LMFDB - Dirichlet character orbit 109744.df

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(109744, base_ring=CyclotomicField(1444)) M = H._module chi = DirichletCharacter(H, M([0,361,1302])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(37, 109744)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("109744.37"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$109744$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$109744$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$1444$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{1444})$
Fixed field:	Number field defined by a degree 1444 polynomial (not computed)

First 31 of 684 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$21$	$23$
$\chi_{109744}(37,\cdot)$	$-1$	$1$	$e\left(\frac{117}{1444}\right)$	$e\left(\frac{857}{1444}\right)$	$e\left(\frac{85}{722}\right)$	$e\left(\frac{117}{722}\right)$	$e\left(\frac{697}{1444}\right)$	$e\left(\frac{1333}{1444}\right)$	$e\left(\frac{487}{722}\right)$	$e\left(\frac{147}{361}\right)$	$e\left(\frac{287}{1444}\right)$	$e\left(\frac{141}{722}\right)$
$\chi_{109744}(189,\cdot)$	$-1$	$1$	$e\left(\frac{1003}{1444}\right)$	$e\left(\frac{1435}{1444}\right)$	$e\left(\frac{235}{722}\right)$	$e\left(\frac{281}{722}\right)$	$e\left(\frac{483}{1444}\right)$	$e\left(\frac{1307}{1444}\right)$	$e\left(\frac{497}{722}\right)$	$e\left(\frac{279}{361}\right)$	$e\left(\frac{29}{1444}\right)$	$e\left(\frac{135}{722}\right)$
$\chi_{109744}(341,\cdot)$	$-1$	$1$	$e\left(\frac{825}{1444}\right)$	$e\left(\frac{341}{1444}\right)$	$e\left(\frac{81}{722}\right)$	$e\left(\frac{103}{722}\right)$	$e\left(\frac{953}{1444}\right)$	$e\left(\frac{217}{1444}\right)$	$e\left(\frac{583}{722}\right)$	$e\left(\frac{259}{361}\right)$	$e\left(\frac{987}{1444}\right)$	$e\left(\frac{661}{722}\right)$
$\chi_{109744}(493,\cdot)$	$-1$	$1$	$e\left(\frac{1027}{1444}\right)$	$e\left(\frac{463}{1444}\right)$	$e\left(\frac{345}{722}\right)$	$e\left(\frac{305}{722}\right)$	$e\left(\frac{663}{1444}\right)$	$e\left(\frac{951}{1444}\right)$	$e\left(\frac{23}{722}\right)$	$e\left(\frac{87}{361}\right)$	$e\left(\frac{273}{1444}\right)$	$e\left(\frac{275}{722}\right)$
$\chi_{109744}(645,\cdot)$	$-1$	$1$	$e\left(\frac{165}{1444}\right)$	$e\left(\frac{357}{1444}\right)$	$e\left(\frac{305}{722}\right)$	$e\left(\frac{165}{722}\right)$	$e\left(\frac{1057}{1444}\right)$	$e\left(\frac{621}{1444}\right)$	$e\left(\frac{261}{722}\right)$	$e\left(\frac{124}{361}\right)$	$e\left(\frac{775}{1444}\right)$	$e\left(\frac{421}{722}\right)$
$\chi_{109744}(797,\cdot)$	$-1$	$1$	$e\left(\frac{1127}{1444}\right)$	$e\left(\frac{23}{1444}\right)$	$e\left(\frac{683}{722}\right)$	$e\left(\frac{405}{722}\right)$	$e\left(\frac{691}{1444}\right)$	$e\left(\frac{671}{1444}\right)$	$e\left(\frac{575}{722}\right)$	$e\left(\frac{9}{361}\right)$	$e\left(\frac{1049}{1444}\right)$	$e\left(\frac{377}{722}\right)$
$\chi_{109744}(949,\cdot)$	$-1$	$1$	$e\left(\frac{1025}{1444}\right)$	$e\left(\frac{905}{1444}\right)$	$e\left(\frac{35}{722}\right)$	$e\left(\frac{303}{722}\right)$	$e\left(\frac{1009}{1444}\right)$	$e\left(\frac{1101}{1444}\right)$	$e\left(\frac{243}{722}\right)$	$e\left(\frac{103}{361}\right)$	$e\left(\frac{1095}{1444}\right)$	$e\left(\frac{143}{722}\right)$
