LMFDB - Embedded newform 105.3.w.a.17.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [105,3,Mod(17,105)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("105.17"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(105, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.w (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.25
Character	$\chi$	$=$	105.17
Dual form			105.3.w.a.68.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.02468 + 0.810462i) q^{2} +(0.887077 + 2.86585i) q^{3} +(5.02776 + 2.90278i) q^{4} +(2.83293 - 4.12001i) q^{5} +(0.360468 + 9.38723i) q^{6} +(-5.96475 - 3.66357i) q^{7} +(3.99791 + 3.99791i) q^{8} +(-7.42619 + 5.08446i) q^{9} +(11.9078 - 10.1658i) q^{10} +(-10.3392 - 5.96936i) q^{11} +(-3.85892 + 16.9838i) q^{12} +(7.11430 + 7.11430i) q^{13} +(-15.0723 - 15.9153i) q^{14} +(14.3204 + 4.46398i) q^{15} +(-2.75886 - 4.77849i) q^{16} +(-3.02956 + 0.811768i) q^{17} +(-26.5826 + 9.36025i) q^{18} +(17.2142 + 29.8159i) q^{19} +(26.2028 - 12.4911i) q^{20} +(5.20803 - 20.3440i) q^{21} +(-26.4350 - 26.4350i) q^{22} +(2.51441 - 9.38391i) q^{23} +(-7.91095 + 15.0039i) q^{24} +(-8.94900 - 23.3434i) q^{25} +(15.7526 + 27.2844i) q^{26} +(-21.1589 - 16.7720i) q^{27} +(-19.3548 - 35.7339i) q^{28} +26.5784 q^{29} +(39.6967 + 25.1082i) q^{30} +(0.677558 + 0.391188i) q^{31} +(-10.3252 - 38.5343i) q^{32} +(7.93558 - 34.9260i) q^{33} -9.82137 q^{34} +(-31.9917 + 14.1962i) q^{35} +(-52.0962 + 4.00687i) q^{36} +(-7.62362 + 28.4517i) q^{37} +(27.9030 + 104.135i) q^{38} +(-14.0776 + 26.6994i) q^{39} +(27.7972 - 5.14563i) q^{40} +43.0909 q^{41} +(32.2406 - 57.3131i) q^{42} +(-40.7104 + 40.7104i) q^{43} +(-34.6554 - 60.0250i) q^{44} +(-0.0898378 + 44.9999i) q^{45} +(15.2106 - 26.3455i) q^{46} +(7.76382 - 28.9750i) q^{47} +(11.2471 - 12.1454i) q^{48} +(22.1566 + 43.7045i) q^{49} +(-8.14895 - 77.8593i) q^{50} +(-5.01386 - 7.96216i) q^{51} +(15.1177 + 56.4202i) q^{52} +(17.1662 - 4.59967i) q^{53} +(-50.4059 - 67.8785i) q^{54} +(-53.8841 + 25.6870i) q^{55} +(-9.19994 - 38.4931i) q^{56} +(-70.1776 + 75.7825i) q^{57} +(80.3912 + 21.5408i) q^{58} +(-62.8463 - 36.2843i) q^{59} +(59.0414 + 64.0127i) q^{60} +(21.4620 - 12.3911i) q^{61} +(1.73236 + 1.73236i) q^{62} +(62.9226 - 3.12123i) q^{63} -102.852i q^{64} +(49.4653 - 9.15668i) q^{65} +(52.3088 - 99.2085i) q^{66} +(-56.2130 + 15.0622i) q^{67} +(-17.5883 - 4.71277i) q^{68} +(29.1233 - 1.11833i) q^{69} +(-108.270 + 17.0111i) q^{70} +43.6004i q^{71} +(-50.0164 - 9.36201i) q^{72} +(0.332612 - 0.0891230i) q^{73} +(-46.1180 + 79.8788i) q^{74} +(58.9603 - 46.3539i) q^{75} +199.877i q^{76} +(39.8018 + 73.4842i) q^{77} +(-64.2191 + 69.3480i) q^{78} +(66.7293 - 38.5262i) q^{79} +(-27.5031 - 2.17059i) q^{80} +(29.2965 - 75.5163i) q^{81} +(130.336 + 34.9235i) q^{82} +(-76.7710 + 76.7710i) q^{83} +(85.2387 - 87.1668i) q^{84} +(-5.23804 + 14.7815i) q^{85} +(-156.130 + 90.1420i) q^{86} +(23.5771 + 76.1697i) q^{87} +(-17.4703 - 65.2002i) q^{88} +(56.8471 - 32.8207i) q^{89} +(-36.7424 + 136.038i) q^{90} +(-16.3713 - 68.4987i) q^{91} +(39.8813 - 39.8813i) q^{92} +(-0.520041 + 2.28879i) q^{93} +(46.9662 - 81.3479i) q^{94} +(171.609 + 13.5436i) q^{95} +(101.274 - 63.7735i) q^{96} +(53.5343 - 53.5343i) q^{97} +(31.5958 + 150.149i) q^{98} +(107.132 - 8.23984i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) $ 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.02468	+	0.810462i	1.51234	+	0.405231i	0.917212	−	0.398399i	$-0.130434\pi$
$2$	3.02468	+	0.810462i	1.51234	+	0.405231i	0.595130	+	0.803630i	$0.297101\pi$
$3$	0.887077	+	2.86585i	0.295692	+	0.955283i
$3$	0.887077	+	2.86585i	0.295692	+	0.955283i
$4$	5.02776	+	2.90278i	1.25694	+	0.725695i
$5$	2.83293	−	4.12001i	0.566586	−	0.824002i
$5$	2.83293	−	4.12001i	0.566586	−	0.824002i
$6$	0.360468	+	9.38723i	0.0600779	+	1.56454i
$7$	−5.96475	−	3.66357i	−0.852108	−	0.523367i
$7$	−5.96475	−	3.66357i	−0.852108	−	0.523367i
$8$	3.99791	+	3.99791i	0.499738	+	0.499738i
$9$	−7.42619	+	5.08446i	−0.825132	+	0.564940i
$10$	11.9078	−	10.1658i	1.19078	−	1.01658i
$11$	−10.3392	−	5.96936i	−0.939930	−	0.542669i	−0.0499915	−	0.998750i	$-0.515919\pi$
$11$	−10.3392	−	5.96936i	−0.939930	−	0.542669i	−0.889938	+	0.456081i	$0.849253\pi$
$12$	−3.85892	+	16.9838i	−0.321576	+	1.41532i
$13$	7.11430	+	7.11430i	0.547254	+	0.547254i	0.925645	−	0.378392i	$-0.123523\pi$
$13$	7.11430	+	7.11430i	0.547254	+	0.547254i	−0.378392	+	0.925645i	$0.623523\pi$
$14$	−15.0723	−	15.9153i	−1.07659	−	1.13681i
$15$	14.3204	+	4.46398i	0.954691	+	0.297599i
$16$	−2.75886	−	4.77849i	−0.172429	−	0.298656i
$17$	−3.02956	+	0.811768i	−0.178209	+	0.0477511i	−0.346820	−	0.937932i	$-0.612739\pi$
$17$	−3.02956	+	0.811768i	−0.178209	+	0.0477511i	0.168611	+	0.985683i	$0.446072\pi$
$18$	−26.5826	+	9.36025i	−1.47681	+	0.520014i
$19$	17.2142	+	29.8159i	0.906013	+	1.56926i	0.819552	+	0.573005i	$0.194222\pi$
$19$	17.2142	+	29.8159i	0.906013	+	1.56926i	0.0864609	+	0.996255i	$0.472444\pi$
$20$	26.2028	−	12.4911i	1.31014	−	0.624553i
$21$	5.20803	−	20.3440i	0.248001	−	0.968760i
$22$	−26.4350	−	26.4350i	−1.20159	−	1.20159i
$23$	2.51441	−	9.38391i	0.109322	−	0.407996i	−0.889477	−	0.456979i	$-0.848931\pi$
$23$	2.51441	−	9.38391i	0.109322	−	0.407996i	0.998800	+	0.0489831i	$0.0155981\pi$
$24$	−7.91095	+	15.0039i	−0.329623	+	0.625161i
$25$	−8.94900	−	23.3434i	−0.357960	−	0.933737i
$26$	15.7526	+	27.2844i	0.605870	+	1.04940i
$27$	−21.1589	−	16.7720i	−0.783663	−	0.621186i
$28$	−19.3548	−	35.7339i	−0.691244	−	1.27621i
$29$	26.5784			0.916496			0.458248	−	0.888824i	$-0.348477\pi$
$29$	26.5784			0.916496			0.458248	+	0.888824i	$0.348477\pi$
$30$	39.6967	+	25.1082i	1.32322	+	0.836942i
$31$	0.677558	+	0.391188i	0.0218567	+	0.0126190i	0.510889	−	0.859647i	$-0.329316\pi$
$31$	0.677558	+	0.391188i	0.0218567	+	0.0126190i	−0.489032	+	0.872266i	$0.662650\pi$
$32$	−10.3252	−	38.5343i	−0.322664	−	1.20420i
$33$	7.93558	−	34.9260i	0.240472	−	1.05836i
$34$	−9.82137			−0.288864
$35$	−31.9917	+	14.1962i	−0.914048	+	0.405607i
$36$	−52.0962	+	4.00687i	−1.44712	+	0.111302i
$37$	−7.62362	+	28.4517i	−0.206044	+	0.768965i	0.783085	+	0.621914i	$0.213645\pi$
$37$	−7.62362	+	28.4517i	−0.206044	+	0.768965i	−0.989129	+	0.147051i	$0.953022\pi$
$38$	27.9030	+	104.135i	0.734288	+	2.74040i
$39$	−14.0776	+	26.6994i	−0.360963	+	0.684601i
$40$	27.7972	−	5.14563i	0.694931	−	0.128641i
$41$	43.0909			1.05100			0.525499	−	0.850794i	$-0.323879\pi$
$41$	43.0909			1.05100			0.525499	+	0.850794i	$0.323879\pi$
$42$	32.2406	−	57.3131i	0.767634	−	1.36460i
$43$	−40.7104	+	40.7104i	−0.946754	+	0.946754i	−0.998652	−	0.0518979i	$-0.983473\pi$
$43$	−40.7104	+	40.7104i	−0.946754	+	0.946754i	0.0518979	+	0.998652i	$0.483473\pi$
$44$	−34.6554	−	60.0250i	−0.787624	−	1.36420i
$45$	−0.0898378	+	44.9999i	−0.00199640	+	0.999998i
$46$	15.2106	−	26.3455i	0.330665	−	0.572729i
$47$	7.76382	−	28.9750i	0.165188	−	0.616489i	−0.832828	−	0.553531i	$-0.813280\pi$
$47$	7.76382	−	28.9750i	0.165188	−	0.616489i	0.998016	−	0.0629579i	$-0.0200534\pi$
$48$	11.2471	−	12.1454i	0.234315	−	0.253029i
$49$	22.1566	+	43.7045i	0.452175	+	0.891929i
$50$	−8.14895	−	77.8593i	−0.162979	−	1.55719i
$51$	−5.01386	−	7.96216i	−0.0983110	−	0.156121i
$52$	15.1177	+	56.4202i	0.290726	+	1.08500i
$53$	17.1662	−	4.59967i	0.323891	−	0.0867863i	−0.0932100	−	0.995646i	$-0.529713\pi$
$53$	17.1662	−	4.59967i	0.323891	−	0.0867863i	0.417101	+	0.908860i	$0.363046\pi$
$54$	−50.4059	−	67.8785i	−0.933443	−	1.25701i
$55$	−53.8841	+	25.6870i	−0.979712	+	0.467036i
$56$	−9.19994	−	38.4931i	−0.164285	−	0.687377i
$57$	−70.1776	+	75.7825i	−1.23119	+	1.32952i
$58$	80.3912	+	21.5408i	1.38606	+	0.371392i
$59$	−62.8463	−	36.2843i	−1.06519	−	0.614988i	−0.138328	−	0.990387i	$-0.544173\pi$
$59$	−62.8463	−	36.2843i	−1.06519	−	0.614988i	−0.926864	+	0.375398i	$0.877506\pi$
$60$	59.0414	+	64.0127i	0.984023	+	1.06688i
$61$	21.4620	−	12.3911i	0.351836	−	0.203132i	−0.313658	−	0.949536i	$-0.601554\pi$
$61$	21.4620	−	12.3911i	0.351836	−	0.203132i	0.665494	+	0.746404i	$0.268221\pi$
$62$	1.73236	+	1.73236i	0.0279412	+	0.0279412i
$63$	62.9226	−	3.12123i	0.998772	−	0.0495433i
$64$		−	102.852i		−	1.60705i
$65$	49.4653	−	9.15668i	0.761005	−	0.140872i
$66$	52.3088	−	99.2085i	0.792557	−	1.50316i
$67$	−56.2130	+	15.0622i	−0.839000	+	0.224809i	−0.652636	−	0.757672i	$-0.726337\pi$
$67$	−56.2130	+	15.0622i	−0.839000	+	0.224809i	−0.186364	+	0.982481i	$0.559670\pi$
$68$	−17.5883	−	4.71277i	−0.258651	−	0.0693054i
$69$	29.1233	−	1.11833i	0.422077	−	0.0162077i
$70$	−108.270	+	17.0111i	−1.54672	+	0.243015i
$71$			43.6004i			0.614091i	0.951695	+	0.307045i	$0.0993403\pi$
$71$			43.6004i			0.614091i	−0.951695	+	0.307045i	$0.900660\pi$
$72$	−50.0164	−	9.36201i	−0.694672	−	0.130028i
$73$	0.332612	−	0.0891230i	0.00455632	−	0.00122086i	−0.256540	−	0.966534i	$-0.582583\pi$
$73$	0.332612	−	0.0891230i	0.00455632	−	0.00122086i	0.261096	+	0.965313i	$0.415916\pi$
$74$	−46.1180	+	79.8788i	−0.623217	+	1.07944i
$75$	58.9603	−	46.3539i	0.786137	−	0.618052i
$76$			199.877i			2.62996i
$77$	39.8018	+	73.4842i	0.516907	+	0.954340i
$78$	−64.2191	+	69.3480i	−0.823321	+	0.889077i
