$0.405113\pi$
$224$	27.8631	−	28.1362i	0.124389	−	0.125608i
$225$	−223.760	−	23.5883i	−0.994489	−	0.104837i
$226$	−12.6123	+	21.8451i	−0.0558066	+	0.0966599i
$227$	−212.531	−	56.9475i	−0.936259	−	0.250870i	−0.241738	−	0.970342i	$-0.577717\pi$
$227$	−212.531	−	56.9475i	−0.936259	−	0.250870i	−0.694522	+	0.719472i	$0.744384\pi$
$228$	86.3473	+	186.042i	0.378716	+	0.815975i
$229$	149.624	−	259.157i	0.653380	−	1.13169i	−0.328917	−	0.944359i	$-0.606684\pi$
$229$	149.624	−	259.157i	0.653380	−	1.13169i	0.982297	−	0.187329i	$-0.0599831\pi$
$230$	−194.244	+	7.10154i	−0.844537	+	0.0308762i
$231$	−114.802	+	53.9646i	−0.496976	+	0.233613i
$232$	13.7333	−	13.7333i	0.0591954	−	0.0591954i
$233$	−31.0526	−	115.890i	−0.133273	−	0.497381i	0.866726	−	0.498784i	$-0.166220\pi$
$233$	−31.0526	−	115.890i	−0.133273	−	0.497381i	−0.999999	+	0.00140324i	$0.999553\pi$
$234$	−44.7087	−	124.220i	−0.191063	−	0.530853i
$235$	117.670	+	26.9634i	0.500722	+	0.114738i
$236$	−113.125	+	195.938i	−0.479342	+	0.830245i
$237$	252.512	+	22.5481i	1.06545	+	0.0951395i
$238$	200.450	+	114.430i	0.842226	+	0.480798i
$239$	−395.609			−1.65527			−0.827634	−	0.561268i	$-0.810314\pi$
$239$	−395.609			−1.65527			−0.827634	+	0.561268i	$0.810314\pi$
$240$	−50.3152	−	32.6861i	−0.209647	−	0.136192i
$241$	−191.579	+	110.608i	−0.794934	+	0.458956i	−0.841697	−	0.539950i	$-0.818443\pi$
$241$	−191.579	+	110.608i	−0.794934	+	0.458956i	0.0467624	+	0.998906i	$0.485110\pi$
$242$	30.9332	−	115.444i	0.127823	−	0.477043i
$243$	137.590	+	200.295i	0.566213	+	0.824259i
$244$	38.9955			0.159818
$245$	−244.737	+	11.3388i	−0.998928	+	0.0462808i
$246$	59.3118	−	49.5876i	0.241105	−	0.201576i
$247$	91.7703	+	342.491i	0.371540	+	1.38660i
$248$	−32.8917	+	122.754i	−0.132628	+	0.494974i
$249$	18.1723	+	6.65109i	0.0729812	+	0.0267112i
$250$	−164.722	+	64.1609i	−0.658889	+	0.256644i
$251$	231.794			0.923482			0.461741	−	0.887015i	$-0.347225\pi$
$251$	231.794			0.923482			0.461741	+	0.887015i	$0.347225\pi$
$252$	−80.8664	+	96.6262i	−0.320898	+	0.383437i
$253$	117.413	+	117.413i	0.464083	+	0.464083i
$254$	−147.938	+	256.236i	−0.582432	+	1.00880i
$255$	108.125	−	332.600i	0.424020	−	1.30431i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	8.34872	+	31.1578i	0.0324853	+	0.121237i	0.980264	−	0.197691i	$-0.0633441\pi$
$257$	8.34872	+	31.1578i	0.0324853	+	0.121237i	−0.947779	+	0.318927i	$0.896677\pi$
$258$	103.132	+	9.20920i	0.399738	+	0.0356946i
$259$	−62.8389	+	239.178i	−0.242621	+	0.923466i
$260$	−75.9753	−	70.6160i	−0.292213	−	0.271600i
$261$	−39.8937	+	47.1989i	−0.152850	+	0.180839i
$262$	−54.7835	+	204.455i	−0.209097	+	0.780362i
$263$	−161.425	−	43.2538i	−0.613785	−	0.164463i	−0.0614840	−	0.998108i	$-0.519583\pi$
$263$	−161.425	−	43.2538i	−0.613785	−	0.164463i	−0.552301	+	0.833645i	$0.686250\pi$
$264$	8.81006	+	50.4933i	0.0333714	+	0.191263i
$265$	272.378	−	293.051i	1.02784	−	1.10585i
$266$	238.118	−	240.452i	0.895180	−	0.903954i
$267$	74.4300	+	6.64621i	0.278764	+	0.0248922i
$268$	21.8594	−	5.85720i	0.0815648	−	0.0218552i
$269$	302.162	−	174.453i	1.12328	−	0.648526i	0.181043	−	0.983475i	$-0.442053\pi$
$269$	302.162	−	174.453i	1.12328	−	0.648526i	0.942236	+	0.334949i	$0.108719\pi$
$270$	168.235	+	90.2607i	0.623093	+	0.334299i
$271$	17.0749	+	9.85817i	0.0630068	+	0.0363770i	0.531172	−	0.847264i	$-0.321752\pi$
$271$	17.0749	+	9.85817i	0.0630068	+	0.0363770i	−0.468166	+	0.883641i	$0.655085\pi$
$272$	65.9464	−	65.9464i	0.242450	−	0.242450i
$273$	−166.429	+	140.528i	−0.609630	+	0.514753i
$274$			35.7425i			0.130447i
$275$	135.947	+	65.7558i	0.494354	+	0.239112i
$276$	154.883	+	56.6875i	0.561171	+	0.205389i
$277$	216.453	+	57.9983i	0.781417	+	0.209380i	0.627409	−	0.778690i	$-0.284115\pi$
$277$	216.453	+	57.9983i	0.781417	+	0.209380i	0.154008	+	0.988070i	$0.450782\pi$
$278$	324.345	−	86.9080i	1.16671	−	0.312619i
$279$	71.6466	−	397.981i	0.256798	−	1.42646i
$280$	−21.6402	+	96.6007i	−0.0772865	+	0.345003i
$281$		−	226.986i		−	0.807780i	−0.914808	−	0.403890i	$-0.867658\pi$
$281$		−	226.986i		−	0.807780i	0.914808	−	0.403890i	$-0.132342\pi$
$282$	−83.8035	−	58.9040i	−0.297176	−	0.208879i
$283$	−92.5997	−	24.8120i	−0.327208	−	0.0876750i	0.0914758	−	0.995807i	$-0.470842\pi$
$283$	−92.5997	−	24.8120i	−0.327208	−	0.0876750i	−0.418683	+	0.908132i	$0.637508\pi$
$284$	−80.6556	−	139.700i	−0.283999	−	0.491900i
$285$	−429.993	−	279.336i	−1.50875	−	0.980125i
$286$			88.6091i			0.309822i
$287$	−110.775	−	63.2379i	−0.385977	−	0.220341i
$288$	29.0521	+	41.8088i	0.100875	+	0.145169i
$289$	220.504	+	127.308i	0.762989	+	0.440512i
$290$	−10.8450	+	47.3281i	−0.0373964	+	0.163200i
$291$	−153.173	−	56.0615i	−0.526368	−	0.192651i
$292$	−3.87746	+	1.03896i	−0.0132790	+	0.00355809i
$293$	−190.809	−	190.809i	−0.651224	−	0.651224i	0.302064	−	0.953288i	$-0.402325\pi$
$293$	−190.809	−	190.809i	−0.651224	−	0.651224i	−0.953288	+	0.302064i	$0.902325\pi$
$294$	195.912	+	69.5448i	0.666367	+	0.236547i
$295$	−20.6654	−	565.246i	−0.0700521	−	1.91609i
$296$	86.5352	+	49.9611i	0.292349	+	0.168787i
$297$	−41.3648	−	157.763i	−0.139275	−	0.531190i
$298$	−14.3896	+	53.7028i	−0.0482874	+	0.180211i
$299$	246.925	+	142.562i	0.825837	+	0.476797i
$300$	149.981	+	2.39559i	0.499936	+	0.00798529i
$301$	−45.0201	−	164.798i	−0.149568	−	0.547502i
$302$	38.1201	+	38.1201i	0.126226	+	0.126226i
$303$	57.5809	+	40.4726i	0.190036	+	0.133573i
$304$	−68.3679	−	118.417i	−0.224895	−	0.389529i
$305$	−82.5905	+	51.7965i	−0.270789	+	0.169824i
$306$	−191.566	+	226.645i	−0.626034	+	0.740671i
$307$	−34.1553	−	34.1553i	−0.111255	−	0.111255i	0.649288	−	0.760543i	$-0.275067\pi$
$307$	−34.1553	−	34.1553i	−0.111255	−	0.111255i	−0.760543	+	0.649288i	$0.775067\pi$
$308$	73.0313	−	42.6408i	0.237114	−	0.138444i
$309$	361.834	+	432.789i	1.17098	+	1.40061i
$310$	−93.3866	−	303.675i	−0.301247	−	0.979597i
$311$	272.168	+	471.409i	0.875139	+	1.51579i	0.856614	+	0.515957i	$0.172564\pi$
$311$	272.168	+	471.409i	0.875139	+	1.51579i	0.0185247	+	0.999828i	$0.494103\pi$
$312$	37.0531	+	79.8339i	0.118760	+	0.255878i
$313$	118.989	+	444.072i	0.380155	+	1.41876i	0.845664	+	0.533716i	$0.179205\pi$
$313$	118.989	+	444.072i	0.380155	+	1.41876i	−0.465509	+	0.885043i	$0.654129\pi$
$314$			84.8163i			0.270116i
$315$	42.9255	−	312.062i	0.136271	−	0.990672i
$316$	−169.011			−0.534846
$317$	17.9678	−	4.81445i	0.0566806	−	0.0151875i	−0.230367	−	0.973104i	$-0.573993\pi$
$317$	17.9678	−	4.81445i	0.0566806	−	0.0151875i	0.287048	+	0.957916i	$0.407326\pi$
$318$	−307.934	+	142.921i	−0.968345	+	0.449436i
$319$	35.9217	−	20.7394i	0.112607	−	0.0650138i
$320$	35.3486	+	18.7210i	0.110464	+	0.0585032i
$321$	−191.347	+	159.975i	−0.596096	+	0.498366i
$322$	−1.32709	−	272.119i	−0.00412139	−	0.845091i
$323$	563.577	−	563.577i	1.74482	−	1.74482i
$324$	−103.239	−	124.842i	−0.318640	−	0.385316i
$325$	254.709	+	48.6454i	0.783719	+	0.149678i
$326$	−7.16033	+	4.13402i	−0.0219642	+	0.0126810i
$327$	−57.7671	+	82.1860i	−0.176658	+	0.251333i
$328$	−36.4442	+	36.4442i	−0.111110	+	0.111110i
