LMFDB - Embedded newform 384.2.o.a.47.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(47,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 4]))

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

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

chi := DirichletCharacter("384.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.o (of order $8$, degree $4$, not 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			47.10
Character	$\chi$	$=$	384.47
Dual form			384.2.o.a.335.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02188 - 1.39848i) q^{3} +(3.14689 - 1.30348i) q^{5} +(-0.663471 - 0.663471i) q^{7} +(-0.911503 - 2.85817i) q^{9} +O(q^{10})$	\(q+(1.02188 - 1.39848i) q^{3} +(3.14689 - 1.30348i) q^{5} +(-0.663471 - 0.663471i) q^{7} +(-0.911503 - 2.85817i) q^{9} +(1.91929 - 0.794997i) q^{11} +(-2.31672 + 5.59306i) q^{13} +(1.39286 - 5.73287i) q^{15} -2.24987 q^{17} +(-3.08841 - 1.27926i) q^{19} +(-1.60584 + 0.249861i) q^{21} +(4.32171 + 4.32171i) q^{23} +(4.66830 - 4.66830i) q^{25} +(-4.92856 - 1.64600i) q^{27} +(-0.546766 + 1.32001i) q^{29} +2.34273i q^{31} +(0.849507 - 3.49649i) q^{33} +(-2.95269 - 1.22305i) q^{35} +(-0.324682 - 0.783851i) q^{37} +(5.45437 + 8.95535i) q^{39} +(4.73908 - 4.73908i) q^{41} +(-0.951664 - 2.29752i) q^{43} +(-6.59398 - 7.80622i) q^{45} -3.02812i q^{47} -6.11961i q^{49} +(-2.29911 + 3.14640i) q^{51} +(3.49549 + 8.43885i) q^{53} +(5.00353 - 5.00353i) q^{55} +(-4.94502 + 3.01183i) q^{57} +(3.11165 + 7.51220i) q^{59} +(-1.01639 - 0.421005i) q^{61} +(-1.29156 + 2.50107i) q^{63} +20.6205i q^{65} +(-3.46052 + 8.35443i) q^{67} +(10.4601 - 1.62755i) q^{69} +(0.167408 - 0.167408i) q^{71} +(3.86922 + 3.86922i) q^{73} +(-1.75807 - 11.2990i) q^{75} +(-1.80085 - 0.745938i) q^{77} -2.44740 q^{79} +(-7.33832 + 5.21047i) q^{81} +(-5.17660 + 12.4974i) q^{83} +(-7.08008 + 2.93267i) q^{85} +(1.28728 + 2.11354i) q^{87} +(-6.63254 - 6.63254i) q^{89} +(5.24791 - 2.17376i) q^{91} +(3.27627 + 2.39400i) q^{93} -11.3864 q^{95} +4.48787 q^{97} +(-4.02168 - 4.76103i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{3} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 56 * q + 4 * q^3 + 8 * q^7 - 4 * q^9	$ 56 q + 4 q^{3} + 8 q^{7} - 4 q^{9} - 8 q^{13} + 8 q^{15} + 8 q^{19} - 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} - 8 q^{37} + 28 q^{39} + 8 q^{43} - 4 q^{45} + 16 q^{51} - 24 q^{55} - 4 q^{57} - 40 q^{61} - 56 q^{67} - 4 q^{69} - 8 q^{73} - 16 q^{75} - 16 q^{79} - 48 q^{85} - 52 q^{87} - 40 q^{91} + 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) $ 56 * q + 4 * q^3 + 8 * q^7 - 4 * q^9 - 8 * q^13 + 8 * q^15 + 8 * q^19 - 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 - 8 * q^37 + 28 * q^39 + 8 * q^43 - 4 * q^45 + 16 * q^51 - 24 * q^55 - 4 * q^57 - 40 * q^61 - 56 * q^67 - 4 * q^69 - 8 * q^73 - 16 * q^75 - 16 * q^79 - 48 * q^85 - 52 * q^87 - 40 * q^91 + 8 * q^93 - 16 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{3}{8}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.02188	−	1.39848i	0.589985	−	0.807414i
$3$	1.02188	−	1.39848i	0.589985	−	0.807414i
$4$		0			0
$5$	3.14689	−	1.30348i	1.40733	−	0.582935i	0.455687	−	0.890140i	$-0.349394\pi$
$5$	3.14689	−	1.30348i	1.40733	−	0.582935i	0.951644	+	0.307205i	$0.0993936\pi$
$6$		0			0
$7$	−0.663471	−	0.663471i	−0.250769	−	0.250769i	0.570517	−	0.821286i	$-0.306743\pi$
$7$	−0.663471	−	0.663471i	−0.250769	−	0.250769i	−0.821286	+	0.570517i	$0.806743\pi$
$8$		0			0
$9$	−0.911503	−	2.85817i	−0.303834	−	0.952725i
$10$		0			0
$11$	1.91929	−	0.794997i	0.578689	−	0.239701i	−0.0740873	−	0.997252i	$-0.523604\pi$
$11$	1.91929	−	0.794997i	0.578689	−	0.239701i	0.652776	+	0.757551i	$0.273604\pi$
$12$		0			0
$13$	−2.31672	+	5.59306i	−0.642543	+	1.55123i	0.180696	+	0.983539i	$0.442165\pi$
$13$	−2.31672	+	5.59306i	−0.642543	+	1.55123i	−0.823238	+	0.567696i	$0.807835\pi$
$14$		0			0
$15$	1.39286	−	5.73287i	0.359634	−	1.48022i
$16$		0			0
$17$	−2.24987			−0.545673			−0.272837	−	0.962060i	$-0.587962\pi$
$17$	−2.24987			−0.545673			−0.272837	+	0.962060i	$0.587962\pi$
$18$		0			0
$19$	−3.08841	−	1.27926i	−0.708530	−	0.293483i	−0.000833646	−	1.00000i	$-0.500265\pi$
$19$	−3.08841	−	1.27926i	−0.708530	−	0.293483i	−0.707696	+	0.706517i	$0.750265\pi$
$20$		0			0
$21$	−1.60584	+	0.249861i	−0.350424	+	0.0545242i
$22$		0			0
$23$	4.32171	+	4.32171i	0.901140	+	0.901140i	0.995535	−	0.0943951i	$-0.0300917\pi$
$23$	4.32171	+	4.32171i	0.901140	+	0.901140i	−0.0943951	+	0.995535i	$0.530092\pi$
$24$		0			0
$25$	4.66830	−	4.66830i	0.933659	−	0.933659i
$26$		0			0
$27$	−4.92856	−	1.64600i	−0.948501	−	0.316774i
$28$		0			0
$29$	−0.546766	+	1.32001i	−0.101532	+	0.245120i	−0.966480	−	0.256741i	$-0.917351\pi$
$29$	−0.546766	+	1.32001i	−0.101532	+	0.245120i	0.864948	+	0.501861i	$0.167351\pi$
$30$		0			0
$31$			2.34273i			0.420767i	0.977619	+	0.210384i	$0.0674713\pi$
$31$			2.34273i			0.420767i	−0.977619	+	0.210384i	$0.932529\pi$
$32$		0			0
$33$	0.849507	−	3.49649i	0.147880	−	0.608661i
$34$		0			0
$35$	−2.95269	−	1.22305i	−0.499096	−	0.206732i
$36$		0			0
$37$	−0.324682	−	0.783851i	−0.0533774	−	0.128864i	0.894941	−	0.446184i	$-0.147217\pi$
$37$	−0.324682	−	0.783851i	−0.0533774	−	0.128864i	−0.948319	+	0.317319i	$0.897217\pi$
$38$		0			0
$39$	5.45437	+	8.95535i	0.873398	+	1.43400i
$40$		0			0
$41$	4.73908	−	4.73908i	0.740120	−	0.740120i	−0.232481	−	0.972601i	$-0.574684\pi$
$41$	4.73908	−	4.73908i	0.740120	−	0.740120i	0.972601	+	0.232481i	$0.0746843\pi$
$42$		0			0
$43$	−0.951664	−	2.29752i	−0.145127	−	0.350369i	0.834555	−	0.550925i	$-0.185725\pi$
$43$	−0.951664	−	2.29752i	−0.145127	−	0.350369i	−0.979682	+	0.200556i	$0.935725\pi$
$44$		0			0
$45$	−6.59398	−	7.80622i	−0.982973	−	1.16368i
$46$		0			0
$47$		−	3.02812i		−	0.441696i	−0.975308	−	0.220848i	$-0.929117\pi$
$47$		−	3.02812i		−	0.441696i	0.975308	−	0.220848i	$-0.0708825\pi$
$48$		0			0
$49$		−	6.11961i		−	0.874230i
$50$		0			0
$51$	−2.29911	+	3.14640i	−0.321939	+	0.440584i
$52$		0			0
$53$	3.49549	+	8.43885i	0.480142	+	1.15916i	0.959541	+	0.281568i	$0.0908545\pi$
$53$	3.49549	+	8.43885i	0.480142	+	1.15916i	−0.479399	+	0.877597i	$0.659145\pi$
$54$		0			0
$55$	5.00353	−	5.00353i	0.674676	−	0.674676i
$56$		0			0
$57$	−4.94502	+	3.01183i	−0.654984	+	0.398926i
$58$		0			0
$59$	3.11165	+	7.51220i	0.405103	+	0.978005i	0.986407	+	0.164318i	$0.0525425\pi$
$59$	3.11165	+	7.51220i	0.405103	+	0.978005i	−0.581305	+	0.813686i	$0.697458\pi$
$60$		0			0
$61$	−1.01639	−	0.421005i	−0.130136	−	0.0539041i	0.316665	−	0.948537i	$-0.397437\pi$
$61$	−1.01639	−	0.421005i	−0.130136	−	0.0539041i	−0.446801	+	0.894633i	$0.647437\pi$
$62$		0			0
$63$	−1.29156	+	2.50107i	−0.162721	+	0.315106i
$64$		0			0
$65$			20.6205i			2.55766i
$66$		0			0
$67$	−3.46052	+	8.35443i	−0.422770	+	1.02066i	0.558757	+	0.829331i	$0.311278\pi$
$67$	−3.46052	+	8.35443i	−0.422770	+	1.02066i	−0.981527	+	0.191325i	$0.938722\pi$
