LMFDB - Embedded newform 126.3.o.a.13.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,3,Mod(13,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.13"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.o (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:	$3.43325133094$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			13.16
Character	$\chi$	$=$	126.13
Dual form			126.3.o.a.97.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 1.22474i) q^{2} +(2.99705 - 0.133043i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(4.98058 + 2.87554i) q^{5} +(2.28218 + 3.57654i) q^{6} +(-6.71501 + 1.97703i) q^{7} -2.82843 q^{8} +(8.96460 - 0.797472i) q^{9} +8.13325i q^{10} +(-8.66094 - 15.0012i) q^{11} +(-2.76661 + 5.32408i) q^{12} +(11.7856 + 6.80443i) q^{13} +(-7.16959 - 6.82620i) q^{14} +(15.3096 + 7.95550i) q^{15} +(-2.00000 - 3.46410i) q^{16} +10.4941i q^{17} +(7.31563 + 10.4154i) q^{18} -23.0584i q^{19} +(-9.96116 + 5.75108i) q^{20} +(-19.8622 + 6.81864i) q^{21} +(12.2484 - 21.2149i) q^{22} +(-13.5925 + 23.5429i) q^{23} +(-8.47693 + 0.376302i) q^{24} +(4.03745 + 6.99307i) q^{25} +19.2458i q^{26} +(26.7612 - 3.58274i) q^{27} +(3.29069 - 13.6078i) q^{28} +(-22.7948 - 39.4817i) q^{29} +(1.08207 + 24.3758i) q^{30} +(-0.774381 - 0.447089i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-27.9531 - 43.8070i) q^{33} +(-12.8526 + 7.42048i) q^{34} +(-39.1297 - 9.46251i) q^{35} +(-7.58334 + 16.3246i) q^{36} +51.1625 q^{37} +(28.2407 - 16.3048i) q^{38} +(36.2274 + 18.8252i) q^{39} +(-14.0872 - 8.13325i) q^{40} +(-21.1730 - 12.2242i) q^{41} +(-22.3958 - 19.5046i) q^{42} +(-5.94767 - 10.3017i) q^{43} +34.6438 q^{44} +(46.9421 + 21.8062i) q^{45} -38.4454 q^{46} +(14.4813 - 8.36076i) q^{47} +(-6.45497 - 10.1160i) q^{48} +(41.1827 - 26.5516i) q^{49} +(-5.70982 + 9.88970i) q^{50} +(1.39617 + 31.4515i) q^{51} +(-23.5712 + 13.6089i) q^{52} -79.0686 q^{53} +(23.3110 + 30.2423i) q^{54} -99.6195i q^{55} +(18.9929 - 5.59189i) q^{56} +(-3.06776 - 69.1071i) q^{57} +(32.2367 - 55.8355i) q^{58} +(-37.5149 - 21.6592i) q^{59} +(-29.0889 + 18.5615i) q^{60} +(-42.3562 + 24.4543i) q^{61} -1.26456i q^{62} +(-58.6207 + 23.0783i) q^{63} +8.00000 q^{64} +(39.1328 + 67.7800i) q^{65} +(33.8866 - 65.2116i) q^{66} +(-5.17274 + 8.95945i) q^{67} +(-18.1764 - 10.4941i) q^{68} +(-37.6051 + 72.3675i) q^{69} +(-16.0797 - 54.6149i) q^{70} +42.0936 q^{71} +(-25.3557 + 2.25559i) q^{72} +109.752i q^{73} +(36.1774 + 62.6610i) q^{74} +(13.0308 + 20.4214i) q^{75} +(39.9383 + 23.0584i) q^{76} +(87.8161 + 83.6102i) q^{77} +(2.56052 + 57.6807i) q^{78} +(56.6624 + 98.1421i) q^{79} -23.0043i q^{80} +(79.7281 - 14.2980i) q^{81} -34.5753i q^{82} +(-82.8440 + 47.8300i) q^{83} +(8.05195 - 41.2209i) q^{84} +(-30.1763 + 52.2669i) q^{85} +(8.41128 - 14.5688i) q^{86} +(-73.5698 - 115.296i) q^{87} +(24.4968 + 42.4298i) q^{88} +123.188i q^{89} +(6.48604 + 72.9114i) q^{90} +(-92.5931 - 22.3913i) q^{91} +(-27.1850 - 47.0858i) q^{92} +(-2.38034 - 1.23692i) q^{93} +(20.4796 + 11.8239i) q^{94} +(66.3053 - 114.844i) q^{95} +(7.82516 - 15.0588i) q^{96} +(20.9168 - 12.0763i) q^{97} +(61.6395 + 31.6635i) q^{98} +(-89.6049 - 127.573i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} - 2 q^{7} + 24 q^{9} - 12 q^{11} - 12 q^{14} + 48 q^{15} - 64 q^{16} - 54 q^{21} + 12 q^{23} + 80 q^{25} + 8 q^{28} - 48 q^{29} - 168 q^{30} + 348 q^{35} - 72 q^{36} - 88 q^{37} + 252 q^{39}+ \cdots - 684 q^{99}+O(q^{100}) $ 32 * q - 32 * q^4 - 2 * q^7 + 24 * q^9 - 12 * q^11 - 12 * q^14 + 48 * q^15 - 64 * q^16 - 54 * q^21 + 12 * q^23 + 80 * q^25 + 8 * q^28 - 48 * q^29 - 168 * q^30 + 348 * q^35 - 72 * q^36 - 88 * q^37 + 252 * q^39 + 32 * q^43 + 48 * q^44 + 48 * q^46 + 50 * q^49 + 48 * q^50 - 372 * q^51 - 864 * q^53 - 24 * q^56 + 372 * q^57 + 48 * q^58 - 24 * q^60 - 114 * q^63 + 256 * q^64 + 120 * q^65 - 140 * q^67 - 108 * q^70 + 552 * q^71 + 96 * q^72 + 144 * q^74 - 258 * q^77 + 288 * q^78 - 176 * q^79 - 360 * q^81 - 60 * q^85 + 96 * q^86 + 372 * q^91 + 24 * q^92 - 456 * q^93 + 528 * q^95 + 624 * q^98 - 684 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$	2.99705	−	0.133043i	0.999016	−	0.0443476i
$3$	2.99705	−	0.133043i	0.999016	−	0.0443476i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	4.98058	+	2.87554i	0.996116	+	0.575108i	0.907097	−	0.420922i	$-0.138293\pi$
$5$	4.98058	+	2.87554i	0.996116	+	0.575108i	0.0890192	+	0.996030i	$0.471627\pi$
$6$	2.28218	+	3.57654i	0.380363	+	0.596091i
$7$	−6.71501	+	1.97703i	−0.959287	+	0.282433i
$7$	−6.71501	+	1.97703i	−0.959287	+	0.282433i
$8$	−2.82843			−0.353553
$9$	8.96460	−	0.797472i	0.996067	−	0.0886080i
$10$			8.13325i			0.813325i
$11$	−8.66094	−	15.0012i	−0.787358	−	1.36374i	−0.927580	−	0.373625i	$-0.878115\pi$
$11$	−8.66094	−	15.0012i	−0.787358	−	1.36374i	0.140222	−	0.990120i	$-0.455218\pi$
$12$	−2.76661	+	5.32408i	−0.230551	+	0.443674i
$13$	11.7856	+	6.80443i	0.906586	+	0.523418i	0.879331	−	0.476211i	$-0.157990\pi$
$13$	11.7856	+	6.80443i	0.906586	+	0.523418i	0.0272552	+	0.999629i	$0.491323\pi$
$14$	−7.16959	−	6.82620i	−0.512113	−	0.487586i
$15$	15.3096	+	7.95550i	1.02064	+	0.530367i
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$			10.4941i			0.617302i	0.951175	+	0.308651i	$0.0998776\pi$
$17$			10.4941i			0.617302i	−0.951175	+	0.308651i	$0.900122\pi$
$18$	7.31563	+	10.4154i	0.406424	+	0.578636i
$19$		−	23.0584i		−	1.21360i	−0.794855	−	0.606800i	$-0.792453\pi$
$19$		−	23.0584i		−	1.21360i	0.794855	−	0.606800i	$-0.207547\pi$
$20$	−9.96116	+	5.75108i	−0.498058	+	0.287554i
$21$	−19.8622	+	6.81864i	−0.945818	+	0.324697i
$22$	12.2484	−	21.2149i	0.556746	−	0.964313i
$23$	−13.5925	+	23.5429i	−0.590978	+	1.02360i	0.403123	+	0.915146i	$0.367925\pi$
$23$	−13.5925	+	23.5429i	−0.590978	+	1.02360i	−0.994101	+	0.108458i	$0.965409\pi$
$24$	−8.47693	+	0.376302i	−0.353206	+	0.0156793i
$25$	4.03745	+	6.99307i	0.161498	+	0.279723i
$26$			19.2458i			0.740225i
$27$	26.7612	−	3.58274i	0.991157	−	0.132694i
$28$	3.29069	−	13.6078i	0.117525	−	0.485992i
$29$	−22.7948	−	39.4817i	−0.786026	−	1.36144i	−0.928384	−	0.371622i	$-0.878802\pi$
$29$	−22.7948	−	39.4817i	−0.786026	−	1.36144i	0.142357	−	0.989815i	$-0.454532\pi$
$30$	1.08207	+	24.3758i	0.0360690	+	0.812525i
$31$	−0.774381	−	0.447089i	−0.0249800	−	0.0144222i	0.487458	−	0.873146i	$-0.337924\pi$
$31$	−0.774381	−	0.447089i	−0.0249800	−	0.0144222i	−0.512438	+	0.858724i	$0.671258\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	−27.9531	−	43.8070i	−0.847063	−	1.32749i
$34$	−12.8526	+	7.42048i	−0.378019	+	0.218249i
$35$	−39.1297	−	9.46251i	−1.11799	−	0.270357i
$36$	−7.58334	+	16.3246i	−0.210648	+	0.453461i
$37$	51.1625			1.38277			0.691386	−	0.722486i	$-0.257001\pi$
$37$	51.1625			1.38277			0.691386	+	0.722486i	$0.257001\pi$
$38$	28.2407	−	16.3048i	0.743175	−	0.429072i
$39$	36.2274	+	18.8252i	0.928907	+	0.482698i
$40$	−14.0872	−	8.13325i	−0.352180	−	0.203331i
$41$	−21.1730	−	12.2242i	−0.516413	−	0.298151i	0.219053	−	0.975713i	$-0.429703\pi$
$41$	−21.1730	−	12.2242i	−0.516413	−	0.298151i	−0.735466	+	0.677562i	$0.763037\pi$
$42$	−22.3958	−	19.5046i	−0.533233	−	0.464395i
$43$	−5.94767	−	10.3017i	−0.138318	−	0.239574i	0.788542	−	0.614981i	$-0.210836\pi$
$43$	−5.94767	−	10.3017i	−0.138318	−	0.239574i	−0.926860	+	0.375407i	$0.877503\pi$
$44$	34.6438			0.787358
$45$	46.9421	+	21.8062i	1.04316	+	0.484582i
$46$	−38.4454			−0.835769
$47$	14.4813	−	8.36076i	0.308112	−	0.177888i	−0.337969	−	0.941157i	$-0.609740\pi$
$47$	14.4813	−	8.36076i	0.308112	−	0.177888i	0.646081	+	0.763269i	$0.276407\pi$
$48$	−6.45497	−	10.1160i	−0.134479	−	0.210750i
$49$	41.1827	−	26.5516i	0.840463	−	0.541869i
$50$	−5.70982	+	9.88970i	−0.114196	+	0.197794i
$51$	1.39617	+	31.4515i	0.0273759	+	0.616695i
$52$	−23.5712	+	13.6089i	−0.453293	+	0.261709i
$53$	−79.0686			−1.49186			−0.745930	−	0.666024i	$-0.767995\pi$
$53$	−79.0686			−1.49186			−0.745930	+	0.666024i	$0.767995\pi$
$54$	23.3110	+	30.2423i	0.431685	+	0.560043i
$55$		−	99.6195i		−	1.81126i
$56$	18.9929	−	5.59189i	0.339159	−	0.0998551i
$57$	−3.06776	−	69.1071i	−0.0538203	−	1.21241i
$58$	32.2367	−	55.8355i	0.555805	−	0.962682i
$59$	−37.5149	−	21.6592i	−0.635846	−	0.367106i	0.147167	−	0.989112i	$-0.452985\pi$
$59$	−37.5149	−	21.6592i	−0.635846	−	0.367106i	−0.783012	+	0.622006i	$0.786318\pi$
$60$	−29.0889	+	18.5615i	−0.484816	+	0.309359i
$61$	−42.3562	+	24.4543i	−0.694363	+	0.400891i	−0.805245	−	0.592943i	$-0.797966\pi$
$61$	−42.3562	+	24.4543i	−0.694363	+	0.400891i	0.110881	+	0.993834i	$0.464633\pi$
$62$		−	1.26456i		−	0.0203961i
$63$	−58.6207	+	23.0783i	−0.930488	+	0.366323i
$64$	8.00000			0.125000
$65$	39.1328	+	67.7800i	0.602043	+	1.04277i
$66$	33.8866	−	65.2116i	0.513434	−	0.988055i
$67$	−5.17274	+	8.95945i	−0.0772051	+	0.133723i	−0.902043	−	0.431646i	$-0.857933\pi$
$67$	−5.17274	+	8.95945i	−0.0772051	+	0.133723i	0.824838	+	0.565369i	$0.191266\pi$
$68$	−18.1764	−	10.4941i	−0.267300	−	0.154326i
$69$	−37.6051	+	72.3675i	−0.545002	+	1.04880i