$\chi_{109744}(1101,\cdot)$	$-1$	$1$	$e\left(\frac{1303}{1444}\right)$	$e\left(\frac{115}{1444}\right)$	$e\left(\frac{527}{722}\right)$	$e\left(\frac{581}{722}\right)$	$e\left(\frac{567}{1444}\right)$	$e\left(\frac{467}{1444}\right)$	$e\left(\frac{709}{722}\right)$	$e\left(\frac{45}{361}\right)$	$e\left(\frac{913}{1444}\right)$	$e\left(\frac{441}{722}\right)$
$\chi_{109744}(1253,\cdot)$	$-1$	$1$	$e\left(\frac{517}{1444}\right)$	$e\left(\frac{541}{1444}\right)$	$e\left(\frac{715}{722}\right)$	$e\left(\frac{517}{722}\right)$	$e\left(\frac{809}{1444}\right)$	$e\left(\frac{213}{1444}\right)$	$e\left(\frac{529}{722}\right)$	$e\left(\frac{196}{361}\right)$	$e\left(\frac{503}{1444}\right)$	$e\left(\frac{549}{722}\right)$
$\chi_{109744}(1405,\cdot)$	$-1$	$1$	$e\left(\frac{111}{1444}\right)$	$e\left(\frac{739}{1444}\right)$	$e\left(\frac{599}{722}\right)$	$e\left(\frac{111}{722}\right)$	$e\left(\frac{291}{1444}\right)$	$e\left(\frac{339}{1444}\right)$	$e\left(\frac{425}{722}\right)$	$e\left(\frac{195}{361}\right)$	$e\left(\frac{1309}{1444}\right)$	$e\left(\frac{467}{722}\right)$
$\chi_{109744}(1557,\cdot)$	$-1$	$1$	$e\left(\frac{85}{1444}\right)$	$e\left(\frac{709}{1444}\right)$	$e\left(\frac{179}{722}\right)$	$e\left(\frac{85}{722}\right)$	$e\left(\frac{457}{1444}\right)$	$e\left(\frac{845}{1444}\right)$	$e\left(\frac{397}{722}\right)$	$e\left(\frac{42}{361}\right)$	$e\left(\frac{443}{1444}\right)$	$e\left(\frac{195}{722}\right)$
$\chi_{109744}(1709,\cdot)$	$-1$	$1$	$e\left(\frac{439}{1444}\right)$	$e\left(\frac{451}{1444}\right)$	$e\left(\frac{177}{722}\right)$	$e\left(\frac{439}{722}\right)$	$e\left(\frac{1307}{1444}\right)$	$e\left(\frac{287}{1444}\right)$	$e\left(\frac{445}{722}\right)$	$e\left(\frac{98}{361}\right)$	$e\left(\frac{793}{1444}\right)$	$e\left(\frac{455}{722}\right)$
$\chi_{109744}(1861,\cdot)$	$-1$	$1$	$e\left(\frac{1173}{1444}\right)$	$e\left(\frac{1409}{1444}\right)$	$e\left(\frac{593}{722}\right)$	$e\left(\frac{451}{722}\right)$	$e\left(\frac{1397}{1444}\right)$	$e\left(\frac{109}{1444}\right)$	$e\left(\frac{569}{722}\right)$	$e\left(\frac{2}{361}\right)$	$e\left(\frac{915}{1444}\right)$	$e\left(\frac{525}{722}\right)$
$\chi_{109744}(2013,\cdot)$	$-1$	$1$	$e\left(\frac{843}{1444}\right)$	$e\left(\frac{695}{1444}\right)$	$e\left(\frac{705}{722}\right)$	$e\left(\frac{121}{722}\right)$	$e\left(\frac{727}{1444}\right)$	$e\left(\frac{311}{1444}\right)$	$e\left(\frac{47}{722}\right)$	$e\left(\frac{115}{361}\right)$	$e\left(\frac{809}{1444}\right)$	$e\left(\frac{405}{722}\right)$
$\chi_{109744}(2317,\cdot)$	$-1$	$1$	$e\left(\frac{1323}{1444}\right)$	$e\left(\frac{27}{1444}\right)$	$e\left(\frac{17}{722}\right)$	$e\left(\frac{601}{722}\right)$	$e\left(\frac{1439}{1444}\right)$	$e\left(\frac{411}{1444}\right)$	$e\left(\frac{675}{722}\right)$	$e\left(\frac{246}{361}\right)$	$e\left(\frac{1357}{1444}\right)$	$e\left(\frac{317}{722}\right)$
