LMFDB - Embedded newform 864.2.bi.a.767.35

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(95,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.95"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 0, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bi (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			767.35
Character	$\chi$	$=$	864.767
Dual form			864.2.bi.a.383.35

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.71055 - 0.272051i) q^{3} +(0.354987 - 0.975319i) q^{5} +(4.63649 + 0.817538i) q^{7} +(2.85198 - 0.930714i) q^{9} +(-2.32491 + 0.846199i) q^{11} +(-2.86530 + 2.40427i) q^{13} +(0.341888 - 1.76491i) q^{15} +(2.82032 - 1.62831i) q^{17} +(3.42322 + 1.97639i) q^{19} +(8.15337 + 0.137081i) q^{21} +(-1.06509 - 6.04044i) q^{23} +(3.00499 + 2.52149i) q^{25} +(4.62525 - 2.36792i) q^{27} +(-5.10059 + 6.07864i) q^{29} +(-10.2706 + 1.81099i) q^{31} +(-3.74667 + 2.07996i) q^{33} +(2.44325 - 4.23184i) q^{35} +(0.0304565 + 0.0527523i) q^{37} +(-4.24716 + 4.89214i) q^{39} +(-4.26685 - 5.08504i) q^{41} +(-3.68141 - 10.1146i) q^{43} +(0.104672 - 3.11198i) q^{45} +(1.20067 - 6.80932i) q^{47} +(14.2508 + 5.18687i) q^{49} +(4.38132 - 3.55258i) q^{51} +6.06507i q^{53} +2.56792i q^{55} +(6.39327 + 2.44944i) q^{57} +(8.99831 + 3.27512i) q^{59} +(-1.05617 + 5.98986i) q^{61} +(13.9840 - 1.98364i) q^{63} +(1.32779 + 3.64807i) q^{65} +(-0.695330 - 0.828662i) q^{67} +(-3.46520 - 10.0427i) q^{69} +(-3.24312 - 5.61724i) q^{71} +(1.27559 - 2.20939i) q^{73} +(5.82616 + 3.49562i) q^{75} +(-11.4712 + 2.02269i) q^{77} +(2.30281 - 2.74438i) q^{79} +(7.26754 - 5.30875i) q^{81} +(-5.87486 - 4.92959i) q^{83} +(-0.586947 - 3.32874i) q^{85} +(-7.07112 + 11.7855i) q^{87} +(5.37546 + 3.10353i) q^{89} +(-15.2505 + 8.80488i) q^{91} +(-17.0757 + 5.89191i) q^{93} +(3.14281 - 2.63713i) q^{95} +(-1.14812 + 0.417883i) q^{97} +(-5.84303 + 4.57717i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) $ 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	1.71055	−	0.272051i	0.987588	−	0.157069i
$3$	1.71055	−	0.272051i	0.987588	−	0.157069i
$4$		0			0
$5$	0.354987	−	0.975319i	0.158755	−	0.436176i	−0.834657	−	0.550770i	$-0.814334\pi$
$5$	0.354987	−	0.975319i	0.158755	−	0.436176i	0.993412	+	0.114593i	$0.0365565\pi$
$6$		0			0
$7$	4.63649	+	0.817538i	1.75243	+	0.309000i	0.955482	−	0.295050i	$-0.0953364\pi$
$7$	4.63649	+	0.817538i	1.75243	+	0.309000i	0.796946	+	0.604051i	$0.206448\pi$
$8$		0			0
$9$	2.85198	−	0.930714i	0.950659	−	0.310238i
$10$		0			0
$11$	−2.32491	+	0.846199i	−0.700987	+	0.255139i	−0.667832	−	0.744312i	$-0.732778\pi$
$11$	−2.32491	+	0.846199i	−0.700987	+	0.255139i	−0.0331549	+	0.999450i	$0.510555\pi$
$12$		0			0
$13$	−2.86530	+	2.40427i	−0.794691	+	0.666825i	−0.946902	−	0.321523i	$-0.895805\pi$
$13$	−2.86530	+	2.40427i	−0.794691	+	0.666825i	0.152211	+	0.988348i	$0.451361\pi$
$14$		0			0
$15$	0.341888	−	1.76491i	0.0882750	−	0.455698i
$16$		0			0
$17$	2.82032	−	1.62831i	0.684028	−	0.394924i	−0.117343	−	0.993091i	$-0.537438\pi$
$17$	2.82032	−	1.62831i	0.684028	−	0.394924i	0.801371	+	0.598168i	$0.204104\pi$
$18$		0			0
$19$	3.42322	+	1.97639i	0.785340	+	0.453416i	0.838319	−	0.545179i	$-0.183539\pi$
$19$	3.42322	+	1.97639i	0.785340	+	0.453416i	−0.0529796	+	0.998596i	$0.516872\pi$
$20$		0			0
$21$	8.15337	+	0.137081i	1.77921	+	0.0299135i
$22$		0			0
$23$	−1.06509	−	6.04044i	−0.222087	−	1.25952i	−0.868176	−	0.496256i	$-0.834708\pi$
$23$	−1.06509	−	6.04044i	−0.222087	−	1.25952i	0.646089	−	0.763262i	$-0.276404\pi$
$24$		0			0
$25$	3.00499	+	2.52149i	0.600998	+	0.504297i
$26$		0			0
$27$	4.62525	−	2.36792i	0.890130	−	0.455706i
$28$		0			0
$29$	−5.10059	+	6.07864i	−0.947155	+	1.12878i	0.0443902	+	0.999014i	$0.485866\pi$
$29$	−5.10059	+	6.07864i	−0.947155	+	1.12878i	−0.991545	+	0.129761i	$0.958579\pi$
$30$		0			0
$31$	−10.2706	+	1.81099i	−1.84466	+	0.325263i	−0.983195	−	0.182560i	$-0.941562\pi$
$31$	−10.2706	+	1.81099i	−1.84466	+	0.325263i	−0.861462	+	0.507823i	$0.830450\pi$
$32$		0			0
$33$	−3.74667	+	2.07996i	−0.652212	+	0.362075i
$34$		0			0
$35$	2.44325	−	4.23184i	0.412985	−	0.715312i
$36$		0			0
$37$	0.0304565	+	0.0527523i	0.00500702	+	0.00867242i	0.868518	−	0.495658i	$-0.165073\pi$
$37$	0.0304565	+	0.0527523i	0.00500702	+	0.00867242i	−0.863511	+	0.504330i	$0.831740\pi$
$38$		0			0
$39$	−4.24716	+	4.89214i	−0.680090	+	0.783369i
$40$		0			0
$41$	−4.26685	−	5.08504i	−0.666370	−	0.794149i	0.321915	−	0.946769i	$-0.395674\pi$
$41$	−4.26685	−	5.08504i	−0.666370	−	0.794149i	−0.988285	+	0.152620i	$0.951229\pi$
$42$		0			0
$43$	−3.68141	−	10.1146i	−0.561410	−	1.54246i	−0.817572	−	0.575826i	$-0.804680\pi$
$43$	−3.68141	−	10.1146i	−0.561410	−	1.54246i	0.256162	−	0.966634i	$-0.417542\pi$
$44$		0			0
$45$	0.104672	−	3.11198i	0.0156036	−	0.463907i
$46$		0			0
$47$	1.20067	−	6.80932i	0.175135	−	0.993241i	−0.762852	−	0.646573i	$-0.776202\pi$
$47$	1.20067	−	6.80932i	0.175135	−	0.993241i	0.937988	−	0.346669i	$-0.112687\pi$
$48$		0			0
$49$	14.2508	+	5.18687i	2.03583	+	0.740981i
$50$		0			0
$51$	4.38132	−	3.55258i	0.613507	−	0.497461i
$52$		0			0
$53$			6.06507i			0.833101i	0.909113	+	0.416551i	$0.136761\pi$
$53$			6.06507i			0.833101i	−0.909113	+	0.416551i	$0.863239\pi$
$54$		0			0
$55$			2.56792i			0.346258i
$56$		0			0
$57$	6.39327	+	2.44944i	0.846809	+	0.324436i
$58$		0			0
$59$	8.99831	+	3.27512i	1.17148	+	0.426384i	0.853185	−	0.521608i	$-0.174668\pi$
$59$	8.99831	+	3.27512i	1.17148	+	0.426384i	0.318295	+	0.947992i	$0.396890\pi$
$60$		0			0
$61$	−1.05617	+	5.98986i	−0.135229	+	0.766924i	0.839470	+	0.543405i	$0.182865\pi$
$61$	−1.05617	+	5.98986i	−0.135229	+	0.766924i	−0.974700	+	0.223518i	$0.928246\pi$
$62$		0			0
$63$	13.9840	−	1.98364i	1.76182	−	0.249916i
$64$		0			0
$65$	1.32779	+	3.64807i	0.164692	+	0.452487i
$66$		0			0
$67$	−0.695330	−	0.828662i	−0.0849481	−	0.101237i	0.721896	−	0.692001i	$-0.243271\pi$
$67$	−0.695330	−	0.828662i	−0.0849481	−	0.101237i	−0.806844	+	0.590764i	$0.798826\pi$
$68$		0			0
$69$	−3.46520	−	10.0427i	−0.417161	−	1.20900i
$70$		0			0
$71$	−3.24312	−	5.61724i	−0.384887	−	0.666644i	0.606867	−	0.794804i	$-0.292426\pi$
$71$	−3.24312	−	5.61724i	−0.384887	−	0.666644i	−0.991754	+	0.128160i	$0.959093\pi$
$72$		0			0
$73$	1.27559	−	2.20939i	0.149297	−	0.258589i	−0.781671	−	0.623691i	$-0.785632\pi$
$73$	1.27559	−	2.20939i	0.149297	−	0.258589i	0.930968	+	0.365102i	$0.118966\pi$
$74$		0			0
$75$	5.82616	+	3.49562i	0.672748	+	0.403640i
$76$		0			0
$77$	−11.4712	+	2.02269i	−1.30727	+	0.230507i
$78$		0			0
$79$	2.30281	−	2.74438i	0.259086	−	0.308767i	−0.620783	−	0.783982i	$-0.713185\pi$
$79$	2.30281	−	2.74438i	0.259086	−	0.308767i	0.879870	+	0.475215i	$0.157630\pi$
$80$		0			0
