LMFDB - Embedded newform 180.2.q.a.11.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,2,Mod(11,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("180.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.q (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	180.11
Dual form			180.2.q.a.131.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.896034 - 1.09413i) q^{2} +(1.60382 + 0.654027i) q^{3} +(-0.394247 + 1.96076i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.721488 - 2.34082i) q^{6} +(1.04714 + 0.604565i) q^{7} +(2.49858 - 1.32555i) q^{8} +(2.14450 + 2.09789i) q^{9} +(1.32305 + 0.499529i) q^{10} +(1.52161 - 2.63550i) q^{11} +(-1.91469 + 2.88686i) q^{12} +(2.53958 + 4.39869i) q^{13} +(-0.276797 - 1.68742i) q^{14} +(-1.71597 + 0.235507i) q^{15} +(-3.68914 - 1.54605i) q^{16} +2.23944i q^{17} +(0.373823 - 4.22614i) q^{18} -2.53835i q^{19} +(-0.638951 - 1.89519i) q^{20} +(1.28402 + 1.65447i) q^{21} +(-4.24700 + 0.696660i) q^{22} +(-3.48067 - 6.02870i) q^{23} +(4.87423 - 0.491800i) q^{24} +(0.500000 - 0.866025i) q^{25} +(2.53719 - 6.72001i) q^{26} +(2.06732 + 4.76720i) q^{27} +(-1.59824 + 1.81484i) q^{28} +(-4.84407 - 2.79673i) q^{29} +(1.79524 + 1.66647i) q^{30} +(2.83759 - 1.63828i) q^{31} +(1.61401 + 5.42171i) q^{32} +(4.16408 - 3.23171i) q^{33} +(2.45024 - 2.00661i) q^{34} -1.20913 q^{35} +(-4.95891 + 3.37775i) q^{36} -10.3514 q^{37} +(-2.77729 + 2.27445i) q^{38} +(1.19618 + 8.71567i) q^{39} +(-1.50106 + 2.39725i) q^{40} +(3.70208 - 2.13740i) q^{41} +(0.659684 - 2.88735i) q^{42} +(-3.74108 - 2.15991i) q^{43} +(4.56769 + 4.02254i) q^{44} +(-2.90613 - 0.744575i) q^{45} +(-3.47739 + 9.21023i) q^{46} +(-5.15071 + 8.92129i) q^{47} +(-4.90557 - 4.89238i) q^{48} +(-2.76900 - 4.79605i) q^{49} +(-1.39556 + 0.228922i) q^{50} +(-1.46465 + 3.59166i) q^{51} +(-9.62598 + 3.24534i) q^{52} +9.42683i q^{53} +(3.36356 - 6.53349i) q^{54} +3.04322i q^{55} +(3.41774 + 0.122528i) q^{56} +(1.66015 - 4.07106i) q^{57} +(1.28047 + 7.80601i) q^{58} +(-4.46335 - 7.73074i) q^{59} +(0.214742 - 3.45744i) q^{60} +(1.32896 - 2.30183i) q^{61} +(-4.33508 - 1.63674i) q^{62} +(0.977274 + 3.49327i) q^{63} +(4.48585 - 6.62398i) q^{64} +(-4.39869 - 2.53958i) q^{65} +(-7.26707 - 1.66033i) q^{66} +(12.4858 - 7.20867i) q^{67} +(-4.39099 - 0.882891i) q^{68} +(-1.63945 - 11.9454i) q^{69} +(1.08342 + 1.32295i) q^{70} +3.49303 q^{71} +(8.13906 + 2.39912i) q^{72} +5.10052 q^{73} +(9.27523 + 11.3258i) q^{74} +(1.36832 - 1.06194i) q^{75} +(4.97709 + 1.00074i) q^{76} +(3.18667 - 1.83982i) q^{77} +(8.46427 - 9.11832i) q^{78} +(-3.26472 - 1.88488i) q^{79} +(3.96791 - 0.505654i) q^{80} +(0.197735 + 8.99783i) q^{81} +(-5.65579 - 2.13538i) q^{82} +(-0.286172 + 0.495665i) q^{83} +(-3.75024 + 1.86538i) q^{84} +(-1.11972 - 1.93941i) q^{85} +(0.988904 + 6.02859i) q^{86} +(-5.93990 - 7.65361i) q^{87} +(0.308386 - 8.60199i) q^{88} +2.40129i q^{89} +(1.78933 + 3.84686i) q^{90} +6.14138i q^{91} +(13.1931 - 4.44795i) q^{92} +(5.62248 - 0.771656i) q^{93} +(14.3763 - 2.35822i) q^{94} +(1.26918 + 2.19828i) q^{95} +(-0.957353 + 9.75108i) q^{96} +(5.82556 - 10.0902i) q^{97} +(-2.76639 + 7.32708i) q^{98} +(8.79207 - 2.45966i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} + 4 q^{9} - 22 q^{12} - 30 q^{14} - 16 q^{18} - 4 q^{21} - 28 q^{24} + 24 q^{25} - 12 q^{29} + 16 q^{30} - 44 q^{33} - 6 q^{34} + 42 q^{36} + 60 q^{38} - 6 q^{40} - 60 q^{41} - 18 q^{42}+ \cdots - 12 q^{97}+O(q^{100}) $ 48 * q + 6 * q^6 + 4 * q^9 - 22 * q^12 - 30 * q^14 - 16 * q^18 - 4 * q^21 - 28 * q^24 + 24 * q^25 - 12 * q^29 + 16 * q^30 - 44 * q^33 - 6 * q^34 + 42 * q^36 + 60 * q^38 - 6 * q^40 - 60 * q^41 - 18 * q^42 - 8 * q^45 - 12 * q^46 - 12 * q^48 + 24 * q^49 - 18 * q^52 - 32 * q^54 - 42 * q^56 - 12 * q^57 - 18 * q^58 + 14 * q^60 - 48 * q^64 + 16 * q^66 + 48 * q^68 + 36 * q^69 + 60 * q^72 - 24 * q^73 + 84 * q^74 + 6 * q^76 + 48 * q^77 + 38 * q^78 - 36 * q^82 + 50 * q^84 - 54 * q^86 - 18 * q^90 + 60 * q^92 - 32 * q^93 + 18 * q^94 - 18 * q^96 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.896034	−	1.09413i	−0.633592	−	0.773668i
$2$	−0.896034	−	1.09413i	−0.633592	−	0.773668i
$3$	1.60382	+	0.654027i	0.925968	+	0.377603i
$3$	1.60382	+	0.654027i	0.925968	+	0.377603i
$4$	−0.394247	+	1.96076i	−0.197124	+	0.980379i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	−0.721488	−	2.34082i	−0.294546	−	0.955637i
$7$	1.04714	+	0.604565i	0.395781	+	0.228504i	0.684662	−	0.728861i	$-0.259950\pi$
$7$	1.04714	+	0.604565i	0.395781	+	0.228504i	−0.288881	+	0.957365i	$0.593283\pi$
$8$	2.49858	−	1.32555i	0.883383	−	0.468651i
$9$	2.14450	+	2.09789i	0.714832	+	0.699296i
$10$	1.32305	+	0.499529i	0.418386	+	0.157965i
$11$	1.52161	−	2.63550i	0.458782	−	0.794634i	−0.540115	−	0.841591i	$-0.681619\pi$
$11$	1.52161	−	2.63550i	0.458782	−	0.794634i	0.998897	+	0.0469575i	$0.0149525\pi$
$12$	−1.91469	+	2.88686i	−0.552724	+	0.833365i
$13$	2.53958	+	4.39869i	0.704354	+	1.21998i	0.966924	+	0.255064i	$0.0820965\pi$
$13$	2.53958	+	4.39869i	0.704354	+	1.21998i	−0.262570	+	0.964913i	$0.584570\pi$
$14$	−0.276797	−	1.68742i	−0.0739771	−	0.450981i
$15$	−1.71597	+	0.235507i	−0.443060	+	0.0608078i
$16$	−3.68914	−	1.54605i	−0.922285	−	0.386512i
$17$			2.23944i			0.543143i	0.962418	+	0.271572i	$0.0875434\pi$
$17$			2.23944i			0.543143i	−0.962418	+	0.271572i	$0.912457\pi$
$18$	0.373823	−	4.22614i	0.0881110	−	0.996111i
$19$		−	2.53835i		−	0.582337i	−0.956672	−	0.291169i	$-0.905956\pi$
$19$		−	2.53835i		−	0.582337i	0.956672	−	0.291169i	$-0.0940441\pi$
$20$	−0.638951	−	1.89519i	−0.142874	−	0.423777i
$21$	1.28402	+	1.65447i	0.280197	+	0.361035i
$22$	−4.24700	+	0.696660i	−0.905463	+	0.148528i
$23$	−3.48067	−	6.02870i	−0.725770	−	1.25707i	−0.958656	−	0.284567i	$-0.908150\pi$
$23$	−3.48067	−	6.02870i	−0.725770	−	1.25707i	0.232886	−	0.972504i	$-0.425183\pi$
$24$	4.87423	−	0.491800i	0.994948	−	0.100388i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	2.53719	−	6.72001i	0.497584	−	1.31790i
$27$	2.06732	+	4.76720i	0.397856	+	0.917448i
$28$	−1.59824	+	1.81484i	−0.302038	+	0.342972i
$29$	−4.84407	−	2.79673i	−0.899521	−	0.519339i	−0.0224766	−	0.999747i	$-0.507155\pi$
$29$	−4.84407	−	2.79673i	−0.899521	−	0.519339i	−0.877045	+	0.480408i	$0.840488\pi$
$30$	1.79524	+	1.66647i	0.327764	+	0.304254i
$31$	2.83759	−	1.63828i	0.509647	−	0.294245i	−0.223042	−	0.974809i	$-0.571599\pi$
$31$	2.83759	−	1.63828i	0.509647	−	0.294245i	0.732688	+	0.680564i	$0.238265\pi$
$32$	1.61401	+	5.42171i	0.285320	+	0.958432i
$33$	4.16408	−	3.23171i	0.724873	−	0.562568i
$34$	2.45024	−	2.00661i	0.420212	−	0.344131i
$35$	−1.20913			−0.204380
$36$	−4.95891	+	3.37775i	−0.826485	+	0.562959i
$37$	−10.3514			−1.70176			−0.850882	−	0.525356i	$-0.823932\pi$
$37$	−10.3514			−1.70176			−0.850882	+	0.525356i	$0.823932\pi$
$38$	−2.77729	+	2.27445i	−0.450536	+	0.368964i
$39$	1.19618	+	8.71567i	0.191542	+	1.39562i
$40$	−1.50106	+	2.39725i	−0.237339	+	0.379038i
$41$	3.70208	−	2.13740i	0.578168	−	0.333806i	−0.182237	−	0.983255i	$-0.558334\pi$
$41$	3.70208	−	2.13740i	0.578168	−	0.333806i	0.760405	+	0.649449i	$0.225000\pi$
$42$	0.659684	−	2.88735i	0.101791	−	0.445528i
$43$	−3.74108	−	2.15991i	−0.570509	−	0.329384i	0.186844	−	0.982390i	$-0.440174\pi$
$43$	−3.74108	−	2.15991i	−0.570509	−	0.329384i	−0.757353	+	0.653006i	$0.773508\pi$
$44$	4.56769	+	4.02254i	0.688605	+	0.606421i
$45$	−2.90613	−	0.744575i	−0.433221	−	0.110995i
$46$	−3.47739	+	9.21023i	−0.512713	+	1.35797i
$47$	−5.15071	+	8.92129i	−0.751308	+	1.30130i	0.195880	+	0.980628i	$0.437244\pi$
$47$	−5.15071	+	8.92129i	−0.751308	+	1.30130i	−0.947189	+	0.320677i	$0.896090\pi$
$48$	−4.90557	−	4.89238i	−0.708058	−	0.706154i
$49$	−2.76900	−	4.79605i	−0.395572	−	0.685150i
$50$	−1.39556	+	0.228922i	−0.197362	+	0.0323745i
$51$	−1.46465	+	3.59166i	−0.205092	+	0.502933i
$52$	−9.62598	+	3.24534i	−1.33488	+	0.450047i
$53$			9.42683i			1.29487i	0.762119	+	0.647437i	$0.224159\pi$
$53$			9.42683i			1.29487i	−0.762119	+	0.647437i	$0.775841\pi$
$54$	3.36356	−	6.53349i	0.457722	−	0.889095i
$55$			3.04322i			0.410347i
$56$	3.41774	+	0.122528i	0.456715	+	0.0163735i
$57$	1.66015	−	4.07106i	0.219892	−	0.539226i
$58$	1.28047	+	7.80601i	0.168133	+	1.02498i
$59$	−4.46335	−	7.73074i	−0.581078	−	1.00646i	−0.995352	−	0.0963045i	$-0.969298\pi$
$59$	−4.46335	−	7.73074i	−0.581078	−	1.00646i	0.414274	−	0.910152i	$-0.364036\pi$
$60$	0.214742	−	3.45744i	0.0277230	−	0.446353i
$61$	1.32896	−	2.30183i	0.170156	−	0.294720i	−0.768318	−	0.640068i	$-0.778906\pi$
$61$	1.32896	−	2.30183i	0.170156	−	0.294720i	0.938474	+	0.345349i	$0.112239\pi$
$62$	−4.33508	−	1.63674i	−0.550555	−	0.207866i
$63$	0.977274	+	3.49327i	0.123125	+	0.440110i
$64$	4.48585	−	6.62398i	0.560732	−	0.827998i
$65$	−4.39869	−	2.53958i	−0.545590	−	0.314997i
$66$	−7.26707	−	1.66033i	−0.894514	−	0.204373i
$67$	12.4858	−	7.20867i	1.52538	−	0.880679i	0.525833	−	0.850588i	$-0.323754\pi$
$67$	12.4858	−	7.20867i	1.52538	−	0.880679i	0.999547	−	0.0300911i	$-0.00957975\pi$
$68$	−4.39099	−	0.882891i	−0.532486	−	0.107066i
$69$	−1.63945	−	11.9454i	−0.197366	−	1.43806i
$70$	1.08342	+	1.32295i	0.129494	+	0.158123i
$71$	3.49303			0.414546			0.207273	−	0.978283i	$-0.433541\pi$
$71$	3.49303			0.414546			0.207273	+	0.978283i	$0.433541\pi$
$72$	8.13906	+	2.39912i	0.959197	+	0.282739i
