LMFDB - Embedded newform 1386.2.bk.d.703.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(703,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("1386.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bk (of order $6$, degree $2$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			703.2
Character	$\chi$	$=$	1386.703
Dual form			1386.2.bk.d.901.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.194145 - 0.112089i) q^{5} +(-2.62785 - 0.307218i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.194145 - 0.112089i) q^{5} +(-2.62785 - 0.307218i) q^{7} +1.00000i q^{8} +(-0.112089 + 0.194145i) q^{10} +(-1.73915 - 2.82407i) q^{11} -5.03153 q^{13} +(2.42940 - 1.04787i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.92826 - 6.80394i) q^{17} +(3.66573 + 6.34924i) q^{19} -0.224179i q^{20} +(2.91818 + 1.57614i) q^{22} +(2.42940 + 4.20784i) q^{23} +(-2.47487 + 4.28660i) q^{25} +(4.35743 - 2.51576i) q^{26} +(-1.57999 + 2.12218i) q^{28} +5.65814i q^{29} +(3.73996 + 2.15927i) q^{31} +(0.866025 + 0.500000i) q^{32} +7.85652i q^{34} +(-0.544620 + 0.234910i) q^{35} +(-0.0891097 - 0.154343i) q^{37} +(-6.34924 - 3.66573i) q^{38} +(0.112089 + 0.194145i) q^{40} -0.568932 q^{41} +6.39391i q^{43} +(-3.31529 + 0.0941129i) q^{44} +(-4.20784 - 2.42940i) q^{46} +(-2.93076 + 1.69208i) q^{47} +(6.81123 + 1.61465i) q^{49} -4.94974i q^{50} +(-2.51576 + 4.35743i) q^{52} +(1.07478 - 1.86157i) q^{53} +(-0.654195 - 0.353338i) q^{55} +(0.307218 - 2.62785i) q^{56} +(-2.82907 - 4.90010i) q^{58} +(2.00911 + 1.15996i) q^{59} +(2.19784 + 3.80677i) q^{61} -4.31854 q^{62} -1.00000 q^{64} +(-0.976845 + 0.563982i) q^{65} +(4.32907 - 7.49817i) q^{67} +(-3.92826 - 6.80394i) q^{68} +(0.354200 - 0.475748i) q^{70} +11.6958 q^{71} +(-5.25571 + 9.10315i) q^{73} +(0.154343 + 0.0891097i) q^{74} +7.33147 q^{76} +(3.70262 + 7.95554i) q^{77} +(-8.75195 + 5.05294i) q^{79} +(-0.194145 - 0.112089i) q^{80} +(0.492709 - 0.284466i) q^{82} +14.2897 q^{83} -1.76127i q^{85} +(-3.19696 - 5.53729i) q^{86} +(2.82407 - 1.73915i) q^{88} +(-9.10315 + 5.25571i) q^{89} +(13.2221 + 1.54578i) q^{91} +4.85879 q^{92} +(1.69208 - 2.93076i) q^{94} +(1.42337 + 0.821781i) q^{95} +3.96123i q^{97} +(-6.70603 + 2.00729i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4}+O(q^{10}) $ 32 * q + 16 * q^4	$ 32 q + 16 q^{4} - 16 q^{16} + 20 q^{22} + 36 q^{25} + 12 q^{31} - 20 q^{37} - 44 q^{49} - 32 q^{64} + 48 q^{67} + 36 q^{70} + 72 q^{82} + 10 q^{88} + 144 q^{91}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 + 36 * q^25 + 12 * q^31 - 20 * q^37 - 44 * q^49 - 32 * q^64 + 48 * q^67 + 36 * q^70 + 72 * q^82 + 10 * q^88 + 144 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.194145	−	0.112089i	0.0868242	−	0.0501279i	−0.455959	−	0.890001i	$-0.650704\pi$
$5$	0.194145	−	0.112089i	0.0868242	−	0.0501279i	0.542783	+	0.839873i	$0.317370\pi$
$6$		0			0
$7$	−2.62785	−	0.307218i	−0.993235	−	0.116117i
$7$	−2.62785	−	0.307218i	−0.993235	−	0.116117i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.112089	+	0.194145i	−0.0354458	+	0.0613939i
$11$	−1.73915	−	2.82407i	−0.524373	−	0.851489i
$11$	−1.73915	−	2.82407i	−0.524373	−	0.851489i
$12$		0			0
$13$	−5.03153			−1.39550			−0.697748	−	0.716344i	$-0.745814\pi$
$13$	−5.03153			−1.39550			−0.697748	+	0.716344i	$0.745814\pi$
$14$	2.42940	−	1.04787i	0.649284	−	0.280055i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.92826	−	6.80394i	0.952743	−	1.65020i	0.213291	−	0.976989i	$-0.431582\pi$
$17$	3.92826	−	6.80394i	0.952743	−	1.65020i	0.739451	−	0.673210i	$-0.235085\pi$
$18$		0			0
$19$	3.66573	+	6.34924i	0.840977	+	1.45662i	0.889070	+	0.457772i	$0.151352\pi$
$19$	3.66573	+	6.34924i	0.840977	+	1.45662i	−0.0480924	+	0.998843i	$0.515314\pi$
$20$		−	0.224179i		−	0.0501279i
$21$		0			0
$22$	2.91818	+	1.57614i	0.622158	+	0.336034i
$23$	2.42940	+	4.20784i	0.506564	+	0.877395i	0.999971	+	0.00759654i	$0.00241808\pi$
$23$	2.42940	+	4.20784i	0.506564	+	0.877395i	−0.493407	+	0.869799i	$0.664249\pi$
$24$		0			0
$25$	−2.47487	+	4.28660i	−0.494974	+	0.857321i
$26$	4.35743	−	2.51576i	0.854563	−	0.493382i
$27$		0			0
$28$	−1.57999	+	2.12218i	−0.298589	+	0.401054i
$29$			5.65814i			1.05069i	0.850889	+	0.525345i	$0.176064\pi$
$29$			5.65814i			1.05069i	−0.850889	+	0.525345i	$0.823936\pi$
$30$		0			0
$31$	3.73996	+	2.15927i	0.671717	+	0.387816i	0.796727	−	0.604340i	$-0.206563\pi$
$31$	3.73996	+	2.15927i	0.671717	+	0.387816i	−0.125010	+	0.992155i	$0.539896\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			7.85652i			1.34738i
$35$	−0.544620	+	0.234910i	−0.0920576	+	0.0397071i
$36$		0			0
$37$	−0.0891097	−	0.154343i	−0.0146495	−	0.0253738i	0.858608	−	0.512633i	$-0.171330\pi$
$37$	−0.0891097	−	0.154343i	−0.0146495	−	0.0253738i	−0.873257	+	0.487259i	$0.837997\pi$
$38$	−6.34924	−	3.66573i	−1.02998	−	0.594661i
$39$		0			0
$40$	0.112089	+	0.194145i	0.0177229	+	0.0306970i
$41$	−0.568932			−0.0888522			−0.0444261	−	0.999013i	$-0.514146\pi$
$41$	−0.568932			−0.0888522			−0.0444261	+	0.999013i	$0.514146\pi$
$42$		0			0
$43$			6.39391i			0.975063i	0.873105	+	0.487531i	$0.162103\pi$
$43$			6.39391i			0.975063i	−0.873105	+	0.487531i	$0.837897\pi$
$44$	−3.31529	+	0.0941129i	−0.499799	+	0.0141881i
$45$		0			0
$46$	−4.20784	−	2.42940i	−0.620412	−	0.358195i
$47$	−2.93076	+	1.69208i	−0.427495	+	0.246815i	−0.698279	−	0.715826i	$-0.746051\pi$
$47$	−2.93076	+	1.69208i	−0.427495	+	0.246815i	0.270784	+	0.962640i	$0.412717\pi$
$48$		0			0
$49$	6.81123	+	1.61465i	0.973033	+	0.230664i
$50$		−	4.94974i		−	0.699999i
$51$		0			0
$52$	−2.51576	+	4.35743i	−0.348874	+	0.604267i
$53$	1.07478	−	1.86157i	0.147632	−	0.255706i	−0.782720	−	0.622374i	$-0.786168\pi$
$53$	1.07478	−	1.86157i	0.147632	−	0.255706i	0.930352	+	0.366668i	$0.119502\pi$
$54$		0			0
$55$	−0.654195	−	0.353338i	−0.0882116	−	0.0476440i
$56$	0.307218	−	2.62785i	0.0410537	−	0.351162i
$57$		0			0
$58$	−2.82907	−	4.90010i	−0.371475	−	0.643414i
$59$	2.00911	+	1.15996i	0.261563	+	0.151014i	0.625048	−	0.780587i	$-0.285080\pi$
$59$	2.00911	+	1.15996i	0.261563	+	0.151014i	−0.363484	+	0.931600i	$0.618413\pi$
$60$		0			0
$61$	2.19784	+	3.80677i	0.281404	+	0.487407i	0.971731	−	0.236091i	$-0.0758665\pi$
$61$	2.19784	+	3.80677i	0.281404	+	0.487407i	−0.690327	+	0.723498i	$0.742533\pi$
$62$	−4.31854			−0.548455
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.976845	+	0.563982i	−0.121163	+	0.0699533i
$66$		0			0
$67$	4.32907	−	7.49817i	0.528880	−	0.916047i	−0.470553	−	0.882372i	$-0.655945\pi$
$67$	4.32907	−	7.49817i	0.528880	−	0.916047i	0.999433	−	0.0336755i	$-0.0107213\pi$
$68$	−3.92826	−	6.80394i	−0.476371	−	0.825099i
$69$		0			0
$70$	0.354200	−	0.475748i	0.0423349	−	0.0568628i
$71$	11.6958			1.38803			0.694015	−	0.719960i	$-0.255840\pi$
$71$	11.6958			1.38803			0.694015	+	0.719960i	$0.255840\pi$
$72$		0			0
$73$	−5.25571	+	9.10315i	−0.615134	+	1.06544i	0.375227	+	0.926933i	$0.377565\pi$
$73$	−5.25571	+	9.10315i	−0.615134	+	1.06544i	−0.990361	+	0.138511i	$0.955769\pi$
$74$	0.154343	+	0.0891097i	0.0179420	+	0.0103588i
$75$		0			0
$76$	7.33147			0.840977
$77$	3.70262	+	7.95554i	0.421953	+	0.906618i
$78$		0			0
$79$	−8.75195	+	5.05294i	−0.984671	+	0.568500i	−0.903677	−	0.428214i	$-0.859143\pi$