$\chi_{109744}(2469,\cdot)$	$-1$	$1$	$e\left(\frac{689}{1444}\right)$	$e\left(\frac{73}{1444}\right)$	$e\left(\frac{661}{722}\right)$	$e\left(\frac{689}{722}\right)$	$e\left(\frac{1377}{1444}\right)$	$e\left(\frac{309}{1444}\right)$	$e\left(\frac{381}{722}\right)$	$e\left(\frac{264}{361}\right)$	$e\left(\frac{567}{1444}\right)$	$e\left(\frac{349}{722}\right)$
$\chi_{109744}(2621,\cdot)$	$-1$	$1$	$e\left(\frac{435}{1444}\right)$	$e\left(\frac{1335}{1444}\right)$	$e\left(\frac{279}{722}\right)$	$e\left(\frac{435}{722}\right)$	$e\left(\frac{555}{1444}\right)$	$e\left(\frac{587}{1444}\right)$	$e\left(\frac{163}{722}\right)$	$e\left(\frac{130}{361}\right)$	$e\left(\frac{993}{1444}\right)$	$e\left(\frac{191}{722}\right)$
$\chi_{109744}(2773,\cdot)$	$-1$	$1$	$e\left(\frac{561}{1444}\right)$	$e\left(\frac{925}{1444}\right)$	$e\left(\frac{315}{722}\right)$	$e\left(\frac{561}{722}\right)$	$e\left(\frac{417}{1444}\right)$	$e\left(\frac{1245}{1444}\right)$	$e\left(\frac{21}{722}\right)$	$e\left(\frac{205}{361}\right)$	$e\left(\frac{1191}{1444}\right)$	$e\left(\frac{565}{722}\right)$
$\chi_{109744}(2925,\cdot)$	$-1$	$1$	$e\left(\frac{1067}{1444}\right)$	$e\left(\frac{287}{1444}\right)$	$e\left(\frac{47}{722}\right)$	$e\left(\frac{345}{722}\right)$	$e\left(\frac{963}{1444}\right)$	$e\left(\frac{839}{1444}\right)$	$e\left(\frac{677}{722}\right)$	$e\left(\frac{128}{361}\right)$	$e\left(\frac{1161}{1444}\right)$	$e\left(\frac{27}{722}\right)$
$\chi_{109744}(3077,\cdot)$	$-1$	$1$	$e\left(\frac{509}{1444}\right)$	$e\left(\frac{865}{1444}\right)$	$e\left(\frac{197}{722}\right)$	$e\left(\frac{509}{722}\right)$	$e\left(\frac{749}{1444}\right)$	$e\left(\frac{813}{1444}\right)$	$e\left(\frac{687}{722}\right)$	$e\left(\frac{260}{361}\right)$	$e\left(\frac{903}{1444}\right)$	$e\left(\frac{21}{722}\right)$
$\chi_{109744}(3229,\cdot)$	$-1$	$1$	$e\left(\frac{331}{1444}\right)$	$e\left(\frac{1215}{1444}\right)$	$e\left(\frac{43}{722}\right)$	$e\left(\frac{331}{722}\right)$	$e\left(\frac{1219}{1444}\right)$	$e\left(\frac{1167}{1444}\right)$	$e\left(\frac{51}{722}\right)$	$e\left(\frac{240}{361}\right)$	$e\left(\frac{417}{1444}\right)$	$e\left(\frac{547}{722}\right)$
$\chi_{109744}(3381,\cdot)$	$-1$	$1$	$e\left(\frac{533}{1444}\right)$	$e\left(\frac{1337}{1444}\right)$	$e\left(\frac{307}{722}\right)$	$e\left(\frac{533}{722}\right)$	$e\left(\frac{929}{1444}\right)$	$e\left(\frac{457}{1444}\right)$	$e\left(\frac{213}{722}\right)$	$e\left(\frac{68}{361}\right)$	$e\left(\frac{1147}{1444}\right)$	$e\left(\frac{161}{722}\right)$
$\chi_{109744}(3533,\cdot)$	$-1$	$1$	$e\left(\frac{1115}{1444}\right)$	$e\left(\frac{1231}{1444}\right)$	$e\left(\frac{267}{722}\right)$	$e\left(\frac{393}{722}\right)$	$e\left(\frac{1323}{1444}\right)$	$e\left(\frac{127}{1444}\right)$	$e\left(\frac{451}{722}\right)$	$e\left(\frac{105}{361}\right)$	$e\left(\frac{205}{1444}\right)$	$e\left(\frac{307}{722}\right)$
$\chi_{109744}(3685,\cdot)$	$-1$	$1$	$e\left(\frac{633}{1444}\right)$	$e\left(\frac{897}{1444}\right)$	$e\left(\frac{645}{722}\right)$	$e\left(\frac{633}{722}\right)$	$e\left(\frac{957}{1444}\right)$	$e\left(\frac{177}{1444}\right)$	$e\left(\frac{43}{722}\right)$	$e\left(\frac{351}{361}\right)$	$e\left(\frac{479}{1444}\right)$	$e\left(\frac{263}{722}\right)$
