LMFDB - Embedded newform 864.2.y.b.97.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

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("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			97.3
Character	$\chi$	$=$	864.97
Dual form			864.2.y.b.481.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06169 - 1.36851i) q^{3} +(0.217711 + 0.0792403i) q^{5} +(0.399809 - 2.26743i) q^{7} +(-0.745646 + 2.90586i) q^{9} +O(q^{10})$	\(q+(-1.06169 - 1.36851i) q^{3} +(0.217711 + 0.0792403i) q^{5} +(0.399809 - 2.26743i) q^{7} +(-0.745646 + 2.90586i) q^{9} +(-2.11152 + 0.768532i) q^{11} +(-4.95385 + 4.15677i) q^{13} +(-0.122699 - 0.382068i) q^{15} +(-0.628922 - 1.08932i) q^{17} +(-0.954408 + 1.65308i) q^{19} +(-3.52747 + 1.86015i) q^{21} +(-1.06030 - 6.01325i) q^{23} +(-3.78910 - 3.17944i) q^{25} +(4.76834 - 2.06468i) q^{27} +(4.03228 + 3.38349i) q^{29} +(1.30900 + 7.42370i) q^{31} +(3.29352 + 2.07371i) q^{33} +(0.266715 - 0.461963i) q^{35} +(3.23198 + 5.59795i) q^{37} +(10.9480 + 2.36621i) q^{39} +(-6.59653 + 5.53515i) q^{41} +(-10.3850 + 3.77983i) q^{43} +(-0.392596 + 0.573552i) q^{45} +(0.621088 - 3.52236i) q^{47} +(1.59646 + 0.581064i) q^{49} +(-0.823036 + 2.01721i) q^{51} -5.55807 q^{53} -0.520601 q^{55} +(3.27554 - 0.448937i) q^{57} +(-5.76771 - 2.09927i) q^{59} +(-0.00799863 + 0.0453625i) q^{61} +(6.29071 + 2.85249i) q^{63} +(-1.40789 + 0.512430i) q^{65} +(-4.70358 + 3.94677i) q^{67} +(-7.10350 + 7.83522i) q^{69} +(-0.202184 - 0.350193i) q^{71} +(0.185158 - 0.320703i) q^{73} +(-0.328256 + 8.56099i) q^{75} +(0.898386 + 5.09500i) q^{77} +(8.47182 + 7.10870i) q^{79} +(-7.88802 - 4.33349i) q^{81} +(-6.17571 - 5.18204i) q^{83} +(-0.0506048 - 0.286994i) q^{85} +(0.349323 - 9.11042i) q^{87} +(-4.29457 + 7.43842i) q^{89} +(7.44459 + 12.8944i) q^{91} +(8.76967 - 9.67301i) q^{93} +(-0.338776 + 0.284267i) q^{95} +(2.35224 - 0.856146i) q^{97} +(-0.658794 - 6.70884i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q+O(q^{10}) $ 54 * q	$ 54 q - 9 q^{11} + 12 q^{17} + 18 q^{19} + 12 q^{21} - 21 q^{27} + 6 q^{29} + 36 q^{31} - 9 q^{33} + 24 q^{39} + 3 q^{41} - 21 q^{43} + 42 q^{45} - 18 q^{49} + 24 q^{51} + 36 q^{53} - 72 q^{55} + 39 q^{57} + 18 q^{59} - 18 q^{61} - 30 q^{63} + 48 q^{65} - 27 q^{67} + 24 q^{69} - 84 q^{75} + 36 q^{77} + 72 q^{79} + 36 q^{81} + 6 q^{87} + 33 q^{89} + 36 q^{91} + 72 q^{93} + 36 q^{95} + 9 q^{97} + 120 q^{99}+O(q^{100}) $ 54 * q - 9 * q^11 + 12 * q^17 + 18 * q^19 + 12 * q^21 - 21 * q^27 + 6 * q^29 + 36 * q^31 - 9 * q^33 + 24 * q^39 + 3 * q^41 - 21 * q^43 + 42 * q^45 - 18 * q^49 + 24 * q^51 + 36 * q^53 - 72 * q^55 + 39 * q^57 + 18 * q^59 - 18 * q^61 - 30 * q^63 + 48 * q^65 - 27 * q^67 + 24 * q^69 - 84 * q^75 + 36 * q^77 + 72 * q^79 + 36 * q^81 + 6 * q^87 + 33 * q^89 + 36 * q^91 + 72 * q^93 + 36 * q^95 + 9 * q^97 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$

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
$3$	−1.06169	−	1.36851i	−0.612965	−	0.790110i
$3$	−1.06169	−	1.36851i	−0.612965	−	0.790110i
$4$		0			0
$5$	0.217711	+	0.0792403i	0.0973633	+	0.0354373i	0.390243	−	0.920712i	$-0.372391\pi$
$5$	0.217711	+	0.0792403i	0.0973633	+	0.0354373i	−0.292879	+	0.956149i	$0.594613\pi$
$6$		0			0
$7$	0.399809	−	2.26743i	0.151114	−	0.857008i	−0.811140	−	0.584852i	$-0.801152\pi$
$7$	0.399809	−	2.26743i	0.151114	−	0.857008i	0.962253	−	0.272155i	$-0.0877364\pi$
$8$		0			0
$9$	−0.745646	+	2.90586i	−0.248549	+	0.968619i
$10$		0			0
$11$	−2.11152	+	0.768532i	−0.636649	+	0.231721i	−0.640123	−	0.768273i	$-0.721116\pi$
$11$	−2.11152	+	0.768532i	−0.636649	+	0.231721i	0.00347397	+	0.999994i	$0.498894\pi$
$12$		0			0
$13$	−4.95385	+	4.15677i	−1.37395	+	1.15288i	−0.402560	+	0.915394i	$0.631879\pi$
$13$	−4.95385	+	4.15677i	−1.37395	+	1.15288i	−0.971391	+	0.237488i	$0.923676\pi$
$14$		0			0
$15$	−0.122699	−	0.382068i	−0.0316808	−	0.0986496i
$16$		0			0
$17$	−0.628922	−	1.08932i	−0.152536	−	0.264200i	0.779623	−	0.626249i	$-0.215411\pi$
$17$	−0.628922	−	1.08932i	−0.152536	−	0.264200i	−0.932159	+	0.362049i	$0.882077\pi$
$18$		0			0
$19$	−0.954408	+	1.65308i	−0.218956	+	0.379243i	−0.954489	−	0.298246i	$-0.903599\pi$
$19$	−0.954408	+	1.65308i	−0.218956	+	0.379243i	0.735533	+	0.677489i	$0.236932\pi$
$20$		0			0
$21$	−3.52747	+	1.86015i	−0.769758	+	0.405919i
$22$		0			0
$23$	−1.06030	−	6.01325i	−0.221088	−	1.25385i	−0.870025	−	0.493008i	$-0.835897\pi$
$23$	−1.06030	−	6.01325i	−0.221088	−	1.25385i	0.648937	−	0.760842i	$-0.275214\pi$
$24$		0			0
$25$	−3.78910	−	3.17944i	−0.757821	−	0.635887i
$26$		0			0
$27$	4.76834	−	2.06468i	0.917668	−	0.397348i
$28$		0			0
$29$	4.03228	+	3.38349i	0.748776	+	0.628298i	0.935179	−	0.354176i	$-0.115239\pi$
$29$	4.03228	+	3.38349i	0.748776	+	0.628298i	−0.186403	+	0.982473i	$0.559683\pi$
$30$		0			0
$31$	1.30900	+	7.42370i	0.235103	+	1.33334i	0.842397	+	0.538858i	$0.181144\pi$
$31$	1.30900	+	7.42370i	0.235103	+	1.33334i	−0.607294	+	0.794477i	$0.707745\pi$
$32$		0			0
$33$	3.29352	+	2.07371i	0.573328	+	0.360986i
$34$		0			0
$35$	0.266715	−	0.461963i	0.0450830	−	0.0780860i
$36$		0			0
$37$	3.23198	+	5.59795i	0.531334	+	0.920298i	0.999331	+	0.0365677i	$0.0116425\pi$
$37$	3.23198	+	5.59795i	0.531334	+	0.920298i	−0.467997	+	0.883730i	$0.655024\pi$
$38$		0			0
$39$	10.9480	+	2.36621i	1.75309	+	0.378897i
$40$		0			0
$41$	−6.59653	+	5.53515i	−1.03021	+	0.864445i	−0.990875	−	0.134781i	$-0.956967\pi$
$41$	−6.59653	+	5.53515i	−1.03021	+	0.864445i	−0.0393299	+	0.999226i	$0.512522\pi$
$42$		0			0
$43$	−10.3850	+	3.77983i	−1.58370	+	0.576419i	−0.976004	−	0.217751i	$-0.930128\pi$
$43$	−10.3850	+	3.77983i	−1.58370	+	0.576419i	−0.607695	+	0.794171i	$0.707906\pi$
$44$		0			0
$45$	−0.392596	+	0.573552i	−0.0585248	+	0.0855001i
$46$		0			0
$47$	0.621088	−	3.52236i	0.0905950	−	0.513790i	−0.905413	−	0.424531i	$-0.860439\pi$
$47$	0.621088	−	3.52236i	0.0905950	−	0.513790i	0.996008	−	0.0892588i	$-0.0284498\pi$
$48$		0			0
$49$	1.59646	+	0.581064i	0.228066	+	0.0830092i
$50$		0			0
$51$	−0.823036	+	2.01721i	−0.115248	+	0.282466i
$52$		0			0
$53$	−5.55807			−0.763460			−0.381730	−	0.924274i	$-0.624672\pi$
$53$	−5.55807			−0.763460			−0.381730	+	0.924274i	$0.624672\pi$
$54$		0			0
$55$	−0.520601			−0.0701978
$56$		0			0
$57$	3.27554	−	0.448937i	0.433856	−	0.0594631i
$58$		0			0
$59$	−5.76771	−	2.09927i	−0.750892	−	0.273302i	−0.0619108	−	0.998082i	$-0.519719\pi$
$59$	−5.76771	−	2.09927i	−0.750892	−	0.273302i	−0.688981	+	0.724779i	$0.741942\pi$
$60$		0			0
$61$	−0.00799863	+	0.0453625i	−0.00102412	+	0.00580807i	−0.985316	−	0.170743i	$-0.945383\pi$
$61$	−0.00799863	+	0.0453625i	−0.00102412	+	0.00580807i	0.984291	+	0.176551i	$0.0564942\pi$
$62$		0			0
$63$	6.29071	+	2.85249i	0.792555	+	0.359380i
$64$		0			0
$65$	−1.40789	+	0.512430i	−0.174627	+	0.0635592i
$66$		0			0
$67$	−4.70358	+	3.94677i	−0.574634	+	0.482175i	−0.883180	−	0.469034i	$-0.844602\pi$
$67$	−4.70358	+	3.94677i	−0.574634	+	0.482175i	0.308546	+	0.951209i	$0.400158\pi$
