LMFDB - Embedded newform 588.2.n.g.275.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(263,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.263"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,4,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.9
Character	$\chi$	$=$	588.275
Dual form			588.2.n.g.263.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.01179 + 0.988071i) q^{2} +(-0.683917 - 1.59131i) q^{3} +(0.0474302 + 1.99944i) q^{4} +(-1.97228 - 1.13870i) q^{5} +(0.880346 - 2.28582i) q^{6} +(-1.92760 + 2.06987i) q^{8} +(-2.06452 + 2.17664i) q^{9} +(-0.870418 - 3.10088i) q^{10} +(-2.15917 - 3.73979i) q^{11} +(3.14928 - 1.44292i) q^{12} +0.406728 q^{13} +(-0.463141 + 3.91729i) q^{15} +(-3.99550 + 0.189667i) q^{16} +(-3.73979 + 2.15917i) q^{17} +(-4.23953 + 0.162413i) q^{18} +(-4.70065 - 2.71392i) q^{19} +(2.18321 - 3.99747i) q^{20} +(1.51056 - 5.91729i) q^{22} +(-0.581371 + 1.00696i) q^{23} +(4.61212 + 1.65178i) q^{24} +(0.0932716 + 0.161551i) q^{25} +(0.411523 + 0.401877i) q^{26} +(4.87566 + 1.79664i) q^{27} -3.72469i q^{29} +(-4.33916 + 3.50585i) q^{30} +(-5.05289 + 2.91729i) q^{31} +(-4.23000 - 3.75594i) q^{32} +(-4.47446 + 5.99360i) q^{33} +(-5.91729 - 1.51056i) q^{34} +(-4.44998 - 4.02463i) q^{36} +(3.91729 - 6.78494i) q^{37} +(-2.07451 - 7.39049i) q^{38} +(-0.278168 - 0.647230i) q^{39} +(6.15873 - 1.88742i) q^{40} -2.56195i q^{41} +11.0211i q^{43} +(7.37506 - 4.49450i) q^{44} +(6.55035 - 1.94210i) q^{45} +(-1.58318 + 0.444399i) q^{46} +(1.16274 - 2.01393i) q^{47} +(3.03441 + 6.22835i) q^{48} +(-0.0652529 + 0.255614i) q^{50} +(5.99360 + 4.47446i) q^{51} +(0.0192912 + 0.813228i) q^{52} +(-4.74675 + 2.74054i) q^{53} +(3.15793 + 6.63532i) q^{54} +9.83457i q^{55} +(-1.10383 + 9.33627i) q^{57} +(3.68026 - 3.76860i) q^{58} +(1.95653 + 3.38881i) q^{59} +(-7.85434 - 0.740224i) q^{60} +(5.22448 - 9.04906i) q^{61} +(-7.99494 - 2.04094i) q^{62} +(-0.568736 - 7.97976i) q^{64} +(-0.802184 - 0.463141i) q^{65} +(-10.4493 + 1.64317i) q^{66} +(6.78494 - 3.91729i) q^{67} +(-4.49450 - 7.37506i) q^{68} +(2.00000 + 0.236460i) q^{69} -4.88743 q^{71} +(-0.525816 - 8.46897i) q^{72} +(1.40673 + 2.43653i) q^{73} +(10.6675 - 2.99436i) q^{74} +(0.193287 - 0.258911i) q^{75} +(5.20336 - 9.52738i) q^{76} +(0.358062 - 0.929710i) q^{78} +(3.46410 + 2.00000i) q^{79} +(8.09624 + 4.17560i) q^{80} +(-0.475549 - 8.98743i) q^{81} +(2.53139 - 2.59215i) q^{82} -0.641735 q^{83} +9.83457 q^{85} +(-10.8896 + 11.1510i) q^{86} +(-5.92712 + 2.54738i) q^{87} +(11.9029 + 2.73961i) q^{88} +(12.1218 + 6.99851i) q^{89} +(8.54650 + 4.50723i) q^{90} +(-2.04094 - 1.11466i) q^{92} +(8.09805 + 6.04551i) q^{93} +(3.16636 - 0.888797i) q^{94} +(6.18068 + 10.7053i) q^{95} +(-3.08388 + 9.29998i) q^{96} +2.00000 q^{97} +(12.5978 + 3.02112i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} + 12 q^{6} + 4 q^{9} + 4 q^{10} - 6 q^{12} - 4 q^{16} + 8 q^{18} - 32 q^{22} + 2 q^{24} + 12 q^{25} - 20 q^{30} - 16 q^{33} - 64 q^{34} - 40 q^{36} + 16 q^{37} + 20 q^{40} + 24 q^{45} - 92 q^{48}+ \cdots + 48 q^{97}+O(q^{100}) $ 24 * q + 4 * q^4 + 12 * q^6 + 4 * q^9 + 4 * q^10 - 6 * q^12 - 4 * q^16 + 8 * q^18 - 32 * q^22 + 2 * q^24 + 12 * q^25 - 20 * q^30 - 16 * q^33 - 64 * q^34 - 40 * q^36 + 16 * q^37 + 20 * q^40 + 24 * q^45 - 92 * q^48 - 28 * q^52 + 10 * q^54 + 32 * q^57 + 32 * q^58 - 28 * q^60 - 16 * q^61 + 40 * q^64 - 12 * q^66 + 48 * q^69 + 32 * q^72 + 24 * q^73 + 120 * q^76 + 40 * q^78 - 28 * q^81 + 8 * q^82 + 80 * q^85 + 56 * q^88 + 160 * q^90 - 24 * q^93 - 34 * q^96 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.01179	+	0.988071i	0.715442	+	0.698672i
$2$	1.01179	+	0.988071i	0.715442	+	0.698672i
$3$	−0.683917	−	1.59131i	−0.394860	−	0.918742i
$3$	−0.683917	−	1.59131i	−0.394860	−	0.918742i
$4$	0.0474302	+	1.99944i	0.0237151	+	0.999719i
$5$	−1.97228	−	1.13870i	−0.882033	−	0.509242i	−0.0107045	−	0.999943i	$-0.503407\pi$
$5$	−1.97228	−	1.13870i	−0.882033	−	0.509242i	−0.871328	+	0.490701i	$0.836741\pi$
$6$	0.880346	−	2.28582i	0.359400	−	0.933184i
$7$		0			0
$7$		0			0
$8$	−1.92760	+	2.06987i	−0.681509	+	0.731810i
$9$	−2.06452	+	2.17664i	−0.688172	+	0.725548i
$10$	−0.870418	−	3.10088i	−0.275250	−	0.980584i
$11$	−2.15917	−	3.73979i	−0.651014	−	1.12759i	−0.982877	−	0.184261i	$-0.941011\pi$
$11$	−2.15917	−	3.73979i	−0.651014	−	1.12759i	0.331864	−	0.943327i	$-0.392323\pi$
$12$	3.14928	−	1.44292i	0.909119	−	0.416537i
$13$	0.406728			0.112806			0.0564031	−	0.998408i	$-0.482037\pi$
$13$	0.406728			0.112806			0.0564031	+	0.998408i	$0.482037\pi$
$14$		0			0
$15$	−0.463141	+	3.91729i	−0.119583	+	1.01144i
$16$	−3.99550	+	0.189667i	−0.998875	+	0.0474169i
$17$	−3.73979	+	2.15917i	−0.907032	+	0.523675i	−0.879475	−	0.475945i	$-0.842106\pi$
$17$	−3.73979	+	2.15917i	−0.907032	+	0.523675i	−0.0275570	+	0.999620i	$0.508773\pi$
$18$	−4.23953	+	0.162413i	−0.999267	+	0.0382810i
$19$	−4.70065	−	2.71392i	−1.07840	−	0.622616i	−0.147938	−	0.988997i	$-0.547264\pi$
$19$	−4.70065	−	2.71392i	−1.07840	−	0.622616i	−0.930465	+	0.366380i	$0.880597\pi$
$20$	2.18321	−	3.99747i	0.488181	−	0.893861i
$21$		0			0
$22$	1.51056	−	5.91729i	0.322052	−	1.26157i
$23$	−0.581371	+	1.00696i	−0.121224	+	0.209967i	−0.920251	−	0.391329i	$-0.872015\pi$
$23$	−0.581371	+	1.00696i	−0.121224	+	0.209967i	0.799026	+	0.601296i	$0.205349\pi$
$24$	4.61212	+	1.65178i	0.941444	+	0.337168i
$25$	0.0932716	+	0.161551i	0.0186543	+	0.0323102i
$26$	0.411523	+	0.401877i	0.0807063	+	0.0788145i
$27$	4.87566	+	1.79664i	0.938322	+	0.345763i
$28$		0			0
$29$		−	3.72469i		−	0.691657i	−0.938298	−	0.345829i	$-0.887598\pi$
$29$		−	3.72469i		−	0.691657i	0.938298	−	0.345829i	$-0.112402\pi$
$30$	−4.33916	+	3.50585i	−0.792218	+	0.640077i
$31$	−5.05289	+	2.91729i	−0.907525	+	0.523960i	−0.879634	−	0.475651i	$-0.842213\pi$
$31$	−5.05289	+	2.91729i	−0.907525	+	0.523960i	−0.0278913	+	0.999611i	$0.508879\pi$
$32$	−4.23000	−	3.75594i	−0.747766	−	0.663962i
$33$	−4.47446	+	5.99360i	−0.778904	+	1.04335i
$34$	−5.91729	−	1.51056i	−1.01481	−	0.259058i
$35$		0			0
$36$	−4.44998	−	4.02463i	−0.741664	−	0.670772i
$37$	3.91729	−	6.78494i	0.643998	−	1.11544i	−0.340534	−	0.940232i	$-0.610608\pi$
$37$	3.91729	−	6.78494i	0.643998	−	1.11544i	0.984532	−	0.175205i	$-0.0560588\pi$
$38$	−2.07451	−	7.39049i	−0.336531	−	1.19890i
$39$	−0.278168	−	0.647230i	−0.0445426	−	0.103640i
$40$	6.15873	−	1.88742i	0.973781	−	0.298428i
$41$		−	2.56195i		−	0.400109i	−0.979785	−	0.200054i	$-0.935888\pi$
$41$		−	2.56195i		−	0.400109i	0.979785	−	0.200054i	$-0.0641119\pi$
$42$		0			0
$43$			11.0211i			1.68070i	0.542041	+	0.840352i	$0.317652\pi$
$43$			11.0211i			1.68070i	−0.542041	+	0.840352i	$0.682348\pi$
$44$	7.37506	−	4.49450i	1.11183	−	0.677571i
$45$	6.55035	−	1.94210i	0.976469	−	0.289511i
$46$	−1.58318	+	0.444399i	−0.233427	+	0.0655230i
$47$	1.16274	−	2.01393i	0.169603	−	0.293762i	−0.768677	−	0.639637i	$-0.779085\pi$
$47$	1.16274	−	2.01393i	0.169603	−	0.293762i	0.938281	+	0.345875i	$0.112418\pi$
$48$	3.03441	+	6.22835i	0.437979	+	0.898985i
$49$		0			0
$50$	−0.0652529	+	0.255614i	−0.00922816	+	0.0361493i
$51$	5.99360	+	4.47446i	0.839272	+	0.626550i
$52$	0.0192912	+	0.813228i	0.00267521	+	0.112774i
$53$	−4.74675	+	2.74054i	−0.652017	+	0.376442i	−0.789228	−	0.614100i	$-0.789519\pi$
$53$	−4.74675	+	2.74054i	−0.652017	+	0.376442i	0.137212	+	0.990542i	$0.456186\pi$
$54$	3.15793	+	6.63532i	0.429740	+	0.902952i
$55$			9.83457i			1.32609i
$56$		0			0
$57$	−1.10383	+	9.33627i	−0.146206	+	1.23662i
$58$	3.68026	−	3.76860i	0.483242	−	0.494841i
$59$	1.95653	+	3.38881i	0.254719	+	0.441186i	0.964819	−	0.262915i	$-0.0846838\pi$
$59$	1.95653	+	3.38881i	0.254719	+	0.441186i	−0.710100	+	0.704100i	$0.751350\pi$
$60$	−7.85434	−	0.740224i	−1.01399	−	0.0955626i
$61$	5.22448	−	9.04906i	0.668926	−	1.15861i	−0.309279	−	0.950971i	$-0.600088\pi$
$61$	5.22448	−	9.04906i	0.668926	−	1.15861i	0.978205	−	0.207642i	$-0.0665791\pi$
$62$	−7.99494	−	2.04094i	−1.01536	−	0.259199i
$63$		0			0
$64$	−0.568736	−	7.97976i	−0.0710920	−	0.997470i
$65$	−0.802184	−	0.463141i	−0.0994987	−	0.0574456i
$66$	−10.4493	+	1.64317i	−1.28622	+	0.202260i
$67$	6.78494	−	3.91729i	0.828912	−	0.478573i	−0.0245679	−	0.999698i	$-0.507821\pi$
$67$	6.78494	−	3.91729i	0.828912	−	0.478573i	0.853480	+	0.521126i	$0.174488\pi$
$68$	−4.49450	−	7.37506i	−0.545038	−	0.894358i
$69$	2.00000	+	0.236460i	0.240772	+	0.0284665i
$70$		0			0
$71$	−4.88743			−0.580031			−0.290016	−	0.957022i	$-0.593661\pi$
$71$	−4.88743			−0.580031			−0.290016	+	0.957022i	$0.593661\pi$
$72$	−0.525816	−	8.46897i	−0.0619680	−	0.998078i
$73$	1.40673	+	2.43653i	0.164645	+	0.285174i	0.936529	−	0.350590i	$-0.114019\pi$
