LMFDB - Embedded newform 900.2.o.c.299.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(299,900)] 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, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.299"); 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.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,6,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == 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			299.19
Character	$\chi$	$=$	900.299
Dual form			900.2.o.c.599.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.09413 - 0.896034i) q^{2} +(0.654027 - 1.60382i) q^{3} +(0.394247 - 1.96076i) q^{4} +(-0.721488 - 2.34082i) q^{6} +(-0.604565 + 1.04714i) q^{7} +(-1.32555 - 2.49858i) q^{8} +(-2.14450 - 2.09789i) q^{9} +(1.52161 - 2.63550i) q^{11} +(-2.88686 - 1.91469i) q^{12} +(4.39869 - 2.53958i) q^{13} +(0.276797 + 1.68742i) q^{14} +(-3.68914 - 1.54605i) q^{16} -2.23944 q^{17} +(-4.22614 - 0.373823i) q^{18} +2.53835i q^{19} +(1.28402 + 1.65447i) q^{21} +(-0.696660 - 4.24700i) q^{22} +(-6.02870 + 3.48067i) q^{23} +(-4.87423 + 0.491800i) q^{24} +(2.53719 - 6.72001i) q^{26} +(-4.76720 + 2.06732i) q^{27} +(1.81484 + 1.59824i) q^{28} +(4.84407 + 2.79673i) q^{29} +(2.83759 - 1.63828i) q^{31} +(-5.42171 + 1.61401i) q^{32} +(-3.23171 - 4.16408i) q^{33} +(-2.45024 + 2.00661i) q^{34} +(-4.95891 + 3.37775i) q^{36} -10.3514i q^{37} +(2.27445 + 2.77729i) q^{38} +(-1.19618 - 8.71567i) q^{39} +(3.70208 - 2.13740i) q^{41} +(2.88735 + 0.659684i) q^{42} +(-2.15991 + 3.74108i) q^{43} +(-4.56769 - 4.02254i) q^{44} +(-3.47739 + 9.21023i) q^{46} +(-8.92129 - 5.15071i) q^{47} +(-4.89238 + 4.90557i) q^{48} +(2.76900 + 4.79605i) q^{49} +(-1.46465 + 3.59166i) q^{51} +(-3.24534 - 9.62598i) q^{52} +9.42683 q^{53} +(-3.36356 + 6.53349i) q^{54} +(3.41774 + 0.122528i) q^{56} +(4.07106 + 1.66015i) q^{57} +(7.80601 - 1.28047i) q^{58} +(4.46335 + 7.73074i) q^{59} +(1.32896 - 2.30183i) q^{61} +(1.63674 - 4.33508i) q^{62} +(3.49327 - 0.977274i) q^{63} +(-4.48585 + 6.62398i) q^{64} +(-7.26707 - 1.66033i) q^{66} +(7.20867 + 12.4858i) q^{67} +(-0.882891 + 4.39099i) q^{68} +(1.63945 + 11.9454i) q^{69} +3.49303 q^{71} +(-2.39912 + 8.13906i) q^{72} -5.10052i q^{73} +(-9.27523 - 11.3258i) q^{74} +(4.97709 + 1.00074i) q^{76} +(1.83982 + 3.18667i) q^{77} +(-9.11832 - 8.46427i) q^{78} +(3.26472 + 1.88488i) q^{79} +(0.197735 + 8.99783i) q^{81} +(2.13538 - 5.65579i) q^{82} +(0.495665 + 0.286172i) q^{83} +(3.75024 - 1.86538i) q^{84} +(0.988904 + 6.02859i) q^{86} +(7.65361 - 5.93990i) q^{87} +(-8.60199 - 0.308386i) q^{88} -2.40129i q^{89} +6.14138i q^{91} +(4.44795 + 13.1931i) q^{92} +(-0.771656 - 5.62248i) q^{93} +(-14.3763 + 2.35822i) q^{94} +(-0.957353 + 9.75108i) q^{96} +(10.0902 + 5.82556i) q^{97} +(7.32708 + 2.76639i) q^{98} +(-8.79207 + 2.45966i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} + 12 q^{8} - 4 q^{9} + 28 q^{12} + 30 q^{14} - 18 q^{18} - 4 q^{21} - 42 q^{22} + 28 q^{24} + 12 q^{29} - 48 q^{33} + 6 q^{34} + 42 q^{36} - 6 q^{38} - 60 q^{41} + 16 q^{42} - 12 q^{46} - 74 q^{48}+ \cdots + 84 q^{98}+O(q^{100}) $ 48 * q + 6 * q^6 + 12 * q^8 - 4 * q^9 + 28 * q^12 + 30 * q^14 - 18 * q^18 - 4 * q^21 - 42 * q^22 + 28 * q^24 + 12 * q^29 - 48 * q^33 + 6 * q^34 + 42 * q^36 - 6 * q^38 - 60 * q^41 + 16 * q^42 - 12 * q^46 - 74 * q^48 - 24 * q^49 - 90 * q^52 + 32 * q^54 - 42 * q^56 - 16 * q^57 + 84 * q^58 + 84 * q^62 + 48 * q^64 + 16 * q^66 + 6 * q^68 - 36 * q^69 - 80 * q^72 - 84 * q^74 + 6 * q^76 - 46 * q^78 - 50 * q^84 - 54 * q^86 + 114 * q^88 - 42 * q^92 - 24 * q^93 - 18 * q^94 - 18 * q^96 - 48 * q^97 + 84 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.09413	−	0.896034i	0.773668	−	0.633592i
$2$	1.09413	−	0.896034i	0.773668	−	0.633592i
$3$	0.654027	−	1.60382i	0.377603	−	0.925968i
$3$	0.654027	−	1.60382i	0.377603	−	0.925968i
$4$	0.394247	−	1.96076i	0.197124	−	0.980379i
$5$		0			0
$5$		0			0
$6$	−0.721488	−	2.34082i	−0.294546	−	0.955637i
$7$	−0.604565	+	1.04714i	−0.228504	+	0.395781i	−0.957365	−	0.288881i	$-0.906717\pi$
$7$	−0.604565	+	1.04714i	−0.228504	+	0.395781i	0.728861	+	0.684662i	$0.240050\pi$
$8$	−1.32555	−	2.49858i	−0.468651	−	0.883383i
$9$	−2.14450	−	2.09789i	−0.714832	−	0.699296i
$10$		0			0
$11$	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	$0.0149525\pi$
$12$	−2.88686	−	1.91469i	−0.833365	−	0.552724i
$13$	4.39869	−	2.53958i	1.21998	−	0.704354i	0.255064	−	0.966924i	$-0.417904\pi$
$13$	4.39869	−	2.53958i	1.21998	−	0.704354i	0.964913	+	0.262570i	$0.0845702\pi$
$14$	0.276797	+	1.68742i	0.0739771	+	0.450981i
$15$		0			0
$16$	−3.68914	−	1.54605i	−0.922285	−	0.386512i
$17$	−2.23944			−0.543143			−0.271572	−	0.962418i	$-0.587543\pi$
$17$	−2.23944			−0.543143			−0.271572	+	0.962418i	$0.587543\pi$
$18$	−4.22614	−	0.373823i	−0.996111	−	0.0881110i
$19$			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
$22$	−0.696660	−	4.24700i	−0.148528	−	0.905463i
$23$	−6.02870	+	3.48067i	−1.25707	+	0.725770i	−0.972504	−	0.232886i	$-0.925183\pi$
$23$	−6.02870	+	3.48067i	−1.25707	+	0.725770i	−0.284567	+	0.958656i	$0.591850\pi$
$24$	−4.87423	+	0.491800i	−0.994948	+	0.100388i
$25$		0			0
$26$	2.53719	−	6.72001i	0.497584	−	1.31790i
$27$	−4.76720	+	2.06732i	−0.917448	+	0.397856i
$28$	1.81484	+	1.59824i	0.342972	+	0.302038i
$29$	4.84407	+	2.79673i	0.899521	+	0.519339i	0.877045	−	0.480408i	$-0.159512\pi$
$29$	4.84407	+	2.79673i	0.899521	+	0.519339i	0.0224766	+	0.999747i	$0.492845\pi$
$30$		0			0
$31$	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	$0.238265\pi$
$32$	−5.42171	+	1.61401i	−0.958432	+	0.285320i
$33$	−3.23171	−	4.16408i	−0.562568	−	0.724873i
$34$	−2.45024	+	2.00661i	−0.420212	+	0.344131i
$35$		0			0
$36$	−4.95891	+	3.37775i	−0.826485	+	0.562959i
$37$		−	10.3514i		−	1.70176i	−0.525356	−	0.850882i	$-0.676068\pi$
$37$		−	10.3514i		−	1.70176i	0.525356	−	0.850882i	$-0.323932\pi$
$38$	2.27445	+	2.77729i	0.368964	+	0.450536i
$39$	−1.19618	−	8.71567i	−0.191542	−	1.39562i
$40$		0			0
$41$	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	$0.225000\pi$
$42$	2.88735	+	0.659684i	0.445528	+	0.101791i
$43$	−2.15991	+	3.74108i	−0.329384	+	0.570509i	−0.982390	−	0.186844i	$-0.940174\pi$
$43$	−2.15991	+	3.74108i	−0.329384	+	0.570509i	0.653006	+	0.757353i	$0.273508\pi$
$44$	−4.56769	−	4.02254i	−0.688605	−	0.606421i
$45$		0			0
$46$	−3.47739	+	9.21023i	−0.512713	+	1.35797i
$47$	−8.92129	−	5.15071i	−1.30130	−	0.751308i	−0.320677	−	0.947189i	$-0.603910\pi$
$47$	−8.92129	−	5.15071i	−1.30130	−	0.751308i	−0.980628	+	0.195880i	$0.937244\pi$
$48$	−4.89238	+	4.90557i	−0.706154	+	0.708058i
$49$	2.76900	+	4.79605i	0.395572	+	0.685150i
$50$		0			0
$51$	−1.46465	+	3.59166i	−0.205092	+	0.502933i
$52$	−3.24534	−	9.62598i	−0.450047	−	1.33488i
$53$	9.42683			1.29487			0.647437	−	0.762119i	$-0.275841\pi$
$53$	9.42683			1.29487			0.647437	+	0.762119i	$0.275841\pi$
$54$	−3.36356	+	6.53349i	−0.457722	+	0.889095i
$55$		0			0
$56$	3.41774	+	0.122528i	0.456715	+	0.0163735i
$57$	4.07106	+	1.66015i	0.539226	+	0.219892i
$58$	7.80601	−	1.28047i	1.02498	−	0.168133i
$59$	4.46335	+	7.73074i	0.581078	+	1.00646i	0.995352	+	0.0963045i	$0.0307023\pi$
$59$	4.46335	+	7.73074i	0.581078	+	1.00646i	−0.414274	+	0.910152i	$0.635964\pi$
$60$		0			0
$61$	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	$0.112239\pi$
$62$	1.63674	−	4.33508i	0.207866	−	0.550555i
$63$	3.49327	−	0.977274i	0.440110	−	0.123125i
$64$	−4.48585	+	6.62398i	−0.560732	+	0.827998i
$65$		0			0
$66$	−7.26707	−	1.66033i	−0.894514	−	0.204373i
$67$	7.20867	+	12.4858i	0.880679	+	1.52538i	0.850588	+	0.525833i	$0.176246\pi$
$67$	7.20867	+	12.4858i	0.880679	+	1.52538i	0.0300911	+	0.999547i	$0.490420\pi$
$68$	−0.882891	+	4.39099i	−0.107066	+	0.532486i
$69$	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	$0.433541\pi$