$81$	7.26754	−	5.30875i	0.807505	−	0.589861i
$82$		0			0
$83$	−5.87486	−	4.92959i	−0.644850	−	0.541093i	0.260654	−	0.965432i	$-0.416062\pi$
$83$	−5.87486	−	4.92959i	−0.644850	−	0.541093i	−0.905503	+	0.424339i	$0.860506\pi$
$84$		0			0
$85$	−0.586947	−	3.32874i	−0.0636634	−	0.361053i
$86$		0			0
$87$	−7.07112	+	11.7855i	−0.758104	+	1.26353i
$88$		0			0
$89$	5.37546	+	3.10353i	0.569798	+	0.328973i	0.757069	−	0.653335i	$-0.226631\pi$
$89$	5.37546	+	3.10353i	0.569798	+	0.328973i	−0.187271	+	0.982308i	$0.559964\pi$
$90$		0			0
$91$	−15.2505	+	8.80488i	−1.59869	+	0.923003i
$92$		0			0
$93$	−17.0757	+	5.89191i	−1.77067	+	0.610963i
$94$		0			0
$95$	3.14281	−	2.63713i	0.322446	−	0.270564i
$96$		0			0
$97$	−1.14812	+	0.417883i	−0.116574	+	0.0424296i	−0.399649	−	0.916668i	$-0.630868\pi$
$97$	−1.14812	+	0.417883i	−0.116574	+	0.0424296i	0.283074	+	0.959098i	$0.408646\pi$
$98$		0			0
$99$	−5.84303	+	4.57717i	−0.587246	+	0.460023i
$100$		0			0
$101$	−1.20697	−	0.212822i	−0.120098	−	0.0211766i	0.113276	−	0.993564i	$-0.463866\pi$
$101$	−1.20697	−	0.212822i	−0.120098	−	0.0211766i	−0.233374	+	0.972387i	$0.574977\pi$
$102$		0			0
$103$	−0.0294082	+	0.0807983i	−0.00289768	+	0.00796130i	−0.941133	−	0.338036i	$-0.890237\pi$
$103$	−0.0294082	+	0.0807983i	−0.00289768	+	0.00796130i	0.938235	+	0.345998i	$0.112460\pi$
$104$		0			0
$105$	3.02804	−	7.90347i	0.295506	−	0.771300i
$106$		0			0
$107$	−5.49195			−0.530927			−0.265463	−	0.964121i	$-0.585525\pi$
$107$	−5.49195			−0.530927			−0.265463	+	0.964121i	$0.585525\pi$
$108$		0			0
$109$	2.30129			0.220424			0.110212	−	0.993908i	$-0.464847\pi$
$109$	2.30129			0.220424			0.110212	+	0.993908i	$0.464847\pi$
$110$		0			0
$111$	0.0664488	+	0.0819498i	0.00630704	+	0.00777833i
$112$		0			0
$113$	−2.55145	+	7.01005i	−0.240020	+	0.659450i	0.759935	+	0.649999i	$0.225231\pi$
$113$	−2.55145	+	7.01005i	−0.240020	+	0.659450i	−0.999955	+	0.00945118i	$0.996992\pi$
$114$		0			0
$115$	−6.26945	−	1.10547i	−0.584629	−	0.103086i
$116$		0			0
$117$	−5.93408	+	9.52370i	−0.548606	+	0.880466i
$118$		0			0
$119$	14.4076	−	5.24393i	1.32074	−	0.480710i
$120$		0			0
$121$	−3.73733	+	3.13599i	−0.339757	+	0.285090i
$122$		0			0
$123$	−8.68206	−	7.53742i	−0.782835	−	0.679626i
$124$		0			0
$125$	8.02028	−	4.63051i	0.717356	−	0.414166i
$126$		0			0
$127$	5.18979	+	2.99632i	0.460519	+	0.265881i	0.712262	−	0.701913i	$-0.247671\pi$
$127$	5.18979	+	2.99632i	0.460519	+	0.265881i	−0.251743	+	0.967794i	$0.581004\pi$
$128$		0			0
$129$	−9.04892	−	16.3000i	−0.796713	−	1.43513i
$130$		0			0
$131$	1.38993	+	7.88269i	0.121439	+	0.688714i	0.983359	+	0.181671i	$0.0581505\pi$
$131$	1.38993	+	7.88269i	0.121439	+	0.688714i	−0.861921	+	0.507043i	$0.830738\pi$
$132$		0			0
$133$	14.2559	+	11.9621i	1.23615	+	1.03725i
$134$		0			0
$135$	−0.667570	−	5.35168i	−0.0574553	−	0.460599i
$136$		0			0
$137$	−9.28580	+	11.0664i	−0.793339	+	0.945465i	−0.999453	−	0.0330630i	$-0.989474\pi$
$137$	−9.28580	+	11.0664i	−0.793339	+	0.945465i	0.206114	+	0.978528i	$0.433918\pi$
$138$		0			0
$139$	−17.3993	+	3.06797i	−1.47579	+	0.260222i	−0.852895	−	0.522083i	$-0.825155\pi$
$139$	−17.3993	+	3.06797i	−1.47579	+	0.260222i	−0.622896	+	0.782305i	$0.714044\pi$
$140$		0			0
$141$	0.201322	−	11.9743i	0.0169544	−	1.00842i
$142$		0			0
$143$	4.62708	−	8.01433i	0.386936	−	0.670192i
$144$		0			0
$145$	4.11797	+	7.13254i	0.341979	+	0.592325i
$146$		0			0
$147$	25.7878	+	4.99547i	2.12694	+	0.412019i
$148$		0			0
$149$	−11.9992	−	14.3001i	−0.983010	−	1.17151i	−0.985183	−	0.171509i	$-0.945136\pi$
$149$	−11.9992	−	14.3001i	−0.983010	−	1.17151i	0.00217220	−	0.999998i	$-0.499309\pi$
$150$		0			0
$151$	5.98345	+	16.4394i	0.486926	+	1.33782i	0.903450	+	0.428693i	$0.141026\pi$
$151$	5.98345	+	16.4394i	0.486926	+	1.33782i	−0.416524	+	0.909125i	$0.636752\pi$
$152$		0			0
$153$	6.52799	−	7.26882i	0.527757	−	0.587649i
$154$		0			0
$155$	−1.87965	+	10.6600i	−0.150977	+	0.856232i
$156$		0			0
$157$	−2.12384	−	0.773014i	−0.169501	−	0.0616932i	0.255876	−	0.966710i	$-0.417636\pi$
$157$	−2.12384	−	0.773014i	−0.169501	−	0.0616932i	−0.425377	+	0.905016i	$0.639858\pi$
$158$		0			0
$159$	1.65001	+	10.3746i	0.130854	+	0.822760i
$160$		0			0
$161$		−	28.8772i		−	2.27584i
$162$		0			0
$163$			8.31889i			0.651586i	0.945441	+	0.325793i	$0.105631\pi$
$163$			8.31889i			0.651586i	−0.945441	+	0.325793i	$0.894369\pi$
$164$		0			0
$165$	0.698605	+	4.39256i	0.0543863	+	0.341961i
$166$		0			0
$167$	−23.2280	−	8.45431i	−1.79744	−	0.654214i	−0.998613	−	0.0526516i	$-0.983233\pi$
$167$	−23.2280	−	8.45431i	−1.79744	−	0.654214i	−0.798826	−	0.601563i	$-0.794545\pi$
$168$		0			0
$169$	0.171991	−	0.975410i	0.0132301	−	0.0750315i
$170$		0			0
$171$	11.6024	+	2.45060i	0.887257	+	0.187402i
$172$		0			0
$173$	−4.89575	−	13.4510i	−0.372217	−	1.02266i	−0.974502	−	0.224377i	$-0.927965\pi$
$173$	−4.89575	−	13.4510i	−0.372217	−	1.02266i	0.602285	−	0.798281i	$-0.294257\pi$
$174$		0			0
$175$	11.8712	+	14.1475i	0.897378	+	1.06945i
$176$		0			0
$177$	16.2831	+	3.15426i	1.22391	+	0.237089i
$178$		0			0
$179$	−5.27954	−	9.14443i	−0.394611	−	0.683486i	0.598440	−	0.801167i	$-0.295787\pi$
$179$	−5.27954	−	9.14443i	−0.394611	−	0.683486i	−0.993051	+	0.117681i	$0.962454\pi$
$180$		0			0
$181$	−3.32337	+	5.75625i	−0.247024	+	0.427859i	−0.962699	−	0.270575i	$-0.912786\pi$
$181$	−3.32337	+	5.75625i	−0.247024	+	0.427859i	0.715675	+	0.698434i	$0.246119\pi$
$182$		0			0
$183$	−0.177095	+	10.5333i	−0.0130912	+	0.778645i
$184$		0			0
$185$	0.0622620	−	0.0109785i	0.00457759	−	0.000807153i
$186$		0			0
$187$	−5.17912	+	6.17223i	−0.378735	+	0.451358i
$188$		0			0
$189$	23.3808	−	7.19750i	1.70070	−	0.523541i
$190$		0			0
$191$	7.13864	+	5.99003i	0.516534	+	0.433423i	0.863421	−	0.504483i	$-0.168317\pi$
$191$	7.13864	+	5.99003i	0.516534	+	0.433423i	−0.346888	+	0.937907i	$0.612762\pi$
$192$		0			0
$193$	−3.18805	−	18.0803i	−0.229481	−	1.30145i	−0.853932	−	0.520385i	$-0.825788\pi$
$193$	−3.18805	−	18.0803i	−0.229481	−	1.30145i	0.624451	−	0.781064i	$-0.285323\pi$
$194$		0			0
$195$	3.26371	+	5.87898i	0.233719	+	0.421003i
$196$		0			0
$197$	−14.5047	−	8.37430i	−1.03342	−	0.596644i	−0.115456	−	0.993313i	$-0.536833\pi$
$197$	−14.5047	−	8.37430i	−1.03342	−	0.596644i	−0.917962	+	0.396669i	$0.870166\pi$
$198$		0			0
$199$	−9.77840	+	5.64556i	−0.693172	+	0.400203i	−0.804799	−	0.593547i	$-0.797727\pi$
$199$	−9.77840	+	5.64556i	−0.693172	+	0.400203i	0.111627	+	0.993750i	$0.464394\pi$
$200$		0			0
$201$	−1.41484	−	1.22830i	−0.0997948	−	0.0866379i
$202$		0			0
$203$	−28.6183	+	24.0136i	−2.00861	+	1.68543i
$204$		0			0
$205$	−6.47421	+	2.35642i	−0.452179	+	0.164580i
$206$		0			0
$207$	−8.65954	−	16.2359i	−0.601880	−	1.12847i
