LMFDB - Embedded newform 512.2.k.a.273.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [512,2,Mod(17,512)] 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("512.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(512, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.k (of order $32$, degree $16$, not 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			273.8
Character	$\chi$	$=$	512.273
Dual form			512.2.k.a.497.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.135634 + 0.0724978i) q^{3} +(2.12942 - 2.59470i) q^{5} +(1.11060 + 0.742082i) q^{7} +(-1.65357 - 2.47474i) q^{9} +(0.181497 + 0.0550566i) q^{11} +(0.374137 - 0.307046i) q^{13} +(0.476932 - 0.197552i) q^{15} +(1.79255 + 0.742500i) q^{17} +(0.487163 - 4.94625i) q^{19} +(0.0968362 + 0.181168i) q^{21} +(-5.40603 - 1.07533i) q^{23} +(-1.22261 - 6.14649i) q^{25} +(-0.0900899 - 0.914698i) q^{27} +(2.45765 + 8.10178i) q^{29} +(-3.30297 + 3.30297i) q^{31} +(0.0206257 + 0.0206257i) q^{33} +(4.29042 - 1.30149i) q^{35} +(8.32789 - 0.820226i) q^{37} +(0.0730059 - 0.0145218i) q^{39} +(0.580168 - 2.91670i) q^{41} +(8.36535 - 4.47137i) q^{43} +(-9.94237 - 0.979238i) q^{45} +(3.57155 - 8.62250i) q^{47} +(-1.99603 - 4.81884i) q^{49} +(0.189301 + 0.230664i) q^{51} +(-3.12341 + 10.2965i) q^{53} +(0.529339 - 0.353693i) q^{55} +(0.424668 - 0.635561i) q^{57} +(10.8483 + 8.90293i) q^{59} +(0.339850 - 0.635815i) q^{61} -3.97554i q^{63} -1.62460i q^{65} +(0.0570291 - 0.106694i) q^{67} +(-0.655283 - 0.537776i) q^{69} +(-8.81399 + 13.1911i) q^{71} +(-1.93431 + 1.29247i) q^{73} +(0.279780 - 0.922310i) q^{75} +(0.160715 + 0.195832i) q^{77} +(3.11404 + 7.51796i) q^{79} +(-3.36290 + 8.11876i) q^{81} +(-14.1505 - 1.39370i) q^{83} +(5.74366 - 3.07005i) q^{85} +(-0.254021 + 1.27705i) q^{87} +(-1.57448 + 0.313183i) q^{89} +(0.643371 - 0.0633666i) q^{91} +(-0.687453 + 0.208537i) q^{93} +(-11.7967 - 11.7967i) q^{95} +(-11.0877 + 11.0877i) q^{97} +(-0.163868 - 0.540199i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{23}{32}\right)$	$1$

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
$3$	0.135634	+	0.0724978i	0.0783083	+	0.0418566i	0.510086	−	0.860123i	$-0.329614\pi$
$3$	0.135634	+	0.0724978i	0.0783083	+	0.0418566i	−0.431778	+	0.901980i	$0.642114\pi$
$4$		0			0
$5$	2.12942	−	2.59470i	0.952305	−	1.16039i	−0.0346516	−	0.999399i	$-0.511032\pi$
$5$	2.12942	−	2.59470i	0.952305	−	1.16039i	0.986956	−	0.160987i	$-0.0514678\pi$
$6$		0			0
$7$	1.11060	+	0.742082i	0.419769	+	0.280480i	0.747463	−	0.664303i	$-0.231272\pi$
$7$	1.11060	+	0.742082i	0.419769	+	0.280480i	−0.327694	+	0.944784i	$0.606272\pi$
$8$		0			0
$9$	−1.65357	−	2.47474i	−0.551190	−	0.824914i
$10$		0			0
$11$	0.181497	+	0.0550566i	0.0547235	+	0.0166002i	0.317528	−	0.948249i	$-0.397147\pi$
$11$	0.181497	+	0.0550566i	0.0547235	+	0.0166002i	−0.262804	+	0.964849i	$0.584647\pi$
$12$		0			0
$13$	0.374137	−	0.307046i	0.103767	−	0.0851593i	−0.581079	−	0.813847i	$-0.697369\pi$
$13$	0.374137	−	0.307046i	0.103767	−	0.0851593i	0.684846	+	0.728688i	$0.259869\pi$
$14$		0			0
$15$	0.476932	−	0.197552i	0.123143	−	0.0510076i
$16$		0			0
$17$	1.79255	+	0.742500i	0.434758	+	0.180083i	0.589319	−	0.807901i	$-0.299396\pi$
$17$	1.79255	+	0.742500i	0.434758	+	0.180083i	−0.154561	+	0.987983i	$0.549396\pi$
$18$		0			0
$19$	0.487163	−	4.94625i	0.111763	−	1.13475i	−0.761724	−	0.647901i	$-0.775647\pi$
$19$	0.487163	−	4.94625i	0.111763	−	1.13475i	0.873487	−	0.486847i	$-0.161853\pi$
$20$		0			0
$21$	0.0968362	+	0.181168i	0.0211314	+	0.0395340i
$22$		0			0
$23$	−5.40603	−	1.07533i	−1.12724	−	0.224221i	−0.403958	−	0.914778i	$-0.632366\pi$
$23$	−5.40603	−	1.07533i	−1.12724	−	0.224221i	−0.723278	+	0.690557i	$0.757366\pi$
$24$		0			0
$25$	−1.22261	−	6.14649i	−0.244523	−	1.22930i
$26$		0			0
$27$	−0.0900899	−	0.914698i	−0.0173378	−	0.176034i
$28$		0			0
$29$	2.45765	+	8.10178i	0.456374	+	1.50446i	0.819695	+	0.572800i	$0.194143\pi$
$29$	2.45765	+	8.10178i	0.456374	+	1.50446i	−0.363321	+	0.931664i	$0.618357\pi$
$30$		0			0
$31$	−3.30297	+	3.30297i	−0.593232	+	0.593232i	−0.938503	−	0.345271i	$-0.887787\pi$
$31$	−3.30297	+	3.30297i	−0.593232	+	0.593232i	0.345271	+	0.938503i	$0.387787\pi$
$32$		0			0
$33$	0.0206257	+	0.0206257i	0.00359047	+	0.00359047i
$34$		0			0
$35$	4.29042	−	1.30149i	0.725214	−	0.219991i
$36$		0			0
$37$	8.32789	−	0.820226i	1.36910	−	0.134844i	0.613404	−	0.789770i	$-0.289800\pi$
$37$	8.32789	−	0.820226i	1.36910	−	0.134844i	0.755694	+	0.654925i	$0.227300\pi$
$38$		0			0
$39$	0.0730059	−	0.0145218i	0.0116903	−	0.00232534i
$40$		0			0
$41$	0.580168	−	2.91670i	0.0906070	−	0.455512i	−0.908671	−	0.417513i	$-0.862902\pi$
$41$	0.580168	−	2.91670i	0.0906070	−	0.455512i	0.999278	−	0.0379988i	$-0.0120983\pi$
$42$		0			0
$43$	8.36535	−	4.47137i	1.27570	−	0.681878i	0.312313	−	0.949979i	$-0.398896\pi$
$43$	8.36535	−	4.47137i	1.27570	−	0.681878i	0.963391	+	0.268101i	$0.0863962\pi$
$44$		0			0
$45$	−9.94237	−	0.979238i	−1.48212	−	0.145976i
$46$		0			0
$47$	3.57155	−	8.62250i	0.520965	−	1.25772i	−0.416340	−	0.909209i	$-0.636687\pi$
$47$	3.57155	−	8.62250i	0.520965	−	1.25772i	0.937305	−	0.348511i	$-0.113313\pi$
$48$		0			0
$49$	−1.99603	−	4.81884i	−0.285147	−	0.688406i
$50$		0			0
$51$	0.189301	+	0.230664i	0.0265075	+	0.0322995i
$52$		0			0
$53$	−3.12341	+	10.2965i	−0.429033	+	1.41433i	0.430194	+	0.902737i	$0.358445\pi$
$53$	−3.12341	+	10.2965i	−0.429033	+	1.41433i	−0.859227	+	0.511595i	$0.829055\pi$
$54$		0			0
$55$	0.529339	−	0.353693i	0.0713761	−	0.0476920i
$56$		0			0
$57$	0.424668	−	0.635561i	0.0562487	−	0.0841822i
$58$		0			0
$59$	10.8483	+	8.90293i	1.41232	+	1.15906i	0.964227	+	0.265077i	$0.0853974\pi$
$59$	10.8483	+	8.90293i	1.41232	+	1.15906i	0.448095	+	0.893986i	$0.352103\pi$
$60$		0			0
$61$	0.339850	−	0.635815i	0.0435134	−	0.0814078i	−0.859225	−	0.511598i	$-0.829054\pi$
$61$	0.339850	−	0.635815i	0.0435134	−	0.0814078i	0.902738	+	0.430190i	$0.141554\pi$
$62$		0			0
$63$		−	3.97554i		−	0.500871i
$64$		0			0
$65$		−	1.62460i		−	0.201507i
$66$		0			0
$67$	0.0570291	−	0.106694i	0.00696721	−	0.0130347i	−0.878414	−	0.477901i	$-0.841398\pi$
$67$	0.0570291	−	0.106694i	0.00696721	−	0.0130347i	0.885381	+	0.464866i	$0.153898\pi$
$68$		0			0
$69$	−0.655283	−	0.537776i	−0.0788867	−	0.0647407i
$70$		0			0
$71$	−8.81399	+	13.1911i	−1.04603	+	1.56549i	−0.242567	+	0.970135i	$0.577989\pi$
$71$	−8.81399	+	13.1911i	−1.04603	+	1.56549i	−0.803461	+	0.595357i	$0.797011\pi$
$72$		0			0
$73$	−1.93431	+	1.29247i	−0.226394	+	0.151272i	−0.663595	−	0.748092i	$-0.730970\pi$
$73$	−1.93431	+	1.29247i	−0.226394	+	0.151272i	0.437200	+	0.899364i	$0.355970\pi$
$74$		0			0
$75$	0.279780	−	0.922310i	0.0323062	−	0.106499i
$76$		0			0
$77$	0.160715	+	0.195832i	0.0183152	+	0.0223171i
$78$		0			0
$79$	3.11404	+	7.51796i	0.350357	+	0.845837i	0.996576	+	0.0826847i	$0.0263494\pi$
