LMFDB - Embedded newform 728.2.cz.a.309.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(309,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.309"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			309.10
Character	$\chi$	$=$	728.309
Dual form			728.2.cz.a.589.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.31721 + 0.514734i) q^{2} +(-0.460788 + 0.266036i) q^{3} +(1.47010 - 1.35603i) q^{4} +0.503361 q^{5} +(0.470018 - 0.587609i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-1.23844 + 2.54289i) q^{8} +(-1.35845 + 2.35290i) q^{9} +(-0.663033 + 0.259097i) q^{10} +(0.0273023 + 0.0472889i) q^{11} +(-0.316651 + 1.01594i) q^{12} +(-3.43333 - 1.10102i) q^{13} +(1.39811 + 0.212834i) q^{14} +(-0.231942 + 0.133912i) q^{15} +(0.322380 - 3.98699i) q^{16} +(1.27667 - 2.21125i) q^{17} +(0.578249 - 3.79852i) q^{18} +(2.62336 - 4.54379i) q^{19} +(0.739990 - 0.682571i) q^{20} +0.532072 q^{21} +(-0.0603041 - 0.0482361i) q^{22} +(0.685700 + 1.18767i) q^{23} +(-0.105841 - 1.50120i) q^{24} -4.74663 q^{25} +(5.08916 - 0.316976i) q^{26} -3.04180i q^{27} +(-1.95116 + 0.439305i) q^{28} +(-7.07541 + 4.08499i) q^{29} +(0.236588 - 0.295779i) q^{30} +8.99735i q^{31} +(1.62759 + 5.41765i) q^{32} +(-0.0251611 - 0.0145268i) q^{33} +(-0.543436 + 3.56983i) q^{34} +(-0.435923 - 0.251680i) q^{35} +(1.19355 + 5.30110i) q^{36} +(-4.90502 - 8.49575i) q^{37} +(-1.11668 + 7.33547i) q^{38} +(1.87495 - 0.406054i) q^{39} +(-0.623382 + 1.27999i) q^{40} +(-2.92300 + 1.68760i) q^{41} +(-0.700852 + 0.273875i) q^{42} +(-4.84378 - 2.79656i) q^{43} +(0.104262 + 0.0324967i) q^{44} +(-0.683790 + 1.18436i) q^{45} +(-1.51454 - 1.21146i) q^{46} -6.59604i q^{47} +(0.912133 + 1.92292i) q^{48} +(0.500000 + 0.866025i) q^{49} +(6.25232 - 2.44325i) q^{50} +1.35856i q^{51} +(-6.54035 + 3.03709i) q^{52} -11.7324i q^{53} +(1.56572 + 4.00670i) q^{54} +(0.0137429 + 0.0238034i) q^{55} +(2.34396 - 1.58298i) q^{56} +2.79163i q^{57} +(7.21714 - 9.02276i) q^{58} +(0.303677 - 0.525983i) q^{59} +(-0.159390 + 0.511384i) q^{60} +(-8.79623 - 5.07851i) q^{61} +(-4.63124 - 11.8514i) q^{62} +(2.35290 - 1.35845i) q^{63} +(-4.93253 - 6.29842i) q^{64} +(-1.72820 - 0.554209i) q^{65} +(0.0406199 + 0.00618358i) q^{66} +(0.0600940 + 0.104086i) q^{67} +(-1.12169 - 4.98195i) q^{68} +(-0.631924 - 0.364842i) q^{69} +(0.703752 + 0.107132i) q^{70} +(3.29717 + 1.90362i) q^{71} +(-4.30081 - 6.36831i) q^{72} +7.23093i q^{73} +(10.8340 + 8.66593i) q^{74} +(2.18719 - 1.26277i) q^{75} +(-2.30491 - 10.2372i) q^{76} -0.0546045i q^{77} +(-2.26069 + 1.49996i) q^{78} -11.5424 q^{79} +(0.162273 - 2.00689i) q^{80} +(-3.26612 - 5.65709i) q^{81} +(2.98155 - 3.72749i) q^{82} +8.30193 q^{83} +(0.782198 - 0.721504i) q^{84} +(0.642623 - 1.11306i) q^{85} +(7.81977 + 1.19041i) q^{86} +(2.17351 - 3.76463i) q^{87} +(-0.154062 + 0.0108621i) q^{88} +(0.726930 - 0.419693i) q^{89} +(0.291068 - 1.91202i) q^{90} +(2.42284 + 2.67017i) q^{91} +(2.61856 + 0.816160i) q^{92} +(-2.39362 - 4.14587i) q^{93} +(3.39521 + 8.68839i) q^{94} +(1.32050 - 2.28716i) q^{95} +(-2.19126 - 2.06339i) q^{96} +(-6.37150 - 3.67859i) q^{97} +(-1.10438 - 0.883373i) q^{98} -0.148355 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 18 q^{6} + 84 q^{9} - 8 q^{10} - 4 q^{12} + 8 q^{16} + 4 q^{17} - 18 q^{22} + 24 q^{23} + 48 q^{24} + 160 q^{25} - 30 q^{26} - 8 q^{30} + 22 q^{36} - 20 q^{38} - 48 q^{39} + 4 q^{40} + 12 q^{41}+ \cdots - 104 q^{95}+O(q^{100}) $ 168 * q - 18 * q^6 + 84 * q^9 - 8 * q^10 - 4 * q^12 + 8 * q^16 + 4 * q^17 - 18 * q^22 + 24 * q^23 + 48 * q^24 + 160 * q^25 - 30 * q^26 - 8 * q^30 + 22 * q^36 - 20 * q^38 - 48 * q^39 + 4 * q^40 + 12 * q^41 - 54 * q^48 + 84 * q^49 - 30 * q^50 - 58 * q^52 + 24 * q^54 - 32 * q^55 - 12 * q^58 + 28 * q^62 - 36 * q^64 + 12 * q^65 - 60 * q^66 - 64 * q^68 - 132 * q^72 + 62 * q^74 - 78 * q^76 + 30 * q^78 - 80 * q^79 + 48 * q^80 - 84 * q^81 - 18 * q^82 - 42 * q^84 - 24 * q^87 + 42 * q^88 + 40 * q^90 - 24 * q^92 + 12 * q^94 - 104 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.31721	+	0.514734i	−0.931410	+	0.363972i
$2$	−1.31721	+	0.514734i	−0.931410	+	0.363972i
$3$	−0.460788	+	0.266036i	−0.266036	+	0.153596i	−0.627085	−	0.778951i	$-0.715752\pi$
$3$	−0.460788	+	0.266036i	−0.266036	+	0.153596i	0.361049	+	0.932547i	$0.382419\pi$
$4$	1.47010	−	1.35603i	0.735049	−	0.678014i
$5$	0.503361			0.225110			0.112555	−	0.993646i	$-0.464097\pi$
$5$	0.503361			0.225110			0.112555	+	0.993646i	$0.464097\pi$
$6$	0.470018	−	0.587609i	0.191884	−	0.239890i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$	−1.23844	+	2.54289i	−0.437855	+	0.899046i
$9$	−1.35845	+	2.35290i	−0.452817	+	0.784301i
$10$	−0.663033	+	0.259097i	−0.209669	+	0.0819335i
$11$	0.0273023	+	0.0472889i	0.00823194	+	0.0142581i	0.870112	−	0.492854i	$-0.164046\pi$
$11$	0.0273023	+	0.0472889i	0.00823194	+	0.0142581i	−0.861880	+	0.507112i	$0.830713\pi$
$12$	−0.316651	+	1.01594i	−0.0914094	+	0.293276i
$13$	−3.43333	−	1.10102i	−0.952235	−	0.305367i
$13$	−3.43333	−	1.10102i	−0.952235	−	0.305367i
$14$	1.39811	+	0.212834i	0.373660	+	0.0568823i
$15$	−0.231942	+	0.133912i	−0.0598873	+	0.0345759i
$16$	0.322380	−	3.98699i	0.0805950	−	0.996747i
$17$	1.27667	−	2.21125i	0.309637	−	0.536307i	−0.668646	−	0.743581i	$-0.733126\pi$
$17$	1.27667	−	2.21125i	0.309637	−	0.536307i	0.978283	+	0.207274i	$0.0664591\pi$
$18$	0.578249	−	3.79852i	0.136295	−	0.895319i
$19$	2.62336	−	4.54379i	0.601840	−	1.04242i	−0.390703	−	0.920517i	$-0.627768\pi$
$19$	2.62336	−	4.54379i	0.601840	−	1.04242i	0.992542	−	0.121900i	$-0.0388987\pi$
$20$	0.739990	−	0.682571i	0.165467	−	0.152627i
$21$	0.532072			0.116108
$22$	−0.0603041	−	0.0482361i	−0.0128569	−	0.0102840i
$23$	0.685700	+	1.18767i	0.142978	+	0.247646i	0.928617	−	0.371040i	$-0.120999\pi$
$23$	0.685700	+	1.18767i	0.142978	+	0.247646i	−0.785639	+	0.618686i	$0.787665\pi$
$24$	−0.105841	−	1.50120i	−0.0216047	−	0.306431i
$25$	−4.74663			−0.949326
$26$	5.08916	−	0.316976i	0.998066	−	0.0621641i
$27$		−	3.04180i		−	0.585395i
$28$	−1.95116	+	0.439305i	−0.368734	+	0.0830208i
$29$	−7.07541	+	4.08499i	−1.31387	+	0.758564i	−0.982735	−	0.185019i	$-0.940765\pi$
$29$	−7.07541	+	4.08499i	−1.31387	+	0.758564i	−0.331137	+	0.943583i	$0.607432\pi$
$30$	0.236588	−	0.295779i	0.0431949	−	0.0540016i
$31$			8.99735i			1.61597i	0.589202	+	0.807986i	$0.299442\pi$
$31$			8.99735i			1.61597i	−0.589202	+	0.807986i	$0.700558\pi$
$32$	1.62759	+	5.41765i	0.287721	+	0.957714i
$33$	−0.0251611	−	0.0145268i	−0.00437998	−	0.00252878i
$34$	−0.543436	+	3.56983i	−0.0931985	+	0.612221i
$35$	−0.435923	−	0.251680i	−0.0736844	−	0.0425417i
$36$	1.19355	+	5.30110i	0.198924	+	0.883516i
$37$	−4.90502	−	8.49575i	−0.806381	−	1.39669i	−0.915355	−	0.402648i	$-0.868090\pi$
$37$	−4.90502	−	8.49575i	−0.806381	−	1.39669i	0.108974	−	0.994045i	$-0.465243\pi$
$38$	−1.11668	+	7.33547i	−0.181149	+	1.18997i
$39$	1.87495	−	0.406054i	0.300232	−	0.0650206i
$40$	−0.623382	+	1.27999i	−0.0985653	+	0.202384i
$41$	−2.92300	+	1.68760i	−0.456496	+	0.263558i	−0.710570	−	0.703627i	$-0.751563\pi$
$41$	−2.92300	+	1.68760i	−0.456496	+	0.263558i	0.254074	+	0.967185i	$0.418229\pi$
$42$	−0.700852	+	0.273875i	−0.108144	+	0.0422599i
$43$	−4.84378	−	2.79656i	−0.738670	−	0.426471i	0.0829158	−	0.996557i	$-0.473577\pi$
$43$	−4.84378	−	2.79656i	−0.738670	−	0.426471i	−0.821585	+	0.570085i	$0.806910\pi$
$44$	0.104262	+	0.0324967i	0.0157181	+	0.00489907i
$45$	−0.683790	+	1.18436i	−0.101933	+	0.176554i
$46$	−1.51454	−	1.21146i	−0.223307	−	0.178620i
$47$		−	6.59604i		−	0.962132i	−0.876684	−	0.481066i	$-0.840250\pi$
$47$		−	6.59604i		−	0.962132i	0.876684	−	0.481066i	$-0.159750\pi$
$48$	0.912133	+	1.92292i	0.131655	+	0.277549i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	6.25232	−	2.44325i	0.884211	−	0.345528i
$51$			1.35856i			0.190236i
$52$	−6.54035	+	3.03709i	−0.906983	+	0.421168i
$53$		−	11.7324i		−	1.61158i	−0.592204	−	0.805788i	$-0.701742\pi$
$53$		−	11.7324i		−	1.61158i	0.592204	−	0.805788i	$-0.298258\pi$
$54$	1.56572	+	4.00670i	0.213067	+	0.545243i
$55$	0.0137429	+	0.0238034i	0.00185309	+	0.00320965i
$56$	2.34396	−	1.58298i	0.313225	−	0.211535i
$57$			2.79163i			0.369760i
$58$	7.21714	−	9.02276i	0.947657	−	1.18475i
$59$	0.303677	−	0.525983i	0.0395353	−	0.0684772i	−0.845581	−	0.533848i	$-0.820746\pi$
$59$	0.303677	−	0.525983i	0.0395353	−	0.0684772i	0.885116	+	0.465370i	$0.154079\pi$
$60$	−0.159390	+	0.511384i	−0.0205771	+	0.0660194i
$61$	−8.79623	−	5.07851i	−1.12624	−	0.650236i	−0.183255	−	0.983065i	$-0.558663\pi$
$61$	−8.79623	−	5.07851i	−1.12624	−	0.650236i	−0.942987	+	0.332829i	$0.891997\pi$
$62$	−4.63124	−	11.8514i	−0.588168	−	1.50513i
$63$	2.35290	−	1.35845i	0.296438	−	0.171149i
$64$	−4.93253	−	6.29842i	−0.616567	−	0.787303i
$65$	−1.72820	−	0.554209i	−0.214357	−	0.0687412i
$66$	0.0406199	+	0.00618358i	0.00499996	+	0.000761146i
$67$	0.0600940	+	0.104086i	0.00734165	+	0.0127161i	0.869673	−	0.493628i	$-0.164330\pi$
$67$	0.0600940	+	0.104086i	0.00734165	+	0.0127161i	−0.862331	+	0.506345i	$0.830996\pi$
$68$	−1.12169	−	4.98195i	−0.136025	−	0.604150i
$69$	−0.631924	−	0.364842i	−0.0760747	−	0.0439218i