$68$		0			0
$69$	10.4601	−	1.62755i	1.25925	−	0.195933i
$70$		0			0
$71$	0.167408	−	0.167408i	0.0198677	−	0.0198677i	−0.697103	−	0.716971i	$-0.745528\pi$
$71$	0.167408	−	0.167408i	0.0198677	−	0.0198677i	0.716971	+	0.697103i	$0.245528\pi$
$72$		0			0
$73$	3.86922	+	3.86922i	0.452858	+	0.452858i	0.896302	−	0.443444i	$-0.146244\pi$
$73$	3.86922	+	3.86922i	0.452858	+	0.452858i	−0.443444	+	0.896302i	$0.646244\pi$
$74$		0			0
$75$	−1.75807	−	11.2990i	−0.203004	−	1.30469i
$76$		0			0
$77$	−1.80085	−	0.745938i	−0.205226	−	0.0850075i
$78$		0			0
$79$	−2.44740			−0.275354			−0.137677	−	0.990477i	$-0.543964\pi$
$79$	−2.44740			−0.275354			−0.137677	+	0.990477i	$0.543964\pi$
$80$		0			0
$81$	−7.33832	+	5.21047i	−0.815369	+	0.578941i
$82$		0			0
$83$	−5.17660	+	12.4974i	−0.568206	+	1.37177i	0.334860	+	0.942268i	$0.391311\pi$
$83$	−5.17660	+	12.4974i	−0.568206	+	1.37177i	−0.903066	+	0.429502i	$0.858689\pi$
$84$		0			0
$85$	−7.08008	+	2.93267i	−0.767943	+	0.318092i
$86$		0			0
$87$	1.28728	+	2.11354i	0.138011	+	0.226595i
$88$		0			0
$89$	−6.63254	−	6.63254i	−0.703048	−	0.703048i	0.262016	−	0.965064i	$-0.415613\pi$
$89$	−6.63254	−	6.63254i	−0.703048	−	0.703048i	−0.965064	+	0.262016i	$0.915613\pi$
$90$		0			0
$91$	5.24791	−	2.17376i	0.550130	−	0.227871i
$92$		0			0
$93$	3.27627	+	2.39400i	0.339733	+	0.248246i
$94$		0			0
$95$	−11.3864			−1.16822
$96$		0			0
$97$	4.48787			0.455674			0.227837	−	0.973699i	$-0.426835\pi$
$97$	4.48787			0.455674			0.227837	+	0.973699i	$0.426835\pi$
$98$		0			0
$99$	−4.02168	−	4.76103i	−0.404194	−	0.478502i
$100$		0			0
$101$	−12.6091	+	5.22285i	−1.25465	+	0.519693i	−0.908263	−	0.418399i	$-0.862591\pi$
$101$	−12.6091	+	5.22285i	−1.25465	+	0.519693i	−0.346386	+	0.938092i	$0.612591\pi$
$102$		0			0
$103$	−5.37192	−	5.37192i	−0.529311	−	0.529311i	0.391056	−	0.920367i	$-0.372110\pi$
$103$	−5.37192	−	5.37192i	−0.529311	−	0.529311i	−0.920367	+	0.391056i	$0.872110\pi$
$104$		0			0
$105$	−4.72772	+	2.87948i	−0.461378	+	0.281008i
$106$		0			0
$107$	13.4838	−	5.58517i	1.30353	−	0.539939i	0.380538	−	0.924765i	$-0.375739\pi$
$107$	13.4838	−	5.58517i	1.30353	−	0.539939i	0.922989	+	0.384826i	$0.125739\pi$
$108$		0			0
$109$	−1.82205	+	4.39883i	−0.174521	+	0.421331i	−0.986801	−	0.161936i	$-0.948226\pi$
$109$	−1.82205	+	4.39883i	−0.174521	+	0.421331i	0.812280	+	0.583268i	$0.198226\pi$
$110$		0			0
$111$	−1.42799	−	0.346944i	−0.135539	−	0.0329305i
$112$		0			0
$113$	5.85162			0.550475			0.275237	−	0.961376i	$-0.411244\pi$
$113$	5.85162			0.550475			0.275237	+	0.961376i	$0.411244\pi$
$114$		0			0
$115$	19.2332	+	7.96666i	1.79351	+	0.742895i
$116$		0			0
$117$	18.0976	+	1.52350i	1.67313	+	0.140848i
$118$		0			0
$119$	1.49272	+	1.49272i	0.136838	+	0.136838i
$120$		0			0
$121$	−4.72651	+	4.72651i	−0.429683	+	0.429683i
$122$		0			0
$123$	−1.78472	−	11.4703i	−0.160923	−	1.03424i
$124$		0			0
$125$	2.08814	−	5.04121i	0.186769	−	0.450899i
$126$		0			0
$127$		−	10.2914i		−	0.913216i	−0.889668	−	0.456608i	$-0.849064\pi$
$127$		−	10.2914i		−	0.913216i	0.889668	−	0.456608i	$-0.150936\pi$
$128$		0			0
$129$	−4.18553	−	1.01692i	−0.368516	−	0.0895345i
$130$		0			0
$131$	−16.3968	−	6.79177i	−1.43259	−	0.593400i	−0.474603	−	0.880200i	$-0.657408\pi$
$131$	−16.3968	−	6.79177i	−1.43259	−	0.593400i	−0.957990	+	0.286800i	$0.907408\pi$
$132$		0			0
$133$	1.20032	+	2.89782i	0.104081	+	0.251273i
$134$		0			0
$135$	−17.6551	+	1.24450i	−1.51951	+	0.107110i
$136$		0			0
$137$	8.43673	−	8.43673i	0.720799	−	0.720799i	−0.247969	−	0.968768i	$-0.579763\pi$
$137$	8.43673	−	8.43673i	0.720799	−	0.720799i	0.968768	+	0.247969i	$0.0797631\pi$
$138$		0			0
$139$	7.74040	+	18.6870i	0.656532	+	1.58501i	0.803124	+	0.595812i	$0.203169\pi$
$139$	7.74040	+	18.6870i	0.656532	+	1.58501i	−0.146592	+	0.989197i	$0.546831\pi$
$140$		0			0
$141$	−4.23477	−	3.09439i	−0.356632	−	0.260594i
$142$		0			0
$143$			12.5765i			1.05170i
$144$		0			0
$145$			4.86662i			0.404151i
$146$		0			0
$147$	−8.55817	−	6.25354i	−0.705866	−	0.515783i
$148$		0			0
$149$	−4.26837	−	10.3048i	−0.349678	−	0.844198i	−0.996658	−	0.0816908i	$-0.973968\pi$
$149$	−4.26837	−	10.3048i	−0.349678	−	0.844198i	0.646979	−	0.762508i	$-0.276032\pi$
$150$		0			0
$151$	−12.1716	+	12.1716i	−0.990514	+	0.990514i	−0.999955	−	0.00944142i	$-0.996995\pi$
$151$	−12.1716	+	12.1716i	−0.990514	+	0.990514i	0.00944142	+	0.999955i	$0.496995\pi$
$152$		0			0
$153$	2.05076	+	6.43052i	0.165794	+	0.519877i
$154$		0			0
$155$	3.05371	+	7.37231i	0.245280	+	0.592159i
$156$		0			0
$157$	−10.1467	−	4.20290i	−0.809795	−	0.335428i	−0.0609231	−	0.998142i	$-0.519404\pi$
$157$	−10.1467	−	4.20290i	−0.809795	−	0.335428i	−0.748872	+	0.662714i	$0.769404\pi$
$158$		0			0
$159$	15.3736	+	3.73516i	1.21920	+	0.296217i
$160$		0			0
$161$		−	5.73467i		−	0.451955i
$162$		0			0
$163$	4.03936	−	9.75187i	0.316387	−	0.763826i	−0.683053	−	0.730369i	$-0.739348\pi$
$163$	4.03936	−	9.75187i	0.316387	−	0.763826i	0.999440	−	0.0334571i	$-0.0106517\pi$
$164$		0			0
$165$	−1.88432	−	12.1104i	−0.146694	−	0.942792i
$166$		0			0
$167$	12.8761	−	12.8761i	0.996385	−	0.996385i	−0.00360853	−	0.999993i	$-0.501149\pi$
$167$	12.8761	−	12.8761i	0.996385	−	0.996385i	0.999993	+	0.00360853i	$0.00114863\pi$
$168$		0			0
$169$	−16.7227	−	16.7227i	−1.28636	−	1.28636i
$170$		0			0
$171$	−0.841256	+	9.99326i	−0.0643325	+	0.764204i
$172$		0			0
$173$	9.91155	+	4.10550i	0.753561	+	0.312135i	0.726194	−	0.687490i	$-0.241288\pi$
$173$	9.91155	+	4.10550i	0.753561	+	0.312135i	0.0273673	+	0.999625i	$0.491288\pi$
$174$		0			0
$175$	−6.19456			−0.468265
$176$		0			0
$177$	13.6854	+	3.32501i	1.02866	+	0.249923i
$178$		0			0
$179$	9.52280	−	22.9901i	0.711768	−	1.71836i	0.0162316	−	0.999868i	$-0.494833\pi$
$179$	9.52280	−	22.9901i	0.711768	−	1.71836i	0.695536	−	0.718491i	$-0.255167\pi$
$180$		0			0
$181$	11.0607	−	4.58151i	0.822139	−	0.340541i	0.0683528	−	0.997661i	$-0.478226\pi$
$181$	11.0607	−	4.58151i	0.822139	−	0.340541i	0.753786	+	0.657120i	$0.228226\pi$
$182$		0			0
$183$	−1.62741	+	0.991192i	−0.120301	+	0.0732710i
$184$		0			0
$185$	−2.04347	−	2.04347i	−0.150239	−	0.150239i
$186$		0			0
$187$	−4.31816	+	1.78864i	−0.315775	+	0.130798i
$188$		0			0
$189$	2.17788	+	4.36203i	0.158417	+	0.317291i
$190$		0			0
$191$	0.133706			0.00967461			0.00483731	−	0.999988i	$-0.498460\pi$
$191$	0.133706			0.00967461			0.00483731	+	0.999988i	$0.498460\pi$
$192$		0			0
$193$	7.48776			0.538981			0.269490	−	0.963003i	$-0.413145\pi$
$193$	7.48776			0.538981			0.269490	+	0.963003i	$0.413145\pi$
$194$		0			0
$195$	28.8374	+	21.0718i	2.06509	+	1.50898i
$196$		0			0
$197$	4.23540	−	1.75436i	0.301759	−	0.124993i	−0.226666	−	0.973973i	$-0.572783\pi$
$197$	4.23540	−	1.75436i	0.301759	−	0.124993i	0.528425	+	0.848980i	$0.322783\pi$
$198$		0			0
$199$	−3.74082	−	3.74082i	−0.265179	−	0.265179i	0.561975	−	0.827154i	$-0.310042\pi$