$72$	−2.39912	+	8.13906i	−0.282739	+	0.959197i
$73$		−	5.10052i		−	0.596970i	−0.954414	−	0.298485i	$-0.903519\pi$
$73$		−	5.10052i		−	0.596970i	0.954414	−	0.298485i	$-0.0964813\pi$
$74$	−9.27523	−	11.3258i	−1.07822	−	1.31660i
$75$		0			0
$76$	4.97709	+	1.00074i	0.570911	+	0.114792i
$77$	1.83982	+	3.18667i	0.209667	+	0.363154i
$78$	−9.11832	−	8.46427i	−1.03245	−	0.958390i
$79$	3.26472	+	1.88488i	0.367309	+	0.212066i	0.672282	−	0.740295i	$-0.265314\pi$
$79$	3.26472	+	1.88488i	0.367309	+	0.212066i	−0.304973	+	0.952361i	$0.598647\pi$
$80$		0			0
$81$	0.197735	+	8.99783i	0.0219706	+	0.999759i
$82$	2.13538	−	5.65579i	0.235814	−	0.624577i
$83$	0.495665	+	0.286172i	0.0544063	+	0.0314115i	0.526956	−	0.849892i	$-0.323333\pi$
$83$	0.495665	+	0.286172i	0.0544063	+	0.0314115i	−0.472550	+	0.881304i	$0.656666\pi$
$84$	3.75024	−	1.86538i	0.409185	−	0.203530i
$85$		0			0
$86$	0.988904	+	6.02859i	0.106636	+	0.650079i
$87$	7.65361	−	5.93990i	0.820553	−	0.636824i
$88$	−8.60199	−	0.308386i	−0.916975	−	0.0328741i
$89$		−	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
$92$	4.44795	+	13.1931i	0.463731	+	1.37547i
$93$	−0.771656	−	5.62248i	−0.0800170	−	0.583024i
$94$	−14.3763	+	2.35822i	−1.48280	+	0.243232i
$95$		0			0
$96$	−0.957353	+	9.75108i	−0.0977094	+	0.995215i
$97$	10.0902	+	5.82556i	1.02450	+	0.591496i	0.915404	−	0.402535i	$-0.131871\pi$
$97$	10.0902	+	5.82556i	1.02450	+	0.591496i	0.109096	+	0.994031i	$0.465204\pi$
$98$	7.32708	+	2.76639i	0.740146	+	0.279448i
$99$	−8.79207	+	2.45966i	−0.883636	+	0.247206i
$100$		0			0
$101$	−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	$0.743059\pi$
$102$	1.61573	+	5.24213i	0.159981	+	0.519048i
$103$	−4.72945	−	8.19166i	−0.466007	−	0.807148i	0.533239	−	0.845964i	$-0.320975\pi$
$103$	−4.72945	−	8.19166i	−0.466007	−	0.807148i	−0.999246	+	0.0388166i	$0.987641\pi$
$104$	−12.1760	−	7.62416i	−1.19396	−	0.747610i
$105$		0			0
$106$	10.3142	−	8.44676i	1.00180	−	0.820422i
$107$		−	18.3014i		−	1.76926i	−0.466294	−	0.884630i	$-0.654411\pi$
$107$		−	18.3014i		−	1.76926i	0.466294	−	0.884630i	$-0.345589\pi$
$108$	2.17405	+	10.1624i	0.209199	+	0.977873i
$109$	10.2589			0.982625			0.491312	−	0.870983i	$-0.336517\pi$
$109$	10.2589			0.982625			0.491312	+	0.870983i	$0.336517\pi$
$110$		0			0
$111$	−16.6019	−	6.77012i	−1.57578	−	0.642591i
$112$	3.84925	−	2.92835i	0.363720	−	0.276703i
$113$	−3.06731	−	5.31273i	−0.288548	−	0.499780i	0.684915	−	0.728623i	$-0.259839\pi$
$113$	−3.06731	−	5.31273i	−0.288548	−	0.499780i	−0.973463	+	0.228843i	$0.926506\pi$
$114$	5.94183	−	1.83139i	0.556503	−	0.171525i
$115$		0			0
$116$	7.39346	−	8.39545i	0.686466	−	0.779498i
$117$	−14.7607	−	3.78182i	−1.36463	−	0.349630i
$118$	11.8105	+	4.45914i	1.08724	+	0.410497i
$119$	1.35389	−	2.34500i	0.124110	−	0.214966i
$120$		0			0
$121$	0.869419	+	1.50588i	0.0790381	+	0.136898i
$122$	−0.608459	−	3.70930i	−0.0550873	−	0.335825i
$123$	−1.00675	−	7.33540i	−0.0907753	−	0.661411i
$124$	−2.09357	−	6.20972i	−0.188008	−	0.557649i
$125$		0			0
$126$	2.94642	−	4.19935i	0.262488	−	0.374108i
$127$	9.41213			0.835192			0.417596	−	0.908633i	$-0.362873\pi$
$127$	9.41213			0.835192			0.417596	+	0.908633i	$0.362873\pi$
$128$	1.02720	+	11.2670i	0.0907922	+	0.995870i
$129$	4.58739	+	5.91088i	0.403897	+	0.520424i
$130$		0			0
$131$	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	$0.803635\pi$
$132$	−9.43884	+	4.69492i	−0.821546	+	0.408640i
$133$	−2.65800	−	1.53460i	−0.230478	−	0.133067i
$134$	19.0749	+	7.20187i	1.64782	+	0.622147i
$135$		0			0
$136$	2.96848	+	5.59542i	0.254545	+	0.479803i
$137$	−8.24344	+	14.2781i	−0.704285	+	1.21986i	0.262665	+	0.964887i	$0.415399\pi$
$137$	−8.24344	+	14.2781i	−0.704285	+	1.21986i	−0.966949	+	0.254969i	$0.917935\pi$
$138$	12.4973	+	11.6009i	1.06384	+	0.987531i
$139$	17.4077	−	10.0504i	1.47650	−	0.852460i	0.476856	−	0.878981i	$-0.341776\pi$
$139$	17.4077	−	10.0504i	1.47650	−	0.852460i	0.999648	+	0.0265213i	$0.00844298\pi$
$140$		0			0
$141$	−14.0956	+	10.9395i	−1.18706	+	0.921270i
$142$	3.82183	−	3.12987i	0.320721	−	0.262653i
$143$		−	15.4570i		−	1.29258i
$144$	4.66792	+	11.0549i	0.388993	+	0.921241i
$145$		0			0
$146$	−4.57023	−	5.58064i	−0.378235	−	0.461857i
$147$	9.50302	−	1.30424i	0.783796	−	0.107572i
$148$	−20.2966	−	4.08102i	−1.66837	−	0.335458i
$149$	−1.63133	+	0.941851i	−0.133644	+	0.0771594i	−0.565331	−	0.824864i	$-0.691252\pi$
$149$	−1.63133	+	0.941851i	−0.133644	+	0.0771594i	0.431687	+	0.902023i	$0.357918\pi$
$150$		0			0
$151$	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	$0.585645\pi$
$152$	6.34228	−	3.36470i	0.514427	−	0.272913i
$153$	4.80246	+	4.69809i	0.388256	+	0.379818i
$154$	4.86837	+	1.83809i	0.392304	+	0.148117i
$155$		0			0
$156$	−17.5609	−	1.09071i	−1.40600	−	0.0873265i
$157$	−1.90546	+	1.10012i	−0.152073	+	0.0877991i	−0.574105	−	0.818781i	$-0.694650\pi$
$157$	−1.90546	+	1.10012i	−0.152073	+	0.0877991i	0.422033	+	0.906581i	$0.361317\pi$
$158$	5.26095	−	0.862984i	0.418539	−	0.0686553i
$159$	6.16540	−	15.1190i	0.488948	−	1.19901i
$160$		0			0
$161$		−	8.41717i		−	0.663366i
$162$	8.27871	+	9.66763i	0.650436	+	0.759561i
$163$	15.3649			1.20347			0.601737	−	0.798694i	$-0.294475\pi$
$163$	15.3649			1.20347			0.601737	+	0.798694i	$0.294475\pi$
$164$	−2.73138	−	8.10155i	−0.213285	−	0.632625i
$165$		0			0
$166$	0.798742	−	0.131022i	0.0619944	−	0.0101693i
$167$	−19.2472	+	11.1124i	−1.48939	+	0.859901i	−0.999927	−	0.0121218i	$-0.996141\pi$
$167$	−19.2472	+	11.1124i	−1.48939	+	0.859901i	−0.489465	+	0.872023i	$0.662808\pi$
$168$	2.43181	−	5.40132i	0.187618	−	0.416721i
$169$	6.39897	−	11.0833i	0.492229	−	0.852565i
$170$		0			0
$171$	5.32517	−	5.44348i	0.407226	−	0.416274i
$172$	6.48381	+	5.70997i	0.494386	+	0.435381i
$173$	−7.70532	+	13.3460i	−0.585825	+	1.01468i	0.408947	+	0.912558i	$0.365896\pi$
$173$	−7.70532	+	13.3460i	−0.585825	+	1.01468i	−0.994772	+	0.102120i	$0.967437\pi$
$174$	3.05170	−	13.3569i	0.231349	−	1.01259i
$175$		0			0
$176$	−9.68803	+	7.37026i	−0.730263	+	0.555554i
$177$	15.3179	−	2.10230i	1.15136	−	0.158019i
$178$	−2.15164	−	2.62733i	−0.161272	−	0.196926i
$179$	−12.8229			−0.958425			−0.479212	−	0.877699i	$-0.659078\pi$
$179$	−12.8229			−0.958425			−0.479212	+	0.877699i	$0.659078\pi$
$180$		0			0
$181$	17.3649			1.29072			0.645360	−	0.763879i	$-0.276707\pi$
$181$	17.3649			1.29072			0.645360	+	0.763879i	$0.276707\pi$
$182$	5.50288	+	6.71947i	0.407901	+	0.498081i
$183$	−2.82255	−	3.63688i	−0.208649	−	0.268846i
$184$	16.6881	+	10.4494i	1.23026	+	0.770342i
$185$		0			0
$186$	−5.88222	−	5.46030i	−0.431306	−	0.400369i
$187$	−3.40754	+	5.90204i	−0.249184	+	0.431600i
$188$	−13.6165	+	15.4618i	−0.993085	+	1.12767i
$189$	0.717316	−	6.24174i	0.0521771	−	0.454020i
$190$		0			0
$191$	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	$-0.0564829\pi$
$192$	7.68982	+	11.5268i	0.554965	+	0.831874i
$193$	4.22934	−	2.44181i	0.304434	−	0.175765i	−0.339999	−	0.940426i	$-0.610427\pi$
$193$	4.22934	−	2.44181i	0.304434	−	0.175765i	0.644433	+	0.764661i	$0.277093\pi$
$194$	16.2599	−	2.66720i	1.16739	−	0.191494i
$195$		0			0
$196$	10.4956	−	3.53851i	0.749683	−	0.252751i
$197$	−16.8173			−1.19818			−0.599090	−	0.800682i	$-0.704471\pi$
$197$	−16.8173			−1.19818			−0.599090	+	0.800682i	$0.704471\pi$
$198$	−7.41574	+	10.5692i	−0.527014	+	0.751119i
$199$			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
$202$	−6.66752	+	1.09371i	−0.469125	+	0.0769534i
$203$	−5.85712	+	3.38161i	−0.411089	+	0.237342i
$204$	6.46494	+	4.28783i	0.452636	+	0.300208i
$205$		0			0
$206$	−12.5146	−	4.72500i	−0.871937	−	0.329206i
$207$	20.2306	+	5.18325i	1.40612	+	0.360260i
$208$	−20.1537	+	2.56830i	−1.39741	+	0.178080i
$209$	6.68983	+	3.86237i	0.462745	+	0.267166i
$210$		0			0
$211$	−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	$0.932494\pi$
$212$	3.71650	−	18.4837i	0.255250	−	1.26947i