$68$		0			0
$69$	−7.10350	+	7.83522i	−0.855161	+	0.943249i
$70$		0			0
$71$	−0.202184	−	0.350193i	−0.0239948	−	0.0415602i	0.853779	−	0.520636i	$-0.174305\pi$
$71$	−0.202184	−	0.350193i	−0.0239948	−	0.0415602i	−0.877773	+	0.479076i	$0.840972\pi$
$72$		0			0
$73$	0.185158	−	0.320703i	0.0216711	−	0.0375354i	−0.854986	−	0.518650i	$-0.826435\pi$
$73$	0.185158	−	0.320703i	0.0216711	−	0.0375354i	0.876658	+	0.481115i	$0.159768\pi$
$74$		0			0
$75$	−0.328256	+	8.56099i	−0.0379037	+	0.988538i
$76$		0			0
$77$	0.898386	+	5.09500i	0.102381	+	0.580629i
$78$		0			0
$79$	8.47182	+	7.10870i	0.953154	+	0.799791i	0.979826	−	0.199853i	$-0.0640465\pi$
$79$	8.47182	+	7.10870i	0.953154	+	0.799791i	−0.0266718	+	0.999644i	$0.508491\pi$
$80$		0			0
$81$	−7.88802	−	4.33349i	−0.876447	−	0.481498i
$82$		0			0
$83$	−6.17571	−	5.18204i	−0.677873	−	0.568803i	0.237511	−	0.971385i	$-0.423668\pi$
$83$	−6.17571	−	5.18204i	−0.677873	−	0.568803i	−0.915384	+	0.402582i	$0.868113\pi$
$84$		0			0
$85$	−0.0506048	−	0.286994i	−0.00548886	−	0.0311289i
$86$		0			0
$87$	0.349323	−	9.11042i	0.0374513	−	0.976740i
$88$		0			0
$89$	−4.29457	+	7.43842i	−0.455224	+	0.788471i	−0.998701	−	0.0509533i	$-0.983774\pi$
$89$	−4.29457	+	7.43842i	−0.455224	+	0.788471i	0.543477	+	0.839424i	$0.317107\pi$
$90$		0			0
$91$	7.44459	+	12.8944i	0.780405	+	1.35170i
$92$		0			0
$93$	8.76967	−	9.67301i	0.909372	−	1.00304i
$94$		0			0
$95$	−0.338776	+	0.284267i	−0.0347577	+	0.0291651i
$96$		0			0
$97$	2.35224	−	0.856146i	0.238834	−	0.0869284i	−0.219830	−	0.975538i	$-0.570550\pi$
$97$	2.35224	−	0.856146i	0.238834	−	0.0869284i	0.458664	+	0.888610i	$0.348328\pi$
$98$		0			0
$99$	−0.658794	−	6.70884i	−0.0662113	−	0.674264i
$100$		0			0
$101$	2.53842	−	14.3961i	0.252582	−	1.43246i	−0.549623	−	0.835413i	$-0.685229\pi$
$101$	2.53842	−	14.3961i	0.252582	−	1.43246i	0.802205	−	0.597049i	$-0.203660\pi$
$102$		0			0
$103$	−4.27106	−	1.55454i	−0.420840	−	0.153173i	0.122915	−	0.992417i	$-0.460776\pi$
$103$	−4.27106	−	1.55454i	−0.420840	−	0.153173i	−0.543755	+	0.839244i	$0.682998\pi$
$104$		0			0
$105$	−0.915369	+	0.125458i	−0.0893308	+	0.0122434i
$106$		0			0
$107$	−6.84780			−0.662002			−0.331001	−	0.943630i	$-0.607386\pi$
$107$	−6.84780			−0.662002			−0.331001	+	0.943630i	$0.607386\pi$
$108$		0			0
$109$	5.10684			0.489146			0.244573	−	0.969631i	$-0.421352\pi$
$109$	5.10684			0.489146			0.244573	+	0.969631i	$0.421352\pi$
$110$		0			0
$111$	4.22951	−	10.3663i	0.401448	−	0.983923i
$112$		0			0
$113$	16.1379	+	5.87370i	1.51812	+	0.552551i	0.960679	−	0.277663i	$-0.0895599\pi$
$113$	16.1379	+	5.87370i	1.51812	+	0.552551i	0.557444	+	0.830215i	$0.311782\pi$
$114$		0			0
$115$	0.245653	−	1.39317i	0.0229073	−	0.129914i
$116$		0			0
$117$	−8.38517	−	17.4947i	−0.775209	−	1.61738i
$118$		0			0
$119$	−2.72142	+	0.990514i	−0.249472	+	0.0908003i
$120$		0			0
$121$	−4.55860	+	3.82512i	−0.414418	+	0.347738i
$122$		0			0
$123$	14.5784	+	3.15084i	1.31449	+	0.284102i
$124$		0			0
$125$	−1.15220	−	1.99566i	−0.103056	−	0.178498i
$126$		0			0
$127$	2.19913	−	3.80900i	0.195141	−	0.337994i	−0.751806	−	0.659385i	$-0.770817\pi$
$127$	2.19913	−	3.80900i	0.195141	−	0.337994i	0.946947	+	0.321390i	$0.104150\pi$
$128$		0			0
$129$	16.1984	+	10.1990i	1.42619	+	0.897972i
$130$		0			0
$131$	−1.00418	−	5.69500i	−0.0877358	−	0.497574i	−0.996733	−	0.0807714i	$-0.974262\pi$
$131$	−1.00418	−	5.69500i	−0.0877358	−	0.497574i	0.908997	−	0.416803i	$-0.136849\pi$
$132$		0			0
$133$	3.36667	+	2.82497i	0.291927	+	0.244956i
$134$		0			0
$135$	1.20173	−	0.0716592i	0.103428	−	0.00616744i
$136$		0			0
$137$	−11.9407	−	10.0194i	−1.02016	−	0.856018i	−0.0305148	−	0.999534i	$-0.509715\pi$
$137$	−11.9407	−	10.0194i	−1.02016	−	0.856018i	−0.989648	+	0.143516i	$0.954159\pi$
$138$		0			0
$139$	0.150962	+	0.856146i	0.0128044	+	0.0726174i	0.990540	−	0.137221i	$-0.0438172\pi$
$139$	0.150962	+	0.856146i	0.0128044	+	0.0726174i	−0.977736	+	0.209839i	$0.932706\pi$
$140$		0			0
$141$	−5.47980	+	2.88968i	−0.461482	+	0.243355i
$142$		0			0
$143$	7.26556	−	12.5843i	0.607577	−	1.05235i
$144$		0			0
$145$	0.609763	+	1.05614i	0.0506381	+	0.0877078i
$146$		0			0
$147$	−0.899747	−	2.80168i	−0.0742099	−	0.231079i
$148$		0			0
$149$	12.2565	−	10.2845i	1.00410	−	0.842536i	0.0165490	−	0.999863i	$-0.494732\pi$
$149$	12.2565	−	10.2845i	1.00410	−	0.842536i	0.987547	+	0.157327i	$0.0502876\pi$
$150$		0			0
$151$	−8.32596	+	3.03040i	−0.677557	+	0.246611i	−0.657798	−	0.753194i	$-0.728512\pi$
$151$	−8.32596	+	3.03040i	−0.677557	+	0.246611i	−0.0197589	+	0.999805i	$0.506290\pi$
$152$		0			0
$153$	3.63438	−	1.01531i	0.293822	−	0.0820827i
$154$		0			0
$155$	−0.303273	+	1.71995i	−0.0243595	+	0.138149i
$156$		0			0
$157$	−2.18624	−	0.795726i	−0.174481	−	0.0635059i	0.253302	−	0.967387i	$-0.418483\pi$
$157$	−2.18624	−	0.795726i	−0.174481	−	0.0635059i	−0.427783	+	0.903881i	$0.640705\pi$
$158$		0			0
$159$	5.90093	+	7.60628i	0.467974	+	0.603218i
$160$		0			0
$161$	−14.0585			−1.10797
$162$		0			0
$163$	−23.1365			−1.81219			−0.906094	−	0.423076i	$-0.860950\pi$
$163$	−23.1365			−1.81219			−0.906094	+	0.423076i	$0.860950\pi$
$164$		0			0
$165$	0.552714	+	0.712448i	0.0430288	+	0.0554640i
$166$		0			0
$167$	−5.61075	−	2.04214i	−0.434173	−	0.158026i	0.115682	−	0.993286i	$-0.463095\pi$
$167$	−5.61075	−	2.04214i	−0.434173	−	0.158026i	−0.549855	+	0.835260i	$0.685317\pi$
$168$		0			0
$169$	5.00443	−	28.3815i	0.384956	−	2.18320i
$170$		0			0
$171$	−4.09197	−	4.00599i	−0.312921	−	0.306346i
$172$		0			0
$173$	23.7036	−	8.62741i	1.80215	−	0.655930i	0.804037	−	0.594579i	$-0.202681\pi$
$173$	23.7036	−	8.62741i	1.80215	−	0.655930i	0.998116	−	0.0613511i	$-0.0195409\pi$
$174$		0			0
$175$	−8.72406	+	7.32036i	−0.659477	+	0.553367i
$176$		0			0
$177$	3.25061	+	10.1219i	0.244331	+	0.760812i
$178$		0			0
$179$	−12.8308	−	22.2236i	−0.959020	−	1.66107i	−0.724888	−	0.688867i	$-0.758109\pi$
$179$	−12.8308	−	22.2236i	−0.959020	−	1.66107i	−0.234132	−	0.972205i	$-0.575225\pi$
$180$		0			0
$181$	0.457169	−	0.791839i	0.0339811	−	0.0588570i	−0.848535	−	0.529140i	$-0.822515\pi$
$181$	0.457169	−	0.791839i	0.0339811	−	0.0588570i	0.882516	+	0.470283i	$0.155848\pi$
$182$		0			0
$183$	0.0705711	−	0.0372145i	0.00521677	−	0.00275097i
$184$		0			0
$185$	0.260054	+	1.47484i	0.0191195	+	0.108432i
$186$		0			0
$187$	2.16516	+	1.81679i	0.158333	+	0.132857i
$188$		0			0
$189$	−2.77510	−	11.6374i	−0.201859	−	0.846493i
$190$		0			0
$191$	−10.0665	−	8.44679i	−0.728386	−	0.611188i	0.201305	−	0.979529i	$-0.435482\pi$
$191$	−10.0665	−	8.44679i	−0.728386	−	0.611188i	−0.929691	+	0.368340i	$0.879926\pi$
$192$		0			0
$193$	−2.84167	−	16.1159i	−0.204548	−	1.16005i	−0.898150	−	0.439690i	$-0.855088\pi$
$193$	−2.84167	−	16.1159i	−0.204548	−	1.16005i	0.693602	−	0.720359i	$-0.256023\pi$
$194$		0			0
$195$	2.19600	+	1.38267i	0.157259	+	0.0990154i
$196$		0			0
$197$	1.76123	−	3.05054i	0.125483	−	0.217342i	−0.796439	−	0.604719i	$-0.793285\pi$
