LMFDB - Embedded newform 93.3.l.b.2.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [93,3,Mod(2,93)] 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("93.2"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(93, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	93.l (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.53406645855$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			2.16
Character	$\chi$	$=$	93.2
Dual form			93.3.l.b.47.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.72290 - 2.37137i) q^{2} +(0.220544 - 2.99188i) q^{3} +(-1.41895 - 4.36707i) q^{4} -1.18691i q^{5} +(-6.71489 - 5.67772i) q^{6} +(2.57067 + 7.91172i) q^{7} +(-1.64979 - 0.536048i) q^{8} +(-8.90272 - 1.31968i) q^{9} +(-2.81460 - 2.04493i) q^{10} +(1.50860 - 0.490174i) q^{11} +(-13.3787 + 3.28219i) q^{12} +(-4.41547 + 3.20803i) q^{13} +(23.1906 + 7.53510i) q^{14} +(-3.55109 - 0.261765i) q^{15} +(10.7458 - 7.80728i) q^{16} +(15.9907 + 5.19568i) q^{17} +(-18.4680 + 18.8380i) q^{18} +(-10.5154 - 7.63990i) q^{19} +(-5.18331 + 1.68416i) q^{20} +(24.2379 - 5.94627i) q^{21} +(1.43679 - 4.42197i) q^{22} +(-23.7062 - 7.70260i) q^{23} +(-1.96764 + 4.81774i) q^{24} +23.5912 q^{25} +15.9979i q^{26} +(-5.91177 + 26.3448i) q^{27} +(30.9033 - 22.4526i) q^{28} +(-16.2622 + 22.3830i) q^{29} +(-6.73893 + 7.96996i) q^{30} +(30.8279 - 3.26159i) q^{31} -45.8723i q^{32} +(-1.13383 - 4.62166i) q^{33} +(39.8713 - 28.9682i) q^{34} +(9.39048 - 3.05115i) q^{35} +(6.86934 + 40.7513i) q^{36} -36.9813 q^{37} +(-36.2341 + 11.7732i) q^{38} +(8.62424 + 13.9181i) q^{39} +(-0.636240 + 1.95815i) q^{40} +(-24.3085 + 33.4578i) q^{41} +(27.6587 - 67.7219i) q^{42} +(31.1808 + 22.6541i) q^{43} +(-4.28124 - 5.89262i) q^{44} +(-1.56634 + 10.5667i) q^{45} +(-59.1092 + 42.9453i) q^{46} +(22.1879 + 30.5390i) q^{47} +(-20.9886 - 33.8720i) q^{48} +(-16.3451 + 11.8754i) q^{49} +(40.6454 - 55.9436i) q^{50} +(19.0715 - 46.6963i) q^{51} +(20.2750 + 14.7306i) q^{52} +(-89.4756 - 29.0724i) q^{53} +(52.2880 + 59.4086i) q^{54} +(-0.581791 - 1.79057i) q^{55} -14.4306i q^{56} +(-25.1768 + 29.7760i) q^{57} +(25.0603 + 77.1276i) q^{58} +(33.1246 + 45.5922i) q^{59} +(3.89566 + 15.8793i) q^{60} -87.3157 q^{61} +(45.3791 - 78.7240i) q^{62} +(-12.4450 - 73.8283i) q^{63} +(-65.7970 - 47.8043i) q^{64} +(3.80764 + 5.24076i) q^{65} +(-12.9132 - 5.27393i) q^{66} -46.1911 q^{67} -77.2047i q^{68} +(-28.2735 + 69.2273i) q^{69} +(8.94347 - 27.5252i) q^{70} +(-19.6473 - 6.38380i) q^{71} +(13.9802 + 6.94948i) q^{72} +(-34.2810 - 105.506i) q^{73} +(-63.7153 + 87.6966i) q^{74} +(5.20290 - 70.5822i) q^{75} +(-18.4431 + 56.7621i) q^{76} +(7.75623 + 10.6755i) q^{77} +(47.8637 + 3.52823i) q^{78} +(42.2073 - 129.901i) q^{79} +(-9.26653 - 12.7543i) q^{80} +(77.5169 + 23.4975i) q^{81} +(37.4597 + 115.289i) q^{82} +(-7.27204 + 10.0091i) q^{83} +(-60.3600 - 97.4110i) q^{84} +(6.16680 - 18.9795i) q^{85} +(107.443 - 34.9103i) q^{86} +(63.3808 + 53.5911i) q^{87} -2.75162 q^{88} +(94.5161 - 30.7102i) q^{89} +(22.3590 + 21.9198i) q^{90} +(-36.7318 - 26.6872i) q^{91} +114.456i q^{92} +(-2.95940 - 92.9529i) q^{93} +110.647 q^{94} +(-9.06786 + 12.4808i) q^{95} +(-137.244 - 10.1168i) q^{96} +(37.9940 + 116.933i) q^{97} +59.2204i q^{98} +(-14.0775 + 2.37301i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 5 q^{3} + 36 q^{4} - 10 q^{6} - 54 q^{7} + 5 q^{9} + 114 q^{10} + 14 q^{12} + 26 q^{13} + 35 q^{15} - 184 q^{16} + 15 q^{18} - 90 q^{19} + 71 q^{21} - 114 q^{22} - 101 q^{24} - 188 q^{25} + 116 q^{27}+ \cdots - 616 q^{99}+O(q^{100}) $ 72 * q + 5 * q^3 + 36 * q^4 - 10 * q^6 - 54 * q^7 + 5 * q^9 + 114 * q^10 + 14 * q^12 + 26 * q^13 + 35 * q^15 - 184 * q^16 + 15 * q^18 - 90 * q^19 + 71 * q^21 - 114 * q^22 - 101 * q^24 - 188 * q^25 + 116 * q^27 - 84 * q^28 - 18 * q^30 + 28 * q^31 - 242 * q^33 - 82 * q^34 + 74 * q^36 + 364 * q^37 + 13 * q^39 + 252 * q^40 - 46 * q^42 - 146 * q^43 + 52 * q^45 - 88 * q^46 - 170 * q^48 - 60 * q^49 - 301 * q^51 - 222 * q^52 - 118 * q^54 + 308 * q^55 - 20 * q^57 - 280 * q^58 - 407 * q^60 + 84 * q^61 + 556 * q^63 + 1450 * q^64 + 550 * q^66 - 324 * q^67 + 355 * q^69 + 728 * q^70 - 631 * q^72 - 140 * q^73 - 17 * q^75 - 622 * q^76 + 679 * q^78 - 200 * q^79 + 5 * q^81 + 598 * q^82 + 1197 * q^84 - 200 * q^85 + 202 * q^87 + 388 * q^88 + 1068 * q^90 + 834 * q^91 + 74 * q^93 - 384 * q^94 - 1016 * q^96 - 1074 * q^97 - 616 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.72290	−	2.37137i	0.861452	−	1.18569i	−0.119770	−	0.992802i	$-0.538216\pi$
$2$	1.72290	−	2.37137i	0.861452	−	1.18569i	0.981221	−	0.192885i	$-0.0617844\pi$
$3$	0.220544	−	2.99188i	0.0735146	−	0.997294i
$3$	0.220544	−	2.99188i	0.0735146	−	0.997294i
$4$	−1.41895	−	4.36707i	−0.354736	−	1.09177i
$5$		−	1.18691i		−	0.237382i	−0.992931	−	0.118691i	$-0.962130\pi$
$5$		−	1.18691i		−	0.237382i	0.992931	−	0.118691i	$-0.0378697\pi$
$6$	−6.71489	−	5.67772i	−1.11915	−	0.946286i
$7$	2.57067	+	7.91172i	0.367239	+	1.13025i	0.948567	+	0.316576i	$0.102533\pi$
$7$	2.57067	+	7.91172i	0.367239	+	1.13025i	−0.581328	+	0.813669i	$0.697467\pi$
$8$	−1.64979	−	0.536048i	−0.206223	−	0.0670060i
$9$	−8.90272	−	1.31968i	−0.989191	−	0.146631i
$10$	−2.81460	−	2.04493i	−0.281460	−	0.204493i
$11$	1.50860	−	0.490174i	0.137145	−	0.0445612i	−0.239640	−	0.970862i	$-0.577029\pi$
$11$	1.50860	−	0.490174i	0.137145	−	0.0445612i	0.376785	+	0.926301i	$0.377029\pi$
$12$	−13.3787	+	3.28219i	−1.11489	+	0.273516i
$13$	−4.41547	+	3.20803i	−0.339652	+	0.246772i	−0.744515	−	0.667606i	$-0.767319\pi$
$13$	−4.41547	+	3.20803i	−0.339652	+	0.246772i	0.404863	+	0.914377i	$0.367319\pi$
$14$	23.1906	+	7.53510i	1.65647	+	0.538221i
$15$	−3.55109	−	0.261765i	−0.236739	−	0.0174510i
$16$	10.7458	−	7.80728i	0.671613	−	0.487955i
$17$	15.9907	+	5.19568i	0.940627	+	0.305628i	0.738901	−	0.673814i	$-0.235345\pi$
$17$	15.9907	+	5.19568i	0.940627	+	0.305628i	0.201726	+	0.979442i	$0.435345\pi$
$18$	−18.4680	+	18.8380i	−1.02600	+	1.04655i
$19$	−10.5154	−	7.63990i	−0.553443	−	0.402100i	0.275610	−	0.961269i	$-0.411120\pi$
$19$	−10.5154	−	7.63990i	−0.553443	−	0.402100i	−0.829053	+	0.559170i	$0.811120\pi$
$20$	−5.18331	+	1.68416i	−0.259165	+	0.0842079i
$21$	24.2379	−	5.94627i	1.15418	−	0.283156i
$22$	1.43679	−	4.42197i	0.0653085	−	0.200999i
$23$	−23.7062	−	7.70260i	−1.03070	−	0.334896i	−0.255635	−	0.966773i	$-0.582284\pi$
$23$	−23.7062	−	7.70260i	−1.03070	−	0.334896i	−0.775068	+	0.631878i	$0.782284\pi$
$24$	−1.96764	+	4.81774i	−0.0819851	+	0.200739i
$25$	23.5912			0.943650
$26$			15.9979i			0.615302i
$27$	−5.91177	+	26.3448i	−0.218955	+	0.975735i
$28$	30.9033	−	22.4526i	1.10369	−	0.801878i
$29$	−16.2622	+	22.3830i	−0.560766	+	0.771828i	−0.991424	−	0.130687i	$-0.958282\pi$
$29$	−16.2622	+	22.3830i	−0.560766	+	0.771828i	0.430658	+	0.902515i	$0.358282\pi$
$30$	−6.73893	+	7.96996i	−0.224631	+	0.265665i
$31$	30.8279	−	3.26159i	0.994450	−	0.105213i
$31$	30.8279	−	3.26159i	0.994450	−	0.105213i
$32$		−	45.8723i		−	1.43351i
$33$	−1.13383	−	4.62166i	−0.0343585	−	0.140050i
$34$	39.8713	−	28.9682i	1.17268	−	0.852005i
$35$	9.39048	−	3.05115i	0.268299	−	0.0871758i
$36$	6.86934	+	40.7513i	0.190815	+	1.13198i
$37$	−36.9813			−0.999496			−0.499748	−	0.866171i	$-0.666574\pi$
$37$	−36.9813			−0.999496			−0.499748	+	0.866171i	$0.666574\pi$
$38$	−36.2341	+	11.7732i	−0.953529	+	0.309820i
$39$	8.62424	+	13.9181i	0.221134	+	0.356874i
$40$	−0.636240	+	1.95815i	−0.0159060	+	0.0489536i
$41$	−24.3085	+	33.4578i	−0.592890	+	0.816043i	−0.995034	−	0.0995330i	$-0.968265\pi$
$41$	−24.3085	+	33.4578i	−0.592890	+	0.816043i	0.402144	+	0.915576i	$0.368265\pi$
$42$	27.6587	−	67.7219i	0.658540	−	1.61243i
$43$	31.1808	+	22.6541i	0.725134	+	0.526841i	0.888020	−	0.459804i	$-0.152080\pi$
$43$	31.1808	+	22.6541i	0.725134	+	0.526841i	−0.162886	+	0.986645i	$0.552080\pi$
$44$	−4.28124	−	5.89262i	−0.0973010	−	0.133923i
$45$	−1.56634	+	10.5667i	−0.0348076	+	0.234816i
$46$	−59.1092	+	42.9453i	−1.28498	+	0.933594i
$47$	22.1879	+	30.5390i	0.472083	+	0.649766i	0.976959	−	0.213425i	$-0.0684620\pi$
$47$	22.1879	+	30.5390i	0.472083	+	0.649766i	−0.504877	+	0.863192i	$0.668462\pi$
$48$	−20.9886	−	33.8720i	−0.437262	−	0.705667i
$49$	−16.3451	+	11.8754i	−0.333573	+	0.242355i
$50$	40.6454	−	55.9436i	0.812909	−	1.11887i
$51$	19.0715	−	46.6963i	0.373951	−	0.915614i
$52$	20.2750	+	14.7306i	0.389904	+	0.283282i
$53$	−89.4756	−	29.0724i	−1.68822	−	0.548535i	−0.701741	−	0.712432i	$-0.747594\pi$
$53$	−89.4756	−	29.0724i	−1.68822	−	0.548535i	−0.986477	+	0.163897i	$0.947594\pi$
$54$	52.2880	+	59.4086i	0.968297	+	1.10016i
$55$	−0.581791	−	1.79057i	−0.0105780	−	0.0325558i
$56$		−	14.4306i		−	0.257690i
$57$	−25.1768	+	29.7760i	−0.441698	+	0.522385i
$58$	25.0603	+	77.1276i	0.432074	+	1.32979i
$59$	33.1246	+	45.5922i	0.561435	+	0.772748i	0.991508	−	0.130045i	$-0.0415123\pi$
$59$	33.1246	+	45.5922i	0.561435	+	0.772748i	−0.430073	+	0.902794i	$0.641512\pi$
$60$	3.89566	+	15.8793i	0.0649277	+	0.264655i
$61$	−87.3157			−1.43140			−0.715702	−	0.698406i	$-0.753893\pi$
$61$	−87.3157			−1.43140			−0.715702	+	0.698406i	$0.753893\pi$
$62$	45.3791	−	78.7240i	0.731921	−	1.26974i
$63$	−12.4450	−	73.8283i	−0.197540	−	1.17188i
$64$	−65.7970	−	47.8043i	−1.02808	−	0.746943i
