LMFDB - Embedded newform 768.2.o.b.95.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(95,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, 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("768.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.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:	$6.13251087523$
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			95.10
Character	$\chi$	$=$	768.95
Dual form			768.2.o.b.671.10

$q$-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 $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{8}\right)$

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	−0.951644	−	0.307205i	$-0.900606\pi$
$5$	−3.14689	+	1.30348i	−1.40733	+	0.582935i	−0.455687	+	0.890140i	$0.650606\pi$
$6$		0			0
$7$	0.663471	+	0.663471i	0.250769	+	0.250769i	0.821286	−	0.570517i	$-0.193257\pi$
$7$	0.663471	+	0.663471i	0.250769	+	0.250769i	−0.570517	+	0.821286i	$0.693257\pi$
$8$		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	$-0.557835\pi$
$13$	2.31672	−	5.59306i	0.642543	−	1.55123i	0.823238	−	0.567696i	$-0.192165\pi$
$14$		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	0.0943951	−	0.995535i	$-0.469908\pi$
$23$	−4.32171	−	4.32171i	−0.901140	−	0.901140i	−0.995535	+	0.0943951i	$0.969908\pi$
$24$		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	−0.864948	−	0.501861i	$-0.832649\pi$
$29$	0.546766	−	1.32001i	0.101532	−	0.245120i	0.966480	+	0.256741i	$0.0826489\pi$
$30$		0			0
$31$		−	2.34273i		−	0.420767i	−0.977619	−	0.210384i	$-0.932529\pi$
$31$		−	2.34273i		−	0.420767i	0.977619	−	0.210384i	$-0.0674713\pi$
$32$		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	0.948319	−	0.317319i	$-0.102783\pi$
$37$	0.324682	+	0.783851i	0.0533774	+	0.128864i	−0.894941	+	0.446184i	$0.852783\pi$
$38$		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	$0.0708825\pi$
$47$			3.02812i			0.441696i	−0.975308	+	0.220848i	$0.929117\pi$
$48$		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	$-0.909145\pi$
$53$	−3.49549	−	8.43885i	−0.480142	−	1.15916i	0.479399	−	0.877597i	$-0.340855\pi$
$54$		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	0.446801	−	0.894633i	$-0.352563\pi$
$61$	1.01639	+	0.421005i	0.130136	+	0.0539041i	−0.316665	+	0.948537i	$0.602563\pi$
$62$		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	−0.716971	−	0.697103i	$-0.754472\pi$
$71$	−0.167408	+	0.167408i	−0.0198677	+	0.0198677i	0.697103	+	0.716971i	$0.254472\pi$
$72$		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	$-0.456036\pi$
$79$	2.44740			0.275354			0.137677	+	0.990477i	$0.456036\pi$
$80$		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	0.346386	−	0.938092i	$-0.387409\pi$
$101$	12.6091	−	5.22285i	1.25465	−	0.519693i	0.908263	+	0.418399i	$0.137409\pi$
$102$		0			0
$103$	5.37192	+	5.37192i	0.529311	+	0.529311i	0.920367	−	0.391056i	$-0.127890\pi$
$103$	5.37192	+	5.37192i	0.529311	+	0.529311i	−0.391056	+	0.920367i	$0.627890\pi$
$104$		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	−0.812280	−	0.583268i	$-0.801774\pi$
$109$	1.82205	−	4.39883i	0.174521	−	0.421331i	0.986801	+	0.161936i	$0.0517739\pi$
$110$		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	$0.150936\pi$
$127$			10.2914i			0.913216i	−0.889668	+	0.456608i	$0.849064\pi$
$128$		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	$0.0260320\pi$
$149$	4.26837	+	10.3048i	0.349678	+	0.844198i	−0.646979	+	0.762508i	$0.723968\pi$
$150$		0			0
$151$	12.1716	−	12.1716i	0.990514	−	0.990514i	−0.00944142	−	0.999955i	$-0.503005\pi$
$151$	12.1716	−	12.1716i	0.990514	−	0.990514i	0.999955	+	0.00944142i	$0.00300534\pi$
$152$		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	0.748872	−	0.662714i	$-0.230596\pi$
$157$	10.1467	+	4.20290i	0.809795	+	0.335428i	0.0609231	+	0.998142i	$0.480596\pi$
$158$		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	−0.999993	−	0.00360853i	$-0.998851\pi$
$167$	−12.8761	+	12.8761i	−0.996385	+	0.996385i	0.00360853	+	0.999993i	$0.498851\pi$
