LMFDB - Embedded newform 900.2.r.f.851.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(551,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, 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("900.551"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,6,0,0,4,0,0,22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			851.17
Character	$\chi$	$=$	900.851
Dual form			900.2.r.f.551.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.896034 - 1.09413i) q^{2} +(-1.60382 + 0.654027i) q^{3} +(-0.394247 - 1.96076i) q^{4} +(-0.721488 + 2.34082i) q^{6} +(-1.04714 + 0.604565i) q^{7} +(-2.49858 - 1.32555i) q^{8} +(2.14450 - 2.09789i) q^{9} +(1.52161 + 2.63550i) q^{11} +(1.91469 + 2.88686i) q^{12} +(-2.53958 + 4.39869i) q^{13} +(-0.276797 + 1.68742i) q^{14} +(-3.68914 + 1.54605i) q^{16} +2.23944i q^{17} +(-0.373823 - 4.22614i) q^{18} +2.53835i q^{19} +(1.28402 - 1.65447i) q^{21} +(4.24700 + 0.696660i) q^{22} +(3.48067 - 6.02870i) q^{23} +(4.87423 + 0.491800i) q^{24} +(2.53719 + 6.72001i) q^{26} +(-2.06732 + 4.76720i) q^{27} +(1.59824 + 1.81484i) q^{28} +(-4.84407 + 2.79673i) q^{29} +(2.83759 + 1.63828i) q^{31} +(-1.61401 + 5.42171i) q^{32} +(-4.16408 - 3.23171i) q^{33} +(2.45024 + 2.00661i) q^{34} +(-4.95891 - 3.37775i) q^{36} +10.3514 q^{37} +(2.77729 + 2.27445i) q^{38} +(1.19618 - 8.71567i) q^{39} +(3.70208 + 2.13740i) q^{41} +(-0.659684 - 2.88735i) q^{42} +(3.74108 - 2.15991i) q^{43} +(4.56769 - 4.02254i) q^{44} +(-3.47739 - 9.21023i) q^{46} +(5.15071 + 8.92129i) q^{47} +(4.90557 - 4.89238i) q^{48} +(-2.76900 + 4.79605i) q^{49} +(-1.46465 - 3.59166i) q^{51} +(9.62598 + 3.24534i) q^{52} +9.42683i q^{53} +(3.36356 + 6.53349i) q^{54} +(3.41774 - 0.122528i) q^{56} +(-1.66015 - 4.07106i) q^{57} +(-1.28047 + 7.80601i) q^{58} +(-4.46335 + 7.73074i) q^{59} +(1.32896 + 2.30183i) q^{61} +(4.33508 - 1.63674i) q^{62} +(-0.977274 + 3.49327i) q^{63} +(4.48585 + 6.62398i) q^{64} +(-7.26707 + 1.66033i) q^{66} +(-12.4858 - 7.20867i) q^{67} +(4.39099 - 0.882891i) q^{68} +(-1.63945 + 11.9454i) q^{69} +3.49303 q^{71} +(-8.13906 + 2.39912i) q^{72} -5.10052 q^{73} +(9.27523 - 11.3258i) q^{74} +(4.97709 - 1.00074i) q^{76} +(-3.18667 - 1.83982i) q^{77} +(-8.46427 - 9.11832i) q^{78} +(-3.26472 + 1.88488i) q^{79} +(0.197735 - 8.99783i) q^{81} +(5.65579 - 2.13538i) q^{82} +(0.286172 + 0.495665i) q^{83} +(-3.75024 - 1.86538i) q^{84} +(0.988904 - 6.02859i) q^{86} +(5.93990 - 7.65361i) q^{87} +(-0.308386 - 8.60199i) q^{88} -2.40129i q^{89} -6.14138i q^{91} +(-13.1931 - 4.44795i) q^{92} +(-5.62248 - 0.771656i) q^{93} +(14.3763 + 2.35822i) q^{94} +(-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} - 12 q^{29} + 44 q^{33} - 6 q^{34} + 42 q^{36} - 60 q^{38} - 60 q^{41} + 18 q^{42} - 12 q^{46} + 12 q^{48} + 24 q^{49}+ \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 - 12 * q^29 + 44 * q^33 - 6 * q^34 + 42 * q^36 - 60 * q^38 - 60 * q^41 + 18 * q^42 - 12 * q^46 + 12 * q^48 + 24 * q^49 + 18 * q^52 - 32 * q^54 - 42 * q^56 + 12 * q^57 + 18 * q^58 - 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 - 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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.896034	−	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			0
$5$		0			0
$6$	−0.721488	+	2.34082i	−0.294546	+	0.955637i
$7$	−1.04714	+	0.604565i	−0.395781	+	0.228504i	−0.684662	−	0.728861i	$-0.740050\pi$
$7$	−1.04714	+	0.604565i	−0.395781	+	0.228504i	0.288881	+	0.957365i	$0.406717\pi$
$8$	−2.49858	−	1.32555i	−0.883383	−	0.468651i
$9$	2.14450	−	2.09789i	0.714832	−	0.699296i
$10$		0			0
$11$	1.52161	+	2.63550i	0.458782	+	0.794634i	0.998897	−	0.0469575i	$-0.0149525\pi$
$11$	1.52161	+	2.63550i	0.458782	+	0.794634i	−0.540115	+	0.841591i	$0.681619\pi$
$12$	1.91469	+	2.88686i	0.552724	+	0.833365i
$13$	−2.53958	+	4.39869i	−0.704354	+	1.21998i	0.262570	+	0.964913i	$0.415430\pi$
$13$	−2.53958	+	4.39869i	−0.704354	+	1.21998i	−0.966924	+	0.255064i	$0.917904\pi$
$14$	−0.276797	+	1.68742i	−0.0739771	+	0.450981i
$15$		0			0
$16$	−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	$0.0940441\pi$
$19$			2.53835i			0.582337i	−0.956672	+	0.291169i	$0.905956\pi$
$20$		0			0
$21$	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	−0.232886	−	0.972504i	$-0.574817\pi$
$23$	3.48067	−	6.02870i	0.725770	−	1.25707i	0.958656	−	0.284567i	$-0.0918498\pi$
$24$	4.87423	+	0.491800i	0.994948	+	0.100388i
$25$		0			0
$26$	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	−0.877045	−	0.480408i	$-0.840488\pi$
$29$	−4.84407	+	2.79673i	−0.899521	+	0.519339i	−0.0224766	+	0.999747i	$0.507155\pi$
$30$		0			0
$31$	2.83759	+	1.63828i	0.509647	+	0.294245i	0.732688	−	0.680564i	$-0.238265\pi$
$31$	2.83759	+	1.63828i	0.509647	+	0.294245i	−0.223042	+	0.974809i	$0.571599\pi$
$32$	−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
$35$		0			0
$36$	−4.95891	−	3.37775i	−0.826485	−	0.562959i
$37$	10.3514			1.70176			0.850882	−	0.525356i	$-0.176068\pi$
$37$	10.3514			1.70176			0.850882	+	0.525356i	$0.176068\pi$
$38$	2.77729	+	2.27445i	0.450536	+	0.368964i
$39$	1.19618	−	8.71567i	0.191542	−	1.39562i
$40$		0			0
$41$	3.70208	+	2.13740i	0.578168	+	0.333806i	0.760405	−	0.649449i	$-0.225000\pi$
$41$	3.70208	+	2.13740i	0.578168	+	0.333806i	−0.182237	+	0.983255i	$0.558334\pi$
$42$	−0.659684	−	2.88735i	−0.101791	−	0.445528i
$43$	3.74108	−	2.15991i	0.570509	−	0.329384i	−0.186844	−	0.982390i	$-0.559826\pi$
$43$	3.74108	−	2.15991i	0.570509	−	0.329384i	0.757353	+	0.653006i	$0.226492\pi$
$44$	4.56769	−	4.02254i	0.688605	−	0.606421i
$45$		0			0
$46$	−3.47739	−	9.21023i	−0.512713	−	1.35797i
$47$	5.15071	+	8.92129i	0.751308	+	1.30130i	0.947189	+	0.320677i	$0.103910\pi$
$47$	5.15071	+	8.92129i	0.751308	+	1.30130i	−0.195880	+	0.980628i	$0.562756\pi$
$48$	4.90557	−	4.89238i	0.708058	−	0.706154i