$208$		0			0
$209$	−9.63110	−	1.69822i	−0.666197	−	0.117469i
$210$		0			0
$211$	6.44678	−	17.7124i	0.443815	−	1.21937i	−0.493149	−	0.869945i	$-0.664154\pi$
$211$	6.44678	−	17.7124i	0.443815	−	1.21937i	0.936964	−	0.349426i	$-0.113624\pi$
$212$		0			0
$213$	−7.07569	−	8.72629i	−0.484818	−	0.597916i
$214$		0			0
$215$	−11.1718			−0.761911
$216$		0			0
$217$	−49.1001			−3.33313
$218$		0			0
$219$	1.58090	−	4.12630i	0.106827	−	0.278829i
$220$		0			0
$221$	−4.16615	+	11.4464i	−0.280246	+	0.769969i
$222$		0			0
$223$	9.44848	+	1.66602i	0.632717	+	0.111565i	0.480803	−	0.876829i	$-0.340345\pi$
$223$	9.44848	+	1.66602i	0.632717	+	0.111565i	0.151914	+	0.988394i	$0.451456\pi$
$224$		0			0
$225$	10.9169	+	4.39443i	0.727796	+	0.292962i
$226$		0			0
$227$	22.6809	−	8.25517i	1.50538	−	0.547915i	0.547935	−	0.836521i	$-0.315414\pi$
$227$	22.6809	−	8.25517i	1.50538	−	0.547915i	0.957448	+	0.288606i	$0.0931917\pi$
$228$		0			0
$229$	7.77014	−	6.51992i	0.513465	−	0.430848i	−0.348881	−	0.937167i	$-0.613438\pi$
$229$	7.77014	−	6.51992i	0.513465	−	0.430848i	0.862347	+	0.506318i	$0.168994\pi$
$230$		0			0
$231$	−19.0719	+	6.58067i	−1.25484	+	0.432976i
$232$		0			0
$233$	−20.3652	+	11.7578i	−1.33417	+	0.770282i	−0.985936	−	0.167126i	$-0.946551\pi$
$233$	−20.3652	+	11.7578i	−1.33417	+	0.770282i	−0.348232	+	0.937408i	$0.613218\pi$
$234$		0			0
$235$	−6.21504	−	3.58826i	−0.405425	−	0.234072i
$236$		0			0
$237$	3.19246	−	5.32089i	0.207373	−	0.345629i
$238$		0			0
$239$	1.68591	+	9.56129i	0.109053	+	0.618468i	0.989524	+	0.144369i	$0.0461152\pi$
$239$	1.68591	+	9.56129i	0.109053	+	0.618468i	−0.880471	+	0.474099i	$0.842774\pi$
$240$		0			0
$241$	12.0056	+	10.0739i	0.773351	+	0.648918i	0.941565	−	0.336832i	$-0.109356\pi$
$241$	12.0056	+	10.0739i	0.773351	+	0.648918i	−0.168214	+	0.985750i	$0.553800\pi$
$242$		0			0
$243$	10.9873	−	11.0580i	0.704833	−	0.709373i
$244$		0			0
$245$	10.1177	−	12.0578i	0.646397	−	0.770345i
$246$		0			0
$247$	−14.5603	+	2.56738i	−0.926451	+	0.163358i
$248$		0			0
$249$	−11.3904	−	6.83406i	−0.721834	−	0.433091i
$250$		0			0
$251$	1.65178	−	2.86096i	0.104259	−	0.180582i	−0.809176	−	0.587566i	$-0.800086\pi$
$251$	1.65178	−	2.86096i	0.104259	−	0.180582i	0.913435	+	0.406984i	$0.133419\pi$
$252$		0			0
$253$	7.58766	+	13.1422i	0.477032	+	0.826244i
$254$		0			0
$255$	−1.90959	−	5.53431i	−0.119583	−	0.346572i
$256$		0			0
$257$	1.50604	+	1.79483i	0.0939443	+	0.111958i	0.810968	−	0.585090i	$-0.198941\pi$
$257$	1.50604	+	1.79483i	0.0939443	+	0.111958i	−0.717024	+	0.697048i	$0.754496\pi$
$258$		0			0
$259$	0.0980844	+	0.269485i	0.00609467	+	0.0167450i
$260$		0			0
$261$	−8.88928	+	22.0833i	−0.550232	+	1.36692i
$262$		0			0
$263$	1.18990	−	6.74826i	0.0733724	−	0.416116i	−0.925893	−	0.377786i	$-0.876685\pi$
$263$	1.18990	−	6.74826i	0.0733724	−	0.416116i	0.999265	−	0.0383292i	$-0.0122036\pi$
$264$		0			0
$265$	5.91538	+	2.15302i	0.363379	+	0.132259i
$266$		0			0
$267$	10.0393	+	3.84634i	0.614397	+	0.235392i
$268$		0			0
$269$			31.7431i			1.93541i	0.252080	+	0.967706i	$0.418885\pi$
$269$			31.7431i			1.93541i	−0.252080	+	0.967706i	$0.581115\pi$
$270$		0			0
$271$			4.28252i			0.260145i	0.991505	+	0.130072i	$0.0415210\pi$
$271$			4.28252i			0.260145i	−0.991505	+	0.130072i	$0.958479\pi$
$272$		0			0
$273$	−23.6914	+	19.2101i	−1.43387	+	1.16265i
$274$		0			0
$275$	−9.12002	−	3.31941i	−0.549958	−	0.200168i
$276$		0			0
$277$	−2.75570	+	15.6284i	−0.165574	+	0.939017i	0.782896	+	0.622152i	$0.213741\pi$
$277$	−2.75570	+	15.6284i	−0.165574	+	0.939017i	−0.948471	+	0.316865i	$0.897370\pi$
$278$		0			0
$279$	−27.6060	+	14.7239i	−1.65273	+	0.881496i
$280$		0			0
$281$	9.95108	+	27.3404i	0.593632	+	1.63099i	0.763710	+	0.645559i	$0.223376\pi$
$281$	9.95108	+	27.3404i	0.593632	+	1.63099i	−0.170079	+	0.985430i	$0.554402\pi$
$282$		0			0
$283$	−11.7848	−	14.0446i	−0.700534	−	0.834864i	0.292053	−	0.956402i	$-0.405662\pi$
$283$	−11.7848	−	14.0446i	−0.700534	−	0.834864i	−0.992587	+	0.121538i	$0.961217\pi$
$284$		0			0
$285$	4.65851	−	5.36596i	0.275947	−	0.317852i
$286$		0			0
$287$	−15.6260	−	27.0650i	−0.922373	−	1.59760i
$288$		0			0
$289$	−3.19720	+	5.53771i	−0.188071	+	0.325748i
$290$		0			0
$291$	−1.85024	+	1.02716i	−0.108463	+	0.0602131i
$292$		0			0
$293$	−2.05437	+	0.362241i	−0.120017	+	0.0211623i	−0.233334	−	0.972397i	$-0.574964\pi$
$293$	−2.05437	+	0.362241i	−0.120017	+	0.0211623i	0.113317	+	0.993559i	$0.463853\pi$
$294$		0			0
$295$	6.38857	−	7.61360i	0.371957	−	0.443281i
$296$		0			0
$297$	−8.74958	+	9.41908i	−0.507702	+	0.546551i
$298$		0			0
$299$	17.5747	+	14.7469i	1.01637	+	0.852835i
$300$		0			0
$301$	−8.79975	−	49.9059i	−0.507209	−	2.87653i
$302$		0			0
$303$	−2.12249	−	0.0356850i	−0.121934	−	0.00205005i
$304$		0			0
$305$	5.46710	+	3.15643i	0.313045	+	0.180737i
$306$		0			0
$307$	−3.72456	+	2.15038i	−0.212572	+	0.122729i	−0.602506	−	0.798114i	$-0.705831\pi$
$307$	−3.72456	+	2.15038i	−0.212572	+	0.122729i	0.389934	+	0.920843i	$0.372498\pi$
$308$		0			0
$309$	−0.0283230	+	0.146210i	−0.00161124	+	0.00831761i
$310$		0			0
$311$	−0.907913	+	0.761830i	−0.0514830	+	0.0431994i	−0.668166	−	0.744012i	$-0.732920\pi$
$311$	−0.907913	+	0.761830i	−0.0514830	+	0.0431994i	0.616683	+	0.787212i	$0.288476\pi$
$312$		0			0
$313$	28.7922	−	10.4795i	1.62743	−	0.592336i	0.642652	−	0.766158i	$-0.277834\pi$
$313$	28.7922	−	10.4795i	1.62743	−	0.592336i	0.984777	+	0.173822i	$0.0556119\pi$
$314$		0			0
$315$	3.02947	−	14.3431i	0.170691	−	0.808141i
$316$		0			0
$317$	15.3113	+	2.69979i	0.859967	+	0.151635i	0.586205	−	0.810162i	$-0.300621\pi$
$317$	15.3113	+	2.69979i	0.859967	+	0.151635i	0.273761	+	0.961798i	$0.411732\pi$
$318$		0			0
$319$	6.71467	−	18.4484i	0.375950	−	1.03291i
$320$		0			0
$321$	−9.39426	+	1.49409i	−0.524337	+	0.0833919i
$322$		0			0
$323$	12.8728			0.716259
$324$		0			0
$325$	−14.6725			−0.813886
$326$		0			0
$327$	3.93648	−	0.626068i	0.217688	−	0.0346216i
$328$		0			0
$329$	11.1338	−	30.5897i	0.613824	−	1.68647i
$330$		0			0
$331$	10.9163	+	1.92484i	0.600013	+	0.105799i	0.465401	−	0.885100i	$-0.345910\pi$
$331$	10.9163	+	1.92484i	0.600013	+	0.105799i	0.134612	+	0.990898i	$0.457021\pi$
$332$		0			0
$333$	0.135959	+	0.122102i	0.00745049	+	0.00669114i
$334$		0			0
$335$	−1.05504	+	0.384004i	−0.0576432	+	0.0209804i
$336$		0			0
$337$	15.1421	−	12.7058i	0.824845	−	0.692127i	−0.129256	−	0.991611i	$-0.541259\pi$
$337$	15.1421	−	12.7058i	0.824845	−	0.692127i	0.954101	+	0.299484i	$0.0968145\pi$
$338$		0			0
$339$	−2.45730	+	12.6852i	−0.133462	+	0.688964i
$340$		0			0
$341$	22.3458	−	12.9014i	1.21009	−	0.698648i
$342$		0			0
$343$	33.2924	+	19.2214i	1.79762	+	1.03786i
$344$		0			0
$345$	−11.0250	−	0.185361i	−0.593564	−	0.00997949i
