LMFDB - Embedded newform 1152.2.i.e.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.e.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	−0.999750	−	0.0223513i	$-0.992885\pi$
$5$	−1.07447	+	1.86104i	−0.480518	+	0.832282i	0.519232	+	0.854633i	$0.326218\pi$
$6$		0			0
$7$	0.153174	+	0.265305i	0.0578942	+	0.100276i	0.893520	−	0.449024i	$-0.148228\pi$
$7$	0.153174	+	0.265305i	0.0578942	+	0.100276i	−0.835626	+	0.549299i	$0.814895\pi$
$8$		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	−0.923893	−	0.382652i	$-0.875011\pi$
$13$	−0.470741	+	0.815346i	−0.130560	+	0.226136i	0.793333	+	0.608788i	$0.208344\pi$
$14$		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	$-0.509256\pi$
$23$	4.08184	−	7.06995i	0.851122	−	1.47419i	0.880197	−	0.474609i	$-0.157410\pi$
$24$		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	0.553286	−	0.832991i	$-0.313374\pi$
$29$	−2.39504	−	4.14834i	−0.444749	−	0.770327i	−0.998035	+	0.0626641i	$0.980040\pi$
$30$		0			0
$31$	−1.29776	+	2.24778i	−0.233084	+	0.403714i	−0.958714	−	0.284371i	$-0.908215\pi$
$31$	−1.29776	+	2.24778i	−0.233084	+	0.403714i	0.725630	+	0.688085i	$0.241548\pi$
$32$		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	$-0.816976\pi$
$37$	−10.2093			−1.67840			−0.839199	+	0.543824i	$0.816976\pi$
$38$		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	0.971402	−	0.237441i	$-0.0763085\pi$
$47$	1.92007	+	3.32566i	0.280072	+	0.485098i	−0.691331	+	0.722539i	$0.742975\pi$
$48$		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	$-0.549056\pi$
$53$	−2.23508			−0.307012			−0.153506	+	0.988148i	$0.549056\pi$
$54$		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	$-0.925678\pi$
$61$	−5.36414	−	9.29097i	−0.686808	−	1.18959i	0.286057	−	0.958213i	$-0.407655\pi$
$62$		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	$-0.568406\pi$
$71$	−3.59379			−0.426505			−0.213252	+	0.976997i	$0.568406\pi$
$72$		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	$0.217286\pi$
$79$	8.30403	+	14.3830i	0.934276	+	1.61821i	0.158356	+	0.987382i	$0.449381\pi$
$80$		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	$0.219380\pi$
$101$	9.41272	+	16.3033i	0.936601	+	1.62224i	0.164847	+	0.986319i	$0.447287\pi$
$102$		0			0
$103$	−2.95014	+	5.10979i	−0.290686	+	0.503483i	−0.973972	−	0.226668i	$-0.927217\pi$
$103$	−2.95014	+	5.10979i	−0.290686	+	0.503483i	0.683286	+	0.730151i	$0.260550\pi$
$104$		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	$-0.674500\pi$
$109$	−10.8821			−1.04232			−0.521159	+	0.853459i	$0.674500\pi$
$110$		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	$-0.325175\pi$
$127$	11.7659			1.04406			0.522028	+	0.852928i	$0.325175\pi$
$128$		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	$0.387478\pi$
$149$	−7.80471	+	13.5181i	−0.639386	+	1.10745i	−0.985568	+	0.169282i	$0.945855\pi$
$150$		0			0
$151$	−8.58275	−	14.8658i	−0.698455	−	1.20976i	−0.969002	−	0.247052i	$-0.920538\pi$
$151$	−8.58275	−	14.8658i	−0.698455	−	1.20976i	0.270547	−	0.962707i	$-0.412795\pi$
$152$		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	−0.950739	−	0.309991i	$-0.899674\pi$
$157$	−2.59257	+	4.49046i	−0.206909	+	0.358378i	0.743830	+	0.668369i	$0.233007\pi$
$158$		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	−0.571776	−	0.820410i	$-0.693745\pi$
$167$	5.48714	−	9.50401i	0.424608	−	0.735442i	0.996384	+	0.0849677i	$0.0270787\pi$
$168$		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	$0.0611865\pi$
$173$	8.63146	+	14.9501i	0.656238	+	1.13664i	−0.325344	+	0.945596i	$0.605480\pi$
$174$		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	$-0.271774\pi$
$181$	17.6813			1.31424			0.657120	+	0.753786i	$0.271774\pi$
$182$		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	$-0.898399\pi$
