LMFDB - Embedded newform 588.2.n.f.275.4

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			275.4
Character	$\chi$	$=$	588.275
Dual form			588.2.n.f.263.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.01179 - 0.988071i) q^{2} +(-1.03615 - 1.38794i) q^{3} +(0.0474302 + 1.99944i) q^{4} +(-1.97228 - 1.13870i) q^{5} +(-0.323018 + 2.42810i) q^{6} +(1.92760 - 2.06987i) q^{8} +(-0.852770 + 2.87624i) q^{9} +(0.870418 + 3.10088i) q^{10} +(2.15917 + 3.73979i) q^{11} +(2.72596 - 2.13756i) q^{12} -0.406728 q^{13} +(0.463141 + 3.91729i) q^{15} +(-3.99550 + 0.189667i) q^{16} +(-3.73979 + 2.15917i) q^{17} +(3.70476 - 2.06755i) 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} +(-4.87015 - 0.530690i) q^{24} +(0.0932716 + 0.161551i) q^{25} +(0.411523 + 0.401877i) q^{26} +(4.87566 - 1.79664i) q^{27} +3.72469i q^{29} +(3.40196 - 4.42108i) q^{30} +(5.05289 - 2.91729i) q^{31} +(4.23000 + 3.75594i) q^{32} +(2.95338 - 6.87180i) q^{33} +(5.91729 + 1.51056i) q^{34} +(-5.79132 - 1.56864i) q^{36} +(3.91729 - 6.78494i) q^{37} +(-2.07451 - 7.39049i) q^{38} +(0.421433 + 0.564516i) q^{39} +(-6.15873 + 1.88742i) q^{40} -2.56195i q^{41} +11.0211i q^{43} +(-7.37506 + 4.49450i) q^{44} +(4.95708 - 4.70172i) q^{45} +(-1.58318 + 0.444399i) q^{46} +(1.16274 - 2.01393i) q^{47} +(4.40320 + 5.34900i) q^{48} +(0.0652529 - 0.255614i) q^{50} +(6.87180 + 2.95338i) q^{51} +(-0.0192912 - 0.813228i) q^{52} +(4.74675 - 2.74054i) q^{53} +(-6.70834 - 2.99969i) q^{54} -9.83457i q^{55} +(-1.10383 - 9.33627i) q^{57} +(3.68026 - 3.76860i) q^{58} +(1.95653 + 3.38881i) q^{59} +(-7.81040 + 1.11182i) 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} +(-9.77802 + 4.03465i) q^{66} +(6.78494 - 3.91729i) q^{67} +(-4.49450 - 7.37506i) q^{68} +(-2.00000 + 0.236460i) q^{69} +4.88743 q^{71} +(4.30966 + 7.30937i) q^{72} +(-1.40673 - 2.43653i) q^{73} +(-10.6675 + 2.99436i) q^{74} +(0.127580 - 0.296847i) q^{75} +(-5.20336 + 9.52738i) q^{76} +(0.131381 - 0.987576i) q^{78} +(3.46410 + 2.00000i) q^{79} +(8.09624 + 4.17560i) q^{80} +(-7.54557 - 4.90555i) q^{81} +(-2.53139 + 2.59215i) q^{82} -0.641735 q^{83} +9.83457 q^{85} +(10.8896 - 11.1510i) q^{86} +(5.16966 - 3.85935i) q^{87} +(11.9029 + 2.73961i) q^{88} +(12.1218 + 6.99851i) q^{89} +(-9.66116 - 0.140802i) q^{90} +(2.04094 + 1.11466i) q^{92} +(-9.28460 - 3.99036i) q^{93} +(-3.16636 + 0.888797i) q^{94} +(-6.18068 - 10.7053i) q^{95} +(0.830089 - 9.76273i) 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
$3$	−1.03615	−	1.38794i	−0.598224	−	0.801329i
$3$	−1.03615	−	1.38794i	−0.598224	−	0.801329i
$4$	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	$0.836741\pi$
$6$	−0.323018	+	2.42810i	−0.131872	+	0.991267i
$7$		0			0
$7$		0			0
$8$	1.92760	−	2.06987i	0.681509	−	0.731810i
$9$	−0.852770	+	2.87624i	−0.284257	+	0.958748i
$10$	0.870418	+	3.10088i	0.275250	+	0.980584i
$11$	2.15917	+	3.73979i	0.651014	+	1.12759i	0.982877	+	0.184261i	$0.0589893\pi$
$11$	2.15917	+	3.73979i	0.651014	+	1.12759i	−0.331864	+	0.943327i	$0.607677\pi$
$12$	2.72596	−	2.13756i	0.786917	−	0.617059i
$13$	−0.406728			−0.112806			−0.0564031	−	0.998408i	$-0.517963\pi$
$13$	−0.406728			−0.112806			−0.0564031	+	0.998408i	$0.517963\pi$
$14$		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	$0.508773\pi$
$18$	3.70476	−	2.06755i	0.873220	−	0.487327i
$19$	4.70065	+	2.71392i	1.07840	+	0.622616i	0.930465	−	0.366380i	$-0.119403\pi$
$19$	4.70065	+	2.71392i	1.07840	+	0.622616i	0.147938	+	0.988997i	$0.452736\pi$
$20$	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	−0.799026	−	0.601296i	$-0.794651\pi$
$23$	0.581371	−	1.00696i	0.121224	−	0.209967i	0.920251	+	0.391329i	$0.127985\pi$
$24$	−4.87015	−	0.530690i	−0.994115	−	0.108327i
$25$	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	$0.112402\pi$
$29$			3.72469i			0.691657i	−0.938298	+	0.345829i	$0.887598\pi$
$30$	3.40196	−	4.42108i	0.621110	−	0.807175i
$31$	5.05289	−	2.91729i	0.907525	−	0.523960i	0.0278913	−	0.999611i	$-0.491121\pi$
$31$	5.05289	−	2.91729i	0.907525	−	0.523960i	0.879634	+	0.475651i	$0.157787\pi$
$32$	4.23000	+	3.75594i	0.747766	+	0.663962i
$33$	2.95338	−	6.87180i	0.514118	−	1.19623i
$34$	5.91729	+	1.51056i	1.01481	+	0.259058i
$35$		0			0
$36$	−5.79132	−	1.56864i	−0.965220	−	0.261440i
$37$	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
$39$	0.421433	+	0.564516i	0.0674833	+	0.0903949i
$40$	−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
$45$	4.95708	−	4.70172i	0.738958	−	0.700892i
$46$	−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	$0.112418\pi$
$48$	4.40320	+	5.34900i	0.635547	+	0.772062i
$49$		0			0
$50$	0.0652529	−	0.255614i	0.00922816	−	0.0361493i
$51$	6.87180	+	2.95338i	0.962244	+	0.413556i
$52$	−0.0192912	−	0.813228i	−0.00267521	−	0.112774i
$53$	4.74675	−	2.74054i	0.652017	−	0.376442i	−0.137212	−	0.990542i	$-0.543814\pi$
$53$	4.74675	−	2.74054i	0.652017	−	0.376442i	0.789228	+	0.614100i	$0.210481\pi$
$54$	−6.70834	−	2.99969i	−0.912890	−	0.408206i
$55$		−	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	$0.751350\pi$
$60$	−7.81040	+	1.11182i	−1.00832	+	0.143535i
$61$	−5.22448	+	9.04906i	−0.668926	+	1.15861i	0.309279	+	0.950971i	$0.399912\pi$
$61$	−5.22448	+	9.04906i	−0.668926	+	1.15861i	−0.978205	+	0.207642i	$0.933421\pi$
$62$	−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
$66$	−9.77802	+	4.03465i	−1.20359	+	0.496631i
$67$	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	$-0.406339\pi$
$71$	4.88743			0.580031			0.290016	+	0.957022i	$0.406339\pi$
$72$	4.30966	+	7.30937i	0.507898	+	0.861417i
$73$	−1.40673	−	2.43653i	−0.164645	−	0.285174i	0.771884	−	0.635763i	$-0.219315\pi$