$79$	3.11404	+	7.51796i	0.350357	+	0.845837i	−0.646219	+	0.763152i	$0.723651\pi$
$80$		0			0
$81$	−3.36290	+	8.11876i	−0.373656	+	0.902085i
$82$		0			0
$83$	−14.1505	−	1.39370i	−1.55322	−	0.152979i	−0.715318	−	0.698799i	$-0.753718\pi$
$83$	−14.1505	−	1.39370i	−1.55322	−	0.152979i	−0.837903	+	0.545820i	$0.816218\pi$
$84$		0			0
$85$	5.74366	−	3.07005i	0.622988	−	0.332994i
$86$		0			0
$87$	−0.254021	+	1.27705i	−0.0272339	+	0.136914i
$88$		0			0
$89$	−1.57448	+	0.313183i	−0.166894	+	0.0331974i	−0.277830	−	0.960630i	$-0.589615\pi$
$89$	−1.57448	+	0.313183i	−0.166894	+	0.0331974i	0.110936	+	0.993828i	$0.464615\pi$
$90$		0			0
$91$	0.643371	−	0.0633666i	0.0674437	−	0.00664262i
$92$		0			0
$93$	−0.687453	+	0.208537i	−0.0712856	+	0.0216243i
$94$		0			0
$95$	−11.7967	−	11.7967i	−1.21031	−	1.21031i
$96$		0			0
$97$	−11.0877	+	11.0877i	−1.12578	+	1.12578i	−0.134927	+	0.990856i	$0.543080\pi$
$97$	−11.0877	+	11.0877i	−1.12578	+	1.12578i	−0.990856	+	0.134927i	$0.956920\pi$
$98$		0			0
$99$	−0.163868	−	0.540199i	−0.0164693	−	0.0542920i
$100$		0			0
$101$	0.150952	+	1.53264i	0.0150203	+	0.152504i	0.999769	−	0.0214772i	$-0.00683695\pi$
$101$	0.150952	+	1.53264i	0.0150203	+	0.152504i	−0.984749	+	0.173981i	$0.944337\pi$
$102$		0			0
$103$	2.60627	+	13.1026i	0.256804	+	1.29104i	0.866808	+	0.498642i	$0.166168\pi$
$103$	2.60627	+	13.1026i	0.256804	+	1.29104i	−0.610004	+	0.792398i	$0.708832\pi$
$104$		0			0
$105$	0.676281	+	0.134521i	0.0659983	+	0.0131279i
$106$		0			0
$107$	−2.08456	−	3.89993i	−0.201522	−	0.377021i	0.760778	−	0.649012i	$-0.224818\pi$
$107$	−2.08456	−	3.89993i	−0.201522	−	0.377021i	−0.962300	+	0.271992i	$0.912318\pi$
$108$		0			0
$109$	−0.181097	+	1.83871i	−0.0173459	+	0.176116i	−0.999954	−	0.00957465i	$-0.996952\pi$
$109$	−0.181097	+	1.83871i	−0.0173459	+	0.176116i	0.982608	+	0.185691i	$0.0594522\pi$
$110$		0			0
$111$	1.18901	+	0.492504i	0.112856	+	0.0467464i
$112$		0			0
$113$	3.84674	−	1.59337i	0.361871	−	0.149892i	−0.194337	−	0.980935i	$-0.562256\pi$
$113$	3.84674	−	1.59337i	0.361871	−	0.149892i	0.556208	+	0.831043i	$0.312256\pi$
$114$		0			0
$115$	−14.3019	+	11.7372i	−1.33366	+	1.09450i
$116$		0			0
$117$	−1.37852	−	0.418170i	−0.127444	−	0.0386599i
$118$		0			0
$119$	1.43982	+	2.15484i	0.131988	+	0.197534i
$120$		0			0
$121$	−9.11626	−	6.09129i	−0.828751	−	0.553753i
$122$		0			0
$123$	0.290145	−	0.353543i	0.0261615	−	0.0318779i
$124$		0			0
$125$	−3.75040	−	2.00463i	−0.335446	−	0.179300i
$126$		0			0
$127$	8.79384			0.780328			0.390164	−	0.920745i	$-0.372418\pi$
$127$	8.79384			0.780328			0.390164	+	0.920745i	$0.372418\pi$
$128$		0			0
$129$	1.45879			0.128439
$130$		0			0
$131$	−12.3982	−	6.62696i	−1.08323	−	0.579000i	−0.169589	−	0.985515i	$-0.554244\pi$
$131$	−12.3982	−	6.62696i	−1.08323	−	0.579000i	−0.913644	+	0.406515i	$0.866744\pi$
$132$		0			0
$133$	4.21157	−	5.13181i	0.365189	−	0.444985i
$134$		0			0
$135$	−2.56521	−	1.71402i	−0.220778	−	0.147519i
$136$		0			0
$137$	5.95510	+	8.91243i	0.508778	+	0.761440i	0.993574	−	0.113187i	$-0.0361060\pi$
$137$	5.95510	+	8.91243i	0.508778	+	0.761440i	−0.484796	+	0.874628i	$0.661106\pi$
$138$		0			0
$139$	0.316667	+	0.0960600i	0.0268594	+	0.00814770i	0.303686	−	0.952772i	$-0.401783\pi$
$139$	0.316667	+	0.0960600i	0.0268594	+	0.00814770i	−0.276826	+	0.960920i	$0.589283\pi$
$140$		0			0
$141$	1.10954	−	0.910573i	0.0934398	−	0.0766840i
$142$		0			0
$143$	0.0848098	−	0.0351294i	0.00709215	−	0.00293766i
$144$		0			0
$145$	26.2551	+	10.8752i	2.18037	+	0.903137i
$146$		0			0
$147$	0.0786262	−	0.798306i	0.00648498	−	0.0658431i
$148$		0			0
$149$	0.739789	+	1.38405i	0.0606059	+	0.113386i	0.910400	−	0.413729i	$-0.135774\pi$
$149$	0.739789	+	1.38405i	0.0606059	+	0.113386i	−0.849794	+	0.527115i	$0.823274\pi$
$150$		0			0
$151$	12.0809	+	2.40303i	0.983126	+	0.195556i	0.660382	−	0.750930i	$-0.270394\pi$
$151$	12.0809	+	2.40303i	0.983126	+	0.195556i	0.322745	+	0.946486i	$0.395394\pi$
$152$		0			0
$153$	−1.12662	−	5.66388i	−0.0910815	−	0.457898i
$154$		0			0
$155$	1.53683	+	15.6036i	0.123441	+	1.25332i
$156$		0			0
$157$	2.19799	+	7.24581i	0.175419	+	0.578278i	0.999923	+	0.0124222i	$0.00395422\pi$
$157$	2.19799	+	7.24581i	0.175419	+	0.578278i	−0.824504	+	0.565856i	$0.808546\pi$
$158$		0			0
$159$	−1.17011	+	1.17011i	−0.0927960	+	0.0927960i
$160$		0			0
$161$	−5.20598	−	5.20598i	−0.410289	−	0.410289i
$162$		0			0
$163$	15.2055	−	4.61255i	1.19099	−	0.361283i	0.368264	−	0.929721i	$-0.379952\pi$
$163$	15.2055	−	4.61255i	1.19099	−	0.361283i	0.822726	+	0.568439i	$0.192452\pi$
$164$		0			0
$165$	0.0974383	−	0.00959683i	0.00758556	−	0.000747113i
$166$		0			0
$167$	−14.9692	+	2.97756i	−1.15835	+	0.230410i	−0.736618	−	0.676310i	$-0.763578\pi$
$167$	−14.9692	+	2.97756i	−1.15835	+	0.230410i	−0.421733	+	0.906720i	$0.638578\pi$
$168$		0			0
$169$	−2.49047	+	12.5205i	−0.191575	+	0.963112i
$170$		0			0
$171$	−13.0463	+	6.97337i	−0.997673	+	0.533267i
$172$		0			0
$173$	−15.3857	−	1.51536i	−1.16975	−	0.115210i	−0.505572	−	0.862784i	$-0.668719\pi$
$173$	−15.3857	−	1.51536i	−1.16975	−	0.115210i	−0.664179	+	0.747574i	$0.731219\pi$
$174$		0			0
$175$	3.20336	−	7.73360i	0.242151	−	0.584605i
$176$		0			0
$177$	0.825948	+	1.99401i	0.0620820	+	0.149879i
$178$		0			0
$179$	8.70051	+	10.6016i	0.650307	+	0.792401i	0.988908	−	0.148529i	$-0.0474538\pi$
$179$	8.70051	+	10.6016i	0.650307	+	0.792401i	−0.338601	+	0.940930i	$0.609954\pi$
$180$		0			0
$181$	2.43393	−	8.02359i	0.180913	−	0.596389i	−0.818837	−	0.574026i	$-0.805381\pi$
$181$	2.43393	−	8.02359i	0.180913	−	0.596389i	0.999750	−	0.0223633i	$-0.00711904\pi$
$182$		0			0
$183$	0.0921905	−	0.0615997i	0.00681492	−	0.00455358i
$184$		0			0
$185$	15.6053	−	23.3550i	1.14733	−	1.71710i
$186$		0			0
$187$	0.284464	+	0.233454i	0.0208021	+	0.0170718i
$188$		0			0
$189$	0.578727	−	1.08272i	0.0420962	−	0.0787564i
$190$		0			0
$191$		−	5.63943i		−	0.408055i	−0.978965	−	0.204027i	$-0.934597\pi$
$191$		−	5.63943i		−	0.408055i	0.978965	−	0.204027i	$-0.0654032\pi$
$192$		0			0
$193$			2.21104i			0.159154i	0.996829	+	0.0795769i	$0.0253569\pi$
$193$			2.21104i			0.159154i	−0.996829	+	0.0795769i	$0.974643\pi$
$194$		0			0
$195$	0.117780	−	0.220351i	0.00843442	−	0.0157797i
$196$		0			0
$197$	−6.53350	−	5.36190i	−0.465493	−	0.382020i	0.372208	−	0.928149i	$-0.378601\pi$
$197$	−6.53350	−	5.36190i	−0.465493	−	0.382020i	−0.837701	+	0.546129i	$0.816101\pi$
$198$		0			0
$199$	7.32240	−	10.9587i	0.519071	−	0.776845i	−0.475631	−	0.879645i	$-0.657780\pi$
$199$	7.32240	−	10.9587i	0.519071	−	0.776845i	0.994702	+	0.102800i	$0.0327802\pi$
$200$		0			0
$201$	0.0154701	−	0.0103368i	0.00109118	−	0.000729103i
$202$		0			0
$203$	−3.28271	+	10.8216i	−0.230401	+	0.759531i
$204$		0			0
$205$	−6.33255	−	7.71624i	−0.442285	−	0.538926i
$206$		0			0
$207$	6.27810	+	15.1567i	0.436358	+	1.05346i
