LMFDB - Embedded newform 290.2.d.a.289.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [290,2,Mod(289,290)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(290, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("290.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 290 = 2 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	290.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.31566165862$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.75200995984.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 10x^{6} + 30x^{4} + 27x^{2} + 4 $ x^8 + 10x^6 + 30x^4 + 27*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			289.3
Root			$1.83507i$ of defining polynomial
Character	$\chi$	$=$	290.289
Dual form			290.2.d.a.289.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -0.367473 q^{3} +1.00000 q^{4} +(1.82635 - 1.29013i) q^{5} +0.367473 q^{6} -2.99580i q^{7} -1.00000 q^{8} -2.86496 q^{9} +(-1.82635 + 1.29013i) q^{10} -1.08988i q^{11} -0.367473 q^{12} +1.37471i q^{13} +2.99580i q^{14} +(-0.671136 + 0.474088i) q^{15} +1.00000 q^{16} +0.212256 q^{17} +2.86496 q^{18} -6.70297i q^{19} +(1.82635 - 1.29013i) q^{20} +1.10088i q^{21} +1.08988i q^{22} +1.06384i q^{23} +0.367473 q^{24} +(1.67114 - 4.71246i) q^{25} -1.37471i q^{26} +2.15522 q^{27} -2.99580i q^{28} +(2.49749 - 4.77101i) q^{29} +(0.671136 - 0.474088i) q^{30} -4.22738i q^{31} -1.00000 q^{32} +0.400501i q^{33} -0.212256 q^{34} +(-3.86496 - 5.47139i) q^{35} -2.86496 q^{36} -5.72993 q^{37} +6.70297i q^{38} -0.505170i q^{39} +(-1.82635 + 1.29013i) q^{40} +10.3731i q^{41} -1.10088i q^{42} +10.8599 q^{43} -1.08988i q^{44} +(-5.23244 + 3.69617i) q^{45} -1.06384i q^{46} +6.38765 q^{47} -0.367473 q^{48} -1.97480 q^{49} +(-1.67114 + 4.71246i) q^{50} -0.0779983 q^{51} +1.37471i q^{52} +10.0993i q^{53} -2.15522 q^{54} +(-1.40608 - 1.99050i) q^{55} +2.99580i q^{56} +2.46316i q^{57} +(-2.49749 + 4.77101i) q^{58} -5.28523 q^{59} +(-0.671136 + 0.474088i) q^{60} +3.38530i q^{61} +4.22738i q^{62} +8.58285i q^{63} +1.00000 q^{64} +(1.77356 + 2.51071i) q^{65} -0.400501i q^{66} -10.2314i q^{67} +0.212256 q^{68} -0.390934i q^{69} +(3.86496 + 5.47139i) q^{70} -5.04538 q^{71} +2.86496 q^{72} +3.51767 q^{73} +5.72993 q^{74} +(-0.614098 + 1.73170i) q^{75} -6.70297i q^{76} -3.26505 q^{77} +0.505170i q^{78} +8.85669i q^{79} +(1.82635 - 1.29013i) q^{80} +7.80291 q^{81} -10.3731i q^{82} +12.4112i q^{83} +1.10088i q^{84} +(0.387654 - 0.273837i) q^{85} -10.8599 q^{86} +(-0.917761 + 1.75322i) q^{87} +1.08988i q^{88} +2.95876i q^{89} +(5.23244 - 3.69617i) q^{90} +4.11836 q^{91} +1.06384i q^{92} +1.55345i q^{93} -6.38765 q^{94} +(-8.64769 - 12.2420i) q^{95} +0.367473 q^{96} -16.0605 q^{97} +1.97480 q^{98} +3.12246i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 4 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} - 8 q^{8} + 8 q^{9} + q^{10} + 4 q^{12} + 3 q^{15} + 8 q^{16} + 2 q^{17} - 8 q^{18} - q^{20} - 4 q^{24} + 5 q^{25} + 10 q^{27} - 4 q^{29} - 3 q^{30}+ \cdots + 6 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 4 * q^3 + 8 * q^4 - q^5 - 4 * q^6 - 8 * q^8 + 8 * q^9 + q^10 + 4 * q^12 + 3 * q^15 + 8 * q^16 + 2 * q^17 - 8 * q^18 - q^20 - 4 * q^24 + 5 * q^25 + 10 * q^27 - 4 * q^29 - 3 * q^30 - 8 * q^32 - 2 * q^34 + 8 * q^36 + 16 * q^37 + q^40 + 8 * q^43 - 4 * q^45 + 6 * q^47 + 4 * q^48 - 6 * q^49 - 5 * q^50 - 24 * q^51 - 10 * q^54 + 11 * q^55 + 4 * q^58 - 18 * q^59 + 3 * q^60 + 8 * q^64 - 15 * q^65 + 2 * q^68 - 12 * q^71 - 8 * q^72 - 34 * q^73 - 16 * q^74 + 11 * q^75 - 40 * q^77 - q^80 - 24 * q^81 - 42 * q^85 - 8 * q^86 + 10 * q^87 + 4 * q^90 - 20 * q^91 - 6 * q^94 + 10 * q^95 - 4 * q^96 - 14 * q^97 + 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/290\mathbb{Z}\right)^\times$.

$n$	$31$	$117$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.367473			−0.212161			−0.106080	−	0.994358i	$-0.533830\pi$
$3$	−0.367473			−0.212161			−0.106080	+	0.994358i	$0.533830\pi$
$4$	1.00000			0.500000
$5$	1.82635	−	1.29013i	0.816770	−	0.576963i
$5$	1.82635	−	1.29013i	0.816770	−	0.576963i
$6$	0.367473			0.150020
$7$		−	2.99580i		−	1.13230i	−0.824301	−	0.566152i	$-0.808431\pi$
$7$		−	2.99580i		−	1.13230i	0.824301	−	0.566152i	$-0.191569\pi$
$8$	−1.00000			−0.353553
$9$	−2.86496			−0.954988
$10$	−1.82635	+	1.29013i	−0.577544	+	0.407974i
$11$		−	1.08988i		−	0.328611i	−0.986410	−	0.164305i	$-0.947462\pi$
$11$		−	1.08988i		−	0.328611i	0.986410	−	0.164305i	$-0.0525382\pi$
$12$	−0.367473			−0.106080
$13$			1.37471i			0.381277i	0.981660	+	0.190638i	$0.0610558\pi$
$13$			1.37471i			0.381277i	−0.981660	+	0.190638i	$0.938944\pi$
$14$			2.99580i			0.800660i
$15$	−0.671136	+	0.474088i	−0.173287	+	0.122409i
$16$	1.00000			0.250000
$17$	0.212256			0.0514796			0.0257398	−	0.999669i	$-0.491806\pi$
$17$	0.212256			0.0514796			0.0257398	+	0.999669i	$0.491806\pi$
$18$	2.86496			0.675278
$19$		−	6.70297i		−	1.53777i	−0.639390	−	0.768883i	$-0.720813\pi$
$19$		−	6.70297i		−	1.53777i	0.639390	−	0.768883i	$-0.279187\pi$
$20$	1.82635	−	1.29013i	0.408385	−	0.288482i
$21$			1.10088i			0.240231i
$22$			1.08988i			0.232363i
$23$			1.06384i			0.221826i	0.993830	+	0.110913i	$0.0353776\pi$
$23$			1.06384i			0.221826i	−0.993830	+	0.110913i	$0.964622\pi$
$24$	0.367473			0.0750102
$25$	1.67114	−	4.71246i	0.334227	−	0.942493i
$26$		−	1.37471i		−	0.269603i
$27$	2.15522			0.414772
$28$		−	2.99580i		−	0.566152i
$29$	2.49749	−	4.77101i	0.463772	−	0.885954i
$29$	2.49749	−	4.77101i	0.463772	−	0.885954i
$30$	0.671136	−	0.474088i	0.122532	−	0.0865562i
$31$		−	4.22738i		−	0.759259i	−0.925139	−	0.379630i	$-0.876051\pi$
$31$		−	4.22738i		−	0.759259i	0.925139	−	0.379630i	$-0.123949\pi$
$32$	−1.00000			−0.176777
$33$			0.400501i			0.0697183i
$34$	−0.212256			−0.0364016
$35$	−3.86496	−	5.47139i	−0.653298	−	0.924833i
$36$	−2.86496			−0.477494
$37$	−5.72993			−0.941994			−0.470997	−	0.882135i	$-0.656106\pi$
$37$	−5.72993			−0.941994			−0.470997	+	0.882135i	$0.656106\pi$
$38$			6.70297i			1.08736i
$39$		−	0.505170i		−	0.0808920i
$40$	−1.82635	+	1.29013i	−0.288772	+	0.203987i
$41$			10.3731i			1.62001i	0.586426	+	0.810003i	$0.300535\pi$
$41$			10.3731i			1.62001i	−0.586426	+	0.810003i	$0.699465\pi$
$42$		−	1.10088i		−	0.169869i
$43$	10.8599			1.65613			0.828063	−	0.560635i	$-0.189443\pi$
$43$	10.8599			1.65613			0.828063	+	0.560635i	$0.189443\pi$
$44$		−	1.08988i		−	0.164305i
$45$	−5.23244	+	3.69617i	−0.780006	+	0.550993i
$46$		−	1.06384i		−	0.156855i
$47$	6.38765			0.931735			0.465868	−	0.884854i	$-0.345742\pi$
$47$	6.38765			0.931735			0.465868	+	0.884854i	$0.345742\pi$
$48$	−0.367473			−0.0530402
$49$	−1.97480			−0.282114
$50$	−1.67114	+	4.71246i	−0.236334	+	0.666443i
$51$	−0.0779983			−0.0109220
$52$			1.37471i			0.190638i
$53$			10.0993i			1.38724i	0.720341	+	0.693620i	$0.243985\pi$
$53$			10.0993i			1.38724i	−0.720341	+	0.693620i	$0.756015\pi$
$54$	−2.15522			−0.293288
$55$	−1.40608	−	1.99050i	−0.189596	−	0.268399i
$56$			2.99580i			0.400330i
$57$			2.46316i			0.326254i
$58$	−2.49749	+	4.77101i	−0.327937	+	0.626464i
$59$	−5.28523			−0.688079			−0.344039	−	0.938955i	$-0.611795\pi$
$59$	−5.28523			−0.688079			−0.344039	+	0.938955i	$0.611795\pi$
$60$	−0.671136	+	0.474088i	−0.0866433	+	0.0612045i
$61$			3.38530i			0.433443i	0.976233	+	0.216722i	$0.0695364\pi$