$65$	3.80764	+	5.24076i	0.0585790	+	0.0806271i
$66$	−12.9132	−	5.27393i	−0.195654	−	0.0799081i
$67$	−46.1911			−0.689420			−0.344710	−	0.938709i	$-0.612023\pi$
$67$	−46.1911			−0.689420			−0.344710	+	0.938709i	$0.612023\pi$
$68$		−	77.2047i		−	1.13536i
$69$	−28.2735	+	69.2273i	−0.409761	+	1.00329i
$70$	8.94347	−	27.5252i	0.127764	−	0.393217i
$71$	−19.6473	−	6.38380i	−0.276723	−	0.0899127i	0.167368	−	0.985895i	$-0.446473\pi$
$71$	−19.6473	−	6.38380i	−0.276723	−	0.0899127i	−0.444091	+	0.895982i	$0.646473\pi$
$72$	13.9802	+	6.94948i	0.194169	+	0.0965205i
$73$	−34.2810	−	105.506i	−0.469603	−	1.44529i	−0.853101	−	0.521746i	$-0.825281\pi$
$73$	−34.2810	−	105.506i	−0.469603	−	1.44529i	0.383498	−	0.923542i	$-0.374719\pi$
$74$	−63.7153	+	87.6966i	−0.861017	+	1.18509i
$75$	5.20290	−	70.5822i	0.0693720	−	0.941097i
$76$	−18.4431	+	56.7621i	−0.242673	+	0.746870i
$77$	7.75623	+	10.6755i	0.100730	+	0.138643i
$78$	47.8637	+	3.52823i	0.613637	+	0.0452337i
$79$	42.2073	−	129.901i	0.534269	−	1.64431i	−0.210953	−	0.977496i	$-0.567657\pi$
$79$	42.2073	−	129.901i	0.534269	−	1.64431i	0.745222	−	0.666816i	$-0.232343\pi$
$80$	−9.26653	−	12.7543i	−0.115832	−	0.159429i
$81$	77.5169	+	23.4975i	0.956999	+	0.290093i
$82$	37.4597	+	115.289i	0.456825	+	1.40596i
$83$	−7.27204	+	10.0091i	−0.0876149	+	0.120592i	−0.850574	−	0.525855i	$-0.823746\pi$
$83$	−7.27204	+	10.0091i	−0.0876149	+	0.120592i	0.762959	+	0.646446i	$0.223746\pi$
$84$	−60.3600	−	97.4110i	−0.718571	−	1.15965i
$85$	6.16680	−	18.9795i	0.0725506	−	0.223288i
$86$	107.443	−	34.9103i	1.24934	−	0.405934i
$87$	63.3808	+	53.5911i	0.728515	+	0.615989i
$88$	−2.75162			−0.0312684
$89$	94.5161	−	30.7102i	1.06198	−	0.345058i	0.274620	−	0.961553i	$-0.411448\pi$
$89$	94.5161	−	30.7102i	1.06198	−	0.345058i	0.787359	+	0.616495i	$0.211448\pi$
$90$	22.3590	+	21.9198i	0.248433	+	0.243553i
$91$	−36.7318	−	26.6872i	−0.403646	−	0.293266i
$92$			114.456i			1.24409i
$93$	−2.95940	−	92.9529i	−0.0318215	−	0.999494i
$94$	110.647			1.17710
$95$	−9.06786	+	12.4808i	−0.0954511	+	0.131377i
$96$	−137.244	−	10.1168i	−1.42963	−	0.105384i
$97$	37.9940	+	116.933i	0.391690	+	1.20550i	0.931509	+	0.363718i	$0.118493\pi$
$97$	37.9940	+	116.933i	0.391690	+	1.20550i	−0.539819	+	0.841781i	$0.681507\pi$
$98$			59.2204i			0.604289i
$99$	−14.0775	+	2.37301i	−0.142197	+	0.0239698i
$100$	−33.4747	−	103.025i	−0.334747	−	1.03025i
$101$	−108.279	−	35.1820i	−1.07207	−	0.348337i	−0.280777	−	0.959773i	$-0.590592\pi$
$101$	−108.279	−	35.1820i	−1.07207	−	0.348337i	−0.791294	+	0.611436i	$0.790592\pi$
$102$	−77.8760	−	125.679i	−0.763490	−	1.23215i
$103$	44.4579	+	32.3006i	0.431631	+	0.313598i	0.782301	−	0.622901i	$-0.214046\pi$
$103$	44.4579	+	32.3006i	0.431631	+	0.313598i	−0.350670	+	0.936499i	$0.614046\pi$
$104$	9.00425	−	2.92566i	0.0865793	−	0.0281313i
$105$	−7.05768	−	28.7681i	−0.0672160	−	0.273982i
$106$	−223.099	+	162.091i	−2.10471	+	1.52916i
$107$	85.9943	+	27.9412i	0.803685	+	0.261133i	0.681921	−	0.731426i	$-0.261145\pi$
$107$	85.9943	+	27.9412i	0.803685	+	0.261133i	0.121764	+	0.992559i	$0.461145\pi$
$108$	123.438	−	11.5648i	1.14295	−	0.107082i
$109$	−122.418	+	88.9422i	−1.12310	+	0.815983i	−0.984677	−	0.174389i	$-0.944205\pi$
$109$	−122.418	+	88.9422i	−1.12310	+	0.815983i	−0.138428	+	0.990373i	$0.544205\pi$
$110$	−5.24848	−	1.70533i	−0.0477134	−	0.0155030i
$111$	−8.15600	+	110.644i	−0.0734775	+	0.996791i
$112$	89.3929	+	64.9478i	0.798151	+	0.579891i
$113$	139.878	−	45.4492i	1.23786	−	0.402205i	0.384304	−	0.923207i	$-0.374441\pi$
$113$	139.878	−	45.4492i	1.23786	−	0.402205i	0.853556	+	0.521002i	$0.174441\pi$
$114$	27.2327	+	111.005i	0.238884	+	0.973725i
$115$	−9.14228	+	28.1370i	−0.0794981	+	0.244670i
$116$	120.823	+	39.2579i	1.04158	+	0.338430i
$117$	43.5433	−	22.7332i	0.372165	−	0.194301i
$118$	165.187			1.39989
$119$			139.870i			1.17538i
$120$	5.71822	+	2.33541i	0.0476518	+	0.0194618i
$121$	−95.8555	+	69.6431i	−0.792194	+	0.575563i
$122$	−150.436	+	207.058i	−1.23309	+	1.69720i
$123$	94.7407	+	80.1071i	0.770249	+	0.651277i
$124$	−57.9868	−	130.000i	−0.467635	−	1.04838i
$125$		−	57.6734i		−	0.461387i
$126$	−196.516	−	97.6872i	−1.55965	−	0.775295i
$127$	122.727	−	89.1667i	0.966358	−	0.702100i	0.0117392	−	0.999931i	$-0.496263\pi$
$127$	122.727	−	89.1667i	0.966358	−	0.702100i	0.954619	+	0.297831i	$0.0962632\pi$
$128$	−52.2153	+	16.9658i	−0.407932	+	0.132545i
$129$	74.6553	−	88.2929i	0.578723	−	0.684441i
$130$	18.9880			0.146062
$131$	144.081	−	46.8148i	1.09986	−	0.357365i	0.297809	−	0.954625i	$-0.403744\pi$
$131$	144.081	−	46.8148i	1.09986	−	0.357365i	0.802047	+	0.597260i	$0.203744\pi$
$132$	−18.5742	+	11.5094i	−0.140714	+	0.0871924i
$133$	33.4130	−	102.835i	0.251226	−	0.773193i
$134$	−79.5829	+	109.536i	−0.593902	+	0.817436i
$135$	31.2689	+	7.01673i	0.231622	+	0.0519758i
$136$	−23.5960	−	17.1435i	−0.173500	−	0.126055i
$137$	−31.6778	−	43.6008i	−0.231225	−	0.318254i	0.677601	−	0.735430i	$-0.263020\pi$
$137$	−31.6778	−	43.6008i	−0.231225	−	0.318254i	−0.908826	+	0.417176i	$0.863020\pi$
$138$	115.451	+	186.319i	0.836603	+	1.35014i
$139$	−46.8961	+	34.0720i	−0.337382	+	0.245123i	−0.743557	−	0.668673i	$-0.766863\pi$
$139$	−46.8961	+	34.0720i	−0.337382	+	0.245123i	0.406174	+	0.913796i	$0.366863\pi$
$140$	−26.6492	−	36.6794i	−0.190351	−	0.261996i
$141$	96.2625	−	59.6484i	0.682713	−	0.423038i
$142$	−48.9888	+	35.5925i	−0.344992	+	0.250651i
$143$	−5.08869	+	7.00398i	−0.0355852	+	0.0489789i
$144$	−105.970	+	55.3250i	−0.735903	+	0.384202i
$145$	26.5666	+	19.3018i	0.183218	+	0.133116i
$146$	−309.257	−	100.484i	−2.11820	−	0.688244i
$147$	31.9249	+	51.5215i	0.217176	+	0.350487i
$148$	52.4745	+	161.500i	0.354558	+	1.09122i
$149$		−	209.253i		−	1.40438i	−0.711988	−	0.702192i	$-0.752205\pi$
$149$		−	209.253i		−	1.40438i	0.711988	−	0.702192i	$-0.247795\pi$
$150$	−158.413	−	133.944i	−1.05608	−	0.892963i
$151$	−65.9661	−	203.023i	−0.436862	−	1.34452i	−0.891167	−	0.453676i	$-0.850112\pi$
$151$	−65.9661	−	203.023i	−0.436862	−	1.34452i	0.454305	−	0.890846i	$-0.349888\pi$
$152$	13.2528	+	18.2410i	0.0871897	+	0.120006i
$153$	−135.504	−	67.3583i	−0.885646	−	0.440250i
$154$	38.6789			0.251162
$155$	−3.87121	−	36.5899i	−0.0249756	−	0.236064i
$156$	48.5439	−	57.4117i	0.311179	−	0.368023i
$157$	55.7837	+	40.5293i	0.355310	+	0.258148i	0.751093	−	0.660196i	$-0.229527\pi$
$157$	55.7837	+	40.5293i	0.355310	+	0.258148i	−0.395783	+	0.918344i	$0.629527\pi$
$158$	−235.324	−	323.896i	−1.48939	−	2.04997i
$159$	−106.714	+	261.289i	−0.671160	+	1.64332i
$160$	−54.4462			−0.340288
$161$		−	207.357i		−	1.28793i
$162$	189.275	−	143.337i	1.16837	−	0.884799i
$163$	89.3469	−	274.981i	0.548140	−	1.68700i	−0.165264	−	0.986249i	$-0.552848\pi$
$163$	89.3469	−	274.981i	0.548140	−	1.68700i	0.713404	−	0.700753i	$-0.247152\pi$
$164$	180.605	+	58.6821i	1.10125	+	0.357817i
$165$	−5.48548	+	1.34575i	−0.0332454	+	0.00815607i
$166$	11.2063	+	34.4894i	0.0675078	+	0.207768i
$167$	63.6406	−	87.5938i	0.381081	−	0.524514i	−0.574789	−	0.818302i	$-0.694916\pi$
$167$	63.6406	−	87.5938i	0.381081	−	0.524514i	0.955871	+	0.293788i	$0.0949159\pi$
$168$	−43.1748	−	3.18259i	−0.256993	−	0.0189440i
$169$	−43.0189	+	132.399i	−0.254550	+	0.783424i
$170$	−34.3826	−	47.3235i	−0.202250	−	0.278374i
$171$	83.5336	+	81.8929i	0.488500	+	0.478906i
$172$	54.6884	−	168.313i	0.317956	−	0.978567i
$173$	63.4628	+	87.3490i	0.366837	+	0.504908i	0.952038	−	0.305981i	$-0.0989843\pi$
$173$	63.4628	+	87.3490i	0.366837	+	0.504908i	−0.585201	+	0.810888i	$0.698984\pi$
$174$	236.284	−	57.9674i	1.35795	−	0.333146i
$175$	60.6454	+	186.647i	0.346545	+	1.06656i
$176$	12.3842	−	17.0454i	0.0703647	−	0.0968487i
$177$	143.712	−	89.0500i	0.811931	−	0.503107i
$178$	90.0169	−	277.044i	0.505713	−	1.55642i
$179$	−100.078	+	32.5172i	−0.559092	+	0.181660i	−0.574913	−	0.818215i	$-0.694964\pi$
$179$	−100.078	+	32.5172i	−0.559092	+	0.181660i	0.0158204	+	0.999875i	$0.494964\pi$
$180$	48.3681	−	8.15328i	0.268712	−	0.0452960i
$181$	−111.385			−0.615386			−0.307693	−	0.951486i	$-0.599557\pi$
$181$	−111.385			−0.615386			−0.307693	+	0.951486i	$0.599557\pi$
$182$	−126.571	+	41.1253i	−0.695442	+	0.225963i
$183$	−19.2569	+	261.238i	−0.105229	+	1.42753i
$184$	34.9811	+	25.4153i	0.190115	+	0.138127i
$185$			43.8935i			0.237262i
$186$	−225.525	−	153.131i	−1.21250	−	0.823285i
$187$	26.6703			0.142622
$188$	101.882	−	140.229i	0.541928	−	0.745900i
$189$	−223.630	+	20.9517i	−1.18323	+	0.110856i
$190$	13.9737	+	43.0065i	0.0735456	+	0.226350i
$191$			202.275i			1.05903i	0.848300	+	0.529516i	$0.177627\pi$
$191$			202.275i			1.05903i	−0.848300	+	0.529516i	$0.822373\pi$
$192$	−157.536	+	186.314i	−0.820500	+	0.970385i
$193$	−87.6122	−	269.643i	−0.453949	−	1.39711i	−0.872364	−	0.488856i	$-0.837414\pi$
$193$	−87.6122	−	269.643i	−0.453949	−	1.39711i	0.418415	−	0.908256i	$-0.362586\pi$
$194$	342.753	+	111.367i	1.76677	+	0.574057i
$195$	16.5195	−	10.2362i	0.0847154	−	0.0524933i
$196$	75.0533	+	54.5294i	0.382925	+	0.278211i
$197$	−221.853	+	72.0843i	−1.12616	+	0.365910i	−0.812114	−	0.583499i	$-0.801683\pi$
$197$	−221.853	+	72.0843i	−1.12616	+	0.365910i	−0.314042	+	0.949409i	$0.601683\pi$
$198$	−18.6269	+	37.4715i	−0.0940753	+	0.189250i