$73$	5.10052			0.596970			0.298485	−	0.954414i	$-0.403519\pi$
$73$	5.10052			0.596970			0.298485	+	0.954414i	$0.403519\pi$
$74$	9.27523	+	11.3258i	1.07822	+	1.31660i
$75$	1.36832	−	1.06194i	0.157999	−	0.122622i
$76$	4.97709	+	1.00074i	0.570911	+	0.114792i
$77$	3.18667	−	1.83982i	0.363154	−	0.209667i
$78$	8.46427	−	9.11832i	0.958390	−	1.03245i
$79$	−3.26472	−	1.88488i	−0.367309	−	0.212066i	0.304973	−	0.952361i	$-0.401353\pi$
$79$	−3.26472	−	1.88488i	−0.367309	−	0.212066i	−0.672282	+	0.740295i	$0.734686\pi$
$80$	3.96791	−	0.505654i	0.443626	−	0.0565338i
$81$	0.197735	+	8.99783i	0.0219706	+	0.999759i
$82$	−5.65579	−	2.13538i	−0.624577	−	0.235814i
$83$	−0.286172	+	0.495665i	−0.0314115	+	0.0544063i	−0.881304	−	0.472550i	$-0.843334\pi$
$83$	−0.286172	+	0.495665i	−0.0314115	+	0.0544063i	0.849892	+	0.526956i	$0.176667\pi$
$84$	−3.75024	+	1.86538i	−0.409185	+	0.203530i
$85$	−1.11972	−	1.93941i	−0.121450	−	0.210358i
$86$	0.988904	+	6.02859i	0.106636	+	0.650079i
$87$	−5.93990	−	7.65361i	−0.636824	−	0.820553i
$88$	0.308386	−	8.60199i	0.0328741	−	0.916975i
$89$			2.40129i			0.254536i	0.991868	+	0.127268i	$0.0406208\pi$
$89$			2.40129i			0.254536i	−0.991868	+	0.127268i	$0.959379\pi$
$90$	1.78933	+	3.84686i	0.188612	+	0.405494i
$91$			6.14138i			0.643791i
$92$	13.1931	−	4.44795i	1.37547	−	0.463731i
$93$	5.62248	−	0.771656i	0.583024	−	0.0800170i
$94$	14.3763	−	2.35822i	1.48280	−	0.243232i
$95$	1.26918	+	2.19828i	0.130215	+	0.225538i
$96$	−0.957353	+	9.75108i	−0.0977094	+	0.995215i
$97$	5.82556	−	10.0902i	0.591496	−	1.02450i	−0.402535	−	0.915404i	$-0.631871\pi$
$97$	5.82556	−	10.0902i	0.591496	−	1.02450i	0.994031	−	0.109096i	$-0.0347957\pi$
$98$	−2.76639	+	7.32708i	−0.279448	+	0.740146i
$99$	8.79207	−	2.45966i	0.883636	−	0.247206i
$100$	1.50094	+	1.32181i	0.150094	+	0.132181i
$101$	−4.13758	−	2.38883i	−0.411704	−	0.237698i	0.279818	−	0.960053i	$-0.409726\pi$
$101$	−4.13758	−	2.38883i	−0.411704	−	0.237698i	−0.691522	+	0.722356i	$0.743059\pi$
$102$	5.24213	−	1.61573i	0.519048	−	0.159981i
$103$	8.19166	−	4.72945i	0.807148	−	0.466007i	−0.0388166	−	0.999246i	$-0.512359\pi$
$103$	8.19166	−	4.72945i	0.807148	−	0.466007i	0.845964	+	0.533239i	$0.179025\pi$
$104$	12.1760	+	7.62416i	1.19396	+	0.747610i
$105$	−1.93923	−	0.790804i	−0.189250	−	0.0771746i
$106$	10.3142	−	8.44676i	1.00180	−	0.820422i
$107$	−18.3014			−1.76926			−0.884630	−	0.466294i	$-0.845589\pi$
$107$	−18.3014			−1.76926			−0.884630	+	0.466294i	$0.845589\pi$
$108$	−10.1624	+	2.17405i	−0.977873	+	0.209199i
$109$	−10.2589			−0.982625			−0.491312	−	0.870983i	$-0.663483\pi$
$109$	−10.2589			−0.982625			−0.491312	+	0.870983i	$0.663483\pi$
$110$	3.32968	−	2.72682i	0.317472	−	0.259992i
$111$	−16.6019	−	6.77012i	−1.57578	−	0.642591i
$112$	−2.92835	−	3.84925i	−0.276703	−	0.363720i
$113$	5.31273	−	3.06731i	0.499780	−	0.288548i	−0.228843	−	0.973463i	$-0.573494\pi$
$113$	5.31273	−	3.06731i	0.499780	−	0.288548i	0.728623	+	0.684915i	$0.240161\pi$
$114$	−5.94183	+	1.83139i	−0.556503	+	0.171525i
$115$	6.02870	+	3.48067i	0.562179	+	0.324574i
$116$	7.39346	−	8.39545i	0.686466	−	0.779498i
$117$	−3.78182	+	14.7607i	−0.349630	+	1.36463i
$118$	−4.45914	+	11.8105i	−0.410497	+	1.08724i
$119$	−1.35389	+	2.34500i	−0.124110	+	0.214966i
$120$	−3.97531	+	2.86303i	−0.362894	+	0.261357i
$121$	0.869419	+	1.50588i	0.0790381	+	0.136898i
$122$	−3.70930	+	0.608459i	−0.335825	+	0.0550873i
$123$	7.33540	−	1.00675i	0.661411	−	0.0907753i
$124$	2.09357	+	6.20972i	0.188008	+	0.557649i
$125$			1.00000i			0.0894427i
$126$	2.94642	−	4.19935i	0.262488	−	0.374108i
$127$		−	9.41213i		−	0.835192i	−0.908633	−	0.417596i	$-0.862873\pi$
$127$		−	9.41213i		−	0.835192i	0.908633	−	0.417596i	$-0.137127\pi$
$128$	−11.2670	+	1.02720i	−0.995870	+	0.0907922i
$129$	−4.58739	−	5.91088i	−0.403897	−	0.520424i
$130$	1.16273	+	7.08830i	0.101979	+	0.621685i
$131$	1.06630	+	1.84689i	0.0931633	+	0.161364i	0.908841	−	0.417144i	$-0.136969\pi$
$131$	1.06630	+	1.84689i	0.0931633	+	0.161364i	−0.815677	+	0.578507i	$0.803635\pi$
$132$	4.69492	+	9.43884i	0.408640	+	0.821546i
$133$	1.53460	−	2.65800i	0.133067	−	0.230478i
$134$	−19.0749	−	7.20187i	−1.64782	−	0.622147i
$135$	−4.17395	−	3.09486i	−0.359236	−	0.266363i
$136$	2.96848	+	5.59542i	0.254545	+	0.479803i
$137$	14.2781	+	8.24344i	1.21986	+	0.704285i	0.964887	−	0.262665i	$-0.0846013\pi$
$137$	14.2781	+	8.24344i	1.21986	+	0.704285i	0.254969	+	0.966949i	$0.417935\pi$
$138$	−11.6009	+	12.4973i	−0.987531	+	1.06384i
$139$	−17.4077	+	10.0504i	−1.47650	+	0.852460i	−0.999648	−	0.0265213i	$-0.991557\pi$
$139$	−17.4077	+	10.0504i	−1.47650	+	0.852460i	−0.476856	+	0.878981i	$0.658224\pi$
$140$	0.476696	−	2.37081i	0.0402882	−	0.200370i
$141$	−14.0956	+	10.9395i	−1.18706	+	0.921270i
$142$	−3.12987	−	3.82183i	−0.262653	−	0.320721i
$143$	15.4570			1.29258
$144$	−4.66792	−	11.0549i	−0.388993	−	0.921241i
$145$	5.59345			0.464511
$146$	−4.57023	−	5.58064i	−0.378235	−	0.461857i
$147$	−1.30424	−	9.50302i	−0.107572	−	0.783796i
$148$	4.08102	−	20.2966i	0.335458	−	1.66837i
$149$	1.63133	−	0.941851i	0.133644	−	0.0771594i	−0.431687	−	0.902023i	$-0.642082\pi$
$149$	1.63133	−	0.941851i	0.133644	−	0.0771594i	0.565331	+	0.824864i	$0.308748\pi$
$150$	−2.38796	−	0.545585i	−0.194976	−	0.0445468i
$151$	5.35919	+	3.09413i	0.436124	+	0.251796i	0.701952	−	0.712224i	$-0.252312\pi$
$151$	5.35919	+	3.09413i	0.436124	+	0.251796i	−0.265828	+	0.964020i	$0.585645\pi$
$152$	−3.36470	−	6.34228i	−0.272913	−	0.514427i
$153$	−4.69809	+	4.80246i	−0.379818	+	0.388256i
$154$	−4.86837	−	1.83809i	−0.392304	−	0.148117i
$155$	−1.63828	+	2.83759i	−0.131590	+	0.227921i
$156$	−17.5609	−	1.09071i	−1.40600	−	0.0873265i
$157$	1.10012	+	1.90546i	0.0877991	+	0.152073i	0.906581	−	0.422033i	$-0.138683\pi$
$157$	1.10012	+	1.90546i	0.0877991	+	0.152073i	−0.818781	+	0.574105i	$0.805350\pi$
$158$	0.862984	+	5.26095i	0.0686553	+	0.418539i
$159$	−6.16540	+	15.1190i	−0.488948	+	1.19901i
$160$	−4.10863	−	3.88833i	−0.324816	−	0.307400i
$161$		−	8.41717i		−	0.663366i
$162$	9.66763	−	8.27871i	0.759561	−	0.650436i
$163$			15.3649i			1.20347i	0.798694	+	0.601737i	$0.205525\pi$
$163$			15.3649i			1.20347i	−0.798694	+	0.601737i	$0.794475\pi$
$164$	2.73138	+	8.10155i	0.213285	+	0.632625i
$165$	−1.99035	+	4.88078i	−0.154948	+	0.379968i
$166$	0.798742	−	0.131022i	0.0619944	−	0.0101693i
$167$	11.1124	+	19.2472i	0.859901	+	1.48939i	0.872023	+	0.489465i	$0.162808\pi$
$167$	11.1124	+	19.2472i	0.859901	+	1.48939i	−0.0121218	+	0.999927i	$0.503859\pi$
$168$	5.40132	+	2.43181i	0.416721	+	0.187618i
$169$	−6.39897	+	11.0833i	−0.492229	+	0.852565i
$170$	−1.11866	+	2.96289i	−0.0857975	+	0.227244i
$171$	5.32517	−	5.44348i	0.407226	−	0.416274i
$172$	5.70997	−	6.48381i	0.435381	−	0.494386i
$173$	−13.3460	−	7.70532i	−1.01468	−	0.585825i	−0.102120	−	0.994772i	$-0.532563\pi$
$173$	−13.3460	−	7.70532i	−1.01468	−	0.585825i	−0.912558	+	0.408947i	$0.865896\pi$
$174$	−3.05170	+	13.3569i	−0.231349	+	1.01259i
$175$	1.04714	−	0.604565i	0.0791562	−	0.0457008i
$176$	−9.68803	+	7.37026i	−0.730263	+	0.555554i
$177$	−2.10230	−	15.3179i	−0.158019	−	1.15136i
$178$	2.62733	−	2.15164i	0.196926	−	0.161272i
$179$	12.8229			0.958425			0.479212	−	0.877699i	$-0.340922\pi$
$179$	12.8229			0.958425			0.479212	+	0.877699i	$0.340922\pi$
$180$	2.60567	−	5.40467i	0.194215	−	0.402841i
$181$	17.3649			1.29072			0.645360	−	0.763879i	$-0.276707\pi$
$181$	17.3649			1.29072			0.645360	+	0.763879i	$0.276707\pi$
$182$	6.71947	−	5.50288i	0.498081	−	0.407901i
$183$	3.63688	−	2.82255i	0.268846	−	0.208649i
$184$	−16.6881	−	10.4494i	−1.23026	−	0.770342i
$185$	8.96460	−	5.17572i	0.659091	−	0.380526i
$186$	−5.88222	−	5.46030i	−0.431306	−	0.400369i
$187$	5.90204	+	3.40754i	0.431600	+	0.249184i
$188$	−15.4618	−	13.6165i	−1.12767	−	0.993085i
$189$	−0.717316	+	6.24174i	−0.0521771	+	0.454020i
$190$	1.26798	−	3.35837i	0.0919889	−	0.243642i
$191$	8.91431	−	15.4400i	0.645017	−	1.11720i	−0.339281	−	0.940685i	$-0.610184\pi$
$191$	8.91431	−	15.4400i	0.645017	−	1.11720i	0.984298	−	0.176516i	$-0.0564829\pi$
$192$	11.5268	−	7.68982i	0.831874	−	0.554965i
$193$	2.44181	+	4.22934i	0.175765	+	0.304434i	0.940426	−	0.339999i	$-0.110427\pi$
$193$	2.44181	+	4.22934i	0.175765	+	0.304434i	−0.764661	+	0.644433i	$0.777093\pi$
$194$	−16.2599	+	2.66720i	−1.16739	+	0.191494i
$195$	−5.39376	−	6.94990i	−0.386255	−	0.497693i
$196$	10.4956	−	3.53851i	0.749683	−	0.252751i
$197$			16.8173i			1.19818i	0.800682	+	0.599090i	$0.204471\pi$
$197$			16.8173i			1.19818i	−0.800682	+	0.599090i	$0.795529\pi$
$198$	−10.5692	−	7.41574i	−0.751119	−	0.527014i
$199$		−	5.91492i		−	0.419297i	−0.977777	−	0.209649i	$-0.932768\pi$
$199$		−	5.91492i		−	0.419297i	0.977777	−	0.209649i	$-0.0672320\pi$
$200$	0.101336	−	2.82661i	0.00716551	−	0.199872i
$201$	24.7396	−	3.39539i	1.74500	−	0.239492i
$202$	1.09371	+	6.66752i	0.0769534	+	0.469125i
$203$	−3.38161	−	5.85712i	−0.237342	−	0.411089i
$204$	−6.46494	−	4.28783i	−0.452636	−	0.300208i
$205$	−2.13740	+	3.70208i	−0.149282	+	0.258565i
$206$	−12.5146	−	4.72500i	−0.871937	−	0.329206i
$207$	5.18325	−	20.2306i	0.360260	−	1.40612i
$208$	−2.56830	−	20.1537i	−0.178080	−	1.39741i
$209$	−6.68983	−	3.86237i	−0.462745	−	0.267166i
$210$	0.872373	+	2.83036i	0.0601995	+	0.195314i
$211$	−23.9485	+	13.8267i	−1.64868	+	0.951868i	−0.671089	+	0.741377i	$0.734173\pi$
