LMFDB - Embedded newform 1024.2.g.a.641.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1024,2,Mod(129,1024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1024, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("1024.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1024 = 2^{10} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1024.g (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.17668116698$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{48})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{8} + 1 $ x^16 - x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			641.2
Root			$-0.608761 - 0.793353i$ of defining polynomial
Character	$\chi$	$=$	1024.641
Dual form			1024.2.g.a.385.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.860919 - 0.356604i) q^{3} +(0.366025 + 0.883663i) q^{5} +(-2.35207 + 2.35207i) q^{7} +(-1.50731 - 1.50731i) q^{9} +O(q^{10})$	\(q+(-0.860919 - 0.356604i) q^{3} +(0.366025 + 0.883663i) q^{5} +(-2.35207 + 2.35207i) q^{7} +(-1.50731 - 1.50731i) q^{9} +(1.81739 - 0.752787i) q^{11} +(0.848387 - 2.04819i) q^{13} -0.891289i q^{15} -6.00997i q^{17} +(-1.54713 + 3.73510i) q^{19} +(2.86370 - 1.18618i) q^{21} +(-2.91236 - 2.91236i) q^{23} +(2.88865 - 2.88865i) q^{25} +(1.82997 + 4.41794i) q^{27} +(9.69383 + 4.01532i) q^{29} +7.52140 q^{31} -1.83307 q^{33} +(-2.93936 - 1.21752i) q^{35} +(0.994652 + 2.40130i) q^{37} +(-1.46078 + 1.46078i) q^{39} +(-1.37894 - 1.37894i) q^{41} +(10.8651 - 4.50046i) q^{43} +(0.780239 - 1.88366i) q^{45} -3.33173i q^{47} -4.06450i q^{49} +(-2.14318 + 5.17409i) q^{51} +(8.02993 - 3.32611i) q^{53} +(1.33042 + 1.33042i) q^{55} +(2.66390 - 2.66390i) q^{57} +(-4.70936 - 11.3694i) q^{59} +(0.166225 + 0.0688525i) q^{61} +7.09059 q^{63} +2.12044 q^{65} +(-8.39629 - 3.47786i) q^{67} +(1.46875 + 3.54587i) q^{69} +(-7.92235 + 7.92235i) q^{71} +(-5.84544 - 5.84544i) q^{73} +(-3.51699 + 1.45679i) q^{75} +(-2.50402 + 6.04524i) q^{77} +1.80100i q^{79} +1.93890i q^{81} +(1.98429 - 4.79049i) q^{83} +(5.31079 - 2.19980i) q^{85} +(-6.91372 - 6.91372i) q^{87} +(6.38134 - 6.38134i) q^{89} +(2.82202 + 6.81296i) q^{91} +(-6.47531 - 2.68216i) q^{93} -3.86686 q^{95} +0.874915 q^{97} +(-3.87404 - 1.60468i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{5} - 16 q^{9}+O(q^{10}) $ 16 * q - 8 * q^5 - 16 * q^9	$ 16 q - 8 q^{5} - 16 q^{9} + 8 q^{13} - 16 q^{21} - 32 q^{25} + 24 q^{29} - 80 q^{33} - 40 q^{37} - 16 q^{41} - 24 q^{45} + 56 q^{53} - 16 q^{57} - 8 q^{61} - 32 q^{65} + 64 q^{69} + 32 q^{73} - 64 q^{77} + 48 q^{85} + 32 q^{89} - 80 q^{93} - 16 q^{97}+O(q^{100}) $ 16 * q - 8 * q^5 - 16 * q^9 + 8 * q^13 - 16 * q^21 - 32 * q^25 + 24 * q^29 - 80 * q^33 - 40 * q^37 - 16 * q^41 - 24 * q^45 + 56 * q^53 - 16 * q^57 - 8 * q^61 - 32 * q^65 + 64 * q^69 + 32 * q^73 - 64 * q^77 + 48 * q^85 + 32 * q^89 - 80 * q^93 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times$.

$n$	$5$	$1023$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$

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
$3$	−0.860919	−	0.356604i	−0.497052	−	0.205886i	0.120052	−	0.992768i	$-0.461694\pi$
$3$	−0.860919	−	0.356604i	−0.497052	−	0.205886i	−0.617103	+	0.786882i	$0.711694\pi$
$4$		0			0
$5$	0.366025	+	0.883663i	0.163692	+	0.395186i	0.984348	−	0.176236i	$-0.0563920\pi$
$5$	0.366025	+	0.883663i	0.163692	+	0.395186i	−0.820656	+	0.571422i	$0.806392\pi$
$6$		0			0
$7$	−2.35207	+	2.35207i	−0.889000	+	0.889000i	−0.994427	−	0.105427i	$-0.966379\pi$
$7$	−2.35207	+	2.35207i	−0.889000	+	0.889000i	0.105427	+	0.994427i	$0.466379\pi$
$8$		0			0
$9$	−1.50731	−	1.50731i	−0.502435	−	0.502435i
$10$		0			0
$11$	1.81739	−	0.752787i	0.547963	−	0.226974i	−0.0914869	−	0.995806i	$-0.529162\pi$
$11$	1.81739	−	0.752787i	0.547963	−	0.226974i	0.639450	+	0.768832i	$0.279162\pi$
$12$		0			0
$13$	0.848387	−	2.04819i	0.235300	−	0.568065i	−0.761485	−	0.648182i	$-0.775529\pi$
$13$	0.848387	−	2.04819i	0.235300	−	0.568065i	0.996785	+	0.0801172i	$0.0255294\pi$
$14$		0			0
$15$		−	0.891289i		−	0.230130i
$16$		0			0
$17$		−	6.00997i		−	1.45763i	−0.684710	−	0.728816i	$-0.740071\pi$
$17$		−	6.00997i		−	1.45763i	0.684710	−	0.728816i	$-0.259929\pi$
$18$		0			0
$19$	−1.54713	+	3.73510i	−0.354935	+	0.856890i	0.641060	+	0.767490i	$0.278495\pi$
$19$	−1.54713	+	3.73510i	−0.354935	+	0.856890i	−0.995996	+	0.0893996i	$0.971505\pi$
$20$		0			0
$21$	2.86370	−	1.18618i	0.624911	−	0.258847i
$22$		0			0
$23$	−2.91236	−	2.91236i	−0.607269	−	0.607269i	0.334962	−	0.942232i	$-0.391276\pi$
$23$	−2.91236	−	2.91236i	−0.607269	−	0.607269i	−0.942232	+	0.334962i	$0.891276\pi$
$24$		0			0
$25$	2.88865	−	2.88865i	0.577729	−	0.577729i
$26$		0			0
$27$	1.82997	+	4.41794i	0.352178	+	0.850232i
$28$		0			0
$29$	9.69383	+	4.01532i	1.80010	+	0.745625i	0.986405	+	0.164332i	$0.0525469\pi$
$29$	9.69383	+	4.01532i	1.80010	+	0.745625i	0.813694	+	0.581293i	$0.197453\pi$
$30$		0			0
$31$	7.52140			1.35088			0.675442	−	0.737413i	$-0.263953\pi$
$31$	7.52140			1.35088			0.675442	+	0.737413i	$0.263953\pi$
$32$		0			0
$33$	−1.83307			−0.319097
$34$		0			0
$35$	−2.93936	−	1.21752i	−0.496843	−	0.205799i
$36$		0			0
$37$	0.994652	+	2.40130i	0.163520	+	0.394772i	0.984308	−	0.176462i	$-0.0564652\pi$
$37$	0.994652	+	2.40130i	0.163520	+	0.394772i	−0.820788	+	0.571233i	$0.806465\pi$
$38$		0			0
$39$	−1.46078	+	1.46078i	−0.233913	+	0.233913i
$40$		0			0
$41$	−1.37894	−	1.37894i	−0.215354	−	0.215354i	0.591183	−	0.806537i	$-0.298661\pi$
$41$	−1.37894	−	1.37894i	−0.215354	−	0.215354i	−0.806537	+	0.591183i	$0.798661\pi$
$42$		0			0
$43$	10.8651	−	4.50046i	1.65691	−	0.686314i	0.659074	−	0.752078i	$-0.270948\pi$
$43$	10.8651	−	4.50046i	1.65691	−	0.686314i	0.997835	+	0.0657637i	$0.0209484\pi$
$44$		0			0
$45$	0.780239	−	1.88366i	0.116311	−	0.280800i
$46$		0			0
$47$		−	3.33173i		−	0.485983i	−0.970028	−	0.242991i	$-0.921871\pi$
$47$		−	3.33173i		−	0.485983i	0.970028	−	0.242991i	$-0.0781286\pi$
$48$		0			0
$49$		−	4.06450i		−	0.580643i
$50$		0			0
$51$	−2.14318	+	5.17409i	−0.300105	+	0.724518i
$52$		0			0
$53$	8.02993	−	3.32611i	1.10300	−	0.456876i	0.244475	−	0.969656i	$-0.421384\pi$
$53$	8.02993	−	3.32611i	1.10300	−	0.456876i	0.858520	+	0.512780i	$0.171384\pi$
$54$		0			0
$55$	1.33042	+	1.33042i	0.179394	+	0.179394i
$56$		0			0
$57$	2.66390	−	2.66390i	0.352843	−	0.352843i
$58$		0			0
$59$	−4.70936	−	11.3694i	−0.613106	−	1.48017i	−0.859570	−	0.511017i	$-0.829269\pi$
$59$	−4.70936	−	11.3694i	−0.613106	−	1.48017i	0.246464	−	0.969152i	$-0.420731\pi$
$60$		0			0
$61$	0.166225	+	0.0688525i	0.0212829	+	0.00881566i	0.393299	−	0.919410i	$-0.371334\pi$
$61$	0.166225	+	0.0688525i	0.0212829	+	0.00881566i	−0.372017	+	0.928226i	$0.621334\pi$
$62$		0			0
$63$	7.09059			0.893330
$64$		0			0
$65$	2.12044			0.263008
$66$		0			0
$67$	−8.39629	−	3.47786i	−1.02577	−	0.424888i	−0.194587	−	0.980885i	$-0.562336\pi$
