LMFDB - Embedded newform 1152.2.i.f.769.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(385,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1152.385");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.8528759163648.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + x^{8} + 9x^{6} - 36x^{5} + 27x^{4} + 27x^{2} - 162x + 243 $ x^10 - 2x^9 + x^8 + 9x^6 - 36x^5 + 27x^4 + 27x^2 - 162x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			769.4
Root			$0.756905 - 1.55791i$ of defining polynomial
Character	$\chi$	$=$	1152.769
Dual form			1152.2.i.f.385.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.970741 - 1.43446i) q^{3} +(1.07447 - 1.86104i) q^{5} +(-0.153174 - 0.265305i) q^{7} +(-1.11533 - 2.78497i) q^{9} +O(q^{10})$	\(q+(0.970741 - 1.43446i) q^{3} +(1.07447 - 1.86104i) q^{5} +(-0.153174 - 0.265305i) q^{7} +(-1.11533 - 2.78497i) q^{9} +(-2.50736 - 4.34288i) q^{11} +(0.470741 - 0.815346i) q^{13} +(-1.62655 - 3.34787i) q^{15} -4.70838 q^{17} -1.61796 q^{19} +(-0.529259 - 0.0378211i) q^{21} +(-4.08184 + 7.06995i) q^{23} +(0.191022 + 0.330859i) q^{25} +(-5.07761 - 1.10360i) q^{27} +(2.39504 + 4.14834i) q^{29} +(1.29776 - 2.24778i) q^{31} +(-8.66367 - 0.619109i) q^{33} -0.658323 q^{35} +10.2093 q^{37} +(-0.712611 - 1.46675i) q^{39} +(3.86537 - 6.69502i) q^{41} +(-0.138140 - 0.239265i) q^{43} +(-6.38132 - 0.916704i) q^{45} +(-1.92007 - 3.32566i) q^{47} +(3.45308 - 5.98090i) q^{49} +(-4.57062 + 6.75396i) q^{51} +2.23508 q^{53} -10.7764 q^{55} +(-1.57062 + 2.32089i) q^{57} +(4.95830 - 8.58802i) q^{59} +(5.36414 + 9.29097i) q^{61} +(-0.568026 + 0.722485i) q^{63} +(-1.01159 - 1.75213i) q^{65} +(-2.02117 + 3.50078i) q^{67} +(6.17912 + 12.7183i) q^{69} +3.59379 q^{71} -5.43811 q^{73} +(0.660035 + 0.0471664i) q^{75} +(-0.768124 + 1.33043i) q^{77} +(-8.30403 - 14.3830i) q^{79} +(-6.51210 + 6.21229i) q^{81} +(-2.91867 - 5.05528i) q^{83} +(-5.05902 + 8.76248i) q^{85} +(8.27557 + 0.591376i) q^{87} -1.94577 q^{89} -0.288420 q^{91} +(-1.96456 - 4.04359i) q^{93} +(-1.73845 + 3.01108i) q^{95} +(7.07283 + 12.2505i) q^{97} +(-9.29826 + 11.8267i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{3} + 4 q^{7} - q^{9}+O(q^{10}) $ 10 * q - q^3 + 4 * q^7 - q^9	$ 10 q - q^{3} + 4 q^{7} - q^{9} + q^{11} - 6 q^{13} - 12 q^{15} - 6 q^{17} - 18 q^{19} - 16 q^{21} - 4 q^{23} + q^{25} + 2 q^{27} + 4 q^{29} + 8 q^{31} - 13 q^{33} + 24 q^{35} + 20 q^{37} + 18 q^{39} - 5 q^{41} + 13 q^{43} + 12 q^{45} + 6 q^{47} + 3 q^{49} - 3 q^{51} - 12 q^{55} + 27 q^{57} + 13 q^{59} - 10 q^{61} + 20 q^{63} + 17 q^{67} + 10 q^{69} - 8 q^{71} - 34 q^{73} + 29 q^{75} - 8 q^{77} + 6 q^{79} - q^{81} - 12 q^{83} - 18 q^{85} - 10 q^{87} + 44 q^{89} - 36 q^{91} - 26 q^{93} + 6 q^{95} + 27 q^{97} - 34 q^{99}+O(q^{100}) $ 10 * q - q^3 + 4 * q^7 - q^9 + q^11 - 6 * q^13 - 12 * q^15 - 6 * q^17 - 18 * q^19 - 16 * q^21 - 4 * q^23 + q^25 + 2 * q^27 + 4 * q^29 + 8 * q^31 - 13 * q^33 + 24 * q^35 + 20 * q^37 + 18 * q^39 - 5 * q^41 + 13 * q^43 + 12 * q^45 + 6 * q^47 + 3 * q^49 - 3 * q^51 - 12 * q^55 + 27 * q^57 + 13 * q^59 - 10 * q^61 + 20 * q^63 + 17 * q^67 + 10 * q^69 - 8 * q^71 - 34 * q^73 + 29 * q^75 - 8 * q^77 + 6 * q^79 - q^81 - 12 * q^83 - 18 * q^85 - 10 * q^87 + 44 * q^89 - 36 * q^91 - 26 * q^93 + 6 * q^95 + 27 * q^97 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	0.970741	−	1.43446i	0.560457	−	0.828183i
$3$	0.970741	−	1.43446i	0.560457	−	0.828183i
$4$		0			0
$5$	1.07447	−	1.86104i	0.480518	−	0.832282i	−0.519232	−	0.854633i	$-0.673782\pi$
$5$	1.07447	−	1.86104i	0.480518	−	0.832282i	0.999750	+	0.0223513i	$0.00711523\pi$
$6$		0			0
$7$	−0.153174	−	0.265305i	−0.0578942	−	0.100276i	0.835626	−	0.549299i	$-0.185105\pi$
$7$	−0.153174	−	0.265305i	−0.0578942	−	0.100276i	−0.893520	+	0.449024i	$0.851772\pi$
$8$		0			0
$9$	−1.11533	−	2.78497i	−0.371775	−	0.928323i
$10$		0			0
$11$	−2.50736	−	4.34288i	−0.755999	−	1.30943i	−0.944876	−	0.327428i	$-0.893818\pi$
$11$	−2.50736	−	4.34288i	−0.755999	−	1.30943i	0.188878	−	0.982001i	$-0.439515\pi$
$12$		0			0
$13$	0.470741	−	0.815346i	0.130560	−	0.226136i	−0.793333	−	0.608788i	$-0.791656\pi$
$13$	0.470741	−	0.815346i	0.130560	−	0.226136i	0.923893	+	0.382652i	$0.124989\pi$
$14$		0			0
$15$	−1.62655	−	3.34787i	−0.419972	−	0.864416i
$16$		0			0
$17$	−4.70838			−1.14195			−0.570975	−	0.820967i	$-0.693435\pi$
$17$	−4.70838			−1.14195			−0.570975	+	0.820967i	$0.693435\pi$
$18$		0			0
$19$	−1.61796			−0.371185			−0.185592	−	0.982627i	$-0.559420\pi$
$19$	−1.61796			−0.371185			−0.185592	+	0.982627i	$0.559420\pi$
$20$		0			0
$21$	−0.529259	−	0.0378211i	−0.115494	−	0.00825323i
$22$		0			0
$23$	−4.08184	+	7.06995i	−0.851122	+	1.47419i	0.0290754	+	0.999577i	$0.490744\pi$
$23$	−4.08184	+	7.06995i	−0.851122	+	1.47419i	−0.880197	+	0.474609i	$0.842590\pi$
$24$		0			0
$25$	0.191022	+	0.330859i	0.0382043	+	0.0661718i
$26$		0			0
$27$	−5.07761	−	1.10360i	−0.977186	−	0.212387i
$28$		0			0
$29$	2.39504	+	4.14834i	0.444749	+	0.770327i	0.998035	−	0.0626641i	$-0.0199597\pi$
$29$	2.39504	+	4.14834i	0.444749	+	0.770327i	−0.553286	+	0.832991i	$0.686626\pi$
$30$		0			0
$31$	1.29776	−	2.24778i	0.233084	−	0.403714i	−0.725630	−	0.688085i	$-0.758452\pi$
$31$	1.29776	−	2.24778i	0.233084	−	0.403714i	0.958714	+	0.284371i	$0.0917848\pi$
$32$		0			0
$33$	−8.66367	−	0.619109i	−1.50815	−	0.107773i
$34$		0			0
$35$	−0.658323			−0.111277
$36$		0			0
$37$	10.2093			1.67840			0.839199	−	0.543824i	$-0.183024\pi$
$37$	10.2093			1.67840			0.839199	+	0.543824i	$0.183024\pi$
$38$		0			0
$39$	−0.712611	−	1.46675i	−0.114109	−	0.234867i
$40$		0			0
$41$	3.86537	−	6.69502i	0.603669	−	1.04559i	−0.388591	−	0.921410i	$-0.627038\pi$
$41$	3.86537	−	6.69502i	0.603669	−	1.04559i	0.992260	−	0.124175i	$-0.0396285\pi$
$42$		0			0
$43$	−0.138140	−	0.239265i	−0.0210661	−	0.0364876i	0.855300	−	0.518133i	$-0.173373\pi$
$43$	−0.138140	−	0.239265i	−0.0210661	−	0.0364876i	−0.876366	+	0.481645i	$0.840039\pi$
$44$		0			0
$45$	−6.38132	−	0.916704i	−0.951271	−	0.136654i
$46$		0			0
$47$	−1.92007	−	3.32566i	−0.280072	−	0.485098i	0.691331	−	0.722539i	$-0.257025\pi$
$47$	−1.92007	−	3.32566i	−0.280072	−	0.485098i	−0.971402	+	0.237441i	$0.923692\pi$
$48$		0			0
$49$	3.45308	−	5.98090i	0.493297	−	0.854415i
$50$		0			0
$51$	−4.57062	+	6.75396i	−0.640014	+	0.945744i
$52$		0			0
$53$	2.23508			0.307012			0.153506	−	0.988148i	$-0.450944\pi$
$53$	2.23508			0.307012			0.153506	+	0.988148i	$0.450944\pi$
$54$		0			0
$55$	−10.7764			−1.45308
$56$		0			0
$57$	−1.57062	+	2.32089i	−0.208033	+	0.307409i
$58$		0			0
$59$	4.95830	−	8.58802i	0.645515	−	1.11807i	−0.338667	−	0.940906i	$-0.609976\pi$
$59$	4.95830	−	8.58802i	0.645515	−	1.11807i	0.984182	−	0.177159i	$-0.0566907\pi$
$60$		0			0
$61$	5.36414	+	9.29097i	0.686808	+	1.18959i	0.972865	+	0.231374i	$0.0743222\pi$