$49$	−2.76900	+	4.79605i	−0.395572	+	0.685150i
$50$		0			0
$51$	−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
$55$		0			0
$56$	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	0.414274	+	0.910152i	$0.364036\pi$
$59$	−4.46335	+	7.73074i	−0.581078	+	1.00646i	−0.995352	+	0.0963045i	$0.969298\pi$
$60$		0			0
$61$	1.32896	+	2.30183i	0.170156	+	0.294720i	0.938474	−	0.345349i	$-0.112239\pi$
$61$	1.32896	+	2.30183i	0.170156	+	0.294720i	−0.768318	+	0.640068i	$0.778906\pi$
$62$	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
$65$		0			0
$66$	−7.26707	+	1.66033i	−0.894514	+	0.204373i
$67$	−12.4858	−	7.20867i	−1.52538	−	0.880679i	−0.999547	−	0.0300911i	$-0.990420\pi$
$67$	−12.4858	−	7.20867i	−1.52538	−	0.880679i	−0.525833	−	0.850588i	$-0.676246\pi$
$68$	4.39099	−	0.882891i	0.532486	−	0.107066i
$69$	−1.63945	+	11.9454i	−0.197366	+	1.43806i
$70$		0			0
$71$	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	$-0.596481\pi$
$73$	−5.10052			−0.596970			−0.298485	+	0.954414i	$0.596481\pi$
$74$	9.27523	−	11.3258i	1.07822	−	1.31660i
$75$		0			0
$76$	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	−0.672282	−	0.740295i	$-0.734686\pi$
$79$	−3.26472	+	1.88488i	−0.367309	+	0.212066i	0.304973	+	0.952361i	$0.401353\pi$
$80$		0			0
$81$	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	$-0.156666\pi$
$83$	0.286172	+	0.495665i	0.0314115	+	0.0544063i	−0.849892	+	0.526956i	$0.823333\pi$
$84$	−3.75024	−	1.86538i	−0.409185	−	0.203530i
$85$		0			0
$86$	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	$-0.959379\pi$
$89$		−	2.40129i		−	0.254536i	0.991868	−	0.127268i	$-0.0406208\pi$
$90$		0			0
$91$		−	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
$95$		0			0
$96$	−0.957353	−	9.75108i	−0.0977094	−	0.995215i
$97$	−5.82556	−	10.0902i	−0.591496	−	1.02450i	−0.994031	−	0.109096i	$-0.965204\pi$
$97$	−5.82556	−	10.0902i	−0.591496	−	1.02450i	0.402535	−	0.915404i	$-0.368129\pi$
$98$	2.76639	+	7.32708i	0.279448	+	0.740146i
$99$	8.79207	+	2.45966i	0.883636	+	0.247206i
$100$		0			0
$101$	−4.13758	+	2.38883i	−0.411704	+	0.237698i	−0.691522	−	0.722356i	$-0.743059\pi$
$101$	−4.13758	+	2.38883i	−0.411704	+	0.237698i	0.279818	+	0.960053i	$0.409726\pi$
$102$	−5.24213	−	1.61573i	−0.519048	−	0.159981i
$103$	−8.19166	−	4.72945i	−0.807148	−	0.466007i	0.0388166	−	0.999246i	$-0.487641\pi$
$103$	−8.19166	−	4.72945i	−0.807148	−	0.466007i	−0.845964	+	0.533239i	$0.820975\pi$
$104$	12.1760	−	7.62416i	1.19396	−	0.747610i
$105$		0			0
$106$	10.3142	+	8.44676i	1.00180	+	0.820422i
$107$	18.3014			1.76926			0.884630	−	0.466294i	$-0.154411\pi$
$107$	18.3014			1.76926			0.884630	+	0.466294i	$0.154411\pi$
$108$	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	$0.663483\pi$
$110$		0			0
$111$	−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	$-0.426506\pi$
$113$	−5.31273	−	3.06731i	−0.499780	−	0.288548i	−0.728623	+	0.684915i	$0.759839\pi$
$114$	−5.94183	−	1.83139i	−0.556503	−	0.171525i
$115$		0			0
$116$	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
$120$		0			0
$121$	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
$125$		0			0
$126$	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
$130$		0			0
$131$	1.06630	−	1.84689i	0.0931633	−	0.161364i	−0.815677	−	0.578507i	$-0.803635\pi$
$131$	1.06630	−	1.84689i	0.0931633	−	0.161364i	0.908841	+	0.417144i	$0.136969\pi$
$132$	−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
$135$		0			0
$136$	2.96848	−	5.59542i	0.254545	−	0.479803i
$137$	−14.2781	+	8.24344i	−1.21986	+	0.704285i	−0.964887	−	0.262665i	$-0.915399\pi$
$137$	−14.2781	+	8.24344i	−1.21986	+	0.704285i	−0.254969	+	0.966949i	$0.582065\pi$
$138$	11.6009	+	12.4973i	0.987531	+	1.06384i
$139$	−17.4077	−	10.0504i	−1.47650	−	0.852460i	−0.476856	−	0.878981i	$-0.658224\pi$
$139$	−17.4077	−	10.0504i	−1.47650	−	0.852460i	−0.999648	+	0.0265213i	$0.991557\pi$
$140$		0			0
$141$	−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
$145$		0			0
$146$	−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	0.565331	−	0.824864i	$-0.308748\pi$
$149$	1.63133	+	0.941851i	0.133644	+	0.0771594i	−0.431687	+	0.902023i	$0.642082\pi$
$150$		0			0
$151$	5.35919	−	3.09413i	0.436124	−	0.251796i	−0.265828	−	0.964020i	$-0.585645\pi$
$151$	5.35919	−	3.09413i	0.436124	−	0.251796i	0.701952	+	0.712224i	$0.252312\pi$
$152$	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
$155$		0			0
$156$	−17.5609	+	1.09071i	−1.40600	+	0.0873265i
$157$	−1.10012	+	1.90546i	−0.0877991	+	0.152073i	−0.906581	−	0.422033i	$-0.861317\pi$
$157$	−1.10012	+	1.90546i	−0.0877991	+	0.152073i	0.818781	+	0.574105i	$0.194650\pi$
$158$	−0.862984	+	5.26095i	−0.0686553	+	0.418539i
$159$	−6.16540	−	15.1190i	−0.488948	−	1.19901i
$160$		0			0
$161$			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
$165$		0			0
$166$	0.798742	+	0.131022i	0.0619944	+	0.0101693i
$167$	−11.1124	+	19.2472i	−0.859901	+	1.48939i	0.0121218	+	0.999927i	$0.496141\pi$
$167$	−11.1124	+	19.2472i	−0.859901	+	1.48939i	−0.872023	+	0.489465i	$0.837192\pi$
$168$	−5.40132	+	2.43181i	−0.416721	+	0.187618i
$169$	−6.39897	−	11.0833i	−0.492229	−	0.852565i
$170$		0			0
$171$	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	$-0.467437\pi$
$173$	13.3460	−	7.70532i	1.01468	−	0.585825i	0.912558	+	0.408947i	$0.134104\pi$
$174$	−3.05170	−	13.3569i	−0.231349	−	1.01259i
$175$		0			0
$176$	−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	$0.340922\pi$
$180$		0			0
$181$	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
$185$		0			0
$186$	−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
$190$		0			0
$191$	8.91431	+	15.4400i	0.645017	+	1.11720i	0.984298	+	0.176516i	$0.0564829\pi$
$191$	8.91431	+	15.4400i	0.645017	+	1.11720i	−0.339281	+	0.940685i	$0.610184\pi$
$192$	−11.5268	−	7.68982i	−0.831874	−	0.554965i
$193$	−2.44181	+	4.22934i	−0.175765	+	0.304434i	−0.940426	−	0.339999i	$-0.889573\pi$
