LMFDB - Embedded newform 1008.2.r.j.673.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(337,1008)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1008.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.r (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			673.3
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	1008.673
Dual form			1008.2.r.j.337.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.71053 - 0.272169i) q^{3} +(-0.119562 - 0.207087i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(2.85185 - 0.931107i) q^{9} +(-2.56238 + 4.43818i) q^{11} +(2.44282 + 4.23109i) q^{13} +(-0.260877 - 0.321688i) q^{15} +3.70370 q^{17} -3.66019 q^{19} +(-0.619562 + 1.61745i) q^{21} +(3.71053 + 6.42683i) q^{23} +(2.47141 - 4.28061i) q^{25} +(4.62476 - 2.36887i) q^{27} +(-1.73229 + 3.00041i) q^{29} +(-0.358685 - 0.621261i) q^{31} +(-3.17511 + 8.28905i) q^{33} +0.239123 q^{35} +4.60301 q^{37} +(5.33009 + 6.57256i) q^{39} +(-2.80150 - 4.85235i) q^{41} +(6.24433 - 10.8155i) q^{43} +(-0.533792 - 0.479256i) q^{45} +(2.16991 - 3.75839i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(6.33530 - 1.00803i) q^{51} -0.942820 q^{53} +1.22545 q^{55} +(-6.26088 + 0.996189i) q^{57} +(3.78947 + 6.56355i) q^{59} +(-2.75404 + 4.77014i) q^{61} +(-0.619562 + 2.93533i) q^{63} +(0.584135 - 1.01175i) q^{65} +(-0.330095 - 0.571741i) q^{67} +(8.09617 + 9.98342i) q^{69} -13.7414 q^{71} -3.66019 q^{73} +(3.06238 - 7.99476i) q^{75} +(-2.56238 - 4.43818i) q^{77} +(-3.11273 + 5.39140i) q^{79} +(7.26608 - 5.31075i) q^{81} +(4.85185 - 8.40365i) q^{83} +(-0.442820 - 0.766987i) q^{85} +(-2.14652 + 5.60377i) q^{87} -7.48865 q^{89} -4.88564 q^{91} +(-0.782630 - 0.965064i) q^{93} +(0.437618 + 0.757977i) q^{95} +(8.57442 - 14.8513i) q^{97} +(-3.17511 + 15.0429i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{3} - q^{5} - 3 q^{7} + 8 q^{9} + 2 q^{11} - 3 q^{13} - q^{15} + 4 q^{17} - 6 q^{19} - 4 q^{21} + 14 q^{23} + 6 q^{25} - 7 q^{27} - q^{29} - 3 q^{31} + 8 q^{33} + 2 q^{35} - 6 q^{37} + 24 q^{39}+ \cdots + 8 q^{99}+O(q^{100}) $ 6 * q + 2 * q^3 - q^5 - 3 * q^7 + 8 * q^9 + 2 * q^11 - 3 * q^13 - q^15 + 4 * q^17 - 6 * q^19 - 4 * q^21 + 14 * q^23 + 6 * q^25 - 7 * q^27 - q^29 - 3 * q^31 + 8 * q^33 + 2 * q^35 - 6 * q^37 + 24 * q^39 + 3 * q^43 + 23 * q^45 + 21 * q^47 - 3 * q^49 - 5 * q^51 + 12 * q^53 - 12 * q^55 - 37 * q^57 + 31 * q^59 - 6 * q^61 - 4 * q^63 - 15 * q^65 + 6 * q^67 + 5 * q^69 - 34 * q^71 - 6 * q^73 + q^75 + 2 * q^77 - 9 * q^79 + 8 * q^81 + 20 * q^83 + 15 * q^85 + 23 * q^87 + 24 * q^89 + 6 * q^91 - 3 * q^93 + 20 * q^95 + 9 * q^97 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.71053	−	0.272169i	0.987577	−	0.157137i
$3$	1.71053	−	0.272169i	0.987577	−	0.157137i
$4$		0			0
$5$	−0.119562	−	0.207087i	−0.0534696	−	0.0926120i	0.838052	−	0.545591i	$-0.183695\pi$
$5$	−0.119562	−	0.207087i	−0.0534696	−	0.0926120i	−0.891521	+	0.452979i	$0.850361\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$		0			0
$9$	2.85185	−	0.931107i	0.950616	−	0.310369i
$10$		0			0
$11$	−2.56238	+	4.43818i	−0.772587	+	1.33816i	0.163554	+	0.986534i	$0.447704\pi$
$11$	−2.56238	+	4.43818i	−0.772587	+	1.33816i	−0.936141	+	0.351626i	$0.885629\pi$
$12$		0			0
$13$	2.44282	+	4.23109i	0.677516	+	1.17349i	0.975727	+	0.218993i	$0.0702770\pi$
$13$	2.44282	+	4.23109i	0.677516	+	1.17349i	−0.298210	+	0.954500i	$0.596390\pi$
$14$		0			0
$15$	−0.260877	−	0.321688i	−0.0673581	−	0.0830595i
$16$		0			0
$17$	3.70370			0.898278			0.449139	−	0.893462i	$-0.351731\pi$
$17$	3.70370			0.898278			0.449139	+	0.893462i	$0.351731\pi$
$18$		0			0
$19$	−3.66019			−0.839705			−0.419853	−	0.907592i	$-0.637918\pi$
$19$	−3.66019			−0.839705			−0.419853	+	0.907592i	$0.637918\pi$
$20$		0			0
$21$	−0.619562	+	1.61745i	−0.135199	+	0.352956i
$22$		0			0
$23$	3.71053	+	6.42683i	0.773700	+	1.34009i	0.935522	+	0.353267i	$0.114929\pi$
$23$	3.71053	+	6.42683i	0.773700	+	1.34009i	−0.161823	+	0.986820i	$0.551737\pi$
$24$		0			0
$25$	2.47141	−	4.28061i	0.494282	−	0.856122i
$26$		0			0
$27$	4.62476	−	2.36887i	0.890036	−	0.455890i
$28$		0			0
$29$	−1.73229	+	3.00041i	−0.321678	+	0.557162i	−0.980834	−	0.194844i	$-0.937580\pi$
$29$	−1.73229	+	3.00041i	−0.321678	+	0.557162i	0.659157	+	0.752006i	$0.270913\pi$
$30$		0			0
$31$	−0.358685	−	0.621261i	−0.0644217	−	0.111582i	0.832016	−	0.554752i	$-0.187187\pi$
$31$	−0.358685	−	0.621261i	−0.0644217	−	0.111582i	−0.896437	+	0.443171i	$0.853854\pi$
$32$		0			0
$33$	−3.17511	+	8.28905i	−0.552715	+	1.44294i
$34$		0			0
$35$	0.239123			0.0404192
$36$		0			0
$37$	4.60301			0.756730			0.378365	−	0.925656i	$-0.376486\pi$
$37$	4.60301			0.756730			0.378365	+	0.925656i	$0.376486\pi$
$38$		0			0
$39$	5.33009	+	6.57256i	0.853498	+	1.05245i
$40$		0			0
$41$	−2.80150	−	4.85235i	−0.437522	−	0.757810i	0.559976	−	0.828509i	$-0.310810\pi$
$41$	−2.80150	−	4.85235i	−0.437522	−	0.757810i	−0.997498	+	0.0706992i	$0.977477\pi$
$42$		0			0
$43$	6.24433	−	10.8155i	0.952251	−	1.64935i	0.211713	−	0.977332i	$-0.432096\pi$
$43$	6.24433	−	10.8155i	0.952251	−	1.64935i	0.740538	−	0.672015i	$-0.234571\pi$
$44$		0			0
$45$	−0.533792	−	0.479256i	−0.0795730	−	0.0714432i
$46$		0			0
$47$	2.16991	−	3.75839i	0.316513	−	0.548217i	−0.663245	−	0.748403i	$-0.730821\pi$
$47$	2.16991	−	3.75839i	0.316513	−	0.548217i	0.979758	+	0.200186i	$0.0641545\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$	6.33530	−	1.00803i	0.887119	−	0.141152i
$52$		0			0
$53$	−0.942820			−0.129506			−0.0647531	−	0.997901i	$-0.520626\pi$
$53$	−0.942820			−0.129506			−0.0647531	+	0.997901i	$0.520626\pi$
$54$		0			0
$55$	1.22545			0.165240
$56$		0			0
$57$	−6.26088	+	0.996189i	−0.829273	+	0.131948i
$58$		0			0
$59$	3.78947	+	6.56355i	0.493347	+	0.854501i	0.999971	−	0.00766579i	$-0.00244012\pi$
$59$	3.78947	+	6.56355i	0.493347	+	0.854501i	−0.506624	+	0.862167i	$0.669107\pi$
$60$		0			0
$61$	−2.75404	+	4.77014i	−0.352619	+	0.610754i	−0.986707	−	0.162507i	$-0.948042\pi$
$61$	−2.75404	+	4.77014i	−0.352619	+	0.610754i	0.634089	+	0.773260i	$0.281375\pi$
$62$		0			0
$63$	−0.619562	+	2.93533i	−0.0780574	+	0.369816i
$64$		0			0
$65$	0.584135	−	1.01175i	0.0724530	−	0.125492i
$66$		0			0
$67$	−0.330095	−	0.571741i	−0.0403275	−	0.0698493i	0.845157	−	0.534518i	$-0.179507\pi$
$67$	−0.330095	−	0.571741i	−0.0403275	−	0.0698493i	−0.885485	+	0.464669i	$0.846173\pi$
$68$		0			0
$69$	8.09617	+	9.98342i	0.974665	+	1.20186i
$70$		0			0
$71$	−13.7414			−1.63081			−0.815405	−	0.578891i	$-0.803486\pi$
$71$	−13.7414			−1.63081			−0.815405	+	0.578891i	$0.803486\pi$
$72$		0			0
$73$	−3.66019			−0.428393			−0.214196	−	0.976791i	$-0.568713\pi$
$73$	−3.66019			−0.428393			−0.214196	+	0.976791i	$0.568713\pi$
$74$		0			0
$75$	3.06238	−	7.99476i	0.353613	−	0.923156i
$76$		0			0
$77$	−2.56238	−	4.43818i	−0.292010	−	0.505777i