$61$	5.36414	+	9.29097i	0.686808	+	1.18959i	−0.286057	+	0.958213i	$0.592345\pi$
$62$		0			0
$63$	−0.568026	+	0.722485i	−0.0715646	+	0.0910245i
$64$		0			0
$65$	−1.01159	−	1.75213i	−0.125473	−	0.217325i
$66$		0			0
$67$	−2.02117	+	3.50078i	−0.246926	+	0.427688i	−0.962671	−	0.270673i	$-0.912754\pi$
$67$	−2.02117	+	3.50078i	−0.246926	+	0.427688i	0.715746	+	0.698361i	$0.246087\pi$
$68$		0			0
$69$	6.17912	+	12.7183i	0.743879	+	1.53110i
$70$		0			0
$71$	3.59379			0.426505			0.213252	−	0.976997i	$-0.431594\pi$
$71$	3.59379			0.426505			0.213252	+	0.976997i	$0.431594\pi$
$72$		0			0
$73$	−5.43811			−0.636483			−0.318242	−	0.948010i	$-0.603092\pi$
$73$	−5.43811			−0.636483			−0.318242	+	0.948010i	$0.603092\pi$
$74$		0			0
$75$	0.660035	+	0.0471664i	0.0762143	+	0.00544630i
$76$		0			0
$77$	−0.768124	+	1.33043i	−0.0875359	+	0.151617i
$78$		0			0
$79$	−8.30403	−	14.3830i	−0.934276	−	1.61821i	−0.775920	−	0.630831i	$-0.782714\pi$
$79$	−8.30403	−	14.3830i	−0.934276	−	1.61821i	−0.158356	−	0.987382i	$-0.550619\pi$
$80$		0			0
$81$	−6.51210	+	6.21229i	−0.723566	+	0.690255i
$82$		0			0
$83$	−2.91867	−	5.05528i	−0.320365	−	0.554889i	0.660198	−	0.751092i	$-0.270472\pi$
$83$	−2.91867	−	5.05528i	−0.320365	−	0.554889i	−0.980563	+	0.196203i	$0.937139\pi$
$84$		0			0
$85$	−5.05902	+	8.76248i	−0.548728	+	0.950425i
$86$		0			0
$87$	8.27557	+	0.591376i	0.887235	+	0.0634021i
$88$		0			0
$89$	−1.94577			−0.206251			−0.103125	−	0.994668i	$-0.532884\pi$
$89$	−1.94577			−0.206251			−0.103125	+	0.994668i	$0.532884\pi$
$90$		0			0
$91$	−0.288420			−0.0302347
$92$		0			0
$93$	−1.96456	−	4.04359i	−0.203715	−	0.419301i
$94$		0			0
$95$	−1.73845	+	3.01108i	−0.178361	+	0.308930i
$96$		0			0
$97$	7.07283	+	12.2505i	0.718137	+	1.24385i	0.961737	+	0.273974i	$0.0883383\pi$
$97$	7.07283	+	12.2505i	0.718137	+	1.24385i	−0.243600	+	0.969876i	$0.578328\pi$
$98$		0			0
$99$	−9.29826	+	11.8267i	−0.934510	+	1.18862i
$100$		0			0
$101$	−9.41272	−	16.3033i	−0.936601	−	1.62224i	−0.771754	−	0.635922i	$-0.780620\pi$
$101$	−9.41272	−	16.3033i	−0.936601	−	1.62224i	−0.164847	−	0.986319i	$-0.552713\pi$
$102$		0			0
$103$	2.95014	−	5.10979i	0.290686	−	0.503483i	−0.683286	−	0.730151i	$-0.739450\pi$
$103$	2.95014	−	5.10979i	0.290686	−	0.503483i	0.973972	+	0.226668i	$0.0727831\pi$
$104$		0			0
$105$	−0.639061	+	0.944335i	−0.0623659	+	0.0921577i
$106$		0			0
$107$	−3.86061			−0.373219			−0.186609	−	0.982434i	$-0.559750\pi$
$107$	−3.86061			−0.373219			−0.186609	+	0.982434i	$0.559750\pi$
$108$		0			0
$109$	10.8821			1.04232			0.521159	−	0.853459i	$-0.325500\pi$
$109$	10.8821			1.04232			0.521159	+	0.853459i	$0.325500\pi$
$110$		0			0
$111$	9.91058	−	14.6448i	0.940671	−	1.39002i
$112$		0			0
$113$	3.15157	−	5.45869i	0.296475	−	0.513510i	−0.678852	−	0.734275i	$-0.737522\pi$
$113$	3.15157	−	5.45869i	0.296475	−	0.513510i	0.975327	+	0.220765i	$0.0708555\pi$
$114$		0			0
$115$	8.77163	+	15.1929i	0.817959	+	1.41675i
$116$		0			0
$117$	−2.79574	−	0.401621i	−0.258467	−	0.0371298i
$118$		0			0
$119$	0.721200	+	1.24915i	0.0661123	+	0.114510i
$120$		0			0
$121$	−7.07375	+	12.2521i	−0.643068	+	1.11383i
$122$		0			0
$123$	−5.85143	−	12.0438i	−0.527606	−	1.08595i
$124$		0			0
$125$	11.5657			1.03447
$126$		0			0
$127$	−11.7659			−1.04406			−0.522028	−	0.852928i	$-0.674825\pi$
$127$	−11.7659			−1.04406			−0.522028	+	0.852928i	$0.674825\pi$
$128$		0			0
$129$	−0.477313	−	0.0341090i	−0.0420251	−	0.00300313i
$130$		0			0
$131$	−2.64077	+	4.57395i	−0.230725	+	0.399628i	−0.958022	−	0.286696i	$-0.907443\pi$
$131$	−2.64077	+	4.57395i	−0.230725	+	0.399628i	0.727297	+	0.686323i	$0.240777\pi$
$132$		0			0
$133$	0.247828	+	0.429251i	0.0214894	+	0.0372208i
$134$		0			0
$135$	−7.50958	+	8.26384i	−0.646322	+	0.711238i
$136$		0			0
$137$	−7.23452	−	12.5306i	−0.618087	−	1.07056i	−0.989834	−	0.142224i	$-0.954575\pi$
$137$	−7.23452	−	12.5306i	−0.618087	−	1.07056i	0.371748	−	0.928334i	$-0.378759\pi$
$138$		0			0
$139$	10.7880	−	18.6854i	0.915026	−	1.58487i	0.108164	−	0.994133i	$-0.465503\pi$
$139$	10.7880	−	18.6854i	0.915026	−	1.58487i	0.806863	−	0.590739i	$-0.201164\pi$
$140$		0			0
$141$	−6.63441	−	0.474097i	−0.558718	−	0.0399262i
$142$		0			0
$143$	−4.72127			−0.394813
$144$		0			0
$145$	10.2936			0.854839
$146$		0			0
$147$	−5.22730	−	10.7592i	−0.431140	−	0.887403i
$148$		0			0
$149$	7.80471	−	13.5181i	0.639386	−	1.10745i	−0.346181	−	0.938168i	$-0.612522\pi$
$149$	7.80471	−	13.5181i	0.639386	−	1.10745i	0.985568	−	0.169282i	$-0.0541449\pi$
$150$		0			0
$151$	8.58275	+	14.8658i	0.698455	+	1.20976i	0.969002	+	0.247052i	$0.0794620\pi$
$151$	8.58275	+	14.8658i	0.698455	+	1.20976i	−0.270547	+	0.962707i	$0.587205\pi$
$152$		0			0
$153$	5.25138	+	13.1127i	0.424549	+	1.06010i
$154$		0			0
$155$	−2.78881	−	4.83036i	−0.224003	−	0.387984i
$156$		0			0
$157$	2.59257	−	4.49046i	0.206909	−	0.358378i	−0.743830	−	0.668369i	$-0.766993\pi$
$157$	2.59257	−	4.49046i	0.206909	−	0.358378i	0.950739	+	0.309991i	$0.100326\pi$
$158$		0			0
$159$	2.16968	−	3.20612i	0.172067	−	0.254262i
$160$		0			0
$161$	2.50092			0.197100
$162$		0			0
$163$	17.8955			1.40168			0.700842	−	0.713317i	$-0.252808\pi$
$163$	17.8955			1.40168			0.700842	+	0.713317i	$0.252808\pi$
$164$		0			0
$165$	−10.4611	+	15.4582i	−0.814392	+	1.20342i
$166$		0			0
$167$	−5.48714	+	9.50401i	−0.424608	+	0.735442i	−0.996384	−	0.0849677i	$-0.972921\pi$
$167$	−5.48714	+	9.50401i	−0.424608	+	0.735442i	0.571776	+	0.820410i	$0.306255\pi$
$168$		0			0
$169$	6.05681	+	10.4907i	0.465908	+	0.806977i
$170$		0			0
$171$	1.80455	+	4.50596i	0.137997	+	0.344579i
$172$		0			0
$173$	−8.63146	−	14.9501i	−0.656238	−	1.13664i	−0.981582	−	0.191042i	$-0.938813\pi$
$173$	−8.63146	−	14.9501i	−0.656238	−	1.13664i	0.325344	−	0.945596i	$-0.394520\pi$
$174$		0			0
$175$	0.0585190	−	0.101358i	0.00442362	−	0.00766193i
$176$		0			0
$177$	−7.50592	−	15.4492i	−0.564179	−	1.16123i
$178$		0			0
$179$	15.0571			1.12542			0.562709	−	0.826655i	$-0.309759\pi$
$179$	15.0571			1.12542			0.562709	+	0.826655i	$0.309759\pi$
$180$		0			0
$181$	−17.6813			−1.31424			−0.657120	−	0.753786i	$-0.728226\pi$
$181$	−17.6813			−1.31424			−0.657120	+	0.753786i	$0.728226\pi$
$182$		0			0
$183$	18.5347	+	1.32449i	1.37012	+	0.0979095i
$184$		0			0
$185$	10.9696	−	18.9999i	0.806501	−	1.39690i
$186$		0			0
$187$	11.8056	+	20.4479i	0.863313	+	1.49530i
$188$		0			0
$189$	0.484966	+	1.51615i	0.0352761	+	0.110284i
$190$		0			0
$191$	10.3168	+	17.8693i	0.746501	+	1.29298i	0.949490	+	0.313796i	$0.101601\pi$
$191$	10.3168	+	17.8693i	0.746501	+	1.29298i	−0.202990	+	0.979181i	$0.565066\pi$
$192$		0			0
$193$	11.6134	−	20.1149i	0.835948	−	1.44791i	−0.0573076	−	0.998357i	$-0.518252\pi$
$193$	11.6134	−	20.1149i	0.835948	−	1.44791i	0.893256	−	0.449548i	$-0.148415\pi$
$194$		0			0
$195$	−3.49535	−	0.249779i	−0.250307	−	0.0178871i
$196$		0			0