$70$	0.703752	+	0.107132i	0.0841144	+	0.0128048i
$71$	3.29717	+	1.90362i	0.391302	+	0.225918i	0.682724	−	0.730676i	$-0.260795\pi$
$71$	3.29717	+	1.90362i	0.391302	+	0.225918i	−0.291422	+	0.956594i	$0.594128\pi$
$72$	−4.30081	−	6.36831i	−0.506855	−	0.750513i
$73$			7.23093i			0.846316i	0.906056	+	0.423158i	$0.139079\pi$
$73$			7.23093i			0.846316i	−0.906056	+	0.423158i	$0.860921\pi$
$74$	10.8340	+	8.66593i	1.25943	+	1.00739i
$75$	2.18719	−	1.26277i	0.252555	−	0.145812i
$76$	−2.30491	−	10.2372i	−0.264391	−	1.17428i
$77$		−	0.0546045i		−	0.00622276i
$78$	−2.26069	+	1.49996i	−0.255973	+	0.169837i
$79$	−11.5424			−1.29863			−0.649313	−	0.760521i	$-0.724943\pi$
$79$	−11.5424			−1.29863			−0.649313	+	0.760521i	$0.724943\pi$
$80$	0.162273	−	2.00689i	0.0181427	−	0.224377i
$81$	−3.26612	−	5.65709i	−0.362902	−	0.628565i
$82$	2.98155	−	3.72749i	0.329257	−	0.411632i
$83$	8.30193			0.911255			0.455628	−	0.890170i	$-0.349415\pi$
$83$	8.30193			0.911255			0.455628	+	0.890170i	$0.349415\pi$
$84$	0.782198	−	0.721504i	0.0853448	−	0.0787225i
$85$	0.642623	−	1.11306i	0.0697023	−	0.120728i
$86$	7.81977	+	1.19041i	0.843228	+	0.128365i
$87$	2.17351	−	3.76463i	0.233025	−	0.403610i
$88$	−0.154062	+	0.0108621i	−0.0164231	+	0.00115790i
$89$	0.726930	−	0.419693i	0.0770544	−	0.0444874i	−0.460978	−	0.887412i	$-0.652501\pi$
$89$	0.726930	−	0.419693i	0.0770544	−	0.0444874i	0.538032	+	0.842924i	$0.319168\pi$
$90$	0.291068	−	1.91202i	0.0306812	−	0.201545i
$91$	2.42284	+	2.67017i	0.253983	+	0.279910i
$92$	2.61856	+	0.816160i	0.273003	+	0.0850906i
$93$	−2.39362	−	4.14587i	−0.248206	−	0.429906i
$94$	3.39521	+	8.68839i	0.350189	+	0.896139i
$95$	1.32050	−	2.28716i	0.135480	−	0.234658i
$96$	−2.19126	−	2.06339i	−0.223645	−	0.210594i
$97$	−6.37150	−	3.67859i	−0.646928	−	0.373504i	0.140350	−	0.990102i	$-0.455177\pi$
$97$	−6.37150	−	3.67859i	−0.646928	−	0.373504i	−0.787278	+	0.616598i	$0.788510\pi$
$98$	−1.10438	−	0.883373i	−0.111559	−	0.0892341i
$99$	−0.148355			−0.0149102
$100$	−6.97801	+	6.43656i	−0.697801	+	0.643656i
$101$	−9.51146	+	5.49144i	−0.946425	+	0.546419i	−0.891969	−	0.452097i	$-0.850676\pi$
$101$	−9.51146	+	5.49144i	−0.946425	+	0.546419i	−0.0544567	+	0.998516i	$0.517343\pi$
$102$	−0.699294	−	1.78951i	−0.0692405	−	0.177188i
$103$	−9.92373			−0.977815			−0.488907	−	0.872336i	$-0.662604\pi$
$103$	−9.92373			−0.977815			−0.488907	+	0.872336i	$0.662604\pi$
$104$	7.05174	−	7.36702i	0.691480	−	0.722396i
$105$	0.267824			0.0261369
$106$	6.03909	+	15.4541i	0.586568	+	1.50104i
$107$	7.36876	−	4.25435i	0.712365	−	0.411284i	−0.0995712	−	0.995030i	$-0.531747\pi$
$107$	7.36876	−	4.25435i	0.712365	−	0.411284i	0.811936	+	0.583746i	$0.198414\pi$
$108$	−4.12476	−	4.47175i	−0.396906	−	0.430294i
$109$	−8.67130			−0.830560			−0.415280	−	0.909694i	$-0.636316\pi$
$109$	−8.67130			−0.830560			−0.415280	+	0.909694i	$0.636316\pi$
$110$	−0.0303547	−	0.0242802i	−0.00289421	−	0.00231502i
$111$	4.52035	+	2.60982i	0.429052	+	0.247714i
$112$	−2.27268	+	3.29164i	−0.214748	+	0.311031i
$113$	−0.278179	+	0.481821i	−0.0261689	+	0.0453259i	−0.878813	−	0.477166i	$-0.841664\pi$
$113$	−0.278179	+	0.481821i	−0.0261689	+	0.0453259i	0.852644	+	0.522492i	$0.174997\pi$
$114$	−1.43695	−	3.67717i	−0.134582	−	0.344399i
$115$	0.345154	+	0.597825i	0.0321858	+	0.0557475i
$116$	−4.86220	+	15.5998i	−0.451444	+	1.44840i
$117$	7.25460	−	6.58262i	0.670688	−	0.608564i
$118$	−0.129265	+	0.849145i	−0.0118998	+	0.0781701i
$119$	−2.21125	+	1.27667i	−0.202705	+	0.117032i
$120$	−0.0532762	−	0.755645i	−0.00486343	−	0.0689806i
$121$	5.49851	−	9.52370i	0.499864	−	0.865791i
$122$	14.2006	+	2.16176i	1.28566	+	0.195716i
$123$	0.897922	−	1.55525i	0.0809629	−	0.140232i
$124$	12.2006	+	13.2270i	1.09565	+	1.18782i
$125$	−4.90607			−0.438812
$126$	−2.40004	+	3.00049i	−0.213812	+	0.267305i
$127$	−5.15315	−	8.92552i	−0.457268	−	0.792012i	0.541547	−	0.840670i	$-0.317839\pi$
$127$	−5.15315	−	8.92552i	−0.457268	−	0.792012i	−0.998815	+	0.0486586i	$0.984505\pi$
$128$	9.73920	+	5.75742i	0.860832	+	0.508889i
$129$	2.97594			0.262017
$130$	2.56168	−	0.159553i	0.224674	−	0.0139937i
$131$			19.1062i			1.66931i	0.550770	+	0.834657i	$0.314334\pi$
$131$			19.1062i			1.66931i	−0.550770	+	0.834657i	$0.685666\pi$
$132$	−0.0566880	+	0.0127633i	−0.00493405	+	0.00111091i
$133$	−4.54379	+	2.62336i	−0.393997	+	0.227474i
$134$	−0.132733	−	0.106171i	−0.0114664	−	0.00917176i
$135$		−	1.53112i		−	0.131778i
$136$	4.04188	+	5.98492i	0.346589	+	0.513202i
$137$	14.1466	+	8.16756i	1.20863	+	0.697802i	0.962459	−	0.271425i	$-0.0874950\pi$
$137$	14.1466	+	8.16756i	1.20863	+	0.697802i	0.246168	+	0.969227i	$0.420828\pi$
$138$	1.02017	+	0.155301i	0.0868430	+	0.0132201i
$139$	1.28244	+	0.740419i	0.108775	+	0.0628015i	0.553401	−	0.832915i	$-0.313330\pi$
$139$	1.28244	+	0.740419i	0.108775	+	0.0628015i	−0.444625	+	0.895717i	$0.646663\pi$
$140$	−0.982135	+	0.221129i	−0.0830056	+	0.0186888i
$141$	1.75478	+	3.03938i	0.147779	+	0.255962i
$142$	−5.32293	−	0.810310i	−0.446690	−	0.0679997i
$143$	−0.0416718	−	0.192419i	−0.00348477	−	0.0160909i
$144$	8.94306	+	6.17465i	0.745255	+	0.514554i
$145$	−3.56149	+	2.05622i	−0.295765	+	0.170760i
$146$	−3.72200	−	9.52467i	−0.308035	−	0.788267i
$147$	−0.460788	−	0.266036i	−0.0380051	−	0.0219423i
$148$	−18.7313	−	5.83825i	−1.53971	−	0.479901i
$149$	3.62234	−	6.27407i	0.296753	−	0.513992i	−0.678638	−	0.734473i	$-0.737429\pi$
$149$	3.62234	−	6.27407i	0.296753	−	0.513992i	0.975391	+	0.220481i	$0.0707628\pi$
$150$	−2.23100	+	2.78916i	−0.182160	+	0.227734i
$151$			14.0199i			1.14092i	0.821326	+	0.570460i	$0.193235\pi$
$151$			14.0199i			1.14092i	−0.821326	+	0.570460i	$0.806765\pi$
$152$	8.30547	+	12.2981i	0.673662	+	0.997508i
$153$	3.46857	+	6.00775i	0.280418	+	0.485697i
$154$	0.0281068	+	0.0719258i	0.00226491	+	0.00579594i
$155$			4.52891i			0.363771i
$156$	2.20574	−	3.13942i	0.176600	−	0.251355i
$157$			23.0946i			1.84315i	0.388203	+	0.921574i	$0.373096\pi$
$157$			23.0946i			1.84315i	−0.388203	+	0.921574i	$0.626904\pi$
$158$	15.2038	−	5.94128i	1.20955	−	0.472663i
$159$	3.12125	+	5.40617i	0.247531	+	0.428737i
$160$	0.819266	+	2.72703i	0.0647687	+	0.215591i
$161$		−	1.37140i		−	0.108081i
$162$	7.21407	+	5.77041i	0.566791	+	0.453366i
$163$	9.72812	−	16.8496i	0.761965	−	1.31976i	−0.179871	−	0.983690i	$-0.557568\pi$
$163$	9.72812	−	16.8496i	0.761965	−	1.31976i	0.941836	−	0.336073i	$-0.109099\pi$
$164$	−2.00868	+	6.44460i	−0.156851	+	0.503239i
$165$	−0.0126651	−	0.00731220i	−0.000985976	−	0.000569254i
$166$	−10.9354	+	4.27328i	−0.848752	+	0.331671i
$167$	3.67924	−	2.12421i	0.284708	−	0.164376i	−0.350845	−	0.936434i	$-0.614106\pi$
$167$	3.67924	−	2.12421i	0.284708	−	0.164376i	0.635553	+	0.772057i	$0.280772\pi$
$168$	−0.658939	+	1.35300i	−0.0508382	+	0.104386i
$169$	10.5755	+	7.56032i	0.813502	+	0.581563i
$170$	−0.273544	+	1.79691i	−0.0209799	+	0.137817i
$171$	7.12740	+	12.3450i	0.545046	+	0.944047i
$172$	−10.9130	+	2.45708i	−0.832112	+	0.187351i
$173$	−8.93839	−	5.16058i	−0.679573	−	0.392352i	0.120121	−	0.992759i	$-0.461672\pi$
$173$	−8.93839	−	5.16058i	−0.679573	−	0.392352i	−0.799694	+	0.600407i	$0.795005\pi$
$174$	−0.925193	+	6.07759i	−0.0701387	+	0.460741i
$175$	4.11070	+	2.37331i	0.310740	+	0.179406i
$176$	0.197342	−	0.0936088i	0.0148752	−	0.00705603i
$177$			0.323156i			0.0242899i
$178$	−0.741491	+	0.927001i	−0.0555771	+	0.0694816i
$179$	−3.47794	+	2.00799i	−0.259953	+	0.150084i	−0.624313	−	0.781174i	$-0.714621\pi$
$179$	−3.47794	+	2.00799i	−0.259953	+	0.150084i	0.364360	+	0.931258i	$0.381288\pi$
$180$	0.600784	+	2.66836i	0.0447798	+	0.198888i
$181$			9.24520i			0.687190i	0.939118	+	0.343595i	$0.111645\pi$
$181$			9.24520i			0.687190i	−0.939118	+	0.343595i	$0.888355\pi$
$182$	−4.56583	−	2.27007i	−0.338442	−	0.168269i
$183$	5.40426			0.399494
$184$	−3.86930	+	0.272802i	−0.285249	+	0.0201112i
$185$	−2.46900	−	4.27643i	−0.181524	−	0.314409i
$186$	5.28692	+	4.22891i	0.387656	+	0.310079i
$187$	0.139423			0.0101957
$188$	−8.94442	−	9.69684i	−0.652339	−	0.707214i
$189$	−1.52090	+	2.63428i	−0.110629	+	0.191615i
$190$	−0.562093	+	3.69239i	−0.0407785	+	0.267874i
$191$	10.7692	−	18.6528i	0.779230	−	1.34967i	−0.153156	−	0.988202i	$-0.548944\pi$
$191$	10.7692	−	18.6528i	0.779230	−	1.34967i	0.932386	−	0.361464i	$-0.117723\pi$
$192$	3.94846	+	1.59000i	0.284955	+	0.114749i
$193$	−5.94892	+	3.43461i	−0.428212	+	0.247228i	−0.698585	−	0.715527i	$-0.746186\pi$
$193$	−5.94892	+	3.43461i	−0.428212	+	0.247228i	0.270372	+	0.962756i	$0.412853\pi$
$194$	10.2861	+	1.56586i	0.738500	+	0.112422i
$195$	0.943774	−	0.204391i	0.0675851	−	0.0146368i
$196$	1.90940	+	0.595129i	0.136386	+	0.0425092i
$197$	12.2509	+	21.2192i	0.872840	+	1.51180i	0.859046	+	0.511899i	$0.171058\pi$
$197$	12.2509	+	21.2192i	0.872840	+	1.51180i	0.0137948	+	0.999905i	$0.495609\pi$
$198$	0.195415	−	0.0763633i	0.0138875	−	0.00542690i
$199$	9.74017	−	16.8705i	0.690463	−	1.19592i	−0.281224	−	0.959642i	$-0.590740\pi$
$199$	9.74017	−	16.8705i	0.690463	−	1.19592i	0.971686	−	0.236274i	$-0.0759263\pi$
$200$	5.87841	−	12.0701i	0.415667	−	0.853487i
$201$	−0.0553811	−	0.0319743i	−0.00390628	−	0.00225529i
$202$	9.70198	−	12.1293i	0.682629	−	0.853412i