$78$		0			0
$79$	−3.11273	+	5.39140i	−0.350209	+	0.606580i	−0.986286	−	0.165046i	$-0.947223\pi$
$79$	−3.11273	+	5.39140i	−0.350209	+	0.606580i	0.636077	+	0.771626i	$0.280556\pi$
$80$		0			0
$81$	7.26608	−	5.31075i	0.807342	−	0.590084i
$82$		0			0
$83$	4.85185	−	8.40365i	0.532560	−	0.922420i	−0.466718	−	0.884406i	$-0.654564\pi$
$83$	4.85185	−	8.40365i	0.532560	−	0.922420i	0.999277	−	0.0380138i	$-0.0121031\pi$
$84$		0			0
$85$	−0.442820	−	0.766987i	−0.0480306	−	0.0831914i
$86$		0			0
$87$	−2.14652	+	5.60377i	−0.230131	+	0.600788i
$88$		0			0
$89$	−7.48865			−0.793795			−0.396898	−	0.917863i	$-0.629913\pi$
$89$	−7.48865			−0.793795			−0.396898	+	0.917863i	$0.629913\pi$
$90$		0			0
$91$	−4.88564			−0.512154
$92$		0			0
$93$	−0.782630	−	0.965064i	−0.0811550	−	0.100072i
$94$		0			0
$95$	0.437618	+	0.757977i	0.0448987	+	0.0777668i
$96$		0			0
$97$	8.57442	−	14.8513i	0.870600	−	1.50792i	0.00922376	−	0.999957i	$-0.497064\pi$
$97$	8.57442	−	14.8513i	0.870600	−	1.50792i	0.861377	−	0.507967i	$-0.169603\pi$
$98$		0			0
$99$	−3.17511	+	15.0429i	−0.319110	+	1.51186i
$100$		0			0
$101$	−3.59097	+	6.21975i	−0.357315	+	0.618888i	−0.987511	−	0.157548i	$-0.949641\pi$
$101$	−3.59097	+	6.21975i	−0.357315	+	0.618888i	0.630196	+	0.776436i	$0.282974\pi$
$102$		0			0
$103$	−6.41423	−	11.1098i	−0.632013	−	1.09468i	−0.987140	−	0.159860i	$-0.948896\pi$
$103$	−6.41423	−	11.1098i	−0.632013	−	1.09468i	0.355127	−	0.934818i	$-0.384438\pi$
$104$		0			0
$105$	0.409028	−	0.0650819i	0.0399171	−	0.00635134i
$106$		0			0
$107$	−7.56526			−0.731361			−0.365681	−	0.930740i	$-0.619164\pi$
$107$	−7.56526			−0.731361			−0.365681	+	0.930740i	$0.619164\pi$
$108$		0			0
$109$	−6.98057			−0.668617			−0.334309	−	0.942464i	$-0.608503\pi$
$109$	−6.98057			−0.668617			−0.334309	+	0.942464i	$0.608503\pi$
$110$		0			0
$111$	7.87360	−	1.25280i	0.747329	−	0.118910i
$112$		0			0
$113$	9.78495	+	16.9480i	0.920491	+	1.59434i	0.798657	+	0.601787i	$0.205544\pi$
$113$	9.78495	+	16.9480i	0.920491	+	1.59434i	0.121834	+	0.992550i	$0.461122\pi$
$114$		0			0
$115$	0.887275	−	1.53681i	0.0827388	−	0.143308i
$116$		0			0
$117$	10.9061	+	9.79190i	1.00827	+	0.905261i
$118$		0			0
$119$	−1.85185	+	3.20750i	−0.169759	+	0.294031i
$120$		0			0
$121$	−7.63160	−	13.2183i	−0.693782	−	1.20167i
$122$		0			0
$123$	−6.11273	−	7.53762i	−0.551166	−	0.679645i
$124$		0			0
$125$	−2.37756			−0.212655
$126$		0			0
$127$	16.8090			1.49156			0.745780	−	0.666192i	$-0.232077\pi$
$127$	16.8090			1.49156			0.745780	+	0.666192i	$0.232077\pi$
$128$		0			0
$129$	7.73749	−	20.1998i	0.681248	−	1.77849i
$130$		0			0
$131$	2.44966	+	4.24293i	0.214027	+	0.370706i	0.952971	−	0.303061i	$-0.0980085\pi$
$131$	2.44966	+	4.24293i	0.214027	+	0.370706i	−0.738944	+	0.673767i	$0.764675\pi$
$132$		0			0
$133$	1.83009	−	3.16982i	0.158689	−	0.274858i
$134$		0			0
$135$	−1.04351	−	0.674501i	−0.0898108	−	0.0580518i
$136$		0			0
$137$	−2.72257	+	4.71563i	−0.232605	+	0.402884i	−0.958574	−	0.284844i	$-0.908058\pi$
$137$	−2.72257	+	4.71563i	−0.232605	+	0.402884i	0.725969	+	0.687727i	$0.241392\pi$
$138$		0			0
$139$	2.83009	+	4.90187i	0.240046	+	0.415771i	0.960727	−	0.277495i	$-0.0895043\pi$
$139$	2.83009	+	4.90187i	0.240046	+	0.415771i	−0.720681	+	0.693266i	$0.756171\pi$
$140$		0			0
$141$	2.68878	−	7.01942i	0.226436	−	0.591142i
$142$		0			0
$143$	−25.0377			−2.09376
$144$		0			0
$145$	0.828460			0.0687999
$146$		0			0
$147$	−1.09097	−	1.34528i	−0.0899818	−	0.110957i
$148$		0			0
$149$	−1.14132	−	1.97682i	−0.0935002	−	0.161947i	0.815481	−	0.578783i	$-0.196472\pi$
$149$	−1.14132	−	1.97682i	−0.0935002	−	0.161947i	−0.908982	+	0.416836i	$0.863139\pi$
$150$		0			0
$151$	5.63160	−	9.75422i	0.458293	−	0.793787i	−0.540578	−	0.841294i	$-0.681794\pi$
$151$	5.63160	−	9.75422i	0.458293	−	0.793787i	0.998871	+	0.0475071i	$0.0151277\pi$
$152$		0			0
$153$	10.5624	−	3.44854i	0.853918	−	0.278798i
$154$		0			0
$155$	−0.0857699	+	0.148558i	−0.00688921	+	0.0119325i
$156$		0			0
$157$	−2.77292	−	4.80283i	−0.221303	−	0.383308i	0.733901	−	0.679256i	$-0.237698\pi$
$157$	−2.77292	−	4.80283i	−0.221303	−	0.383308i	−0.955204	+	0.295949i	$0.904364\pi$
$158$		0			0
$159$	−1.61273	+	0.256606i	−0.127897	+	0.0203502i
$160$		0			0
$161$	−7.42107			−0.584862
$162$		0			0
$163$	−6.66019			−0.521666			−0.260833	−	0.965384i	$-0.583997\pi$
$163$	−6.66019			−0.521666			−0.260833	+	0.965384i	$0.583997\pi$
$164$		0			0
$165$	2.09617	−	0.333529i	0.163187	−	0.0259652i
$166$		0			0
$167$	2.20370	+	3.81691i	0.170527	+	0.295362i	0.938604	−	0.344996i	$-0.112120\pi$
$167$	2.20370	+	3.81691i	0.170527	+	0.295362i	−0.768077	+	0.640357i	$0.778786\pi$
$168$		0			0
$169$	−5.43474	+	9.41325i	−0.418057	+	0.724096i
$170$		0			0
$171$	−10.4383	+	3.40803i	−0.798237	+	0.260619i
$172$		0			0
$173$	−12.6654	+	21.9371i	−0.962932	+	1.66785i	−0.247860	+	0.968796i	$0.579727\pi$
$173$	−12.6654	+	21.9371i	−0.962932	+	1.66785i	−0.715072	+	0.699051i	$0.753606\pi$
$174$		0			0
$175$	2.47141	+	4.28061i	0.186821	+	0.323584i
$176$		0			0
$177$	8.26840	+	10.1958i	0.621491	+	0.766363i
$178$		0			0
$179$	−9.54583			−0.713489			−0.356744	−	0.934202i	$-0.616113\pi$
$179$	−9.54583			−0.713489			−0.356744	+	0.934202i	$0.616113\pi$
$180$		0			0
$181$	12.3743			0.919774			0.459887	−	0.887978i	$-0.347890\pi$
$181$	12.3743			0.919774			0.459887	+	0.887978i	$0.347890\pi$
$182$		0			0
$183$	−3.41260	+	8.90904i	−0.252266	+	0.658575i
$184$		0			0
$185$	−0.550343	−	0.953223i	−0.0404621	−	0.0700823i
$186$		0			0
$187$	−9.49028	+	16.4377i	−0.693998	+	1.20204i
$188$		0			0
$189$	−0.260877	+	5.18960i	−0.0189760	+	0.377488i
$190$		0			0
$191$	6.58414	−	11.4041i	0.476411	−	0.825169i	−0.523223	−	0.852196i	$-0.675271\pi$
$191$	6.58414	−	11.4041i	0.476411	−	0.825169i	0.999635	+	0.0270270i	$0.00860400\pi$
$192$		0			0
$193$	−5.57442	−	9.65518i	−0.401256	−	0.694995i	0.592622	−	0.805481i	$-0.298093\pi$
$193$	−5.57442	−	9.65518i	−0.401256	−	0.694995i	−0.993878	+	0.110486i	$0.964759\pi$
$194$		0			0
$195$	0.723815	−	1.88962i	0.0518335	−	0.135318i
$196$		0			0
$197$	−0.144194			−0.0102734			−0.00513669	−	0.999987i	$-0.501635\pi$
$197$	−0.144194			−0.0102734			−0.00513669	+	0.999987i	$0.501635\pi$
$198$		0			0
$199$	19.4692			1.38014			0.690068	−	0.723744i	$-0.257581\pi$
$199$	19.4692			1.38014			0.690068	+	0.723744i	$0.257581\pi$
$200$		0			0
$201$	−0.720248	−	0.888141i	−0.0508024	−	0.0626446i
$202$		0			0
$203$	−1.73229	−	3.00041i	−0.121583	−	0.210587i
$204$		0			0
$205$	−0.669905	+	1.16031i	−0.0467882	+	0.0810395i
$206$		0			0
$207$	16.5659	+	14.8734i	1.15141	+	1.03378i
$208$		0			0
$209$	9.37880	−	16.2446i	0.648745	−	1.12366i
$210$		0			0
$211$	−1.61436	−	2.79615i	−0.111137	−	0.192495i	0.805092	−	0.593150i	$-0.202116\pi$
$211$	−1.61436	−	2.79615i	−0.111137	−	0.192495i	−0.916229	+	0.400655i	$0.868783\pi$