$346$		0			0
$347$	−0.454724	−	2.57887i	−0.0244109	−	0.138441i	0.970167	−	0.242439i	$-0.0779475\pi$
$347$	−0.454724	−	2.57887i	−0.0244109	−	0.138441i	−0.994577	+	0.103998i	$0.966836\pi$
$348$		0			0
$349$	−1.49726	−	1.25635i	−0.0801463	−	0.0672507i	0.601834	−	0.798621i	$-0.294437\pi$
$349$	−1.49726	−	1.25635i	−0.0801463	−	0.0672507i	−0.681981	+	0.731370i	$0.738881\pi$
$350$		0			0
$351$	−7.55962	+	17.9052i	−0.403503	+	0.955706i
$352$		0			0
$353$	−16.8463	+	20.0767i	−0.896639	+	1.06857i	0.100645	+	0.994922i	$0.467909\pi$
$353$	−16.8463	+	20.0767i	−0.896639	+	1.06857i	−0.997284	+	0.0736501i	$0.976535\pi$
$354$		0			0
$355$	−6.62987	+	1.16902i	−0.351877	+	0.0620454i
$356$		0			0
$357$	23.2183	−	12.8896i	1.22884	−	0.682191i
$358$		0			0
$359$	5.19681	−	9.00114i	0.274277	−	0.475062i	−0.695675	−	0.718356i	$-0.744895\pi$
$359$	5.19681	−	9.00114i	0.274277	−	0.475062i	0.969953	+	0.243294i	$0.0782281\pi$
$360$		0			0
$361$	−1.68773	−	2.92323i	−0.0888277	−	0.153854i
$362$		0			0
$363$	−5.53974	+	6.38101i	−0.290761	+	0.334916i
$364$		0			0
$365$	−1.70204	−	2.02841i	−0.0890888	−	0.106172i
$366$		0			0
$367$	−6.33789	−	17.4132i	−0.330835	−	0.908962i	−0.987895	−	0.155124i	$-0.950422\pi$
$367$	−6.33789	−	17.4132i	−0.330835	−	0.908962i	0.657060	−	0.753838i	$-0.271800\pi$
$368$		0			0
$369$	−16.9017	−	10.5312i	−0.879866	−	0.548232i
$370$		0			0
$371$	−4.95842	+	28.1206i	−0.257428	+	1.45995i
$372$		0			0
$373$	5.82444	+	2.11992i	0.301578	+	0.109766i	0.488377	−	0.872633i	$-0.337589\pi$
$373$	5.82444	+	2.11992i	0.301578	+	0.109766i	−0.186799	+	0.982398i	$0.559811\pi$
$374$		0			0
$375$	12.4594	−	10.1027i	0.643400	−	0.521699i
$376$		0			0
$377$		−	29.6803i		−	1.52861i
$378$		0			0
$379$		−	19.5023i		−	1.00177i	−0.865515	−	0.500883i	$-0.833009\pi$
$379$		−	19.5023i		−	1.00177i	0.865515	−	0.500883i	$-0.166991\pi$
$380$		0			0
$381$	9.69255	+	3.71348i	0.496564	+	0.190248i
$382$		0			0
$383$	26.3076	+	9.57518i	1.34426	+	0.489269i	0.911150	−	0.412075i	$-0.135196\pi$
$383$	26.3076	+	9.57518i	1.34426	+	0.489269i	0.433105	+	0.901343i	$0.357418\pi$
$384$		0			0
$385$	−2.09937	+	11.9061i	−0.106994	+	0.606793i
$386$		0			0
$387$	−19.9131	−	25.4202i	−1.01224	−	1.29218i
$388$		0			0
$389$	9.67172	+	26.5728i	0.490375	+	1.34730i	0.900337	+	0.435193i	$0.143320\pi$
$389$	9.67172	+	26.5728i	0.490375	+	1.34730i	−0.409962	+	0.912103i	$0.634458\pi$
$390$		0			0
$391$	−12.8396	−	15.3017i	−0.649328	−	0.773838i
$392$		0			0
$393$	4.52204	+	13.1056i	0.228107	+	0.661091i
$394$		0			0
$395$	−1.85918	−	3.22019i	−0.0935455	−	0.162026i
$396$		0			0
$397$	13.1024	−	22.6940i	0.657590	−	1.13898i	−0.323648	−	0.946178i	$-0.604909\pi$
$397$	13.1024	−	22.6940i	0.657590	−	1.13898i	0.981238	−	0.192802i	$-0.0617574\pi$
$398$		0			0
$399$	27.6398	+	16.5835i	1.38372	+	0.830215i
$400$		0			0
$401$	−6.23291	+	1.09903i	−0.311257	+	0.0548830i	−0.327095	−	0.944992i	$-0.606070\pi$
$401$	−6.23291	+	1.09903i	−0.311257	+	0.0548830i	0.0158378	+	0.999875i	$0.494958\pi$
$402$		0			0
$403$	25.0743	−	29.8823i	1.24904	−	1.48855i
$404$		0			0
$405$	−2.59784	−	8.97271i	−0.129088	−	0.445858i
$406$		0			0
$407$	−0.115448	−	0.0968721i	−0.00572253	−	0.00480177i
$408$		0			0
$409$	6.65238	+	37.7275i	0.328939	+	1.86550i	0.480411	+	0.877043i	$0.340487\pi$
$409$	6.65238	+	37.7275i	0.328939	+	1.86550i	−0.151472	+	0.988462i	$0.548401\pi$
$410$		0			0
$411$	−12.8732	+	21.4558i	−0.634989	+	1.05834i
$412$		0			0
$413$	39.0430	+	22.5415i	1.92118	+	1.10919i
$414$		0			0
$415$	−6.89343	+	3.97992i	−0.338385	+	0.195367i
$416$		0			0
$417$	−28.9278	+	9.98141i	−1.41660	+	0.488792i
$418$		0			0
$419$	15.8147	−	13.2701i	0.772601	−	0.648289i	−0.168773	−	0.985655i	$-0.553980\pi$
$419$	15.8147	−	13.2701i	0.772601	−	0.648289i	0.941374	+	0.337366i	$0.109536\pi$
$420$		0			0
$421$	22.1786	−	8.07235i	1.08092	−	0.393422i	0.260669	−	0.965428i	$-0.416057\pi$
$421$	22.1786	−	8.07235i	1.08092	−	0.393422i	0.820250	+	0.572006i	$0.193835\pi$
$422$		0			0
$423$	−2.91326	−	20.5375i	−0.141647	−	0.998567i
$424$		0			0
$425$	12.5808	+	2.21833i	0.610258	+	0.107605i
$426$		0			0
$427$	−9.79388	+	26.9085i	−0.473959	+	1.30219i
$428$		0			0
$429$	5.73455	−	14.9677i	0.276867	−	0.722649i
$430$		0			0
$431$	16.5976			0.799478			0.399739	−	0.916629i	$-0.369101\pi$
$431$	16.5976			0.799478			0.399739	+	0.916629i	$0.369101\pi$
$432$		0			0
$433$	−20.5776			−0.988898			−0.494449	−	0.869207i	$-0.664630\pi$
$433$	−20.5776			−0.988898			−0.494449	+	0.869207i	$0.664630\pi$
$434$		0			0
$435$	8.98442	+	11.0803i	0.430770	+	0.531259i
$436$		0			0
$437$	8.29225	−	22.7828i	0.396672	−	1.08985i
$438$		0			0
$439$	0.237133	+	0.0418129i	0.0113177	+	0.00199562i	0.179304	−	0.983794i	$-0.442615\pi$
$439$	0.237133	+	0.0418129i	0.0113177	+	0.00199562i	−0.167986	+	0.985789i	$0.553726\pi$
$440$		0			0
$441$	45.4704	+	1.52941i	2.16526	+	0.0728288i
$442$		0			0
$443$	22.4320	−	8.16459i	1.06578	−	0.387911i	0.251181	−	0.967940i	$-0.419181\pi$
$443$	22.4320	−	8.16459i	1.06578	−	0.387911i	0.814596	+	0.580029i	$0.196959\pi$
$444$		0			0
$445$	4.93515	−	4.14108i	0.233949	−	0.196306i
$446$		0			0
$447$	−24.4155	−	21.1966i	−1.15482	−	1.00257i
$448$		0			0
$449$	16.5811	−	9.57311i	0.782511	−	0.451783i	−0.0548085	−	0.998497i	$-0.517455\pi$
$449$	16.5811	−	9.57311i	0.782511	−	0.451783i	0.837319	+	0.546714i	$0.184122\pi$
$450$		0			0
$451$	14.2230	+	8.21166i	0.669735	+	0.386672i
$452$		0			0
$453$	14.7073	+	26.4926i	0.691011	+	1.24473i
$454$		0			0
$455$	3.17384	+	17.9997i	0.148792	+	0.843841i
$456$		0			0
$457$	−30.3262	−	25.4467i	−1.41860	−	1.19035i	−0.952085	−	0.305834i	$-0.901065\pi$
$457$	−30.3262	−	25.4467i	−1.41860	−	1.19035i	−0.466515	−	0.884513i	$-0.654491\pi$
$458$		0			0
$459$	9.18898	−	14.2096i	0.428905	−	0.663249i
$460$		0			0
$461$	−3.24779	+	3.87056i	−0.151264	+	0.180270i	−0.836355	−	0.548188i	$-0.815318\pi$
$461$	−3.24779	+	3.87056i	−0.151264	+	0.180270i	0.685091	+	0.728458i	$0.259762\pi$
$462$		0			0
$463$	31.2054	−	5.50235i	1.45024	−	0.255716i	0.607619	−	0.794229i	$-0.292125\pi$
$463$	31.2054	−	5.50235i	1.45024	−	0.255716i	0.842617	+	0.538513i	$0.181014\pi$
$464$		0			0
$465$	−0.315171	+	18.7458i	−0.0146157	+	0.869318i
$466$		0			0
$467$	−15.3648	+	26.6126i	−0.710998	+	1.23148i	0.253485	+	0.967339i	$0.418423\pi$
$467$	−15.3648	+	26.6126i	−0.710998	+	1.23148i	−0.964483	+	0.264145i	$0.914910\pi$
$468$		0			0
$469$	−2.54643	−	4.41054i	−0.117583	−	0.203660i
$470$		0			0
$471$	−3.84323	−	0.744489i	−0.177087	−	0.0343042i
$472$		0			0
$473$	17.1179	+	20.4003i	0.787082	+	0.938008i
$474$		0			0
$475$	5.30328	+	14.5706i	0.243331	+	0.668547i
$476$		0			0
$477$	5.64484	+	17.2974i	0.258460	+	0.791995i
$478$		0			0
