LMFDB - Embedded newform 110.4.k.a.7.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,4,Mod(7,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 14])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.7"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	110.k (of order $20$, degree $8$, 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:	$6.49021010063$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.17
Character	$\chi$	$=$	110.7
Dual form			110.4.k.a.63.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.97538 - 0.312869i) q^{2} +(3.05899 + 6.00362i) q^{3} +(3.80423 - 1.23607i) q^{4} +(10.3687 + 4.18211i) q^{5} +(7.92101 + 10.9023i) q^{6} +(-6.69380 - 3.41066i) q^{7} +(7.12805 - 3.63192i) q^{8} +(-10.8157 + 14.8866i) q^{9} +(21.7905 + 5.01720i) q^{10} +(-10.0463 + 35.0724i) q^{11} +(19.0580 + 19.0580i) q^{12} +(-13.2463 - 83.6339i) q^{13} +(-14.2899 - 4.64306i) q^{14} +(6.61002 + 75.0427i) q^{15} +(12.9443 - 9.40456i) q^{16} +(-17.8428 + 112.655i) q^{17} +(-16.7076 + 32.7906i) q^{18} +(17.8986 - 55.0863i) q^{19} +(44.6143 + 3.09328i) q^{20} -50.6202i q^{21} +(-8.87209 + 72.4243i) q^{22} +(4.14181 - 4.14181i) q^{23} +(43.6094 + 31.6840i) q^{24} +(90.0199 + 86.7261i) q^{25} +(-52.3329 - 161.064i) q^{26} +(57.2279 + 9.06400i) q^{27} +(-29.6806 - 4.70094i) q^{28} +(-84.3925 - 259.733i) q^{29} +(36.5358 + 146.170i) q^{30} +(-42.6332 - 30.9749i) q^{31} +(22.6274 - 22.6274i) q^{32} +(-241.293 + 46.9724i) q^{33} +228.119i q^{34} +(-55.1423 - 63.3584i) q^{35} +(-22.7447 + 70.0010i) q^{36} +(118.837 - 233.230i) q^{37} +(18.1217 - 114.416i) q^{38} +(461.586 - 335.362i) q^{39} +(89.0977 - 7.84803i) q^{40} +(98.2775 + 31.9323i) q^{41} +(-15.8375 - 99.9940i) q^{42} +(-14.0489 - 14.0489i) q^{43} +(5.13362 + 145.841i) q^{44} +(-174.403 + 109.122i) q^{45} +(6.88580 - 9.47749i) q^{46} +(-511.548 + 260.647i) q^{47} +(96.0578 + 48.9439i) q^{48} +(-168.436 - 231.832i) q^{49} +(204.957 + 143.152i) q^{50} +(-730.919 + 237.490i) q^{51} +(-153.769 - 301.789i) q^{52} +(-29.5620 + 4.68216i) q^{53} +115.882 q^{54} +(-250.843 + 321.641i) q^{55} -60.1011 q^{56} +(385.469 - 61.0523i) q^{57} +(-247.970 - 486.668i) q^{58} +(14.7271 - 4.78513i) q^{59} +(117.904 + 277.309i) q^{60} +(-240.012 - 330.347i) q^{61} +(-93.9078 - 47.8484i) q^{62} +(123.172 - 62.7591i) q^{63} +(37.6183 - 51.7771i) q^{64} +(212.419 - 922.573i) q^{65} +(-461.948 + 168.281i) q^{66} +(459.956 + 459.956i) q^{67} +(71.3712 + 450.620i) q^{68} +(37.5357 + 12.1961i) q^{69} +(-128.750 - 107.904i) q^{70} +(58.0796 - 42.1973i) q^{71} +(-23.0282 + 145.394i) q^{72} +(160.356 - 314.716i) q^{73} +(161.777 - 497.898i) q^{74} +(-245.300 + 805.740i) q^{75} -231.685i q^{76} +(186.868 - 200.503i) q^{77} +(806.881 - 806.881i) q^{78} +(-407.935 - 296.382i) q^{79} +(173.546 - 43.3787i) q^{80} +(274.170 + 843.807i) q^{81} +(204.126 + 32.3303i) q^{82} +(831.952 + 131.768i) q^{83} +(-62.5700 - 192.571i) q^{84} +(-656.143 + 1093.47i) q^{85} +(-32.1474 - 23.3565i) q^{86} +(1301.18 - 1301.18i) q^{87} +(55.7700 + 286.485i) q^{88} +642.498i q^{89} +(-310.370 + 270.122i) q^{90} +(-196.579 + 605.008i) q^{91} +(10.6368 - 20.8760i) q^{92} +(55.5463 - 350.705i) q^{93} +(-928.952 + 674.923i) q^{94} +(415.963 - 496.319i) q^{95} +(205.063 + 66.6292i) q^{96} +(54.0877 + 341.497i) q^{97} +(-405.258 - 405.258i) q^{98} +(-413.451 - 528.889i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{3} + 32 q^{5} - 40 q^{7} - 44 q^{11} + 128 q^{12} - 256 q^{15} + 576 q^{16} - 640 q^{17} - 64 q^{20} + 312 q^{22} - 984 q^{23} - 520 q^{25} + 304 q^{26} - 364 q^{27} + 240 q^{28} - 432 q^{31}+ \cdots + 7044 q^{97}+O(q^{100}) $ 144 * q + 8 * q^3 + 32 * q^5 - 40 * q^7 - 44 * q^11 + 128 * q^12 - 256 * q^15 + 576 * q^16 - 640 * q^17 - 64 * q^20 + 312 * q^22 - 984 * q^23 - 520 * q^25 + 304 * q^26 - 364 * q^27 + 240 * q^28 - 432 * q^31 + 2368 * q^33 + 1808 * q^36 - 960 * q^37 + 72 * q^38 + 740 * q^41 + 2440 * q^42 + 2656 * q^45 + 720 * q^46 - 1980 * q^47 - 128 * q^48 - 1360 * q^50 - 3880 * q^51 - 1920 * q^52 - 3060 * q^53 - 3044 * q^55 - 64 * q^56 - 4400 * q^57 - 2016 * q^58 - 1120 * q^60 - 960 * q^61 + 80 * q^62 + 1800 * q^63 + 1552 * q^66 + 10160 * q^67 + 2560 * q^68 + 2304 * q^70 + 1312 * q^71 - 2460 * q^73 + 8644 * q^75 - 1272 * q^77 - 5312 * q^78 + 768 * q^80 + 2116 * q^81 + 1280 * q^82 + 320 * q^85 - 5488 * q^86 + 1248 * q^88 - 8480 * q^90 + 11796 * q^91 - 704 * q^92 + 688 * q^93 - 1280 * q^95 + 7044 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	1.97538	−	0.312869i	0.698401	−	0.110616i
$2$	1.97538	−	0.312869i	0.698401	−	0.110616i
$3$	3.05899	+	6.00362i	0.588704	+	1.15540i	0.972701	+	0.232062i	$0.0745472\pi$
$3$	3.05899	+	6.00362i	0.588704	+	1.15540i	−0.383997	+	0.923334i	$0.625453\pi$
$4$	3.80423	−	1.23607i	0.475528	−	0.154508i
$5$	10.3687	+	4.18211i	0.927405	+	0.374059i
$5$	10.3687	+	4.18211i	0.927405	+	0.374059i
$6$	7.92101	+	10.9023i	0.538957	+	0.741810i
$7$	−6.69380	−	3.41066i	−0.361431	−	0.184159i	0.263839	−	0.964567i	$-0.415011\pi$
$7$	−6.69380	−	3.41066i	−0.361431	−	0.184159i	−0.625270	+	0.780408i	$0.715011\pi$
$8$	7.12805	−	3.63192i	0.315018	−	0.160510i
$9$	−10.8157	+	14.8866i	−0.400583	+	0.551356i
$10$	21.7905	+	5.01720i	0.689077	+	0.158658i
$11$	−10.0463	+	35.0724i	−0.275369	+	0.961339i
$11$	−10.0463	+	35.0724i	−0.275369	+	0.961339i
$12$	19.0580	+	19.0580i	0.458464	+	0.458464i
$13$	−13.2463	−	83.6339i	−0.282605	−	1.78430i	−0.565092	−	0.825028i	$-0.691160\pi$
$13$	−13.2463	−	83.6339i	−0.282605	−	1.78430i	0.282487	−	0.959271i	$-0.408840\pi$
$14$	−14.2899	−	4.64306i	−0.272795	−	0.0886365i
$15$	6.61002	+	75.0427i	0.113780	+	1.29173i
$16$	12.9443	−	9.40456i	0.202254	−	0.146946i
$17$	−17.8428	+	112.655i	−0.254560	+	1.60723i	0.446944	+	0.894562i	$0.352512\pi$
$17$	−17.8428	+	112.655i	−0.254560	+	1.60723i	−0.701504	+	0.712665i	$0.747488\pi$
$18$	−16.7076	+	32.7906i	−0.218779	+	0.429378i
$19$	17.8986	−	55.0863i	0.216117	−	0.665140i	−0.782955	−	0.622078i	$-0.786289\pi$
$19$	17.8986	−	55.0863i	0.216117	−	0.665140i	0.999072	−	0.0430622i	$-0.0137114\pi$
$20$	44.6143	+	3.09328i	0.498803	+	0.0345839i
$21$		−	50.6202i		−	0.526011i
$22$	−8.87209	+	72.4243i	−0.0859789	+	0.701860i
$23$	4.14181	−	4.14181i	0.0375490	−	0.0375490i	−0.688083	−	0.725632i	$-0.741548\pi$
$23$	4.14181	−	4.14181i	0.0375490	−	0.0375490i	0.725632	+	0.688083i	$0.241548\pi$
$24$	43.6094	+	31.6840i	0.370905	+	0.269478i
$25$	90.0199	+	86.7261i	0.720159	+	0.693809i
$26$	−52.3329	−	161.064i	−0.394743	−	1.21490i
$27$	57.2279	+	9.06400i	0.407908	+	0.0646062i
$28$	−29.6806	−	4.70094i	−0.200325	−	0.0317284i
$29$	−84.3925	−	259.733i	−0.540390	−	1.66315i	−0.731707	−	0.681620i	$-0.761276\pi$
$29$	−84.3925	−	259.733i	−0.540390	−	1.66315i	0.191317	−	0.981528i	$-0.438724\pi$
$30$	36.5358	+	146.170i	0.222350	+	0.889560i
$31$	−42.6332	−	30.9749i	−0.247005	−	0.179460i	0.457393	−	0.889264i	$-0.348783\pi$
$31$	−42.6332	−	30.9749i	−0.247005	−	0.179460i	−0.704398	+	0.709805i	$0.748783\pi$
$32$	22.6274	−	22.6274i	0.125000	−	0.125000i
$33$	−241.293	+	46.9724i	−1.27284	+	0.247783i
$34$			228.119i			1.15065i
$35$	−55.1423	−	63.3584i	−0.266307	−	0.305986i
$36$	−22.7447	+	70.0010i	−0.105300	+	0.324079i
$37$	118.837	−	233.230i	0.528018	−	1.03629i	−0.460847	−	0.887479i	$-0.652454\pi$
$37$	118.837	−	233.230i	0.528018	−	1.03629i	0.988865	−	0.148814i	$-0.0475456\pi$
$38$	18.1217	−	114.416i	0.0773614	−	0.488441i
$39$	461.586	−	335.362i	1.89520	−	1.37694i
$40$	89.0977	−	7.84803i	0.352190	−	0.0310221i
$41$	98.2775	+	31.9323i	0.374350	+	0.121634i	0.490148	−	0.871639i	$-0.336943\pi$
$41$	98.2775	+	31.9323i	0.374350	+	0.121634i	−0.115798	+	0.993273i	$0.536943\pi$
$42$	−15.8375	−	99.9940i	−0.0581852	−	0.367367i
$43$	−14.0489	−	14.0489i	−0.0498243	−	0.0498243i	0.681756	−	0.731580i	$-0.261217\pi$
$43$	−14.0489	−	14.0489i	−0.0498243	−	0.0498243i	−0.731580	+	0.681756i	$0.761217\pi$
$44$	5.13362	+	145.841i	0.0175891	+	0.499691i
$45$	−174.403	+	109.122i	−0.577743	+	0.361488i
$46$	6.88580	−	9.47749i	0.0220708	−	0.0303778i
$47$	−511.548	+	260.647i	−1.58759	+	0.808920i	−1.00000		0.000235997i	$-0.999925\pi$
$47$	−511.548	+	260.647i	−1.58759	+	0.808920i	−0.587594	+	0.809156i	$0.699925\pi$
$48$	96.0578	+	48.9439i	0.288849	+	0.147176i
$49$	−168.436	−	231.832i	−0.491067	−	0.675896i
$50$	204.957	+	143.152i	0.579706	+	0.404896i
$51$	−730.919	+	237.490i	−2.00684	+	0.652063i
$52$	−153.769	−	301.789i	−0.410076	−	0.804820i
$53$	−29.5620	+	4.68216i	−0.0766161	+	0.0121348i	−0.194625	−	0.980878i	$-0.562349\pi$
$53$	−29.5620	+	4.68216i	−0.0766161	+	0.0121348i	0.118009	+	0.993013i	$0.462349\pi$
$54$	115.882			0.292030
$55$	−250.843	+	321.641i	−0.614976	+	0.788546i
$56$	−60.1011			−0.143417
$57$	385.469	−	61.0523i	0.895730	−	0.141870i
$58$	−247.970	−	486.668i	−0.561379	−	1.10177i
$59$	14.7271	−	4.78513i	0.0324967	−	0.0105588i	−0.292724	−	0.956197i	$-0.594562\pi$
$59$	14.7271	−	4.78513i	0.0324967	−	0.0105588i	0.325220	+	0.945638i	$0.394562\pi$
$60$	117.904	+	277.309i	0.253689	+	0.596674i
$61$	−240.012	−	330.347i	−0.503776	−	0.693388i	0.479078	−	0.877772i	$-0.340971\pi$
$61$	−240.012	−	330.347i	−0.503776	−	0.693388i	−0.982854	+	0.184384i	$0.940971\pi$
$62$	−93.9078	−	47.8484i	−0.192360	−	0.0980121i
$63$	123.172	−	62.7591i	0.246320	−	0.125506i
$64$	37.6183	−	51.7771i	0.0734732	−	0.101127i
$65$	212.419	−	922.573i	0.405344	−	1.76048i
$66$	−461.948	+	168.281i	−0.861543	+	0.313848i