$212$		0			0
$213$	−23.5052	+	3.73999i	−1.61055	+	0.256260i
$214$		0			0
$215$	−2.98633			−0.203666
$216$		0			0
$217$	0.717370			0.0486982
$218$		0			0
$219$	−6.26088	+	0.996189i	−0.423071	+	0.0673162i
$220$		0			0
$221$	9.04746	+	15.6707i	0.608598	+	1.05412i
$222$		0			0
$223$	10.3856	−	17.9885i	0.695474	−	1.20460i	−0.274547	−	0.961574i	$-0.588528\pi$
$223$	10.3856	−	17.9885i	0.695474	−	1.20460i	0.970021	−	0.243022i	$-0.0781389\pi$
$224$		0			0
$225$	3.06238	−	14.5088i	0.204159	−	0.967253i
$226$		0			0
$227$	10.9714	−	19.0030i	0.728198	−	1.26128i	−0.229446	−	0.973321i	$-0.573691\pi$
$227$	10.9714	−	19.0030i	0.728198	−	1.26128i	0.957644	−	0.287955i	$-0.0929752\pi$
$228$		0			0
$229$	−11.3856	−	19.7205i	−0.752384	−	1.30317i	−0.946664	−	0.322222i	$-0.895570\pi$
$229$	−11.3856	−	19.7205i	−0.752384	−	1.30317i	0.194280	−	0.980946i	$-0.437763\pi$
$230$		0			0
$231$	−5.59097	−	6.89425i	−0.367859	−	0.453608i
$232$		0			0
$233$	−25.7817			−1.68901			−0.844507	−	0.535544i	$-0.820106\pi$
$233$	−25.7817			−1.68901			−0.844507	+	0.535544i	$0.820106\pi$
$234$		0			0
$235$	−1.03775			−0.0676953
$236$		0			0
$237$	−3.85705	+	10.0694i	−0.250542	+	0.654075i
$238$		0			0
$239$	−13.6488	−	23.6405i	−0.882870	−	1.52918i	−0.848136	−	0.529779i	$-0.822275\pi$
$239$	−13.6488	−	23.6405i	−0.882870	−	1.52918i	−0.0347345	−	0.999397i	$-0.511059\pi$
$240$		0			0
$241$	−5.01724	+	8.69011i	−0.323189	+	0.559779i	−0.981144	−	0.193277i	$-0.938088\pi$
$241$	−5.01724	+	8.69011i	−0.323189	+	0.559779i	0.657955	+	0.753057i	$0.271422\pi$
$242$		0			0
$243$	10.9834	−	11.0618i	0.704589	−	0.709616i
$244$		0			0
$245$	−0.119562	+	0.207087i	−0.00763851	+	0.0132303i
$246$		0			0
$247$	−8.94119	−	15.4866i	−0.568914	−	0.985388i
$248$		0			0
$249$	6.01204	−	15.6952i	0.380997	−	0.994645i
$250$		0			0
$251$	28.3171			1.78736			0.893680	−	0.448705i	$-0.148115\pi$
$251$	28.3171			1.78736			0.893680	+	0.448705i	$0.148115\pi$
$252$		0			0
$253$	−38.0312			−2.39100
$254$		0			0
$255$	−0.966208	−	1.19143i	−0.0605063	−	0.0746105i
$256$		0			0
$257$	−14.4315	−	24.9960i	−0.900210	−	1.55921i	−0.827221	−	0.561877i	$-0.810079\pi$
$257$	−14.4315	−	24.9960i	−0.900210	−	1.55921i	−0.0729899	−	0.997333i	$-0.523254\pi$
$258$		0			0
$259$	−2.30150	+	3.98632i	−0.143009	+	0.247698i
$260$		0			0
$261$	−2.14652	+	10.1697i	−0.132866	+	0.629486i
$262$		0			0
$263$	−0.604645	+	1.04728i	−0.0372840	+	0.0645778i	−0.884065	−	0.467363i	$-0.845204\pi$
$263$	−0.604645	+	1.04728i	−0.0372840	+	0.0645778i	0.846781	+	0.531941i	$0.178537\pi$
$264$		0			0
$265$	0.112725	+	0.195246i	0.00692465	+	0.0119938i
$266$		0			0
$267$	−12.8096	+	2.03818i	−0.783934	+	0.124734i
$268$		0			0
$269$	9.01367			0.549573			0.274787	−	0.961505i	$-0.411393\pi$
$269$	9.01367			0.549573			0.274787	+	0.961505i	$0.411393\pi$
$270$		0			0
$271$	−17.6030			−1.06931			−0.534653	−	0.845071i	$-0.679558\pi$
$271$	−17.6030			−1.06931			−0.534653	+	0.845071i	$0.679558\pi$
$272$		0			0
$273$	−8.35705	+	1.32972i	−0.505792	+	0.0804782i
$274$		0			0
$275$	12.6654	+	21.9371i	0.763752	+	1.32286i
$276$		0			0
$277$	−0.727085	+	1.25935i	−0.0436863	+	0.0756669i	−0.887042	−	0.461689i	$-0.847244\pi$
$277$	−0.727085	+	1.25935i	−0.0436863	+	0.0756669i	0.843355	+	0.537356i	$0.180577\pi$
$278$		0			0
$279$	−1.60138	−	1.43777i	−0.0958718	−	0.0860768i
$280$		0			0
$281$	10.1482	−	17.5771i	0.605388	−	1.04856i	−0.386602	−	0.922247i	$-0.626351\pi$
$281$	10.1482	−	17.5771i	0.605388	−	1.04856i	0.991990	−	0.126316i	$-0.0403154\pi$
$282$		0			0
$283$	−2.30150	−	3.98632i	−0.136810	−	0.236962i	0.789477	−	0.613780i	$-0.210352\pi$
$283$	−2.30150	−	3.98632i	−0.136810	−	0.236962i	−0.926288	+	0.376817i	$0.877018\pi$
$284$		0			0
$285$	0.954858	+	1.17744i	0.0565609	+	0.0697455i
$286$		0			0
$287$	5.60301			0.330735
$288$		0			0
$289$	−3.28263			−0.193096
$290$		0			0
$291$	10.6248	−	27.7374i	0.622835	−	1.62599i
$292$		0			0
$293$	3.53667	+	6.12569i	0.206614	+	0.357867i	0.950646	−	0.310278i	$-0.100422\pi$
$293$	3.53667	+	6.12569i	0.206614	+	0.357867i	−0.744031	+	0.668145i	$0.767089\pi$
$294$		0			0
$295$	0.906150	−	1.56950i	0.0527581	−	0.0913797i
$296$		0			0
$297$	−1.33693	+	26.5955i	−0.0775766	+	1.54323i
$298$		0			0
$299$	−18.1283	+	31.3992i	−1.04839	+	1.81586i
$300$		0			0
$301$	6.24433	+	10.8155i	0.359917	+	0.623394i
$302$		0			0
$303$	−4.44966	+	11.6164i	−0.255626	+	0.667347i
$304$		0			0
$305$	1.31711			0.0754175
$306$		0			0
$307$	−15.7518			−0.899006			−0.449503	−	0.893279i	$-0.648399\pi$
$307$	−15.7518			−0.899006			−0.449503	+	0.893279i	$0.648399\pi$
$308$		0			0
$309$	−13.9955	−	17.2579i	−0.796175	−	0.981767i
$310$		0			0
$311$	−9.81191	−	16.9947i	−0.556382	−	0.963682i	−0.997795	−	0.0663780i	$-0.978856\pi$
$311$	−9.81191	−	16.9947i	−0.556382	−	0.963682i	0.441412	−	0.897304i	$-0.354478\pi$
$312$		0			0
$313$	12.7427	−	22.0710i	0.720259	−	1.24753i	−0.240636	−	0.970615i	$-0.577356\pi$
$313$	12.7427	−	22.0710i	0.720259	−	1.24753i	0.960896	−	0.276911i	$-0.0893106\pi$
$314$		0			0
$315$	0.681943	−	0.222649i	0.0384232	−	0.0125449i
$316$		0			0
$317$	−4.14132	+	7.17297i	−0.232599	+	0.402874i	−0.958572	−	0.284849i	$-0.908056\pi$
$317$	−4.14132	+	7.17297i	−0.232599	+	0.402874i	0.725973	+	0.687723i	$0.241390\pi$
$318$		0			0
$319$	−8.87756	−	15.3764i	−0.497048	−	0.860912i
$320$		0			0
$321$	−12.9406	+	2.05903i	−0.722276	+	0.114924i
$322$		0			0
$323$	−13.5562			−0.754289
$324$		0			0
$325$	24.1488			1.33954
$326$		0			0
$327$	−11.9405	+	1.89989i	−0.660311	+	0.105064i
$328$		0			0
$329$	2.16991	+	3.75839i	0.119631	+	0.207207i
$330$		0			0
$331$	−5.99028	+	10.3755i	−0.329256	+	0.570288i	−0.982364	−	0.186976i	$-0.940131\pi$
$331$	−5.99028	+	10.3755i	−0.329256	+	0.570288i	0.653109	+	0.757264i	$0.273465\pi$
$332$		0			0
$333$	13.1271	−	4.28590i	0.719360	−	0.234866i
$334$		0			0
$335$	−0.0789334	+	0.136717i	−0.00431259	+	0.00746963i
$336$		0			0
$337$	6.46006	+	11.1892i	0.351902	+	0.609512i	0.986583	−	0.163262i	$-0.0522017\pi$
$337$	6.46006	+	11.1892i	0.351902	+	0.609512i	−0.634681	+	0.772774i	$0.718868\pi$
$338$		0			0
$339$	21.3502	+	26.3270i	1.15958	+	1.42989i
$340$		0			0
$341$	3.67635			0.199086
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	1.09944	−	2.87024i	0.0591920	−	0.154529i
$346$		0			0
$347$	8.09329	+	14.0180i	0.434471	+	0.752526i	0.997252	−	0.0740802i	$-0.0236021\pi$
$347$	8.09329	+	14.0180i	0.434471	+	0.752526i	−0.562781	+	0.826606i	$0.690269\pi$
$348$		0			0
$349$	9.05718	−	15.6875i	0.484820	−	0.839732i	−0.515028	−	0.857173i	$-0.672219\pi$
$349$	9.05718	−	15.6875i	0.484820	−	0.839732i	0.999848	+	0.0174409i	$0.00555188\pi$
$350$		0			0
$351$	21.3204	+	13.7811i	1.13800	+	0.735578i
$352$		0			0
$353$	5.84897	−	10.1307i	0.311309	−	0.539203i	−0.667337	−	0.744756i	$-0.732566\pi$