$191$	−10.3168	−	17.8693i	−0.746501	−	1.29298i	0.202990	−	0.979181i	$-0.434934\pi$
$192$		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	$-0.554525\pi$
$197$	−4.78497			−0.340915			−0.170458	+	0.985365i	$0.554525\pi$
$198$		0			0
$199$	11.5938			0.821862			0.410931	−	0.911666i	$-0.365204\pi$
$199$	11.5938			0.821862			0.410931	+	0.911666i	$0.365204\pi$
$200$		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	0.647315	−	0.762223i	$-0.275892\pi$
$223$	−5.02422	−	8.70221i	−0.336447	−	0.582743i	−0.983762	+	0.179480i	$0.942559\pi$
$224$		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	$-0.561920\pi$
$229$	11.3955	−	19.7377i	0.753039	−	1.30430i	0.946343	−	0.323163i	$-0.104746\pi$
$230$		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	−0.990114	−	0.140264i	$-0.955205\pi$
$239$	−5.77549	+	10.0034i	−0.373585	+	0.647069i	0.616529	+	0.787332i	$0.288538\pi$
$240$		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	$-0.923377\pi$
$263$	−11.2231	−	19.4389i	−0.692044	−	1.19866i	0.279123	−	0.960255i	$-0.409956\pi$
$264$		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	$-0.208307\pi$
$269$	26.0256			1.58681			0.793403	+	0.608696i	$0.208307\pi$
$270$		0			0
$271$	−5.59761			−0.340031			−0.170015	−	0.985441i	$-0.554382\pi$
$271$	−5.59761			−0.340031			−0.170015	+	0.985441i	$0.554382\pi$
$272$		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	0.909570	−	0.415551i	$-0.136411\pi$
$277$	1.57957	+	2.73589i	0.0949069	+	0.164384i	−0.814663	+	0.579935i	$0.803078\pi$
$278$		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	−0.980746	−	0.195290i	$-0.937435\pi$
$293$	−5.49886	+	9.52431i	−0.321247	+	0.556416i	0.659499	+	0.751706i	$0.270769\pi$
$294$		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	−0.739651	−	0.672991i	$-0.765009\pi$
$311$	3.75633	−	6.50616i	0.213002	−	0.368930i	0.952653	+	0.304061i	$0.0983426\pi$
$312$		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	$-0.923405\pi$
$317$	−12.3204	−	21.3395i	−0.691980	−	1.19854i	0.279208	−	0.960231i	$-0.409928\pi$
$318$		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	0.824843	−	0.565362i	$-0.191264\pi$
$349$	−1.44215	−	2.49788i	−0.0771966	−	0.133708i	−0.902039	+	0.431654i	$0.857930\pi$
$350$		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	$-0.748059\pi$
$359$	−26.6316			−1.40556			−0.702782	+	0.711406i	$0.748059\pi$
$360$		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	$-0.937278\pi$
$367$	−12.6413	−	21.8953i	−0.659869	−	1.14293i	0.320780	−	0.947154i	$-0.396055\pi$
$368$		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	−0.876891	−	0.480689i	$-0.840387\pi$
$373$	−0.427926	+	0.741189i	−0.0221571	+	0.0383773i	0.854734	+	0.519066i	$0.173720\pi$
$374$		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	−0.869389	−	0.494128i	$-0.835487\pi$
$383$	−0.132433	+	0.229381i	−0.00676702	+	0.0117208i	0.862622	+	0.505849i	$0.168821\pi$
$384$		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	$-0.978931\pi$
$389$	−10.9697	−	19.0001i	−0.556187	−	0.963343i	0.441624	−	0.897200i	$-0.354403\pi$
$390$		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	$-0.482479\pi$
$397$	2.19238			0.110032			0.0550161	+	0.998485i	$0.482479\pi$
$398$		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	0.990535	−	0.137261i	$-0.0438299\pi$
$421$	7.72300	+	13.3766i	0.376396	+	0.651937i	−0.614139	+	0.789198i	$0.710497\pi$
$422$		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	$-0.348784\pi$
$431$	18.9913			0.914779			0.457390	+	0.889266i	$0.348784\pi$
$432$		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	$-0.922831\pi$
$439$	−14.5259	−	25.1595i	−0.693281	−	1.20080i	0.277476	−	0.960733i	$-0.410502\pi$
