LMFDB - Dirichlet character orbit 56644.ga

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(56644, base_ring=CyclotomicField(5712)) M = H._module chi = DirichletCharacter(H, M([0,3944,4809])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,56644)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$56644$
Conductor:	$14161$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$5712$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 14161.da	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{5712})$
Fixed field:	Number field defined by a degree 5712 polynomial (not computed)

First 31 of 1536 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$19$	$23$	$25$	$27$
$\chi_{56644}(5,\cdot)$	$1$	$1$	$e\left(\frac{3041}{5712}\right)$	$e\left(\frac{4693}{5712}\right)$	$e\left(\frac{185}{2856}\right)$	$e\left(\frac{5615}{5712}\right)$	$e\left(\frac{381}{476}\right)$	$e\left(\frac{337}{952}\right)$	$e\left(\frac{389}{408}\right)$	$e\left(\frac{5623}{5712}\right)$	$e\left(\frac{1837}{2856}\right)$	$e\left(\frac{1137}{1904}\right)$
$\chi_{56644}(45,\cdot)$	$1$	$1$	$e\left(\frac{3355}{5712}\right)$	$e\left(\frac{5063}{5712}\right)$	$e\left(\frac{499}{2856}\right)$	$e\left(\frac{325}{5712}\right)$	$e\left(\frac{387}{476}\right)$	$e\left(\frac{451}{952}\right)$	$e\left(\frac{295}{408}\right)$	$e\left(\frac{2477}{5712}\right)$	$e\left(\frac{2207}{2856}\right)$	$e\left(\frac{1451}{1904}\right)$
$\chi_{56644}(61,\cdot)$	$1$	$1$	$e\left(\frac{1223}{5712}\right)$	$e\left(\frac{3715}{5712}\right)$	$e\left(\frac{1223}{2856}\right)$	$e\left(\frac{2153}{5712}\right)$	$e\left(\frac{131}{476}\right)$	$e\left(\frac{823}{952}\right)$	$e\left(\frac{203}{408}\right)$	$e\left(\frac{1681}{5712}\right)$	$e\left(\frac{859}{2856}\right)$	$e\left(\frac{1223}{1904}\right)$
$\chi_{56644}(73,\cdot)$	$1$	$1$	$e\left(\frac{2785}{5712}\right)$	$e\left(\frac{2645}{5712}\right)$	$e\left(\frac{2785}{2856}\right)$	$e\left(\frac{1087}{5712}\right)$	$e\left(\frac{461}{476}\right)$	$e\left(\frac{905}{952}\right)$	$e\left(\frac{133}{408}\right)$	$e\left(\frac{4295}{5712}\right)$	$e\left(\frac{2645}{2856}\right)$	$e\left(\frac{881}{1904}\right)$
$\chi_{56644}(173,\cdot)$	$1$	$1$	$e\left(\frac{4349}{5712}\right)$	$e\left(\frac{2305}{5712}\right)$	$e\left(\frac{1493}{2856}\right)$	$e\left(\frac{2243}{5712}\right)$	$e\left(\frac{121}{476}\right)$	$e\left(\frac{157}{952}\right)$	$e\left(\frac{65}{408}\right)$	$e\left(\frac{5179}{5712}\right)$	$e\left(\frac{2305}{2856}\right)$	$e\left(\frac{541}{1904}\right)$
$\chi_{56644}(201,\cdot)$	$1$	$1$	$e\left(\frac{2117}{5712}\right)$	$e\left(\frac{4441}{5712}\right)$	$e\left(\frac{2117}{2856}\right)$	$e\left(\frac{1499}{5712}\right)$	$e\left(\frac{45}{476}\right)$	$e\left(\frac{141}{952}\right)$	$e\left(\frac{281}{408}\right)$	$e\left(\frac{5203}{5712}\right)$	$e\left(\frac{1585}{2856}\right)$	$e\left(\frac{213}{1904}\right)$
$\chi_{56644}(241,\cdot)$	$1$	$1$	$e\left(\frac{205}{5712}\right)$	$e\left(\frac{3425}{5712}\right)$	$e\left(\frac{205}{2856}\right)$	$e\left(\frac{2131}{5712}\right)$	$e\left(\frac{345}{476}\right)$	$e\left(\frac{605}{952}\right)$	$e\left(\frac{1}{408}\right)$	$e\left(\frac{2603}{5712}\right)$	$e\left(\frac{569}{2856}\right)$	$e\left(\frac{205}{1904}\right)$