$79$	−8.75195	+	5.05294i	−0.984671	+	0.568500i	−0.0809939	+	0.996715i	$0.525809\pi$
$80$	−0.194145	−	0.112089i	−0.0217060	−	0.0125320i
$81$		0			0
$82$	0.492709	−	0.284466i	0.0544106	−	0.0314140i
$83$	14.2897			1.56849			0.784247	−	0.620448i	$-0.213049\pi$
$83$	14.2897			1.56849			0.784247	+	0.620448i	$0.213049\pi$
$84$		0			0
$85$		−	1.76127i		−	0.191036i
$86$	−3.19696	−	5.53729i	−0.344737	−	0.597102i
$87$		0			0
$88$	2.82407	−	1.73915i	0.301047	−	0.185394i
$89$	−9.10315	+	5.25571i	−0.964932	+	0.557104i	−0.897688	−	0.440633i	$-0.854754\pi$
$89$	−9.10315	+	5.25571i	−0.964932	+	0.557104i	−0.0672448	+	0.997737i	$0.521421\pi$
$90$		0			0
$91$	13.2221	+	1.54578i	1.38606	+	0.162041i
$92$	4.85879			0.506564
$93$		0			0
$94$	1.69208	−	2.93076i	0.174524	−	0.302285i
$95$	1.42337	+	0.821781i	0.146034	+	0.0843129i
$96$		0			0
$97$			3.96123i			0.402202i	0.979571	+	0.201101i	$0.0644519\pi$
$97$			3.96123i			0.402202i	−0.979571	+	0.201101i	$0.935548\pi$
$98$	−6.70603	+	2.00729i	−0.677411	+	0.202767i
$99$		0			0
$100$	2.47487	+	4.28660i	0.247487	+	0.428660i
$101$	−3.38364	+	5.86063i	−0.336685	+	0.583155i	−0.983807	−	0.179231i	$-0.942639\pi$
$101$	−3.38364	+	5.86063i	−0.336685	+	0.583155i	0.647122	+	0.762386i	$0.275972\pi$
$102$		0			0
$103$	−12.4945	+	7.21371i	−1.23112	+	0.710788i	−0.967263	−	0.253774i	$-0.918328\pi$
$103$	−12.4945	+	7.21371i	−1.23112	+	0.710788i	−0.263857	+	0.964562i	$0.584995\pi$
$104$		−	5.03153i		−	0.493382i
$105$		0			0
$106$			2.14956i			0.208783i
$107$	14.9528	−	8.63301i	1.44554	−	0.834585i	0.447332	−	0.894368i	$-0.352374\pi$
$107$	14.9528	−	8.63301i	1.44554	−	0.834585i	0.998211	+	0.0597828i	$0.0190408\pi$
$108$		0			0
$109$	2.87038	+	1.65721i	0.274932	+	0.158732i	0.631127	−	0.775680i	$-0.282593\pi$
$109$	2.87038	+	1.65721i	0.274932	+	0.158732i	−0.356195	+	0.934412i	$0.615926\pi$
$110$	0.743218	−	0.0210981i	0.0708631	−	0.00201163i
$111$		0			0
$112$	1.04787	+	2.42940i	0.0990143	+	0.229556i
$113$	−17.4297			−1.63965			−0.819825	−	0.572613i	$-0.805930\pi$
$113$	−17.4297			−1.63965			−0.819825	+	0.572613i	$0.805930\pi$
$114$		0			0
$115$	0.943309	+	0.544620i	0.0879640	+	0.0507861i
$116$	4.90010	+	2.82907i	0.454962	+	0.262673i
$117$		0			0
$118$	−2.31992			−0.213566
$119$	−12.4132	+	16.6729i	−1.13791	+	1.52841i
$120$		0			0
$121$	−4.95072	+	9.82295i	−0.450066	+	0.892995i
$122$	−3.80677	−	2.19784i	−0.344649	−	0.198983i
$123$		0			0
$124$	3.73996	−	2.15927i	0.335858	−	0.193908i
$125$			2.23052i			0.199504i
$126$		0			0
$127$		−	8.23722i		−	0.730935i	−0.930824	−	0.365468i	$-0.880909\pi$
$127$		−	8.23722i		−	0.730935i	0.930824	−	0.365468i	$-0.119091\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	0.563982	−	0.976845i	0.0494645	−	0.0856750i
$131$	1.07003	+	1.85334i	0.0934888	+	0.161927i	0.908977	−	0.416846i	$-0.136865\pi$
$131$	1.07003	+	1.85334i	0.0934888	+	0.161927i	−0.815488	+	0.578774i	$0.803531\pi$
$132$		0			0
$133$	−7.68241	−	17.8111i	−0.666150	−	1.54441i
$134$			8.65814i			0.747950i
$135$		0			0
$136$	6.80394	+	3.92826i	0.583433	+	0.336845i
$137$	−5.69013	+	9.85559i	−0.486140	+	0.842020i	−0.999873	−	0.0159306i	$-0.994929\pi$
$137$	−5.69013	+	9.85559i	−0.486140	+	0.842020i	0.513733	+	0.857950i	$0.328262\pi$
$138$		0			0
$139$	14.0998			1.19593			0.597963	−	0.801523i	$-0.295977\pi$
$139$	14.0998			1.19593			0.597963	+	0.801523i	$0.295977\pi$
$140$	−0.0688718	+	0.589110i	−0.00582073	+	0.0497889i
$141$		0			0
$142$	−10.1288	+	5.84788i	−0.849991	+	0.490743i
$143$	8.75058	+	14.2094i	0.731760	+	1.18825i
$144$		0			0
$145$	0.634218	+	1.09850i	0.0526690	+	0.0912253i
$146$		−	10.5114i		−	0.869931i
$147$		0			0
$148$	−0.178219			−0.0146495
$149$	−11.8830	+	6.86063i	−0.973491	+	0.562045i	−0.900299	−	0.435273i	$-0.856652\pi$
$149$	−11.8830	+	6.86063i	−0.973491	+	0.562045i	−0.0731920	+	0.997318i	$0.523319\pi$
$150$		0			0
$151$	−15.1576	−	8.75126i	−1.23351	−	0.712167i	−0.265750	−	0.964042i	$-0.585620\pi$
$151$	−15.1576	−	8.75126i	−1.23351	−	0.712167i	−0.967760	+	0.251875i	$0.918953\pi$
$152$	−6.34924	+	3.66573i	−0.514991	+	0.297330i
$153$		0			0
$154$	−7.18434	−	5.03838i	−0.578930	−	0.406005i
$155$	0.968125			0.0777617
$156$		0			0
$157$	−2.73267	−	1.57771i	−0.218091	−	0.125915i	0.386975	−	0.922090i	$-0.373520\pi$
$157$	−2.73267	−	1.57771i	−0.218091	−	0.125915i	−0.605066	+	0.796175i	$0.706853\pi$
$158$	5.05294	−	8.75195i	0.401990	−	0.696268i
$159$		0			0
$160$	0.224179			0.0177229
$161$	−5.09138	−	11.8039i	−0.401257	−	0.930281i
$162$		0			0
$163$	−6.07127	−	10.5158i	−0.475539	−	0.823657i	0.524069	−	0.851676i	$-0.324414\pi$
$163$	−6.07127	−	10.5158i	−0.475539	−	0.823657i	−0.999607	+	0.0280187i	$0.991080\pi$
$164$	−0.284466	+	0.492709i	−0.0222130	+	0.0384741i
$165$		0			0
$166$	−12.3752	+	7.14483i	−0.960503	+	0.554547i
$167$	14.4274			1.11643			0.558213	−	0.829697i	$-0.311487\pi$
$167$	14.4274			1.11643			0.558213	+	0.829697i	$0.311487\pi$
$168$		0			0
$169$	12.3163			0.947407
$170$	0.880633	+	1.52530i	0.0675415	+	0.116985i
$171$		0			0
$172$	5.53729	+	3.19696i	0.422215	+	0.243766i
$173$	−1.80593	−	3.12796i	−0.137302	−	0.237815i	0.789172	−	0.614172i	$-0.210510\pi$
$173$	−1.80593	−	3.12796i	−0.137302	−	0.237815i	−0.926475	+	0.376357i	$0.877177\pi$
$174$		0			0
$175$	7.82052	−	10.5042i	0.591176	−	0.794046i
$176$	−1.57614	+	2.91818i	−0.118806	+	0.219966i
$177$		0			0
$178$	5.25571	−	9.10315i	0.393932	−	0.682310i
$179$	−1.27355	+	2.20585i	−0.0951895	+	0.164873i	−0.909688	−	0.415293i	$-0.863679\pi$
$179$	−1.27355	+	2.20585i	−0.0951895	+	0.164873i	0.814498	+	0.580166i	$0.197012\pi$
$180$		0			0
$181$			6.92820i			0.514969i	0.966282	+	0.257485i	$0.0828937\pi$
$181$			6.92820i			0.514969i	−0.966282	+	0.257485i	$0.917106\pi$
$182$	−12.2236	+	5.27238i	−0.906072	+	0.390815i
$183$		0			0
$184$	−4.20784	+	2.42940i	−0.310206	+	0.179098i
$185$	−0.0346003	−	0.0199765i	−0.00254387	−	0.00146870i
$186$		0			0
$187$	−26.0466	+	0.739400i	−1.90472	+	0.0540703i
$188$			3.38415i			0.246815i
$189$		0			0
$190$	−1.64356			−0.119236
$191$	−0.339220	−	0.587546i	−0.0245451	−	0.0425133i	0.853492	−	0.521106i	$-0.174480\pi$
$191$	−0.339220	−	0.587546i	−0.0245451	−	0.0425133i	−0.878037	+	0.478593i	$0.841147\pi$
$192$		0			0
$193$	20.7803	+	11.9975i	1.49580	+	0.863600i	0.999988	−	0.00483004i	$-0.00153746\pi$
$193$	20.7803	+	11.9975i	1.49580	+	0.863600i	0.495811	+	0.868430i	$0.334871\pi$
$194$	−1.98061	−	3.43052i	−0.142200	−	0.246297i
$195$		0			0
$196$	4.80394	−	5.09138i	0.343139	−	0.363670i
$197$			13.4945i			0.961444i	0.876873	+	0.480722i	$0.159625\pi$
$197$			13.4945i			0.961444i	−0.876873	+	0.480722i	$0.840375\pi$
$198$		0			0
$199$	15.6225	+	9.01964i	1.10745	+	0.639385i	0.938167	−	0.346183i	$-0.112522\pi$
$199$	15.6225	+	9.01964i	1.10745	+	0.639385i	0.169280	+	0.985568i	$0.445856\pi$
$200$	−4.28660	−	2.47487i	−0.303109	−	0.175000i
$201$		0			0
$202$		−	6.76728i		−	0.476144i
$203$	1.73828	−	14.8688i	0.122004	−	1.04358i
$204$		0			0
$205$	−0.110455	+	0.0637712i	−0.00771451	+	0.00445398i
$206$	7.21371	−	12.4945i	0.502603	−	0.870533i
$207$		0			0
$208$	2.51576	+	4.35743i	0.174437	+	0.302134i
$209$	11.5554	−	21.3946i	0.799305	−	1.47989i
$210$		0			0
$211$			10.1699i			0.700124i	0.936727	+	0.350062i	$0.113839\pi$