$440$		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	0.685704	−	0.727880i	$-0.259494\pi$
$461$	−6.17311	−	10.6921i	−0.287510	−	0.497983i	−0.973215	+	0.229897i	$0.926161\pi$
$462$		0			0
$463$	18.6089	−	32.2316i	0.864830	−	1.49793i	−0.00238525	−	0.999997i	$-0.500759\pi$
$463$	18.6089	−	32.2316i	0.864830	−	1.49793i	0.867216	−	0.497933i	$-0.165907\pi$
$464$		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	0.687906	−	0.725799i	$-0.258530\pi$
$479$	−6.22894	−	10.7888i	−0.284608	−	0.492955i	−0.972514	+	0.232845i	$0.925197\pi$
$480$		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	$-0.591592\pi$
$487$	−12.5254			−0.567580			−0.283790	+	0.958886i	$0.591592\pi$
$488$		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	$-0.319056\pi$
$503$	24.1469			1.07666			0.538328	+	0.842736i	$0.319056\pi$
$504$		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	−0.747164	−	0.664640i	$-0.768585\pi$
$509$	4.55763	−	7.89404i	0.202013	−	0.349897i	0.949177	+	0.314743i	$0.101918\pi$
$510$		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	$-0.693929\pi$
$541$	−26.6203			−1.14450			−0.572249	+	0.820080i	$0.693929\pi$
$542$		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	$-0.563400\pi$
$557$	−9.33947			−0.395726			−0.197863	+	0.980230i	$0.563400\pi$
$558$		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	$0.502578\pi$
$599$	−21.2939	+	36.8822i	−0.870047	+	1.50697i	−0.861947	+	0.506998i	$0.830755\pi$
$600$		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	$0.338828\pi$
$607$	−12.6852	+	21.9714i	−0.514875	+	0.891790i	−0.999851	+	0.0172622i	$0.994505\pi$
$608$		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	$-0.415802\pi$
$613$	12.9459			0.522882			0.261441	+	0.965220i	$0.415802\pi$
$614$		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	$-0.327856\pi$
$631$	25.8646			1.02965			0.514827	+	0.857294i	$0.327856\pi$
$632$		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	$-0.657669\pi$
$647$	−24.1808			−0.950647			−0.475324	+	0.879811i	$0.657669\pi$
$648$		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	−0.778321	−	0.627867i	$-0.783928\pi$
$653$	3.95033	−	6.84218i	0.154589	−	0.267755i	0.932909	+	0.360112i	$0.117261\pi$
$654$		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	−0.870927	−	0.491412i	$-0.836481\pi$
$661$	−0.254233	+	0.440344i	−0.00988850	+	0.0171274i	0.861039	+	0.508539i	$0.169814\pi$
$662$		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	0.817329	−	0.576171i	$-0.195454\pi$
$677$	−2.34992	−	4.07018i	−0.0903147	−	0.156430i	−0.907644	+	0.419742i	$0.862121\pi$
$678$		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	$-0.544257\pi$
$701$	−7.33870			−0.277179			−0.138589	+	0.990350i	$0.544257\pi$
$702$		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	0.695298	−	0.718722i	$-0.255273\pi$
$709$	−7.31665	−	12.6728i	−0.274783	−	0.475938i	−0.970080	+	0.242784i	$0.921939\pi$
$710$		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	$-0.320162\pi$
$719$	28.7125			1.07080			0.535398	+	0.844600i	$0.320162\pi$
$720$		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	0.521537	−	0.853229i	$-0.325359\pi$
$727$	−12.8923	−	22.3301i	−0.478149	−	0.828178i	−0.999686	+	0.0250502i	$0.992025\pi$
$728$		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	−0.750289	−	0.661110i	$-0.770086\pi$
$733$	5.34424	−	9.25649i	0.197394	−	0.341896i	0.947683	+	0.319214i	$0.103419\pi$
$734$		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	−0.873213	−	0.487339i	$-0.837968\pi$
$743$	−0.396827	+	0.687325i	−0.0145582	+	0.0252155i	0.858655	+	0.512555i	$0.171301\pi$
$744$		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	−0.815723	−	0.578443i	$-0.803661\pi$
$751$	2.55092	−	4.41832i	0.0930844	−	0.161227i	0.908808	+	0.417216i	$0.136994\pi$