$73$	1.40673	+	2.43653i	0.164645	+	0.285174i	−0.771884	+	0.635763i	$0.780685\pi$
$74$	10.6675	−	2.99436i	1.24007	−	0.348087i
$75$	0.193287	−	0.258911i	0.0223189	−	0.0298965i
$76$	5.20336	−	9.52738i	0.596867	−	1.09287i
$77$		0			0
$78$	0.358062	−	0.929710i	0.0405425	−	0.105269i
$79$	3.46410	+	2.00000i	0.389742	+	0.225018i	0.682048	−	0.731307i	$-0.261089\pi$
$79$	3.46410	+	2.00000i	0.389742	+	0.225018i	−0.292306	+	0.956325i	$0.594423\pi$
$80$	8.09624	+	4.17560i	0.905187	+	0.466846i
$81$	−0.475549	−	8.98743i	−0.0528388	−	0.998603i
$82$	2.53139	−	2.59215i	0.279545	−	0.286255i
$83$	−0.641735			−0.0704395			−0.0352198	−	0.999380i	$-0.511213\pi$
$83$	−0.641735			−0.0704395			−0.0352198	+	0.999380i	$0.511213\pi$
$84$		0			0
$85$	9.83457			1.06671
$86$	−10.8896	+	11.1510i	−1.17426	+	1.20245i
$87$	−5.92712	+	2.54738i	−0.635454	+	0.273108i
$88$	11.9029	+	2.73961i	1.26885	+	0.292043i
$89$	12.1218	+	6.99851i	1.28491	+	0.741841i	0.977741	−	0.209815i	$-0.0672863\pi$
$89$	12.1218	+	6.99851i	1.28491	+	0.741841i	0.307165	+	0.951656i	$0.400620\pi$
$90$	8.54650	+	4.50723i	0.900880	+	0.475103i
$91$		0			0
$92$	−2.04094	−	1.11466i	−0.212782	−	0.116211i
$93$	8.09805	+	6.04551i	0.839729	+	0.626891i
$94$	3.16636	−	0.888797i	0.326585	−	0.0916724i
$95$	6.18068	+	10.7053i	0.634124	+	1.09834i
$96$	−3.08388	+	9.29998i	−0.314747	+	0.949176i
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		0			0
$99$	12.5978	+	3.02112i	1.26613	+	0.303633i
$100$	−0.318587	+	0.194153i	−0.0318587	+	0.0194153i
$101$	−7.52122	+	4.34238i	−0.748390	+	0.432083i	−0.825112	−	0.564970i	$-0.808888\pi$
$101$	−7.52122	+	4.34238i	−0.748390	+	0.432083i	0.0767221	+	0.997053i	$0.475555\pi$
$102$	1.64317	+	10.4493i	0.162698	+	1.03464i
$103$	−9.22146	−	5.32401i	−0.908618	−	0.524591i	−0.0286316	−	0.999590i	$-0.509115\pi$
$103$	−9.22146	−	5.32401i	−0.908618	−	0.524591i	−0.879986	+	0.474999i	$0.842448\pi$
$104$	−0.784009	+	0.841876i	−0.0768784	+	0.0825527i
$105$		0			0
$106$	−7.51056	−	1.91729i	−0.729490	−	0.186223i
$107$	4.20011	−	7.27480i	0.406040	−	0.703281i	−0.588402	−	0.808568i	$-0.700243\pi$
$107$	4.20011	−	7.27480i	0.406040	−	0.703281i	0.994442	+	0.105287i	$0.0335762\pi$
$108$	−3.36101	+	9.83380i	−0.323413	+	0.946258i
$109$	5.24130	+	9.07820i	0.502026	+	0.869534i	0.999997	+	0.00234046i	$0.000744993\pi$
$109$	5.24130	+	9.07820i	0.502026	+	0.869534i	−0.497972	+	0.867193i	$0.665922\pi$
$110$	−9.71726	+	9.95050i	−0.926504	+	0.948743i
$111$	−13.4760	−	1.59327i	−1.27909	−	0.151227i
$112$		0			0
$113$		−	9.56296i		−	0.899607i	−0.893128	−	0.449804i	$-0.851494\pi$
$113$		−	9.56296i		−	0.899607i	0.893128	−	0.449804i	$-0.148506\pi$
$114$	−10.3417	+	8.35567i	−0.968593	+	0.782580i
$115$	2.29326	−	1.32401i	0.213848	−	0.123465i
$116$	7.44728	−	0.176663i	0.691463	−	0.0164027i
$117$	−0.839697	+	0.885303i	−0.0776300	+	0.0818463i
$118$	−1.36879	+	5.36195i	−0.126008	+	0.493608i
$119$		0			0
$120$	−7.21553	−	8.50959i	−0.658685	−	0.776816i
$121$	−3.82401	+	6.62339i	−0.347638	+	0.602126i
$122$	14.2272	−	3.99358i	1.28807	−	0.361561i
$123$	−4.07684	+	1.75216i	−0.367597	+	0.157987i
$124$	−6.07259	−	9.96457i	−0.545335	−	0.894844i
$125$			10.9622i			0.980485i
$126$		0			0
$127$		−	6.20766i		−	0.550841i	−0.961324	−	0.275420i	$-0.911183\pi$
$127$		−	6.20766i		−	0.550841i	0.961324	−	0.275420i	$-0.0888170\pi$
$128$	7.30913	−	8.63578i	0.646042	−	0.763302i
$129$	17.5380	−	7.53753i	1.54413	−	0.663642i
$130$	−0.354024	−	1.26122i	−0.0310499	−	0.110616i
$131$	−7.20115	+	12.4728i	−0.629167	+	1.08975i	0.358552	+	0.933510i	$0.383271\pi$
$131$	−7.20115	+	12.4728i	−0.629167	+	1.08975i	−0.987719	+	0.156240i	$0.950063\pi$
$132$	−12.1961	−	8.66213i	−1.06153	−	0.753941i
$133$		0			0
$134$	10.7355	+	2.74054i	0.927404	+	0.236747i
$135$	−7.57037	−	9.09539i	−0.651554	−	0.782807i
$136$	2.73961	−	11.9029i	0.234919	−	1.02066i
$137$	−2.01393	+	1.16274i	−0.172062	+	0.0993398i	−0.583558	−	0.812072i	$-0.698340\pi$
$137$	−2.01393	+	1.16274i	−0.172062	+	0.0993398i	0.411496	+	0.911412i	$0.365006\pi$
$138$	1.78994	+	2.21539i	0.152370	+	0.188587i
$139$		−	9.22019i		−	0.782046i	−0.920381	−	0.391023i	$-0.872121\pi$
$139$		−	9.22019i		−	0.782046i	0.920381	−	0.391023i	$-0.127879\pi$
$140$		0			0
$141$	−4.00000	−	0.472921i	−0.336861	−	0.0398271i
$142$	−4.94505	−	4.82913i	−0.414979	−	0.405252i
$143$	−0.878195	−	1.52108i	−0.0734384	−	0.127199i
$144$	7.83594	−	9.08835i	0.652995	−	0.757363i
$145$	−4.24130	+	7.34615i	−0.352221	+	0.610064i
$146$	−0.984149	+	3.85520i	−0.0814488	+	0.319058i
$147$		0			0
$148$	13.7519	+	7.51056i	1.13040	+	0.617364i
$149$	−15.0594	−	8.69454i	−1.23371	−	0.712284i	−0.265911	−	0.963998i	$-0.585673\pi$
$149$	−15.0594	−	8.69454i	−1.23371	−	0.712284i	−0.967802	+	0.251713i	$0.919006\pi$
$150$	0.451389	−	0.0709815i	0.0368557	−	0.00579562i
$151$	−3.60737	+	2.08271i	−0.293563	+	0.169489i	−0.639548	−	0.768751i	$-0.720878\pi$
$151$	−3.60737	+	2.08271i	−0.293563	+	0.169489i	0.345984	+	0.938240i	$0.387545\pi$
$152$	14.6784	−	4.49839i	1.19058	−	0.364868i
$153$	3.02112	−	12.5978i	0.244243	−	1.01847i
$154$		0			0
$155$	13.2876			1.06729
$156$	1.28090	−	0.586879i	0.102554	−	0.0469879i
$157$	−9.63121	−	16.6817i	−0.768654	−	1.33135i	−0.938293	−	0.345842i	$-0.887593\pi$
$157$	−9.63121	−	16.6817i	−0.768654	−	1.33135i	0.169639	−	0.985506i	$-0.445740\pi$
$158$	1.52879	+	5.44636i	0.121624	+	0.433289i
$159$	7.60742	+	5.67924i	0.603308	+	0.450393i
$160$	4.06589	+	12.2245i	0.321437	+	0.966430i
$161$		0			0
$162$	8.39906	−	9.56325i	0.659893	−	0.751360i
$163$	−7.48941	−	4.32401i	−0.586616	−	0.338683i	0.177142	−	0.984185i	$-0.443315\pi$
$163$	−7.48941	−	4.32401i	−0.586616	−	0.338683i	−0.763758	+	0.645502i	$0.776648\pi$
$164$	5.12245	−	0.121514i	0.399996	−	0.00948862i
$165$	15.6498	−	6.72603i	1.21834	−	0.523621i
$166$	−0.649300	−	0.634080i	−0.0503954	−	0.0492141i
$167$	1.75639			0.135914			0.0679568	−	0.997688i	$-0.478352\pi$
$167$	1.75639			0.135914			0.0679568	+	0.997688i	$0.478352\pi$
$168$		0			0
$169$	−12.8346			−0.987275
$170$	9.95050	+	9.71726i	0.763169	+	0.745280i
$171$	15.6118	−	4.62870i	1.19386	−	0.353966i
$172$	−22.0360	+	0.522734i	−1.68023	+	0.0398581i
$173$	−6.81927	−	3.93711i	−0.518459	−	0.299333i	0.217845	−	0.975983i	$-0.430097\pi$
$173$	−6.81927	−	3.93711i	−0.518459	−	0.299333i	−0.736304	+	0.676651i	$0.763431\pi$
$174$	−8.51398	−	3.27902i	−0.645443	−	0.248581i
$175$		0			0
$176$	9.33627	+	14.5328i	0.703748	+	1.09545i
$177$	4.05453	−	5.43111i	0.304757	−	0.408227i
$178$	5.34964	+	19.0582i	0.400973	+	1.42847i
$179$	4.67303	+	8.09392i	0.349278	+	0.604968i	0.986121	−	0.166026i	$-0.0530934\pi$
$179$	4.67303	+	8.09392i	0.349278	+	0.604968i	−0.636843	+	0.770993i	$0.719760\pi$
$180$	4.19379	+	13.0049i	0.312586	+	0.969329i
$181$	−16.8893			−1.25537			−0.627687	−	0.778466i	$-0.715998\pi$
$181$	−16.8893			−1.25537			−0.627687	+	0.778466i	$0.715998\pi$
$182$		0			0
$183$	−17.9729	−	2.12494i	−1.32860	−	0.157080i
$184$	−0.963638	−	3.14439i	−0.0710403	−	0.231807i
$185$	−15.4520	+	8.92122i	−1.13605	+	0.655901i
$186$	2.22011	+	14.1182i	0.162787	+	1.03520i
$187$	16.1497	+	9.32401i	1.18098	+	0.681839i
$188$	4.08188	+	2.22931i	0.297701	+	0.162589i
$189$		0			0
$190$	−4.32401	+	16.9384i	−0.313697	+	1.22884i
$191$	−10.1541	+	17.5874i	−0.734725	+	1.27258i	0.220118	+	0.975473i	$0.429356\pi$
$191$	−10.1541	+	17.5874i	−0.734725	+	1.27258i	−0.954844	+	0.297108i	$0.903978\pi$
$192$	−12.3093	+	6.36252i	−0.888346	+	0.459176i
$193$	−3.42784	−	5.93720i	−0.246742	−	0.427369i	0.715878	−	0.698225i	$-0.246027\pi$
$193$	−3.42784	−	5.93720i	−0.246742	−	0.427369i	−0.962620	+	0.270856i	$0.912693\pi$
$194$	2.02358	+	1.97614i	0.145284	+	0.141879i
$195$	−0.188373	+	1.59327i	−0.0134897	+	0.114097i
$196$		0			0
$197$			1.96830i			0.140235i	0.997539	+	0.0701177i	$0.0223375\pi$
$197$			1.96830i			0.140235i	−0.997539	+	0.0701177i	$0.977662\pi$
$198$	9.76125	+	15.5043i	0.693702	+	1.10184i
$199$	5.51925	−	3.18654i	0.391250	−	0.225888i	−0.291452	−	0.956586i	$-0.594138\pi$
$199$	5.51925	−	3.18654i	0.391250	−	0.225888i	0.682701	+	0.730697i	$0.260805\pi$
$200$	−0.514180	−	0.118345i	−0.0363580	−	0.00836828i
$201$	−10.8739	−	8.11782i	−0.766988	−	0.572587i
$202$	−11.9005	−	3.03794i	−0.837314	−	0.213748i
$203$		0			0
$204$	−8.66213	+	12.1961i	−0.606470	+	0.853895i
$205$	−2.91729	+	5.05289i	−0.203752	+	0.352909i
$206$	−4.06966	−	14.4982i	−0.283547	−	1.01014i
$207$	−0.991553	−	3.34433i	−0.0689177	−	0.232447i
$208$	−1.62508	+	0.0771431i	−0.112679	+	0.00534891i
$209$			23.4393i			1.62133i
$210$		0			0
$211$		−	25.1306i		−	1.73006i	−0.501717	−	0.865032i	$-0.667298\pi$
$211$		−	25.1306i		−	1.73006i	0.501717	−	0.865032i	$-0.332702\pi$
