LMFDB - Embedded newform 210.3.w.a.17.2

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			17.2
Character	$\chi$	$=$	210.17
Dual form			210.3.w.a.173.2

$q$-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 $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

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

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	0.242996	−	0.970027i	$-0.421870\pi$
$11$	−5.23131	−	3.02030i	−0.475574	−	0.274573i	−0.718570	+	0.695455i	$0.755203\pi$
$12$	−3.45026	−	4.90874i	−0.287522	−	0.409061i
$13$	−7.33446	−	7.33446i	−0.564189	−	0.564189i	0.366305	−	0.930495i	$-0.380623\pi$
$13$	−7.33446	−	7.33446i	−0.564189	−	0.564189i	−0.930495	+	0.366305i	$0.880623\pi$
$14$	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	0.474008	−	0.880520i	$-0.342807\pi$
$17$	22.5211	−	6.03451i	1.32477	−	0.354971i	0.850763	+	0.525549i	$0.176140\pi$
$18$	−5.42036	−	11.5161i	−0.301131	−	0.639781i
$19$	17.0920	+	29.6042i	0.899578	+	1.55811i	0.828034	+	0.560678i	$0.189459\pi$
$19$	17.0920	+	29.6042i	0.899578	+	1.55811i	0.0715438	+	0.997437i	$0.477207\pi$
$20$	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	0.619826	+	0.784739i	$0.287203\pi$
$23$	−7.11456	+	26.5519i	−0.309329	+	1.15443i	−0.929155	+	0.369691i	$0.879464\pi$
$24$	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	0.972138	−	0.234407i	$-0.0753150\pi$
$31$	38.9114	+	22.4655i	1.25520	+	0.724693i	0.283066	+	0.959100i	$0.408648\pi$
$32$	−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	0.725183	+	0.688556i	$0.241755\pi$
$37$	−9.14352	+	34.1241i	−0.247122	+	0.922272i	−0.972305	+	0.233716i	$0.924911\pi$
$38$	−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	−0.477372	−	0.878701i	$-0.658411\pi$
$43$	17.2571	−	17.2571i	0.401329	−	0.401329i	0.878701	+	0.477372i	$0.158411\pi$
$44$	−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	−0.999998	−	0.00203792i	$-0.999351\pi$
$47$	−6.24890	+	23.3212i	−0.132955	+	0.496196i	0.867043	+	0.498234i	$0.166018\pi$
$48$	−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	−0.898907	−	0.438139i	$-0.855638\pi$
$53$	−77.2906	+	20.7100i	−1.45831	+	0.390754i	−0.559407	+	0.828893i	$0.688971\pi$
$54$	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	−0.972481	−	0.232982i	$-0.925152\pi$
$59$	−97.9689	−	56.5624i	−1.66049	−	0.958684i	−0.688009	−	0.725702i	$-0.741515\pi$
$60$	−13.6156	+	26.7323i	−0.226926	+	0.445538i
$61$	16.8856	−	9.74888i	0.276812	−	0.159818i	−0.355167	−	0.934803i	$-0.615576\pi$
$61$	16.8856	−	9.74888i	0.276812	−	0.159818i	0.631979	+	0.774985i	$0.282243\pi$
$62$	−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	−0.176330	−	0.984331i	$-0.556423\pi$
$67$	10.9297	−	2.92860i	0.163130	−	0.0437104i	0.339459	+	0.940621i	$0.389756\pi$
$68$	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	$0.192282\pi$
$71$			80.6556i			1.13599i	−0.823030	+	0.567997i	$0.807718\pi$
$72$	2.12771	−	25.3668i	0.0295516	−	0.352316i
$73$	−1.93873	+	0.519481i	−0.0265579	+	0.00711618i	−0.272074	−	0.962276i	$-0.587709\pi$
$73$	−1.93873	+	0.519481i	−0.0265579	+	0.00711618i	0.245516	+	0.969393i	$0.421043\pi$
$74$	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	−0.885665	−	0.464325i	$-0.846297\pi$
$79$	−73.1841	+	42.2528i	−0.926381	+	0.534846i	−0.0407156	+	0.999171i	$0.512964\pi$
$80$	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	−0.734049	−	0.679096i	$-0.762372\pi$
$83$	−4.56113	+	4.56113i	−0.0549533	+	0.0549533i	0.679096	+	0.734049i	$0.262372\pi$
$84$	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	−0.616269	−	0.787536i	$-0.711357\pi$