$67$	459.956	+	459.956i	0.838695	+	0.838695i	0.988687	−	0.149992i	$-0.0479249\pi$
$67$	459.956	+	459.956i	0.838695	+	0.838695i	−0.149992	+	0.988687i	$0.547925\pi$
$68$	71.3712	+	450.620i	0.127280	+	0.803614i
$69$	37.5357	+	12.1961i	0.0654893	+	0.0212788i
$70$	−128.750	−	107.904i	−0.219836	−	0.184243i
$71$	58.0796	−	42.1973i	0.0970814	−	0.0705337i	−0.538186	−	0.842826i	$-0.680890\pi$
$71$	58.0796	−	42.1973i	0.0970814	−	0.0705337i	0.635267	+	0.772293i	$0.280890\pi$
$72$	−23.0282	+	145.394i	−0.0376931	+	0.237985i
$73$	160.356	−	314.716i	0.257099	−	0.504585i	−0.725992	−	0.687703i	$-0.758619\pi$
$73$	160.356	−	314.716i	0.257099	−	0.504585i	0.983091	+	0.183118i	$0.0586191\pi$
$74$	161.777	−	497.898i	0.254138	−	0.782156i
$75$	−245.300	+	805.740i	−0.377664	+	1.24052i
$76$		−	231.685i		−	0.349685i
$77$	186.868	−	200.503i	0.276566	−	0.296746i
$78$	806.881	−	806.881i	1.17130	−	1.17130i
$79$	−407.935	−	296.382i	−0.580965	−	0.422096i	0.258107	−	0.966116i	$-0.416901\pi$
$79$	−407.935	−	296.382i	−0.580965	−	0.422096i	−0.839072	+	0.544020i	$0.816901\pi$
$80$	173.546	−	43.3787i	0.242538	−	0.0606236i
$81$	274.170	+	843.807i	0.376090	+	1.15749i
$82$	204.126	+	32.3303i	0.274901	+	0.0435401i
$83$	831.952	+	131.768i	1.10022	+	0.174258i	0.680036	−	0.733179i	$-0.261964\pi$
$83$	831.952	+	131.768i	1.10022	+	0.174258i	0.420188	+	0.907437i	$0.361964\pi$
$84$	−62.5700	−	192.571i	−0.0812732	−	0.250133i
$85$	−656.143	+	1093.47i	−0.837278	+	1.39533i
$86$	−32.1474	−	23.3565i	−0.0403087	−	0.0292860i
$87$	1301.18	−	1301.18i	1.60347	−	1.60347i
$88$	55.7700	+	286.485i	0.0675580	+	0.347039i
$89$			642.498i			0.765221i	0.923910	+	0.382611i	$0.124975\pi$
$89$			642.498i			0.765221i	−0.923910	+	0.382611i	$0.875025\pi$
$90$	−310.370	+	270.122i	−0.363510	+	0.316371i
$91$	−196.579	+	605.008i	−0.226451	+	0.696946i
$92$	10.6368	−	20.8760i	0.0120540	−	0.0236573i
$93$	55.5463	−	350.705i	0.0619342	−	0.391037i
$94$	−928.952	+	674.923i	−1.01930	+	0.740564i
$95$	415.963	−	496.319i	0.449230	−	0.536014i
$96$	205.063	+	66.6292i	0.218013	+	0.0708366i
$97$	54.0877	+	341.497i	0.0566163	+	0.357461i	0.999690	+	0.0248787i	$0.00791994\pi$
$97$	54.0877	+	341.497i	0.0566163	+	0.357461i	−0.943074	+	0.332582i	$0.892080\pi$
$98$	−405.258	−	405.258i	−0.417726	−	0.417726i
$99$	−413.451	−	528.889i	−0.419731	−	0.536922i
$100$	449.655	+	218.655i	0.449655	+	0.218655i
$101$	−1010.27	+	1390.52i	−0.995303	+	1.36992i	−0.0671397	+	0.997744i	$0.521387\pi$
$101$	−1010.27	+	1390.52i	−0.995303	+	1.36992i	−0.928163	+	0.372173i	$0.878613\pi$
$102$	−1369.54	+	697.814i	−1.32945	+	0.677391i
$103$	1019.49	+	519.455i	0.975273	+	0.496926i	0.867602	−	0.497260i	$-0.165661\pi$
$103$	1019.49	+	519.455i	0.975273	+	0.496926i	0.107672	+	0.994187i	$0.465661\pi$
$104$	−398.173	−	548.037i	−0.375423	−	0.516726i
$105$	211.699	−	524.866i	0.196759	−	0.487825i
$106$	−56.9312	+	18.4981i	−0.0521664	+	0.0169499i
$107$	724.541	+	1421.99i	0.654617	+	1.28476i	0.944756	+	0.327774i	$0.106299\pi$
$107$	724.541	+	1421.99i	0.654617	+	1.28476i	−0.290139	+	0.956985i	$0.593701\pi$
$108$	228.911	−	36.2560i	0.203954	−	0.0323031i
$109$	−1038.01			−0.912137			−0.456068	−	0.889945i	$-0.650743\pi$
$109$	−1038.01			−0.912137			−0.456068	+	0.889945i	$0.650743\pi$
$110$	−394.879	+	713.842i	−0.342275	+	0.618747i
$111$	1763.75			1.50818
$112$	−118.722	+	18.8038i	−0.100162	+	0.0158642i
$113$	100.937	+	198.100i	0.0840299	+	0.164918i	0.929198	−	0.369583i	$-0.120500\pi$
$113$	100.937	+	198.100i	0.0840299	+	0.164918i	−0.845168	+	0.534501i	$0.820500\pi$
$114$	742.345	−	241.202i	0.609886	−	0.198164i
$115$	60.2668	−	25.6237i	0.0488687	−	0.0207776i
$116$	−642.096	−	883.770i	−0.513941	−	0.707379i
$117$	1388.29	+	707.371i	1.09699	+	0.558944i
$118$	27.5945	−	14.0601i	0.0215278	−	0.0109689i
$119$	503.665	−	693.235i	0.387990	−	0.534023i
$120$	319.666	+	510.902i	0.243178	+	0.388656i
$121$	−1129.15	−	704.693i	−0.848344	−	0.529446i
$122$	−577.469	−	577.469i	−0.428537	−	0.428537i
$123$	108.921	+	687.701i	0.0798462	+	0.504129i
$124$	−200.473	−	65.1378i	−0.145186	−	0.0471738i
$125$	570.691	+	1275.71i	0.408353	+	0.912824i
$126$	223.675	−	162.509i	0.158147	−	0.114901i
$127$	−177.540	+	1120.94i	−0.124048	+	0.783209i	0.844714	+	0.535218i	$0.179770\pi$
$127$	−177.540	+	1120.94i	−0.124048	+	0.783209i	−0.968762	+	0.247991i	$0.920230\pi$
$128$	58.1108	−	114.049i	0.0401275	−	0.0787546i
$129$	41.3688	−	127.320i	0.0282351	−	0.0868986i
$130$	130.964	−	1888.89i	0.0883560	−	1.27436i
$131$		−	1449.08i		−	0.966464i	−0.875492	−	0.483232i	$-0.839463\pi$
$131$		−	1449.08i		−	0.966464i	0.875492	−	0.483232i	$-0.160537\pi$
$132$	−859.871	+	476.948i	−0.566986	+	0.314492i
$133$	−307.691	+	307.691i	−0.200603	+	0.200603i
$134$	1052.49	+	764.680i	0.678518	+	0.492972i
$135$	555.472	+	333.315i	0.354129	+	0.212498i
$136$	281.970	+	867.815i	0.177785	+	0.547165i
$137$	−2049.61	−	324.626i	−1.27817	−	0.202443i	−0.519815	−	0.854279i	$-0.673999\pi$
$137$	−2049.61	−	324.626i	−1.27817	−	0.202443i	−0.758360	+	0.651836i	$0.773999\pi$
$138$	77.9628	+	12.3481i	0.0480916	+	0.00761696i
$139$	590.482	+	1817.32i	0.360317	+	1.10894i	0.952862	+	0.303404i	$0.0981230\pi$
$139$	590.482	+	1817.32i	0.360317	+	1.10894i	−0.592545	+	0.805537i	$0.701877\pi$
$140$	−288.089	−	172.870i	−0.173914	−	0.104358i
$141$	−3129.64	−	2273.82i	−1.86925	−	1.35809i
$142$	101.527	−	101.527i	0.0599996	−	0.0599996i
$143$	3066.32	+	375.628i	1.79314	+	0.219662i
$144$			294.414i			0.170378i
$145$	211.193	−	3046.04i	0.120956	−	1.74455i
$146$	218.298	−	671.853i	0.123743	−	0.380842i
$147$	876.587	−	1720.40i	0.491834	−	0.965279i
$148$	163.794	−	1034.15i	0.0909713	−	0.574370i
$149$	1066.45	−	774.824i	0.586357	−	0.426014i	−0.254653	−	0.967033i	$-0.581961\pi$
$149$	1066.45	−	774.824i	0.586357	−	0.426014i	0.841010	+	0.541019i	$0.181961\pi$
$150$	−232.469	+	1668.39i	−0.126540	+	0.908154i
$151$	−1578.54	−	512.900i	−0.850728	−	0.276418i	−0.148977	−	0.988841i	$-0.547598\pi$
$151$	−1578.54	−	512.900i	−0.850728	−	0.276418i	−0.701751	+	0.712422i	$0.747598\pi$
$152$	−72.4869	−	457.665i	−0.0386807	−	0.244220i
$153$	−1484.07	−	1484.07i	−0.784181	−	0.784181i
$154$	306.403	−	454.535i	0.160329	−	0.237841i
$155$	−312.511	−	499.466i	−0.161945	−	0.258826i
$156$	1341.45	−	1846.34i	0.688472	−	0.947601i
$157$	951.464	−	484.795i	0.483663	−	0.246439i	−0.195117	−	0.980780i	$-0.562509\pi$
$157$	951.464	−	484.795i	0.483663	−	0.246439i	0.678780	+	0.734341i	$0.262509\pi$
$158$	−898.554	−	457.836i	−0.452437	−	0.230528i
$159$	−118.540	−	163.156i	−0.0591247	−	0.0813781i
$160$	329.247	−	139.987i	0.162683	−	0.0691682i
$161$	−41.8508	+	13.5982i	−0.0204864	+	0.00665643i
$162$	805.589	+	1581.06i	0.390698	+	0.766788i
$163$	−3186.48	+	504.689i	−1.53119	+	0.242517i	−0.864430	−	0.502753i	$-0.832321\pi$
$163$	−3186.48	+	504.689i	−1.53119	+	0.242517i	−0.666763	+	0.745270i	$0.732321\pi$
$164$	413.340			0.196808
$165$	−2698.33	−	522.070i	−1.27312	−	0.246322i
$166$	1684.65			0.787674
$167$	−1216.28	+	192.640i	−0.563586	+	0.0892632i	−0.431725	−	0.902005i	$-0.642095\pi$
$167$	−1216.28	+	192.640i	−0.563586	+	0.0892632i	−0.131860	+	0.991268i	$0.542095\pi$
$168$	−183.849	−	360.824i	−0.0844300	−	0.165703i
$169$	−4729.70	+	1536.77i	−2.15280	+	0.699487i
$170$	−954.017	+	2365.29i	−0.430410	+	1.06712i
$171$	626.461	+	862.249i	0.280156	+	0.385601i
$172$	−70.8108	−	36.0799i	−0.0313911	−	0.0159946i
$173$	−1678.71	+	855.347i	−0.737746	+	0.375901i	−0.782131	−	0.623114i	$-0.785867\pi$
$173$	−1678.71	+	855.347i	−0.737746	+	0.375901i	0.0443847	+	0.999015i	$0.485867\pi$
$174$	2163.23	−	2977.43i	0.942494	−	1.29723i
$175$	−306.782	−	887.555i	−0.132517	−	0.383388i
$176$	199.799	+	548.467i	0.0855706	+	0.234899i
$177$	73.7782	+	73.7782i	0.0313306	+	0.0313306i
$178$	201.018	+	1269.18i	0.0846456	+	0.534431i
$179$	472.240	+	153.440i	0.197189	+	0.0640706i	0.405947	−	0.913897i	$-0.366942\pi$
$179$	472.240	+	153.440i	0.197189	+	0.0640706i	−0.208757	+	0.977967i	$0.566942\pi$
$180$	−528.585	+	630.698i	−0.218880	+	0.261164i
$181$	−1227.80	+	892.047i	−0.504207	+	0.366328i	−0.810622	−	0.585570i	$-0.800871\pi$
$181$	−1227.80	+	892.047i	−0.504207	+	0.366328i	0.306415	+	0.951898i	$0.400871\pi$
$182$	−199.029	+	1256.62i	−0.0810607	+	0.511797i
$183$	1249.09	−	2451.47i	0.504563	−	0.990261i
$184$	14.4803	−	44.5658i	0.00580165	−	0.0178556i
$185$	2207.58	−	1921.31i	0.877322	−	0.763553i
$186$		−	710.154i		−	0.279952i
$187$	−3771.83	−	1757.55i	−1.47499	−	0.687299i
$188$	−1623.87	+	1623.87i	−0.629961	+	0.629961i
$189$	−352.158	−	255.858i	−0.135533	−	0.0984704i
$190$	666.400	−	1110.56i	0.254451	−	0.424045i
$191$	195.594	+	601.975i	0.0740977	+	0.228049i	0.981245	−	0.192763i	$-0.0617450\pi$
$191$	195.594	+	601.975i	0.0740977	+	0.228049i	−0.907148	+	0.420813i	$0.861745\pi$
$192$	425.924	+	67.4597i	0.160096	+	0.0253567i
$193$	529.229	+	83.8216i	0.197382	+	0.0312622i	0.254343	−	0.967114i	$-0.418141\pi$
$193$	529.229	+	83.8216i	0.197382	+	0.0312622i	−0.0569606	+	0.998376i	$0.518141\pi$
$194$	213.687	+	657.662i	0.0790817	+	0.243389i
$195$	6188.56	−	1546.86i	2.27268	−	0.568067i
$196$	−927.329	−	673.744i	−0.337948	−	0.245533i
$197$	1151.01	−	1151.01i	0.416275	−	0.416275i	−0.467643	−	0.883918i	$-0.654897\pi$
$197$	1151.01	−	1151.01i	0.416275	−	0.416275i	0.883918	+	0.467643i	$0.154897\pi$
$198$	−982.194	−	915.399i	−0.352533	−	0.328558i
$199$		−	1820.60i		−	0.648539i	−0.945965	−	0.324269i	$-0.894882\pi$
