LMFDB - Embedded newform 900.2.r.g.851.22

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 = [48,0,0,2,0,0,0,0,12,0,0,0] 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			851.22
Character	$\chi$	$=$	900.851
Dual form			900.2.r.g.551.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36866 - 0.356046i) q^{2} +(1.14213 + 1.30213i) q^{3} +(1.74646 - 0.974612i) q^{4} +(2.02680 + 1.37553i) q^{6} +(2.87089 - 1.65751i) q^{7} +(2.04331 - 1.95573i) q^{8} +(-0.391092 + 2.97440i) q^{9} +(-1.17952 - 2.04298i) q^{11} +(3.26375 + 1.16099i) q^{12} +(-2.20004 + 3.81058i) q^{13} +(3.33912 - 3.29074i) q^{14} +(2.10026 - 3.40425i) q^{16} -0.889368i q^{17} +(0.523750 + 4.21019i) q^{18} +3.03537i q^{19} +(5.43722 + 1.84519i) q^{21} +(-2.34176 - 2.37619i) q^{22} +(3.63703 - 6.29952i) q^{23} +(4.88034 + 0.426960i) q^{24} +(-1.65437 + 5.99870i) q^{26} +(-4.31973 + 2.88789i) q^{27} +(3.39848 - 5.69278i) q^{28} +(-1.03714 + 0.598791i) q^{29} +(-0.205172 - 0.118456i) q^{31} +(1.66248 - 5.40705i) q^{32} +(1.31308 - 3.86923i) q^{33} +(-0.316656 - 1.21724i) q^{34} +(2.21586 + 5.57584i) q^{36} -11.4975 q^{37} +(1.08073 + 4.15440i) q^{38} +(-7.47460 + 1.48743i) q^{39} +(2.45213 + 1.41574i) q^{41} +(8.09868 + 0.589541i) q^{42} +(-7.23369 + 4.17637i) q^{43} +(-4.05110 - 2.41842i) q^{44} +(2.73494 - 9.91686i) q^{46} +(3.78624 + 6.55796i) q^{47} +(6.83154 - 1.15326i) q^{48} +(1.99467 - 3.45488i) q^{49} +(1.15807 - 1.01577i) q^{51} +(-0.128451 + 8.79922i) q^{52} -0.772055i q^{53} +(-4.88403 + 5.49056i) q^{54} +(2.62447 - 9.00150i) q^{56} +(-3.95246 + 3.46678i) q^{57} +(-1.20629 + 1.18881i) q^{58} +(1.06446 - 1.84370i) q^{59} +(1.91303 + 3.31346i) q^{61} +(-0.322986 - 0.0890754i) q^{62} +(3.80731 + 9.18741i) q^{63} +(0.350216 - 7.99233i) q^{64} +(0.419529 - 5.76318i) q^{66} +(-5.49472 - 3.17238i) q^{67} +(-0.866788 - 1.55325i) q^{68} +(12.3568 - 2.45896i) q^{69} +11.7244 q^{71} +(5.01801 + 6.84248i) q^{72} -6.10889 q^{73} +(-15.7362 + 4.09365i) q^{74} +(2.95831 + 5.30117i) q^{76} +(-6.77253 - 3.91012i) q^{77} +(-9.70059 + 4.69708i) q^{78} +(8.94873 - 5.16655i) q^{79} +(-8.69409 - 2.32653i) q^{81} +(3.86020 + 1.06459i) q^{82} +(-1.29963 - 2.25103i) q^{83} +(11.2942 - 2.07662i) q^{84} +(-8.41349 + 8.29156i) q^{86} +(-1.96425 - 0.666593i) q^{87} +(-6.40565 - 1.86763i) q^{88} +4.68130i q^{89} +14.5863i q^{91} +(0.212351 - 14.5466i) q^{92} +(-0.0800869 - 0.402452i) q^{93} +(7.51702 + 7.62755i) q^{94} +(8.93945 - 4.01077i) q^{96} +(3.08700 + 5.34684i) q^{97} +(1.49994 - 5.43875i) q^{98} +(6.53795 - 2.70936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{4} + 12 q^{9} + 42 q^{14} + 30 q^{16} - 12 q^{21} + 6 q^{24} + 4 q^{34} + 96 q^{36} + 96 q^{41} + 4 q^{46} - 32 q^{49} + 30 q^{54} + 6 q^{56} + 8 q^{61} + 20 q^{64} + 36 q^{66} + 96 q^{69} - 72 q^{74}+ \cdots + 54 q^{96}+O(q^{100}) $ 48 * q + 2 * q^4 + 12 * q^9 + 42 * q^14 + 30 * q^16 - 12 * q^21 + 6 * q^24 + 4 * q^34 + 96 * q^36 + 96 * q^41 + 4 * q^46 - 32 * q^49 + 30 * q^54 + 6 * q^56 + 8 * q^61 + 20 * q^64 + 36 * q^66 + 96 * q^69 - 72 * q^74 + 36 * q^81 + 6 * q^84 + 108 * q^86 + 62 * q^94 + 54 * q^96

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 $

$2$	1.36866	−	0.356046i	0.967789	−	0.251762i
$2$	1.36866	−	0.356046i	0.967789	−	0.251762i
$3$	1.14213	+	1.30213i	0.659407	+	0.751786i
$3$	1.14213	+	1.30213i	0.659407	+	0.751786i
$4$	1.74646	−	0.974612i	0.873231	−	0.487306i
$5$		0			0
$5$		0			0
$6$	2.02680	+	1.37553i	0.827439	+	0.561556i
$7$	2.87089	−	1.65751i	1.08509	−	0.626480i	0.152828	−	0.988253i	$-0.451162\pi$
$7$	2.87089	−	1.65751i	1.08509	−	0.626480i	0.932266	+	0.361773i	$0.117828\pi$
$8$	2.04331	−	1.95573i	0.722418	−	0.691456i
$9$	−0.391092	+	2.97440i	−0.130364	+	0.991466i
$10$		0			0
$11$	−1.17952	−	2.04298i	−0.355638	−	0.615983i	0.631589	−	0.775303i	$-0.282403\pi$
$11$	−1.17952	−	2.04298i	−0.355638	−	0.615983i	−0.987227	+	0.159320i	$0.949070\pi$
$12$	3.26375	+	1.16099i	0.942165	+	0.335150i
$13$	−2.20004	+	3.81058i	−0.610181	+	1.05686i	0.381029	+	0.924563i	$0.375570\pi$
$13$	−2.20004	+	3.81058i	−0.610181	+	1.05686i	−0.991210	+	0.132301i	$0.957763\pi$
$14$	3.33912	−	3.29074i	0.892419	−	0.879486i
$15$		0			0
$16$	2.10026	−	3.40425i	0.525066	−	0.851061i
$17$		−	0.889368i		−	0.215703i	−0.994167	−	0.107852i	$-0.965603\pi$
$17$		−	0.889368i		−	0.215703i	0.994167	−	0.107852i	$-0.0343972\pi$
$18$	0.523750	+	4.21019i	0.123449	+	0.992351i
$19$			3.03537i			0.696363i	0.937427	+	0.348181i	$0.113201\pi$
$19$			3.03537i			0.696363i	−0.937427	+	0.348181i	$0.886799\pi$
$20$		0			0
$21$	5.43722	+	1.84519i	1.18650	+	0.402654i
$22$	−2.34176	−	2.37619i	−0.499264	−	0.506605i
$23$	3.63703	−	6.29952i	0.758374	−	1.31354i	−0.185306	−	0.982681i	$-0.559328\pi$
$23$	3.63703	−	6.29952i	0.758374	−	1.31354i	0.943680	−	0.330861i	$-0.107339\pi$
$24$	4.88034	+	0.426960i	0.996195	+	0.0871528i
$25$		0			0
$26$	−1.65437	+	5.99870i	−0.324448	+	1.17644i
$27$	−4.31973	+	2.88789i	−0.831333	+	0.555774i
$28$	3.39848	−	5.69278i	0.642251	−	1.07583i
$29$	−1.03714	+	0.598791i	−0.192592	+	0.111193i	−0.593195	−	0.805059i	$-0.702134\pi$
$29$	−1.03714	+	0.598791i	−0.192592	+	0.111193i	0.400604	+	0.916251i	$0.368800\pi$
$30$		0			0
$31$	−0.205172	−	0.118456i	−0.0368499	−	0.0212753i	0.481462	−	0.876467i	$-0.340106\pi$
$31$	−0.205172	−	0.118456i	−0.0368499	−	0.0212753i	−0.518312	+	0.855192i	$0.673439\pi$
$32$	1.66248	−	5.40705i	0.293888	−	0.955840i
$33$	1.31308	−	3.86923i	0.228577	−	0.673547i
$34$	−0.316656	−	1.21724i	−0.0543060	−	0.208755i
$35$		0			0
$36$	2.21586	+	5.57584i	0.369309	+	0.929307i
$37$	−11.4975			−1.89018			−0.945091	−	0.326807i	$-0.894027\pi$
$37$	−11.4975			−1.89018			−0.945091	+	0.326807i	$0.894027\pi$
$38$	1.08073	+	4.15440i	0.175318	+	0.673932i
$39$	−7.47460	+	1.48743i	−1.19689	+	0.238179i
$40$		0			0
$41$	2.45213	+	1.41574i	0.382958	+	0.221101i	0.679105	−	0.734042i	$-0.262368\pi$
$41$	2.45213	+	1.41574i	0.382958	+	0.221101i	−0.296146	+	0.955143i	$0.595702\pi$
$42$	8.09868	+	0.589541i	1.24965	+	0.0909681i
$43$	−7.23369	+	4.17637i	−1.10313	+	0.636891i	−0.937041	−	0.349220i	$-0.886447\pi$
$43$	−7.23369	+	4.17637i	−1.10313	+	0.636891i	−0.166087	+	0.986111i	$0.553113\pi$
$44$	−4.05110	−	2.41842i	−0.610726	−	0.364591i
$45$		0			0
$46$	2.73494	−	9.91686i	0.403245	−	1.46216i
$47$	3.78624	+	6.55796i	0.552280	+	0.956577i	0.998110	+	0.0614594i	$0.0195755\pi$
$47$	3.78624	+	6.55796i	0.552280	+	0.956577i	−0.445829	+	0.895118i	$0.647091\pi$
$48$	6.83154	−	1.15326i	0.986048	−	0.166459i
$49$	1.99467	−	3.45488i	0.284954	−	0.493554i
$50$		0			0
$51$	1.15807	−	1.01577i	0.162163	−	0.142236i
$52$	−0.128451	+	8.79922i	−0.0178130	+	1.22023i
$53$		−	0.772055i		−	0.106050i	−0.998593	−	0.0530249i	$-0.983114\pi$
$53$		−	0.772055i		−	0.106050i	0.998593	−	0.0530249i	$-0.0168863\pi$
$54$	−4.88403	+	5.49056i	−0.664632	+	0.747171i
$55$		0			0
$56$	2.62447	−	9.00150i	0.350709	−	1.20288i
$57$	−3.95246	+	3.46678i	−0.523516	+	0.459187i
$58$	−1.20629	+	1.18881i	−0.158394	+	0.156098i
$59$	1.06446	−	1.84370i	0.138581	−	0.240029i	−0.788379	−	0.615190i	$-0.789079\pi$
$59$	1.06446	−	1.84370i	0.138581	−	0.240029i	0.926960	+	0.375161i	$0.122413\pi$
$60$		0			0
$61$	1.91303	+	3.31346i	0.244938	+	0.424245i	0.962114	−	0.272647i	$-0.0878990\pi$
$61$	1.91303	+	3.31346i	0.244938	+	0.424245i	−0.717176	+	0.696892i	$0.754566\pi$
$62$	−0.322986	−	0.0890754i	−0.0410193	−	0.0113126i
$63$	3.80731	+	9.18741i	0.479676	+	1.15751i
$64$	0.350216	−	7.99233i	0.0437769	−	0.999041i
$65$		0			0
$66$	0.419529	−	5.76318i	0.0516405	−	0.709399i
$67$	−5.49472	−	3.17238i	−0.671287	−	0.387567i	0.125277	−	0.992122i	$-0.460018\pi$
$67$	−5.49472	−	3.17238i	−0.671287	−	0.387567i	−0.796564	+	0.604554i	$0.793351\pi$
$68$	−0.866788	−	1.55325i	−0.105113	−	0.188359i
$69$	12.3568	−	2.45896i	1.48758	−	0.296024i
$70$		0			0
$71$	11.7244			1.39143			0.695717	−	0.718316i	$-0.255087\pi$
$71$	11.7244			1.39143			0.695717	+	0.718316i	$0.255087\pi$
$72$	5.01801	+	6.84248i	0.591378	+	0.806395i
$73$	−6.10889			−0.714992			−0.357496	−	0.933915i	$-0.616369\pi$
$73$	−6.10889			−0.714992			−0.357496	+	0.933915i	$0.616369\pi$
$74$	−15.7362	+	4.09365i	−1.82930	+	0.475877i
$75$		0			0
$76$	2.95831	+	5.30117i	0.339342	+	0.608086i
$77$	−6.77253	−	3.91012i	−0.771802	−	0.445600i
