LMFDB - Embedded newform 714.2.bl.a.367.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [714,2,Mod(31,714)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(714, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([0, 8, 27])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("714.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.bl (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [192,0,0,0,0,0,0,0,0,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$5.70131870432$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$12$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			367.7
Character	$\chi$	$=$	714.367
Dual form			714.2.bl.a.607.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.991445 - 0.130526i) q^{2} +(0.442289 + 0.896873i) q^{3} +(0.965926 - 0.258819i) q^{4} +(-2.94516 + 2.58284i) q^{5} +(0.555570 + 0.831470i) q^{6} +(-2.43751 + 1.02886i) q^{7} +(0.923880 - 0.382683i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(-2.58284 + 2.94516i) q^{10} +(-0.0584024 + 0.00382789i) q^{11} +(0.659346 + 0.751840i) q^{12} +(-3.92397 - 3.92397i) q^{13} +(-2.28236 + 1.33821i) q^{14} +(-3.61909 - 1.49907i) q^{15} +(0.866025 - 0.500000i) q^{16} +(-1.36037 - 3.89222i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(0.607113 + 4.61148i) q^{19} +(-2.17632 + 3.25709i) q^{20} +(-2.00084 - 1.73109i) q^{21} +(-0.0574031 + 0.0114182i) q^{22} +(-1.58016 - 0.779247i) q^{23} +(0.751840 + 0.659346i) q^{24} +(1.35029 - 10.2565i) q^{25} +(-4.40259 - 3.37822i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(-2.08817 + 1.62467i) q^{28} +(1.83587 + 9.22956i) q^{29} +(-3.78379 - 1.01386i) q^{30} +(-3.30549 + 1.63009i) q^{31} +(0.793353 - 0.608761i) q^{32} +(-0.0292639 - 0.0506865i) q^{33} +(-1.85677 - 3.68136i) q^{34} +(4.52149 - 9.32583i) q^{35} +(-0.382683 + 0.923880i) q^{36} +(0.137713 - 2.10109i) q^{37} +(1.20384 + 4.49279i) q^{38} +(1.78378 - 5.25484i) q^{39} +(-1.73256 + 3.51329i) q^{40} +(-2.01165 + 10.1132i) q^{41} +(-2.20967 - 1.45511i) q^{42} +(1.12696 + 2.72072i) q^{43} +(-0.0554216 + 0.0188131i) q^{44} +(-0.256202 - 3.90888i) q^{45} +(-1.66835 - 0.566329i) q^{46} +(-3.06102 + 11.4239i) q^{47} +(0.831470 + 0.555570i) q^{48} +(4.88291 - 5.01569i) q^{49} -10.3450i q^{50} +(2.88915 - 2.94156i) q^{51} +(-4.80587 - 2.77467i) q^{52} +(6.05849 + 7.89558i) q^{53} +(-0.997859 - 0.0654031i) q^{54} +(0.162118 - 0.162118i) q^{55} +(-1.85824 + 1.88333i) q^{56} +(-3.86739 + 2.58411i) q^{57} +(3.02487 + 8.91097i) q^{58} +(4.06869 + 0.535653i) q^{59} +(-3.88376 - 0.511306i) q^{60} +(1.60031 + 4.71437i) q^{61} +(-3.06444 + 2.04760i) q^{62} +(0.667617 - 2.56013i) q^{63} +(0.707107 - 0.707107i) q^{64} +(21.6917 + 1.42175i) q^{65} +(-0.0356294 - 0.0464331i) q^{66} +(-8.49844 - 4.90657i) q^{67} +(-2.32140 - 3.40751i) q^{68} -1.76185i q^{69} +(3.26555 - 9.83622i) q^{70} +(4.77482 + 3.19043i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-4.96680 - 1.68600i) q^{73} +(-0.137713 - 2.10109i) q^{74} +(9.79600 - 3.32529i) q^{75} +(1.77997 + 4.29722i) q^{76} +(0.138418 - 0.0694181i) q^{77} +(1.08262 - 5.44271i) q^{78} +(3.95145 - 8.01275i) q^{79} +(-1.25917 + 3.70938i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(-0.674395 + 10.2893i) q^{82} +(3.46655 - 8.36899i) q^{83} +(-2.38070 - 1.15425i) q^{84} +(14.0595 + 7.94961i) q^{85} +(1.47245 + 2.55035i) q^{86} +(-7.46576 + 5.72868i) q^{87} +(-0.0524919 + 0.0258861i) q^{88} +(-0.739906 - 0.198257i) q^{89} +(-0.764221 - 3.84200i) q^{90} +(13.6019 + 5.52753i) q^{91} +(-1.72800 - 0.343720i) q^{92} +(-2.92396 - 2.24364i) q^{93} +(-1.54372 + 11.7257i) q^{94} +(-13.6987 - 12.0135i) q^{95} +(0.896873 + 0.442289i) q^{96} +(-4.91058 + 0.976775i) q^{97} +(4.18646 - 5.61013i) q^{98} +(0.0325162 - 0.0486640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 48 q^{10} + 16 q^{11} - 16 q^{14} + 32 q^{15} - 96 q^{18} + 32 q^{22} + 16 q^{25} + 32 q^{28} - 32 q^{29} + 64 q^{35} - 48 q^{37} - 64 q^{43} - 16 q^{46} + 48 q^{47} + 64 q^{49} + 16 q^{53} + 16 q^{58}+ \cdots - 32 q^{99}+O(q^{100}) $ 192 * q - 48 * q^10 + 16 * q^11 - 16 * q^14 + 32 * q^15 - 96 * q^18 + 32 * q^22 + 16 * q^25 + 32 * q^28 - 32 * q^29 + 64 * q^35 - 48 * q^37 - 64 * q^43 - 16 * q^46 + 48 * q^47 + 64 * q^49 + 16 * q^53 + 16 * q^58 + 48 * q^61 - 64 * q^65 + 16 * q^70 - 32 * q^71 + 240 * q^73 + 48 * q^74 + 16 * q^77 - 64 * q^78 - 64 * q^79 + 48 * q^80 - 64 * q^85 + 32 * q^86 + 144 * q^87 + 16 * q^88 + 144 * q^89 - 64 * q^91 + 48 * q^94 + 80 * q^95 - 80 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{16}\right)$

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 $

$2$	0.991445	−	0.130526i	0.701057	−	0.0922960i
$2$	0.991445	−	0.130526i	0.701057	−	0.0922960i
$3$	0.442289	+	0.896873i	0.255355	+	0.517810i
$3$	0.442289	+	0.896873i	0.255355	+	0.517810i
$4$	0.965926	−	0.258819i	0.482963	−	0.129410i
$5$	−2.94516	+	2.58284i	−1.31712	+	1.15508i	−0.340462	+	0.940258i	$0.610583\pi$
$5$	−2.94516	+	2.58284i	−1.31712	+	1.15508i	−0.976653	+	0.214821i	$0.931083\pi$
$6$	0.555570	+	0.831470i	0.226811	+	0.339446i
$7$	−2.43751	+	1.02886i	−0.921292	+	0.388871i
$7$	−2.43751	+	1.02886i	−0.921292	+	0.388871i
$8$	0.923880	−	0.382683i	0.326641	−	0.135299i
$9$	−0.608761	+	0.793353i	−0.202920	+	0.264451i
$10$	−2.58284	+	2.94516i	−0.816764	+	0.931341i
$11$	−0.0584024	+	0.00382789i	−0.0176090	+	0.00115415i	−0.0742051	−	0.997243i	$-0.523642\pi$
$11$	−0.0584024	+	0.00382789i	−0.0176090	+	0.00115415i	0.0565961	+	0.998397i	$0.481975\pi$
$12$	0.659346	+	0.751840i	0.190337	+	0.217037i
$13$	−3.92397	−	3.92397i	−1.08831	−	1.08831i	−0.995702	−	0.0926125i	$-0.970478\pi$
$13$	−3.92397	−	3.92397i	−1.08831	−	1.08831i	−0.0926125	−	0.995702i	$-0.529522\pi$
$14$	−2.28236	+	1.33821i	−0.609988	+	0.357652i
$15$	−3.61909	−	1.49907i	−0.934444	−	0.387059i
$16$	0.866025	−	0.500000i	0.216506	−	0.125000i
$17$	−1.36037	−	3.89222i	−0.329938	−	0.944003i
$17$	−1.36037	−	3.89222i	−0.329938	−	0.944003i
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	0.607113	+	4.61148i	0.139281	+	1.05795i	0.908181	+	0.418577i	$0.137471\pi$
$19$	0.607113	+	4.61148i	0.139281	+	1.05795i	−0.768900	+	0.639369i	$0.779196\pi$
$20$	−2.17632	+	3.25709i	−0.486640	+	0.728308i
$21$	−2.00084	−	1.73109i	−0.436618	−	0.377754i
$22$	−0.0574031	+	0.0114182i	−0.0122384	+	0.00243437i
$23$	−1.58016	−	0.779247i	−0.329485	−	0.162484i	0.270020	−	0.962855i	$-0.412970\pi$
$23$	−1.58016	−	0.779247i	−0.329485	−	0.162484i	−0.599506	+	0.800370i	$0.704636\pi$
$24$	0.751840	+	0.659346i	0.153469	+	0.134588i
$25$	1.35029	−	10.2565i	0.270059	−	2.05130i
$26$	−4.40259	−	3.37822i	−0.863418	−	0.662524i
$27$	−0.980785	−	0.195090i	−0.188752	−	0.0375451i
$28$	−2.08817	+	1.62467i	−0.394626	+	0.307034i
$29$	1.83587	+	9.22956i	0.340913	+	1.71389i	0.647519	+	0.762050i	$0.275807\pi$
$29$	1.83587	+	9.22956i	0.340913	+	1.71389i	−0.306605	+	0.951837i	$0.599193\pi$
$30$	−3.78379	−	1.01386i	−0.690823	−	0.185105i
$31$	−3.30549	+	1.63009i	−0.593684	+	0.292772i	−0.714203	−	0.699939i	$-0.753211\pi$
$31$	−3.30549	+	1.63009i	−0.593684	+	0.292772i	0.120519	+	0.992711i	$0.461544\pi$
$32$	0.793353	−	0.608761i	0.140246	−	0.107615i
$33$	−0.0292639	−	0.0506865i	−0.00509418	−	0.00882338i
$34$	−1.85677	−	3.68136i	−0.318433	−	0.631348i
$35$	4.52149	−	9.32583i	0.764272	−	1.57635i
$36$	−0.382683	+	0.923880i	−0.0637806	+	0.153980i
$37$	0.137713	−	2.10109i	0.0226399	−	0.345418i	−0.971479	−	0.237125i	$-0.923795\pi$
$37$	0.137713	−	2.10109i	0.0226399	−	0.345418i	0.994119	−	0.108293i	$-0.0345384\pi$
$38$	1.20384	+	4.49279i	0.195288	+	0.728826i
$39$	1.78378	−	5.25484i	0.285633	−	0.841447i
$40$	−1.73256	+	3.51329i	−0.273942	+	0.555500i
$41$	−2.01165	+	10.1132i	−0.314166	+	1.57942i	0.424550	+	0.905405i	$0.360432\pi$
$41$	−2.01165	+	10.1132i	−0.314166	+	1.57942i	−0.738716	+	0.674017i	$0.764568\pi$
$42$	−2.20967	−	1.45511i	−0.340959	−	0.224529i
$43$	1.12696	+	2.72072i	0.171860	+	0.414906i	0.986217	−	0.165458i	$-0.0529102\pi$
$43$	1.12696	+	2.72072i	0.171860	+	0.414906i	−0.814357	+	0.580364i	$0.802910\pi$
$44$	−0.0554216	+	0.0188131i	−0.00835513	+	0.00283618i
$45$	−0.256202	−	3.90888i	−0.0381923	−	0.582702i
$46$	−1.66835	−	0.566329i	−0.245985	−	0.0835006i
$47$	−3.06102	+	11.4239i	−0.446495	+	1.66634i	0.265462	+	0.964121i	$0.414475\pi$
$47$	−3.06102	+	11.4239i	−0.446495	+	1.66634i	−0.711958	+	0.702222i	$0.752191\pi$
$48$	0.831470	+	0.555570i	0.120012	+	0.0801897i
$49$	4.88291	−	5.01569i	0.697559	−	0.716527i
$50$		−	10.3450i		−	1.46300i
$51$	2.88915	−	2.94156i	0.404562	−	0.411901i
$52$	−4.80587	−	2.77467i	−0.666454	−	0.384777i
$53$	6.05849	+	7.89558i	0.832197	+	1.08454i	0.995195	+	0.0979143i	$0.0312171\pi$
$53$	6.05849	+	7.89558i	0.832197	+	1.08454i	−0.162997	+	0.986626i	$0.552116\pi$
$54$	−0.997859	−	0.0654031i	−0.135791	−	0.00890024i
$55$	0.162118	−	0.162118i	0.0218599	−	0.0218599i
$56$	−1.85824	+	1.88333i	−0.248318	+	0.251671i
$57$	−3.86739	+	2.58411i	−0.512249	+	0.342274i
$58$	3.02487	+	8.91097i	0.397185	+	1.17007i
$59$	4.06869	+	0.535653i	0.529698	+	0.0697360i	0.390632	−	0.920547i	$-0.372257\pi$
$59$	4.06869	+	0.535653i	0.529698	+	0.0697360i	0.139066	+	0.990283i	$0.455590\pi$
$60$	−3.88376	−	0.511306i	−0.501391	−	0.0660094i
$61$	1.60031	+	4.71437i	0.204899	+	0.603613i	0.999996	−	0.00286947i	$-0.000913381\pi$
$61$	1.60031	+	4.71437i	0.204899	+	0.603613i	−0.795097	+	0.606482i	$0.792580\pi$
$62$	−3.06444	+	2.04760i	−0.389185	+	0.260045i
$63$	0.667617	−	2.56013i	0.0841118	−	0.322547i
$64$	0.707107	−	0.707107i	0.0883883	−	0.0883883i
$65$	21.6917	+	1.42175i	2.69053	+	0.176346i
$66$	−0.0356294	−	0.0464331i	−0.00438568	−	0.00571553i