$213$	2.28453	−	5.60220i	0.156534	−	0.383856i
$214$	−16.3986	−	20.0241i	−1.12099	−	1.36882i
$215$		0			0
$216$	11.4845	+	9.17093i	0.781422	+	0.624003i
$217$			3.96180i			0.268945i
$218$	11.2246	−	9.19232i	0.760225	−	0.622583i
$219$	−8.18033	−	3.33588i	−0.552775	−	0.225418i
$220$		0			0
$221$	−9.85058	+	5.68724i	−0.662622	+	0.382565i
$222$	−24.2309	+	7.46843i	−1.62627	+	0.501248i
$223$	−11.9737	+	20.7390i	−0.801815	+	1.38878i	0.116605	+	0.993178i	$0.462799\pi$
$223$	−11.9737	+	20.7390i	−0.801815	+	1.38878i	−0.918420	+	0.395606i	$0.870535\pi$
$224$	1.58768	−	6.65306i	0.106082	−	0.444526i
$225$		0			0
$226$	−8.11643	−	3.06442i	−0.539897	−	0.203842i
$227$	−5.99253	−	3.45979i	−0.397739	−	0.229634i	0.287769	−	0.957700i	$-0.407086\pi$
$227$	−5.99253	−	3.45979i	−0.397739	−	0.229634i	−0.685508	+	0.728065i	$0.740420\pi$
$228$	4.86016	−	7.32786i	0.321872	−	0.485299i
$229$	−7.65837	−	13.2647i	−0.506080	−	0.876556i	−0.999975	−	0.00703439i	$-0.997761\pi$
$229$	−7.65837	−	13.2647i	−0.506080	−	0.876556i	0.493896	−	0.869521i	$-0.335572\pi$
$230$		0			0
$231$	6.31414	−	0.866584i	0.415440	−	0.0570170i
$232$	0.566816	−	15.8105i	0.0372133	−	1.03801i
$233$	6.61050			0.433068			0.216534	−	0.976275i	$-0.430525\pi$
$233$	6.61050			0.433068			0.216534	+	0.976275i	$0.430525\pi$
$234$	−19.5388	+	9.08830i	−1.27729	+	0.594121i
$235$		0			0
$236$	16.9178	−	5.70371i	1.10125	−	0.371280i
$237$	5.15823	−	4.00326i	0.335063	−	0.260040i
$238$	−0.619869	−	3.77886i	−0.0401801	−	0.244947i
$239$	−4.11060	−	7.11976i	−0.265892	−	0.460539i	0.701905	−	0.712271i	$-0.252333\pi$
$239$	−4.11060	−	7.11976i	−0.265892	−	0.460539i	−0.967797	+	0.251732i	$0.919000\pi$
$240$		0			0
$241$	−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	$0.322678\pi$
$242$	2.30058	+	0.868600i	0.147887	+	0.0558357i
$243$	14.5602	+	5.56769i	0.934040	+	0.357168i
$244$	−3.98940	−	3.51327i	−0.255395	−	0.224914i
$245$		0			0
$246$	−7.67428	−	7.12382i	−0.489294	−	0.454198i
$247$	6.44635	+	11.1654i	0.410172	+	0.710438i
$248$	−7.85475	−	4.91834i	−0.498777	−	0.312315i
$249$	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	$0.475949\pi$
$252$	−0.538987	−	7.23473i	−0.0339530	−	0.455745i
$253$			21.1849i			1.33188i
$254$	10.2981	−	8.43359i	0.646161	−	0.529170i
$255$		0			0
$256$	11.2195	+	11.4072i	0.701218	+	0.712947i
$257$	4.22474	+	7.31747i	0.263532	+	0.456451i	0.967178	−	0.254100i	$-0.0817791\pi$
$257$	4.22474	+	7.31747i	0.263532	+	0.456451i	−0.703646	+	0.710551i	$0.748446\pi$
$258$	10.3156	+	2.35683i	0.642218	+	0.146730i
$259$	10.8394	+	6.25812i	0.673526	+	0.388860i
$260$		0			0
$261$	−4.52088	−	16.1599i	−0.279835	−	1.00027i
$262$	2.82155	+	1.06530i	0.174316	+	0.0658143i
$263$	5.59733	+	3.23162i	0.345146	+	0.199270i	0.662545	−	0.749022i	$-0.269476\pi$
$263$	5.59733	+	3.23162i	0.345146	+	0.199270i	−0.317399	+	0.948292i	$0.602810\pi$
$264$	−6.12053	+	13.5944i	−0.376693	+	0.836676i
$265$		0			0
$266$	−4.28326	+	0.702607i	−0.262623	+	0.0430796i
$267$	−3.85124	−	1.57051i	−0.235692	−	0.0961135i
$268$	27.3236	−	9.21196i	1.66905	−	0.562710i
$269$			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	$-0.995680\pi$
$271$		−	0.446839i		−	0.0271436i	0.999908	−	0.0135718i	$-0.00432016\pi$
$272$	8.26159	+	3.46227i	0.500932	+	0.209931i
$273$	9.84968	+	4.01663i	0.596130	+	0.243097i
$274$	3.77421	+	23.0085i	0.228009	+	1.38999i
$275$		0			0
$276$	24.0684	+	1.49489i	1.44875	+	0.0899818i
$277$	−5.91710	−	3.41624i	−0.355524	−	0.205262i	0.311592	−	0.950216i	$-0.399138\pi$
$277$	−5.91710	−	3.41624i	−0.355524	−	0.205262i	−0.667115	+	0.744954i	$0.732471\pi$
$278$	10.0409	−	26.5943i	0.602212	−	1.59502i
$279$	−9.52214	−	2.43965i	−0.570076	−	0.146058i
$280$		0			0
$281$	−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	$0.697969\pi$
$282$	−5.62030	+	24.5993i	−0.334684	+	1.46487i
$283$	11.7187	+	20.2974i	0.696603	+	1.20655i	0.969637	+	0.244548i	$0.0786395\pi$
$283$	11.7187	+	20.2974i	0.696603	+	1.20655i	−0.273034	+	0.962004i	$0.588027\pi$
$284$	1.37712	−	6.84898i	0.0817168	−	0.406412i
$285$		0			0
$286$	−13.8500	−	16.9120i	−0.818967	−	1.00003i
$287$			5.16879i			0.305104i
$288$	15.0129	+	7.91289i	0.884642	+	0.466272i
$289$	−11.9849			−0.704996
$290$		0			0
$291$	15.9424	−	12.3728i	0.934560	−	0.725304i
$292$	−10.0009	−	2.01086i	−0.585257	−	0.117677i
$293$	−13.9565	−	24.1734i	−0.815349	−	1.41223i	−0.909077	−	0.416628i	$-0.863212\pi$
$293$	−13.9565	−	24.1734i	−0.815349	−	1.41223i	0.0937278	−	0.995598i	$-0.470122\pi$
$294$	9.22891	−	9.94204i	0.538241	−	0.579831i
$295$		0			0
$296$	−25.8639	+	13.7213i	−1.50331	+	0.797535i
$297$	−1.80539	+	15.7096i	−0.104759	+	0.911564i
$298$	−0.940963	+	2.49224i	−0.0545085	+	0.144371i
$299$	−17.6789	+	30.6208i	−1.02240	+	1.77085i
$300$		0			0
$301$	−2.61162	−	4.52345i	−0.150531	−	0.260727i
$302$	8.63610	−	1.41663i	0.496951	−	0.0815178i
$303$	−6.53735	+	5.07358i	−0.375561	+	0.291470i
$304$	3.92441	−	9.36432i	0.225080	−	0.537081i
$305$		0			0
$306$	9.46417	+	0.837153i	0.541031	+	0.0478569i
$307$	−22.5939			−1.28950			−0.644750	−	0.764393i	$-0.723039\pi$
$307$	−22.5939			−1.28950			−0.644750	+	0.764393i	$0.723039\pi$
$308$	6.97362	−	2.35111i	0.397359	−	0.133967i
$309$	−16.2312	+	2.22764i	−0.923358	+	0.126726i
$310$		0			0
$311$	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	$0.779919\pi$
$312$	−20.1913	+	14.5418i	−1.14310	+	0.823267i
$313$	6.72675	+	3.88369i	0.380218	+	0.219519i	0.677913	−	0.735142i	$-0.262885\pi$
$313$	6.72675	+	3.88369i	0.380218	+	0.219519i	−0.297695	+	0.954661i	$0.596218\pi$
$314$	−1.09908	+	2.91104i	−0.0620249	+	0.164279i
$315$		0			0
$316$	4.98291	−	5.65820i	0.280310	−	0.318299i
$317$	5.88545	−	10.1939i	0.330560	−	0.572547i	−0.652062	−	0.758166i	$-0.726096\pi$
$317$	5.88545	−	10.1939i	0.330560	−	0.572547i	0.982622	+	0.185619i	$0.0594291\pi$
$318$	−6.80134	−	22.0665i	−0.381400	−	1.23743i
$319$	14.7416	−	8.51104i	0.825369	−	0.476527i
$320$		0			0
$321$	−29.3522	−	11.9696i	−1.63828	−	0.668077i
$322$	−7.54207	−	9.20949i	−0.420303	−	0.513225i
$323$		−	5.68447i		−	0.316293i
$324$	17.7205	+	3.15966i	0.984473	+	0.175537i
$325$		0			0
$326$	16.8113	−	13.7675i	0.931089	−	0.762511i
$327$	6.70960	−	16.4535i	0.371042	−	0.909879i
$328$	−10.2478	−	6.41675i	−0.565838	−	0.354306i
$329$	10.7870	−	6.22788i	0.594707	−	0.343354i
$330$		0			0
$331$	−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	$0.704582\pi$
$332$	0.756529	−	0.859056i	0.0415199	−	0.0471468i
$333$	−21.7161	+	22.1986i	−1.19004	+	1.21648i
$334$	−11.1019	+	29.4045i	−0.607469	+	1.60894i
$335$		0			0
$336$	−2.17904	−	8.08873i	−0.118877	−	0.441277i
$337$	6.72910	−	3.88505i	0.366558	−	0.211632i	−0.305396	−	0.952225i	$-0.598789\pi$
$337$	6.72910	−	3.88505i	0.366558	−	0.211632i	0.671953	+	0.740593i	$0.265455\pi$
$338$	−2.92973	−	17.8603i	−0.159357	−	0.971474i
$339$	−10.5268	+	1.44475i	−0.571737	+	0.0784679i
$340$		0			0
$341$		−	9.97131i		−	0.539977i
$342$	0.948894	−	10.7274i	0.0513103	−	0.580073i
$343$	−15.1601			−0.818568
$344$	12.2105	+	0.437752i	0.658344	+	0.0236020i
$345$		0			0
$346$	3.52784	+	21.5065i	0.189658	+	1.15620i
$347$	9.75677	−	5.63307i	0.523771	−	0.302399i	−0.214705	−	0.976679i	$-0.568879\pi$
$347$	9.75677	−	5.63307i	0.523771	−	0.302399i	0.738476	+	0.674280i	$0.235546\pi$
$348$	−8.62929	−	17.3487i	−0.462578	−	0.929986i
$349$	−11.1403	+	19.2956i	−0.596326	+	1.03287i	0.397032	+	0.917805i	$0.370040\pi$
$349$	−11.1403	+	19.2956i	−0.596326	+	1.03287i	−0.993358	+	0.115063i	$0.963293\pi$
$350$		0			0
$351$	−15.7193	+	21.2002i	−0.839034	+	1.13158i
$352$	−3.99598	+	16.7448i	−0.212986	+	0.892502i
$353$	−11.0323	+	19.1084i	−0.587188	+	1.01704i	0.407411	+	0.913245i	$0.366432\pi$
$353$	−11.0323	+	19.1084i	−0.587188	+	1.01704i	−0.994599	+	0.103794i	$0.966902\pi$
$354$	14.8761	−	16.0255i	0.790653	−	0.851748i
$355$		0			0
