LMFDB - Embedded newform 484.2.g.f.239.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [484,2,Mod(215,484)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("484.215"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(484, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	484.g (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-5,0,-1,4,10,0,-5,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$3.86475945783$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 13 x^{14} - 25 x^{13} + 35 x^{12} - 30 x^{11} - 2 x^{10} + 60 x^{9} - 116 x^{8} + \cdots + 256 $ x^16 - 5x^15 + 13x^14 - 25x^13 + 35x^12 - 30x^11 - 2x^10 + 60x^9 - 116x^8 + 120x^7 - 8x^6 - 240x^5 + 560x^4 - 800x^3 + 832x^2 - 640*x + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			239.1
Root			$-0.204982 + 1.39928i$ of defining polynomial
Character	$\chi$	$=$	484.239
Dual form			484.2.g.f.403.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26745 + 0.627351i) q^{2} +(0.873506 - 0.283819i) q^{3} +(1.21286 - 1.59027i) q^{4} +(-1.38723 - 1.00788i) q^{5} +(-0.929072 + 0.907722i) q^{6} +(-0.738720 + 2.27355i) q^{7} +(-0.539585 + 2.77648i) q^{8} +(-1.74459 + 1.26752i) q^{9} +(2.39055 + 0.407162i) q^{10} +(0.608093 - 1.73335i) q^{12} +(-0.945515 - 1.30139i) q^{13} +(-0.490020 - 3.34504i) q^{14} +(-1.49781 - 0.486669i) q^{15} +(-1.05793 - 3.85756i) q^{16} +(-3.55361 + 4.89112i) q^{17} +(1.41600 - 2.70099i) q^{18} +(-0.409609 - 1.26065i) q^{19} +(-3.28533 + 0.983654i) q^{20} +2.19562i q^{21} +7.25726i q^{23} +(0.316689 + 2.57842i) q^{24} +(-0.636498 - 1.95894i) q^{25} +(2.01482 + 1.05628i) q^{26} +(-2.78373 + 3.83148i) q^{27} +(2.71959 + 3.93226i) q^{28} +(0.516085 + 0.167686i) q^{29} +(2.20372 - 0.322825i) q^{30} +(4.83783 + 6.65870i) q^{31} +(3.76092 + 4.22558i) q^{32} +(1.43557 - 8.42861i) q^{34} +(3.31625 - 2.40939i) q^{35} +(-0.100248 + 4.31170i) q^{36} +(0.114237 - 0.351585i) q^{37} +(1.31003 + 1.34084i) q^{38} +(-1.19527 - 0.868417i) q^{39} +(3.54690 - 3.30779i) q^{40} +(-4.84269 + 1.57349i) q^{41} +(-1.37742 - 2.78284i) q^{42} -9.45922 q^{43} +3.69767 q^{45} +(-4.55285 - 9.19822i) q^{46} +(-3.81125 + 1.23835i) q^{47} +(-2.01896 - 3.06934i) q^{48} +(1.03982 + 0.755472i) q^{49} +(2.03567 + 2.08355i) q^{50} +(-1.71590 + 5.28101i) q^{51} +(-3.21634 - 0.0747804i) q^{52} +(2.00527 - 1.45691i) q^{53} +(1.12456 - 6.60259i) q^{54} +(-5.91385 - 3.27781i) q^{56} +(-0.715591 - 0.984927i) q^{57} +(-0.759311 + 0.111232i) q^{58} +(-6.70659 - 2.17910i) q^{59} +(-2.59058 + 1.79167i) q^{60} +(5.81666 - 8.00595i) q^{61} +(-10.3090 - 5.40456i) q^{62} +(-1.59300 - 4.90275i) q^{63} +(-7.41770 - 2.99629i) q^{64} +2.75830i q^{65} +4.79085i q^{67} +(3.46818 + 11.5835i) q^{68} +(2.05975 + 6.33927i) q^{69} +(-2.69164 + 5.13424i) q^{70} +(-2.06424 + 2.84118i) q^{71} +(-2.57789 - 5.52776i) q^{72} +(1.99912 + 0.649555i) q^{73} +(0.0757774 + 0.517283i) q^{74} +(-1.11197 - 1.53050i) q^{75} +(-2.50157 - 0.877601i) q^{76} +(2.05975 + 0.350820i) q^{78} +(2.08801 - 1.51703i) q^{79} +(-2.42038 + 6.41761i) q^{80} +(0.654963 - 2.01577i) q^{81} +(5.15074 - 5.03238i) q^{82} +(-3.21257 - 2.33407i) q^{83} +(3.49163 + 2.66298i) q^{84} +(9.85937 - 3.20350i) q^{85} +(11.9891 - 5.93425i) q^{86} +0.498396 q^{87} -8.45225 q^{89} +(-4.68661 + 2.31973i) q^{90} +(3.65724 - 1.18831i) q^{91} +(11.5410 + 8.80206i) q^{92} +(6.11574 + 4.44334i) q^{93} +(4.05370 - 3.96054i) q^{94} +(-0.702362 + 2.16165i) q^{95} +(4.48449 + 2.62365i) q^{96} +(6.73607 - 4.89404i) q^{97} +(-1.79186 - 0.305193i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{2} - q^{4} + 4 q^{5} + 10 q^{6} - 5 q^{8} + 10 q^{9} - 22 q^{12} - 2 q^{14} - 17 q^{16} - 10 q^{17} - 15 q^{18} - 24 q^{20} + 40 q^{24} - 4 q^{25} + 16 q^{26} - 30 q^{28} + 40 q^{29} + 30 q^{30}+ \cdots + 72 q^{97}+O(q^{100}) $ 16 * q - 5 * q^2 - q^4 + 4 * q^5 + 10 * q^6 - 5 * q^8 + 10 * q^9 - 22 * q^12 - 2 * q^14 - 17 * q^16 - 10 * q^17 - 15 * q^18 - 24 * q^20 + 40 * q^24 - 4 * q^25 + 16 * q^26 - 30 * q^28 + 40 * q^29 + 30 * q^30 - 6 * q^34 + 5 * q^36 - 12 * q^37 + 17 * q^38 - 50 * q^41 + 24 * q^42 + 40 * q^45 - 40 * q^46 - q^48 + 16 * q^49 + 25 * q^50 - 20 * q^52 - 12 * q^53 - 12 * q^56 - 50 * q^57 - 48 * q^60 + 20 * q^61 - 30 * q^62 - 37 * q^64 + 35 * q^68 + 4 * q^69 + 22 * q^70 - 10 * q^72 - 30 * q^73 + 60 * q^74 + 4 * q^78 + 32 * q^80 + 16 * q^81 + 46 * q^82 - 10 * q^84 + 60 * q^85 + 46 * q^86 - 36 * q^89 - 40 * q^90 - 54 * q^92 + 2 * q^93 + 60 * q^94 - 55 * q^96 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$-1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−1.26745	+	0.627351i	−0.896223	+	0.443604i
$2$	−1.26745	+	0.627351i	−0.896223	+	0.443604i
$3$	0.873506	−	0.283819i	0.504319	−	0.163863i	−0.0457980	−	0.998951i	$-0.514583\pi$
$3$	0.873506	−	0.283819i	0.504319	−	0.163863i	0.550117	+	0.835088i	$0.314583\pi$
$4$	1.21286	−	1.59027i	0.606431	−	0.795136i
$5$	−1.38723	−	1.00788i	−0.620390	−	0.450740i	0.232668	−	0.972556i	$-0.425254\pi$
$5$	−1.38723	−	1.00788i	−0.620390	−	0.450740i	−0.853058	+	0.521817i	$0.825254\pi$
$6$	−0.929072	+	0.907722i	−0.379292	+	0.370576i
$7$	−0.738720	+	2.27355i	−0.279210	+	0.859319i	0.708865	+	0.705344i	$0.249208\pi$
$7$	−0.738720	+	2.27355i	−0.279210	+	0.859319i	−0.988075	+	0.153975i	$0.950792\pi$
$8$	−0.539585	+	2.77648i	−0.190772	+	0.981634i
$9$	−1.74459	+	1.26752i	−0.581530	+	0.422507i
$10$	2.39055	+	0.407162i	0.755957	+	0.128756i
$11$		0			0
$11$		0			0
$12$	0.608093	−	1.73335i	0.175541	−	0.500374i
$13$	−0.945515	−	1.30139i	−0.262239	−	0.360941i	0.657512	−	0.753444i	$-0.271609\pi$
$13$	−0.945515	−	1.30139i	−0.262239	−	0.360941i	−0.919750	+	0.392504i	$0.871609\pi$
$14$	−0.490020	−	3.34504i	−0.130963	−	0.894000i
$15$	−1.49781	−	0.486669i	−0.386734	−	0.125658i
$16$	−1.05793	−	3.85756i	−0.264483	−	0.964390i
$17$	−3.55361	+	4.89112i	−0.861877	+	1.18627i	0.119242	+	0.992865i	$0.461954\pi$
$17$	−3.55361	+	4.89112i	−0.861877	+	1.18627i	−0.981119	+	0.193406i	$0.938046\pi$
$18$	1.41600	−	2.70099i	0.333755	−	0.636629i
$19$	−0.409609	−	1.26065i	−0.0939707	−	0.289212i	0.893013	−	0.450030i	$-0.148587\pi$
$19$	−0.409609	−	1.26065i	−0.0939707	−	0.289212i	−0.986984	+	0.160818i	$0.948587\pi$
$20$	−3.28533	+	0.983654i	−0.734623	+	0.219952i
$21$			2.19562i			0.479123i
$22$		0			0
$23$			7.25726i			1.51324i	0.653853	+	0.756622i	$0.273152\pi$
$23$			7.25726i			1.51324i	−0.653853	+	0.756622i	$0.726848\pi$
$24$	0.316689	+	2.57842i	0.0646438	+	0.526317i
$25$	−0.636498	−	1.95894i	−0.127300	−	0.391788i
$26$	2.01482	+	1.05628i	0.395139	+	0.207153i
$27$	−2.78373	+	3.83148i	−0.535730	+	0.737369i
$28$	2.71959	+	3.93226i	0.513954	+	0.743128i
$29$	0.516085	+	0.167686i	0.0958346	+	0.0311386i	0.356542	−	0.934279i	$-0.383956\pi$
$29$	0.516085	+	0.167686i	0.0958346	+	0.0311386i	−0.260707	+	0.965418i	$0.583956\pi$
$30$	2.20372	−	0.322825i	0.402342	−	0.0589396i
$31$	4.83783	+	6.65870i	0.868899	+	1.19594i	0.979373	+	0.202058i	$0.0647631\pi$
$31$	4.83783	+	6.65870i	0.868899	+	1.19594i	−0.110474	+	0.993879i	$0.535237\pi$
$32$	3.76092	+	4.22558i	0.664843	+	0.746983i
$33$		0			0
$34$	1.43557	−	8.42861i	0.246199	−	1.44550i
$35$	3.31625	−	2.40939i	0.560548	−	0.407262i
$36$	−0.100248	+	4.31170i	−0.0167079	+	0.718617i
$37$	0.114237	−	0.351585i	0.0187804	−	0.0578002i	−0.941227	−	0.337774i	$-0.890326\pi$
$37$	0.114237	−	0.351585i	0.0187804	−	0.0578002i	0.960008	+	0.279974i	$0.0903259\pi$
$38$	1.31003	+	1.34084i	0.212514	+	0.217513i
$39$	−1.19527	−	0.868417i	−0.191397	−	0.139058i
$40$	3.54690	−	3.30779i	0.560814	−	0.523007i
$41$	−4.84269	+	1.57349i	−0.756301	+	0.245737i	−0.661690	−	0.749777i	$-0.730161\pi$
$41$	−4.84269	+	1.57349i	−0.756301	+	0.245737i	−0.0946108	+	0.995514i	$0.530161\pi$
$42$	−1.37742	−	2.78284i	−0.212541	−	0.429401i
$43$	−9.45922			−1.44252			−0.721259	−	0.692666i	$-0.756436\pi$
$43$	−9.45922			−1.44252			−0.721259	+	0.692666i	$0.756436\pi$
$44$		0			0
$45$	3.69767			0.551216
$46$	−4.55285	−	9.19822i	−0.671281	−	1.35620i
$47$	−3.81125	+	1.23835i	−0.555928	+	0.180632i	−0.573488	−	0.819214i	$-0.694410\pi$
$47$	−3.81125	+	1.23835i	−0.555928	+	0.180632i	0.0175599	+	0.999846i	$0.494410\pi$
$48$	−2.01896	−	3.06934i	−0.291412	−	0.443022i
$49$	1.03982	+	0.755472i	0.148545	+	0.107925i
$50$	2.03567	+	2.08355i	0.287888	+	0.294659i
$51$	−1.71590	+	5.28101i	−0.240275	+	0.739489i
$52$	−3.21634	−	0.0747804i	−0.446027	−	0.0103702i
$53$	2.00527	−	1.45691i	0.275445	−	0.200122i	−0.441483	−	0.897269i	$-0.645548\pi$
$53$	2.00527	−	1.45691i	0.275445	−	0.200122i	0.716928	+	0.697147i	$0.245548\pi$
$54$	1.12456	−	6.60259i	0.153034	−	0.898499i
$55$		0			0
$56$	−5.91385	−	3.27781i	−0.790272	−	0.438016i
$57$	−0.715591	−	0.984927i	−0.0947824	−	0.130457i
$58$	−0.759311	+	0.111232i	−0.0997024	+	0.0146055i
$59$	−6.70659	−	2.17910i	−0.873124	−	0.283695i	−0.162025	−	0.986787i	$-0.551802\pi$
$59$	−6.70659	−	2.17910i	−0.873124	−	0.283695i	−0.711099	+	0.703091i	$0.751802\pi$
$60$	−2.59058	+	1.79167i	−0.334442	+	0.231304i
$61$	5.81666	−	8.00595i	0.744747	−	1.02506i	−0.253584	−	0.967313i	$-0.581609\pi$
$61$	5.81666	−	8.00595i	0.744747	−	1.02506i	0.998331	−	0.0577436i	$-0.0183906\pi$