$212$	−5.70468	−	9.36085i	−0.391799	−	0.642906i
$213$	3.34260	+	7.77740i	0.229031	+	0.532899i
$214$	11.4376	−	3.21055i	0.781861	−	0.219469i
$215$	12.5497	−	21.7368i	0.855885	−	1.48244i
$216$	−13.1171	+	6.62881i	−0.892507	+	0.451033i
$217$		0			0
$218$	−3.66682	+	14.3640i	−0.248349	+	0.972852i
$219$	2.91517	−	3.90492i	0.196989	−	0.263870i
$220$	−19.6636	+	0.466456i	−1.32572	+	0.0314484i
$221$	−1.52108	+	0.878195i	−0.102319	+	0.0590738i
$222$	−12.0606	−	14.9273i	−0.809455	−	1.00186i
$223$		−	9.22877i		−	0.618004i	−0.951061	−	0.309002i	$-0.900005\pi$
$223$		−	9.22877i		−	0.618004i	0.951061	−	0.309002i	$-0.0999950\pi$
$224$		0			0
$225$	−0.544200	−	0.130506i	−0.0362800	−	0.00870039i
$226$	9.44888	−	9.67568i	0.628530	−	0.643617i
$227$	9.76310	+	16.9102i	0.647999	+	1.12237i	0.983600	+	0.180364i	$0.0577274\pi$
$227$	9.76310	+	16.9102i	0.647999	+	1.12237i	−0.335601	+	0.942004i	$0.608939\pi$
$228$	−18.7197	−	1.76422i	−1.23974	−	0.116838i
$229$	1.01682	−	1.76119i	0.0671934	−	0.116382i	−0.830471	−	0.557061i	$-0.811929\pi$
$229$	1.01682	−	1.76119i	0.0671934	−	0.116382i	0.897665	+	0.440679i	$0.145262\pi$
$230$	3.62851	+	0.926283i	0.239257	+	0.0610773i
$231$		0			0
$232$	7.70963	+	7.17970i	0.506162	+	0.471370i
$233$	2.83305	+	1.63566i	0.185599	+	0.107156i	0.589921	−	0.807461i	$-0.299159\pi$
$233$	2.83305	+	1.63566i	0.185599	+	0.107156i	−0.404321	+	0.914617i	$0.632492\pi$
$234$	−1.72434	+	0.0660578i	−0.112723	+	0.00431833i
$235$	−4.58652	+	2.64803i	−0.299192	+	0.172738i
$236$	−6.68292	+	4.07269i	−0.435021	+	0.265110i
$237$	0.813457	−	6.88028i	0.0528397	−	0.446922i
$238$		0			0
$239$	−24.5058			−1.58515			−0.792575	−	0.609775i	$-0.791260\pi$
$239$	−24.5058			−1.58515			−0.792575	+	0.609775i	$0.791260\pi$
$240$	1.10750	−	15.7394i	0.0714888	−	1.01597i
$241$	9.20766	+	15.9481i	0.593117	+	1.02731i	0.993810	+	0.111097i	$0.0354363\pi$
$241$	9.20766	+	15.9481i	0.593117	+	1.02731i	−0.400692	+	0.916213i	$0.631230\pi$
$242$	−10.4135	+	2.92307i	−0.669403	+	0.187902i
$243$	−13.9765	+	6.90340i	−0.896594	+	0.442853i
$244$	18.3408	+	10.0168i	1.17415	+	0.641261i
$245$		0			0
$246$	−5.85616	−	2.25540i	−0.373375	−	0.143799i
$247$	−1.91189	−	1.10383i	−0.121651	−	0.0702350i
$248$	3.70153	−	16.0822i	0.235047	−	1.02122i
$249$	0.438893	+	1.02120i	0.0278137	+	0.0647157i
$250$	−10.8314	+	11.0914i	−0.685038	+	0.701481i
$251$	15.4443			0.974837			0.487418	−	0.873169i	$-0.337939\pi$
$251$	15.4443			0.974837			0.487418	+	0.873169i	$0.337939\pi$
$252$		0			0
$253$	5.02112			0.315675
$254$	6.13361	−	6.28083i	0.384857	−	0.394095i
$255$	−6.72603	−	15.6498i	−0.421200	−	0.980030i
$256$	15.9281	−	1.51563i	0.995503	−	0.0947271i
$257$	−7.76765	−	4.48465i	−0.484533	−	0.279745i	0.237771	−	0.971321i	$-0.423583\pi$
$257$	−7.76765	−	4.48465i	−0.484533	−	0.279745i	−0.722303	+	0.691576i	$0.756917\pi$
$258$	25.1923	+	9.70239i	1.56841	+	0.604045i
$259$		0			0
$260$	0.887974	−	1.62588i	0.0550698	−	0.100833i
$261$	8.10732	+	7.68968i	0.501830	+	0.475979i
$262$	−19.6100	+	5.50454i	−1.21151	+	0.340071i
$263$	−9.68119	−	16.7683i	−0.596967	−	1.03398i	−0.993266	−	0.115856i	$-0.963039\pi$
$263$	−9.68119	−	16.7683i	−0.596967	−	1.03398i	0.396299	−	0.918122i	$-0.370295\pi$
$264$	−3.78103	−	20.8148i	−0.232706	−	1.28106i
$265$	12.4826			0.766800
$266$		0			0
$267$	2.84649	−	24.0759i	0.174203	−	1.47342i
$268$	8.15418	+	13.3803i	0.498096	+	0.817330i
$269$	−0.0416451	+	0.0240438i	−0.00253914	+	0.00146598i	−0.501269	−	0.865291i	$-0.667133\pi$
$269$	−0.0416451	+	0.0240438i	−0.00253914	+	0.00146598i	0.498730	+	0.866757i	$0.333800\pi$
$270$	1.32729	−	16.6827i	0.0807760	−	1.01528i
$271$	17.2138	+	9.93840i	1.04566	+	0.603715i	0.921433	−	0.388538i	$-0.127020\pi$
$271$	17.2138	+	9.93840i	1.04566	+	0.603715i	0.124232	+	0.992253i	$0.460353\pi$
$272$	14.5328	−	9.33627i	0.881181	−	0.566095i
$273$		0			0
$274$	−3.18654	−	0.813457i	−0.192506	−	0.0491427i
$275$	0.402778	−	0.697632i	0.0242884	−	0.0420688i
$276$	−0.377927	+	4.01009i	−0.0227485	+	0.241379i
$277$	−5.13747	−	8.89836i	−0.308681	−	0.534651i	0.669393	−	0.742908i	$-0.266554\pi$
$277$	−5.13747	−	8.89836i	−0.308681	−	0.534651i	−0.978074	+	0.208257i	$0.933221\pi$
$278$	9.11020	−	9.32887i	0.546394	−	0.559509i
$279$	4.08188	−	17.0211i	0.244376	−	1.01903i
$280$		0			0
$281$		−	6.78411i		−	0.404706i	−0.979313	−	0.202353i	$-0.935141\pi$
$281$		−	6.78411i		−	0.404706i	0.979313	−	0.202353i	$-0.0648588\pi$
$282$	−3.57987	−	4.43078i	−0.213178	−	0.263849i
$283$	−4.70065	+	2.71392i	−0.279425	+	0.161326i	−0.633163	−	0.774019i	$-0.718244\pi$
$283$	−4.70065	+	2.71392i	−0.279425	+	0.161326i	0.353738	+	0.935344i	$0.384910\pi$
$284$	−0.231812	−	9.77212i	−0.0137555	−	0.579868i
$285$	12.8083	−	17.1569i	0.758697	−	1.01628i
$286$	0.614387	−	2.40673i	0.0363294	−	0.142313i
$287$		0			0
$288$	16.9082	−	1.45302i	0.996328	−	0.0856201i
$289$	0.824014	−	1.42723i	0.0484714	−	0.0839550i
$290$	−11.5498	+	3.24204i	−0.678228	+	0.190379i
$291$	−1.36783	−	3.18261i	−0.0801838	−	0.186568i
$292$	−4.80496	+	2.92823i	−0.281189	+	0.171362i
$293$		−	28.1874i		−	1.64673i	−0.567515	−	0.823363i	$-0.692095\pi$
$293$		−	28.1874i		−	1.64673i	0.567515	−	0.823363i	$-0.307905\pi$
$294$		0			0
$295$		−	8.91160i		−	0.518853i
$296$	6.49300	+	21.1869i	0.377398	+	1.23146i
$297$	−3.80834	−	22.1132i	−0.220982	−	1.28314i
$298$	−6.64608	−	23.6768i	−0.384997	−	1.37156i
$299$	−0.236460	+	0.409561i	−0.0136749	+	0.0236855i
$300$	0.526844	+	0.374186i	0.0304174	+	0.0216036i
$301$		0			0
$302$	−5.70776	−	1.45707i	−0.328445	−	0.0838450i
$303$	12.0540	+	8.99875i	0.692481	+	0.516965i
$304$	19.2962	+	9.95192i	1.10671	+	0.570782i
$305$	−20.6083	+	11.8982i	−1.18003	+	0.681290i
$306$	15.5043	−	9.76125i	0.886320	−	0.558013i
$307$		−	2.24130i		−	0.127918i	−0.997953	−	0.0639589i	$-0.979627\pi$
$307$		−	2.24130i		−	0.127918i	0.997953	−	0.0639589i	$-0.0203727\pi$
$308$		0			0
$309$	−2.16543	+	18.3154i	−0.123187	+	1.04192i
$310$	13.4443	+	13.1291i	0.763584	+	0.745685i
$311$	−13.2396	−	22.9316i	−0.750746	−	1.30033i	−0.947461	−	0.319870i	$-0.896361\pi$
$311$	−13.2396	−	22.9316i	−0.750746	−	1.30033i	0.196715	−	0.980461i	$-0.436973\pi$
$312$	1.87588	+	0.671826i	0.106201	+	0.0380346i
$313$	0.220185	−	0.381372i	0.0124456	−	0.0215564i	−0.859736	−	0.510739i	$-0.829372\pi$
$313$	0.220185	−	0.381372i	0.0124456	−	0.0215564i	0.872181	+	0.489183i	$0.162705\pi$
$314$	6.73801	−	26.3947i	0.380248	−	1.48954i
$315$		0			0
$316$	−3.83457	+	7.02112i	−0.215712	+	0.394969i
$317$	−10.2124	−	5.89613i	−0.573586	−	0.331160i	0.184995	−	0.982740i	$-0.440773\pi$
$317$	−10.2124	−	5.89613i	−0.573586	−	0.331160i	−0.758580	+	0.651580i	$0.774107\pi$
$318$	2.08561	+	13.2629i	0.116955	+	0.743745i
$319$	−13.9296	+	8.04223i	−0.779905	+	0.450278i
$320$	−7.96484	+	16.3860i	−0.445248	+	0.916004i
$321$	−14.4490	−	1.70830i	−0.806462	−	0.0953482i
$322$		0			0
$323$	23.4393			1.30419
$324$	17.9472	−	1.37711i	0.997069	−	0.0765059i
$325$	0.0379362	+	0.0657074i	0.00210432	+	0.00364479i
$326$	−3.30526	−	11.7751i	−0.183062	−	0.652160i
$327$	10.8616	−	14.5492i	0.600647	−	0.804575i
$328$	5.30290	+	4.93840i	0.292804	+	0.272678i
$329$		0			0
$330$	22.4801	+	8.65783i	1.23749	+	0.476598i
$331$	−1.13427	−	0.654870i	−0.0623451	−	0.0359949i	0.468503	−	0.883462i	$-0.344793\pi$
$331$	−1.13427	−	0.654870i	−0.0623451	−	0.0359949i	−0.530849	+	0.847467i	$0.678127\pi$
$332$	−0.0304376	−	1.28311i	−0.00167048	−	0.0704197i
$333$	6.68109	+	22.5341i	0.366121	+	1.23486i
$334$	1.77709	+	1.73544i	0.0972383	+	0.0949590i
$335$	−17.8424			−0.974837
$336$		0			0
$337$	−15.4615			−0.842241			−0.421120	−	0.907005i	$-0.638363\pi$
$337$	−15.4615			−0.842241			−0.421120	+	0.907005i	$0.638363\pi$
$338$	−12.9859	−	12.6815i	−0.706338	−	0.689781i
$339$	−15.2176	+	6.54027i	−0.826506	+	0.355218i
$340$	0.466456	+	19.6636i	0.0252971	+	1.06641i
$341$	21.8201	+	12.5978i	1.18162	+	0.682210i
$342$	20.3693	+	10.7423i	1.10145	+	0.580878i
$343$		0			0
$344$	−22.8123	−	21.2443i	−1.22996	−	1.14541i
$345$	−3.67531	−	2.74377i	−0.197872	−	0.147719i
$346$	−3.00951	−	10.7214i	−0.161792	−	0.576388i
$347$	−13.8307	−	23.9555i	−0.742471	−	1.28600i	−0.951367	−	0.308060i	$-0.900320\pi$
$347$	−13.8307	−	23.9555i	−0.742471	−	1.28600i	0.208896	−	0.977938i	$-0.433013\pi$
$348$	−5.37445	−	11.7301i	−0.288101	−	0.628799i
$349$	18.9316			1.01338			0.506692	−	0.862127i	$-0.330868\pi$
$349$	18.9316			1.01338			0.506692	+	0.862127i	$0.330868\pi$
$350$		0			0
$351$	1.98307	+	0.730743i	0.105849	+	0.0390042i
$352$	−4.91312	+	23.9290i	−0.261870	+	1.27542i
$353$	−1.72586	+	0.996425i	−0.0918582	+	0.0530344i	−0.545225	−	0.838289i	$-0.683556\pi$