$211$	−23.9485	+	13.8267i	−1.64868	+	0.951868i	−0.977596	+	0.210491i	$0.932494\pi$
$212$	−18.4837	−	3.71650i	−1.26947	−	0.255250i
$213$	5.60220	+	2.28453i	0.383856	+	0.156534i
$214$	16.3986	+	20.0241i	1.12099	+	1.36882i
$215$	4.31983			0.294610
$216$	11.4845	+	9.17093i	0.781422	+	0.624003i
$217$	3.96180			0.268945
$218$	9.19232	+	11.2246i	0.622583	+	0.760225i
$219$	8.18033	+	3.33588i	0.552775	+	0.225418i
$220$	−5.96701	−	1.19978i	−0.402296	−	0.0808891i
$221$	−9.85058	+	5.68724i	−0.662622	+	0.382565i
$222$	7.46843	+	24.2309i	0.501248	+	1.62627i
$223$	−20.7390	−	11.9737i	−1.38878	−	0.801815i	−0.395606	−	0.918420i	$-0.629465\pi$
$223$	−20.7390	−	11.9737i	−1.38878	−	0.801815i	−0.993178	+	0.116605i	$0.962799\pi$
$224$	−1.58768	+	6.65306i	−0.106082	+	0.444526i
$225$	2.88907	−	0.808245i	0.192605	−	0.0538830i
$226$	−8.11643	−	3.06442i	−0.539897	−	0.203842i
$227$	−3.45979	+	5.99253i	−0.229634	+	0.397739i	−0.957700	−	0.287769i	$-0.907086\pi$
$227$	−3.45979	+	5.99253i	−0.229634	+	0.397739i	0.728065	+	0.685508i	$0.240420\pi$
$228$	7.32786	+	4.86016i	0.485299	+	0.321872i
$229$	7.65837	+	13.2647i	0.506080	+	0.876556i	0.999975	+	0.00703439i	$0.00223914\pi$
$229$	7.65837	+	13.2647i	0.506080	+	0.876556i	−0.493896	+	0.869521i	$0.664428\pi$
$230$	−1.59361	−	9.71499i	−0.105079	−	0.640587i
$231$	6.31414	−	0.866584i	0.415440	−	0.0570170i
$232$	−15.8105	−	0.566816i	−1.03801	−	0.0372133i
$233$			6.61050i			0.433068i	0.976275	+	0.216534i	$0.0694753\pi$
$233$			6.61050i			0.433068i	−0.976275	+	0.216534i	$0.930525\pi$
$234$	19.5388	−	9.08830i	1.27729	−	0.594121i
$235$		−	10.3014i		−	0.671991i
$236$	16.9178	−	5.70371i	1.10125	−	0.371280i
$237$	−4.00326	−	5.15823i	−0.260040	−	0.335063i
$238$	3.77886	−	0.619869i	0.244947	−	0.0401801i
$239$	4.11060	+	7.11976i	0.265892	+	0.460539i	0.967797	−	0.251732i	$-0.0810001\pi$
$239$	4.11060	+	7.11976i	0.265892	+	0.460539i	−0.701905	+	0.712271i	$0.747667\pi$
$240$	6.69454	+	1.78414i	0.432131	+	0.115166i
$241$	−7.30777	+	12.6574i	−0.470735	+	0.815337i	−0.999440	−	0.0334691i	$-0.989344\pi$
$241$	−7.30777	+	12.6574i	−0.470735	+	0.815337i	0.528705	+	0.848806i	$0.322678\pi$
$242$	0.868600	−	2.30058i	0.0558357	−	0.147887i
$243$	−5.56769	+	14.5602i	−0.357168	+	0.934040i
$244$	3.98940	+	3.51327i	0.255395	+	0.224914i
$245$	4.79605	+	2.76900i	0.306408	+	0.176905i
$246$	−7.67428	−	7.12382i	−0.489294	−	0.454198i
$247$	11.1654	−	6.44635i	0.710438	−	0.410172i
$248$	4.91834	−	7.85475i	0.312315	−	0.498777i
$249$	−0.783148	+	0.607794i	−0.0496300	+	0.0385174i
$250$	1.09413	−	0.896034i	0.0691989	−	0.0566701i
$251$	2.39191			0.150976			0.0754880	−	0.997147i	$-0.475949\pi$
$251$	2.39191			0.150976			0.0754880	+	0.997147i	$0.475949\pi$
$252$	−7.23473	+	0.538987i	−0.455745	+	0.0339530i
$253$	−21.1849			−1.33188
$254$	−10.2981	+	8.43359i	−0.646161	+	0.529170i
$255$	−0.527404	−	3.84279i	−0.0330273	−	0.240645i
$256$	11.2195	+	11.4072i	0.701218	+	0.712947i
$257$	7.31747	−	4.22474i	0.456451	−	0.263532i	−0.254100	−	0.967178i	$-0.581779\pi$
$257$	7.31747	−	4.22474i	0.456451	−	0.263532i	0.710551	+	0.703646i	$0.248446\pi$
$258$	−2.35683	+	10.3156i	−0.146730	+	0.642218i
$259$	−10.8394	−	6.25812i	−0.673526	−	0.388860i
$260$	6.71368	−	7.62354i	0.416365	−	0.472792i
$261$	−4.52088	−	16.1599i	−0.279835	−	1.00027i
$262$	1.06530	−	2.82155i	0.0658143	−	0.174316i
$263$	−3.23162	+	5.59733i	−0.199270	+	0.345146i	−0.948292	−	0.317399i	$-0.897190\pi$
$263$	−3.23162	+	5.59733i	−0.199270	+	0.345146i	0.749022	+	0.662545i	$0.230524\pi$
$264$	6.12053	−	13.5944i	0.376693	−	0.836676i
$265$	−4.71342	−	8.16388i	−0.289543	−	0.501503i
$266$	−4.28326	+	0.702607i	−0.262623	+	0.0430796i
$267$	−1.57051	+	3.85124i	−0.0961135	+	0.235692i
$268$	9.21196	+	27.3236i	0.562710	+	1.66905i
$269$		−	6.14888i		−	0.374904i	−0.982274	−	0.187452i	$-0.939977\pi$
$269$		−	6.14888i		−	0.374904i	0.982274	−	0.187452i	$-0.0600229\pi$
$270$	0.353820	+	7.33995i	0.0215328	+	0.446695i
$271$		−	0.446839i		−	0.0271436i	−0.999908	−	0.0135718i	$-0.995680\pi$
$271$		−	0.446839i		−	0.0271436i	0.999908	−	0.0135718i	$-0.00432016\pi$
$272$	3.46227	−	8.26159i	0.209931	−	0.500932i
$273$	−4.01663	+	9.84968i	−0.243097	+	0.596130i
$274$	−3.77421	−	23.0085i	−0.228009	−	1.38999i
$275$	−1.52161	−	2.63550i	−0.0917564	−	0.158927i
$276$	24.0684	+	1.49489i	1.44875	+	0.0899818i
$277$	−3.41624	+	5.91710i	−0.205262	+	0.355524i	−0.950216	−	0.311592i	$-0.899138\pi$
$277$	−3.41624	+	5.91710i	−0.205262	+	0.355524i	0.744954	+	0.667115i	$0.232471\pi$
$278$	26.5943	+	10.0409i	1.59502	+	0.602212i
$279$	9.52214	+	2.43965i	0.570076	+	0.146058i
$280$	−3.02112	+	1.60276i	−0.180546	+	0.0957832i
$281$	−2.85059	−	1.64579i	−0.170052	−	0.0981794i	0.412559	−	0.910931i	$-0.364635\pi$
$281$	−2.85059	−	1.64579i	−0.170052	−	0.0981794i	−0.582610	+	0.812752i	$0.697969\pi$
$282$	24.5993	+	5.62030i	1.46487	+	0.334684i
$283$	−20.2974	+	11.7187i	−1.20655	+	0.696603i	−0.962004	−	0.273034i	$-0.911973\pi$
$283$	−20.2974	+	11.7187i	−1.20655	+	0.696603i	−0.244548	+	0.969637i	$0.578640\pi$
$284$	−1.37712	+	6.84898i	−0.0817168	+	0.406412i
$285$	0.597800	+	4.35572i	0.0354106	+	0.258011i
$286$	−13.8500	−	16.9120i	−0.818967	−	1.00003i
$287$	5.16879			0.305104
$288$	−7.91289	+	15.0129i	−0.466272	+	0.884642i
$289$	11.9849			0.704996
$290$	−5.01192	−	6.11997i	−0.294310	−	0.359377i
$291$	15.9424	−	12.3728i	0.934560	−	0.725304i
$292$	−2.01086	+	10.0009i	−0.117677	+	0.585257i
$293$	24.1734	−	13.9565i	1.41223	−	0.815349i	0.416628	−	0.909077i	$-0.363212\pi$
$293$	24.1734	−	13.9565i	1.41223	−	0.815349i	0.995598	+	0.0937278i	$0.0298784\pi$
$294$	−9.22891	+	9.94204i	−0.538241	+	0.579831i
$295$	7.73074	+	4.46335i	0.450101	+	0.259866i
$296$	−25.8639	+	13.7213i	−1.50331	+	0.797535i
$297$	15.7096	+	1.80539i	0.911564	+	0.104759i
$298$	−2.49224	−	0.940963i	−0.144371	−	0.0545085i
$299$	17.6789	−	30.6208i	1.02240	−	1.77085i
$300$	1.54275	+	3.10160i	0.0890706	+	0.179071i
$301$	−2.61162	−	4.52345i	−0.150531	−	0.260727i
$302$	−1.41663	−	8.63610i	−0.0815178	−	0.496951i
$303$	−5.07358	−	6.53735i	−0.291470	−	0.375561i
$304$	−3.92441	+	9.36432i	−0.225080	+	0.537081i
$305$			2.65793i			0.152193i
$306$	9.46417	+	0.837153i	0.541031	+	0.0478569i
$307$			22.5939i			1.28950i	0.764393	+	0.644750i	$0.223039\pi$
$307$			22.5939i			1.28950i	−0.764393	+	0.644750i	$0.776961\pi$
$308$	2.35111	+	6.97362i	0.133967	+	0.397359i
$309$	16.2312	−	2.22764i	0.923358	−	0.126726i
$310$	4.57266	−	0.750080i	0.259709	−	0.0426017i
$311$	2.94543	+	5.10164i	0.167020	+	0.289287i	0.937371	−	0.348333i	$-0.113252\pi$
$311$	2.94543	+	5.10164i	0.167020	+	0.289287i	−0.770351	+	0.637620i	$0.779919\pi$
$312$	14.5418	+	20.1913i	0.823267	+	1.14310i
$313$	−3.88369	+	6.72675i	−0.219519	+	0.380218i	−0.954661	−	0.297695i	$-0.903782\pi$
$313$	−3.88369	+	6.72675i	−0.219519	+	0.380218i	0.735142	+	0.677913i	$0.237115\pi$
$314$	1.09908	−	2.91104i	0.0620249	−	0.164279i
$315$	−2.59298	−	2.53662i	−0.146098	−	0.142922i
$316$	4.98291	−	5.65820i	0.280310	−	0.318299i
$317$	−10.1939	−	5.88545i	−0.572547	−	0.330560i	0.185619	−	0.982622i	$-0.440571\pi$
$317$	−10.1939	−	5.88545i	−0.572547	−	0.330560i	−0.758166	+	0.652062i	$0.773904\pi$
$318$	22.0665	−	6.80134i	1.23743	−	0.381400i
$319$	−14.7416	+	8.51104i	−0.825369	+	0.476527i
$320$	−0.572873	+	7.97946i	−0.0320246	+	0.446065i
$321$	−29.3522	−	11.9696i	−1.63828	−	0.668077i
$322$	−9.20949	+	7.54207i	−0.513225	+	0.420303i
$323$	5.68447			0.316293
$324$	−17.7205	−	3.15966i	−0.984473	−	0.175537i
$325$	5.07917			0.281742
$326$	16.8113	−	13.7675i	0.931089	−	0.762511i
$327$	−16.4535	−	6.70960i	−0.909879	−	0.371042i
$328$	6.41675	−	10.2478i	0.354306	−	0.565838i
$329$	−10.7870	+	6.22788i	−0.594707	+	0.343354i
$330$	7.12363	−	2.19564i	0.392143	−	0.120866i
$331$	−3.74464	−	2.16197i	−0.205824	−	0.118833i	0.393545	−	0.919305i	$-0.371249\pi$
$331$	−3.74464	−	2.16197i	−0.205824	−	0.118833i	−0.599369	+	0.800473i	$0.704582\pi$
$332$	−0.859056	−	0.756529i	−0.0471468	−	0.0415199i
$333$	−22.1986	−	21.7161i	−1.21648	−	1.19004i
$334$	11.1019	−	29.4045i	0.607469	−	1.60894i
$335$	−7.20867	+	12.4858i	−0.393852	+	0.682171i
$336$	−2.17904	−	8.08873i	−0.118877	−	0.441277i
$337$	−3.88505	−	6.72910i	−0.211632	−	0.366558i	0.740593	−	0.671953i	$-0.234545\pi$
$337$	−3.88505	−	6.72910i	−0.211632	−	0.366558i	−0.952225	+	0.305396i	$0.901211\pi$
$338$	17.8603	−	2.92973i	0.971474	−	0.159357i
$339$	10.5268	−	1.44475i	0.571737	−	0.0784679i
$340$	4.24416	−	1.43089i	0.230172	−	0.0776009i
$341$		−	9.97131i		−	0.539977i
$342$	−10.7274	−	0.948894i	−0.580073	−	0.0513103i
$343$		−	15.1601i		−	0.818568i
$344$	−12.2105	−	0.437752i	−0.658344	−	0.0236020i
$345$	7.39252	+	9.52532i	0.398000	+	0.512826i
$346$	3.52784	+	21.5065i	0.189658	+	1.15620i
$347$	−5.63307	−	9.75677i	−0.302399	−	0.523771i	0.674280	−	0.738476i	$-0.264454\pi$
$347$	−5.63307	−	9.75677i	−0.302399	−	0.523771i	−0.976679	+	0.214705i	$0.931121\pi$
$348$	17.3487	−	8.62929i	0.929986	−	0.462578i
$349$	11.1403	−	19.2956i	0.596326	−	1.03287i	−0.397032	−	0.917805i	$-0.629960\pi$
$349$	11.1403	−	19.2956i	0.596326	−	1.03287i	0.993358	−	0.115063i	$-0.0367069\pi$
$350$	−1.59974	−	0.603996i	−0.0855100	−	0.0322849i
$351$	−15.7193	+	21.2002i	−0.839034	+	1.13158i
$352$	16.7448	+	3.99598i	0.892502	+	0.212986i
$353$	−19.1084	−	11.0323i	−1.01704	−	0.587188i	−0.103794	−	0.994599i	$-0.533098\pi$