$79$	66.7293	−	38.5262i	0.844674	−	0.487673i	−0.0141761	−	0.999900i	$-0.504513\pi$
$79$	66.7293	−	38.5262i	0.844674	−	0.487673i	0.858850	+	0.512227i	$0.171179\pi$
$80$	−27.5031	−	2.17059i	−0.343789	−	0.0271323i
$81$	29.2965	−	75.5163i	0.361685	−	0.932300i
$82$	130.336	+	34.9235i	1.58947	+	0.425897i
$83$	−76.7710	+	76.7710i	−0.924952	+	0.924952i	−0.997374	−	0.0724223i	$-0.976927\pi$
$83$	−76.7710	+	76.7710i	−0.924952	+	0.924952i	0.0724223	+	0.997374i	$0.476927\pi$
$84$	85.2387	−	87.1668i	1.01475	−	1.03770i
$85$	−5.23804	+	14.7815i	−0.0616240	+	0.173900i
$86$	−156.130	+	90.1420i	−1.81547	+	1.04816i
$87$	23.5771	+	76.1697i	0.271001	+	0.875513i
$88$	−17.4703	−	65.2002i	−0.198527	−	0.740911i
$89$	56.8471	−	32.8207i	0.638731	−	0.368772i	−0.145394	−	0.989374i	$-0.546445\pi$
$89$	56.8471	−	32.8207i	0.638731	−	0.368772i	0.784126	+	0.620602i	$0.213112\pi$
$90$	−36.7424	+	136.038i	−0.408249	+	1.51153i
$91$	−16.3713	−	68.4987i	−0.179905	−	0.752733i
$92$	39.8813	−	39.8813i	0.433492	−	0.433492i
$93$	−0.520041	+	2.28879i	−0.00559184	+	0.0246107i
$94$	46.9662	−	81.3479i	0.499641	−	0.865403i
$95$	171.609	+	13.5436i	1.80641	+	0.142564i
$96$	101.274	−	63.7735i	1.05494	−	0.664308i
$97$	53.5343	−	53.5343i	0.551900	−	0.551900i	−0.375089	−	0.926989i	$-0.622388\pi$
$97$	53.5343	−	53.5343i	0.551900	−	0.551900i	0.926989	+	0.375089i	$0.122388\pi$
$98$	31.5958	+	150.149i	0.322406	+	1.53214i
$99$	107.132	−	8.23984i	1.08214	−	0.0832307i
$100$	22.7674	−	143.342i	0.227674	−	1.43342i
$101$	11.5407	−	19.9891i	0.114264	−	0.197912i	−0.803221	−	0.595681i	$-0.796882\pi$
$101$	11.5407	−	19.9891i	0.114264	−	0.197912i	0.917485	+	0.397769i	$0.130216\pi$
$102$	−8.71231	−	28.1466i	−0.0854148	−	0.275947i
$103$	−42.5642	+	158.852i	−0.413245	+	1.54225i	0.375081	+	0.926992i	$0.377615\pi$
$103$	−42.5642	+	158.852i	−0.413245	+	1.54225i	−0.788325	+	0.615259i	$0.789052\pi$
$104$			56.8846i			0.546967i
$105$	−69.0633	−	79.0902i	−0.657746	−	0.753240i
$106$	55.6502			0.525002
$107$	83.4520	+	22.3609i	0.779925	+	0.208980i	0.626752	−	0.779219i	$-0.284384\pi$
$107$	83.4520	+	22.3609i	0.779925	+	0.208980i	0.153173	+	0.988199i	$0.451051\pi$
$108$	−57.6964	−	145.745i	−0.534226	−	1.34949i
$109$	−88.6816	−	51.2003i	−0.813593	−	0.469728i	0.0346094	−	0.999401i	$-0.488981\pi$
$109$	−88.6816	−	51.2003i	−0.813593	−	0.469728i	−0.848202	+	0.529673i	$0.822315\pi$
$110$	−183.801	+	34.0239i	−1.67092	+	0.309309i
$111$	−88.3011	+	3.39074i	−0.795505	+	0.0305472i
$112$	−1.05038	+	38.6098i	−0.00937837	+	0.344730i
$113$	−88.2611	−	88.2611i	−0.781072	−	0.781072i	0.198940	−	0.980012i	$-0.436250\pi$
$113$	−88.2611	−	88.2611i	−0.781072	−	0.781072i	−0.980012	+	0.198940i	$0.936250\pi$
$114$	−273.684	+	172.342i	−2.40074	+	1.51177i
$115$	−31.5387	−	36.9434i	−0.274249	−	0.321247i
$116$	133.630	+	77.1512i	1.15198	+	0.665096i
$117$	−89.0044	−	16.6597i	−0.760722	−	0.142391i
$118$	−160.683	−	160.683i	−1.36172	−	1.36172i
$119$	21.0445	+	6.25700i	0.176845	+	0.0525798i
$120$	39.4049	+	75.0981i	0.328374	+	0.625817i
$121$	10.7664	+	18.6480i	0.0889787	+	0.154116i
$122$	74.9582	−	20.0850i	0.614411	−	0.164631i
$123$	38.2250	+	123.492i	0.310772	+	1.00400i
$124$	2.27107	+	3.93360i	0.0183151	+	0.0317226i
$125$	−121.527	−	29.2603i	−0.972217	−	0.234082i
$126$	192.851	+	41.5556i	1.53056	+	0.329807i
$127$	−139.976	−	139.976i	−1.10217	−	1.10217i	−0.994149	−	0.108021i	$-0.965549\pi$
$127$	−139.976	−	139.976i	−1.10217	−	1.10217i	−0.108021	−	0.994149i	$-0.534451\pi$
$128$	42.0562	−	156.956i	0.328564	−	1.22622i
$129$	−152.783	−	80.5567i	−1.18437	−	0.624470i
$130$	157.038	+	12.3937i	1.20798	+	0.0953359i
$131$	−90.9080	−	157.457i	−0.693954	−	1.20196i	−0.970532	−	0.240972i	$-0.922534\pi$
$131$	−90.9080	−	157.457i	−0.693954	−	1.20196i	0.276578	−	0.960991i	$-0.410800\pi$
$132$	141.281	−	152.564i	1.07031	−	1.15579i
$133$	6.55395	−	240.910i	0.0492778	−	1.81136i
$134$	−182.234			−1.35995
$135$	−129.043	+	39.6609i	−0.955872	+	0.293785i
$136$	−15.3573	−	8.86653i	−0.112921	−	0.0651950i
$137$	−28.1852	−	105.189i	−0.205731	−	0.767800i	−0.989225	−	0.146401i	$-0.953231\pi$
$137$	−28.1852	−	105.189i	−0.205731	−	0.767800i	0.783494	−	0.621399i	$-0.213436\pi$
$138$	88.9953	+	20.2208i	0.644893	+	0.146527i
$139$	181.388			1.30495			0.652475	−	0.757810i	$-0.273731\pi$
$139$	181.388			1.30495			0.652475	+	0.757810i	$0.273731\pi$
$140$	−202.055	−	21.4895i	−1.44325	−	0.153497i
$141$	89.9251	−	3.45310i	0.637766	−	0.0244901i
$142$	−35.3365	+	131.878i	−0.248848	+	0.928715i
$143$	−31.0886	−	116.024i	−0.217403	−	0.811357i
$144$	44.7839	+	21.4586i	0.310999	+	0.149018i
$145$	75.2947	−	109.503i	0.519274	−	0.755195i
$146$	1.07828			0.00738545
$147$	−105.596	+	102.267i	−0.718340	+	0.695692i
$148$	−120.919	+	120.919i	−0.817019	+	0.817019i
$149$	103.679	+	179.578i	0.695834	+	1.20522i	0.969899	+	0.243508i	$0.0782983\pi$
$149$	103.679	+	179.578i	0.695834	+	1.20522i	−0.274065	+	0.961711i	$0.588368\pi$
$150$	215.904	−	92.4209i	1.43936	−	0.616139i
$151$	8.73623	−	15.1316i	0.0578558	−	0.100209i	−0.835647	−	0.549267i	$-0.814907\pi$
$151$	8.73623	−	15.1316i	0.0578558	−	0.100209i	0.893503	+	0.449058i	$0.148240\pi$
$152$	−50.3804	+	188.022i	−0.331450	+	1.23699i
$153$	18.3707	−	21.4320i	0.120070	−	0.140079i
$154$	60.8318	+	254.524i	0.395012	+	1.65275i
$155$	3.53118	−	1.68334i	0.0227818	−	0.0108602i
$156$	−148.281	+	93.3743i	−0.950521	+	0.598553i
$157$	29.4104	+	109.761i	0.187327	+	0.699116i	0.994120	+	0.108281i	$0.0345347\pi$
$157$	29.4104	+	109.761i	0.187327	+	0.699116i	−0.806793	+	0.590834i	$0.798799\pi$
$158$	233.059	−	62.4479i	1.47506	−	0.395240i
$159$	28.4097	+	45.1155i	0.178678	+	0.283745i
$160$	−188.013	−	66.6250i	−1.17508	−	0.416406i
$161$	−49.3764	+	46.7610i	−0.306686	+	0.290441i
$162$	149.816	−	204.669i	0.924789	−	1.26339i
$163$	170.009	+	45.5539i	1.04300	+	0.279472i	0.739357	−	0.673313i	$-0.235130\pi$
$163$	170.009	+	45.5539i	1.04300	+	0.279472i	0.303645	+	0.952785i	$0.401796\pi$
$164$	216.651	+	125.083i	1.32104	+	0.762704i
$165$	−121.414	−	131.638i	−0.735845	−	0.797803i
$166$	−294.428	+	169.988i	−1.77366	+	1.02402i
$167$	23.5359	+	23.5359i	0.140933	+	0.140933i	0.774053	−	0.633120i	$-0.218226\pi$
$167$	23.5359	+	23.5359i	0.140933	+	0.140933i	−0.633120	+	0.774053i	$0.718226\pi$
$168$	102.154	−	60.5120i	0.608062	−	0.360191i
$169$		−	67.7736i		−	0.401027i
$170$	−27.8233	+	40.4642i	−0.163666	+	0.238024i
$171$	−279.434	−	133.894i	−1.63412	−	0.783004i
$172$	−322.856	+	86.5090i	−1.87707	+	0.502959i
$173$	30.7585	+	8.24173i	0.177795	+	0.0476400i	0.346618	−	0.938006i	$-0.387330\pi$
$173$	30.7585	+	8.24173i	0.177795	+	0.0476400i	−0.168823	+	0.985646i	$0.553997\pi$
$174$	9.58065	+	249.497i	0.0550612	+	1.43389i
$175$	−32.1416	+	172.023i	−0.183666	+	0.982989i
$176$			65.8745i			0.374287i
$177$	48.2359	−	212.295i	0.272519	−	1.19941i
$178$	198.544	−	53.1998i	1.11542	−	0.298875i
$179$	−13.1960	+	22.8561i	−0.0737207	+	0.127688i	−0.900529	−	0.434795i	$-0.856821\pi$
$179$	−13.1960	+	22.8561i	−0.0737207	+	0.127688i	0.826809	+	0.562483i	$0.190154\pi$
$180$	−131.076	+	225.988i	−0.728203	+	1.25549i
$181$			32.4648i			0.179364i	0.995970	+	0.0896818i	$0.0285850\pi$
$181$			32.4648i			0.179364i	−0.995970	+	0.0896818i	$0.971415\pi$
$182$	5.99747	−	220.455i	0.0329531	−	1.21129i
$183$	54.5494	+	50.5150i	0.298084	+	0.276038i
$184$	47.5684	−	27.4636i	0.258524	−	0.149259i
$185$	95.6243	+	112.011i	0.516888	+	0.605466i
$186$	−3.42794	+	6.50141i	−0.0184298	+	0.0349538i
$187$	36.1690	+	9.69147i	0.193417	+	0.0518260i
$188$	123.143	−	123.143i	0.655014	−	0.655014i
$189$	64.7622	+	177.558i	0.342657	+	0.939460i
$190$	508.086	+	180.048i	2.67414	+	0.947619i
$191$	283.840	−	163.875i	1.48607	−	0.857985i	0.486199	−	0.873848i	$-0.338383\pi$
$191$	283.840	−	163.875i	1.48607	−	0.857985i	0.999874	+	0.0158629i	$0.00504953\pi$
$192$	294.757	−	91.2372i	1.53519	−	0.475194i
$193$	−18.4194	−	68.7422i	−0.0954373	−	0.356177i	0.901648	−	0.432471i	$-0.142358\pi$
$193$	−18.4194	−	68.7422i	−0.0954373	−	0.356177i	−0.997085	+	0.0762936i	$0.975691\pi$
$194$	205.312	−	118.537i	1.05831	−	0.611015i
$195$	70.1212	+	133.637i	0.359596	+	0.685320i
$196$	−15.4667	+	284.052i	−0.0789115	+	1.44924i
$197$	−63.4729	+	63.4729i	−0.322198	+	0.322198i	−0.849610	−	0.527412i	$-0.823162\pi$
$197$	−63.4729	+	63.4729i	−0.322198	+	0.322198i	0.527412	+	0.849610i	$0.323162\pi$
$198$	330.718	+	61.9035i	1.67030	+	0.312644i
$199$	−149.531	+	258.996i	−0.751413	+	1.30149i	0.195725	+	0.980659i	$0.437294\pi$
$199$	−149.531	+	258.996i	−0.751413	+	1.30149i	−0.947138	+	0.320826i	$0.896039\pi$
$200$	57.5476	−	129.102i	0.287738	−	0.645511i
$201$	−93.0313	−	147.737i	−0.462842	−	0.735008i
$202$	51.1074	−	51.1074i	0.253007	−	0.253007i
$203$	−158.534	−	97.3717i	−0.780953	−	0.479663i
$204$	−2.09609	−	54.5860i	−0.0102749	−	0.267578i
$205$	122.074	−	177.535i	0.595481	−	0.866025i
$206$	−257.487	+	445.980i	−1.24993	+	2.16495i
$207$	29.0396	+	82.4711i	0.140288	+	0.398411i
$208$	14.3682	−	53.6230i	0.0690780	−	0.257803i
$209$		−	411.032i		−	1.96666i
$210$	−144.795	−	295.196i	−0.689501	−	1.40569i