$197$	1.76123	−	3.05054i	0.125483	−	0.217342i	0.921921	+	0.387377i	$0.126619\pi$
$198$		0			0
$199$	2.01650	+	3.49268i	0.142946	+	0.247590i	0.928605	−	0.371070i	$-0.121009\pi$
$199$	2.01650	+	3.49268i	0.142946	+	0.247590i	−0.785659	+	0.618660i	$0.787676\pi$
$200$		0			0
$201$	10.3949	+	2.24667i	0.733202	+	0.158468i
$202$		0			0
$203$	9.28396	−	7.79017i	0.651606	−	0.546762i
$204$		0			0
$205$	−1.87474	+	0.682351i	−0.130938	+	0.0476575i
$206$		0			0
$207$	18.2643	+	1.40268i	1.26945	+	0.0974932i
$208$		0			0
$209$	0.744808	−	4.22402i	0.0515195	−	0.292181i
$210$		0			0
$211$	13.1689	+	4.79310i	0.906586	+	0.329970i	0.752889	−	0.658148i	$-0.228660\pi$
$211$	13.1689	+	4.79310i	0.906586	+	0.329970i	0.153697	+	0.988118i	$0.450882\pi$
$212$		0			0
$213$	−0.264587	+	0.648486i	−0.0181292	+	0.0444335i
$214$		0			0
$215$	−2.56045			−0.174621
$216$		0			0
$217$	17.3561			1.17821
$218$		0			0
$219$	−0.635465	+	0.0870951i	−0.0429408	+	0.00588534i
$220$		0			0
$221$	7.64366	+	2.78206i	0.514168	+	0.187142i
$222$		0			0
$223$	−3.81932	+	21.6604i	−0.255761	+	1.45049i	0.538352	+	0.842720i	$0.319047\pi$
$223$	−3.81932	+	21.6604i	−0.255761	+	1.45049i	−0.794113	+	0.607771i	$0.792064\pi$
$224$		0			0
$225$	12.0643	−	8.63986i	0.804288	−	0.575991i
$226$		0			0
$227$	2.34562	−	0.853736i	0.155684	−	0.0566645i	−0.263002	−	0.964795i	$-0.584713\pi$
$227$	2.34562	−	0.853736i	0.155684	−	0.0566645i	0.418687	+	0.908131i	$0.362491\pi$
$228$		0			0
$229$	−19.7082	+	16.5371i	−1.30235	+	1.09280i	−0.312619	+	0.949879i	$0.601206\pi$
$229$	−19.7082	+	16.5371i	−1.30235	+	1.09280i	−0.989734	+	0.142924i	$0.954349\pi$
$230$		0			0
$231$	6.01876	−	6.63874i	0.396005	−	0.436797i
$232$		0			0
$233$	−7.66748	−	13.2805i	−0.502313	−	0.870032i	−0.999996	−	0.00267305i	$-0.999149\pi$
$233$	−7.66748	−	13.2805i	−0.502313	−	0.870032i	0.497683	−	0.867359i	$-0.334184\pi$
$234$		0			0
$235$	0.414331	−	0.717642i	0.0270280	−	0.0468138i
$236$		0			0
$237$	0.733926	−	19.1410i	0.0476736	−	1.24334i
$238$		0			0
$239$	4.21317	+	23.8941i	0.272527	+	1.54558i	0.746708	+	0.665152i	$0.231633\pi$
$239$	4.21317	+	23.8941i	0.272527	+	1.54558i	−0.474181	+	0.880427i	$0.657256\pi$
$240$		0			0
$241$	−15.2364	−	12.7848i	−0.981462	−	0.823544i	0.00284754	−	0.999996i	$-0.499094\pi$
$241$	−15.2364	−	12.7848i	−0.981462	−	0.823544i	−0.984309	+	0.176452i	$0.943538\pi$
$242$		0			0
$243$	2.44418	+	15.3956i	0.156794	+	0.987631i
$244$		0			0
$245$	0.301523	+	0.253008i	0.0192636	+	0.0161641i
$246$		0			0
$247$	−2.14350	−	12.1564i	−0.136388	−	0.773492i
$248$		0			0
$249$	−0.535011	+	13.9532i	−0.0339050	+	0.884250i
$250$		0			0
$251$	−13.2793	+	23.0004i	−0.838180	+	1.45177i	0.0532354	+	0.998582i	$0.483047\pi$
$251$	−13.2793	+	23.0004i	−0.838180	+	1.45177i	−0.891415	+	0.453188i	$0.850287\pi$
$252$		0			0
$253$	6.86023	+	11.8823i	0.431299	+	0.747031i
$254$		0			0
$255$	−0.339028	+	0.373951i	−0.0212308	+	0.0234177i
$256$		0			0
$257$	−21.2279	+	17.8124i	−1.32416	+	1.11110i	−0.338758	+	0.940873i	$0.610007\pi$
$257$	−21.2279	+	17.8124i	−1.32416	+	1.11110i	−0.985404	+	0.170231i	$0.945549\pi$
$258$		0			0
$259$	13.9851	−	5.09017i	0.868994	−	0.316288i
$260$		0			0
$261$	−12.8386	+	9.19436i	−0.794689	+	0.569116i
$262$		0			0
$263$	4.05887	−	23.0190i	0.250281	−	1.41941i	−0.557622	−	0.830095i	$-0.688286\pi$
$263$	4.05887	−	23.0190i	0.250281	−	1.41941i	0.807902	−	0.589317i	$-0.200603\pi$
$264$		0			0
$265$	−1.21005	−	0.440423i	−0.0743330	−	0.0270550i
$266$		0			0
$267$	14.7390	−	2.02009i	0.902015	−	0.123628i
$268$		0			0
$269$	−2.10847			−0.128556			−0.0642779	−	0.997932i	$-0.520474\pi$
$269$	−2.10847			−0.128556			−0.0642779	+	0.997932i	$0.520474\pi$
$270$		0			0
$271$	−5.90936			−0.358968			−0.179484	−	0.983761i	$-0.557443\pi$
$271$	−5.90936			−0.358968			−0.179484	+	0.983761i	$0.557443\pi$
$272$		0			0
$273$	9.74233	−	23.8778i	0.589633	−	1.44515i
$274$		0			0
$275$	10.4443	+	3.80141i	0.629814	+	0.229233i
$276$		0			0
$277$	1.79706	−	10.1916i	0.107975	−	0.612355i	−0.882016	−	0.471220i	$-0.843814\pi$
$277$	1.79706	−	10.1916i	0.107975	−	0.612355i	0.989990	−	0.141135i	$-0.0450751\pi$
$278$		0			0
$279$	−22.5483	−	1.73169i	−1.34993	−	0.103674i
$280$		0			0
$281$	23.7267	−	8.63580i	1.41541	−	0.515168i	0.482700	−	0.875786i	$-0.339656\pi$
$281$	23.7267	−	8.63580i	1.41541	−	0.515168i	0.932714	+	0.360617i	$0.117434\pi$
$282$		0			0
$283$	14.4266	−	12.1054i	0.857572	−	0.719589i	−0.103871	−	0.994591i	$-0.533123\pi$
$283$	14.4266	−	12.1054i	0.857572	−	0.719589i	0.961444	+	0.275002i	$0.0886785\pi$
$284$		0			0
$285$	0.748696	+	0.161817i	0.0443489	+	0.00958519i
$286$		0			0
$287$	9.91320	+	17.1702i	0.585158	+	1.01352i
$288$		0			0
$289$	7.70891	−	13.3522i	0.453466	−	0.785425i
$290$		0			0
$291$	−3.66899	−	2.31011i	−0.215080	−	0.135421i
$292$		0			0
$293$	4.31963	+	24.4978i	0.252355	+	1.43118i	0.802771	+	0.596287i	$0.203358\pi$
$293$	4.31963	+	24.4978i	0.252355	+	1.43118i	−0.550416	+	0.834891i	$0.685531\pi$
$294$		0			0
$295$	−1.08935	−	0.914070i	−0.0634242	−	0.0532192i
$296$		0			0
$297$	−8.48170	+	8.02425i	−0.492158	+	0.465614i
$298$		0			0
$299$	30.2483	+	25.3813i	1.74930	+	1.46784i
$300$		0			0
$301$	4.41849	+	25.0585i	0.254677	+	1.44435i
$302$		0			0
$303$	−22.3962	+	11.8103i	−1.28663	+	0.678481i
$304$		0			0
$305$	−0.00533593	+	0.00924210i	−0.000305534	+	0.000529201i
$306$		0			0
$307$	8.26117	+	14.3088i	0.471490	+	0.816645i	0.999468	−	0.0326134i	$-0.0103830\pi$
$307$	8.26117	+	14.3088i	0.471490	+	0.816645i	−0.527978	+	0.849258i	$0.677050\pi$
$308$		0			0
$309$	2.40712	+	7.49542i	0.136936	+	0.426399i
$310$		0			0
$311$	−22.4012	+	18.7968i	−1.27025	+	1.06587i	−0.275742	+	0.961232i	$0.588924\pi$
$311$	−22.4012	+	18.7968i	−1.27025	+	1.06587i	−0.994510	+	0.104637i	$0.966632\pi$
$312$		0			0
$313$	15.3550	−	5.58878i	0.867918	−	0.315896i	0.130594	−	0.991436i	$-0.458311\pi$
$313$	15.3550	−	5.58878i	0.867918	−	0.315896i	0.737324	+	0.675540i	$0.236089\pi$
$314$		0			0
$315$	1.14352	+	1.11950i	0.0644303	+	0.0630764i
$316$		0			0
$317$	2.04942	−	11.6229i	0.115107	−	0.652805i	−0.871590	−	0.490235i	$-0.836911\pi$
$317$	2.04942	−	11.6229i	0.115107	−	0.652805i	0.986697	−	0.162569i	$-0.0519781\pi$
$318$		0			0
$319$	−11.1146	−	4.04538i	−0.622297	−	0.226498i
$320$		0			0
$321$	7.27021	+	9.37129i	0.405784	+	0.523055i
$322$		0			0
$323$	2.40099			0.133595
$324$		0			0
$325$	31.9868			1.77431
$326$		0			0
$327$	−5.42186	−	6.98877i	−0.299829	−	0.386480i
$328$		0			0
$329$	−7.73840	−	2.81655i	−0.426632	−	0.155281i
$330$		0			0
$331$	0.241369	−	1.36887i	0.0132669	−	0.0752401i	−0.977456	−	0.211141i	$-0.932282\pi$
$331$	0.241369	−	1.36887i	0.0132669	−	0.0752401i	0.990722	+	0.135901i	$0.0433930\pi$
$332$		0			0
$333$	−18.6768	+	5.21758i	−1.02348	+	0.285922i
$334$		0			0
$335$	−1.33676	+	0.486543i	−0.0730353	+	0.0265827i
$336$		0			0
$337$	−24.3595	+	20.4401i	−1.32695	+	1.11344i	−0.342169	+	0.939639i	$0.611161\pi$
$337$	−24.3595	+	20.4401i	−1.32695	+	1.11344i	−0.984780	+	0.173804i	$0.944394\pi$