$193$	−2.44181	+	4.22934i	−0.175765	+	0.304434i	0.764661	+	0.644433i	$0.222907\pi$
$194$	−16.2599	−	2.66720i	−1.16739	−	0.191494i
$195$		0			0
$196$	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	$0.0672320\pi$
$199$			5.91492i			0.419297i	−0.977777	+	0.209649i	$0.932768\pi$
$200$		0			0
$201$	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
$205$		0			0
$206$	−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			0
$211$	−23.9485	−	13.8267i	−1.64868	−	0.951868i	−0.977596	−	0.210491i	$-0.932494\pi$
$211$	−23.9485	−	13.8267i	−1.64868	−	0.951868i	−0.671089	−	0.741377i	$-0.734173\pi$
$212$	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
$215$		0			0
$216$	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
$220$		0			0
$221$	−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	$-0.370535\pi$
$223$	20.7390	−	11.9737i	1.38878	−	0.801815i	0.993178	+	0.116605i	$0.0372013\pi$
$224$	−1.58768	−	6.65306i	−0.106082	−	0.444526i
$225$		0			0
$226$	−8.11643	+	3.06442i	−0.539897	+	0.203842i
$227$	3.45979	+	5.99253i	0.229634	+	0.397739i	0.957700	−	0.287769i	$-0.0929136\pi$
$227$	3.45979	+	5.99253i	0.229634	+	0.397739i	−0.728065	+	0.685508i	$0.759580\pi$
$228$	−7.32786	+	4.86016i	−0.485299	+	0.321872i
$229$	7.65837	−	13.2647i	0.506080	−	0.876556i	−0.493896	−	0.869521i	$-0.664428\pi$
$229$	7.65837	−	13.2647i	0.506080	−	0.876556i	0.999975	−	0.00703439i	$-0.00223914\pi$
$230$		0			0
$231$	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
$235$		0			0
$236$	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	−0.701905	−	0.712271i	$-0.747667\pi$
$239$	4.11060	−	7.11976i	0.265892	−	0.460539i	0.967797	+	0.251732i	$0.0810001\pi$
$240$		0			0
$241$	−7.30777	−	12.6574i	−0.470735	−	0.815337i	0.528705	−	0.848806i	$-0.322678\pi$
$241$	−7.30777	−	12.6574i	−0.470735	−	0.815337i	−0.999440	+	0.0334691i	$0.989344\pi$
$242$	−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
$245$		0			0
$246$	−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
$250$		0			0
$251$	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			0
$256$	11.2195	−	11.4072i	0.701218	−	0.712947i
$257$	−7.31747	−	4.22474i	−0.456451	−	0.263532i	0.254100	−	0.967178i	$-0.418221\pi$
$257$	−7.31747	−	4.22474i	−0.456451	−	0.263532i	−0.710551	+	0.703646i	$0.751554\pi$
$258$	2.35683	+	10.3156i	0.146730	+	0.642218i
$259$	−10.8394	+	6.25812i	−0.673526	+	0.388860i
$260$		0			0
$261$	−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	$-0.102810\pi$
$263$	3.23162	+	5.59733i	0.199270	+	0.345146i	−0.749022	+	0.662545i	$0.769476\pi$
$264$	6.12053	+	13.5944i	0.376693	+	0.836676i
$265$		0			0
$266$	−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	$0.0600229\pi$
$269$			6.14888i			0.374904i	−0.982274	+	0.187452i	$0.939977\pi$
$270$		0			0
$271$			0.446839i			0.0271436i	0.999908	+	0.0135718i	$0.00432016\pi$
$271$			0.446839i			0.0271436i	−0.999908	+	0.0135718i	$0.995680\pi$
$272$	−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
$275$		0			0
$276$	24.0684	−	1.49489i	1.44875	−	0.0899818i
$277$	3.41624	+	5.91710i	0.205262	+	0.355524i	0.950216	−	0.311592i	$-0.100862\pi$
$277$	3.41624	+	5.91710i	0.205262	+	0.355524i	−0.744954	+	0.667115i	$0.767529\pi$
$278$	−26.5943	+	10.0409i	−1.59502	+	0.602212i
$279$	9.52214	−	2.43965i	0.570076	−	0.146058i
$280$		0			0
$281$	−2.85059	+	1.64579i	−0.170052	+	0.0981794i	−0.582610	−	0.812752i	$-0.697969\pi$
$281$	−2.85059	+	1.64579i	−0.170052	+	0.0981794i	0.412559	+	0.910931i	$0.364635\pi$
$282$	−24.5993	+	5.62030i	−1.46487	+	0.334684i
$283$	20.2974	+	11.7187i	1.20655	+	0.696603i	0.962004	−	0.273034i	$-0.0880271\pi$
$283$	20.2974	+	11.7187i	1.20655	+	0.696603i	0.244548	+	0.969637i	$0.421360\pi$
$284$	−1.37712	−	6.84898i	−0.0817168	−	0.406412i
$285$		0			0
$286$	−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
$290$		0			0
$291$	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	$-0.636788\pi$
$293$	−24.1734	−	13.9565i	−1.41223	−	0.815349i	−0.995598	+	0.0937278i	$0.970122\pi$
$294$	−9.22891	−	9.94204i	−0.538241	−	0.579831i
$295$		0			0
$296$	−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
$300$		0			0
$301$	−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
$305$		0			0
$306$	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
$310$		0			0
$311$	2.94543	−	5.10164i	0.167020	−	0.289287i	−0.770351	−	0.637620i	$-0.779919\pi$
$311$	2.94543	−	5.10164i	0.167020	−	0.289287i	0.937371	+	0.348333i	$0.113252\pi$
$312$	−14.5418	+	20.1913i	−0.823267	+	1.14310i
$313$	3.88369	+	6.72675i	0.219519	+	0.380218i	0.954661	−	0.297695i	$-0.0962178\pi$
$313$	3.88369	+	6.72675i	0.219519	+	0.380218i	−0.735142	+	0.677913i	$0.762885\pi$
$314$	1.09908	+	2.91104i	0.0620249	+	0.164279i
$315$		0			0
$316$	4.98291	+	5.65820i	0.280310	+	0.318299i
$317$	10.1939	−	5.88545i	0.572547	−	0.330560i	−0.185619	−	0.982622i	$-0.559429\pi$
$317$	10.1939	−	5.88545i	0.572547	−	0.330560i	0.758166	+	0.652062i	$0.226096\pi$
$318$	−22.0665	−	6.80134i	−1.23743	−	0.381400i
$319$	−14.7416	−	8.51104i	−0.825369	−	0.476527i
$320$		0			0
$321$	−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
$325$		0			0
$326$	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
$330$		0			0
$331$	−3.74464	+	2.16197i	−0.205824	+	0.118833i	−0.599369	−	0.800473i	$-0.704582\pi$
$331$	−3.74464	+	2.16197i	−0.205824	+	0.118833i	0.393545	+	0.919305i	$0.371249\pi$
$332$	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
$335$		0			0
$336$	−2.17904	+	8.08873i	−0.118877	+	0.441277i
$337$	3.88505	−	6.72910i	0.211632	−	0.366558i	−0.740593	−	0.671953i	$-0.765455\pi$
$337$	3.88505	−	6.72910i	0.211632	−	0.366558i	0.952225	+	0.305396i	$0.0987888\pi$
$338$	−17.8603	−	2.92973i	−0.971474	−	0.159357i
$339$	10.5268	+	1.44475i	0.571737	+	0.0784679i
$340$		0			0