$211$	151.609			0.718525			0.359263	−	0.933236i	$-0.383028\pi$
$211$	151.609			0.718525			0.359263	+	0.933236i	$0.383028\pi$
$212$	99.6595	+	26.7037i	0.470092	+	0.125961i
$213$	−124.952	+	38.6770i	−0.586631	+	0.181582i
$214$	234.293	+	135.269i	1.09483	+	0.632099i
$215$	52.3976	+	283.057i	0.243710	+	1.31655i
$216$	−17.5383	−	151.644i	−0.0811959	−	0.702057i
$217$	−2.60832	−	4.81562i	−0.0120199	−	0.0221918i
$218$	−226.738	−	226.738i	−1.04008	−	1.04008i
$219$	0.550465	+	0.874156i	0.00251354	+	0.00399158i
$220$	−345.480	−	27.2658i	−1.57036	−	0.123936i
$221$	−27.3283	−	15.7780i	−0.123658	−	0.0713938i
$222$	−269.831	−	61.3087i	−1.21545	−	0.276165i
$223$	−24.9405	−	24.9405i	−0.111841	−	0.111841i	0.648972	−	0.760813i	$-0.275199\pi$
$223$	−24.9405	−	24.9405i	−0.111841	−	0.111841i	−0.760813	+	0.648972i	$0.775199\pi$
$224$	−79.5856	+	267.675i	−0.355293	+	1.19498i
$225$	185.146	+	127.852i	0.822870	+	0.568230i
$226$	−195.430	−	338.494i	−0.864734	−	1.49776i
$227$	−315.536	+	84.5475i	−1.39003	+	0.372456i	−0.874752	−	0.484570i	$-0.838976\pi$
$227$	−315.536	+	84.5475i	−1.39003	+	0.372456i	−0.515273	+	0.857026i	$0.672309\pi$
$228$	−572.816	+	177.306i	−2.51235	+	0.777658i
$229$	−76.9204	−	133.230i	−0.335897	−	0.581790i	0.647760	−	0.761845i	$-0.275706\pi$
$229$	−76.9204	−	133.230i	−0.335897	−	0.581790i	−0.983657	+	0.180054i	$0.942373\pi$
$230$	−65.4533	−	137.303i	−0.284580	−	0.596969i
$231$	−175.287	+	179.252i	−0.758820	+	0.775983i
$232$	106.258	+	106.258i	0.458008	+	0.458008i
$233$	13.6040	−	50.7709i	0.0583864	−	0.217901i	−0.930569	−	0.366118i	$-0.880687\pi$
$233$	13.6040	−	50.7709i	0.0583864	−	0.217901i	0.988955	+	0.148217i	$0.0473534\pi$
$234$	−255.708	−	122.525i	−1.09277	−	0.523612i
$235$	−97.3829	−	114.071i	−0.414395	−	0.485409i
$236$	−210.651	−	364.858i	−0.892588	−	1.54601i
$237$	169.604	+	157.060i	0.715629	+	0.662702i
$238$	58.5820	+	35.9812i	0.246143	+	0.151182i
$239$	127.602			0.533902			0.266951	−	0.963710i	$-0.413984\pi$
$239$	127.602			0.533902			0.266951	+	0.963710i	$0.413984\pi$
$240$	−18.1768	−	80.7452i	−0.0757367	−	0.336439i
$241$	115.480	+	66.6725i	0.479171	+	0.276650i	0.720071	−	0.693900i	$-0.244109\pi$
$241$	115.480	+	66.6725i	0.479171	+	0.276650i	−0.240900	+	0.970550i	$0.577443\pi$
$242$	17.4515	+	65.1300i	0.0721138	+	0.269132i
$243$	242.407	+	16.9706i	0.997558	+	0.0698379i
$244$	143.874			0.589649
$245$	242.831	+	32.5266i	0.991148	+	0.132762i
$246$	15.5329	+	404.504i	0.0631418	+	1.64433i
$247$	−89.6522	+	334.587i	−0.362964	+	1.35460i
$248$	1.14488	+	4.27275i	0.00461645	+	0.0172288i
$249$	−288.116	−	151.912i	−1.15709	−	0.610090i
$250$	−343.867	−	186.996i	−1.37547	−	0.747985i
$251$	264.593			1.05416			0.527078	−	0.849817i	$-0.323288\pi$
$251$	264.593			1.05416			0.527078	+	0.849817i	$0.323288\pi$
$252$	325.420	+	166.958i	1.29135	+	0.662531i
$253$	−82.0130	+	82.0130i	−0.324162	+	0.324162i
$254$	−309.937	−	536.826i	−1.22022	−	2.11349i
$255$	−47.0081	−	1.89909i	−0.184346	−	0.00744743i
$256$	48.7104	−	84.3689i	0.190275	−	0.329566i
$257$	−37.0832	+	138.397i	−0.144293	+	0.538508i	0.855493	+	0.517814i	$0.173254\pi$
$257$	−37.0832	+	138.397i	−0.144293	+	0.538508i	−0.999786	+	0.0206937i	$0.993413\pi$
$258$	−396.833	−	367.483i	−1.53811	−	1.42435i
$259$	149.708	−	141.778i	0.578022	−	0.547405i
$260$	275.279	+	97.5493i	1.05877	+	0.375189i
$261$	−197.376	+	135.137i	−0.756230	+	0.517765i
$262$	−147.355	−	549.936i	−0.562423	−	2.09899i
$263$	−350.851	+	94.0103i	−1.33403	+	0.357454i	−0.854218	−	0.519915i	$-0.825964\pi$
$263$	−350.851	+	94.0103i	−1.33403	+	0.357454i	−0.479817	+	0.877369i	$0.659297\pi$
$264$	171.356	−	107.905i	0.649077	−	0.408731i
$265$	29.6800	−	83.7556i	0.112000	−	0.316059i
$266$	215.072	−	723.366i	0.808542	−	2.71942i
$267$	144.487	+	133.801i	0.541149	+	0.501126i
$268$	−326.348	−	87.4446i	−1.21772	−	0.326286i
$269$	454.286	+	262.282i	1.68879	+	0.975026i	0.955443	+	0.295176i	$0.0953782\pi$
$269$	454.286	+	262.282i	1.68879	+	0.975026i	0.733351	+	0.679850i	$0.237955\pi$
$270$	−422.457	+	15.3777i	−1.56466	+	0.0569544i
$271$	81.8541	−	47.2585i	0.302045	−	0.174386i	−0.341316	−	0.939948i	$-0.610873\pi$
$271$	81.8541	−	47.2585i	0.302045	−	0.174386i	0.643361	+	0.765563i	$0.277539\pi$
$272$	12.2372	+	12.2372i	0.0449896	+	0.0449896i
$273$	181.784	−	107.681i	0.665877	−	0.394437i
$274$		−	341.005i		−	1.24454i
$275$	−46.8194	+	294.773i	−0.170252	+	1.07190i
$276$	149.671	+	78.9159i	0.542288	+	0.285927i
$277$	257.471	−	68.9893i	0.929500	−	0.249059i	0.237858	−	0.971300i	$-0.423555\pi$
$277$	257.471	−	68.9893i	0.929500	−	0.249059i	0.691641	+	0.722241i	$0.256888\pi$
$278$	548.642	+	147.008i	1.97353	+	0.528806i
$279$	−7.02066	+	0.539980i	−0.0251636	+	0.00193541i
$280$	−184.655	−	71.1445i	−0.659482	−	0.254088i
$281$		−	104.628i		−	0.372343i	−0.982517	−	0.186171i	$-0.940392\pi$
$281$		−	104.628i		−	0.372343i	0.982517	−	0.186171i	$-0.0596079\pi$
$282$	274.793	+	62.4363i	0.974445	+	0.221405i
$283$	−92.4866	+	24.7817i	−0.326808	+	0.0875679i	−0.418493	−	0.908220i	$-0.637441\pi$
$283$	−92.4866	+	24.7817i	−0.326808	+	0.0875679i	0.0916849	+	0.995788i	$0.470775\pi$
$284$	−126.562	+	219.213i	−0.445643	+	0.771875i
$285$	113.416	+	503.819i	0.397952	+	1.76779i
$286$		−	376.132i		−	1.31515i
$287$	−257.027	−	157.866i	−0.895563	−	0.550057i
$288$	272.604	+	233.665i	0.946540	+	0.811337i
$289$	−241.762	+	139.581i	−0.836547	+	0.482981i
$290$	316.491	−	270.189i	1.09135	−	0.931687i
$291$	200.910	+	105.932i	0.690414	+	0.364028i
$292$	1.93100	+	0.517409i	0.00661300	+	0.00177195i
$293$	43.5663	−	43.5663i	0.148690	−	0.148690i	−0.628842	−	0.777533i	$-0.716471\pi$
$293$	43.5663	−	43.5663i	0.148690	−	0.148690i	0.777533	+	0.628842i	$0.216471\pi$
$294$	−402.278	+	223.743i	−1.36829	+	0.761030i
$295$	−327.531	+	156.136i	−1.11027	+	0.529276i
$296$	−144.226	+	83.2688i	−0.487249	+	0.281314i
$297$	118.649	+	299.715i	0.399490	+	1.00914i
$298$	168.056	+	627.194i	0.563946	+	2.10468i
$299$	84.6482	−	48.8716i	0.283104	−	0.163450i
$300$	430.993	−	61.9077i	1.43664	−	0.206359i
$301$	391.973	−	93.6824i	1.30224	−	0.311237i
$302$	38.6879	−	38.6879i	0.128106	−	0.128106i
$303$	67.5233	+	15.3421i	0.222849	+	0.0506339i
$304$	94.9835	−	164.516i	0.312446	−	0.541172i
$305$	9.74891	−	123.527i	0.0319636	−	0.405006i
$306$	72.9353	−	49.9364i	0.238351	−	0.163191i
$307$	341.970	−	341.970i	1.11391	−	1.11391i	0.121293	−	0.992617i	$-0.461296\pi$
$307$	341.970	−	341.970i	1.11391	−	1.11391i	0.992617	−	0.121293i	$-0.0387041\pi$
$308$	−13.1943	+	484.997i	−0.0428387	+	1.57466i
$309$	−493.003	+	18.9312i	−1.59548	+	0.0612661i
$310$	12.0450	−	2.22968i	0.0388548	−	0.00719253i
$311$	−157.476	+	272.756i	−0.506353	+	0.877029i	0.493620	+	0.869678i	$0.335673\pi$
$311$	−157.476	+	272.756i	−0.506353	+	0.877029i	−0.999973	+	0.00735136i	$0.997660\pi$
$312$	−163.023	+	50.4610i	−0.522509	+	0.161734i
$313$	−77.3027	+	288.498i	−0.246973	+	0.921717i	0.725408	+	0.688319i	$0.241651\pi$
$313$	−77.3027	+	288.498i	−0.246973	+	0.921717i	−0.972381	+	0.233398i	$0.925015\pi$
$314$			355.829i			1.13321i
$315$	165.396	−	268.084i	0.525067	−	0.851061i
$316$	447.332			1.41561
$317$	−114.539	−	30.6907i	−0.361323	−	0.0968162i	0.0735902	−	0.997289i	$-0.476554\pi$
$317$	−114.539	−	30.6907i	−0.361323	−	0.0968162i	−0.434913	+	0.900472i	$0.643221\pi$
$318$	49.3661	+	159.485i	0.155239	+	0.501526i
$319$	−274.800	−	158.656i	−0.861442	−	0.497354i
$320$	−423.749	−	291.371i	−1.32422	−	0.910535i
$321$	9.94542	+	258.997i	0.0309826	+	0.806843i
$322$	−187.246	+	101.420i	−0.581509	+	0.314967i
$323$	−76.3552	−	76.3552i	−0.236394	−	0.236394i
$324$	366.503	−	294.637i	1.13118	−	0.909372i
$325$	102.406	−	229.738i	0.315096	−	0.706886i
$326$	477.305	+	275.572i	1.46413	+	0.845313i
$327$	68.0650	−	299.567i	0.208150	−	0.916106i
$328$	172.273	+	172.273i	0.525224	+	0.525224i
$329$	−152.461	+	144.385i	−0.463408	+	0.438861i
$330$	−260.553	−	496.564i	−0.789555	−	1.50474i
$331$	97.3575	+	168.628i	0.294131	+	0.509450i	0.974782	−	0.223157i	$-0.0716363\pi$
$331$	97.3575	+	168.628i	0.294131	+	0.509450i	−0.680651	+	0.732608i	$0.738303\pi$
$332$	−608.835	+	163.137i	−1.83384	+	0.491376i
$333$	−88.0472	−	250.050i	−0.264406	−	0.750900i
$334$	52.1136	+	90.2634i	0.156029	+	0.270250i
$335$	−97.1910	+	274.268i	−0.290122	+	0.818712i
$336$	−111.582	+	31.2397i	−0.332088	+	0.0929751i
$337$	−76.8819	−	76.8819i	−0.228136	−	0.228136i	0.583777	−	0.811914i	$-0.301574\pi$
$337$	−76.8819	−	76.8819i	−0.228136	−	0.228136i	−0.811914	+	0.583777i	$0.801574\pi$
$338$	54.9279	−	204.994i	0.162509	−	0.606490i
$339$	174.649	−	331.238i	0.515188	−	0.977102i
$340$	−69.2431	+	59.1130i	−0.203656	+	0.173862i
$341$	−4.67029	−	8.08917i	−0.0136959	−	0.0237219i
$342$	−736.684	−	631.457i	−2.15405	−	1.84636i
$343$	27.9559	−	341.859i	0.0815042	−	0.996673i
$344$	−325.513			−0.946259
$345$	77.8969	−	123.157i	0.225788	−	0.356976i
$346$	86.3553	+	49.8572i	0.249582	+	0.144096i
$347$	−33.0067	−	123.182i	−0.0951200	−	0.354993i	0.901918	−	0.431908i	$-0.142160\pi$
$347$	−33.0067	−	123.182i	−0.0951200	−	0.354993i	−0.997038	+	0.0769154i	$0.975493\pi$
$348$	−102.564	+	451.402i	−0.294723	+	1.29713i