$197$	4.78497			0.340915			0.170458	−	0.985365i	$-0.445475\pi$
$197$	4.78497			0.340915			0.170458	+	0.985365i	$0.445475\pi$
$198$		0			0
$199$	−11.5938			−0.821862			−0.410931	−	0.911666i	$-0.634796\pi$
$199$	−11.5938			−0.821862			−0.410931	+	0.911666i	$0.634796\pi$
$200$		0			0
$201$	3.05967	+	6.29763i	0.215813	+	0.444200i
$202$		0			0
$203$	0.733715	−	1.27083i	0.0514967	−	0.0891950i
$204$		0			0
$205$	−8.30646	−	14.3872i	−0.580148	−	1.00485i
$206$		0			0
$207$	24.2422	+	3.48249i	1.68495	+	0.242050i
$208$		0			0
$209$	4.05681	+	7.02660i	0.280615	+	0.486040i
$210$		0			0
$211$	−0.888671	+	1.53922i	−0.0611786	+	0.105964i	−0.894993	−	0.446081i	$-0.852819\pi$
$211$	−0.888671	+	1.53922i	−0.0611786	+	0.105964i	0.833814	+	0.552046i	$0.186153\pi$
$212$		0			0
$213$	3.48864	−	5.15513i	0.239038	−	0.353224i
$214$		0			0
$215$	−0.593709			−0.0404906
$216$		0			0
$217$	−0.795130			−0.0539769
$218$		0			0
$219$	−5.27900	+	7.80073i	−0.356722	+	0.527125i
$220$		0			0
$221$	−2.21643	+	3.83896i	−0.149093	+	0.258237i
$222$		0			0
$223$	5.02422	+	8.70221i	0.336447	+	0.582743i	0.983762	−	0.179480i	$-0.0574415\pi$
$223$	5.02422	+	8.70221i	0.336447	+	0.582743i	−0.647315	+	0.762223i	$0.724108\pi$
$224$		0			0
$225$	0.708381	−	0.901005i	0.0472254	−	0.0600670i
$226$		0			0
$227$	−5.27671	−	9.13953i	−0.350228	−	0.606612i	0.636061	−	0.771638i	$-0.280562\pi$
$227$	−5.27671	−	9.13953i	−0.350228	−	0.606612i	−0.986289	+	0.165026i	$0.947229\pi$
$228$		0			0
$229$	−11.3955	+	19.7377i	−0.753039	+	1.30430i	0.193304	+	0.981139i	$0.438080\pi$
$229$	−11.3955	+	19.7377i	−0.753039	+	1.30430i	−0.946343	+	0.323163i	$0.895254\pi$
$230$		0			0
$231$	1.16279	+	2.39334i	0.0765062	+	0.157470i
$232$		0			0
$233$	5.97108			0.391179			0.195589	−	0.980686i	$-0.437338\pi$
$233$	5.97108			0.391179			0.195589	+	0.980686i	$0.437338\pi$
$234$		0			0
$235$	−8.25226			−0.538318
$236$		0			0
$237$	−28.6928	−	2.05040i	−1.86380	−	0.133188i
$238$		0			0
$239$	5.77549	−	10.0034i	0.373585	−	0.647069i	−0.616529	−	0.787332i	$-0.711462\pi$
$239$	5.77549	−	10.0034i	0.373585	−	0.647069i	0.990114	+	0.140264i	$0.0447950\pi$
$240$		0			0
$241$	7.75827	+	13.4377i	0.499754	+	0.865600i	1.00000		0.000283894i	$-9.03662e-5\pi$
$241$	7.75827	+	13.4377i	0.499754	+	0.865600i	−0.500246	+	0.865883i	$0.666757\pi$
$242$		0			0
$243$	2.58970	+	15.3718i	0.166129	+	0.986104i
$244$		0			0
$245$	−7.42046	−	12.8526i	−0.474076	−	0.821124i
$246$		0			0
$247$	−0.761638	+	1.31920i	−0.0484619	+	0.0839384i
$248$		0			0
$249$	−10.0848	−	0.720666i	−0.639101	−	0.0456704i
$250$		0			0
$251$	14.5685			0.919557			0.459778	−	0.888034i	$-0.347929\pi$
$251$	14.5685			0.919557			0.459778	+	0.888034i	$0.347929\pi$
$252$		0			0
$253$	40.9386			2.57379
$254$		0			0
$255$	7.65839	+	15.7630i	0.479587	+	0.987120i
$256$		0			0
$257$	−7.78071	+	13.4766i	−0.485347	+	0.840646i	−0.999858	−	0.0168376i	$-0.994640\pi$
$257$	−7.78071	+	13.4766i	−0.485347	+	0.840646i	0.514511	+	0.857484i	$0.327974\pi$
$258$		0			0
$259$	−1.56380	−	2.70857i	−0.0971695	−	0.168303i
$260$		0			0
$261$	8.88174	−	11.2969i	0.549766	−	0.699259i
$262$		0			0
$263$	11.2231	+	19.4389i	0.692044	+	1.19866i	0.971167	+	0.238400i	$0.0766229\pi$
$263$	11.2231	+	19.4389i	0.692044	+	1.19866i	−0.279123	+	0.960255i	$0.590044\pi$
$264$		0			0
$265$	2.40153	−	4.15957i	0.147525	−	0.255521i
$266$		0			0
$267$	−1.88884	+	2.79112i	−0.115595	+	0.170814i
$268$		0			0
$269$	−26.0256			−1.58681			−0.793403	−	0.608696i	$-0.791693\pi$
$269$	−26.0256			−1.58681			−0.793403	+	0.608696i	$0.791693\pi$
$270$		0			0
$271$	5.59761			0.340031			0.170015	−	0.985441i	$-0.445618\pi$
$271$	5.59761			0.340031			0.170015	+	0.985441i	$0.445618\pi$
$272$		0			0
$273$	−0.279981	+	0.413726i	−0.0169452	+	0.0250398i
$274$		0			0
$275$	0.957922	−	1.65917i	0.0577648	−	0.100052i
$276$		0			0
$277$	−1.57957	−	2.73589i	−0.0949069	−	0.164384i	0.814663	−	0.579935i	$-0.196922\pi$
$277$	−1.57957	−	2.73589i	−0.0949069	−	0.164384i	−0.909570	+	0.415551i	$0.863589\pi$
$278$		0			0
$279$	−7.70743	−	1.10721i	−0.461432	−	0.0662867i
$280$		0			0
$281$	−8.02031	−	13.8916i	−0.478452	−	0.828703i	0.521243	−	0.853408i	$-0.325468\pi$
$281$	−8.02031	−	13.8916i	−0.478452	−	0.828703i	−0.999695	+	0.0247057i	$0.992135\pi$
$282$		0			0
$283$	−1.87142	+	3.24140i	−0.111245	+	0.192681i	−0.916272	−	0.400556i	$-0.868817\pi$
$283$	−1.87142	+	3.24140i	−0.111245	+	0.192681i	0.805028	+	0.593237i	$0.202150\pi$
$284$		0			0
$285$	2.63168	+	5.41671i	0.155887	+	0.320858i
$286$		0			0
$287$	−2.36829			−0.139796
$288$		0			0
$289$	5.16885			0.304050
$290$		0			0
$291$	24.4387	+	1.74640i	1.43262	+	0.102376i
$292$		0			0
$293$	5.49886	−	9.52431i	0.321247	−	0.556416i	−0.659499	−	0.751706i	$-0.729231\pi$
$293$	5.49886	−	9.52431i	0.321247	−	0.556416i	0.980746	+	0.195290i	$0.0625647\pi$
$294$		0			0
$295$	−10.6551	−	18.4552i	−0.620364	−	1.07450i
$296$		0			0
$297$	7.93862	+	24.8186i	0.460645	+	1.44012i
$298$		0			0
$299$	3.84297	+	6.65622i	0.222245	+	0.384939i
$300$		0			0
$301$	−0.0423188	+	0.0732983i	−0.00243921	+	0.00422484i
$302$		0			0
$303$	−32.5237	−	2.32416i	−1.86844	−	0.133519i
$304$		0			0
$305$	23.0545			1.32010
$306$		0			0
$307$	−6.08416			−0.347241			−0.173621	−	0.984813i	$-0.555547\pi$
$307$	−6.08416			−0.347241			−0.173621	+	0.984813i	$0.555547\pi$
$308$		0			0
$309$	−4.46595	−	9.19213i	−0.254059	−	0.522922i
$310$		0			0
$311$	−3.75633	+	6.50616i	−0.213002	+	0.368930i	−0.952653	−	0.304061i	$-0.901657\pi$
$311$	−3.75633	+	6.50616i	−0.213002	+	0.368930i	0.739651	+	0.672991i	$0.234991\pi$
$312$		0			0
$313$	6.18076	+	10.7054i	0.349357	+	0.605105i	0.986135	−	0.165942i	$-0.0530666\pi$
$313$	6.18076	+	10.7054i	0.349357	+	0.605105i	−0.636778	+	0.771047i	$0.719733\pi$
$314$		0			0
$315$	0.734245	+	1.83341i	0.0413700	+	0.103301i
$316$		0			0
$317$	12.3204	+	21.3395i	0.691980	+	1.19854i	0.971188	+	0.238314i	$0.0765947\pi$
$317$	12.3204	+	21.3395i	0.691980	+	1.19854i	−0.279208	+	0.960231i	$0.590072\pi$
$318$		0			0
$319$	12.0105	−	20.8028i	0.672459	−	1.16473i
$320$		0			0
$321$	−3.74765	+	5.53787i	−0.209173	+	0.309094i
$322$		0			0
$323$	7.61796			0.423874
$324$		0			0
$325$	0.359686			0.0199518
$326$		0			0
$327$	10.5637	−	15.6099i	0.584175	−	0.863231i
$328$		0			0
$329$	−0.588209	+	1.01881i	−0.0324290	+	0.0561687i
$330$		0			0
$331$	11.0695	+	19.1730i	0.608436	+	1.05384i	0.991498	+	0.130119i	$0.0415360\pi$
$331$	11.0695	+	19.1730i	0.608436	+	1.05384i	−0.383063	+	0.923722i	$0.625131\pi$
$332$		0			0
$333$	−11.3867	−	28.4326i	−0.623987	−	1.55810i
$334$		0			0
$335$	4.34339	+	7.52297i	0.237305	+	0.411024i
$336$		0			0
$337$	−5.63803	+	9.76536i	−0.307123	+	0.531953i	−0.977732	−	0.209858i	$-0.932700\pi$
$337$	−5.63803	+	9.76536i	−0.307123	+	0.531953i	0.670609	+	0.741811i	$0.266033\pi$
$338$		0			0
$339$	−4.77088	−	9.81976i	−0.259119	−	0.533336i
$340$		0			0