$341$			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
$345$		0			0
$346$	3.52784	−	21.5065i	0.189658	−	1.15620i
$347$	5.63307	−	9.75677i	0.302399	−	0.523771i	−0.674280	−	0.738476i	$-0.735546\pi$
$347$	5.63307	−	9.75677i	0.302399	−	0.523771i	0.976679	+	0.214705i	$0.0688791\pi$
$348$	−17.3487	−	8.62929i	−0.929986	−	0.462578i
$349$	11.1403	+	19.2956i	0.596326	+	1.03287i	0.993358	+	0.115063i	$0.0367069\pi$
$349$	11.1403	+	19.2956i	0.596326	+	1.03287i	−0.397032	+	0.917805i	$0.629960\pi$
$350$		0			0
$351$	−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	$-0.466902\pi$
$353$	19.1084	−	11.0323i	1.01704	−	0.587188i	0.913245	+	0.407411i	$0.133568\pi$
$354$	−14.8761	−	16.0255i	−0.790653	−	0.851748i
$355$		0			0
$356$	−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	$0.514313\pi$
$360$		0			0
$361$	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
$365$		0			0
$366$	−6.34702	+	1.45013i	−0.331764	+	0.0757993i
$367$	−8.15927	+	4.71076i	−0.425910	+	0.245900i	−0.697603	−	0.716485i	$-0.745750\pi$
$367$	−8.15927	+	4.71076i	−0.425910	+	0.245900i	0.271692	+	0.962384i	$0.412417\pi$
$368$	−3.52003	+	27.6220i	−0.183494	+	1.43990i
$369$	12.4231	−	3.18291i	0.646722	−	0.165696i
$370$		0			0
$371$	−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	$-0.710081\pi$
$373$	7.29277	−	12.6314i	0.377605	−	0.654031i	0.990713	+	0.135968i	$0.0434143\pi$
$374$	−1.56013	+	9.51088i	−0.0806721	+	0.491796i
$375$		0			0
$376$	−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	$-0.921875\pi$
$379$		−	9.46065i		−	0.485961i	0.970031	−	0.242980i	$-0.0781251\pi$
$380$		0			0
$381$	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	$-0.889413\pi$
$383$	−3.43007	+	5.94105i	−0.175268	+	0.303573i	0.764986	+	0.644047i	$0.222746\pi$
$384$	−18.7421	+	5.72147i	−0.956427	+	0.291973i
$385$		0			0
$386$	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	−0.308622	−	0.951185i	$-0.599868\pi$
$389$	7.11643	−	4.10868i	0.360818	−	0.208318i	0.669439	+	0.742867i	$0.266534\pi$
$390$		0			0
$391$	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
$395$		0			0
$396$	1.35656	−	18.2088i	0.0681695	−	0.915028i
$397$	7.07936			0.355303			0.177651	−	0.984093i	$-0.443150\pi$
$397$	7.07936			0.355303			0.177651	+	0.984093i	$0.443150\pi$
$398$	6.47170	+	5.29996i	0.324397	+	0.265663i
$399$	4.19963	+	3.25930i	0.210244	+	0.163169i
$400$		0			0
$401$	−15.3220	−	8.84615i	−0.765143	−	0.441755i	0.0659963	−	0.997820i	$-0.478977\pi$
$401$	−15.3220	−	8.84615i	−0.765143	−	0.441755i	−0.831139	+	0.556064i	$0.812311\pi$
$402$	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
$405$		0			0
$406$	−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	−0.435944	−	0.899974i	$-0.643585\pi$
$409$	11.3542	−	19.6660i	0.561428	−	0.972422i	0.997372	−	0.0724482i	$-0.0230812\pi$
$410$		0			0
$411$	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			0
$416$	−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	0.340645	+	0.940192i	$0.389355\pi$
$419$	−13.1805	+	22.8292i	−0.643908	+	1.11528i	−0.984553	+	0.175089i	$0.943979\pi$
$420$		0			0
$421$	−8.57768	−	14.8570i	−0.418050	−	0.724084i	0.577693	−	0.816254i	$-0.303953\pi$
$421$	−8.57768	−	14.8570i	−0.418050	−	0.724084i	−0.995743	+	0.0921697i	$0.970620\pi$
$422$	−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
$425$		0			0
$426$	−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
$430$		0			0
$431$	−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	$-0.408945\pi$
$433$	11.7433			0.564346			0.282173	+	0.959364i	$0.408945\pi$
$434$	−3.54991	+	4.33473i	−0.170401	+	0.208074i
$435$		0			0
$436$	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	−0.534375	−	0.845247i	$-0.679453\pi$
$439$	−1.45738	+	0.841421i	−0.0695571	+	0.0401588i	0.464818	+	0.885406i	$0.346120\pi$
$440$		0			0
$441$	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	$-0.172406\pi$
$443$	−0.379510	−	0.657331i	−0.0180311	−	0.0312307i	−0.874900	+	0.484303i	$0.839073\pi$
$444$	19.8198	+	29.8831i	0.940606	+	1.41819i
$445$		0			0
$446$	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	$-0.864850\pi$
$449$		−	17.4579i		−	0.823887i	0.911209	−	0.411943i	$-0.135150\pi$
$450$		0			0
$451$			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
$455$		0			0
$456$	−1.24836	+	12.3725i	−0.0584598	+	0.579396i
$457$	−17.4319	−	30.1929i	−0.815430	−	1.41237i	−0.909019	−	0.416756i	$-0.863167\pi$
$457$	−17.4319	−	30.1929i	−0.815430	−	1.41237i	0.0935884	−	0.995611i	$-0.470166\pi$
$458$	−7.65116	−	20.2649i	−0.357515	−	0.946916i
$459$	−10.6758	−	4.62963i	−0.498306	−	0.216093i
$460$		0			0
$461$	27.0906	−	15.6407i	1.26173	−	0.728462i	0.288324	−	0.957533i	$-0.406902\pi$
$461$	27.0906	−	15.6407i	1.26173	−	0.728462i	0.973410	+	0.229071i	$0.0735688\pi$
$462$	6.60584	−	6.13201i	0.307332	−	0.285287i
$463$	−8.90511	−	5.14137i	−0.413856	−	0.238940i	0.278589	−	0.960410i	$-0.410133\pi$
$463$	−8.90511	−	5.14137i	−0.413856	−	0.238940i	−0.692445	+	0.721471i	$0.743466\pi$
$464$	13.5466	−	17.8067i	0.628884	−	0.826654i
$465$		0			0
$466$	7.23276	+	5.92323i	0.335051	+	0.274388i
$467$	−2.90585			−0.134467			−0.0672333	−	0.997737i	$-0.521417\pi$
$467$	−2.90585			−0.134467			−0.0672333	+	0.997737i	$0.521417\pi$
$468$	27.4512	−	13.2346i	1.26893	−	0.611770i
$469$	17.4324			0.804955
$470$		0			0
$471$	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
$475$		0			0
$476$	−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	0.996939	−	0.0781799i	$-0.0249109\pi$
$479$	9.42773	+	16.3293i	0.430764	+	0.746105i	−0.566175	+	0.824285i	$0.691578\pi$
$480$		0			0
$481$	−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
$485$		0			0
$486$	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
$490$		0			0
$491$	−0.747617	+	1.29491i	−0.0337395	+	0.0584385i	−0.882402	−	0.470496i	$-0.844075\pi$
$491$	−0.747617	+	1.29491i	−0.0337395	+	0.0584385i	0.848663	+	0.528935i	$0.177408\pi$