$349$	−51.0844			−0.146374			−0.0731869	−	0.997318i	$-0.523317\pi$
$349$	−51.0844			−0.146374			−0.0731869	+	0.997318i	$0.523317\pi$
$350$	−236.636	+	494.266i	−0.676103	+	1.41219i
$351$	−31.2095	−	269.852i	−0.0889161	−	0.768809i
$352$	−123.270	+	460.050i	−0.350199	+	1.30696i
$353$	−22.4299	−	83.7097i	−0.0635409	−	0.237138i	0.926850	−	0.375431i	$-0.122505\pi$
$353$	−22.4299	−	83.7097i	−0.0635409	−	0.237138i	−0.990391	+	0.138293i	$0.955839\pi$
$354$	317.955	−	603.032i	0.898178	−	1.70348i
$355$	179.634	+	123.517i	0.506012	+	0.347935i
$356$	381.085			1.07046
$357$	0.736533	+	65.8609i	0.00206312	+	0.184484i
$358$	−58.4378	+	58.4378i	−0.163234	+	0.163234i
$359$	−289.434	−	501.315i	−0.806224	−	1.39642i	−0.915462	−	0.402405i	$-0.868174\pi$
$359$	−289.434	−	501.315i	−0.806224	−	1.39642i	0.109238	−	0.994016i	$-0.465159\pi$
$360$	−180.265	+	179.546i	−0.500735	+	0.498740i
$361$	−412.160	+	713.883i	−1.14172	+	1.97751i
$362$	−26.3115	+	98.1958i	−0.0726837	+	0.271259i
$363$	−43.8917	+	47.3972i	−0.120914	+	0.130571i
$364$	116.525	−	391.918i	0.320125	−	1.07670i
$365$	0.575078	−	1.62284i	0.00157556	−	0.00444615i
$366$	124.054	+	197.002i	0.338946	+	0.538257i
$367$	77.7404	+	290.131i	0.211827	+	0.790548i	0.987260	+	0.159118i	$0.0508650\pi$
$367$	77.7404	+	290.131i	0.211827	+	0.790548i	−0.775433	+	0.631430i	$0.782468\pi$
$368$	−51.7778	+	13.8738i	−0.140701	+	0.0377006i
$369$	−320.001	+	219.094i	−0.867212	+	0.593751i
$370$	198.452	+	416.298i	0.536358	+	1.12513i
$371$	−119.243	−	35.4536i	−0.321411	−	0.0955624i
$372$	−9.25851	+	9.99795i	−0.0248885	+	0.0268762i
$373$	−458.973	−	122.982i	−1.23049	−	0.329709i	−0.415721	−	0.909492i	$-0.636471\pi$
$373$	−458.973	−	122.982i	−1.23049	−	0.329709i	−0.814771	+	0.579783i	$0.803137\pi$
$374$	101.545	+	58.6272i	0.271512	+	0.156757i
$375$	−23.9483	−	374.235i	−0.0638621	−	0.997959i
$376$	146.878	−	84.8003i	0.390634	−	0.225533i
$377$	189.086	+	189.086i	0.501556	+	0.501556i
$378$	51.9813	+	589.544i	0.137517	+	1.55964i
$379$			497.374i			1.31233i	0.754617	+	0.656166i	$0.227823\pi$
$379$			497.374i			1.31233i	−0.754617	+	0.656166i	$0.772177\pi$
$380$	823.494	+	566.237i	2.16709	+	1.49010i
$381$	276.980	−	525.318i	0.726981	−	1.37879i
$382$	991.341	−	265.629i	2.59513	−	0.695364i
$383$	−572.466	−	153.392i	−1.49469	−	0.400501i	−0.583372	−	0.812205i	$-0.698267\pi$
$383$	−572.466	−	153.392i	−1.49469	−	0.400501i	−0.911317	+	0.411705i	$0.864934\pi$
$384$	487.119	−	18.7053i	1.26854	−	0.0487116i
$385$	415.512	+	44.1916i	1.07925	+	0.114783i
$386$		−	222.851i		−	0.577335i
$387$	95.3327	−	509.314i	0.246338	−	1.31606i
$388$	424.556	−	113.759i	1.09422	−	0.293194i
$389$	39.0172	−	67.5798i	0.100301	−	0.173727i	−0.811507	−	0.584342i	$-0.801353\pi$
$389$	39.0172	−	67.5798i	0.100301	−	0.173727i	0.911809	+	0.410615i	$0.134686\pi$
$390$	103.786	+	461.041i	0.266119	+	1.18216i
$391$			30.4702i			0.0779290i
$392$	−86.1468	+	263.307i	−0.219762	+	0.671700i
$393$	370.606	−	400.205i	0.943019	−	1.01833i
$394$	−243.428	+	140.543i	−0.617837	+	0.356709i
$395$	30.3112	−	384.067i	0.0767371	−	0.972322i
$396$	562.553	+	269.553i	1.42059	+	0.680688i
$397$	−335.039	−	89.7734i	−0.843927	−	0.226129i	−0.189146	−	0.981949i	$-0.560572\pi$
$397$	−335.039	−	89.7734i	−0.843927	−	0.226129i	−0.654780	+	0.755819i	$0.727239\pi$
$398$	−662.190	+	662.190i	−1.66379	+	1.66379i
$399$	696.226	−	194.923i	1.74493	−	0.488530i
$400$	−86.8572	+	107.164i	−0.217143	+	0.267910i
$401$	−635.125	+	366.690i	−1.58385	+	0.914438i	−0.589563	+	0.807722i	$0.700700\pi$
$401$	−635.125	+	366.690i	−1.58385	+	0.914438i	−0.994290	+	0.106716i	$0.965966\pi$
$402$	−161.655	−	522.255i	−0.402128	−	1.29914i
$403$	2.03732	+	7.60338i	0.00505538	+	0.0188670i
$404$	116.048	−	67.0003i	0.287247	−	0.165842i
$405$	−228.133	−	334.635i	−0.563292	−	0.826258i
$406$	−400.598	−	423.004i	−0.986694	−	1.04188i
$407$	248.661	−	248.661i	0.610960	−	0.610960i
$408$	11.7870	−	51.8769i	0.0288898	−	0.127149i
$409$	−237.092	+	410.656i	−0.579687	+	1.00405i	0.415828	+	0.909443i	$0.363492\pi$
$409$	−237.092	+	410.656i	−0.579687	+	1.00405i	−0.995515	+	0.0946043i	$0.969841\pi$
$410$	513.119	−	438.051i	1.25151	−	1.06842i
$411$	276.452	−	174.085i	0.672633	−	0.423564i
$412$	−675.115	+	675.115i	−1.63863	+	1.63863i
$413$	241.933	+	446.668i	0.585793	+	1.08152i
$414$	20.9960	+	272.984i	0.0507151	+	0.659383i
$415$	98.8105	+	533.784i	0.238098	+	1.28623i
$416$	200.688	−	347.602i	0.482423	−	0.835581i
$417$	160.905	+	519.831i	0.385864	+	1.24660i
$418$	333.125	−	1243.24i	0.796951	−	2.97426i
$419$		−	124.867i		−	0.298012i	−0.988836	−	0.149006i	$-0.952393\pi$
$419$		−	124.867i		−	0.298012i	0.988836	−	0.149006i	$-0.0476073\pi$
$420$	−117.653	−	598.122i	−0.280125	−	1.42410i
$421$	−385.564			−0.915829			−0.457914	−	0.888996i	$-0.651403\pi$
$421$	−385.564			−0.915829			−0.457914	+	0.888996i	$0.651403\pi$
$422$	458.569	+	122.873i	1.08666	+	0.291169i
$423$	89.6666	+	254.649i	0.211978	+	0.602006i
$424$	87.0180	+	50.2399i	0.205231	+	0.118490i
$425$	46.0610	+	63.4558i	0.108379	+	0.149308i
$426$	−409.287	+	15.7165i	−0.960769	+	0.0368933i
$427$	−173.411	−	4.71764i	−0.406115	−	0.0110483i
$428$	354.668	+	354.668i	0.828664	+	0.828664i
$429$	304.930	−	192.017i	0.710792	−	0.447593i
$430$	−70.9209	+	898.625i	−0.164932	+	2.08983i
$431$	−143.931	−	83.0986i	−0.333947	−	0.192804i	0.323645	−	0.946178i	$-0.395092\pi$
$431$	−143.931	−	83.0986i	−0.333947	−	0.192804i	−0.657592	+	0.753374i	$0.728425\pi$
$432$	−21.7705	+	147.379i	−0.0503946	+	0.341156i
$433$	223.442	+	223.442i	0.516033	+	0.516033i	0.916369	−	0.400335i	$-0.131106\pi$
$433$	223.442	+	223.442i	0.516033	+	0.516033i	−0.400335	+	0.916369i	$0.631106\pi$
$434$	−3.98648	−	16.6797i	−0.00918543	−	0.0384324i
$435$	380.612	+	118.646i	0.874971	+	0.272748i
$436$	−297.247	−	514.846i	−0.681758	−	1.18084i
$437$	323.074	−	86.5674i	0.739299	−	0.198095i
$438$	0.956514	+	3.09018i	0.00218382	+	0.00705520i
$439$	−160.351	−	277.735i	−0.365263	−	0.632655i	0.623555	−	0.781779i	$-0.285688\pi$
$439$	−160.351	−	277.735i	−0.365263	−	0.632655i	−0.988818	+	0.149125i	$0.952354\pi$
$440$	−318.118	−	112.730i	−0.722995	−	0.256204i
$441$	−386.753	−	211.904i	−0.876991	−	0.480508i
$442$	−69.8721	−	69.8721i	−0.158082	−	0.158082i
$443$	−95.6047	+	356.801i	−0.215812	+	0.805421i	0.770067	+	0.637963i	$0.220223\pi$
$443$	−95.6047	+	356.801i	−0.215812	+	0.805421i	−0.985879	+	0.167458i	$0.946444\pi$
$444$	−453.799	−	239.271i	−1.02207	−	0.538898i
$445$	25.8223	−	327.189i	0.0580276	−	0.735257i
$446$	−55.2238	−	95.6505i	−0.123820	−	0.214463i
$447$	−422.671	+	456.428i	−0.945573	+	1.02109i
$448$	−376.803	+	613.484i	−0.841079	+	1.36938i
$449$	40.2211			0.0895793			0.0447897	−	0.998996i	$-0.485738\pi$
$449$	40.2211			0.0895793			0.0447897	+	0.998996i	$0.485738\pi$
$450$	456.388	+	536.765i	1.01420	+	1.19281i
$451$	−445.527	−	257.225i	−0.987864	−	0.570344i
$452$	−187.553	−	699.959i	−0.414941	−	1.54858i
$453$	51.1146	+	11.6138i	0.112836	+	0.0256376i
$454$	−1022.92			−2.25312
$455$	−328.594	−	126.602i	−0.722185	−	0.278246i
$456$	−583.535	+	22.4076i	−1.27968	+	0.0491395i
$457$	215.217	−	803.200i	0.470934	−	1.75755i	−0.165491	−	0.986211i	$-0.552921\pi$
$457$	215.217	−	803.200i	0.470934	−	1.75755i	0.636425	−	0.771338i	$-0.280412\pi$
$458$	−124.682	−	465.320i	−0.272231	−	1.01598i
$459$	77.7172	+	33.6357i	0.169318	+	0.0732805i
$460$	−51.3304	−	277.292i	−0.111588	−	0.602809i
$461$	100.425			0.217841			0.108920	−	0.994050i	$-0.465261\pi$
$461$	100.425			0.217841			0.108920	+	0.994050i	$0.465261\pi$
$462$	−675.466	+	400.118i	−1.46205	+	0.866055i
$463$	155.475	−	155.475i	0.335799	−	0.335799i	−0.518984	−	0.854784i	$-0.673690\pi$
$463$	155.475	−	155.475i	0.335799	−	0.335799i	0.854784	+	0.518984i	$0.173690\pi$
$464$	−73.3261	−	127.005i	−0.158030	−	0.273717i
$465$	7.95662	+	8.62657i	0.0171110	+	0.0185518i
$466$	82.2957	−	142.540i	0.176600	−	0.305881i
$467$	−97.2752	+	363.036i	−0.208298	+	0.777379i	0.780121	+	0.625629i	$0.215158\pi$
$467$	−97.2752	+	363.036i	−0.208298	+	0.777379i	−0.988419	+	0.151750i	$0.951509\pi$
$468$	−399.134	−	342.121i	−0.852849	−	0.731029i
$469$	390.478	+	116.097i	0.832576	+	0.247543i
$470$	−202.102	−	423.954i	−0.430005	−	0.902031i
$471$	−288.470	+	181.652i	−0.612462	+	0.385674i
$472$	−106.192	−	396.315i	−0.224984	−	0.839650i
$473$	663.930	−	177.899i	1.40366	−	0.376109i
$474$	385.708	+	612.515i	0.813729	+	1.29223i
$475$	541.956	−	668.662i	1.14096	−	1.40771i
$476$	87.6443	+	92.5463i	0.184127	+	0.194425i
$477$	−104.093	+	121.439i	−0.218224	+	0.254589i
$478$	385.957	+	103.417i	0.807442	+	0.216353i
$479$	−79.5325	−	45.9181i	−0.166039	−	0.0958625i	0.414678	−	0.909968i	$-0.363894\pi$
$479$	−79.5325	−	45.9181i	−0.166039	−	0.0958625i	−0.580717	+	0.814106i	$0.697228\pi$
$480$	24.1554	−	597.918i	0.0503238	−	1.24566i
$481$	−256.651	+	148.177i	−0.533577	+	0.308061i
$482$	295.256	+	295.256i	0.612564	+	0.612564i
$483$	−177.811	−	100.025i	−0.368138	−	0.207091i
$484$			125.010i			0.258286i
$485$	−68.9030	−	372.221i	−0.142068	−	0.767466i
$486$	719.449	+	247.792i	1.48035	+	0.509860i
$487$	−41.9994	+	11.2537i	−0.0862411	+	0.0231082i	−0.301682	−	0.953409i	$-0.597548\pi$