$61$			3.38530i			0.433443i	−0.976233	+	0.216722i	$0.930464\pi$
$62$			4.22738i			0.536877i
$63$			8.58285i			1.08134i
$64$	1.00000			0.125000
$65$	1.77356	+	2.51071i	0.219983	+	0.311415i
$66$		−	0.400501i		−	0.0492983i
$67$		−	10.2314i		−	1.24996i	−0.780639	−	0.624982i	$-0.785106\pi$
$67$		−	10.2314i		−	1.24996i	0.780639	−	0.624982i	$-0.214894\pi$
$68$	0.212256			0.0257398
$69$		−	0.390934i		−	0.0470629i
$70$	3.86496	+	5.47139i	0.461951	+	0.653956i
$71$	−5.04538			−0.598777			−0.299388	−	0.954131i	$-0.596783\pi$
$71$	−5.04538			−0.598777			−0.299388	+	0.954131i	$0.596783\pi$
$72$	2.86496			0.337639
$73$	3.51767			0.411712			0.205856	−	0.978582i	$-0.434002\pi$
$73$	3.51767			0.411712			0.205856	+	0.978582i	$0.434002\pi$
$74$	5.72993			0.666090
$75$	−0.614098	+	1.73170i	−0.0709099	+	0.199960i
$76$		−	6.70297i		−	0.768883i
$77$	−3.26505			−0.372087
$78$			0.505170i			0.0571993i
$79$			8.85669i			0.996455i	0.867046	+	0.498227i	$0.166016\pi$
$79$			8.85669i			0.996455i	−0.867046	+	0.498227i	$0.833984\pi$
$80$	1.82635	−	1.29013i	0.204193	−	0.144241i
$81$	7.80291			0.866989
$82$		−	10.3731i		−	1.14552i
$83$			12.4112i			1.36230i	0.732143	+	0.681151i	$0.238520\pi$
$83$			12.4112i			1.36230i	−0.732143	+	0.681151i	$0.761480\pi$
$84$			1.10088i			0.120115i
$85$	0.387654	−	0.273837i	0.0420470	−	0.0297018i
$86$	−10.8599			−1.17106
$87$	−0.917761	+	1.75322i	−0.0983943	+	0.187965i
$88$			1.08988i			0.116181i
$89$			2.95876i			0.313628i	0.987628	+	0.156814i	$0.0501224\pi$
$89$			2.95876i			0.313628i	−0.987628	+	0.156814i	$0.949878\pi$
$90$	5.23244	−	3.69617i	0.551547	−	0.389611i
$91$	4.11836			0.431721
$92$			1.06384i			0.110913i
$93$			1.55345i			0.161085i
$94$	−6.38765			−0.658836
$95$	−8.64769	−	12.2420i	−0.887234	−	1.25600i
$96$	0.367473			0.0375051
$97$	−16.0605			−1.63070			−0.815351	−	0.578968i	$-0.803456\pi$
$97$	−16.0605			−1.63070			−0.815351	+	0.578968i	$0.803456\pi$
$98$	1.97480			0.199485
$99$			3.12246i			0.313819i
$100$	1.67114	−	4.71246i	0.167114	−	0.471246i
$101$			13.7584i			1.36901i	0.729007	+	0.684506i	$0.239982\pi$
$101$			13.7584i			1.36901i	−0.729007	+	0.684506i	$0.760018\pi$
$102$	0.0779983			0.00772299
$103$		−	9.16613i		−	0.903165i	−0.892229	−	0.451583i	$-0.850860\pi$
$103$		−	9.16613i		−	0.903165i	0.892229	−	0.451583i	$-0.149140\pi$
$104$		−	1.37471i		−	0.134802i
$105$	1.42027	+	2.01059i	0.138604	+	0.196213i
$106$		−	10.0993i		−	0.980927i
$107$			2.34345i			0.226550i	0.993564	+	0.113275i	$0.0361341\pi$
$107$			2.34345i			0.226550i	−0.993564	+	0.113275i	$0.963866\pi$
$108$	2.15522			0.207386
$109$	−1.12260			−0.107526			−0.0537628	−	0.998554i	$-0.517121\pi$
$109$	−1.12260			−0.107526			−0.0537628	+	0.998554i	$0.517121\pi$
$110$	1.40608	+	1.99050i	0.134065	+	0.189787i
$111$	2.10560			0.199854
$112$		−	2.99580i		−	0.283076i
$113$	14.7451			1.38710			0.693551	−	0.720408i	$-0.256045\pi$
$113$	14.7451			1.38710			0.693551	+	0.720408i	$0.256045\pi$
$114$		−	2.46316i		−	0.230696i
$115$	1.37249	+	1.94295i	0.127986	+	0.181181i
$116$	2.49749	−	4.77101i	0.231886	−	0.442977i
$117$		−	3.93850i		−	0.364115i
$118$	5.28523			0.486545
$119$		−	0.635875i		−	0.0582906i
$120$	0.671136	−	0.474088i	0.0612661	−	0.0432781i
$121$	9.81217			0.892015
$122$		−	3.38530i		−	0.306491i
$123$		−	3.81184i		−	0.343702i
$124$		−	4.22738i		−	0.379630i
$125$	−3.02760	−	10.7626i	−0.270796	−	0.962637i
$126$		−	8.58285i		−	0.764621i
$127$	−2.57047			−0.228092			−0.114046	−	0.993475i	$-0.536381\pi$
$127$	−2.57047			−0.228092			−0.114046	+	0.993475i	$0.536381\pi$
$128$	−1.00000			−0.0883883
$129$	−3.99074			−0.351365
$130$	−1.77356	−	2.51071i	−0.155551	−	0.220204i
$131$			1.20697i			0.105454i	0.998609	+	0.0527269i	$0.0167913\pi$
$131$			1.20697i			0.105454i	−0.998609	+	0.0527269i	$0.983209\pi$
$132$			0.400501i			0.0348591i
$133$	−20.0807			−1.74122
$134$			10.2314i			0.883858i
$135$	3.93619	−	2.78051i	0.338773	−	0.239308i
$136$	−0.212256			−0.0182008
$137$	5.81534			0.496838			0.248419	−	0.968653i	$-0.420089\pi$
$137$	5.81534			0.496838			0.248419	+	0.968653i	$0.420089\pi$
$138$			0.390934i			0.0332785i
$139$	15.0428			1.27591			0.637955	−	0.770074i	$-0.279781\pi$
$139$	15.0428			1.27591			0.637955	+	0.770074i	$0.279781\pi$
$140$	−3.86496	−	5.47139i	−0.326649	−	0.462416i
$141$	−2.34729			−0.197678
$142$	5.04538			0.423399
$143$	1.49827			0.125292
$144$	−2.86496			−0.238747
$145$	−1.59392	−	11.9356i	−0.132368	−	0.991201i
$146$	−3.51767			−0.291125
$147$	0.725686			0.0598536
$148$	−5.72993			−0.470997
$149$	0.968162			0.0793150			0.0396575	−	0.999213i	$-0.487373\pi$
$149$	0.968162			0.0793150			0.0396575	+	0.999213i	$0.487373\pi$
$150$	0.614098	−	1.73170i	0.0501409	−	0.141393i
$151$	−10.3004			−0.838234			−0.419117	−	0.907932i	$-0.637660\pi$
$151$	−10.3004			−0.838234			−0.419117	+	0.907932i	$0.637660\pi$
$152$			6.70297i			0.543682i
$153$	−0.608105			−0.0491624
$154$	3.26505			0.263105
$155$	−5.45386	−	7.72069i	−0.438065	−	0.620140i
$156$		−	0.505170i		−	0.0404460i
$157$	11.5654			0.923023			0.461512	−	0.887134i	$-0.347307\pi$
$157$	11.5654			0.923023			0.461512	+	0.887134i	$0.347307\pi$
$158$		−	8.85669i		−	0.704600i
$159$		−	3.71121i		−	0.294318i
$160$	−1.82635	+	1.29013i	−0.144386	+	0.101994i
$161$	3.18706			0.251175
$162$	−7.80291			−0.613054
$163$	−3.50675			−0.274670			−0.137335	−	0.990525i	$-0.543854\pi$
$163$	−3.50675			−0.274670			−0.137335	+	0.990525i	$0.543854\pi$
$164$			10.3731i			0.810003i
$165$	0.516698	+	0.731457i	0.0402249	+	0.0569438i
$166$		−	12.4112i		−	0.963292i
$167$		−	6.80763i		−	0.526791i	−0.964688	−	0.263395i	$-0.915158\pi$
$167$		−	6.80763i		−	0.526791i	0.964688	−	0.263395i	$-0.0848423\pi$
$168$		−	1.10088i		−	0.0849344i
$169$	11.1102			0.854628
$170$	−0.387654	+	0.273837i	−0.0297317	+	0.0210024i
$171$			19.2038i			1.46855i
$172$	10.8599			0.828063
$173$		−	12.6960i		−	0.965258i	−0.875825	−	0.482629i	$-0.839682\pi$
$173$		−	12.6960i		−	0.965258i	0.875825	−	0.482629i	$-0.160318\pi$
$174$	0.917761	−	1.75322i	0.0695753	−	0.132911i
$175$	−14.1176	−	5.00638i	−1.06719	−	0.378447i
$176$		−	1.08988i		−	0.0821527i
$177$	1.94218			0.145983
$178$		−	2.95876i		−	0.221769i
$179$	−3.44971			−0.257844			−0.128922	−	0.991655i	$-0.541152\pi$
$179$	−3.44971			−0.257844			−0.128922	+	0.991655i	$0.541152\pi$
$180$	−5.23244	+	3.69617i	−0.390003	+	0.275496i
$181$	19.3826			1.44070			0.720350	−	0.693611i	$-0.243981\pi$
$181$	19.3826			1.44070			0.720350	+	0.693611i	$0.243981\pi$
$182$	−4.11836			−0.305273
$183$		−	1.24401i		−	0.0919597i
$184$		−	1.06384i		−	0.0784275i
$185$	−10.4649	+	7.39234i	−0.769393	+	0.543496i
$186$		−	1.55345i		−	0.113904i
$187$		−	0.231333i		−	0.0169167i
$188$	6.38765			0.465868
$189$		−	6.45659i		−	0.469648i
$190$	8.64769	+	12.2420i	0.627369	+	0.888127i
$191$		−	24.5210i		−	1.77428i	−0.461503	−	0.887139i	$-0.652689\pi$
$191$		−	24.5210i		−	1.77428i	0.461503	−	0.887139i	$-0.347311\pi$
$192$	−0.367473			−0.0265201
$193$	−10.0101			−0.720546			−0.360273	−	0.932847i	$-0.617316\pi$
$193$	−10.0101			−0.720546			−0.360273	+	0.932847i	$0.617316\pi$
$194$	16.0605			1.15308
$195$	−0.651735	−	0.922620i	−0.0466717	−	0.0660702i
$196$	−1.97480			−0.141057
$197$			19.1667i			1.36557i	0.730618	+	0.682786i	$0.239232\pi$