$67$	−8.39629	−	3.47786i	−1.02577	−	0.424888i	−0.831184	+	0.555997i	$0.812336\pi$
$68$		0			0
$69$	1.46875	+	3.54587i	0.176816	+	0.426872i
$70$		0			0
$71$	−7.92235	+	7.92235i	−0.940210	+	0.940210i	−0.998311	−	0.0581008i	$-0.981496\pi$
$71$	−7.92235	+	7.92235i	−0.940210	+	0.940210i	0.0581008	+	0.998311i	$0.481496\pi$
$72$		0			0
$73$	−5.84544	−	5.84544i	−0.684157	−	0.684157i	0.276777	−	0.960934i	$-0.410734\pi$
$73$	−5.84544	−	5.84544i	−0.684157	−	0.684157i	−0.960934	+	0.276777i	$0.910734\pi$
$74$		0			0
$75$	−3.51699	+	1.45679i	−0.406108	+	0.168215i
$76$		0			0
$77$	−2.50402	+	6.04524i	−0.285360	+	0.688919i
$78$		0			0
$79$			1.80100i			0.202628i	0.994855	+	0.101314i	$0.0323046\pi$
$79$			1.80100i			0.202628i	−0.994855	+	0.101314i	$0.967695\pi$
$80$		0			0
$81$			1.93890i			0.215433i
$82$		0			0
$83$	1.98429	−	4.79049i	0.217804	−	0.525825i	−0.776779	−	0.629773i	$-0.783148\pi$
$83$	1.98429	−	4.79049i	0.217804	−	0.525825i	0.994583	+	0.103949i	$0.0331478\pi$
$84$		0			0
$85$	5.31079	−	2.19980i	0.576036	−	0.238602i
$86$		0			0
$87$	−6.91372	−	6.91372i	−0.741229	−	0.741229i
$88$		0			0
$89$	6.38134	−	6.38134i	0.676421	−	0.676421i	−0.282768	−	0.959188i	$-0.591253\pi$
$89$	6.38134	−	6.38134i	0.676421	−	0.676421i	0.959188	+	0.282768i	$0.0912525\pi$
$90$		0			0
$91$	2.82202	+	6.81296i	0.295828	+	0.714192i
$92$		0			0
$93$	−6.47531	−	2.68216i	−0.671459	−	0.278127i
$94$		0			0
$95$	−3.86686			−0.396731
$96$		0			0
$97$	0.874915			0.0888342			0.0444171	−	0.999013i	$-0.485857\pi$
$97$	0.874915			0.0888342			0.0444171	+	0.999013i	$0.485857\pi$
$98$		0			0
$99$	−3.87404	−	1.60468i	−0.389356	−	0.161276i
$100$		0			0
$101$	0.000704119		0.00169989i	7.00625e−5		0.000169146i	0.923915	−	0.382599i	$-0.124971\pi$
$101$	0.000704119		0.00169989i	7.00625e−5		0.000169146i	−0.923844	+	0.382768i	$0.874971\pi$
$102$		0			0
$103$	8.93098	−	8.93098i	0.879996	−	0.879996i	−0.113538	−	0.993534i	$-0.536218\pi$
$103$	8.93098	−	8.93098i	0.879996	−	0.879996i	0.993534	+	0.113538i	$0.0362184\pi$
$104$		0			0
$105$	2.09638	+	2.09638i	0.204585	+	0.204585i
$106$		0			0
$107$	3.07786	−	1.27489i	0.297548	−	0.123248i	−0.228915	−	0.973446i	$-0.573518\pi$
$107$	3.07786	−	1.27489i	0.297548	−	0.123248i	0.526463	+	0.850198i	$0.323518\pi$
$108$		0			0
$109$	3.19445	−	7.71209i	0.305973	−	0.738684i	−0.693855	−	0.720115i	$-0.744089\pi$
$109$	3.19445	−	7.71209i	0.305973	−	0.738684i	0.999828	−	0.0185691i	$-0.00591107\pi$
$110$		0			0
$111$		−	2.42202i		−	0.229888i
$112$		0			0
$113$		−	7.03528i		−	0.661823i	−0.943662	−	0.330912i	$-0.892644\pi$
$113$		−	7.03528i		−	0.661823i	0.943662	−	0.330912i	$-0.107356\pi$
$114$		0			0
$115$	1.50755	−	3.63955i	0.140580	−	0.339389i
$116$		0			0
$117$	−4.36603	+	1.80847i	−0.403639	+	0.167193i
$118$		0			0
$119$	14.1359	+	14.1359i	1.29583	+	1.29583i
$120$		0			0
$121$	−5.04196	+	5.04196i	−0.458360	+	0.458360i
$122$		0			0
$123$	0.695418	+	1.67889i	0.0627037	+	0.151380i
$124$		0			0
$125$	8.02823	+	3.32540i	0.718067	+	0.297433i
$126$		0			0
$127$	1.09821			0.0974502			0.0487251	−	0.998812i	$-0.484484\pi$
$127$	1.09821			0.0974502			0.0487251	+	0.998812i	$0.484484\pi$
$128$		0			0
$129$	−10.9588			−0.964872
$130$		0			0
$131$	17.0608	+	7.06683i	1.49061	+	0.617431i	0.971450	−	0.237245i	$-0.0762443\pi$
$131$	17.0608	+	7.06683i	1.49061	+	0.617431i	0.519161	+	0.854676i	$0.326244\pi$
$132$		0			0
$133$	−5.14626	−	12.4242i	−0.446238	−	1.07731i
$134$		0			0
$135$	−3.23415	+	3.23415i	−0.278352	+	0.278352i
$136$		0			0
$137$	5.83183	+	5.83183i	0.498247	+	0.498247i	0.910892	−	0.412645i	$-0.135395\pi$
$137$	5.83183	+	5.83183i	0.498247	+	0.498247i	−0.412645	+	0.910892i	$0.635395\pi$
$138$		0			0
$139$	−12.4088	+	5.13991i	−1.05250	+	0.435961i	−0.840785	−	0.541369i	$-0.817906\pi$
$139$	−12.4088	+	5.13991i	−1.05250	+	0.435961i	−0.211719	+	0.977331i	$0.567906\pi$
$140$		0			0
$141$	−1.18811	+	2.86835i	−0.100057	+	0.241558i
$142$		0			0
$143$		−	4.36101i		−	0.364686i
$144$		0			0
$145$			10.0358i			0.833427i
$146$		0			0
$147$	−1.44942	+	3.49920i	−0.119546	+	0.288609i
$148$		0			0
$149$	−16.6186	+	6.88366i	−1.36145	+	0.563932i	−0.939457	−	0.342667i	$-0.888670\pi$
$149$	−16.6186	+	6.88366i	−1.36145	+	0.563932i	−0.421994	+	0.906598i	$0.638670\pi$
$150$		0			0
$151$	−8.54877	−	8.54877i	−0.695689	−	0.695689i	0.267789	−	0.963478i	$-0.413707\pi$
$151$	−8.54877	−	8.54877i	−0.695689	−	0.695689i	−0.963478	+	0.267789i	$0.913707\pi$
$152$		0			0
$153$	−9.05886	+	9.05886i	−0.732365	+	0.732365i
$154$		0			0
$155$	2.75302	+	6.64639i	0.221128	+	0.533851i
$156$		0			0
$157$	−5.46821	−	2.26500i	−0.436410	−	0.180767i	0.153652	−	0.988125i	$-0.450897\pi$
$157$	−5.46821	−	2.26500i	−0.436410	−	0.180767i	−0.590062	+	0.807358i	$0.700897\pi$
$158$		0			0
$159$	−8.09922			−0.642310
$160$		0			0
$161$	13.7002			1.07973
$162$		0			0
$163$	7.16282	+	2.96694i	0.561035	+	0.232388i	0.645135	−	0.764069i	$-0.276801\pi$
$163$	7.16282	+	2.96694i	0.561035	+	0.232388i	−0.0840992	+	0.996457i	$0.526801\pi$
$164$		0			0
$165$	−0.670951	−	1.61982i	−0.0522334	−	0.126103i
$166$		0			0
$167$	14.5948	−	14.5948i	1.12938	−	1.12938i	0.139100	−	0.990278i	$-0.455579\pi$
$167$	14.5948	−	14.5948i	1.12938	−	1.12938i	0.990278	−	0.139100i	$-0.0444209\pi$
$168$		0			0
$169$	5.71707	+	5.71707i	0.439775	+	0.439775i
$170$		0			0
$171$	7.96193	−	3.29794i	0.608864	−	0.252200i
$172$		0			0
$173$	−2.74788	+	6.63397i	−0.208918	+	0.504372i	−0.993253	−	0.115965i	$-0.963004\pi$
$173$	−2.74788	+	6.63397i	−0.208918	+	0.504372i	0.784336	+	0.620337i	$0.213004\pi$
$174$		0			0
$175$			13.5886i			1.02720i
$176$		0			0
$177$			11.4675i			0.861950i
$178$		0			0
$179$	0.333419	−	0.804946i	0.0249209	−	0.0601645i	−0.910929	−	0.412563i	$-0.864634\pi$
$179$	0.333419	−	0.804946i	0.0249209	−	0.0601645i	0.935850	+	0.352398i	$0.114634\pi$
$180$		0			0
$181$	−15.9365	+	6.60110i	−1.18455	+	0.490656i	−0.885976	−	0.463731i	$-0.846510\pi$
$181$	−15.9365	+	6.60110i	−1.18455	+	0.490656i	−0.298572	+	0.954387i	$0.596510\pi$
$182$		0			0
$183$	−0.118553	−	0.118553i	−0.00876367	−	0.00876367i
$184$		0			0
$185$	−1.75787	+	1.75787i	−0.129242	+	0.129242i
$186$		0			0
$187$	−4.52423	−	10.9225i	−0.330844	−	0.798729i
$188$		0			0
$189$	−14.6955	−	6.08709i	−1.06894	−	0.442770i
$190$		0			0
$191$	−21.7629			−1.57471			−0.787356	−	0.616499i	$-0.788551\pi$
$191$	−21.7629			−1.57471			−0.787356	+	0.616499i	$0.788551\pi$
$192$		0			0
$193$	0.640834			0.0461283			0.0230641	−	0.999734i	$-0.492658\pi$
$193$	0.640834			0.0461283			0.0230641	+	0.999734i	$0.492658\pi$
$194$		0			0
$195$	−1.82553	−	0.756158i	−0.130729	−	0.0541496i
$196$		0			0
$197$	7.91794	+	19.1156i	0.564130	+	1.36193i	0.906436	+	0.422342i	$0.138792\pi$
$197$	7.91794	+	19.1156i	0.564130	+	1.36193i	−0.342306	+	0.939588i	$0.611208\pi$
$198$		0			0
