LMFDB - Embedded newform 207.2.g.a.137.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(68,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("207.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.57352136505929721.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{9} + x^{6} - 24x^{3} + 64 $ x^12 - 3x^9 + x^6 - 24x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label			137.4
Root			$1.09400 - 0.896196i$ of defining polynomial
Character	$\chi$	$=$	207.137
Dual form			207.2.g.a.68.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.864870 + 0.499333i) q^{2} +(0.929461 - 1.46154i) q^{3} +(-0.501333 - 0.868335i) q^{4} +(1.53366 - 0.799932i) q^{6} -2.99866i q^{8} +(-1.27220 - 2.71689i) q^{9} +O(q^{10})$	\(q+(0.864870 + 0.499333i) q^{2} +(0.929461 - 1.46154i) q^{3} +(-0.501333 - 0.868335i) q^{4} +(1.53366 - 0.799932i) q^{6} -2.99866i q^{8} +(-1.27220 - 2.71689i) q^{9} +(-1.73508 - 0.0743641i) q^{12} +(3.57572 + 6.19332i) q^{13} +(0.494663 - 0.856782i) q^{16} +(0.256342 - 2.98501i) q^{18} +(-4.15331 + 2.39792i) q^{23} +(-4.38267 - 2.78714i) q^{24} +(2.50000 - 4.33013i) q^{25} +7.14189i q^{26} +(-5.15331 - 0.665865i) q^{27} +(4.87526 + 2.81473i) q^{29} +(5.17700 + 8.96682i) q^{31} +(-4.33819 + 2.50466i) q^{32} +(-1.72137 + 2.46677i) q^{36} +(12.3753 + 0.530395i) q^{39} +(-5.21963 + 3.01356i) q^{41} -4.78943 q^{46} +(-9.28313 - 5.35962i) q^{47} +(-0.792451 - 1.51932i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(4.32435 - 2.49666i) q^{50} +(3.58525 - 6.20984i) q^{52} +(-4.12446 - 3.14910i) q^{54} +(2.81098 + 4.86875i) q^{58} +(-4.84669 + 2.79824i) q^{59} +10.3402i q^{62} -6.98128 q^{64} +(-0.355689 + 8.29901i) q^{69} -16.3838i q^{71} +(-8.14703 + 3.81491i) q^{72} +12.3860 q^{73} +(-4.00501 - 7.67854i) q^{75} +(10.4382 + 6.63811i) q^{78} +(-5.76299 + 6.91288i) q^{81} -6.01907 q^{82} +(8.64521 - 4.50921i) q^{87} +(4.16439 + 2.40431i) q^{92} +(17.9172 + 0.767917i) q^{93} +(-5.35246 - 9.27074i) q^{94} +(-0.371522 + 8.66843i) q^{96} -6.99066i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{4} - 3 q^{6}+O(q^{10}) $ 12 * q + 12 * q^4 - 3 * q^6	$ 12 q + 12 q^{4} - 3 q^{6} - 30 q^{12} - 24 q^{16} - 21 q^{18} - 12 q^{24} + 30 q^{25} - 12 q^{27} + 54 q^{32} + 33 q^{36} + 24 q^{39} + 48 q^{48} - 42 q^{49} - 3 q^{52} + 15 q^{58} - 108 q^{59} - 54 q^{64} + 42 q^{72} + 51 q^{78} - 66 q^{82} + 96 q^{87} + 6 q^{93} - 39 q^{94} - 69 q^{96}+O(q^{100}) $ 12 * q + 12 * q^4 - 3 * q^6 - 30 * q^12 - 24 * q^16 - 21 * q^18 - 12 * q^24 + 30 * q^25 - 12 * q^27 + 54 * q^32 + 33 * q^36 + 24 * q^39 + 48 * q^48 - 42 * q^49 - 3 * q^52 + 15 * q^58 - 108 * q^59 - 54 * q^64 + 42 * q^72 + 51 * q^78 - 66 * q^82 + 96 * q^87 + 6 * q^93 - 39 * q^94 - 69 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.864870	+	0.499333i	0.611555	+	0.353082i	0.773574	−	0.633706i	$-0.218467\pi$
$2$	0.864870	+	0.499333i	0.611555	+	0.353082i	−0.162019	+	0.986788i	$0.551800\pi$
$3$	0.929461	−	1.46154i	0.536625	−	0.843821i
$3$	0.929461	−	1.46154i	0.536625	−	0.843821i
$4$	−0.501333	−	0.868335i	−0.250667	−	0.434167i
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$	1.53366	−	0.799932i	0.626113	−	0.326571i
$7$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$7$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$8$		−	2.99866i		−	1.06019i
$9$	−1.27220	−	2.71689i	−0.424068	−	0.905630i
$10$		0			0
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	−1.73508	−	0.0743641i	−0.500874	−	0.0214671i
$13$	3.57572	+	6.19332i	0.991725	+	1.71772i	0.607042	+	0.794670i	$0.292356\pi$
$13$	3.57572	+	6.19332i	0.991725	+	1.71772i	0.384684	+	0.923049i	$0.374311\pi$
$14$		0			0
$15$		0			0
$16$	0.494663	−	0.856782i	0.123666	−	0.214195i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$	0.256342	−	2.98501i	0.0604203	−	0.703574i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.15331	+	2.39792i	−0.866025	+	0.500000i
$23$	−4.15331	+	2.39792i	−0.866025	+	0.500000i
$24$	−4.38267	−	2.78714i	−0.894608	−	0.568922i
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$			7.14189i			1.40064i
$27$	−5.15331	−	0.665865i	−0.991755	−	0.128146i
$28$		0			0
$29$	4.87526	+	2.81473i	0.905312	+	0.522682i	0.878920	−	0.476969i	$-0.158265\pi$
$29$	4.87526	+	2.81473i	0.905312	+	0.522682i	0.0263925	+	0.999652i	$0.491598\pi$
$30$		0			0
$31$	5.17700	+	8.96682i	0.929816	+	1.61049i	0.783627	+	0.621232i	$0.213367\pi$
$31$	5.17700	+	8.96682i	0.929816	+	1.61049i	0.146189	+	0.989257i	$0.453299\pi$
$32$	−4.33819	+	2.50466i	−0.766892	+	0.442765i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−1.72137	+	2.46677i	−0.286895	+	0.411128i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$		0			0
$39$	12.3753	+	0.530395i	1.98163	+	0.0849312i
$40$		0			0
$41$	−5.21963	+	3.01356i	−0.815170	+	0.470638i	−0.848748	−	0.528798i	$-0.822643\pi$
$41$	−5.21963	+	3.01356i	−0.815170	+	0.470638i	0.0335783	+	0.999436i	$0.489310\pi$
$42$		0			0
$43$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$43$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$44$		0			0
$45$		0			0
$46$	−4.78943			−0.706163
$47$	−9.28313	−	5.35962i	−1.35408	−	0.781780i	−0.365265	−	0.930904i	$-0.619021\pi$
$47$	−9.28313	−	5.35962i	−1.35408	−	0.781780i	−0.988819	+	0.149124i	$0.952355\pi$
$48$	−0.792451	−	1.51932i	−0.114381	−	0.219294i