$62$	−10.3090	−	5.40456i	−1.30925	−	0.686379i
$63$	−1.59300	−	4.90275i	−0.200699	−	0.617688i
$64$	−7.41770	−	2.99629i	−0.927212	−	0.374537i
$65$			2.75830i			0.342125i
$66$		0			0
$67$			4.79085i			0.585296i	0.956220	+	0.292648i	$0.0945364\pi$
$67$			4.79085i			0.585296i	−0.956220	+	0.292648i	$0.905464\pi$
$68$	3.46818	+	11.5835i	0.420578	+	1.40470i
$69$	2.05975	+	6.33927i	0.247965	+	0.763158i
$70$	−2.69164	+	5.13424i	−0.321713	+	0.613659i
$71$	−2.06424	+	2.84118i	−0.244980	+	0.337187i	−0.913745	−	0.406287i	$-0.866823\pi$
$71$	−2.06424	+	2.84118i	−0.244980	+	0.337187i	0.668765	+	0.743474i	$0.266823\pi$
$72$	−2.57789	−	5.52776i	−0.303807	−	0.651453i
$73$	1.99912	+	0.649555i	0.233980	+	0.0760246i	0.423660	−	0.905821i	$-0.360745\pi$
$73$	1.99912	+	0.649555i	0.233980	+	0.0760246i	−0.189680	+	0.981846i	$0.560745\pi$
$74$	0.0757774	+	0.517283i	0.00880894	+	0.0601329i
$75$	−1.11197	−	1.53050i	−0.128399	−	0.176727i
$76$	−2.50157	−	0.877601i	−0.286950	−	0.100668i
$77$		0			0
$78$	2.05975	+	0.350820i	0.233221	+	0.0397226i
$79$	2.08801	−	1.51703i	0.234919	−	0.170679i	−0.464098	−	0.885784i	$-0.653621\pi$
$79$	2.08801	−	1.51703i	0.234919	−	0.170679i	0.699017	+	0.715105i	$0.253621\pi$
$80$	−2.42038	+	6.41761i	−0.270607	+	0.717511i
$81$	0.654963	−	2.01577i	0.0727737	−	0.223974i
$82$	5.15074	−	5.03238i	0.568804	−	0.555733i
$83$	−3.21257	−	2.33407i	−0.352625	−	0.256197i	0.397344	−	0.917670i	$-0.369932\pi$
$83$	−3.21257	−	2.33407i	−0.352625	−	0.256197i	−0.749970	+	0.661472i	$0.769932\pi$
$84$	3.49163	+	2.66298i	0.380968	+	0.290555i
$85$	9.85937	−	3.20350i	1.06940	−	0.347469i
$86$	11.9891	−	5.93425i	1.29282	−	0.639906i
$87$	0.498396			0.0534337
$88$		0			0
$89$	−8.45225			−0.895937			−0.447969	−	0.894049i	$-0.647852\pi$
$89$	−8.45225			−0.895937			−0.447969	+	0.894049i	$0.647852\pi$
$90$	−4.68661	+	2.31973i	−0.494012	+	0.244522i
$91$	3.65724	−	1.18831i	0.383383	−	0.124569i
$92$	11.5410	+	8.80206i	1.20323	+	0.917678i
$93$	6.11574	+	4.44334i	0.634173	+	0.460753i
$94$	4.05370	−	3.96054i	0.418107	−	0.408499i
$95$	−0.702362	+	2.16165i	−0.0720608	+	0.221780i
$96$	4.48449	+	2.62365i	0.457696	+	0.267775i
$97$	6.73607	−	4.89404i	0.683944	−	0.496914i	−0.190720	−	0.981645i	$-0.561082\pi$
$97$	6.73607	−	4.89404i	0.683944	−	0.496914i	0.874664	+	0.484730i	$0.161082\pi$
$98$	−1.79186	−	0.305193i	−0.181005	−	0.0308291i
$99$		0			0
$100$	−3.88723	−	1.36372i	−0.388723	−	0.136372i
$101$	5.30760	+	7.30528i	0.528126	+	0.726903i	0.986843	−	0.161679i	$-0.0516910\pi$
$101$	5.30760	+	7.30528i	0.528126	+	0.726903i	−0.458718	+	0.888582i	$0.651691\pi$
$102$	−1.13822	−	7.76989i	−0.112701	−	0.769334i
$103$	8.55390	+	2.77933i	0.842840	+	0.273855i	0.698444	−	0.715665i	$-0.253876\pi$
$103$	8.55390	+	2.77933i	0.842840	+	0.273855i	0.144396	+	0.989520i	$0.453876\pi$
$104$	4.12347	−	1.92300i	0.404340	−	0.188565i
$105$	2.21293	−	3.04584i	0.215960	−	0.297243i
$106$	−1.62758	+	3.10457i	−0.158085	+	0.301543i
$107$	−0.952709	−	2.93214i	−0.0921019	−	0.283460i	0.894386	−	0.447297i	$-0.147613\pi$
$107$	−0.952709	−	2.93214i	−0.0921019	−	0.283460i	−0.986488	+	0.163836i	$0.947613\pi$
$108$	2.71681	+	9.07395i	0.261425	+	0.873142i
$109$		−	9.68863i		−	0.928002i	−0.885835	−	0.464001i	$-0.846413\pi$
$109$		−	9.68863i		−	0.928002i	0.885835	−	0.464001i	$-0.153587\pi$
$110$		0			0
$111$		−	0.339534i		−	0.0322271i
$112$	9.55186	+	0.444404i	0.902566	+	0.0419922i
$113$	−3.32368	−	10.2292i	−0.312666	−	0.962287i	−0.976705	−	0.214588i	$-0.931159\pi$
$113$	−3.32368	−	10.2292i	−0.312666	−	0.962287i	0.664039	−	0.747698i	$-0.268841\pi$
$114$	1.52487	+	0.799420i	0.142817	+	0.0748725i
$115$	7.31448	−	10.0675i	0.682079	−	0.938801i
$116$	0.892607	−	0.617336i	0.0828765	−	0.0573182i
$117$	3.29908	+	1.07193i	0.305000	+	0.0991004i
$118$	9.86734	−	1.44548i	0.908362	−	0.133067i
$119$	−8.49507	−	11.6925i	−0.778742	−	1.07185i
$120$	2.15943	−	3.89605i	0.197128	−	0.355659i
$121$		0			0
$122$	−2.34980	+	13.7962i	−0.212740	+	1.24905i
$123$	−3.78353	+	2.74890i	−0.341150	+	0.247860i
$124$	16.4568	+	0.382622i	1.47786	+	0.0343605i
$125$	−3.74079	+	11.5130i	−0.334587	+	1.02975i
$126$	5.09479	+	5.21462i	0.453880	+	0.464556i
$127$	−0.264088	−	0.191871i	−0.0234340	−	0.0170258i	0.576007	−	0.817445i	$-0.304610\pi$
$127$	−0.264088	−	0.191871i	−0.0234340	−	0.0170258i	−0.599441	+	0.800419i	$0.704610\pi$
$128$	11.2813	−	0.855842i	0.997135	−	0.0756465i
$129$	−8.26269	+	2.68471i	−0.727489	+	0.236376i
$130$	−1.73042	−	3.49601i	−0.151768	−	0.306621i
$131$	10.8360			0.946745			0.473372	−	0.880862i	$-0.343037\pi$
$131$	10.8360			0.946745			0.473372	+	0.880862i	$0.343037\pi$
$132$		0			0
$133$	3.16872			0.274763
$134$	−3.00554	−	6.07217i	−0.259639	−	0.524555i
$135$	7.72338	−	2.50948i	0.664723	−	0.215982i
$136$	−11.6626	−	12.5057i	−1.00006	−	1.07236i
$137$	1.02135	+	0.742056i	0.0872601	+	0.0633981i	0.630560	−	0.776141i	$-0.282825\pi$
$137$	1.02135	+	0.742056i	0.0872601	+	0.0633981i	−0.543300	+	0.839539i	$0.682825\pi$
$138$	−6.58758	−	6.74252i	−0.560772	−	0.573961i
$139$	3.10550	−	9.55775i	0.263405	−	0.810678i	−0.728651	−	0.684885i	$-0.759852\pi$
$139$	3.10550	−	9.55775i	0.263405	−	0.810678i	0.992057	−	0.125793i	$-0.0401475\pi$
$140$	0.190558	−	8.19600i	0.0161051	−	0.692688i
$141$	−2.97769	+	2.16342i	−0.250766	+	0.182192i
$142$	0.833905	−	4.89606i	0.0699797	−	0.410869i
$143$		0			0
$144$	6.73519	+	5.38892i	0.561266	+	0.449077i
$145$	−0.546923	−	0.752774i	−0.0454194	−	0.0625145i
$146$	−2.94129	+	0.430873i	−0.243423	+	0.0356593i
$147$	1.12270	+	0.364789i	0.0925991	+	0.0300873i
$148$	−0.420562	−	0.608091i	−0.0345700	−	0.0499848i
$149$	1.38899	−	1.91178i	0.113790	−	0.156619i	−0.748323	−	0.663335i	$-0.769141\pi$
$149$	1.38899	−	1.91178i	0.113790	−	0.156619i	0.862113	+	0.506716i	$0.169141\pi$
$150$	2.36953	+	1.24223i	0.193471	+	0.101428i
$151$	5.90285	+	18.1671i	0.480367	+	1.47842i	0.838580	+	0.544779i	$0.183386\pi$
$151$	5.90285	+	18.1671i	0.480367	+	1.47842i	−0.358213	+	0.933640i	$0.616614\pi$
$152$	3.72118	−	0.457045i	0.301827	−	0.0370713i
$153$		−	13.0373i		−	1.05400i
$154$		0			0
$155$		−	14.1131i		−	1.13359i
$156$	−2.83072	+	0.847540i	−0.226639	+	0.0678575i
$157$	3.03166	+	9.33049i	0.241953	+	0.744654i	0.996123	+	0.0879750i	$0.0280396\pi$
$157$	3.03166	+	9.33049i	0.241953	+	0.744654i	−0.754170	+	0.656679i	$0.771960\pi$
$158$	−1.69474	+	3.23267i	−0.134826	+	0.257177i
$159$	1.33811	−	1.84176i	0.106119	−	0.146061i
$160$	−0.958382	−	9.65243i	−0.0757667	−	0.763092i
$161$	−16.4997	−	5.36108i	−1.30036	−	0.422513i
$162$	0.434461	+	2.96578i	0.0341344	+	0.233014i
$163$	8.37426	+	11.5262i	0.655923	+	0.902800i	0.999338	−	0.0363837i	$-0.0115839\pi$
$163$	8.37426	+	11.5262i	0.655923	+	0.902800i	−0.343415	+	0.939184i	$0.611584\pi$
$164$	−3.37125	+	9.60962i	−0.263250	+	0.750385i
$165$		0			0
$166$	5.53605	+	0.942909i	0.429681	+	0.0731839i
$167$	0.0567326	−	0.0412187i	0.00439010	−	0.00318960i	−0.585588	−	0.810609i	$-0.699136\pi$
$167$	0.0567326	−	0.0412187i	0.00439010	−	0.00318960i	0.589978	+	0.807419i	$0.299136\pi$
$168$	−6.09610	−	1.18472i	−0.470324	−	0.0914033i
$169$	3.21760	−	9.90277i	0.247508	−	0.761751i
$170$	−10.4865	+	10.2456i	−0.804281	+	0.785799i
$171$	2.31249	+	1.68012i	0.176841	+	0.128482i
$172$	−11.4727	+	15.0427i	−0.874788	+	1.14700i
$173$	18.8576	−	6.12721i	1.43372	−	0.465843i	0.513785	−	0.857919i	$-0.328243\pi$
$173$	18.8576	−	6.12721i	1.43372	−	0.465843i	0.919933	+	0.392076i	$0.128243\pi$
$174$	−0.631693	+	0.312669i	−0.0478885	+	0.0237034i
$175$	4.92393			0.372214
$176$		0			0
$177$	−6.47672			−0.486820
$178$	10.7128	−	5.30253i	0.802959	−	0.397441i
$179$	−3.27708	+	1.06479i	−0.244941	+	0.0795861i	−0.428915	−	0.903345i	$-0.641104\pi$
$179$	−3.27708	+	1.06479i	−0.244941	+	0.0795861i	0.183974	+	0.982931i	$0.441104\pi$
$180$	4.48476	−	5.88030i	0.334274	−	0.438292i
$181$	−12.7504	−	9.26371i	−0.947730	−	0.688566i	0.00253904	−	0.999997i	$-0.499192\pi$
$181$	−12.7504	−	9.26371i	−0.947730	−	0.688566i	−0.950269	+	0.311431i	$0.899192\pi$
$182$	−3.88989	+	3.80050i	−0.288337	+	0.281712i
$183$	2.80865	−	8.64413i	0.207621	−	0.638993i
$184$	−20.1497	−	3.91591i	−1.48545	−	0.288685i
$185$	−0.512830	+	0.372593i	−0.0377040	+	0.0273936i
$186$	−10.5389	−	1.79501i	−0.772752	−	0.131616i
$187$		0			0
$188$	−2.65321	+	7.56288i	−0.193505	+	0.551580i
$189$	−6.65465	−	9.15934i	−0.484054	−	0.666244i
$190$	−0.465902	−	3.18041i	−0.0338001	−	0.230731i
$191$	6.77521	+	2.20140i	0.490237	+	0.159288i	0.543696	−	0.839282i	$-0.317025\pi$
$191$	6.77521	+	2.20140i	0.490237	+	0.159288i	−0.0534587	+	0.998570i	$0.517025\pi$
$192$	−7.32981	−	0.511995i	−0.528984	−	0.0369501i
$193$	−9.91153	+	13.6420i	−0.713447	+	0.981976i	0.286269	+	0.958149i	$0.407585\pi$
$193$	−9.91153	+	13.6420i	−0.713447	+	0.981976i	−0.999716	+	0.0238267i	$0.992415\pi$
$194$	−5.46735	+	10.4288i	−0.392533	+	0.748746i
$195$	0.782860	+	2.40939i	0.0560618	+	0.172540i
$196$	2.46256	−	0.737310i	0.175897	−	0.0526650i
$197$			24.6863i			1.75883i	0.476058	+	0.879414i	$0.342065\pi$
$197$			24.6863i			1.75883i	−0.476058	+	0.879414i	$0.657935\pi$
$198$		0			0
$199$		−	15.7596i		−	1.11717i	−0.829449	−	0.558583i	$-0.811345\pi$
$199$		−	15.7596i		−	1.11717i	0.829449	−	0.558583i	$-0.188655\pi$