$208$		0			0
$209$	0.360743	−	0.870910i	0.0249531	−	0.0602421i
$210$		0			0
$211$	5.77547	+	0.568835i	0.397600	+	0.0391602i	0.294842	−	0.955546i	$-0.404733\pi$
$211$	5.77547	+	0.568835i	0.397600	+	0.0391602i	0.102758	+	0.994706i	$0.467233\pi$
$212$		0			0
$213$	−2.15180	+	1.15016i	−0.147439	+	0.0788077i
$214$		0			0
$215$	6.21144	−	31.2270i	0.423617	−	2.12967i
$216$		0			0
$217$	−6.11937	+	1.21722i	−0.415410	+	0.0826302i
$218$		0			0
$219$	−0.356060	+	0.0350688i	−0.0240603	+	0.00236973i
$220$		0			0
$221$	0.898642	−	0.272600i	0.0604492	−	0.0183371i
$222$		0			0
$223$	−1.95160	−	1.95160i	−0.130689	−	0.130689i	0.638737	−	0.769425i	$-0.279457\pi$
$223$	−1.95160	−	1.95160i	−0.130689	−	0.130689i	−0.769425	+	0.638737i	$0.779457\pi$
$224$		0			0
$225$	−13.1893	+	13.1893i	−0.879287	+	0.879287i
$226$		0			0
$227$	−4.38810	−	14.4656i	−0.291248	−	0.960117i	−0.973440	−	0.228944i	$-0.926473\pi$
$227$	−4.38810	−	14.4656i	−0.291248	−	0.960117i	0.682191	−	0.731174i	$-0.261027\pi$
$228$		0			0
$229$	0.0144057	+	0.146264i	0.000951955	+	0.00966536i	0.995649	−	0.0931833i	$-0.0297043\pi$
$229$	0.0144057	+	0.146264i	0.000951955	+	0.00966536i	−0.994697	+	0.102849i	$0.967204\pi$
$230$		0			0
$231$	0.00760102	+	0.0382129i	0.000500111	+	0.00251423i
$232$		0			0
$233$	−20.2728	−	4.03251i	−1.32811	−	0.264178i	−0.520486	−	0.853870i	$-0.674249\pi$
$233$	−20.2728	−	4.03251i	−1.32811	−	0.264178i	−0.807628	+	0.589692i	$0.799249\pi$
$234$		0			0
$235$	−14.7675	−	27.6280i	−0.963325	−	1.80225i
$236$		0			0
$237$	−0.122666	+	1.24545i	−0.00796803	+	0.0809008i
$238$		0			0
$239$	12.4323	+	5.14962i	0.804177	+	0.333101i	0.746628	−	0.665242i	$-0.231671\pi$
$239$	12.4323	+	5.14962i	0.804177	+	0.333101i	0.0575490	+	0.998343i	$0.481671\pi$
$240$		0			0
$241$	16.5636	−	6.86086i	1.06695	−	0.441947i	0.221039	−	0.975265i	$-0.429055\pi$
$241$	16.5636	−	6.86086i	1.06695	−	0.441947i	0.845915	+	0.533318i	$0.179055\pi$
$242$		0			0
$243$	−3.17619	+	2.60664i	−0.203753	+	0.167216i
$244$		0			0
$245$	−16.7538	−	5.08222i	−1.07036	−	0.324691i
$246$		0			0
$247$	−1.33646	−	2.00016i	−0.0850371	−	0.127267i
$248$		0			0
$249$	−1.81825	−	1.21492i	−0.115227	−	0.0769921i
$250$		0			0
$251$	10.4175	−	12.6937i	0.657546	−	0.801222i	−0.332329	−	0.943164i	$-0.607834\pi$
$251$	10.4175	−	12.6937i	0.657546	−	0.801222i	0.989875	+	0.141941i	$0.0453344\pi$
$252$		0			0
$253$	−0.921976	−	0.492807i	−0.0579642	−	0.0309825i
$254$		0			0
$255$	1.00161			0.0627231
$256$		0			0
$257$	4.49360			0.280303			0.140152	−	0.990130i	$-0.455241\pi$
$257$	4.49360			0.280303			0.140152	+	0.990130i	$0.455241\pi$
$258$		0			0
$259$	9.85766	+	5.26903i	0.612525	+	0.327402i
$260$		0			0
$261$	15.9859	−	19.4789i	0.989504	−	1.20571i
$262$		0			0
$263$	−14.2440	−	9.51756i	−0.878325	−	0.586878i	0.0325916	−	0.999469i	$-0.489624\pi$
$263$	−14.2440	−	9.51756i	−0.878325	−	0.586878i	−0.910916	+	0.412591i	$0.864624\pi$
$264$		0			0
$265$	20.0653	+	30.0299i	1.23260	+	1.84472i
$266$		0			0
$267$	−0.236258	−	0.0716680i	−0.0144587	−	0.00438601i
$268$		0			0
$269$	11.4987	−	9.43672i	0.701087	−	0.575367i	−0.214870	−	0.976643i	$-0.568933\pi$
$269$	11.4987	−	9.43672i	0.701087	−	0.575367i	0.915957	+	0.401275i	$0.131433\pi$
$270$		0			0
$271$	11.5173	−	4.77061i	0.699624	−	0.289794i	−0.00437943	−	0.999990i	$-0.501394\pi$
$271$	11.5173	−	4.77061i	0.699624	−	0.289794i	0.704003	+	0.710197i	$0.251394\pi$
$272$		0			0
$273$	0.0918569	+	0.0380484i	0.00555943	+	0.00230279i
$274$		0			0
$275$	0.116504	−	1.18288i	0.00702545	−	0.0713306i
$276$		0			0
$277$	5.09008	+	9.52286i	0.305833	+	0.572173i	0.987146	−	0.159819i	$-0.0510909\pi$
$277$	5.09008	+	9.52286i	0.305833	+	0.572173i	−0.681313	+	0.731992i	$0.738591\pi$
$278$		0			0
$279$	13.6357	+	2.71231i	0.816348	+	0.162382i
$280$		0			0
$281$	5.00511	+	25.1624i	0.298580	+	1.50106i	0.780671	+	0.624942i	$0.214877\pi$
$281$	5.00511	+	25.1624i	0.298580	+	1.50106i	−0.482091	+	0.876121i	$0.660123\pi$
$282$		0			0
$283$	1.47858	+	15.0123i	0.0878928	+	0.892390i	0.933498	+	0.358582i	$0.116740\pi$
$283$	1.47858	+	15.0123i	0.0878928	+	0.892390i	−0.845606	+	0.533808i	$0.820760\pi$
$284$		0			0
$285$	−0.744796	−	2.45526i	−0.0441179	−	0.145437i
$286$		0			0
$287$	2.80877	−	2.80877i	0.165796	−	0.165796i
$288$		0			0
$289$	−9.35887	−	9.35887i	−0.550522	−	0.550522i
$290$		0			0
$291$	−2.30770	+	0.700032i	−0.135280	+	0.0410366i
$292$		0			0
$293$	0.107888	−	0.0106261i	0.00630290	−	0.000620782i	−0.0948652	−	0.995490i	$-0.530242\pi$
$293$	0.107888	−	0.0106261i	0.00630290	−	0.000620782i	0.101168	+	0.994869i	$0.467742\pi$
$294$		0			0
$295$	46.2009	−	9.18994i	2.68992	−	0.535059i
$296$		0			0
$297$	0.0340091	−	0.170975i	0.00197341	−	0.00992099i
$298$		0			0
$299$	−2.35277	+	1.25758i	−0.136064	+	0.0727279i
$300$		0			0
$301$	12.6087	+	1.24185i	0.726754	+	0.0715790i
$302$		0			0
$303$	−0.0906390	+	0.218822i	−0.00520707	+	0.0125710i
$304$		0			0
$305$	−0.926069	−	2.23573i	−0.0530266	−	0.128017i
$306$		0			0
$307$	−11.1702	−	13.6110i	−0.637518	−	0.776818i	0.349585	−	0.936905i	$-0.386323\pi$
$307$	−11.1702	−	13.6110i	−0.637518	−	0.776818i	−0.987103	+	0.160087i	$0.948823\pi$
$308$		0			0
$309$	−0.596413	+	1.96611i	−0.0339287	+	0.111848i
$310$		0			0
$311$	−18.5250	+	12.3780i	−1.05045	+	0.701891i	−0.955919	−	0.293630i	$-0.905137\pi$
$311$	−18.5250	+	12.3780i	−1.05045	+	0.701891i	−0.0945355	+	0.995521i	$0.530137\pi$
$312$		0			0
$313$	8.47932	−	12.6902i	0.479279	−	0.717292i	−0.510503	−	0.859876i	$-0.670541\pi$
$313$	8.47932	−	12.6902i	0.479279	−	0.717292i	0.989783	+	0.142583i	$0.0455409\pi$
$314$		0			0
$315$	−10.3154	−	8.46559i	−0.581204	−	0.476982i
$316$		0			0
$317$	0.174406	−	0.326290i	0.00979561	−	0.0183263i	−0.876976	−	0.480534i	$-0.840443\pi$
$317$	0.174406	−	0.326290i	0.00979561	−	0.0183263i	0.886771	+	0.462208i	$0.152943\pi$
$318$		0			0
$319$			1.60576i			0.0899054i
$320$		0			0
$321$		−	0.680089i		−	0.0379589i
$322$		0			0
$323$	4.54586	−	8.50470i	0.252938	−	0.473214i
$324$		0			0
$325$	−2.34468	−	1.92423i	−0.130060	−	0.106737i
$326$		0			0
$327$	−0.157865	+	0.236262i	−0.00872995	+	0.0130653i
$328$		0			0
$329$	10.3652	−	6.92579i	0.571451	−	0.381831i
$330$		0			0
$331$	2.83863	−	9.35771i	0.156025	−	0.514346i	−0.843723	−	0.536779i	$-0.819641\pi$
$331$	2.83863	−	9.35771i	0.156025	−	0.514346i	0.999748	+	0.0224324i	$0.00714106\pi$
$332$		0			0
$333$	−15.8006	−	19.2531i	−0.865868	−	1.05506i
$334$		0			0
$335$	−0.155400	−	0.375169i	−0.00849042	−	0.0204977i
$336$		0			0
$337$	1.79808	−	4.34094i	0.0979475	−	0.236466i	−0.867309	−	0.497770i	$-0.834152\pi$
$337$	1.79808	−	4.34094i	0.0979475	−	0.236466i	0.965257	+	0.261304i	$0.0841524\pi$
$338$		0			0
$339$	0.637265	+	0.0627651i	0.0346115	+	0.00340893i
$340$		0			0
$341$	−0.781331	+	0.417630i	−0.0423114	+	0.0226159i
$342$		0			0
$343$	3.18327	−	16.0034i	0.171880	−	0.864100i
