LMFDB - Embedded newform 728.2.cz.a.309.19

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			309.19
Character	$\chi$	$=$	728.309
Dual form			728.2.cz.a.589.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.10438 + 0.883373i) q^{2} +(0.460788 - 0.266036i) q^{3} +(0.439305 - 1.95116i) q^{4} -0.503361 q^{5} +(-0.273875 + 0.700852i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(1.23844 + 2.54289i) q^{8} +(-1.35845 + 2.35290i) q^{9} +(0.555901 - 0.444655i) 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} +(-3.61402 - 1.71430i) q^{16} +(1.27667 - 2.21125i) q^{17} +(-0.578249 - 3.79852i) q^{18} +(-2.62336 + 4.54379i) q^{19} +(-0.221129 + 0.982135i) q^{20} -0.532072 q^{21} +(0.0719258 + 0.0281068i) q^{22} +(0.685700 + 1.18767i) q^{23} +(1.24716 + 0.842261i) q^{24} -4.74663 q^{25} +(-4.76431 + 1.81697i) q^{26} +3.04180i q^{27} +(-1.35603 + 1.47010i) q^{28} +(7.07541 - 4.08499i) q^{29} +(0.137858 - 0.352781i) q^{30} +8.99735i q^{31} +(5.50562 - 1.29929i) q^{32} +(-0.0251611 - 0.0145268i) q^{33} +(0.543436 + 3.56983i) q^{34} +(0.435923 + 0.251680i) q^{35} +(3.99411 + 3.68419i) 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} +(0.587609 - 0.470018i) q^{42} +(4.84378 + 2.79656i) q^{43} +(-0.104262 + 0.0324967i) q^{44} +(0.683790 - 1.18436i) q^{45} +(-1.80643 - 0.705906i) q^{46} -6.59604i q^{47} +(-2.12136 + 0.171529i) q^{48} +(0.500000 + 0.866025i) q^{49} +(5.24208 - 4.19304i) q^{50} -1.35856i q^{51} +(3.65654 - 6.21528i) q^{52} +11.7324i q^{53} +(-2.68704 - 3.35930i) q^{54} +(0.0137429 + 0.0238034i) q^{55} +(0.198922 - 2.82142i) q^{56} +2.79163i q^{57} +(-4.20537 + 10.7616i) q^{58} +(-0.303677 + 0.525983i) q^{59} +(0.159390 + 0.511384i) q^{60} +(8.79623 + 5.07851i) q^{61} +(-7.94801 - 9.93648i) 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} +(-3.75365 - 3.46239i) q^{68} +(0.631924 + 0.364842i) q^{69} +(-0.703752 + 0.107132i) q^{70} +(3.29717 + 1.90362i) q^{71} +(-7.66552 - 0.540452i) q^{72} +7.23093i q^{73} +(-12.9219 - 5.04956i) q^{74} +(-2.18719 + 1.26277i) q^{75} +(7.71319 + 7.11469i) q^{76} +0.0546045i q^{77} +(-1.71195 + 2.10471i) q^{78} -11.5424 q^{79} +(1.81916 + 0.862913i) q^{80} +(-3.26612 - 5.65709i) q^{81} +(1.73732 - 4.44585i) q^{82} -8.30193 q^{83} +(-0.233742 + 1.03816i) q^{84} +(-0.642623 + 1.11306i) q^{85} +(-7.81977 + 1.19041i) q^{86} +(2.17351 - 3.76463i) q^{87} +(0.0864380 - 0.127991i) 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} +(5.82677 + 7.28453i) q^{94} +(1.32050 - 2.28716i) q^{95} +(2.19126 - 2.06339i) q^{96} +(-6.37150 - 3.67859i) q^{97} +(-1.31721 - 0.514734i) 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 $

$2$	−1.10438	+	0.883373i	−0.780914	+	0.624639i
$2$	−1.10438	+	0.883373i	−0.780914	+	0.624639i
$3$	0.460788	−	0.266036i	0.266036	−	0.153596i	−0.361049	−	0.932547i	$-0.617581\pi$
$3$	0.460788	−	0.266036i	0.266036	−	0.153596i	0.627085	+	0.778951i	$0.284248\pi$
$4$	0.439305	−	1.95116i	0.219652	−	0.975578i
$5$	−0.503361			−0.225110			−0.112555	−	0.993646i	$-0.535903\pi$
$5$	−0.503361			−0.225110			−0.112555	+	0.993646i	$0.535903\pi$
$6$	−0.273875	+	0.700852i	−0.111809	+	0.286121i
$7$	−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
$10$	0.555901	−	0.444655i	0.175791	−	0.140612i
$11$	−0.0273023	−	0.0472889i	−0.00823194	−	0.0142581i	0.861880	−	0.507112i	$-0.169287\pi$
$11$	−0.0273023	−	0.0472889i	−0.00823194	−	0.0142581i	−0.870112	+	0.492854i	$0.835954\pi$
$12$	−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
$16$	−3.61402	−	1.71430i	−0.903506	−	0.428576i
$17$	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	$0.372232\pi$
$19$	−2.62336	+	4.54379i	−0.601840	+	1.04242i	−0.992542	+	0.121900i	$0.961101\pi$
$20$	−0.221129	+	0.982135i	−0.0494459	+	0.219612i
$21$	−0.532072			−0.116108
$22$	0.0719258	+	0.0281068i	0.0153346	+	0.00599238i
$23$	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	$0.787665\pi$
$24$	1.24716	+	0.842261i	0.254575	+	0.171926i
$25$	−4.74663			−0.949326
$26$	−4.76431	+	1.81697i	−0.934357	+	0.356337i
$27$			3.04180i			0.585395i
$28$	−1.35603	+	1.47010i	−0.256265	+	0.277823i
$29$	7.07541	−	4.08499i	1.31387	−	0.758564i	0.331137	−	0.943583i	$-0.392568\pi$
$29$	7.07541	−	4.08499i	1.31387	−	0.758564i	0.982735	+	0.185019i	$0.0592346\pi$
$30$	0.137858	−	0.352781i	0.0251693	−	0.0644087i
$31$			8.99735i			1.61597i	0.589202	+	0.807986i	$0.299442\pi$
$31$			8.99735i			1.61597i	−0.589202	+	0.807986i	$0.700558\pi$
$32$	5.50562	−	1.29929i	0.973265	−	0.229684i
$33$	−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
$36$	3.99411	+	3.68419i	0.665685	+	0.614032i
$37$	4.90502	+	8.49575i	0.806381	+	1.39669i	0.915355	+	0.402648i	$0.131910\pi$
$37$	4.90502	+	8.49575i	0.806381	+	1.39669i	−0.108974	+	0.994045i	$0.534757\pi$
$38$	−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	$0.418229\pi$
$42$	0.587609	−	0.470018i	0.0906700	−	0.0725253i
$43$	4.84378	+	2.79656i	0.738670	+	0.426471i	0.821585	−	0.570085i	$-0.193090\pi$
$43$	4.84378	+	2.79656i	0.738670	+	0.426471i	−0.0829158	+	0.996557i	$0.526423\pi$
$44$	−0.104262	+	0.0324967i	−0.0157181	+	0.00489907i
$45$	0.683790	−	1.18436i	0.101933	−	0.176554i
$46$	−1.80643	−	0.705906i	−0.266343	−	0.104080i
$47$		−	6.59604i		−	0.962132i	−0.876684	−	0.481066i	$-0.840250\pi$
$47$		−	6.59604i		−	0.962132i	0.876684	−	0.481066i	$-0.159750\pi$
$48$	−2.12136	+	0.171529i	−0.306192	+	0.0247581i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	5.24208	−	4.19304i	0.741341	−	0.592986i
$51$		−	1.35856i		−	0.190236i
$52$	3.65654	−	6.21528i	0.507070	−	0.861905i
$53$			11.7324i			1.61158i	0.592204	+	0.805788i	$0.298258\pi$
$53$			11.7324i			1.61158i	−0.592204	+	0.805788i	$0.701742\pi$
$54$	−2.68704	−	3.35930i	−0.365660	−	0.457143i
$55$	0.0137429	+	0.0238034i	0.00185309	+	0.00320965i
$56$	0.198922	−	2.82142i	0.0265821	−	0.377029i
$57$			2.79163i			0.369760i
$58$	−4.20537	+	10.7616i	−0.552192	+	1.41307i
$59$	−0.303677	+	0.525983i	−0.0395353	+	0.0684772i	−0.885116	−	0.465370i	$-0.845921\pi$
$59$	−0.303677	+	0.525983i	−0.0395353	+	0.0684772i	0.845581	+	0.533848i	$0.179254\pi$
$60$	0.159390	+	0.511384i	0.0205771	+	0.0660194i
$61$	8.79623	+	5.07851i	1.12624	+	0.650236i	0.942987	−	0.332829i	$-0.108003\pi$
$61$	8.79623	+	5.07851i	1.12624	+	0.650236i	0.183255	+	0.983065i	$0.441337\pi$
$62$	−7.94801	−	9.93648i	−1.00940	−	1.26193i
$63$	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	0.862331	−	0.506345i	$-0.169004\pi$
$67$	−0.0600940	−	0.104086i	−0.00734165	−	0.0127161i	−0.869673	+	0.493628i	$0.835670\pi$