$199$	−7.96053	+	7.96053i	−0.564307	+	0.564307i	−0.930528	−	0.366221i	$-0.880651\pi$
$199$	−7.96053	+	7.96053i	−0.564307	+	0.564307i	0.366221	+	0.930528i	$0.380651\pi$
$200$		0			0
$201$	5.98831	+	5.98831i	0.422383	+	0.422383i
$202$		0			0
$203$	−32.2449	+	13.3563i	−2.26315	+	0.937427i
$204$		0			0
$205$	0.713791	−	1.72324i	0.0498533	−	0.120356i
$206$		0			0
$207$			8.77964i			0.610227i
$208$		0			0
$209$			7.95278i			0.550105i
$210$		0			0
$211$	2.27691	−	5.49696i	0.156749	−	0.378426i	−0.825922	−	0.563785i	$-0.809345\pi$
$211$	2.27691	−	5.49696i	0.156749	−	0.378426i	0.982671	+	0.185359i	$0.0593447\pi$
$212$		0			0
$213$	9.64564	−	3.99536i	0.660909	−	0.273757i
$214$		0			0
$215$	7.95379	+	7.95379i	0.542444	+	0.542444i
$216$		0			0
$217$	−17.6909	+	17.6909i	−1.20094	+	1.20094i
$218$		0			0
$219$	2.94794	+	7.11696i	0.199203	+	0.480920i
$220$		0			0
$221$	−12.3095	−	5.09878i	−0.828030	−	0.342981i
$222$		0			0
$223$	−15.3054			−1.02493			−0.512464	−	0.858709i	$-0.671267\pi$
$223$	−15.3054			−1.02493			−0.512464	+	0.858709i	$0.671267\pi$
$224$		0			0
$225$	−8.70815			−0.580543
$226$		0			0
$227$	16.1228	+	6.67827i	1.07011	+	0.443252i	0.847028	−	0.531548i	$-0.178390\pi$
$227$	16.1228	+	6.67827i	1.07011	+	0.443252i	0.223078	+	0.974801i	$0.428390\pi$
$228$		0			0
$229$	−5.84666	−	14.1151i	−0.386358	−	0.932752i	−0.990705	−	0.136030i	$-0.956566\pi$
$229$	−5.84666	−	14.1151i	−0.386358	−	0.932752i	0.604346	−	0.796722i	$-0.293434\pi$
$230$		0			0
$231$	4.31152	−	4.31152i	0.283677	−	0.283677i
$232$		0			0
$233$	−8.21582	−	8.21582i	−0.538236	−	0.538236i	0.384774	−	0.923011i	$-0.374279\pi$
$233$	−8.21582	−	8.21582i	−0.538236	−	0.538236i	−0.923011	+	0.384774i	$0.874279\pi$
$234$		0			0
$235$	2.94413	−	1.21950i	0.192054	−	0.0795512i
$236$		0			0
$237$	0.642242	−	1.55051i	0.0417181	−	0.100716i
$238$		0			0
$239$			4.21394i			0.272577i	0.990669	+	0.136289i	$0.0435175\pi$
$239$			4.21394i			0.272577i	−0.990669	+	0.136289i	$0.956483\pi$
$240$		0			0
$241$			20.9382i			1.34875i	0.738391	+	0.674373i	$0.235586\pi$
$241$			20.9382i			1.34875i	−0.738391	+	0.674373i	$0.764414\pi$
$242$		0			0
$243$	6.18133	−	14.9230i	0.396532	−	0.957314i
$244$		0			0
$245$	3.59165	−	1.48771i	0.229462	−	0.0950463i
$246$		0			0
$247$	6.33762	+	6.33762i	0.403253	+	0.403253i
$248$		0			0
$249$	−3.41662	+	3.41662i	−0.216519	+	0.216519i
$250$		0			0
$251$	−6.98106	−	16.8538i	−0.440641	−	1.06380i	−0.975724	−	0.219002i	$-0.929720\pi$
$251$	−6.98106	−	16.8538i	−0.440641	−	1.06380i	0.535084	−	0.844799i	$-0.320280\pi$
$252$		0			0
$253$	−7.48528	−	3.10051i	−0.470596	−	0.194927i
$254$		0			0
$255$	−5.35662			−0.335444
$256$		0			0
$257$	15.7839			0.984570			0.492285	−	0.870434i	$-0.336162\pi$
$257$	15.7839			0.984570			0.492285	+	0.870434i	$0.336162\pi$
$258$		0			0
$259$	−7.98753	−	3.30854i	−0.496321	−	0.205583i
$260$		0			0
$261$	−8.55926	−	20.6639i	−0.529805	−	1.27906i
$262$		0			0
$263$	15.7140	−	15.7140i	0.968967	−	0.968967i	−0.0305653	−	0.999533i	$-0.509731\pi$
$263$	15.7140	−	15.7140i	0.968967	−	0.968967i	0.999533	+	0.0305653i	$0.00973076\pi$
$264$		0			0
$265$	5.87832	+	5.87832i	0.361102	+	0.361102i
$266$		0			0
$267$	−7.76943	+	3.21820i	−0.475481	+	0.196951i
$268$		0			0
$269$	3.62542	−	8.75253i	0.221045	−	0.533651i	−0.773987	−	0.633201i	$-0.781740\pi$
$269$	3.62542	−	8.75253i	0.221045	−	0.533651i	0.995033	+	0.0995505i	$0.0317405\pi$
$270$		0			0
$271$		−	6.69345i		−	0.406598i	−0.979117	−	0.203299i	$-0.934834\pi$
$271$		−	6.69345i		−	0.406598i	0.979117	−	0.203299i	$-0.0651664\pi$
$272$		0			0
$273$		−	6.87175i		−	0.415897i
$274$		0			0
$275$	3.07526	−	7.42433i	0.185445	−	0.447704i
$276$		0			0
$277$	−23.3643	+	9.67781i	−1.40382	+	0.581483i	−0.950741	−	0.309985i	$-0.899676\pi$
$277$	−23.3643	+	9.67781i	−1.40382	+	0.581483i	−0.453083	+	0.891468i	$0.649676\pi$
$278$		0			0
$279$	−11.3371	−	11.3371i	−0.678731	−	0.678731i
$280$		0			0
$281$	13.6559	−	13.6559i	0.814640	−	0.814640i	−0.170685	−	0.985326i	$-0.554598\pi$
$281$	13.6559	−	13.6559i	0.814640	−	0.814640i	0.985326	+	0.170685i	$0.0545982\pi$
$282$		0			0
$283$	5.28083	+	12.7490i	0.313913	+	0.757852i	0.999553	+	0.0299113i	$0.00952250\pi$
$283$	5.28083	+	12.7490i	0.313913	+	0.757852i	−0.685640	+	0.727941i	$0.740478\pi$
$284$		0			0
$285$	3.32905	+	1.37894i	0.197196	+	0.0816812i
$286$		0			0
$287$	6.48672			0.382899
$288$		0			0
$289$	−19.1197			−1.12469
$290$		0			0
$291$	−0.753231	−	0.311998i	−0.0441552	−	0.0182897i
$292$		0			0
$293$	6.15402	+	14.8571i	0.359521	+	0.867962i	0.995367	+	0.0961455i	$0.0306514\pi$
$293$	6.15402	+	14.8571i	0.359521	+	0.867962i	−0.635846	+	0.771816i	$0.719349\pi$
$294$		0			0
$295$	8.32298	−	8.32298i	0.484582	−	0.484582i
$296$		0			0
$297$	6.65153	+	6.65153i	0.385961	+	0.385961i
$298$		0			0
$299$	−8.43587	+	3.49425i	−0.487859	+	0.202078i
$300$		0			0
$301$	−14.9700	+	36.1409i	−0.862859	+	2.08313i
$302$		0			0
$303$		−	0.00171456i		−	9.84990e-5i
$304$		0			0
$305$			0.172088i			0.00985375i
$306$		0			0
$307$	2.65468	−	6.40896i	0.151511	−	0.365779i	−0.829841	−	0.558000i	$-0.811569\pi$
$307$	2.65468	−	6.40896i	0.151511	−	0.365779i	0.981352	+	0.192221i	$0.0615690\pi$
$308$		0			0
$309$	−10.8737	+	4.50402i	−0.618582	+	0.256225i
$310$		0			0
$311$	21.7524	+	21.7524i	1.23347	+	1.23347i	0.962624	+	0.270841i	$0.0873018\pi$
$311$	21.7524	+	21.7524i	1.23347	+	1.23347i	0.270841	+	0.962624i	$0.412698\pi$
$312$		0			0
$313$	2.78658	−	2.78658i	0.157507	−	0.157507i	−0.623954	−	0.781461i	$-0.714475\pi$
$313$	2.78658	−	2.78658i	0.157507	−	0.157507i	0.781461	+	0.623954i	$0.214475\pi$
$314$		0			0
$315$	2.59534	+	6.26569i	0.146231	+	0.353032i
$316$		0			0
$317$	3.91065	+	1.61984i	0.219644	+	0.0909794i	0.489792	−	0.871839i	$-0.337073\pi$
$317$	3.91065	+	1.61984i	0.219644	+	0.0909794i	−0.270148	+	0.962819i	$0.587073\pi$
$318$		0			0
$319$	20.6401			1.15563
$320$		0			0
$321$	−3.10442			−0.173272
$322$		0			0
$323$	22.4478	+	9.29819i	1.24903	+	0.517365i
$324$		0			0
$325$	−3.46580	−	8.36719i	−0.192248	−	0.464128i
$326$		0			0
$327$	−5.50033	+	5.50033i	−0.304169	+	0.304169i
$328$		0			0
$329$	7.83647	+	7.83647i	0.432039	+	0.432039i
$330$		0			0
$331$	14.9631	−	6.19790i	0.822444	−	0.340668i	0.0685372	−	0.997649i	$-0.478167\pi$
$331$	14.9631	−	6.19790i	0.822444	−	0.340668i	0.753907	+	0.656981i	$0.228167\pi$
$332$		0			0
$333$	2.12025	−	5.11874i	0.116189	−	0.280505i
$334$		0			0
$335$		−	8.69248i		−	0.474921i
$336$		0			0
$337$		−	2.16071i		−	0.117702i	−0.998267	−	0.0588508i	$-0.981256\pi$
$337$		−	2.16071i		−	0.117702i	0.998267	−	0.0588508i	$-0.0187436\pi$
$338$		0			0
$339$	−2.50881	+	6.05680i	−0.136260	+	0.328960i
$340$		0			0
$341$	13.6693	−	5.66201i	0.740235	−	0.306615i
$342$		0			0
$343$	−6.90451	−	6.90451i	−0.372809	−	0.372809i
$344$		0			0
$345$	−2.59575	+	2.59575i	−0.139751	+	0.139751i
$346$		0			0
