LMFDB - Embedded newform 1024.2.g.f.641.3

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			641.3
Root			$0.608761 + 0.793353i$ of defining polynomial
Character	$\chi$	$=$	1024.641
Dual form			1024.2.g.f.385.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.860919 + 0.356604i) q^{3} +(-0.366025 - 0.883663i) q^{5} +(-2.35207 + 2.35207i) q^{7} +(-1.50731 - 1.50731i) q^{9} +O(q^{10})$	\(q+(0.860919 + 0.356604i) q^{3} +(-0.366025 - 0.883663i) q^{5} +(-2.35207 + 2.35207i) q^{7} +(-1.50731 - 1.50731i) q^{9} +(-1.81739 + 0.752787i) q^{11} +(-0.848387 + 2.04819i) q^{13} -0.891289i q^{15} -6.00997i q^{17} +(1.54713 - 3.73510i) q^{19} +(-2.86370 + 1.18618i) q^{21} +(-2.91236 - 2.91236i) q^{23} +(2.88865 - 2.88865i) q^{25} +(-1.82997 - 4.41794i) q^{27} +(-9.69383 - 4.01532i) q^{29} +7.52140 q^{31} -1.83307 q^{33} +(2.93936 + 1.21752i) q^{35} +(-0.994652 - 2.40130i) q^{37} +(-1.46078 + 1.46078i) q^{39} +(-1.37894 - 1.37894i) q^{41} +(-10.8651 + 4.50046i) q^{43} +(-0.780239 + 1.88366i) q^{45} -3.33173i q^{47} -4.06450i q^{49} +(2.14318 - 5.17409i) q^{51} +(-8.02993 + 3.32611i) q^{53} +(1.33042 + 1.33042i) q^{55} +(2.66390 - 2.66390i) q^{57} +(4.70936 + 11.3694i) q^{59} +(-0.166225 - 0.0688525i) q^{61} +7.09059 q^{63} +2.12044 q^{65} +(8.39629 + 3.47786i) q^{67} +(-1.46875 - 3.54587i) q^{69} +(-7.92235 + 7.92235i) q^{71} +(-5.84544 - 5.84544i) q^{73} +(3.51699 - 1.45679i) q^{75} +(2.50402 - 6.04524i) q^{77} +1.80100i q^{79} +1.93890i q^{81} +(-1.98429 + 4.79049i) q^{83} +(-5.31079 + 2.19980i) q^{85} +(-6.91372 - 6.91372i) q^{87} +(6.38134 - 6.38134i) q^{89} +(-2.82202 - 6.81296i) q^{91} +(6.47531 + 2.68216i) q^{93} -3.86686 q^{95} +0.874915 q^{97} +(3.87404 + 1.60468i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	0.617103	−	0.786882i	$-0.288306\pi$
$3$	0.860919	+	0.356604i	0.497052	+	0.205886i	−0.120052	+	0.992768i	$0.538306\pi$
$4$		0			0
$5$	−0.366025	−	0.883663i	−0.163692	−	0.395186i	0.820656	−	0.571422i	$-0.193608\pi$
$5$	−0.366025	−	0.883663i	−0.163692	−	0.395186i	−0.984348	+	0.176236i	$0.943608\pi$
$6$		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	−0.639450	−	0.768832i	$-0.720838\pi$
$11$	−1.81739	+	0.752787i	−0.547963	+	0.226974i	0.0914869	+	0.995806i	$0.470838\pi$
$12$		0			0
$13$	−0.848387	+	2.04819i	−0.235300	+	0.568065i	−0.996785	−	0.0801172i	$-0.974471\pi$
$13$	−0.848387	+	2.04819i	−0.235300	+	0.568065i	0.761485	+	0.648182i	$0.224471\pi$
$14$		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	$-0.721505\pi$
$19$	1.54713	−	3.73510i	0.354935	−	0.856890i	0.995996	−	0.0893996i	$-0.0284948\pi$
$20$		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	$-0.947453\pi$
$29$	−9.69383	−	4.01532i	−1.80010	−	0.745625i	−0.813694	−	0.581293i	$-0.802547\pi$
$30$		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	0.820788	−	0.571233i	$-0.193535\pi$
$37$	−0.994652	−	2.40130i	−0.163520	−	0.394772i	−0.984308	+	0.176462i	$0.943535\pi$
$38$		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	−0.997835	−	0.0657637i	$-0.979052\pi$
$43$	−10.8651	+	4.50046i	−1.65691	+	0.686314i	−0.659074	+	0.752078i	$0.729052\pi$
$44$		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	−0.858520	−	0.512780i	$-0.828616\pi$
$53$	−8.02993	+	3.32611i	−1.10300	+	0.456876i	−0.244475	+	0.969656i	$0.578616\pi$
$54$		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	$0.170731\pi$
$59$	4.70936	+	11.3694i	0.613106	+	1.48017i	−0.246464	+	0.969152i	$0.579269\pi$
$60$		0			0
$61$	−0.166225	−	0.0688525i	−0.0212829	−	0.00881566i	0.372017	−	0.928226i	$-0.378666\pi$
$61$	−0.166225	−	0.0688525i	−0.0212829	−	0.00881566i	−0.393299	+	0.919410i	$0.628666\pi$