$329$	−42.9457	+	163.460i	−0.130534	+	0.496839i
$330$	−85.7279	−	95.2402i	−0.259782	−	0.288607i
$331$	−82.1070	+	142.213i	−0.248057	+	0.429648i	−0.962987	−	0.269549i	$-0.913125\pi$
$331$	−82.1070	+	142.213i	−0.248057	+	0.429648i	0.714929	+	0.699197i	$0.246459\pi$
$332$	−12.4612	−	3.33898i	−0.0375338	−	0.0100572i
$333$	−287.678	−	135.404i	−0.863896	−	0.406618i
$334$	6.13829	−	10.6318i	0.0183781	−	0.0318318i
$335$	−38.5171	+	41.4403i	−0.114976	+	0.123702i
$336$	47.9679	−	68.9571i	0.142762	−	0.205229i
$337$	182.945	−	182.945i	0.542865	−	0.542865i	−0.381503	−	0.924368i	$-0.624593\pi$
$337$	182.945	−	182.945i	0.542865	−	0.542865i	0.924368	+	0.381503i	$0.124593\pi$
$338$	−22.4781	−	83.8894i	−0.0665033	−	0.248194i
$339$	−18.3914	+	50.2495i	−0.0542519	+	0.148229i
$340$	−52.0766	+	227.266i	−0.153167	+	0.668428i
$341$	−135.705	+	235.048i	−0.397962	+	0.689290i
$342$	248.279	+	357.298i	0.725961	+	1.04473i
$343$	−5.01807	−	342.963i	−0.0146300	−	0.999893i
$344$	−69.0285			−0.200664
$345$	−403.331	+	85.6653i	−1.16908	+	0.248305i
$346$	−246.710	+	142.438i	−0.713033	+	0.411670i
$347$	−19.7736	+	73.7960i	−0.0569844	+	0.212669i	−0.988547	−	0.150912i	$-0.951779\pi$
$347$	−19.7736	+	73.7960i	−0.0569844	+	0.212669i	0.931563	+	0.363580i	$0.118446\pi$
$348$	23.6918	−	33.7067i	0.0680799	−	0.0968583i
$349$	−601.421			−1.72327			−0.861634	−	0.507529i	$-0.830559\pi$
$349$	−601.421			−1.72327			−0.861634	+	0.507529i	$0.830559\pi$
$350$	−82.4787	−	233.339i	−0.235653	−	0.666684i
$351$	−138.723	−	243.286i	−0.395221	−	0.693123i
$352$	−8.84405	−	33.0064i	−0.0251251	−	0.0937683i
$353$	117.673	−	439.162i	0.333351	−	1.24408i	−0.572294	−	0.820048i	$-0.693946\pi$
$353$	117.673	−	439.162i	0.333351	−	1.24408i	0.905645	−	0.424036i	$-0.139387\pi$
$354$	−164.960	+	450.708i	−0.465988	+	1.27319i
$355$	356.383	+	188.744i	1.00390	+	0.531674i
$356$	−49.8174			−0.139937
$357$	460.613	+	166.042i	1.29023	+	0.465104i
$358$	35.2872	+	35.2872i	0.0985676	+	0.0985676i
$359$	−99.2457	+	171.899i	−0.276450	+	0.478826i	−0.970500	−	0.241101i	$-0.922491\pi$
$359$	−99.2457	+	171.899i	−0.276450	+	0.478826i	0.694050	+	0.719927i	$0.255825\pi$
$360$	−117.064	−	49.9600i	−0.325178	−	0.138778i
$361$	−403.772	−	699.353i	−1.11848	−	1.93727i
$362$	−71.2207	−	265.799i	−0.196742	−	0.734252i
$363$	22.5495	−	252.529i	0.0621199	−	0.695672i
$364$	102.180	−	103.182i	0.280716	−	0.283467i
$365$	6.83224	−	7.35077i	0.0187185	−	0.0201391i
$366$	81.4909	−	14.2185i	0.222653	−	0.0388484i
$367$	121.793	−	454.536i	0.331860	−	1.23852i	−0.575373	−	0.817891i	$-0.695143\pi$
$367$	121.793	−	454.536i	0.331860	−	1.23852i	0.907233	−	0.420628i	$-0.138190\pi$
$368$	−106.208	−	28.4582i	−0.288607	−	0.0773321i
$369$	105.866	−	125.252i	0.286900	−	0.339436i
$370$	−249.639	+	9.12678i	−0.674699	+	0.0246670i
$371$	397.992	+	394.129i	1.07275	+	1.06234i
$372$	−23.9772	+	268.517i	−0.0644549	+	0.721821i
$373$	261.696	−	70.1213i	0.701599	−	0.187993i	0.109652	−	0.993970i	$-0.465026\pi$
$373$	261.696	−	70.1213i	0.701599	−	0.187993i	0.591947	+	0.805977i	$0.298360\pi$
$374$	172.493	−	99.5889i	0.461211	−	0.266281i
$375$	−320.834	+	194.141i	−0.855557	+	0.517709i
$376$	59.1402	+	34.1446i	0.157288	+	0.0908102i
$377$	50.3633	−	50.3633i	0.133590	−	0.133590i
$378$	−133.759	+	231.410i	−0.353859	+	0.612196i
$379$		−	478.536i		−	1.26263i	−0.775528	−	0.631314i	$-0.782516\pi$
$379$		−	478.536i		−	1.26263i	0.775528	−	0.631314i	$-0.217484\pi$
$380$	302.089	+	159.990i	0.794971	+	0.421025i
$381$	−215.725	+	589.409i	−0.566206	+	1.54701i
$382$	180.493	+	48.3630i	0.472495	+	0.126605i
$383$	−412.087	+	110.418i	−1.07595	+	0.288299i	−0.752934	−	0.658096i	$-0.771362\pi$
$383$	−412.087	+	110.418i	−1.07595	+	0.288299i	−0.323012	+	0.946395i	$0.604695\pi$
$384$	−21.7703	−	26.0395i	−0.0566935	−	0.0678111i
$385$	−98.0380	+	187.316i	−0.254644	+	0.486535i
$386$			297.239i			0.770049i
$387$	218.879	−	18.3591i	0.565578	−	0.0474396i
$388$	105.035	+	28.1440i	0.270708	+	0.0725361i
$389$	116.515	+	201.810i	0.299524	+	0.518791i	0.976027	−	0.217649i	$-0.0698387\pi$
$389$	116.515	+	201.810i	0.299524	+	0.518791i	−0.676503	+	0.736440i	$0.736505\pi$
$390$	−184.517	−	119.868i	−0.473121	−	0.307353i
$391$		−	640.911i		−	1.63916i
$392$	−134.214	−	34.5631i	−0.342383	−	0.0881711i
$393$	−39.9357	+	447.234i	−0.101618	+	1.13800i
$394$	163.700	+	94.5121i	0.415482	+	0.239878i
$395$	357.957	−	224.492i	0.906221	−	0.568335i
$396$	36.8216	+	102.306i	0.0929839	+	0.258349i
$397$	52.8700	−	14.1665i	0.133174	−	0.0356838i	−0.191616	−	0.981470i	$-0.561373\pi$
$397$	52.8700	−	14.1665i	0.133174	−	0.0356838i	0.324790	+	0.945786i	$0.394706\pi$
$398$	−365.549	−	365.549i	−0.918465	−	0.918465i
$399$	409.934	−	589.307i	1.02740	−	1.47696i
$400$	−99.7330	+	7.30223i	−0.249333	+	0.0182556i
$401$	−396.262	−	228.782i	−0.988184	−	0.570528i	−0.0834527	−	0.996512i	$-0.526595\pi$
$401$	−396.262	−	228.782i	−0.988184	−	0.570528i	−0.904731	+	0.425984i	$0.859928\pi$
$402$	43.5449	−	20.2104i	0.108321	−	0.0502747i
$403$	−120.622	+	450.166i	−0.299309	+	1.11704i
$404$	−40.6349	−	23.4606i	−0.100582	−	0.0580708i
$405$	384.480	+	127.281i	0.949333	+	0.314273i
$406$	−65.7453	−	17.2732i	−0.161934	−	0.0425449i
$407$	150.897	+	150.897i	0.370755	+	0.370755i
$408$	113.766	−	161.857i	0.278839	−	0.396708i
$409$	−166.436	−	288.276i	−0.406935	−	0.704832i	0.587609	−	0.809145i	$-0.300069\pi$
$409$	−166.436	−	288.276i	−0.406935	−	0.704832i	−0.994545	+	0.104312i	$0.966736\pi$
$410$	28.7793	−	125.595i	0.0701935	−	0.306329i
$411$	13.0324	+	74.6930i	0.0317090	+	0.181735i
$412$	−265.928	−	265.928i	−0.645457	−	0.645457i
$413$	791.864	−	3.86181i	1.91735	−	0.00935064i
$414$	344.337	+	61.9892i	0.831731	+	0.149732i
$415$	30.8273	−	9.48006i	0.0742827	−	0.0228435i
$416$	−29.3379	−	50.8146i	−0.0705237	−	0.122151i
$417$	646.112	−	299.878i	1.54943	−	0.719133i
$418$	−75.5812	−	282.073i	−0.180816	−	0.674815i
$419$			377.243i			0.900341i	0.892943	+	0.450171i	$0.148637\pi$
$419$			377.243i			0.900341i	−0.892943	+	0.450171i	$0.851363\pi$
$420$	−10.0002	+	209.762i	−0.0238101	+	0.499433i
$421$	197.759			0.469736			0.234868	−	0.972027i	$-0.424534\pi$
$421$	197.759			0.469736			0.234868	+	0.972027i	$0.424534\pi$
$422$	−67.5389	+	18.0970i	−0.160045	+	0.0428839i
$423$	−196.606	−	92.5382i	−0.464789	−	0.218766i
$424$	196.001	−	113.161i	0.462267	−	0.266890i
$425$	−191.574	−	550.508i	−0.450762	−	1.29531i
$426$	−219.487	−	262.529i	−0.515228	−	0.616265i
$427$	−68.8178	−	117.865i	−0.161166	−	0.276030i
$428$	117.573	−	117.573i	0.274704	−	0.274704i
$429$	32.3085	+	185.171i	0.0753113	+	0.431633i
$430$	146.199	−	91.6883i	0.339997	−	0.213229i
$431$	−142.518	+	82.2828i	−0.330668	+	0.190911i	−0.656138	−	0.754641i	$-0.727811\pi$
$431$	−142.518	+	82.2828i	−0.330668	+	0.190911i	0.325469	+	0.945553i	$0.394478\pi$
$432$	75.9558	+	76.7770i	0.175824	+	0.177725i
$433$	−346.623	+	346.623i	−0.800515	+	0.800515i	−0.983176	−	0.182661i	$-0.941529\pi$
$433$	−346.623	+	346.623i	−0.800515	+	0.800515i	0.182661	+	0.983176i	$0.441529\pi$