$199$		−	1820.60i		−	0.648539i	0.945965	−	0.324269i	$-0.105118\pi$
$200$	956.649	+	291.243i	0.338227	+	0.102970i
$201$	−1354.40	+	4168.40i	−0.475282	+	1.46277i
$202$	−1560.61	+	3062.88i	−0.543586	+	1.06685i
$203$	−320.956	+	2026.44i	−0.110969	+	0.700631i
$204$	−2487.03	+	1806.93i	−0.853562	+	0.620149i
$205$	885.465	+	742.103i	0.301676	+	0.252833i
$206$	2176.39	+	707.153i	0.736100	+	0.239173i
$207$	16.8607	+	106.454i	0.00566136	+	0.0357444i
$208$	−958.005	−	958.005i	−0.319354	−	0.319354i
$209$	1752.19	+	1181.16i	0.579913	+	0.390921i
$210$	253.972	−	1103.04i	0.0834558	−	0.362463i
$211$	−171.507	+	236.060i	−0.0559576	+	0.0770190i	−0.836079	−	0.548609i	$-0.815157\pi$
$211$	−171.507	+	236.060i	−0.0559576	+	0.0770190i	0.780121	+	0.625628i	$0.215157\pi$
$212$	−106.673	+	54.3526i	−0.0345582	+	0.0176083i
$213$	431.001	+	219.606i	0.138647	+	0.0706440i
$214$	1876.14	+	2582.28i	0.599300	+	0.824866i
$215$	−86.9151	−	204.424i	−0.0275700	−	0.0648445i
$216$	440.843	−	143.239i	0.138868	−	0.0451211i
$217$	179.734	+	352.747i	0.0562264	+	0.110350i
$218$	−2050.45	+	324.760i	−0.637037	+	0.100897i
$219$	2379.96			0.734351
$220$	−556.695	+	1533.65i	−0.170602	+	0.469995i
$221$	9658.14			2.93971
$222$	3484.07	−	551.822i	1.05331	−	0.166828i
$223$	1716.41	+	3368.65i	0.515423	+	1.01157i	0.991245	+	0.132033i	$0.0421506\pi$
$223$	1716.41	+	3368.65i	0.515423	+	1.01157i	−0.475822	+	0.879542i	$0.657849\pi$
$224$	−228.638	+	74.2890i	−0.0681987	+	0.0221591i
$225$	−2264.69	+	402.083i	−0.671019	+	0.119136i
$226$	261.369	+	359.743i	0.0769291	+	0.105884i
$227$	3999.03	+	2037.61i	1.16927	+	0.595775i	0.927231	−	0.374491i	$-0.122182\pi$
$227$	3999.03	+	2037.61i	1.16927	+	0.595775i	0.242043	+	0.970265i	$0.422182\pi$
$228$	1390.95	−	708.722i	0.404025	−	0.205861i
$229$	437.764	−	602.530i	0.126324	−	0.173870i	−0.741170	−	0.671317i	$-0.765729\pi$
$229$	437.764	−	602.530i	0.126324	−	0.173870i	0.867495	+	0.497447i	$0.165729\pi$
$230$	111.033	−	69.4721i	0.0318316	−	0.0199168i
$231$	1775.37	+	508.544i	0.505675	+	0.144847i
$232$	−1544.89	−	1544.89i	−0.437184	−	0.437184i
$233$	−257.617	−	1626.53i	−0.0724336	−	0.457328i	−0.997071	−	0.0764795i	$-0.975632\pi$
$233$	−257.617	−	1626.53i	−0.0724336	−	0.457328i	0.924638	−	0.380848i	$-0.124368\pi$
$234$	2963.72	+	962.970i	0.827967	+	0.269023i
$235$	−6394.14	+	563.217i	−1.77493	+	0.156341i
$236$	50.1105	−	36.4074i	0.0138217	−	0.0100420i
$237$	531.493	−	3355.72i	0.145672	−	0.919735i
$238$	778.036	−	1526.98i	0.211902	−	0.415880i
$239$	−8.53436	+	26.2661i	−0.00230980	+	0.00710883i	−0.952205	−	0.305460i	$-0.901190\pi$
$239$	−8.53436	+	26.2661i	−0.00230980	+	0.00710883i	0.949895	+	0.312569i	$0.101190\pi$
$240$	791.306	+	909.209i	0.212827	+	0.244538i
$241$			1580.59i			0.422467i	0.977436	+	0.211233i	$0.0677480\pi$
$241$			1580.59i			0.422467i	−0.977436	+	0.211233i	$0.932252\pi$
$242$	−2450.96	−	1038.76i	−0.651049	−	0.275925i
$243$	−3121.01	+	3121.01i	−0.823920	+	0.823920i
$244$	−1321.39	−	960.046i	−0.346694	−	0.251888i
$245$	−776.914	−	3108.22i	−0.202593	−	0.810517i
$246$	430.320	+	1324.39i	0.111529	+	0.343252i
$247$	−4844.18	−	767.242i	−1.24788	−	0.197646i
$248$	−416.390	−	65.9497i	−0.106616	−	0.0168863i
$249$	1753.85	+	5397.80i	0.446369	+	1.37378i
$250$	1526.46	+	2341.46i	0.386167	+	0.592347i
$251$	683.210	+	496.381i	0.171808	+	0.124826i	0.670366	−	0.742030i	$-0.266137\pi$
$251$	683.210	+	496.381i	0.171808	+	0.124826i	−0.498558	+	0.866856i	$0.666137\pi$
$252$	390.998	−	390.998i	0.0977404	−	0.0977404i
$253$	103.654	+	186.873i	0.0257575	+	0.0464372i
$254$			2269.83i			0.560715i
$255$	−8571.88	−	594.321i	−2.10507	−	0.145952i
$256$	79.1084	−	243.470i	0.0193136	−	0.0594410i
$257$	2789.44	−	5474.58i	0.677045	−	1.32877i	−0.255180	−	0.966894i	$-0.582135\pi$
$257$	2789.44	−	5474.58i	0.677045	−	1.32877i	0.932224	−	0.361881i	$-0.117865\pi$
$258$	41.8845	−	264.448i	0.0101070	−	0.0638133i
$259$	−1590.94	+	1155.89i	−0.381685	+	0.277310i
$260$	−332.272	−	3772.24i	−0.0792562	−	0.899786i
$261$	4779.32	+	1552.89i	1.13346	+	0.368282i
$262$	−453.372	−	2862.48i	−0.106906	−	0.674979i
$263$	2517.68	+	2517.68i	0.590292	+	0.590292i	0.937710	−	0.347418i	$-0.112941\pi$
$263$	2517.68	+	2517.68i	0.590292	+	0.590292i	−0.347418	+	0.937710i	$0.612941\pi$
$264$	−1549.35	+	1211.18i	−0.361196	+	0.282359i
$265$	−326.101	−	75.0836i	−0.0755932	−	0.0174051i
$266$	−511.538	+	704.072i	−0.117911	+	0.162291i
$267$	−3857.31	+	1965.40i	−0.884134	+	0.450489i
$268$	2318.31	+	1181.24i	0.528408	+	0.269238i
$269$	−2594.79	−	3571.43i	−0.588132	−	0.809494i	0.406426	−	0.913684i	$-0.366775\pi$
$269$	−2594.79	−	3571.43i	−0.588132	−	0.809494i	−0.994557	+	0.104190i	$0.966775\pi$
$270$	1201.55	+	484.633i	0.270830	+	0.109236i
$271$	5798.41	−	1884.02i	1.29974	−	0.422310i	0.424246	−	0.905547i	$-0.360539\pi$
$271$	5798.41	−	1884.02i	1.29974	−	0.422310i	0.875489	+	0.483237i	$0.160539\pi$
$272$	828.509	+	1626.04i	0.184690	+	0.362475i
$273$	−4233.57	+	670.531i	−0.938561	+	0.148654i
$274$	−4150.32			−0.915072
$275$	−3946.06	+	2285.94i	−0.865295	+	0.501263i
$276$	157.869			0.0344298
$277$	8564.73	−	1356.52i	1.85778	−	0.294243i	0.875721	−	0.482818i	$-0.160387\pi$
$277$	8564.73	−	1356.52i	1.85778	−	0.294243i	0.982059	+	0.188575i	$0.0603869\pi$
$278$	1735.01	+	3405.14i	0.374312	+	0.734629i
$279$	922.221	−	299.648i	0.197892	−	0.0642991i
$280$	−623.170	−	251.349i	−0.133005	−	0.0536464i
$281$	−1933.62	−	2661.40i	−0.410499	−	0.565004i	0.552841	−	0.833287i	$-0.313544\pi$
$281$	−1933.62	−	2661.40i	−0.410499	−	0.565004i	−0.963340	+	0.268283i	$0.913544\pi$
$282$	−6893.64	−	3512.48i	−1.45571	−	0.741721i
$283$	−2387.38	+	1216.43i	−0.501467	+	0.255510i	−0.686378	−	0.727245i	$-0.740800\pi$
$283$	−2387.38	+	1216.43i	−0.501467	+	0.255510i	0.184911	+	0.982755i	$0.440800\pi$
$284$	168.789	−	232.318i	0.0352669	−	0.0485407i
$285$	4252.14	+	979.041i	0.883772	+	0.203485i
$286$	6174.66	−	217.348i	1.27663	−	0.0449373i
$287$	−548.940	−	548.940i	−0.112902	−	0.112902i
$288$	92.1129	+	581.578i	0.0188465	+	0.118992i
$289$	−7700.25	−	2501.96i	−1.56732	−	0.509254i
$290$	−535.824	−	6083.15i	−0.108499	−	1.23177i
$291$	−1884.76	+	1369.36i	−0.379679	+	0.275853i
$292$	221.019	−	1395.46i	0.0442951	−	0.279668i
$293$	−343.378	+	673.917i	−0.0684653	+	0.134371i	−0.922703	−	0.385513i	$-0.874025\pi$
$293$	−343.378	+	673.917i	−0.0684653	+	0.134371i	0.854237	+	0.519883i	$0.174025\pi$
$294$	1193.33	−	3672.69i	0.236722	−	0.728557i
$295$	172.713	+	11.9748i	0.0340872	+	0.00236340i
$296$		−	2094.09i		−	0.411204i
$297$	−892.822	+	1916.06i	−0.174434	+	0.374347i
$298$	1864.23	−	1864.23i	0.362389	−	0.362389i
$299$	−401.260	−	291.533i	−0.0776103	−	0.0563872i
$300$	62.7731	+	3368.42i	0.0120807	+	0.648253i
$301$	46.1247	+	141.957i	0.00883250	+	0.0271836i
$302$	−3278.69	−	519.293i	−0.624726	−	0.0989469i
$303$	−11438.5	−	1811.69i	−2.16874	−	0.343494i
$304$	−286.378	−	881.381i	−0.0540293	−	0.166285i
$305$	−1107.06	−	4429.03i	−0.207836	−	0.831493i
$306$	−3395.91	−	2467.27i	−0.634416	−	0.460930i
$307$	5621.21	−	5621.21i	1.04501	−	1.04501i	0.0460758	−	0.998938i	$-0.485328\pi$
$307$	5621.21	−	5621.21i	1.04501	−	1.04501i	0.998938	−	0.0460758i	$-0.0146716\pi$
$308$	463.052	−	993.741i	0.0856650	−	0.183843i
$309$			7709.62i			1.41937i
$310$	−773.594	−	888.858i	−0.141733	−	0.162851i
$311$	2703.67	−	8321.05i	0.492962	−	1.51718i	−0.327146	−	0.944974i	$-0.606087\pi$
$311$	2703.67	−	8321.05i	0.492962	−	1.51718i	0.820109	−	0.572208i	$-0.193913\pi$
$312$	2072.20	−	4066.92i	0.376010	−	0.737961i
$313$	241.055	−	1521.96i	0.0435311	−	0.274845i	−0.956316	−	0.292335i	$-0.905568\pi$
$313$	241.055	−	1521.96i	0.0435311	−	0.274845i	0.999847	+	0.0174906i	$0.00556772\pi$
$314$	1727.82	−	1255.34i	0.310531	−	0.225614i
$315$	1539.60	−	135.613i	0.275385	−	0.0242569i
$316$	−1918.22	−	623.269i	−0.341483	−	0.110955i
$317$	1679.74	+	10605.5i	0.297614	+	1.87906i	0.453456	+	0.891279i	$0.350191\pi$
$317$	1679.74	+	10605.5i	0.297614	+	1.87906i	−0.155842	+	0.987782i	$0.549809\pi$
$318$	−285.207	−	285.207i	−0.0502944	−	0.0502944i
$319$	9957.30	−	350.498i	1.74766	−	0.0615175i
$320$	606.590	−	379.537i	0.105967	−	0.0663025i
$321$	−6320.73	+	8699.74i	−1.09903	+	1.51269i
$322$	−78.4167	+	39.9553i	−0.0135714	+	0.00691498i
$323$	5886.39	+	2999.26i	1.01402	+	0.516667i
$324$	2086.01	+	2871.14i	0.357683	+	0.492308i
$325$	6060.81	−	8677.52i	1.03444	−	1.48105i
$326$	−6136.60	+	1993.90i	−1.04256	+	0.338749i
$327$	−3175.25	−	6231.79i	−0.536978	−	1.05388i
$328$	816.502	−	129.321i	0.137451	−	0.0217700i
$329$	4313.18			0.722776
$330$	−5493.57	−	187.060i	−0.916397	−	0.0312039i
$331$	−1937.09			−0.321667			−0.160834	−	0.986982i	$-0.551418\pi$
$331$	−1937.09			−0.321667			−0.160834	+	0.986982i	$0.551418\pi$
$332$	3327.81	−	527.073i	0.550112	−	0.0871292i
$333$	2186.70	+	4291.64i	0.359851	+	0.706247i
$334$	−2342.35	+	761.074i	−0.383735	+	0.124683i
$335$	2845.56	+	6692.73i	0.464088	+	1.09153i
$336$	−476.061	−	655.242i	−0.0772954	−	0.106388i
$337$	−1030.43	−	525.030i	−0.166561	−	0.0848670i	0.368723	−	0.929539i	$-0.379795\pi$
$337$	−1030.43	−	525.030i	−0.166561	−	0.0848670i	−0.535284	+	0.844672i	$0.679795\pi$
$338$	−8862.13	+	4515.48i	−1.42614	+	0.726656i
$339$	−880.553	+	1211.98i	−0.141077	+	0.194176i
$340$	−1144.52	+	4970.83i	−0.182559	+	0.792885i
$341$	1514.67	−	1184.07i	0.240539	−	0.188038i
$342$	1507.27	+	1507.27i	0.238315	+	0.238315i
$343$	739.881	+	4671.43i	0.116472	+	0.735374i