$73$	−1.40673	−	2.43653i	−0.164645	−	0.285174i	−0.936529	+	0.350590i	$0.885981\pi$
$74$	−10.6675	+	2.99436i	−1.24007	+	0.348087i
$75$	0.127580	−	0.296847i	0.0147317	−	0.0342770i
$76$	−5.20336	+	9.52738i	−0.596867	+	1.09287i
$77$		0			0
$78$	0.131381	−	0.987576i	0.0148759	−	0.111821i
$79$	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
$81$	−7.54557	−	4.90555i	−0.838396	−	0.545061i
$82$	−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
$87$	5.16966	−	3.85935i	0.554245	−	0.413766i
$88$	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	$0.400620\pi$
$90$	−9.66116	−	0.140802i	−1.01838	−	0.0148419i
$91$		0			0
$92$	2.04094	+	1.11466i	0.212782	+	0.116211i
$93$	−9.28460	−	3.99036i	−0.962768	−	0.413781i
$94$	−3.16636	+	0.888797i	−0.326585	+	0.0916724i
$95$	−6.18068	−	10.7053i	−0.634124	−	1.09834i
$96$	0.830089	−	9.76273i	0.0847206	−	0.996405i
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		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	$0.475555\pi$
$102$	−4.03465	−	9.77802i	−0.399490	−	0.968169i
$103$	9.22146	+	5.32401i	0.908618	+	0.524591i	0.879986	−	0.474999i	$-0.157552\pi$
$103$	9.22146	+	5.32401i	0.908618	+	0.524591i	0.0286316	+	0.999590i	$0.490885\pi$
$104$	−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	−0.994442	−	0.105287i	$-0.966424\pi$
$107$	−4.20011	+	7.27480i	−0.406040	+	0.703281i	0.588402	+	0.808568i	$0.299757\pi$
$108$	3.82351	+	9.66337i	0.367918	+	0.929858i
$109$	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	$0.148506\pi$
$113$			9.56296i			0.899607i	−0.893128	+	0.449804i	$0.851494\pi$
$114$	−8.10806	+	10.5370i	−0.759390	+	0.986880i
$115$	−2.29326	+	1.32401i	−0.213848	+	0.123465i
$116$	−7.44728	+	0.176663i	−0.691463	+	0.0164027i
$117$	0.346846	−	1.16985i	0.0320659	−	0.108153i
$118$	1.36879	−	5.36195i	0.126008	−	0.493608i
$119$		0			0
$120$	9.00103	+	6.59231i	0.821678	+	0.601793i
$121$	−3.82401	+	6.62339i	−0.347638	+	0.602126i
$122$	14.2272	−	3.99358i	1.28807	−	0.361561i
$123$	−3.55583	+	2.65457i	−0.320619	+	0.239355i
$124$	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
$129$	15.2967	−	11.4196i	1.34680	−	1.00544i
$130$	−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	$0.950063\pi$
$132$	13.8798	+	5.57917i	1.20808	+	0.485605i
$133$		0			0
$134$	−10.7355	−	2.74054i	−0.927404	−	0.236747i
$135$	−11.6620	−	2.00844i	−1.00371	−	0.172859i
$136$	−2.73961	+	11.9029i	−0.234919	+	1.02066i
$137$	2.01393	−	1.16274i	0.172062	−	0.0993398i	−0.411496	−	0.911412i	$-0.634994\pi$
$137$	2.01393	−	1.16274i	0.172062	−	0.0993398i	0.583558	+	0.812072i	$0.301660\pi$
$138$	2.25722	+	1.73689i	0.192147	+	0.147854i
$139$			9.22019i			0.782046i	0.920381	+	0.391023i	$0.127879\pi$
$139$			9.22019i			0.782046i	−0.920381	+	0.391023i	$0.872121\pi$
$140$		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
$144$	2.86171	−	11.6538i	0.238476	−	0.971148i
$145$	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	0.967802	−	0.251713i	$-0.0809940\pi$
$149$	15.0594	+	8.69454i	1.23371	+	0.712284i	0.265911	+	0.963998i	$0.414327\pi$
$150$	−0.422390	+	0.174289i	−0.0344880	+	0.0142306i
$151$	−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
$156$	−1.10873	+	0.869405i	−0.0887691	+	0.0696081i
$157$	9.63121	+	16.6817i	0.768654	+	1.33135i	0.938293	+	0.345842i	$0.112407\pi$
$157$	9.63121	+	16.6817i	0.768654	+	1.33135i	−0.169639	+	0.985506i	$0.554260\pi$
$158$	−1.52879	−	5.44636i	−0.121624	−	0.433289i
$159$	−8.72208	−	3.74860i	−0.691706	−	0.297283i
$160$	−4.06589	−	12.2245i	−0.321437	−	0.966430i
$161$		0			0
$162$	2.78748	+	12.4189i	0.219005	+	0.975724i
$163$	−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
$165$	−13.6498	+	10.1901i	−1.06264	+	0.793301i
$166$	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
$171$	−11.8145	+	11.2059i	−0.903476	+	0.856934i
$172$	−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	$0.763431\pi$
$174$	−9.04391	−	1.20314i	−0.685617	−	0.0912100i
$175$		0			0
$176$	−9.33627	−	14.5328i	−0.703748	−	1.09545i
$177$	2.67621	−	6.22688i	0.201156	−	0.468041i
$178$	−5.34964	−	19.0582i	−0.400973	−	1.42847i
$179$	−4.67303	−	8.09392i	−0.349278	−	0.604968i	0.636843	−	0.770993i	$-0.280240\pi$
$179$	−4.67303	−	8.09392i	−0.349278	−	0.604968i	−0.986121	+	0.166026i	$0.946907\pi$
$180$	9.63592	+	9.68837i	0.718219	+	0.722129i
$181$	16.8893			1.25537			0.627687	−	0.778466i	$-0.284002\pi$
$181$	16.8893			1.25537			0.627687	+	0.778466i	$0.284002\pi$
$182$		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
$186$	5.45128	+	13.2112i	0.399707	+	0.968695i
$187$	−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	$-0.570644\pi$
$191$	10.1541	−	17.5874i	0.734725	−	1.27258i	0.954844	−	0.297108i	$-0.0960223\pi$
$192$	−10.4861	+	9.05763i	−0.756773	+	0.653678i
$193$	−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	$-0.977662\pi$
$197$		−	1.96830i		−	0.140235i	0.997539	−	0.0701177i	$-0.0223375\pi$
$198$	15.7314	+	9.39082i	1.11798	+	0.667376i
$199$	−5.51925	+	3.18654i	−0.391250	+	0.225888i	−0.682701	−	0.730697i	$-0.739195\pi$
$199$	−5.51925	+	3.18654i	−0.391250	+	0.225888i	0.291452	+	0.956586i	$0.405862\pi$
$200$	0.514180	+	0.118345i	0.0363580	+	0.00836828i
$201$	−12.4672	−	5.35819i	−0.879369	−	0.377938i
$202$	11.9005	+	3.03794i	0.837314	+	0.213748i
$203$		0			0
$204$	−5.57917	+	13.8798i	−0.390620	+	0.971781i
$205$	−2.91729	+	5.05289i	−0.203752	+	0.352909i
$206$	−4.06966	−	14.4982i	−0.283547	−	1.01014i
$207$	2.40050	+	2.53088i	0.166846	+	0.175908i
$208$	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
$213$	−5.06413	−	6.78348i	−0.346989	−	0.464796i