$353$	5.84897	−	10.1307i	0.311309	−	0.539203i	0.978646	+	0.205553i	$0.0658992\pi$
$354$		0			0
$355$	1.64295	+	2.84567i	0.0871987	+	0.151033i
$356$		0			0
$357$	−2.29467	+	5.99054i	−0.121447	+	0.317053i
$358$		0			0
$359$	−35.7245			−1.88547			−0.942734	−	0.333547i	$-0.891755\pi$
$359$	−35.7245			−1.88547			−0.942734	+	0.333547i	$0.891755\pi$
$360$		0			0
$361$	−5.60301			−0.294895
$362$		0			0
$363$	−16.6517	−	20.5333i	−0.873989	−	1.07772i
$364$		0			0
$365$	0.437618	+	0.757977i	0.0229060	+	0.0396743i
$366$		0			0
$367$	8.52696	−	14.7691i	0.445103	−	0.770942i	−0.552956	−	0.833210i	$-0.686500\pi$
$367$	8.52696	−	14.7691i	0.445103	−	0.770942i	0.998059	+	0.0622687i	$0.0198336\pi$
$368$		0			0
$369$	−12.5075	−	11.2297i	−0.651116	−	0.584593i
$370$		0			0
$371$	0.471410	−	0.816506i	0.0244744	−	0.0423909i
$372$		0			0
$373$	12.9617	+	22.4503i	0.671131	+	1.16243i	0.977584	+	0.210547i	$0.0675246\pi$
$373$	12.9617	+	22.4503i	0.671131	+	1.16243i	−0.306453	+	0.951886i	$0.599142\pi$
$374$		0			0
$375$	−4.06690	+	0.647097i	−0.210014	+	0.0334160i
$376$		0			0
$377$	−16.9267			−0.871767
$378$		0			0
$379$	−26.8446			−1.37892			−0.689458	−	0.724326i	$-0.742151\pi$
$379$	−26.8446			−1.37892			−0.689458	+	0.724326i	$0.742151\pi$
$380$		0			0
$381$	28.7524	−	4.57489i	1.47303	−	0.234379i
$382$		0			0
$383$	12.4263	+	21.5229i	0.634953	+	1.09977i	0.986525	+	0.163610i	$0.0523137\pi$
$383$	12.4263	+	21.5229i	0.634953	+	1.09977i	−0.351573	+	0.936161i	$0.614353\pi$
$384$		0			0
$385$	−0.612725	+	1.06127i	−0.0312274	+	0.0540874i
$386$		0			0
$387$	7.73749	−	36.6583i	0.393319	−	1.86344i
$388$		0			0
$389$	9.12640	−	15.8074i	0.462727	−	0.801466i	−0.536369	−	0.843984i	$-0.680204\pi$
$389$	9.12640	−	15.8074i	0.462727	−	0.801466i	0.999096	+	0.0425174i	$0.0135378\pi$
$390$		0			0
$391$	13.7427	+	23.8030i	0.694998	+	1.20377i
$392$		0			0
$393$	5.34501	+	6.59095i	0.269620	+	0.332470i
$394$		0			0
$395$	1.48865			0.0749021
$396$		0			0
$397$	12.3743			0.621048			0.310524	−	0.950566i	$-0.399496\pi$
$397$	12.3743			0.621048			0.310524	+	0.950566i	$0.399496\pi$
$398$		0			0
$399$	2.26771	−	5.92017i	0.113528	−	0.296379i
$400$		0			0
$401$	5.48113	+	9.49359i	0.273714	+	0.474087i	0.969810	−	0.243862i	$-0.0784144\pi$
$401$	5.48113	+	9.49359i	0.273714	+	0.474087i	−0.696096	+	0.717949i	$0.745081\pi$
$402$		0			0
$403$	1.75241	−	3.03526i	0.0872935	−	0.151197i
$404$		0			0
$405$	−1.96853	−	0.869747i	−0.0978171	−	0.0432181i
$406$		0			0
$407$	−11.7947	+	20.4290i	−0.584640	+	1.01263i
$408$		0			0
$409$	6.66019	+	11.5358i	0.329325	+	0.570408i	0.982378	−	0.186904i	$-0.0598454\pi$
$409$	6.66019	+	11.5358i	0.329325	+	0.570408i	−0.653053	+	0.757312i	$0.726512\pi$
$410$		0			0
$411$	−3.37360	+	8.80724i	−0.166408	+	0.434429i
$412$		0			0
$413$	−7.57893			−0.372935
$414$		0			0
$415$	−2.32038			−0.113903
$416$		0			0
$417$	6.17511	+	7.61455i	0.302396	+	0.372886i
$418$		0			0
$419$	2.35705	+	4.08253i	0.115149	+	0.199445i	0.917839	−	0.396952i	$-0.129932\pi$
$419$	2.35705	+	4.08253i	0.115149	+	0.199445i	−0.802690	+	0.596396i	$0.796599\pi$
$420$		0			0
$421$	−9.65856	+	16.7291i	−0.470729	+	0.815327i	−0.999440	−	0.0334755i	$-0.989342\pi$
$421$	−9.65856	+	16.7291i	−0.470729	+	0.815327i	0.528710	+	0.848802i	$0.322676\pi$
$422$		0			0
$423$	2.68878	−	12.7388i	0.130733	−	0.619380i
$424$		0			0
$425$	9.15335	−	15.8541i	0.444003	−	0.769036i
$426$		0			0
$427$	−2.75404	−	4.77014i	−0.133277	−	0.230843i
$428$		0			0
$429$	−42.8279	+	6.81449i	−2.06775	+	0.329007i
$430$		0			0
$431$	30.2794			1.45851			0.729253	−	0.684244i	$-0.239868\pi$
$431$	30.2794			1.45851			0.729253	+	0.684244i	$0.239868\pi$
$432$		0			0
$433$	34.2060			1.64384			0.821918	−	0.569606i	$-0.192904\pi$
$433$	34.2060			1.64384			0.821918	+	0.569606i	$0.192904\pi$
$434$		0			0
$435$	1.41711	−	0.225481i	0.0679452	−	0.0108110i
$436$		0			0
$437$	−13.5813	−	23.5234i	−0.649680	−	1.12528i
$438$		0			0
$439$	−0.311220	+	0.539049i	−0.0148537	+	0.0257274i	−0.873357	−	0.487081i	$-0.838062\pi$
$439$	−0.311220	+	0.539049i	−0.0148537	+	0.0257274i	0.858503	+	0.512809i	$0.171395\pi$
$440$		0			0
$441$	−2.23229	−	2.00422i	−0.106299	−	0.0954390i
$442$		0			0
$443$	−2.58934	+	4.48486i	−0.123023	+	0.213082i	−0.920958	−	0.389661i	$-0.872592\pi$
$443$	−2.58934	+	4.48486i	−0.123023	+	0.213082i	0.797935	+	0.602743i	$0.205926\pi$
$444$		0			0
$445$	0.895355	+	1.55080i	0.0424439	+	0.0735150i
$446$		0			0
$447$	−2.49028	−	3.07078i	−0.117786	−	0.145243i
$448$		0			0
$449$	−10.4977			−0.495416			−0.247708	−	0.968835i	$-0.579677\pi$
$449$	−10.4977			−0.495416			−0.247708	+	0.968835i	$0.579677\pi$
$450$		0			0
$451$	28.7141			1.35209
$452$		0			0
$453$	6.97825	−	18.2177i	0.327867	−	0.855940i
$454$		0			0
$455$	0.584135	+	1.01175i	0.0273847	+	0.0474317i
$456$		0			0
$457$	1.60464	−	2.77933i	0.0750621	−	0.130011i	−0.826051	−	0.563595i	$-0.809418\pi$
$457$	1.60464	−	2.77933i	0.0750621	−	0.130011i	0.901113	+	0.433584i	$0.142751\pi$
$458$		0			0
$459$	17.1287	−	8.77359i	0.799500	−	0.409516i
$460$		0			0
$461$	18.1150	−	31.3762i	0.843702	−	1.46133i	−0.0430418	−	0.999073i	$-0.513705\pi$
$461$	18.1150	−	31.3762i	0.843702	−	1.46133i	0.886744	−	0.462261i	$-0.152962\pi$
$462$		0			0
$463$	14.5253	+	25.1586i	0.675049	+	1.16922i	0.976455	+	0.215723i	$0.0692108\pi$
$463$	14.5253	+	25.1586i	0.675049	+	1.16922i	−0.301406	+	0.953496i	$0.597456\pi$
$464$		0			0
$465$	−0.106279	+	0.277457i	−0.00492859	+	0.0128668i
$466$		0			0
$467$	37.4933			1.73498			0.867491	−	0.497452i	$-0.165731\pi$
$467$	37.4933			1.73498			0.867491	+	0.497452i	$0.165731\pi$
$468$		0			0
$469$	0.660190			0.0304847
$470$		0			0
$471$	−6.05034	−	7.46070i	−0.278785	−	0.343771i
$472$		0			0
$473$	32.0007	+	55.4268i	1.47139	+	2.54853i
$474$		0			0
$475$	−9.04583	+	15.6678i	−0.415051	+	0.718890i
$476$		0			0
$477$	−2.68878	+	0.877867i	−0.123111	+	0.0401948i
$478$		0			0
$479$	14.9549	−	25.9026i	0.683305	−	1.18352i	−0.290661	−	0.956826i	$-0.593875\pi$
$479$	14.9549	−	25.9026i	0.683305	−	1.18352i	0.973966	−	0.226693i	$-0.0727914\pi$
$480$		0			0
$481$	11.2443	+	19.4757i	0.512697	+	0.888017i
$482$		0			0
$483$	−12.6940	+	2.01978i	−0.577596	+	0.0919033i
$484$		0			0
$485$	−4.10069			−0.186203
$486$		0			0
$487$	−21.2632			−0.963528			−0.481764	−	0.876301i	$-0.660004\pi$
$487$	−21.2632			−0.963528			−0.481764	+	0.876301i	$0.660004\pi$
$488$		0			0
$489$	−11.3925	+	1.81270i	−0.515186	+	0.0819729i
$490$		0			0
$491$	−10.6985	−	18.5303i	−0.482816	−	0.836262i	0.516989	−	0.855992i	$-0.327053\pi$
$491$	−10.6985	−	18.5303i	−0.482816	−	0.836262i	−0.999805	+	0.0197296i	$0.993719\pi$
$492$		0			0
$493$	−6.41586	+	11.1126i	−0.288956	+	0.500487i
$494$		0			0
$495$	3.49480	−	1.14103i	0.157079	−	0.0512853i
$496$		0			0
$497$	6.87072	−	11.9004i	0.308194	−	0.533808i