$344$	−151.166	−	49.1169i	−0.0236929	−	0.00769828i
$345$	338.191	+	283.436i	0.0527756	+	0.0442309i
$346$	−3048.48	+	2214.85i	−0.473662	+	0.344136i
$347$	−907.467	+	5729.52i	−0.140390	+	0.886389i	0.812475	+	0.582996i	$0.198120\pi$
$347$	−907.467	+	5729.52i	−0.140390	+	0.886389i	−0.952865	+	0.303393i	$0.901880\pi$
$348$	3341.65	−	6558.35i	0.514744	−	1.01024i
$349$	558.207	−	1717.99i	0.0856165	−	0.263500i	−0.899078	−	0.437788i	$-0.855762\pi$
$349$	558.207	−	1717.99i	0.0856165	−	0.263500i	0.984695	+	0.174287i	$0.0557621\pi$
$350$	−883.698	−	1657.27i	−0.134959	−	0.253100i
$351$		−	4906.26i		−	0.746087i
$352$	566.277	+	1020.92i	0.0857462	+	0.154588i
$353$	8280.99	−	8280.99i	1.24859	−	1.24859i	0.292249	−	0.956342i	$-0.405596\pi$
$353$	8280.99	−	8280.99i	1.24859	−	1.24859i	0.956342	−	0.292249i	$-0.0944036\pi$
$354$	168.823	+	122.657i	0.0253470	+	0.0184156i
$355$	778.683	−	194.636i	0.116418	−	0.0290991i
$356$	794.171	+	2444.21i	0.118233	+	0.363884i
$357$	5702.62	+	903.207i	0.845420	+	0.133901i
$358$	980.858	+	155.353i	0.144804	+	0.0229347i
$359$	−2926.34	−	9006.36i	−0.430213	−	1.32406i	−0.897913	−	0.440173i	$-0.854917\pi$
$359$	−2926.34	−	9006.36i	−0.430213	−	1.32406i	0.467700	−	0.883887i	$-0.345083\pi$
$360$	−846.828	+	1411.24i	−0.123977	+	0.206609i
$361$	2834.91	+	2059.68i	0.413312	+	0.300289i
$362$	−2146.27	+	2146.27i	−0.311617	+	0.311617i
$363$	776.655	−	8934.61i	0.112297	−	1.29186i
$364$			2544.57i			0.366406i
$365$	2978.86	−	2592.57i	0.427180	−	0.371784i
$366$	1700.43	−	5233.37i	0.242849	−	0.747412i
$367$	4.86023	−	9.53873i	0.000691285	−	0.00135672i	−0.890661	−	0.454669i	$-0.849758\pi$
$367$	4.86023	−	9.53873i	0.000691285	−	0.00135672i	0.891352	+	0.453312i	$0.149758\pi$
$368$	14.6608	−	92.5647i	0.00207676	−	0.0131121i
$369$	−1538.31	+	1117.65i	−0.217022	+	0.157676i
$370$	3759.68	−	4485.99i	0.528261	−	0.630312i
$371$	213.851	+	69.4845i	0.0299262	+	0.00972361i
$372$	−222.185	−	1402.82i	−0.0309671	−	0.195519i
$373$	353.978	+	353.978i	0.0491375	+	0.0491375i	0.731249	−	0.682111i	$-0.238938\pi$
$373$	353.978	+	353.978i	0.0491375	+	0.0491375i	−0.682111	+	0.731249i	$0.738938\pi$
$374$	−8000.66	−	2291.74i	−1.10616	−	0.316853i
$375$	−5913.13	+	7328.60i	−0.814274	+	1.00919i
$376$	−2699.69	+	3715.81i	−0.370282	+	0.509649i
$377$	−20604.6	+	10498.6i	−2.81484	+	1.43423i
$378$	−775.694	−	395.236i	−0.105549	−	0.0537797i
$379$	2554.79	+	3516.37i	0.346255	+	0.476580i	0.946255	−	0.323420i	$-0.104833\pi$
$379$	2554.79	+	3516.37i	0.346255	+	0.476580i	−0.600000	+	0.800000i	$0.704833\pi$
$380$	968.931	−	2402.27i	0.130803	−	0.324299i
$381$	−7272.80	+	2363.07i	−0.977944	+	0.317753i
$382$	574.710	+	1127.93i	0.0769758	+	0.151073i
$383$	−11555.3	+	1830.19i	−1.54164	+	0.244173i	−0.868632	−	0.495458i	$-0.835000\pi$
$383$	−11555.3	+	1830.19i	−1.54164	+	0.244173i	−0.673013	+	0.739631i	$0.735000\pi$
$384$	862.466			0.114616
$385$	2776.10	−	1297.46i	0.367489	−	0.171752i
$386$	1071.65			0.141310
$387$	361.091	−	57.1912i	0.0474297	−	0.00751212i
$388$	627.875	+	1232.27i	0.0821534	+	0.161235i
$389$	1474.44	−	479.075i	0.192178	−	0.0624423i	−0.211347	−	0.977411i	$-0.567785\pi$
$389$	1474.44	−	479.075i	0.192178	−	0.0624423i	0.403525	+	0.914969i	$0.367785\pi$
$390$	11740.8	−	4991.84i	1.52440	−	0.648133i
$391$	392.695	+	540.498i	0.0507914	+	0.0699083i
$392$	−2042.62	−	1040.77i	−0.263183	−	0.134098i
$393$	8699.72	−	4432.73i	1.11665	−	0.568961i
$394$	1913.57	−	2633.80i	0.244680	−	0.336773i
$395$	−2990.25	−	4779.13i	−0.380901	−	0.608769i
$396$	−2226.60	−	1500.96i	−0.282553	−	0.190470i
$397$	−2722.88	−	2722.88i	−0.344225	−	0.344225i	0.513728	−	0.857953i	$-0.328264\pi$
$397$	−2722.88	−	2722.88i	−0.344225	−	0.344225i	−0.857953	+	0.513728i	$0.828264\pi$
$398$	−569.610	−	3596.38i	−0.0717387	−	0.452940i
$399$	−2788.48	−	906.033i	−0.349871	−	0.113680i
$400$	1980.86	+	276.008i	0.247608	+	0.0345010i
$401$	3606.99	−	2620.63i	0.449189	−	0.326355i	−0.340087	−	0.940394i	$-0.610456\pi$
$401$	3606.99	−	2620.63i	0.449189	−	0.326355i	0.789275	+	0.614039i	$0.210456\pi$
$402$	−1371.28	+	8657.91i	−0.170132	+	1.07417i
$403$	−2025.82	+	3975.89i	−0.250405	+	0.491447i
$404$	−2124.52	+	6538.60i	−0.261631	+	0.805217i
$405$	−686.113	+	9895.79i	−0.0841808	+	1.21414i
$406$			4103.40i			0.501597i
$407$	6986.08	+	6510.99i	0.850829	+	0.792967i
$408$	−4347.48	+	4347.48i	−0.527530	+	0.527530i
$409$	−4265.26	−	3098.89i	−0.515656	−	0.374646i	0.299309	−	0.954156i	$-0.403244\pi$
$409$	−4265.26	−	3098.89i	−0.515656	−	0.374646i	−0.814965	+	0.579510i	$0.803244\pi$
$410$	1981.31	+	1188.90i	0.238658	+	0.143209i
$411$	−4320.81	−	13298.1i	−0.518564	−	1.59598i
$412$	4520.44	+	715.968i	0.540549	+	0.0856146i
$413$	−114.901	−	18.1985i	−0.0136898	−	0.00216826i
$414$	66.6125	+	205.012i	0.00790779	+	0.0243377i
$415$	8075.19	+	4845.58i	0.955170	+	0.573157i
$416$	−2192.15	−	1592.69i	−0.258363	−	0.187712i
$417$	−9104.19	+	9104.19i	−1.06915	+	1.06915i
$418$	3830.79	+	1785.03i	0.448254	+	0.208872i
$419$		−	14770.7i		−	1.72218i	−0.508450	−	0.861092i	$-0.669781\pi$
$419$		−	14770.7i		−	1.72218i	0.508450	−	0.861092i	$-0.330219\pi$
$420$	156.582	−	2258.38i	0.0181915	−	0.262376i
$421$	3429.15	−	10553.8i	0.396975	−	1.22176i	−0.530437	−	0.847724i	$-0.677972\pi$
$421$	3429.15	−	10553.8i	0.396975	−	1.22176i	0.927413	−	0.374040i	$-0.122028\pi$
$422$	−264.936	+	519.966i	−0.0305613	+	0.0599799i
$423$	1652.63	−	10434.3i	0.189961	−	1.19937i
$424$	−193.714	+	140.742i	−0.0221877	+	0.0161203i
$425$	−11376.3	+	8593.76i	−1.29843	+	0.980844i
$426$	920.098	+	298.958i	0.104645	+	0.0340013i
$427$	479.886	+	3029.88i	0.0543871	+	0.343387i
$428$	4514.00	+	4514.00i	0.509795	+	0.509795i
$429$	7124.72	+	19558.0i	0.801830	+	2.20110i
$430$	−235.648	−	376.621i	−0.0264278	−	0.0422378i
$431$	−2912.77	+	4009.09i	−0.325530	+	0.448053i	−0.940145	−	0.340773i	$-0.889311\pi$
$431$	−2912.77	+	4009.09i	−0.325530	+	0.448053i	0.614616	+	0.788827i	$0.289311\pi$
$432$	826.016	−	420.876i	0.0919947	−	0.0468736i
$433$	14629.7	+	7454.20i	1.62369	+	0.827311i	0.998918	+	0.0465041i	$0.0148081\pi$
$433$	14629.7	+	7454.20i	1.62369	+	0.827311i	0.624772	+	0.780807i	$0.285192\pi$
$434$	465.405	+	640.576i	0.0514751	+	0.0708493i
$435$	18933.3	−	8049.89i	2.08685	−	0.887270i
$436$	−3948.81	+	1283.05i	−0.433747	+	0.140933i
$437$	−154.024	−	302.290i	−0.0168604	−	0.0330904i
$438$	4701.32	−	744.616i	0.512872	−	0.0812309i
$439$	4799.77			0.521823			0.260912	−	0.965363i	$-0.415977\pi$
$439$	4799.77			0.521823			0.260912	+	0.965363i	$0.415977\pi$
$440$	−619.850	+	3203.71i	−0.0671595	+	0.347116i
$441$	5272.95			0.569372
$442$	19078.5	−	3021.73i	2.05310	−	0.325179i
$443$	−6926.61	−	13594.2i	−0.742874	−	1.45797i	−0.883757	−	0.467945i	$-0.844994\pi$
$443$	−6926.61	−	13594.2i	−0.742874	−	1.45797i	0.140884	−	0.990026i	$-0.455006\pi$
$444$	6709.69	−	2180.11i	0.717180	−	0.233026i
$445$	−2687.00	+	6661.87i	−0.286238	+	0.709670i
$446$	4444.50	+	6117.33i	0.471868	+	0.649471i
$447$	7914.02	+	4032.39i	0.837406	+	0.426679i
$448$	−428.403	+	218.282i	−0.0451789	+	0.0230198i
$449$	4895.24	−	6737.72i	0.514522	−	0.708179i	−0.470151	−	0.882586i	$-0.655801\pi$
$449$	4895.24	−	6737.72i	0.514522	−	0.708179i	0.984674	+	0.174407i	$0.0558007\pi$
$450$	−4347.82	+	1502.82i	−0.455462	+	0.157430i
$451$	−2107.26	+	3126.03i	−0.220016	+	0.326383i
$452$	628.854	+	628.854i	0.0654398	+	0.0654398i
$453$	−1749.50	−	11045.9i	−0.181454	−	1.14566i
$454$	8537.10	+	2773.87i	0.882524	+	0.286750i
$455$	−4568.48	+	5451.03i	−0.470711	+	0.561645i
$456$	2525.90	−	1835.18i	0.259400	−	0.188465i
$457$	−981.827	+	6199.01i	−0.100499	+	0.634524i	0.885097	+	0.465406i	$0.154092\pi$
$457$	−981.827	+	6199.01i	−0.100499	+	0.634524i	−0.985596	+	0.169118i	$0.945908\pi$
$458$	676.235	−	1327.19i	0.0689921	−	0.135405i
$459$	−2042.21	+	6285.28i	−0.207674	+	0.639154i
$460$	197.596	−	171.972i	0.0200282	−	0.0174310i
$461$			11510.8i			1.16293i	0.813570	+	0.581467i	$0.197521\pi$
$461$			11510.8i			1.16293i	−0.813570	+	0.581467i	$0.802479\pi$
$462$	3666.14	+	449.107i	0.369186	+	0.0452259i
$463$	−8635.81	+	8635.81i	−0.866825	+	0.866825i	−0.992120	−	0.125295i	$-0.960012\pi$
$463$	−8635.81	+	8635.81i	−0.866825	+	0.866825i	0.125295	+	0.992120i	$0.460012\pi$
$464$	−3535.08	−	2568.39i	−0.353690	−	0.256971i
$465$	2042.63	−	3404.06i	0.203709	−	0.339483i
$466$	−1017.78	−	3132.40i	−0.101175	−	0.311386i
$467$	−7153.93	−	1133.07i	−0.708875	−	0.112275i	−0.208422	−	0.978039i	$-0.566833\pi$
$467$	−7153.93	−	1133.07i	−0.708875	−	0.112275i	−0.500452	+	0.865764i	$0.666833\pi$
$468$	6155.74	+	974.974i	0.608011	+	0.0962995i
$469$	−1510.10	−	4647.61i	−0.148678	−	0.457583i
$470$	−12454.6	+	3113.09i	−1.22232	+	0.305524i
$471$	5821.05	+	4229.24i	0.569469	+	0.413743i
$472$	87.5964	−	87.5964i	0.00854227	−	0.00854227i
$473$	633.870	−	351.591i	0.0616181	−	0.0341779i
$474$		−	6795.09i		−	0.658457i
$475$	6388.65	−	3406.59i	0.617119	−	0.329063i
$476$	1059.17	−	3259.79i	0.101989	−	0.313891i
$477$	250.034	−	490.719i	0.0240005	−	0.0471037i
$478$	−8.64075	+	54.5555i	−0.000826817	+	0.00522032i
$479$	−10929.3	+	7940.61i	−1.04253	+	0.757444i	−0.970778	−	0.239978i	$-0.922860\pi$
$479$	−10929.3	+	7940.61i	−1.04253	+	0.757444i	−0.0717545	+	0.997422i	$0.522860\pi$
$480$	1847.59	+	1548.46i	0.175689	+	0.147244i
$481$	−21080.1	−	6849.35i	−1.99828	−	0.649280i
$482$	494.516	+	3122.25i	0.0467315	+	0.295051i
$483$	−209.660	−	209.660i	−0.0197512	−	0.0197512i