$338$		0			0
$339$	−9.09511	−	28.3209i	−0.493979	−	1.53818i
$340$		0			0
$341$	−8.46933	−	14.6693i	−0.458640	−	0.794388i
$342$		0			0
$343$	10.0142	−	17.3452i	0.540718	−	0.936550i
$344$		0			0
$345$	−2.16738	+	1.14293i	−0.116688	+	0.0615332i
$346$		0			0
$347$	−4.23207	−	24.0012i	−0.227189	−	1.28845i	−0.858455	−	0.512888i	$-0.828576\pi$
$347$	−4.23207	−	24.0012i	−0.227189	−	1.28845i	0.631266	−	0.775566i	$-0.282536\pi$
$348$		0			0
$349$	−20.1385	−	16.8982i	−1.07799	−	0.904542i	−0.0822384	−	0.996613i	$-0.526207\pi$
$349$	−20.1385	−	16.8982i	−1.07799	−	0.904542i	−0.995752	+	0.0920710i	$0.970651\pi$
$350$		0			0
$351$	−15.0392	+	30.0490i	−0.802735	+	1.60390i
$352$		0			0
$353$	10.4957	+	8.80692i	0.558629	+	0.468745i	0.877850	−	0.478935i	$-0.158977\pi$
$353$	10.4957	+	8.80692i	0.558629	+	0.468745i	−0.319222	+	0.947680i	$0.603421\pi$
$354$		0			0
$355$	−0.0162683	−	0.0922619i	−0.000863430	−	0.00489675i
$356$		0			0
$357$	4.24482	+	2.67267i	0.224660	+	0.141453i
$358$		0			0
$359$	5.44724	−	9.43489i	0.287494	−	0.497955i	−0.685717	−	0.727869i	$-0.740511\pi$
$359$	5.44724	−	9.43489i	0.287494	−	0.497955i	0.973211	+	0.229914i	$0.0738444\pi$
$360$		0			0
$361$	7.67821	+	13.2991i	0.404116	+	0.699950i
$362$		0			0
$363$	10.0745	+	2.17742i	0.528775	+	0.114285i
$364$		0			0
$365$	0.0657235	−	0.0551486i	0.00344013	−	0.00288661i
$366$		0			0
$367$	27.3970	−	9.97169i	1.43011	−	0.520518i	0.493148	−	0.869946i	$-0.335846\pi$
$367$	27.3970	−	9.97169i	1.43011	−	0.520518i	0.936963	+	0.349428i	$0.113624\pi$
$368$		0			0
$369$	−11.1657	−	23.2958i	−0.581262	−	1.21273i
$370$		0			0
$371$	−2.22217	+	12.6025i	−0.115369	+	0.654291i
$372$		0			0
$373$	−1.28503	−	0.467714i	−0.0665365	−	0.0242173i	0.308537	−	0.951212i	$-0.400160\pi$
$373$	−1.28503	−	0.467714i	−0.0665365	−	0.0242173i	−0.375074	+	0.926995i	$0.622383\pi$
$374$		0			0
$375$	−1.50782	+	3.69556i	−0.0778634	+	0.190838i
$376$		0			0
$377$	−34.0397			−1.75313
$378$		0			0
$379$	−10.5561			−0.542229			−0.271115	−	0.962547i	$-0.587392\pi$
$379$	−10.5561			−0.542229			−0.271115	+	0.962547i	$0.587392\pi$
$380$		0			0
$381$	−7.54745	+	1.03443i	−0.386668	+	0.0529956i
$382$		0			0
$383$	−9.43581	−	3.43436i	−0.482148	−	0.175487i	0.0894997	−	0.995987i	$-0.471473\pi$
$383$	−9.43581	−	3.43436i	−0.482148	−	0.175487i	−0.571647	+	0.820499i	$0.693695\pi$
$384$		0			0
$385$	−0.208141	+	1.18043i	−0.0106078	+	0.0601600i
$386$		0			0
$387$	−3.24012	−	32.9958i	−0.164704	−	1.67727i
$388$		0			0
$389$	−20.2225	+	7.36039i	−1.02532	+	0.373187i	−0.799298	−	0.600935i	$-0.794795\pi$
$389$	−20.2225	+	7.36039i	−1.02532	+	0.373187i	−0.226024	+	0.974122i	$0.572573\pi$
$390$		0			0
$391$	−5.88354	+	4.93688i	−0.297543	+	0.249669i
$392$		0			0
$393$	−6.72755	+	7.42053i	−0.339360	+	0.374316i
$394$		0			0
$395$	1.28111	+	2.21895i	0.0644597	+	0.111648i
$396$		0			0
$397$	−13.5799	+	23.5212i	−0.681558	+	1.18049i	0.292947	+	0.956129i	$0.405364\pi$
$397$	−13.5799	+	23.5212i	−0.681558	+	1.18049i	−0.974505	+	0.224364i	$0.927969\pi$
$398$		0			0
$399$	0.291660	−	7.60655i	0.0146012	−	0.380804i
$400$		0			0
$401$	5.92115	+	33.5805i	0.295688	+	1.67693i	0.664392	+	0.747385i	$0.268691\pi$
$401$	5.92115	+	33.5805i	0.295688	+	1.67693i	−0.368703	+	0.929547i	$0.620198\pi$
$402$		0			0
$403$	−37.3432	−	31.3347i	−1.86020	−	1.56089i
$404$		0			0
$405$	−1.37392	−	1.56850i	−0.0682707	−	0.0779392i
$406$		0			0
$407$	−11.1266	−	9.33633i	−0.551526	−	0.462785i
$408$		0			0
$409$	2.35563	+	13.3594i	0.116478	+	0.660582i	0.986008	+	0.166700i	$0.0533112\pi$
$409$	2.35563	+	13.3594i	0.116478	+	0.660582i	−0.869529	+	0.493881i	$0.835578\pi$
$410$		0			0
$411$	−1.03444	+	26.9785i	−0.0510252	+	1.33075i
$412$		0			0
$413$	−7.06594	+	12.2386i	−0.347692	+	0.602220i
$414$		0			0
$415$	−0.933894	−	1.61755i	−0.0458431	−	0.0794025i
$416$		0			0
$417$	1.01137	−	1.11555i	0.0495271	−	0.0546288i
$418$		0			0
$419$	9.90202	−	8.30878i	0.483745	−	0.405911i	−0.368033	−	0.929813i	$-0.619969\pi$
$419$	9.90202	−	8.30878i	0.483745	−	0.405911i	0.851779	+	0.523902i	$0.175524\pi$
$420$		0			0
$421$	7.12696	−	2.59400i	0.347347	−	0.126424i	−0.162455	−	0.986716i	$-0.551941\pi$
$421$	7.12696	−	2.59400i	0.347347	−	0.126424i	0.509801	+	0.860292i	$0.329719\pi$
$422$		0			0
$423$	9.77238	+	4.43123i	0.475149	+	0.215454i
$424$		0			0
$425$	−1.08039	+	6.12718i	−0.0524065	+	0.297212i
$426$		0			0
$427$	0.0996583	+	0.0362727i	0.00482280	+	0.00175536i
$428$		0			0
$429$	−24.9355	+	3.41759i	−1.20390	+	0.165003i
$430$		0			0
$431$	12.0397			0.579931			0.289965	−	0.957037i	$-0.406356\pi$
$431$	12.0397			0.579931			0.289965	+	0.957037i	$0.406356\pi$
$432$		0			0
$433$	0.862397			0.0414442			0.0207221	−	0.999785i	$-0.493403\pi$
$433$	0.862397			0.0414442			0.0207221	+	0.999785i	$0.493403\pi$
$434$		0			0
$435$	0.797964	−	1.95576i	0.0382594	−	0.0937714i
$436$		0			0
$437$	10.9524	+	3.98634i	0.523923	+	0.190692i
$438$		0			0
$439$	0.140119	−	0.794654i	0.00668751	−	0.0379268i	−0.981281	−	0.192579i	$-0.938315\pi$
$439$	0.140119	−	0.794654i	0.00668751	−	0.0379268i	0.987969	+	0.154653i	$0.0494258\pi$
$440$		0			0
$441$	−2.87889	+	4.20582i	−0.137090	+	0.200277i
$442$		0			0
$443$	17.8534	−	6.49812i	0.848243	−	0.308735i	0.118919	−	0.992904i	$-0.462057\pi$
$443$	17.8534	−	6.49812i	0.848243	−	0.308735i	0.729324	+	0.684169i	$0.239835\pi$
$444$		0			0
$445$	−1.52440	+	1.27912i	−0.0722634	+	0.0606362i
$446$		0			0
$447$	−27.0870	−	5.85435i	−1.28117	−	0.276901i
$448$		0			0
$449$	4.05922	+	7.03078i	0.191567	+	0.331803i	0.945770	−	0.324838i	$-0.105310\pi$
$449$	4.05922	+	7.03078i	0.191567	+	0.331803i	−0.754203	+	0.656641i	$0.771977\pi$
$450$		0			0
$451$	9.67480	−	16.7572i	0.455569	−	0.789068i
$452$		0			0
$453$	12.9867	+	8.17684i	0.610168	+	0.384181i
$454$		0			0
$455$	0.599012	+	3.39717i	0.0280821	+	0.159262i
$456$		0			0
$457$	2.65134	+	2.22474i	0.124025	+	0.104069i	0.702690	−	0.711496i	$-0.251982\pi$
$457$	2.65134	+	2.22474i	0.124025	+	0.104069i	−0.578666	+	0.815565i	$0.696426\pi$
$458$		0			0
$459$	−5.24802	−	3.89575i	−0.244957	−	0.181838i
$460$		0			0
$461$	3.95171	+	3.31588i	0.184049	+	0.154436i	0.730157	−	0.683279i	$-0.239447\pi$
$461$	3.95171	+	3.31588i	0.184049	+	0.154436i	−0.546108	+	0.837715i	$0.683891\pi$
$462$		0			0
$463$	0.813887	+	4.61578i	0.0378245	+	0.214513i	0.997862	−	0.0653585i	$-0.0208191\pi$
$463$	0.813887	+	4.61578i	0.0378245	+	0.214513i	−0.960037	+	0.279872i	$0.909708\pi$
$464$		0			0
$465$	2.67574	−	1.41101i	0.124085	−	0.0654340i
$466$		0			0
$467$	3.61817	−	6.26686i	0.167429	−	0.289996i	−0.770086	−	0.637940i	$-0.779787\pi$
$467$	3.61817	−	6.26686i	0.167429	−	0.289996i	0.937515	+	0.347944i	$0.113120\pi$
$468$		0			0
$469$	7.06849	+	12.2430i	0.326393	+	0.565329i
$470$		0			0
$471$	1.23214	+	3.83671i	0.0567740	+	0.176786i
$472$		0			0
$473$	19.0233	−	15.9624i	0.874691	−	0.733953i
$474$		0			0
$475$	8.87222	−	3.22922i	0.407085	−	0.148167i
$476$		0			0
$477$	4.14436	−	16.1510i	0.189757	−	0.739502i