$70$	−16.0797	−	54.6149i	−0.229710	−	0.780212i
$71$	42.0936			0.592868			0.296434	−	0.955053i	$-0.404203\pi$
$71$	42.0936			0.592868			0.296434	+	0.955053i	$0.404203\pi$
$72$	−25.3557	+	2.25559i	−0.352163	+	0.0313277i
$73$			109.752i			1.50345i	0.659476	+	0.751726i	$0.270778\pi$
$73$			109.752i			1.50345i	−0.659476	+	0.751726i	$0.729222\pi$
$74$	36.1774	+	62.6610i	0.488883	+	0.846771i
$75$	13.0308	+	20.4214i	0.173744	+	0.272286i
$76$	39.9383	+	23.0584i	0.525504	+	0.303400i
$77$	87.8161	+	83.6102i	1.14047	+	1.08585i
$78$	2.56052	+	57.6807i	0.0328272	+	0.739496i
$79$	56.6624	+	98.1421i	0.717245	+	1.24231i	0.962087	+	0.272742i	$0.0879306\pi$
$79$	56.6624	+	98.1421i	0.717245	+	1.24231i	−0.244842	+	0.969563i	$0.578736\pi$
$80$		−	23.0043i		−	0.287554i
$81$	79.7281	−	14.2980i	0.984297	−	0.176519i
$82$		−	34.5753i		−	0.421650i
$83$	−82.8440	+	47.8300i	−0.998121	+	0.576265i	−0.907692	−	0.419638i	$-0.862157\pi$
$83$	−82.8440	+	47.8300i	−0.998121	+	0.576265i	−0.0904289	+	0.995903i	$0.528824\pi$
$84$	8.05195	−	41.2209i	0.0958565	−	0.490726i
$85$	−30.1763	+	52.2669i	−0.355016	+	0.614905i
$86$	8.41128	−	14.5688i	0.0978056	−	0.169404i
$87$	−73.5698	−	115.296i	−0.845630	−	1.32524i
$88$	24.4968	+	42.4298i	0.278373	+	0.482157i
$89$			123.188i			1.38414i	0.721831	+	0.692070i	$0.243301\pi$
$89$			123.188i			1.38414i	−0.721831	+	0.692070i	$0.756699\pi$
$90$	6.48604	+	72.9114i	0.0720671	+	0.810126i
$91$	−92.5931	−	22.3913i	−1.01751	−	0.246058i
$92$	−27.1850	−	47.0858i	−0.295489	−	0.511802i
$93$	−2.38034	−	1.23692i	−0.0255950	−	0.0133002i
$94$	20.4796	+	11.8239i	0.217868	+	0.125786i
$95$	66.3053	−	114.844i	0.697951	−	1.20889i
$96$	7.82516	−	15.0588i	0.0815121	−	0.156862i
$97$	20.9168	−	12.0763i	0.215637	−	0.124498i	−0.388291	−	0.921537i	$-0.626935\pi$
$97$	20.9168	−	12.0763i	0.215637	−	0.124498i	0.603929	+	0.797038i	$0.293601\pi$
$98$	61.6395	+	31.6635i	0.628974	+	0.323097i
$99$	−89.6049	−	127.573i	−0.905100	−	1.28861i
$100$	−16.1498			−0.161498
$101$	21.0830	−	12.1723i	0.208743	−	0.120518i	−0.391984	−	0.919972i	$-0.628211\pi$
$101$	21.0830	−	12.1723i	0.208743	−	0.120518i	0.600727	+	0.799454i	$0.294878\pi$
$102$	−37.5328	+	23.9495i	−0.367968	+	0.234799i
$103$	126.643	+	73.1173i	1.22954	+	0.709876i	0.966934	−	0.255026i	$-0.0820841\pi$
$103$	126.643	+	73.1173i	1.22954	+	0.709876i	0.262608	+	0.964903i	$0.415417\pi$
$104$	−33.3348	−	19.2458i	−0.320527	−	0.185056i
$105$	−118.532	−	23.1537i	−1.12888	−	0.220511i
$106$	−55.9099	−	96.8388i	−0.527452	−	0.913574i
$107$	39.3576			0.367828			0.183914	−	0.982942i	$-0.441123\pi$
$107$	39.3576			0.367828			0.183914	+	0.982942i	$0.441123\pi$
$108$	−20.5558	+	49.9346i	−0.190331	+	0.462357i
$109$	84.9847			0.779676			0.389838	−	0.920884i	$-0.372531\pi$
$109$	84.9847			0.779676			0.389838	+	0.920884i	$0.372531\pi$
$110$	122.008	−	70.4416i	1.10917	−	0.640378i
$111$	153.337	−	6.80681i	1.38141	−	0.0613226i
$112$	20.2787	+	19.3074i	0.181059	+	0.172388i
$113$	−25.6093	+	44.3566i	−0.226631	+	0.392536i	−0.956807	−	0.290722i	$-0.906104\pi$
$113$	−25.6093	+	44.3566i	−0.226631	+	0.392536i	0.730177	+	0.683258i	$0.239438\pi$
$114$	82.4694	−	52.6233i	0.723416	−	0.461608i
$115$	−135.397	+	78.1715i	−1.17736	+	0.679752i
$116$	91.1791			0.786026
$117$	111.080	+	51.6003i	0.949399	+	0.441028i
$118$		−	61.2616i		−	0.519166i
$119$	−20.7472	−	70.4683i	−0.174347	−	0.592170i
$120$	−43.3021	−	22.5016i	−0.360851	−	0.187513i
$121$	−89.5238	+	155.060i	−0.739866	+	1.28149i
$122$	−59.9007	−	34.5837i	−0.490989	−	0.283473i
$123$	−65.0827	−	33.8196i	−0.529128	−	0.274956i
$124$	1.54876	−	0.894178i	0.0124900	−	0.00721111i
$125$		−	97.3376i		−	0.778700i
$126$	−69.7162	−	55.4766i	−0.553303	−	0.440291i
$127$	−139.901			−1.10158			−0.550790	−	0.834644i	$-0.685673\pi$
$127$	−139.901			−1.10158			−0.550790	+	0.834644i	$0.685673\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	−19.1960	−	30.0833i	−0.148806	−	0.233204i
$130$	−55.3422	+	95.8555i	−0.425709	+	0.737350i
$131$	−36.7121	−	21.1958i	−0.280245	−	0.161800i	0.353289	−	0.935514i	$-0.385063\pi$
$131$	−36.7121	−	21.1958i	−0.280245	−	0.161800i	−0.633534	+	0.773714i	$0.718397\pi$
$132$	103.829	−	4.60911i	0.786584	−	0.0349175i
$133$	45.5872	+	154.837i	0.342761	+	1.16419i
$134$	−14.6307			−0.109184
$135$	143.589	+	59.1089i	1.06362	+	0.437844i
$136$		−	29.6819i		−	0.218249i
$137$	45.9094	+	79.5175i	0.335105	+	0.580420i	0.983505	−	0.180881i	$-0.0578947\pi$
$137$	45.9094	+	79.5175i	0.335105	+	0.580420i	−0.648400	+	0.761300i	$0.724561\pi$
$138$	−115.223	+	5.11488i	−0.834946	+	0.0370644i
$139$	−43.1971	−	24.9399i	−0.310771	−	0.179423i	0.336501	−	0.941683i	$-0.390757\pi$
$139$	−43.1971	−	24.9399i	−0.310771	−	0.179423i	−0.647271	+	0.762260i	$0.724090\pi$
$140$	55.5192	−	58.3121i	0.396566	−	0.416515i
$141$	42.2887	−	26.9842i	0.299920	−	0.191378i
$142$	29.7647	+	51.5540i	0.209611	+	0.363056i
$143$		−	235.731i		−	1.64847i
$144$	−20.6917	−	29.4593i	−0.143693	−	0.204579i
$145$		−	262.189i		−	1.80820i
$146$	−134.418	+	77.6063i	−0.920672	+	0.531550i
$147$	119.894	−	85.0554i	0.815606	−	0.578608i
$148$	−51.1625	+	88.6161i	−0.345693	+	0.598757i
$149$	35.3502	−	61.2284i	0.237250	−	0.410929i	−0.722674	−	0.691189i	$-0.757087\pi$
$149$	35.3502	−	61.2284i	0.237250	−	0.410929i	0.959924	+	0.280260i	$0.0904207\pi$
$150$	−15.7969	+	30.3995i	−0.105312	+	0.202664i
$151$	−57.5780	−	99.7279i	−0.381311	−	0.660450i	0.609939	−	0.792448i	$-0.291194\pi$
$151$	−57.5780	−	99.7279i	−0.381311	−	0.660450i	−0.991250	+	0.131998i	$0.957861\pi$
$152$			65.2190i			0.429072i
$153$	8.36878	+	94.0758i	0.0546979	+	0.614874i
$154$	−40.3058	+	166.674i	−0.261726	+	1.08230i
$155$	−2.57124	−	4.45353i	−0.0165887	−	0.0287324i
$156$	−68.8336	+	43.9224i	−0.441241	+	0.281554i
$157$	177.402	+	102.423i	1.12995	+	0.652376i	0.943922	−	0.330169i	$-0.107106\pi$
$157$	177.402	+	102.423i	1.12995	+	0.652376i	0.186026	+	0.982545i	$0.440439\pi$
$158$	−80.1327	+	138.794i	−0.507169	+	0.878442i
$159$	−236.972	+	10.5195i	−1.49039	+	0.0661605i
$160$	28.1744	−	16.2665i	0.176090	−	0.101666i
$161$	44.7287	−	184.963i	0.277818	−	1.14884i
$162$	73.8877	+	87.5363i	0.456097	+	0.540348i
$163$	−200.360			−1.22920			−0.614601	−	0.788838i	$-0.710683\pi$
$163$	−200.360			−1.22920			−0.614601	+	0.788838i	$0.710683\pi$
$164$	42.3459	−	24.4484i	0.258207	−	0.149076i
$165$	−13.2537	−	298.565i	−0.0803253	−	1.80948i
$166$	−117.159	−	67.6418i	−0.705778	−	0.407481i
$167$	−20.5934	−	11.8896i	−0.123314	−	0.0711953i	0.437074	−	0.899425i	$-0.356015\pi$
$167$	−20.5934	−	11.8896i	−0.123314	−	0.0711953i	−0.560388	+	0.828230i	$0.689348\pi$
$168$	56.1787	−	19.2860i	0.334397	−	0.114798i
$169$	8.10061	+	14.0307i	0.0479326	+	0.0830217i
$170$	−85.3515			−0.502068
$171$	−18.3884	−	206.709i	−0.107535	−	1.20883i
$172$	23.7907			0.138318
$173$	−141.525	+	81.7094i	−0.818062	+	0.472309i	−0.849748	−	0.527189i	$-0.823246\pi$
$173$	−141.525	+	81.7094i	−0.818062	+	0.472309i	0.0316855	+	0.999498i	$0.489913\pi$
$174$	89.1863	−	171.631i	0.512565	−	0.986383i
$175$	−40.9370	−	38.9764i	−0.233926	−	0.222722i
$176$	−34.6438	+	60.0048i	−0.196840	+	0.340936i
$177$	−115.316	−	59.9227i	−0.651500	−	0.338546i
$178$	−150.874	+	87.1074i	−0.847609	+	0.489367i
$179$	189.491			1.05861			0.529304	−	0.848432i	$-0.322453\pi$
$179$	189.491			1.05861			0.529304	+	0.848432i	$0.322453\pi$
$180$	−84.7115	+	59.4999i	−0.470619	+	0.330555i
$181$		−	162.121i		−	0.895698i	−0.894109	−	0.447849i	$-0.852190\pi$
$181$		−	162.121i		−	0.895698i	0.894109	−	0.447849i	$-0.147810\pi$
$182$	−38.0496	−	129.236i	−0.209064	−	0.710088i
$183$	−123.690	+	78.9260i	−0.675902	+	0.431290i
$184$	38.4454	−	66.5893i	0.208942	−	0.361898i
$185$	254.819	+	147.120i	1.37740	+	0.795243i
$186$	−0.168241	−	3.78994i	−0.000904519	−	0.0203760i
$187$	157.425	−	90.8892i	0.841843	−	0.486038i
$188$			33.4430i			0.177888i
$189$	−172.619	+	76.9659i	−0.913327	+	0.407227i
$190$	187.540			0.987052
$191$	48.8766	+	84.6567i	0.255898	+	0.443229i	0.965139	−	0.261737i	$-0.0842955\pi$
$191$	48.8766	+	84.6567i	0.255898	+	0.443229i	−0.709241	+	0.704966i	$0.750962\pi$
$192$	23.9764	−	1.06434i	0.124877	−	0.00554345i
$193$	173.476	−	300.468i	0.898837	−	1.55683i	0.0698539	−	0.997557i	$-0.477747\pi$
$193$	173.476	−	300.468i	0.898837	−	1.55683i	0.828983	−	0.559274i	$-0.188920\pi$
$194$	29.5808	+	17.0785i	0.152479	+	0.0880335i
$195$	126.301	+	197.934i	0.647696	+	1.01504i
$196$	4.80595	+	97.8821i	0.0245202	+	0.499398i
$197$	15.5388			0.0788769			0.0394385	−	0.999222i	$-0.487443\pi$
$197$	15.5388			0.0788769			0.0394385	+	0.999222i	$0.487443\pi$
$198$	92.8839	−	199.951i	0.469111	−	1.00985i
$199$			286.352i			1.43895i	0.694516	+	0.719477i	$0.255619\pi$
$199$			286.352i			1.43895i	−0.694516	+	0.719477i	$0.744381\pi$
$200$	−11.4196	−	19.7794i	−0.0570982	−	0.0988970i
$201$	−14.3110	+	27.5401i	−0.0711988	+	0.137015i
$202$	29.8159	+	17.2142i	0.147604	+	0.0852190i
$203$	231.124	+	220.054i	1.13854	+	1.08401i
$204$	−55.8717	−	29.0332i	−0.273881	−	0.142320i