$\chi_{56644}(269,\cdot)$	$1$	$1$	$e\left(\frac{3541}{5712}\right)$	$e\left(\frac{4409}{5712}\right)$	$e\left(\frac{685}{2856}\right)$	$e\left(\frac{1339}{5712}\right)$	$e\left(\frac{433}{476}\right)$	$e\left(\frac{373}{952}\right)$	$e\left(\frac{73}{408}\right)$	$e\left(\frac{1523}{5712}\right)$	$e\left(\frac{1553}{2856}\right)$	$e\left(\frac{1637}{1904}\right)$
$\chi_{56644}(369,\cdot)$	$1$	$1$	$e\left(\frac{233}{5712}\right)$	$e\left(\frac{2221}{5712}\right)$	$e\left(\frac{233}{2856}\right)$	$e\left(\frac{4679}{5712}\right)$	$e\left(\frac{9}{476}\right)$	$e\left(\frac{409}{952}\right)$	$e\left(\frac{29}{408}\right)$	$e\left(\frac{1231}{5712}\right)$	$e\left(\frac{2221}{2856}\right)$	$e\left(\frac{233}{1904}\right)$
$\chi_{56644}(381,\cdot)$	$1$	$1$	$e\left(\frac{3823}{5712}\right)$	$e\left(\frac{4523}{5712}\right)$	$e\left(\frac{967}{2856}\right)$	$e\left(\frac{481}{5712}\right)$	$e\left(\frac{211}{476}\right)$	$e\left(\frac{439}{952}\right)$	$e\left(\frac{355}{408}\right)$	$e\left(\frac{3209}{5712}\right)$	$e\left(\frac{1667}{2856}\right)$	$e\left(\frac{15}{1904}\right)$
$\chi_{56644}(397,\cdot)$	$1$	$1$	$e\left(\frac{563}{5712}\right)$	$e\left(\frac{2719}{5712}\right)$	$e\left(\frac{563}{2856}\right)$	$e\left(\frac{29}{5712}\right)$	$e\left(\frac{367}{476}\right)$	$e\left(\frac{547}{952}\right)$	$e\left(\frac{359}{408}\right)$	$e\left(\frac{1381}{5712}\right)$	$e\left(\frac{2719}{2856}\right)$	$e\left(\frac{563}{1904}\right)$
$\chi_{56644}(437,\cdot)$	$1$	$1$	$e\left(\frac{3481}{5712}\right)$	$e\left(\frac{5357}{5712}\right)$	$e\left(\frac{625}{2856}\right)$	$e\left(\frac{3223}{5712}\right)$	$e\left(\frac{65}{476}\right)$	$e\left(\frac{521}{952}\right)$	$e\left(\frac{13}{408}\right)$	$e\left(\frac{2015}{5712}\right)$	$e\left(\frac{2501}{2856}\right)$	$e\left(\frac{1577}{1904}\right)$
$\chi_{56644}(453,\cdot)$	$1$	$1$	$e\left(\frac{1643}{5712}\right)$	$e\left(\frac{2791}{5712}\right)$	$e\left(\frac{1643}{2856}\right)$	$e\left(\frac{389}{5712}\right)$	$e\left(\frac{327}{476}\right)$	$e\left(\frac{739}{952}\right)$	$e\left(\frac{215}{408}\right)$	$e\left(\frac{3949}{5712}\right)$	$e\left(\frac{2791}{2856}\right)$	$e\left(\frac{1643}{1904}\right)$
$\chi_{56644}(465,\cdot)$	$1$	$1$	$e\left(\frac{4339}{5712}\right)$	$e\left(\frac{4367}{5712}\right)$	$e\left(\frac{1483}{2856}\right)$	$e\left(\frac{2557}{5712}\right)$	$e\left(\frac{139}{476}\right)$	$e\left(\frac{499}{952}\right)$	$e\left(\frac{55}{408}\right)$	$e\left(\frac{2405}{5712}\right)$	$e\left(\frac{1511}{2856}\right)$	$e\left(\frac{531}{1904}\right)$
$\chi_{56644}(481,\cdot)$	$1$	$1$	$e\left(\frac{4241}{5712}\right)$	$e\left(\frac{2869}{5712}\right)$	$e\left(\frac{1385}{2856}\right)$	$e\left(\frac{2207}{5712}\right)$	$e\left(\frac{125}{476}\right)$	$e\left(\frac{233}{952}\right)$	$e\left(\frac{365}{408}\right)$	$e\left(\frac{1495}{5712}\right)$	$e\left(\frac{13}{2856}\right)$	$e\left(\frac{433}{1904}\right)$