$353$	−19.1084	−	11.0323i	−1.01704	−	0.587188i	−0.913245	+	0.407411i	$0.866432\pi$
$354$	−14.8761	+	16.0255i	−0.790653	+	0.851748i
$355$	−3.02505	+	1.74651i	−0.160553	+	0.0926953i
$356$	−4.70835	−	0.946702i	−0.249542	−	0.0501751i
$357$	−3.70509	+	2.87548i	−0.196094	+	0.152187i
$358$	−11.4897	−	14.0299i	−0.607250	−	0.741502i
$359$	−1.70332			−0.0898978			−0.0449489	−	0.998989i	$-0.514313\pi$
$359$	−1.70332			−0.0898978			−0.0449489	+	0.998989i	$0.514313\pi$
$360$	−8.24819	+	1.99183i	−0.434718	+	0.104979i
$361$	12.5568			0.660883
$362$	−15.5595	−	18.9994i	−0.817789	−	0.998588i
$363$	0.409509	+	2.98379i	0.0214937	+	0.156608i
$364$	−12.0418	−	2.42122i	−0.631159	−	0.126906i
$365$	−4.41718	+	2.55026i	−0.231206	+	0.133487i
$366$	−6.34702	−	1.45013i	−0.331764	−	0.0757993i
$367$	8.15927	+	4.71076i	0.425910	+	0.245900i	0.697603	−	0.716485i	$-0.254250\pi$
$367$	8.15927	+	4.71076i	0.425910	+	0.245900i	−0.271692	+	0.962384i	$0.587583\pi$
$368$	3.52003	+	27.6220i	0.183494	+	1.43990i
$369$	12.4231	+	3.18291i	0.646722	+	0.165696i
$370$	−13.6955	−	5.17084i	−0.711995	−	0.268819i
$371$	−5.69914	+	9.87119i	−0.295884	+	0.512487i
$372$	−0.703615	+	11.3285i	−0.0364808	+	0.587357i
$373$	−7.29277	−	12.6314i	−0.377605	−	0.654031i	0.613108	−	0.789999i	$-0.289919\pi$
$373$	−7.29277	−	12.6314i	−0.377605	−	0.654031i	−0.990713	+	0.135968i	$0.956586\pi$
$374$	−1.56013	−	9.51088i	−0.0806721	−	0.491796i
$375$	−0.654027	+	1.60382i	−0.0337738	+	0.0828211i
$376$	−1.04390	+	29.1181i	−0.0538351	+	1.50165i
$377$		−	28.4101i		−	1.46319i
$378$	7.47203	−	4.80798i	0.384320	−	0.247296i
$379$			9.46065i			0.485961i	0.970031	+	0.242980i	$0.0781251\pi$
$379$			9.46065i			0.485961i	−0.970031	+	0.242980i	$0.921875\pi$
$380$	−4.81065	+	1.62188i	−0.246781	+	0.0832007i
$381$	6.15579	−	15.0954i	0.315371	−	0.773361i
$382$	−24.8809	+	4.08137i	−1.27302	+	0.208821i
$383$	3.43007	+	5.94105i	0.175268	+	0.303573i	0.940254	−	0.340474i	$-0.110587\pi$
$383$	3.43007	+	5.94105i	0.175268	+	0.303573i	−0.764986	+	0.644047i	$0.777254\pi$
$384$	−18.7421	−	5.72147i	−0.956427	−	0.291973i
$385$	−1.83982	+	3.18667i	−0.0937661	+	0.162408i
$386$	2.43951	−	6.46129i	0.124168	−	0.328871i
$387$	−3.49148	−	12.4803i	−0.177482	−	0.634409i
$388$	17.4876	+	15.4005i	0.887801	+	0.781843i
$389$	7.11643	+	4.10868i	0.360818	+	0.208318i	0.669439	−	0.742867i	$-0.266534\pi$
$389$	7.11643	+	4.10868i	0.360818	+	0.208318i	−0.308622	+	0.951185i	$0.599868\pi$
$390$	−2.77112	+	12.1288i	−0.140321	+	0.614167i
$391$	13.5009	−	7.79474i	0.682769	−	0.394197i
$392$	−13.2760	−	8.31290i	−0.670538	−	0.419865i
$393$	0.502244	+	3.65948i	0.0253349	+	0.184596i
$394$	18.4003	−	15.0688i	0.926993	−	0.759157i
$395$	3.76977			0.189678
$396$	1.35656	+	18.2088i	0.0681695	+	0.915028i
$397$	−7.07936			−0.355303			−0.177651	−	0.984093i	$-0.556850\pi$
$397$	−7.07936			−0.355303			−0.177651	+	0.984093i	$0.556850\pi$
$398$	−6.47170	+	5.29996i	−0.324397	+	0.265663i
$399$	4.19963	−	3.25930i	0.210244	−	0.163169i
$400$	−3.18348	+	2.42186i	−0.159174	+	0.121093i
$401$	−15.3220	+	8.84615i	−0.765143	+	0.441755i	−0.831139	−	0.556064i	$-0.812311\pi$
$401$	−15.3220	+	8.84615i	−0.765143	+	0.441755i	0.0659963	+	0.997820i	$0.478977\pi$
$402$	−25.8826	−	24.0260i	−1.29090	−	1.19831i
$403$	14.4126	+	8.32112i	0.717943	+	0.414505i
$404$	6.31514	−	7.17099i	0.314190	−	0.356770i
$405$	−4.67016	−	7.69348i	−0.232062	−	0.382292i
$406$	−3.37842	+	8.94810i	−0.167668	+	0.444087i
$407$	−15.7508	+	27.2812i	−0.780739	+	1.35228i
$408$	1.10135	+	10.9155i	0.0545251	+	0.540399i
$409$	11.3542	+	19.6660i	0.561428	+	0.972422i	0.997372	+	0.0724482i	$0.0230812\pi$
$409$	11.3542	+	19.6660i	0.561428	+	0.972422i	−0.435944	+	0.899974i	$0.643585\pi$
$410$	5.96575	−	0.978596i	0.294627	−	0.0483294i
$411$	17.5080	+	22.5593i	0.863608	+	1.11277i
$412$	6.04377	+	17.9264i	0.297755	+	0.883171i
$413$		−	10.7935i		−	0.531115i
$414$	−26.7793	+	12.4561i	−1.31613	+	0.612186i
$415$		−	0.572344i		−	0.0280953i
$416$	−19.7495	+	20.8684i	−0.968299	+	1.02316i
$417$	−34.4921	+	4.73387i	−1.68909	+	0.231818i
$418$	1.76837	+	10.7804i	0.0864936	+	0.527285i
$419$	−13.1805	−	22.8292i	−0.643908	−	1.11528i	−0.984553	−	0.175089i	$-0.943979\pi$
$419$	−13.1805	−	22.8292i	−0.643908	−	1.11528i	0.340645	−	0.940192i	$-0.389355\pi$
$420$	2.31511	−	3.49059i	0.112966	−	0.170323i
$421$	−8.57768	+	14.8570i	−0.418050	+	0.724084i	−0.995743	−	0.0921697i	$-0.970620\pi$
$421$	−8.57768	+	14.8570i	−0.418050	+	0.724084i	0.577693	+	0.816254i	$0.303953\pi$
$422$	36.5869	+	13.8137i	1.78102	+	0.672438i
$423$	−29.7616	+	8.32607i	−1.44706	+	0.404828i
$424$	12.4957	+	23.5537i	0.606845	+	1.14387i
$425$	1.93941	+	1.11972i	0.0940751	+	0.0543143i
$426$	−2.52018	−	8.17656i	−0.122103	−	0.396156i
$427$	2.78322	−	1.60689i	0.134689	−	0.0777629i
$428$	7.21526	−	35.8845i	0.348763	−	1.73454i
$429$	24.7903	+	10.1093i	1.19689	+	0.488082i
$430$	−3.87071	−	4.72646i	−0.186662	−	0.227930i
$431$	−12.5816			−0.606037			−0.303018	−	0.952985i	$-0.597994\pi$
$431$	−12.5816			−0.606037			−0.303018	+	0.952985i	$0.597994\pi$
$432$	−0.256313	−	20.7830i	−0.0123319	−	0.999924i
$433$	−11.7433			−0.564346			−0.282173	−	0.959364i	$-0.591055\pi$
$433$	−11.7433			−0.564346			−0.282173	+	0.959364i	$0.591055\pi$
$434$	−3.54991	−	4.33473i	−0.170401	−	0.208074i
$435$	8.97091	+	3.65827i	0.430122	+	0.175401i
$436$	4.04454	−	20.1152i	0.193698	−	0.963344i
$437$	−15.3030	+	8.83516i	−0.732039	+	0.422643i
$438$	−3.67996	−	11.9394i	−0.175835	−	0.570487i
$439$	−1.45738	−	0.841421i	−0.0695571	−	0.0401588i	0.464818	−	0.885406i	$-0.346120\pi$
$439$	−1.45738	−	0.841421i	−0.0695571	−	0.0401588i	−0.534375	+	0.845247i	$0.679453\pi$
$440$	4.03392	+	7.60373i	0.192310	+	0.362494i
$441$	4.12346	−	16.0942i	0.196355	−	0.766389i
$442$	15.0490	+	5.68188i	0.715810	+	0.270259i
$443$	0.379510	−	0.657331i	0.0180311	−	0.0312307i	−0.856869	−	0.515534i	$-0.827594\pi$
$443$	0.379510	−	0.657331i	0.0180311	−	0.0312307i	0.874900	+	0.484303i	$0.160927\pi$
$444$	19.8198	−	29.8831i	0.940606	−	1.41819i
$445$	−1.20064	−	2.07958i	−0.0569160	−	0.0985814i
$446$	5.48207	+	33.4200i	0.259584	+	1.58248i
$447$	3.23237	−	0.443626i	0.152886	−	0.0209828i
$448$	8.70194	−	4.22423i	0.411128	−	0.199576i
$449$			17.4579i			0.823887i	0.911209	+	0.411943i	$0.135150\pi$
$449$			17.4579i			0.823887i	−0.911209	+	0.411943i	$0.864850\pi$
$450$	−3.47303	−	2.43681i	−0.163720	−	0.114872i
$451$		−	13.0091i		−	0.612576i
$452$	3.91972	+	11.6263i	0.184368	+	0.546853i
$453$	6.57154	+	8.46749i	0.308758	+	0.397837i
$454$	9.65671	−	1.58405i	0.453212	−	0.0743430i
$455$	−3.07069	−	5.31859i	−0.143956	−	0.249339i
$456$	−1.24836	−	12.3725i	−0.0584598	−	0.579396i
$457$	17.4319	−	30.1929i	0.815430	−	1.41237i	−0.0935884	−	0.995611i	$-0.529834\pi$
$457$	17.4319	−	30.1929i	0.815430	−	1.41237i	0.909019	−	0.416756i	$-0.136833\pi$
$458$	7.65116	−	20.2649i	0.357515	−	0.946916i
$459$	−10.6758	+	4.62963i	−0.498306	+	0.216093i
$460$	−9.20155	+	10.4486i	−0.429025	+	0.487167i
$461$	27.0906	+	15.6407i	1.26173	+	0.728462i	0.973410	−	0.229071i	$-0.0735688\pi$
$461$	27.0906	+	15.6407i	1.26173	+	0.728462i	0.288324	+	0.957533i	$0.406902\pi$
$462$	−6.60584	−	6.13201i	−0.307332	−	0.285287i
$463$	8.90511	−	5.14137i	0.413856	−	0.238940i	−0.278589	−	0.960410i	$-0.589867\pi$
$463$	8.90511	−	5.14137i	0.413856	−	0.238940i	0.692445	+	0.721471i	$0.256534\pi$
$464$	13.5466	+	17.8067i	0.628884	+	0.826654i
$465$	−4.48338	+	3.47951i	−0.207912	+	0.161359i
$466$	7.23276	−	5.92323i	0.335051	−	0.274388i
$467$	2.90585			0.134467			0.0672333	−	0.997737i	$-0.478583\pi$
$467$	2.90585			0.134467			0.0672333	+	0.997737i	$0.478583\pi$
$468$	−27.4512	−	13.2346i	−1.26893	−	0.611770i
$469$	17.4324			0.804955
$470$	−11.2711	+	9.23042i	−0.519898	+	0.425768i
$471$	0.518173	+	3.77554i	0.0238761	+	0.173967i
$472$	−21.3995	−	13.3995i	−0.984992	−	0.616764i
$473$	−11.3849	+	6.57308i	−0.523479	+	0.302231i
$474$	−2.05673	+	9.00204i	−0.0944687	+	0.413478i
$475$	−2.19828	−	1.26918i	−0.100864	−	0.0582337i
$476$	−4.06421	−	3.57915i	−0.186283	−	0.164050i
$477$	−19.7764	+	20.2158i	−0.905501	+	0.925618i
$478$	4.10672	−	10.8771i	0.187837	−	0.497506i
$479$	9.42773	−	16.3293i	0.430764	−	0.746105i	−0.566175	−	0.824285i	$-0.691578\pi$
$479$	9.42773	−	16.3293i	0.430764	−	0.746105i	0.996939	+	0.0781799i	$0.0249109\pi$
$480$	−4.04645	−	8.92336i	−0.184694	−	0.407294i
$481$	−26.2883	−	45.5327i	−1.19864	−	2.07611i
$482$	20.3969	−	3.34582i	0.929053	−	0.152398i
$483$	5.50506	−	13.4997i	0.250489	−	0.614256i
$484$	−3.29543	+	1.11103i	−0.149792	+	0.0505014i
$485$			11.6511i			0.529050i
$486$	20.9197	−	6.95469i	0.948935	−	0.315471i
$487$		−	11.5696i		−	0.524268i	−0.965031	−	0.262134i	$-0.915574\pi$
$487$		−	11.5696i		−	0.524268i	0.965031	−	0.262134i	$-0.0844263\pi$
$488$	0.269343	−	7.51293i	0.0121926	−	0.340094i
$489$	−10.0491	+	24.6426i	−0.454435	+	1.11438i
$490$	−1.26777	−	7.72863i	−0.0572721	−	0.349144i
$491$	−0.747617	−	1.29491i	−0.0337395	−	0.0584385i	0.848663	−	0.528935i	$-0.177408\pi$
$491$	−0.747617	−	1.29491i	−0.0337395	−	0.0584385i	−0.882402	+	0.470496i	$0.844075\pi$
$492$	−0.917977	+	14.7799i	−0.0413856	+	0.666327i
$493$	6.26309	−	10.8480i	0.282075	−	0.488569i
$494$	−17.0577	−	6.44028i	−0.767464	−	0.289762i
$495$	−6.38432	+	6.52617i	−0.286954	+	0.293329i