$434$	429.071	−	117.215i	0.988644	−	0.270081i
$435$	−5.40656	+	102.858i	−0.0124289	+	0.236455i
$436$	33.4856	−	57.9988i	0.0768019	−	0.133025i
$437$	−907.649	−	243.204i	−2.07700	−	0.556530i
$438$	−7.72409	+	3.58497i	−0.0176349	+	0.00818485i
$439$	−269.647	+	467.043i	−0.614230	+	1.06388i	0.376289	+	0.926502i	$0.377200\pi$
$439$	−269.647	+	467.043i	−0.614230	+	1.06388i	−0.990519	+	0.137376i	$0.956133\pi$
$440$	62.5726	+	58.1587i	0.142210	+	0.132179i
$441$	434.764	+	73.8981i	0.985860	+	0.167569i
$442$	241.841	−	241.841i	0.547151	−	0.547151i
$443$	91.4437	+	341.272i	0.206419	+	0.770367i	0.989012	+	0.147833i	$0.0472299\pi$
$443$	91.4437	+	341.272i	0.206419	+	0.770367i	−0.782593	+	0.622533i	$0.786103\pi$
$444$	199.054	+	72.8538i	0.448319	+	0.164085i
$445$	105.511	−	66.1709i	0.237103	−	0.148699i
$446$	147.669	−	255.771i	0.331097	−	0.573478i
$447$	−10.4897	+	117.472i	−0.0234668	+	0.262801i
$448$	−27.7632	+	48.6334i	−0.0619713	+	0.108557i
$449$	436.761			0.972742			0.486371	−	0.873752i	$-0.338320\pi$
$449$	436.761			0.972742			0.486371	+	0.873752i	$0.338320\pi$
$450$	314.296	−	49.6797i	0.698435	−	0.110399i
$451$	−95.3255	+	55.0362i	−0.211365	+	0.122032i
$452$	9.23284	−	34.4574i	0.0204266	−	0.0762333i
$453$	93.5609	+	65.7622i	0.206536	+	0.145170i
$454$	311.167			0.685389
$455$	−79.3597	+	354.257i	−0.174417	+	0.778587i
$456$	−186.049	−	222.533i	−0.408002	−	0.488011i
$457$	−8.13289	−	30.3524i	−0.0177963	−	0.0664166i	0.956457	−	0.291874i	$-0.0942789\pi$
$457$	−8.13289	−	30.3524i	−0.0177963	−	0.0664166i	−0.974253	+	0.225458i	$0.927612\pi$
$458$	−109.532	+	408.781i	−0.239154	+	0.892534i
$459$	−317.687	+	543.481i	−0.692128	+	1.18405i
$460$	262.742	−	80.7989i	0.571179	−	0.175650i
$461$	−154.115			−0.334305			−0.167152	−	0.985931i	$-0.553457\pi$
$461$	−154.115			−0.334305			−0.167152	+	0.985931i	$0.553457\pi$
$462$	137.069	−	115.737i	0.296687	−	0.250514i
$463$	−200.474	−	200.474i	−0.432989	−	0.432989i	0.456655	−	0.889644i	$-0.349047\pi$
$463$	−200.474	−	200.474i	−0.432989	−	0.432989i	−0.889644	+	0.456655i	$0.849047\pi$
$464$	−13.7333	+	23.7868i	−0.0295977	+	0.0512648i
$465$	−305.880	−	600.554i	−0.657807	−	1.29151i
$466$	84.8372	+	146.942i	0.182054	+	0.315327i
$467$	−25.0817	−	93.6060i	−0.0537081	−	0.200441i	0.933858	−	0.357643i	$-0.116419\pi$
$467$	−25.0817	−	93.6060i	−0.0537081	−	0.200441i	−0.987567	+	0.157202i	$0.949753\pi$
$468$	106.541	+	153.323i	0.227651	+	0.327612i
$469$	−56.2800	−	55.7338i	−0.120000	−	0.118835i
$470$	−170.609	+	6.23747i	−0.362998	+	0.0132712i
$471$	30.9256	+	177.245i	0.0656595	+	0.376316i
$472$	82.8131	−	309.063i	0.175451	−	0.654794i
$473$	−142.399	−	38.1557i	−0.301055	−	0.0806675i
$474$	−353.191	+	61.6247i	−0.745130	+	0.130010i
$475$	−852.318	+	62.4048i	−1.79435	+	0.131379i
$476$	−315.704	−	82.9446i	−0.663243	−	0.174253i
$477$	−591.393	+	410.947i	−1.23982	+	0.861523i
$478$	540.412	−	144.803i	1.13057	−	0.302935i
$479$	−92.7005	+	53.5207i	−0.193529	+	0.111734i	−0.593634	−	0.804735i	$-0.702307\pi$
$479$	−92.7005	+	53.5207i	−0.193529	+	0.111734i	0.400104	+	0.916470i	$0.368974\pi$
$480$	80.6958	+	26.2335i	0.168116	+	0.0546531i
$481$	317.344	+	183.219i	0.659760	+	0.380912i
$482$	221.217	−	221.217i	0.458956	−	0.458956i
$483$	−101.993	−	568.177i	−0.211166	−	1.17635i
$484$			169.022i			0.349220i
$485$	−259.841	+	79.9068i	−0.535755	+	0.164756i
$486$	−261.264	−	223.247i	−0.537581	−	0.459355i
$487$	456.200	+	122.238i	0.936756	+	0.251003i	0.694733	−	0.719268i	$-0.255522\pi$
$487$	456.200	+	122.238i	0.936756	+	0.251003i	0.242023	+	0.970271i	$0.422189\pi$
$488$	−53.2689	+	14.2734i	−0.109158	+	0.0292487i
$489$	−13.4560	+	11.2499i	−0.0275173	+	0.0230059i
$490$	330.167	−	105.069i	0.673811	−	0.214427i
$491$			228.035i			0.464431i	0.972664	+	0.232215i	$0.0745974\pi$
$491$			228.035i			0.464431i	−0.972664	+	0.232215i	$0.925403\pi$
$492$	−62.8711	+	89.4476i	−0.127787	+	0.181804i
$493$	−154.645	−	41.4370i	−0.313682	−	0.0840508i
$494$	−250.721	−	434.262i	−0.507532	−	0.879072i
$495$	−213.876	−	167.770i	−0.432073	−	0.338930i
$496$		−	179.724i		−	0.362346i
$497$	−279.907	+	490.320i	−0.563193	+	0.986559i
$498$	−27.2583	−	2.43403i	−0.0547356	−	0.00488760i
$499$	706.586	+	407.948i	1.41600	+	0.817530i	0.995945	−	0.0899668i	$-0.0286761\pi$
$499$	706.586	+	407.948i	1.41600	+	0.817530i	0.420059	+	0.907497i	$0.362009\pi$
$500$	201.530	−	147.938i	0.403060	−	0.295876i
$501$	8.95092	−	24.4560i	0.0178661	−	0.0488143i
$502$	−316.636	+	84.8425i	−0.630750	+	0.169009i
$503$	493.203	+	493.203i	0.980522	+	0.980522i	0.999814	−	0.0192915i	$-0.00614106\pi$
$503$	493.203	+	493.203i	0.980522	+	0.980522i	−0.0192915	+	0.999814i	$0.506141\pi$
$504$	75.0979	−	161.593i	0.149004	−	0.320621i
$505$	117.225	−	4.28573i	0.232128	−	0.00848659i
$506$	−203.365	−	117.413i	−0.401908	−	0.232042i
$507$	−77.5613	−	167.112i	−0.152981	−	0.329609i
$508$	108.298	−	404.174i	0.213185	−	0.795617i
$509$	−715.344	−	413.004i	−1.40539	−	0.811403i	−0.410452	−	0.911882i	$-0.634629\pi$
$509$	−715.344	−	413.004i	−1.40539	−	0.811403i	−0.994939	+	0.100479i	$0.967962\pi$
$510$	−25.9619	+	493.916i	−0.0509056	+	0.968463i
$511$	9.98307	+	9.88617i	0.0195363	+	0.0193467i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	649.118	+	656.136i	1.26534	+	1.27902i
$514$	−22.8091	−	39.5066i	−0.0443757	−	0.0768610i
$515$	916.446	+	209.999i	1.77951	+	0.407764i
$516$	−144.252	+	25.1691i	−0.279559	+	0.0487773i
$517$	103.127	+	103.127i	0.199472	+	0.199472i
$518$	−1.70555	−	349.724i	−0.00329258	−	0.675142i
$519$	−463.626	+	387.614i	−0.893306	+	0.746848i
$520$	129.631	+	68.6543i	0.249291	+	0.132028i
$521$	−70.0727	−	121.369i	−0.134497	−	0.232955i	0.790908	−	0.611934i	$-0.209608\pi$
$521$	−70.0727	−	121.369i	−0.134497	−	0.232955i	−0.925405	+	0.378980i	$0.876275\pi$
$522$	37.2199	−	79.0770i	0.0713024	−	0.151489i
$523$	−44.3611	−	165.558i	−0.0848204	−	0.316554i	0.910460	−	0.413598i	$-0.135728\pi$
$523$	−44.3611	−	165.558i	−0.0848204	−	0.316554i	−0.995280	+	0.0970437i	$0.969061\pi$
$524$		−	299.343i		−	0.571264i
$525$	−257.440	−	457.548i	−0.490361	−	0.871519i
$526$	236.343			0.449322
$527$	1011.90	−	271.137i	1.92011	−	0.514491i
$528$	−30.5166	−	65.7505i	−0.0577966	−	0.124527i
$529$	−196.258	+	113.310i	−0.370999	+	0.214196i
$530$	−264.812	+	500.012i	−0.499645	+	0.943419i
$531$	−180.388	+	1002.02i	−0.339714	+	1.88703i
$532$	−237.264	+	415.621i	−0.445984	+	0.781242i
$533$	−133.649	+	133.649i	−0.250749	+	0.250749i
$534$	−104.106	+	18.1644i	−0.194955	+	0.0340157i
$535$	−92.8455	+	405.183i	−0.173543	+	0.757352i
$536$	−27.7166	+	16.0022i	−0.0517100	+	0.0298548i
$537$	86.6078	+	60.8751i	0.161281	+	0.113361i
$538$	−348.907	+	348.907i	−0.648526	+	0.648526i
$539$	−257.765	−	145.487i	−0.478229	−	0.269921i
$540$	−262.851	−	61.7201i	−0.486761	−	0.114297i
$541$	271.403	−	470.083i	0.501669	−	0.868916i	−0.498329	−	0.866988i	$-0.666053\pi$
$541$	271.403	−	470.083i	0.501669	−	0.868916i	0.999998	−	0.00192801i	$-0.000613704\pi$
$542$	−26.9330	−	7.21668i	−0.0496919	−	0.0133149i
$543$	−245.749	−	529.485i	−0.452576	−	0.975111i