$341$	−13.0158			−0.704846
$342$		0			0
$343$	−4.26011			−0.230024
$344$		0			0
$345$	30.3085	+	2.16586i	1.63176	+	0.116606i
$346$		0			0
$347$	11.3903	−	19.7286i	0.611465	−	1.05909i	−0.379529	−	0.925180i	$-0.623914\pi$
$347$	11.3903	−	19.7286i	0.611465	−	1.05909i	0.990994	−	0.133908i	$-0.0427527\pi$
$348$		0			0
$349$	1.44215	+	2.49788i	0.0771966	+	0.133708i	0.902039	−	0.431654i	$-0.142070\pi$
$349$	1.44215	+	2.49788i	0.0771966	+	0.133708i	−0.824843	+	0.565362i	$0.808736\pi$
$350$		0			0
$351$	−3.29005	+	3.62050i	−0.175610	+	0.193248i
$352$		0			0
$353$	9.41192	+	16.3019i	0.500946	+	0.867663i	0.999999	+	0.00109240i	$0.000347720\pi$
$353$	9.41192	+	16.3019i	0.500946	+	0.867663i	−0.499054	+	0.866571i	$0.666319\pi$
$354$		0			0
$355$	3.86143	−	6.68819i	0.204943	−	0.354972i
$356$		0			0
$357$	2.49196	+	0.178076i	0.131888	+	0.00942478i
$358$		0			0
$359$	26.6316			1.40556			0.702782	−	0.711406i	$-0.251941\pi$
$359$	26.6316			1.40556			0.702782	+	0.711406i	$0.251941\pi$
$360$		0			0
$361$	−16.3822			−0.862222
$362$		0			0
$363$	10.7083	+	22.0406i	0.562040	+	1.15683i
$364$		0			0
$365$	−5.84310	+	10.1205i	−0.305842	+	0.529733i
$366$		0			0
$367$	12.6413	+	21.8953i	0.659869	+	1.14293i	0.980649	+	0.195773i	$0.0627216\pi$
$367$	12.6413	+	21.8953i	0.659869	+	1.14293i	−0.320780	+	0.947154i	$0.603945\pi$
$368$		0			0
$369$	−22.9566	−	3.29781i	−1.19507	−	0.171677i
$370$		0			0
$371$	−0.342356	−	0.592977i	−0.0177742	−	0.0307858i
$372$		0			0
$373$	0.427926	−	0.741189i	0.0221571	−	0.0383773i	−0.854734	−	0.519066i	$-0.826280\pi$
$373$	0.427926	−	0.741189i	0.0221571	−	0.0383773i	0.876891	+	0.480689i	$0.159613\pi$
$374$		0			0
$375$	11.2273	−	16.5905i	0.579775	−	0.856729i
$376$		0			0
$377$	4.50978			0.232265
$378$		0			0
$379$	−5.34571			−0.274591			−0.137295	−	0.990530i	$-0.543841\pi$
$379$	−5.34571			−0.274591			−0.137295	+	0.990530i	$0.543841\pi$
$380$		0			0
$381$	−11.4217	+	16.8777i	−0.585149	+	0.864671i
$382$		0			0
$383$	0.132433	−	0.229381i	0.00676702	−	0.0117208i	−0.862622	−	0.505849i	$-0.831179\pi$
$383$	0.132433	−	0.229381i	0.00676702	−	0.0117208i	0.869389	+	0.494128i	$0.164513\pi$
$384$		0			0
$385$	1.65066	+	2.85902i	0.0841252	+	0.145709i
$386$		0			0
$387$	−0.512275	+	0.651574i	−0.0260404	+	0.0331214i
$388$		0			0
$389$	10.9697	+	19.0001i	0.556187	+	0.963343i	0.997810	+	0.0661429i	$0.0210693\pi$
$389$	10.9697	+	19.0001i	0.556187	+	0.963343i	−0.441624	+	0.897200i	$0.645597\pi$
$390$		0			0
$391$	19.2188	−	33.2880i	0.971938	−	1.68345i
$392$		0			0
$393$	3.99762	+	8.22819i	0.201653	+	0.415057i
$394$		0			0
$395$	−35.6898			−1.79575
$396$		0			0
$397$	−2.19238			−0.110032			−0.0550161	−	0.998485i	$-0.517521\pi$
$397$	−2.19238			−0.110032			−0.0550161	+	0.998485i	$0.517521\pi$
$398$		0			0
$399$	0.856319	+	0.0611929i	0.0428696	+	0.00306347i
$400$		0			0
$401$	−18.8864	+	32.7121i	−0.943140	+	1.63357i	−0.183707	+	0.982981i	$0.558810\pi$
$401$	−18.8864	+	32.7121i	−0.943140	+	1.63357i	−0.759433	+	0.650585i	$0.774524\pi$
$402$		0			0
$403$	−1.22182	−	2.11625i	−0.0608630	−	0.105418i
$404$		0			0
$405$	4.56426	+	18.7942i	0.226800	+	0.933891i
$406$		0			0
$407$	−25.5984	−	44.3378i	−1.26887	−	2.19774i
$408$		0			0
$409$	15.9676	−	27.6566i	0.789546	−	1.36753i	−0.136700	−	0.990612i	$-0.543650\pi$
$409$	15.9676	−	27.6566i	0.789546	−	1.36753i	0.926246	−	0.376920i	$-0.123017\pi$
$410$		0			0
$411$	−24.9974	−	1.78632i	−1.23303	−	0.0881127i
$412$		0			0
$413$	−3.03792			−0.149486
$414$		0			0
$415$	−12.5441			−0.615766
$416$		0			0
$417$	−16.3310	−	33.6136i	−0.799731	−	1.64606i
$418$		0			0
$419$	−1.83505	+	3.17840i	−0.0896480	+	0.155275i	−0.907362	−	0.420349i	$-0.861908\pi$
$419$	−1.83505	+	3.17840i	−0.0896480	+	0.155275i	0.817714	+	0.575624i	$0.195241\pi$
$420$		0			0
$421$	−7.72300	−	13.3766i	−0.376396	−	0.651937i	0.614139	−	0.789198i	$-0.289503\pi$
$421$	−7.72300	−	13.3766i	−0.376396	−	0.651937i	−0.990535	+	0.137261i	$0.956170\pi$
$422$		0			0
$423$	−7.12036	+	9.05654i	−0.346204	+	0.440344i
$424$		0			0
$425$	−0.899403	−	1.55781i	−0.0436274	−	0.0755649i
$426$		0			0
$427$	1.64329	−	2.84626i	0.0795244	−	0.137740i
$428$		0			0
$429$	−4.58313	+	6.77245i	−0.221276	+	0.326977i
$430$		0			0
$431$	−18.9913			−0.914779			−0.457390	−	0.889266i	$-0.651216\pi$
$431$	−18.9913			−0.914779			−0.457390	+	0.889266i	$0.651216\pi$
$432$		0			0
$433$	12.7931			0.614796			0.307398	−	0.951581i	$-0.400542\pi$
$433$	12.7931			0.614796			0.307398	+	0.951581i	$0.400542\pi$
$434$		0			0
$435$	9.99244	−	14.7658i	0.479101	−	0.707964i
$436$		0			0
$437$	6.60423	−	11.4389i	0.315923	−	0.547195i
$438$		0			0
$439$	14.5259	+	25.1595i	0.693281	+	1.20080i	0.970757	+	0.240065i	$0.0771689\pi$
$439$	14.5259	+	25.1595i	0.693281	+	1.20080i	−0.277476	+	0.960733i	$0.589498\pi$
$440$		0			0
$441$	−20.5079	−	2.94605i	−0.976568	−	0.140288i
$442$		0			0
$443$	18.4010	+	31.8714i	0.874256	+	1.51426i	0.857554	+	0.514395i	$0.171983\pi$
$443$	18.4010	+	31.8714i	0.874256	+	1.51426i	0.0167020	+	0.999861i	$0.494683\pi$
$444$		0			0
$445$	−2.09067	+	3.62115i	−0.0991073	+	0.171659i
$446$		0			0
$447$	−11.8148	−	24.3181i	−0.558823	−	1.15021i
$448$		0			0
$449$	−18.4952			−0.872842			−0.436421	−	0.899743i	$-0.643754\pi$
$449$	−18.4952			−0.872842			−0.436421	+	0.899743i	$0.643754\pi$
$450$		0			0
$451$	−38.7675			−1.82549
$452$		0			0
$453$	29.6559	+	2.11922i	1.39336	+	0.0995697i
$454$		0			0
$455$	−0.309899	+	0.536761i	−0.0145283	+	0.0251638i
$456$		0			0
$457$	9.79321	+	16.9623i	0.458107	+	0.793465i	0.998861	−	0.0477162i	$-0.0151943\pi$
$457$	9.79321	+	16.9623i	0.458107	+	0.793465i	−0.540754	+	0.841181i	$0.681861\pi$
$458$		0			0
$459$	23.9073	+	5.19615i	1.11590	+	0.242536i
$460$		0			0
$461$	6.17311	+	10.6921i	0.287510	+	0.497983i	0.973215	−	0.229897i	$-0.0738391\pi$
$461$	6.17311	+	10.6921i	0.287510	+	0.497983i	−0.685704	+	0.727880i	$0.740506\pi$
$462$		0			0
$463$	−18.6089	+	32.2316i	−0.864830	+	1.49793i	0.00238525	+	0.999997i	$0.499241\pi$
$463$	−18.6089	+	32.2316i	−0.864830	+	1.49793i	−0.867216	+	0.497933i	$0.834093\pi$
$464$		0			0
$465$	−9.63615	−	0.688603i	−0.446866	−	0.0319332i
$466$		0			0
$467$	−10.6412			−0.492415			−0.246208	−	0.969217i	$-0.579185\pi$
$467$	−10.6412			−0.492415			−0.246208	+	0.969217i	$0.579185\pi$
$468$		0			0
$469$	1.23836			0.0571823
$470$		0			0
$471$	−3.92465	−	8.07799i	−0.180838	−	0.372214i
$472$		0			0
$473$	−0.692734	+	1.19985i	−0.0318519	+	0.0551692i
$474$		0			0
$475$	−0.309065	−	0.535316i	−0.0141809	−	0.0245620i
$476$		0			0
$477$	−2.49284	−	6.22463i	−0.114139	−	0.285006i
$478$		0			0
$479$	6.22894	+	10.7888i	0.284608	+	0.492955i	0.972514	−	0.232845i	$-0.0748034\pi$
$479$	6.22894	+	10.7888i	0.284608	+	0.492955i	−0.687906	+	0.725799i	$0.741470\pi$
$480$		0			0
$481$	4.80593	−	8.32412i	0.219132	−	0.379547i
$482$		0			0
$483$	2.42774	−	3.58746i	0.110466	−	0.163235i