$199$	−3.74082	−	3.74082i	−0.265179	−	0.265179i	−0.827154	+	0.561975i	$0.810042\pi$
$200$		0			0
$201$	8.14727	+	13.3767i	0.574664	+	0.943522i
$202$		0			0
$203$	1.23855	−	0.513025i	0.0869293	−	0.0360073i
$204$		0			0
$205$	8.73604	−	21.0907i	0.610152	−	1.47304i
$206$		0			0
$207$	8.41296	−	16.2915i	0.584741	−	1.13234i
$208$		0			0
$209$	−6.94457			−0.480366
$210$		0			0
$211$	−0.564367	−	0.233768i	−0.0388526	−	0.0160933i	0.363173	−	0.931722i	$-0.381694\pi$
$211$	−0.564367	−	0.233768i	−0.0388526	−	0.0160933i	−0.402025	+	0.915629i	$0.631694\pi$
$212$		0			0
$213$	−0.0630455	−	0.405189i	−0.00431980	−	0.0277631i
$214$		0			0
$215$	−5.98956	−	5.98956i	−0.408485	−	0.408485i
$216$		0			0
$217$	1.55434	−	1.55434i	0.105515	−	0.105515i
$218$		0			0
$219$	9.36493	−	1.45714i	0.632823	−	0.0984642i
$220$		0			0
$221$	5.21232	−	12.5836i	0.350618	−	0.846468i
$222$		0			0
$223$		−	10.6887i		−	0.715768i	−0.933766	−	0.357884i	$-0.883498\pi$
$223$		−	10.6887i		−	0.715768i	0.933766	−	0.357884i	$-0.116502\pi$
$224$		0			0
$225$	−17.5980	−	9.08764i	−1.17320	−	0.605842i
$226$		0			0
$227$	1.76729	+	0.732035i	0.117299	+	0.0485869i	0.440561	−	0.897723i	$-0.354780\pi$
$227$	1.76729	+	0.732035i	0.117299	+	0.0485869i	−0.323262	+	0.946309i	$0.604780\pi$
$228$		0			0
$229$	−4.83167	−	11.6647i	−0.319286	−	0.770824i	−0.999292	−	0.0376176i	$-0.988023\pi$
$229$	−4.83167	−	11.6647i	−0.319286	−	0.770824i	0.680007	−	0.733206i	$-0.261977\pi$
$230$		0			0
$231$	−2.88345	+	1.75620i	−0.189717	+	0.115549i
$232$		0			0
$233$	−6.98725	+	6.98725i	−0.457750	+	0.457750i	−0.897916	−	0.440166i	$-0.854920\pi$
$233$	−6.98725	+	6.98725i	−0.457750	+	0.457750i	0.440166	+	0.897916i	$0.354920\pi$
$234$		0			0
$235$	−3.94710	−	9.52914i	−0.257480	−	0.621613i
$236$		0			0
$237$	−2.50096	+	3.42265i	−0.162455	+	0.222325i
$238$		0			0
$239$		−	6.60970i		−	0.427546i	−0.976883	−	0.213773i	$-0.931425\pi$
$239$		−	6.60970i		−	0.427546i	0.976883	−	0.213773i	$-0.0685752\pi$
$240$		0			0
$241$			13.3092i			0.857322i	0.903466	+	0.428661i	$0.141014\pi$
$241$			13.3092i			0.857322i	−0.903466	+	0.428661i	$0.858986\pi$
$242$		0			0
$243$	−0.212173	+	15.5870i	−0.0136109	+	0.999907i
$244$		0			0
$245$	−7.97681	−	19.2577i	−0.509620	−	1.23033i
$246$		0			0
$247$	14.3100	−	14.3100i	0.910521	−	0.910521i
$248$		0			0
$249$	12.1875	+	20.0103i	0.772353	+	1.26810i
$250$		0			0
$251$	−5.55430	−	13.4093i	−0.350584	−	0.846385i	−0.996548	−	0.0830174i	$-0.973544\pi$
$251$	−5.55430	−	13.4093i	−0.350584	−	0.846385i	0.645964	−	0.763368i	$-0.276456\pi$
$252$		0			0
$253$	11.7304	+	4.85889i	0.737483	+	0.305476i
$254$		0			0
$255$	−3.13375	+	12.8982i	−0.196243	+	0.807718i
$256$		0			0
$257$		−	12.0491i		−	0.751605i	−0.926700	−	0.375803i	$-0.877367\pi$
$257$		−	12.0491i		−	0.751605i	0.926700	−	0.375803i	$-0.122633\pi$
$258$		0			0
$259$	−0.304646	+	0.735480i	−0.0189298	+	0.0457005i
$260$		0			0
$261$	4.27120	+	0.359559i	0.264380	+	0.0222562i
$262$		0			0
$263$	2.42769	−	2.42769i	0.149698	−	0.149698i	−0.628285	−	0.777983i	$-0.716243\pi$
$263$	2.42769	−	2.42769i	0.149698	−	0.149698i	0.777983	+	0.628285i	$0.216243\pi$
$264$		0			0
$265$	21.9998	+	21.9998i	1.35144	+	1.35144i
$266$		0			0
$267$	−16.0532	+	2.49780i	−0.982439	+	0.152863i
$268$		0			0
$269$	11.0872	+	4.59246i	0.675997	+	0.280007i	0.694153	−	0.719828i	$-0.255779\pi$
$269$	11.0872	+	4.59246i	0.675997	+	0.280007i	−0.0181552	+	0.999835i	$0.505779\pi$
$270$		0			0
$271$	−16.6609			−1.01208			−0.506038	−	0.862511i	$-0.668891\pi$
$271$	−16.6609			−1.01208			−0.506038	+	0.862511i	$0.668891\pi$
$272$		0			0
$273$	2.32280	−	9.56043i	0.140582	−	0.578624i
$274$		0			0
$275$	5.24854	−	12.6711i	0.316499	−	0.764097i
$276$		0			0
$277$	−26.2888	+	10.8892i	−1.57954	+	0.654267i	−0.988341	−	0.152259i	$-0.951345\pi$
$277$	−26.2888	+	10.8892i	−1.57954	+	0.654267i	−0.591199	+	0.806526i	$0.701345\pi$
$278$		0			0
$279$	6.69594	−	2.13541i	0.400875	−	0.127844i
$280$		0			0
$281$	0.109141	+	0.109141i	0.00651081	+	0.00651081i	0.710355	−	0.703844i	$-0.248535\pi$
$281$	0.109141	+	0.109141i	0.00651081	+	0.00651081i	−0.703844	+	0.710355i	$0.748535\pi$
$282$		0			0
$283$	−11.5159	+	4.77003i	−0.684547	+	0.283549i	−0.697726	−	0.716364i	$-0.745805\pi$
$283$	−11.5159	+	4.77003i	−0.684547	+	0.283549i	0.0131791	+	0.999913i	$0.495805\pi$
$284$		0			0
$285$	−11.6356	+	15.9236i	−0.689231	+	0.943235i
$286$		0			0
$287$	−6.28849			−0.371198
$288$		0			0
$289$	−11.9381			−0.702240
$290$		0			0
$291$	4.58609	−	6.27621i	0.268841	−	0.367918i
$292$		0			0
$293$	−14.6551	+	6.07035i	−0.856161	+	0.354634i	−0.767205	−	0.641402i	$-0.778353\pi$
$293$	−14.6551	+	6.07035i	−0.856161	+	0.354634i	−0.0889561	+	0.996036i	$0.528353\pi$
$294$		0			0
$295$	19.5840	+	19.5840i	1.14023	+	1.14023i
$296$		0			0
$297$	−10.7679	+	0.759024i	−0.624818	+	0.0440430i
$298$		0			0
$299$	−34.1838	+	14.1594i	−1.97690	+	0.818859i
$300$		0			0
$301$	−0.892937	+	2.15574i	−0.0514680	+	0.124255i
$302$		0			0
$303$	−5.58096	+	22.9707i	−0.320618	+	1.31963i
$304$		0			0
$305$	−3.74725			−0.214567
$306$		0			0
$307$	−17.9759	−	7.44586i	−1.02594	−	0.424958i	−0.194694	−	0.980864i	$-0.562371\pi$
$307$	−17.9759	−	7.44586i	−1.02594	−	0.424958i	−0.831245	+	0.555906i	$0.812371\pi$
$308$		0			0
$309$	−13.0020	+	2.02305i	−0.739659	+	0.115087i
$310$		0			0
$311$	−14.7567	−	14.7567i	−0.836776	−	0.836776i	0.151657	−	0.988433i	$-0.451539\pi$
$311$	−14.7567	−	14.7567i	−0.836776	−	0.836776i	−0.988433	+	0.151657i	$0.951539\pi$
$312$		0			0
$313$	−3.76309	+	3.76309i	−0.212703	+	0.212703i	−0.805415	−	0.592712i	$-0.798057\pi$
$313$	−3.76309	+	3.76309i	−0.212703	+	0.212703i	0.592712	+	0.805415i	$0.298057\pi$
$314$		0			0
$315$	−0.804289	+	9.55412i	−0.0453165	+	0.538314i
$316$		0			0
$317$	−5.65481	+	13.6519i	−0.317606	+	0.766768i	0.681774	+	0.731562i	$0.261209\pi$
$317$	−5.65481	+	13.6519i	−0.317606	+	0.766768i	−0.999380	+	0.0352055i	$0.988791\pi$
$318$		0			0
$319$			2.96816i			0.166185i
$320$		0			0
$321$	5.96812	−	24.5642i	0.333108	−	1.37104i
$322$		0			0
$323$	6.94852	+	2.87817i	0.386626	+	0.160146i
$324$		0			0
$325$	15.2949	+	36.9252i	0.848409	+	2.04824i
$326$		0			0
$327$	4.28975	+	7.04321i	0.237224	+	0.389490i
$328$		0			0
$329$	−2.00907	+	2.00907i	−0.110764	+	0.110764i
$330$		0			0
$331$	−3.87845	−	9.36340i	−0.213179	−	0.514659i	0.780730	−	0.624869i	$-0.214848\pi$
$331$	−3.87845	−	9.36340i	−0.213179	−	0.514659i	−0.993908	+	0.110210i	$0.964848\pi$
$332$		0			0
$333$	−1.94443	+	1.64248i	−0.106554	+	0.0900073i
$334$		0			0
$335$			30.8012i			1.68285i
$336$		0			0
$337$		−	18.4557i		−	1.00535i	−0.864476	−	0.502674i	$-0.832350\pi$
$337$		−	18.4557i		−	1.00535i	0.864476	−	0.502674i	$-0.167650\pi$
$338$		0			0
$339$	5.97969	−	8.18339i	0.324772	−	0.444461i
$340$		0			0
$341$	1.86247	+	4.49639i	0.100858	+	0.243493i
$342$		0			0
$343$	−8.70449	+	8.70449i	−0.469998	+	0.469998i