$353$	−1.72586	+	0.996425i	−0.0918582	+	0.0530344i	0.453367	+	0.891324i	$0.350223\pi$
$354$	9.46865	−	1.48896i	0.503253	−	0.0791373i
$355$	9.63941	+	5.56531i	0.511607	+	0.295376i
$356$	−13.4182	+	24.5687i	−0.711161	+	1.30214i
$357$		0			0
$358$	−3.26926	+	12.8066i	−0.172786	+	0.676851i
$359$	1.17502	−	2.03519i	0.0620151	−	0.107413i	−0.833351	−	0.552744i	$-0.813581\pi$
$359$	1.17502	−	2.03519i	0.0620151	−	0.107413i	0.895366	+	0.445331i	$0.146914\pi$
$360$	−8.60656	+	17.3020i	−0.453605	+	0.911894i
$361$	5.23074	+	9.05991i	0.275302	+	0.476837i
$362$	−17.0884	−	16.6879i	−0.898148	−	0.877095i
$363$	13.1551	+	1.55534i	0.690466	+	0.0816339i
$364$		0			0
$365$		−	6.40736i		−	0.335377i
$366$	−16.0852	−	19.9085i	−0.840788	−	1.04064i
$367$	29.6129	−	17.0970i	1.54578	−	0.892455i	0.547321	−	0.836923i	$-0.315648\pi$
$367$	29.6129	−	17.0970i	1.54578	−	0.892455i	0.998457	−	0.0555330i	$-0.0176858\pi$
$368$	2.13188	−	4.13360i	0.111132	−	0.215479i
$369$	5.57644	+	5.28918i	0.290298	+	0.275344i
$370$	−24.4490	−	6.24130i	−1.27104	−	0.324470i
$371$		0			0
$372$	−11.7035	+	16.4783i	−0.606800	+	0.854359i
$373$	8.83457	−	15.3019i	0.457437	−	0.792304i	−0.541388	−	0.840773i	$-0.682101\pi$
$373$	8.83457	−	15.3019i	0.457437	−	0.792304i	0.998825	+	0.0484692i	$0.0154343\pi$
$374$	7.12725	+	25.3909i	0.368541	+	1.31293i
$375$	17.4442	−	7.49720i	0.900813	−	0.387154i
$376$	1.92728	+	6.28877i	0.0993916	+	0.324319i
$377$		−	1.51494i		−	0.0780232i
$378$		0			0
$379$			5.39420i			0.277082i	0.990357	+	0.138541i	$0.0442412\pi$
$379$			5.39420i			0.277082i	−0.990357	+	0.138541i	$0.955759\pi$
$380$	−21.1113	+	12.8656i	−1.08299	+	0.659993i
$381$	−9.87829	+	4.24552i	−0.506080	+	0.217505i
$382$	−27.6514	+	7.76177i	−1.41477	+	0.397127i
$383$	0.926283	−	1.60437i	0.0473308	−	0.0819794i	−0.841389	−	0.540429i	$-0.818262\pi$
$383$	0.926283	−	1.60437i	0.0473308	−	0.0819794i	0.888720	+	0.458450i	$0.151595\pi$
$384$	−18.7410	−	5.72492i	−0.956373	−	0.292149i
$385$		0			0
$386$	2.39812	−	9.39414i	0.122061	−	0.478149i
$387$	−23.9890	−	22.7533i	−1.21943	−	1.15661i
$388$	0.0948604	+	3.99888i	0.00481581	+	0.203012i
$389$	−4.66346	+	2.69245i	−0.236447	+	0.136513i	−0.613543	−	0.789662i	$-0.710256\pi$
$389$	−4.66346	+	2.69245i	−0.236447	+	0.136513i	0.377096	+	0.926174i	$0.376923\pi$
$390$	−1.76486	+	1.42593i	−0.0893671	+	0.0722046i
$391$		−	5.02112i		−	0.253929i
$392$		0			0
$393$	24.7730	+	2.92891i	1.24963	+	0.147744i
$394$	−1.94482	+	1.99150i	−0.0979786	+	0.100330i
$395$	−4.55480	−	7.88914i	−0.229177	−	0.396946i
$396$	−5.44301	+	25.3319i	−0.273522	+	1.27297i
$397$	−10.8178	+	18.7369i	−0.542927	+	0.940378i	0.455807	+	0.890079i	$0.349351\pi$
$397$	−10.8178	+	18.7369i	−0.542927	+	0.940378i	−0.998734	+	0.0502990i	$0.983983\pi$
$398$	8.73285	+	2.22931i	0.437738	+	0.111745i
$399$		0			0
$400$	−0.403308	−	0.627787i	−0.0201654	−	0.0313893i
$401$	33.1440	+	19.1357i	1.65513	+	0.955591i	0.974914	+	0.222580i	$0.0714480\pi$
$401$	33.1440	+	19.1357i	1.65513	+	0.955591i	0.680217	+	0.733010i	$0.261885\pi$
$402$	−2.98113	−	18.9577i	−0.148685	−	0.945526i
$403$	−2.05515	+	1.18654i	−0.102374	+	0.0591059i
$404$	−9.03905	−	14.8323i	−0.449710	−	0.737932i
$405$	−9.29606	+	18.2673i	−0.461925	+	0.907708i
$406$		0			0
$407$	−33.8323			−1.67701
$408$	−20.8148	+	3.78103i	−1.03049	+	0.187189i
$409$	2.38561	+	4.13200i	0.117961	+	0.204314i	0.918960	−	0.394352i	$-0.129031\pi$
$409$	2.38561	+	4.13200i	0.117961	+	0.204314i	−0.800999	+	0.598666i	$0.795698\pi$
$410$	−7.94429	+	2.22996i	−0.392340	+	0.110130i
$411$	3.22764	+	2.40956i	0.159208	+	0.118855i
$412$	10.2077	−	18.6903i	0.502895	−	0.920803i
$413$		0			0
$414$	2.30120	−	4.36348i	0.113098	−	0.214453i
$415$	1.26568	+	0.730743i	0.0621300	+	0.0358708i
$416$	−1.72046	−	1.52765i	−0.0843527	−	0.0748990i
$417$	−14.6721	+	6.30584i	−0.718498	+	0.308798i
$418$	−23.1597	+	23.7156i	−1.13278	+	1.15997i
$419$	8.33257			0.407072			0.203536	−	0.979067i	$-0.434757\pi$
$419$	8.33257			0.407072			0.203536	+	0.979067i	$0.434757\pi$
$420$		0			0
$421$	−20.7325			−1.01044			−0.505220	−	0.862991i	$-0.668589\pi$
$421$	−20.7325			−1.01044			−0.505220	+	0.862991i	$0.668589\pi$
$422$	24.8309	−	25.4269i	1.20875	−	1.23776i
$423$	1.98311	+	6.68867i	0.0964219	+	0.325214i
$424$	3.47727	−	15.1078i	0.168871	−	0.733701i
$425$	−0.697632	−	0.402778i	−0.0338401	−	0.0195376i
$426$	−4.30263	+	11.1718i	−0.208463	+	0.541276i
$427$		0			0
$428$	14.7447	+	8.05280i	0.712713	+	0.389247i
$429$	−1.81989	+	2.43777i	−0.0878651	+	0.117697i
$430$	34.1752	−	9.59298i	1.64807	−	0.462615i
$431$	17.4975	+	30.3066i	0.842826	+	1.45982i	0.887496	+	0.460816i	$0.152443\pi$
$431$	17.4975	+	30.3066i	0.842826	+	1.45982i	−0.0446692	+	0.999002i	$0.514223\pi$
$432$	−19.8215	−	6.25370i	−0.953662	−	0.300882i
$433$	−17.3383			−0.833225			−0.416612	−	0.909084i	$-0.636783\pi$
$433$	−17.3383			−0.833225			−0.416612	+	0.909084i	$0.636783\pi$
$434$		0			0
$435$	14.5907	+	1.72506i	0.699569	+	0.0827102i
$436$	−17.9027	+	10.9102i	−0.857384	+	0.522505i
$437$	5.46565	−	3.15559i	0.261457	−	0.150953i
$438$	6.80788	−	1.07055i	0.325293	−	0.0511528i
$439$	−28.8352	−	16.6480i	−1.37623	−	0.794567i	−0.384527	−	0.923114i	$-0.625635\pi$
$439$	−28.8352	−	16.6480i	−1.37623	−	0.794567i	−0.991703	+	0.128547i	$0.958969\pi$
$440$	−20.3563	−	18.9571i	−0.970449	−	0.903744i
$441$		0			0
$442$	−2.40673	−	0.614387i	−0.114476	−	0.0292234i
$443$	4.43657	−	7.68436i	0.210788	−	0.365095i	−0.741174	−	0.671313i	$-0.765730\pi$
$443$	4.43657	−	7.68436i	0.210788	−	0.365095i	0.951961	+	0.306218i	$0.0990638\pi$
$444$	2.54648	−	27.0200i	0.120850	−	1.28231i
$445$	−15.9384	−	27.6061i	−0.755553	−	1.30866i
$446$	9.11869	−	9.33756i	0.431782	−	0.442146i
$447$	−3.53632	+	29.9104i	−0.167262	+	1.41472i
$448$		0			0
$449$			26.3829i			1.24509i	0.782585	+	0.622544i	$0.213901\pi$
$449$			26.3829i			1.24509i	−0.782585	+	0.622544i	$0.786099\pi$
$450$	−0.421666	−	0.669752i	−0.0198775	−	0.0315724i
$451$	−9.58114	+	5.53167i	−0.451158	+	0.260476i
$452$	19.1205	−	0.453573i	0.899354	−	0.0213343i
$453$	5.78138	+	4.31602i	0.271633	+	0.202785i
$454$	−6.83028	+	26.7562i	−0.320561	+	1.25573i
$455$		0			0
$456$	−17.1971	−	20.2814i	−0.805330	−	0.949762i
$457$	−15.1249	+	26.1972i	−0.707515	+	1.22545i	0.258261	+	0.966075i	$0.416851\pi$
$457$	−15.1249	+	26.1972i	−0.707515	+	1.22545i	−0.965776	+	0.259377i	$0.916483\pi$
$458$	2.76898	−	0.777255i	0.129386	−	0.0363187i
$459$	−22.1132	+	3.80834i	−1.03216	+	0.177758i
$460$	2.75605	+	4.52243i	0.128502	+	0.210859i
$461$		−	1.56302i		−	0.0727973i	−0.999337	−	0.0363987i	$-0.988411\pi$
$461$		−	1.56302i		−	0.0727973i	0.999337	−	0.0363987i	$-0.0115886\pi$
$462$		0			0
$463$			33.2961i			1.54740i	0.633553	+	0.773700i	$0.281596\pi$
$463$			33.2961i			1.54740i	−0.633553	+	0.773700i	$0.718404\pi$
$464$	0.706452	+	14.8820i	0.0327962	+	0.690879i
$465$	−9.08764	−	21.1447i	−0.421429	−	0.980563i
$466$	1.25030	+	4.45420i	0.0579189	+	0.206337i
$467$	−8.64844	+	14.9795i	−0.400202	+	0.693170i	−0.993750	−	0.111628i	$-0.964393\pi$
$467$	−8.64844	+	14.9795i	−0.400202	+	0.693170i	0.593548	+	0.804799i	$0.297727\pi$
$468$	−1.80993	−	1.63693i	−0.0836642	−	0.0756672i
$469$		0			0
$470$	−7.25703	−	1.85257i	−0.334742	−	0.0854525i
$471$	−19.9588	+	26.7351i	−0.919654	+	1.23189i
$472$	−10.7858	−	2.48250i	−0.496457	−	0.114266i
$473$	41.2166	−	23.7964i	1.89514	−	1.09416i
$474$	7.62126	−	6.15763i	0.350056	−	0.282830i
$475$		−	1.01253i		−	0.0464579i
$476$		0			0
$477$	3.83457	−	15.9899i	0.175573	−	0.732126i
$478$	−24.7947	−	24.2135i	−1.13408	−	1.10750i
$479$	8.30404	+	14.3830i	0.379421	+	0.657177i	0.990978	−	0.134024i	$-0.0427898\pi$
$479$	8.30404	+	14.3830i	0.379421	+	0.657177i	−0.611557	+	0.791200i	$0.709456\pi$
$480$	16.6722	−	14.8306i	0.760977	−	0.676922i
$481$	1.59327	−	2.75963i	0.0726469	−	0.125828i
$482$	−6.44169	+	25.2340i	−0.293411	+	1.14938i
$483$		0			0
$484$	−13.4244	−	7.33173i	−0.610201	−	0.333260i
$485$	−3.94457	−	2.27740i	−0.179114	−	0.103411i
$486$	−20.9623	−	6.82502i	−0.950870	−	0.309589i
$487$	21.0010	−	12.1249i	0.951647	−	0.549434i	0.0580548	−	0.998313i	$-0.481510\pi$
$487$	21.0010	−	12.1249i	0.951647	−	0.549434i	0.893592	+	0.448880i	$0.148177\pi$
$488$	8.65971	+	28.2570i	0.392006	+	1.27913i
$489$	−1.75870	+	14.8752i	−0.0795311	+	0.672681i
$490$		0			0
$491$	20.3082			0.916497			0.458248	−	0.888824i	$-0.348477\pi$
$491$	20.3082			0.916497			0.458248	+	0.888824i	$0.348477\pi$
$492$	−3.69670	−	8.06829i	−0.166660	−	0.363746i
$493$	8.04223	+	13.9296i	0.362204	+	0.627355i
$494$	−0.843764	−	3.00592i	−0.0379627	−	0.135243i
$495$	−21.4064	−	20.3036i	−0.962144	−	0.912580i
$496$	19.6355	−	12.6144i	0.881660	−	0.566403i
$497$		0			0