$199$	55.4667	−	40.2989i	0.278727	−	0.202507i	−0.439635	−	0.898177i	$-0.644892\pi$
$199$	55.4667	−	40.2989i	0.278727	−	0.202507i	0.718362	+	0.695669i	$0.244892\pi$
$200$	−38.9205	−	12.6460i	−0.194603	−	0.0632302i
$201$	−10.1872	+	138.198i	−0.0506824	+	0.687555i
$202$	−269.984	+	196.155i	−1.33656	+	0.971065i
$203$	−218.893	−	71.1226i	−1.07829	−	0.350358i
$204$	−230.987	−	17.0270i	−1.13229	−	0.0834657i
$205$	39.7113	+	28.8520i	0.193714	+	0.140741i
$206$	153.193	−	49.7756i	0.743658	−	0.241629i
$207$	200.884	+	99.8587i	0.970456	+	0.482409i
$208$	−22.4018	+	68.9457i	−0.107701	+	0.331470i
$209$	−19.6084	−	6.37116i	−0.0938202	−	0.0304840i
$210$	−80.3797	−	32.8283i	−0.382760	−	0.156325i
$211$	−97.9627			−0.464278			−0.232139	−	0.972683i	$-0.574572\pi$
$211$	−97.9627			−0.464278			−0.232139	+	0.972683i	$0.574572\pi$
$212$			431.998i			2.03773i
$213$	−23.4327	+	57.3746i	−0.110013	+	0.269364i
$214$	214.419	−	155.784i	1.00196	−	0.727965i
$215$	26.8884	−	37.0087i	0.125062	−	0.172133i
$216$	23.8753	−	40.2944i	0.110534	−	0.186548i
$217$	105.053	+	235.517i	0.484117	+	1.08533i
$218$			443.538i			2.03458i
$219$	−323.222	+	79.2960i	−1.47590	+	0.362082i
$220$	−6.99400	+	5.08144i	−0.0317909	+	0.0230975i
$221$	−87.2743	+	28.3571i	−0.394906	+	0.128313i
$222$	248.326	+	209.970i	1.11858	+	0.945809i
$223$	−97.6519			−0.437901			−0.218950	−	0.975736i	$-0.570263\pi$
$223$	−97.6519			−0.437901			−0.218950	+	0.975736i	$0.570263\pi$
$224$	362.928	−	117.923i	1.62022	−	0.526440i
$225$	−210.026	−	31.1329i	−0.933450	−	0.138369i
$226$	133.220	−	410.008i	0.589467	−	1.81419i
$227$	19.9862	−	27.5087i	0.0880450	−	0.121184i	−0.762722	−	0.646726i	$-0.776138\pi$
$227$	19.9862	−	27.5087i	0.0880450	−	0.121184i	0.850767	+	0.525543i	$0.176138\pi$
$228$	165.758	+	67.6982i	0.727009	+	0.296922i
$229$	112.014	+	81.3832i	0.489146	+	0.355385i	0.804856	−	0.593470i	$-0.202243\pi$
$229$	112.014	+	81.3832i	0.489146	+	0.355385i	−0.315710	+	0.948856i	$0.602243\pi$
$230$	50.9722	+	70.1571i	0.221618	+	0.305031i
$231$	33.6505	−	20.8513i	0.145673	−	0.0902654i
$232$	38.8276	−	28.2099i	0.167360	−	0.121594i
$233$	−249.722	−	343.713i	−1.07177	−	1.47516i	−0.868272	−	0.496088i	$-0.834769\pi$
$233$	−249.722	−	343.713i	−1.07177	−	1.47516i	−0.203497	−	0.979076i	$-0.565231\pi$
$234$	21.1121	−	142.424i	0.0902226	−	0.608652i
$235$	36.2470	−	26.3350i	0.154243	−	0.112064i
$236$	152.102	−	209.350i	0.644500	−	0.887078i
$237$	−379.339	−	154.928i	−1.60059	−	0.653705i
$238$	331.684	+	240.982i	1.39363	+	1.01253i
$239$	52.8039	+	17.1570i	0.220937	+	0.0717867i	0.417394	−	0.908726i	$-0.362944\pi$
$239$	52.8039	+	17.1570i	0.220937	+	0.0717867i	−0.196457	+	0.980512i	$0.562944\pi$
$240$	−40.2030	+	24.9115i	−0.167512	+	0.103798i
$241$	55.6894	+	171.394i	0.231076	+	0.711179i	0.997618	+	0.0689847i	$0.0219760\pi$
$241$	55.6894	+	171.394i	0.231076	+	0.711179i	−0.766542	+	0.642195i	$0.778024\pi$
$242$			347.297i			1.43511i
$243$	87.3977	−	226.739i	0.359661	−	0.933083i
$244$	123.896	+	381.313i	0.507771	+	1.56276i
$245$	14.0950	+	19.4001i	0.0575306	+	0.0791840i
$246$	353.193	−	86.6487i	1.43574	−	0.352230i
$247$	70.9396			0.287205
$248$	−52.6079	−	11.1443i	−0.212129	−	0.0449368i
$249$	28.3422	+	23.9645i	0.113824	+	0.0962431i
$250$	−136.765	−	99.3656i	−0.547060	−	0.397462i
$251$	145.984	+	200.930i	0.581611	+	0.800519i	0.993871	−	0.110547i	$-0.0352603\pi$
$251$	145.984	+	200.930i	0.581611	+	0.800519i	−0.412259	+	0.911066i	$0.635260\pi$
$252$	−304.754	+	159.107i	−1.20934	+	0.631375i
$253$	−39.5387			−0.156279
$254$		−	444.658i		−	1.75062i
$255$	−55.4242	−	22.6361i	−0.217350	−	0.0887692i
$256$	50.7991	−	156.344i	0.198434	−	0.610717i
$257$	324.659	+	105.488i	1.26326	+	0.410460i	0.862657	−	0.505790i	$-0.168799\pi$
$257$	324.659	+	105.488i	1.26326	+	0.410460i	0.400608	+	0.916250i	$0.368799\pi$
$258$	−80.7517	−	329.156i	−0.312991	−	1.27580i
$259$	−95.0669	−	292.586i	−0.367054	−	1.12968i
$260$	17.4839	−	24.0646i	0.0672459	−	0.0925560i
$261$	174.316	−	177.809i	0.667879	−	0.681260i
$262$	137.223	−	422.328i	0.523750	−	1.61194i
$263$	50.1214	+	68.9861i	0.190576	+	0.262305i	0.893603	−	0.448858i	$-0.148169\pi$
$263$	50.1214	+	68.9861i	0.190576	+	0.262305i	−0.703028	+	0.711162i	$0.748169\pi$
$264$	−0.606853	+	8.23253i	−0.00229869	+	0.0311838i
$265$	−34.5062	+	106.199i	−0.130212	+	0.400752i
$266$	−186.292	−	256.409i	−0.700346	−	0.963943i
$267$	−71.0362	−	289.554i	−0.266053	−	1.08447i
$268$	65.5427	+	201.720i	0.244562	+	0.752686i
$269$	−253.760	+	349.270i	−0.943345	+	1.29840i	0.0110760	+	0.999939i	$0.496474\pi$
$269$	−253.760	+	349.270i	−0.943345	+	1.29840i	−0.954421	+	0.298464i	$0.903526\pi$
$270$	70.5126	−	62.0611i	0.261158	−	0.229856i
$271$	−17.0358	+	52.4309i	−0.0628629	+	0.193472i	−0.977555	−	0.210678i	$-0.932433\pi$
$271$	−17.0358	+	52.4309i	−0.0628629	+	0.193472i	0.914693	+	0.404150i	$0.132433\pi$
$272$	212.397	−	69.0119i	0.780870	−	0.253720i
$273$	−87.9459	+	104.011i	−0.322146	+	0.380994i
$274$	−157.972			−0.576538
$275$	35.5897	−	11.5638i	0.129417	−	0.0420502i
$276$	342.439	+	25.2425i	1.24072	+	0.0914585i
$277$	146.427	+	106.386i	0.528618	+	0.384063i	0.819840	−	0.572592i	$-0.194062\pi$
$277$	146.427	+	106.386i	0.528618	+	0.384063i	−0.291223	+	0.956655i	$0.594062\pi$
$278$			169.911i			0.611191i
$279$	−278.757	−	11.6460i	−0.999128	−	0.0417419i
$280$	−17.1279			−0.0611709
$281$	100.565	−	138.416i	0.357882	−	0.492582i	−0.591675	−	0.806176i	$-0.701533\pi$
$281$	100.565	−	138.416i	0.357882	−	0.492582i	0.949557	+	0.313594i	$0.101533\pi$
$282$	24.4025	−	331.043i	0.0865337	−	1.17391i
$283$	29.3166	+	90.2273i	0.103592	+	0.318824i	0.989397	−	0.145233i	$-0.0463931\pi$
$283$	29.3166	+	90.2273i	0.103592	+	0.318824i	−0.885805	+	0.464057i	$0.846393\pi$
$284$			94.8595i			0.334012i
$285$	35.3413	+	29.8825i	0.124005	+	0.104851i
$286$	7.84173	+	24.1344i	0.0274186	+	0.0843859i
$287$	−327.198	−	106.313i	−1.14006	−	0.370428i
$288$	−60.5368	+	408.388i	−0.210197	+	1.41801i
$289$	−5.09965	−	3.70512i	−0.0176459	−	0.0128205i
$290$	91.5434	−	29.7442i	0.315667	−	0.102566i
$291$	358.230	−	87.8845i	1.23103	−	0.302009i
$292$	−412.109	+	299.415i	−1.41133	+	1.02539i
$293$	234.087	+	76.0595i	0.798932	+	0.259589i	0.679903	−	0.733302i	$-0.262022\pi$
$293$	234.087	+	76.0595i	0.798932	+	0.259589i	0.119029	+	0.992891i	$0.462022\pi$
$294$	177.180	+	13.0607i	0.602654	+	0.0444241i
$295$	54.1137	−	39.3159i	0.183436	−	0.133274i
$296$	61.0113	+	19.8238i	0.206119	+	0.0669722i
$297$	3.99505	+	42.6416i	0.0134514	+	0.143574i
$298$	−496.217	−	360.523i	−1.66516	−	1.20981i
$299$	129.384	−	42.0394i	0.432723	−	0.140600i
$300$	−315.620	+	77.4310i	−1.05207	+	0.258103i
$301$	−99.0777	+	304.930i	−0.329162	+	1.01306i
$302$	−595.096	−	193.358i	−1.97052	−	0.640260i
$303$	−129.141	+	316.199i	−0.426207	+	1.04356i
$304$	−172.643			−0.567906
$305$			103.636i			0.339789i
$306$	−393.192	+	205.278i	−1.28494	+	0.670844i
$307$	39.0136	−	28.3450i	0.127080	−	0.0923291i	−0.522430	−	0.852682i	$-0.674974\pi$
$307$	39.0136	−	28.3450i	0.127080	−	0.0923291i	0.649510	+	0.760353i	$0.274974\pi$
$308$	35.6151	−	49.0200i	0.115633	−	0.159156i
$309$	106.444	−	125.889i	0.344481	−	0.407409i
$310$	−93.4381	−	53.8608i	−0.301413	−	0.173745i
$311$			163.395i			0.525387i	0.964879	+	0.262693i	$0.0846108\pi$
$311$			163.395i			0.525387i	−0.964879	+	0.262693i	$0.915389\pi$
$312$	−6.76739	−	27.5849i	−0.0216904	−	0.0884131i
$313$	−141.363	+	102.706i	−0.451639	+	0.328135i	−0.790243	−	0.612794i	$-0.790045\pi$
$313$	−141.363	+	102.706i	−0.451639	+	0.328135i	0.338603	+	0.940929i	$0.390045\pi$
$314$	192.220	−	62.4561i	0.612166	−	0.198905i
$315$	−87.6274	+	14.7711i	−0.278182	+	0.0468924i
$316$	−627.175			−1.98473
$317$	225.253	−	73.1890i	0.710576	−	0.230880i	0.0686434	−	0.997641i	$-0.478133\pi$
$317$	225.253	−	73.1890i	0.710576	−	0.230880i	0.641933	+	0.766761i	$0.278133\pi$
$318$	435.754	+	703.235i	1.37030	+	2.21143i
$319$	−13.5616	+	41.7383i	−0.0425129	+	0.130841i
$320$	−56.7394	+	78.0950i	−0.177310	+	0.244047i
$321$	102.562	−	251.123i	0.319509	−	0.782313i
$322$	−491.721	−	357.256i	−1.52708	−	1.10949i
$323$	−128.454	−	176.802i	−0.397690	−	0.547374i
$324$	−7.37705	−	371.863i	−0.0227687	−	1.14773i
$325$	−104.167	+	75.6814i	−0.320512	+	0.232866i
$326$	−498.147	−	685.641i	−1.52806	−	2.10319i
$327$	239.106	+	385.877i	0.731211	+	1.18005i
$328$	58.0388	−	42.1677i	0.176948	−	0.128560i
$329$	−184.578	+	254.050i	−0.561028	+	0.772189i
$330$	−6.25968	+	15.3267i	−0.0189687	+	0.0464446i
$331$	110.715	+	80.4393i	0.334487	+	0.243019i	0.742332	−	0.670032i	$-0.233720\pi$
$331$	110.715	+	80.4393i	0.334487	+	0.243019i	−0.407845	+	0.913051i	$0.633720\pi$
$332$	54.0290	+	17.5551i	0.162738	+	0.0528768i
$333$	329.235	+	48.8036i	0.988692	+	0.146557i
$334$	−98.0709	−	301.831i	−0.293625	−	0.903686i
$335$			54.8247i			0.163656i
$336$	214.031	−	253.129i	0.636997	−	0.753361i
$337$	101.739	+	313.121i	0.301897	+	0.929143i	0.980817	+	0.194931i	$0.0624482\pi$
$337$	101.739	+	313.121i	0.301897	+	0.929143i	−0.678920	+	0.734212i	$0.737552\pi$
$338$	239.849	+	330.124i	0.709613	+	0.976698i
$339$	−105.129	−	428.523i	−0.310116	−	1.26408i
$340$	−91.6349			−0.269514
$341$	44.9083	−	20.0315i	0.131696	−	0.0587434i
