LMFDB - Embedded newform 900.2.r.g.851.4

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			851.4
Character	$\chi$	$=$	900.851
Dual form			900.2.r.g.551.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34329 - 0.442228i) q^{2} +(1.72840 - 0.112475i) q^{3} +(1.60887 + 1.18808i) q^{4} +(-2.37148 - 0.613258i) q^{6} +(-0.993605 + 0.573658i) q^{7} +(-1.63578 - 2.30743i) q^{8} +(2.97470 - 0.388803i) q^{9} +(0.629615 + 1.09053i) q^{11} +(2.91439 + 1.87252i) q^{12} +(-2.53890 + 4.39750i) q^{13} +(1.58839 - 0.331191i) q^{14} +(1.17692 + 3.82294i) q^{16} +3.29816i q^{17} +(-4.16783 - 0.793219i) q^{18} +3.62414i q^{19} +(-1.65282 + 1.10326i) q^{21} +(-0.363497 - 1.74333i) q^{22} +(1.78942 - 3.09936i) q^{23} +(-3.08680 - 3.80416i) q^{24} +(5.35518 - 4.78436i) q^{26} +(5.09772 - 1.00658i) q^{27} +(-2.28013 - 0.257544i) q^{28} +(0.184856 - 0.106727i) q^{29} +(9.12339 + 5.26739i) q^{31} +(0.109664 - 5.65579i) q^{32} +(1.21088 + 1.81404i) q^{33} +(1.45854 - 4.43039i) q^{34} +(5.24783 + 2.90866i) q^{36} -4.72925 q^{37} +(1.60269 - 4.86827i) q^{38} +(-3.89361 + 7.88619i) q^{39} +(5.81019 + 3.35452i) q^{41} +(2.70811 - 0.751083i) q^{42} +(-2.45255 + 1.41598i) q^{43} +(-0.282666 + 2.50255i) q^{44} +(-3.77433 + 3.37202i) q^{46} +(0.534497 + 0.925776i) q^{47} +(2.46417 + 6.47517i) q^{48} +(-2.84183 + 4.92220i) q^{49} +(0.370961 + 5.70053i) q^{51} +(-9.30936 + 4.05858i) q^{52} -9.12493i q^{53} +(-7.29287 - 0.902219i) q^{54} +(2.94899 + 1.35430i) q^{56} +(0.407625 + 6.26394i) q^{57} +(-0.295514 + 0.0616167i) q^{58} +(4.87018 - 8.43539i) q^{59} +(-5.24521 - 9.08497i) q^{61} +(-9.92600 - 11.1103i) q^{62} +(-2.73264 + 2.09278i) q^{63} +(-2.64846 + 7.54889i) q^{64} +(-0.824347 - 2.97228i) q^{66} +(12.8589 + 7.42407i) q^{67} +(-3.91849 + 5.30631i) q^{68} +(2.74422 - 5.55818i) q^{69} -9.68598 q^{71} +(-5.76308 - 6.22791i) q^{72} -9.08215 q^{73} +(6.35277 + 2.09141i) q^{74} +(-4.30577 + 5.83076i) q^{76} +(-1.25118 - 0.722368i) q^{77} +(8.71775 - 8.87159i) q^{78} +(5.78563 - 3.34033i) q^{79} +(8.69767 - 2.31314i) q^{81} +(-6.32133 - 7.07552i) q^{82} +(2.84920 + 4.93496i) q^{83} +(-3.96994 - 0.188680i) q^{84} +(3.92068 - 0.817489i) q^{86} +(0.307501 - 0.205258i) q^{87} +(1.48640 - 3.23665i) q^{88} +2.26303i q^{89} -5.82584i q^{91} +(6.56123 - 2.86049i) q^{92} +(16.3613 + 8.07798i) q^{93} +(-0.308582 - 1.47996i) q^{94} +(-0.446593 - 9.78778i) q^{96} +(3.86692 + 6.69770i) q^{97} +(5.99415 - 5.35521i) q^{98} +(2.29692 + 2.99919i) 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 $

$2$	−1.34329	−	0.442228i	−0.949851	−	0.312702i
$2$	−1.34329	−	0.442228i	−0.949851	−	0.312702i
$3$	1.72840	−	0.112475i	0.997889	−	0.0649375i
$3$	1.72840	−	0.112475i	0.997889	−	0.0649375i
$4$	1.60887	+	1.18808i	0.804435	+	0.594041i
$5$		0			0
$5$		0			0
$6$	−2.37148	−	0.613258i	−0.968152	−	0.250361i
$7$	−0.993605	+	0.573658i	−0.375547	+	0.216822i	−0.675879	−	0.737012i	$-0.736236\pi$
$7$	−0.993605	+	0.573658i	−0.375547	+	0.216822i	0.300332	+	0.953835i	$0.402903\pi$
$8$	−1.63578	−	2.30743i	−0.578335	−	0.815799i
$9$	2.97470	−	0.388803i	0.991566	−	0.129601i
$10$		0			0
$11$	0.629615	+	1.09053i	0.189836	+	0.328806i	0.945196	−	0.326505i	$-0.105871\pi$
$11$	0.629615	+	1.09053i	0.189836	+	0.328806i	−0.755359	+	0.655311i	$0.772538\pi$
$12$	2.91439	+	1.87252i	0.841312	+	0.540550i
$13$	−2.53890	+	4.39750i	−0.704164	+	1.21965i	0.262828	+	0.964843i	$0.415345\pi$
$13$	−2.53890	+	4.39750i	−0.704164	+	1.21965i	−0.966992	+	0.254805i	$0.917989\pi$
$14$	1.58839	−	0.331191i	0.424515	−	0.0885145i
$15$		0			0
$16$	1.17692	+	3.82294i	0.294230	+	0.955735i
$17$			3.29816i			0.799922i	0.916532	+	0.399961i	$0.130976\pi$
$17$			3.29816i			0.799922i	−0.916532	+	0.399961i	$0.869024\pi$
$18$	−4.16783	−	0.793219i	−0.982367	−	0.186964i
$19$			3.62414i			0.831434i	0.909494	+	0.415717i	$0.136469\pi$
$19$			3.62414i			0.831434i	−0.909494	+	0.415717i	$0.863531\pi$
$20$		0			0
$21$	−1.65282	+	1.10326i	−0.360675	+	0.240752i
$22$	−0.363497	−	1.74333i	−0.0774978	−	0.371679i
$23$	1.78942	−	3.09936i	0.373119	−	0.646261i	−0.616924	−	0.787022i	$-0.711622\pi$
$23$	1.78942	−	3.09936i	0.373119	−	0.646261i	0.990044	+	0.140761i	$0.0449549\pi$
$24$	−3.08680	−	3.80416i	−0.630090	−	0.776522i
$25$		0			0
$26$	5.35518	−	4.78436i	1.05024	−	0.938290i
$27$	5.09772	−	1.00658i	0.981057	−	0.193717i
$28$	−2.28013	−	0.257544i	−0.430905	−	0.0486713i
$29$	0.184856	−	0.106727i	0.0343270	−	0.0198187i	−0.482738	−	0.875765i	$-0.660358\pi$
$29$	0.184856	−	0.106727i	0.0343270	−	0.0198187i	0.517065	+	0.855946i	$0.327024\pi$
$30$		0			0
$31$	9.12339	+	5.26739i	1.63861	+	0.946052i	0.981313	+	0.192420i	$0.0616337\pi$
$31$	9.12339	+	5.26739i	1.63861	+	0.946052i	0.657297	+	0.753632i	$0.271700\pi$
$32$	0.109664	−	5.65579i	0.0193860	−	0.999812i
$33$	1.21088	+	1.81404i	0.210787	+	0.315784i
$34$	1.45854	−	4.43039i	0.250137	−	0.759806i
$35$		0			0
$36$	5.24783	+	2.90866i	0.874638	+	0.484776i
$37$	−4.72925			−0.777484			−0.388742	−	0.921347i	$-0.627090\pi$
$37$	−4.72925			−0.777484			−0.388742	+	0.921347i	$0.627090\pi$
$38$	1.60269	−	4.86827i	0.259991	−	0.789738i
$39$	−3.89361	+	7.88619i	−0.623477	+	1.26280i
$40$		0			0
$41$	5.81019	+	3.35452i	0.907399	+	0.523887i	0.879594	−	0.475726i	$-0.157815\pi$
$41$	5.81019	+	3.35452i	0.907399	+	0.523887i	0.0278059	+	0.999613i	$0.491148\pi$
$42$	2.70811	−	0.751083i	0.417871	−	0.115895i
$43$	−2.45255	+	1.41598i	−0.374010	+	0.215935i	−0.675209	−	0.737626i	$-0.735947\pi$
$43$	−2.45255	+	1.41598i	−0.374010	+	0.215935i	0.301199	+	0.953561i	$0.402613\pi$
$44$	−0.282666	+	2.50255i	−0.0426135	+	0.377273i
$45$		0			0
$46$	−3.77433	+	3.37202i	−0.556495	+	0.497177i
$47$	0.534497	+	0.925776i	0.0779644	+	0.135038i	0.902372	−	0.430959i	$-0.141825\pi$
$47$	0.534497	+	0.925776i	0.0779644	+	0.135038i	−0.824407	+	0.565997i	$0.808491\pi$
$48$	2.46417	+	6.47517i	0.355672	+	0.934611i
$49$	−2.84183	+	4.92220i	−0.405976	+	0.703171i
$50$		0			0
$51$	0.370961	+	5.70053i	0.0519449	+	0.798233i
$52$	−9.30936	+	4.05858i	−1.29098	+	0.562824i
$53$		−	9.12493i		−	1.25341i	−0.779258	−	0.626703i	$-0.784404\pi$
$53$		−	9.12493i		−	1.25341i	0.779258	−	0.626703i	$-0.215596\pi$
$54$	−7.29287	−	0.902219i	−0.992434	−	0.122776i
$55$		0			0
$56$	2.94899	+	1.35430i	0.394076	+	0.180975i
$57$	0.407625	+	6.26394i	0.0539912	+	0.829679i
$58$	−0.295514	+	0.0616167i	−0.0388028	+	0.00809067i
$59$	4.87018	−	8.43539i	0.634043	−	1.09819i	−0.352674	−	0.935746i	$-0.614728\pi$
$59$	4.87018	−	8.43539i	0.634043	−	1.09819i	0.986717	−	0.162449i	$-0.0519391\pi$
$60$		0			0
$61$	−5.24521	−	9.08497i	−0.671580	−	1.16321i	−0.977456	−	0.211140i	$-0.932282\pi$
$61$	−5.24521	−	9.08497i	−0.671580	−	1.16321i	0.305876	−	0.952072i	$-0.401051\pi$
$62$	−9.92600	−	11.1103i	−1.26060	−	1.41101i
$63$	−2.73264	+	2.09278i	−0.344280	+	0.263665i
$64$	−2.64846	+	7.54889i	−0.331057	+	0.943611i
$65$		0			0
$66$	−0.824347	−	2.97228i	−0.101470	−	0.365862i
$67$	12.8589	+	7.42407i	1.57096	+	0.906994i	0.996052	+	0.0887767i	$0.0282957\pi$
$67$	12.8589	+	7.42407i	1.57096	+	0.906994i	0.574909	+	0.818218i	$0.305038\pi$
$68$	−3.91849	+	5.30631i	−0.475186	+	0.643484i
$69$	2.74422	−	5.55818i	0.330365	−	0.669127i
$70$		0			0
$71$	−9.68598			−1.14951			−0.574757	−	0.818324i	$-0.694903\pi$
$71$	−9.68598			−1.14951			−0.574757	+	0.818324i	$0.694903\pi$
$72$	−5.76308	−	6.22791i	−0.679186	−	0.733966i
$73$	−9.08215			−1.06299			−0.531493	−	0.847063i	$-0.678369\pi$
$73$	−9.08215			−1.06299			−0.531493	+	0.847063i	$0.678369\pi$
$74$	6.35277	+	2.09141i	0.738494	+	0.243121i
$75$		0			0
$76$	−4.30577	+	5.83076i	−0.493906	+	0.668834i
$77$	−1.25118	−	0.722368i	−0.142585	−	0.0823215i
$78$	8.71775	−	8.87159i	0.987091	−	1.00451i
$79$	5.78563	−	3.34033i	0.650934	−	0.375817i	−0.137880	−	0.990449i	$-0.544029\pi$
$79$	5.78563	−	3.34033i	0.650934	−	0.375817i	0.788814	+	0.614632i	$0.210695\pi$
$80$		0			0
$81$	8.69767	−	2.31314i	0.966407	−	0.257016i
$82$	−6.32133	−	7.07552i	−0.698074	−	0.781361i
$83$	2.84920	+	4.93496i	0.312740	+	0.541682i	0.978955	−	0.204078i	$-0.0654197\pi$
$83$	2.84920	+	4.93496i	0.312740	+	0.541682i	−0.666214	+	0.745760i	$0.732086\pi$
$84$	−3.96994	−	0.188680i	−0.433156	−	0.0205867i