$68$	−3.75365	−	3.46239i	−0.455197	−	0.419876i
$69$	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	$0.594128\pi$
$72$	−7.66552	−	0.540452i	−0.903391	−	0.0636929i
$73$			7.23093i			0.846316i	0.906056	+	0.423158i	$0.139079\pi$
$73$			7.23093i			0.846316i	−0.906056	+	0.423158i	$0.860921\pi$
$74$	−12.9219	−	5.04956i	−1.50214	−	0.587000i
$75$	−2.18719	+	1.26277i	−0.252555	+	0.145812i
$76$	7.71319	+	7.11469i	0.884764	+	0.816111i
$77$			0.0546045i			0.00622276i
$78$	−1.71195	+	2.10471i	−0.193841	+	0.238312i
$79$	−11.5424			−1.29863			−0.649313	−	0.760521i	$-0.724943\pi$
$79$	−11.5424			−1.29863			−0.649313	+	0.760521i	$0.724943\pi$
$80$	1.81916	+	0.862913i	0.203388	+	0.0964766i
$81$	−3.26612	−	5.65709i	−0.362902	−	0.628565i
$82$	1.73732	−	4.44585i	0.191855	−	0.490962i
$83$	−8.30193			−0.911255			−0.455628	−	0.890170i	$-0.650585\pi$
$83$	−8.30193			−0.911255			−0.455628	+	0.890170i	$0.650585\pi$
$84$	−0.233742	+	1.03816i	−0.0255033	+	0.113272i
$85$	−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
$88$	0.0864380	−	0.127991i	0.00921433	−	0.0136439i
$89$	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
$94$	5.82677	+	7.28453i	0.600985	+	0.751342i
$95$	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	$0.788510\pi$
$98$	−1.31721	−	0.514734i	−0.133059	−	0.0519959i
$99$	0.148355			0.0149102
$100$	−2.08522	+	9.26141i	−0.208522	+	0.926141i
$101$	9.51146	−	5.49144i	0.946425	−	0.546419i	0.0544567	−	0.998516i	$-0.482657\pi$
$101$	9.51146	−	5.49144i	0.946425	−	0.546419i	0.891969	+	0.452097i	$0.149324\pi$
$102$	1.20011	+	1.50036i	0.118829	+	0.148558i
$103$	−9.92373			−0.977815			−0.488907	−	0.872336i	$-0.662604\pi$
$103$	−9.92373			−0.977815			−0.488907	+	0.872336i	$0.662604\pi$
$104$	1.45221	+	10.0941i	0.142401	+	0.989809i
$105$	0.267824			0.0261369
$106$	−10.3641	−	12.9571i	−1.00665	−	1.25850i
$107$	−7.36876	+	4.25435i	−0.712365	+	0.411284i	−0.811936	−	0.583746i	$-0.801586\pi$
$107$	−7.36876	+	4.25435i	−0.712365	+	0.411284i	0.0995712	+	0.995030i	$0.468253\pi$
$108$	5.93503	+	1.33628i	0.571098	+	0.128583i
$109$	8.67130			0.830560			0.415280	−	0.909694i	$-0.363684\pi$
$109$	8.67130			0.830560			0.415280	+	0.909694i	$0.363684\pi$
$110$	−0.0362046	−	0.0141478i	−0.00345197	−	0.00134894i
$111$	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	$0.174997\pi$
$114$	−2.46605	−	3.08302i	−0.230967	−	0.288751i
$115$	−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
$120$	−0.627769	−	0.423961i	−0.0573072	−	0.0387022i
$121$	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
$124$	17.5552	+	3.95258i	1.57651	+	0.354952i
$125$	4.90607			0.438812
$126$	−1.39848	+	3.57873i	−0.124586	+	0.318819i
$127$	−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	$0.984505\pi$
$128$	−0.116470	−	11.3131i	−0.0102946	−	0.999947i
$129$	2.97594			0.262017
$130$	2.39816	−	0.914591i	0.210333	−	0.0802150i
$131$		−	19.1062i		−	1.66931i	−0.550770	−	0.834657i	$-0.685666\pi$
$131$		−	19.1062i		−	1.66931i	0.550770	−	0.834657i	$-0.314334\pi$
$132$	−0.0393974	+	0.0427115i	−0.00342910	+	0.00371756i
$133$	4.54379	−	2.62336i	0.393997	−	0.227474i
$134$	0.158313	+	0.0618648i	0.0136762	+	0.00534431i
$135$		−	1.53112i		−	0.131778i
$136$	7.20403	+	0.507915i	0.617741	+	0.0435533i
$137$	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	0.444625	−	0.895717i	$-0.353337\pi$
$139$	−1.28244	−	0.740419i	−0.108775	−	0.0628015i	−0.553401	+	0.832915i	$0.686670\pi$
$140$	0.682571	−	0.739990i	0.0576878	−	0.0625405i
$141$	−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
$146$	−6.38761	−	7.98568i	−0.528642	−	0.660900i
$147$	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	−0.975391	−	0.220481i	$-0.929237\pi$
$149$	−3.62234	+	6.27407i	−0.296753	+	0.513992i	0.678638	+	0.734473i	$0.262571\pi$
$150$	1.29998	−	3.32668i	0.106143	−	0.271622i
$151$			14.0199i			1.14092i	0.821326	+	0.570460i	$0.193235\pi$
$151$			14.0199i			1.14092i	−0.821326	+	0.570460i	$0.806765\pi$
$152$	−14.8032	−	1.04369i	−1.20070	−	0.0846544i
$153$	3.46857	+	6.00775i	0.280418	+	0.485697i
$154$	−0.0482361	−	0.0603041i	−0.00388698	−	0.00485944i
$155$		−	4.52891i		−	0.363771i
$156$	0.0313985	−	3.83670i	0.00251389	−	0.307181i
$157$		−	23.0946i		−	1.84315i	−0.388203	−	0.921574i	$-0.626904\pi$
$157$		−	23.0946i		−	1.84315i	0.388203	−	0.921574i	$-0.373096\pi$
$158$	12.7472	−	10.1963i	1.01411	−	0.811172i
$159$	3.12125	+	5.40617i	0.247531	+	0.428737i
$160$	−2.77131	+	0.654011i	−0.219091	+	0.0517041i
$161$		−	1.37140i		−	0.108081i
$162$	8.60435	+	3.36236i	0.676022	+	0.264172i
$163$	−9.72812	+	16.8496i	−0.761965	+	1.31976i	0.179871	+	0.983690i	$0.442432\pi$
$163$	−9.72812	+	16.8496i	−0.761965	+	1.31976i	−0.941836	+	0.336073i	$0.890901\pi$
$164$	2.00868	+	6.44460i	0.156851	+	0.503239i
$165$	0.0126651	+	0.00731220i	0.000985976	+	0.000569254i
$166$	9.16848	−	7.33370i	0.711612	−	0.569206i
$167$	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
$172$	7.58442	−	8.22243i	0.578306	−	0.626955i
$173$	8.93839	+	5.16058i	0.679573	+	0.392352i	0.799694	−	0.600407i	$-0.204995\pi$
$173$	8.93839	+	5.16058i	0.679573	+	0.392352i	−0.120121	+	0.992759i	$0.538328\pi$
$174$	0.925193	+	6.07759i	0.0701387	+	0.460741i
$175$	4.11070	+	2.37331i	0.310740	+	0.179406i
$176$	0.0176034	+	0.217708i	0.00132691	+	0.0164103i
$177$			0.323156i			0.0242899i
$178$	−0.432061	+	1.10565i	−0.0323843	+	0.0828720i
$179$	3.47794	−	2.00799i	0.259953	−	0.150084i	−0.364360	−	0.931258i	$-0.618712\pi$
$179$	3.47794	−	2.00799i	0.259953	−	0.150084i	0.624313	+	0.781174i	$0.285379\pi$
$180$	−2.01048	−	1.85448i	−0.149852	−	0.138224i
$181$		−	9.24520i		−	0.687190i	−0.939118	−	0.343595i	$-0.888355\pi$
$181$		−	9.24520i		−	0.687190i	0.939118	−	0.343595i	$-0.111645\pi$
$182$	5.03450	+	0.808611i	0.373182	+	0.0599382i
$183$	5.40426			0.399494
$184$	−2.17090	+	3.21451i	−0.160041	+	0.236977i
$185$	−2.46900	−	4.27643i	−0.181524	−	0.314409i
$186$	−6.30580	−	2.46415i	−0.462364	−	0.180680i
$187$	−0.139423			−0.0101957
$188$	−12.8699	−	2.89767i	−0.938635	−	0.211335i
$189$	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	$-0.117723\pi$
$192$	−0.597244	+	4.21447i	−0.0431024	+	0.304153i
$193$	−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	$-0.828942\pi$
$197$	−12.2509	−	21.2192i	−0.872840	−	1.51180i	−0.0137948	−	0.999905i	$-0.504391\pi$
$198$	−0.163840	+	0.131053i	−0.0116436	+	0.00931351i
$199$	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
$202$	−5.65326	+	14.4668i	−0.397762	+	1.01788i
$203$	−8.16999			−0.573421
$204$	−2.65075	−	0.596820i	−0.185590	−	0.0417858i