$484$	−5166.57	−	1285.11i	−0.485215	−	0.120690i
$485$	−867.357	+	3767.08i	−0.0812054	+	0.352689i
$486$	−5188.70	+	7141.63i	−0.484288	+	0.666565i
$487$	8107.19	−	4130.82i	0.754357	−	0.384364i	−0.0341286	−	0.999417i	$-0.510866\pi$
$487$	8107.19	−	4130.82i	0.754357	−	0.384364i	0.788485	+	0.615053i	$0.210866\pi$
$488$	−2910.61	−	1483.03i	−0.269994	−	0.137569i
$489$	−12777.4	−	17586.6i	−1.18162	−	1.62636i
$490$	−2507.16	−	5896.83i	−0.231147	−	0.543656i
$491$	−10202.8	+	3315.08i	−0.937768	+	0.304699i	−0.737735	−	0.675090i	$-0.764105\pi$
$491$	−10202.8	+	3315.08i	−0.937768	+	0.304699i	−0.200032	+	0.979789i	$0.564105\pi$
$492$	1264.41	+	2481.54i	0.115861	+	0.227391i
$493$	30766.1	−	4872.87i	2.81062	−	0.445158i
$494$	−9809.12			−0.893387
$495$	−2075.08	−	7212.99i	−0.188420	−	0.654949i
$496$	−843.161			−0.0763287
$497$	−532.694	+	84.3704i	−0.0480776	+	0.00761475i
$498$	5153.32	+	10114.0i	0.463706	+	0.910075i
$499$	−5114.63	+	1661.84i	−0.458842	+	0.149087i	−0.529312	−	0.848427i	$-0.677550\pi$
$499$	−5114.63	+	1661.84i	−0.458842	+	0.149087i	0.0704702	+	0.997514i	$0.477550\pi$
$500$	3747.90	+	4147.68i	0.335223	+	0.370980i
$501$	−4877.14	−	6712.81i	−0.434919	−	0.598615i
$502$	1504.90	+	766.784i	0.133799	+	0.0681738i
$503$	−11547.3	+	5883.66i	−1.02360	+	0.521550i	−0.883423	−	0.468577i	$-0.844767\pi$
$503$	−11547.3	+	5883.66i	−1.02360	+	0.521550i	−0.140176	+	0.990127i	$0.544767\pi$
$504$	650.038	−	894.700i	0.0574504	−	0.0790737i
$505$	−16290.5	+	10192.8i	−1.43548	+	0.898165i
$506$	263.222	+	336.715i	0.0231258	+	0.0295826i
$507$	−23694.3	−	23694.3i	−2.07555	−	2.07555i
$508$	710.159	+	4483.77i	0.0620240	+	0.391604i
$509$	17582.5	+	5712.90i	1.53110	+	0.497485i	0.948905	−	0.315563i	$-0.102193\pi$
$509$	17582.5	+	5712.90i	1.53110	+	0.497485i	0.582197	+	0.813048i	$0.302193\pi$
$510$	−17118.6	+	1507.87i	−1.48633	+	0.130921i
$511$	−2146.78	+	1559.73i	−0.185847	+	0.135026i
$512$	80.0944	−	505.696i	0.00691349	−	0.0436501i
$513$	1523.60	−	2990.24i	0.131128	−	0.257353i
$514$	3797.37	−	11687.1i	0.325865	−	1.00291i
$515$	8398.35	+	9649.69i	0.718593	+	0.825662i
$516$		−	535.489i		−	0.0456853i
$517$	−4002.36	−	20559.7i	−0.340471	−	1.74897i
$518$	−2781.07	+	2781.07i	−0.235894	+	0.235894i
$519$	−10270.3	−	7461.84i	−0.868628	−	0.631095i
$520$	−1836.58	−	7347.64i	−0.154883	−	0.619645i
$521$	478.973	+	1474.13i	0.0402768	+	0.123959i	0.969173	−	0.246381i	$-0.0792413\pi$
$521$	478.973	+	1474.13i	0.0402768	+	0.123959i	−0.928896	+	0.370340i	$0.879241\pi$
$522$	9926.80	+	1572.25i	0.832346	+	0.131831i
$523$	15153.5	+	2400.08i	1.26695	+	0.200665i	0.753497	−	0.657451i	$-0.228365\pi$
$523$	15153.5	+	2400.08i	1.26695	+	0.200665i	0.513455	+	0.858117i	$0.328365\pi$
$524$	−1791.16	−	5512.63i	−0.149327	−	0.459581i
$525$	4390.10	−	4556.83i	0.364951	−	0.378812i
$526$	5761.07	+	4185.67i	0.477557	+	0.346965i
$527$	4250.17	−	4250.17i	0.351310	−	0.351310i
$528$	−2681.60	+	2877.28i	−0.221026	+	0.237154i
$529$			12132.7i			0.997180i
$530$	−667.663	−	46.2916i	−0.0547197	−	0.00379392i
$531$	−88.0504	+	270.991i	−0.00719597	+	0.0221469i
$532$	−790.199	+	1550.85i	−0.0643975	+	0.126387i
$533$	1368.81	−	8642.32i	0.111238	−	0.702327i
$534$	−7004.73	+	5089.24i	−0.567649	+	0.412421i
$535$	1565.62	+	17774.3i	0.126519	+	1.43636i
$536$	4949.11	+	1608.06i	0.398823	+	0.129585i
$537$	523.384	+	3304.52i	0.0420590	+	0.265550i
$538$	−6243.08	−	6243.08i	−0.500295	−	0.500295i
$539$	9823.06	−	3578.41i	0.784989	−	0.285961i
$540$	2525.14	+	581.405i	0.201231	+	0.0463328i
$541$	−6750.13	+	9290.76i	−0.536434	+	0.738338i	−0.988094	−	0.153852i	$-0.950832\pi$
$541$	−6750.13	+	9290.76i	−0.536434	+	0.738338i	0.451660	+	0.892190i	$0.350832\pi$
$542$	10864.6	−	5535.79i	0.861023	−	0.438713i
$543$	−9111.33	−	4642.46i	−0.720082	−	0.366900i
$544$	2145.36	+	2952.83i	0.169083	+	0.232723i
$545$	−10762.8	−	4341.05i	−0.845920	−	0.341193i
$546$	−8153.11	+	2649.10i	−0.639049	+	0.207640i
$547$	−10249.0	−	20114.8i	−0.801126	−	1.57230i	−0.819923	−	0.572474i	$-0.805984\pi$
$547$	−10249.0	−	20114.8i	−0.801126	−	1.57230i	0.0187970	−	0.999823i	$-0.494016\pi$
$548$	−8198.44	+	1298.50i	−0.639087	+	0.101221i
$549$	7513.65			0.584107
$550$	−7079.75	+	5750.19i	−0.548875	+	0.445798i
$551$	−15818.3			−1.22301
$552$	311.851	−	49.3924i	0.0240458	−	0.00380848i
$553$	1719.78	+	3375.25i	0.132247	+	0.259549i
$554$	16494.2	−	5359.28i	1.26493	−	0.411000i
$555$	18287.8	+	7376.19i	1.39869	+	0.564147i
$556$	4492.65	+	6183.61i	0.342681	+	0.471661i
$557$	17457.0	+	8894.79i	1.32797	+	0.676632i	0.966720	−	0.255838i	$-0.0823515\pi$
$557$	17457.0	+	8894.79i	1.32797	+	0.676632i	0.361246	+	0.932471i	$0.382351\pi$
$558$	1727.98	−	880.451i	0.131096	−	0.0667965i
$559$	−988.872	+	1361.07i	−0.0748208	+	0.102982i
$560$	−1309.63	−	301.539i	−0.0988253	−	0.0227542i
$561$	−986.339	−	28020.9i	−0.0742304	−	2.10882i
$562$	−4652.31	−	4652.31i	−0.349192	−	0.349192i
$563$	−2031.29	−	12825.1i	−0.152058	−	0.960056i	−0.939221	−	0.343312i	$-0.888451\pi$
$563$	−2031.29	−	12825.1i	−0.152058	−	0.960056i	0.787163	−	0.616744i	$-0.211549\pi$
$564$	−14716.5	−	4781.67i	−1.09872	−	0.356994i
$565$	218.110	+	2476.18i	0.0162406	+	0.184378i
$566$	−4335.39	+	3149.85i	−0.321961	+	0.233919i
$567$	1042.71	−	6583.38i	0.0772302	−	0.487612i
$568$	260.737	−	511.725i	0.0192611	−	0.0378019i
$569$	4429.91	−	13633.8i	0.326382	−	1.00450i	−0.644431	−	0.764662i	$-0.722906\pi$
$569$	4429.91	−	13633.8i	0.326382	−	1.00450i	0.970813	−	0.239838i	$-0.0770943\pi$
$570$	8705.89	+	603.612i	0.639736	+	0.0443553i
$571$			1875.04i			0.137422i	0.997637	+	0.0687110i	$0.0218886\pi$
$571$			1875.04i			0.137422i	−0.997637	+	0.0687110i	$0.978111\pi$
$572$	12129.3	−	2361.20i	0.886626	−	0.172599i
$573$	−3015.71	+	3015.71i	−0.219866	+	0.219866i
$574$	−1256.11	−	912.617i	−0.0913397	−	0.0663622i
$575$	732.049	−	13.6423i	0.0530932	−	0.000989430i
$576$	363.915	+	1120.02i	0.0263249	+	0.0810197i
$577$	19506.8	+	3089.58i	1.40742	+	0.222913i	0.813478	−	0.581596i	$-0.197571\pi$
$577$	19506.8	+	3089.58i	1.40742	+	0.222913i	0.593941	+	0.804509i	$0.297571\pi$
$578$	−15993.7	−	2533.15i	−1.15095	−	0.182293i
$579$	1115.67	+	3433.69i	0.0800792	+	0.246458i
$580$	−2961.68	−	11848.9i	−0.212030	−	0.848271i
$581$	−5119.51	−	3719.54i	−0.365564	−	0.265598i
$582$	−3294.68	+	3294.68i	−0.234655	+	0.234655i
$583$	132.773	−	1083.85i	0.00943206	−	0.0769955i
$584$		−	2825.71i		−	0.200221i
$585$	11436.5	+	13140.5i	0.808275	+	0.928707i
$586$	−467.453	+	1438.67i	−0.0329527	+	0.101418i
$587$	307.649	−	603.795i	0.0216321	−	0.0424554i	−0.879938	−	0.475089i	$-0.842416\pi$
$587$	307.649	−	603.795i	0.0216321	−	0.0424554i	0.901570	+	0.432634i	$0.142416\pi$
$588$	1208.20	−	7628.30i	0.0847373	−	0.535010i
$589$	−2469.37	+	1794.10i	−0.172748	+	0.125509i
$590$	344.920	−	30.3817i	0.0240680	−	0.00211999i
$591$	10431.2	+	3389.29i	0.726025	+	0.235900i
$592$	−655.174	−	4136.61i	−0.0454856	−	0.287185i
$593$	−4583.31	−	4583.31i	−0.317393	−	0.317393i	0.530372	−	0.847765i	$-0.322052\pi$
$593$	−4583.31	−	4583.31i	−0.317393	−	0.317393i	−0.847765	+	0.530372i	$0.822052\pi$
$594$	−1164.18	+	4064.27i	−0.0804160	+	0.280739i
$595$	8121.53	−	5081.56i	0.559581	−	0.350124i
$596$	3099.29	−	4265.81i	0.213007	−	0.293179i
$597$	10930.2	−	5569.22i	0.749319	−	0.381797i
$598$	−883.851	−	450.345i	−0.0604404	−	0.0307959i
$599$	−6705.15	−	9228.84i	−0.457370	−	0.629516i	0.516590	−	0.856233i	$-0.327201\pi$
$599$	−6705.15	−	9228.84i	−0.457370	−	0.629516i	−0.973961	+	0.226716i	$0.927201\pi$
$600$	1177.88	+	6634.26i	0.0801443	+	0.451404i
$601$	6261.06	−	2034.34i	0.424949	−	0.138074i	−0.0887322	−	0.996056i	$-0.528282\pi$
$601$	6261.06	−	2034.34i	0.424949	−	0.138074i	0.513681	+	0.857981i	$0.328282\pi$
$602$	135.528	+	265.988i	0.00917557	+	0.0180081i
$603$	−11821.9	+	1872.41i	−0.798386	+	0.126452i
$604$	−6639.11			−0.447254
$605$	−8760.67	−	12029.0i	−0.588714	−	0.808342i
$606$	−23162.2			−1.55264
$607$	−23249.3	+	3682.32i	−1.55463	+	0.246229i	−0.873826	−	0.486239i	$-0.838368\pi$
$607$	−23249.3	+	3682.32i	−1.55463	+	0.246229i	−0.680802	+	0.732468i	$0.738368\pi$
$608$	−841.461	−	1651.46i	−0.0561279	−	0.110157i
$609$	−13147.8	+	4271.97i	−0.874835	+	0.284251i
$610$	−3572.56	−	8402.64i	−0.237129	−	0.557726i
$611$	28575.0	+	39330.2i	1.89202	+	2.60414i
$612$	−7480.14	−	3811.32i	−0.494063	−	0.251738i
$613$	−19713.8	+	10044.7i	−1.29891	+	0.661828i	−0.960266	−	0.279087i	$-0.909968\pi$
$613$	−19713.8	+	10044.7i	−1.29891	+	0.661828i	−0.338644	+	0.940914i	$0.609968\pi$
$614$	9345.30	−	12862.7i	0.614244	−	0.845434i
$615$	−1746.67	+	7586.08i	−0.114524	+	0.497399i
$616$	603.791	−	2107.89i	0.0394926	−	0.137872i
$617$	3218.68	+	3218.68i	0.210015	+	0.210015i	0.804274	−	0.594259i	$-0.202555\pi$
$617$	3218.68	+	3218.68i	0.210015	+	0.210015i	−0.594259	+	0.804274i	$0.702555\pi$
$618$	2412.10	+	15229.4i	0.157005	+	0.991289i
$619$	4244.92	+	1379.26i	0.275635	+	0.0895592i	0.443573	−	0.896238i	$-0.353711\pi$
$619$	4244.92	+	1379.26i	0.275635	+	0.0895592i	−0.167938	+	0.985798i	$0.553711\pi$
$620$	−1806.24	−	1513.80i	−0.117000	−	0.0980573i
$621$	274.569	−	199.486i	0.0177424	−	0.0128906i
$622$	2737.37	−	17283.1i	0.176461	−	1.11413i
$623$	2191.35	−	4300.76i	0.140922	−	0.276575i
$624$	2820.96	−	8682.02i	0.180976	−	0.556986i
$625$	582.165	+	15614.2i	0.0372586	+	0.999306i
$626$		−	3081.87i		−	0.196767i
$627$	−1731.27	+	14132.7i	−0.110272	+	0.900166i
$628$	3020.34	−	3020.34i	0.191919	−	0.191919i