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$	4.32435	−	2.49666i	0.611555	−	0.353082i
$51$		0			0
$52$	3.58525	−	6.20984i	0.497185	−	0.861150i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	−4.12446	−	3.14910i	−0.561267	−	0.428539i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	2.81098	+	4.86875i	0.369099	+	0.639298i
$59$	−4.84669	+	2.79824i	−0.630985	+	0.364299i	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−4.84669	+	2.79824i	−0.630985	+	0.364299i	0.150148	+	0.988663i	$0.452025\pi$
$60$		0			0
$61$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$61$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$62$			10.3402i			1.31320i
$63$		0			0
$64$	−6.98128			−0.872660
$65$		0			0
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$		0			0
$69$	−0.355689	+	8.29901i	−0.0428199	+	0.999083i
$70$		0			0
$71$		−	16.3838i		−	1.94440i	−0.234151	−	0.972200i	$-0.575231\pi$
$71$		−	16.3838i		−	1.94440i	0.234151	−	0.972200i	$-0.424769\pi$
$72$	−8.14703	+	3.81491i	−0.960137	+	0.449591i
$73$	12.3860			1.44967			0.724836	−	0.688921i	$-0.241915\pi$
$73$	12.3860			1.44967			0.724836	+	0.688921i	$0.241915\pi$
$74$		0			0
$75$	−4.00501	−	7.67854i	−0.462458	−	0.886641i
$76$		0			0
$77$		0			0
$78$	10.4382	+	6.63811i	1.18189	+	0.751618i
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$		0			0
$81$	−5.76299	+	6.91288i	−0.640332	+	0.768098i
$82$	−6.01907			−0.664695
$83$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$83$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	8.64521	−	4.50921i	0.926863	−	0.483438i
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$		0			0
$92$	4.16439	+	2.40431i	0.434167	+	0.250667i
$93$	17.9172	+	0.767917i	1.85793	+	0.0796293i
$94$	−5.35246	−	9.27074i	−0.552065	−	0.956204i
$95$		0			0
$96$	−0.371522	+	8.66843i	−0.0379183	+	0.884718i
$97$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$97$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$98$		−	6.99066i		−	0.706163i
$99$		0			0
$100$	−5.01333			−0.501333
$101$	3.80662	+	2.19776i	0.378773	+	0.218685i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	3.80662	+	2.19776i	0.378773	+	0.218685i	−0.298511	+	0.954406i	$0.596490\pi$
$102$		0			0
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$	18.5717	−	10.7224i	1.82110	−	1.05141i
$105$		0			0
$106$		0			0
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$	2.00533	+	4.80862i	0.192963	+	0.462710i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$113$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$114$		0			0
$115$		0			0
$116$		−	5.64447i		−	0.524076i
$117$	12.2775	−	17.5940i	1.13506	−	1.62657i
$118$	−5.58901			−0.514510
$119$		0			0
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$		0			0
$123$	−0.447009	+	10.4297i	−0.0403054	+	0.940413i
$124$	5.19080	−	8.99073i	0.466148	−	0.807392i
$125$		0			0
$126$		0			0
$127$	−19.1377			−1.69819			−0.849096	−	0.528239i	$-0.822853\pi$
$127$	−19.1377			−1.69819			−0.849096	+	0.528239i	$0.822853\pi$
$128$	2.63849	+	1.52333i	0.233211	+	0.134645i
$129$		0			0
$130$		0			0
$131$	4.43828	−	2.56244i	0.387775	−	0.223882i	−0.293421	−	0.955983i	$-0.594794\pi$
$131$	4.43828	−	2.56244i	0.387775	−	0.223882i	0.681195	+	0.732102i	$0.261460\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$137$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$138$	−4.45159	+	6.99995i	−0.378945	+	0.595876i
$139$	−3.56349	−	6.17215i	−0.302252	−	0.523515i	0.674394	−	0.738372i	$-0.264405\pi$
$139$	−3.56349	−	6.17215i	−0.302252	−	0.523515i	−0.976646	+	0.214857i	$0.931072\pi$
$140$		0			0
$141$	−16.4616	+	8.58612i	−1.38632	+	0.723081i
$142$	8.18097	−	14.1699i	0.686532	−	1.18911i
$143$		0			0
$144$	−2.95709	−	0.253944i	−0.246425	−	0.0211620i
$145$		0			0
$146$	10.7123	+	6.18474i	0.886555	+	0.511853i
$147$	−12.1132	−	0.519164i	−0.999083	−	0.0428199i
$148$		0			0
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$	0.370337	−	8.64077i	0.0302379	−	0.705516i
$151$	1.21372	−	2.10222i	0.0987709	−	0.171076i	−0.812405	−	0.583093i	$-0.801842\pi$
$151$	1.21372	−	2.10222i	0.0987709	−	0.171076i	0.911176	+	0.412017i	$0.135176\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−5.74358	−	11.0118i	−0.459855	−	0.881649i
$157$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$157$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−8.43607	+	3.10109i	−0.662800	+	0.243645i
$163$	−11.8754			−0.930156			−0.465078	−	0.885270i	$-0.653974\pi$
$163$	−11.8754			−0.930156			−0.465078	+	0.885270i	$0.653974\pi$
$164$	5.23355	+	3.02159i	0.408672	+	0.235947i
$165$		0			0
$166$		0			0
$167$	22.1533	−	12.7902i	1.71427	−	0.989737i	0.785687	−	0.618624i	$-0.212310\pi$
$167$	22.1533	−	12.7902i	1.71427	−	0.989737i	0.928588	−	0.371113i	$-0.121024\pi$
$168$		0			0
$169$	−19.0715	+	33.0328i	−1.46704	+	2.54098i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−16.6132	−	9.59166i	−1.26308	−	0.729241i	−0.289412	−	0.957205i	$-0.593460\pi$
$173$	−16.6132	−	9.59166i	−1.26308	−	0.729241i	−0.973670	+	0.227964i	$0.926793\pi$
$174$	9.72857	+	0.416959i	0.737521	+	0.0316096i
$175$		0			0
$176$		0			0
$177$	−0.415070	+	9.68449i	−0.0311986	+	0.727931i
$178$		0			0
$179$		−	22.7735i		−	1.70217i	−0.525030	−	0.851084i	$-0.675946\pi$
$179$		−	22.7735i		−	1.70217i	0.525030	−	0.851084i	$-0.324054\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$		0			0