$205$	1.47132	−	0.849469i	0.102762	−	0.0593295i
$206$	10.9596	−	8.76636i	0.763589	−	0.610781i
$207$	−3.72596			−0.258972
$208$	−10.5207	−	9.86488i	−0.729476	−	0.684006i
$209$	0.286494			0.0198172
$210$	−0.295779	+	0.236588i	−0.0204107	+	0.0163262i
$211$	−1.25291	+	0.723371i	−0.0862542	+	0.0497989i	−0.542507	−	0.840051i	$-0.682525\pi$
$211$	−1.25291	+	0.723371i	−0.0862542	+	0.0497989i	0.456253	+	0.889850i	$0.349191\pi$
$212$	22.8918	+	5.15412i	1.57222	+	0.353986i
$213$	2.02572			0.138800
$214$	4.37972	−	11.2078i	0.299391	−	0.766148i
$215$	−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
$218$	−9.57640	+	7.65999i	−0.648595	+	0.518800i
$219$	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	$0.374358\pi$
$224$	−5.41765	−	1.62759i	−0.361982	−	0.108748i
$225$	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	$-0.607242\pi$
$227$	9.82414	−	17.0159i	0.652051	−	1.12939i	0.982624	−	0.185605i	$-0.0594246\pi$
$228$	5.44691	+	1.22638i	0.360730	+	0.0812187i
$229$	13.5568			0.895861			0.447931	−	0.894068i	$-0.352161\pi$
$229$	13.5568			0.895861			0.447931	+	0.894068i	$0.352161\pi$
$230$	0.909283	+	0.355325i	0.0599564	+	0.0234294i
$231$	0.0145268	+	0.0251611i	0.000955790	+	0.00165548i
$232$	19.1501	+	12.9330i	1.25727	+	0.849090i
$233$	−29.1230			−1.90791			−0.953955	−	0.299950i	$-0.903030\pi$
$233$	−29.1230			−1.90791			−0.953955	+	0.299950i	$0.903030\pi$
$234$	2.19691	−	13.6782i	0.143617	−	0.894173i
$235$			3.32019i			0.216585i
$236$	0.892869	+	0.823588i	0.0581208	+	0.0536110i
$237$	−5.31861	+	3.07070i	−0.345481	+	0.199464i
$238$	1.31429	−	3.36328i	0.0851925	−	0.218009i
$239$			9.08693i			0.587784i	0.955839	+	0.293892i	$0.0949507\pi$
$239$			9.08693i			0.587784i	−0.955839	+	0.293892i	$0.905049\pi$
$240$	1.06781	−	0.0863411i	0.0689269	−	0.00557330i
$241$	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
$244$	13.7732	−	14.9318i	0.881738	−	0.955911i
$245$	−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
$250$	−5.41816	+	4.33389i	−0.342674	+	0.274099i
$251$	−24.4196	−	14.0987i	−1.54135	−	0.889901i	−0.998754	−	0.0499092i	$-0.984107\pi$
$251$	−24.4196	−	14.0987i	−1.54135	−	0.889901i	−0.542599	−	0.839992i	$-0.682560\pi$
$252$	−1.61691	−	5.18766i	−0.101856	−	0.326792i
$253$	0.0374423	−	0.0648520i	0.00235398	−	0.00407721i
$254$	13.5756	+	5.30500i	0.851808	+	0.332865i
$255$			0.683843i			0.0428239i
$256$	10.1223	+	12.3911i	0.632645	+	0.774442i
$257$	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	$0.684562\pi$
$258$	−3.28656	+	2.62886i	−0.204613	+	0.163666i
$259$		−	9.81005i		−	0.609567i
$260$	−1.84056	+	3.12853i	−0.114146	+	0.194023i
$261$			22.1970i			1.37396i
$262$	16.8779	+	21.1005i	1.04272	+	1.30359i
$263$	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	$0.734552\pi$
$264$	0.00577939	−	0.0819723i	0.000355697	−	0.00504504i
$265$		−	5.90565i		−	0.362781i
$266$	−2.70066	+	6.91104i	−0.165588	+	0.423743i
$267$	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	0.0360294	−	0.999351i	$-0.488529\pi$
$269$	−13.3083	−	7.68353i	−0.811419	−	0.468473i	−0.847448	+	0.530878i	$0.821862\pi$
$270$	1.35255	+	1.69094i	0.0823137	+	0.102907i
$271$	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
$276$	0.989470	−	1.07271i	0.0595591	−	0.0645693i
$277$	16.3247	+	9.42507i	0.980856	+	0.566297i	0.902528	−	0.430630i	$-0.141709\pi$
$277$	16.3247	+	9.42507i	0.980856	+	0.566297i	0.0783274	+	0.996928i	$0.475042\pi$
$278$	2.07037	−	0.315173i	0.124173	−	0.0189028i
$279$	−21.1699	−	12.2224i	−1.26741	−	0.731739i
$280$	−0.100130	+	1.42019i	−0.00598389	+	0.0848728i
$281$		−	9.97434i		−	0.595019i	−0.954719	−	0.297510i	$-0.903844\pi$
$281$		−	9.97434i		−	0.595019i	0.954719	−	0.297510i	$-0.0961560\pi$
$282$	4.62285	+	1.80649i	0.275287	+	0.107575i
$283$	−5.94568	+	3.43274i	−0.353434	+	0.204055i	−0.666197	−	0.745776i	$-0.732079\pi$
$283$	−5.94568	+	3.43274i	−0.353434	+	0.204055i	0.312763	+	0.949831i	$0.398746\pi$
$284$	5.16272	−	5.59702i	0.306351	−	0.332122i
$285$		−	1.40520i		−	0.0832366i
$286$	0.215999	+	0.175691i	0.0127723	+	0.0103888i
$287$	3.37519			0.199231
$288$	−4.42201	+	14.7192i	−0.260569	+	0.867338i
$289$	5.24025	+	9.07637i	0.308250	+	0.533904i
$290$	2.11682	−	5.41697i	0.124304	−	0.318095i
$291$	−3.91455			−0.229475
$292$	14.1087	+	3.17658i	0.825648	+	0.185895i
$293$	−12.2555	+	21.2272i	−0.715977	+	1.24011i	0.246605	+	0.969116i	$0.420685\pi$
$293$	−12.2555	+	21.2272i	−0.715977	+	1.24011i	−0.962582	+	0.270992i	$0.912648\pi$
$294$	−0.743893	+	0.113243i	−0.0433847	+	0.00660446i
$295$	0.152859	−	0.264759i	0.00889979	−	0.0154149i
$296$	−15.5291	+	22.9944i	−0.902613	+	1.33652i
$297$	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
$302$	−12.3848	−	15.4832i	−0.712663	−	0.890960i
$303$	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
$306$	−9.13770	−	3.57078i	−0.522367	−	0.204128i
$307$	−24.7808			−1.41431			−0.707157	−	0.707056i	$-0.750023\pi$
$307$	−24.7808			−1.41431			−0.707157	+	0.707056i	$0.750023\pi$
$308$	0.106542	+	0.0239880i	0.00607079	+	0.00136684i
$309$	−4.57273	+	2.64007i	−0.260134	+	0.150188i
$310$	4.00072	+	5.00163i	0.227225	+	0.284074i
$311$	−19.4192			−1.10116			−0.550580	−	0.834782i	$-0.685593\pi$
$311$	−19.4192			−1.10116			−0.550580	+	0.834782i	$0.685593\pi$
$312$	3.35456	+	4.26490i	0.189914	+	0.241452i
$313$	−0.799731			−0.0452035			−0.0226017	−	0.999745i	$-0.507195\pi$
$313$	−0.799731			−0.0452035			−0.0226017	+	0.999745i	$0.507195\pi$
$314$	20.4011	+	25.5052i	1.15130	+	1.43934i
$315$	−1.18436	+	0.683790i	−0.0667311	+	0.0385272i
$316$	−5.07065	+	22.5211i	−0.285246	+	1.26691i
$317$	−4.02472			−0.226051			−0.113025	−	0.993592i	$-0.536054\pi$
$317$	−4.02472			−0.226051			−0.113025	+	0.993592i	$0.536054\pi$
$318$	−8.22271	−	3.21323i	−0.461106	−	0.180189i
$319$	−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
$322$	1.21146	+	1.51454i	0.0675119	+	0.0844023i
$323$	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
$328$	−7.91133	−	5.34287i	−0.436830	−	0.295011i
$329$	−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	−0.838152	−	0.545436i	$-0.816364\pi$
$331$	0.969444	−	1.67913i	0.0532854	−	0.0922931i	0.891438	+	0.453143i	$0.149697\pi$
$332$	−3.64708	+	16.1984i	−0.200159	+	0.889001i
$333$	−26.6529			−1.46057
$334$	−2.18680	+	5.59607i	−0.119656	+	0.306203i
$335$	0.0302490	+	0.0523927i	0.00165268	+	0.00286252i
$336$	1.92292	+	0.912133i	0.104904	+	0.0497609i
$337$	−21.2705			−1.15868			−0.579340	−	0.815086i	$-0.696690\pi$
$337$	−21.2705			−1.15868			−0.579340	+	0.815086i	$0.696690\pi$