$62$		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	0.831184	−	0.555997i	$-0.187664\pi$
$67$	8.39629	+	3.47786i	1.02577	+	0.424888i	0.194587	+	0.980885i	$0.437664\pi$
$68$		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	−0.994583	−	0.103949i	$-0.966852\pi$
$83$	−1.98429	+	4.79049i	−0.217804	+	0.525825i	0.776779	+	0.629773i	$0.216852\pi$
$84$		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	0.923844	−	0.382768i	$-0.125029\pi$
$101$	−0.000704119	−	0.00169989i	−7.00625e−5	−	0.000169146i	−0.923915	+	0.382599i	$0.875029\pi$
$102$		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	−0.526463	−	0.850198i	$-0.676482\pi$
$107$	−3.07786	+	1.27489i	−0.297548	+	0.123248i	0.228915	+	0.973446i	$0.426482\pi$
$108$		0			0
$109$	−3.19445	+	7.71209i	−0.305973	+	0.738684i	0.693855	+	0.720115i	$0.255911\pi$
$109$	−3.19445	+	7.71209i	−0.305973	+	0.738684i	−0.999828	+	0.0185691i	$0.994089\pi$
$110$		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	−0.519161	−	0.854676i	$-0.673756\pi$
$131$	−17.0608	−	7.06683i	−1.49061	−	0.617431i	−0.971450	+	0.237245i	$0.923756\pi$
$132$		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	0.211719	−	0.977331i	$-0.432094\pi$
$139$	12.4088	−	5.13991i	1.05250	−	0.435961i	0.840785	+	0.541369i	$0.182094\pi$
$140$		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	0.421994	−	0.906598i	$-0.361330\pi$
$149$	16.6186	−	6.88366i	1.36145	−	0.563932i	0.939457	+	0.342667i	$0.111330\pi$
$150$		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	0.590062	−	0.807358i	$-0.299103\pi$
$157$	5.46821	+	2.26500i	0.436410	+	0.180767i	−0.153652	+	0.988125i	$0.549103\pi$
$158$		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	0.0840992	−	0.996457i	$-0.473199\pi$
$163$	−7.16282	−	2.96694i	−0.561035	−	0.232388i	−0.645135	+	0.764069i	$0.723199\pi$
$164$		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	−0.784336	−	0.620337i	$-0.786996\pi$
$173$	2.74788	−	6.63397i	0.208918	−	0.504372i	0.993253	+	0.115965i	$0.0369960\pi$
$174$		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	−0.935850	−	0.352398i	$-0.885366\pi$
$179$	−0.333419	+	0.804946i	−0.0249209	+	0.0601645i	0.910929	+	0.412563i	$0.135366\pi$
$180$		0			0
$181$	15.9365	−	6.60110i	1.18455	−	0.490656i	0.298572	−	0.954387i	$-0.403490\pi$
$181$	15.9365	−	6.60110i	1.18455	−	0.490656i	0.885976	+	0.463731i	$0.153490\pi$
$182$		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	$-0.861208\pi$
$197$	−7.91794	−	19.1156i	−0.564130	−	1.36193i	0.342306	−	0.939588i	$-0.388792\pi$
$198$		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	−0.982671	−	0.185359i	$-0.940655\pi$
$211$	−2.27691	+	5.49696i	−0.156749	+	0.378426i	0.825922	+	0.563785i	$0.190655\pi$
$212$		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	−0.223078	−	0.974801i	$-0.571610\pi$
$227$	−16.1228	−	6.67827i	−1.07011	−	0.443252i	−0.847028	+	0.531548i	$0.821610\pi$
$228$		0			0
$229$	5.84666	+	14.1151i	0.386358	+	0.932752i	0.990705	+	0.136030i	$0.0434343\pi$
$229$	5.84666	+	14.1151i	0.386358	+	0.932752i	−0.604346	+	0.796722i	$0.706566\pi$
$230$		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	$0.0702800\pi$
$251$	6.98106	+	16.8538i	0.440641	+	1.06380i	−0.535084	+	0.844799i	$0.679720\pi$
$252$		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	−0.995033	−	0.0995505i	$-0.968260\pi$
$269$	−3.62542	+	8.75253i	−0.221045	+	0.533651i	0.773987	+	0.633201i	$0.218260\pi$
$270$		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	0.453083	−	0.891468i	$-0.350324\pi$
$277$	23.3643	−	9.67781i	1.40382	−	0.581483i	0.950741	+	0.309985i	$0.100324\pi$