$344$		0			0
$345$	30.7954	−	18.7563i	1.65797	−	1.00981i
$346$		0			0
$347$	2.01715	+	4.86983i	0.108286	+	0.261426i	0.968729	−	0.248121i	$-0.0798130\pi$
$347$	2.01715	+	4.86983i	0.108286	+	0.261426i	−0.860443	+	0.509547i	$0.829813\pi$
$348$		0			0
$349$	19.0402	+	7.88672i	1.01920	+	0.422166i	0.828803	−	0.559541i	$-0.189023\pi$
$349$	19.0402	+	7.88672i	1.01920	+	0.422166i	0.190397	+	0.981707i	$0.439023\pi$
$350$		0			0
$351$	20.6243	−	23.7524i	1.10084	−	1.26781i
$352$		0			0
$353$			13.3595i			0.711053i	0.934666	+	0.355527i	$0.115699\pi$
$353$			13.3595i			0.711053i	−0.934666	+	0.355527i	$0.884301\pi$
$354$		0			0
$355$	0.308601	−	0.745029i	0.0163788	−	0.0395420i
$356$		0			0
$357$	3.61294	−	0.562156i	0.191217	−	0.0297524i
$358$		0			0
$359$	−0.514805	+	0.514805i	−0.0271704	+	0.0271704i	−0.720561	−	0.693391i	$-0.756116\pi$
$359$	−0.514805	+	0.514805i	−0.0271704	+	0.0271704i	0.693391	+	0.720561i	$0.256116\pi$
$360$		0			0
$361$	−5.53327	−	5.53327i	−0.291225	−	0.291225i
$362$		0			0
$363$	1.77999	+	11.4399i	0.0934252	+	0.600438i
$364$		0			0
$365$	17.2195	+	7.13254i	0.901308	+	0.373334i
$366$		0			0
$367$	37.5921			1.96229			0.981145	−	0.193271i	$-0.0619096\pi$
$367$	37.5921			1.96229			0.981145	+	0.193271i	$0.0619096\pi$
$368$		0			0
$369$	−17.8648	−	9.22543i	−0.930005	−	0.480257i
$370$		0			0
$371$	3.27978	−	7.91809i	0.170278	−	0.411087i
$372$		0			0
$373$	22.6229	−	9.37070i	1.17137	−	0.485196i	0.289723	−	0.957111i	$-0.406437\pi$
$373$	22.6229	−	9.37070i	1.17137	−	0.485196i	0.881644	+	0.471914i	$0.156437\pi$
$374$		0			0
$375$	−4.91620	−	8.07176i	−0.253872	−	0.416824i
$376$		0			0
$377$	−6.11619	−	6.11619i	−0.315000	−	0.315000i
$378$		0			0
$379$	14.1576	−	5.86429i	0.727229	−	0.301228i	0.0118165	−	0.999930i	$-0.496239\pi$
$379$	14.1576	−	5.86429i	0.727229	−	0.301228i	0.715413	+	0.698702i	$0.246239\pi$
$380$		0			0
$381$	−14.3924	−	10.5167i	−0.737344	−	0.538784i
$382$		0			0
$383$	16.0682			0.821048			0.410524	−	0.911850i	$-0.365346\pi$
$383$	16.0682			0.821048			0.410524	+	0.911850i	$0.365346\pi$
$384$		0			0
$385$	−6.63940			−0.338375
$386$		0			0
$387$	−5.69927	+	4.81422i	−0.289710	+	0.244721i
$388$		0			0
$389$	−31.0923	+	12.8788i	−1.57644	+	0.652983i	−0.987845	−	0.155444i	$-0.950319\pi$
$389$	−31.0923	+	12.8788i	−1.57644	+	0.652983i	−0.588596	+	0.808427i	$0.700319\pi$
$390$		0			0
$391$	−9.72329	−	9.72329i	−0.491728	−	0.491728i
$392$		0			0
$393$	−26.2538	+	15.9902i	−1.32433	+	0.806599i
$394$		0			0
$395$	−7.70170	+	3.19015i	−0.387514	+	0.160514i
$396$		0			0
$397$	−8.21223	+	19.8261i	−0.412160	+	0.995042i	0.572397	+	0.819977i	$0.306014\pi$
$397$	−8.21223	+	19.8261i	−0.412160	+	0.995042i	−0.984557	+	0.175065i	$0.943986\pi$
$398$		0			0
$399$	5.27914	+	1.28262i	0.264288	+	0.0642113i
$400$		0			0
$401$	15.2053			0.759315			0.379657	−	0.925127i	$-0.376042\pi$
$401$	15.2053			0.759315			0.379657	+	0.925127i	$0.376042\pi$
$402$		0			0
$403$	−13.1030	−	5.42745i	−0.652709	−	0.270361i
$404$		0			0
$405$	−16.3011	+	25.9621i	−0.810009	+	1.29007i
$406$		0			0
$407$	−1.24632	−	1.24632i	−0.0617777	−	0.0617777i
$408$		0			0
$409$	23.0147	−	23.0147i	1.13800	−	1.13800i	0.149193	−	0.988808i	$-0.452332\pi$
$409$	23.0147	−	23.0147i	1.13800	−	1.13800i	0.988808	−	0.149193i	$-0.0476677\pi$
$410$		0			0
$411$	−3.17725	−	20.4200i	−0.156722	−	1.00724i
$412$		0			0
$413$	2.91963	−	7.04862i	0.143666	−	0.346840i
$414$		0			0
$415$			46.0756i			2.26176i
$416$		0			0
$417$	34.0432	+	8.27113i	1.66710	+	0.405039i
$418$		0			0
$419$	10.8187	+	4.48124i	0.528527	+	0.218923i	0.630958	−	0.775817i	$-0.282662\pi$
$419$	10.8187	+	4.48124i	0.528527	+	0.218923i	−0.102431	+	0.994740i	$0.532662\pi$
$420$		0			0
$421$	−11.0208	−	26.6066i	−0.537121	−	1.29673i	−0.926724	−	0.375742i	$-0.877388\pi$
$421$	−11.0208	−	26.6066i	−0.537121	−	1.29673i	0.389603	−	0.920983i	$-0.372612\pi$
$422$		0			0
$423$	−8.65489	+	2.76014i	−0.420815	+	0.134203i
$424$		0			0
$425$	−10.5031	+	10.5031i	−0.509473	+	0.509473i
$426$		0			0
$427$	0.395024	+	0.953673i	0.0191166	+	0.0461515i
$428$		0			0
$429$	17.5880	+	12.8517i	0.849157	+	0.620488i
$430$		0			0
$431$			0.278342i			0.0134073i	0.999978	+	0.00670363i	$0.00213385\pi$
$431$			0.278342i			0.0134073i	−0.999978	+	0.00670363i	$0.997866\pi$
$432$		0			0
$433$		−	11.0862i		−	0.532769i	−0.963867	−	0.266385i	$-0.914171\pi$
$433$		−	11.0862i		−	0.532769i	0.963867	−	0.266385i	$-0.0858292\pi$
$434$		0			0
$435$	6.80588	+	4.97313i	0.326317	+	0.238443i
$436$		0			0
$437$	−7.81862	−	18.8758i	−0.374015	−	0.902953i
$438$		0			0
$439$	−18.4802	+	18.4802i	−0.882011	+	0.882011i	−0.993739	−	0.111728i	$-0.964361\pi$
$439$	−18.4802	+	18.4802i	−0.882011	+	0.882011i	0.111728	+	0.993739i	$0.464361\pi$
$440$		0			0
$441$	−17.4909	+	5.57805i	−0.832901	+	0.265621i
$442$		0			0
$443$	15.7855	+	38.1095i	0.749991	+	1.81064i	0.559251	+	0.828998i	$0.311089\pi$
$443$	15.7855	+	38.1095i	0.749991	+	1.81064i	0.190740	+	0.981641i	$0.438911\pi$
$444$		0			0
$445$	−29.5173	−	12.2265i	−1.39925	−	0.579590i
$446$		0			0
$447$	−18.7728	−	4.56103i	−0.887923	−	0.215730i
$448$		0			0
$449$		−	23.9532i		−	1.13042i	−0.824946	−	0.565211i	$-0.808795\pi$
$449$		−	23.9532i		−	1.13042i	0.824946	−	0.565211i	$-0.191205\pi$
$450$		0			0
$451$	5.32813	−	12.8632i	0.250892	−	0.605706i
$452$		0			0
$453$	4.58380	+	29.4598i	0.215366	+	1.38414i
$454$		0			0
$455$	13.6811	−	13.6811i	0.641381	−	0.641381i
$456$		0			0
$457$	−3.61836	−	3.61836i	−0.169260	−	0.169260i	0.617394	−	0.786654i	$-0.288188\pi$
$457$	−3.61836	−	3.61836i	−0.169260	−	0.169260i	−0.786654	+	0.617394i	$0.788188\pi$
$458$		0			0
$459$	11.0886	+	3.70329i	0.517572	+	0.172855i
$460$		0			0
$461$	11.0476	+	4.57608i	0.514539	+	0.213129i	0.624816	−	0.780772i	$-0.285174\pi$
$461$	11.0476	+	4.57608i	0.514539	+	0.213129i	−0.110277	+	0.993901i	$0.535174\pi$
$462$		0			0
$463$	27.8395			1.29381			0.646906	−	0.762569i	$-0.276062\pi$
$463$	27.8395			1.29381			0.646906	+	0.762569i	$0.276062\pi$
$464$		0			0
$465$	13.4306	+	3.26309i	0.622829	+	0.151322i
$466$		0			0
$467$	−15.3748	+	37.1181i	−0.711462	+	1.71762i	−0.0151469	+	0.999885i	$0.504822\pi$
$467$	−15.3748	+	37.1181i	−0.711462	+	1.71762i	−0.696315	+	0.717736i	$0.745178\pi$
$468$		0			0
$469$	7.83888	−	3.24697i	0.361966	−	0.149931i
$470$		0			0
$471$	−16.2465	+	9.89510i	−0.748597	+	0.455942i
$472$		0			0
$473$	−3.65304	−	3.65304i	−0.167967	−	0.167967i
$474$		0			0
$475$	−20.3896	+	8.44564i	−0.935538	+	0.387512i
$476$		0			0
$477$	20.9336	−	17.6827i	0.958482	−	0.809637i
$478$		0			0
$479$	−23.6720			−1.08160			−0.540800	−	0.841151i	$-0.681878\pi$
$479$	−23.6720			−1.08160			−0.540800	+	0.841151i	$0.681878\pi$
$480$		0			0
$481$	5.13632			0.234196
$482$		0			0
$483$	−8.01983	−	5.86017i	−0.364915	−	0.266647i
$484$		0			0
$485$	14.1228	−	5.84987i	0.641284	−	0.265629i
$486$		0			0