$498$	−0.564949	+	1.46689i	−0.0253160	+	0.0657330i
$499$	9.12662	+	5.26926i	0.408564	+	0.235884i	0.690172	−	0.723645i	$-0.257535\pi$
$499$	9.12662	+	5.26926i	0.408564	+	0.235884i	−0.281609	+	0.959529i	$0.590868\pi$
$500$	−21.9182	+	0.519937i	−0.980210	+	0.0232523i
$501$	−1.20122	−	2.79496i	−0.0536668	−	0.124869i
$502$	15.6264	+	15.2601i	0.697439	+	0.681091i
$503$	−27.6664			−1.23358			−0.616792	−	0.787126i	$-0.711568\pi$
$503$	−27.6664			−1.23358			−0.616792	+	0.787126i	$0.711568\pi$
$504$		0			0
$505$	19.7787			0.880139
$506$	5.08030	+	4.96122i	0.225847	+	0.220553i
$507$	8.77778	+	20.4237i	0.389835	+	0.907050i
$508$	12.4118	−	0.294430i	0.550686	−	0.0130632i
$509$	−24.4110	−	14.0937i	−1.08200	−	0.624693i	−0.150564	−	0.988600i	$-0.548109\pi$
$509$	−24.4110	−	14.0937i	−1.08200	−	0.624693i	−0.931435	+	0.363908i	$0.881442\pi$
$510$	8.65783	−	22.4801i	0.383375	−	0.995436i
$511$		0			0
$512$	17.6134	+	14.2046i	0.778408	+	0.627758i
$513$	−18.0429	−	21.6775i	−0.796612	−	0.957086i
$514$	−3.42806	−	12.2125i	−0.151205	−	0.538671i
$515$	12.1249	+	21.0009i	0.534287	+	0.925412i
$516$	15.9026	+	34.7086i	0.700075	+	1.52796i
$517$	−10.0422			−0.441657
$518$		0			0
$519$	−1.60133	+	13.5442i	−0.0702907	+	0.594524i
$520$	2.50493	−	0.767668i	0.109849	−	0.0336645i
$521$	20.7962	−	12.0067i	0.911097	−	0.526022i	0.0303127	−	0.999540i	$-0.490350\pi$
$521$	20.7962	−	12.0067i	0.911097	−	0.526022i	0.880784	+	0.473519i	$0.157016\pi$
$522$	0.604936	+	15.7909i	0.0264773	+	0.691150i
$523$	−2.40739	−	1.38991i	−0.105268	−	0.0607764i	0.446442	−	0.894813i	$-0.352691\pi$
$523$	−2.40739	−	1.38991i	−0.105268	−	0.0607764i	−0.551710	+	0.834036i	$0.686024\pi$
$524$	−25.2801	−	13.8067i	−1.10436	−	0.603147i
$525$		0			0
$526$	6.77297	−	26.5317i	0.295316	−	1.15684i
$527$	12.5978	−	21.8201i	0.548770	−	0.950497i
$528$	16.7409	−	24.7961i	0.728555	−	1.07911i
$529$	10.8240	+	18.7477i	0.470609	+	0.815119i
$530$	12.6297	+	12.3337i	0.548601	+	0.535742i
$531$	−11.4155	−	2.73758i	−0.495391	−	0.118801i
$532$		0			0
$533$		−	1.04202i		−	0.0451347i
$534$	26.6687	−	21.5471i	1.15407	−	0.932436i
$535$	−16.5676	+	9.56531i	−0.716280	+	0.413545i
$536$	−4.97035	+	21.5949i	−0.214687	+	0.932758i
$537$	9.68395	−	12.9718i	0.417893	−	0.559774i
$538$	−0.0658929	−	0.0168211i	−0.00284085	−	0.000725208i
$539$		0			0
$540$	17.8266	−	15.5679i	0.767135	−	0.669935i
$541$	−4.15859	+	7.20288i	−0.178792	+	0.309676i	−0.941467	−	0.337105i	$-0.890552\pi$
$541$	−4.15859	+	7.20288i	−0.178792	+	0.309676i	0.762675	+	0.646782i	$0.223885\pi$
$542$	7.59688	+	27.0640i	0.326314	+	1.16250i
$543$	11.5509	+	26.8761i	0.495696	+	1.15336i
$544$	23.9290	+	4.91312i	1.02595	+	0.210648i
$545$		−	23.8731i		−	1.02261i
$546$		0			0
$547$			15.4364i			0.660014i	0.943978	+	0.330007i	$0.107051\pi$
$547$			15.4364i			0.660014i	−0.943978	+	0.330007i	$0.892949\pi$
$548$	−2.42035	−	3.97158i	−0.103392	−	0.169657i
$549$	8.91056	+	30.0538i	0.380293	+	1.28266i
$550$	1.09684	−	0.307882i	0.0467693	−	0.0131281i
$551$	−10.1085	+	17.5085i	−0.430637	+	0.745886i
$552$	−4.34464	+	3.68394i	−0.184920	+	0.156799i
$553$		0			0
$554$	3.59418	−	14.0794i	0.152702	−	0.598178i
$555$	24.7643	+	18.4875i	1.05119	+	0.784751i
$556$	18.4352	−	0.437315i	0.781826	−	0.0185463i
$557$	11.6502	−	6.72624i	0.493634	−	0.285000i	−0.232447	−	0.972609i	$-0.574673\pi$
$557$	11.6502	−	6.72624i	0.493634	−	0.285000i	0.726081	+	0.687609i	$0.241340\pi$
$558$	20.9481	−	13.1886i	0.886802	−	0.558317i
$559$			4.48260i			0.189594i
$560$		0			0
$561$	3.79234	−	32.0759i	0.160113	−	1.35425i
$562$	6.70318	−	6.86408i	0.282757	−	0.289544i
$563$	17.0006	+	29.4458i	0.716488	+	1.24099i	0.962383	+	0.271698i	$0.0875851\pi$
$563$	17.0006	+	29.4458i	0.716488	+	1.24099i	−0.245894	+	0.969297i	$0.579082\pi$
$564$	0.755854	−	8.02018i	0.0318272	−	0.337711i
$565$	−10.8893	+	18.8609i	−0.458118	+	0.793483i
$566$	−7.43761	−	1.89866i	−0.312626	−	0.0798068i
$567$		0			0
$568$	9.42100	−	10.1164i	0.395296	−	0.424473i
$569$	−23.0318	−	13.2974i	−0.965544	−	0.557457i	−0.0676690	−	0.997708i	$-0.521556\pi$
$569$	−23.0318	−	13.2974i	−0.965544	−	0.557457i	−0.897875	+	0.440251i	$0.854890\pi$
$570$	29.9115	−	4.70362i	1.25285	−	0.197013i
$571$	−7.12974	+	4.11636i	−0.298370	+	0.172264i	−0.641711	−	0.766947i	$-0.721775\pi$
$571$	−7.12974	+	4.11636i	−0.298370	+	0.172264i	0.343340	+	0.939211i	$0.388442\pi$
$572$	2.99965	−	1.82804i	0.125422	−	0.0764342i
$573$	34.9316	+	4.12996i	1.45929	+	0.172532i
$574$		0			0
$575$	−0.216902			−0.00904543
$576$	18.5432	+	15.2364i	0.772635	+	0.634850i
$577$	0.792342	+	1.37238i	0.0329856	+	0.0571328i	0.882047	−	0.471162i	$-0.156165\pi$
$577$	0.792342	+	1.37238i	0.0329856	+	0.0571328i	−0.849061	+	0.528294i	$0.822832\pi$
$578$	2.24394	−	0.629874i	0.0933355	−	0.0261993i
$579$	−7.10355	+	9.51530i	−0.295213	+	0.395442i
$580$	−14.8893	−	8.13179i	−0.618246	−	0.337654i
$581$		0			0
$582$	1.76069	−	4.57165i	0.0729830	−	0.189501i
$583$	20.4981	+	11.8346i	0.848944	+	0.490138i
$584$	−7.75490	−	1.78489i	−0.320900	−	0.0738594i
$585$	2.66422	−	0.789906i	0.110152	−	0.0326586i
$586$	27.8512	−	28.5197i	1.15052	−	1.17814i
$587$	30.8651			1.27394			0.636969	−	0.770889i	$-0.280188\pi$
$587$	30.8651			1.27394			0.636969	+	0.770889i	$0.280188\pi$
$588$		0			0
$589$	31.6691			1.30490
$590$	8.80530	−	9.01665i	0.362508	−	0.371210i
$591$	3.13217	−	1.34615i	0.128840	−	0.0553733i
$592$	−14.3646	+	27.8522i	−0.590383	+	1.14472i
$593$	−5.58714	−	3.22574i	−0.229436	−	0.132465i	0.380876	−	0.924626i	$-0.375623\pi$
$593$	−5.58714	−	3.22574i	−0.229436	−	0.132465i	−0.610312	+	0.792161i	$0.708956\pi$
$594$	17.9962	−	26.1368i	0.738392	−	1.07240i
$595$		0			0
$596$	16.6699	−	30.5227i	0.682826	−	1.25026i
$597$	−8.84548	−	6.60350i	−0.362021	−	0.270263i
$598$	−0.643923	+	0.180750i	−0.0263320	+	0.00739140i
$599$	−6.40487	−	11.0936i	−0.261696	−	0.453270i	0.704997	−	0.709210i	$-0.250948\pi$
$599$	−6.40487	−	11.0936i	−0.261696	−	0.453270i	−0.966693	+	0.255940i	$0.917615\pi$
$600$	0.163333	+	0.899157i	0.00666803	+	0.0367079i
$601$	37.2710			1.52032			0.760158	−	0.649738i	$-0.225122\pi$
$601$	37.2710			1.52032			0.760158	+	0.649738i	$0.225122\pi$
$602$		0			0
$603$	−5.48108	+	22.8557i	−0.223207	+	0.930756i
$604$	−4.33535	−	7.11392i	−0.176403	−	0.289461i
$605$	15.0841	−	8.70880i	0.613256	−	0.354063i
$606$	3.30464	+	21.0150i	0.134242	+	0.853676i
$607$	18.0250	+	10.4067i	0.731611	+	0.422396i	0.819011	−	0.573777i	$-0.194522\pi$
$607$	18.0250	+	10.4067i	0.731611	+	0.422396i	−0.0873999	+	0.996173i	$0.527856\pi$
$608$	9.69046	+	29.1352i	0.393000	+	1.18159i
$609$		0			0
$610$	−32.6075	−	8.32401i	−1.32024	−	0.337029i
$611$	0.472921	−	0.819123i	0.0191323	−	0.0331382i
$612$	25.3319	+	5.44301i	1.02398	+	0.220021i
$613$	−9.61439	−	16.6526i	−0.388321	−	0.672592i	0.603902	−	0.797058i	$-0.293612\pi$
$613$	−9.61439	−	16.6526i	−0.388321	−	0.672592i	−0.992224	+	0.124466i	$0.960278\pi$
$614$	2.21456	−	2.26772i	0.0893726	−	0.0915178i
$615$	10.0359	+	1.18654i	0.404686	+	0.0478460i
$616$		0			0
$617$		−	29.3933i		−	1.18333i	−0.806185	−	0.591664i	$-0.798471\pi$
$617$		−	29.3933i		−	1.18333i	0.806185	−	0.591664i	$-0.201529\pi$
$618$	−20.2878	+	16.3917i	−0.816097	+	0.659370i
$619$	−17.2548	+	9.96206i	−0.693529	+	0.400409i	−0.804933	−	0.593366i	$-0.797799\pi$
$619$	−17.2548	+	9.96206i	−0.693529	+	0.400409i	0.111404	+	0.993775i	$0.464465\pi$
$620$	0.630236	+	26.5678i	0.0253109	+	1.06699i
$621$	−4.64372	+	3.86511i	−0.186346	+	0.155102i
$622$	9.26242	−	36.2835i	0.371389	−	1.45484i
$623$		0			0
$624$	1.23418	+	2.53325i	0.0494068	+	0.101411i
$625$	12.9490	−	22.4283i	0.517958	−	0.897130i
$626$	0.599604	−	0.168309i	0.0239650	−	0.00672698i
$627$	37.2990	−	16.0305i	1.48958	−	0.640196i
$628$	32.8973	−	20.0482i	1.31274	−	0.800011i
$629$			33.8323i			1.34898i
$630$		0			0
$631$			17.6269i			0.701716i	0.936429	+	0.350858i	$0.114110\pi$
$631$			17.6269i			0.701716i	−0.936429	+	0.350858i	$0.885890\pi$
$632$	−10.8171	+	3.31505i	−0.430283	+	0.131866i
$633$	−39.9905	+	17.1873i	−1.58948	+	0.683132i
$634$	−4.50699	−	16.0562i	−0.178995	−	0.637674i
$635$	−7.06866	+	12.2433i	−0.280511	+	0.485859i
$636$	−10.9945	+	15.4799i	−0.435959	+	0.613819i
$637$		0			0
$638$	−22.0401	−	5.62636i	−0.872574	−	0.222750i
$639$	10.0902	−	10.6382i	0.399161	−	0.420840i
$640$	−24.2492	+	8.70931i	−0.958535	+	0.344266i
$641$	19.0040	−	10.9719i	0.750611	−	0.433365i	−0.0753036	−	0.997161i	$-0.523993\pi$
$641$	19.0040	−	10.9719i	0.750611	−	0.433365i	0.825915	+	0.563795i	$0.190659\pi$
$642$	−12.9314	−	16.0050i	−0.510360	−	0.631669i
$643$			49.5796i			1.95523i	0.210406	+	0.977614i	$0.432521\pi$
$643$			49.5796i			1.95523i	−0.210406	+	0.977614i	$0.567479\pi$