$498$		0			0
$499$	7.28263	+	12.6139i	0.326015	+	0.564675i	0.981717	−	0.190345i	$-0.0609606\pi$
$499$	7.28263	+	12.6139i	0.326015	+	0.564675i	−0.655702	+	0.755020i	$0.727627\pi$
$500$		0			0
$501$	4.80834	+	5.92918i	0.214821	+	0.264896i
$502$		0			0
$503$	−2.92339			−0.130348			−0.0651738	−	0.997874i	$-0.520760\pi$
$503$	−2.92339			−0.130348			−0.0651738	+	0.997874i	$0.520760\pi$
$504$		0			0
$505$	1.71737			0.0764220
$506$		0			0
$507$	−6.73431	+	17.5808i	−0.299081	+	0.780792i
$508$		0			0
$509$	9.62025	+	16.6628i	0.426410	+	0.738564i	0.996551	−	0.0829830i	$-0.0264447\pi$
$509$	9.62025	+	16.6628i	0.426410	+	0.738564i	−0.570141	+	0.821547i	$0.693111\pi$
$510$		0			0
$511$	1.83009	−	3.16982i	0.0809586	−	0.140224i
$512$		0			0
$513$	−16.9275	+	8.67053i	−0.747368	+	0.382813i
$514$		0			0
$515$	−1.53379	+	2.65661i	−0.0675869	+	0.117064i
$516$		0			0
$517$	11.1202	+	19.2608i	0.489068	+	0.847091i
$518$		0			0
$519$	−15.6940	+	40.9713i	−0.688889	+	1.79844i
$520$		0			0
$521$	27.7486			1.21569			0.607844	−	0.794057i	$-0.292035\pi$
$521$	27.7486			1.21569			0.607844	+	0.794057i	$0.292035\pi$
$522$		0			0
$523$	2.73680			0.119672			0.0598360	−	0.998208i	$-0.480942\pi$
$523$	2.73680			0.119672			0.0598360	+	0.998208i	$0.480942\pi$
$524$		0			0
$525$	5.39248	+	6.64948i	0.235347	+	0.290207i
$526$		0			0
$527$	−1.32846	−	2.30096i	−0.0578686	−	0.100231i
$528$		0			0
$529$	−16.0361	+	27.7754i	−0.697222	+	1.20762i
$530$		0			0
$531$	16.9184	+	15.1898i	0.734194	+	0.659183i
$532$		0			0
$533$	13.6871	−	23.7068i	0.592856	−	1.02686i
$534$		0			0
$535$	0.904515	+	1.56667i	0.0391056	+	0.0677329i
$536$		0			0
$537$	−16.3285	+	2.59808i	−0.704625	+	0.112115i
$538$		0			0
$539$	5.12476			0.220739
$540$		0			0
$541$	−11.9773			−0.514944			−0.257472	−	0.966286i	$-0.582890\pi$
$541$	−11.9773			−0.514944			−0.257472	+	0.966286i	$0.582890\pi$
$542$		0			0
$543$	21.1666	−	3.36789i	0.908347	−	0.144530i
$544$		0			0
$545$	0.834608	+	1.44558i	0.0357507	+	0.0619220i
$546$		0			0
$547$	−10.7346	+	18.5929i	−0.458979	+	0.794975i	−0.998907	−	0.0467363i	$-0.985118\pi$
$547$	−10.7346	+	18.5929i	−0.458979	+	0.794975i	0.539928	+	0.841711i	$0.318451\pi$
$548$		0			0
$549$	−3.41260	+	16.1680i	−0.145646	+	0.690034i
$550$		0			0
$551$	6.34050	−	10.9821i	0.270114	−	0.467852i
$552$		0			0
$553$	−3.11273	−	5.39140i	−0.132367	−	0.229266i
$554$		0			0
$555$	−1.20082	−	1.48073i	−0.0509719	−	0.0628536i
$556$		0			0
$557$	−31.8493			−1.34950			−0.674748	−	0.738048i	$-0.735748\pi$
$557$	−31.8493			−1.34950			−0.674748	+	0.738048i	$0.735748\pi$
$558$		0			0
$559$	61.0150			2.58066
$560$		0			0
$561$	−11.7596	+	30.7001i	−0.496492	+	1.29616i
$562$		0			0
$563$	17.7742	+	30.7857i	0.749091	+	1.29746i	0.948259	+	0.317499i	$0.102843\pi$
$563$	17.7742	+	30.7857i	0.749091	+	1.29746i	−0.199167	+	0.979966i	$0.563824\pi$
$564$		0			0
$565$	2.33981	−	4.05267i	0.0984366	−	0.170497i
$566$		0			0
$567$	0.966208	+	8.94799i	0.0405769	+	0.375780i
$568$		0			0
$569$	−10.8743	+	18.8348i	−0.455874	+	0.789597i	−0.998738	−	0.0502237i	$-0.984007\pi$
$569$	−10.8743	+	18.8348i	−0.455874	+	0.789597i	0.542864	+	0.839821i	$0.317340\pi$
$570$		0			0
$571$	−4.79987	−	8.31362i	−0.200868	−	0.347914i	0.747940	−	0.663766i	$-0.231043\pi$
$571$	−4.79987	−	8.31362i	−0.200868	−	0.347914i	−0.948808	+	0.315852i	$0.897710\pi$
$572$		0			0
$573$	8.15856	−	21.2990i	0.340829	−	0.889779i
$574$		0			0
$575$	36.6810			1.52970
$576$		0			0
$577$	13.0183			0.541960			0.270980	−	0.962585i	$-0.412652\pi$
$577$	13.0183			0.541960			0.270980	+	0.962585i	$0.412652\pi$
$578$		0			0
$579$	−12.1631	−	14.9983i	−0.505480	−	0.623309i
$580$		0			0
$581$	4.85185	+	8.40365i	0.201289	+	0.348642i
$582$		0			0
$583$	2.41586	−	4.18440i	0.100055	−	0.173300i
$584$		0			0
$585$	0.723815	−	3.42926i	0.0299261	−	0.141782i
$586$		0			0
$587$	8.64364	−	14.9712i	0.356761	−	0.617928i	−0.630657	−	0.776062i	$-0.717214\pi$
$587$	8.64364	−	14.9712i	0.356761	−	0.617928i	0.987418	+	0.158134i	$0.0505477\pi$
$588$		0			0
$589$	1.31285	+	2.27393i	0.0540952	+	0.0936957i
$590$		0			0
$591$	−0.246648	+	0.0392450i	−0.0101457	+	0.00161432i
$592$		0			0
$593$	12.4153			0.509836			0.254918	−	0.966963i	$-0.417952\pi$
$593$	12.4153			0.509836			0.254918	+	0.966963i	$0.417952\pi$
$594$		0			0
$595$	0.885640			0.0363077
$596$		0			0
$597$	33.3027	−	5.29891i	1.36299	−	0.216870i
$598$		0			0
$599$	−3.94282	−	6.82916i	−0.161099	−	0.279032i	0.774164	−	0.632985i	$-0.218171\pi$
$599$	−3.94282	−	6.82916i	−0.161099	−	0.279032i	−0.935263	+	0.353953i	$0.884837\pi$
$600$		0			0
$601$	−11.1413	+	19.2973i	−0.454464	+	0.787154i	−0.998657	−	0.0518055i	$-0.983502\pi$
$601$	−11.1413	+	19.2973i	−0.454464	+	0.787154i	0.544193	+	0.838960i	$0.316836\pi$
$602$		0			0
$603$	−1.47373	−	1.32317i	−0.0600151	−	0.0538835i
$604$		0			0
$605$	−1.82489	+	3.16081i	−0.0741925	+	0.128505i
$606$		0			0
$607$	11.0458	+	19.1319i	0.448336	+	0.776541i	0.998278	−	0.0586617i	$-0.0186833\pi$
$607$	11.0458	+	19.1319i	0.448336	+	0.776541i	−0.549942	+	0.835203i	$0.685350\pi$
$608$		0			0
$609$	−3.77975	−	4.66082i	−0.153163	−	0.188866i
$610$		0			0
$611$	21.2028			0.857771
$612$		0			0
$613$	−29.5264			−1.19256			−0.596280	−	0.802777i	$-0.703355\pi$
$613$	−29.5264			−1.19256			−0.596280	+	0.802777i	$0.703355\pi$
$614$		0			0
$615$	−0.830095	+	2.16708i	−0.0334727	+	0.0873849i
$616$		0			0
$617$	5.01655	+	8.68892i	0.201959	+	0.349803i	0.949159	−	0.314796i	$-0.101936\pi$
$617$	5.01655	+	8.68892i	0.201959	+	0.349803i	−0.747201	+	0.664598i	$0.768603\pi$
$618$		0			0
$619$	−19.1283	+	33.1312i	−0.768833	+	1.33166i	0.169364	+	0.985554i	$0.445829\pi$
$619$	−19.1283	+	33.1312i	−0.768833	+	1.33166i	−0.938196	+	0.346103i	$0.887505\pi$
$620$		0			0
$621$	32.3847	+	20.9328i	1.29955	+	0.840004i
$622$		0			0
$623$	3.74433	−	6.48536i	0.150013	−	0.259831i
$624$		0			0
$625$	−12.0728	−	20.9107i	−0.482911	−	0.836427i
$626$		0			0
$627$	11.6215	−	30.3395i	0.464118	−	1.21164i
$628$		0			0
$629$	17.0482			0.679754
$630$		0			0
$631$	23.0377			0.917118			0.458559	−	0.888664i	$-0.348366\pi$
$631$	23.0377			0.917118			0.458559	+	0.888664i	$0.348366\pi$
$632$		0			0
$633$	−3.52244	−	4.34354i	−0.140004	−	0.172640i
$634$		0			0
$635$	−2.00972	−	3.48093i	−0.0797531	−	0.138136i
$636$		0			0
$637$	2.44282	−	4.23109i	0.0967881	−	0.167642i
$638$		0			0
$639$	−39.1885	+	12.7948i	−1.55027	+	0.506153i
$640$		0			0
$641$	8.68646	−	15.0454i	0.343094	−	0.594257i	−0.641911	−	0.766779i	$-0.721858\pi$
$641$	8.68646	−	15.0454i	0.343094	−	0.594257i	0.985006	+	0.172522i	$0.0551916\pi$
$642$		0			0
$643$	−9.47949	−	16.4190i	−0.373835	−	0.647501i	0.616317	−	0.787498i	$-0.288624\pi$
$643$	−9.47949	−	16.4190i	−0.373835	−	0.647501i	−0.990152	+	0.139997i	$0.955291\pi$
$644$		0			0