$496$	−13.0011	+	1.65681i	−0.583768	+	0.0743930i
$497$	3.65768	+	2.11176i	0.164069	+	0.0947255i
$498$	1.36673	+	0.312263i	0.0612448	+	0.0139928i
$499$	27.2612	−	15.7393i	1.22038	−	0.704586i	0.255380	−	0.966841i	$-0.417799\pi$
$499$	27.2612	−	15.7393i	1.22038	−	0.704586i	0.964999	+	0.262254i	$0.0844660\pi$
$500$	−1.96076	−	0.394247i	−0.0876877	−	0.0176313i
$501$	5.23409	+	38.1369i	0.233842	+	1.70383i
$502$	−2.14323	−	2.61706i	−0.0956571	−	0.116805i
$503$	−1.90449			−0.0849171			−0.0424585	−	0.999098i	$-0.513519\pi$
$503$	−1.90449			−0.0849171			−0.0424585	+	0.999098i	$0.513519\pi$
$504$	7.07229	+	7.43280i	0.315025	+	0.331083i
$505$	4.77766			0.212603
$506$	18.9824	+	23.1790i	0.843869	+	1.03043i
$507$	−17.5116	+	13.5906i	−0.777719	+	0.603581i
$508$	18.4549	+	3.71071i	0.818804	+	0.164636i
$509$	27.2228	−	15.7171i	1.20663	−	0.696647i	0.244607	−	0.969622i	$-0.421341\pi$
$509$	27.2228	−	15.7171i	1.20663	−	0.696647i	0.962021	+	0.272975i	$0.0880078\pi$
$510$	−3.73195	+	4.02032i	−0.165254	+	0.178023i
$511$	5.34094	+	3.08360i	0.236269	+	0.136410i
$512$	2.42789	−	22.4968i	0.107299	−	0.994227i
$513$	12.1008	−	5.24758i	0.534264	−	0.231686i
$514$	−11.1791	−	4.22076i	−0.493090	−	0.186170i
$515$	−4.72945	+	8.19166i	−0.208405	+	0.360967i
$516$	13.3984	−	6.66440i	0.589831	−	0.293384i
$517$	15.6747	+	27.1494i	0.689374	+	1.19403i
$518$	2.86524	+	17.4672i	0.125892	+	0.767464i
$519$	−16.3652	−	21.0866i	−0.718350	−	0.925600i
$520$	−14.3568	−	0.514701i	−0.629589	−	0.0225711i
$521$			23.2742i			1.01966i	0.860275	+	0.509831i	$0.170292\pi$
$521$			23.2742i			1.01966i	−0.860275	+	0.509831i	$0.829708\pi$
$522$	−13.6302	+	19.4262i	−0.596577	+	0.850263i
$523$		−	10.8804i		−	0.475769i	−0.971293	−	0.237884i	$-0.923546\pi$
$523$		−	10.8804i		−	0.475769i	0.971293	−	0.237884i	$-0.0764539\pi$
$524$	−4.04169	+	1.36263i	−0.176562	+	0.0595267i
$525$	2.07483	−	0.284759i	0.0905528	−	0.0124279i
$526$	9.01985	−	1.47958i	0.393284	−	0.0645127i
$527$	3.66883	+	6.35461i	0.159817	+	0.276811i
$528$	−20.3582	+	5.48435i	−0.885978	+	0.238676i
$529$	−12.7302	+	22.0493i	−0.553485	+	0.958664i
$530$	−4.70897	+	12.4722i	−0.204545	+	0.541758i
$531$	6.64660	−	25.9422i	0.288438	−	1.12579i
$532$	4.60669	+	4.05689i	0.199725	+	0.175888i
$533$	18.8035	+	10.8562i	0.814470	+	0.470235i
$534$	5.62099	−	1.73250i	0.243244	−	0.0749727i
$535$	15.8495	−	9.15068i	0.685231	−	0.395619i
$536$	21.6414	−	34.5619i	0.934764	−	1.49285i
$537$	20.5656	+	8.38649i	0.887471	+	0.361904i
$538$	−6.72769	+	5.50961i	−0.290051	+	0.237536i
$539$	−16.8533			−0.725925
$540$	7.71383	−	6.96396i	0.331950	−	0.299681i
$541$	−6.53795			−0.281088			−0.140544	−	0.990074i	$-0.544885\pi$
$541$	−6.53795			−0.281088			−0.140544	+	0.990074i	$0.544885\pi$
$542$	−0.488901	+	0.400383i	−0.0210001	+	0.0171979i
$543$	27.8502	+	11.3571i	1.19516	+	0.487379i
$544$	−12.1416	+	3.61448i	−0.520566	+	0.154970i
$545$	8.88447	−	5.12945i	0.380569	−	0.219722i
$546$	14.3759	−	4.43093i	0.615231	−	0.189626i
$547$	23.0165	+	13.2886i	0.984113	+	0.568178i	0.903509	−	0.428569i	$-0.140982\pi$
$547$	23.0165	+	13.2886i	0.984113	+	0.568178i	0.0806034	+	0.996746i	$0.474315\pi$
$548$	−21.7925	+	24.7458i	−0.930928	+	1.05709i
$549$	7.67895	−	2.14826i	0.327729	−	0.0916854i
$550$	−1.52017	+	4.02634i	−0.0648204	+	0.171684i
$551$	−7.09907	+	12.2959i	−0.302431	+	0.523825i
$552$	−19.9305	−	27.6735i	−0.848299	−	1.17786i
$553$	−2.27907	−	3.94747i	−0.0969160	−	0.167863i
$554$	9.53514	−	1.56411i	0.405109	−	0.0664525i
$555$	17.7627	−	2.43784i	0.753984	−	0.103481i
$556$	−12.8434	−	38.0947i	−0.544680	−	1.61557i
$557$			8.68248i			0.367889i	0.982937	+	0.183944i	$0.0588866\pi$
$557$			8.68248i			0.367889i	−0.982937	+	0.183944i	$0.941113\pi$
$558$	−5.86286	−	12.6045i	−0.248195	−	0.533591i
$559$		−	21.9411i		−	0.928010i
$560$	4.46065	+	1.86937i	0.188497	+	0.0789954i
$561$	7.23720	+	9.32519i	0.305555	+	0.393710i
$562$	0.753514	+	4.59360i	0.0317851	+	0.193769i
$563$	−15.8324	−	27.4226i	−0.667257	−	1.15572i	−0.978668	−	0.205448i	$-0.934135\pi$
$563$	−15.8324	−	27.4226i	−0.667257	−	1.15572i	0.311411	−	0.950275i	$-0.399199\pi$
$564$	−15.8925	−	31.9509i	−0.669195	−	1.34538i
$565$	−3.06731	+	5.31273i	−0.129043	+	0.223508i
$566$	31.0089	+	11.7076i	1.30340	+	0.492109i
$567$	−5.23272	+	9.54151i	−0.219754	+	0.400706i
$568$	8.72762	−	4.63017i	0.366203	−	0.194278i
$569$	27.9697	+	16.1483i	1.17255	+	0.676973i	0.954280	−	0.298915i	$-0.0966248\pi$
$569$	27.9697	+	16.1483i	1.17255	+	0.676973i	0.218272	+	0.975888i	$0.429958\pi$
$570$	4.23008	−	4.55694i	0.177179	−	0.190869i
$571$	12.7245	−	7.34651i	0.532505	−	0.307442i	−0.209531	−	0.977802i	$-0.567194\pi$
$571$	12.7245	−	7.34651i	0.532505	−	0.307442i	0.742036	+	0.670360i	$0.233860\pi$
$572$	−6.09388	+	30.3074i	−0.254798	+	1.26722i
$573$	24.3952	−	18.9329i	1.01912	−	0.790932i
$574$	−4.63141	−	5.65534i	−0.193311	−	0.236049i
$575$	−6.96134			−0.290308
$576$	23.5163	−	4.79429i	0.979844	−	0.199762i
$577$	−22.4886			−0.936214			−0.468107	−	0.883672i	$-0.655064\pi$
$577$	−22.4886			−0.936214			−0.468107	+	0.883672i	$0.655064\pi$
$578$	−10.7389	−	13.1131i	−0.446679	−	0.545432i
$579$	1.15013	+	8.38012i	0.0477977	+	0.348266i
$580$	−2.20520	+	10.9674i	−0.0915661	+	0.455397i
$581$	−0.599324	+	0.346020i	−0.0248641	+	0.0143553i
$582$	−27.8224	−	6.35667i	−1.15327	−	0.263493i
$583$	24.8444	+	14.3439i	1.02895	+	0.594065i
$584$	12.7441	−	6.76097i	0.527354	−	0.279771i
$585$	−4.10521	−	14.6741i	−0.169730	−	0.606699i
$586$	−36.9305	−	13.9434i	−1.52558	−	0.575996i
$587$	17.2484	−	29.8752i	0.711919	−	1.23308i	−0.252217	−	0.967671i	$-0.581160\pi$
$587$	17.2484	−	29.8752i	0.711919	−	1.23308i	0.964136	−	0.265409i	$-0.0855069\pi$
$588$	19.1473	+	1.18924i	0.789622	+	0.0490434i
$589$	−4.15854	−	7.20280i	−0.171350	−	0.296786i
$590$	−2.04352	−	12.4578i	−0.0841303	−	0.512878i
$591$	−10.9989	+	26.9719i	−0.452436	+	1.10948i
$592$	38.1879	+	16.0038i	1.56951	+	0.657752i
$593$			11.5133i			0.472794i	0.971656	+	0.236397i	$0.0759667\pi$
$593$			11.5133i			0.472794i	−0.971656	+	0.236397i	$0.924033\pi$
$594$	−12.1010	−	18.8061i	−0.496511	−	0.771622i
$595$		−	2.70777i		−	0.111008i
$596$	1.20359	+	3.56997i	0.0493011	+	0.146232i
$597$	3.86852	−	9.48648i	0.158328	−	0.388256i
$598$	−49.3441	+	8.09419i	−2.01783	+	0.330996i
$599$	17.8060	+	30.8410i	0.727535	+	1.26013i	0.957922	+	0.287028i	$0.0926674\pi$
$599$	17.8060	+	30.8410i	0.727535	+	1.26013i	−0.230387	+	0.973099i	$0.573999\pi$
$600$	2.01120	−	4.46711i	0.0821071	−	0.182369i
$601$	−20.4137	+	35.3576i	−0.832693	+	1.44227i	0.0632021	+	0.998001i	$0.479869\pi$
$601$	−20.4137	+	35.3576i	−0.832693	+	1.44227i	−0.895895	+	0.444266i	$0.853465\pi$
$602$	−2.60916	+	6.91062i	−0.106341	+	0.281656i
$603$	41.8987	+	10.7348i	1.70625	+	0.437155i
$604$	−8.17968	+	9.28821i	−0.332826	+	0.377932i
$605$	−1.50588	−	0.869419i	−0.0612226	−	0.0353469i
$606$	−2.60662	+	11.4088i	−0.105887	+	0.463453i
$607$	1.90026	−	1.09711i	0.0771290	−	0.0445304i	−0.460940	−	0.887432i	$-0.652487\pi$
$607$	1.90026	−	1.09711i	0.0771290	−	0.0445304i	0.538069	+	0.842901i	$0.319154\pi$
$608$	13.7622	−	4.09693i	0.558131	−	0.166153i
$609$	−1.59279	−	11.6054i	−0.0645430	−	0.470276i
$610$	2.90812	−	2.38159i	0.117746	−	0.0964279i
$611$	−52.3227			−2.11675
$612$	−7.56426	−	11.1052i	−0.305767	−	0.448900i
$613$	38.7673			1.56580			0.782899	−	0.622149i	$-0.213740\pi$
$613$	38.7673			1.56580			0.782899	+	0.622149i	$0.213740\pi$
$614$	24.7207	−	20.2449i	0.997645	−	0.817017i
$615$	−5.84927	+	4.53957i	−0.235865	+	0.183053i
$616$	5.52339	−	8.82103i	0.222544	−	0.355409i
$617$	−12.8653	+	7.42778i	−0.517937	+	0.299031i	−0.736090	−	0.676884i	$-0.763330\pi$
$617$	−12.8653	+	7.42778i	−0.517937	+	0.299031i	0.218153	+	0.975915i	$0.429997\pi$
$618$	−16.9810	−	15.7630i	−0.683076	−	0.634080i
$619$	12.3383	+	7.12352i	0.495918	+	0.286318i	0.727026	−	0.686610i	$-0.240902\pi$
$619$	12.3383	+	7.12352i	0.495918	+	0.286318i	−0.231108	+	0.972928i	$0.574235\pi$
$620$	−4.91794	−	4.33099i	−0.197509	−	0.173937i
$621$	21.5444	−	29.0563i	0.864545	−	1.16599i
$622$	2.94266	−	7.79393i	0.117990	−	0.312508i
$623$	−1.45174	+	2.51448i	−0.0581626	+	0.100741i
$624$	9.06196	−	34.0027i	0.362769	−	1.36120i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	10.8399	−	1.77813i	0.433248	−	0.0710682i
$627$	−8.20320	−	10.5699i	−0.327604	−	0.422121i
$628$	−4.16987	+	1.40584i	−0.166396	+	0.0560993i
$629$		−	23.1814i		−	0.924302i
$630$	−0.452001	+	5.10996i	−0.0180082	+	0.203585i
$631$		−	38.8200i		−	1.54540i	−0.634772	−	0.772700i	$-0.718906\pi$
$631$		−	38.8200i		−	1.54540i	0.634772	−	0.772700i	$-0.281094\pi$
$632$	−10.6557	−	0.382012i	−0.423860	−	0.0151956i
$633$	−47.4522	+	6.51258i	−1.88606	+	0.258852i
$634$	2.69462	+	16.4270i	0.107017	+	0.652401i
$635$	4.70607	+	8.15115i	0.186755	+	0.323468i
$636$	−27.2139	−	18.0495i	−1.07910	−	0.715708i
$637$	14.0642	−	24.3599i	0.557245	−	0.965176i
$638$	22.5211	+	8.50302i	0.891620	+	0.336638i
$639$	7.49078	+	7.32798i	0.296331	+	0.289890i
$640$	9.24389	−	6.52307i	0.365397	−	0.257847i
$641$	16.5595	+	9.56061i	0.654060	+	0.377621i	0.790010	−	0.613094i	$-0.210075\pi$
$641$	16.5595	+	9.56061i	0.654060	+	0.377621i	−0.135950	+	0.990716i	$0.543409\pi$
$642$	13.2042	+	42.8403i	0.521129	+	1.69077i
$643$	−5.69143	+	3.28595i	−0.224448	+	0.129585i	−0.608008	−	0.793931i	$-0.708031\pi$
