LMFDB - Dirichlet character orbit 39326.bo

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(39326, base_ring=CyclotomicField(4134)) M = H._module chi = DirichletCharacter(H, M([2756,2910])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(81, 39326)) 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("39326.81"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$39326$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$19663$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$2067$	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:	no, induced from 19663.bo	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{2067})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 2067 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 1248 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{39326}(81,\cdot)$	$1$	$1$	$e\left(\frac{139}{2067}\right)$	$e\left(\frac{1097}{2067}\right)$	$e\left(\frac{278}{2067}\right)$	$e\left(\frac{1294}{2067}\right)$	$e\left(\frac{473}{689}\right)$	$e\left(\frac{412}{689}\right)$	$e\left(\frac{1069}{2067}\right)$	$e\left(\frac{1172}{2067}\right)$	$e\left(\frac{128}{159}\right)$	$e\left(\frac{127}{2067}\right)$
$\chi_{39326}(95,\cdot)$	$1$	$1$	$e\left(\frac{1084}{2067}\right)$	$e\left(\frac{2012}{2067}\right)$	$e\left(\frac{101}{2067}\right)$	$e\left(\frac{1288}{2067}\right)$	$e\left(\frac{556}{689}\right)$	$e\left(\frac{343}{689}\right)$	$e\left(\frac{604}{2067}\right)$	$e\left(\frac{173}{2067}\right)$	$e\left(\frac{122}{159}\right)$	$e\left(\frac{1957}{2067}\right)$
$\chi_{39326}(121,\cdot)$	$1$	$1$	$e\left(\frac{647}{2067}\right)$	$e\left(\frac{1567}{2067}\right)$	$e\left(\frac{1294}{2067}\right)$	$e\left(\frac{1562}{2067}\right)$	$e\left(\frac{670}{689}\right)$	$e\left(\frac{49}{689}\right)$	$e\left(\frac{1169}{2067}\right)$	$e\left(\frac{1009}{2067}\right)$	$e\left(\frac{25}{159}\right)$	$e\left(\frac{1067}{2067}\right)$
$\chi_{39326}(205,\cdot)$	$1$	$1$	$e\left(\frac{653}{2067}\right)$	$e\left(\frac{1540}{2067}\right)$	$e\left(\frac{1306}{2067}\right)$	$e\left(\frac{1142}{2067}\right)$	$e\left(\frac{279}{689}\right)$	$e\left(\frac{42}{689}\right)$	$e\left(\frac{1691}{2067}\right)$	$e\left(\frac{1357}{2067}\right)$	$e\left(\frac{82}{159}\right)$	$e\left(\frac{1013}{2067}\right)$
$\chi_{39326}(261,\cdot)$	$1$	$1$	$e\left(\frac{1865}{2067}\right)$	$e\left(\frac{220}{2067}\right)$	$e\left(\frac{1663}{2067}\right)$	$e\left(\frac{1049}{2067}\right)$	$e\left(\frac{532}{689}\right)$	$e\left(\frac{6}{689}\right)$	$e\left(\frac{1718}{2067}\right)$	$e\left(\frac{1375}{2067}\right)$	$e\left(\frac{148}{159}\right)$	$e\left(\frac{440}{2067}\right)$
$\chi_{39326}(275,\cdot)$	$1$	$1$	$e\left(\frac{872}{2067}\right)$	$e\left(\frac{1588}{2067}\right)$	$e\left(\frac{1744}{2067}\right)$	$e\left(\frac{281}{2067}\right)$	$e\left(\frac{132}{689}\right)$	$e\left(\frac{131}{689}\right)$	$e\left(\frac{74}{2067}\right)$	$e\left(\frac{1657}{2067}\right)$	$e\left(\frac{16}{159}\right)$	$e\left(\frac{1109}{2067}\right)$