$203$	8.16999			0.573421
$204$	1.84224	+	1.99721i	0.128983	+	0.139833i
$205$	−1.47132	+	0.849469i	−0.102762	+	0.0593295i
$206$	13.0717	−	5.10808i	0.910746	−	0.355897i
$207$	−3.72596			−0.258972
$208$	−5.49658	+	13.3337i	−0.381119	+	0.924526i
$209$	0.286494			0.0198172
$210$	−0.352781	+	0.137858i	−0.0243442	+	0.00951310i
$211$	1.25291	−	0.723371i	0.0862542	−	0.0497989i	−0.456253	−	0.889850i	$-0.650809\pi$
$211$	1.25291	−	0.723371i	0.0862542	−	0.0497989i	0.542507	+	0.840051i	$0.317475\pi$
$212$	−15.9095	−	17.2479i	−1.09267	−	1.18459i
$213$	−2.02572			−0.138800
$214$	−7.51636	+	9.39684i	−0.513808	+	0.642355i
$215$	−2.43817	−	1.40768i	−0.166282	−	0.0960028i
$216$	7.73495	+	3.76709i	0.526297	+	0.256318i
$217$	4.49867	−	7.79193i	0.305390	−	0.528951i
$218$	11.4219	−	4.46341i	0.773592	−	0.302300i
$219$	−1.92369	−	3.33192i	−0.129991	−	0.225150i
$220$	0.0524814	+	0.0163576i	0.00353830	+	0.00110283i
$221$	−6.81784	+	6.18632i	−0.458618	+	0.416137i
$222$	−7.29762	−	1.11092i	−0.489784	−	0.0745600i
$223$	−3.32430	+	1.91929i	−0.222612	+	0.128525i	−0.607159	−	0.794580i	$-0.707691\pi$
$223$	−3.32430	+	1.91929i	−0.222612	+	0.128525i	0.384547	+	0.923105i	$0.374358\pi$
$224$	1.29929	−	5.50562i	0.0868124	−	0.367860i
$225$	6.44806	−	11.1684i	0.429870	−	0.744557i
$226$	0.118412	−	0.777849i	0.00787666	−	0.0517417i
$227$	−9.82414	+	17.0159i	−0.652051	+	1.12939i	0.330573	+	0.943780i	$0.392758\pi$
$227$	−9.82414	+	17.0159i	−0.652051	+	1.12939i	−0.982624	+	0.185605i	$0.940575\pi$
$228$	3.78553	+	4.10397i	0.250703	+	0.271792i
$229$	−13.5568			−0.895861			−0.447931	−	0.894068i	$-0.647839\pi$
$229$	−13.5568			−0.895861			−0.447931	+	0.894068i	$0.647839\pi$
$230$	−0.762362	−	0.609800i	−0.0502687	−	0.0402090i
$231$	0.0145268	+	0.0251611i	0.000955790	+	0.00165548i
$232$	−1.62519	−	23.0510i	−0.106699	−	1.51337i
$233$	−29.1230			−1.90791			−0.953955	−	0.299950i	$-0.903030\pi$
$233$	−29.1230			−1.90791			−0.953955	+	0.299950i	$0.903030\pi$
$234$	−6.16755	+	12.4049i	−0.403185	+	0.810933i
$235$		−	3.32019i		−	0.216585i
$236$	−0.266813	−	1.18504i	−0.0173681	−	0.0771396i
$237$	5.31861	−	3.07070i	0.345481	−	0.199464i
$238$	2.25554	−	2.81985i	0.146205	−	0.182783i
$239$			9.08693i			0.587784i	0.955839	+	0.293892i	$0.0949507\pi$
$239$			9.08693i			0.587784i	−0.955839	+	0.293892i	$0.905049\pi$
$240$	0.459132	+	0.967922i	0.0296368	+	0.0624791i
$241$	20.7330	+	11.9702i	1.33553	+	0.771069i	0.986141	−	0.165908i	$-0.0530554\pi$
$241$	20.7330	+	11.9702i	1.33553	+	0.771069i	0.349390	+	0.936977i	$0.386389\pi$
$242$	−2.34054	+	15.3750i	−0.150456	+	0.988343i
$243$	10.9128	+	6.30051i	0.700057	+	0.404178i
$244$	−19.8179	+	4.46202i	−1.26871	+	0.285652i
$245$	0.251680	+	0.435923i	0.0160793	+	0.0278501i
$246$	−0.382217	+	2.51078i	−0.0243692	+	0.160082i
$247$	−14.0097	+	12.7120i	−0.891413	+	0.808843i
$248$	−22.8792	−	11.1427i	−1.45283	−	0.707560i
$249$	−3.82543	+	2.20861i	−0.242427	+	0.139965i
$250$	6.46234	−	2.52532i	0.408714	−	0.159715i
$251$	24.4196	+	14.0987i	1.54135	+	0.889901i	0.998754	+	0.0499092i	$0.0158932\pi$
$251$	24.4196	+	14.0987i	1.54135	+	0.889901i	0.542599	+	0.839992i	$0.317440\pi$
$252$	1.61691	−	5.18766i	0.101856	−	0.326792i
$253$	−0.0374423	+	0.0648520i	−0.00235398	+	0.00407721i
$254$	11.3821	+	9.10431i	0.714174	+	0.571255i
$255$			0.683843i			0.0428239i
$256$	−15.7921	−	2.57065i	−0.987009	−	0.160666i
$257$	7.22285	+	12.5103i	0.450549	+	0.780374i	0.998420	−	0.0561888i	$-0.0178949\pi$
$257$	7.22285	+	12.5103i	0.450549	+	0.780374i	−0.547871	+	0.836563i	$0.684562\pi$
$258$	−3.91994	+	1.53182i	−0.244045	+	0.0953667i
$259$			9.81005i			0.609567i
$260$	−3.29215	+	1.52875i	−0.204171	+	0.0948090i
$261$		−	22.1970i		−	1.37396i
$262$	−9.83459	−	25.1669i	−0.607583	−	1.55482i
$263$	4.95232	+	8.57768i	0.305373	+	0.528922i	0.977344	−	0.211655i	$-0.0678854\pi$
$263$	4.95232	+	8.57768i	0.305373	+	0.528922i	−0.671971	+	0.740577i	$0.734552\pi$
$264$	0.0681004	−	0.0459912i	0.00419129	−	0.00283056i
$265$		−	5.90565i		−	0.362781i
$266$	4.63481	−	5.79436i	0.284178	−	0.355275i
$267$	−0.223307	+	0.386779i	−0.0136662	+	0.0236705i
$268$	0.229487	+	0.0715274i	0.0140182	+	0.00436923i
$269$	13.3083	+	7.68353i	0.811419	+	0.468473i	0.847448	−	0.530878i	$-0.178138\pi$
$269$	13.3083	+	7.68353i	0.811419	+	0.468473i	−0.0360294	+	0.999351i	$0.511471\pi$
$270$	0.788120	+	2.01681i	0.0479635	+	0.122739i
$271$	25.0763	−	14.4778i	1.52328	−	0.879464i	0.523656	−	0.851930i	$-0.324568\pi$
$271$	25.0763	−	14.4778i	1.52328	−	0.879464i	0.999621	−	0.0275341i	$-0.00876548\pi$
$272$	−8.40466	−	5.80292i	−0.509607	−	0.351853i
$273$	−1.82678	−	0.585820i	−0.110562	−	0.0354555i
$274$	−22.8382	−	3.47667i	−1.37971	−	0.210033i
$275$	−0.129594	−	0.224463i	−0.00781479	−	0.0135356i
$276$	−1.42373	+	0.320553i	−0.0856982	+	0.0192950i
$277$	−16.3247	−	9.42507i	−0.980856	−	0.566297i	−0.0783274	−	0.996928i	$-0.524958\pi$
$277$	−16.3247	−	9.42507i	−0.980856	−	0.566297i	−0.902528	+	0.430630i	$0.858291\pi$
$278$	−2.07037	−	0.315173i	−0.124173	−	0.0189028i
$279$	−21.1699	−	12.2224i	−1.26741	−	0.731739i
$280$	1.17986	−	0.796812i	0.0705100	−	0.0476186i
$281$		−	9.97434i		−	0.595019i	−0.954719	−	0.297510i	$-0.903844\pi$
$281$		−	9.97434i		−	0.595019i	0.954719	−	0.297510i	$-0.0961560\pi$
$282$	−3.87589	−	3.10026i	−0.230806	−	0.184618i
$283$	5.94568	−	3.43274i	0.353434	−	0.204055i	−0.312763	−	0.949831i	$-0.601254\pi$
$283$	5.94568	−	3.43274i	0.353434	−	0.204055i	0.666197	+	0.745776i	$0.267921\pi$
$284$	7.42852	−	1.67254i	0.440802	−	0.0992469i
$285$			1.40520i			0.0832366i
$286$	0.153935	+	0.232006i	0.00910236	+	0.0137188i
$287$	3.37519			0.199231
$288$	−14.9582	−	3.53004i	−0.881421	−	0.208009i
$289$	5.24025	+	9.07637i	0.308250	+	0.533904i
$290$	3.63283	−	4.54170i	0.213327	−	0.266698i
$291$	3.91455			0.229475
$292$	9.80534	+	10.6302i	0.573814	+	0.622084i
$293$	12.2555	−	21.2272i	0.715977	−	1.24011i	−0.246605	−	0.969116i	$-0.579315\pi$
$293$	12.2555	−	21.2272i	0.715977	−	1.24011i	0.962582	−	0.270992i	$-0.0873517\pi$
$294$	0.743893	+	0.113243i	0.0433847	+	0.00660446i
$295$	0.152859	−	0.264759i	0.00889979	−	0.0154149i
$296$	27.6783	−	1.95144i	1.60877	−	0.113425i
$297$	0.143843	−	0.0830480i	0.00834664	−	0.00481893i
$298$	−1.54191	+	10.1288i	−0.0893206	+	0.586747i
$299$	−1.04659	−	4.83262i	−0.0605260	−	0.279478i
$300$	1.50303	−	4.82229i	0.0867773	−	0.278415i
$301$	2.79656	+	4.84378i	0.161191	+	0.279191i
$302$	−7.21649	−	18.4671i	−0.415262	−	1.06266i
$303$	2.92184	−	5.06078i	0.167855	−	0.290734i
$304$	−17.2703	−	11.9241i	−0.990521	−	0.683895i
$305$	−4.42768	−	2.55632i	−0.253528	−	0.146374i
$306$	−7.66124	−	6.12809i	−0.437964	−	0.350319i
$307$	24.7808			1.41431			0.707157	−	0.707056i	$-0.249977\pi$
$307$	24.7808			1.41431			0.707157	+	0.707056i	$0.249977\pi$
$308$	−0.0740452	−	0.0802740i	−0.00421912	−	0.00457404i
$309$	4.57273	−	2.64007i	0.260134	−	0.150188i
$310$	−2.33118	−	5.96554i	−0.132402	−	0.338820i
$311$	−19.4192			−1.10116			−0.550580	−	0.834782i	$-0.685593\pi$
$311$	−19.4192			−1.10116			−0.550580	+	0.834782i	$0.685593\pi$
$312$	−1.28946	+	5.27065i	−0.0730013	+	0.298392i
$313$	−0.799731			−0.0452035			−0.0226017	−	0.999745i	$-0.507195\pi$
$313$	−0.799731			−0.0452035			−0.0226017	+	0.999745i	$0.507195\pi$
$314$	−11.8876	−	30.4205i	−0.670853	−	1.71673i
$315$	1.18436	−	0.683790i	0.0667311	−	0.0385272i
$316$	−16.9685	+	15.6519i	−0.954554	+	0.880486i
$317$	4.02472			0.226051			0.113025	−	0.993592i	$-0.463946\pi$
$317$	4.02472			0.226051			0.113025	+	0.993592i	$0.463946\pi$
$318$	−6.89409	−	5.51446i	−0.386601	−	0.309235i
$319$	−0.386350	−	0.223059i	−0.0216314	−	0.0124889i
$320$	−2.48284	−	3.17038i	−0.138795	−	0.177229i
$321$	−2.26362	+	3.92071i	−0.126343	+	0.218833i
$322$	0.705906	+	1.80643i	0.0393386	+	0.100668i
$323$	−6.69831	−	11.6018i	−0.372704	−	0.645542i
$324$	−12.4727	−	3.88753i	−0.692927	−	0.215974i
$325$	16.2967	+	5.22612i	0.903981	+	0.289893i
$326$	−4.14095	+	27.2019i	−0.229346	+	1.50657i
$327$	3.99563	−	2.30688i	0.220959	−	0.127571i
$328$	−0.671401	−	9.52285i	−0.0370719	−	0.525811i
$329$	−3.29802	+	5.71234i	−0.181826	+	0.314932i
$330$	0.0204465	+	0.00311257i	0.00112554	+	0.000171341i
$331$	−0.969444	+	1.67913i	−0.0532854	+	0.0922931i	−0.891438	−	0.453143i	$-0.850303\pi$
$331$	−0.969444	+	1.67913i	−0.0532854	+	0.0922931i	0.838152	+	0.545436i	$0.183636\pi$
$332$	12.2047	−	11.2576i	0.669818	−	0.617843i
$333$	26.6529			1.46057
$334$	−3.75294	+	4.69186i	−0.205351	+	0.256727i
$335$	0.0302490	+	0.0523927i	0.00165268	+	0.00286252i
$336$	0.171529	−	2.12136i	0.00935769	−	0.115730i
$337$	−21.2705			−1.15868			−0.579340	−	0.815086i	$-0.696690\pi$
$337$	−21.2705			−1.15868			−0.579340	+	0.815086i	$0.696690\pi$
$338$	−17.8218	−	4.51497i	−0.969376	−	0.245582i
$339$		−	0.296023i		−	0.0160778i
$340$	−0.564615	−	2.50772i	−0.0306205	−	0.136000i
$341$	−0.425475	+	0.245648i	−0.0230407	+	0.0133026i
$342$	−15.7427	−	12.5923i	−0.851268	−	0.680914i
$343$		−	1.00000i		−	0.0539949i
$344$	13.1101	−	8.85381i	0.706847	−	0.477365i
$345$	−0.318086	−	0.183647i	−0.0171252	−	0.00988721i
$346$	14.4301	+	2.19669i	0.775766	+	0.118095i