$89$	−21.5716	+	12.4544i	−0.242377	+	0.139937i	0.373892	+	0.927472i	$0.378023\pi$
$90$	−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	−0.480597	−	0.876942i	$-0.659580\pi$
$97$	38.4454	−	38.4454i	0.396345	−	0.396345i	0.876942	+	0.480597i	$0.159580\pi$
$98$	−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	−0.918235	−	0.396035i	$-0.870386\pi$
$101$	−11.7303	+	20.3175i	−0.116142	+	0.201163i	0.802094	+	0.597198i	$0.203719\pi$
$102$	89.7264	+	41.6445i	0.879670	+	0.408279i
$103$	−48.6683	+	181.632i	−0.472507	+	1.76342i	0.158207	+	0.987406i	$0.449429\pi$
$103$	−48.6683	+	181.632i	−0.472507	+	1.76342i	−0.630714	+	0.776015i	$0.717238\pi$
$104$			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	0.613742	−	0.789506i	$-0.289663\pi$
$107$	80.3041	+	21.5174i	0.750506	+	0.201097i	0.136763	+	0.990604i	$0.456330\pi$
$108$	13.6956	−	52.2344i	0.126811	−	0.483652i
$109$	28.9994	+	16.7428i	0.266049	+	0.153604i	0.627091	−	0.778946i	$-0.284245\pi$
$109$	28.9994	+	16.7428i	0.266049	+	0.153604i	−0.361042	+	0.932550i	$0.617579\pi$
$110$	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	0.760708	−	0.649095i	$-0.224852\pi$
$113$	12.6123	+	12.6123i	0.111613	+	0.111613i	−0.649095	+	0.760708i	$0.724852\pi$
$114$	−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	0.983397	+	0.181467i	$0.0580847\pi$
$127$	147.938	+	147.938i	1.16486	+	1.16486i	0.181467	+	0.983397i	$0.441915\pi$
$128$	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	0.996436	+	0.0843465i	$0.0268803\pi$
$131$	74.8356	+	129.619i	0.571264	+	0.989459i	−0.425172	+	0.905113i	$0.639786\pi$
$132$	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	0.985681	−	0.168619i	$-0.0539306\pi$
$137$	6.54134	+	24.4126i	0.0477470	+	0.178194i	−0.937934	+	0.346813i	$0.887264\pi$
$138$	−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	0.924418	−	0.381381i	$-0.124551\pi$
$149$	19.6566	+	34.0462i	0.131924	+	0.228498i	−0.792494	+	0.609879i	$0.791218\pi$
$150$	−102.000	+	29.0846i	−0.680003	+	0.193897i
$151$	−19.0601	+	33.0130i	−0.126226	+	0.218629i	−0.922211	−	0.386686i	$-0.873620\pi$
$151$	−19.0601	+	33.0130i	−0.126226	+	0.218629i	0.795986	+	0.605315i	$0.206953\pi$
$152$	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	0.997578	−	0.0695618i	$-0.0221601\pi$
$157$	15.5225	+	57.9306i	0.0988692	+	0.368985i	−0.898708	+	0.438547i	$0.855493\pi$
$158$	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	0.276100	−	0.961129i	$-0.410958\pi$
$163$	5.64718	+	1.51316i	0.0346453	+	0.00928317i	−0.241455	+	0.970412i	$0.577625\pi$
$164$	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	0.688490	−	0.725246i	$-0.258274\pi$
$167$	−6.13829	−	6.13829i	−0.0367562	−	0.0367562i	−0.725246	+	0.688490i	$0.758274\pi$
$168$	−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	0.772785	−	0.634668i	$-0.218863\pi$
$173$	194.574	+	52.1359i	1.12470	+	0.301363i	0.351918	+	0.936031i	$0.385530\pi$
$174$	−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	−0.911092	−	0.412203i	$-0.864759\pi$
$179$	−17.6436	+	30.5596i	−0.0985676	+	0.170724i	0.812524	+	0.582927i	$0.198093\pi$
$180$	70.8129	−	55.5475i	0.393405	−	0.308597i
$181$		−	194.579i		−	1.07502i	−0.843258	−	0.537510i	$-0.819365\pi$
$181$		−	194.579i		−	1.07502i	0.843258	−	0.537510i	$-0.180635\pi$
$182$	−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	−0.768687	−	0.639625i	$-0.779090\pi$
$191$	−114.428	+	66.0651i	−0.599100	+	0.345890i	0.169588	+	0.985515i	$0.445756\pi$
$192$	10.1038	−	21.7695i	0.0526242	−	0.113383i
$193$	54.3985	+	203.018i	0.281858	+	1.05191i	0.951105	+	0.308867i	$0.0999498\pi$