$78$	−9.70059	+	4.69708i	−1.09838	+	0.531839i
$79$	8.94873	−	5.16655i	1.00681	−	0.581283i	0.0965546	−	0.995328i	$-0.469218\pi$
$79$	8.94873	−	5.16655i	1.00681	−	0.581283i	0.910256	+	0.414045i	$0.135884\pi$
$80$		0			0
$81$	−8.69409	−	2.32653i	−0.966010	−	0.258503i
$82$	3.86020	+	1.06459i	0.426288	+	0.117565i
$83$	−1.29963	−	2.25103i	−0.142653	−	0.247083i	0.785842	−	0.618428i	$-0.212230\pi$
$83$	−1.29963	−	2.25103i	−0.142653	−	0.247083i	−0.928495	+	0.371345i	$0.878897\pi$
$84$	11.2942	−	2.07662i	1.23230	−	0.226578i
$85$		0			0
$86$	−8.41349	+	8.29156i	−0.907250	+	0.894102i
$87$	−1.96425	−	0.666593i	−0.210589	−	0.0714663i
$88$	−6.40565	−	1.86763i	−0.682845	−	0.199089i
$89$			4.68130i			0.496217i	0.968732	+	0.248108i	$0.0798089\pi$
$89$			4.68130i			0.496217i	−0.968732	+	0.248108i	$0.920191\pi$
$90$		0			0
$91$			14.5863i			1.52906i
$92$	0.212351	−	14.5466i	0.0221391	−	1.51659i
$93$	−0.0800869	−	0.402452i	−0.00830463	−	0.0417324i
$94$	7.51702	+	7.62755i	0.775321	+	0.786722i
$95$		0			0
$96$	8.93945	−	4.01077i	0.912379	−	0.409347i
$97$	3.08700	+	5.34684i	0.313438	+	0.542890i	0.979104	−	0.203360i	$-0.0651860\pi$
$97$	3.08700	+	5.34684i	0.313438	+	0.542890i	−0.665667	+	0.746249i	$0.731853\pi$
$98$	1.49994	−	5.43875i	0.151517	−	0.549397i
$99$	6.53795	−	2.70936i	0.657089	−	0.272301i
$100$		0			0
$101$	−6.72336	+	3.88174i	−0.669000	+	0.386247i	−0.795697	−	0.605694i	$-0.792895\pi$
$101$	−6.72336	+	3.88174i	−0.669000	+	0.386247i	0.126698	+	0.991941i	$0.459562\pi$
$102$	1.22335	−	1.80257i	0.121130	−	0.178481i
$103$	−11.3975	−	6.58033i	−1.12302	−	0.648379i	−0.180853	−	0.983510i	$-0.557886\pi$
$103$	−11.3975	−	6.58033i	−1.12302	−	0.648379i	−0.942171	+	0.335131i	$0.891219\pi$
$104$	2.95712	+	12.0889i	0.289969	+	1.18541i
$105$		0			0
$106$	−0.274887	−	1.05668i	−0.0266994	−	0.102634i
$107$	−0.252175			−0.0243786			−0.0121893	−	0.999926i	$-0.503880\pi$
$107$	−0.252175			−0.0243786			−0.0121893	+	0.999926i	$0.503880\pi$
$108$	−4.72969	+	9.25365i	−0.455114	+	0.890433i
$109$	−0.459068			−0.0439708			−0.0219854	−	0.999758i	$-0.506999\pi$
$109$	−0.459068			−0.0439708			−0.0219854	+	0.999758i	$0.506999\pi$
$110$		0			0
$111$	−13.1316	−	14.9713i	−1.24640	−	1.42101i
$112$	0.387059	−	13.2544i	0.0365736	−	1.25243i
$113$	−15.0958	−	8.71557i	−1.42009	−	0.819892i	−0.423788	−	0.905761i	$-0.639300\pi$
$113$	−15.0958	−	8.71557i	−1.42009	−	0.819892i	−0.996306	+	0.0858696i	$0.972633\pi$
$114$	−4.17524	+	6.15210i	−0.391047	+	0.576197i
$115$		0			0
$116$	−1.22773	+	2.05657i	−0.113992	+	0.190948i
$117$	−10.4738	−	8.03408i	−0.968300	−	0.742751i
$118$	0.800444	−	2.90240i	0.0736868	−	0.267187i
$119$	−1.47414	−	2.55328i	−0.135134	−	0.234059i
$120$		0			0
$121$	2.71748	−	4.70681i	0.247043	−	0.427891i
$122$	3.79803	+	3.85388i	0.343857	+	0.348914i
$123$	0.957167	+	4.80995i	0.0863048	+	0.433698i
$124$	−0.473773	−	0.00691615i	−0.0425461	−	0.000621089i
$125$		0			0
$126$	8.48206	+	11.2189i	0.755642	+	0.999456i
$127$			10.5666i			0.937635i	0.883295	+	0.468817i	$0.155320\pi$
$127$			10.5666i			0.937635i	−0.883295	+	0.468817i	$0.844680\pi$
$128$	−2.36631	−	11.0635i	−0.209154	−	0.977883i
$129$	−13.7000	−	4.64927i	−1.20622	−	0.409345i
$130$		0			0
$131$	8.12900	−	14.0798i	0.710234	−	1.23016i	−0.254535	−	0.967064i	$-0.581922\pi$
$131$	8.12900	−	14.0798i	0.710234	−	1.23016i	0.964769	−	0.263098i	$-0.0847444\pi$
$132$	−1.47776	−	8.03721i	−0.128623	−	0.699550i
$133$	5.03116	+	8.71423i	0.436257	+	0.755619i
$134$	−8.64991	−	2.38554i	−0.747239	−	0.206079i
$135$		0			0
$136$	−1.73937	−	1.81725i	−0.149149	−	0.155828i
$137$	−11.4244	+	6.59587i	−0.976051	+	0.563523i	−0.901076	−	0.433662i	$-0.857221\pi$
$137$	−11.4244	+	6.59587i	−0.976051	+	0.563523i	−0.0749753	+	0.997185i	$0.523888\pi$
$138$	16.0367	−	7.76506i	1.36513	−	0.661006i
$139$	−5.61535	−	3.24202i	−0.476288	−	0.274985i	0.242580	−	0.970131i	$-0.422006\pi$
$139$	−5.61535	−	3.24202i	−0.476288	−	0.274985i	−0.718868	+	0.695146i	$0.755340\pi$
$140$		0			0
$141$	−4.21496	+	12.4202i	−0.354964	+	1.04597i
$142$	16.0468	−	4.17443i	1.34661	−	0.350311i
$143$	10.3799			0.868014
$144$	9.30419	+	7.57840i	0.775349	+	0.631533i
$145$		0			0
$146$	−8.36100	+	2.17505i	−0.691961	+	0.180008i
$147$	6.77688	−	1.34858i	0.558947	−	0.111229i
$148$	−20.0800	+	11.2056i	−1.65057	+	0.921097i
$149$	−7.25009	−	4.18584i	−0.593950	−	0.342917i	0.172708	−	0.984973i	$-0.444748\pi$
$149$	−7.25009	−	4.18584i	−0.593950	−	0.342917i	−0.766658	+	0.642056i	$0.778082\pi$
$150$		0			0
$151$	−14.2008	+	8.19886i	−1.15565	+	0.667214i	−0.950257	−	0.311466i	$-0.899180\pi$
$151$	−14.2008	+	8.19886i	−1.15565	+	0.667214i	−0.205391	+	0.978680i	$0.565847\pi$
$152$	5.93638	+	6.20220i	0.481504	+	0.503065i
$153$	2.64533	+	0.347825i	0.213863	+	0.0281200i
$154$	−10.6615	−	2.94030i	−0.859127	−	0.236936i
$155$		0			0
$156$	−11.6044	+	9.88256i	−0.929099	+	0.791238i
$157$	5.35608	−	9.27700i	0.427462	−	0.740386i	−0.569185	−	0.822209i	$-0.692741\pi$
$157$	5.35608	−	9.27700i	0.427462	−	0.740386i	0.996647	+	0.0818239i	$0.0260745\pi$
$158$	10.4082	−	10.2574i	0.828036	−	0.816036i
$159$	1.00532	−	0.881785i	0.0797268	−	0.0699301i
$160$		0			0
$161$		−	24.1137i		−	1.90042i
$162$	−12.7276	−	0.0887308i	−0.999976	−	0.00697135i
$163$		−	1.33584i		−	0.104631i	−0.998631	−	0.0523153i	$-0.983340\pi$
$163$		−	1.33584i		−	0.104631i	0.998631	−	0.0523153i	$-0.0166601\pi$
$164$	5.66235	+	0.0826590i	0.442155	+	0.00645459i
$165$		0			0
$166$	−2.58023	−	2.61817i	−0.200265	−	0.203209i
$167$	3.58501	−	6.20942i	0.277417	−	0.480500i	−0.693325	−	0.720625i	$-0.743855\pi$
$167$	3.58501	−	6.20942i	0.277417	−	0.480500i	0.970742	+	0.240125i	$0.0771884\pi$
$168$	14.7186	−	6.86345i	1.13557	−	0.529527i
$169$	−3.18034	−	5.50851i	−0.244641	−	0.423731i
$170$		0			0
$171$	−9.02841	−	1.18711i	−0.690420	−	0.0907806i
$172$	−8.56303	+	14.3439i	−0.652925	+	1.09371i
$173$	−2.23027	+	1.28765i	−0.169564	+	0.0978979i	−0.582380	−	0.812916i	$-0.697879\pi$
$173$	−2.23027	+	1.28765i	−0.169564	+	0.0978979i	0.412816	+	0.910814i	$0.364545\pi$
$174$	−2.92573	−	0.212977i	−0.221799	−	0.0161458i
$175$		0			0
$176$	−9.43212	−	0.275439i	−0.710973	−	0.0207620i
$177$	3.61649	−	0.719672i	0.271832	−	0.0540939i
$178$	1.66676	+	6.40711i	0.124929	+	0.480233i
$179$	10.1847			0.761243			0.380622	−	0.924731i	$-0.375710\pi$
$179$	10.1847			0.761243			0.380622	+	0.924731i	$0.375710\pi$
$180$		0			0
$181$	4.17537			0.310353			0.155176	−	0.987887i	$-0.450405\pi$
$181$	4.17537			0.310353			0.155176	+	0.987887i	$0.450405\pi$
$182$	5.19340	+	19.9637i	0.384961	+	1.47981i
$183$	−2.12964	+	6.27541i	−0.157428	+	0.463891i
$184$	−4.88861	−	19.9849i	−0.360393	−	1.47331i
$185$		0			0
$186$	−0.252903	−	0.522306i	−0.0185438	−	0.0382973i
$187$	−1.81696	+	1.04902i	−0.132870	+	0.0767123i
$188$	13.0040	+	7.76312i	0.948414	+	0.566184i
$189$	−7.61478	+	15.4508i	−0.553894	+	1.12388i
$190$		0			0
$191$	12.5152	+	21.6770i	0.905570	+	1.56849i	0.820151	+	0.572147i	$0.193889\pi$
$191$	12.5152	+	21.6770i	0.905570	+	1.56849i	0.0854186	+	0.996345i	$0.472777\pi$
$192$	10.8071	−	8.67223i	0.779932	−	0.625864i
$193$	9.45871	−	16.3830i	0.680853	−	1.17927i	−0.293868	−	0.955846i	$-0.594943\pi$
$193$	9.45871	−	16.3830i	0.680853	−	1.17927i	0.974721	−	0.223426i	$-0.0717241\pi$
$194$	6.12878	+	6.21890i	0.440021	+	0.446491i
$195$		0			0
$196$	0.116461	−	7.97785i	0.00831863	−	0.569846i
$197$		−	5.25418i		−	0.374345i	−0.982327	−	0.187172i	$-0.940068\pi$
$197$		−	5.25418i		−	0.374345i	0.982327	−	0.187172i	$-0.0599323\pi$
$198$	7.98358	−	6.03600i	0.567368	−	0.428960i
$199$			18.8487i			1.33615i	0.744095	+	0.668074i	$0.232881\pi$
$199$			18.8487i			1.33615i	−0.744095	+	0.668074i	$0.767119\pi$
$200$		0			0
$201$	−2.14481	−	10.7781i	−0.151284	−	0.760229i
$202$	−7.81993	+	7.70660i	−0.550208	+	0.542235i
$203$	−1.98500	+	3.43813i	−0.139320	+	0.241309i
$204$	1.03255	−	2.90268i	0.0722930	−	0.203228i
$205$		0			0
$206$	−17.9421	−	4.94821i	−1.25009	−	0.344758i
$207$	17.3149	+	13.2817i	1.20347	+	0.923140i
$208$	8.35148	+	15.4927i	0.579071	+	1.07423i
$209$	6.20122	−	3.58028i	0.428948	−	0.247653i
$210$		0			0
$211$	3.96081	+	2.28678i	0.272674	+	0.157428i	0.630102	−	0.776512i	$-0.283013\pi$
$211$	3.96081	+	2.28678i	0.272674	+	0.157428i	−0.357428	+	0.933941i	$0.616346\pi$
$212$	−0.752454	−	1.34837i	−0.0516787	−	0.0926061i