$544$	−65.9464	+	114.223i	−0.121225	+	0.209968i
$545$	6.11708	+	167.316i	0.0112240	+	0.307002i
$546$	175.910	−	252.882i	0.322179	−	0.463153i
$547$	−764.656	+	764.656i	−1.39791	+	1.39791i	−0.591892	+	0.806017i	$0.701619\pi$
$547$	−764.656	+	764.656i	−1.39791	+	1.39791i	−0.806017	+	0.591892i	$0.798381\pi$
$548$	−13.0827	−	48.8252i	−0.0238735	−	0.0890971i
$549$	165.111	−	59.4262i	0.300749	−	0.108244i
$550$	−209.776	−	40.0639i	−0.381411	−	0.0728435i
$551$	−117.365	+	203.282i	−0.213004	+	0.368933i
$552$	−232.324	−	20.7453i	−0.420876	−	0.0375821i
$553$	298.265	+	510.840i	0.539358	+	0.923761i
$554$	−316.909			−0.572037
$555$	−518.355	+	110.096i	−0.933972	+	0.198371i
$556$	−411.253	+	237.437i	−0.739664	+	0.427045i
$557$	−0.745171	+	2.78102i	−0.00133783	+	0.00499285i	−0.966592	−	0.256322i	$-0.917489\pi$
$557$	−0.745171	+	2.78102i	−0.00133783	+	0.00499285i	0.965254	+	0.261315i	$0.0841560\pi$
$558$	47.8001	+	569.877i	0.0856633	+	1.02128i
$559$	−253.144			−0.452851
$560$	−5.79721	−	139.880i	−0.0103522	−	0.249786i
$561$	324.155	−	271.010i	0.577817	−	0.483084i
$562$	83.0827	+	310.069i	0.147834	+	0.551724i
$563$	58.0850	−	216.776i	0.103171	−	0.385038i	−0.894961	−	0.446145i	$-0.852797\pi$
$563$	58.0850	−	216.776i	0.103171	−	0.385038i	0.998131	+	0.0611074i	$0.0194632\pi$
$564$	136.038	+	49.7901i	0.241202	+	0.0882803i
$565$	26.2140	+	85.2428i	0.0463965	+	0.150872i
$566$	135.575			0.239533
$567$	−195.146	+	532.360i	−0.344173	+	0.938906i
$568$	161.311	+	161.311i	0.283999	+	0.283999i
$569$	−395.156	+	684.429i	−0.694474	+	1.20286i	0.275884	+	0.961191i	$0.411029\pi$
$569$	−395.156	+	684.429i	−0.694474	+	1.20286i	−0.970358	+	0.241673i	$0.922304\pi$
$570$	689.625	+	224.191i	1.20987	+	0.393318i
$571$	−124.910	−	216.351i	−0.218757	−	0.378899i	0.735671	−	0.677339i	$-0.236867\pi$
$571$	−124.910	−	216.351i	−0.218757	−	0.378899i	−0.954428	+	0.298440i	$0.903534\pi$
$572$	−32.4332	−	121.042i	−0.0567013	−	0.211612i
$573$	394.820	+	35.2553i	0.689039	+	0.0615277i
$574$	174.469	+	45.8380i	0.303953	+	0.0798571i
$575$	−449.152	+	520.120i	−0.781134	+	0.904556i
$576$	−54.9890	−	46.4781i	−0.0954669	−	0.0806912i
$577$	22.1831	−	82.7885i	0.0384456	−	0.143481i	−0.944035	−	0.329845i	$-0.893004\pi$
$577$	22.1831	−	82.7885i	0.0384456	−	0.143481i	0.982481	+	0.186364i	$0.0596703\pi$
$578$	−347.812	−	93.1959i	−0.601751	−	0.161239i
$579$	108.379	+	621.155i	0.187183	+	1.07281i
$580$	−2.50878	−	68.6209i	−0.00432548	−	0.118312i
$581$	11.8990	+	43.5568i	0.0204802	+	0.0749687i
$582$	229.758	+	20.5162i	0.394774	+	0.0352513i
$583$	466.882	−	125.101i	0.800826	−	0.214581i
$584$	4.91642	−	2.83850i	0.00841853	−	0.00486044i
$585$	−429.301	−	183.215i	−0.733848	−	0.313188i
$586$	330.490	+	190.809i	0.563977	+	0.325612i
$587$	−198.002	+	198.002i	−0.337312	+	0.337312i	−0.855355	−	0.518043i	$-0.826661\pi$
$587$	−198.002	+	198.002i	−0.337312	+	0.337312i	0.518043	+	0.855355i	$0.326661\pi$
$588$	−293.076	−	23.2912i	−0.498429	−	0.0396109i
$589$		−	1535.92i		−	2.60767i
$590$	235.124	+	764.577i	0.398515	+	1.29589i
$591$	376.552	+	137.819i	0.637144	+	0.233196i
$592$	−136.496	−	36.5741i	−0.230568	−	0.0617805i
$593$	−957.421	+	256.540i	−1.61454	+	0.432614i	−0.949391	−	0.314097i	$-0.898298\pi$
$593$	−957.421	+	256.540i	−1.61454	+	0.432614i	−0.665148	+	0.746712i	$0.731631\pi$
$594$	114.251	+	200.368i	0.192341	+	0.337320i
$595$	778.817	−	243.667i	1.30894	−	0.409524i
$596$		−	78.6264i		−	0.131924i
$597$	−897.192	−	630.620i	−1.50283	−	1.05631i
$598$	−389.488	−	104.363i	−0.651317	−	0.174520i
$599$	−58.5042	−	101.332i	−0.0976698	−	0.169169i	0.813050	−	0.582194i	$-0.197806\pi$
$599$	−58.5042	−	101.332i	−0.0976698	−	0.169169i	−0.910720	+	0.413025i	$0.864472\pi$
$600$	−205.755	+	51.6244i	−0.342924	+	0.0860406i
$601$		−	258.350i		−	0.429867i	−0.976629	−	0.214933i	$-0.931047\pi$
$601$		−	258.350i		−	0.429867i	0.976629	−	0.214933i	$-0.0689534\pi$
$602$	121.819	+	208.640i	0.202357	+	0.346578i
$603$	83.6289	−	58.1120i	0.138688	−	0.0963715i
$604$	−66.0260	−	38.1201i	−0.109315	−	0.0631128i
$605$	−224.507	−	357.981i	−0.371086	−	0.591704i
$606$	−93.4710	−	34.2105i	−0.154243	−	0.0564530i
$607$	−920.381	+	246.615i	−1.51628	+	0.406285i	−0.918514	−	0.395387i	$-0.870610\pi$
$607$	−920.381	+	246.615i	−1.51628	+	0.406285i	−0.597763	+	0.801673i	$0.703944\pi$
$608$	136.736	+	136.736i	0.224895	+	0.224895i
$609$	−143.689	−	12.1247i	−0.235943	−	0.0199092i
$610$	93.8619	−	100.986i	0.153872	−	0.165550i
$611$	216.881	+	125.216i	0.354961	+	0.204937i
$612$	178.727	−	379.721i	0.292037	−	0.620460i
$613$	60.5569	−	226.001i	0.0987878	−	0.368681i	−0.898779	−	0.438403i	$-0.855544\pi$
$613$	60.5569	−	226.001i	0.0987878	−	0.368681i	0.997566	+	0.0697216i	$0.0222111\pi$
$614$	59.1587	+	34.1553i	0.0963497	+	0.0556275i
$615$	14.3474	−	272.955i	0.0233291	−	0.443829i
$616$	−84.1549	+	84.9798i	−0.136615	+	0.137954i
$617$	722.963	+	722.963i	1.17174	+	1.17174i	0.981795	+	0.189945i	$0.0608308\pi$
$617$	722.963	+	722.963i	1.17174	+	1.17174i	0.189945	+	0.981795i	$0.439169\pi$
$618$	−652.686	−	458.761i	−1.05613	−	0.742332i
$619$	164.472	+	284.874i	0.265706	+	0.460217i	0.967748	−	0.251919i	$-0.0810616\pi$
$619$	164.472	+	284.874i	0.265706	+	0.460217i	−0.702042	+	0.712135i	$0.747728\pi$
$620$	238.721	+	380.646i	0.385034	+	0.613945i
$621$	742.180	+	3.99039i	1.19514	+	0.00642574i
$622$	−544.337	−	544.337i	−0.875139	−	0.875139i
$623$	87.9159	+	150.574i	0.141117	+	0.241692i
$624$	−79.8367	−	95.4928i	−0.127943	−	0.153033i
$625$	−230.329	+	581.011i	−0.368527	+	0.929617i
$626$	−325.083	−	563.060i	−0.519302	−	0.899457i
$627$	−260.795	−	561.903i	−0.415941	−	0.896177i
$628$	−31.0449	−	115.861i	−0.0494346	−	0.184492i
$629$		−	823.689i		−	1.30952i
$630$	55.5851	+	441.996i	0.0882304	+	0.701581i
$631$	−184.344			−0.292145			−0.146073	−	0.989274i	$-0.546663\pi$
$631$	−184.344			−0.292145			−0.146073	+	0.989274i	$0.546663\pi$
$632$	230.874	−	61.8625i	0.365307	−	0.0978836i
$633$	−134.541	+	62.4442i	−0.212545	+	0.0986480i
$634$	−22.7822	+	13.1533i	−0.0359341	+	0.0207465i
$635$	307.481	+	999.867i	0.484222	+	1.57459i
$636$	368.333	−	307.945i	0.579139	−	0.484190i
$637$	−492.194	−	126.751i	−0.772675	−	0.198981i
$638$	−41.4788	+	41.4788i	−0.0650138	+	0.0650138i
$639$	−554.396	−	468.590i	−0.867600	−	0.733318i
$640$	−55.1395	−	12.6349i	−0.0861554	−	0.0197420i
$641$	706.892	−	408.124i	1.10280	−	0.636699i	0.165841	−	0.986152i	$-0.446966\pi$
$641$	706.892	−	408.124i	1.10280	−	0.636699i	0.936954	+	0.349453i	$0.113633\pi$
$642$	202.829	−	288.568i	0.315934	−	0.449483i
$643$	18.6427	−	18.6427i	0.0289933	−	0.0289933i	−0.692462	−	0.721455i	$-0.743474\pi$
$643$	18.6427	−	18.6427i	0.0289933	−	0.0289933i	0.721455	+	0.692462i	$0.243474\pi$
$644$	101.415	+	371.236i	0.157477	+	0.576454i
$645$	272.088	−	244.913i	0.421842	−	0.379709i
$646$	−563.577	+	976.145i	−0.872411	+	1.51106i
$647$	−936.314	−	250.884i	−1.44716	−	0.387766i	−0.552126	−	0.833761i	$-0.686183\pi$
$647$	−936.314	−	250.884i	−1.44716	−	0.387766i	−0.895036	+	0.445995i	$0.852850\pi$