$347$	−3.36433	−	8.12222i	−0.180607	−	0.436024i	0.807485	−	0.589888i	$-0.200828\pi$
$347$	−3.36433	−	8.12222i	−0.180607	−	0.436024i	−0.988092	+	0.153864i	$0.950828\pi$
$348$		0			0
$349$	−14.8014	−	6.13095i	−0.792302	−	0.328182i	−0.0504332	−	0.998727i	$-0.516060\pi$
$349$	−14.8014	−	6.13095i	−0.792302	−	0.328182i	−0.741869	+	0.670545i	$0.766060\pi$
$350$		0			0
$351$	10.6013			0.565855
$352$		0			0
$353$	−2.59235			−0.137977			−0.0689885	−	0.997617i	$-0.521977\pi$
$353$	−2.59235			−0.137977			−0.0689885	+	0.997617i	$0.521977\pi$
$354$		0			0
$355$	−9.90047	−	4.10091i	−0.525463	−	0.217654i
$356$		0			0
$357$	−7.12893	−	17.2108i	−0.377303	−	0.910890i
$358$		0			0
$359$	4.94678	−	4.94678i	0.261081	−	0.261081i	−0.564412	−	0.825493i	$-0.690897\pi$
$359$	4.94678	−	4.94678i	0.261081	−	0.261081i	0.825493	+	0.564412i	$0.190897\pi$
$360$		0			0
$361$	1.87768	+	1.87768i	0.0988255	+	0.0988255i
$362$		0			0
$363$	6.13870	−	2.54273i	0.322198	−	0.133459i
$364$		0			0
$365$	3.02582	−	7.30499i	0.158379	−	0.382360i
$366$		0			0
$367$		−	19.5663i		−	1.02135i	−0.859774	−	0.510675i	$-0.829395\pi$
$367$		−	19.5663i		−	1.02135i	0.859774	−	0.510675i	$-0.170605\pi$
$368$		0			0
$369$			4.15696i			0.216403i
$370$		0			0
$371$	−11.0637	+	26.7102i	−0.574401	+	1.38673i
$372$		0			0
$373$	20.3665	−	8.43606i	1.05454	−	0.436803i	0.213026	−	0.977046i	$-0.431668\pi$
$373$	20.3665	−	8.43606i	1.05454	−	0.436803i	0.841509	+	0.540244i	$0.181668\pi$
$374$		0			0
$375$	−5.72580	−	5.72580i	−0.295679	−	0.295679i
$376$		0			0
$377$	16.4482	−	16.4482i	0.847128	−	0.847128i
$378$		0			0
$379$	−1.60971	−	3.88618i	−0.0826851	−	0.199620i	0.877130	−	0.480253i	$-0.159455\pi$
$379$	−1.60971	−	3.88618i	−0.0826851	−	0.199620i	−0.959815	+	0.280634i	$0.909455\pi$
$380$		0			0
$381$	−0.945468	−	0.391626i	−0.0484378	−	0.0200636i
$382$		0			0
$383$	−20.6568			−1.05552			−0.527758	−	0.849395i	$-0.676967\pi$
$383$	−20.6568			−1.05552			−0.527758	+	0.849395i	$0.676967\pi$
$384$		0			0
$385$	−6.25850			−0.318963
$386$		0			0
$387$	−23.1606	−	9.59343i	−1.17732	−	0.487661i
$388$		0			0
$389$	6.58576	+	15.8994i	0.333911	+	0.806133i	0.998274	+	0.0587232i	$0.0187029\pi$
$389$	6.58576	+	15.8994i	0.333911	+	0.806133i	−0.664363	+	0.747410i	$0.731297\pi$
$390$		0			0
$391$	−17.5032	+	17.5032i	−0.885175	+	0.885175i
$392$		0			0
$393$	−12.1679	−	12.1679i	−0.613791	−	0.613791i
$394$		0			0
$395$	−1.59147	+	0.659210i	−0.0800757	+	0.0331685i
$396$		0			0
$397$	7.38205	−	17.8218i	0.370494	−	0.894452i	−0.623172	−	0.782084i	$-0.714157\pi$
$397$	7.38205	−	17.8218i	0.370494	−	0.894452i	0.993667	−	0.112368i	$-0.0358435\pi$
$398$		0			0
$399$			12.5314i			0.627354i
$400$		0			0
$401$			0.119032i			0.00594418i	0.999996	+	0.00297209i	$0.000946048\pi$
$401$			0.119032i			0.00594418i	−0.999996	+	0.00297209i	$0.999054\pi$
$402$		0			0
$403$	6.38106	−	15.4052i	0.317863	−	0.767390i
$404$		0			0
$405$	−1.71334	+	0.709687i	−0.0851363	+	0.0352646i
$406$		0			0
$407$	3.61534	+	3.61534i	0.179206	+	0.179206i
$408$		0			0
$409$	−10.5505	+	10.5505i	−0.521689	+	0.521689i	−0.918081	−	0.396392i	$-0.870262\pi$
$409$	−10.5505	+	10.5505i	−0.521689	+	0.521689i	0.396392	+	0.918081i	$0.370262\pi$
$410$		0			0
$411$	−2.94107	−	7.10038i	−0.145073	−	0.350236i
$412$		0			0
$413$	37.8184	+	15.6649i	1.86092	+	0.770819i
$414$		0			0
$415$	4.95948			0.243451
$416$		0			0
$417$	12.5159			0.612907
$418$		0			0
$419$	−8.44401	−	3.49762i	−0.412517	−	0.170870i	0.166766	−	0.985996i	$-0.446667\pi$
$419$	−8.44401	−	3.49762i	−0.412517	−	0.170870i	−0.579283	+	0.815126i	$0.696667\pi$
$420$		0			0
$421$	10.4476	+	25.2227i	0.509184	+	1.22928i	0.944354	+	0.328930i	$0.106688\pi$
$421$	10.4476	+	25.2227i	0.509184	+	1.22928i	−0.435171	+	0.900348i	$0.643312\pi$
$422$		0			0
$423$	−5.02193	+	5.02193i	−0.244175	+	0.244175i
$424$		0			0
$425$	−17.3607	−	17.3607i	−0.842117	−	0.842117i
$426$		0			0
$427$	−0.552918	+	0.229026i	−0.0267576	+	0.0110834i
$428$		0			0
$429$	−1.55515	+	3.75447i	−0.0750836	+	0.181268i
$430$		0			0
$431$			3.31726i			0.159787i	0.996803	+	0.0798934i	$0.0254580\pi$
$431$			3.31726i			0.159787i	−0.996803	+	0.0798934i	$0.974542\pi$
$432$		0			0
$433$		−	22.3224i		−	1.07275i	−0.843981	−	0.536374i	$-0.819794\pi$
$433$		−	22.3224i		−	1.07275i	0.843981	−	0.536374i	$-0.180206\pi$
$434$		0			0
$435$	3.57881	−	8.64000i	0.171591	−	0.414256i
$436$		0			0
$437$	15.3837	−	6.37216i	0.735904	−	0.304822i
$438$		0			0
$439$	−21.1260	−	21.1260i	−1.00829	−	1.00829i	−0.999965	−	0.00832228i	$-0.997351\pi$
$439$	−21.1260	−	21.1260i	−1.00829	−	1.00829i	−0.00832228	−	0.999965i	$-0.502649\pi$
$440$		0			0
$441$	−6.12644	+	6.12644i	−0.291735	+	0.291735i
$442$		0			0
$443$	−0.0916028	−	0.221149i	−0.00435218	−	0.0105071i	0.921689	−	0.387931i	$-0.126810\pi$
$443$	−0.0916028	−	0.221149i	−0.00435218	−	0.0105071i	−0.926041	+	0.377424i	$0.876810\pi$
$444$		0			0
$445$	7.97469	+	3.30323i	0.378037	+	0.156588i
$446$		0			0
$447$	16.7620			0.792817
$448$		0			0
$449$	21.5081			1.01503			0.507515	−	0.861643i	$-0.330564\pi$
$449$	21.5081			1.01503			0.507515	+	0.861643i	$0.330564\pi$
$450$		0			0
$451$	−3.54411	−	1.46802i	−0.166886	−	0.0691263i
$452$		0			0
$453$	4.31127	+	10.4083i	0.202561	+	0.489026i
$454$		0			0
$455$	−4.98743	+	4.98743i	−0.233814	+	0.233814i
$456$		0			0
$457$	−9.73721	−	9.73721i	−0.455487	−	0.455487i	0.441683	−	0.897171i	$-0.354381\pi$
$457$	−9.73721	−	9.73721i	−0.455487	−	0.455487i	−0.897171	+	0.441683i	$0.854381\pi$
$458$		0			0
$459$	26.5516	−	10.9981i	1.23932	−	0.513345i
$460$		0			0
$461$	−11.3049	+	27.2925i	−0.526523	+	1.27114i	0.407265	+	0.913310i	$0.366483\pi$
$461$	−11.3049	+	27.2925i	−0.526523	+	1.27114i	−0.933787	+	0.357828i	$0.883517\pi$
$462$		0			0
$463$			39.6338i			1.84194i	0.389635	+	0.920969i	$0.372601\pi$
$463$			39.6338i			1.84194i	−0.389635	+	0.920969i	$0.627399\pi$
$464$		0			0
$465$		−	6.70374i		−	0.310878i
$466$		0			0
$467$	−8.16422	+	19.7102i	−0.377795	+	0.912077i	0.614584	+	0.788852i	$0.289324\pi$
$467$	−8.16422	+	19.7102i	−0.377795	+	0.912077i	−0.992379	+	0.123226i	$0.960676\pi$
$468$		0			0
$469$	27.9289	−	11.5685i	1.28964	−	0.534185i
$470$		0			0
$471$	3.89997	+	3.89997i	0.179701	+	0.179701i
$472$		0			0
$473$	16.3582	−	16.3582i	0.752150	−	0.752150i
$474$		0			0
$475$	6.32027	+	15.2585i	0.289994	+	0.700107i
$476$		0			0
$477$	−17.1170	−	7.09010i	−0.783734	−	0.324633i
$478$		0			0
$479$	−3.07863			−0.140666			−0.0703331	−	0.997524i	$-0.522406\pi$
$479$	−3.07863			−0.140666			−0.0703331	+	0.997524i	$0.522406\pi$
$480$		0			0
$481$	5.76217			0.262732
$482$		0			0
$483$	−11.7947	−	4.88554i	−0.536679	−	0.222300i
$484$		0			0
$485$	0.320241	+	0.773131i	0.0145414	+	0.0351061i
$486$		0			0
$487$	−21.0643	+	21.0643i	−0.954517	+	0.954517i	−0.999010	−	0.0444931i	$-0.985833\pi$