$200$	5.78241	−	0.710211i	0.408878	−	0.0502195i
$201$	1.35974	+	4.18484i	0.0959084	+	0.295176i
$202$	−11.3101	−	5.92936i	−0.795775	−	0.417188i
$203$	−0.762485	+	1.04947i	−0.0535159	+	0.0736584i
$204$	6.31709	+	9.13389i	0.442284	+	0.639500i
$205$	8.30383	+	2.69808i	0.579965	+	0.188442i
$206$	−12.5853	+	1.84363i	−0.876856	+	0.128452i
$207$	−9.19872	−	12.6610i	−0.639356	−	0.879997i
$208$	−4.01990	+	5.02416i	−0.278730	+	0.348363i
$209$		0			0
$210$	−0.893972	+	5.24873i	−0.0616899	+	0.362197i
$211$	−19.3303	+	14.0443i	−1.33076	+	0.966851i	−0.331026	+	0.943622i	$0.607395\pi$
$211$	−19.3303	+	14.0443i	−1.33076	+	0.966851i	−0.999730	+	0.0232291i	$0.992605\pi$
$212$	0.115227	−	4.95595i	0.00791380	−	0.340376i
$213$	−0.996744	+	3.06766i	−0.0682958	+	0.210193i
$214$	3.04699	+	3.11866i	0.208288	+	0.213187i
$215$	13.1221	+	9.53380i	0.894923	+	0.650200i
$216$	−9.13598	−	9.79640i	−0.621624	−	0.666560i
$217$	−18.7126	+	6.08011i	−1.27030	+	0.412745i
$218$	6.07817	+	12.2799i	0.411665	+	0.831697i
$219$	1.93060			0.130458
$220$		0			0
$221$	9.72525			0.654191
$222$	0.213007	+	0.430343i	0.0142961	+	0.0288827i
$223$	−17.9430	+	5.83003i	−1.20155	+	0.390408i	−0.840331	−	0.542073i	$-0.817640\pi$
$223$	−17.9430	+	5.83003i	−1.20155	+	0.390408i	−0.361220	+	0.932481i	$0.617640\pi$
$224$	−12.3853	+	5.42910i	−0.827528	+	0.362747i
$225$	3.59343	+	2.61078i	0.239562	+	0.174052i
$226$	10.6299	+	10.8800i	0.707093	+	0.723724i
$227$	3.48214	−	10.7169i	0.231118	−	0.711308i	−0.766495	−	0.642251i	$-0.778001\pi$
$227$	3.48214	−	10.7169i	0.231118	−	0.711308i	0.997613	−	0.0690573i	$-0.0219991\pi$
$228$	−2.43422	−	0.0565958i	−0.161210	−	0.00374815i
$229$	−17.6785	+	12.8442i	−1.16823	+	0.848766i	−0.990795	−	0.135368i	$-0.956778\pi$
$229$	−17.6785	+	12.8442i	−1.16823	+	0.848766i	−0.177430	+	0.984133i	$0.556778\pi$
$230$	−2.95488	+	17.3488i	−0.194839	+	1.14395i
$231$		0			0
$232$	−0.744050	+	1.34242i	−0.0488492	+	0.0881342i
$233$	3.73432	+	5.13984i	0.244643	+	0.336722i	0.913626	−	0.406555i	$-0.133270\pi$
$233$	3.73432	+	5.13984i	0.244643	+	0.336722i	−0.668983	+	0.743278i	$0.733270\pi$
$234$	−4.85389	+	0.711053i	−0.317309	+	0.0464830i
$235$	6.53521	+	2.12342i	0.426310	+	0.138517i
$236$	−11.5995	+	8.02236i	−0.755066	+	0.522211i
$237$	1.39333	−	1.91775i	0.0905062	−	0.124571i
$238$	18.1023	+	9.49023i	1.17340	+	0.615160i
$239$	−4.62139	−	14.2232i	−0.298933	−	0.920021i	−0.981872	−	0.189546i	$-0.939298\pi$
$239$	−4.62139	−	14.2232i	−0.298933	−	0.920021i	0.682939	−	0.730476i	$-0.260702\pi$
$240$	−0.292774	+	6.29277i	−0.0188985	+	0.406197i
$241$		−	0.457365i		−	0.0294615i	−0.999891	−	0.0147307i	$-0.995311\pi$
$241$		−	0.457365i		−	0.0294615i	0.999891	−	0.0147307i	$-0.00468911\pi$
$242$		0			0
$243$		−	16.1546i		−	1.03632i
$244$	−5.67683	−	18.9602i	−0.363422	−	1.21380i
$245$	−0.681042	−	2.09603i	−0.0435102	−	0.133911i
$246$	3.07092	−	5.85770i	0.195795	−	0.373473i
$247$	−1.25330	+	1.72502i	−0.0797456	+	0.109760i
$248$	−21.0982	+	9.83920i	−1.33973	+	0.624790i
$249$	−3.46865	−	1.12703i	−0.219817	−	0.0714229i
$250$	−2.48140	−	16.9389i	−0.156938	−	1.07131i
$251$	−7.47418	−	10.2873i	−0.471766	−	0.649330i	0.505130	−	0.863043i	$-0.331444\pi$
$251$	−7.47418	−	10.2873i	−0.471766	−	0.649330i	−0.976897	+	0.213713i	$0.931444\pi$
$252$	−9.72879	−	3.41306i	−0.612856	−	0.215002i
$253$		0			0
$254$	0.455090	+	0.0775115i	0.0285549	+	0.00486351i
$255$	7.70301	−	5.59656i	0.482381	−	0.350470i
$256$	−13.7616	+	8.16206i	−0.860098	+	0.510129i
$257$	−0.460724	+	1.41796i	−0.0287392	+	0.0884501i	−0.964397	−	0.264458i	$-0.914807\pi$
$257$	−0.460724	+	1.41796i	−0.0287392	+	0.0884501i	0.935658	+	0.352908i	$0.114807\pi$
$258$	8.78830	−	8.58634i	0.547135	−	0.534562i
$259$	0.714955	+	0.519445i	0.0444251	+	0.0322767i
$260$	4.38645	+	3.34544i	0.272036	+	0.207475i
$261$	−1.11290	+	0.361604i	−0.0688870	+	0.0223827i
$262$	−13.7341	+	6.79797i	−0.848494	+	0.419980i
$263$	14.7580			0.910017			0.455008	−	0.890487i	$-0.349636\pi$
$263$	14.7580			0.910017			0.455008	+	0.890487i	$0.349636\pi$
$264$		0			0
$265$	−4.25017			−0.261086
$266$	−4.01620	+	1.98790i	−0.246249	+	0.121886i
$267$	−7.38310	+	2.39891i	−0.451838	+	0.146811i
$268$	7.61876	+	5.81064i	0.465390	+	0.354942i
$269$	−10.6338	−	7.72593i	−0.648356	−	0.471059i	0.214354	−	0.976756i	$-0.431235\pi$
$269$	−10.6338	−	7.72593i	−0.648356	−	0.471059i	−0.862711	+	0.505697i	$0.831235\pi$
$270$	−8.21468	+	8.02591i	−0.499930	+	0.488441i
$271$	3.49273	−	10.7495i	0.212168	−	0.652987i	−0.787174	−	0.616731i	$-0.788457\pi$
$271$	3.49273	−	10.7495i	0.212168	−	0.652987i	0.999343	−	0.0362561i	$-0.0115432\pi$
$272$	22.6273	+	8.53380i	1.37198	+	0.517437i
$273$	2.85736	−	2.07599i	0.172935	−	0.125645i
$274$	−1.76004	−	0.299773i	−0.106328	−	0.0181100i
$275$		0			0
$276$	12.5794	+	4.41309i	0.757188	+	0.265637i
$277$	−0.929657	−	1.27956i	−0.0558577	−	0.0768815i	0.780174	−	0.625562i	$-0.215130\pi$
$277$	−0.929657	−	1.27956i	−0.0558577	−	0.0768815i	−0.836032	+	0.548681i	$0.815130\pi$
$278$	2.05999	+	14.0622i	0.123550	+	0.843396i
$279$	−16.8801	−	5.48466i	−1.01058	−	0.328358i
$280$	4.90024	+	10.5076i	0.292846	+	0.627947i
$281$	−5.18136	+	7.13153i	−0.309094	+	0.425431i	−0.935098	−	0.354388i	$-0.884689\pi$
$281$	−5.18136	+	7.13153i	−0.309094	+	0.425431i	0.626005	+	0.779819i	$0.284689\pi$
$282$	2.41685	−	4.61008i	0.143921	−	0.274526i
$283$	6.26632	+	19.2857i	0.372494	+	1.14642i	0.945154	+	0.326625i	$0.105911\pi$
$283$	6.26632	+	19.2857i	0.372494	+	1.14642i	−0.572660	+	0.819793i	$0.694089\pi$
$284$	2.01462	+	6.72867i	0.119545	+	0.399273i
$285$			2.08756i			0.123656i
$286$		0			0
$287$		−	12.1724i		−	0.718516i
$288$	−11.9173	−	2.60486i	−0.702232	−	0.153493i
$289$	−6.04165	−	18.5943i	−0.355391	−	1.09378i
$290$	1.16545	+	0.610992i	0.0684376	+	0.0358787i
$291$	4.49497	−	6.18680i	0.263500	−	0.362677i
$292$	3.45763	−	2.39133i	0.202342	−	0.139942i
$293$	13.2689	+	4.31133i	0.775178	+	0.251871i	0.669780	−	0.742559i	$-0.266388\pi$
$293$	13.2689	+	4.31133i	0.775178	+	0.251871i	0.105398	+	0.994430i	$0.466388\pi$
$294$	−1.65182	+	0.241978i	−0.0963363	+	0.0141124i
$295$	7.10733	+	9.78240i	0.413805	+	0.569553i
$296$	0.914528	+	0.506886i	0.0531558	+	0.0294621i
$297$		0			0
$298$	−0.561118	+	3.29446i	−0.0325047	+	0.190843i
$299$	9.44453	−	6.86185i	0.546191	−	0.396831i
$300$	−3.78257	−	0.0879453i	−0.218387	−	0.00507753i
$301$	6.98771	−	21.5060i	0.402765	−	1.23958i
$302$	−18.8787	−	19.3228i	−1.08635	−	1.11190i
$303$	6.70960	+	4.87481i	0.385457	+	0.280051i
$304$	−4.42968	+	2.91377i	−0.254060	+	0.167116i
$305$	−16.1381	+	5.24360i	−0.924067	+	0.300248i
$306$	8.17894	+	16.5241i	0.467559	+	0.944620i
$307$	−5.88829			−0.336062			−0.168031	−	0.985782i	$-0.553741\pi$
$307$	−5.88829			−0.336062			−0.168031	+	0.985782i	$0.553741\pi$
$308$		0			0
$309$	8.26071			0.469935
$310$	8.85389	+	17.8877i	0.502867	+	1.01595i
$311$	24.9494	−	8.10657i	1.41475	−	0.459681i	0.500822	−	0.865550i	$-0.333031\pi$
$311$	24.9494	−	8.10657i	1.41475	−	0.459681i	0.913931	+	0.405869i	$0.133031\pi$
$312$	3.05610	−	2.85007i	0.173017	−	0.161353i
$313$	13.8600	+	10.0699i	0.783411	+	0.569182i	0.906001	−	0.423276i	$-0.139120\pi$
$313$	13.8600	+	10.0699i	0.783411	+	0.569182i	−0.122589	+	0.992457i	$0.539120\pi$
$314$	−9.69597	−	9.92403i	−0.547175	−	0.560045i
$315$	−2.73154	+	8.40682i	−0.153905	+	0.473670i
$316$	0.119981	−	5.16044i	0.00674945	−	0.290297i
$317$	−0.644937	+	0.468574i	−0.0362233	+	0.0263177i	−0.605750	−	0.795655i	$-0.707127\pi$
$317$	−0.644937	+	0.468574i	−0.0362233	+	0.0263177i	0.569526	+	0.821973i	$0.307127\pi$
$318$	−0.540567	+	3.17380i	−0.0303135	+	0.177978i
$319$		0			0
$320$	7.27016	+	11.6327i	0.406414	+	0.650290i
$321$	−1.66439	−	2.29084i	−0.0928975	−	0.127862i
$322$	24.2759	−	3.55620i	1.35284	−	0.198179i
$323$	7.62156	+	2.47640i	0.424075	+	0.137790i
$324$	−2.41124	−	3.48642i	−0.133958	−	0.193690i
$325$	−1.94753	+	2.68054i	−0.108029	+	0.148690i
$326$	−17.8449	−	9.35526i	−0.988338	−	0.518140i
$327$	−2.74982	−	8.46308i	−0.152065	−	0.468009i
$328$	−1.75571	−	14.2947i	−0.0969429	−	0.789291i
$329$		−	9.57985i		−	0.528154i
$330$		0			0
$331$			21.2979i			1.17064i	0.810803	+	0.585319i	$0.199031\pi$
$331$			21.2979i			1.17064i	−0.810803	+	0.585319i	$0.800969\pi$
$332$	−7.60821	+	2.27796i	−0.417555	+	0.125019i
$333$	0.246344	+	0.758169i	0.0134996	+	0.0415474i
$334$	−0.0460473	+	0.0878339i	−0.00251959	+	0.00480606i
$335$	4.82862	−	6.64603i	0.263816	−	0.363111i
$336$	8.46974	−	2.32281i	0.462062	−	0.126720i
$337$	−10.3436	−	3.36083i	−0.563450	−	0.183076i	0.0134229	−	0.999910i	$-0.495727\pi$
$337$	−10.3436	−	3.36083i	−0.563450	−	0.183076i	−0.576873	+	0.816834i	$0.695727\pi$
$338$	2.13435	+	14.5698i	0.116093	+	0.792494i
$339$	−5.80652	−	7.99199i	−0.315367	−	0.434065i
$340$	6.86362	−	19.5645i	0.372232	−	1.06103i
$341$		0			0
$342$	−3.98500	−	0.678731i	−0.215484	−	0.0367016i
$343$	−16.0237	+	11.6419i	−0.865198	+	0.628603i
$344$	5.10405	−	26.2633i	0.275192	−	1.41602i
$345$	3.53189	−	10.8700i	0.190150	−	0.585223i
$346$	−20.0572	+	19.5963i	−1.07828	+	1.05350i
$347$	0.520630	+	0.378260i	0.0279489	+	0.0203061i	0.601672	−	0.798743i	$-0.294501\pi$