$342$	338.119	−	56.9958i	0.988651	−	0.166654i
$343$	193.803	+	140.806i	0.565023	+	0.410513i
$344$	−39.2979	−	54.0889i	−0.114238	−	0.157235i
$345$	82.1664	+	33.5581i	0.238164	+	0.0972698i
$346$	316.477			0.914674
$347$		−	476.545i		−	1.37333i	−0.726974	−	0.686665i	$-0.759074\pi$
$347$		−	476.545i		−	1.37333i	0.726974	−	0.686665i	$-0.240926\pi$
$348$	144.102	−	352.831i	0.414086	−	1.01388i
$349$	59.9175	−	184.407i	0.171683	−	0.528387i	−0.827783	−	0.561048i	$-0.810398\pi$
$349$	59.9175	−	184.407i	0.171683	−	0.528387i	0.999466	+	0.0326613i	$0.0103983\pi$
$350$	547.096	+	177.762i	1.56313	+	0.507893i
$351$	−58.4118	−	135.290i	−0.166415	−	0.385442i
$352$	−22.4854	−	69.2029i	−0.0638789	−	0.196599i
$353$	−58.1247	+	80.0018i	−0.164659	+	0.226634i	−0.883371	−	0.468674i	$-0.844732\pi$
$353$	−58.1247	+	80.0018i	−0.164659	+	0.226634i	0.718712	+	0.695308i	$0.244732\pi$
$354$	36.4309	−	494.219i	0.102912	−	1.39610i
$355$	−7.57699	+	23.3196i	−0.0213436	+	0.0656889i
$356$	−268.227	−	369.182i	−0.753445	−	1.03703i
$357$	418.475	+	30.8474i	1.17220	+	0.0864074i
$358$	−95.3136	+	293.345i	−0.266239	+	0.819400i
$359$	−10.3003	−	14.1772i	−0.0286917	−	0.0394907i	0.794430	−	0.607356i	$-0.207770\pi$
$359$	−10.3003	−	14.1772i	−0.0286917	−	0.0394907i	−0.823122	+	0.567865i	$0.807770\pi$
$360$	8.24839	−	16.5932i	0.0229122	−	0.0460922i
$361$	−59.3492	−	182.658i	−0.164402	−	0.505978i
$362$	−191.905	+	264.135i	−0.530126	+	0.729655i
$363$	187.224	+	302.148i	0.515767	+	0.832363i
$364$	−64.4243	+	198.278i	−0.176990	+	0.544719i
$365$	−125.226	+	40.6884i	−0.343085	+	0.111475i
$366$	586.315	+	495.754i	1.60195	+	1.35452i
$367$	575.094			1.56701			0.783507	−	0.621382i	$-0.213429\pi$
$367$	575.094			1.56701			0.783507	+	0.621382i	$0.213429\pi$
$368$	−314.878	+	102.310i	−0.855647	+	0.278017i
$369$	260.565	−	265.786i	0.706139	−	0.720287i
$370$	104.088	+	75.6242i	0.281318	+	0.204390i
$371$		−	782.641i		−	2.10954i
$372$	−401.732	+	144.819i	−1.07993	+	0.389299i
$373$	22.6117			0.0606212			0.0303106	−	0.999541i	$-0.490350\pi$
$373$	22.6117			0.0606212			0.0303106	+	0.999541i	$0.490350\pi$
$374$	45.9503	−	63.2452i	0.122862	−	0.169105i
$375$	−172.552	−	12.7195i	−0.460138	−	0.0339187i
$376$	−20.2349	−	62.2766i	−0.0538162	−	0.165629i
$377$		−	151.001i		−	0.400534i
$378$	−335.609	+	566.408i	−0.887854	+	1.49843i
$379$	91.4229	+	281.371i	0.241221	+	0.742403i	0.996235	+	0.0866939i	$0.0276302\pi$
$379$	91.4229	+	281.371i	0.241221	+	0.742403i	−0.755014	+	0.655709i	$0.772370\pi$
$380$	67.3714	+	21.8903i	0.177293	+	0.0576061i
$381$	−239.710	−	386.851i	−0.629159	−	1.01536i
$382$	479.670	+	348.501i	1.25568	+	0.912305i
$383$	−490.549	+	159.389i	−1.28081	+	0.416160i	−0.868865	−	0.495050i	$-0.835150\pi$
$383$	−490.549	+	159.389i	−1.28081	+	0.416160i	−0.411943	+	0.911209i	$0.635150\pi$
$384$	39.2439	+	159.964i	0.102198	+	0.416573i
$385$	12.6709	−	9.20593i	0.0329114	−	0.0239115i
$386$	−790.370	−	256.807i	−2.04759	−	0.665303i
$387$	−247.697	−	242.832i	−0.640045	−	0.627473i
$388$	456.745	−	331.844i	1.17718	−	0.855269i
$389$	683.603	+	222.116i	1.75733	+	0.570992i	0.996918	−	0.0784455i	$-0.0249957\pi$
$389$	683.603	+	222.116i	1.75733	+	0.570992i	0.760415	+	0.649438i	$0.224996\pi$
$390$	4.18768	−	56.8098i	0.0107376	−	0.145666i
$391$	−339.057	−	246.339i	−0.867153	−	0.630024i
$392$	33.3316	−	10.8301i	0.0850296	−	0.0276278i
$393$	−108.288	−	441.399i	−0.275543	−	1.12315i
$394$	−211.292	+	650.290i	−0.536274	+	1.65048i
$395$	−154.180	−	50.0962i	−0.390330	−	0.126826i
$396$	30.3383	+	58.1103i	0.0766119	+	0.146743i
$397$	−192.096			−0.483869			−0.241934	−	0.970293i	$-0.577782\pi$
$397$	−192.096			−0.483869			−0.241934	+	0.970293i	$0.577782\pi$
$398$		−	200.963i		−	0.504933i
$399$	−300.300	−	122.647i	−0.752632	−	0.307387i
$400$	253.507	−	184.184i	0.633767	−	0.460459i
$401$	−402.274	+	553.682i	−1.00318	+	1.38075i	−0.0798203	+	0.996809i	$0.525435\pi$
$401$	−402.274	+	553.682i	−1.00318	+	1.38075i	−0.923356	+	0.383945i	$0.874565\pi$
$402$	310.169	+	262.260i	0.771564	+	0.652388i
$403$	−125.657	+	113.298i	−0.311803	+	0.281138i
$404$			522.784i			1.29402i
$405$	27.8894	−	92.0054i	0.0688627	−	0.227174i
$406$	−545.790	+	396.539i	−1.34431	+	0.976698i
$407$	−55.7900	+	18.1273i	−0.137076	+	0.0445388i
$408$	−56.4954	+	66.8157i	−0.138469	+	0.163764i
$409$	423.204			1.03473			0.517364	−	0.855765i	$-0.326913\pi$
$409$	423.204			1.03473			0.517364	+	0.855765i	$0.326913\pi$
$410$	136.838	−	44.4612i	0.333750	−	0.108442i
$411$	−137.435	+	85.1604i	−0.334391	+	0.207203i
$412$	77.9754	−	239.984i	0.189261	−	0.582484i
$413$	−275.560	+	379.275i	−0.667214	+	0.918342i
$414$	582.906	−	304.325i	1.40799	−	0.735084i
$415$	11.8799	+	8.63124i	0.0286262	+	0.0207982i
$416$	147.160	+	202.548i	0.353749	+	0.486894i
$417$	91.5969	+	147.822i	0.219657	+	0.354489i
$418$	−48.8918	+	35.5220i	−0.116966	+	0.0849808i
$419$	438.296	+	603.262i	1.04605	+	1.43977i	0.892182	+	0.451676i	$0.149174\pi$
$419$	438.296	+	603.262i	1.04605	+	1.43977i	0.153870	+	0.988091i	$0.450826\pi$
$420$	−115.618	+	71.6418i	−0.275281	+	0.170576i
$421$	195.522	−	142.055i	0.464422	−	0.337423i	−0.330841	−	0.943686i	$-0.607332\pi$
$421$	195.522	−	142.055i	0.464422	−	0.337423i	0.795264	+	0.606264i	$0.207332\pi$
$422$	−168.780	+	232.306i	−0.399953	+	0.550489i
$423$	−157.231	−	301.161i	−0.371704	−	0.711965i
$424$	132.031	+	95.9264i	0.311395	+	0.226242i
$425$	377.240	+	122.573i	0.887623	+	0.288406i
$426$	95.6843	+	154.418i	0.224611	+	0.362485i
$427$	−224.460	−	690.817i	−0.525667	−	1.61784i
$428$		−	415.190i		−	0.970070i
$429$	19.8328	+	16.7694i	0.0462303	+	0.0390896i
$430$	−41.4353	−	127.525i	−0.0963612	−	0.296569i
$431$	−44.7946	−	61.6545i	−0.103932	−	0.143050i	0.753883	−	0.657009i	$-0.228178\pi$
$431$	−44.7946	−	61.6545i	−0.103932	−	0.143050i	−0.857815	+	0.513959i	$0.828178\pi$
$432$	142.155	+	329.251i	0.329062	+	0.762156i
$433$	−316.128			−0.730088			−0.365044	−	0.930990i	$-0.618946\pi$
$433$	−316.128			−0.730088			−0.365044	+	0.930990i	$0.618946\pi$
$434$	739.496	+	156.653i	1.70391	+	0.360952i
$435$	63.6077	−	75.2273i	0.146225	−	0.172936i
$436$	562.121	+	408.405i	1.28927	+	0.936709i
$437$	190.433	+	262.109i	0.435774	+	0.599791i
$438$	−368.840	+	903.099i	−0.842101	+	2.06187i
$439$	464.085			1.05714			0.528571	−	0.848889i	$-0.322728\pi$
$439$	464.085			1.05714			0.528571	+	0.848889i	$0.322728\pi$
$440$			3.26592i			0.00742256i
$441$	161.187	−	84.1529i	0.365504	−	0.190823i
$442$	−83.1198	+	255.816i	−0.188054	+	0.578770i
$443$	531.659	+	172.747i	1.20013	+	0.389947i	0.839810	−	0.542880i	$-0.182666\pi$
$443$	531.659	+	172.747i	1.20013	+	0.389947i	0.360323	+	0.932827i	$0.382666\pi$
$444$	494.762	−	121.380i	1.11433	−	0.273378i
$445$	−36.4501	−	112.182i	−0.0819104	−	0.252094i
$446$	−168.245	+	231.569i	−0.377230	+	0.519213i
$447$	−626.061	−	46.1494i	−1.40058	−	0.103243i
$448$	209.072	−	643.456i	0.466678	−	1.43629i
$449$	−91.2814	−	125.638i	−0.203299	−	0.279818i	0.695178	−	0.718838i	$-0.255326\pi$
$449$	−91.2814	−	125.638i	−0.203299	−	0.279818i	−0.898477	+	0.439020i	$0.855326\pi$
$450$	−435.683	+	444.412i	−0.968184	+	0.987581i
$451$	−20.2717	+	62.3898i	−0.0449483	+	0.138337i
$452$	−396.959	−	546.367i	−0.878228	−	1.20878i
$453$	−621.969	+	152.587i	−1.37300	+	0.336838i
$454$	−30.7990	−	94.7895i	−0.0678392	−	0.208787i
$455$	−31.6752	+	43.5972i	−0.0696159	+	0.0958181i
$456$	57.4976	−	35.6280i	0.126091	−	0.0781316i
$457$	118.627	−	365.095i	0.259577	−	0.798895i	−0.733317	−	0.679887i	$-0.762029\pi$
$457$	118.627	−	365.095i	0.259577	−	0.798895i	0.992893	−	0.119008i	$-0.0379714\pi$
$458$	385.980	−	125.412i	0.842751	−	0.273826i
$459$	−231.413	+	390.556i	−0.504167	+	0.850884i
$460$	135.849			0.295323
$461$	390.343	−	126.830i	0.846731	−	0.275120i	0.146655	−	0.989188i	$-0.453149\pi$
$461$	390.343	−	126.830i	0.846731	−	0.275120i	0.700076	+	0.714068i	$0.253149\pi$
$462$	8.53039	−	115.723i	0.0184640	−	0.250482i
$463$	125.750	+	91.3624i	0.271597	+	0.197327i	0.715244	−	0.698875i	$-0.246316\pi$
$463$	125.750	+	91.3624i	0.271597	+	0.197327i	−0.443647	+	0.896202i	$0.646316\pi$
$464$			367.487i			0.791998i
$465$	−110.327	+	3.51254i	−0.237261	+	0.00755384i
$466$	−1245.32			−2.67236
$467$	327.208	−	450.364i	0.700660	−	0.964376i	−0.299288	−	0.954163i	$-0.596749\pi$
$467$	327.208	−	450.364i	0.700660	−	0.964376i	0.999948	−	0.0102130i	$-0.00325095\pi$
$468$	−161.063	−	157.899i	−0.344151	−	0.337392i
$469$	−118.742	−	365.451i	−0.253182	−	0.779214i
$470$		−	131.328i		−	0.279421i
$471$	133.562	−	157.960i	0.283570	−	0.335371i
$472$	−30.2090	−	92.9737i	−0.0640021	−	0.196978i
$473$	58.1437	+	18.8920i	0.122925	+	0.0399409i
$474$	−1020.96	+	632.628i	−2.15392	+	1.33466i
$475$	−248.072	−	180.235i	−0.522256	−	0.379441i
$476$	610.822	−	198.468i	1.28324	−	0.416950i
$477$	758.210	+	376.903i	1.58954	+	0.790152i
$478$	131.662	−	95.6578i	0.275443	−	0.200121i
$479$	−487.498	−	158.398i	−1.01774	−	0.330684i	−0.247808	−	0.968809i	$-0.579710\pi$
$479$	−487.498	−	158.398i	−1.01774	−	0.330684i	−0.769932	+	0.638125i	$0.779710\pi$
$480$	−12.0078	+	162.897i	−0.0250162	+	0.339368i
$481$	163.290	−	118.637i	0.339481	−	0.246647i
$482$	502.387	+	163.235i	1.04230	+	0.338663i
$483$	−620.388	−	45.7313i	−1.28445	−	0.0946819i