$205$	−70.3024	−	121.767i	−0.342938	−	0.593987i
$206$			206.807i			1.00392i
$207$	−103.076	+	221.892i	−0.497954	+	1.07194i
$208$		−	54.4355i		−	0.261709i
$209$	−345.903	+	199.707i	−1.65504	+	0.955538i
$210$	−55.4577	−	161.544i	−0.264084	−	0.769258i
$211$	71.1281	−	123.197i	0.337100	−	0.583874i	−0.646786	−	0.762672i	$-0.723887\pi$
$211$	71.1281	−	123.197i	0.337100	−	0.583874i	0.983886	+	0.178797i	$0.0572206\pi$
$212$	79.0686	−	136.951i	0.372965	−	0.645994i
$213$	126.157	−	5.60026i	0.592285	−	0.0262923i
$214$	27.8300	+	48.2030i	0.130047	+	0.225247i
$215$		−	68.4111i		−	0.318191i
$216$	−75.6922	+	10.1335i	−0.350427	+	0.0469144i
$217$	6.08388	+	1.47123i	0.0280363	+	0.00677987i
$218$	60.0932	+	104.085i	0.275657	+	0.477452i
$219$	14.6017	+	328.932i	0.0666745	+	1.50197i
$220$	172.546	+	99.6195i	0.784300	+	0.452816i
$221$	−71.4067	+	123.680i	−0.323107	+	0.559638i
$222$	116.762	+	182.985i	0.525955	+	0.824257i
$223$	98.4840	−	56.8598i	0.441632	−	0.254977i	−0.262657	−	0.964889i	$-0.584599\pi$
$223$	98.4840	−	56.8598i	0.441632	−	0.254977i	0.704290	+	0.709913i	$0.251266\pi$
$224$	−9.30748	+	38.4886i	−0.0415513	+	0.171824i
$225$	41.7709	+	59.4703i	0.185649	+	0.264313i
$226$	−72.4340			−0.320504
$227$	130.245	−	75.1969i	0.573766	−	0.331264i	−0.184886	−	0.982760i	$-0.559192\pi$
$227$	130.245	−	75.1969i	0.573766	−	0.331264i	0.758652	+	0.651496i	$0.225858\pi$
$228$	122.765	+	63.7936i	0.538442	+	0.279797i
$229$	−31.0059	−	17.9012i	−0.135397	−	0.0781714i	0.430772	−	0.902461i	$-0.358241\pi$
$229$	−31.0059	−	17.9012i	−0.135397	−	0.0781714i	−0.566168	+	0.824290i	$0.691575\pi$
$230$	−191.480	−	110.551i	−0.832522	−	0.480657i
$231$	274.313	+	238.900i	1.18750	+	1.03420i
$232$	64.4733	+	111.671i	0.277902	+	0.481341i
$233$	−397.747			−1.70707			−0.853533	−	0.521038i	$-0.825545\pi$
$233$	−397.747			−1.70707			−0.853533	+	0.521038i	$0.825545\pi$
$234$	15.3480	+	172.531i	0.0655898	+	0.737313i
$235$	96.1668			0.409220
$236$	75.0298	−	43.3185i	0.317923	−	0.183553i
$237$	182.877	+	286.598i	0.771633	+	1.20927i
$238$	71.6351	−	75.2387i	0.300988	−	0.316129i
$239$	85.1346	−	147.458i	0.356212	−	0.616977i	−0.631113	−	0.775691i	$-0.717401\pi$
$239$	85.1346	−	147.458i	0.356212	−	0.616977i	0.987325	+	0.158714i	$0.0507348\pi$
$240$	−3.06056	−	68.9450i	−0.0127523	−	0.287271i
$241$	−62.5220	+	36.0971i	−0.259427	+	0.149780i	−0.624073	−	0.781366i	$-0.714523\pi$
$241$	−62.5220	+	36.0971i	−0.259427	+	0.149780i	0.364646	+	0.931146i	$0.381190\pi$
$242$	−253.212			−1.04633
$243$	237.047	−	53.4591i	0.975501	−	0.219996i
$244$		−	97.8174i		−	0.400891i
$245$	281.464	−	13.8197i	1.14883	−	0.0564070i
$246$	−4.60000	−	103.624i	−0.0186992	−	0.421235i
$247$	156.899	−	271.758i	0.635220	−	1.10023i
$248$	2.19028	+	1.26456i	0.00883177	+	0.00509903i
$249$	−241.924	+	154.371i	−0.971583	+	0.619962i
$250$	119.214	−	68.8280i	0.476855	−	0.275312i
$251$			220.918i			0.880153i	0.897960	+	0.440076i	$0.145049\pi$
$251$			220.918i			0.880153i	−0.897960	+	0.440076i	$0.854951\pi$
$252$	18.6479	−	124.612i	0.0739997	−	0.494494i
$253$	470.895			1.86124
$254$	−98.9246	−	171.343i	−0.389467	−	0.674577i
$255$	−83.4861	+	160.661i	−0.327397	+	0.630044i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−307.432	−	177.496i	−1.19623	−	0.690645i	−0.236519	−	0.971627i	$-0.576006\pi$
$257$	−307.432	−	177.496i	−1.19623	−	0.690645i	−0.959713	+	0.280982i	$0.909340\pi$
$258$	23.2707	−	44.7823i	0.0901967	−	0.173575i
$259$	−343.557	+	101.150i	−1.32647	+	0.390540i
$260$	−156.531			−0.602043
$261$	−235.831	−	335.759i	−0.903569	−	1.28643i
$262$		−	59.9507i		−	0.228819i
$263$	−107.394	−	186.012i	−0.408341	−	0.707268i	0.586363	−	0.810049i	$-0.300559\pi$
$263$	−107.394	−	186.012i	−0.408341	−	0.707268i	−0.994704	+	0.102781i	$0.967226\pi$
$264$	79.0632	+	123.905i	0.299482	+	0.469337i
$265$	−393.807	−	227.365i	−1.48607	−	0.857980i
$266$	−157.401	+	165.319i	−0.591734	+	0.621501i
$267$	16.3893	+	369.202i	0.0613833	+	1.38278i
$268$	−10.3455	−	17.9189i	−0.0386025	−	0.0668615i
$269$		−	99.1640i		−	0.368639i	−0.982866	−	0.184320i	$-0.940992\pi$
$269$		−	99.1640i		−	0.368639i	0.982866	−	0.184320i	$-0.0590082\pi$
$270$	29.1393	+	217.656i	0.107923	+	0.806133i
$271$			487.080i			1.79734i	0.438622	+	0.898672i	$0.355467\pi$
$271$			487.080i			1.79734i	−0.438622	+	0.898672i	$0.644533\pi$
$272$	36.3528	−	20.9883i	0.133650	−	0.0771628i
$273$	−280.485	−	54.7889i	−1.02742	−	0.200692i
$274$	−64.9258	+	112.455i	−0.236955	+	0.410419i
$275$	69.9363	−	121.133i	0.254314	−	0.440484i
$276$	−87.7391	−	137.502i	−0.317895	−	0.498194i
$277$	−161.811	−	280.265i	−0.584155	−	1.01179i	−0.994980	−	0.100072i	$-0.968093\pi$
$277$	−161.811	−	280.265i	−0.584155	−	1.01179i	0.410825	−	0.911714i	$-0.365241\pi$
$278$		−	70.5406i		−	0.253743i
$279$	−7.29855	−	3.39043i	−0.0261597	−	0.0121521i
$280$	110.675	+	26.7640i	0.395269	+	0.0955858i
$281$	103.963	+	180.070i	0.369976	+	0.640817i	0.989561	−	0.144112i	$-0.0460326\pi$
$281$	103.963	+	180.070i	0.369976	+	0.640817i	−0.619585	+	0.784929i	$0.712699\pi$
$282$	62.9514	+	32.7121i	0.223232	+	0.116000i
$283$	−235.533	−	135.985i	−0.832273	−	0.480513i	0.0223573	−	0.999750i	$-0.492883\pi$
$283$	−235.533	−	135.985i	−0.832273	−	0.480513i	−0.854630	+	0.519237i	$0.826216\pi$
$284$	−42.0936	+	72.9083i	−0.148217	+	0.256719i
$285$	183.441	−	353.015i	0.643653	−	1.23865i
$286$	288.711	−	166.687i	1.00948	−	0.582822i
$287$	166.344	+	40.2261i	0.579597	+	0.140161i
$288$	21.4489	−	46.1730i	0.0744754	−	0.160323i
$289$	178.873			0.618938
$290$	321.115	−	185.396i	1.10729	−	0.639295i
$291$	61.0820	−	38.9762i	0.209904	−	0.133939i
$292$	−190.096	−	109.752i	−0.651014	−	0.375863i
$293$	239.193	+	138.098i	0.816357	+	0.471324i	0.849158	−	0.528138i	$-0.177110\pi$
$293$	239.193	+	138.098i	0.816357	+	0.471324i	−0.0328018	+	0.999462i	$0.510443\pi$
$294$	188.949	+	86.6964i	0.642684	+	0.294886i
$295$	−124.564	−	215.751i	−0.422251	−	0.731360i
$296$	−144.709			−0.488883
$297$	−285.523	−	370.421i	−0.961357	−	1.24721i
$298$	99.9855			0.335522
$299$	−320.392	+	184.978i	−1.07154	+	0.618657i
$300$	−48.4018	+	2.14862i	−0.161339	+	0.00716206i
$301$	60.3054	+	57.4171i	0.200350	+	0.190754i
$302$	81.4275	−	141.037i	0.269628	−	0.467009i
$303$	61.5675	−	39.2859i	0.203193	−	0.129657i
$304$	−79.8766	+	46.1168i	−0.262752	+	0.151700i
$305$	−281.278			−0.922222
$306$	−109.301	+	76.7712i	−0.357193	+	0.250886i
$307$		−	418.849i		−	1.36433i	−0.731199	−	0.682165i	$-0.761039\pi$
$307$		−	418.849i		−	1.36433i	0.731199	−	0.682165i	$-0.238961\pi$
$308$	−232.633	+	68.4918i	−0.755303	+	0.222376i
$309$	389.282	+	202.287i	1.25981	+	0.654651i
$310$	3.63629	−	6.29824i	0.0117300	−	0.0203169i
$311$	−168.685	−	97.3905i	−0.542397	−	0.313153i	0.203653	−	0.979043i	$-0.434719\pi$
$311$	−168.685	−	97.3905i	−0.542397	−	0.313153i	−0.746050	+	0.665890i	$0.768052\pi$
$312$	−102.466	−	53.2458i	−0.328418	−	0.170660i
$313$	82.2059	−	47.4616i	0.262639	−	0.151634i	−0.362899	−	0.931828i	$-0.618213\pi$
$313$	82.2059	−	47.4616i	0.262639	−	0.151634i	0.625538	+	0.780194i	$0.284880\pi$
$314$			289.696i			0.922599i
$315$	−358.328	−	53.6228i	−1.13755	−	0.170231i
$316$	−226.649			−0.717245
$317$	−77.4057	−	134.071i	−0.244182	−	0.422936i	0.717719	−	0.696333i	$-0.245186\pi$
$317$	−77.4057	−	134.071i	−0.244182	−	0.422936i	−0.961901	+	0.273397i	$0.911853\pi$
$318$	−180.449	−	282.792i	−0.567448	−	0.889284i
$319$	−394.848	+	683.897i	−1.23777	+	2.14388i
$320$	39.8446	+	23.0043i	0.124515	+	0.0718885i
$321$	117.956	−	5.23624i	0.367466	−	0.0163123i
$322$	258.161	−	76.0077i	0.801742	−	0.236049i
$323$	241.978			0.749158
$324$	−54.9632	+	152.391i	−0.169639	+	0.470343i
$325$			109.890i			0.338124i
$326$	−141.676	−	245.390i	−0.434588	−	0.752729i
$327$	254.703	−	11.3066i	0.778909	−	0.0345768i
$328$	59.8862	+	34.5753i	0.182580	+	0.105412i
$329$	−80.7123	+	84.7725i	−0.245326	+	0.257667i
$330$	356.294	−	227.349i	1.07968	−	0.688937i
$331$	−87.2053	−	151.044i	−0.263460	−	0.456326i	0.703699	−	0.710498i	$-0.251530\pi$
$331$	−87.2053	−	151.044i	−0.263460	−	0.456326i	−0.967159	+	0.254172i	$0.918197\pi$
$332$		−	191.320i		−	0.576265i
$333$	458.652	−	40.8007i	1.37733	−	0.122525i
$334$		−	33.6289i		−	0.100685i
$335$	−51.5265	+	29.7488i	−0.153810	+	0.0888025i
$336$	63.3448	+	55.1673i	0.188526	+	0.164188i
$337$	−40.8311	+	70.7216i	−0.121161	+	0.209856i	−0.920226	−	0.391388i	$-0.871995\pi$
$337$	−40.8311	+	70.7216i	−0.121161	+	0.209856i	0.799065	+	0.601245i	$0.205328\pi$
$338$	−11.4560	+	19.8424i	−0.0338935	+	0.0587052i
$339$	−70.8510	+	136.346i	−0.209000	+	0.402201i
$340$	−60.3526	−	104.534i	−0.177508	−	0.307452i
$341$			15.4888i			0.0454218i
$342$	240.164	−	168.687i	0.702233	−	0.493236i
$343$	−224.049	+	259.713i	−0.653204	+	0.757182i
$344$	16.8226	+	29.1375i	0.0489028	+	0.0847021i
$345$	−395.391	+	252.297i	−1.14606	+	0.731296i
$346$	−200.146	−	115.555i	−0.578457	−	0.333973i
$347$	242.992	−	420.875i	0.700266	−	1.21290i	−0.268106	−	0.963389i	$-0.586398\pi$