$347$	−31.5600	−	18.2212i	−1.69423	−	0.978164i	−0.951032	−	0.309091i	$-0.899975\pi$
$347$	−31.5600	−	18.2212i	−1.69423	−	0.978164i	−0.743197	−	0.669073i	$-0.766691\pi$
$348$	−1.90967	−	8.48171i	−0.102369	−	0.454667i
$349$	−1.65377	−	2.86442i	−0.0885243	−	0.153329i	0.818363	−	0.574701i	$-0.194882\pi$
$349$	−1.65377	−	2.86442i	−0.0885243	−	0.153329i	−0.906888	+	0.421373i	$0.861548\pi$
$350$	−6.63629	−	1.01024i	−0.354725	−	0.0539998i
$351$	−3.34908	+	10.4435i	−0.178760	+	0.557433i
$352$	−0.211758	+	0.224881i	−0.0112867	+	0.0119862i
$353$	10.3258	−	5.96159i	0.549586	−	0.317304i	−0.199369	−	0.979924i	$-0.563889\pi$
$353$	10.3258	−	5.96159i	0.549586	−	0.317304i	0.748955	+	0.662621i	$0.230556\pi$
$354$	−0.166339	−	0.425665i	−0.00884082	−	0.0226238i
$355$	1.65966	+	0.958207i	0.0880858	+	0.0508564i
$356$	0.499544	−	1.60273i	0.0264758	−	0.0849444i
$357$	0.679278	−	1.17654i	0.0359512	−	0.0622693i
$358$	3.54760	−	4.43516i	0.187497	−	0.234405i
$359$			17.1081i			0.902932i	0.892288	+	0.451466i	$0.149099\pi$
$359$			17.1081i			0.902932i	−0.892288	+	0.451466i	$0.850901\pi$
$360$	−2.16486	−	3.20556i	−0.114098	−	0.168948i
$361$	−4.26402	−	7.38550i	−0.224422	−	0.388710i
$362$	−4.75881	−	12.1779i	−0.250118	−	0.640056i
$363$			5.85120i			0.307108i
$364$	7.18265	+	0.639979i	0.376473	+	0.0335440i
$365$			3.63976i			0.190514i
$366$	−7.11856	+	2.78175i	−0.372093	+	0.145405i
$367$	6.83700	+	11.8420i	0.356889	+	0.618149i	0.987439	−	0.157999i	$-0.0505042\pi$
$367$	6.83700	+	11.8420i	0.356889	+	0.618149i	−0.630551	+	0.776148i	$0.717171\pi$
$368$	4.95627	−	2.35100i	0.258363	−	0.122554i
$369$		−	9.17006i		−	0.477374i
$370$	5.45341	+	4.36209i	0.283509	+	0.226774i
$371$	−5.86622	+	10.1606i	−0.304559	+	0.527512i
$372$	−9.14076	−	2.84902i	−0.473926	−	0.147715i
$373$	−14.4489	−	8.34206i	−0.748135	−	0.431936i	0.0768849	−	0.997040i	$-0.475503\pi$
$373$	−14.4489	−	8.34206i	−0.748135	−	0.431936i	−0.825019	+	0.565104i	$0.808836\pi$
$374$	−0.183650	+	0.0717659i	−0.00949633	+	0.00371093i
$375$	2.26066	−	1.30519i	0.116740	−	0.0673997i
$376$	16.7730	+	8.16880i	0.865001	+	0.421274i
$377$	28.7899	−	6.23497i	1.48275	−	0.321117i
$378$	0.647399	−	4.25276i	0.0332986	−	0.218738i
$379$	−7.90038	−	13.6839i	−0.405815	−	0.702893i	0.588601	−	0.808424i	$-0.299679\pi$
$379$	−7.90038	−	13.6839i	−0.405815	−	0.702893i	−0.994416	+	0.105531i	$0.966346\pi$
$380$	−1.16020	−	5.15299i	−0.0595170	−	0.264343i
$381$	4.74902	+	2.74185i	0.243299	+	0.140469i
$382$	−4.58409	+	30.1129i	−0.234543	+	1.54071i
$383$	−22.3355	−	12.8954i	−1.14129	−	0.658925i	−0.194542	−	0.980894i	$-0.562322\pi$
$383$	−22.3355	−	12.8954i	−1.14129	−	0.658925i	−0.946750	+	0.321969i	$0.895655\pi$
$384$	−6.01939	−	0.0619704i	−0.307175	−	0.00316241i
$385$		−	0.0274858i		−	0.00140080i
$386$	6.06808	−	7.58622i	0.308857	−	0.386128i
$387$	13.1601	−	7.59797i	0.668964	−	0.386226i
$388$	−14.3550	+	3.23204i	−0.728765	+	0.164082i
$389$		−	2.80781i		−	0.142362i	−0.997463	−	0.0711808i	$-0.977323\pi$
$389$		−	2.80781i		−	0.142362i	0.997463	−	0.0711808i	$-0.0226767\pi$
$390$	−1.13794	+	0.755019i	−0.0576220	+	0.0382319i
$391$	3.50164			0.177086
$392$	−2.82142	+	0.198922i	−0.142503	+	0.0100471i
$393$	−5.08293	−	8.80389i	−0.256400	−	0.444097i
$394$	−27.0593	−	21.6442i	−1.36323	−	1.09042i
$395$	−5.81001			−0.292333
$396$	−0.218096	+	0.201173i	−0.0109598	+	0.0101093i
$397$	−4.61339	+	7.99062i	−0.231539	+	0.401038i	−0.958261	−	0.285894i	$-0.907709\pi$
$397$	−4.61339	+	7.99062i	−0.231539	+	0.401038i	0.726722	+	0.686932i	$0.241043\pi$
$398$	−4.14608	+	27.2356i	−0.207824	+	1.36520i
$399$	1.39581	−	2.41762i	0.0698781	−	0.121032i
$400$	−1.53022	+	18.9247i	−0.0765109	+	0.946237i
$401$	10.1480	−	5.85893i	0.506765	−	0.292581i	−0.224738	−	0.974419i	$-0.572153\pi$
$401$	10.1480	−	5.85893i	0.506765	−	0.292581i	0.731503	+	0.681838i	$0.238819\pi$
$402$	0.0894070	+	0.0136104i	0.00445922	+	0.000678827i
$403$	9.90624	−	30.8909i	0.493465	−	1.53878i
$404$	−6.53623	+	20.9708i	−0.325190	+	1.04333i
$405$	−1.64404	−	2.84756i	−0.0816929	−	0.141496i
$406$	−10.7616	+	4.20537i	−0.534090	+	0.208709i
$407$	0.267836	−	0.463906i	0.0132762	−	0.0229950i
$408$	−3.45465	−	1.68249i	−0.171031	−	0.0832957i
$409$	−27.7538	−	16.0237i	−1.37234	−	0.792320i	−0.381116	−	0.924527i	$-0.624460\pi$
$409$	−27.7538	−	16.0237i	−1.37234	−	0.792320i	−0.991222	+	0.132207i	$0.957793\pi$
$410$	1.50080	−	1.87627i	0.0741190	−	0.0926625i
$411$	−8.69145			−0.428718
$412$	−14.5889	+	13.4569i	−0.718742	+	0.662972i
$413$	−0.525983	+	0.303677i	−0.0258820	+	0.0149430i
$414$	4.90788	−	1.91787i	0.241209	−	0.0942584i
$415$	4.17886			0.205132
$416$	0.376864	−	20.3926i	0.0184773	−	0.999829i
$417$	−0.787912			−0.0385842
$418$	−0.377374	+	0.147468i	−0.0184580	+	0.00721291i
$419$	−29.5374	+	17.0535i	−1.44300	+	0.833116i	−0.998049	−	0.0624398i	$-0.980112\pi$
$419$	−29.5374	+	17.0535i	−1.44300	+	0.833116i	−0.444950	+	0.895555i	$0.646779\pi$
$420$	0.393728	−	0.363177i	0.0192119	−	0.0177212i
$421$	25.1111			1.22384			0.611921	−	0.790919i	$-0.290397\pi$
$421$	25.1111			1.22384			0.611921	+	0.790919i	$0.290397\pi$
$422$	−1.27801	+	1.59775i	−0.0622127	+	0.0777773i
$423$	15.5199	+	8.96040i	0.754601	+	0.435669i
$424$	29.8343	+	14.5299i	1.44888	+	0.705636i
$425$	−6.05986	+	10.4960i	−0.293946	+	0.509130i
$426$	2.66831	−	1.04271i	0.129280	−	0.0505194i
$427$	5.07851	+	8.79623i	0.245766	+	0.425679i
$428$	5.06378	−	16.2466i	0.244767	−	0.785307i
$429$	0.0703921	+	0.0775780i	0.00339856	+	0.00374550i
$430$	3.93617	+	0.599203i	0.189819	+	0.0288961i
$431$	−15.0064	+	8.66396i	−0.722834	+	0.417328i	−0.815795	−	0.578341i	$-0.803700\pi$
$431$	−15.0064	+	8.66396i	−0.722834	+	0.417328i	0.0929610	+	0.995670i	$0.470367\pi$
$432$	−12.1276	−	0.980616i	−0.583490	−	0.0471799i
$433$	−5.07244	+	8.78572i	−0.243766	+	0.422215i	−0.961784	−	0.273810i	$-0.911716\pi$
$433$	−5.07244	+	8.78572i	−0.243766	+	0.422215i	0.718018	+	0.696025i	$0.245050\pi$
$434$	−1.91494	+	12.5792i	−0.0919201	+	0.603823i
$435$	1.09406	−	1.89497i	0.0524561	−	0.0908566i
$436$	−12.7477	+	11.7585i	−0.610502	+	0.563131i
$437$	7.19535			0.344200
$438$	4.24896	+	3.39866i	0.203023	+	0.162394i
$439$	4.81405	+	8.33818i	0.229762	+	0.397960i	0.957738	−	0.287644i	$-0.0928718\pi$
$439$	4.81405	+	8.33818i	0.229762	+	0.397960i	−0.727975	+	0.685603i	$0.759538\pi$
$440$	−0.0775490	+	0.00546753i	−0.00369700	+	0.000260654i
$441$	−2.71690			−0.129376
$442$	5.79624	−	11.6581i	0.275699	−	0.554518i
$443$			4.68124i			0.222413i	0.993797	+	0.111206i	$0.0354714\pi$
$443$			4.68124i			0.222413i	−0.993797	+	0.111206i	$0.964529\pi$
$444$	10.1844	−	2.29302i	0.483328	−	0.108822i
$445$	0.365908	−	0.211257i	0.0173457	−	0.0100145i
$446$	3.39089	−	4.23924i	0.160563	−	0.200734i
$447$			3.85468i			0.182320i
$448$	1.12249	+	7.92086i	0.0530326	+	0.374225i
$449$	−4.05715	−	2.34240i	−0.191469	−	0.110544i	0.401201	−	0.915990i	$-0.368593\pi$
$449$	−4.05715	−	2.34240i	−0.191469	−	0.110544i	−0.592670	+	0.805445i	$0.701926\pi$
$450$	−2.74473	+	18.0301i	−0.129388	+	0.849949i
$451$	−0.159609	−	0.0921504i	−0.00751570	−	0.00433919i
$452$	0.244411	+	1.08554i	0.0114961	+	0.0510597i
$453$	−3.72978	−	6.46017i	−0.175241	−	0.303525i
$454$	4.18182	−	27.4704i	0.196263	−	1.28925i
$455$	1.21956	+	1.34406i	0.0571740	+	0.0630105i
$456$	−7.09879	−	3.45727i	−0.332431	−	0.161901i
$457$	−4.98012	+	2.87527i	−0.232960	+	0.134500i	−0.611937	−	0.790907i	$-0.709609\pi$
$457$	−4.98012	+	2.87527i	−0.232960	+	0.134500i	0.378977	+	0.925406i	$0.376276\pi$
$458$	17.8572	−	6.97816i	0.834414	−	0.326068i
$459$	−6.72618	−	3.88336i	−0.313951	−	0.181260i
$460$	1.31808	+	0.410823i	0.0614557	+	0.0191547i
$461$	−13.2508	+	22.9511i	−0.617151	+	1.06894i	0.372851	+	0.927891i	$0.378380\pi$
$461$	−13.2508	+	22.9511i	−0.617151	+	1.06894i	−0.990003	+	0.141047i	$0.954953\pi$
$462$	−0.0320861	−	0.0256651i	−0.00149278	−	0.00119405i
$463$		−	16.3328i		−	0.759049i	−0.925182	−	0.379524i	$-0.876088\pi$
$463$		−	16.3328i		−	0.759049i	0.925182	−	0.379524i	$-0.123912\pi$
$464$	14.0058	+	29.5265i	0.650205	+	1.37073i
$465$	−1.20485	−	2.08687i	−0.0558737	−	0.0967761i
$466$	38.3612	−	14.9906i	1.77705	−	0.694425i
$467$		−	6.35367i		−	0.294013i	−0.989136	−	0.147006i	$-0.953036\pi$
$467$		−	6.35367i		−	0.294013i	0.989136	−	0.147006i	$-0.0469638\pi$
$468$	1.73876	−	19.5145i	0.0803742	−	0.902060i
$469$		−	0.120188i		−	0.00554977i
$470$	1.70901	+	4.37340i	0.0788309	+	0.201730i
$471$	−6.14398	−	10.6417i	−0.283100	−	0.490343i
$472$	0.961430	+	1.42361i	0.0442534	+	0.0655271i
$473$		−	0.305409i		−	0.0140427i
$474$	−5.42515	+	6.78244i	−0.249185	+	0.311528i
$475$	−12.4521	+	21.5677i	−0.571342	+	0.989593i
$476$	−1.51956	+	4.87534i	−0.0696490	+	0.223461i
$477$	27.6053	+	15.9379i	1.26396	+	0.729748i
$478$	−4.67735	−	11.9694i	−0.213937	−	0.547468i
$479$	11.0433	−	6.37585i	0.504581	−	0.291320i	−0.226022	−	0.974122i	$-0.572572\pi$
$479$	11.0433	−	6.37585i	0.504581	−	0.291320i	0.730603	+	0.682802i	$0.239239\pi$
$480$	−1.10300	−	1.03863i	−0.0503447	−	0.0474067i
$481$	7.48660	+	34.5692i	0.341359	+	1.57622i
$482$	−33.4713	−	5.09534i	−1.52457	−	0.232086i
$483$	0.364842	+	0.631924i	0.0166009	+	0.0287535i
$484$	−4.83104	−	21.4569i	−0.219593	−	0.975314i