$338$	−18.3580	+	0.992675i	−0.998541	+	0.0539944i
$339$			0.296023i			0.0160778i
$340$	1.88944	+	1.74283i	0.102469	+	0.0945182i
$341$	0.425475	−	0.245648i	0.0230407	−	0.0133026i
$342$	18.7766	+	7.33743i	1.01532	+	0.396763i
$343$		−	1.00000i		−	0.0539949i
$344$	−1.11260	+	15.7805i	−0.0599871	+	0.850830i
$345$	−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	$0.100025\pi$
$347$	31.5600	+	18.2212i	1.69423	+	0.978164i	0.743197	+	0.669073i	$0.233309\pi$
$348$	−6.39055	−	5.89467i	−0.342569	−	0.315988i
$349$	1.65377	+	2.86442i	0.0885243	+	0.153329i	0.906888	−	0.421373i	$-0.138452\pi$
$349$	1.65377	+	2.86442i	0.0885243	+	0.153329i	−0.818363	+	0.574701i	$0.805118\pi$
$350$	−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	$0.230556\pi$
$354$	−0.285467	−	0.356886i	−0.0151724	−	0.0189683i
$355$	−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
$358$	−2.06716	+	5.28989i	−0.109253	+	0.279580i
$359$			17.1081i			0.902932i	0.892288	+	0.451466i	$0.149099\pi$
$359$			17.1081i			0.902932i	−0.892288	+	0.451466i	$0.850901\pi$
$360$	3.85852	+	0.272042i	0.203362	+	0.0143379i
$361$	−4.26402	−	7.38550i	−0.224422	−	0.388710i
$362$	8.16696	+	10.2102i	0.429246	+	0.536636i
$363$		−	5.85120i		−	0.307108i
$364$	−6.27429	+	3.55432i	−0.328862	+	0.186297i
$365$		−	3.63976i		−	0.190514i
$366$	−5.96835	+	4.77398i	−0.311971	+	0.249540i
$367$	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	$0.717171\pi$
$368$	−0.442112	−	5.46775i	−0.0230467	−	0.285026i
$369$		−	9.17006i		−	0.477374i
$370$	6.50438	+	2.54175i	0.338147	+	0.132139i
$371$	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	0.825019	−	0.565104i	$-0.191164\pi$
$373$	14.4489	+	8.34206i	0.748135	+	0.431936i	−0.0768849	+	0.997040i	$0.524497\pi$
$374$	0.153976	−	0.123163i	0.00796193	−	0.00636860i
$375$	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	0.994416	−	0.105531i	$-0.0336543\pi$
$379$	7.90038	+	13.6839i	0.405815	+	0.702893i	−0.588601	+	0.808424i	$0.700321\pi$
$380$	−3.88252	−	3.58126i	−0.199169	−	0.183715i
$381$	−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	$0.895655\pi$
$384$	−3.06336	−	5.18196i	−0.156326	−	0.264441i
$385$		−	0.0274858i		−	0.00140080i
$386$	3.53582	−	9.04822i	0.179968	−	0.460542i
$387$	−13.1601	+	7.59797i	−0.668964	+	0.386226i
$388$	−9.97653	+	10.8158i	−0.506482	+	0.549088i
$389$			2.80781i			0.142362i	0.997463	+	0.0711808i	$0.0226767\pi$
$389$			2.80781i			0.142362i	−0.997463	+	0.0711808i	$0.977323\pi$
$390$	0.861730	−	1.05943i	0.0436354	−	0.0536463i
$391$	3.50164			0.177086
$392$	−1.58298	+	2.34396i	−0.0799527	+	0.118388i
$393$	−5.08293	−	8.80389i	−0.256400	−	0.444097i
$394$	32.2741	+	12.6119i	1.62594	+	0.635378i
$395$	5.81001			0.292333
$396$	0.0651730	−	0.289464i	0.00327507	−	0.0145461i
$397$	4.61339	−	7.99062i	0.231539	−	0.401038i	−0.726722	−	0.686932i	$-0.758957\pi$
$397$	4.61339	−	7.99062i	0.231539	−	0.401038i	0.958261	+	0.285894i	$0.0922905\pi$
$398$	4.14608	+	27.2356i	0.207824	+	1.36520i
$399$	1.39581	−	2.41762i	0.0698781	−	0.121032i
$400$	17.1544	+	8.13717i	0.857721	+	0.406858i
$401$	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
$406$	9.02276	−	7.21714i	0.447792	−	0.358181i
$407$	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	$0.957793\pi$
$410$	−0.874501	+	2.23786i	−0.0431885	+	0.110520i
$411$	8.69145			0.428718
$412$	−4.35954	+	19.3628i	−0.214779	+	0.953935i
$413$	0.525983	−	0.303677i	0.0258820	−	0.0149430i
$414$	4.11487	−	3.29141i	0.202235	−	0.161764i
$415$	4.17886			0.205132
$416$	20.3332	+	1.60090i	0.996915	+	0.0784905i
$417$	−0.787912			−0.0385842
$418$	−0.316398	+	0.253081i	−0.0154755	+	0.0123786i
$419$	29.5374	−	17.0535i	1.44300	−	0.833116i	0.444950	−	0.895555i	$-0.353221\pi$
$419$	29.5374	−	17.0535i	1.44300	−	0.833116i	0.998049	+	0.0624398i	$0.0198881\pi$
$420$	0.117656	−	0.522566i	0.00574104	−	0.0254986i
$421$	−25.1111			−1.22384			−0.611921	−	0.790919i	$-0.709603\pi$
$421$	−25.1111			−1.22384			−0.611921	+	0.790919i	$0.709603\pi$
$422$	0.744686	−	1.90567i	0.0362508	−	0.0927664i
$423$	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
$426$	−2.23717	+	1.78947i	−0.108391	+	0.0867001i
$427$	−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	$0.470367\pi$
$432$	5.21457	−	10.9931i	0.250886	−	0.528908i
$433$	−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
$436$	3.80934	−	16.9191i	0.182434	−	0.810276i
$437$	−7.19535			−0.344200
$438$	−5.06781	−	1.98037i	−0.242149	−	0.0946258i
$439$	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	$0.759538\pi$
$440$	−0.0435095	+	0.0644256i	−0.00207423	+	0.00307137i
$441$	−2.71690			−0.129376
$442$	−2.06465	+	12.8547i	−0.0982055	+	0.611438i
$443$		−	4.68124i		−	0.222413i	−0.993797	−	0.111206i	$-0.964529\pi$
$443$		−	4.68124i		−	0.222413i	0.993797	−	0.111206i	$-0.0354714\pi$
$444$	7.07799	−	7.67340i	0.335906	−	0.364163i
$445$	−0.365908	+	0.211257i	−0.0173457	+	0.0100145i
$446$	1.97584	−	5.05622i	0.0935589	−	0.239419i
$447$			3.85468i			0.182320i
$448$	7.42091	−	2.98833i	0.350605	−	0.141185i
$449$	−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
$452$	0.817903	+	0.754438i	0.0384709	+	0.0354858i
$453$	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	$0.376276\pi$
$458$	−14.9719	+	11.9757i	−0.699590	+	0.559590i
$459$	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	$-0.621620\pi$
$461$	13.2508	−	22.9511i	0.617151	−	1.06894i	0.990003	−	0.141047i	$-0.0450468\pi$
$462$	−0.0382697	−	0.0149548i	−0.00178047	−	0.000695761i
$463$		−	16.3328i		−	0.759049i	−0.925182	−	0.379524i	$-0.876088\pi$
$463$		−	16.3328i		−	0.759049i	0.925182	−	0.379524i	$-0.123912\pi$
$464$	−32.5736	+	2.63384i	−1.51219	+	0.122273i
$465$	−1.20485	−	2.08687i	−0.0558737	−	0.0967761i
$466$	32.1628	−	25.7265i	1.48991	−	1.19175i
$467$			6.35367i			0.294013i	0.989136	+	0.147006i	$0.0469638\pi$
$467$			6.35367i			0.294013i	−0.989136	+	0.147006i	$0.953036\pi$
$468$	9.65674	+	17.0466i	0.446383	+	0.787981i
$469$			0.120188i			0.00554977i
$470$	−2.93296	−	3.66675i	−0.135288	−	0.169134i
$471$	−6.14398	−	10.6417i	−0.283100	−	0.490343i
$472$	−1.71360	−	0.120816i	−0.0788749	−	0.00556101i
$473$		−	0.305409i		−	0.0140427i
$474$	3.16119	−	8.08954i	0.145198	−	0.371565i
$475$	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
$478$	−8.02714	−	10.0354i	−0.367153	−	0.459009i
$479$	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
$484$	−16.1667	−	14.9123i	−0.734850	−	0.677830i
$485$	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	$0.931199\pi$
$488$	−2.02046	+	28.6572i	−0.0914618	+	1.29725i