$487$	−41.9994	+	11.2537i	−0.0862411	+	0.0231082i	0.215440	+	0.976517i	$0.430881\pi$
$488$	135.341	+	36.2646i	0.277339	+	0.0743127i
$489$	20.2609	+	527.631i	0.0414334	+	1.07900i
$490$	708.126	+	295.188i	1.44516	+	0.602425i
$491$			147.820i			0.301059i	0.988605	+	0.150530i	$0.0480979\pi$
$491$			147.820i			0.301059i	−0.988605	+	0.150530i	$0.951902\pi$
$492$	−166.284	+	731.847i	−0.337976	+	1.48749i
$493$	−80.5208	+	21.5755i	−0.163328	+	0.0437637i
$494$	−542.339	+	939.359i	−1.09785	+	1.90154i
$495$	269.549	−	464.728i	0.544544	−	0.938845i
$496$		−	4.31694i		−	0.00870351i
$497$	159.733	−	260.066i	0.321395	−	0.523271i
$498$	−748.340	−	692.994i	−1.50269	−	1.39155i
$499$	285.561	−	164.869i	0.572267	−	0.330399i	−0.185787	−	0.982590i	$-0.559483\pi$
$499$	285.561	−	164.869i	0.572267	−	0.330399i	0.758054	+	0.652191i	$0.226150\pi$
$500$	−526.073	−	499.880i	−1.05215	−	0.999760i
$501$	−46.5721	+	88.3283i	−0.0929583	+	0.176304i
$502$	800.310	+	214.442i	1.59424	+	0.427176i
$503$	−202.943	+	202.943i	−0.403465	+	0.403465i	−0.879452	−	0.475987i	$-0.842091\pi$
$503$	−202.943	+	202.943i	−0.403465	+	0.403465i	0.475987	+	0.879452i	$0.342091\pi$
$504$	264.037	+	239.080i	0.523883	+	0.474366i
$505$	−49.6613	−	104.176i	−0.0983392	−	0.206288i
$506$	−314.532	+	181.595i	−0.621604	+	0.358883i
$507$	194.229	−	60.1204i	0.383095	−	0.118581i
$508$	−297.445	−	1110.08i	−0.585523	−	2.18520i
$509$	−391.137	+	225.823i	−0.768442	+	0.443660i	−0.832319	−	0.554297i	$-0.812987\pi$
$509$	−391.137	+	225.823i	−0.768442	+	0.443660i	0.0638764	+	0.997958i	$0.479654\pi$
$510$	−140.646	−	43.8424i	−0.275776	−	0.0859656i
$511$	−2.31045	−	0.686948i	−0.00452144	−	0.00134432i
$512$	−243.887	+	243.887i	−0.476343	+	0.476343i
$513$	135.839	−	919.590i	0.264794	−	1.79257i
$514$	−224.330	+	388.551i	−0.436440	+	0.755936i
$515$	533.890	+	625.381i	1.03668	+	1.21433i
$516$	−534.320	−	848.516i	−1.03550	−	1.64441i
$517$	−253.234	+	253.234i	−0.489814	+	0.489814i
$518$	567.724	−	307.501i	1.09599	−	0.593631i
$519$	3.66566	+	95.4604i	0.00706293	+	0.183931i
$520$	234.365	+	161.150i	0.450702	+	0.309904i
$521$	−79.6615	+	137.978i	−0.152901	+	0.264833i	−0.932293	−	0.361704i	$-0.882195\pi$
$521$	−79.6615	+	137.978i	−0.152901	+	0.264833i	0.779392	+	0.626537i	$0.215528\pi$
$522$	−706.523	+	248.780i	−1.35349	+	0.476590i
$523$	61.4111	−	229.189i	0.117421	−	0.438221i	−0.882036	−	0.471183i	$-0.843827\pi$
$523$	61.4111	−	229.189i	0.117421	−	0.438221i	0.999457	+	0.0329618i	$0.0104940\pi$
$524$		−	1055.54i		−	2.01440i
$525$	−521.504	+	60.4848i	−0.993341	+	0.115209i
$526$	−1137.41			−2.16237
$527$	−2.37026	−	0.635109i	−0.00449764	−	0.00120514i
$528$	−188.787	+	58.4358i	−0.357550	+	0.110674i
$529$	376.392	+	217.310i	0.711516	+	0.410794i
$530$	157.653	−	229.280i	0.297459	−	0.432603i
$531$	651.194	−	50.0853i	1.22635	−	0.0943226i
$532$	732.261	−	1192.21i	1.37643	−	2.24100i
$533$	306.561	+	306.561i	0.575162	+	0.575162i
$534$	328.587	+	521.806i	0.615331	+	0.977165i
$535$	328.541	−	280.476i	0.614095	−	0.524255i
$536$	−284.952	−	164.517i	−0.531626	−	0.306935i
$537$	−77.2082	−	17.5426i	−0.143777	−	0.0326678i
$538$	1161.50	+	1161.50i	2.15892	+	2.15892i
$539$	31.8061	−	584.132i	0.0590094	−	1.08373i
$540$	−763.923	−	175.177i	−1.41467	−	0.324401i
$541$	337.537	+	584.631i	0.623913	+	1.08065i	0.988750	+	0.149578i	$0.0477914\pi$
$541$	337.537	+	584.631i	0.623913	+	1.08065i	−0.364837	+	0.931071i	$0.618875\pi$
$542$	285.884	−	76.6024i	0.527461	−	0.141333i
$543$	−93.0393	+	28.7988i	−0.171343	+	0.0530365i
$544$	62.5619	+	108.360i	0.115004	+	0.199192i
$545$	−462.175	+	220.322i	−0.848027	+	0.404261i
$546$	637.112	−	178.373i	1.16687	−	0.326691i
$547$	−734.930	−	734.930i	−1.34356	−	1.34356i	−0.892483	−	0.451081i	$-0.851039\pi$
$547$	−734.930	−	734.930i	−1.34356	−	1.34356i	−0.451081	−	0.892483i	$-0.648961\pi$
$548$	163.631	−	610.679i	0.298596	−	1.11438i
$549$	−96.3787	+	201.141i	−0.175553	+	0.366377i
$550$	−380.516	+	853.649i	−0.691847	+	1.55209i
$551$	457.527	+	792.460i	0.830357	+	1.43822i
$552$	120.903	+	111.961i	0.219028	+	0.202829i
$553$	−539.167	−	14.6680i	−0.974985	−	0.0265244i
$554$	834.683			1.50665
$555$	−236.181	+	373.407i	−0.425551	+	0.672806i
$556$	911.976	+	526.530i	1.64025	+	0.946996i
$557$	−188.451	−	703.308i	−0.338332	−	1.26267i	−0.900212	−	0.435452i	$-0.856588\pi$
$557$	−188.451	−	703.308i	−0.338332	−	1.26267i	0.561880	−	0.827219i	$-0.310078\pi$
$558$	−21.6729	−	4.05671i	−0.0388403	−	0.00727008i
$559$	−579.252			−1.03623
$560$	156.097	+	113.706i	0.278745	+	0.203047i
$561$	4.31046	+	112.252i	0.00768352	+	0.200093i
$562$	84.7972	−	316.467i	0.150885	−	0.563109i
$563$	−16.0681	−	59.9668i	−0.0285401	−	0.106513i	0.950187	−	0.311682i	$-0.100892\pi$
$563$	−16.0681	−	59.9668i	−0.0285401	−	0.106513i	−0.978727	+	0.205169i	$0.934226\pi$
$564$	462.145	+	243.671i	0.819407	+	0.432041i
$565$	−613.675	+	113.599i	−1.08615	+	0.201061i
$566$	−299.827			−0.529730
$567$	−451.406	+	343.106i	−0.796130	+	0.605126i
$568$	−174.311	+	174.311i	−0.306885	+	0.306885i
$569$	362.028	+	627.052i	0.636254	+	1.10202i	0.986248	+	0.165272i	$0.0528502\pi$
$569$	362.028	+	627.052i	0.636254	+	1.10202i	−0.349994	+	0.936752i	$0.613816\pi$
$570$	−65.2777	+	1615.81i	−0.114522	+	2.83476i
$571$	238.498	−	413.091i	0.417685	−	0.723451i	−0.578021	−	0.816022i	$-0.696175\pi$
$571$	238.498	−	413.091i	0.417685	−	0.723451i	0.995706	+	0.0925704i	$0.0295083\pi$
$572$	180.486	−	673.585i	0.315536	−	1.17760i
$573$	721.430	+	668.073i	1.25904	+	1.16592i
$574$	−649.480	−	685.806i	−1.13150	−	1.19478i
$575$	−241.554	+	25.2817i	−0.420094	+	0.0439681i
$576$	522.944	+	763.795i	0.907890	+	1.32603i
$577$	65.7596	+	245.418i	0.113968	+	0.425335i	0.999208	−	0.0398006i	$-0.0126723\pi$
$577$	65.7596	+	245.418i	0.113968	+	0.425335i	−0.885240	+	0.465135i	$0.846006\pi$
$578$	−844.379	+	226.251i	−1.46086	+	0.391437i
$579$	180.665	−	113.767i	0.312030	−	0.196489i
$580$	696.428	−	331.992i	1.20074	−	0.572401i
$581$	739.176	−	176.664i	1.27225	−	0.304070i
$582$	521.836	+	483.241i	0.896626	+	0.830312i
$583$	−204.943	−	54.9142i	−0.351531	−	0.0941924i
$584$	1.68606	+	0.973445i	0.00288708	+	0.00166686i
$585$	−320.782	+	319.504i	−0.548345	+	0.546160i
$586$	167.083	−	96.4655i	0.285125	−	0.164617i
$587$	−324.936	−	324.936i	−0.553554	−	0.553554i	0.373911	−	0.927465i	$-0.378017\pi$
$587$	−324.936	−	324.936i	−0.553554	−	0.553554i	−0.927465	+	0.373911i	$0.878017\pi$
$588$	−827.769	+	207.651i	−1.40777	+	0.353147i
$589$			26.9361i			0.0457318i
$590$	−1117.22	+	206.812i	−1.89359	+	0.350529i
$591$	−238.209	−	125.598i	−0.403061	−	0.212519i
$592$	156.989	−	42.0650i	0.265184	−	0.0710558i
$593$	616.787	+	165.267i	1.04011	+	0.278697i	0.738160	−	0.674626i	$-0.235695\pi$
$593$	616.787	+	165.267i	1.04011	+	0.278697i	0.301952	+	0.953323i	$0.402362\pi$
$594$	115.967	+	1002.70i	0.195230	+	1.68805i
$595$	85.3966	−	68.9782i	0.143524	−	0.115930i
$596$			1203.83i			2.01985i
$597$	−874.888	−	198.785i	−1.46547	−	0.332973i
$598$	295.642	−	79.2172i	0.494385	−	0.132470i
$599$	−342.953	+	594.012i	−0.572542	+	0.991672i	0.423762	+	0.905774i	$0.360709\pi$
$599$	−342.953	+	594.012i	−0.572542	+	0.991672i	−0.996304	+	0.0858986i	$0.972624\pi$
$600$	421.036	+	50.3991i	0.701727	+	0.0839985i
$601$		−	491.319i		−	0.817502i	−0.912646	−	0.408751i	$-0.865964\pi$
$601$		−	491.319i		−	0.817502i	0.912646	−	0.408751i	$-0.134036\pi$
$602$	1261.52	+	34.3196i	2.09555	+	0.0570093i
$603$	340.865	−	397.668i	0.565282	−	0.659482i
$604$	87.8474	−	50.7187i	0.145443	−	0.0839714i
$605$	107.330	+	8.47068i	0.177406	+	0.0140011i
$606$	191.802	+	101.130i	0.316506	+	0.166881i
$607$	603.657	+	161.749i	0.994493	+	0.266473i	0.719136	−	0.694869i	$-0.244538\pi$
$607$	603.657	+	161.749i	0.994493	+	0.266473i	0.275356	+	0.961342i	$0.411204\pi$
$608$	971.197	−	971.197i	1.59736	−	1.59736i
$609$	138.421	−	540.709i	0.227292	−	0.887864i
$610$	129.601	−	365.728i	0.212461	−	0.599554i
$611$	261.371	−	150.902i	0.427775	−	0.246976i
$612$	154.576	−	54.4291i	0.252575	−	0.0889364i
$613$	248.162	+	926.155i	0.404833	+	1.51086i	0.804364	+	0.594137i	$0.202506\pi$
$613$	248.162	+	926.155i	0.404833	+	1.51086i	−0.399531	+	0.916719i	$0.630827\pi$
$614$	1311.51	−	757.198i	2.13600	−	1.23322i
$615$	617.078	+	192.357i	1.00338	+	0.312776i
$616$	−134.659	+	452.907i	−0.218602	+	0.735238i
$617$	519.079	−	519.079i	0.841294	−	0.841294i	−0.147733	−	0.989027i	$-0.547198\pi$
$617$	519.079	−	519.079i	0.841294	−	0.841294i	0.989027	+	0.147733i	$0.0471976\pi$
$618$	−1506.52	−	342.299i	−2.43774	−	0.553882i
$619$	370.531	−	641.779i	0.598597	−	1.03680i	−0.394432	−	0.918925i	$-0.629059\pi$
$619$	370.531	−	641.779i	0.598597	−	1.03680i	0.993029	−	0.117874i	$-0.0376080\pi$
$620$	22.6403	+	1.78680i	0.0365166	+	0.00288194i
$621$	−210.589	+	156.381i	−0.339113	+	0.251822i
$622$	−697.373	+	697.373i	−1.12118	+	1.12118i
$623$	−459.320	−	12.4958i	−0.737271	−	0.0200574i
$624$	166.421	−	6.39053i	0.266700	−	0.0102412i
$625$	−464.831	+	417.801i	−0.743729	+	0.668481i
$626$	−467.632	+	809.963i	−0.747016	+	1.29387i
$627$	1177.96	−	364.617i	1.87872	−	0.581526i
$628$	−170.744	+	637.225i	−0.271885	+	1.01469i