$\chi_{109744}(3837,\cdot)$	$-1$	$1$	$e\left(\frac{531}{1444}\right)$	$e\left(\frac{335}{1444}\right)$	$e\left(\frac{719}{722}\right)$	$e\left(\frac{531}{722}\right)$	$e\left(\frac{1275}{1444}\right)$	$e\left(\frac{607}{1444}\right)$	$e\left(\frac{433}{722}\right)$	$e\left(\frac{84}{361}\right)$	$e\left(\frac{525}{1444}\right)$	$e\left(\frac{29}{722}\right)$
$\chi_{109744}(3989,\cdot)$	$-1$	$1$	$e\left(\frac{809}{1444}\right)$	$e\left(\frac{989}{1444}\right)$	$e\left(\frac{489}{722}\right)$	$e\left(\frac{87}{722}\right)$	$e\left(\frac{833}{1444}\right)$	$e\left(\frac{1417}{1444}\right)$	$e\left(\frac{177}{722}\right)$	$e\left(\frac{26}{361}\right)$	$e\left(\frac{343}{1444}\right)$	$e\left(\frac{327}{722}\right)$
$\chi_{109744}(4141,\cdot)$	$-1$	$1$	$e\left(\frac{23}{1444}\right)$	$e\left(\frac{1415}{1444}\right)$	$e\left(\frac{677}{722}\right)$	$e\left(\frac{23}{722}\right)$	$e\left(\frac{1075}{1444}\right)$	$e\left(\frac{1163}{1444}\right)$	$e\left(\frac{719}{722}\right)$	$e\left(\frac{177}{361}\right)$	$e\left(\frac{1377}{1444}\right)$	$e\left(\frac{435}{722}\right)$
$\chi_{109744}(4293,\cdot)$	$-1$	$1$	$e\left(\frac{1061}{1444}\right)$	$e\left(\frac{169}{1444}\right)$	$e\left(\frac{561}{722}\right)$	$e\left(\frac{339}{722}\right)$	$e\left(\frac{557}{1444}\right)$	$e\left(\frac{1289}{1444}\right)$	$e\left(\frac{615}{722}\right)$	$e\left(\frac{176}{361}\right)$	$e\left(\frac{739}{1444}\right)$	$e\left(\frac{353}{722}\right)$
$\chi_{109744}(4445,\cdot)$	$-1$	$1$	$e\left(\frac{1035}{1444}\right)$	$e\left(\frac{139}{1444}\right)$	$e\left(\frac{141}{722}\right)$	$e\left(\frac{313}{722}\right)$	$e\left(\frac{723}{1444}\right)$	$e\left(\frac{351}{1444}\right)$	$e\left(\frac{587}{722}\right)$	$e\left(\frac{23}{361}\right)$	$e\left(\frac{1317}{1444}\right)$	$e\left(\frac{81}{722}\right)$
$\chi_{109744}(4597,\cdot)$	$-1$	$1$	$e\left(\frac{1389}{1444}\right)$	$e\left(\frac{1325}{1444}\right)$	$e\left(\frac{139}{722}\right)$	$e\left(\frac{667}{722}\right)$	$e\left(\frac{129}{1444}\right)$	$e\left(\frac{1237}{1444}\right)$	$e\left(\frac{635}{722}\right)$	$e\left(\frac{79}{361}\right)$	$e\left(\frac{223}{1444}\right)$	$e\left(\frac{341}{722}\right)$
$\chi_{109744}(4749,\cdot)$	$-1$	$1$	$e\left(\frac{679}{1444}\right)$	$e\left(\frac{839}{1444}\right)$	$e\left(\frac{555}{722}\right)$	$e\left(\frac{679}{722}\right)$	$e\left(\frac{219}{1444}\right)$	$e\left(\frac{1059}{1444}\right)$	$e\left(\frac{37}{722}\right)$	$e\left(\frac{344}{361}\right)$	$e\left(\frac{345}{1444}\right)$	$e\left(\frac{411}{722}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)
\(\chi_{109744}(37,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{117}{1444}\right)\)	\(e\left(\frac{857}{1444}\right)\)	\(e\left(\frac{85}{722}\right)\)	\(e\left(\frac{117}{722}\right)\)	\(e\left(\frac{697}{1444}\right)\)	\(e\left(\frac{1333}{1444}\right)\)	\(e\left(\frac{487}{722}\right)\)	\(e\left(\frac{147}{361}\right)\)	\(e\left(\frac{287}{1444}\right)\)	\(e\left(\frac{141}{722}\right)\)