$356$	−4.70835	−	0.946702i	−0.249542	−	0.0501751i
$357$	−2.87548	−	3.70509i	−0.152187	−	0.196094i
$358$	−14.0299	+	11.4897i	−0.741502	+	0.607250i
$359$	1.70332			0.0898978			0.0449489	−	0.998989i	$-0.485687\pi$
$359$	1.70332			0.0898978			0.0449489	+	0.998989i	$0.485687\pi$
$360$		0			0
$361$	12.5568			0.660883
$362$	18.9994	−	15.5595i	0.998588	−	0.817789i
$363$	2.98379	−	0.409509i	0.156608	−	0.0214937i
$364$	12.0418	+	2.42122i	0.631159	+	0.126906i
$365$		0			0
$366$	−6.34702	−	1.45013i	−0.331764	−	0.0757993i
$367$	−4.71076	+	8.15927i	−0.245900	+	0.425910i	−0.962384	−	0.271692i	$-0.912417\pi$
$367$	−4.71076	+	8.15927i	−0.245900	+	0.425910i	0.716485	+	0.697603i	$0.245750\pi$
$368$	27.6220	−	3.52003i	1.43990	−	0.183494i
$369$	−12.4231	−	3.18291i	−0.646722	−	0.165696i
$370$		0			0
$371$	−5.69914	+	9.87119i	−0.295884	+	0.512487i
$372$	−11.3285	−	0.703615i	−0.587357	−	0.0364808i
$373$	−12.6314	+	7.29277i	−0.654031	+	0.377605i	−0.789999	−	0.613108i	$-0.789919\pi$
$373$	−12.6314	+	7.29277i	−0.654031	+	0.377605i	0.135968	+	0.990713i	$0.456586\pi$
$374$	1.56013	+	9.51088i	0.0806721	+	0.491796i
$375$		0			0
$376$	−1.04390	+	29.1181i	−0.0538351	+	1.50165i
$377$	28.4101			1.46319
$378$	−4.80798	−	7.47203i	−0.247296	−	0.384320i
$379$		−	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
$382$	−4.08137	−	24.8809i	−0.208821	−	1.27302i
$383$	5.94105	−	3.43007i	0.303573	−	0.175268i	−0.340474	−	0.940254i	$-0.610587\pi$
$383$	5.94105	−	3.43007i	0.303573	−	0.175268i	0.644047	+	0.764986i	$0.277254\pi$
$384$	18.7421	+	5.72147i	0.956427	+	0.291973i
$385$		0			0
$386$	2.43951	−	6.46129i	0.124168	−	0.328871i
$387$	12.4803	−	3.49148i	0.634409	−	0.177482i
$388$	15.4005	−	17.4876i	0.781843	−	0.887801i
$389$	−7.11643	−	4.10868i	−0.360818	−	0.208318i	0.308622	−	0.951185i	$-0.400132\pi$
$389$	−7.11643	−	4.10868i	−0.360818	−	0.208318i	−0.669439	+	0.742867i	$0.733466\pi$
$390$		0			0
$391$	13.5009	−	7.79474i	0.682769	−	0.394197i
$392$	8.31290	−	13.2760i	0.419865	−	0.670538i
$393$	3.65948	−	0.502244i	0.184596	−	0.0253349i
$394$	−18.4003	+	15.0688i	−0.926993	+	0.759157i
$395$		0			0
$396$	1.35656	+	18.2088i	0.0681695	+	0.915028i
$397$		−	7.07936i		−	0.355303i	−0.984093	−	0.177651i	$-0.943150\pi$
$397$		−	7.07936i		−	0.355303i	0.984093	−	0.177651i	$-0.0568499\pi$
$398$	5.29996	+	6.47170i	0.265663	+	0.324397i
$399$	−4.19963	+	3.25930i	−0.210244	+	0.163169i
$400$		0			0
$401$	−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	$0.478977\pi$
$402$	24.0260	−	25.8826i	1.19831	−	1.29090i
$403$	8.32112	−	14.4126i	0.414505	−	0.717943i
$404$	−6.31514	+	7.17099i	−0.314190	+	0.356770i
$405$		0			0
$406$	−3.37842	+	8.94810i	−0.167668	+	0.444087i
$407$	−27.2812	−	15.7508i	−1.35228	−	0.780739i
$408$	10.9155	−	1.10135i	0.540399	−	0.0545251i
$409$	−11.3542	−	19.6660i	−0.561428	−	0.972422i	−0.997372	−	0.0724482i	$-0.976919\pi$
$409$	−11.3542	−	19.6660i	−0.561428	−	0.972422i	0.435944	−	0.899974i	$-0.356415\pi$
$410$		0			0
$411$	17.5080	+	22.5593i	0.863608	+	1.11277i
$412$	−17.9264	+	6.04377i	−0.883171	+	0.297755i
$413$	−10.7935			−0.531115
$414$	26.7793	−	12.4561i	1.31613	−	0.612186i
$415$		0			0
$416$	−19.7495	+	20.8684i	−0.968299	+	1.02316i
$417$	−4.73387	−	34.4921i	−0.231818	−	1.68909i
$418$	10.7804	−	1.76837i	0.527285	−	0.0864936i
$419$	13.1805	+	22.8292i	0.643908	+	1.11528i	0.984553	+	0.175089i	$0.0560212\pi$
$419$	13.1805	+	22.8292i	0.643908	+	1.11528i	−0.340645	+	0.940192i	$0.610645\pi$
$420$		0			0
$421$	−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	$0.303953\pi$
$422$	−13.8137	+	36.5869i	−0.672438	+	1.78102i
$423$	8.32607	+	29.7616i	0.404828	+	1.44706i
$424$	−12.4957	−	23.5537i	−0.606845	−	1.14387i
$425$		0			0
$426$	−2.52018	−	8.17656i	−0.122103	−	0.396156i
$427$	1.60689	+	2.78322i	0.0777629	+	0.134689i
$428$	−35.8845	−	7.21526i	−1.73454	−	0.348763i
$429$	−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	$0.597994\pi$
$432$	20.7830	−	0.256313i	0.999924	−	0.0123319i
$433$			11.7433i			0.564346i	0.959364	+	0.282173i	$0.0910553\pi$
$433$			11.7433i			0.564346i	−0.959364	+	0.282173i	$0.908945\pi$
$434$	3.54991	+	4.33473i	0.170401	+	0.208074i
$435$		0			0
$436$	4.04454	−	20.1152i	0.193698	−	0.963344i
$437$	−8.83516	−	15.3030i	−0.422643	−	0.732039i
$438$	−11.9394	+	3.67996i	−0.570487	+	0.175835i
$439$	1.45738	+	0.841421i	0.0695571	+	0.0401588i	0.534375	−	0.845247i	$-0.320547\pi$
$439$	1.45738	+	0.841421i	0.0695571	+	0.0401588i	−0.464818	+	0.885406i	$0.653880\pi$
$440$		0			0
$441$	4.12346	−	16.0942i	0.196355	−	0.766389i
$442$	−5.68188	+	15.0490i	−0.270259	+	0.715810i
$443$	−0.657331	−	0.379510i	−0.0312307	−	0.0180311i	0.484303	−	0.874900i	$-0.339073\pi$
$443$	−0.657331	−	0.379510i	−0.0312307	−	0.0180311i	−0.515534	+	0.856869i	$0.672406\pi$
$444$	−19.8198	+	29.8831i	−0.940606	+	1.41819i
$445$		0			0
$446$	5.48207	+	33.4200i	0.259584	+	1.58248i
$447$	0.443626	+	3.23237i	0.0209828	+	0.152886i
$448$	−4.22423	−	8.70194i	−0.199576	−	0.411128i
$449$		−	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
$452$	−11.6263	+	3.91972i	−0.546853	+	0.184368i
$453$	8.46749	−	6.57154i	0.397837	−	0.308758i
$454$	−9.65671	+	1.58405i	−0.453212	+	0.0743430i
$455$		0			0
$456$	−1.24836	−	12.3725i	−0.0584598	−	0.579396i
$457$	30.1929	+	17.4319i	1.41237	+	0.815430i	0.995611	−	0.0935884i	$-0.0298338\pi$
$457$	30.1929	+	17.4319i	1.41237	+	0.815430i	0.416756	+	0.909019i	$0.363167\pi$
$458$	−20.2649	−	7.65116i	−0.946916	−	0.357515i
$459$	10.6758	−	4.62963i	0.498306	−	0.216093i
$460$		0			0
$461$	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	$0.406902\pi$
$462$	6.13201	−	6.60584i	0.285287	−	0.307332i
$463$	−5.14137	−	8.90511i	−0.238940	−	0.413856i	0.721471	−	0.692445i	$-0.243466\pi$
$463$	−5.14137	−	8.90511i	−0.238940	−	0.413856i	−0.960410	+	0.278589i	$0.910133\pi$
$464$	−13.5466	−	17.8067i	−0.628884	−	0.826654i
$465$		0			0
$466$	7.23276	−	5.92323i	0.335051	−	0.274388i
$467$			2.90585i			0.134467i	0.997737	+	0.0672333i	$0.0214172\pi$
$467$			2.90585i			0.134467i	−0.997737	+	0.0672333i	$0.978583\pi$
$468$	−13.2346	+	27.4512i	−0.611770	+	1.26893i
$469$	−17.4324			−0.804955
$470$		0			0
$471$	0.518173	+	3.77554i	0.0238761	+	0.173967i
$472$	13.3995	−	21.3995i	0.616764	−	0.984992i
$473$	6.57308	+	11.3849i	0.302231	+	0.523479i
$474$	2.05673	−	9.00204i	0.0944687	−	0.413478i
$475$		0			0
$476$	−4.06421	−	3.57915i	−0.186283	−	0.164050i
$477$	−20.2158	−	19.7764i	−0.925618	−	0.905501i
$478$	−10.8771	−	4.10672i	−0.497506	−	0.187837i
$479$	−9.42773	+	16.3293i	−0.430764	+	0.746105i	−0.996939	−	0.0781799i	$-0.975089\pi$
$479$	−9.42773	+	16.3293i	−0.430764	+	0.746105i	0.566175	+	0.824285i	$0.308422\pi$
$480$		0			0
$481$	−26.2883	−	45.5327i	−1.19864	−	2.07611i
$482$	3.34582	+	20.3969i	0.152398	+	0.929053i
$483$	−13.4997	−	5.50506i	−0.614256	−	0.250489i
$484$	3.29543	−	1.11103i	0.149792	−	0.0505014i
$485$		0			0
$486$	20.9197	−	6.95469i	0.948935	−	0.315471i
$487$	11.5696			0.524268			0.262134	−	0.965031i	$-0.415574\pi$
$487$	11.5696			0.524268			0.262134	+	0.965031i	$0.415574\pi$
$488$	−7.51293	−	0.269343i	−0.340094	−	0.0121926i
$489$	10.0491	−	24.6426i	0.454435	−	1.11438i
$490$		0			0
$491$	−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	$0.844075\pi$
$492$	−14.7799	−	0.917977i	−0.666327	−	0.0413856i
$493$	−10.8480	−	6.26309i	−0.488569	−	0.282075i
$494$	17.0577	+	6.44028i	0.767464	+	0.289762i
$495$		0			0
$496$	−13.0011	+	1.65681i	−0.583768	+	0.0743930i
$497$	−2.11176	+	3.65768i	−0.0947255	+	0.164069i
$498$	0.312263	−	1.36673i	0.0139928	−	0.0612448i
$499$	−27.2612	+	15.7393i	−1.22038	+	0.704586i	−0.964999	−	0.262254i	$-0.915534\pi$
$499$	−27.2612	+	15.7393i	−1.22038	+	0.704586i	−0.255380	+	0.966841i	$0.582201\pi$
$500$		0			0
$501$	5.23409	+	38.1369i	0.233842	+	1.70383i
$502$	2.61706	−	2.14323i	0.116805	−	0.0956571i