$\chi_{39326}(289,\cdot)$	$1$	$1$	$e\left(\frac{1568}{2067}\right)$	$e\left(\frac{523}{2067}\right)$	$e\left(\frac{1069}{2067}\right)$	$e\left(\frac{1169}{2067}\right)$	$e\left(\frac{250}{689}\right)$	$e\left(\frac{8}{689}\right)$	$e\left(\frac{683}{2067}\right)$	$e\left(\frac{685}{2067}\right)$	$e\left(\frac{109}{159}\right)$	$e\left(\frac{1046}{2067}\right)$
$\chi_{39326}(331,\cdot)$	$1$	$1$	$e\left(\frac{1697}{2067}\right)$	$e\left(\frac{976}{2067}\right)$	$e\left(\frac{1327}{2067}\right)$	$e\left(\frac{407}{2067}\right)$	$e\left(\frac{456}{689}\right)$	$e\left(\frac{202}{689}\right)$	$e\left(\frac{1571}{2067}\right)$	$e\left(\frac{1966}{2067}\right)$	$e\left(\frac{142}{159}\right)$	$e\left(\frac{1952}{2067}\right)$
$\chi_{39326}(333,\cdot)$	$1$	$1$	$e\left(\frac{634}{2067}\right)$	$e\left(\frac{1970}{2067}\right)$	$e\left(\frac{1268}{2067}\right)$	$e\left(\frac{1783}{2067}\right)$	$e\left(\frac{254}{689}\right)$	$e\left(\frac{179}{689}\right)$	$e\left(\frac{727}{2067}\right)$	$e\left(\frac{944}{2067}\right)$	$e\left(\frac{140}{159}\right)$	$e\left(\frac{1873}{2067}\right)$
$\chi_{39326}(387,\cdot)$	$1$	$1$	$e\left(\frac{1832}{2067}\right)$	$e\left(\frac{1402}{2067}\right)$	$e\left(\frac{1597}{2067}\right)$	$e\left(\frac{1292}{2067}\right)$	$e\left(\frac{271}{689}\right)$	$e\left(\frac{389}{689}\right)$	$e\left(\frac{914}{2067}\right)$	$e\left(\frac{1528}{2067}\right)$	$e\left(\frac{73}{159}\right)$	$e\left(\frac{737}{2067}\right)$
$\chi_{39326}(415,\cdot)$	$1$	$1$	$e\left(\frac{1376}{2067}\right)$	$e\left(\frac{1387}{2067}\right)$	$e\left(\frac{685}{2067}\right)$	$e\left(\frac{140}{2067}\right)$	$e\left(\frac{360}{689}\right)$	$e\left(\frac{232}{689}\right)$	$e\left(\frac{515}{2067}\right)$	$e\left(\frac{1951}{2067}\right)$	$e\left(\frac{34}{159}\right)$	$e\left(\frac{707}{2067}\right)$
$\chi_{39326}(417,\cdot)$	$1$	$1$	$e\left(\frac{484}{2067}\right)$	$e\left(\frac{578}{2067}\right)$	$e\left(\frac{968}{2067}\right)$	$e\left(\frac{1948}{2067}\right)$	$e\left(\frac{383}{689}\right)$	$e\left(\frac{354}{689}\right)$	$e\left(\frac{79}{2067}\right)$	$e\left(\frac{512}{2067}\right)$	$e\left(\frac{146}{159}\right)$	$e\left(\frac{1156}{2067}\right)$
$\chi_{39326}(471,\cdot)$	$1$	$1$	$e\left(\frac{41}{2067}\right)$	$e\left(\frac{160}{2067}\right)$	$e\left(\frac{82}{2067}\right)$	$e\left(\frac{575}{2067}\right)$	$e\left(\frac{199}{689}\right)$	$e\left(\frac{67}{689}\right)$	$e\left(\frac{122}{2067}\right)$	$e\left(\frac{1000}{2067}\right)$	$e\left(\frac{151}{159}\right)$	$e\left(\frac{320}{2067}\right)$
$\chi_{39326}(473,\cdot)$	$1$	$1$	$e\left(\frac{19}{2067}\right)$	$e\left(\frac{1637}{2067}\right)$	$e\left(\frac{38}{2067}\right)$	$e\left(\frac{1426}{2067}\right)$	$e\left(\frac{25}{689}\right)$	$e\left(\frac{552}{689}\right)$	$e\left(\frac{964}{2067}\right)$	$e\left(\frac{413}{2067}\right)$	$e\left(\frac{101}{159}\right)$	$e\left(\frac{1207}{2067}\right)$
$\chi_{39326}(487,\cdot)$	$1$	$1$	$e\left(\frac{508}{2067}\right)$	$e\left(\frac{470}{2067}\right)$	$e\left(\frac{1016}{2067}\right)$	$e\left(\frac{268}{2067}\right)$	$e\left(\frac{197}{689}\right)$	$e\left(\frac{326}{689}\right)$	$e\left(\frac{100}{2067}\right)$	$e\left(\frac{1904}{2067}\right)$	$e\left(\frac{56}{159}\right)$	$e\left(\frac{940}{2067}\right)$