$489$			10.3521i			0.468139i
$490$	0.663033	+	0.259097i	0.0299528	+	0.0117048i
$491$	15.4408	−	8.91477i	0.696835	−	0.402318i	−0.109333	−	0.994005i	$-0.534871\pi$
$491$	15.4408	−	8.91477i	0.696835	−	0.402318i	0.806167	+	0.591687i	$0.201538\pi$
$492$	2.64007	+	2.43521i	0.119023	+	0.109788i
$493$		−	20.8607i		−	0.939518i
$494$	4.24255	−	26.4146i	0.190881	−	1.18845i
$495$	−0.0746761			−0.00335644
$496$	15.4242	−	32.5166i	0.692567	−	1.46004i
$497$	−1.90362	−	3.29717i	−0.0853890	−	0.147898i
$498$	2.27369	−	5.81842i	0.101887	−	0.260730i
$499$	9.30760			0.416665			0.208333	−	0.978058i	$-0.433196\pi$
$499$	9.30760			0.416665			0.208333	+	0.978058i	$0.433196\pi$
$500$	2.15526	−	9.57251i	0.0963861	−	0.428096i
$501$	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	$-0.0203909\pi$
$504$	6.36831	+	4.30081i	0.283667	+	0.191573i
$505$	−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	0.967254	−	0.253811i	$-0.0816842\pi$
$509$	5.95205	+	10.3093i	0.263820	+	0.456950i	−0.703434	+	0.710761i	$0.748351\pi$
$510$	−0.604089	−	0.755222i	−0.0267495	−	0.0334418i
$511$	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
$514$	−19.0281	−	7.43569i	−0.839292	−	0.327974i
$515$	4.99522			0.220116
$516$	1.30734	−	5.80652i	0.0575526	−	0.255618i
$517$	−0.311920	+	0.180087i	−0.0137182	+	0.00792021i
$518$	8.66593	+	10.8340i	0.380759	+	0.476019i
$519$	5.49160			0.241054
$520$	−0.730986	−	5.08098i	−0.0320559	−	0.222816i
$521$	24.9432			1.09278			0.546391	−	0.837530i	$-0.316001\pi$
$521$	24.9432			1.09278			0.546391	+	0.837530i	$0.316001\pi$
$522$	−19.6083	−	24.5139i	−0.858230	−	1.07295i
$523$	−6.91876	+	3.99455i	−0.302536	+	0.174669i	−0.643582	−	0.765377i	$-0.722552\pi$
$523$	−6.91876	+	3.99455i	−0.302536	+	0.174669i	0.341046	+	0.940047i	$0.389219\pi$
$524$	−37.2791	−	8.39343i	−1.62855	−	0.366669i
$525$	2.52555			0.110224
$526$	−13.0465	−	5.09826i	−0.568856	−	0.222295i
$527$	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
$530$	5.21689	+	6.52208i	0.226607	+	0.283301i
$531$	−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
$536$	0.190256	−	0.281716i	0.00821779	−	0.0121683i
$537$	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
$540$	−2.98746	−	0.672629i	−0.128560	−	0.0289454i
$541$	−3.88519			−0.167037			−0.0835187	−	0.996506i	$-0.526616\pi$
$541$	−3.88519			−0.167037			−0.0835187	+	0.996506i	$0.526616\pi$
$542$	−14.9044	+	38.1407i	−0.640200	+	1.63828i
$543$	−2.45955	−	4.26007i	−0.105550	−	0.182817i
$544$	4.15579	−	13.8331i	0.178178	−	0.593088i
$545$	−4.36479			−0.186967
$546$	2.53495	−	0.966759i	0.108486	−	0.0413735i
$547$			17.1661i			0.733968i	0.930227	+	0.366984i	$0.119610\pi$
$547$			17.1661i			0.733968i	−0.930227	+	0.366984i	$0.880390\pi$
$548$	22.1509	−	24.0142i	0.946238	−	1.02584i
$549$	−23.8985	+	13.7978i	−1.01996	+	0.588875i
$550$	−0.341405	−	0.133412i	−0.0145576	−	0.00568872i
$551$			42.8656i			1.82614i
$552$	−0.145150	+	2.05874i	−0.00617801	+	0.0876260i
$553$	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
$556$	−2.00806	+	2.17698i	−0.0851606	+	0.0923245i
$557$	−4.73492	−	8.20111i	−0.200625	−	0.347492i	0.748105	−	0.663580i	$-0.230964\pi$
$557$	−4.73492	−	8.20111i	−0.200625	−	0.347492i	−0.948730	+	0.316088i	$0.897631\pi$
$558$	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
$562$	8.81106	+	11.0154i	0.371672	+	0.464659i
$563$	29.1619	+	16.8366i	1.22903	+	0.709580i	0.966827	−	0.255433i	$-0.0822181\pi$
$563$	29.1619	+	16.8366i	1.22903	+	0.709580i	0.262202	+	0.965013i	$0.415551\pi$
$564$	−6.70118	+	2.08865i	−0.282171	+	0.0879479i
$565$	0.140025	−	0.242530i	0.00589088	−	0.0102033i
$566$	3.53389	−	9.04330i	0.148541	−	0.380118i
$567$			6.53224i			0.274328i
$568$	−0.757345	+	10.7418i	−0.0317775	+	0.450717i
$569$	−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	$0.856593\pi$
$570$	1.24131	+	1.55187i	0.0519929	+	0.0650006i
$571$			32.6908i			1.36807i	0.729451	+	0.684033i	$0.239776\pi$
$571$			32.6908i			1.36807i	−0.729451	+	0.684033i	$0.760224\pi$
$572$	−0.393746	−	0.00322231i	−0.0164633	−	0.000134732i
$573$		−	11.4599i		−	0.478746i
$574$	−3.72749	+	2.98155i	−0.155582	+	0.124448i
$575$	−3.25476	−	5.63741i	−0.135733	−	0.235096i
$576$	−8.11898	−	20.1619i	−0.338291	−	0.840078i
$577$		−	44.5079i		−	1.85289i	−0.376435	−	0.926443i	$-0.622850\pi$
$577$		−	44.5079i		−	1.85289i	0.376435	−	0.926443i	$-0.377150\pi$
$578$	−13.8050	−	5.39466i	−0.574214	−	0.224388i
$579$	−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
$582$	4.32314	−	3.45800i	0.179200	−	0.143339i
$583$	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	0.705969	−	0.708243i	$-0.250512\pi$
$587$	−6.30830	−	10.9263i	−0.260371	−	0.450977i	−0.966341	+	0.257266i	$0.917178\pi$
$588$	0.721504	−	0.782198i	0.0297543	−	0.0322573i
$589$	−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
$592$	−3.16256	−	39.1125i	−0.129981	−	1.60752i
$593$		−	32.4280i		−	1.33166i	−0.746105	−	0.665828i	$-0.768078\pi$
$593$		−	32.4280i		−	1.33166i	0.746105	−	0.665828i	$-0.231922\pi$
$594$	−0.0854952	+	0.218784i	−0.00350791	+	0.00897681i
$595$	1.11306	−	0.642623i	0.0456309	−	0.0263450i
$596$	10.6504	+	9.82397i	0.436257	+	0.402406i
$597$		−	10.3649i		−	0.424209i
$598$	−5.42484	−	4.41251i	−0.221838	−	0.180441i
$599$	6.28240			0.256692			0.128346	−	0.991729i	$-0.459033\pi$
$599$	6.28240			0.256692			0.128346	+	0.991729i	$0.459033\pi$
$600$	−5.91979	−	3.99790i	−0.241674	−	0.163214i
$601$	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	$0.832302\pi$
$602$	7.36732	+	2.87896i	0.300270	+	0.117338i
$603$	0.326539			0.0132977
$604$	27.3549	+	6.15899i	1.11306	+	0.250606i
$605$	−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	$0.263395\pi$
$608$	−8.53952	+	28.4249i	−0.346323	+	1.15278i
$609$	−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	0.996506	−	0.0835236i	$-0.0266174\pi$
$613$	10.5453	+	18.2649i	0.425919	+	0.737714i	−0.570586	+	0.821238i	$0.693284\pi$
$614$	27.3674	−	21.8907i	1.10446	−	0.883436i
$615$	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	$0.550747\pi$
$618$	2.71786	−	6.95506i	0.109329	−	0.279774i
$619$	−8.68923			−0.349250			−0.174625	−	0.984635i	$-0.555871\pi$
$619$	−8.68923			−0.349250			−0.174625	+	0.984635i	$0.555871\pi$
$620$	−8.83661	−	1.98957i	−0.354887	−	0.0799031i
$621$	−3.61265	+	2.08576i	−0.144971	+	0.0836988i
$622$	21.4461	−	17.1544i	0.859911	−	0.687827i
$623$	−0.839387			−0.0336293
$624$	−7.47220	−	1.74674i	−0.299127	−	0.0699256i
$625$	21.2636			0.850545
$626$	0.883206	−	0.706461i	0.0353000	−	0.0282359i
$627$	0.132013	−	0.0762178i	0.00527209	−	0.00304384i