$344$		0			0
$345$	−2.79074	+	0.555113i	−0.150248	+	0.0298863i
$346$		0			0
$347$	−20.0724	+	1.97696i	−1.07754	+	0.106129i	−0.621182	−	0.783666i	$-0.713347\pi$
$347$	−20.0724	+	1.97696i	−1.07754	+	0.106129i	−0.456360	+	0.889795i	$0.650847\pi$
$348$		0			0
$349$	27.5367	−	8.35317i	1.47401	−	0.447135i	0.551847	−	0.833946i	$-0.313923\pi$
$349$	27.5367	−	8.35317i	1.47401	−	0.447135i	0.922159	+	0.386811i	$0.126423\pi$
$350$		0			0
$351$	−0.314561	−	0.314561i	−0.0167900	−	0.0167900i
$352$		0			0
$353$	12.0137	−	12.0137i	0.639425	−	0.639425i	−0.310989	−	0.950414i	$-0.600660\pi$
$353$	12.0137	−	12.0137i	0.639425	−	0.639425i	0.950414	+	0.310989i	$0.100660\pi$
$354$		0			0
$355$	15.4582	+	50.9590i	0.820438	+	2.70462i
$356$		0			0
$357$	0.0390670	+	0.396654i	0.00206764	+	0.0209931i
$358$		0			0
$359$	6.61583	+	33.2600i	0.349170	+	1.75540i	0.612290	+	0.790633i	$0.290248\pi$
$359$	6.61583	+	33.2600i	0.349170	+	1.75540i	−0.263120	+	0.964763i	$0.584752\pi$
$360$		0			0
$361$	−5.59318	−	1.11255i	−0.294378	−	0.0585554i
$362$		0			0
$363$	−0.794868	−	1.48709i	−0.0417198	−	0.0780522i
$364$		0			0
$365$	−0.765394	+	7.77117i	−0.0400625	+	0.406762i
$366$		0			0
$367$	−22.3629	−	9.26301i	−1.16733	−	0.483525i	−0.287023	−	0.957924i	$-0.592666\pi$
$367$	−22.3629	−	9.26301i	−1.16733	−	0.483525i	−0.880310	+	0.474399i	$0.842666\pi$
$368$		0			0
$369$	−8.17743	+	3.38720i	−0.425700	+	0.176331i
$370$		0			0
$371$	−11.1097	+	9.11750i	−0.576787	+	0.473357i
$372$		0			0
$373$	−31.7137	−	9.62025i	−1.64207	−	0.498118i	−0.671923	−	0.740621i	$-0.734532\pi$
$373$	−31.7137	−	9.62025i	−1.64207	−	0.498118i	−0.970151	+	0.242503i	$0.922032\pi$
$374$		0			0
$375$	−0.363350	−	0.543792i	−0.0187633	−	0.0280813i
$376$		0			0
$377$	3.40712	+	2.27657i	0.175476	+	0.117249i
$378$		0			0
$379$	3.38631	−	4.12623i	0.173943	−	0.211950i	−0.678740	−	0.734379i	$-0.737474\pi$
$379$	3.38631	−	4.12623i	0.173943	−	0.211950i	0.852683	+	0.522428i	$0.174974\pi$
$380$		0			0
$381$	1.19274	+	0.637535i	0.0611061	+	0.0326619i
$382$		0			0
$383$	−13.1180			−0.670298			−0.335149	−	0.942165i	$-0.608787\pi$
$383$	−13.1180			−0.670298			−0.335149	+	0.942165i	$0.608787\pi$
$384$		0			0
$385$	0.850355			0.0433381
$386$		0			0
$387$	−24.8982	−	13.3084i	−1.26565	−	0.676502i
$388$		0			0
$389$	−0.145657	+	0.177483i	−0.00738509	+	0.00899876i	−0.776690	−	0.629883i	$-0.783103\pi$
$389$	−0.145657	+	0.177483i	−0.00738509	+	0.00899876i	0.769305	+	0.638882i	$0.220603\pi$
$390$		0			0
$391$	−8.89217	−	5.94156i	−0.449697	−	0.300478i
$392$		0			0
$393$	−1.20117	−	1.79768i	−0.0605911	−	0.0906810i
$394$		0			0
$395$	26.1380	+	7.92887i	1.31515	+	0.398945i
$396$		0			0
$397$	14.6428	−	12.0170i	0.734899	−	0.603116i	−0.190688	−	0.981651i	$-0.561072\pi$
$397$	14.6428	−	12.0170i	0.734899	−	0.603116i	0.925587	+	0.378535i	$0.123572\pi$
$398$		0			0
$399$	0.943277	−	0.390718i	0.0472229	−	0.0195604i
$400$		0			0
$401$	−31.8230	−	13.1815i	−1.58917	−	0.658254i	−0.599334	−	0.800499i	$-0.704568\pi$
$401$	−31.8230	−	13.1815i	−1.58917	−	0.658254i	−0.989831	+	0.142245i	$0.954568\pi$
$402$		0			0
$403$	−0.221599	+	2.24993i	−0.0110386	+	0.112077i
$404$		0			0
$405$	13.9048	+	26.0140i	0.690933	+	1.29265i
$406$		0			0
$407$	1.55665	+	0.309637i	0.0771602	+	0.0153481i
$408$		0			0
$409$	5.18514	+	26.0675i	0.256389	+	1.28895i	0.867511	+	0.497418i	$0.165718\pi$
$409$	5.18514	+	26.0675i	0.256389	+	1.28895i	−0.611122	+	0.791536i	$0.709282\pi$
$410$		0			0
$411$	0.161581	+	1.64056i	0.00797020	+	0.0809228i
$412$		0			0
$413$	5.44141	+	17.9379i	0.267754	+	0.882667i
$414$		0			0
$415$	−33.7486	+	33.7486i	−1.65665	+	1.65665i
$416$		0			0
$417$	0.0359867	+	0.0359867i	0.00176228	+	0.00176228i
$418$		0			0
$419$	21.7315	−	6.59218i	1.06165	−	0.322049i	0.289298	−	0.957239i	$-0.406578\pi$
$419$	21.7315	−	6.59218i	1.06165	−	0.322049i	0.772356	+	0.635190i	$0.219078\pi$
$420$		0			0
$421$	−29.7632	+	2.93141i	−1.45057	+	0.142868i	−0.792399	−	0.610003i	$-0.791168\pi$
$421$	−29.7632	+	2.93141i	−1.45057	+	0.142868i	−0.658168	+	0.752871i	$0.728668\pi$
$422$		0			0
$423$	−27.2443	+	5.41922i	−1.32466	+	0.263492i
$424$		0			0
$425$	2.37217	−	11.9257i	0.115067	−	0.578482i
$426$		0			0
$427$	0.849266	−	0.453942i	0.0410989	−	0.0219678i
$428$		0			0
$429$	0.0140499	+	0.00138379i	0.000678335	+	6.68101e-5i
$430$		0			0
$431$	−5.85086	+	14.1252i	−0.281826	+	0.680388i	−0.999878	−	0.0156011i	$-0.995034\pi$
$431$	−5.85086	+	14.1252i	−0.281826	+	0.680388i	0.718052	+	0.695989i	$0.245034\pi$
$432$		0			0
$433$	−11.6465	−	28.1171i	−0.559694	−	1.35122i	−0.910009	−	0.414589i	$-0.863925\pi$
$433$	−11.6465	−	28.1171i	−0.559694	−	1.35122i	0.350315	−	0.936632i	$-0.386075\pi$
$434$		0			0
$435$	2.77265	+	3.37848i	0.132938	+	0.161986i
$436$		0			0
$437$	−7.95246	+	26.2158i	−0.380418	+	1.25407i
$438$		0			0
$439$	−1.85148	+	1.23712i	−0.0883664	+	0.0590445i	−0.598968	−	0.800773i	$-0.704423\pi$
$439$	−1.85148	+	1.23712i	−0.0883664	+	0.0590445i	0.510602	+	0.859817i	$0.329423\pi$
$440$		0			0
$441$	−8.62481	+	12.9079i	−0.410705	+	0.614664i
$442$		0			0
$443$	16.0609	+	13.1808i	0.763075	+	0.626239i	0.933272	−	0.359171i	$-0.116940\pi$
$443$	16.0609	+	13.1808i	0.763075	+	0.626239i	−0.170197	+	0.985410i	$0.554440\pi$
$444$		0			0
$445$	−2.54011	+	4.75221i	−0.120413	+	0.225276i
$446$		0			0
$447$			0.241357i			0.0114158i
$448$		0			0
$449$		−	12.0240i		−	0.567447i	−0.958906	−	0.283724i	$-0.908430\pi$
$449$		−	12.0240i		−	0.567447i	0.958906	−	0.283724i	$-0.0915698\pi$
$450$		0			0
$451$	0.265882	−	0.497431i	0.0125199	−	0.0234231i
$452$		0			0
$453$	1.46436	+	1.20177i	0.0688016	+	0.0564640i
$454$		0			0
$455$	1.20559	−	1.80429i	0.0565189	−	0.0845865i
$456$		0			0
$457$	9.55723	−	6.38594i	0.447068	−	0.298722i	−0.311582	−	0.950219i	$-0.600859\pi$
$457$	9.55723	−	6.38594i	0.447068	−	0.298722i	0.758651	+	0.651498i	$0.225859\pi$
$458$		0			0
$459$	0.517672	−	1.70654i	0.0241629	−	0.0796543i
$460$		0			0
$461$	8.79720	+	10.7194i	0.409727	+	0.499253i	0.936459	−	0.350778i	$-0.114083\pi$
$461$	8.79720	+	10.7194i	0.409727	+	0.499253i	−0.526732	+	0.850031i	$0.676583\pi$
$462$		0			0
$463$	3.77259	+	9.10783i	0.175327	+	0.423277i	0.986976	−	0.160869i	$-0.0514297\pi$
$463$	3.77259	+	9.10783i	0.175327	+	0.423277i	−0.811649	+	0.584146i	$0.801430\pi$
$464$		0			0
$465$	−0.922785	+	2.22780i	−0.0427931	+	0.103312i
$466$		0			0
$467$	29.6180	+	2.91712i	1.37056	+	0.134988i	0.756356	−	0.654161i	$-0.226978\pi$
$467$	29.6180	+	2.91712i	1.37056	+	0.134988i	0.614202	+	0.789149i	$0.289478\pi$
$468$		0			0
$469$	0.142512	−	0.0761744i	0.00658060	−	0.00351741i
$470$		0			0
$471$	−0.227183	+	1.14213i	−0.0104680	+	0.0526264i
$472$		0			0
$473$	1.76447	−	0.350974i	0.0811303	−	0.0161378i
$474$		0			0
$475$	−30.9977	+	3.05301i	−1.42227	+	0.140082i
$476$		0			0
$477$	30.6459	−	9.29634i	1.40318	−	0.425650i