$648$	186.723	+	132.750i	0.288153	+	0.204861i
$649$	341.671	−	591.791i	0.526457	−	0.911850i
$650$	−365.744	+	26.7790i	−0.562683	+	0.0411984i
$651$	853.913	−	401.397i	1.31169	−	0.616586i
$652$	8.26804	−	8.26804i	0.0126810	−	0.0126810i
$653$	15.6346	+	58.3491i	0.0239427	+	0.0893554i	0.976863	−	0.213864i	$-0.0686050\pi$
$653$	15.6346	+	58.3491i	0.0239427	+	0.0893554i	−0.952921	+	0.303220i	$0.901938\pi$
$654$	48.8291	−	133.412i	0.0746622	−	0.203995i
$655$	397.607	+	633.992i	0.607033	+	0.967927i
$656$	36.4442	−	63.1233i	0.0555552	−	0.0962245i
$657$	−14.8343	+	10.3080i	−0.0225788	+	0.0156895i
$658$	−1.16562	−	239.010i	−0.00177145	−	0.363236i
$659$	397.461			0.603127			0.301564	−	0.953446i	$-0.402491\pi$
$659$	397.461			0.603127			0.301564	+	0.953446i	$0.402491\pi$
$660$	151.967	+	98.7219i	0.230253	+	0.149579i
$661$	417.970	−	241.315i	0.632330	−	0.365076i	−0.149324	−	0.988788i	$-0.547710\pi$
$661$	417.970	−	241.315i	0.632330	−	0.365076i	0.781654	+	0.623712i	$0.214376\pi$
$662$	60.1065	−	224.320i	0.0907953	−	0.338853i
$663$	417.207	−	593.566i	0.629271	−	0.895273i
$664$	18.2445			0.0274767
$665$	−49.5429	−	1195.41i	−0.0745007	−	1.79761i
$666$	442.536	+	79.6676i	0.664468	+	0.119621i
$667$	48.8533	+	182.323i	0.0732434	+	0.273348i
$668$	−4.49354	+	16.7701i	−0.00672685	+	0.0251050i
$669$	215.333	−	588.340i	0.321873	−	0.879433i
$670$	37.4471	−	70.7068i	0.0558912	−	0.105532i
$671$	−117.778			−0.175526
$672$	−40.2854	+	111.755i	−0.0599485	+	0.166301i
$673$	594.528	+	594.528i	0.883400	+	0.883400i	0.993879	−	0.110479i	$-0.0352384\pi$
$673$	594.528	+	594.528i	0.883400	+	0.883400i	−0.110479	+	0.993879i	$0.535238\pi$
$674$	−182.945	+	316.871i	−0.271432	+	0.470135i
$675$	638.686	−	218.416i	0.946201	−	0.323580i
$676$	61.4113	+	106.368i	0.0908451	+	0.157348i
$677$	28.8163	+	107.544i	0.0425647	+	0.158854i	0.983937	−	0.178516i	$-0.0571295\pi$
$677$	28.8163	+	107.544i	0.0425647	+	0.158854i	−0.941372	+	0.337369i	$0.890463\pi$
$678$	6.73050	−	75.3739i	0.00992699	−	0.111171i
$679$	−100.296	−	367.137i	−0.147711	−	0.540703i
$680$	−12.0469	−	329.512i	−0.0177161	−	0.484576i
$681$	650.261	−	113.457i	0.954861	−	0.166604i
$682$	99.3429	−	370.753i	0.145664	−	0.543626i
$683$	380.211	+	101.877i	0.556678	+	0.149161i	0.526180	−	0.850373i	$-0.323624\pi$
$683$	380.211	+	101.877i	0.556678	+	0.149161i	0.0304984	+	0.999535i	$0.490291\pi$
$684$	−469.935	−	397.202i	−0.687040	−	0.580704i
$685$	92.5614	+	86.0320i	0.135126	+	0.125594i
$686$	132.388	+	466.660i	0.192986	+	0.680262i
$687$	−79.8463	+	894.187i	−0.116225	+	1.30158i
$688$	94.2947	−	25.2662i	0.137056	−	0.0367241i
$689$	718.782	−	414.989i	1.04322	−	0.602306i
$690$	519.605	−	264.650i	0.753050	−	0.383551i
$691$	675.459	+	389.977i	0.977510	+	0.564366i	0.901517	−	0.432743i	$-0.142454\pi$
$691$	675.459	+	389.977i	0.977510	+	0.564366i	0.0759924	+	0.997108i	$0.475788\pi$
$692$	284.876	−	284.876i	0.411670	−	0.411670i
$693$	244.241	−	291.840i	0.352440	−	0.421125i
$694$		−	108.045i		−	0.155684i
$695$	555.633	−	1049.13i	0.799472	−	1.50954i
$696$	−20.0261	+	54.7160i	−0.0287732	+	0.0786149i
$697$	410.382	+	109.962i	0.588784	+	0.157764i
$698$	821.556	−	220.135i	1.17701	−	0.315380i
$699$	230.866	+	276.139i	0.330281	+	0.395049i
$700$	198.076	+	288.558i	0.282966	+	0.412226i
$701$		−	1193.31i		−	1.70229i	−0.524928	−	0.851147i	$-0.675908\pi$
$701$		−	1193.31i		−	1.70229i	0.524928	−	0.851147i	$-0.324092\pi$
$702$	278.548	+	281.559i	0.396792	+	0.401081i
$703$	−1166.50	−	312.562i	−1.65931	−	0.444611i
$704$	24.1624	+	41.8505i	0.0343216	+	0.0594467i
$705$	−354.256	+	75.2421i	−0.502491	+	0.106726i
$706$			642.977i			0.910733i
$707$	0.800889	+	164.222i	0.00113280	+	0.232280i
$708$	60.3685	−	676.059i	0.0852663	−	0.954885i
$709$	−787.987	−	454.944i	−1.11141	−	0.641671i	−0.172213	−	0.985060i	$-0.555092\pi$
$709$	−787.987	−	454.944i	−1.11141	−	0.641671i	−0.939193	+	0.343389i	$0.888425\pi$
$710$	−555.913	−	127.384i	−0.782977	−	0.179415i
$711$	−715.612	+	257.560i	−1.00649	+	0.362251i
$712$	68.0519	−	18.2344i	0.0955785	−	0.0256102i
$713$	−873.338	−	873.338i	−1.22488	−	1.22488i
$714$	−689.985	−	58.2218i	−0.966366	−	0.0815431i
$715$	229.468	+	213.281i	0.320935	+	0.298296i
$716$	−61.1192	−	35.2872i	−0.0853621	−	0.0492838i
$717$	1076.53	−	499.647i	1.50143	−	0.696857i
$718$	72.6529	−	271.144i	0.101188	−	0.377638i
$719$	−276.671	−	159.736i	−0.384800	−	0.222164i	0.295105	−	0.955465i	$-0.404645\pi$
$719$	−276.671	−	159.736i	−0.384800	−	0.222164i	−0.679905	+	0.733301i	$0.737979\pi$
$720$	178.199	+	25.3982i	0.247499	+	0.0352753i
$721$	−334.473	+	1273.07i	−0.463902	+	1.76570i
$722$	807.544	+	807.544i	1.11848	+	1.11848i
$723$	381.628	−	542.947i	0.527839	−	0.750964i
$724$	194.579	+	337.020i	0.268755	+	0.465497i
$725$	96.4603	+	142.003i	0.133049	+	0.195866i
$726$	61.6287	+	353.214i	0.0848881	+	0.486521i
$727$	962.101	+	962.101i	1.32338	+	1.32338i	0.911018	+	0.412367i	$0.135298\pi$
$727$	962.101	+	962.101i	1.32338	+	1.32338i	0.412367	+	0.911018i	$0.364702\pi$
$728$	−101.814	+	178.350i	−0.139854	+	0.244986i
$729$	−627.377	−	371.268i	−0.860599	−	0.509283i
$730$	−6.64244	+	12.5421i	−0.00909924	+	0.0171810i
$731$	284.511	+	492.788i	0.389209	+	0.674129i
$732$	−106.114	+	49.2506i	−0.144965	+	0.0672822i
$733$	−101.038	−	377.079i	−0.137842	−	0.514433i	−0.999970	−	0.00774251i	$-0.997535\pi$
$733$	−101.038	−	377.079i	−0.137842	−	0.514433i	0.862128	−	0.506690i	$-0.169131\pi$
$734$			665.487i			0.906658i
$735$	651.657	−	339.954i	0.886608	−	0.462522i
$736$	155.499			0.211275
$737$	−66.0218	+	17.6905i	−0.0895818	+	0.0240034i
$738$	−98.7705	+	209.847i	−0.133835	+	0.284346i
$739$	−665.653	+	384.315i	−0.900749	+	0.520047i	−0.877443	−	0.479681i	$-0.840752\pi$
$739$	−665.653	+	384.315i	−0.900749	+	0.520047i	−0.0233056	+	0.999728i	$0.507419\pi$
$740$	337.672	−	103.842i	0.456314	−	0.140326i
$741$	−682.284	−	816.080i	−0.920761	−	1.10132i
$742$	−687.928	−	392.715i	−0.927126	−	0.529265i
$743$	−411.294	+	411.294i	−0.553559	+	0.553559i	−0.927466	−	0.373907i	$-0.878018\pi$
$743$	−411.294	+	411.294i	−0.553559	+	0.553559i	0.373907	+	0.927466i	$0.378018\pi$
$744$	−65.5307	−	375.578i	−0.0880789	−	0.504809i
$745$	104.437	+	166.527i	0.140184	+	0.223526i
$746$	−331.818	+	191.575i	−0.444796	+	0.256803i
$747$	−57.8505	+	4.85239i	−0.0774438	+	0.00649583i
$748$	−199.178	+	199.178i	−0.266281	+	0.266281i
$749$	−562.857	−	147.879i	−0.751477	−	0.197435i
$750$	367.207	−	382.635i	0.489609	−	0.510180i
$751$	569.327	−	986.103i	0.758091	−	1.31305i	−0.185731	−	0.982601i	$-0.559465\pi$
$751$	569.327	−	986.103i	0.758091	−	1.31305i	0.943823	−	0.330452i	$-0.107201\pi$
$752$	−93.2849	−	24.9956i	−0.124049	−	0.0332388i
$753$	−630.756	+	292.751i	−0.837657	+	0.388780i
$754$	−50.3633	+	87.2319i	−0.0667949	+	0.115692i
$755$	190.473	−	6.96370i	0.252283	−	0.00922345i
$756$	98.0160	−	365.071i	0.129651	−	0.482898i
$757$	−264.443	+	264.443i	−0.349331	+	0.349331i	−0.859860	−	0.510530i	$-0.829449\pi$
$757$	−264.443	+	264.443i	−0.349331	+	0.349331i	0.510530	+	0.859860i	$0.329449\pi$