$628$	−45.0611	−	10.1456i	−1.79813	−	0.404852i
$629$	25.0483			0.998742
$630$	0.703939	−	1.80139i	0.0280456	−	0.0717693i
$631$	−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
$634$	4.44481	−	3.55533i	0.176526	−	0.141200i
$635$	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
$640$	0.0586264	+	5.69457i	0.00231741	+	0.225098i
$641$	−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	$-0.561645\pi$
$643$	19.1096	−	33.0987i	0.753608	−	1.30529i	0.946064	−	0.323981i	$-0.105021\pi$
$644$	−2.67582	−	0.602462i	−0.105442	−	0.0237403i
$645$	−1.49797			−0.0589825
$646$	−17.6462	−	6.89569i	−0.694280	−	0.271307i
$647$	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	$0.608263\pi$
$648$	10.3404	−	15.3113i	0.406211	−	0.601486i
$649$	0.0331642			0.00130181
$650$	22.6144	−	8.62448i	0.887009	−	0.338280i
$651$		−	4.78723i		−	0.187626i
$652$	28.6026	+	26.3832i	1.12016	+	1.03325i
$653$	23.9076	−	13.8030i	0.935576	−	0.540155i	0.0470050	−	0.998895i	$-0.485032\pi$
$653$	23.9076	−	13.8030i	0.935576	−	0.540155i	0.888571	+	0.458740i	$0.151699\pi$
$654$	−2.37485	+	6.07729i	−0.0928641	+	0.237641i
$655$			9.61730i			0.375779i
$656$	13.4568	−	1.08809i	0.525402	−	0.0424830i
$657$	−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	$0.00112384\pi$
$659$	38.5847	+	22.2769i	1.50305	+	0.867785i	0.503055	+	0.864255i	$0.332209\pi$
$660$	0.0198311	−	0.0214993i	0.000771924	−	0.000836859i
$661$	−7.27753	−	12.6051i	−0.283063	−	0.490280i	0.689075	−	0.724690i	$-0.258017\pi$
$661$	−7.27753	−	12.6051i	−0.283063	−	0.490280i	−0.972138	+	0.234411i	$0.924684\pi$
$662$	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
$666$	29.4349	−	23.5445i	1.14058	−	0.912329i
$667$	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
$670$	−0.0796886	−	0.0311403i	−0.00307864	−	0.00120305i
$671$		−	0.554619i		−	0.0214108i
$672$	−2.92938	+	0.691315i	−0.113003	+	0.0266680i
$673$	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	$0.621410\pi$
$674$	23.4907	−	18.7898i	0.904829	−	0.723757i
$675$		−	14.4383i		−	0.555730i
$676$	19.3972	−	17.3132i	0.746048	−	0.665893i
$677$			40.8143i			1.56862i	0.620369	+	0.784310i	$0.286983\pi$
$677$			40.8143i			1.56862i	−0.620369	+	0.784310i	$0.713017\pi$
$678$	−0.261499	−	0.326921i	−0.0100428	−	0.0125553i
$679$	3.67859	+	6.37150i	0.141171	+	0.244516i
$680$	−3.62623	−	0.255664i	−0.139059	−	0.00980428i
$681$		−	10.4543i		−	0.400609i
$682$	−0.252886	+	0.647141i	−0.00968352	+	0.0247803i
$683$	−3.76037	+	6.51315i	−0.143887	+	0.249219i	−0.928957	−	0.370188i	$-0.879293\pi$
$683$	−3.76037	+	6.51315i	−0.143887	+	0.249219i	0.785070	+	0.619407i	$0.212627\pi$
$684$	−27.2182	+	8.48345i	−1.04071	+	0.324373i
$685$	−7.12086	−	4.11123i	−0.272074	−	0.157082i
$686$	0.883373	+	1.10438i	0.0337273	+	0.0421654i
$687$	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	0.760879	−	0.648893i	$-0.224768\pi$
$691$	−4.77155	−	8.26457i	−0.181518	−	0.314399i	−0.942398	+	0.334494i	$0.891435\pi$
$692$	13.9958	−	15.1731i	0.532040	−	0.576796i
$693$	−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
$696$	12.2648	+	0.864719i	0.464895	+	0.0327771i
$697$			8.61799i			0.326430i
$698$	−4.35674	−	1.70250i	−0.164905	−	0.0644407i
$699$	−13.4195	+	7.74776i	−0.507572	+	0.293047i
$700$	6.43656	−	6.97801i	0.243279	−	0.263744i
$701$		−	12.9010i		−	0.487265i	−0.969868	−	0.243632i	$-0.921661\pi$
$701$		−	12.9010i		−	0.487265i	0.969868	−	0.243632i	$-0.0783390\pi$
$702$	−5.52686	−	14.4921i	−0.208598	−	0.546968i
$703$	−51.4705			−1.94125
$704$	0.432515	+	0.0612929i	0.0163010	+	0.00231006i
$705$	0.883289	+	1.52990i	0.0332666	+	0.0576194i
$706$	−6.13726	+	15.7054i	−0.230979	+	0.591080i
$707$	−10.9829			−0.413054
$708$	0.630527	+	0.141964i	0.0236967	+	0.00533532i
$709$	−4.86115	+	8.41977i	−0.182565	+	0.316211i	−0.942753	−	0.333491i	$-0.891773\pi$
$709$	−4.86115	+	8.41977i	−0.182565	+	0.316211i	0.760189	+	0.649702i	$0.225107\pi$
$710$	2.67935	−	0.407878i	0.100554	−	0.0153074i
$711$	15.6798	−	27.1583i	0.588039	−	1.01851i
$712$	1.96749	+	1.32874i	0.0737349	+	0.0497965i
$713$	−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
$718$	−15.1129	−	18.8939i	−0.564007	−	0.705112i
$719$	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
$722$	11.2332	+	4.38967i	0.418058	+	0.163366i
$723$	12.7380			0.473732
$724$	−18.0388	−	4.06146i	−0.670408	−	0.150943i
$725$	−33.5844	+	19.3899i	−1.24729	+	0.720124i
$726$	5.16879	+	6.46194i	0.191832	+	0.239825i
$727$	37.1208			1.37673			0.688367	−	0.725363i	$-0.258328\pi$
$727$	37.1208			1.37673			0.688367	+	0.725363i	$0.258328\pi$
$728$	3.78940	−	9.46786i	0.140445	−	0.350902i
$729$	12.8921			0.477484
$730$	3.21527	+	4.01968i	0.119002	+	0.148775i
$731$	12.3678	−	7.14054i	0.457439	−	0.264102i
$732$	2.37412	−	10.5446i	0.0877499	−	0.389738i
$733$	9.84743			0.363723			0.181862	−	0.983324i	$-0.441788\pi$
$733$	9.84743			0.363723			0.181862	+	0.983324i	$0.441788\pi$
$734$	−18.0116	−	7.03847i	−0.664820	−	0.259795i
$735$	−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
$738$	8.10058	+	10.1272i	0.298186	+	0.372788i
$739$	25.7194	+	44.5473i	0.946104	+	1.63870i	0.753526	+	0.657418i	$0.228352\pi$
$739$	25.7194	+	44.5473i	0.946104	+	1.63870i	0.192578	+	0.981282i	$0.438315\pi$
$740$	−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	$0.643712\pi$
$744$	−7.57811	+	11.2211i	−0.277827	+	0.411385i
$745$	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
$748$	−0.0612494	+	0.272037i	−0.00223950	+	0.00994666i
$749$	8.50871			0.310901
$750$	−1.34365	+	3.43843i	−0.0490632	+	0.125554i
$751$	−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	$0.851885\pi$
$752$	−11.3076	+	23.8383i	−0.412347	+	0.869292i
$753$	−15.0030			−0.546740
$754$	−26.2871	+	32.3180i	−0.957321	+	1.17695i
$755$		−	7.05704i		−	0.256832i
$756$	−4.47175	−	4.12476i	−0.162636	−	0.150016i
$757$	−3.50546	+	2.02388i	−0.127408	+	0.0735591i	−0.562349	−	0.826900i	$-0.690102\pi$
$757$	−3.50546	+	2.02388i	−0.127408	+	0.0735591i	0.434941	+	0.900459i	$0.356769\pi$
$758$	−20.8130	−	8.13318i	−0.755961	−	0.295410i
$759$		−	0.0398440i		−	0.00144625i
$760$	7.45135	+	0.525352i	0.270289	+	0.0190565i
$761$	−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
$764$	−31.6635	−	29.2066i	−1.14554	−	1.05666i
$765$	−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	$0.0881070\pi$
$770$	0.0242802	+	0.0303547i	0.000874997	+	0.00109391i
$771$	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	−0.825970	−	0.563715i	$-0.809372\pi$
$773$	2.09096	−	3.62164i	0.0752065	−	0.130261i	0.901176	+	0.433453i	$0.142705\pi$