$\chi_{39326}(501,\cdot)$	$1$	$1$	$e\left(\frac{268}{2067}\right)$	$e\left(\frac{1550}{2067}\right)$	$e\left(\frac{536}{2067}\right)$	$e\left(\frac{532}{2067}\right)$	$e\left(\frac{679}{689}\right)$	$e\left(\frac{606}{689}\right)$	$e\left(\frac{1957}{2067}\right)$	$e\left(\frac{386}{2067}\right)$	$e\left(\frac{2}{159}\right)$	$e\left(\frac{1033}{2067}\right)$
$\chi_{39326}(513,\cdot)$	$1$	$1$	$e\left(\frac{914}{2067}\right)$	$e\left(\frac{1399}{2067}\right)$	$e\left(\frac{1828}{2067}\right)$	$e\left(\frac{1475}{2067}\right)$	$e\left(\frac{151}{689}\right)$	$e\left(\frac{82}{689}\right)$	$e\left(\frac{1661}{2067}\right)$	$e\left(\frac{2026}{2067}\right)$	$e\left(\frac{97}{159}\right)$	$e\left(\frac{731}{2067}\right)$
$\chi_{39326}(543,\cdot)$	$1$	$1$	$e\left(\frac{1099}{2067}\right)$	$e\left(\frac{911}{2067}\right)$	$e\left(\frac{131}{2067}\right)$	$e\left(\frac{238}{2067}\right)$	$e\left(\frac{612}{689}\right)$	$e\left(\frac{670}{689}\right)$	$e\left(\frac{1909}{2067}\right)$	$e\left(\frac{1043}{2067}\right)$	$e\left(\frac{26}{159}\right)$	$e\left(\frac{1822}{2067}\right)$
$\chi_{39326}(599,\cdot)$	$1$	$1$	$e\left(\frac{571}{2067}\right)$	$e\left(\frac{1220}{2067}\right)$	$e\left(\frac{1142}{2067}\right)$	$e\left(\frac{2059}{2067}\right)$	$e\left(\frac{570}{689}\right)$	$e\left(\frac{597}{689}\right)$	$e\left(\frac{1447}{2067}\right)$	$e\left(\frac{1424}{2067}\right)$	$e\left(\frac{98}{159}\right)$	$e\left(\frac{373}{2067}\right)$
$\chi_{39326}(611,\cdot)$	$1$	$1$	$e\left(\frac{503}{2067}\right)$	$e\left(\frac{148}{2067}\right)$	$e\left(\frac{1006}{2067}\right)$	$e\left(\frac{1307}{2067}\right)$	$e\left(\frac{408}{689}\right)$	$e\left(\frac{217}{689}\right)$	$e\left(\frac{1043}{2067}\right)$	$e\left(\frac{925}{2067}\right)$	$e\left(\frac{88}{159}\right)$	$e\left(\frac{296}{2067}\right)$
$\chi_{39326}(625,\cdot)$	$1$	$1$	$e\left(\frac{1097}{2067}\right)$	$e\left(\frac{1609}{2067}\right)$	$e\left(\frac{127}{2067}\right)$	$e\left(\frac{1067}{2067}\right)$	$e\left(\frac{283}{689}\right)$	$e\left(\frac{213}{689}\right)$	$e\left(\frac{1046}{2067}\right)$	$e\left(\frac{238}{2067}\right)$	$e\left(\frac{7}{159}\right)$	$e\left(\frac{1151}{2067}\right)$
$\chi_{39326}(627,\cdot)$	$1$	$1$	$e\left(\frac{1168}{2067}\right)$	$e\left(\frac{1634}{2067}\right)$	$e\left(\frac{269}{2067}\right)$	$e\left(\frac{1609}{2067}\right)$	$e\left(\frac{594}{689}\right)$	$e\left(\frac{245}{689}\right)$	$e\left(\frac{1711}{2067}\right)$	$e\left(\frac{911}{2067}\right)$	$e\left(\frac{125}{159}\right)$	$e\left(\frac{1201}{2067}\right)$
$\chi_{39326}(683,\cdot)$	$1$	$1$	$e\left(\frac{418}{2067}\right)$	$e\left(\frac{875}{2067}\right)$	$e\left(\frac{836}{2067}\right)$	$e\left(\frac{367}{2067}\right)$	$e\left(\frac{550}{689}\right)$	$e\left(\frac{431}{689}\right)$	$e\left(\frac{538}{2067}\right)$	$e\left(\frac{818}{2067}\right)$	$e\left(\frac{155}{159}\right)$	$e\left(\frac{1750}{2067}\right)$
$\chi_{39326}(725,\cdot)$	$1$	$1$	$e\left(\frac{277}{2067}\right)$	$e\left(\frac{476}{2067}\right)$	$e\left(\frac{554}{2067}\right)$	$e\left(\frac{1969}{2067}\right)$	$e\left(\frac{437}{689}\right)$	$e\left(\frac{251}{689}\right)$	$e\left(\frac{673}{2067}\right)$	$e\left(\frac{908}{2067}\right)$	$e\left(\frac{8}{159}\right)$	$e\left(\frac{952}{2067}\right)$