$197$			19.1667i			1.36557i	−0.730618	+	0.682786i	$0.760768\pi$
$198$		−	3.12246i		−	0.221904i
$199$	14.7249			1.04382			0.521910	−	0.853000i	$-0.325219\pi$
$199$	14.7249			1.04382			0.521910	+	0.853000i	$0.325219\pi$
$200$	−1.67114	+	4.71246i	−0.118167	+	0.333221i
$201$			3.75977i			0.265193i
$202$		−	13.7584i		−	0.968038i
$203$	−14.2930	−	7.48197i	−1.00317	−	0.525132i
$204$	−0.0779983			−0.00546098
$205$	13.3826	+	18.9450i	0.934684	+	1.32317i
$206$			9.16613i			0.638634i
$207$		−	3.04787i		−	0.211842i
$208$			1.37471i			0.0953192i
$209$	−7.30542			−0.505326
$210$	−1.42027	−	2.01059i	−0.0980080	−	0.138744i
$211$			8.19596i			0.564233i	0.959380	+	0.282116i	$0.0910365\pi$
$211$			8.19596i			0.564233i	−0.959380	+	0.282116i	$0.908964\pi$
$212$			10.0993i			0.693620i
$213$	1.85404			0.127037
$214$		−	2.34345i		−	0.160195i
$215$	19.8341	−	14.0107i	1.35267	−	0.955523i
$216$	−2.15522			−0.146644
$217$	−12.6644			−0.859713
$218$	1.12260			0.0760321
$219$	−1.29265			−0.0873492
$220$	−1.40608	−	1.99050i	−0.0947981	−	0.134200i
$221$			0.291791i			0.0196280i
$222$	−2.10560			−0.141318
$223$			6.32850i			0.423788i	0.977293	+	0.211894i	$0.0679631\pi$
$223$			6.32850i			0.423788i	−0.977293	+	0.211894i	$0.932037\pi$
$224$			2.99580i			0.200165i
$225$	−4.78774	+	13.5010i	−0.319183	+	0.900069i
$226$	−14.7451			−0.980829
$227$			20.8358i			1.38292i	0.722413	+	0.691461i	$0.243033\pi$
$227$			20.8358i			1.38292i	−0.722413	+	0.691461i	$0.756967\pi$
$228$			2.46316i			0.163127i
$229$			14.2925i			0.944473i	0.881472	+	0.472236i	$0.156553\pi$
$229$			14.2925i			0.944473i	−0.881472	+	0.472236i	$0.843447\pi$
$230$	−1.37249	−	1.94295i	−0.0904995	−	0.128114i
$231$	1.19982			0.0789424
$232$	−2.49749	+	4.77101i	−0.163968	+	0.313232i
$233$		−	13.5230i		−	0.885923i	−0.896541	−	0.442961i	$-0.853928\pi$
$233$		−	13.5230i		−	0.885923i	0.896541	−	0.442961i	$-0.146072\pi$
$234$			3.93850i			0.257468i
$235$	11.6661	−	8.24090i	0.761014	−	0.537577i
$236$	−5.28523			−0.344039
$237$		−	3.25460i		−	0.211409i
$238$			0.635875i			0.0412177i
$239$	−18.6697			−1.20764			−0.603822	−	0.797119i	$-0.706356\pi$
$239$	−18.6697			−1.20764			−0.603822	+	0.797119i	$0.706356\pi$
$240$	−0.671136	+	0.474088i	−0.0433217	+	0.0306022i
$241$	−19.6628			−1.26660			−0.633298	−	0.773908i	$-0.718299\pi$
$241$	−19.6628			−1.26660			−0.633298	+	0.773908i	$0.718299\pi$
$242$	−9.81217			−0.630750
$243$	−9.33301			−0.598713
$244$			3.38530i			0.216722i
$245$	−3.60668	+	2.54775i	−0.230422	+	0.162769i
$246$			3.81184i			0.243034i
$247$	9.21465			0.586314
$248$			4.22738i			0.268439i
$249$		−	4.56077i		−	0.289027i
$250$	3.02760	+	10.7626i	0.191482	+	0.680687i
$251$			11.5370i			0.728212i	0.931358	+	0.364106i	$0.118625\pi$
$251$			11.5370i			0.728212i	−0.931358	+	0.364106i	$0.881375\pi$
$252$			8.58285i			0.540669i
$253$	1.15946			0.0728945
$254$	2.57047			0.161286
$255$	−0.142453	+	0.100628i	−0.00892073	+	0.00630156i
$256$	1.00000			0.0625000
$257$		−	7.27525i		−	0.453817i	−0.973916	−	0.226909i	$-0.927138\pi$
$257$		−	7.27525i		−	0.453817i	0.973916	−	0.226909i	$-0.0728619\pi$
$258$	3.99074			0.248453
$259$			17.1657i			1.06662i
$260$	1.77356	+	2.51071i	0.109991	+	0.155708i
$261$	−7.15522	+	13.6688i	−0.442897	+	0.846076i
$262$		−	1.20697i		−	0.0745671i
$263$	29.7334			1.83344			0.916721	−	0.399528i	$-0.130826\pi$
$263$	29.7334			1.83344			0.916721	+	0.399528i	$0.130826\pi$
$264$		−	0.400501i		−	0.0246491i
$265$	13.0293	+	18.4448i	0.800387	+	1.13306i
$266$	20.0807			1.23123
$267$		−	1.08727i		−	0.0665396i
$268$		−	10.2314i		−	0.624982i
$269$		−	26.5290i		−	1.61750i	−0.588152	−	0.808750i	$-0.700144\pi$
$269$		−	26.5290i		−	1.61750i	0.588152	−	0.808750i	$-0.299856\pi$
$270$	−3.93619	+	2.78051i	−0.239549	+	0.169216i
$271$		−	19.2989i		−	1.17232i	−0.810195	−	0.586161i	$-0.800639\pi$
$271$		−	19.2989i		−	1.17232i	0.810195	−	0.586161i	$-0.199361\pi$
$272$	0.212256			0.0128699
$273$	−1.51339			−0.0915944
$274$	−5.81534			−0.351318
$275$	−5.13601	−	1.82133i	−0.309713	−	0.109831i
$276$		−	0.390934i		−	0.0235314i
$277$			11.2042i			0.673194i	0.941649	+	0.336597i	$0.109276\pi$
$277$			11.2042i			0.673194i	−0.941649	+	0.336597i	$0.890724\pi$
$278$	−15.0428			−0.902205
$279$			12.1113i			0.725083i
$280$	3.86496	+	5.47139i	0.230976	+	0.326978i
$281$	−7.60493			−0.453672			−0.226836	−	0.973933i	$-0.572838\pi$
$281$	−7.60493			−0.453672			−0.226836	+	0.973933i	$0.572838\pi$
$282$	2.34729			0.139779
$283$		−	4.75740i		−	0.282798i	−0.989953	−	0.141399i	$-0.954840\pi$
$283$		−	4.75740i		−	0.282798i	0.989953	−	0.141399i	$-0.0451601\pi$
$284$	−5.04538			−0.299388
$285$	3.17779	+	4.49860i	0.188236	+	0.266474i
$286$	−1.49827			−0.0885945
$287$	31.0757			1.83434
$288$	2.86496			0.168820
$289$	−16.9549			−0.997350
$290$	1.59392	+	11.9356i	0.0935980	+	0.700885i
$291$	5.90182			0.345971
$292$	3.51767			0.205856
$293$	−22.2904			−1.30222			−0.651108	−	0.758985i	$-0.725696\pi$
$293$	−22.2904			−1.30222			−0.651108	+	0.758985i	$0.725696\pi$
$294$	−0.725686			−0.0423229
$295$	−9.65271	+	6.81863i	−0.562002	+	0.396996i
$296$	5.72993			0.333045
$297$		−	2.34892i		−	0.136298i
$298$	−0.968162			−0.0560841
$299$	−1.46248			−0.0845772
$300$	−0.614098	+	1.73170i	−0.0354550	+	0.0999800i
$301$		−	32.5342i		−	1.87524i
$302$	10.3004			0.592721
$303$		−	5.05585i		−	0.290451i
$304$		−	6.70297i		−	0.384441i
$305$	4.36747	+	6.18276i	0.250081	+	0.354024i
$306$	0.608105			0.0347631
$307$	−19.9531			−1.13878			−0.569392	−	0.822066i	$-0.692821\pi$
$307$	−19.9531			−1.13878			−0.569392	+	0.822066i	$0.692821\pi$
$308$	−3.26505			−0.186044
$309$			3.36831i			0.191616i
$310$	5.45386	+	7.72069i	0.309758	+	0.438506i
$311$		−	15.8156i		−	0.896820i	−0.893828	−	0.448410i	$-0.851990\pi$
$311$		−	15.8156i		−	0.896820i	0.893828	−	0.448410i	$-0.148010\pi$
$312$			0.505170i			0.0285996i
$313$			9.71119i			0.548909i	0.961600	+	0.274454i	$0.0884973\pi$
$313$			9.71119i			0.548909i	−0.961600	+	0.274454i	$0.911503\pi$
$314$	−11.5654			−0.652676
$315$	11.0730	+	15.6753i	0.623892	+	0.883204i
$316$			8.85669i			0.498227i
$317$	31.6058			1.77516			0.887580	−	0.460654i	$-0.152385\pi$
$317$	31.6058			1.77516			0.887580	+	0.460654i	$0.152385\pi$
$318$			3.71121i			0.208114i
$319$	−5.19982	−	2.72196i	−0.291134	−	0.152400i
$320$	1.82635	−	1.29013i	0.102096	−	0.0721204i
$321$		−	0.861157i		−	0.0480651i
$322$	−3.18706			−0.177608
$323$		−	1.42274i		−	0.0791636i
$324$	7.80291			0.433495
$325$	6.47828	+	2.29733i	0.359350	+	0.127433i
$326$	3.50675			0.194221
$327$	0.412526			0.0228127
$328$		−	10.3731i		−	0.572759i
$329$		−	19.1361i		−	1.05501i
$330$	−0.516698	−	0.731457i	−0.0284433	−	0.0402654i
$331$			18.4649i			1.01492i	0.861674	+	0.507462i	$0.169416\pi$
$331$			18.4649i			1.01492i	−0.861674	+	0.507462i	$0.830584\pi$
$332$			12.4112i			0.681151i
$333$	16.4160			0.899593
$334$			6.80763i			0.372497i
$335$	−13.1998	−	18.6862i	−0.721183	−	1.02093i
$336$			1.10088i			0.0600577i
$337$	11.7729			0.641311			0.320656	−	0.947196i	$-0.396097\pi$
$337$	11.7729			0.641311			0.320656	+	0.947196i	$0.396097\pi$
$338$	−11.1102			−0.604313
$339$	−5.41843			−0.294289
$340$	0.387654	−	0.273837i	0.0210235	−	0.0148509i
$341$	−4.60733			−0.249501
$342$		−	19.2038i		−	1.03842i
$343$		−	15.0545i		−	0.812866i
$344$	−10.8599			−0.585529
