LMFDB - Embedded newform 171.3.j.a.68.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [171,3,Mod(68,171)] 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("171.68"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	171.j (of order $6$, degree $2$, 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:	$4.65941252056$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.6
Character	$\chi$	$=$	171.68
Dual form			171.3.j.a.83.33

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.10239i q^{2} +(2.99536 + 0.166742i) q^{3} -5.62485 q^{4} +(3.72606 - 2.15124i) q^{5} +(0.517300 - 9.29280i) q^{6} +(0.122000 + 0.211310i) q^{7} +5.04093i q^{8} +(8.94439 + 0.998906i) q^{9} +(-6.67400 - 11.5597i) q^{10} +(1.58563 - 0.915463i) q^{11} +(-16.8485 - 0.937899i) q^{12} -7.20231 q^{13} +(0.655567 - 0.378492i) q^{14} +(11.5196 - 5.82246i) q^{15} -6.86046 q^{16} +(4.73531 + 2.73393i) q^{17} +(3.09900 - 27.7490i) q^{18} +(-1.81089 - 18.9135i) q^{19} +(-20.9585 + 12.1004i) q^{20} +(0.330200 + 0.653293i) q^{21} +(-2.84013 - 4.91925i) q^{22} +29.8957i q^{23} +(-0.840535 + 15.0994i) q^{24} +(-3.24432 + 5.61933i) q^{25} +22.3444i q^{26} +(26.6251 + 4.48349i) q^{27} +(-0.686231 - 1.18859i) q^{28} +(-5.36039 - 3.09482i) q^{29} +(-18.0636 - 35.7383i) q^{30} +(-12.5185 + 21.6826i) q^{31} +41.4476i q^{32} +(4.90218 - 2.47775i) q^{33} +(8.48174 - 14.6908i) q^{34} +(0.909158 + 0.524902i) q^{35} +(-50.3109 - 5.61870i) q^{36} +25.8584 q^{37} +(-58.6771 + 5.61811i) q^{38} +(-21.5735 - 1.20093i) q^{39} +(10.8442 + 18.7828i) q^{40} +(-50.3865 + 29.0907i) q^{41} +(2.02677 - 1.02441i) q^{42} +16.1357 q^{43} +(-8.91893 + 5.14934i) q^{44} +(35.4762 - 15.5196i) q^{45} +92.7484 q^{46} +(27.2821 + 15.7513i) q^{47} +(-20.5496 - 1.14393i) q^{48} +(24.4702 - 42.3837i) q^{49} +(17.4334 + 10.0652i) q^{50} +(13.7281 + 8.97870i) q^{51} +40.5119 q^{52} +(55.2531 - 31.9004i) q^{53} +(13.9096 - 82.6017i) q^{54} +(3.93876 - 6.82214i) q^{55} +(-1.06520 + 0.614992i) q^{56} +(-2.27061 - 56.9548i) q^{57} +(-9.60136 + 16.6300i) q^{58} +(19.6012 - 11.3168i) q^{59} +(-64.7960 + 32.7504i) q^{60} +(-0.694666 + 1.20320i) q^{61} +(67.2681 + 38.8372i) q^{62} +(0.880136 + 2.01191i) q^{63} +101.145 q^{64} +(-26.8362 + 15.4939i) q^{65} +(-7.68697 - 15.2085i) q^{66} -18.1418 q^{67} +(-26.6354 - 15.3780i) q^{68} +(-4.98488 + 89.5486i) q^{69} +(1.62845 - 2.82057i) q^{70} +(94.7332 + 54.6943i) q^{71} +(-5.03541 + 45.0880i) q^{72} +(5.53115 - 9.58024i) q^{73} -80.2230i q^{74} +(-10.6549 + 16.2910i) q^{75} +(10.1860 + 106.386i) q^{76} +(0.386893 + 0.223373i) q^{77} +(-3.72575 + 66.9296i) q^{78} -118.751 q^{79} +(-25.5625 + 14.7585i) q^{80} +(79.0044 + 17.8692i) q^{81} +(90.2508 + 156.319i) q^{82} +(-62.7808 + 36.2465i) q^{83} +(-1.85732 - 3.67467i) q^{84} +23.5254 q^{85} -50.0594i q^{86} +(-15.5403 - 10.1639i) q^{87} +(4.61478 + 7.99304i) q^{88} +(37.8306 - 21.8415i) q^{89} +(-48.1478 - 110.061i) q^{90} +(-0.878681 - 1.52192i) q^{91} -168.159i q^{92} +(-41.1128 + 62.8600i) q^{93} +(48.8668 - 84.6398i) q^{94} +(-47.4350 - 66.5772i) q^{95} +(-6.91105 + 124.150i) q^{96} -182.445 q^{97} +(-131.491 - 75.9163i) q^{98} +(15.0970 - 6.60437i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 5 q^{3} - 146 q^{4} - 3 q^{5} + 23 q^{6} - q^{7} - 13 q^{9} + 6 q^{10} - 24 q^{11} + 15 q^{12} + 8 q^{13} - 3 q^{14} - 14 q^{15} + 262 q^{16} - 135 q^{17} + 30 q^{18} + 4 q^{19} + 69 q^{20} - 40 q^{21}+ \cdots - 64 q^{99}+O(q^{100}) $ 76 * q - 5 * q^3 - 146 * q^4 - 3 * q^5 + 23 * q^6 - q^7 - 13 * q^9 + 6 * q^10 - 24 * q^11 + 15 * q^12 + 8 * q^13 - 3 * q^14 - 14 * q^15 + 262 * q^16 - 135 * q^17 + 30 * q^18 + 4 * q^19 + 69 * q^20 - 40 * q^21 - 3 * q^22 - 81 * q^24 + 151 * q^25 - 59 * q^27 + 14 * q^28 - 30 * q^29 + 265 * q^30 + 14 * q^31 + 31 * q^33 - 33 * q^34 - 75 * q^35 + 41 * q^36 + 14 * q^37 + 63 * q^38 - 78 * q^39 + 12 * q^40 - 201 * q^41 - 122 * q^42 - 58 * q^43 + 183 * q^44 + 145 * q^45 - 84 * q^46 - 21 * q^47 + 159 * q^48 - 171 * q^49 - 363 * q^50 - 103 * q^51 - 202 * q^52 + 36 * q^53 - 370 * q^54 - 27 * q^55 + 300 * q^56 - 3 * q^57 + 6 * q^58 - 84 * q^59 - 145 * q^60 + 8 * q^61 + 120 * q^62 + 3 * q^63 - 680 * q^64 - 6 * q^65 + 271 * q^66 - 16 * q^67 + 666 * q^68 + 81 * q^69 - 42 * q^70 + 135 * q^71 + 381 * q^72 + 65 * q^73 - 139 * q^75 - 155 * q^76 - 366 * q^77 - 514 * q^78 + 32 * q^79 - 66 * q^80 + 179 * q^81 - 42 * q^82 - 177 * q^83 + 546 * q^84 - 102 * q^85 - 375 * q^87 + 162 * q^88 + 216 * q^89 - 575 * q^90 + 265 * q^91 + 201 * q^93 + 6 * q^94 + 789 * q^95 + 511 * q^96 + 254 * q^97 + 882 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	3.10239i		−	1.55120i	−0.631226	−	0.775599i	$-0.717448\pi$
$2$		−	3.10239i		−	1.55120i	0.631226	−	0.775599i	$-0.282552\pi$
$3$	2.99536	+	0.166742i	0.998454	+	0.0555807i
$3$	2.99536	+	0.166742i	0.998454	+	0.0555807i
$4$	−5.62485			−1.40621
$5$	3.72606	−	2.15124i	0.745212	−	0.430248i	−0.0787494	−	0.996894i	$-0.525093\pi$
$5$	3.72606	−	2.15124i	0.745212	−	0.430248i	0.823961	+	0.566646i	$0.191759\pi$
$6$	0.517300	−	9.29280i	0.0862166	−	1.54880i
$7$	0.122000	+	0.211310i	0.0174286	+	0.0301872i	0.874608	−	0.484830i	$-0.161119\pi$
$7$	0.122000	+	0.211310i	0.0174286	+	0.0301872i	−0.857180	+	0.515018i	$0.827785\pi$
$8$			5.04093i			0.630116i
$9$	8.94439	+	0.998906i	0.993822	+	0.110990i
$10$	−6.67400	−	11.5597i	−0.667400	−	1.15597i
$11$	1.58563	−	0.915463i	0.144148	−	0.0832239i	−0.426191	−	0.904633i	$-0.640145\pi$
$11$	1.58563	−	0.915463i	0.144148	−	0.0832239i	0.570339	+	0.821409i	$0.306812\pi$
$12$	−16.8485	−	0.937899i	−1.40404	−	0.0781583i
$13$	−7.20231			−0.554024			−0.277012	−	0.960866i	$-0.589344\pi$
$13$	−7.20231			−0.554024			−0.277012	+	0.960866i	$0.589344\pi$
$14$	0.655567	−	0.378492i	0.0468262	−	0.0270351i
$15$	11.5196	−	5.82246i	0.767973	−	0.388164i
$16$	−6.86046			−0.428779
$17$	4.73531	+	2.73393i	0.278548	+	0.160820i	0.632766	−	0.774343i	$-0.281920\pi$
$17$	4.73531	+	2.73393i	0.278548	+	0.160820i	−0.354218	+	0.935163i	$0.615253\pi$
$18$	3.09900	−	27.7490i	0.172167	−	1.54161i
$19$	−1.81089	−	18.9135i	−0.0953102	−	0.995448i
$19$	−1.81089	−	18.9135i	−0.0953102	−	0.995448i
$20$	−20.9585	+	12.1004i	−1.04793	+	0.605020i
$21$	0.330200	+	0.653293i	0.0157238	+	0.0311092i
$22$	−2.84013	−	4.91925i	−0.129097	−	0.223602i
$23$			29.8957i			1.29981i	0.760013	+	0.649907i	$0.225192\pi$
$23$			29.8957i			1.29981i	−0.760013	+	0.649907i	$0.774808\pi$
$24$	−0.840535	+	15.0994i	−0.0350223	+	0.629142i
$25$	−3.24432	+	5.61933i	−0.129773	+	0.224773i
$26$			22.3444i			0.859400i
$27$	26.6251	+	4.48349i	0.986116	+	0.166055i
$28$	−0.686231	−	1.18859i	−0.0245083	−	0.0424495i
$29$	−5.36039	−	3.09482i	−0.184841	−	0.106718i	0.404724	−	0.914439i	$-0.367368\pi$
$29$	−5.36039	−	3.09482i	−0.184841	−	0.106718i	−0.589565	+	0.807721i	$0.700701\pi$
$30$	−18.0636	−	35.7383i	−0.602118	−	1.19128i
$31$	−12.5185	+	21.6826i	−0.403822	+	0.699440i	−0.994184	−	0.107699i	$-0.965652\pi$
$31$	−12.5185	+	21.6826i	−0.403822	+	0.699440i	0.590362	+	0.807139i	$0.298985\pi$
$32$			41.4476i			1.29524i
$33$	4.90218	−	2.47775i	0.148551	−	0.0750834i
$34$	8.48174	−	14.6908i	0.249463	−	0.432083i
$35$	0.909158	+	0.524902i	0.0259759	+	0.0149972i
$36$	−50.3109	−	5.61870i	−1.39752	−	0.156075i
$37$	25.8584			0.698876			0.349438	−	0.936959i	$-0.386372\pi$
$37$	25.8584			0.698876			0.349438	+	0.936959i	$0.386372\pi$
$38$	−58.6771	+	5.61811i	−1.54414	+	0.147845i
$39$	−21.5735	−	1.20093i	−0.553168	−	0.0307930i
$40$	10.8442	+	18.7828i	0.271106	+	0.469570i
$41$	−50.3865	+	29.0907i	−1.22894	+	0.709529i	−0.966808	−	0.255503i	$-0.917759\pi$
$41$	−50.3865	+	29.0907i	−1.22894	+	0.709529i	−0.262132	+	0.965032i	$0.584426\pi$
$42$	2.02677	−	1.02441i	0.0482565	−	0.0243907i
$43$	16.1357			0.375250			0.187625	−	0.982241i	$-0.439921\pi$
$43$	16.1357			0.375250			0.187625	+	0.982241i	$0.439921\pi$
$44$	−8.91893	+	5.14934i	−0.202703	+	0.117031i
$45$	35.4762	−	15.5196i	0.788361	−	0.344879i
$46$	92.7484			2.01627
$47$	27.2821	+	15.7513i	0.580470	+	0.335135i	0.761320	−	0.648376i	$-0.224552\pi$
$47$	27.2821	+	15.7513i	0.580470	+	0.335135i	−0.180850	+	0.983511i	$0.557885\pi$
$48$	−20.5496	−	1.14393i	−0.428116	−	0.0238318i
$49$	24.4702	−	42.3837i	0.499392	−	0.864973i
$50$	17.4334	+	10.0652i	0.348668	+	0.201303i
$51$	13.7281	+	8.97870i	0.269179	+	0.176053i
$52$	40.5119			0.779075
$53$	55.2531	−	31.9004i	1.04251	−	0.601894i	0.121967	−	0.992534i	$-0.461080\pi$
$53$	55.2531	−	31.9004i	1.04251	−	0.601894i	0.920543	+	0.390640i	$0.127746\pi$
$54$	13.9096	−	82.6017i	0.257585	−	1.52966i
$55$	3.93876	−	6.82214i	0.0716139	−	0.124039i
$56$	−1.06520	+	0.614992i	−0.0190214	+	0.0109820i
$57$	−2.27061	−	56.9548i	−0.0398352	−	0.999206i
$58$	−9.60136	+	16.6300i	−0.165541	+	0.286725i
$59$	19.6012	−	11.3168i	0.332224	−	0.191810i	−0.324604	−	0.945850i	$-0.605231\pi$
$59$	19.6012	−	11.3168i	0.332224	−	0.191810i	0.656828	+	0.754040i	$0.271898\pi$
$60$	−64.7960	+	32.7504i	−1.07993	+	0.545841i
$61$	−0.694666	+	1.20320i	−0.0113880	+	0.0197245i	−0.871663	−	0.490105i	$-0.836958\pi$