$629$		−	92.3848i		−	0.146876i
$630$	717.542	−	676.823i	1.13896	−	1.07432i
$631$	1132.04			1.79404			0.897022	−	0.441985i	$-0.145726\pi$
$631$	1132.04			1.79404			0.897022	+	0.441985i	$0.145726\pi$
$632$	420.801	+	112.753i	0.665825	+	0.178407i
$633$	134.489	+	434.488i	0.212463	+	0.686395i
$634$	−321.572	−	185.660i	−0.507211	−	0.292838i
$635$	−973.242	+	180.160i	−1.53266	+	0.283716i
$636$	11.8769	+	309.297i	0.0186744	+	0.486317i
$637$	−153.299	+	468.555i	−0.240657	+	0.735566i
$638$	−702.599	−	702.599i	−1.10125	−	1.10125i
$639$	−221.685	−	323.785i	−0.346925	−	0.506706i
$640$	−527.518	−	617.917i	−0.824247	−	0.965496i
$641$	−715.066	−	412.844i	−1.11555	−	0.644062i	−0.175287	−	0.984517i	$-0.556085\pi$
$641$	−715.066	−	412.844i	−1.11555	−	0.644062i	−0.940261	+	0.340455i	$0.889419\pi$
$642$	−179.825	+	791.444i	−0.280101	+	1.23278i
$643$	40.3544	+	40.3544i	0.0627595	+	0.0627595i	0.737790	−	0.675030i	$-0.235870\pi$
$643$	40.3544	+	40.3544i	0.0627595	+	0.0627595i	−0.675030	+	0.737790i	$0.735870\pi$
$644$	−383.990	+	91.7743i	−0.596257	+	0.142507i
$645$	−764.719	+	401.258i	−1.18561	+	0.622105i
$646$	−169.067	−	292.833i	−0.261714	−	0.453302i
$647$	474.537	−	127.152i	0.733442	−	0.196525i	0.127281	−	0.991867i	$-0.459375\pi$
$647$	474.537	−	127.152i	0.733442	−	0.196525i	0.606162	+	0.795342i	$0.292708\pi$
$648$	419.032	−	184.782i	0.646654	−	0.285158i
$649$	433.188	+	750.304i	0.667470	+	1.15609i
$650$	495.940	−	611.888i	0.762984	−	0.941366i
$651$	11.4871	−	11.7469i	0.0176453	−	0.0180444i
$652$	722.534	+	722.534i	1.10818	+	1.10818i
$653$	113.367	−	423.092i	0.173610	−	0.647921i	−0.823174	−	0.567789i	$-0.807799\pi$
$653$	113.367	−	423.092i	0.173610	−	0.647921i	0.996784	−	0.0801323i	$-0.0255343\pi$
$654$	448.663	−	850.931i	0.686028	−	1.30112i
$655$	−906.262	−	71.5235i	−1.38361	−	0.109196i
$656$	−118.882	−	205.910i	−0.181222	−	0.313886i
$657$	−2.01689	+	2.35299i	−0.00306985	+	0.00358142i
$658$	−578.165	+	313.156i	−0.878671	+	0.475921i
$659$	−777.010			−1.17907			−0.589537	−	0.807741i	$-0.700690\pi$
$659$	−777.010			−1.17907			−0.589537	+	0.807741i	$0.700690\pi$
$660$	−228.328	−	1014.28i	−0.345951	−	1.53679i
$661$	8.95181	+	5.16833i	0.0135428	+	0.00781896i	0.506756	−	0.862089i	$-0.330844\pi$
$661$	8.95181	+	5.16833i	0.0135428	+	0.00781896i	−0.493213	+	0.869908i	$0.664178\pi$
$662$	157.809	+	588.951i	0.238382	+	0.889654i
$663$	20.9751	−	92.3153i	0.0316366	−	0.139239i
$664$	−613.847			−0.924468
$665$	−973.986	−	709.485i	−1.46464	−	1.06689i
$666$	−63.6594	−	827.680i	−0.0955846	−	1.24276i
$667$	66.8290	−	249.409i	0.100193	−	0.373927i
$668$	50.0133	+	186.652i	0.0748702	+	0.279419i
$669$	49.3516	−	93.5999i	0.0737692	−	0.139910i
$670$	−516.256	+	750.806i	−0.770531	+	1.12061i
$671$	−295.867			−0.440935
$672$	−837.715	+	9.36830i	−1.24660	+	0.0139409i
$673$	179.773	−	179.773i	0.267121	−	0.267121i	−0.560818	−	0.827939i	$-0.689513\pi$
$673$	179.773	−	179.773i	0.267121	−	0.267121i	0.827939	+	0.560818i	$0.189513\pi$
$674$	−170.234	−	294.853i	−0.252572	−	0.437468i
$675$	−202.165	+	644.014i	−0.299504	+	0.954095i
$676$	196.732	−	340.749i	0.291023	−	0.504067i
$677$	−157.225	+	586.770i	−0.232237	+	0.866721i	0.747138	+	0.664669i	$0.231428\pi$
$677$	−157.225	+	586.770i	−0.232237	+	0.866721i	−0.979375	+	0.202052i	$0.935239\pi$
$678$	796.712	−	860.343i	1.17509	−	1.26894i
$679$	−515.445	+	123.192i	−0.759124	+	0.181432i
$680$	−80.0363	+	38.1539i	−0.117700	+	0.0561087i
$681$	−522.205	−	829.278i	−0.766821	−	1.21774i
$682$	−7.57018	−	28.2523i	−0.0111000	−	0.0414256i
$683$	188.011	−	50.3773i	0.275272	−	0.0737589i	−0.118542	−	0.992949i	$-0.537822\pi$
$683$	188.011	−	50.3773i	0.275272	−	0.0737589i	0.393814	+	0.919190i	$0.371155\pi$
$684$	−1016.26	−	1484.32i	−1.48577	−	2.17006i
$685$	−513.225	−	181.869i	−0.749234	−	0.265502i
$686$	361.621	−	1011.36i	0.527145	−	1.47428i
$687$	313.583	−	338.628i	0.456452	−	0.492908i
$688$	306.849	+	82.2199i	0.446001	+	0.119506i
$689$	154.849	+	89.4021i	0.224745	+	0.129756i
$690$	335.427	−	309.378i	0.486126	−	0.448373i
$691$	853.990	−	493.052i	1.23588	−	0.713533i	0.267627	−	0.963523i	$-0.413760\pi$
$691$	853.990	−	493.052i	1.23588	−	0.713533i	0.968249	+	0.249989i	$0.0804271\pi$
$692$	130.723	+	130.723i	0.188906	+	0.188906i
$693$	−669.203	−	343.337i	−0.965661	−	0.495435i
$694$		−	399.339i		−	0.575416i
$695$	513.860	−	747.321i	0.739367	−	1.07528i
$696$	−210.260	+	398.778i	−0.302098	+	0.572957i
$697$	−130.547	+	34.9798i	−0.187298	+	0.0501863i
$698$	−154.514	−	41.4020i	−0.221367	−	0.0593152i
$699$	157.570	−	6.05064i	0.225421	−	0.00865613i
$700$	−660.945	+	771.591i	−0.944207	+	1.10227i
$701$			693.931i			0.989917i	0.868917	+	0.494958i	$0.164817\pi$
$701$			693.931i			0.989917i	−0.868917	+	0.494958i	$0.835183\pi$
$702$	124.306	−	841.511i	0.177073	−	1.19873i
$703$	−979.550	+	262.470i	−1.39338	+	0.373356i
$704$	−613.957	+	1063.41i	−0.872098	+	1.51052i
$705$	240.525	−	380.275i	0.341170	−	0.539397i
$706$		−	271.374i		−	0.384382i
$707$	−142.069	+	76.9499i	−0.200946	+	0.108840i
$708$	858.764	−	927.350i	1.21294	−	1.30982i
$709$	281.100	−	162.293i	0.396473	−	0.228904i	−0.288488	−	0.957484i	$-0.593152\pi$
$709$	281.100	−	162.293i	0.396473	−	0.228904i	0.684961	+	0.728580i	$0.259819\pi$
$710$	443.231	+	519.187i	0.624269	+	0.731249i
$711$	−299.659	+	625.385i	−0.421462	+	0.879585i
$712$	358.483	+	96.0553i	0.503488	+	0.134909i
$713$	5.37454	−	5.37454i	0.00753792	−	0.00753792i
$714$	−51.1500	+	199.805i	−0.0716386	+	0.279840i
$715$	−566.092	−	200.603i	−0.791738	−	0.280564i
$716$	−132.693	+	76.6102i	−0.185325	+	0.106997i
$717$	113.193	+	365.689i	0.157871	+	0.510027i
$718$	−469.151	−	1750.89i	−0.653413	−	2.43857i
$719$	529.025	−	305.433i	0.735779	−	0.424802i	−0.0847533	−	0.996402i	$-0.527010\pi$
$719$	529.025	−	305.433i	0.735779	−	0.424802i	0.820533	+	0.571600i	$0.193677\pi$
$720$	215.279	−	123.719i	0.298999	−	0.171832i
$721$	835.849	−	791.575i	1.15929	−	1.09789i
$722$	−1825.23	+	1825.23i	−2.52802	+	2.52802i
$723$	−88.6336	+	390.093i	−0.122591	+	0.539547i
$724$	−94.2382	+	163.225i	−0.130163	+	0.225449i
$725$	−237.850	−	620.431i	−0.328069	−	0.855766i
$726$	−171.172	+	107.789i	−0.235774	+	0.148470i
$727$	104.280	−	104.280i	0.143439	−	0.143439i	−0.631741	−	0.775180i	$-0.717659\pi$
$727$	104.280	−	104.280i	0.143439	−	0.143439i	0.775180	+	0.631741i	$0.217659\pi$
$728$	208.400	−	339.303i	0.286264	−	0.466075i
$729$	166.398	+	709.755i	0.228256	+	0.973601i
$730$	3.05468	−	4.44251i	0.00418449	−	0.00608563i
$731$	90.2873	−	156.382i	0.123512	−	0.213929i
$732$	127.628	+	412.322i	0.174355	+	0.563282i
$733$	−9.31513	+	34.7645i	−0.0127082	+	0.0474277i	−0.971989	−	0.235027i	$-0.924482\pi$
$733$	−9.31513	+	34.7645i	−0.0127082	+	0.0474277i	0.959281	+	0.282455i	$0.0911488\pi$
$734$			940.560i			1.28142i
$735$	122.194	+	724.771i	0.166250	+	0.986084i
$736$	−387.565			−0.526582
$737$	671.111	+	179.824i	0.910598	+	0.243994i
$738$	−1145.47	+	403.341i	−1.55213	+	0.546533i
$739$	−235.115	−	135.743i	−0.318152	−	0.183685i	0.332416	−	0.943133i	$-0.392136\pi$
$739$	−235.115	−	135.743i	−0.318152	−	0.183685i	−0.650569	+	0.759447i	$0.725469\pi$
$740$	155.632	+	840.741i	0.210314	+	1.13614i
$741$	−1038.40	+	39.8745i	−1.40135	+	0.0538117i
$742$	−331.940	−	203.878i	−0.447358	−	0.274769i
$743$	389.786	+	389.786i	0.524611	+	0.524611i	0.918961	−	0.394349i	$-0.129030\pi$
$743$	389.786	+	389.786i	0.524611	+	0.524611i	−0.394349	+	0.918961i	$0.629030\pi$
$744$	−11.2295	+	7.07131i	−0.0150934	+	0.00950446i
$745$	1033.58	+	81.5715i	1.38735	+	0.109492i
$746$	−1288.58	−	743.960i	−1.72732	−	0.997266i
$747$	179.777	−	960.455i	0.240665	−	1.28575i
$748$	153.717	+	153.717i	0.205504	+	0.205504i
$749$	−415.850	−	439.109i	−0.555207	−	0.586261i
$750$	230.867	−	1151.35i	0.307822	−	1.53513i
$751$	515.279	+	892.489i	0.686124	+	1.18840i	0.973082	+	0.230458i	$0.0740225\pi$
$751$	515.279	+	892.489i	0.686124	+	1.18840i	−0.286958	+	0.957943i	$0.592644\pi$
$752$	−159.876	+	42.8387i	−0.212601	+	0.0569663i
$753$	234.714	+	758.284i	0.311706	+	1.00702i
$754$	418.679	+	725.174i	0.555278	+	0.961769i
$755$	−37.5932	−	78.8602i	−0.0497924	−	0.104451i
$756$	−189.803	+	1080.71i	−0.251062	+	1.42951i
$757$	770.070	+	770.070i	1.01727	+	1.01727i	0.999848	+	0.0174177i	$0.00554450\pi$
$757$	770.070	+	770.070i	1.01727	+	1.01727i	0.0174177	+	0.999848i	$0.494455\pi$
$758$	−403.102	+	1504.40i	−0.531797	+	1.98469i
$759$	−307.789	−	162.285i	−0.405519	−	0.213814i
$760$	631.930	+	740.222i	0.831487	+	0.973977i
$761$	−198.598	−	343.982i	−0.260970	−	0.452013i	0.705530	−	0.708680i	$-0.250709\pi$
$761$	−198.598	−	343.982i	−0.260970	−	0.452013i	−0.966500	+	0.256667i	$0.917376\pi$
$762$	1263.53	−	1364.44i	1.65817	−	1.79060i
$763$	341.388	+	630.288i	0.447429	+	0.826066i
$764$	1902.77			2.49054
$765$	−36.2573	−	136.403i	−0.0473952	−	0.178304i
$766$	−1607.21	−	927.923i	−2.09819	−	1.21139i
$767$	−188.970	−	705.244i	−0.246375	−	0.919484i
$768$	284.998	+	64.7549i	0.371092	+	0.0843163i
$769$	−548.417			−0.713156			−0.356578	−	0.934266i	$-0.616057\pi$
$769$	−548.417			−0.713156			−0.356578	+	0.934266i	$0.616057\pi$
$770$	1220.98	+	470.422i	1.58568	+	0.610937i