$214$	11.4376	−	3.21055i	0.781861	−	0.219469i
$215$	12.5497	−	21.7368i	0.855885	−	1.48244i
$216$	5.67951	−	13.5552i	0.386442	−	0.922314i
$217$		0			0
$218$	3.66682	−	14.3640i	0.248349	−	0.972852i
$219$	−1.92417	+	4.47707i	−0.130023	+	0.302533i
$220$	19.6636	−	0.466456i	1.32572	−	0.0314484i
$221$	1.52108	−	0.878195i	0.102319	−	0.0590738i
$222$	15.2091	+	11.7032i	1.02077	+	0.785468i
$223$			9.22877i			0.618004i	0.951061	+	0.309002i	$0.0999950\pi$
$223$			9.22877i			0.618004i	−0.951061	+	0.309002i	$0.900005\pi$
$224$		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	$0.608939\pi$
$228$	18.6149	−	2.64986i	1.23280	−	0.175491i
$229$	−1.01682	+	1.76119i	−0.0671934	+	0.116382i	−0.897665	−	0.440679i	$-0.854738\pi$
$229$	−1.01682	+	1.76119i	−0.0671934	+	0.116382i	0.830471	+	0.557061i	$0.188071\pi$
$230$	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	0.404321	−	0.914617i	$-0.367508\pi$
$233$	−2.83305	−	1.63566i	−0.185599	−	0.107156i	−0.589921	+	0.807461i	$0.700841\pi$
$234$	−1.50683	+	0.840932i	−0.0985046	+	0.0549735i
$235$	−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	$-0.208740\pi$
$239$	24.5058			1.58515			0.792575	+	0.609775i	$0.208740\pi$
$240$	−2.59346	−	15.5637i	−0.167407	−	1.00463i
$241$	−9.20766	−	15.9481i	−0.593117	−	1.02731i	−0.993810	−	0.111097i	$-0.964564\pi$
$241$	−9.20766	−	15.9481i	−0.593117	−	1.02731i	0.400692	−	0.916213i	$-0.368770\pi$
$242$	10.4135	−	2.92307i	0.669403	−	0.187902i
$243$	1.00974	+	15.5557i	0.0647750	+	0.997900i
$244$	−18.3408	−	10.0168i	−1.17415	−	0.641261i
$245$		0			0
$246$	6.22066	+	0.827555i	0.396615	+	0.0527630i
$247$	−1.91189	−	1.10383i	−0.121651	−	0.0702350i
$248$	3.70153	−	16.0822i	0.235047	−	1.02122i
$249$	0.664936	+	0.890691i	0.0421386	+	0.0564453i
$250$	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
$255$	−10.1901	−	13.6498i	−0.638131	−	0.854785i
$256$	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	$0.756917\pi$
$258$	−26.7603	−	3.56002i	−1.66603	−	0.221637i
$259$		0			0
$260$	−0.887974	+	1.62588i	−0.0550698	+	0.100833i
$261$	−10.7131	−	3.17630i	−0.663125	−	0.196608i
$262$	19.6100	−	5.50454i	1.21151	−	0.340071i
$263$	9.68119	+	16.7683i	0.596967	+	1.03398i	0.993266	+	0.115856i	$0.0369612\pi$
$263$	9.68119	+	16.7683i	0.596967	+	1.03398i	−0.396299	+	0.918122i	$0.629705\pi$
$264$	−8.53081	−	19.3592i	−0.525035	−	1.19148i
$265$	−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	$0.333800\pi$
$270$	9.81502	+	13.5550i	0.597323	+	0.824933i
$271$	−17.2138	−	9.93840i	−1.04566	−	0.603715i	−0.124232	−	0.992253i	$-0.539647\pi$
$271$	−17.2138	−	9.93840i	−1.04566	−	0.603715i	−0.921433	+	0.388538i	$0.872980\pi$
$272$	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
$276$	−0.567648	−	3.98766i	−0.0341684	−	0.240029i
$277$	−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	$0.0648588\pi$
$281$			6.78411i			0.404706i	−0.979313	+	0.202353i	$0.935141\pi$
$282$	4.51443	+	3.47379i	0.268830	+	0.206861i
$283$	4.70065	−	2.71392i	0.279425	−	0.161326i	−0.353738	−	0.935344i	$-0.615090\pi$
$283$	4.70065	−	2.71392i	0.279425	−	0.161326i	0.633163	+	0.774019i	$0.281756\pi$
$284$	0.231812	+	9.77212i	0.0137555	+	0.579868i
$285$	−8.45414	+	19.6707i	−0.500780	+	1.16519i
$286$	−0.614387	+	2.40673i	−0.0363294	+	0.142313i
$287$		0			0
$288$	−14.4102	+	8.96358i	−0.849130	+	0.528184i
$289$	0.824014	−	1.42723i	0.0484714	−	0.0839550i
$290$	−11.5498	+	3.24204i	−0.678228	+	0.190379i
$291$	2.07231	+	2.77589i	0.121481	+	0.162725i
$292$	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
$297$	17.2464	+	14.3547i	1.00074	+	0.832945i
$298$	−6.64608	−	23.6768i	−0.384997	−	1.37156i
$299$	−0.236460	+	0.409561i	−0.0136749	+	0.0236855i
$300$	0.599579	+	0.241009i	0.0346167	+	0.0139146i
$301$		0			0
$302$	5.70776	+	1.45707i	0.328445	+	0.0838450i
$303$	13.8201	+	5.93965i	0.793945	+	0.341224i
$304$	−19.2962	−	9.95192i	−1.10671	−	0.570782i
$305$	20.6083	−	11.8982i	1.18003	−	0.681290i
$306$	−9.39082	+	15.7314i	−0.536837	+	0.899304i
$307$			2.24130i			0.127918i	0.997953	+	0.0639589i	$0.0203727\pi$
$307$			2.24130i			0.127918i	−0.997953	+	0.0639589i	$0.979627\pi$
$308$		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	$-0.436973\pi$
$312$	1.98083	+	0.215847i	0.112142	+	0.0122199i
$313$	−0.220185	+	0.381372i	−0.0124456	+	0.0215564i	−0.872181	−	0.489183i	$-0.837295\pi$
$313$	−0.220185	+	0.381372i	−0.0124456	+	0.0215564i	0.859736	+	0.510739i	$0.170628\pi$
$314$	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	0.758580	−	0.651580i	$-0.225893\pi$
$317$	10.2124	+	5.89613i	0.573586	+	0.331160i	−0.184995	+	0.982740i	$0.559227\pi$
$318$	5.12101	+	12.4108i	0.287172	+	0.695965i
$319$	−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
$324$	9.45046	−	15.3196i	0.525025	−	0.851087i
$325$	−0.0379362	−	0.0657074i	−0.00210432	−	0.00364479i
$326$	3.30526	+	11.7751i	0.183062	+	0.652160i
$327$	7.16923	−	16.6810i	0.396459	−	0.922463i
$328$	−5.30290	−	4.93840i	−0.292804	−	0.272678i
$329$		0			0
$330$	23.8793	+	3.17675i	1.31451	+	0.174874i
$331$	−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
$333$	16.1746	+	17.0531i	0.886362	+	0.934502i
$334$	−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
$339$	13.2728	−	9.90869i	0.720881	−	0.538166i
$340$	0.466456	+	19.6636i	0.0252971	+	1.06641i
$341$	21.8201	+	12.5978i	1.18162	+	0.682210i
$342$	23.0259	+	0.335582i	1.24510	+	0.0181462i
$343$		0			0
$344$	22.8123	+	21.2443i	1.22996	+	1.14541i
$345$	4.21383	+	1.81103i	0.226865	+	0.0975026i
$346$	3.00951	+	10.7214i	0.161792	+	0.576388i
$347$	13.8307	+	23.9555i	0.742471	+	1.28600i	0.951367	+	0.308060i	$0.0996798\pi$
