LMFDB - Embedded newform 768.2.o.a.671.6

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			671.6
Character	$\chi$	$=$	768.671
Dual form			768.2.o.a.95.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.266294 - 1.71146i) q^{3} +(3.14689 + 1.30348i) q^{5} +(-0.663471 + 0.663471i) q^{7} +(-2.85817 + 0.911503i) q^{9} +O(q^{10})$	\(q+(-0.266294 - 1.71146i) q^{3} +(3.14689 + 1.30348i) q^{5} +(-0.663471 + 0.663471i) q^{7} +(-2.85817 + 0.911503i) q^{9} +(1.91929 + 0.794997i) q^{11} +(2.31672 + 5.59306i) q^{13} +(1.39286 - 5.73287i) q^{15} +2.24987 q^{17} +(3.08841 - 1.27926i) q^{19} +(1.31218 + 0.958824i) q^{21} +(-4.32171 + 4.32171i) q^{23} +(4.66830 + 4.66830i) q^{25} +(2.32111 + 4.64892i) q^{27} +(-0.546766 - 1.32001i) q^{29} -2.34273i q^{31} +(0.849507 - 3.49649i) q^{33} +(-2.95269 + 1.22305i) q^{35} +(0.324682 - 0.783851i) q^{37} +(8.95535 - 5.45437i) q^{39} +(-4.73908 - 4.73908i) q^{41} +(0.951664 - 2.29752i) q^{43} +(-10.1825 - 0.857185i) q^{45} -3.02812i q^{47} +6.11961i q^{49} +(-0.599128 - 3.85056i) q^{51} +(3.49549 - 8.43885i) q^{53} +(5.00353 + 5.00353i) q^{55} +(-3.01183 - 4.94502i) q^{57} +(3.11165 - 7.51220i) q^{59} +(1.01639 - 0.421005i) q^{61} +(1.29156 - 2.50107i) q^{63} +20.6205i q^{65} +(3.46052 + 8.35443i) q^{67} +(8.54728 + 6.24558i) q^{69} +(-0.167408 - 0.167408i) q^{71} +(3.86922 - 3.86922i) q^{73} +(6.74645 - 9.23273i) q^{75} +(-1.80085 + 0.745938i) q^{77} -2.44740 q^{79} +(7.33832 - 5.21047i) q^{81} +(-5.17660 - 12.4974i) q^{83} +(7.08008 + 2.93267i) q^{85} +(-2.11354 + 1.28728i) q^{87} +(6.63254 - 6.63254i) q^{89} +(-5.24791 - 2.17376i) q^{91} +(-4.00949 + 0.623856i) q^{93} +11.3864 q^{95} +4.48787 q^{97} +(-6.21032 - 0.522799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{8}\right)$

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
$3$	−0.266294	−	1.71146i	−0.153745	−	0.988111i
$3$	−0.266294	−	1.71146i	−0.153745	−	0.988111i
$4$		0			0
$5$	3.14689	+	1.30348i	1.40733	+	0.582935i	0.951644	−	0.307205i	$-0.0993936\pi$
$5$	3.14689	+	1.30348i	1.40733	+	0.582935i	0.455687	+	0.890140i	$0.349394\pi$
$6$		0			0
$7$	−0.663471	+	0.663471i	−0.250769	+	0.250769i	−0.821286	−	0.570517i	$-0.806743\pi$
$7$	−0.663471	+	0.663471i	−0.250769	+	0.250769i	0.570517	+	0.821286i	$0.306743\pi$
$8$		0			0
$9$	−2.85817	+	0.911503i	−0.952725	+	0.303834i
$10$		0			0
$11$	1.91929	+	0.794997i	0.578689	+	0.239701i	0.652776	−	0.757551i	$-0.273604\pi$
$11$	1.91929	+	0.794997i	0.578689	+	0.239701i	−0.0740873	+	0.997252i	$0.523604\pi$
$12$		0			0
$13$	2.31672	+	5.59306i	0.642543	+	1.55123i	0.823238	+	0.567696i	$0.192165\pi$
$13$	2.31672	+	5.59306i	0.642543	+	1.55123i	−0.180696	+	0.983539i	$0.557835\pi$
$14$		0			0
$15$	1.39286	−	5.73287i	0.359634	−	1.48022i
$16$		0			0
$17$	2.24987			0.545673			0.272837	−	0.962060i	$-0.412038\pi$
$17$	2.24987			0.545673			0.272837	+	0.962060i	$0.412038\pi$
$18$		0			0
$19$	3.08841	−	1.27926i	0.708530	−	0.293483i	0.000833646	−	1.00000i	$-0.499735\pi$
$19$	3.08841	−	1.27926i	0.708530	−	0.293483i	0.707696	+	0.706517i	$0.249735\pi$
$20$		0			0
$21$	1.31218	+	0.958824i	0.286342	+	0.209233i
$22$		0			0
$23$	−4.32171	+	4.32171i	−0.901140	+	0.901140i	−0.995535	−	0.0943951i	$-0.969908\pi$
$23$	−4.32171	+	4.32171i	−0.901140	+	0.901140i	0.0943951	+	0.995535i	$0.469908\pi$
$24$		0			0
$25$	4.66830	+	4.66830i	0.933659	+	0.933659i
$26$		0			0
$27$	2.32111	+	4.64892i	0.446699	+	0.894684i
$28$		0			0
$29$	−0.546766	−	1.32001i	−0.101532	−	0.245120i	0.864948	−	0.501861i	$-0.167351\pi$
$29$	−0.546766	−	1.32001i	−0.101532	−	0.245120i	−0.966480	+	0.256741i	$0.917351\pi$
$30$		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	−0.894941	−	0.446184i	$-0.852783\pi$
$37$	0.324682	−	0.783851i	0.0533774	−	0.128864i	0.948319	+	0.317319i	$0.102783\pi$
$38$		0			0
$39$	8.95535	−	5.45437i	1.43400	−	0.873398i
$40$		0			0
$41$	−4.73908	−	4.73908i	−0.740120	−	0.740120i	0.232481	−	0.972601i	$-0.425316\pi$
$41$	−4.73908	−	4.73908i	−0.740120	−	0.740120i	−0.972601	+	0.232481i	$0.925316\pi$
$42$		0			0
$43$	0.951664	−	2.29752i	0.145127	−	0.350369i	−0.834555	−	0.550925i	$-0.814275\pi$
$43$	0.951664	−	2.29752i	0.145127	−	0.350369i	0.979682	+	0.200556i	$0.0642750\pi$
$44$		0			0
$45$	−10.1825	−	0.857185i	−1.51791	−	0.127782i
$46$		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
$51$	−0.599128	−	3.85056i	−0.0838946	−	0.539186i
$52$		0			0
$53$	3.49549	−	8.43885i	0.480142	−	1.15916i	−0.479399	−	0.877597i	$-0.659145\pi$
$53$	3.49549	−	8.43885i	0.480142	−	1.15916i	0.959541	−	0.281568i	$-0.0908545\pi$
$54$		0			0
$55$	5.00353	+	5.00353i	0.674676	+	0.674676i
$56$		0			0
$57$	−3.01183	−	4.94502i	−0.398926	−	0.654984i
$58$		0			0
$59$	3.11165	−	7.51220i	0.405103	−	0.978005i	−0.581305	−	0.813686i	$-0.697458\pi$
$59$	3.11165	−	7.51220i	0.405103	−	0.978005i	0.986407	−	0.164318i	$-0.0525425\pi$
$60$		0			0
$61$	1.01639	−	0.421005i	0.130136	−	0.0539041i	−0.316665	−	0.948537i	$-0.602563\pi$
$61$	1.01639	−	0.421005i	0.130136	−	0.0539041i	0.446801	+	0.894633i	$0.352563\pi$
$62$		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	0.981527	+	0.191325i	$0.0612784\pi$