$478$		0			0
$479$	−4.08143	+	23.1469i	−0.186485	+	1.05761i	0.737547	+	0.675296i	$0.235984\pi$
$479$	−4.08143	+	23.1469i	−0.186485	+	1.05761i	−0.924032	+	0.382315i	$0.875127\pi$
$480$		0			0
$481$	−39.2802	−	14.2968i	−1.79102	−	0.651878i
$482$		0			0
$483$	14.9258	+	19.2393i	0.679146	+	0.875417i
$484$		0			0
$485$	0.579950			0.0263342
$486$		0			0
$487$	−23.8351			−1.08007			−0.540035	−	0.841642i	$-0.681589\pi$
$487$	−23.8351			−1.08007			−0.540035	+	0.841642i	$0.681589\pi$
$488$		0			0
$489$	24.5637	+	31.6625i	1.11081	+	1.43183i
$490$		0			0
$491$	27.6046	+	10.0473i	1.24578	+	0.453427i	0.878973	−	0.476871i	$-0.158229\pi$
$491$	27.6046	+	10.0473i	1.24578	+	0.453427i	0.366806	+	0.930297i	$0.380451\pi$
$492$		0			0
$493$	1.14972	−	6.52041i	0.0517810	−	0.293665i
$494$		0			0
$495$	0.388184	−	1.51279i	0.0174476	−	0.0679949i
$496$		0			0
$497$	−0.874872	+	0.318427i	−0.0392434	+	0.0142834i
$498$		0			0
$499$	31.5060	−	26.4367i	1.41040	−	1.18347i	0.454148	−	0.890926i	$-0.349944\pi$
$499$	31.5060	−	26.4367i	1.41040	−	1.18347i	0.956253	−	0.292541i	$-0.0945008\pi$
$500$		0			0
$501$	3.16215	+	9.84648i	0.141275	+	0.439908i
$502$		0			0
$503$	7.82999	+	13.5619i	0.349122	+	0.604697i	0.986094	−	0.166190i	$-0.0531465\pi$
$503$	7.82999	+	13.5619i	0.349122	+	0.604697i	−0.636972	+	0.770887i	$0.719813\pi$
$504$		0			0
$505$	1.69339	−	2.93304i	0.0753548	−	0.130518i
$506$		0			0
$507$	−44.1536	+	23.2837i	−1.96093	+	1.03406i
$508$		0			0
$509$	2.24686	+	12.7426i	0.0995904	+	0.564805i	0.993244	+	0.116047i	$0.0370224\pi$
$509$	2.24686	+	12.7426i	0.0995904	+	0.564805i	−0.893653	+	0.448758i	$0.851867\pi$
$510$		0			0
$511$	−0.653144	−	0.548052i	−0.0288934	−	0.0242444i
$512$		0			0
$513$	−1.13785	+	9.85302i	−0.0502374	+	0.435021i
$514$		0			0
$515$	−0.806674	−	0.676879i	−0.0355463	−	0.0298269i
$516$		0			0
$517$	1.39561	+	7.91488i	0.0613788	+	0.348096i
$518$		0			0
$519$	−36.9725	−	23.2791i	−1.62291	−	1.02184i
$520$		0			0
$521$	−14.7537	+	25.5541i	−0.646370	+	1.11955i	0.337613	+	0.941285i	$0.390380\pi$
$521$	−14.7537	+	25.5541i	−0.646370	+	1.11955i	−0.983983	+	0.178261i	$0.942953\pi$
$522$		0			0
$523$	15.3764	+	26.6326i	0.672361	+	1.16456i	0.977233	+	0.212170i	$0.0680531\pi$
$523$	15.3764	+	26.6326i	0.672361	+	1.16456i	−0.304872	+	0.952393i	$0.598614\pi$
$524$		0			0
$525$	19.2802	+	4.16706i	0.841457	+	0.181865i
$526$		0			0
$527$	7.26356	−	6.09485i	0.316406	−	0.265496i
$528$		0			0
$529$	−13.4221	+	4.88523i	−0.583568	+	0.212401i
$530$		0			0
$531$	10.4009	−	15.1948i	0.451359	−	0.659399i
$532$		0			0
$533$	9.66987	−	54.8406i	0.418849	−	2.37541i
$534$		0			0
$535$	−1.49084	−	0.542622i	−0.0644547	−	0.0234596i
$536$		0			0
$537$	−16.7910	+	41.1536i	−0.724584	+	1.77591i
$538$		0			0
$539$	−3.81753			−0.164433
$540$		0			0
$541$	−35.1137			−1.50966			−0.754828	−	0.655922i	$-0.772280\pi$
$541$	−35.1137			−1.50966			−0.754828	+	0.655922i	$0.772280\pi$
$542$		0			0
$543$	−1.56901	+	0.215044i	−0.0673327	+	0.00922843i
$544$		0			0
$545$	1.11181	+	0.404667i	0.0476249	+	0.0173340i
$546$		0			0
$547$	3.67992	−	20.8699i	0.157342	−	0.892332i	−0.799271	−	0.600971i	$-0.794781\pi$
$547$	3.67992	−	20.8699i	0.157342	−	0.892332i	0.956613	−	0.291361i	$-0.0941081\pi$
$548$		0			0
$549$	−0.125853	−	0.0570673i	−0.00537127	−	0.00243557i
$550$		0			0
$551$	−9.44163	+	3.43647i	−0.402227	+	0.146399i
$552$		0			0
$553$	19.5056	−	16.3671i	0.829462	−	0.696001i
$554$		0			0
$555$	1.74224	−	1.92170i	0.0739539	−	0.0815717i
$556$		0			0
$557$	5.00418	+	8.66750i	0.212034	+	0.367254i	0.952351	−	0.305004i	$-0.0986579\pi$
$557$	5.00418	+	8.66750i	0.212034	+	0.367254i	−0.740317	+	0.672258i	$0.765325\pi$
$558$		0			0
$559$	35.7339	−	61.8928i	1.51138	−	2.61779i
$560$		0			0
$561$	0.187571	−	4.89191i	0.00791927	−	0.206537i
$562$		0			0
$563$	4.99803	+	28.3453i	0.210642	+	1.19461i	0.888311	+	0.459243i	$0.151879\pi$
$563$	4.99803	+	28.3453i	0.210642	+	1.19461i	−0.677669	+	0.735367i	$0.737010\pi$
$564$		0			0
$565$	3.04796	+	2.55754i	0.128228	+	0.107596i
$566$		0			0
$567$	−12.9796	+	16.1530i	−0.545091	+	0.678361i
$568$		0			0
$569$	−28.9360	−	24.2802i	−1.21306	−	1.01788i	−0.999158	−	0.0410246i	$-0.986938\pi$
$569$	−28.9360	−	24.2802i	−1.21306	−	1.01788i	−0.213903	−	0.976855i	$-0.568618\pi$
$570$		0			0
$571$	0.778451	+	4.41481i	0.0325771	+	0.184754i	0.996754	−	0.0805054i	$-0.0256534\pi$
$571$	0.778451	+	4.41481i	0.0325771	+	0.184754i	−0.964177	+	0.265260i	$0.914542\pi$
$572$		0			0
$573$	−0.872075	+	22.7439i	−0.0364315	+	0.950142i
$574$		0			0
$575$	−15.1012	+	26.1560i	−0.629762	+	1.09078i
$576$		0			0
$577$	0.179029	+	0.310087i	0.00745307	+	0.0129091i	0.869728	−	0.493532i	$-0.164294\pi$
$577$	0.179029	+	0.310087i	0.00745307	+	0.0129091i	−0.862275	+	0.506441i	$0.830961\pi$
$578$		0			0
$579$	−19.0378	+	20.9989i	−0.791186	+	0.872684i
$580$		0			0
$581$	−14.2190	+	11.9312i	−0.589904	+	0.494988i
$582$		0			0
$583$	11.7360	−	4.27156i	0.486056	−	0.176910i
$584$		0			0
$585$	−0.439261	−	4.47322i	−0.0181612	−	0.184945i
$586$		0			0
$587$	−3.93692	+	22.3274i	−0.162494	+	0.921550i	0.789116	+	0.614244i	$0.210539\pi$
$587$	−3.93692	+	22.3274i	−0.162494	+	0.921550i	−0.951611	+	0.307307i	$0.900572\pi$
$588$		0			0
$589$	−13.5213	−	4.92135i	−0.557136	−	0.202781i
$590$		0			0
$591$	−6.04458	+	0.828452i	−0.248641	+	0.0340780i
$592$		0			0
$593$	−7.47045			−0.306774			−0.153387	−	0.988166i	$-0.549018\pi$
$593$	−7.47045			−0.306774			−0.153387	+	0.988166i	$0.549018\pi$
$594$		0			0
$595$	−0.670970			−0.0275071
$596$		0			0
$597$	2.63888	−	6.46773i	0.108002	−	0.264707i
$598$		0			0
$599$	21.9158	+	7.97668i	0.895453	+	0.325918i	0.748429	−	0.663215i	$-0.230808\pi$
$599$	21.9158	+	7.97668i	0.895453	+	0.325918i	0.147024	+	0.989133i	$0.453031\pi$
$600$		0			0
$601$	0.0913889	−	0.518292i	0.00372783	−	0.0211416i	−0.982887	−	0.184209i	$-0.941028\pi$
$601$	0.0913889	−	0.518292i	0.00372783	−	0.0211416i	0.986615	+	0.163067i	$0.0521388\pi$
$602$		0			0
$603$	−7.96156	−	16.6108i	−0.324220	−	0.676446i
$604$		0			0
$605$	−1.29556	+	0.471545i	−0.0526720	+	0.0191710i
$606$		0			0
$607$	−14.9417	+	12.5376i	−0.606465	+	0.508884i	−0.893516	−	0.449031i	$-0.851769\pi$
$607$	−14.9417	+	12.5376i	−0.606465	+	0.508884i	0.287051	+	0.957915i	$0.407325\pi$
$608$		0			0
$609$	−20.5176	−	4.43449i	−0.831414	−	0.179695i
$610$		0			0
$611$	11.5649	+	20.0310i	0.467866	+	0.810367i
$612$		0			0
$613$	7.85317	−	13.6021i	0.317187	−	0.549383i	−0.662713	−	0.748873i	$-0.730595\pi$
$613$	7.85317	−	13.6021i	0.317187	−	0.549383i	0.979900	+	0.199490i	$0.0639285\pi$
$614$		0			0
$615$	2.92419	+	1.84117i	0.117915	+	0.0742430i
$616$		0			0
$617$	0.416168	+	2.36021i	0.0167543	+	0.0950184i	0.992038	−	0.125937i	$-0.0401937\pi$
$617$	0.416168	+	2.36021i	0.0167543	+	0.0950184i	−0.975284	+	0.220955i	$0.929083\pi$
$618$		0			0
$619$	−1.21076	−	1.01595i	−0.0486647	−	0.0408345i	0.618131	−	0.786075i	$-0.287890\pi$
$619$	−1.21076	−	1.01595i	−0.0486647	−	0.0408345i	−0.666796	+	0.745241i	$0.732335\pi$