$\chi_{56644}(537,\cdot)$	$1$	$1$	$e\left(\frac{1415}{5712}\right)$	$e\left(\frac{5251}{5712}\right)$	$e\left(\frac{1415}{2856}\right)$	$e\left(\frac{4121}{5712}\right)$	$e\left(\frac{71}{476}\right)$	$e\left(\frac{159}{952}\right)$	$e\left(\frac{395}{408}\right)$	$e\left(\frac{1249}{5712}\right)$	$e\left(\frac{2395}{2856}\right)$	$e\left(\frac{1415}{1904}\right)$
$\chi_{56644}(549,\cdot)$	$1$	$1$	$e\left(\frac{1537}{5712}\right)$	$e\left(\frac{4085}{5712}\right)$	$e\left(\frac{1537}{2856}\right)$	$e\left(\frac{2575}{5712}\right)$	$e\left(\frac{137}{476}\right)$	$e\left(\frac{937}{952}\right)$	$e\left(\frac{109}{408}\right)$	$e\left(\frac{4247}{5712}\right)$	$e\left(\frac{1229}{2856}\right)$	$e\left(\frac{1537}{1904}\right)$
$\chi_{56644}(605,\cdot)$	$1$	$1$	$e\left(\frac{3463}{5712}\right)$	$e\left(\frac{4499}{5712}\right)$	$e\left(\frac{607}{2856}\right)$	$e\left(\frac{361}{5712}\right)$	$e\left(\frac{383}{476}\right)$	$e\left(\frac{375}{952}\right)$	$e\left(\frac{403}{408}\right)$	$e\left(\frac{449}{5712}\right)$	$e\left(\frac{1643}{2856}\right)$	$e\left(\frac{1559}{1904}\right)$
$\chi_{56644}(649,\cdot)$	$1$	$1$	$e\left(\frac{1181}{5712}\right)$	$e\left(\frac{5521}{5712}\right)$	$e\left(\frac{1181}{2856}\right)$	$e\left(\frac{1187}{5712}\right)$	$e\left(\frac{397}{476}\right)$	$e\left(\frac{165}{952}\right)$	$e\left(\frac{161}{408}\right)$	$e\left(\frac{3739}{5712}\right)$	$e\left(\frac{2665}{2856}\right)$	$e\left(\frac{1181}{1904}\right)$
$\chi_{56644}(677,\cdot)$	$1$	$1$	$e\left(\frac{3653}{5712}\right)$	$e\left(\frac{5305}{5712}\right)$	$e\left(\frac{797}{2856}\right)$	$e\left(\frac{107}{5712}\right)$	$e\left(\frac{41}{476}\right)$	$e\left(\frac{541}{952}\right)$	$e\left(\frac{185}{408}\right)$	$e\left(\frac{1747}{5712}\right)$	$e\left(\frac{2449}{2856}\right)$	$e\left(\frac{1749}{1904}\right)$
$\chi_{56644}(745,\cdot)$	$1$	$1$	$e\left(\frac{2629}{5712}\right)$	$e\left(\frac{2825}{5712}\right)$	$e\left(\frac{2629}{2856}\right)$	$e\left(\frac{4843}{5712}\right)$	$e\left(\frac{361}{476}\right)$	$e\left(\frac{909}{952}\right)$	$e\left(\frac{385}{408}\right)$	$e\left(\frac{2147}{5712}\right)$	$e\left(\frac{2825}{2856}\right)$	$e\left(\frac{725}{1904}\right)$
$\chi_{56644}(789,\cdot)$	$1$	$1$	$e\left(\frac{3503}{5712}\right)$	$e\left(\frac{1963}{5712}\right)$	$e\left(\frac{647}{2856}\right)$	$e\left(\frac{4817}{5712}\right)$	$e\left(\frac{311}{476}\right)$	$e\left(\frac{911}{952}\right)$	$e\left(\frac{35}{408}\right)$	$e\left(\frac{121}{5712}\right)$	$e\left(\frac{1963}{2856}\right)$	$e\left(\frac{1599}{1904}\right)$
$\chi_{56644}(845,\cdot)$	$1$	$1$	$e\left(\frac{3113}{5712}\right)$	$e\left(\frac{2413}{5712}\right)$	$e\left(\frac{257}{2856}\right)$	$e\left(\frac{5639}{5712}\right)$	$e\left(\frac{61}{476}\right)$	$e\left(\frac{921}{952}\right)$	$e\left(\frac{53}{408}\right)$	$e\left(\frac{463}{5712}\right)$	$e\left(\frac{2413}{2856}\right)$	$e\left(\frac{1209}{1904}\right)$
$\chi_{56644}(857,\cdot)$	$1$	$1$	$e\left(\frac{5263}{5712}\right)$	$e\left(\frac{4619}{5712}\right)$	$e\left(\frac{2407}{2856}\right)$	$e\left(\frac{961}{5712}\right)$	$e\left(\frac{475}{476}\right)$	$e\left(\frac{695}{952}\right)$	$e\left(\frac{163}{408}\right)$	$e\left(\frac{2825}{5712}\right)$	$e\left(\frac{1763}{2856}\right)$	$e\left(\frac{1455}{1904}\right)$