$347$	13.8307	+	23.9555i	0.742471	+	1.28600i	−0.208896	+	0.977938i	$0.566987\pi$
$348$	7.96173	+	10.1534i	0.426793	+	0.544277i
$349$	−18.9316			−1.01338			−0.506692	−	0.862127i	$-0.669132\pi$
$349$	−18.9316			−1.01338			−0.506692	+	0.862127i	$0.669132\pi$
$350$		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	$0.350223\pi$
$354$	−8.86036	+	3.65600i	−0.470923	+	0.194314i
$355$	−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	−0.895366	−	0.445331i	$-0.853086\pi$
$359$	−1.17502	+	2.03519i	−0.0620151	+	0.107413i	0.833351	+	0.552744i	$0.186419\pi$
$360$	−0.176705	−	19.3236i	−0.00931317	−	1.01844i
$361$	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
$366$	−20.2844	−	15.6086i	−1.06028	−	0.815872i
$367$	−29.6129	+	17.0970i	−1.54578	+	0.892455i	−0.547321	+	0.836923i	$0.684352\pi$
$367$	−29.6129	+	17.0970i	−1.54578	+	0.892455i	−0.998457	+	0.0555330i	$0.982314\pi$
$368$	−2.13188	+	4.13360i	−0.111132	+	0.215479i
$369$	7.36878	+	2.18475i	0.383604	+	0.113734i
$370$	24.4490	+	6.24130i	1.27104	+	0.324470i
$371$		0			0
$372$	7.53811	−	18.7532i	0.390833	−	0.972310i
$373$	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
$375$	15.2148	−	11.3585i	0.785691	−	0.586550i
$376$	−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
$381$	−8.61587	+	6.43209i	−0.441405	+	0.329526i
$382$	−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	$0.151595\pi$
$384$	19.5593	+	1.19666i	0.998134	+	0.0610669i
$385$		0			0
$386$	−2.39812	+	9.39414i	−0.122061	+	0.478149i
$387$	−31.6994	−	9.39848i	−1.61137	−	0.477752i
$388$	−0.0948604	−	3.99888i	−0.00481581	−	0.203012i
$389$	4.66346	−	2.69245i	0.236447	−	0.136513i	−0.377096	−	0.926174i	$-0.623077\pi$
$389$	4.66346	−	2.69245i	0.236447	−	0.136513i	0.613543	+	0.789662i	$0.289744\pi$
$390$	−1.38367	+	1.79818i	−0.0700650	+	0.0910543i
$391$			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
$396$	−6.63805	−	25.0453i	−0.333574	−	1.25857i
$397$	10.8178	−	18.7369i	0.542927	−	0.940378i	−0.455807	−	0.890079i	$-0.650649\pi$
$397$	10.8178	−	18.7369i	0.542927	−	0.940378i	0.998734	−	0.0502990i	$-0.0160174\pi$
$398$	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	$-0.928552\pi$
$401$	−33.1440	−	19.1357i	−1.65513	−	0.955591i	−0.680217	−	0.733010i	$-0.738115\pi$
$402$	7.31989	+	17.7398i	0.365083	+	0.884783i
$403$	−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
$408$	19.3592	−	8.53081i	0.958422	−	0.422338i
$409$	−2.38561	−	4.13200i	−0.117961	−	0.204314i	0.800999	−	0.598666i	$-0.204302\pi$
$409$	−2.38561	−	4.13200i	−0.117961	−	0.204314i	−0.918960	+	0.394352i	$0.870969\pi$
$410$	7.94429	−	2.22996i	0.392340	−	0.110130i
$411$	−3.70056	−	1.59044i	−0.182535	−	0.0784506i
$412$	−10.2077	+	18.6903i	−0.502895	+	0.920803i
$413$		0			0
$414$	0.0718878	−	4.93258i	0.00353309	−	0.242423i
$415$	1.26568	+	0.730743i	0.0621300	+	0.0358708i
$416$	−1.72046	−	1.52765i	−0.0843527	−	0.0748990i
$417$	12.7971	−	9.55353i	0.626676	−	0.467838i
$418$	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
$423$	4.80100	+	5.06175i	0.233433	+	0.246111i
$424$	3.47727	−	15.1078i	0.168871	−	0.733701i
$425$	−0.697632	−	0.402778i	−0.0338401	−	0.0195376i
$426$	−1.57873	+	11.8672i	−0.0764897	+	0.574966i
$427$		0			0
$428$	−14.7447	−	8.05280i	−0.712713	−	0.389247i
$429$	−1.20122	+	2.79496i	−0.0579957	+	0.134942i
$430$	−34.1752	+	9.59298i	−1.64807	+	0.462615i
$431$	−17.4975	−	30.3066i	−0.842826	−	1.45982i	−0.887496	−	0.460816i	$-0.847557\pi$
$431$	−17.4975	−	30.3066i	−0.842826	−	1.45982i	0.0446692	−	0.999002i	$-0.485777\pi$
$432$	−19.1400	+	8.10321i	−0.920872	+	0.389866i
$433$	17.3383			0.833225			0.416612	−	0.909084i	$-0.363217\pi$
$433$	17.3383			0.833225			0.416612	+	0.909084i	$0.363217\pi$
$434$		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
$438$	6.37052	−	2.62863i	0.304395	−	0.125601i
$439$	28.8352	+	16.6480i	1.37623	+	0.794567i	0.991703	−	0.128547i	$-0.0410312\pi$
$439$	28.8352	+	16.6480i	1.37623	+	0.794567i	0.384527	+	0.923114i	$0.374365\pi$
$440$	−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	−0.951961	−	0.306218i	$-0.900936\pi$
$443$	−4.43657	+	7.68436i	−0.210788	+	0.365095i	0.741174	+	0.671313i	$0.234270\pi$
$444$	−3.82482	−	26.8689i	−0.181518	−	1.27514i
$445$	−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	$-0.786099\pi$
$449$		−	26.3829i		−	1.24509i	0.782585	−	0.622544i	$-0.213901\pi$
$450$	0.679564	+	0.405664i	0.0320349	+	0.0191232i
$451$	9.58114	−	5.53167i	0.451158	−	0.260476i
$452$	−19.1205	+	0.453573i	−0.899354	+	0.0213343i
$453$	6.62847	+	2.84881i	0.311433	+	0.133849i
$454$	6.83028	−	26.7562i	0.320561	−	1.25573i
$455$		0			0
$456$	−21.4526	−	15.7118i	−1.00461	−	0.735772i
$457$	−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
$459$	−14.3547	+	17.2464i	−0.670021	+	0.804994i
$460$	−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
$465$	13.7680	+	18.4425i	0.638478	+	0.855250i
$466$	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	$0.297727\pi$
$468$	2.35549	+	0.638010i	0.108883	+	0.0294920i
$469$		0			0
$470$	7.25703	+	1.85257i	0.334742	+	0.0854525i
$471$	13.1739	−	30.6524i	0.607021	−	1.41239i
$472$	10.7858	+	2.48250i	0.496457	+	0.114266i
$473$	−41.2166	+	23.7964i	−1.89514	+	1.09416i
$474$	−5.97516	+	7.76514i	−0.274448	+	0.356665i
$475$			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	$0.709456\pi$
$480$	−12.7540	+	18.3097i	−0.582137	+	0.835718i
$481$	−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
$486$	14.3485	−	16.7368i	0.650862	−	0.759196i
$487$	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	$-0.651523\pi$
$491$	−20.3082			−0.916497			−0.458248	+	0.888824i	$0.651523\pi$