$487$	−21.0643	+	21.0643i	−0.954517	+	0.954517i	0.0444931	+	0.999010i	$0.485833\pi$
$488$		0			0
$489$	−5.10858	−	5.10858i	−0.231018	−	0.231018i
$490$		0			0
$491$	16.0818	−	6.66130i	0.725761	−	0.300620i	0.0109525	−	0.999940i	$-0.496514\pi$
$491$	16.0818	−	6.66130i	0.725761	−	0.300620i	0.714809	+	0.699320i	$0.246514\pi$
$492$		0			0
$493$	24.1319	−	58.2596i	1.08685	−	2.62388i
$494$		0			0
$495$		−	4.01070i		−	0.180268i
$496$		0			0
$497$		−	37.2679i		−	1.67169i
$498$		0			0
$499$	−7.69930	+	18.5877i	−0.344668	+	0.832102i	0.652563	+	0.757734i	$0.273694\pi$
$499$	−7.69930	+	18.5877i	−0.344668	+	0.832102i	−0.997231	+	0.0743674i	$0.976306\pi$
$500$		0			0
$501$	−17.7695	+	7.36036i	−0.793882	+	0.328837i
$502$		0			0
$503$	−11.0921	−	11.0921i	−0.494572	−	0.494572i	0.415172	−	0.909743i	$-0.363722\pi$
$503$	−11.0921	−	11.0921i	−0.494572	−	0.494572i	−0.909743	+	0.415172i	$0.863722\pi$
$504$		0			0
$505$	−0.00124441	+	0.00124441i	−5.53755e−5	+	5.53755e-5i
$506$		0			0
$507$	−2.88320	−	6.96067i	−0.128048	−	0.309134i
$508$		0			0
$509$	33.5605	+	13.9012i	1.48754	+	0.616160i	0.970780	−	0.239970i	$-0.0771377\pi$
$509$	33.5605	+	13.9012i	1.48754	+	0.616160i	0.516761	+	0.856130i	$0.327138\pi$
$510$		0			0
$511$	27.4978			1.21643
$512$		0			0
$513$	−19.3326			−0.853556
$514$		0			0
$515$	11.1609	+	4.62301i	0.491810	+	0.203714i
$516$		0			0
$517$	−2.50808	−	6.05505i	−0.110305	−	0.266301i
$518$		0			0
$519$	4.73141	−	4.73141i	0.207686	−	0.207686i
$520$		0			0
$521$	5.27400	+	5.27400i	0.231058	+	0.231058i	0.813134	−	0.582076i	$-0.197759\pi$
$521$	5.27400	+	5.27400i	0.231058	+	0.231058i	−0.582076	+	0.813134i	$0.697759\pi$
$522$		0			0
$523$	5.67885	−	2.35226i	0.248319	−	0.102857i	−0.255053	−	0.966927i	$-0.582093\pi$
$523$	5.67885	−	2.35226i	0.248319	−	0.102857i	0.503371	+	0.864070i	$0.332093\pi$
$524$		0			0
$525$	4.84576	−	11.6987i	0.211486	−	0.510573i
$526$		0			0
$527$		−	45.2034i		−	1.96909i
$528$		0			0
$529$		−	6.03631i		−	0.262448i
$530$		0			0
$531$	−10.0387	+	24.2356i	−0.435643	+	1.05174i
$532$		0			0
$533$	−3.99420	+	1.65445i	−0.173008	+	0.0716622i
$534$		0			0
$535$	2.25315	+	2.25315i	0.0974122	+	0.0974122i
$536$		0			0
$537$	−0.574094	+	0.574094i	−0.0247740	+	0.0247740i
$538$		0			0
$539$	−3.05970	−	7.38678i	−0.131791	−	0.318171i
$540$		0			0
$541$	19.5140	+	8.08295i	0.838971	+	0.347513i	0.760448	−	0.649399i	$-0.224980\pi$
$541$	19.5140	+	8.08295i	0.838971	+	0.347513i	0.0785232	+	0.996912i	$0.474980\pi$
$542$		0			0
$543$	16.0740			0.689801
$544$		0			0
$545$	7.98414			0.342003
$546$		0			0
$547$	−3.60625	−	1.49376i	−0.154192	−	0.0638684i	0.304253	−	0.952591i	$-0.401593\pi$
$547$	−3.60625	−	1.49376i	−0.154192	−	0.0638684i	−0.458445	+	0.888723i	$0.651593\pi$
$548$		0			0
$549$	−0.146770	−	0.354333i	−0.00626397	−	0.0151226i
$550$		0			0
$551$	−29.9952	+	29.9952i	−1.27784	+	1.27784i
$552$		0			0
$553$	−4.23607	−	4.23607i	−0.180136	−	0.180136i
$554$		0			0
$555$	2.14025	−	0.886522i	0.0908487	−	0.0376308i
$556$		0			0
$557$	−7.31781	+	17.6668i	−0.310066	+	0.748565i	0.689636	+	0.724156i	$0.257770\pi$
$557$	−7.31781	+	17.6668i	−0.310066	+	0.748565i	−0.999702	+	0.0244089i	$0.992230\pi$
$558$		0			0
$559$		−	26.0719i		−	1.10272i
$560$		0			0
$561$			11.0167i			0.465125i
$562$		0			0
$563$	−1.12618	+	2.71884i	−0.0474628	+	0.114585i	−0.945833	−	0.324654i	$-0.894752\pi$
$563$	−1.12618	+	2.71884i	−0.0474628	+	0.114585i	0.898370	+	0.439240i	$0.144752\pi$
$564$		0			0
$565$	6.21682	−	2.57509i	0.261543	−	0.108335i
$566$		0			0
$567$	−4.56044	−	4.56044i	−0.191520	−	0.191520i
$568$		0			0
$569$	10.4042	−	10.4042i	0.436169	−	0.436169i	−0.454552	−	0.890720i	$-0.650201\pi$
$569$	10.4042	−	10.4042i	0.436169	−	0.436169i	0.890720	+	0.454552i	$0.150201\pi$
$570$		0			0
$571$	15.6556	+	37.7960i	0.655167	+	1.58171i	0.805181	+	0.593030i	$0.202068\pi$
$571$	15.6556	+	37.7960i	0.655167	+	1.58171i	−0.150013	+	0.988684i	$0.547932\pi$
$572$		0			0
$573$	18.7361	+	7.76076i	0.782713	+	0.324210i
$574$		0			0
$575$	−16.8256			−0.701675
$576$		0			0
$577$	−30.1981			−1.25716			−0.628582	−	0.777744i	$-0.716364\pi$
$577$	−30.1981			−1.25716			−0.628582	+	0.777744i	$0.716364\pi$
$578$		0			0
$579$	−0.551706	−	0.228524i	−0.0229281	−	0.00949714i
$580$		0			0
$581$	6.60040	+	15.9348i	0.273831	+	0.661086i
$582$		0			0
$583$	12.0897	−	12.0897i	0.500702	−	0.500702i
$584$		0			0
$585$	−3.19615	−	3.19615i	−0.132145	−	0.132145i
$586$		0			0
$587$	20.0997	−	8.32558i	0.829605	−	0.343634i	0.0728586	−	0.997342i	$-0.476788\pi$
$587$	20.0997	−	8.32558i	0.829605	−	0.343634i	0.756746	+	0.653709i	$0.226788\pi$
$588$		0			0
$589$	−11.6366	+	28.0932i	−0.479476	+	1.15756i
$590$		0			0
$591$		−	19.2806i		−	0.793096i
$592$		0			0
$593$		−	38.2715i		−	1.57162i	−0.618468	−	0.785810i	$-0.712246\pi$
$593$		−	38.2715i		−	1.57162i	0.618468	−	0.785810i	$-0.287754\pi$
$594$		0			0
$595$	−7.31727	+	17.6655i	−0.299979	+	0.724213i
$596$		0			0
$597$	9.69213	−	4.01461i	0.396672	−	0.164307i
$598$		0			0
$599$	2.76223	+	2.76223i	0.112862	+	0.112862i	0.761282	−	0.648421i	$-0.224570\pi$
$599$	2.76223	+	2.76223i	0.112862	+	0.112862i	−0.648421	+	0.761282i	$0.724570\pi$
$600$		0			0
$601$	20.7961	−	20.7961i	0.848289	−	0.848289i	−0.141630	−	0.989920i	$-0.545234\pi$
$601$	20.7961	−	20.7961i	0.848289	−	0.848289i	0.989920	+	0.141630i	$0.0452344\pi$
$602$		0			0
$603$	7.41359	+	17.8980i	0.301905	+	0.728862i
$604$		0			0
$605$	−6.30088	−	2.60991i	−0.256167	−	0.106108i
$606$		0			0
$607$	18.7402			0.760642			0.380321	−	0.924855i	$-0.375813\pi$
$607$	18.7402			0.760642			0.380321	+	0.924855i	$0.375813\pi$
$608$		0			0
$609$	32.5232			1.31790
$610$		0			0
$611$	−6.82401	−	2.82660i	−0.276070	−	0.114352i
$612$		0			0
$613$	−6.19497	−	14.9560i	−0.250212	−	0.604066i	0.748009	−	0.663689i	$-0.231010\pi$
$613$	−6.19497	−	14.9560i	−0.250212	−	0.604066i	−0.998221	+	0.0596229i	$0.981010\pi$
$614$		0			0
$615$	−1.22903	+	1.22903i	−0.0495593	+	0.0495593i
$616$		0			0
$617$	25.7897	+	25.7897i	1.03825	+	1.03825i	0.999239	+	0.0390142i	$0.0124218\pi$
$617$	25.7897	+	25.7897i	1.03825	+	1.03825i	0.0390142	+	0.999239i	$0.487578\pi$
$618$		0			0
$619$	5.34111	−	2.21236i	0.214677	−	0.0889222i	−0.272753	−	0.962084i	$-0.587934\pi$
$619$	5.34111	−	2.21236i	0.214677	−	0.0889222i	0.487431	+	0.873162i	$0.337934\pi$
$620$		0			0
$621$	7.53709	−	18.1962i	0.302453	−	0.730186i
$622$		0			0
$623$			30.0188i			1.20268i
$624$		0			0
$625$		−	12.1144i		−	0.484576i
$626$		0			0
$627$	2.83600	−	6.84670i	0.113259	−	0.273431i
$628$		0			0
$629$	14.4317	−	5.97782i	0.575431	−	0.238351i
$630$		0			0
$631$	−5.43699	−	5.43699i	−0.216443	−	0.216443i	0.590555	−	0.806998i	$-0.298909\pi$
$631$	−5.43699	−	5.43699i	−0.216443	−	0.216443i	−0.806998	+	0.590555i	$0.798909\pi$
$632$		0			0
$633$	−3.92048	+	3.92048i	−0.155825	+	0.155825i
$634$		0			0
$635$	0.401972	+	0.970446i	0.0159518	+	0.0385110i