$67$	3.46052	+	8.35443i	0.422770	+	1.02066i	−0.558757	+	0.829331i	$0.688722\pi$
$68$		0			0
$69$	8.54728	+	6.24558i	1.02897	+	0.751880i
$70$		0			0
$71$	−0.167408	−	0.167408i	−0.0198677	−	0.0198677i	0.697103	−	0.716971i	$-0.254472\pi$
$71$	−0.167408	−	0.167408i	−0.0198677	−	0.0198677i	−0.716971	+	0.697103i	$0.754472\pi$
$72$		0			0
$73$	3.86922	−	3.86922i	0.452858	−	0.452858i	−0.443444	−	0.896302i	$-0.646244\pi$
$73$	3.86922	−	3.86922i	0.452858	−	0.452858i	0.896302	+	0.443444i	$0.146244\pi$
$74$		0			0
$75$	6.74645	−	9.23273i	0.779013	−	1.06610i
$76$		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	−0.903066	−	0.429502i	$-0.858689\pi$
$83$	−5.17660	−	12.4974i	−0.568206	−	1.37177i	0.334860	−	0.942268i	$-0.391311\pi$
$84$		0			0
$85$	7.08008	+	2.93267i	0.767943	+	0.318092i
$86$		0			0
$87$	−2.11354	+	1.28728i	−0.226595	+	0.138011i
$88$		0			0
$89$	6.63254	−	6.63254i	0.703048	−	0.703048i	−0.262016	−	0.965064i	$-0.584387\pi$
$89$	6.63254	−	6.63254i	0.703048	−	0.703048i	0.965064	+	0.262016i	$0.0843872\pi$
$90$		0			0
$91$	−5.24791	−	2.17376i	−0.550130	−	0.227871i
$92$		0			0
$93$	−4.00949	+	0.623856i	−0.415764	+	0.0646909i
$94$		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
$99$	−6.21032	−	0.522799i	−0.624160	−	0.0525433i
$100$		0			0
$101$	−12.6091	−	5.22285i	−1.25465	−	0.519693i	−0.346386	−	0.938092i	$-0.612591\pi$
$101$	−12.6091	−	5.22285i	−1.25465	−	0.519693i	−0.908263	+	0.418399i	$0.862591\pi$
$102$		0			0
$103$	−5.37192	+	5.37192i	−0.529311	+	0.529311i	−0.920367	−	0.391056i	$-0.872110\pi$
$103$	−5.37192	+	5.37192i	−0.529311	+	0.529311i	0.391056	+	0.920367i	$0.372110\pi$
$104$		0			0
$105$	2.87948	+	4.72772i	0.281008	+	0.461378i
$106$		0			0
$107$	13.4838	+	5.58517i	1.30353	+	0.539939i	0.922989	−	0.384826i	$-0.125739\pi$
$107$	13.4838	+	5.58517i	1.30353	+	0.539939i	0.380538	+	0.924765i	$0.375739\pi$
$108$		0			0
$109$	1.82205	+	4.39883i	0.174521	+	0.421331i	0.986801	−	0.161936i	$-0.0517739\pi$
$109$	1.82205	+	4.39883i	0.174521	+	0.421331i	−0.812280	+	0.583268i	$0.801774\pi$
$110$		0			0
$111$	−1.42799	−	0.346944i	−0.135539	−	0.0329305i
$112$		0			0
$113$	−5.85162			−0.550475			−0.275237	−	0.961376i	$-0.588756\pi$
$113$	−5.85162			−0.550475			−0.275237	+	0.961376i	$0.588756\pi$
$114$		0			0
$115$	−19.2332	+	7.96666i	−1.79351	+	0.742895i
$116$		0			0
$117$	−11.7197	−	13.8742i	−1.08348	−	1.28267i
$118$		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
$123$	−6.84875	+	9.37273i	−0.617531	+	0.845110i
$124$		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	−0.957990	−	0.286800i	$-0.907408\pi$
$131$	−16.3968	+	6.79177i	−1.43259	+	0.593400i	−0.474603	+	0.880200i	$0.657408\pi$
$132$		0			0
$133$	−1.20032	+	2.89782i	−0.104081	+	0.251273i
$134$		0			0
$135$	1.24450	+	17.6551i	0.107110	+	1.51951i
$136$		0			0
$137$	−8.43673	−	8.43673i	−0.720799	−	0.720799i	0.247969	−	0.968768i	$-0.420237\pi$
$137$	−8.43673	−	8.43673i	−0.720799	−	0.720799i	−0.968768	+	0.247969i	$0.920237\pi$
$138$		0			0
$139$	−7.74040	+	18.6870i	−0.656532	+	1.58501i	0.146592	+	0.989197i	$0.453169\pi$
$139$	−7.74040	+	18.6870i	−0.656532	+	1.58501i	−0.803124	+	0.595812i	$0.796831\pi$
$140$		0			0
$141$	−5.18249	+	0.806371i	−0.436445	+	0.0679086i
$142$		0			0
$143$			12.5765i			1.05170i
$144$		0			0
$145$		−	4.86662i		−	0.404151i
$146$		0			0
$147$	10.4735	−	1.62962i	0.863836	−	0.134409i
$148$		0			0
$149$	−4.26837	+	10.3048i	−0.349678	+	0.844198i	0.646979	+	0.762508i	$0.276032\pi$
$149$	−4.26837	+	10.3048i	−0.349678	+	0.844198i	−0.996658	+	0.0816908i	$0.973968\pi$
$150$		0			0
$151$	−12.1716	−	12.1716i	−0.990514	−	0.990514i	0.00944142	−	0.999955i	$-0.496995\pi$
$151$	−12.1716	−	12.1716i	−0.990514	−	0.990514i	−0.999955	+	0.00944142i	$0.996995\pi$
$152$		0			0
$153$	−6.43052	+	2.05076i	−0.519877	+	0.165794i
$154$		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	$-0.480596\pi$
$157$	10.1467	−	4.20290i	0.809795	−	0.335428i	0.748872	+	0.662714i	$0.230596\pi$
$158$		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	−0.999440	−	0.0334571i	$-0.989348\pi$
$163$	−4.03936	−	9.75187i	−0.316387	−	0.763826i	0.683053	−	0.730369i	$-0.260652\pi$
$164$		0			0
$165$	7.23092	−	9.89575i	0.562926	−	0.770383i
$166$		0			0
$167$	−12.8761	−	12.8761i	−0.996385	−	0.996385i	0.00360853	−	0.999993i	$-0.498851\pi$
$167$	−12.8761	−	12.8761i	−0.996385	−	0.996385i	−0.999993	+	0.00360853i	$0.998851\pi$
$168$		0			0
$169$	−16.7227	+	16.7227i	−1.28636	+	1.28636i
$170$		0			0
$171$	−7.66116	+	6.47145i	−0.585864	+	0.494884i
$172$		0			0
$173$	9.91155	−	4.10550i	0.753561	−	0.312135i	0.0273673	−	0.999625i	$-0.491288\pi$
$173$	9.91155	−	4.10550i	0.753561	−	0.312135i	0.726194	+	0.687490i	$0.241288\pi$
$174$		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	0.695536	+	0.718491i	$0.255167\pi$
$179$	9.52280	+	22.9901i	0.711768	+	1.71836i	0.0162316	+	0.999868i	$0.494833\pi$
$180$		0			0
$181$	−11.0607	−	4.58151i	−0.822139	−	0.340541i	−0.0683528	−	0.997661i	$-0.521774\pi$
$181$	−11.0607	−	4.58151i	−0.822139	−	0.340541i	−0.753786	+	0.657120i	$0.771774\pi$
$182$		0			0
$183$	−0.991192	−	1.62741i	−0.0732710	−	0.120301i