$347$	242.992	−	420.875i	0.700266	−	1.21290i	0.968373	−	0.249508i	$-0.0802688\pi$
$348$	273.268	−	12.1307i	0.785253	−	0.0348584i
$349$	423.870	−	244.722i	1.21453	−	0.701208i	0.250786	−	0.968043i	$-0.419311\pi$
$349$	423.870	−	244.722i	1.21453	−	0.701208i	0.963742	+	0.266834i	$0.0859777\pi$
$350$	18.7893	−	77.6979i	0.0536836	−	0.221994i
$351$	339.776	+	139.870i	0.968024	+	0.398491i
$352$	−97.9874			−0.278373
$353$	−148.587	+	85.7870i	−0.420927	+	0.243023i	−0.695474	−	0.718551i	$-0.744806\pi$
$353$	−148.587	+	85.7870i	−0.420927	+	0.243023i	0.274547	+	0.961574i	$0.411472\pi$
$354$	−8.15041	−	183.604i	−0.0230238	−	0.518655i
$355$	209.651	+	121.042i	0.590565	+	0.340963i
$356$	−213.369	−	123.188i	−0.599350	−	0.346035i
$357$	−71.5558	−	208.437i	−0.200436	−	0.583856i
$358$	133.990	+	232.078i	0.374275	+	0.648263i
$359$	−111.557			−0.310744			−0.155372	−	0.987856i	$-0.549658\pi$
$359$	−111.557			−0.310744			−0.155372	+	0.987856i	$0.549658\pi$
$360$	−132.772	−	61.6772i	−0.368812	−	0.171326i
$361$	−170.690			−0.472825
$362$	198.557	−	114.637i	0.548501	−	0.316677i
$363$	−247.678	+	476.632i	−0.682308	+	1.31304i
$364$	131.376	−	137.985i	0.360923	−	0.379079i
$365$	−315.596	+	546.628i	−0.864647	+	1.49761i
$366$	−184.126	−	95.6796i	−0.503077	−	0.261420i
$367$	502.284	−	289.994i	1.36862	−	0.790174i	0.377869	−	0.925859i	$-0.376657\pi$
$367$	502.284	−	289.994i	1.36862	−	0.790174i	0.990752	+	0.135686i	$0.0433237\pi$
$368$	108.740			0.295489
$369$	−199.555	−	92.7003i	−0.540801	−	0.251220i
$370$			416.118i			1.12464i
$371$	530.946	−	156.321i	1.43112	−	0.421350i
$372$	4.52275	−	2.88595i	0.0121579	−	0.00775792i
$373$	159.831	−	276.835i	0.428501	−	0.742185i	−0.568240	−	0.822863i	$-0.692375\pi$
$373$	159.831	−	276.835i	0.428501	−	0.742185i	0.996740	+	0.0806784i	$0.0257087\pi$
$374$	222.632	+	128.537i	0.595273	+	0.343681i
$375$	−12.9501	−	291.725i	−0.0345335	−	0.777934i
$376$	−40.9592	+	23.6478i	−0.108934	+	0.0628931i
$377$		−	620.422i		−	1.64568i
$378$	−216.324	−	156.991i	−0.572284	−	0.415320i
$379$	105.877			0.279359			0.139679	−	0.990197i	$-0.455393\pi$
$379$	105.877			0.279359			0.139679	+	0.990197i	$0.455393\pi$
$380$	132.611	+	229.688i	0.348975	+	0.604443i
$381$	−419.289	+	18.6128i	−1.10050	+	0.0488524i
$382$	−69.1219	+	119.723i	−0.180947	+	0.313410i
$383$	111.394	+	64.3133i	0.290846	+	0.167920i	0.638323	−	0.769769i	$-0.279628\pi$
$383$	111.394	+	64.3133i	0.290846	+	0.167920i	−0.347478	+	0.937688i	$0.612962\pi$
$384$	18.2574	+	28.6124i	0.0475454	+	0.0745113i
$385$	196.951	+	668.946i	0.511561	+	1.73752i
$386$	490.663			1.27115
$387$	−61.5338	−	87.6072i	−0.159002	−	0.226375i
$388$			48.3053i			0.124498i
$389$	75.0565	+	130.002i	0.192947	+	0.334195i	0.946226	−	0.323507i	$-0.104862\pi$
$389$	75.0565	+	130.002i	0.192947	+	0.334195i	−0.753278	+	0.657702i	$0.771529\pi$
$390$	−153.110	+	294.646i	−0.392590	+	0.755503i
$391$	−247.062	−	142.641i	−0.631873	−	0.364812i
$392$	−116.482	+	75.0992i	−0.297149	+	0.191579i
$393$	−112.848	−	58.6404i	−0.287145	−	0.149212i
$394$	10.9876	+	19.0310i	0.0278872	+	0.0483021i
$395$			651.740i			1.64997i
$396$	310.567	−	27.6274i	0.784261	−	0.0697662i
$397$			305.431i			0.769347i	0.923053	+	0.384674i	$0.125686\pi$
$397$			305.431i			0.769347i	−0.923053	+	0.384674i	$0.874314\pi$
$398$	−350.708	+	202.481i	−0.881176	+	0.508747i
$399$	157.227	+	457.990i	0.394053	+	1.14784i
$400$	16.1498	−	27.9723i	0.0403745	−	0.0699307i
$401$	131.258	−	227.346i	0.327327	−	0.566947i	−0.654653	−	0.755929i	$-0.727185\pi$
$401$	131.258	−	227.346i	0.327327	−	0.566947i	0.981981	+	0.188982i	$0.0605188\pi$
$402$	−43.8490	+	1.94651i	−0.109077	+	0.00484207i
$403$	−6.08437	−	10.5384i	−0.0150977	−	0.0261500i
$404$			48.6892i			0.120518i
$405$	438.207	+	158.049i	1.08199	+	0.390244i
$406$	−106.081	+	438.669i	−0.261283	+	1.08047i
$407$	−443.116	−	767.499i	−1.08874	−	1.88575i
$408$	−3.94897	−	88.9581i	−0.00967884	−	0.218035i
$409$	−305.530	−	176.398i	−0.747017	−	0.431291i	0.0775980	−	0.996985i	$-0.475275\pi$
$409$	−305.530	−	176.398i	−0.747017	−	0.431291i	−0.824615	+	0.565694i	$0.808608\pi$
$410$	99.4226	−	172.205i	0.242494	−	0.420012i
$411$	148.172	+	232.210i	0.360516	+	0.564987i
$412$	−253.286	+	146.235i	−0.614771	+	0.354938i
$413$	294.734	+	71.2739i	0.713641	+	0.172576i
$414$	−344.647	+	30.6591i	−0.832481	+	0.0740558i
$415$	−550.148			−1.32566
$416$	66.6696	−	38.4917i	0.160263	−	0.0925281i
$417$	−132.782	−	68.9989i	−0.318422	−	0.165465i
$418$	−489.181	−	282.429i	−1.17029	−	0.675667i
$419$	−604.426	−	348.965i	−1.44254	−	0.832853i	−0.444524	−	0.895767i	$-0.646627\pi$
$419$	−604.426	−	348.965i	−1.44254	−	0.832853i	−0.998019	+	0.0629143i	$0.979961\pi$
$420$	158.636	−	182.151i	0.377704	−	0.433692i
$421$	−15.2619	−	26.4343i	−0.0362514	−	0.0627894i	0.847330	−	0.531066i	$-0.178208\pi$
$421$	−15.2619	−	26.4343i	−0.0362514	−	0.0627894i	−0.883582	+	0.468277i	$0.844875\pi$
$422$	201.181			0.476731
$423$	123.151	−	86.4992i	0.291138	−	0.204490i
$424$	223.640			0.527452
$425$	−73.3863	+	42.3696i	−0.172674	+	0.0996932i
$426$	96.0651	+	150.550i	0.225505	+	0.353403i
$427$	236.075	−	247.951i	0.552869	−	0.580680i
$428$	−39.3576	+	68.1693i	−0.0919569	+	0.159274i
$429$	−31.3624	−	706.498i	−0.0731057	−	1.64685i
$430$	83.7861	−	48.3739i	0.194851	−	0.112497i
$431$	214.726			0.498205			0.249103	−	0.968477i	$-0.419864\pi$
$431$	214.726			0.498205			0.249103	+	0.968477i	$0.419864\pi$
$432$	−65.9334	−	85.5382i	−0.152624	−	0.198005i
$433$			49.9849i			0.115439i	0.998333	+	0.0577193i	$0.0183828\pi$
$433$			49.9849i			0.115439i	−0.998333	+	0.0577193i	$0.981617\pi$
$434$	2.50007	+	8.49152i	0.00576053	+	0.0195657i
$435$	−34.8824	−	785.793i	−0.0801894	−	1.80642i
$436$	−84.9847	+	147.198i	−0.194919	+	0.337609i
$437$	542.861	+	313.421i	1.24224	+	0.717210i
$438$	−392.533	+	250.473i	−0.896193	+	0.571857i
$439$	−174.953	+	101.009i	−0.398527	+	0.230090i	−0.685848	−	0.727745i	$-0.740569\pi$
$439$	−174.953	+	101.009i	−0.398527	+	0.230090i	0.287321	+	0.957834i	$0.407235\pi$
$440$			281.767i			0.640378i
$441$	348.012	−	270.866i	0.789143	−	0.614209i
$442$	−201.969			−0.456943
$443$	410.792	+	711.513i	0.927296	+	1.60612i	0.787826	+	0.615898i	$0.211207\pi$
$443$	410.792	+	711.513i	0.927296	+	1.60612i	0.139470	+	0.990226i	$0.455460\pi$
$444$	−141.547	+	272.394i	−0.318799	+	0.613499i
$445$	−354.233	+	613.550i	−0.796030	+	1.37876i
$446$	139.277	+	80.4119i	0.312281	+	0.180296i
$447$	97.8003	−	188.207i	0.218793	−	0.421046i
$448$	−53.7201	+	15.8162i	−0.119911	+	0.0353041i
$449$	324.954			0.723729			0.361864	−	0.932231i	$-0.382140\pi$
$449$	324.954			0.723729			0.361864	+	0.932231i	$0.382140\pi$
$450$	−43.2995	+	93.2106i	−0.0962211	+	0.207135i
$451$			423.493i			0.939008i
$452$	−51.2186	−	88.7132i	−0.113315	−	0.196268i
$453$	−185.832	−	291.229i	−0.410225	−	0.642890i
$454$	184.194	+	106.345i	0.405714	+	0.234239i
$455$	−396.781	−	377.777i	−0.872045	−	0.830279i
$456$	8.67692	+	195.465i	0.0190283	+	0.428650i
$457$	370.766	+	642.186i	0.811305	+	1.40522i	0.911951	+	0.410298i	$0.134575\pi$
$457$	370.766	+	642.186i	0.811305	+	1.40522i	−0.100647	+	0.994922i	$0.532091\pi$
$458$		−	50.6324i		−	0.110551i
$459$	37.5978	+	280.836i	0.0819123	+	0.611844i
$460$		−	312.686i		−	0.679752i
$461$	573.356	−	331.027i	1.24372	−	0.718063i	0.273872	−	0.961766i	$-0.411695\pi$
$461$	573.356	−	331.027i	1.24372	−	0.718063i	0.969850	+	0.243703i	$0.0783621\pi$
$462$	−98.6236	+	504.891i	−0.213471	+	1.09284i
$463$	−323.675	+	560.622i	−0.699083	+	1.21085i	0.269702	+	0.962944i	$0.413075\pi$
$463$	−323.675	+	560.622i	−0.699083	+	1.21085i	−0.968785	+	0.247903i	$0.920258\pi$
$464$	−91.1791	+	157.927i	−0.196507	+	0.340359i
$465$	−8.29865	−	13.0053i	−0.0178466	−	0.0279685i
$466$	−281.249	−	487.138i	−0.603539	−	1.04536i
$467$			17.5828i			0.0376506i	0.999823	+	0.0188253i	$0.00599263\pi$
$467$			17.5828i			0.0376506i	−0.999823	+	0.0188253i	$0.994007\pi$
$468$	−200.454	+	140.795i	−0.428321	+	0.300845i
$469$	17.0219	−	70.3894i	0.0362940	−	0.150084i
$470$	68.0002	+	117.780i	0.144681	+	0.250595i
$471$	545.309	+	283.365i	1.15777	+	0.601624i
$472$	106.108	+	61.2616i	0.224805	+	0.129791i
$473$	−103.025	+	178.444i	−0.217812	+	0.377261i
$474$	−221.696	+	426.633i	−0.467713	+	0.900070i
$475$	161.249	−	93.0972i	0.339472	−	0.195994i
$476$	142.802	+	34.5330i	0.300004	+	0.0725483i
$477$	−708.818	+	63.0550i	−1.48599	+	0.132191i
$478$	240.797			0.503760
$479$	599.109	−	345.896i	1.25075	−	0.722121i	0.279491	−	0.960148i	$-0.409834\pi$
$479$	599.109	−	345.896i	1.25075	−	0.722121i	0.971258	+	0.238028i	$0.0765009\pi$
$480$	82.2759	−	52.4999i	0.171408	−	0.109375i
$481$	602.982	+	348.132i	1.25360	+	0.723767i
$482$	−88.4194	−	51.0490i	−0.183443	−	0.105911i
$483$	109.446	−	560.295i	0.226596	−	1.16003i
$484$	−179.048	−	310.120i	−0.369933	−	0.640743i
$485$	138.904			0.286400
$486$	233.091	+	252.520i	0.479611	+	0.519589i
$487$	782.871			1.60754			0.803769	−	0.594941i	$-0.202825\pi$
$487$	782.871			1.60754			0.803769	+	0.594941i	$0.202825\pi$