$345$	−0.504355	−	0.713983i	−0.0271535	−	0.0384396i
$346$			12.6960i			0.682541i
$347$			12.1497i			0.652232i	0.945330	+	0.326116i	$0.105740\pi$
$347$			12.1497i			0.652232i	−0.945330	+	0.326116i	$0.894260\pi$
$348$	−0.917761	+	1.75322i	−0.0491972	+	0.0939824i
$349$	−8.13241			−0.435318			−0.217659	−	0.976025i	$-0.569842\pi$
$349$	−8.13241			−0.435318			−0.217659	+	0.976025i	$0.569842\pi$
$350$	14.1176	+	5.00638i	0.754616	+	0.267603i
$351$			2.96280i			0.158143i
$352$			1.08988i			0.0580907i
$353$		−	17.7354i		−	0.943958i	−0.881610	−	0.471979i	$-0.843540\pi$
$353$		−	17.7354i		−	0.943958i	0.881610	−	0.471979i	$-0.156460\pi$
$354$	−1.94218			−0.103226
$355$	−9.21465	+	6.50919i	−0.489063	+	0.345472i
$356$			2.95876i			0.156814i
$357$			0.233667i			0.0123670i
$358$	3.44971			0.182323
$359$		−	9.14009i		−	0.482396i	−0.970476	−	0.241198i	$-0.922460\pi$
$359$		−	9.14009i		−	0.482396i	0.970476	−	0.241198i	$-0.0775402\pi$
$360$	5.23244	−	3.69617i	0.275774	−	0.194805i
$361$	−25.9297			−1.36472
$362$	−19.3826			−1.01873
$363$	−3.60571			−0.189251
$364$	4.11836			0.215861
$365$	6.42451	−	4.53825i	0.336274	−	0.237543i
$366$			1.24401i			0.0650253i
$367$	−25.5654			−1.33451			−0.667253	−	0.744831i	$-0.732530\pi$
$367$	−25.5654			−1.33451			−0.667253	+	0.744831i	$0.732530\pi$
$368$			1.06384i			0.0554566i
$369$		−	29.7186i		−	1.54709i
$370$	10.4649	−	7.39234i	0.544043	−	0.384310i
$371$	30.2553			1.57078
$372$			1.55345i			0.0805425i
$373$		−	21.8731i		−	1.13255i	−0.824217	−	0.566273i	$-0.808385\pi$
$373$		−	21.8731i		−	1.13255i	0.824217	−	0.566273i	$-0.191615\pi$
$374$			0.231333i			0.0119619i
$375$	1.11256	+	3.95497i	0.0574524	+	0.204234i
$376$	−6.38765			−0.329418
$377$	6.55877	+	3.43333i	0.337794	+	0.176826i
$378$			6.45659i			0.332091i
$379$			32.8410i			1.68693i	0.537184	+	0.843465i	$0.319488\pi$
$379$			32.8410i			1.68693i	−0.537184	+	0.843465i	$0.680512\pi$
$380$	−8.64769	−	12.2420i	−0.443617	−	0.628001i
$381$	0.944579			0.0483922
$382$			24.5210i			1.25460i
$383$		−	34.6298i		−	1.76950i	−0.466064	−	0.884751i	$-0.654328\pi$
$383$		−	34.6298i		−	1.76950i	0.466064	−	0.884751i	$-0.345672\pi$
$384$	0.367473			0.0187525
$385$	−5.96314	+	4.21234i	−0.303910	+	0.214681i
$386$	10.0101			0.509503
$387$	−31.1133			−1.58158
$388$	−16.0605			−0.815351
$389$		−	12.9103i		−	0.654580i	−0.944924	−	0.327290i	$-0.893865\pi$
$389$		−	12.9103i		−	0.654580i	0.944924	−	0.327290i	$-0.106135\pi$
$390$	0.651735	+	0.922620i	0.0330019	+	0.0467187i
$391$			0.225807i			0.0114195i
$392$	1.97480			0.0997424
$393$		−	0.443531i		−	0.0223732i
$394$		−	19.1667i		−	0.965605i
$395$	11.4263	+	16.1754i	0.574918	+	0.813875i
$396$			3.12246i			0.156910i
$397$		−	28.7398i		−	1.44241i	−0.692723	−	0.721204i	$-0.743589\pi$
$397$		−	28.7398i		−	1.44241i	0.692723	−	0.721204i	$-0.256411\pi$
$398$	−14.7249			−0.738093
$399$	7.37913			0.369419
$400$	1.67114	−	4.71246i	0.0835568	−	0.235623i
$401$	24.2030			1.20864			0.604320	−	0.796742i	$-0.293445\pi$
$401$	24.2030			1.20864			0.604320	+	0.796742i	$0.293445\pi$
$402$		−	3.75977i		−	0.187520i
$403$	5.81143			0.289488
$404$			13.7584i			0.684506i
$405$	14.2509	−	10.0668i	0.708131	−	0.500221i
$406$	14.2930	+	7.48197i	0.709349	+	0.371324i
$407$			6.24492i			0.309549i
$408$	0.0779983			0.00386149
$409$		−	17.4820i		−	0.864431i	−0.901770	−	0.432216i	$-0.857732\pi$
$409$		−	17.4820i		−	0.864431i	0.901770	−	0.432216i	$-0.142268\pi$
$410$	−13.3826	−	18.9450i	−0.660921	−	0.935624i
$411$	−2.13698			−0.105410
$412$		−	9.16613i		−	0.451583i
$413$			15.8335i			0.779115i
$414$			3.04787i			0.149795i
$415$	16.0120	+	22.6672i	0.785997	+	1.11269i
$416$		−	1.37471i		−	0.0674008i
$417$	−5.52781			−0.270698
$418$	7.30542			0.357320
$419$	26.2378			1.28180			0.640900	−	0.767625i	$-0.278561\pi$
$419$	26.2378			1.28180			0.640900	+	0.767625i	$0.278561\pi$
$420$	1.42027	+	2.01059i	0.0693021	+	0.0981066i
$421$			13.6673i			0.666105i	0.942908	+	0.333053i	$0.108079\pi$
$421$			13.6673i			0.666105i	−0.942908	+	0.333053i	$0.891921\pi$
$422$		−	8.19596i		−	0.398973i
$423$	−18.3004			−0.889796
$424$		−	10.0993i		−	0.490464i
$425$	0.354708	−	1.00025i	0.0172059	−	0.0485191i
$426$	−1.85404			−0.0898287
$427$	10.1417			0.490790
$428$			2.34345i			0.113275i
$429$	−0.550574			−0.0265820
$430$	−19.8341	+	14.0107i	−0.956485	+	0.675657i
$431$	−20.1544			−0.970805			−0.485403	−	0.874291i	$-0.661327\pi$
$431$	−20.1544			−0.970805			−0.485403	+	0.874291i	$0.661327\pi$
$432$	2.15522			0.103693
$433$	9.30542			0.447190			0.223595	−	0.974682i	$-0.428221\pi$
$433$	9.30542			0.447190			0.223595	+	0.974682i	$0.428221\pi$
$434$	12.6644			0.607909
$435$	0.585722	+	4.38603i	0.0280832	+	0.210294i
$436$	−1.12260			−0.0537628
$437$	7.13090			0.341117
$438$	1.29265			0.0617652
$439$	38.2655			1.82631			0.913156	−	0.407610i	$-0.133638\pi$
$439$	38.2655			1.82631			0.913156	+	0.407610i	$0.133638\pi$
$440$	1.40608	+	1.99050i	0.0670324	+	0.0948935i
$441$	5.65773			0.269416
$442$		−	0.291791i		−	0.0138791i
$443$	−34.1561			−1.62281			−0.811403	−	0.584488i	$-0.801296\pi$
$443$	−34.1561			−1.62281			−0.811403	+	0.584488i	$0.801296\pi$
$444$	2.10560			0.0999271
$445$	3.81719	+	5.40375i	0.180952	+	0.256162i
$446$		−	6.32850i		−	0.299663i
$447$	−0.355774			−0.0168275
$448$		−	2.99580i		−	0.141538i
$449$		−	2.90669i		−	0.137175i	−0.997645	−	0.0685876i	$-0.978151\pi$
$449$		−	2.90669i		−	0.137175i	0.997645	−	0.0685876i	$-0.0218493\pi$
$450$	4.78774	−	13.5010i	0.225696	−	0.636445i
$451$	11.3054			0.532351
$452$	14.7451			0.693551
$453$	3.78512			0.177840
$454$		−	20.8358i		−	0.977874i
$455$	7.52158	−	5.31321i	0.352617	−	0.249087i
$456$		−	2.46316i		−	0.115348i
$457$		−	2.65336i		−	0.124119i	−0.998072	−	0.0620596i	$-0.980233\pi$
$457$		−	2.65336i		−	0.124119i	0.998072	−	0.0620596i	$-0.0197669\pi$
$458$		−	14.2925i		−	0.667843i
$459$	0.457457			0.0213523
$460$	1.37249	+	1.94295i	0.0639928	+	0.0905906i
$461$			6.53979i			0.304589i	0.988335	+	0.152294i	$0.0486662\pi$
$461$			6.53979i			0.304589i	−0.988335	+	0.152294i	$0.951334\pi$
$462$	−1.19982			−0.0558207
$463$			27.1658i			1.26250i	0.775579	+	0.631250i	$0.217458\pi$
$463$			27.1658i			1.26250i	−0.775579	+	0.631250i	$0.782542\pi$
$464$	2.49749	−	4.77101i	0.115943	−	0.221489i
$465$	2.00415	+	2.83715i	0.0929401	+	0.131570i
$466$			13.5230i			0.626442i
$467$	−32.2561			−1.49264			−0.746318	−	0.665590i	$-0.768180\pi$
$467$	−32.2561			−1.49264			−0.746318	+	0.665590i	$0.768180\pi$
$468$		−	3.93850i		−	0.182057i
$469$	−30.6512			−1.41534
$470$	−11.6661	+	8.24090i	−0.538118	+	0.380124i
$471$	−4.24999			−0.195829
$472$	5.28523			0.243273
$473$		−	11.8360i		−	0.544221i
$474$			3.25460i			0.149489i
$475$	−31.5875	−	11.2016i	−1.44933	−	0.513963i
$476$		−	0.635875i		−	0.0291453i
$477$		−	28.9340i		−	1.32480i
$478$	18.6697			0.853933
$479$			25.8295i			1.18018i	0.807337	+	0.590090i	$0.200908\pi$
$479$			25.8295i			1.18018i	−0.807337	+	0.590090i	$0.799092\pi$
$480$	0.671136	−	0.474088i	0.0306330	−	0.0216391i
$481$		−	7.87700i		−	0.359160i
$482$	19.6628			0.895618
$483$	−1.17116			−0.0532895
$484$	9.81217			0.446008
$485$	−29.3322	+	20.7202i	−1.33191	+	0.940854i
$486$	9.33301			0.423354
$487$		−	1.63351i		−	0.0740215i	−0.999315	−	0.0370107i	$-0.988216\pi$