$184$		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
$189$	−4.62442	−	1.54443i	−0.336377	−	0.112341i
$190$		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
$195$	35.2912	−	5.49113i	2.52725	−	0.393228i
$196$		0			0
$197$	4.23540	+	1.75436i	0.301759	+	0.124993i	0.528425	−	0.848980i	$-0.322783\pi$
$197$	4.23540	+	1.75436i	0.301759	+	0.124993i	−0.226666	+	0.973973i	$0.572783\pi$
$198$		0			0
$199$	−3.74082	+	3.74082i	−0.265179	+	0.265179i	−0.827154	−	0.561975i	$-0.810042\pi$
$199$	−3.74082	+	3.74082i	−0.265179	+	0.265179i	0.561975	+	0.827154i	$0.310042\pi$
$200$		0			0
$201$	13.3767	−	8.14727i	0.943522	−	0.574664i
$202$		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	$-0.618306\pi$
$211$	0.564367	−	0.233768i	0.0388526	−	0.0160933i	0.402025	+	0.915629i	$0.368306\pi$
$212$		0			0
$213$	−0.241932	+	0.331092i	−0.0165769	+	0.0226861i
$214$		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
$219$	−7.65236	−	5.59165i	−0.517098	−	0.377849i
$220$		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	−0.323262	−	0.946309i	$-0.604780\pi$
$227$	1.76729	−	0.732035i	0.117299	−	0.0485869i	0.440561	+	0.897723i	$0.354780\pi$
$228$		0			0
$229$	4.83167	−	11.6647i	0.319286	−	0.770824i	−0.680007	−	0.733206i	$-0.738023\pi$
$229$	4.83167	−	11.6647i	0.319286	−	0.770824i	0.999292	−	0.0376176i	$-0.0119769\pi$
$230$		0			0
$231$	1.75620	+	2.88345i	0.115549	+	0.189717i
$232$		0			0
$233$	6.98725	+	6.98725i	0.457750	+	0.457750i	0.897916	−	0.440166i	$-0.145080\pi$
$233$	6.98725	+	6.98725i	0.457750	+	0.457750i	−0.440166	+	0.897916i	$0.645080\pi$
$234$		0			0
$235$	3.94710	−	9.52914i	0.257480	−	0.621613i
$236$		0			0
$237$	0.651729	+	4.18862i	0.0423344	+	0.272080i
$238$		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	$-0.858986\pi$
$241$		−	13.3092i		−	0.857322i	0.903466	−	0.428661i	$-0.141014\pi$
$242$		0			0
$243$	−10.8717	−	11.1717i	−0.697417	−	0.716666i
$244$		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
$249$	−20.0103	+	12.1875i	−1.26810	+	0.772353i
$250$		0			0
$251$	−5.55430	+	13.4093i	−0.350584	+	0.846385i	0.645964	+	0.763368i	$0.276456\pi$
$251$	−5.55430	+	13.4093i	−0.350584	+	0.846385i	−0.996548	+	0.0830174i	$0.973544\pi$
$252$		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
$261$	2.76595	+	3.27444i	0.171208	+	0.202683i
$262$		0			0
$263$	−2.42769	−	2.42769i	−0.149698	−	0.149698i	0.628285	−	0.777983i	$-0.283757\pi$
$263$	−2.42769	−	2.42769i	−0.149698	−	0.149698i	−0.777983	+	0.628285i	$0.783757\pi$
$264$		0			0
$265$	21.9998	−	21.9998i	1.35144	−	1.35144i
$266$		0			0
$267$	−13.1175	−	9.58511i	−0.802780	−	0.586599i
$268$		0			0
$269$	11.0872	−	4.59246i	0.675997	−	0.280007i	−0.0181552	−	0.999835i	$-0.505779\pi$
$269$	11.0872	−	4.59246i	0.675997	−	0.280007i	0.694153	+	0.719828i	$0.255779\pi$
$270$		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	$-0.0486547\pi$
$277$	26.2888	+	10.8892i	1.57954	+	0.654267i	0.591199	+	0.806526i	$0.298655\pi$
$278$		0			0
$279$	2.13541	+	6.69594i	0.127844	+	0.400875i
$280$		0			0
$281$	−0.109141	+	0.109141i	−0.00651081	+	0.00651081i	−0.710355	−	0.703844i	$-0.751465\pi$
$281$	−0.109141	+	0.109141i	−0.00651081	+	0.00651081i	0.703844	+	0.710355i	$0.251465\pi$
$282$		0			0
$283$	11.5159	+	4.77003i	0.684547	+	0.283549i	0.697726	−	0.716364i	$-0.254195\pi$
$283$	11.5159	+	4.77003i	0.684547	+	0.283549i	−0.0131791	+	0.999913i	$0.504195\pi$
$284$		0			0
$285$	−3.03213	−	19.4873i	−0.179608	−	1.15433i
$286$		0			0
$287$	6.28849			0.371198
$288$		0			0
$289$	−11.9381			−0.702240
$290$		0			0
$291$	−1.19510	−	7.68080i	−0.0700577	−	0.450257i
$292$		0			0
$293$	−14.6551	−	6.07035i	−0.856161	−	0.354634i	−0.0889561	−	0.996036i	$-0.528353\pi$
$293$	−14.6551	−	6.07035i	−0.856161	−	0.354634i	−0.767205	+	0.641402i	$0.778353\pi$
$294$		0			0
$295$	19.5840	−	19.5840i	1.14023	−	1.14023i
$296$		0			0
$297$	0.759024	+	10.7679i	0.0440430	+	0.624818i
$298$		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	$-0.437629\pi$
$307$	17.9759	−	7.44586i	1.02594	−	0.424958i	0.831245	+	0.555906i	$0.187629\pi$
$308$		0			0
$309$	10.6243	+	7.76330i	0.604397	+	0.441639i
$310$		0			0
$311$	14.7567	−	14.7567i	0.836776	−	0.836776i	−0.151657	−	0.988433i	$-0.548461\pi$
$311$	14.7567	−	14.7567i	0.836776	−	0.836776i	0.988433	+	0.151657i	$0.0484609\pi$
$312$		0			0
$313$	−3.76309	−	3.76309i	−0.212703	−	0.212703i	0.592712	−	0.805415i	$-0.298057\pi$
$313$	−3.76309	−	3.76309i	−0.212703	−	0.212703i	−0.805415	+	0.592712i	$0.798057\pi$
$314$		0			0
$315$	7.32450	−	6.18707i	0.412689	−	0.348602i
$316$		0			0
$317$	−5.65481	−	13.6519i	−0.317606	−	0.766768i	−0.999380	−	0.0352055i	$-0.988791\pi$
$317$	−5.65481	−	13.6519i	−0.317606	−	0.766768i	0.681774	−	0.731562i	$-0.261209\pi$
$318$		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
$327$	7.04321	−	4.28975i	0.389490	−	0.237224i
$328$		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	$-0.785152\pi$
$331$	3.87845	−	9.36340i	0.213179	−	0.514659i	0.993908	+	0.110210i	$0.0351523\pi$
$332$		0			0
$333$	−0.213514	+	2.53633i	−0.0117005	+	0.138990i
$334$		0			0
$335$			30.8012i			1.68285i
$336$		0			0