$478$		0			0
$479$	1.25772	+	1.25772i	0.0574668	+	0.0574668i	0.735256	−	0.677789i	$-0.237062\pi$
$479$	1.25772	+	1.25772i	0.0574668	+	0.0574668i	−0.677789	+	0.735256i	$0.737062\pi$
$480$		0			0
$481$	2.86393	−	2.86393i	0.130584	−	0.130584i
$482$		0			0
$483$	−0.328685	−	1.08353i	−0.0149557	−	0.0493023i
$484$		0			0
$485$	5.15893	+	52.3795i	0.234255	+	2.37843i
$486$		0			0
$487$	−2.68056	−	13.4761i	−0.121468	−	0.610661i	−0.992782	−	0.119935i	$-0.961732\pi$
$487$	−2.68056	−	13.4761i	−0.121468	−	0.610661i	0.871314	−	0.490726i	$-0.163268\pi$
$488$		0			0
$489$	2.39679	+	0.476750i	0.108386	+	0.0215594i
$490$		0			0
$491$	−14.1771	−	26.5235i	−0.639804	−	1.19699i	−0.967659	−	0.252261i	$-0.918826\pi$
$491$	−14.1771	−	26.5235i	−0.639804	−	1.19699i	0.327856	−	0.944728i	$-0.393674\pi$
$492$		0			0
$493$	−1.61011	+	16.3477i	−0.0725155	+	0.736263i
$494$		0			0
$495$	−1.75060	−	0.725122i	−0.0786836	−	0.0325918i
$496$		0			0
$497$	−19.5777	+	8.10935i	−0.878180	+	0.363754i
$498$		0			0
$499$	3.93306	−	3.22778i	0.176068	−	0.144495i	−0.542232	−	0.840229i	$-0.682421\pi$
$499$	3.93306	−	3.22778i	0.176068	−	0.144495i	0.718300	+	0.695734i	$0.244921\pi$
$500$		0			0
$501$	−2.24620	−	0.681376i	−0.100353	−	0.0304416i
$502$		0			0
$503$	−8.17711	−	12.2379i	−0.364599	−	0.545661i	0.603134	−	0.797640i	$-0.293919\pi$
$503$	−8.17711	−	12.2379i	−0.364599	−	0.545661i	−0.967733	+	0.251979i	$0.918919\pi$
$504$		0			0
$505$	4.29819	+	2.87196i	0.191267	+	0.127800i
$506$		0			0
$507$	−1.24550	+	1.51764i	−0.0553145	+	0.0674009i
$508$		0			0
$509$	−14.7190	−	7.86746i	−0.652407	−	0.348719i	0.111762	−	0.993735i	$-0.464351\pi$
$509$	−14.7190	−	7.86746i	−0.652407	−	0.348719i	−0.764169	+	0.645016i	$0.776851\pi$
$510$		0			0
$511$	−3.10737			−0.137462
$512$		0			0
$513$	−4.56822			−0.201692
$514$		0			0
$515$	39.5473	+	21.1385i	1.74266	+	0.931472i
$516$		0			0
$517$	1.12295	−	1.36832i	0.0493874	−	0.0601787i
$518$		0			0
$519$	−1.97696	−	1.32096i	−0.0867789	−	0.0579838i
$520$		0			0
$521$	−5.06833	−	7.58529i	−0.222047	−	0.332317i	0.703674	−	0.710523i	$-0.251541\pi$
$521$	−5.06833	−	7.58529i	−0.222047	−	0.332317i	−0.925722	+	0.378205i	$0.876541\pi$
$522$		0			0
$523$	−1.12932	−	0.342577i	−0.0493819	−	0.0149798i	0.265497	−	0.964112i	$-0.414464\pi$
$523$	−1.12932	−	0.342577i	−0.0493819	−	0.0149798i	−0.314879	+	0.949132i	$0.601964\pi$
$524$		0			0
$525$	0.995153	−	0.816701i	0.0434320	−	0.0356438i
$526$		0			0
$527$	−8.37321	+	3.46830i	−0.364743	+	0.151081i
$528$		0			0
$529$	6.81964	+	2.82479i	0.296506	+	0.122817i
$530$		0			0
$531$	4.09412	−	41.5683i	0.177669	−	1.80391i
$532$		0			0
$533$	−0.678500	−	1.26938i	−0.0293891	−	0.0549831i
$534$		0			0
$535$	−14.5581	−	2.89578i	−0.629400	−	0.125195i
$536$		0			0
$537$	0.411491	+	2.06870i	0.0177571	+	0.0892712i
$538$		0			0
$539$	−0.0969649	−	0.984501i	−0.00417657	−	0.0424054i
$540$		0			0
$541$	5.23802	+	17.2674i	0.225200	+	0.742386i	0.994615	+	0.103636i	$0.0330478\pi$
$541$	5.23802	+	17.2674i	0.225200	+	0.742386i	−0.769415	+	0.638749i	$0.779452\pi$
$542$		0			0
$543$	0.911816	−	0.911816i	0.0391298	−	0.0391298i
$544$		0			0
$545$	4.38527	+	4.38527i	0.187844	+	0.187844i
$546$		0			0
$547$	−0.760300	+	0.230635i	−0.0325081	+	0.00986122i	−0.306497	−	0.951872i	$-0.599157\pi$
$547$	−0.760300	+	0.230635i	−0.0325081	+	0.00986122i	0.273989	+	0.961733i	$0.411657\pi$
$548$		0			0
$549$	−2.13545	+	0.210323i	−0.0911386	+	0.00897637i
$550$		0			0
$551$	41.2708	−	8.20926i	1.75819	−	0.349726i
$552$		0			0
$553$	−2.12048	+	10.6604i	−0.0901718	+	0.453324i
$554$		0			0
$555$	3.80980	−	2.03638i	0.161717	−	0.0864395i
$556$		0			0
$557$	−18.2234	−	1.79485i	−0.772152	−	0.0760504i	−0.295735	−	0.955270i	$-0.595565\pi$
$557$	−18.2234	−	1.79485i	−0.772152	−	0.0760504i	−0.476417	+	0.879220i	$0.658065\pi$
$558$		0			0
$559$	1.75687	−	4.24146i	0.0743076	−	0.179395i
$560$		0			0
$561$	0.0216581	+	0.0522872i	0.000914405	+	0.00220757i
$562$		0			0
$563$	9.14512	+	11.1434i	0.385421	+	0.469637i	0.929192	−	0.369597i	$-0.120504\pi$
$563$	9.14512	+	11.1434i	0.385421	+	0.469637i	−0.543771	+	0.839233i	$0.683004\pi$
$564$		0			0
$565$	4.05700	−	13.3741i	0.170679	−	0.562654i
$566$		0			0
$567$	−9.75964	+	6.52118i	−0.409866	+	0.273864i
$568$		0			0
$569$	0.0300548	−	0.0449802i	0.00125996	−	0.00188567i	−0.830839	−	0.556513i	$-0.812139\pi$
$569$	0.0300548	−	0.0449802i	0.00125996	−	0.00188567i	0.832099	+	0.554627i	$0.187139\pi$
$570$		0			0
$571$	−19.2334	−	15.7845i	−0.804893	−	0.660559i	0.139190	−	0.990266i	$-0.455550\pi$
$571$	−19.2334	−	15.7845i	−0.804893	−	0.660559i	−0.944083	+	0.329707i	$0.893050\pi$
$572$		0			0
$573$	0.408846	−	0.764898i	0.0170798	−	0.0319541i
$574$		0			0
$575$			34.5429i			1.44054i
$576$		0			0
$577$		−	8.94718i		−	0.372476i	−0.982505	−	0.186238i	$-0.940370\pi$
$577$		−	8.94718i		−	0.372476i	0.982505	−	0.186238i	$-0.0596295\pi$
$578$		0			0
$579$	−0.160295	+	0.299891i	−0.00666164	+	0.0124631i
$580$		0			0
$581$	−14.6814	−	12.0487i	−0.609086	−	0.499864i
$582$		0			0
$583$	−1.13378	+	1.69682i	−0.0469563	+	0.0702751i
$584$		0			0
$585$	−4.02048	+	2.68640i	−0.166226	+	0.111069i
$586$		0			0
$587$	−7.89764	+	26.0350i	−0.325971	+	1.07458i	0.628882	+	0.777501i	$0.283513\pi$
$587$	−7.89764	+	26.0350i	−0.325971	+	1.07458i	−0.954853	+	0.297080i	$0.903987\pi$
$588$		0			0
$589$	14.7283	+	17.9464i	0.606867	+	0.739470i
$590$		0			0
$591$	−0.497438	−	1.20092i	−0.0204618	−	0.0493993i
$592$		0			0
$593$	−1.82052	+	4.39513i	−0.0747599	+	0.180486i	−0.956841	−	0.290610i	$-0.906142\pi$
$593$	−1.82052	+	4.39513i	−0.0747599	+	0.180486i	0.882082	+	0.471097i	$0.156142\pi$
$594$		0			0
$595$	8.65716	+	0.852656i	0.354909	+	0.0349555i
$596$		0			0
$597$	1.78765	−	0.955519i	0.0731637	−	0.0391068i
$598$		0			0
$599$	2.80655	−	14.1095i	0.114672	−	0.576497i	−0.880135	−	0.474723i	$-0.842548\pi$
$599$	2.80655	−	14.1095i	0.114672	−	0.576497i	0.994808	−	0.101774i	$-0.0324519\pi$
$600$		0			0
$601$	−42.4056	+	8.43499i	−1.72976	+	0.344070i	−0.956880	−	0.290483i	$-0.906184\pi$
$601$	−42.4056	+	8.43499i	−1.72976	+	0.344070i	−0.772879	+	0.634554i	$0.781184\pi$
$602$		0			0
$603$	−0.358341	+	0.0352936i	−0.0145928	+	0.00143726i
$604$		0			0
$605$	−35.2174	+	10.6831i	−1.43179	+	0.434329i
$606$		0			0
$607$	16.1357	+	16.1357i	0.654930	+	0.654930i	0.954176	−	0.299246i	$-0.0967352\pi$
$607$	16.1357	+	16.1357i	0.654930	+	0.654930i	−0.299246	+	0.954176i	$0.596735\pi$
$608$		0			0
$609$	−1.22979	+	1.22979i	−0.0498337	+	0.0498337i
$610$		0			0
$611$	−1.31125	−	4.32263i	−0.0530477	−	0.174875i
$612$		0			0
$613$	−0.498594	−	5.06231i	−0.0201380	−	0.204465i	−0.999989	−	0.00473379i	$-0.998493\pi$
$613$	−0.498594	−	5.06231i	−0.0201380	−	0.204465i	0.979851	−	0.199731i	$-0.0640068\pi$
$614$		0			0
$615$	−0.299498	−	1.50568i	−0.0120769	−	0.0607149i
$616$		0			0