$629$	24154.2	+	17549.1i	1.53115	+	1.11244i
$630$	2998.85	−	749.578i	0.189646	−	0.0474030i
$631$	−1817.41	−	5593.40i	−0.114659	−	0.352884i	0.877217	−	0.480094i	$-0.159398\pi$
$631$	−1817.41	−	5593.40i	−0.114659	−	0.352884i	−0.991876	+	0.127211i	$0.959398\pi$
$632$	−3984.22	−	631.038i	−0.250765	−	0.0397173i
$633$	−1941.85	−	307.559i	−0.121930	−	0.0193118i
$634$	6636.24	+	20424.3i	0.415708	+	1.27942i
$635$	−6528.76	+	10880.2i	−0.408009	+	0.679950i
$636$	−652.624	−	474.159i	−0.0406891	−	0.0295623i
$637$	−17157.9	+	17157.9i	−1.06722	+	1.06722i
$638$	19559.8	−	3807.70i	1.21376	−	0.236282i
$639$			1321.00i			0.0817810i
$640$	1079.50	−	939.512i	0.0666733	−	0.0580273i
$641$	8626.00	−	26548.1i	0.531524	−	1.63586i	−0.219519	−	0.975608i	$-0.570449\pi$
$641$	8626.00	−	26548.1i	0.531524	−	1.63586i	0.751043	−	0.660254i	$-0.229551\pi$
$642$	−9763.94	+	19162.8i	−0.600237	+	1.17803i
$643$	3459.71	−	21843.8i	0.212189	−	1.33971i	−0.619730	−	0.784815i	$-0.712758\pi$
$643$	3459.71	−	21843.8i	0.212189	−	1.33971i	0.831920	−	0.554896i	$-0.187242\pi$
$644$	−142.402	+	103.461i	−0.00871338	+	0.00633064i
$645$	961.408	−	1147.14i	0.0586905	−	0.0700285i
$646$	12566.2	+	4083.01i	0.765342	+	0.248675i
$647$	2770.80	+	17494.2i	0.168364	+	1.06301i	0.916667	+	0.399652i	$0.130869\pi$
$647$	2770.80	+	17494.2i	0.168364	+	1.06301i	−0.748303	+	0.663357i	$0.769131\pi$
$648$	5018.94	+	5018.94i	0.304263	+	0.304263i
$649$	19.8735	+	564.587i	0.00120201	+	0.0341479i
$650$	9257.46	−	19037.6i	0.558627	−	1.14879i
$651$	−1567.95	+	2158.10i	−0.0943978	+	0.129927i
$652$	−11498.3	+	5858.66i	−0.690655	+	0.351906i
$653$	4376.97	+	2230.18i	0.262304	+	0.133650i	0.580197	−	0.814476i	$-0.302975\pi$
$653$	4376.97	+	2230.18i	0.262304	+	0.133650i	−0.317894	+	0.948126i	$0.602975\pi$
$654$	−8222.05	−	11316.7i	−0.491602	−	0.676632i
$655$	6060.22	−	15025.1i	0.361515	−	0.896303i
$656$	1572.44	−	510.917i	0.0935876	−	0.0304084i
$657$	2950.68	+	5791.04i	0.175216	+	0.343881i
$658$	8520.15	−	1349.46i	0.504788	−	0.0799505i
$659$	−4997.03			−0.295382			−0.147691	−	0.989034i	$-0.547184\pi$
$659$	−4997.03			−0.295382			−0.147691	+	0.989034i	$0.547184\pi$
$660$	−10910.4	+	1349.25i	−0.643464	+	0.0795752i
$661$	29077.8			1.71104			0.855520	−	0.517770i	$-0.173238\pi$
$661$	29077.8			1.71104			0.855520	+	0.517770i	$0.173238\pi$
$662$	−3826.47	+	606.054i	−0.224653	+	0.0355815i
$663$	29544.2	+	57983.7i	1.73062	+	3.39653i
$664$	6408.77	−	2082.34i	0.374561	−	0.121702i
$665$	−4477.15	+	1903.56i	−0.261077	+	0.111003i
$666$	5662.28	+	7793.45i	0.329443	+	0.453439i
$667$	−1425.31	−	726.230i	−0.0827407	−	0.0421585i
$668$	−4388.90	+	2236.26i	−0.254209	+	0.129526i
$669$	−14973.6	+	20609.3i	−0.865338	+	1.19104i
$670$	7715.00	+	12330.4i	0.444860	+	0.710991i
$671$	13997.3	−	5099.02i	0.805305	−	0.293361i
$672$	−1145.41	−	1145.41i	−0.0657514	−	0.0657514i
$673$	−4783.03	−	30198.9i	−0.273956	−	1.72969i	−0.614023	−	0.789288i	$-0.710450\pi$
$673$	−4783.03	−	30198.9i	−0.273956	−	1.72969i	0.340067	−	0.940401i	$-0.389550\pi$
$674$	−2199.75	−	714.742i	−0.125714	−	0.0408469i
$675$	4365.56	+	5779.09i	0.248934	+	0.329537i
$676$	−16093.3	+	11692.5i	−0.915640	+	0.665252i
$677$	−473.680	+	2990.70i	−0.0268907	+	0.169781i	−0.997479	−	0.0709650i	$-0.977392\pi$
$677$	−473.680	+	2990.70i	−0.0268907	+	0.169781i	0.970588	+	0.240746i	$0.0773921\pi$
$678$	−1360.23	+	2669.61i	−0.0770493	+	0.151218i
$679$	802.677	−	2470.39i	0.0453666	−	0.139624i
$680$	−705.634	+	10177.3i	−0.0397939	+	0.573946i
$681$			30241.7i			1.70171i
$682$	2621.58	−	2812.87i	0.147193	−	0.157933i
$683$	−15516.2	+	15516.2i	−0.869270	+	0.869270i	−0.992392	−	0.123122i	$-0.960709\pi$
$683$	−15516.2	+	15516.2i	−0.869270	+	0.869270i	0.123122	+	0.992392i	$0.460709\pi$
$684$	3449.00	+	2505.84i	0.192801	+	0.140078i
$685$	−19894.2	−	11937.6i	−1.10966	−	0.665860i
$686$	2923.09	+	8996.34i	0.162688	+	0.500702i
$687$	4956.47	+	785.028i	0.275257	+	0.0435964i
$688$	−313.978	−	49.7292i	−0.0173987	−	0.00275568i
$689$	783.175	+	2410.36i	0.0433042	+	0.133277i
$690$	756.732	+	454.083i	0.0417512	+	0.0250531i
$691$	−8128.46	−	5905.67i	−0.447498	−	0.325126i	0.341109	−	0.940024i	$-0.389197\pi$
$691$	−8128.46	−	5905.67i	−0.447498	−	0.325126i	−0.788607	+	0.614897i	$0.789197\pi$
$692$	−5328.93	+	5328.93i	−0.292739	+	0.292739i
$693$	963.697	+	4950.42i	0.0528252	+	0.271358i
$694$			11601.9i			0.634584i
$695$	−1477.69	+	21312.7i	−0.0806502	+	1.16322i
$696$	4549.10	−	14000.7i	0.247749	−	0.762493i
$697$	−5350.88	+	10501.7i	−0.290788	+	0.570703i
$698$	565.165	−	3568.31i	0.0306473	−	0.193500i
$699$	8977.00	−	6522.17i	0.485753	−	0.352920i
$700$	−2264.15	−	2997.26i	−0.122252	−	0.161837i
$701$	−15863.8	−	5154.48i	−0.854735	−	0.277720i	−0.151307	−	0.988487i	$-0.548348\pi$
$701$	−15863.8	−	5154.48i	−0.854735	−	0.277720i	−0.703428	+	0.710767i	$0.748348\pi$
$702$	−1535.01	−	9691.70i	−0.0825291	−	0.521068i
$703$	−10720.8	−	10720.8i	−0.575167	−	0.575167i
$704$	1438.02	+	1839.53i	0.0769852	+	0.0984799i
$705$	−22941.0	−	36665.1i	−1.22554	−	1.95870i
$706$	13767.2	−	18948.9i	0.733904	−	1.01013i
$707$	11505.1	−	5862.16i	0.612016	−	0.311838i
$708$	371.864	+	189.474i	0.0197394	+	0.0100577i
$709$	11429.6	+	15731.6i	0.605429	+	0.833302i	0.996192	−	0.0871899i	$-0.0277887\pi$
$709$	11429.6	+	15731.6i	0.605429	+	0.833302i	−0.390763	+	0.920491i	$0.627789\pi$
$710$	1477.30	−	628.105i	0.0780873	−	0.0332005i
$711$	8824.24	−	2867.17i	0.465450	−	0.151234i
$712$	2333.50	+	4579.76i	0.122826	+	0.241059i
$713$	−304.871	+	48.2868i	−0.0160133	+	0.00253626i
$714$	11547.4			0.605254
$715$	30222.8	+	16718.5i	1.58080	+	0.874455i
$716$	1986.17			0.103668
$717$	−183.798	+	29.1107i	−0.00957331	+	0.00151626i
$718$	−8598.44	−	16875.4i	−0.446923	−	0.877137i
$719$	25487.3	−	8281.32i	1.32200	−	0.429543i	0.438817	−	0.898577i	$-0.355398\pi$
$719$	25487.3	−	8281.32i	1.32200	−	0.429543i	0.883180	+	0.469034i	$0.155398\pi$
$720$	−1231.27	+	3052.69i	−0.0637316	+	0.158010i
$721$	−5052.57	−	6954.26i	−0.260981	−	0.359210i
$722$	6244.42	+	3181.69i	0.321874	+	0.164003i
$723$	−9489.23	+	4835.00i	−0.488117	+	0.248708i
$724$	−3568.19	+	4911.19i	−0.183164	+	0.252103i
$725$	14928.7	−	30700.2i	0.764740	−	1.57266i
$726$	−1261.18	−	17892.2i	−0.0644719	−	0.914658i
$727$	9901.76	+	9901.76i	0.505139	+	0.505139i	0.913030	−	0.407892i	$-0.133736\pi$
$727$	9901.76	+	9901.76i	0.505139	+	0.505139i	−0.407892	+	0.913030i	$0.633736\pi$
$728$	796.118	+	5026.49i	0.0405303	+	0.255898i
$729$	−5501.65	−	1787.60i	−0.279513	−	0.0908193i
$730$	5073.23	−	6053.29i	0.257217	−	0.306907i
$731$	1833.36	−	1332.01i	0.0927622	−	0.0673957i
$732$	1721.62	−	10869.9i	0.0869303	−	0.548856i
$733$	1764.72	−	3463.45i	0.0889239	−	0.174523i	−0.842261	−	0.539070i	$-0.818776\pi$
$733$	1764.72	−	3463.45i	0.0889239	−	0.174523i	0.931185	+	0.364547i	$0.118776\pi$
$734$	6.61641	−	20.3632i	0.000332719	−	0.00102400i
$735$	16284.0	−	14172.3i	0.817201	−	0.711229i
$736$		−	187.437i		−	0.00938726i
$737$	−20752.6	+	11510.9i	−1.03722	+	0.575319i
$738$	−2689.06	+	2689.06i	−0.134127	+	0.134127i
$739$	16569.2	+	12038.2i	0.824775	+	0.599234i	0.918076	−	0.396404i	$-0.129742\pi$
$739$	16569.2	+	12038.2i	0.824775	+	0.599234i	−0.0933012	+	0.995638i	$0.529742\pi$
$740$	6023.26	−	10037.8i	0.299216	−	0.498645i
$741$	−10212.1	−	31429.6i	−0.506276	−	1.55816i
$742$	444.177	+	70.3507i	0.0219761	+	0.00348067i
$743$	−24111.2	−	3818.84i	−1.19052	−	0.188559i	−0.470426	−	0.882440i	$-0.655900\pi$
$743$	−24111.2	−	3818.84i	−1.19052	−	0.188559i	−0.720090	+	0.693880i	$0.755900\pi$
$744$	−877.799	−	2701.59i	−0.0432549	−	0.133125i
$745$	14298.1	−	3573.89i	0.703145	−	0.175755i
$746$	809.989	+	588.492i	0.0397531	+	0.0288823i
$747$	−10959.8	+	10959.8i	−0.536810	+	0.536810i
$748$	−16521.3	−	2023.89i	−0.807594	−	0.0989314i
$749$		−	11989.7i		−	0.584906i
$750$	−9387.77	+	16326.8i	−0.457057	+	0.794893i
$751$	−2131.84	+	6561.12i	−0.103584	+	0.318800i	−0.989396	−	0.145246i	$-0.953603\pi$
$751$	−2131.84	+	6561.12i	−0.103584	+	0.318800i	0.885811	+	0.464046i	$0.153603\pi$
$752$	−4170.35	+	8184.77i	−0.202230	+	0.396899i
$753$	−890.145	+	5620.15i	−0.0430793	+	0.271992i
$754$	−37417.3	+	27185.2i	−1.80724	+	1.31303i
$755$	−14222.4	−	11919.7i	−0.685573	−	0.574575i
$756$	−1655.95	−	538.049i	−0.0796642	−	0.0258845i
$757$	−1787.83	−	11287.9i	−0.0858386	−	0.541964i	−0.992707	−	0.120550i	$-0.961534\pi$
$757$	−1787.83	−	11287.9i	−0.0858386	−	0.541964i	0.906869	−	0.421413i	$-0.138466\pi$
$758$	6146.84	+	6146.84i	0.294542	+	0.294542i
$759$	−804.838	+	1193.94i	−0.0384898	+	0.0570979i
$760$	1162.41	−	5048.53i	0.0554802	−	0.240960i
$761$	4054.89	−	5581.08i	0.193153	−	0.265853i	−0.701445	−	0.712723i	$-0.747462\pi$
$761$	4054.89	−	5581.08i	0.193153	−	0.265853i	0.894599	+	0.446871i	$0.147462\pi$
$762$	−13627.2	+	6943.40i	−0.647849	+	0.330095i
$763$	6948.21	+	3540.29i	0.329675	+	0.167978i
$764$	1488.16	+	2048.28i	0.0704711	+	0.0969951i
$765$	−9181.32	−	21594.4i	−0.433923	−	1.02058i
$766$	−22253.5	+	7230.61i	−1.04968	+	0.341061i
$767$	−595.279	−	1168.30i	−0.0280238	−	0.0549999i
$768$	1703.70	−	269.839i	0.0800479	−	0.0126783i
$769$	716.792			0.0336127			0.0168063	−	0.999859i	$-0.494650\pi$
$769$	716.792			0.0336127			0.0168063	+	0.999859i	$0.494650\pi$
$770$	5077.92	−	3431.52i	0.237656	−	0.160602i
$771$	41400.2			1.93384
$772$	2116.91	−	335.286i	0.0986909	−	0.0156311i
$773$	−148.145	−	290.752i	−0.00689317	−	0.0135286i	0.887534	−	0.460742i	$-0.152417\pi$