$193$	54.3985	+	203.018i	0.281858	+	1.05191i	−0.669248	+	0.743039i	$0.733383\pi$
$194$	−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	−0.905054	−	0.425297i	$-0.860170\pi$
$197$	−94.5121	+	94.5121i	−0.479757	+	0.479757i	0.425297	+	0.905054i	$0.360170\pi$
$198$	−6.42633	+	76.6152i	−0.0324562	+	0.386945i
$199$	182.775	−	316.575i	0.918465	−	1.59083i	0.116717	−	0.993165i	$-0.462763\pi$
$199$	182.775	−	316.575i	0.918465	−	1.59083i	0.801748	−	0.597663i	$-0.203904\pi$
$200$	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	0.293702	−	0.955897i	$-0.405113\pi$
$223$	−147.669	−	147.669i	−0.662195	−	0.662195i	−0.955897	+	0.293702i	$0.905113\pi$
$224$	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	−0.694522	−	0.719472i	$-0.744384\pi$
$227$	−212.531	+	56.9475i	−0.936259	+	0.250870i	−0.241738	+	0.970342i	$0.577717\pi$
$228$	86.3473	−	186.042i	0.378716	−	0.815975i
$229$	149.624	+	259.157i	0.653380	+	1.13169i	0.982297	+	0.187329i	$0.0599831\pi$
$229$	149.624	+	259.157i	0.653380	+	1.13169i	−0.328917	+	0.944359i	$0.606684\pi$
$230$	−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	−0.999999	−	0.00140324i	$-0.999553\pi$
$233$	−31.0526	+	115.890i	−0.133273	+	0.497381i	0.866726	+	0.498784i	$0.166220\pi$
$234$	−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	0.0467624	−	0.998906i	$-0.485110\pi$
$241$	−191.579	−	110.608i	−0.794934	−	0.458956i	−0.841697	+	0.539950i	$0.818443\pi$
$242$	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	−0.947779	−	0.318927i	$-0.896677\pi$
$257$	8.34872	−	31.1578i	0.0324853	−	0.121237i	0.980264	+	0.197691i	$0.0633441\pi$
$258$	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	−0.552301	−	0.833645i	$-0.686250\pi$
$263$	−161.425	+	43.2538i	−0.613785	+	0.164463i	−0.0614840	+	0.998108i	$0.519583\pi$
$264$	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	0.942236	−	0.334949i	$-0.108719\pi$
$269$	302.162	+	174.453i	1.12328	+	0.648526i	0.181043	+	0.983475i	$0.442053\pi$
$270$	168.235	−	90.2607i	0.623093	−	0.334299i
$271$	17.0749	−	9.85817i	0.0630068	−	0.0363770i	−0.468166	−	0.883641i	$-0.655085\pi$
$271$	17.0749	−	9.85817i	0.0630068	−	0.0363770i	0.531172	+	0.847264i	$0.321752\pi$
$272$	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	0.154008	−	0.988070i	$-0.450782\pi$
$277$	216.453	−	57.9983i	0.781417	−	0.209380i	0.627409	+	0.778690i	$0.284115\pi$
$278$	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	$0.132342\pi$
$281$			226.986i			0.807780i	−0.914808	+	0.403890i	$0.867658\pi$
$282$	−83.8035	+	58.9040i	−0.297176	+	0.208879i
$283$	−92.5997	+	24.8120i	−0.327208	+	0.0876750i	−0.418683	−	0.908132i	$-0.637508\pi$
$283$	−92.5997	+	24.8120i	−0.327208	+	0.0876750i	0.0914758	+	0.995807i	$0.470842\pi$
$284$	−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	−0.953288	−	0.302064i	$-0.902325\pi$
$293$	−190.809	+	190.809i	−0.651224	+	0.651224i	0.302064	+	0.953288i	$0.402325\pi$
$294$	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	−0.760543	−	0.649288i	$-0.775067\pi$
$307$	−34.1553	+	34.1553i	−0.111255	+	0.111255i	0.649288	+	0.760543i	$0.275067\pi$
$308$	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	0.0185247	−	0.999828i	$-0.494103\pi$
$311$	272.168	−	471.409i	0.875139	−	1.51579i	0.856614	−	0.515957i	$-0.172564\pi$
$312$	37.0531	−	79.8339i	0.118760	−	0.255878i
$313$	118.989	−	444.072i	0.380155	−	1.41876i	−0.465509	−	0.885043i	$-0.654129\pi$
$313$	118.989	−	444.072i	0.380155	−	1.41876i	0.845664	−	0.533716i	$-0.179205\pi$
$314$		−	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	0.287048	−	0.957916i	$-0.407326\pi$
$317$	17.9678	+	4.81445i	0.0566806	+	0.0151875i	−0.230367	+	0.973104i	$0.573993\pi$