$503$			1.90449i			0.0849171i	0.999098	+	0.0424585i	$0.0135190\pi$
$503$			1.90449i			0.0849171i	−0.999098	+	0.0424585i	$0.986481\pi$
$504$	−7.07229	−	7.43280i	−0.315025	−	0.331083i
$505$		0			0
$506$	18.9824	+	23.1790i	0.843869	+	1.03043i
$507$	−13.5906	−	17.5116i	−0.603581	−	0.777719i
$508$	3.71071	−	18.4549i	0.164636	−	0.818804i
$509$	−27.2228	+	15.7171i	−1.20663	+	0.696647i	−0.962021	−	0.272975i	$-0.911992\pi$
$509$	−27.2228	+	15.7171i	−1.20663	+	0.696647i	−0.244607	+	0.969622i	$0.578659\pi$
$510$		0			0
$511$	5.34094	+	3.08360i	0.236269	+	0.136410i
$512$	22.4968	+	2.42789i	0.994227	+	0.107299i
$513$	−5.24758	−	12.1008i	−0.231686	−	0.534264i
$514$	11.1791	+	4.22076i	0.493090	+	0.186170i
$515$		0			0
$516$	13.3984	−	6.66440i	0.589831	−	0.293384i
$517$	−27.1494	+	15.6747i	−1.19403	+	0.689374i
$518$	17.4672	−	2.86524i	0.767464	−	0.125892i
$519$	16.3652	+	21.0866i	0.718350	+	0.925600i
$520$		0			0
$521$			23.2742i			1.01966i	0.860275	+	0.509831i	$0.170292\pi$
$521$			23.2742i			1.01966i	−0.860275	+	0.509831i	$0.829708\pi$
$522$	−19.4262	−	13.6302i	−0.850263	−	0.596577i
$523$	−10.8804			−0.475769			−0.237884	−	0.971293i	$-0.576454\pi$
$523$	−10.8804			−0.475769			−0.237884	+	0.971293i	$0.576454\pi$
$524$	4.04169	−	1.36263i	0.176562	−	0.0595267i
$525$		0			0
$526$	9.01985	−	1.47958i	0.393284	−	0.0645127i
$527$	−6.35461	+	3.66883i	−0.276811	+	0.159817i
$528$	5.48435	+	20.3582i	0.238676	+	0.885978i
$529$	12.7302	−	22.0493i	0.553485	−	0.958664i
$530$		0			0
$531$	6.64660	−	25.9422i	0.288438	−	1.12579i
$532$	−4.05689	+	4.60669i	−0.175888	+	0.199725i
$533$	10.8562	−	18.8035i	0.470235	−	0.814470i
$534$	−5.62099	+	1.73250i	−0.243244	+	0.0749727i
$535$		0			0
$536$	21.6414	−	34.5619i	0.934764	−	1.49285i
$537$	−8.38649	+	20.5656i	−0.361904	+	0.887471i
$538$	5.50961	+	6.72769i	0.237536	+	0.290051i
$539$	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	$0.544885\pi$
$542$	−0.400383	−	0.488901i	−0.0171979	−	0.0210001i
$543$	11.3571	−	27.8502i	0.487379	−	1.19516i
$544$	12.1416	−	3.61448i	0.520566	−	0.154970i
$545$		0			0
$546$	14.3759	−	4.43093i	0.615231	−	0.189626i
$547$	−13.2886	+	23.0165i	−0.568178	+	0.984113i	0.428569	+	0.903509i	$0.359018\pi$
$547$	−13.2886	+	23.0165i	−0.568178	+	0.984113i	−0.996746	+	0.0806034i	$0.974315\pi$
$548$	24.7458	+	21.7925i	1.05709	+	0.930928i
$549$	−7.67895	+	2.14826i	−0.327729	+	0.0916854i
$550$		0			0
$551$	−7.09907	+	12.2959i	−0.302431	+	0.523825i
$552$	27.6735	−	19.9305i	1.17786	−	0.848299i
$553$	−3.94747	+	2.27907i	−0.167863	+	0.0969160i
$554$	−9.53514	+	1.56411i	−0.405109	+	0.0664525i
$555$		0			0
$556$	−12.8434	−	38.0947i	−0.544680	−	1.61557i
$557$	−8.68248			−0.367889			−0.183944	−	0.982937i	$-0.558887\pi$
$557$	−8.68248			−0.367889			−0.183944	+	0.982937i	$0.558887\pi$
$558$	−12.6045	+	5.86286i	−0.533591	+	0.248195i
$559$			21.9411i			0.928010i
$560$		0			0
$561$	7.23720	+	9.32519i	0.305555	+	0.393710i
$562$	−4.59360	+	0.753514i	−0.193769	+	0.0317851i
$563$	−27.4226	+	15.8324i	−1.15572	+	0.667257i	−0.950275	−	0.311411i	$-0.899199\pi$
$563$	−27.4226	+	15.8324i	−1.15572	+	0.667257i	−0.205448	+	0.978668i	$0.565865\pi$
$564$	15.8925	+	31.9509i	0.669195	+	1.34538i
$565$		0			0
$566$	31.0089	+	11.7076i	1.30340	+	0.492109i
$567$	−9.54151	−	5.23272i	−0.400706	−	0.219754i
$568$	−4.63017	−	8.72762i	−0.194278	−	0.366203i
$569$	−27.9697	−	16.1483i	−1.17255	−	0.676973i	−0.218272	−	0.975888i	$-0.570042\pi$
$569$	−27.9697	−	16.1483i	−1.17255	−	0.676973i	−0.954280	+	0.298915i	$0.903375\pi$
$570$		0			0
$571$	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	$0.233860\pi$
$572$	−30.3074	−	6.09388i	−1.26722	−	0.254798i
$573$	−18.9329	−	24.3952i	−0.790932	−	1.01912i
$574$	4.63141	+	5.65534i	0.193311	+	0.236049i
$575$		0			0
$576$	23.5163	−	4.79429i	0.979844	−	0.199762i
$577$		−	22.4886i		−	0.936214i	−0.883672	−	0.468107i	$-0.844936\pi$
$577$		−	22.4886i		−	0.936214i	0.883672	−	0.468107i	$-0.155064\pi$
$578$	−13.1131	+	10.7389i	−0.545432	+	0.446679i
$579$	−1.15013	−	8.38012i	−0.0477977	−	0.348266i
$580$		0			0
$581$	−0.599324	+	0.346020i	−0.0248641	+	0.0143553i
$582$	6.35667	−	27.8224i	0.263493	−	1.15327i
$583$	14.3439	−	24.8444i	0.594065	−	1.02895i
$584$	−12.7441	+	6.76097i	−0.527354	+	0.279771i
$585$		0			0
$586$	−36.9305	−	13.9434i	−1.52558	−	0.575996i
$587$	29.8752	+	17.2484i	1.23308	+	0.711919i	0.967671	−	0.252217i	$-0.0811597\pi$
$587$	29.8752	+	17.2484i	1.23308	+	0.711919i	0.265409	+	0.964136i	$0.414493\pi$
$588$	1.18924	−	19.1473i	0.0490434	−	0.789622i
$589$	4.15854	+	7.20280i	0.171350	+	0.296786i
$590$		0			0
$591$	−10.9989	+	26.9719i	−0.452436	+	1.10948i
$592$	−16.0038	+	38.1879i	−0.657752	+	1.56951i
$593$	11.5133			0.472794			0.236397	−	0.971656i	$-0.424033\pi$
$593$	11.5133			0.472794			0.236397	+	0.971656i	$0.424033\pi$
$594$	12.1010	+	18.8061i	0.496511	+	0.771622i
$595$		0			0
$596$	1.20359	+	3.56997i	0.0493011	+	0.146232i
$597$	9.48648	+	3.86852i	0.388256	+	0.158328i
$598$	8.09419	+	49.3441i	0.330996	+	2.01783i
$599$	−17.8060	−	30.8410i	−0.727535	−	1.26013i	−0.957922	−	0.287028i	$-0.907333\pi$
$599$	−17.8060	−	30.8410i	−0.727535	−	1.26013i	0.230387	−	0.973099i	$-0.426001\pi$
$600$		0			0
$601$	−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	$0.853465\pi$
$602$	−6.91062	−	2.60916i	−0.281656	−	0.106341i
$603$	10.7348	−	41.8987i	0.437155	−	1.70625i
$604$	8.17968	−	9.28821i	0.332826	−	0.377932i
$605$		0			0
$606$	−2.60662	+	11.4088i	−0.105887	+	0.463453i
$607$	1.09711	+	1.90026i	0.0445304	+	0.0771290i	0.887432	−	0.460940i	$-0.152487\pi$
$607$	1.09711	+	1.90026i	0.0445304	+	0.0771290i	−0.842901	+	0.538069i	$0.819154\pi$
$608$	−4.09693	−	13.7622i	−0.166153	−	0.558131i
$609$	1.59279	+	11.6054i	0.0645430	+	0.470276i
$610$		0			0
$611$	−52.3227			−2.11675
$612$	11.1052	−	7.56426i	0.448900	−	0.305767i
$613$		−	38.7673i		−	1.56580i	−0.622149	−	0.782899i	$-0.713740\pi$
$613$		−	38.7673i		−	1.56580i	0.622149	−	0.782899i	$-0.286260\pi$
$614$	−24.7207	+	20.2449i	−0.997645	+	0.817017i
$615$		0			0
$616$	5.52339	−	8.82103i	0.222544	−	0.355409i
$617$	−7.42778	−	12.8653i	−0.299031	−	0.517937i	0.676884	−	0.736090i	$-0.263330\pi$
$617$	−7.42778	−	12.8653i	−0.299031	−	0.517937i	−0.975915	+	0.218153i	$0.929997\pi$
$618$	−15.7630	+	16.9810i	−0.634080	+	0.683076i
$619$	−12.3383	−	7.12352i	−0.495918	−	0.286318i	0.231108	−	0.972928i	$-0.425765\pi$
$619$	−12.3383	−	7.12352i	−0.495918	−	0.286318i	−0.727026	+	0.686610i	$0.759098\pi$
$620$		0			0
$621$	21.5444	−	29.0563i	0.864545	−	1.16599i
$622$	7.79393	+	2.94266i	0.312508	+	0.117990i
$623$	2.51448	+	1.45174i	0.100741	+	0.0581626i
$624$	−9.06196	+	34.0027i	−0.362769	+	1.36120i
$625$		0			0
$626$	10.8399	−	1.77813i	0.433248	−	0.0710682i
$627$	10.5699	−	8.20320i	0.422121	−	0.327604i
$628$	1.40584	+	4.16987i	0.0560993	+	0.166396i
$629$			23.1814i			0.924302i
$630$		0			0
$631$		−	38.8200i		−	1.54540i	−0.634772	−	0.772700i	$-0.718906\pi$
$631$		−	38.8200i		−	1.54540i	0.634772	−	0.772700i	$-0.281094\pi$
$632$	0.382012	−	10.6557i	0.0151956	−	0.423860i
$633$	6.51258	+	47.4522i	0.258852	+	1.88606i
$634$	−2.69462	−	16.4270i	−0.107017	−	0.652401i
$635$		0			0
$636$	−27.2139	−	18.0495i	−1.07910	−	0.715708i
$637$	24.3599	+	14.0642i	0.965176	+	0.557245i
$638$	8.50302	−	22.5211i	0.336638	−	0.891620i
$639$	−7.49078	−	7.32798i	−0.296331	−	0.289890i
$640$		0			0
$641$	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	$0.543409\pi$
$642$	−42.8403	+	13.2042i	−1.69077	+	0.521129i
$643$	3.28595	+	5.69143i	0.129585	+	0.224448i	0.923516	−	0.383560i	$-0.125302\pi$
$643$	3.28595	+	5.69143i	0.129585	+	0.224448i	−0.793931	+	0.608008i	$0.791969\pi$
$644$	−16.5040	−	3.31845i	−0.650350	−	0.130765i
$645$		0			0
$646$	−5.09348	−	6.21956i	−0.200400	−	0.244705i
$647$		−	12.7191i		−	0.500040i	−0.968241	−	0.250020i	$-0.919563\pi$