$492$	−5.47630	−	6.98376i	−0.246891	−	0.314852i
$493$	−8.04223	−	13.9296i	−0.362204	−	0.627355i
$494$	0.843764	+	3.00592i	0.0379627	+	0.135243i
$495$	28.2866	+	8.38663i	1.27139	+	0.376951i
$496$	−19.6355	+	12.6144i	−0.881660	+	0.566403i
$497$		0			0
$498$	0.207292	−	1.55819i	0.00928898	−	0.0698244i
$499$	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
$501$	−1.81989	−	2.43777i	−0.0813067	−	0.108911i
$502$	−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
$507$	13.2986	+	17.8137i	0.590611	+	0.791132i
$508$	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	$0.881442\pi$
$510$	−3.17675	+	23.8793i	−0.140669	+	1.05739i
$511$		0			0
$512$	−17.6134	−	14.2046i	−0.778408	−	0.627758i
$513$	27.7947	+	4.78681i	1.22717	+	0.211343i
$514$	3.42806	+	12.2125i	0.151205	+	0.538671i
$515$	−12.1249	−	21.0009i	−0.534287	−	0.925412i
$516$	23.5582	+	30.0431i	1.03709	+	1.32257i
$517$	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	$0.157016\pi$
$522$	7.70099	+	13.7991i	0.337063	+	0.603969i
$523$	2.40739	+	1.38991i	0.105268	+	0.0607764i	0.551710	−	0.834036i	$-0.313976\pi$
$523$	2.40739	+	1.38991i	0.105268	+	0.0607764i	−0.446442	+	0.894813i	$0.647309\pi$
$524$	−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
$528$	−10.4969	+	28.0164i	−0.456818	+	1.21926i
$529$	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
$534$	−20.9086	+	27.1722i	−0.904805	+	1.17586i
$535$	16.5676	−	9.56531i	0.716280	−	0.413545i
$536$	4.97035	−	21.5949i	0.214687	−	0.932758i
$537$	−6.39192	+	14.8724i	−0.275832	+	0.641793i
$538$	0.0658929	+	0.0168211i	0.00284085	+	0.000725208i
$539$		0			0
$540$	3.46261	−	23.4128i	0.149007	−	1.00752i
$541$	−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
$543$	−17.4999	−	23.4414i	−0.750994	−	1.00597i
$544$	−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
$549$	−21.5720	−	22.7437i	−0.920672	−	0.970675i
$550$	1.09684	−	0.307882i	0.0467693	−	0.0131281i
$551$	−10.1085	+	17.5085i	−0.430637	+	0.745886i
$552$	−3.36575	+	4.59554i	−0.143256	+	0.195599i
$553$		0			0
$554$	−3.59418	+	14.0794i	−0.152702	+	0.598178i
$555$	28.3928	+	12.2027i	1.20521	+	0.517978i
$556$	−18.4352	+	0.437315i	−0.781826	+	0.0185463i
$557$	−11.6502	+	6.72624i	−0.493634	+	0.285000i	−0.726081	−	0.687609i	$-0.758660\pi$
$557$	−11.6502	+	6.72624i	−0.493634	+	0.285000i	0.232447	+	0.972609i	$0.425327\pi$
$558$	12.6881	−	21.2549i	0.537129	−	0.899794i
$559$		−	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	$0.579082\pi$
$564$	−1.13530	−	7.97532i	−0.0478046	−	0.335822i
$565$	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	0.897875	−	0.440251i	$-0.145110\pi$
$569$	23.0318	+	13.2974i	0.965544	+	0.557457i	0.0676690	+	0.997708i	$0.478444\pi$
$570$	27.9899	−	11.5493i	1.17237	−	0.483747i
$571$	−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
$576$	23.4367	+	5.16908i	0.976531	+	0.215378i
$577$	−0.792342	−	1.37238i	−0.0329856	−	0.0571328i	0.849061	−	0.528294i	$-0.177168\pi$
$577$	−0.792342	−	1.37238i	−0.0329856	−	0.0571328i	−0.882047	+	0.471162i	$0.843835\pi$
$578$	−2.24394	+	0.629874i	−0.0933355	+	0.0261993i
$579$	−4.68872	+	10.9095i	−0.194857	+	0.453383i
$580$	14.8893	+	8.13179i	0.618246	+	0.337654i
$581$		0			0
$582$	0.646037	−	4.85620i	0.0267791	−	0.201296i
$583$	20.4981	+	11.8346i	0.848944	+	0.490138i
$584$	−7.75490	−	1.78489i	−0.320900	−	0.0738594i
$585$	−2.01619	+	1.91233i	−0.0833591	+	0.0790649i
$586$	−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
$591$	−2.73189	+	2.03946i	−0.112375	+	0.0838922i
$592$	−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	$0.708956\pi$
$594$	−3.26624	−	31.5646i	−0.134015	−	1.29511i
$595$		0			0
$596$	−16.6699	+	30.5227i	−0.682826	+	1.25026i
$597$	10.1415	+	4.35866i	0.415065	+	0.178388i
$598$	0.643923	−	0.180750i	0.0263320	−	0.00739140i
$599$	6.40487	+	11.0936i	0.261696	+	0.453270i	0.966693	−	0.255940i	$-0.0823850\pi$
$599$	6.40487	+	11.0936i	0.261696	+	0.453270i	−0.704997	+	0.709210i	$0.749052\pi$
$600$	−0.368513	−	0.836276i	−0.0150445	−	0.0341408i
$601$	−37.2710			−1.52032			−0.760158	−	0.649738i	$-0.774878\pi$
$601$	−37.2710			−1.52032			−0.760158	+	0.649738i	$0.774878\pi$
$602$		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
$606$	−8.11423	−	19.6649i	−0.329618	−	0.798833i
$607$	−18.0250	−	10.4067i	−0.731611	−	0.422396i	0.0873999	−	0.996173i	$-0.472144\pi$
$607$	−18.0250	−	10.4067i	−0.731611	−	0.422396i	−0.819011	+	0.573777i	$0.805478\pi$
$608$	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
$612$	25.0453	−	6.63805i	1.01239	−	0.268327i
$613$	−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	$0.201529\pi$
$617$			29.3933i			1.18333i	−0.806185	+	0.591664i	$0.798471\pi$
$618$	−15.9059	+	20.6709i	−0.639830	+	0.831504i
$619$	17.2548	−	9.96206i	0.693529	−	0.400409i	−0.111404	−	0.993775i	$-0.535535\pi$
$619$	17.2548	−	9.96206i	0.693529	−	0.400409i	0.804933	+	0.593366i	$0.202201\pi$
$620$	−0.630236	−	26.5678i	−0.0253109	−	1.06699i
$621$	1.02542	−	5.95414i	0.0411488	−	0.238931i
$622$	−9.26242	+	36.2835i	−0.371389	+	1.45484i
$623$		0			0
$624$	−1.79091	−	2.17559i	−0.0716937	−	0.0870933i
$625$	12.9490	−	22.4283i	0.517958	−	0.897130i
$626$	0.599604	−	0.168309i	0.0239650	−	0.00672698i
$627$	32.5323	−	24.2867i	1.29922	−	0.969916i
$628$	−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
$633$	−34.8799	+	26.0392i	−1.38635	+	1.03497i
$634$	−4.50699	−	16.0562i	−0.178995	−	0.637674i
$635$	−7.06866	+	12.2433i	−0.280511	+	0.485859i
$636$	7.08141	−	17.6171i	0.280796	−	0.698561i
$637$		0			0
$638$	22.0401	+	5.62636i	0.872574	+	0.222750i
$639$	−4.16786	+	14.0575i	−0.164878	+	0.556104i