$318$	−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	0.714929	−	0.699197i	$-0.246459\pi$
$331$	−82.1070	−	142.213i	−0.248057	−	0.429648i	−0.962987	+	0.269549i	$0.913125\pi$
$332$	−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	0.924368	−	0.381503i	$-0.124593\pi$
$337$	182.945	+	182.945i	0.542865	+	0.542865i	−0.381503	+	0.924368i	$0.624593\pi$
$338$	−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	0.931563	−	0.363580i	$-0.118446\pi$
$347$	−19.7736	−	73.7960i	−0.0569844	−	0.212669i	−0.988547	+	0.150912i	$0.951779\pi$
$348$	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	0.905645	+	0.424036i	$0.139387\pi$
$353$	117.673	+	439.162i	0.333351	+	1.24408i	−0.572294	+	0.820048i	$0.693946\pi$
$354$	−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	0.694050	−	0.719927i	$-0.255825\pi$
$359$	−99.2457	−	171.899i	−0.276450	−	0.478826i	−0.970500	+	0.241101i	$0.922491\pi$
$360$	−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	0.907233	+	0.420628i	$0.138190\pi$
$367$	121.793	+	454.536i	0.331860	+	1.23852i	−0.575373	+	0.817891i	$0.695143\pi$
$368$	−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	0.591947	−	0.805977i	$-0.298360\pi$
$373$	261.696	+	70.1213i	0.701599	+	0.187993i	0.109652	+	0.993970i	$0.465026\pi$
$374$	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	$0.217484\pi$
$379$			478.536i			1.26263i	−0.775528	+	0.631314i	$0.782516\pi$
$380$	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	−0.323012	−	0.946395i	$-0.604695\pi$
$383$	−412.087	−	110.418i	−1.07595	−	0.288299i	−0.752934	+	0.658096i	$0.771362\pi$
$384$	−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	−0.676503	−	0.736440i	$-0.736505\pi$
$389$	116.515	−	201.810i	0.299524	−	0.518791i	0.976027	+	0.217649i	$0.0698387\pi$
$390$	−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	0.324790	−	0.945786i	$-0.394706\pi$
$397$	52.8700	+	14.1665i	0.133174	+	0.0356838i	−0.191616	+	0.981470i	$0.561373\pi$
$398$	−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	−0.904731	−	0.425984i	$-0.859928\pi$
$401$	−396.262	+	228.782i	−0.988184	+	0.570528i	−0.0834527	+	0.996512i	$0.526595\pi$
$402$	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	−0.994545	−	0.104312i	$-0.966736\pi$
$409$	−166.436	+	288.276i	−0.406935	+	0.704832i	0.587609	+	0.809145i	$0.300069\pi$
$410$	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	$-0.851363\pi$
$419$		−	377.243i		−	0.900341i	0.892943	−	0.450171i	$-0.148637\pi$
$420$	−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	0.325469	−	0.945553i	$-0.394478\pi$
$431$	−142.518	−	82.2828i	−0.330668	−	0.190911i	−0.656138	+	0.754641i	$0.727811\pi$
$432$	75.9558	−	76.7770i	0.175824	−	0.177725i
$433$	−346.623	−	346.623i	−0.800515	−	0.800515i	0.182661	−	0.983176i	$-0.441529\pi$
$433$	−346.623	−	346.623i	−0.800515	−	0.800515i	−0.983176	+	0.182661i	$0.941529\pi$
$434$	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	−0.990519	−	0.137376i	$-0.956133\pi$
$439$	−269.647	−	467.043i	−0.614230	−	1.06388i	0.376289	−	0.926502i	$-0.377200\pi$
$440$	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	−0.782593	−	0.622533i	$-0.786103\pi$
$443$	91.4437	−	341.272i	0.206419	−	0.770367i	0.989012	−	0.147833i	$-0.0472299\pi$
$444$	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	−0.974253	−	0.225458i	$-0.927612\pi$
$457$	−8.13289	+	30.3524i	−0.0177963	+	0.0664166i	0.956457	+	0.291874i	$0.0942789\pi$
$458$	−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	−0.889644	−	0.456655i	$-0.849047\pi$
$463$	−200.474	+	200.474i	−0.432989	+	0.432989i	0.456655	+	0.889644i	$0.349047\pi$