$485$	−3.20716	−	1.85166i	−0.145630	−	0.0840794i
$486$	−17.6176	−	2.68193i	−0.799149	−	0.121655i
$487$	−28.2331	−	16.3004i	−1.27937	−	0.738642i	−0.302634	−	0.953107i	$-0.597866\pi$
$487$	−28.2331	−	16.3004i	−1.27937	−	0.738642i	−0.976732	+	0.214465i	$0.931199\pi$
$488$	23.8077	−	16.0784i	1.07772	−	0.727834i
$489$			10.3521i			0.468139i
$490$	−0.555901	−	0.444655i	−0.0251130	−	0.0200875i
$491$	−15.4408	+	8.91477i	−0.696835	+	0.402318i	−0.806167	−	0.591687i	$-0.798462\pi$
$491$	−15.4408	+	8.91477i	−0.696835	+	0.402318i	0.109333	+	0.994005i	$0.465129\pi$
$492$	−0.788923	−	3.50397i	−0.0355674	−	0.157971i
$493$			20.8607i			0.939518i
$494$	11.9104	−	23.9556i	0.535875	−	1.07781i
$495$	−0.0746761			−0.00335644
$496$	35.8723	+	2.90057i	1.61071	+	0.130239i
$497$	−1.90362	−	3.29717i	−0.0853890	−	0.147898i
$498$	3.90205	−	4.87829i	0.174855	−	0.218601i
$499$	−9.30760			−0.416665			−0.208333	−	0.978058i	$-0.566804\pi$
$499$	−9.30760			−0.416665			−0.208333	+	0.978058i	$0.566804\pi$
$500$	−7.21240	+	6.65276i	−0.322549	+	0.297521i
$501$	−1.13023	+	1.95762i	−0.0504950	+	0.0874599i
$502$	−39.4229	−	6.00136i	−1.75953	−	0.267854i
$503$	12.4342	−	21.5367i	0.554414	−	0.960273i	−0.443535	−	0.896257i	$-0.646276\pi$
$503$	12.4342	−	21.5367i	0.554414	−	0.960273i	0.997949	−	0.0640160i	$-0.0203909\pi$
$504$	0.540452	+	7.66552i	0.0240736	+	0.341450i
$505$	−4.78769	+	2.76418i	−0.213050	+	0.123004i
$506$	0.0159380	−	0.104697i	0.000708530	−	0.00465433i
$507$	−6.88438	−	0.670233i	−0.305746	−	0.0297661i
$508$	−19.6789	−	6.13358i	−0.873109	−	0.272134i
$509$	−5.95205	−	10.3093i	−0.263820	−	0.456950i	0.703434	−	0.710761i	$-0.251649\pi$
$509$	−5.95205	−	10.3093i	−0.263820	−	0.456950i	−0.967254	+	0.253811i	$0.918316\pi$
$510$	−0.351997	−	0.900767i	−0.0155867	−	0.0398866i
$511$	3.61546	−	6.26217i	0.159939	−	0.277022i
$512$	22.1248	−	4.74265i	0.977788	−	0.209598i
$513$	−13.8213	−	7.97973i	−0.610225	−	0.352314i
$514$	−15.9535	−	12.7609i	−0.703680	−	0.562861i
$515$	−4.99522			−0.220116
$516$	4.37492	−	4.03545i	0.192595	−	0.177651i
$517$	0.311920	−	0.180087i	0.0137182	−	0.00792021i
$518$	−5.04956	−	12.9219i	−0.221865	−	0.567757i
$519$	5.49160			0.241054
$520$	3.54957	−	3.70827i	0.155659	−	0.162618i
$521$	24.9432			1.09278			0.546391	−	0.837530i	$-0.316001\pi$
$521$	24.9432			1.09278			0.546391	+	0.837530i	$0.316001\pi$
$522$	11.4256	+	29.2382i	0.500083	+	1.27972i
$523$	6.91876	−	3.99455i	0.302536	−	0.174669i	−0.341046	−	0.940047i	$-0.610781\pi$
$523$	6.91876	−	3.99455i	0.302536	−	0.174669i	0.643582	+	0.765377i	$0.277448\pi$
$524$	25.9085	+	28.0880i	1.13182	+	1.22703i
$525$	−2.52555			−0.110224
$526$	−10.9385	−	8.74950i	−0.476941	−	0.381496i
$527$	19.8954	+	11.4866i	0.866657	+	0.500364i
$528$	−0.0660294	+	0.0956338i	−0.00287356	+	0.00416193i
$529$	10.5596	−	18.2898i	0.459114	−	0.795209i
$530$	3.03984	+	7.77900i	0.132042	+	0.337898i
$531$	0.825059	+	1.42904i	0.0358045	+	0.0620152i
$532$	−3.12247	+	10.0181i	−0.135376	+	0.434340i
$533$	11.8937	−	2.57580i	0.515174	−	0.111570i
$534$	0.0950546	−	0.624414i	0.00411342	−	0.0270210i
$535$	3.70914	−	2.14147i	0.160360	−	0.0925840i
$536$	−0.339101	+	0.0239081i	−0.0146469	+	0.00103267i
$537$	1.06839	−	1.85051i	0.0461046	−	0.0798555i
$538$	−21.4848	−	3.27063i	−0.926275	−	0.141007i
$539$	−0.0273023	+	0.0472889i	−0.00117599	+	0.00203688i
$540$	−2.07624	−	2.25090i	−0.0893473	−	0.0968634i
$541$	3.88519			0.167037			0.0835187	−	0.996506i	$-0.473384\pi$
$541$	3.88519			0.167037			0.0835187	+	0.996506i	$0.473384\pi$
$542$	−25.5786	+	31.9780i	−1.09870	+	1.37357i
$543$	−2.45955	−	4.26007i	−0.105550	−	0.182817i
$544$	14.0577	+	3.31751i	0.602718	+	0.142237i
$545$	−4.36479			−0.186967
$546$	2.70780	−	0.168654i	0.115883	−	0.00721772i
$547$		−	17.1661i		−	0.733968i	−0.930227	−	0.366984i	$-0.880390\pi$
$547$		−	17.1661i		−	0.733968i	0.930227	−	0.366984i	$-0.119610\pi$
$548$	31.8724	−	7.17609i	1.36152	−	0.306548i
$549$	23.8985	−	13.7978i	1.01996	−	0.588875i
$550$	0.286241	+	0.228959i	0.0122054	+	0.00976285i
$551$			42.8656i			1.82614i
$552$	1.71035	−	1.15508i	0.0727973	−	0.0491633i
$553$	9.99605	+	5.77122i	0.425075	+	0.245417i
$554$	26.3545	+	4.01195i	1.11970	+	0.170451i
$555$	2.27537	+	1.31368i	0.0965839	+	0.0557627i
$556$	2.88935	−	0.650539i	0.122536	−	0.0275890i
$557$	4.73492	+	8.20111i	0.200625	+	0.347492i	0.948730	−	0.316088i	$-0.102369\pi$
$557$	4.73492	+	8.20111i	0.200625	+	0.347492i	−0.748105	+	0.663580i	$0.769036\pi$
$558$	34.1766	+	5.20270i	1.44681	+	0.220248i
$559$	13.5512	+	14.9346i	0.573156	+	0.631666i
$560$	−1.14398	+	1.65688i	−0.0483419	+	0.0700161i
$561$	−0.0642446	+	0.0370916i	−0.00271241	+	0.00156601i
$562$	5.13413	+	13.1383i	0.216570	+	0.554207i
$563$	−29.1619	−	16.8366i	−1.22903	−	0.709580i	−0.262202	−	0.965013i	$-0.584449\pi$
$563$	−29.1619	−	16.8366i	−1.22903	−	0.709580i	−0.966827	+	0.255433i	$0.917782\pi$
$564$	6.70118	+	2.08865i	0.282171	+	0.0879479i
$565$	−0.140025	+	0.242530i	−0.00589088	+	0.0102033i
$566$	−6.06478	+	7.58209i	−0.254922	+	0.318699i
$567$			6.53224i			0.274328i
$568$	−8.92403	+	6.02680i	−0.374444	+	0.252879i
$569$	−1.74147	−	3.01631i	−0.0730060	−	0.126450i	0.827211	−	0.561891i	$-0.189926\pi$
$569$	−1.74147	−	3.01631i	−0.0730060	−	0.126450i	−0.900217	+	0.435441i	$0.856593\pi$
$570$	−0.723302	−	1.85094i	−0.0302958	−	0.0775274i
$571$		−	32.6908i		−	1.36807i	−0.729451	−	0.684033i	$-0.760224\pi$
$571$		−	32.6908i		−	1.36807i	0.729451	−	0.684033i	$-0.239776\pi$
$572$	−0.322187	−	0.226366i	−0.0134713	−	0.00946485i
$573$			11.4599i			0.478746i
$574$	−4.44585	+	1.73732i	−0.185566	+	0.0725145i
$575$	−3.25476	−	5.63741i	−0.135733	−	0.235096i
$576$	21.5202	−	3.04969i	0.896674	−	0.127070i
$577$		−	44.5079i		−	1.85289i	−0.376435	−	0.926443i	$-0.622850\pi$
$577$		−	44.5079i		−	1.85289i	0.376435	−	0.926443i	$-0.377150\pi$
$578$	−11.5744	−	9.25818i	−0.481433	−	0.385090i
$579$	1.82746	−	3.16525i	0.0759465	−	0.131543i
$580$	−2.44744	+	7.85232i	−0.101624	+	0.326050i
$581$	−7.18968	−	4.15097i	−0.298278	−	0.172211i
$582$	−5.15629	+	2.01495i	−0.213735	+	0.0835223i
$583$	0.554815	−	0.320322i	0.0229781	−	0.0132664i
$584$	−18.3874	−	8.95507i	−0.760877	−	0.370563i
$585$	3.65168	−	3.31343i	0.150978	−	0.136994i
$586$	−5.21680	+	34.2691i	−0.215504	+	1.41564i
$587$	6.30830	+	10.9263i	0.260371	+	0.450977i	0.966341	−	0.257266i	$-0.0828217\pi$
$587$	6.30830	+	10.9263i	0.260371	+	0.450977i	−0.705969	+	0.708243i	$0.749488\pi$
$588$	−1.03816	+	0.233742i	−0.0428128	+	0.00963934i
$589$	40.8821	+	23.6033i	1.68452	+	0.972556i
$590$	−0.0650671	+	0.427426i	−0.00267877	+	0.0175968i
$591$	−11.2901	−	6.51836i	−0.464414	−	0.268129i
$592$	−35.4537	+	16.8174i	−1.45714	+	0.691191i
$593$		−	32.4280i		−	1.33166i	−0.746105	−	0.665828i	$-0.768078\pi$
$593$		−	32.4280i		−	1.33166i	0.746105	−	0.665828i	$-0.231922\pi$
$594$	−0.146725	+	0.183433i	−0.00602019	+	0.00752634i
$595$	−1.11306	+	0.642623i	−0.0456309	+	0.0263450i
$596$	−3.18262	−	14.1355i	−0.130365	−	0.579012i
$597$			10.3649i			0.424209i
$598$	3.86610	+	5.82687i	0.158096	+	0.238279i
$599$	6.28240			0.256692			0.128346	−	0.991729i	$-0.459033\pi$
$599$	6.28240			0.256692			0.128346	+	0.991729i	$0.459033\pi$
$600$	0.502388	+	7.12564i	0.0205099	+	0.290903i
$601$	0.0794138	+	0.137549i	0.00323936	+	0.00561073i	0.867641	−	0.497192i	$-0.165636\pi$
$601$	0.0794138	+	0.137549i	0.00323936	+	0.00561073i	−0.864401	+	0.502803i	$0.832302\pi$
$602$	−6.17692	−	4.94081i	−0.251752	−	0.201372i
$603$	−0.326539			−0.0132977
$604$	19.0113	+	20.6106i	0.773559	+	0.838632i
$605$	2.76773	−	4.79385i	0.112524	−	0.194898i
$606$	−1.24373	+	8.17009i	−0.0505232	+	0.331887i
$607$	−7.37212	+	12.7689i	−0.299225	+	0.518273i	−0.975959	−	0.217955i	$-0.930062\pi$
$607$	−7.37212	+	12.7689i	−0.299225	+	0.518273i	0.676734	+	0.736228i	$0.263395\pi$
$608$	28.8864	+	6.81700i	1.17150	+	0.276466i
$609$	−3.76463	+	2.17351i	−0.152550	+	0.0880750i
$610$	7.14801	+	1.08814i	0.289415	+	0.0440576i
$611$	−7.26236	+	22.6464i	−0.293804	+	0.916175i
$612$	13.2458	+	4.12850i	0.535430	+	0.166885i
$613$	−10.5453	−	18.2649i	−0.425919	−	0.737714i	0.570586	−	0.821238i	$-0.306716\pi$
$613$	−10.5453	−	18.2649i	−0.425919	−	0.737714i	−0.996506	+	0.0835236i	$0.973383\pi$
$614$	−32.6416	+	12.7555i	−1.31731	+	0.514770i
$615$	0.451979	−	0.782850i	0.0182255	−	0.0315676i
$616$	0.138853	+	0.0676244i	0.00559455	+	0.00272466i
$617$	15.3239	+	8.84723i	0.616915	+	0.356176i	0.775667	−	0.631142i	$-0.217414\pi$
$617$	15.3239	+	8.84723i	0.616915	+	0.356176i	−0.158752	+	0.987319i	$0.550747\pi$
$618$	−4.66433	+	5.83127i	−0.187627	+	0.234568i
$619$	8.68923			0.349250			0.174625	−	0.984635i	$-0.444129\pi$
$619$	8.68923			0.349250			0.174625	+	0.984635i	$0.444129\pi$
$620$	6.14132	+	6.65794i	0.246642	+	0.267389i
$621$	3.61265	−	2.08576i	0.144971	−	0.0836988i
$622$	25.5792	−	9.99570i	1.02563	−	0.400791i
$623$	−0.839387			−0.0336293
$624$	−1.01449	−	7.60629i	−0.0406119	−	0.304495i
$625$	21.2636			0.850545
$626$	1.05342	−	0.411649i	0.0421030	−	0.0164528i
$627$	−0.132013	+	0.0762178i	−0.00527209	+	0.00304384i
$628$	31.3169	+	33.9513i	1.24968	+	1.35480i
$629$	−25.0483			−0.998742