$184$	7.19054	+	12.4544i	0.530093	+	0.918148i
$185$		0			0
$186$	15.1126	+	9.61079i	1.10811	+	0.704697i
$187$		0			0
$188$			10.7478i			0.783865i
$189$		0			0
$190$		0			0
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	−6.48883	+	10.2034i	−0.468291	+	0.736369i
$193$	0.560826	+	0.971380i	0.0403692	+	0.0699214i	0.885504	−	0.464632i	$-0.153813\pi$
$193$	0.560826	+	0.971380i	0.0403692	+	0.0699214i	−0.845135	+	0.534553i	$0.820480\pi$
$194$		0			0
$195$		0			0
$196$	−3.50933	+	6.07834i	−0.250667	+	0.434167i
$197$			27.4656i			1.95684i	0.206623	+	0.978421i	$0.433752\pi$
$197$			27.4656i			1.95684i	−0.206623	+	0.978421i	$0.566248\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	−12.9846	−	7.49665i	−0.918148	−	0.530093i
$201$		0			0
$202$	2.19482	+	3.80154i	0.154427	+	0.267476i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	11.7987	+	8.23346i	0.820069	+	0.572265i
$208$	7.07510			0.490570
$209$		0			0
$210$		0			0
$211$	−13.4599	−	23.3133i	−0.926620	−	1.60495i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	−13.4599	−	23.3133i	−0.926620	−	1.60495i	−0.137686	−	0.990476i	$-0.543966\pi$
$212$		0			0
$213$	−23.9456	−	15.2281i	−1.64073	−	1.04341i
$214$		0			0
$215$		0			0
$216$	−1.99670	+	15.4530i	−0.135858	+	1.05145i
$217$		0			0
$218$		0			0
$219$	11.5123	−	18.1027i	0.777930	−	1.22326i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−10.4599	+	18.1171i	−0.700449	+	1.21321i	0.267860	+	0.963458i	$0.413684\pi$
$223$	−10.4599	+	18.1171i	−0.700449	+	1.21321i	−0.968309	+	0.249756i	$0.919650\pi$
$224$		0			0
$225$	−14.9450	−	1.28342i	−0.996333	−	0.0855613i
$226$		0			0
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$		0			0
$229$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$229$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$230$		0			0
$231$		0			0
$232$	8.44042	−	14.6192i	0.554141	−	0.959800i
$233$			28.3051i			1.85433i	0.374657	+	0.927163i	$0.377760\pi$
$233$			28.3051i			1.85433i	−0.374657	+	0.927163i	$0.622240\pi$
$234$	19.4037	−	9.08595i	1.26846	−	0.593967i
$235$		0			0
$236$	4.85961	+	2.80570i	0.316334	+	0.182635i
$237$		0			0
$238$		0			0
$239$	−26.2426	+	15.1512i	−1.69750	+	0.980050i	−0.749372	+	0.662150i	$0.769644\pi$
$239$	−26.2426	+	15.1512i	−1.69750	+	0.980050i	−0.948124	+	0.317900i	$0.897022\pi$
$240$		0			0
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$			10.9853i			0.706163i
$243$	4.74698	+	14.8481i	0.304519	+	0.952506i
$244$		0			0
$245$		0			0
$246$	−5.59449	+	8.79712i	−0.356692	+	0.560884i
$247$		0			0
$248$	26.8884	−	15.5241i	1.70742	−	0.985778i
$249$		0			0
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		0			0
$254$	−16.5516	−	9.55606i	−1.03854	−	0.599600i
$255$		0			0
$256$	8.50258	+	14.7269i	0.531411	+	0.920431i
$257$	−23.5023	+	13.5691i	−1.46604	+	0.846416i	−0.999279	−	0.0379700i	$-0.987911\pi$
$257$	−23.5023	+	13.5691i	−1.46604	+	0.846416i	−0.466756	+	0.884386i	$0.654578\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	1.44499	−	16.8265i	0.0894428	−	1.04153i
$262$	5.11805			0.316194
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	24.3104i		−	1.48223i	−0.671377	−	0.741116i	$-0.734297\pi$
$269$		−	24.3104i		−	1.48223i	0.671377	−	0.741116i	$-0.265703\pi$
$270$		0			0
$271$	32.9199			1.99974			0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	32.9199			1.99974			0.999870	+	0.0161307i	$0.00513477\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	7.38463	−	3.85171i	0.444503	−	0.231846i
$277$	16.5470	−	28.6602i	0.994213	−	1.72203i	0.404069	−	0.914728i	$-0.367596\pi$
$277$	16.5470	−	28.6602i	0.994213	−	1.72203i	0.590144	−	0.807298i	$-0.299071\pi$
$278$		−	7.11748i		−	0.426878i
$279$	17.7757	−	25.4730i	1.06420	−	1.52503i
$280$		0			0
$281$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$281$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$282$	−18.5245	−	0.793945i	−1.10312	−	0.0472787i
$283$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$283$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$284$	−14.2266	+	8.21375i	−0.844195	+	0.487396i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	12.3240	+	8.59996i	0.726196	+	0.506758i
$289$	−17.0000			−1.00000
$290$		0			0
$291$		0			0
$292$	−6.20952	−	10.7552i	−0.363385	−	0.629401i
$293$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$293$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$294$	−10.2171	−	6.49755i	−0.595876	−	0.378945i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−29.7021	−	17.1485i	−1.71772	−	0.991725i
$300$	−4.65970	+	7.32719i	−0.269028	+	0.423036i
$301$		0			0
$302$	2.09941	−	1.21210i	0.120808	−	0.0697484i
$303$	6.75022	−	3.52081i	0.387790	−	0.202265i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	14.9199			0.851522			0.425761	−	0.904836i	$-0.360006\pi$
$307$	14.9199			0.851522			0.425761	+	0.904836i	$0.360006\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	19.3237	−	11.1565i	1.09575	−	0.632629i	0.160646	−	0.987012i	$-0.448642\pi$
$311$	19.3237	−	11.1565i	1.09575	−	0.632629i	0.935100	+	0.354383i	$0.115309\pi$
$312$	1.59048	−	37.1093i	0.0900429	−	2.10090i
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	30.8066	+	17.7862i	1.73027	+	0.998973i	0.887788	+	0.460252i	$0.152241\pi$