$337$			18.4557i			1.00535i	0.864476	+	0.502674i	$0.167650\pi$
$337$			18.4557i			1.00535i	−0.864476	+	0.502674i	$0.832350\pi$
$338$		0			0
$339$	1.55825	+	10.0148i	0.0846328	+	0.543930i
$340$		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
$345$	18.7563	+	30.7954i	1.00981	+	1.65797i
$346$		0			0
$347$	2.01715	−	4.86983i	0.108286	−	0.261426i	−0.860443	−	0.509547i	$-0.829813\pi$
$347$	2.01715	−	4.86983i	0.108286	−	0.261426i	0.968729	+	0.248121i	$0.0798130\pi$
$348$		0			0
$349$	−19.0402	+	7.88672i	−1.01920	+	0.422166i	−0.828803	−	0.559541i	$-0.810977\pi$
$349$	−19.0402	+	7.88672i	−1.01920	+	0.422166i	−0.190397	+	0.981707i	$0.560977\pi$
$350$		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
$357$	2.95224	+	2.15723i	0.156249	+	0.114173i
$358$		0			0
$359$	0.514805	+	0.514805i	0.0271704	+	0.0271704i	0.720561	−	0.693391i	$-0.243884\pi$
$359$	0.514805	+	0.514805i	0.0271704	+	0.0271704i	−0.693391	+	0.720561i	$0.743884\pi$
$360$		0			0
$361$	−5.53327	+	5.53327i	−0.291225	+	0.291225i
$362$		0			0
$363$	−6.83058	+	9.34786i	−0.358512	+	0.490636i
$364$		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	$-0.593563\pi$
$373$	−22.6229	−	9.37070i	−1.17137	−	0.485196i	−0.881644	+	0.471914i	$0.843563\pi$
$374$		0			0
$375$	8.07176	−	4.91620i	0.416824	−	0.253872i
$376$		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	$-0.503761\pi$
$379$	−14.1576	−	5.86429i	−0.727229	−	0.301228i	−0.715413	+	0.698702i	$0.753761\pi$
$380$		0			0
$381$	17.6133	−	2.74055i	0.902359	−	0.140403i
$382$		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
$387$	−0.625825	+	7.43416i	−0.0318125	+	0.377900i
$388$		0			0
$389$	−31.0923	−	12.8788i	−1.57644	−	0.652983i	−0.588596	−	0.808427i	$-0.700319\pi$
$389$	−31.0923	−	12.8788i	−1.57644	−	0.652983i	−0.987845	+	0.155444i	$0.950319\pi$
$390$		0			0
$391$	−9.72329	+	9.72329i	−0.491728	+	0.491728i
$392$		0			0
$393$	15.9902	+	26.2538i	0.806599	+	1.32433i
$394$		0			0
$395$	−7.70170	−	3.19015i	−0.387514	−	0.160514i
$396$		0			0
$397$	8.21223	+	19.8261i	0.412160	+	0.995042i	0.984557	+	0.175065i	$0.0560136\pi$
$397$	8.21223	+	19.8261i	0.412160	+	0.995042i	−0.572397	+	0.819977i	$0.693986\pi$
$398$		0			0
$399$	5.27914	+	1.28262i	0.264288	+	0.0642113i
$400$		0			0
$401$	−15.2053			−0.759315			−0.379657	−	0.925127i	$-0.623958\pi$
$401$	−15.2053			−0.759315			−0.379657	+	0.925127i	$0.623958\pi$
$402$		0			0
$403$	13.1030	−	5.42745i	0.652709	−	0.270361i
$404$		0			0
$405$	29.8846	−	6.83138i	1.48498	−	0.339454i
$406$		0			0
$407$	1.24632	−	1.24632i	0.0617777	−	0.0617777i
$408$		0			0
$409$	23.0147	+	23.0147i	1.13800	+	1.13800i	0.988808	+	0.149193i	$0.0476677\pi$
$409$	23.0147	+	23.0147i	1.13800	+	1.13800i	0.149193	+	0.988808i	$0.452332\pi$
$410$		0			0
$411$	−12.1925	+	16.6858i	−0.601410	+	0.823048i
$412$		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	−0.102431	−	0.994740i	$-0.532662\pi$
$419$	10.8187	−	4.48124i	0.528527	−	0.218923i	0.630958	+	0.775817i	$0.282662\pi$
$420$		0			0
$421$	11.0208	−	26.6066i	0.537121	−	1.29673i	−0.389603	−	0.920983i	$-0.627388\pi$
$421$	11.0208	−	26.6066i	0.537121	−	1.29673i	0.926724	−	0.375742i	$-0.122612\pi$
$422$		0			0
$423$	2.76014	+	8.65489i	0.134203	+	0.420815i
$424$		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
$429$	21.5241	−	3.34905i	1.03920	−	0.161694i
$430$		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	$0.0858292\pi$
$433$			11.0862i			0.532769i	−0.963867	+	0.266385i	$0.914171\pi$
$434$		0			0
$435$	−8.32902	+	1.29595i	−0.399346	+	0.0621362i
$436$		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	$-0.464361\pi$
$439$	−18.4802	−	18.4802i	−0.882011	−	0.882011i	−0.993739	+	0.111728i	$0.964361\pi$
$440$		0			0
$441$	−5.57805	−	17.4909i	−0.265621	−	0.832901i
$442$		0			0
$443$	15.7855	−	38.1095i	0.749991	−	1.81064i	0.190740	−	0.981641i	$-0.438911\pi$
$443$	15.7855	−	38.1095i	0.749991	−	1.81064i	0.559251	−	0.828998i	$-0.311089\pi$
$444$		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
$453$	−17.5900	+	24.0725i	−0.826451	+	1.13102i
$454$		0			0
$455$	−13.6811	−	13.6811i	−0.641381	−	0.641381i
$456$		0			0
$457$	−3.61836	+	3.61836i	−0.169260	+	0.169260i	−0.786654	−	0.617394i	$-0.788188\pi$
$457$	−3.61836	+	3.61836i	−0.169260	+	0.169260i	0.617394	+	0.786654i	$0.288188\pi$
$458$		0			0
$459$	5.22221	+	10.4595i	0.243752	+	0.488206i
$460$		0			0
$461$	11.0476	−	4.57608i	0.514539	−	0.213129i	−0.110277	−	0.993901i	$-0.535174\pi$
$461$	11.0476	−	4.57608i	0.514539	−	0.213129i	0.624816	+	0.780772i	$0.285174\pi$
$462$		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	−0.696315	−	0.717736i	$-0.745178\pi$
$467$	−15.3748	−	37.1181i	−0.711462	−	1.71762i	−0.0151469	−	0.999885i	$-0.504822\pi$
$468$		0			0
$469$	−7.83888	−	3.24697i	−0.361966	−	0.149931i
$470$		0			0
$471$	−9.89510	−	16.2465i	−0.455942	−	0.748597i
$472$		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
$477$	−2.29867	+	27.3058i	−0.105249	+	1.25025i
$478$		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
$483$	−9.81464	+	1.52711i	−0.446582	+	0.0694859i
$484$		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	$-0.739115\pi$