$492$	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
$495$		0			0
$496$	−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	0.964999	−	0.262254i	$-0.0844660\pi$
$499$	27.2612	+	15.7393i	1.22038	+	0.704586i	0.255380	+	0.966841i	$0.417799\pi$
$500$		0			0
$501$	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	$-0.486481\pi$
$503$	1.90449			0.0849171			0.0424585	+	0.999098i	$0.486481\pi$
$504$	7.07229	−	7.43280i	0.315025	−	0.331083i
$505$		0			0
$506$	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	0.962021	−	0.272975i	$-0.0880078\pi$
$509$	27.2228	+	15.7171i	1.20663	+	0.696647i	0.244607	+	0.969622i	$0.421341\pi$
$510$		0			0
$511$	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
$515$		0			0
$516$	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
$520$		0			0
$521$		−	23.2742i		−	1.01966i	−0.860275	−	0.509831i	$-0.829708\pi$
$521$		−	23.2742i		−	1.01966i	0.860275	−	0.509831i	$-0.170292\pi$
$522$	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
$525$		0			0
$526$	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
$530$		0			0
$531$	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
$535$		0			0
$536$	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
$540$		0			0
$541$	−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
$545$		0			0
$546$	14.3759	+	4.43093i	0.615231	+	0.189626i
$547$	−23.0165	+	13.2886i	−0.984113	+	0.568178i	−0.903509	−	0.428569i	$-0.859018\pi$
$547$	−23.0165	+	13.2886i	−0.984113	+	0.568178i	−0.0806034	+	0.996746i	$0.525685\pi$
$548$	21.7925	+	24.7458i	0.930928	+	1.05709i
$549$	7.67895	+	2.14826i	0.327729	+	0.0916854i
$550$		0			0
$551$	−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
$555$		0			0
$556$	−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
$560$		0			0
$561$	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	−0.311411	−	0.950275i	$-0.600801\pi$
$563$	15.8324	−	27.4226i	0.667257	−	1.15572i	0.978668	−	0.205448i	$-0.0658652\pi$
$564$	−15.8925	+	31.9509i	−0.669195	+	1.34538i
$565$		0			0
$566$	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	0.218272	−	0.975888i	$-0.429958\pi$
$569$	27.9697	−	16.1483i	1.17255	−	0.676973i	0.954280	+	0.298915i	$0.0966248\pi$
$570$		0			0
$571$	12.7245	+	7.34651i	0.532505	+	0.307442i	0.742036	−	0.670360i	$-0.233860\pi$
$571$	12.7245	+	7.34651i	0.532505	+	0.307442i	−0.209531	+	0.977802i	$0.567194\pi$
$572$	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
$575$		0			0
$576$	23.5163	+	4.79429i	0.979844	+	0.199762i
$577$	22.4886			0.936214			0.468107	−	0.883672i	$-0.344936\pi$
$577$	22.4886			0.936214			0.468107	+	0.883672i	$0.344936\pi$
$578$	10.7389	−	13.1131i	0.446679	−	0.545432i
$579$	1.15013	−	8.38012i	0.0477977	−	0.348266i
$580$		0			0
$581$	−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
$585$		0			0
$586$	−36.9305	+	13.9434i	−1.52558	+	0.575996i
$587$	−17.2484	−	29.8752i	−0.711919	−	1.23308i	−0.964136	−	0.265409i	$-0.914493\pi$
$587$	−17.2484	−	29.8752i	−0.711919	−	1.23308i	0.252217	−	0.967671i	$-0.418840\pi$
$588$	−19.1473	+	1.18924i	−0.789622	+	0.0490434i
$589$	−4.15854	+	7.20280i	−0.171350	+	0.296786i
$590$		0			0
$591$	−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
$595$		0			0
$596$	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	−0.230387	−	0.973099i	$-0.573999\pi$
$599$	17.8060	−	30.8410i	0.727535	−	1.26013i	0.957922	−	0.287028i	$-0.0926674\pi$
$600$		0			0
$601$	−20.4137	−	35.3576i	−0.832693	−	1.44227i	−0.895895	−	0.444266i	$-0.853465\pi$
$601$	−20.4137	−	35.3576i	−0.832693	−	1.44227i	0.0632021	−	0.998001i	$-0.479869\pi$
$602$	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
$605$		0			0
$606$	−2.60662	−	11.4088i	−0.105887	−	0.463453i
$607$	−1.90026	−	1.09711i	−0.0771290	−	0.0445304i	0.460940	−	0.887432i	$-0.347513\pi$
$607$	−1.90026	−	1.09711i	−0.0771290	−	0.0445304i	−0.538069	+	0.842901i	$0.680846\pi$
$608$	−13.7622	−	4.09693i	−0.558131	−	0.166153i
$609$	−1.59279	+	11.6054i	−0.0645430	+	0.470276i
$610$		0			0
$611$	−52.3227			−2.11675
$612$	7.56426	−	11.1052i	0.305767	−	0.448900i
$613$	−38.7673			−1.56580			−0.782899	−	0.622149i	$-0.786260\pi$
$613$	−38.7673			−1.56580			−0.782899	+	0.622149i	$0.786260\pi$
$614$	24.7207	+	20.2449i	0.997645	+	0.817017i
$615$		0			0
$616$	5.52339	+	8.82103i	0.222544	+	0.355409i
$617$	12.8653	+	7.42778i	0.517937	+	0.299031i	0.736090	−	0.676884i	$-0.236670\pi$
$617$	12.8653	+	7.42778i	0.517937	+	0.299031i	−0.218153	+	0.975915i	$0.570003\pi$
$618$	16.9810	−	15.7630i	0.683076	−	0.634080i
$619$	12.3383	−	7.12352i	0.495918	−	0.286318i	−0.231108	−	0.972928i	$-0.574235\pi$
$619$	12.3383	−	7.12352i	0.495918	−	0.286318i	0.727026	+	0.686610i	$0.240902\pi$
$620$		0			0
$621$	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			0
$626$	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			0
$631$			38.8200i			1.54540i	0.634772	+	0.772700i	$0.281094\pi$
$631$			38.8200i			1.54540i	−0.634772	+	0.772700i	$0.718906\pi$
$632$	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
$635$		0			0
$636$	−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
$640$		0			0
$641$	16.5595	−	9.56061i	0.654060	−	0.377621i	−0.135950	−	0.990716i	$-0.543409\pi$
$641$	16.5595	−	9.56061i	0.654060	−	0.377621i	0.790010	+	0.613094i	$0.210075\pi$
$642$	−13.2042	+	42.8403i	−0.521129	+	1.69077i
$643$	5.69143	+	3.28595i	0.224448	+	0.129585i	0.608008	−	0.793931i	$-0.291969\pi$
$643$	5.69143	+	3.28595i	0.224448	+	0.129585i	−0.383560	+	0.923516i	$0.625302\pi$
$644$	16.5040	−	3.31845i	0.650350	−	0.130765i
$645$		0			0
$646$	−5.09348	+	6.21956i	−0.200400	+	0.244705i
$647$	12.7191			0.500040			0.250020	−	0.968241i	$-0.419563\pi$
$647$	12.7191			0.500040			0.250020	+	0.968241i	$0.419563\pi$
$648$	−12.4211	+	22.2197i	−0.487947	+	0.872873i
$649$	−27.1658			−1.06635
$650$		0			0