$61$	−0.694666	+	1.20320i	−0.0113880	+	0.0197245i	0.860275	+	0.509830i	$0.170292\pi$
$62$	67.2681	+	38.8372i	1.08497	+	0.626407i
$63$	0.880136	+	2.01191i	0.0139704	+	0.0319350i
$64$	101.145			1.58039
$65$	−26.8362	+	15.4939i	−0.412865	+	0.238368i
$66$	−7.68697	−	15.2085i	−0.116469	−	0.230432i
$67$	−18.1418			−0.270774			−0.135387	−	0.990793i	$-0.543228\pi$
$67$	−18.1418			−0.270774			−0.135387	+	0.990793i	$0.543228\pi$
$68$	−26.6354	−	15.3780i	−0.391697	−	0.226147i
$69$	−4.98488	+	89.5486i	−0.0722446	+	1.29781i
$70$	1.62845	−	2.82057i	0.0232636	−	0.0402938i
$71$	94.7332	+	54.6943i	1.33427	+	0.770342i	0.985951	−	0.167034i	$-0.0534190\pi$
$71$	94.7332	+	54.6943i	1.33427	+	0.770342i	0.348320	+	0.937376i	$0.386752\pi$
$72$	−5.03541	+	45.0880i	−0.0699363	+	0.626223i
$73$	5.53115	−	9.58024i	0.0757692	−	0.131236i	−0.825651	−	0.564181i	$-0.809192\pi$
$73$	5.53115	−	9.58024i	0.0757692	−	0.131236i	0.901421	+	0.432945i	$0.142525\pi$
$74$		−	80.2230i		−	1.08410i
$75$	−10.6549	+	16.2910i	−0.142065	+	0.217213i
$76$	10.1860	+	106.386i	0.134026	+	1.39981i
$77$	0.386893	+	0.223373i	0.00502459	+	0.00290095i
$78$	−3.72575	+	66.9296i	−0.0477661	+	0.858072i
$79$	−118.751			−1.50317			−0.751587	−	0.659634i	$-0.770711\pi$
$79$	−118.751			−1.50317			−0.751587	+	0.659634i	$0.770711\pi$
$80$	−25.5625	+	14.7585i	−0.319531	+	0.184481i
$81$	79.0044	+	17.8692i	0.975363	+	0.220608i
$82$	90.2508	+	156.319i	1.10062	+	1.90633i
$83$	−62.7808	+	36.2465i	−0.756395	+	0.436705i	−0.828000	−	0.560728i	$-0.810521\pi$
$83$	−62.7808	+	36.2465i	−0.756395	+	0.436705i	0.0716052	+	0.997433i	$0.477188\pi$
$84$	−1.85732	−	3.67467i	−0.0221110	−	0.0437461i
$85$	23.5254			0.276769
$86$		−	50.0594i		−	0.582087i
$87$	−15.5403	−	10.1639i	−0.178624	−	0.116827i
$88$	4.61478	+	7.99304i	0.0524407	+	0.0908300i
$89$	37.8306	−	21.8415i	0.425063	−	0.245410i	−0.272178	−	0.962247i	$-0.587744\pi$
$89$	37.8306	−	21.8415i	0.425063	−	0.245410i	0.697241	+	0.716837i	$0.254411\pi$
$90$	−48.1478	−	110.061i	−0.534976	−	1.22290i
$91$	−0.878681	−	1.52192i	−0.00965584	−	0.0167244i
$92$		−	168.159i		−	1.82782i
$93$	−41.1128	+	62.8600i	−0.442073	+	0.675914i
$94$	48.8668	−	84.6398i	0.519860	−	0.900424i
$95$	−47.4350	−	66.5772i	−0.499316	−	0.700812i
$96$	−6.91105	+	124.150i	−0.0719901	+	1.29323i
$97$	−182.445			−1.88087			−0.940436	−	0.339972i	$-0.889582\pi$
$97$	−182.445			−1.88087			−0.940436	+	0.339972i	$0.889582\pi$
$98$	−131.491	−	75.9163i	−1.34174	−	0.774656i
$99$	15.0970	−	6.60437i	0.152494	−	0.0667108i
$100$	18.2488	−	31.6079i	0.182488	−	0.316079i
$101$	55.0667	+	31.7928i	0.545215	+	0.314780i	0.747190	−	0.664611i	$-0.231403\pi$
$101$	55.0667	+	31.7928i	0.545215	+	0.314780i	−0.201975	+	0.979391i	$0.564736\pi$
$102$	27.8555	−	42.5900i	0.273093	−	0.417549i
$103$	−34.0216	+	58.9272i	−0.330307	+	0.572108i	−0.982572	−	0.185883i	$-0.940486\pi$
$103$	−34.0216	+	58.9272i	−0.330307	+	0.572108i	0.652265	+	0.757991i	$0.273819\pi$
$104$		−	36.3063i		−	0.349099i
$105$	2.63573	+	1.72387i	0.0251022	+	0.0164178i
$106$	−98.9676	−	171.417i	−0.933656	−	1.61714i
$107$		−	53.8099i		−	0.502897i	−0.967871	−	0.251448i	$-0.919093\pi$
$107$		−	53.8099i		−	0.502897i	0.967871	−	0.251448i	$-0.0809068\pi$
$108$	−149.762	−	25.2190i	−1.38669	−	0.233509i
$109$	1.25329	−	2.17076i	0.0114980	−	0.0199152i	−0.860219	−	0.509925i	$-0.829673\pi$
$109$	1.25329	−	2.17076i	0.0114980	−	0.0199152i	0.871717	+	0.490009i	$0.163007\pi$
$110$	−21.1650	−	12.2196i	−0.192409	−	0.111087i
$111$	77.4554	+	4.31169i	0.697796	+	0.0388440i
$112$	−0.836976	−	1.44968i	−0.00747300	−	0.0129436i
$113$	−179.813	−	103.815i	−1.59127	−	0.918718i	−0.993090	−	0.117353i	$-0.962559\pi$
$113$	−179.813	−	103.815i	−1.59127	−	0.918718i	−0.598176	−	0.801365i	$-0.704108\pi$
$114$	−176.696	+	7.04432i	−1.54997	+	0.0617923i
$115$	64.3129	+	111.393i	0.559243	+	0.968637i
$116$	30.1514	+	17.4079i	0.259926	+	0.150068i
$117$	−64.4203	−	7.19443i	−0.550601	−	0.0614909i
$118$	−35.1091	−	60.8108i	−0.297535	−	0.515346i
$119$			1.33416i			0.0112114i
$120$	29.3506	+	58.0694i	0.244588	+	0.483912i
$121$	−58.8239	+	101.886i	−0.486148	+	0.842032i
$122$	3.73279	+	2.15513i	0.0305966	+	0.0176650i
$123$	−155.777	+	78.7356i	−1.26648	+	0.640127i
$124$	70.4145	−	121.962i	0.567859	−	0.983561i
$125$			135.479i			1.08383i
$126$	6.24173	−	2.73053i	0.0495375	−	0.0216709i
$127$	−74.4050	−	128.873i	−0.585866	−	1.01475i	−0.994767	−	0.102171i	$-0.967421\pi$
$127$	−74.4050	−	128.873i	−0.585866	−	1.01475i	0.408900	−	0.912579i	$-0.365912\pi$
$128$		−	148.001i		−	1.15626i
$129$	48.3324	+	2.69051i	0.374670	+	0.0208567i
$130$	48.0682	+	83.2566i	0.369755	+	0.640435i
$131$	45.9094	−	26.5058i	0.350454	−	0.202335i	−0.314431	−	0.949280i	$-0.601814\pi$
$131$	45.9094	−	26.5058i	0.350454	−	0.202335i	0.664885	+	0.746946i	$0.268481\pi$
$132$	−27.5740	+	13.9370i	−0.208894	+	0.105583i
$133$	3.77568	−	2.69011i	0.0283886	−	0.0202264i
$134$			56.2831i			0.420023i
$135$	108.852	−	40.5713i	0.806311	−	0.300528i
$136$	−13.7816	+	23.8704i	−0.101335	+	0.175517i
$137$	189.263	+	109.271i	1.38148	+	0.797598i	0.992335	−	0.123578i	$-0.0394370\pi$
$137$	189.263	+	109.271i	1.38148	+	0.797598i	0.389146	+	0.921176i	$0.372770\pi$
$138$	277.815	+	15.4651i	2.01315	+	0.112066i
$139$	40.5748			0.291905			0.145953	−	0.989292i	$-0.453375\pi$
$139$	40.5748			0.291905			0.145953	+	0.989292i	$0.453375\pi$
$140$	−5.11388	−	2.95250i	−0.0365277	−	0.0210893i
$141$	79.0934	+	51.7300i	0.560946	+	0.366880i
$142$	169.683	−	293.900i	1.19495	−	2.06972i
$143$	−11.4202	+	6.59345i	−0.0798615	+	0.0461081i
$144$	−61.3627	−	6.85296i	−0.426130	−	0.0475900i
$145$	−26.6308			−0.183661
$146$	−29.7217	−	17.1598i	−0.203573	−	0.117533i
$147$	80.3644	−	122.874i	0.546696	−	0.835880i
$148$	−145.450			−0.982769
$149$	−39.7078	+	22.9253i	−0.266495	+	0.153861i	−0.627294	−	0.778783i	$-0.715837\pi$
$149$	−39.7078	+	22.9253i	−0.266495	+	0.153861i	0.360799	+	0.932644i	$0.382504\pi$
$150$	50.5410	+	33.0557i	0.336940	+	0.220371i
$151$	89.9816	+	155.853i	0.595904	+	1.03214i	0.993419	+	0.114541i	$0.0365396\pi$
$151$	89.9816	+	155.853i	0.595904	+	1.03214i	−0.397514	+	0.917596i	$0.630127\pi$
$152$	95.3416	−	9.12858i	0.627247	−	0.0600565i
$153$	39.6236	+	29.1835i	0.258977	+	0.190742i
$154$	0.692991	−	1.20030i	0.00449994	−	0.00779413i
$155$			107.721i			0.694974i
$156$	121.348	+	6.75504i	0.777871	+	0.0433016i
$157$	−71.8821	−	124.503i	−0.457848	−	0.793015i	0.540999	−	0.841023i	$-0.318046\pi$
$157$	−71.8821	−	124.503i	−0.457848	−	0.793015i	−0.998847	+	0.0480077i	$0.984713\pi$
$158$			368.412i			2.33172i
$159$	170.822	−	86.3402i	1.07435	−	0.543020i
$160$	89.1637	+	154.436i	0.557273	+	0.965225i
$161$	−6.31727	+	3.64728i	−0.0392377	+	0.0226539i
$162$	55.4374	−	245.103i	0.342206	−	1.51298i
$163$	−305.866			−1.87648			−0.938240	−	0.345984i	$-0.887545\pi$
$163$	−305.866			−1.87648			−0.938240	+	0.345984i	$0.887545\pi$
$164$	283.417	−	163.631i	1.72815	−	0.997748i
$165$	12.9356	−	19.7780i	0.0783974	−	0.119867i
$166$	112.451	+	194.771i	0.677415	+	1.17332i
$167$			69.0811i			0.413659i	0.978377	+	0.206830i	$0.0663146\pi$
$167$			69.0811i			0.413659i	−0.978377	+	0.206830i	$0.933685\pi$
$168$	−3.29320	+	1.66451i	−0.0196024	+	0.00990781i
$169$	−117.127			−0.693057
$170$		−	72.9851i		−	0.429324i
$171$	2.69546	−	170.979i	0.0157630	−	0.999876i
$172$	−90.7612			−0.527681
$173$		−	240.294i		−	1.38898i	−0.719502	−	0.694490i	$-0.755630\pi$
$173$		−	240.294i		−	1.38898i	0.719502	−	0.694490i	$-0.244370\pi$
$174$	−31.5325	+	48.2120i	−0.181221	+	0.277081i
$175$	−1.58323			−0.00904702
$176$	−10.8781	+	6.28050i	−0.0618077	+	0.0356847i
$177$	60.5998	−	30.6295i	0.342372	−	0.173048i
$178$	−67.7610	−	117.365i	−0.380680	−	0.659356i
$179$			114.747i			0.641042i	0.947241	+	0.320521i	$0.103858\pi$
$179$			114.747i			0.641042i	−0.947241	+	0.320521i	$0.896142\pi$
$180$	−199.548	+	87.2952i	−1.10860	+	0.484973i
$181$	−155.928	−	270.076i	−0.861483	−	1.49213i	−0.870497	−	0.492173i	$-0.836203\pi$
$181$	−155.928	−	270.076i	−0.861483	−	1.49213i	0.00901439	−	0.999959i	$-0.497131\pi$
$182$	−4.72160	+	2.72602i	−0.0259428	+	0.0149781i
$183$	−2.28140	+	3.48818i	−0.0124667	+	0.0190611i
$184$	−150.702			−0.819034
$185$	96.3500	−	55.6277i	0.520811	−	0.300690i
$186$	195.016	+	127.548i	1.04848	+	0.685742i
$187$	10.0113			0.0535362
$188$	−153.458	−	88.5989i	−0.816265	−	0.471271i
$189$	2.30086	+	6.17315i	0.0121739	+	0.0326622i
$190$	−206.549	+	147.162i	−1.08710	+	0.774537i
$191$	37.6935	−	21.7623i	0.197348	−	0.113939i	−0.398070	−	0.917355i	$-0.630320\pi$
$191$	37.6935	−	21.7623i	0.197348	−	0.113939i	0.595418	+	0.803416i	$0.296987\pi$
$192$	302.965	+	16.8651i	1.57794	+	0.0878391i
$193$	−27.0004	−	46.7660i	−0.139898	−	0.242311i	0.787560	−	0.616238i	$-0.211344\pi$
$193$	−27.0004	−	46.7660i	−0.139898	−	0.242311i	−0.927458	+	0.373927i	$0.878011\pi$
$194$			566.015i			2.91760i
$195$	−82.9677	+	41.9351i	−0.425476	+	0.215052i
$196$	−137.641	+	238.402i	−0.702252	+	1.21634i
$197$		−	350.299i		−	1.77817i	−0.457743	−	0.889085i	$-0.651342\pi$
$197$		−	350.299i		−	1.77817i	0.457743	−	0.889085i	$-0.348658\pi$