$67$	−8.49844	−	4.90657i	−1.03825	−	0.599434i	−0.118912	−	0.992905i	$-0.537941\pi$
$67$	−8.49844	−	4.90657i	−1.03825	−	0.599434i	−0.919337	+	0.393471i	$0.871274\pi$
$68$	−2.32140	−	3.40751i	−0.281511	−	0.413221i
$69$		−	1.76185i		−	0.212102i
$70$	3.26555	−	9.83622i	0.390307	−	1.17565i
$71$	4.77482	+	3.19043i	0.566666	+	0.378634i	0.805652	−	0.592389i	$-0.201815\pi$
$71$	4.77482	+	3.19043i	0.566666	+	0.378634i	−0.238986	+	0.971023i	$0.576815\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	−4.96680	−	1.68600i	−0.581320	−	0.197331i	0.0152624	−	0.999884i	$-0.495142\pi$
$73$	−4.96680	−	1.68600i	−0.581320	−	0.197331i	−0.596582	+	0.802552i	$0.703475\pi$
$74$	−0.137713	−	2.10109i	−0.0160088	−	0.244247i
$75$	9.79600	−	3.32529i	1.13114	−	0.383972i
$76$	1.77997	+	4.29722i	0.204176	+	0.492925i
$77$	0.138418	−	0.0694181i	0.0157742	−	0.00791093i
$78$	1.08262	−	5.44271i	0.122583	−	0.616265i
$79$	3.95145	−	8.01275i	0.444573	−	0.901504i	−0.553087	−	0.833124i	$-0.686550\pi$
$79$	3.95145	−	8.01275i	0.444573	−	0.901504i	0.997659	−	0.0683805i	$-0.0217832\pi$
$80$	−1.25917	+	3.70938i	−0.140779	+	0.414721i
$81$	−0.258819	−	0.965926i	−0.0287577	−	0.107325i
$82$	−0.674395	+	10.2893i	−0.0744745	+	1.13626i
$83$	3.46655	−	8.36899i	0.380503	−	0.918616i	−0.611365	−	0.791349i	$-0.709379\pi$
$83$	3.46655	−	8.36899i	0.380503	−	0.918616i	0.991868	−	0.127268i	$-0.0406207\pi$
$84$	−2.38070	−	1.15425i	−0.259755	−	0.125939i
$85$	14.0595	+	7.94961i	1.52496	+	0.862256i
$86$	1.47245	+	2.55035i	0.158778	+	0.275011i
$87$	−7.46576	+	5.72868i	−0.800413	+	0.614179i
$88$	−0.0524919	+	0.0258861i	−0.00559566	+	0.00275947i
$89$	−0.739906	−	0.198257i	−0.0784299	−	0.0210152i	0.219391	−	0.975637i	$-0.429593\pi$
$89$	−0.739906	−	0.198257i	−0.0784299	−	0.0210152i	−0.297821	+	0.954622i	$0.596260\pi$
$90$	−0.764221	−	3.84200i	−0.0805560	−	0.404982i
$91$	13.6019	+	5.52753i	1.42587	+	0.579442i
$92$	−1.72800	−	0.343720i	−0.180156	−	0.0358353i
$93$	−2.92396	−	2.24364i	−0.303201	−	0.232654i
$94$	−1.54372	+	11.7257i	−0.159222	+	1.20941i
$95$	−13.6987	−	12.0135i	−1.40546	−	1.23256i
$96$	0.896873	+	0.442289i	0.0915367	+	0.0451409i
$97$	−4.91058	+	0.976775i	−0.498594	+	0.0991765i	−0.437980	−	0.898985i	$-0.644306\pi$
$97$	−4.91058	+	0.976775i	−0.498594	+	0.0991765i	−0.0606140	+	0.998161i	$0.519306\pi$
$98$	4.18646	−	5.61013i	0.422896	−	0.566709i
$99$	0.0325162	−	0.0486640i	0.00326801	−	0.00489092i
$100$	−1.35029	−	10.2565i	−0.135029	−	1.02565i
$101$	−0.0339779	+	0.0588514i	−0.00338093	+	0.00585593i	−0.867711	−	0.497069i	$-0.834410\pi$
$101$	−0.0339779	+	0.0588514i	−0.00338093	+	0.00585593i	0.864330	+	0.502925i	$0.167743\pi$
$102$	2.48048	−	3.29351i	0.245605	−	0.326106i
$103$	−5.70708	+	3.29499i	−0.562336	+	0.324665i	−0.754082	−	0.656780i	$-0.771918\pi$
$103$	−5.70708	+	3.29499i	−0.562336	+	0.324665i	0.191747	+	0.981444i	$0.438585\pi$
$104$	−5.12692	−	2.12364i	−0.502736	−	0.208240i
$105$	10.3639	−	0.0695051i	1.01141	−	0.00678301i
$106$	7.03724	+	7.03724i	0.683517	+	0.683517i
$107$	4.58955	+	5.23338i	0.443688	+	0.505930i	0.929850	−	0.367939i	$-0.119937\pi$
$107$	4.58955	+	5.23338i	0.443688	+	0.505930i	−0.486161	+	0.873869i	$0.661603\pi$
$108$	−0.997859	+	0.0654031i	−0.0960190	+	0.00629342i
$109$	−12.0214	+	13.7078i	−1.15144	+	1.31297i	−0.209262	+	0.977860i	$0.567106\pi$
$109$	−12.0214	+	13.7078i	−1.15144	+	1.31297i	−0.942180	+	0.335108i	$0.891227\pi$
$110$	0.139570	−	0.181891i	0.0133075	−	0.0173426i
$111$	1.94532	−	0.805779i	0.184642	−	0.0764812i
$112$	−1.59652	+	2.10977i	−0.150857	+	0.199355i
$113$	−7.36634	−	11.0245i	−0.692967	−	1.03710i	−0.996444	−	0.0842598i	$-0.973147\pi$
$113$	−7.36634	−	11.0245i	−0.692967	−	1.03710i	0.303477	−	0.952839i	$-0.401853\pi$
$114$	−3.49701	+	3.06680i	−0.327525	+	0.287232i
$115$	6.66648	−	1.78628i	0.621652	−	0.166571i
$116$	4.16210	+	8.43991i	0.386442	+	0.783626i
$117$	5.50186	−	0.724334i	0.508647	−	0.0669647i
$118$	4.10379			0.377785
$119$	7.32045	+	8.08771i	0.671064	+	0.741399i
$120$	−3.91727			−0.357596
$121$	−10.9025	+	1.43534i	−0.991136	+	0.130486i
$122$	2.20197	+	4.46515i	0.199357	+	0.404256i
$123$	−9.96001	+	2.66878i	−0.898064	+	0.240635i
$124$	−2.77096	+	2.43007i	−0.248840	+	0.218227i
$125$	11.6324	+	17.4092i	1.04044	+	1.55712i
$126$	0.327741	−	2.62537i	0.0291975	−	0.233887i
$127$	2.27184	−	0.941026i	0.201593	−	0.0835026i	−0.279603	−	0.960116i	$-0.590203\pi$
$127$	2.27184	−	0.941026i	0.201593	−	0.0835026i	0.481196	+	0.876613i	$0.340203\pi$
$128$	0.608761	−	0.793353i	0.0538074	−	0.0701232i
$129$	−1.94170	+	2.21409i	−0.170957	+	0.194939i
$130$	21.6917	−	1.42175i	1.90249	−	0.124696i
$131$	−2.21202	−	2.52233i	−0.193265	−	0.220377i	0.647089	−	0.762415i	$-0.275986\pi$
$131$	−2.21202	−	2.52233i	−0.193265	−	0.220377i	−0.840354	+	0.542038i	$0.817653\pi$
$132$	−0.0413853	−	0.0413853i	−0.00360213	−	0.00360213i
$133$	−6.22439	−	10.6159i	−0.539723	−	0.920516i
$134$	−9.06617	−	3.75533i	−0.783198	−	0.324411i
$135$	3.39246	−	1.95864i	0.291976	−	0.168572i
$136$	−2.74631	−	3.07535i	−0.235494	−	0.263709i
$137$	8.82237	−	15.2808i	0.753746	−	1.30553i	−0.192250	−	0.981346i	$-0.561578\pi$
$137$	8.82237	−	15.2808i	0.753746	−	1.30553i	0.945996	−	0.324180i	$-0.105088\pi$
$138$	−0.229968	−	1.74678i	−0.0195762	−	0.148696i
$139$	7.37612	−	11.0391i	0.625634	−	0.936327i	−0.374325	−	0.927297i	$-0.622126\pi$
$139$	7.37612	−	11.0391i	0.625634	−	0.936327i	0.999959	−	0.00902987i	$-0.00287434\pi$
$140$	1.95372	−	10.1783i	0.165120	−	0.860224i
$141$	−11.5996	+	2.30731i	−0.976864	+	0.194310i
$142$	5.15040	+	2.53990i	0.432212	+	0.213143i
$143$	0.244190	+	0.214149i	0.0204202	+	0.0179080i
$144$	−0.130526	+	0.991445i	−0.0108772	+	0.0826204i
$145$	−29.2454	−	22.4408i	−2.42870	−	1.86360i
$146$	−5.14437	−	1.02328i	−0.425751	−	0.0846872i
$147$	6.65809	+	2.16097i	0.549150	+	0.178234i
$148$	−0.410783	−	2.06514i	−0.0337661	−	0.169754i
$149$	−15.3620	−	4.11624i	−1.25851	−	0.337216i	−0.432889	−	0.901447i	$-0.642506\pi$
$149$	−15.3620	−	4.11624i	−1.25851	−	0.337216i	−0.825616	+	0.564232i	$0.809172\pi$
$150$	9.27815	−	4.57548i	0.757558	−	0.373586i
$151$	−0.923070	+	0.708297i	−0.0751184	+	0.0576404i	−0.645638	−	0.763644i	$-0.723408\pi$
$151$	−0.923070	+	0.708297i	−0.0751184	+	0.0576404i	0.570520	+	0.821284i	$0.306742\pi$
$152$	2.32564	+	4.02812i	0.188634	+	0.326724i
$153$	3.91605	+	1.29018i	0.316594	+	0.104305i
$154$	0.128173	−	0.0868914i	0.0103285	−	0.00700191i
$155$	5.52495	−	13.3384i	0.443775	−	1.07137i
$156$	0.362944	−	5.53746i	0.0290588	−	0.443351i
$157$	−2.00923	−	7.49854i	−0.160354	−	0.598449i	−0.998587	−	0.0531372i	$-0.983078\pi$
$157$	−2.00923	−	7.49854i	−0.160354	−	0.598449i	0.838233	−	0.545312i	$-0.183589\pi$
$158$	2.87177	−	8.45996i	0.228466	−	0.673039i
$159$	−4.40173	+	8.92582i	−0.349080	+	0.707863i
$160$	−0.764221	+	3.84200i	−0.0604170	+	0.303737i
$161$	4.65338	+	0.273671i	0.366738	+	0.0215683i
$162$	−0.382683	−	0.923880i	−0.0300665	−	0.0725868i
$163$	7.69551	−	2.61227i	0.602759	−	0.204609i	−0.00334527	−	0.999994i	$-0.501065\pi$
$163$	7.69551	−	2.61227i	0.602759	−	0.204609i	0.606104	+	0.795385i	$0.292732\pi$
$164$	0.674395	+	10.2893i	0.0526614	+	0.803458i
$165$	0.217102	+	0.0736960i	0.0169013	+	0.00573723i
$166$	2.34452	−	8.74987i	0.181970	−	0.679122i
$167$	16.9409	+	11.3195i	1.31093	+	0.875933i	0.997287	−	0.0736096i	$-0.0234519\pi$
$167$	16.9409	+	11.3195i	1.31093	+	0.875933i	0.313639	+	0.949542i	$0.398452\pi$
$168$	−2.51099	−	0.833628i	−0.193727	−	0.0643158i
$169$			17.7952i			1.36886i
$170$	14.9768	+	6.04647i	1.14867	+	0.463743i
$171$	−4.02812	−	2.32564i	−0.308038	−	0.177846i
$172$	1.79274	+	2.33634i	0.136695	+	0.178144i
$173$	5.49145	+	0.359929i	0.417507	+	0.0273649i	0.272710	−	0.962096i	$-0.412080\pi$
$173$	5.49145	+	0.359929i	0.417507	+	0.0273649i	0.144798	+	0.989461i	$0.453747\pi$
$174$	−6.65414	+	6.65414i	−0.504449	+	0.504449i
$175$	7.26110	+	26.3896i	0.548887	+	1.99487i
$176$	−0.0486640	+	0.0325162i	−0.00366819	+	0.00245100i
$177$	1.31912	+	3.88601i	0.0991512	+	0.292090i
$178$	−0.759454	−	0.0999840i	−0.0569235	−	0.00749412i
$179$	10.2414	+	1.34831i	0.765478	+	0.100777i	0.503147	−	0.864201i	$-0.332175\pi$
$179$	10.2414	+	1.34831i	0.765478	+	0.100777i	0.262331	+	0.964978i	$0.415509\pi$
$180$	−1.25917	−	3.70938i	−0.0938526	−	0.276481i
$181$	3.36119	−	2.24587i	0.249835	−	0.166935i	−0.424347	−	0.905500i	$-0.639496\pi$
$181$	3.36119	−	2.24587i	0.249835	−	0.166935i	0.674182	+	0.738565i	$0.264496\pi$
$182$	14.2071	+	3.70483i	1.05310	+	0.274620i
$183$	−3.52039	+	3.52039i	−0.260235	+	0.260235i
$184$	−1.75808	−	0.115231i	−0.129607	−	0.00849491i
$185$	5.02119	+	6.54375i	0.369166	+	0.481106i
$186$	−3.19180	−	1.84279i	−0.234034	−	0.135120i
$187$	0.0943478	+	0.222108i	0.00689939	+	0.0162421i
$188$			11.8269i			0.862563i
$189$	2.59139	−	0.533551i	0.188496	−	0.0388101i
$190$	−15.1496	−	10.1227i	−1.09907	−	0.734374i
$191$	−2.58310	+	9.64027i	−0.186907	+	0.697546i	0.807308	+	0.590131i	$0.200924\pi$
$191$	−2.58310	+	9.64027i	−0.186907	+	0.697546i	−0.994214	+	0.107415i	$0.965743\pi$
$192$	0.946930	+	0.321439i	0.0683388	+	0.0231979i
$193$	0.848538	+	12.9462i	0.0610791	+	0.931887i	0.912933	+	0.408108i	$0.133811\pi$
$193$	0.848538	+	12.9462i	0.0610791	+	0.931887i	−0.851854	+	0.523779i	$0.824522\pi$
$194$	−4.74108	+	1.60938i	−0.340389	+	0.115547i
$195$	8.31887	+	20.0835i	0.595727	+	1.43821i
$196$	3.41838	−	6.10858i	0.244170	−	0.436327i
$197$	0.0140523	−	0.0706457i	0.00100119	−	0.00503330i	−0.980281	−	0.197606i	$-0.936683\pi$
$197$	0.0140523	−	0.0706457i	0.00100119	−	0.00503330i	0.981283	+	0.192573i	$0.0616832\pi$
$198$	0.0258861	−	0.0524919i	0.00183965	−	0.00373044i