$617$	−29.6709	−	5.90191i	−1.19451	−	0.237602i	−0.442506	−	0.896766i	$-0.645910\pi$
$617$	−29.6709	−	5.90191i	−1.19451	−	0.237602i	−0.752000	+	0.659164i	$0.770910\pi$
$618$		0			0
$619$	8.63894	+	16.1623i	0.347228	+	0.649618i	0.993543	−	0.113452i	$-0.0361909\pi$
$619$	8.63894	+	16.1623i	0.347228	+	0.649618i	−0.646315	+	0.763071i	$0.723691\pi$
$620$		0			0
$621$	−0.496571	+	5.04177i	−0.0199267	+	0.202319i
$622$		0			0
$623$	−1.98103	−	0.820570i	−0.0793683	−	0.0328754i
$624$		0			0
$625$	15.7617	−	6.52873i	0.630470	−	0.261149i
$626$		0			0
$627$	0.112068	−	0.0919718i	0.00447556	−	0.00367300i
$628$		0			0
$629$	15.5372	+	4.71316i	0.619509	+	0.187926i
$630$		0			0
$631$	18.9104	+	28.3014i	0.752812	+	1.12666i	0.987961	+	0.154703i	$0.0494422\pi$
$631$	18.9104	+	28.3014i	0.752812	+	1.12666i	−0.235149	+	0.971959i	$0.575558\pi$
$632$		0			0
$633$	0.742111	+	0.495863i	0.0294963	+	0.0197088i
$634$		0			0
$635$	18.7258	−	22.8174i	0.743110	−	0.905482i
$636$		0			0
$637$	−2.22640	−	1.19003i	−0.0882130	−	0.0471508i
$638$		0			0
$639$	47.2190			1.86796
$640$		0			0
$641$	11.0097			0.434858			0.217429	−	0.976076i	$-0.430233\pi$
$641$	11.0097			0.434858			0.217429	+	0.976076i	$0.430233\pi$
$642$		0			0
$643$	−42.0290	−	22.4650i	−1.65746	−	0.885932i	−0.989964	−	0.141321i	$-0.954865\pi$
$643$	−42.0290	−	22.4650i	−1.65746	−	0.885932i	−0.667498	−	0.744611i	$-0.732635\pi$
$644$		0			0
$645$	3.10637	−	3.78513i	0.122313	−	0.149039i
$646$		0			0
$647$	−29.4587	−	19.6837i	−1.15814	−	0.773846i	−0.180387	−	0.983596i	$-0.557735\pi$
$647$	−29.4587	−	19.6837i	−1.15814	−	0.773846i	−0.977755	+	0.209750i	$0.932735\pi$
$648$		0			0
$649$	1.47876	+	2.21313i	0.0580465	+	0.0868728i
$650$		0			0
$651$	−0.918240	−	0.278545i	−0.0359886	−	0.0109170i
$652$		0			0
$653$	3.90577	−	3.20538i	0.152844	−	0.125436i	−0.554863	−	0.831942i	$-0.687229\pi$
$653$	3.90577	−	3.20538i	0.152844	−	0.125436i	0.707708	+	0.706505i	$0.249729\pi$
$654$		0			0
$655$	−43.5959	+	18.0580i	−1.70343	+	0.705584i
$656$		0			0
$657$	6.39705	+	2.64974i	0.249573	+	0.103376i
$658$		0			0
$659$	−2.04620	+	20.7754i	−0.0797086	+	0.809295i	0.869350	+	0.494197i	$0.164538\pi$
$659$	−2.04620	+	20.7754i	−0.0797086	+	0.809295i	−0.949059	+	0.315099i	$0.897962\pi$
$660$		0			0
$661$	−17.0403	−	31.8801i	−0.662789	−	1.23999i	−0.958603	−	0.284746i	$-0.908091\pi$
$661$	−17.0403	−	31.8801i	−0.662789	−	1.23999i	0.295813	−	0.955246i	$-0.404409\pi$
$662$		0			0
$663$	0.141649	+	0.0281758i	0.00550120	+	0.00109426i
$664$		0			0
$665$	−4.34734	−	21.8555i	−0.168583	−	0.847522i
$666$		0			0
$667$	−4.57407	−	46.4413i	−0.177109	−	1.79821i
$668$		0			0
$669$	−0.123216	−	0.406189i	−0.00476381	−	0.0157042i
$670$		0			0
$671$	0.0966877	−	0.0966877i	0.00373259	−	0.00373259i
$672$		0			0
$673$	−18.7729	−	18.7729i	−0.723642	−	0.723642i	0.245703	−	0.969345i	$-0.420981\pi$
$673$	−18.7729	−	18.7729i	−0.723642	−	0.723642i	−0.969345	+	0.245703i	$0.920981\pi$
$674$		0			0
$675$	−5.51204	+	1.67206i	−0.212159	+	0.0643576i
$676$		0			0
$677$	27.0517	−	2.66436i	1.03968	−	0.102400i	0.436259	−	0.899821i	$-0.356303\pi$
$677$	27.0517	−	2.66436i	1.03968	−	0.102400i	0.603423	+	0.797421i	$0.293803\pi$
$678$		0			0
$679$	−20.5420	+	4.08605i	−0.788328	+	0.156808i
$680$		0			0
$681$	0.453551	−	2.28016i	0.0173801	−	0.0873758i
$682$		0			0
$683$	−8.04037	+	4.29767i	−0.307656	+	0.164446i	−0.617999	−	0.786179i	$-0.712056\pi$
$683$	−8.04037	+	4.29767i	−0.307656	+	0.164446i	0.310342	+	0.950625i	$0.399556\pi$
$684$		0			0
$685$	35.8060	+	3.52658i	1.36808	+	0.134744i
$686$		0			0
$687$	−0.00864988	+	0.0208827i	−0.000330014	+	0.000796724i
$688$		0			0
$689$	1.99292	+	4.81133i	0.0759241	+	0.183297i
$690$		0			0
$691$	24.5094	+	29.8648i	0.932382	+	1.13611i	0.990460	+	0.137798i	$0.0440026\pi$
$691$	24.5094	+	29.8648i	0.932382	+	1.13611i	−0.0580785	+	0.998312i	$0.518497\pi$
$692$		0			0
$693$	0.218880	−	0.721550i	0.00831456	−	0.0274094i
$694$		0			0
$695$	0.923565	−	0.617106i	0.0350328	−	0.0234082i
$696$		0			0
$697$	3.20563	−	4.79757i	0.121422	−	0.181721i
$698$		0			0
$699$	−2.45733	−	2.01668i	−0.0929447	−	0.0762778i
$700$		0			0
$701$	14.6991	−	27.5000i	0.555176	−	1.03866i	−0.435210	−	0.900329i	$-0.643326\pi$
$701$	14.6991	−	27.5000i	0.555176	−	1.03866i	0.990386	−	0.138332i	$-0.0441740\pi$
$702$		0			0
$703$		−	41.5915i		−	1.56865i
$704$		0			0
$705$		−	4.81791i		−	0.181453i
$706$		0			0
$707$	−0.969697	+	1.81418i	−0.0364692	+	0.0682291i
$708$		0			0
$709$	2.31868	+	1.90289i	0.0870797	+	0.0714645i	0.676926	−	0.736051i	$-0.263312\pi$
$709$	2.31868	+	1.90289i	0.0870797	+	0.0714645i	−0.589846	+	0.807516i	$0.700812\pi$
$710$		0			0
$711$	13.4557	−	20.1379i	0.504630	−	0.755232i
$712$		0			0
$713$	21.4078	−	14.3042i	0.801727	−	0.535697i
$714$		0			0
$715$	0.0894452	−	0.294861i	0.00334506	−	0.0110272i
$716$		0			0
$717$	1.31290	+	1.59978i	0.0490312	+	0.0597447i
$718$		0			0
$719$	6.09932	+	14.7251i	0.227466	+	0.549152i	0.995868	−	0.0908161i	$-0.0289475\pi$
$719$	6.09932	+	14.7251i	0.227466	+	0.549152i	−0.768401	+	0.639968i	$0.778948\pi$
$720$		0			0
$721$	−6.82868	+	16.4859i	−0.254313	+	0.613967i
$722$		0			0
$723$	2.74398	+	0.270259i	0.102050	+	0.0100510i
$724$		0			0
$725$	46.7928	−	25.0113i	1.73784	−	0.928895i
$726$		0			0
$727$	−6.02809	+	30.3052i	−0.223569	+	1.12396i	0.692031	+	0.721868i	$0.256716\pi$
$727$	−6.02809	+	30.3052i	−0.223569	+	1.12396i	−0.915600	+	0.402091i	$0.868284\pi$
$728$		0			0
$729$	25.2367	−	5.01990i	0.934694	−	0.185922i
$730$		0			0
$731$	18.3153	−	1.80390i	0.677417	−	0.0667197i
$732$		0			0
$733$	−16.5818	+	5.03003i	−0.612463	+	0.185789i	−0.581251	−	0.813724i	$-0.697437\pi$
$733$	−16.5818	+	5.03003i	−0.612463	+	0.185789i	−0.0312116	+	0.999513i	$0.509937\pi$
$734$		0			0
$735$	−1.90394	−	1.90394i	−0.0702278	−	0.0702278i
$736$		0			0
$737$	0.0162248	−	0.0162248i	0.000597649	−	0.000597649i
$738$		0			0
$739$	−5.77788	−	19.0471i	−0.212543	−	0.700660i	−0.996779	−	0.0801974i	$-0.974445\pi$
$739$	−5.77788	−	19.0471i	−0.212543	−	0.700660i	0.784236	−	0.620462i	$-0.213055\pi$
$740$		0			0
$741$	−0.0362626	−	0.368180i	−0.00133214	−	0.0135254i
$742$		0			0
$743$	−7.74710	−	38.9473i	−0.284213	−	1.42884i	−0.814078	−	0.580755i	$-0.802757\pi$
$743$	−7.74710	−	38.9473i	−0.284213	−	1.42884i	0.529865	−	0.848082i	$-0.322243\pi$
$744$		0			0
$745$	5.16652	+	1.02768i	0.189287	+	0.0376514i
$746$		0			0
$747$	19.9498	+	37.3235i	0.729925	+	1.36559i
$748$		0			0
$749$	0.578951	−	5.87819i	0.0211544	−	0.214784i
$750$		0			0
$751$	−30.2032	−	12.5106i	−1.10213	−	0.456518i	−0.243910	−	0.969798i	$-0.578430\pi$
$751$	−30.2032	−	12.5106i	−1.10213	−	0.456518i	−0.858221	+	0.513280i	$0.828430\pi$
$752$		0			0
$753$	2.33323	−	0.966457i	0.0850278	−	0.0352196i
$754$		0			0
$755$	31.9604	−	26.2292i	1.16316	−	0.954578i
$756$		0			0
$757$	17.5361	+	5.31953i	0.637362	+	0.193342i	0.592396	−	0.805647i	$-0.298182\pi$