$488$	119.801	−	69.1673i	0.245495	−	0.141736i
$489$	−600.488	+	26.6565i	−1.22799	+	0.0545122i
$490$	215.951	+	334.949i	0.440715	+	0.683570i
$491$	−169.949	+	294.361i	−0.346129	+	0.599513i	−0.985558	−	0.169337i	$-0.945837\pi$
$491$	−169.949	+	294.361i	−0.346129	+	0.599513i	0.639429	+	0.768850i	$0.279171\pi$
$492$	123.660	−	78.9069i	0.251342	−	0.160380i
$493$	414.327	−	239.212i	0.840419	−	0.485216i
$494$	443.778			0.898337
$495$	−79.4438	−	893.049i	−0.160492	−	1.80414i
$496$			3.57671i			0.00721111i
$497$	−282.659	+	83.2204i	−0.568731	+	0.167446i
$498$	−360.131	−	187.139i	−0.723154	−	0.375781i
$499$	108.860	−	188.551i	0.218156	−	0.377857i	−0.736088	−	0.676885i	$-0.763329\pi$
$499$	108.860	−	188.551i	0.218156	−	0.377857i	0.954244	+	0.299028i	$0.0966626\pi$
$500$	168.594	+	97.3376i	0.337187	+	0.194675i
$501$	−63.3013	−	32.8939i	−0.126350	−	0.0656566i
$502$	−270.569	+	156.213i	−0.538981	+	0.311181i
$503$			732.558i			1.45638i	0.685377	+	0.728189i	$0.259637\pi$
$503$			732.558i			1.45638i	−0.685377	+	0.728189i	$0.740363\pi$
$504$	165.804	−	65.2753i	0.328977	−	0.129515i
$505$	140.008			0.277243
$506$	332.973	+	576.726i	0.658049	+	1.13977i
$507$	26.1446	+	40.9729i	0.0515673	+	0.0808143i
$508$	139.901	−	242.315i	0.275395	−	0.476998i
$509$	−22.4840	−	12.9812i	−0.0441730	−	0.0255033i	0.477751	−	0.878495i	$-0.341452\pi$
$509$	−22.4840	−	12.9812i	−0.0441730	−	0.0255033i	−0.521924	+	0.852992i	$0.674785\pi$
$510$	−255.803	+	11.3554i	−0.501574	+	0.0222655i
$511$	−216.983	−	736.985i	−0.424624	−	1.44224i
$512$	−22.6274			−0.0441942
$513$	−82.6122	−	617.071i	−0.161037	−	1.20287i
$514$		−	502.034i		−	0.976719i
$515$	420.503	+	728.333i	0.816511	+	1.41424i
$516$	71.3018	−	3.16518i	0.138182	−	0.00613407i
$517$	−250.843	−	144.824i	−0.485189	−	0.280124i
$518$	−366.814	−	349.246i	−0.708136	−	0.674220i
$519$	−413.286	+	263.716i	−0.796312	+	0.508123i
$520$	−110.684	−	191.711i	−0.212855	−	0.368675i
$521$		−	152.333i		−	0.292385i	−0.989256	−	0.146193i	$-0.953298\pi$
$521$		−	152.333i		−	0.292385i	0.989256	−	0.146193i	$-0.0467019\pi$
$522$	244.462	−	526.251i	0.468317	−	1.00814i
$523$		−	343.250i		−	0.656310i	−0.944624	−	0.328155i	$-0.893573\pi$
$523$		−	343.250i		−	0.656310i	0.944624	−	0.328155i	$-0.106427\pi$
$524$	73.4243	−	42.3915i	0.140123	−	0.0808999i
$525$	−127.876	−	111.368i	−0.243573	−	0.212129i
$526$	151.878	−	263.060i	0.288741	−	0.500114i
$527$	4.69182	−	8.12646i	0.00890288	−	0.0154202i
$528$	−95.8458	+	184.446i	−0.181526	+	0.349330i
$529$	−105.011	−	181.885i	−0.198509	−	0.343828i
$530$		−	643.085i		−	1.21337i
$531$	−353.579	−	164.249i	−0.665873	−	0.309321i
$532$	−313.773	−	75.8781i	−0.589800	−	0.142628i
$533$	−166.358	−	288.140i	−0.312116	−	0.540600i
$534$	−440.589	+	281.138i	−0.825073	+	0.526475i
$535$	196.023	+	113.174i	0.366399	+	0.211541i
$536$	14.6307	−	25.3411i	0.0272961	−	0.0472782i
$537$	567.914	−	25.2104i	1.05757	−	0.0469468i
$538$	121.451	−	70.1195i	0.225745	−	0.130334i
$539$	−754.986	−	387.828i	−1.40072	−	0.719533i
$540$	−245.968	+	189.594i	−0.455497	+	0.351100i
$541$	−941.180			−1.73970			−0.869852	−	0.493313i	$-0.835786\pi$
$541$	−941.180			−1.73970			−0.869852	+	0.493313i	$0.835786\pi$
$542$	−596.549	+	344.418i	−1.10064	+	0.635457i
$543$	−21.5691	−	485.885i	−0.0397221	−	0.894816i
$544$	51.4106	+	29.6819i	0.0945048	+	0.0545623i
$545$	423.273	+	244.377i	0.776647	+	0.448398i
$546$	−131.230	−	382.264i	−0.240349	−	0.700118i
$547$	102.142	+	176.916i	0.186732	+	0.323429i	0.944159	−	0.329491i	$-0.106877\pi$
$547$	102.142	+	176.916i	0.186732	+	0.323429i	−0.757427	+	0.652920i	$0.773544\pi$
$548$	−183.638			−0.335105
$549$	−360.204	+	253.001i	−0.656110	+	0.460840i
$550$	197.810			0.359654
$551$	−910.385	+	525.611i	−1.65224	+	0.953922i
$552$	106.363	−	204.686i	0.192687	−	0.370808i
$553$	−574.518	−	547.002i	−1.03891	−	0.989154i
$554$	228.835	−	396.354i	0.413060	−	0.715441i
$555$	783.278	+	407.024i	1.41131	+	0.733376i
$556$	86.3942	−	49.8797i	0.155385	−	0.0897117i
$557$	−693.807			−1.24561			−0.622807	−	0.782375i	$-0.714008\pi$
$557$	−693.807			−1.24561			−0.622807	+	0.782375i	$0.714008\pi$
$558$	−1.00845	−	11.3363i	−0.00180726	−	0.0203159i
$559$		−	161.882i		−	0.289592i
$560$	45.4802	+	154.474i	0.0812147	+	0.275847i
$561$	459.717	−	293.343i	0.819460	−	0.522894i
$562$	−147.026	+	254.657i	−0.261613	+	0.453126i
$563$	−63.9135	−	36.9005i	−0.113523	−	0.0655426i	0.442163	−	0.896935i	$-0.354211\pi$
$563$	−63.9135	−	36.9005i	−0.113523	−	0.0655426i	−0.555686	+	0.831392i	$0.687544\pi$
$564$	4.44936	+	100.230i	0.00788893	+	0.177713i
$565$	−255.098	+	147.281i	−0.451501	+	0.260674i
$566$		−	384.624i		−	0.679548i
$567$	−507.107	+	253.636i	−0.894369	+	0.447330i
$568$	−119.059			−0.209611
$569$	−490.396	−	849.391i	−0.861856	−	1.49278i	−0.870135	−	0.492813i	$-0.835969\pi$
$569$	−490.396	−	849.391i	−0.861856	−	1.49278i	0.00827871	−	0.999966i	$-0.497365\pi$
$570$	562.066	−	24.9508i	0.986080	−	0.0437734i
$571$	−173.666	+	300.798i	−0.304143	+	0.526791i	−0.977070	−	0.212918i	$-0.931703\pi$
$571$	−173.666	+	300.798i	−0.304143	+	0.526791i	0.672927	+	0.739709i	$0.265037\pi$
$572$	408.298	+	235.731i	0.713808	+	0.412117i
$573$	157.748	+	247.218i	0.275303	+	0.431444i
$574$	68.3564	+	232.173i	0.119088	+	0.404483i
$575$	−219.516			−0.381767
$576$	71.7168	−	6.37978i	0.124508	−	0.0110760i
$577$		−	268.872i		−	0.465982i	−0.972479	−	0.232991i	$-0.925149\pi$
$577$		−	268.872i		−	0.465982i	0.972479	−	0.232991i	$-0.0748512\pi$
$578$	126.482	+	219.074i	0.218828	+	0.379020i
$579$	479.939	−	923.598i	0.828911	−	1.59516i
$580$	454.125	+	262.189i	0.782974	+	0.452050i
$581$	461.737	−	484.964i	0.794728	−	0.834706i
$582$	90.9274	+	47.2496i	0.156233	+	0.0811848i
$583$	684.808	+	1186.12i	1.17463	+	2.03452i
$584$		−	310.425i		−	0.531550i
$585$	404.863	+	576.414i	0.692073	+	0.985322i
$586$			390.600i			0.666552i
$587$	822.447	−	474.840i	1.40110	−	0.808927i	0.406596	−	0.913608i	$-0.366716\pi$
$587$	822.447	−	474.840i	1.40110	−	0.808927i	0.994506	+	0.104681i	$0.0333823\pi$
$588$	27.4262	+	292.718i	0.0466432	+	0.497820i
$589$	−10.3092	+	17.8560i	−0.0175028	+	0.0303158i
$590$	176.160	−	305.118i	0.298576	−	0.517149i
$591$	46.5704	−	2.06732i	0.0787993	−	0.00349800i
$592$	−102.325	−	177.232i	−0.172846	−	0.299379i
$593$		−	738.022i		−	1.24456i	−0.782796	−	0.622278i	$-0.786207\pi$
$593$		−	738.022i		−	1.24456i	0.782796	−	0.622278i	$-0.213793\pi$
$594$	251.776	−	611.620i	0.423865	−	1.02966i
$595$	99.3010	−	410.632i	0.166892	−	0.690138i
$596$	70.7004	+	122.457i	0.118625	+	0.205464i
$597$	38.0971	+	858.211i	0.0638142	+	1.43754i
$598$	−453.102	−	261.599i	−0.757696	−	0.437456i
$599$	−134.612	+	233.156i	−0.224729	+	0.389241i	−0.956238	−	0.292590i	$-0.905483\pi$
$599$	−134.612	+	233.156i	−0.224729	+	0.389241i	0.731509	+	0.681831i	$0.238816\pi$
$600$	−36.8567	−	57.7605i	−0.0614279	−	0.0962675i
$601$	−669.416	+	386.488i	−1.11384	+	0.643074i	−0.939821	−	0.341668i	$-0.889008\pi$
$601$	−669.416	+	386.488i	−1.11384	+	0.643074i	−0.174017	+	0.984743i	$0.555675\pi$
$602$	−27.6789	+	114.459i	−0.0459783	+	0.190131i
$603$	−39.2266	+	84.4430i	−0.0650524	+	0.140038i
$604$	230.312			0.381311
$605$	−891.761	+	514.859i	−1.47399	+	0.851006i
$606$	91.6500	+	47.6251i	0.151238	+	0.0785893i
$607$	−341.516	−	197.174i	−0.562629	−	0.324834i	0.191571	−	0.981479i	$-0.438642\pi$
$607$	−341.516	−	197.174i	−0.562629	−	0.324834i	−0.754200	+	0.656645i	$0.771975\pi$
$608$	−112.963	−	65.2190i	−0.185794	−	0.107268i
$609$	721.965	+	628.763i	1.18549	+	1.03245i
$610$	−198.893	−	344.493i	−0.326055	−	0.564743i
$611$	227.561			0.372440
$612$	−171.313	−	79.5806i	−0.279923	−	0.130034i
$613$	855.275			1.39523			0.697614	−	0.716474i	$-0.254245\pi$
$613$	855.275			1.39523			0.697614	+	0.716474i	$0.254245\pi$
$614$	512.983	−	296.171i	0.835477	−	0.482363i
$615$	−226.900	−	355.589i	−0.368943	−	0.578194i
$616$	−248.382	−	236.485i	−0.403217	−	0.383905i
$617$	−187.827	+	325.326i	−0.304420	+	0.527271i	−0.977132	−	0.212634i	$-0.931796\pi$
$617$	−187.827	+	325.326i	−0.304420	+	0.527271i	0.672712	+	0.739904i	$0.265129\pi$
$618$	27.5142	+	619.810i	0.0445213	+	1.00293i
$619$	−750.475	+	433.287i	−1.21240	+	0.699979i	−0.963281	−	0.268494i	$-0.913474\pi$
$619$	−750.475	+	433.287i	−1.21240	+	0.699979i	−0.249118	+	0.968473i	$0.580141\pi$
$620$	10.2850			0.0165887
$621$	−279.404	+	678.735i	−0.449926	+	1.09297i
$622$		−	275.462i		−	0.442865i
$623$	−243.547	−	827.211i	−0.390927	−	1.32779i
$624$	−7.24225	−	163.146i	−0.0116062	−	0.261451i
$625$	380.834	−	659.624i	0.609335	−	1.05540i
$626$	116.257	+	67.1208i	0.185713	+	0.107222i
$627$	−1010.12	+	644.553i	−1.61104	+	1.02800i
$628$	−354.804	+	204.846i	−0.564974	+	0.326188i
$629$			536.907i			0.853588i
$630$	−187.702	−	476.777i	−0.297939	−	0.756789i
$631$	−1131.47			−1.79314			−0.896571	−	0.442900i	$-0.853950\pi$
$631$	−1131.47			−1.79314			−0.896571	+	0.442900i	$0.853950\pi$
$632$	−160.265	−	277.588i	−0.253584	−	0.439221i
$633$	196.784	−	378.692i	0.310875	−	0.598249i