$85$		0			0
$86$	3.92068	−	0.817489i	0.422777	−	0.0881521i
$87$	0.307501	−	0.205258i	0.0329675	−	0.0220060i
$88$	1.48640	−	3.23665i	0.158451	−	0.345028i
$89$			2.26303i			0.239881i	0.992781	+	0.119940i	$0.0382703\pi$
$89$			2.26303i			0.239881i	−0.992781	+	0.119940i	$0.961730\pi$
$90$		0			0
$91$		−	5.82584i		−	0.610714i
$92$	6.56123	−	2.86049i	0.684056	−	0.298227i
$93$	16.3613	+	8.07798i	1.69659	+	0.837648i
$94$	−0.308582	−	1.47996i	−0.0318278	−	0.152646i
$95$		0			0
$96$	−0.446593	−	9.78778i	−0.0455802	−	0.998961i
$97$	3.86692	+	6.69770i	0.392626	+	0.680048i	0.992795	−	0.119825i	$-0.0382333\pi$
$97$	3.86692	+	6.69770i	0.392626	+	0.680048i	−0.600169	+	0.799873i	$0.704900\pi$
$98$	5.99415	−	5.35521i	0.605500	−	0.540958i
$99$	2.29692	+	2.99919i	0.230849	+	0.301430i
$100$		0			0
$101$	−16.4845	+	9.51736i	−1.64027	+	0.947012i	−0.659538	+	0.751671i	$0.729248\pi$
$101$	−16.4845	+	9.51736i	−1.64027	+	0.947012i	−0.980735	+	0.195341i	$0.937419\pi$
$102$	2.02262	−	7.82152i	0.200269	−	0.774446i
$103$	6.64918	+	3.83891i	0.655164	+	0.378259i	0.790432	−	0.612550i	$-0.209856\pi$
$103$	6.64918	+	3.83891i	0.655164	+	0.378259i	−0.135268	+	0.990809i	$0.543190\pi$
$104$	14.3000	−	1.33501i	1.40223	−	0.130908i
$105$		0			0
$106$	−4.03530	+	12.2575i	−0.391943	+	1.19055i
$107$	11.8511			1.14569			0.572843	−	0.819665i	$-0.305840\pi$
$107$	11.8511			1.14569			0.572843	+	0.819665i	$0.305840\pi$
$108$	9.39747	+	4.43706i	0.904272	+	0.426956i
$109$	−1.38567			−0.132723			−0.0663615	−	0.997796i	$-0.521139\pi$
$109$	−1.38567			−0.132723			−0.0663615	+	0.997796i	$0.521139\pi$
$110$		0			0
$111$	−8.17402	+	0.531923i	−0.775843	+	0.0504879i
$112$	−3.36245	−	3.12334i	−0.317722	−	0.295128i
$113$	−0.504944	−	0.291530i	−0.0475012	−	0.0274248i	0.476061	−	0.879412i	$-0.342064\pi$
$113$	−0.504944	−	0.291530i	−0.0475012	−	0.0274248i	−0.523563	+	0.851987i	$0.675397\pi$
$114$	2.22253	−	8.59456i	0.208159	−	0.804955i
$115$		0			0
$116$	0.424210	+	0.0479151i	0.0393869	+	0.00444880i
$117$	−5.84270	+	14.0684i	−0.540158	+	1.30062i
$118$	−10.2724	+	9.17747i	−0.945655	+	0.844855i
$119$	−1.89202	−	3.27707i	−0.173441	−	0.300408i
$120$		0			0
$121$	4.70717	−	8.15306i	0.427924	−	0.741187i
$122$	3.02822	+	14.5234i	0.274163	+	1.31488i
$123$	10.4196	+	5.14443i	0.939504	+	0.463857i
$124$	8.42025	+	19.3139i	0.756160	+	1.73444i
$125$		0			0
$126$	4.59621	−	1.60276i	0.409463	−	0.142785i
$127$		−	10.3137i		−	0.915191i	−0.889161	−	0.457595i	$-0.848711\pi$
$127$		−	10.3137i		−	0.915191i	0.889161	−	0.457595i	$-0.151289\pi$
$128$	6.89598	−	8.96914i	0.609524	−	0.792767i
$129$	−4.07971	+	2.72322i	−0.359199	+	0.239766i
$130$		0			0
$131$	7.18947	−	12.4525i	0.628147	−	1.08798i	−0.359776	−	0.933039i	$-0.617147\pi$
$131$	7.18947	−	12.4525i	0.628147	−	1.08798i	0.987923	−	0.154944i	$-0.0495196\pi$
$132$	−0.207085	+	4.35719i	−0.0180244	+	0.379244i
$133$	−2.07902	−	3.60096i	−0.180274	−	0.312243i
$134$	−13.9901	−	15.6592i	−1.20856	−	1.35275i
$135$		0			0
$136$	7.61027	−	5.39506i	0.652576	−	0.462623i
$137$	6.40593	−	3.69847i	0.547296	−	0.315981i	−0.200735	−	0.979646i	$-0.564333\pi$
$137$	6.40593	−	3.69847i	0.547296	−	0.315981i	0.748031	+	0.663664i	$0.231000\pi$
$138$	−6.14427	+	6.25270i	−0.523035	+	0.532265i
$139$	1.44892	+	0.836533i	0.122896	+	0.0709538i	0.560188	−	0.828366i	$-0.310729\pi$
$139$	1.44892	+	0.836533i	0.122896	+	0.0709538i	−0.437292	+	0.899320i	$0.644062\pi$
$140$		0			0
$141$	1.02795	+	1.53999i	0.0865689	+	0.129690i
$142$	13.0111	+	4.28341i	1.09187	+	0.359456i
$143$	−6.39412			−0.534703
$144$	4.98735	+	10.9145i	0.415612	+	0.909542i
$145$		0			0
$146$	12.2000	+	4.01638i	1.00968	+	0.332398i
$147$	−4.35818	+	8.82714i	−0.359457	+	0.728050i
$148$	−7.60875	−	5.61874i	−0.625435	−	0.461858i
$149$	−3.87075	−	2.23478i	−0.317104	−	0.183080i	0.332997	−	0.942928i	$-0.391940\pi$
$149$	−3.87075	−	2.23478i	−0.317104	−	0.183080i	−0.650101	+	0.759848i	$0.725273\pi$
$150$		0			0
$151$	11.2428	−	6.49105i	0.914928	−	0.528234i	0.0329149	−	0.999458i	$-0.489521\pi$
$151$	11.2428	−	6.49105i	0.914928	−	0.528234i	0.882014	+	0.471224i	$0.156188\pi$
$152$	8.36244	−	5.92828i	0.678283	−	0.480847i
$153$	1.28233	+	9.81104i	0.103671	+	0.793175i
$154$	1.36125	+	1.52366i	0.109692	+	0.122780i
$155$		0			0
$156$	−15.6338	+	8.06191i	−1.25170	+	0.645469i
$157$	−3.67874	+	6.37177i	−0.293595	+	0.508522i	−0.974657	−	0.223704i	$-0.928185\pi$
$157$	−3.67874	+	6.37177i	−0.293595	+	0.508522i	0.681062	+	0.732226i	$0.261519\pi$
$158$	−9.24898	+	1.92848i	−0.735809	+	0.153422i
$159$	−1.02633	−	15.7715i	−0.0813930	−	1.25076i
$160$		0			0
$161$			4.10605i			0.323602i
$162$	−12.7064	−	0.739125i	−0.998312	−	0.0580711i
$163$		−	6.48159i		−	0.507678i	−0.967247	−	0.253839i	$-0.918307\pi$
$163$		−	6.48159i		−	0.507678i	0.967247	−	0.253839i	$-0.0816933\pi$
$164$	5.36240	+	12.3000i	0.418733	+	0.960466i
$165$		0			0
$166$	−1.64493	−	7.88909i	−0.127671	−	0.612312i
$167$	−6.53280	+	11.3151i	−0.505523	+	0.875592i	0.494456	+	0.869203i	$0.335367\pi$
$167$	−6.53280	+	11.3151i	−0.505523	+	0.875592i	−0.999980	+	0.00638974i	$0.997966\pi$
$168$	5.24935	+	2.00907i	0.404996	+	0.155003i
$169$	−6.39203	−	11.0713i	−0.491694	−	0.851639i
$170$		0			0
$171$	1.40907	+	10.7807i	0.107755	+	0.824422i
$172$	−5.62813	−	0.635705i	−0.429141	−	0.0484720i
$173$	4.87725	−	2.81588i	0.370810	−	0.214087i	−0.303002	−	0.952990i	$-0.597989\pi$
$173$	4.87725	−	2.81588i	0.370810	−	0.214087i	0.673812	+	0.738902i	$0.264656\pi$
$174$	−0.503834	+	0.139736i	−0.0381956	+	0.0105934i
$175$		0			0
$176$	−3.42801	+	3.69044i	−0.258396	+	0.278178i
$177$	7.46882	−	15.1275i	0.561391	−	1.13705i
$178$	1.00078	−	3.03991i	0.0750113	−	0.227851i
$179$	−14.3831			−1.07504			−0.537520	−	0.843251i	$-0.680639\pi$
$179$	−14.3831			−1.07504			−0.537520	+	0.843251i	$0.680639\pi$
$180$		0			0
$181$	−11.3978			−0.847194			−0.423597	−	0.905851i	$-0.639233\pi$
$181$	−11.3978			−0.847194			−0.423597	+	0.905851i	$0.639233\pi$
$182$	−2.57635	+	7.82581i	−0.190972	+	0.580088i
$183$	−10.0876	−	15.1125i	−0.745699	−	1.11715i
$184$	−10.0786	+	0.940914i	−0.743007	+	0.0693651i
$185$		0			0
$186$	−18.4057	−	18.0865i	−1.34957	−	1.32617i
$187$	−3.59673	+	2.07657i	−0.263019	+	0.151854i
$188$	−0.239963	+	2.12448i	−0.0175011	+	0.154944i
$189$	−4.48769	+	3.92450i	−0.326431	+	0.285465i
$190$		0			0
$191$	−8.04586	−	13.9358i	−0.582178	−	1.00836i	−0.995221	−	0.0976507i	$-0.968867\pi$
$191$	−8.04586	−	13.9358i	−0.582178	−	1.00836i	0.413042	−	0.910712i	$-0.364466\pi$
$192$	−3.72852	+	13.3453i	−0.269083	+	0.963117i
$193$	−6.06256	+	10.5007i	−0.436393	+	0.755854i	−0.997408	−	0.0719511i	$-0.977077\pi$
$193$	−6.06256	+	10.5007i	−0.436393	+	0.755854i	0.561016	+	0.827805i	$0.310411\pi$
$194$	−2.23249	−	10.7070i	−0.160284	−	0.768720i
$195$		0			0
$196$	−10.4201	+	4.54284i	−0.744294	+	0.324489i
$197$		−	3.58143i		−	0.255166i	−0.991828	−	0.127583i	$-0.959278\pi$
$197$		−	3.58143i		−	0.255166i	0.991828	−	0.127583i	$-0.0407219\pi$
$198$	−1.75910	−	5.04455i	−0.125014	−	0.358501i
$199$		−	6.39345i		−	0.453219i	−0.973986	−	0.226610i	$-0.927236\pi$
$199$		−	6.39345i		−	0.453219i	0.973986	−	0.226610i	$-0.0727642\pi$
$200$		0			0
$201$	23.0602	+	11.3854i	1.62654	+	0.803066i
$202$	26.3524	−	5.49467i	1.85415	−	0.386603i
$203$	−0.122449	+	0.212089i	−0.00859427	+	0.0148857i
$204$	−6.17587	+	9.61213i	−0.432397	+	0.672984i
$205$		0			0
$206$	−7.23413	−	8.09723i	−0.504025	−	0.564161i
$207$	4.11794	−	9.91539i	0.286216	−	0.689168i
$208$	−19.7995	−	4.53055i	−1.37285	−	0.314137i
$209$	−3.95221	+	2.28181i	−0.273380	+	0.157836i
$210$		0			0
$211$	−12.6167	−	7.28424i	−0.868568	−	0.501468i	−0.00169595	−	0.999999i	$-0.500540\pi$
$211$	−12.6167	−	7.28424i	−0.868568	−	0.501468i	−0.866872	+	0.498531i	$0.833873\pi$
$212$	10.8412	−	14.6808i	0.744575	−	1.00828i
$213$	−16.7412	+	1.08943i	−1.14709	+	0.0746466i
$214$	−15.9195	−	5.24088i	−1.08823	−	0.358259i
$215$		0			0
$216$	−10.6614	−	10.1161i	−0.725414	−	0.688313i
$217$	−12.0867			−0.820501
$218$	1.86136	+	0.612781i	0.126067	+	0.0415028i
$219$	−15.6975	+	1.02152i	−1.06074	+	0.0690276i
$220$		0			0
$221$	−14.5037	−	8.37370i	−0.975623	−	0.563276i