$620$		0			0
$621$	−17.4713	−	26.4841i	−0.701100	−	1.06277i
$622$		0			0
$623$	15.1491	+	12.7116i	0.606935	+	0.509279i
$624$		0			0
$625$	4.20189	+	23.8301i	0.168076	+	0.953204i
$626$		0			0
$627$	−6.57137	+	3.46530i	−0.262435	+	0.138391i
$628$		0			0
$629$	4.06533	−	7.04135i	0.162095	−	0.280757i
$630$		0			0
$631$	6.07148	+	10.5161i	0.241702	+	0.418640i	0.961199	−	0.275855i	$-0.0889611\pi$
$631$	6.07148	+	10.5161i	0.241702	+	0.418640i	−0.719497	+	0.694495i	$0.755628\pi$
$632$		0			0
$633$	−7.42185	−	23.1106i	−0.294992	−	0.918563i
$634$		0			0
$635$	0.780601	−	0.655002i	0.0309772	−	0.0259930i
$636$		0			0
$637$	−10.3240	+	3.75762i	−0.409051	+	0.148882i
$638$		0			0
$639$	1.16837	−	0.326398i	0.0462199	−	0.0129121i
$640$		0			0
$641$	−0.185717	+	1.05325i	−0.00733538	+	0.0416010i	−0.988256	−	0.152809i	$-0.951168\pi$
$641$	−0.185717	+	1.05325i	−0.00733538	+	0.0416010i	0.980920	+	0.194410i	$0.0622792\pi$
$642$		0			0
$643$	12.3154	+	4.48244i	0.485672	+	0.176770i	0.573238	−	0.819389i	$-0.305687\pi$
$643$	12.3154	+	4.48244i	0.485672	+	0.176770i	−0.0875667	+	0.996159i	$0.527909\pi$
$644$		0			0
$645$	2.71839	+	3.50400i	0.107036	+	0.137970i
$646$		0			0
$647$	43.2226			1.69925			0.849627	−	0.527384i	$-0.176827\pi$
$647$	43.2226			1.69925			0.849627	+	0.527384i	$0.176827\pi$
$648$		0			0
$649$	13.7920			0.541384
$650$		0			0
$651$	−18.4267	−	23.7520i	−0.722198	−	0.930913i
$652$		0			0
$653$	25.3272	+	9.21834i	0.991130	+	0.360742i	0.786158	−	0.618026i	$-0.212067\pi$
$653$	25.3272	+	9.21834i	0.991130	+	0.360742i	0.204972	+	0.978768i	$0.434290\pi$
$654$		0			0
$655$	0.232652	−	1.31944i	0.00909047	−	0.0515546i
$656$		0			0
$657$	0.793855	+	0.777174i	0.0309712	+	0.0303204i
$658$		0			0
$659$	−31.4302	+	11.4396i	−1.22435	+	0.445625i	−0.871657	−	0.490116i	$-0.836955\pi$
$659$	−31.4302	+	11.4396i	−1.22435	+	0.445625i	−0.352688	+	0.935741i	$0.614732\pi$
$660$		0			0
$661$	18.8487	−	15.8159i	0.733129	−	0.615168i	−0.197854	−	0.980232i	$-0.563397\pi$
$661$	18.8487	−	15.8159i	0.733129	−	0.615168i	0.930983	+	0.365063i	$0.118953\pi$
$662$		0			0
$663$	−4.30788	−	13.4141i	−0.167304	−	0.520961i
$664$		0			0
$665$	0.509109	+	0.881803i	0.0197424	+	0.0341948i
$666$		0			0
$667$	16.0703	−	27.8346i	0.622246	−	1.07776i
$668$		0			0
$669$	33.6975	−	17.7698i	1.30282	−	0.687020i
$670$		0			0
$671$	−0.0179732	−	0.101931i	−0.000693848	−	0.00393501i
$672$		0			0
$673$	9.88171	+	8.29174i	0.380912	+	0.319623i	0.813060	−	0.582179i	$-0.197800\pi$
$673$	9.88171	+	8.29174i	0.380912	+	0.319623i	−0.432148	+	0.901803i	$0.642244\pi$
$674$		0			0
$675$	−24.6323	−	7.33734i	−0.948096	−	0.282414i
$676$		0			0
$677$	26.8925	+	22.5655i	1.03356	+	0.867261i	0.991270	−	0.131844i	$-0.0420898\pi$
$677$	26.8925	+	22.5655i	1.03356	+	0.867261i	0.0422912	+	0.999105i	$0.486534\pi$
$678$		0			0
$679$	−1.00080	−	5.67584i	−0.0384073	−	0.217819i
$680$		0			0
$681$	−3.65866	−	2.30361i	−0.140200	−	0.0882745i
$682$		0			0
$683$	5.00531	−	8.66946i	0.191523	−	0.331728i	−0.754232	−	0.656608i	$-0.771991\pi$
$683$	5.00531	−	8.66946i	0.191523	−	0.331728i	0.945755	+	0.324880i	$0.105324\pi$
$684$		0			0
$685$	−1.80568	−	3.12753i	−0.0689914	−	0.119497i
$686$		0			0
$687$	43.5551	+	9.41363i	1.66173	+	0.359152i
$688$		0			0
$689$	27.5338	−	23.1036i	1.04896	−	0.880179i
$690$		0			0
$691$	−34.3946	+	12.5186i	−1.30843	+	0.476230i	−0.899733	−	0.436440i	$-0.856239\pi$
$691$	−34.3946	+	12.5186i	−1.30843	+	0.476230i	−0.408698	+	0.912670i	$0.634017\pi$
$692$		0			0
$693$	−15.4752	−	1.18849i	−0.587855	−	0.0451468i
$694$		0			0
$695$	−0.0349753	+	0.198355i	−0.00132669	+	0.00752402i
$696$		0			0
$697$	10.1783	+	3.70459i	0.385530	+	0.140321i
$698$		0			0
$699$	−10.0340	+	24.5927i	−0.379521	+	0.930182i
$700$		0			0
$701$	−20.2108			−0.763352			−0.381676	−	0.924296i	$-0.624653\pi$
$701$	−20.2108			−0.763352			−0.381676	+	0.924296i	$0.624653\pi$
$702$		0			0
$703$	−12.3385			−0.465356
$704$		0			0
$705$	−1.42199	+	0.194894i	−0.0535553	+	0.00734013i
$706$		0			0
$707$	−31.6272	−	11.5114i	−1.18946	−	0.432929i
$708$		0			0
$709$	1.64212	−	9.31291i	0.0616710	−	0.349754i	−0.938321	−	0.345765i	$-0.887619\pi$
$709$	1.64212	−	9.31291i	0.0616710	−	0.349754i	0.999992	−	0.00398835i	$-0.00126953\pi$
$710$		0			0
$711$	−26.9739	+	19.3173i	−1.01160	+	0.724456i
$712$		0			0
$713$	43.2526	−	15.7427i	1.61982	−	0.589568i
$714$		0			0
$715$	2.57898	−	2.16402i	0.0964483	−	0.0809297i
$716$		0			0
$717$	28.2262	−	31.1338i	1.05413	−	1.16271i
$718$		0			0
$719$	7.77273	+	13.4628i	0.289874	+	0.502076i	0.973779	−	0.227494i	$-0.0730533\pi$
$719$	7.77273	+	13.4628i	0.289874	+	0.502076i	−0.683905	+	0.729571i	$0.739720\pi$
$720$		0			0
$721$	−5.23241	+	9.06280i	−0.194865	+	0.337516i
$722$		0			0
$723$	−1.31995	+	34.4247i	−0.0490895	+	1.28027i
$724$		0			0
$725$	−4.52116	−	25.6408i	−0.167912	−	0.952274i
$726$		0			0
$727$	22.0259	+	18.4820i	0.816897	+	0.685458i	0.952243	−	0.305340i	$-0.0987702\pi$
$727$	22.0259	+	18.4820i	0.816897	+	0.685458i	−0.135346	+	0.990798i	$0.543215\pi$
$728$		0			0
$729$	18.4742	−	19.6902i	0.684228	−	0.729268i
$730$		0			0
$731$	10.6488	+	8.93543i	0.393861	+	0.330489i
$732$		0			0
$733$	−3.45356	−	19.5861i	−0.127560	−	0.723429i	−0.979754	−	0.200204i	$-0.935840\pi$
$733$	−3.45356	−	19.5861i	−0.127560	−	0.723429i	0.852194	−	0.523226i	$-0.175271\pi$
$734$		0			0
$735$	0.0261214	−	0.681253i	0.000963503	−	0.0251284i
$736$		0			0
$737$	6.89850	−	11.9486i	0.254110	−	0.440131i
$738$		0			0
$739$	15.3249	+	26.5436i	0.563737	+	0.976421i	0.997166	+	0.0752331i	$0.0239701\pi$
$739$	15.3249	+	26.5436i	0.563737	+	0.976421i	−0.433429	+	0.901188i	$0.642697\pi$
$740$		0			0
$741$	−14.3604	+	15.8397i	−0.527543	+	0.581884i
$742$		0			0
$743$	−8.54021	+	7.16609i	−0.313310	+	0.262898i	−0.785858	−	0.618406i	$-0.787779\pi$
$743$	−8.54021	+	7.16609i	−0.313310	+	0.262898i	0.472549	+	0.881305i	$0.343334\pi$
$744$		0			0
$745$	3.48333	−	1.26783i	0.127619	−	0.0464496i
$746$		0			0
$747$	19.6632	−	14.0818i	0.719438	−	0.515225i
$748$		0			0
$749$	−2.73781	+	15.5269i	−0.100037	+	0.567341i
$750$		0			0
$751$	−28.4587	−	10.3581i	−1.03847	−	0.377974i	−0.234173	−	0.972195i	$-0.575238\pi$
$751$	−28.4587	−	10.3581i	−1.03847	−	0.377974i	−0.804302	+	0.594221i	$0.797460\pi$
$752$		0			0
$753$	45.5747	−	6.24633i	1.66083	−	0.227629i
$754$		0			0
$755$	−2.05278			−0.0747084
$756$		0			0
$757$	29.1450			1.05929			0.529646	−	0.848219i	$-0.322325\pi$
$757$	29.1450			1.05929			0.529646	+	0.848219i	$0.322325\pi$
$758$		0			0
$759$	8.97760	−	22.0035i	0.325866	−	0.798677i
$760$		0			0
$761$	−17.2923	−	6.29388i	−0.626846	−	0.228153i	0.00901218	−	0.999959i	$-0.497131\pi$
$761$	−17.2923	−	6.29388i	−0.626846	−	0.228153i	−0.635858	+	0.771806i	$0.719354\pi$
$762$		0			0
$763$	2.04176	−	11.5794i	0.0739167	−	0.419202i
$764$		0			0
$765$	0.871697	+	0.0669457i	0.0315163	+	0.00242043i
$766$		0			0
$767$	37.2986	−	13.5756i	1.34677	−	0.490185i
$768$		0			0