$487$	1.06704	−	1.06704i	0.0483522	−	0.0483522i	0.730869	+	0.682517i	$0.239115\pi$
$488$		0			0
$489$	−15.6143	+	9.51006i	−0.706101	+	0.430060i
$490$		0			0
$491$	24.4454	+	10.1256i	1.10321	+	0.456964i	0.858594	−	0.512657i	$-0.171339\pi$
$491$	24.4454	+	10.1256i	1.10321	+	0.456964i	0.244614	+	0.969621i	$0.421339\pi$
$492$		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	$-0.430059\pi$
$499$	23.7276	−	9.82828i	1.06219	−	0.439974i	0.844229	+	0.535983i	$0.180059\pi$
$500$		0			0
$501$	−18.6081	+	25.4658i	−0.831349	+	1.13773i
$502$		0			0
$503$	8.35178	−	8.35178i	0.372387	−	0.372387i	−0.495959	−	0.868346i	$-0.665183\pi$
$503$	8.35178	−	8.35178i	0.372387	−	0.372387i	0.868346	+	0.495959i	$0.165183\pi$
$504$		0			0
$505$	−32.8714	−	32.8714i	−1.46276	−	1.46276i
$506$		0			0
$507$	33.0734	+	24.1670i	1.46884	+	1.07330i
$508$		0			0
$509$	2.98703	+	7.21134i	0.132398	+	0.319637i	0.976150	−	0.217096i	$-0.0696584\pi$
$509$	2.98703	+	7.21134i	0.132398	+	0.319637i	−0.843752	+	0.536733i	$0.819658\pi$
$510$		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
$519$	−9.66577	−	15.8699i	−0.424280	−	0.696612i
$520$		0			0
$521$	−5.48494	−	5.48494i	−0.240299	−	0.240299i	0.576675	−	0.816974i	$-0.304350\pi$
$521$	−5.48494	−	5.48494i	−0.240299	−	0.240299i	−0.816974	+	0.576675i	$0.804350\pi$
$522$		0			0
$523$	6.43166	−	15.5274i	0.281237	−	0.678966i	−0.718628	−	0.695394i	$-0.755230\pi$
$523$	6.43166	−	15.5274i	0.281237	−	0.678966i	0.999865	+	0.0164288i	$0.00522969\pi$
$524$		0			0
$525$	1.64958	+	10.6017i	0.0719934	+	0.462697i
$526$		0			0
$527$		−	5.27084i		−	0.229601i
$528$		0			0
$529$		−	14.3544i		−	0.624106i
$530$		0			0
$531$	−2.04626	+	24.3074i	−0.0888000	+	1.05485i
$532$		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
$537$	36.8107	−	22.4200i	1.58850	−	0.967495i
$538$		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	$-0.598522\pi$
$541$	3.57097	−	1.47914i	0.153528	−	0.0635934i	0.458124	+	0.888888i	$0.348522\pi$
$542$		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	$-0.0897339\pi$
$547$	1.97916	+	4.77812i	0.0846228	+	0.204298i	−0.875904	+	0.482486i	$0.839734\pi$
$548$		0			0
$549$	−2.52129	+	2.12975i	−0.107606	+	0.0908956i
$550$		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
$555$	−4.04148	−	2.95315i	−0.171551	−	0.125354i
$556$		0			0
$557$	−30.8826	+	12.7920i	−1.30854	+	0.542014i	−0.924457	−	0.381286i	$-0.875481\pi$
$557$	−30.8826	+	12.7920i	−1.30854	+	0.542014i	−0.384080	+	0.923300i	$0.625481\pi$
$558$		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	0.998636	−	0.0522151i	$-0.0166281\pi$
$563$	6.06412	+	14.6401i	0.255572	+	0.617005i	−0.743064	+	0.669221i	$0.766628\pi$
$564$		0			0
$565$	−18.4144	−	7.62750i	−0.774700	−	0.320891i
$566$		0			0
$567$	−1.41177	+	8.32577i	−0.0592888	+	0.349649i
$568$		0			0
$569$	−24.5419	+	24.5419i	−1.02885	+	1.02885i	−0.0292808	+	0.999571i	$0.509322\pi$
$569$	−24.5419	+	24.5419i	−1.02885	+	1.02885i	−0.999571	+	0.0292808i	$0.990678\pi$
$570$		0			0
$571$	−37.5798	−	15.5661i	−1.57266	−	0.651419i	−0.585435	−	0.810720i	$-0.699076\pi$
$571$	−37.5798	−	15.5661i	−1.57266	−	0.651419i	−0.987230	+	0.159301i	$0.949076\pi$
$572$		0			0
$573$	0.0356051	+	0.228832i	0.00148743	+	0.00955959i
$574$		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
$579$	−1.99395	−	12.8150i	−0.0828657	−	0.532573i
$580$		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
$585$	−18.7957	−	58.9371i	−0.777105	−	2.43675i
$586$		0			0
$587$	16.1148	+	6.67499i	0.665131	+	0.275506i	0.689596	−	0.724195i	$-0.257788\pi$
$587$	16.1148	+	6.67499i	0.665131	+	0.275506i	−0.0244651	+	0.999701i	$0.507788\pi$
$588$		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	$-0.757624\pi$
$593$	−35.2533			−1.44768			−0.723839	+	0.689969i	$0.757624\pi$
$594$		0			0
$595$	−6.64317	+	2.75169i	−0.272344	+	0.112808i
$596$		0			0
$597$	7.39841	+	5.40609i	0.302797	+	0.221257i
$598$		0			0
$599$	−12.1323	+	12.1323i	−0.495712	+	0.495712i	−0.910100	−	0.414388i	$-0.863996\pi$
$599$	−12.1323	+	12.1323i	−0.495712	+	0.495712i	0.414388	+	0.910100i	$0.363996\pi$
$600$		0			0
$601$	0.0132863	+	0.0132863i	0.000541959	+	0.000541959i	0.707378	−	0.706836i	$-0.249878\pi$
$601$	0.0132863	+	0.0132863i	0.000541959	+	0.000541959i	−0.706836	+	0.707378i	$0.749878\pi$
$602$		0			0
$603$	−17.5059	−	20.7241i	−0.712894	−	0.843953i
$604$		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	−0.471362	−	0.881940i	$-0.656237\pi$
$613$	12.0221	−	29.0239i	0.485567	−	1.17226i	0.956929	−	0.290322i	$-0.0937626\pi$
$614$		0			0
$615$	−33.7694	+	20.5677i	−1.36171	+	0.829369i
$616$		0			0
$617$	−12.5126	−	12.5126i	−0.503739	−	0.503739i	0.408859	−	0.912598i	$-0.365927\pi$
$617$	−12.5126	−	12.5126i	−0.503739	−	0.503739i	−0.912598	+	0.408859i	$0.865927\pi$
$618$		0			0
$619$	9.64869	−	23.2940i	0.387814	−	0.936265i	−0.602589	−	0.798052i	$-0.705864\pi$
$619$	9.64869	−	23.2940i	0.387814	−	0.936265i	0.990402	−	0.138213i	$-0.0441359\pi$
$620$		0			0
$621$	−30.1225	−	10.0601i	−1.20877	−	0.403698i
$622$		0			0
$623$			8.80100i			0.352605i
$624$		0			0
$625$		−	14.4239i		−	0.576955i