$278$		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	$-0.990478\pi$
$283$	−5.28083	−	12.7490i	−0.313913	−	0.757852i	0.685640	−	0.727941i	$-0.259522\pi$
$284$		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	$-0.969349\pi$
$293$	−6.15402	−	14.8571i	−0.359521	−	0.867962i	0.635846	−	0.771816i	$-0.280651\pi$
$294$		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	−0.981352	−	0.192221i	$-0.938431\pi$
$307$	−2.65468	+	6.40896i	−0.151511	+	0.365779i	0.829841	+	0.558000i	$0.188431\pi$
$308$		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	0.270148	−	0.962819i	$-0.412927\pi$
$317$	−3.91065	−	1.61984i	−0.219644	−	0.0909794i	−0.489792	+	0.871839i	$0.662927\pi$
$318$		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	−0.753907	−	0.656981i	$-0.771833\pi$
$331$	−14.9631	+	6.19790i	−0.822444	+	0.340668i	−0.0685372	+	0.997649i	$0.521833\pi$
$332$		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	0.988092	−	0.153864i	$-0.0491719\pi$
$347$	3.36433	+	8.12222i	0.180607	+	0.436024i	−0.807485	+	0.589888i	$0.799172\pi$
$348$		0			0
$349$	14.8014	+	6.13095i	0.792302	+	0.328182i	0.741869	−	0.670545i	$-0.233940\pi$
$349$	14.8014	+	6.13095i	0.792302	+	0.328182i	0.0504332	+	0.998727i	$0.483940\pi$
$350$		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	−0.841509	−	0.540244i	$-0.818332\pi$
$373$	−20.3665	+	8.43606i	−1.05454	+	0.436803i	−0.213026	+	0.977046i	$0.568332\pi$
$374$		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	0.959815	−	0.280634i	$-0.0905447\pi$
$379$	1.60971	+	3.88618i	0.0826851	+	0.199620i	−0.877130	+	0.480253i	$0.840545\pi$
$380$		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	$-0.981297\pi$
$389$	−6.58576	−	15.8994i	−0.333911	−	0.806133i	0.664363	−	0.747410i	$-0.268703\pi$
$390$		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	$0.285843\pi$
$397$	−7.38205	+	17.8218i	−0.370494	+	0.894452i	−0.993667	+	0.112368i	$0.964157\pi$
$398$		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	0.579283	−	0.815126i	$-0.303333\pi$
$419$	8.44401	+	3.49762i	0.412517	+	0.170870i	−0.166766	+	0.985996i	$0.553333\pi$
$420$		0			0
$421$	−10.4476	−	25.2227i	−0.509184	−	1.22928i	−0.944354	−	0.328930i	$-0.893312\pi$
$421$	−10.4476	−	25.2227i	−0.509184	−	1.22928i	0.435171	−	0.900348i	$-0.356688\pi$
$422$		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	0.926041	−	0.377424i	$-0.123190\pi$
$443$	0.0916028	+	0.221149i	0.00435218	+	0.0105071i	−0.921689	+	0.387931i	$0.873190\pi$
$444$		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	$-0.633517\pi$
$461$	11.3049	−	27.2925i	0.526523	−	1.27114i	0.933787	−	0.357828i	$-0.116483\pi$
$462$		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	$-0.710676\pi$
$467$	8.16422	−	19.7102i	0.377795	−	0.912077i	0.992379	−	0.123226i	$-0.0393240\pi$
$468$		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	−0.714809	−	0.699320i	$-0.753486\pi$
$491$	−16.0818	+	6.66130i	−0.725761	+	0.300620i	−0.0109525	+	0.999940i	$0.503486\pi$
$492$		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	$-0.726306\pi$
$499$	7.69930	−	18.5877i	0.344668	−	0.832102i	0.997231	−	0.0743674i	$-0.0236937\pi$
$500$		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	−0.516761	−	0.856130i	$-0.672862\pi$
$509$	−33.5605	−	13.9012i	−1.48754	−	0.616160i	−0.970780	+	0.239970i	$0.922862\pi$
$510$		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	−0.503371	−	0.864070i	$-0.667907\pi$
$523$	−5.67885	+	2.35226i	−0.248319	+	0.102857i	0.255053	+	0.966927i	$0.417907\pi$
$524$		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	−0.0785232	−	0.996912i	$-0.525020\pi$
$541$	−19.5140	−	8.08295i	−0.838971	−	0.347513i	−0.760448	+	0.649399i	$0.775020\pi$