$199$	4.64018	−	13.6695i	0.328933	−	0.969007i	−0.649126	−	0.760681i	$-0.724865\pi$
$199$	4.64018	−	13.6695i	0.328933	−	0.969007i	0.978059	−	0.208326i	$-0.0668015\pi$
$200$	−2.67748	−	9.99251i	−0.189327	−	0.706577i
$201$	0.641811	−	9.79214i	0.0452698	−	0.690684i
$202$	−0.0260055	+	0.0627829i	−0.00182974	+	0.00441739i
$203$	−13.9708	−	20.6083i	−0.980561	−	1.44642i
$204$	2.02937	−	3.58910i	0.142085	−	0.251287i
$205$	−20.1962	−	34.9808i	−1.41056	−	2.44317i
$206$	−5.22818	+	4.01172i	−0.364264	+	0.279510i
$207$	1.58016	−	0.779247i	0.109828	−	0.0541614i
$208$	−5.36025	−	1.43627i	−0.371666	−	0.0995877i
$209$	−0.0531091	−	0.266998i	−0.00367363	−	0.0184686i
$210$	10.2662	−	1.42167i	0.708432	−	0.0981045i
$211$	8.58347	+	1.70736i	0.590911	+	0.117539i	0.481483	−	0.876455i	$-0.340098\pi$
$211$	8.58347	+	1.70736i	0.590911	+	0.117539i	0.109427	+	0.993995i	$0.465098\pi$
$212$	7.89558	+	6.05849i	0.542270	+	0.416099i
$213$	−0.749563	+	5.69349i	−0.0513592	+	0.390112i
$214$	5.23338	+	4.58955i	0.357746	+	0.313735i
$215$	−10.3463	−	5.10221i	−0.705609	−	0.347968i
$216$	−0.980785	+	0.195090i	−0.0667340	+	0.0132742i
$217$	6.38004	−	7.37423i	0.433106	−	0.500595i
$218$	−10.1293	+	15.1596i	−0.686045	+	1.02674i
$219$	−0.684630	−	5.20028i	−0.0462630	−	0.351403i
$220$	0.114634	−	0.198553i	0.00772865	−	0.0133864i
$221$	−9.93493	+	20.6110i	−0.668296	+	1.38645i
$222$	1.82351	−	1.05280i	0.122386	−	0.0706594i
$223$	12.1533	+	5.03405i	0.813843	+	0.337105i	0.750486	−	0.660886i	$-0.229819\pi$
$223$	12.1533	+	5.03405i	0.813843	+	0.337105i	0.0633565	+	0.997991i	$0.479819\pi$
$224$	−1.30748	+	2.30011i	−0.0873597	+	0.153682i
$225$	7.31502	+	7.31502i	0.487668	+	0.487668i
$226$	−8.74231	−	9.96869i	−0.581530	−	0.663108i
$227$	19.5616	−	1.28214i	1.29835	−	0.0850984i	0.599505	−	0.800371i	$-0.295364\pi$
$227$	19.5616	−	1.28214i	1.29835	−	0.0850984i	0.698846	+	0.715272i	$0.253697\pi$
$228$	−3.06680	+	3.49701i	−0.203104	+	0.231595i
$229$	14.2735	−	18.6016i	0.943221	−	1.22923i	−0.0300448	−	0.999549i	$-0.509565\pi$
$229$	14.2735	−	18.6016i	0.943221	−	1.22923i	0.973266	−	0.229681i	$-0.0737683\pi$
$230$	6.37629	−	2.64115i	0.420440	−	0.174152i
$231$	0.123480	+	0.0934406i	0.00812439	+	0.00614794i
$232$	5.22813	+	7.82444i	0.343243	+	0.513700i
$233$	−1.01040	+	0.886093i	−0.0661932	+	0.0580499i	−0.691803	−	0.722086i	$-0.743183\pi$
$233$	−1.01040	+	0.886093i	−0.0661932	+	0.0580499i	0.625610	+	0.780136i	$0.284850\pi$
$234$	5.36025	−	1.43627i	0.350410	−	0.0938922i
$235$	−20.4908	−	41.5513i	−1.33667	−	2.71050i
$236$	4.06869	−	0.535653i	0.264849	−	0.0348680i
$237$	8.93409			0.580332
$238$	8.31348	+	7.06301i	0.538883	+	0.457827i
$239$	−27.6716			−1.78993			−0.894964	−	0.446139i	$-0.852799\pi$
$239$	−27.6716			−1.78993			−0.894964	+	0.446139i	$0.852799\pi$
$240$	−3.88376	+	0.511306i	−0.250695	+	0.0330047i
$241$	−3.09286	−	6.27171i	−0.199229	−	0.403996i	0.774215	−	0.632923i	$-0.218145\pi$
$241$	−3.09286	−	6.27171i	−0.199229	−	0.403996i	−0.973444	+	0.228927i	$0.926478\pi$
$242$	−10.6219	+	2.84612i	−0.682800	+	0.182956i
$243$	0.751840	−	0.659346i	0.0482305	−	0.0422971i
$244$	2.76595	+	4.13954i	0.177072	+	0.265007i
$245$	−1.42626	+	27.3838i	−0.0911204	+	1.74949i
$246$	−9.52645	+	3.94599i	−0.607385	+	0.251587i
$247$	15.7130	−	20.4776i	0.999797	−	1.30296i
$248$	−2.43007	+	2.77096i	−0.154309	+	0.175956i
$249$	9.03914	−	0.592456i	0.572832	−	0.0375454i
$250$	13.8053	+	15.7419i	0.873122	+	0.995605i
$251$	9.59545	+	9.59545i	0.605659	+	0.605659i	0.941809	−	0.336149i	$-0.109125\pi$
$251$	9.59545	+	9.59545i	0.605659	+	0.605659i	−0.336149	+	0.941809i	$0.609125\pi$
$252$	−0.0177433	−	2.64569i	−0.00111772	−	0.166663i
$253$	0.0952678	+	0.0394612i	0.00598943	+	0.00248090i
$254$	2.12957	−	1.22951i	0.133621	−	0.0771463i
$255$	−0.911441	+	16.1256i	−0.0570766	+	1.00982i
$256$	0.500000	−	0.866025i	0.0312500	−	0.0541266i
$257$	2.46145	+	18.6965i	0.153541	+	1.16626i	0.878595	+	0.477567i	$0.158481\pi$
$257$	2.46145	+	18.6965i	0.153541	+	1.16626i	−0.725055	+	0.688691i	$0.758186\pi$
$258$	−1.63609	+	2.44859i	−0.101859	+	0.152442i
$259$	1.82604	+	5.26313i	0.113465	+	0.327035i
$260$	21.3206	−	4.24092i	1.32225	−	0.263011i
$261$	−8.43991	−	4.16210i	−0.522417	−	0.257628i
$262$	−2.52233	−	2.21202i	−0.155830	−	0.136659i
$263$	2.43106	−	18.4657i	0.149905	−	1.13864i	−0.736734	−	0.676183i	$-0.763633\pi$
$263$	2.43106	−	18.4657i	0.149905	−	1.13864i	0.886639	−	0.462462i	$-0.153034\pi$
$264$	−0.0464331	−	0.0356294i	−0.00285776	−	0.00219284i
$265$	−38.2362	−	7.60565i	−2.34883	−	0.467211i
$266$	−7.55679	−	9.71264i	−0.463337	−	0.595520i
$267$	−0.149441	−	0.751288i	−0.00914561	−	0.0459781i
$268$	−9.47877	−	2.53983i	−0.579008	−	0.155145i
$269$	−20.4495	+	10.0846i	−1.24683	+	0.614866i	−0.941382	−	0.337343i	$-0.890472\pi$
$269$	−20.4495	+	10.0846i	−1.24683	+	0.614866i	−0.305444	+	0.952210i	$0.598805\pi$
$270$	3.10778	−	2.38468i	0.189133	−	0.145127i
$271$	8.99513	+	15.5800i	0.546415	+	0.946419i	0.998516	+	0.0544524i	$0.0173413\pi$
$271$	8.99513	+	15.5800i	0.546415	+	0.946419i	−0.452101	+	0.891967i	$0.649325\pi$
$272$	−3.12423	−	2.69058i	−0.189434	−	0.163140i
$273$	1.05849	+	14.6440i	0.0640628	+	0.886293i
$274$	6.75235	−	16.3016i	0.407924	−	0.984816i
$275$	−0.0395996	+	0.604173i	−0.00238795	+	0.0364330i
$276$	−0.456001	−	1.70182i	−0.0274480	−	0.102437i
$277$	0.177919	−	0.524133i	0.0106901	−	0.0314921i	−0.941454	−	0.337141i	$-0.890540\pi$
$277$	0.177919	−	0.524133i	0.0106901	−	0.0314921i	0.952144	+	0.305649i	$0.0988734\pi$
$278$	5.87211	−	11.9075i	0.352186	−	0.714163i
$279$	0.719020	−	3.61476i	0.0430466	−	0.216410i
$280$	0.608474	−	10.3462i	0.0363633	−	0.618306i
$281$	11.1133	+	26.8300i	0.662967	+	1.60054i	0.793131	+	0.609051i	$0.208449\pi$
$281$	11.1133	+	26.8300i	0.662967	+	1.60054i	−0.130165	+	0.991492i	$0.541551\pi$
$282$	−11.1992	+	3.80162i	−0.666904	+	0.226383i
$283$	−1.23915	−	18.9057i	−0.0736597	−	1.12383i	−0.861435	−	0.507868i	$-0.830434\pi$
$283$	−1.23915	−	18.9057i	−0.0736597	−	1.12383i	0.787775	−	0.615963i	$-0.211233\pi$
$284$	5.43786	+	1.84591i	0.322678	+	0.109534i
$285$	4.71576	−	17.5995i	0.279337	−	1.04250i
$286$	0.270053	+	0.180444i	0.0159686	+	0.0106699i
$287$	−5.50164	−	26.7208i	−0.324751	−	1.57728i
$288$			1.00000i			0.0589256i
$289$	−13.2988	+	10.5897i	−0.782282	+	0.622924i
$290$	−31.9243	−	18.4315i	−1.87466	−	1.08233i
$291$	−3.04794	−	3.97215i	−0.178673	−	0.232852i
$292$	−5.23393	−	0.343050i	−0.306292	−	0.0200755i
$293$	6.27497	−	6.27497i	0.366588	−	0.366588i	−0.499643	−	0.866231i	$-0.666536\pi$
$293$	6.27497	−	6.27497i	0.366588	−	0.366588i	0.866231	+	0.499643i	$0.166536\pi$
$294$	6.88320	+	1.27343i	0.401436	+	0.0742678i
$295$	−13.3664	+	8.93116i	−0.778224	+	0.519992i
$296$	−0.676824	−	1.99386i	−0.0393396	−	0.115891i
$297$	0.0580270	+	0.00763940i	0.00336707	+	0.000443283i
$298$	−15.7679	−	2.07588i	−0.913408	−	0.120252i
$299$	3.14275	+	9.25824i	0.181750	+	0.535418i
$300$	8.60156	−	5.74738i	0.496611	−	0.331825i
$301$	−5.54621	−	5.47231i	−0.319678	−	0.315419i
$302$	−0.822722	+	0.822722i	−0.0473423	+	0.0473423i
$303$	−0.0678103	−	0.00444452i	−0.00389560	−	0.000255331i
$304$	2.83152	+	3.69010i	0.162399	+	0.211642i
$305$	−16.8896	−	9.75122i	−0.967096	−	0.558353i
$306$	4.05095	+	0.767998i	0.231577	+	0.0439035i
$307$			22.4455i			1.28103i	0.767945	+	0.640516i	$0.221279\pi$
$307$			22.4455i			1.28103i	−0.767945	+	0.640516i	$0.778721\pi$
$308$	0.115735	−	0.102878i	0.00659461	−	0.00586202i
$309$	−5.47936	−	3.66119i	−0.311710	−	0.208278i
$310$	3.73667	−	13.9454i	0.212229	−	0.792048i
$311$	−32.6953	−	11.0986i	−1.85398	−	0.629342i	−0.992607	−	0.121369i	$-0.961271\pi$
$311$	−32.6953	−	11.0986i	−1.85398	−	0.629342i	−0.861373	−	0.507972i	$-0.830395\pi$
$312$	−0.362944	−	5.53746i	−0.0205477	−	0.313497i
$313$	7.71893	−	2.62022i	0.436300	−	0.148104i	−0.0946433	−	0.995511i	$-0.530171\pi$
$313$	7.71893	−	2.62022i	0.436300	−	0.148104i	0.530943	+	0.847407i	$0.321838\pi$
$314$	−2.97080	−	7.17214i	−0.167652	−	0.404747i
$315$	4.64617	+	9.26435i	0.261782	+	0.521987i
$316$	1.74296	−	8.76243i	0.0980489	−	0.492925i
$317$	−14.5470	+	29.4984i	−0.817041	+	1.65680i	−0.0648091	+	0.997898i	$0.520644\pi$
$317$	−14.5470	+	29.4984i	−0.817041	+	1.65680i	−0.752232	+	0.658898i	$0.771023\pi$
$318$	−3.19902	+	9.42400i	−0.179392	+	0.528471i
$319$	−0.142549	−	0.532001i	−0.00798122	−	0.0297863i
$320$	−0.256202	+	3.90888i	−0.0143221	+	0.218513i
$321$	−2.66377	+	6.43090i	−0.148677	+	0.358938i
$322$	4.64929	−	0.336059i	0.259095	−	0.0187278i
$323$	17.1230	−	8.63633i	0.952750	−	0.480538i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−45.5448	+	34.9477i	−2.52637	+	1.93855i
$326$	7.28870	−	3.59439i	0.403684	−	0.199075i
$327$	−17.6111	−	4.71887i	−0.973894	−	0.260954i
$328$	2.01165	+	10.1132i	0.111075	+	0.558410i
$329$	−4.29225	−	30.9952i	−0.236639	−	1.70882i
$330$	0.224863	+	0.0447281i	0.0123783	+	0.00246220i
$331$	21.3096	+	16.3514i	1.17128	+	0.898755i	0.996311	−	0.0858184i	$-0.0273505\pi$
$331$	21.3096	+	16.3514i	1.17128	+	0.898755i	0.174970	+	0.984574i	$0.444017\pi$
$332$	1.18238	−	8.98104i	0.0648913	−	0.492898i
$333$	1.58308	+	1.38832i	0.0867520	+	0.0760795i
$334$	18.2735	+	9.01147i	0.999879	+	0.493086i
$335$	37.7021	−	7.49942i	2.05989	−	0.409737i
$336$	−2.59832	−	0.498747i	−0.141750	−	0.0272089i
$337$	−10.0623	+	15.0593i	−0.548130	+	0.820335i	−0.997325	−	0.0730993i	$-0.976711\pi$
$337$	−10.0623	+	15.0593i	−0.548130	+	0.820335i	0.449195	+	0.893434i	$0.351711\pi$
$338$	2.32273	+	17.6429i	0.126340	+	0.959648i
$339$	6.62953	−	11.4827i	0.360067	−	0.623654i
$340$	15.6379	+	4.03987i	0.848085	+	0.219093i
$341$	0.186809	−	0.107854i	0.0101163	−	0.00584063i