$640$	24.2492	−	8.70931i	0.958535	−	0.344266i
$641$	−19.0040	+	10.9719i	−0.750611	+	0.433365i	−0.825915	−	0.563795i	$-0.809341\pi$
$641$	−19.0040	+	10.9719i	−0.750611	+	0.433365i	0.0753036	+	0.997161i	$0.476007\pi$
$642$	−16.3072	−	12.5482i	−0.643594	−	0.495236i
$643$		−	49.5796i		−	1.95523i	−0.210406	−	0.977614i	$-0.567479\pi$
$643$		−	49.5796i		−	1.95523i	0.210406	−	0.977614i	$-0.432521\pi$
$644$		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	$0.989095\pi$
$648$	−24.6987	+	6.16242i	−0.970256	+	0.242083i
$649$	−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	$-0.967013\pi$
$653$	−40.4145	−	23.3333i	−1.58154	−	0.913103i	−0.586905	−	0.809656i	$-0.699654\pi$
$654$	−23.7358	+	9.79397i	−0.928143	+	0.382974i
$655$	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	$-0.702165\pi$
$659$	−30.4598			−1.18655			−0.593273	+	0.805001i	$0.702165\pi$
$660$	−21.0219	−	26.8086i	−0.818278	−	1.04353i
$661$	24.6523	+	42.6991i	0.958864	+	1.66080i	0.725266	+	0.688468i	$0.241717\pi$
$661$	24.6523	+	42.6991i	0.958864	+	1.66080i	0.233598	+	0.972333i	$0.424950\pi$
$662$	0.500581	+	1.78333i	0.0194556	+	0.0693110i
$663$	−2.79496	−	1.20122i	−0.108547	−	0.0466517i
$664$	−1.23701	+	1.32831i	−0.0480052	+	0.0515484i
$665$		0			0
$666$	0.484380	−	33.2357i	0.0187694	−	1.28786i
$667$	3.75063	+	2.16543i	0.145225	+	0.0838457i
$668$	0.0833059	+	3.51179i	0.00322320	+	0.135875i
$669$	12.8090	−	9.56243i	0.495225	−	0.369705i
$670$	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
$675$	0.745009	+	0.620094i	0.0286754	+	0.0238674i
$676$	−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	$0.728020\pi$
$678$	−23.2198	−	3.08901i	−0.891751	−	0.118633i
$679$		0			0
$680$	18.9571	−	20.3563i	0.726971	−	0.780628i
$681$	13.3543	−	31.0722i	0.511737	−	1.19069i
$682$	−9.62974	−	34.3061i	−0.368742	−	1.31365i
$683$	14.8051	+	25.6431i	0.566501	+	0.981208i	0.996908	+	0.0785732i	$0.0250364\pi$
$683$	14.8051	+	25.6431i	0.566501	+	0.981208i	−0.430408	+	0.902635i	$0.641630\pi$
$684$	−22.9658	−	23.0908i	−0.878119	−	0.882899i
$685$	−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
$690$	−2.47407	−	5.99594i	−0.0941863	−	0.228262i
$691$	38.2440	+	22.0802i	1.45487	+	0.839969i	0.998752	−	0.0499504i	$-0.0159063\pi$
$691$	38.2440	+	22.0802i	1.45487	+	0.839969i	0.456117	+	0.889920i	$0.349240\pi$
$692$	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
$696$	1.97665	−	18.1398i	0.0749249	−	0.687587i
$697$	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	$-0.742880\pi$
$701$		−	38.2714i		−	1.44549i	0.691115	−	0.722745i	$-0.257120\pi$
$702$	2.72847	+	1.22006i	0.102980	+	0.0460482i
$703$	36.8276	−	21.2624i	1.38898	−	0.801927i
$704$	28.6146	−	19.3566i	1.07845	−	0.729529i
$705$	8.42765	+	3.62206i	0.317404	+	0.136415i
$706$	2.73074	+	0.697101i	0.102773	+	0.0262357i
$707$		0			0
$708$	12.5772	+	5.05557i	0.472680	+	0.190000i
$709$	−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
$711$	−8.70657	+	8.25806i	−0.326522	+	0.309702i
$712$	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
$717$	−25.3918	−	34.0127i	−0.948274	−	1.27023i
$718$	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	$-0.00983056\pi$
$720$	−18.9143	+	19.7259i	−0.704893	+	0.735142i
$721$		0			0
$722$	3.65944	−	14.3351i	0.136190	−	0.533496i
$723$	−12.5945	+	29.3044i	−0.468396	+	1.08984i
$724$	0.801064	+	33.7692i	0.0297713	+	1.25502i
$725$	−0.601728	+	0.347408i	−0.0223476	+	0.0129024i
$726$	−14.8470	−	11.4246i	−0.551024	−	0.424005i
$727$		−	27.3942i		−	1.01599i	−0.861359	−	0.507997i	$-0.830386\pi$
$727$		−	27.3942i		−	1.01599i	0.861359	−	0.507997i	$-0.169614\pi$
$728$		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
$732$	5.10115	+	35.8350i	0.188544	+	1.32450i
$733$	14.8514	−	25.7234i	0.548549	−	0.950114i	−0.449826	−	0.893116i	$-0.648514\pi$
$733$	14.8514	−	25.7234i	0.548549	−	0.950114i	0.998374	−	0.0569978i	$-0.0181528\pi$
$734$	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
$738$	−5.29696	−	9.49139i	−0.194984	−	0.349383i
$739$	−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	$-0.486561\pi$
$743$	2.30093			0.0844131			0.0422065	+	0.999109i	$0.486561\pi$
$744$	−26.1565	+	11.5261i	−0.958944	+	0.422568i
$745$	−19.8009	−	34.2962i	−0.725450	−	1.25652i
$746$	−24.0581	+	6.75312i	−0.880830	+	0.247249i
$747$	0.547252	−	1.84579i	0.0200229	−	0.0675338i
$748$	17.8768	−	32.7325i	0.653641	−	1.19682i
$749$		0			0
$750$	−26.6172	−	3.54098i	−0.971922	−	0.129298i
$751$	−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
$753$	−16.0027	−	21.4358i	−0.583170	−	0.781165i
$754$	−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
$759$	−5.20265	−	6.96902i	−0.188844	−	0.252959i
$760$	−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	$0.594594\pi$
$762$	15.0728	+	2.00519i	0.546030	+	0.0726403i
$763$		0			0
$764$	35.6466	+	19.4683i	1.28965	+	0.704339i
$765$	−8.38663	+	28.2866i	−0.303219	+	1.02271i
$766$	−2.52243	+	0.708048i	−0.0911392	+	0.0255828i
$767$	−0.795777	−	1.37833i	−0.0287338	−	0.0497685i
$768$	−18.6075	−	20.5368i	−0.671441	−	0.741058i
$769$	45.0074			1.62301			0.811505	−	0.584346i	$-0.198649\pi$
$769$	45.0074			1.62301			0.811505	+	0.584346i	$0.198649\pi$
$770$		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	$-0.0432979\pi$
$774$	22.7867	+	40.8306i	0.819052	+	1.46762i
$775$	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
$780$	3.17671	−	0.452209i	0.113745	−	0.0161917i
$781$	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
$786$	−27.9590	−	21.5140i	−0.997264	−	0.767380i
$787$	−35.6977	+	20.6101i	−1.27249	+	0.734670i	−0.975455	−	0.220197i	$-0.929330\pi$