$213$	13.3908	+	15.2667i	0.917521	+	1.04606i
$214$	−0.345141	+	0.0897857i	−0.0235934	+	0.00613762i
$215$		0			0
$216$	−3.17861	+	14.3491i	−0.216277	+	0.976332i
$217$	−0.785367			−0.0533142
$218$	−0.628309	+	0.163449i	−0.0425544	+	0.0110702i
$219$	−6.97713	−	7.95458i	−0.471471	−	0.537521i
$220$		0			0
$221$	3.38900	+	1.95664i	0.227969	+	0.131618i
$222$	−23.3032	−	15.8152i	−1.56401	−	1.06144i
$223$	20.5711	−	11.8767i	1.37754	−	0.795323i	0.385677	−	0.922634i	$-0.373968\pi$
$223$	20.5711	−	11.8767i	1.37754	−	0.795323i	0.991863	+	0.127310i	$0.0406344\pi$
$224$	−4.18943	−	18.2786i	−0.279918	−	1.22129i
$225$		0			0
$226$	−23.7642	−	6.55386i	−1.58077	−	0.435956i
$227$	−13.9287	−	24.1252i	−0.924478	−	1.60124i	−0.792398	−	0.610005i	$-0.791168\pi$
$227$	−13.9287	−	24.1252i	−0.924478	−	1.60124i	−0.132081	−	0.991239i	$-0.542166\pi$
$228$	−3.52405	+	9.90672i	−0.233386	+	0.656088i
$229$	−8.35991	+	14.4798i	−0.552439	+	0.956852i	0.445659	+	0.895203i	$0.352969\pi$
$229$	−8.35991	+	14.4798i	−0.552439	+	0.956852i	−0.998098	+	0.0616492i	$0.980364\pi$
$230$		0			0
$231$	−2.64360	−	13.2846i	−0.173936	−	0.874061i
$232$	−0.948115	+	3.25188i	−0.0622468	+	0.213496i
$233$		−	1.67938i		−	0.110020i	−0.998486	−	0.0550101i	$-0.982481\pi$
$233$		−	1.67938i		−	0.110020i	0.998486	−	0.0550101i	$-0.0175191\pi$
$234$	−17.1955	−	7.26679i	−1.12411	−	0.475045i
$235$		0			0
$236$	0.0621495	−	4.25739i	0.00404559	−	0.277133i
$237$	16.9481	+	5.75157i	1.10090	+	0.373604i
$238$	−2.92667	−	2.96971i	−0.189708	−	0.192498i
$239$	5.41085	−	9.37186i	0.349999	−	0.606215i	−0.636250	−	0.771483i	$-0.719515\pi$
$239$	5.41085	−	9.37186i	0.349999	−	0.606215i	0.986249	+	0.165267i	$0.0528487\pi$
$240$		0			0
$241$	−5.45657	−	9.45105i	−0.351488	−	0.608796i	0.635022	−	0.772494i	$-0.280991\pi$
$241$	−5.45657	−	9.45105i	−0.351488	−	0.608796i	−0.986510	+	0.163698i	$0.947658\pi$
$242$	2.04346	−	7.40957i	0.131359	−	0.476305i
$243$	−6.90031	−	13.9780i	−0.442655	−	0.896692i
$244$	6.57037	+	3.92238i	0.420625	+	0.251104i
$245$		0			0
$246$	3.02260	+	6.24239i	0.192714	+	0.398000i
$247$	−11.5665	−	6.67794i	−0.735961	−	0.424907i
$248$	−0.650897	+	0.159219i	−0.0413320	+	0.0101104i
$249$	1.44679	−	4.26326i	0.0916867	−	0.270173i
$250$		0			0
$251$	5.05766			0.319237			0.159618	−	0.987179i	$-0.448974\pi$
$251$	5.05766			0.319237			0.159618	+	0.987179i	$0.448974\pi$
$252$	15.6035	+	12.3348i	0.982927	+	0.777021i
$253$	−17.1598			−1.07883
$254$	3.76220	+	14.4621i	0.236061	+	0.907433i
$255$		0			0
$256$	−7.17778	−	14.2996i	−0.448611	−	0.893727i
$257$	11.5968	+	6.69541i	0.723388	+	0.417649i	0.815999	−	0.578054i	$-0.196188\pi$
$257$	11.5968	+	6.69541i	0.723388	+	0.417649i	−0.0926101	+	0.995702i	$0.529521\pi$
$258$	−20.4060	−	1.48545i	−1.27042	−	0.0924799i
$259$	−33.0081	+	19.0573i	−2.05103	+	1.18416i
$260$		0			0
$261$	−1.37543	−	3.31904i	−0.0851369	−	0.205444i
$262$	6.11278	−	22.1648i	0.377649	−	1.36935i
$263$	5.44564	+	9.43213i	0.335793	+	0.581610i	0.983637	−	0.180163i	$-0.0576626\pi$
$263$	5.44564	+	9.43213i	0.335793	+	0.581610i	−0.647844	+	0.761773i	$0.724329\pi$
$264$	−4.88417	−	10.4741i	−0.300600	−	0.644634i
$265$		0			0
$266$	9.98862	+	10.1355i	0.612441	+	0.621447i
$267$	−6.09567	+	5.34664i	−0.373049	+	0.327209i
$268$	−12.6882	−	0.185222i	−0.775052	−	0.0113142i
$269$		−	21.5020i		−	1.31100i	−0.755195	−	0.655500i	$-0.772458\pi$
$269$		−	21.5020i		−	1.31100i	0.755195	−	0.655500i	$-0.227542\pi$
$270$		0			0
$271$			18.9445i			1.15080i	0.817873	+	0.575399i	$0.195153\pi$
$271$			18.9445i			1.15080i	−0.817873	+	0.575399i	$0.804847\pi$
$272$	−3.02763	−	1.86791i	−0.183577	−	0.113258i
$273$	−18.9933	+	16.6594i	−1.14953	+	1.00828i
$274$	−13.2877	+	13.0951i	−0.802737	+	0.791105i
$275$		0			0
$276$	19.1841	−	16.3375i	1.15475	−	0.983404i
$277$	9.33092	+	16.1616i	0.560641	+	0.971058i	0.997441	+	0.0714994i	$0.0227784\pi$
$277$	9.33092	+	16.1616i	0.560641	+	0.971058i	−0.436800	+	0.899559i	$0.643888\pi$
$278$	−8.83982	−	2.43791i	−0.530177	−	0.146216i
$279$	0.432576	−	0.563935i	0.0258977	−	0.0337619i
$280$		0			0
$281$	−5.84683	+	3.37567i	−0.348792	+	0.201375i	−0.664153	−	0.747596i	$-0.731208\pi$
$281$	−5.84683	+	3.37567i	−0.348792	+	0.201375i	0.315361	+	0.948972i	$0.397874\pi$
$282$	−1.34669	+	18.4998i	−0.0801940	+	1.10165i
$283$	−4.56374	−	2.63488i	−0.271286	−	0.156627i	0.358186	−	0.933650i	$-0.383395\pi$
$283$	−4.56374	−	2.63488i	−0.271286	−	0.156627i	−0.629472	+	0.777023i	$0.716729\pi$
$284$	20.4763	−	11.4268i	1.21504	−	0.678054i
$285$		0			0
$286$	14.2066	−	3.69573i	0.840054	−	0.218533i
$287$	9.38639			0.554061
$288$	15.4325	+	7.05953i	0.909371	+	0.415987i
$289$	16.2090			0.953472
$290$		0			0
$291$	−3.43655	+	10.1265i	−0.201454	+	0.593623i
$292$	−10.6690	+	5.95380i	−0.624353	+	0.348420i
$293$	19.3041	+	11.1453i	1.12776	+	0.651113i	0.943371	−	0.331741i	$-0.107636\pi$
$293$	19.3041	+	11.1453i	1.12776	+	0.651113i	0.184390	+	0.982853i	$0.440969\pi$
$294$	8.79509	−	4.25863i	0.512940	−	0.248368i
$295$		0			0
$296$	−23.4930	+	22.4861i	−1.36550	+	1.30698i
$297$	10.9951	+	5.41884i	0.638001	+	0.314433i
$298$	−11.4133	−	3.14763i	−0.661153	−	0.182337i
$299$	16.0032	+	27.7184i	0.925490	+	1.60300i
$300$		0			0
$301$	−13.8448	+	23.9798i	−0.797999	+	1.38217i
$302$	−16.5170	+	16.2776i	−0.950444	+	0.936671i
$303$	−12.7335	−	4.32127i	−0.731518	−	0.248250i
$304$	10.3332	+	6.37509i	0.592647	+	0.365636i
$305$		0			0
$306$	3.74440	−	0.465806i	0.214053	−	0.0266284i
$307$		−	0.415414i		−	0.0237089i	−0.999930	−	0.0118545i	$-0.996227\pi$
$307$		−	0.415414i		−	0.0237089i	0.999930	−	0.0118545i	$-0.00377348\pi$
$308$	−15.6388	−	0.228296i	−0.891105	−	0.0130084i
$309$	−4.44890	−	22.3566i	−0.253089	−	1.27182i
$310$		0			0
$311$	0.284562	−	0.492876i	0.0161360	−	0.0279484i	−0.857845	−	0.513909i	$-0.828197\pi$
$311$	0.284562	−	0.492876i	0.0161360	−	0.0279484i	0.873981	+	0.485961i	$0.161530\pi$
$312$	−12.3639	+	17.6576i	−0.699968	+	0.999664i
$313$	14.0312	+	24.3028i	0.793091	+	1.37367i	0.924044	+	0.382285i	$0.124863\pi$
$313$	14.0312	+	24.3028i	0.793091	+	1.37367i	−0.130954	+	0.991388i	$0.541804\pi$
$314$	4.02762	−	14.6041i	0.227292	−	0.824156i
$315$		0			0
$316$	10.5932	−	17.7447i	0.595917	−	0.998219i
$317$	11.4952	−	6.63676i	0.645635	−	0.372758i	−0.141147	−	0.989989i	$-0.545079\pi$
$317$	11.4952	−	6.63676i	0.645635	−	0.372758i	0.786782	+	0.617231i	$0.211746\pi$
$318$	1.06198	−	1.56480i	0.0595530	−	0.0877498i
$319$	2.44664	+	1.41257i	0.136986	+	0.0790887i
$320$		0			0
$321$	−0.288015	−	0.328364i	−0.0160754	−	0.0183275i
$322$	−8.58557	−	33.0034i	−0.478455	−	1.83921i
$323$	2.69956			0.150208
$324$	−17.4514	+	4.41017i	−0.969521	+	0.245010i
$325$		0			0
$326$	−0.475619	−	1.82830i	−0.0263421	−	0.101260i
$327$	−0.524314	−	0.597767i	−0.0289947	−	0.0330566i
$328$	7.77926	−	1.90292i	0.429538	−	0.105071i
$329$	21.7398	+	12.5515i	1.19855	+	0.691985i
$330$		0			0
$331$	−7.43989	+	4.29542i	−0.408933	+	0.236098i	−0.690331	−	0.723493i	$-0.742535\pi$
$331$	−7.43989	+	4.29542i	−0.408933	+	0.236098i	0.281398	+	0.959591i	$0.409202\pi$
$332$	−4.46364	−	2.66471i	−0.244974	−	0.146245i
$333$	4.49659	−	34.1982i	0.246412	−	1.87405i
$334$	2.69583	−	9.77502i	0.147509	−	0.534865i
$335$		0			0
$336$	17.7011	−	14.6342i	0.965673	−	0.798363i
$337$	−0.527708	+	0.914017i	−0.0287461	+	0.0497897i	−0.880041	−	0.474899i	$-0.842485\pi$
$337$	−0.527708	+	0.914017i	−0.0287461	+	0.0497897i	0.851294	+	0.524688i	$0.175818\pi$
$338$	−6.31409	−	6.40693i	−0.343441	−	0.348491i
$339$	−5.89251	−	29.6110i	−0.320037	−	1.60825i
$340$		0			0
$341$			0.558884i			0.0302652i
$342$	−12.7795	+	1.58978i	−0.691036	+	0.0859653i
$343$			9.98036i			0.538889i
$344$	−6.61279	+	22.6808i	−0.356538	+	1.22287i
$345$		0			0
$346$	−2.59402	+	2.55643i	−0.139455	+	0.137434i
$347$	−3.45165	+	5.97844i	−0.185294	+	0.320939i	−0.943676	−	0.330872i	$-0.892657\pi$
$347$	−3.45165	+	5.97844i	−0.185294	+	0.320939i	0.758381	+	0.651811i	$0.225991\pi$
$348$	−4.08015	+	0.750199i	−0.218719	+	0.0402149i
$349$	15.5145	+	26.8719i	0.830473	+	1.43842i	0.897663	+	0.440682i	$0.145263\pi$
$349$	15.5145	+	26.8719i	0.830473	+	1.43842i	−0.0671899	+	0.997740i	$0.521403\pi$
$350$		0			0
$351$	−1.50094	−	22.8142i	−0.0801142	−	1.21773i
$352$	−13.0074	+	2.98128i	−0.693299	+	0.158903i
$353$	13.2995	−	7.67847i	0.707861	−	0.408684i	−0.102408	−	0.994743i	$-0.532655\pi$