$645$	−5.10821	+	0.812785i	−0.201136	+	0.0320034i
$646$		0			0
$647$	−19.0194			−0.747731			−0.373865	−	0.927483i	$-0.621968\pi$
$647$	−19.0194			−0.747731			−0.373865	+	0.927483i	$0.621968\pi$
$648$		0			0
$649$	−38.8402			−1.52461
$650$		0			0
$651$	1.22708	−	0.195246i	0.0480933	−	0.00765228i
$652$		0			0
$653$	3.59329	+	6.22377i	0.140616	+	0.243555i	0.927729	−	0.373255i	$-0.121758\pi$
$653$	3.59329	+	6.22377i	0.140616	+	0.243555i	−0.787112	+	0.616810i	$0.788425\pi$
$654$		0			0
$655$	0.585770	−	1.01458i	0.0228879	−	0.0396430i
$656$		0			0
$657$	−10.4383	+	3.40803i	−0.407237	+	0.132960i
$658$		0			0
$659$	12.7261	−	22.0423i	0.495740	−	0.858647i	−0.504248	−	0.863559i	$-0.668230\pi$
$659$	12.7261	−	22.0423i	0.495740	−	0.858647i	0.999988	+	0.00491209i	$0.00156357\pi$
$660$		0			0
$661$	−4.14295	−	7.17580i	−0.161142	−	0.279106i	0.774136	−	0.633019i	$-0.218184\pi$
$661$	−4.14295	−	7.17580i	−0.161142	−	0.279106i	−0.935279	+	0.353912i	$0.884851\pi$
$662$		0			0
$663$	19.7411	+	24.3428i	0.766679	+	0.945395i
$664$		0			0
$665$	−0.875237			−0.0339402
$666$		0			0
$667$	−25.7108			−0.995527
$668$		0			0
$669$	12.8691	−	33.5965i	0.497548	−	1.29892i
$670$		0			0
$671$	−14.1138	−	24.4458i	−0.544857	−	0.943721i
$672$		0			0
$673$	5.91586	−	10.2466i	0.228040	−	0.394977i	−0.729187	−	0.684314i	$-0.760102\pi$
$673$	5.91586	−	10.2466i	0.228040	−	0.394977i	0.957227	+	0.289338i	$0.0934350\pi$
$674$		0			0
$675$	1.28947	−	25.6513i	0.0496316	−	0.987317i
$676$		0			0
$677$	−6.80314	+	11.7834i	−0.261466	+	0.452872i	−0.966632	−	0.256170i	$-0.917539\pi$
$677$	−6.80314	+	11.7834i	−0.261466	+	0.452872i	0.705166	+	0.709042i	$0.250873\pi$
$678$		0			0
$679$	8.57442	+	14.8513i	0.329056	+	0.569942i
$680$		0			0
$681$	13.5949	−	35.4914i	0.520959	−	1.36003i
$682$		0			0
$683$	−3.58142			−0.137039			−0.0685196	−	0.997650i	$-0.521828\pi$
$683$	−3.58142			−0.137039			−0.0685196	+	0.997650i	$0.521828\pi$
$684$		0			0
$685$	1.30206			0.0497492
$686$		0			0
$687$	−24.8428	−	30.6338i	−0.947813	−	1.16875i
$688$		0			0
$689$	−2.30314	−	3.98916i	−0.0877426	−	0.151975i
$690$		0			0
$691$	5.85868	−	10.1475i	0.222875	−	0.386031i	−0.732805	−	0.680439i	$-0.761789\pi$
$691$	5.85868	−	10.1475i	0.222875	−	0.386031i	0.955680	+	0.294408i	$0.0951225\pi$
$692$		0			0
$693$	−11.4399	−	10.2712i	−0.434567	−	0.390169i
$694$		0			0
$695$	0.676742	−	1.17215i	0.0256703	−	0.0444622i
$696$		0			0
$697$	−10.3759	−	17.9716i	−0.393016	−	0.680724i
$698$		0			0
$699$	−44.1004	+	7.01697i	−1.66803	+	0.265406i
$700$		0			0
$701$	−10.5926			−0.400077			−0.200039	−	0.979788i	$-0.564107\pi$
$701$	−10.5926			−0.400077			−0.200039	+	0.979788i	$0.564107\pi$
$702$		0			0
$703$	−16.8479			−0.635430
$704$		0			0
$705$	−1.77511	+	0.282443i	−0.0668543	+	0.0106374i
$706$		0			0
$707$	−3.59097	−	6.21975i	−0.135052	−	0.233918i
$708$		0			0
$709$	−19.1488	+	33.1668i	−0.719150	+	1.24560i	0.242187	+	0.970230i	$0.422135\pi$
$709$	−19.1488	+	33.1668i	−0.719150	+	1.24560i	−0.961337	+	0.275374i	$0.911198\pi$
$710$		0			0
$711$	−3.85705	+	18.2737i	−0.144651	+	0.685318i
$712$		0			0
$713$	2.66182	−	4.61042i	0.0996861	−	0.172661i
$714$		0			0
$715$	2.99355	+	5.18499i	0.111953	+	0.193908i
$716$		0			0
$717$	−29.7810	−	36.7230i	−1.11219	−	1.37145i
$718$		0			0
$719$	−41.6752			−1.55422			−0.777112	−	0.629362i	$-0.783316\pi$
$719$	−41.6752			−1.55422			−0.777112	+	0.629362i	$0.783316\pi$
$720$		0			0
$721$	12.8285			0.477757
$722$		0			0
$723$	−6.21698	+	16.2303i	−0.231212	+	0.603610i
$724$		0			0
$725$	8.56238	+	14.8305i	0.317999	+	0.550790i
$726$		0			0
$727$	−16.4126	+	28.4274i	−0.608709	+	1.05432i	0.382744	+	0.923854i	$0.374979\pi$
$727$	−16.4126	+	28.4274i	−0.608709	+	1.05432i	−0.991453	+	0.130461i	$0.958354\pi$
$728$		0			0
$729$	15.7769	−	21.9110i	0.584329	−	0.811517i
$730$		0			0
$731$	23.1271	−	40.0573i	0.855386	−	1.48157i
$732$		0			0
$733$	−4.64884	−	8.05203i	−0.171709	−	0.297408i	0.767309	−	0.641278i	$-0.221595\pi$
$733$	−4.64884	−	8.05203i	−0.171709	−	0.297408i	−0.939017	+	0.343870i	$0.888262\pi$
$734$		0			0
$735$	−0.148152	+	0.386770i	−0.00546465	+	0.0142662i
$736$		0			0
$737$	3.38332			0.124626
$738$		0			0
$739$	−11.3776			−0.418530			−0.209265	−	0.977859i	$-0.567107\pi$
$739$	−11.3776			−0.418530			−0.209265	+	0.977859i	$0.567107\pi$
$740$		0			0
$741$	−19.5092	−	24.0568i	−0.716687	−	0.883749i
$742$		0			0
$743$	−1.16182	−	2.01234i	−0.0426232	−	0.0738256i	0.843927	−	0.536458i	$-0.180238\pi$
$743$	−1.16182	−	2.01234i	−0.0426232	−	0.0738256i	−0.886550	+	0.462633i	$0.846905\pi$
$744$		0			0
$745$	−0.272915	+	0.472703i	−0.00999883	+	0.0173185i
$746$		0			0
$747$	6.01204	−	28.4835i	0.219969	−	1.04216i
$748$		0			0
$749$	3.78263	−	6.55171i	0.138214	−	0.239394i
$750$		0			0
$751$	−5.56690	−	9.64215i	−0.203139	−	0.351847i	0.746399	−	0.665498i	$-0.231781\pi$
$751$	−5.56690	−	9.64215i	−0.203139	−	0.351847i	−0.949538	+	0.313652i	$0.898448\pi$
$752$		0			0
$753$	48.4374	−	7.70703i	1.76516	−	0.280860i
$754$		0			0
$755$	−2.69329			−0.0980190
$756$		0			0
$757$	52.1639			1.89593			0.947964	−	0.318376i	$-0.103138\pi$
$757$	52.1639			1.89593			0.947964	+	0.318376i	$0.103138\pi$
$758$		0			0
$759$	−65.0537	+	10.3509i	−2.36130	+	0.375714i
$760$		0			0
$761$	23.5127	+	40.7252i	0.852336	+	1.47629i	0.879095	+	0.476647i	$0.158148\pi$
$761$	23.5127	+	40.7252i	0.852336	+	1.47629i	−0.0267592	+	0.999642i	$0.508519\pi$
$762$		0			0
$763$	3.49028	−	6.04535i	0.126357	−	0.218856i
$764$		0			0
$765$	−1.97700	−	1.77502i	−0.0714787	−	0.0641759i
$766$		0			0
$767$	−18.5140	+	32.0671i	−0.668501	+	1.15788i
$768$		0			0
$769$	3.30314	+	5.72121i	0.119114	+	0.206312i	0.919417	−	0.393284i	$-0.128661\pi$
$769$	3.30314	+	5.72121i	0.119114	+	0.206312i	−0.800303	+	0.599596i	$0.795328\pi$
$770$		0			0
$771$	−31.4887	−	38.8288i	−1.13404	−	1.39838i
$772$		0			0
$773$	19.0870			0.686512			0.343256	−	0.939242i	$-0.388470\pi$
$773$	19.0870			0.686512			0.343256	+	0.939242i	$0.388470\pi$
$774$		0			0
$775$	−3.54583			−0.127370
$776$		0			0
$777$	−2.85185	+	7.44514i	−0.102309	+	0.267093i
$778$		0			0
$779$	10.2540	+	17.7605i	0.367389	+	0.636337i
$780$		0			0
$781$	35.2108	−	60.9869i	1.25994	−	2.18228i
$782$		0			0
$783$	−0.903827	+	17.9797i	−0.0323001	+	0.642544i
$784$		0			0
$785$	−0.663069	+	1.14847i	−0.0236659	+	0.0409906i
$786$		0			0
$787$	25.4503	+	44.0813i	0.907207	+	1.57133i	0.817927	+	0.575322i	$0.195123\pi$
$787$	25.4503	+	44.0813i	0.907207	+	1.57133i	0.0892796	+	0.996007i	$0.471544\pi$
$788$		0			0
$789$	−0.749229	+	1.95596i	−0.0266733	+	0.0696342i
$790$		0			0
$791$	−19.5699			−0.695826
$792$		0			0
$793$	−26.9105			−0.955620
$794$		0			0
$795$	0.245960	+	0.303294i	0.00872330	+	0.0107567i
$796$		0			0
$797$	−4.38727	−	7.59898i	−0.155405	−	0.269170i	0.777801	−	0.628510i	$-0.216335\pi$