$752$		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	$-0.617424\pi$
$757$	−19.8422			−0.721177			−0.360589	+	0.932725i	$0.617424\pi$
$758$		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	$-0.599814\pi$
$773$	−17.1522			−0.616923			−0.308461	+	0.951237i	$0.599814\pi$
$774$		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	−0.946329	−	0.323204i	$-0.895240\pi$
$797$	−5.45601	+	9.45009i	−0.193262	+	0.334739i	0.753067	+	0.657943i	$0.228573\pi$
$798$		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	$-0.979070\pi$
$821$	−15.9260	−	27.5847i	−0.555822	−	0.962712i	0.442017	−	0.897007i	$-0.354263\pi$
$822$		0			0
$823$	5.06901	−	8.77978i	0.176694	−	0.306044i	−0.764052	−	0.645155i	$-0.776793\pi$
$823$	5.06901	−	8.77978i	0.176694	−	0.306044i	0.940746	+	0.339111i	$0.110126\pi$
$824$		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	$-0.379454\pi$
$829$	21.2902			0.739439			0.369720	+	0.929143i	$0.379454\pi$
$830$		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	0.882169	−	0.470932i	$-0.156082\pi$
$839$	0.962971	+	1.66791i	0.0332454	+	0.0575828i	−0.848924	+	0.528515i	$0.822749\pi$
$840$		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	$0.0695763\pi$
$853$	19.7403	+	34.1912i	0.675895	+	1.17069i	−0.300311	+	0.953841i	$0.597090\pi$
$854$		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	$-0.492083\pi$
$863$	1.46113			0.0497374			0.0248687	+	0.999691i	$0.492083\pi$
$864$		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	−0.767475	−	0.641078i	$-0.778487\pi$
$877$	5.07742	−	8.79435i	0.171452	−	0.296964i	0.938928	+	0.344114i	$0.111821\pi$
$878$		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	$-0.451287\pi$
$887$	27.7610	−	48.0835i	0.932124	−	1.61449i	0.779685	−	0.626172i	$-0.215379\pi$
$888$		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	0.695732	−	0.718301i	$-0.255080\pi$
$911$	−8.27615	−	14.3347i	−0.274201	−	0.474930i	−0.969933	+	0.243371i	$0.921747\pi$
$912$		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	$-0.768675\pi$
$919$	−45.3120			−1.49470			−0.747352	+	0.664428i	$0.768675\pi$
$920$		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	$-0.649328\pi$
$941$	16.7615	−	29.0318i	0.546409	−	0.946409i	0.998517	−	0.0544452i	$-0.0173390\pi$
$942$		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	−0.996144	−	0.0877283i	$-0.972039\pi$
$967$	−13.1258	+	22.7346i	−0.422097	+	0.731094i	0.574047	+	0.818822i	$0.305373\pi$
$968$		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	0.954454	−	0.298359i	$-0.0964393\pi$
$983$	6.86126	+	11.8841i	0.218840	+	0.379042i	−0.735613	+	0.677402i	$0.763106\pi$
$984$		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	$-0.693976\pi$
$991$	−36.0366			−1.14474			−0.572370	+	0.819996i	$0.693976\pi$
$992$		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	0.990847	−	0.134992i	$-0.0431009\pi$
$997$	11.9518	+	20.7011i	0.378517	+	0.655610i	−0.612330	+	0.790602i	$0.709768\pi$
$998$		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.e.769.4	yes	10
3.2	odd	2		3456.2.i.e.2305.4		10
4.3	odd	2		1152.2.i.h.769.2	yes	10
8.3	odd	2		1152.2.i.f.769.4	yes	10
8.5	even	2		1152.2.i.g.769.2	yes	10
9.2	odd	6		3456.2.i.e.1153.4		10
9.7	even	3	inner	1152.2.i.e.385.4	✓	10
12.11	even	2		3456.2.i.h.2305.4		10
24.5	odd	2		3456.2.i.f.2305.2		10
24.11	even	2		3456.2.i.g.2305.2		10
36.7	odd	6		1152.2.i.h.385.2	yes	10
36.11	even	6		3456.2.i.h.1153.4		10
72.11	even	6		3456.2.i.g.1153.2		10
72.29	odd	6		3456.2.i.f.1153.2		10
72.43	odd	6		1152.2.i.f.385.4	yes	10
72.61	even	6		1152.2.i.g.385.2	yes	10

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

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Database

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