$787$	−35.6977	+	20.6101i	−1.27249	+	0.734670i	−0.297031	+	0.954868i	$0.595997\pi$
$788$	3.93549	−	0.0933568i	0.140196	−	0.00332570i
$789$	13.2422	−	30.8115i	0.471437	−	1.09692i
$790$	−3.18654	+	12.4826i	−0.113372	+	0.444111i
$791$		0			0
$792$	−18.0302	+	31.8994i	−0.640676	+	1.13349i
$793$	2.12494	−	3.68051i	0.0754590	−	0.130699i
$794$	−29.4587	+	8.26906i	−1.04545	+	0.293458i
$795$	12.9339	+	17.3251i	0.458718	+	0.614459i
$796$	−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
$801$	−30.4665	+	28.8971i	−1.07648	+	1.02103i
$802$	14.6273	+	52.1099i	0.516507	+	1.84006i
$803$	6.07473	−	10.5217i	0.214372	−	0.371304i
$804$	10.1221	−	25.1815i	0.356977	−	0.888085i
$805$		0			0
$806$	3.25177	+	0.830108i	0.114539	+	0.0292393i
$807$	0.0765221	+	0.0328879i	0.00269370	+	0.00115771i
$808$	−5.50972	+	23.9383i	−0.193831	+	0.842147i
$809$	45.3040	−	26.1563i	1.59280	−	0.919605i	0.599979	−	0.800016i	$-0.295175\pi$
$809$	45.3040	−	26.1563i	1.59280	−	0.919605i	0.992823	−	0.119589i	$-0.0381578\pi$
$810$	8.64373	−	27.6678i	0.303710	−	0.972147i
$811$			25.3719i			0.890929i	0.895300	+	0.445464i	$0.146961\pi$
$811$			25.3719i			0.890929i	−0.895300	+	0.445464i	$0.853039\pi$
$812$		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
$816$	−28.0164	−	10.4969i	−0.980771	−	0.367464i
$817$	−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	−0.00833206	−	0.999965i	$-0.502652\pi$
$821$	−25.1716	−	14.5328i	−0.878493	−	0.507198i	−0.870161	+	0.492767i	$0.835986\pi$
$822$	2.17272	+	5.26561i	0.0757822	+	0.183659i
$823$	−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	$-0.527081\pi$
$827$	−4.88743			−0.169953			−0.0849763	+	0.996383i	$0.527081\pi$
$828$	−4.94647	+	4.91969i	−0.171902	+	0.170971i
$829$	19.4658	+	33.7157i	0.676074	+	1.17100i	0.976154	+	0.217081i	$0.0696536\pi$
$829$	19.4658	+	33.7157i	0.676074	+	1.17100i	−0.300079	+	0.953914i	$0.597013\pi$
$830$	−0.558578	−	1.98994i	−0.0193885	−	0.0690719i
$831$	−7.02721	+	16.3506i	−0.243771	+	0.567196i
$832$	0.231321	+	3.24559i	0.00801961	+	0.112521i
$833$		0			0
$834$	−22.3875	−	2.97829i	−0.775216	−	0.103130i
$835$	−3.46410	−	2.00000i	−0.119880	−	0.0692129i
$836$	−46.8653	+	1.11173i	−1.62087	+	0.0384499i
$837$	19.3949	−	23.3019i	0.670385	−	0.805432i
$838$	−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
$843$	9.41595	−	7.02938i	0.324303	−	0.242105i
$844$	50.2471	−	1.19195i	1.72958	−	0.0410286i
$845$	25.3134	+	14.6147i	0.870809	+	0.502762i
$846$	0.143776	−	9.86515i	0.00494310	−	0.339171i
$847$		0			0
$848$	−18.4459	+	11.8501i	−0.633434	+	0.406935i
$849$	−8.63737	−	3.71219i	−0.296434	−	0.127402i
$850$	0.307882	+	1.09684i	0.0105603	+	0.0376212i
$851$	−4.55480	−	7.88914i	−0.156136	−	0.270436i
$852$	13.3229	−	10.4472i	0.456437	−	0.357914i
$853$	36.4912			1.24943			0.624717	−	0.780851i	$-0.285214\pi$
$853$	36.4912			1.24943			0.624717	+	0.780851i	$0.285214\pi$
$854$		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	$0.119474\pi$
$858$	3.97700	−	1.64101i	0.135773	−	0.0560231i
$859$	10.2782	+	5.93411i	0.350687	+	0.202469i	0.664988	−	0.746854i	$-0.268437\pi$
$859$	10.2782	+	5.93411i	0.350687	+	0.202469i	−0.314301	+	0.949323i	$0.601770\pi$
$860$	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	−0.693028	−	0.720910i	$-0.743724\pi$
$863$	8.16126	−	14.1357i	0.277812	−	0.481185i	0.970841	+	0.239725i	$0.0770573\pi$
$864$	27.3721	+	10.7129i	0.931219	+	0.364460i
$865$	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
$870$	16.4671	+	12.6712i	0.558289	+	0.429595i
$871$	−2.75963	+	1.59327i	−0.0935064	+	0.0539859i
$872$	28.8938	+	6.65030i	0.978468	+	0.225207i
$873$	1.70554	−	5.75249i	0.0577238	−	0.194692i
$874$	−8.64803	−	2.20766i	−0.292524	−	0.0746752i
$875$		0			0
$876$	−9.04289	−	3.63491i	−0.305531	−	0.122812i
$877$	−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
$879$	−39.1225	+	29.2065i	−1.31957	+	0.985111i
$880$	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
$885$	−12.3688	+	9.23379i	−0.415772	+	0.310390i
$886$	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	$-0.101613\pi$
$888$	−22.6785	+	30.9648i	−0.761040	+	1.03911i
$889$		0			0
$890$	−11.1505	+	43.6798i	−0.373767	+	1.46415i
$891$	2.05358	−	38.8107i	0.0687976	−	1.30021i
$892$	−18.4524	+	0.437723i	−0.617831	+	0.0146560i
$893$	10.9313	−	6.31119i	0.365802	−	0.211196i
$894$	−25.9756	+	33.7572i	−0.868756	+	1.12901i
$895$			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
$900$	−0.286750	−	1.08190i	−0.00955833	−	0.0360634i
$901$	−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
$906$	−3.89179	−	9.43179i	−0.129296	−	0.313350i
$907$	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	$-0.459205\pi$
$911$	7.71538			0.255622			0.127811	+	0.991799i	$0.459205\pi$
$912$	6.18114	+	37.0937i	0.204678	+	1.22830i
$913$	−1.38561	−	2.39995i	−0.0458571	−	0.0794268i
$914$	41.1879	−	11.5615i	1.36238	−	0.382419i
$915$	−37.8674	−	16.2748i	−1.25186	−	0.538028i
$916$	−3.56961	−	1.94954i	−0.117943	−	0.0644145i
$917$		0			0
$918$	31.5646	−	3.26624i	1.04179	−	0.107802i
$919$	−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
$921$	3.11080	−	2.32233i	0.102504	−	0.0765234i
$922$	−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
$927$	−23.1770	+	21.9830i	−0.761231	+	0.722017i
$928$	−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	$0.650310\pi$
$930$	4.29215	−	32.2637i	0.140745	−	1.05797i
$931$		0			0
$932$	3.13603	−	5.74209i	0.102724	−	0.188088i
$933$	−18.1095	+	42.1364i	−0.592879	+	1.37948i
$934$	23.5512	−	6.61084i	0.770620	−	0.216313i
$935$	21.2345	+	36.7792i	0.694442	+	1.20281i
$936$	−1.75286	−	2.97293i	−0.0572940	−	0.0971732i