$774$	7.82186	−	20.0163i	0.281151	−	0.719470i
$775$		−	42.7071i		−	1.53408i
$776$	1.46351	−	20.7577i	0.0525368	−	0.745158i
$777$	−2.60982	−	4.52035i	−0.0936269	−	0.162167i
$778$	−2.48034	−	3.10088i	−0.0889246	−	0.111172i
$779$		−	17.7087i		−	0.634479i
$780$	−0.0158048	+	1.93124i	−0.000565902	+	0.0691495i
$781$		−	0.207892i		−	0.00743898i
$782$	−3.86714	+	3.09325i	−0.138289	+	0.110615i
$783$	12.4257	+	21.5220i	0.444059	+	0.769134i
$784$	−0.322380	−	3.98699i	−0.0115136	−	0.142392i
$785$			11.6249i			0.414910i
$786$	13.3906	+	5.23271i	0.477627	+	0.186644i
$787$	−3.98138	+	6.89596i	−0.141921	+	0.245814i	−0.928220	−	0.372032i	$-0.878661\pi$
$787$	−3.98138	+	6.89596i	−0.141921	+	0.245814i	0.786299	+	0.617846i	$0.211995\pi$
$788$	−46.7838	+	14.5817i	−1.66660	+	0.519453i
$789$	4.56394	+	2.63499i	0.162481	+	0.0938082i
$790$	−6.41645	+	5.13240i	−0.228287	+	0.182603i
$791$	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
$796$	−28.6380	−	26.4159i	−1.01505	−	0.936286i
$797$	−4.53112	−	2.61604i	−0.160501	−	0.0926650i	0.417598	−	0.908632i	$-0.362872\pi$
$797$	−4.53112	−	2.61604i	−0.160501	−	0.0926650i	−0.578099	+	0.815967i	$0.696205\pi$
$798$	0.594154	+	3.90300i	0.0210328	+	0.138165i
$799$	−14.5855	−	8.42095i	−0.515998	−	0.297912i
$800$	−26.1331	+	6.16724i	−0.923946	+	0.218045i
$801$			2.28053i			0.0805785i
$802$	−6.03157	+	15.4349i	−0.212982	+	0.545025i
$803$	0.341943	−	0.197421i	0.0120669	−	0.00696682i
$804$	−0.0867161	+	0.0940108i	−0.00305824	+	0.00331551i
$805$			0.690309i			0.0243302i
$806$	−16.3479	−	42.8661i	−0.575831	−	1.50989i
$807$	−8.17638			−0.287822
$808$	25.7435	+	17.3857i	0.905652	+	0.611628i
$809$	−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	$-0.361800\pi$
$810$	−4.33109	−	1.69248i	−0.152179	−	0.0594678i
$811$	−18.8176			−0.660774			−0.330387	−	0.943846i	$-0.607179\pi$
$811$	−18.8176			−0.660774			−0.330387	+	0.943846i	$0.607179\pi$
$812$	−3.58911	+	15.9409i	−0.125953	+	0.559417i
$813$	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
$816$	−2.32898	+	4.90985i	−0.0815305	+	0.171879i
$817$	−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	0.800119	−	0.599841i	$-0.204769\pi$
$821$	−3.42168	−	5.92653i	−0.119418	−	0.206837i	−0.919537	+	0.393003i	$0.871436\pi$
$822$	−9.59866	+	7.67780i	−0.334792	+	0.267794i
$823$	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
$826$	−0.312625	+	0.800014i	−0.0108776	+	0.0278360i
$827$	55.5607			1.93204			0.966018	−	0.258476i	$-0.0832204\pi$
$827$	55.5607			1.93204			0.966018	+	0.258476i	$0.0832204\pi$
$828$	−1.63683	+	7.26992i	−0.0568838	+	0.252647i
$829$	−2.87809	+	1.66167i	−0.0999603	+	0.0577121i	−0.549147	−	0.835726i	$-0.685047\pi$
$829$	−2.87809	+	1.66167i	−0.0999603	+	0.0577121i	0.449187	+	0.893438i	$0.351714\pi$
$830$	−4.61505	+	3.69150i	−0.160191	+	0.128134i
$831$	10.0296			0.347924
$832$	−23.8697	+	16.1938i	−0.827533	+	0.561418i
$833$	2.55333			0.0884677
$834$	0.870154	−	0.696020i	0.0301310	−	0.0241012i
$835$	−1.85198	+	1.06924i	−0.0640905	+	0.0370027i
$836$	0.125858	−	0.558995i	0.00435290	−	0.0193333i
$837$	−27.3681			−0.945981
$838$	−17.5560	+	44.9260i	−0.606461	+	1.55194i
$839$	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
$842$	27.7322	−	22.1825i	0.955715	−	0.764459i
$843$	−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
$848$	20.1130	−	42.4013i	0.690683	−	1.45607i
$849$	−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
$852$	0.889910	−	3.95251i	0.0304878	−	0.135411i
$853$	14.1217			0.483518			0.241759	−	0.970336i	$-0.422276\pi$
$853$	14.1217			0.483518			0.241759	+	0.970336i	$0.422276\pi$
$854$	13.3789	+	5.22816i	0.457818	+	0.178904i
$855$	3.58765	+	6.21400i	0.122695	+	0.212514i
$856$	−19.9441	−	13.4691i	−0.681675	−	0.460366i
$857$	−44.6183			−1.52413			−0.762067	−	0.647498i	$-0.775815\pi$
$857$	−44.6183			−1.52413			−0.762067	+	0.647498i	$0.775815\pi$
$858$	0.146270	+	0.0234930i	0.00499357	+	0.000802037i
$859$			33.7518i			1.15160i	0.817592	+	0.575798i	$0.195308\pi$
$859$			33.7518i			1.15160i	−0.817592	+	0.575798i	$0.804692\pi$
$860$	−3.81770	+	4.13885i	−0.130182	+	0.141134i
$861$	1.55525	−	0.897922i	0.0530027	−	0.0306011i
$862$	8.91926	−	22.8246i	0.303791	−	0.777408i
$863$			29.1278i			0.991521i	0.868459	+	0.495761i	$0.165111\pi$
$863$			29.1278i			0.991521i	−0.868459	+	0.495761i	$0.834889\pi$
$864$	3.95218	+	16.7470i	0.134456	+	0.569744i
$865$	−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
$868$	−13.2270	−	12.2006i	−0.448953	−	0.414117i
$869$	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
$874$	7.94639	−	6.35617i	0.268791	−	0.215001i
$875$	−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	−0.854878	−	0.518829i	$-0.826368\pi$
$877$	0.647947	−	1.12228i	0.0218796	−	0.0378966i	0.876758	+	0.480932i	$0.159702\pi$
$878$	−12.6823	−	4.95591i	−0.428006	−	0.167254i
$879$			13.0417i			0.439884i
$880$	−0.00886086	−	0.109585i	−0.000298700	−	0.00369412i
$881$	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	$0.762076\pi$
$882$	3.00049	−	2.40004i	0.101032	−	0.0808134i
$883$			28.9841i			0.975392i	0.873014	+	0.487696i	$0.162163\pi$
$883$			28.9841i			0.975392i	−0.873014	+	0.487696i	$0.837837\pi$
$884$	−9.07537	−	16.0204i	−0.305238	−	0.538823i
$885$		−	0.162664i		−	0.00546788i
$886$	4.13528	+	5.16987i	0.138928	+	0.173685i
$887$	−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	$0.924929\pi$
$888$	−1.03830	+	14.7268i	−0.0348432	+	0.494200i
$889$			10.3063i			0.345662i
$890$	0.217482	−	0.556541i	0.00729002	−	0.0186553i
$891$	−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
$894$	−3.40512	−	4.25703i	−0.113884	−	0.142376i
$895$	−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
$900$	−18.9586	−	17.4875i	−0.631952	−	0.582916i
$901$	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
$904$	−1.56972	−	0.110672i	−0.0522082	−	0.00368090i
$905$			4.65367i			0.154693i
$906$	−9.82584	−	3.83969i	−0.326442	−	0.127565i
$907$	20.1526	−	11.6351i	0.669157	−	0.386338i	−0.126600	−	0.991954i	$-0.540407\pi$
$907$	20.1526	−	11.6351i	0.669157	−	0.386338i	0.795757	+	0.605616i	$0.207073\pi$
$908$	−28.8849	−	26.6436i	−0.958579	−	0.884199i
$909$			29.8394i			0.989710i
$910$	−2.53417	−	0.407023i	−0.0840068	−	0.0134927i
$911$	44.0432			1.45922			0.729608	−	0.683866i	$-0.239703\pi$
$911$	44.0432			1.45922			0.729608	+	0.683866i	$0.239703\pi$
$912$	4.78570	−	10.0890i	0.158470	−	0.334081i
$913$	0.226661	+	0.392589i	0.00750140	+	0.0129928i
$914$	2.96000	−	7.57469i	0.0979080	−	0.250548i
$915$	−2.72029			−0.0899300