$487$	1.06704	+	1.06704i	0.0483522	+	0.0483522i	0.730869	−	0.682517i	$-0.239115\pi$
$487$	1.06704	+	1.06704i	0.0483522	+	0.0483522i	−0.682517	+	0.730869i	$0.739115\pi$
$488$		0			0
$489$	−9.51006	−	15.6143i	−0.430060	−	0.706101i
$490$		0			0
$491$	24.4454	−	10.1256i	1.10321	−	0.456964i	0.244614	−	0.969621i	$-0.421339\pi$
$491$	24.4454	−	10.1256i	1.10321	−	0.456964i	0.858594	+	0.512657i	$0.171339\pi$
$492$		0			0
$493$	1.23015	−	2.96985i	0.0554033	−	0.133755i
$494$		0			0
$495$	−18.8617	−	9.74023i	−0.847771	−	0.437791i
$496$		0			0
$497$	−0.222141			−0.00996439
$498$		0			0
$499$	−23.7276	−	9.82828i	−1.06219	−	0.439974i	−0.217963	−	0.975957i	$-0.569941\pi$
$499$	−23.7276	−	9.82828i	−1.06219	−	0.439974i	−0.844229	+	0.535983i	$0.819941\pi$
$500$		0			0
$501$	−4.84911	−	31.1650i	−0.216642	−	1.39235i
$502$		0			0
$503$	−8.35178	−	8.35178i	−0.372387	−	0.372387i	0.495959	−	0.868346i	$-0.334817\pi$
$503$	−8.35178	−	8.35178i	−0.372387	−	0.372387i	−0.868346	+	0.495959i	$0.834817\pi$
$504$		0			0
$505$	−32.8714	+	32.8714i	−1.46276	+	1.46276i
$506$		0			0
$507$	−40.4751	+	6.29772i	−1.79756	+	0.279692i
$508$		0			0
$509$	2.98703	−	7.21134i	0.132398	−	0.319637i	−0.843752	−	0.536733i	$-0.819658\pi$
$509$	2.98703	−	7.21134i	0.132398	−	0.319637i	0.976150	+	0.217096i	$0.0696584\pi$
$510$		0			0
$511$		−	5.13423i		−	0.227125i
$512$		0			0
$513$	13.1157	+	11.3884i	0.579074	+	0.502812i
$514$		0			0
$515$	−23.9070	−	9.90262i	−1.05347	−	0.436361i
$516$		0			0
$517$	−2.40734	−	5.81184i	−0.105875	−	0.255605i
$518$		0			0
$519$	15.8699	−	9.66577i	0.696612	−	0.424280i
$520$		0			0
$521$	5.48494	−	5.48494i	0.240299	−	0.240299i	−0.576675	−	0.816974i	$-0.695650\pi$
$521$	5.48494	−	5.48494i	0.240299	−	0.240299i	0.816974	+	0.576675i	$0.195650\pi$
$522$		0			0
$523$	−6.43166	−	15.5274i	−0.281237	−	0.678966i	0.718628	−	0.695394i	$-0.244770\pi$
$523$	−6.43166	−	15.5274i	−0.281237	−	0.678966i	−0.999865	+	0.0164288i	$0.994770\pi$
$524$		0			0
$525$	−6.33013	+	8.66298i	−0.276269	+	0.378083i
$526$		0			0
$527$		−	5.27084i		−	0.229601i
$528$		0			0
$529$			14.3544i			0.624106i
$530$		0			0
$531$	18.6349	−	15.7410i	0.808685	−	0.683103i
$532$		0			0
$533$	15.5268	+	37.4851i	0.672542	+	1.62366i
$534$		0			0
$535$	35.1518	−	35.1518i	1.51974	−	1.51974i
$536$		0			0
$537$	−22.4200	−	36.8107i	−0.967495	−	1.58850i
$538$		0			0
$539$	−4.86507	−	11.7453i	−0.209554	−	0.505907i
$540$		0			0
$541$	−3.57097	−	1.47914i	−0.153528	−	0.0635934i	0.304596	−	0.952482i	$-0.401478\pi$
$541$	−3.57097	−	1.47914i	−0.153528	−	0.0635934i	−0.458124	+	0.888888i	$0.651478\pi$
$542$		0			0
$543$	4.89565	−	20.1500i	0.210092	−	0.864720i
$544$		0			0
$545$			16.2176i			0.694687i
$546$		0			0
$547$	−1.97916	+	4.77812i	−0.0846228	+	0.204298i	−0.960527	−	0.278188i	$-0.910266\pi$
$547$	−1.97916	+	4.77812i	−0.0846228	+	0.204298i	0.875904	+	0.482486i	$0.160266\pi$
$548$		0			0
$549$	−0.276857	+	3.28878i	−0.0118160	+	0.140362i
$550$		0			0
$551$	3.37727	−	3.37727i	0.143877	−	0.143877i
$552$		0			0
$553$	1.62378	+	1.62378i	0.0690502	+	0.0690502i
$554$		0			0
$555$	−4.94596	+	0.769566i	−0.209944	+	0.0326663i
$556$		0			0
$557$	−30.8826	−	12.7920i	−1.30854	−	0.542014i	−0.384080	−	0.923300i	$-0.625481\pi$
$557$	−30.8826	−	12.7920i	−1.30854	−	0.542014i	−0.924457	+	0.381286i	$0.875481\pi$
$558$		0			0
$559$	15.0549			0.636755
$560$		0			0
$561$	−1.91128	+	7.86665i	−0.0806943	+	0.332130i
$562$		0			0
$563$	6.06412	−	14.6401i	0.255572	−	0.617005i	−0.743064	−	0.669221i	$-0.766628\pi$
$563$	6.06412	−	14.6401i	0.255572	−	0.617005i	0.998636	+	0.0522151i	$0.0166281\pi$
$564$		0			0
$565$	18.4144	−	7.62750i	0.774700	−	0.320891i
$566$		0			0
$567$	8.32577	+	1.41177i	0.349649	+	0.0592888i
$568$		0			0
$569$	24.5419	+	24.5419i	1.02885	+	1.02885i	0.999571	+	0.0292808i	$0.00932170\pi$
$569$	24.5419	+	24.5419i	1.02885	+	1.02885i	0.0292808	+	0.999571i	$0.490678\pi$
$570$		0			0
$571$	37.5798	−	15.5661i	1.57266	−	0.651419i	0.585435	−	0.810720i	$-0.300924\pi$
$571$	37.5798	−	15.5661i	1.57266	−	0.651419i	0.987230	+	0.159301i	$0.0509239\pi$
$572$		0			0
$573$	0.136632	−	0.186985i	0.00570788	−	0.00781142i
$574$		0			0
$575$	40.3501			1.68271
$576$		0			0
$577$	−37.6825			−1.56874			−0.784371	−	0.620292i	$-0.787014\pi$
$577$	−37.6825			−1.56874			−0.784371	+	0.620292i	$0.787014\pi$
$578$		0			0
$579$	7.65163	−	10.4715i	0.317991	−	0.435181i
$580$		0			0
$581$	11.7262	−	4.85715i	0.486485	−	0.201509i
$582$		0			0
$583$	13.4177	+	13.4177i	0.555705	+	0.555705i
$584$		0			0
$585$	58.9371	−	18.7957i	2.43675	−	0.777105i
$586$		0			0
$587$	16.1148	−	6.67499i	0.665131	−	0.275506i	−0.0244651	−	0.999701i	$-0.507788\pi$
$587$	16.1148	−	6.67499i	0.665131	−	0.275506i	0.689596	+	0.724195i	$0.257788\pi$
$588$		0			0
$589$	2.99697	−	7.23532i	0.123488	−	0.298126i
$590$		0			0
$591$	1.87465	−	7.71588i	0.0771127	−	0.317389i
$592$		0			0
$593$	35.2533			1.44768			0.723839	−	0.689969i	$-0.242376\pi$
$593$	35.2533			1.44768			0.723839	+	0.689969i	$0.242376\pi$
$594$		0			0
$595$	6.64317	+	2.75169i	0.272344	+	0.112808i
$596$		0			0
$597$	−9.05415	+	1.40878i	−0.370562	+	0.0576576i
$598$		0			0
$599$	12.1323	+	12.1323i	0.495712	+	0.495712i	0.910100	−	0.414388i	$-0.136004\pi$
$599$	12.1323	+	12.1323i	0.495712	+	0.495712i	−0.414388	+	0.910100i	$0.636004\pi$
$600$		0			0
$601$	0.0132863	−	0.0132863i	0.000541959	−	0.000541959i	−0.706836	−	0.707378i	$-0.749878\pi$
$601$	0.0132863	−	0.0132863i	0.000541959	−	0.000541959i	0.707378	+	0.706836i	$0.249878\pi$
$602$		0			0
$603$	27.0327	+	2.27568i	1.10086	+	0.0926727i
$604$		0			0
$605$	−8.71287	+	21.0347i	−0.354228	+	0.855183i
$606$		0			0
$607$		−	5.69469i		−	0.231140i	−0.993299	−	0.115570i	$-0.963130\pi$
$607$		−	5.69469i		−	0.231140i	0.993299	−	0.115570i	$-0.0368695\pi$
$608$		0			0
$609$	0.548201	−	2.25635i	0.0222142	−	0.0914317i
$610$		0			0
$611$	16.9364	+	7.01530i	0.685175	+	0.283809i
$612$		0			0
$613$	−12.0221	−	29.0239i	−0.485567	−	1.17226i	−0.956929	−	0.290322i	$-0.906237\pi$
$613$	−12.0221	−	29.0239i	−0.485567	−	1.17226i	0.471362	−	0.881940i	$-0.343763\pi$
$614$		0			0
$615$	−20.5677	−	33.7694i	−0.829369	−	1.36171i
$616$		0			0
$617$	12.5126	−	12.5126i	0.503739	−	0.503739i	−0.408859	−	0.912598i	$-0.634073\pi$
$617$	12.5126	−	12.5126i	0.503739	−	0.503739i	0.912598	+	0.408859i	$0.134073\pi$
$618$		0			0
$619$	−9.64869	−	23.2940i	−0.387814	−	0.936265i	−0.990402	−	0.138213i	$-0.955864\pi$
$619$	−9.64869	−	23.2940i	−0.387814	−	0.936265i	0.602589	−	0.798052i	$-0.294136\pi$
$620$		0			0
$621$	−14.1863	−	28.4134i	−0.569275	−	1.14019i
$622$		0			0
$623$			8.80100i			0.352605i
$624$		0			0
$625$			14.4239i			0.576955i
$626$		0			0
$627$	−7.09655	+	9.71186i	−0.283409	+	0.387854i
$628$		0			0
$629$	0.730492	+	1.76356i	0.0291266	+	0.0703178i
$630$		0			0
$631$	−14.0643	+	14.0643i	−0.559893	+	0.559893i	−0.929277	−	0.369384i	$-0.879569\pi$