$630$	−1.20808	+	1.51033i	−0.0481312	+	0.0601728i
$631$	−9.43527	−	5.44746i	−0.375612	−	0.216860i	0.300295	−	0.953846i	$-0.402915\pi$
$631$	−9.43527	−	5.44746i	−0.375612	−	0.216860i	−0.675908	+	0.736986i	$0.736248\pi$
$632$	14.2946	−	29.3511i	0.568609	−	1.16752i
$633$	−0.384885	+	0.666641i	−0.0152978	+	0.0264966i
$634$	−5.30141	+	2.07166i	−0.210546	+	0.0822760i
$635$	−2.59389	−	4.49275i	−0.102935	−	0.178290i
$636$	11.9195	+	3.71510i	0.472637	+	0.147313i
$637$	−0.763156	−	3.52386i	−0.0302373	−	0.139620i
$638$	0.623721	+	0.0949491i	0.0246933	+	0.00375907i
$639$	−8.95807	+	5.17194i	−0.354376	+	0.204599i
$640$	4.90233	+	2.89806i	0.193782	+	0.114556i
$641$	−13.4895	+	23.3645i	−0.532804	+	0.922843i	0.466462	+	0.884541i	$0.345528\pi$
$641$	−13.4895	+	23.3645i	−0.532804	+	0.922843i	−0.999266	+	0.0383023i	$0.987805\pi$
$642$	0.963551	−	6.32957i	0.0380283	−	0.249808i
$643$	−19.1096	+	33.0987i	−0.753608	+	1.30529i	0.192456	+	0.981306i	$0.438355\pi$
$643$	−19.1096	+	33.0987i	−0.753608	+	1.30529i	−0.946064	+	0.323981i	$0.894979\pi$
$644$	−1.85966	−	2.01609i	−0.0732807	−	0.0794452i
$645$	1.49797			0.0589825
$646$	14.7949	+	11.8342i	0.582099	+	0.465610i
$647$	16.5238	+	28.6200i	0.649616	+	1.12517i	0.983215	+	0.182453i	$0.0584036\pi$
$647$	16.5238	+	28.6200i	0.649616	+	1.12517i	−0.333599	+	0.942715i	$0.608263\pi$
$648$	18.4302	−	1.29941i	0.724008	−	0.0510456i
$649$	0.0331642			0.00130181
$650$	−24.1563	+	1.50457i	−0.947490	+	0.0590140i
$651$			4.78723i			0.187626i
$652$	−8.54722	−	37.9622i	−0.334735	−	1.48671i
$653$	−23.9076	+	13.8030i	−0.935576	+	0.540155i	−0.888571	−	0.458740i	$-0.848301\pi$
$653$	−23.9076	+	13.8030i	−0.935576	+	0.540155i	−0.0470050	+	0.998895i	$0.514968\pi$
$654$	−4.07566	+	5.09533i	−0.159371	+	0.199243i
$655$			9.61730i			0.375779i
$656$	5.78611	+	12.1980i	0.225910	+	0.476253i
$657$	−17.0137	−	9.82285i	−0.663767	−	0.383226i
$658$	1.40386	−	9.22197i	0.0547283	−	0.359510i
$659$	−38.5847	−	22.2769i	−1.50305	−	0.867785i	−0.999994	−	0.00353064i	$-0.998876\pi$
$659$	−38.5847	−	22.2769i	−1.50305	−	0.867785i	−0.503055	−	0.864255i	$-0.667791\pi$
$660$	−0.0285345	+	0.00642457i	−0.00111070	+	0.000250076i
$661$	7.27753	+	12.6051i	0.283063	+	0.490280i	0.972138	−	0.234411i	$-0.0753161\pi$
$661$	7.27753	+	12.6051i	0.283063	+	0.490280i	−0.689075	+	0.724690i	$0.741983\pi$
$662$	0.412661	−	2.71077i	0.0160385	−	0.105357i
$663$	1.49579	−	4.66437i	0.0580918	−	0.181149i
$664$	−10.2814	+	21.1109i	−0.398997	+	0.819260i
$665$	−2.28716	+	1.32050i	−0.0886924	+	0.0512066i
$666$	−35.1076	+	13.7192i	−1.36039	+	0.531606i
$667$	−9.70322	−	5.60216i	−0.375710	−	0.216916i
$668$	2.52836	−	8.11194i	0.0978250	−	0.313860i
$669$	1.02120	−	1.76877i	0.0394818	−	0.0683845i
$670$	−0.0668126	−	0.0534422i	−0.00258120	−	0.00206465i
$671$		−	0.554619i		−	0.0214108i
$672$	0.865996	+	2.88258i	0.0334065	+	0.111198i
$673$	16.0237	+	27.7539i	0.617669	+	1.06983i	0.989910	+	0.141698i	$0.0452563\pi$
$673$	16.0237	+	27.7539i	0.617669	+	1.06983i	−0.372241	+	0.928136i	$0.621410\pi$
$674$	28.0178	−	10.9487i	1.07921	−	0.421727i
$675$			14.4383i			0.555730i
$676$	25.7991	−	3.22628i	0.992271	−	0.124088i
$677$		−	40.8143i		−	1.56862i	−0.620369	−	0.784310i	$-0.713017\pi$
$677$		−	40.8143i		−	1.56862i	0.620369	−	0.784310i	$-0.286983\pi$
$678$	0.152373	+	0.389925i	0.00585185	+	0.0149750i
$679$	3.67859	+	6.37150i	0.141171	+	0.244516i
$680$	2.03452	+	3.01257i	0.0780205	+	0.115527i
$681$		−	10.4543i		−	0.400609i
$682$	0.433997	−	0.542577i	0.0166186	−	0.0207763i
$683$	3.76037	−	6.51315i	0.143887	−	0.249219i	−0.785070	−	0.619407i	$-0.787373\pi$
$683$	3.76037	−	6.51315i	0.143887	−	0.249219i	0.928957	+	0.370188i	$0.120707\pi$
$684$	27.2182	+	8.48345i	1.04071	+	0.324373i
$685$	7.12086	+	4.11123i	0.272074	+	0.157082i
$686$	0.514734	+	1.31721i	0.0196526	+	0.0502914i
$687$	6.24682	−	3.60661i	0.238331	−	0.137601i
$688$	−12.7114	+	18.4105i	−0.484617	+	0.701895i
$689$	−12.9176	+	40.2814i	−0.492123	+	1.53460i
$690$	0.513516	+	0.0781726i	0.0195492	+	0.00297598i
$691$	4.77155	+	8.26457i	0.181518	+	0.314399i	0.942398	−	0.334494i	$-0.108565\pi$
$691$	4.77155	+	8.26457i	0.181518	+	0.314399i	−0.760879	+	0.648893i	$0.775232\pi$
$692$	−20.1382	+	4.53414i	−0.765540	+	0.172362i
$693$	0.128479	+	0.0741775i	0.00488052	+	0.00281777i
$694$	50.9503	+	7.75617i	1.93405	+	0.294420i
$695$	0.645532	+	0.372698i	0.0244864	+	0.0141372i
$696$	6.88126	+	10.1892i	0.260833	+	0.386223i
$697$			8.61799i			0.326430i
$698$	3.65278	+	2.92179i	0.138260	+	0.110592i
$699$	13.4195	−	7.74776i	0.507572	−	0.293047i
$700$	9.26141	−	2.08522i	0.350049	−	0.0788138i
$701$			12.9010i			0.487265i	0.969868	+	0.243632i	$0.0783390\pi$
$701$			12.9010i			0.487265i	−0.969868	+	0.243632i	$0.921661\pi$
$702$	−0.964178	−	15.4802i	−0.0363906	−	0.584263i
$703$	−51.4705			−1.94125
$704$	0.163176	−	0.405215i	0.00614993	−	0.0152721i
$705$	0.883289	+	1.52990i	0.0332666	+	0.0576194i
$706$	−10.5326	+	13.1677i	−0.396400	+	0.495573i
$707$	10.9829			0.413054
$708$	0.438208	+	0.475071i	0.0164689	+	0.0178542i
$709$	4.86115	−	8.41977i	0.182565	−	0.316211i	−0.760189	−	0.649702i	$-0.774893\pi$
$709$	4.86115	−	8.41977i	0.182565	−	0.316211i	0.942753	+	0.333491i	$0.108227\pi$
$710$	−2.67935	−	0.407878i	−0.100554	−	0.0153074i
$711$	15.6798	−	27.1583i	0.588039	−	1.01851i
$712$	0.166973	+	2.36827i	0.00625757	+	0.0887545i
$713$	−10.6859	+	6.16948i	−0.400188	+	0.231049i
$714$	−0.289147	+	1.89941i	−0.0108210	+	0.0710835i
$715$	−0.0209759	−	0.0968560i	−0.000784455	−	0.00362221i
$716$	−2.39002	+	7.66812i	−0.0893194	+	0.286571i
$717$	−2.41745	−	4.18714i	−0.0902813	−	0.156372i
$718$	−8.80613	−	22.5350i	−0.328642	−	0.841000i
$719$	1.04838	−	1.81585i	0.0390980	−	0.0677198i	−0.845814	−	0.533478i	$-0.820885\pi$
$719$	1.04838	−	1.81585i	0.0390980	−	0.0677198i	0.884912	+	0.465758i	$0.154218\pi$
$720$	4.50159	+	3.10808i	0.167764	+	0.115831i
$721$	8.59421	+	4.96187i	0.320065	+	0.184790i
$722$	9.41818	+	7.53344i	0.350508	+	0.280365i
$723$	−12.7380			−0.473732
$724$	12.5367	+	13.5914i	0.465924	+	0.505119i
$725$	33.5844	−	19.3899i	1.24729	−	0.720124i
$726$	−3.01181	−	7.70728i	−0.111779	−	0.286044i
$727$	37.1208			1.37673			0.688367	−	0.725363i	$-0.258328\pi$
$727$	37.1208			1.37673			0.688367	+	0.725363i	$0.258328\pi$
$728$	−9.79049	+	2.85416i	−0.362860	+	0.105782i
$729$	12.8921			0.477484
$730$	−1.87351	−	4.79434i	−0.0693417	−	0.177447i
$731$	−12.3678	+	7.14054i	−0.457439	+	0.264102i
$732$	7.94479	−	7.32832i	0.293648	−	0.270863i
$733$	−9.84743			−0.363723			−0.181862	−	0.983324i	$-0.558212\pi$
$733$	−9.84743			−0.363723			−0.181862	+	0.983324i	$0.558212\pi$
$734$	−15.1013	−	12.0792i	−0.557399	−	0.445853i
$735$	−0.231942	−	0.133912i	−0.00855532	−	0.00493942i
$736$	−5.31833	+	5.64792i	−0.196036	+	0.208185i
$737$	−0.00328140	+	0.00568356i	−0.000120872	+	0.000209357i
$738$	4.72014	+	12.0789i	0.173751	+	0.444631i
$739$	−25.7194	−	44.5473i	−0.946104	−	1.63870i	−0.753526	−	0.657418i	$-0.771648\pi$
$739$	−25.7194	−	44.5473i	−0.946104	−	1.63870i	−0.192578	−	0.981282i	$-0.561685\pi$
$740$	−9.42862	−	2.93874i	−0.346603	−	0.108030i
$741$	3.07363	−	9.58459i	0.112913	−	0.352099i
$742$	2.49706	−	16.4032i	0.0916701	−	0.602181i
$743$	−39.0799	+	22.5628i	−1.43370	+	0.827748i	−0.997401	−	0.0720525i	$-0.977045\pi$
$743$	−39.0799	+	22.5628i	−1.43370	+	0.827748i	−0.436301	+	0.899801i	$0.643712\pi$
$744$	13.5068	−	0.952288i	0.495184	−	0.0349126i
$745$	1.82334	−	3.15812i	0.0668020	−	0.115705i
$746$	23.3262	+	3.55095i	0.854032	+	0.130009i
$747$	−11.2778	+	19.5336i	−0.412632	+	0.714699i
$748$	0.204966	−	0.189062i	0.00749431	−	0.00691279i
$749$	−8.50871			−0.310901
$750$	−2.30594	+	2.88285i	−0.0842010	+	0.105267i
$751$	−1.59624	−	2.76477i	−0.0582477	−	0.100888i	0.835431	−	0.549595i	$-0.185218\pi$
$751$	−1.59624	−	2.76477i	−0.0582477	−	0.100888i	−0.893679	+	0.448707i	$0.851885\pi$
$752$	−26.2983	−	2.12643i	−0.959002	−	0.0775431i
$753$	−15.0030			−0.546740
$754$	−34.7131	+	23.0319i	−1.26417	+	0.838773i
$755$			7.05704i			0.256832i
$756$	1.33628	+	5.93503i	0.0485999	+	0.215855i
$757$	3.50546	−	2.02388i	0.127408	−	0.0735591i	−0.434941	−	0.900459i	$-0.643231\pi$
$757$	3.50546	−	2.02388i	0.127408	−	0.0735591i	0.562349	+	0.826900i	$0.309898\pi$
$758$	17.4500	+	13.9580i	0.633813	+	0.506976i
$759$		−	0.0398440i		−	0.00144625i
$760$	4.18064	+	6.19038i	0.151648	+	0.224549i
$761$	−6.73194	−	3.88669i	−0.244033	−	0.140892i	0.372996	−	0.927833i	$-0.378330\pi$
$761$	−6.73194	−	3.88669i	−0.244033	−	0.140892i	−0.617029	+	0.786941i	$0.711664\pi$
$762$	−7.66678	−	1.16712i	−0.277738	−	0.0422801i
$763$	7.50956	+	4.33565i	0.271864	+	0.156961i
$764$	−9.46190	−	42.0247i	−0.342319	−	1.52040i
$765$	1.74594	+	3.02406i	0.0631247	+	0.109335i
$766$	36.0583	+	5.48917i	1.30284	+	0.198332i
$767$	−1.62174	+	1.47152i	−0.0585576	+	0.0531336i
$768$	7.96071	−	3.01675i	0.287257	−	0.108858i
$769$	33.4501	−	19.3124i	1.20624	−	0.696423i	0.244305	−	0.969699i	$-0.421440\pi$
$769$	33.4501	−	19.3124i	1.20624	−	0.696423i	0.961936	+	0.273275i	$0.0881070\pi$
$770$	0.0141478	+	0.0362046i	0.000509853	+	0.00130472i
$771$	−6.65640	−	3.84308i	−0.239724	−	0.138405i