$222$	11.2153	+	2.90025i	0.752723	+	0.194652i
$223$	1.07945	−	0.623219i	0.0722851	−	0.0417338i	−0.463422	−	0.886138i	$-0.653379\pi$
$223$	1.07945	−	0.623219i	0.0722851	−	0.0417338i	0.535707	+	0.844404i	$0.320045\pi$
$224$	3.13553	+	5.68253i	0.209501	+	0.379680i
$225$		0			0
$226$	0.549365	+	0.614910i	0.0365432	+	0.0409032i
$227$	−5.42338	−	9.39358i	−0.359963	−	0.623474i	0.627992	−	0.778220i	$-0.283877\pi$
$227$	−5.42338	−	9.39358i	−0.359963	−	0.623474i	−0.987954	+	0.154747i	$0.950544\pi$
$228$	−6.78626	+	10.5621i	−0.449431	+	0.699495i
$229$	12.0859	−	20.9333i	0.798656	−	1.38331i	−0.121836	−	0.992550i	$-0.538878\pi$
$229$	12.0859	−	20.9333i	0.798656	−	1.38331i	0.920492	−	0.390762i	$-0.127788\pi$
$230$		0			0
$231$	−2.24378	−	1.10781i	−0.147630	−	0.0728886i
$232$	−0.548649	−	0.251961i	−0.0360205	−	0.0165421i
$233$		−	8.94645i		−	0.586102i	−0.956097	−	0.293051i	$-0.905329\pi$
$233$		−	8.94645i		−	0.586102i	0.956097	−	0.293051i	$-0.0946705\pi$
$234$	14.0699	−	16.3141i	0.919777	−	1.06649i
$235$		0			0
$236$	17.8574	−	7.78527i	1.16242	−	0.506778i
$237$	9.62415	−	6.42416i	0.625156	−	0.417294i
$238$	1.09232	+	5.23877i	0.0708046	+	0.339579i
$239$	−7.59415	+	13.1535i	−0.491225	+	0.850826i	−0.999949	−	0.0101033i	$-0.996784\pi$
$239$	−7.59415	+	13.1535i	−0.491225	+	0.850826i	0.508724	+	0.860930i	$0.330117\pi$
$240$		0			0
$241$	−0.235922	−	0.408630i	−0.0151971	−	0.0263222i	0.858327	−	0.513103i	$-0.171504\pi$
$241$	−0.235922	−	0.408630i	−0.0151971	−	0.0263222i	−0.873524	+	0.486781i	$0.838171\pi$
$242$	−9.92861	+	8.87030i	−0.638235	+	0.570204i
$243$	14.7728	−	4.97629i	0.947678	−	0.319229i
$244$	2.35484	−	20.8483i	0.150753	−	1.33467i
$245$		0			0
$246$	−11.7216	−	11.5183i	−0.747340	−	0.734381i
$247$	−15.9372	−	9.20132i	−1.01406	−	0.585466i
$248$	−2.76971	−	29.6679i	−0.175877	−	1.88391i
$249$	5.47960	+	8.20909i	0.347256	+	0.520230i
$250$		0			0
$251$	−24.1551			−1.52465			−0.762327	−	0.647192i	$-0.775943\pi$
$251$	−24.1551			−1.52465			−0.762327	+	0.647192i	$0.775943\pi$
$252$	−6.88285	+	0.120406i	−0.433579	+	0.00758484i
$253$	4.50658			0.283326
$254$	−4.56099	+	13.8543i	−0.286182	+	0.869295i
$255$		0			0
$256$	−13.2297	+	8.99858i	−0.826858	+	0.562411i
$257$	−12.7715	−	7.37360i	−0.796661	−	0.459953i	0.0456410	−	0.998958i	$-0.485467\pi$
$257$	−12.7715	−	7.37360i	−0.796661	−	0.459953i	−0.842302	+	0.539005i	$0.818800\pi$
$258$	6.68453	−	1.85392i	0.416161	−	0.115420i
$259$	4.69901	−	2.71297i	0.291982	−	0.168576i
$260$		0			0
$261$	0.508396	−	0.389353i	0.0314689	−	0.0241003i
$262$	−15.1644	+	13.5480i	−0.936861	+	0.836998i
$263$	0.654834	+	1.13421i	0.0403788	+	0.0699381i	0.885509	−	0.464623i	$-0.153810\pi$
$263$	0.654834	+	1.13421i	0.0403788	+	0.0699381i	−0.845130	+	0.534561i	$0.820477\pi$
$264$	2.20504	−	5.76140i	0.135711	−	0.354589i
$265$		0			0
$266$	1.20028	+	5.75654i	0.0735939	+	0.352956i
$267$	0.254534	+	3.91141i	0.0155773	+	0.239374i
$268$	11.8678	+	27.2217i	0.724942	+	1.66283i
$269$			21.5574i			1.31438i	0.753725	+	0.657190i	$0.228255\pi$
$269$			21.5574i			1.31438i	−0.753725	+	0.657190i	$0.771745\pi$
$270$		0			0
$271$			1.58111i			0.0960453i	0.998846	+	0.0480227i	$0.0152920\pi$
$271$			1.58111i			0.0960453i	−0.998846	+	0.0480227i	$0.984708\pi$
$272$	−12.6087	+	3.88167i	−0.764513	+	0.235361i
$273$	−0.655262	−	10.0694i	−0.0396583	−	0.609425i
$274$	−10.2406	+	2.13524i	−0.618658	+	0.128995i
$275$		0			0
$276$	11.0187	−	5.68203i	0.663246	−	0.342018i
$277$	−3.97015	−	6.87650i	−0.238543	−	0.413169i	0.721753	−	0.692150i	$-0.243337\pi$
$277$	−3.97015	−	6.87650i	−0.238543	−	0.413169i	−0.960297	+	0.278981i	$0.910003\pi$
$278$	−1.57638	−	1.76446i	−0.0945451	−	0.105825i
$279$	29.1873	+	12.1217i	1.74740	+	0.725708i
$280$		0			0
$281$	−5.88352	+	3.39685i	−0.350982	+	0.202639i	−0.665118	−	0.746739i	$-0.731619\pi$
$281$	−5.88352	+	3.39685i	−0.350982	+	0.202639i	0.314136	+	0.949378i	$0.398285\pi$
$282$	−0.699809	−	2.52324i	−0.0416730	−	0.150257i
$283$	6.58918	+	3.80426i	0.391686	+	0.226140i	0.682890	−	0.730521i	$-0.260723\pi$
$283$	6.58918	+	3.80426i	0.391686	+	0.226140i	−0.291204	+	0.956661i	$0.594056\pi$
$284$	−15.5835	−	11.5077i	−0.924709	−	0.682859i
$285$		0			0
$286$	8.58918	+	2.82766i	0.507889	+	0.167203i
$287$	−7.69738			−0.454362
$288$	−1.87277	−	16.8669i	−0.110354	−	0.993892i
$289$	6.12213			0.360126
$290$		0			0
$291$	7.43689	+	11.1413i	0.435958	+	0.653117i
$292$	−14.6120	−	10.7903i	−0.855102	−	0.631457i
$293$	8.58215	+	4.95491i	0.501375	+	0.289469i	0.729281	−	0.684214i	$-0.239855\pi$
$293$	8.58215	+	4.95491i	0.501375	+	0.289469i	−0.227906	+	0.973683i	$0.573188\pi$
$294$	9.75792	−	9.93012i	0.569094	−	0.579136i
$295$		0			0
$296$	7.73601	+	10.9124i	0.449646	+	0.634271i
$297$	4.30731	+	4.92544i	0.249936	+	0.285803i
$298$	4.21127	+	4.71372i	0.243952	+	0.273058i
$299$	9.08630	+	15.7379i	0.525474	+	0.910148i
$300$		0			0
$301$	1.62458	−	2.81385i	0.0936391	−	0.162188i
$302$	−17.9729	+	3.74749i	−1.03423	+	0.215644i
$303$	−27.4213	+	18.3039i	−1.57531	+	1.05153i
$304$	−13.8549	+	4.26531i	−0.794630	+	0.244633i
$305$		0			0
$306$	2.61616	−	13.7462i	0.149556	−	0.785816i
$307$			7.97501i			0.455158i	0.973760	+	0.227579i	$0.0730810\pi$
$307$			7.97501i			0.455158i	−0.973760	+	0.227579i	$0.926919\pi$
$308$	−1.15475	−	2.64870i	−0.0657979	−	0.150924i
$309$	11.9242	+	5.88728i	0.678344	+	0.334916i
$310$		0			0
$311$	3.50301	−	6.06739i	0.198637	−	0.344050i	−0.749449	−	0.662062i	$-0.769682\pi$
$311$	3.50301	−	6.06739i	0.198637	−	0.344050i	0.948087	+	0.318011i	$0.103015\pi$
$312$	24.5659	−	3.91582i	1.39077	−	0.221689i
$313$	−7.35028	−	12.7311i	−0.415462	−	0.719602i	0.580014	−	0.814606i	$-0.303047\pi$
$313$	−7.35028	−	12.7311i	−0.415462	−	0.719602i	−0.995477	+	0.0950041i	$0.969714\pi$
$314$	7.75940	−	6.93230i	0.437888	−	0.391212i
$315$		0			0
$316$	13.2769	+	1.49965i	0.746885	+	0.0843616i
$317$	−2.01274	+	1.16205i	−0.113047	+	0.0652675i	−0.555457	−	0.831545i	$-0.687457\pi$
$317$	−2.01274	+	1.16205i	−0.113047	+	0.0652675i	0.442411	+	0.896813i	$0.354123\pi$
$318$	−5.59593	+	21.6396i	−0.313804	+	1.21349i
$319$	0.232777	+	0.134394i	0.0130330	+	0.00752460i
$320$		0			0
$321$	20.4833	−	1.33295i	1.14327	−	0.0743980i
$322$	1.81581	−	5.51563i	0.101191	−	0.307374i
$323$	−11.9530			−0.665082
$324$	16.7416	+	6.61200i	0.930089	+	0.367334i
$325$		0			0
$326$	−2.86634	+	8.70668i	−0.158752	+	0.482218i
$327$	−2.39498	+	0.155853i	−0.132443	+	0.00861870i
$328$	−1.76388	−	18.8938i	−0.0973938	−	1.04324i
$329$	−1.06216	−	0.613237i	−0.0585587	−	0.0338089i
$330$		0			0
$331$	13.0699	−	7.54592i	0.718388	−	0.414762i	−0.0957711	−	0.995403i	$-0.530532\pi$
$331$	13.0699	−	7.54592i	0.718388	−	0.414762i	0.814159	+	0.580642i	$0.197198\pi$
$332$	−1.27915	+	11.3248i	−0.0702025	+	0.621528i
$333$	−14.0681	+	1.83875i	−0.770927	+	0.100763i
$334$	13.7793	−	12.3106i	0.753972	−	0.673604i
$335$		0			0
$336$	−6.16295	−	5.02018i	−0.336216	−	0.273873i
$337$	10.8759	−	18.8375i	0.592445	−	1.02615i	−0.401456	−	0.915878i	$-0.631496\pi$
$337$	10.8759	−	18.8375i	0.592445	−	1.02615i	0.993902	−	0.110268i	$-0.0351708\pi$
$338$	3.69032	+	17.6987i	0.200727	+	0.962685i
$339$	−0.905533	−	0.447085i	−0.0491818	−	0.0242823i
$340$		0			0
$341$			13.2657i			0.718380i
$342$	2.87473	−	15.1048i	0.155448	−	0.816773i
$343$		−	14.5522i		−	0.785744i
$344$	7.27910	+	3.34285i	0.392463	+	0.180235i
$345$		0			0
$346$	−7.79683	+	1.62570i	−0.419160	+	0.0873979i
$347$	13.6590	−	23.6580i	0.733251	−	1.27003i	−0.222236	−	0.974993i	$-0.571335\pi$
$347$	13.6590	−	23.6580i	0.733251	−	1.27003i	0.955487	−	0.295035i	$-0.0953312\pi$
$348$	0.738592	+	0.0351032i	0.0395927	+	0.00188173i
$349$	1.77750	+	3.07872i	0.0951472	+	0.164800i	0.909670	−	0.415332i	$-0.136334\pi$
$349$	1.77750	+	3.07872i	0.0951472	+	0.164800i	−0.814523	+	0.580132i	$0.803001\pi$
$350$		0			0
$351$	−8.51615	+	24.9729i	−0.454559	+	1.33295i
$352$	6.23683	−	3.44138i	0.332424	−	0.183426i
$353$	−2.26731	+	1.30903i	−0.120677	+	0.0696727i	−0.559123	−	0.829085i	$-0.688862\pi$
$353$	−2.26731	+	1.30903i	−0.120677	+	0.0696727i	0.438447	+	0.898757i	$0.355529\pi$
$354$	−16.7226	+	17.0177i	−0.888796	+	0.904480i
$355$		0			0
$356$	−2.68867	+	3.64092i	−0.142499	+	0.192968i