$484$	440.150	+	319.787i	0.909400	+	0.660718i
$485$	138.789	−	45.0953i	0.286163	−	0.0929801i
$486$	−387.105	−	597.902i	−0.796513	−	1.23025i
$487$	−101.999	+	313.922i	−0.209444	+	0.644603i	0.790057	+	0.613033i	$0.210051\pi$
$487$	−101.999	+	313.922i	−0.209444	+	0.644603i	−0.999502	+	0.0315703i	$0.989949\pi$
$488$	144.052	+	46.8054i	0.295189	+	0.0959127i
$489$	−803.007	−	327.961i	−1.64214	−	0.670676i
$490$	70.2891			0.143447
$491$			252.085i			0.513412i	0.966489	+	0.256706i	$0.0826373\pi$
$491$			252.085i			0.513412i	−0.966489	+	0.256706i	$0.917363\pi$
$492$	215.401	−	527.406i	0.437807	−	1.07196i
$493$	−376.339	+	273.426i	−0.763365	+	0.554617i
$494$	122.222	−	168.224i	0.247413	−	0.340535i
$495$	2.81654	+	16.7087i	0.00568999	+	0.0337550i
$496$	305.807	−	275.731i	0.616546	−	0.555909i
$497$		−	171.855i		−	0.345784i
$498$	105.660	−	25.9215i	0.212168	−	0.0520512i
$499$	−704.527	+	511.868i	−1.41188	+	1.02579i	−0.418831	+	0.908064i	$0.637560\pi$
$499$	−704.527	+	511.868i	−1.41188	+	1.02579i	−0.993046	+	0.117724i	$0.962440\pi$
$500$	−251.863	+	81.8354i	−0.503727	+	0.163671i
$501$	−248.035	−	209.723i	−0.495079	−	0.418610i
$502$	727.998			1.45020
$503$	−531.874	+	172.816i	−1.05740	+	0.343571i	−0.785570	−	0.618773i	$-0.787630\pi$
$503$	−531.874	+	172.816i	−1.05740	+	0.343571i	−0.271834	+	0.962344i	$0.587630\pi$
$504$	−19.0439	+	128.472i	−0.0377854	+	0.254905i
$505$	−41.7579	+	128.517i	−0.0826888	+	0.254490i
$506$	−68.1214	+	93.7610i	−0.134627	+	0.185298i
$507$	386.634	+	157.907i	0.762591	+	0.311454i
$508$	−563.541	−	409.436i	−1.10933	−	0.805977i
$509$	−409.663	−	563.853i	−0.804839	−	1.10777i	−0.992099	−	0.125455i	$-0.959961\pi$
$509$	−409.663	−	563.853i	−0.804839	−	1.10777i	0.187261	−	0.982310i	$-0.440039\pi$
$510$	−149.169	+	92.4317i	−0.292489	+	0.181239i
$511$	746.609	−	542.443i	1.46107	−	1.06153i
$512$	−412.310	−	567.497i	−0.805294	−	1.10839i
$513$	263.437	−	231.862i	0.513522	−	0.451972i
$514$	809.508	−	588.142i	1.57492	−	1.14424i
$515$	38.3378	−	52.7675i	0.0744424	−	0.102461i
$516$	−491.513	−	200.742i	−0.952544	−	0.389034i
$517$	48.4421	+	35.1952i	0.0936984	+	0.0680758i
$518$	−857.621	−	278.658i	−1.65564	−	0.537950i
$519$	275.334	−	170.609i	0.530509	−	0.328726i
$520$	−3.47249	−	10.6872i	−0.00667786	−	0.0205523i
$521$			765.661i			1.46960i	0.678285	+	0.734799i	$0.262724\pi$
$521$			765.661i			1.46960i	−0.678285	+	0.734799i	$0.737276\pi$
$522$	−121.321	−	719.717i	−0.232415	−	1.37877i
$523$	−110.474	−	340.005i	−0.211232	−	0.650104i	−0.999400	−	0.0346442i	$-0.988970\pi$
$523$	−110.474	−	340.005i	−0.211232	−	0.650104i	0.788168	−	0.615460i	$-0.211030\pi$
$524$	−408.887	−	562.785i	−0.780319	−	1.07402i
$525$	571.802	−	140.280i	1.08915	−	0.267200i
$526$	249.946			0.475183
$527$	509.906	+	108.017i	0.967563	+	0.204966i
$528$	−48.2665	−	40.8113i	−0.0914138	−	0.0772941i
$529$	74.6820	+	54.2596i	0.141176	+	0.102570i
$530$	192.387	+	264.798i	0.362995	+	0.499619i
$531$	−234.732	−	449.608i	−0.442057	−	0.846720i
$532$	−496.497			−0.933265
$533$		−	225.714i		−	0.423479i
$534$	−809.029	−	330.420i	−1.51504	−	0.618765i
$535$	33.1637	−	102.067i	0.0619882	−	0.190780i
$536$	76.2055	+	24.7607i	0.142174	+	0.0461953i
$537$	75.2160	+	306.592i	0.140067	+	0.570934i
$538$	391.047	+	1203.52i	0.726853	+	2.23702i
$539$	−18.8371	+	25.9271i	−0.0349483	+	0.0481022i
$540$	−13.7264	−	146.510i	−0.0254192	−	0.271314i
$541$	−306.707	+	943.946i	−0.566925	+	1.74482i	0.0952346	+	0.995455i	$0.469640\pi$
$541$	−306.707	+	943.946i	−0.566925	+	1.74482i	−0.662160	+	0.749362i	$0.730360\pi$
$542$	94.9822	+	130.732i	0.175244	+	0.241203i
$543$	−24.5652	+	333.251i	−0.0452399	+	0.613721i
$544$	238.338	−	733.528i	0.438121	−	1.34840i
$545$	105.566	+	145.299i	0.193699	+	0.266604i
$546$	95.1276	+	387.754i	0.174226	+	0.710172i
$547$	−80.2192	−	246.889i	−0.146653	−	0.451352i	0.850567	−	0.525867i	$-0.176259\pi$
$547$	−80.2192	−	246.889i	−0.146653	−	0.451352i	−0.997220	+	0.0745154i	$0.976259\pi$
$548$	−145.458	+	200.206i	−0.265435	+	0.365340i
$549$	777.347	+	115.229i	1.41593	+	0.209889i
$550$	33.8956	−	104.320i	0.0616283	−	0.189673i
$551$	342.008	−	111.125i	0.620704	−	0.201679i
$552$	83.7544	−	99.0543i	0.151729	−	0.179446i
$553$	1136.24			2.05468
$554$	504.560	−	163.941i	0.910757	−	0.295923i
$555$	131.324	+	9.68043i	0.236620	+	0.0174422i
$556$	215.338	+	156.452i	0.387298	+	0.281389i
$557$		−	368.636i		−	0.661824i	−0.943662	−	0.330912i	$-0.892644\pi$
$557$		−	368.636i		−	0.661824i	0.943662	−	0.330912i	$-0.107356\pi$
$558$	−507.888	+	640.971i	−0.910194	+	1.14869i
$559$	−210.353			−0.376302
$560$	77.0871	−	106.101i	0.137655	−	0.189466i
$561$	5.88197	−	79.7944i	0.0104848	−	0.142236i
$562$	−154.972	−	476.953i	−0.275750	−	0.848671i
$563$		−	572.005i		−	1.01599i	−0.861359	−	0.507997i	$-0.830386\pi$
$563$		−	572.005i		−	1.01599i	0.861359	−	0.507997i	$-0.169614\pi$
$564$	−397.080	−	335.747i	−0.704042	−	0.595296i
$565$	−53.9440	−	166.023i	−0.0954761	−	0.293845i
$566$	264.472	+	85.9323i	0.467266	+	0.151824i
$567$	13.3648	+	673.696i	0.0235711	+	1.18818i
$568$	28.9919	+	21.0638i	0.0510420	+	0.0370842i
$569$	−246.925	+	80.2307i	−0.433963	+	0.141003i	−0.517848	−	0.855472i	$-0.673267\pi$
$569$	−246.925	+	80.2307i	−0.433963	+	0.141003i	0.0838859	+	0.996475i	$0.473267\pi$
$570$	131.752	−	32.3228i	0.231144	−	0.0567066i
$571$	−406.065	+	295.024i	−0.711148	+	0.516679i	−0.883544	−	0.468349i	$-0.844849\pi$
$571$	−406.065	+	295.024i	−0.711148	+	0.516679i	0.172396	+	0.985028i	$0.444849\pi$
$572$	37.8074	+	12.2844i	0.0660969	+	0.0214762i
$573$	605.184	+	44.6105i	1.05617	+	0.0778543i
$574$	−815.838	+	592.741i	−1.42132	+	1.03265i
$575$	−559.258	−	181.714i	−0.972622	−	0.316024i
$576$	522.686	+	512.420i	0.907441	+	0.889617i
$577$	−315.362	−	229.124i	−0.546555	−	0.397096i	0.279959	−	0.960012i	$-0.409679\pi$
$577$	−315.362	−	229.124i	−0.546555	−	0.397096i	−0.826514	+	0.562916i	$0.809679\pi$
$578$	−17.5724	+	5.70963i	−0.0304021	+	0.00987824i
$579$	−826.061	+	202.657i	−1.42670	+	0.350013i
$580$	46.5955	−	143.406i	0.0803371	−	0.247252i
$581$	−97.8832	−	31.8042i	−0.168474	−	0.0547404i
$582$	408.789	−	1000.91i	0.702387	−	1.71978i
$583$	−149.233			−0.255975
$584$			192.439i			0.329518i
$585$	−26.9822	−	51.6819i	−0.0461234	−	0.0883452i
$586$	583.675	−	424.065i	0.996033	−	0.723660i
$587$	33.6677	−	46.3396i	0.0573555	−	0.0789431i	−0.779376	−	0.626557i	$-0.784464\pi$
$587$	33.6677	−	46.3396i	0.0573555	−	0.0789431i	0.836731	+	0.547614i	$0.184464\pi$
$588$	179.698	−	212.525i	0.305609	−	0.361436i
$589$	−349.087	−	201.225i	−0.592677	−	0.341639i
$590$		−	196.061i		−	0.332307i
$591$	166.740	+	679.655i	0.282131	+	1.15001i
$592$	−397.394	+	288.724i	−0.671274	+	0.487709i
$593$	599.877	−	194.912i	1.01160	−	0.328688i	0.244107	−	0.969748i	$-0.421505\pi$
$593$	599.877	−	194.912i	1.01160	−	0.328688i	0.767490	+	0.641061i	$0.221505\pi$
$594$	108.002	+	63.9936i	0.181822	+	0.107733i
$595$	166.013			0.279013
$596$	−913.822	+	296.919i	−1.53326	+	0.498186i
$597$	−108.337	−	174.838i	−0.181469	−	0.292860i
$598$	123.225	−	379.248i	0.206062	−	0.634194i
$599$	−333.787	+	459.418i	−0.557240	+	0.766975i	−0.990972	−	0.134067i	$-0.957196\pi$
$599$	−333.787	+	459.418i	−0.557240	+	0.766975i	0.433732	+	0.901042i	$0.357196\pi$
$600$	−46.4191	+	113.657i	−0.0773652	+	0.189428i
$601$	476.466	+	346.173i	0.792789	+	0.575995i	0.908790	−	0.417254i	$-0.137008\pi$
$601$	476.466	+	346.173i	0.792789	+	0.575995i	−0.116001	+	0.993249i	$0.537008\pi$
$602$	552.401	+	760.314i	0.917609	+	1.26298i
$603$	411.227	+	60.9576i	0.681968	+	0.101091i
$604$	−793.012	+	576.157i	−1.31293	+	0.953902i
$605$	82.6599	+	113.772i	0.136628	+	0.188052i
$606$	527.330	+	851.022i	0.870181	+	1.40433i
$607$	−598.444	+	434.795i	−0.985904	+	0.716301i	−0.959020	−	0.283337i	$-0.908558\pi$
$607$	−598.444	+	434.795i	−0.985904	+	0.716301i	−0.0268840	+	0.999639i	$0.508558\pi$
$608$	−350.459	+	482.366i	−0.576413	+	0.793365i
$609$	−261.066	+	639.216i	−0.428680	+	1.04962i
$610$	245.759	+	178.554i	0.402883	+	0.292712i
$611$	−195.940	−	63.6648i	−0.320688	−	0.104198i
$612$	−101.886	+	687.332i	−0.166480	+	1.12309i
$613$	243.923	+	750.717i	0.397916	+	1.22466i	0.926667	+	0.375883i	$0.122661\pi$
$613$	243.923	+	750.717i	0.397916	+	1.22466i	−0.528751	+	0.848777i	$0.677339\pi$
$614$		−	141.351i		−	0.230214i
$615$	95.0798	−	112.448i	0.154601	−	0.182843i
$616$	−7.07352	−	21.7701i	−0.0114830	−	0.0353410i
$617$	−379.143	−	521.846i	−0.614495	−	0.845780i	0.382443	−	0.923979i	$-0.375083\pi$
$617$	−379.143	−	521.846i	−0.614495	−	0.845780i	−0.996938	+	0.0781995i	$0.975083\pi$
$618$	−115.137	−	469.315i	−0.186306	−	0.759409i
$619$	373.731			0.603766			0.301883	−	0.953345i	$-0.402385\pi$
$619$	373.731			0.603766			0.301883	+	0.953345i	$0.402385\pi$
$620$	−154.298	+	68.8250i	−0.248867	+	0.111008i
$621$	343.069	−	578.999i	0.552446	−	0.932366i
$622$	387.471	+	281.514i	0.622944	+	0.452595i
$623$	485.940	+	668.839i	0.780000	+	1.07358i
$624$	201.337	+	82.2292i	0.322655	+	0.131777i
$625$	521.328			0.834125
$626$			512.177i			0.818175i
$627$	−23.3863	+	57.2610i	−0.0372987	+	0.0913253i
$628$	97.8399	−	301.120i	0.155796	−	0.479491i
$629$	−591.356	−	192.143i	−0.940153	−	0.305474i
$630$	−115.946	+	233.246i	−0.184041	+	0.370232i