$211$			10.1699i			0.700124i	−0.936727	+	0.350062i	$0.886161\pi$
$212$	−1.07478	−	1.86157i	−0.0738160	−	0.127853i
$213$		0			0
$214$	−8.63301	+	14.9528i	−0.590141	+	1.02215i
$215$	0.716691	+	1.24134i	0.0488779	+	0.0846590i
$216$		0			0
$217$	−9.16471	−	6.82322i	−0.622141	−	0.463191i
$218$	−3.31442			−0.224481
$219$		0			0
$220$	−0.633097	+	0.389881i	−0.0426834	+	0.0262857i
$221$	−19.7651	+	34.2342i	−1.32955	+	2.30284i
$222$		0			0
$223$			20.6489i			1.38276i	0.722494	+	0.691378i	$0.242996\pi$
$223$			20.6489i			1.38276i	−0.722494	+	0.691378i	$0.757004\pi$
$224$	−2.12218	−	1.57999i	−0.141794	−	0.105567i
$225$		0			0
$226$	15.0946	−	8.71486i	1.00408	−	0.579704i
$227$	1.61465	−	2.79665i	0.107168	−	0.185620i	−0.807454	−	0.589931i	$-0.799155\pi$
$227$	1.61465	−	2.79665i	0.107168	−	0.185620i	0.914622	+	0.404310i	$0.132488\pi$
$228$		0			0
$229$	−6.90120	+	3.98441i	−0.456044	+	0.263297i	−0.710379	−	0.703819i	$-0.751477\pi$
$229$	−6.90120	+	3.98441i	−0.456044	+	0.263297i	0.254335	+	0.967116i	$0.418143\pi$
$230$	−1.08924			−0.0718223
$231$		0			0
$232$	−5.65814			−0.371475
$233$	9.88963	−	5.70978i	0.647891	−	0.374060i	−0.139757	−	0.990186i	$-0.544632\pi$
$233$	9.88963	−	5.70978i	0.647891	−	0.374060i	0.787648	+	0.616126i	$0.211299\pi$
$234$		0			0
$235$	−0.379328	+	0.657015i	−0.0247446	+	0.0428589i
$236$	2.00911	−	1.15996i	0.130782	−	0.0755068i
$237$		0			0
$238$	2.41366	−	20.6458i	0.156455	−	1.33827i
$239$			3.67272i			0.237569i	0.992920	+	0.118784i	$0.0378997\pi$
$239$			3.67272i			0.237569i	−0.992920	+	0.118784i	$0.962100\pi$
$240$		0			0
$241$	10.4731	−	18.1399i	0.674632	−	1.16850i	−0.301945	−	0.953325i	$-0.597636\pi$
$241$	10.4731	−	18.1399i	0.674632	−	1.16850i	0.976576	−	0.215171i	$-0.0690308\pi$
$242$	−0.624023	−	10.9823i	−0.0401137	−	0.705968i
$243$		0			0
$244$	4.39568			0.281404
$245$	1.50335	−	0.449992i	0.0960455	−	0.0287490i
$246$		0			0
$247$	−18.4442	−	31.9464i	−1.17358	−	2.03270i
$248$	−2.15927	+	3.73996i	−0.137114	+	0.237488i
$249$		0			0
$250$	−1.11526	−	1.93169i	−0.0705353	−	0.122171i
$251$			20.8713i			1.31739i	0.752411	+	0.658694i	$0.228891\pi$
$251$			20.8713i			1.31739i	−0.752411	+	0.658694i	$0.771109\pi$
$252$		0			0
$253$	7.65814	−	14.1788i	0.481463	−	0.891416i
$254$	4.11861	+	7.13364i	0.258425	+	0.447605i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	17.0414	−	9.83888i	1.06302	−	0.613732i	0.136751	−	0.990605i	$-0.456334\pi$
$257$	17.0414	−	9.83888i	1.06302	−	0.613732i	0.926265	+	0.376873i	$0.123001\pi$
$258$		0			0
$259$	0.186750	+	0.432966i	0.0116041	+	0.0269032i
$260$			1.12796i			0.0699533i
$261$		0			0
$262$	−1.85334	−	1.07003i	−0.114500	−	0.0661066i
$263$	−18.4604	−	10.6581i	−1.13832	−	0.657209i	−0.192306	−	0.981335i	$-0.561597\pi$
$263$	−18.4604	−	10.6581i	−1.13832	−	0.657209i	−0.946014	+	0.324126i	$0.894930\pi$
$264$		0			0
$265$		−	0.481885i		−	0.0296020i
$266$	15.5587	+	11.5836i	0.953965	+	0.710237i
$267$		0			0
$268$	−4.32907	−	7.49817i	−0.264440	−	0.458024i
$269$	−13.6201	−	7.86359i	−0.830434	−	0.479451i	0.0235673	−	0.999722i	$-0.492498\pi$
$269$	−13.6201	−	7.86359i	−0.830434	−	0.479451i	−0.854001	+	0.520271i	$0.825831\pi$
$270$		0			0
$271$	8.18151	+	14.1708i	0.496991	+	0.860814i	0.999994	−	0.00347047i	$-0.00110469\pi$
$271$	8.18151	+	14.1708i	0.496991	+	0.860814i	−0.503003	+	0.864285i	$0.667771\pi$
$272$	−7.85652			−0.476371
$273$		0			0
$274$		−	11.3803i		−	0.687506i
$275$	16.4098	−	0.465835i	0.989550	−	0.0280909i
$276$		0			0
$277$	−6.09136	−	3.51685i	−0.365994	−	0.211307i	0.305713	−	0.952124i	$-0.401105\pi$
$277$	−6.09136	−	3.51685i	−0.365994	−	0.211307i	−0.671707	+	0.740817i	$0.734439\pi$
$278$	−12.2108	+	7.04988i	−0.732353	+	0.422824i
$279$		0			0
$280$	−0.234910	−	0.544620i	−0.0140386	−	0.0325473i
$281$			17.9643i			1.07166i	0.844325	+	0.535831i	$0.180002\pi$
$281$			17.9643i			1.07166i	−0.844325	+	0.535831i	$0.819998\pi$
$282$		0			0
$283$	10.3239	−	17.8816i	0.613693	−	1.06295i	−0.376919	−	0.926246i	$-0.623016\pi$
$283$	10.3239	−	17.8816i	0.613693	−	1.06295i	0.990612	−	0.136702i	$-0.0436502\pi$
$284$	5.84788	−	10.1288i	0.347008	−	0.601035i
$285$		0			0
$286$	−14.6829	−	7.93040i	−0.868219	−	0.468934i
$287$	1.49507	+	0.174786i	0.0882511	+	0.0103173i
$288$		0			0
$289$	−22.3624	−	38.7329i	−1.31544	−	2.27840i
$290$	−1.09850	−	0.634218i	−0.0645061	−	0.0372426i
$291$		0			0
$292$	5.25571	+	9.10315i	0.307567	+	0.532722i
$293$	5.05047			0.295051			0.147526	−	0.989058i	$-0.452869\pi$
$293$	5.05047			0.295051			0.147526	+	0.989058i	$0.452869\pi$
$294$		0			0
$295$	0.520076			0.0302800
$296$	0.154343	−	0.0891097i	0.00897098	−	0.00517940i
$297$		0			0
$298$	6.86063	−	11.8830i	0.397426	−	0.688362i
$299$	−12.2236	−	21.1719i	−0.706908	−	1.22440i
$300$		0			0
$301$	1.96433	−	16.8023i	0.113222	−	0.968467i
$302$	17.5025			1.00716
$303$		0			0
$304$	3.66573	−	6.34924i	0.210244	−	0.364154i
$305$	0.853397	+	0.492709i	0.0488654	+	0.0282124i
$306$		0			0
$307$	2.61678			0.149348			0.0746738	−	0.997208i	$-0.476208\pi$
$307$	2.61678			0.149348			0.0746738	+	0.997208i	$0.476208\pi$
$308$	8.74101	+	0.771201i	0.498065	+	0.0439433i
$309$		0			0
$310$	−0.838421	+	0.484063i	−0.0476191	+	0.0274929i
$311$	15.6292	+	9.02354i	0.886253	+	0.511678i	0.872715	−	0.488230i	$-0.162357\pi$
$311$	15.6292	+	9.02354i	0.886253	+	0.511678i	0.0135378	+	0.999908i	$0.495691\pi$
$312$		0			0
$313$	6.23405	−	3.59923i	0.352370	−	0.203441i	−0.313359	−	0.949635i	$-0.601454\pi$
$313$	6.23405	−	3.59923i	0.352370	−	0.203441i	0.665728	+	0.746194i	$0.268121\pi$
$314$	3.15542			0.178070
$315$		0			0
$316$			10.1059i			0.568500i
$317$	−15.5781	−	26.9821i	−0.874955	−	1.51547i	−0.856810	−	0.515632i	$-0.827557\pi$
$317$	−15.5781	−	26.9821i	−0.874955	−	1.51547i	−0.0181453	−	0.999835i	$-0.505776\pi$
$318$		0			0
$319$	15.9790	−	9.84035i	0.894651	−	0.550954i
$320$	−0.194145	+	0.112089i	−0.0108530	+	0.00626599i
$321$		0			0
$322$	10.3112	+	7.67683i	0.574623	+	0.427813i
$323$	57.5998			3.20494
$324$		0			0
$325$	12.4524	−	21.5682i	0.690734	−	1.19639i
$326$	10.5158	+	6.07127i	0.582414	+	0.336257i
$327$		0			0
$328$		−	0.568932i		−	0.0314140i
$329$	8.22145	−	3.54614i	0.453263	−	0.195505i
$330$		0			0
$331$	5.87847	+	10.1818i	0.323110	+	0.559643i	0.981128	−	0.193359i	$-0.0619383\pi$
$331$	5.87847	+	10.1818i	0.323110	+	0.559643i	−0.658018	+	0.753002i	$0.728605\pi$
$332$	7.14483	−	12.3752i	0.392124	−	0.679178i
$333$		0			0
$334$	−12.4945	+	7.21371i	−0.683669	+	0.394716i
$335$		−	1.94097i		−	0.106047i
$336$		0			0
$337$		−	23.0213i		−	1.25405i	−0.779000	−	0.627024i	$-0.784273\pi$
$337$		−	23.0213i		−	1.25405i	0.779000	−	0.627024i	$-0.215727\pi$
$338$	−10.6662	+	6.15814i	−0.580166	+	0.334959i
$339$		0			0
$340$	−1.52530	−	0.880633i	−0.0827211	−	0.0477590i
$341$	−0.406430	−	14.3172i	−0.0220094	−	0.775320i
$342$		0			0
$343$	−17.4029	−	6.33559i	−0.939667	−	0.342090i
$344$	−6.39391			−0.344737
$345$		0			0
$346$	3.12796	+	1.80593i	0.168160	+	0.0970874i
$347$	−25.6752	−	14.8236i	−1.37832	−	0.795771i	−0.386360	−	0.922348i	$-0.626268\pi$
$347$	−25.6752	−	14.8236i	−1.37832	−	0.795771i	−0.991957	+	0.126577i	$0.959601\pi$
$348$		0			0
$349$	8.53049			0.456627			0.228313	−	0.973588i	$-0.426679\pi$
$349$	8.53049			0.456627			0.228313	+	0.973588i	$0.426679\pi$