$357$	−3.63874	−	5.45127i	−0.192583	−	0.288512i
$358$	19.3207	+	6.36059i	1.02113	+	0.336168i
$359$	−21.9608			−1.15904			−0.579522	−	0.814956i	$-0.696761\pi$
$359$	−21.9608			−1.15904			−0.579522	+	0.814956i	$0.696761\pi$
$360$		0			0
$361$	5.86564			0.308718
$362$	15.3106	+	5.04044i	0.804709	+	0.264920i
$363$	7.21883	−	14.6211i	0.378890	−	0.767411i
$364$	6.92158	−	9.37302i	0.362790	−	0.491280i
$365$		0			0
$366$	6.86748	+	24.7615i	0.358969	+	1.29430i
$367$	−17.5533	+	10.1344i	−0.916276	+	0.529012i	−0.882445	−	0.470415i	$-0.844104\pi$
$367$	−17.5533	+	10.1344i	−0.916276	+	0.529012i	−0.0338310	+	0.999428i	$0.510771\pi$
$368$	13.9547	+	3.19313i	0.727437	+	0.166454i
$369$	18.5878	+	7.71966i	0.967643	+	0.401869i
$370$		0			0
$371$	5.23459	+	9.06658i	0.271767	+	0.470713i
$372$	16.7258	+	32.4350i	0.867194	+	1.68167i
$373$	6.18110	−	10.7060i	0.320045	−	0.554334i	−0.660452	−	0.750868i	$-0.729635\pi$
$373$	6.18110	−	10.7060i	0.320045	−	0.554334i	0.980497	+	0.196534i	$0.0629686\pi$
$374$	5.74978	−	1.19887i	0.297314	−	0.0619921i
$375$		0			0
$376$	1.26184	−	2.74768i	0.0650746	−	0.141701i
$377$			1.08388i			0.0558224i
$378$	7.76380	−	3.28717i	0.399327	−	0.169074i
$379$		−	6.92628i		−	0.355779i	−0.984050	−	0.177889i	$-0.943073\pi$
$379$		−	6.92628i		−	0.355779i	0.984050	−	0.177889i	$-0.0569270\pi$
$380$		0			0
$381$	−1.16003	−	17.8261i	−0.0594302	−	0.913259i
$382$	4.64513	+	22.2780i	0.237665	+	1.13984i
$383$	0.722230	−	1.25094i	0.0369042	−	0.0639200i	−0.846983	−	0.531619i	$-0.821584\pi$
$383$	0.722230	−	1.25094i	0.0369042	−	0.0639200i	0.883888	+	0.467699i	$0.154917\pi$
$384$	10.9102	−	16.2778i	0.556758	−	0.830675i
$385$		0			0
$386$	12.7875	−	11.4244i	0.650865	−	0.581488i
$387$	−6.74506	+	5.16567i	−0.342871	+	0.262586i
$388$	−1.73606	+	15.3699i	−0.0881349	+	0.780290i
$389$	−0.707497	+	0.408474i	−0.0358715	+	0.0207104i	−0.517829	−	0.855484i	$-0.673259\pi$
$389$	−0.707497	+	0.408474i	−0.0358715	+	0.0207104i	0.481957	+	0.876195i	$0.339926\pi$
$390$		0			0
$391$	10.2222	+	5.90178i	0.516958	+	0.298466i
$392$	16.0062	−	1.49430i	0.808437	−	0.0754734i
$393$	11.0256	−	22.3315i	0.556170	−	1.12648i
$394$	−1.58381	+	4.81090i	−0.0797910	+	0.242370i
$395$		0			0
$396$	0.132151	+	7.55423i	0.00664082	+	0.379614i
$397$	29.4855			1.47984			0.739918	−	0.672697i	$-0.234864\pi$
$397$	29.4855			1.47984			0.739918	+	0.672697i	$0.234864\pi$
$398$	−2.82736	+	8.58827i	−0.141723	+	0.430491i
$399$	−3.99838	−	5.99004i	−0.200169	−	0.299877i
$400$		0			0
$401$	−1.19058	−	0.687380i	−0.0594546	−	0.0343261i	0.469978	−	0.882678i	$-0.344262\pi$
$401$	−1.19058	−	0.687380i	−0.0594546	−	0.0343261i	−0.529433	+	0.848352i	$0.677595\pi$
$402$	−25.9417	−	25.4918i	−1.29385	−	1.27142i
$403$	−46.3268	+	26.7468i	−2.30770	+	1.33235i
$404$	−37.8289	−	4.27282i	−1.88206	−	0.212581i
$405$		0			0
$406$	0.258277	−	0.230747i	0.0128181	−	0.0114518i
$407$	−2.97761	−	5.15737i	−0.147595	−	0.255642i
$408$	12.5467	−	10.1808i	0.621157	−	0.504023i
$409$	1.66076	−	2.87653i	0.0821195	−	0.142235i	−0.822041	−	0.569429i	$-0.807164\pi$
$409$	1.66076	−	2.87653i	0.0821195	−	0.142235i	0.904160	+	0.427194i	$0.140498\pi$
$410$		0			0
$411$	10.6560	−	7.11292i	0.525621	−	0.350854i
$412$	6.13673	+	14.0761i	0.302335	+	0.693479i
$413$			11.1753i			0.549899i
$414$	−9.91646	+	11.4982i	−0.487367	+	0.565106i
$415$		0			0
$416$	24.5929	+	14.8417i	1.20577	+	0.727676i
$417$	2.59839	+	1.28289i	0.127244	+	0.0628235i
$418$	6.31806	−	1.31736i	0.309026	−	0.0644343i
$419$	17.6346	−	30.5441i	0.861508	−	1.49218i	−0.00896441	−	0.999960i	$-0.502853\pi$
$419$	17.6346	−	30.5441i	0.861508	−	1.49218i	0.870473	−	0.492217i	$-0.163813\pi$
$420$		0			0
$421$	−14.6171	−	25.3175i	−0.712392	−	1.23390i	−0.963957	−	0.266059i	$-0.914278\pi$
$421$	−14.6171	−	25.3175i	−0.712392	−	1.23390i	0.251565	−	0.967841i	$-0.419055\pi$
$422$	13.7266	+	15.3643i	0.668200	+	0.747923i
$423$	1.94991	+	2.54609i	0.0948079	+	0.123795i
$424$	−21.0551	+	14.9264i	−1.02253	+	0.724888i
$425$		0			0
$426$	22.9701	+	5.94000i	1.11290	+	0.287794i
$427$	10.4233	+	6.01792i	0.504421	+	0.291227i
$428$	19.0668	+	14.0801i	0.921630	+	0.680585i
$429$	−11.0516	+	0.719179i	−0.533575	+	0.0347223i
$430$		0			0
$431$	15.7242			0.757408			0.378704	−	0.925518i	$-0.376370\pi$
$431$	15.7242			0.757408			0.378704	+	0.925518i	$0.376370\pi$
$432$	9.84772	+	18.3036i	0.473798	+	0.880633i
$433$	40.6371			1.95289			0.976447	−	0.215758i	$-0.0692222\pi$
$433$	40.6371			1.95289			0.976447	+	0.215758i	$0.0692222\pi$
$434$	16.2360	+	5.34509i	0.779354	+	0.256573i
$435$		0			0
$436$	−2.22936	−	1.64629i	−0.106767	−	0.0788429i
$437$	11.2325	+	6.48509i	0.537324	+	0.310224i
$438$	21.5381	+	5.56970i	1.02913	+	0.266130i
$439$	−19.5385	+	11.2806i	−0.932523	+	0.538392i	−0.887608	−	0.460599i	$-0.847635\pi$
$439$	−19.5385	+	11.2806i	−0.932523	+	0.538392i	−0.0449140	+	0.998991i	$0.514301\pi$
$440$		0			0
$441$	−6.53983	+	15.7470i	−0.311421	+	0.749856i
$442$	15.7796	+	17.6623i	0.750559	+	0.840108i
$443$	−7.20347	−	12.4768i	−0.342247	−	0.592789i	0.642603	−	0.766200i	$-0.277855\pi$
$443$	−7.20347	−	12.4768i	−0.342247	−	0.592789i	−0.984850	+	0.173410i	$0.944521\pi$
$444$	−13.7829	−	8.85561i	−0.654107	−	0.420269i
$445$		0			0
$446$	−1.72562	+	0.359804i	−0.0817104	+	0.0170372i
$447$	−6.94154	−	3.42722i	−0.328324	−	0.162102i
$448$	−1.69896	−	9.01992i	−0.0802682	−	0.426151i
$449$		−	14.7482i		−	0.696008i	−0.937493	−	0.348004i	$-0.886860\pi$
$449$		−	14.7482i		−	0.696008i	0.937493	−	0.348004i	$-0.113140\pi$
$450$		0			0
$451$			8.44822i			0.397811i
$452$	−0.466028	−	1.06895i	−0.0219201	−	0.0502791i
$453$	18.7020	−	12.4836i	0.878695	−	0.586532i
$454$	3.13109	+	15.0167i	0.146949	+	0.704768i
$455$		0			0
$456$	13.7868	−	11.1870i	0.645627	−	0.523878i
$457$	−0.510332	−	0.883921i	−0.0238723	−	0.0413481i	0.853842	−	0.520532i	$-0.174266\pi$
$457$	−0.510332	−	0.883921i	−0.0238723	−	0.0413481i	−0.877715	+	0.479183i	$0.840933\pi$
$458$	−25.4921	+	22.7749i	−1.19117	+	1.06420i
$459$	3.31988	+	16.8131i	0.154959	+	0.784769i
$460$		0			0
$461$	0.679602	−	0.392368i	0.0316522	−	0.0182744i	−0.484090	−	0.875018i	$-0.660849\pi$
$461$	0.679602	−	0.392368i	0.0316522	−	0.0182744i	0.515743	+	0.856744i	$0.327516\pi$
$462$	2.52415	+	2.48038i	0.117434	+	0.115398i
$463$	28.2095	+	16.2867i	1.31101	+	0.756909i	0.982263	−	0.187510i	$-0.0600418\pi$
$463$	28.2095	+	16.2867i	1.31101	+	0.756909i	0.328743	+	0.944420i	$0.393375\pi$
$464$	0.625571	+	0.581086i	0.0290414	+	0.0269762i
$465$		0			0
$466$	−3.95637	+	12.0177i	−0.183275	+	0.556709i
$467$	−26.0874			−1.20718			−0.603590	−	0.797295i	$-0.706264\pi$
$467$	−26.0874			−1.20718			−0.603590	+	0.797295i	$0.706264\pi$
$468$	−26.1145	+	15.6926i	−1.20714	+	0.725389i
$469$	−17.0355			−0.786627
$470$		0			0
$471$	−5.64165	+	11.4267i	−0.259954	+	0.526514i
$472$	−27.4306	+	2.56085i	−1.26260	+	0.117872i
$473$	−3.08833	−	1.78305i	−0.142001	−	0.0819845i
$474$	−15.7690	+	4.37345i	−0.724294	+	0.200879i
$475$		0			0
$476$	0.849422	−	7.52025i	0.0389332	−	0.344690i
$477$	−3.54780	−	27.1439i	−0.162443	−	1.24284i
$478$	16.0180	−	14.3106i	0.732646	−	0.654551i
$479$	15.0858	+	26.1294i	0.689288	+	1.19388i	0.972068	+	0.234698i	$0.0754101\pi$
$479$	15.0858	+	26.1294i	0.689288	+	1.19388i	−0.282780	+	0.959185i	$0.591257\pi$
$480$		0			0
$481$	12.0071	−	20.7969i	0.547477	−	0.948257i
$482$	0.136205	+	0.653241i	0.00620399	+	0.0297543i
$483$	0.461829	+	7.09688i	0.0210139	+	0.322919i
$484$	17.2597	−	7.52469i	0.784533	−	0.342031i
$485$		0			0
$486$	−22.0449	+	0.151658i	−0.999976	+	0.00687935i
$487$		−	22.2802i		−	1.00961i	−0.863233	−	0.504806i	$-0.831564\pi$
$487$		−	22.2802i		−	1.00961i	0.863233	−	0.504806i	$-0.168436\pi$
$488$	−12.3829	+	26.9639i	−0.560549	+	1.22060i
$489$	−0.729018	−	11.2028i	−0.0329673	−	0.506606i
$490$		0			0
$491$	−10.7024	+	18.5371i	−0.482992	+	0.836566i	−0.999809	−	0.0195292i	$-0.993783\pi$
$491$	−10.7024	+	18.5371i	−0.482992	+	0.836566i	0.516817	+	0.856096i	$0.327117\pi$
$492$	10.6518	+	20.6561i	0.480219	+	0.931247i
$493$	0.352002	+	0.609686i	0.0158534	+	0.0274589i
$494$	17.3392	+	19.4079i	0.780126	+	0.873203i
$495$		0			0
$496$	−9.39943	+	41.0775i	−0.422047	+	1.84443i