$771$	−429.519	+	16.4934i	−0.557094	+	0.0213923i
$772$	106.935	−	399.087i	0.138517	−	0.516952i
$773$	−141.402	−	527.718i	−0.182926	−	0.682688i	−0.995065	−	0.0992245i	$-0.968364\pi$
$773$	−141.402	−	527.718i	−0.182926	−	0.682688i	0.812139	−	0.583463i	$-0.198303\pi$
$774$	701.131	−	1463.25i	0.905854	−	1.89050i
$775$	3.06821	−	19.3173i	0.00395898	−	0.0249255i
$776$	428.050			0.551611
$777$	539.116	+	303.272i	0.693844	+	0.390311i
$778$	172.785	−	172.785i	0.222089	−	0.222089i
$779$	741.777	+	1284.80i	0.952217	+	1.64929i
$780$	−35.3673	+	875.443i	−0.0453427	+	1.12236i
$781$	260.267	−	450.795i	0.333248	−	0.577202i
$782$	−24.6950	+	92.1628i	−0.0315792	+	0.117855i
$783$	−562.369	−	445.773i	−0.718224	−	0.569315i
$784$	147.715	−	226.450i	0.188412	−	0.288839i
$785$	535.535	+	189.775i	0.682210	+	0.241751i
$786$	1445.32	−	910.132i	1.83883	−	1.15793i
$787$	249.035	+	929.410i	0.316435	+	1.18095i	0.922646	+	0.385649i	$0.126022\pi$
$787$	249.035	+	929.410i	0.316435	+	1.18095i	−0.606210	+	0.795305i	$0.707311\pi$
$788$	−503.375	+	134.879i	−0.638800	+	0.171166i
$789$	−580.652	−	922.092i	−0.735933	−	1.16868i
$790$	402.953	−	1137.12i	0.510068	−	1.43939i
$791$	203.105	+	849.807i	0.256771	+	1.07434i
$792$	461.246	+	395.362i	0.582381	+	0.499194i
$793$	240.841	+	64.5331i	0.303708	+	0.0813784i
$794$	−940.629	−	543.072i	−1.18467	−	0.683970i
$795$	266.359	+	10.7607i	0.335043	+	0.0135355i
$796$	−1503.61	+	868.112i	−1.88896	+	1.09059i
$797$	673.373	+	673.373i	0.844885	+	0.844885i	0.989490	−	0.144605i	$-0.0461910\pi$
$797$	673.373	+	673.373i	0.844885	+	0.844885i	−0.144605	+	0.989490i	$0.546191\pi$
$798$	2263.84	−	25.3169i	2.83690	−	0.0317254i
$799$			94.0839i			0.117752i
$800$	−807.123	+	585.871i	−1.00890	+	0.732338i
$801$	−255.282	+	532.769i	−0.318704	+	0.665130i
$802$	−2218.24	+	594.376i	−2.76589	+	0.741117i
$803$	−3.97095	−	1.06401i	−0.00494515	−	0.00132505i
$804$	−38.8926	−	1012.83i	−0.0483739	−	1.25974i
$805$	52.7759	+	335.902i	0.0655601	+	0.417270i
$806$			24.6490i			0.0305819i
$807$	−348.674	+	1534.58i	−0.432062	+	1.90158i
$808$	126.053	−	33.7759i	0.156007	−	0.0418018i
$809$	−247.264	+	428.274i	−0.305641	+	0.529386i	−0.977404	−	0.211380i	$-0.932204\pi$
$809$	−247.264	+	428.274i	−0.305641	+	0.529386i	0.671763	+	0.740767i	$0.265538\pi$
$810$	−418.822	−	1197.06i	−0.517064	−	1.47785i
$811$		−	809.347i		−	0.997962i	−0.866613	−	0.498981i	$-0.833708\pi$
$811$		−	809.347i		−	0.997962i	0.866613	−	0.498981i	$-0.166292\pi$
$812$	−514.420	−	949.749i	−0.633522	−	1.16964i
$813$	208.047	+	192.660i	0.255900	+	0.236974i
$814$	953.650	−	550.590i	1.17156	−	0.676401i
$815$	669.308	−	571.390i	0.821236	−	0.701092i
$816$	−24.2146	+	45.9252i	−0.0296747	+	0.0562809i
$817$	−1914.62	−	513.021i	−2.34348	−	0.627932i
$818$	−1049.95	+	1049.95i	−1.28356	+	1.28356i
$819$	469.856	+	425.445i	0.573694	+	0.519469i
$820$	1129.10	−	538.251i	1.37695	−	0.656404i
$821$	827.948	−	478.016i	1.00846	−	0.582236i	0.0977213	−	0.995214i	$-0.468845\pi$
$821$	827.948	−	478.016i	1.00846	−	0.582236i	0.910741	+	0.412978i	$0.135511\pi$
$822$	977.270	−	302.498i	1.18889	−	0.368002i
$823$	68.7769	+	256.679i	0.0835686	+	0.311882i	0.995039	−	0.0994828i	$-0.0317188\pi$
$823$	68.7769	+	256.679i	0.0835686	+	0.311882i	−0.911471	+	0.411365i	$0.865052\pi$
$824$	−805.243	+	464.907i	−0.977236	+	0.564208i
$825$	−886.307	+	127.309i	−1.07431	+	0.154314i
$826$	369.762	+	1547.11i	0.447654	+	1.87301i
$827$	775.831	−	775.831i	0.938127	−	0.938127i	−0.0600672	−	0.998194i	$-0.519131\pi$
$827$	775.831	−	775.831i	0.938127	−	0.938127i	0.998194	+	0.0600672i	$0.0191315\pi$
$828$	−93.3910	+	498.941i	−0.112791	+	0.602585i
$829$	660.449	−	1143.93i	0.796682	−	1.37989i	−0.125084	−	0.992146i	$-0.539920\pi$
$829$	660.449	−	1143.93i	0.796682	−	1.37989i	0.921766	−	0.387747i	$-0.126747\pi$
$830$	−133.741	+	1694.61i	−0.161134	+	2.04170i
$831$	426.110	+	676.675i	0.512768	+	0.814291i
$832$	731.716	−	731.716i	0.879466	−	0.879466i
$833$	−102.603	−	114.420i	−0.123172	−	0.137358i
$834$	65.3845	+	1702.73i	0.0783987	+	2.04165i
$835$	163.643	−	30.2926i	0.195980	−	0.0362785i
$836$	1193.13	−	2066.57i	1.42719	−	2.47197i
$837$	−7.77537	−	19.6411i	−0.00928957	−	0.0234661i
$838$	101.200	−	377.683i	0.120764	−	0.450696i
$839$		−	1167.63i		−	1.39169i	−0.718193	−	0.695843i	$-0.755031\pi$
$839$		−	1167.63i		−	1.39169i	0.718193	−	0.695843i	$-0.244969\pi$
$840$	40.0863	−	592.304i	0.0477218	−	0.705124i
$841$	−134.589			−0.160035
$842$	−1166.21	−	312.485i	−1.38505	−	0.371122i
$843$	299.849	−	92.8134i	0.355693	−	0.110099i
$844$	762.253	+	440.087i	0.903143	+	0.521430i
$845$	−279.228	−	191.998i	−0.330447	−	0.227216i
$846$	64.8301	+	842.903i	0.0766314	+	0.996339i
$847$	4.09908	−	150.674i	0.00483953	−	0.177892i
$848$	−69.3387	−	69.3387i	−0.0817674	−	0.0817674i
$849$	−153.063	−	243.069i	−0.180287	−	0.286301i
$850$	87.8914	+	229.264i	0.103402	+	0.269723i
$851$	247.819	+	143.079i	0.291210	+	0.168130i
$852$	−740.501	−	168.250i	−0.869133	−	0.197477i
$853$	196.296	+	196.296i	0.230124	+	0.230124i	0.812744	−	0.582621i	$-0.197973\pi$
$853$	196.296	+	196.296i	0.230124	+	0.230124i	−0.582621	+	0.812744i	$0.697973\pi$
$854$	−520.690	−	154.812i	−0.609707	−	0.181279i
$855$	−1343.26	+	771.961i	−1.57107	+	0.902878i
$856$	244.237	+	423.030i	0.285323	+	0.494194i
$857$	−1041.66	+	279.112i	−1.21547	+	0.325684i	−0.808906	−	0.587938i	$-0.799940\pi$
$857$	−1041.66	+	279.112i	−1.21547	+	0.325684i	−0.406564	+	0.913622i	$0.633273\pi$
$858$	1077.94	−	333.658i	1.25634	−	0.388879i
$859$	380.060	+	658.283i	0.442444	+	0.766336i	0.997870	−	0.0652300i	$-0.0207781\pi$
$859$	380.060	+	658.283i	0.442444	+	0.766336i	−0.555426	+	0.831566i	$0.687445\pi$
$860$	−558.210	+	1575.24i	−0.649082	+	1.83168i
$861$	224.419	−	876.639i	0.260649	−	1.01816i
$862$	−367.997	−	367.997i	−0.426911	−	0.426911i
$863$	−52.4932	+	195.907i	−0.0608264	+	0.227007i	−0.989647	−	0.143522i	$-0.954157\pi$
$863$	−52.4932	+	195.907i	−0.0608264	+	0.227007i	0.928821	+	0.370530i	$0.120824\pi$
$864$	−427.828	+	988.520i	−0.495171	+	1.14412i
$865$	121.093	−	103.377i	0.139992	−	0.119511i
$866$	494.751	+	856.934i	0.571306	+	0.989531i
$867$	−614.481	−	569.034i	−0.708744	−	0.656326i
$868$	0.864660	−	31.7832i	0.000996152	−	0.0366166i
$869$	−919.905			−1.05858
$870$	1055.07	+	667.337i	1.21273	+	0.767054i
$871$	−507.073	−	292.759i	−0.582173	−	0.336118i
$872$	−149.847	−	559.235i	−0.171842	−	0.641324i
$873$	−125.363	+	669.749i	−0.143600	+	0.767181i
$874$	1047.36			1.19835
$875$	617.682	+	619.753i	0.705922	+	0.708289i
$876$	0.230127	+	5.99293i	0.000262702	+	0.00684124i
$877$	340.203	−	1269.66i	0.387917	−	1.44773i	−0.445599	−	0.895233i	$-0.647009\pi$
$877$	340.203	−	1269.66i	0.387917	−	1.44773i	0.833516	−	0.552495i	$-0.186324\pi$
$878$	−259.916	−	970.019i	−0.296032	−	1.10481i
$879$	163.501	+	86.2078i	0.186008	+	0.0980749i
$880$	271.404	+	186.618i	0.308414	+	0.212066i
$881$	175.429			0.199125			0.0995623	−	0.995031i	$-0.468256\pi$
$881$	175.429			0.199125			0.0995623	+	0.995031i	$0.468256\pi$
$882$	−998.065	−	954.390i	−1.13159	−	1.08208i
$883$	21.1868	−	21.1868i	0.0239941	−	0.0239941i	−0.695008	−	0.719002i	$-0.744599\pi$
$883$	21.1868	−	21.1868i	0.0239941	−	0.0239941i	0.719002	+	0.695008i	$0.244599\pi$
$884$	−91.6003	−	158.656i	−0.103620	−	0.179475i
$885$	−738.009	−	800.149i	−0.833908	−	0.904124i
$886$	−578.348	+	1001.73i	−0.652763	+	1.13062i
$887$	−159.580	+	595.560i	−0.179909	+	0.671431i	0.815754	+	0.578399i	$0.196322\pi$
$887$	−159.580	+	595.560i	−0.179909	+	0.671431i	−0.995663	+	0.0930318i	$0.970344\pi$
$888$	−366.575	−	339.464i	−0.412810	−	0.382279i
$889$	322.110	+	1347.73i	0.362328	+	1.51601i
$890$	343.279	−	968.716i	0.385706	−	1.08845i
$891$	−753.687	+	605.899i	−0.845889	+	0.680021i
$892$	−52.9981	−	197.792i	−0.0594150	−	0.221740i
$893$	997.565	−	267.297i	1.11709	−	0.299324i
$894$	−1648.36	+	1037.99i	−1.84381	+	1.16107i
$895$	56.7842	+	119.118i	0.0634461	+	0.133092i
$896$	−825.873	+	782.128i	−0.921733	+	0.872910i
$897$	215.148	+	199.236i	0.239853	+	0.222114i
$898$	121.656	+	32.5977i	0.135475	+	0.0363003i
$899$	18.0084	+	10.3972i	0.0200316	+	0.0115652i
$900$	559.743	+	1180.25i	0.621936	+	1.31138i
$901$	−48.2722	+	27.8700i	−0.0535763	+	0.0309323i
$902$	−1139.11	−	1139.11i	−1.26287	−	1.26287i
$903$	616.190	+	1040.23i	0.682381	+	1.15197i
$904$		−	705.720i		−	0.780663i
$905$	133.755	+	91.9706i	0.147796	+	0.101625i
$906$	145.193	+	76.5546i	0.160257	+	0.0844973i
$907$	1251.30	−	335.284i	1.37960	−	0.369663i	0.508625	−	0.860988i	$-0.330154\pi$
$907$	1251.30	−	335.284i	1.37960	−	0.369663i	0.870976	+	0.491325i	$0.163487\pi$
$908$	−1831.86	−	490.846i	−2.01747	−	0.540579i
$909$	15.9303	+	207.121i	0.0175251	+	0.227856i
$910$	−891.288	−	649.244i	−0.979437	−	0.713455i
$911$		−	1273.56i		−	1.39798i	−0.715132	−	0.698989i	$-0.753634\pi$
$911$		−	1273.56i		−	1.39798i	0.715132	−	0.698989i	$-0.246366\pi$
$912$	555.736	+	126.270i	0.609360	+	0.138454i
$913$	1252.03	−	335.479i	1.37133	−	0.367447i
$914$	1301.93	−	2255.00i	1.42443	−	2.46718i
$915$	362.657	−	81.6388i	0.396346	−	0.0892228i
$916$		−	893.132i		−	0.975034i