$342$	−4.29722	−	1.77997i	−0.232367	−	0.0962495i
$343$	−6.74174	+	17.2496i	−0.364020	+	0.931391i
$344$	2.08235	+	2.08235i	0.112273	+	0.112273i
$345$	4.55057	+	5.18893i	0.244995	+	0.279363i
$346$	5.49145	−	0.359929i	0.295222	−	0.0193499i
$347$	8.91725	−	10.1682i	0.478703	−	0.545856i	−0.461201	−	0.887296i	$-0.652581\pi$
$347$	8.91725	−	10.1682i	0.478703	−	0.545856i	0.939904	+	0.341440i	$0.110915\pi$
$348$	−5.72868	+	7.46576i	−0.307089	+	0.400207i
$349$	−15.0309	+	6.22601i	−0.804587	+	0.333271i	−0.746792	−	0.665058i	$-0.768407\pi$
$349$	−15.0309	+	6.22601i	−0.804587	+	0.333271i	−0.0577948	+	0.998328i	$0.518407\pi$
$350$	10.6435	+	25.2161i	0.568920	+	1.34786i
$351$	3.08305	+	4.61411i	0.164561	+	0.246283i
$352$	−0.0440035	+	0.0385900i	−0.00234539	+	0.00205685i
$353$	−22.8109	+	6.11216i	−1.21410	+	0.325318i	−0.808370	−	0.588675i	$-0.799650\pi$
$353$	−22.8109	+	6.11216i	−1.21410	+	0.325318i	−0.405732	+	0.913992i	$0.632983\pi$
$354$	1.81506	+	3.68058i	0.0964694	+	0.195621i
$355$	−22.3030	+	2.93624i	−1.18372	+	0.155839i
$356$	−0.766007			−0.0405983
$357$	−4.01590	+	10.1426i	−0.212544	+	0.536804i
$358$	10.3298			0.545945
$359$	7.77347	−	1.02340i	0.410268	−	0.0540128i	0.0774322	−	0.996998i	$-0.475328\pi$
$359$	7.77347	−	1.02340i	0.410268	−	0.0540128i	0.332836	+	0.942985i	$0.391995\pi$
$360$	−1.73256	−	3.51329i	−0.0913142	−	0.185167i
$361$	−2.54458	+	0.681819i	−0.133925	+	0.0358852i
$362$	3.03929	−	2.66538i	0.159741	−	0.140089i
$363$	−6.10937	−	9.14332i	−0.320659	−	0.479900i
$364$	14.5691	+	1.81874i	0.763628	+	0.0953281i
$365$	18.9827	−	7.86288i	0.993598	−	0.411562i
$366$	−3.03077	+	3.94977i	−0.158421	+	0.206458i
$367$	−5.86608	+	6.68898i	−0.306207	+	0.349162i	−0.884393	−	0.466743i	$-0.845427\pi$
$367$	−5.86608	+	6.68898i	−0.306207	+	0.349162i	0.578186	+	0.815905i	$0.303761\pi$
$368$	−1.75808	+	0.115231i	−0.0916462	+	0.00600681i
$369$	−6.79875	−	7.75249i	−0.353929	−	0.403579i
$370$	5.83237	+	5.83237i	0.303210	+	0.303210i
$371$	−22.8910	−	13.0122i	−1.18844	−	0.675562i
$372$	−3.40503	−	1.41041i	−0.176542	−	0.0731262i
$373$	9.47370	−	5.46965i	0.490530	−	0.283208i	−0.234264	−	0.972173i	$-0.575268\pi$
$373$	9.47370	−	5.46965i	0.490530	−	0.283208i	0.724794	+	0.688965i	$0.241935\pi$
$374$	0.122532	+	0.207893i	0.00633595	+	0.0107499i
$375$	−10.4689	+	18.1327i	−0.540612	+	0.936368i
$376$	1.54372	+	11.7257i	0.0796111	+	0.604706i
$377$	29.0126	−	43.4205i	1.49423	−	2.23627i
$378$	2.49958	−	0.867231i	0.128565	−	0.0446056i
$379$	13.9672	−	2.77825i	0.717447	−	0.142709i	0.177150	−	0.984184i	$-0.443312\pi$
$379$	13.9672	−	2.77825i	0.717447	−	0.142709i	0.540296	+	0.841475i	$0.318312\pi$
$380$	−16.3413	−	8.05863i	−0.838290	−	0.413399i
$381$	1.84879	+	1.62134i	0.0947163	+	0.0830640i
$382$	−1.30270	+	9.89496i	−0.0666517	+	0.506270i
$383$	4.22906	+	3.24507i	0.216095	+	0.165816i	0.711137	−	0.703054i	$-0.248181\pi$
$383$	4.22906	+	3.24507i	0.216095	+	0.165816i	−0.495042	+	0.868869i	$0.664847\pi$
$384$	0.980785	+	0.195090i	0.0500505	+	0.00995566i
$385$	−0.228368	+	0.561959i	−0.0116387	+	0.0286401i
$386$	2.53110	+	12.7247i	0.128829	+	0.647669i
$387$	−2.84455	−	0.762194i	−0.144596	−	0.0387445i
$388$	−4.49045	+	2.21444i	−0.227968	+	0.112421i
$389$	−0.429520	+	0.329582i	−0.0217775	+	0.0167105i	−0.619593	−	0.784923i	$-0.712702\pi$
$389$	−0.429520	+	0.329582i	−0.0217775	+	0.0167105i	0.597815	+	0.801634i	$0.296036\pi$
$390$	10.8691	+	18.8259i	0.550380	+	0.953286i
$391$	−0.883407	+	7.21038i	−0.0446758	+	0.364645i
$392$	2.59180	−	6.50250i	0.130906	−	0.328426i
$393$	1.28385	−	3.09950i	0.0647619	−	0.156349i
$394$	0.00471097	−	0.0718755i	0.000237335	−	0.00362104i
$395$	9.05796	+	33.8048i	0.455755	+	1.70090i
$396$	0.0188131	−	0.0554216i	0.000945395	−	0.00278504i
$397$	2.33030	−	4.72539i	0.116955	−	0.237160i	−0.830522	−	0.556986i	$-0.811958\pi$
$397$	2.33030	−	4.72539i	0.116955	−	0.237160i	0.947476	+	0.319826i	$0.103624\pi$
$398$	2.81625	−	14.1582i	0.141166	−	0.709689i
$399$	6.76814	−	10.2778i	0.338831	−	0.514533i
$400$	−3.95886	−	9.55754i	−0.197943	−	0.477877i
$401$	−17.5453	+	5.95584i	−0.876172	+	0.297420i	−0.723057	−	0.690788i	$-0.757264\pi$
$401$	−17.5453	+	5.95584i	−0.876172	+	0.297420i	−0.153115	+	0.988208i	$0.548930\pi$
$402$	−0.641811	−	9.79214i	−0.0320106	−	0.488387i
$403$	19.3671	+	6.57424i	0.964743	+	0.327486i
$404$	−0.0175882	+	0.0656402i	−0.000875048	+	0.00326572i
$405$	3.25709	+	2.17632i	0.161846	+	0.108142i
$406$	−16.5412	−	18.6084i	−0.820928	−	0.923521i
$407$			0.123236i			0.00610858i
$408$	1.54354	−	3.82328i	0.0764167	−	0.189281i
$409$	7.44692	+	4.29948i	0.368227	+	0.212596i	0.672683	−	0.739930i	$-0.265142\pi$
$409$	7.44692	+	4.29948i	0.368227	+	0.212596i	−0.304457	+	0.952526i	$0.598475\pi$
$410$	−24.5893	−	32.0454i	−1.21438	−	1.58261i
$411$	17.6070	+	1.15402i	0.868487	+	0.0569236i
$412$	−4.65981	+	4.65981i	−0.229573	+	0.229573i
$413$	−10.4686	+	2.88043i	−0.515125	+	0.141737i
$414$	1.46493	−	0.978832i	0.0719972	−	0.0481070i
$415$	11.4062	+	33.6016i	0.559908	+	1.64944i
$416$	−5.50186	−	0.724334i	−0.269751	−	0.0355134i
$417$	13.1631	+	1.73295i	0.644598	+	0.0848630i
$418$	−0.0875049	−	0.257781i	−0.00428001	−	0.0126085i
$419$	−22.8827	+	15.2897i	−1.11789	+	0.746953i	−0.970254	−	0.242089i	$-0.922168\pi$
$419$	−22.8827	+	15.2897i	−1.11789	+	0.746953i	−0.147639	+	0.989041i	$0.547168\pi$
$420$	9.99276	−	2.74951i	0.487597	−	0.134162i
$421$	−21.9966	+	21.9966i	−1.07205	+	1.07205i	−0.0748526	+	0.997195i	$0.523849\pi$
$421$	−21.9966	+	21.9966i	−1.07205	+	1.07205i	−0.997195	+	0.0748526i	$0.976151\pi$
$422$	8.73289	+	0.572384i	0.425111	+	0.0278632i
$423$	−7.19974	−	9.38289i	−0.350063	−	0.456211i
$424$	8.61882	+	4.97608i	0.418567	+	0.241660i
$425$	−41.7575	+	8.69698i	−2.02554	+	0.421865i
$426$			5.74262i			0.278231i
$427$	−8.75118	−	9.84483i	−0.423499	−	0.476425i
$428$	5.78766	+	3.86719i	0.279757	+	0.186928i
$429$	−0.0840618	+	0.313723i	−0.00405854	+	0.0151467i
$430$	−10.9237	−	3.70810i	−0.526789	−	0.178821i
$431$	−1.14154	−	17.4165i	−0.0549859	−	0.838923i	−0.932907	−	0.360118i	$-0.882737\pi$
$431$	−1.14154	−	17.4165i	−0.0549859	−	0.838923i	0.877921	−	0.478806i	$-0.158930\pi$
$432$	−0.946930	+	0.321439i	−0.0455592	+	0.0154653i
$433$	14.7168	+	35.5296i	0.707246	+	1.70744i	0.706771	+	0.707443i	$0.250151\pi$
$433$	14.7168	+	35.5296i	0.707246	+	1.70744i	0.000475398		1.00000i	$0.499849\pi$
$434$	5.36293	−	8.14390i	0.257429	−	0.390920i
$435$	7.19161	−	36.1547i	0.344811	−	1.73348i
$436$	−8.06395	+	16.3521i	−0.386193	+	0.783122i
$437$	2.63415	−	7.75995i	0.126008	−	0.371209i
$438$	−1.35755	−	5.06643i	−0.0648661	−	0.242083i
$439$	2.21390	−	33.7777i	0.105664	−	1.61212i	−0.535377	−	0.844613i	$-0.679831\pi$
$439$	2.21390	−	33.7777i	0.105664	−	1.61212i	0.641041	−	0.767507i	$-0.278503\pi$
$440$	0.0877374	−	0.211817i	0.00418272	−	0.0100980i
$441$	1.00668	+	6.92724i	0.0479373	+	0.329868i
$442$	−7.15966	+	21.7315i	−0.340550	+	1.03366i
$443$	5.39176	+	9.33880i	0.256170	+	0.443700i	0.965213	−	0.261466i	$-0.0842060\pi$
$443$	5.39176	+	9.33880i	0.256170	+	0.443700i	−0.709043	+	0.705166i	$0.750873\pi$
$444$	1.67049	−	1.28181i	0.0792778	−	0.0608320i
$445$	2.69121	−	1.32716i	0.127575	−	0.0629132i
$446$	12.7064	+	3.40466i	0.601664	+	0.161215i
$447$	−3.10270	−	15.5983i	−0.146753	−	0.737776i
$448$	−0.996070	+	2.45109i	−0.0470599	+	0.115803i
$449$	−14.2714	−	2.83877i	−0.673511	−	0.133970i	−0.153525	−	0.988145i	$-0.549063\pi$
$449$	−14.2714	−	2.83877i	−0.673511	−	0.133970i	−0.519986	+	0.854175i	$0.674063\pi$
$450$	8.20724	+	6.29764i	0.386893	+	0.296874i
$451$	0.0787726	−	0.598337i	0.00370926	−	0.0281746i
$452$	−9.96869	−	8.74231i	−0.468888	−	0.411204i
$453$	−1.04352	−	0.514605i	−0.0490286	−	0.0241782i
$454$	19.2269	−	3.82447i	0.902364	−	0.179491i
$455$	−54.3366	+	18.8521i	−2.54734	+	0.883800i
$456$	−2.58411	+	3.86739i	−0.121012	+	0.181107i
$457$	2.01274	+	15.2883i	0.0941522	+	0.715157i	0.971793	+	0.235837i	$0.0757833\pi$
$457$	2.01274	+	15.2883i	0.0941522	+	0.715157i	−0.877640	+	0.479320i	$0.840883\pi$
$458$	11.7234	−	20.3055i	0.547799	−	0.948816i
$459$	0.574894	+	4.08283i	0.0268338	+	0.190570i
$460$	5.97700	−	3.45082i	0.278679	−	0.160895i
$461$	−21.0951	−	8.73786i	−0.982495	−	0.406963i	−0.167146	−	0.985932i	$-0.553455\pi$
$461$	−21.0951	−	8.73786i	−0.982495	−	0.406963i	−0.815349	+	0.578970i	$0.803455\pi$
$462$	0.134620	+	0.0765238i	0.00626309	+	0.00356021i
$463$	−25.9336	−	25.9336i	−1.20524	−	1.20524i	−0.972552	−	0.232685i	$-0.925249\pi$
$463$	−25.9336	−	25.9336i	−1.20524	−	1.20524i	−0.232685	−	0.972552i	$-0.574751\pi$
$464$	6.20469	+	7.07510i	0.288046	+	0.328453i
$465$	14.4065	−	0.944250i	0.668084	−	0.0437886i
$466$	−0.886093	+	1.01040i	−0.0410475	+	0.0468057i
$467$	−6.34356	+	8.26709i	−0.293545	+	0.382555i	−0.916722	−	0.399526i	$-0.869175\pi$
$467$	−6.34356	+	8.26709i	−0.293545	+	0.382555i	0.623177	+	0.782081i	$0.285842\pi$
$468$	5.12692	−	2.12364i	0.236992	−	0.0981653i
$469$	25.7632	+	3.21617i	1.18963	+	0.148509i
$470$	−25.7390	−	38.5212i	−1.18725	−	1.77685i
$471$	5.83658	−	5.11854i	0.268935	−	0.235850i
$472$	3.96396	−	1.06214i	0.182456	−	0.0488890i
$473$	−0.0762318	−	0.154583i	−0.00350514	−	0.00710773i
$474$	8.85766	−	1.16613i	0.406846	−	0.0535623i
$475$	48.1175			2.20778
$476$	9.16426	+	5.91746i	0.420043	+	0.271226i
$477$	−9.95216			−0.455678
$478$	−27.4349	+	3.61187i	−1.25484	+	0.165203i
$479$	−10.8405	−	21.9824i	−0.495316	−	1.00440i	−0.990743	−	0.135752i	$-0.956655\pi$
$479$	−10.8405	−	21.9824i	−0.495316	−	1.00440i	0.495426	−	0.868650i	$-0.335012\pi$
$480$	−3.78379	+	1.01386i	−0.172706	+	0.0462764i
$481$	−8.78502	+	7.70426i	−0.400562	+	0.351284i