$484$		0			0
$485$	30.3982			1.38031
$486$		0			0
$487$	12.5254			0.567580			0.283790	−	0.958886i	$-0.408408\pi$
$487$	12.5254			0.567580			0.283790	+	0.958886i	$0.408408\pi$
$488$		0			0
$489$	17.3719	−	25.6703i	0.785584	−	1.16085i
$490$		0			0
$491$	0.581151	−	1.00658i	0.0262270	−	0.0454264i	−0.852614	−	0.522541i	$-0.824984\pi$
$491$	0.581151	−	1.00658i	0.0262270	−	0.0454264i	0.878841	+	0.477115i	$0.158317\pi$
$492$		0			0
$493$	−11.2768	−	19.5320i	−0.507881	−	0.879675i
$494$		0			0
$495$	12.0192	+	30.0118i	0.540221	+	1.34893i
$496$		0			0
$497$	−0.550474	−	0.953449i	−0.0246921	−	0.0427680i
$498$		0			0
$499$	12.8699	−	22.2912i	0.576134	−	0.997893i	−0.419784	−	0.907624i	$-0.637894\pi$
$499$	12.8699	−	22.2912i	0.576134	−	0.997893i	0.995917	−	0.0902688i	$-0.0287726\pi$
$500$		0			0
$501$	8.30648	+	17.0970i	0.371106	+	0.763837i
$502$		0			0
$503$	−24.1469			−1.07666			−0.538328	−	0.842736i	$-0.680944\pi$
$503$	−24.1469			−1.07666			−0.538328	+	0.842736i	$0.680944\pi$
$504$		0			0
$505$	−40.4548			−1.80022
$506$		0			0
$507$	20.9280	+	1.49552i	0.929446	+	0.0664186i
$508$		0			0
$509$	−4.55763	+	7.89404i	−0.202013	+	0.349897i	−0.949177	−	0.314743i	$-0.898082\pi$
$509$	−4.55763	+	7.89404i	−0.202013	+	0.349897i	0.747164	+	0.664640i	$0.231415\pi$
$510$		0			0
$511$	0.832976	+	1.44276i	0.0368487	+	0.0638238i
$512$		0			0
$513$	8.21535	+	1.78557i	0.362716	+	0.0788349i
$514$		0			0
$515$	−6.33969	−	10.9807i	−0.279360	−	0.483866i
$516$		0			0
$517$	−9.62865	+	16.6773i	−0.423467	+	0.733467i
$518$		0			0
$519$	−29.8242	−	2.13125i	−1.30914	−	0.0935514i
$520$		0			0
$521$	−9.18121			−0.402236			−0.201118	−	0.979567i	$-0.564458\pi$
$521$	−9.18121			−0.402236			−0.201118	+	0.979567i	$0.564458\pi$
$522$		0			0
$523$	−8.94824			−0.391279			−0.195640	−	0.980676i	$-0.562678\pi$
$523$	−8.94824			−0.391279			−0.195640	+	0.980676i	$0.562678\pi$
$524$		0			0
$525$	−0.0885866	−	0.182335i	−0.00386623	−	0.00795775i
$526$		0			0
$527$	−6.11034	+	10.5834i	−0.266171	+	0.461021i
$528$		0			0
$529$	−21.8228	−	37.7981i	−0.948816	−	1.64340i
$530$		0			0
$531$	−29.4475	−	4.23026i	−1.27791	−	0.183578i
$532$		0			0
$533$	−3.63917	−	6.30323i	−0.157630	−	0.273023i
$534$		0			0
$535$	−4.14811	+	7.18474i	−0.179338	+	0.310623i
$536$		0			0
$537$	14.6165	−	21.5987i	0.630749	−	0.932053i
$538$		0			0
$539$	−34.6325			−1.49173
$540$		0			0
$541$	26.6203			1.14450			0.572249	−	0.820080i	$-0.306071\pi$
$541$	26.6203			1.14450			0.572249	+	0.820080i	$0.306071\pi$
$542$		0			0
$543$	−17.1640	+	25.3630i	−0.736576	+	1.08843i
$544$		0			0
$545$	11.6925	−	20.2521i	0.500853	−	0.867503i
$546$		0			0
$547$	2.18028	+	3.77635i	0.0932219	+	0.161465i	0.908865	−	0.417090i	$-0.136950\pi$
$547$	2.18028	+	3.77635i	0.0932219	+	0.161465i	−0.815643	+	0.578555i	$0.803617\pi$
$548$		0			0
$549$	19.8923	−	25.3014i	0.848982	−	1.07984i
$550$		0			0
$551$	−3.87508	−	6.71183i	−0.165084	−	0.285934i
$552$		0			0
$553$	−2.54392	+	4.40619i	−0.108178	+	0.187370i
$554$		0			0
$555$	−16.6059	−	34.1794i	−0.704881	−	1.45083i
$556$		0			0
$557$	9.33947			0.395726			0.197863	−	0.980230i	$-0.436600\pi$
$557$	9.33947			0.395726			0.197863	+	0.980230i	$0.436600\pi$
$558$		0			0
$559$	−0.260112			−0.0110016
$560$		0			0
$561$	40.7919	+	2.91500i	1.72223	+	0.123071i
$562$		0			0
$563$	0.603050	−	1.04451i	0.0254155	−	0.0440210i	−0.853038	−	0.521849i	$-0.825242\pi$
$563$	0.603050	−	1.04451i	0.0254155	−	0.0440210i	0.878453	+	0.477828i	$0.158576\pi$
$564$		0			0
$565$	−6.77255	−	11.7304i	−0.284923	−	0.493502i
$566$		0			0
$567$	2.64563	+	0.776129i	0.111106	+	0.0325944i
$568$		0			0
$569$	−3.83998	−	6.65104i	−0.160980	−	0.278826i	0.774240	−	0.632892i	$-0.218132\pi$
$569$	−3.83998	−	6.65104i	−0.160980	−	0.278826i	−0.935221	+	0.354066i	$0.884799\pi$
$570$		0			0
$571$	−4.44038	+	7.69097i	−0.185824	+	0.321857i	−0.943854	−	0.330363i	$-0.892829\pi$
$571$	−4.44038	+	7.69097i	−0.185824	+	0.321857i	0.758030	+	0.652220i	$0.226162\pi$
$572$		0			0
$573$	35.6477	+	2.54740i	1.48920	+	0.106419i
$574$		0			0
$575$	−3.11888			−0.130066
$576$		0			0
$577$	−33.1358			−1.37946			−0.689732	−	0.724065i	$-0.742271\pi$
$577$	−33.1358			−1.37946			−0.689732	+	0.724065i	$0.742271\pi$
$578$		0			0
$579$	−17.5804	−	36.1852i	−0.730617	−	1.50381i
$580$		0			0
$581$	−0.894126	+	1.54867i	−0.0370946	+	0.0642497i
$582$		0			0
$583$	−5.60416	−	9.70669i	−0.232101	−	0.402010i
$584$		0			0
$585$	−3.75138	+	4.77146i	−0.155100	+	0.197276i
$586$		0			0
$587$	18.0712	+	31.3002i	0.745877	+	1.29190i	0.949784	+	0.312906i	$0.101302\pi$
$587$	18.0712	+	31.3002i	0.745877	+	1.29190i	−0.203908	+	0.978990i	$0.565364\pi$
$588$		0			0
$589$	−2.09972	+	3.63682i	−0.0865174	+	0.149852i
$590$		0			0
$591$	4.64496	−	6.86383i	0.191068	−	0.282340i
$592$		0			0
$593$	−34.4076			−1.41295			−0.706476	−	0.707737i	$-0.749716\pi$
$593$	−34.4076			−1.41295			−0.706476	+	0.707737i	$0.749716\pi$
$594$		0			0
$595$	3.09964			0.127073
$596$		0			0
$597$	−11.2546	+	16.6308i	−0.460619	+	0.680652i
$598$		0			0
$599$	21.2939	−	36.8822i	0.870047	−	1.50697i	0.00809947	−	0.999967i	$-0.497422\pi$
$599$	21.2939	−	36.8822i	0.870047	−	1.50697i	0.861947	−	0.506998i	$-0.169245\pi$
$600$		0			0
$601$	−11.6910	−	20.2495i	−0.476888	−	0.825994i	0.522762	−	0.852479i	$-0.324902\pi$
$601$	−11.6910	−	20.2495i	−0.476888	−	0.825994i	−0.999649	+	0.0264854i	$0.991568\pi$
$602$		0			0
$603$	12.0038	+	1.72440i	0.488833	+	0.0702230i
$604$		0			0
$605$	15.2011	+	26.3291i	0.618012	+	1.07043i
$606$		0			0
$607$	12.6852	−	21.9714i	0.514875	−	0.891790i	−0.484976	−	0.874527i	$-0.661172\pi$
$607$	12.6852	−	21.9714i	0.514875	−	0.891790i	0.999851	−	0.0172622i	$-0.00549499\pi$
$608$		0			0
$609$	−1.11071	−	2.28613i	−0.0450081	−	0.0926387i
$610$		0			0
$611$	−3.61543			−0.146264
$612$		0			0
$613$	−12.9459			−0.522882			−0.261441	−	0.965220i	$-0.584198\pi$
$613$	−12.9459			−0.522882			−0.261441	+	0.965220i	$0.584198\pi$
$614$		0			0
$615$	−28.7012	−	2.05100i	−1.15735	−	0.0827043i
$616$		0			0
$617$	6.01514	−	10.4185i	0.242161	−	0.419434i	−0.719169	−	0.694835i	$-0.755477\pi$
$617$	6.01514	−	10.4185i	0.242161	−	0.419434i	0.961329	+	0.275401i	$0.0888106\pi$
$618$		0			0
$619$	−21.9475	−	38.0142i	−0.882144	−	1.52792i	−0.848952	−	0.528469i	$-0.822766\pi$
$619$	−21.9475	−	38.0142i	−0.882144	−	1.52792i	−0.0331916	−	0.999449i	$-0.510567\pi$
$620$		0			0
$621$	28.5283	−	31.3937i	1.14480	−	1.25979i
$622$		0			0
$623$	0.298040	+	0.516221i	0.0119407	+	0.0206820i
$624$		0			0
$625$	11.4719	−	19.8699i	0.458877	−	0.794797i
$626$		0			0
$627$	14.0174	+	1.00169i	0.559803	+	0.0400037i
$628$		0			0
$629$	−48.0693			−1.91665
$630$		0			0
$631$	−25.8646			−1.02965			−0.514827	−	0.857294i	$-0.672144\pi$
$631$	−25.8646			−1.02965			−0.514827	+	0.857294i	$0.672144\pi$
$632$		0			0
$633$	1.34528	+	2.76895i	0.0534700	+	0.110056i