$937$	−47.0325			−1.53648			−0.768242	−	0.640159i	$-0.778868\pi$
$937$	−47.0325			−1.53648			−0.768242	+	0.640159i	$0.778868\pi$
$938$		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	$0.451483\pi$
$942$	−43.6160	+	17.9970i	−1.42108	+	0.586374i
$943$	−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	$0.352552\pi$
$947$	−16.9667	+	29.3873i	−0.551345	+	0.954958i	−0.998178	+	0.0603402i	$0.980781\pi$
$948$	13.7181	−	1.95279i	0.445544	−	0.0634236i
$949$	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	$-0.893555\pi$
$953$		−	20.2641i		−	0.656419i	0.944605	−	0.328209i	$-0.106445\pi$
$954$	11.9194	−	19.9672i	0.385904	−	0.646462i
$955$	−40.0536	+	23.1249i	−1.29610	+	0.748306i
$956$	1.16232	+	48.9979i	0.0375920	+	1.58470i
$957$	25.5953	+	11.0004i	0.827379	+	0.355593i
$958$	5.80952	−	22.7575i	0.187697	−	0.735263i
$959$		0			0
$960$	30.9956	−	5.92366i	1.00038	−	0.191185i
$961$	1.52112	−	2.63465i	0.0490682	−	0.0849887i
$962$	4.33876	−	1.21789i	0.139887	−	0.0392664i
$963$	−17.3424	−	18.2843i	−0.558850	−	0.589202i
$964$	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
$969$	24.2867	+	32.5323i	0.780200	+	1.04509i
$970$	−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	$0.147903\pi$
$972$	−31.0548	+	2.75673i	−0.996083	+	0.0884221i
$973$		0			0
$974$	−33.2289	−	8.48263i	−1.06472	−	0.271801i
$975$	−0.0518904	+	0.120736i	−0.00166182	+	0.00386666i
$976$	19.1581	−	37.1465i	0.613236	−	1.18903i
$977$	−29.5088	+	17.0369i	−0.944069	+	0.545058i	−0.891233	−	0.453545i	$-0.850159\pi$
$977$	−29.5088	+	17.0369i	−0.944069	+	0.545058i	−0.0528352	+	0.998603i	$0.516826\pi$
$978$	12.9183	−	16.7883i	0.413083	−	0.536830i
$979$			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	$-0.499758\pi$
$984$	−1.35960	+	12.4771i	−0.0433424	+	0.397754i
$985$	−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
$990$	−20.3335	−	36.4347i	−0.646241	−	1.15797i
$991$	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
$996$	−1.74934	+	1.37174i	−0.0554301	+	0.0434654i
$997$	−10.7282	−	18.5818i	−0.339765	−	0.588491i	0.644623	−	0.764501i	$-0.277014\pi$
$997$	−10.7282	−	18.5818i	−0.339765	−	0.588491i	−0.984388	+	0.176010i	$0.943681\pi$
$998$	−4.02780	−	14.3491i	−0.127498	−	0.454214i
$999$	6.90931	−	40.1190i	0.218601	−	1.26931i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.e.a.71.5	✓	12	84.23	even	6
84.2.e.a.71.6	yes	12	7.2	even	3
84.2.e.a.71.7	yes	12	21.2	odd	6
84.2.e.a.71.8	yes	12	28.23	odd	6
588.2.e.c.491.5		12	84.47	odd	6
588.2.e.c.491.6		12	7.5	odd	6
588.2.e.c.491.7		12	21.5	even	6
588.2.e.c.491.8		12	28.19	even	6
588.2.n.f.263.2		24	21.11	odd	6	inner
588.2.n.f.263.4		24	84.11	even	6	inner
588.2.n.f.263.9		24	28.11	odd	6	inner
588.2.n.f.263.11		24	7.4	even	3	inner
588.2.n.f.275.2		24	4.3	odd	2	inner
588.2.n.f.275.4		24	1.1	even	1	trivial
588.2.n.f.275.9		24	3.2	odd	2	inner
588.2.n.f.275.11		24	12.11	even	2	inner
588.2.n.g.263.2		24	21.17	even	6
588.2.n.g.263.4		24	84.59	odd	6
588.2.n.g.263.9		24	28.3	even	6
588.2.n.g.263.11		24	7.3	odd	6
588.2.n.g.275.2		24	28.27	even	2
588.2.n.g.275.4		24	7.6	odd	2
588.2.n.g.275.9		24	21.20	even	2
588.2.n.g.275.11		24	84.83	odd	2
1344.2.h.h.575.1		12	168.107	even	6
1344.2.h.h.575.2		12	56.37	even	6
1344.2.h.h.575.11		12	56.51	odd	6
1344.2.h.h.575.12		12	168.149	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} +(-1.03615 - 1.38794i) q^{3} +(0.0474302 + 1.99944i) q^{4} +(-1.97228 - 1.13870i) q^{5} +(-0.323018 + 2.42810i) q^{6} +(1.92760 - 2.06987i) q^{8} +(-0.852770 + 2.87624i) q^{9} +(0.870418 + 3.10088i) q^{10} +(2.15917 + 3.73979i) q^{11} +(2.72596 - 2.13756i) q^{12} -0.406728 q^{13} +(0.463141 + 3.91729i) q^{15} +(-3.99550 + 0.189667i) q^{16} +(-3.73979 + 2.15917i) q^{17} +(3.70476 - 2.06755i) 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} +(-4.87015 - 0.530690i) q^{24} +(0.0932716 + 0.161551i) q^{25} +(0.411523 + 0.401877i) q^{26} +(4.87566 - 1.79664i) q^{27} +3.72469i q^{29} +(3.40196 - 4.42108i) q^{30} +(5.05289 - 2.91729i) q^{31} +(4.23000 + 3.75594i) q^{32} +(2.95338 - 6.87180i) q^{33} +(5.91729 + 1.51056i) q^{34} +(-5.79132 - 1.56864i) q^{36} +(3.91729 - 6.78494i) q^{37} +(-2.07451 - 7.39049i) q^{38} +(0.421433 + 0.564516i) q^{39} +(-6.15873 + 1.88742i) q^{40} -2.56195i q^{41} +11.0211i q^{43} +(-7.37506 + 4.49450i) q^{44} +(4.95708 - 4.70172i) q^{45} +(-1.58318 + 0.444399i) q^{46} +(1.16274 - 2.01393i) q^{47} +(4.40320 + 5.34900i) q^{48} +(0.0652529 - 0.255614i) q^{50} +(6.87180 + 2.95338i) q^{51} +(-0.0192912 - 0.813228i) q^{52} +(4.74675 - 2.74054i) q^{53} +(-6.70834 - 2.99969i) q^{54} -9.83457i q^{55} +(-1.10383 - 9.33627i) q^{57} +(3.68026 - 3.76860i) q^{58} +(1.95653 + 3.38881i) q^{59} +(-7.81040 + 1.11182i) 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} +(-9.77802 + 4.03465i) q^{66} +(6.78494 - 3.91729i) q^{67} +(-4.49450 - 7.37506i) q^{68} +(-2.00000 + 0.236460i) q^{69} +4.88743 q^{71} +(4.30966 + 7.30937i) q^{72} +(-1.40673 - 2.43653i) q^{73} +(-10.6675 + 2.99436i) q^{74} +(0.127580 - 0.296847i) q^{75} +(-5.20336 + 9.52738i) q^{76} +(0.131381 - 0.987576i) q^{78} +(3.46410 + 2.00000i) q^{79} +(8.09624 + 4.17560i) q^{80} +(-7.54557 - 4.90555i) q^{81} +(-2.53139 + 2.59215i) q^{82} -0.641735 q^{83} +9.83457 q^{85} +(10.8896 - 11.1510i) q^{86} +(5.16966 - 3.85935i) q^{87} +(11.9029 + 2.73961i) q^{88} +(12.1218 + 6.99851i) q^{89} +(-9.66116 - 0.140802i) q^{90} +(2.04094 + 1.11466i) q^{92} +(-9.28460 - 3.99036i) q^{93} +(-3.16636 + 0.888797i) q^{94} +(-6.18068 - 10.7053i) q^{95} +(0.830089 - 9.76273i) 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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