$631$	−14.0643	+	14.0643i	−0.559893	+	0.559893i	0.369384	+	0.929277i	$0.379569\pi$
$632$		0			0
$633$	−0.903639	+	0.550373i	−0.0359164	+	0.0218753i
$634$		0			0
$635$	−13.4147	−	32.3860i	−0.532346	−	1.28520i
$636$		0			0
$637$	34.2273	+	14.1774i	1.35614	+	0.561730i
$638$		0			0
$639$	−0.631075	−	0.325889i	−0.0249649	−	0.0128920i
$640$		0			0
$641$			2.18451i			0.0862828i	0.999069	+	0.0431414i	$0.0137366\pi$
$641$			2.18451i			0.0862828i	−0.999069	+	0.0431414i	$0.986263\pi$
$642$		0			0
$643$	−10.9947	+	26.5434i	−0.433587	+	1.04677i	0.544535	+	0.838738i	$0.316706\pi$
$643$	−10.9947	+	26.5434i	−0.433587	+	1.04677i	−0.978122	+	0.208033i	$0.933294\pi$
$644$		0			0
$645$	−14.4969	+	2.25565i	−0.570816	+	0.0888162i
$646$		0			0
$647$	−18.0436	+	18.0436i	−0.709366	+	0.709366i	−0.966402	−	0.257036i	$-0.917254\pi$
$647$	−18.0436	+	18.0436i	−0.709366	+	0.709366i	0.257036	+	0.966402i	$0.417254\pi$
$648$		0			0
$649$	11.9443	+	11.9443i	0.468857	+	0.468857i
$650$		0			0
$651$	−0.585358	−	3.76206i	−0.0229420	−	0.147447i
$652$		0			0
$653$	9.04305	+	3.74575i	0.353882	+	0.146583i	0.552540	−	0.833486i	$-0.313658\pi$
$653$	9.04305	+	3.74575i	0.353882	+	0.146583i	−0.198659	+	0.980069i	$0.563658\pi$
$654$		0			0
$655$	−60.4518			−2.36205
$656$		0			0
$657$	7.53210	−	14.5857i	0.293855	−	0.569043i
$658$		0			0
$659$	6.74648	−	16.2874i	0.262805	−	0.634468i	−0.736305	−	0.676650i	$-0.763431\pi$
$659$	6.74648	−	16.2874i	0.262805	−	0.634468i	0.999110	+	0.0421820i	$0.0134309\pi$
$660$		0			0
$661$	−20.2135	+	8.37271i	−0.786215	+	0.325661i	−0.739421	−	0.673244i	$-0.764900\pi$
$661$	−20.2135	+	8.37271i	−0.786215	+	0.325661i	−0.0467942	+	0.998905i	$0.514900\pi$
$662$		0			0
$663$	−12.2716	−	20.1484i	−0.476590	−	0.782498i
$664$		0			0
$665$	7.55453	+	7.55453i	0.292952	+	0.292952i
$666$		0			0
$667$	−8.06767	+	3.34174i	−0.312381	+	0.129393i
$668$		0			0
$669$	−14.9480	−	10.9226i	−0.577921	−	0.422293i
$670$		0			0
$671$	−2.28546			−0.0882291
$672$		0			0
$673$	−12.4887			−0.481404			−0.240702	−	0.970599i	$-0.577378\pi$
$673$	−12.4887			−0.481404			−0.240702	+	0.970599i	$0.577378\pi$
$674$		0			0
$675$	−30.6920	+	15.3239i	−1.18134	+	0.589818i
$676$		0			0
$677$	40.9040	−	16.9430i	1.57207	−	0.651173i	0.584937	−	0.811078i	$-0.301119\pi$
$677$	40.9040	−	16.9430i	1.57207	−	0.651173i	0.987132	+	0.159906i	$0.0511190\pi$
$678$		0			0
$679$	−2.97757	−	2.97757i	−0.114269	−	0.114269i
$680$		0			0
$681$	2.82970	−	1.72347i	0.108434	−	0.0660433i
$682$		0			0
$683$	8.56803	−	3.54899i	0.327846	−	0.135798i	−0.212688	−	0.977120i	$-0.568222\pi$
$683$	8.56803	−	3.54899i	0.327846	−	0.135798i	0.540535	+	0.841322i	$0.318222\pi$
$684$		0			0
$685$	15.5523	−	37.5466i	0.594223	−	1.43458i
$686$		0			0
$687$	−21.2502	−	5.16296i	−0.810748	−	0.196979i
$688$		0			0
$689$	−55.2970			−2.10665
$690$		0			0
$691$	32.2776	+	13.3698i	1.22790	+	0.508611i	0.899912	−	0.436072i	$-0.143631\pi$
$691$	32.2776	+	13.3698i	1.22790	+	0.508611i	0.327984	+	0.944683i	$0.393631\pi$
$692$		0			0
$693$	−0.490537	+	5.82708i	−0.0186340	+	0.221352i
$694$		0			0
$695$	48.7163	+	48.7163i	1.84792	+	1.84792i
$696$		0			0
$697$	−10.6623	+	10.6623i	−0.403864	+	0.403864i
$698$		0			0
$699$	2.63138	+	16.9117i	0.0995279	+	0.639660i
$700$		0			0
$701$	7.31376	−	17.6570i	0.276237	−	0.666895i	−0.723488	−	0.690337i	$-0.757462\pi$
$701$	7.31376	−	17.6570i	0.276237	−	0.666895i	0.999725	+	0.0234415i	$0.00746235\pi$
$702$		0			0
$703$			2.83621i			0.106970i
$704$		0			0
$705$	−17.3598	−	4.21774i	−0.653808	−	0.158849i
$706$		0			0
$707$	11.8310	+	4.90055i	0.444949	+	0.184304i
$708$		0			0
$709$	17.1483	+	41.3997i	0.644019	+	1.55480i	0.821212	+	0.570624i	$0.193299\pi$
$709$	17.1483	+	41.3997i	0.644019	+	1.55480i	−0.177192	+	0.984176i	$0.556701\pi$
$710$		0			0
$711$	2.23081	+	6.99510i	0.0836621	+	0.262337i
$712$		0			0
$713$	−10.1246	+	10.1246i	−0.379170	+	0.379170i
$714$		0			0
$715$	16.3933	+	39.5768i	0.613073	+	1.48009i
$716$		0			0
$717$	−9.24354	−	6.75435i	−0.345206	−	0.252246i
$718$		0			0
$719$		−	41.1609i		−	1.53504i	−0.641023	−	0.767522i	$-0.721490\pi$
$719$		−	41.1609i		−	1.53504i	0.641023	−	0.767522i	$-0.278510\pi$
$720$		0			0
$721$			7.12823i			0.265469i
$722$		0			0
$723$	18.6127	+	13.6005i	0.692213	+	0.505807i
$724$		0			0
$725$	3.60973	+	8.71466i	0.134062	+	0.323654i
$726$		0			0
$727$	2.53270	−	2.53270i	0.0939328	−	0.0939328i	−0.658579	−	0.752512i	$-0.728842\pi$
$727$	2.53270	−	2.53270i	0.0939328	−	0.0939328i	0.752512	+	0.658579i	$0.228842\pi$
$728$		0			0
$729$	21.5813	+	16.2249i	0.799309	+	0.600920i
$730$		0			0
$731$	2.14112	+	5.16912i	0.0791922	+	0.191187i
$732$		0			0
$733$	−12.2518	−	5.07484i	−0.452529	−	0.187444i	0.144765	−	0.989466i	$-0.453757\pi$
$733$	−12.2518	−	5.07484i	−0.452529	−	0.187444i	−0.597294	+	0.802023i	$0.703757\pi$
$734$		0			0
$735$	−35.0830	−	8.52375i	−1.29405	−	0.314403i
$736$		0			0
$737$			18.7857i			0.691980i
$738$		0			0
$739$	−0.871699	+	2.10447i	−0.0320659	+	0.0774141i	−0.939101	−	0.343640i	$-0.888340\pi$
$739$	−0.871699	+	2.10447i	−0.0320659	+	0.0774141i	0.907035	+	0.421054i	$0.138340\pi$
$740$		0			0
$741$	−5.38909	−	34.6353i	−0.197973	−	1.27236i
$742$		0			0
$743$	−37.5946	+	37.5946i	−1.37921	+	1.37921i	−0.533262	+	0.845950i	$0.679034\pi$
$743$	−37.5946	+	37.5946i	−1.37921	+	1.37921i	−0.845950	+	0.533262i	$0.820966\pi$
$744$		0			0
$745$	−26.8642	−	26.8642i	−0.984226	−	0.984226i
$746$		0			0
$747$	40.4383	+	3.40419i	1.47956	+	0.124553i
$748$		0			0
$749$	−12.6517	−	5.24051i	−0.462283	−	0.191484i
$750$		0			0
$751$	−33.5914			−1.22577			−0.612885	−	0.790172i	$-0.709991\pi$
$751$	−33.5914			−1.22577			−0.612885	+	0.790172i	$0.709991\pi$
$752$		0			0
$753$	−24.4285	−	5.93514i	−0.890223	−	0.216288i
$754$		0			0
$755$	−22.4372	+	54.1683i	−0.816575	+	1.97139i
$756$		0			0
$757$	30.7254	−	12.7269i	1.11673	−	0.462567i	0.253483	−	0.967340i	$-0.418424\pi$
$757$	30.7254	−	12.7269i	1.11673	−	0.462567i	0.863252	+	0.504773i	$0.168424\pi$
$758$		0			0
$759$	18.7822	−	11.4395i	0.681749	−	0.415228i
$760$		0			0
$761$	−8.23145	−	8.23145i	−0.298390	−	0.298390i	0.541993	−	0.840383i	$-0.317670\pi$
$761$	−8.23145	−	8.23145i	−0.298390	−	0.298390i	−0.840383	+	0.541993i	$0.817670\pi$
$762$		0			0
$763$	4.12738	−	1.70962i	0.149421	−	0.0618922i
$764$		0			0
$765$	14.8356	+	17.5630i	0.536382	+	0.634991i
$766$		0			0
$767$	−49.2250			−1.77741
$768$		0			0
$769$	28.7476			1.03667			0.518333	−	0.855179i	$-0.326553\pi$
$769$	28.7476			1.03667			0.518333	+	0.855179i	$0.326553\pi$
$770$		0			0
$771$	−16.8505	−	12.3128i	−0.606856	−	0.443436i
$772$		0			0
$773$	19.1137	−	7.91717i	0.687474	−	0.284761i	−0.0114736	−	0.999934i	$-0.503652\pi$
$773$	19.1137	−	7.91717i	0.687474	−	0.284761i	0.698947	+	0.715173i	$0.253652\pi$
$774$		0			0
$775$	10.9366	+	10.9366i	0.392853	+	0.392853i
$776$		0			0
$777$	0.717242	+	1.17762i	0.0257309	+	0.0422468i
$778$		0			0