$482$	−3.88503	−	5.81435i	−0.176958	−	0.264836i
$483$	1.81269	+	4.29453i	0.0824802	+	0.195408i
$484$	−10.1595	+	4.20821i	−0.461796	+	0.191282i
$485$	11.9396	−	15.5600i	0.542149	−	0.706542i
$486$	0.659346	−	0.751840i	0.0299085	−	0.0341041i
$487$	−28.6396	+	1.87714i	−1.29778	+	0.0850612i	−0.698578	−	0.715534i	$-0.746183\pi$
$487$	−28.6396	+	1.87714i	−1.29778	+	0.0850612i	−0.599205	+	0.800595i	$0.704517\pi$
$488$	3.28261	+	3.74310i	0.148597	+	0.169442i
$489$	5.74651	+	5.74651i	0.259866	+	0.259866i
$490$	2.16024	+	27.3357i	0.0975898	+	1.23490i
$491$	−2.45369	−	1.01635i	−0.110733	−	0.0458673i	0.326629	−	0.945153i	$-0.394087\pi$
$491$	−2.45369	−	1.01635i	−0.110733	−	0.0458673i	−0.437362	+	0.899285i	$0.644087\pi$
$492$	−8.92990	+	5.15568i	−0.402591	+	0.232436i
$493$	33.4260	−	19.7012i	1.50543	−	0.887299i
$494$	12.9057	−	22.3534i	0.580657	−	1.00573i
$495$	0.0299256	+	0.227307i	0.00134506	+	0.0102167i
$496$	−2.04760	+	3.06444i	−0.0919397	+	0.137598i
$497$	−14.9212	−	2.86411i	−0.669305	−	0.128473i
$498$	8.88448	−	1.76723i	0.398123	−	0.0791916i
$499$	7.00340	+	3.45369i	0.313515	+	0.154609i	0.592238	−	0.805763i	$-0.298244\pi$
$499$	7.00340	+	3.45369i	0.313515	+	0.154609i	−0.278723	+	0.960372i	$0.589911\pi$
$500$	15.7419	+	13.8053i	0.703999	+	0.617390i
$501$	−2.65942	+	20.2003i	−0.118814	+	0.902484i
$502$	10.7658	+	8.26090i	0.480502	+	0.368702i
$503$	−31.8666	−	6.33865i	−1.42086	−	0.282627i	−0.575928	−	0.817501i	$-0.695359\pi$
$503$	−31.8666	−	6.33865i	−1.42086	−	0.282627i	−0.844932	+	0.534874i	$0.820359\pi$
$504$	−0.362924	−	2.62074i	−0.0161659	−	0.116737i
$505$	−0.0519333	−	0.261086i	−0.00231100	−	0.0116182i
$506$	0.0996035	+	0.0266887i	0.00442791	+	0.00118646i
$507$	−15.9600	+	7.87059i	−0.708808	+	0.349545i
$508$	1.95087	−	1.49696i	0.0865559	−	0.0664167i
$509$	13.7039	+	23.7359i	0.607415	+	1.05207i	0.991665	+	0.128845i	$0.0411268\pi$
$509$	13.7039	+	23.7359i	0.607415	+	1.05207i	−0.384250	+	0.923229i	$0.625540\pi$
$510$	1.20117	+	16.1066i	0.0531886	+	0.713212i
$511$	13.8413	−	1.00047i	0.612302	−	0.0442582i
$512$	0.382683	−	0.923880i	0.0169124	−	0.0408301i
$513$	0.304208	−	4.64131i	0.0134311	−	0.204919i
$514$	4.88078	+	18.2153i	0.215282	+	0.803443i
$515$	8.29786	−	24.4447i	0.365648	−	1.07716i
$516$	−1.30249	+	2.64119i	−0.0573390	+	0.116272i
$517$	0.135041	−	0.678899i	0.00593911	−	0.0298579i
$518$	2.49740	+	4.97975i	0.109729	+	0.218798i
$519$	2.10600	+	5.08433i	0.0924430	+	0.223177i
$520$	20.5846	−	6.98753i	0.902695	−	0.306424i
$521$	1.82321	+	27.8168i	0.0798762	+	1.21868i	0.830147	+	0.557545i	$0.188256\pi$
$521$	1.82321	+	27.8168i	0.0798762	+	1.21868i	−0.750271	+	0.661131i	$0.770077\pi$
$522$	−8.91097	−	3.02487i	−0.390023	−	0.132395i
$523$	9.32093	−	34.7862i	0.407576	−	1.52109i	−0.391680	−	0.920102i	$-0.628106\pi$
$523$	9.32093	−	34.7862i	0.407576	−	1.52109i	0.799255	−	0.600992i	$-0.205228\pi$
$524$	−2.78948	−	1.86387i	−0.121859	−	0.0814235i
$525$	−20.4566	+	18.1841i	−0.892799	+	0.793619i
$526$		−	18.6251i		−	0.812091i
$527$	10.8413	+	10.6482i	0.472257	+	0.463842i
$528$	−0.0506865	−	0.0292639i	−0.00220585	−	0.00127355i
$529$	−12.1118	−	15.7845i	−0.526602	−	0.686281i
$530$	−38.9018	−	2.54976i	−1.68979	−	0.110754i
$531$	−2.90182	+	2.90182i	−0.125928	+	0.125928i
$532$	−8.75990	−	8.64318i	−0.379790	−	0.374730i
$533$	47.5777	−	31.7904i	2.06082	−	1.37700i
$534$	−0.246225	−	0.725355i	−0.0106552	−	0.0313892i
$535$	−27.0339	−	3.55908i	−1.16878	−	0.153873i
$536$	−9.72920	−	1.28087i	−0.420237	−	0.0553253i
$537$	3.32039	+	9.78157i	0.143286	+	0.422106i
$538$	−18.9582	+	12.6675i	−0.817347	+	0.546134i
$539$	−0.265974	+	0.311620i	−0.0114563	+	0.0134224i
$540$	2.76993	−	2.76993i	0.119199	−	0.119199i
$541$	−0.857856	−	0.0562269i	−0.0368821	−	0.00241738i	0.0469509	−	0.998897i	$-0.485050\pi$
$541$	−0.857856	−	0.0562269i	−0.0368821	−	0.00241738i	−0.0838330	+	0.996480i	$0.526716\pi$
$542$	10.9518	+	14.2726i	0.470419	+	0.613062i
$543$	3.50088	+	2.02123i	0.150237	+	0.0867395i
$544$	−3.44869	−	2.25977i	−0.147861	−	0.0968868i
$545$		−	71.4209i		−	3.05934i
$546$	2.96086	+	14.3805i	0.126713	+	0.615429i
$547$	29.0682	+	19.4228i	1.24287	+	0.830457i	0.990545	−	0.137186i	$-0.0438060\pi$
$547$	29.0682	+	19.4228i	1.24287	+	0.830457i	0.252321	+	0.967643i	$0.418806\pi$
$548$	4.56679	−	17.0435i	0.195084	−	0.728062i
$549$	−4.71437	−	1.60031i	−0.201204	−	0.0682997i
$550$	0.0395996	+	0.604173i	0.00168853	+	0.0257620i
$551$	−41.4474	+	14.0695i	−1.76572	+	0.599380i
$552$	−0.674231	−	1.62774i	−0.0286972	−	0.0692811i
$553$	−1.38774	+	23.5966i	−0.0590129	+	1.00343i
$554$	0.107984	−	0.542873i	0.00458780	−	0.0230644i
$555$	−3.64809	+	7.39760i	−0.154853	+	0.314011i
$556$	4.26764	−	12.5721i	0.180988	−	0.533174i
$557$	1.69766	+	6.33575i	0.0719321	+	0.268454i	0.992520	−	0.122081i	$-0.0389567\pi$
$557$	1.69766	+	6.33575i	0.0719321	+	0.268454i	−0.920588	+	0.390535i	$0.872290\pi$
$558$	0.241048	−	3.67768i	0.0102044	−	0.155689i
$559$	6.25389	−	15.0982i	0.264511	−	0.638586i
$560$	−0.747187	−	10.3372i	−0.0315744	−	0.436824i
$561$	−0.157473	+	0.182854i	−0.00664853	+	0.00772009i
$562$	14.5203	+	25.1499i	0.612501	+	1.06088i
$563$	−3.88324	+	2.97971i	−0.163659	+	0.125580i	−0.687344	−	0.726332i	$-0.741224\pi$
$563$	−3.88324	+	2.97971i	−0.163659	+	0.125580i	0.523685	+	0.851912i	$0.324557\pi$
$564$	−10.6072	+	5.23089i	−0.446644	+	0.220260i
$565$	50.1696	+	13.4429i	2.11065	+	0.565547i
$566$	−3.69624	−	18.5823i	−0.155365	−	0.781071i
$567$	1.62467	+	2.08817i	0.0682298	+	0.0876948i
$568$	5.63228	+	1.12033i	0.236325	+	0.0470080i
$569$	−10.8598	−	8.33305i	−0.455269	−	0.349340i	0.355530	−	0.934665i	$-0.384300\pi$
$569$	−10.8598	−	8.33305i	−0.455269	−	0.349340i	−0.810799	+	0.585325i	$0.800967\pi$
$570$	2.37823	−	18.0644i	0.0996129	−	0.756635i
$571$	8.38820	+	7.35625i	0.351035	+	0.307850i	0.816645	−	0.577141i	$-0.195832\pi$
$571$	8.38820	+	7.35625i	0.351035	+	0.307850i	−0.465610	+	0.884990i	$0.654165\pi$
$572$	0.291295	+	0.143651i	0.0121797	+	0.00600635i
$573$	−9.78858	+	1.94707i	−0.408924	+	0.0813400i
$574$	−8.94233	−	25.7741i	−0.373246	−	1.07579i
$575$	−10.1260	+	15.1547i	−0.422284	+	0.631993i
$576$	0.130526	+	0.991445i	0.00543859	+	0.0413102i
$577$	8.65505	−	14.9910i	0.360314	−	0.624083i	−0.627698	−	0.778457i	$-0.716003\pi$
$577$	8.65505	−	14.9910i	0.360314	−	0.624083i	0.988012	+	0.154374i	$0.0493361\pi$
$578$	−11.8028	+	12.2350i	−0.490931	+	0.508907i
$579$	−11.2358	+	6.48698i	−0.466943	+	0.269590i
$580$	−34.0570	−	14.1069i	−1.41414	−	0.585755i
$581$	0.160728	+	23.9661i	0.00666812	+	0.994281i
$582$	−3.54033	−	3.54033i	−0.146751	−	0.146751i
$583$	−0.384054	−	0.437929i	−0.0159059	−	0.0181372i
$584$	−5.23393	+	0.343050i	−0.216581	+	0.0141955i
$585$	−14.3330	+	16.3437i	−0.592598	+	0.675728i
$586$	5.40224	−	7.04033i	0.223164	−	0.290834i
$587$	21.3504	−	8.84364i	0.881227	−	0.365016i	0.104255	−	0.994551i	$-0.466754\pi$
$587$	21.3504	−	8.84364i	0.881227	−	0.365016i	0.776973	+	0.629534i	$0.216754\pi$
$588$	6.99052	+	0.364095i	0.288284	+	0.0150150i
$589$	−9.52392	−	14.2536i	−0.392426	−	0.587308i
$590$	−12.0863	+	10.5994i	−0.497586	+	0.436371i
$591$	0.0695754	−	0.0186427i	0.00286195	−	0.000766857i
$592$	−0.931284	−	1.88846i	−0.0382755	−	0.0776151i
$593$	−40.3470	+	5.31179i	−1.65685	+	0.218129i	−0.900135	−	0.435611i	$-0.856532\pi$
$593$	−40.3470	+	5.31179i	−1.65685	+	0.218129i	−0.756719	+	0.653740i	$0.773199\pi$
$594$	0.0585277			0.00240142
$595$	−42.4491	−	4.91209i	−1.74024	−	0.201376i
$596$	−15.9039			−0.651450
$597$	14.3121	−	1.88423i	0.585756	−	0.0771163i
$598$	4.32430	+	8.76882i	0.176834	+	0.358584i
$599$	21.4307	−	5.74235i	0.875636	−	0.234626i	0.207113	−	0.978317i	$-0.433593\pi$
$599$	21.4307	−	5.74235i	0.875636	−	0.234626i	0.668523	+	0.743691i	$0.266927\pi$
$600$	7.77779	−	6.82094i	0.317527	−	0.278464i
$601$	7.81757	+	11.6998i	0.318886	+	0.477246i	0.955936	−	0.293577i	$-0.0948456\pi$
$601$	7.81757	+	11.6998i	0.318886	+	0.477246i	−0.637050	+	0.770822i	$0.719846\pi$
$602$	−6.21304	−	4.70157i	−0.253225	−	0.191622i
$603$	9.06617	−	3.75533i	0.369203	−	0.152929i
$604$	−0.708297	+	0.923070i	−0.0288202	+	0.0375592i
$605$	28.4023	−	32.3867i	1.15472	−	1.31671i
$606$	−0.0678103	+	0.00444452i	−0.00275460	+	0.000180546i
$607$	24.9586	+	28.4598i	1.01304	+	1.15515i	0.987841	+	0.155465i	$0.0496877\pi$
$607$	24.9586	+	28.4598i	1.01304	+	1.15515i	0.0251960	+	0.999683i	$0.491979\pi$
$608$	3.28895	+	3.28895i	0.133384	+	0.133384i
$609$	12.3039	−	21.6449i	0.498578	−	0.877095i
$610$	−18.0179	−	7.46326i	−0.729524	−	0.302179i
$611$	56.8384	−	32.8156i	2.29943	−	1.32758i
$612$	4.11654	+	0.232672i	0.166401	+	0.00940523i
$613$	17.8198	−	30.8648i	0.719735	−	1.24662i	−0.241370	−	0.970433i	$-0.577597\pi$
$613$	17.8198	−	30.8648i	0.719735	−	1.24662i	0.961105	−	0.276184i	$-0.0890700\pi$
$614$	2.92972	+	22.2535i	0.118234	+	0.898076i
$615$	22.4408	−	33.5850i	0.904901	−	1.35428i
$616$	0.101316	−	0.117104i	0.00408216	−	0.00471827i
$617$	−8.27744	+	1.64649i	−0.333237	+	0.0662850i	−0.358873	−	0.933386i	$-0.616839\pi$
$617$	−8.27744	+	1.64649i	−0.333237	+	0.0662850i	0.0256360	+	0.999671i	$0.491839\pi$
$618$	−5.91037	−	2.91467i	−0.237750	−	0.117245i
$619$	−11.4874	−	10.0742i	−0.461716	−	0.404914i	0.396635	−	0.917976i	$-0.370178\pi$
$619$	−11.4874	−	10.0742i	−0.461716	−	0.404914i	−0.858352	+	0.513062i	$0.828511\pi$
$620$	1.88446	−	14.3139i	0.0756816	−	0.574859i
$621$	1.39777	+	1.07255i	0.0560906	+	0.0430398i
$622$	−33.8642	−	6.73602i	−1.35783	−	0.270090i
$623$	2.00751	−	0.278002i	0.0804290	−	0.0111379i
$624$	−1.08262	−	5.44271i	−0.0433396	−	0.217883i
$625$	−29.2619	−	7.84069i	−1.17047	−	0.313628i
$626$	7.31089	−	3.60533i	0.292202	−	0.144098i