$643$	−5.69143	+	3.28595i	−0.224448	+	0.129585i	0.383560	+	0.923516i	$0.374698\pi$
$644$	16.5040	+	3.31845i	0.650350	+	0.130765i
$645$	6.92824	+	2.82528i	0.272799	+	0.111245i
$646$	−5.09348	−	6.21956i	−0.200400	−	0.244705i
$647$	−12.7191			−0.500040			−0.250020	−	0.968241i	$-0.580437\pi$
$647$	−12.7191			−0.500040			−0.250020	+	0.968241i	$0.580437\pi$
$648$	12.4211	+	22.2197i	0.487947	+	0.872873i
$649$	−27.1658			−1.06635
$650$	−4.55111	−	5.55728i	−0.178509	−	0.217974i
$651$	6.35403	+	2.59112i	0.249034	+	0.101554i
$652$	−30.1269	−	6.05758i	−1.17986	−	0.237233i
$653$	−38.1762	+	22.0410i	−1.49395	+	0.862532i	−0.999976	−	0.00694441i	$-0.997790\pi$
$653$	−38.1762	+	22.0410i	−1.49395	+	0.862532i	−0.493974	+	0.869477i	$0.664456\pi$
$654$	7.40167	+	24.0143i	0.289428	+	0.939033i
$655$	−1.84689	−	1.06630i	−0.0721640	−	0.0416639i
$656$	−16.9620	+	2.16157i	−0.662256	+	0.0843951i
$657$	10.9380	+	10.7003i	0.426734	+	0.417459i
$658$	16.4796	+	6.22201i	0.642444	+	0.242559i
$659$	−10.8929	+	18.8671i	−0.424328	+	0.734957i	−0.996357	−	0.0852757i	$-0.972823\pi$
$659$	−10.8929	+	18.8671i	−0.424328	+	0.734957i	0.572030	+	0.820233i	$0.306156\pi$
$660$	−8.78534	−	5.82682i	−0.341969	−	0.226809i
$661$	−10.2756	−	17.7979i	−0.399676	−	0.692260i	0.594009	−	0.804458i	$-0.297544\pi$
$661$	−10.2756	−	17.7979i	−0.399676	−	0.692260i	−0.993686	+	0.112198i	$0.964211\pi$
$662$	0.989845	+	6.03433i	0.0384714	+	0.234531i
$663$	−19.5182	+	2.67877i	−0.758024	+	0.104035i
$664$	−0.0579989	+	1.61780i	−0.00225079	+	0.0627826i
$665$			3.06920i			0.119018i
$666$	−3.86960	+	43.7466i	−0.149944	+	1.69515i
$667$			38.9379i			1.50768i
$668$	−42.1201	+	14.2005i	−1.62967	+	0.549434i
$669$	−25.4305	−	32.7675i	−0.983202	−	1.26686i
$670$	20.1203	−	3.30045i	0.777315	−	0.127507i
$671$	−4.04432	−	7.00497i	−0.156129	−	0.270424i
$672$	−6.89764	+	9.63194i	−0.266082	+	0.371560i
$673$	1.08874	−	1.88576i	0.0419680	−	0.0726906i	−0.844278	−	0.535905i	$-0.819971\pi$
$673$	1.08874	−	1.88576i	0.0419680	−	0.0726906i	0.886246	+	0.463214i	$0.153304\pi$
$674$	−3.88139	+	10.2803i	−0.149505	+	0.395981i
$675$	5.16218	+	0.593250i	0.198692	+	0.0228342i
$676$	−19.2090	−	16.9164i	−0.738807	−	0.650631i
$677$	1.92840	+	1.11336i	0.0741143	+	0.0427899i	0.536599	−	0.843837i	$-0.319709\pi$
$677$	1.92840	+	1.11336i	0.0741143	+	0.0427899i	−0.462485	+	0.886627i	$0.653042\pi$
$678$	−11.0131	−	10.2231i	−0.422956	−	0.392618i
$679$	12.2003	−	7.04386i	0.468205	−	0.270319i
$680$	−5.36849	−	3.36154i	−0.205872	−	0.128909i
$681$	−9.46817	+	7.34817i	−0.362821	+	0.281582i
$682$	−10.9099	+	8.93463i	−0.417762	+	0.342125i
$683$	−12.9800			−0.496665			−0.248333	−	0.968675i	$-0.579883\pi$
$683$	−12.9800			−0.496665			−0.248333	+	0.968675i	$0.579883\pi$
$684$	8.57392	+	12.5875i	0.327832	+	0.481293i
$685$	−16.4869			−0.629931
$686$	−16.5871	+	13.5839i	−0.633299	+	0.518637i
$687$	3.60721	+	26.2830i	0.137624	+	1.00276i
$688$	10.4620	+	13.7521i	0.398861	+	0.524294i
$689$	−41.4657	+	23.9402i	−1.57972	+	0.912050i
$690$	3.79800	−	16.6234i	0.144588	−	0.632842i
$691$	−24.1859	−	13.9637i	−0.920074	−	0.531205i	−0.0364156	−	0.999337i	$-0.511594\pi$
$691$	−24.1859	−	13.9637i	−0.920074	−	0.531205i	−0.883659	+	0.468132i	$0.844927\pi$
$692$	20.3699	−	23.1305i	0.774347	−	0.879289i
$693$	10.6935	+	2.73977i	0.406214	+	0.104075i
$694$	−5.62776	+	14.9057i	−0.213627	+	0.565813i
$695$	10.0504	−	17.4077i	0.381232	−	0.660313i
$696$	−24.9866	−	11.2496i	−0.947113	−	0.426414i
$697$	4.78657	+	8.29058i	0.181304	+	0.314028i
$698$	−31.0940	+	5.10052i	−1.17692	+	0.193058i
$699$	−4.32345	+	10.6021i	−0.163528	+	0.401007i
$700$	0.772575	+	2.29153i	0.0292006	+	0.0866117i
$701$		−	31.0643i		−	1.17328i	−0.809847	−	0.586641i	$-0.800450\pi$
$701$		−	31.0643i		−	1.17328i	0.809847	−	0.586641i	$-0.199550\pi$
$702$	37.2808	−	1.79711i	1.40707	−	0.0678276i
$703$			26.2756i			0.991001i
$704$	−10.6318	−	21.9016i	−0.400701	−	0.825447i
$705$	6.73741	−	16.5217i	0.253746	−	0.622242i
$706$	5.05106	+	30.7924i	0.190099	+	1.15889i
$707$	−2.88841	−	5.00287i	−0.108630	−	0.188152i
$708$	30.8635	+	1.91693i	1.15992	+	0.0720427i
$709$	21.7239	−	37.6269i	0.815859	−	1.41311i	−0.0928511	−	0.995680i	$-0.529598\pi$
$709$	21.7239	−	37.6269i	0.815859	−	1.41311i	0.908710	−	0.417429i	$-0.137069\pi$
$710$	4.62146	+	1.74487i	0.173440	+	0.0654837i
$711$	−3.04690	−	10.8911i	−0.114268	−	0.408449i
$712$	3.18302	+	5.99982i	0.119289	+	0.224853i
$713$	−19.7535	−	11.4047i	−0.739773	−	0.427108i
$714$	6.46604	+	1.47732i	0.241985	+	0.0552873i
$715$	−13.3862	+	7.72850i	−0.500614	+	0.289030i
$716$	−5.05537	+	25.1425i	−0.188928	+	0.939619i
$717$	1.93615	+	14.1073i	0.0723069	+	0.526846i
$718$	1.52623	+	1.86366i	0.0569585	+	0.0695510i
$719$	12.6495			0.471747			0.235874	−	0.971784i	$-0.424205\pi$
$719$	12.6495			0.471747			0.235874	+	0.971784i	$0.424205\pi$
$720$	9.56998	+	7.23986i	0.356652	+	0.269814i
$721$	11.4371			0.425938
$722$	−11.2513	−	13.7388i	−0.418730	−	0.511304i
$723$	−19.9987	+	15.5208i	−0.743759	+	0.577225i
$724$	−6.84605	+	34.0483i	−0.254431	+	1.26539i
$725$	−4.84407	+	2.79673i	−0.179904	+	0.103868i
$726$	2.89772	−	3.12163i	0.107544	−	0.115855i
$727$	−43.4035	−	25.0590i	−1.60975	−	0.929389i	−0.989425	−	0.145042i	$-0.953668\pi$
$727$	−43.4035	−	25.0590i	−1.60975	−	0.929389i	−0.620323	−	0.784347i	$-0.712998\pi$
$728$	8.14068	+	15.3448i	0.301714	+	0.568714i
$729$	−18.4524	+	19.7106i	−0.683422	+	0.730024i
$730$	6.74826	+	2.54785i	0.249764	+	0.0943003i
$731$	4.83699	−	8.37791i	0.178902	−	0.309868i
$732$	4.10051	+	8.24383i	0.151559	+	0.304701i
$733$	14.7327	+	25.5178i	0.544166	+	0.942523i	0.998659	+	0.0517728i	$0.0164872\pi$
$733$	14.7327	+	25.5178i	0.544166	+	0.942523i	−0.454493	+	0.890750i	$0.650179\pi$
$734$	−2.15679	−	13.1483i	−0.0796087	−	0.485313i
$735$	5.88102	+	7.57774i	0.216925	+	0.279509i
$736$	27.0680	−	28.6016i	0.997740	−	1.05427i
$737$		−	43.8751i		−	1.61616i
$738$	−7.64902	−	16.4445i	−0.281564	−	0.605332i
$739$			45.3131i			1.66687i	0.552618	+	0.833435i	$0.313629\pi$
$739$			45.3131i			1.66687i	−0.552618	+	0.833435i	$0.686371\pi$
$740$	6.61405	+	19.6179i	0.243137	+	0.721169i
$741$	22.1234	−	3.03633i	0.812725	−	0.111542i
$742$	15.9070	−	2.60932i	0.583964	−	0.0957911i
$743$	4.03779	+	6.99366i	0.148132	+	0.256573i	0.930537	−	0.366197i	$-0.119341\pi$
$743$	4.03779	+	6.99366i	0.148132	+	0.256573i	−0.782405	+	0.622770i	$0.786007\pi$
$744$	13.0254	−	9.38090i	0.477533	−	0.343921i
$745$	−0.941851	+	1.63133i	−0.0345067	+	0.0597674i
$746$	−7.28589	+	19.2974i	−0.266756	+	0.706530i
$747$	−1.65354	+	0.462595i	−0.0605000	+	0.0169255i
$748$	−9.00823	+	10.2291i	−0.329373	+	0.374011i
$749$	−19.1641	−	11.0644i	−0.700239	−	0.404283i
$750$	2.34082	−	0.721488i	0.0854748	−	0.0263450i
$751$	−9.71367	+	5.60819i	−0.354457	+	0.204646i	−0.666646	−	0.745374i	$-0.732271\pi$
$751$	−9.71367	+	5.60819i	−0.354457	+	0.204646i	0.312190	+	0.950020i	$0.398938\pi$
$752$	32.7944	−	24.9486i	1.19589	−	0.909784i
$753$	3.83620	+	1.56437i	0.139799	+	0.0570090i
$754$	−31.0844	+	25.4564i	−1.13203	+	0.927067i
$755$	−6.18825			−0.225214
$756$	−11.9557	−	3.86727i	−0.434826	−	0.140651i
$757$	−26.9148			−0.978236			−0.489118	−	0.872218i	$-0.662681\pi$
$757$	−26.9148			−0.978236			−0.489118	+	0.872218i	$0.662681\pi$
$758$	10.3512	−	8.47706i	0.375972	−	0.307901i
$759$	−33.9768	−	13.8555i	−1.23328	−	0.502922i
$760$	6.08506	+	3.81023i	0.220728	+	0.138212i
$761$	6.74550	−	3.89451i	0.244524	−	0.141176i	−0.372730	−	0.927940i	$-0.621578\pi$
$761$	6.74550	−	3.89451i	0.244524	−	0.141176i	0.617254	+	0.786764i	$0.288245\pi$
$762$	−22.0321	+	6.79074i	−0.798140	+	0.246003i
$763$	−10.7425	−	6.20218i	−0.388904	−	0.224534i
$764$	26.7597	+	23.5660i	0.968132	+	0.852587i
$765$	1.66743	−	6.50810i	0.0602860	−	0.235301i
$766$	3.42683	−	9.07632i	0.123816	−	0.327941i
$767$	22.6701	−	39.2657i	0.818569	−	1.41780i
$768$	10.5335	+	25.6329i	0.380094	+	0.924948i
$769$	−3.36491	−	5.82819i	−0.121342	−	0.210170i	0.798955	−	0.601390i	$-0.205386\pi$
$769$	−3.36491	−	5.82819i	−0.121342	−	0.210170i	−0.920297	+	0.391220i	$0.872053\pi$
$770$	5.13518	−	0.842353i	0.185059	−	0.0303563i
$771$	14.4990	−	1.98992i	0.522170	−	0.0716651i
$772$	−9.25538	+	3.12039i	−0.333108	+	0.112305i
$773$		−	16.5270i		−	0.594435i	−0.954810	−	0.297217i	$-0.903941\pi$
$773$		−	16.5270i		−	0.594435i	0.954810	−	0.297217i	$-0.0960586\pi$
$774$	−10.5266	+	15.0029i	−0.378371	+	0.539268i
$775$		−	3.27657i		−	0.117698i
$776$	1.18067	−	32.9332i	0.0423837	−	1.18223i
$777$	−13.2915	−	17.1262i	−0.476829	−	0.614398i
$778$	−1.88113	−	11.4678i	−0.0674419	−	0.411141i
$779$	−5.42547	−	9.39719i	−0.194388	−	0.336689i
$780$	15.7536	−	7.83588i	0.564068	−	0.280569i
$781$	5.31502	−	9.20588i	0.190186	−	0.329412i
$782$	−20.6257	−	7.78740i	−0.737574	−	0.278477i
$783$	3.31831	−	28.8744i	0.118587	−	1.03189i
$784$	2.80031	+	21.9743i	0.100011	+	0.784796i
$785$	−1.90546	−	1.10012i	−0.0680089	−	0.0392650i
$786$	3.55392	−	3.82853i	0.126764	−	0.136559i
$787$	−2.38973	+	1.37971i	−0.0851847	+	0.0491814i	−0.541987	−	0.840387i	$-0.682328\pi$
$787$	−2.38973	+	1.37971i	−0.0851847	+	0.0491814i	0.456803	+	0.889568i	$0.348995\pi$
$788$	−32.9746	−	6.63016i	−1.17467	−	0.236190i
$789$	−8.84375	+	6.86356i	−0.314846	+	0.244349i
$790$	−3.37784	−	4.12462i	−0.120178	−	0.146747i
$791$	7.41755			0.263738
$792$	18.7073	−	17.8000i	0.664736	−	0.632495i