$487$		−	1.63351i		−	0.0740215i	0.999315	−	0.0370107i	$-0.0117836\pi$
$488$		−	3.38530i		−	0.153245i
$489$	1.28864			0.0582742
$490$	3.60668	−	2.54775i	0.162933	−	0.115095i
$491$			10.3456i			0.466892i	0.972370	+	0.233446i	$0.0750002\pi$
$491$			10.3456i			0.466892i	−0.972370	+	0.233446i	$0.925000\pi$
$492$		−	3.81184i		−	0.171851i
$493$	0.530107	−	1.01267i	0.0238748	−	0.0456086i
$494$	−9.21465			−0.414587
$495$	4.02838	+	5.70272i	0.181062	+	0.256318i
$496$		−	4.22738i		−	0.189815i
$497$			15.1149i			0.677998i
$498$			4.56077i			0.204373i
$499$	0.704726			0.0315479			0.0157739	−	0.999876i	$-0.494979\pi$
$499$	0.704726			0.0315479			0.0157739	+	0.999876i	$0.494979\pi$
$500$	−3.02760	−	10.7626i	−0.135398	−	0.481318i
$501$			2.50162i			0.111764i
$502$		−	11.5370i		−	0.514924i
$503$	6.19285			0.276126			0.138063	−	0.990423i	$-0.455912\pi$
$503$	6.19285			0.276126			0.138063	+	0.990423i	$0.455912\pi$
$504$		−	8.58285i		−	0.382310i
$505$	17.7501	+	25.1277i	0.789869	+	1.11817i
$506$	−1.15946			−0.0515442
$507$	−4.08269			−0.181319
$508$	−2.57047			−0.114046
$509$	−14.6292			−0.648426			−0.324213	−	0.945984i	$-0.605100\pi$
$509$	−14.6292			−0.648426			−0.324213	+	0.945984i	$0.605100\pi$
$510$	0.142453	−	0.100628i	0.00630791	−	0.00445588i
$511$		−	10.5382i		−	0.466184i
$512$	−1.00000			−0.0441942
$513$		−	14.4463i		−	0.637822i
$514$			7.27525i			0.320897i
$515$	−11.8255	−	16.7406i	−0.521093	−	0.737679i
$516$	−3.99074			−0.175683
$517$		−	6.96176i		−	0.306178i
$518$		−	17.1657i		−	0.754217i
$519$			4.66544i			0.204790i
$520$	−1.77356	−	2.51071i	−0.0777756	−	0.110102i
$521$	−6.40511			−0.280613			−0.140306	−	0.990108i	$-0.544809\pi$
$521$	−6.40511			−0.280613			−0.140306	+	0.990108i	$0.544809\pi$
$522$	7.15522	−	13.6688i	0.313175	−	0.598266i
$523$			16.5805i			0.725013i	0.931981	+	0.362507i	$0.118079\pi$
$523$			16.5805i			0.725013i	−0.931981	+	0.362507i	$0.881921\pi$
$524$			1.20697i			0.0527269i
$525$	5.18783	+	1.83971i	0.226416	+	0.0802917i
$526$	−29.7334			−1.29644
$527$		−	0.897285i		−	0.0390864i
$528$			0.400501i			0.0174296i
$529$	21.8682			0.950793
$530$	−13.0293	−	18.4448i	−0.565959	−	0.801192i
$531$	15.1420			0.657107
$532$	−20.0807			−0.870610
$533$	−14.2600			−0.617671
$534$			1.08727i			0.0470506i
$535$	3.02336	+	4.27997i	0.130711	+	0.185039i
$536$			10.2314i			0.441929i
$537$	1.26768			0.0547043
$538$			26.5290i			1.14375i
$539$			2.15229i			0.0927057i
$540$	3.93619	−	2.78051i	0.169387	−	0.119654i
$541$		−	40.5567i		−	1.74367i	−0.489803	−	0.871833i	$-0.662931\pi$
$541$		−	40.5567i		−	1.74367i	0.489803	−	0.871833i	$-0.337069\pi$
$542$			19.2989i			0.828957i
$543$	−7.12260			−0.305660
$544$	−0.212256			−0.00910039
$545$	−2.05027	+	1.44830i	−0.0878238	+	0.0620383i
$546$	1.51339			0.0647670
$547$			43.0100i			1.83897i	0.393119	+	0.919487i	$0.371396\pi$
$547$			43.0100i			1.83897i	−0.393119	+	0.919487i	$0.628604\pi$
$548$	5.81534			0.248419
$549$		−	9.69876i		−	0.413933i
$550$	5.13601	+	1.82133i	0.219000	+	0.0776620i
$551$	−31.9799	−	16.7406i	−1.36239	−	0.713173i
$552$			0.390934i			0.0166392i
$553$	26.5328			1.12829
$554$		−	11.2042i		−	0.476020i
$555$	3.84556	−	2.71649i	0.163235	−	0.115309i
$556$	15.0428			0.637955
$557$			35.0002i			1.48301i	0.670949	+	0.741503i	$0.265887\pi$
$557$			35.0002i			1.48301i	−0.670949	+	0.741503i	$0.734113\pi$
$558$		−	12.1113i		−	0.512711i
$559$			14.9293i			0.631442i
$560$	−3.86496	−	5.47139i	−0.163325	−	0.231208i
$561$			0.0850087i			0.00358907i
$562$	7.60493			0.320795
$563$	7.82733			0.329882			0.164941	−	0.986303i	$-0.447257\pi$
$563$	7.82733			0.329882			0.164941	+	0.986303i	$0.447257\pi$
$564$	−2.34729			−0.0988388
$565$	26.9297	−	19.0231i	1.13294	−	0.800306i
$566$			4.75740i			0.199969i
$567$		−	23.3759i		−	0.981696i
$568$	5.04538			0.211700
$569$			16.3098i			0.683741i	0.939747	+	0.341870i	$0.111060\pi$
$569$			16.3098i			0.683741i	−0.939747	+	0.341870i	$0.888940\pi$
$570$	−3.17779	−	4.49860i	−0.133103	−	0.188426i
$571$	−26.6814			−1.11658			−0.558291	−	0.829645i	$-0.688543\pi$
$571$	−26.6814			−1.11658			−0.558291	+	0.829645i	$0.688543\pi$
$572$	1.49827			0.0626458
$573$			9.01082i			0.376432i
$574$	−31.0757			−1.29707
$575$	5.01332	+	1.77783i	0.209070	+	0.0741404i
$576$	−2.86496			−0.119373
$577$	34.3986			1.43203			0.716016	−	0.698084i	$-0.245964\pi$
$577$	34.3986			1.43203			0.716016	+	0.698084i	$0.245964\pi$
$578$	16.9549			0.705233
$579$	3.67846			0.152872
$580$	−1.59392	−	11.9356i	−0.0661838	−	0.495600i
$581$	37.1813			1.54254
$582$	−5.90182			−0.244638
$583$	11.0070			0.455862
$584$	−3.51767			−0.145562
$585$	−5.08117	−	7.19310i	−0.210081	−	0.297398i
$586$	22.2904			0.920806
$587$		−	25.7402i		−	1.06241i	−0.847243	−	0.531205i	$-0.821739\pi$
$587$		−	25.7402i		−	1.06241i	0.847243	−	0.531205i	$-0.178261\pi$
$588$	0.725686			0.0299268
$589$	−28.3360			−1.16756
$590$	9.65271	−	6.81863i	0.397396	−	0.280719i
$591$		−	7.04326i		−	0.289721i
$592$	−5.72993			−0.235499
$593$			8.07625i			0.331652i	0.986155	+	0.165826i	$0.0530290\pi$
$593$			8.07625i			0.331652i	−0.986155	+	0.165826i	$0.946971\pi$
$594$			2.34892i			0.0963775i
$595$	−0.820361	−	1.16133i	−0.0336315	−	0.0476100i
$596$	0.968162			0.0396575
$597$	−5.41101			−0.221458
$598$	1.46248			0.0598051
$599$		−	6.48120i		−	0.264815i	−0.991195	−	0.132407i	$-0.957729\pi$
$599$		−	6.48120i		−	0.264815i	0.991195	−	0.132407i	$-0.0422707\pi$
$600$	0.614098	−	1.73170i	0.0250704	−	0.0706965i
$601$			9.59123i			0.391235i	0.980680	+	0.195617i	$0.0626710\pi$
$601$			9.59123i			0.391235i	−0.980680	+	0.195617i	$0.937329\pi$
$602$			32.5342i			1.32599i
$603$			29.3126i			1.19370i
$604$	−10.3004			−0.419117
$605$	17.9205	−	12.6590i	0.728571	−	0.514660i
$606$			5.05585i			0.205380i
$607$	28.1680			1.14330			0.571652	−	0.820496i	$-0.306303\pi$
$607$	28.1680			1.14330			0.571652	+	0.820496i	$0.306303\pi$
$608$			6.70297i			0.271841i
$609$	5.25229	+	2.74943i	0.212833	+	0.111412i
$610$	−4.36747	−	6.18276i	−0.176834	−	0.250333i
$611$			8.78119i			0.355249i
$612$	−0.608105			−0.0245812
$613$			41.3758i			1.67115i	0.549373	+	0.835577i	$0.314867\pi$
$613$			41.3758i			1.67115i	−0.549373	+	0.835577i	$0.685133\pi$
$614$	19.9531			0.805242
$615$	−4.91776	−	6.96176i	−0.198303	−	0.280725i
$616$	3.26505			0.131553
$617$	−9.70399			−0.390668			−0.195334	−	0.980737i	$-0.562579\pi$
$617$	−9.70399			−0.390668			−0.195334	+	0.980737i	$0.562579\pi$
$618$		−	3.36831i		−	0.135493i
$619$			29.7952i			1.19757i	0.800909	+	0.598786i	$0.204350\pi$
$619$			29.7952i			1.19757i	−0.800909	+	0.598786i	$0.795650\pi$
$620$	−5.45386	−	7.72069i	−0.219032	−	0.310070i
$621$			2.29281i			0.0920073i
$622$			15.8156i			0.634147i
$623$	8.86386			0.355123
$624$		−	0.505170i		−	0.0202230i
$625$	−19.4146	−	15.7503i	−0.776584	−	0.630013i
$626$		−	9.71119i		−	0.388137i
$627$	2.68455			0.107210
$628$	11.5654			0.461512
$629$	−1.21621			−0.0484935
$630$	−11.0730	−	15.6753i	−0.441158	−	0.624520i
$631$	−35.9799			−1.43234			−0.716169	−	0.697927i	$-0.754106\pi$
$631$	−35.9799			−1.43234			−0.716169	+	0.697927i	$0.754106\pi$
$632$		−	8.85669i		−	0.352300i
$633$		−	3.01180i		−	0.119708i
$634$	−31.6058			−1.25523
$635$	−4.69458	+	3.31623i	−0.186299	+	0.131601i
$636$		−	3.71121i		−	0.147159i
$637$		−	2.71478i		−	0.107564i
$638$	5.19982	+	2.72196i	0.205863	+	0.107763i