$769$	−6.06997	+	5.09331i	−0.218889	+	0.183669i	−0.745638	−	0.666351i	$-0.767855\pi$
$769$	−6.06997	+	5.09331i	−0.218889	+	0.183669i	0.526749	+	0.850021i	$0.323411\pi$
$770$		0			0
$771$	46.9138	+	10.1396i	1.68956	+	0.365167i
$772$		0			0
$773$	−20.0630	−	34.7502i	−0.721617	−	1.24988i	−0.960352	−	0.278792i	$-0.910066\pi$
$773$	−20.0630	−	34.7502i	−0.721617	−	1.24988i	0.238735	−	0.971085i	$-0.423267\pi$
$774$		0			0
$775$	18.6432	−	32.2910i	0.669685	−	1.15993i
$776$		0			0
$777$	−21.8138	−	13.7347i	−0.782565	−	0.492728i
$778$		0			0
$779$	−2.85428	−	16.1874i	−0.102265	−	0.579974i
$780$		0			0
$781$	0.696050	+	0.584056i	0.0249066	+	0.0208992i
$782$		0			0
$783$	26.2131	+	7.80824i	0.936781	+	0.279044i
$784$		0			0
$785$	−0.412915	−	0.346477i	−0.0147376	−	0.0123663i
$786$		0			0
$787$	−6.67124	−	37.8345i	−0.237804	−	1.34865i	−0.836627	−	0.547773i	$-0.815476\pi$
$787$	−6.67124	−	37.8345i	−0.237804	−	1.34865i	0.598823	−	0.800881i	$-0.295635\pi$
$788$		0			0
$789$	−35.8110	+	18.8843i	−1.27491	+	0.672300i
$790$		0			0
$791$	19.7703	−	34.2431i	0.702950	−	1.21754i
$792$		0			0
$793$	−0.148938	−	0.257967i	−0.00528893	−	0.00916069i
$794$		0			0
$795$	0.681972	+	2.12356i	0.0241871	+	0.0753150i
$796$		0			0
$797$	−26.6990	+	22.4031i	−0.945726	+	0.793558i	−0.978573	−	0.205902i	$-0.933987\pi$
$797$	−26.6990	+	22.4031i	−0.945726	+	0.793558i	0.0328470	+	0.999460i	$0.489543\pi$
$798$		0			0
$799$	−4.22761	+	1.53873i	−0.149562	+	0.0544362i
$800$		0			0
$801$	−18.4128	−	18.0258i	−0.650583	−	0.636912i
$802$		0			0
$803$	−0.144495	+	0.819472i	−0.00509912	+	0.0289185i
$804$		0			0
$805$	−3.06070	−	1.11400i	−0.107875	−	0.0392635i
$806$		0			0
$807$	2.23853	+	2.88547i	0.0788001	+	0.101573i
$808$		0			0
$809$	38.2217			1.34380			0.671902	−	0.740640i	$-0.265478\pi$
$809$	38.2217			1.34380			0.671902	+	0.740640i	$0.265478\pi$
$810$		0			0
$811$	−18.3939			−0.645899			−0.322949	−	0.946416i	$-0.604674\pi$
$811$	−18.3939			−0.645899			−0.322949	+	0.946416i	$0.604674\pi$
$812$		0			0
$813$	6.27388	+	8.08702i	0.220035	+	0.283624i
$814$		0			0
$815$	−5.03706	−	1.83334i	−0.176441	−	0.0642191i
$816$		0			0
$817$	3.66316	−	20.7748i	0.128158	−	0.726818i
$818$		0			0
$819$	−43.0204	+	12.0183i	−1.50325	+	0.419952i
$820$		0			0
$821$	−36.3448	+	13.2284i	−1.26844	+	0.461675i	−0.886593	−	0.462550i	$-0.846934\pi$
$821$	−36.3448	+	13.2284i	−1.26844	+	0.461675i	−0.381848	+	0.924225i	$0.624712\pi$
$822$		0			0
$823$	−11.7273	+	9.84034i	−0.408787	+	0.343013i	−0.823878	−	0.566767i	$-0.808194\pi$
$823$	−11.7273	+	9.84034i	−0.408787	+	0.343013i	0.415091	+	0.909780i	$0.363750\pi$
$824$		0			0
$825$	−5.88628	−	18.3290i	−0.204934	−	0.638134i
$826$		0			0
$827$	−10.8112	−	18.7256i	−0.375943	−	0.651152i	0.614525	−	0.788897i	$-0.289348\pi$
$827$	−10.8112	−	18.7256i	−0.375943	−	0.651152i	−0.990468	+	0.137745i	$0.956014\pi$
$828$		0			0
$829$	17.4229	−	30.1773i	0.605121	−	1.04810i	−0.386912	−	0.922117i	$-0.626458\pi$
$829$	17.4229	−	30.1773i	0.605121	−	1.04810i	0.992032	−	0.125983i	$-0.0402085\pi$
$830$		0			0
$831$	−15.8552	+	8.36100i	−0.550012	+	0.290040i
$832$		0			0
$833$	−0.371082	−	2.10451i	−0.0128572	−	0.0729169i
$834$		0			0
$835$	−1.05970	−	0.889194i	−0.0366724	−	0.0307718i
$836$		0			0
$837$	21.5693	+	32.6961i	0.745545	+	1.13014i
$838$		0			0
$839$	−26.1650	−	21.9550i	−0.903316	−	0.757972i	0.0675198	−	0.997718i	$-0.478491\pi$
$839$	−26.1650	−	21.9550i	−0.903316	−	0.757972i	−0.970836	+	0.239746i	$0.922936\pi$
$840$		0			0
$841$	−0.224478	−	1.27308i	−0.00774062	−	0.0438992i
$842$		0			0
$843$	−37.0084	−	23.3017i	−1.27464	−	0.802553i
$844$		0			0
$845$	3.33848	−	5.78242i	0.114847	−	0.198921i
$846$		0			0
$847$	6.85061	+	11.8656i	0.235390	+	0.407707i
$848$		0			0
$849$	−31.8828	−	6.89088i	−1.09422	−	0.236494i
$850$		0			0
$851$	30.2351	−	25.3702i	1.03644	−	0.869680i
$852$		0			0
$853$	33.7121	−	12.2702i	1.15428	−	0.420124i	0.307229	−	0.951636i	$-0.400598\pi$
$853$	33.7121	−	12.2702i	1.15428	−	0.420124i	0.847051	+	0.531512i	$0.178376\pi$
$854$		0			0
$855$	−0.573432	−	1.19640i	−0.0196110	−	0.0409159i
$856$		0			0
$857$	−3.83440	+	21.7459i	−0.130980	+	0.742827i	0.846594	+	0.532239i	$0.178649\pi$
$857$	−3.83440	+	21.7459i	−0.130980	+	0.742827i	−0.977575	+	0.210588i	$0.932462\pi$
$858$		0			0
$859$	2.29163	+	0.834087i	0.0781896	+	0.0284587i	0.380819	−	0.924650i	$-0.375642\pi$
$859$	2.29163	+	0.834087i	0.0781896	+	0.0284587i	−0.302629	+	0.953108i	$0.597864\pi$
$860$		0			0
$861$	12.9729	−	31.7957i	0.442114	−	1.08359i
$862$		0			0
$863$	−26.9506			−0.917410			−0.458705	−	0.888589i	$-0.651687\pi$
$863$	−26.9506			−0.917410			−0.458705	+	0.888589i	$0.651687\pi$
$864$		0			0
$865$	5.84418			0.198708
$866$		0			0
$867$	−26.4571	+	3.62614i	−0.898531	+	0.123150i
$868$		0			0
$869$	−23.3517	−	8.49933i	−0.792153	−	0.288320i
$870$		0			0
$871$	6.89499	−	39.1034i	0.233628	−	1.32497i
$872$		0			0
$873$	0.733898	+	7.47366i	0.0248387	+	0.252945i
$874$		0			0
$875$	−4.98569	+	1.81464i	−0.168547	+	0.0613461i
$876$		0			0
$877$	−12.0230	+	10.0885i	−0.405988	+	0.340665i	−0.822803	−	0.568327i	$-0.807591\pi$
$877$	−12.0230	+	10.0885i	−0.405988	+	0.340665i	0.416815	+	0.908992i	$0.363146\pi$
$878$		0			0
$879$	28.9395	−	31.9205i	0.976104	−	1.07665i
$880$		0			0
$881$	−2.65316	−	4.59541i	−0.0893873	−	0.154823i	0.817865	−	0.575410i	$-0.195158\pi$
$881$	−2.65316	−	4.59541i	−0.0893873	−	0.154823i	−0.907252	+	0.420587i	$0.861824\pi$
$882$		0			0
$883$	−21.4252	+	37.1096i	−0.721017	+	1.24884i	0.239576	+	0.970878i	$0.422992\pi$
$883$	−21.4252	+	37.1096i	−0.721017	+	1.24884i	−0.960593	+	0.277960i	$0.910342\pi$
$884$		0			0
$885$	−0.0943717	+	2.46124i	−0.00317227	+	0.0827336i
$886$		0			0
$887$	8.43065	+	47.8126i	0.283074	+	1.60539i	0.712086	+	0.702092i	$0.247751\pi$
$887$	8.43065	+	47.8126i	0.283074	+	1.60539i	−0.429012	+	0.903299i	$0.641138\pi$
$888$		0			0
$889$	−7.75742	−	6.50924i	−0.260175	−	0.218313i
$890$		0			0
$891$	19.9862	+	3.08806i	0.669562	+	0.103454i
$892$		0			0
$893$	5.22999	+	4.38848i	0.175015	+	0.146855i
$894$		0			0
$895$	−1.03240	−	5.85504i	−0.0345094	−	0.195713i
$896$		0			0
$897$	2.62046	−	68.3421i	0.0874944	−	2.28188i
$898$		0			0
$899$	−19.8397	+	34.3634i	−0.661692	+	1.14608i
$900$		0			0
$901$	3.49559	+	6.05455i	0.116455	+	0.201706i
$902$		0			0
$903$	29.6018	−	32.6510i	0.985085	−	1.08656i
$904$		0			0
$905$	0.162276	−	0.136166i	0.00539424	−	0.00452631i
$906$		0			0
$907$	−19.7538	+	7.18980i	−0.655915	+	0.238733i	−0.648472	−	0.761239i	$-0.724591\pi$
$907$	−19.7538	+	7.18980i	−0.655915	+	0.238733i	−0.00744320	+	0.999972i	$0.502369\pi$
$908$		0			0
$909$	39.9402	+	18.1106i	1.32473	+	0.600692i
$910$		0			0
$911$	9.74624	−	55.2737i	0.322907	−	1.83130i	−0.201083	−	0.979574i	$-0.564446\pi$
$911$	9.74624	−	55.2737i	0.322907	−	1.83130i	0.523990	−	0.851724i	$-0.324443\pi$
$912$		0			0
$913$	17.0227	+	6.19577i	0.563370	+	0.205050i
$914$		0			0
$915$	0.0183130	−	0.00250993i	0.000605409	−	8.29756e-5i