$168$		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	−0.0273673	−	0.999625i	$-0.508712\pi$
$173$	−9.91155	−	4.10550i	−0.753561	−	0.312135i	−0.726194	+	0.687490i	$0.758712\pi$
$174$		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	−0.753786	−	0.657120i	$-0.771774\pi$
$181$	−11.0607	+	4.58151i	−0.822139	+	0.340541i	−0.0683528	+	0.997661i	$0.521774\pi$
$182$		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	$-0.501540\pi$
$191$	−0.133706			−0.00967461			−0.00483731	+	0.999988i	$0.501540\pi$
$192$		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	−0.528425	−	0.848980i	$-0.677217\pi$
$197$	−4.23540	+	1.75436i	−0.301759	+	0.124993i	0.226666	+	0.973973i	$0.427217\pi$
$198$		0			0
$199$	3.74082	+	3.74082i	0.265179	+	0.265179i	0.827154	−	0.561975i	$-0.189958\pi$
$199$	3.74082	+	3.74082i	0.265179	+	0.265179i	−0.561975	+	0.827154i	$0.689958\pi$
$200$		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	$0.116502\pi$
$223$			10.6887i			0.715768i	−0.933766	+	0.357884i	$0.883498\pi$
$224$		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	$0.0119769\pi$
$229$	4.83167	+	11.6647i	0.319286	+	0.770824i	−0.680007	+	0.733206i	$0.738023\pi$
$230$		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	$0.0685752\pi$
$239$			6.60970i			0.427546i	−0.976883	+	0.213773i	$0.931425\pi$
$240$		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	−0.777983	−	0.628285i	$-0.783757\pi$
$263$	−2.42769	+	2.42769i	−0.149698	+	0.149698i	0.628285	+	0.777983i	$0.283757\pi$
$264$		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	0.0181552	−	0.999835i	$-0.494221\pi$
$269$	−11.0872	−	4.59246i	−0.675997	−	0.280007i	−0.694153	+	0.719828i	$0.744221\pi$
$270$		0			0
$271$	16.6609			1.01208			0.506038	−	0.862511i	$-0.331109\pi$
$271$	16.6609			1.01208			0.506038	+	0.862511i	$0.331109\pi$
$272$		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	0.591199	−	0.806526i	$-0.298655\pi$
$277$	26.2888	−	10.8892i	1.57954	−	0.654267i	0.988341	+	0.152259i	$0.0486547\pi$
$278$		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	0.0889561	−	0.996036i	$-0.471647\pi$
$293$	14.6551	−	6.07035i	0.856161	−	0.354634i	0.767205	+	0.641402i	$0.221647\pi$
$294$		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	0.988433	−	0.151657i	$-0.0484609\pi$
$311$	14.7567	+	14.7567i	0.836776	+	0.836776i	−0.151657	+	0.988433i	$0.548461\pi$
$312$		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	$-0.738791\pi$
$317$	5.65481	−	13.6519i	0.317606	−	0.766768i	0.999380	−	0.0352055i	$-0.0112086\pi$
$318$		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	−0.190397	−	0.981707i	$-0.560977\pi$
$349$	−19.0402	−	7.88672i	−1.01920	−	0.422166i	−0.828803	+	0.559541i	$0.810977\pi$
$350$		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	−0.693391	−	0.720561i	$-0.743884\pi$
$359$	0.514805	−	0.514805i	0.0271704	−	0.0271704i	0.720561	+	0.693391i	$0.243884\pi$
$360$		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	$-0.938090\pi$
$367$	−37.5921			−1.96229			−0.981145	+	0.193271i	$0.938090\pi$
$368$		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	−0.881644	−	0.471914i	$-0.843563\pi$
$373$	−22.6229	+	9.37070i	−1.17137	+	0.485196i	−0.289723	+	0.957111i	$0.593563\pi$
$374$		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	$-0.634654\pi$
$383$	−16.0682			−0.821048			−0.410524	+	0.911850i	$0.634654\pi$
$384$		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	0.588596	−	0.808427i	$-0.299681\pi$
$389$	31.0923	−	12.8788i	1.57644	−	0.652983i	0.987845	+	0.155444i	$0.0496807\pi$
$390$		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	$-0.693986\pi$
$397$	8.21223	−	19.8261i	0.412160	−	0.995042i	0.984557	−	0.175065i	$-0.0560136\pi$
$398$		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	$0.122612\pi$
$421$	11.0208	+	26.6066i	0.537121	+	1.29673i	−0.389603	+	0.920983i	$0.627388\pi$
$422$		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	$-0.997866\pi$
$431$		−	0.278342i		−	0.0134073i	0.999978	−	0.00670363i	$-0.00213385\pi$