$347$	0.520630	+	0.378260i	0.0279489	+	0.0203061i	−0.573723	+	0.819049i	$0.694501\pi$
$348$	0.604486	−	0.792586i	0.0324039	−	0.0424871i
$349$	16.4340	−	5.33972i	0.879690	−	0.285829i	0.165861	−	0.986149i	$-0.446960\pi$
$349$	16.4340	−	5.33972i	0.879690	−	0.285829i	0.713829	+	0.700321i	$0.246960\pi$
$350$	−6.24084	+	3.08903i	−0.333587	+	0.165116i
$351$	7.61832			0.406636
$352$		0			0
$353$	−28.3825			−1.51065			−0.755324	−	0.655352i	$-0.772520\pi$
$353$	−28.3825			−1.51065			−0.755324	+	0.655352i	$0.772520\pi$
$354$	8.20893	−	4.06318i	0.436300	−	0.215955i
$355$	5.72717	−	1.86087i	0.303967	−	0.0987647i
$356$	−10.2514	+	13.4414i	−0.543324	+	0.712392i
$357$	−10.7390	−	7.80237i	−0.568370	−	0.412945i
$358$	3.48555	−	3.40545i	0.184217	−	0.179984i
$359$	−8.82347	+	27.1558i	−0.465685	+	1.43323i	0.392434	+	0.919780i	$0.371633\pi$
$359$	−8.82347	+	27.1558i	−0.465685	+	1.43323i	−0.858119	+	0.513451i	$0.828367\pi$
$360$	−1.99521	+	10.2665i	−0.105157	+	0.541092i
$361$	13.9499	−	10.1352i	0.734204	−	0.533430i
$362$	21.9721	+	3.74232i	1.15483	+	0.196692i
$363$		0			0
$364$	2.54599	−	7.25726i	0.133446	−	0.380384i
$365$	−2.11858	−	2.91597i	−0.110891	−	0.152629i
$366$	1.86308	+	12.7180i	0.0973847	+	0.664781i
$367$	0.370369	+	0.120340i	0.0193331	+	0.00628170i	0.318668	−	0.947867i	$-0.396765\pi$
$367$	0.370369	+	0.120340i	0.0193331	+	0.00628170i	−0.299334	+	0.954148i	$0.596765\pi$
$368$	27.9953	−	7.67768i	1.45936	−	0.400227i
$369$	6.45409	−	8.88329i	0.335987	−	0.462446i
$370$	0.416240	−	0.793967i	0.0216393	−	0.0412764i
$371$	1.83103	+	5.63532i	0.0950621	+	0.292571i
$372$	14.4837	−	4.33652i	0.750944	−	0.224838i
$373$			9.95150i			0.515269i	0.966242	+	0.257635i	$0.0829430\pi$
$373$			9.95150i			0.515269i	−0.966242	+	0.257635i	$0.917057\pi$
$374$		0			0
$375$			11.1184i			0.574150i
$376$	−1.38177	−	11.2501i	−0.0712591	−	0.580178i
$377$	−0.269741	−	0.830178i	−0.0138924	−	0.0427564i
$378$	14.1806	+	7.43421i	0.729369	+	0.382374i
$379$	−11.8218	+	16.2713i	−0.607244	+	0.835800i	−0.996347	−	0.0853946i	$-0.972785\pi$
$379$	−11.8218	+	16.2713i	−0.607244	+	0.835800i	0.389103	+	0.921194i	$0.372785\pi$
$380$	2.58574	+	3.73873i	0.132646	+	0.191793i
$381$	−0.285140	−	0.0926475i	−0.0146081	−	0.00474647i
$382$	−9.96829	+	1.46027i	−0.510022	+	0.0747138i
$383$	6.04340	+	8.31802i	0.308803	+	0.425031i	0.935007	−	0.354628i	$-0.115392\pi$
$383$	6.04340	+	8.31802i	0.308803	+	0.425031i	−0.626204	+	0.779659i	$0.715392\pi$
$384$	9.61137	−	3.94943i	0.490478	−	0.201544i
$385$		0			0
$386$	4.00402	−	23.5086i	0.203799	−	1.19656i
$387$	16.5025	−	11.9897i	0.838868	−	0.609473i
$388$	0.387068	−	16.6480i	0.0196504	−	0.845173i
$389$	−5.95780	+	18.3362i	−0.302073	+	0.929684i	0.678681	+	0.734433i	$0.262552\pi$
$389$	−5.95780	+	18.3362i	−0.302073	+	0.929684i	−0.980753	+	0.195251i	$0.937448\pi$
$390$	−2.50377	−	2.56266i	−0.126783	−	0.129765i
$391$	−35.4962	−	25.7895i	−1.79512	−	1.30423i
$392$	−2.65862	+	2.47939i	−0.134281	+	0.125228i
$393$	9.46530	−	3.07546i	0.477461	−	0.155137i
$394$	−15.4870	−	31.2887i	−0.780223	−	1.57630i
$395$	−4.42554			−0.222673
$396$		0			0
$397$	38.1030			1.91233			0.956167	−	0.292823i	$-0.0945945\pi$
$397$	38.1030			1.91233			0.956167	+	0.292823i	$0.0945945\pi$
$398$	9.88677	+	19.9745i	0.495579	+	1.00123i
$399$	2.76790	−	0.899345i	0.138568	−	0.0450235i
$400$	−6.88336	+	4.52776i	−0.344168	+	0.226388i
$401$	3.35886	+	2.44035i	0.167733	+	0.121866i	0.668485	−	0.743725i	$-0.266943\pi$
$401$	3.35886	+	2.44035i	0.167733	+	0.121866i	−0.500752	+	0.865591i	$0.666943\pi$
$402$	−4.34876	−	4.45105i	−0.216896	−	0.221998i
$403$	4.09132	−	12.5918i	0.203803	−	0.627242i
$404$	18.0548	+	0.419776i	0.898259	+	0.0208846i
$405$	−2.94025	+	2.13622i	−0.146102	+	0.106149i
$406$	0.308026	−	1.80850i	0.0152871	−	0.0897542i
$407$		0			0
$408$	−13.7367	−	7.61373i	−0.680070	−	0.376936i
$409$	6.65491	+	9.15969i	0.329064	+	0.452918i	0.941208	−	0.337829i	$-0.109693\pi$
$409$	6.65491	+	9.15969i	0.329064	+	0.452918i	−0.612144	+	0.790747i	$0.709693\pi$
$410$	−12.2173	+	1.78973i	−0.603371	+	0.0883886i
$411$	1.10277	+	0.358311i	0.0543955	+	0.0176742i
$412$	14.7946	−	10.2321i	0.728877	−	0.504098i
$413$	9.90859	−	13.6380i	0.487570	−	0.671082i
$414$	19.6018	+	10.2763i	0.963375	+	0.505053i
$415$	2.10411	+	6.47580i	0.103287	+	0.317884i
$416$	1.94312	−	8.88977i	0.0952692	−	0.435857i
$417$		−	9.23016i		−	0.452003i
$418$		0			0
$419$			21.2095i			1.03615i	0.855335	+	0.518075i	$0.173351\pi$
$419$			21.2095i			1.03615i	−0.855335	+	0.518075i	$0.826649\pi$
$420$	−2.15973	−	7.21334i	−0.105384	−	0.351975i
$421$	7.65848	+	23.5704i	0.373251	+	1.14875i	0.944651	+	0.328077i	$0.106401\pi$
$421$	7.65848	+	23.5704i	0.373251	+	1.14875i	−0.571399	+	0.820672i	$0.693599\pi$
$422$	15.6895	−	29.9274i	0.763755	−	1.45684i
$423$	5.07944	−	6.99126i	0.246971	−	0.339926i
$424$	2.96308	+	6.35372i	0.143900	+	0.308564i
$425$	11.8433	+	3.84812i	0.574484	+	0.186661i
$426$	−0.661177	−	4.51342i	−0.0320341	−	0.218676i
$427$	13.9050	+	19.1386i	0.672911	+	0.926182i
$428$	−5.81840	−	2.04121i	−0.281243	−	0.0986657i
$429$		0			0
$430$	−22.6127	−	3.85143i	−1.09048	−	0.185732i
$431$	−1.42978	+	1.03880i	−0.0688703	+	0.0500372i	−0.621688	−	0.783265i	$-0.713553\pi$
$431$	−1.42978	+	1.03880i	−0.0688703	+	0.0500372i	0.552817	+	0.833302i	$0.313553\pi$
$432$	17.7252	+	6.68499i	0.852803	+	0.321632i
$433$	−10.1825	+	31.3386i	−0.489342	+	1.50604i	0.336251	+	0.941773i	$0.390841\pi$
$433$	−10.1825	+	31.3386i	−0.489342	+	1.50604i	−0.825592	+	0.564267i	$0.809159\pi$
$434$	19.9030	−	19.4456i	0.955374	−	0.933420i
$435$	−0.691392	−	0.502326i	−0.0331497	−	0.0240847i
$436$	−15.4076	−	11.7510i	−0.737888	−	0.562769i
$437$	9.14884	−	2.97264i	0.437648	−	0.142201i
$438$	−2.44694	+	1.21117i	−0.116920	+	0.0578717i
$439$	−27.3520			−1.30544			−0.652719	−	0.757600i	$-0.726372\pi$
$439$	−27.3520			−1.30544			−0.652719	+	0.757600i	$0.726372\pi$
$440$		0			0
$441$	−2.77163			−0.131982
$442$	−12.3263	+	6.10114i	−0.586301	+	0.290202i
$443$	−1.61235	+	0.523885i	−0.0766051	+	0.0248905i	−0.347069	−	0.937840i	$-0.612823\pi$
$443$	−1.61235	+	0.523885i	−0.0766051	+	0.0248905i	0.270464	+	0.962730i	$0.412823\pi$
$444$	−0.539951	−	0.411808i	−0.0256250	−	0.0195435i
$445$	11.7253	+	8.51889i	0.555830	+	0.403834i
$446$	19.0844	−	18.6458i	0.903672	−	0.882905i
$447$	0.670689	−	2.06417i	0.0317225	−	0.0976319i
$448$	12.2918	−	14.6510i	0.580733	−	0.692197i
$449$	14.9936	−	10.8935i	0.707590	−	0.514095i	−0.174805	−	0.984603i	$-0.555929\pi$
$449$	14.9936	−	10.8935i	0.707590	−	0.514095i	0.882395	+	0.470508i	$0.155929\pi$
$450$	−6.19236	−	1.05469i	−0.291911	−	0.0497187i
$451$		0			0
$452$	−20.2985	−	7.12111i	−0.954759	−	0.334949i
$453$	10.3124	+	14.1937i	0.484517	+	0.666880i
$454$	2.30983	+	15.7677i	0.108406	+	0.740015i
$455$	−6.27113	−	2.03761i	−0.293995	−	0.0955247i
$456$	3.12075	−	1.45537i	0.146143	−	0.0681542i
$457$	6.39687	−	8.80454i	0.299233	−	0.411859i	−0.632753	−	0.774354i	$-0.718075\pi$
$457$	6.39687	−	8.80454i	0.299233	−	0.411859i	0.931986	+	0.362495i	$0.118075\pi$
$458$	14.3488	−	27.3699i	0.670475	−	1.27891i
$459$	−8.84794	−	27.2312i	−0.412987	−	1.27104i
$460$	−7.13864	−	23.8425i	−0.332841	−	1.11166i
$461$		−	13.8278i		−	0.644024i	−0.946736	−	0.322012i	$-0.895641\pi$
$461$		−	13.8278i		−	0.644024i	0.946736	−	0.322012i	$-0.104359\pi$
$462$		0			0
$463$			37.3657i			1.73653i	0.496099	+	0.868266i	$0.334765\pi$
$463$			37.3657i			1.73653i	−0.496099	+	0.868266i	$0.665235\pi$
$464$	0.100878	−	2.16823i	0.00468314	−	0.100658i
$465$	−4.00558	−	12.3279i	−0.185754	−	0.571693i
$466$	−7.95754	−	4.17177i	−0.368626	−	0.193254i
$467$	−8.10864	+	11.1606i	−0.375223	+	0.516450i	−0.954311	−	0.298815i	$-0.903409\pi$
$467$	−8.10864	+	11.1606i	−0.375223	+	0.516450i	0.579088	+	0.815265i	$0.303409\pi$
$468$	5.70599	−	3.94632i	0.263760	−	0.182419i
$469$	−10.8922	−	3.53910i	−0.502956	−	0.163420i
$470$	−9.61519	+	1.40854i	−0.443516	+	0.0649712i
$471$	5.29635	+	7.28980i	0.244043	+	0.335896i
$472$	9.66902	−	17.4449i	0.445053	−	0.802968i
$473$		0			0
$474$	−0.562871	+	3.30475i	−0.0258535	+	0.151792i
$475$	−2.20882	+	1.60480i	−0.101347	+	0.0736332i
$476$	−28.8975	−	0.671872i	−1.32452	−	0.0307952i
$477$	−1.65171	+	5.08343i	−0.0756265	+	0.232754i
$478$	14.7803	+	15.1280i	0.676036	+	0.691936i
$479$	10.9275	+	7.93926i	0.499288	+	0.362754i	0.808745	−	0.588159i	$-0.200147\pi$
$479$	10.9275	+	7.93926i	0.499288	+	0.362754i	−0.309457	+	0.950913i	$0.600147\pi$
$480$	−3.57670	−	8.15945i	−0.163253	−	0.372426i
$481$	−0.565561	+	0.183762i	−0.0257874	+	0.00837883i
$482$	0.286928	+	0.579688i	0.0130692	+	0.0264041i
$483$	−15.9342			−0.725031
$484$		0			0
$485$	−14.2771			−0.648291
$486$	10.1346	+	20.4751i	0.459715	+	0.928772i
$487$	−33.9895	+	11.0438i	−1.54021	+	0.500445i	−0.951434	−	0.307852i	$-0.900390\pi$
$487$	−33.9895	+	11.0438i	−1.54021	+	0.500445i	−0.588776	+	0.808296i	$0.700390\pi$
$488$	19.0898	+	20.4697i	0.864154	+	0.926622i
$489$	10.5863	+	7.69141i	0.478730	+	0.347818i
$490$	2.17813	+	2.22936i	0.0983980	+	0.100712i
$491$	−12.4684	+	38.3738i	−0.562690	+	1.73178i	0.112025	+	0.993705i	$0.464266\pi$
$491$	−12.4684	+	38.3738i	−0.562690	+	1.73178i	−0.674716	+	0.738078i	$0.735734\pi$