$639$	14.4548			0.571824
$640$	−1.82635	+	1.29013i	−0.0721930	+	0.0509968i
$641$		−	7.21413i		−	0.284941i	−0.989799	−	0.142471i	$-0.954495\pi$
$641$		−	7.21413i		−	0.284941i	0.989799	−	0.142471i	$-0.0455046\pi$
$642$			0.861157i			0.0339871i
$643$		−	16.4543i		−	0.648895i	−0.945904	−	0.324448i	$-0.894822\pi$
$643$		−	16.4543i		−	0.648895i	0.945904	−	0.324448i	$-0.105178\pi$
$644$	3.18706			0.125588
$645$	−7.28850	+	5.14857i	−0.286984	+	0.202725i
$646$			1.42274i			0.0559771i
$647$			30.8486i			1.21278i	0.795166	+	0.606392i	$0.207384\pi$
$647$			30.8486i			1.21278i	−0.795166	+	0.606392i	$0.792616\pi$
$648$	−7.80291			−0.306527
$649$			5.76026i			0.226110i
$650$	−6.47828	−	2.29733i	−0.254099	−	0.0901088i
$651$	4.65382			0.182397
$652$	−3.50675			−0.137335
$653$	−22.3089			−0.873014			−0.436507	−	0.899701i	$-0.643785\pi$
$653$	−22.3089			−0.873014			−0.436507	+	0.899701i	$0.643785\pi$
$654$	−0.412526			−0.0161310
$655$	1.55715	+	2.20436i	0.0608430	+	0.0861316i
$656$			10.3731i			0.405002i
$657$	−10.0780			−0.393180
$658$			19.1361i			0.746003i
$659$			27.0186i			1.05249i	0.850332	+	0.526247i	$0.176401\pi$
$659$			27.0186i			1.05249i	−0.850332	+	0.526247i	$0.823599\pi$
$660$	0.516698	+	0.731457i	0.0201124	+	0.0284719i
$661$	−9.63068			−0.374590			−0.187295	−	0.982304i	$-0.559972\pi$
$661$	−9.63068			−0.374590			−0.187295	+	0.982304i	$0.559972\pi$
$662$		−	18.4649i		−	0.717659i
$663$		−	0.107225i		−	0.00416429i
$664$		−	12.4112i		−	0.481646i
$665$	−36.6745	+	25.9067i	−1.42218	+	1.00462i
$666$	−16.4160			−0.636108
$667$	5.07560	+	2.65694i	0.196528	+	0.102877i
$668$		−	6.80763i		−	0.263395i
$669$		−	2.32555i		−	0.0899111i
$670$	13.1998	+	18.6862i	0.509954	+	0.721909i
$671$	3.68956			0.142434
$672$		−	1.10088i		−	0.0424672i
$673$			46.9574i			1.81007i	0.425334	+	0.905037i	$0.360157\pi$
$673$			46.9574i			1.81007i	−0.425334	+	0.905037i	$0.639843\pi$
$674$	−11.7729			−0.453476
$675$	3.60166	−	10.1564i	0.138628	−	0.390919i
$676$	11.1102			0.427314
$677$	−28.1645			−1.08245			−0.541224	−	0.840878i	$-0.682039\pi$
$677$	−28.1645			−1.08245			−0.541224	+	0.840878i	$0.682039\pi$
$678$	5.41843			0.208093
$679$			48.1141i			1.84645i
$680$	−0.387654	+	0.273837i	−0.0148659	+	0.0105012i
$681$		−	7.65661i		−	0.293402i
$682$	4.60733			0.176424
$683$			19.8006i			0.757650i	0.925468	+	0.378825i	$0.123672\pi$
$683$			19.8006i			0.757650i	−0.925468	+	0.378825i	$0.876328\pi$
$684$			19.2038i			0.734274i
$685$	10.6209	−	7.50254i	0.405803	−	0.286657i
$686$			15.0545i			0.574783i
$687$		−	5.25210i		−	0.200380i
$688$	10.8599			0.414031
$689$	−13.8836			−0.528922
$690$	0.504355	+	0.713983i	0.0192005	+	0.0271809i
$691$	3.64179			0.138540			0.0692701	−	0.997598i	$-0.477933\pi$
$691$	3.64179			0.138540			0.0692701	+	0.997598i	$0.477933\pi$
$692$		−	12.6960i		−	0.482629i
$693$	9.35426			0.355339
$694$		−	12.1497i		−	0.461198i
$695$	27.4734	−	19.4071i	1.04213	−	0.736153i
$696$	0.917761	−	1.75322i	0.0347876	−	0.0664556i
$697$			2.20175i			0.0833973i
$698$	8.13241			0.307816
$699$			4.96935i			0.187958i
$700$	−14.1176	−	5.00638i	−0.533594	−	0.189224i
$701$	−24.5639			−0.927767			−0.463883	−	0.885896i	$-0.653544\pi$
$701$	−24.5639			−0.927767			−0.463883	+	0.885896i	$0.653544\pi$
$702$		−	2.96280i		−	0.111824i
$703$			38.4075i			1.44857i
$704$		−	1.08988i		−	0.0410763i
$705$	−4.28699	+	3.02831i	−0.161457	+	0.114053i
$706$			17.7354i			0.667479i
$707$	41.2174			1.55014
$708$	1.94218			0.0729917
$709$	36.5676			1.37333			0.686663	−	0.726976i	$-0.259075\pi$
$709$	36.5676			1.37333			0.686663	+	0.726976i	$0.259075\pi$
$710$	9.21465	−	6.50919i	0.345820	−	0.244286i
$711$		−	25.3741i		−	0.951602i
$712$		−	2.95876i		−	0.110884i
$713$	4.49726			0.168424
$714$		−	0.233667i		−	0.00874477i
$715$	2.73637	−	1.93296i	0.102334	−	0.0722886i
$716$	−3.44971			−0.128922
$717$	6.86062			0.256215
$718$			9.14009i			0.341105i
$719$	−4.40968			−0.164453			−0.0822267	−	0.996614i	$-0.526203\pi$
$719$	−4.40968			−0.164453			−0.0822267	+	0.996614i	$0.526203\pi$
$720$	−5.23244	+	3.69617i	−0.195001	+	0.137748i
$721$	−27.4599			−1.02266
$722$	25.9297			0.965005
$723$	7.22557			0.268722
$724$	19.3826			0.720350
$725$	−18.3096	−	19.7423i	−0.680000	−	0.733212i
$726$	3.60571			0.133820
$727$	−37.9900			−1.40897			−0.704485	−	0.709719i	$-0.748822\pi$
$727$	−37.9900			−1.40897			−0.704485	+	0.709719i	$0.748822\pi$
$728$	−4.11836			−0.152637
$729$	−19.9791			−0.739966
$730$	−6.42451	+	4.53825i	−0.237782	+	0.167968i
$731$	2.30509			0.0852567
$732$		−	1.24401i		−	0.0459798i
$733$	−6.57895			−0.242999			−0.121500	−	0.992591i	$-0.538770\pi$
$733$	−6.57895			−0.242999			−0.121500	+	0.992591i	$0.538770\pi$
$734$	25.5654			0.943638
$735$	1.32536	−	0.936228i	0.0488866	−	0.0345333i
$736$		−	1.06384i		−	0.0392137i
$737$	−11.1510			−0.410752
$738$			29.7186i			1.09396i
$739$			26.6171i			0.979127i	0.871968	+	0.489563i	$0.162844\pi$
$739$			26.6171i			0.979127i	−0.871968	+	0.489563i	$0.837156\pi$
$740$	−10.4649	+	7.39234i	−0.384696	+	0.271748i
$741$	−3.38614			−0.124393
$742$	−30.2553			−1.11071
$743$	4.67606			0.171548			0.0857741	−	0.996315i	$-0.472664\pi$
$743$	4.67606			0.171548			0.0857741	+	0.996315i	$0.472664\pi$
$744$		−	1.55345i		−	0.0569522i
$745$	1.76821	−	1.24905i	0.0647821	−	0.0457618i
$746$			21.8731i			0.800832i
$747$		−	35.5575i		−	1.30098i
$748$		−	0.231333i		−	0.00845837i
$749$	7.02051			0.256524
$750$	−1.11256	−	3.95497i	−0.0406250	−	0.144415i
$751$		−	12.3371i		−	0.450187i	−0.974337	−	0.225093i	$-0.927731\pi$
$751$		−	12.3371i		−	0.450187i	0.974337	−	0.225093i	$-0.0722687\pi$
$752$	6.38765			0.232934
$753$		−	4.23956i		−	0.154498i
$754$	−6.55877	−	3.43333i	−0.238856	−	0.125035i
$755$	−18.8122	+	13.2888i	−0.684645	+	0.483630i
$756$		−	6.45659i		−	0.234824i
$757$	−10.2685			−0.373216			−0.186608	−	0.982434i	$-0.559749\pi$
$757$	−10.2685			−0.373216			−0.186608	+	0.982434i	$0.559749\pi$
$758$		−	32.8410i		−	1.19284i
$759$	−0.426070			−0.0154654
$760$	8.64769	+	12.2420i	0.313685	+	0.444064i
$761$	49.1824			1.78286			0.891430	−	0.453159i	$-0.149703\pi$
$761$	49.1824			1.78286			0.891430	+	0.453159i	$0.149703\pi$
$762$	−0.944579			−0.0342185
$763$			3.36308i			0.121752i
$764$		−	24.5210i		−	0.887139i
$765$	−1.11062	+	0.784534i	−0.0401544	+	0.0283649i
$766$			34.6298i			1.25123i
$767$		−	7.26568i		−	0.262348i
$768$	−0.367473			−0.0132601
$769$		−	36.4972i		−	1.31612i	−0.752964	−	0.658062i	$-0.771376\pi$
$769$		−	36.4972i		−	1.31612i	0.752964	−	0.658062i	$-0.228624\pi$
$770$	5.96314	−	4.21234i	0.214897	−	0.151802i
$771$			2.67346i			0.0962823i
$772$	−10.0101			−0.360273
$773$	29.4854			1.06052			0.530258	−	0.847836i	$-0.322095\pi$
$773$	29.4854			1.06052			0.530258	+	0.847836i	$0.322095\pi$
$774$	31.1133			1.11835
$775$	−19.9214	−	7.06452i	−0.715596	−	0.253765i
$776$	16.0605			0.576540
$777$		−	6.30794i		−	0.226296i
$778$			12.9103i			0.462858i
$779$	69.5305			2.49119
$780$	−0.651735	−	0.922620i	−0.0233358	−	0.0330351i
$781$			5.49885i			0.196764i
$782$		−	0.225807i		−	0.00807483i
$783$	5.38263	−	10.2826i	0.192360	−	0.367469i
$784$	−1.97480			−0.0705285
$785$	21.1226	−	14.9209i	0.753898	−	0.532550i
$786$			0.443531i			0.0158202i
$787$		−	38.4961i		−	1.37224i	−0.727490	−	0.686119i	$-0.759313\pi$