$350$	−1.52065	+	13.0072i	−0.0812822	+	0.695264i
$351$		0			0
$352$	−0.0941129	−	3.31529i	−0.00501624	−	0.176706i
$353$	−23.5882	−	13.6187i	−1.25548	−	0.724849i	−0.283284	−	0.959036i	$-0.591424\pi$
$353$	−23.5882	−	13.6187i	−1.25548	−	0.724849i	−0.972192	+	0.234187i	$0.924757\pi$
$354$		0			0
$355$	2.27067	−	1.31097i	0.120515	−	0.0695791i
$356$			10.5114i			0.557104i
$357$		0			0
$358$		−	2.54710i		−	0.134618i
$359$	−15.2798	+	8.82178i	−0.806436	+	0.465596i	−0.845717	−	0.533632i	$-0.820827\pi$
$359$	−15.2798	+	8.82178i	−0.806436	+	0.465596i	0.0392810	+	0.999228i	$0.487493\pi$
$360$		0			0
$361$	−17.3752	+	30.0948i	−0.914485	+	1.58393i
$362$	−3.46410	−	6.00000i	−0.182069	−	0.315353i
$363$		0			0
$364$	7.94974	−	10.6778i	0.416680	−	0.559669i
$365$			2.35644i			0.123342i
$366$		0			0
$367$	6.03328	+	3.48331i	0.314934	+	0.181827i	0.649132	−	0.760675i	$-0.275132\pi$
$367$	6.03328	+	3.48331i	0.314934	+	0.181827i	−0.334198	+	0.942503i	$0.608465\pi$
$368$	2.42940	−	4.20784i	0.126641	−	0.219349i
$369$		0			0
$370$	0.0399530			0.00207706
$371$	−3.39627	+	4.56174i	−0.176325	+	0.236834i
$372$		0			0
$373$	25.1206	−	14.5034i	1.30069	−	0.750956i	0.320170	−	0.947360i	$-0.396260\pi$
$373$	25.1206	−	14.5034i	1.30069	−	0.750956i	0.980523	+	0.196404i	$0.0629265\pi$
$374$	22.1873	−	13.6637i	1.14728	−	0.706531i
$375$		0			0
$376$	−1.69208	−	2.93076i	−0.0872621	−	0.151142i
$377$		−	28.4691i		−	1.46623i
$378$		0			0
$379$	−11.7569			−0.603914			−0.301957	−	0.953322i	$-0.597640\pi$
$379$	−11.7569			−0.603914			−0.301957	+	0.953322i	$0.597640\pi$
$380$	1.42337	−	0.821781i	0.0730171	−	0.0421565i
$381$		0			0
$382$	0.587546	+	0.339220i	0.0300615	+	0.0173560i
$383$	−24.8948	+	14.3730i	−1.27206	+	0.734426i	−0.975376	−	0.220549i	$-0.929215\pi$
$383$	−24.8948	+	14.3730i	−1.27206	+	0.734426i	−0.296687	+	0.954975i	$0.595882\pi$
$384$		0			0
$385$	1.61058	+	1.12950i	0.0820826	+	0.0575647i
$386$	−23.9950			−1.22132
$387$		0			0
$388$	3.43052	+	1.98061i	0.174158	+	0.100550i
$389$	15.4023	−	26.6775i	0.780926	−	1.35260i	−0.150477	−	0.988613i	$-0.548081\pi$
$389$	15.4023	−	26.6775i	0.780926	−	1.35260i	0.931403	−	0.363990i	$-0.118586\pi$
$390$		0			0
$391$	38.1732			1.93050
$392$	−1.61465	+	6.81123i	−0.0815520	+	0.344019i
$393$		0			0
$394$	−6.74725	−	11.6866i	−0.339922	−	0.588762i
$395$	−1.13276	+	1.96200i	−0.0569955	+	0.0987191i
$396$		0			0
$397$	−30.8496	+	17.8111i	−1.54830	+	0.893911i	−0.550027	+	0.835147i	$0.685383\pi$
$397$	−30.8496	+	17.8111i	−1.54830	+	0.893911i	−0.998272	+	0.0587644i	$0.981284\pi$
$398$	−18.0393			−0.904227
$399$		0			0
$400$	4.94974			0.247487
$401$	1.53512	+	2.65891i	0.0766602	+	0.132779i	0.901807	−	0.432139i	$-0.142241\pi$
$401$	1.53512	+	2.65891i	0.0766602	+	0.132779i	−0.825147	+	0.564918i	$0.808908\pi$
$402$		0			0
$403$	−18.8177	−	10.8644i	−0.937378	−	0.541195i
$404$	3.38364	+	5.86063i	0.168342	+	0.291577i
$405$		0			0
$406$	5.92899	+	13.7459i	0.294251	+	0.682196i
$407$	−0.280899	+	0.520076i	−0.0139236	+	0.0257792i
$408$		0			0
$409$	−1.51423	+	2.62272i	−0.0748737	+	0.129685i	−0.901031	−	0.433754i	$-0.857189\pi$
$409$	−1.51423	+	2.62272i	−0.0748737	+	0.129685i	0.826158	+	0.563439i	$0.190522\pi$
$410$	0.0637712	−	0.110455i	0.00314944	−	0.00545499i
$411$		0			0
$412$			14.4274i			0.710788i
$413$	−4.92328	−	3.66543i	−0.242259	−	0.180364i
$414$		0			0
$415$	2.77426	−	1.60172i	0.136183	−	0.0786254i
$416$	−4.35743	−	2.51576i	−0.213641	−	0.123346i
$417$		0			0
$418$	0.689986	+	24.3059i	0.0337483	+	1.18884i
$419$			0.668585i			0.0326625i	0.999867	+	0.0163312i	$0.00519863\pi$
$419$			0.668585i			0.0326625i	−0.999867	+	0.0163312i	$0.994801\pi$
$420$		0			0
$421$	−8.07771			−0.393683			−0.196842	−	0.980435i	$-0.563068\pi$
$421$	−8.07771			−0.393683			−0.196842	+	0.980435i	$0.563068\pi$
$422$	−5.08494	−	8.80738i	−0.247531	−	0.428736i
$423$		0			0
$424$	1.86157	+	1.07478i	0.0904058	+	0.0521958i
$425$	19.4439	+	33.6778i	0.943166	+	1.63361i
$426$		0			0
$427$	−4.60609	−	10.6788i	−0.222904	−	0.516786i
$428$		−	17.2660i		−	0.834585i
$429$		0			0
$430$	−1.24134	−	0.716691i	−0.0598630	−	0.0345619i
$431$	8.26452	+	4.77152i	0.398088	+	0.229836i	0.685659	−	0.727923i	$-0.259514\pi$
$431$	8.26452	+	4.77152i	0.398088	+	0.229836i	−0.287571	+	0.957759i	$0.592848\pi$
$432$		0			0
$433$		−	0.729857i		−	0.0350747i	−0.999846	−	0.0175374i	$-0.994417\pi$
$433$		−	0.729857i		−	0.0350747i	0.999846	−	0.0175374i	$-0.00558260\pi$
$434$	11.3485	+	1.32673i	0.544745	+	0.0636852i
$435$		0			0
$436$	2.87038	−	1.65721i	0.137466	−	0.0793661i
$437$	−17.8111	+	30.8496i	−0.852018	+	1.47574i
$438$		0			0
$439$	12.9809	+	22.4835i	0.619542	+	1.07308i	0.989569	+	0.144058i	$0.0460151\pi$
$439$	12.9809	+	22.4835i	0.619542	+	1.07308i	−0.370027	+	0.929021i	$0.620652\pi$
$440$	0.353338	−	0.654195i	0.0168447	−	0.0311875i
$441$		0			0
$442$		−	39.5303i		−	1.88026i
$443$	8.80056	+	15.2430i	0.418127	+	0.724218i	0.995751	−	0.0920854i	$-0.0293533\pi$
$443$	8.80056	+	15.2430i	0.418127	+	0.724218i	−0.577624	+	0.816303i	$0.696020\pi$
$444$		0			0
$445$	−1.17822	+	2.04074i	−0.0558530	+	0.0967402i
$446$	−10.3245	−	17.8825i	−0.488878	−	0.846761i
$447$		0			0
$448$	2.62785	+	0.307218i	0.124154	+	0.0145147i
$449$	−8.92251			−0.421079			−0.210540	−	0.977585i	$-0.567522\pi$
$449$	−8.92251			−0.421079			−0.210540	+	0.977585i	$0.567522\pi$
$450$		0			0
$451$	0.989457	+	1.60670i	0.0465917	+	0.0756566i
$452$	−8.71486	+	15.0946i	−0.409913	+	0.709990i
$453$		0			0
$454$			3.22930i			0.151558i
$455$	2.74027	−	1.18196i	0.128466	−	0.0554110i
$456$		0			0
$457$	−24.3327	+	14.0485i	−1.13823	+	0.657160i	−0.945993	−	0.324188i	$-0.894909\pi$
$457$	−24.3327	+	14.0485i	−1.13823	+	0.657160i	−0.192241	+	0.981348i	$0.561576\pi$
$458$	3.98441	−	6.90120i	0.186179	−	0.322472i
$459$		0			0
$460$	0.943309	−	0.544620i	0.0439820	−	0.0253930i
$461$	18.7712			0.874262			0.437131	−	0.899398i	$-0.355995\pi$
$461$	18.7712			0.874262			0.437131	+	0.899398i	$0.355995\pi$
$462$		0			0
$463$	7.57221			0.351911			0.175955	−	0.984398i	$-0.443699\pi$
$463$	7.57221			0.351911			0.175955	+	0.984398i	$0.443699\pi$
$464$	4.90010	−	2.82907i	0.227481	−	0.131336i
$465$		0			0
$466$	−5.70978	+	9.88963i	−0.264501	+	0.458128i
$467$	34.4353	−	19.8812i	1.59347	−	0.919993i	0.600770	−	0.799422i	$-0.294861\pi$
$467$	34.4353	−	19.8812i	1.59347	−	0.919993i	0.992705	−	0.120571i	$-0.0384725\pi$
$468$		0			0
$469$	−13.6797	+	18.3741i	−0.631672	+	0.848439i
$470$		−	0.758655i		−	0.0349942i
$471$		0			0
$472$	−1.15996	+	2.00911i	−0.0533914	+	0.0924766i
$473$	18.0569	−	11.1200i	0.830255	−	0.511297i
$474$		0			0
$475$	−36.2889			−1.66505
$476$	8.23260	+	19.0866i	0.377340	+	0.874833i
$477$		0			0
$478$	−1.83636	−	3.18067i	−0.0839933	−	0.145481i
$479$	9.30307	−	16.1134i	0.425068	−	0.736239i	−0.571359	−	0.820700i	$-0.693584\pi$
$479$	9.30307	−	16.1134i	0.425068	−	0.736239i	0.996427	+	0.0844611i	$0.0269169\pi$
$480$		0			0
$481$	0.448358	+	0.776579i	0.0204434	+	0.0354089i
$482$			20.9462i			0.954073i
$483$		0			0
$484$	6.03156	+	9.19893i	0.274162	+	0.418133i
$485$	0.444012	+	0.769051i	0.0201615	+	0.0349208i
$486$		0			0
$487$	−10.2345	+	17.7266i	−0.463768	+	0.803270i	−0.999145	−	0.0413435i	$-0.986836\pi$