$479$	4.96632	−	28.1654i	0.226917	−	1.28691i	−0.632070	−	0.774911i	$-0.717794\pi$
$479$	4.96632	−	28.1654i	0.226917	−	1.28691i	0.858987	−	0.511998i	$-0.171094\pi$
$480$		0			0
$481$	−0.214098	−	0.0779253i	−0.00976202	−	0.00355309i
$482$		0			0
$483$	−7.85606	−	49.3959i	−0.357463	−	2.24759i
$484$		0			0
$485$			1.26813i			0.0575828i
$486$		0			0
$487$		−	2.87205i		−	0.130145i	−0.997881	−	0.0650725i	$-0.979272\pi$
$487$		−	2.87205i		−	0.130145i	0.997881	−	0.0650725i	$-0.0207279\pi$
$488$		0			0
$489$	2.26316	+	14.2299i	0.102344	+	0.643498i
$490$		0			0
$491$	−16.1231	−	5.86832i	−0.727625	−	0.264834i	−0.0484657	−	0.998825i	$-0.515433\pi$
$491$	−16.1231	−	5.86832i	−0.727625	−	0.264834i	−0.679159	+	0.733991i	$0.737655\pi$
$492$		0			0
$493$	−4.48736	+	25.4491i	−0.202100	+	1.14617i
$494$		0			0
$495$	2.39000	+	7.32365i	0.107423	+	0.329174i
$496$		0			0
$497$	−10.4444	−	28.6956i	−0.468493	−	1.28718i
$498$		0			0
$499$	−24.1598	−	28.7926i	−1.08154	−	1.28893i	−0.954881	−	0.296987i	$-0.904018\pi$
$499$	−24.1598	−	28.7926i	−1.08154	−	1.28893i	−0.126662	−	0.991946i	$-0.540426\pi$
$500$		0			0
$501$	−42.0327	−	8.14234i	−1.87788	−	0.363773i
$502$		0			0
$503$	13.3677	+	23.1536i	0.596038	+	1.03237i	0.993399	+	0.114706i	$0.0365927\pi$
$503$	13.3677	+	23.1536i	0.596038	+	1.03237i	−0.397361	+	0.917662i	$0.630074\pi$
$504$		0			0
$505$	−0.636029	+	1.10163i	−0.0283029	+	0.0490221i
$506$		0			0
$507$	0.0288387	−	1.71528i	0.00128077	−	0.0761783i
$508$		0			0
$509$	−24.3407	+	4.29192i	−1.07888	+	0.190236i	−0.684720	−	0.728806i	$-0.740076\pi$
$509$	−24.3407	+	4.29192i	−1.07888	+	0.190236i	−0.394160	+	0.919042i	$0.628965\pi$
$510$		0			0
$511$	7.72052	−	9.20095i	0.341536	−	0.407026i
$512$		0			0
$513$	20.5132	+	1.03543i	0.905679	+	0.0457155i
$514$		0			0
$515$	0.0683647	+	0.0573648i	0.00301251	+	0.00252779i
$516$		0			0
$517$	2.97059	+	16.8471i	0.130647	+	0.740933i
$518$		0			0
$519$	−12.0338	−	21.6767i	−0.528225	−	0.951501i
$520$		0			0
$521$	2.69784	+	1.55760i	0.118194	+	0.0682395i	0.557932	−	0.829887i	$-0.311595\pi$
$521$	2.69784	+	1.55760i	0.118194	+	0.0682395i	−0.439737	+	0.898126i	$0.644928\pi$
$522$		0			0
$523$	9.27535	−	5.35512i	0.405583	−	0.234163i	−0.283307	−	0.959029i	$-0.591432\pi$
$523$	9.27535	−	5.35512i	0.405583	−	0.234163i	0.688890	+	0.724866i	$0.258098\pi$
$524$		0			0
$525$	24.1551	+	20.9705i	1.05422	+	0.915229i
$526$		0			0
$527$	−26.0176	+	21.8313i	−1.13334	+	0.950987i
$528$		0			0
$529$	−13.7396	+	5.00079i	−0.597372	+	0.217426i
$530$		0			0
$531$	28.7112	+	0.965705i	1.24596	+	0.0419080i
$532$		0			0
$533$	24.4516	+	4.31148i	1.05912	+	0.186751i
$534$		0			0
$535$	−1.94957	+	5.35640i	−0.0842873	+	0.231577i
$536$		0			0
$537$	−11.5187	−	14.2057i	−0.497067	−	0.613022i
$538$		0			0
$539$	−37.5210			−1.61614
$540$		0			0
$541$	−3.32479			−0.142944			−0.0714720	−	0.997443i	$-0.522770\pi$
$541$	−3.32479			−0.142944			−0.0714720	+	0.997443i	$0.522770\pi$
$542$		0			0
$543$	−4.11881	+	10.7505i	−0.176755	+	0.461348i
$544$		0			0
$545$	0.816929	−	2.24449i	0.0349934	−	0.0961435i
$546$		0			0
$547$	10.4493	+	1.84250i	0.446781	+	0.0787796i	0.392512	−	0.919747i	$-0.371606\pi$
$547$	10.4493	+	1.84250i	0.446781	+	0.0787796i	0.0542689	+	0.998526i	$0.482717\pi$
$548$		0			0
$549$	2.56266	+	18.0660i	0.109372	+	0.771036i
$550$		0			0
$551$	−29.4742	+	10.7277i	−1.25564	+	0.457017i
$552$		0			0
$553$	12.9206	−	10.8417i	0.549439	−	0.461034i
$554$		0			0
$555$	0.103516	−	0.0357177i	0.00439400	−	0.00151613i
$556$		0			0
$557$	34.3902	−	19.8552i	1.45716	−	0.841291i	0.458288	−	0.888804i	$-0.348463\pi$
$557$	34.3902	−	19.8552i	1.45716	−	0.841291i	0.998871	+	0.0475133i	$0.0151297\pi$
$558$		0			0
$559$	34.8665	+	20.1302i	1.47470	+	0.851417i
$560$		0			0
$561$	−7.17999	+	11.9669i	−0.303139	+	0.505243i
$562$		0			0
$563$	7.04951	+	39.9798i	0.297101	+	1.68495i	0.658536	+	0.752549i	$0.271176\pi$
$563$	7.04951	+	39.9798i	0.297101	+	1.68495i	−0.361435	+	0.932397i	$0.617713\pi$
$564$		0			0
$565$	5.93131	+	4.97696i	0.249532	+	0.209382i
$566$		0			0
$567$	38.0360	−	18.6725i	1.59736	−	0.784170i
$568$		0			0
$569$	−16.5625	+	19.7384i	−0.694337	+	0.827478i	−0.991873	−	0.127232i	$-0.959391\pi$
$569$	−16.5625	+	19.7384i	−0.694337	+	0.827478i	0.297536	+	0.954711i	$0.403835\pi$
$570$		0			0
$571$	15.6655	−	2.76225i	0.655581	−	0.115597i	0.164044	−	0.986453i	$-0.447546\pi$
$571$	15.6655	−	2.76225i	0.655581	−	0.115597i	0.491537	+	0.870857i	$0.336435\pi$
$572$		0			0
$573$	13.8406	+	8.30418i	0.578199	+	0.346912i
$574$		0			0
$575$	12.0303	−	20.8371i	0.501698	−	0.868966i
$576$		0			0
$577$	4.52882	+	7.84415i	0.188537	+	0.326556i	0.944763	−	0.327755i	$-0.106292\pi$
$577$	4.52882	+	7.84415i	0.188537	+	0.326556i	−0.756225	+	0.654311i	$0.772959\pi$
$578$		0			0
$579$	−10.3721	−	30.0600i	−0.431049	−	1.24925i
$580$		0			0
$581$	−23.2086	−	27.6589i	−0.962854	−	1.14749i
$582$		0			0
$583$	−5.13225	−	14.1007i	−0.212556	−	0.583993i
$584$		0			0
$585$	7.18213	+	9.16841i	0.296944	+	0.379067i
$586$		0			0
$587$	2.00218	−	11.3549i	0.0826387	−	0.468667i	−0.915203	−	0.402994i	$-0.867969\pi$
$587$	2.00218	−	11.3549i	0.0826387	−	0.468667i	0.997841	−	0.0656730i	$-0.0209194\pi$
$588$		0			0
$589$	−38.7377	−	14.0994i	−1.59616	−	0.580955i
$590$		0			0
$591$	−27.0893	−	10.3787i	−1.11430	−	0.426921i
$592$		0			0
$593$		−	3.14084i		−	0.128979i	−0.997918	−	0.0644895i	$-0.979458\pi$
$593$		−	3.14084i		−	0.128979i	0.997918	−	0.0644895i	$-0.0205419\pi$
$594$		0			0
$595$		−	15.9135i		−	0.652391i
$596$		0			0
$597$	−15.1906	+	12.3173i	−0.621709	+	0.504112i
$598$		0			0
$599$	6.29887	+	2.29260i	0.257365	+	0.0936732i	0.467481	−	0.884003i	$-0.345162\pi$
$599$	6.29887	+	2.29260i	0.257365	+	0.0936732i	−0.210116	+	0.977677i	$0.567384\pi$
$600$		0			0
$601$	7.89908	−	44.7979i	0.322210	−	1.82735i	−0.206384	−	0.978471i	$-0.566170\pi$
$601$	7.89908	−	44.7979i	0.322210	−	1.82735i	0.528594	−	0.848875i	$-0.322719\pi$
$602$		0			0
$603$	−2.75431	−	1.71617i	−0.112164	−	0.0698879i
$604$		0			0
$605$	1.73189	+	4.75832i	0.0704113	+	0.193453i
$606$		0			0
$607$	−1.93769	−	2.30924i	−0.0786482	−	0.0937293i	0.725285	−	0.688448i	$-0.241708\pi$
$607$	−1.93769	−	2.30924i	−0.0786482	−	0.0937293i	−0.803934	+	0.594719i	$0.797263\pi$
$608$		0			0
$609$	−42.4202	+	48.8622i	−1.71895	+	1.98000i
$610$		0			0
$611$	12.9312	+	22.3975i	0.523140	+	0.906104i
$612$		0			0
$613$	24.1313	−	41.7966i	0.974652	−	1.68815i	0.293574	−	0.955936i	$-0.405155\pi$
$613$	24.1313	−	41.7966i	0.974652	−	1.68815i	0.681079	−	0.732210i	$-0.261511\pi$
$614$		0			0
$615$	−10.4334	+	5.79209i	−0.420716	+	0.233560i
$616$		0			0
$617$	27.8944	−	4.91854i	1.12299	−	0.198013i	0.418836	−	0.908062i	$-0.362438\pi$