$634$		0			0
$635$	−12.6422	+	21.8968i	−0.501688	+	0.868950i
$636$		0			0
$637$	−3.25101	−	5.63091i	−0.128810	−	0.223105i
$638$		0			0
$639$	−4.00825	−	10.0086i	−0.158564	−	0.395934i
$640$		0			0
$641$	3.81826	+	6.61342i	0.150812	+	0.261215i	0.931526	−	0.363674i	$-0.118478\pi$
$641$	3.81826	+	6.61342i	0.150812	+	0.261215i	−0.780714	+	0.624888i	$0.785144\pi$
$642$		0			0
$643$	21.8623	−	37.8667i	0.862166	−	1.49332i	−0.00766794	−	0.999971i	$-0.502441\pi$
$643$	21.8623	−	37.8667i	0.862166	−	1.49332i	0.869834	−	0.493345i	$-0.164226\pi$
$644$		0			0
$645$	−0.576338	+	0.851650i	−0.0226933	+	0.0335337i
$646$		0			0
$647$	24.1808			0.950647			0.475324	−	0.879811i	$-0.342331\pi$
$647$	24.1808			0.950647			0.475324	+	0.879811i	$0.342331\pi$
$648$		0			0
$649$	−49.7290			−1.95203
$650$		0			0
$651$	−0.771865	+	1.14058i	−0.0302518	+	0.0447028i
$652$		0			0
$653$	−3.95033	+	6.84218i	−0.154589	+	0.267755i	−0.932909	−	0.360112i	$-0.882739\pi$
$653$	−3.95033	+	6.84218i	−0.154589	+	0.267755i	0.778321	+	0.627867i	$0.216072\pi$
$654$		0			0
$655$	5.67487	+	9.82916i	0.221735	+	0.384057i
$656$		0			0
$657$	6.06527	+	15.1450i	0.236629	+	0.590862i
$658$		0			0
$659$	−12.9895	−	22.4985i	−0.506001	−	0.876419i	−0.999976	−	0.00694272i	$-0.997790\pi$
$659$	−12.9895	−	22.4985i	−0.506001	−	0.876419i	0.493975	−	0.869476i	$-0.335543\pi$
$660$		0			0
$661$	0.254233	−	0.440344i	0.00988850	−	0.0171274i	−0.861039	−	0.508539i	$-0.830186\pi$
$661$	0.254233	−	0.440344i	0.00988850	−	0.0171274i	0.870927	+	0.491412i	$0.163519\pi$
$662$		0			0
$663$	3.35525	+	6.90600i	0.130307	+	0.268207i
$664$		0			0
$665$	1.06514			0.0413043
$666$		0			0
$667$	−39.1047			−1.51414
$668$		0			0
$669$	17.3601	+	1.24056i	0.671182	+	0.0479629i
$670$		0			0
$671$	26.8997	−	46.5917i	1.03845	−	1.79865i
$672$		0			0
$673$	11.2425	+	19.4726i	0.433367	+	0.750613i	0.997161	−	0.0753024i	$-0.0239922\pi$
$673$	11.2425	+	19.4726i	0.433367	+	0.750613i	−0.563794	+	0.825915i	$0.690659\pi$
$674$		0			0
$675$	−0.604797	−	1.89078i	−0.0232787	−	0.0727763i
$676$		0			0
$677$	2.34992	+	4.07018i	0.0903147	+	0.156430i	0.907644	−	0.419742i	$-0.137879\pi$
$677$	2.34992	+	4.07018i	0.0903147	+	0.156430i	−0.817329	+	0.576171i	$0.804546\pi$
$678$		0			0
$679$	2.16674	−	3.75291i	0.0831520	−	0.144023i
$680$		0			0
$681$	−18.2326	−	1.30291i	−0.698674	−	0.0499275i
$682$		0			0
$683$	15.4013			0.589315			0.294657	−	0.955603i	$-0.404794\pi$
$683$	15.4013			0.589315			0.294657	+	0.955603i	$0.404794\pi$
$684$		0			0
$685$	−31.0932			−1.18801
$686$		0			0
$687$	17.2507	+	35.5066i	0.658155	+	1.35466i
$688$		0			0
$689$	1.05214	−	1.82237i	0.0400835	−	0.0694266i
$690$		0			0
$691$	−13.9618	−	24.1825i	−0.531131	−	0.919945i	−0.999340	−	0.0363275i	$-0.988434\pi$
$691$	−13.9618	−	24.1825i	−0.531131	−	0.919945i	0.468209	−	0.883618i	$-0.344899\pi$
$692$		0			0
$693$	4.56191	+	0.655339i	0.173293	+	0.0248943i
$694$		0			0
$695$	−23.1828	−	40.1538i	−0.879374	−	1.52312i
$696$		0			0
$697$	−18.1996	+	31.5227i	−0.689360	+	1.19401i
$698$		0			0
$699$	5.79637	−	8.56525i	0.219239	−	0.323968i
$700$		0			0
$701$	7.33870			0.277179			0.138589	−	0.990350i	$-0.455743\pi$
$701$	7.33870			0.277179			0.138589	+	0.990350i	$0.455743\pi$
$702$		0			0
$703$	−16.5182			−0.622996
$704$		0			0
$705$	−8.01080	+	11.8375i	−0.301704	+	0.445826i
$706$		0			0
$707$	−2.88356	+	4.99448i	−0.108448	+	0.187837i
$708$		0			0
$709$	7.31665	+	12.6728i	0.274783	+	0.475938i	0.970080	−	0.242784i	$-0.0780608\pi$
$709$	7.31665	+	12.6728i	0.274783	+	0.475938i	−0.695298	+	0.718722i	$0.744727\pi$
$710$		0			0
$711$	−30.7945	+	39.1682i	−1.15488	+	1.46892i
$712$		0			0
$713$	10.5945	+	18.3502i	0.396766	+	0.687219i
$714$		0			0
$715$	−5.07287	+	8.78647i	−0.189715	+	0.328595i
$716$		0			0
$717$	−8.74299	−	17.9954i	−0.326513	−	0.672051i
$718$		0			0
$719$	−28.7125			−1.07080			−0.535398	−	0.844600i	$-0.679838\pi$
$719$	−28.7125			−1.07080			−0.535398	+	0.844600i	$0.679838\pi$
$720$		0			0
$721$	−1.80754			−0.0673161
$722$		0			0
$723$	26.8071	+	1.91564i	0.996966	+	0.0712435i
$724$		0			0
$725$	−0.915011	+	1.58484i	−0.0339826	+	0.0588597i
$726$		0			0
$727$	12.8923	+	22.3301i	0.478149	+	0.828178i	0.999686	−	0.0250502i	$-0.00797457\pi$
$727$	12.8923	+	22.3301i	0.478149	+	0.828178i	−0.521537	+	0.853229i	$0.674641\pi$
$728$		0			0
$729$	24.5641	+	11.2073i	0.909783	+	0.415083i
$730$		0			0
$731$	0.650415	+	1.12655i	0.0240565	+	0.0416670i
$732$		0			0
$733$	−5.34424	+	9.25649i	−0.197394	+	0.341896i	−0.947683	−	0.319214i	$-0.896581\pi$
$733$	−5.34424	+	9.25649i	−0.197394	+	0.341896i	0.750289	+	0.661110i	$0.229914\pi$
$734$		0			0
$735$	−25.6399	−	1.83223i	−0.945740	−	0.0675829i
$736$		0			0
$737$	20.2713			0.746702
$738$		0			0
$739$	−19.5440			−0.718937			−0.359469	−	0.933157i	$-0.617042\pi$
$739$	−19.5440			−0.718937			−0.359469	+	0.933157i	$0.617042\pi$
$740$		0			0
$741$	1.15297	+	2.37313i	0.0423556	+	0.0871792i
$742$		0			0
$743$	0.396827	−	0.687325i	0.0145582	−	0.0252155i	−0.858655	−	0.512555i	$-0.828699\pi$
$743$	0.396827	−	0.687325i	0.0145582	−	0.0252155i	0.873213	+	0.487339i	$0.162032\pi$
$744$		0			0
$745$	−16.7719	−	29.0497i	−0.614474	−	1.06430i
$746$		0			0
$747$	−10.8235	+	13.7667i	−0.396012	+	0.503696i
$748$		0			0
$749$	0.591343	+	1.02424i	0.0216072	+	0.0374248i
$750$		0			0
$751$	−2.55092	+	4.41832i	−0.0930844	+	0.161227i	−0.908808	−	0.417216i	$-0.863006\pi$
$751$	−2.55092	+	4.41832i	−0.0930844	+	0.161227i	0.815723	+	0.578443i	$0.196339\pi$
$752$		0			0
$753$	14.1423	−	20.8979i	0.515372	−	0.761562i
$754$		0			0
$755$	36.8877			1.34248
$756$		0			0
$757$	19.8422			0.721177			0.360589	−	0.932725i	$-0.382576\pi$
$757$	19.8422			0.721177			0.360589	+	0.932725i	$0.382576\pi$
$758$		0			0
$759$	39.7408	−	58.7246i	1.44250	−	2.13157i
$760$		0			0
$761$	−21.3960	+	37.0590i	−0.775605	+	1.34339i	0.158849	+	0.987303i	$0.449222\pi$
$761$	−21.3960	+	37.0590i	−0.775605	+	1.34339i	−0.934454	+	0.356084i	$0.884112\pi$
$762$		0			0
$763$	−1.66686	−	2.88708i	−0.0603442	−	0.104519i
$764$		0			0
$765$	30.0457	+	4.31619i	1.08630	+	0.156052i
$766$		0			0
$767$	−4.66814	−	8.08546i	−0.168557	−	0.291949i
$768$		0			0
$769$	17.8574	−	30.9300i	0.643955	−	1.11536i	−0.340587	−	0.940213i	$-0.610626\pi$
$769$	17.8574	−	30.9300i	0.643955	−	1.11536i	0.984542	−	0.175150i	$-0.0560410\pi$
$770$		0			0
$771$	11.7785	+	24.2433i	0.424193	+	0.873103i
$772$		0			0
$773$	17.1522			0.616923			0.308461	−	0.951237i	$-0.400186\pi$
$773$	17.1522			0.616923			0.308461	+	0.951237i	$0.400186\pi$
$774$		0			0
$775$	0.991600			0.0356193
$776$		0			0
$777$	−5.40337	−	0.386127i	−0.193845	−	0.0138522i
$778$		0			0
$779$	−6.25400	+	10.8322i	−0.224073	+	0.388105i
$780$		0			0
$781$	−9.01094	−	15.6074i	−0.322437	−	0.558477i
$782$		0			0
$783$	−7.58300	−	23.7068i	−0.270994	−	0.847212i
$784$		0			0