$\chi_{56644}(873,\cdot)$	$1$	$1$	$e\left(\frac{1427}{5712}\right)$	$e\left(\frac{3919}{5712}\right)$	$e\left(\frac{1427}{2856}\right)$	$e\left(\frac{317}{5712}\right)$	$e\left(\frac{335}{476}\right)$	$e\left(\frac{891}{952}\right)$	$e\left(\frac{407}{408}\right)$	$e\left(\frac{2293}{5712}\right)$	$e\left(\frac{1063}{2856}\right)$	$e\left(\frac{1427}{1904}\right)$
$\chi_{56644}(929,\cdot)$	$1$	$1$	$e\left(\frac{4859}{5712}\right)$	$e\left(\frac{5671}{5712}\right)$	$e\left(\frac{2003}{2856}\right)$	$e\left(\frac{3365}{5712}\right)$	$e\left(\frac{155}{476}\right)$	$e\left(\frac{803}{952}\right)$	$e\left(\frac{167}{408}\right)$	$e\left(\frac{3853}{5712}\right)$	$e\left(\frac{2815}{2856}\right)$	$e\left(\frac{1051}{1904}\right)$
$\chi_{56644}(941,\cdot)$	$1$	$1$	$e\left(\frac{2755}{5712}\right)$	$e\left(\frac{3119}{5712}\right)$	$e\left(\frac{2755}{2856}\right)$	$e\left(\frac{2029}{5712}\right)$	$e\left(\frac{39}{476}\right)$	$e\left(\frac{27}{952}\right)$	$e\left(\frac{103}{408}\right)$	$e\left(\frac{1685}{5712}\right)$	$e\left(\frac{263}{2856}\right)$	$e\left(\frac{851}{1904}\right)$
$\chi_{56644}(957,\cdot)$	$1$	$1$	$e\left(\frac{5441}{5712}\right)$	$e\left(\frac{1045}{5712}\right)$	$e\left(\frac{2585}{2856}\right)$	$e\left(\frac{4511}{5712}\right)$	$e\left(\frac{345}{476}\right)$	$e\left(\frac{129}{952}\right)$	$e\left(\frac{341}{408}\right)$	$e\left(\frac{3079}{5712}\right)$	$e\left(\frac{1045}{2856}\right)$	$e\left(\frac{1633}{1904}\right)$
$\chi_{56644}(997,\cdot)$	$1$	$1$	$e\left(\frac{4891}{5712}\right)$	$e\left(\frac{215}{5712}\right)$	$e\left(\frac{2035}{2856}\right)$	$e\left(\frac{4645}{5712}\right)$	$e\left(\frac{383}{476}\right)$	$e\left(\frac{851}{952}\right)$	$e\left(\frac{199}{408}\right)$	$e\left(\frac{4733}{5712}\right)$	$e\left(\frac{215}{2856}\right)$	$e\left(\frac{1083}{1904}\right)$
$\chi_{56644}(1013,\cdot)$	$1$	$1$	$e\left(\frac{1607}{5712}\right)$	$e\left(\frac{1075}{5712}\right)$	$e\left(\frac{1607}{2856}\right)$	$e\left(\frac{377}{5712}\right)$	$e\left(\frac{11}{476}\right)$	$e\left(\frac{447}{952}\right)$	$e\left(\frac{179}{408}\right)$	$e\left(\frac{817}{5712}\right)$	$e\left(\frac{1075}{2856}\right)$	$e\left(\frac{1607}{1904}\right)$
$\chi_{56644}(1125,\cdot)$	$1$	$1$	$e\left(\frac{3725}{5712}\right)$	$e\left(\frac{3025}{5712}\right)$	$e\left(\frac{869}{2856}\right)$	$e\left(\frac{131}{5712}\right)$	$e\left(\frac{197}{476}\right)$	$e\left(\frac{173}{952}\right)$	$e\left(\frac{257}{408}\right)$	$e\left(\frac{2299}{5712}\right)$	$e\left(\frac{169}{2856}\right)$	$e\left(\frac{1821}{1904}\right)$

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 $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{56644}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3041}{5712}\right)\)	\(e\left(\frac{4693}{5712}\right)\)	\(e\left(\frac{185}{2856}\right)\)	\(e\left(\frac{5615}{5712}\right)\)	\(e\left(\frac{381}{476}\right)\)	\(e\left(\frac{337}{952}\right)\)	\(e\left(\frac{389}{408}\right)\)	\(e\left(\frac{5623}{5712}\right)\)	\(e\left(\frac{1837}{2856}\right)\)	\(e\left(\frac{1137}{1904}\right)\)