$317$	30.8066	+	17.7862i	1.73027	+	0.998973i	0.842484	+	0.538721i	$0.181092\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	8.89188	+	1.53855i	0.493993	+	0.0854749i
$325$	35.7572			1.98345
$326$	−10.2707	−	5.92979i	−0.568842	−	0.328421i
$327$		0			0
$328$	9.03663	+	15.6519i	0.498964	+	0.864232i
$329$		0			0
$330$		0			0
$331$	−3.14498	+	5.44727i	−0.172864	+	0.299409i	−0.939420	−	0.342768i	$-0.888635\pi$
$331$	−3.14498	+	5.44727i	−0.172864	+	0.299409i	0.766556	+	0.642177i	$0.221969\pi$
$332$		0			0
$333$		0			0
$334$	25.5463			1.39783
$335$		0			0
$336$		0			0
$337$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$337$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$338$	−32.9887	+	19.0460i	−1.79435	+	1.03597i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−9.57887	−	16.5911i	−0.514963	−	0.891942i
$347$	−8.30662	+	4.79583i	−0.445923	+	0.257454i	−0.706107	−	0.708105i	$-0.749550\pi$
$347$	−8.30662	+	4.79583i	−0.445923	+	0.257454i	0.260184	+	0.965559i	$0.416217\pi$
$348$	−8.24963	−	5.24632i	−0.442227	−	0.281232i
$349$	18.5768	−	32.1760i	0.994395	−	1.72234i	0.405631	−	0.914037i	$-0.367052\pi$
$349$	18.5768	−	32.1760i	0.994395	−	1.72234i	0.588764	−	0.808305i	$-0.299615\pi$
$350$		0			0
$351$	−14.3029	−	34.2971i	−0.763430	−	1.83064i
$352$		0			0
$353$	31.4319	+	18.1472i	1.67295	+	0.965878i	0.965974	+	0.258640i	$0.0832744\pi$
$353$	31.4319	+	18.1472i	1.67295	+	0.965878i	0.706976	+	0.707238i	$0.250059\pi$
$354$	−5.19476	+	8.16856i	−0.276099	+	0.434154i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	11.3715	−	19.6961i	0.601004	−	1.04097i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	19.0000			1.00000
$362$		0			0
$363$	19.0351	+	0.815829i	0.999083	+	0.0428199i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$			4.74464i			0.247332i
$369$	14.8279	+	10.3473i	0.771912	+	0.538660i
$370$		0			0
$371$		0			0
$372$	−8.31568	−	15.9431i	−0.431148	−	0.826611i
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$		0			0
$376$	−16.0717	+	27.8369i	−0.828833	+	1.43558i
$377$			40.2587i			2.07343i
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	−17.7877	+	27.9705i	−0.911292	+	1.43297i
$382$		0			0
$383$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$383$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$384$	4.67878	−	2.44038i	0.238763	−	0.124535i
$385$		0			0
$386$			1.12016i			0.0570144i
$387$		0			0
$388$		0			0
$389$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$389$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$390$		0			0
$391$		0			0
$392$	−18.1784	+	10.4953i	−0.918148	+	0.530093i
$393$	0.380094	−	8.86842i	0.0191732	−	0.447353i
$394$	−13.7145	+	23.7541i	−0.690925	+	1.19672i
$395$		0			0
$396$		0			0
$397$	−10.8890			−0.546504			−0.273252	−	0.961942i	$-0.588099\pi$
$397$	−10.8890			−0.546504			−0.273252	+	0.961942i	$0.588099\pi$
$398$		0			0
$399$		0			0
$400$	−2.47332	−	4.28391i	−0.123666	−	0.214195i
$401$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$401$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$402$		0			0
$403$	−37.0229	+	64.1256i	−1.84424	+	3.19432i
$404$		−	4.40723i		−	0.219268i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−14.5150	−	25.1407i	−0.717720	−	1.24313i	−0.961901	−	0.273397i	$-0.911853\pi$
$409$	−14.5150	−	25.1407i	−0.717720	−	1.24313i	0.244182	−	0.969730i	$-0.421481\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	6.09314	+	13.0124i	0.299461	+	0.639523i
$415$		0			0
$416$	−31.0243	−	17.9119i	−1.52109	−	0.878203i
$417$	−12.3330	−	0.528582i	−0.603949	−	0.0258848i
$418$		0			0
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$		0			0
$421$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$421$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$422$		−	26.8840i		−	1.30869i
$423$	−2.75145	+	32.0398i	−0.133780	+	1.55783i
$424$		0			0
$425$		0			0
$426$	−13.1059	−	25.1272i	−0.634985	−	1.21742i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	−3.11965	+	4.08588i	−0.150094	+	0.196582i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	18.9959	−	9.90797i	0.907659	−	0.473421i
$439$	−15.5166	+	26.8755i	−0.740566	+	1.28270i	0.211672	+	0.977341i	$0.432109\pi$
$439$	−15.5166	+	26.8755i	−0.740566	+	1.28270i	−0.952238	+	0.305357i	$0.901224\pi$
$440$		0			0
$441$	−12.0176	+	17.2214i	−0.572265	+	0.820069i
$442$		0			0
$443$	15.8642	+	9.15921i	0.753731	+	0.435167i	0.827041	−	0.562142i	$-0.190023\pi$
$443$	15.8642	+	9.15921i	0.753731	+	0.435167i	−0.0733092	+	0.997309i	$0.523356\pi$
$444$		0			0
$445$		0			0
$446$	−18.0930	+	10.4460i	−0.856727	+	0.494631i
$447$		0			0
$448$		0			0
$449$		−	38.3667i		−	1.81063i	−0.424736	−	0.905317i	$-0.639633\pi$
$449$		−	38.3667i		−	1.81063i	0.424736	−	0.905317i	$-0.360367\pi$
$450$	−12.2846	−	8.57252i	−0.579103	−	0.404112i
$451$		0			0
$452$		0			0
$453$	−1.94438	−	3.72783i	−0.0913548	−	0.175149i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	34.2251	+	19.7599i	1.59402	+	0.920310i	0.992607	+	0.121375i	$0.0387304\pi$
$461$	34.2251	+	19.7599i	1.59402	+	0.920310i	0.601417	+	0.798935i	$0.294603\pi$
$462$		0			0
$463$	−4.45994	−	7.72484i	−0.207271	−	0.359004i	0.743583	−	0.668644i	$-0.233125\pi$
$463$	−4.45994	−	7.72484i	−0.207271	−	0.359004i	−0.950854	+	0.309640i	$0.899791\pi$
$464$	4.82322	−	2.78469i	0.223912	−	0.129276i
$465$		0			0
$466$	−14.1337	+	24.4802i	−0.654729	+	1.13402i