$464$	−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	−0.987567	−	0.157202i	$-0.949753\pi$
$467$	−25.0817	+	93.6060i	−0.0537081	+	0.200441i	0.933858	+	0.357643i	$0.116419\pi$
$468$	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	0.400104	−	0.916470i	$-0.368974\pi$
$479$	−92.7005	−	53.5207i	−0.193529	−	0.111734i	−0.593634	+	0.804735i	$0.702307\pi$
$480$	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	0.242023	−	0.970271i	$-0.422189\pi$
$487$	456.200	−	122.238i	0.936756	−	0.251003i	0.694733	+	0.719268i	$0.255522\pi$
$488$	−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	$-0.925403\pi$
$491$		−	228.035i		−	0.464431i	0.972664	−	0.232215i	$-0.0745974\pi$
$492$	−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	0.420059	−	0.907497i	$-0.362009\pi$
$499$	706.586	−	407.948i	1.41600	−	0.817530i	0.995945	+	0.0899668i	$0.0286761\pi$
$500$	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	−0.0192915	−	0.999814i	$-0.506141\pi$
$503$	493.203	−	493.203i	0.980522	−	0.980522i	0.999814	+	0.0192915i	$0.00614106\pi$
$504$	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	−0.994939	−	0.100479i	$-0.967962\pi$
$509$	−715.344	+	413.004i	−1.40539	+	0.811403i	−0.410452	+	0.911882i	$0.634629\pi$
$510$	−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	−0.925405	−	0.378980i	$-0.876275\pi$
$521$	−70.0727	+	121.369i	−0.134497	+	0.232955i	0.790908	+	0.611934i	$0.209608\pi$
$522$	37.2199	+	79.0770i	0.0713024	+	0.151489i
$523$	−44.3611	+	165.558i	−0.0848204	+	0.316554i	−0.995280	−	0.0970437i	$-0.969061\pi$
$523$	−44.3611	+	165.558i	−0.0848204	+	0.316554i	0.910460	+	0.413598i	$0.135728\pi$
$524$			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	0.999998	+	0.00192801i	$0.000613704\pi$
$541$	271.403	+	470.083i	0.501669	+	0.868916i	−0.498329	+	0.866988i	$0.666053\pi$
$542$	−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	−0.806017	−	0.591892i	$-0.798381\pi$
$547$	−764.656	−	764.656i	−1.39791	−	1.39791i	−0.591892	−	0.806017i	$-0.701619\pi$
$548$	−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	0.965254	−	0.261315i	$-0.0841560\pi$
$557$	−0.745171	−	2.78102i	−0.00133783	−	0.00499285i	−0.966592	+	0.256322i	$0.917489\pi$
$558$	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	0.998131	−	0.0611074i	$-0.0194632\pi$
$563$	58.0850	+	216.776i	0.103171	+	0.385038i	−0.894961	+	0.446145i	$0.852797\pi$
$564$	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	−0.970358	−	0.241673i	$-0.922304\pi$
$569$	−395.156	−	684.429i	−0.694474	−	1.20286i	0.275884	−	0.961191i	$-0.411029\pi$
$570$	689.625	−	224.191i	1.20987	−	0.393318i
$571$	−124.910	+	216.351i	−0.218757	+	0.378899i	−0.954428	−	0.298440i	$-0.903534\pi$
$571$	−124.910	+	216.351i	−0.218757	+	0.378899i	0.735671	+	0.677339i	$0.236867\pi$
$572$	−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	0.982481	−	0.186364i	$-0.0596703\pi$
$577$	22.1831	+	82.7885i	0.0384456	+	0.143481i	−0.944035	+	0.329845i	$0.893004\pi$
$578$	−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	0.518043	−	0.855355i	$-0.326661\pi$
$587$	−198.002	−	198.002i	−0.337312	−	0.337312i	−0.855355	+	0.518043i	$0.826661\pi$
$588$	−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	−0.665148	−	0.746712i	$-0.731631\pi$
$593$	−957.421	−	256.540i	−1.61454	−	0.432614i	−0.949391	+	0.314097i	$0.898298\pi$
$594$	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	−0.910720	−	0.413025i	$-0.864472\pi$
$599$	−58.5042	+	101.332i	−0.0976698	+	0.169169i	0.813050	+	0.582194i	$0.197806\pi$
$600$	−205.755	−	51.6244i	−0.342924	−	0.0860406i