$\chi_{39326}(823,\cdot)$	$1$	$1$	$e\left(\frac{373}{2067}\right)$	$e\left(\frac{44}{2067}\right)$	$e\left(\frac{746}{2067}\right)$	$e\left(\frac{1450}{2067}\right)$	$e\left(\frac{382}{689}\right)$	$e\left(\frac{139}{689}\right)$	$e\left(\frac{757}{2067}\right)$	$e\left(\frac{275}{2067}\right)$	$e\left(\frac{125}{159}\right)$	$e\left(\frac{88}{2067}\right)$
$\chi_{39326}(837,\cdot)$	$1$	$1$	$e\left(\frac{1240}{2067}\right)$	$e\left(\frac{1310}{2067}\right)$	$e\left(\frac{413}{2067}\right)$	$e\left(\frac{703}{2067}\right)$	$e\left(\frac{36}{689}\right)$	$e\left(\frac{161}{689}\right)$	$e\left(\frac{1774}{2067}\right)$	$e\left(\frac{953}{2067}\right)$	$e\left(\frac{14}{159}\right)$	$e\left(\frac{553}{2067}\right)$
$\chi_{39326}(863,\cdot)$	$1$	$1$	$e\left(\frac{257}{2067}\right)$	$e\left(\frac{1255}{2067}\right)$	$e\left(\frac{514}{2067}\right)$	$e\left(\frac{1991}{2067}\right)$	$e\left(\frac{592}{689}\right)$	$e\left(\frac{504}{689}\right)$	$e\left(\frac{311}{2067}\right)$	$e\left(\frac{1126}{2067}\right)$	$e\left(\frac{136}{159}\right)$	$e\left(\frac{443}{2067}\right)$
$\chi_{39326}(947,\cdot)$	$1$	$1$	$e\left(\frac{1784}{2067}\right)$	$e\left(\frac{1618}{2067}\right)$	$e\left(\frac{1501}{2067}\right)$	$e\left(\frac{518}{2067}\right)$	$e\left(\frac{643}{689}\right)$	$e\left(\frac{445}{689}\right)$	$e\left(\frac{872}{2067}\right)$	$e\left(\frac{811}{2067}\right)$	$e\left(\frac{94}{159}\right)$	$e\left(\frac{1169}{2067}\right)$
$\chi_{39326}(1003,\cdot)$	$1$	$1$	$e\left(\frac{227}{2067}\right)$	$e\left(\frac{1390}{2067}\right)$	$e\left(\frac{454}{2067}\right)$	$e\left(\frac{2024}{2067}\right)$	$e\left(\frac{480}{689}\right)$	$e\left(\frac{539}{689}\right)$	$e\left(\frac{1835}{2067}\right)$	$e\left(\frac{1453}{2067}\right)$	$e\left(\frac{10}{159}\right)$	$e\left(\frac{713}{2067}\right)$
$\chi_{39326}(1017,\cdot)$	$1$	$1$	$e\left(\frac{287}{2067}\right)$	$e\left(\frac{1120}{2067}\right)$	$e\left(\frac{574}{2067}\right)$	$e\left(\frac{1958}{2067}\right)$	$e\left(\frac{15}{689}\right)$	$e\left(\frac{469}{689}\right)$	$e\left(\frac{854}{2067}\right)$	$e\left(\frac{799}{2067}\right)$	$e\left(\frac{103}{159}\right)$	$e\left(\frac{173}{2067}\right)$
$\chi_{39326}(1031,\cdot)$	$1$	$1$	$e\left(\frac{1841}{2067}\right)$	$e\left(\frac{328}{2067}\right)$	$e\left(\frac{1615}{2067}\right)$	$e\left(\frac{662}{2067}\right)$	$e\left(\frac{29}{689}\right)$	$e\left(\frac{34}{689}\right)$	$e\left(\frac{1697}{2067}\right)$	$e\left(\frac{2050}{2067}\right)$	$e\left(\frac{79}{159}\right)$	$e\left(\frac{656}{2067}\right)$

Overview	Random
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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	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{39326}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{2067}\right)\)	\(e\left(\frac{1097}{2067}\right)\)	\(e\left(\frac{278}{2067}\right)\)	\(e\left(\frac{1294}{2067}\right)\)	\(e\left(\frac{473}{689}\right)\)	\(e\left(\frac{412}{689}\right)\)	\(e\left(\frac{1069}{2067}\right)\)	\(e\left(\frac{1172}{2067}\right)\)	\(e\left(\frac{128}{159}\right)\)	\(e\left(\frac{127}{2067}\right)\)