$198$	−20.4894	−	46.8367i	−0.103482	−	0.236549i
$199$	29.9017	+	51.7913i	0.150260	+	0.260258i	0.931323	−	0.364194i	$-0.118656\pi$
$199$	29.9017	+	51.7913i	0.150260	+	0.260258i	−0.781063	+	0.624452i	$0.785322\pi$
$200$	−28.3266	−	16.3544i	−0.141633	−	0.0817720i
$201$	−54.3414	−	3.02501i	−0.270355	−	0.0150498i
$202$	98.6337	−	170.839i	0.488285	−	0.845735i
$203$		−	1.51027i		−	0.00743976i
$204$	−77.2186	−	50.5038i	−0.378523	−	0.247568i
$205$	−125.162	+	216.787i	−0.610547	+	1.05750i
$206$	182.815	+	105.548i	0.887453	+	0.512371i
$207$	−29.8630	+	267.399i	−0.144266	+	1.29178i
$208$	49.4112			0.237554
$209$	−20.1860	−	28.3320i	−0.0965839	−	0.135560i
$210$	5.34812	−	8.17709i	0.0254672	−	0.0389385i
$211$	−160.525	−	278.037i	−0.760781	−	1.31771i	−0.942448	−	0.334352i	$-0.891483\pi$
$211$	−160.525	−	278.037i	−0.760781	−	1.31771i	0.181667	−	0.983360i	$-0.441851\pi$
$212$	−310.790	+	179.435i	−1.46599	+	0.846391i
$213$	274.641	+	179.625i	1.28939	+	0.843311i
$214$	−166.940			−0.780092
$215$	60.1227	−	34.7119i	0.279641	−	0.161451i
$216$	−22.6010	+	134.215i	−0.104634	+	0.621367i
$217$	−6.10901			−0.0281521
$218$	−6.73454	−	3.88819i	−0.0308924	−	0.0178357i
$219$	18.1652	−	27.7740i	0.0829463	−	0.126822i
$220$	−22.1550	+	38.3735i	−0.100704	+	0.174425i
$221$	−34.1052	−	19.6906i	−0.154322	−	0.0890979i
$222$	13.3766	−	240.297i	0.0602548	−	1.08242i
$223$	362.065			1.62361			0.811806	−	0.583927i	$-0.198485\pi$
$223$	362.065			1.62361			0.811806	+	0.583927i	$0.198485\pi$
$224$	−8.75829	+	5.05660i	−0.0390995	+	0.0225741i
$225$	−34.6317	+	47.0208i	−0.153919	+	0.208981i
$226$	−322.075	+	557.851i	−1.42511	+	2.46837i
$227$	137.742	−	79.5252i	0.606792	−	0.350331i	−0.164917	−	0.986307i	$-0.552736\pi$
$227$	137.742	−	79.5252i	0.606792	−	0.350331i	0.771709	+	0.635976i	$0.219402\pi$
$228$	12.7718	+	320.362i	0.0560168	+	1.40510i
$229$	127.999	−	221.700i	0.558946	−	0.968124i	−0.438638	−	0.898664i	$-0.644539\pi$
$229$	127.999	−	221.700i	0.558946	−	0.968124i	0.997585	−	0.0694600i	$-0.0221276\pi$
$230$	345.586	−	199.524i	1.50255	−	0.867496i
$231$	1.12164	+	0.733594i	0.00485558	+	0.00317573i
$232$	15.6008	−	27.0213i	0.0672447	−	0.116471i
$233$	−184.915	−	106.761i	−0.793626	−	0.458200i	0.0476116	−	0.998866i	$-0.484839\pi$
$233$	−184.915	−	106.761i	−0.793626	−	0.458200i	−0.841237	+	0.540666i	$0.818172\pi$
$234$	−22.3200	+	199.857i	−0.0953845	+	0.854091i
$235$	135.540			0.576764
$236$	−110.254	+	63.6552i	−0.467178	+	0.269725i
$237$	−355.702	−	19.8008i	−1.50085	−	0.0835475i
$238$	4.13909			0.0173911
$239$	331.738	+	191.529i	1.38802	+	0.801376i	0.993092	−	0.117335i	$-0.0374351\pi$
$239$	331.738	+	191.529i	1.38802	+	0.801376i	0.394931	+	0.918711i	$0.370768\pi$
$240$	−79.0298	+	39.9447i	−0.329291	+	0.166436i
$241$	−79.3519	+	137.441i	−0.329261	+	0.570297i	−0.982365	−	0.186971i	$-0.940133\pi$
$241$	−79.3519	+	137.441i	−0.329261	+	0.570297i	0.653105	+	0.757268i	$0.273466\pi$
$242$	316.090	+	182.495i	1.30616	+	0.754111i
$243$	233.667	+	66.6982i	0.961593	+	0.274478i
$244$	3.90739	−	6.76780i	0.0160139	−	0.0277369i
$245$		−	210.565i		−	0.859451i
$246$	244.269	+	483.280i	0.992963	+	1.96455i
$247$	13.0426	+	136.221i	0.0528042	+	0.551502i
$248$	−109.300	−	63.1047i	−0.440728	−	0.254454i
$249$	−194.095	+	98.1032i	−0.779498	+	0.393989i
$250$	420.310			1.68124
$251$	−53.4985	+	30.8874i	−0.213141	+	0.123057i	−0.602771	−	0.797915i	$-0.705937\pi$
$251$	−53.4985	+	30.8874i	−0.213141	+	0.123057i	0.389629	+	0.920972i	$0.372603\pi$
$252$	−4.95064	−	11.3167i	−0.0196454	−	0.0449074i
$253$	27.3685	+	47.4035i	0.108176	+	0.187366i
$254$	−399.816	+	230.834i	−1.57408	+	0.908794i
$255$	70.4671	+	3.92268i	0.276342	+	0.0153830i
$256$	−54.5778			−0.213194
$257$		−	402.498i		−	1.56614i	−0.621935	−	0.783069i	$-0.713653\pi$
$257$		−	402.498i		−	1.56614i	0.621935	−	0.783069i	$-0.286347\pi$
$258$	8.34702	−	149.946i	0.0323528	−	0.581187i
$259$	3.15473	+	5.46415i	0.0121804	+	0.0210971i
$260$	150.950	−	87.1509i	0.580576	−	0.335196i
$261$	−44.8540	−	33.0358i	−0.171854	−	0.126574i
$262$	−82.2315	−	142.429i	−0.313861	−	0.543623i
$263$			4.90234i			0.0186401i	0.999957	+	0.00932004i	$0.00296670\pi$
$263$			4.90234i			0.0186401i	−0.999957	+	0.00932004i	$0.997033\pi$
$264$	12.4902	+	24.7115i	0.0473112	+	0.0936043i
$265$	137.251	−	237.725i	0.517928	−	0.897077i
$266$	−8.34577	−	11.7137i	−0.0313751	−	0.0440363i
$267$	116.958	−	59.1153i	0.438046	−	0.221406i
$268$	102.045			0.380765
$269$	169.855	+	98.0660i	0.631432	+	0.364558i	0.781307	−	0.624148i	$-0.214554\pi$
$269$	169.855	+	98.0660i	0.631432	+	0.364558i	−0.149874	+	0.988705i	$0.547887\pi$
$270$	−125.868	−	337.702i	−0.466179	−	1.25075i
$271$	−141.237	+	244.629i	−0.521169	+	0.902691i	0.478528	+	0.878072i	$0.341171\pi$
$271$	−141.237	+	244.629i	−0.521169	+	0.902691i	−0.999697	+	0.0246188i	$0.992163\pi$
$272$	−32.4864	−	18.7561i	−0.119435	−	0.0689561i
$273$	−2.37820	−	4.70522i	−0.00871136	−	0.0172352i
$274$	339.002	−	587.168i	1.23723	−	2.14295i
$275$			11.8802i			0.0432009i
$276$	28.0392	−	503.697i	0.101591	−	1.82499i
$277$	−23.6491	−	40.9615i	−0.0853759	−	0.147875i	0.820175	−	0.572112i	$-0.193876\pi$
$277$	−23.6491	−	40.9615i	−0.0853759	−	0.147875i	−0.905551	+	0.424237i	$0.860542\pi$
$278$		−	125.879i		−	0.452803i
$279$	−133.629	+	181.433i	−0.478957	+	0.650298i
$280$	−2.64599	+	4.58300i	−0.00944998	+	0.0163678i
$281$	−434.565	−	250.896i	−1.54649	−	0.892869i	−0.998406	−	0.0564480i	$-0.982022\pi$
$281$	−434.565	−	250.896i	−1.54649	−	0.892869i	−0.548088	−	0.836421i	$-0.684644\pi$
$282$	160.487	−	245.379i	0.569103	−	0.870138i
$283$	175.209	+	303.470i	0.619111	+	1.07233i	0.989648	+	0.143515i	$0.0458404\pi$
$283$	175.209	+	303.470i	0.619111	+	1.07233i	−0.370537	+	0.928818i	$0.620826\pi$
$284$	−532.860	−	307.647i	−1.87627	−	1.08326i
$285$	−130.984	−	207.332i	−0.459592	−	0.727481i
$286$	20.4555	+	35.4299i	0.0715227	+	0.123881i
$287$	−12.2943	−	7.09812i	−0.0428373	−	0.0247321i
$288$	−41.4022	+	370.723i	−0.143758	+	1.28723i
$289$	−129.551	−	224.389i	−0.448274	−	0.776433i
$290$			82.6193i			0.284894i
$291$	−546.487	−	30.4212i	−1.87796	−	0.104540i
$292$	−31.1119	+	53.8874i	−0.106548	+	0.184546i
$293$	−432.408	−	249.651i	−1.47580	−	0.852051i	−0.476168	−	0.879354i	$-0.657975\pi$
$293$	−432.408	−	249.651i	−1.47580	−	0.852051i	−0.999627	+	0.0273032i	$0.991308\pi$
$294$	−381.204	−	249.322i	−1.29661	−	0.848034i
$295$	48.6902	−	84.3340i	0.165052	−	0.285878i
$296$			130.350i			0.440373i
$297$	46.3221	−	17.2652i	0.155967	−	0.0581319i
$298$	71.1233	+	123.189i	0.238669	+	0.413386i
$299$		−	215.318i		−	0.720128i
$300$	59.9322	−	91.6343i	0.199774	−	0.305448i
$301$	1.96856	+	3.40965i	0.00654007	+	0.0113277i
$302$	483.516	−	279.158i	1.60105	−	0.924365i
$303$	159.643	+	104.413i	0.526876	+	0.344597i
$304$	12.4236	+	129.755i	0.0408670	+	0.426827i
$305$			5.97757i			0.0195986i
$306$	90.5388	−	122.928i	0.295878	−	0.401725i
$307$	287.121	−	497.309i	0.935249	−	1.61990i	0.161059	−	0.986945i	$-0.448509\pi$
$307$	287.121	−	497.309i	0.935249	−	1.61990i	0.774190	−	0.632953i	$-0.218158\pi$
$308$	−2.17622	−	1.25644i	−0.00706564	−	0.00407935i
$309$	−111.733	+	170.835i	−0.361595	+	0.552865i
$310$	334.193			1.07804
$311$	−47.8179	−	27.6077i	−0.153755	−	0.0887707i	0.421148	−	0.906992i	$-0.361627\pi$
$311$	−47.8179	−	27.6077i	−0.153755	−	0.0887707i	−0.574904	+	0.818221i	$0.694960\pi$
$312$	6.05379	−	108.751i	0.0194032	−	0.348560i
$313$	87.5165	−	151.583i	0.279605	−	0.484291i	−0.691681	−	0.722203i	$-0.743130\pi$
$313$	87.5165	−	151.583i	0.279605	−	0.484291i	0.971287	+	0.237912i	$0.0764630\pi$
$314$	−386.259	+	223.007i	−1.23012	+	0.710212i
$315$	7.60754	+	5.60310i	0.0241509	+	0.0177876i
$316$	667.955			2.11378
$317$	−18.2304	−	10.5253i	−0.0575091	−	0.0332029i	0.470970	−	0.882149i	$-0.343904\pi$
$317$	−18.2304	−	10.5253i	−0.0575091	−	0.0332029i	−0.528479	+	0.848946i	$0.677237\pi$
$318$	−267.861	−	529.958i	−0.842331	−	1.66653i
$319$	−11.3328			−0.0355260
$320$	376.872	−	217.587i	1.17772	−	0.679959i
$321$	8.97238	−	161.180i	0.0279513	−	0.502119i
$322$	11.3153	+	19.5987i	0.0351407	+	0.0608654i
$323$	43.1331	−	94.5122i	0.133539	−	0.292607i
$324$	−444.388	−	100.512i	−1.37157	−	0.310221i
$325$	23.3666	−	40.4722i	0.0718973	−	0.124530i
$326$			948.918i			2.91079i
$327$	4.11601	−	6.29323i	0.0125872	−	0.0192453i
$328$	−146.644	−	253.995i	−0.447085	−	0.774374i
$329$			7.68664i			0.0233637i
$330$	−61.3592	−	40.1312i	−0.185937	−	0.121610i
$331$	218.982	+	379.288i	0.661578	+	1.14589i	0.980201	+	0.198005i	$0.0634462\pi$
$331$	218.982	+	379.288i	0.661578	+	1.14589i	−0.318623	+	0.947881i	$0.603220\pi$
$332$	353.132	−	203.881i	1.06365	−	0.614100i
$333$	231.288	+	25.8301i	0.694559	+	0.0775680i
$334$	214.317			0.641667
$335$	−67.5976	+	39.0275i	−0.201784	+	0.116500i
$336$	−2.26532	−	4.48189i	−0.00674203	−	0.0133390i
$337$	293.744	+	508.780i	0.871644	+	1.50973i	0.860295	+	0.509797i	$0.170279\pi$
$337$	293.744	+	508.780i	0.871644	+	1.50973i	0.0113493	+	0.999936i	$0.496387\pi$
$338$			363.373i			1.07507i
$339$	−521.295	−	340.946i	−1.53774	−	1.00574i
$340$	−132.327			−0.389197
$341$			45.8408i			0.134430i