$757$	17.5361	+	5.31953i	0.637362	+	0.193342i	0.0449660	+	0.998989i	$0.485682\pi$
$758$		0			0
$759$	−0.0893238	−	0.133683i	−0.00324225	−	0.00485237i
$760$		0			0
$761$	10.7889	+	7.20891i	0.391097	+	0.261323i	0.735536	−	0.677486i	$-0.236931\pi$
$761$	10.7889	+	7.20891i	0.391097	+	0.261323i	−0.344438	+	0.938809i	$0.611931\pi$
$762$		0			0
$763$	−1.56560	+	1.90768i	−0.0566784	+	0.0690628i
$764$		0			0
$765$	−17.0951	−	9.13754i	−0.618076	−	0.330368i
$766$		0			0
$767$	6.79235			0.245257
$768$		0			0
$769$	55.4296			1.99884			0.999422	−	0.0339985i	$-0.0108241\pi$
$769$	55.4296			1.99884			0.999422	+	0.0339985i	$0.0108241\pi$
$770$		0			0
$771$	0.609484	+	0.325776i	0.0219500	+	0.0117325i
$772$		0			0
$773$	−29.5336	+	35.9867i	−1.06225	+	1.29435i	−0.108386	+	0.994109i	$0.534568\pi$
$773$	−29.5336	+	35.9867i	−1.06225	+	1.29435i	−0.953862	+	0.300244i	$0.902932\pi$
$774$		0			0
$775$	24.3400	+	16.2634i	0.874317	+	0.584200i
$776$		0			0
$777$	0.955040	+	1.42932i	0.0342619	+	0.0512765i
$778$		0			0
$779$	−14.1441	−	4.29057i	−0.506765	−	0.153726i
$780$		0			0
$781$	−2.32597	+	1.90887i	−0.0832297	+	0.0683049i
$782$		0			0
$783$	7.18928	−	2.97790i	0.256924	−	0.106421i
$784$		0			0
$785$	23.4812	+	9.72622i	0.838079	+	0.347144i
$786$		0			0
$787$	2.46437	−	25.0212i	0.0878455	−	0.891910i	−0.845750	−	0.533580i	$-0.820846\pi$
$787$	2.46437	−	25.0212i	0.0878455	−	0.891910i	0.933595	−	0.358330i	$-0.116654\pi$
$788$		0			0
$789$	−1.24197	−	2.32357i	−0.0442154	−	0.0827211i
$790$		0			0
$791$	5.45462	+	1.08499i	0.193944	+	0.0385779i
$792$		0			0
$793$	−0.0680742	−	0.342232i	−0.00241738	−	0.0121530i
$794$		0			0
$795$	0.544437	+	5.52776i	0.0193092	+	0.196049i
$796$		0			0
$797$	−6.23492	−	20.5538i	−0.220852	−	0.728052i	−0.995423	−	0.0955650i	$-0.969534\pi$
$797$	−6.23492	−	20.5538i	−0.220852	−	0.728052i	0.774571	−	0.632487i	$-0.217966\pi$
$798$		0			0
$799$	12.8044	−	12.8044i	0.452987	−	0.452987i
$800$		0			0
$801$	3.37856	+	3.37856i	0.119376	+	0.119376i
$802$		0			0
$803$	−0.422231	+	0.128082i	−0.0149002	+	0.00451993i
$804$		0			0
$805$	−24.5937	+	2.42227i	−0.866814	+	0.0853737i
$806$		0			0
$807$	2.24375	−	0.446310i	0.0789838	−	0.0157109i
$808$		0			0
$809$	7.10502	−	35.7193i	0.249799	−	1.25582i	−0.628537	−	0.777780i	$-0.716346\pi$
$809$	7.10502	−	35.7193i	0.249799	−	1.25582i	0.878336	−	0.478045i	$-0.158654\pi$
$810$		0			0
$811$	5.53266	−	2.95727i	0.194278	−	0.103844i	−0.371390	−	0.928477i	$-0.621119\pi$
$811$	5.53266	−	2.95727i	0.194278	−	0.103844i	0.565667	+	0.824633i	$0.308619\pi$
$812$		0			0
$813$	1.90799	+	0.187921i	0.0669161	+	0.00659066i
$814$		0			0
$815$	20.4107	−	49.2759i	0.714957	−	1.72606i
$816$		0			0
$817$	−18.0413	−	43.5554i	−0.631183	−	1.52381i
$818$		0			0
$819$	−1.22068	−	1.48740i	−0.0426539	−	0.0519739i
$820$		0			0
$821$	8.45214	−	27.8630i	0.294982	−	0.972424i	−0.676725	−	0.736235i	$-0.736602\pi$
$821$	8.45214	−	27.8630i	0.294982	−	0.972424i	0.971707	−	0.236189i	$-0.0758984\pi$
$822$		0			0
$823$	11.9092	−	7.95748i	0.415129	−	0.277380i	−0.330416	−	0.943835i	$-0.607189\pi$
$823$	11.9092	−	7.95748i	0.415129	−	0.277380i	0.745545	+	0.666455i	$0.232189\pi$
$824$		0			0
$825$	0.101558	−	0.151993i	0.00353581	−	0.00529171i
$826$		0			0
$827$	22.9146	+	18.8055i	0.796819	+	0.653933i	0.942053	−	0.335465i	$-0.108893\pi$
$827$	22.9146	+	18.8055i	0.796819	+	0.653933i	−0.145234	+	0.989397i	$0.546393\pi$
$828$		0			0
$829$	8.94431	−	16.7336i	0.310649	−	0.581183i	−0.677347	−	0.735664i	$-0.736870\pi$
$829$	8.94431	−	16.7336i	0.310649	−	0.581183i	0.987996	+	0.154481i	$0.0493705\pi$
$830$		0			0
$831$			1.66064i			0.0576070i
$832$		0			0
$833$		−	10.1201i		−	0.350640i
$834$		0			0
$835$	−24.1498	+	45.1811i	−0.835738	+	1.56356i
$836$		0			0
$837$	3.31879	+	2.72366i	0.114714	+	0.0941435i
$838$		0			0
$839$	−7.42607	+	11.1139i	−0.256376	+	0.383694i	−0.937222	−	0.348732i	$-0.886612\pi$
$839$	−7.42607	+	11.1139i	−0.256376	+	0.383694i	0.680846	+	0.732427i	$0.261612\pi$
$840$		0			0
$841$	−35.4862	+	23.7111i	−1.22366	+	0.817626i
$842$		0			0
$843$	−1.14536	+	3.77573i	−0.0394482	+	0.130043i
$844$		0			0
$845$	27.1836	+	33.1233i	0.935145	+	1.13948i
$846$		0			0
$847$	−5.60431	−	13.5300i	−0.192567	−	0.464897i
$848$		0			0
$849$	−0.887815	+	2.14337i	−0.0304697	+	0.0735604i
$850$		0			0
$851$	−45.9029	−	4.52104i	−1.57353	−	0.154979i
$852$		0			0
$853$	−11.2584	+	6.01773i	−0.385479	+	0.206043i	−0.652741	−	0.757581i	$-0.726381\pi$
$853$	−11.2584	+	6.01773i	−0.385479	+	0.206043i	0.267262	+	0.963624i	$0.413881\pi$
$854$		0			0
$855$	−9.68711	+	48.7004i	−0.331292	+	1.66552i
$856$		0			0
$857$	36.9270	−	7.34524i	1.26140	−	0.250909i	0.481298	−	0.876557i	$-0.340166\pi$
$857$	36.9270	−	7.34524i	1.26140	−	0.250909i	0.780105	+	0.625649i	$0.215166\pi$
$858$		0			0
$859$	14.8740	−	1.46496i	0.507494	−	0.0499838i	0.158970	−	0.987283i	$-0.449183\pi$
$859$	14.8740	−	1.46496i	0.507494	−	0.0499838i	0.348524	+	0.937300i	$0.386683\pi$
$860$		0			0
$861$	0.584593	−	0.177334i	0.0199229	−	0.00604354i
$862$		0			0
$863$	−38.0460	−	38.0460i	−1.29510	−	1.29510i	−0.931590	−	0.363511i	$-0.881578\pi$
$863$	−38.0460	−	38.0460i	−1.29510	−	1.29510i	−0.363511	−	0.931590i	$-0.618422\pi$
$864$		0			0
$865$	−36.6944	+	36.6944i	−1.24765	+	1.24765i
$866$		0			0
$867$	−0.590882	−	1.94788i	−0.0200674	−	0.0661534i
$868$		0			0
$869$	0.151277	+	1.53594i	0.00513171	+	0.0521031i
$870$		0			0
$871$	−0.0114233	−	0.0574287i	−0.000387063	−	0.00194590i
$872$		0			0
$873$	45.7734	+	9.10489i	1.54919	+	0.308154i
$874$		0			0
$875$	−2.67761	−	5.00946i	−0.0905198	−	0.169351i
$876$		0			0
$877$	0.261117	−	2.65116i	0.00881729	−	0.0895234i	−0.989769	−	0.142680i	$-0.954428\pi$
$877$	0.261117	−	2.65116i	0.00881729	−	0.0895234i	0.998586	+	0.0531562i	$0.0169281\pi$
$878$		0			0
$879$	0.0154037	+	0.00638041i	0.000519553	+	0.000215206i
$880$		0			0
$881$	−20.2346	+	8.38144i	−0.681720	+	0.282378i	−0.696546	−	0.717512i	$-0.745281\pi$
$881$	−20.2346	+	8.38144i	−0.681720	+	0.282378i	0.0148256	+	0.999890i	$0.495281\pi$
$882$		0			0
$883$	−11.5623	+	9.48892i	−0.389102	+	0.319328i	−0.808523	−	0.588464i	$-0.799733\pi$
$883$	−11.5623	+	9.48892i	−0.389102	+	0.319328i	0.419422	+	0.907792i	$0.362233\pi$
$884$		0			0
$885$	6.93266	+	2.10300i	0.233039	+	0.0706916i
$886$		0			0
$887$	−3.14343	−	4.70448i	−0.105546	−	0.157961i	0.774937	−	0.632039i	$-0.217782\pi$
$887$	−3.14343	−	4.70448i	−0.105546	−	0.157961i	−0.880483	+	0.474078i	$0.842782\pi$
$888$		0			0
$889$	9.76648	+	6.52575i	0.327557	+	0.218867i
$890$		0			0
$891$	−1.05735	+	1.28838i	−0.0354225	+	0.0431625i
$892$		0			0
$893$	−40.9091	−	21.8664i	−1.36897	−	0.731730i
$894$		0			0
$895$	46.0350			1.53878
$896$		0			0
$897$	−0.410288			−0.0136991
$898$		0			0
$899$	−34.8775	−	18.6424i	−1.16323	−	0.621760i
$900$		0			0