$787$		−	38.4961i		−	1.37224i	0.727490	−	0.686119i	$-0.240687\pi$
$788$			19.1667i			0.682786i
$789$	−10.9262			−0.388985
$790$	−11.4263	−	16.1754i	−0.406528	−	0.575496i
$791$		−	44.1733i		−	1.57062i
$792$		−	3.12246i		−	0.110952i
$793$	−4.65382			−0.165262
$794$			28.7398i			1.01994i
$795$	−4.78794	−	6.77798i	−0.169811	−	0.240390i
$796$	14.7249			0.521910
$797$	−44.1311			−1.56320			−0.781602	−	0.623777i	$-0.785597\pi$
$797$	−44.1311			−1.56320			−0.781602	+	0.623777i	$0.785597\pi$
$798$	−7.37913			−0.261218
$799$	1.35582			0.0479653
$800$	−1.67114	+	4.71246i	−0.0590836	+	0.166611i
$801$		−	8.47675i		−	0.299511i
$802$	−24.2030			−0.854637
$803$		−	3.83383i		−	0.135293i
$804$			3.75977i			0.132597i
$805$	5.82069	−	4.11171i	0.205152	−	0.144919i
$806$	−5.81143			−0.204699
$807$			9.74869i			0.343170i
$808$		−	13.7584i		−	0.484019i
$809$			8.79023i			0.309048i	0.987989	+	0.154524i	$0.0493844\pi$
$809$			8.79023i			0.309048i	−0.987989	+	0.154524i	$0.950616\pi$
$810$	−14.2509	+	10.0668i	−0.500724	+	0.353710i
$811$	−3.91186			−0.137364			−0.0686820	−	0.997639i	$-0.521879\pi$
$811$	−3.91186			−0.137364			−0.0686820	+	0.997639i	$0.521879\pi$
$812$	−14.2930	−	7.48197i	−0.501585	−	0.262566i
$813$			7.09181i			0.248721i
$814$		−	6.24492i		−	0.218884i
$815$	−6.40457	+	4.52416i	−0.224342	+	0.158474i
$816$	−0.0779983			−0.00273049
$817$		−	72.7938i		−	2.54673i
$818$			17.4820i			0.611245i
$819$	−11.7990			−0.412289
$820$	13.3826	+	18.9450i	0.467342	+	0.661586i
$821$	−8.59729			−0.300047			−0.150024	−	0.988682i	$-0.547935\pi$
$821$	−8.59729			−0.300047			−0.150024	+	0.988682i	$0.547935\pi$
$822$	2.13698			0.0745358
$823$	2.31892			0.0808323			0.0404162	−	0.999183i	$-0.487132\pi$
$823$	2.31892			0.0808323			0.0404162	+	0.999183i	$0.487132\pi$
$824$			9.16613i			0.319317i
$825$	1.88735	+	0.669292i	0.0657090	+	0.0233018i
$826$		−	15.8335i		−	0.550918i
$827$	13.5864			0.472446			0.236223	−	0.971699i	$-0.424090\pi$
$827$	13.5864			0.472446			0.236223	+	0.971699i	$0.424090\pi$
$828$		−	3.04787i		−	0.105921i
$829$		−	24.1451i		−	0.838594i	−0.907849	−	0.419297i	$-0.862277\pi$
$829$		−	24.1451i		−	0.838594i	0.907849	−	0.419297i	$-0.137723\pi$
$830$	−16.0120	−	22.6672i	−0.555784	−	0.786789i
$831$		−	4.11724i		−	0.142825i
$832$			1.37471i			0.0476596i
$833$	−0.419163			−0.0145231
$834$	5.52781			0.191412
$835$	−8.78272	−	12.4331i	−0.303939	−	0.430267i
$836$	−7.30542			−0.252663
$837$		−	9.11092i		−	0.314919i
$838$	−26.2378			−0.906369
$839$		−	19.9698i		−	0.689434i	−0.938707	−	0.344717i	$-0.887975\pi$
$839$		−	19.9698i		−	0.689434i	0.938707	−	0.344717i	$-0.112025\pi$
$840$	−1.42027	−	2.01059i	−0.0490040	−	0.0693719i
$841$	−16.5251	−	23.8311i	−0.569831	−	0.821762i
$842$		−	13.6673i		−	0.471008i
$843$	2.79461			0.0962514
$844$			8.19596i			0.282116i
$845$	20.2911	−	14.3335i	0.698035	−	0.493089i
$846$	18.3004			0.629181
$847$		−	29.3953i		−	1.01003i
$848$			10.0993i			0.346810i
$849$			1.74822i			0.0599987i
$850$	−0.354708	+	1.00025i	−0.0121664	+	0.0343082i
$851$		−	6.09574i		−	0.208959i
$852$	1.85404			0.0635185
$853$	36.0840			1.23549			0.617746	−	0.786378i	$-0.288046\pi$
$853$	36.0840			1.23549			0.617746	+	0.786378i	$0.288046\pi$
$854$	−10.1417			−0.347041
$855$	24.7753	+	35.0728i	0.847298	+	1.19947i
$856$		−	2.34345i		−	0.0800976i
$857$			19.0491i			0.650705i	0.945593	+	0.325352i	$0.105483\pi$
$857$			19.0491i			0.650705i	−0.945593	+	0.325352i	$0.894517\pi$
$858$	0.550574			0.0187963
$859$		−	43.1051i		−	1.47073i	−0.677673	−	0.735364i	$-0.737011\pi$
$859$		−	43.1051i		−	1.47073i	0.677673	−	0.735364i	$-0.262989\pi$
$860$	19.8341	−	14.0107i	0.676337	−	0.477762i
$861$	−11.4195			−0.389175
$862$	20.1544			0.686463
$863$		−	25.9382i		−	0.882947i	−0.897274	−	0.441474i	$-0.854456\pi$
$863$		−	25.9382i		−	0.882947i	0.897274	−	0.441474i	$-0.145544\pi$
$864$	−2.15522			−0.0733220
$865$	−16.3795	−	23.1874i	−0.556918	−	0.788394i
$866$	−9.30542			−0.316211
$867$	6.23049			0.211599
$868$	−12.6644			−0.429857
$869$	9.65271			0.327446
$870$	−0.585722	−	4.38603i	−0.0198578	−	0.148700i
$871$	14.0652			0.476582
$872$	1.12260			0.0380161
$873$	46.0129			1.55730
$874$	−7.13090			−0.241206
$875$	−32.2426	+	9.07007i	−1.09000	+	0.306624i
$876$	−1.29265			−0.0436746
$877$			43.0492i			1.45367i	0.686812	+	0.726835i	$0.259009\pi$
$877$			43.0492i			1.45367i	−0.686812	+	0.726835i	$0.740991\pi$
$878$	−38.2655			−1.29140
$879$	8.19111			0.276279
$880$	−1.40608	−	1.99050i	−0.0473990	−	0.0670998i
$881$			49.8210i			1.67851i	0.543736	+	0.839256i	$0.317009\pi$
$881$			49.8210i			1.67851i	−0.543736	+	0.839256i	$0.682991\pi$
$882$	−5.65773			−0.190506
$883$			9.29618i			0.312841i	0.987691	+	0.156421i	$0.0499955\pi$
$883$			9.29618i			0.312841i	−0.987691	+	0.156421i	$0.950004\pi$
$884$			0.291791i			0.00981398i
$885$	3.54711	−	2.50567i	0.119235	−	0.0842270i
$886$	34.1561			1.14750
$887$	1.49827			0.0503070			0.0251535	−	0.999684i	$-0.491993\pi$
$887$	1.49827			0.0503070			0.0251535	+	0.999684i	$0.491993\pi$
$888$	−2.10560			−0.0706591
$889$			7.70060i			0.258270i
$890$	−3.81719	−	5.40375i	−0.127952	−	0.181134i
$891$		−	8.50422i		−	0.284902i
$892$			6.32850i			0.211894i
$893$		−	42.8162i		−	1.43279i
$894$	0.355774			0.0118989
$895$	−6.30040	+	4.45057i	−0.210599	+	0.148766i
$896$			2.99580i			0.100083i
$897$	0.537421			0.0179440
$898$			2.90669i			0.0969976i
$899$	−20.1689	−	10.5578i	−0.672669	−	0.352123i
$900$	−4.78774	+	13.5010i	−0.159591	+	0.450034i
$901$			2.14363i			0.0714146i
$902$	−11.3054			−0.376429
$903$			11.9554i			0.397852i
$904$	−14.7451			−0.490414
$905$	35.3995	−	25.0061i	1.17672	−	0.831231i
$906$	−3.78512			−0.125752
$907$	32.7075			1.08603			0.543017	−	0.839722i	$-0.317282\pi$
$907$	32.7075			1.08603			0.543017	+	0.839722i	$0.317282\pi$
$908$			20.8358i			0.691461i
$909$		−	39.4173i		−	1.30739i
$910$	−7.52158	+	5.31321i	−0.249338	+	0.176131i
$911$		−	38.5452i		−	1.27706i	−0.769598	−	0.638529i	$-0.779543\pi$
$911$		−	38.5452i		−	1.27706i	0.769598	−	0.638529i	$-0.220457\pi$
$912$			2.46316i			0.0815634i
$913$	13.5266			0.447667
$914$			2.65336i			0.0877655i
$915$	−1.60493	−	2.27200i	−0.0530573	−	0.0751099i
$916$			14.2925i			0.472236i
$917$	3.61585			0.119406
$918$	−0.457457			−0.0150983
$919$	−36.8375			−1.21516			−0.607579	−	0.794259i	$-0.707859\pi$
$919$	−36.8375			−1.21516			−0.607579	+	0.794259i	$0.707859\pi$
$920$	−1.37249	−	1.94295i	−0.0452498	−	0.0640572i
$921$	7.33223			0.241605
$922$		−	6.53979i		−	0.215377i
$923$		−	6.93595i		−	0.228300i
$924$	1.19982			0.0394712
$925$	−9.57549	+	27.0021i	−0.314840	+	0.887822i
$926$		−	27.1658i		−	0.892722i
$927$			26.2606i			0.862512i
$928$	−2.49749	+	4.77101i	−0.0819841	+	0.156616i
$929$	29.3787			0.963885			0.481942	−	0.876203i	$-0.339931\pi$
$929$	29.3787			0.963885			0.481942	+	0.876203i	$0.339931\pi$
$930$	−2.00415	−	2.83715i	−0.0657186	−	0.0930337i
$931$			13.2370i			0.433826i
$932$		−	13.5230i		−	0.442961i
$933$			5.81181i			0.190270i
$934$	32.2561			1.05545
$935$	−0.298449	−	0.422496i	−0.00976033	−	0.0138171i
$936$			3.93850i			0.128734i
$937$		−	29.1188i		−	0.951270i	−0.879643	−	0.475635i	$-0.842218\pi$
$937$		−	29.1188i		−	0.951270i	0.879643	−	0.475635i	$-0.157782\pi$
$938$	30.6512			1.00080
$939$		−	3.56860i		−	0.116457i