$353$	13.2995	−	7.67847i	0.707861	−	0.408684i	0.810269	+	0.586059i	$0.199321\pi$
$354$	4.69351	−	2.27262i	0.249457	−	0.120789i
$355$		0			0
$356$	4.56245	+	8.17572i	0.241809	+	0.433312i
$357$	1.64105	−	4.83568i	0.0868537	−	0.255932i
$358$	13.9394	−	3.62623i	0.736723	−	0.191652i
$359$	−8.51196			−0.449244			−0.224622	−	0.974446i	$-0.572115\pi$
$359$	−8.51196			−0.449244			−0.224622	+	0.974446i	$0.572115\pi$
$360$		0			0
$361$	9.78650			0.515079
$362$	5.71466	−	1.48662i	0.300356	−	0.0781352i
$363$	9.23258	−	1.83726i	0.484585	−	0.0964311i
$364$	14.2160	+	25.4745i	0.745122	+	1.33523i
$365$		0			0
$366$	−0.680423	+	9.34715i	−0.0355663	+	0.488583i
$367$	1.11984	−	0.646542i	0.0584553	−	0.0337492i	−0.470488	−	0.882407i	$-0.655922\pi$
$367$	1.11984	−	0.646542i	0.0584553	−	0.0337492i	0.528943	+	0.848657i	$0.322589\pi$
$368$	−13.8064	−	25.6120i	−0.719708	−	1.33512i
$369$	−5.16998	+	6.73993i	−0.269138	+	0.350867i
$370$		0			0
$371$	−1.27969	−	2.21648i	−0.0664381	−	0.115074i
$372$	−0.532103	−	0.624814i	−0.0275883	−	0.0323951i
$373$	8.18898	−	14.1837i	0.424010	−	0.734406i	−0.572318	−	0.820032i	$-0.693956\pi$
$373$	8.18898	−	14.1837i	0.424010	−	0.734406i	0.996327	+	0.0856259i	$0.0272890\pi$
$374$	−2.11331	+	2.08268i	−0.109276	+	0.107693i
$375$		0			0
$376$	20.5621	+	5.99506i	1.06041	+	0.309172i
$377$		−	5.26946i		−	0.271391i
$378$	−4.92086	+	23.8581i	−0.253102	+	1.22713i
$379$		−	11.7940i		−	0.605818i	−0.953020	−	0.302909i	$-0.902042\pi$
$379$		−	11.7940i		−	0.605818i	0.953020	−	0.302909i	$-0.0979578\pi$
$380$		0			0
$381$	−13.7591	+	12.0684i	−0.704901	+	0.618283i
$382$	24.8471	+	25.2125i	1.27129	+	1.28998i
$383$	−5.63455	+	9.75933i	−0.287912	+	0.498678i	−0.973311	−	0.229489i	$-0.926294\pi$
$383$	−5.63455	+	9.75933i	−0.287912	+	0.498678i	0.685399	+	0.728168i	$0.259628\pi$
$384$	11.7035	−	15.7171i	0.597241	−	0.802062i
$385$		0			0
$386$	7.11268	−	25.7905i	0.362026	−	1.31270i
$387$	−9.59316	−	23.1492i	−0.487648	−	1.17674i
$388$	10.6024	+	6.32944i	0.538257	+	0.321328i
$389$	−17.4583	+	10.0796i	−0.885172	+	0.511054i	−0.872360	−	0.488864i	$-0.837411\pi$
$389$	−17.4583	+	10.0796i	−0.885172	+	0.511054i	−0.0128115	+	0.999918i	$0.504078\pi$
$390$		0			0
$391$	−5.60259	−	3.23466i	−0.283335	−	0.163584i
$392$	−2.68108	−	10.9604i	−0.135415	−	0.553585i
$393$	27.6182	−	5.49594i	1.39315	−	0.277234i
$394$	−1.87073	−	7.19119i	−0.0942460	−	0.362287i
$395$		0			0
$396$	8.77771	−	11.1038i	0.441097	−	0.557985i
$397$	5.11859			0.256895			0.128447	−	0.991716i	$-0.459001\pi$
$397$	5.11859			0.256895			0.128447	+	0.991716i	$0.459001\pi$
$398$	6.71100	+	25.7975i	0.336392	+	1.29311i
$399$	−5.60084	+	16.5040i	−0.280393	+	0.826233i
$400$		0			0
$401$	9.58291	+	5.53269i	0.478548	+	0.276290i	0.719811	−	0.694170i	$-0.244228\pi$
$401$	9.58291	+	5.53269i	0.478548	+	0.276290i	−0.241263	+	0.970460i	$0.577562\pi$
$402$	−6.77302	−	13.9879i	−0.337808	−	0.697653i
$403$	0.902771	−	0.521215i	0.0449702	−	0.0259636i
$404$	−7.95892	+	13.3320i	−0.395971	+	0.663291i
$405$		0			0
$406$	−1.49267	+	5.41238i	−0.0740798	+	0.268612i
$407$	13.5615	+	23.4893i	0.672221	+	1.16432i
$408$	0.379724	−	4.34041i	0.0187992	−	0.214883i
$409$	8.08315	−	14.0004i	0.399686	−	0.692276i	−0.594001	−	0.804464i	$-0.702452\pi$
$409$	8.08315	−	14.0004i	0.399686	−	0.692276i	0.993687	+	0.112188i	$0.0357858\pi$
$410$		0			0
$411$	−21.6368	−	7.34273i	−1.06726	−	0.362190i
$412$	−26.3185	−	0.384198i	−1.29662	−	0.0189281i
$413$		−	7.05742i		−	0.347273i
$414$	28.4271	+	12.0132i	1.39711	+	0.590417i
$415$		0			0
$416$	16.9465	+	18.2307i	0.830868	+	0.893835i
$417$	−2.19190	−	11.0147i	−0.107338	−	0.539394i
$418$	7.21263	−	7.10810i	0.352781	−	0.347669i
$419$	3.65564	−	6.33176i	0.178590	−	0.309327i	−0.762808	−	0.646625i	$-0.776180\pi$
$419$	3.65564	−	6.33176i	0.178590	−	0.309327i	0.941398	+	0.337298i	$0.109513\pi$
$420$		0			0
$421$	14.9731	+	25.9341i	0.729742	+	1.26395i	0.956992	+	0.290114i	$0.0936932\pi$
$421$	14.9731	+	25.9341i	0.729742	+	1.26395i	−0.227250	+	0.973836i	$0.572973\pi$
$422$	6.23521	+	1.71959i	0.303525	+	0.0837083i
$423$	−20.9868	+	8.69702i	−1.02041	+	0.422864i
$424$	−1.50993	−	1.57755i	−0.0733288	−	0.0766124i
$425$		0			0
$426$	23.7631	+	16.1273i	1.15133	+	0.781368i
$427$	10.9842	+	6.34172i	0.531562	+	0.306897i
$428$	−0.440413	+	0.245772i	−0.0212882	+	0.0118798i
$429$	11.8552	+	13.5160i	0.572375	+	0.652561i
$430$		0			0
$431$	30.7505			1.48120			0.740599	−	0.671947i	$-0.234542\pi$
$431$	30.7505			1.48120			0.740599	+	0.671947i	$0.234542\pi$
$432$	0.758495	+	20.7708i	0.0364931	+	0.999334i
$433$	−29.3734			−1.41160			−0.705798	−	0.708413i	$-0.749411\pi$
$433$	−29.3734			−1.41160			−0.705798	+	0.708413i	$0.749411\pi$
$434$	−1.07490	+	0.279627i	−0.0515969	+	0.0134225i
$435$		0			0
$436$	−0.801746	+	0.447413i	−0.0383967	+	0.0214272i
$437$	19.1214	+	11.0398i	0.914701	+	0.528103i
$438$	−12.3815	−	8.40294i	−0.591612	−	0.401508i
$439$	6.77418	−	3.91108i	0.323314	−	0.186665i	−0.329555	−	0.944136i	$-0.606899\pi$
$439$	6.77418	−	3.91108i	0.323314	−	0.186665i	0.652869	+	0.757471i	$0.273565\pi$
$440$		0			0
$441$	9.49608	+	7.28413i	0.452194	+	0.346863i
$442$	5.33505	+	1.47134i	0.253763	+	0.0699844i
$443$	−13.3520	−	23.1263i	−0.634371	−	1.09876i	−0.986648	−	0.162867i	$-0.947926\pi$
$443$	−13.3520	−	23.1263i	−0.634371	−	1.09876i	0.352277	−	0.935896i	$-0.385408\pi$
$444$	−37.5251	−	13.3486i	−1.78086	−	0.633495i
$445$		0			0
$446$	23.9261	−	23.5794i	1.13294	−	1.11652i
$447$	−2.83001	−	14.2213i	−0.133855	−	0.672646i
$448$	−12.2419	−	23.5256i	−0.578377	−	1.11148i
$449$		−	23.8441i		−	1.12527i	−0.826704	−	0.562637i	$-0.809787\pi$
$449$		−	23.8441i		−	1.12527i	0.826704	−	0.562637i	$-0.190213\pi$
$450$		0			0
$451$		−	6.67955i		−	0.314528i
$452$	−34.8586	−	0.508866i	−1.63961	−	0.0239350i
$453$	−26.8952	−	9.12722i	−1.26364	−	0.428834i
$454$	−27.6533	−	28.0599i	−1.29783	−	1.31692i
$455$		0			0
$456$	−1.29598	+	14.8137i	−0.0606900	+	0.693713i
$457$	−7.87798	−	13.6451i	−0.368516	−	0.638289i	0.620817	−	0.783955i	$-0.286801\pi$
$457$	−7.87798	−	13.6451i	−0.368516	−	0.638289i	−0.989334	+	0.145666i	$0.953468\pi$
$458$	−6.28641	+	22.7944i	−0.293745	+	1.06511i
$459$	2.56839	+	3.84183i	0.119882	+	0.179321i
$460$		0			0
$461$	9.24515	−	5.33769i	0.430590	−	0.248601i	−0.269008	−	0.963138i	$-0.586696\pi$
$461$	9.24515	−	5.33769i	0.430590	−	0.248601i	0.699598	+	0.714537i	$0.253363\pi$
$462$	−8.34811	−	17.2408i	−0.388389	−	0.802117i
$463$	5.50175	+	3.17644i	0.255688	+	0.147622i	0.622366	−	0.782726i	$-0.286172\pi$
$463$	5.50175	+	3.17644i	0.255688	+	0.147622i	−0.366678	+	0.930348i	$0.619505\pi$
$464$	−0.139829	+	4.78829i	−0.00649139	+	0.222291i
$465$		0			0
$466$	−0.597938	−	2.29851i	−0.0276989	−	0.106476i
$467$	−7.76191			−0.359179			−0.179589	−	0.983742i	$-0.557477\pi$
$467$	−7.76191			−0.359179			−0.179589	+	0.983742i	$0.557477\pi$
$468$	−26.1221	−	3.82337i	−1.20750	−	0.176735i
$469$	−21.0330			−0.971213
$470$		0			0
$471$	18.1972	−	3.62120i	0.838483	−	0.166856i
$472$	−1.43076	−	5.84905i	−0.0658563	−	0.269224i
$473$	17.0645	+	9.85221i	0.784628	+	0.453005i
$474$	25.2440	+	1.83763i	1.15950	+	0.0844053i
$475$		0			0
$476$	−5.06298	−	3.02249i	−0.232061	−	0.138536i
$477$	2.29640	+	0.301945i	0.105145	+	0.0138251i
$478$	4.06880	−	14.7534i	0.186103	−	0.674805i
$479$	−3.56565	−	6.17588i	−0.162919	−	0.282183i	0.772996	−	0.634411i	$-0.218757\pi$
$479$	−3.56565	−	6.17588i	−0.162919	−	0.282183i	−0.935914	+	0.352228i	$0.885424\pi$
$480$		0			0
$481$	25.2950	−	43.8122i	1.15335	−	1.99767i
$482$	−10.8332	−	10.9925i	−0.493439	−	0.500694i
$483$	31.3992	−	27.5409i	1.42871	−	1.25315i
$484$	0.158662	−	10.8687i	0.00721192	−	0.494034i
$485$		0			0
$486$	−14.4210	−	16.6744i	−0.654150	−	0.756365i
$487$		−	15.1089i		−	0.684649i	−0.939582	−	0.342325i	$-0.888786\pi$
$487$		−	15.1089i		−	0.684649i	0.939582	−	0.342325i	$-0.111214\pi$
$488$	10.3891	+	3.02905i	0.470295	+	0.137119i
$489$	1.73943	−	1.52569i	0.0786599	−	0.0689942i
$490$		0			0
$491$	14.7215	−	25.4984i	0.664372	−	1.15073i	−0.315083	−	0.949064i	$-0.602032\pi$
$491$	14.7215	−	25.4984i	0.664372	−	1.15073i	0.979455	−	0.201662i	$-0.0646342\pi$
$492$	6.35949	+	7.46753i	0.286708	+	0.336662i
$493$	0.532546	+	0.922396i	0.0239847	+	0.0415426i
$494$	−18.2083	−	5.02162i	−0.819230	−	0.225933i