$636$		0			0
$637$	−8.32486	−	3.44827i	−0.329843	−	0.136625i
$638$		0			0
$639$	23.8828			0.944789
$640$		0			0
$641$	11.1732			0.441315			0.220658	−	0.975351i	$-0.429180\pi$
$641$	11.1732			0.441315			0.220658	+	0.975351i	$0.429180\pi$
$642$		0			0
$643$	−35.7957	−	14.8270i	−1.41164	−	0.584722i	−0.458897	−	0.888490i	$-0.651755\pi$
$643$	−35.7957	−	14.8270i	−1.41164	−	0.584722i	−0.952746	+	0.303768i	$0.901755\pi$
$644$		0			0
$645$	−4.01121	−	9.68392i	−0.157941	−	0.381304i
$646$		0			0
$647$	−3.05035	+	3.05035i	−0.119922	+	0.119922i	−0.764521	−	0.644599i	$-0.777024\pi$
$647$	−3.05035	+	3.05035i	−0.119922	+	0.119922i	0.644599	+	0.764521i	$0.277024\pi$
$648$		0			0
$649$	−17.1175	−	17.1175i	−0.671920	−	0.671920i
$650$		0			0
$651$	21.5391	−	8.92177i	0.844182	−	0.349672i
$652$		0			0
$653$	6.45384	−	15.5810i	0.252558	−	0.609730i	−0.745851	−	0.666113i	$-0.767957\pi$
$653$	6.45384	−	15.5810i	0.252558	−	0.609730i	0.998409	+	0.0563832i	$0.0179568\pi$
$654$		0			0
$655$			17.6627i			0.690138i
$656$		0			0
$657$			17.6217i			0.687490i
$658$		0			0
$659$	16.0504	−	38.7490i	0.625233	−	1.50945i	−0.220250	−	0.975444i	$-0.570687\pi$
$659$	16.0504	−	38.7490i	0.625233	−	1.50945i	0.845483	−	0.534003i	$-0.179313\pi$
$660$		0			0
$661$	−22.6719	+	9.39102i	−0.881836	+	0.365268i	−0.777208	−	0.629243i	$-0.783365\pi$
$661$	−22.6719	+	9.39102i	−0.881836	+	0.365268i	−0.104627	+	0.994512i	$0.533365\pi$
$662$		0			0
$663$	8.77927	+	8.77927i	0.340959	+	0.340959i
$664$		0			0
$665$	9.09513	−	9.09513i	0.352694	−	0.352694i
$666$		0			0
$667$	−16.5379	−	39.9260i	−0.640349	−	1.54594i
$668$		0			0
$669$	13.1767	+	5.45798i	0.509442	+	0.211018i
$670$		0			0
$671$	0.353926			0.0136632
$672$		0			0
$673$	−19.5003			−0.751680			−0.375840	−	0.926685i	$-0.622646\pi$
$673$	−19.5003			−0.751680			−0.375840	+	0.926685i	$0.622646\pi$
$674$		0			0
$675$	18.0480	+	7.47572i	0.694668	+	0.287741i
$676$		0			0
$677$	6.44466	+	15.5588i	0.247688	+	0.597972i	0.998007	−	0.0631039i	$-0.0200999\pi$
$677$	6.44466	+	15.5588i	0.247688	+	0.597972i	−0.750319	+	0.661076i	$0.770100\pi$
$678$		0			0
$679$	−2.05787	+	2.05787i	−0.0789736	+	0.0789736i
$680$		0			0
$681$	−11.4989	−	11.4989i	−0.440639	−	0.440639i
$682$		0			0
$683$	−45.3415	+	18.7811i	−1.73495	+	0.718638i	−0.735805	+	0.677193i	$0.763196\pi$
$683$	−45.3415	+	18.7811i	−1.73495	+	0.718638i	−0.999141	+	0.0414451i	$0.986804\pi$
$684$		0			0
$685$	−3.01878	+	7.28797i	−0.115341	+	0.278459i
$686$		0			0
$687$			14.2369i			0.543171i
$688$		0			0
$689$		−	19.2686i		−	0.734076i
$690$		0			0
$691$	−3.36470	+	8.12311i	−0.127999	+	0.309018i	−0.974868	−	0.222785i	$-0.928485\pi$
$691$	−3.36470	+	8.12311i	−0.127999	+	0.309018i	0.846868	+	0.531803i	$0.178485\pi$
$692$		0			0
$693$	12.8864	−	5.33770i	0.489512	−	0.202763i
$694$		0			0
$695$	−9.08390	−	9.08390i	−0.344572	−	0.344572i
$696$		0			0
$697$	−8.28737	+	8.28737i	−0.313906	+	0.313906i
$698$		0			0
$699$	4.14336	+	10.0029i	0.156716	+	0.378346i
$700$		0			0
$701$	−25.6052	−	10.6060i	−0.967094	−	0.400584i	−0.157465	−	0.987525i	$-0.550332\pi$
$701$	−25.6052	−	10.6060i	−0.967094	−	0.400584i	−0.809630	+	0.586941i	$0.800332\pi$
$702$		0			0
$703$	−10.5079			−0.396315
$704$		0			0
$705$	−2.96953			−0.111839
$706$		0			0
$707$	−0.00565442	−	0.00234214i	−0.000212656	−	8.80851e-5i
$708$		0			0
$709$	8.52863	+	20.5899i	0.320299	+	0.773271i	0.999236	+	0.0390744i	$0.0124409\pi$
$709$	8.52863	+	20.5899i	0.320299	+	0.773271i	−0.678937	+	0.734197i	$0.737559\pi$
$710$		0			0
$711$	2.71465	−	2.71465i	0.101807	−	0.101807i
$712$		0			0
$713$	−21.9050	−	21.9050i	−0.820350	−	0.820350i
$714$		0			0
$715$	3.85367	−	1.59624i	0.144119	−	0.0596960i
$716$		0			0
$717$	1.50271	−	3.62786i	0.0561197	−	0.135485i
$718$		0			0
$719$		−	33.6036i		−	1.25320i	−0.779340	−	0.626601i	$-0.784445\pi$
$719$		−	33.6036i		−	1.25320i	0.779340	−	0.626601i	$-0.215555\pi$
$720$		0			0
$721$			42.0126i			1.56463i
$722$		0			0
$723$	7.46664	−	18.0261i	0.277687	−	0.670396i
$724$		0			0
$725$	39.6009	−	16.4032i	1.47074	−	0.609200i
$726$		0			0
$727$	6.49728	+	6.49728i	0.240971	+	0.240971i	0.817252	−	0.576281i	$-0.195497\pi$
$727$	6.49728	+	6.49728i	0.240971	+	0.240971i	−0.576281	+	0.817252i	$0.695497\pi$
$728$		0			0
$729$	−6.53021	+	6.53021i	−0.241860	+	0.241860i
$730$		0			0
$731$	−27.0476	−	65.2988i	−1.00039	−	2.41516i
$732$		0			0
$733$	−14.3970	−	5.96344i	−0.531766	−	0.220265i	0.100611	−	0.994926i	$-0.467920\pi$
$733$	−14.3970	−	5.96344i	−0.531766	−	0.220265i	−0.632376	+	0.774661i	$0.717920\pi$
$734$		0			0
$735$	−3.62264			−0.133623
$736$		0			0
$737$	−17.8774			−0.658523
$738$		0			0
$739$	9.18771	+	3.80567i	0.337975	+	0.139994i	0.545215	−	0.838296i	$-0.316448\pi$
$739$	9.18771	+	3.80567i	0.337975	+	0.139994i	−0.207240	+	0.978290i	$0.566448\pi$
$740$		0			0
$741$	−3.19615	−	7.71619i	−0.117414	−	0.283461i
$742$		0			0
$743$	3.28243	−	3.28243i	0.120421	−	0.120421i	−0.644328	−	0.764749i	$-0.722863\pi$
$743$	3.28243	−	3.28243i	0.120421	−	0.120421i	0.764749	+	0.644328i	$0.222863\pi$
$744$		0			0
$745$	−12.1657	−	12.1657i	−0.445716	−	0.445716i
$746$		0			0
$747$	−10.2117	+	4.22981i	−0.373625	+	0.154761i
$748$		0			0
$749$	−4.24072	+	10.2380i	−0.154952	+	0.374088i
$750$		0			0
$751$		−	5.40568i		−	0.197256i	−0.995124	−	0.0986280i	$-0.968555\pi$
$751$		−	5.40568i		−	0.197256i	0.995124	−	0.0986280i	$-0.0314454\pi$
$752$		0			0
$753$			16.9992i			0.619485i
$754$		0			0
$755$	4.42517	−	10.6833i	0.161048	−	0.388805i
$756$		0			0
$757$	−0.532954	+	0.220757i	−0.0193705	+	0.00802354i	−0.392348	−	0.919817i	$-0.628337\pi$
$757$	−0.532954	+	0.220757i	−0.0193705	+	0.00802354i	0.372977	+	0.927841i	$0.378337\pi$
$758$		0			0
$759$	5.33857	+	5.33857i	0.193778	+	0.193778i
$760$		0			0
$761$	−3.74202	+	3.74202i	−0.135648	+	0.135648i	−0.771671	−	0.636022i	$-0.780579\pi$
$761$	−3.74202	+	3.74202i	−0.135648	+	0.135648i	0.636022	+	0.771671i	$0.280579\pi$
$762$		0			0
$763$	10.6258	+	25.6530i	0.384680	+	0.928701i
$764$		0			0
$765$	−11.3208	−	4.68921i	−0.409303	−	0.169539i
$766$		0			0
$767$	−27.2820			−0.985097
$768$		0			0
$769$	43.7699			1.57838			0.789192	−	0.614146i	$-0.210499\pi$
$769$	43.7699			1.57838			0.789192	+	0.614146i	$0.210499\pi$
$770$		0			0
$771$	−13.5886	−	5.62859i	−0.489382	−	0.202709i
$772$		0			0
$773$	−18.2653	−	44.0963i	−0.656956	−	1.58603i	−0.802481	−	0.596678i	$-0.796487\pi$
$773$	−18.2653	−	44.0963i	−0.656956	−	1.58603i	0.145525	−	0.989355i	$-0.453513\pi$
$774$		0			0
$775$	21.7267	−	21.7267i	0.780445	−	0.780445i
$776$		0			0
$777$	5.69677	+	5.69677i	0.204371	+	0.204371i
$778$		0			0
$779$	7.28386	−	3.01707i	0.260971	−	0.108098i
$780$		0			0
$781$	−8.43415	+	20.3618i	−0.301798	+	0.728604i
$782$		0			0
$783$			50.1746i			1.79309i
$784$		0			0
$785$		−	5.66110i		−	0.202053i
$786$		0			0