$542$		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	0.458445	−	0.888723i	$-0.348407\pi$
$547$	3.60625	+	1.49376i	0.154192	+	0.0638684i	−0.304253	+	0.952591i	$0.598407\pi$
$548$		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	$-0.742230\pi$
$557$	7.31781	−	17.6668i	0.310066	−	0.748565i	0.999702	−	0.0244089i	$-0.00777037\pi$
$558$		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	−0.898370	−	0.439240i	$-0.855248\pi$
$563$	1.12618	−	2.71884i	0.0474628	−	0.114585i	0.945833	+	0.324654i	$0.105248\pi$
$564$		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	$-0.797932\pi$
$571$	−15.6556	−	37.7960i	−0.655167	−	1.58171i	0.150013	−	0.988684i	$-0.452068\pi$
$572$		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	−0.756746	−	0.653709i	$-0.773212\pi$
$587$	−20.0997	+	8.32558i	−0.829605	+	0.343634i	−0.0728586	+	0.997342i	$0.523212\pi$
$588$		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	0.998221	−	0.0596229i	$-0.0189898\pi$
$613$	6.19497	+	14.9560i	0.250212	+	0.604066i	−0.748009	+	0.663689i	$0.768990\pi$
$614$		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	−0.487431	−	0.873162i	$-0.662066\pi$
$619$	−5.34111	+	2.21236i	−0.214677	+	0.0889222i	0.272753	+	0.962084i	$0.412066\pi$
$620$		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	0.952746	−	0.303768i	$-0.0982448\pi$
$643$	35.7957	+	14.8270i	1.41164	+	0.584722i	0.458897	+	0.888490i	$0.348245\pi$
$644$		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	−0.998409	−	0.0563832i	$-0.982043\pi$
$653$	−6.45384	+	15.5810i	−0.252558	+	0.609730i	0.745851	+	0.666113i	$0.232043\pi$
$654$		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	$0.429313\pi$
$659$	−16.0504	+	38.7490i	−0.625233	+	1.50945i	−0.845483	+	0.534003i	$0.820687\pi$
$660$		0			0
$661$	22.6719	−	9.39102i	0.881836	−	0.365268i	0.104627	−	0.994512i	$-0.466635\pi$
$661$	22.6719	−	9.39102i	0.881836	−	0.365268i	0.777208	+	0.629243i	$0.216635\pi$
$662$		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	0.750319	−	0.661076i	$-0.229900\pi$
$677$	−6.44466	−	15.5588i	−0.247688	−	0.597972i	−0.998007	+	0.0631039i	$0.979900\pi$
$678$		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	$-0.236804\pi$
$683$	45.3415	−	18.7811i	1.73495	−	0.718638i	0.999141	−	0.0414451i	$-0.0131962\pi$
$684$		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	−0.846868	−	0.531803i	$-0.821515\pi$
$691$	3.36470	−	8.12311i	0.127999	−	0.309018i	0.974868	+	0.222785i	$0.0715148\pi$
$692$		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	0.809630	−	0.586941i	$-0.199668\pi$
$701$	25.6052	+	10.6060i	0.967094	+	0.400584i	0.157465	+	0.987525i	$0.449668\pi$
$702$		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	$-0.987559\pi$
$709$	−8.52863	−	20.5899i	−0.320299	−	0.773271i	0.678937	−	0.734197i	$-0.262441\pi$
$710$		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	0.632376	−	0.774661i	$-0.282080\pi$
$733$	14.3970	+	5.96344i	0.531766	+	0.220265i	−0.100611	+	0.994926i	$0.532080\pi$
$734$		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	0.207240	−	0.978290i	$-0.433552\pi$
$739$	−9.18771	−	3.80567i	−0.337975	−	0.139994i	−0.545215	+	0.838296i	$0.683552\pi$
$740$		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	−0.372977	−	0.927841i	$-0.621663\pi$
$757$	0.532954	−	0.220757i	0.0193705	−	0.00802354i	0.392348	+	0.919817i	$0.371663\pi$
$758$		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	$0.203513\pi$
$773$	18.2653	+	44.0963i	0.656956	+	1.58603i	−0.145525	+	0.989355i	$0.546487\pi$
$774$		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	$-0.632526\pi$