$631$	37.6818	+	115.973i	0.0597175	+	0.183792i	0.976465	−	0.215675i	$-0.0691953\pi$
$631$	37.6818	+	115.973i	0.0597175	+	0.183792i	−0.916748	+	0.399467i	$0.869195\pi$
$632$	−139.266	+	191.683i	−0.220358	+	0.303296i
$633$	−21.6051	+	293.093i	−0.0341312	+	0.463022i
$634$	214.530	−	660.255i	0.338375	−	1.04141i
$635$	−105.833	−	145.666i	−0.166666	−	0.229396i
$636$	1292.49	+	95.2744i	2.03221	+	0.149803i
$637$	34.0746	−	104.871i	0.0534923	−	0.164632i
$638$	75.6118	+	104.071i	0.118514	+	0.163120i
$639$	166.490	+	82.7614i	0.260548	+	0.129517i
$640$	20.1368	+	61.9748i	0.0314638	+	0.0968357i
$641$	−150.551	+	207.215i	−0.234868	+	0.323269i	−0.910140	−	0.414300i	$-0.864026\pi$
$641$	−150.551	+	207.215i	−0.234868	+	0.323269i	0.675272	+	0.737569i	$0.264026\pi$
$642$	−418.800	−	675.874i	−0.652337	−	1.05276i
$643$	150.132	−	462.057i	0.233486	−	0.718596i	−0.763833	−	0.645414i	$-0.776685\pi$
$643$	150.132	−	462.057i	0.233486	−	0.718596i	0.997319	−	0.0731817i	$-0.0233153\pi$
$644$	−905.543	+	294.229i	−1.40612	+	0.456877i
$645$	−104.796	−	88.6090i	−0.162474	−	0.137378i
$646$	−640.577			−0.991605
$647$	−55.8034	+	18.1316i	−0.0862495	+	0.0280241i	−0.351824	−	0.936066i	$-0.614438\pi$
$647$	−55.8034	+	18.1316i	−0.0862495	+	0.0280241i	0.265574	+	0.964090i	$0.414438\pi$
$648$	−115.290	−	80.3187i	−0.177917	−	0.123949i
$649$	72.3199	+	52.5435i	0.111433	+	0.0809607i
$650$			377.410i			0.580630i
$651$	727.809	−	262.365i	1.11799	−	0.403019i
$652$	−1327.64			−2.03626
$653$	670.621	−	923.031i	1.02698	−	1.41352i	0.119796	−	0.992798i	$-0.461776\pi$
$653$	670.621	−	923.031i	1.02698	−	1.41352i	0.907188	−	0.420725i	$-0.138224\pi$
$654$	1327.01	+	97.8196i	2.02907	+	0.149571i
$655$	−55.5649	−	171.011i	−0.0848319	−	0.261086i
$656$			549.314i			0.837369i
$657$	165.960	+	984.531i	0.252602	+	1.49852i
$658$	284.437	+	875.407i	0.432275	+	1.33041i
$659$	−642.898	−	208.890i	−0.975566	−	0.316980i	−0.222505	−	0.974932i	$-0.571423\pi$
$659$	−642.898	−	208.890i	−0.975566	−	0.316980i	−0.753061	+	0.657951i	$0.771423\pi$
$660$	13.6606	+	22.0459i	0.0206979	+	0.0334029i
$661$	−504.661	−	366.658i	−0.763481	−	0.554702i	0.136495	−	0.990641i	$-0.456416\pi$
$661$	−504.661	−	366.658i	−0.763481	−	0.554702i	−0.899976	+	0.435939i	$0.856416\pi$
$662$	381.503	−	123.958i	0.576289	−	0.187248i
$663$	65.5934	+	267.368i	0.0989342	+	0.403271i
$664$	17.3627	−	12.6147i	0.0261486	−	0.0189981i
$665$	−122.055	−	39.6582i	−0.183542	−	0.0596363i
$666$	682.971	−	696.654i	1.02548	−	1.04603i
$667$	557.922	−	405.354i	0.836465	−	0.607727i
$668$	−472.830	−	153.632i	−0.707830	−	0.229988i
$669$	−21.5365	+	292.163i	−0.0321921	+	0.436716i
$670$	130.010	+	94.4576i	0.194044	+	0.140981i
$671$	−131.724	+	42.7998i	−0.196311	+	0.0637852i
$672$	−272.769	−	1111.85i	−0.405906	−	1.65453i
$673$	202.004	−	621.704i	0.300154	−	0.923780i	−0.681287	−	0.732016i	$-0.738579\pi$
$673$	202.004	−	621.704i	0.300154	−	0.923780i	0.981441	−	0.191763i	$-0.0614206\pi$
$674$	917.814	+	298.216i	1.36174	+	0.442457i
$675$	−139.466	+	621.508i	−0.206616	+	0.920752i
$676$	639.235			0.945614
$677$		−	66.2687i		−	0.0978858i	−0.998802	−	0.0489429i	$-0.984415\pi$
$677$		−	66.2687i		−	0.0978858i	0.998802	−	0.0489429i	$-0.0155852\pi$
$678$	−1197.31	−	489.002i	−1.76595	−	0.721242i
$679$	−827.474	+	601.195i	−1.21867	+	0.885412i
$680$	−20.3478	+	28.0063i	−0.0299232	+	0.0411858i
$681$	−77.8948	−	65.8633i	−0.114383	−	0.0967155i
$682$	29.8705	−	141.007i	0.0437984	−	0.206754i
$683$		−	65.0347i		−	0.0952192i	−0.998866	−	0.0476096i	$-0.984840\pi$
$683$		−	65.0347i		−	0.0952192i	0.998866	−	0.0476096i	$-0.0151603\pi$
$684$	239.102	−	480.998i	0.349564	−	0.703214i
$685$	−51.7501	+	37.5987i	−0.0755476	+	0.0548886i
$686$	667.807	−	216.984i	0.973480	−	0.316303i
$687$	268.193	−	317.185i	0.390383	−	0.461696i
$688$	511.930			0.744084
$689$	488.342	−	158.672i	0.708769	−	0.230293i
$690$	221.144	−	137.030i	0.320498	−	0.198594i
$691$	170.310	−	524.161i	0.246469	−	0.758554i	−0.748922	−	0.662658i	$-0.769428\pi$
$691$	170.310	−	524.161i	0.246469	−	0.758554i	0.995391	−	0.0958959i	$-0.0305716\pi$
$692$	291.409	−	401.090i	0.421111	−	0.579609i
$693$	−54.9632	−	105.277i	−0.0793120	−	0.151915i
$694$	−1130.07	−	821.041i	−1.62834	−	1.18306i
$695$	40.4404	+	55.6614i	0.0581876	+	0.0800884i
$696$	−75.8375	−	122.389i	−0.108962	−	0.175846i
$697$	−562.545	+	408.713i	−0.807095	+	0.586389i
$698$	−334.066	−	459.802i	−0.478604	−	0.658742i
$699$	−1083.42	+	671.336i	−1.54996	+	0.960423i
$700$	729.048	−	529.685i	1.04150	−	0.756692i
$701$	−125.631	+	172.916i	−0.179217	+	0.246671i	−0.889169	−	0.457579i	$-0.848717\pi$
$701$	−125.631	+	172.916i	−0.179217	+	0.246671i	0.709952	+	0.704250i	$0.248717\pi$
$702$	−421.461	−	94.5757i	−0.600372	−	0.134723i
$703$	388.874	+	282.534i	0.553164	+	0.401897i
$704$	−122.694	−	39.8656i	−0.174281	−	0.0566273i
$705$	−70.7972	−	114.255i	−0.100421	−	0.162064i
$706$	89.5709	+	275.671i	0.126871	+	0.390468i
$707$		−	947.116i		−	1.33963i
$708$	−592.806	−	501.242i	−0.837297	−	0.707969i
$709$	177.578	+	546.528i	0.250462	+	0.770844i	0.994690	+	0.102918i	$0.0328178\pi$
$709$	177.578	+	546.528i	0.250462	+	0.770844i	−0.744228	+	0.667926i	$0.767182\pi$
$710$	42.2450	+	58.1452i	0.0595000	+	0.0818947i
$711$	−547.187	+	1100.77i	−0.769602	+	1.54820i
$712$	−172.394			−0.242126
$713$	−755.935	−	160.135i	−1.06022	−	0.224594i
$714$	794.142	−	939.212i	1.11224	−	1.31542i
$715$	8.31308	+	6.03981i	0.0116267	+	0.00844728i
$716$	284.009	+	390.905i	0.396661	+	0.545957i
$717$	62.9773	−	154.199i	0.0878345	−	0.215061i
$718$	−51.3658			−0.0715401
$719$		−	1402.29i		−	1.95033i	−0.221475	−	0.975166i	$-0.571087\pi$
$719$		−	1402.29i		−	1.95033i	0.221475	−	0.975166i	$-0.428913\pi$
$720$	65.6657	+	125.777i	0.0912024	+	0.174690i
$721$	−141.266	+	434.773i	−0.195931	+	0.603014i
$722$	−535.403	−	173.963i	−0.741556	−	0.240946i
$723$	525.073	−	128.816i	0.726243	−	0.178169i
$724$	158.049	+	486.425i	0.218300	+	0.671858i
$725$	−383.646	+	528.043i	−0.529167	+	0.728336i
$726$	1039.07	+	76.5942i	1.43123	+	0.105502i
$727$	−226.673	+	697.627i	−0.311792	+	0.959597i	0.665263	+	0.746609i	$0.268320\pi$
$727$	−226.673	+	697.627i	−0.311792	+	0.959597i	−0.977055	+	0.212988i	$0.931680\pi$
$728$	46.2939	+	63.7181i	0.0635906	+	0.0875249i
$729$	−659.102	−	311.489i	−0.904118	−	0.427283i
$730$	−119.265	+	367.060i	−0.163377	+	0.502821i
$731$	380.897	+	524.260i	0.521063	+	0.717182i
$732$	1168.17	−	286.587i	1.59586	−	0.391512i
$733$	−150.454	−	463.051i	−0.205258	−	0.631720i	−0.999703	−	0.0243830i	$-0.992238\pi$
$733$	−150.454	−	463.051i	−0.205258	−	0.631720i	0.794445	−	0.607337i	$-0.207762\pi$
$734$	990.832	−	1363.76i	1.34991	−	1.85799i
$735$	61.1513	−	37.8920i	0.0831991	−	0.0515537i
$736$	−353.336	+	1087.45i	−0.480075	+	1.47752i
$737$	−69.6839	+	22.6417i	−0.0945508	+	0.0307214i
$738$	−181.348	−	1075.82i	−0.245729	−	1.45775i
$739$	438.481			0.593343			0.296672	−	0.954980i	$-0.404123\pi$
$739$	438.481			0.593343			0.296672	+	0.954980i	$0.404123\pi$
$740$	191.686	−	62.2825i	0.259035	−	0.0841655i
$741$	15.6453	−	212.243i	0.0211137	−	0.286428i
$742$	−1855.93	−	1348.41i	−2.50126	−	1.81727i
$743$			729.590i			0.981952i	0.871173	+	0.490976i	$0.163360\pi$
$743$			729.590i			0.981952i	−0.871173	+	0.490976i	$0.836640\pi$
$744$	−44.9448	+	154.939i	−0.0604097	+	0.208251i
$745$	−248.364			−0.333375
$746$	38.9578	−	53.6208i	0.0522222	−	0.0718778i
$747$	77.9497	−	79.5115i	0.104350	−	0.106441i
$748$	−37.8437	−	116.471i	−0.0505932	−	0.155710i
$749$			752.190i			1.00426i
$750$	−327.453	+	387.270i	−0.436604	+	0.516361i
$751$	73.2843	+	225.546i	0.0975823	+	0.300327i	0.987918	−	0.154977i	$-0.0495304\pi$
$751$	73.2843	+	225.546i	0.0975823	+	0.300327i	−0.890336	+	0.455304i	$0.849530\pi$
$752$	476.853	+	154.939i	0.634114	+	0.206036i
$753$	633.356	−	392.454i	0.841110	−	0.521188i
$754$	−358.080	−	260.161i	−0.474908	−	0.345041i
$755$	−240.970	+	78.2957i	−0.319165	+	0.103703i
$756$	408.817	+	946.879i	0.540763	+	1.25248i
$757$	559.493	−	406.495i	0.739092	−	0.536982i	−0.153335	−	0.988174i	$-0.549001\pi$
$757$	559.493	−	406.495i	0.739092	−	0.536982i	0.892427	+	0.451193i	$0.149001\pi$
$758$	824.748	+	267.977i	1.08806	+	0.353531i
$759$	−8.72001	+	118.295i	−0.0114888	+	0.155857i
$760$	21.6504	−	15.7299i	0.0284873	−	0.0206972i
$761$	208.181	+	67.6422i	0.273563	+	0.0888860i	0.442586	−	0.896726i	$-0.354061\pi$
$761$	208.181	+	67.6422i	0.273563	+	0.0888860i	−0.169023	+	0.985612i	$0.554061\pi$
$762$	−1330.36	−	98.0666i	−1.74589	−	0.128696i
$763$	−1018.38	−	739.898i	−1.33471	−	0.969723i
$764$	883.349	−	287.018i	1.15622	−	0.375677i
$765$	−79.9481	+	160.831i	−0.104507	+	0.210236i
$766$	−467.198	+	1437.89i	−0.609919	+	1.87714i
$767$	−292.522	−	95.0462i	−0.381385	−	0.123919i
$768$	−456.558	−	186.466i	−0.594477	−	0.242794i
$769$	−1400.37			−1.82103			−0.910514	−	0.413478i	$-0.864314\pi$
$769$	−1400.37			−1.82103			−0.910514	+	0.413478i	$0.864314\pi$
$770$		−	45.9083i		−	0.0596212i
$771$	387.210	−	948.077i	0.502217	−	1.22967i
$772$	−1053.23	+	765.217i	−1.36429	+	0.991213i
$773$	414.808	−	570.934i	0.536620	−	0.738595i	−0.451501	−	0.892271i	$-0.649111\pi$
$773$	414.808	−	570.934i	0.536620	−	0.738595i	0.988121	+	0.153676i	$0.0491112\pi$