$779$	−20.6987	+	8.57370i	−0.741609	+	0.307185i
$780$		0			0
$781$	0.188216	−	0.454395i	0.00673491	−	0.0162595i
$782$		0			0
$783$	4.86751	−	5.60576i	0.173951	−	0.200334i
$784$		0			0
$785$	−37.4090			−1.33518
$786$		0			0
$787$	30.1761	+	12.4993i	1.07566	+	0.445554i	0.848985	−	0.528417i	$-0.177214\pi$
$787$	30.1761	+	12.4993i	1.07566	+	0.445554i	0.226676	+	0.973970i	$0.427214\pi$
$788$		0			0
$789$	−0.914263	−	5.87591i	−0.0325486	−	0.209188i
$790$		0			0
$791$	−3.88239	−	3.88239i	−0.138042	−	0.138042i
$792$		0			0
$793$	4.70940	−	4.70940i	0.167236	−	0.167236i
$794$		0			0
$795$	53.2476	−	8.28506i	1.88850	−	0.293841i
$796$		0			0
$797$	−15.0856	+	36.4199i	−0.534360	+	1.29006i	0.394251	+	0.919003i	$0.371004\pi$
$797$	−15.0856	+	36.4199i	−0.534360	+	1.29006i	−0.928611	+	0.371055i	$0.878996\pi$
$798$		0			0
$799$			6.81287i			0.241022i
$800$		0			0
$801$	−12.9114	+	25.0026i	−0.456201	+	0.883422i
$802$		0			0
$803$	10.5022	+	4.35015i	0.370614	+	0.153513i
$804$		0			0
$805$	−7.47504	−	18.0464i	−0.263461	−	0.636050i
$806$		0			0
$807$	17.7523	−	10.8123i	0.624910	−	0.380609i
$808$		0			0
$809$	−12.2843	+	12.2843i	−0.431893	+	0.431893i	−0.889272	−	0.457379i	$-0.848788\pi$
$809$	−12.2843	+	12.2843i	−0.431893	+	0.431893i	0.457379	+	0.889272i	$0.348788\pi$
$810$		0			0
$811$	2.03182	+	4.90525i	0.0713468	+	0.172246i	0.955530	−	0.294894i	$-0.0952843\pi$
$811$	2.03182	+	4.90525i	0.0713468	+	0.172246i	−0.884183	+	0.467140i	$0.845284\pi$
$812$		0			0
$813$	−17.0255	+	23.2999i	−0.597110	+	0.817165i
$814$		0			0
$815$		−	35.9533i		−	1.25939i
$816$		0			0
$817$			8.31311i			0.290839i
$818$		0			0
$819$	−10.9965	−	13.0181i	−0.384247	−	0.454888i
$820$		0			0
$821$	5.58979	+	13.4949i	0.195085	+	0.470977i	0.990906	−	0.134555i	$-0.0429605\pi$
$821$	5.58979	+	13.4949i	0.195085	+	0.470977i	−0.795821	+	0.605532i	$0.792960\pi$
$822$		0			0
$823$	−16.7820	+	16.7820i	−0.584983	+	0.584983i	−0.936268	−	0.351286i	$-0.885745\pi$
$823$	−16.7820	+	16.7820i	−0.584983	+	0.584983i	0.351286	+	0.936268i	$0.385745\pi$
$824$		0			0
$825$	−12.3569	−	20.2884i	−0.430212	−	0.706352i
$826$		0			0
$827$	−14.4882	−	34.9777i	−0.503806	−	1.21629i	−0.947396	−	0.320065i	$-0.896295\pi$
$827$	−14.4882	−	34.9777i	−0.503806	−	1.21629i	0.443590	−	0.896230i	$-0.353705\pi$
$828$		0			0
$829$	15.7971	+	6.54339i	0.548657	+	0.227261i	0.639753	−	0.768581i	$-0.279037\pi$
$829$	15.7971	+	6.54339i	0.548657	+	0.227261i	−0.0910953	+	0.995842i	$0.529037\pi$
$830$		0			0
$831$	−11.6358	+	47.8919i	−0.403641	+	1.66135i
$832$		0			0
$833$			13.7683i			0.477044i
$834$		0			0
$835$	23.7359	−	57.3036i	0.821415	−	1.98307i
$836$		0			0
$837$	3.85615	−	11.5463i	0.133288	−	0.399098i
$838$		0			0
$839$	−24.3139	+	24.3139i	−0.839409	+	0.839409i	−0.988781	−	0.149372i	$-0.952275\pi$
$839$	−24.3139	+	24.3139i	−0.839409	+	0.839409i	0.149372	+	0.988781i	$0.452275\pi$
$840$		0			0
$841$	19.0626	+	19.0626i	0.657332	+	0.657332i
$842$		0			0
$843$	0.264161	−	0.0411022i	0.00909820	−	0.00141564i
$844$		0			0
$845$	−74.4222	−	30.8267i	−2.56020	−	1.06047i
$846$		0			0
$847$	6.27181			0.215502
$848$		0			0
$849$	−5.09709	+	20.9791i	−0.174932	+	0.720003i
$850$		0			0
$851$	1.98440	−	4.79076i	0.0680243	−	0.164225i
$852$		0			0
$853$	1.86280	−	0.771599i	0.0637812	−	0.0264190i	−0.350565	−	0.936538i	$-0.614010\pi$
$853$	1.86280	−	0.771599i	0.0637812	−	0.0264190i	0.414346	+	0.910119i	$0.364010\pi$
$854$		0			0
$855$	10.3787	+	32.5442i	0.354944	+	1.11299i
$856$		0			0
$857$	−16.8878	−	16.8878i	−0.576875	−	0.576875i	0.357166	−	0.934041i	$-0.383743\pi$
$857$	−16.8878	−	16.8878i	−0.576875	−	0.576875i	−0.934041	+	0.357166i	$0.883743\pi$
$858$		0			0
$859$	−46.4891	+	19.2564i	−1.58619	+	0.657020i	−0.989378	−	0.145363i	$-0.953565\pi$
$859$	−46.4891	+	19.2564i	−1.58619	+	0.657020i	−0.596809	+	0.802383i	$0.703565\pi$
$860$		0			0
$861$	−6.42611	+	8.79434i	−0.219001	+	0.299710i
$862$		0			0
$863$	51.6586			1.75848			0.879239	−	0.476381i	$-0.158052\pi$
$863$	51.6586			1.75848			0.879239	+	0.476381i	$0.158052\pi$
$864$		0			0
$865$	36.5420			1.24246
$866$		0			0
$867$	−12.1993	+	16.6952i	−0.414312	+	0.566999i
$868$		0			0
$869$	−4.69728	+	1.94568i	−0.159344	+	0.0660026i
$870$		0			0
$871$	−38.7098	−	38.7098i	−1.31163	−	1.31163i
$872$		0			0
$873$	−4.09071	−	12.8271i	−0.138450	−	0.434132i
$874$		0			0
$875$	−4.73012	+	1.95928i	−0.159907	+	0.0662357i
$876$		0			0
$877$	−15.0174	+	36.2552i	−0.507101	+	1.22425i	0.438444	+	0.898759i	$0.355530\pi$
$877$	−15.0174	+	36.2552i	−0.507101	+	1.22425i	−0.945545	+	0.325492i	$0.894470\pi$
$878$		0			0
$879$	−6.48657	+	26.6981i	−0.218787	+	0.900505i
$880$		0			0
$881$	54.2455			1.82758			0.913788	−	0.406192i	$-0.133144\pi$
$881$	54.2455			1.82758			0.913788	+	0.406192i	$0.133144\pi$
$882$		0			0
$883$	−12.5424	−	5.19524i	−0.422086	−	0.174834i	0.161522	−	0.986869i	$-0.448360\pi$
$883$	−12.5424	−	5.19524i	−0.422086	−	0.174834i	−0.583608	+	0.812035i	$0.698360\pi$
$884$		0			0
$885$	47.4006	−	7.37529i	1.59335	−	0.247918i
$886$		0			0
$887$	17.2169	+	17.2169i	0.578086	+	0.578086i	0.934376	−	0.356289i	$-0.115958\pi$
$887$	17.2169	+	17.2169i	0.578086	+	0.578086i	−0.356289	+	0.934376i	$0.615958\pi$
$888$		0			0
$889$	−6.82807	+	6.82807i	−0.229006	+	0.229006i
$890$		0			0
$891$	−9.94208	+	15.8344i	−0.333072	+	0.530471i
$892$		0			0
$893$	−3.87375	+	9.35206i	−0.129630	+	0.312955i
$894$		0			0
$895$		−	84.7600i		−	2.83321i
$896$		0			0
$897$	−15.1302	+	62.2747i	−0.505184	+	2.07929i
$898$		0			0
$899$	−3.09243	−	1.28093i	−0.103138	−	0.0427213i
$900$		0			0
$901$	−7.86439	−	18.9863i	−0.262001	−	0.632526i
$902$		0			0
$903$	2.10229	+	3.45168i	0.0699597	+	0.114865i
$904$		0			0
$905$	28.8350	−	28.8350i	0.958507	−	0.958507i
$906$		0			0
$907$	−0.183637	−	0.443339i	−0.00609756	−	0.0147208i	0.920801	−	0.390032i	$-0.127536\pi$
$907$	−0.183637	−	0.443339i	−0.00609756	−	0.0147208i	−0.926899	+	0.375311i	$0.877536\pi$
$908$		0			0
$909$	26.4210	+	31.2783i	0.876330	+	1.03744i
$910$		0			0
$911$		−	3.96023i		−	0.131208i	−0.997846	−	0.0656041i	$-0.979103\pi$
$911$		−	3.96023i		−	0.131208i	0.997846	−	0.0656041i	$-0.0208974\pi$
$912$		0			0
$913$			28.1016i			0.930027i
$914$		0			0
$915$	−3.82926	+	5.24046i	−0.126591	+	0.173244i
$916$		0			0
$917$	6.37265	+	15.3849i	0.210443	+	0.508056i
$918$		0			0
$919$	17.2218	−	17.2218i	0.568095	−	0.568095i	−0.363500	−	0.931594i	$-0.618418\pi$
$919$	17.2218	−	17.2218i	0.568095	−	0.568095i	0.931594	+	0.363500i	$0.118418\pi$
$920$		0			0
$921$	−28.7822	+	17.5302i	−0.948406	+	0.577638i
$922$		0			0
$923$	0.548486	+	1.32416i	0.0180536	+	0.0435853i
$924$		0			0
$925$	−5.17496	−	2.14354i	−0.170152	−	0.0704791i
$926$		0			0
$927$	−10.4574	+	20.2504i	−0.343465	+	0.665111i
$928$		0			0
$929$		−	31.0543i		−	1.01886i	−0.860513	−	0.509429i	$-0.829857\pi$
$929$		−	31.0543i		−	1.01886i	0.860513	−	0.509429i	$-0.170143\pi$
$930$		0			0