\(\chi_{56644}(45,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3355}{5712}\right)\)	\(e\left(\frac{5063}{5712}\right)\)	\(e\left(\frac{499}{2856}\right)\)	\(e\left(\frac{325}{5712}\right)\)	\(e\left(\frac{387}{476}\right)\)	\(e\left(\frac{451}{952}\right)\)	\(e\left(\frac{295}{408}\right)\)	\(e\left(\frac{2477}{5712}\right)\)	\(e\left(\frac{2207}{2856}\right)\)	\(e\left(\frac{1451}{1904}\right)\)
\(\chi_{56644}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1223}{5712}\right)\)	\(e\left(\frac{3715}{5712}\right)\)	\(e\left(\frac{1223}{2856}\right)\)	\(e\left(\frac{2153}{5712}\right)\)	\(e\left(\frac{131}{476}\right)\)	\(e\left(\frac{823}{952}\right)\)	\(e\left(\frac{203}{408}\right)\)	\(e\left(\frac{1681}{5712}\right)\)	\(e\left(\frac{859}{2856}\right)\)	\(e\left(\frac{1223}{1904}\right)\)
\(\chi_{56644}(73,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2785}{5712}\right)\)	\(e\left(\frac{2645}{5712}\right)\)	\(e\left(\frac{2785}{2856}\right)\)	\(e\left(\frac{1087}{5712}\right)\)	\(e\left(\frac{461}{476}\right)\)	\(e\left(\frac{905}{952}\right)\)	\(e\left(\frac{133}{408}\right)\)	\(e\left(\frac{4295}{5712}\right)\)	\(e\left(\frac{2645}{2856}\right)\)	\(e\left(\frac{881}{1904}\right)\)
\(\chi_{56644}(173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4349}{5712}\right)\)	\(e\left(\frac{2305}{5712}\right)\)	\(e\left(\frac{1493}{2856}\right)\)	\(e\left(\frac{2243}{5712}\right)\)	\(e\left(\frac{121}{476}\right)\)	\(e\left(\frac{157}{952}\right)\)	\(e\left(\frac{65}{408}\right)\)	\(e\left(\frac{5179}{5712}\right)\)	\(e\left(\frac{2305}{2856}\right)\)	\(e\left(\frac{541}{1904}\right)\)
\(\chi_{56644}(201,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2117}{5712}\right)\)	\(e\left(\frac{4441}{5712}\right)\)	\(e\left(\frac{2117}{2856}\right)\)	\(e\left(\frac{1499}{5712}\right)\)	\(e\left(\frac{45}{476}\right)\)	\(e\left(\frac{141}{952}\right)\)	\(e\left(\frac{281}{408}\right)\)	\(e\left(\frac{5203}{5712}\right)\)	\(e\left(\frac{1585}{2856}\right)\)	\(e\left(\frac{213}{1904}\right)\)
\(\chi_{56644}(241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{205}{5712}\right)\)	\(e\left(\frac{3425}{5712}\right)\)	\(e\left(\frac{205}{2856}\right)\)	\(e\left(\frac{2131}{5712}\right)\)	\(e\left(\frac{345}{476}\right)\)	\(e\left(\frac{605}{952}\right)\)	\(e\left(\frac{1}{408}\right)\)	\(e\left(\frac{2603}{5712}\right)\)	\(e\left(\frac{569}{2856}\right)\)	\(e\left(\frac{205}{1904}\right)\)
\(\chi_{56644}(269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3541}{5712}\right)\)	\(e\left(\frac{4409}{5712}\right)\)	\(e\left(\frac{685}{2856}\right)\)	\(e\left(\frac{1339}{5712}\right)\)	\(e\left(\frac{433}{476}\right)\)	\(e\left(\frac{373}{952}\right)\)	\(e\left(\frac{73}{408}\right)\)	\(e\left(\frac{1523}{5712}\right)\)	\(e\left(\frac{1553}{2856}\right)\)	\(e\left(\frac{1637}{1904}\right)\)
\(\chi_{56644}(369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{233}{5712}\right)\)	\(e\left(\frac{2221}{5712}\right)\)	\(e\left(\frac{233}{2856}\right)\)	\(e\left(\frac{4679}{5712}\right)\)	\(e\left(\frac{9}{476}\right)\)	\(e\left(\frac{409}{952}\right)\)	\(e\left(\frac{29}{408}\right)\)	\(e\left(\frac{1231}{5712}\right)\)	\(e\left(\frac{2221}{2856}\right)\)	\(e\left(\frac{233}{1904}\right)\)