$432$		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	−0.111728	−	0.993739i	$-0.535639\pi$
$439$	18.4802	−	18.4802i	0.882011	−	0.882011i	0.993739	+	0.111728i	$0.0356386\pi$
$440$		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	0.110277	−	0.993901i	$-0.464826\pi$
$461$	−11.0476	−	4.57608i	−0.514539	−	0.213129i	−0.624816	+	0.780772i	$0.714826\pi$
$462$		0			0
$463$	−27.8395			−1.29381			−0.646906	−	0.762569i	$-0.723938\pi$
$463$	−27.8395			−1.29381			−0.646906	+	0.762569i	$0.723938\pi$
$464$		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	$-0.318122\pi$
$479$	23.6720			1.08160			0.540800	+	0.841151i	$0.318122\pi$
$480$		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	0.682517	−	0.730869i	$-0.260885\pi$
$487$	−1.06704	−	1.06704i	−0.0483522	−	0.0483522i	−0.730869	+	0.682517i	$0.760885\pi$
$488$		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	0.868346	−	0.495959i	$-0.165183\pi$
$503$	8.35178	+	8.35178i	0.372387	+	0.372387i	−0.495959	+	0.868346i	$0.665183\pi$
$504$		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	−0.976150	−	0.217096i	$-0.930342\pi$
$509$	−2.98703	+	7.21134i	−0.132398	+	0.319637i	0.843752	+	0.536733i	$0.180342\pi$
$510$		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	0.458124	−	0.888888i	$-0.348522\pi$
$541$	3.57097	+	1.47914i	0.153528	+	0.0635934i	−0.304596	+	0.952482i	$0.598522\pi$
$542$		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	0.924457	−	0.381286i	$-0.124519\pi$
$557$	30.8826	+	12.7920i	1.30854	+	0.542014i	0.384080	+	0.923300i	$0.374519\pi$
$558$		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	0.414388	−	0.910100i	$-0.363996\pi$
$599$	−12.1323	−	12.1323i	−0.495712	−	0.495712i	−0.910100	+	0.414388i	$0.863996\pi$
$600$		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	$0.0368695\pi$
$607$			5.69469i			0.231140i	−0.993299	+	0.115570i	$0.963130\pi$
$608$		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	$0.0937626\pi$
$613$	12.0221	+	29.0239i	0.485567	+	1.17226i	−0.471362	+	0.881940i	$0.656237\pi$
$614$		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	−0.369384	−	0.929277i	$-0.620431\pi$
$631$	14.0643	−	14.0643i	0.559893	−	0.559893i	0.929277	+	0.369384i	$0.120431\pi$
$632$		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	−0.257036	−	0.966402i	$-0.582746\pi$
$647$	18.0436	−	18.0436i	0.709366	−	0.709366i	0.966402	+	0.257036i	$0.0827458\pi$
$648$		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	0.198659	−	0.980069i	$-0.436342\pi$
$653$	−9.04305	−	3.74575i	−0.353882	−	0.146583i	−0.552540	+	0.833486i	$0.686342\pi$
$654$		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	0.0467942	−	0.998905i	$-0.485100\pi$
$661$	20.2135	−	8.37271i	0.786215	−	0.325661i	0.739421	+	0.673244i	$0.235100\pi$
$662$		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	−0.987132	−	0.159906i	$-0.948881\pi$
$677$	−40.9040	+	16.9430i	−1.57207	+	0.651173i	−0.584937	+	0.811078i	$0.698881\pi$
$678$		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	−0.999725	−	0.0234415i	$-0.992538\pi$
$701$	−7.31376	+	17.6570i	−0.276237	+	0.666895i	0.723488	+	0.690337i	$0.242538\pi$
$702$		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	$-0.806701\pi$
$709$	−17.1483	−	41.3997i	−0.644019	−	1.55480i	0.177192	−	0.984176i	$-0.443299\pi$
$710$		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	$0.278510\pi$
$719$			41.1609i			1.53504i	−0.641023	+	0.767522i	$0.721490\pi$
$720$		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	−0.752512	−	0.658579i	$-0.771158\pi$
$727$	−2.53270	+	2.53270i	−0.0939328	+	0.0939328i	0.658579	+	0.752512i	$0.271158\pi$
$728$		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	0.597294	−	0.802023i	$-0.296243\pi$
$733$	12.2518	+	5.07484i	0.452529	+	0.187444i	−0.144765	+	0.989466i	$0.546243\pi$
$734$		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	$-0.320966\pi$
$743$	37.5946	−	37.5946i	1.37921	−	1.37921i	0.845950	−	0.533262i	$-0.179034\pi$
$744$		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	$-0.290009\pi$