$342$	−530.444	−	8.36239i	−1.55100	−	0.0244514i
$343$	23.8975			0.0696719
$344$			81.3391i			0.236451i
$345$	174.067	+	344.387i	0.504541	+	0.998223i
$346$	−745.486			−2.15458
$347$	−254.357	+	146.853i	−0.733016	+	0.423207i	−0.819525	−	0.573044i	$-0.805762\pi$
$347$	−254.357	+	146.853i	−0.733016	+	0.423207i	0.0865082	+	0.996251i	$0.472429\pi$
$348$	87.4117	+	57.1705i	0.251183	+	0.164283i
$349$	60.3052	+	104.452i	0.172794	+	0.299289i	0.939396	−	0.342835i	$-0.111387\pi$
$349$	60.3052	+	104.452i	0.172794	+	0.299289i	−0.766601	+	0.642123i	$0.778054\pi$
$350$			4.91180i			0.0140337i
$351$	−191.763	−	32.2915i	−0.546332	−	0.0919986i
$352$	37.9437	+	65.7205i	0.107795	+	0.186706i
$353$	302.080	−	174.406i	0.855750	−	0.494068i	−0.00683651	−	0.999977i	$-0.502176\pi$
$353$	302.080	−	174.406i	0.855750	−	0.494068i	0.862587	+	0.505909i	$0.168843\pi$
$354$	−95.0248	−	188.004i	−0.268432	−	0.531086i
$355$	470.642			1.32575
$356$	−212.791	+	122.855i	−0.597729	+	0.345099i
$357$	−0.222460	+	3.99629i	−0.000623139	+	0.0111941i
$358$	355.989			0.994383
$359$	277.550	+	160.244i	0.773121	+	0.446362i	0.833987	−	0.551784i	$-0.186053\pi$
$359$	277.550	+	160.244i	0.773121	+	0.446362i	−0.0608659	+	0.998146i	$0.519386\pi$
$360$	78.2330	+	178.833i	0.217314	+	0.496758i
$361$	−354.441	+	68.5007i	−0.981832	+	0.189753i
$362$	−837.882	+	483.751i	−2.31459	+	1.33633i
$363$	−193.187	+	295.377i	−0.532197	+	0.813710i
$364$	4.94245	+	8.56058i	0.0135782	+	0.0235181i
$365$		−	47.5954i		−	0.130398i
$366$	10.8217	+	7.07780i	0.0295675	+	0.0193382i
$367$	−14.8859	+	25.7831i	−0.0405609	+	0.0702536i	−0.885593	−	0.464462i	$-0.846248\pi$
$367$	−14.8859	+	25.7831i	−0.0405609	+	0.0702536i	0.845032	+	0.534715i	$0.179581\pi$
$368$		−	205.099i		−	0.557333i
$369$	−479.736	+	209.867i	−1.30010	+	0.568746i
$370$	−172.579	−	298.916i	−0.466430	−	0.807880i
$371$	13.4817	+	7.78369i	0.0363389	+	0.0209803i
$372$	231.253	−	353.578i	0.621648	−	0.950478i
$373$	−6.86222	+	11.8857i	−0.0183974	+	0.0318652i	−0.875078	−	0.483983i	$-0.839190\pi$
$373$	−6.86222	+	11.8857i	−0.0183974	+	0.0318652i	0.856680	+	0.515848i	$0.172523\pi$
$374$		−	31.0589i		−	0.0830452i
$375$	−22.5901	+	405.810i	−0.0602403	+	1.08216i
$376$	−79.4013	+	137.527i	−0.211174	+	0.365763i
$377$	38.6072	+	22.2899i	0.102406	+	0.0591243i
$378$	19.1515	−	7.13817i	0.0506654	−	0.0188840i
$379$	343.933			0.907476			0.453738	−	0.891135i	$-0.350090\pi$
$379$	343.933			0.907476			0.453738	+	0.891135i	$0.350090\pi$
$380$	266.815	+	374.487i	0.702144	+	0.985491i
$381$	−201.381	−	398.429i	−0.528560	−	1.04574i
$382$	−67.5153	−	116.940i	−0.176742	−	0.306126i
$383$	−400.837	+	231.423i	−1.04657	+	0.604238i	−0.921687	−	0.387934i	$-0.873189\pi$
$383$	−400.837	+	231.423i	−1.04657	+	0.604238i	−0.124883	+	0.992171i	$0.539856\pi$
$384$	24.6780	−	443.316i	0.0642656	−	1.15447i
$385$	1.92212			0.00499251
$386$	−145.087	+	83.7658i	−0.375872	+	0.217010i
$387$	144.324	+	16.1181i	0.372931	+	0.0416488i
$388$	1026.22			2.64490
$389$	96.6413	+	55.7959i	0.248435	+	0.143434i	0.619048	−	0.785354i	$-0.287519\pi$
$389$	96.6413	+	55.7959i	0.248435	+	0.143434i	−0.370612	+	0.928788i	$0.620852\pi$
$390$	130.099	+	257.399i	0.333588	+	0.659997i
$391$	−81.7330	+	141.566i	−0.209036	+	0.362061i
$392$	213.653	+	123.353i	0.545033	+	0.314675i
$393$	141.935	−	71.7395i	0.361158	−	0.182543i
$394$	−1086.77			−2.75829
$395$	−442.472	+	255.462i	−1.12018	+	0.646738i
$396$	−84.9181	+	37.1486i	−0.214440	+	0.0938096i
$397$	−300.313	+	520.157i	−0.756455	+	1.31022i	0.188193	+	0.982132i	$0.439737\pi$
$397$	−300.313	+	520.157i	−0.756455	+	1.31022i	−0.944648	+	0.328086i	$0.893596\pi$
$398$	160.677	−	92.7669i	0.403711	−	0.233083i
$399$	11.7581	−	7.42828i	0.0294689	−	0.0186172i
$400$	22.2576	−	38.5512i	0.0556439	−	0.0963781i
$401$	402.565	−	232.421i	1.00390	−	0.579603i	0.0945015	−	0.995525i	$-0.469874\pi$
$401$	402.565	−	232.421i	1.00390	−	0.579603i	0.909400	+	0.415922i	$0.136541\pi$
$402$	−9.38477	+	168.588i	−0.0233452	+	0.419374i
$403$	90.1619	−	156.165i	0.223727	−	0.387506i
$404$	−309.742	−	178.829i	−0.766687	−	0.442647i
$405$	332.816	−	103.376i	0.821768	−	0.255249i
$406$	−4.68546			−0.0115405
$407$	41.0019	−	23.6724i	0.100742	−	0.0581633i
$408$	−45.2610	+	69.2024i	−0.110934	+	0.169614i
$409$	−315.977			−0.772561			−0.386281	−	0.922381i	$-0.626240\pi$
$409$	−315.977			−0.772561			−0.386281	+	0.922381i	$0.626240\pi$
$410$	672.559	+	388.302i	1.64039	+	0.947079i
$411$	548.691	+	358.864i	1.33501	+	0.873149i
$412$	191.366	−	331.456i	0.464482	−	0.804506i
$413$	4.78270	+	2.76129i	0.0115804	+	0.00668594i
$414$	829.578	+	92.6469i	2.00381	+	0.223785i
$415$	−155.950	+	270.113i	−0.375783	+	0.650875i
$416$		−	298.518i		−	0.717592i
$417$	121.536	+	6.76554i	0.291454	+	0.0162243i
$418$	−87.8970	+	62.6250i	−0.210280	+	0.149821i
$419$	−191.611	−	110.627i	−0.457306	−	0.264026i	0.253605	−	0.967308i	$-0.418384\pi$
$419$	−191.611	−	110.627i	−0.457306	−	0.264026i	−0.710911	+	0.703282i	$0.751717\pi$
$420$	−14.8256	−	9.69650i	−0.0352991	−	0.0230869i
$421$	−255.233			−0.606255			−0.303128	−	0.952950i	$-0.598031\pi$
$421$	−255.233			−0.606255			−0.303128	+	0.952950i	$0.598031\pi$
$422$	−862.581	+	498.011i	−2.04403	+	1.18012i
$423$	228.288	+	168.138i	0.539687	+	0.397490i
$424$	160.807	+	278.527i	0.379263	+	0.656902i
$425$	−30.7258	+	17.7395i	−0.0722959	+	0.0417401i
$426$	557.268	−	852.043i	1.30814	−	2.00010i
$427$	−0.338997			−0.000793903
$428$			302.673i			0.707179i
$429$	−35.3070	+	17.8456i	−0.0823008	+	0.0415980i
$430$	−107.690	−	186.524i	−0.250442	−	0.433778i
$431$	515.063	−	297.372i	1.19504	−	0.689957i	0.235595	−	0.971851i	$-0.424296\pi$
$431$	515.063	−	297.372i	1.19504	−	0.689957i	0.959446	+	0.281894i	$0.0909627\pi$
$432$	−182.661	−	30.7588i	−0.422826	−	0.0712010i
$433$	−213.469	−	369.739i	−0.493000	−	0.853902i	0.506967	−	0.861965i	$-0.330767\pi$
$433$	−213.469	−	369.739i	−0.493000	−	0.853902i	−0.999967	+	0.00806366i	$0.997433\pi$
$434$			18.9526i			0.0436695i
$435$	−79.7690	−	4.44048i	−0.183377	−	0.0102080i
$436$	−7.04955	+	12.2102i	−0.0161687	+	0.0280050i
$437$	565.433	−	54.1380i	1.29390	−	0.123886i
$438$	−86.1659	−	56.3557i	−0.196726	−	0.128666i
$439$	266.774			0.607686			0.303843	−	0.952722i	$-0.401730\pi$
$439$	266.774			0.607686			0.303843	+	0.952722i	$0.401730\pi$
$440$	34.3899	+	19.8550i	0.0781589	+	0.0451250i
$441$	261.209	−	354.653i	0.592310	−	0.804202i
$442$	−61.0881	+	105.808i	−0.138208	+	0.239384i
$443$	−313.524	−	181.013i	−0.707728	−	0.408607i	0.102491	−	0.994734i	$-0.467319\pi$
$443$	−313.524	−	181.013i	−0.707728	−	0.408607i	−0.810219	+	0.586127i	$0.800652\pi$
$444$	−435.675	−	24.2526i	−0.981250	−	0.0546230i
$445$	93.9727	−	162.766i	0.211175	−	0.365765i
$446$		−	1123.27i		−	2.51854i
$447$	−122.762	+	62.0486i	−0.274635	+	0.138811i
$448$	12.3397	+	21.3729i	0.0275439	+	0.0477074i
$449$			482.220i			1.07399i	0.843587	+	0.536993i	$0.180440\pi$
$449$			482.220i			1.07399i	−0.843587	+	0.536993i	$0.819560\pi$
$450$	145.877	+	107.441i	0.324171	+	0.238758i
$451$	−53.2629	+	92.2541i	−0.118100	+	0.204554i
$452$	1011.42	+	583.945i	2.23766	+	1.29191i
$453$	243.540	+	481.839i	0.537616	+	1.06366i
$454$	−246.719	−	427.329i	−0.543433	−	0.941254i
$455$	−6.54804	−	3.78051i	−0.0143913	−	0.00830882i
$456$	287.105	−	11.4460i	0.629616	−	0.0251008i
$457$	−118.786	−	205.744i	−0.259926	−	0.450205i	0.706296	−	0.707917i	$-0.250365\pi$
$457$	−118.786	−	205.744i	−0.259926	−	0.450205i	−0.966222	+	0.257712i	$0.917032\pi$
$458$	−687.802	−	397.103i	−1.50175	−	0.867036i
$459$	113.821	+	94.0221i	0.247976	+	0.204841i
$460$	−361.751	−	626.570i	−0.786414	−	1.36211i
$461$			146.611i			0.318028i	0.987276	+	0.159014i	$0.0508314\pi$
$461$			146.611i			0.318028i	−0.987276	+	0.159014i	$0.949169\pi$
$462$	2.27590	−	3.47977i	0.00492619	−	0.00753197i
$463$	−252.501	+	437.345i	−0.545359	+	0.944590i	0.453225	+	0.891396i	$0.350274\pi$
$463$	−252.501	+	437.345i	−0.545359	+	0.944590i	−0.998584	+	0.0531940i	$0.983060\pi$
$464$	36.7747	+	21.2319i	0.0792559	+	0.0457584i
$465$	−17.9616	+	322.663i	−0.0386272	+	0.693900i
$466$	−331.214	+	573.679i	−0.710759	+	1.23107i
$467$			793.589i			1.69934i	0.527319	+	0.849668i	$0.323197\pi$
$467$			793.589i			1.69934i	−0.527319	+	0.849668i	$0.676803\pi$
$468$	362.355	+	40.4676i	0.774262	+	0.0864693i
$469$	−2.21330	−	3.83355i	−0.00471920	−	0.00817389i
$470$		−	420.497i		−	0.894675i
$471$	−194.553	−	384.919i	−0.413063	−	0.817237i
$472$	57.0470	+	98.8084i	0.120862	+	0.209340i
$473$	25.5853	−	14.7717i	0.0540916	−	0.0312298i
$474$	−61.4298	+	1103.53i	−0.129599	+	2.32812i
$475$	112.156	+	51.1855i	0.236119	+	0.107759i
$476$		−	7.50444i		−	0.0157656i
$477$	526.071	−	230.137i	1.10287	−	0.482467i
$478$	594.198	−	1029.18i	1.24309	−	2.15310i
$479$	670.583	+	387.161i	1.39996	+	0.808270i	0.994388	−	0.105792i	$-0.0337377\pi$
$479$	670.583	+	387.161i	1.39996	+	0.808270i	0.405576	+	0.914061i	$0.367071\pi$
$480$	241.327	+	477.459i	0.502764	+	0.994707i
$481$	−186.240			−0.387194
$482$	426.398	+	246.181i	0.884642	+	0.510749i
$483$	−19.5307	+	9.87156i	−0.0404362	+	0.0204380i