$651$	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	$-0.00221049\pi$
$653$	38.1762	+	22.0410i	1.49395	+	0.862532i	0.493974	+	0.869477i	$0.335544\pi$
$654$	7.40167	−	24.0143i	0.289428	−	0.939033i
$655$		0			0
$656$	−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	0.572030	−	0.820233i	$-0.306156\pi$
$659$	−10.8929	−	18.8671i	−0.424328	−	0.734957i	−0.996357	+	0.0852757i	$0.972823\pi$
$660$		0			0
$661$	−10.2756	+	17.7979i	−0.399676	+	0.692260i	−0.993686	−	0.112198i	$-0.964211\pi$
$661$	−10.2756	+	17.7979i	−0.399676	+	0.692260i	0.594009	+	0.804458i	$0.297544\pi$
$662$	−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
$665$		0			0
$666$	−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
$670$		0			0
$671$	−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	$-0.180029\pi$
$673$	−1.08874	−	1.88576i	−0.0419680	−	0.0726906i	−0.886246	+	0.463214i	$0.846696\pi$
$674$	−3.88139	−	10.2803i	−0.149505	−	0.395981i
$675$		0			0
$676$	−19.2090	+	16.9164i	−0.738807	+	0.650631i
$677$	−1.92840	+	1.11336i	−0.0741143	+	0.0427899i	−0.536599	−	0.843837i	$-0.680291\pi$
$677$	−1.92840	+	1.11336i	−0.0741143	+	0.0427899i	0.462485	+	0.886627i	$0.346958\pi$
$678$	11.0131	−	10.2231i	0.422956	−	0.392618i
$679$	12.2003	+	7.04386i	0.468205	+	0.270319i
$680$		0			0
$681$	−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	$-0.420117\pi$
$683$	12.9800			0.496665			0.248333	+	0.968675i	$0.420117\pi$
$684$	8.57392	−	12.5875i	0.327832	−	0.481293i
$685$		0			0
$686$	−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
$690$		0			0
$691$	−24.1859	+	13.9637i	−0.920074	+	0.531205i	−0.883659	−	0.468132i	$-0.844927\pi$
$691$	−24.1859	+	13.9637i	−0.920074	+	0.531205i	−0.0364156	+	0.999337i	$0.511594\pi$
$692$	−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
$695$		0			0
$696$	−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			0
$701$			31.0643i			1.17328i	0.809847	+	0.586641i	$0.199550\pi$
$701$			31.0643i			1.17328i	−0.809847	+	0.586641i	$0.800450\pi$
$702$	−37.2808	−	1.79711i	−1.40707	−	0.0678276i
$703$			26.2756i			0.991001i
$704$	−10.6318	+	21.9016i	−0.400701	+	0.825447i
$705$		0			0
$706$	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	0.908710	+	0.417429i	$0.137069\pi$
$709$	21.7239	+	37.6269i	0.815859	+	1.41311i	−0.0928511	+	0.995680i	$0.529598\pi$
$710$		0			0
$711$	−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
$715$		0			0
$716$	−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	$0.424205\pi$
$720$		0			0
$721$	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
$725$		0			0
$726$	2.89772	+	3.12163i	0.107544	+	0.115855i
$727$	43.4035	−	25.0590i	1.60975	−	0.929389i	0.620323	−	0.784347i	$-0.287002\pi$
$727$	43.4035	−	25.0590i	1.60975	−	0.929389i	0.989425	−	0.145042i	$-0.0463318\pi$
$728$	−8.14068	+	15.3448i	−0.301714	+	0.568714i
$729$	−18.4524	−	19.7106i	−0.683422	−	0.730024i
$730$		0			0
$731$	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	0.454493	+	0.890750i	$0.349821\pi$
$733$	−14.7327	+	25.5178i	−0.544166	+	0.942523i	−0.998659	+	0.0517728i	$0.983513\pi$
$734$	−2.15679	+	13.1483i	−0.0796087	+	0.485313i
$735$		0			0
$736$	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	$-0.686371\pi$
$739$		−	45.3131i		−	1.66687i	0.552618	−	0.833435i	$-0.313629\pi$
$740$		0			0
$741$	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	$-0.880659\pi$
$743$	−4.03779	+	6.99366i	−0.148132	+	0.256573i	0.782405	+	0.622770i	$0.213993\pi$
$744$	13.0254	+	9.38090i	0.477533	+	0.343921i
$745$		0			0
$746$	−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
$750$		0			0
$751$	−9.71367	−	5.60819i	−0.354457	−	0.204646i	0.312190	−	0.950020i	$-0.398938\pi$
$751$	−9.71367	−	5.60819i	−0.354457	−	0.204646i	−0.666646	+	0.745374i	$0.732271\pi$
$752$	−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
$755$		0			0
$756$	−11.9557	+	3.86727i	−0.434826	+	0.140651i
$757$	26.9148			0.978236			0.489118	−	0.872218i	$-0.337319\pi$
$757$	26.9148			0.978236			0.489118	+	0.872218i	$0.337319\pi$
$758$	−10.3512	−	8.47706i	−0.375972	−	0.307901i
$759$	−33.9768	+	13.8555i	−1.23328	+	0.502922i
$760$		0			0
$761$	6.74550	+	3.89451i	0.244524	+	0.141176i	0.617254	−	0.786764i	$-0.288245\pi$
$761$	6.74550	+	3.89451i	0.244524	+	0.141176i	−0.372730	+	0.927940i	$0.621578\pi$
$762$	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
$765$		0			0
$766$	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	−0.920297	−	0.391220i	$-0.872053\pi$
$769$	−3.36491	+	5.82819i	−0.121342	+	0.210170i	0.798955	+	0.601390i	$0.205386\pi$
$770$		0			0
$771$	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
$775$		0			0
$776$	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
$780$		0			0
$781$	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
$785$		0			0
$786$	3.55392	+	3.82853i	0.126764	+	0.136559i
$787$	2.38973	+	1.37971i	0.0851847	+	0.0491814i	0.541987	−	0.840387i	$-0.317672\pi$
$787$	2.38973	+	1.37971i	0.0851847	+	0.0491814i	−0.456803	+	0.889568i	$0.651005\pi$
$788$	32.9746	−	6.63016i	1.17467	−	0.236190i
$789$	−8.84375	−	6.86356i	−0.314846	−	0.244349i
$790$		0			0
$791$	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
$795$		0			0
$796$	11.5977	−	2.33194i	0.411070	−	0.0826534i
$797$	−4.54011	−	2.62123i	−0.160819	−	0.0928488i	0.417431	−	0.908709i	$-0.362931\pi$
$797$	−4.54011	−	2.62123i	−0.160819	−	0.0928488i	−0.578250	+	0.815860i	$0.696264\pi$
$798$	7.32911	−	1.67451i	0.259448	−	0.0592769i
$799$	−19.9787	+	11.5347i	−0.706794	+	0.408068i
$800$		0			0
$801$	−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
$805$		0			0
$806$	−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	$0.311319\pi$
$809$			47.1813i			1.65881i	−0.558650	+	0.829403i	$0.688681\pi$
$810$		0			0
$811$			18.8666i			0.662495i	0.943544	+	0.331247i	$0.107469\pi$