$751$	33.5914			1.22577			0.612885	+	0.790172i	$0.290009\pi$
$752$		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	−0.863252	−	0.504773i	$-0.831576\pi$
$757$	−30.7254	+	12.7269i	−1.11673	+	0.462567i	−0.253483	+	0.967340i	$0.581576\pi$
$758$		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	−0.698947	−	0.715173i	$-0.746348\pi$
$773$	−19.1137	+	7.91717i	−0.687474	+	0.284761i	0.0114736	+	0.999934i	$0.496348\pi$
$774$		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	$-0.628996\pi$
$797$	15.0856	−	36.4199i	0.534360	−	1.29006i	0.928611	−	0.371055i	$-0.121004\pi$
$798$		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	0.795821	−	0.605532i	$-0.207040\pi$
$821$	−5.58979	−	13.4949i	−0.195085	−	0.470977i	−0.990906	+	0.134555i	$0.957040\pi$
$822$		0			0
$823$	16.7820	−	16.7820i	0.584983	−	0.584983i	−0.351286	−	0.936268i	$-0.614255\pi$
$823$	16.7820	−	16.7820i	0.584983	−	0.584983i	0.936268	+	0.351286i	$0.114255\pi$
$824$		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	0.0910953	−	0.995842i	$-0.470963\pi$
$829$	−15.7971	−	6.54339i	−0.548657	−	0.227261i	−0.639753	+	0.768581i	$0.720963\pi$
$830$		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	−0.149372	−	0.988781i	$-0.547725\pi$
$839$	24.3139	−	24.3139i	0.839409	−	0.839409i	0.988781	+	0.149372i	$0.0477252\pi$
$840$		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	−0.414346	−	0.910119i	$-0.635990\pi$
$853$	−1.86280	+	0.771599i	−0.0637812	+	0.0264190i	0.350565	+	0.936538i	$0.385990\pi$
$854$		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	$-0.841948\pi$
$863$	−51.6586			−1.75848			−0.879239	+	0.476381i	$0.841948\pi$
$864$		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	$-0.644470\pi$
$877$	15.0174	−	36.2552i	0.507101	−	1.22425i	0.945545	−	0.325492i	$-0.105530\pi$
$878$		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	0.356289	−	0.934376i	$-0.384042\pi$
$887$	−17.2169	−	17.2169i	−0.578086	−	0.578086i	−0.934376	+	0.356289i	$0.884042\pi$
$888$		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	$0.0208974\pi$
$911$			3.96023i			0.131208i	−0.997846	+	0.0656041i	$0.979103\pi$
$912$		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	−0.931594	−	0.363500i	$-0.881582\pi$
$919$	−17.2218	+	17.2218i	−0.568095	+	0.568095i	0.363500	+	0.931594i	$0.381582\pi$
$920$		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	0.656064	−	0.754705i	$-0.272220\pi$
$941$	17.9856	+	7.44989i	0.586315	+	0.242859i	−0.0697497	+	0.997565i	$0.522220\pi$
$942$		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	0.581691	−	0.813410i	$-0.302391\pi$
$967$	−7.20570	−	7.20570i	−0.231720	−	0.231720i	−0.813410	+	0.581691i	$0.802391\pi$
$968$		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	0.914831	−	0.403837i	$-0.132324\pi$
$983$	16.0211	+	16.0211i	0.510994	+	0.510994i	−0.403837	+	0.914831i	$0.632324\pi$
$984$		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	$-0.874485\pi$
$991$		−	24.1879i		−	0.768355i	0.923259	−	0.384177i	$-0.125515\pi$
$992$		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	$-0.897744\pi$
$997$	−15.8249	−	38.2046i	−0.501178	−	1.20995i	0.447664	−	0.894202i	$-0.352256\pi$
$998$		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	768.2.o.b.95.10		56
3.2	odd	2	inner	768.2.o.b.95.9		56
4.3	odd	2		768.2.o.a.95.5		56
8.3	odd	2		384.2.o.a.47.10		56
8.5	even	2		96.2.o.a.35.10	yes	56
12.11	even	2		768.2.o.a.95.6		56
24.5	odd	2		96.2.o.a.35.5	yes	56
24.11	even	2		384.2.o.a.47.9		56
32.5	even	8		384.2.o.a.335.9		56
32.11	odd	8	inner	768.2.o.b.671.9		56
32.21	even	8		768.2.o.a.671.6		56
32.27	odd	8		96.2.o.a.11.5	✓	56
96.5	odd	8		384.2.o.a.335.10		56
96.11	even	8	inner	768.2.o.b.671.10		56
96.53	odd	8		768.2.o.a.671.5		56
96.59	even	8		96.2.o.a.11.10	yes	56

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

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.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

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