$772$	−4.08807	+	13.1161i	−0.147133	+	0.472059i
$773$	−2.09096	+	3.62164i	−0.0752065	+	0.130261i	−0.901176	−	0.433453i	$-0.857295\pi$
$773$	−2.09096	+	3.62164i	−0.0752065	+	0.130261i	0.825970	+	0.563715i	$0.190628\pi$
$774$	−13.4237	+	16.7821i	−0.482504	+	0.603219i
$775$		−	42.7071i		−	1.53408i
$776$	17.2450	−	11.6463i	0.619058	−	0.418077i
$777$	−2.60982	−	4.52035i	−0.0936269	−	0.162167i
$778$	1.44527	+	3.69848i	0.0518156	+	0.132597i
$779$			17.7087i			0.634479i
$780$	1.11028	−	1.58026i	0.0397544	−	0.0565824i
$781$			0.207892i			0.00743898i
$782$	−4.61240	+	1.80241i	−0.164939	+	0.0644541i
$783$	12.4257	+	21.5220i	0.444059	+	0.769134i
$784$	3.61402	−	1.71430i	0.129072	−	0.0612252i
$785$			11.6249i			0.414910i
$786$	11.2270	+	8.98024i	0.400452	+	0.320315i
$787$	3.98138	−	6.89596i	0.141921	−	0.245814i	−0.786299	−	0.617846i	$-0.788005\pi$
$787$	3.98138	−	6.89596i	0.141921	−	0.245814i	0.928220	+	0.372032i	$0.121339\pi$
$788$	46.7838	+	14.5817i	1.66660	+	0.519453i
$789$	−4.56394	−	2.63499i	−0.162481	−	0.0938082i
$790$	7.65302	−	2.99061i	0.272282	−	0.106401i
$791$	0.481821	−	0.278179i	0.0171316	−	0.00989092i
$792$	0.183729	−	0.377250i	0.00652852	−	0.0134050i
$793$	24.6088	+	27.1210i	0.873886	+	0.963095i
$794$	1.96377	−	12.9000i	0.0696916	−	0.457804i
$795$	1.57112	+	2.72125i	0.0557217	+	0.0965128i
$796$	−8.55781	−	38.0092i	−0.303323	−	1.34720i
$797$	4.53112	+	2.61604i	0.160501	+	0.0926650i	0.578099	−	0.815967i	$-0.303795\pi$
$797$	4.53112	+	2.61604i	0.160501	+	0.0926650i	−0.417598	+	0.908632i	$0.637128\pi$
$798$	−0.594154	+	3.90300i	−0.0210328	+	0.138165i
$799$	−14.5855	−	8.42095i	−0.515998	−	0.297912i
$800$	−7.72558	−	25.7156i	−0.273140	−	0.909183i
$801$			2.28053i			0.0805785i
$802$	−10.3512	+	12.9409i	−0.365515	+	0.456961i
$803$	−0.341943	+	0.197421i	−0.0120669	+	0.00696682i
$804$	−0.124774	+	0.0280929i	−0.00440043	+	0.000990762i
$805$		−	0.690309i		−	0.0243302i
$806$	2.85194	+	45.7889i	0.100455	+	1.61285i
$807$	−8.17638			−0.287822
$808$	−2.18474	−	30.9874i	−0.0768589	−	1.09013i
$809$	−16.3646	−	28.3443i	−0.575348	−	0.996532i	−0.996004	−	0.0893114i	$-0.971533\pi$
$809$	−16.3646	−	28.3443i	−0.575348	−	0.996532i	0.420656	−	0.907220i	$-0.361800\pi$
$810$	3.63128	+	2.90460i	0.127590	+	0.102057i
$811$	18.8176			0.660774			0.330387	−	0.943846i	$-0.392821\pi$
$811$	18.8176			0.660774			0.330387	+	0.943846i	$0.392821\pi$
$812$	12.0107	−	11.0787i	0.421492	−	0.388787i
$813$	−7.70323	+	13.3424i	−0.270164	+	0.467938i
$814$	−0.114009	+	0.748928i	−0.00399603	+	0.0262499i
$815$	4.89675	−	8.48143i	0.171526	−	0.297091i
$816$	5.41655	+	0.437971i	0.189617	+	0.0153321i
$817$	−25.4139	+	14.6727i	−0.889121	+	0.513334i
$818$	44.8056	+	6.82077i	1.56659	+	0.238482i
$819$	−9.57398	+	2.07342i	−0.334542	+	0.0724511i
$820$	−1.01109	+	3.24396i	−0.0353087	+	0.113284i
$821$	3.42168	+	5.92653i	0.119418	+	0.206837i	0.919537	−	0.393003i	$-0.128564\pi$
$821$	3.42168	+	5.92653i	0.119418	+	0.206837i	−0.800119	+	0.599841i	$0.795231\pi$
$822$	11.4485	−	4.47378i	0.399312	−	0.156041i
$823$	1.91909	−	3.32396i	0.0668953	−	0.115866i	−0.830638	−	0.556813i	$-0.812024\pi$
$823$	1.91909	−	3.32396i	0.0668953	−	0.115866i	0.897533	+	0.440947i	$0.145357\pi$
$824$	12.2899	−	25.2349i	0.428141	−	0.879100i
$825$	0.119430	+	0.0689531i	0.00415803	+	0.00240064i
$826$	0.536519	−	0.670748i	0.0186679	−	0.0233383i
$827$	−55.5607			−1.93204			−0.966018	−	0.258476i	$-0.916780\pi$
$827$	−55.5607			−1.93204			−0.966018	+	0.258476i	$0.916780\pi$
$828$	−5.47752	+	5.05250i	−0.190357	+	0.175586i
$829$	2.87809	−	1.66167i	0.0999603	−	0.0577121i	−0.449187	−	0.893438i	$-0.648286\pi$
$829$	2.87809	−	1.66167i	0.0999603	−	0.0577121i	0.549147	+	0.835726i	$0.314953\pi$
$830$	−5.50445	+	2.15100i	−0.191062	+	0.0746624i
$831$	10.0296			0.347924
$832$	10.0003	+	27.0554i	0.346700	+	0.937976i
$833$	2.55333			0.0884677
$834$	1.03785	−	0.405565i	0.0359377	−	0.0140436i
$835$	1.85198	−	1.06924i	0.0640905	−	0.0370027i
$836$	0.421175	−	0.388494i	0.0145666	−	0.0134364i
$837$	27.3681			0.945981
$838$	30.1291	−	37.6669i	1.04079	−	1.30118i
$839$	1.14859	+	0.663140i	0.0396538	+	0.0228941i	0.519696	−	0.854351i	$-0.326045\pi$
$839$	1.14859	+	0.663140i	0.0396538	+	0.0228941i	−0.480042	+	0.877245i	$0.659379\pi$
$840$	−0.331684	+	0.681046i	−0.0114442	+	0.0234983i
$841$	18.8743	−	32.6913i	0.650839	−	1.12729i
$842$	−33.0767	+	12.9255i	−1.13990	+	0.445444i
$843$	2.65353	+	4.59605i	0.0913925	+	0.158296i
$844$	0.860998	−	2.76241i	0.0296368	−	0.0950862i
$845$	5.32330	+	3.80557i	0.183127	+	0.130915i
$846$	−25.0552	−	3.81415i	−0.861415	−	0.131133i
$847$	−9.52370	+	5.49851i	−0.327238	+	0.188931i
$848$	−46.7771	−	3.78231i	−1.60633	−	0.129885i
$849$	−1.82646	+	3.16353i	−0.0626841	+	0.108572i
$850$	2.57949	−	16.9447i	0.0884757	−	0.581197i
$851$	6.72675	−	11.6511i	0.230590	−	0.399394i
$852$	−2.97801	+	2.74694i	−0.102025	+	0.0941085i
$853$	−14.1217			−0.483518			−0.241759	−	0.970336i	$-0.577724\pi$
$853$	−14.1217			−0.483518			−0.241759	+	0.970336i	$0.577724\pi$
$854$	−11.2172	−	8.97243i	−0.383844	−	0.307030i
$855$	3.58765	+	6.21400i	0.122695	+	0.212514i
$856$	1.69257	+	24.0067i	0.0578509	+	0.820531i
$857$	−44.6183			−1.52413			−0.762067	−	0.647498i	$-0.775815\pi$
$857$	−44.6183			−1.52413			−0.762067	+	0.647498i	$0.775815\pi$
$858$	−0.132653	−	0.0659535i	−0.00452871	−	0.00225162i
$859$		−	33.7518i		−	1.15160i	−0.817592	−	0.575798i	$-0.804692\pi$
$859$		−	33.7518i		−	1.15160i	0.817592	−	0.575798i	$-0.195308\pi$
$860$	−5.49320	+	1.23680i	−0.187316	+	0.0421745i
$861$	−1.55525	+	0.897922i	−0.0530027	+	0.0306011i
$862$	15.3070	−	19.1366i	0.521359	−	0.651795i
$863$			29.1278i			0.991521i	0.868459	+	0.495761i	$0.165111\pi$
$863$			29.1278i			0.991521i	−0.868459	+	0.495761i	$0.834889\pi$
$864$	16.4794	−	4.95081i	0.560641	−	0.168430i
$865$	−4.49923	−	2.59763i	−0.152979	−	0.0883222i
$866$	2.15918	−	14.1836i	0.0733718	−	0.481979i
$867$	−4.82928	−	2.78819i	−0.164011	−	0.0946918i
$868$	−3.95258	−	17.5552i	−0.134159	−	0.595863i
$869$	−0.315135	−	0.545829i	−0.0106902	−	0.0185160i
$870$	−0.465706	+	3.05922i	−0.0157889	+	0.103717i
$871$	−0.0917222	−	0.423526i	−0.00310789	−	0.0143506i
$872$	10.7389	−	22.0501i	0.363664	−	0.746711i
$873$	17.3107	−	9.99436i	0.585879	−	0.338258i
$874$	−9.47780	+	3.70369i	−0.320591	+	0.125279i
$875$	4.24878	+	2.45303i	0.143635	+	0.0829277i
$876$	−7.34619	−	2.28968i	−0.248205	−	0.0773612i
$877$	−0.647947	+	1.12228i	−0.0218796	+	0.0378966i	−0.876758	−	0.480932i	$-0.840298\pi$
$877$	−0.647947	+	1.12228i	−0.0218796	+	0.0378966i	0.854878	+	0.518829i	$0.173632\pi$
$878$	−10.6331	−	8.50521i	−0.358849	−	0.287037i
$879$			13.0417i			0.439884i
$880$	0.0993342	−	0.0471190i	0.00334855	−	0.00158838i
$881$	6.58921	+	11.4128i	0.221996	+	0.384508i	0.955414	−	0.295270i	$-0.0954095\pi$
$881$	6.58921	+	11.4128i	0.221996	+	0.384508i	−0.733418	+	0.679778i	$0.762076\pi$
$882$	3.57873	−	1.39848i	0.120502	−	0.0470893i
$883$		−	28.9841i		−	0.975392i	−0.873014	−	0.487696i	$-0.837837\pi$
$883$		−	28.9841i		−	0.975392i	0.873014	−	0.487696i	$-0.162163\pi$
$884$	−1.63408	+	18.3397i	−0.0549601	+	0.616830i
$885$			0.162664i			0.00546788i
$886$	−2.40959	−	6.16620i	−0.0809519	−	0.207157i
$887$	−8.45230	−	14.6398i	−0.283801	−	0.491557i	0.688517	−	0.725220i	$-0.258262\pi$
$887$	−8.45230	−	14.6398i	−0.283801	−	0.491557i	−0.972318	+	0.233663i	$0.924929\pi$
$888$	−12.2347	+	8.26262i	−0.410568	+	0.277275i
$889$			10.3063i			0.345662i
$890$	−0.373238	+	0.466616i	−0.0125110	+	0.0156410i
$891$	0.178345	−	0.308903i	0.00597478	−	0.0103486i
$892$	−2.28445	+	7.32938i	−0.0764889	+	0.245406i
$893$	−29.9710	−	17.3038i	−1.00294	−	0.579049i
$894$	−1.98414	−	5.07744i	−0.0663594	−	0.169815i
$895$	−1.75066	+	1.01074i	−0.0585180	+	0.0337854i
$896$	−5.55569	−	9.85567i	−0.185603	−	0.329255i
$897$	1.76791	+	1.94838i	0.0590287	+	0.0650546i
$898$	6.54984	+	0.997083i	0.218571	+	0.0332731i
$899$	−36.7541	−	63.6600i	−1.22582	−	2.12318i
$900$	−5.66532	−	25.1623i	−0.188844	−	0.838744i
$901$	−25.9434	−	14.9784i	−0.864299	−	0.499004i
$902$	0.257672	+	0.0392255i	0.00857954	+	0.00130606i
$903$	−2.57724	−	1.48797i	−0.0857651	−	0.0495165i
$904$	−0.880707	−	1.30408i	−0.0292919	−	0.0433732i
$905$			4.65367i			0.154693i
$906$	8.23819	+	6.58958i	0.273695	+	0.218924i
$907$	−20.1526	+	11.6351i	−0.669157	+	0.386338i	−0.795757	−	0.605616i	$-0.792927\pi$
$907$	−20.1526	+	11.6351i	−0.669157	+	0.386338i	0.126600	+	0.991954i	$0.459593\pi$
$908$	8.63158	+	38.3369i	0.286449	+	1.27225i
$909$		−	29.8394i		−	0.989710i
$910$	−2.29826	−	1.14266i	−0.0761865	−	0.0378789i
$911$	44.0432			1.45922			0.729608	−	0.683866i	$-0.239703\pi$
$911$	44.0432			1.45922			0.729608	+	0.683866i	$0.239703\pi$
$912$	11.1302	+	0.899966i	0.368558	+	0.0298009i
$913$	0.226661	+	0.392589i	0.00750140	+	0.0129928i
$914$	5.07987	−	6.35078i	0.168027	−	0.210065i
$915$	2.72029			0.0899300
$916$	−19.9299	+	18.3834i	−0.658502	+	0.607406i
$917$	9.55309	−	16.5464i	0.315471	−	0.546411i
$918$	10.8587	+	1.65302i	0.358391	+	0.0545579i
$919$	−4.02391	+	6.96962i	−0.132737	+	0.229907i	−0.924731	−	0.380622i	$-0.875710\pi$
$919$	−4.02391	+	6.96962i	−0.132737	+	0.229907i	0.791994	+	0.610529i	$0.209043\pi$