$647$		−	12.7191i		−	0.500040i	0.968241	−	0.250020i	$-0.0804373\pi$
$648$	22.2197	−	12.4211i	0.872873	−	0.487947i
$649$	27.1658			1.06635
$650$		0			0
$651$	6.35403	+	2.59112i	0.249034	+	0.101554i
$652$	6.05758	−	30.1269i	0.237233	−	1.17986i
$653$	22.0410	+	38.1762i	0.862532	+	1.49395i	0.869477	+	0.493974i	$0.164456\pi$
$653$	22.0410	+	38.1762i	0.862532	+	1.49395i	−0.00694441	+	0.999976i	$0.502210\pi$
$654$	−7.40167	−	24.0143i	−0.289428	−	0.939033i
$655$		0			0
$656$	−16.9620	+	2.16157i	−0.662256	+	0.0843951i
$657$	−10.7003	+	10.9380i	−0.417459	+	0.426734i
$658$	6.22201	−	16.4796i	0.242559	−	0.642444i
$659$	10.8929	−	18.8671i	0.424328	−	0.734957i	−0.572030	−	0.820233i	$-0.693844\pi$
$659$	10.8929	−	18.8671i	0.424328	−	0.734957i	0.996357	+	0.0852757i	$0.0271771\pi$
$660$		0			0
$661$	−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	$0.964211\pi$
$662$	−6.03433	+	0.989845i	−0.234531	+	0.0384714i
$663$	2.67877	+	19.5182i	0.104035	+	0.758024i
$664$	0.0579989	−	1.61780i	0.00225079	−	0.0627826i
$665$		0			0
$666$	−3.86960	+	43.7466i	−0.149944	+	1.69515i
$667$	−38.9379			−1.50768
$668$	14.2005	+	42.1201i	0.549434	+	1.62967i
$669$	25.4305	+	32.7675i	0.983202	+	1.26686i
$670$		0			0
$671$	−4.04432	−	7.00497i	−0.156129	−	0.270424i
$672$	−9.63194	−	6.89764i	−0.371560	−	0.266082i
$673$	−1.88576	−	1.08874i	−0.0726906	−	0.0419680i	0.463214	−	0.886246i	$-0.346696\pi$
$673$	−1.88576	−	1.08874i	−0.0726906	−	0.0419680i	−0.535905	+	0.844278i	$0.680029\pi$
$674$	3.88139	−	10.2803i	0.149505	−	0.395981i
$675$		0			0
$676$	−19.2090	−	16.9164i	−0.738807	−	0.650631i
$677$	−1.11336	+	1.92840i	−0.0427899	+	0.0741143i	−0.886627	−	0.462485i	$-0.846958\pi$
$677$	−1.11336	+	1.92840i	−0.0427899	+	0.0741143i	0.843837	+	0.536599i	$0.180291\pi$
$678$	−10.2231	+	11.0131i	−0.392618	+	0.422956i
$679$	−12.2003	+	7.04386i	−0.468205	+	0.270319i
$680$		0			0
$681$	−9.46817	+	7.34817i	−0.362821	+	0.281582i
$682$	−8.93463	−	10.9099i	−0.342125	−	0.417762i
$683$			12.9800i			0.496665i	0.968675	+	0.248333i	$0.0798826\pi$
$683$			12.9800i			0.496665i	−0.968675	+	0.248333i	$0.920117\pi$
$684$	−8.57392	−	12.5875i	−0.327832	−	0.481293i
$685$		0			0
$686$	−16.5871	+	13.5839i	−0.633299	+	0.518637i
$687$	−26.2830	+	3.60721i	−1.00276	+	0.137624i
$688$	13.7521	−	10.4620i	0.524294	−	0.398861i
$689$	41.4657	−	23.9402i	1.57972	−	0.912050i
$690$		0			0
$691$	−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	$0.844927\pi$
$692$	23.1305	+	20.3699i	0.879289	+	0.774347i
$693$	2.73977	−	10.6935i	0.104075	−	0.406214i
$694$	5.62776	−	14.9057i	0.213627	−	0.565813i
$695$		0			0
$696$	−24.9866	−	11.2496i	−0.947113	−	0.426414i
$697$	−8.29058	+	4.78657i	−0.314028	+	0.181304i
$698$	5.10052	+	31.0940i	0.193058	+	1.17692i
$699$	4.32345	−	10.6021i	0.163528	−	0.401007i
$700$		0			0
$701$		−	31.0643i		−	1.17328i	−0.809847	−	0.586641i	$-0.800450\pi$
$701$		−	31.0643i		−	1.17328i	0.809847	−	0.586641i	$-0.199550\pi$
$702$	1.79711	+	37.2808i	0.0678276	+	1.40707i
$703$	26.2756			0.991001
$704$	10.6318	+	21.9016i	0.400701	+	0.825447i
$705$		0			0
$706$	5.05106	+	30.7924i	0.190099	+	1.15889i
$707$	5.00287	−	2.88841i	0.188152	−	0.108630i
$708$	1.91693	−	30.8635i	0.0720427	−	1.15992i
$709$	−21.7239	+	37.6269i	−0.815859	+	1.41311i	0.0928511	+	0.995680i	$0.470402\pi$
$709$	−21.7239	+	37.6269i	−0.815859	+	1.41311i	−0.908710	+	0.417429i	$0.862931\pi$
$710$		0			0
$711$	−3.04690	−	10.8911i	−0.114268	−	0.408449i
$712$	−5.99982	+	3.18302i	−0.224853	+	0.119289i
$713$	−11.4047	+	19.7535i	−0.427108	+	0.739773i
$714$	−6.46604	−	1.47732i	−0.241985	−	0.0552873i
$715$		0			0
$716$	−5.05537	+	25.1425i	−0.188928	+	0.939619i
$717$	−14.1073	+	1.93615i	−0.526846	+	0.0723069i
$718$	1.86366	−	1.52623i	0.0695510	−	0.0569585i
$719$	−12.6495			−0.471747			−0.235874	−	0.971784i	$-0.575795\pi$
$719$	−12.6495			−0.471747			−0.235874	+	0.971784i	$0.575795\pi$
$720$		0			0
$721$	11.4371			0.425938
$722$	13.7388	−	11.2513i	0.511304	−	0.418730i
$723$	15.5208	+	19.9987i	0.577225	+	0.743759i
$724$	6.84605	−	34.0483i	0.254431	−	1.26539i
$725$		0			0
$726$	2.89772	−	3.12163i	0.107544	−	0.115855i
$727$	25.0590	−	43.4035i	0.929389	−	1.60975i	0.145042	−	0.989425i	$-0.453668\pi$
$727$	25.0590	−	43.4035i	0.929389	−	1.60975i	0.784347	−	0.620323i	$-0.212998\pi$
$728$	15.3448	−	8.14068i	0.568714	−	0.301714i
$729$	18.4524	−	19.7106i	0.683422	−	0.730024i
$730$		0			0
$731$	4.83699	−	8.37791i	0.178902	−	0.309868i
$732$	−8.24383	+	4.10051i	−0.304701	+	0.151559i
$733$	25.5178	−	14.7327i	0.942523	−	0.544166i	0.0517728	−	0.998659i	$-0.483513\pi$
$733$	25.5178	−	14.7327i	0.942523	−	0.544166i	0.890750	+	0.454493i	$0.150179\pi$
$734$	2.15679	+	13.1483i	0.0796087	+	0.485313i
$735$		0			0
$736$	27.0680	−	28.6016i	0.997740	−	1.05427i
$737$	43.8751			1.61616
$738$	−16.4445	+	7.64902i	−0.605332	+	0.281564i
$739$		−	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
$742$	2.60932	+	15.9070i	0.0957911	+	0.583964i
$743$	6.99366	−	4.03779i	0.256573	−	0.148132i	−0.366197	−	0.930537i	$-0.619341\pi$
$743$	6.99366	−	4.03779i	0.256573	−	0.148132i	0.622770	+	0.782405i	$0.286007\pi$
$744$	−13.0254	+	9.38090i	−0.477533	+	0.343921i
$745$		0			0
$746$	−7.28589	+	19.2974i	−0.266756	+	0.706530i
$747$	−0.462595	−	1.65354i	−0.0169255	−	0.0605000i
$748$	10.2291	+	9.00823i	0.374011	+	0.329373i
$749$	19.1641	+	11.0644i	0.700239	+	0.404283i
$750$		0			0
$751$	−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	$0.398938\pi$
$752$	24.9486	+	32.7944i	0.909784	+	1.19589i
$753$	1.56437	−	3.83620i	0.0570090	−	0.139799i
$754$	31.0844	−	25.4564i	1.13203	−	0.927067i
$755$		0			0
$756$	−11.9557	−	3.86727i	−0.434826	−	0.140651i
$757$		−	26.9148i		−	0.978236i	−0.872218	−	0.489118i	$-0.837319\pi$
$757$		−	26.9148i		−	0.978236i	0.872218	−	0.489118i	$-0.162681\pi$
$758$	−8.47706	−	10.3512i	−0.307901	−	0.375972i
$759$	33.9768	+	13.8555i	1.23328	+	0.502922i
$760$		0			0
$761$	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	$0.288245\pi$
$762$	−6.79074	−	22.0321i	−0.246003	−	0.798140i
$763$	−6.20218	+	10.7425i	−0.224534	+	0.388904i
$764$	−26.7597	−	23.5660i	−0.968132	−	0.852587i
$765$		0			0
$766$	3.42683	−	9.07632i	0.123816	−	0.327941i
$767$	39.2657	+	22.6701i	1.41780	+	0.818569i
$768$	25.6329	−	10.5335i	0.924948	−	0.380094i
$769$	3.36491	+	5.82819i	0.121342	+	0.210170i	0.920297	−	0.391220i	$-0.127947\pi$
$769$	3.36491	+	5.82819i	0.121342	+	0.210170i	−0.798955	+	0.601390i	$0.794614\pi$
$770$		0			0
$771$	14.4990	−	1.98992i	0.522170	−	0.0716651i
$772$	−3.12039	−	9.25538i	−0.112305	−	0.333108i
$773$	−16.5270			−0.594435			−0.297217	−	0.954810i	$-0.596059\pi$
$773$	−16.5270			−0.594435			−0.297217	+	0.954810i	$0.596059\pi$
$774$	10.5266	−	15.0029i	0.378371	−	0.539268i
$775$		0			0
$776$	1.18067	−	32.9332i	0.0423837	−	1.18223i
$777$	17.1262	−	13.2915i	0.614398	−	0.476829i
$778$	−11.4678	+	1.88113i	−0.411141	+	0.0674419i
$779$	5.42547	+	9.39719i	0.194388	+	0.336689i
$780$		0			0
$781$	5.31502	−	9.20588i	0.190186	−	0.329412i
$782$	7.78740	−	20.6257i	0.278477	−	0.737574i
$783$	−28.8744	−	3.31831i	−1.03189	−	0.118587i
$784$	−2.80031	−	21.9743i	−0.100011	−	0.784796i
$785$		0			0
$786$	3.55392	−	3.82853i	0.126764	−	0.136559i
$787$	−1.37971	−	2.38973i	−0.0491814	−	0.0851847i	0.840387	−	0.541987i	$-0.182328\pi$
$787$	−1.37971	−	2.38973i	−0.0491814	−	0.0851847i	−0.889568	+	0.456803i	$0.848995\pi$
$788$	−6.63016	+	32.9746i	−0.236190	+	1.17467i
$789$	8.84375	−	6.86356i	0.314846	−	0.244349i
$790$		0			0
$791$	7.41755			0.263738
$792$	17.8000	+	18.7073i	0.632495	+	0.664736i
$793$		−	13.5001i		−	0.479401i
$794$	−6.34334	−	7.74575i	−0.225117	−	0.274886i
$795$		0			0
$796$	11.5977	+	2.33194i	0.411070	+	0.0826534i
$797$	2.62123	+	4.54011i	0.0928488	+	0.160819i	0.908709	−	0.417431i	$-0.137069\pi$