$793$	13.5001			0.479401
$794$	6.34334	+	7.74575i	0.225117	+	0.274886i
$795$	−2.22009	−	16.1761i	−0.0787384	−	0.573708i
$796$	11.5977	+	2.33194i	0.411070	+	0.0826534i
$797$	4.54011	−	2.62123i	0.160819	−	0.0928488i	−0.417431	−	0.908709i	$-0.637069\pi$
$797$	4.54011	−	2.62123i	0.160819	−	0.0928488i	0.578250	+	0.815860i	$0.303736\pi$
$798$	−7.32911	−	1.67451i	−0.259448	−	0.0592769i
$799$	−19.9787	−	11.5347i	−0.706794	−	0.408068i
$800$	5.50235	+	1.31308i	0.194537	+	0.0464243i
$801$	−5.03763	+	5.14956i	−0.177996	+	0.181951i
$802$	23.4079	+	8.83781i	0.826560	+	0.312074i
$803$	7.76099	−	13.4424i	0.273879	−	0.474373i
$804$	−3.09600	+	49.8471i	−0.109187	+	1.75797i
$805$	4.20859	+	7.28949i	0.148333	+	0.256921i
$806$	−3.80978	−	23.2253i	−0.134194	−	0.818076i
$807$	4.02154	−	9.86172i	0.141565	−	0.347149i
$808$	−13.5046	−	0.484147i	−0.475090	−	0.0170322i
$809$		−	47.1813i		−	1.65881i	−0.558650	−	0.829403i	$-0.688681\pi$
$809$		−	47.1813i		−	1.65881i	0.558650	−	0.829403i	$-0.311319\pi$
$810$	−4.23306	+	12.0034i	−0.148735	+	0.421756i
$811$		−	18.8666i		−	0.662495i	−0.943544	−	0.331247i	$-0.892531\pi$
$811$		−	18.8666i		−	0.662495i	0.943544	−	0.331247i	$-0.107469\pi$
$812$	12.8176	−	4.32136i	0.449809	−	0.151650i
$813$	0.292245	−	0.716651i	0.0102495	−	0.0251341i
$814$	43.9625	−	7.21143i	1.54089	−	0.252760i
$815$	−7.68247	−	13.3064i	−0.269105	−	0.466104i
$816$	10.9562	−	10.9857i	0.383543	−	0.384577i
$817$	−5.48261	+	9.49617i	−0.191812	+	0.332229i
$818$	11.3435	−	30.0444i	0.396615	−	1.05048i
$819$	−12.8839	+	13.1702i	−0.450201	+	0.460203i
$820$	−6.41622	−	5.65046i	−0.224064	−	0.197323i
$821$	1.12399	+	0.648938i	0.0392277	+	0.0226481i	0.519486	−	0.854479i	$-0.326124\pi$
$821$	1.12399	+	0.648938i	0.0392277	+	0.0226481i	−0.480258	+	0.877127i	$0.659457\pi$
$822$	8.99499	−	39.3699i	0.313736	−	1.37318i
$823$	−5.77693	+	3.33531i	−0.201371	+	0.116262i	−0.597295	−	0.802022i	$-0.703758\pi$
$823$	−5.77693	+	3.33531i	−0.201371	+	0.116262i	0.395924	+	0.918283i	$0.370424\pi$
$824$	14.1984	−	22.6754i	0.494626	−	0.789934i
$825$	−0.716700	−	5.22205i	−0.0249523	−	0.181809i
$826$	−11.8095	+	9.67137i	−0.410907	+	0.336510i
$827$	37.4924			1.30374			0.651869	−	0.758331i	$-0.273985\pi$
$827$	37.4924			1.30374			0.651869	+	0.758331i	$0.273985\pi$
$828$	37.6238	+	18.1389i	1.30752	+	0.630372i
$829$	−22.9261			−0.796255			−0.398127	−	0.917330i	$-0.630340\pi$
$829$	−22.9261			−0.796255			−0.398127	+	0.917330i	$0.630340\pi$
$830$	−0.626220	+	0.512840i	−0.0217364	+	0.0178009i
$831$	−9.34898	+	7.25566i	−0.324313	+	0.251696i
$832$	40.5290	+	2.90972i	1.40509	+	0.100876i
$833$	10.7405	−	6.20100i	0.372135	−	0.214852i
$834$	36.0856	+	33.4972i	1.24954	+	1.15991i
$835$	−19.2472	−	11.1124i	−0.666076	−	0.384559i
$836$	10.2106	−	11.5944i	0.353142	−	0.401001i
$837$	13.6762	+	10.1405i	0.472720	+	0.350507i
$838$	−13.1680	+	34.8769i	−0.454882	+	1.20480i
$839$	−9.11048	+	15.7798i	−0.314529	+	0.544780i	−0.979337	−	0.202234i	$-0.935180\pi$
$839$	−9.11048	+	15.7798i	−0.314529	+	0.544780i	0.664808	+	0.747014i	$0.268513\pi$
$840$	−5.89358	+	0.594650i	−0.203348	+	0.0205174i
$841$	1.14335	+	1.98034i	0.0394259	+	0.0682877i
$842$	23.9414	−	3.92724i	0.825074	−	0.135342i
$843$	−3.49545	−	4.50391i	−0.120390	−	0.155123i
$844$	−17.6691	−	52.4084i	−0.608197	−	1.80397i
$845$		−	12.7979i		−	0.440263i
$846$	35.7772	+	25.1026i	1.23004	+	0.863046i
$847$			2.10248i			0.0722422i
$848$	14.5743	−	34.7769i	0.500484	−	1.19424i
$849$	−40.2177	+	5.51967i	−1.38027	+	0.189435i
$850$	−0.512657	−	3.12527i	−0.0175840	−	0.107196i
$851$	36.0299	+	62.4057i	1.23509	+	2.13924i
$852$	−6.68807	+	10.0839i	−0.229129	+	0.345468i
$853$	0.975478	−	1.68958i	0.0333997	−	0.0578500i	−0.848842	−	0.528646i	$-0.822700\pi$
$853$	0.975478	−	1.68958i	0.0333997	−	0.0578500i	0.882242	+	0.470796i	$0.156033\pi$
$854$	−4.25201	−	1.60538i	−0.145501	−	0.0549349i
$855$	−1.88999	+	7.37678i	−0.0646364	+	0.252281i
$856$	−45.7275	+	24.2593i	−1.56293	+	0.829166i
$857$	11.2785	+	6.51166i	0.385267	+	0.222434i	0.680107	−	0.733113i	$-0.261933\pi$
$857$	11.2785	+	6.51166i	0.385267	+	0.222434i	−0.294840	+	0.955546i	$0.595267\pi$
$858$	−11.1520	−	36.1821i	−0.380724	−	1.23524i
$859$	−3.50034	+	2.02092i	−0.119430	+	0.0689530i	−0.558525	−	0.829488i	$-0.688633\pi$
$859$	−3.50034	+	2.02092i	−0.119430	+	0.0689530i	0.439095	+	0.898441i	$0.355299\pi$
$860$	−1.70308	+	8.47013i	−0.0580745	+	0.288829i
$861$	8.28982	+	3.38053i	0.282516	+	0.115208i
$862$	11.2736	+	13.7660i	0.383980	+	0.468871i
$863$	10.6258			0.361705			0.180853	−	0.983510i	$-0.442114\pi$
$863$	10.6258			0.361705			0.180853	+	0.983510i	$0.442114\pi$
$864$	−22.5097	+	18.9027i	−0.765796	+	0.643084i
$865$	15.4106			0.523978
$866$	10.5224	+	12.8487i	0.357565	+	0.436616i
$867$	19.2217	+	7.83847i	0.652803	+	0.266208i
$868$	−1.56193	+	7.76813i	−0.0530153	+	0.263667i
$869$	−9.93523	+	5.73611i	−0.337030	+	0.194584i
$870$	−4.03561	−	13.0933i	−0.136820	−	0.443904i
$871$	63.4174	+	36.6140i	2.14882	+	1.24062i
$872$	−25.6327	+	13.5986i	−0.868034	+	0.460508i
$873$	33.6609	−	9.41696i	1.13925	−	0.318716i
$874$	23.3788	+	8.82684i	0.790799	+	0.298572i
$875$	−0.604565	+	1.04714i	−0.0204380	+	0.0353997i
$876$	−9.76591	+	14.7245i	−0.329960	+	0.497494i
$877$	26.5530	+	45.9911i	0.896631	+	1.55301i	0.831774	+	0.555115i	$0.187326\pi$
$877$	26.5530	+	45.9911i	0.896631	+	1.55301i	0.0648570	+	0.997895i	$0.479341\pi$
$878$	0.385240	+	2.34851i	0.0130012	+	0.0792584i
$879$	47.8978	−	6.57373i	1.61555	−	0.221727i
$880$	4.70495	−	11.2268i	0.158604	−	0.378457i
$881$		−	10.8244i		−	0.364685i	−0.983235	−	0.182342i	$-0.941632\pi$
$881$		−	10.8244i		−	0.364685i	0.983235	−	0.182342i	$-0.0583679\pi$
$882$	−21.3039	+	9.90931i	−0.717340	+	0.333664i
$883$		−	21.6083i		−	0.727178i	−0.931559	−	0.363589i	$-0.881551\pi$
$883$		−	21.6083i		−	0.727178i	0.931559	−	0.363589i	$-0.118449\pi$
$884$	−7.26773	−	21.5568i	−0.244440	−	0.725033i
$885$	9.47959	+	12.2145i	0.318653	+	0.410587i
$886$	−1.05926	+	0.173757i	−0.0355865	+	0.00583747i
$887$	−0.264026	−	0.457306i	−0.00886511	−	0.0153548i	0.861559	−	0.507658i	$-0.169489\pi$
$887$	−0.264026	−	0.457306i	−0.00886511	−	0.0153548i	−0.870424	+	0.492303i	$0.836155\pi$
$888$	−50.4553	+	5.09083i	−1.69317	+	0.170837i
$889$	5.69025	−	9.85580i	0.190845	−	0.330553i
$890$	−1.19951	+	3.17703i	−0.0402078	+	0.106494i
$891$	24.0147	+	13.1700i	0.804522	+	0.441213i
$892$	31.6537	−	35.9435i	1.05984	−	1.20348i
$893$	22.6454	+	13.0743i	0.757798	+	0.437515i
$894$	−3.38169	−	3.13913i	−0.113101	−	0.104988i
$895$	−11.1049	+	6.41143i	−0.371196	+	0.214310i
$896$	−12.4191	−	5.73601i	−0.414893	−	0.191627i
$897$	48.3807	−	37.5478i	1.61538	−	1.25369i
$898$	19.1012	−	15.6428i	0.637415	−	0.522008i
$899$	−18.3273			−0.611251
$900$	0.445764	+	5.98342i	0.0148588	+	0.199447i
$901$	−21.1108			−0.703302
$902$	−14.2337	+	11.6566i	−0.473930	+	0.388123i
$903$	−1.23011	−	8.96289i	−0.0409355	−	0.298266i
$904$	9.20846	−	14.7062i	0.306269	−	0.489121i
$905$	−15.0384	+	8.68243i	−0.499894	+	0.288614i
$906$	3.37622	−	14.7773i	0.112167	−	0.490942i
$907$	−40.9884	−	23.6647i	−1.36100	−	0.785773i	−0.371242	−	0.928536i	$-0.621068\pi$
$907$	−40.9884	−	23.6647i	−1.36100	−	0.785773i	−0.989757	+	0.142763i	$0.954401\pi$
$908$	−10.3859	−	9.14635i	−0.344668	−	0.303532i
$909$	−3.86152	−	13.8030i	−0.128079	−	0.457817i
$910$	−3.06779	+	8.12537i	−0.101696	+	0.269353i
$911$	18.8160	−	32.5902i	0.623401	−	1.07976i	−0.365447	−	0.930832i	$-0.619084\pi$
$911$	18.8160	−	32.5902i	0.623401	−	1.07976i	0.988848	−	0.148930i	$-0.0475829\pi$
$912$	−12.4186	+	12.4521i	−0.411220	+	0.412329i
$913$	0.870884	+	1.50841i	0.0288220	+	0.0499213i
$914$	−48.6546	+	7.98110i	−1.60935	+	0.263991i
$915$	−1.73836	+	4.26285i	−0.0574683	+	0.140925i
$916$	−29.0281	+	9.78664i	−0.959117	+	0.323360i
$917$			2.57860i			0.0851528i
$918$	14.6313	+	7.53247i	0.482906	+	0.248609i
$919$			42.9157i			1.41566i	0.706383	+	0.707830i	$0.250326\pi$
$919$			42.9157i			1.41566i	−0.706383	+	0.707830i	$0.749674\pi$
$920$	19.6770	+	0.705432i	0.648732	+	0.0232574i
$921$	−14.7770	+	36.2366i	−0.486919	+	1.19404i
$922$	−7.16103	−	43.6553i	−0.235836	−	1.43771i
$923$	8.87083	+	15.3647i	0.291987	+	0.505736i
$924$	−0.790173	+	12.7222i	−0.0259948	+	0.418528i
$925$	−5.17572	+	8.96460i	−0.170176	+	0.294754i
$926$	−13.6046	−	5.13652i	−0.447075	−	0.168797i
$927$	27.4888	+	7.04287i	0.902852	+	0.231318i
$928$	7.34464	−	30.7771i	0.241100	−	1.01031i
$929$	−25.1609	−	14.5267i	−0.825503	−	0.476605i	0.0268072	−	0.999641i	$-0.491466\pi$
$929$	−25.1609	−	14.5267i	−0.825503	−	0.476605i	−0.852311	+	0.523036i	$0.824799\pi$
$930$	7.82431	+	1.78765i	0.256569	+	0.0586192i
$931$	−12.1741	+	7.02870i	−0.398989	+	0.230356i
$932$	−12.9616	−	2.60617i	−0.424571	−	0.0853680i
$933$	1.38734	+	10.1085i	0.0454196	+	0.330938i
$934$	−2.60374	−	3.17938i	−0.0851969	−	0.104033i
$935$	−6.81509			−0.222877
$936$	10.1168	+	41.8939i	0.330679	+	1.36935i
$937$	51.0143			1.66656			0.833282	−	0.552848i	$-0.186459\pi$
$937$	51.0143			1.66656			0.833282	+	0.552848i	$0.186459\pi$
$938$	−15.6201	−	19.0734i	−0.510013	−	0.622768i
$939$	−10.6282	+	8.24847i	−0.346839	+	0.269179i
$940$	20.1986	+	4.06131i	0.658805	+	0.132465i
$941$	7.54730	−	4.35743i	0.246035	−	0.142048i	−0.371912	−	0.928268i	$-0.621298\pi$