$495$		0			0
$496$	−0.834168	+	0.449666i	−0.0374552	+	0.0201906i
$497$	33.6595	−	19.4333i	1.50984	−	0.871705i
$498$	0.462252	−	6.35008i	0.0207140	−	0.284554i
$499$	18.0795	+	10.4382i	0.809351	+	0.467279i	0.846730	−	0.532022i	$-0.178568\pi$
$499$	18.0795	+	10.4382i	0.809351	+	0.467279i	−0.0373795	+	0.999301i	$0.511901\pi$
$500$		0			0
$501$	12.1800	−	2.42379i	0.544163	−	0.108287i
$502$	6.92222	−	1.80076i	0.308954	−	0.0803718i
$503$	−22.6713			−1.01086			−0.505431	−	0.862867i	$-0.668667\pi$
$503$	−22.6713			−1.01086			−0.505431	+	0.862867i	$0.668667\pi$
$504$	25.7476	+	11.3266i	1.14689	+	0.504528i
$505$		0			0
$506$	−23.4859	+	6.10967i	−1.04408	+	0.271608i
$507$	3.54045	−	10.4326i	0.157237	−	0.463330i
$508$	10.2983	+	18.4542i	0.456915	+	0.818772i
$509$	23.5593	+	13.6020i	1.04425	+	0.602896i	0.921033	−	0.389484i	$-0.127347\pi$
$509$	23.5593	+	13.6020i	1.04425	+	0.602896i	0.123213	+	0.992380i	$0.460680\pi$
$510$		0			0
$511$	−17.5380	+	10.1255i	−0.775834	+	0.447928i
$512$	−14.9153	−	17.0157i	−0.659168	−	0.751996i
$513$	−8.76582	−	13.1120i	−0.387020	−	0.578909i
$514$	18.2560	+	5.03476i	0.805236	+	0.222074i
$515$		0			0
$516$	−28.4577	+	5.23239i	−1.25278	+	0.230343i
$517$	8.93188	−	15.4705i	0.392824	−	0.680390i
$518$	−38.3917	+	37.8353i	−1.68683	+	1.66239i
$519$	−4.22393	−	1.43345i	−0.185410	−	0.0629213i
$520$		0			0
$521$		−	2.18176i		−	0.0955847i	−0.998857	−	0.0477924i	$-0.984781\pi$
$521$		−	2.18176i		−	0.0955847i	0.998857	−	0.0477924i	$-0.0152186\pi$
$522$	−3.06423	−	4.05293i	−0.134117	−	0.177392i
$523$			28.8185i			1.26014i	0.776537	+	0.630071i	$0.216974\pi$
$523$			28.8185i			1.26014i	−0.776537	+	0.630071i	$0.783026\pi$
$524$	0.474619	−	32.5126i	0.0207338	−	1.42032i
$525$		0			0
$526$	10.8115	+	10.9705i	0.471404	+	0.478336i
$527$	−0.105351	+	0.182473i	−0.00458916	+	0.00794865i
$528$	−10.4140	−	12.5964i	−0.453212	−	0.548190i
$529$	−14.9560	−	25.9046i	−0.650261	−	1.12629i
$530$		0			0
$531$	5.06760	+	3.88719i	0.219915	+	0.168690i
$532$	17.2797	+	10.3156i	0.749171	+	0.447240i
$533$	−10.7896	+	6.22935i	−0.467348	+	0.269823i
$534$	−6.43925	+	9.48807i	−0.278654	+	0.410589i
$535$		0			0
$536$	−17.4317	+	4.26406i	−0.752936	+	0.184179i
$537$	11.6323	+	13.2619i	0.501969	+	0.572292i
$538$	−7.65570	−	29.4290i	−0.330061	−	1.26877i
$539$	−9.41102			−0.405361
$540$		0			0
$541$	3.32257			0.142848			0.0714242	−	0.997446i	$-0.477246\pi$
$541$	3.32257			0.142848			0.0714242	+	0.997446i	$0.477246\pi$
$542$	6.74512	+	25.9286i	0.289728	+	1.11373i
$543$	4.76880	+	5.43688i	0.204649	+	0.233319i
$544$	−4.80885	−	1.47856i	−0.206178	−	0.0633926i
$545$		0			0
$546$	−20.0639	+	29.5636i	−0.858655	+	1.26521i
$547$	24.0231	−	13.8697i	1.02715	−	0.593027i	0.110986	−	0.993822i	$-0.464599\pi$
$547$	24.0231	−	13.8697i	1.02715	−	0.593027i	0.916168	+	0.400795i	$0.131266\pi$
$548$	−13.5238	+	22.6538i	−0.577710	+	0.967721i
$549$	−10.6037	+	4.39424i	−0.452556	+	0.187541i
$550$		0			0
$551$	−1.81756	−	3.14810i	−0.0774305	−	0.134114i
$552$	20.4396	−	29.1909i	0.869967	−	1.24245i
$553$	17.1272	−	29.6652i	0.728323	−	1.26149i
$554$	18.5251	+	18.7975i	0.787058	+	0.798631i
$555$		0			0
$556$	−12.9667	−	0.189288i	−0.549911	−	0.00802761i
$557$			30.0401i			1.27284i	0.771344	+	0.636419i	$0.219585\pi$
$557$			30.0401i			1.27284i	−0.771344	+	0.636419i	$0.780415\pi$
$558$	0.391263	−	0.925853i	0.0165635	−	0.0391945i
$559$		−	36.7527i		−	1.55447i
$560$		0			0
$561$	−3.44117	−	1.16781i	−0.145286	−	0.0493048i
$562$	−6.80043	+	6.70188i	−0.286859	+	0.282702i
$563$	−0.883109	+	1.52959i	−0.0372186	+	0.0644645i	−0.884035	−	0.467421i	$-0.845183\pi$
$563$	−0.883109	+	1.52959i	−0.0372186	+	0.0644645i	0.846816	+	0.531886i	$0.178516\pi$
$564$	4.74361	+	25.7994i	0.199742	+	1.08635i
$565$		0			0
$566$	−7.18435	−	1.98135i	−0.301981	−	0.0832824i
$567$	−28.8160	+	7.73134i	−1.21016	+	0.324686i
$568$	23.9566	−	22.9298i	1.00520	−	0.962115i
$569$	−31.9951	+	18.4724i	−1.34131	+	0.774403i	−0.986999	−	0.160726i	$-0.948616\pi$
$569$	−31.9951	+	18.4724i	−1.34131	+	0.774403i	−0.354306	+	0.935129i	$0.615283\pi$
$570$		0			0
$571$	26.5164	+	15.3092i	1.10968	+	0.640672i	0.938745	−	0.344612i	$-0.111989\pi$
$571$	26.5164	+	15.3092i	1.10968	+	0.640672i	0.170930	+	0.985283i	$0.445323\pi$
$572$	18.1282	−	10.1164i	0.757977	−	0.422988i
$573$	−13.9323	+	41.0543i	−0.582031	+	1.71507i
$574$	12.8468	−	3.34199i	0.536214	−	0.139492i
$575$		0			0
$576$	23.6354	+	4.16742i	0.984809	+	0.173642i
$577$	23.6405			0.984168			0.492084	−	0.870548i	$-0.336235\pi$
$577$	23.6405			0.984168			0.492084	+	0.870548i	$0.336235\pi$
$578$	22.1847	−	5.77116i	0.922760	−	0.240048i
$579$	32.1358	−	6.39495i	1.33552	−	0.265765i
$580$		0			0
$581$	−7.46221	−	4.30831i	−0.309585	−	0.178739i
$582$	−1.09798	+	15.0832i	−0.0455128	+	0.625221i
$583$	−1.57730	+	0.910652i	−0.0653249	+	0.0377154i
$584$	−12.4824	+	11.9474i	−0.516523	+	0.494385i
$585$		0			0
$586$	30.3890	+	8.38091i	1.25536	+	0.346212i
$587$	−0.0296509	−	0.0513568i	−0.00122382	−	0.00211972i	0.865413	−	0.501059i	$-0.167056\pi$
$587$	−0.0296509	−	0.0513568i	−0.00122382	−	0.00211972i	−0.866637	+	0.498940i	$0.833723\pi$
$588$	10.5212	−	8.96007i	0.433888	−	0.369507i
$589$	0.359558	−	0.622773i	0.0148153	−	0.0256609i
$590$		0			0
$591$	6.84163	−	6.00094i	0.281427	−	0.246846i
$592$	−24.1478	+	39.1404i	−0.992471	+	1.60866i
$593$			44.6245i			1.83251i	0.400596	+	0.916255i	$0.368803\pi$
$593$			44.6245i			1.83251i	−0.400596	+	0.916255i	$0.631197\pi$
$594$	16.9779	+	3.50178i	0.696613	+	0.143680i
$595$		0			0
$596$	−16.7416	−	0.244394i	−0.685762	−	0.0100108i
$597$	−24.5435	+	21.5276i	−1.00450	+	0.881066i
$598$	31.7720	+	32.2392i	1.29925	+	1.31836i
$599$	11.5001	−	19.9187i	0.469881	−	0.813857i	−0.529526	−	0.848294i	$-0.677630\pi$
$599$	11.5001	−	19.9187i	0.469881	−	0.813857i	0.999407	+	0.0344362i	$0.0109636\pi$
$600$		0			0
$601$	0.981232	+	1.69954i	0.0400253	+	0.0693259i	0.885344	−	0.464936i	$-0.153923\pi$
$601$	0.981232	+	1.69954i	0.0400253	+	0.0693259i	−0.845319	+	0.534262i	$0.820589\pi$
$602$	−10.4109	+	37.7496i	−0.424315	+	1.53856i
$603$	11.5849	−	15.1028i	0.471772	−	0.615033i
$604$	−16.8105	+	28.1593i	−0.684011	+	1.14579i
$605$		0			0
$606$	−18.9664	−	1.38065i	−0.770456	−	0.0560851i
$607$	17.5023	+	10.1049i	0.710394	+	0.410146i	0.811207	−	0.584759i	$-0.198811\pi$
$607$	17.5023	+	10.1049i	0.710394	+	0.410146i	−0.100813	+	0.994905i	$0.532144\pi$
$608$	16.4124	+	5.04625i	0.665611	+	0.204653i
$609$	−6.74402	+	1.34204i	−0.273282	+	0.0543823i
$610$		0			0
$611$	−33.3195			−1.34796
$612$	4.95897	−	1.97071i	0.200455	−	0.0796612i
$613$	24.8672			1.00438			0.502189	−	0.864758i	$-0.332528\pi$
$613$	24.8672			1.00438			0.502189	+	0.864758i	$0.332528\pi$
$614$	−0.147906	−	0.568560i	−0.00596901	−	0.0229452i
$615$		0			0
$616$	−21.4855	+	5.25568i	−0.865677	+	0.211757i
$617$	−28.3549	−	16.3707i	−1.14152	−	0.659059i	−0.194717	−	0.980860i	$-0.562379\pi$
$617$	−28.3549	−	16.3707i	−1.14152	−	0.659059i	−0.946808	+	0.321800i	$0.895712\pi$
$618$	−14.0490	−	29.0145i	−0.565133	−	1.16714i
$619$	11.9754	−	6.91400i	0.481332	−	0.277897i	−0.239640	−	0.970862i	$-0.577029\pi$
$619$	11.9754	−	6.91400i	0.481332	−	0.277897i	0.720971	+	0.692965i	$0.243696\pi$
$620$		0			0
$621$	2.48130	+	37.7156i	0.0995713	+	1.51348i
$622$	0.213982	−	0.775897i	0.00857991	−	0.0311106i
$623$	7.75930	+	13.4395i	0.310870	+	0.538442i
$624$	−10.6351	+	28.5694i	−0.425743	+	1.14369i
$625$		0			0
$626$	27.8569	+	28.2665i	1.11338	+	1.12976i
$627$	11.7446	+	3.98568i	0.469033	+	0.159173i
$628$	0.312719	−	21.4220i	0.0124789	−	0.854833i
$629$			10.2255i			0.407719i
$630$		0			0
$631$		−	0.298908i		−	0.0118994i	−0.999982	−	0.00594968i	$-0.998106\pi$
$631$		−	0.298908i		−	0.0118994i	0.999982	−	0.00594968i	$-0.00189385\pi$
$632$	8.18062	−	28.0582i	0.325407	−	1.11609i
$633$	1.54607	+	7.76929i	0.0614507	+	0.308802i
$634$	13.3700	−	13.1763i	0.530992	−	0.523297i
$635$		0			0
$636$	0.896351	−	2.51980i	0.0355426	−	0.0999165i
$637$	8.77672	+	15.2017i	0.347746	+	0.602314i
$638$	3.85156	+	1.06221i	0.152485	+	0.0420534i
$639$	−4.58533	+	34.8731i	−0.181393	+	1.37956i
$640$		0			0
$641$	12.2453	−	7.06982i	0.483660	−	0.279241i	−0.238281	−	0.971196i	$-0.576584\pi$
$641$	12.2453	−	7.06982i	0.483660	−	0.279241i	0.721940	+	0.691955i	$0.243250\pi$