\(\chi_{109744}(189,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1003}{1444}\right)\)	\(e\left(\frac{1435}{1444}\right)\)	\(e\left(\frac{235}{722}\right)\)	\(e\left(\frac{281}{722}\right)\)	\(e\left(\frac{483}{1444}\right)\)	\(e\left(\frac{1307}{1444}\right)\)	\(e\left(\frac{497}{722}\right)\)	\(e\left(\frac{279}{361}\right)\)	\(e\left(\frac{29}{1444}\right)\)	\(e\left(\frac{135}{722}\right)\)
\(\chi_{109744}(341,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{825}{1444}\right)\)	\(e\left(\frac{341}{1444}\right)\)	\(e\left(\frac{81}{722}\right)\)	\(e\left(\frac{103}{722}\right)\)	\(e\left(\frac{953}{1444}\right)\)	\(e\left(\frac{217}{1444}\right)\)	\(e\left(\frac{583}{722}\right)\)	\(e\left(\frac{259}{361}\right)\)	\(e\left(\frac{987}{1444}\right)\)	\(e\left(\frac{661}{722}\right)\)
\(\chi_{109744}(493,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1027}{1444}\right)\)	\(e\left(\frac{463}{1444}\right)\)	\(e\left(\frac{345}{722}\right)\)	\(e\left(\frac{305}{722}\right)\)	\(e\left(\frac{663}{1444}\right)\)	\(e\left(\frac{951}{1444}\right)\)	\(e\left(\frac{23}{722}\right)\)	\(e\left(\frac{87}{361}\right)\)	\(e\left(\frac{273}{1444}\right)\)	\(e\left(\frac{275}{722}\right)\)
\(\chi_{109744}(645,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{165}{1444}\right)\)	\(e\left(\frac{357}{1444}\right)\)	\(e\left(\frac{305}{722}\right)\)	\(e\left(\frac{165}{722}\right)\)	\(e\left(\frac{1057}{1444}\right)\)	\(e\left(\frac{621}{1444}\right)\)	\(e\left(\frac{261}{722}\right)\)	\(e\left(\frac{124}{361}\right)\)	\(e\left(\frac{775}{1444}\right)\)	\(e\left(\frac{421}{722}\right)\)
\(\chi_{109744}(797,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1127}{1444}\right)\)	\(e\left(\frac{23}{1444}\right)\)	\(e\left(\frac{683}{722}\right)\)	\(e\left(\frac{405}{722}\right)\)	\(e\left(\frac{691}{1444}\right)\)	\(e\left(\frac{671}{1444}\right)\)	\(e\left(\frac{575}{722}\right)\)	\(e\left(\frac{9}{361}\right)\)	\(e\left(\frac{1049}{1444}\right)\)	\(e\left(\frac{377}{722}\right)\)
\(\chi_{109744}(949,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1025}{1444}\right)\)	\(e\left(\frac{905}{1444}\right)\)	\(e\left(\frac{35}{722}\right)\)	\(e\left(\frac{303}{722}\right)\)	\(e\left(\frac{1009}{1444}\right)\)	\(e\left(\frac{1101}{1444}\right)\)	\(e\left(\frac{243}{722}\right)\)	\(e\left(\frac{103}{361}\right)\)	\(e\left(\frac{1095}{1444}\right)\)	\(e\left(\frac{143}{722}\right)\)
\(\chi_{109744}(1101,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1303}{1444}\right)\)	\(e\left(\frac{115}{1444}\right)\)	\(e\left(\frac{527}{722}\right)\)	\(e\left(\frac{581}{722}\right)\)	\(e\left(\frac{567}{1444}\right)\)	\(e\left(\frac{467}{1444}\right)\)	\(e\left(\frac{709}{722}\right)\)	\(e\left(\frac{45}{361}\right)\)	\(e\left(\frac{913}{1444}\right)\)	\(e\left(\frac{441}{722}\right)\)
\(\chi_{109744}(1253,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{517}{1444}\right)\)	\(e\left(\frac{541}{1444}\right)\)	\(e\left(\frac{715}{722}\right)\)	\(e\left(\frac{517}{722}\right)\)	\(e\left(\frac{809}{1444}\right)\)	\(e\left(\frac{213}{1444}\right)\)	\(e\left(\frac{529}{722}\right)\)	\(e\left(\frac{196}{361}\right)\)	\(e\left(\frac{503}{1444}\right)\)	\(e\left(\frac{549}{722}\right)\)