$920$	−1.94765	+	0.137318i	−0.0642122	+	0.00452723i
$921$	−11.4187	+	6.59258i	−0.376258	+	0.217233i
$922$	5.64044	−	37.0521i	0.185758	−	1.22024i
$923$	−9.22434	−	10.1660i	−0.303623	−	0.334618i
$924$	0.0554749	+	0.0172906i	0.00182499	+	0.000568819i
$925$	23.2823	+	40.3262i	0.765518	+	1.32592i
$926$	8.40703	+	21.5137i	0.276272	+	0.706985i
$927$	13.4809	−	23.3496i	0.442771	−	0.766901i
$928$	−33.6470	−	31.6834i	−1.10452	−	1.04006i
$929$	−36.2832	−	20.9481i	−1.19041	−	0.687285i	−0.232012	−	0.972713i	$-0.574531\pi$
$929$	−36.2832	−	20.9481i	−1.19041	−	0.687285i	−0.958400	+	0.285428i	$0.907864\pi$
$930$	2.66123	+	2.12867i	0.0872651	+	0.0698018i
$931$	5.24672			0.171954
$932$	−42.8137	+	39.4916i	−1.40241	+	1.29359i
$933$	8.94811	−	5.16619i	0.292948	−	0.169134i
$934$	3.27045	+	8.36913i	0.107012	+	0.273846i
$935$	0.0701803			0.00229514
$936$	7.75447	+	26.5998i	0.253463	+	0.869441i
$937$	−23.6005			−0.770995			−0.385498	−	0.922709i	$-0.625970\pi$
$937$	−23.6005			−0.770995			−0.385498	+	0.922709i	$0.625970\pi$
$938$	0.0618648	+	0.158313i	0.00201996	+	0.00516911i
$939$	0.368506	−	0.212757i	0.0120257	−	0.00694307i
$940$	−4.50227	−	4.88101i	−0.146848	−	0.159201i
$941$	11.6270			0.379028			0.189514	−	0.981878i	$-0.439309\pi$
$941$	11.6270			0.379028			0.189514	+	0.981878i	$0.439309\pi$
$942$	13.5706	+	10.8549i	0.442153	+	0.353670i
$943$	−4.00860	−	2.31437i	−0.130538	−	0.0753662i
$944$	−1.99919	−	1.38032i	−0.0650681	−	0.0449256i
$945$	−0.765561	+	1.32599i	−0.0249037	+	0.0431345i
$946$	0.157204	+	0.402289i	0.00511116	+	0.0130795i
$947$	11.8585	+	20.5394i	0.385348	+	0.667442i	0.991817	−	0.127664i	$-0.0407481\pi$
$947$	11.8585	+	20.5394i	0.385348	+	0.667442i	−0.606469	+	0.795107i	$0.707415\pi$
$948$	3.65493	−	11.7264i	0.118707	−	0.380856i
$949$	7.96138	−	24.8262i	0.258437	−	0.805892i
$950$	5.30046	−	34.8187i	0.171970	−	1.12967i
$951$	−1.85454	+	1.07072i	−0.0601376	+	0.0347204i
$952$	−0.507915	−	7.20403i	−0.0164616	−	0.233484i
$953$	−3.80024	+	6.58221i	−0.123102	+	0.213219i	−0.920989	−	0.389588i	$-0.872617\pi$
$953$	−3.80024	+	6.58221i	−0.123102	+	0.213219i	0.797888	+	0.602806i	$0.205951\pi$
$954$	−44.5659	−	6.78427i	−1.44287	−	0.219649i
$955$	5.42078	−	9.38906i	0.175412	−	0.303823i
$956$	12.3221	+	13.3587i	0.398526	+	0.432051i
$957$	0.237367			0.00767298
$958$	−11.2645	+	14.0827i	−0.363939	+	0.454991i
$959$	−8.16756	−	14.1466i	−0.263744	−	0.456818i
$960$	1.98750	+	0.800345i	0.0641462	+	0.0258310i
$961$	−49.9522			−1.61136
$962$	−27.6554	−	41.6814i	−0.891645	−	1.34386i
$963$			23.1173i			0.744945i
$964$	46.7115	−	10.5171i	1.50448	−	0.338734i
$965$	−2.99445	+	1.72885i	−0.0963947	+	0.0556535i
$966$	−0.805846	−	0.644582i	−0.0259277	−	0.0207391i
$967$			31.8272i			1.02349i	0.859136	+	0.511747i	$0.171002\pi$
$967$			31.8272i			1.02349i	−0.859136	+	0.511747i	$0.828998\pi$
$968$	17.4081	+	25.7766i	0.559517	+	0.828491i
$969$	6.17299	+	3.56398i	0.198305	+	0.114491i
$970$	5.17763	+	0.788191i	0.166244	+	0.0253073i
$971$	17.8057	+	10.2801i	0.571411	+	0.329904i	0.757713	−	0.652588i	$-0.226317\pi$
$971$	17.8057	+	10.2801i	0.571411	+	0.329904i	−0.186302	+	0.982493i	$0.559650\pi$
$972$	24.5866	−	5.53569i	0.788615	−	0.177557i
$973$	−0.740419	−	1.28244i	−0.0237368	−	0.0411133i
$974$	45.5794	+	6.93856i	1.46046	+	0.222326i
$975$	−8.89967	+	1.92739i	−0.285018	+	0.0617258i
$976$	−23.0837	+	33.4333i	−0.738890	+	1.07017i
$977$	11.5310	−	6.65743i	0.368909	−	0.212990i	−0.304073	−	0.952649i	$-0.598347\pi$
$977$	11.5310	−	6.65743i	0.368909	−	0.212990i	0.672982	+	0.739659i	$0.265013\pi$
$978$	−5.32858	−	13.6359i	−0.170389	−	0.436029i
$979$	0.0396937	+	0.0229172i	0.00126862	+	0.000732435i
$980$	0.961118	+	0.299565i	0.0307018	+	0.00956924i
$981$	11.7795	−	20.4027i	0.376091	−	0.651409i
$982$	15.7501	−	19.6906i	0.502607	−	0.628351i
$983$			10.0970i			0.322045i	0.986951	+	0.161022i	$0.0514791\pi$
$983$			10.0970i			0.322045i	−0.986951	+	0.161022i	$0.948521\pi$
$984$	2.84279	+	4.20939i	0.0906249	+	0.134191i
$985$	6.16662	+	10.6809i	0.196485	+	0.340322i
$986$	−10.7377	−	27.4780i	−0.341958	−	0.875077i
$987$		−	3.50957i		−	0.111711i
$988$	−3.35779	+	37.6853i	−0.106826	+	1.19893i
$989$		−	7.67040i		−	0.243904i
$990$	0.0983642	−	0.0384383i	0.00312622	−	0.00122165i
$991$	11.6485	+	20.1758i	0.370026	+	0.640904i	0.989569	−	0.144058i	$-0.0460153\pi$
$991$	11.6485	+	20.1758i	0.370026	+	0.640904i	−0.619543	+	0.784963i	$0.712682\pi$
$992$	−48.7445	+	14.6440i	−1.54764	+	0.464948i
$993$		−	1.03163i		−	0.0327377i
$994$	4.20463	+	3.36321i	0.133363	+	0.106675i
$995$	4.90282	−	8.49193i	0.155430	−	0.269212i
$996$	−2.62882	+	8.43426i	−0.0832973	+	0.267250i
$997$	13.4272	+	7.75219i	0.425243	+	0.245514i	0.697318	−	0.716762i	$-0.254376\pi$
$997$	13.4272	+	7.75219i	0.425243	+	0.245514i	−0.272075	+	0.962276i	$0.587710\pi$
$998$	12.2601	−	4.79094i	0.388086	−	0.151654i
$999$	−25.8424	+	14.9201i	−0.817617	+	0.472051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.cz.a.309.10	✓	168
8.5	even	2	inner	728.2.cz.a.309.19	yes	168
13.4	even	6	inner	728.2.cz.a.589.19	yes	168
104.69	even	6	inner	728.2.cz.a.589.10	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.cz.a.309.10	✓	168	1.1	even	1	trivial
728.2.cz.a.309.19	yes	168	8.5	even	2	inner
728.2.cz.a.589.10	yes	168	104.69	even	6	inner
728.2.cz.a.589.19	yes	168	13.4	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31721 + 0.514734i) q^{2} +(-0.460788 + 0.266036i) q^{3} +(1.47010 - 1.35603i) q^{4} +0.503361 q^{5} +(0.470018 - 0.587609i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-1.23844 + 2.54289i) q^{8} +(-1.35845 + 2.35290i) q^{9} +(-0.663033 + 0.259097i) q^{10} +(0.0273023 + 0.0472889i) q^{11} +(-0.316651 + 1.01594i) q^{12} +(-3.43333 - 1.10102i) q^{13} +(1.39811 + 0.212834i) q^{14} +(-0.231942 + 0.133912i) q^{15} +(0.322380 - 3.98699i) q^{16} +(1.27667 - 2.21125i) q^{17} +(0.578249 - 3.79852i) q^{18} +(2.62336 - 4.54379i) q^{19} +(0.739990 - 0.682571i) q^{20} +0.532072 q^{21} +(-0.0603041 - 0.0482361i) q^{22} +(0.685700 + 1.18767i) q^{23} +(-0.105841 - 1.50120i) q^{24} -4.74663 q^{25} +(5.08916 - 0.316976i) q^{26} -3.04180i q^{27} +(-1.95116 + 0.439305i) q^{28} +(-7.07541 + 4.08499i) q^{29} +(0.236588 - 0.295779i) q^{30} +8.99735i q^{31} +(1.62759 + 5.41765i) q^{32} +(-0.0251611 - 0.0145268i) q^{33} +(-0.543436 + 3.56983i) q^{34} +(-0.435923 - 0.251680i) q^{35} +(1.19355 + 5.30110i) q^{36} +(-4.90502 - 8.49575i) q^{37} +(-1.11668 + 7.33547i) q^{38} +(1.87495 - 0.406054i) q^{39} +(-0.623382 + 1.27999i) q^{40} +(-2.92300 + 1.68760i) q^{41} +(-0.700852 + 0.273875i) q^{42} +(-4.84378 - 2.79656i) q^{43} +(0.104262 + 0.0324967i) q^{44} +(-0.683790 + 1.18436i) q^{45} +(-1.51454 - 1.21146i) q^{46} -6.59604i q^{47} +(0.912133 + 1.92292i) q^{48} +(0.500000 + 0.866025i) q^{49} +(6.25232 - 2.44325i) q^{50} +1.35856i q^{51} +(-6.54035 + 3.03709i) q^{52} -11.7324i q^{53} +(1.56572 + 4.00670i) q^{54} +(0.0137429 + 0.0238034i) q^{55} +(2.34396 - 1.58298i) q^{56} +2.79163i q^{57} +(7.21714 - 9.02276i) q^{58} +(0.303677 - 0.525983i) q^{59} +(-0.159390 + 0.511384i) q^{60} +(-8.79623 - 5.07851i) q^{61} +(-4.63124 - 11.8514i) q^{62} +(2.35290 - 1.35845i) q^{63} +(-4.93253 - 6.29842i) q^{64} +(-1.72820 - 0.554209i) q^{65} +(0.0406199 + 0.00618358i) q^{66} +(0.0600940 + 0.104086i) q^{67} +(-1.12169 - 4.98195i) q^{68} +(-0.631924 - 0.364842i) q^{69} +(0.703752 + 0.107132i) q^{70} +(3.29717 + 1.90362i) q^{71} +(-4.30081 - 6.36831i) q^{72} +7.23093i q^{73} +(10.8340 + 8.66593i) q^{74} +(2.18719 - 1.26277i) q^{75} +(-2.30491 - 10.2372i) q^{76} -0.0546045i q^{77} +(-2.26069 + 1.49996i) q^{78} -11.5424 q^{79} +(0.162273 - 2.00689i) q^{80} +(-3.26612 - 5.65709i) q^{81} +(2.98155 - 3.72749i) q^{82} +8.30193 q^{83} +(0.782198 - 0.721504i) q^{84} +(0.642623 - 1.11306i) q^{85} +(7.81977 + 1.19041i) q^{86} +(2.17351 - 3.76463i) q^{87} +(-0.154062 + 0.0108621i) q^{88} +(0.726930 - 0.419693i) q^{89} +(0.291068 - 1.91202i) q^{90} +(2.42284 + 2.67017i) q^{91} +(2.61856 + 0.816160i) q^{92} +(-2.39362 - 4.14587i) q^{93} +(3.39521 + 8.68839i) q^{94} +(1.32050 - 2.28716i) q^{95} +(-2.19126 - 2.06339i) q^{96} +(-6.37150 - 3.67859i) q^{97} +(-1.10438 - 0.883373i) q^{98} -0.148355 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 18 q^{6} + 84 q^{9} - 8 q^{10} - 4 q^{12} + 8 q^{16} + 4 q^{17} - 18 q^{22} + 24 q^{23} + 48 q^{24} + 160 q^{25} - 30 q^{26} - 8 q^{30} + 22 q^{36} - 20 q^{38} - 48 q^{39} + 4 q^{40} + 12 q^{41}+ \cdots - 104 q^{95}+O(q^{100}) \) 168 * q - 18 * q^6 + 84 * q^9 - 8 * q^10 - 4 * q^12 + 8 * q^16 + 4 * q^17 - 18 * q^22 + 24 * q^23 + 48 * q^24 + 160 * q^25 - 30 * q^26 - 8 * q^30 + 22 * q^36 - 20 * q^38 - 48 * q^39 + 4 * q^40 + 12 * q^41 - 54 * q^48 + 84 * q^49 - 30 * q^50 - 58 * q^52 + 24 * q^54 - 32 * q^55 - 12 * q^58 + 28 * q^62 - 36 * q^64 + 12 * q^65 - 60 * q^66 - 64 * q^68 - 132 * q^72 + 62 * q^74 - 78 * q^76 + 30 * q^78 - 80 * q^79 + 48 * q^80 - 84 * q^81 - 18 * q^82 - 42 * q^84 - 24 * q^87 + 42 * q^88 + 40 * q^90 - 24 * q^92 + 12 * q^94 - 104 * q^95

Introduction

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