$626$		0			0
$627$	−1.84930	−	11.8853i	−0.0738539	−	0.474655i
$628$		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	$-0.379569\pi$
$631$	−14.0643	−	14.0643i	−0.559893	−	0.559893i	−0.929277	+	0.369384i	$0.879569\pi$
$632$		0			0
$633$	−0.550373	−	0.903639i	−0.0218753	−	0.0359164i
$634$		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	0.978122	+	0.208033i	$0.0667062\pi$
$643$	10.9947	+	26.5434i	0.433587	+	1.04677i	−0.544535	+	0.838738i	$0.683294\pi$
$644$		0			0
$645$	−11.8459	−	8.65589i	−0.466430	−	0.340825i
$646$		0			0
$647$	18.0436	+	18.0436i	0.709366	+	0.709366i	0.966402	−	0.257036i	$-0.0827458\pi$
$647$	18.0436	+	18.0436i	0.709366	+	0.709366i	−0.257036	+	0.966402i	$0.582746\pi$
$648$		0			0
$649$	11.9443	−	11.9443i	0.468857	−	0.468857i
$650$		0			0
$651$	2.24627	−	3.07409i	0.0880382	−	0.120483i
$652$		0			0
$653$	9.04305	−	3.74575i	0.353882	−	0.146583i	−0.198659	−	0.980069i	$-0.563658\pi$
$653$	9.04305	−	3.74575i	0.353882	−	0.146583i	0.552540	+	0.833486i	$0.313658\pi$
$654$		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	0.999110	−	0.0421820i	$-0.0134309\pi$
$659$	6.74648	+	16.2874i	0.262805	+	0.634468i	−0.736305	+	0.676650i	$0.763431\pi$
$660$		0			0
$661$	20.2135	+	8.37271i	0.786215	+	0.325661i	0.739421	−	0.673244i	$-0.235100\pi$
$661$	20.2135	+	8.37271i	0.786215	+	0.325661i	0.0467942	+	0.998905i	$0.485100\pi$
$662$		0			0
$663$	20.1484	−	12.2716i	0.782498	−	0.476590i
$664$		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
$669$	18.2933	−	2.84634i	0.707258	−	0.110046i
$670$		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
$675$	−10.8669	+	32.5382i	−0.418266	+	1.25239i
$676$		0			0
$677$	40.9040	+	16.9430i	1.57207	+	0.651173i	0.987132	−	0.159906i	$-0.0511190\pi$
$677$	40.9040	+	16.9430i	1.57207	+	0.651173i	0.584937	+	0.811078i	$0.301119\pi$
$678$		0			0
$679$	−2.97757	+	2.97757i	−0.114269	+	0.114269i
$680$		0			0
$681$	−1.72347	−	2.82970i	−0.0660433	−	0.108434i
$682$		0			0
$683$	8.56803	+	3.54899i	0.327846	+	0.135798i	0.540535	−	0.841322i	$-0.318222\pi$
$683$	8.56803	+	3.54899i	0.327846	+	0.135798i	−0.212688	+	0.977120i	$0.568222\pi$
$684$		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	$-0.856369\pi$
$691$	−32.2776	+	13.3698i	−1.22790	+	0.508611i	−0.327984	+	0.944683i	$0.606369\pi$
$692$		0			0
$693$	4.46723	−	3.77350i	0.169696	−	0.143344i
$694$		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
$699$	10.0977	−	13.8191i	0.381931	−	0.522685i
$700$		0			0
$701$	7.31376	+	17.6570i	0.276237	+	0.666895i	0.999725	−	0.0234415i	$-0.00746235\pi$
$701$	7.31376	+	17.6570i	0.276237	+	0.666895i	−0.723488	+	0.690337i	$0.757462\pi$
$702$		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	0.177192	+	0.984176i	$0.443299\pi$
$709$	−17.1483	+	41.3997i	−0.644019	+	1.55480i	−0.821212	+	0.570624i	$0.806701\pi$
$710$		0			0
$711$	6.99510	−	2.23081i	0.262337	−	0.0836621i
$712$		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
$717$	−11.3122	+	1.76013i	−0.422462	+	0.0657331i
$718$		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
$723$	−22.7781	+	3.54417i	−0.847128	+	0.131809i
$724$		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	$-0.228842\pi$
$727$	2.53270	+	2.53270i	0.0939328	+	0.0939328i	−0.658579	+	0.752512i	$0.728842\pi$
$728$		0			0
$729$	−16.2249	+	21.5813i	−0.600920	+	0.799309i
$730$		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	$-0.546243\pi$
$733$	12.2518	−	5.07484i	0.452529	−	0.187444i	0.597294	+	0.802023i	$0.296243\pi$
$734$		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	$-0.111660\pi$
$739$	0.871699	+	2.10447i	0.0320659	+	0.0774141i	−0.907035	+	0.421054i	$0.861660\pi$
$740$		0			0
$741$	20.6802	−	28.3015i	0.759707	−	1.03968i
$742$		0			0
$743$	37.5946	+	37.5946i	1.37921	+	1.37921i	0.845950	+	0.533262i	$0.179034\pi$
$743$	37.5946	+	37.5946i	1.37921	+	1.37921i	0.533262	+	0.845950i	$0.320966\pi$
$744$		0			0
$745$	−26.8642	+	26.8642i	−0.984226	+	0.984226i
$746$		0			0
$747$	26.1871	+	31.0013i	0.958134	+	1.13428i
$748$		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	$-0.581576\pi$
$757$	−30.7254	−	12.7269i	−1.11673	−	0.462567i	−0.863252	+	0.504773i	$0.831576\pi$
$758$		0			0
$759$	11.4395	+	18.7822i	0.415228	+	0.681749i
$760$		0			0
$761$	8.23145	−	8.23145i	0.298390	−	0.298390i	−0.541993	−	0.840383i	$-0.682330\pi$
$761$	8.23145	−	8.23145i	0.298390	−	0.298390i	0.840383	+	0.541993i	$0.182330\pi$
$762$		0			0
$763$	−4.12738	−	1.70962i	−0.149421	−	0.0618922i
$764$		0			0
$765$	−22.9093	−	1.92856i	−0.828286	−	0.0697271i
$766$		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
$771$	−20.6216	+	3.20862i	−0.742669	+	0.115556i
$772$		0			0
$773$	19.1137	+	7.91717i	0.687474	+	0.284761i	0.698947	−	0.715173i	$-0.253652\pi$
$773$	19.1137	+	7.91717i	0.687474	+	0.284761i	−0.0114736	+	0.999934i	$0.503652\pi$
$774$		0			0
$775$	10.9366	−	10.9366i	0.392853	−	0.392853i
$776$		0			0
$777$	1.17762	−	0.717242i	0.0422468	−	0.0257309i
$778$		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	$-0.822786\pi$
$787$	−30.1761	+	12.4993i	−1.07566	+	0.445554i	−0.226676	+	0.973970i	$0.572786\pi$
$788$		0			0