\(\chi_{56644}(381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3823}{5712}\right)\)	\(e\left(\frac{4523}{5712}\right)\)	\(e\left(\frac{967}{2856}\right)\)	\(e\left(\frac{481}{5712}\right)\)	\(e\left(\frac{211}{476}\right)\)	\(e\left(\frac{439}{952}\right)\)	\(e\left(\frac{355}{408}\right)\)	\(e\left(\frac{3209}{5712}\right)\)	\(e\left(\frac{1667}{2856}\right)\)	\(e\left(\frac{15}{1904}\right)\)
\(\chi_{56644}(397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{563}{5712}\right)\)	\(e\left(\frac{2719}{5712}\right)\)	\(e\left(\frac{563}{2856}\right)\)	\(e\left(\frac{29}{5712}\right)\)	\(e\left(\frac{367}{476}\right)\)	\(e\left(\frac{547}{952}\right)\)	\(e\left(\frac{359}{408}\right)\)	\(e\left(\frac{1381}{5712}\right)\)	\(e\left(\frac{2719}{2856}\right)\)	\(e\left(\frac{563}{1904}\right)\)
\(\chi_{56644}(437,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3481}{5712}\right)\)	\(e\left(\frac{5357}{5712}\right)\)	\(e\left(\frac{625}{2856}\right)\)	\(e\left(\frac{3223}{5712}\right)\)	\(e\left(\frac{65}{476}\right)\)	\(e\left(\frac{521}{952}\right)\)	\(e\left(\frac{13}{408}\right)\)	\(e\left(\frac{2015}{5712}\right)\)	\(e\left(\frac{2501}{2856}\right)\)	\(e\left(\frac{1577}{1904}\right)\)
\(\chi_{56644}(453,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1643}{5712}\right)\)	\(e\left(\frac{2791}{5712}\right)\)	\(e\left(\frac{1643}{2856}\right)\)	\(e\left(\frac{389}{5712}\right)\)	\(e\left(\frac{327}{476}\right)\)	\(e\left(\frac{739}{952}\right)\)	\(e\left(\frac{215}{408}\right)\)	\(e\left(\frac{3949}{5712}\right)\)	\(e\left(\frac{2791}{2856}\right)\)	\(e\left(\frac{1643}{1904}\right)\)
\(\chi_{56644}(465,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4339}{5712}\right)\)	\(e\left(\frac{4367}{5712}\right)\)	\(e\left(\frac{1483}{2856}\right)\)	\(e\left(\frac{2557}{5712}\right)\)	\(e\left(\frac{139}{476}\right)\)	\(e\left(\frac{499}{952}\right)\)	\(e\left(\frac{55}{408}\right)\)	\(e\left(\frac{2405}{5712}\right)\)	\(e\left(\frac{1511}{2856}\right)\)	\(e\left(\frac{531}{1904}\right)\)
\(\chi_{56644}(481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4241}{5712}\right)\)	\(e\left(\frac{2869}{5712}\right)\)	\(e\left(\frac{1385}{2856}\right)\)	\(e\left(\frac{2207}{5712}\right)\)	\(e\left(\frac{125}{476}\right)\)	\(e\left(\frac{233}{952}\right)\)	\(e\left(\frac{365}{408}\right)\)	\(e\left(\frac{1495}{5712}\right)\)	\(e\left(\frac{13}{2856}\right)\)	\(e\left(\frac{433}{1904}\right)\)
\(\chi_{56644}(537,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1415}{5712}\right)\)	\(e\left(\frac{5251}{5712}\right)\)	\(e\left(\frac{1415}{2856}\right)\)	\(e\left(\frac{4121}{5712}\right)\)	\(e\left(\frac{71}{476}\right)\)	\(e\left(\frac{159}{952}\right)\)	\(e\left(\frac{395}{408}\right)\)	\(e\left(\frac{1249}{5712}\right)\)	\(e\left(\frac{2395}{2856}\right)\)	\(e\left(\frac{1415}{1904}\right)\)
\(\chi_{56644}(549,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1537}{5712}\right)\)	\(e\left(\frac{4085}{5712}\right)\)	\(e\left(\frac{1537}{2856}\right)\)	\(e\left(\frac{2575}{5712}\right)\)	\(e\left(\frac{137}{476}\right)\)	\(e\left(\frac{937}{952}\right)\)	\(e\left(\frac{109}{408}\right)\)	\(e\left(\frac{4247}{5712}\right)\)	\(e\left(\frac{1229}{2856}\right)\)	\(e\left(\frac{1537}{1904}\right)\)