$487$	−10.2345	+	17.7266i	−0.463768	+	0.803270i	0.535377	+	0.844613i	$0.320170\pi$
$488$	−3.80677	+	2.19784i	−0.172324	+	0.0994915i
$489$		0			0
$490$	−1.07694	+	1.14138i	−0.0486513	+	0.0515623i
$491$		−	29.5933i		−	1.33553i	−0.744373	−	0.667764i	$-0.767252\pi$
$491$		−	29.5933i		−	1.33553i	0.744373	−	0.667764i	$-0.232748\pi$
$492$		0			0
$493$	38.4977	+	22.2266i	1.73385	+	1.00104i
$494$	31.9464	+	18.4442i	1.43734	+	0.829846i
$495$		0			0
$496$		−	4.31854i		−	0.193908i
$497$	−30.7347	−	3.59314i	−1.37864	−	0.161175i
$498$		0			0
$499$	−3.72298	−	6.44839i	−0.166664	−	0.288670i	0.770581	−	0.637342i	$-0.219966\pi$
$499$	−3.72298	−	6.44839i	−0.166664	−	0.288670i	−0.937245	+	0.348672i	$0.886633\pi$
$500$	1.93169	+	1.11526i	0.0863878	+	0.0498760i
$501$		0			0
$502$	−10.4357	−	18.0751i	−0.465767	−	0.806732i
$503$	−8.83120			−0.393764			−0.196882	−	0.980427i	$-0.563082\pi$
$503$	−8.83120			−0.393764			−0.196882	+	0.980427i	$0.563082\pi$
$504$		0			0
$505$			1.51708i			0.0675092i
$506$	0.457275	+	16.1083i	0.0203284	+	0.716102i
$507$		0			0
$508$	−7.13364	−	4.11861i	−0.316504	−	0.182734i
$509$	−2.15760	+	1.24569i	−0.0956341	+	0.0552144i	−0.547054	−	0.837097i	$-0.684251\pi$
$509$	−2.15760	+	1.24569i	−0.0956341	+	0.0552144i	0.451420	+	0.892311i	$0.350918\pi$
$510$		0			0
$511$	16.6079	−	22.3071i	0.734690	−	0.986809i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−9.83888	+	17.0414i	−0.433974	+	0.751666i
$515$	−1.61716	+	2.80101i	−0.0712606	+	0.123427i
$516$		0			0
$517$	9.87556	+	5.33390i	0.434327	+	0.234584i
$518$	−0.378213	−	0.281584i	−0.0166177	−	0.0123721i
$519$		0			0
$520$	−0.563982	−	0.976845i	−0.0247322	−	0.0428375i
$521$	8.03642	+	4.63983i	0.352082	+	0.203275i	0.665602	−	0.746307i	$-0.268175\pi$
$521$	8.03642	+	4.63983i	0.352082	+	0.203275i	−0.313520	+	0.949582i	$0.601508\pi$
$522$		0			0
$523$	−4.35899	−	7.55000i	−0.190605	−	0.330138i	0.754846	−	0.655903i	$-0.227712\pi$
$523$	−4.35899	−	7.55000i	−0.190605	−	0.330138i	−0.945451	+	0.325764i	$0.894378\pi$
$524$	2.14006			0.0934888
$525$		0			0
$526$	21.3163			0.929434
$527$	29.3831	−	16.9643i	1.27995	−	0.738978i
$528$		0			0
$529$	−0.303943	+	0.526445i	−0.0132149	+	0.0228889i
$530$	0.240943	+	0.417325i	0.0104659	+	0.0181274i
$531$		0			0
$532$	−19.2660	−	2.25236i	−0.835288	−	0.0976521i
$533$	2.86260			0.123993
$534$		0			0
$535$	1.93534	−	3.35211i	0.0836721	−	0.144924i
$536$	7.49817	+	4.32907i	0.323872	+	0.186987i
$537$		0			0
$538$	15.7272			0.678047
$539$	−7.28587	−	22.0435i	−0.313825	−	0.949481i
$540$		0			0
$541$	−38.5195	+	22.2392i	−1.65608	+	0.956139i	−0.681583	+	0.731740i	$0.738708\pi$
$541$	−38.5195	+	22.2392i	−1.65608	+	0.956139i	−0.974497	+	0.224398i	$0.927958\pi$
$542$	−14.1708	−	8.18151i	−0.608688	−	0.351426i
$543$		0			0
$544$	6.80394	−	3.92826i	0.291717	−	0.168423i
$545$	0.743024			0.0318277
$546$		0			0
$547$		−	22.6133i		−	0.966874i	−0.875379	−	0.483437i	$-0.839388\pi$
$547$		−	22.6133i		−	0.966874i	0.875379	−	0.483437i	$-0.160612\pi$
$548$	5.69013	+	9.85559i	0.243070	+	0.421010i
$549$		0			0
$550$	−13.9784	+	8.60834i	−0.596042	+	0.367061i
$551$	−35.9249	+	20.7412i	−1.53045	+	0.883607i
$552$		0			0
$553$	24.5512	−	10.5896i	1.04402	−	0.450317i
$554$	7.03370			0.298833
$555$		0			0
$556$	7.04988	−	12.2108i	0.298982	−	0.517851i
$557$	−19.8094	−	11.4370i	−0.839351	−	0.484599i	0.0176926	−	0.999843i	$-0.494368\pi$
$557$	−19.8094	−	11.4370i	−0.839351	−	0.484599i	−0.857044	+	0.515244i	$0.827701\pi$
$558$		0			0
$559$		−	32.1712i		−	1.36070i
$560$	0.475748	+	0.354200i	0.0201040	+	0.0149677i
$561$		0			0
$562$	−8.98216	−	15.5576i	−0.378890	−	0.656256i
$563$	−16.6837	+	28.8971i	−0.703136	+	1.21787i	0.264224	+	0.964461i	$0.414884\pi$
$563$	−16.6837	+	28.8971i	−0.703136	+	1.21787i	−0.967360	+	0.253406i	$0.918449\pi$
$564$		0			0
$565$	−3.38389	+	1.95369i	−0.142361	+	0.0821923i
$566$			20.6478i			0.867894i
$567$		0			0
$568$			11.6958i			0.490743i
$569$	−31.7920	+	18.3551i	−1.33279	+	0.769487i	−0.985727	−	0.168354i	$-0.946155\pi$
$569$	−31.7920	+	18.3551i	−1.33279	+	0.769487i	−0.347065	+	0.937841i	$0.612822\pi$
$570$		0			0
$571$	14.9063	+	8.60618i	0.623811	+	0.360158i	0.778351	−	0.627829i	$-0.216056\pi$
$571$	14.9063	+	8.60618i	0.623811	+	0.360158i	−0.154540	+	0.987987i	$0.549390\pi$
$572$	16.6810	−	0.473532i	0.697467	−	0.0197994i
$573$		0			0
$574$	−1.38216	+	0.596165i	−0.0576903	+	0.0248835i
$575$	−24.0498			−1.00295
$576$		0			0
$577$	34.1924	+	19.7410i	1.42345	+	0.821827i	0.996592	−	0.0824929i	$-0.0262882\pi$
$577$	34.1924	+	19.7410i	1.42345	+	0.821827i	0.426855	+	0.904320i	$0.359622\pi$
$578$	38.7329	+	22.3624i	1.61107	+	0.930154i
$579$		0			0
$580$	1.26844			0.0526690
$581$	−37.5512	−	4.39004i	−1.55788	−	0.182130i
$582$		0			0
$583$	−7.12640	+	0.202301i	−0.295145	+	0.00837845i
$584$	−9.10315	−	5.25571i	−0.376691	−	0.217483i
$585$		0			0
$586$	−4.37383	+	2.52523i	−0.180681	+	0.104316i
$587$		−	33.2111i		−	1.37077i	−0.728182	−	0.685384i	$-0.759634\pi$
$587$		−	33.2111i		−	1.37077i	0.728182	−	0.685384i	$-0.240366\pi$
$588$		0			0
$589$			31.6612i			1.30458i
$590$	−0.450399	+	0.260038i	−0.0185426	+	0.0107056i
$591$		0			0
$592$	−0.0891097	+	0.154343i	−0.00366239	+	0.00634344i
$593$	−7.18187	−	12.4394i	−0.294924	−	0.510823i	0.680043	−	0.733172i	$-0.261961\pi$
$593$	−7.18187	−	12.4394i	−0.294924	−	0.510823i	−0.974967	+	0.222349i	$0.928628\pi$
$594$		0			0
$595$	−0.541093	+	4.62835i	−0.0221826	+	0.189744i
$596$			13.7213i			0.562045i
$597$		0			0
$598$	21.1719	+	12.2236i	0.865782	+	0.499860i
$599$	7.17073	−	12.4201i	0.292988	−	0.507470i	−0.681527	−	0.731793i	$-0.738684\pi$
$599$	7.17073	−	12.4201i	0.292988	−	0.507470i	0.974515	+	0.224323i	$0.0720171\pi$
$600$		0			0
$601$	−10.9630			−0.447192			−0.223596	−	0.974682i	$-0.571780\pi$
$601$	−10.9630			−0.447192			−0.223596	+	0.974682i	$0.571780\pi$
$602$	6.69998	+	15.5334i	0.273071	+	0.633092i
$603$		0			0
$604$	−15.1576	+	8.75126i	−0.616755	+	0.356084i
$605$	0.139893	+	2.46200i	0.00568745	+	0.100094i
$606$		0			0
$607$	3.89629	+	6.74857i	0.158146	+	0.273916i	0.934200	−	0.356750i	$-0.116115\pi$
$607$	3.89629	+	6.74857i	0.158146	+	0.273916i	−0.776054	+	0.630666i	$0.782782\pi$
$608$			7.33147i			0.297330i
$609$		0			0
$610$	−0.985418			−0.0398984
$611$	14.7462	−	8.51373i	0.596568	−	0.344428i
$612$		0			0
$613$	21.9788	+	12.6895i	0.887715	+	0.512522i	0.873194	−	0.487372i	$-0.162045\pi$
$613$	21.9788	+	12.6895i	0.887715	+	0.512522i	0.0145204	+	0.999895i	$0.495378\pi$
$614$	−2.26620	+	1.30839i	−0.0914563	+	0.0528023i
$615$		0			0
$616$	−7.95554	+	3.70262i	−0.320538	+	0.149183i
$617$	−41.0360			−1.65205			−0.826024	−	0.563635i	$-0.809402\pi$
$617$	−41.0360			−1.65205			−0.826024	+	0.563635i	$0.809402\pi$
$618$		0			0
$619$	7.48172	+	4.31957i	0.300716	+	0.173618i	0.642764	−	0.766064i	$-0.277787\pi$
$619$	7.48172	+	4.31957i	0.300716	+	0.173618i	−0.342049	+	0.939682i	$0.611121\pi$
$620$	0.484063	−	0.838421i	0.0194404	−	0.0336718i
$621$		0			0
$622$	−18.0471			−0.723622
$623$	25.5364	−	11.0146i	1.02309	−	0.441290i
$624$		0			0
$625$	−12.1243	−	21.0000i	−0.484974	−	0.839999i
$626$	−3.59923	+	6.23405i	−0.143854	+	0.249163i
$627$		0			0
$628$	−2.73267	+	1.57771i	−0.109045	+	0.0629574i