$789$	−3.50842	+	4.80138i	−0.124903	+	0.170934i
$790$		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
$795$	−43.5101	−	31.7933i	−1.54315	−	1.12759i
$796$		0			0
$797$	−15.0856	−	36.4199i	−0.534360	−	1.29006i	−0.928611	−	0.371055i	$-0.878996\pi$
$797$	−15.0856	−	36.4199i	−0.534360	−	1.29006i	0.394251	−	0.919003i	$-0.371004\pi$
$798$		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
$807$	−10.8123	−	17.7523i	−0.380609	−	0.624910i
$808$		0			0
$809$	12.2843	+	12.2843i	0.431893	+	0.431893i	0.889272	−	0.457379i	$-0.151212\pi$
$809$	12.2843	+	12.2843i	0.431893	+	0.431893i	−0.457379	+	0.889272i	$0.651212\pi$
$810$		0			0
$811$	−2.03182	+	4.90525i	−0.0713468	+	0.172246i	−0.955530	−	0.294894i	$-0.904716\pi$
$811$	−2.03182	+	4.90525i	−0.0713468	+	0.172246i	0.884183	+	0.467140i	$0.154716\pi$
$812$		0			0
$813$	4.43670	+	28.5144i	0.155602	+	1.00004i
$814$		0			0
$815$		−	35.9533i		−	1.25939i
$816$		0			0
$817$		−	8.31311i		−	0.290839i
$818$		0			0
$819$	16.9808	+	1.42949i	0.593358	+	0.0499503i
$820$		0			0
$821$	5.58979	−	13.4949i	0.195085	−	0.470977i	−0.795821	−	0.605532i	$-0.792960\pi$
$821$	5.58979	−	13.4949i	0.195085	−	0.470977i	0.990906	+	0.134555i	$0.0429605\pi$
$822$		0			0
$823$	−16.7820	−	16.7820i	−0.584983	−	0.584983i	0.351286	−	0.936268i	$-0.385745\pi$
$823$	−16.7820	−	16.7820i	−0.584983	−	0.584983i	−0.936268	+	0.351286i	$0.885745\pi$
$824$		0			0
$825$	20.2884	−	12.3569i	0.706352	−	0.430212i
$826$		0			0
$827$	−14.4882	+	34.9777i	−0.503806	+	1.21629i	0.443590	+	0.896230i	$0.353705\pi$
$827$	−14.4882	+	34.9777i	−0.503806	+	1.21629i	−0.947396	+	0.320065i	$0.896295\pi$
$828$		0			0
$829$	−15.7971	+	6.54339i	−0.548657	+	0.227261i	−0.639753	−	0.768581i	$-0.720963\pi$
$829$	−15.7971	+	6.54339i	−0.548657	+	0.227261i	0.0910953	+	0.995842i	$0.470963\pi$
$830$		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
$837$	10.8912	−	5.43775i	0.376454	−	0.187956i
$838$		0			0
$839$	24.3139	+	24.3139i	0.839409	+	0.839409i	0.988781	−	0.149372i	$-0.0477252\pi$
$839$	24.3139	+	24.3139i	0.839409	+	0.839409i	−0.149372	+	0.988781i	$0.547725\pi$
$840$		0			0
$841$	19.0626	−	19.0626i	0.657332	−	0.657332i
$842$		0			0
$843$	0.215854	+	0.157727i	0.00743441	+	0.00543240i
$844$		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	$-0.385990\pi$
$853$	−1.86280	−	0.771599i	−0.0637812	−	0.0264190i	−0.414346	+	0.910119i	$0.635990\pi$
$854$		0			0
$855$	−32.5442	+	10.3787i	−1.11299	+	0.354944i
$856$		0			0
$857$	16.8878	−	16.8878i	0.576875	−	0.576875i	−0.357166	−	0.934041i	$-0.616257\pi$
$857$	16.8878	−	16.8878i	0.576875	−	0.576875i	0.934041	+	0.357166i	$0.116257\pi$
$858$		0			0
$859$	46.4891	+	19.2564i	1.58619	+	0.657020i	0.989378	−	0.145363i	$-0.0464349\pi$
$859$	46.4891	+	19.2564i	1.58619	+	0.657020i	0.596809	+	0.802383i	$0.296435\pi$
$860$		0			0
$861$	−1.67459	−	10.7625i	−0.0570699	−	0.366784i
$862$		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
$867$	3.17905	+	20.4315i	0.107966	+	0.693891i
$868$		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
$873$	−12.8271	+	4.09071i	−0.434132	+	0.138450i
$874$		0			0
$875$	−4.73012	−	1.95928i	−0.159907	−	0.0662357i
$876$		0			0
$877$	15.0174	+	36.2552i	0.507101	+	1.22425i	0.945545	+	0.325492i	$0.105530\pi$
$877$	15.0174	+	36.2552i	0.507101	+	1.22425i	−0.438444	+	0.898759i	$0.644470\pi$
$878$		0			0
$879$	−6.48657	+	26.6981i	−0.218787	+	0.900505i
$880$		0			0
$881$	−54.2455			−1.82758			−0.913788	−	0.406192i	$-0.866856\pi$
$881$	−54.2455			−1.82758			−0.913788	+	0.406192i	$0.866856\pi$
$882$		0			0
$883$	12.5424	−	5.19524i	0.422086	−	0.174834i	−0.161522	−	0.986869i	$-0.551640\pi$
$883$	12.5424	−	5.19524i	0.422086	−	0.174834i	0.583608	+	0.812035i	$0.301640\pi$
$884$		0			0
$885$	−38.7324	−	28.3021i	−1.30197	−	0.951366i
$886$		0			0
$887$	−17.2169	+	17.2169i	−0.578086	+	0.578086i	−0.934376	−	0.356289i	$-0.884042\pi$
$887$	−17.2169	+	17.2169i	−0.578086	+	0.578086i	0.356289	+	0.934376i	$0.384042\pi$
$888$		0			0
$889$	−6.82807	−	6.82807i	−0.229006	−	0.229006i
$890$		0			0
$891$	18.2267	−	4.16647i	0.610618	−	0.139582i
$892$		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
$903$	3.45168	−	2.10229i	0.114865	−	0.0699597i
$904$		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	$-0.872464\pi$
$907$	0.183637	−	0.443339i	0.00609756	−	0.0147208i	0.926899	+	0.375311i	$0.122464\pi$
$908$		0			0
$909$	40.7996	+	3.43461i	1.35324	+	0.113919i
$910$		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
$915$	−0.997872	−	6.41326i	−0.0329886	−	0.212016i
$916$		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	$-0.118418\pi$
$919$	17.2218	+	17.2218i	0.568095	+	0.568095i	−0.363500	+	0.931594i	$0.618418\pi$
$920$		0			0
$921$	−17.5302	−	28.7822i	−0.577638	−	0.948406i
$922$		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
$933$	−29.1851	−	21.3259i	−0.955478	−	0.698177i
$934$		0			0
$935$	11.2573	+	11.2573i	0.368153	+	0.368153i
$936$		0			0
$937$	−35.2447	+	35.2447i	−1.15139	+	1.15139i	−0.165120	+	0.986273i	$0.552801\pi$
$937$	−35.2447	+	35.2447i	−1.15139	+	1.15139i	−0.986273	+	0.165120i	$0.947199\pi$
$938$		0			0