$773$	−148.145	−	290.752i	−0.00689317	−	0.0135286i	−0.894427	+	0.447213i	$0.852417\pi$
$774$	695.397	−	225.948i	0.0322940	−	0.0104929i
$775$	−1151.51	−	6485.77i	−0.0533722	−	0.300614i
$776$	1625.83	+	2237.76i	0.0752112	+	0.103519i
$777$	−11806.2	−	6015.55i	−0.545102	−	0.277743i
$778$	2762.69	−	1407.66i	0.127310	−	0.0648677i
$779$	3518.06	−	4842.20i	0.161807	−	0.222708i
$780$	21630.7	−	13534.1i	0.992951	−	0.621280i
$781$	896.477	+	2460.91i	0.0410736	+	0.112751i
$782$	944.825	+	944.825i	0.0432057	+	0.0432057i
$783$	−2475.38	−	15628.9i	−0.112979	−	0.713323i
$784$	−4360.56	−	1416.83i	−0.198641	−	0.0645423i
$785$	11892.9	−	1047.57i	0.540734	−	0.0476297i
$786$	15798.4	−	11478.2i	0.716933	−	0.520882i
$787$	3569.73	−	22538.4i	0.161686	−	1.02085i	−0.764731	−	0.644349i	$-0.777128\pi$
$787$	3569.73	−	22538.4i	0.161686	−	1.02085i	0.926418	−	0.376497i	$-0.122872\pi$
$788$	2955.98	−	5801.44i	0.133632	−	0.262268i
$789$	−7413.62	+	22816.8i	−0.334514	+	1.02953i
$790$	−7402.11	−	8505.02i	−0.333361	−	0.383032i
$791$		−	1670.31i		−	0.0750813i
$792$	−4867.98	−	2268.32i	−0.218404	−	0.101769i
$793$	−24449.0	+	24449.0i	−1.09484	+	1.09484i
$794$	−6230.62	−	4526.81i	−0.278484	−	0.202330i
$795$	−546.767	−	2187.46i	−0.0243922	−	0.0975866i
$796$	−2250.39	−	6925.99i	−0.100205	−	0.308398i
$797$	19211.6	+	3042.82i	0.853840	+	0.135235i	0.567986	−	0.823038i	$-0.307723\pi$
$797$	19211.6	+	3042.82i	0.853840	+	0.135235i	0.285854	+	0.958273i	$0.407723\pi$
$798$	−5791.77	−	917.326i	−0.256925	−	0.0406930i
$799$	−20235.7	−	62279.1i	−0.895980	−	2.75754i
$800$	3999.31	−	74.5300i	0.176746	−	0.00329379i
$801$	−9564.61	−	6949.10i	−0.421909	−	0.306535i
$802$	6305.26	−	6305.26i	0.277614	−	0.277614i
$803$	9426.86	+	8785.78i	0.414280	+	0.386106i
$804$			17531.7i			0.769022i
$805$	−490.808	−	34.0296i	−0.0214891	−	0.00148992i
$806$	−2757.82	+	8487.69i	−0.120521	+	0.370926i
$807$	13504.0	−	26503.1i	0.589051	−	1.15608i
$808$	−2151.00	+	13580.9i	−0.0936535	+	0.591305i
$809$	−12423.6	+	9026.26i	−0.539914	+	0.392270i	−0.824053	−	0.566513i	$-0.808292\pi$
$809$	−12423.6	+	9026.26i	−0.539914	+	0.392270i	0.284139	+	0.958783i	$0.408292\pi$
$810$	1740.75	+	19762.6i	0.0755110	+	0.857267i
$811$	−2469.28	−	802.318i	−0.106915	−	0.0347388i	0.255071	−	0.966922i	$-0.417901\pi$
$811$	−2469.28	−	802.318i	−0.106915	−	0.0347388i	−0.361986	+	0.932184i	$0.617901\pi$
$812$	1283.83	+	8105.76i	0.0554846	+	0.350316i
$813$	29048.2	+	29048.2i	1.25309	+	1.25309i
$814$	15837.2	+	10675.9i	0.681935	+	0.459694i
$815$	−35150.3	−	8093.25i	−1.51075	−	0.347846i
$816$	−7227.72	+	9948.10i	−0.310075	+	0.426781i
$817$	−1025.36	+	522.448i	−0.0439080	+	0.0223723i
$818$	−9395.04	−	4787.01i	−0.401577	−	0.204614i
$819$	−6880.36	−	9470.01i	−0.293552	−	0.404040i
$820$	4285.80	+	1728.63i	0.182520	+	0.0736177i
$821$	−24082.1	+	7824.76i	−1.02372	+	0.332626i	−0.772304	−	0.635253i	$-0.780896\pi$
$821$	−24082.1	+	7824.76i	−1.02372	+	0.332626i	−0.251414	+	0.967880i	$0.580896\pi$
$822$	−12695.8	−	24916.9i	−0.538706	−	1.05727i
$823$	−15470.8	+	2450.33i	−0.655258	+	0.103783i	−0.475206	−	0.879874i	$-0.657627\pi$
$823$	−15470.8	+	2450.33i	−0.655258	+	0.103783i	−0.180052	+	0.983657i	$0.557627\pi$
$824$	9153.58			0.386991
$825$	−25794.9	−	16697.9i	−1.08856	−	0.704663i
$826$	−232.666			−0.00980084
$827$	−27349.5	+	4331.73i	−1.14998	+	0.182139i	−0.702184	−	0.711996i	$-0.747792\pi$
$827$	−27349.5	+	4331.73i	−1.14998	+	0.182139i	−0.447798	+	0.894135i	$0.647792\pi$
$828$	195.727	+	384.135i	0.00821495	+	0.0161227i
$829$	−23902.8	+	7766.50i	−1.00142	+	0.325382i	−0.763434	−	0.645886i	$-0.776488\pi$
$829$	−23902.8	+	7766.50i	−1.00142	+	0.325382i	−0.237989	+	0.971268i	$0.576488\pi$
$830$	17467.6	+	7045.37i	0.730492	+	0.294637i
$831$	34343.5	+	47269.8i	1.43365	+	1.97325i
$832$	−4828.63	−	2460.31i	−0.201205	−	0.102519i
$833$	29122.4	−	14838.6i	1.21132	−	0.617200i
$834$	−15135.8	+	20832.6i	−0.628428	+	0.864957i
$835$	−13416.9	−	3089.20i	−0.556062	−	0.128031i
$836$	8125.74	+	2327.56i	0.336166	+	0.0962925i
$837$	−2159.05	−	2159.05i	−0.0891610	−	0.0891610i
$838$	−4621.29	−	29177.7i	−0.190501	−	1.20277i
$839$	−27152.4	−	8822.34i	−1.11729	−	0.363029i	−0.308556	−	0.951206i	$-0.599846\pi$
$839$	−27152.4	−	8822.34i	−1.11729	−	0.363029i	−0.808732	+	0.588177i	$0.799846\pi$
$840$	−397.269	−	4510.15i	−0.0163180	−	0.185256i
$841$	−40608.3	+	29503.6i	−1.66502	+	1.20971i
$842$	3471.90	−	21920.7i	0.142101	−	0.897193i
$843$	10063.1	−	19750.0i	0.411141	−	0.806909i
$844$	−360.667	+	1110.02i	−0.0147093	+	0.0452706i
$845$	−55467.8	−	3845.79i	−2.25817	−	0.156567i
$846$		−	21128.7i		−	0.858653i
$847$	5154.81	+	8568.21i	0.209116	+	0.347588i
$848$	−338.625	+	338.625i	−0.0137128	+	0.0137128i
$849$	−14606.0	−	10611.9i	−0.590431	−	0.428973i
$850$	−19783.8	+	20535.2i	−0.798329	+	0.828649i
$851$	−473.797	−	1458.20i	−0.0190853	−	0.0587384i
$852$	1911.07	+	302.684i	0.0768455	+	0.0121711i
$853$	−9674.05	−	1532.22i	−0.388316	−	0.0615032i	−0.0407757	−	0.999168i	$-0.512983\pi$
$853$	−9674.05	−	1532.22i	−0.388316	−	0.0615032i	−0.347540	+	0.937665i	$0.612983\pi$
$854$	1895.91	+	5835.01i	0.0759681	+	0.233806i
$855$	2889.56	+	11560.3i	0.115580	+	0.462404i
$856$	10329.1	+	7504.56i	0.412433	+	0.299650i
$857$	23049.9	−	23049.9i	0.918750	−	0.918750i	−0.0781883	−	0.996939i	$-0.524914\pi$
$857$	23049.9	−	23049.9i	0.918750	−	0.918750i	0.996939	+	0.0781883i	$0.0249135\pi$
$858$	20193.1	+	36405.4i	0.803475	+	1.44855i
$859$			48969.2i			1.94506i	0.232775	+	0.972531i	$0.425219\pi$
$859$			48969.2i			1.94506i	−0.232775	+	0.972531i	$0.574781\pi$
$860$	−583.326	−	670.241i	−0.0231294	−	0.0265756i
$861$	1616.42	−	4974.83i	0.0639808	−	0.196913i
$862$	−4499.50	+	8830.77i	−0.177789	+	0.348930i
$863$	−4270.25	+	26961.3i	−0.168437	+	1.06347i	0.748120	+	0.663564i	$0.230957\pi$
$863$	−4270.25	+	26961.3i	−0.168437	+	1.06347i	−0.916556	+	0.399905i	$0.869043\pi$
$864$	1500.01	−	1089.82i	0.0590642	−	0.0429127i
$865$	−20983.2	+	1848.27i	−0.824799	+	0.0726510i
$866$	31231.3	+	10147.7i	1.22550	+	0.398189i
$867$	−8534.20	−	53882.8i	−0.334298	−	2.11068i
$868$	1119.77	+	1119.77i	0.0437873	+	0.0437873i
$869$	14493.0	−	11329.7i	0.565757	−	0.442272i
$870$	34881.8	−	21825.2i	1.35931	−	0.850510i
$871$	32375.2	−	44560.6i	1.25946	−	1.73350i
$872$	−7398.96	+	3769.96i	−0.287340	+	0.146407i
$873$	−5668.72	−	2888.36i	−0.219768	−	0.111977i
$874$	−398.834	−	548.947i	−0.0154356	−	0.0212453i
$875$	530.923	−	10485.8i	0.0205125	−	0.405125i
$876$	9053.91	−	2941.79i	0.349205	−	0.113463i
$877$	−4359.44	−	8555.88i	−0.167854	−	0.329432i	0.791722	−	0.610881i	$-0.209185\pi$
$877$	−4359.44	−	8555.88i	−0.167854	−	0.329432i	−0.959576	+	0.281450i	$0.909185\pi$
$878$	9481.35	−	1501.70i	0.364442	−	0.0577219i
$879$	−5096.33			−0.195557
$880$	−222.095	+	6522.47i	−0.00850773	+	0.249855i
$881$	26264.4			1.00439			0.502196	−	0.864754i	$-0.332526\pi$
$881$	26264.4			1.00439			0.502196	+	0.864754i	$0.332526\pi$
$882$	10416.1	−	1649.74i	0.397650	−	0.0629816i
$883$	4152.97	+	8150.66i	0.158277	+	0.310636i	0.956503	−	0.291722i	$-0.0942281\pi$
$883$	4152.97	+	8150.66i	0.158277	+	0.310636i	−0.798226	+	0.602358i	$0.794228\pi$
$884$	36741.7	−	11938.1i	1.39792	−	0.454211i
$885$	456.435	+	1073.53i	0.0173366	+	0.0407756i
$886$	−17935.9	−	24686.6i	−0.680099	−	0.936075i
$887$	36730.0	+	18714.9i	1.39039	+	0.708437i	0.979159	−	0.203096i	$-0.0651005\pi$
$887$	36730.0	+	18714.9i	1.39039	+	0.708437i	0.411227	+	0.911533i	$0.365101\pi$
$888$	12572.1	−	6405.80i	0.475103	−	0.242077i
$889$	5011.57	−	6897.84i	0.189069	−	0.260232i
$890$	−3223.54	+	14000.4i	−0.121408	+	0.527297i
$891$	−32348.7	+	1138.68i	−1.21630	+	0.0428138i
$892$	10693.5	+	10693.5i	0.401395	+	0.401395i
$893$	5202.06	+	32844.5i	0.194939	+	1.23079i
$894$	16894.8	+	5489.45i	0.632042	+	0.205363i
$895$	4254.81	+	3565.93i	0.158908	+	0.133180i
$896$	−777.964	+	565.224i	−0.0290067	+	0.0210746i
$897$	522.797	−	3300.81i	0.0194601	−	0.122866i
$898$	7561.91	−	14841.1i	0.281007	−	0.551507i
$899$	−4447.28	+	13687.3i	−0.164989	+	0.507784i
$900$	−8118.39	+	4328.92i	−0.300681	+	0.160330i
$901$		−	3413.85i		−	0.126228i
$902$	−3184.60	+	6834.38i	−0.117556	+	0.252284i
$903$	−711.161	+	711.161i	−0.0262081	+	0.0262081i
$904$	1438.97	+	1045.47i	0.0529419	+	0.0384645i
$905$	−16461.3	+	4114.58i	−0.604632	+	0.151131i
$906$	−6911.85	−	21272.5i	−0.253456	−	0.780056i
$907$	23472.7	+	3717.71i	0.859315	+	0.136102i	0.570515	−	0.821287i	$-0.306744\pi$
$907$	23472.7	+	3717.71i	0.859315	+	0.136102i	0.288800	+	0.957389i	$0.406744\pi$
$908$	17731.9	+	2808.45i	0.648075	+	0.102645i
$909$	−9773.25	−	30079.0i	−0.356610	−	1.09753i
$910$	−7319.01	+	12197.2i	−0.266618	+	0.444321i
$911$	38180.2	+	27739.5i	1.38855	+	1.00884i	0.996023	+	0.0890950i	$0.0283975\pi$
$911$	38180.2	+	27739.5i	1.38855	+	1.00884i	0.392522	+	0.919742i	$0.371603\pi$
$912$	4415.44	−	4415.44i	0.160318	−	0.160318i
$913$	−12979.4	+	27854.8i	−0.470489	+	1.00970i
$914$			12552.6i			0.454269i
$915$	23203.7	−	20194.7i	0.838351	−	0.729636i
$916$	920.584	−	2833.27i	0.0332063	−	0.102198i
$917$	−4942.33	+	9699.86i	−0.177983	+	0.349310i
$918$	−2067.67	+	13054.7i	−0.0743390	+	0.469358i
$919$	11769.2	−	8550.82i	0.422448	−	0.306927i	−0.356174	−	0.934420i	$-0.615919\pi$
$919$	11769.2	−	8550.82i	0.422448	−	0.306927i	0.778622	+	0.627493i	$0.215919\pi$
$920$	336.521	−	401.531i	0.0120595	−	0.0143892i
$921$	50942.8	+	16552.3i	1.82261	+	0.592201i
$922$	3601.38	+	22738.2i	0.128639	+	0.812195i