\(\chi_{56644}(605,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3463}{5712}\right)\)	\(e\left(\frac{4499}{5712}\right)\)	\(e\left(\frac{607}{2856}\right)\)	\(e\left(\frac{361}{5712}\right)\)	\(e\left(\frac{383}{476}\right)\)	\(e\left(\frac{375}{952}\right)\)	\(e\left(\frac{403}{408}\right)\)	\(e\left(\frac{449}{5712}\right)\)	\(e\left(\frac{1643}{2856}\right)\)	\(e\left(\frac{1559}{1904}\right)\)
\(\chi_{56644}(649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1181}{5712}\right)\)	\(e\left(\frac{5521}{5712}\right)\)	\(e\left(\frac{1181}{2856}\right)\)	\(e\left(\frac{1187}{5712}\right)\)	\(e\left(\frac{397}{476}\right)\)	\(e\left(\frac{165}{952}\right)\)	\(e\left(\frac{161}{408}\right)\)	\(e\left(\frac{3739}{5712}\right)\)	\(e\left(\frac{2665}{2856}\right)\)	\(e\left(\frac{1181}{1904}\right)\)
\(\chi_{56644}(677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3653}{5712}\right)\)	\(e\left(\frac{5305}{5712}\right)\)	\(e\left(\frac{797}{2856}\right)\)	\(e\left(\frac{107}{5712}\right)\)	\(e\left(\frac{41}{476}\right)\)	\(e\left(\frac{541}{952}\right)\)	\(e\left(\frac{185}{408}\right)\)	\(e\left(\frac{1747}{5712}\right)\)	\(e\left(\frac{2449}{2856}\right)\)	\(e\left(\frac{1749}{1904}\right)\)
\(\chi_{56644}(745,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2629}{5712}\right)\)	\(e\left(\frac{2825}{5712}\right)\)	\(e\left(\frac{2629}{2856}\right)\)	\(e\left(\frac{4843}{5712}\right)\)	\(e\left(\frac{361}{476}\right)\)	\(e\left(\frac{909}{952}\right)\)	\(e\left(\frac{385}{408}\right)\)	\(e\left(\frac{2147}{5712}\right)\)	\(e\left(\frac{2825}{2856}\right)\)	\(e\left(\frac{725}{1904}\right)\)
\(\chi_{56644}(789,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3503}{5712}\right)\)	\(e\left(\frac{1963}{5712}\right)\)	\(e\left(\frac{647}{2856}\right)\)	\(e\left(\frac{4817}{5712}\right)\)	\(e\left(\frac{311}{476}\right)\)	\(e\left(\frac{911}{952}\right)\)	\(e\left(\frac{35}{408}\right)\)	\(e\left(\frac{121}{5712}\right)\)	\(e\left(\frac{1963}{2856}\right)\)	\(e\left(\frac{1599}{1904}\right)\)
\(\chi_{56644}(845,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3113}{5712}\right)\)	\(e\left(\frac{2413}{5712}\right)\)	\(e\left(\frac{257}{2856}\right)\)	\(e\left(\frac{5639}{5712}\right)\)	\(e\left(\frac{61}{476}\right)\)	\(e\left(\frac{921}{952}\right)\)	\(e\left(\frac{53}{408}\right)\)	\(e\left(\frac{463}{5712}\right)\)	\(e\left(\frac{2413}{2856}\right)\)	\(e\left(\frac{1209}{1904}\right)\)
\(\chi_{56644}(857,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5263}{5712}\right)\)	\(e\left(\frac{4619}{5712}\right)\)	\(e\left(\frac{2407}{2856}\right)\)	\(e\left(\frac{961}{5712}\right)\)	\(e\left(\frac{475}{476}\right)\)	\(e\left(\frac{695}{952}\right)\)	\(e\left(\frac{163}{408}\right)\)	\(e\left(\frac{2825}{5712}\right)\)	\(e\left(\frac{1763}{2856}\right)\)	\(e\left(\frac{1455}{1904}\right)\)