$601$			258.350i			0.429867i	0.976629	+	0.214933i	$0.0689534\pi$
$601$			258.350i			0.429867i	−0.976629	+	0.214933i	$0.931047\pi$
$602$	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	−0.597763	−	0.801673i	$-0.703944\pi$
$607$	−920.381	−	246.615i	−1.51628	−	0.406285i	−0.918514	+	0.395387i	$0.870610\pi$
$608$	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	0.997566	−	0.0697216i	$-0.0222111\pi$
$613$	60.5569	+	226.001i	0.0987878	+	0.368681i	−0.898779	+	0.438403i	$0.855544\pi$
$614$	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	0.189945	−	0.981795i	$-0.439169\pi$
$617$	722.963	−	722.963i	1.17174	−	1.17174i	0.981795	−	0.189945i	$-0.0608308\pi$
$618$	−652.686	+	458.761i	−1.05613	+	0.742332i
$619$	164.472	−	284.874i	0.265706	−	0.460217i	−0.702042	−	0.712135i	$-0.747728\pi$
$619$	164.472	−	284.874i	0.265706	−	0.460217i	0.967748	+	0.251919i	$0.0810616\pi$
$620$	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	0.936954	−	0.349453i	$-0.113633\pi$
$641$	706.892	+	408.124i	1.10280	+	0.636699i	0.165841	+	0.986152i	$0.446966\pi$
$642$	202.829	+	288.568i	0.315934	+	0.449483i
$643$	18.6427	+	18.6427i	0.0289933	+	0.0289933i	0.721455	−	0.692462i	$-0.243474\pi$
$643$	18.6427	+	18.6427i	0.0289933	+	0.0289933i	−0.692462	+	0.721455i	$0.743474\pi$
$644$	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	−0.895036	−	0.445995i	$-0.852850\pi$
$647$	−936.314	+	250.884i	−1.44716	+	0.387766i	−0.552126	+	0.833761i	$0.686183\pi$
$648$	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	−0.952921	−	0.303220i	$-0.901938\pi$
$653$	15.6346	−	58.3491i	0.0239427	−	0.0893554i	0.976863	+	0.213864i	$0.0686050\pi$
$654$	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	0.781654	−	0.623712i	$-0.214376\pi$
$661$	417.970	+	241.315i	0.632330	+	0.365076i	−0.149324	+	0.988788i	$0.547710\pi$
$662$	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	−0.110479	−	0.993879i	$-0.535238\pi$
$673$	594.528	−	594.528i	0.883400	−	0.883400i	0.993879	+	0.110479i	$0.0352384\pi$
$674$	−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	−0.941372	−	0.337369i	$-0.890463\pi$
$677$	28.8163	−	107.544i	0.0425647	−	0.158854i	0.983937	+	0.178516i	$0.0571295\pi$
$678$	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	0.0304984	−	0.999535i	$-0.490291\pi$
$683$	380.211	−	101.877i	0.556678	−	0.149161i	0.526180	+	0.850373i	$0.323624\pi$
$684$	−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	0.0759924	−	0.997108i	$-0.475788\pi$
$691$	675.459	−	389.977i	0.977510	−	0.564366i	0.901517	+	0.432743i	$0.142454\pi$
$692$	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	$0.324092\pi$
$701$			1193.31i			1.70229i	−0.524928	+	0.851147i	$0.675908\pi$
$702$	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	−0.939193	−	0.343389i	$-0.888425\pi$
$709$	−787.987	+	454.944i	−1.11141	+	0.641671i	−0.172213	+	0.985060i	$0.555092\pi$
$710$	−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	−0.679905	−	0.733301i	$-0.737979\pi$
$719$	−276.671	+	159.736i	−0.384800	+	0.222164i	0.295105	+	0.955465i	$0.404645\pi$
$720$	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	0.412367	−	0.911018i	$-0.364702\pi$
$727$	962.101	−	962.101i	1.32338	−	1.32338i	0.911018	−	0.412367i	$-0.135298\pi$
$728$	−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	0.862128	+	0.506690i	$0.169131\pi$
$733$	−101.038	+	377.079i	−0.137842	+	0.514433i	−0.999970	+	0.00774251i	$0.997535\pi$
$734$		−	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	−0.0233056	−	0.999728i	$-0.507419\pi$
$739$	−665.653	−	384.315i	−0.900749	−	0.520047i	−0.877443	+	0.479681i	$0.840752\pi$