$758$	175.156	+	653.692i	0.231077	+	0.862390i
$759$	−467.794	−	171.213i	−0.616329	−	0.225577i
$760$	−471.221	−	107.978i	−0.620028	−	0.142076i
$761$	692.515	−	1199.47i	0.910006	−	1.57618i	0.0959541	−	0.995386i	$-0.469410\pi$
$761$	692.515	−	1199.47i	0.910006	−	1.57618i	0.814052	−	0.580792i	$-0.197257\pi$
$762$	78.9464	−	884.109i	0.103604	−	1.16025i
$763$	−234.397	+	1.14312i	−0.307204	+	0.00149819i
$764$	−264.260			−0.345890
$765$	125.837	+	1041.63i	0.164493	+	1.36160i
$766$	522.505	−	301.669i	0.682122	−	0.393823i
$767$	303.695	−	1133.40i	0.395951	−	1.47771i
$768$	39.2699	+	27.6021i	0.0511327	+	0.0359402i
$769$	1084.88			1.41077			0.705386	−	0.708823i	$-0.250773\pi$
$769$	1084.88			1.41077			0.705386	+	0.708823i	$0.250773\pi$
$770$	65.3600	−	291.763i	0.0848831	−	0.378913i
$771$	−62.0702	−	74.2422i	−0.0805061	−	0.0962933i
$772$	−108.797	−	406.036i	−0.140929	−	0.525953i
$773$	−371.358	+	1385.93i	−0.480411	+	1.79292i	0.119480	+	0.992837i	$0.461877\pi$
$773$	−371.358	+	1385.93i	−0.480411	+	1.79292i	−0.599891	+	0.800082i	$0.704789\pi$
$774$	−292.274	+	105.194i	−0.377615	+	0.135910i
$775$	−1011.20	−	489.103i	−1.30477	−	0.631100i
$776$	−153.782			−0.198172
$777$	−131.080	−	730.213i	−0.168700	−	0.939785i
$778$	−233.030	−	233.030i	−0.299524	−	0.299524i
$779$	311.452	−	539.451i	0.399810	−	0.692492i
$780$	295.930	+	96.2042i	0.379397	+	0.123339i
$781$	243.604	+	421.935i	0.311913	+	0.540249i
$782$	234.590	+	875.501i	0.299987	+	1.11957i
$783$	48.9472	−	178.822i	0.0625124	−	0.228381i
$784$	195.991	−	1.91169i	0.249988	−	0.00243837i
$785$	219.646	+	204.152i	0.279804	+	0.260066i
$786$	−109.146	−	625.551i	−0.138863	−	0.795866i
$787$	−127.483	+	475.774i	−0.161986	+	0.604542i	0.836419	+	0.548091i	$0.184645\pi$
$787$	−127.483	+	475.774i	−0.161986	+	0.604542i	−0.998405	+	0.0564509i	$0.982022\pi$
$788$	−258.212	−	69.1876i	−0.327680	−	0.0878016i
$789$	493.898	−	86.1752i	0.625980	−	0.109221i
$790$	−406.809	+	437.684i	−0.514948	+	0.554030i
$791$	−120.442	+	32.9027i	−0.152265	+	0.0415963i
$792$	−87.7459	−	126.275i	−0.110790	−	0.159438i
$793$	−195.349	+	52.3437i	−0.246342	+	0.0660072i
$794$	−67.0365	+	38.7035i	−0.0844288	+	0.0487450i
$795$	−371.077	+	1141.46i	−0.466763	+	1.43579i
$796$	633.149	+	365.549i	0.795414	+	0.459232i
$797$	183.570	−	183.570i	0.230326	−	0.230326i	−0.582503	−	0.812829i	$-0.697926\pi$
$797$	183.570	−	183.570i	0.230326	−	0.230326i	0.812829	+	0.582503i	$0.197926\pi$
$798$	−344.279	+	955.054i	−0.431427	+	1.19681i
$799$		−	562.929i		−	0.704542i
$800$	133.565	−	46.4799i	0.166956	−	0.0580998i
$801$	−210.932	+	75.9180i	−0.263336	+	0.0947790i
$802$	625.043	+	167.480i	0.779356	+	0.208828i
$803$	11.7111	−	3.13798i	0.0145842	−	0.00390781i
$804$	−52.0860	+	43.5465i	−0.0647836	+	0.0541623i
$805$	−707.894	−	651.552i	−0.879371	−	0.809382i
$806$		−	659.089i		−	0.817728i
$807$	−601.910	+	856.346i	−0.745861	+	1.06115i
$808$	64.0955	+	17.1743i	0.0793261	+	0.0212554i
$809$	554.415	+	960.275i	0.685309	+	1.18699i	0.973340	+	0.229369i	$0.0736663\pi$
$809$	554.415	+	960.275i	0.685309	+	1.18699i	−0.288030	+	0.957621i	$0.593000\pi$
$810$	−571.797	−	33.1392i	−0.705922	−	0.0409126i
$811$		−	715.199i		−	0.881873i	−0.897538	−	0.440937i	$-0.854646\pi$
$811$		−	715.199i		−	0.881873i	0.897538	−	0.440937i	$-0.145354\pi$
$812$	96.1323	−	0.468824i	0.118389	−	0.000577369i
$813$	−58.9146	−	5.26077i	−0.0724657	−	0.00647081i
$814$	−261.362	−	150.897i	−0.321084	−	0.185378i
$815$	−6.52912	+	28.4935i	−0.00801119	+	0.0349613i
$816$	−96.1638	+	262.742i	−0.117848	+	0.321987i
$817$	805.842	−	215.925i	0.986343	−	0.264290i
$818$	332.873	+	332.873i	0.406935	+	0.406935i
$819$	275.402	−	592.599i	0.336266	−	0.723564i
$820$	6.65755	+	182.100i	0.00811897	+	0.222073i
$821$	−1269.36	−	732.866i	−1.54612	−	0.892650i	−0.998433	−	0.0559644i	$-0.982177\pi$
$821$	−1269.36	−	732.866i	−1.54612	−	0.892650i	−0.547683	−	0.836686i	$-0.684490\pi$
$822$	−45.1421	−	97.2623i	−0.0549174	−	0.118324i
$823$	251.704	−	939.371i	0.305837	−	1.14140i	−0.626386	−	0.779513i	$-0.715467\pi$
$823$	251.704	−	939.371i	0.305837	−	1.14140i	0.932223	−	0.361885i	$-0.117867\pi$
$824$	460.601	+	265.928i	0.558982	+	0.322728i
$825$	−452.987	−	7.23539i	−0.549075	−	0.00877016i
$826$	−1080.29	+	295.118i	−1.30786	+	0.357285i
$827$	−618.411	−	618.411i	−0.747776	−	0.747776i	0.226285	−	0.974061i	$-0.427342\pi$
$827$	−618.411	−	618.411i	−0.747776	−	0.747776i	−0.974061	+	0.226285i	$0.927342\pi$
$828$	−493.062	+	41.3571i	−0.595486	+	0.0499481i
$829$	678.323	+	1174.89i	0.818242	+	1.41724i	0.906976	+	0.421182i	$0.138385\pi$
$829$	678.323	+	1174.89i	0.818242	+	1.41724i	−0.0887341	+	0.996055i	$0.528282\pi$
$830$	−38.6409	+	24.2336i	−0.0465553	+	0.0291971i
$831$	−662.260	+	115.551i	−0.796943	+	0.139050i
$832$	58.6757	+	58.6757i	0.0705237	+	0.0705237i
$833$	306.440	+	1100.60i	0.367876	+	1.32125i
$834$	−772.842	+	646.135i	−0.926669	+	0.774742i
$835$	−12.7581	−	41.4868i	−0.0152792	−	0.0496848i
$836$	206.492	+	357.654i	0.246999	+	0.427816i
$837$	307.678	+	1173.47i	0.367596	+	1.40200i
$838$	−138.080	−	515.323i	−0.164774	−	0.614944i
$839$		−	1498.76i		−	1.78637i	−0.449693	−	0.893183i	$-0.648467\pi$
$839$		−	1498.76i		−	1.78637i	0.449693	−	0.893183i	$-0.351533\pi$
$840$	−63.1176	−	290.200i	−0.0751400	−	0.345476i
$841$	−793.849			−0.943934
$842$	−270.143	+	72.3847i	−0.320835	+	0.0859676i
$843$	286.679	+	617.673i	0.340070	+	0.732708i
$844$	85.6360	−	49.4419i	0.101464	−	0.0585805i
$845$	−271.350	−	143.710i	−0.321125	−	0.170071i
$846$	302.440	+	54.4468i	0.357494	+	0.0643579i
$847$	510.873	−	298.284i	0.603156	−	0.352165i
$848$	−226.323	+	226.323i	−0.266890	+	0.266890i
$849$	283.319	−	49.4334i	0.333709	−	0.0582254i
$850$	463.195	+	681.888i	0.544935	+	0.802221i
$851$	−841.006	+	485.555i	−0.988256	+	0.570570i
$852$	395.917	+	278.283i	0.464692	+	0.326623i
$853$	4.38891	−	4.38891i	0.00514527	−	0.00514527i	−0.704529	−	0.709675i	$-0.748842\pi$
$853$	4.38891	−	4.38891i	0.00514527	−	0.00514527i	0.709675	+	0.704529i	$0.248842\pi$
$854$	137.148	+	135.817i	0.160595	+	0.159036i
$855$	1522.89	+	217.053i	1.78116	+	0.253863i
$856$	−117.573	+	203.643i	−0.137352	+	0.237901i
$857$	741.882	+	198.787i	0.865673	+	0.231956i	0.664216	−	0.747541i	$-0.268766\pi$
$857$	741.882	+	198.787i	0.865673	+	0.231956i	0.201457	+	0.979497i	$0.435432\pi$
$858$	−111.911	−	241.122i	−0.130433	−	0.281028i
$859$	−506.657	+	877.555i	−0.589821	+	1.02160i	0.404434	+	0.914567i	$0.367469\pi$
$859$	−506.657	+	877.555i	−0.589821	+	1.02160i	−0.994255	+	0.107033i	$0.965865\pi$
$860$	−166.151	+	178.761i	−0.193199	+	0.207862i
$861$	381.309	+	32.1754i	0.442868	+	0.0373698i
$862$	164.566	−	164.566i	0.190911	−	0.190911i
$863$	−226.732	−	846.176i	−0.262726	−	0.980505i	−0.963628	−	0.267248i	$-0.913886\pi$
$863$	−226.732	−	846.176i	−0.262726	−	0.980505i	0.700902	−	0.713257i	$-0.252781\pi$
$864$	−131.860	−	77.0776i	−0.152616	−	0.0892102i
$865$	−224.961	+	981.743i	−0.260070	+	1.13496i
$866$	346.623	−	600.369i	0.400258	−	0.693267i
$867$	−760.821	−	67.9374i	−0.877533	−	0.0783591i