$787$	14.8193	−	35.7769i	0.528250	−	1.27531i	0.932668	−	0.360735i	$-0.117474\pi$
$788$		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	−0.133520	−	0.991046i	$-0.542628\pi$
$797$	−26.2186	−	10.8601i	−0.928709	−	0.384684i	−0.795188	+	0.606362i	$0.792628\pi$
$798$		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	−0.301852	−	0.953355i	$-0.597605\pi$
$811$	4.52316	−	1.87355i	0.158829	−	0.0657893i	0.460682	+	0.887565i	$0.347605\pi$
$812$		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	0.150235	−	0.988650i	$-0.451997\pi$
$821$	27.3794	−	11.3409i	0.955549	−	0.395801i	0.805314	+	0.592849i	$0.201997\pi$
$822$		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	$-0.989461\pi$
$827$	−9.09145	−	21.9487i	−0.316141	−	0.763231i	0.683311	−	0.730127i	$-0.260539\pi$
$828$		0			0
$829$	46.0340	+	19.0679i	1.59883	+	0.662256i	0.991249	−	0.132004i	$-0.0421412\pi$
$829$	46.0340	+	19.0679i	1.59883	+	0.662256i	0.607578	+	0.794260i	$0.292141\pi$
$830$		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	−0.387034	−	0.922065i	$-0.626501\pi$
$853$	−0.254393	+	0.105373i	−0.00871025	+	0.00360790i	0.378324	+	0.925673i	$0.376501\pi$
$854$		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	0.927349	−	0.374197i	$-0.122082\pi$
$859$	0.205658	+	0.496502i	0.00701695	+	0.0169404i	−0.920332	+	0.391138i	$0.872082\pi$
$860$		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	−0.891355	−	0.453306i	$-0.850244\pi$
$877$	1.76098	−	4.25139i	0.0594642	−	0.143559i	0.950819	+	0.309747i	$0.100244\pi$
$878$		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	$0.300789\pi$
$883$	−11.9313	+	28.8046i	−0.401519	+	0.969353i	−0.987298	+	0.158881i	$0.949211\pi$
$884$		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	−0.478524	−	0.878074i	$-0.658828\pi$
$907$	−5.90281	+	2.44502i	−0.196000	+	0.0811857i	0.282525	+	0.959260i	$0.408828\pi$
$908$		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	−0.848138	−	0.529775i	$-0.822276\pi$
$941$	3.87108	−	9.34561i	0.126194	−	0.304658i	0.974332	+	0.225117i	$0.0722764\pi$
$942$		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	$-0.677663\pi$
$947$	13.6842	−	33.0365i	0.444676	−	1.07354i	0.974289	−	0.225303i	$-0.0723372\pi$
$948$		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	−0.266621	−	0.963801i	$-0.585907\pi$
$971$	7.05357	−	2.92168i	0.226360	−	0.0937613i	0.492981	+	0.870040i	$0.335907\pi$
$972$		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	$0.0625910\pi$
$997$	13.4320	+	32.4278i	0.425397	+	1.02700i	−0.555333	+	0.831628i	$0.687409\pi$
$998$		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.f.641.3	yes	16
4.3	odd	2	inner	1024.2.g.f.641.2	yes	16
8.3	odd	2		1024.2.g.a.641.3	yes	16
8.5	even	2		1024.2.g.a.641.2	yes	16
16.3	odd	4		1024.2.g.g.129.3	yes	16
16.5	even	4		1024.2.g.d.129.3	yes	16
16.11	odd	4		1024.2.g.d.129.2	yes	16
16.13	even	4		1024.2.g.g.129.2	yes	16
32.3	odd	8		1024.2.g.d.897.2	yes	16
32.5	even	8		1024.2.g.a.385.2	✓	16
32.11	odd	8	inner	1024.2.g.f.385.2	yes	16
32.13	even	8		1024.2.g.g.897.2	yes	16
32.19	odd	8		1024.2.g.g.897.3	yes	16
32.21	even	8	inner	1024.2.g.f.385.3	yes	16
32.27	odd	8		1024.2.g.a.385.3	yes	16
32.29	even	8		1024.2.g.d.897.3	yes	16
64.11	odd	16		4096.2.a.s.1.2		8
64.21	even	16		4096.2.a.s.1.1		8
64.43	odd	16		4096.2.a.i.1.7		8
64.53	even	16		4096.2.a.i.1.8		8

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

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Varieties

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Representations

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Database

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