$629$	−1.40018			−0.0558290
$630$		0			0
$631$	−1.12348			−0.0447252			−0.0223626	−	0.999750i	$-0.507119\pi$
$631$	−1.12348			−0.0447252			−0.0223626	+	0.999750i	$0.507119\pi$
$632$	−5.05294	−	8.75195i	−0.200995	−	0.348134i
$633$		0			0
$634$	26.9821	+	15.5781i	1.07160	+	0.618687i
$635$	−0.923306	−	1.59921i	−0.0366403	−	0.0634628i
$636$		0			0
$637$	−34.2709	−	8.12415i	−1.35786	−	0.321891i
$638$	−8.91803	+	16.5115i	−0.353068	+	0.653696i
$639$		0			0
$640$	0.112089	−	0.194145i	0.00443073	−	0.00767424i
$641$	−4.29911	+	7.44628i	−0.169805	+	0.294110i	−0.938351	−	0.345684i	$-0.887647\pi$
$641$	−4.29911	+	7.44628i	−0.169805	+	0.294110i	0.768546	+	0.639794i	$0.220980\pi$
$642$		0			0
$643$			21.6511i			0.853837i	0.904290	+	0.426919i	$0.140401\pi$
$643$			21.6511i			0.853837i	−0.904290	+	0.426919i	$0.859599\pi$
$644$	−12.7682	−	1.49271i	−0.503138	−	0.0588210i
$645$		0			0
$646$	−49.8829	+	28.7999i	−1.96262	+	1.13312i
$647$	2.74766	+	1.58636i	0.108022	+	0.0623664i	0.553038	−	0.833156i	$-0.313469\pi$
$647$	2.74766	+	1.58636i	0.108022	+	0.0623664i	−0.445016	+	0.895523i	$0.646802\pi$
$648$		0			0
$649$	−0.218334	−	7.69119i	−0.00857036	−	0.301906i
$650$			24.9048i			0.976846i
$651$		0			0
$652$	−12.1425			−0.475539
$653$	−14.7215	−	25.4983i	−0.576095	−	0.997826i	−0.995922	−	0.0902218i	$-0.971242\pi$
$653$	−14.7215	−	25.4983i	−0.576095	−	0.997826i	0.419826	−	0.907604i	$-0.362091\pi$
$654$		0			0
$655$	0.415481	+	0.239878i	0.0162342	+	0.00937280i
$656$	0.284466	+	0.492709i	0.0111065	+	0.0192371i
$657$		0			0
$658$	−5.34691	+	7.18177i	−0.208444	+	0.279975i
$659$			0.469820i			0.0183016i	0.999958	+	0.00915080i	$0.00291283\pi$
$659$			0.469820i			0.0183016i	−0.999958	+	0.00915080i	$0.997087\pi$
$660$		0			0
$661$	−6.13937	−	3.54456i	−0.238794	−	0.137868i	0.375829	−	0.926689i	$-0.377358\pi$
$661$	−6.13937	−	3.54456i	−0.238794	−	0.137868i	−0.614622	+	0.788822i	$0.710692\pi$
$662$	−10.1818	−	5.87847i	−0.395727	−	0.228473i
$663$		0			0
$664$			14.2897i			0.554547i
$665$	−3.48793	−	2.59680i	−0.135256	−	0.100700i
$666$		0			0
$667$	−23.8086	+	13.7459i	−0.921871	+	0.532243i
$668$	7.21371	−	12.4945i	0.279107	−	0.483427i
$669$		0			0
$670$	0.970487	+	1.68093i	0.0374932	+	0.0649401i
$671$	6.92820	−	12.8274i	0.267460	−	0.495196i
$672$		0			0
$673$			43.2330i			1.66651i	0.552889	+	0.833255i	$0.313525\pi$
$673$			43.2330i			1.66651i	−0.552889	+	0.833255i	$0.686475\pi$
$674$	11.5106	+	19.9370i	0.443373	+	0.767944i
$675$		0			0
$676$	6.15814	−	10.6662i	0.236852	−	0.410239i
$677$	10.8282	+	18.7550i	0.416161	+	0.720812i	0.995550	−	0.0942398i	$-0.0300420\pi$
$677$	10.8282	+	18.7550i	0.416161	+	0.720812i	−0.579389	+	0.815051i	$0.696709\pi$
$678$		0			0
$679$	1.21696	−	10.4095i	0.0467027	−	0.399481i
$680$	1.76127			0.0675415
$681$		0			0
$682$	7.51058	+	12.1958i	0.287595	+	0.467003i
$683$	−8.93736	+	15.4800i	−0.341978	+	0.592324i	−0.984800	−	0.173692i	$-0.944430\pi$
$683$	−8.93736	+	15.4800i	−0.341978	+	0.592324i	0.642822	+	0.766016i	$0.277764\pi$
$684$		0			0
$685$			2.55121i			0.0974769i
$686$	18.2391	−	3.21466i	0.696373	−	0.122736i
$687$		0			0
$688$	5.53729	−	3.19696i	0.211107	−	0.121883i
$689$	−5.40778	+	9.36654i	−0.206020	+	0.356837i
$690$		0			0
$691$	−15.7085	+	9.06930i	−0.597579	+	0.345012i	−0.768089	−	0.640344i	$-0.778792\pi$
$691$	−15.7085	+	9.06930i	−0.597579	+	0.345012i	0.170510	+	0.985356i	$0.445459\pi$
$692$	−3.61186			−0.137302
$693$		0			0
$694$	29.6472			1.12539
$695$	2.73740	−	1.58044i	0.103835	−	0.0599494i
$696$		0			0
$697$	−2.23491	+	3.87098i	−0.0846533	+	0.146624i
$698$	−7.38762	+	4.26524i	−0.279626	+	0.161442i
$699$		0			0
$700$	−5.18668	−	12.0249i	−0.196038	−	0.454498i
$701$		−	37.5868i		−	1.41963i	−0.704386	−	0.709817i	$-0.748778\pi$
$701$		−	37.5868i		−	1.41963i	0.704386	−	0.709817i	$-0.251222\pi$
$702$		0			0
$703$	0.653305	−	1.13156i	0.0246399	−	0.0426775i
$704$	1.73915	+	2.82407i	0.0655466	+	0.106436i
$705$		0			0
$706$	27.2374			1.02509
$707$	10.6922	−	14.3614i	0.402122	−	0.540115i
$708$		0			0
$709$	7.63216	+	13.2193i	0.286632	+	0.496461i	0.973004	−	0.230790i	$-0.0741311\pi$
$709$	7.63216	+	13.2193i	0.286632	+	0.496461i	−0.686372	+	0.727251i	$0.740798\pi$
$710$	−1.31097	+	2.27067i	−0.0491999	+	0.0852167i
$711$		0			0
$712$	−5.25571	−	9.10315i	−0.196966	−	0.341155i
$713$			20.9829i			0.785815i
$714$		0			0
$715$	3.29160	+	1.77783i	0.123099	+	0.0664870i
$716$	1.27355	+	2.20585i	0.0475947	+	0.0824365i
$717$		0			0
$718$	8.82178	−	15.2798i	0.329226	−	0.570236i
$719$	30.5794	−	17.6550i	1.14042	−	0.658422i	0.193886	−	0.981024i	$-0.437891\pi$
$719$	30.5794	−	17.6550i	1.14042	−	0.658422i	0.946535	+	0.322602i	$0.104557\pi$
$720$		0			0
$721$	35.0499	−	15.1180i	1.30533	−	0.563025i
$722$		−	34.7504i		−	1.29328i
$723$		0			0
$724$	6.00000	+	3.46410i	0.222988	+	0.128742i
$725$	−24.2542	−	14.0032i	−0.900779	−	0.520065i
$726$		0			0
$727$			17.0371i			0.631870i	0.948781	+	0.315935i	$0.102318\pi$
$727$			17.0371i			0.631870i	−0.948781	+	0.315935i	$0.897682\pi$
$728$	−1.54578	+	13.2221i	−0.0572903	+	0.490045i
$729$		0			0
$730$	−1.17822	−	2.04074i	−0.0436079	−	0.0755310i
$731$	43.5038	+	25.1169i	1.60905	+	0.928984i
$732$		0			0
$733$	21.3208	+	36.9287i	0.787501	+	1.36399i	0.927493	+	0.373839i	$0.121959\pi$
$733$	21.3208	+	36.9287i	0.787501	+	1.36399i	−0.139992	+	0.990153i	$0.544708\pi$
$734$	−6.96663			−0.257143
$735$		0			0
$736$			4.85879i			0.179098i
$737$	−28.7042	+	0.814843i	−1.05733	+	0.0300151i
$738$		0			0
$739$	27.8460	+	16.0769i	1.02433	+	0.591398i	0.915356	−	0.402646i	$-0.131909\pi$
$739$	27.8460	+	16.0769i	1.02433	+	0.591398i	0.108976	+	0.994044i	$0.465243\pi$
$740$	−0.0346003	+	0.0199765i	−0.00127193	+	0.000734351i
$741$		0			0
$742$	0.660382	−	5.64872i	0.0242434	−	0.207371i
$743$			52.5029i			1.92614i	0.269243	+	0.963072i	$0.413226\pi$
$743$			52.5029i			1.92614i	−0.269243	+	0.963072i	$0.586774\pi$
$744$		0			0
$745$	−1.53801	+	2.66391i	−0.0563483	+	0.0975982i
$746$	−14.5034	+	25.1206i	−0.531006	+	0.919729i
$747$		0			0
$748$	−12.3830	+	22.9267i	−0.452766	+	0.838285i
$749$	−41.9460	+	18.0925i	−1.53268	+	0.661087i
$750$		0			0
$751$	12.3478	+	21.3871i	0.450579	+	0.780426i	0.998422	−	0.0561550i	$-0.0178841\pi$
$751$	12.3478	+	21.3871i	0.450579	+	0.780426i	−0.547843	+	0.836581i	$0.684551\pi$
$752$	2.93076	+	1.69208i	0.106874	+	0.0617036i
$753$		0			0
$754$	14.2346	+	24.6550i	0.518392	+	0.897881i
$755$	−3.92370			−0.142798
$756$		0			0
$757$	40.8108			1.48329			0.741647	−	0.670791i	$-0.234045\pi$
$757$	40.8108			1.48329			0.741647	+	0.670791i	$0.234045\pi$
$758$	10.1818	−	5.87847i	0.369820	−	0.213516i
$759$		0			0
$760$	−0.821781	+	1.42337i	−0.0298091	+	0.0516309i
$761$	21.0095	+	36.3894i	0.761592	+	1.31912i	0.942030	+	0.335530i	$0.108915\pi$
$761$	21.0095	+	36.3894i	0.761592	+	1.31912i	−0.180438	+	0.983586i	$0.557751\pi$
$762$		0			0
$763$	−7.03380	−	5.23674i	−0.254641	−	0.189583i
$764$	−0.678440			−0.0245451
$765$		0			0
$766$	14.3730	−	24.8948i	0.519318	−	0.899484i
$767$	−10.1089	−	5.83636i	−0.365010	−	0.210739i
$768$		0			0
$769$	−15.6284			−0.563574			−0.281787	−	0.959477i	$-0.590927\pi$
$769$	−15.6284			−0.563574			−0.281787	+	0.959477i	$0.590927\pi$
$770$	−1.95955	−	0.172887i	−0.0706173	−	0.00623042i