$868$	−543.219	+	317.170i	−0.625828	+	0.365403i
$869$	510.465			0.587416
$870$	−30.2632	−	142.486i	−0.0347853	−	0.163777i
$871$	−101.643	+	58.6836i	−0.116697	+	0.0673750i
$872$	−24.5132	+	91.4844i	−0.0281114	+	0.104913i
$873$	487.618	−	40.9004i	0.558554	−	0.0468504i
$874$	1328.89			1.52047
$875$	−802.797	−	348.053i	−0.917483	−	0.397775i
$876$	9.23912	−	7.72437i	0.0105469	−	0.00881777i
$877$	332.001	+	1239.04i	0.378564	+	1.41282i	0.848067	+	0.529890i	$0.177767\pi$
$877$	332.001	+	1239.04i	0.378564	+	1.41282i	−0.469502	+	0.882931i	$0.655567\pi$
$878$	197.395	−	736.690i	0.224824	−	0.839054i
$879$	760.214	+	278.239i	0.864863	+	0.316541i
$880$	−106.763	−	56.5431i	−0.121322	−	0.0642535i
$881$	1186.25			1.34648			0.673241	−	0.739423i	$-0.264902\pi$
$881$	1186.25			1.34648			0.673241	+	0.739423i	$0.264902\pi$
$882$	−620.948	+	58.1882i	−0.704022	+	0.0659730i
$883$	459.415	+	459.415i	0.520289	+	0.520289i	0.917659	−	0.397369i	$-0.130077\pi$
$883$	459.415	+	459.415i	0.520289	+	0.520289i	−0.397369	+	0.917659i	$0.630077\pi$
$884$	−241.841	+	418.880i	−0.273575	+	0.473847i
$885$	770.129	+	1512.04i	0.870202	+	1.70852i
$886$	−249.829	−	432.716i	−0.281974	−	0.488393i
$887$	231.193	+	862.823i	0.260646	+	0.972743i	0.964862	+	0.262758i	$0.0846320\pi$
$887$	231.193	+	862.823i	0.260646	+	0.972743i	−0.704216	+	0.709986i	$0.748701\pi$
$888$	−298.579	−	26.6615i	−0.336237	−	0.0300242i
$889$	−1412.74	+	385.937i	−1.58914	+	0.434125i
$890$	−119.910	+	129.011i	−0.134730	+	0.144956i
$891$	311.813	+	377.062i	0.349959	+	0.423189i
$892$	−108.102	+	403.441i	−0.121190	+	0.452288i
$893$	−797.212	−	213.612i	−0.892734	−	0.239207i
$894$	−28.6687	−	164.310i	−0.0320679	−	0.183791i
$895$	176.318	−	6.44619i	0.197004	−	0.00720245i
$896$	20.1241	−	76.5965i	0.0224600	−	0.0854871i
$897$	−851.984	−	76.0778i	−0.949815	−	0.0848136i
$898$	−596.627	+	159.866i	−0.664395	+	0.178024i
$899$	−267.191	+	154.263i	−0.297210	+	0.171594i
$900$	−411.152	+	182.904i	−0.456836	+	0.203227i
$901$	−1615.70	−	932.823i	−1.79323	−	1.03532i
$902$	110.072	−	110.072i	0.122032	−	0.122032i
$903$	330.645	+	391.588i	0.366163	+	0.433652i
$904$			50.4492i			0.0558066i
$905$	−859.760	−	455.339i	−0.950011	−	0.503137i
$906$	−151.877	−	55.5872i	−0.167635	−	0.0613546i
$907$	−607.910	−	162.889i	−0.670242	−	0.179591i	−0.0923782	−	0.995724i	$-0.529447\pi$
$907$	−607.910	−	162.889i	−0.670242	−	0.179591i	−0.577864	+	0.816133i	$0.696114\pi$
$908$	−425.062	+	113.895i	−0.468130	+	0.125435i
$909$	−207.805	−	37.4101i	−0.228608	−	0.0411552i
$910$	−21.2597	−	512.972i	−0.0233623	−	0.563706i
$911$		−	911.280i		−	1.00031i	−0.865937	−	0.500154i	$-0.833277\pi$
$911$		−	911.280i		−	1.00031i	0.865937	−	0.500154i	$-0.166723\pi$
$912$	335.600	+	235.887i	0.367983	+	0.258648i
$913$	37.6366	+	10.0847i	0.0412230	+	0.0110457i
$914$	22.2195	+	38.4853i	0.0243102	+	0.0421064i
$915$	159.327	−	245.258i	0.174127	−	0.268042i
$916$		−	598.496i		−	0.653380i
$917$	−904.768	+	528.268i	−0.986661	+	0.576083i
$918$	235.041	−	858.690i	0.256036	−	0.935392i
$919$	687.784	+	397.092i	0.748404	+	0.432092i	0.825117	−	0.564962i	$-0.191109\pi$
$919$	687.784	+	397.092i	0.748404	+	0.432092i	−0.0767126	+	0.997053i	$0.524442\pi$
$920$	−329.338	+	206.544i	−0.357976	+	0.224504i
$921$	136.081	+	49.8056i	0.147753	+	0.0540778i
$922$	210.524	−	56.4099i	0.228335	−	0.0611821i
$923$	591.566	+	591.566i	0.640916	+	0.640916i
$924$	−144.877	+	208.271i	−0.156794	+	0.225401i
$925$	−577.243	+	668.450i	−0.624046	+	0.722649i
$926$	347.231	+	200.474i	0.374979	+	0.216494i
$927$	−1531.22	−	720.714i	−1.65180	−	0.777469i
$928$	10.0535	−	37.5202i	0.0108335	−	0.0404312i
$929$	445.001	+	256.922i	0.479011	+	0.276557i	0.720004	−	0.693970i	$-0.244140\pi$
$929$	445.001	+	256.922i	0.479011	+	0.276557i	−0.240993	+	0.970527i	$0.577473\pi$
$930$	637.658	+	708.412i	0.685654	+	0.761734i
$931$	1674.93	−	16.3372i	1.79907	−	0.0175481i
$932$	−169.674	−	169.674i	−0.182054	−	0.182054i
$933$	−1336.00	−	939.052i	−1.43194	−	1.00649i
$934$	68.5244	+	118.688i	0.0733666	+	0.127075i
$935$	157.287	−	686.410i	0.168221	−	0.734128i
$936$	−201.657	−	170.446i	−0.215446	−	0.182100i
$937$	−35.0323	−	35.0323i	−0.0373877	−	0.0373877i	0.688166	−	0.725553i	$-0.258416\pi$
$937$	−35.0323	−	35.0323i	−0.0373877	−	0.0373877i	−0.725553	+	0.688166i	$0.758416\pi$
$938$	97.2799	+	55.5338i	0.103710	+	0.0592045i
$939$	−884.644	−	1058.12i	−0.942113	−	1.12686i
$940$	230.773	−	70.9678i	0.245504	−	0.0754977i
$941$	423.536	+	733.586i	0.450091	+	0.779581i	0.998391	−	0.0567009i	$-0.0180581\pi$
$941$	423.536	+	733.586i	0.450091	+	0.779581i	−0.548300	+	0.836282i	$0.684725\pi$
$942$	−107.121	−	230.801i	−0.113717	−	0.245012i
$943$	−129.642	−	483.832i	−0.137479	−	0.513077i
$944$			452.499i			0.479342i
$945$	277.319	+	903.393i	0.293459	+	0.955972i
$946$	208.487			0.220388
$947$	1461.39	−	391.578i	1.54318	−	0.413493i	0.615887	−	0.787835i	$-0.288798\pi$
$947$	1461.39	−	391.578i	1.54318	−	0.413493i	0.927291	+	0.374341i	$0.122131\pi$
$948$	459.912	−	213.458i	0.485140	−	0.225167i
$949$	18.0297	−	10.4094i	0.0189986	−	0.0109688i
$950$	1141.45	−	397.216i	1.20152	−	0.418123i
$951$	−42.8132	+	35.7939i	−0.0450191	+	0.0376382i
$952$	461.619	−	2.25125i	0.484894	−	0.00236476i
$953$	−88.2376	+	88.2376i	−0.0925893	+	0.0925893i	−0.751884	−	0.659295i	$-0.770855\pi$
$953$	−88.2376	+	88.2376i	−0.0925893	+	0.0925893i	0.659295	+	0.751884i	$0.270855\pi$
$954$	657.441	−	777.828i	0.689141	−	0.815334i
$955$	559.690	−	351.008i	0.586063	−	0.367548i
$956$	−685.215	+	395.609i	−0.716752	+	0.413817i
$957$	−71.5563	+	101.804i	−0.0747715	+	0.106379i
$958$	107.041	−	107.041i	0.111734	−	0.111734i
$959$	−124.487	+	125.708i	−0.129810	+	0.131082i
$960$	−119.835	−	6.29890i	−0.124828	−	0.00656135i
$961$	528.896	−	916.074i	0.550360	−	0.953251i
$962$	−500.563	−	134.126i	−0.520336	−	0.139424i
$963$	318.645	−	676.991i	0.330888	−	0.703002i
$964$	−221.217	+	383.158i	−0.229478	+	0.397467i
$965$	769.751	+	715.452i	0.797669	+	0.741401i
$966$	347.293	+	738.813i	0.359516	+	0.764816i
$967$	−11.0507	+	11.0507i	−0.0114278	+	0.0114278i	−0.712798	−	0.701370i	$-0.752572\pi$
$967$	−11.0507	+	11.0507i	−0.0114278	+	0.0114278i	0.701370	+	0.712798i	$0.252572\pi$
$968$	−61.8665	−	230.889i	−0.0639117	−	0.238522i
$969$	−821.815	+	2245.39i	−0.848106	+	2.31722i
$970$	325.702	−	204.263i	0.335775	−	0.210581i
$971$	528.106	−	914.707i	0.543879	−	0.942025i	−0.454798	−	0.890595i	$-0.650289\pi$
$971$	528.106	−	914.707i	0.543879	−	0.942025i	0.998677	−	0.0514307i	$-0.0163781\pi$
$972$	438.607	+	209.331i	0.451242	+	0.215361i
$973$	1443.42	+	824.000i	1.48348	+	0.846866i
$974$	−667.923			−0.685753
$975$	−754.549	+	189.319i	−0.773897	+	0.194173i
$976$	67.5422	−	38.9955i	0.0692031	−	0.0399544i
$977$	414.973	−	1548.70i	0.424743	−	1.58516i	−0.339742	−	0.940519i	$-0.610340\pi$
$977$	414.973	−	1548.70i	0.424743	−	1.58516i	0.764484	−	0.644642i	$-0.222994\pi$
$978$	14.2635	−	20.2928i	0.0145843	−	0.0207493i
$979$	150.463			0.153691
$980$	−412.559	+	264.377i	−0.420979	+	0.269772i