$642$	−0.511108	−	0.346873i	−0.0201718	−	0.0136900i
$643$	31.6633	+	18.2808i	1.24868	+	0.720925i	0.970846	−	0.239704i	$-0.0770505\pi$
$643$	31.6633	+	18.2808i	1.24868	+	0.720925i	0.277833	+	0.960629i	$0.410384\pi$
$644$	−23.5015	−	42.1136i	−0.926087	−	1.65951i
$645$		0			0
$646$	3.69479	−	0.961168i	0.145369	−	0.0378167i
$647$	−25.4645			−1.00111			−0.500556	−	0.865704i	$-0.666871\pi$
$647$	−25.4645			−1.00111			−0.500556	+	0.865704i	$0.666871\pi$
$648$	−22.3148	+	12.2495i	−0.876607	+	0.481206i
$649$	−5.02220			−0.197139
$650$		0			0
$651$	−0.896989	−	1.02265i	−0.0351558	−	0.0400809i
$652$	−1.30192	−	2.33299i	−0.0509871	−	0.0913668i
$653$	−19.4203	−	11.2123i	−0.759976	−	0.438772i	0.0693112	−	0.997595i	$-0.477920\pi$
$653$	−19.4203	−	11.2123i	−0.759976	−	0.438772i	−0.829287	+	0.558823i	$0.811253\pi$
$654$	−0.930441	−	0.631461i	−0.0363831	−	0.0246921i
$655$		0			0
$656$	9.96964	−	5.37423i	0.389249	−	0.209828i
$657$	2.38914	−	18.1703i	0.0932092	−	0.708890i
$658$	34.2233	+	9.43834i	1.33416	+	0.367945i
$659$	3.28193	+	5.68446i	0.127846	+	0.221435i	0.922842	−	0.385179i	$-0.125860\pi$
$659$	3.28193	+	5.68446i	0.127846	+	0.221435i	−0.794996	+	0.606615i	$0.792527\pi$
$660$		0			0
$661$	−9.44856	+	16.3654i	−0.367506	+	0.636540i	−0.989175	−	0.146741i	$-0.953122\pi$
$661$	−9.44856	+	16.3654i	−0.367506	+	0.636540i	0.621669	+	0.783280i	$0.286455\pi$
$662$	−8.65332	+	8.52792i	−0.336321	+	0.331447i
$663$	1.32287	+	6.64766i	0.0513759	+	0.258174i
$664$	−7.05797	−	2.05781i	−0.273902	−	0.0798587i
$665$		0			0
$666$	−6.02183	−	48.4068i	−0.233341	−	1.87572i
$667$			8.71129i			0.337303i
$668$	0.209314	−	14.3385i	0.00809860	−	0.554774i
$669$	38.9598	+	13.2215i	1.50627	+	0.511173i
$670$		0			0
$671$	4.51290	−	7.81657i	0.174219	−	0.301755i
$672$	19.0163	−	26.3317i	0.733570	−	1.01577i
$673$	15.6611	+	27.1258i	0.603690	+	1.04562i	0.992257	+	0.124201i	$0.0396367\pi$
$673$	15.6611	+	27.1258i	0.603690	+	1.04562i	−0.388567	+	0.921420i	$0.627030\pi$
$674$	−0.396821	+	1.43887i	−0.0152850	+	0.0554231i
$675$		0			0
$676$	−10.9230	−	6.52081i	−0.420115	−	0.250800i
$677$	−35.4936	+	20.4922i	−1.36413	+	0.787580i	−0.990171	−	0.139866i	$-0.955333\pi$
$677$	−35.4936	+	20.4922i	−1.36413	+	0.787580i	−0.373958	+	0.927446i	$0.622000\pi$
$678$	−18.6077	−	38.4294i	−0.714626	−	1.47587i
$679$	17.7249	+	10.2335i	0.680219	+	0.392724i
$680$		0			0
$681$	15.5058	−	45.6910i	0.594185	−	1.75088i
$682$	0.198988	+	0.764922i	0.00761965	+	0.0292904i
$683$	−42.0703			−1.60978			−0.804888	−	0.593427i	$-0.797775\pi$
$683$	−42.0703			−1.60978			−0.804888	+	0.593427i	$0.797775\pi$
$684$	−16.9248	+	6.72595i	−0.647134	+	0.257173i
$685$		0			0
$686$	3.55347	+	13.6597i	0.135672	+	0.521531i
$687$	−28.4027	+	5.65206i	−1.08363	+	0.215639i
$688$	−0.975261	+	33.3968i	−0.0371815	+	1.27324i
$689$	2.94198	+	1.69855i	0.112080	+	0.0647096i
$690$		0			0
$691$	30.3277	−	17.5097i	1.15372	−	0.666101i	0.203930	−	0.978986i	$-0.434629\pi$
$691$	30.3277	−	17.5097i	1.15372	−	0.666101i	0.949791	+	0.312885i	$0.101295\pi$
$692$	−2.64012	+	4.42247i	−0.100362	+	0.168117i
$693$	14.2789	−	18.6150i	0.542412	−	0.707125i
$694$	−2.59554	+	9.41140i	−0.0985255	+	0.357252i
$695$		0			0
$696$	−5.31724	+	2.47949i	−0.201549	+	0.0939848i
$697$	1.25911	−	2.18084i	0.0476922	−	0.0826054i
$698$	30.8018	+	31.2547i	1.16586	+	1.18301i
$699$	2.18678	−	1.91807i	0.0827116	−	0.0725481i
$700$		0			0
$701$			41.5315i			1.56862i	0.620366	+	0.784312i	$0.286984\pi$
$701$			41.5315i			1.56862i	−0.620366	+	0.784312i	$0.713016\pi$
$702$	−10.1772	−	30.6904i	−0.384112	−	1.15834i
$703$		−	34.8993i		−	1.31625i
$704$	−16.7413	+	8.71161i	−0.630961	+	0.328331i
$705$		0			0
$706$	15.4686	−	15.2445i	0.582169	−	0.573732i
$707$	−12.8680	+	22.2881i	−0.483952	+	0.838229i
$708$	5.61466	−	4.78155i	0.211012	−	0.179702i
$709$	−5.69139	−	9.85778i	−0.213745	−	0.370217i	0.739139	−	0.673553i	$-0.235233\pi$
$709$	−5.69139	−	9.85778i	−0.213745	−	0.370217i	−0.952883	+	0.303337i	$0.901899\pi$
$710$		0			0
$711$	11.8676	+	28.6377i	0.445070	+	1.07400i
$712$	9.15538	+	9.56534i	0.343112	+	0.358476i
$713$	−1.49243	+	0.861656i	−0.0558920	+	0.0322693i
$714$	0.524319	−	7.20270i	0.0196221	−	0.269554i
$715$		0			0
$716$	17.7873	−	9.92616i	0.664741	−	0.370958i
$717$	18.3833	−	3.65822i	0.686536	−	0.136619i
$718$	−11.6500	+	3.03065i	−0.434774	+	0.113103i
$719$	−24.0599			−0.897282			−0.448641	−	0.893712i	$-0.648092\pi$
$719$	−24.0599			−0.897282			−0.448641	+	0.893712i	$0.648092\pi$
$720$		0			0
$721$	−43.6278			−1.62478
$722$	13.3944	−	3.48444i	0.498488	−	0.129678i
$723$	6.07442	−	17.8995i	0.225910	−	0.665689i
$724$	7.29213	−	4.06936i	0.271010	−	0.151237i
$725$		0			0
$726$	11.9821	−	5.80181i	0.444698	−	0.215325i
$727$	−4.94944	+	2.85756i	−0.183565	+	0.105981i	−0.588966	−	0.808158i	$-0.700465\pi$
$727$	−4.94944	+	2.85756i	−0.183565	+	0.105981i	0.405402	+	0.914139i	$0.367132\pi$
$728$	28.5270	+	29.8044i	1.05728	+	1.10462i
$729$	10.3202	−	24.9498i	0.382230	−	0.924067i
$730$		0			0
$731$	3.71433	+	6.43341i	0.137380	+	0.237948i
$732$	2.39674	+	13.0353i	0.0885862	+	0.481800i
$733$	12.9269	−	22.3900i	0.477465	−	0.826994i	−0.522201	−	0.852822i	$-0.674889\pi$
$733$	12.9269	−	22.3900i	0.477465	−	0.826994i	0.999666	+	0.0258286i	$0.00822241\pi$
$734$	1.30249	−	1.28361i	0.0480756	−	0.0473790i
$735$		0			0
$736$	−28.0153	−	30.1384i	−1.03266	−	1.11092i
$737$			14.9675i			0.551335i
$738$	−4.67622	+	11.0654i	−0.172134	+	0.407324i
$739$			18.0774i			0.664989i	0.943105	+	0.332495i	$0.107890\pi$
$739$			18.0774i			0.664989i	−0.943105	+	0.332495i	$0.892110\pi$
$740$		0			0
$741$	−4.51489	−	22.6882i	−0.165859	−	0.833472i
$742$	−2.54063	−	2.57799i	−0.0932694	−	0.0946409i
$743$	9.00512	−	15.5973i	0.330366	−	0.572210i	−0.652218	−	0.758032i	$-0.726161\pi$
$743$	9.00512	−	15.5973i	0.330366	−	0.572210i	0.982584	+	0.185821i	$0.0594946\pi$
$744$	−0.950731	−	0.665705i	−0.0348555	−	0.0244059i
$745$		0			0
$746$	6.15788	−	22.3284i	0.225456	−	0.817500i
$747$	7.20374	−	2.98527i	0.263571	−	0.109225i
$748$	−2.15087	+	3.60292i	−0.0786435	+	0.131736i
$749$	−0.723965	+	0.417982i	−0.0264531	+	0.0152727i
$750$		0			0
$751$	−35.2487	−	20.3509i	−1.28624	−	0.742613i	−0.308262	−	0.951302i	$-0.599747\pi$
$751$	−35.2487	−	20.3509i	−1.28624	−	0.742613i	−0.977982	+	0.208689i	$0.933081\pi$
$752$	30.2770	+	0.884158i	1.10409	+	0.0322419i
$753$	5.77649	+	6.58574i	0.210507	+	0.239998i
$754$	−1.87617	−	7.21210i	−0.0683260	−	0.262649i
$755$		0			0
$756$	1.75960	+	34.4057i	0.0639961	+	1.25132i
$757$	−35.4823			−1.28963			−0.644813	−	0.764340i	$-0.723065\pi$
$757$	−35.4823			−1.28963			−0.644813	+	0.764340i	$0.723065\pi$
$758$	−4.19921	−	16.1420i	−0.152522	−	0.586304i
$759$	−19.5986	−	22.3443i	−0.711386	−	0.811046i
$760$		0			0
$761$	−34.0009	−	19.6304i	−1.23253	−	0.711602i	−0.264974	−	0.964256i	$-0.585363\pi$
$761$	−34.0009	−	19.6304i	−1.23253	−	0.711602i	−0.967557	+	0.252654i	$0.918697\pi$
$762$	−14.5346	+	21.4164i	−0.526535	+	0.775835i
$763$	−1.31794	+	0.760910i	−0.0477125	+	0.0275468i
$764$	42.9840	+	25.6606i	1.55511	+	0.928367i
$765$		0			0
$766$	−4.23702	+	15.3634i	−0.153090	+	0.555101i
$767$	4.68371	+	8.11242i	0.169119	+	0.292923i
$768$	10.4221	−	25.6784i	0.376074	−	0.926590i
$769$	3.27941	−	5.68011i	0.118259	−	0.204830i	−0.800819	−	0.598906i	$-0.795602\pi$
$769$	3.27941	−	5.68011i	0.118259	−	0.204830i	0.919078	+	0.394076i	$0.128935\pi$
$770$		0			0
$771$	4.52671	+	22.7476i	0.163025	+	0.819234i
$772$	0.552255	−	37.8308i	0.0198761	−	1.36156i
$773$		−	34.2118i		−	1.23051i	−0.788327	−	0.615256i	$-0.789053\pi$
$773$		−	34.2118i		−	1.23051i	0.788327	−	0.615256i	$-0.210947\pi$
$774$	−21.3720	−	28.2678i	−0.768199	−	1.01607i
$775$		0			0
$776$	16.7647	+	4.88790i	0.601817	+	0.175465i
$777$	−62.5146	−	21.2151i	−2.24270	−	0.761089i
$778$	−20.3057	+	20.0115i	−0.727995	+	0.717445i
$779$	−4.29729	+	7.44313i	−0.153967	+	0.266678i
$780$		0			0
$781$	−13.8292	−	23.9528i	−0.494847	−	0.857099i
$782$	−8.81973	−	2.43237i	−0.315393	−	0.0869813i
$783$	2.75092	−	5.58176i	0.0983097	−	0.199476i
$784$	−7.57191	−	14.0465i	−0.270425	−	0.501661i
$785$		0			0
$786$	35.8431	−	17.3554i	1.27848	−	0.619047i
$787$	15.0505	+	8.68943i	0.536494	+	0.309745i	0.743657	−	0.668562i	$-0.233090\pi$
$787$	15.0505	+	8.68943i	0.536494	+	0.309745i	−0.207163	+	0.978306i	$0.566423\pi$