$771$		0			0
$772$	20.7803	−	11.9975i	0.747900	−	0.431800i
$773$	−2.74004	−	1.58196i	−0.0985523	−	0.0568992i	0.449914	−	0.893072i	$-0.351455\pi$
$773$	−2.74004	−	1.58196i	−0.0985523	−	0.0568992i	−0.548466	+	0.836173i	$0.684788\pi$
$774$		0			0
$775$	−18.5119	+	10.6878i	−0.664965	+	0.383918i
$776$	−3.96123			−0.142200
$777$		0			0
$778$			30.8045i			1.10440i
$779$	−2.08555	−	3.61228i	−0.0747226	−	0.129423i
$780$		0			0
$781$	−20.3407	−	33.0296i	−0.727846	−	1.18189i
$782$	−33.0590	+	19.0866i	−1.18219	+	0.682535i
$783$		0			0
$784$	−2.00729	−	6.70603i	−0.0716890	−	0.239501i
$785$	−0.707378			−0.0252474
$786$		0			0
$787$	−18.2920	+	31.6827i	−0.652039	+	1.12936i	0.330588	+	0.943775i	$0.392753\pi$
$787$	−18.2920	+	31.6827i	−0.652039	+	1.12936i	−0.982627	+	0.185590i	$0.940581\pi$
$788$	11.6866	+	6.74725i	0.416317	+	0.240361i
$789$		0			0
$790$		−	2.26553i		−	0.0806038i
$791$	45.8028	+	5.35473i	1.62856	+	0.190392i
$792$		0			0
$793$	−11.0585	−	19.1539i	−0.392698	−	0.680174i
$794$	17.8111	−	30.8496i	0.632091	−	1.09481i
$795$		0			0
$796$	15.6225	−	9.01964i	0.553724	−	0.319693i
$797$		−	8.72925i		−	0.309206i	−0.987977	−	0.154603i	$-0.950590\pi$
$797$		−	8.72925i		−	0.309206i	0.987977	−	0.154603i	$-0.0494098\pi$
$798$		0			0
$799$			26.5876i			0.940603i
$800$	−4.28660	+	2.47487i	−0.151554	+	0.0874999i
$801$		0			0
$802$	−2.65891	−	1.53512i	−0.0938892	−	0.0542070i
$803$	34.8484	−	0.989260i	1.22977	−	0.0349102i
$804$		0			0
$805$	−2.31156	−	1.72098i	−0.0814719	−	0.0606567i
$806$	21.7288			0.765366
$807$		0			0
$808$	−5.86063	−	3.38364i	−0.206176	−	0.119036i
$809$	−25.2367	−	14.5704i	−0.887275	−	0.512269i	−0.0142249	−	0.999899i	$-0.504528\pi$
$809$	−25.2367	−	14.5704i	−0.887275	−	0.512269i	−0.873050	+	0.487630i	$0.837861\pi$
$810$		0			0
$811$	−32.7260			−1.14917			−0.574583	−	0.818446i	$-0.694836\pi$
$811$	−32.7260			−1.14917			−0.574583	+	0.818446i	$0.694836\pi$
$812$	−12.0076	−	8.93978i	−0.421384	−	0.313725i
$813$		0			0
$814$	−0.0167727	−	0.590849i	−0.000587884	−	0.0207092i
$815$	−2.35741	−	1.36105i	−0.0825765	−	0.0476756i
$816$		0			0
$817$	−40.5965	+	23.4384i	−1.42029	+	0.820006i
$818$		−	3.02845i		−	0.105887i
$819$		0			0
$820$			0.127542i			0.00445398i
$821$	−10.8680	+	6.27462i	−0.379294	+	0.218986i	−0.677511	−	0.735512i	$-0.736941\pi$
$821$	−10.8680	+	6.27462i	−0.379294	+	0.218986i	0.298217	+	0.954498i	$0.403608\pi$
$822$		0			0
$823$	−2.32728	+	4.03096i	−0.0811237	+	0.140510i	−0.903733	−	0.428097i	$-0.859184\pi$
$823$	−2.32728	+	4.03096i	−0.0811237	+	0.140510i	0.822609	+	0.568607i	$0.192518\pi$
$824$	−7.21371	−	12.4945i	−0.251301	−	0.435267i
$825$		0			0
$826$	6.09640	+	0.712720i	0.212121	+	0.0247987i
$827$			1.60601i			0.0558463i	0.999610	+	0.0279232i	$0.00888938\pi$
$827$			1.60601i			0.0558463i	−0.999610	+	0.0279232i	$0.991111\pi$
$828$		0			0
$829$	30.6111	+	17.6733i	1.06317	+	0.613819i	0.926306	−	0.376771i	$-0.122966\pi$
$829$	30.6111	+	17.6733i	1.06317	+	0.613819i	0.136860	+	0.990590i	$0.456299\pi$
$830$	−1.60172	+	2.77426i	−0.0555966	+	0.0962961i
$831$		0			0
$832$	5.03153			0.174437
$833$	37.7423	−	40.0005i	1.30769	−	1.38594i
$834$		0			0
$835$	2.80101	−	1.61716i	0.0969328	−	0.0559642i
$836$	−12.7505	−	20.7046i	−0.440986	−	0.716082i
$837$		0			0
$838$	−0.334292	−	0.579011i	−0.0115479	−	0.0200016i
$839$			20.3870i			0.703837i	0.936031	+	0.351918i	$0.114471\pi$
$839$			20.3870i			0.703837i	−0.936031	+	0.351918i	$0.885529\pi$
$840$		0			0
$841$	−3.01458			−0.103951
$842$	6.99550	−	4.03885i	0.241081	−	0.139188i
$843$		0			0
$844$	8.80738	+	5.08494i	0.303162	+	0.175031i
$845$	2.39114	−	1.38053i	0.0822578	−	0.0474915i
$846$		0			0
$847$	16.0276	−	24.2923i	0.550714	−	0.834694i
$848$	−2.14956			−0.0738160
$849$		0			0
$850$	−33.6778	−	19.4439i	−1.15514	−	0.666919i
$851$	0.432966	−	0.749919i	0.0148419	−	0.0257069i
$852$		0			0
$853$	−13.6020			−0.465723			−0.232861	−	0.972510i	$-0.574809\pi$
$853$	−13.6020			−0.465723			−0.232861	+	0.972510i	$0.574809\pi$
$854$	9.32841	+	6.94511i	0.319212	+	0.237657i
$855$		0			0
$856$	8.63301	+	14.9528i	0.295070	+	0.511077i
$857$	−14.5169	+	25.1439i	−0.495886	+	0.858900i	−0.999989	−	0.00474364i	$-0.998490\pi$
$857$	−14.5169	+	25.1439i	−0.495886	+	0.858900i	0.504102	+	0.863644i	$0.331823\pi$
$858$		0			0
$859$	17.6354	−	10.1818i	0.601713	−	0.347399i	−0.168002	−	0.985787i	$-0.553732\pi$
$859$	17.6354	−	10.1818i	0.601713	−	0.347399i	0.769715	+	0.638388i	$0.220398\pi$
$860$	1.43338			0.0488779
$861$		0			0
$862$	−9.54305			−0.325038
$863$	−3.55527	−	6.15791i	−0.121023	−	0.209618i	0.799148	−	0.601134i	$-0.205284\pi$
$863$	−3.55527	−	6.15791i	−0.121023	−	0.209618i	−0.920171	+	0.391516i	$0.871951\pi$
$864$		0			0
$865$	−0.701224	−	0.404852i	−0.0238423	−	0.0137654i
$866$	0.364929	+	0.632075i	0.0124008	+	0.0214788i
$867$		0			0
$868$	−10.4914	+	4.52526i	−0.356103	+	0.153597i
$869$	29.4908	+	15.9283i	1.00041	+	0.540330i
$870$		0			0
$871$	−21.7818	+	37.7273i	−0.738050	+	1.27834i
$872$	−1.65721	+	2.87038i	−0.0561203	+	0.0972032i
$873$		0			0
$874$		−	35.6221i		−	1.20494i
$875$	0.685257	−	5.86149i	0.0231659	−	0.198155i
$876$		0			0
$877$	19.7715	−	11.4151i	0.667636	−	0.385460i	−0.127544	−	0.991833i	$-0.540709\pi$
$877$	19.7715	−	11.4151i	0.667636	−	0.385460i	0.795180	+	0.606373i	$0.207376\pi$
$878$	−22.4835	−	12.9809i	−0.758781	−	0.438082i
$879$		0			0
$880$	0.0210981	+	0.743218i	0.000711218	+	0.0250539i
$881$		−	28.5824i		−	0.962967i	−0.876455	−	0.481483i	$-0.840098\pi$
$881$		−	28.5824i		−	0.962967i	0.876455	−	0.481483i	$-0.159902\pi$
$882$		0			0
$883$	40.1298			1.35048			0.675238	−	0.737600i	$-0.264041\pi$
$883$	40.1298			1.35048			0.675238	+	0.737600i	$0.264041\pi$
$884$	19.7651	+	34.2342i	0.664774	+	1.15142i
$885$		0			0
$886$	−15.2430	−	8.80056i	−0.512099	−	0.295661i
$887$	8.30087	+	14.3775i	0.278716	+	0.482750i	0.971066	−	0.238812i	$-0.0767579\pi$
$887$	8.30087	+	14.3775i	0.278716	+	0.482750i	−0.692350	+	0.721562i	$0.743425\pi$
$888$		0			0
$889$	−2.53062	+	21.6462i	−0.0848744	+	0.725991i
$890$		−	2.35644i		−	0.0789880i
$891$		0			0
$892$	17.8825	+	10.3245i	0.598751	+	0.345689i
$893$	−21.4868	−	12.4054i	−0.719028	−	0.415131i
$894$		0			0
$895$			0.571006i			0.0190866i
$896$	−2.42940	+	1.04787i	−0.0811605	+	0.0350068i
$897$		0			0
$898$	7.72712	−	4.46125i	0.257857	−	0.148874i
$899$	−12.2174	+	21.1612i	−0.407475	+	0.705767i
$900$		0			0
$901$	−8.44401	−	14.6255i	−0.281311	−	0.487245i
$902$	−1.66025	−	0.896716i	−0.0552801	−	0.0298574i
$903$		0			0
$904$		−	17.4297i		−	0.579704i
$905$	0.776579	+	1.34507i	0.0258144	+	0.0447118i
$906$		0			0
$907$	−12.6308	+	21.8771i	−0.419398	+	0.726419i	−0.995879	−	0.0906919i	$-0.971092\pi$
$907$	−12.6308	+	21.8771i	−0.419398	+	0.726419i	0.576481	+	0.817111i	$0.304425\pi$
$908$	−1.61465	−	2.79665i	−0.0535840	−	0.0928102i
$909$		0			0
$910$	−1.78217	+	2.39374i	−0.0590782	+	0.0793517i
$911$	−0.530745			−0.0175844			−0.00879219	−	0.999961i	$-0.502799\pi$
$911$	−0.530745			−0.0175844			−0.00879219	+	0.999961i	$0.502799\pi$
$912$		0			0
$913$	−24.8519	−	40.3550i	−0.822477	−	1.33556i
$914$	14.0485	−	24.3327i	0.464682	−	0.804853i
$915$		0			0
$916$			7.96882i			0.263297i
$917$	−2.24250	−	5.19905i	−0.0740538	−	0.171688i