$492$	−0.217409	+	9.35089i	−0.00980157	+	0.421570i
$493$	−2.65414	+	1.92834i	−0.119536	+	0.0868483i
$494$	0.506304	−	2.97264i	0.0227797	−	0.133745i
$495$		0			0
$496$	20.5683	−	25.7067i	0.923542	−	1.15426i
$497$	−4.93467	−	6.79198i	−0.221350	−	0.304662i
$498$	5.10339	−	0.747602i	0.228688	−	0.0335009i
$499$	3.87103	+	1.25777i	0.173291	+	0.0563057i	0.394377	−	0.918949i	$-0.370960\pi$
$499$	3.87103	+	1.25777i	0.173291	+	0.0563057i	−0.221086	+	0.975254i	$0.570960\pi$
$500$	13.7717	+	19.9125i	0.615889	+	0.890516i
$501$	0.0378577	−	0.0521066i	0.00169136	−	0.00232795i
$502$	15.9269	+	8.34975i	0.710853	+	0.372668i
$503$	−6.03101	−	18.5615i	−0.268909	−	0.827618i	−0.990767	−	0.135576i	$-0.956712\pi$
$503$	−6.03101	−	18.5615i	−0.268909	−	0.827618i	0.721858	−	0.692041i	$-0.243288\pi$
$504$	14.4719	−	1.77749i	0.644632	−	0.0791755i
$505$		−	15.4836i		−	0.689010i
$506$		0			0
$507$		−	9.56335i		−	0.424723i
$508$	−0.625430	+	0.187259i	−0.0277490	+	0.00830826i
$509$	7.25254	+	22.3210i	0.321463	+	0.989362i	0.973012	+	0.230755i	$0.0741196\pi$
$509$	7.25254	+	22.3210i	0.321463	+	0.989362i	−0.651549	+	0.758607i	$0.725880\pi$
$510$	−6.25217	+	11.9258i	−0.276851	+	0.528086i
$511$	−2.95358	+	4.06526i	−0.130659	+	0.179836i
$512$	12.3216	−	18.9783i	0.544544	−	0.838732i
$513$	5.97038	+	1.93990i	0.263599	+	0.0856485i
$514$	−0.305615	−	2.08623i	−0.0134801	−	0.0920199i
$515$	−9.06501	−	12.4769i	−0.399452	−	0.549799i
$516$	−5.75208	+	16.3961i	−0.253221	+	0.721798i
$517$		0			0
$518$	−1.23204	−	0.209844i	−0.0541329	−	0.00922000i
$519$	14.7332	−	10.7043i	0.646717	−	0.469867i
$520$	−7.65838	−	1.48834i	−0.335842	−	0.0652679i
$521$	6.32368	−	19.4623i	0.277046	−	0.852659i	−0.711625	−	0.702559i	$-0.752041\pi$
$521$	6.32368	−	19.4623i	0.277046	−	0.852659i	0.988671	−	0.150100i	$-0.0479594\pi$
$522$	1.18370	−	1.15650i	0.0518090	−	0.0506185i
$523$	−6.66151	−	4.83987i	−0.291287	−	0.211633i	0.432538	−	0.901616i	$-0.357618\pi$
$523$	−6.66151	−	4.83987i	−0.291287	−	0.211633i	−0.723826	+	0.689983i	$0.757618\pi$
$524$	13.1426	−	17.2322i	0.574136	−	0.752791i
$525$	4.30109	−	1.39751i	0.187715	−	0.0609923i
$526$	−18.7050	+	9.25844i	−0.815578	+	0.403687i
$527$	−49.7602			−2.16759
$528$		0			0
$529$	−29.6679			−1.28991
$530$	5.38689	−	2.66635i	0.233991	−	0.115819i
$531$	14.4623	−	4.69909i	0.627611	−	0.203923i
$532$	3.84322	−	5.03913i	0.166625	−	0.218474i
$533$	6.62656	+	4.81448i	0.287028	+	0.208538i
$534$	7.85275	−	7.67230i	0.339822	−	0.332013i
$535$	−1.63362	+	5.02778i	−0.0706278	+	0.217370i
$536$	−13.3017	−	2.58507i	−0.574546	−	0.111658i
$537$	−2.56035	+	1.86020i	−0.110487	+	0.0802736i
$538$	18.3247	+	3.12110i	0.790035	+	0.134560i
$539$		0			0
$540$	5.37664	−	15.3259i	0.231374	−	0.659523i
$541$	−12.9257	−	17.7907i	−0.555719	−	0.764882i	0.435055	−	0.900404i	$-0.356729\pi$
$541$	−12.9257	−	17.7907i	−0.555719	−	0.764882i	−0.990774	+	0.135522i	$0.956729\pi$
$542$	2.31685	+	15.8157i	0.0995174	+	0.679340i
$543$	−13.7668	−	4.47310i	−0.590789	−	0.191959i
$544$	−34.0326	+	3.37907i	−1.45914	+	0.144876i
$545$	−9.76502	+	13.4404i	−0.418287	+	0.575723i
$546$	−2.31918	+	4.42378i	−0.0992519	+	0.189320i
$547$	−7.83614	−	24.1171i	−0.335049	−	1.03117i	−0.966698	−	0.255920i	$-0.917622\pi$
$547$	−7.83614	−	24.1171i	−0.335049	−	1.03117i	0.631649	−	0.775255i	$-0.282378\pi$
$548$	2.41883	−	0.724217i	0.103327	−	0.0309370i
$549$			21.3398i			0.910762i
$550$		0			0
$551$		−	0.719286i		−	0.0306426i
$552$	−18.7123	+	2.29829i	−0.796447	+	0.0978218i
$553$	1.90657	+	5.86783i	0.0810758	+	0.249526i
$554$	1.98103	+	1.03856i	0.0841659	+	0.0441243i
$555$	−0.342211	+	0.471013i	−0.0145260	+	0.0199934i
$556$	−11.4329	−	16.5308i	−0.484862	−	0.701063i
$557$	−4.30585	−	1.39905i	−0.182445	−	0.0592798i	0.216370	−	0.976311i	$-0.430578\pi$
$557$	−4.30585	−	1.39905i	−0.182445	−	0.0592798i	−0.398815	+	0.917032i	$0.630578\pi$
$558$	24.8354	−	3.63818i	1.05137	−	0.154016i
$559$	8.94384	+	12.3101i	0.378284	+	0.520663i
$560$	−12.8027	−	10.2437i	−0.541015	−	0.432874i
$561$		0			0
$562$	2.09315	−	12.2894i	0.0882940	−	0.518396i
$563$	31.5504	−	22.9227i	1.32969	−	0.966076i	0.329933	−	0.944004i	$-0.392974\pi$
$563$	31.5504	−	22.9227i	1.32969	−	0.966076i	0.999756	−	0.0220712i	$-0.00702604\pi$
$564$	−0.171104	+	7.35926i	−0.00720476	+	0.309881i
$565$	−5.69917	+	17.5402i	−0.239766	+	0.737924i
$566$	−20.0412	−	20.5125i	−0.842393	−	0.862206i
$567$	4.09911	+	2.97818i	0.172146	+	0.125072i
$568$	−6.77466	−	7.26439i	−0.284258	−	0.304807i
$569$	−33.4766	+	10.8772i	−1.40341	+	0.455996i	−0.910293	−	0.413965i	$-0.864144\pi$
$569$	−33.4766	+	10.8772i	−1.40341	+	0.455996i	−0.493120	+	0.869961i	$0.664144\pi$
$570$	−1.30963	−	2.64588i	−0.0548544	−	0.110824i
$571$	28.8320			1.20658			0.603291	−	0.797521i	$-0.293856\pi$
$571$	28.8320			1.20658			0.603291	+	0.797521i	$0.293856\pi$
$572$		0			0
$573$	6.54299			0.273337
$574$	7.63639	+	15.4280i	0.318737	+	0.643951i
$575$	14.2165	−	4.61924i	0.592871	−	0.192635i
$576$	16.7387	−	4.17477i	0.697446	−	0.173949i
$577$	4.61336	+	3.35180i	0.192057	+	0.139537i	0.679658	−	0.733529i	$-0.262128\pi$
$577$	4.61336	+	3.35180i	0.192057	+	0.139537i	−0.487602	+	0.873066i	$0.662128\pi$
$578$	19.3226	+	19.7771i	0.803716	+	0.822620i
$579$	−4.78590	+	14.7295i	−0.198895	+	0.612137i
$580$	−1.86046	−	0.0432559i	−0.0772513	−	0.00179610i
$581$	7.67980	−	5.57970i	0.318612	−	0.231485i
$582$	−1.81586	+	10.6614i	−0.0752700	+	0.441929i
$583$		0			0
$584$	−2.88217	+	5.20004i	−0.119265	+	0.215179i
$585$	−3.49620	−	4.81211i	−0.144550	−	0.198956i
$586$	−19.5224	+	2.85986i	−0.806464	+	0.118140i
$587$	−40.1885	−	13.0580i	−1.65876	−	0.538962i	−0.678145	−	0.734928i	$-0.737216\pi$
$587$	−40.1885	−	13.0580i	−1.65876	−	0.538962i	−0.980611	+	0.195966i	$0.937216\pi$
$588$	1.94180	−	1.34297i	0.0800785	−	0.0553830i
$589$	6.41264	−	8.82625i	0.264228	−	0.363679i
$590$	−15.1452	−	7.93992i	−0.623517	−	0.326881i
$591$	7.00646	+	21.5637i	0.288207	+	0.887010i
$592$	−1.47711	−	0.0687233i	−0.0607090	−	0.00282451i
$593$			21.6694i			0.889855i	0.895567	+	0.444927i	$0.146771\pi$
$593$			21.6694i			0.889855i	−0.895567	+	0.444927i	$0.853229\pi$
$594$		0			0
$595$			24.7822i			1.01597i
$596$	−1.35559	−	4.52759i	−0.0555273	−	0.185457i
$597$	−4.47287	−	13.7661i	−0.183062	−	0.563408i
$598$	−7.66569	+	14.6221i	−0.313473	+	0.597942i
$599$	−11.0726	+	15.2401i	−0.452414	+	0.622694i	−0.972914	−	0.231167i	$-0.925746\pi$
$599$	−11.0726	+	15.2401i	−0.452414	+	0.622694i	0.520500	+	0.853862i	$0.325746\pi$
$600$	4.84940	−	2.26153i	0.197976	−	0.0923267i
$601$	−14.4069	−	4.68109i	−0.587670	−	0.190946i	6.34538e−5	−	1.00000i	$-0.499980\pi$
$601$	−14.4069	−	4.68109i	−0.587670	−	0.190946i	−0.587734	+	0.809054i	$0.699980\pi$
$602$	4.63520	+	31.6415i	0.188917	+	1.28961i
$603$	−6.07250	−	8.35808i	−0.247291	−	0.340367i
$604$	36.0500	+	12.6471i	1.46685	+	0.514602i
$605$		0			0
$606$	−11.5623	−	1.96931i	−0.469687	−	0.0799977i
$607$	−5.49233	+	3.99041i	−0.222927	+	0.161966i	−0.693643	−	0.720319i	$-0.743996\pi$
$607$	−5.49233	+	3.99041i	−0.222927	+	0.161966i	0.470716	+	0.882285i	$0.343996\pi$
$608$	3.78645	−	6.47202i	0.153561	−	0.262475i
$609$	−0.368175	+	1.13313i	−0.0149192	+	0.0459166i
$610$	17.1647	−	16.7703i	0.694979	−	0.679009i
$611$	5.21518	+	3.78905i	0.210984	+	0.153288i
$612$	−20.7328	−	15.8124i	−0.838074	−	0.639179i
$613$	8.52662	−	2.77047i	0.344387	−	0.111898i	−0.131716	−	0.991287i	$-0.542049\pi$
$613$	8.52662	−	2.77047i	0.344387	−	0.111898i	0.476103	+	0.879389i	$0.342049\pi$
$614$	7.46312	−	3.69402i	0.301187	−	0.149079i
$615$	8.01922			0.323366
$616$		0			0
$617$	41.7476			1.68069			0.840347	−	0.542049i	$-0.182351\pi$
$617$	41.7476			1.68069			0.840347	+	0.542049i	$0.182351\pi$
$618$	−10.4700	+	5.18236i	−0.421167	+	0.208465i
$619$	−5.76294	+	1.87249i	−0.231632	+	0.0752619i	−0.422533	−	0.906347i	$-0.638859\pi$
$619$	−5.76294	+	1.87249i	−0.231632	+	0.0752619i	0.190901	+	0.981609i	$0.438859\pi$
$620$	−22.4437	−	17.1173i	−0.901362	−	0.687447i
$621$	−27.8061	−	20.2023i	−1.11582	−	0.810690i
$622$	−26.5365	+	25.9267i	−1.06402	+	1.03957i
$623$	6.24385	−	19.2166i	0.250154	−	0.769896i
$624$	−2.08546	+	5.52957i	−0.0834851	+	0.221360i
$625$	8.46123	−	6.14745i	0.338449	−	0.245898i
$626$	−23.8841	−	4.06798i	−0.954603	−	0.162589i
$627$		0			0
$628$	18.5150	+	6.49544i	0.738829	+	0.259196i
$629$	1.31369	+	1.80814i	0.0523803	+	0.0720953i
$630$	−1.81193	−	12.3689i	−0.0721890	−	0.492787i
$631$	15.2719	+	4.96214i	0.607965	+	0.197540i	0.596789	−	0.802398i	$-0.296443\pi$
$631$	15.2719	+	4.96214i	0.607965	+	0.197540i	0.0111752	+	0.999938i	$0.496443\pi$
$632$	3.08534	+	6.61587i	0.122728	+	0.263165i
$633$	−12.8991	+	17.7541i	−0.512694	+	0.705663i
$634$	0.523465	−	0.998496i	0.0207895	−	0.0396553i
$635$	0.172968	+	0.532341i	0.00686403	+	0.0211253i
$636$	−1.30594	−	4.36176i	−0.0517841	−	0.172955i
$637$		−	2.06752i		−	0.0819181i
$638$		0			0
$639$		−	7.57317i		−	0.299590i
$640$	−16.5124	−	10.1830i	−0.652709	−	0.402518i
$641$	−6.20653	−	19.1017i	−0.245143	−	0.754473i	−0.995613	−	0.0935681i	$-0.970173\pi$
$641$	−6.20653	−	19.1017i	−0.245143	−	0.754473i	0.750470	−	0.660905i	$-0.229827\pi$