$484$	330.875	−	573.093i	0.683627	−	1.18408i
$485$	−679.799	+	392.482i	−1.40165	+	0.809241i
$486$	206.924	−	724.928i	0.425769	−	1.49162i
$487$	368.935			0.757567			0.378783	−	0.925485i	$-0.376343\pi$
$487$	368.935			0.757567			0.378783	+	0.925485i	$0.376343\pi$
$488$	−6.06522	−	3.50176i	−0.0124287	−	0.00717573i
$489$	−916.181	−	51.0008i	−1.87358	−	0.104296i
$490$	−653.257			−1.33318
$491$	−80.9819	+	46.7549i	−0.164933	+	0.0952238i	−0.580194	−	0.814478i	$-0.697023\pi$
$491$	−80.9819	+	46.7549i	−0.164933	+	0.0952238i	0.415262	+	0.909702i	$0.363690\pi$
$492$	876.220	−	442.876i	1.78094	−	0.900154i
$493$	−16.9221	−	29.3099i	−0.0343247	−	0.0594521i
$494$	422.611	−	40.4634i	0.855488	−	0.0819096i
$495$	42.0445	−	57.0855i	0.0849385	−	0.115324i
$496$	85.8825	−	148.753i	0.173150	−	0.299905i
$497$			26.6908i			0.0537038i
$498$	304.355	+	602.159i	0.611154	+	1.20915i
$499$	217.683	+	377.038i	0.436238	+	0.755587i	0.997396	−	0.0721221i	$-0.0229771\pi$
$499$	217.683	+	377.038i	0.436238	+	0.755587i	−0.561157	+	0.827709i	$0.689644\pi$
$500$		−	762.051i		−	1.52410i
$501$	−11.5187	+	206.923i	−0.0229915	+	0.413020i
$502$	95.8248	+	165.973i	0.190886	+	0.330624i
$503$	−44.8428	+	25.8900i	−0.0891507	+	0.0514712i	−0.543913	−	0.839142i	$-0.683058\pi$
$503$	−44.8428	+	25.8900i	−0.0891507	+	0.0514712i	0.454762	+	0.890613i	$0.349724\pi$
$504$	−10.1419	+	4.43670i	−0.0201228	+	0.00880298i
$505$	273.576			0.541734
$506$	147.064	−	84.9077i	0.290641	−	0.167802i
$507$	−350.837	−	19.5300i	−0.691986	−	0.0385206i
$508$	418.517	+	724.893i	0.823853	+	1.42695i
$509$			432.694i			0.850087i	0.905173	+	0.425043i	$0.139741\pi$
$509$			432.694i			0.850087i	−0.905173	+	0.425043i	$0.860259\pi$
$510$	12.1697	−	218.617i	0.0238621	−	0.428660i
$511$	2.69920			0.00528219
$512$		−	422.682i		−	0.825550i
$513$	36.5833	−	511.694i	0.0713124	−	0.997454i
$514$	−1248.71			−2.42939
$515$			292.755i			0.568456i
$516$	−271.863	−	15.1337i	−0.526865	−	0.0293289i
$517$	57.6791			0.111565
$518$	16.9519	−	9.78720i	0.0327257	−	0.0188942i
$519$	40.0671	−	719.767i	0.0772005	−	1.38683i
$520$	−78.1036	−	135.279i	−0.150199	−	0.260153i
$521$			156.298i			0.299996i	0.988686	+	0.149998i	$0.0479267\pi$
$521$			156.298i			0.299996i	−0.988686	+	0.149998i	$0.952073\pi$
$522$	−102.490	+	139.155i	−0.196341	+	0.266580i
$523$	−96.3542	−	166.890i	−0.184234	−	0.319102i	0.759084	−	0.650992i	$-0.225647\pi$
$523$	−96.3542	−	166.890i	−0.184234	−	0.319102i	−0.943318	+	0.331890i	$0.892314\pi$
$524$	−258.234	+	149.091i	−0.492812	+	0.284525i
$525$	−4.74234	−	0.263991i	−0.00903304	−	0.000502840i
$526$	15.2090			0.0289144
$527$	−118.558	+	68.4493i	−0.224967	+	0.129885i
$528$	−33.6312	+	16.9985i	−0.0636955	+	0.0321942i
$529$	−364.755			−0.689518
$530$	−737.518	−	425.806i	−1.39154	−	0.803408i
$531$	186.626	−	81.6419i	0.351461	−	0.153751i
$532$	−21.2377	+	15.1314i	−0.0399204	+	0.0284426i
$533$	362.900	−	209.520i	0.680862	−	0.393096i
$534$	−183.399	−	362.851i	−0.343444	−	0.679496i
$535$	−115.758	−	200.499i	−0.216370	−	0.374764i
$536$		−	91.4517i		−	0.170619i
$537$	−19.1331	+	343.708i	−0.0356296	+	0.640051i
$538$	304.239	−	526.958i	0.565501	−	0.979476i
$539$		−	89.6064i		−	0.166246i
$540$	−612.276	+	228.208i	−1.13384	+	0.422607i
$541$	298.072	+	516.277i	0.550966	+	0.954301i	0.998205	+	0.0598864i	$0.0190738\pi$
$541$	298.072	+	516.277i	0.550966	+	0.954301i	−0.447239	+	0.894414i	$0.647593\pi$
$542$	758.937	+	438.172i	1.40025	+	0.808436i
$543$	−422.029	−	834.975i	−0.777218	−	1.53771i
$544$	−113.315	+	196.267i	−0.208299	+	0.360785i
$545$		−	10.7845i		−	0.0197881i
$546$	−14.5974	+	7.37812i	−0.0267352	+	0.0135130i
$547$	449.618	−	778.762i	0.821971	−	1.42370i	−0.0822407	−	0.996612i	$-0.526208\pi$
$547$	449.618	−	778.762i	0.821971	−	1.42370i	0.904212	−	0.427084i	$-0.140459\pi$
$548$	−1064.57	−	614.633i	−1.94265	−	1.12159i
$549$	−7.41524	+	10.0680i	−0.0135068	+	0.0183387i
$550$	36.8572			0.0670131
$551$	−48.8268	+	106.988i	−0.0886149	+	0.194171i
$552$	−451.408	−	25.1284i	−0.817768	−	0.0455225i
$553$	−14.4876	−	25.0932i	−0.0261982	−	0.0453766i
$554$	−127.079	+	73.3689i	−0.229384	+	0.132435i
$555$	297.879	−	150.560i	0.536718	−	0.271278i
$556$	−228.227			−0.410481
$557$	317.565	−	183.346i	0.570134	−	0.329167i	−0.187069	−	0.982347i	$-0.559899\pi$
$557$	317.565	−	183.346i	0.570134	−	0.329167i	0.757203	+	0.653180i	$0.226565\pi$
$558$	562.877	+	414.570i	1.00874	+	0.742957i
$559$	−116.215			−0.207897
$560$	−6.23724	−	3.60107i	−0.0111379	−	0.00643049i
$561$	29.9874	+	1.66930i	0.0534534	+	0.00297558i
$562$	−778.379	+	1348.19i	−1.38502	+	2.39892i
$563$	−684.854	−	395.400i	−1.21644	−	0.702310i	−0.252282	−	0.967654i	$-0.581181\pi$
$563$	−684.854	−	395.400i	−1.21644	−	0.702310i	−0.964154	+	0.265344i	$0.914515\pi$
$564$	−444.888	−	290.974i	−0.788809	−	0.515911i
$565$	−893.326			−1.58111
$566$	941.484	−	543.566i	1.66340	−	0.960364i
$567$	5.86258	+	18.8745i	0.0103396	+	0.0332883i
$568$	−275.710	+	477.543i	−0.485404	+	0.840745i
$569$	686.573	−	396.393i	1.20663	−	0.696648i	0.244609	−	0.969622i	$-0.421341\pi$
$569$	686.573	−	396.393i	1.20663	−	0.696648i	0.962022	+	0.272974i	$0.0880072\pi$
$570$	−643.226	+	406.363i	−1.12847	+	0.712918i
$571$	284.891	−	493.446i	0.498934	−	0.864179i	−0.501065	−	0.865409i	$-0.667058\pi$
$571$	284.891	−	493.446i	0.498934	−	0.864179i	0.999999	+	0.00123074i	$0.000391755\pi$
$572$	64.2369	−	37.0872i	0.112302	−	0.0648377i
$573$	116.534	−	58.9010i	0.203376	−	0.102794i
$574$	−22.0212	+	38.1418i	−0.0383644	+	0.0664491i
$575$	−167.994	−	96.9915i	−0.292164	−	0.168681i
$576$	904.679	+	101.034i	1.57062	+	0.175407i
$577$	678.670			1.17620			0.588102	−	0.808786i	$-0.299875\pi$
$577$	678.670			1.17620			0.588102	+	0.808786i	$0.299875\pi$
$578$	−696.144	+	401.919i	−1.20440	+	0.695361i
$579$	−73.0780	−	144.583i	−0.126214	−	0.249712i
$580$	149.794			0.258266
$581$	−15.3185	−	8.84414i	−0.0263657	−	0.0152223i
$582$	−94.3785	+	1695.42i	−0.162162	+	2.91309i
$583$	58.4073	−	101.164i	0.100184	−	0.173524i
$584$	48.2933	+	27.8821i	0.0826939	+	0.0477434i
$585$	−255.511	+	111.777i	−0.436771	+	0.191071i
$586$	−774.516	+	1341.50i	−1.32170	+	2.28925i
$587$			485.817i			0.827627i	0.910362	+	0.413813i	$0.135803\pi$
$587$			485.817i			0.827627i	−0.910362	+	0.413813i	$0.864197\pi$
$588$	−452.037	+	691.149i	−0.768771	+	1.17542i
$589$	432.764	+	197.503i	0.734744	+	0.335320i
$590$	−261.637	−	151.056i	−0.443453	−	0.256028i
$591$	58.4097	−	1049.27i	0.0988319	−	1.77542i
$592$	−177.401			−0.299663
$593$	−54.2566	+	31.3251i	−0.0914951	+	0.0528247i	−0.545049	−	0.838404i	$-0.683489\pi$
$593$	−54.2566	+	31.3251i	−0.0914951	+	0.0528247i	0.453554	+	0.891229i	$0.350156\pi$
$594$	−53.5634	−	143.709i	−0.0901741	−	0.241935i
$595$	2.87010	+	4.97115i	0.00482369	+	0.00835488i
$596$	223.350	−	128.951i	0.374749	−	0.216361i
$597$	80.9307	+	160.120i	0.135562	+	0.268207i
$598$	−668.003			−1.11706
$599$			847.178i			1.41432i	0.707053	+	0.707160i	$0.250024\pi$
$599$			847.178i			1.41432i	−0.707053	+	0.707160i	$0.749976\pi$
$600$	−82.1216	−	53.7106i	−0.136869	−	0.0895176i
$601$	−178.361	−	308.930i	−0.296774	−	0.514027i	0.678622	−	0.734487i	$-0.262577\pi$
$601$	−178.361	−	308.930i	−0.296774	−	0.514027i	−0.975396	+	0.220461i	$0.929244\pi$
$602$	10.5781	−	6.10725i	0.0175715	−	0.0101449i
$603$	−162.268	−	18.1220i	−0.269101	−	0.0300531i
$604$	−506.133	−	876.648i	−0.837968	−	1.45140i
$605$			506.177i			0.836656i
$606$	323.930	−	495.277i	0.534537	−	0.817289i
$607$	357.464	−	619.147i	0.588904	−	1.02001i	−0.405473	−	0.914107i	$-0.632893\pi$
$607$	357.464	−	619.147i	0.588904	−	1.02001i	0.994376	−	0.105904i	$-0.0337736\pi$
$608$	783.919	−	75.0572i	1.28934	−	0.123449i
$609$	0.251826	−	4.52381i	0.000413507	−	0.00742826i
$610$	18.5448			0.0304013
$611$	−196.494	−	113.446i	−0.321594	−	0.185673i
$612$	−222.877	−	164.153i	−0.364177	−	0.268224i
$613$	−0.225456	+	0.390501i	−0.000367791	+	0.000637032i	−0.866209	−	0.499681i	$-0.833450\pi$
$613$	−0.225456	+	0.390501i	−0.000367791	+	0.000637032i	0.865841	+	0.500318i	$0.166784\pi$
$614$	−1542.85	−	890.764i	−2.51278	−	1.45075i
$615$	−411.054	+	628.487i	−0.668380	+	1.02193i
$616$	−1.12601	+	1.95030i	−0.00182793	+	0.00316607i
$617$		−	895.034i		−	1.45062i	−0.688421	−	0.725311i	$-0.741696\pi$
$617$		−	895.034i		−	1.45062i	0.688421	−	0.725311i	$-0.258304\pi$
$618$	529.999	+	346.639i	0.857603	+	0.560904i
$619$	93.6789	+	162.257i	0.151339	+	0.262127i	0.931720	−	0.363177i	$-0.118308\pi$
$619$	93.6789	+	162.257i	0.151339	+	0.262127i	−0.780381	+	0.625304i	$0.784975\pi$
$620$		−	605.914i		−	0.977281i
$621$	−134.037	+	795.978i	−0.215841	+	1.28177i
$622$	−85.6499	+	148.350i	−0.137701	+	0.238505i
$623$	9.23066	+	5.32933i	0.0148165	+	0.00855429i
$624$	148.004	+	8.23893i	0.237187	+	0.0132034i
$625$	210.341	+	364.321i	0.336545	+	0.582913i
$626$	−470.270	−	271.511i	−0.751231	−	0.433723i
$627$	−55.7403	−	88.2305i	−0.0889001	−	0.140718i
$628$	404.326	+	700.313i	0.643831	+	1.11515i
$629$	122.448	+	70.6952i	0.194670	+	0.112393i
$630$	17.3830	−	23.6016i	0.0275921	−	0.0374628i