$787$	−14.8193	+	35.7769i	−0.528250	+	1.27531i	0.404418	+	0.914574i	$0.367474\pi$
$787$	−14.8193	+	35.7769i	−0.528250	+	1.27531i	−0.932668	+	0.360735i	$0.882526\pi$
$788$		0			0
$789$	−19.1322	+	7.92480i	−0.681123	+	0.282130i
$790$		0			0
$791$	16.5475	+	16.5475i	0.588361	+	0.588361i
$792$		0			0
$793$	0.282046	−	0.282046i	0.0100157	−	0.0100157i
$794$		0			0
$795$	−2.96452	−	7.15698i	−0.105141	−	0.253832i
$796$		0			0
$797$	26.2186	+	10.8601i	0.928709	+	0.384684i	0.795188	−	0.606362i	$-0.207372\pi$
$797$	26.2186	+	10.8601i	0.928709	+	0.384684i	0.133520	+	0.991046i	$0.457372\pi$
$798$		0			0
$799$	−20.0236			−0.708383
$800$		0			0
$801$	−19.2373			−0.679715
$802$		0			0
$803$	−15.0238	−	6.22307i	−0.530179	−	0.219607i
$804$		0			0
$805$	5.01461	+	12.1063i	0.176742	+	0.426693i
$806$		0			0
$807$	−6.24238	+	6.24238i	−0.219742	+	0.219742i
$808$		0			0
$809$	36.1908	+	36.1908i	1.27240	+	1.27240i	0.944825	+	0.327575i	$0.106231\pi$
$809$	36.1908	+	36.1908i	1.27240	+	1.27240i	0.327575	+	0.944825i	$0.393769\pi$
$810$		0			0
$811$	−4.52316	+	1.87355i	−0.158829	+	0.0657893i	−0.460682	−	0.887565i	$-0.652395\pi$
$811$	−4.52316	+	1.87355i	−0.158829	+	0.0657893i	0.301852	+	0.953355i	$0.402395\pi$
$812$		0			0
$813$	−2.38691	+	5.76252i	−0.0837127	+	0.202100i
$814$		0			0
$815$			7.41550i			0.259754i
$816$		0			0
$817$			47.5449i			1.66339i
$818$		0			0
$819$	6.01557	−	14.5229i	0.210201	−	0.507470i
$820$		0			0
$821$	−27.3794	+	11.3409i	−0.955549	+	0.395801i	−0.805314	−	0.592849i	$-0.798003\pi$
$821$	−27.3794	+	11.3409i	−0.955549	+	0.395801i	−0.150235	+	0.988650i	$0.548003\pi$
$822$		0			0
$823$	−17.6023	−	17.6023i	−0.613576	−	0.613576i	0.330300	−	0.943876i	$-0.392850\pi$
$823$	−17.6023	−	17.6023i	−0.613576	−	0.613576i	−0.943876	+	0.330300i	$0.892850\pi$
$824$		0			0
$825$	−5.29510	+	5.29510i	−0.184352	+	0.184352i
$826$		0			0
$827$	9.09145	+	21.9487i	0.316141	+	0.763231i	0.999452	+	0.0331040i	$0.0105393\pi$
$827$	9.09145	+	21.9487i	0.316141	+	0.763231i	−0.683311	+	0.730127i	$0.739461\pi$
$828$		0			0
$829$	−46.0340	−	19.0679i	−1.59883	−	0.662256i	−0.607578	−	0.794260i	$-0.707859\pi$
$829$	−46.0340	−	19.0679i	−1.59883	−	0.662256i	−0.991249	+	0.132004i	$0.957859\pi$
$830$		0			0
$831$	23.5659			0.817492
$832$		0			0
$833$	−24.4275			−0.846363
$834$		0			0
$835$	18.2389	+	7.55482i	0.631185	+	0.261445i
$836$		0			0
$837$	13.7639	+	33.2291i	0.475751	+	1.14856i
$838$		0			0
$839$	32.6558	−	32.6558i	1.12740	−	1.12740i	0.136807	−	0.990598i	$-0.456316\pi$
$839$	32.6558	−	32.6558i	1.12740	−	1.12740i	0.990598	−	0.136807i	$-0.0436841\pi$
$840$		0			0
$841$	57.3415	+	57.3415i	1.97729	+	1.97729i
$842$		0			0
$843$	−16.6263	+	6.88685i	−0.572641	+	0.237196i
$844$		0			0
$845$	−2.95938	+	7.14456i	−0.101806	+	0.245780i
$846$		0			0
$847$		−	23.7181i		−	0.814964i
$848$		0			0
$849$		−	12.8591i		−	0.441322i
$850$		0			0
$851$	4.09667	−	9.89024i	0.140432	−	0.339033i
$852$		0			0
$853$	0.254393	−	0.105373i	0.00871025	−	0.00360790i	−0.378324	−	0.925673i	$-0.623499\pi$
$853$	0.254393	−	0.105373i	0.00871025	−	0.00360790i	0.387034	+	0.922065i	$0.373499\pi$
$854$		0			0
$855$	5.82854	+	5.82854i	0.199332	+	0.199332i
$856$		0			0
$857$	−15.7107	+	15.7107i	−0.536666	+	0.536666i	−0.922548	−	0.385882i	$-0.873897\pi$
$857$	−15.7107	+	15.7107i	−0.536666	+	0.536666i	0.385882	+	0.922548i	$0.373897\pi$
$858$		0			0
$859$	−0.205658	−	0.496502i	−0.00701695	−	0.0169404i	0.920332	−	0.391138i	$-0.127918\pi$
$859$	−0.205658	−	0.496502i	−0.00701695	−	0.0169404i	−0.927349	+	0.374197i	$0.877918\pi$
$860$		0			0
$861$	−5.58454	−	2.31319i	−0.190321	−	0.0788334i
$862$		0			0
$863$	−11.3841			−0.387520			−0.193760	−	0.981049i	$-0.562068\pi$
$863$	−11.3841			−0.387520			−0.193760	+	0.981049i	$0.562068\pi$
$864$		0			0
$865$	−6.86800			−0.233519
$866$		0			0
$867$	16.4605	+	6.81817i	0.559028	+	0.231557i
$868$		0			0
$869$	1.35577	+	3.27311i	0.0459912	+	0.111033i
$870$		0			0
$871$	−14.2466	+	14.2466i	−0.482728	+	0.482728i
$872$		0			0
$873$	−1.31877	−	1.31877i	−0.0446334	−	0.0446334i
$874$		0			0
$875$	−26.7046	+	11.0614i	−0.902779	+	0.373943i
$876$		0			0
$877$	−1.76098	+	4.25139i	−0.0594642	+	0.143559i	−0.950819	−	0.309747i	$-0.899756\pi$
$877$	−1.76098	+	4.25139i	−0.0594642	+	0.143559i	0.891355	+	0.453306i	$0.149756\pi$
$878$		0			0
$879$		−	14.9853i		−	0.505442i
$880$		0			0
$881$			41.1185i			1.38532i	0.721266	+	0.692658i	$0.243561\pi$
$881$			41.1185i			1.38532i	−0.721266	+	0.692658i	$0.756439\pi$
$882$		0			0
$883$	11.9313	−	28.8046i	0.401519	−	0.969353i	−0.585779	−	0.810471i	$-0.699211\pi$
$883$	11.9313	−	28.8046i	0.401519	−	0.969353i	0.987298	−	0.158881i	$-0.0507888\pi$
$884$		0			0
$885$	−10.1334	+	4.19740i	−0.340631	+	0.141094i
$886$		0			0
$887$	−8.97107	−	8.97107i	−0.301219	−	0.301219i	0.540272	−	0.841491i	$-0.318321\pi$
$887$	−8.97107	−	8.97107i	−0.301219	−	0.301219i	−0.841491	+	0.540272i	$0.818321\pi$
$888$		0			0
$889$	−2.58307	+	2.58307i	−0.0866333	+	0.0866333i
$890$		0			0
$891$	1.45958	+	3.52374i	0.0488977	+	0.118050i
$892$		0			0
$893$	12.4443	+	5.15461i	0.416434	+	0.172492i
$894$		0			0
$895$	0.833341			0.0278555
$896$		0			0
$897$	8.50867			0.284096
$898$		0			0
$899$	72.9112	+	30.2008i	2.43172	+	1.00725i
$900$		0			0
$901$	−19.9898	−	48.2596i	−0.665956	−	1.60776i
$902$		0			0
$903$	25.7760	−	25.7760i	0.857771	−	0.857771i
$904$		0			0
$905$	−11.6663	−	11.6663i	−0.387801	−	0.387801i
$906$		0			0
$907$	5.90281	−	2.44502i	0.196000	−	0.0811857i	−0.282525	−	0.959260i	$-0.591172\pi$
$907$	5.90281	−	2.44502i	0.196000	−	0.0811857i	0.478524	+	0.878074i	$0.341172\pi$
$908$		0			0
$909$	0.00150094	−	0.00362358i	4.97830e−5	−	0.000120187i
$910$		0			0
$911$		−	2.93353i		−	0.0971921i	−0.998819	−	0.0485961i	$-0.984525\pi$
$911$		−	2.93353i		−	0.0971921i	0.998819	−	0.0485961i	$-0.0154747\pi$
$912$		0			0
$913$		−	10.1999i		−	0.337568i
$914$		0			0
$915$	0.0613674	−	0.148154i	0.00202874	−	0.00489782i
$916$		0			0
$917$	−56.7500	+	23.5066i	−1.87405	+	0.776257i
$918$		0			0
$919$	31.0406	+	31.0406i	1.02393	+	1.02393i	0.999706	+	0.0242270i	$0.00771244\pi$
$919$	31.0406	+	31.0406i	1.02393	+	1.02393i	0.0242270	+	0.999706i	$0.492288\pi$
$920$		0			0
$921$	−4.57093	+	4.57093i	−0.150617	+	0.150617i
$922$		0			0
$923$	9.50524	+	22.9477i	0.312869	+	0.755332i
$924$		0			0
$925$	9.80971	+	4.06332i	0.322541	+	0.133601i
$926$		0			0
$927$	−26.9234			−0.884282
$928$		0			0
$929$	−11.7583			−0.385776			−0.192888	−	0.981221i	$-0.561785\pi$
$929$	−11.7583			−0.385776			−0.192888	+	0.981221i	$0.561785\pi$
$930$		0			0
$931$	15.1813	+	6.28830i	0.497547	+	0.206091i
$932$		0			0
$933$	−10.9700	−	26.4840i	−0.359143	−	0.867048i
$934$		0			0
$935$	7.99579	−	7.99579i	0.261490	−	0.261490i
$936$		0			0
$937$	−1.46723	−	1.46723i	−0.0479325	−	0.0479325i	0.682734	−	0.730667i	$-0.260791\pi$