\(\chi_{56644}(873,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1427}{5712}\right)\)	\(e\left(\frac{3919}{5712}\right)\)	\(e\left(\frac{1427}{2856}\right)\)	\(e\left(\frac{317}{5712}\right)\)	\(e\left(\frac{335}{476}\right)\)	\(e\left(\frac{891}{952}\right)\)	\(e\left(\frac{407}{408}\right)\)	\(e\left(\frac{2293}{5712}\right)\)	\(e\left(\frac{1063}{2856}\right)\)	\(e\left(\frac{1427}{1904}\right)\)
\(\chi_{56644}(929,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4859}{5712}\right)\)	\(e\left(\frac{5671}{5712}\right)\)	\(e\left(\frac{2003}{2856}\right)\)	\(e\left(\frac{3365}{5712}\right)\)	\(e\left(\frac{155}{476}\right)\)	\(e\left(\frac{803}{952}\right)\)	\(e\left(\frac{167}{408}\right)\)	\(e\left(\frac{3853}{5712}\right)\)	\(e\left(\frac{2815}{2856}\right)\)	\(e\left(\frac{1051}{1904}\right)\)
\(\chi_{56644}(941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2755}{5712}\right)\)	\(e\left(\frac{3119}{5712}\right)\)	\(e\left(\frac{2755}{2856}\right)\)	\(e\left(\frac{2029}{5712}\right)\)	\(e\left(\frac{39}{476}\right)\)	\(e\left(\frac{27}{952}\right)\)	\(e\left(\frac{103}{408}\right)\)	\(e\left(\frac{1685}{5712}\right)\)	\(e\left(\frac{263}{2856}\right)\)	\(e\left(\frac{851}{1904}\right)\)
\(\chi_{56644}(957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5441}{5712}\right)\)	\(e\left(\frac{1045}{5712}\right)\)	\(e\left(\frac{2585}{2856}\right)\)	\(e\left(\frac{4511}{5712}\right)\)	\(e\left(\frac{345}{476}\right)\)	\(e\left(\frac{129}{952}\right)\)	\(e\left(\frac{341}{408}\right)\)	\(e\left(\frac{3079}{5712}\right)\)	\(e\left(\frac{1045}{2856}\right)\)	\(e\left(\frac{1633}{1904}\right)\)
\(\chi_{56644}(997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4891}{5712}\right)\)	\(e\left(\frac{215}{5712}\right)\)	\(e\left(\frac{2035}{2856}\right)\)	\(e\left(\frac{4645}{5712}\right)\)	\(e\left(\frac{383}{476}\right)\)	\(e\left(\frac{851}{952}\right)\)	\(e\left(\frac{199}{408}\right)\)	\(e\left(\frac{4733}{5712}\right)\)	\(e\left(\frac{215}{2856}\right)\)	\(e\left(\frac{1083}{1904}\right)\)
\(\chi_{56644}(1013,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1607}{5712}\right)\)	\(e\left(\frac{1075}{5712}\right)\)	\(e\left(\frac{1607}{2856}\right)\)	\(e\left(\frac{377}{5712}\right)\)	\(e\left(\frac{11}{476}\right)\)	\(e\left(\frac{447}{952}\right)\)	\(e\left(\frac{179}{408}\right)\)	\(e\left(\frac{817}{5712}\right)\)	\(e\left(\frac{1075}{2856}\right)\)	\(e\left(\frac{1607}{1904}\right)\)
\(\chi_{56644}(1125,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3725}{5712}\right)\)	\(e\left(\frac{3025}{5712}\right)\)	\(e\left(\frac{869}{2856}\right)\)	\(e\left(\frac{131}{5712}\right)\)	\(e\left(\frac{197}{476}\right)\)	\(e\left(\frac{173}{952}\right)\)	\(e\left(\frac{257}{408}\right)\)	\(e\left(\frac{2299}{5712}\right)\)	\(e\left(\frac{169}{2856}\right)\)	\(e\left(\frac{1821}{1904}\right)\)

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First 31 of 1536 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	56644.ga
Modulus	$56644$
Conductor	$14161$
Order	$5712$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(56644\)
Conductor:	\(14161\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(5712\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 14161.da	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)