$631$	63.5948	+	110.149i	0.100784	+	0.174563i	0.912008	−	0.410173i	$-0.134532\pi$
$631$	63.5948	+	110.149i	0.100784	+	0.174563i	−0.811224	+	0.584736i	$0.801198\pi$
$632$		−	598.614i		−	0.947174i
$633$	−434.470	−	859.589i	−0.686366	−	1.35796i
$634$	−32.6537	+	56.5579i	−0.0515043	+	0.0892080i
$635$	−554.475	−	320.126i	−0.873189	−	0.504136i
$636$	−960.849	+	485.651i	−1.51077	+	0.763602i
$637$	−176.242	+	305.260i	−0.276675	+	0.479216i
$638$			35.1588i			0.0551078i
$639$	792.697	+	583.837i	1.24053	+	0.913672i
$640$	−318.386	−	551.460i	−0.497477	−	0.861656i
$641$		−	376.791i		−	0.587818i	−0.955833	−	0.293909i	$-0.905044\pi$
$641$		−	376.791i		−	0.587818i	0.955833	−	0.293909i	$-0.0949562\pi$
$642$	−500.045	−	27.8359i	−0.778886	−	0.0433580i
$643$	−253.177	−	438.515i	−0.393743	−	0.681983i	0.599197	−	0.800602i	$-0.295487\pi$
$643$	−253.177	−	438.515i	−0.393743	−	0.681983i	−0.992940	+	0.118619i	$0.962153\pi$
$644$	35.5337	−	20.5154i	0.0551765	−	0.0318562i
$645$	185.877	−	93.9497i	0.288182	−	0.145658i
$646$	−293.214	−	133.816i	−0.453892	−	0.207145i
$647$		−	497.371i		−	0.768734i	−0.923180	−	0.384367i	$-0.874420\pi$
$647$		−	497.371i		−	0.768734i	0.923180	−	0.384367i	$-0.125580\pi$
$648$	−90.0774	+	398.255i	−0.139008	+	0.614591i
$649$	20.7202	−	35.8884i	0.0319263	−	0.0552980i
$650$	−125.561	−	72.4925i	−0.193170	−	0.111527i
$651$	−18.2987	−	1.01863i	−0.0281086	−	0.00156471i
$652$	1720.45			2.63873
$653$	1112.53	+	642.317i	1.70371	+	0.983640i	0.941930	+	0.335811i	$0.109010\pi$
$653$	1112.53	+	642.317i	1.70371	+	0.983640i	0.761785	+	0.647830i	$0.224323\pi$
$654$	−19.5241	−	12.7695i	−0.0298533	−	0.0195252i
$655$	114.041	−	197.525i	0.174108	−	0.301564i
$656$	345.675	−	199.576i	0.526944	−	0.304231i
$657$	59.0426	−	80.1643i	0.0898669	−	0.122016i
$658$	23.8470			0.0362416
$659$	−623.936	−	360.230i	−0.946793	−	0.546631i	−0.0547095	−	0.998502i	$-0.517423\pi$
$659$	−623.936	−	360.230i	−0.946793	−	0.546631i	−0.892083	+	0.451871i	$0.850757\pi$
$660$	−72.7606	+	111.248i	−0.110243	+	0.168558i
$661$	152.843			0.231230			0.115615	−	0.993294i	$-0.463116\pi$
$661$	152.843			0.231230			0.115615	+	0.993294i	$0.463116\pi$
$662$	1176.70	−	679.369i	1.77750	−	1.02624i
$663$	−98.8742	−	64.6674i	−0.149131	−	0.0975375i
$664$	−182.716	−	316.473i	−0.275174	−	0.476616i
$665$	8.28136	−	18.1459i	0.0124532	−	0.0272871i
$666$	80.1353	−	717.547i	0.120323	−	1.07740i
$667$	92.5220	−	160.253i	0.138714	−	0.240259i
$668$		−	388.571i		−	0.581693i
$669$	1084.52	+	60.3716i	1.62110	+	0.0902415i
$670$	121.079	+	209.714i	0.180714	+	0.313006i
$671$			2.54376i			0.00379100i
$672$	−27.0774	+	13.6860i	−0.0402937	+	0.0203660i
$673$	−134.985	−	233.801i	−0.200572	−	0.347402i	0.748141	−	0.663540i	$-0.230947\pi$
$673$	−134.985	−	233.801i	−0.200572	−	0.347402i	−0.948713	+	0.316139i	$0.897614\pi$
$674$	1578.44	−	911.310i	2.34189	−	1.35209i
$675$	−111.575	+	135.070i	−0.165296	+	0.200103i
$676$	658.820			0.974586
$677$	212.209	−	122.519i	0.313455	−	0.180973i	−0.335017	−	0.942212i	$-0.608742\pi$
$677$	212.209	−	122.519i	0.313455	−	0.180973i	0.648471	+	0.761239i	$0.275409\pi$
$678$	−1057.75	+	1617.26i	−1.56010	+	2.38534i
$679$	−22.2582	−	38.5524i	−0.0327809	−	0.0567781i
$680$			118.590i			0.174397i
$681$	425.847	−	215.240i	0.625325	−	0.316064i
$682$	142.216			0.208528
$683$		−	298.653i		−	0.437266i	−0.975807	−	0.218633i	$-0.929840\pi$
$683$		−	298.653i		−	0.437266i	0.975807	−	0.218633i	$-0.0701597\pi$
$684$	−15.1616	+	961.730i	−0.0221661	+	1.40604i
$685$	940.272			1.37266
$686$		−	74.1393i		−	0.108075i
$687$	420.369	−	642.730i	0.611891	−	0.935561i
$688$	−110.699			−0.160899
$689$	−397.950	+	229.756i	−0.577576	+	0.333464i
$690$	1068.42	−	540.023i	1.54844	−	0.782642i
$691$	−385.934	−	668.458i	−0.558516	−	0.967378i	−0.997621	−	0.0689420i	$-0.978038\pi$
$691$	−385.934	−	668.458i	−0.558516	−	0.967378i	0.439105	−	0.898436i	$-0.355296\pi$
$692$			1351.62i			1.95320i
$693$	3.23740	+	2.38441i	0.00467157	+	0.00344070i
$694$	455.596	+	789.115i	0.656478	+	1.13705i
$695$	151.184	−	87.2863i	0.217531	−	0.125592i
$696$	51.2355	−	78.3373i	0.0736143	−	0.112554i
$697$	−318.128			−0.456425
$698$	324.050	−	187.091i	0.464256	−	0.268038i
$699$	−536.085	−	350.620i	−0.766932	−	0.501602i
$700$	8.90543			0.0127220
$701$	343.160	+	198.123i	0.489529	+	0.282630i	0.724379	−	0.689402i	$-0.242127\pi$
$701$	343.160	+	198.123i	0.489529	+	0.282630i	−0.234850	+	0.972032i	$0.575460\pi$
$702$	−100.181	+	594.923i	−0.142708	+	0.847469i
$703$	−46.8269	−	489.074i	−0.0666101	−	0.695695i
$704$	160.378	−	92.5944i	0.227810	−	0.131526i
$705$	405.990	+	22.6002i	0.575873	+	0.0320570i
$706$	−541.076	−	937.171i	−0.766396	−	1.32744i
$707$			15.5149i			0.0219446i
$708$	−340.865	+	172.286i	−0.481447	+	0.243342i
$709$	−669.131	+	1158.97i	−0.943767	+	1.63465i	−0.185567	+	0.982632i	$0.559412\pi$
$709$	−669.131	+	1158.97i	−0.943767	+	1.63465i	−0.758200	+	0.652022i	$0.773921\pi$
$710$		−	1460.12i		−	2.05650i
$711$	−1062.15	−	118.621i	−1.49389	−	0.166837i
$712$	110.101	+	190.701i	0.154637	+	0.267839i
$713$	−648.218	−	374.249i	−0.909142	−	0.524893i
$714$	12.3981	+	0.690160i	0.0173642	+	0.000966611i
$715$	−28.3682	+	49.1352i	−0.0396758	+	0.0687205i
$716$		−	645.432i		−	0.901442i
$717$	961.739	+	629.013i	1.34134	+	0.877284i
$718$	497.139	−	861.071i	0.692395	−	1.19926i
$719$	−552.103	−	318.757i	−0.767876	−	0.443333i	0.0642405	−	0.997934i	$-0.479538\pi$
$719$	−552.103	−	318.757i	−0.767876	−	0.443333i	−0.832116	+	0.554601i	$0.812871\pi$
$720$	−243.383	+	106.471i	−0.338032	+	0.147877i
$721$	−16.6025			−0.0230271
$722$	212.516	+	1099.62i	0.294344	+	1.52301i
$723$	−260.605	+	398.456i	−0.360449	+	0.551114i
$724$	877.074	+	1519.14i	1.21143	+	2.09826i
$725$	34.7817	−	20.0812i	0.0479747	−	0.0276982i
$726$	916.375	+	599.344i	1.26222	+	0.825542i
$727$	527.230			0.725213			0.362606	−	0.931942i	$-0.381887\pi$
$727$	527.230			0.725213			0.362606	+	0.931942i	$0.381887\pi$
$728$	7.67189	−	4.42937i	0.0105383	−	0.00608430i
$729$	688.797	+	238.747i	0.944851	+	0.327500i
$730$	−147.660			−0.202273
$731$	76.4078	+	44.1141i	0.104525	+	0.0603476i
$732$	12.8325	−	19.6205i	0.0175308	−	0.0268039i
$733$	−40.8186	+	70.6999i	−0.0556870	+	0.0964528i	−0.892525	−	0.450998i	$-0.851068\pi$
$733$	−40.8186	+	70.6999i	−0.0556870	+	0.0964528i	0.836838	+	0.547451i	$0.184402\pi$
$734$	79.9893	+	46.1818i	0.108977	+	0.0629180i
$735$	35.1101	−	630.720i	0.0477689	−	0.858122i
$736$	−1239.11			−1.68357
$737$	−28.7662	+	16.6082i	−0.0390315	+	0.0225349i
$738$	651.091	+	1488.33i	0.882237	+	2.01671i
$739$	−261.428	+	452.807i	−0.353759	+	0.612729i	−0.986905	−	0.161304i	$-0.948430\pi$
$739$	−261.428	+	452.807i	−0.353759	+	0.612729i	0.633145	+	0.774033i	$0.281764\pi$
$740$	−541.954	+	312.898i	−0.732371	+	0.422835i
$741$	16.3536	+	410.206i	0.0220697	+	0.553584i
$742$	24.1481	−	41.8257i	0.0325446	−	0.0563688i
$743$	−470.273	+	271.512i	−0.632938	+	0.365427i	−0.781889	−	0.623418i	$-0.785744\pi$
$743$	−470.273	+	271.512i	−0.632938	+	0.365427i	0.148951	+	0.988845i	$0.452410\pi$
$744$	−316.872	−	207.246i	−0.425904	−	0.278557i
$745$	−98.6356	+	170.842i	−0.132397	+	0.229318i
$746$	36.8742	+	21.2893i	0.0494292	+	0.0285380i
$747$	−597.743	+	261.491i	−0.800191	+	0.350055i
$748$	−56.3119			−0.0752832
$749$	11.3706	−	6.56481i	0.0151810	−	0.00876476i
$750$	1258.98	+	70.0834i	1.67864	+	0.0934446i
$751$	85.4078			0.113725			0.0568627	−	0.998382i	$-0.481890\pi$
$751$	85.4078			0.113725			0.0568627	+	0.998382i	$0.481890\pi$
$752$	−187.168	−	108.061i	−0.248893	−	0.143699i
$753$	−165.398	+	83.5984i	−0.219652	+	0.111021i
$754$	69.1520	−	119.775i	0.0917135	−	0.158852i
$755$	670.553	+	387.144i	0.888150	+	0.512774i
$756$	−12.9420	−	34.7230i	−0.0171190	−	0.0459299i
$757$	−471.884	+	817.326i	−0.623360	+	1.07969i	0.365496	+	0.930813i	$0.380900\pi$
$757$	−471.884	+	817.326i	−0.623360	+	1.07969i	−0.988856	+	0.148878i	$0.952434\pi$
$758$		−	1067.02i		−	1.40767i
$759$	74.0743	+	146.554i	0.0975946	+	0.193089i
$760$	335.610	−	239.116i	0.441593	−	0.314627i
$761$	−36.1731	−	20.8846i	−0.0475337	−	0.0274436i	0.476045	−	0.879421i	$-0.342070\pi$
$761$	−36.1731	−	20.8846i	−0.0475337	−	0.0274436i	−0.523579	+	0.851977i	$0.675403\pi$
$762$	−1236.08	+	624.765i	−1.62216	+	0.819901i
$763$	0.611604			0.000801578
$764$	−212.020	+	122.410i	−0.277513	+	0.160222i
$765$	210.420	+	23.4997i	0.275059	+	0.0307185i
$766$	717.966	+	1243.55i	0.937292	+	1.62344i
$767$	−141.174	+	81.5070i	−0.184060	+	0.106267i
$768$	−163.480	−	9.10041i	−0.212865	−	0.0118495i
$769$	−841.969			−1.09489			−0.547444	−	0.836842i	$-0.684399\pi$
$769$	−841.969			−1.09489			−0.547444	+	0.836842i	$0.684399\pi$
$770$		−	5.96316i		−	0.00774436i
$771$	67.1133	−	1205.63i	0.0870471	−	1.56372i
$772$	151.873	+	263.052i	0.196727	+	0.340741i
$773$	−733.888	+	423.711i	−0.949403	+	0.548138i	−0.892895	−	0.450264i	$-0.851330\pi$
$773$	−733.888	+	423.711i	−0.949403	+	0.548138i	−0.0565075	+	0.998402i	$0.517996\pi$
$774$	50.0047	−	447.751i	0.0646055	−	0.578490i
$775$	−81.2279	−	140.691i	−0.104810	−	0.181537i
$776$		−	919.689i		−	1.18517i
$777$	8.53845	+	16.8931i	0.0109890	+	0.0217415i