$497$	9.62404	−	5.55644i	0.431697	−	0.249240i
$498$	−3.73042	−	13.4504i	−0.167164	−	0.602729i
$499$	14.4771	+	8.35834i	0.648083	+	0.374171i	0.787721	−	0.616032i	$-0.211261\pi$
$499$	14.4771	+	8.35834i	0.648083	+	0.374171i	−0.139638	+	0.990203i	$0.544594\pi$
$500$		0			0
$501$	−10.0186	+	20.2918i	−0.447598	+	0.906572i
$502$	32.4473	+	10.6820i	1.44819	+	0.476763i
$503$	37.4827			1.67127			0.835635	−	0.549285i	$-0.185100\pi$
$503$	37.4827			1.67127			0.835635	+	0.549285i	$0.185100\pi$
$504$	9.29892	+	2.88205i	0.414207	+	0.128377i
$505$		0			0
$506$	−6.05365	−	1.99293i	−0.269118	−	0.0885967i
$507$	−12.2932	−	18.4167i	−0.545960	−	0.817912i
$508$	12.2535	−	16.5934i	0.543661	−	0.736211i
$509$	−23.3737	−	13.4948i	−1.03602	−	0.598148i	−0.117318	−	0.993094i	$-0.537430\pi$
$509$	−23.3737	−	13.4948i	−1.03602	−	0.598148i	−0.918704	+	0.394947i	$0.870763\pi$
$510$		0			0
$511$	9.02407	−	5.21005i	0.399201	−	0.230479i
$512$	21.7508	−	6.23717i	0.961259	−	0.275647i
$513$	3.64800	+	18.4748i	0.161063	+	0.815684i
$514$	13.8950	+	15.5528i	0.612881	+	0.686004i
$515$		0			0
$516$	−9.79913	−	0.465725i	−0.431383	−	0.0205024i
$517$	−0.673055	+	1.16577i	−0.0296009	+	0.0512703i
$518$	−7.51190	+	1.56629i	−0.330054	+	0.0688186i
$519$	8.11309	−	5.41552i	0.356125	−	0.237715i
$520$		0			0
$521$			26.5168i			1.16172i	0.814003	+	0.580860i	$0.197284\pi$
$521$			26.5168i			1.16172i	−0.814003	+	0.580860i	$0.802716\pi$
$522$	−0.855107	+	0.298188i	−0.0374270	+	0.0130513i
$523$		−	31.5217i		−	1.37835i	−0.724596	−	0.689174i	$-0.757974\pi$
$523$		−	31.5217i		−	1.37835i	0.724596	−	0.689174i	$-0.242026\pi$
$524$	26.3615	−	11.4928i	1.15161	−	0.502065i
$525$		0			0
$526$	−0.378056	−	1.81316i	−0.0164840	−	0.0790574i
$527$	−17.3727	+	30.0904i	−0.756767	+	1.31076i
$528$	−5.50987	+	6.76411i	−0.239786	+	0.294370i
$529$	5.09598	+	8.82649i	0.221564	+	0.383760i
$530$		0			0
$531$	11.2076	−	26.9863i	0.486369	−	1.17111i
$532$	0.933375	−	8.26352i	0.0404669	−	0.358269i
$533$	−29.5030	+	17.0336i	−1.27792	+	0.737805i
$534$	1.38782	−	5.36673i	0.0600569	−	0.232241i
$535$		0			0
$536$	−3.90374	−	41.8150i	−0.168616	−	1.80613i
$537$	−24.8596	+	1.61774i	−1.07277	+	0.0698105i
$538$	9.53329	−	28.9579i	0.411009	−	1.24846i
$539$	−7.15705			−0.308276
$540$		0			0
$541$	−0.0570124			−0.00245116			−0.00122558	−	0.999999i	$-0.500390\pi$
$541$	−0.0570124			−0.00245116			−0.00122558	+	0.999999i	$0.500390\pi$
$542$	0.699209	−	2.12389i	0.0300336	−	0.0912288i
$543$	−19.7000	+	1.28197i	−0.845406	+	0.0550147i
$544$	18.6537	+	0.361689i	0.799771	+	0.0155073i
$545$		0			0
$546$	−3.57274	+	13.8159i	−0.152899	+	0.591265i
$547$	−3.09710	+	1.78811i	−0.132422	+	0.0764541i	−0.564748	−	0.825264i	$-0.691027\pi$
$547$	−3.09710	+	1.78811i	−0.132422	+	0.0764541i	0.432325	+	0.901718i	$0.357693\pi$
$548$	14.7004	+	1.66043i	0.627970	+	0.0709300i
$549$	−19.1352	−	24.9857i	−0.816670	−	1.06636i
$550$		0			0
$551$	0.386793	+	0.669944i	0.0164779	+	0.0285406i
$552$	−17.3140	+	2.75987i	−0.736935	+	0.117468i
$553$	−3.83242	+	6.63795i	−0.162971	+	0.282274i
$554$	2.29209	+	10.9929i	0.0973817	+	0.467042i
$555$		0			0
$556$	1.33725	+	3.06730i	0.0567119	+	0.130083i
$557$		−	15.0861i		−	0.639217i	−0.947550	−	0.319609i	$-0.896449\pi$
$557$		−	15.0861i		−	0.639217i	0.947550	−	0.319609i	$-0.103551\pi$
$558$	−33.8466	−	29.1904i	−1.43284	−	1.23573i
$559$		−	14.3801i		−	0.608214i
$560$		0			0
$561$	−5.98301	+	3.99368i	−0.252603	+	0.168613i
$562$	9.40548	−	1.96111i	0.396746	−	0.0827244i
$563$	−4.21208	+	7.29553i	−0.177518	+	0.307470i	−0.941030	−	0.338324i	$-0.890140\pi$
$563$	−4.21208	+	7.29553i	−0.177518	+	0.307470i	0.763512	+	0.645794i	$0.223473\pi$
$564$	−0.175800	+	3.69893i	−0.00740250	+	0.155753i
$565$		0			0
$566$	−7.16884	−	8.02416i	−0.301329	−	0.337280i
$567$	−7.31509	+	7.28784i	−0.307205	+	0.306060i
$568$	15.8441	+	22.3497i	0.664804	+	0.937773i
$569$	3.05453	−	1.76353i	0.128053	−	0.0739312i	−0.434605	−	0.900621i	$-0.643112\pi$
$569$	3.05453	−	1.76353i	0.128053	−	0.0739312i	0.562658	+	0.826690i	$0.309779\pi$
$570$		0			0
$571$	29.6633	+	17.1261i	1.24137	+	0.716705i	0.969373	−	0.245593i	$-0.0789826\pi$
$571$	29.6633	+	17.1261i	1.24137	+	0.716705i	0.271997	+	0.962298i	$0.412316\pi$
$572$	−10.2873	−	7.59675i	−0.430134	−	0.317636i
$573$	−15.4739	−	23.1817i	−0.646430	−	0.968429i
$574$	10.3398	+	3.40400i	0.431576	+	0.142080i
$575$		0			0
$576$	−4.94334	+	23.4854i	−0.205973	+	0.978558i
$577$	1.78616			0.0743587			0.0371793	−	0.999309i	$-0.488163\pi$
$577$	1.78616			0.0743587			0.0371793	+	0.999309i	$0.488163\pi$
$578$	−8.22382	−	2.70738i	−0.342066	−	0.112612i
$579$	−9.29744	+	18.8312i	−0.386388	+	0.782597i
$580$		0			0
$581$	−5.66196	−	3.26893i	−0.234898	−	0.135618i
$582$	−5.06290	−	18.2549i	−0.209864	−	0.756689i
$583$	9.95098	−	5.74520i	0.412127	−	0.237942i
$584$	14.8564	+	20.9564i	0.614762	+	0.867183i
$585$		0			0
$586$	−9.33714	−	10.4512i	−0.385714	−	0.431733i
$587$	7.84570	+	13.5891i	0.323826	+	0.560884i	0.981274	−	0.192616i	$-0.0616973\pi$
$587$	7.84570	+	13.5891i	0.323826	+	0.560884i	−0.657448	+	0.753500i	$0.728364\pi$
$588$	−17.4991	+	9.02383i	−0.721651	+	0.372136i
$589$	−19.0898	+	33.0644i	−0.786579	+	1.36240i
$590$		0			0
$591$	−0.402821	−	6.19012i	−0.0165698	−	0.254627i
$592$	−5.56595	−	18.0796i	−0.228759	−	0.743069i
$593$			46.6356i			1.91510i	0.288273	+	0.957548i	$0.406919\pi$
$593$			46.6356i			1.91510i	−0.288273	+	0.957548i	$0.593081\pi$
$594$	−3.60781	−	8.52112i	−0.148030	−	0.349626i
$595$		0			0
$596$	−3.57243	−	8.19424i	−0.146332	−	0.335649i
$597$	−0.719103	−	11.0504i	−0.0294309	−	0.452263i
$598$	−5.24580	−	25.1589i	−0.214517	−	1.02882i
$599$	21.3211	−	36.9292i	0.871156	−	1.50889i	0.0103549	−	0.999946i	$-0.496704\pi$
$599$	21.3211	−	36.9292i	0.871156	−	1.50889i	0.860802	−	0.508941i	$-0.169963\pi$
$600$		0			0
$601$	10.7999	+	18.7061i	0.440539	+	0.763036i	0.997729	−	0.0673489i	$-0.0214541\pi$
$601$	10.7999	+	18.7061i	0.440539	+	0.763036i	−0.557191	+	0.830385i	$0.688121\pi$
$602$	−3.42664	+	3.06139i	−0.139660	+	0.124773i
$603$	41.1377	+	17.0848i	1.67526	+	0.695747i
$604$	25.8001	+	2.91416i	1.04979	+	0.118576i
$605$		0			0
$606$	44.9294	−	12.4609i	1.82513	−	0.506191i
$607$	2.59588	+	1.49873i	0.105363	+	0.0608316i	0.551756	−	0.834006i	$-0.313958\pi$
$607$	2.59588	+	1.49873i	0.105363	+	0.0608316i	−0.446392	+	0.894837i	$0.647291\pi$
$608$	20.4974	+	0.397436i	0.831278	+	0.0161182i
$609$	−0.187786	+	0.380346i	−0.00760949	+	0.0154124i
$610$		0			0
$611$	−5.42814			−0.219599
$612$	−9.59321	+	17.3082i	−0.387783	+	0.699642i
$613$	14.2081			0.573858			0.286929	−	0.957952i	$-0.407366\pi$
$613$	14.2081			0.573858			0.286929	+	0.957952i	$0.407366\pi$
$614$	3.52677	−	10.7128i	0.142329	−	0.432332i
$615$		0			0
$616$	0.379837	+	4.06864i	0.0153041	+	0.163930i
$617$	22.9723	+	13.2631i	0.924832	+	0.533952i	0.885173	−	0.465262i	$-0.154040\pi$
$617$	22.9723	+	13.2631i	0.924832	+	0.533952i	0.0396583	+	0.999213i	$0.487373\pi$
$618$	−13.4142	−	13.1816i	−0.539597	−	0.530240i
$619$	13.2974	−	7.67724i	0.534466	−	0.308574i	−0.208367	−	0.978051i	$-0.566815\pi$
$619$	13.2974	−	7.67724i	0.534466	−	0.308574i	0.742833	+	0.669476i	$0.233481\pi$
$620$		0			0
$621$	6.00219	−	17.6009i	0.240859	−	0.706299i
$622$	−7.38874	+	6.60115i	−0.296261	+	0.264682i
$623$	−1.29821	−	2.24856i	−0.0520115	−	0.0900866i
$624$	−34.7309	−	5.60364i	−1.39035	−	0.224325i
$625$		0			0
$626$	4.24355	+	20.3520i	0.169606	+	0.813431i
$627$	−6.57434	+	4.38840i	−0.262554	+	0.175256i
$628$	−13.4888	+	5.88069i	−0.538262	+	0.234665i
$629$		−	15.5978i		−	0.621927i
$630$		0			0
$631$			4.30213i			0.171265i	0.996327	+	0.0856326i	$0.0272911\pi$
$631$			4.30213i			0.171265i	−0.996327	+	0.0856326i	$0.972709\pi$
$632$	−17.1716	−	7.88588i	−0.683049	−	0.313684i
$633$	−22.6259	−	11.1710i	−0.899299	−	0.444007i
$634$	3.21759	−	0.670890i	0.127787	−	0.0266445i
$635$		0			0
$636$	17.0866	−	26.5936i	0.677528	−	1.05451i
$637$	−14.4303	−	24.9939i	−0.571748	−	0.990296i
$638$	−0.253255	−	0.283470i	−0.0100264	−	0.0112227i
$639$	−28.8129	+	3.76593i	−1.13982	+	0.148978i
$640$		0			0
$641$	26.3204	−	15.1961i	1.03959	−	0.600209i	0.119875	−	0.992789i	$-0.461751\pi$