$617$	27.8944	−	4.91854i	1.12299	−	0.198013i	0.704152	+	0.710049i	$0.251327\pi$
$618$		0			0
$619$	16.8930	−	20.1323i	0.678988	−	0.809186i	−0.310989	−	0.950413i	$-0.600660\pi$
$619$	16.8930	−	20.1323i	0.678988	−	0.809186i	0.989977	+	0.141227i	$0.0451048\pi$
$620$		0			0
$621$	−19.2296	−	25.4165i	−0.771657	−	1.01993i
$622$		0			0
$623$	22.3860	+	18.7841i	0.896877	+	0.752569i
$624$		0			0
$625$	1.73675	+	9.84959i	0.0694700	+	0.393984i
$626$		0			0
$627$	−16.9365	−	0.284750i	−0.676379	−	0.0113718i
$628$		0			0
$629$	0.171794	+	0.0991855i	0.00684989	+	0.00395479i
$630$		0			0
$631$	−25.2286	+	14.5657i	−1.00434	+	0.579853i	−0.909528	−	0.415642i	$-0.863557\pi$
$631$	−25.2286	+	14.5657i	−1.00434	+	0.579853i	−0.0948072	+	0.995496i	$0.530223\pi$
$632$		0			0
$633$	6.20889	−	32.0518i	0.246781	−	1.27395i
$634$		0			0
$635$	4.76468	−	3.99804i	0.189081	−	0.158657i
$636$		0			0
$637$	−53.3034	+	19.4009i	−2.11196	+	0.768690i
$638$		0			0
$639$	−14.4773	−	13.0018i	−0.572714	−	0.514344i
$640$		0			0
$641$	10.0975	+	1.78047i	0.398828	+	0.0703242i	0.369465	−	0.929245i	$-0.379541\pi$
$641$	10.0975	+	1.78047i	0.398828	+	0.0703242i	0.0293632	+	0.999569i	$0.490652\pi$
$642$		0			0
$643$	−5.56679	+	15.2946i	−0.219533	+	0.603161i	−0.999750	−	0.0223470i	$-0.992886\pi$
$643$	−5.56679	+	15.2946i	−0.219533	+	0.603161i	0.780218	+	0.625508i	$0.215108\pi$
$644$		0			0
$645$	−19.1100	+	3.03930i	−0.752454	+	0.119672i
$646$		0			0
$647$	−14.7952			−0.581661			−0.290830	−	0.956775i	$-0.593932\pi$
$647$	−14.7952			−0.581661			−0.290830	+	0.956775i	$0.593932\pi$
$648$		0			0
$649$	−23.6917			−0.929980
$650$		0			0
$651$	−83.9883	+	13.3577i	−3.29176	+	0.523530i
$652$		0			0
$653$	−0.685785	+	1.88418i	−0.0268368	+	0.0737336i	−0.952388	−	0.304890i	$-0.901380\pi$
$653$	−0.685785	+	1.88418i	−0.0268368	+	0.0737336i	0.925551	+	0.378624i	$0.123603\pi$
$654$		0			0
$655$	8.18155	+	1.44263i	0.319680	+	0.0563681i
$656$		0			0
$657$	1.58165	−	7.48833i	0.0617059	−	0.292148i
$658$		0			0
$659$	−0.340176	+	0.123814i	−0.0132514	+	0.00482310i	−0.348637	−	0.937258i	$-0.613356\pi$
$659$	−0.340176	+	0.123814i	−0.0132514	+	0.00482310i	0.335386	+	0.942081i	$0.391133\pi$
$660$		0			0
$661$	2.76874	−	2.32325i	0.107692	−	0.0903640i	−0.587352	−	0.809332i	$-0.699830\pi$
$661$	2.76874	−	2.32325i	0.107692	−	0.0903640i	0.695044	+	0.718968i	$0.255385\pi$
$662$		0			0
$663$	−4.01242	+	20.7131i	−0.155829	+	0.804430i
$664$		0			0
$665$	16.7276	−	9.65767i	0.648668	−	0.374508i
$666$		0			0
$667$	42.1503	+	24.3355i	1.63206	+	0.942273i
$668$		0			0
$669$	16.6154	+	0.279351i	0.642387	+	0.0108003i
$670$		0			0
$671$	−2.61310	−	14.8196i	−0.100878	−	0.572106i
$672$		0			0
$673$	3.29929	+	2.76843i	0.127178	+	0.106715i	0.704158	−	0.710043i	$-0.251325\pi$
$673$	3.29929	+	2.76843i	0.127178	+	0.106715i	−0.576980	+	0.816758i	$0.695769\pi$
$674$		0			0
$675$	19.8695	+	4.54694i	0.764778	+	0.175012i
$676$		0			0
$677$	16.4123	−	19.5594i	0.630774	−	0.751728i	−0.352108	−	0.935959i	$-0.614535\pi$
$677$	16.4123	−	19.5594i	0.630774	−	0.751728i	0.982883	+	0.184232i	$0.0589796\pi$
$678$		0			0
$679$	−5.66489	+	0.998874i	−0.217399	+	0.0383333i
$680$		0			0
$681$	36.5510	−	20.2912i	1.40064	−	0.777562i
$682$		0			0
$683$	−9.05123	+	15.6772i	−0.346336	+	0.599871i	−0.985596	−	0.169120i	$-0.945908\pi$
$683$	−9.05123	+	15.6772i	−0.346336	+	0.599871i	0.639260	+	0.768991i	$0.279241\pi$
$684$		0			0
$685$	7.49692	+	12.9850i	0.286443	+	0.496133i
$686$		0			0
$687$	11.5175	−	13.2665i	0.439419	−	0.506150i
$688$		0			0
$689$	−14.5821	−	17.3782i	−0.555532	−	0.662058i
$690$		0			0
$691$	−3.68849	−	10.1340i	−0.140317	−	0.385517i	0.849552	−	0.527506i	$-0.176873\pi$
$691$	−3.68849	−	10.1340i	−0.140317	−	0.385517i	−0.989868	+	0.141989i	$0.954650\pi$
$692$		0			0
$693$	−30.8331	+	16.4451i	−1.17125	+	0.624697i
$694$		0			0
$695$	−3.18428	+	18.0590i	−0.120787	+	0.685016i
$696$		0			0
$697$	−20.3139	−	7.39366i	−0.769444	−	0.280055i
$698$		0			0
$699$	−31.6370	+	25.6528i	−1.19662	+	0.970277i
$700$		0			0
$701$		−	12.4174i		−	0.469000i	−0.972116	−	0.234500i	$-0.924655\pi$
$701$		−	12.4174i		−	0.469000i	0.972116	−	0.234500i	$-0.0753453\pi$
$702$		0			0
$703$			0.240777i			0.00908106i
$704$		0			0
$705$	−11.6073	−	4.44709i	−0.437158	−	0.167487i
$706$		0			0
$707$	−5.42212	−	1.97349i	−0.203920	−	0.0742208i
$708$		0			0
$709$	−1.72675	+	9.79290i	−0.0648496	+	0.367780i	0.935062	+	0.354484i	$0.115343\pi$
$709$	−1.72675	+	9.79290i	−0.0648496	+	0.367780i	−0.999912	+	0.0132960i	$0.995768\pi$
$710$		0			0
$711$	4.01332	−	9.97017i	0.150511	−	0.373910i
$712$		0			0
$713$	21.8783	+	60.1101i	0.819349	+	2.25114i
$714$		0			0
$715$	−6.17398	−	7.35786i	−0.230894	−	0.275168i
$716$		0			0
$717$	5.48500	+	15.8964i	0.204841	+	0.593663i
$718$		0			0
$719$	−4.47701	−	7.75440i	−0.166964	−	0.289190i	0.770387	−	0.637577i	$-0.220063\pi$
$719$	−4.47701	−	7.75440i	−0.166964	−	0.289190i	−0.937351	+	0.348386i	$0.886730\pi$
$720$		0			0
$721$	−0.202406	+	0.350578i	−0.00753801	+	0.0130562i
$722$		0			0
$723$	23.2769	+	13.9658i	0.865676	+	0.519395i
$724$		0			0
$725$	−30.6544	+	5.40520i	−1.13848	+	0.200744i
$726$		0			0
$727$	11.5744	−	13.7938i	0.429270	−	0.511584i	−0.507442	−	0.861686i	$-0.669409\pi$
$727$	11.5744	−	13.7938i	0.429270	−	0.511584i	0.936711	+	0.350102i	$0.113853\pi$
$728$		0			0
$729$	15.7859	−	21.9044i	0.584664	−	0.811275i
$730$		0			0
$731$	−26.8525	−	22.5319i	−0.993174	−	0.833372i
$732$		0			0
$733$	−1.01377	−	5.74939i	−0.0374445	−	0.212359i	0.960345	−	0.278815i	$-0.0899417\pi$
$733$	−1.01377	−	5.74939i	−0.0374445	−	0.212359i	−0.997789	+	0.0664567i	$0.978831\pi$
$734$		0			0
$735$	14.0265	−	23.3780i	0.517376	−	0.862312i
$736$		0			0
$737$	2.31779	+	1.33818i	0.0853770	+	0.0492924i
$738$		0			0
$739$	−39.6890	+	22.9145i	−1.45998	+	0.842922i	−0.999010	−	0.0444922i	$-0.985833\pi$
$739$	−39.6890	+	22.9145i	−1.45998	+	0.842922i	−0.460974	+	0.887414i	$0.652500\pi$
$740$		0			0
$741$	−24.2077	+	8.35278i	−0.889294	+	0.306847i
$742$		0			0
$743$	23.1581	−	19.4320i	0.849588	−	0.712889i	−0.110111	−	0.993919i	$-0.535121\pi$
$743$	23.1581	−	19.4320i	0.849588	−	0.712889i	0.959699	+	0.281030i	$0.0906761\pi$
$744$		0			0
$745$	−18.2067	+	6.62669i	−0.667041	+	0.242783i
$746$		0			0
$747$	−21.3430	−	8.59127i	−0.780900	−	0.314338i
$748$		0			0
$749$	−25.4633	−	4.48988i	−0.930410	−	0.164056i
$750$		0			0
$751$	1.50126	−	4.12468i	0.0547818	−	0.150512i	−0.909283	−	0.416178i	$-0.863369\pi$
$751$	1.50126	−	4.12468i	0.0547818	−	0.150512i	0.964065	+	0.265666i	$0.0855917\pi$
$752$		0			0
$753$	2.04713	−	5.34320i	0.0746014	−	0.194717i
$754$		0			0
$755$	18.1577			0.660826
$756$		0			0
$757$	13.3993			0.487005			0.243503	−	0.969900i	$-0.421704\pi$