$740$	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	0.373907	−	0.927466i	$-0.378018\pi$
$743$	−411.294	−	411.294i	−0.553559	−	0.553559i	−0.927466	+	0.373907i	$0.878018\pi$
$744$	−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	0.943823	+	0.330452i	$0.107201\pi$
$751$	569.327	+	986.103i	0.758091	+	1.31305i	−0.185731	+	0.982601i	$0.559465\pi$
$752$	−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	0.510530	−	0.859860i	$-0.329449\pi$
$757$	−264.443	−	264.443i	−0.349331	−	0.349331i	−0.859860	+	0.510530i	$0.829449\pi$
$758$	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	0.814052	+	0.580792i	$0.197257\pi$
$761$	692.515	+	1199.47i	0.910006	+	1.57618i	0.0959541	+	0.995386i	$0.469410\pi$
$762$	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	−0.599891	−	0.800082i	$-0.704789\pi$
$773$	−371.358	−	1385.93i	−0.480411	−	1.79292i	0.119480	−	0.992837i	$-0.461877\pi$
$774$	−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	−0.998405	−	0.0564509i	$-0.982022\pi$
$787$	−127.483	−	475.774i	−0.161986	−	0.604542i	0.836419	−	0.548091i	$-0.184645\pi$
$788$	−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	0.812829	−	0.582503i	$-0.197926\pi$
$797$	183.570	+	183.570i	0.230326	+	0.230326i	−0.582503	+	0.812829i	$0.697926\pi$
$798$	−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	−0.288030	−	0.957621i	$-0.593000\pi$
$809$	554.415	−	960.275i	0.685309	−	1.18699i	0.973340	−	0.229369i	$-0.0736663\pi$
$810$	−571.797	+	33.1392i	−0.705922	+	0.0409126i
$811$			715.199i			0.881873i	0.897538	+	0.440937i	$0.145354\pi$
$811$			715.199i			0.881873i	−0.897538	+	0.440937i	$0.854646\pi$
$812$	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	−0.547683	+	0.836686i	$0.684490\pi$
$821$	−1269.36	+	732.866i	−1.54612	+	0.892650i	−0.998433	+	0.0559644i	$0.982177\pi$
$822$	−45.1421	+	97.2623i	−0.0549174	+	0.118324i
$823$	251.704	+	939.371i	0.305837	+	1.14140i	0.932223	+	0.361885i	$0.117867\pi$
$823$	251.704	+	939.371i	0.305837	+	1.14140i	−0.626386	+	0.779513i	$0.715467\pi$
$824$	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	−0.974061	−	0.226285i	$-0.927342\pi$
$827$	−618.411	+	618.411i	−0.747776	+	0.747776i	0.226285	+	0.974061i	$0.427342\pi$
$828$	−493.062	−	41.3571i	−0.595486	−	0.0499481i
$829$	678.323	−	1174.89i	0.818242	−	1.41724i	−0.0887341	−	0.996055i	$-0.528282\pi$
$829$	678.323	−	1174.89i	0.818242	−	1.41724i	0.906976	−	0.421182i	$-0.138385\pi$
$830$	−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	$0.351533\pi$
$839$			1498.76i			1.78637i	−0.449693	+	0.893183i	$0.648467\pi$
$840$	−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	0.709675	−	0.704529i	$-0.248842\pi$
$853$	4.38891	+	4.38891i	0.00514527	+	0.00514527i	−0.704529	+	0.709675i	$0.748842\pi$
$854$	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	0.201457	−	0.979497i	$-0.435432\pi$
$857$	741.882	−	198.787i	0.865673	−	0.231956i	0.664216	+	0.747541i	$0.268766\pi$
$858$	−111.911	+	241.122i	−0.130433	+	0.281028i
$859$	−506.657	−	877.555i	−0.589821	−	1.02160i	−0.994255	−	0.107033i	$-0.965865\pi$
$859$	−506.657	−	877.555i	−0.589821	−	1.02160i	0.404434	−	0.914567i	$-0.367469\pi$
$860$	−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	0.700902	+	0.713257i	$0.252781\pi$
$863$	−226.732	+	846.176i	−0.262726	+	0.980505i	−0.963628	+	0.267248i	$0.913886\pi$
$864$	−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	−0.469502	−	0.882931i	$-0.655567\pi$
$877$	332.001	−	1239.04i	0.378564	−	1.41282i	0.848067	−	0.529890i	$-0.177767\pi$
$878$	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	−0.397369	−	0.917659i	$-0.630077\pi$