$634$	109.468	−	189.604i	0.172663	−	0.299061i
$635$	−696.786	−	402.290i	−1.09730	−	0.633527i
$636$	218.752	−	420.968i	0.343950	−	0.661899i
$637$	666.032	−	32.7018i	1.04558	−	0.0513372i
$638$	−1116.80			−1.75047
$639$	377.353	−	33.5685i	0.590536	−	0.0525329i
$640$			65.0660i			0.101666i
$641$	205.779	+	356.420i	0.321028	+	0.556038i	0.980701	−	0.195516i	$-0.0626381\pi$
$641$	205.779	+	356.420i	0.321028	+	0.556038i	−0.659672	+	0.751554i	$0.729305\pi$
$642$	89.8209	+	140.764i	0.139908	+	0.219259i
$643$	984.048	+	568.140i	1.53040	+	0.883577i	0.999343	+	0.0362419i	$0.0115387\pi$
$643$	984.048	+	568.140i	1.53040	+	0.883577i	0.531058	+	0.847336i	$0.321795\pi$
$644$	275.637	+	262.436i	0.428008	+	0.407509i
$645$	−9.10160	−	205.031i	−0.0141110	−	0.317878i
$646$	171.104	+	296.361i	0.264867	+	0.458764i
$647$			52.9830i			0.0818902i	0.999161	+	0.0409451i	$0.0130369\pi$
$647$			52.9830i			0.0818902i	−0.999161	+	0.0409451i	$0.986963\pi$
$648$	−225.505	+	40.4409i	−0.348002	+	0.0624089i
$649$			750.357i			1.15617i
$650$	−134.588	+	77.7042i	−0.207058	+	0.119545i
$651$	18.4294	+	3.59994i	0.0283094	+	0.00552986i
$652$	200.360	−	347.034i	0.307300	−	0.532260i
$653$	−24.9889	+	43.2821i	−0.0382679	+	0.0662820i	−0.884525	−	0.466493i	$-0.845517\pi$
$653$	−24.9889	+	43.2821i	−0.0382679	+	0.0662820i	0.846257	+	0.532775i	$0.178851\pi$
$654$	193.950	+	303.951i	0.296560	+	0.464757i
$655$	−121.898	−	211.134i	−0.186105	−	0.322343i
$656$			97.7937i			0.149076i
$657$	87.5241	+	983.882i	0.133218	+	1.49754i
$658$	−160.897	−	38.9088i	−0.244524	−	0.0591319i
$659$	−226.144	−	391.692i	−0.343162	−	0.594374i	0.641856	−	0.766825i	$-0.278165\pi$
$659$	−226.144	−	391.692i	−0.343162	−	0.594374i	−0.985018	+	0.172451i	$0.944831\pi$
$660$	530.383	+	275.608i	0.803610	+	0.417589i
$661$	472.830	+	272.988i	0.715325	+	0.412993i	0.813030	−	0.582222i	$-0.197817\pi$
$661$	472.830	+	272.988i	0.715325	+	0.412993i	−0.0977046	+	0.995215i	$0.531150\pi$
$662$	123.327	−	213.609i	0.186294	−	0.322671i
$663$	−197.555	+	380.175i	−0.297971	+	0.573416i
$664$	234.318	−	135.284i	0.352889	−	0.203741i
$665$	−218.190	+	902.268i	−0.328106	+	1.35679i
$666$	374.286	+	532.881i	0.561991	+	0.800121i
$667$	1239.35			1.85810
$668$	41.1868	−	23.7792i	0.0616569	−	0.0355976i
$669$	287.597	−	183.514i	0.429890	−	0.274311i
$670$	−72.8694	−	42.0712i	−0.108760	−	0.0627928i
$671$	733.689	+	423.595i	1.09343	+	0.631290i
$672$	−22.7743	+	116.590i	−0.0338904	+	0.173498i
$673$	−208.424	−	361.001i	−0.309694	−	0.536406i	0.668601	−	0.743621i	$-0.266893\pi$
$673$	−208.424	−	361.001i	−0.309694	−	0.536406i	−0.978295	+	0.207215i	$0.933560\pi$
$674$	−115.488			−0.171347
$675$	133.102	+	172.678i	0.197187	+	0.255819i
$676$	−32.4024			−0.0479326
$677$	−423.242	+	244.359i	−0.625173	+	0.360944i	−0.778880	−	0.627173i	$-0.784212\pi$
$677$	−423.242	+	244.359i	−0.625173	+	0.360944i	0.153707	+	0.988116i	$0.450879\pi$
$678$	−217.088	+	9.63683i	−0.320189	+	0.0142136i
$679$	−116.581	+	122.446i	−0.171696	+	0.180333i
$680$	85.3515	−	147.833i	0.125517	−	0.217402i
$681$	380.346	−	242.697i	0.558511	−	0.356383i
$682$	−18.9699	+	10.9523i	−0.0278151	+	0.0160590i
$683$	−546.916			−0.800756			−0.400378	−	0.916350i	$-0.631121\pi$
$683$	−546.916			−0.800756			−0.400378	+	0.916350i	$0.631121\pi$
$684$	376.419	+	174.860i	0.550321	+	0.255643i
$685$			528.058i			0.770887i
$686$	−476.509	−	90.7577i	−0.694620	−	0.132300i
$687$	−95.3077	−	49.5258i	−0.138730	−	0.0720899i
$688$	−23.7907	+	41.2067i	−0.0345795	+	0.0598934i
$689$	−931.873	−	538.017i	−1.35250	−	0.780866i
$690$	−588.583	−	305.852i	−0.853019	−	0.443264i
$691$	575.708	−	332.385i	0.833152	−	0.481020i	−0.0217788	−	0.999763i	$-0.506933\pi$
$691$	575.708	−	332.385i	0.833152	−	0.481020i	0.854931	+	0.518742i	$0.173600\pi$
$692$		−	326.837i		−	0.472309i
$693$	853.913	+	679.501i	1.23220	+	0.980521i
$694$	687.286			0.990326
$695$	−143.431	−	248.430i	−0.206376	−	0.357453i
$696$	208.087	+	326.106i	0.298975	+	0.468543i
$697$	128.283	−	222.192i	0.184050	−	0.318783i
$698$	599.443	+	346.089i	0.858801	+	0.495829i
$699$	−1192.07	+	52.9174i	−1.70539	+	0.0757044i
$700$	108.446	−	31.9287i	0.154923	−	0.0456124i
$701$	125.029			0.178358			0.0891789	−	0.996016i	$-0.471576\pi$
$701$	125.029			0.178358			0.0891789	+	0.996016i	$0.471576\pi$
$702$	68.9528	+	515.043i	0.0982234	+	0.733679i
$703$		−	1179.73i		−	1.67813i
$704$	−69.2875	−	120.010i	−0.0984198	−	0.170468i
$705$	288.216	−	12.7943i	0.408818	−	0.0181479i
$706$	−210.134	−	121.321i	−0.297641	−	0.171843i
$707$	−117.508	+	123.419i	−0.166206	+	0.174567i
$708$	219.105	−	139.810i	0.309470	−	0.197471i
$709$	−212.052	−	367.285i	−0.299086	−	0.518033i	0.676841	−	0.736129i	$-0.263349\pi$
$709$	−212.052	−	367.285i	−0.299086	−	0.518033i	−0.975927	+	0.218097i	$0.930015\pi$
$710$			342.358i			0.482195i
$711$	586.221	+	834.618i	0.824502	+	1.17387i
$712$		−	348.429i		−	0.489367i
$713$	21.0515	−	12.1541i	0.0295253	−	0.0170464i
$714$	204.684	−	235.024i	0.286672	−	0.329166i
$715$	677.854	−	1174.08i	0.948048	−	1.64207i
$716$	−189.491	+	328.208i	−0.264652	+	0.458391i
$717$	235.534	−	453.264i	0.328500	−	0.632167i
$718$	−78.8828	−	136.629i	−0.109865	−	0.190291i
$719$			852.338i			1.18545i	0.805405	+	0.592724i	$0.201948\pi$
$719$			852.338i			1.18545i	−0.805405	+	0.592724i	$0.798052\pi$
$720$	−18.3453	−	206.224i	−0.0254796	−	0.286423i
$721$	−994.963	−	240.606i	−1.37998	−	0.333712i
$722$	−120.696	−	209.051i	−0.167169	−	0.289545i
$723$	−182.579	+	116.503i	−0.252530	+	0.161138i
$724$	280.802	+	162.121i	0.387848	+	0.223924i
$725$	184.066	−	318.811i	0.253884	−	0.439739i
$726$	−758.888	+	33.6880i	−1.04530	+	0.0464022i
$727$	−1127.09	+	650.723i	−1.55032	+	0.895080i	−0.552209	+	0.833705i	$0.686215\pi$
$727$	−1127.09	+	650.723i	−1.55032	+	0.895080i	−0.998115	+	0.0613747i	$0.980452\pi$
$728$	261.893	+	63.3321i	0.359743	+	0.0869947i
$729$	703.328	−	191.757i	0.964785	−	0.263041i
$730$	−892.640			−1.22280
$731$	108.107	−	62.4157i	0.147889	−	0.0853840i
$732$	−13.0139	−	293.163i	−0.0177786	−	0.400496i
$733$	989.572	+	571.330i	1.35003	+	0.779440i	0.988253	−	0.152825i	$-0.0488370\pi$
$733$	989.572	+	571.330i	1.35003	+	0.779440i	0.361777	+	0.932265i	$0.382170\pi$
$734$	710.337	+	410.113i	0.967761	+	0.558737i
$735$	841.722	−	78.8651i	1.14520	−	0.107299i
$736$	76.8907	+	133.179i	0.104471	+	0.180949i
$737$	179.203			0.243152
$738$	−27.5728	−	309.954i	−0.0373615	−	0.419991i
$739$	847.380			1.14666			0.573329	−	0.819325i	$-0.305652\pi$
$739$	847.380			1.14666			0.573329	+	0.819325i	$0.305652\pi$
$740$	−509.638	+	294.240i	−0.688700	+	0.397621i
$741$	434.079	−	835.345i	0.585802	−	1.12732i
$742$	566.889	+	539.738i	0.764002	+	0.727410i
$743$	−74.5649	+	129.150i	−0.100356	+	0.173823i	−0.911832	−	0.410565i	$-0.865332\pi$
$743$	−74.5649	+	129.150i	−0.100356	+	0.173823i	0.811475	+	0.584387i	$0.198665\pi$
$744$	6.73262	+	3.49854i	0.00904921	+	0.00470234i
$745$	352.129	−	203.302i	0.472656	−	0.272888i
$746$	452.069			0.605991
$747$	−704.520	+	494.843i	−0.943133	+	0.662440i
$748$			363.557i			0.486038i
$749$	−264.286	+	77.8111i	−0.352852	+	0.103887i
$750$	348.132	−	222.142i	0.464176	−	0.296189i
$751$	−89.4819	+	154.987i	−0.119150	+	0.206374i	−0.919431	−	0.393251i	$-0.871350\pi$
$751$	−89.4819	+	154.987i	−0.119150	+	0.206374i	0.800281	+	0.599625i	$0.204684\pi$
$752$	−57.9250	−	33.4430i	−0.0770280	−	0.0444721i
$753$	29.3916	+	662.103i	0.0390327	+	0.879287i
$754$	759.858	−	438.705i	1.00777	−	0.581836i
$755$		−	662.271i		−	0.877180i
$756$	39.3099	−	375.950i	0.0519972	−	0.497289i
$757$	549.096			0.725358			0.362679	−	0.931914i	$-0.381862\pi$
$757$	549.096			0.725358			0.362679	+	0.931914i	$0.381862\pi$
$758$	74.8663	+	129.672i	0.0987682	+	0.171071i
$759$	1411.29	−	62.6492i	1.85941	−	0.0825418i
$760$	−187.540	+	324.828i	−0.246763	+	0.427406i
$761$	1100.15	+	635.174i	1.44567	+	0.834657i	0.998219	−	0.0596526i	$-0.0189993\pi$
$761$	1100.15	+	635.174i	1.44567	+	0.834657i	0.447449	+	0.894309i	$0.352333\pi$
$762$	−319.278	−	500.361i	−0.419000	−	0.656641i
$763$	−570.673	+	168.017i	−0.747933	+	0.220206i
$764$	−195.506			−0.255898
$765$	−228.837	+	492.617i	−0.299134	+	0.643943i
$766$			181.905i			0.237474i
$767$	−294.758	−	510.535i	−0.384299	−	0.665626i
$768$	−22.1329	+	42.5927i	−0.0288189	+	0.0554592i
$769$	−683.143	−	394.413i	−0.888353	−	0.512891i	−0.0149496	−	0.999888i	$-0.504759\pi$
$769$	−683.143	−	394.413i	−0.888353	−	0.512891i	−0.873403	+	0.486997i	$0.838092\pi$
$770$	−680.023	+	714.231i	−0.883147	+	0.927572i
$771$	−945.002	−	491.062i	−1.22568	−	0.636915i
$772$	346.951	+	600.937i	0.449418	+	0.778416i
$773$			98.1910i			0.127026i	0.997981	+	0.0635130i	$0.0202304\pi$
$773$			98.1910i			0.127026i	−0.997981	+	0.0635130i	$0.979770\pi$
$774$	63.7856	−	137.311i	0.0824103	−	0.177404i
$775$		−	7.22040i		−	0.00931665i
$776$	−59.1617	+	34.1570i	−0.0762393	+	0.0440168i
$777$	−1016.20	+	348.859i	−1.30785	+	0.448982i
$778$	−106.146	+	183.850i	−0.136434	+	0.236311i
$779$	−281.871	+	488.214i	−0.361837	+	0.626719i