$757$	13.3993			0.487005			0.243503	+	0.969900i	$0.421704\pi$
$758$		0			0
$759$	16.5544	+	20.4162i	0.600888	+	0.741061i
$760$		0			0
$761$	−13.0545	+	35.8670i	−0.473226	+	1.30018i	0.441920	+	0.897054i	$0.354297\pi$
$761$	−13.0545	+	35.8670i	−0.473226	+	1.30018i	−0.915146	+	0.403122i	$0.867925\pi$
$762$		0			0
$763$	10.6699	+	1.88139i	0.386276	+	0.0681110i
$764$		0			0
$765$	−4.77207	−	8.94722i	−0.172534	−	0.323487i
$766$		0			0
$767$	−33.6571	+	12.2502i	−1.21529	+	0.442329i
$768$		0			0
$769$	13.8319	−	11.6063i	0.498791	−	0.418535i	−0.358373	−	0.933578i	$-0.616668\pi$
$769$	13.8319	−	11.6063i	0.498791	−	0.418535i	0.857164	+	0.515043i	$0.172224\pi$
$770$		0			0
$771$	3.06445	+	2.66043i	0.110363	+	0.0958131i
$772$		0			0
$773$	−20.4862	+	11.8277i	−0.736836	+	0.425413i	−0.820918	−	0.571046i	$-0.806538\pi$
$773$	−20.4862	+	11.8277i	−0.736836	+	0.425413i	0.0840816	+	0.996459i	$0.473204\pi$
$774$		0			0
$775$	−35.4295	−	20.4552i	−1.27266	−	0.734773i
$776$		0			0
$777$	0.241092	+	0.434284i	0.00864913	+	0.0155798i
$778$		0			0
$779$	−4.55632	−	25.8402i	−0.163247	−	0.925820i
$780$		0			0
$781$	12.2933	+	10.3153i	0.439887	+	0.369109i
$782$		0			0
$783$	−9.19778	+	40.1930i	−0.328702	+	1.43638i
$784$		0			0
$785$	−1.50787	+	1.79701i	−0.0538182	+	0.0641381i
$786$		0			0
$787$	17.4793	−	3.08207i	0.623069	−	0.109864i	0.146804	−	0.989166i	$-0.453101\pi$
$787$	17.4793	−	3.08207i	0.623069	−	0.109864i	0.476265	+	0.879302i	$0.341990\pi$
$788$		0			0
$789$	0.199517	−	11.8670i	0.00710300	−	0.422475i
$790$		0			0
$791$	−17.5607	+	30.4161i	−0.624388	+	1.08147i
$792$		0			0
$793$	−11.3750	−	19.7021i	−0.403938	−	0.699641i
$794$		0			0
$795$	10.7043	+	2.07357i	0.379642	+	0.0735420i
$796$		0			0
$797$	9.94374	+	11.8505i	0.352225	+	0.419766i	0.912844	−	0.408308i	$-0.133881\pi$
$797$	9.94374	+	11.8505i	0.352225	+	0.419766i	−0.560619	+	0.828074i	$0.689437\pi$
$798$		0			0
$799$	−7.70143	−	21.1595i	−0.272457	−	0.748570i
$800$		0			0
$801$	18.2192	+	3.84816i	0.643743	+	0.135968i
$802$		0			0
$803$	−1.09605	+	6.21603i	−0.0386789	+	0.219359i
$804$		0			0
$805$	−28.1645	−	10.2510i	−0.992667	−	0.361301i
$806$		0			0
$807$	8.63574	+	54.2983i	0.303993	+	1.91139i
$808$		0			0
$809$			20.4367i			0.718516i	0.933238	+	0.359258i	$0.116970\pi$
$809$			20.4367i			0.718516i	−0.933238	+	0.359258i	$0.883030\pi$
$810$		0			0
$811$		−	29.0699i		−	1.02078i	−0.859943	−	0.510391i	$-0.829501\pi$
$811$		−	29.0699i		−	1.02078i	0.859943	−	0.510391i	$-0.170499\pi$
$812$		0			0
$813$	1.16506	+	7.32548i	0.0408606	+	0.256916i
$814$		0			0
$815$	8.11357	+	2.95310i	0.284206	+	0.103443i
$816$		0			0
$817$	7.38816	−	41.9003i	0.258479	−	1.46591i
$818$		0			0
$819$	−35.2993	+	39.3052i	−1.23346	+	1.37343i
$820$		0			0
$821$	−11.9380	−	32.7995i	−0.416640	−	1.14471i	−0.953593	−	0.301097i	$-0.902647\pi$
$821$	−11.9380	−	32.7995i	−0.416640	−	1.14471i	0.536953	−	0.843612i	$-0.319575\pi$
$822$		0			0
$823$	−11.6062	−	13.8317i	−0.404567	−	0.482144i	0.524840	−	0.851201i	$-0.324125\pi$
$823$	−11.6062	−	13.8317i	−0.404567	−	0.482144i	−0.929407	+	0.369057i	$0.879681\pi$
$824$		0			0
$825$	−16.5033	−	3.19692i	−0.574572	−	0.111303i
$826$		0			0
$827$	5.11628	+	8.86165i	0.177910	+	0.308150i	0.941165	−	0.337948i	$-0.109733\pi$
$827$	5.11628	+	8.86165i	0.177910	+	0.308150i	−0.763254	+	0.646098i	$0.776400\pi$
$828$		0			0
$829$	16.8214	−	29.1355i	0.584231	−	1.01192i	−0.410740	−	0.911752i	$-0.634730\pi$
$829$	16.8214	−	29.1355i	0.584231	−	1.01192i	0.994971	−	0.100165i	$-0.0319370\pi$
$830$		0			0
$831$	−0.462064	+	27.4828i	−0.0160288	+	0.953368i
$832$		0			0
$833$	48.6377	−	8.57613i	1.68519	−	0.297145i
$834$		0			0
$835$	−16.4913	+	19.6536i	−0.570705	+	0.680140i
$836$		0			0
$837$	−43.2159	+	32.6962i	−1.49376	+	1.13015i
$838$		0			0
$839$	42.8076	+	35.9198i	1.47788	+	1.24009i	0.908411	+	0.418078i	$0.137296\pi$
$839$	42.8076	+	35.9198i	1.47788	+	1.24009i	0.569470	+	0.822012i	$0.307148\pi$
$840$		0			0
$841$	−5.89811	−	33.4498i	−0.203383	−	1.15344i
$842$		0			0
$843$	24.4598	+	44.0599i	0.842440	+	1.51750i
$844$		0			0
$845$	−0.890282	−	0.514004i	−0.0306266	−	0.0176823i
$846$		0			0
$847$	−19.8919	+	11.4846i	−0.683492	+	0.394614i
$848$		0			0
$849$	−23.9794	−	20.8179i	−0.822970	−	0.714470i
$850$		0			0
$851$	0.286208	−	0.240157i	0.00981108	−	0.00823247i
$852$		0			0
$853$	2.16235	−	0.787030i	0.0740373	−	0.0269474i	−0.304736	−	0.952437i	$-0.598568\pi$
$853$	2.16235	−	0.787030i	0.0740373	−	0.0269474i	0.378773	+	0.925489i	$0.376346\pi$
$854$		0			0
$855$	6.50882	−	10.4461i	0.222597	−	0.357249i
$856$		0			0
$857$	−52.9090	−	9.32928i	−1.80734	−	0.318682i	−0.834646	−	0.550787i	$-0.814328\pi$
$857$	−52.9090	−	9.32928i	−1.80734	−	0.318682i	−0.972691	+	0.232105i	$0.925439\pi$
$858$		0			0
$859$	−8.64745	+	23.7587i	−0.295047	+	0.810636i	0.700262	+	0.713886i	$0.253067\pi$
$859$	−8.64745	+	23.7587i	−0.295047	+	0.810636i	−0.995309	+	0.0967492i	$0.969156\pi$
$860$		0			0
$861$	−34.0921	−	42.0451i	−1.16186	−	1.43289i
$862$		0			0
$863$	−9.84682			−0.335190			−0.167595	−	0.985856i	$-0.553600\pi$
$863$	−9.84682			−0.335190			−0.167595	+	0.985856i	$0.553600\pi$
$864$		0			0
$865$	−14.8569			−0.505150
$866$		0			0
$867$	−3.96244	+	10.3423i	−0.134571	+	0.351244i
$868$		0			0
$869$	−3.03154	+	8.32908i	−0.102838	+	0.282545i
$870$		0			0
$871$	3.98466	+	0.702602i	0.135015	+	0.0238068i
$872$		0			0
$873$	−2.88549	+	2.26037i	−0.0976591	+	0.0765018i
$874$		0			0
$875$	40.9716	−	14.9124i	1.38509	−	0.504132i
$876$		0			0
$877$	22.3672	−	18.7683i	0.755286	−	0.633760i	−0.181609	−	0.983371i	$-0.558131\pi$
$877$	22.3672	−	18.7683i	0.755286	−	0.633760i	0.936895	+	0.349611i	$0.113686\pi$
$878$		0			0
$879$	−3.41556	+	1.17852i	−0.115204	+	0.0397506i
$880$		0			0
$881$	23.3146	−	13.4607i	0.785487	−	0.453501i	−0.0528841	−	0.998601i	$-0.516841\pi$
$881$	23.3146	−	13.4607i	0.785487	−	0.453501i	0.838371	+	0.545099i	$0.183508\pi$
$882$		0			0
$883$	26.4888	+	15.2933i	0.891418	+	0.514660i	0.874406	−	0.485195i	$-0.161251\pi$
$883$	26.4888	+	15.2933i	0.891418	+	0.514660i	0.0170120	+	0.999855i	$0.494585\pi$
$884$		0			0
$885$	8.85670	−	14.7615i	0.297715	−	0.496202i
$886$		0			0
$887$	7.45008	+	42.2515i	0.250149	+	1.41867i	0.808224	+	0.588875i	$0.200429\pi$
$887$	7.45008	+	42.2515i	0.250149	+	1.41867i	−0.558075	+	0.829791i	$0.688460\pi$
$888$		0			0
$889$	21.6128	+	18.1353i	0.724869	+	0.608237i
$890$		0			0
$891$	−12.4041	+	18.4922i	−0.415554	+	0.619511i
$892$		0			0
$893$	17.5680	−	20.9368i	0.587892	−	0.700623i
$894$		0			0
$895$	−10.7929	+	1.90308i	−0.360767	+	0.0636130i
$896$		0			0
$897$	34.0743	+	20.4441i	1.13771	+	0.682610i
$898$		0			0
$899$	41.3778	−	71.6685i	1.38003	−	2.39028i
$900$		0			0