$917$	−34.6112	+	1272.24i	−0.0377440	+	1.38739i
$918$	207.809	+	164.724i	0.226372	+	0.179438i
$919$	−908.766	+	524.676i	−0.988864	+	0.570921i	−0.904935	−	0.425551i	$-0.860080\pi$
$919$	−908.766	+	524.676i	−0.988864	+	0.570921i	−0.0839294	+	0.996472i	$0.526747\pi$
$920$	21.6075	−	273.785i	0.0234864	−	0.297592i
$921$	1283.39	+	676.681i	1.39347	+	0.734725i
$922$	303.752	+	81.3902i	0.329449	+	0.0882757i
$923$	−310.186	+	310.186i	−0.336063	+	0.336063i
$924$	−1401.63	+	392.417i	−1.51692	+	0.424693i
$925$	732.384	−	76.6532i	0.791767	−	0.0828683i
$926$	596.269	−	344.256i	0.643919	−	0.371767i
$927$	−491.586	−	1396.08i	−0.530298	−	1.50602i
$928$	−274.428	−	1024.18i	−0.295720	−	1.10364i
$929$	−244.701	+	141.278i	−0.263403	+	0.152076i	−0.625886	−	0.779915i	$-0.715262\pi$
$929$	−244.701	+	141.278i	−0.263403	+	0.152076i	0.362483	+	0.931990i	$0.381929\pi$
$930$	17.0748	+	32.5412i	0.0183600	+	0.0349905i
$931$	−921.683	+	1412.96i	−0.989993	+	1.51768i
$932$	215.775	−	215.775i	0.231518	−	0.231518i
$933$	−921.371	−	209.346i	−0.987536	−	0.224380i
$934$	−588.453	+	1019.23i	−0.630036	+	1.09125i
$935$	142.393	−	121.562i	0.152292	−	0.130012i
$936$	−289.227	−	422.436i	−0.309004	−	0.451320i
$937$	−271.472	+	271.472i	−0.289725	+	0.289725i	−0.836971	−	0.547247i	$-0.815676\pi$
$937$	−271.472	+	271.472i	−0.289725	+	0.289725i	0.547247	+	0.836971i	$0.315676\pi$
$938$	1086.98	+	667.626i	1.15883	+	0.711754i
$939$	−895.364	+	34.3818i	−0.953529	+	0.0366153i
$940$	−158.495	−	856.204i	−0.168611	−	0.910855i
$941$	−244.200	+	422.967i	−0.259511	+	0.449486i	−0.966111	−	0.258127i	$-0.916895\pi$
$941$	−244.200	+	422.967i	−0.259511	+	0.449486i	0.706600	+	0.707613i	$0.250228\pi$
$942$	−1019.75	+	315.648i	−1.08254	+	0.335082i
$943$	108.348	−	404.361i	0.114897	−	0.428803i
$944$			400.414i			0.424167i
$945$	915.008	+	236.189i	0.968263	+	0.249935i
$946$	2152.36			2.27522
$947$	−1101.67	−	295.191i	−1.16332	−	0.311711i	−0.375030	−	0.927013i	$-0.622368\pi$
$947$	−1101.67	−	295.191i	−1.16332	−	0.311711i	−0.788292	+	0.615301i	$0.789034\pi$
$948$	396.818	+	1281.99i	0.418584	+	1.35231i
$949$	3.00034	+	1.73225i	0.00316159	+	0.00182534i
$950$	2181.17	−	1583.26i	2.29597	−	1.66659i
$951$	−13.6503	−	355.478i	−0.0143536	−	0.373794i
$952$	59.1193	+	109.149i	0.0621001	+	0.114652i
$953$	354.436	+	354.436i	0.371916	+	0.371916i	0.868175	−	0.496258i	$-0.165293\pi$
$953$	354.436	+	354.436i	0.371916	+	0.371916i	−0.496258	+	0.868175i	$0.665293\pi$
$954$	−413.269	+	282.951i	−0.433196	+	0.296595i
$955$	128.932	−	1633.67i	0.135007	−	1.71065i
$956$	641.555	+	370.402i	0.671082	+	0.387450i
$957$	210.915	−	928.275i	0.220392	−	0.969985i
$958$	−203.346	−	203.346i	−0.212261	−	0.212261i
$959$	−217.248	+	730.682i	−0.226536	+	0.761921i
$960$	459.128	−	1472.87i	0.478258	−	1.53424i
$961$	−480.194	−	831.720i	−0.499682	−	0.865474i
$962$	−896.379	+	240.184i	−0.931787	+	0.249671i
$963$	−733.423	+	258.252i	−0.761603	+	0.268175i
$964$	387.071	+	670.427i	0.401526	+	0.695464i
$965$	−335.399	−	118.854i	−0.347564	−	0.123164i
$966$	−456.755	−	446.652i	−0.472831	−	0.462373i
$967$	−563.373	−	563.373i	−0.582599	−	0.582599i	0.353018	−	0.935617i	$-0.385155\pi$
$967$	−563.373	−	563.373i	−0.582599	−	0.582599i	−0.935617	+	0.353018i	$0.885155\pi$
$968$	−31.5098	+	117.596i	−0.0325514	+	0.121484i
$969$	151.090	−	286.556i	0.155923	−	0.295723i
$970$	93.2610	−	1181.69i	0.0961454	−	1.21824i
$971$	−673.469	−	1166.48i	−0.693583	−	1.20132i	−0.970656	−	0.240472i	$-0.922698\pi$
$971$	−673.469	−	1166.48i	−0.693583	−	1.20132i	0.277073	−	0.960849i	$-0.410635\pi$
$972$	1169.50	+	788.977i	1.20319	+	0.811705i
$973$	−1081.94	−	664.527i	−1.11196	−	0.682968i
$974$	−136.156			−0.139790
$975$	749.236	+	89.6854i	0.768447	+	0.0919850i
$976$	−118.421	−	68.3706i	−0.121333	−	0.0700518i
$977$	386.710	+	1443.22i	0.395814	+	1.47720i	0.820389	+	0.571806i	$0.193757\pi$
$977$	386.710	+	1443.22i	0.395814	+	1.47720i	−0.424575	+	0.905393i	$0.639577\pi$
$978$	−366.342	+	1612.34i	−0.374583	+	1.64861i
$979$	−783.673			−0.800483
$980$	1126.48	+	868.421i	1.14947	+	0.886144i
$981$	918.892	−	70.6747i	0.936689	−	0.0720436i
$982$	−119.803	+	447.109i	−0.121999	+	0.455305i
$983$	13.9523	+	52.0708i	0.0141936	+	0.0529713i	0.972659	−	0.232236i	$-0.0746042\pi$
$983$	13.9523	+	52.0708i	0.0141936	+	0.0529713i	−0.958466	+	0.285207i	$0.907938\pi$
$984$	−340.890	+	646.530i	−0.346433	+	0.657042i
$985$	81.6948	+	441.324i	0.0829389	+	0.448044i
$986$	−261.036			−0.264743
$987$	−549.032	−	308.849i	−0.556263	−	0.312917i
$988$	−1421.98	+	1421.98i	−1.43925	+	1.43925i
$989$	279.660	+	484.386i	0.282771	+	0.489773i
$990$	1191.95	−	1187.20i	1.20399	−	1.19919i
$991$	−448.670	+	777.120i	−0.452745	+	0.784177i	−0.998555	−	0.0537313i	$-0.982889\pi$
$991$	−448.670	+	777.120i	−0.452745	+	0.784177i	0.545810	+	0.837909i	$0.316222\pi$
$992$	8.07824	−	30.1484i	0.00814338	−	0.0303915i
$993$	−396.899	+	428.598i	−0.399697	+	0.431619i
$994$	693.916	−	657.160i	0.698104	−	0.661126i
$995$	643.453	+	1349.79i	0.646687	+	1.35657i
$996$	−1007.61	−	1600.12i	−1.01166	−	1.60654i
$997$	225.975	+	843.351i	0.226655	+	0.845889i	0.981735	+	0.190256i	$0.0609317\pi$
$997$	225.975	+	843.351i	0.226655	+	0.845889i	−0.755079	+	0.655634i	$0.772402\pi$
$998$	997.353	−	267.240i	0.999351	−	0.267775i
$999$	638.500	−	474.144i	0.639139	−	0.474618i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.w.a.17.25	yes	112
3.2	odd	2	inner	105.3.w.a.17.4	✓	112
5.3	odd	4	inner	105.3.w.a.38.25	yes	112
7.5	odd	6	inner	105.3.w.a.47.4	yes	112
15.8	even	4	inner	105.3.w.a.38.4	yes	112
21.5	even	6	inner	105.3.w.a.47.25	yes	112
35.33	even	12	inner	105.3.w.a.68.4	yes	112
105.68	odd	12	inner	105.3.w.a.68.25	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.4	✓	112	3.2	odd	2	inner
105.3.w.a.17.25	yes	112	1.1	even	1	trivial
105.3.w.a.38.4	yes	112	15.8	even	4	inner
105.3.w.a.38.25	yes	112	5.3	odd	4	inner
105.3.w.a.47.4	yes	112	7.5	odd	6	inner
105.3.w.a.47.25	yes	112	21.5	even	6	inner
105.3.w.a.68.4	yes	112	35.33	even	12	inner
105.3.w.a.68.25	yes	112	105.68	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.02468 + 0.810462i) q^{2} +(0.887077 + 2.86585i) q^{3} +(5.02776 + 2.90278i) q^{4} +(2.83293 - 4.12001i) q^{5} +(0.360468 + 9.38723i) q^{6} +(-5.96475 - 3.66357i) q^{7} +(3.99791 + 3.99791i) q^{8} +(-7.42619 + 5.08446i) q^{9} +(11.9078 - 10.1658i) q^{10} +(-10.3392 - 5.96936i) q^{11} +(-3.85892 + 16.9838i) q^{12} +(7.11430 + 7.11430i) q^{13} +(-15.0723 - 15.9153i) q^{14} +(14.3204 + 4.46398i) q^{15} +(-2.75886 - 4.77849i) q^{16} +(-3.02956 + 0.811768i) q^{17} +(-26.5826 + 9.36025i) q^{18} +(17.2142 + 29.8159i) q^{19} +(26.2028 - 12.4911i) q^{20} +(5.20803 - 20.3440i) q^{21} +(-26.4350 - 26.4350i) q^{22} +(2.51441 - 9.38391i) q^{23} +(-7.91095 + 15.0039i) q^{24} +(-8.94900 - 23.3434i) q^{25} +(15.7526 + 27.2844i) q^{26} +(-21.1589 - 16.7720i) q^{27} +(-19.3548 - 35.7339i) q^{28} +26.5784 q^{29} +(39.6967 + 25.1082i) q^{30} +(0.677558 + 0.391188i) q^{31} +(-10.3252 - 38.5343i) q^{32} +(7.93558 - 34.9260i) q^{33} -9.82137 q^{34} +(-31.9917 + 14.1962i) q^{35} +(-52.0962 + 4.00687i) q^{36} +(-7.62362 + 28.4517i) q^{37} +(27.9030 + 104.135i) q^{38} +(-14.0776 + 26.6994i) q^{39} +(27.7972 - 5.14563i) q^{40} +43.0909 q^{41} +(32.2406 - 57.3131i) q^{42} +(-40.7104 + 40.7104i) q^{43} +(-34.6554 - 60.0250i) q^{44} +(-0.0898378 + 44.9999i) q^{45} +(15.2106 - 26.3455i) q^{46} +(7.76382 - 28.9750i) q^{47} +(11.2471 - 12.1454i) q^{48} +(22.1566 + 43.7045i) q^{49} +(-8.14895 - 77.8593i) q^{50} +(-5.01386 - 7.96216i) q^{51} +(15.1177 + 56.4202i) q^{52} +(17.1662 - 4.59967i) q^{53} +(-50.4059 - 67.8785i) q^{54} +(-53.8841 + 25.6870i) q^{55} +(-9.19994 - 38.4931i) q^{56} +(-70.1776 + 75.7825i) q^{57} +(80.3912 + 21.5408i) q^{58} +(-62.8463 - 36.2843i) q^{59} +(59.0414 + 64.0127i) q^{60} +(21.4620 - 12.3911i) q^{61} +(1.73236 + 1.73236i) q^{62} +(62.9226 - 3.12123i) q^{63} -102.852i q^{64} +(49.4653 - 9.15668i) q^{65} +(52.3088 - 99.2085i) q^{66} +(-56.2130 + 15.0622i) q^{67} +(-17.5883 - 4.71277i) q^{68} +(29.1233 - 1.11833i) q^{69} +(-108.270 + 17.0111i) q^{70} +43.6004i q^{71} +(-50.0164 - 9.36201i) q^{72} +(0.332612 - 0.0891230i) q^{73} +(-46.1180 + 79.8788i) q^{74} +(58.9603 - 46.3539i) q^{75} +199.877i q^{76} +(39.8018 + 73.4842i) q^{77} +(-64.2191 + 69.3480i) q^{78} +(66.7293 - 38.5262i) q^{79} +(-27.5031 - 2.17059i) q^{80} +(29.2965 - 75.5163i) q^{81} +(130.336 + 34.9235i) q^{82} +(-76.7710 + 76.7710i) q^{83} +(85.2387 - 87.1668i) q^{84} +(-5.23804 + 14.7815i) q^{85} +(-156.130 + 90.1420i) q^{86} +(23.5771 + 76.1697i) q^{87} +(-17.4703 - 65.2002i) q^{88} +(56.8471 - 32.8207i) q^{89} +(-36.7424 + 136.038i) q^{90} +(-16.3713 - 68.4987i) q^{91} +(39.8813 - 39.8813i) q^{92} +(-0.520041 + 2.28879i) q^{93} +(46.9662 - 81.3479i) q^{94} +(171.609 + 13.5436i) q^{95} +(101.274 - 63.7735i) q^{96} +(53.5343 - 53.5343i) q^{97} +(31.5958 + 150.149i) q^{98} +(107.132 - 8.23984i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) \) 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Introduction

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