$811$			18.8666i			0.662495i	−0.943544	+	0.331247i	$0.892531\pi$
$812$	−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
$815$		0			0
$816$	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
$820$		0			0
$821$	1.12399	−	0.648938i	0.0392277	−	0.0226481i	−0.480258	−	0.877127i	$-0.659457\pi$
$821$	1.12399	−	0.648938i	0.0392277	−	0.0226481i	0.519486	+	0.854479i	$0.326124\pi$
$822$	−8.99499	−	39.3699i	−0.313736	−	1.37318i
$823$	5.77693	+	3.33531i	0.201371	+	0.116262i	0.597295	−	0.802022i	$-0.296242\pi$
$823$	5.77693	+	3.33531i	0.201371	+	0.116262i	−0.395924	+	0.918283i	$0.629576\pi$
$824$	14.1984	+	22.6754i	0.494626	+	0.789934i
$825$		0			0
$826$	−11.8095	−	9.67137i	−0.410907	−	0.336510i
$827$	−37.4924			−1.30374			−0.651869	−	0.758331i	$-0.726015\pi$
$827$	−37.4924			−1.30374			−0.651869	+	0.758331i	$0.726015\pi$
$828$	−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			0
$831$	−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
$835$		0			0
$836$	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	0.664808	−	0.747014i	$-0.268513\pi$
$839$	−9.11048	−	15.7798i	−0.314529	−	0.544780i	−0.979337	+	0.202234i	$0.935180\pi$
$840$		0			0
$841$	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
$845$		0			0
$846$	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			0
$851$	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	$-0.177300\pi$
$853$	−0.975478	−	1.68958i	−0.0333997	−	0.0578500i	−0.882242	+	0.470796i	$0.843967\pi$
$854$	−4.25201	+	1.60538i	−0.145501	+	0.0549349i
$855$		0			0
$856$	−45.7275	−	24.2593i	−1.56293	−	0.829166i
$857$	−11.2785	+	6.51166i	−0.385267	+	0.222434i	−0.680107	−	0.733113i	$-0.738067\pi$
$857$	−11.2785	+	6.51166i	−0.385267	+	0.222434i	0.294840	+	0.955546i	$0.404733\pi$
$858$	11.1520	−	36.1821i	0.380724	−	1.23524i
$859$	−3.50034	−	2.02092i	−0.119430	−	0.0689530i	0.439095	−	0.898441i	$-0.355299\pi$
$859$	−3.50034	−	2.02092i	−0.119430	−	0.0689530i	−0.558525	+	0.829488i	$0.688633\pi$
$860$		0			0
$861$	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	$-0.557886\pi$
$863$	−10.6258			−0.361705			−0.180853	+	0.983510i	$0.557886\pi$
$864$	−22.5097	−	18.9027i	−0.765796	−	0.643084i
$865$		0			0
$866$	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
$870$		0			0
$871$	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			0
$876$	−9.76591	−	14.7245i	−0.329960	−	0.497494i
$877$	−26.5530	+	45.9911i	−0.896631	+	1.55301i	−0.0648570	+	0.997895i	$0.520659\pi$
$877$	−26.5530	+	45.9911i	−0.896631	+	1.55301i	−0.831774	+	0.555115i	$0.812674\pi$
$878$	−0.385240	+	2.34851i	−0.0130012	+	0.0792584i
$879$	47.8978	+	6.57373i	1.61555	+	0.221727i
$880$		0			0
$881$			10.8244i			0.364685i	0.983235	+	0.182342i	$0.0583679\pi$
$881$			10.8244i			0.364685i	−0.983235	+	0.182342i	$0.941632\pi$
$882$	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
$885$		0			0
$886$	−1.05926	−	0.173757i	−0.0355865	−	0.00583747i
$887$	0.264026	−	0.457306i	0.00886511	−	0.0153548i	−0.861559	−	0.507658i	$-0.830511\pi$
$887$	0.264026	−	0.457306i	0.00886511	−	0.0153548i	0.870424	+	0.492303i	$0.163845\pi$
$888$	50.4553	+	5.09083i	1.69317	+	0.170837i
$889$	5.69025	+	9.85580i	0.190845	+	0.330553i
$890$		0			0
$891$	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
$895$		0			0
$896$	−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			0
$901$	−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
$905$		0			0
$906$	3.37622	+	14.7773i	0.112167	+	0.490942i
$907$	40.9884	−	23.6647i	1.36100	−	0.785773i	0.371242	−	0.928536i	$-0.378932\pi$
$907$	40.9884	−	23.6647i	1.36100	−	0.785773i	0.989757	+	0.142763i	$0.0455988\pi$
$908$	10.3859	−	9.14635i	0.344668	−	0.303532i
$909$	−3.86152	+	13.8030i	−0.128079	+	0.457817i
$910$		0			0
$911$	18.8160	+	32.5902i	0.623401	+	1.07976i	0.988848	+	0.148930i	$0.0475829\pi$
$911$	18.8160	+	32.5902i	0.623401	+	1.07976i	−0.365447	+	0.930832i	$0.619084\pi$
$912$	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
$915$		0			0
$916$	−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	$-0.749674\pi$
$919$		−	42.9157i		−	1.41566i	0.706383	−	0.707830i	$-0.250326\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$	−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	−0.852311	−	0.523036i	$-0.824799\pi$
$929$	−25.1609	+	14.5267i	−0.825503	+	0.476605i	0.0268072	+	0.999641i	$0.491466\pi$
$930$		0			0
$931$	−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
$935$		0			0
$936$	10.1168	−	41.8939i	0.330679	−	1.36935i
$937$	−51.0143			−1.66656			−0.833282	−	0.552848i	$-0.813541\pi$
$937$	−51.0143			−1.66656			−0.833282	+	0.552848i	$0.813541\pi$
$938$	15.6201	−	19.0734i	0.510013	−	0.622768i
$939$	−10.6282	−	8.24847i	−0.346839	−	0.269179i
$940$		0			0
$941$	7.54730	+	4.35743i	0.246035	+	0.142048i	0.617947	−	0.786220i	$-0.287964\pi$
$941$	7.54730	+	4.35743i	0.246035	+	0.142048i	−0.371912	+	0.928268i	$0.621298\pi$
$942$	−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
$945$		0			0
$946$	17.3931	−	6.56689i	0.565498	−	0.213508i
$947$	−19.0803	−	33.0481i	−0.620028	−	1.07392i	−0.989480	−	0.144670i	$-0.953788\pi$
$947$	−19.0803	−	33.0481i	−0.620028	−	1.07392i	0.369452	−	0.929250i	$-0.379545\pi$
$948$	−11.6923	−	5.81580i	−0.379749	−	0.188888i
$949$	12.9532	−	22.4356i	0.420478	−	0.728290i
$950$		0			0
$951$	−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
$955$		0			0
$956$	−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
$960$		0			0
$961$	−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
$965$		0			0
$966$	−19.7031	−	6.07289i	−0.633938	−	0.195392i
$967$	14.5754	+	8.41511i	0.468713	+	0.270612i	0.715701	−	0.698407i	$-0.246107\pi$
$967$	14.5754	+	8.41511i	0.468713	+	0.270612i	−0.246988	+	0.969019i	$0.579441\pi$
$968$	−4.16843	+	2.61011i	−0.133978	+	0.0838921i
$969$	9.11689	−	3.71780i	0.292877	−	0.119433i
$970$		0			0