$644$		0			0
$645$	−43.1729	−	5.10433i	−1.69993	−	0.200983i
$646$	23.7156	+	23.1597i	0.933076	+	0.911204i
$647$	−11.9561	−	20.7086i	−0.470042	−	0.814137i	0.529371	−	0.848391i	$-0.322428\pi$
$647$	−11.9561	−	20.7086i	−0.470042	−	0.814137i	−0.999413	+	0.0342534i	$0.989095\pi$
$648$	19.5195	+	16.3398i	0.766798	+	0.641889i
$649$	8.44896	−	14.6340i	0.331651	−	0.574436i
$650$	−0.0265402	+	0.103966i	−0.00104099	+	0.00407787i
$651$		0			0
$652$	8.29037	−	15.1797i	0.324676	−	0.594483i
$653$	40.4145	+	23.3333i	1.58154	+	0.913103i	0.994635	+	0.103447i	$0.0329872\pi$
$653$	40.4145	+	23.3333i	1.58154	+	0.913103i	0.586905	+	0.809656i	$0.300346\pi$
$654$	25.3653	−	3.98873i	0.991863	−	0.155972i
$655$	28.4054	−	16.3999i	1.10989	−	0.640797i
$656$	0.485918	+	10.2363i	0.0189719	+	0.399659i
$657$	−8.20766	−	1.96830i	−0.320211	−	0.0767907i
$658$		0			0
$659$	30.4598			1.18655			0.593273	−	0.805001i	$-0.297835\pi$
$659$	30.4598			1.18655			0.593273	+	0.805001i	$0.297835\pi$
$660$	14.1905	+	30.9718i	0.552366	+	1.20558i
$661$	−24.6523	−	42.6991i	−0.958864	−	1.66080i	−0.725266	−	0.688468i	$-0.758283\pi$
$661$	−24.6523	−	42.6991i	−0.958864	−	1.66080i	−0.233598	−	0.972333i	$-0.575050\pi$
$662$	−0.500581	−	1.78333i	−0.0194556	−	0.0693110i
$663$	2.43777	+	1.81989i	0.0946751	+	0.0706787i
$664$	1.23701	−	1.32831i	0.0480052	−	0.0515484i
$665$		0			0
$666$	−15.5055	+	29.4012i	−0.600826	+	1.13927i
$667$	3.75063	+	2.16543i	0.145225	+	0.0838457i
$668$	0.0833059	+	3.51179i	0.00322320	+	0.135875i
$669$	−14.6858	+	6.31171i	−0.567786	+	0.244025i
$670$	−18.0528	−	17.6296i	−0.697439	−	0.681091i
$671$	−45.1221			−1.74192
$672$		0			0
$673$	−19.4364			−0.749219			−0.374610	−	0.927183i	$-0.622223\pi$
$673$	−19.4364			−0.749219			−0.374610	+	0.927183i	$0.622223\pi$
$674$	−15.6437	−	15.2771i	−0.602575	−	0.588450i
$675$	0.164512	+	0.955244i	0.00633208	+	0.0367674i
$676$	−0.608746	−	25.6619i	−0.0234133	−	0.986997i
$677$	−8.63274	−	4.98411i	−0.331783	−	0.191555i	0.324849	−	0.945766i	$-0.394686\pi$
$677$	−8.63274	−	4.98411i	−0.331783	−	0.191555i	−0.656633	+	0.754211i	$0.728020\pi$
$678$	−21.8592	−	8.41871i	−0.839499	−	0.323319i
$679$		0			0
$680$	−18.9571	+	20.3563i	−0.726971	+	0.780628i
$681$	20.2321	−	27.1012i	0.775297	−	1.03852i
$682$	9.62974	+	34.3061i	0.368742	+	1.31365i
$683$	−14.8051	−	25.6431i	−0.566501	−	0.981208i	−0.996908	−	0.0785732i	$-0.974964\pi$
$683$	−14.8051	−	25.6431i	−0.566501	−	0.981208i	0.430408	−	0.902635i	$-0.358370\pi$
$684$	9.99527	+	30.9953i	0.382179	+	1.18513i
$685$	5.29606			0.202352
$686$		0			0
$687$	−3.49801	−	0.413570i	−0.133457	−	0.0157787i
$688$	−2.09035	−	44.0349i	−0.0796937	−	1.67881i
$689$	−1.93064	+	1.11466i	−0.0735515	+	0.0424650i
$690$	−1.00760	−	6.40758i	−0.0383587	−	0.243932i
$691$	−38.2440	−	22.0802i	−1.45487	−	0.839969i	−0.456117	−	0.889920i	$-0.650760\pi$
$691$	−38.2440	−	22.0802i	−1.45487	−	0.839969i	−0.998752	+	0.0499504i	$0.984094\pi$
$692$	7.54856	−	13.8214i	0.286953	−	0.525412i
$693$		0			0
$694$	9.67599	−	37.9036i	0.367295	−	1.43880i
$695$	−10.4990	+	18.1848i	−0.398250	+	0.689790i
$696$	6.15237	−	17.1787i	0.233205	−	0.651157i
$697$	5.53167	+	9.58114i	0.209527	+	0.362911i
$698$	19.1547	+	18.7057i	0.725017	+	0.708022i
$699$	0.665271	−	5.62691i	0.0251629	−	0.212829i
$700$		0			0
$701$			38.2714i			1.44549i	0.691115	+	0.722745i	$0.257120\pi$
$701$			38.2714i			1.44549i	−0.691115	+	0.722745i	$0.742880\pi$
$702$	1.28442	+	2.69877i	0.0484774	+	0.101859i
$703$	−36.8276	+	21.2624i	−1.38898	+	0.801927i
$704$	−28.6146	+	19.3566i	−1.07845	+	0.729529i
$705$	7.35062	+	5.48753i	0.276841	+	0.206672i
$706$	−2.73074	−	0.697101i	−0.102773	−	0.0262357i
$707$		0			0
$708$	11.0515	+	7.84919i	0.415339	+	0.294991i
$709$	−3.44896	+	5.97377i	−0.129528	+	0.224350i	−0.923494	−	0.383613i	$-0.874680\pi$
$709$	−3.44896	+	5.97377i	−0.129528	+	0.224350i	0.793966	+	0.607963i	$0.208013\pi$
$710$	4.25411	+	15.1553i	0.159654	+	0.568770i
$711$	−11.5050	+	3.41108i	−0.431470	+	0.127926i
$712$	−37.8519	+	11.6002i	−1.41856	+	0.434736i
$713$		−	6.78411i		−	0.254067i
$714$		0			0
$715$			4.00000i			0.149592i
$716$	−15.9616	+	9.72732i	−0.596515	+	0.363527i
$717$	16.7599	+	38.9963i	0.625912	+	1.45634i
$718$	3.19978	−	0.898181i	0.119415	−	0.0335198i
$719$	14.1178	−	24.4527i	0.526503	−	0.911930i	−0.473020	−	0.881052i	$-0.656836\pi$
$719$	14.1178	−	24.4527i	0.526503	−	0.911930i	0.999523	−	0.0308787i	$-0.00983056\pi$
$720$	−25.8036	+	9.00204i	−0.961643	+	0.335486i
$721$		0			0
$722$	−3.65944	+	14.3351i	−0.136190	+	0.533496i
$723$	19.0811	−	25.5594i	0.709634	−	0.950565i
$724$	−0.801064	−	33.7692i	−0.0297713	−	1.25502i
$725$	0.601728	−	0.347408i	0.0223476	−	0.0129024i
$726$	11.7734	+	14.5719i	0.436953	+	0.540814i
$727$			27.3942i			1.01599i	0.861359	+	0.507997i	$0.169614\pi$
$727$			27.3942i			1.01599i	−0.861359	+	0.507997i	$0.830386\pi$
$728$		0			0
$729$	20.5442	+	17.5196i	0.760896	+	0.648874i
$730$	6.33093	−	6.48289i	0.234318	−	0.239943i
$731$	−23.7964	−	41.2166i	−0.880143	−	1.52445i
$732$	3.39623	−	36.0366i	0.125528	−	1.33195i
$733$	−14.8514	+	25.7234i	−0.548549	+	0.950114i	0.449826	+	0.893116i	$0.351486\pi$
$733$	−14.8514	+	25.7234i	−0.548549	+	0.950114i	−0.998374	+	0.0569978i	$0.981847\pi$
$734$	46.8550	+	11.9611i	1.72945	+	0.441492i
$735$		0			0
$736$	6.24130	−	2.07587i	0.230057	−	0.0765177i
$737$	−29.2996	−	16.9162i	−1.07927	−	0.623115i
$738$	0.416092	+	10.8615i	0.0153166	+	0.399816i
$739$	−23.7606	+	13.7182i	−0.874050	+	0.504633i	−0.868692	−	0.495353i	$-0.835039\pi$
$739$	−23.7606	+	13.7182i	−0.874050	+	0.504633i	−0.00535770	+	0.999986i	$0.501705\pi$
$740$	−18.5703	−	30.4722i	−0.682658	−	1.12018i
$741$	−0.448959	+	3.79733i	−0.0164929	+	0.139498i
$742$		0			0
$743$	−2.30093			−0.0844131			−0.0422065	−	0.999109i	$-0.513439\pi$
$743$	−2.30093			−0.0844131			−0.0422065	+	0.999109i	$0.513439\pi$
$744$	−28.1232	+	5.10861i	−1.03105	+	0.187291i
$745$	19.8009	+	34.2962i	0.725450	+	1.25652i
$746$	24.0581	−	6.75312i	0.880830	−	0.247249i
$747$	1.32487	−	1.39683i	0.0484745	−	0.0511072i
$748$	−17.8768	+	32.7325i	−0.653641	+	1.19682i
$749$		0			0
$750$	25.0576	+	9.65049i	0.914973	+	0.352386i
$751$	−16.8176	−	9.70963i	−0.613682	−	0.354309i	0.160723	−	0.987000i	$-0.448617\pi$
$751$	−16.8176	−	9.70963i	−0.613682	−	0.354309i	−0.774405	+	0.632690i	$0.781951\pi$
$752$	−4.26376	+	8.26719i	−0.155483	+	0.301474i
$753$	−10.5626	−	24.5766i	−0.384924	−	0.895623i
$754$	1.49687	−	1.53280i	0.0545126	−	0.0558211i
$755$	9.48634			0.345243
$756$		0			0
$757$	13.9327			0.506393			0.253197	−	0.967415i	$-0.418518\pi$
$757$	13.9327			0.506393			0.253197	+	0.967415i	$0.418518\pi$
$758$	−5.32986	+	5.45779i	−0.193589	+	0.198236i
$759$	−3.43402	−	7.99014i	−0.124647	−	0.290024i
$760$	−34.0724	−	7.84220i	−1.23593	−	0.284467i
$761$	10.7265	+	6.19296i	0.388836	+	0.224495i	0.681656	−	0.731673i	$-0.261260\pi$
$761$	10.7265	+	6.19296i	0.388836	+	0.224495i	−0.292820	+	0.956168i	$0.594594\pi$
$762$	−14.1896	−	5.46489i	−0.514035	−	0.197972i
$763$		0			0
$764$	−35.6466	−	19.4683i	−1.28965	−	0.704339i
$765$	−20.3036	+	21.4064i	−0.734079	+	0.773948i
$766$	2.52243	−	0.708048i	0.0911392	−	0.0255828i
$767$	0.795777	+	1.37833i	0.0287338	+	0.0497685i
$768$	−13.3053	−	24.3099i	−0.480114	−	0.877206i
$769$	−45.0074			−1.62301			−0.811505	−	0.584346i	$-0.801351\pi$
$769$	−45.0074			−1.62301			−0.811505	+	0.584346i	$0.801351\pi$
$770$		0			0
$771$	−1.82404	+	15.4278i	−0.0656911	+	0.555620i
$772$	11.7085	−	7.13536i	0.421397	−	0.256807i
$773$	44.5842	−	25.7407i	1.60358	−	0.925828i	0.612819	−	0.790223i	$-0.290035\pi$
$773$	44.5842	−	25.7407i	1.60358	−	0.925828i	0.990763	−	0.135605i	$-0.0432979\pi$
$774$	−1.78997	−	46.7244i	−0.0643391	−	1.67947i
$775$	−0.942582	−	0.544200i	−0.0338585	−	0.0195482i
$776$	−3.85520	+	4.13974i	−0.138393	+	0.148608i
$777$		0			0
$778$	−7.37877	−	1.88364i	−0.264542	−	0.0675319i
$779$	−6.95292	+	12.0428i	−0.249114	+	0.431479i
$780$	−3.19458	−	0.301070i	−0.114384	−	0.0107800i
$781$	10.5528	+	18.2780i	0.377608	+	0.654037i
$782$	4.96122	−	5.08030i	0.177413	−	0.181671i
$783$	6.69191	−	18.1603i	0.239149	−	0.648997i
$784$		0			0
$785$			43.8682i			1.56572i
$786$	22.1710	+	27.4409i	0.790814	+	0.978785i
$787$	35.6977	−	20.6101i	1.27249	−	0.734670i	0.297031	−	0.954868i	$-0.404003\pi$
$787$	35.6977	−	20.6101i	1.27249	−	0.734670i	0.975455	+	0.220197i	$0.0706701\pi$
$788$	−3.93549	+	0.0933568i	−0.140196	+	0.00332570i
$789$	−20.0624	+	26.8739i	−0.714240	+	0.956735i
$790$	3.18654	−	12.4826i	0.113372	−	0.444111i
$791$		0			0
$792$	−30.5369	+	20.2524i	−1.08508	+	0.719637i
$793$	2.12494	−	3.68051i	0.0754590	−	0.130699i