$797$	2.62123	+	4.54011i	0.0928488	+	0.160819i	−0.815860	+	0.578250i	$0.803736\pi$
$798$	−1.67451	+	7.32911i	−0.0592769	+	0.259448i
$799$	19.9787	+	11.5347i	0.706794	+	0.408068i
$800$		0			0
$801$	−5.03763	+	5.14956i	−0.177996	+	0.181951i
$802$	−8.83781	+	23.4079i	−0.312074	+	0.826560i
$803$	−13.4424	−	7.76099i	−0.474373	−	0.273879i
$804$	3.09600	−	49.8471i	0.109187	−	1.75797i
$805$		0			0
$806$	−3.80978	−	23.2253i	−0.134194	−	0.818076i
$807$	9.86172	+	4.02154i	0.347149	+	0.141565i
$808$	−0.484147	+	13.5046i	−0.0170322	+	0.475090i
$809$			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	$-0.892531\pi$
$811$		−	18.8666i		−	0.662495i	0.943544	−	0.331247i	$-0.107469\pi$
$812$	4.32136	+	12.8176i	0.151650	+	0.449809i
$813$	−0.716651	−	0.292245i	−0.0251341	−	0.0102495i
$814$	−43.9625	+	7.21143i	−1.54089	+	0.252760i
$815$		0			0
$816$	10.9562	−	10.9857i	0.383543	−	0.384577i
$817$	−9.49617	−	5.48261i	−0.332229	−	0.191812i
$818$	−30.0444	−	11.3435i	−1.05048	−	0.396615i
$819$	12.8839	−	13.1702i	0.450201	−	0.460203i
$820$		0			0
$821$	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	$0.659457\pi$
$822$	39.3699	+	8.99499i	1.37318	+	0.313736i
$823$	3.33531	+	5.77693i	0.116262	+	0.201371i	0.918283	−	0.395924i	$-0.129576\pi$
$823$	3.33531	+	5.77693i	0.116262	+	0.201371i	−0.802022	+	0.597295i	$0.796242\pi$
$824$	−14.1984	+	22.6754i	−0.494626	+	0.789934i
$825$		0			0
$826$	−11.8095	+	9.67137i	−0.410907	+	0.336510i
$827$			37.4924i			1.30374i	0.758331	+	0.651869i	$0.226015\pi$
$827$			37.4924i			1.30374i	−0.758331	+	0.651869i	$0.773985\pi$
$828$	18.1389	−	37.6238i	0.630372	−	1.30752i
$829$	22.9261			0.796255			0.398127	−	0.917330i	$-0.369660\pi$
$829$	22.9261			0.796255			0.398127	+	0.917330i	$0.369660\pi$
$830$		0			0
$831$	−9.34898	+	7.25566i	−0.324313	+	0.251696i
$832$	−2.90972	+	40.5290i	−0.100876	+	1.40509i
$833$	−6.20100	−	10.7405i	−0.214852	−	0.372135i
$834$	−36.0856	−	33.4972i	−1.24954	−	1.15991i
$835$		0			0
$836$	10.2106	−	11.5944i	0.353142	−	0.401001i
$837$	−10.1405	+	13.6762i	−0.350507	+	0.472720i
$838$	34.8769	+	13.1680i	1.20480	+	0.454882i
$839$	9.11048	−	15.7798i	0.314529	−	0.544780i	−0.664808	−	0.747014i	$-0.731487\pi$
$839$	9.11048	−	15.7798i	0.314529	−	0.544780i	0.979337	+	0.202234i	$0.0648202\pi$
$840$		0			0
$841$	1.14335	+	1.98034i	0.0394259	+	0.0682877i
$842$	3.92724	+	23.9414i	0.135342	+	0.825074i
$843$	−4.50391	+	3.49545i	−0.155123	+	0.120390i
$844$	17.6691	+	52.4084i	0.608197	+	1.80397i
$845$		0			0
$846$	35.7772	+	25.1026i	1.23004	+	0.863046i
$847$	−2.10248			−0.0722422
$848$	−34.7769	−	14.5743i	−1.19424	−	0.500484i
$849$	40.2177	−	5.51967i	1.38027	−	0.189435i
$850$		0			0
$851$	36.0299	+	62.4057i	1.23509	+	2.13924i
$852$	−10.0839	−	6.68807i	−0.345468	−	0.229129i
$853$	−1.68958	−	0.975478i	−0.0578500	−	0.0333997i	0.470796	−	0.882242i	$-0.343967\pi$
$853$	−1.68958	−	0.975478i	−0.0578500	−	0.0333997i	−0.528646	+	0.848842i	$0.677300\pi$
$854$	4.25201	+	1.60538i	0.145501	+	0.0549349i
$855$		0			0
$856$	−45.7275	+	24.2593i	−1.56293	+	0.829166i
$857$	−6.51166	+	11.2785i	−0.222434	+	0.385267i	−0.955546	−	0.294840i	$-0.904733\pi$
$857$	−6.51166	+	11.2785i	−0.222434	+	0.385267i	0.733113	+	0.680107i	$0.238067\pi$
$858$	−36.1821	+	11.1520i	−1.23524	+	0.380724i
$859$	3.50034	−	2.02092i	0.119430	−	0.0689530i	−0.439095	−	0.898441i	$-0.644701\pi$
$859$	3.50034	−	2.02092i	0.119430	−	0.0689530i	0.558525	+	0.829488i	$0.311367\pi$
$860$		0			0
$861$	8.28982	+	3.38053i	0.282516	+	0.115208i
$862$	−13.7660	+	11.2736i	−0.468871	+	0.383980i
$863$		−	10.6258i		−	0.361705i	−0.983510	−	0.180853i	$-0.942114\pi$
$863$		−	10.6258i		−	0.361705i	0.983510	−	0.180853i	$-0.0578857\pi$
$864$	22.5097	−	18.9027i	0.765796	−	0.643084i
$865$		0			0
$866$	10.5224	+	12.8487i	0.357565	+	0.436616i
$867$	−7.83847	+	19.2217i	−0.266208	+	0.652803i
$868$	7.76813	+	1.56193i	0.263667	+	0.0530153i
$869$	9.93523	−	5.73611i	0.337030	−	0.194584i
$870$		0			0
$871$	63.4174	+	36.6140i	2.14882	+	1.24062i
$872$	−13.5986	−	25.6327i	−0.460508	−	0.868034i
$873$	−9.41696	−	33.6609i	−0.318716	−	1.13925i
$874$	−23.3788	−	8.82684i	−0.790799	−	0.298572i
$875$		0			0
$876$	−9.76591	+	14.7245i	−0.329960	+	0.497494i
$877$	−45.9911	+	26.5530i	−1.55301	+	0.896631i	−0.555115	+	0.831774i	$0.687326\pi$
$877$	−45.9911	+	26.5530i	−1.55301	+	0.896631i	−0.997895	+	0.0648570i	$0.979341\pi$
$878$	2.34851	−	0.385240i	0.0792584	−	0.0130012i
$879$	−47.8978	+	6.57373i	−1.61555	+	0.221727i
$880$		0			0
$881$		−	10.8244i		−	0.364685i	−0.983235	−	0.182342i	$-0.941632\pi$
$881$		−	10.8244i		−	0.364685i	0.983235	−	0.182342i	$-0.0583679\pi$
$882$	−9.90931	−	21.3039i	−0.333664	−	0.717340i
$883$	−21.6083			−0.727178			−0.363589	−	0.931559i	$-0.618449\pi$
$883$	−21.6083			−0.727178			−0.363589	+	0.931559i	$0.618449\pi$
$884$	7.26773	+	21.5568i	0.244440	+	0.725033i
$885$		0			0
$886$	−1.05926	+	0.173757i	−0.0355865	+	0.00583747i
$887$	0.457306	−	0.264026i	0.0153548	−	0.00886511i	−0.492303	−	0.870424i	$-0.663845\pi$
$887$	0.457306	−	0.264026i	0.0153548	−	0.00886511i	0.507658	+	0.861559i	$0.330511\pi$
$888$	5.09083	+	50.4553i	0.170837	+	1.69317i
$889$	−5.69025	+	9.85580i	−0.190845	+	0.330553i
$890$		0			0
$891$	24.0147	+	13.1700i	0.804522	+	0.441213i
$892$	35.9435	+	31.6537i	1.20348	+	1.05984i
$893$	13.0743	−	22.6454i	0.437515	−	0.757798i
$894$	3.38169	+	3.13913i	0.113101	+	0.104988i
$895$		0			0
$896$	−12.4191	−	5.73601i	−0.414893	−	0.191627i
$897$	37.5478	+	48.3807i	1.25369	+	1.61538i
$898$	−15.6428	−	19.1012i	−0.522008	−	0.637415i
$899$	18.3273			0.611251
$900$		0			0
$901$	−21.1108			−0.703302
$902$	−11.6566	−	14.2337i	−0.388123	−	0.473930i
$903$	−8.96289	+	1.23011i	−0.298266	+	0.0409355i
$904$	−9.20846	+	14.7062i	−0.306269	+	0.489121i
$905$		0			0
$906$	3.37622	−	14.7773i	0.112167	−	0.490942i
$907$	23.6647	−	40.9884i	0.785773	−	1.36100i	−0.142763	−	0.989757i	$-0.545599\pi$
$907$	23.6647	−	40.9884i	0.785773	−	1.36100i	0.928536	−	0.371242i	$-0.121068\pi$
$908$	−9.14635	+	10.3859i	−0.303532	+	0.344668i
$909$	3.86152	+	13.8030i	0.128079	+	0.457817i
$910$		0			0
$911$	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	$-0.0475829\pi$
$912$	−12.4521	−	12.4186i	−0.412329	−	0.411220i
$913$	1.50841	−	0.870884i	0.0499213	−	0.0288220i
$914$	48.6546	−	7.98110i	1.60935	−	0.263991i
$915$		0			0
$916$	−29.0281	+	9.78664i	−0.959117	+	0.323360i
$917$	−2.57860			−0.0851528
$918$	7.53247	−	14.6313i	0.248609	−	0.482906i
$919$		−	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
$922$	43.6553	−	7.16103i	1.43771	−	0.235836i
$923$	15.3647	−	8.87083i	0.505736	−	0.291987i
$924$	0.790173	−	12.7222i	0.0259948	−	0.418528i
$925$		0			0
$926$	−13.6046	−	5.13652i	−0.447075	−	0.168797i
$927$	−7.04287	+	27.4888i	−0.231318	+	0.902852i
$928$	−30.7771	−	7.34464i	−1.01031	−	0.241100i
$929$	25.1609	+	14.5267i	0.825503	+	0.476605i	0.852311	−	0.523036i	$-0.175201\pi$
$929$	25.1609	+	14.5267i	0.825503	+	0.476605i	−0.0268072	+	0.999641i	$0.508534\pi$
$930$		0			0
$931$	−12.1741	+	7.02870i	−0.398989	+	0.230356i
$932$	2.60617	−	12.9616i	0.0853680	−	0.424571i
$933$	10.1085	−	1.38734i	0.330938	−	0.0454196i
$934$	2.60374	+	3.17938i	0.0851969	+	0.104033i
$935$		0			0
$936$	10.1168	+	41.8939i	0.330679	+	1.36935i
$937$			51.0143i			1.66656i	0.552848	+	0.833282i	$0.313541\pi$
$937$			51.0143i			1.66656i	−0.552848	+	0.833282i	$0.686459\pi$
$938$	−19.0734	+	15.6201i	−0.622768	+	0.510013i
$939$	10.6282	−	8.24847i	0.346839	−	0.269179i
$940$		0			0
$941$	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	$0.287964\pi$
$942$	3.94996	+	3.66663i	0.128697	+	0.119465i
$943$	−14.8792	+	25.7715i	−0.484532	+	0.839235i
$944$	−4.51382	−	35.4203i	−0.146912	−	1.15283i
$945$		0			0
$946$	17.3931	+	6.56689i	0.565498	+	0.213508i
$947$	33.0481	+	19.0803i	1.07392	+	0.620028i	0.929250	−	0.369452i	$-0.120455\pi$