$785$	−5.57128	−	9.64974i	−0.198848	−	0.344414i
$786$		0			0
$787$	−10.5790	+	18.3233i	−0.377100	+	0.653156i	−0.990639	−	0.136509i	$-0.956412\pi$
$787$	−10.5790	+	18.3233i	−0.377100	+	0.653156i	0.613539	+	0.789664i	$0.289745\pi$
$788$		0			0
$789$	38.7790	+	2.77116i	1.38057	+	0.0986559i
$790$		0			0
$791$	−1.93095			−0.0686568
$792$		0			0
$793$	10.1005			0.358679
$794$		0			0
$795$	−3.63546	−	7.48276i	−0.128936	−	0.265386i
$796$		0			0
$797$	5.45601	−	9.45009i	0.193262	−	0.334739i	−0.753067	−	0.657943i	$-0.771427\pi$
$797$	5.45601	−	9.45009i	0.193262	−	0.334739i	0.946329	+	0.323204i	$0.104760\pi$
$798$		0			0
$799$	9.04044	+	15.6585i	0.319828	+	0.553958i
$800$		0			0
$801$	2.17016	+	5.41890i	0.0766790	+	0.191467i
$802$		0			0
$803$	13.6353	+	23.6171i	0.481180	+	0.833429i
$804$		0			0
$805$	2.68717	−	4.65431i	0.0947102	−	0.164043i
$806$		0			0
$807$	−25.2641	+	37.3325i	−0.889337	+	1.31417i
$808$		0			0
$809$	14.6688			0.515729			0.257865	−	0.966181i	$-0.416981\pi$
$809$	14.6688			0.515729			0.257865	+	0.966181i	$0.416981\pi$
$810$		0			0
$811$	7.96618			0.279731			0.139865	−	0.990171i	$-0.455333\pi$
$811$	7.96618			0.279731			0.139865	+	0.990171i	$0.455333\pi$
$812$		0			0
$813$	5.43383	−	8.02952i	0.190573	−	0.281608i
$814$		0			0
$815$	19.2282	−	33.3042i	0.673535	−	1.16660i
$816$		0			0
$817$	0.223504	+	0.387121i	0.00781943	+	0.0135436i
$818$		0			0
$819$	0.321682	+	0.803241i	0.0112405	+	0.0280675i
$820$		0			0
$821$	15.9260	+	27.5847i	0.555822	+	0.962712i	0.997839	+	0.0657057i	$0.0209298\pi$
$821$	15.9260	+	27.5847i	0.555822	+	0.962712i	−0.442017	+	0.897007i	$0.645737\pi$
$822$		0			0
$823$	−5.06901	+	8.77978i	−0.176694	+	0.306044i	−0.940746	−	0.339111i	$-0.889874\pi$
$823$	−5.06901	+	8.77978i	−0.176694	+	0.306044i	0.764052	+	0.645155i	$0.223207\pi$
$824$		0			0
$825$	−1.45011	−	2.98472i	−0.0504864	−	0.103915i
$826$		0			0
$827$	−16.2236			−0.564148			−0.282074	−	0.959393i	$-0.591022\pi$
$827$	−16.2236			−0.564148			−0.282074	+	0.959393i	$0.591022\pi$
$828$		0			0
$829$	−21.2902			−0.739439			−0.369720	−	0.929143i	$-0.620546\pi$
$829$	−21.2902			−0.739439			−0.369720	+	0.929143i	$0.620546\pi$
$830$		0			0
$831$	−5.45786	−	0.390020i	−0.189331	−	0.0135297i
$832$		0			0
$833$	−16.2584	+	28.1604i	−0.563320	+	0.975699i
$834$		0			0
$835$	11.7916	+	20.4236i	0.408063	+	0.706787i
$836$		0			0
$837$	−9.07015	+	9.98116i	−0.313510	+	0.344999i
$838$		0			0
$839$	−0.962971	−	1.66791i	−0.0332454	−	0.0575828i	0.848924	−	0.528515i	$-0.177251\pi$
$839$	−0.962971	−	1.66791i	−0.0332454	−	0.0575828i	−0.882169	+	0.470932i	$0.843918\pi$
$840$		0			0
$841$	3.02752	−	5.24382i	0.104397	−	0.180821i
$842$		0			0
$843$	−27.7125	−	1.98035i	−0.954469	−	0.0682067i
$844$		0			0
$845$	26.0315			0.895510
$846$		0			0
$847$	4.33405			0.148920
$848$		0			0
$849$	2.83298	+	5.83103i	0.0972275	+	0.200120i
$850$		0			0
$851$	−41.6727	+	72.1792i	−1.42852	+	2.47427i
$852$		0			0
$853$	−19.7403	−	34.1912i	−0.675895	−	1.17069i	−0.976206	−	0.216844i	$-0.930424\pi$
$853$	−19.7403	−	34.1912i	−0.675895	−	1.17069i	0.300311	−	0.953841i	$-0.402910\pi$
$854$		0			0
$855$	10.3247	+	1.48319i	0.353097	+	0.0507240i
$856$		0			0
$857$	15.0539	+	26.0742i	0.514233	+	0.890677i	0.999864	+	0.0165134i	$0.00525662\pi$
$857$	15.0539	+	26.0742i	0.514233	+	0.890677i	−0.485631	+	0.874164i	$0.661410\pi$
$858$		0			0
$859$	20.2994	−	35.1597i	0.692608	−	1.19963i	−0.278373	−	0.960473i	$-0.589795\pi$
$859$	20.2994	−	35.1597i	0.692608	−	1.19963i	0.970980	−	0.239159i	$-0.0768716\pi$
$860$		0			0
$861$	−2.29900	+	3.39721i	−0.0783496	+	0.115777i
$862$		0			0
$863$	−1.46113			−0.0497374			−0.0248687	−	0.999691i	$-0.507917\pi$
$863$	−1.46113			−0.0497374			−0.0248687	+	0.999691i	$0.507917\pi$
$864$		0			0
$865$	−37.0970			−1.26134
$866$		0			0
$867$	5.01761	−	7.41449i	0.170407	−	0.251809i
$868$		0			0
$869$	−41.6424	+	72.1268i	−1.41262	+	2.44673i
$870$		0			0
$871$	1.90290	+	3.29591i	0.0644772	+	0.111678i
$872$		0			0
$873$	26.2288	−	33.3609i	0.887709	−	1.12910i
$874$		0			0
$875$	−1.77156	−	3.06843i	−0.0598897	−	0.103732i
$876$		0			0
$877$	−5.07742	+	8.79435i	−0.171452	+	0.296964i	−0.938928	−	0.344114i	$-0.888179\pi$
$877$	−5.07742	+	8.79435i	−0.171452	+	0.296964i	0.767475	+	0.641078i	$0.221513\pi$
$878$		0			0
$879$	−8.32423	−	17.1335i	−0.280769	−	0.577899i
$880$		0			0
$881$	12.6952			0.427711			0.213855	−	0.976865i	$-0.431398\pi$
$881$	12.6952			0.427711			0.213855	+	0.976865i	$0.431398\pi$
$882$		0			0
$883$	−35.3754			−1.19048			−0.595238	−	0.803549i	$-0.702942\pi$
$883$	−35.3754			−1.19048			−0.595238	+	0.803549i	$0.702942\pi$
$884$		0			0
$885$	−36.8165	−	2.63092i	−1.23757	−	0.0884373i
$886$		0			0
$887$	−27.7610	+	48.0835i	−0.932124	+	1.61449i	−0.152439	+	0.988313i	$0.548713\pi$
$887$	−27.7610	+	48.0835i	−0.932124	+	1.61449i	−0.779685	+	0.626172i	$0.784621\pi$
$888$		0			0
$889$	1.80223	+	3.12155i	0.0604448	+	0.104694i
$890$		0			0
$891$	43.3075	+	12.7048i	1.45085	+	0.425626i
$892$		0			0
$893$	3.10660	+	5.38078i	0.103958	+	0.180061i
$894$		0			0
$895$	16.1784	−	28.0218i	0.540784	−	0.936666i
$896$		0			0
$897$	13.2786	+	0.948892i	0.443359	+	0.0316826i
$898$		0			0
$899$	12.4328			0.414656
$900$		0			0
$901$	−10.5236			−0.350592
$902$		0			0
$903$	0.0640626	+	0.131858i	0.00213187	+	0.00438796i
$904$		0			0
$905$	−18.9981	+	32.9056i	−0.631517	+	1.09382i
$906$		0			0
$907$	17.1123	+	29.6393i	0.568204	+	0.984158i	0.996744	+	0.0806350i	$0.0256948\pi$
$907$	17.1123	+	29.6393i	0.568204	+	0.984158i	−0.428540	+	0.903523i	$0.640972\pi$
$908$		0			0
$909$	−34.9060	+	44.3976i	−1.15776	+	1.47258i
$910$		0			0
$911$	8.27615	+	14.3347i	0.274201	+	0.474930i	0.969933	−	0.243371i	$-0.0782533\pi$
$911$	8.27615	+	14.3347i	0.274201	+	0.474930i	−0.695732	+	0.718301i	$0.744920\pi$
$912$		0			0
$913$	−14.6363	+	25.3509i	−0.484392	+	0.838991i
$914$		0			0
$915$	22.3799	−	33.0706i	0.739857	−	1.09328i
$916$		0			0
$917$	1.61799			0.0534306
$918$		0			0
$919$	45.3120			1.49470			0.747352	−	0.664428i	$-0.231325\pi$
$919$	45.3120			1.49470			0.747352	+	0.664428i	$0.231325\pi$
$920$		0			0
$921$	−5.90614	+	8.72745i	−0.194614	+	0.287579i
$922$		0			0
$923$	1.69174	−	2.93019i	0.0556844	−	0.0964482i
$924$		0			0
$925$	1.95020	+	3.37784i	0.0641221	+	0.111063i
$926$		0			0
$927$	−17.5210	−	2.51696i	−0.575465	−	0.0826680i
$928$		0			0
$929$	−10.0403	−	17.3903i	−0.329412	−	0.570558i	0.652984	−	0.757372i	$-0.273517\pi$
$929$	−10.0403	−	17.3903i	−0.329412	−	0.570558i	−0.982395	+	0.186814i	$0.940184\pi$
$930$		0			0
$931$	−5.58693	+	9.67684i	−0.183104	+	0.317146i
$932$		0			0
$933$	5.68637	+	11.7041i	0.186163	+	0.383174i
$934$		0			0
$935$	50.7392			1.65935
$936$		0			0
$937$	57.3842			1.87466			0.937330	−	0.348443i	$-0.113289\pi$
$937$	57.3842			1.87466			0.937330	+	0.348443i	$0.113289\pi$
$938$		0			0