\(\chi_{109744}(1405,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{111}{1444}\right)\)	\(e\left(\frac{739}{1444}\right)\)	\(e\left(\frac{599}{722}\right)\)	\(e\left(\frac{111}{722}\right)\)	\(e\left(\frac{291}{1444}\right)\)	\(e\left(\frac{339}{1444}\right)\)	\(e\left(\frac{425}{722}\right)\)	\(e\left(\frac{195}{361}\right)\)	\(e\left(\frac{1309}{1444}\right)\)	\(e\left(\frac{467}{722}\right)\)
\(\chi_{109744}(1557,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{1444}\right)\)	\(e\left(\frac{709}{1444}\right)\)	\(e\left(\frac{179}{722}\right)\)	\(e\left(\frac{85}{722}\right)\)	\(e\left(\frac{457}{1444}\right)\)	\(e\left(\frac{845}{1444}\right)\)	\(e\left(\frac{397}{722}\right)\)	\(e\left(\frac{42}{361}\right)\)	\(e\left(\frac{443}{1444}\right)\)	\(e\left(\frac{195}{722}\right)\)
\(\chi_{109744}(1709,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{439}{1444}\right)\)	\(e\left(\frac{451}{1444}\right)\)	\(e\left(\frac{177}{722}\right)\)	\(e\left(\frac{439}{722}\right)\)	\(e\left(\frac{1307}{1444}\right)\)	\(e\left(\frac{287}{1444}\right)\)	\(e\left(\frac{445}{722}\right)\)	\(e\left(\frac{98}{361}\right)\)	\(e\left(\frac{793}{1444}\right)\)	\(e\left(\frac{455}{722}\right)\)
\(\chi_{109744}(1861,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1173}{1444}\right)\)	\(e\left(\frac{1409}{1444}\right)\)	\(e\left(\frac{593}{722}\right)\)	\(e\left(\frac{451}{722}\right)\)	\(e\left(\frac{1397}{1444}\right)\)	\(e\left(\frac{109}{1444}\right)\)	\(e\left(\frac{569}{722}\right)\)	\(e\left(\frac{2}{361}\right)\)	\(e\left(\frac{915}{1444}\right)\)	\(e\left(\frac{525}{722}\right)\)
\(\chi_{109744}(2013,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{843}{1444}\right)\)	\(e\left(\frac{695}{1444}\right)\)	\(e\left(\frac{705}{722}\right)\)	\(e\left(\frac{121}{722}\right)\)	\(e\left(\frac{727}{1444}\right)\)	\(e\left(\frac{311}{1444}\right)\)	\(e\left(\frac{47}{722}\right)\)	\(e\left(\frac{115}{361}\right)\)	\(e\left(\frac{809}{1444}\right)\)	\(e\left(\frac{405}{722}\right)\)
\(\chi_{109744}(2317,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1323}{1444}\right)\)	\(e\left(\frac{27}{1444}\right)\)	\(e\left(\frac{17}{722}\right)\)	\(e\left(\frac{601}{722}\right)\)	\(e\left(\frac{1439}{1444}\right)\)	\(e\left(\frac{411}{1444}\right)\)	\(e\left(\frac{675}{722}\right)\)	\(e\left(\frac{246}{361}\right)\)	\(e\left(\frac{1357}{1444}\right)\)	\(e\left(\frac{317}{722}\right)\)
\(\chi_{109744}(2469,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{689}{1444}\right)\)	\(e\left(\frac{73}{1444}\right)\)	\(e\left(\frac{661}{722}\right)\)	\(e\left(\frac{689}{722}\right)\)	\(e\left(\frac{1377}{1444}\right)\)	\(e\left(\frac{309}{1444}\right)\)	\(e\left(\frac{381}{722}\right)\)	\(e\left(\frac{264}{361}\right)\)	\(e\left(\frac{567}{1444}\right)\)	\(e\left(\frac{349}{722}\right)\)
\(\chi_{109744}(2621,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{435}{1444}\right)\)	\(e\left(\frac{1335}{1444}\right)\)	\(e\left(\frac{279}{722}\right)\)	\(e\left(\frac{435}{722}\right)\)	\(e\left(\frac{555}{1444}\right)\)	\(e\left(\frac{587}{1444}\right)\)	\(e\left(\frac{163}{722}\right)\)	\(e\left(\frac{130}{361}\right)\)	\(e\left(\frac{993}{1444}\right)\)	\(e\left(\frac{191}{722}\right)\)