$788$	−5.12079	−	9.17623i	−0.182420	−	0.326890i
$789$	−6.06225	+	17.8636i	−0.215822	+	0.635962i
$790$		0			0
$791$	−57.7846			−2.05458
$792$	8.06026	−	18.3225i	0.286409	−	0.651063i
$793$	−16.8349			−0.597826
$794$	7.00561	−	1.82245i	0.248620	−	0.0646764i
$795$		0			0
$796$	18.3702	+	32.9185i	0.651113	+	1.16677i
$797$	6.07314	+	3.50633i	0.215122	+	0.124201i	0.603689	−	0.797220i	$-0.293697\pi$
$797$	6.07314	+	3.50633i	0.215122	+	0.124201i	−0.388568	+	0.921420i	$0.627030\pi$
$798$	−1.78948	+	24.5825i	−0.0633468	+	0.870211i
$799$	5.83244	−	3.36736i	0.206337	−	0.119129i
$800$		0			0
$801$	−13.9241	−	1.83082i	−0.491982	−	0.0646889i
$802$	15.0856	+	4.16042i	0.532692	+	0.146910i
$803$	7.20555	+	12.4804i	0.254278	+	0.440423i
$804$	−14.2503	−	16.7332i	−0.502569	−	0.590134i
$805$		0			0
$806$	1.05001	−	1.03479i	0.0369851	−	0.0364491i
$807$	27.9984	−	24.5580i	0.985592	−	0.864483i
$808$	−6.14626	+	21.0807i	−0.216225	+	0.741616i
$809$		−	38.9234i		−	1.36847i	−0.729261	−	0.684236i	$-0.760136\pi$
$809$		−	38.9234i		−	1.36847i	0.729261	−	0.684236i	$-0.239864\pi$
$810$		0			0
$811$		−	35.7891i		−	1.25673i	−0.777920	−	0.628363i	$-0.783725\pi$
$811$		−	35.7891i		−	1.25673i	0.777920	−	0.628363i	$-0.216275\pi$
$812$	−0.115896	+	7.93917i	−0.00406716	+	0.278610i
$813$	−24.6683	+	21.6371i	−0.865154	+	0.758845i
$814$	26.9244	+	27.3203i	0.943700	+	0.957576i
$815$		0			0
$816$	−1.02567	−	6.07575i	−0.0359057	−	0.212694i
$817$	−12.6769	−	21.9570i	−0.443507	−	0.768177i
$818$	6.07829	−	22.0398i	0.212523	−	0.770604i
$819$	−43.3856	−	5.70460i	−1.51601	−	0.199335i
$820$		0			0
$821$	−27.8765	+	16.0945i	−0.972895	+	0.561701i	−0.900118	−	0.435647i	$-0.856520\pi$
$821$	−27.8765	+	16.0945i	−0.972895	+	0.561701i	−0.0727775	+	0.997348i	$0.523186\pi$
$822$	−32.2278	−	2.34601i	−1.12407	−	0.0818265i
$823$	−14.9963	−	8.65813i	−0.522739	−	0.301804i	0.215315	−	0.976545i	$-0.430922\pi$
$823$	−14.9963	−	8.65813i	−0.522739	−	0.301804i	−0.738055	+	0.674741i	$0.764255\pi$
$824$	−36.1579	+	8.84475i	−1.25962	+	0.308122i
$825$		0			0
$826$	−2.51276	−	9.65921i	−0.0874302	−	0.336087i
$827$	15.5363			0.540249			0.270124	−	0.962825i	$-0.412935\pi$
$827$	15.5363			0.540249			0.270124	+	0.962825i	$0.412935\pi$
$828$	43.1843	+	6.32067i	1.50076	+	0.219658i
$829$	27.4645			0.953882			0.476941	−	0.878935i	$-0.341746\pi$
$829$	27.4645			0.953882			0.476941	+	0.878935i	$0.341746\pi$
$830$		0			0
$831$	−10.3875	+	30.6087i	−0.360337	+	1.06180i
$832$	29.6849	+	18.9180i	1.02914	+	0.655862i
$833$	−3.07266	−	1.77400i	−0.106461	−	0.0614654i
$834$	−6.92172	−	14.2950i	−0.239679	−	0.494995i
$835$		0			0
$836$	7.34082	−	12.2966i	0.253888	−	0.425287i
$837$	1.22837	−	0.0808146i	0.0424588	−	0.00279336i
$838$	2.74894	−	9.96761i	0.0949605	−	0.344325i
$839$	−6.91476	−	11.9767i	−0.238724	−	0.413482i	0.721624	−	0.692285i	$-0.243396\pi$
$839$	−6.91476	−	11.9767i	−0.238724	−	0.413482i	−0.960348	+	0.278803i	$0.910062\pi$
$840$		0			0
$841$	−13.7829	+	23.8727i	−0.475272	+	0.823196i
$842$	29.7268	+	30.1639i	1.02445	+	1.03952i
$843$	−11.0734	−	3.75790i	−0.381387	−	0.129429i
$844$	9.14613	+	0.133515i	0.314823	+	0.00459579i
$845$		0			0
$846$	−25.6272	+	19.3755i	−0.881082	+	0.666144i
$847$		−	18.0170i		−	0.619070i
$848$	−2.62826	−	1.62152i	−0.0902550	−	0.0556832i
$849$	−1.78142	−	8.95196i	−0.0611380	−	0.307230i
$850$		0			0
$851$	−41.8169	+	72.4290i	−1.43346	+	2.48283i
$852$	38.2656	+	13.6120i	1.31096	+	0.466339i
$853$	−18.0633	−	31.2866i	−0.618476	−	1.07123i	−0.989764	−	0.142714i	$-0.954417\pi$
$853$	−18.0633	−	31.2866i	−0.618476	−	1.07123i	0.371288	−	0.928518i	$-0.378916\pi$
$854$	17.2916	+	4.76879i	0.591705	+	0.163185i
$855$		0			0
$856$	−0.515270	+	0.493186i	−0.0176116	+	0.0168568i
$857$	−6.41713	+	3.70493i	−0.219205	+	0.126558i	−0.605582	−	0.795783i	$-0.707060\pi$
$857$	−6.41713	+	3.70493i	−0.219205	+	0.126558i	0.386377	+	0.922341i	$0.373726\pi$
$858$	21.0381	+	14.2779i	0.718228	+	0.487439i
$859$	−35.7586	−	20.6452i	−1.22007	−	0.704407i	−0.255136	−	0.966905i	$-0.582120\pi$
$859$	−35.7586	−	20.6452i	−1.22007	−	0.704407i	−0.964932	+	0.262499i	$0.915453\pi$
$860$		0			0
$861$	10.7205	+	12.2223i	0.365352	+	0.416535i
$862$	42.0870	−	10.9486i	1.43349	−	0.372910i
$863$	46.7922			1.59282			0.796412	−	0.604754i	$-0.206729\pi$
$863$	46.7922			1.59282			0.796412	+	0.604754i	$0.206729\pi$
$864$	8.43347	+	28.1581i	0.286912	+	0.957957i
$865$		0			0
$866$	−40.2022	+	10.4583i	−1.36613	+	0.355387i
$867$	18.5128	+	21.1063i	0.628726	+	0.716807i
$868$	−1.37161	+	0.765428i	−0.0465556	+	0.0259803i
$869$	−21.1104	−	12.1881i	−0.716120	−	0.413452i
$870$		0			0
$871$	24.1772	−	13.9587i	0.819213	−	0.472973i
$872$	−0.938018	+	0.897815i	−0.0317653	+	0.0304039i
$873$	−17.1109	+	7.09086i	−0.579118	+	0.239989i
$874$	30.1014	+	8.30157i	1.01819	+	0.280805i
$875$		0			0
$876$	−19.9379	−	7.09239i	−0.673640	−	0.239630i
$877$	7.07692	−	12.2576i	0.238970	−	0.413909i	−0.721449	−	0.692468i	$-0.756523\pi$
$877$	7.07692	−	12.2576i	0.238970	−	0.413909i	0.960419	+	0.278559i	$0.0898567\pi$
$878$	7.87903	−	7.76485i	0.265904	−	0.262051i
$879$	7.53520	+	37.8658i	0.254156	+	1.27718i
$880$		0			0
$881$		−	13.5705i		−	0.457200i	−0.973520	−	0.228600i	$-0.926585\pi$
$881$		−	13.5705i		−	0.457200i	0.973520	−	0.228600i	$-0.0734148\pi$
$882$	15.5904	+	6.58846i	0.524956	+	0.221845i
$883$			46.0353i			1.54921i	0.632444	+	0.774606i	$0.282052\pi$
$883$			46.0353i			1.54921i	−0.632444	+	0.774606i	$0.717948\pi$
$884$	7.82574	+	0.114240i	0.263208	+	0.00384232i
$885$		0			0
$886$	−26.5083	−	26.8981i	−0.890565	−	0.903660i
$887$	9.90855	−	17.1621i	0.332696	−	0.576247i	−0.650343	−	0.759641i	$-0.725375\pi$
$887$	9.90855	−	17.1621i	0.332696	−	0.576247i	0.983040	+	0.183393i	$0.0587082\pi$
$888$	−56.1118	−	4.90898i	−1.88299	−	0.164735i
$889$	17.5143	+	30.3356i	0.587409	+	1.01742i
$890$		0			0
$891$	5.50178	+	20.5061i	0.184316	+	0.686980i
$892$	24.3514	−	40.7910i	0.815346	−	1.36578i
$893$	−19.9059	+	11.4927i	−0.666125	+	0.384587i
$894$	−8.93676	−	18.4566i	−0.298890	−	0.617280i
$895$		0			0
$896$	−25.1312	−	27.8399i	−0.839576	−	0.930064i
$897$	−17.8153	+	52.4962i	−0.594835	+	1.75280i
$898$	−8.48960	−	32.6345i	−0.283302	−	1.08903i
$899$	0.283722			0.00946265
$900$		0			0
$901$	−0.686641			−0.0228753
$902$	−2.37823	−	9.14204i	−0.0791863	−	0.304396i
$903$	−47.0374	+	9.36031i	−1.56531	+	0.311492i
$904$	−47.8907	+	11.7148i	−1.59282	+	0.389628i
$905$		0			0
$906$	−40.0600	−	2.91616i	−1.33091	−	0.0968829i
$907$	−42.3752	+	24.4653i	−1.40705	+	0.812358i	−0.995102	−	0.0988513i	$-0.968483\pi$
$907$	−42.3752	+	24.4653i	−1.40705	+	0.812358i	−0.411943	+	0.911209i	$0.635150\pi$
$908$	−47.8386	−	28.5587i	−1.58758	−	0.947752i
$909$	−8.91637	−	21.5161i	−0.295737	−	0.713643i
$910$		0			0
$911$	−16.0978	−	27.8822i	−0.533343	−	0.923778i	−0.999242	−	0.0389396i	$-0.987602\pi$
$911$	−16.0978	−	27.8822i	−0.533343	−	0.923778i	0.465898	−	0.884838i	$-0.345731\pi$
$912$	3.50058	+	20.7363i	0.115916	+	0.686647i
$913$	−3.06588	+	5.31026i	−0.101466	+	0.175744i
$914$	−15.6406	−	15.8705i	−0.517343	−	0.524951i
$915$		0			0
$916$	−0.488101	+	33.4361i	−0.0161273	+	1.10476i
$917$		−	53.8956i		−	1.77979i
$918$	4.88313	+	4.34370i	0.161167	+	0.143363i
$919$			37.8553i			1.24873i	0.781133	+	0.624365i	$0.214642\pi$
$919$			37.8553i			1.24873i	−0.781133	+	0.624365i	$0.785358\pi$
$920$		0			0
$921$	0.540923	−	0.474455i	0.0178240	−	0.0156338i
$922$	10.7530	−	10.5972i	0.354132	−	0.349000i
$923$	−25.7942	+	44.6768i	−0.849026	+	1.47056i
$924$	−17.5643	−	20.6246i	−0.577822	−	0.678498i
$925$		0			0
$926$	8.66098	+	2.38859i	0.284618	+	0.0784939i
$927$	24.0300	−	31.3271i	0.789248	−	1.02892i
$928$	1.51347	+	6.60333i	0.0496822	+	0.216765i
$929$	−14.4535	+	8.34474i	−0.474205	+	0.273782i	−0.717998	−	0.696045i	$-0.754941\pi$
$929$	−14.4535	+	8.34474i	−0.474205	+	0.273782i	0.243794	+	0.969827i	$0.421608\pi$
$930$		0			0
$931$	10.4868	+	6.05458i	0.343693	+	0.198431i
$932$	−1.63675	−	2.93298i	−0.0536135	−	0.0960730i
$933$	0.966795	−	0.192390i	0.0316514	−	0.00629855i
$934$	−10.6234	+	2.76360i	−0.347609	+	0.0904277i
$935$		0			0
$936$	−37.1136	+	4.06778i	−1.21310	+	0.132960i
$937$	−41.7514			−1.36396			−0.681979	−	0.731372i	$-0.738880\pi$
$937$	−41.7514			−1.36396			−0.681979	+	0.731372i	$0.738880\pi$
$938$	−28.7870	+	7.48870i	−0.939929	+	0.244515i