\(\chi_{39326}(95,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1084}{2067}\right)\)	\(e\left(\frac{2012}{2067}\right)\)	\(e\left(\frac{101}{2067}\right)\)	\(e\left(\frac{1288}{2067}\right)\)	\(e\left(\frac{556}{689}\right)\)	\(e\left(\frac{343}{689}\right)\)	\(e\left(\frac{604}{2067}\right)\)	\(e\left(\frac{173}{2067}\right)\)	\(e\left(\frac{122}{159}\right)\)	\(e\left(\frac{1957}{2067}\right)\)
\(\chi_{39326}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{647}{2067}\right)\)	\(e\left(\frac{1567}{2067}\right)\)	\(e\left(\frac{1294}{2067}\right)\)	\(e\left(\frac{1562}{2067}\right)\)	\(e\left(\frac{670}{689}\right)\)	\(e\left(\frac{49}{689}\right)\)	\(e\left(\frac{1169}{2067}\right)\)	\(e\left(\frac{1009}{2067}\right)\)	\(e\left(\frac{25}{159}\right)\)	\(e\left(\frac{1067}{2067}\right)\)
\(\chi_{39326}(205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{653}{2067}\right)\)	\(e\left(\frac{1540}{2067}\right)\)	\(e\left(\frac{1306}{2067}\right)\)	\(e\left(\frac{1142}{2067}\right)\)	\(e\left(\frac{279}{689}\right)\)	\(e\left(\frac{42}{689}\right)\)	\(e\left(\frac{1691}{2067}\right)\)	\(e\left(\frac{1357}{2067}\right)\)	\(e\left(\frac{82}{159}\right)\)	\(e\left(\frac{1013}{2067}\right)\)
\(\chi_{39326}(261,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1865}{2067}\right)\)	\(e\left(\frac{220}{2067}\right)\)	\(e\left(\frac{1663}{2067}\right)\)	\(e\left(\frac{1049}{2067}\right)\)	\(e\left(\frac{532}{689}\right)\)	\(e\left(\frac{6}{689}\right)\)	\(e\left(\frac{1718}{2067}\right)\)	\(e\left(\frac{1375}{2067}\right)\)	\(e\left(\frac{148}{159}\right)\)	\(e\left(\frac{440}{2067}\right)\)
\(\chi_{39326}(275,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{872}{2067}\right)\)	\(e\left(\frac{1588}{2067}\right)\)	\(e\left(\frac{1744}{2067}\right)\)	\(e\left(\frac{281}{2067}\right)\)	\(e\left(\frac{132}{689}\right)\)	\(e\left(\frac{131}{689}\right)\)	\(e\left(\frac{74}{2067}\right)\)	\(e\left(\frac{1657}{2067}\right)\)	\(e\left(\frac{16}{159}\right)\)	\(e\left(\frac{1109}{2067}\right)\)
\(\chi_{39326}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1568}{2067}\right)\)	\(e\left(\frac{523}{2067}\right)\)	\(e\left(\frac{1069}{2067}\right)\)	\(e\left(\frac{1169}{2067}\right)\)	\(e\left(\frac{250}{689}\right)\)	\(e\left(\frac{8}{689}\right)\)	\(e\left(\frac{683}{2067}\right)\)	\(e\left(\frac{685}{2067}\right)\)	\(e\left(\frac{109}{159}\right)\)	\(e\left(\frac{1046}{2067}\right)\)
\(\chi_{39326}(331,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1697}{2067}\right)\)	\(e\left(\frac{976}{2067}\right)\)	\(e\left(\frac{1327}{2067}\right)\)	\(e\left(\frac{407}{2067}\right)\)	\(e\left(\frac{456}{689}\right)\)	\(e\left(\frac{202}{689}\right)\)	\(e\left(\frac{1571}{2067}\right)\)	\(e\left(\frac{1966}{2067}\right)\)	\(e\left(\frac{142}{159}\right)\)	\(e\left(\frac{1952}{2067}\right)\)
\(\chi_{39326}(333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{634}{2067}\right)\)	\(e\left(\frac{1970}{2067}\right)\)	\(e\left(\frac{1268}{2067}\right)\)	\(e\left(\frac{1783}{2067}\right)\)	\(e\left(\frac{254}{689}\right)\)	\(e\left(\frac{179}{689}\right)\)	\(e\left(\frac{727}{2067}\right)\)	\(e\left(\frac{944}{2067}\right)\)	\(e\left(\frac{140}{159}\right)\)	\(e\left(\frac{1873}{2067}\right)\)