$916$		0			0
$917$	−13.3145			−0.439683
$918$		0			0
$919$	−31.9396			−1.05359			−0.526795	−	0.849992i	$-0.676607\pi$
$919$	−31.9396			−1.05359			−0.526795	+	0.849992i	$0.676607\pi$
$920$		0			0
$921$	10.8109	−	26.4969i	0.356233	−	0.873103i
$922$		0			0
$923$	2.45726	+	0.894369i	0.0808817	+	0.0294385i
$924$		0			0
$925$	5.55202	−	31.4871i	0.182549	−	1.03529i
$926$		0			0
$927$	7.70196	−	11.2519i	0.252966	−	0.369562i
$928$		0			0
$929$	32.8158	−	11.9440i	1.07665	−	0.391869i	0.257992	−	0.966147i	$-0.416939\pi$
$929$	32.8158	−	11.9440i	1.07665	−	0.391869i	0.818661	+	0.574278i	$0.194717\pi$
$930$		0			0
$931$	−2.48422	+	2.08451i	−0.0814171	+	0.0683171i
$932$		0			0
$933$	49.5066	+	10.6999i	1.62077	+	0.350300i
$934$		0			0
$935$	0.327417	+	0.567103i	0.0107077	+	0.0185463i
$936$		0			0
$937$	0.485981	−	0.841744i	0.0158763	−	0.0274986i	−0.857978	−	0.513686i	$-0.828280\pi$
$937$	0.485981	−	0.841744i	0.0158763	−	0.0274986i	0.873854	+	0.486188i	$0.161613\pi$
$938$		0			0
$939$	−23.9505	−	15.0800i	−0.781596	−	0.492118i
$940$		0			0
$941$	−2.66422	−	15.1096i	−0.0868512	−	0.492558i	−0.996942	−	0.0781482i	$-0.975099\pi$
$941$	−2.66422	−	15.1096i	−0.0868512	−	0.492558i	0.910091	−	0.414409i	$-0.136012\pi$
$942$		0			0
$943$	40.2786	+	33.7977i	1.31165	+	1.10061i
$944$		0			0
$945$	0.317979	−	2.75348i	0.0103438	−	0.0895707i
$946$		0			0
$947$	25.2384	+	21.1776i	0.820139	+	0.688178i	0.953005	−	0.302956i	$-0.0979735\pi$
$947$	25.2384	+	21.1776i	0.820139	+	0.688178i	−0.132866	+	0.991134i	$0.542418\pi$
$948$		0			0
$949$	0.415845	+	2.35837i	0.0134989	+	0.0765561i
$950$		0			0
$951$	−18.0819	+	9.53516i	−0.586344	+	0.309199i
$952$		0			0
$953$	24.2827	−	42.0589i	0.786595	−	1.36242i	−0.141447	−	0.989946i	$-0.545176\pi$
$953$	24.2827	−	42.0589i	0.786595	−	1.36242i	0.928042	−	0.372476i	$-0.121491\pi$
$954$		0			0
$955$	−1.52226	−	2.63663i	−0.0492591	−	0.0853193i
$956$		0			0
$957$	6.26405	+	19.5053i	0.202488	+	0.630518i
$958$		0			0
$959$	−27.4924	+	23.0688i	−0.887775	+	0.744931i
$960$		0			0
$961$	−24.2673	+	8.83258i	−0.782817	+	0.284922i
$962$		0			0
$963$	5.10604	−	19.8987i	0.164540	−	0.641228i
$964$		0			0
$965$	0.658367	−	3.73378i	0.0211936	−	0.120195i
$966$		0			0
$967$	35.5287	+	12.9314i	1.14252	+	0.415845i	0.842825	−	0.538188i	$-0.180891\pi$
$967$	35.5287	+	12.9314i	1.14252	+	0.415845i	0.299700	+	0.954033i	$0.403113\pi$
$968$		0			0
$969$	−2.54910	−	3.28579i	−0.0818889	−	0.105555i
$970$		0			0
$971$	−61.8689			−1.98547			−0.992734	−	0.120332i	$-0.961604\pi$
$971$	−61.8689			−1.98547			−0.992734	+	0.120332i	$0.961604\pi$
$972$		0			0
$973$	2.00161			0.0641685
$974$		0			0
$975$	−33.9600	−	43.7743i	−1.08759	−	1.40190i
$976$		0			0
$977$	13.0796	+	4.76060i	0.418455	+	0.152305i	0.542662	−	0.839951i	$-0.317416\pi$
$977$	13.0796	+	4.76060i	0.418455	+	0.152305i	−0.124207	+	0.992256i	$0.539639\pi$
$978$		0			0
$979$	3.35143	−	19.0069i	0.107112	−	0.607464i
$980$		0			0
$981$	−3.80790	+	14.8397i	−0.121577	+	0.473797i
$982$		0			0
$983$	−19.6920	+	7.16729i	−0.628076	+	0.228601i	−0.636394	−	0.771364i	$-0.719575\pi$
$983$	−19.6920	+	7.16729i	−0.628076	+	0.228601i	0.00831755	+	0.999965i	$0.497352\pi$
$984$		0			0
$985$	0.625165	−	0.524576i	0.0199194	−	0.0167144i
$986$		0			0
$987$	4.36127	+	13.5804i	0.138821	+	0.432268i
$988$		0			0
$989$	33.7403	+	58.4400i	1.07288	+	1.85828i
$990$		0			0
$991$	11.6607	−	20.1970i	0.370415	−	0.641578i	−0.619214	−	0.785222i	$-0.712549\pi$
$991$	11.6607	−	20.1970i	0.370415	−	0.641578i	0.989629	+	0.143644i	$0.0458820\pi$
$992$		0			0
$993$	−2.12958	+	1.12300i	−0.0675801	+	0.0356372i
$994$		0			0
$995$	0.162253	+	0.920183i	0.00514377	+	0.0291718i
$996$		0			0
$997$	−19.9947	−	16.7775i	−0.633239	−	0.531350i	0.268695	−	0.963225i	$-0.413408\pi$
$997$	−19.9947	−	16.7775i	−0.633239	−	0.531350i	−0.901933	+	0.431875i	$0.857852\pi$
$998$		0			0
$999$	26.9692	+	20.0199i	0.853267	+	0.633403i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.b.97.3	✓	54
4.3	odd	2		864.2.y.c.97.7	yes	54
27.22	even	9	inner	864.2.y.b.481.3	yes	54
108.103	odd	18		864.2.y.c.481.7	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.b.97.3	✓	54	1.1	even	1	trivial
864.2.y.b.481.3	yes	54	27.22	even	9	inner
864.2.y.c.97.7	yes	54	4.3	odd	2
864.2.y.c.481.7	yes	54	108.103	odd	18

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06169 - 1.36851i) q^{3} +(0.217711 + 0.0792403i) q^{5} +(0.399809 - 2.26743i) q^{7} +(-0.745646 + 2.90586i) q^{9} +O(q^{10})\)	\(q+(-1.06169 - 1.36851i) q^{3} +(0.217711 + 0.0792403i) q^{5} +(0.399809 - 2.26743i) q^{7} +(-0.745646 + 2.90586i) q^{9} +(-2.11152 + 0.768532i) q^{11} +(-4.95385 + 4.15677i) q^{13} +(-0.122699 - 0.382068i) q^{15} +(-0.628922 - 1.08932i) q^{17} +(-0.954408 + 1.65308i) q^{19} +(-3.52747 + 1.86015i) q^{21} +(-1.06030 - 6.01325i) q^{23} +(-3.78910 - 3.17944i) q^{25} +(4.76834 - 2.06468i) q^{27} +(4.03228 + 3.38349i) q^{29} +(1.30900 + 7.42370i) q^{31} +(3.29352 + 2.07371i) q^{33} +(0.266715 - 0.461963i) q^{35} +(3.23198 + 5.59795i) q^{37} +(10.9480 + 2.36621i) q^{39} +(-6.59653 + 5.53515i) q^{41} +(-10.3850 + 3.77983i) q^{43} +(-0.392596 + 0.573552i) q^{45} +(0.621088 - 3.52236i) q^{47} +(1.59646 + 0.581064i) q^{49} +(-0.823036 + 2.01721i) q^{51} -5.55807 q^{53} -0.520601 q^{55} +(3.27554 - 0.448937i) q^{57} +(-5.76771 - 2.09927i) q^{59} +(-0.00799863 + 0.0453625i) q^{61} +(6.29071 + 2.85249i) q^{63} +(-1.40789 + 0.512430i) q^{65} +(-4.70358 + 3.94677i) q^{67} +(-7.10350 + 7.83522i) q^{69} +(-0.202184 - 0.350193i) q^{71} +(0.185158 - 0.320703i) q^{73} +(-0.328256 + 8.56099i) q^{75} +(0.898386 + 5.09500i) q^{77} +(8.47182 + 7.10870i) q^{79} +(-7.88802 - 4.33349i) q^{81} +(-6.17571 - 5.18204i) q^{83} +(-0.0506048 - 0.286994i) q^{85} +(0.349323 - 9.11042i) q^{87} +(-4.29457 + 7.43842i) q^{89} +(7.44459 + 12.8944i) q^{91} +(8.76967 - 9.67301i) q^{93} +(-0.338776 + 0.284267i) q^{95} +(2.35224 - 0.856146i) q^{97} +(-0.658794 - 6.70884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q+O(q^{10}) \) 54 * q	\( 54 q - 9 q^{11} + 12 q^{17} + 18 q^{19} + 12 q^{21} - 21 q^{27} + 6 q^{29} + 36 q^{31} - 9 q^{33} + 24 q^{39} + 3 q^{41} - 21 q^{43} + 42 q^{45} - 18 q^{49} + 24 q^{51} + 36 q^{53} - 72 q^{55} + 39 q^{57} + 18 q^{59} - 18 q^{61} - 30 q^{63} + 48 q^{65} - 27 q^{67} + 24 q^{69} - 84 q^{75} + 36 q^{77} + 72 q^{79} + 36 q^{81} + 6 q^{87} + 33 q^{89} + 36 q^{91} + 72 q^{93} + 36 q^{95} + 9 q^{97} + 120 q^{99}+O(q^{100}) \) 54 * q - 9 * q^11 + 12 * q^17 + 18 * q^19 + 12 * q^21 - 21 * q^27 + 6 * q^29 + 36 * q^31 - 9 * q^33 + 24 * q^39 + 3 * q^41 - 21 * q^43 + 42 * q^45 - 18 * q^49 + 24 * q^51 + 36 * q^53 - 72 * q^55 + 39 * q^57 + 18 * q^59 - 18 * q^61 - 30 * q^63 + 48 * q^65 - 27 * q^67 + 24 * q^69 - 84 * q^75 + 36 * q^77 + 72 * q^79 + 36 * q^81 + 6 * q^87 + 33 * q^89 + 36 * q^91 + 72 * q^93 + 36 * q^95 + 9 * q^97 + 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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