$627$	0.215973	−	0.165722i	0.00862514	−	0.00661830i
$628$	−3.88153	−	6.72301i	−0.154890	−	0.268277i
$629$	−8.36527	+	2.32225i	−0.333545	+	0.0925943i
$630$	5.81566	+	8.57864i	0.231701	+	0.341781i
$631$	−6.76800	+	16.3394i	−0.269430	+	0.650461i	−0.999457	−	0.0329571i	$-0.989508\pi$
$631$	−6.76800	+	16.3394i	−0.269430	+	0.650461i	0.730027	+	0.683418i	$0.239508\pi$
$632$	0.584318	−	8.91497i	0.0232429	−	0.354618i
$633$	2.26509	+	8.45343i	0.0900292	+	0.335994i
$634$	−10.5722	+	31.1448i	−0.419877	+	1.23692i
$635$	−4.26041	+	8.63926i	−0.169069	+	0.342838i
$636$	−1.94157	+	9.76093i	−0.0769882	+	0.387046i
$637$	−38.8419	+	0.521007i	−1.53897	+	0.0206431i
$638$	−0.210770	−	0.508843i	−0.00834445	−	0.0201453i
$639$	−5.43786	+	1.84591i	−0.215119	+	0.0730229i
$640$	0.256202	+	3.90888i	0.0101273	+	0.154512i
$641$	16.6555	+	5.65376i	0.657851	+	0.223310i	0.630349	−	0.776311i	$-0.282912\pi$
$641$	16.6555	+	5.65376i	0.657851	+	0.223310i	0.0275014	+	0.999622i	$0.491245\pi$
$642$	−1.80158	+	6.72358i	−0.0711026	+	0.265359i
$643$	−23.8119	−	15.9106i	−0.939051	−	0.627454i	−0.0110131	−	0.999939i	$-0.503506\pi$
$643$	−23.8119	−	15.9106i	−0.939051	−	0.627454i	−0.928038	+	0.372485i	$0.878506\pi$
$644$	4.56565	−	0.940038i	0.179912	−	0.0370427i
$645$		−	11.5359i		−	0.454227i
$646$	15.8493	−	10.7975i	0.623581	−	0.424820i
$647$	25.8777	+	14.9405i	1.01736	+	0.587372i	0.913338	−	0.407203i	$-0.133496\pi$
$647$	25.8777	+	14.9405i	1.01736	+	0.587372i	0.104021	+	0.994575i	$0.466829\pi$
$648$	−0.608761	−	0.793353i	−0.0239144	−	0.0311659i
$649$	−0.239671	−	0.0157089i	−0.00940792	−	0.000616628i
$650$	−40.5935	+	40.5935i	−1.59221	+	1.59221i
$651$	9.43556	+	2.46055i	0.369809	+	0.0964366i
$652$	6.75718	−	4.51501i	0.264632	−	0.176821i
$653$	6.53918	+	19.2638i	0.255898	+	0.753851i	0.996628	+	0.0820486i	$0.0261463\pi$
$653$	6.53918	+	19.2638i	0.255898	+	0.753851i	−0.740730	+	0.671802i	$0.765520\pi$
$654$	−18.0763	−	2.37979i	−0.706841	−	0.0930573i
$655$	13.0295	+	1.71537i	0.509105	+	0.0670250i
$656$	3.31448	+	9.76414i	0.129409	+	0.381225i
$657$	4.36119	−	2.91405i	0.170146	−	0.113688i
$658$	−8.30121	−	30.1697i	−0.323615	−	1.17614i
$659$	5.06298	−	5.06298i	0.197226	−	0.197226i	−0.601584	−	0.798810i	$-0.705463\pi$
$659$	5.06298	−	5.06298i	0.197226	−	0.197226i	0.798810	+	0.601584i	$0.205463\pi$
$660$	0.228778	+	0.0149949i	0.00890517	+	0.000583676i
$661$	16.9960	+	22.1496i	0.661068	+	0.861520i	0.996758	−	0.0804521i	$-0.0256364\pi$
$661$	16.9960	+	22.1496i	0.661068	+	0.861520i	−0.335691	+	0.941972i	$0.608970\pi$
$662$	23.2616	+	13.4301i	0.904087	+	0.521975i
$663$	−22.8796	+	0.205658i	−0.888569	+	0.00798711i
$664$		−	9.05853i		−	0.351539i
$665$	45.7510	+	15.1890i	1.77415	+	0.589002i
$666$	1.75074	+	1.16981i	0.0678400	+	0.0453292i
$667$	4.29114	−	16.0147i	0.166154	−	0.620094i
$668$	19.2934	+	6.54921i	0.746483	+	0.253397i
$669$	0.860352	+	13.1264i	0.0332631	+	0.507497i
$670$	36.4007	−	12.3564i	1.40628	−	0.477368i
$671$	−0.111508	−	0.269205i	−0.00430472	−	0.0103925i
$672$	−2.64119	−	0.155331i	−0.101886	−	0.00599203i
$673$	−2.10363	+	10.5757i	−0.0810890	+	0.407662i	0.918827	+	0.394662i	$0.129138\pi$
$673$	−2.10363	+	10.5757i	−0.0810890	+	0.407662i	−0.999915	+	0.0130001i	$0.995862\pi$
$674$	−8.01061	+	16.2439i	−0.308557	+	0.625692i
$675$	−3.32529	+	9.79600i	−0.127991	+	0.377048i
$676$	4.60572	+	17.1888i	0.177143	+	0.661108i
$677$	1.44862	−	22.1016i	0.0556749	−	0.849434i	−0.875123	−	0.483900i	$-0.839220\pi$
$677$	1.44862	−	22.1016i	0.0556749	−	0.849434i	0.930798	−	0.365534i	$-0.119114\pi$
$678$	5.07402	−	12.2498i	0.194867	−	0.470450i
$679$	10.9646	−	7.43318i	0.420784	−	0.285259i
$680$	16.0314	+	1.96415i	0.614778	+	0.0753218i
$681$	9.80180	+	16.9772i	0.375606	+	0.650568i
$682$	0.171133	−	0.131315i	0.00655301	−	0.00502830i
$683$	−40.9561	+	20.1973i	−1.56714	+	0.772830i	−0.998753	−	0.0499293i	$-0.984100\pi$
$683$	−40.9561	+	20.1973i	−1.56714	+	0.772830i	−0.568391	+	0.822759i	$0.692434\pi$
$684$	−4.49279	−	1.20384i	−0.171786	−	0.0460299i
$685$	13.4845	+	67.7911i	0.515216	+	2.59016i
$686$	−4.43254	+	17.9820i	−0.169235	+	0.686556i
$687$	22.9963	+	4.57425i	0.877364	+	0.174519i
$688$	2.33634	+	1.79274i	0.0890721	+	0.0683474i
$689$	7.20868	−	54.7554i	0.274629	−	2.08601i
$690$	5.18893	+	4.55057i	0.197539	+	0.173237i
$691$	31.0754	+	15.3247i	1.18216	+	0.582978i	0.923728	−	0.383050i	$-0.125126\pi$
$691$	31.0754	+	15.3247i	1.18216	+	0.582978i	0.258436	+	0.966028i	$0.416793\pi$
$692$	5.39749	−	1.07363i	0.205182	−	0.0408132i
$693$	−0.0291905	+	0.152074i	−0.00110885	+	0.00577680i
$694$	7.51374	−	11.2451i	0.285218	−	0.426859i
$695$	6.78844	+	51.5633i	0.257500	+	1.95591i
$696$	−4.70519	+	8.14963i	−0.178350	+	0.308911i
$697$	42.0995	−	5.92794i	1.59463	−	0.224537i
$698$	−14.0897	+	8.13468i	−0.533302	+	0.307902i
$699$	−1.24160	−	0.514287i	−0.0469616	−	0.0194521i
$700$	13.8438	+	23.6111i	0.523247	+	0.892415i
$701$	10.9482	+	10.9482i	0.413510	+	0.413510i	0.882959	−	0.469450i	$-0.155548\pi$
$701$	10.9482	+	10.9482i	0.413510	+	0.413510i	−0.469450	+	0.882959i	$0.655548\pi$
$702$	3.65893	+	4.17221i	0.138098	+	0.157470i
$703$	9.77276	−	0.640541i	0.368587	−	0.0241585i
$704$	−0.0385900	+	0.0440035i	−0.00145442	+	0.00165844i
$705$	28.2033	−	36.7553i	1.06220	−	1.38428i
$706$	−21.8180	+	9.03729i	−0.821129	+	0.340123i
$707$	0.0222719	−	0.178409i	0.000837620	−	0.00670977i
$708$	2.27995	+	3.41218i	0.0856856	+	0.128238i
$709$	21.7452	−	19.0701i	0.816659	−	0.716191i	−0.145299	−	0.989388i	$-0.546414\pi$
$709$	21.7452	−	19.0701i	0.816659	−	0.716191i	0.961958	+	0.273197i	$0.0880810\pi$
$710$	−21.7289	+	5.82224i	−0.815471	+	0.218505i
$711$	3.95145	+	8.01275i	0.148191	+	0.300501i
$712$	−0.759454	+	0.0999840i	−0.0284617	+	0.00374706i
$713$	6.49343			0.243181
$714$	−2.65766	+	10.5800i	−0.0994606	+	0.395947i
$715$	−1.27229			−0.0475810
$716$	10.2414	−	1.34831i	0.382739	−	0.0503885i
$717$	−12.2388	−	24.8179i	−0.457068	−	0.926842i
$718$	7.57339	−	2.02928i	0.282636	−	0.0757321i
$719$	7.25393	−	6.36152i	0.270526	−	0.237245i	−0.513325	−	0.858195i	$-0.671586\pi$
$719$	7.25393	−	6.36152i	0.270526	−	0.237245i	0.783850	+	0.620950i	$0.213253\pi$
$720$	−2.17632	−	3.25709i	−0.0811066	−	0.121385i
$721$	10.5210	−	13.9033i	0.391823	−	0.517787i
$722$	−2.43382	+	1.00812i	−0.0905773	+	0.0375184i
$723$	4.25698	−	5.54781i	0.158319	−	0.206325i
$724$	2.66538	−	3.03929i	0.0990582	−	0.112954i
$725$	97.1420	−	6.36702i	3.60776	−	0.236465i
$726$	−7.25055	−	8.26766i	−0.269093	−	0.306842i
$727$	6.39504	+	6.39504i	0.237179	+	0.237179i	0.815681	−	0.578502i	$-0.196363\pi$
$727$	6.39504	+	6.39504i	0.237179	+	0.237179i	−0.578502	+	0.815681i	$0.696363\pi$
$728$	14.6818	−	0.0984633i	0.544145	−	0.00364929i
$729$	0.923880	+	0.382683i	0.0342178	+	0.0141735i
$730$	17.7940	−	10.2733i	0.658584	−	0.380234i
$731$	9.05658	−	8.08757i	0.334970	−	0.299130i
$732$	−2.48929	+	4.31158i	−0.0920068	+	0.159360i
$733$	−2.06883	−	15.7143i	−0.0764140	−	0.580422i	−0.986226	−	0.165402i	$-0.947108\pi$
$733$	−2.06883	−	15.7143i	−0.0764140	−	0.580422i	0.909812	−	0.415020i	$-0.136225\pi$
$734$	−4.94280	+	7.39743i	−0.182442	+	0.273044i
$735$	−25.1906	+	10.8324i	−0.929168	+	0.399558i
$736$	−1.72800	+	0.343720i	−0.0636948	+	0.0126697i
$737$	0.515111	+	0.254025i	0.0189744	+	0.00935712i
$738$	−7.75249	−	6.79875i	−0.285373	−	0.250266i
$739$	1.92792	−	14.6440i	0.0709197	−	0.538688i	−0.918698	−	0.394961i	$-0.870758\pi$
$739$	1.92792	−	14.6440i	0.0709197	−	0.538688i	0.989617	−	0.143727i	$-0.0459087\pi$
$740$	6.54375	+	5.02119i	0.240553	+	0.184583i
$741$	25.3155	+	5.03557i	0.929989	+	0.184986i
$742$	−24.3936	−	9.91304i	−0.895518	−	0.363919i
$743$	−3.63488	−	18.2738i	−0.133351	−	0.670400i	−0.988402	−	0.151857i	$-0.951475\pi$
$743$	−3.63488	−	18.2738i	−0.133351	−	0.670400i	0.855052	−	0.518543i	$-0.173525\pi$
$744$	−3.55999	−	0.953897i	−0.130516	−	0.0349715i
$745$	55.8752	−	27.5546i	2.04711	−	1.00952i
$746$	8.67872	−	6.65942i	0.317751	−	0.243819i
$747$	4.52927	+	7.84492i	0.165717	+	0.287031i
$748$	0.148619	+	0.190121i	0.00543404	+	0.00695150i
$749$	−16.5715	−	8.03443i	−0.605508	−	0.293572i
$750$	−8.01256	+	19.3440i	−0.292577	+	0.706344i
$751$	−0.431450	+	6.58266i	−0.0157438	+	0.240205i	0.982733	+	0.185030i	$0.0592382\pi$
$751$	−0.431450	+	6.58266i	−0.0157438	+	0.240205i	−0.998477	+	0.0551746i	$0.982428\pi$
$752$	3.06102	+	11.4239i	0.111624	+	0.416586i
$753$	−4.36194	+	12.8499i	−0.158958	+	0.468275i
$754$	23.0969	−	46.8359i	0.841140	−	1.70566i
$755$	0.889175	−	4.47018i	0.0323604	−	0.162687i
$756$	2.36500	−	1.18607i	0.0860143	−	0.0431371i
$757$	4.08013	+	9.85031i	0.148295	+	0.358016i	0.980519	−	0.196424i	$-0.0629328\pi$
$757$	4.08013	+	9.85031i	0.148295	+	0.358016i	−0.832224	+	0.554439i	$0.812933\pi$
$758$	13.4851	−	4.57756i	0.489800	−	0.166265i
$759$	0.00674418	+	0.102896i	0.000244798	+	0.00373490i
$760$	−17.2533	−	5.85672i	−0.625845	−	0.212446i
$761$	8.62893	−	32.2036i	0.312798	−	1.16738i	−0.613223	−	0.789910i	$-0.710127\pi$
$761$	8.62893	−	32.2036i	0.312798	−	1.16738i	0.926022	−	0.377470i	$-0.123206\pi$
$762$	2.04460	+	1.36616i	0.0740680	+	0.0494907i
$763$	15.1990	−	45.7811i	0.550240	−	1.65739i
$764$			9.98034i			0.361076i
$765$	−14.8657	+	6.31472i	−0.537471	+	0.228309i
$766$	4.61645	+	2.66531i	0.166799	+	0.0963015i
$767$	−13.8635	−	18.0673i	−0.500583	−	0.652372i
$768$	0.997859	+	0.0654031i	0.0360071	+	0.00236003i
$769$	17.0363	−	17.0363i	0.614344	−	0.614344i	−0.329731	−	0.944075i	$-0.606958\pi$
$769$	17.0363	−	17.0363i	0.614344	−	0.614344i	0.944075	+	0.329731i	$0.106958\pi$
$770$	−0.153064	+	0.586959i	−0.00551603	+	0.0211525i
$771$	−15.6797	+	10.4769i	−0.564692	+	0.377315i