\(\chi_{39326}(387,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1832}{2067}\right)\)	\(e\left(\frac{1402}{2067}\right)\)	\(e\left(\frac{1597}{2067}\right)\)	\(e\left(\frac{1292}{2067}\right)\)	\(e\left(\frac{271}{689}\right)\)	\(e\left(\frac{389}{689}\right)\)	\(e\left(\frac{914}{2067}\right)\)	\(e\left(\frac{1528}{2067}\right)\)	\(e\left(\frac{73}{159}\right)\)	\(e\left(\frac{737}{2067}\right)\)
\(\chi_{39326}(415,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1376}{2067}\right)\)	\(e\left(\frac{1387}{2067}\right)\)	\(e\left(\frac{685}{2067}\right)\)	\(e\left(\frac{140}{2067}\right)\)	\(e\left(\frac{360}{689}\right)\)	\(e\left(\frac{232}{689}\right)\)	\(e\left(\frac{515}{2067}\right)\)	\(e\left(\frac{1951}{2067}\right)\)	\(e\left(\frac{34}{159}\right)\)	\(e\left(\frac{707}{2067}\right)\)
\(\chi_{39326}(417,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{484}{2067}\right)\)	\(e\left(\frac{578}{2067}\right)\)	\(e\left(\frac{968}{2067}\right)\)	\(e\left(\frac{1948}{2067}\right)\)	\(e\left(\frac{383}{689}\right)\)	\(e\left(\frac{354}{689}\right)\)	\(e\left(\frac{79}{2067}\right)\)	\(e\left(\frac{512}{2067}\right)\)	\(e\left(\frac{146}{159}\right)\)	\(e\left(\frac{1156}{2067}\right)\)
\(\chi_{39326}(471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{2067}\right)\)	\(e\left(\frac{160}{2067}\right)\)	\(e\left(\frac{82}{2067}\right)\)	\(e\left(\frac{575}{2067}\right)\)	\(e\left(\frac{199}{689}\right)\)	\(e\left(\frac{67}{689}\right)\)	\(e\left(\frac{122}{2067}\right)\)	\(e\left(\frac{1000}{2067}\right)\)	\(e\left(\frac{151}{159}\right)\)	\(e\left(\frac{320}{2067}\right)\)
\(\chi_{39326}(473,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{2067}\right)\)	\(e\left(\frac{1637}{2067}\right)\)	\(e\left(\frac{38}{2067}\right)\)	\(e\left(\frac{1426}{2067}\right)\)	\(e\left(\frac{25}{689}\right)\)	\(e\left(\frac{552}{689}\right)\)	\(e\left(\frac{964}{2067}\right)\)	\(e\left(\frac{413}{2067}\right)\)	\(e\left(\frac{101}{159}\right)\)	\(e\left(\frac{1207}{2067}\right)\)
\(\chi_{39326}(487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{508}{2067}\right)\)	\(e\left(\frac{470}{2067}\right)\)	\(e\left(\frac{1016}{2067}\right)\)	\(e\left(\frac{268}{2067}\right)\)	\(e\left(\frac{197}{689}\right)\)	\(e\left(\frac{326}{689}\right)\)	\(e\left(\frac{100}{2067}\right)\)	\(e\left(\frac{1904}{2067}\right)\)	\(e\left(\frac{56}{159}\right)\)	\(e\left(\frac{940}{2067}\right)\)
\(\chi_{39326}(501,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{268}{2067}\right)\)	\(e\left(\frac{1550}{2067}\right)\)	\(e\left(\frac{536}{2067}\right)\)	\(e\left(\frac{532}{2067}\right)\)	\(e\left(\frac{679}{689}\right)\)	\(e\left(\frac{606}{689}\right)\)	\(e\left(\frac{1957}{2067}\right)\)	\(e\left(\frac{386}{2067}\right)\)	\(e\left(\frac{2}{159}\right)\)	\(e\left(\frac{1033}{2067}\right)\)
\(\chi_{39326}(513,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{914}{2067}\right)\)	\(e\left(\frac{1399}{2067}\right)\)	\(e\left(\frac{1828}{2067}\right)\)	\(e\left(\frac{1475}{2067}\right)\)	\(e\left(\frac{151}{689}\right)\)	\(e\left(\frac{82}{689}\right)\)	\(e\left(\frac{1661}{2067}\right)\)	\(e\left(\frac{2026}{2067}\right)\)	\(e\left(\frac{97}{159}\right)\)	\(e\left(\frac{731}{2067}\right)\)