$939$	21.3563	+	1.52613i	0.696937	+	0.0498034i
$940$		0			0
$941$	−16.7615	+	29.0318i	−0.546409	+	0.946409i	0.452107	+	0.891963i	$0.350672\pi$
$941$	−16.7615	+	29.0318i	−0.546409	+	0.946409i	−0.998517	+	0.0544452i	$0.982661\pi$
$942$		0			0
$943$	31.5556	+	54.6559i	1.02759	+	1.77984i
$944$		0			0
$945$	3.34270	+	0.726523i	0.108738	+	0.0236338i
$946$		0			0
$947$	3.66775	+	6.35274i	0.119186	+	0.206436i	0.919445	−	0.393218i	$-0.128638\pi$
$947$	3.66775	+	6.35274i	0.119186	+	0.206436i	−0.800259	+	0.599654i	$0.795305\pi$
$948$		0			0
$949$	−2.55994	+	4.43395i	−0.0830992	+	0.143932i
$950$		0			0
$951$	42.5704	+	3.04210i	1.38044	+	0.0986467i
$952$		0			0
$953$	−7.30761			−0.236717			−0.118358	−	0.992971i	$-0.537763\pi$
$953$	−7.30761			−0.236717			−0.118358	+	0.992971i	$0.537763\pi$
$954$		0			0
$955$	44.3406			1.43483
$956$		0			0
$957$	−18.1816	−	37.4226i	−0.587728	−	1.20970i
$958$		0			0
$959$	−2.21628	+	3.83870i	−0.0715673	+	0.123958i
$960$		0			0
$961$	12.1316	+	21.0126i	0.391343	+	0.677827i
$962$		0			0
$963$	4.30583	+	10.7517i	0.138754	+	0.346468i
$964$		0			0
$965$	−24.9565	−	43.2259i	−0.803377	−	1.39149i
$966$		0			0
$967$	13.1258	−	22.7346i	0.422097	−	0.731094i	−0.574047	−	0.818822i	$-0.694627\pi$
$967$	13.1258	−	22.7346i	0.422097	−	0.731094i	0.996144	+	0.0877283i	$0.0279607\pi$
$968$		0			0
$969$	7.39506	−	10.9276i	0.237564	−	0.351046i
$970$		0			0
$971$	15.9643			0.512318			0.256159	−	0.966635i	$-0.417543\pi$
$971$	15.9643			0.512318			0.256159	+	0.966635i	$0.417543\pi$
$972$		0			0
$973$	−6.60975			−0.211899
$974$		0			0
$975$	0.349162	−	0.515954i	0.0111821	−	0.0165238i
$976$		0			0
$977$	3.96119	−	6.86099i	0.126730	−	0.219502i	−0.795678	−	0.605720i	$-0.792885\pi$
$977$	3.96119	−	6.86099i	0.126730	−	0.219502i	0.922408	+	0.386217i	$0.126219\pi$
$978$		0			0
$979$	4.87875	+	8.45024i	0.155925	+	0.270071i
$980$		0			0
$981$	−12.1371	−	30.3064i	−0.387508	−	0.967608i
$982$		0			0
$983$	−6.86126	−	11.8841i	−0.218840	−	0.379042i	0.735613	−	0.677402i	$-0.236894\pi$
$983$	−6.86126	−	11.8841i	−0.218840	−	0.379042i	−0.954454	+	0.298359i	$0.903561\pi$
$984$		0			0
$985$	5.14131	−	8.90502i	0.163816	−	0.283737i
$986$		0			0
$987$	0.890437	+	1.83276i	0.0283429	+	0.0583374i
$988$		0			0
$989$	2.25546			0.0717194
$990$		0			0
$991$	36.0366			1.14474			0.572370	−	0.819996i	$-0.306024\pi$
$991$	36.0366			1.14474			0.572370	+	0.819996i	$0.306024\pi$
$992$		0			0
$993$	38.2484	+	2.73324i	1.21378	+	0.0867369i
$994$		0			0
$995$	−12.4572	+	21.5765i	−0.394920	+	0.684021i
$996$		0			0
$997$	−11.9518	−	20.7011i	−0.378517	−	0.655610i	0.612330	−	0.790602i	$-0.290232\pi$
$997$	−11.9518	−	20.7011i	−0.378517	−	0.655610i	−0.990847	+	0.134992i	$0.956899\pi$
$998$		0			0
$999$	−51.8388	−	11.2669i	−1.64011	−	0.356470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.i.f.769.4	yes	10
3.2	odd	2		3456.2.i.g.2305.2		10
4.3	odd	2		1152.2.i.g.769.2	yes	10
8.3	odd	2		1152.2.i.e.769.4	yes	10
8.5	even	2		1152.2.i.h.769.2	yes	10
9.2	odd	6		3456.2.i.g.1153.2		10
9.7	even	3	inner	1152.2.i.f.385.4	yes	10
12.11	even	2		3456.2.i.f.2305.2		10
24.5	odd	2		3456.2.i.h.2305.4		10
24.11	even	2		3456.2.i.e.2305.4		10
36.7	odd	6		1152.2.i.g.385.2	yes	10
36.11	even	6		3456.2.i.f.1153.2		10
72.11	even	6		3456.2.i.e.1153.4		10
72.29	odd	6		3456.2.i.h.1153.4		10
72.43	odd	6		1152.2.i.e.385.4	✓	10
72.61	even	6		1152.2.i.h.385.2	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.i.e.385.4	✓	10	72.43	odd	6
1152.2.i.e.769.4	yes	10	8.3	odd	2
1152.2.i.f.385.4	yes	10	9.7	even	3	inner
1152.2.i.f.769.4	yes	10	1.1	even	1	trivial
1152.2.i.g.385.2	yes	10	36.7	odd	6
1152.2.i.g.769.2	yes	10	4.3	odd	2
1152.2.i.h.385.2	yes	10	72.61	even	6
1152.2.i.h.769.2	yes	10	8.5	even	2
3456.2.i.e.1153.4		10	72.11	even	6
3456.2.i.e.2305.4		10	24.11	even	2
3456.2.i.f.1153.2		10	36.11	even	6
3456.2.i.f.2305.2		10	12.11	even	2
3456.2.i.g.1153.2		10	9.2	odd	6
3456.2.i.g.2305.2		10	3.2	odd	2
3456.2.i.h.1153.4		10	72.29	odd	6
3456.2.i.h.2305.4		10	24.5	odd	2

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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.970741 - 1.43446i) q^{3} +(1.07447 - 1.86104i) q^{5} +(-0.153174 - 0.265305i) q^{7} +(-1.11533 - 2.78497i) q^{9} +O(q^{10})\)	\(q+(0.970741 - 1.43446i) q^{3} +(1.07447 - 1.86104i) q^{5} +(-0.153174 - 0.265305i) q^{7} +(-1.11533 - 2.78497i) q^{9} +(-2.50736 - 4.34288i) q^{11} +(0.470741 - 0.815346i) q^{13} +(-1.62655 - 3.34787i) q^{15} -4.70838 q^{17} -1.61796 q^{19} +(-0.529259 - 0.0378211i) q^{21} +(-4.08184 + 7.06995i) q^{23} +(0.191022 + 0.330859i) q^{25} +(-5.07761 - 1.10360i) q^{27} +(2.39504 + 4.14834i) q^{29} +(1.29776 - 2.24778i) q^{31} +(-8.66367 - 0.619109i) q^{33} -0.658323 q^{35} +10.2093 q^{37} +(-0.712611 - 1.46675i) q^{39} +(3.86537 - 6.69502i) q^{41} +(-0.138140 - 0.239265i) q^{43} +(-6.38132 - 0.916704i) q^{45} +(-1.92007 - 3.32566i) q^{47} +(3.45308 - 5.98090i) q^{49} +(-4.57062 + 6.75396i) q^{51} +2.23508 q^{53} -10.7764 q^{55} +(-1.57062 + 2.32089i) q^{57} +(4.95830 - 8.58802i) q^{59} +(5.36414 + 9.29097i) q^{61} +(-0.568026 + 0.722485i) q^{63} +(-1.01159 - 1.75213i) q^{65} +(-2.02117 + 3.50078i) q^{67} +(6.17912 + 12.7183i) q^{69} +3.59379 q^{71} -5.43811 q^{73} +(0.660035 + 0.0471664i) q^{75} +(-0.768124 + 1.33043i) q^{77} +(-8.30403 - 14.3830i) q^{79} +(-6.51210 + 6.21229i) q^{81} +(-2.91867 - 5.05528i) q^{83} +(-5.05902 + 8.76248i) q^{85} +(8.27557 + 0.591376i) q^{87} -1.94577 q^{89} -0.288420 q^{91} +(-1.96456 - 4.04359i) q^{93} +(-1.73845 + 3.01108i) q^{95} +(7.07283 + 12.2505i) q^{97} +(-9.29826 + 11.8267i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{3} + 4 q^{7} - q^{9}+O(q^{10}) \) 10 * q - q^3 + 4 * q^7 - q^9	\( 10 q - q^{3} + 4 q^{7} - q^{9} + q^{11} - 6 q^{13} - 12 q^{15} - 6 q^{17} - 18 q^{19} - 16 q^{21} - 4 q^{23} + q^{25} + 2 q^{27} + 4 q^{29} + 8 q^{31} - 13 q^{33} + 24 q^{35} + 20 q^{37} + 18 q^{39} - 5 q^{41} + 13 q^{43} + 12 q^{45} + 6 q^{47} + 3 q^{49} - 3 q^{51} - 12 q^{55} + 27 q^{57} + 13 q^{59} - 10 q^{61} + 20 q^{63} + 17 q^{67} + 10 q^{69} - 8 q^{71} - 34 q^{73} + 29 q^{75} - 8 q^{77} + 6 q^{79} - q^{81} - 12 q^{83} - 18 q^{85} - 10 q^{87} + 44 q^{89} - 36 q^{91} - 26 q^{93} + 6 q^{95} + 27 q^{97} - 34 q^{99}+O(q^{100}) \) 10 * q - q^3 + 4 * q^7 - q^9 + q^11 - 6 * q^13 - 12 * q^15 - 6 * q^17 - 18 * q^19 - 16 * q^21 - 4 * q^23 + q^25 + 2 * q^27 + 4 * q^29 + 8 * q^31 - 13 * q^33 + 24 * q^35 + 20 * q^37 + 18 * q^39 - 5 * q^41 + 13 * q^43 + 12 * q^45 + 6 * q^47 + 3 * q^49 - 3 * q^51 - 12 * q^55 + 27 * q^57 + 13 * q^59 - 10 * q^61 + 20 * q^63 + 17 * q^67 + 10 * q^69 - 8 * q^71 - 34 * q^73 + 29 * q^75 - 8 * q^77 + 6 * q^79 - q^81 - 12 * q^83 - 18 * q^85 - 10 * q^87 + 44 * q^89 - 36 * q^91 - 26 * q^93 + 6 * q^95 + 27 * q^97 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more