$940$	11.6661	−	8.24090i	0.380507	−	0.268788i
$941$	−34.4784			−1.12396			−0.561982	−	0.827149i	$-0.689961\pi$
$941$	−34.4784			−1.12396			−0.561982	+	0.827149i	$0.689961\pi$
$942$	4.24999			0.138472
$943$	−11.0353			−0.359360
$944$	−5.28523			−0.172020
$945$	−8.32984	−	11.7920i	−0.270970	−	0.383595i
$946$			11.8360i			0.384822i
$947$	−16.7368			−0.543873			−0.271936	−	0.962315i	$-0.587664\pi$
$947$	−16.7368			−0.543873			−0.271936	+	0.962315i	$0.587664\pi$
$948$		−	3.25460i		−	0.105704i
$949$			4.83579i			0.156976i
$950$	31.5875	+	11.2016i	1.02483	+	0.363427i
$951$	−11.6143			−0.376619
$952$			0.635875i			0.0206088i
$953$			49.5247i			1.60426i	0.597149	+	0.802131i	$0.296300\pi$
$953$			49.5247i			1.60426i	−0.597149	+	0.802131i	$0.703700\pi$
$954$			28.9340i			0.936773i
$955$	−31.6353	−	44.7840i	−1.02369	−	1.44918i
$956$	−18.6697			−0.603822
$957$	1.91080	+	1.00025i	0.0617672	+	0.0323334i
$958$		−	25.8295i		−	0.834514i
$959$		−	17.4216i		−	0.562572i
$960$	−0.671136	+	0.474088i	−0.0216608	+	0.0153011i
$961$	13.1293			0.423525
$962$			7.87700i			0.253965i
$963$		−	6.71391i		−	0.216353i
$964$	−19.6628			−0.633298
$965$	−18.2821	+	12.9144i	−0.588520	+	0.415728i
$966$	1.17116			0.0376814
$967$	−28.3924			−0.913040			−0.456520	−	0.889713i	$-0.650904\pi$
$967$	−28.3924			−0.913040			−0.456520	+	0.889713i	$0.650904\pi$
$968$	−9.81217			−0.315375
$969$			0.522820i			0.0167954i
$970$	29.3322	−	20.7202i	0.941801	−	0.665284i
$971$			4.86155i			0.156014i	0.996953	+	0.0780072i	$0.0248557\pi$
$971$			4.86155i			0.156014i	−0.996953	+	0.0780072i	$0.975144\pi$
$972$	−9.33301			−0.299356
$973$		−	45.0650i		−	1.44472i
$974$			1.63351i			0.0523411i
$975$	−2.38060	−	0.844208i	−0.0762401	−	0.0270363i
$976$			3.38530i			0.108361i
$977$			34.0078i			1.08801i	0.839083	+	0.544003i	$0.183092\pi$
$977$			34.0078i			1.08801i	−0.839083	+	0.544003i	$0.816908\pi$
$978$	−1.28864			−0.0412061
$979$	3.22469			0.103062
$980$	−3.60668	+	2.54775i	−0.115211	+	0.0813847i
$981$	3.21621			0.102686
$982$		−	10.3456i		−	0.330142i
$983$	−38.6176			−1.23171			−0.615855	−	0.787860i	$-0.711189\pi$
$983$	−38.6176			−1.23171			−0.615855	+	0.787860i	$0.711189\pi$
$984$			3.81184i			0.121517i
$985$	24.7275	+	35.0052i	0.787885	+	1.11536i
$986$	−0.530107	+	1.01267i	−0.0168820	+	0.0322501i
$987$			7.03201i			0.223831i
$988$	9.21465			0.293157
$989$			11.5533i			0.367372i
$990$	−4.02838	−	5.70272i	−0.128030	−	0.181244i
$991$	26.3189			0.836048			0.418024	−	0.908436i	$-0.362723\pi$
$991$	26.3189			0.836048			0.418024	+	0.908436i	$0.362723\pi$
$992$			4.22738i			0.134219i
$993$		−	6.78536i		−	0.215327i
$994$		−	15.1149i		−	0.479417i
$995$	26.8929	−	18.9970i	0.852562	−	0.602246i
$996$		−	4.56077i		−	0.144513i
$997$	34.2096			1.08343			0.541715	−	0.840562i	$-0.317775\pi$
$997$	34.2096			1.08343			0.541715	+	0.840562i	$0.317775\pi$
$998$	−0.704726			−0.0223077
$999$	−12.3492			−0.390713

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	290.2.d.a.289.3	✓	8
3.2	odd	2		2610.2.b.f.289.2		8
4.3	odd	2		2320.2.j.d.289.5		8
5.2	odd	4		1450.2.c.g.1101.6		16
5.3	odd	4		1450.2.c.g.1101.11		16
5.4	even	2		290.2.d.b.289.6	yes	8
15.14	odd	2		2610.2.b.d.289.1		8
20.19	odd	2		2320.2.j.e.289.4		8
29.28	even	2		290.2.d.b.289.5	yes	8
87.86	odd	2		2610.2.b.d.289.2		8
116.115	odd	2		2320.2.j.e.289.3		8
145.28	odd	4		1450.2.c.g.1101.5		16
145.57	odd	4		1450.2.c.g.1101.12		16
145.144	even	2	inner	290.2.d.a.289.4	yes	8
435.434	odd	2		2610.2.b.f.289.1		8
580.579	odd	2		2320.2.j.d.289.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.d.a.289.3	✓	8	1.1	even	1	trivial
290.2.d.a.289.4	yes	8	145.144	even	2	inner
290.2.d.b.289.5	yes	8	29.28	even	2
290.2.d.b.289.6	yes	8	5.4	even	2
1450.2.c.g.1101.5		16	145.28	odd	4
1450.2.c.g.1101.6		16	5.2	odd	4
1450.2.c.g.1101.11		16	5.3	odd	4
1450.2.c.g.1101.12		16	145.57	odd	4
2320.2.j.d.289.5		8	4.3	odd	2
2320.2.j.d.289.6		8	580.579	odd	2
2320.2.j.e.289.3		8	116.115	odd	2
2320.2.j.e.289.4		8	20.19	odd	2
2610.2.b.d.289.1		8	15.14	odd	2
2610.2.b.d.289.2		8	87.86	odd	2
2610.2.b.f.289.1		8	435.434	odd	2
2610.2.b.f.289.2		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 290 = 2 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	290.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.367473 q^{3} +1.00000 q^{4} +(1.82635 - 1.29013i) q^{5} +0.367473 q^{6} -2.99580i q^{7} -1.00000 q^{8} -2.86496 q^{9} +(-1.82635 + 1.29013i) q^{10} -1.08988i q^{11} -0.367473 q^{12} +1.37471i q^{13} +2.99580i q^{14} +(-0.671136 + 0.474088i) q^{15} +1.00000 q^{16} +0.212256 q^{17} +2.86496 q^{18} -6.70297i q^{19} +(1.82635 - 1.29013i) q^{20} +1.10088i q^{21} +1.08988i q^{22} +1.06384i q^{23} +0.367473 q^{24} +(1.67114 - 4.71246i) q^{25} -1.37471i q^{26} +2.15522 q^{27} -2.99580i q^{28} +(2.49749 - 4.77101i) q^{29} +(0.671136 - 0.474088i) q^{30} -4.22738i q^{31} -1.00000 q^{32} +0.400501i q^{33} -0.212256 q^{34} +(-3.86496 - 5.47139i) q^{35} -2.86496 q^{36} -5.72993 q^{37} +6.70297i q^{38} -0.505170i q^{39} +(-1.82635 + 1.29013i) q^{40} +10.3731i q^{41} -1.10088i q^{42} +10.8599 q^{43} -1.08988i q^{44} +(-5.23244 + 3.69617i) q^{45} -1.06384i q^{46} +6.38765 q^{47} -0.367473 q^{48} -1.97480 q^{49} +(-1.67114 + 4.71246i) q^{50} -0.0779983 q^{51} +1.37471i q^{52} +10.0993i q^{53} -2.15522 q^{54} +(-1.40608 - 1.99050i) q^{55} +2.99580i q^{56} +2.46316i q^{57} +(-2.49749 + 4.77101i) q^{58} -5.28523 q^{59} +(-0.671136 + 0.474088i) q^{60} +3.38530i q^{61} +4.22738i q^{62} +8.58285i q^{63} +1.00000 q^{64} +(1.77356 + 2.51071i) q^{65} -0.400501i q^{66} -10.2314i q^{67} +0.212256 q^{68} -0.390934i q^{69} +(3.86496 + 5.47139i) q^{70} -5.04538 q^{71} +2.86496 q^{72} +3.51767 q^{73} +5.72993 q^{74} +(-0.614098 + 1.73170i) q^{75} -6.70297i q^{76} -3.26505 q^{77} +0.505170i q^{78} +8.85669i q^{79} +(1.82635 - 1.29013i) q^{80} +7.80291 q^{81} -10.3731i q^{82} +12.4112i q^{83} +1.10088i q^{84} +(0.387654 - 0.273837i) q^{85} -10.8599 q^{86} +(-0.917761 + 1.75322i) q^{87} +1.08988i q^{88} +2.95876i q^{89} +(5.23244 - 3.69617i) q^{90} +4.11836 q^{91} +1.06384i q^{92} +1.55345i q^{93} -6.38765 q^{94} +(-8.64769 - 12.2420i) q^{95} +0.367473 q^{96} -16.0605 q^{97} +1.97480 q^{98} +3.12246i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 4 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} - 8 q^{8} + 8 q^{9} + q^{10} + 4 q^{12} + 3 q^{15} + 8 q^{16} + 2 q^{17} - 8 q^{18} - q^{20} - 4 q^{24} + 5 q^{25} + 10 q^{27} - 4 q^{29} - 3 q^{30}+ \cdots + 6 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 4 * q^3 + 8 * q^4 - q^5 - 4 * q^6 - 8 * q^8 + 8 * q^9 + q^10 + 4 * q^12 + 3 * q^15 + 8 * q^16 + 2 * q^17 - 8 * q^18 - q^20 - 4 * q^24 + 5 * q^25 + 10 * q^27 - 4 * q^29 - 3 * q^30 - 8 * q^32 - 2 * q^34 + 8 * q^36 + 16 * q^37 + q^40 + 8 * q^43 - 4 * q^45 + 6 * q^47 + 4 * q^48 - 6 * q^49 - 5 * q^50 - 24 * q^51 - 10 * q^54 + 11 * q^55 + 4 * q^58 - 18 * q^59 + 3 * q^60 + 8 * q^64 - 15 * q^65 + 2 * q^68 - 12 * q^71 - 8 * q^72 - 34 * q^73 - 16 * q^74 + 11 * q^75 - 40 * q^77 - q^80 - 24 * q^81 - 42 * q^85 - 8 * q^86 + 10 * q^87 + 4 * q^90 - 20 * q^91 - 6 * q^94 + 10 * q^95 - 4 * q^96 - 14 * q^97 + 6 * q^98

Introduction

L-functions

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Database

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