\(\chi_{39326}(543,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1099}{2067}\right)\)	\(e\left(\frac{911}{2067}\right)\)	\(e\left(\frac{131}{2067}\right)\)	\(e\left(\frac{238}{2067}\right)\)	\(e\left(\frac{612}{689}\right)\)	\(e\left(\frac{670}{689}\right)\)	\(e\left(\frac{1909}{2067}\right)\)	\(e\left(\frac{1043}{2067}\right)\)	\(e\left(\frac{26}{159}\right)\)	\(e\left(\frac{1822}{2067}\right)\)
\(\chi_{39326}(599,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{571}{2067}\right)\)	\(e\left(\frac{1220}{2067}\right)\)	\(e\left(\frac{1142}{2067}\right)\)	\(e\left(\frac{2059}{2067}\right)\)	\(e\left(\frac{570}{689}\right)\)	\(e\left(\frac{597}{689}\right)\)	\(e\left(\frac{1447}{2067}\right)\)	\(e\left(\frac{1424}{2067}\right)\)	\(e\left(\frac{98}{159}\right)\)	\(e\left(\frac{373}{2067}\right)\)
\(\chi_{39326}(611,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{503}{2067}\right)\)	\(e\left(\frac{148}{2067}\right)\)	\(e\left(\frac{1006}{2067}\right)\)	\(e\left(\frac{1307}{2067}\right)\)	\(e\left(\frac{408}{689}\right)\)	\(e\left(\frac{217}{689}\right)\)	\(e\left(\frac{1043}{2067}\right)\)	\(e\left(\frac{925}{2067}\right)\)	\(e\left(\frac{88}{159}\right)\)	\(e\left(\frac{296}{2067}\right)\)
\(\chi_{39326}(625,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1097}{2067}\right)\)	\(e\left(\frac{1609}{2067}\right)\)	\(e\left(\frac{127}{2067}\right)\)	\(e\left(\frac{1067}{2067}\right)\)	\(e\left(\frac{283}{689}\right)\)	\(e\left(\frac{213}{689}\right)\)	\(e\left(\frac{1046}{2067}\right)\)	\(e\left(\frac{238}{2067}\right)\)	\(e\left(\frac{7}{159}\right)\)	\(e\left(\frac{1151}{2067}\right)\)
\(\chi_{39326}(627,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1168}{2067}\right)\)	\(e\left(\frac{1634}{2067}\right)\)	\(e\left(\frac{269}{2067}\right)\)	\(e\left(\frac{1609}{2067}\right)\)	\(e\left(\frac{594}{689}\right)\)	\(e\left(\frac{245}{689}\right)\)	\(e\left(\frac{1711}{2067}\right)\)	\(e\left(\frac{911}{2067}\right)\)	\(e\left(\frac{125}{159}\right)\)	\(e\left(\frac{1201}{2067}\right)\)
\(\chi_{39326}(683,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{418}{2067}\right)\)	\(e\left(\frac{875}{2067}\right)\)	\(e\left(\frac{836}{2067}\right)\)	\(e\left(\frac{367}{2067}\right)\)	\(e\left(\frac{550}{689}\right)\)	\(e\left(\frac{431}{689}\right)\)	\(e\left(\frac{538}{2067}\right)\)	\(e\left(\frac{818}{2067}\right)\)	\(e\left(\frac{155}{159}\right)\)	\(e\left(\frac{1750}{2067}\right)\)
\(\chi_{39326}(725,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{277}{2067}\right)\)	\(e\left(\frac{476}{2067}\right)\)	\(e\left(\frac{554}{2067}\right)\)	\(e\left(\frac{1969}{2067}\right)\)	\(e\left(\frac{437}{689}\right)\)	\(e\left(\frac{251}{689}\right)\)	\(e\left(\frac{673}{2067}\right)\)	\(e\left(\frac{908}{2067}\right)\)	\(e\left(\frac{8}{159}\right)\)	\(e\left(\frac{952}{2067}\right)\)