$981$	53.3959	−	296.603i	0.0544301	−	0.302347i
$982$	−83.4668	−	311.502i	−0.0849967	−	0.317212i
$983$	−203.226	+	758.449i	−0.206740	+	0.771565i	0.782172	+	0.623063i	$0.214112\pi$
$983$	−203.226	+	758.449i	−0.206740	+	0.771565i	−0.988912	+	0.148502i	$0.952555\pi$
$984$	53.1434	−	145.200i	0.0540075	−	0.147561i
$985$	638.779	−	196.438i	0.648507	−	0.199430i
$986$	226.416			0.229631
$987$	−89.5832	−	499.045i	−0.0907632	−	0.505618i
$988$	501.442	+	501.442i	0.507532	+	0.507532i
$989$	335.433	−	580.986i	0.339163	−	0.587448i
$990$	353.568	+	150.894i	0.357140	+	0.152418i
$991$	517.260	+	895.920i	0.521957	+	0.904056i	0.999674	+	0.0255424i	$0.00813127\pi$
$991$	517.260	+	895.920i	0.521957	+	0.904056i	−0.477717	+	0.878514i	$0.658535\pi$
$992$	65.7835	+	245.507i	0.0663140	+	0.247487i
$993$	43.8160	−	490.690i	0.0441249	−	0.494149i
$994$	202.890	−	772.242i	0.204115	−	0.776903i
$995$	−1826.52	+	66.7777i	−1.83570	+	0.0671133i
$996$	38.1265	−	6.65229i	0.0382796	−	0.00667901i
$997$	50.5660	−	188.715i	0.0507181	−	0.189283i	−0.935919	−	0.352215i	$-0.885429\pi$
$997$	50.5660	−	188.715i	0.0507181	−	0.189283i	0.986637	+	0.162932i	$0.0520953\pi$
$998$	−1114.53	−	298.638i	−1.11677	−	0.299237i
$999$	953.838	+	5.12838i	0.954792	+	0.00513352i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.w.a.173.2	yes	64
3.2	odd	2		210.3.w.b.173.5	yes	64
5.2	odd	4		210.3.w.b.47.11	yes	64
7.3	odd	6	inner	210.3.w.a.143.3	yes	64
15.2	even	4	inner	210.3.w.a.47.3	yes	64
21.17	even	6		210.3.w.b.143.11	yes	64
35.17	even	12		210.3.w.b.17.5	yes	64
105.17	odd	12	inner	210.3.w.a.17.2	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.w.a.17.2	✓	64	105.17	odd	12	inner
210.3.w.a.47.3	yes	64	15.2	even	4	inner
210.3.w.a.143.3	yes	64	7.3	odd	6	inner
210.3.w.a.173.2	yes	64	1.1	even	1	trivial
210.3.w.b.17.5	yes	64	35.17	even	12
210.3.w.b.47.11	yes	64	5.2	odd	4
210.3.w.b.143.11	yes	64	21.17	even	6
210.3.w.b.173.5	yes	64	3.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 0.366025i) q^{2} +(-2.72119 + 1.26298i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-2.34013 + 4.41857i) q^{5} +(3.25493 - 2.72129i) q^{6} +(-6.07917 - 3.47039i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(5.80976 - 6.87362i) q^{9} +O(q^{10})\)	\(q+(-1.36603 + 0.366025i) q^{2} +(-2.72119 + 1.26298i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-2.34013 + 4.41857i) q^{5} +(3.25493 - 2.72129i) q^{6} +(-6.07917 - 3.47039i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(5.80976 - 6.87362i) q^{9} +(1.57936 - 6.89243i) q^{10} +(-5.23131 + 3.02030i) q^{11} +(-3.45026 + 4.90874i) q^{12} +(-7.33446 + 7.33446i) q^{13} +(9.57456 + 2.51551i) q^{14} +(0.787362 - 14.9793i) q^{15} +(2.00000 - 3.46410i) q^{16} +(22.5211 + 6.03451i) q^{17} +(-5.42036 + 11.5161i) q^{18} +(17.0920 - 29.6042i) q^{19} +(0.365356 + 9.99332i) q^{20} +(20.9256 + 1.76573i) q^{21} +(6.04060 - 6.04060i) q^{22} +(-7.11456 - 26.5519i) q^{23} +(2.91642 - 7.96834i) q^{24} +(-14.0476 - 20.6801i) q^{25} +(7.33446 - 12.7037i) q^{26} +(-7.12823 + 26.0420i) q^{27} +(-13.9998 + 0.0682753i) q^{28} -6.86667 q^{29} +(4.40726 + 20.7503i) q^{30} +(38.9114 - 22.4655i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(10.4208 - 14.8258i) q^{33} -32.9732 q^{34} +(29.5602 - 18.7401i) q^{35} +(3.18919 - 17.7152i) q^{36} +(-9.14352 - 34.1241i) q^{37} +(-12.5122 + 46.6962i) q^{38} +(10.6952 - 29.2218i) q^{39} +(-4.15690 - 13.5174i) q^{40} +18.2221 q^{41} +(-29.2313 + 5.24728i) q^{42} +(17.2571 + 17.2571i) q^{43} +(-6.04060 + 10.4626i) q^{44} +(16.7760 + 41.7560i) q^{45} +(19.4373 + 33.6664i) q^{46} +(-6.24890 - 23.3212i) q^{47} +(-1.06729 + 11.9524i) q^{48} +(24.9127 + 42.1943i) q^{49} +(26.7588 + 23.1077i) q^{50} +(-68.9057 + 12.0226i) q^{51} +(-5.36920 + 20.0381i) q^{52} +(-77.2906 - 20.7100i) q^{53} +(0.205295 - 38.1832i) q^{54} +(-1.10348 - 30.1828i) q^{55} +(19.0991 - 5.21756i) q^{56} +(-9.12106 + 102.145i) q^{57} +(9.38005 - 2.51338i) q^{58} +(-97.9689 + 56.5624i) q^{59} +(-13.6156 - 26.7323i) q^{60} +(16.8856 + 9.74888i) q^{61} +(-44.9310 + 44.9310i) q^{62} +(-59.1727 + 21.6238i) q^{63} -8.00000i q^{64} +(-15.2443 - 49.5715i) q^{65} +(-8.80847 + 24.0668i) q^{66} +(10.9297 + 2.92860i) q^{67} +(45.0422 - 12.0690i) q^{68} +(52.8946 + 63.2672i) q^{69} +(-33.5207 + 36.4193i) q^{70} -80.6556i q^{71} +(2.12771 + 25.3668i) q^{72} +(-1.93873 - 0.519481i) q^{73} +(24.9805 + 43.2676i) q^{74} +(64.3447 + 38.5325i) q^{75} -68.3679i q^{76} +(42.2837 - 0.206212i) q^{77} +(-3.91400 + 43.8324i) q^{78} +(-73.1841 - 42.2528i) q^{79} +(10.6261 + 16.9436i) q^{80} +(-13.4933 - 79.8682i) q^{81} +(-24.8919 + 6.66976i) q^{82} +(-4.56113 - 4.56113i) q^{83} +(38.0100 - 17.8673i) q^{84} +(-79.3662 + 85.3897i) q^{85} +(-29.8902 - 17.2571i) q^{86} +(18.6855 - 8.67247i) q^{87} +(4.42202 - 16.5032i) q^{88} +(-21.5716 - 12.4544i) q^{89} +(-38.2002 - 50.8993i) q^{90} +(70.0410 - 19.1340i) q^{91} +(-38.8747 - 38.8747i) q^{92} +(-77.5118 + 110.277i) q^{93} +(17.0723 + 29.5701i) q^{94} +(90.8109 + 144.800i) q^{95} +(-2.91695 - 16.7180i) q^{96} +(38.4454 + 38.4454i) q^{97} +(-49.4756 - 48.5197i) q^{98} +(-9.63229 + 53.5053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 32 q^{2} - 6 q^{3} - 12 q^{5} + 4 q^{7} - 128 q^{8} - 16 q^{9}+O(q^{10}) \) 64 * q - 32 * q^2 - 6 * q^3 - 12 * q^5 + 4 * q^7 - 128 * q^8 - 16 * q^9	\( 64 q - 32 q^{2} - 6 q^{3} - 12 q^{5} + 4 q^{7} - 128 q^{8} - 16 q^{9} + 24 q^{10} + 12 q^{12} - 16 q^{14} - 44 q^{15} + 128 q^{16} - 20 q^{18} + 36 q^{21} + 16 q^{22} - 12 q^{23} - 16 q^{25} + 8 q^{28} - 112 q^{29} + 26 q^{30} + 128 q^{32} + 30 q^{33} + 16 q^{36} - 32 q^{37} + 24 q^{38} + 64 q^{39} - 136 q^{42} + 32 q^{43} - 16 q^{44} - 114 q^{45} - 24 q^{46} - 96 q^{47} + 40 q^{50} - 84 q^{51} + 56 q^{53} - 72 q^{54} - 316 q^{57} + 56 q^{58} + 672 q^{59} + 8 q^{60} + 600 q^{61} - 210 q^{63} + 28 q^{65} + 16 q^{67} + 24 q^{72} - 624 q^{73} - 64 q^{74} + 48 q^{75} + 208 q^{77} - 8 q^{78} - 48 q^{80} - 64 q^{81} - 192 q^{82} + 160 q^{84} - 152 q^{85} + 60 q^{87} - 16 q^{88} + 144 q^{89} - 232 q^{91} + 48 q^{92} - 170 q^{93} + 136 q^{95} - 48 q^{96} + 128 q^{98} + 160 q^{99}+O(q^{100}) \) 64 * q - 32 * q^2 - 6 * q^3 - 12 * q^5 + 4 * q^7 - 128 * q^8 - 16 * q^9 + 24 * q^10 + 12 * q^12 - 16 * q^14 - 44 * q^15 + 128 * q^16 - 20 * q^18 + 36 * q^21 + 16 * q^22 - 12 * q^23 - 16 * q^25 + 8 * q^28 - 112 * q^29 + 26 * q^30 + 128 * q^32 + 30 * q^33 + 16 * q^36 - 32 * q^37 + 24 * q^38 + 64 * q^39 - 136 * q^42 + 32 * q^43 - 16 * q^44 - 114 * q^45 - 24 * q^46 - 96 * q^47 + 40 * q^50 - 84 * q^51 + 56 * q^53 - 72 * q^54 - 316 * q^57 + 56 * q^58 + 672 * q^59 + 8 * q^60 + 600 * q^61 - 210 * q^63 + 28 * q^65 + 16 * q^67 + 24 * q^72 - 624 * q^73 - 64 * q^74 + 48 * q^75 + 208 * q^77 - 8 * q^78 - 48 * q^80 - 64 * q^81 - 192 * q^82 + 160 * q^84 - 152 * q^85 + 60 * q^87 - 16 * q^88 + 144 * q^89 - 232 * q^91 + 48 * q^92 - 170 * q^93 + 136 * q^95 - 48 * q^96 + 128 * q^98 + 160 * q^99

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