$780$	−469.132	+	20.8254i	−0.601451	+	0.0266992i
$781$	−364.571	−	631.455i	−0.466800	−	0.808521i
$782$		−	403.451i		−	0.515922i
$783$	−751.469	−	974.911i	−0.959730	−	1.24510i
$784$	−174.343	−	89.5579i	−0.222376	−	0.114232i
$785$	589.043	+	1020.25i	0.750373	+	1.29968i
$786$	−7.97601	−	179.675i	−0.0101476	−	0.228594i
$787$	−457.230	−	263.982i	−0.580978	−	0.335428i	0.180544	−	0.983567i	$-0.442214\pi$
$787$	−457.230	−	263.982i	−0.580978	−	0.335428i	−0.761522	+	0.648139i	$0.775548\pi$
$788$	−15.5388	+	26.9139i	−0.0197192	+	0.0341547i
$789$	−346.612	−	543.198i	−0.439305	−	0.688463i
$790$	−798.215	+	460.849i	−1.01040	+	0.583354i
$791$	84.2723	−	348.485i	0.106539	−	0.440563i
$792$	253.441	+	360.830i	0.320001	+	0.455594i
$793$	−665.592			−0.839334
$794$	−374.075	+	215.972i	−0.471127	+	0.272005i
$795$	−1210.51	−	629.030i	−1.52265	−	0.791233i
$796$	−495.976	−	286.352i	−0.623086	−	0.359739i
$797$	−455.600	−	263.041i	−0.571643	−	0.330038i	0.186162	−	0.982519i	$-0.440395\pi$
$797$	−455.600	−	263.041i	−0.571643	−	0.330038i	−0.757805	+	0.652481i	$0.773728\pi$
$798$	−449.745	+	516.411i	−0.563590	+	0.647131i
$799$	87.7390	+	151.968i	0.109811	+	0.190198i
$800$	45.6786			0.0570982
$801$	98.2393	+	1104.33i	0.122646	+	1.37870i
$802$	371.254			0.462910
$803$	1646.41	−	950.555i	2.05032	−	1.18375i
$804$	−33.3899	−	52.3274i	−0.0415297	−	0.0650838i
$805$	754.644	−	792.606i	0.937446	−	0.984604i
$806$	8.60460	−	14.9036i	0.0106757	−	0.0184908i
$807$	−13.1931	−	297.199i	−0.0163483	−	0.368277i
$808$	−59.6319	+	34.4285i	−0.0738018	+	0.0426095i
$809$	87.2827			0.107890			0.0539448	−	0.998544i	$-0.482820\pi$
$809$	87.2827			0.107890			0.0539448	+	0.998544i	$0.482820\pi$
$810$	116.290	+	648.449i	0.143567	+	0.800554i
$811$			455.489i			0.561639i	0.959761	+	0.280819i	$0.0906062\pi$
$811$			455.489i			0.561639i	−0.959761	+	0.280819i	$0.909394\pi$
$812$	−612.268	+	180.264i	−0.754025	+	0.222000i
$813$	64.8025	+	1459.80i	0.0797079	+	1.79557i
$814$	626.660	−	1085.41i	0.769853	−	1.33342i
$815$	−997.909	−	576.143i	−1.22443	−	0.706924i
$816$	106.159	−	67.7394i	0.130096	−	0.0830140i
$817$	−237.540	+	137.144i	−0.290747	+	0.167863i
$818$		−	498.928i		−	0.609937i
$819$	−847.917	−	126.889i	−1.03531	−	0.154931i
$820$	281.210			0.342938
$821$	578.892	+	1002.67i	0.705106	+	1.22128i	0.966653	+	0.256089i	$0.0824339\pi$
$821$	578.892	+	1002.67i	0.705106	+	1.22128i	−0.261547	+	0.965191i	$0.584233\pi$
$822$	−179.624	+	345.670i	−0.218521	+	0.420523i
$823$	−288.372	+	499.474i	−0.350391	+	0.606895i	−0.986318	−	0.164855i	$-0.947285\pi$
$823$	−288.372	+	499.474i	−0.350391	+	0.606895i	0.635927	+	0.771749i	$0.280618\pi$
$824$	−358.200	−	206.807i	−0.434709	−	0.250979i
$825$	193.486	−	372.347i	0.234529	−	0.451329i
$826$	121.116	+	411.372i	0.146630	+	0.498029i
$827$	1015.60			1.22805			0.614026	−	0.789286i	$-0.289549\pi$
$827$	1015.60			1.22805			0.614026	+	0.789286i	$0.289549\pi$
$828$	−281.252	−	400.426i	−0.339676	−	0.483606i
$829$		−	1345.23i		−	1.62271i	−0.584554	−	0.811355i	$-0.698730\pi$
$829$		−	1345.23i		−	1.62271i	0.584554	−	0.811355i	$-0.301270\pi$
$830$	−389.014	−	673.791i	−0.468691	−	0.811797i
$831$	−522.243	−	818.440i	−0.628451	−	0.984885i
$832$	94.2850	+	54.4355i	0.113323	+	0.0654272i
$833$	278.636	+	432.177i	0.334497	+	0.518820i
$834$	−9.38492	−	211.414i	−0.0112529	−	0.253493i
$835$	−68.3781	−	118.434i	−0.0818899	−	0.141838i
$836$		−	798.830i		−	0.955538i
$837$	−22.3252	−	9.19025i	−0.0266729	−	0.0109800i
$838$		−	987.023i		−	1.17783i
$839$	1030.38	−	594.890i	1.22810	−	0.709047i	0.261472	−	0.965211i	$-0.415792\pi$
$839$	1030.38	−	594.890i	1.22810	−	0.709047i	0.966633	+	0.256165i	$0.0824589\pi$
$840$	335.260	+	65.4885i	0.399119	+	0.0779625i
$841$	−618.703	+	1071.62i	−0.735675	+	1.27423i
$842$	21.5835	−	37.3838i	0.0256336	−	0.0443988i
$843$	335.540	+	525.846i	0.398031	+	0.623779i
$844$	142.256	+	246.395i	0.168550	+	0.291937i
$845$			93.1745i			0.110266i
$846$	193.021	+	89.6646i	0.228157	+	0.105987i
$847$	294.595	−	1218.22i	0.347810	−	1.43828i
$848$	158.137	+	273.902i	0.186483	+	0.322997i
$849$	−723.996	−	376.218i	−0.852764	−	0.443131i
$850$	−103.784	−	59.9197i	−0.122099	−	0.0704937i
$851$	−695.426	+	1204.51i	−0.817187	+	1.41541i
$852$	−116.457	+	224.110i	−0.136686	+	0.263040i
$853$	−1394.66	+	805.206i	−1.63500	+	0.943969i	−0.652485	+	0.757802i	$0.726273\pi$
$853$	−1394.66	+	805.206i	−1.63500	+	0.943969i	−0.982518	+	0.186168i	$0.940393\pi$
$854$	470.606	+	113.804i	0.551061	+	0.133260i
$855$	502.816	−	1082.41i	0.588089	−	1.26598i
$856$	−111.320			−0.130047
$857$	−637.918	+	368.302i	−0.744361	+	0.429757i	−0.823653	−	0.567094i	$-0.808068\pi$
$857$	−637.918	+	368.302i	−0.744361	+	0.429757i	0.0792915	+	0.996851i	$0.474734\pi$
$858$	843.103	−	537.980i	0.982638	−	0.627017i
$859$	−449.010	−	259.236i	−0.522712	−	0.301788i	0.215331	−	0.976541i	$-0.430917\pi$
$859$	−449.010	−	259.236i	−0.522712	−	0.301788i	−0.738044	+	0.674753i	$0.764250\pi$
$860$	118.491	+	68.4111i	0.137781	+	0.0795477i
$861$	503.893	+	98.4287i	0.585242	+	0.114319i
$862$	151.835	+	262.985i	0.176142	+	0.305087i
$863$	319.670			0.370417			0.185209	−	0.982699i	$-0.440704\pi$
$863$	319.670			0.370417			0.185209	+	0.982699i	$0.440704\pi$
$864$	58.1405	−	141.236i	0.0672922	−	0.163468i
$865$	−939.834			−1.08651
$866$	−61.2187	+	35.3447i	−0.0706914	+	0.0408137i
$867$	536.091	−	23.7978i	0.618329	−	0.0274484i
$868$	−8.63213	+	9.06636i	−0.00994485	+	0.0104451i
$869$	981.499	−	1700.01i	1.12946	−	1.95628i
$870$	937.731	−	598.362i	1.07785	−	0.687772i
$871$	−121.928	+	70.3951i	−0.139986	+	0.0808210i
$872$	−240.373			−0.275657
$873$	177.880	−	124.940i	0.203757	−	0.143116i
$874$			886.488i			1.01429i
$875$	192.439	+	653.623i	0.219931	+	0.746997i
$876$	−584.328	−	303.641i	−0.667042	−	0.346622i
$877$	120.744	−	209.135i	0.137679	−	0.238467i	−0.788939	−	0.614472i	$-0.789369\pi$
$877$	120.744	−	209.135i	0.137679	−	0.238467i	0.926618	+	0.376005i	$0.122703\pi$
$878$	−247.422	−	142.849i	−0.281801	−	0.162698i
$879$	735.245	+	382.063i	0.836456	+	0.434657i
$880$	−345.092	+	199.239i	−0.392150	+	0.226408i
$881$		−	1263.93i		−	1.43466i	−0.696735	−	0.717328i	$-0.745365\pi$
$881$		−	1263.93i		−	1.43466i	0.696735	−	0.717328i	$-0.254635\pi$
$882$	577.824	+	234.695i	0.655129	+	0.266094i
$883$	84.6550			0.0958720			0.0479360	−	0.998850i	$-0.484736\pi$
$883$	84.6550			0.0958720			0.0479360	+	0.998850i	$0.484736\pi$
$884$	−142.813	−	247.360i	−0.161554	−	0.279819i
$885$	−402.028	−	630.044i	−0.454269	−	0.711914i
$886$	−580.948	+	1006.23i	−0.655697	+	1.13570i
$887$	−322.314	−	186.088i	−0.363375	−	0.209795i	0.307185	−	0.951650i	$-0.400613\pi$
$887$	−322.314	−	186.088i	−0.363375	−	0.209795i	−0.670560	+	0.741855i	$0.733946\pi$
$888$	−433.701	+	19.2526i	−0.488402	+	0.0216808i
$889$	939.434	−	276.588i	1.05673	−	0.311122i
$890$	−1001.92			−1.12576
$891$	−905.008	−	1072.18i	−1.01572	−	1.20335i
$892$			227.439i			0.254977i
$893$	−192.786	−	333.915i	−0.215885	−	0.373925i
$894$	299.661	−	13.3024i	0.335192	−	0.0148796i
$895$	943.775	+	544.889i	1.05450	+	0.608814i
$896$	−57.3567	−	54.6096i	−0.0640142	−	0.0609482i
$897$	−935.620	+	597.015i	−1.04305	+	0.665568i
$898$	229.777	+	397.986i	0.255877	+	0.443192i
$899$			40.7652i			0.0453450i
$900$	−144.777	+	12.8790i	−0.160863	+	0.0143100i
$901$		−	829.757i		−	0.920929i
$902$	−518.670	+	299.455i	−0.575023	+	0.331990i
$903$	188.377	+	164.059i	0.208613	+	0.181682i
$904$	72.4340	−	125.459i	0.0801261	−	0.138783i
$905$	466.186	−	807.458i	0.515123	−	0.892219i
$906$	225.278	−	433.527i	0.248652	−	0.478506i
$907$	−680.264	−	1178.25i	−0.750015	−	1.29906i	−0.947815	−	0.318822i	$-0.896713\pi$
$907$	−680.264	−	1178.25i	−0.750015	−	1.29906i	0.197799	−	0.980243i	$-0.436621\pi$
$908$			300.788i			0.331264i
$909$	179.294	−	125.933i	0.197243	−	0.138540i
$910$	182.114	−	753.083i	0.200125	−	0.827564i
$911$	−23.2739	−	40.3116i	−0.0255477	−	0.0442498i	0.852969	−	0.521962i	$-0.174800\pi$
$911$	−23.2739	−	40.3116i	−0.0255477	−	0.0442498i	−0.878517	+	0.477712i	$0.841466\pi$
$912$	−233.259	+	148.841i	−0.255766	+	0.163203i
$913$	1435.01	+	828.506i	1.57176	+	0.907454i
$914$	−524.343	+	908.188i	−0.573679	+	0.993641i
$915$	−843.003	+	37.4220i	−0.921315	+	0.0408984i
$916$	62.0117	−	35.8025i	0.0676984	−	0.0390857i
$917$	288.427	+	69.7487i	0.314533	+	0.0760618i
$918$	−317.367	+	244.629i	−0.345716	+	0.266480i
$919$	−326.576			−0.355360			−0.177680	−	0.984088i	$-0.556859\pi$
$919$	−326.576			−0.355360			−0.177680	+	0.984088i	$0.556859\pi$
$920$	382.960	−	221.102i	0.416261	−	0.240329i
$921$	−55.7249	−	1255.31i	−0.0605048	−	1.36299i
$922$	810.848	+	468.143i	0.879445	+	0.507748i
$923$	496.100	+	286.423i	0.537486	+	0.310318i
$924$	−688.101	+	236.223i	−0.744698	+	0.255653i
$925$	206.566	+	357.783i	0.223315	+	0.386793i
$926$	−915.492			−0.988653
$927$	1193.61	+	554.473i	1.28761	+	0.598137i
$928$	−257.893			−0.277902
$929$	508.153	−	293.382i	0.546989	−	0.315804i	−0.200918	−	0.979608i	$-0.564392\pi$