$923$	−4298.46	−	4298.46i	−0.153289	−	0.153289i
$924$	7382.51	−	259.865i	0.262843	−	0.00925208i
$925$	30924.9	−	10689.1i	1.09925	−	0.379953i
$926$	−14357.1	+	19760.8i	−0.509507	+	0.701276i
$927$	−18759.4	+	9558.41i	−0.664661	+	0.338662i
$928$	−7786.68	−	3967.51i	−0.275442	−	0.140345i
$929$	15669.6	+	21567.4i	0.553395	+	0.761683i	0.990468	−	0.137743i	$-0.0439849\pi$
$929$	15669.6	+	21567.4i	0.553395	+	0.761683i	−0.437073	+	0.899426i	$0.643985\pi$
$930$	2969.94	−	7363.38i	0.104719	−	0.259629i
$931$	−15785.6	+	5129.04i	−0.555693	+	0.180556i
$932$	−2990.53	−	5869.25i	−0.105105	−	0.206281i
$933$	58226.9	−	9222.24i	2.04315	−	0.323604i
$934$	−14486.2			−0.507498
$935$	−31758.7	−	33997.7i	−1.11082	−	1.18914i
$936$	12464.9			0.435288
$937$	−29836.2	+	4725.60i	−1.04024	+	0.164758i	−0.653108	−	0.757265i	$-0.726535\pi$
$937$	−29836.2	+	4725.60i	−1.04024	+	0.164758i	−0.387135	+	0.922023i	$0.626535\pi$
$938$	−4437.11	−	8708.31i	−0.154453	−	0.303131i
$939$	9874.66	−	3208.47i	0.343181	−	0.111506i
$940$	−23628.6	+	10046.2i	−0.819872	+	0.348586i
$941$	−6079.01	−	8367.03i	−0.210595	−	0.289859i	0.690632	−	0.723206i	$-0.257332\pi$
$941$	−6079.01	−	8367.03i	−0.210595	−	0.289859i	−0.901227	+	0.433347i	$0.857332\pi$
$942$	12822.0	+	6533.11i	0.443484	+	0.225966i
$943$	539.305	−	274.789i	0.0186237	−	0.00948926i
$944$	145.630	−	200.442i	0.00502102	−	0.00691084i
$945$	−2581.39	−	4125.67i	−0.0888600	−	0.142019i
$946$	1142.13	−	892.842i	0.0392535	−	0.0306858i
$947$	−6886.74	−	6886.74i	−0.236314	−	0.236314i	0.579008	−	0.815322i	$-0.303440\pi$
$947$	−6886.74	−	6886.74i	−0.236314	−	0.236314i	−0.815322	+	0.579008i	$0.803440\pi$
$948$	−2125.97	−	13422.9i	−0.0728358	−	0.459867i
$949$	−28445.1	−	9242.36i	−0.972988	−	0.316143i
$950$	11554.2	−	8728.10i	0.394597	−	0.298081i
$951$	−58532.8	+	42526.6i	−1.99585	+	1.45007i
$952$	1072.37	−	6770.69i	0.0365081	−	0.230503i
$953$	−134.840	+	264.638i	−0.00458331	+	0.00899524i	−0.893287	−	0.449487i	$-0.851607\pi$
$953$	−134.840	+	264.638i	−0.00458331	+	0.00899524i	0.888704	+	0.458482i	$0.151607\pi$
$954$	340.380	−	1047.58i	0.0115516	−	0.0355521i
$955$	−489.476	+	7059.70i	−0.0165854	+	0.239211i
$956$			110.471i			0.00373733i
$957$	32563.6	+	58707.7i	1.09993	+	1.98302i
$958$	−19105.1	+	19105.1i	−0.644321	+	0.644321i
$959$	12612.5	+	9163.51i	0.424691	+	0.308556i
$960$	4134.15	+	2480.73i	0.138989	+	0.0834013i
$961$	−8347.77	−	25691.8i	−0.280211	−	0.862402i
$962$	−43784.2	−	6934.73i	−1.46742	−	0.232416i
$963$	−29005.1	−	4593.96i	−0.970588	−	0.153726i
$964$	1953.71	+	6012.91i	0.0652747	+	0.200895i
$965$	5136.86	+	3082.41i	0.171359	+	0.102825i
$966$	−479.753	−	348.561i	−0.0159791	−	0.0116095i
$967$	31358.1	−	31358.1i	1.04282	−	1.04282i	0.0437810	−	0.999041i	$-0.486060\pi$
$967$	31358.1	−	31358.1i	1.04282	−	1.04282i	0.999041	−	0.0437810i	$-0.0139404\pi$
$968$	−10608.0	−	922.117i	−0.352225	−	0.0306177i
$969$			44514.3i			1.47576i
$970$	−534.755	+	7712.76i	−0.0177010	+	0.255301i
$971$	−12188.8	+	37513.1i	−0.402838	+	1.23981i	0.519849	+	0.854258i	$0.325988\pi$
$971$	−12188.8	+	37513.1i	−0.402838	+	1.23981i	−0.922687	+	0.385550i	$0.874012\pi$
$972$	−8015.23	+	15730.8i	−0.264495	+	0.519100i
$973$	2245.68	−	14178.7i	0.0739911	−	0.467161i
$974$	14722.3	−	10696.4i	0.484327	−	0.351884i
$975$	70636.5	+	9842.31i	2.32018	+	0.323288i
$976$	−6213.55	−	2018.90i	−0.203782	−	0.0662127i
$977$	−4517.48	−	28522.3i	−0.147929	−	0.933990i	−0.944277	−	0.329151i	$-0.893238\pi$
$977$	−4517.48	−	28522.3i	−0.147929	−	0.933990i	0.796348	−	0.604839i	$-0.206762\pi$
$978$	−30742.4	−	30742.4i	−1.00515	−	1.00515i
$979$	−22533.9	−	6454.70i	−0.735636	−	0.210718i
$980$	−6797.52	−	10864.0i	−0.221570	−	0.354121i
$981$	11226.8	−	15452.4i	0.365387	−	0.502912i
$982$	−19117.1	+	9740.65i	−0.621233	+	0.316534i
$983$	8596.23	+	4380.00i	0.278919	+	0.142116i	0.587854	−	0.808967i	$-0.299973\pi$
$983$	8596.23	+	4380.00i	0.278919	+	0.142116i	−0.308936	+	0.951083i	$0.599973\pi$
$984$	3274.07	+	4506.37i	0.106071	+	0.145994i
$985$	16748.1	−	7120.83i	0.541767	−	0.230344i
$986$	59250.0	−	19251.5i	1.91370	−	0.621798i
$987$	13194.0	+	25894.7i	0.425501	+	0.835093i
$988$	−19376.7	+	3068.97i	−0.623942	+	0.0988228i
$989$	−116.376			−0.00374171
$990$	−6355.78	−	13599.1i	−0.204040	−	0.436575i
$991$	38768.3			1.24270			0.621351	−	0.783533i	$-0.286584\pi$
$991$	38768.3			1.24270			0.621351	+	0.783533i	$0.286584\pi$
$992$	−1665.56	+	263.799i	−0.0533081	+	0.00844317i
$993$	−5925.54	−	11629.5i	−0.189367	−	0.371653i
$994$	−1025.87	+	333.327i	−0.0327352	+	0.0106363i
$995$	7613.97	−	18877.3i	0.242592	−	0.601458i
$996$	13344.1	+	18366.6i	0.424522	+	0.584304i
$997$	−15163.0	−	7725.92i	−0.481661	−	0.245419i	0.196262	−	0.980551i	$-0.437120\pi$
$997$	−15163.0	−	7725.92i	−0.481661	−	0.245419i	−0.677923	+	0.735133i	$0.737120\pi$
$998$	−9583.38	+	4882.98i	−0.303964	+	0.154878i
$999$	8914.78	−	12270.1i	0.282334	−	0.388599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.4.k.a.7.17	✓	144
5.3	odd	4	inner	110.4.k.a.73.2	yes	144
11.8	odd	10	inner	110.4.k.a.107.2	yes	144
55.8	even	20	inner	110.4.k.a.63.17	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.4.k.a.7.17	✓	144	1.1	even	1	trivial
110.4.k.a.63.17	yes	144	55.8	even	20	inner
110.4.k.a.73.2	yes	144	5.3	odd	4	inner
110.4.k.a.107.2	yes	144	11.8	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	110.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.97538 - 0.312869i) q^{2} +(3.05899 + 6.00362i) q^{3} +(3.80423 - 1.23607i) q^{4} +(10.3687 + 4.18211i) q^{5} +(7.92101 + 10.9023i) q^{6} +(-6.69380 - 3.41066i) q^{7} +(7.12805 - 3.63192i) q^{8} +(-10.8157 + 14.8866i) q^{9} +(21.7905 + 5.01720i) q^{10} +(-10.0463 + 35.0724i) q^{11} +(19.0580 + 19.0580i) q^{12} +(-13.2463 - 83.6339i) q^{13} +(-14.2899 - 4.64306i) q^{14} +(6.61002 + 75.0427i) q^{15} +(12.9443 - 9.40456i) q^{16} +(-17.8428 + 112.655i) q^{17} +(-16.7076 + 32.7906i) q^{18} +(17.8986 - 55.0863i) q^{19} +(44.6143 + 3.09328i) q^{20} -50.6202i q^{21} +(-8.87209 + 72.4243i) q^{22} +(4.14181 - 4.14181i) q^{23} +(43.6094 + 31.6840i) q^{24} +(90.0199 + 86.7261i) q^{25} +(-52.3329 - 161.064i) q^{26} +(57.2279 + 9.06400i) q^{27} +(-29.6806 - 4.70094i) q^{28} +(-84.3925 - 259.733i) q^{29} +(36.5358 + 146.170i) q^{30} +(-42.6332 - 30.9749i) q^{31} +(22.6274 - 22.6274i) q^{32} +(-241.293 + 46.9724i) q^{33} +228.119i q^{34} +(-55.1423 - 63.3584i) q^{35} +(-22.7447 + 70.0010i) q^{36} +(118.837 - 233.230i) q^{37} +(18.1217 - 114.416i) q^{38} +(461.586 - 335.362i) q^{39} +(89.0977 - 7.84803i) q^{40} +(98.2775 + 31.9323i) q^{41} +(-15.8375 - 99.9940i) q^{42} +(-14.0489 - 14.0489i) q^{43} +(5.13362 + 145.841i) q^{44} +(-174.403 + 109.122i) q^{45} +(6.88580 - 9.47749i) q^{46} +(-511.548 + 260.647i) q^{47} +(96.0578 + 48.9439i) q^{48} +(-168.436 - 231.832i) q^{49} +(204.957 + 143.152i) q^{50} +(-730.919 + 237.490i) q^{51} +(-153.769 - 301.789i) q^{52} +(-29.5620 + 4.68216i) q^{53} +115.882 q^{54} +(-250.843 + 321.641i) q^{55} -60.1011 q^{56} +(385.469 - 61.0523i) q^{57} +(-247.970 - 486.668i) q^{58} +(14.7271 - 4.78513i) q^{59} +(117.904 + 277.309i) q^{60} +(-240.012 - 330.347i) q^{61} +(-93.9078 - 47.8484i) q^{62} +(123.172 - 62.7591i) q^{63} +(37.6183 - 51.7771i) q^{64} +(212.419 - 922.573i) q^{65} +(-461.948 + 168.281i) q^{66} +(459.956 + 459.956i) q^{67} +(71.3712 + 450.620i) q^{68} +(37.5357 + 12.1961i) q^{69} +(-128.750 - 107.904i) q^{70} +(58.0796 - 42.1973i) q^{71} +(-23.0282 + 145.394i) q^{72} +(160.356 - 314.716i) q^{73} +(161.777 - 497.898i) q^{74} +(-245.300 + 805.740i) q^{75} -231.685i q^{76} +(186.868 - 200.503i) q^{77} +(806.881 - 806.881i) q^{78} +(-407.935 - 296.382i) q^{79} +(173.546 - 43.3787i) q^{80} +(274.170 + 843.807i) q^{81} +(204.126 + 32.3303i) q^{82} +(831.952 + 131.768i) q^{83} +(-62.5700 - 192.571i) q^{84} +(-656.143 + 1093.47i) q^{85} +(-32.1474 - 23.3565i) q^{86} +(1301.18 - 1301.18i) q^{87} +(55.7700 + 286.485i) q^{88} +642.498i q^{89} +(-310.370 + 270.122i) q^{90} +(-196.579 + 605.008i) q^{91} +(10.6368 - 20.8760i) q^{92} +(55.5463 - 350.705i) q^{93} +(-928.952 + 674.923i) q^{94} +(415.963 - 496.319i) q^{95} +(205.063 + 66.6292i) q^{96} +(54.0877 + 341.497i) q^{97} +(-405.258 - 405.258i) q^{98} +(-413.451 - 528.889i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{3} + 32 q^{5} - 40 q^{7} - 44 q^{11} + 128 q^{12} - 256 q^{15} + 576 q^{16} - 640 q^{17} - 64 q^{20} + 312 q^{22} - 984 q^{23} - 520 q^{25} + 304 q^{26} - 364 q^{27} + 240 q^{28} - 432 q^{31}+ \cdots + 7044 q^{97}+O(q^{100}) \) 144 * q + 8 * q^3 + 32 * q^5 - 40 * q^7 - 44 * q^11 + 128 * q^12 - 256 * q^15 + 576 * q^16 - 640 * q^17 - 64 * q^20 + 312 * q^22 - 984 * q^23 - 520 * q^25 + 304 * q^26 - 364 * q^27 + 240 * q^28 - 432 * q^31 + 2368 * q^33 + 1808 * q^36 - 960 * q^37 + 72 * q^38 + 740 * q^41 + 2440 * q^42 + 2656 * q^45 + 720 * q^46 - 1980 * q^47 - 128 * q^48 - 1360 * q^50 - 3880 * q^51 - 1920 * q^52 - 3060 * q^53 - 3044 * q^55 - 64 * q^56 - 4400 * q^57 - 2016 * q^58 - 1120 * q^60 - 960 * q^61 + 80 * q^62 + 1800 * q^63 + 1552 * q^66 + 10160 * q^67 + 2560 * q^68 + 2304 * q^70 + 1312 * q^71 - 2460 * q^73 + 8644 * q^75 - 1272 * q^77 - 5312 * q^78 + 768 * q^80 + 2116 * q^81 + 1280 * q^82 + 320 * q^85 - 5488 * q^86 + 1248 * q^88 - 8480 * q^90 + 11796 * q^91 - 704 * q^92 + 688 * q^93 - 1280 * q^95 + 7044 * q^97

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