\(\chi_{109744}(2773,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{561}{1444}\right)\)	\(e\left(\frac{925}{1444}\right)\)	\(e\left(\frac{315}{722}\right)\)	\(e\left(\frac{561}{722}\right)\)	\(e\left(\frac{417}{1444}\right)\)	\(e\left(\frac{1245}{1444}\right)\)	\(e\left(\frac{21}{722}\right)\)	\(e\left(\frac{205}{361}\right)\)	\(e\left(\frac{1191}{1444}\right)\)	\(e\left(\frac{565}{722}\right)\)
\(\chi_{109744}(2925,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1067}{1444}\right)\)	\(e\left(\frac{287}{1444}\right)\)	\(e\left(\frac{47}{722}\right)\)	\(e\left(\frac{345}{722}\right)\)	\(e\left(\frac{963}{1444}\right)\)	\(e\left(\frac{839}{1444}\right)\)	\(e\left(\frac{677}{722}\right)\)	\(e\left(\frac{128}{361}\right)\)	\(e\left(\frac{1161}{1444}\right)\)	\(e\left(\frac{27}{722}\right)\)
\(\chi_{109744}(3077,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{509}{1444}\right)\)	\(e\left(\frac{865}{1444}\right)\)	\(e\left(\frac{197}{722}\right)\)	\(e\left(\frac{509}{722}\right)\)	\(e\left(\frac{749}{1444}\right)\)	\(e\left(\frac{813}{1444}\right)\)	\(e\left(\frac{687}{722}\right)\)	\(e\left(\frac{260}{361}\right)\)	\(e\left(\frac{903}{1444}\right)\)	\(e\left(\frac{21}{722}\right)\)
\(\chi_{109744}(3229,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{331}{1444}\right)\)	\(e\left(\frac{1215}{1444}\right)\)	\(e\left(\frac{43}{722}\right)\)	\(e\left(\frac{331}{722}\right)\)	\(e\left(\frac{1219}{1444}\right)\)	\(e\left(\frac{1167}{1444}\right)\)	\(e\left(\frac{51}{722}\right)\)	\(e\left(\frac{240}{361}\right)\)	\(e\left(\frac{417}{1444}\right)\)	\(e\left(\frac{547}{722}\right)\)
\(\chi_{109744}(3381,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{533}{1444}\right)\)	\(e\left(\frac{1337}{1444}\right)\)	\(e\left(\frac{307}{722}\right)\)	\(e\left(\frac{533}{722}\right)\)	\(e\left(\frac{929}{1444}\right)\)	\(e\left(\frac{457}{1444}\right)\)	\(e\left(\frac{213}{722}\right)\)	\(e\left(\frac{68}{361}\right)\)	\(e\left(\frac{1147}{1444}\right)\)	\(e\left(\frac{161}{722}\right)\)
\(\chi_{109744}(3533,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1115}{1444}\right)\)	\(e\left(\frac{1231}{1444}\right)\)	\(e\left(\frac{267}{722}\right)\)	\(e\left(\frac{393}{722}\right)\)	\(e\left(\frac{1323}{1444}\right)\)	\(e\left(\frac{127}{1444}\right)\)	\(e\left(\frac{451}{722}\right)\)	\(e\left(\frac{105}{361}\right)\)	\(e\left(\frac{205}{1444}\right)\)	\(e\left(\frac{307}{722}\right)\)
\(\chi_{109744}(3685,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{633}{1444}\right)\)	\(e\left(\frac{897}{1444}\right)\)	\(e\left(\frac{645}{722}\right)\)	\(e\left(\frac{633}{722}\right)\)	\(e\left(\frac{957}{1444}\right)\)	\(e\left(\frac{177}{1444}\right)\)	\(e\left(\frac{43}{722}\right)\)	\(e\left(\frac{351}{361}\right)\)	\(e\left(\frac{479}{1444}\right)\)	\(e\left(\frac{263}{722}\right)\)