$971$	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
$975$		0			0
$976$	−8.46147	−	6.43714i	−0.270845	−	0.206048i
$977$	−0.748148	−	0.431943i	−0.0239354	−	0.0138191i	0.487985	−	0.872852i	$-0.337732\pi$
$977$	−0.748148	−	0.431943i	−0.0239354	−	0.0138191i	−0.511920	+	0.859033i	$0.671066\pi$
$978$	−35.9666	−	11.0856i	−1.15008	−	0.354479i
$979$	6.32860	−	3.65382i	0.202263	−	0.116777i
$980$		0			0
$981$	−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	0.994596	+	0.103821i	$0.0331069\pi$
$983$	18.4107	+	31.8882i	0.587209	+	1.01708i	−0.407387	+	0.913256i	$0.633560\pi$
$984$	16.9936	+	12.2389i	0.541738	+	0.390161i
$985$		0			0
$986$	−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
$990$		0			0
$991$		−	35.9773i		−	1.14286i	−0.820652	−	0.571428i	$-0.806390\pi$
$991$		−	35.9773i		−	1.14286i	0.820652	−	0.571428i	$-0.193610\pi$
$992$	−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
$995$		0			0
$996$	−0.882983	+	1.77518i	−0.0279784	+	0.0562489i
$997$	−16.7322	−	28.9811i	−0.529915	−	0.917840i	−0.999391	−	0.0348944i	$-0.988891\pi$
$997$	−16.7322	−	28.9811i	−0.529915	−	0.917840i	0.469476	−	0.882945i	$-0.344443\pi$
$998$	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	900.2.r.f.851.17		48
4.3	odd	2	inner	900.2.r.f.851.24		48
5.2	odd	4		900.2.o.c.599.19		48
5.3	odd	4		900.2.o.b.599.6		48
5.4	even	2		180.2.q.a.131.8	yes	48
9.2	odd	6	inner	900.2.r.f.551.24		48
15.14	odd	2		540.2.q.a.71.17		48
20.3	even	4		900.2.o.b.599.11		48
20.7	even	4		900.2.o.c.599.14		48
20.19	odd	2		180.2.q.a.131.1	yes	48
36.11	even	6	inner	900.2.r.f.551.17		48
45.2	even	12		900.2.o.b.299.11		48
45.4	even	6		1620.2.e.b.971.17		48
45.14	odd	6		1620.2.e.b.971.32		48
45.29	odd	6		180.2.q.a.11.1	✓	48
45.34	even	6		540.2.q.a.251.24		48
45.38	even	12		900.2.o.c.299.14		48
60.59	even	2		540.2.q.a.71.24		48
180.47	odd	12		900.2.o.b.299.6		48
180.59	even	6		1620.2.e.b.971.18		48
180.79	odd	6		540.2.q.a.251.17		48
180.83	odd	12		900.2.o.c.299.19		48
180.119	even	6		180.2.q.a.11.8	yes	48
180.139	odd	6		1620.2.e.b.971.31		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.1	✓	48	45.29	odd	6
180.2.q.a.11.8	yes	48	180.119	even	6
180.2.q.a.131.1	yes	48	20.19	odd	2
180.2.q.a.131.8	yes	48	5.4	even	2
540.2.q.a.71.17		48	15.14	odd	2
540.2.q.a.71.24		48	60.59	even	2
540.2.q.a.251.17		48	180.79	odd	6
540.2.q.a.251.24		48	45.34	even	6
900.2.o.b.299.6		48	180.47	odd	12
900.2.o.b.299.11		48	45.2	even	12
900.2.o.b.599.6		48	5.3	odd	4
900.2.o.b.599.11		48	20.3	even	4
900.2.o.c.299.14		48	45.38	even	12
900.2.o.c.299.19		48	180.83	odd	12
900.2.o.c.599.14		48	20.7	even	4
900.2.o.c.599.19		48	5.2	odd	4
900.2.r.f.551.17		48	36.11	even	6	inner
900.2.r.f.551.24		48	9.2	odd	6	inner
900.2.r.f.851.17		48	1.1	even	1	trivial
900.2.r.f.851.24		48	4.3	odd	2	inner
1620.2.e.b.971.17		48	45.4	even	6
1620.2.e.b.971.18		48	180.59	even	6
1620.2.e.b.971.31		48	180.139	odd	6
1620.2.e.b.971.32		48	45.14	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.r (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} +(-0.721488 + 2.34082i) q^{6} +(-1.04714 + 0.604565i) q^{7} +(-2.49858 - 1.32555i) q^{8} +(2.14450 - 2.09789i) q^{9} +(1.52161 + 2.63550i) q^{11} +(1.91469 + 2.88686i) q^{12} +(-2.53958 + 4.39869i) q^{13} +(-0.276797 + 1.68742i) q^{14} +(-3.68914 + 1.54605i) q^{16} +2.23944i q^{17} +(-0.373823 - 4.22614i) q^{18} +2.53835i q^{19} +(1.28402 - 1.65447i) q^{21} +(4.24700 + 0.696660i) q^{22} +(3.48067 - 6.02870i) q^{23} +(4.87423 + 0.491800i) q^{24} +(2.53719 + 6.72001i) q^{26} +(-2.06732 + 4.76720i) q^{27} +(1.59824 + 1.81484i) q^{28} +(-4.84407 + 2.79673i) q^{29} +(2.83759 + 1.63828i) q^{31} +(-1.61401 + 5.42171i) q^{32} +(-4.16408 - 3.23171i) q^{33} +(2.45024 + 2.00661i) q^{34} +(-4.95891 - 3.37775i) q^{36} +10.3514 q^{37} +(2.77729 + 2.27445i) q^{38} +(1.19618 - 8.71567i) q^{39} +(3.70208 + 2.13740i) q^{41} +(-0.659684 - 2.88735i) q^{42} +(3.74108 - 2.15991i) q^{43} +(4.56769 - 4.02254i) q^{44} +(-3.47739 - 9.21023i) q^{46} +(5.15071 + 8.92129i) q^{47} +(4.90557 - 4.89238i) q^{48} +(-2.76900 + 4.79605i) q^{49} +(-1.46465 - 3.59166i) q^{51} +(9.62598 + 3.24534i) q^{52} +9.42683i q^{53} +(3.36356 + 6.53349i) q^{54} +(3.41774 - 0.122528i) q^{56} +(-1.66015 - 4.07106i) q^{57} +(-1.28047 + 7.80601i) q^{58} +(-4.46335 + 7.73074i) q^{59} +(1.32896 + 2.30183i) q^{61} +(4.33508 - 1.63674i) q^{62} +(-0.977274 + 3.49327i) q^{63} +(4.48585 + 6.62398i) q^{64} +(-7.26707 + 1.66033i) q^{66} +(-12.4858 - 7.20867i) q^{67} +(4.39099 - 0.882891i) q^{68} +(-1.63945 + 11.9454i) q^{69} +3.49303 q^{71} +(-8.13906 + 2.39912i) q^{72} -5.10052 q^{73} +(9.27523 - 11.3258i) q^{74} +(4.97709 - 1.00074i) q^{76} +(-3.18667 - 1.83982i) q^{77} +(-8.46427 - 9.11832i) q^{78} +(-3.26472 + 1.88488i) q^{79} +(0.197735 - 8.99783i) q^{81} +(5.65579 - 2.13538i) q^{82} +(0.286172 + 0.495665i) q^{83} +(-3.75024 - 1.86538i) q^{84} +(0.988904 - 6.02859i) q^{86} +(5.93990 - 7.65361i) q^{87} +(-0.308386 - 8.60199i) q^{88} -2.40129i q^{89} -6.14138i q^{91} +(-13.1931 - 4.44795i) q^{92} +(-5.62248 - 0.771656i) q^{93} +(14.3763 + 2.35822i) q^{94} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} + 4 q^{9} + 22 q^{12} - 30 q^{14} + 16 q^{18} - 4 q^{21} - 28 q^{24} - 12 q^{29} + 44 q^{33} - 6 q^{34} + 42 q^{36} - 60 q^{38} - 60 q^{41} + 18 q^{42} - 12 q^{46} + 12 q^{48} + 24 q^{49}+ \cdots + 12 q^{97}+O(q^{100}) \) 48 * q + 6 * q^6 + 4 * q^9 + 22 * q^12 - 30 * q^14 + 16 * q^18 - 4 * q^21 - 28 * q^24 - 12 * q^29 + 44 * q^33 - 6 * q^34 + 42 * q^36 - 60 * q^38 - 60 * q^41 + 18 * q^42 - 12 * q^46 + 12 * q^48 + 24 * q^49 + 18 * q^52 - 32 * q^54 - 42 * q^56 + 12 * q^57 + 18 * q^58 - 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 - 60 * q^92 + 32 * q^93 + 18 * q^94 - 18 * q^96 + 12 * q^97

Introduction

L-functions

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