$916$	5.95558	−	26.4515i	0.196778	−	0.873983i
$917$	−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	$0.209043\pi$
$920$	1.09275	−	1.61806i	0.0360268	−	0.0533458i
$921$	−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
$926$	14.4279	+	18.0376i	0.474131	+	0.592751i
$927$	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	$0.907864\pi$
$930$	3.17409	+	1.24036i	0.104083	+	0.0406729i
$931$	−5.24672			−0.171954
$932$	−12.7939	+	56.8235i	−0.419077	+	1.86132i
$933$	−8.94811	+	5.16619i	−0.292948	+	0.169134i
$934$	−5.61266	−	7.01685i	−0.183652	−	0.229598i
$935$	0.0701803			0.00229514
$936$	−25.7232	−	10.2954i	−0.840790	−	0.336517i
$937$	−23.6005			−0.770995			−0.385498	−	0.922709i	$-0.625970\pi$
$937$	−23.6005			−0.770995			−0.385498	+	0.922709i	$0.625970\pi$
$938$	−0.106171	−	0.132733i	−0.00346660	−	0.00433389i
$939$	−0.368506	+	0.212757i	−0.0120257	+	0.00694307i
$940$	6.47821	+	1.45857i	0.211296	+	0.0475735i
$941$	−11.6270			−0.379028			−0.189514	−	0.981878i	$-0.560691\pi$
$941$	−11.6270			−0.379028			−0.189514	+	0.981878i	$0.560691\pi$
$942$	16.1859	+	6.32503i	0.527364	+	0.206081i
$943$	−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
$946$	0.269790	+	0.337288i	0.00877164	+	0.0109662i
$947$	−11.8585	−	20.5394i	−0.385348	−	0.667442i	0.606469	−	0.795107i	$-0.292585\pi$
$947$	−11.8585	−	20.5394i	−0.385348	−	0.667442i	−0.991817	+	0.127664i	$0.959252\pi$
$948$	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
$952$	−5.98492	−	4.04188i	−0.193972	−	0.130998i
$953$	−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
$956$	17.7300	+	3.99193i	0.573430	+	0.129108i
$957$	−0.237367			−0.00767298
$958$	−6.56373	+	16.7967i	−0.212064	+	0.542677i
$959$	−8.16756	−	14.1466i	−0.263744	−	0.456818i
$960$	0.300629	−	2.12140i	0.00970277	−	0.0684678i
$961$	−49.9522			−1.61136
$962$	−38.8056	−	31.5641i	−1.25114	−	1.01767i
$963$		−	23.1173i		−	0.744945i
$964$	32.4639	−	35.1948i	1.04559	−	1.13355i
$965$	2.99445	−	1.72885i	0.0963947	−	0.0556535i
$966$	0.961148	+	0.375592i	0.0309244	+	0.0120845i
$967$			31.8272i			1.02349i	0.859136	+	0.511747i	$0.171002\pi$
$967$			31.8272i			1.02349i	−0.859136	+	0.511747i	$0.828998\pi$
$968$	31.0272	+	2.18755i	0.997253	+	0.0703106i
$969$	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	0.186302	−	0.982493i	$-0.440350\pi$
$971$	−17.8057	−	10.2801i	−0.571411	−	0.329904i	−0.757713	+	0.652588i	$0.773683\pi$
$972$	−17.0873	+	18.5247i	−0.548076	+	0.594182i
$973$	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	$0.265013\pi$
$978$	−9.14478	−	11.4327i	−0.292418	−	0.365576i
$979$	−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
$982$	−9.17746	+	23.4853i	−0.292865	+	0.749446i
$983$			10.0970i			0.322045i	0.986951	+	0.161022i	$0.0514791\pi$
$983$			10.0970i			0.322045i	−0.986951	+	0.161022i	$0.948521\pi$
$984$	−5.06684	−	0.357234i	−0.161525	−	0.0113882i
$985$	6.16662	+	10.6809i	0.196485	+	0.340322i
$986$	18.4278	+	23.0381i	0.586860	+	0.733683i
$987$			3.50957i			0.111711i
$988$	18.6485	+	32.9194i	0.593289	+	1.04731i
$989$			7.67040i			0.243904i
$990$	0.0824706	−	0.0659668i	0.00262109	−	0.00209656i
$991$	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	$0.712682\pi$
$992$	11.6901	+	49.5360i	0.371163	+	1.57277i
$993$		−	1.03163i		−	0.0327377i
$994$	5.01494	+	1.95971i	0.159064	+	0.0621584i
$995$	−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	0.272075	−	0.962276i	$-0.412290\pi$
$997$	−13.4272	−	7.75219i	−0.425243	−	0.245514i	−0.697318	+	0.716762i	$0.745624\pi$
$998$	−10.2791	+	8.22208i	−0.325380	+	0.260265i
$999$	−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.309.19	yes	168
8.5	even	2	inner	728.2.cz.a.309.10	✓	168
13.4	even	6	inner	728.2.cz.a.589.10	yes	168
104.69	even	6	inner	728.2.cz.a.589.19	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.cz.a.309.10	✓	168	8.5	even	2	inner
728.2.cz.a.309.19	yes	168	1.1	even	1	trivial
728.2.cz.a.589.10	yes	168	13.4	even	6	inner
728.2.cz.a.589.19	yes	168	104.69	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+(-1.10438 + 0.883373i) q^{2} +(0.460788 - 0.266036i) q^{3} +(0.439305 - 1.95116i) q^{4} -0.503361 q^{5} +(-0.273875 + 0.700852i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(1.23844 + 2.54289i) q^{8} +(-1.35845 + 2.35290i) q^{9} +(0.555901 - 0.444655i) 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} +(-3.61402 - 1.71430i) q^{16} +(1.27667 - 2.21125i) q^{17} +(-0.578249 - 3.79852i) q^{18} +(-2.62336 + 4.54379i) q^{19} +(-0.221129 + 0.982135i) q^{20} -0.532072 q^{21} +(0.0719258 + 0.0281068i) q^{22} +(0.685700 + 1.18767i) q^{23} +(1.24716 + 0.842261i) q^{24} -4.74663 q^{25} +(-4.76431 + 1.81697i) q^{26} +3.04180i q^{27} +(-1.35603 + 1.47010i) q^{28} +(7.07541 - 4.08499i) q^{29} +(0.137858 - 0.352781i) q^{30} +8.99735i q^{31} +(5.50562 - 1.29929i) q^{32} +(-0.0251611 - 0.0145268i) q^{33} +(0.543436 + 3.56983i) q^{34} +(0.435923 + 0.251680i) q^{35} +(3.99411 + 3.68419i) 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} +(0.587609 - 0.470018i) q^{42} +(4.84378 + 2.79656i) q^{43} +(-0.104262 + 0.0324967i) q^{44} +(0.683790 - 1.18436i) q^{45} +(-1.80643 - 0.705906i) q^{46} -6.59604i q^{47} +(-2.12136 + 0.171529i) q^{48} +(0.500000 + 0.866025i) q^{49} +(5.24208 - 4.19304i) q^{50} -1.35856i q^{51} +(3.65654 - 6.21528i) q^{52} +11.7324i q^{53} +(-2.68704 - 3.35930i) q^{54} +(0.0137429 + 0.0238034i) q^{55} +(0.198922 - 2.82142i) q^{56} +2.79163i q^{57} +(-4.20537 + 10.7616i) q^{58} +(-0.303677 + 0.525983i) q^{59} +(0.159390 + 0.511384i) q^{60} +(8.79623 + 5.07851i) q^{61} +(-7.94801 - 9.93648i) 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} +(-3.75365 - 3.46239i) q^{68} +(0.631924 + 0.364842i) q^{69} +(-0.703752 + 0.107132i) q^{70} +(3.29717 + 1.90362i) q^{71} +(-7.66552 - 0.540452i) q^{72} +7.23093i q^{73} +(-12.9219 - 5.04956i) q^{74} +(-2.18719 + 1.26277i) q^{75} +(7.71319 + 7.11469i) q^{76} +0.0546045i q^{77} +(-1.71195 + 2.10471i) q^{78} -11.5424 q^{79} +(1.81916 + 0.862913i) q^{80} +(-3.26612 - 5.65709i) q^{81} +(1.73732 - 4.44585i) q^{82} -8.30193 q^{83} +(-0.233742 + 1.03816i) q^{84} +(-0.642623 + 1.11306i) q^{85} +(-7.81977 + 1.19041i) q^{86} +(2.17351 - 3.76463i) q^{87} +(0.0864380 - 0.127991i) 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} +(5.82677 + 7.28453i) q^{94} +(1.32050 - 2.28716i) q^{95} +(2.19126 - 2.06339i) q^{96} +(-6.37150 - 3.67859i) q^{97} +(-1.31721 - 0.514734i) 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

L-functions

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