$794$	−29.4587	+	8.26906i	−1.04545	+	0.293458i
$795$	−8.53706	−	19.8636i	−0.302778	−	0.704491i
$796$	6.63307	+	10.8843i	0.235103	+	0.385783i
$797$		−	37.0164i		−	1.31119i	−0.755113	−	0.655595i	$-0.772418\pi$
$797$		−	37.0164i		−	1.31119i	0.755113	−	0.655595i	$-0.227582\pi$
$798$		0			0
$799$			10.0422i			0.355269i
$800$	0.212236	−	1.03368i	0.00750369	−	0.0365463i
$801$	−40.2589	+	11.9362i	−1.42248	+	0.421747i
$802$	14.6273	+	52.1099i	0.516507	+	1.84006i
$803$	6.07473	−	10.5217i	0.214372	−	0.371304i
$804$	15.7153	−	22.1268i	0.554237	−	0.780352i
$805$		0			0
$806$	−3.25177	−	0.830108i	−0.114539	−	0.0292393i
$807$	0.0667428	+	0.0498261i	0.00234946	+	0.00175396i
$808$	5.50972	−	23.9383i	0.193831	−	0.842147i
$809$	−45.3040	+	26.1563i	−1.59280	+	0.919605i	−0.599979	+	0.800016i	$0.704825\pi$
$809$	−45.3040	+	26.1563i	−1.59280	+	0.919605i	−0.992823	+	0.119589i	$0.961842\pi$
$810$	−27.4550	+	9.29744i	−0.964671	+	0.326679i
$811$		−	25.3719i		−	0.890929i	−0.895300	−	0.445464i	$-0.853039\pi$
$811$		−	25.3719i		−	0.890929i	0.895300	−	0.445464i	$-0.146961\pi$
$812$		0			0
$813$	4.04223	−	34.1895i	0.141767	−	1.19908i
$814$	−34.2311	−	33.4287i	−1.19980	−	1.17168i
$815$	9.84750	+	17.0564i	0.344943	+	0.597459i
$816$	−24.7961	−	16.7409i	−0.868037	−	0.586049i
$817$	29.9104	−	51.8064i	1.04643	−	1.81248i
$818$	−1.66898	+	6.53787i	−0.0583545	+	0.228591i
$819$		0			0
$820$	−10.2413	−	5.59327i	−0.357642	−	0.195326i
$821$	25.1716	+	14.5328i	0.878493	+	0.507198i	0.870161	−	0.492767i	$-0.164014\pi$
$821$	25.1716	+	14.5328i	0.878493	+	0.507198i	0.00833206	+	0.999965i	$0.497348\pi$
$822$	0.884871	+	5.62711i	0.0308634	+	0.196268i
$823$	−24.7981	+	14.3172i	−0.864406	+	0.499065i	−0.865485	−	0.500934i	$-0.832990\pi$
$823$	−24.7981	+	14.3172i	−0.864406	+	0.499065i	0.00107900	+	0.999999i	$0.499657\pi$
$824$	28.7953	−	8.82469i	1.00313	−	0.307423i
$825$	−1.38561	−	0.163821i	−0.0482409	−	0.00570352i
$826$		0			0
$827$	4.88743			0.169953			0.0849763	−	0.996383i	$-0.472919\pi$
$827$	4.88743			0.169953			0.0849763	+	0.996383i	$0.472919\pi$
$828$	6.63976	−	2.14117i	0.230747	−	0.0744108i
$829$	−19.4658	−	33.7157i	−0.676074	−	1.17100i	−0.976154	−	0.217081i	$-0.930346\pi$
$829$	−19.4658	−	33.7157i	−0.676074	−	1.17100i	0.300079	−	0.953914i	$-0.402987\pi$
$830$	0.558578	+	1.98994i	0.0193885	+	0.0690719i
$831$	−10.6464	+	14.2610i	−0.369320	+	0.494710i
$832$	−0.231321	−	3.24559i	−0.00801961	−	0.112521i
$833$		0			0
$834$	−21.0757	−	8.11695i	−0.729793	−	0.281067i
$835$	−3.46410	−	2.00000i	−0.119880	−	0.0692129i
$836$	−46.8653	+	1.11173i	−1.62087	+	0.0384499i
$837$	−29.8775	+	5.14551i	−1.03272	+	0.177855i
$838$	8.43079	+	8.23317i	0.291237	+	0.284410i
$839$	49.3493			1.70373			0.851863	−	0.523765i	$-0.175473\pi$
$839$	49.3493			1.70373			0.851863	+	0.523765i	$0.175473\pi$
$840$		0			0
$841$	15.1267			0.521610
$842$	−20.9769	−	20.4852i	−0.722911	−	0.705966i
$843$	−10.7956	+	4.63976i	−0.371820	+	0.159802i
$844$	50.2471	−	1.19195i	1.72958	−	0.0410286i
$845$	25.3134	+	14.6147i	0.870809	+	0.502762i
$846$	−4.60240	+	8.72696i	−0.158234	+	0.300039i
$847$		0			0
$848$	18.4459	−	11.8501i	0.633434	−	0.406935i
$849$	7.53354	+	5.62408i	0.258550	+	0.193018i
$850$	−0.307882	−	1.09684i	−0.0105603	−	0.0376212i
$851$	4.55480	+	7.88914i	0.156136	+	0.270436i
$852$	−15.3919	+	7.05220i	−0.527318	+	0.241604i
$853$	−36.4912			−1.24943			−0.624717	−	0.780851i	$-0.714786\pi$
$853$	−36.4912			−1.24943			−0.624717	+	0.780851i	$0.714786\pi$
$854$		0			0
$855$	−36.0616	−	8.64803i	−1.23328	−	0.295756i
$856$	6.96178	+	22.7166i	0.237949	+	0.776436i
$857$	31.5609	−	18.2217i	1.07810	−	0.622441i	0.147716	−	0.989030i	$-0.452808\pi$
$857$	31.5609	−	18.2217i	1.07810	−	0.622441i	0.930383	+	0.366589i	$0.119474\pi$
$858$	−4.25003	+	0.668324i	−0.145094	+	0.0228162i
$859$	−10.2782	−	5.93411i	−0.350687	−	0.202469i	0.314301	−	0.949323i	$-0.398230\pi$
$859$	−10.2782	−	5.93411i	−0.350687	−	0.202469i	−0.664988	+	0.746854i	$0.731563\pi$
$860$	44.0566	+	24.0614i	1.50232	+	0.820488i
$861$		0			0
$862$	−12.2413	+	47.9527i	−0.416940	+	1.63327i
$863$	−8.16126	+	14.1357i	−0.277812	+	0.481185i	−0.970841	−	0.239725i	$-0.922943\pi$
$863$	−8.16126	+	14.1357i	−0.277812	+	0.481185i	0.693028	+	0.720910i	$0.256276\pi$
$864$	−13.8760	−	25.9125i	−0.472072	−	0.881560i
$865$	8.96636	+	15.5302i	0.304865	+	0.528042i
$866$	−17.5427	−	17.1315i	−0.596124	−	0.582151i
$867$	−2.83473	−	0.335150i	−0.0962723	−	0.0113823i
$868$		0			0
$869$		−	17.2733i		−	0.585958i
$870$	13.0582	+	16.1620i	0.442714	+	0.547944i
$871$	2.75963	−	1.59327i	0.0935064	−	0.0539859i
$872$	−28.8938	−	6.65030i	−0.978468	−	0.225207i
$873$	−4.12903	+	4.35329i	−0.139747	+	0.147336i
$874$	8.64803	+	2.20766i	0.292524	+	0.0746752i
$875$		0			0
$876$	7.94591	+	5.64350i	0.268467	+	0.190676i
$877$	−3.40673	+	5.90063i	−0.115037	+	0.199250i	−0.917795	−	0.397056i	$-0.870032\pi$
$877$	−3.40673	+	5.90063i	−0.115037	+	0.199250i	0.802758	+	0.596306i	$0.203365\pi$
$878$	−12.7257	−	45.3355i	−0.429472	−	1.53000i
$879$	−44.8548	+	19.2778i	−1.51292	+	0.650226i
$880$	−1.86530	−	39.2940i	−0.0628792	−	1.32460i
$881$			10.1075i			0.340530i	0.985398	+	0.170265i	$0.0544624\pi$
$881$			10.1075i			0.340530i	−0.985398	+	0.170265i	$0.945538\pi$
$882$		0			0
$883$		−	29.4615i		−	0.991458i	−0.868477	−	0.495729i	$-0.834901\pi$
$883$		−	29.4615i		−	0.991458i	0.868477	−	0.495729i	$-0.165099\pi$
$884$	−1.82804	−	2.99965i	−0.0614837	−	0.100889i
$885$	−14.1811	+	6.09479i	−0.476692	+	0.204874i
$886$	12.0816	−	3.39130i	0.405888	−	0.113933i
$887$	22.2334	−	38.5094i	0.746525	−	1.29302i	−0.202954	−	0.979188i	$-0.565054\pi$
$887$	22.2334	−	38.5094i	0.746525	−	1.29302i	0.949479	−	0.313831i	$-0.101613\pi$
$888$	29.2742	−	24.8224i	0.982378	−	0.832986i
$889$		0			0
$890$	11.1505	−	43.6798i	0.373767	−	1.46415i
$891$	−32.5843	+	21.1838i	−1.09161	+	0.709685i
$892$	18.4524	−	0.437723i	0.617831	−	0.0146560i
$893$	−10.9313	+	6.31119i	−0.365802	+	0.211196i
$894$	−33.1317	+	26.7689i	−1.10809	+	0.895286i
$895$		−	21.2847i		−	0.711469i
$896$		0			0
$897$	0.813457	+	0.0961751i	0.0271605	+	0.00321119i
$898$	−26.0682	+	26.6939i	−0.869908	+	0.890788i
$899$	10.8660	+	18.8204i	0.362401	+	0.627697i
$900$	0.235127	−	1.09428i	0.00783756	−	0.0364761i
$901$	11.8346	−	20.4981i	0.394267	−	0.682890i
$902$	−15.1598	−	3.86997i	−0.504765	−	0.128856i
$903$		0			0
$904$	19.7941	+	18.4335i	0.658342	+	0.613090i
$905$	33.3106	+	19.2319i	1.10728	+	0.639289i
$906$	1.58499	+	10.0793i	0.0526577	+	0.334863i
$907$	48.4273	−	27.9595i	1.60800	−	0.928380i	0.618186	−	0.786032i	$-0.287868\pi$
$907$	48.4273	−	27.9595i	1.60800	−	0.928380i	0.989817	−	0.142348i	$-0.0454653\pi$
$908$	−33.3478	+	20.3228i	−1.10668	+	0.674434i
$909$	6.07587	−	25.3359i	0.201524	−	0.840340i
$910$		0			0
$911$	−7.71538			−0.255622			−0.127811	−	0.991799i	$-0.540795\pi$
$911$	−7.71538			−0.255622			−0.127811	+	0.991799i	$0.540795\pi$
$912$	2.63956	−	37.5125i	0.0874047	−	1.24216i
$913$	1.38561	+	2.39995i	0.0458571	+	0.0794268i
$914$	−41.1879	+	11.5615i	−1.36238	+	0.382419i
$915$	33.0281	+	24.6568i	1.09188	+	0.815128i
$916$	3.56961	+	1.94954i	0.117943	+	0.0644145i
$917$		0			0
$918$	−26.1368	−	17.9962i	−0.862642	−	0.593962i
$919$	−8.69683	−	5.02112i	−0.286882	−	0.165631i	0.349653	−	0.936879i	$-0.386300\pi$
$919$	−8.69683	−	5.02112i	−0.286882	−	0.165631i	−0.636535	+	0.771248i	$0.719633\pi$
$920$	−1.67994	+	7.29892i	−0.0553861	+	0.240638i
$921$	−3.56660	+	1.53286i	−0.117523	+	0.0505095i
$922$	1.54438	−	1.58145i	0.0508614	−	0.0520823i
$923$	−1.98786			−0.0654311
$924$		0			0
$925$	1.46149			0.0480534
$926$	−32.8989	+	33.6886i	−1.08112	+	1.10707i
$927$	30.6263	−	9.08032i	1.00590	−	0.298237i
$928$	−13.9897	+	15.7555i	−0.459234	+	0.517198i
$929$	2.71156	+	1.56552i	0.0889635	+	0.0513631i	0.543822	−	0.839201i	$-0.316977\pi$
$929$	2.71156	+	1.56552i	0.0889635	+	0.0513631i	−0.454858	+	0.890564i	$0.650310\pi$
$930$	11.6977	−	30.3732i	0.383583	−	0.995977i
$931$		0			0
$932$	−3.13603	+	5.74209i	−0.102724	+	0.188088i
$933$	−27.4364	+	36.7515i	−0.898229	+	1.20319i
$934$	−23.5512	+	6.61084i	−0.770620	+	0.216313i
$935$	−21.2345	−	36.7792i	−0.694442	−	1.20281i
$936$	−0.213864	−	3.44457i	−0.00699037	−	0.112589i
$937$	47.0325			1.53648			0.768242	−	0.640159i	$-0.221132\pi$
$937$	47.0325			1.53648			0.768242	+	0.640159i	$0.221132\pi$
$938$		0			0
$939$	−0.757468	−	0.0895556i	−0.0247190	−	0.00292254i
$940$	−5.51211	−	9.04486i	−0.179785	−	0.295011i
$941$	−19.2716	+	11.1265i	−0.628238	+	0.362713i	−0.780069	−	0.625693i	$-0.784816\pi$
$941$	−19.2716	+	11.1265i	−0.628238	+	0.362713i	0.151832	+	0.988406i	$0.451483\pi$
$942$	−46.6103	+	7.32954i	−1.51865	+	0.238809i