$641$	26.3204	−	15.1961i	1.03959	−	0.600209i	0.919718	+	0.392580i	$0.128417\pi$
$642$	−28.1046	−	7.26776i	−1.10920	−	0.286836i
$643$	−23.2202	−	13.4062i	−0.915714	−	0.528688i	−0.0334490	−	0.999440i	$-0.510649\pi$
$643$	−23.2202	−	13.4062i	−0.915714	−	0.528688i	−0.882265	+	0.470753i	$0.843982\pi$
$644$	−4.87833	+	6.60610i	−0.192233	+	0.260317i
$645$		0			0
$646$	16.0564	+	5.28594i	0.631729	+	0.207973i
$647$	9.51887			0.374225			0.187113	−	0.982338i	$-0.440087\pi$
$647$	9.51887			0.374225			0.187113	+	0.982338i	$0.440087\pi$
$648$	−19.5649	−	16.2855i	−0.768580	−	0.639753i
$649$	12.2654			0.481457
$650$		0			0
$651$	−20.8907	+	1.35946i	−0.818769	+	0.0532813i
$652$	7.70067	−	10.4280i	0.301581	−	0.408393i
$653$	−13.3577	−	7.71208i	−0.522728	−	0.301797i	0.215322	−	0.976543i	$-0.430920\pi$
$653$	−13.3577	−	7.71208i	−0.522728	−	0.301797i	−0.738050	+	0.674746i	$0.764253\pi$
$654$	3.28608	+	0.849772i	0.128496	+	0.0332287i
$655$		0			0
$656$	−5.98598	+	26.1600i	−0.233713	+	1.02138i
$657$	−27.0167	+	3.53116i	−1.05402	+	0.137764i
$658$	1.15560	+	1.29347i	0.0450499	+	0.0504248i
$659$	−17.3345	−	30.0242i	−0.675256	−	1.16958i	−0.976394	−	0.215998i	$-0.930700\pi$
$659$	−17.3345	−	30.0242i	−0.675256	−	1.16958i	0.301137	−	0.953581i	$-0.402634\pi$
$660$		0			0
$661$	−10.7043	+	18.5404i	−0.416350	+	0.721139i	−0.995569	−	0.0940328i	$-0.970024\pi$
$661$	−10.7043	+	18.5404i	−0.416350	+	0.721139i	0.579219	+	0.815172i	$0.303357\pi$
$662$	−20.8937	+	4.35650i	−0.812059	+	0.169320i
$663$	−26.0099	−	12.8418i	−1.01014	−	0.498733i
$664$	6.72641	−	14.6468i	0.261035	−	0.568407i
$665$		0			0
$666$	19.7107	+	3.75133i	0.763775	+	0.145361i
$667$		−	0.763915i		−	0.0295789i
$668$	−23.9538	+	10.4431i	−0.926799	+	0.404055i
$669$	1.79561	−	1.19858i	0.0694225	−	0.0463398i
$670$		0			0
$671$	6.60493	−	11.4401i	0.254981	−	0.441639i
$672$	6.05858	+	9.46899i	0.233715	+	0.365274i
$673$	−12.8764	−	22.3026i	−0.496349	−	0.859702i	0.503642	−	0.863913i	$-0.331993\pi$
$673$	−12.8764	−	22.3026i	−0.496349	−	0.859702i	−0.999991	+	0.00421032i	$0.998660\pi$
$674$	−22.9399	+	20.4947i	−0.883613	+	0.789427i
$675$		0			0
$676$	2.86970	−	25.4065i	0.110373	−	0.977175i
$677$	−25.1994	+	14.5489i	−0.968492	+	0.559159i	−0.898776	−	0.438408i	$-0.855542\pi$
$677$	−25.1994	+	14.5489i	−0.968492	+	0.559159i	−0.0697156	+	0.997567i	$0.522209\pi$
$678$	1.01868	+	1.00102i	0.0391223	+	0.0384439i
$679$	−7.68438	−	4.43658i	−0.294899	−	0.170260i
$680$		0			0
$681$	−10.4303	−	15.6258i	−0.399690	−	0.598783i
$682$	5.86648	−	17.8198i	0.224639	−	0.682354i
$683$	−0.973163			−0.0372370			−0.0186185	−	0.999827i	$-0.505927\pi$
$683$	−0.973163			−0.0372370			−0.0186185	+	0.999827i	$0.505927\pi$
$684$	−10.5414	+	19.0189i	−0.403059	+	0.727204i
$685$		0			0
$686$	−6.43538	+	19.5478i	−0.245704	+	0.746340i
$687$	18.5347	−	37.5404i	0.707141	−	1.43225i
$688$	−8.29966	−	7.70945i	−0.316421	−	0.293920i
$689$	40.1269	+	23.1673i	1.52871	+	0.882604i
$690$		0			0
$691$	−14.2382	+	8.22045i	−0.541648	+	0.312721i	−0.745747	−	0.666230i	$-0.767907\pi$
$691$	−14.2382	+	8.22045i	−0.541648	+	0.312721i	0.204099	+	0.978950i	$0.434574\pi$
$692$	11.1924	+	1.26419i	0.425469	+	0.0480573i
$693$	−4.00274	−	1.66237i	−0.152051	−	0.0631481i
$694$	−28.8102	+	25.7392i	−1.09362	+	0.977048i
$695$		0			0
$696$	−0.976621	−	0.373780i	−0.0370187	−	0.0141681i
$697$	−11.0637	+	19.1629i	−0.419069	+	0.725848i
$698$	−1.02620	−	4.92167i	−0.0388424	−	0.186288i
$699$	−1.00625	−	15.4630i	−0.0380600	−	0.584865i
$700$		0			0
$701$		−	12.3225i		−	0.465415i	−0.972547	−	0.232707i	$-0.925242\pi$
$701$		−	12.3225i		−	0.465415i	0.972547	−	0.232707i	$-0.0747585\pi$
$702$	22.4834	−	29.7798i	0.848581	−	1.12397i
$703$		−	17.1395i		−	0.646427i
$704$	−9.89977	+	1.86468i	−0.373111	+	0.0702778i
$705$		0			0
$706$	3.62455	−	0.755744i	0.136412	−	0.0284428i
$707$	10.9194	−	18.9130i	0.410667	−	0.711296i
$708$	29.9890	−	15.4645i	1.12706	−	0.581193i
$709$	−2.75578	−	4.77314i	−0.103495	−	0.179259i	0.809627	−	0.586945i	$-0.199669\pi$
$709$	−2.75578	−	4.77314i	−0.103495	−	0.179259i	−0.913122	+	0.407685i	$0.866336\pi$
$710$		0			0
$711$	15.9118	−	12.1860i	0.596738	−	0.457009i
$712$	5.22178	−	3.70182i	0.195695	−	0.138731i
$713$	32.6511	−	18.8511i	1.22279	−	0.705980i
$714$	2.47719	+	8.93180i	0.0927066	+	0.334264i
$715$		0			0
$716$	−23.1405	−	17.0883i	−0.864800	−	0.638619i
$717$	−11.6463	+	23.5885i	−0.434937	+	0.880929i
$718$	29.4997	+	9.71166i	1.10092	+	0.362436i
$719$	13.7828			0.514012			0.257006	−	0.966410i	$-0.417264\pi$
$719$	13.7828			0.514012			0.257006	+	0.966410i	$0.417264\pi$
$720$		0			0
$721$	−8.80888			−0.328060
$722$	−7.87927	−	2.59395i	−0.293236	−	0.0965368i
$723$	−0.453728	−	0.679738i	−0.0168743	−	0.0252797i
$724$	−18.3376	−	13.5416i	−0.681512	−	0.503268i
$725$		0			0
$726$	−16.1629	+	16.4481i	−0.599861	+	0.610446i
$727$	40.0622	−	23.1299i	1.48583	−	0.857842i	0.485956	−	0.873983i	$-0.338472\pi$
$727$	40.0622	−	23.1299i	1.48583	−	0.857842i	0.999870	+	0.0161416i	$0.00513827\pi$
$728$	−13.4427	+	9.52979i	−0.498220	+	0.353197i
$729$	24.9736	−	10.2626i	0.924947	−	0.380095i
$730$		0			0
$731$	−4.67013	−	8.08890i	−0.172731	−	0.299179i
$732$	1.72518	−	36.2989i	0.0637646	−	1.34165i
$733$	−14.9365	+	25.8707i	−0.551690	+	0.955556i	0.446462	+	0.894802i	$0.352684\pi$
$733$	−14.9365	+	25.8707i	−0.551690	+	0.955556i	−0.998153	+	0.0607534i	$0.980650\pi$
$734$	28.0610	−	5.85092i	1.03575	−	0.215961i
$735$		0			0
$736$	−17.3331	−	10.4605i	−0.638907	−	0.385577i
$737$			18.6972i			0.688721i
$738$	−21.5550	−	18.5898i	−0.793451	−	0.684300i
$739$			37.3592i			1.37428i	0.726526	+	0.687139i	$0.241134\pi$
$739$			37.3592i			1.37428i	−0.726526	+	0.687139i	$0.758866\pi$
$740$		0			0
$741$	−28.5806	−	14.1110i	−1.04994	−	0.518380i
$742$	−3.02209	−	14.4940i	−0.110945	−	0.532090i
$743$	−12.2440	+	21.2072i	−0.449188	+	0.778016i	−0.998333	−	0.0577104i	$-0.981620\pi$
$743$	−12.2440	+	21.2072i	−0.449188	+	0.778016i	0.549145	+	0.835727i	$0.314953\pi$
$744$	−8.12405	−	50.9663i	−0.297842	−	1.86851i
$745$		0			0
$746$	−13.0375	+	11.6478i	−0.477337	+	0.426456i
$747$	10.3942	+	13.5722i	0.380305	+	0.496582i
$748$	−8.25381	−	0.932279i	−0.301789	−	0.0340875i
$749$	−11.7753	+	6.79847i	−0.430260	+	0.248411i
$750$		0			0
$751$	−20.1320	−	11.6232i	−0.734629	−	0.424138i	0.0854843	−	0.996340i	$-0.472756\pi$
$751$	−20.1320	−	11.6232i	−0.734629	−	0.424138i	−0.820113	+	0.572201i	$0.806090\pi$
$752$	−2.91012	+	3.13291i	−0.106121	+	0.114246i
$753$	−41.7495	+	2.71684i	−1.52144	+	0.0990072i
$754$	0.479320	−	1.45596i	0.0174558	−	0.0530230i
$755$		0			0
$756$	−11.8827	+	0.982257i	−0.432171	+	0.0357243i
$757$	31.5549			1.14688			0.573442	−	0.819246i	$-0.305608\pi$
$757$	31.5549			1.14688			0.573442	+	0.819246i	$0.305608\pi$
$758$	−3.06299	+	9.30402i	−0.111253	+	0.337937i
$759$	7.78915	−	0.506878i	0.282728	−	0.0183985i
$760$		0			0
$761$	22.9687	+	13.2610i	0.832616	+	0.480711i	0.854747	−	0.519044i	$-0.173712\pi$
$761$	22.9687	+	13.2610i	0.832616	+	0.480711i	−0.0221316	+	0.999755i	$0.507045\pi$
$762$	−6.32494	+	24.4587i	−0.229128	+	0.886044i
$763$	1.37681	−	0.794900i	0.0498438	−	0.0287773i
$764$	3.61220	−	31.9801i	0.130685	−	1.15700i
$765$		0			0
$766$	−1.52337	+	1.36099i	−0.0550415	+	0.0491745i
$767$	24.7298	+	42.8332i	0.892941	+	1.54662i
$768$	−21.8541	+	17.0411i	−0.788591	+	0.614918i
$769$	−2.70091	+	4.67812i	−0.0973974	+	0.168697i	−0.910607	−	0.413274i	$-0.864385\pi$
$769$	−2.70091	+	4.67812i	−0.0973974	+	0.168697i	0.813209	+	0.581971i	$0.197718\pi$
$770$		0			0
$771$	−22.9035	−	11.3080i	−0.824848	−	0.407249i
$772$	−22.2295	+	9.69137i	−0.800058	+	0.348800i
$773$		−	10.0058i		−	0.359884i	−0.983677	−	0.179942i	$-0.942409\pi$
$773$		−	10.0058i		−	0.359884i	0.983677	−	0.179942i	$-0.0575910\pi$
$774$	11.3450	−	3.95615i	0.407787	−	0.142201i
$775$		0			0
$776$	9.12905	−	19.8786i	0.327714	−	0.713600i
$777$	7.81660	−	5.21761i	0.280419	−	0.187181i
$778$	1.13101	−	0.235825i	0.0405488	−	0.00845472i
$779$	−12.1572	+	21.0569i	−0.435578	+	0.754443i
$780$		0			0
$781$	−6.09844	−	10.5628i	−0.218219	−	0.377967i
$782$	−11.1215	−	12.4484i	−0.397702	−	0.445152i
$783$	0.834917	−	0.730137i	0.0298375	−	0.0260930i