$929$	508.153	−	293.382i	0.546989	−	0.315804i	0.747907	+	0.663804i	$0.231059\pi$
$930$	10.0602	−	19.3599i	0.0108174	−	0.0208171i
$931$	−612.236	−	949.607i	−0.657612	−	1.01999i
$932$	397.747	−	688.917i	0.426767	−	0.739182i
$933$	−518.515	−	269.442i	−0.555751	−	0.288791i
$934$	−21.5345	+	12.4329i	−0.0230562	+	0.0133115i
$935$	1045.42			1.11810
$936$	−314.181	−	145.948i	−0.335663	−	0.155927i
$937$			858.055i			0.915747i	0.889017	+	0.457873i	$0.151389\pi$
$937$			858.055i			0.915747i	−0.889017	+	0.457873i	$0.848611\pi$
$938$	98.2454	−	28.9254i	0.104739	−	0.0308373i
$939$	240.060	−	153.182i	0.255655	−	0.163133i
$940$	−96.1668	+	166.566i	−0.102305	+	0.177198i
$941$	−293.858	−	169.659i	−0.312283	−	0.180296i	0.335665	−	0.941981i	$-0.391039\pi$
$941$	−293.858	−	169.659i	−0.312283	−	0.180296i	−0.647947	+	0.761685i	$0.724372\pi$
$942$	38.5420	+	868.233i	0.0409151	+	0.921691i
$943$	575.586	−	332.315i	0.610378	−	0.352402i
$944$			173.274i			0.183553i
$945$	−1081.06	−	113.037i	−1.14398	−	0.119616i
$946$	−291.398			−0.308032
$947$	145.781	+	252.501i	0.153940	+	0.266632i	0.932673	−	0.360724i	$-0.117470\pi$
$947$	145.781	+	252.501i	0.153940	+	0.266632i	−0.778732	+	0.627356i	$0.784137\pi$
$948$	−679.280	+	30.1541i	−0.716540	+	0.0318081i
$949$	−746.800	+	1293.50i	−0.786933	+	1.36301i
$950$	228.041	+	131.659i	0.240043	+	0.138589i
$951$	−249.826	−	391.518i	−0.262698	−	0.411691i
$952$	58.6821	+	199.314i	0.0616408	+	0.209364i
$953$	1099.85			1.15409			0.577046	−	0.816712i	$-0.304205\pi$
$953$	1099.85			1.15409			0.577046	+	0.816712i	$0.304205\pi$
$954$	−578.436	−	823.535i	−0.606327	−	0.863244i
$955$			562.186i			0.588676i
$956$	170.269	+	294.915i	0.178106	+	0.308489i
$957$	−1092.39	+	2102.21i	−1.14148	+	2.19666i
$958$	847.268	+	489.171i	0.884414	+	0.510616i
$959$	−465.491	−	443.196i	−0.485392	−	0.462144i
$960$	122.477	+	63.6440i	0.127580	+	0.0662958i
$961$	−480.100	−	831.558i	−0.499584	−	0.865305i
$962$			984.666i			1.02356i
$963$	352.825	−	31.3865i	0.366381	−	0.0325925i
$964$		−	144.388i		−	0.149780i
$965$	1728.02	−	997.671i	1.79069	−	1.03386i
$966$	763.609	−	262.145i	0.790485	−	0.271372i
$967$	−206.206	+	357.160i	−0.213243	+	0.369348i	−0.952728	−	0.303825i	$-0.901736\pi$
$967$	−206.206	+	357.160i	−0.213243	+	0.369348i	0.739484	+	0.673174i	$0.235069\pi$
$968$	253.212	−	438.575i	0.261582	−	0.453074i
$969$	725.220	−	32.1935i	0.748421	−	0.0332234i
$970$	98.2198	+	170.122i	0.101258	+	0.175383i
$971$			1193.06i			1.22869i	0.789038	+	0.614344i	$0.210579\pi$
$971$			1193.06i			1.22869i	−0.789038	+	0.614344i	$0.789421\pi$
$972$	−144.453	+	464.036i	−0.148614	+	0.477403i
$973$	339.376	+	82.0694i	0.348793	+	0.0843468i
$974$	553.574	+	958.818i	0.568351	+	0.984412i
$975$	14.6201	+	329.346i	0.0149950	+	0.337791i
$976$	169.425	+	97.8174i	0.173591	+	0.100223i
$977$	962.075	−	1666.36i	0.984723	−	1.70559i	0.341564	−	0.939858i	$-0.389043\pi$
$977$	962.075	−	1666.36i	0.984723	−	1.70559i	0.643159	−	0.765733i	$-0.277623\pi$
$978$	−457.257	−	716.596i	−0.467543	−	0.732716i
$979$	1847.97	−	1066.93i	1.88761	−	1.08981i
$980$	−257.527	+	501.329i	−0.262783	+	0.511560i
$981$	761.853	−	67.7729i	0.776609	−	0.0690855i
$982$	−480.689			−0.489500
$983$	−1122.96	+	648.340i	−1.14238	+	0.659552i	−0.947018	−	0.321180i	$-0.895921\pi$
$983$	−1122.96	+	648.340i	−1.14238	+	0.659552i	−0.195359	+	0.980732i	$0.562587\pi$
$984$	184.082	+	95.6564i	0.187075	+	0.0972118i
$985$	77.3920	+	44.6823i	0.0785706	+	0.0453627i
$986$	585.946	+	338.296i	0.594266	+	0.343100i
$987$	−230.620	+	264.805i	−0.233658	+	0.268293i
$988$	313.799	+	543.515i	0.317610	+	0.550117i
$989$	323.375			0.326971
$990$	1037.58	−	728.779i	1.04806	−	0.736141i
$991$	232.207			0.234315			0.117158	−	0.993113i	$-0.462622\pi$
$991$	232.207			0.234315			0.117158	+	0.993113i	$0.462622\pi$
$992$	−4.38056	+	2.52912i	−0.00441589	+	0.00254951i
$993$	−281.454	−	441.084i	−0.283438	−	0.444194i
$994$	−301.794	−	287.340i	−0.303616	−	0.289074i
$995$	−823.416	+	1426.20i	−0.827554	+	1.43337i
$996$	−25.4538	−	573.395i	−0.0255560	−	0.575698i
$997$	−1177.97	+	680.103i	−1.18152	+	0.682149i	−0.956365	−	0.292174i	$-0.905621\pi$
$997$	−1177.97	+	680.103i	−1.18152	+	0.682149i	−0.225152	+	0.974324i	$0.572288\pi$
$998$	307.902			0.308519
$999$	1369.17	−	183.302i	1.37054	−	0.183485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.o.a.13.16	yes	32
3.2	odd	2		378.3.o.a.307.2		32
7.6	odd	2	inner	126.3.o.a.13.9	✓	32
9.2	odd	6		378.3.o.a.181.7		32
9.4	even	3		1134.3.c.e.811.2		16
9.5	odd	6		1134.3.c.d.811.15		16
9.7	even	3	inner	126.3.o.a.97.9	yes	32
21.20	even	2		378.3.o.a.307.7		32
63.13	odd	6		1134.3.c.e.811.7		16
63.20	even	6		378.3.o.a.181.2		32
63.34	odd	6	inner	126.3.o.a.97.16	yes	32
63.41	even	6		1134.3.c.d.811.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.o.a.13.9	✓	32	7.6	odd	2	inner
126.3.o.a.13.16	yes	32	1.1	even	1	trivial
126.3.o.a.97.9	yes	32	9.7	even	3	inner
126.3.o.a.97.16	yes	32	63.34	odd	6	inner
378.3.o.a.181.2		32	63.20	even	6
378.3.o.a.181.7		32	9.2	odd	6
378.3.o.a.307.2		32	3.2	odd	2
378.3.o.a.307.7		32	21.20	even	2
1134.3.c.d.811.10		16	63.41	even	6
1134.3.c.d.811.15		16	9.5	odd	6
1134.3.c.e.811.2		16	9.4	even	3
1134.3.c.e.811.7		16	63.13	odd	6

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(2.99705 - 0.133043i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(4.98058 + 2.87554i) q^{5} +(2.28218 + 3.57654i) q^{6} +(-6.71501 + 1.97703i) q^{7} -2.82843 q^{8} +(8.96460 - 0.797472i) q^{9} +8.13325i q^{10} +(-8.66094 - 15.0012i) q^{11} +(-2.76661 + 5.32408i) q^{12} +(11.7856 + 6.80443i) q^{13} +(-7.16959 - 6.82620i) q^{14} +(15.3096 + 7.95550i) q^{15} +(-2.00000 - 3.46410i) q^{16} +10.4941i q^{17} +(7.31563 + 10.4154i) q^{18} -23.0584i q^{19} +(-9.96116 + 5.75108i) q^{20} +(-19.8622 + 6.81864i) q^{21} +(12.2484 - 21.2149i) q^{22} +(-13.5925 + 23.5429i) q^{23} +(-8.47693 + 0.376302i) q^{24} +(4.03745 + 6.99307i) q^{25} +19.2458i q^{26} +(26.7612 - 3.58274i) q^{27} +(3.29069 - 13.6078i) q^{28} +(-22.7948 - 39.4817i) q^{29} +(1.08207 + 24.3758i) q^{30} +(-0.774381 - 0.447089i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-27.9531 - 43.8070i) q^{33} +(-12.8526 + 7.42048i) q^{34} +(-39.1297 - 9.46251i) q^{35} +(-7.58334 + 16.3246i) q^{36} +51.1625 q^{37} +(28.2407 - 16.3048i) q^{38} +(36.2274 + 18.8252i) q^{39} +(-14.0872 - 8.13325i) q^{40} +(-21.1730 - 12.2242i) q^{41} +(-22.3958 - 19.5046i) q^{42} +(-5.94767 - 10.3017i) q^{43} +34.6438 q^{44} +(46.9421 + 21.8062i) q^{45} -38.4454 q^{46} +(14.4813 - 8.36076i) q^{47} +(-6.45497 - 10.1160i) q^{48} +(41.1827 - 26.5516i) q^{49} +(-5.70982 + 9.88970i) q^{50} +(1.39617 + 31.4515i) q^{51} +(-23.5712 + 13.6089i) q^{52} -79.0686 q^{53} +(23.3110 + 30.2423i) q^{54} -99.6195i q^{55} +(18.9929 - 5.59189i) q^{56} +(-3.06776 - 69.1071i) q^{57} +(32.2367 - 55.8355i) q^{58} +(-37.5149 - 21.6592i) q^{59} +(-29.0889 + 18.5615i) q^{60} +(-42.3562 + 24.4543i) q^{61} -1.26456i q^{62} +(-58.6207 + 23.0783i) q^{63} +8.00000 q^{64} +(39.1328 + 67.7800i) q^{65} +(33.8866 - 65.2116i) q^{66} +(-5.17274 + 8.95945i) q^{67} +(-18.1764 - 10.4941i) q^{68} +(-37.6051 + 72.3675i) q^{69} +(-16.0797 - 54.6149i) q^{70} +42.0936 q^{71} +(-25.3557 + 2.25559i) q^{72} +109.752i q^{73} +(36.1774 + 62.6610i) q^{74} +(13.0308 + 20.4214i) q^{75} +(39.9383 + 23.0584i) q^{76} +(87.8161 + 83.6102i) q^{77} +(2.56052 + 57.6807i) q^{78} +(56.6624 + 98.1421i) q^{79} -23.0043i q^{80} +(79.7281 - 14.2980i) q^{81} -34.5753i q^{82} +(-82.8440 + 47.8300i) q^{83} +(8.05195 - 41.2209i) q^{84} +(-30.1763 + 52.2669i) q^{85} +(8.41128 - 14.5688i) q^{86} +(-73.5698 - 115.296i) q^{87} +(24.4968 + 42.4298i) q^{88} +123.188i q^{89} +(6.48604 + 72.9114i) q^{90} +(-92.5931 - 22.3913i) q^{91} +(-27.1850 - 47.0858i) q^{92} +(-2.38034 - 1.23692i) q^{93} +(20.4796 + 11.8239i) q^{94} +(66.3053 - 114.844i) q^{95} +(7.82516 - 15.0588i) q^{96} +(20.9168 - 12.0763i) q^{97} +(61.6395 + 31.6635i) q^{98} +(-89.6049 - 127.573i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} - 2 q^{7} + 24 q^{9} - 12 q^{11} - 12 q^{14} + 48 q^{15} - 64 q^{16} - 54 q^{21} + 12 q^{23} + 80 q^{25} + 8 q^{28} - 48 q^{29} - 168 q^{30} + 348 q^{35} - 72 q^{36} - 88 q^{37} + 252 q^{39}+ \cdots - 684 q^{99}+O(q^{100}) \) 32 * q - 32 * q^4 - 2 * q^7 + 24 * q^9 - 12 * q^11 - 12 * q^14 + 48 * q^15 - 64 * q^16 - 54 * q^21 + 12 * q^23 + 80 * q^25 + 8 * q^28 - 48 * q^29 - 168 * q^30 + 348 * q^35 - 72 * q^36 - 88 * q^37 + 252 * q^39 + 32 * q^43 + 48 * q^44 + 48 * q^46 + 50 * q^49 + 48 * q^50 - 372 * q^51 - 864 * q^53 - 24 * q^56 + 372 * q^57 + 48 * q^58 - 24 * q^60 - 114 * q^63 + 256 * q^64 + 120 * q^65 - 140 * q^67 - 108 * q^70 + 552 * q^71 + 96 * q^72 + 144 * q^74 - 258 * q^77 + 288 * q^78 - 176 * q^79 - 360 * q^81 - 60 * q^85 + 96 * q^86 + 372 * q^91 + 24 * q^92 - 456 * q^93 + 528 * q^95 + 624 * q^98 - 684 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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