$642$	3.54670	+	1.85937i	0.139977	+	0.0733835i
$643$	−2.56484	+	3.53021i	−0.101148	+	0.139218i	−0.856591	−	0.515997i	$-0.827422\pi$
$643$	−2.56484	+	3.53021i	−0.101148	+	0.139218i	0.755443	+	0.655214i	$0.227422\pi$
$644$	−28.5375	+	19.7368i	−1.12453	+	0.777738i
$645$	14.1682	+	4.60351i	0.557871	+	0.181263i
$646$	−11.2135	+	1.64268i	−0.441190	+	0.0646305i
$647$	5.66148	+	7.79236i	0.222576	+	0.306349i	0.905672	−	0.423979i	$-0.139367\pi$
$647$	5.66148	+	7.79236i	0.222576	+	0.306349i	−0.683096	+	0.730329i	$0.739367\pi$
$648$	5.24334	+	2.90617i	0.205978	+	0.114165i
$649$		0			0
$650$	0.786755	−	4.61924i	0.0308591	−	0.181181i
$651$	−14.6200	+	10.6220i	−0.573002	+	0.416310i
$652$	28.4866	+	0.662317i	1.11562	+	0.0259383i
$653$	5.64612	−	17.3770i	0.220950	−	0.680014i	−0.777728	−	0.628601i	$-0.783628\pi$
$653$	5.64612	−	17.3770i	0.220950	−	0.680014i	0.998678	−	0.0514125i	$-0.0163723\pi$
$654$	8.79458	+	9.00143i	0.343895	+	0.351984i
$655$	−15.0320	−	10.9214i	−0.587351	−	0.426735i
$656$	11.1930	+	17.0163i	0.437015	+	0.664376i
$657$	−4.31098	+	1.40072i	−0.168187	+	0.0546473i
$658$	6.00993	+	12.1420i	0.234291	+	0.473344i
$659$	17.9779			0.700318			0.350159	−	0.936690i	$-0.386128\pi$
$659$	17.9779			0.700318			0.350159	+	0.936690i	$0.386128\pi$
$660$		0			0
$661$	2.57645			0.100212			0.0501062	−	0.998744i	$-0.484044\pi$
$661$	2.57645			0.100212			0.0501062	+	0.998744i	$0.484044\pi$
$662$	−13.3612	−	26.9940i	−0.519299	−	1.04915i
$663$	8.49507	−	2.76021i	0.329921	−	0.107198i
$664$	8.21395	−	7.66021i	0.318763	−	0.297274i
$665$	−4.39576	−	3.19370i	−0.170460	−	0.123847i
$666$	−0.787867	−	0.806397i	−0.0305292	−	0.0312473i
$667$	−1.21694	+	3.74537i	−0.0471202	+	0.145021i
$668$	0.00325997	−	0.140213i	0.000126132	−	0.00542500i
$669$	−14.0186	+	10.1851i	−0.541992	+	0.393780i
$670$	−1.95065	+	11.4528i	−0.0753602	+	0.442459i
$671$		0			0
$672$	−9.27776	+	8.25754i	−0.357897	+	0.318542i
$673$	20.1822	+	27.7784i	0.777966	+	1.07078i	0.995503	+	0.0947261i	$0.0301975\pi$
$673$	20.1822	+	27.7784i	0.777966	+	1.07078i	−0.217538	+	0.976052i	$0.569802\pi$
$674$	15.2184	−	2.22936i	0.586190	−	0.0858717i
$675$	9.27749	+	3.01444i	0.357091	+	0.116026i
$676$	−11.8456	−	17.1276i	−0.455599	−	0.658752i
$677$	10.1454	−	13.9639i	0.389919	−	0.536677i	−0.568259	−	0.822850i	$-0.692383\pi$
$677$	10.1454	−	13.9639i	0.389919	−	0.536677i	0.958178	+	0.286172i	$0.0923829\pi$
$678$	12.3733	+	6.48673i	0.475192	+	0.249121i
$679$	6.15076	+	18.9301i	0.236044	+	0.726470i
$680$	3.57450	+	29.1029i	0.137076	+	1.11605i
$681$		−	10.3496i		−	0.396598i
$682$		0			0
$683$		−	0.254052i		−	0.00972104i	−0.999988	−	0.00486052i	$-0.998453\pi$
$683$		−	0.254052i		−	0.00972104i	0.999988	−	0.00486052i	$-0.00154716\pi$
$684$	5.47659	−	1.63973i	0.209403	−	0.0626968i
$685$	−0.668948	−	2.05881i	−0.0255592	−	0.0786631i
$686$	13.0057	−	24.8080i	0.496559	−	0.947173i
$687$	−11.7968	+	16.2369i	−0.450077	+	0.619478i
$688$	10.0072	+	36.4895i	0.381521	+	1.39115i
$689$	−3.79202	−	1.23210i	−0.144465	−	0.0469394i
$690$	2.34283	+	15.9930i	0.0891900	+	0.608842i
$691$	5.57531	+	7.67375i	0.212095	+	0.291923i	0.901788	−	0.432178i	$-0.142255\pi$
$691$	5.57531	+	7.67375i	0.212095	+	0.291923i	−0.689694	+	0.724101i	$0.742255\pi$
$692$	13.1278	−	37.4202i	0.499043	−	1.42250i
$693$		0			0
$694$	−0.897175	−	0.152808i	−0.0340563	−	0.00580052i
$695$	−13.9412	+	10.1288i	−0.528818	+	0.384209i
$696$	−0.268927	+	1.38379i	−0.0101937	+	0.0524524i
$697$	9.51291	−	29.2777i	0.360327	−	1.10897i
$698$	−17.4794	+	17.0777i	−0.661604	+	0.646400i
$699$	4.72074	+	3.42981i	0.178555	+	0.129728i
$700$	5.97205	−	7.83040i	0.225722	−	0.295961i
$701$	8.15984	−	2.65129i	0.308193	−	0.100138i	−0.150837	−	0.988559i	$-0.548197\pi$
$701$	8.15984	−	2.65129i	0.308193	−	0.100138i	0.459030	+	0.888421i	$0.348197\pi$
$702$	−9.65584	+	4.77936i	−0.364436	+	0.180385i
$703$	−0.490016			−0.0184813
$704$		0			0
$705$	6.31122			0.237694
$706$	35.9734	−	17.8058i	1.35388	−	0.670129i
$707$	−20.5297	+	6.67051i	−0.772100	+	0.250870i
$708$	−7.85537	+	10.2998i	−0.295223	+	0.387088i
$709$	−5.59572	−	4.06553i	−0.210152	−	0.152684i	0.477731	−	0.878506i	$-0.341459\pi$
$709$	−5.59572	−	4.06553i	−0.210152	−	0.152684i	−0.687882	+	0.725822i	$0.741459\pi$
$710$	−6.09149	+	5.95150i	−0.228609	+	0.223356i
$711$	−1.71986	+	5.29318i	−0.0644997	+	0.198510i
$712$	4.56071	−	23.4675i	0.170920	−	0.879483i
$713$	−48.3239	+	35.1094i	−1.80975	+	1.31486i
$714$	18.5060	+	3.15197i	0.692571	+	0.117960i
$715$		0			0
$716$	−2.28135	+	6.50290i	−0.0852580	+	0.243025i
$717$	−8.07363	−	11.1124i	−0.301515	−	0.415000i
$718$	−5.85293	−	39.9541i	−0.218429	−	1.49107i
$719$	18.1005	+	5.88121i	0.675035	+	0.219332i	0.626421	−	0.779485i	$-0.284519\pi$
$719$	18.1005	+	5.88121i	0.675035	+	0.219332i	0.0486149	+	0.998818i	$0.484519\pi$
$720$	−3.91188	−	14.2640i	−0.145787	−	0.531587i
$721$	−12.6379	+	17.3945i	−0.470659	+	0.647806i
$722$	−11.3225	+	21.5973i	−0.421379	+	0.803768i
$723$	−0.129809	−	0.399511i	−0.00482765	−	0.0148580i
$724$	−30.1963	+	9.04100i	−1.12224	+	0.336006i
$725$		−	1.11771i		−	0.0415108i
$726$		0			0
$727$		−	19.7014i		−	0.730685i	−0.930873	−	0.365342i	$-0.880952\pi$
$727$		−	19.7014i		−	0.730685i	0.930873	−	0.365342i	$-0.119048\pi$
$728$	1.32593	+	10.7955i	0.0491422	+	0.400106i
$729$	−2.62010	−	8.06383i	−0.0970407	−	0.298661i
$730$	4.51453	+	2.36676i	0.167090	+	0.0875976i
$731$	33.6144	−	46.2662i	1.24327	−	1.71122i
$732$	−10.3400	−	14.9507i	−0.382178	−	0.552592i
$733$	47.3926	+	15.3988i	1.75049	+	0.568767i	0.996146	−	0.0877158i	$-0.0279567\pi$
$733$	47.3926	+	15.3988i	1.75049	+	0.568767i	0.754341	+	0.656483i	$0.227957\pi$
$734$	−0.544919	+	0.0798259i	−0.0201133	+	0.00294643i
$735$	−1.18979	−	1.63760i	−0.0438860	−	0.0604039i
$736$	−30.6661	+	27.2940i	−1.13037	+	1.00607i
$737$		0			0
$738$	−2.60730	+	15.3081i	−0.0959761	+	0.563500i
$739$	−13.2872	+	9.65373i	−0.488778	+	0.355118i	−0.804714	−	0.593662i	$-0.797682\pi$
$739$	−13.2872	+	9.65373i	−0.488778	+	0.355118i	0.315936	+	0.948781i	$0.397682\pi$
$740$	−0.0294682	+	1.26744i	−0.00108327	+	0.0465921i
$741$	−0.605172	+	1.86253i	−0.0222315	+	0.0684217i
$742$	−5.85605	−	5.99379i	−0.214983	−	0.220039i
$743$	−2.41980	−	1.75809i	−0.0887737	−	0.0644979i	0.542513	−	0.840047i	$-0.317473\pi$
$743$	−2.41980	−	1.75809i	−0.0887737	−	0.0644979i	−0.631287	+	0.775549i	$0.717473\pi$
$744$	−15.6368	+	14.5827i	−0.573274	+	0.534627i
$745$	−3.85370	+	1.25214i	−0.141189	+	0.0458749i
$746$	−6.24308	−	12.6130i	−0.228575	−	0.461796i
$747$	8.56310			0.313307
$748$		0			0
$749$	7.37013			0.269299
$750$	−6.97512	−	14.0920i	−0.254695	−	0.514567i
$751$	39.5784	−	12.8598i	1.44424	−	0.469261i	0.521021	−	0.853544i	$-0.325551\pi$
$751$	39.5784	−	12.8598i	1.44424	−	0.469261i	0.923215	+	0.384283i	$0.125551\pi$
$752$	8.80906	+	13.3921i	0.321233	+	0.488358i
$753$	−9.44849	−	6.86473i	−0.344322	−	0.250165i
$754$	0.862697	+	0.882988i	0.0314176	+	0.0321565i
$755$	10.1217	−	31.1514i	0.368367	−	1.13372i
$756$	−22.6370	−	0.526313i	−0.823300	−	0.0191418i
$757$	18.5203	−	13.4558i	0.673131	−	0.489058i	−0.197941	−	0.980214i	$-0.563425\pi$
$757$	18.5203	−	13.4558i	0.673131	−	0.489058i	0.871072	+	0.491156i	$0.163425\pi$
$758$	4.77572	−	28.0394i	0.173462	−	1.01844i
$759$		0			0
$760$	−5.62279	−	3.11649i	−0.203960	−	0.113047i
$761$	−28.1805	−	38.7871i	−1.02154	−	1.40603i	−0.911117	−	0.412147i	$-0.864779\pi$
$761$	−28.1805	−	38.7871i	−1.02154	−	1.40603i	−0.110425	−	0.993884i	$-0.535221\pi$
$762$	0.419523	−	0.0614564i	0.0151977	−	0.00222633i
$763$	22.0275	+	7.15718i	0.797450	+	0.259107i
$764$	11.7182	−	8.10443i	0.423950	−	0.293208i
$765$	−13.1401	+	18.0857i	−0.475080	+	0.653892i
$766$	−12.8780	−	6.75135i	−0.465302	−	0.243936i
$767$	3.50532	+	10.7883i	0.126570	+	0.389542i
$768$	−9.70426	+	11.0354i	−0.350172	+	0.398206i
$769$			43.0718i			1.55321i	0.629989	+	0.776604i	$0.283059\pi$
$769$			43.0718i			1.55321i	−0.629989	+	0.776604i	$0.716941\pi$
$770$		0			0
$771$			1.36936i			0.0493164i
$772$	9.67325	+	32.3079i	0.348148	+	1.16279i
$773$	−3.97191	−	12.2243i	−0.142860	−	0.439677i	0.853870	−	0.520486i	$-0.174249\pi$
$773$	−3.97191	−	12.2243i	−0.142860	−	0.439677i	−0.996730	+	0.0808097i	$0.974249\pi$
$774$	−13.3943	+	25.5493i	−0.481448	+	0.918349i
$775$	9.96472	−	13.7153i	0.357943	−	0.492667i
$776$	9.95353	+	21.3433i	0.357311	+	0.766180i
$777$	0.771946	+	0.250820i	0.0276934	+	0.00899813i
$778$	−3.95203	−	26.9779i	−0.141687	−	0.967205i
$779$	3.96722	+	5.46040i	0.142140	+	0.195639i
$780$	4.78109	+	1.67730i	0.171191	+	0.0600571i
$781$		0			0
$782$	61.1687	+	10.4183i	2.18739	+	0.372559i
$783$	−2.07913	+	1.51058i	−0.0743021	+	0.0539836i
$784$	1.81422	−	4.81040i	0.0647937	−	0.171800i
$785$	5.19844	−	15.9991i	0.185540	−	0.571034i
$786$	−10.0674	+	9.83606i	−0.359093	+	0.350841i
$787$	32.2532	+	23.4333i	1.14970	+	0.835308i	0.988441	−	0.151604i	$-0.0484439\pi$
$787$	32.2532	+	23.4333i	1.14970	+	0.835308i	0.161261	+	0.986912i	$0.448444\pi$
$788$	39.2580	+	29.9411i	1.39851	+	1.06661i
$789$	12.8912	−	4.18860i	0.458939	−	0.149118i
$790$	5.60915	−	2.77636i	0.199565	−	0.0987786i
$791$	25.7119			0.914211
$792$		0			0
$793$	−15.9186			−0.565287