$784$	−22.1619	−	5.07112i	−0.791495	−	0.181112i
$785$		0			0
$786$	−24.6863	+	25.1219i	−0.880531	+	0.896069i
$787$	−1.99517	−	1.15191i	−0.0711202	−	0.0410613i	0.464018	−	0.885826i	$-0.346407\pi$
$787$	−1.99517	−	1.15191i	−0.0711202	−	0.0410613i	−0.535138	+	0.844764i	$0.679741\pi$
$788$	4.25503	−	5.76204i	0.151579	−	0.205264i
$789$	1.25938	+	1.88670i	0.0448352	+	0.0671684i
$790$		0			0
$791$	0.668954			0.0237853
$792$	3.16317	−	10.2060i	0.112398	−	0.362654i
$793$	53.2683			1.89161
$794$	−39.6077	−	13.0393i	−1.40562	−	0.462748i
$795$		0			0
$796$	7.59594	−	10.2862i	0.269231	−	0.364585i
$797$	8.50066	+	4.90786i	0.301109	+	0.173845i	0.642941	−	0.765916i	$-0.277714\pi$
$797$	8.50066	+	4.90786i	0.301109	+	0.173845i	−0.341832	+	0.939761i	$0.611047\pi$
$798$	2.72203	+	9.81458i	0.0963587	+	0.347432i
$799$	−3.05336	+	1.76286i	−0.108020	+	0.0623654i
$800$		0			0
$801$	0.879872	+	6.73183i	0.0310888	+	0.237858i
$802$	1.29532	+	1.44986i	0.0457392	+	0.0511963i
$803$	−5.71826	−	9.90432i	−0.201793	−	0.349516i
$804$	23.5740	+	45.7151i	0.831393	+	1.61225i
$805$		0			0
$806$	74.0586	−	15.4417i	2.60860	−	0.543912i
$807$	2.42467	+	37.2597i	0.0853525	+	1.31161i
$808$	48.9257	+	22.4686i	1.72120	+	0.790444i
$809$			2.25430i			0.0792571i	0.999214	+	0.0396285i	$0.0126175\pi$
$809$			2.25430i			0.0792571i	−0.999214	+	0.0396285i	$0.987383\pi$
$810$		0			0
$811$		−	43.2702i		−	1.51942i	−0.650260	−	0.759711i	$-0.725340\pi$
$811$		−	43.2702i		−	1.51942i	0.650260	−	0.759711i	$-0.274660\pi$
$812$	−0.448984	+	0.195743i	−0.0157563	+	0.00686923i
$813$	0.177835	+	2.73278i	0.00623694	+	0.0958426i
$814$	1.71907	+	8.24464i	0.0602533	+	0.288975i
$815$		0			0
$816$	−21.3562	+	8.12722i	−0.747615	+	0.284509i
$817$	−5.13170	−	8.88837i	−0.179536	−	0.310965i
$818$	−3.50297	+	3.12958i	−0.122478	+	0.109423i
$819$	−2.26510	−	17.3301i	−0.0791491	−	0.605564i
$820$		0			0
$821$	14.9032	−	8.60434i	0.520124	−	0.300293i	−0.216862	−	0.976202i	$-0.569582\pi$
$821$	14.9032	−	8.60434i	0.520124	−	0.300293i	0.736985	+	0.675909i	$0.236249\pi$
$822$	−17.4596	+	4.84235i	−0.608975	+	0.168896i
$823$	13.3192	+	7.68986i	0.464279	+	0.268052i	0.713842	−	0.700307i	$-0.246954\pi$
$823$	13.3192	+	7.68986i	0.464279	+	0.268052i	−0.249563	+	0.968359i	$0.580287\pi$
$824$	−2.01858	−	21.6221i	−0.0703206	−	0.753242i
$825$		0			0
$826$	4.94202	−	15.0117i	0.171955	−	0.522322i
$827$	0.827927			0.0287899			0.0143949	−	0.999896i	$-0.495418\pi$
$827$	0.827927			0.0287899			0.0143949	+	0.999896i	$0.495418\pi$
$828$	18.4055	−	11.0601i	0.639636	−	0.384366i
$829$	−30.8355			−1.07096			−0.535481	−	0.844547i	$-0.679870\pi$
$829$	−30.8355			−1.07096			−0.535481	+	0.844547i	$0.679870\pi$
$830$		0			0
$831$	−7.63542	−	11.4388i	−0.264870	−	0.396807i
$832$	−26.4721	−	30.8125i	−0.917754	−	1.06823i
$833$	−16.2342	−	9.37282i	−0.562482	−	0.324749i
$834$	−2.92307	−	2.87238i	−0.101218	−	0.0994624i
$835$		0			0
$836$	−9.06958	−	1.02442i	−0.313678	−	0.0354303i
$837$	51.8106	+	17.6683i	1.79084	+	0.610704i
$838$	−37.1959	+	33.2311i	−1.28491	+	1.14795i
$839$	7.49176	+	12.9761i	0.258644	+	0.447985i	0.965879	−	0.258994i	$-0.0833909\pi$
$839$	7.49176	+	12.9761i	0.258644	+	0.447985i	−0.707235	+	0.706979i	$0.750058\pi$
$840$		0			0
$841$	−14.4772	+	25.0753i	−0.499214	+	0.864665i
$842$	8.43889	+	40.4729i	0.290823	+	1.39479i
$843$	−9.78699	+	6.53286i	−0.337082	+	0.225004i
$844$	−11.6443	−	26.7091i	−0.400813	−	0.919364i
$845$		0			0
$846$	−1.49335	−	4.28245i	−0.0513424	−	0.147234i
$847$			10.8012i			0.371134i
$848$	34.8841	−	10.7393i	1.19792	−	0.368789i
$849$	11.8166	+	5.83415i	0.405544	+	0.200228i
$850$		0			0
$851$	−8.46260	+	14.6577i	−0.290094	+	0.502458i
$852$	−28.2287	−	18.1372i	−0.967100	−	0.621369i
$853$	1.45764	+	2.52471i	0.0499088	+	0.0864445i	0.889901	−	0.456155i	$-0.150774\pi$
$853$	1.45764	+	2.52471i	0.0499088	+	0.0864445i	−0.839992	+	0.542599i	$0.817440\pi$
$854$	−11.3403	−	12.6933i	−0.388057	−	0.434356i
$855$		0			0
$856$	−19.3857	−	27.3455i	−0.662591	−	0.934650i
$857$	−45.3198	+	26.1654i	−1.54810	+	0.893794i	−0.549809	+	0.835291i	$0.685299\pi$
$857$	−45.3198	+	26.1654i	−1.54810	+	0.893794i	−0.998287	+	0.0585032i	$0.981367\pi$
$858$	15.1635	+	3.92124i	0.517674	+	0.133869i
$859$	−1.52668	−	0.881431i	−0.0520897	−	0.0300740i	0.473729	−	0.880671i	$-0.342908\pi$
$859$	−1.52668	−	0.881431i	−0.0520897	−	0.0300740i	−0.525819	+	0.850597i	$0.676241\pi$
$860$		0			0
$861$	−13.3041	+	0.865763i	−0.453403	+	0.0295051i
$862$	−21.1222	−	6.95368i	−0.719425	−	0.236843i
$863$	−16.9992			−0.578658			−0.289329	−	0.957230i	$-0.593432\pi$
$863$	−16.9992			−0.578658			−0.289329	+	0.957230i	$0.593432\pi$
$864$	−5.13399	−	28.9420i	−0.174662	−	0.984628i
$865$		0			0
$866$	−54.5875	−	17.9709i	−1.85496	−	0.610674i
$867$	10.5815	−	0.688587i	0.359365	−	0.0233857i
$868$	−19.4460	−	14.3600i	−0.660039	−	0.487412i
$869$	7.28544	+	4.20625i	0.247142	+	0.142687i
$870$		0			0
$871$	−65.2947	+	37.6979i	−2.21243	+	1.27735i
$872$	2.26665	+	3.19733i	0.0767583	+	0.108275i
$873$	14.1070	+	18.4202i	0.477450	+	0.623428i
$874$	−12.2207	−	13.6787i	−0.413370	−	0.462689i
$875$		0			0
$876$	−26.4689	−	17.0065i	−0.894302	−	0.574596i
$877$	−18.7837	+	32.5343i	−0.634279	+	1.09860i	0.352388	+	0.935854i	$0.385370\pi$
$877$	−18.7837	+	32.5343i	−0.634279	+	1.09860i	−0.986667	+	0.162750i	$0.947964\pi$
$878$	31.2345	−	6.51262i	1.05411	−	0.219790i
$879$	15.3907	+	7.59876i	0.519114	+	0.256300i
$880$		0			0
$881$		−	32.8340i		−	1.10620i	−0.833114	−	0.553102i	$-0.813444\pi$
$881$		−	32.8340i		−	1.10620i	0.833114	−	0.553102i	$-0.186556\pi$
$882$	15.7487	−	18.2607i	0.530285	−	0.614869i
$883$			57.6883i			1.94137i	0.240363	+	0.970683i	$0.422734\pi$
$883$			57.6883i			1.94137i	−0.240363	+	0.970683i	$0.577266\pi$
$884$	−13.3859	−	30.7038i	−0.450215	−	1.03268i
$885$		0			0
$886$	4.15879	+	19.9455i	0.139717	+	0.670083i
$887$	18.8010	−	32.5642i	0.631275	−	1.09340i	−0.356017	−	0.934479i	$-0.615865\pi$
$887$	18.8010	−	32.5642i	0.631275	−	1.09340i	0.987291	−	0.158920i	$-0.0508012\pi$
$888$	14.5983	+	17.9909i	0.489885	+	0.603734i
$889$	5.91652	+	10.2477i	0.198434	+	0.343698i
$890$		0			0
$891$	7.99873	+	8.02864i	0.267967	+	0.268970i
$892$	2.47712	+	0.279795i	0.0829403	+	0.00936821i
$893$	−3.35514	+	1.93709i	−0.112275	+	0.0648222i
$894$	7.80891	+	7.67350i	0.261169	+	0.256640i
$895$		0			0
$896$	−1.70666	+	12.8677i	−0.0570157	+	0.429880i
$897$	17.4748	+	26.1794i	0.583468	+	0.874104i
$898$	−6.52204	+	19.8111i	−0.217643	+	0.661104i
$899$	2.24869			0.0749980
$900$		0			0
$901$	30.0955			1.00263
$902$	3.73604	−	11.3484i	0.124396	−	0.377861i
$903$	2.49142	−	5.04617i	0.0829094	−	0.167926i
$904$	0.153293	+	1.64200i	0.00509844	+	0.0546122i
$905$		0			0
$906$	−30.6428	+	8.49864i	−1.01804	+	0.282349i
$907$	−22.1806	+	12.8060i	−0.736494	+	0.425215i	−0.820793	−	0.571225i	$-0.806468\pi$
$907$	−22.1806	+	12.8060i	−0.736494	+	0.425215i	0.0842990	+	0.996441i	$0.473135\pi$
$908$	2.43483	−	21.5565i	0.0808027	−	0.715376i
$909$	−45.3362	+	34.7205i	−1.50371	+	1.15161i
$910$		0			0
$911$	−0.996781	−	1.72648i	−0.0330248	−	0.0572007i	0.849041	−	0.528328i	$-0.177181\pi$
$911$	−0.996781	−	1.72648i	−0.0330248	−	0.0572007i	−0.882065	+	0.471127i	$0.843847\pi$
$912$	−23.4669	+	8.93047i	−0.777067	+	0.295718i
$913$	−3.58780	+	6.21425i	−0.118739	+	0.205662i
$914$	0.294631	+	1.41305i	0.00974552	+	0.0467395i
$915$		0			0
$916$	44.3151	−	19.3200i	1.46421	−	0.638349i
$917$			16.4972i			0.544785i
$918$	2.97566	−	24.0531i	0.0982115	−	0.793870i
$919$			13.2072i			0.435667i	0.975986	+	0.217833i	$0.0698989\pi$
$919$			13.2072i			0.435667i	−0.975986	+	0.217833i	$0.930101\pi$
$920$		0			0
$921$	0.896990	+	13.7840i	0.0295568	+	0.454197i
$922$	−1.08642	+	0.226526i	−0.0357793	+	0.00746025i
$923$	24.5917	−	42.5941i	0.809446	−	1.40200i
$924$	−2.29377	−	4.44812i	−0.0754597	−	0.146332i
$925$		0			0
$926$	−30.6911	−	34.3529i	−1.00857	−	1.12891i
$927$	21.2719	+	8.83437i	0.698661	+	0.290159i
$928$	−0.583353	−	1.05721i	−0.0191495	−	0.0347047i
$929$	14.7794	−	8.53291i	0.484897	−	0.279956i	−0.237558	−	0.971373i	$-0.576347\pi$
$929$	14.7794	−	8.53291i	0.484897	−	0.279956i	0.722455	+	0.691418i	$0.243014\pi$