$778$	173.101	−	299.819i	0.222495	−	0.385372i
$779$	641.452	+	900.306i	0.823429	+	1.15572i
$780$	466.681	−	235.879i	0.598309	−	0.302409i
$781$	200.282			0.256443
$782$	439.192	+	253.568i	0.561627	+	0.324256i
$783$	−128.846	−	106.433i	−0.164554	−	0.135930i
$784$	−167.877	+	290.772i	−0.214129	+	0.370882i
$785$	−535.674	−	309.271i	−0.682387	−	0.393976i
$786$	−222.564	−	440.338i	−0.283161	−	0.560227i
$787$	352.339	−	610.268i	0.447698	−	0.775436i	−0.550538	−	0.834810i	$-0.685577\pi$
$787$	352.339	−	610.268i	0.447698	−	0.775436i	0.998236	+	0.0593743i	$0.0189106\pi$
$788$			1970.38i			2.50048i
$789$	−0.817426	+	14.6843i	−0.00103603	+	0.0186113i
$790$	792.543	+	1372.72i	1.00322	+	1.73763i
$791$		−	50.6618i		−	0.0640477i
$792$	33.2921	+	76.1026i	0.0420355	+	0.0960892i
$793$	5.00320	−	8.66579i	0.00630920	−	0.0109279i
$794$	1613.73	+	931.688i	2.03241	+	1.17341i
$795$	450.755	−	689.188i	0.566987	−	0.866903i
$796$	−168.193	−	291.318i	−0.211297	−	0.365978i
$797$	423.299	+	244.392i	0.531115	+	0.306639i	0.741470	−	0.670986i	$-0.234129\pi$
$797$	423.299	+	244.392i	0.531115	+	0.306639i	−0.210355	+	0.977625i	$0.567462\pi$
$798$	−23.0454	−	36.4783i	−0.0288790	−	0.0457121i
$799$	86.1262	+	149.175i	0.107792	+	0.186702i
$800$	−232.908	−	134.469i	−0.291135	−	0.168087i
$801$	360.189	−	157.570i	0.449675	−	0.196716i
$802$	−721.061	−	1248.91i	−0.899079	−	1.55725i
$803$		−	20.2543i		−	0.0252232i
$804$	305.662	+	17.0152i	0.380177	+	0.0211632i
$805$	−15.6923	+	27.1799i	−0.0194936	+	0.0337639i
$806$	−484.485	−	279.718i	−0.601099	−	0.347044i
$807$	492.426	+	322.065i	0.610194	+	0.399089i
$808$	−160.265	+	277.587i	−0.198348	+	0.343548i
$809$			515.502i			0.637209i	0.947888	+	0.318604i	$0.103214\pi$
$809$			515.502i			0.637209i	−0.947888	+	0.318604i	$0.896786\pi$
$810$	−320.712	−	1032.53i	−0.395941	−	1.27472i
$811$	−173.236	−	300.054i	−0.213608	−	0.369980i	0.739233	−	0.673450i	$-0.235188\pi$
$811$	−173.236	−	300.054i	−0.213608	−	0.369980i	−0.952841	+	0.303470i	$0.901855\pi$
$812$			8.49505i			0.0104619i
$813$	−463.845	+	709.203i	−0.570536	+	0.872329i
$814$	−73.4413	−	127.204i	−0.0902227	−	0.156270i
$815$	−1139.68	+	657.992i	−1.39838	+	0.807352i
$816$	−94.1812	−	61.5980i	−0.115418	−	0.0754878i
$817$	−29.2201	−	305.184i	−0.0357652	−	0.373542i
$818$			980.287i			1.19839i
$819$	−6.33902	−	14.4904i	−0.00773995	−	0.0176928i
$820$	704.018	−	1219.40i	0.858559	−	1.48707i
$821$	717.637	+	414.328i	0.874101	+	0.504663i	0.868709	−	0.495323i	$-0.164950\pi$
$821$	717.637	+	414.328i	0.874101	+	0.504663i	0.00539240	+	0.999985i	$0.498284\pi$
$822$	1113.34	−	1702.25i	1.35443	−	2.07087i
$823$	−1260.62			−1.53174			−0.765868	−	0.642998i	$-0.777690\pi$
$823$	−1260.62			−1.53174			−0.765868	+	0.642998i	$0.777690\pi$
$824$	−297.047	−	171.500i	−0.360494	−	0.208132i
$825$	−1.98094	+	35.5856i	−0.00240113	+	0.0431341i
$826$	8.56662	−	14.8378i	0.0103712	−	0.0179635i
$827$	−637.979	+	368.337i	−0.771438	+	0.445390i	−0.833387	−	0.552689i	$-0.813602\pi$
$827$	−637.979	+	368.337i	−0.771438	+	0.445390i	0.0619494	+	0.998079i	$0.480268\pi$
$828$	167.975	−	1504.08i	0.202869	−	1.81652i
$829$	−230.711			−0.278301			−0.139150	−	0.990271i	$-0.544437\pi$
$829$	−230.711			−0.278301			−0.139150	+	0.990271i	$0.544437\pi$
$830$	837.997	+	483.818i	1.00964	+	0.582913i
$831$	−64.0077	−	126.638i	−0.0770249	−	0.152392i
$832$	−728.477			−0.875573
$833$	231.748	−	133.800i	0.278209	−	0.160624i
$834$	20.9894	−	377.054i	0.0251671	−	0.452103i
$835$	148.610	+	257.400i	0.177976	+	0.308264i
$836$	113.543	+	159.363i	0.135817	+	0.190626i
$837$	−430.520	+	521.177i	−0.514361	+	0.622672i
$838$	−343.208	+	594.454i	−0.409556	+	0.709372i
$839$			1032.26i			1.23035i	0.788392	+	0.615173i	$0.210914\pi$
$839$			1032.26i			1.23035i	−0.788392	+	0.615173i	$0.789086\pi$
$840$	−8.68989	+	13.2865i	−0.0103451	+	0.0158173i
$841$	−401.344	−	695.148i	−0.477223	−	0.826574i
$842$			791.835i			0.940422i
$843$	−1259.84	−	823.985i	−1.49448	−	0.977444i
$844$	902.928	+	1563.92i	1.06982	+	1.85298i
$845$	−436.421	+	251.968i	−0.516475	+	0.298187i
$846$	521.632	−	708.239i	0.616586	−	0.837162i
$847$	−28.7060			−0.0338914
$848$	−379.062	+	218.851i	−0.447007	+	0.258079i
$849$	474.212	+	938.217i	0.558553	+	1.10509i
$850$	55.0350	+	95.3235i	0.0647471	+	0.112145i
$851$			773.057i			0.908410i
$852$	−1544.81	−	1010.36i	−1.81316	−	1.18587i
$853$	1184.35			1.38845			0.694224	−	0.719759i	$-0.255748\pi$
$853$	1184.35			1.38845			0.694224	+	0.719759i	$0.255748\pi$
$854$			1.05170i			0.00123150i
$855$	−357.773	−	642.875i	−0.418448	−	0.751901i
$856$	271.252			0.316883
$857$			1367.92i			1.59617i	0.602546	+	0.798084i	$0.294153\pi$
$857$			1367.92i			1.59617i	−0.602546	+	0.798084i	$0.705847\pi$
$858$	55.3639	+	109.536i	0.0645267	+	0.127665i
$859$	1359.42			1.58256			0.791279	−	0.611455i	$-0.209415\pi$
$859$	1359.42			1.58256			0.791279	+	0.611455i	$0.209415\pi$
$860$	−338.181	+	195.249i	−0.393234	+	0.227034i
$861$	−35.6424	−	23.3114i	−0.0413965	−	0.0270748i
$862$	−922.564	−	1597.93i	−1.07026	−	1.85374i
$863$			493.046i			0.571317i	0.958332	+	0.285658i	$0.0922122\pi$
$863$			493.046i			0.571317i	−0.958332	+	0.285658i	$0.907788\pi$
$864$	−185.830	+	1103.55i	−0.215081	+	1.27725i
$865$	−516.930	−	895.348i	−0.597606	−	1.03508i
$866$	−1147.08	+	662.266i	−1.32457	+	0.764741i
$867$	−350.638	−	693.729i	−0.404426	−	0.800149i
$868$	34.3623			0.0395879
$869$	−188.295	+	108.712i	−0.216680	+	0.125100i
$870$	−13.7761	+	247.475i	−0.0158346	+	0.284454i
$871$	130.663			0.150015
$872$	10.9426	+	6.31773i	0.0125489	+	0.00724510i
$873$	−1631.86	−	182.245i	−1.86925	−	0.208757i
$874$	−167.957	−	1754.20i	−0.192171	−	2.00709i
$875$	−28.6281	+	16.5285i	−0.0327179	+	0.0188897i
$876$	−102.177	+	156.225i	−0.116640	+	0.178339i
$877$	−668.930	−	1158.62i	−0.762748	−	1.32112i	−0.941429	−	0.337211i	$-0.890516\pi$
$877$	−668.930	−	1158.62i	−0.762748	−	1.32112i	0.178681	−	0.983907i	$-0.442817\pi$
$878$		−	827.639i		−	0.942641i
$879$	−1253.59	−	819.896i	−1.42616	−	0.932760i
$880$	−27.0217	+	46.8030i	−0.0307065	+	0.0531853i
$881$			789.581i			0.896233i	0.893975	+	0.448116i	$0.147905\pi$
$881$			789.581i			0.896233i	−0.893975	+	0.448116i	$0.852095\pi$
$882$	−1100.27	−	810.372i	−1.24748	−	0.918790i
$883$	406.118	+	703.417i	0.459930	+	0.796622i	0.998957	−	0.0456667i	$-0.0145412\pi$
$883$	406.118	+	703.417i	0.459930	+	0.796622i	−0.539027	+	0.842289i	$0.681208\pi$
$884$	191.837	+	110.757i	0.217010	+	0.125291i
$885$	159.907	−	244.492i	0.180686	−	0.276262i
$886$	−561.574	+	972.674i	−0.633830	+	1.09783i
$887$		−	169.788i		−	0.191419i	−0.995409	−	0.0957093i	$-0.969488\pi$
$887$		−	169.788i		−	0.191419i	0.995409	−	0.0957093i	$-0.0305119\pi$
$888$	−21.7349	+	390.447i	−0.0244762	+	0.439692i
$889$	18.1548	−	31.4451i	0.0204216	−	0.0353713i
$890$	−504.963	−	291.540i	−0.567374	−	0.327573i
$891$	141.630	−	43.9916i	0.158956	−	0.0493733i
$892$	−2036.56			−2.28314
$893$	248.508	−	544.524i	0.278284	−	0.609770i
$894$	192.499	+	380.855i	0.215323	+	0.426013i
$895$	246.848	+	427.553i	0.275807	+	0.477712i
$896$	31.2741	−	18.0561i	0.0349041	−	0.0201519i
$897$	35.9027	−	644.957i	0.0400253	−	0.719015i
$898$	1496.04			1.66596
$899$	134.208	−	77.4849i	0.149286	−	0.0861901i
$900$	194.798	−	264.485i	0.216442	−	0.293872i
$901$	348.854			0.387185
$902$	286.208	+	165.243i	0.317304	+	0.183196i
$903$	5.32802	+	10.5414i	0.00590035	+	0.0116737i
$904$	523.324	−	906.424i	0.578899	−	1.00268i
$905$	−1162.00	−	670.879i	−1.28397	−	0.741303i
$906$	1494.85	−	755.558i	1.64995	−	0.833949i
$907$	673.575			0.742641			0.371320	−	0.928505i	$-0.378905\pi$
$907$	673.575			0.742641			0.371320	+	0.928505i	$0.378905\pi$
$908$	−774.777	+	447.317i	−0.853278	+	0.492640i
$909$	460.780	+	339.373i	0.506909	+	0.373348i
$910$	−11.7286	+	20.3146i	−0.0128886	+	0.0223237i
$911$	918.101	−	530.066i	1.00779	−	0.581851i	0.0972495	−	0.995260i	$-0.468996\pi$
$911$	918.101	−	530.066i	1.00779	−	0.581851i	0.910545	+	0.413409i	$0.135662\pi$
$912$	15.5774	+	390.736i	0.0170805	+	0.428439i
$913$	−66.3647	+	114.947i	−0.0726886	+	0.125900i
$914$	−638.298	+	368.522i	−0.698357	+	0.403197i
$915$	−0.996713	+	17.9050i	−0.00108930	+	0.0195683i
$916$	−719.974	+	1247.03i	−0.785997	+	1.36139i
$917$	11.2019	+	6.46742i	0.0122158	+	0.00705280i
$918$	291.694	−	353.117i	0.317749	−	0.384659i
$919$	−402.026			−0.437461			−0.218730	−	0.975785i	$-0.570191\pi$
$919$	−402.026			−0.437461			−0.218730	+	0.975785i	$0.570191\pi$
$920$	−561.525	+	324.197i	−0.610353	+	0.352388i
$921$	942.955	−	1441.74i	1.02384	−	1.56541i
$922$	454.844			0.493324
$923$	−682.298	−	393.925i	−0.739218	−	0.426788i
$924$	−6.30906	−	4.12636i	−0.00682798	−	0.00446575i
$925$	−83.8931	+	145.307i	−0.0906953	+	0.157089i
$926$	1356.82	+	783.359i	1.46525	+	0.845960i
$927$	−363.165	+	493.083i	−0.391764	+	0.531913i
$928$	128.273	−	222.175i	0.138225	−	0.239413i
$929$		−	1589.77i		−	1.71127i	−0.517576	−	0.855637i	$-0.673166\pi$
$929$		−	1589.77i		−	1.71127i	0.517576	−	0.855637i	$-0.326834\pi$
$930$	1001.03	+	55.7240i	1.07638	+	0.0599183i
$931$	−845.937	−	386.065i	−0.908633	−	0.414678i