$772$	4.17035	+	12.2854i	0.150094	+	0.442163i
$773$	21.5908	+	2.84248i	0.776567	+	0.102237i	0.508384	−	0.861131i	$-0.330243\pi$
$773$	21.5908	+	2.84248i	0.776567	+	0.102237i	0.268184	+	0.963368i	$0.413577\pi$
$774$	−2.91970	−	0.384385i	−0.104946	−	0.0138164i
$775$	12.2556	+	36.1039i	0.440235	+	1.29689i
$776$	−4.16299	+	2.78162i	−0.149443	+	0.0998544i
$777$	−3.91271	+	3.96555i	−0.140368	+	0.142263i
$778$	−0.382826	+	0.382826i	−0.0137250	+	0.0137250i
$779$	−47.8583	−	3.13680i	−1.71470	−	0.112387i
$780$	13.2334	+	17.2461i	0.473832	+	0.617510i
$781$	−0.291073	−	0.168051i	−0.0104154	−	0.00601335i
$782$	0.0652942	+	7.26401i	0.00233492	+	0.259760i
$783$		−	9.41038i		−	0.336300i
$784$	1.72088	−	6.78517i	0.0614601	−	0.242328i
$785$	25.2850	+	16.8949i	0.902461	+	0.603005i
$786$	0.868305	−	3.24056i	0.0309714	−	0.115587i
$787$	2.72015	+	0.923366i	0.0969629	+	0.0329145i	0.369499	−	0.929231i	$-0.379529\pi$
$787$	2.72015	+	0.923366i	0.0969629	+	0.0329145i	−0.272536	+	0.962145i	$0.587863\pi$
$788$	−0.00471097	−	0.0718755i	−0.000167821	−	0.00256046i
$789$	17.6366	−	5.98683i	0.627880	−	0.213137i
$790$	13.3929	+	32.3333i	0.476497	+	1.15037i
$791$	29.2982	+	19.2935i	1.04172	+	0.685996i
$792$	0.0114182	−	0.0574031i	0.000405728	−	0.00203973i
$793$	12.2195	−	24.7786i	0.433926	−	0.879915i
$794$	1.69358	−	4.98912i	0.0601029	−	0.177057i
$795$	−10.0901	−	37.6569i	−0.357860	−	1.33555i
$796$	0.944135	−	14.4047i	0.0334640	−	0.510561i
$797$	−14.9882	+	36.1846i	−0.530908	+	1.28173i	0.400015	+	0.916509i	$0.369005\pi$
$797$	−14.9882	+	36.1846i	−0.530908	+	1.28173i	−0.930923	+	0.365217i	$0.880995\pi$
$798$	5.36871	−	11.0733i	0.190050	−	0.391990i
$799$	48.6284	−	3.62652i	1.72035	−	0.128297i
$800$	−5.17250	−	8.95904i	−0.182876	−	0.316750i
$801$	0.607714	−	0.466316i	0.0214725	−	0.0164764i
$802$	−16.6178	+	8.19501i	−0.586796	+	0.289376i
$803$	0.296527	+	0.0794541i	0.0104642	+	0.00280387i
$804$	−1.91445	−	9.62459i	−0.0675175	−	0.339433i
$805$	−14.4118	+	11.2129i	−0.507949	+	0.395203i
$806$	20.0595	+	3.99008i	0.706566	+	0.140545i
$807$	−18.0891	−	13.8803i	−0.636768	−	0.488609i
$808$	−0.00887001	+	0.0673744i	−0.000312046	+	0.00237022i
$809$	7.54554	+	6.61726i	0.265287	+	0.232650i	0.781647	−	0.623721i	$-0.214380\pi$
$809$	7.54554	+	6.61726i	0.265287	+	0.232650i	−0.516360	+	0.856372i	$0.672713\pi$
$810$	3.51329	+	1.73256i	0.123445	+	0.0608761i
$811$	7.72911	−	1.53742i	0.271406	−	0.0539859i	−0.0575111	−	0.998345i	$-0.518316\pi$
$811$	7.72911	−	1.53742i	0.271406	−	0.0539859i	0.328917	+	0.944359i	$0.393316\pi$
$812$	−18.8286	−	16.2902i	−0.660755	−	0.571673i
$813$	−9.99486	+	14.9584i	−0.350535	+	0.524613i
$814$	0.0160855	+	0.122182i	0.000563798	+	0.00428247i
$815$	−15.9174	+	27.5698i	−0.557563	+	0.965728i
$816$	1.03130	−	3.99205i	0.0361026	−	0.139750i
$817$	−11.8624	+	6.84875i	−0.415012	+	0.239607i
$818$	7.94441	+	3.29068i	0.277770	+	0.115056i
$819$	−12.6656	+	7.42619i	−0.442572	+	0.259492i
$820$	−28.5617	−	28.5617i	−0.997419	−	0.997419i
$821$	1.25641	+	1.43266i	0.0438489	+	0.0500001i	0.773348	−	0.633981i	$-0.218580\pi$
$821$	1.25641	+	1.43266i	0.0438489	+	0.0500001i	−0.729500	+	0.683981i	$0.760247\pi$
$822$	17.6070	−	1.15402i	0.614113	−	0.0402511i
$823$	−35.9175	+	40.9561i	−1.25201	+	1.42764i	−0.389944	+	0.920838i	$0.627506\pi$
$823$	−35.9175	+	40.9561i	−1.25201	+	1.42764i	−0.862063	+	0.506802i	$0.830828\pi$
$824$	−4.01172	+	5.22818i	−0.139755	+	0.182132i
$825$	−0.559381	+	0.231703i	−0.0194751	+	0.00806687i
$826$	−10.0030	+	4.22221i	−0.348050	+	0.146909i
$827$	5.77584	+	8.64415i	0.200845	+	0.300587i	0.918196	−	0.396126i	$-0.129646\pi$
$827$	5.77584	+	8.64415i	0.200845	+	0.300587i	−0.717351	+	0.696712i	$0.754646\pi$
$828$	1.32463	−	1.16167i	0.0460341	−	0.0403708i
$829$	18.9155	−	5.06840i	0.656963	−	0.176033i	0.0850881	−	0.996373i	$-0.472883\pi$
$829$	18.9155	−	5.06840i	0.656963	−	0.176033i	0.571875	+	0.820341i	$0.306216\pi$
$830$	15.6945	+	31.8253i	0.544764	+	1.10467i
$831$	0.548773	−	0.0722473i	0.0190367	−	0.00250623i
$832$	−5.54934			−0.192389
$833$	−26.1647	−	12.1822i	−0.906555	−	0.422088i
$834$	13.2767			0.459733
$835$	−79.1302	+	10.4177i	−2.73841	+	0.360519i
$836$	−0.120404	−	0.244154i	−0.00416424	−	0.00844425i
$837$	3.55999	−	0.953897i	0.123051	−	0.0329715i
$838$	−20.6912	+	18.1457i	−0.714767	+	0.626834i
$839$	7.00078	+	10.4774i	0.241694	+	0.361720i	0.932408	−	0.361408i	$-0.117704\pi$
$839$	7.00078	+	10.4774i	0.241694	+	0.361720i	−0.690714	+	0.723128i	$0.742704\pi$
$840$	9.54839	−	4.03030i	0.329451	−	0.139059i
$841$	−55.0219	+	22.7908i	−1.89731	+	0.785890i
$842$	−18.9373	+	24.6795i	−0.652621	+	0.850512i
$843$	−19.1478	+	21.8339i	−0.659485	+	0.751998i
$844$	8.73289	−	0.572384i	0.300599	−	0.0197023i
$845$	−45.9619	−	52.4096i	−1.58114	−	1.80294i
$846$	−8.36286	−	8.36286i	−0.287521	−	0.287521i
$847$	25.0982	−	14.7157i	0.862384	−	0.505639i
$848$	9.19459	+	3.80853i	0.315744	+	0.130785i
$849$	16.4080	−	9.47316i	0.563121	−	0.325118i
$850$	−40.2651	+	14.0730i	−1.38108	+	0.482701i
$851$	−1.85488	+	3.21274i	−0.0635844	+	0.110131i
$852$	0.749563	+	5.69349i	0.0256796	+	0.195056i
$853$	28.3510	−	42.4302i	0.970718	−	1.45278i	0.0807638	−	0.996733i	$-0.474264\pi$
$853$	28.3510	−	42.4302i	0.970718	−	1.45278i	0.889954	−	0.456049i	$-0.150736\pi$
$854$	−9.96132	−	8.61835i	−0.340869	−	0.294914i
$855$	17.8702	−	3.55460i	0.611148	−	0.121565i
$856$	6.24292	+	3.07867i	0.213379	+	0.105227i
$857$	−26.7398	−	23.4501i	−0.913413	−	0.801041i	0.0670494	−	0.997750i	$-0.478641\pi$
$857$	−26.7398	−	23.4501i	−0.913413	−	0.801041i	−0.980462	+	0.196708i	$0.936975\pi$
$858$	−0.0423936	+	0.322011i	−0.00144729	+	0.0109933i
$859$	−16.6598	−	12.7836i	−0.568427	−	0.436169i	0.284144	−	0.958782i	$-0.408291\pi$
$859$	−16.6598	−	12.7836i	−0.568427	−	0.436169i	−0.852570	+	0.522613i	$0.824957\pi$
$860$	−11.3143	−	2.25055i	−0.385813	−	0.0767431i
$861$	21.5318	−	16.7526i	0.733803	−	0.570926i
$862$	−3.40508	−	17.1185i	−0.115978	−	0.583058i
$863$	43.7096	+	11.7120i	1.48789	+	0.398679i	0.909025	−	0.416742i	$-0.136828\pi$
$863$	43.7096	+	11.7120i	1.48789	+	0.398679i	0.578867	+	0.815422i	$0.303495\pi$
$864$	−0.896873	+	0.442289i	−0.0305122	+	0.0150470i
$865$	−17.1028	+	13.1235i	−0.581514	+	0.446211i
$866$	19.2285	+	33.3047i	0.653410	+	1.13174i
$867$	−15.3795	−	7.24362i	−0.522316	−	0.246006i
$868$	4.25406	−	8.77423i	0.144392	−	0.297817i
$869$	−0.200102	+	0.483089i	−0.00678800	+	0.0163877i
$870$	2.41096	−	36.7841i	0.0817390	−	1.24710i
$871$	14.0944	+	52.6009i	0.477570	+	1.78231i
$872$	−5.86059	+	17.2647i	−0.198464	+	0.584658i
$873$	2.21444	−	4.49045i	0.0749476	−	0.151979i
$874$	1.59874	−	8.03739i	0.0540781	−	0.271869i
$875$	−46.2657	−	30.4669i	−1.56407	−	1.02997i
$876$	−2.00723	−	4.84589i	−0.0678182	−	0.163728i
$877$	−12.1658	+	4.12972i	−0.410809	+	0.139451i	−0.519191	−	0.854658i	$-0.673767\pi$
$877$	−12.1658	+	4.12972i	−0.410809	+	0.139451i	0.108382	+	0.994109i	$0.465433\pi$
$878$	−2.21390	−	33.7777i	−0.0747157	−	1.13994i
$879$	8.40320	+	2.85250i	0.283433	+	0.0962125i
$880$	0.0593391	−	0.221457i	0.00200032	−	0.00746530i
$881$	−14.3925	−	9.61674i	−0.484895	−	0.323996i	0.288980	−	0.957335i	$-0.406684\pi$
$881$	−14.3925	−	9.61674i	−0.484895	−	0.323996i	−0.773875	+	0.633339i	$0.781684\pi$
$882$	1.90226	+	6.73657i	0.0640523	+	0.226832i
$883$		−	1.60446i		−	0.0539942i	−0.999636	−	0.0269971i	$-0.991406\pi$
$883$		−	1.60446i		−	0.0539942i	0.999636	−	0.0269971i	$-0.00859449\pi$
$884$	−4.26188	+	22.4801i	−0.143342	+	0.756087i
$885$	−13.9219	−	8.03783i	−0.467981	−	0.270189i
$886$	6.56459	+	8.55514i	0.220542	+	0.287415i
$887$	34.5310	+	2.26328i	1.15944	+	0.0759936i	0.632953	−	0.774191i	$-0.281843\pi$
$887$	34.5310	+	2.26328i	1.15944	+	0.0759936i	0.526485	+	0.850184i	$0.323509\pi$
$888$	1.48889	−	1.48889i	0.0499637	−	0.0499637i
$889$	−4.56945	+	4.63115i	−0.153254	+	0.155324i
$890$	2.49495	−	1.66708i	0.0836311	−	0.0558805i
$891$	0.0188131	+	0.0554216i	0.000630263	+	0.00185669i
$892$	13.0421	+	1.71702i	0.436680	+	0.0574901i
$893$	−54.5394	−	7.18025i	−1.82509	−	0.240278i
$894$	−5.11215	−	15.0599i	−0.170976	−	0.503679i
$895$	−33.6450	+	22.4809i	−1.12463	+	0.751452i
$896$	−0.667617	+	2.56013i	−0.0223035	+	0.0855281i
$897$	−6.91346	+	6.91346i	−0.230834	+	0.230834i
$898$	−14.5199	−	0.951683i	−0.484535	−	0.0317581i
$899$	−21.1135	−	27.5156i	−0.704173	−	0.917696i
$900$	8.95904	+	5.17250i	0.298635	+	0.172417i
$901$	22.4896	−	34.3219i	0.749236	−	1.14343i
$902$		−	0.603500i		−	0.0200944i
$903$	2.45494	−	7.39459i	0.0816954	−	0.246076i
$904$	−11.0245	−	7.36634i	−0.366670	−	0.245001i
$905$	−4.09851	+	15.2959i	−0.136239	+	0.508452i
$906$	−1.10176	−	0.373996i	−0.0366034	−	0.0124252i
$907$	3.08975	+	47.1405i	0.102594	+	1.56527i	0.670329	+	0.742064i	$0.266153\pi$
$907$	3.08975	+	47.1405i	0.102594	+	1.56527i	−0.567736	+	0.823211i	$0.692180\pi$
$908$	18.5632	−	6.30137i	0.616043	−	0.209118i
$909$	−0.0260055	−	0.0627829i	−0.000862549	−	0.00208238i
$910$	−51.4110	+	25.7832i	−1.70426	+	0.854703i
$911$	4.56970	−	22.9734i	0.151401	−	0.761144i	−0.828238	−	0.560377i	$-0.810656\pi$
$911$	4.56970	−	22.9734i	0.151401	−	0.761144i	0.979639	−	0.200767i	$-0.0643436\pi$
$912$	−2.05721	+	4.17160i	−0.0681209	+	0.138135i
$913$	−0.170419	+	0.502039i	−0.00564005	+	0.0166151i
$914$	3.99105	+	14.8948i	0.132012	+	0.492676i
$915$	1.27552	−	19.4607i	0.0421674	−	0.643351i
$916$	8.97271	−	21.6620i	0.296467	−	0.715734i
$917$	7.98694	+	3.87235i	0.263752	+	0.127876i
$918$	1.10289	+	3.97286i	0.0364009	+	0.131124i
$919$	−11.0978	−	19.2220i	−0.366083	−	0.634074i	0.622866	−	0.782328i	$-0.285968\pi$
$919$	−11.0978	−	19.2220i	−0.366083	−	0.634074i	−0.988949	+	0.148254i	$0.952635\pi$