$467$		0			0			−	1.00000i	$-0.5\pi$
$467$		0			0				1.00000i	$0.5\pi$
$468$	−21.4326	−	1.84055i	−0.990723	−	0.0850796i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	8.39096	+	14.5336i	0.386225	+	0.668962i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−30.2620			−1.38415
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	5.51467	−	9.55168i	0.250667	−	0.434167i
$485$		0			0
$486$	−3.30862	+	15.2120i	−0.150082	+	0.690030i
$487$	43.1590			1.95572			0.977860	−	0.209259i	$-0.0671053\pi$
$487$	43.1590			1.95572			0.977860	+	0.209259i	$0.0671053\pi$
$488$		0			0
$489$	−11.0378	+	17.3564i	−0.499144	+	0.784885i
$490$		0			0
$491$	38.2886	−	22.1060i	1.72794	−	0.997628i	0.829553	−	0.558429i	$-0.188595\pi$
$491$	38.2886	−	22.1060i	1.72794	−	0.997628i	0.898390	−	0.439199i	$-0.144738\pi$
$492$	9.28056	−	4.84060i	0.418400	−	0.218231i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	10.2435			0.459946
$497$		0			0
$498$		0			0
$499$	−20.2406	−	35.0577i	−0.906093	−	1.56940i	−0.819444	−	0.573160i	$-0.805717\pi$
$499$	−20.2406	−	35.0577i	−0.906093	−	1.56940i	−0.0866493	−	0.996239i	$-0.527616\pi$
$500$		0			0
$501$	1.89721	−	44.2660i	0.0847610	−	1.97766i
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	30.5526	+	58.5765i	1.35689	+	2.60147i
$508$	9.59434	+	16.6179i	0.425680	+	0.737300i
$509$	34.8913	−	20.1445i	1.54653	−	0.892891i	0.548129	−	0.836394i	$-0.315340\pi$
$509$	34.8913	−	20.1445i	1.54653	−	0.892891i	0.998403	−	0.0564968i	$-0.0179931\pi$
$510$		0			0
$511$		0			0
$512$			10.8892i			0.481237i
$513$		0			0
$514$	−27.1019			−1.19542
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−29.4600	+	15.3659i	−1.29315	+	0.674487i
$520$		0			0
$521$		0			0			−	1.00000i	$-0.5\pi$
$521$		0			0				1.00000i	$0.5\pi$
$522$	9.65173	−	13.8312i	0.422445	−	0.605373i
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$	−4.45012	−	2.56928i	−0.194404	−	0.112239i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$		0			0
$531$	13.7685	+	9.60799i	0.597501	+	0.416951i
$532$		0			0
$533$	−37.3278	−	21.5512i	−1.61685	−	0.933488i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−33.2843	−	21.1670i	−1.43633	−	0.913425i
$538$	12.1390	−	21.0253i	0.523349	−	0.906467i
$539$		0			0
$540$		0			0
$541$	−16.4500			−0.707242			−0.353621	−	0.935389i	$-0.615050\pi$
$541$	−16.4500			−0.707242			−0.353621	+	0.935389i	$0.615050\pi$
$542$	28.4714	+	16.4380i	1.22295	+	0.706071i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−8.44717	+	14.6309i	−0.361175	+	0.625574i	−0.988155	−	0.153462i	$-0.950958\pi$
$547$	−8.44717	+	14.6309i	−0.361175	+	0.625574i	0.626979	+	0.779036i	$0.284291\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	24.8859	+	1.06659i	1.05921	+	0.0453971i
$553$		0			0
$554$	28.6220	−	16.5249i	1.21603	−	0.702077i
$555$		0			0
$556$	−3.57300	+	6.18861i	−0.151529	+	0.262456i
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$	28.0931	−	13.1548i	1.18928	−	0.556888i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$563$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$564$	15.7084	+	9.98968i	0.661442	+	0.420641i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−49.1295			−2.06143
$569$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$569$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$570$		0			0
$571$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$571$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			23.9792i			1.00000i
$576$	8.88162	+	18.9674i	0.370068	+	0.790308i
$577$	2.29657			0.0956073			0.0478037	−	0.998857i	$-0.484778\pi$
$577$	2.29657			0.0956073			0.0478037	+	0.998857i	$0.484778\pi$
$578$	−14.7028	−	8.48866i	−0.611555	−	0.353082i
$579$	1.94098	+	0.0831888i	0.0806643	+	0.00345721i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		−	37.1414i		−	1.53692i
$585$		0			0
$586$		0			0
$587$	32.8159	+	18.9463i	1.35446	+	0.781996i	0.988870	−	0.148782i	$-0.0475353\pi$
$587$	32.8159	+	18.9463i	1.35446	+	0.781996i	0.365586	+	0.930778i	$0.380869\pi$
$588$	5.62196	+	10.7786i	0.231846	+	0.444503i
$589$		0			0
$590$		0			0
$591$	40.1421	+	25.5282i	1.65122	+	1.05009i
$592$		0			0
$593$		−	6.79744i		−	0.279137i	−0.990212	−	0.139569i	$-0.955428\pi$
$593$		−	6.79744i		−	0.279137i	0.990212	−	0.139569i	$-0.0445716\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−17.1257	−	29.6625i	−0.700320	−	1.21299i
$599$	−31.8467	+	18.3867i	−1.30122	+	0.751260i	−0.980613	−	0.195952i	$-0.937220\pi$
$599$	−31.8467	+	18.3867i	−1.30122	+	0.751260i	−0.320607	+	0.947212i	$0.603887\pi$
$600$	−23.0253	+	12.0097i	−0.940005	+	0.490292i
$601$	8.29972	−	14.3755i	0.338552	−	0.586390i	−0.645608	−	0.763669i	$-0.723396\pi$
$601$	8.29972	−	14.3755i	0.338552	−	0.586390i	0.984161	+	0.177279i	$0.0567294\pi$
$602$		0			0
$603$		0			0
$604$	−2.43391			−0.0990342
$605$		0			0
$606$	7.59612	+	0.325564i	0.308571	+	0.0132251i
$607$	−22.4599	−	38.9017i	−0.911621	−	1.57897i	−0.811775	−	0.583970i	$-0.801498\pi$
$607$	−22.4599	−	38.9017i	−0.911621	−	1.57897i	−0.0998457	−	0.995003i	$-0.531835\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	76.6579i		−	3.10124i
$612$		0			0
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$	12.9037	+	7.44998i	0.520753	+	0.300657i
$615$		0			0
$616$		0			0