$794$	−48.2936	+	23.9039i	−1.71388	+	0.848319i
$795$	−3.71255	+	1.20628i	−0.131671	+	0.0427824i
$796$	−25.0620	−	19.1142i	−0.888299	−	0.677484i
$797$	21.7562	+	15.8068i	0.770643	+	0.559905i	0.902156	−	0.431409i	$-0.141984\pi$
$797$	21.7562	+	15.8068i	0.770643	+	0.559905i	−0.131513	+	0.991314i	$0.541984\pi$
$798$	−2.94397	+	2.87632i	−0.104215	+	0.101821i
$799$	7.48677	−	23.0419i	0.264863	−	0.815165i
$800$	5.88383	−	10.0570i	0.208025	−	0.355568i
$801$	14.7457	−	10.7134i	0.521015	−	0.378539i
$802$	−5.78815	−	0.985846i	−0.204387	−	0.0348114i
$803$		0			0
$804$	8.30421	+	2.91328i	0.292867	+	0.102744i
$805$	17.4856	+	24.0669i	0.616287	+	0.848246i
$806$	2.71392	+	18.5262i	0.0955939	+	0.652557i
$807$	−11.4815	−	3.73056i	−0.404168	−	0.131322i
$808$	−23.1469	+	10.7946i	−0.814304	+	0.379754i
$809$	−6.81793	+	9.38407i	−0.239706	+	0.329926i	−0.911873	−	0.410473i	$-0.865364\pi$
$809$	−6.81793	+	9.38407i	−0.239706	+	0.329926i	0.672167	+	0.740399i	$0.265364\pi$
$810$	2.38646	−	4.55211i	0.0838518	−	0.159945i
$811$	11.3129	+	34.8176i	0.397251	+	1.22261i	0.927195	+	0.374580i	$0.122213\pi$
$811$	11.3129	+	34.8176i	0.397251	+	1.22261i	−0.529944	+	0.848033i	$0.677787\pi$
$812$	0.744154	+	2.48542i	0.0261147	+	0.0872212i
$813$		−	10.3811i		−	0.364080i
$814$		0			0
$815$		−	24.4298i		−	0.855738i
$816$	22.1871	+	1.03227i	0.776705	+	0.0361365i
$817$	3.87458	+	11.9247i	0.135554	+	0.417193i
$818$	−14.1811	−	7.43450i	−0.495831	−	0.259941i
$819$	−4.87418	+	6.70874i	−0.170318	+	0.234422i
$820$	14.3621	−	9.93296i	0.501546	−	0.346874i
$821$	−30.1599	−	9.79956i	−1.05259	−	0.342007i	−0.268905	−	0.963167i	$-0.586662\pi$
$821$	−30.1599	−	9.79956i	−1.05259	−	0.342007i	−0.783684	+	0.621160i	$0.786662\pi$
$822$	−1.62249	+	0.237681i	−0.0565909	+	0.00829007i
$823$	−10.8506	−	14.9345i	−0.378226	−	0.520584i	0.576887	−	0.816824i	$-0.304267\pi$
$823$	−10.8506	−	14.9345i	−0.378226	−	0.520584i	−0.955114	+	0.296240i	$0.904267\pi$
$824$	−12.3323	+	22.2500i	−0.429616	+	0.775117i
$825$		0			0
$826$	−4.00284	+	23.5016i	−0.139276	+	0.817727i
$827$	−15.3185	+	11.1295i	−0.532676	+	0.387012i	−0.821358	−	0.570413i	$-0.806783\pi$
$827$	−15.3185	+	11.1295i	−0.532676	+	0.387012i	0.288682	+	0.957425i	$0.406783\pi$
$828$	−31.2912	−	0.727523i	−1.08744	−	0.0252832i
$829$	2.53131	−	7.79058i	0.0879162	−	0.270578i	−0.897427	−	0.441164i	$-0.854566\pi$
$829$	2.53131	−	7.79058i	0.0879162	−	0.270578i	0.985343	+	0.170585i	$0.0545659\pi$
$830$	−6.72946	−	6.88773i	−0.233583	−	0.239077i
$831$	−1.17523	−	0.853852i	−0.0407681	−	0.0296198i
$832$	3.11420	+	12.4864i	0.107965	+	0.432887i
$833$	−7.39021	+	2.40122i	−0.256055	+	0.0831975i
$834$	5.79055	+	11.6988i	0.200510	+	0.405095i
$835$	−0.120245			−0.00416125
$836$		0			0
$837$	−38.9799			−1.34734
$838$	−13.3058	−	26.8819i	−0.459640	−	0.928621i
$839$	−34.5606	+	11.2294i	−1.19316	+	0.387682i	−0.837242	−	0.546833i	$-0.815833\pi$
$839$	−34.5606	+	11.2294i	−1.19316	+	0.387682i	−0.355922	+	0.934516i	$0.615833\pi$
$840$	7.26265	+	7.78765i	0.250585	+	0.268699i
$841$	−23.2233	−	16.8727i	−0.800802	−	0.581817i
$842$	−24.4936	−	25.0697i	−0.844106	−	0.863960i
$843$	−2.50188	+	7.70000i	−0.0861694	+	0.265202i
$844$	−1.11076	+	47.7743i	−0.0382339	+	1.64446i
$845$	−14.4444	+	10.4945i	−0.496903	+	0.361021i
$846$	−2.05198	+	12.0477i	−0.0705484	+	0.414207i
$847$		0			0
$848$	−7.74156	−	6.19413i	−0.265846	−	0.212707i
$849$	10.9473	+	15.0677i	0.375711	+	0.517123i
$850$	−17.4249	+	2.55260i	−0.597669	+	0.0875533i
$851$	2.55154	+	0.829046i	0.0874657	+	0.0284193i
$852$	3.66951	+	5.30575i	0.125715	+	0.181772i
$853$	−6.98930	+	9.61995i	−0.239309	+	0.329381i	−0.911731	−	0.410787i	$-0.865254\pi$
$853$	−6.98930	+	9.61995i	−0.239309	+	0.329381i	0.672422	+	0.740168i	$0.265254\pi$
$854$	−29.6305	−	15.5339i	−1.01394	−	0.531560i
$855$	−1.51460	−	4.66145i	−0.0517981	−	0.159418i
$856$	8.65509	−	1.06304i	0.295825	−	0.0363340i
$857$		−	35.7039i		−	1.21962i	−0.792547	−	0.609811i	$-0.791245\pi$
$857$		−	35.7039i		−	1.21962i	0.792547	−	0.609811i	$-0.208755\pi$
$858$		0			0
$859$		−	40.2518i		−	1.37337i	−0.726953	−	0.686687i	$-0.759064\pi$
$859$		−	40.2518i		−	1.37337i	0.726953	−	0.686687i	$-0.240936\pi$
$860$	31.0767	−	9.30460i	1.05971	−	0.317284i
$861$	−3.45477	−	10.6327i	−0.117738	−	0.362362i
$862$	1.16049	−	2.21360i	0.0395264	−	0.0753956i
$863$	10.6919	−	14.7161i	0.363955	−	0.500941i	−0.587290	−	0.809376i	$-0.699805\pi$
$863$	10.6919	−	14.7161i	0.363955	−	0.500941i	0.951245	+	0.308435i	$0.0998053\pi$
$864$	−26.6596	+	2.64701i	−0.906979	+	0.0900531i
$865$	−32.3354	−	10.5064i	−1.09944	−	0.357229i
$866$	−6.75445	−	46.1082i	−0.229526	−	1.56682i
$867$	−10.5548	−	14.5275i	−0.358461	−	0.493380i
$868$	−13.0268	+	37.1325i	−0.442160	+	1.26036i
$869$		0			0
$870$	1.19144	+	0.202928i	0.0403936	+	0.00687990i
$871$	6.23477	−	4.52982i	0.211257	−	0.153487i
$872$	26.9003	+	5.22784i	0.910959	+	0.177037i
$873$	−5.54839	+	17.0762i	−0.187785	+	0.577942i
$874$	−9.73082	+	9.50720i	−0.329150	+	0.321586i
$875$	−23.4119	−	17.0097i	−0.791466	−	0.575034i
$876$	2.34156	−	3.07018i	0.0791138	−	0.103732i
$877$	−37.9877	+	12.3429i	−1.28275	+	0.416791i	−0.869549	−	0.493847i	$-0.835590\pi$
$877$	−37.9877	+	12.3429i	−1.28275	+	0.416791i	−0.413203	+	0.910639i	$0.635590\pi$
$878$	34.6673	−	17.1593i	1.16996	−	0.579097i
$879$	12.8141			0.432210
$880$		0			0
$881$	21.8173			0.735045			0.367522	−	0.930015i	$-0.380206\pi$
$881$	21.8173			0.735045			0.367522	+	0.930015i	$0.380206\pi$
$882$	3.51291	−	1.73878i	0.118286	−	0.0585479i
$883$	−14.6757	+	4.76844i	−0.493878	+	0.160471i	−0.545358	−	0.838203i	$-0.683606\pi$
$883$	−14.6757	+	4.76844i	−0.493878	+	0.160471i	0.0514797	+	0.998674i	$0.483606\pi$
$884$	11.7954	−	15.4658i	0.396722	−	0.520171i
$885$	8.98473	+	6.52779i	0.302018	+	0.219429i
$886$	1.71492	−	1.67551i	0.0576137	−	0.0562898i
$887$	5.23296	−	16.1054i	0.175706	−	0.540767i	−0.823959	−	0.566649i	$-0.808240\pi$
$887$	5.23296	−	16.1054i	0.175706	−	0.540767i	0.999665	+	0.0258824i	$0.00823956\pi$
$888$	0.942710	+	0.183207i	0.0316353	+	0.00614804i
$889$	0.631316	−	0.458678i	0.0211736	−	0.0153836i
$890$	−20.2055	−	3.44143i	−0.677290	−	0.115357i
$891$		0			0
$892$	−12.4910	+	35.6053i	−0.418231	+	1.19215i
$893$	3.12224	+	4.29740i	0.104482	+	0.143807i
$894$	0.444893	+	3.03699i	0.0148794	+	0.101572i
$895$	5.61927	+	1.82581i	0.187831	+	0.0610301i
$896$	−6.38792	+	26.2808i	−0.213405	+	0.877978i
$897$	6.30233	−	8.67441i	0.210429	−	0.289630i
$898$	−12.1696	+	23.2132i	−0.406104	+	0.774633i
$899$	1.38016	+	4.24769i	0.0460309	+	0.141668i
$900$	8.51017	−	2.54801i	0.283672	−	0.0849337i
$901$			14.9853i			0.499233i
$902$		0			0
$903$		−	20.7688i		−	0.691144i
$904$	30.1947	−	3.70860i	1.00426	−	0.123346i
$905$	8.35104	+	25.7019i	0.277598	+	0.854359i
$906$	−21.9749	−	11.5204i	−0.730066	−	0.382740i
$907$	−14.6614	+	20.1797i	−0.486825	+	0.670057i	−0.979799	−	0.199987i	$-0.935910\pi$
$907$	−14.6614	+	20.1797i	−0.486825	+	0.670057i	0.492973	+	0.870044i	$0.335910\pi$
$908$	−12.8195	−	18.5357i	−0.425429	−	0.615129i
$909$	−18.5192	−	6.01725i	−0.614242	−	0.199579i
$910$	9.22664	−	1.35162i	0.305860	−	0.0448058i
$911$	−26.1026	−	35.9271i	−0.864818	−	1.19032i	−0.980399	−	0.197021i	$-0.936873\pi$
$911$	−26.1026	−	35.9271i	−0.864818	−	1.19032i	0.115582	−	0.993298i	$-0.463127\pi$
$912$	−3.04237	+	3.80242i	−0.100743	+	0.125911i
$913$		0			0
$914$	−2.58419	+	15.1724i	−0.0854773	+	0.501858i
$915$	−12.6085	+	9.16064i	−0.416825	+	0.302841i
$916$	−1.01584	+	43.6918i	−0.0335643	+	1.44362i
$917$	−8.00476	+	24.6361i	−0.264340	+	0.813556i
$918$	28.2978	+	28.9634i	0.933967	+	0.955935i
$919$	39.2030	+	28.4827i	1.29319	+	0.939556i	0.999865	−	0.0164566i	$-0.00523854\pi$
$919$	39.2030	+	28.4827i	1.29319	+	0.939556i	0.293324	+	0.956013i	$0.405239\pi$
$920$	24.0055	+	25.7408i	0.791438	+	0.848649i
$921$	−5.14346	+	1.67121i	−0.169483	+	0.0550683i
$922$	8.67487	+	17.5260i	0.285692	+	0.577189i
$923$	5.64926			0.185948
$924$		0			0
$925$	−0.761445			−0.0250362
$926$	−23.4414	−	47.3592i	−0.770333	−	1.55632i
$927$	−18.4459	+	5.99344i	−0.605843	+	0.196850i
$928$	1.23238	+	2.81141i	0.0404550	+	0.0922891i
$929$	−18.1130	−	13.1598i	−0.594267	−	0.431761i	0.249572	−	0.968356i	$-0.419710\pi$
$929$	−18.1130	−	13.1598i	−0.594267	−	0.431761i	−0.843839	+	0.536596i	$0.819710\pi$
$930$	12.8108	+	13.1121i	0.420083	+	0.429963i
$931$	0.526464	−	1.62029i	0.0172542	−	0.0531028i
$932$	12.7030	+	0.295346i	0.416099	+	0.00967436i
$933$	19.4927	−	14.1623i	0.638162	−	0.463652i
$934$	3.27570	−	19.2324i	0.107184	−	0.629305i
$935$		0			0
$936$	−4.75634	+	8.58142i	−0.155466	+	0.280493i
$937$	−21.1435	−	29.1016i	−0.690729	−	0.950707i	0.309271	−	0.950974i	$-0.399915\pi$
$937$	−21.1435	−	29.1016i	−0.690729	−	0.950707i	−1.00000		0.000266837i	$0.999915\pi$
$938$	16.0256	−	2.34761i	0.523255	−	0.0766522i
$939$	14.9648	+	4.86235i	0.488357	+	0.158677i
$940$	11.3031	−	7.81735i	0.368667	−	0.254974i
$941$	29.1444	−	40.1139i	0.950082	−	1.30768i	−0.00140961	−	0.999999i	$-0.500449\pi$
$941$	29.1444	−	40.1139i	0.950082	−	1.30768i	0.951491	−	0.307676i	$-0.0995513\pi$
$942$	−11.2861	−	5.91679i	−0.367722	−	0.192780i
$943$	−11.4192	−	35.1447i	−0.371860	−	1.14447i