\(\chi_{39326}(823,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{373}{2067}\right)\)	\(e\left(\frac{44}{2067}\right)\)	\(e\left(\frac{746}{2067}\right)\)	\(e\left(\frac{1450}{2067}\right)\)	\(e\left(\frac{382}{689}\right)\)	\(e\left(\frac{139}{689}\right)\)	\(e\left(\frac{757}{2067}\right)\)	\(e\left(\frac{275}{2067}\right)\)	\(e\left(\frac{125}{159}\right)\)	\(e\left(\frac{88}{2067}\right)\)
\(\chi_{39326}(837,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1240}{2067}\right)\)	\(e\left(\frac{1310}{2067}\right)\)	\(e\left(\frac{413}{2067}\right)\)	\(e\left(\frac{703}{2067}\right)\)	\(e\left(\frac{36}{689}\right)\)	\(e\left(\frac{161}{689}\right)\)	\(e\left(\frac{1774}{2067}\right)\)	\(e\left(\frac{953}{2067}\right)\)	\(e\left(\frac{14}{159}\right)\)	\(e\left(\frac{553}{2067}\right)\)
\(\chi_{39326}(863,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{257}{2067}\right)\)	\(e\left(\frac{1255}{2067}\right)\)	\(e\left(\frac{514}{2067}\right)\)	\(e\left(\frac{1991}{2067}\right)\)	\(e\left(\frac{592}{689}\right)\)	\(e\left(\frac{504}{689}\right)\)	\(e\left(\frac{311}{2067}\right)\)	\(e\left(\frac{1126}{2067}\right)\)	\(e\left(\frac{136}{159}\right)\)	\(e\left(\frac{443}{2067}\right)\)
\(\chi_{39326}(947,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1784}{2067}\right)\)	\(e\left(\frac{1618}{2067}\right)\)	\(e\left(\frac{1501}{2067}\right)\)	\(e\left(\frac{518}{2067}\right)\)	\(e\left(\frac{643}{689}\right)\)	\(e\left(\frac{445}{689}\right)\)	\(e\left(\frac{872}{2067}\right)\)	\(e\left(\frac{811}{2067}\right)\)	\(e\left(\frac{94}{159}\right)\)	\(e\left(\frac{1169}{2067}\right)\)
\(\chi_{39326}(1003,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{2067}\right)\)	\(e\left(\frac{1390}{2067}\right)\)	\(e\left(\frac{454}{2067}\right)\)	\(e\left(\frac{2024}{2067}\right)\)	\(e\left(\frac{480}{689}\right)\)	\(e\left(\frac{539}{689}\right)\)	\(e\left(\frac{1835}{2067}\right)\)	\(e\left(\frac{1453}{2067}\right)\)	\(e\left(\frac{10}{159}\right)\)	\(e\left(\frac{713}{2067}\right)\)
\(\chi_{39326}(1017,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{287}{2067}\right)\)	\(e\left(\frac{1120}{2067}\right)\)	\(e\left(\frac{574}{2067}\right)\)	\(e\left(\frac{1958}{2067}\right)\)	\(e\left(\frac{15}{689}\right)\)	\(e\left(\frac{469}{689}\right)\)	\(e\left(\frac{854}{2067}\right)\)	\(e\left(\frac{799}{2067}\right)\)	\(e\left(\frac{103}{159}\right)\)	\(e\left(\frac{173}{2067}\right)\)
\(\chi_{39326}(1031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1841}{2067}\right)\)	\(e\left(\frac{328}{2067}\right)\)	\(e\left(\frac{1615}{2067}\right)\)	\(e\left(\frac{662}{2067}\right)\)	\(e\left(\frac{29}{689}\right)\)	\(e\left(\frac{34}{689}\right)\)	\(e\left(\frac{1697}{2067}\right)\)	\(e\left(\frac{2050}{2067}\right)\)	\(e\left(\frac{79}{159}\right)\)	\(e\left(\frac{656}{2067}\right)\)

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First 31 of 1248 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	39326.bo
Modulus	$39326$
Conductor	$19663$
Order	$2067$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(39326\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(19663\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(2067\)	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:	no, induced from 19663.bo	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);