$901$	9.87582	+	17.1054i	0.329011	+	0.569864i
$902$		0			0
$903$	−28.6294	−	82.9726i	−0.952725	−	2.76115i
$904$		0			0
$905$	4.43443	+	5.28474i	0.147405	+	0.175671i
$906$		0			0
$907$	4.73257	+	13.0026i	0.157142	+	0.431745i	0.993132	−	0.117000i	$-0.0373278\pi$
$907$	4.73257	+	13.0026i	0.157142	+	0.431745i	−0.835989	+	0.548746i	$0.815106\pi$
$908$		0			0
$909$	−3.64033	+	0.516383i	−0.120742	+	0.0171274i
$910$		0			0
$911$	−3.91731	+	22.2162i	−0.129786	+	0.736055i	0.848563	+	0.529094i	$0.177468\pi$
$911$	−3.91731	+	22.2162i	−0.129786	+	0.736055i	−0.978349	+	0.206960i	$0.933643\pi$
$912$		0			0
$913$	17.8299	+	6.48957i	0.590085	+	0.214773i
$914$		0			0
$915$	10.2105	+	3.91191i	0.337548	+	0.129324i
$916$		0			0
$917$			37.6843i			1.24445i
$918$		0			0
$919$		−	51.1914i		−	1.68865i	−0.535833	−	0.844324i	$-0.680003\pi$
$919$		−	51.1914i		−	1.68865i	0.535833	−	0.844324i	$-0.319997\pi$
$920$		0			0
$921$	−5.78605	+	4.69160i	−0.190657	+	0.154594i
$922$		0			0
$923$	22.7979	+	8.29774i	0.750401	+	0.273124i
$924$		0			0
$925$	−0.0414925	+	0.235316i	−0.00136427	+	0.00773714i
$926$		0			0
$927$	−0.00867133	+	0.257806i	−0.000284804	+	0.00846745i
$928$		0			0
$929$	−12.8844	−	35.3996i	−0.422723	−	1.16142i	−0.950142	−	0.311817i	$-0.899063\pi$
$929$	−12.8844	−	35.3996i	−0.422723	−	1.16142i	0.527419	−	0.849605i	$-0.323160\pi$
$930$		0			0
$931$	38.5323	+	45.9210i	1.26284	+	1.50500i
$932$		0			0
$933$	−1.34578	+	1.55015i	−0.0440588	+	0.0507496i
$934$		0			0
$935$	4.18138	+	7.24236i	0.136746	+	0.236850i
$936$		0			0
$937$	1.91697	−	3.32029i	0.0626247	−	0.108469i	−0.833013	−	0.553253i	$-0.813386\pi$
$937$	1.91697	−	3.32029i	0.0626247	−	0.108469i	0.895638	+	0.444784i	$0.146720\pi$
$938$		0			0
$939$	46.3995	−	25.7586i	1.51419	−	0.840601i
$940$		0			0
$941$	1.49218	−	0.263112i	0.0486438	−	0.00857721i	−0.149273	−	0.988796i	$-0.547693\pi$
$941$	1.49218	−	0.263112i	0.0486438	−	0.00857721i	0.197917	+	0.980219i	$0.436582\pi$
$942$		0			0
$943$	−26.1713	+	31.1897i	−0.852253	+	1.01568i
$944$		0			0
$945$	1.28002	−	25.3588i	0.0416391	−	0.824921i
$946$		0			0
$947$	−23.4786	−	19.7009i	−0.762952	−	0.640193i	0.175941	−	0.984401i	$-0.443703\pi$
$947$	−23.4786	−	19.7009i	−0.762952	−	0.640193i	−0.938893	+	0.344208i	$0.888148\pi$
$948$		0			0
$949$	1.65702	+	9.39742i	0.0537891	+	0.305053i
$950$		0			0
$951$	26.9252	+	0.452689i	0.873110	+	0.0146794i
$952$		0			0
$953$	−16.5100	−	9.53205i	−0.534811	−	0.308773i	0.208162	−	0.978094i	$-0.433252\pi$
$953$	−16.5100	−	9.53205i	−0.534811	−	0.308773i	−0.742973	+	0.669321i	$0.766585\pi$
$954$		0			0
$955$	8.37631	−	4.83607i	0.271051	−	0.156491i
$956$		0			0
$957$	6.46689	−	33.3837i	0.209045	−	1.07914i
$958$		0			0
$959$	−52.1007	+	43.7177i	−1.68242	+	1.41172i
$960$		0			0
$961$	73.0753	−	26.5972i	2.35727	−	0.857975i
$962$		0			0
$963$	−15.6629	+	5.11143i	−0.504730	+	0.164714i
$964$		0			0
$965$	−18.7658	−	3.30891i	−0.604092	−	0.106518i
$966$		0			0
$967$	−11.0559	+	30.3760i	−0.355535	+	0.976825i	0.625025	+	0.780605i	$0.285089\pi$
$967$	−11.0559	+	30.3760i	−0.355535	+	0.976825i	−0.980560	+	0.196220i	$0.937133\pi$
$968$		0			0
$969$	22.0195	−	3.50204i	0.707369	−	0.112502i
$970$		0			0
$971$	21.3765			0.686005			0.343003	−	0.939334i	$-0.388556\pi$
$971$	21.3765			0.686005			0.343003	+	0.939334i	$0.388556\pi$
$972$		0			0
$973$	−83.1799			−2.66662
$974$		0			0
$975$	−25.0981	+	3.99167i	−0.803783	+	0.127836i
$976$		0			0
$977$	15.0358	−	41.3104i	0.481037	−	1.32164i	−0.427569	−	0.903983i	$-0.640630\pi$
$977$	15.0358	−	41.3104i	0.481037	−	1.32164i	0.908606	−	0.417655i	$-0.137148\pi$
$978$		0			0
$979$	−15.1237	−	2.66671i	−0.483355	−	0.0852285i
$980$		0			0
$981$	6.56323	−	2.14184i	0.209548	−	0.0683838i
$982$		0			0
$983$	−1.12861	+	0.410780i	−0.0359970	+	0.0131018i	−0.359956	−	0.932969i	$-0.617208\pi$
$983$	−1.12861	+	0.410780i	−0.0359970	+	0.0131018i	0.323959	+	0.946071i	$0.394986\pi$
$984$		0			0
$985$	−13.3166	+	11.1740i	−0.424302	+	0.356032i
$986$		0			0
$987$	10.7229	−	55.3543i	0.341314	−	1.76195i
$988$		0			0
$989$	−57.1755	+	33.0103i	−1.81808	+	1.04967i
$990$		0			0
$991$	−4.22942	−	2.44186i	−0.134352	−	0.0775682i	0.431318	−	0.902200i	$-0.358049\pi$
$991$	−4.22942	−	2.44186i	−0.134352	−	0.0775682i	−0.565670	+	0.824632i	$0.691382\pi$
$992$		0			0
$993$	19.1965	+	0.322748i	0.609183	+	0.0102421i
$994$		0			0
$995$	2.03502	+	11.5412i	0.0645144	+	0.365880i
$996$		0			0
$997$	−9.25562	−	7.76639i	−0.293128	−	0.245964i	0.484349	−	0.874875i	$-0.339057\pi$
$997$	−9.25562	−	7.76639i	−0.293128	−	0.245964i	−0.777477	+	0.628911i	$0.783501\pi$
$998$		0			0
$999$	0.265782	+	0.171874i	0.00840898	+	0.00543785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.767.35	yes	216
4.3	odd	2	inner	864.2.bi.a.767.2	yes	216
27.5	odd	18	inner	864.2.bi.a.383.2	✓	216
108.59	even	18	inner	864.2.bi.a.383.35	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.383.2	✓	216	27.5	odd	18	inner
864.2.bi.a.383.35	yes	216	108.59	even	18	inner
864.2.bi.a.767.2	yes	216	4.3	odd	2	inner
864.2.bi.a.767.35	yes	216	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.71055 - 0.272051i) q^{3} +(0.354987 - 0.975319i) q^{5} +(4.63649 + 0.817538i) q^{7} +(2.85198 - 0.930714i) q^{9} +(-2.32491 + 0.846199i) q^{11} +(-2.86530 + 2.40427i) q^{13} +(0.341888 - 1.76491i) q^{15} +(2.82032 - 1.62831i) q^{17} +(3.42322 + 1.97639i) q^{19} +(8.15337 + 0.137081i) q^{21} +(-1.06509 - 6.04044i) q^{23} +(3.00499 + 2.52149i) q^{25} +(4.62525 - 2.36792i) q^{27} +(-5.10059 + 6.07864i) q^{29} +(-10.2706 + 1.81099i) q^{31} +(-3.74667 + 2.07996i) q^{33} +(2.44325 - 4.23184i) q^{35} +(0.0304565 + 0.0527523i) q^{37} +(-4.24716 + 4.89214i) q^{39} +(-4.26685 - 5.08504i) q^{41} +(-3.68141 - 10.1146i) q^{43} +(0.104672 - 3.11198i) q^{45} +(1.20067 - 6.80932i) q^{47} +(14.2508 + 5.18687i) q^{49} +(4.38132 - 3.55258i) q^{51} +6.06507i q^{53} +2.56792i q^{55} +(6.39327 + 2.44944i) q^{57} +(8.99831 + 3.27512i) q^{59} +(-1.05617 + 5.98986i) q^{61} +(13.9840 - 1.98364i) q^{63} +(1.32779 + 3.64807i) q^{65} +(-0.695330 - 0.828662i) q^{67} +(-3.46520 - 10.0427i) q^{69} +(-3.24312 - 5.61724i) q^{71} +(1.27559 - 2.20939i) q^{73} +(5.82616 + 3.49562i) q^{75} +(-11.4712 + 2.02269i) q^{77} +(2.30281 - 2.74438i) q^{79} +(7.26754 - 5.30875i) q^{81} +(-5.87486 - 4.92959i) q^{83} +(-0.586947 - 3.32874i) q^{85} +(-7.07112 + 11.7855i) q^{87} +(5.37546 + 3.10353i) q^{89} +(-15.2505 + 8.80488i) q^{91} +(-17.0757 + 5.89191i) q^{93} +(3.14281 - 2.63713i) q^{95} +(-1.14812 + 0.417883i) q^{97} +(-5.84303 + 4.57717i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) \) 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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