$939$	−15.6200	+	46.0273i	−0.509739	+	1.50204i
$940$		0			0
$941$	9.78882	+	5.65158i	0.319106	+	0.184236i	0.650994	−	0.759083i	$-0.274352\pi$
$941$	9.78882	+	5.65158i	0.319106	+	0.184236i	−0.331888	+	0.943319i	$0.607686\pi$
$942$	23.6165	−	11.4352i	0.769466	−	0.372580i
$943$	17.8369	−	10.2982i	0.580851	−	0.335354i
$944$	−4.04076	−	7.49595i	−0.131516	−	0.243972i
$945$		0			0
$946$	26.8634	+	7.40858i	0.873404	+	0.240874i
$947$	−2.56935	−	4.45025i	−0.0834928	−	0.144614i	0.821255	−	0.570561i	$-0.193274\pi$
$947$	−2.56935	−	4.45025i	−0.0834928	−	0.144614i	−0.904748	+	0.425947i	$0.859941\pi$
$948$	35.2048	−	6.47294i	1.14340	−	0.210231i
$949$	13.4398	−	23.2784i	0.436274	−	0.755649i
$950$		0			0
$951$	21.7709	+	7.38824i	0.705970	+	0.239580i
$952$	−8.00564	−	2.33412i	−0.259464	−	0.0756491i
$953$		−	22.9718i		−	0.744131i	−0.928206	−	0.372066i	$-0.878650\pi$
$953$		−	22.9718i		−	0.744131i	0.928206	−	0.372066i	$-0.121350\pi$
$954$	3.25050	−	0.404364i	0.105239	−	0.0130918i
$955$		0			0
$956$	0.315917	−	21.6411i	0.0102175	−	0.699923i
$957$	0.955025	+	4.79919i	0.0308716	+	0.155136i
$958$	−7.07906	−	7.18315i	−0.228714	−	0.232077i
$959$	−21.8654	+	37.8720i	−0.706072	+	1.22295i
$960$		0			0
$961$	−15.4719	−	26.7982i	−0.499095	−	0.864457i
$962$	19.0211	−	68.9703i	0.613265	−	2.22369i
$963$	0.0986235	−	0.750067i	0.00317810	−	0.0241706i
$964$	−18.7408	−	11.1879i	−0.603601	−	0.360337i
$965$		0			0
$966$	33.1690	−	48.8736i	1.06719	−	1.57248i
$967$	−36.5239	−	21.0871i	−1.17453	−	0.678115i	−0.219787	−	0.975548i	$-0.570536\pi$
$967$	−36.5239	−	21.0871i	−1.17453	−	0.678115i	−0.954743	+	0.297433i	$0.903869\pi$
$968$	−3.65262	−	14.9321i	−0.117400	−	0.479936i
$969$	3.08324	+	3.51519i	0.0990481	+	0.112924i
$970$		0			0
$971$	29.9678			0.961712			0.480856	−	0.876799i	$-0.340326\pi$
$971$	29.9678			0.961712			0.480856	+	0.876799i	$0.340326\pi$
$972$	−25.6743	−	17.6870i	−0.823504	−	0.567311i
$973$	−21.4947			−0.689090
$974$	−5.37946	−	20.6789i	−0.172369	−	0.662596i
$975$		0			0
$976$	15.2977	+	0.446727i	0.489667	+	0.0142994i
$977$	−32.1452	−	18.5590i	−1.02842	−	0.593756i	−0.111885	−	0.993721i	$-0.535689\pi$
$977$	−32.1452	−	18.5590i	−1.02842	−	0.593756i	−0.916530	+	0.399965i	$0.869022\pi$
$978$	1.83748	−	2.70747i	0.0587560	−	0.0865755i
$979$	9.56383	−	5.52168i	0.305661	−	0.176474i
$980$		0			0
$981$	0.179538	−	1.36545i	0.00573221	−	0.0435955i
$982$	11.0701	−	40.1402i	0.353262	−	1.28092i
$983$	14.3704	+	24.8903i	0.458345	+	0.793876i	0.998874	−	0.0474493i	$-0.0151093\pi$
$983$	14.3704	+	24.8903i	0.458345	+	0.793876i	−0.540529	+	0.841325i	$0.681776\pi$
$984$	11.3628	+	7.95624i	0.362232	+	0.253636i
$985$		0			0
$986$	1.05729	+	1.07284i	0.0336710	+	0.0341661i
$987$	8.48593	+	42.6434i	0.270110	+	1.35735i
$988$	−26.7089	−	0.389897i	−0.849724	−	0.0124043i
$989$			60.7584i			1.93201i
$990$		0			0
$991$		−	5.20653i		−	0.165391i	−0.996575	−	0.0826954i	$-0.973647\pi$
$991$		−	5.20653i		−	0.165391i	0.996575	−	0.0826954i	$-0.0263529\pi$
$992$	−0.981591	+	0.912442i	−0.0311655	+	0.0289701i
$993$	−14.0905	−	4.78180i	−0.447149	−	0.151746i
$994$	39.1493	−	38.5820i	1.24174	−	1.22375i
$995$		0			0
$996$	−1.62825	−	8.85568i	−0.0515931	−	0.280603i
$997$	10.4918	+	18.1724i	0.332279	+	0.575525i	0.982958	−	0.183828i	$-0.0588490\pi$
$997$	10.4918	+	18.1724i	0.332279	+	0.575525i	−0.650679	+	0.759353i	$0.725516\pi$
$998$	28.4612	+	7.84924i	0.900924	+	0.248463i
$999$	49.6663	−	33.2036i	1.57137	−	1.05051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.r.g.851.22		48
4.3	odd	2	inner	900.2.r.g.851.18		48
5.2	odd	4		180.2.n.d.59.15	yes	48
5.3	odd	4		180.2.n.d.59.10	yes	48
5.4	even	2	inner	900.2.r.g.851.3		48
9.2	odd	6	inner	900.2.r.g.551.18		48
15.2	even	4		540.2.n.d.179.10		48
15.8	even	4		540.2.n.d.179.15		48
20.3	even	4		180.2.n.d.59.6	✓	48
20.7	even	4		180.2.n.d.59.19	yes	48
20.19	odd	2	inner	900.2.r.g.851.7		48
36.11	even	6	inner	900.2.r.g.551.22		48
45.2	even	12		180.2.n.d.119.6	yes	48
45.7	odd	12		540.2.n.d.359.19		48
45.29	odd	6	inner	900.2.r.g.551.7		48
45.38	even	12		180.2.n.d.119.19	yes	48
45.43	odd	12		540.2.n.d.359.6		48
60.23	odd	4		540.2.n.d.179.19		48
60.47	odd	4		540.2.n.d.179.6		48
180.7	even	12		540.2.n.d.359.15		48
180.43	even	12		540.2.n.d.359.10		48
180.47	odd	12		180.2.n.d.119.10	yes	48
180.83	odd	12		180.2.n.d.119.15	yes	48
180.119	even	6	inner	900.2.r.g.551.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.6	✓	48	20.3	even	4
180.2.n.d.59.10	yes	48	5.3	odd	4
180.2.n.d.59.15	yes	48	5.2	odd	4
180.2.n.d.59.19	yes	48	20.7	even	4
180.2.n.d.119.6	yes	48	45.2	even	12
180.2.n.d.119.10	yes	48	180.47	odd	12
180.2.n.d.119.15	yes	48	180.83	odd	12
180.2.n.d.119.19	yes	48	45.38	even	12
540.2.n.d.179.6		48	60.47	odd	4
540.2.n.d.179.10		48	15.2	even	4
540.2.n.d.179.15		48	15.8	even	4
540.2.n.d.179.19		48	60.23	odd	4
540.2.n.d.359.6		48	45.43	odd	12
540.2.n.d.359.10		48	180.43	even	12
540.2.n.d.359.15		48	180.7	even	12
540.2.n.d.359.19		48	45.7	odd	12
900.2.r.g.551.3		48	180.119	even	6	inner
900.2.r.g.551.7		48	45.29	odd	6	inner
900.2.r.g.551.18		48	9.2	odd	6	inner
900.2.r.g.551.22		48	36.11	even	6	inner
900.2.r.g.851.3		48	5.4	even	2	inner
900.2.r.g.851.7		48	20.19	odd	2	inner
900.2.r.g.851.18		48	4.3	odd	2	inner
900.2.r.g.851.22		48	1.1	even	1	trivial

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+(1.36866 - 0.356046i) q^{2} +(1.14213 + 1.30213i) q^{3} +(1.74646 - 0.974612i) q^{4} +(2.02680 + 1.37553i) q^{6} +(2.87089 - 1.65751i) q^{7} +(2.04331 - 1.95573i) q^{8} +(-0.391092 + 2.97440i) q^{9} +(-1.17952 - 2.04298i) q^{11} +(3.26375 + 1.16099i) q^{12} +(-2.20004 + 3.81058i) q^{13} +(3.33912 - 3.29074i) q^{14} +(2.10026 - 3.40425i) q^{16} -0.889368i q^{17} +(0.523750 + 4.21019i) q^{18} +3.03537i q^{19} +(5.43722 + 1.84519i) q^{21} +(-2.34176 - 2.37619i) q^{22} +(3.63703 - 6.29952i) q^{23} +(4.88034 + 0.426960i) q^{24} +(-1.65437 + 5.99870i) q^{26} +(-4.31973 + 2.88789i) q^{27} +(3.39848 - 5.69278i) q^{28} +(-1.03714 + 0.598791i) q^{29} +(-0.205172 - 0.118456i) q^{31} +(1.66248 - 5.40705i) q^{32} +(1.31308 - 3.86923i) q^{33} +(-0.316656 - 1.21724i) q^{34} +(2.21586 + 5.57584i) q^{36} -11.4975 q^{37} +(1.08073 + 4.15440i) q^{38} +(-7.47460 + 1.48743i) q^{39} +(2.45213 + 1.41574i) q^{41} +(8.09868 + 0.589541i) q^{42} +(-7.23369 + 4.17637i) q^{43} +(-4.05110 - 2.41842i) q^{44} +(2.73494 - 9.91686i) q^{46} +(3.78624 + 6.55796i) q^{47} +(6.83154 - 1.15326i) q^{48} +(1.99467 - 3.45488i) q^{49} +(1.15807 - 1.01577i) q^{51} +(-0.128451 + 8.79922i) q^{52} -0.772055i q^{53} +(-4.88403 + 5.49056i) q^{54} +(2.62447 - 9.00150i) q^{56} +(-3.95246 + 3.46678i) q^{57} +(-1.20629 + 1.18881i) q^{58} +(1.06446 - 1.84370i) q^{59} +(1.91303 + 3.31346i) q^{61} +(-0.322986 - 0.0890754i) q^{62} +(3.80731 + 9.18741i) q^{63} +(0.350216 - 7.99233i) q^{64} +(0.419529 - 5.76318i) q^{66} +(-5.49472 - 3.17238i) q^{67} +(-0.866788 - 1.55325i) q^{68} +(12.3568 - 2.45896i) q^{69} +11.7244 q^{71} +(5.01801 + 6.84248i) q^{72} -6.10889 q^{73} +(-15.7362 + 4.09365i) q^{74} +(2.95831 + 5.30117i) q^{76} +(-6.77253 - 3.91012i) q^{77} +(-9.70059 + 4.69708i) q^{78} +(8.94873 - 5.16655i) q^{79} +(-8.69409 - 2.32653i) q^{81} +(3.86020 + 1.06459i) q^{82} +(-1.29963 - 2.25103i) q^{83} +(11.2942 - 2.07662i) q^{84} +(-8.41349 + 8.29156i) q^{86} +(-1.96425 - 0.666593i) q^{87} +(-6.40565 - 1.86763i) q^{88} +4.68130i q^{89} +14.5863i q^{91} +(0.212351 - 14.5466i) q^{92} +(-0.0800869 - 0.402452i) q^{93} +(7.51702 + 7.62755i) q^{94} +(8.93945 - 4.01077i) q^{96} +(3.08700 + 5.34684i) q^{97} +(1.49994 - 5.43875i) q^{98} +(6.53795 - 2.70936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{4} + 12 q^{9} + 42 q^{14} + 30 q^{16} - 12 q^{21} + 6 q^{24} + 4 q^{34} + 96 q^{36} + 96 q^{41} + 4 q^{46} - 32 q^{49} + 30 q^{54} + 6 q^{56} + 8 q^{61} + 20 q^{64} + 36 q^{66} + 96 q^{69} - 72 q^{74}+ \cdots + 54 q^{96}+O(q^{100}) \) 48 * q + 2 * q^4 + 12 * q^9 + 42 * q^14 + 30 * q^16 - 12 * q^21 + 6 * q^24 + 4 * q^34 + 96 * q^36 + 96 * q^41 + 4 * q^46 - 32 * q^49 + 30 * q^54 + 6 * q^56 + 8 * q^61 + 20 * q^64 + 36 * q^66 + 96 * q^69 - 72 * q^74 + 36 * q^81 + 6 * q^84 + 108 * q^86 + 62 * q^94 + 54 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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