$930$		0			0
$931$	−17.8387	−	10.2992i	−0.584640	−	0.337542i
$932$	10.6291	−	14.3937i	0.348169	−	0.471480i
$933$	5.37215	−	10.8808i	0.175876	−	0.356223i
$934$	35.0430	+	11.5366i	1.14664	+	0.377488i
$935$		0			0
$936$	42.0192	−	9.53113i	1.37344	−	0.311535i
$937$	20.0658			0.655523			0.327761	−	0.944761i	$-0.393706\pi$
$937$	20.0658			0.655523			0.327761	+	0.944761i	$0.393706\pi$
$938$	22.8837	+	7.53358i	0.747178	+	0.245980i
$939$	−14.1361	−	21.1776i	−0.461315	−	0.691104i
$940$		0			0
$941$	−28.5447	−	16.4803i	−0.930532	−	0.537243i	−0.0435520	−	0.999051i	$-0.513867\pi$
$941$	−28.5447	−	16.4803i	−0.930532	−	0.537243i	−0.886980	+	0.461808i	$0.847201\pi$
$942$	12.6316	−	12.8545i	0.411559	−	0.418822i
$943$	20.7937	−	12.0053i	0.677136	−	0.390945i
$944$	37.9798	+	8.69061i	1.23614	+	0.282855i
$945$		0			0
$946$	3.36001	+	3.76090i	0.109243	+	0.122277i
$947$	−25.6271	−	44.3874i	−0.832767	−	1.44240i	−0.895835	−	0.444386i	$-0.853422\pi$
$947$	−25.6271	−	44.3874i	−0.832767	−	1.44240i	0.0630680	−	0.998009i	$-0.479912\pi$
$948$	23.1164	+	1.09866i	0.750787	+	0.0356828i
$949$	23.0587	−	39.9388i	0.748516	−	1.29647i
$950$		0			0
$951$	−3.34810	+	2.23487i	−0.108570	+	0.0724707i
$952$	−4.46669	+	9.72626i	−0.144766	+	0.315230i
$953$			23.0185i			0.745641i	0.927903	+	0.372821i	$0.121609\pi$
$953$			23.0185i			0.745641i	−0.927903	+	0.372821i	$0.878391\pi$
$954$	−7.23807	+	38.0312i	−0.234341	+	1.23130i
$955$		0			0
$956$	−27.8454	+	12.1397i	−0.900584	+	0.392626i
$957$	0.417446	+	0.206104i	0.0134941	+	0.00666239i
$958$	−8.70951	−	41.7708i	−0.281392	−	1.34955i
$959$	−4.24331	+	7.34963i	−0.137024	+	0.237332i
$960$		0			0
$961$	39.9909	+	69.2662i	1.29003	+	2.23439i
$962$	−25.3260	+	22.6265i	−0.816544	+	0.729506i
$963$	35.2534	−	4.60773i	1.13602	−	0.148482i
$964$	0.105918	−	0.937727i	0.00341137	−	0.0302022i
$965$		0			0
$966$	2.51807	−	9.73742i	0.0810175	−	0.313296i
$967$	38.8737	+	22.4438i	1.25010	+	0.721743i	0.971128	−	0.238558i	$-0.0766747\pi$
$967$	38.8737	+	22.4438i	1.25010	+	0.721743i	0.278967	+	0.960301i	$0.410008\pi$
$968$	−26.5125	+	2.47513i	−0.852143	+	0.0795538i
$969$	−20.6595	+	1.34441i	−0.663678	+	0.0431888i
$970$		0			0
$971$	49.5015			1.58858			0.794290	−	0.607539i	$-0.207843\pi$
$971$	49.5015			1.58858			0.794290	+	0.607539i	$0.207843\pi$
$972$	29.6798	+	9.54514i	0.951980	+	0.306161i
$973$	−1.91954			−0.0615375
$974$	−9.85293	+	29.9288i	−0.315708	+	0.958982i
$975$		0			0
$976$	28.5581	−	30.7444i	0.914123	−	0.984104i
$977$	−27.1220	−	15.6589i	−0.867710	−	0.500972i	−0.00112320	−	0.999999i	$-0.500358\pi$
$977$	−27.1220	−	15.6589i	−0.867710	−	0.500972i	−0.866586	+	0.499027i	$0.833691\pi$
$978$	−3.97489	+	15.3710i	−0.127103	+	0.491509i
$979$	−2.46789	+	1.42484i	−0.0788742	+	0.0455380i
$980$		0			0
$981$	−4.12195	+	0.538752i	−0.131604	+	0.0172010i
$982$	22.5740	−	20.1678i	0.720367	−	0.643581i
$983$	27.7206	+	48.0135i	0.884149	+	1.53139i	0.846686	+	0.532094i	$0.178595\pi$
$983$	27.7206	+	48.0135i	0.884149	+	1.53139i	0.0374637	+	0.999298i	$0.488072\pi$
$984$	−5.17376	−	32.4576i	−0.164934	−	1.03471i
$985$		0			0
$986$	−0.203222	−	0.974652i	−0.00647190	−	0.0310392i
$987$	−1.90480	−	0.940450i	−0.0606305	−	0.0299348i
$988$	−14.7089	−	33.7384i	−0.467951	−	1.07336i
$989$			10.1351i			0.322278i
$990$		0			0
$991$			5.66060i			0.179815i	0.995950	+	0.0899075i	$0.0286571\pi$
$991$			5.66060i			0.179815i	−0.995950	+	0.0899075i	$0.971343\pi$
$992$	30.7918	−	51.0224i	0.977640	−	1.61996i
$993$	21.7413	−	14.5124i	0.689938	−	0.460536i
$994$	−15.3851	+	3.20791i	−0.487986	+	0.101749i
$995$		0			0
$996$	−0.937120	+	19.7176i	−0.0296938	+	0.624775i
$997$	9.37172	+	16.2323i	0.296805	+	0.514082i	0.975403	−	0.220428i	$-0.0707454\pi$
$997$	9.37172	+	16.2323i	0.296805	+	0.514082i	−0.678598	+	0.734510i	$0.737412\pi$
$998$	−15.7507	−	17.6299i	−0.498578	−	0.558064i
$999$	−24.1084	+	4.76039i	−0.762757	+	0.150612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.r.g.851.4		48
4.3	odd	2	inner	900.2.r.g.851.10		48
5.2	odd	4		180.2.n.d.59.16	yes	48
5.3	odd	4		180.2.n.d.59.9	yes	48
5.4	even	2	inner	900.2.r.g.851.21		48
9.2	odd	6	inner	900.2.r.g.551.10		48
15.2	even	4		540.2.n.d.179.9		48
15.8	even	4		540.2.n.d.179.16		48
20.3	even	4		180.2.n.d.59.22	yes	48
20.7	even	4		180.2.n.d.59.3	✓	48
20.19	odd	2	inner	900.2.r.g.851.15		48
36.11	even	6	inner	900.2.r.g.551.4		48
45.2	even	12		180.2.n.d.119.22	yes	48
45.7	odd	12		540.2.n.d.359.3		48
45.29	odd	6	inner	900.2.r.g.551.15		48
45.38	even	12		180.2.n.d.119.3	yes	48
45.43	odd	12		540.2.n.d.359.22		48
60.23	odd	4		540.2.n.d.179.3		48
60.47	odd	4		540.2.n.d.179.22		48
180.7	even	12		540.2.n.d.359.16		48
180.43	even	12		540.2.n.d.359.9		48
180.47	odd	12		180.2.n.d.119.9	yes	48
180.83	odd	12		180.2.n.d.119.16	yes	48
180.119	even	6	inner	900.2.r.g.551.21		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.3	✓	48	20.7	even	4
180.2.n.d.59.9	yes	48	5.3	odd	4
180.2.n.d.59.16	yes	48	5.2	odd	4
180.2.n.d.59.22	yes	48	20.3	even	4
180.2.n.d.119.3	yes	48	45.38	even	12
180.2.n.d.119.9	yes	48	180.47	odd	12
180.2.n.d.119.16	yes	48	180.83	odd	12
180.2.n.d.119.22	yes	48	45.2	even	12
540.2.n.d.179.3		48	60.23	odd	4
540.2.n.d.179.9		48	15.2	even	4
540.2.n.d.179.16		48	15.8	even	4
540.2.n.d.179.22		48	60.47	odd	4
540.2.n.d.359.3		48	45.7	odd	12
540.2.n.d.359.9		48	180.43	even	12
540.2.n.d.359.16		48	180.7	even	12
540.2.n.d.359.22		48	45.43	odd	12
900.2.r.g.551.4		48	36.11	even	6	inner
900.2.r.g.551.10		48	9.2	odd	6	inner
900.2.r.g.551.15		48	45.29	odd	6	inner
900.2.r.g.551.21		48	180.119	even	6	inner
900.2.r.g.851.4		48	1.1	even	1	trivial
900.2.r.g.851.10		48	4.3	odd	2	inner
900.2.r.g.851.15		48	20.19	odd	2	inner
900.2.r.g.851.21		48	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.34329 - 0.442228i) q^{2} +(1.72840 - 0.112475i) q^{3} +(1.60887 + 1.18808i) q^{4} +(-2.37148 - 0.613258i) q^{6} +(-0.993605 + 0.573658i) q^{7} +(-1.63578 - 2.30743i) q^{8} +(2.97470 - 0.388803i) q^{9} +(0.629615 + 1.09053i) q^{11} +(2.91439 + 1.87252i) q^{12} +(-2.53890 + 4.39750i) q^{13} +(1.58839 - 0.331191i) q^{14} +(1.17692 + 3.82294i) q^{16} +3.29816i q^{17} +(-4.16783 - 0.793219i) q^{18} +3.62414i q^{19} +(-1.65282 + 1.10326i) q^{21} +(-0.363497 - 1.74333i) q^{22} +(1.78942 - 3.09936i) q^{23} +(-3.08680 - 3.80416i) q^{24} +(5.35518 - 4.78436i) q^{26} +(5.09772 - 1.00658i) q^{27} +(-2.28013 - 0.257544i) q^{28} +(0.184856 - 0.106727i) q^{29} +(9.12339 + 5.26739i) q^{31} +(0.109664 - 5.65579i) q^{32} +(1.21088 + 1.81404i) q^{33} +(1.45854 - 4.43039i) q^{34} +(5.24783 + 2.90866i) q^{36} -4.72925 q^{37} +(1.60269 - 4.86827i) q^{38} +(-3.89361 + 7.88619i) q^{39} +(5.81019 + 3.35452i) q^{41} +(2.70811 - 0.751083i) q^{42} +(-2.45255 + 1.41598i) q^{43} +(-0.282666 + 2.50255i) q^{44} +(-3.77433 + 3.37202i) q^{46} +(0.534497 + 0.925776i) q^{47} +(2.46417 + 6.47517i) q^{48} +(-2.84183 + 4.92220i) q^{49} +(0.370961 + 5.70053i) q^{51} +(-9.30936 + 4.05858i) q^{52} -9.12493i q^{53} +(-7.29287 - 0.902219i) q^{54} +(2.94899 + 1.35430i) q^{56} +(0.407625 + 6.26394i) q^{57} +(-0.295514 + 0.0616167i) q^{58} +(4.87018 - 8.43539i) q^{59} +(-5.24521 - 9.08497i) q^{61} +(-9.92600 - 11.1103i) q^{62} +(-2.73264 + 2.09278i) q^{63} +(-2.64846 + 7.54889i) q^{64} +(-0.824347 - 2.97228i) q^{66} +(12.8589 + 7.42407i) q^{67} +(-3.91849 + 5.30631i) q^{68} +(2.74422 - 5.55818i) q^{69} -9.68598 q^{71} +(-5.76308 - 6.22791i) q^{72} -9.08215 q^{73} +(6.35277 + 2.09141i) q^{74} +(-4.30577 + 5.83076i) q^{76} +(-1.25118 - 0.722368i) q^{77} +(8.71775 - 8.87159i) q^{78} +(5.78563 - 3.34033i) q^{79} +(8.69767 - 2.31314i) q^{81} +(-6.32133 - 7.07552i) q^{82} +(2.84920 + 4.93496i) q^{83} +(-3.96994 - 0.188680i) q^{84} +(3.92068 - 0.817489i) q^{86} +(0.307501 - 0.205258i) q^{87} +(1.48640 - 3.23665i) q^{88} +2.26303i q^{89} -5.82584i q^{91} +(6.56123 - 2.86049i) q^{92} +(16.3613 + 8.07798i) q^{93} +(-0.308582 - 1.47996i) q^{94} +(-0.446593 - 9.78778i) q^{96} +(3.86692 + 6.69770i) q^{97} +(5.99415 - 5.35521i) q^{98} +(2.29692 + 2.99919i) 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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