$774$	−1002.60	+	169.006i	−1.29535	+	0.218354i
$775$	727.270	−	76.9451i	0.938412	−	0.0992840i
$776$		−	213.282i		−	0.274848i
$777$	−896.349	+	219.901i	−1.15360	+	0.283013i
$778$	1704.50	−	1238.39i	2.19088	−	1.59176i
$779$	511.228	−	166.108i	0.656262	−	0.213232i
$780$	−68.1424	−	57.6172i	−0.0873620	−	0.0738681i
$781$	−32.7691			−0.0419579
$782$	−1168.32	+	379.612i	−1.49402	+	0.485437i
$783$	−493.539	−	560.749i	−0.630318	−	0.716154i
$784$	−82.9263	+	255.221i	−0.105773	+	0.325537i
$785$	48.1045	−	66.2102i	0.0612796	−	0.0843442i
$786$	−1233.29	−	503.696i	−1.56907	−	0.640834i
$787$	−524.846	−	381.323i	−0.666894	−	0.484527i	0.202090	−	0.979367i	$-0.435227\pi$
$787$	−524.846	−	381.323i	−0.666894	−	0.484527i	−0.868984	+	0.494840i	$0.835227\pi$
$788$	629.594	+	866.562i	0.798977	+	1.09970i
$789$	217.452	−	134.743i	0.275605	−	0.170777i
$790$	−384.434	+	279.308i	−0.486626	+	0.353554i
$791$	719.162	+	989.841i	0.909181	+	1.25138i
$792$	24.4969	+	3.63127i	0.0309305	+	0.00458493i
$793$	385.540	−	280.111i	0.486179	−	0.353230i
$794$	−330.963	+	455.531i	−0.416830	+	0.573717i
$795$	310.126	+	126.660i	0.390095	+	0.159321i
$796$	−254.692	−	185.045i	−0.319965	−	0.232468i
$797$	836.524	+	271.803i	1.04959	+	0.341033i	0.782508	−	0.622641i	$-0.213940\pi$
$797$	836.524	+	271.803i	1.04959	+	0.341033i	0.267083	+	0.963673i	$0.413940\pi$
$798$	−808.231	+	500.814i	−1.01282	+	0.627587i
$799$	196.128	+	603.620i	0.245467	+	0.755470i
$800$		−	1082.18i		−	1.35273i
$801$	−881.978	+	148.673i	−1.10110	+	0.185609i
$802$	619.909	+	1907.88i	0.772953	+	2.37891i
$803$	−103.433	−	142.363i	−0.128808	−	0.177289i
$804$	617.977	−	151.608i	0.768628	−	0.188567i
$805$	−246.114			−0.305732
$806$	52.1785	+	493.181i	0.0647376	+	0.611887i
$807$	989.011	+	836.249i	1.22554	+	1.03624i
$808$	159.778	+	116.086i	0.197745	+	0.143670i
$809$	−348.170	−	479.215i	−0.430371	−	0.592355i	0.537667	−	0.843157i	$-0.319306\pi$
$809$	−348.170	−	479.215i	−0.430371	−	0.592355i	−0.968038	+	0.250802i	$0.919306\pi$
$810$	−170.128	−	224.653i	−0.210035	−	0.277349i
$811$	−981.426			−1.21014			−0.605071	−	0.796171i	$-0.706855\pi$
$811$	−981.426			−1.21014			−0.605071	+	0.796171i	$0.706855\pi$
$812$			1056.84i			1.30153i
$813$	153.110	+	62.5326i	0.188327	+	0.0769158i
$814$	−53.1343	+	163.531i	−0.0652755	+	0.200897i
$815$	−326.378	−	106.047i	−0.400463	−	0.130118i
$816$	−159.633	−	650.686i	−0.195628	−	0.797409i
$817$	−154.803	−	476.435i	−0.189478	−	0.583152i
$818$	729.140	−	1003.57i	0.891369	−	1.22686i
$819$	291.794	+	286.063i	0.356281	+	0.349283i
$820$	69.6502	−	214.361i	0.0849393	−	0.261416i
$821$	480.148	+	660.867i	0.584833	+	0.804954i	0.994215	−	0.107409i	$-0.0342556\pi$
$821$	480.148	+	660.867i	0.584833	+	0.804954i	−0.409382	+	0.912363i	$0.634256\pi$
$822$	−34.8396	+	472.632i	−0.0423840	+	0.574978i
$823$	101.764	−	313.196i	0.123650	−	0.380554i	−0.870003	−	0.493046i	$-0.835883\pi$
$823$	101.764	−	313.196i	0.123650	−	0.380554i	0.993653	+	0.112492i	$0.0358833\pi$
$824$	−56.0314	−	77.1207i	−0.0679993	−	0.0935930i
$825$	−26.7485	−	109.031i	−0.0324224	−	0.132158i
$826$	424.641	+	1306.91i	0.514093	+	1.58221i
$827$	−80.2377	+	110.438i	−0.0970226	+	0.133540i	−0.854768	−	0.519010i	$-0.826301\pi$
$827$	−80.2377	+	110.438i	−0.0970226	+	0.133540i	0.757746	+	0.652550i	$0.226301\pi$
$828$	151.045	−	1018.97i	0.182422	−	1.23064i
$829$	4.46082	−	13.7290i	0.00538096	−	0.0165609i	−0.948330	−	0.317286i	$-0.897229\pi$
$829$	4.46082	−	13.7290i	0.00538096	−	0.0165609i	0.953711	+	0.300725i	$0.0972286\pi$
$830$	40.9358	−	13.3008i	0.0493202	−	0.0160251i
$831$	350.587	−	414.630i	0.421885	−	0.498953i
$832$	443.883			0.533513
$833$	−323.069	+	104.971i	−0.387838	+	0.126016i
$834$	508.354	+	37.4728i	0.609537	+	0.0449314i
$835$	−103.966	−	75.5356i	−0.124510	−	0.0904618i
$836$			94.6716i			0.113244i
$837$	−96.3215	+	831.439i	−0.115079	+	0.993356i
$838$	2185.70			2.60824
$839$	−914.140	+	1258.21i	−1.08956	+	1.49965i	−0.241016	+	0.970521i	$0.577481\pi$
$839$	−914.140	+	1258.21i	−1.08956	+	1.49965i	−0.848542	+	0.529127i	$0.822519\pi$
$840$	−3.77744	+	51.2445i	−0.00449695	+	0.0610054i
$841$	23.3433	+	71.8433i	0.0277566	+	0.0854261i
$842$		−	708.402i		−	0.841333i
$843$	−391.944	−	331.405i	−0.464940	−	0.393125i
$844$	139.004	+	427.810i	0.164696	+	0.506884i
$845$	157.145	+	51.0595i	0.185970	+	0.0604255i
$846$	−985.059	−	146.019i	−1.16437	−	0.172599i
$847$	−797.409	−	579.352i	−0.941451	−	0.684004i
$848$	−1188.46	+	386.155i	−1.40149	+	0.455372i
$849$	276.415	−	67.8129i	0.325577	−	0.0798738i
$850$	940.613	−	683.395i	1.10660	−	0.803995i
$851$	876.686	+	284.852i	1.03018	+	0.334727i
$852$	283.808	+	20.9207i	0.333108	+	0.0245548i
$853$	−41.2660	+	29.9815i	−0.0483774	+	0.0351483i	−0.611711	−	0.791081i	$-0.709519\pi$
$853$	−41.2660	+	29.9815i	−0.0483774	+	0.0351483i	0.563334	+	0.826229i	$0.309519\pi$
$854$	−2024.91	−	657.932i	−2.37109	−	0.770412i
$855$	97.1993	−	99.1467i	0.113683	−	0.115961i
$856$	−126.894	−	92.1941i	−0.148241	−	0.107703i
$857$	−623.196	+	202.489i	−0.727183	+	0.236276i	−0.649135	−	0.760674i	$-0.724869\pi$
$857$	−623.196	+	202.489i	−0.727183	+	0.236276i	−0.0780482	+	0.996950i	$0.524869\pi$
$858$	73.9366	−	18.1389i	0.0861732	−	0.0211409i
$859$	507.171	−	1560.91i	0.590420	−	1.81713i	0.0141014	−	0.999901i	$-0.495511\pi$
$859$	507.171	−	1560.91i	0.590420	−	1.81713i	0.576319	−	0.817225i	$-0.304489\pi$
$860$	−199.773	−	64.9101i	−0.232294	−	0.0754768i
$861$	−390.237	+	955.490i	−0.453237	+	1.10974i
$862$	−223.383			−0.259145
$863$		−	39.3450i		−	0.0455909i	−0.999740	−	0.0227955i	$-0.992743\pi$
$863$		−	39.3450i		−	0.0455909i	0.999740	−	0.0227955i	$-0.00725665\pi$
$864$	1208.50	+	271.186i	1.39872	+	0.313873i
$865$	103.675	−	75.3245i	0.119856	−	0.0870803i
$866$	−544.658	+	749.657i	−0.628935	+	0.865655i
$867$	−12.2100	+	14.4404i	−0.0140830	+	0.0166556i
$868$	879.455	−	792.961i	1.01320	−	0.913550i
$869$		−	216.657i		−	0.249318i
$870$	−68.8020	−	280.447i	−0.0790827	−	0.322353i
$871$	203.956	−	148.183i	0.234163	−	0.170129i
$872$	249.641	−	81.1134i	0.286286	−	0.0930200i
$873$	−183.935	−	1091.17i	−0.210693	−	1.24990i
$874$	949.655			1.08656
$875$	456.295	−	148.259i	0.521480	−	0.169439i
$876$	804.926	+	1299.02i	0.918865	+	1.48289i
$877$	−219.436	+	675.354i	−0.250212	+	0.770073i	0.744524	+	0.667596i	$0.232677\pi$
$877$	−219.436	+	675.354i	−0.250212	+	0.770073i	−0.994735	+	0.102477i	$0.967323\pi$
$878$	799.574	−	1100.52i	0.910677	−	1.25344i
$879$	279.188	−	683.587i	0.317620	−	0.777687i
$880$	−20.2313	−	14.6989i	−0.0229901	−	0.0167033i
$881$	−372.976	−	513.357i	−0.423355	−	0.582698i	0.543057	−	0.839696i	$-0.317267\pi$
$881$	−372.976	−	513.357i	−0.423355	−	0.582698i	−0.966412	+	0.256997i	$0.917267\pi$
$882$	78.1520	−	527.222i	0.0886077	−	0.597758i
$883$	−123.885	+	90.0076i	−0.140300	+	0.101934i	−0.655721	−	0.755003i	$-0.727635\pi$
$883$	−123.885	+	90.0076i	−0.140300	+	0.101934i	0.515421	+	0.856937i	$0.327635\pi$
$884$	247.675	+	340.895i	0.280175	+	0.385628i
$885$	−105.694	−	170.573i	−0.119428	−	0.192738i
$886$	1325.64	−	963.136i	1.49621	−	1.08706i
$887$	984.997	−	1355.73i	1.11048	−	1.52845i	0.289777	−	0.957094i	$-0.406419\pi$
$887$	984.997	−	1355.73i	1.11048	−	1.52845i	0.820705	−	0.571353i	$-0.193581\pi$
$888$	72.7661	−	178.167i	0.0819438	−	0.200638i
$889$	1020.95	+	741.766i	1.14843	+	0.834383i
$890$	−328.825	−	106.842i	−0.369467	−	0.120047i
$891$	128.460	−	2.54839i	0.144175	−	0.00286015i
$892$	138.563	+	426.452i	0.155339	+	0.478085i
$893$		−	490.644i		−	0.549433i
$894$	−1188.08	+	1405.11i	−1.32895	+	1.57171i
$895$	38.5949	+	118.783i	0.0431228	+	0.132718i
$896$	−268.457	−	369.499i	−0.299617	−	0.412388i
$897$	−97.2422	−	396.374i	−0.108408	−	0.441888i
$898$	−455.204			−0.506908
$899$	−428.326	+	743.063i	−0.476448	+	0.826544i
$900$	162.056	+	961.375i	0.180063	+	1.06819i
$901$	−1279.72	−	929.773i	−1.42034	−	1.03193i
$902$	113.023	+	155.563i	0.125303	+	0.172465i
$903$	890.463	+	363.679i	0.986116	+	0.402745i
$904$	−255.132			−0.282226
$905$			132.204i			0.146081i
$906$	−709.750	+	1737.81i	−0.783389	+	1.91812i
$907$	192.606	−	592.779i	0.212355	−	0.653561i	−0.786976	−	0.616983i	$-0.788355\pi$
$907$	192.606	−	592.779i	0.212355	−	0.653561i	0.999331	−	0.0365771i	$-0.0116455\pi$
$908$	−148.492	−	48.2478i	−0.163537	−	0.0531364i
$909$	917.550	+	456.110i	1.00941	+	0.501771i
$910$	48.8119	+	150.228i	0.0536395	+	0.165085i
$911$	235.308	−	323.874i	0.258297	−	0.355515i	−0.660099	−	0.751179i	$-0.729486\pi$
$911$	235.308	−	323.874i	0.258297	−	0.355515i	0.918395	+	0.395664i	$0.129486\pi$
$912$	−38.0754	+	516.529i	−0.0417494	+	0.566369i
$913$	−6.06439	+	18.6643i	−0.00664227	+	0.0204428i
$914$	−661.395	−	910.332i	−0.723626	−	0.995986i
$915$	310.066	+	22.8562i	0.338870	+	0.0249795i
$916$	196.464	−	604.653i	0.214480	−	0.660101i
$917$	740.771	+	1019.58i	0.807820	+	1.11187i
$918$	527.452	+	1221.66i	0.574567	+	1.33078i
$919$	128.078	+	394.185i	0.139367	+	0.428928i	0.996244	−	0.0865937i	$-0.0275982\pi$
$919$	128.078	+	394.185i	0.139367	+	0.428928i	−0.856877	+	0.515522i	$0.827598\pi$
$920$	30.1656	−	41.5194i	0.0327887	−	0.0451298i
$921$	−76.2008	−	122.975i	−0.0827370	−	0.133524i
$922$	371.762	−	1144.17i	0.403212	−	1.24096i
$923$	107.232	−	34.8417i	0.116177	−	0.0377483i