$943$	2.57979	+	1.48944i	0.0840095	+	0.0485029i
$944$	−8.46007	−	13.1689i	−0.275352	−	0.428611i
$945$		0			0
$946$	65.2151	+	16.6480i	2.12033	+	0.541274i
$947$	16.9667	−	29.3873i	0.551345	−	0.954958i	−0.446833	−	0.894617i	$-0.647448\pi$
$947$	16.9667	−	29.3873i	0.551345	−	0.954958i	0.998178	−	0.0603402i	$-0.0192185\pi$
$948$	13.7953	+	1.30012i	0.448050	+	0.0422260i
$949$	0.572156	+	0.991004i	0.0185730	+	0.0321694i
$950$	1.00045	−	1.02446i	0.0324588	−	0.0332380i
$951$	−2.39812	+	20.2835i	−0.0777645	+	0.657739i
$952$		0			0
$953$			20.2641i			0.656419i	0.944605	+	0.328209i	$0.106445\pi$
$953$			20.2641i			0.656419i	−0.944605	+	0.328209i	$0.893555\pi$
$954$	19.6789	−	12.3895i	0.637128	−	0.401126i
$955$	40.0536	−	23.1249i	1.29610	−	0.748306i
$956$	−1.16232	−	48.9979i	−0.0375920	−	1.58470i
$957$	22.3243	+	16.6660i	0.721642	+	0.538735i
$958$	−5.80952	+	22.7575i	−0.187697	+	0.735263i
$959$		0			0
$960$	31.5224	+	1.46786i	1.01738	+	0.0473748i
$961$	1.52112	−	2.63465i	0.0490682	−	0.0849887i
$962$	4.33876	−	1.21789i	0.139887	−	0.0392664i
$963$	7.16345	+	24.1611i	0.230839	+	0.778579i
$964$	−31.4506	+	19.1666i	−1.01295	+	0.617313i
$965$			15.6131i			0.502604i
$966$		0			0
$967$		−	43.5882i		−	1.40170i	−0.713308	−	0.700851i	$-0.752804\pi$
$967$		−	43.5882i		−	1.40170i	0.713308	−	0.700851i	$-0.247196\pi$
$968$	−6.33840	−	20.6824i	−0.203724	−	0.664759i
$969$	−16.0305	−	37.2990i	−0.514974	−	1.19822i
$970$	−1.74084	−	6.20176i	−0.0558949	−	0.199127i
$971$	1.83580	−	3.17971i	0.0589138	−	0.102042i	−0.835064	−	0.550152i	$-0.814570\pi$
$971$	1.83580	−	3.17971i	0.0589138	−	0.102042i	0.893978	+	0.448111i	$0.147903\pi$
$972$	−14.4658	−	27.6177i	−0.463991	−	0.885840i
$973$		0			0
$974$	33.2289	+	8.48263i	1.06472	+	0.271801i
$975$	0.0786155	−	0.105307i	0.00251771	−	0.00337251i
$976$	−19.1581	+	37.1465i	−0.613236	+	1.18903i
$977$	29.5088	−	17.0369i	0.944069	−	0.545058i	0.0528352	−	0.998603i	$-0.483174\pi$
$977$	29.5088	−	17.0369i	0.944069	−	0.545058i	0.891233	+	0.453545i	$0.149841\pi$
$978$	−16.4772	+	13.3129i	−0.526883	+	0.425698i
$979$		−	60.4439i		−	1.93179i
$980$		0			0
$981$	−30.5807	−	7.33364i	−0.976368	−	0.234145i
$982$	20.5476	+	20.0660i	0.655700	+	0.640331i
$983$	−27.1404	−	47.0086i	−0.865645	−	1.49934i	−0.866406	−	0.499341i	$-0.833576\pi$
$983$	−27.1404	−	47.0086i	−0.865645	−	1.49934i	0.000761201	−	1.00000i	$-0.499758\pi$
$984$	4.23177	−	11.8160i	0.134904	−	0.376680i
$985$	2.24130	−	3.88205i	0.0714138	−	0.123692i
$986$	−5.62636	+	22.0401i	−0.179180	+	0.701898i
$987$		0			0
$988$	2.11636	−	3.87506i	0.0673303	−	0.123282i
$989$	−11.0979	−	6.40736i	−0.352892	−	0.203742i
$990$	−1.59726	−	41.6940i	−0.0507642	−	1.32512i
$991$	9.09990	−	5.25383i	0.289068	−	0.166893i	−0.348454	−	0.937326i	$-0.613293\pi$
$991$	9.09990	−	5.25383i	0.289068	−	0.166893i	0.637521	+	0.770433i	$0.279960\pi$
$992$	32.3309	+	6.63819i	1.02651	+	0.210763i
$993$	−0.266354	+	2.25285i	−0.00845250	+	0.0714919i
$994$		0			0
$995$	−14.5141			−0.460127
$996$	−2.02100	+	0.925975i	−0.0640379	+	0.0293406i
$997$	10.7282	+	18.5818i	0.339765	+	0.588491i	0.984388	−	0.176010i	$-0.0563190\pi$
$997$	10.7282	+	18.5818i	0.339765	+	0.588491i	−0.644623	+	0.764501i	$0.722986\pi$
$998$	4.02780	+	14.3491i	0.127498	+	0.454214i
$999$	31.2894	−	26.0431i	0.989954	−	0.823969i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.n.g.275.9		24
3.2	odd	2	inner	588.2.n.g.275.4		24
4.3	odd	2	inner	588.2.n.g.275.11		24
7.2	even	3		588.2.e.c.491.7		12
7.3	odd	6		588.2.n.f.263.2		24
7.4	even	3	inner	588.2.n.g.263.2		24
7.5	odd	6		84.2.e.a.71.7	yes	12
7.6	odd	2		588.2.n.f.275.9		24
12.11	even	2	inner	588.2.n.g.275.2		24
21.2	odd	6		588.2.e.c.491.6		12
21.5	even	6		84.2.e.a.71.6	yes	12
21.11	odd	6	inner	588.2.n.g.263.11		24
21.17	even	6		588.2.n.f.263.11		24
21.20	even	2		588.2.n.f.275.4		24
28.3	even	6		588.2.n.f.263.4		24
28.11	odd	6	inner	588.2.n.g.263.4		24
28.19	even	6		84.2.e.a.71.5	✓	12
28.23	odd	6		588.2.e.c.491.5		12
28.27	even	2		588.2.n.f.275.11		24
56.5	odd	6		1344.2.h.h.575.12		12
56.19	even	6		1344.2.h.h.575.1		12
84.11	even	6	inner	588.2.n.g.263.9		24
84.23	even	6		588.2.e.c.491.8		12
84.47	odd	6		84.2.e.a.71.8	yes	12
84.59	odd	6		588.2.n.f.263.9		24
84.83	odd	2		588.2.n.f.275.2		24
168.5	even	6		1344.2.h.h.575.2		12
168.131	odd	6		1344.2.h.h.575.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.e.a.71.5	✓	12	28.19	even	6
84.2.e.a.71.6	yes	12	21.5	even	6
84.2.e.a.71.7	yes	12	7.5	odd	6
84.2.e.a.71.8	yes	12	84.47	odd	6
588.2.e.c.491.5		12	28.23	odd	6
588.2.e.c.491.6		12	21.2	odd	6
588.2.e.c.491.7		12	7.2	even	3
588.2.e.c.491.8		12	84.23	even	6
588.2.n.f.263.2		24	7.3	odd	6
588.2.n.f.263.4		24	28.3	even	6
588.2.n.f.263.9		24	84.59	odd	6
588.2.n.f.263.11		24	21.17	even	6
588.2.n.f.275.2		24	84.83	odd	2
588.2.n.f.275.4		24	21.20	even	2
588.2.n.f.275.9		24	7.6	odd	2
588.2.n.f.275.11		24	28.27	even	2
588.2.n.g.263.2		24	7.4	even	3	inner
588.2.n.g.263.4		24	28.11	odd	6	inner
588.2.n.g.263.9		24	84.11	even	6	inner
588.2.n.g.263.11		24	21.11	odd	6	inner
588.2.n.g.275.2		24	12.11	even	2	inner
588.2.n.g.275.4		24	3.2	odd	2	inner
588.2.n.g.275.9		24	1.1	even	1	trivial
588.2.n.g.275.11		24	4.3	odd	2	inner
1344.2.h.h.575.1		12	56.19	even	6
1344.2.h.h.575.2		12	168.5	even	6
1344.2.h.h.575.11		12	168.131	odd	6
1344.2.h.h.575.12		12	56.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.01179 + 0.988071i) q^{2} +(-0.683917 - 1.59131i) q^{3} +(0.0474302 + 1.99944i) q^{4} +(-1.97228 - 1.13870i) q^{5} +(0.880346 - 2.28582i) q^{6} +(-1.92760 + 2.06987i) q^{8} +(-2.06452 + 2.17664i) q^{9} +(-0.870418 - 3.10088i) q^{10} +(-2.15917 - 3.73979i) q^{11} +(3.14928 - 1.44292i) q^{12} +0.406728 q^{13} +(-0.463141 + 3.91729i) q^{15} +(-3.99550 + 0.189667i) q^{16} +(-3.73979 + 2.15917i) q^{17} +(-4.23953 + 0.162413i) q^{18} +(-4.70065 - 2.71392i) q^{19} +(2.18321 - 3.99747i) q^{20} +(1.51056 - 5.91729i) q^{22} +(-0.581371 + 1.00696i) q^{23} +(4.61212 + 1.65178i) q^{24} +(0.0932716 + 0.161551i) q^{25} +(0.411523 + 0.401877i) q^{26} +(4.87566 + 1.79664i) q^{27} -3.72469i q^{29} +(-4.33916 + 3.50585i) q^{30} +(-5.05289 + 2.91729i) q^{31} +(-4.23000 - 3.75594i) q^{32} +(-4.47446 + 5.99360i) q^{33} +(-5.91729 - 1.51056i) q^{34} +(-4.44998 - 4.02463i) q^{36} +(3.91729 - 6.78494i) q^{37} +(-2.07451 - 7.39049i) q^{38} +(-0.278168 - 0.647230i) q^{39} +(6.15873 - 1.88742i) q^{40} -2.56195i q^{41} +11.0211i q^{43} +(7.37506 - 4.49450i) q^{44} +(6.55035 - 1.94210i) q^{45} +(-1.58318 + 0.444399i) q^{46} +(1.16274 - 2.01393i) q^{47} +(3.03441 + 6.22835i) q^{48} +(-0.0652529 + 0.255614i) q^{50} +(5.99360 + 4.47446i) q^{51} +(0.0192912 + 0.813228i) q^{52} +(-4.74675 + 2.74054i) q^{53} +(3.15793 + 6.63532i) q^{54} +9.83457i q^{55} +(-1.10383 + 9.33627i) q^{57} +(3.68026 - 3.76860i) q^{58} +(1.95653 + 3.38881i) q^{59} +(-7.85434 - 0.740224i) q^{60} +(5.22448 - 9.04906i) q^{61} +(-7.99494 - 2.04094i) q^{62} +(-0.568736 - 7.97976i) q^{64} +(-0.802184 - 0.463141i) q^{65} +(-10.4493 + 1.64317i) q^{66} +(6.78494 - 3.91729i) q^{67} +(-4.49450 - 7.37506i) q^{68} +(2.00000 + 0.236460i) q^{69} -4.88743 q^{71} +(-0.525816 - 8.46897i) q^{72} +(1.40673 + 2.43653i) q^{73} +(10.6675 - 2.99436i) q^{74} +(0.193287 - 0.258911i) q^{75} +(5.20336 - 9.52738i) q^{76} +(0.358062 - 0.929710i) q^{78} +(3.46410 + 2.00000i) q^{79} +(8.09624 + 4.17560i) q^{80} +(-0.475549 - 8.98743i) q^{81} +(2.53139 - 2.59215i) q^{82} -0.641735 q^{83} +9.83457 q^{85} +(-10.8896 + 11.1510i) q^{86} +(-5.92712 + 2.54738i) q^{87} +(11.9029 + 2.73961i) q^{88} +(12.1218 + 6.99851i) q^{89} +(8.54650 + 4.50723i) q^{90} +(-2.04094 - 1.11466i) q^{92} +(8.09805 + 6.04551i) q^{93} +(3.16636 - 0.888797i) q^{94} +(6.18068 + 10.7053i) q^{95} +(-3.08388 + 9.29998i) q^{96} +2.00000 q^{97} +(12.5978 + 3.02112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} + 12 q^{6} + 4 q^{9} + 4 q^{10} - 6 q^{12} - 4 q^{16} + 8 q^{18} - 32 q^{22} + 2 q^{24} + 12 q^{25} - 20 q^{30} - 16 q^{33} - 64 q^{34} - 40 q^{36} + 16 q^{37} + 20 q^{40} + 24 q^{45} - 92 q^{48}+ \cdots + 48 q^{97}+O(q^{100}) \) 24 * q + 4 * q^4 + 12 * q^6 + 4 * q^9 + 4 * q^10 - 6 * q^12 - 4 * q^16 + 8 * q^18 - 32 * q^22 + 2 * q^24 + 12 * q^25 - 20 * q^30 - 16 * q^33 - 64 * q^34 - 40 * q^36 + 16 * q^37 + 20 * q^40 + 24 * q^45 - 92 * q^48 - 28 * q^52 + 10 * q^54 + 32 * q^57 + 32 * q^58 - 28 * q^60 - 16 * q^61 + 40 * q^64 - 12 * q^66 + 48 * q^69 + 32 * q^72 + 24 * q^73 + 120 * q^76 + 40 * q^78 - 28 * q^81 + 8 * q^82 + 80 * q^85 + 56 * q^88 + 160 * q^90 - 24 * q^93 - 34 * q^96 + 48 * q^97

Introduction

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