$617$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$617$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$618$		0			0
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$	23.0000	−	9.59166i	0.922958	−	0.384900i
$622$	22.2833			0.893479
$623$		0			0
$624$	6.57603	−	10.3405i	0.263252	−	0.413953i
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$	−46.5838	−	1.99655i	−1.85154	−	0.0793556i
$634$	17.7625	+	30.7655i	0.705438	+	1.22185i
$635$		0			0
$636$		0			0
$637$	25.0300	−	43.3533i	0.991725	−	1.71772i
$638$		0			0
$639$	−44.5130	+	20.8436i	−1.76091	+	0.824558i
$640$		0			0
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$		0			0
$643$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$643$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			38.9017i			1.52938i	0.644397	+	0.764691i	$0.277108\pi$
$647$			38.9017i			1.52938i	−0.644397	+	0.764691i	$0.722892\pi$
$648$	20.7294	+	17.2813i	0.814327	+	0.678872i
$649$		0			0
$650$	30.9253	+	17.8547i	1.21299	+	0.700320i
$651$		0			0
$652$	5.95355	+	10.3119i	0.233159	+	0.403843i
$653$	−2.90736	+	1.67856i	−0.113774	+	0.0656872i	−0.555807	−	0.831311i	$-0.687591\pi$
$653$	−2.90736	+	1.67856i	−0.113774	+	0.0656872i	0.442033	+	0.896999i	$0.354257\pi$
$654$		0			0
$655$		0			0
$656$			5.96278i			0.232807i
$657$	−15.7575	−	33.6514i	−0.614760	−	1.31287i
$658$		0			0
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$		0			0
$661$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$661$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$662$	−5.44000	+	3.14079i	−0.211432	+	0.122070i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−26.9979			−1.04536
$668$	−22.2124	−	12.8243i	−0.859423	−	0.496188i
$669$	16.7568	+	32.1268i	0.647857	+	1.24209i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	2.12897	−	3.68749i	0.0820659	−	0.142142i	−0.822071	−	0.569385i	$-0.807182\pi$
$673$	2.12897	−	3.68749i	0.0820659	−	0.142142i	0.904137	+	0.427242i	$0.140515\pi$
$674$		0			0
$675$	−15.7666	+	20.6498i	−0.606855	+	0.794812i
$676$	38.2447			1.47095
$677$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$677$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	20.1035i		−	0.769238i	−0.923075	−	0.384619i	$-0.874333\pi$
$683$		−	20.1035i		−	0.769238i	0.923075	−	0.384619i	$-0.125667\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−1.45994	+	2.52868i	−0.0555386	+	0.0961956i	−0.892458	−	0.451130i	$-0.851021\pi$
$691$	−1.45994	+	2.52868i	−0.0555386	+	0.0961956i	0.836919	+	0.547326i	$0.184354\pi$
$692$			19.2345i			0.731185i
$693$		0			0
$694$	−9.57887			−0.363609
$695$		0			0
$696$	−13.5216	−	25.9240i	−0.512534	−	0.982648i
$697$		0			0
$698$	32.1331	−	18.5520i	1.21625	−	0.702205i
$699$	41.3690	+	26.3085i	1.56472	+	0.995077i
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	4.75553	−	36.8044i	0.179486	−	1.38909i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	18.1230	+	31.3899i	0.682068	+	1.18138i
$707$		0			0
$708$	8.61746	−	4.49474i	0.323864	−	0.168923i
$709$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$709$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−43.0034	−	24.8280i	−1.61049	−	0.929816i
$714$		0			0
$715$		0			0
$716$	−19.7750	+	11.4171i	−0.739026	+	0.426677i
$717$	−2.24742	+	52.4372i	−0.0839313	+	1.95830i
$718$		0			0
$719$		−	3.19455i		−	0.119137i	−0.998224	−	0.0595683i	$-0.981028\pi$
$719$		−	3.19455i		−	0.119137i	0.998224	−	0.0595683i	$-0.0189724\pi$
$720$		0			0
$721$		0			0
$722$	16.4325	+	9.48732i	0.611555	+	0.353082i
$723$		0			0
$724$		0			0
$725$	24.3763	−	14.0737i	0.905312	−	0.522682i
$726$	16.0555	+	10.2104i	0.595876	+	0.378945i
$727$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$727$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$728$		0			0
$729$	26.1132	+	6.86282i	0.967157	+	0.254179i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$733$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$734$		0			0
$735$		0			0
$736$	12.0119	−	20.8052i	0.442765	−	0.766892i
$737$		0			0
$738$	7.65749	+	16.3532i	0.281876	+	0.601968i
$739$	−45.3360			−1.66771			−0.833856	−	0.551981i	$-0.813872\pi$
$739$	−45.3360			−1.66771			−0.833856	+	0.551981i	$0.813872\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$743$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$744$	2.30272	−	53.7276i	0.0844219	−	1.96975i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$	−9.18404	+	5.30241i	−0.334907	+	0.193359i
$753$		0			0
$754$	−20.1025	+	34.8186i	−0.732090	+	1.26802i
$755$		0			0
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−10.6750	+	6.16321i	−0.386968	+	0.223416i	−0.680846	−	0.732427i	$-0.738388\pi$
$761$	−10.6750	+	6.16321i	−0.386968	+	0.223416i	0.293878	+	0.955843i	$0.405054\pi$
$762$	−29.3506	+	15.3088i	−1.06326	+	0.554580i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−34.6608	−	20.0114i	−1.25153	−	0.722570i
$768$	29.4268	+	1.26121i	1.06185	+	0.0455100i
$769$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$769$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$770$		0			0
$771$	−2.01274	+	46.9616i	−0.0724870	+	1.69128i
$772$	0.562322	−	0.973970i	0.0202384	−	0.0350539i
$773$		0			0			−	1.00000i	$-0.5\pi$
$773$		0			0				1.00000i	$0.5\pi$
$774$		0			0
$775$	51.7700			1.85963
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−23.2495	−	17.7514i	−0.830869	−	0.634385i