$901$	−13.2440	+	16.1379i	−0.441222	+	0.537631i
$902$		0			0
$903$	1.62014	+	1.08254i	0.0539148	+	0.0360247i
$904$		0			0
$905$	−15.6360	−	23.4009i	−0.519758	−	0.777873i
$906$		0			0
$907$	−6.34426	−	1.92451i	−0.210658	−	0.0639023i	0.183192	−	0.983077i	$-0.441357\pi$
$907$	−6.34426	−	1.92451i	−0.210658	−	0.0639023i	−0.393850	+	0.919175i	$0.628857\pi$
$908$		0			0
$909$	3.54328	−	2.90790i	0.117523	−	0.0964489i
$910$		0			0
$911$	−8.63355	+	3.57614i	−0.286042	+	0.118483i	−0.521091	−	0.853501i	$-0.674475\pi$
$911$	−8.63355	+	3.57614i	−0.286042	+	0.118483i	0.235049	+	0.971984i	$0.424475\pi$
$912$		0			0
$913$	−2.49155	−	1.03203i	−0.0824582	−	0.0341553i
$914$		0			0
$915$	0.0364791	−	0.370378i	0.00120596	−	0.0122443i
$916$		0			0
$917$	−8.85170	−	16.5604i	−0.292309	−	0.546872i
$918$		0			0
$919$	9.57985	+	1.90555i	0.316010	+	0.0628583i	0.350547	−	0.936545i	$-0.385996\pi$
$919$	9.57985	+	1.90555i	0.316010	+	0.0628583i	−0.0345370	+	0.999403i	$0.510996\pi$
$920$		0			0
$921$	−0.528296	−	2.65592i	−0.0174079	−	0.0875156i
$922$		0			0
$923$	0.752629	+	7.64157i	0.0247731	+	0.251525i
$924$		0			0
$925$	−15.2233	−	50.1845i	−0.500539	−	1.65006i
$926$		0			0
$927$	28.1160	−	28.1160i	0.923450	−	0.923450i
$928$		0			0
$929$	39.9272	+	39.9272i	1.30997	+	1.30997i	0.921434	+	0.388534i	$0.127018\pi$
$929$	39.9272	+	39.9272i	1.30997	+	1.30997i	0.388534	+	0.921434i	$0.372982\pi$
$930$		0			0
$931$	−24.8076	+	7.52530i	−0.813036	+	0.246632i
$932$		0			0
$933$	−3.40999	+	0.335855i	−0.111638	+	0.0109954i
$934$		0			0
$935$	1.21149	−	0.240979i	0.0396198	−	0.00788087i
$936$		0			0
$937$	−1.71770	+	8.63545i	−0.0561147	+	0.282108i	−0.998647	−	0.0520083i	$-0.983438\pi$
$937$	−1.71770	+	8.63545i	−0.0561147	+	0.282108i	0.942532	+	0.334116i	$0.108438\pi$
$938$		0			0
$939$	2.07009	−	1.10649i	0.0675550	−	0.0361089i
$940$		0			0
$941$	−25.7216	−	2.53336i	−0.838502	−	0.0825852i	−0.330356	−	0.943856i	$-0.607169\pi$
$941$	−25.7216	−	2.53336i	−0.838502	−	0.0825852i	−0.508146	+	0.861271i	$0.669669\pi$
$942$		0			0
$943$	−6.27281	+	15.1439i	−0.204271	+	0.493154i
$944$		0			0
$945$	−1.57699	−	3.80719i	−0.0512995	−	0.123848i
$946$		0			0
$947$	3.75302	+	4.57307i	0.121957	+	0.148605i	0.830410	−	0.557154i	$-0.188107\pi$
$947$	3.75302	+	4.57307i	0.121957	+	0.148605i	−0.708453	+	0.705758i	$0.750607\pi$
$948$		0			0
$949$	−0.326851	+	1.07748i	−0.0106100	+	0.0349766i
$950$		0			0
$951$	0.0473107	−	0.0316120i	0.00153415	−	0.00102509i
$952$		0			0
$953$	−11.0052	+	16.4704i	−0.356492	+	0.533528i	−0.965760	−	0.259436i	$-0.916463\pi$
$953$	−11.0052	+	16.4704i	−0.356492	+	0.533528i	0.609268	+	0.792964i	$0.291463\pi$
$954$		0			0
$955$	−14.6326	−	12.0087i	−0.473501	−	0.388593i
$956$		0			0
$957$	−0.116414	+	0.217796i	−0.00376314	+	0.00704033i
$958$		0			0
$959$			14.3173i			0.462331i
$960$		0			0
$961$			9.18073i			0.296153i
$962$		0			0
$963$	−6.20437	+	11.6076i	−0.199933	+	0.374048i
$964$		0			0
$965$	5.73698	+	4.70822i	0.184680	+	0.151563i
$966$		0			0
$967$	7.85147	−	11.7506i	0.252486	−	0.377872i	−0.683476	−	0.729973i	$-0.739533\pi$
$967$	7.85147	−	11.7506i	0.252486	−	0.377872i	0.935962	+	0.352101i	$0.114533\pi$
$968$		0			0
$969$	1.23315	−	0.823961i	0.0396143	−	0.0264694i
$970$		0			0
$971$	−4.95320	+	16.3285i	−0.158956	+	0.524007i	−0.999852	−	0.0171891i	$-0.994528\pi$
$971$	−4.95320	+	16.3285i	−0.158956	+	0.524007i	0.840897	+	0.541196i	$0.182028\pi$
$972$		0			0
$973$	0.280408	+	0.341678i	0.00898946	+	0.0109537i
$974$		0			0
$975$	−0.178516	−	0.430975i	−0.00571708	−	0.0138023i
$976$		0			0
$977$	−15.1737	+	36.6326i	−0.485450	+	1.17198i	0.471536	+	0.881847i	$0.343700\pi$
$977$	−15.1737	+	36.6326i	−0.485450	+	1.17198i	−0.956986	+	0.290133i	$0.906300\pi$
$978$		0			0
$979$	−0.303006	−	0.0298435i	−0.00968413	−	0.000953804i
$980$		0			0
$981$	4.84978	−	2.59226i	0.154842	−	0.0827645i
$982$		0			0
$983$	−1.18564	+	5.96062i	−0.0378161	+	0.190114i	−0.995076	−	0.0991147i	$-0.968399\pi$
$983$	−1.18564	+	5.96062i	−0.0378161	+	0.190114i	0.957260	+	0.289229i	$0.0933989\pi$
$984$		0			0
$985$	−27.8251	+	5.53476i	−0.886582	+	0.176352i
$986$		0			0
$987$	1.90797	−	0.187919i	0.0607315	−	0.00598153i
$988$		0			0
$989$	−50.0316	+	15.1769i	−1.59091	+	0.482598i
$990$		0			0
$991$	15.6471	+	15.6471i	0.497048	+	0.497048i	0.910518	−	0.413470i	$-0.135683\pi$
$991$	15.6471	+	15.6471i	0.497048	+	0.497048i	−0.413470	+	0.910518i	$0.635683\pi$
$992$		0			0
$993$	1.06343	−	1.06343i	0.0337469	−	0.0337469i
$994$		0			0
$995$	−12.8422	−	42.3352i	−0.407127	−	1.34212i
$996$		0			0
$997$	−4.19514	−	42.5940i	−0.132861	−	1.34896i	−0.798186	−	0.602411i	$-0.794207\pi$
$997$	−4.19514	−	42.5940i	−0.132861	−	1.34896i	0.665325	−	0.746554i	$-0.268293\pi$
$998$		0			0
$999$	−1.50052	−	7.54362i	−0.0474743	−	0.238669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.273.8		240
4.3	odd	2		128.2.k.a.109.8	yes	240
128.27	odd	32		128.2.k.a.101.8	✓	240
128.101	even	32	inner	512.2.k.a.497.8		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.101.8	✓	240	128.27	odd	32
128.2.k.a.109.8	yes	240	4.3	odd	2
512.2.k.a.273.8		240	1.1	even	1	trivial
512.2.k.a.497.8		240	128.101	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.k (of order \(32\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.135634 + 0.0724978i) q^{3} +(2.12942 - 2.59470i) q^{5} +(1.11060 + 0.742082i) q^{7} +(-1.65357 - 2.47474i) q^{9} +(0.181497 + 0.0550566i) q^{11} +(0.374137 - 0.307046i) q^{13} +(0.476932 - 0.197552i) q^{15} +(1.79255 + 0.742500i) q^{17} +(0.487163 - 4.94625i) q^{19} +(0.0968362 + 0.181168i) q^{21} +(-5.40603 - 1.07533i) q^{23} +(-1.22261 - 6.14649i) q^{25} +(-0.0900899 - 0.914698i) q^{27} +(2.45765 + 8.10178i) q^{29} +(-3.30297 + 3.30297i) q^{31} +(0.0206257 + 0.0206257i) q^{33} +(4.29042 - 1.30149i) q^{35} +(8.32789 - 0.820226i) q^{37} +(0.0730059 - 0.0145218i) q^{39} +(0.580168 - 2.91670i) q^{41} +(8.36535 - 4.47137i) q^{43} +(-9.94237 - 0.979238i) q^{45} +(3.57155 - 8.62250i) q^{47} +(-1.99603 - 4.81884i) q^{49} +(0.189301 + 0.230664i) q^{51} +(-3.12341 + 10.2965i) q^{53} +(0.529339 - 0.353693i) q^{55} +(0.424668 - 0.635561i) q^{57} +(10.8483 + 8.90293i) q^{59} +(0.339850 - 0.635815i) q^{61} -3.97554i q^{63} -1.62460i q^{65} +(0.0570291 - 0.106694i) q^{67} +(-0.655283 - 0.537776i) q^{69} +(-8.81399 + 13.1911i) q^{71} +(-1.93431 + 1.29247i) q^{73} +(0.279780 - 0.922310i) q^{75} +(0.160715 + 0.195832i) q^{77} +(3.11404 + 7.51796i) q^{79} +(-3.36290 + 8.11876i) q^{81} +(-14.1505 - 1.39370i) q^{83} +(5.74366 - 3.07005i) q^{85} +(-0.254021 + 1.27705i) q^{87} +(-1.57448 + 0.313183i) q^{89} +(0.643371 - 0.0633666i) q^{91} +(-0.687453 + 0.208537i) q^{93} +(-11.7967 - 11.7967i) q^{95} +(-11.0877 + 11.0877i) q^{97} +(-0.163868 - 0.540199i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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