$941$	7.54730	−	4.35743i	0.246035	−	0.142048i	0.617947	+	0.786220i	$0.287964\pi$
$942$	3.66663	−	3.94996i	0.119465	−	0.128697i
$943$	−25.7715	−	14.8792i	−0.839235	−	0.484532i
$944$	4.51382	+	35.4203i	0.146912	+	1.15283i
$945$	−2.49966	−	5.76417i	−0.0813139	−	0.187508i
$946$	17.3931	+	6.56689i	0.565498	+	0.213508i
$947$	19.0803	−	33.0481i	0.620028	−	1.07392i	−0.369452	−	0.929250i	$-0.620455\pi$
$947$	19.0803	−	33.0481i	0.620028	−	1.07392i	0.989480	−	0.144670i	$-0.0462120\pi$
$948$	11.6923	−	5.81580i	0.379749	−	0.188888i
$949$	12.9532	+	22.4356i	0.420478	+	0.728290i
$950$	0.581085	+	3.54243i	0.0188529	+	0.114931i
$951$	−12.5000	−	16.1063i	−0.405339	−	0.522283i
$952$	−0.274394	+	7.65382i	−0.00889315	+	0.248062i
$953$			40.4395i			1.30996i	0.755645	+	0.654982i	$0.227324\pi$
$953$			40.4395i			1.30996i	−0.755645	+	0.654982i	$0.772676\pi$
$954$	39.8391	+	3.52397i	1.28984	+	0.114093i
$955$			17.8286i			0.576920i
$956$	−15.5807	+	5.25293i	−0.503916	+	0.169892i
$957$	−29.2093	+	4.00883i	−0.944202	+	0.129587i
$958$	−26.3140	+	4.31643i	−0.850166	+	0.139458i
$959$	9.96739	+	17.2640i	0.321864	+	0.557485i
$960$	−6.13757	+	12.4230i	−0.198089	+	0.400950i
$961$	−10.1320	+	17.5492i	−0.326840	+	0.566104i
$962$	−26.2636	+	69.5617i	−0.846771	+	2.24276i
$963$	−39.2472	−	38.3942i	−1.26472	−	1.23724i
$964$	−21.9371	−	19.3189i	−0.706546	−	0.622220i
$965$	−4.22934	−	2.44181i	−0.136147	−	0.0786046i
$966$	−19.7031	+	6.07289i	−0.633938	+	0.195392i
$967$	−14.5754	+	8.41511i	−0.468713	+	0.270612i	−0.715701	−	0.698407i	$-0.753893\pi$
$967$	−14.5754	+	8.41511i	−0.468713	+	0.270612i	0.246988	+	0.969019i	$0.420559\pi$
$968$	4.16843	+	2.61011i	0.133978	+	0.0838921i
$969$	9.11689	+	3.71780i	0.292877	+	0.119433i
$970$	12.7479	−	10.4398i	0.409309	−	0.335202i
$971$	34.0951			1.09416			0.547082	−	0.837079i	$-0.315738\pi$
$971$	34.0951			1.09416			0.547082	+	0.837079i	$0.315738\pi$
$972$	−26.3541	−	16.6572i	−0.845307	−	0.534281i
$973$	−24.3044			−0.779163
$974$	−12.6587	+	10.3667i	−0.405609	+	0.332172i
$975$	8.14609	+	3.32191i	0.260884	+	0.106386i
$976$	−8.46147	+	6.43714i	−0.270845	+	0.206048i
$977$	0.748148	−	0.431943i	0.0239354	−	0.0138191i	−0.487985	−	0.872852i	$-0.662268\pi$
$977$	0.748148	−	0.431943i	0.0239354	−	0.0138191i	0.511920	+	0.859033i	$0.328934\pi$
$978$	35.9666	−	11.0856i	1.15008	−	0.354479i
$979$	6.32860	+	3.65382i	0.202263	+	0.116777i
$980$	−7.32017	+	8.31222i	−0.233834	+	0.265524i
$981$	−22.0002	−	21.5220i	−0.702412	−	0.687145i
$982$	−0.746913	+	1.97828i	−0.0238349	+	0.0631293i
$983$	−18.4107	+	31.8882i	−0.587209	+	1.01708i	0.407387	+	0.913256i	$0.366440\pi$
$983$	−18.4107	+	31.8882i	−0.587209	+	1.01708i	−0.994596	+	0.103821i	$0.966893\pi$
$984$	16.9936	−	12.2389i	0.541738	−	0.390161i
$985$	−8.40863	−	14.5642i	−0.267921	−	0.464053i
$986$	−17.4811	+	2.86752i	−0.556711	+	0.0913205i
$987$	−21.3737	+	2.93343i	−0.680331	+	0.0933720i
$988$	8.23780	+	24.4341i	0.262079	+	0.777353i
$989$			30.0718i			0.956227i
$990$	12.8611	+	1.13762i	0.408751	+	0.0361561i
$991$			35.9773i			1.14286i	0.820652	+	0.571428i	$0.193610\pi$
$991$			35.9773i			1.14286i	−0.820652	+	0.571428i	$0.806390\pi$
$992$	13.4622	+	12.7404i	0.427426	+	0.404508i
$993$	−4.59175	−	5.91651i	−0.145715	−	0.187755i
$994$	−0.966859	−	5.89419i	−0.0306669	−	0.186952i
$995$	2.95746	+	5.12247i	0.0937577	+	0.162393i
$996$	−0.882983	−	1.77518i	−0.0279784	−	0.0562489i
$997$	16.7322	−	28.9811i	0.529915	−	0.917840i	−0.469476	−	0.882945i	$-0.655557\pi$
$997$	16.7322	−	28.9811i	0.529915	−	0.917840i	0.999391	−	0.0348944i	$-0.0111095\pi$
$998$	−41.6478	−	15.7244i	−1.31834	−	0.497748i
$999$	−21.3997	−	49.3473i	−0.677057	−	1.56128i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.q.a.11.8	yes	48
3.2	odd	2		540.2.q.a.251.17		48
4.3	odd	2	inner	180.2.q.a.11.1	✓	48
5.2	odd	4		900.2.o.c.299.19		48
5.3	odd	4		900.2.o.b.299.6		48
5.4	even	2		900.2.r.f.551.17		48
9.2	odd	6		1620.2.e.b.971.31		48
9.4	even	3		540.2.q.a.71.24		48
9.5	odd	6	inner	180.2.q.a.131.1	yes	48
9.7	even	3		1620.2.e.b.971.18		48
12.11	even	2		540.2.q.a.251.24		48
20.3	even	4		900.2.o.b.299.11		48
20.7	even	4		900.2.o.c.299.14		48
20.19	odd	2		900.2.r.f.551.24		48
36.7	odd	6		1620.2.e.b.971.32		48
36.11	even	6		1620.2.e.b.971.17		48
36.23	even	6	inner	180.2.q.a.131.8	yes	48
36.31	odd	6		540.2.q.a.71.17		48
45.14	odd	6		900.2.r.f.851.24		48
45.23	even	12		900.2.o.c.599.14		48
45.32	even	12		900.2.o.b.599.11		48
180.23	odd	12		900.2.o.c.599.19		48
180.59	even	6		900.2.r.f.851.17		48
180.167	odd	12		900.2.o.b.599.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.1	✓	48	4.3	odd	2	inner
180.2.q.a.11.8	yes	48	1.1	even	1	trivial
180.2.q.a.131.1	yes	48	9.5	odd	6	inner
180.2.q.a.131.8	yes	48	36.23	even	6	inner
540.2.q.a.71.17		48	36.31	odd	6
540.2.q.a.71.24		48	9.4	even	3
540.2.q.a.251.17		48	3.2	odd	2
540.2.q.a.251.24		48	12.11	even	2
900.2.o.b.299.6		48	5.3	odd	4
900.2.o.b.299.11		48	20.3	even	4
900.2.o.b.599.6		48	180.167	odd	12
900.2.o.b.599.11		48	45.32	even	12
900.2.o.c.299.14		48	20.7	even	4
900.2.o.c.299.19		48	5.2	odd	4
900.2.o.c.599.14		48	45.23	even	12
900.2.o.c.599.19		48	180.23	odd	12
900.2.r.f.551.17		48	5.4	even	2
900.2.r.f.551.24		48	20.19	odd	2
900.2.r.f.851.17		48	180.59	even	6
900.2.r.f.851.24		48	45.14	odd	6
1620.2.e.b.971.17		48	36.11	even	6
1620.2.e.b.971.18		48	9.7	even	3
1620.2.e.b.971.31		48	9.2	odd	6
1620.2.e.b.971.32		48	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.896034 - 1.09413i) q^{2} +(1.60382 + 0.654027i) q^{3} +(-0.394247 + 1.96076i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.721488 - 2.34082i) q^{6} +(1.04714 + 0.604565i) q^{7} +(2.49858 - 1.32555i) q^{8} +(2.14450 + 2.09789i) q^{9} +(1.32305 + 0.499529i) q^{10} +(1.52161 - 2.63550i) q^{11} +(-1.91469 + 2.88686i) q^{12} +(2.53958 + 4.39869i) q^{13} +(-0.276797 - 1.68742i) q^{14} +(-1.71597 + 0.235507i) q^{15} +(-3.68914 - 1.54605i) q^{16} +2.23944i q^{17} +(0.373823 - 4.22614i) q^{18} -2.53835i q^{19} +(-0.638951 - 1.89519i) q^{20} +(1.28402 + 1.65447i) q^{21} +(-4.24700 + 0.696660i) q^{22} +(-3.48067 - 6.02870i) q^{23} +(4.87423 - 0.491800i) q^{24} +(0.500000 - 0.866025i) q^{25} +(2.53719 - 6.72001i) q^{26} +(2.06732 + 4.76720i) q^{27} +(-1.59824 + 1.81484i) q^{28} +(-4.84407 - 2.79673i) q^{29} +(1.79524 + 1.66647i) q^{30} +(2.83759 - 1.63828i) q^{31} +(1.61401 + 5.42171i) q^{32} +(4.16408 - 3.23171i) q^{33} +(2.45024 - 2.00661i) q^{34} -1.20913 q^{35} +(-4.95891 + 3.37775i) q^{36} -10.3514 q^{37} +(-2.77729 + 2.27445i) q^{38} +(1.19618 + 8.71567i) q^{39} +(-1.50106 + 2.39725i) q^{40} +(3.70208 - 2.13740i) q^{41} +(0.659684 - 2.88735i) q^{42} +(-3.74108 - 2.15991i) q^{43} +(4.56769 + 4.02254i) q^{44} +(-2.90613 - 0.744575i) q^{45} +(-3.47739 + 9.21023i) q^{46} +(-5.15071 + 8.92129i) q^{47} +(-4.90557 - 4.89238i) q^{48} +(-2.76900 - 4.79605i) q^{49} +(-1.39556 + 0.228922i) q^{50} +(-1.46465 + 3.59166i) q^{51} +(-9.62598 + 3.24534i) q^{52} +9.42683i q^{53} +(3.36356 - 6.53349i) q^{54} +3.04322i q^{55} +(3.41774 + 0.122528i) q^{56} +(1.66015 - 4.07106i) q^{57} +(1.28047 + 7.80601i) q^{58} +(-4.46335 - 7.73074i) q^{59} +(0.214742 - 3.45744i) q^{60} +(1.32896 - 2.30183i) q^{61} +(-4.33508 - 1.63674i) q^{62} +(0.977274 + 3.49327i) q^{63} +(4.48585 - 6.62398i) q^{64} +(-4.39869 - 2.53958i) q^{65} +(-7.26707 - 1.66033i) q^{66} +(12.4858 - 7.20867i) q^{67} +(-4.39099 - 0.882891i) q^{68} +(-1.63945 - 11.9454i) q^{69} +(1.08342 + 1.32295i) q^{70} +3.49303 q^{71} +(8.13906 + 2.39912i) q^{72} +5.10052 q^{73} +(9.27523 + 11.3258i) q^{74} +(1.36832 - 1.06194i) q^{75} +(4.97709 + 1.00074i) q^{76} +(3.18667 - 1.83982i) q^{77} +(8.46427 - 9.11832i) q^{78} +(-3.26472 - 1.88488i) q^{79} +(3.96791 - 0.505654i) q^{80} +(0.197735 + 8.99783i) q^{81} +(-5.65579 - 2.13538i) q^{82} +(-0.286172 + 0.495665i) q^{83} +(-3.75024 + 1.86538i) q^{84} +(-1.11972 - 1.93941i) q^{85} +(0.988904 + 6.02859i) q^{86} +(-5.93990 - 7.65361i) q^{87} +(0.308386 - 8.60199i) q^{88} +2.40129i q^{89} +(1.78933 + 3.84686i) q^{90} +6.14138i q^{91} +(13.1931 - 4.44795i) q^{92} +(5.62248 - 0.771656i) q^{93} +(14.3763 - 2.35822i) q^{94} +(1.26918 + 2.19828i) q^{95} +(-0.957353 + 9.75108i) q^{96} +(5.82556 - 10.0902i) q^{97} +(-2.76639 + 7.32708i) q^{98} +(8.79207 - 2.45966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} + 4 q^{9} - 22 q^{12} - 30 q^{14} - 16 q^{18} - 4 q^{21} - 28 q^{24} + 24 q^{25} - 12 q^{29} + 16 q^{30} - 44 q^{33} - 6 q^{34} + 42 q^{36} + 60 q^{38} - 6 q^{40} - 60 q^{41} - 18 q^{42}+ \cdots - 12 q^{97}+O(q^{100}) \) 48 * q + 6 * q^6 + 4 * q^9 - 22 * q^12 - 30 * q^14 - 16 * q^18 - 4 * q^21 - 28 * q^24 + 24 * q^25 - 12 * q^29 + 16 * q^30 - 44 * q^33 - 6 * q^34 + 42 * q^36 + 60 * q^38 - 6 * q^40 - 60 * q^41 - 18 * q^42 - 8 * q^45 - 12 * q^46 - 12 * q^48 + 24 * q^49 - 18 * q^52 - 32 * q^54 - 42 * q^56 - 12 * q^57 - 18 * q^58 + 14 * q^60 - 48 * q^64 + 16 * q^66 + 48 * q^68 + 36 * q^69 + 60 * q^72 - 24 * q^73 + 84 * q^74 + 6 * q^76 + 48 * q^77 + 38 * q^78 - 36 * q^82 + 50 * q^84 - 54 * q^86 - 18 * q^90 + 60 * q^92 - 32 * q^93 + 18 * q^94 - 18 * q^96 - 12 * q^97

Introduction

L-functions

Modular forms

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Representations

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Database

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