$784$	−6.92528			−0.247332
$785$		0			0
$786$	4.75703	−	7.48024i	0.169678	−	0.266811i
$787$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$787$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$788$	23.8493	−	13.7694i	0.849597	−	0.490515i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−9.41758	−	5.43724i	−0.334217	−	0.192961i
$795$		0			0
$796$		0			0
$797$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$797$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$798$		0			0
$799$		0			0
$800$			25.0466i			0.885530i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−64.0401	+	36.9735i	−2.25571	+	1.30234i
$807$	−35.5307	−	22.5956i	−1.25074	−	0.795402i
$808$	6.59032	−	11.4148i	0.231847	−	0.401570i
$809$			55.5564i			1.95326i	0.214930	+	0.976629i	$0.431048\pi$
$809$			55.5564i			1.95326i	−0.214930	+	0.976629i	$0.568952\pi$
$810$		0			0
$811$	−55.8340			−1.96060			−0.980298	−	0.197523i	$-0.936710\pi$
$811$	−55.8340			−1.96060			−0.980298	+	0.197523i	$0.936710\pi$
$812$		0			0
$813$	30.5977	−	48.1137i	1.07311	−	1.68742i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		−	28.9912i		−	1.01365i
$819$		0			0
$820$		0			0
$821$	−16.6132	−	9.59166i	−0.579806	−	0.334751i	0.181250	−	0.983437i	$-0.441986\pi$
$821$	−16.6132	−	9.59166i	−0.579806	−	0.334751i	−0.761056	+	0.648686i	$0.775319\pi$
$822$		0			0
$823$	27.3920	+	47.4444i	0.954826	+	1.65381i	0.734767	+	0.678320i	$0.237292\pi$
$823$	27.3920	+	47.4444i	0.954826	+	1.65381i	0.220059	+	0.975487i	$0.429375\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$	1.23430	−	14.3730i	0.0428947	−	0.499495i
$829$	−50.8397			−1.76574			−0.882869	−	0.469620i	$-0.844391\pi$
$829$	−50.8397			−1.76574			−0.882869	+	0.469620i	$0.844391\pi$
$830$		0			0
$831$	−26.5083	−	50.8227i	−0.919564	−	1.76302i
$832$	−24.9631	−	43.2373i	−0.865439	−	1.49898i
$833$		0			0
$834$	−10.4025	−	6.61542i	−0.360209	−	0.229073i
$835$		0			0
$836$		0			0
$837$	−20.7080	−	49.6560i	−0.715773	−	1.71636i
$838$		0			0
$839$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$839$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$840$		0			0
$841$	1.34542	+	2.33033i	0.0463937	+	0.0803563i
$842$		0			0
$843$		0			0
$844$	−13.4958	+	23.3755i	−0.464546	+	0.804617i
$845$		0			0
$846$	−18.3782	+	26.3363i	−0.631854	+	0.905462i
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	−1.21837	+	28.4272i	−0.0417406	+	0.973899i
$853$	22.4199	−	38.8324i	0.767642	−	1.32959i	−0.171197	−	0.985237i	$-0.554763\pi$
$853$	22.4199	−	38.8324i	0.767642	−	1.32959i	0.938839	−	0.344358i	$-0.111903\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	31.9129	+	18.4249i	1.09012	+	0.629383i	0.933609	−	0.358293i	$-0.116641\pi$
$857$	31.9129	+	18.4249i	1.09012	+	0.629383i	0.156514	+	0.987676i	$0.449974\pi$
$858$		0			0
$859$	27.5848	+	47.7783i	0.941182	+	1.63018i	0.763221	+	0.646138i	$0.223617\pi$
$859$	27.5848	+	47.7783i	0.941182	+	1.63018i	0.177961	+	0.984037i	$0.443050\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			46.2811i			1.57543i	0.616043	+	0.787713i	$0.288735\pi$
$863$			46.2811i			1.57543i	−0.616043	+	0.787713i	$0.711265\pi$
$864$	24.0238	−	10.0186i	0.817307	−	0.340841i
$865$		0			0
$866$		0			0
$867$	−15.8008	+	24.8462i	−0.536625	+	0.843821i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$	−21.4907	−	0.921074i	−0.726103	−	0.0311202i
$877$	28.4199	+	49.2247i	0.959671	+	1.66220i	0.723298	+	0.690536i	$0.242625\pi$
$877$	28.4199	+	49.2247i	0.959671	+	1.66220i	0.236373	+	0.971662i	$0.424041\pi$
$878$	−26.8396	+	15.4959i	−0.905794	+	0.522961i
$879$		0			0
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$	−18.9929	+	8.89355i	−0.639523	+	0.299461i
$883$	50.9199			1.71359			0.856795	−	0.515657i	$-0.172452\pi$
$883$	50.9199			1.71359			0.856795	+	0.515657i	$0.172452\pi$
$884$		0			0
$885$		0			0
$886$	9.14699	+	15.8430i	0.307299	+	0.532257i
$887$	−48.7279	+	28.1331i	−1.63612	+	0.944616i	−0.653973	+	0.756518i	$0.726899\pi$
$887$	−48.7279	+	28.1331i	−1.63612	+	0.944616i	−0.982150	+	0.188098i	$0.939768\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	20.9757			0.702317
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−52.6703	+	27.4720i	−1.75861	+	0.917263i
$898$	19.1577	−	33.1822i	0.639302	−	1.10730i
$899$			58.2874i			1.94399i
$900$	6.37799	+	13.6207i	0.212600	+	0.454023i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	0.179794	−	4.19498i	0.00597324	−	0.139369i
$907$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$907$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$908$		0			0
$909$	1.12826	−	13.1382i	0.0374219	−	0.435766i
$910$		0			0
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$	13.8674	−	21.8060i	0.456948	−	0.718532i
$922$	19.7335	+	34.1795i	0.649889	+	1.12564i
$923$	101.470	−	58.5839i	3.33993	−	1.92831i
$924$		0			0
$925$		0			0
$926$		−	8.90797i		−	0.292734i
$927$		0			0
$928$	−28.1997			−0.925702
$929$	−52.7914	−	30.4791i	−1.73203	−	0.999988i	−0.868485	−	0.495716i	$-0.834906\pi$
$929$	−52.7914	−	30.4791i	−1.73203	−	0.999988i	−0.863545	−	0.504272i	$-0.831761\pi$
$930$		0			0
$931$		0			0
$932$	24.5783	−	14.1903i	0.805088	−	0.464818i
$933$	1.65488	−	38.6119i	0.0541783	−	1.26410i
$934$		0			0
$935$		0			0
$936$	−52.7584	−	36.8162i	−1.72446	−	1.20337i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$941$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$942$		0			0