$883$	459.415	−	459.415i	0.520289	−	0.520289i	0.917659	+	0.397369i	$0.130077\pi$
$884$	−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	−0.704216	−	0.709986i	$-0.748701\pi$
$887$	231.193	−	862.823i	0.260646	−	0.972743i	0.964862	−	0.262758i	$-0.0846320\pi$
$888$	−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	−0.577864	−	0.816133i	$-0.696114\pi$
$907$	−607.910	+	162.889i	−0.670242	+	0.179591i	−0.0923782	+	0.995724i	$0.529447\pi$
$908$	−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	$0.166723\pi$
$911$			911.280i			1.00031i	−0.865937	+	0.500154i	$0.833277\pi$
$912$	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	−0.0767126	−	0.997053i	$-0.524442\pi$
$919$	687.784	−	397.092i	0.748404	−	0.432092i	0.825117	+	0.564962i	$0.191109\pi$
$920$	−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	−0.240993	−	0.970527i	$-0.577473\pi$
$929$	445.001	−	256.922i	0.479011	−	0.276557i	0.720004	+	0.693970i	$0.244140\pi$
$930$	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	−0.725553	−	0.688166i	$-0.758416\pi$
$937$	−35.0323	+	35.0323i	−0.0373877	+	0.0373877i	0.688166	+	0.725553i	$0.258416\pi$
$938$	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	−0.548300	−	0.836282i	$-0.684725\pi$
$941$	423.536	−	733.586i	0.450091	−	0.779581i	0.998391	+	0.0567009i	$0.0180581\pi$
$942$	−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	0.927291	−	0.374341i	$-0.122131\pi$
$947$	1461.39	+	391.578i	1.54318	+	0.413493i	0.615887	+	0.787835i	$0.288798\pi$
$948$	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	0.659295	−	0.751884i	$-0.270855\pi$
$953$	−88.2376	−	88.2376i	−0.0925893	−	0.0925893i	−0.751884	+	0.659295i	$0.770855\pi$
$954$	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	0.701370	−	0.712798i	$-0.252572\pi$
$967$	−11.0507	−	11.0507i	−0.0114278	−	0.0114278i	−0.712798	+	0.701370i	$0.752572\pi$
$968$	−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	0.998677	+	0.0514307i	$0.0163781\pi$
$971$	528.106	+	914.707i	0.543879	+	0.942025i	−0.454798	+	0.890595i	$0.650289\pi$
$972$	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	0.764484	+	0.644642i	$0.222994\pi$
$977$	414.973	+	1548.70i	0.424743	+	1.58516i	−0.339742	+	0.940519i	$0.610340\pi$
$978$	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	−0.988912	−	0.148502i	$-0.952555\pi$
$983$	−203.226	−	758.449i	−0.206740	−	0.771565i	0.782172	−	0.623063i	$-0.214112\pi$
$984$	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	−0.477717	−	0.878514i	$-0.658535\pi$
$991$	517.260	−	895.920i	0.521957	−	0.904056i	0.999674	−	0.0255424i	$-0.00813127\pi$
$992$	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	0.986637	−	0.162932i	$-0.0520953\pi$
$997$	50.5660	+	188.715i	0.0507181	+	0.189283i	−0.935919	+	0.352215i	$0.885429\pi$
$998$	−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.17.2	✓	64
3.2	odd	2		210.3.w.b.17.5	yes	64
5.3	odd	4		210.3.w.b.143.11	yes	64
7.5	odd	6	inner	210.3.w.a.47.3	yes	64
15.8	even	4	inner	210.3.w.a.143.3	yes	64
21.5	even	6		210.3.w.b.47.11	yes	64
35.33	even	12		210.3.w.b.173.5	yes	64
105.68	odd	12	inner	210.3.w.a.173.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.w.a.17.2	✓	64	1.1	even	1	trivial
210.3.w.a.47.3	yes	64	7.5	odd	6	inner
210.3.w.a.143.3	yes	64	15.8	even	4	inner
210.3.w.a.173.2	yes	64	105.68	odd	12	inner
210.3.w.b.17.5	yes	64	3.2	odd	2
210.3.w.b.47.11	yes	64	21.5	even	6
210.3.w.b.143.11	yes	64	5.3	odd	4
210.3.w.b.173.5	yes	64	35.33	even	12

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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