$939$	−5.43828	+	7.44246i	−0.177472	+	0.242876i
$940$		0			0
$941$	−17.9856	+	7.44989i	−0.586315	+	0.242859i	−0.656064	−	0.754705i	$-0.727780\pi$
$941$	−17.9856	+	7.44989i	−0.586315	+	0.242859i	0.0697497	+	0.997565i	$0.477780\pi$
$942$		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	0.738110	−	0.674680i	$-0.235718\pi$
$947$	−8.02826	−	19.3819i	−0.260883	−	0.629828i	−0.998994	+	0.0448519i	$0.985718\pi$
$948$		0			0
$949$	30.6047	+	12.6769i	0.993470	+	0.411509i
$950$		0			0
$951$	−21.8588	+	13.3134i	−0.708821	+	0.431716i
$952$		0			0
$953$	−30.6881	+	30.6881i	−0.994084	+	0.994084i	−0.999983	−	0.00589861i	$-0.998122\pi$
$953$	−30.6881	+	30.6881i	−0.994084	+	0.994084i	0.00589861	+	0.999983i	$0.498122\pi$
$954$		0			0
$955$	−0.420757	−	0.174283i	−0.0136154	−	0.00563968i
$956$		0			0
$957$	−5.07988	+	0.790405i	−0.164209	+	0.0255502i
$958$		0			0
$959$	11.1951			0.361507
$960$		0			0
$961$	25.5116			0.822955
$962$		0			0
$963$	−43.6299	−	3.67287i	−1.40595	−	0.118357i
$964$		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	$-0.697609\pi$
$967$	7.20570	−	7.20570i	0.231720	−	0.231720i	0.813410	+	0.581691i	$0.197609\pi$
$968$		0			0
$969$	−6.77622	−	11.1257i	−0.217683	−	0.357407i
$970$		0			0
$971$	18.8717	+	7.81690i	0.605621	+	0.250856i	0.664355	−	0.747417i	$-0.268706\pi$
$971$	18.8717	+	7.81690i	0.605621	+	0.250856i	−0.0587340	+	0.998274i	$0.518706\pi$
$972$		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	$-0.444616\pi$
$977$	10.8222			0.346234			0.173117	+	0.984901i	$0.444616\pi$
$978$		0			0
$979$	18.0026	−	7.45694i	0.575367	−	0.238325i
$980$		0			0
$981$	−9.21729	−	10.9118i	−0.294286	−	0.348387i
$982$		0			0
$983$	16.0211	−	16.0211i	0.510994	−	0.510994i	−0.403837	−	0.914831i	$-0.632324\pi$
$983$	16.0211	−	16.0211i	0.510994	−	0.510994i	0.914831	+	0.403837i	$0.132324\pi$
$984$		0			0
$985$	11.0415	+	11.0415i	0.351813	+	0.351813i
$986$		0			0
$987$	2.90343	−	3.97344i	0.0924173	−	0.126476i
$988$		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	0.447664	+	0.894202i	$0.352256\pi$
$997$	−15.8249	+	38.2046i	−0.501178	+	1.20995i	−0.948842	+	0.315750i	$0.897744\pi$
$998$		0			0
$999$	4.39768	−	0.309990i	0.139137	−	0.00980765i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.o.a.671.6		56
3.2	odd	2	inner	768.2.o.a.671.5		56
4.3	odd	2		768.2.o.b.671.9		56
8.3	odd	2		96.2.o.a.11.5	✓	56
8.5	even	2		384.2.o.a.335.9		56
12.11	even	2		768.2.o.b.671.10		56
24.5	odd	2		384.2.o.a.335.10		56
24.11	even	2		96.2.o.a.11.10	yes	56
32.3	odd	8	inner	768.2.o.a.95.5		56
32.13	even	8		96.2.o.a.35.10	yes	56
32.19	odd	8		384.2.o.a.47.10		56
32.29	even	8		768.2.o.b.95.10		56
96.29	odd	8		768.2.o.b.95.9		56
96.35	even	8	inner	768.2.o.a.95.6		56
96.77	odd	8		96.2.o.a.35.5	yes	56
96.83	even	8		384.2.o.a.47.9		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.11.5	✓	56	8.3	odd	2
96.2.o.a.11.10	yes	56	24.11	even	2
96.2.o.a.35.5	yes	56	96.77	odd	8
96.2.o.a.35.10	yes	56	32.13	even	8
384.2.o.a.47.9		56	96.83	even	8
384.2.o.a.47.10		56	32.19	odd	8
384.2.o.a.335.9		56	8.5	even	2
384.2.o.a.335.10		56	24.5	odd	2
768.2.o.a.95.5		56	32.3	odd	8	inner
768.2.o.a.95.6		56	96.35	even	8	inner
768.2.o.a.671.5		56	3.2	odd	2	inner
768.2.o.a.671.6		56	1.1	even	1	trivial
768.2.o.b.95.9		56	96.29	odd	8
768.2.o.b.95.10		56	32.29	even	8
768.2.o.b.671.9		56	4.3	odd	2
768.2.o.b.671.10		56	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.o (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.266294 - 1.71146i) q^{3} +(3.14689 + 1.30348i) q^{5} +(-0.663471 + 0.663471i) q^{7} +(-2.85817 + 0.911503i) q^{9} +O(q^{10})\)	\(q+(-0.266294 - 1.71146i) q^{3} +(3.14689 + 1.30348i) q^{5} +(-0.663471 + 0.663471i) q^{7} +(-2.85817 + 0.911503i) q^{9} +(1.91929 + 0.794997i) q^{11} +(2.31672 + 5.59306i) q^{13} +(1.39286 - 5.73287i) q^{15} +2.24987 q^{17} +(3.08841 - 1.27926i) q^{19} +(1.31218 + 0.958824i) q^{21} +(-4.32171 + 4.32171i) q^{23} +(4.66830 + 4.66830i) q^{25} +(2.32111 + 4.64892i) q^{27} +(-0.546766 - 1.32001i) q^{29} -2.34273i q^{31} +(0.849507 - 3.49649i) q^{33} +(-2.95269 + 1.22305i) q^{35} +(0.324682 - 0.783851i) q^{37} +(8.95535 - 5.45437i) q^{39} +(-4.73908 - 4.73908i) q^{41} +(0.951664 - 2.29752i) q^{43} +(-10.1825 - 0.857185i) q^{45} -3.02812i q^{47} +6.11961i q^{49} +(-0.599128 - 3.85056i) q^{51} +(3.49549 - 8.43885i) q^{53} +(5.00353 + 5.00353i) q^{55} +(-3.01183 - 4.94502i) q^{57} +(3.11165 - 7.51220i) q^{59} +(1.01639 - 0.421005i) q^{61} +(1.29156 - 2.50107i) q^{63} +20.6205i q^{65} +(3.46052 + 8.35443i) q^{67} +(8.54728 + 6.24558i) q^{69} +(-0.167408 - 0.167408i) q^{71} +(3.86922 - 3.86922i) q^{73} +(6.74645 - 9.23273i) q^{75} +(-1.80085 + 0.745938i) q^{77} -2.44740 q^{79} +(7.33832 - 5.21047i) q^{81} +(-5.17660 - 12.4974i) q^{83} +(7.08008 + 2.93267i) q^{85} +(-2.11354 + 1.28728i) q^{87} +(6.63254 - 6.63254i) q^{89} +(-5.24791 - 2.17376i) q^{91} +(-4.00949 + 0.623856i) q^{93} +11.3864 q^{95} +4.48787 q^{97} +(-6.21032 - 0.522799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 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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