$943$	14.4525	−	25.0325i	0.470638	−	0.815170i
$944$			5.53674i			0.180205i
$945$		0			0
$946$		0			0
$947$	−15.0627	−	8.69648i	−0.489473	−	0.282598i	0.234883	−	0.972024i	$-0.424529\pi$
$947$	−15.0627	−	8.69648i	−0.489473	−	0.282598i	−0.724356	+	0.689426i	$0.757863\pi$
$948$		0			0
$949$	44.2888	+	76.7105i	1.43768	+	2.49013i
$950$		0			0
$951$	54.6288	−	28.4936i	1.77146	−	0.923967i
$952$		0			0
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$		0			0
$955$		0			0
$956$	26.3126	+	15.1916i	0.851011	+	0.491332i
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−38.1026	+	65.9956i	−1.22912	+	2.12889i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−9.24102	−	16.0059i	−0.297171	−	0.514716i	0.678316	−	0.734770i	$-0.262710\pi$
$967$	−9.24102	−	16.0059i	−0.297171	−	0.514716i	−0.975488	+	0.220054i	$0.929377\pi$
$968$	28.5661	−	16.4926i	0.918148	−	0.530093i
$969$		0			0
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$	10.5133	−	11.5658i	0.337214	−	0.370974i
$973$		0			0
$974$	37.3269	+	21.5507i	1.19603	+	0.690529i
$975$	33.2349	−	52.2606i	1.06437	−	1.67368i
$976$		0			0
$977$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$977$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$978$	−18.2129	+	9.49954i	−0.582383	+	0.303762i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	44.1529			1.40898
$983$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$983$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$984$	31.2751	+	1.34043i	0.997014	+	0.0427313i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−3.08013			−0.0978435			−0.0489218	−	0.998803i	$-0.515578\pi$
$991$	−3.08013			−0.0978435			−0.0489218	+	0.998803i	$0.515578\pi$
$992$	−44.9176	−	25.9332i	−1.42614	−	0.823380i
$993$	5.03827	+	9.65954i	0.159885	+	0.306536i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	31.4199	−	54.4208i	0.995077	−	1.72352i	0.411714	−	0.911313i	$-0.364930\pi$
$997$	31.4199	−	54.4208i	0.995077	−	1.72352i	0.583363	−	0.812211i	$-0.301736\pi$
$998$		−	40.4272i		−	1.27970i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.g.a.137.4	yes	12
3.2	odd	2		621.2.g.a.413.3		12
9.2	odd	6		1863.2.c.a.1862.8		12
9.4	even	3		621.2.g.a.206.3		12
9.5	odd	6	inner	207.2.g.a.68.4	✓	12
9.7	even	3		1863.2.c.a.1862.5		12
23.22	odd	2	CM	207.2.g.a.137.4	yes	12
69.68	even	2		621.2.g.a.413.3		12
207.22	odd	6		621.2.g.a.206.3		12
207.68	even	6	inner	207.2.g.a.68.4	✓	12
207.137	even	6		1863.2.c.a.1862.8		12
207.160	odd	6		1863.2.c.a.1862.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.g.a.68.4	✓	12	9.5	odd	6	inner
207.2.g.a.68.4	✓	12	207.68	even	6	inner
207.2.g.a.137.4	yes	12	1.1	even	1	trivial
207.2.g.a.137.4	yes	12	23.22	odd	2	CM
621.2.g.a.206.3		12	9.4	even	3
621.2.g.a.206.3		12	207.22	odd	6
621.2.g.a.413.3		12	3.2	odd	2
621.2.g.a.413.3		12	69.68	even	2
1863.2.c.a.1862.5		12	9.7	even	3
1863.2.c.a.1862.5		12	207.160	odd	6
1863.2.c.a.1862.8		12	9.2	odd	6
1863.2.c.a.1862.8		12	207.137	even	6

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.864870 + 0.499333i) q^{2} +(0.929461 - 1.46154i) q^{3} +(-0.501333 - 0.868335i) q^{4} +(1.53366 - 0.799932i) q^{6} -2.99866i q^{8} +(-1.27220 - 2.71689i) q^{9} +O(q^{10})\)	\(q+(0.864870 + 0.499333i) q^{2} +(0.929461 - 1.46154i) q^{3} +(-0.501333 - 0.868335i) q^{4} +(1.53366 - 0.799932i) q^{6} -2.99866i q^{8} +(-1.27220 - 2.71689i) q^{9} +(-1.73508 - 0.0743641i) q^{12} +(3.57572 + 6.19332i) q^{13} +(0.494663 - 0.856782i) q^{16} +(0.256342 - 2.98501i) q^{18} +(-4.15331 + 2.39792i) q^{23} +(-4.38267 - 2.78714i) q^{24} +(2.50000 - 4.33013i) q^{25} +7.14189i q^{26} +(-5.15331 - 0.665865i) q^{27} +(4.87526 + 2.81473i) q^{29} +(5.17700 + 8.96682i) q^{31} +(-4.33819 + 2.50466i) q^{32} +(-1.72137 + 2.46677i) q^{36} +(12.3753 + 0.530395i) q^{39} +(-5.21963 + 3.01356i) q^{41} -4.78943 q^{46} +(-9.28313 - 5.35962i) q^{47} +(-0.792451 - 1.51932i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(4.32435 - 2.49666i) q^{50} +(3.58525 - 6.20984i) q^{52} +(-4.12446 - 3.14910i) q^{54} +(2.81098 + 4.86875i) q^{58} +(-4.84669 + 2.79824i) q^{59} +10.3402i q^{62} -6.98128 q^{64} +(-0.355689 + 8.29901i) q^{69} -16.3838i q^{71} +(-8.14703 + 3.81491i) q^{72} +12.3860 q^{73} +(-4.00501 - 7.67854i) q^{75} +(10.4382 + 6.63811i) q^{78} +(-5.76299 + 6.91288i) q^{81} -6.01907 q^{82} +(8.64521 - 4.50921i) q^{87} +(4.16439 + 2.40431i) q^{92} +(17.9172 + 0.767917i) q^{93} +(-5.35246 - 9.27074i) q^{94} +(-0.371522 + 8.66843i) q^{96} -6.99066i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{4} - 3 q^{6}+O(q^{10}) \) 12 * q + 12 * q^4 - 3 * q^6	\( 12 q + 12 q^{4} - 3 q^{6} - 30 q^{12} - 24 q^{16} - 21 q^{18} - 12 q^{24} + 30 q^{25} - 12 q^{27} + 54 q^{32} + 33 q^{36} + 24 q^{39} + 48 q^{48} - 42 q^{49} - 3 q^{52} + 15 q^{58} - 108 q^{59} - 54 q^{64} + 42 q^{72} + 51 q^{78} - 66 q^{82} + 96 q^{87} + 6 q^{93} - 39 q^{94} - 69 q^{96}+O(q^{100}) \) 12 * q + 12 * q^4 - 3 * q^6 - 30 * q^12 - 24 * q^16 - 21 * q^18 - 12 * q^24 + 30 * q^25 - 12 * q^27 + 54 * q^32 + 33 * q^36 + 24 * q^39 + 48 * q^48 - 42 * q^49 - 3 * q^52 + 15 * q^58 - 108 * q^59 - 54 * q^64 + 42 * q^72 + 51 * q^78 - 66 * q^82 + 96 * q^87 + 6 * q^93 - 39 * q^94 - 69 * q^96

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