$931$	−7.82858	+	18.8999i	−0.256571	+	0.619418i
$932$		0			0
$933$	−35.7166	+	5.55733i	−1.16931	+	0.181939i
$934$		0			0
$935$	−11.2573	+	11.2573i	−0.368153	+	0.368153i
$936$		0			0
$937$	−35.2447	−	35.2447i	−1.15139	−	1.15139i	−0.986273	−	0.165120i	$-0.947199\pi$
$937$	−35.2447	−	35.2447i	−1.15139	−	1.15139i	−0.165120	−	0.986273i	$-0.552801\pi$
$938$		0			0
$939$	1.41717	+	9.10806i	0.0462476	+	0.297230i
$940$		0			0
$941$	−17.9856	−	7.44989i	−0.586315	−	0.242859i	0.0697497	−	0.997565i	$-0.477780\pi$
$941$	−17.9856	−	7.44989i	−0.586315	−	0.242859i	−0.656064	+	0.754705i	$0.727780\pi$
$942$		0			0
$943$	40.9619			1.33390
$944$		0			0
$945$	12.5394	+	10.8880i	0.407906	+	0.354186i
$946$		0			0
$947$	−8.02826	+	19.3819i	−0.260883	+	0.629828i	−0.998994	−	0.0448519i	$-0.985718\pi$
$947$	−8.02826	+	19.3819i	−0.260883	+	0.629828i	0.738110	+	0.674680i	$0.235718\pi$
$948$		0			0
$949$	−30.6047	+	12.6769i	−0.993470	+	0.411509i
$950$		0			0
$951$	13.3134	+	21.8588i	0.431716	+	0.708821i
$952$		0			0
$953$	30.6881	+	30.6881i	0.994084	+	0.994084i	0.999983	−	0.00589861i	$-0.00187760\pi$
$953$	30.6881	+	30.6881i	0.994084	+	0.994084i	−0.00589861	+	0.999983i	$0.501878\pi$
$954$		0			0
$955$	0.420757	−	0.174283i	0.0136154	−	0.00563968i
$956$		0			0
$957$	4.15092	+	3.03312i	0.134180	+	0.0980469i
$958$		0			0
$959$	−11.1951			−0.361507
$960$		0			0
$961$	25.5116			0.822955
$962$		0			0
$963$	−28.2539	−	33.4481i	−0.910469	−	1.07785i
$964$		0			0
$965$	23.5631	−	9.76017i	0.758524	−	0.314191i
$966$		0			0
$967$	7.20570	+	7.20570i	0.231720	+	0.231720i	0.813410	−	0.581691i	$-0.197609\pi$
$967$	7.20570	+	7.20570i	0.231720	+	0.231720i	−0.581691	+	0.813410i	$0.697609\pi$
$968$		0			0
$969$	11.1257	−	6.77622i	0.357407	−	0.217683i
$970$		0			0
$971$	18.8717	−	7.81690i	0.605621	−	0.250856i	−0.0587340	−	0.998274i	$-0.518706\pi$
$971$	18.8717	−	7.81690i	0.605621	−	0.250856i	0.664355	+	0.747417i	$0.268706\pi$
$972$		0			0
$973$	7.26274	−	17.5338i	0.232833	−	0.562108i
$974$		0			0
$975$	67.2688	+	16.3436i	2.15433	+	0.523415i
$976$		0			0
$977$	−10.8222			−0.346234			−0.173117	−	0.984901i	$-0.555384\pi$
$977$	−10.8222			−0.346234			−0.173117	+	0.984901i	$0.555384\pi$
$978$		0			0
$979$	−18.0026	−	7.45694i	−0.575367	−	0.238325i
$980$		0			0
$981$	14.2334	+	1.19820i	0.454438	+	0.0382557i
$982$		0			0
$983$	−16.0211	−	16.0211i	−0.510994	−	0.510994i	0.403837	−	0.914831i	$-0.367676\pi$
$983$	−16.0211	−	16.0211i	−0.510994	−	0.510994i	−0.914831	+	0.403837i	$0.867676\pi$
$984$		0			0
$985$	11.0415	−	11.0415i	0.351813	−	0.351813i
$986$		0			0
$987$	0.756610	+	4.86268i	0.0240831	+	0.154781i
$988$		0			0
$989$	5.81641	−	14.0420i	0.184951	−	0.446511i
$990$		0			0
$991$			24.1879i			0.768355i	0.923259	+	0.384177i	$0.125515\pi$
$991$			24.1879i			0.768355i	−0.923259	+	0.384177i	$0.874485\pi$
$992$		0			0
$993$	−17.0579	−	4.14438i	−0.541315	−	0.131518i
$994$		0			0
$995$	−16.6480	−	6.89584i	−0.527778	−	0.218613i
$996$		0			0
$997$	15.8249	+	38.2046i	0.501178	+	1.20995i	0.948842	+	0.315750i	$0.102256\pi$
$997$	15.8249	+	38.2046i	0.501178	+	1.20995i	−0.447664	+	0.894202i	$0.647744\pi$
$998$		0			0
$999$	0.309990	+	4.39768i	0.00980765	+	0.139137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.o.a.47.10		56
3.2	odd	2	inner	384.2.o.a.47.9		56
4.3	odd	2		96.2.o.a.35.10	yes	56
8.3	odd	2		768.2.o.b.95.10		56
8.5	even	2		768.2.o.a.95.5		56
12.11	even	2		96.2.o.a.35.5	yes	56
24.5	odd	2		768.2.o.a.95.6		56
24.11	even	2		768.2.o.b.95.9		56
32.5	even	8		768.2.o.b.671.9		56
32.11	odd	8	inner	384.2.o.a.335.9		56
32.21	even	8		96.2.o.a.11.5	✓	56
32.27	odd	8		768.2.o.a.671.6		56
96.5	odd	8		768.2.o.b.671.10		56
96.11	even	8	inner	384.2.o.a.335.10		56
96.53	odd	8		96.2.o.a.11.10	yes	56
96.59	even	8		768.2.o.a.671.5		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.11.5	✓	56	32.21	even	8
96.2.o.a.11.10	yes	56	96.53	odd	8
96.2.o.a.35.5	yes	56	12.11	even	2
96.2.o.a.35.10	yes	56	4.3	odd	2
384.2.o.a.47.9		56	3.2	odd	2	inner
384.2.o.a.47.10		56	1.1	even	1	trivial
384.2.o.a.335.9		56	32.11	odd	8	inner
384.2.o.a.335.10		56	96.11	even	8	inner
768.2.o.a.95.5		56	8.5	even	2
768.2.o.a.95.6		56	24.5	odd	2
768.2.o.a.671.5		56	96.59	even	8
768.2.o.a.671.6		56	32.27	odd	8
768.2.o.b.95.9		56	24.11	even	2
768.2.o.b.95.10		56	8.3	odd	2
768.2.o.b.671.9		56	32.5	even	8
768.2.o.b.671.10		56	96.5	odd	8

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.o (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.02188 - 1.39848i) q^{3} +(3.14689 - 1.30348i) q^{5} +(-0.663471 - 0.663471i) q^{7} +(-0.911503 - 2.85817i) q^{9} +O(q^{10})\)	\(q+(1.02188 - 1.39848i) q^{3} +(3.14689 - 1.30348i) q^{5} +(-0.663471 - 0.663471i) q^{7} +(-0.911503 - 2.85817i) q^{9} +(1.91929 - 0.794997i) q^{11} +(-2.31672 + 5.59306i) q^{13} +(1.39286 - 5.73287i) q^{15} -2.24987 q^{17} +(-3.08841 - 1.27926i) q^{19} +(-1.60584 + 0.249861i) q^{21} +(4.32171 + 4.32171i) q^{23} +(4.66830 - 4.66830i) q^{25} +(-4.92856 - 1.64600i) q^{27} +(-0.546766 + 1.32001i) q^{29} +2.34273i q^{31} +(0.849507 - 3.49649i) q^{33} +(-2.95269 - 1.22305i) q^{35} +(-0.324682 - 0.783851i) q^{37} +(5.45437 + 8.95535i) q^{39} +(4.73908 - 4.73908i) q^{41} +(-0.951664 - 2.29752i) q^{43} +(-6.59398 - 7.80622i) q^{45} -3.02812i q^{47} -6.11961i q^{49} +(-2.29911 + 3.14640i) q^{51} +(3.49549 + 8.43885i) q^{53} +(5.00353 - 5.00353i) q^{55} +(-4.94502 + 3.01183i) q^{57} +(3.11165 + 7.51220i) q^{59} +(-1.01639 - 0.421005i) q^{61} +(-1.29156 + 2.50107i) q^{63} +20.6205i q^{65} +(-3.46052 + 8.35443i) q^{67} +(10.4601 - 1.62755i) q^{69} +(0.167408 - 0.167408i) q^{71} +(3.86922 + 3.86922i) q^{73} +(-1.75807 - 11.2990i) q^{75} +(-1.80085 - 0.745938i) q^{77} -2.44740 q^{79} +(-7.33832 + 5.21047i) q^{81} +(-5.17660 + 12.4974i) q^{83} +(-7.08008 + 2.93267i) q^{85} +(1.28728 + 2.11354i) q^{87} +(-6.63254 - 6.63254i) q^{89} +(5.24791 - 2.17376i) q^{91} +(3.27627 + 2.39400i) q^{93} -11.3864 q^{95} +4.48787 q^{97} +(-4.02168 - 4.76103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 56 * q + 4 * q^3 + 8 * q^7 - 4 * q^9	\( 56 q + 4 q^{3} + 8 q^{7} - 4 q^{9} - 8 q^{13} + 8 q^{15} + 8 q^{19} - 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} - 8 q^{37} + 28 q^{39} + 8 q^{43} - 4 q^{45} + 16 q^{51} - 24 q^{55} - 4 q^{57} - 40 q^{61} - 56 q^{67} - 4 q^{69} - 8 q^{73} - 16 q^{75} - 16 q^{79} - 48 q^{85} - 52 q^{87} - 40 q^{91} + 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) \) 56 * q + 4 * q^3 + 8 * q^7 - 4 * q^9 - 8 * q^13 + 8 * q^15 + 8 * q^19 - 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 - 8 * q^37 + 28 * q^39 + 8 * q^43 - 4 * q^45 + 16 * q^51 - 24 * q^55 - 4 * q^57 - 40 * q^61 - 56 * q^67 - 4 * q^69 - 8 * q^73 - 16 * q^75 - 16 * q^79 - 48 * q^85 - 52 * q^87 - 40 * q^91 + 8 * q^93 - 16 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

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