$797$	−4.38727	−	7.59898i	−0.155405	−	0.269170i	−0.933207	+	0.359341i	$0.883002\pi$
$798$		0			0
$799$	8.03667	−	13.9199i	0.284317	−	0.492451i
$800$		0			0
$801$	−21.3565	+	6.97274i	−0.754595	+	0.246370i
$802$		0			0
$803$	9.37880	−	16.2446i	0.330971	−	0.573258i
$804$		0			0
$805$	0.887275	+	1.53681i	0.0312723	+	0.0541653i
$806$		0			0
$807$	15.4182	−	2.45324i	0.542746	−	0.0863581i
$808$		0			0
$809$	−9.51384			−0.334489			−0.167244	−	0.985915i	$-0.553487\pi$
$809$	−9.51384			−0.334489			−0.167244	+	0.985915i	$0.553487\pi$
$810$		0			0
$811$	25.0118			0.878282			0.439141	−	0.898418i	$-0.355283\pi$
$811$	25.0118			0.878282			0.439141	+	0.898418i	$0.355283\pi$
$812$		0			0
$813$	−30.1105	+	4.79099i	−1.05602	+	0.168027i
$814$		0			0
$815$	0.796303	+	1.37924i	0.0278933	+	0.0483126i
$816$		0			0
$817$	−22.8554	+	39.5867i	−0.799610	+	1.38496i
$818$		0			0
$819$	−13.9331	+	4.54906i	−0.486862	+	0.158957i
$820$		0			0
$821$	17.7970	−	30.8253i	0.621119	−	1.07581i	−0.368158	−	0.929763i	$-0.620012\pi$
$821$	17.7970	−	30.8253i	0.621119	−	1.07581i	0.989278	−	0.146047i	$-0.0466551\pi$
$822$		0			0
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$		0			0
$825$	27.6352	+	34.0770i	0.962133	+	1.18641i
$826$		0			0
$827$	25.4531			0.885090			0.442545	−	0.896746i	$-0.354076\pi$
$827$	25.4531			0.885090			0.442545	+	0.896746i	$0.354076\pi$
$828$		0			0
$829$	−17.5458			−0.609392			−0.304696	−	0.952450i	$-0.598555\pi$
$829$	−17.5458			−0.609392			−0.304696	+	0.952450i	$0.598555\pi$
$830$		0			0
$831$	−0.900948	+	2.35205i	−0.0312535	+	0.0815916i
$832$		0			0
$833$	−1.85185	−	3.20750i	−0.0641627	−	0.111133i
$834$		0			0
$835$	0.526955	−	0.912713i	0.0182360	−	0.0315857i
$836$		0			0
$837$	−3.13052	−	2.02350i	−0.108207	−	0.0699425i
$838$		0			0
$839$	12.0562	−	20.8820i	0.416227	−	0.720927i	−0.579329	−	0.815094i	$-0.696685\pi$
$839$	12.0562	−	20.8820i	0.416227	−	0.720927i	0.995556	+	0.0941668i	$0.0300187\pi$
$840$		0			0
$841$	8.49837	+	14.7196i	0.293047	+	0.507572i
$842$		0			0
$843$	12.5748	−	32.8282i	0.433099	−	1.13066i
$844$		0			0
$845$	2.59915			0.0894133
$846$		0			0
$847$	15.2632			0.524450
$848$		0			0
$849$	−5.02175	−	6.19234i	−0.172346	−	0.212521i
$850$		0			0
$851$	17.0796	+	29.5828i	0.585482	+	1.01408i
$852$		0			0
$853$	−16.2616	+	28.1659i	−0.556785	+	0.964381i	0.440977	+	0.897518i	$0.354632\pi$
$853$	−16.2616	+	28.1659i	−0.556785	+	0.964381i	−0.997762	+	0.0668621i	$0.978701\pi$
$854$		0			0
$855$	1.95378	+	1.75417i	0.0668178	+	0.0599912i
$856$		0			0
$857$	0.299870	−	0.519390i	0.0102434	−	0.0177420i	−0.860858	−	0.508845i	$-0.830073\pi$
$857$	0.299870	−	0.519390i	0.0102434	−	0.0177420i	0.871102	+	0.491103i	$0.163406\pi$
$858$		0			0
$859$	−13.2174	−	22.8932i	−0.450971	−	0.781104i	0.547476	−	0.836822i	$-0.315589\pi$
$859$	−13.2174	−	22.8932i	−0.450971	−	0.781104i	−0.998447	+	0.0557171i	$0.982255\pi$
$860$		0			0
$861$	9.58414	−	1.52496i	0.326626	−	0.0519706i
$862$		0			0
$863$	−19.8454			−0.675545			−0.337773	−	0.941228i	$-0.609674\pi$
$863$	−19.8454			−0.675545			−0.337773	+	0.941228i	$0.609674\pi$
$864$		0			0
$865$	6.05718			0.205950
$866$		0			0
$867$	−5.61505	+	0.893429i	−0.190697	+	0.0303424i
$868$		0			0
$869$	−15.9520	−	27.6296i	−0.541134	−	0.937271i
$870$		0			0
$871$	1.61273	−	2.79332i	0.0546451	−	0.0946481i
$872$		0			0
$873$	10.6248	−	50.3374i	0.359594	−	1.70366i
$874$		0			0
$875$	1.18878	−	2.05903i	0.0401881	−	0.0696078i
$876$		0			0
$877$	−10.2352	−	17.7278i	−0.345617	−	0.598626i	0.639849	−	0.768501i	$-0.278997\pi$
$877$	−10.2352	−	17.7278i	−0.345617	−	0.598626i	−0.985466	+	0.169875i	$0.945664\pi$
$878$		0			0
$879$	7.71681	+	9.51563i	0.260282	+	0.320954i
$880$		0			0
$881$	−31.1683			−1.05009			−0.525043	−	0.851076i	$-0.675951\pi$
$881$	−31.1683			−1.05009			−0.525043	+	0.851076i	$0.675951\pi$
$882$		0			0
$883$	2.64187			0.0889060			0.0444530	−	0.999011i	$-0.485846\pi$
$883$	2.64187			0.0889060			0.0444530	+	0.999011i	$0.485846\pi$
$884$		0			0
$885$	1.12283	−	2.93130i	0.0377436	−	0.0985347i
$886$		0			0
$887$	−11.5825	−	20.0615i	−0.388902	−	0.673599i	0.603400	−	0.797439i	$-0.293812\pi$
$887$	−11.5825	−	20.0615i	−0.388902	−	0.673599i	−0.992302	+	0.123840i	$0.960479\pi$
$888$		0			0
$889$	−8.40451	+	14.5570i	−0.281878	+	0.488228i
$890$		0			0
$891$	4.95159	+	45.8563i	0.165884	+	1.53624i
$892$		0			0
$893$	−7.94226	+	13.7564i	−0.265778	+	0.460341i
$894$		0			0
$895$	1.14132	+	1.97682i	0.0381500	+	0.0660777i
$896$		0			0
$897$	−22.4632	+	58.6433i	−0.750026	+	1.95804i
$898$		0			0
$899$	2.48538			0.0828921
$900$		0			0
$901$	−3.49192			−0.116333
$902$		0			0
$903$	13.6248	+	16.8007i	0.453404	+	0.559094i
$904$		0			0
$905$	−1.47949	−	2.56255i	−0.0491799	−	0.0851821i
$906$		0			0
$907$	−25.0264	+	43.3470i	−0.830988	+	1.43931i	0.0662676	+	0.997802i	$0.478891\pi$
$907$	−25.0264	+	43.3470i	−0.830988	+	1.43931i	−0.897256	+	0.441511i	$0.854442\pi$
$908$		0			0
$909$	−4.44966	+	21.0814i	−0.147586	+	0.699224i
$910$		0			0
$911$	−5.42231	+	9.39172i	−0.179649	+	0.311161i	−0.941760	−	0.336285i	$-0.890830\pi$
$911$	−5.42231	+	9.39172i	−0.179649	+	0.311161i	0.762111	+	0.647446i	$0.224163\pi$
$912$		0			0
$913$	24.8646	+	43.0667i	0.822897	+	1.42530i
$914$		0			0
$915$	2.25296	−	0.358476i	0.0744806	−	0.0118509i
$916$		0			0
$917$	−4.89931			−0.161790
$918$		0			0
$919$	−11.1910			−0.369156			−0.184578	−	0.982818i	$-0.559092\pi$
$919$	−11.1910			−0.369156			−0.184578	+	0.982818i	$0.559092\pi$
$920$		0			0
$921$	−26.9441	+	4.28716i	−0.887837	+	0.141267i
$922$		0			0
$923$	−33.5679	−	58.1413i	−1.10490	−	1.91374i
$924$		0			0
$925$	11.3759	−	19.7037i	0.374038	−	0.647853i
$926$		0			0
$927$	−28.6368	−	25.7111i	−0.940556	−	0.844462i
$928$		0			0
$929$	−20.6478	+	35.7630i	−0.677431	+	1.17335i	0.298321	+	0.954466i	$0.403573\pi$
$929$	−20.6478	+	35.7630i	−0.677431	+	1.17335i	−0.975752	+	0.218879i	$0.929760\pi$
$930$		0			0
$931$	1.83009	+	3.16982i	0.0599789	+	0.103887i
$932$		0			0
$933$	−21.4090	−	26.3995i	−0.700900	−	0.864282i
$934$		0			0
$935$	4.53870			0.148431
$936$		0			0
$937$	−33.5620			−1.09642			−0.548211	−	0.836340i	$-0.684691\pi$
$937$	−33.5620			−1.09642			−0.548211	+	0.836340i	$0.684691\pi$
$938$		0			0
$939$	15.7898	−	41.2213i	0.515279	−	1.34521i
$940$		0			0
$941$	−25.2112	−	43.6671i	−0.821862	−	1.42351i	−0.904294	−	0.426911i	$-0.859602\pi$
$941$	−25.2112	−	43.6671i	−0.821862	−	1.42351i	0.0824315	−	0.996597i	$-0.473731\pi$
$942$		0			0
$943$	20.7902	−	36.0096i	0.677021	−	1.17263i
$944$		0			0
$945$	1.10589	−	0.566453i	0.0359746	−	0.0184267i
$946$		0			0
$947$	10.1212	−	17.5304i	0.328895	−	0.569662i	−0.653398	−	0.757014i	$-0.726657\pi$
$947$	10.1212	−	17.5304i	0.328895	−	0.569662i	0.982293	+	0.187352i	$0.0599905\pi$
$948$		0			0
$949$	−8.94119	−	15.4866i	−0.290243	−	0.502716i