$932$	1040.12	+	600.512i	1.11601	+	0.644327i
$933$	−138.629	−	90.6683i	−0.148584	−	0.0971793i
$934$	2462.03			2.63600
$935$	37.3026	−	21.5366i	0.0398958	−	0.0230338i
$936$	36.2666	−	324.738i	0.0387464	−	0.346942i
$937$	53.1253	+	92.0157i	0.0566972	+	0.0982025i	0.892981	−	0.450094i	$-0.148610\pi$
$937$	53.1253	+	92.0157i	0.0566972	+	0.0982025i	−0.836284	+	0.548297i	$0.815276\pi$
$938$	−11.8932	+	6.86654i	−0.0126793	+	0.00732040i
$939$	287.419	−	439.454i	0.306091	−	0.468002i
$940$	−762.390			−0.811053
$941$		−	1416.59i		−	1.50541i	−0.658360	−	0.752703i	$-0.728749\pi$
$941$		−	1416.59i		−	1.50541i	0.658360	−	0.752703i	$-0.271251\pi$
$942$	−1194.17	+	603.580i	−1.26770	+	0.640743i
$943$	−869.688	−	1506.34i	−0.922256	−	1.59739i
$944$	−134.474	+	77.6384i	−0.142451	+	0.0822440i
$945$	21.8531	+	18.0518i	0.0231249	+	0.0191024i
$946$	−45.8276	−	79.3757i	−0.0484435	−	0.0839067i
$947$			830.359i			0.876831i	0.898772	+	0.438416i	$0.144460\pi$
$947$			830.359i			0.876831i	−0.898772	+	0.438416i	$0.855540\pi$
$948$	2000.77	+	111.376i	2.11052	+	0.117486i
$949$	−39.8371	+	68.9998i	−0.0419780	+	0.0727079i
$950$	158.798	−	347.953i	0.167155	−	0.366267i
$951$	−52.8516	−	34.5669i	−0.0555748	−	0.0363480i
$952$	−6.72539			−0.00706449
$953$	909.963	+	525.367i	0.954840	+	0.551277i	0.894581	−	0.446906i	$-0.147474\pi$
$953$	909.963	+	525.367i	0.954840	+	0.551277i	0.0602589	+	0.998183i	$0.480807\pi$
$954$	−713.975	−	1632.08i	−0.748402	−	1.71077i
$955$	93.6320	−	162.175i	0.0980440	−	0.169817i
$956$	−1865.97	−	1077.32i	−1.95186	−	1.12690i
$957$	−33.9458	−	1.88965i	−0.0354711	−	0.00197456i
$958$	1201.13	−	2080.41i	1.25379	−	2.17162i
$959$			53.3242i			0.0556039i
$960$	1165.15	−	588.911i	1.21370	−	0.613449i
$961$	167.076	+	289.384i	0.173856	+	0.301128i
$962$			577.791i			0.600615i
$963$	53.7511	−	481.297i	0.0558163	−	0.499789i
$964$	446.342	−	773.088i	0.463011	−	0.801958i
$965$	−201.210	−	116.169i	−0.208508	−	0.120382i
$966$	30.6255	+	60.5918i	0.0317034	+	0.0627245i
$967$	694.807	+	1203.44i	0.718518	+	1.24451i	0.961587	+	0.274501i	$0.0885127\pi$
$967$	694.807	+	1203.44i	0.718518	+	1.24451i	−0.243069	+	0.970009i	$0.578154\pi$
$968$	−513.599	−	296.527i	−0.530578	−	0.306329i
$969$	144.959	−	275.906i	0.149596	−	0.284733i
$970$	1217.63	+	2109.00i	1.25529	+	2.17423i
$971$	350.798	+	202.533i	0.361275	+	0.208582i	0.669640	−	0.742686i	$-0.266448\pi$
$971$	350.798	+	202.533i	0.361275	+	0.208582i	−0.308365	+	0.951268i	$0.599782\pi$
$972$	−1314.34	−	375.167i	−1.35220	−	0.385974i
$973$	4.95013	+	8.57387i	0.00508749	+	0.00881179i
$974$		−	1144.58i		−	1.17514i
$975$	76.7400	−	117.333i	0.0787076	−	0.120341i
$976$	4.76573	−	8.25448i	0.00488292	−	0.00845746i
$977$	720.527	+	415.996i	0.737489	+	0.425790i	0.821156	−	0.570704i	$-0.193330\pi$
$977$	720.527	+	415.996i	0.737489	+	0.425790i	−0.0836664	+	0.996494i	$0.526663\pi$
$978$	−158.225	+	2842.35i	−0.161784	+	2.90629i
$979$	39.9902	−	69.2651i	0.0408480	−	0.0707508i
$980$			1184.40i			1.20857i
$981$	13.3783	−	18.1642i	0.0136374	−	0.0185160i
$982$	145.052	+	251.238i	0.147711	+	0.255843i
$983$		−	780.993i		−	0.794500i	−0.917710	−	0.397250i	$-0.869965\pi$
$983$		−	780.993i		−	0.794500i	0.917710	−	0.397250i	$-0.130035\pi$
$984$	−396.900	−	785.258i	−0.403354	−	0.798027i
$985$	−753.578	−	1305.24i	−0.765054	−	1.32511i
$986$	−90.9309	+	52.4990i	−0.0922220	+	0.0532444i
$987$	−1.28169	+	23.0243i	−0.00129857	+	0.0233275i
$988$	−73.3628	−	766.222i	−0.0742539	−	0.775529i
$989$			482.390i			0.487755i
$990$	−177.102	−	130.439i	−0.178890	−	0.131756i
$991$	−452.505	+	783.761i	−0.456614	+	0.790879i	−0.998779	−	0.0493930i	$-0.984271\pi$
$991$	−452.505	+	783.761i	−0.456614	+	0.790879i	0.542165	+	0.840272i	$0.317605\pi$
$992$	−898.692	−	518.860i	−0.905939	−	0.523044i
$993$	592.688	+	1172.62i	0.596866	+	1.18089i
$994$	82.8053			0.0833052
$995$	222.831	+	128.652i	0.223951	+	0.129298i
$996$	1091.75	−	551.816i	1.09614	−	0.554032i
$997$	105.284	−	182.358i	0.105601	−	0.182906i	−0.808383	−	0.588657i	$-0.799657\pi$
$997$	105.284	−	182.358i	0.105601	−	0.182906i	0.913984	+	0.405751i	$0.132990\pi$
$998$	1169.72	−	675.338i	1.17206	−	0.676692i
$999$	688.484	+	115.936i	0.689174	+	0.116052i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.j.a.68.6	✓	76
3.2	odd	2		513.3.j.a.125.33		76
9.2	odd	6		171.3.n.a.11.33	yes	76
9.7	even	3		513.3.n.a.467.6		76
19.7	even	3		171.3.n.a.140.33	yes	76
57.26	odd	6		513.3.n.a.368.6		76
171.7	even	3		513.3.j.a.197.6		76
171.83	odd	6	inner	171.3.j.a.83.33	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.3.j.a.68.6	✓	76	1.1	even	1	trivial
171.3.j.a.83.33	yes	76	171.83	odd	6	inner
171.3.n.a.11.33	yes	76	9.2	odd	6
171.3.n.a.140.33	yes	76	19.7	even	3
513.3.j.a.125.33		76	3.2	odd	2
513.3.j.a.197.6		76	171.7	even	3
513.3.n.a.368.6		76	57.26	odd	6
513.3.n.a.467.6		76	9.7	even	3

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-3.10239i q^{2} +(2.99536 + 0.166742i) q^{3} -5.62485 q^{4} +(3.72606 - 2.15124i) q^{5} +(0.517300 - 9.29280i) q^{6} +(0.122000 + 0.211310i) q^{7} +5.04093i q^{8} +(8.94439 + 0.998906i) q^{9} +(-6.67400 - 11.5597i) q^{10} +(1.58563 - 0.915463i) q^{11} +(-16.8485 - 0.937899i) q^{12} -7.20231 q^{13} +(0.655567 - 0.378492i) q^{14} +(11.5196 - 5.82246i) q^{15} -6.86046 q^{16} +(4.73531 + 2.73393i) q^{17} +(3.09900 - 27.7490i) q^{18} +(-1.81089 - 18.9135i) q^{19} +(-20.9585 + 12.1004i) q^{20} +(0.330200 + 0.653293i) q^{21} +(-2.84013 - 4.91925i) q^{22} +29.8957i q^{23} +(-0.840535 + 15.0994i) q^{24} +(-3.24432 + 5.61933i) q^{25} +22.3444i q^{26} +(26.6251 + 4.48349i) q^{27} +(-0.686231 - 1.18859i) q^{28} +(-5.36039 - 3.09482i) q^{29} +(-18.0636 - 35.7383i) q^{30} +(-12.5185 + 21.6826i) q^{31} +41.4476i q^{32} +(4.90218 - 2.47775i) q^{33} +(8.48174 - 14.6908i) q^{34} +(0.909158 + 0.524902i) q^{35} +(-50.3109 - 5.61870i) q^{36} +25.8584 q^{37} +(-58.6771 + 5.61811i) q^{38} +(-21.5735 - 1.20093i) q^{39} +(10.8442 + 18.7828i) q^{40} +(-50.3865 + 29.0907i) q^{41} +(2.02677 - 1.02441i) q^{42} +16.1357 q^{43} +(-8.91893 + 5.14934i) q^{44} +(35.4762 - 15.5196i) q^{45} +92.7484 q^{46} +(27.2821 + 15.7513i) q^{47} +(-20.5496 - 1.14393i) q^{48} +(24.4702 - 42.3837i) q^{49} +(17.4334 + 10.0652i) q^{50} +(13.7281 + 8.97870i) q^{51} +40.5119 q^{52} +(55.2531 - 31.9004i) q^{53} +(13.9096 - 82.6017i) q^{54} +(3.93876 - 6.82214i) q^{55} +(-1.06520 + 0.614992i) q^{56} +(-2.27061 - 56.9548i) q^{57} +(-9.60136 + 16.6300i) q^{58} +(19.6012 - 11.3168i) q^{59} +(-64.7960 + 32.7504i) q^{60} +(-0.694666 + 1.20320i) q^{61} +(67.2681 + 38.8372i) q^{62} +(0.880136 + 2.01191i) q^{63} +101.145 q^{64} +(-26.8362 + 15.4939i) q^{65} +(-7.68697 - 15.2085i) q^{66} -18.1418 q^{67} +(-26.6354 - 15.3780i) q^{68} +(-4.98488 + 89.5486i) q^{69} +(1.62845 - 2.82057i) q^{70} +(94.7332 + 54.6943i) q^{71} +(-5.03541 + 45.0880i) q^{72} +(5.53115 - 9.58024i) q^{73} -80.2230i q^{74} +(-10.6549 + 16.2910i) q^{75} +(10.1860 + 106.386i) q^{76} +(0.386893 + 0.223373i) q^{77} +(-3.72575 + 66.9296i) q^{78} -118.751 q^{79} +(-25.5625 + 14.7585i) q^{80} +(79.0044 + 17.8692i) q^{81} +(90.2508 + 156.319i) q^{82} +(-62.7808 + 36.2465i) q^{83} +(-1.85732 - 3.67467i) q^{84} +23.5254 q^{85} -50.0594i q^{86} +(-15.5403 - 10.1639i) q^{87} +(4.61478 + 7.99304i) q^{88} +(37.8306 - 21.8415i) q^{89} +(-48.1478 - 110.061i) q^{90} +(-0.878681 - 1.52192i) q^{91} -168.159i q^{92} +(-41.1128 + 62.8600i) q^{93} +(48.8668 - 84.6398i) q^{94} +(-47.4350 - 66.5772i) q^{95} +(-6.91105 + 124.150i) q^{96} -182.445 q^{97} +(-131.491 - 75.9163i) q^{98} +(15.0970 - 6.60437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 5 q^{3} - 146 q^{4} - 3 q^{5} + 23 q^{6} - q^{7} - 13 q^{9} + 6 q^{10} - 24 q^{11} + 15 q^{12} + 8 q^{13} - 3 q^{14} - 14 q^{15} + 262 q^{16} - 135 q^{17} + 30 q^{18} + 4 q^{19} + 69 q^{20} - 40 q^{21}+ \cdots - 64 q^{99}+O(q^{100}) \) 76 * q - 5 * q^3 - 146 * q^4 - 3 * q^5 + 23 * q^6 - q^7 - 13 * q^9 + 6 * q^10 - 24 * q^11 + 15 * q^12 + 8 * q^13 - 3 * q^14 - 14 * q^15 + 262 * q^16 - 135 * q^17 + 30 * q^18 + 4 * q^19 + 69 * q^20 - 40 * q^21 - 3 * q^22 - 81 * q^24 + 151 * q^25 - 59 * q^27 + 14 * q^28 - 30 * q^29 + 265 * q^30 + 14 * q^31 + 31 * q^33 - 33 * q^34 - 75 * q^35 + 41 * q^36 + 14 * q^37 + 63 * q^38 - 78 * q^39 + 12 * q^40 - 201 * q^41 - 122 * q^42 - 58 * q^43 + 183 * q^44 + 145 * q^45 - 84 * q^46 - 21 * q^47 + 159 * q^48 - 171 * q^49 - 363 * q^50 - 103 * q^51 - 202 * q^52 + 36 * q^53 - 370 * q^54 - 27 * q^55 + 300 * q^56 - 3 * q^57 + 6 * q^58 - 84 * q^59 - 145 * q^60 + 8 * q^61 + 120 * q^62 + 3 * q^63 - 680 * q^64 - 6 * q^65 + 271 * q^66 - 16 * q^67 + 666 * q^68 + 81 * q^69 - 42 * q^70 + 135 * q^71 + 381 * q^72 + 65 * q^73 - 139 * q^75 - 155 * q^76 - 366 * q^77 - 514 * q^78 + 32 * q^79 - 66 * q^80 + 179 * q^81 - 42 * q^82 - 177 * q^83 + 546 * q^84 - 102 * q^85 - 375 * q^87 + 162 * q^88 + 216 * q^89 - 575 * q^90 + 265 * q^91 + 201 * q^93 + 6 * q^94 + 789 * q^95 + 511 * q^96 + 254 * q^97 + 882 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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