$920$	5.47544	−	4.20146i	0.180520	−	0.138518i
$921$	−20.1307	+	9.92738i	−0.663330	+	0.327118i
$922$	−22.0551	−	5.90965i	−0.726346	−	0.194624i
$923$	−6.21709	−	31.2554i	−0.204638	−	1.02878i
$924$	0.143457	+	0.0582977i	0.00471938	+	0.00191785i
$925$	−21.3639	−	4.24955i	−0.702441	−	0.139724i
$926$	−29.0968	−	22.3267i	−0.956179	−	0.733702i
$927$	0.860164	−	6.53359i	0.0282515	−	0.214591i
$928$	7.07510	+	6.20469i	0.232251	+	0.203679i
$929$	12.5957	+	6.21153i	0.413252	+	0.203794i	0.637017	−	0.770850i	$-0.280168\pi$
$929$	12.5957	+	6.21153i	0.413252	+	0.203794i	−0.223765	+	0.974643i	$0.571835\pi$
$930$	14.1600	−	2.81659i	0.464324	−	0.0923598i
$931$	26.0942	+	19.4724i	0.855204	+	0.638181i
$932$	−0.746630	+	1.11741i	−0.0244567	+	0.0366020i
$933$	−4.50677	−	34.2323i	−0.147545	−	1.12072i
$934$	−5.21022	+	9.02436i	−0.170484	+	0.295286i
$935$	−0.851537	−	0.410458i	−0.0278482	−	0.0134234i
$936$	4.80587	−	2.77467i	0.157085	−	0.0906929i
$937$	−52.1683	−	21.6088i	−1.70426	−	0.705929i	−0.704271	−	0.709932i	$-0.748726\pi$
$937$	−52.1683	−	21.6088i	−1.70426	−	0.705929i	−0.999992	+	0.00400277i	$0.998726\pi$
$938$	25.9626	−	0.174117i	0.847708	−	0.00568513i
$939$	5.76400	+	5.76400i	0.188101	+	0.188101i
$940$	−30.5469	−	34.8320i	−0.996329	−	1.13610i
$941$	−20.7294	+	1.35868i	−0.675760	+	0.0442916i	−0.399420	−	0.916768i	$-0.630788\pi$
$941$	−20.7294	+	1.35868i	−0.675760	+	0.0442916i	−0.276340	+	0.961060i	$0.589122\pi$
$942$	5.11854	−	5.83658i	0.166771	−	0.190166i
$943$	11.0594	−	14.4129i	0.360144	−	0.469349i
$944$	3.79141	−	1.57045i	0.123400	−	0.0511139i
$945$	−6.25399	+	8.26454i	−0.203442	+	0.268845i
$946$	−0.0957568	−	0.143310i	−0.00311332	−	0.00465942i
$947$	20.9840	−	18.4025i	0.681888	−	0.598000i	−0.246709	−	0.969090i	$-0.579349\pi$
$947$	20.9840	−	18.4025i	0.681888	−	0.598000i	0.928597	+	0.371090i	$0.121016\pi$
$948$	8.62967	−	2.31231i	0.280279	−	0.0751005i
$949$	12.8738	+	26.1054i	0.417900	+	0.847417i
$950$	47.7058	−	6.28059i	1.54778	−	0.203769i
$951$	−32.8903			−1.06654
$952$	9.85824	+	4.67066i	0.319507	+	0.151377i
$953$	−0.0602407			−0.00195139			−0.000975694	−	1.00000i	$-0.500311\pi$
$953$	−0.0602407			−0.00195139			−0.000975694		1.00000i	$0.500311\pi$
$954$	−9.86701	+	1.29902i	−0.319456	+	0.0420572i
$955$	−17.2916	−	35.0639i	−0.559543	−	1.13464i
$956$	−26.7287	+	7.16194i	−0.864468	+	0.231634i
$957$	0.414089	−	0.363146i	0.0133856	−	0.0117389i
$958$	−13.6171	−	20.3794i	−0.439947	−	0.658428i
$959$	−5.78290	+	46.3240i	−0.186739	+	1.49588i
$960$	−3.61909	+	1.49907i	−0.116805	+	0.0483824i
$961$	−10.6025	+	13.8175i	−0.342017	+	0.445725i
$962$	−7.70426	+	8.78502i	−0.248395	+	0.283240i
$963$	−6.94586	+	0.455256i	−0.223827	+	0.0146704i
$964$	−4.61071	−	5.25751i	−0.148501	−	0.169333i
$965$	−35.9370	−	35.9370i	−1.15685	−	1.15685i
$966$	2.35773	+	4.02119i	0.0758587	+	0.129380i
$967$	4.32572	+	1.79177i	0.139106	+	0.0576195i	0.451150	−	0.892448i	$-0.351014\pi$
$967$	4.32572	+	1.79177i	0.139106	+	0.0576195i	−0.312045	+	0.950067i	$0.601014\pi$
$968$	−9.52331	+	5.49829i	−0.306091	+	0.176722i
$969$	15.3190	+	11.5374i	0.492117	+	0.370635i
$970$	9.80646	−	16.9853i	0.314867	−	0.545365i
$971$	−2.84725	−	21.6270i	−0.0913726	−	0.694044i	−0.974416	−	0.224752i	$-0.927843\pi$
$971$	−2.84725	−	21.6270i	−0.0913726	−	0.694044i	0.883043	−	0.469291i	$-0.155491\pi$
$972$	0.555570	−	0.831470i	0.0178199	−	0.0266694i
$973$	−6.62169	+	34.4970i	−0.212282	+	1.10592i
$974$	−28.1495	+	5.59929i	−0.901970	+	0.179413i
$975$	−51.4876	−	25.3909i	−1.64892	−	0.813159i
$976$	3.74310	+	3.28261i	0.119814	+	0.105074i
$977$	−1.72603	+	13.1105i	−0.0552204	+	0.419441i	0.941400	+	0.337293i	$0.109511\pi$
$977$	−1.72603	+	13.1105i	−0.0552204	+	0.419441i	−0.996620	+	0.0821478i	$0.973822\pi$
$978$	6.44742	+	4.94728i	0.206166	+	0.158197i
$979$	0.0439712	+	0.00874641i	0.00140533	+	0.000279537i
$980$	5.70978	+	26.8198i	0.182392	+	0.856728i
$981$	−3.55695	−	17.8820i	−0.113565	−	0.570928i
$982$	−2.56536	−	0.687385i	−0.0818638	−	0.0219353i
$983$	37.0960	−	18.2937i	1.18318	−	0.583478i	0.259162	−	0.965834i	$-0.416554\pi$
$983$	37.0960	−	18.2937i	1.18318	−	0.583478i	0.924015	+	0.382355i	$0.124887\pi$
$984$	−8.18055	+	6.27716i	−0.260786	+	0.200108i
$985$	0.141080	+	0.244358i	0.00449518	+	0.00778588i
$986$	30.5686	−	23.8957i	0.973501	−	0.760993i
$987$	25.9003	−	17.5584i	0.824416	−	0.558890i
$988$	9.87763	−	23.8467i	0.314249	−	0.758665i
$989$	0.339341	−	5.17735i	0.0107904	−	0.164630i
$990$	0.0593391	+	0.221457i	0.00188592	+	0.00703836i
$991$	−16.6570	+	49.0699i	−0.529127	+	1.55876i	0.273252	+	0.961942i	$0.411901\pi$
$991$	−16.6570	+	49.0699i	−0.529127	+	1.55876i	−0.802379	+	0.596815i	$0.796433\pi$
$992$	−1.63009	+	3.30549i	−0.0517553	+	0.104949i
$993$	−5.24015	+	26.3440i	−0.166291	+	0.836003i
$994$	−15.1673	−	0.892009i	−0.481079	−	0.0282928i
$995$	21.6401	+	52.2437i	0.686036	+	1.65624i
$996$	8.57780	−	2.91177i	0.271798	−	0.0922630i
$997$	−2.63459	−	40.1960i	−0.0834382	−	1.27302i	−0.810209	−	0.586141i	$-0.800646\pi$
$997$	−2.63459	−	40.1960i	−0.0834382	−	1.27302i	0.726771	−	0.686880i	$-0.241020\pi$
$998$	7.39428	+	2.51002i	0.234062	+	0.0794533i
$999$	−0.544970	+	2.03386i	−0.0172421	+	0.0643483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.bl.a.367.7	yes	192
7.5	odd	6	inner	714.2.bl.a.61.7	✓	192
17.12	odd	16	inner	714.2.bl.a.199.7	yes	192
119.12	even	48	inner	714.2.bl.a.607.7	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.bl.a.61.7	✓	192	7.5	odd	6	inner
714.2.bl.a.199.7	yes	192	17.12	odd	16	inner
714.2.bl.a.367.7	yes	192	1.1	even	1	trivial
714.2.bl.a.607.7	yes	192	119.12	even	48	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:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.991445 - 0.130526i) q^{2} +(0.442289 + 0.896873i) q^{3} +(0.965926 - 0.258819i) q^{4} +(-2.94516 + 2.58284i) q^{5} +(0.555570 + 0.831470i) q^{6} +(-2.43751 + 1.02886i) q^{7} +(0.923880 - 0.382683i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(-2.58284 + 2.94516i) q^{10} +(-0.0584024 + 0.00382789i) q^{11} +(0.659346 + 0.751840i) q^{12} +(-3.92397 - 3.92397i) q^{13} +(-2.28236 + 1.33821i) q^{14} +(-3.61909 - 1.49907i) q^{15} +(0.866025 - 0.500000i) q^{16} +(-1.36037 - 3.89222i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(0.607113 + 4.61148i) q^{19} +(-2.17632 + 3.25709i) q^{20} +(-2.00084 - 1.73109i) q^{21} +(-0.0574031 + 0.0114182i) q^{22} +(-1.58016 - 0.779247i) q^{23} +(0.751840 + 0.659346i) q^{24} +(1.35029 - 10.2565i) q^{25} +(-4.40259 - 3.37822i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(-2.08817 + 1.62467i) q^{28} +(1.83587 + 9.22956i) q^{29} +(-3.78379 - 1.01386i) q^{30} +(-3.30549 + 1.63009i) q^{31} +(0.793353 - 0.608761i) q^{32} +(-0.0292639 - 0.0506865i) q^{33} +(-1.85677 - 3.68136i) q^{34} +(4.52149 - 9.32583i) q^{35} +(-0.382683 + 0.923880i) q^{36} +(0.137713 - 2.10109i) q^{37} +(1.20384 + 4.49279i) q^{38} +(1.78378 - 5.25484i) q^{39} +(-1.73256 + 3.51329i) q^{40} +(-2.01165 + 10.1132i) q^{41} +(-2.20967 - 1.45511i) q^{42} +(1.12696 + 2.72072i) q^{43} +(-0.0554216 + 0.0188131i) q^{44} +(-0.256202 - 3.90888i) q^{45} +(-1.66835 - 0.566329i) q^{46} +(-3.06102 + 11.4239i) q^{47} +(0.831470 + 0.555570i) q^{48} +(4.88291 - 5.01569i) q^{49} -10.3450i q^{50} +(2.88915 - 2.94156i) q^{51} +(-4.80587 - 2.77467i) q^{52} +(6.05849 + 7.89558i) q^{53} +(-0.997859 - 0.0654031i) q^{54} +(0.162118 - 0.162118i) q^{55} +(-1.85824 + 1.88333i) q^{56} +(-3.86739 + 2.58411i) q^{57} +(3.02487 + 8.91097i) q^{58} +(4.06869 + 0.535653i) q^{59} +(-3.88376 - 0.511306i) q^{60} +(1.60031 + 4.71437i) q^{61} +(-3.06444 + 2.04760i) q^{62} +(0.667617 - 2.56013i) q^{63} +(0.707107 - 0.707107i) q^{64} +(21.6917 + 1.42175i) q^{65} +(-0.0356294 - 0.0464331i) q^{66} +(-8.49844 - 4.90657i) q^{67} +(-2.32140 - 3.40751i) q^{68} -1.76185i q^{69} +(3.26555 - 9.83622i) q^{70} +(4.77482 + 3.19043i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-4.96680 - 1.68600i) q^{73} +(-0.137713 - 2.10109i) q^{74} +(9.79600 - 3.32529i) q^{75} +(1.77997 + 4.29722i) q^{76} +(0.138418 - 0.0694181i) q^{77} +(1.08262 - 5.44271i) q^{78} +(3.95145 - 8.01275i) q^{79} +(-1.25917 + 3.70938i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(-0.674395 + 10.2893i) q^{82} +(3.46655 - 8.36899i) q^{83} +(-2.38070 - 1.15425i) q^{84} +(14.0595 + 7.94961i) q^{85} +(1.47245 + 2.55035i) q^{86} +(-7.46576 + 5.72868i) q^{87} +(-0.0524919 + 0.0258861i) q^{88} +(-0.739906 - 0.198257i) q^{89} +(-0.764221 - 3.84200i) q^{90} +(13.6019 + 5.52753i) q^{91} +(-1.72800 - 0.343720i) q^{92} +(-2.92396 - 2.24364i) q^{93} +(-1.54372 + 11.7257i) q^{94} +(-13.6987 - 12.0135i) q^{95} +(0.896873 + 0.442289i) q^{96} +(-4.91058 + 0.976775i) q^{97} +(4.18646 - 5.61013i) q^{98} +(0.0325162 - 0.0486640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 48 q^{10} + 16 q^{11} - 16 q^{14} + 32 q^{15} - 96 q^{18} + 32 q^{22} + 16 q^{25} + 32 q^{28} - 32 q^{29} + 64 q^{35} - 48 q^{37} - 64 q^{43} - 16 q^{46} + 48 q^{47} + 64 q^{49} + 16 q^{53} + 16 q^{58}+ \cdots - 32 q^{99}+O(q^{100}) \) 192 * q - 48 * q^10 + 16 * q^11 - 16 * q^14 + 32 * q^15 - 96 * q^18 + 32 * q^22 + 16 * q^25 + 32 * q^28 - 32 * q^29 + 64 * q^35 - 48 * q^37 - 64 * q^43 - 16 * q^46 + 48 * q^47 + 64 * q^49 + 16 * q^53 + 16 * q^58 + 48 * q^61 - 64 * q^65 + 16 * q^70 - 32 * q^71 + 240 * q^73 + 48 * q^74 + 16 * q^77 - 64 * q^78 - 64 * q^79 + 48 * q^80 - 64 * q^85 + 32 * q^86 + 144 * q^87 + 16 * q^88 + 144 * q^89 - 64 * q^91 + 48 * q^94 + 80 * q^95 - 80 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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