$944$	−1.31092	+	28.1764i	−0.0426668	+	0.917065i
$945$			19.4133i			0.631513i
$946$		0			0
$947$		−	45.1846i		−	1.46830i	−0.678985	−	0.734152i	$-0.737580\pi$
$947$		−	45.1846i		−	1.46830i	0.678985	−	0.734152i	$-0.262420\pi$
$948$	−1.35983	−	4.54173i	−0.0441652	−	0.147509i
$949$	−1.04488	−	3.21580i	−0.0339182	−	0.104389i
$950$	1.79279	−	3.41970i	0.0581659	−	0.110950i
$951$	−0.430366	+	0.592348i	−0.0139556	+	0.0192082i
$952$	37.0477	−	17.2773i	1.20072	−	0.559961i
$953$	28.3348	+	9.20654i	0.917855	+	0.298229i	0.729586	−	0.683889i	$-0.239713\pi$
$953$	28.3348	+	9.20654i	0.917855	+	0.298229i	0.188268	+	0.982118i	$0.439713\pi$
$954$	−1.09564	−	7.47920i	−0.0354726	−	0.242148i
$955$	−7.18004	−	9.88248i	−0.232341	−	0.319790i
$956$	−28.2239	−	9.90149i	−0.912825	−	0.320237i
$957$		0			0
$958$	−18.8307	−	3.20728i	−0.608393	−	0.103622i
$959$	−2.44159	+	1.77392i	−0.0788431	+	0.0572829i
$960$	9.65213	+	8.09786i	0.311521	+	0.261357i
$961$	−11.3542	+	34.9445i	−0.366263	+	1.12724i
$962$	0.601538	−	0.587715i	0.0193944	−	0.0189487i
$963$	5.37863	+	3.90780i	0.173324	+	0.125927i
$964$	−0.727335	−	0.554721i	−0.0234259	−	0.0178664i
$965$	27.4992	−	8.93503i	0.885231	−	0.287629i
$966$	20.1958	−	9.99632i	0.649789	−	0.321626i
$967$	−2.10906			−0.0678227			−0.0339113	−	0.999425i	$-0.510796\pi$
$967$	−2.10906			−0.0678227			−0.0339113	+	0.999425i	$0.510796\pi$
$968$		0			0
$969$	7.36033			0.236448
$970$	18.0956	−	8.95676i	0.581013	−	0.287584i
$971$	54.6230	−	17.7481i	1.75293	−	0.569563i	0.756504	−	0.653989i	$-0.226906\pi$
$971$	54.6230	−	17.7481i	1.75293	−	0.569563i	0.996430	+	0.0844257i	$0.0269056\pi$
$972$	−25.6902	−	19.5933i	−0.824013	−	0.628455i
$973$	19.4359	+	14.1210i	0.623086	+	0.452698i
$974$	36.1516	−	35.3209i	1.15837	−	1.13175i
$975$	−0.940388	+	2.89422i	−0.0301165	+	0.0926891i
$976$	−37.0371	−	13.9684i	−1.18553	−	0.447118i
$977$	−4.23080	+	3.07386i	−0.135355	+	0.0983414i	−0.653403	−	0.757011i	$-0.726659\pi$
$977$	−4.23080	+	3.07386i	−0.135355	+	0.0983414i	0.518047	+	0.855352i	$0.326659\pi$
$978$	−18.2429	−	3.10715i	−0.583342	−	0.0993557i
$979$		0			0
$980$	−4.15927	−	1.45916i	−0.132863	−	0.0466110i
$981$	12.2805	+	16.9027i	0.392087	+	0.539662i
$982$	−8.27073	−	56.4589i	−0.263930	−	1.80168i
$983$	−27.1601	−	8.82486i	−0.866273	−	0.281469i	−0.158027	−	0.987435i	$-0.550513\pi$
$983$	−27.1601	−	8.82486i	−0.866273	−	0.281469i	−0.708246	+	0.705966i	$0.750513\pi$
$984$	−5.59073	−	11.9882i	−0.178226	−	0.382169i
$985$	24.8809	−	34.2457i	0.792773	−	1.09116i
$986$	2.15424	−	4.10916i	0.0686050	−	0.130862i
$987$	−2.71895	−	8.36806i	−0.0865451	−	0.266358i
$988$	1.22317	+	4.08530i	0.0389143	+	0.129971i
$989$		−	68.6481i		−	2.18288i
$990$		0			0
$991$		−	0.537995i		−	0.0170900i	−0.999963	−	0.00854499i	$-0.997280\pi$
$991$		−	0.537995i		−	0.0170900i	0.999963	−	0.00854499i	$-0.00271999\pi$
$992$	−9.94216	+	45.4854i	−0.315664	+	1.44416i
$993$	6.04475	+	18.6038i	0.191824	+	0.590375i
$994$	10.5154	+	5.51274i	0.333528	+	0.174853i
$995$	−15.8838	+	21.8622i	−0.503551	+	0.693078i
$996$	−5.99929	+	4.14917i	−0.190095	+	0.131471i
$997$	−23.1078	−	7.50819i	−0.731832	−	0.237787i	−0.0806867	−	0.996740i	$-0.525711\pi$
$997$	−23.1078	−	7.50819i	−0.731832	−	0.237787i	−0.651146	+	0.758953i	$0.725711\pi$
$998$	−5.69540	+	0.834326i	−0.180285	+	0.0264101i
$999$	1.02909	+	1.41641i	0.0325588	+	0.0448134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.2.g.f.239.1		16
4.3	odd	2	inner	484.2.g.f.239.4		16
11.2	odd	10		484.2.c.d.483.1		16
11.3	even	5		44.2.g.a.39.4	yes	16
11.4	even	5		484.2.g.j.403.1		16
11.5	even	5		484.2.g.i.475.2		16
11.6	odd	10		44.2.g.a.35.3	✓	16
11.7	odd	10	inner	484.2.g.f.403.4		16
11.8	odd	10		484.2.g.i.215.1		16
11.9	even	5		484.2.c.d.483.16		16
11.10	odd	2		484.2.g.j.239.4		16
33.14	odd	10		396.2.r.a.127.1		16
33.17	even	10		396.2.r.a.343.2		16
44.3	odd	10		44.2.g.a.39.3	yes	16
44.7	even	10	inner	484.2.g.f.403.1		16
44.15	odd	10		484.2.g.j.403.4		16
44.19	even	10		484.2.g.i.215.2		16
44.27	odd	10		484.2.g.i.475.1		16
44.31	odd	10		484.2.c.d.483.2		16
44.35	even	10		484.2.c.d.483.15		16
44.39	even	10		44.2.g.a.35.4	yes	16
44.43	even	2		484.2.g.j.239.1		16
88.3	odd	10		704.2.u.c.127.2		16
88.61	odd	10		704.2.u.c.255.2		16
88.69	even	10		704.2.u.c.127.3		16
88.83	even	10		704.2.u.c.255.3		16
132.47	even	10		396.2.r.a.127.2		16
132.83	odd	10		396.2.r.a.343.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.g.a.35.3	✓	16	11.6	odd	10
44.2.g.a.35.4	yes	16	44.39	even	10
44.2.g.a.39.3	yes	16	44.3	odd	10
44.2.g.a.39.4	yes	16	11.3	even	5
396.2.r.a.127.1		16	33.14	odd	10
396.2.r.a.127.2		16	132.47	even	10
396.2.r.a.343.1		16	132.83	odd	10
396.2.r.a.343.2		16	33.17	even	10
484.2.c.d.483.1		16	11.2	odd	10
484.2.c.d.483.2		16	44.31	odd	10
484.2.c.d.483.15		16	44.35	even	10
484.2.c.d.483.16		16	11.9	even	5
484.2.g.f.239.1		16	1.1	even	1	trivial
484.2.g.f.239.4		16	4.3	odd	2	inner
484.2.g.f.403.1		16	44.7	even	10	inner
484.2.g.f.403.4		16	11.7	odd	10	inner
484.2.g.i.215.1		16	11.8	odd	10
484.2.g.i.215.2		16	44.19	even	10
484.2.g.i.475.1		16	44.27	odd	10
484.2.g.i.475.2		16	11.5	even	5
484.2.g.j.239.1		16	44.43	even	2
484.2.g.j.239.4		16	11.10	odd	2
484.2.g.j.403.1		16	11.4	even	5
484.2.g.j.403.4		16	44.15	odd	10
704.2.u.c.127.2		16	88.3	odd	10
704.2.u.c.127.3		16	88.69	even	10
704.2.u.c.255.2		16	88.61	odd	10
704.2.u.c.255.3		16	88.83	even	10

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:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	484.g (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.26745 + 0.627351i) q^{2} +(0.873506 - 0.283819i) q^{3} +(1.21286 - 1.59027i) q^{4} +(-1.38723 - 1.00788i) q^{5} +(-0.929072 + 0.907722i) q^{6} +(-0.738720 + 2.27355i) q^{7} +(-0.539585 + 2.77648i) q^{8} +(-1.74459 + 1.26752i) q^{9} +(2.39055 + 0.407162i) q^{10} +(0.608093 - 1.73335i) q^{12} +(-0.945515 - 1.30139i) q^{13} +(-0.490020 - 3.34504i) q^{14} +(-1.49781 - 0.486669i) q^{15} +(-1.05793 - 3.85756i) q^{16} +(-3.55361 + 4.89112i) q^{17} +(1.41600 - 2.70099i) q^{18} +(-0.409609 - 1.26065i) q^{19} +(-3.28533 + 0.983654i) q^{20} +2.19562i q^{21} +7.25726i q^{23} +(0.316689 + 2.57842i) q^{24} +(-0.636498 - 1.95894i) q^{25} +(2.01482 + 1.05628i) q^{26} +(-2.78373 + 3.83148i) q^{27} +(2.71959 + 3.93226i) q^{28} +(0.516085 + 0.167686i) q^{29} +(2.20372 - 0.322825i) q^{30} +(4.83783 + 6.65870i) q^{31} +(3.76092 + 4.22558i) q^{32} +(1.43557 - 8.42861i) q^{34} +(3.31625 - 2.40939i) q^{35} +(-0.100248 + 4.31170i) q^{36} +(0.114237 - 0.351585i) q^{37} +(1.31003 + 1.34084i) q^{38} +(-1.19527 - 0.868417i) q^{39} +(3.54690 - 3.30779i) q^{40} +(-4.84269 + 1.57349i) q^{41} +(-1.37742 - 2.78284i) q^{42} -9.45922 q^{43} +3.69767 q^{45} +(-4.55285 - 9.19822i) q^{46} +(-3.81125 + 1.23835i) q^{47} +(-2.01896 - 3.06934i) q^{48} +(1.03982 + 0.755472i) q^{49} +(2.03567 + 2.08355i) q^{50} +(-1.71590 + 5.28101i) q^{51} +(-3.21634 - 0.0747804i) q^{52} +(2.00527 - 1.45691i) q^{53} +(1.12456 - 6.60259i) q^{54} +(-5.91385 - 3.27781i) q^{56} +(-0.715591 - 0.984927i) q^{57} +(-0.759311 + 0.111232i) q^{58} +(-6.70659 - 2.17910i) q^{59} +(-2.59058 + 1.79167i) q^{60} +(5.81666 - 8.00595i) q^{61} +(-10.3090 - 5.40456i) q^{62} +(-1.59300 - 4.90275i) q^{63} +(-7.41770 - 2.99629i) q^{64} +2.75830i q^{65} +4.79085i q^{67} +(3.46818 + 11.5835i) q^{68} +(2.05975 + 6.33927i) q^{69} +(-2.69164 + 5.13424i) q^{70} +(-2.06424 + 2.84118i) q^{71} +(-2.57789 - 5.52776i) q^{72} +(1.99912 + 0.649555i) q^{73} +(0.0757774 + 0.517283i) q^{74} +(-1.11197 - 1.53050i) q^{75} +(-2.50157 - 0.877601i) q^{76} +(2.05975 + 0.350820i) q^{78} +(2.08801 - 1.51703i) q^{79} +(-2.42038 + 6.41761i) q^{80} +(0.654963 - 2.01577i) q^{81} +(5.15074 - 5.03238i) q^{82} +(-3.21257 - 2.33407i) q^{83} +(3.49163 + 2.66298i) q^{84} +(9.85937 - 3.20350i) q^{85} +(11.9891 - 5.93425i) q^{86} +0.498396 q^{87} -8.45225 q^{89} +(-4.68661 + 2.31973i) q^{90} +(3.65724 - 1.18831i) q^{91} +(11.5410 + 8.80206i) q^{92} +(6.11574 + 4.44334i) q^{93} +(4.05370 - 3.96054i) q^{94} +(-0.702362 + 2.16165i) q^{95} +(4.48449 + 2.62365i) q^{96} +(6.73607 - 4.89404i) q^{97} +(-1.79186 - 0.305193i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{2} - q^{4} + 4 q^{5} + 10 q^{6} - 5 q^{8} + 10 q^{9} - 22 q^{12} - 2 q^{14} - 17 q^{16} - 10 q^{17} - 15 q^{18} - 24 q^{20} + 40 q^{24} - 4 q^{25} + 16 q^{26} - 30 q^{28} + 40 q^{29} + 30 q^{30}+ \cdots + 72 q^{97}+O(q^{100}) \) 16 * q - 5 * q^2 - q^4 + 4 * q^5 + 10 * q^6 - 5 * q^8 + 10 * q^9 - 22 * q^12 - 2 * q^14 - 17 * q^16 - 10 * q^17 - 15 * q^18 - 24 * q^20 + 40 * q^24 - 4 * q^25 + 16 * q^26 - 30 * q^28 + 40 * q^29 + 30 * q^30 - 6 * q^34 + 5 * q^36 - 12 * q^37 + 17 * q^38 - 50 * q^41 + 24 * q^42 + 40 * q^45 - 40 * q^46 - q^48 + 16 * q^49 + 25 * q^50 - 20 * q^52 - 12 * q^53 - 12 * q^56 - 50 * q^57 - 48 * q^60 + 20 * q^61 - 30 * q^62 - 37 * q^64 + 35 * q^68 + 4 * q^69 + 22 * q^70 - 10 * q^72 - 30 * q^73 + 60 * q^74 + 4 * q^78 + 32 * q^80 + 16 * q^81 + 46 * q^82 - 10 * q^84 + 60 * q^85 + 46 * q^86 - 36 * q^89 - 40 * q^90 - 54 * q^92 + 2 * q^93 + 60 * q^94 - 55 * q^96 + 72 * q^97

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