$918$		0			0
$919$	−21.2350	+	12.2601i	−0.700480	+	0.404422i	−0.807526	−	0.589832i	$-0.799194\pi$
$919$	−21.2350	+	12.2601i	−0.700480	+	0.404422i	0.107046	+	0.994254i	$0.465861\pi$
$920$	−0.544620	+	0.943309i	−0.0179556	+	0.0311000i
$921$		0			0
$922$	−16.2563	+	9.38560i	−0.535374	+	0.309098i
$923$	−58.8475			−1.93699
$924$		0			0
$925$	0.882140			0.0290046
$926$	−6.55773	+	3.78611i	−0.215500	+	0.124419i
$927$		0			0
$928$	−2.82907	+	4.90010i	−0.0928688	+	0.160854i
$929$	20.0150	−	11.5557i	0.656671	−	0.379129i	−0.134336	−	0.990936i	$-0.542890\pi$
$929$	20.0150	−	11.5557i	0.656671	−	0.379129i	0.791008	+	0.611806i	$0.209557\pi$
$930$		0			0
$931$	14.7164	+	49.1650i	0.482310	+	1.61132i
$932$		−	11.4196i		−	0.374060i
$933$		0			0
$934$	−19.8812	+	34.4353i	−0.650533	+	1.12676i
$935$	−4.97394	+	3.06310i	−0.162665	+	0.100174i
$936$		0			0
$937$	21.7695			0.711180			0.355590	−	0.934642i	$-0.384280\pi$
$937$	21.7695			0.711180			0.355590	+	0.934642i	$0.384280\pi$
$938$	2.65994	−	22.7523i	0.0868500	−	0.742890i
$939$		0			0
$940$	0.379328	+	0.657015i	0.0123723	+	0.0214295i
$941$	5.39515	−	9.34467i	0.175877	−	0.304628i	−0.764588	−	0.644520i	$-0.777057\pi$
$941$	5.39515	−	9.34467i	0.175877	−	0.304628i	0.940464	+	0.339892i	$0.110391\pi$
$942$		0			0
$943$	−1.38216	−	2.39397i	−0.0450093	−	0.0779585i
$944$		−	2.31992i		−	0.0755068i
$945$		0			0
$946$	−10.0777	+	18.6586i	−0.327655	+	0.606643i
$947$	−4.56068	−	7.89933i	−0.148202	−	0.256694i	0.782361	−	0.622825i	$-0.214015\pi$
$947$	−4.56068	−	7.89933i	−0.148202	−	0.256694i	−0.930563	+	0.366132i	$0.880682\pi$
$948$		0			0
$949$	26.4442	−	45.8028i	0.858417	−	1.48682i
$950$	31.4271	−	18.1444i	1.01963	−	0.588684i
$951$		0			0
$952$	−16.6729	−	12.4132i	−0.540373	−	0.402314i
$953$		−	48.6873i		−	1.57714i	−0.614947	−	0.788568i	$-0.710823\pi$
$953$		−	48.6873i		−	1.57714i	0.614947	−	0.788568i	$-0.289177\pi$
$954$		0			0
$955$	−0.131715	−	0.0760460i	−0.00426221	−	0.00246079i
$956$	3.18067	+	1.83636i	0.102870	+	0.0593922i
$957$		0			0
$958$			18.6061i			0.601137i
$959$	17.9806	−	24.1509i	0.580625	−	0.779874i
$960$		0			0
$961$	−6.17512	−	10.6956i	−0.199198	−	0.345020i
$962$	−0.776579	−	0.448358i	−0.0250379	−	0.0144556i
$963$		0			0
$964$	−10.4731	−	18.1399i	−0.337316	−	0.584248i
$965$	5.37918			0.173162
$966$		0			0
$967$		−	38.8957i		−	1.25080i	−0.780304	−	0.625401i	$-0.784935\pi$
$967$		−	38.8957i		−	1.25080i	0.780304	−	0.625401i	$-0.215065\pi$
$968$	−9.82295	−	4.95072i	−0.315722	−	0.159122i
$969$		0			0
$970$	−0.769051	−	0.444012i	−0.0246928	−	0.0142564i
$971$	15.1953	−	8.77301i	0.487640	−	0.281539i	−0.235955	−	0.971764i	$-0.575822\pi$
$971$	15.1953	−	8.77301i	0.487640	−	0.281539i	0.723595	+	0.690225i	$0.242488\pi$
$972$		0			0
$973$	−37.0521	−	4.33170i	−1.18784	−	0.138868i
$974$		−	20.4689i		−	0.655867i
$975$		0			0
$976$	2.19784	−	3.80677i	0.0703511	−	0.121852i
$977$	−30.2650	+	52.4205i	−0.968263	+	1.67708i	−0.267683	+	0.963507i	$0.586258\pi$
$977$	−30.2650	+	52.4205i	−0.968263	+	1.67708i	−0.700580	+	0.713574i	$0.747075\pi$
$978$		0			0
$979$	30.6742	+	16.5675i	0.980352	+	0.529499i
$980$	0.361970	−	1.52694i	0.0115627	−	0.0487762i
$981$		0			0
$982$	14.7967	+	25.6286i	0.472180	+	0.817840i
$983$	33.6952	+	19.4539i	1.07471	+	0.620484i	0.929464	−	0.368912i	$-0.120270\pi$
$983$	33.6952	+	19.4539i	1.07471	+	0.620484i	0.145245	+	0.989396i	$0.453603\pi$
$984$		0			0
$985$	1.51259	+	2.61989i	0.0481952	+	0.0834765i
$986$	−44.4533			−1.41568
$987$		0			0
$988$	−36.8885			−1.17358
$989$	−26.9046	+	15.5334i	−0.855515	+	0.493932i
$990$		0			0
$991$	−7.41269	+	12.8391i	−0.235472	+	0.407849i	−0.959410	−	0.282016i	$-0.908997\pi$
$991$	−7.41269	+	12.8391i	−0.235472	+	0.407849i	0.723938	+	0.689865i	$0.242330\pi$
$992$	2.15927	+	3.73996i	0.0685568	+	0.118744i
$993$		0			0
$994$	28.4136	−	12.2556i	0.901225	−	0.388724i
$995$	4.04403			0.128204
$996$		0			0
$997$	2.94741	−	5.10507i	0.0933456	−	0.161679i	−0.815571	−	0.578657i	$-0.803577\pi$
$997$	2.94741	−	5.10507i	0.0933456	−	0.161679i	0.908917	+	0.416977i	$0.136911\pi$
$998$	6.44839	+	3.72298i	0.204120	+	0.117849i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bk.d.703.2	yes	32
3.2	odd	2	inner	1386.2.bk.d.703.9	yes	32
7.5	odd	6	inner	1386.2.bk.d.901.10	yes	32
11.10	odd	2	inner	1386.2.bk.d.703.10	yes	32
21.5	even	6	inner	1386.2.bk.d.901.1	yes	32
33.32	even	2	inner	1386.2.bk.d.703.1	✓	32
77.54	even	6	inner	1386.2.bk.d.901.2	yes	32
231.131	odd	6	inner	1386.2.bk.d.901.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bk.d.703.1	✓	32	33.32	even	2	inner
1386.2.bk.d.703.2	yes	32	1.1	even	1	trivial
1386.2.bk.d.703.9	yes	32	3.2	odd	2	inner
1386.2.bk.d.703.10	yes	32	11.10	odd	2	inner
1386.2.bk.d.901.1	yes	32	21.5	even	6	inner
1386.2.bk.d.901.2	yes	32	77.54	even	6	inner
1386.2.bk.d.901.9	yes	32	231.131	odd	6	inner
1386.2.bk.d.901.10	yes	32	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.194145 - 0.112089i) q^{5} +(-2.62785 - 0.307218i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.194145 - 0.112089i) q^{5} +(-2.62785 - 0.307218i) q^{7} +1.00000i q^{8} +(-0.112089 + 0.194145i) q^{10} +(-1.73915 - 2.82407i) q^{11} -5.03153 q^{13} +(2.42940 - 1.04787i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.92826 - 6.80394i) q^{17} +(3.66573 + 6.34924i) q^{19} -0.224179i q^{20} +(2.91818 + 1.57614i) q^{22} +(2.42940 + 4.20784i) q^{23} +(-2.47487 + 4.28660i) q^{25} +(4.35743 - 2.51576i) q^{26} +(-1.57999 + 2.12218i) q^{28} +5.65814i q^{29} +(3.73996 + 2.15927i) q^{31} +(0.866025 + 0.500000i) q^{32} +7.85652i q^{34} +(-0.544620 + 0.234910i) q^{35} +(-0.0891097 - 0.154343i) q^{37} +(-6.34924 - 3.66573i) q^{38} +(0.112089 + 0.194145i) q^{40} -0.568932 q^{41} +6.39391i q^{43} +(-3.31529 + 0.0941129i) q^{44} +(-4.20784 - 2.42940i) q^{46} +(-2.93076 + 1.69208i) q^{47} +(6.81123 + 1.61465i) q^{49} -4.94974i q^{50} +(-2.51576 + 4.35743i) q^{52} +(1.07478 - 1.86157i) q^{53} +(-0.654195 - 0.353338i) q^{55} +(0.307218 - 2.62785i) q^{56} +(-2.82907 - 4.90010i) q^{58} +(2.00911 + 1.15996i) q^{59} +(2.19784 + 3.80677i) q^{61} -4.31854 q^{62} -1.00000 q^{64} +(-0.976845 + 0.563982i) q^{65} +(4.32907 - 7.49817i) q^{67} +(-3.92826 - 6.80394i) q^{68} +(0.354200 - 0.475748i) q^{70} +11.6958 q^{71} +(-5.25571 + 9.10315i) q^{73} +(0.154343 + 0.0891097i) q^{74} +7.33147 q^{76} +(3.70262 + 7.95554i) q^{77} +(-8.75195 + 5.05294i) q^{79} +(-0.194145 - 0.112089i) q^{80} +(0.492709 - 0.284466i) q^{82} +14.2897 q^{83} -1.76127i q^{85} +(-3.19696 - 5.53729i) q^{86} +(2.82407 - 1.73915i) q^{88} +(-9.10315 + 5.25571i) q^{89} +(13.2221 + 1.54578i) q^{91} +4.85879 q^{92} +(1.69208 - 2.93076i) q^{94} +(1.42337 + 0.821781i) q^{95} +3.96123i q^{97} +(-6.70603 + 2.00729i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4}+O(q^{10}) \) 32 * q + 16 * q^4	\( 32 q + 16 q^{4} - 16 q^{16} + 20 q^{22} + 36 q^{25} + 12 q^{31} - 20 q^{37} - 44 q^{49} - 32 q^{64} + 48 q^{67} + 36 q^{70} + 72 q^{82} + 10 q^{88} + 144 q^{91}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 + 36 * q^25 + 12 * q^31 - 20 * q^37 - 44 * q^49 - 32 * q^64 + 48 * q^67 + 36 * q^70 + 72 * q^82 + 10 * q^88 + 144 * q^91

Introduction

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