\(\chi_{109744}(3837,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{531}{1444}\right)\)	\(e\left(\frac{335}{1444}\right)\)	\(e\left(\frac{719}{722}\right)\)	\(e\left(\frac{531}{722}\right)\)	\(e\left(\frac{1275}{1444}\right)\)	\(e\left(\frac{607}{1444}\right)\)	\(e\left(\frac{433}{722}\right)\)	\(e\left(\frac{84}{361}\right)\)	\(e\left(\frac{525}{1444}\right)\)	\(e\left(\frac{29}{722}\right)\)
\(\chi_{109744}(3989,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{809}{1444}\right)\)	\(e\left(\frac{989}{1444}\right)\)	\(e\left(\frac{489}{722}\right)\)	\(e\left(\frac{87}{722}\right)\)	\(e\left(\frac{833}{1444}\right)\)	\(e\left(\frac{1417}{1444}\right)\)	\(e\left(\frac{177}{722}\right)\)	\(e\left(\frac{26}{361}\right)\)	\(e\left(\frac{343}{1444}\right)\)	\(e\left(\frac{327}{722}\right)\)
\(\chi_{109744}(4141,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{1444}\right)\)	\(e\left(\frac{1415}{1444}\right)\)	\(e\left(\frac{677}{722}\right)\)	\(e\left(\frac{23}{722}\right)\)	\(e\left(\frac{1075}{1444}\right)\)	\(e\left(\frac{1163}{1444}\right)\)	\(e\left(\frac{719}{722}\right)\)	\(e\left(\frac{177}{361}\right)\)	\(e\left(\frac{1377}{1444}\right)\)	\(e\left(\frac{435}{722}\right)\)
\(\chi_{109744}(4293,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1061}{1444}\right)\)	\(e\left(\frac{169}{1444}\right)\)	\(e\left(\frac{561}{722}\right)\)	\(e\left(\frac{339}{722}\right)\)	\(e\left(\frac{557}{1444}\right)\)	\(e\left(\frac{1289}{1444}\right)\)	\(e\left(\frac{615}{722}\right)\)	\(e\left(\frac{176}{361}\right)\)	\(e\left(\frac{739}{1444}\right)\)	\(e\left(\frac{353}{722}\right)\)
\(\chi_{109744}(4445,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1035}{1444}\right)\)	\(e\left(\frac{139}{1444}\right)\)	\(e\left(\frac{141}{722}\right)\)	\(e\left(\frac{313}{722}\right)\)	\(e\left(\frac{723}{1444}\right)\)	\(e\left(\frac{351}{1444}\right)\)	\(e\left(\frac{587}{722}\right)\)	\(e\left(\frac{23}{361}\right)\)	\(e\left(\frac{1317}{1444}\right)\)	\(e\left(\frac{81}{722}\right)\)
\(\chi_{109744}(4597,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1389}{1444}\right)\)	\(e\left(\frac{1325}{1444}\right)\)	\(e\left(\frac{139}{722}\right)\)	\(e\left(\frac{667}{722}\right)\)	\(e\left(\frac{129}{1444}\right)\)	\(e\left(\frac{1237}{1444}\right)\)	\(e\left(\frac{635}{722}\right)\)	\(e\left(\frac{79}{361}\right)\)	\(e\left(\frac{223}{1444}\right)\)	\(e\left(\frac{341}{722}\right)\)
\(\chi_{109744}(4749,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{679}{1444}\right)\)	\(e\left(\frac{839}{1444}\right)\)	\(e\left(\frac{555}{722}\right)\)	\(e\left(\frac{679}{722}\right)\)	\(e\left(\frac{219}{1444}\right)\)	\(e\left(\frac{1059}{1444}\right)\)	\(e\left(\frac{37}{722}\right)\)	\(e\left(\frac{344}{361}\right)\)	\(e\left(\frac{345}{1444}\right)\)	\(e\left(\frac{411}{722}\right)\)

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First 31 of 684 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	109744.df
Modulus	$109744$
Conductor	$109744$
Order	$1444$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(109744\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(109744\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(1444\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);