$947$	33.0481	+	19.0803i	1.07392	+	0.620028i	0.144670	+	0.989480i	$0.453788\pi$
$948$	−5.81580	−	11.6923i	−0.188888	−	0.379749i
$949$	−12.9532	−	22.4356i	−0.420478	−	0.728290i
$950$		0			0
$951$	−12.5000	−	16.1063i	−0.405339	−	0.522283i
$952$	−7.65382	−	0.274394i	−0.248062	−	0.00889315i
$953$	40.4395			1.30996			0.654982	−	0.755645i	$-0.272676\pi$
$953$	40.4395			1.30996			0.654982	+	0.755645i	$0.272676\pi$
$954$	−39.8391	−	3.52397i	−1.28984	−	0.114093i
$955$		0			0
$956$	−15.5807	+	5.25293i	−0.503916	+	0.169892i
$957$	−4.00883	−	29.2093i	−0.129587	−	0.944202i
$958$	4.31643	+	26.3140i	0.139458	+	0.850166i
$959$	−9.96739	−	17.2640i	−0.321864	−	0.557485i
$960$		0			0
$961$	−10.1320	+	17.5492i	−0.326840	+	0.566104i
$962$	−69.5617	−	26.2636i	−2.24276	−	0.846771i
$963$	−38.3942	+	39.2472i	−1.23724	+	1.26472i
$964$	21.9371	+	19.3189i	0.706546	+	0.622220i
$965$		0			0
$966$	−19.7031	+	6.07289i	−0.633938	+	0.195392i
$967$	−8.41511	−	14.5754i	−0.270612	−	0.468713i	0.698407	−	0.715701i	$-0.253893\pi$
$967$	−8.41511	−	14.5754i	−0.270612	−	0.468713i	−0.969019	+	0.246988i	$0.920559\pi$
$968$	2.61011	−	4.16843i	0.0838921	−	0.133978i
$969$	−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	$0.315738\pi$
$972$	16.6572	−	26.3541i	0.534281	−	0.845307i
$973$			24.3044i			0.779163i
$974$	12.6587	−	10.3667i	0.405609	−	0.332172i
$975$		0			0
$976$	−8.46147	+	6.43714i	−0.270845	+	0.206048i
$977$	0.431943	+	0.748148i	0.0138191	+	0.0239354i	0.872852	−	0.487985i	$-0.162268\pi$
$977$	0.431943	+	0.748148i	0.0138191	+	0.0239354i	−0.859033	+	0.511920i	$0.828934\pi$
$978$	−11.0856	−	35.9666i	−0.354479	−	1.15008i
$979$	−6.32860	−	3.65382i	−0.202263	−	0.116777i
$980$		0			0
$981$	−22.0002	−	21.5220i	−0.702412	−	0.687145i
$982$	−1.97828	−	0.746913i	−0.0631293	−	0.0238349i
$983$	31.8882	+	18.4107i	1.01708	+	0.587209i	0.913256	−	0.407387i	$-0.133560\pi$
$983$	31.8882	+	18.4107i	1.01708	+	0.587209i	0.103821	+	0.994596i	$0.466893\pi$
$984$	−16.9936	+	12.2389i	−0.541738	+	0.390161i
$985$		0			0
$986$	−17.4811	+	2.86752i	−0.556711	+	0.0913205i
$987$	−2.93343	−	21.3737i	−0.0933720	−	0.680331i
$988$	24.4341	−	8.23780i	0.777353	−	0.262079i
$989$		−	30.0718i		−	0.956227i
$990$		0			0
$991$			35.9773i			1.14286i	0.820652	+	0.571428i	$0.193610\pi$
$991$			35.9773i			1.14286i	−0.820652	+	0.571428i	$0.806390\pi$
$992$	−12.7404	+	13.4622i	−0.404508	+	0.427426i
$993$	−5.91651	+	4.59175i	−0.187755	+	0.145715i
$994$	0.966859	+	5.89419i	0.0306669	+	0.186952i
$995$		0			0
$996$	−0.882983	−	1.77518i	−0.0279784	−	0.0562489i
$997$	28.9811	+	16.7322i	0.917840	+	0.529915i	0.882945	−	0.469476i	$-0.155557\pi$
$997$	28.9811	+	16.7322i	0.917840	+	0.529915i	0.0348944	+	0.999391i	$0.488891\pi$
$998$	−15.7244	+	41.6478i	−0.497748	+	1.31834i
$999$	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.o.c.299.19		48
4.3	odd	2	inner	900.2.o.c.299.14		48
5.2	odd	4		900.2.r.f.551.17		48
5.3	odd	4		180.2.q.a.11.8	yes	48
5.4	even	2		900.2.o.b.299.6		48
9.5	odd	6		900.2.o.b.599.11		48
15.8	even	4		540.2.q.a.251.17		48
20.3	even	4		180.2.q.a.11.1	✓	48
20.7	even	4		900.2.r.f.551.24		48
20.19	odd	2		900.2.o.b.299.11		48
36.23	even	6		900.2.o.b.599.6		48
45.13	odd	12		540.2.q.a.71.24		48
45.14	odd	6	inner	900.2.o.c.599.14		48
45.23	even	12		180.2.q.a.131.1	yes	48
45.32	even	12		900.2.r.f.851.24		48
45.38	even	12		1620.2.e.b.971.31		48
45.43	odd	12		1620.2.e.b.971.18		48
60.23	odd	4		540.2.q.a.251.24		48
180.23	odd	12		180.2.q.a.131.8	yes	48
180.43	even	12		1620.2.e.b.971.32		48
180.59	even	6	inner	900.2.o.c.599.19		48
180.83	odd	12		1620.2.e.b.971.17		48
180.103	even	12		540.2.q.a.71.17		48
180.167	odd	12		900.2.r.f.851.17		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.1	✓	48	20.3	even	4
180.2.q.a.11.8	yes	48	5.3	odd	4
180.2.q.a.131.1	yes	48	45.23	even	12
180.2.q.a.131.8	yes	48	180.23	odd	12
540.2.q.a.71.17		48	180.103	even	12
540.2.q.a.71.24		48	45.13	odd	12
540.2.q.a.251.17		48	15.8	even	4
540.2.q.a.251.24		48	60.23	odd	4
900.2.o.b.299.6		48	5.4	even	2
900.2.o.b.299.11		48	20.19	odd	2
900.2.o.b.599.6		48	36.23	even	6
900.2.o.b.599.11		48	9.5	odd	6
900.2.o.c.299.14		48	4.3	odd	2	inner
900.2.o.c.299.19		48	1.1	even	1	trivial
900.2.o.c.599.14		48	45.14	odd	6	inner
900.2.o.c.599.19		48	180.59	even	6	inner
900.2.r.f.551.17		48	5.2	odd	4
900.2.r.f.551.24		48	20.7	even	4
900.2.r.f.851.17		48	180.167	odd	12
900.2.r.f.851.24		48	45.32	even	12
1620.2.e.b.971.17		48	180.83	odd	12
1620.2.e.b.971.18		48	45.43	odd	12
1620.2.e.b.971.31		48	45.38	even	12
1620.2.e.b.971.32		48	180.43	even	12

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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.09413 - 0.896034i) q^{2} +(0.654027 - 1.60382i) q^{3} +(0.394247 - 1.96076i) q^{4} +(-0.721488 - 2.34082i) q^{6} +(-0.604565 + 1.04714i) q^{7} +(-1.32555 - 2.49858i) q^{8} +(-2.14450 - 2.09789i) q^{9} +(1.52161 - 2.63550i) q^{11} +(-2.88686 - 1.91469i) q^{12} +(4.39869 - 2.53958i) q^{13} +(0.276797 + 1.68742i) q^{14} +(-3.68914 - 1.54605i) q^{16} -2.23944 q^{17} +(-4.22614 - 0.373823i) q^{18} +2.53835i q^{19} +(1.28402 + 1.65447i) q^{21} +(-0.696660 - 4.24700i) q^{22} +(-6.02870 + 3.48067i) q^{23} +(-4.87423 + 0.491800i) q^{24} +(2.53719 - 6.72001i) q^{26} +(-4.76720 + 2.06732i) q^{27} +(1.81484 + 1.59824i) q^{28} +(4.84407 + 2.79673i) q^{29} +(2.83759 - 1.63828i) q^{31} +(-5.42171 + 1.61401i) q^{32} +(-3.23171 - 4.16408i) q^{33} +(-2.45024 + 2.00661i) q^{34} +(-4.95891 + 3.37775i) q^{36} -10.3514i q^{37} +(2.27445 + 2.77729i) q^{38} +(-1.19618 - 8.71567i) q^{39} +(3.70208 - 2.13740i) q^{41} +(2.88735 + 0.659684i) q^{42} +(-2.15991 + 3.74108i) q^{43} +(-4.56769 - 4.02254i) q^{44} +(-3.47739 + 9.21023i) q^{46} +(-8.92129 - 5.15071i) q^{47} +(-4.89238 + 4.90557i) q^{48} +(2.76900 + 4.79605i) q^{49} +(-1.46465 + 3.59166i) q^{51} +(-3.24534 - 9.62598i) q^{52} +9.42683 q^{53} +(-3.36356 + 6.53349i) q^{54} +(3.41774 + 0.122528i) q^{56} +(4.07106 + 1.66015i) q^{57} +(7.80601 - 1.28047i) q^{58} +(4.46335 + 7.73074i) q^{59} +(1.32896 - 2.30183i) q^{61} +(1.63674 - 4.33508i) q^{62} +(3.49327 - 0.977274i) q^{63} +(-4.48585 + 6.62398i) q^{64} +(-7.26707 - 1.66033i) q^{66} +(7.20867 + 12.4858i) q^{67} +(-0.882891 + 4.39099i) q^{68} +(1.63945 + 11.9454i) q^{69} +3.49303 q^{71} +(-2.39912 + 8.13906i) q^{72} -5.10052i q^{73} +(-9.27523 - 11.3258i) q^{74} +(4.97709 + 1.00074i) q^{76} +(1.83982 + 3.18667i) q^{77} +(-9.11832 - 8.46427i) q^{78} +(3.26472 + 1.88488i) q^{79} +(0.197735 + 8.99783i) q^{81} +(2.13538 - 5.65579i) q^{82} +(0.495665 + 0.286172i) q^{83} +(3.75024 - 1.86538i) q^{84} +(0.988904 + 6.02859i) q^{86} +(7.65361 - 5.93990i) q^{87} +(-8.60199 - 0.308386i) q^{88} -2.40129i q^{89} +6.14138i q^{91} +(4.44795 + 13.1931i) q^{92} +(-0.771656 - 5.62248i) q^{93} +(-14.3763 + 2.35822i) q^{94} +(-0.957353 + 9.75108i) q^{96} +(10.0902 + 5.82556i) q^{97} +(7.32708 + 2.76639i) q^{98} +(-8.79207 + 2.45966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} + 12 q^{8} - 4 q^{9} + 28 q^{12} + 30 q^{14} - 18 q^{18} - 4 q^{21} - 42 q^{22} + 28 q^{24} + 12 q^{29} - 48 q^{33} + 6 q^{34} + 42 q^{36} - 6 q^{38} - 60 q^{41} + 16 q^{42} - 12 q^{46} - 74 q^{48}+ \cdots + 84 q^{98}+O(q^{100}) \) 48 * q + 6 * q^6 + 12 * q^8 - 4 * q^9 + 28 * q^12 + 30 * q^14 - 18 * q^18 - 4 * q^21 - 42 * q^22 + 28 * q^24 + 12 * q^29 - 48 * q^33 + 6 * q^34 + 42 * q^36 - 6 * q^38 - 60 * q^41 + 16 * q^42 - 12 * q^46 - 74 * q^48 - 24 * q^49 - 90 * q^52 + 32 * q^54 - 42 * q^56 - 16 * q^57 + 84 * q^58 + 84 * q^62 + 48 * q^64 + 16 * q^66 + 6 * q^68 - 36 * q^69 - 80 * q^72 - 84 * q^74 + 6 * q^76 - 46 * q^78 - 50 * q^84 - 54 * q^86 + 114 * q^88 - 42 * q^92 - 24 * q^93 - 18 * q^94 - 18 * q^96 - 48 * q^97 + 84 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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