$937$	−1.46723	−	1.46723i	−0.0479325	−	0.0479325i	−0.730667	+	0.682734i	$0.760791\pi$
$938$		0			0
$939$	−3.39273	+	1.40531i	−0.110718	+	0.0458607i
$940$		0			0
$941$	−3.87108	+	9.34561i	−0.126194	+	0.304658i	−0.974332	−	0.225117i	$-0.927724\pi$
$941$	−3.87108	+	9.34561i	−0.126194	+	0.304658i	0.848138	+	0.529775i	$0.177724\pi$
$942$		0			0
$943$			8.03193i			0.261556i
$944$		0			0
$945$		−	15.2139i		−	0.494909i
$946$		0			0
$947$	−13.6842	+	33.0365i	−0.444676	+	1.07354i	0.529613	+	0.848240i	$0.322337\pi$
$947$	−13.6842	+	33.0365i	−0.444676	+	1.07354i	−0.974289	+	0.225303i	$0.927663\pi$
$948$		0			0
$949$	−16.9318	+	7.01337i	−0.549628	+	0.227664i
$950$		0			0
$951$	−2.78911	−	2.78911i	−0.0904430	−	0.0904430i
$952$		0			0
$953$	−11.2740	+	11.2740i	−0.365201	+	0.365201i	−0.865723	−	0.500523i	$-0.833141\pi$
$953$	−11.2740	+	11.2740i	−0.365201	+	0.365201i	0.500523	+	0.865723i	$0.333141\pi$
$954$		0			0
$955$	−7.96579	−	19.2311i	−0.257767	−	0.622305i
$956$		0			0
$957$	−17.7695	−	7.36036i	−0.574406	−	0.237927i
$958$		0			0
$959$	−27.4338			−0.885883
$960$		0			0
$961$	25.5715			0.824886
$962$		0			0
$963$	−6.56093	−	2.71763i	−0.211423	−	0.0875743i
$964$		0			0
$965$	0.234562	+	0.566282i	0.00755080	+	0.0182293i
$966$		0			0
$967$	25.1865	−	25.1865i	0.809944	−	0.809944i	−0.174681	−	0.984625i	$-0.555889\pi$
$967$	25.1865	−	25.1865i	0.809944	−	0.809944i	0.984625	+	0.174681i	$0.0558893\pi$
$968$		0			0
$969$	−16.0100	−	16.0100i	−0.514314	−	0.514314i
$970$		0			0
$971$	−7.05357	+	2.92168i	−0.226360	+	0.0937613i	−0.492981	−	0.870040i	$-0.664093\pi$
$971$	−7.05357	+	2.92168i	−0.226360	+	0.0937613i	0.266621	+	0.963801i	$0.414093\pi$
$972$		0			0
$973$	17.0971	−	41.2759i	0.548106	−	1.32325i
$974$		0			0
$975$			8.43939i			0.270277i
$976$		0			0
$977$			21.0511i			0.673484i	0.941597	+	0.336742i	$0.109325\pi$
$977$			21.0511i			0.673484i	−0.941597	+	0.336742i	$0.890675\pi$
$978$		0			0
$979$	6.79359	−	16.4012i	0.217124	−	0.524184i
$980$		0			0
$981$	−16.4395	+	6.80946i	−0.524873	+	0.217409i
$982$		0			0
$983$	23.6221	+	23.6221i	0.753429	+	0.753429i	0.975117	−	0.221689i	$-0.0711569\pi$
$983$	23.6221	+	23.6221i	0.753429	+	0.753429i	−0.221689	+	0.975117i	$0.571157\pi$
$984$		0			0
$985$	−13.9936	+	13.9936i	−0.445873	+	0.445873i
$986$		0			0
$987$	−3.95205	−	9.54108i	−0.125795	−	0.303696i
$988$		0			0
$989$	−44.7500	−	18.5361i	−1.42297	−	0.589412i
$990$		0			0
$991$	−27.0358			−0.858822			−0.429411	−	0.903109i	$-0.641279\pi$
$991$	−27.0358			−0.858822			−0.429411	+	0.903109i	$0.641279\pi$
$992$		0			0
$993$	−15.0922			−0.478936
$994$		0			0
$995$	−9.94819	−	4.12067i	−0.315379	−	0.130634i
$996$		0			0
$997$	−13.4320	−	32.4278i	−0.425397	−	1.02700i	−0.980729	−	0.195371i	$-0.937409\pi$
$997$	−13.4320	−	32.4278i	−0.425397	−	1.02700i	0.555333	−	0.831628i	$-0.312591\pi$
$998$		0			0
$999$	−8.78861	+	8.78861i	−0.278059	+	0.278059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1024.2.g.a.641.2	yes	16
4.3	odd	2	inner	1024.2.g.a.641.3	yes	16
8.3	odd	2		1024.2.g.f.641.2	yes	16
8.5	even	2		1024.2.g.f.641.3	yes	16
16.3	odd	4		1024.2.g.d.129.2	yes	16
16.5	even	4		1024.2.g.g.129.2	yes	16
16.11	odd	4		1024.2.g.g.129.3	yes	16
16.13	even	4		1024.2.g.d.129.3	yes	16
32.3	odd	8		1024.2.g.g.897.3	yes	16
32.5	even	8		1024.2.g.f.385.3	yes	16
32.11	odd	8	inner	1024.2.g.a.385.3	yes	16
32.13	even	8		1024.2.g.d.897.3	yes	16
32.19	odd	8		1024.2.g.d.897.2	yes	16
32.21	even	8	inner	1024.2.g.a.385.2	✓	16
32.27	odd	8		1024.2.g.f.385.2	yes	16
32.29	even	8		1024.2.g.g.897.2	yes	16
64.11	odd	16		4096.2.a.i.1.7		8
64.21	even	16		4096.2.a.i.1.8		8
64.43	odd	16		4096.2.a.s.1.2		8
64.53	even	16		4096.2.a.s.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1024.2.g.a.385.2	✓	16	32.21	even	8	inner
1024.2.g.a.385.3	yes	16	32.11	odd	8	inner
1024.2.g.a.641.2	yes	16	1.1	even	1	trivial
1024.2.g.a.641.3	yes	16	4.3	odd	2	inner
1024.2.g.d.129.2	yes	16	16.3	odd	4
1024.2.g.d.129.3	yes	16	16.13	even	4
1024.2.g.d.897.2	yes	16	32.19	odd	8
1024.2.g.d.897.3	yes	16	32.13	even	8
1024.2.g.f.385.2	yes	16	32.27	odd	8
1024.2.g.f.385.3	yes	16	32.5	even	8
1024.2.g.f.641.2	yes	16	8.3	odd	2
1024.2.g.f.641.3	yes	16	8.5	even	2
1024.2.g.g.129.2	yes	16	16.5	even	4
1024.2.g.g.129.3	yes	16	16.11	odd	4
1024.2.g.g.897.2	yes	16	32.29	even	8
1024.2.g.g.897.3	yes	16	32.3	odd	8
4096.2.a.i.1.7		8	64.11	odd	16
4096.2.a.i.1.8		8	64.21	even	16
4096.2.a.s.1.1		8	64.53	even	16
4096.2.a.s.1.2		8	64.43	odd	16

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:	\( N \)	\(=\)	\( 1024 = 2^{10} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1024.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.860919 - 0.356604i) q^{3} +(0.366025 + 0.883663i) q^{5} +(-2.35207 + 2.35207i) q^{7} +(-1.50731 - 1.50731i) q^{9} +O(q^{10})\)	\(q+(-0.860919 - 0.356604i) q^{3} +(0.366025 + 0.883663i) q^{5} +(-2.35207 + 2.35207i) q^{7} +(-1.50731 - 1.50731i) q^{9} +(1.81739 - 0.752787i) q^{11} +(0.848387 - 2.04819i) q^{13} -0.891289i q^{15} -6.00997i q^{17} +(-1.54713 + 3.73510i) q^{19} +(2.86370 - 1.18618i) q^{21} +(-2.91236 - 2.91236i) q^{23} +(2.88865 - 2.88865i) q^{25} +(1.82997 + 4.41794i) q^{27} +(9.69383 + 4.01532i) q^{29} +7.52140 q^{31} -1.83307 q^{33} +(-2.93936 - 1.21752i) q^{35} +(0.994652 + 2.40130i) q^{37} +(-1.46078 + 1.46078i) q^{39} +(-1.37894 - 1.37894i) q^{41} +(10.8651 - 4.50046i) q^{43} +(0.780239 - 1.88366i) q^{45} -3.33173i q^{47} -4.06450i q^{49} +(-2.14318 + 5.17409i) q^{51} +(8.02993 - 3.32611i) q^{53} +(1.33042 + 1.33042i) q^{55} +(2.66390 - 2.66390i) q^{57} +(-4.70936 - 11.3694i) q^{59} +(0.166225 + 0.0688525i) q^{61} +7.09059 q^{63} +2.12044 q^{65} +(-8.39629 - 3.47786i) q^{67} +(1.46875 + 3.54587i) q^{69} +(-7.92235 + 7.92235i) q^{71} +(-5.84544 - 5.84544i) q^{73} +(-3.51699 + 1.45679i) q^{75} +(-2.50402 + 6.04524i) q^{77} +1.80100i q^{79} +1.93890i q^{81} +(1.98429 - 4.79049i) q^{83} +(5.31079 - 2.19980i) q^{85} +(-6.91372 - 6.91372i) q^{87} +(6.38134 - 6.38134i) q^{89} +(2.82202 + 6.81296i) q^{91} +(-6.47531 - 2.68216i) q^{93} -3.86686 q^{95} +0.874915 q^{97} +(-3.87404 - 1.60468i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{5} - 16 q^{9}+O(q^{10}) \) 16 * q - 8 * q^5 - 16 * q^9	\( 16 q - 8 q^{5} - 16 q^{9} + 8 q^{13} - 16 q^{21} - 32 q^{25} + 24 q^{29} - 80 q^{33} - 40 q^{37} - 16 q^{41} - 24 q^{45} + 56 q^{53} - 16 q^{57} - 8 q^{61} - 32 q^{65} + 64 q^{69} + 32 q^{73} - 64 q^{77} + 48 q^{85} + 32 q^{89} - 80 q^{93} - 16 q^{97}+O(q^{100}) \) 16 * q - 8 * q^5 - 16 * q^9 + 8 * q^13 - 16 * q^21 - 32 * q^25 + 24 * q^29 - 80 * q^33 - 40 * q^37 - 16 * q^41 - 24 * q^45 + 56 * q^53 - 16 * q^57 - 8 * q^61 - 32 * q^65 + 64 * q^69 + 32 * q^73 - 64 * q^77 + 48 * q^85 + 32 * q^89 - 80 * q^93 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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