$950$		0			0
$951$	−5.13160	+	13.3967i	−0.166404	+	0.434419i
$952$		0			0
$953$	−29.3685			−0.951340			−0.475670	−	0.879624i	$-0.657794\pi$
$953$	−29.3685			−0.951340			−0.475670	+	0.879624i	$0.657794\pi$
$954$		0			0
$955$	−3.14884			−0.101894
$956$		0			0
$957$	−19.3703	−	23.8856i	−0.626154	−	0.772113i
$958$		0			0
$959$	−2.72257	−	4.71563i	−0.0879164	−	0.152276i
$960$		0			0
$961$	15.2427	−	26.4011i	0.491700	−	0.851649i
$962$		0			0
$963$	−21.5750	+	7.04407i	−0.695244	+	0.226992i
$964$		0			0
$965$	−1.33297	+	2.30878i	−0.0429099	+	0.0743222i
$966$		0			0
$967$	−15.2157	−	26.3544i	−0.489305	−	0.847501i	0.510619	−	0.859807i	$-0.329416\pi$
$967$	−15.2157	−	26.3544i	−0.489305	−	0.847501i	−0.999924	+	0.0123057i	$0.996083\pi$
$968$		0			0
$969$	−23.1884	+	3.68958i	−0.744918	+	0.118526i
$970$		0			0
$971$	−7.18659			−0.230629			−0.115314	−	0.993329i	$-0.536788\pi$
$971$	−7.18659			−0.230629			−0.115314	+	0.993329i	$0.536788\pi$
$972$		0			0
$973$	−5.66019			−0.181457
$974$		0			0
$975$	41.3074	−	6.57256i	1.32290	−	0.210490i
$976$		0			0
$977$	−14.2713	−	24.7186i	−0.456579	−	0.790818i	0.542199	−	0.840250i	$-0.317592\pi$
$977$	−14.2713	−	24.7186i	−0.456579	−	0.790818i	−0.998777	+	0.0494328i	$0.984259\pi$
$978$		0			0
$979$	19.1888	−	33.2359i	0.613276	−	1.06223i
$980$		0			0
$981$	−19.9075	+	6.49966i	−0.635598	+	0.207518i
$982$		0			0
$983$	2.20821	−	3.82473i	0.0704310	−	0.121990i	−0.828659	−	0.559753i	$-0.810896\pi$
$983$	2.20821	−	3.82473i	0.0704310	−	0.121990i	0.899090	+	0.437763i	$0.144229\pi$
$984$		0			0
$985$	0.0172400	+	0.0298606i	0.000549313	+	0.000951438i
$986$		0			0
$987$	4.73461	+	5.83826i	0.150704	+	0.185834i
$988$		0			0
$989$	92.6791			2.94702
$990$		0			0
$991$	5.81341			0.184669			0.0923345	−	0.995728i	$-0.470567\pi$
$991$	5.81341			0.184669			0.0923345	+	0.995728i	$0.470567\pi$
$992$		0			0
$993$	−7.42270	+	19.3780i	−0.235552	+	0.614941i
$994$		0			0
$995$	−2.32777	−	4.03182i	−0.0737953	−	0.127817i
$996$		0			0
$997$	26.3204	−	45.5882i	0.833575	−	1.44379i	−0.0616108	−	0.998100i	$-0.519624\pi$
$997$	26.3204	−	45.5882i	0.833575	−	1.44379i	0.895186	−	0.445694i	$-0.147043\pi$
$998$		0			0
$999$	21.2878	−	10.9040i	0.673517	−	0.344986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.r.j.673.3		6
3.2	odd	2		3024.2.r.j.2017.2		6
4.3	odd	2		252.2.j.a.169.1	yes	6
9.2	odd	6		9072.2.a.bv.1.2		3
9.4	even	3	inner	1008.2.r.j.337.3		6
9.5	odd	6		3024.2.r.j.1009.2		6
9.7	even	3		9072.2.a.by.1.2		3
12.11	even	2		756.2.j.b.505.2		6
28.3	even	6		1764.2.l.f.961.1		6
28.11	odd	6		1764.2.l.e.961.3		6
28.19	even	6		1764.2.i.d.1537.2		6
28.23	odd	6		1764.2.i.g.1537.2		6
28.27	even	2		1764.2.j.e.1177.3		6
36.7	odd	6		2268.2.a.i.1.2		3
36.11	even	6		2268.2.a.h.1.2		3
36.23	even	6		756.2.j.b.253.2		6
36.31	odd	6		252.2.j.a.85.1	✓	6
84.11	even	6		5292.2.l.e.3313.2		6
84.23	even	6		5292.2.i.f.2125.2		6
84.47	odd	6		5292.2.i.e.2125.2		6
84.59	odd	6		5292.2.l.f.3313.2		6
84.83	odd	2		5292.2.j.d.3529.2		6
252.23	even	6		5292.2.l.e.361.2		6
252.31	even	6		1764.2.i.d.373.2		6
252.59	odd	6		5292.2.i.e.1549.2		6
252.67	odd	6		1764.2.i.g.373.2		6
252.95	even	6		5292.2.i.f.1549.2		6
252.103	even	6		1764.2.l.f.949.1		6
252.131	odd	6		5292.2.l.f.361.2		6
252.139	even	6		1764.2.j.e.589.3		6
252.167	odd	6		5292.2.j.d.1765.2		6
252.247	odd	6		1764.2.l.e.949.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.j.a.85.1	✓	6	36.31	odd	6
252.2.j.a.169.1	yes	6	4.3	odd	2
756.2.j.b.253.2		6	36.23	even	6
756.2.j.b.505.2		6	12.11	even	2
1008.2.r.j.337.3		6	9.4	even	3	inner
1008.2.r.j.673.3		6	1.1	even	1	trivial
1764.2.i.d.373.2		6	252.31	even	6
1764.2.i.d.1537.2		6	28.19	even	6
1764.2.i.g.373.2		6	252.67	odd	6
1764.2.i.g.1537.2		6	28.23	odd	6
1764.2.j.e.589.3		6	252.139	even	6
1764.2.j.e.1177.3		6	28.27	even	2
1764.2.l.e.949.3		6	252.247	odd	6
1764.2.l.e.961.3		6	28.11	odd	6
1764.2.l.f.949.1		6	252.103	even	6
1764.2.l.f.961.1		6	28.3	even	6
2268.2.a.h.1.2		3	36.11	even	6
2268.2.a.i.1.2		3	36.7	odd	6
3024.2.r.j.1009.2		6	9.5	odd	6
3024.2.r.j.2017.2		6	3.2	odd	2
5292.2.i.e.1549.2		6	252.59	odd	6
5292.2.i.e.2125.2		6	84.47	odd	6
5292.2.i.f.1549.2		6	252.95	even	6
5292.2.i.f.2125.2		6	84.23	even	6
5292.2.j.d.1765.2		6	252.167	odd	6
5292.2.j.d.3529.2		6	84.83	odd	2
5292.2.l.e.361.2		6	252.23	even	6
5292.2.l.e.3313.2		6	84.11	even	6
5292.2.l.f.361.2		6	252.131	odd	6
5292.2.l.f.3313.2		6	84.59	odd	6
9072.2.a.bv.1.2		3	9.2	odd	6
9072.2.a.by.1.2		3	9.7	even	3

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.71053 - 0.272169i) q^{3} +(-0.119562 - 0.207087i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(2.85185 - 0.931107i) q^{9} +(-2.56238 + 4.43818i) q^{11} +(2.44282 + 4.23109i) q^{13} +(-0.260877 - 0.321688i) q^{15} +3.70370 q^{17} -3.66019 q^{19} +(-0.619562 + 1.61745i) q^{21} +(3.71053 + 6.42683i) q^{23} +(2.47141 - 4.28061i) q^{25} +(4.62476 - 2.36887i) q^{27} +(-1.73229 + 3.00041i) q^{29} +(-0.358685 - 0.621261i) q^{31} +(-3.17511 + 8.28905i) q^{33} +0.239123 q^{35} +4.60301 q^{37} +(5.33009 + 6.57256i) q^{39} +(-2.80150 - 4.85235i) q^{41} +(6.24433 - 10.8155i) q^{43} +(-0.533792 - 0.479256i) q^{45} +(2.16991 - 3.75839i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(6.33530 - 1.00803i) q^{51} -0.942820 q^{53} +1.22545 q^{55} +(-6.26088 + 0.996189i) q^{57} +(3.78947 + 6.56355i) q^{59} +(-2.75404 + 4.77014i) q^{61} +(-0.619562 + 2.93533i) q^{63} +(0.584135 - 1.01175i) q^{65} +(-0.330095 - 0.571741i) q^{67} +(8.09617 + 9.98342i) q^{69} -13.7414 q^{71} -3.66019 q^{73} +(3.06238 - 7.99476i) q^{75} +(-2.56238 - 4.43818i) q^{77} +(-3.11273 + 5.39140i) q^{79} +(7.26608 - 5.31075i) q^{81} +(4.85185 - 8.40365i) q^{83} +(-0.442820 - 0.766987i) q^{85} +(-2.14652 + 5.60377i) q^{87} -7.48865 q^{89} -4.88564 q^{91} +(-0.782630 - 0.965064i) q^{93} +(0.437618 + 0.757977i) q^{95} +(8.57442 - 14.8513i) q^{97} +(-3.17511 + 15.0429i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{3} - q^{5} - 3 q^{7} + 8 q^{9} + 2 q^{11} - 3 q^{13} - q^{15} + 4 q^{17} - 6 q^{19} - 4 q^{21} + 14 q^{23} + 6 q^{25} - 7 q^{27} - q^{29} - 3 q^{31} + 8 q^{33} + 2 q^{35} - 6 q^{37} + 24 q^{39}+ \cdots + 8 q^{99}+O(q^{100}) \) 6 * q + 2 * q^3 - q^5 - 3 * q^7 + 8 * q^9 + 2 * q^11 - 3 * q^13 - q^15 + 4 * q^17 - 6 * q^19 - 4 * q^21 + 14 * q^23 + 6 * q^25 - 7 * q^27 - q^29 - 3 * q^31 + 8 * q^33 + 2 * q^35 - 6 * q^37 + 24 * q^39 + 3 * q^43 + 23 * q^45 + 21 * q^47 - 3 * q^49 - 5 * q^51 + 12 * q^53 - 12 * q^55 - 37 * q^57 + 31 * q^59 - 6 * q^61 - 4 * q^63 - 15 * q^65 + 6 * q^67 + 5 * q^69 - 34 * q^71 - 6 * q^73 + q^75 + 2 * q^77 - 9 * q^79 + 8 * q^81 + 20 * q^83 + 15 * q^85 + 23 * q^87 + 24 * q^89 + 6 * q^91 - 3 * q^93 + 20 * q^95 + 9 * q^97 + 8 * q^99

Introduction

L-functions

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