$924$	−138.807	−	117.367i	−0.150224	−	0.127021i
$925$	−872.436			−0.943174
$926$	433.309	−	140.791i	0.467936	−	0.152042i
$927$	−353.170	−	346.233i	−0.380982	−	0.373499i
$928$	1026.76	+	745.985i	1.10642	+	0.803863i
$929$			354.879i			0.382001i	0.981590	+	0.191001i	$0.0611732\pi$
$929$			354.879i			0.382001i	−0.981590	+	0.191001i	$0.938827\pi$
$930$	−181.752	+	267.677i	−0.195433	+	0.287825i
$931$	262.602			0.282064
$932$	−1146.68	+	1578.26i	−1.23034	+	1.69342i
$933$	488.860	+	36.0358i	0.523965	+	0.0386236i
$934$	−504.232	−	1551.87i	−0.539863	−	1.66153i
$935$		−	31.6552i		−	0.0338558i
$936$	−84.0232	+	14.1636i	−0.0897684	+	0.0151320i
$937$	111.377	+	342.783i	0.118866	+	0.365831i	0.992734	−	0.120332i	$-0.0383961\pi$
$937$	111.377	+	342.783i	0.118866	+	0.365831i	−0.873868	+	0.486163i	$0.838396\pi$
$938$	−1071.20	−	348.055i	−1.14201	−	0.371061i
$939$	276.108	+	445.593i	0.294045	+	0.474540i
$940$	−166.439	−	120.925i	−0.177063	−	0.128644i
$941$	−1227.50	+	398.838i	−1.30446	+	0.423845i	−0.877131	−	0.480251i	$-0.840546\pi$
$941$	−1227.50	+	398.838i	−1.30446	+	0.423845i	−0.427329	+	0.904096i	$0.640546\pi$
$942$	−144.468	−	588.874i	−0.153363	−	0.625132i
$943$	833.973	−	605.917i	0.884383	−	0.642542i
$944$	711.902	+	231.311i	0.754133	+	0.245033i
$945$	24.8678	+	265.429i	0.0263151	+	0.280877i
$946$	144.976	−	105.331i	0.153252	−	0.111344i
$947$	−388.615	−	126.269i	−0.410364	−	0.133335i	0.0965576	−	0.995327i	$-0.469217\pi$
$947$	−388.615	−	126.269i	−0.410364	−	0.133335i	−0.506922	+	0.861992i	$0.669217\pi$
$948$	−138.319	+	1876.43i	−0.145907	+	1.97936i
$949$	489.833	+	355.885i	0.516157	+	0.375010i
$950$	−854.807	+	277.744i	−0.899797	+	0.292362i
$951$	−169.295	−	690.071i	−0.178018	−	0.725626i
$952$	74.9770	−	230.756i	0.0787574	−	0.242390i
$953$	567.853	+	184.507i	0.595858	+	0.193606i	0.591392	−	0.806384i	$-0.298578\pi$
$953$	567.853	+	184.507i	0.595858	+	0.193606i	0.00446592	+	0.999990i	$0.498578\pi$
$954$	2200.10	−	1148.63i	2.30618	−	1.20402i
$955$	240.082			0.251395
$956$		−	254.943i		−	0.266677i
$957$	121.885	+	49.7798i	0.127362	+	0.0520166i
$958$	−1215.53	+	883.135i	−1.26882	+	0.921853i
$959$	263.524	−	362.709i	0.274790	−	0.378216i
$960$	221.138	+	186.981i	0.230352	+	0.194772i
$961$	939.724	−	201.097i	0.977861	−	0.209258i
$962$		−	591.622i		−	0.614992i
$963$	−728.710	−	362.238i	−0.756708	−	0.376156i
$964$	669.470	−	486.398i	0.694471	−	0.504563i
$965$	−320.041	+	103.988i	−0.331649	+	0.107759i
$966$	−1177.32	+	1392.38i	−1.21875	+	1.44139i
$967$	440.596			0.455632			0.227816	−	0.973704i	$-0.426842\pi$
$967$	440.596			0.455632			0.227816	+	0.973704i	$0.426842\pi$
$968$	195.473	−	63.5130i	0.201935	−	0.0656126i
$969$	−557.300	+	345.327i	−0.575129	+	0.356374i
$970$	132.183	−	406.816i	0.136271	−	0.419398i
$971$	−54.9606	+	75.6468i	−0.0566021	+	0.0779061i	−0.836380	−	0.548150i	$-0.815332\pi$
$971$	−54.9606	+	75.6468i	−0.0566021	+	0.0779061i	0.779778	+	0.626057i	$0.215332\pi$
$972$	−1114.20	−	59.9408i	−1.14629	−	0.0616675i
$973$	−390.123	−	283.441i	−0.400948	−	0.291306i
$974$	568.691	+	782.736i	0.583871	+	0.803630i
$975$	203.457	+	328.345i	0.208673	+	0.336764i
$976$	−938.277	+	681.698i	−0.961349	+	0.698461i
$977$	165.720	+	228.094i	0.169622	+	0.233464i	0.885362	−	0.464902i	$-0.153911\pi$
$977$	165.720	+	228.094i	0.169622	+	0.233464i	−0.715740	+	0.698366i	$0.753911\pi$
$978$	−2161.22	+	1339.18i	−2.20984	+	1.36931i
$979$	127.534	−	92.6586i	0.130269	−	0.0946462i
$980$	64.7214	−	89.0814i	0.0660423	−	0.0908994i
$981$	1207.23	−	630.274i	1.23061	−	0.642481i
$982$	597.789	+	434.319i	0.608746	+	0.442280i
$983$	−343.953	−	111.757i	−0.349902	−	0.113690i	0.128793	−	0.991672i	$-0.458890\pi$
$983$	−343.953	−	111.757i	−0.349902	−	0.113690i	−0.478694	+	0.877982i	$0.658890\pi$
$984$	−113.361	−	182.945i	−0.115204	−	0.185920i
$985$	85.5575	+	263.319i	0.0868604	+	0.267329i
$986$			1363.53i			1.38289i
$987$	719.380	+	608.265i	0.728856	+	0.616277i
$988$	−100.659	−	309.798i	−0.101882	−	0.313560i
$989$	−564.680	−	777.216i	−0.570961	−	0.785860i
$990$	44.4752	+	22.1084i	0.0449245	+	0.0223317i
$991$	−830.830			−0.838376			−0.419188	−	0.907900i	$-0.637685\pi$
$991$	−830.830			−0.838376			−0.419188	+	0.907900i	$0.637685\pi$
$992$	−149.617	−	1414.15i	−0.150823	−	1.42555i
$993$	265.082	−	313.506i	0.266951	−	0.315716i
$994$	−407.532	−	296.089i	−0.409992	−	0.297876i
$995$	−47.8311	−	65.8339i	−0.0480715	−	0.0661647i
$996$	64.4386	−	157.777i	0.0646973	−	0.158411i
$997$	−1159.32			−1.16281			−0.581406	−	0.813614i	$-0.697497\pi$
$997$	−1159.32			−1.16281			−0.581406	+	0.813614i	$0.697497\pi$
$998$			2552.60i			2.55771i
$999$	218.625	−	974.268i	0.218844	−	0.975243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.3.l.b.2.16	yes	72
3.2	odd	2	inner	93.3.l.b.2.3	✓	72
31.16	even	5	inner	93.3.l.b.47.3	yes	72
93.47	odd	10	inner	93.3.l.b.47.16	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.3.l.b.2.3	✓	72	3.2	odd	2	inner
93.3.l.b.2.16	yes	72	1.1	even	1	trivial
93.3.l.b.47.3	yes	72	31.16	even	5	inner
93.3.l.b.47.16	yes	72	93.47	odd	10	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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	93.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72290 - 2.37137i) q^{2} +(0.220544 - 2.99188i) q^{3} +(-1.41895 - 4.36707i) q^{4} -1.18691i q^{5} +(-6.71489 - 5.67772i) q^{6} +(2.57067 + 7.91172i) q^{7} +(-1.64979 - 0.536048i) q^{8} +(-8.90272 - 1.31968i) q^{9} +(-2.81460 - 2.04493i) q^{10} +(1.50860 - 0.490174i) q^{11} +(-13.3787 + 3.28219i) q^{12} +(-4.41547 + 3.20803i) q^{13} +(23.1906 + 7.53510i) q^{14} +(-3.55109 - 0.261765i) q^{15} +(10.7458 - 7.80728i) q^{16} +(15.9907 + 5.19568i) q^{17} +(-18.4680 + 18.8380i) q^{18} +(-10.5154 - 7.63990i) q^{19} +(-5.18331 + 1.68416i) q^{20} +(24.2379 - 5.94627i) q^{21} +(1.43679 - 4.42197i) q^{22} +(-23.7062 - 7.70260i) q^{23} +(-1.96764 + 4.81774i) q^{24} +23.5912 q^{25} +15.9979i q^{26} +(-5.91177 + 26.3448i) q^{27} +(30.9033 - 22.4526i) q^{28} +(-16.2622 + 22.3830i) q^{29} +(-6.73893 + 7.96996i) q^{30} +(30.8279 - 3.26159i) q^{31} -45.8723i q^{32} +(-1.13383 - 4.62166i) q^{33} +(39.8713 - 28.9682i) q^{34} +(9.39048 - 3.05115i) q^{35} +(6.86934 + 40.7513i) q^{36} -36.9813 q^{37} +(-36.2341 + 11.7732i) q^{38} +(8.62424 + 13.9181i) q^{39} +(-0.636240 + 1.95815i) q^{40} +(-24.3085 + 33.4578i) q^{41} +(27.6587 - 67.7219i) q^{42} +(31.1808 + 22.6541i) q^{43} +(-4.28124 - 5.89262i) q^{44} +(-1.56634 + 10.5667i) q^{45} +(-59.1092 + 42.9453i) q^{46} +(22.1879 + 30.5390i) q^{47} +(-20.9886 - 33.8720i) q^{48} +(-16.3451 + 11.8754i) q^{49} +(40.6454 - 55.9436i) q^{50} +(19.0715 - 46.6963i) q^{51} +(20.2750 + 14.7306i) q^{52} +(-89.4756 - 29.0724i) q^{53} +(52.2880 + 59.4086i) q^{54} +(-0.581791 - 1.79057i) q^{55} -14.4306i q^{56} +(-25.1768 + 29.7760i) q^{57} +(25.0603 + 77.1276i) q^{58} +(33.1246 + 45.5922i) q^{59} +(3.89566 + 15.8793i) q^{60} -87.3157 q^{61} +(45.3791 - 78.7240i) q^{62} +(-12.4450 - 73.8283i) q^{63} +(-65.7970 - 47.8043i) q^{64} +(3.80764 + 5.24076i) q^{65} +(-12.9132 - 5.27393i) q^{66} -46.1911 q^{67} -77.2047i q^{68} +(-28.2735 + 69.2273i) q^{69} +(8.94347 - 27.5252i) q^{70} +(-19.6473 - 6.38380i) q^{71} +(13.9802 + 6.94948i) q^{72} +(-34.2810 - 105.506i) q^{73} +(-63.7153 + 87.6966i) q^{74} +(5.20290 - 70.5822i) q^{75} +(-18.4431 + 56.7621i) q^{76} +(7.75623 + 10.6755i) q^{77} +(47.8637 + 3.52823i) q^{78} +(42.2073 - 129.901i) q^{79} +(-9.26653 - 12.7543i) q^{80} +(77.5169 + 23.4975i) q^{81} +(37.4597 + 115.289i) q^{82} +(-7.27204 + 10.0091i) q^{83} +(-60.3600 - 97.4110i) q^{84} +(6.16680 - 18.9795i) q^{85} +(107.443 - 34.9103i) q^{86} +(63.3808 + 53.5911i) q^{87} -2.75162 q^{88} +(94.5161 - 30.7102i) q^{89} +(22.3590 + 21.9198i) q^{90} +(-36.7318 - 26.6872i) q^{91} +114.456i q^{92} +(-2.95940 - 92.9529i) q^{93} +110.647 q^{94} +(-9.06786 + 12.4808i) q^{95} +(-137.244 - 10.1168i) q^{96} +(37.9940 + 116.933i) q^{97} +59.2204i q^{98} +(-14.0775 + 2.37301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 5 q^{3} + 36 q^{4} - 10 q^{6} - 54 q^{7} + 5 q^{9} + 114 q^{10} + 14 q^{12} + 26 q^{13} + 35 q^{15} - 184 q^{16} + 15 q^{18} - 90 q^{19} + 71 q^{21} - 114 q^{22} - 101 q^{24} - 188 q^{25} + 116 q^{27}+ \cdots - 616 q^{99}+O(q^{100}) \) 72 * q + 5 * q^3 + 36 * q^4 - 10 * q^6 - 54 * q^7 + 5 * q^9 + 114 * q^10 + 14 * q^12 + 26 * q^13 + 35 * q^15 - 184 * q^16 + 15 * q^18 - 90 * q^19 + 71 * q^21 - 114 * q^22 - 101 * q^24 - 188 * q^25 + 116 * q^27 - 84 * q^28 - 18 * q^30 + 28 * q^31 - 242 * q^33 - 82 * q^34 + 74 * q^36 + 364 * q^37 + 13 * q^39 + 252 * q^40 - 46 * q^42 - 146 * q^43 + 52 * q^45 - 88 * q^46 - 170 * q^48 - 60 * q^49 - 301 * q^51 - 222 * q^52 - 118 * q^54 + 308 * q^55 - 20 * q^57 - 280 * q^58 - 407 * q^60 + 84 * q^61 + 556 * q^63 + 1450 * q^64 + 550 * q^66 - 324 * q^67 + 355 * q^69 + 728 * q^70 - 631 * q^72 - 140 * q^73 - 17 * q^75 - 622 * q^76 + 679 * q^78 - 200 * q^79 + 5 * q^81 + 598 * q^82 + 1197 * q^84 - 200 * q^85 + 202 * q^87 + 388 * q^88 + 1068 * q^90 + 834 * q^91 + 74 * q^93 - 384 * q^94 - 1016 * q^96 - 1074 * q^97 - 616 * q^99

Introduction

L-functions

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