LMFDB - Dirichlet character orbit 7742.cn

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7742, base_ring=CyclotomicField(546)) M = H._module chi = DirichletCharacter(H, M([260,126])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(65,7742)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$7742$
Conductor:	$3871$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$273$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 3871.cn	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:	$\Q(\zeta_{273})$
Fixed field:	Number field defined by a degree 273 polynomial (not computed)

First 31 of 144 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{7742}(65,\cdot)$	$1$	$1$	$e\left(\frac{193}{273}\right)$	$e\left(\frac{32}{273}\right)$	$e\left(\frac{113}{273}\right)$	$e\left(\frac{202}{273}\right)$	$e\left(\frac{51}{91}\right)$	$e\left(\frac{75}{91}\right)$	$e\left(\frac{205}{273}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{64}{273}\right)$
$\chi_{7742}(179,\cdot)$	$1$	$1$	$e\left(\frac{215}{273}\right)$	$e\left(\frac{187}{273}\right)$	$e\left(\frac{157}{273}\right)$	$e\left(\frac{242}{273}\right)$	$e\left(\frac{62}{91}\right)$	$e\left(\frac{43}{91}\right)$	$e\left(\frac{251}{273}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{101}{273}\right)$
$\chi_{7742}(247,\cdot)$	$1$	$1$	$e\left(\frac{127}{273}\right)$	$e\left(\frac{113}{273}\right)$	$e\left(\frac{254}{273}\right)$	$e\left(\frac{82}{273}\right)$	$e\left(\frac{18}{91}\right)$	$e\left(\frac{80}{91}\right)$	$e\left(\frac{67}{273}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{226}{273}\right)$
$\chi_{7742}(289,\cdot)$	$1$	$1$	$e\left(\frac{199}{273}\right)$	$e\left(\frac{248}{273}\right)$	$e\left(\frac{125}{273}\right)$	$e\left(\frac{64}{273}\right)$	$e\left(\frac{54}{91}\right)$	$e\left(\frac{58}{91}\right)$	$e\left(\frac{19}{273}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{223}{273}\right)$
$\chi_{7742}(403,\cdot)$	$1$	$1$	$e\left(\frac{29}{273}\right)$	$e\left(\frac{43}{273}\right)$	$e\left(\frac{58}{273}\right)$	$e\left(\frac{152}{273}\right)$	$e\left(\frac{60}{91}\right)$	$e\left(\frac{24}{91}\right)$	$e\left(\frac{11}{273}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{86}{273}\right)$
$\chi_{7742}(417,\cdot)$	$1$	$1$	$e\left(\frac{83}{273}\right)$	$e\left(\frac{76}{273}\right)$	$e\left(\frac{166}{273}\right)$	$e\left(\frac{2}{273}\right)$	$e\left(\frac{87}{91}\right)$	$e\left(\frac{53}{91}\right)$	$e\left(\frac{248}{273}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{152}{273}\right)$
$\chi_{7742}(457,\cdot)$	$1$	$1$	$e\left(\frac{67}{273}\right)$	$e\left(\frac{137}{273}\right)$	$e\left(\frac{134}{273}\right)$	$e\left(\frac{97}{273}\right)$	$e\left(\frac{79}{91}\right)$	$e\left(\frac{68}{91}\right)$	$e\left(\frac{16}{273}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{273}\right)$
$\chi_{7742}(541,\cdot)$	$1$	$1$	$e\left(\frac{64}{273}\right)$	$e\left(\frac{29}{273}\right)$	$e\left(\frac{128}{273}\right)$	$e\left(\frac{166}{273}\right)$	$e\left(\frac{32}{91}\right)$	$e\left(\frac{31}{91}\right)$	$e\left(\frac{109}{273}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{58}{273}\right)$
$\chi_{7742}(571,\cdot)$	$1$	$1$	$e\left(\frac{47}{273}\right)$	$e\left(\frac{145}{273}\right)$	$e\left(\frac{94}{273}\right)$	$e\left(\frac{11}{273}\right)$	$e\left(\frac{69}{91}\right)$	$e\left(\frac{64}{91}\right)$	$e\left(\frac{272}{273}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{17}{273}\right)$
$\chi_{7742}(599,\cdot)$	$1$	$1$	$e\left(\frac{92}{273}\right)$	$e\left(\frac{127}{273}\right)$	$e\left(\frac{184}{273}\right)$	$e\left(\frac{68}{273}\right)$	$e\left(\frac{46}{91}\right)$	$e\left(\frac{73}{91}\right)$	$e\left(\frac{242}{273}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{254}{273}\right)$
$\chi_{7742}(653,\cdot)$	$1$	$1$	$e\left(\frac{46}{273}\right)$	$e\left(\frac{200}{273}\right)$	$e\left(\frac{92}{273}\right)$	$e\left(\frac{34}{273}\right)$	$e\left(\frac{23}{91}\right)$	$e\left(\frac{82}{91}\right)$	$e\left(\frac{121}{273}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{127}{273}\right)$
$\chi_{7742}(697,\cdot)$	$1$	$1$	$e\left(\frac{50}{273}\right)$	$e\left(\frac{253}{273}\right)$	$e\left(\frac{100}{273}\right)$	$e\left(\frac{215}{273}\right)$	$e\left(\frac{25}{91}\right)$	$e\left(\frac{10}{91}\right)$	$e\left(\frac{179}{273}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{233}{273}\right)$
$\chi_{7742}(877,\cdot)$	$1$	$1$	$e\left(\frac{94}{273}\right)$	$e\left(\frac{17}{273}\right)$	$e\left(\frac{188}{273}\right)$	$e\left(\frac{22}{273}\right)$	$e\left(\frac{47}{91}\right)$	$e\left(\frac{37}{91}\right)$	$e\left(\frac{271}{273}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{34}{273}\right)$
$\chi_{7742}(879,\cdot)$	$1$	$1$	$e\left(\frac{101}{273}\right)$	$e\left(\frac{178}{273}\right)$	$e\left(\frac{202}{273}\right)$	$e\left(\frac{134}{273}\right)$	$e\left(\frac{5}{91}\right)$	$e\left(\frac{2}{91}\right)$	$e\left(\frac{236}{273}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{83}{273}\right)$
$\chi_{7742}(891,\cdot)$	$1$	$1$	$e\left(\frac{265}{273}\right)$	$e\left(\frac{167}{273}\right)$	$e\left(\frac{257}{273}\right)$	$e\left(\frac{184}{273}\right)$	$e\left(\frac{87}{91}\right)$	$e\left(\frac{53}{91}\right)$	$e\left(\frac{157}{273}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{61}{273}\right)$
$\chi_{7742}(907,\cdot)$	$1$	$1$	$e\left(\frac{230}{273}\right)$	$e\left(\frac{181}{273}\right)$	$e\left(\frac{187}{273}\right)$	$e\left(\frac{170}{273}\right)$	$e\left(\frac{24}{91}\right)$	$e\left(\frac{46}{91}\right)$	$e\left(\frac{59}{273}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{89}{273}\right)$
$\chi_{7742}(921,\cdot)$	$1$	$1$	$e\left(\frac{95}{273}\right)$	$e\left(\frac{235}{273}\right)$	$e\left(\frac{190}{273}\right)$	$e\left(\frac{272}{273}\right)$	$e\left(\frac{2}{91}\right)$	$e\left(\frac{19}{91}\right)$	$e\left(\frac{149}{273}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{197}{273}\right)$
$\chi_{7742}(933,\cdot)$	$1$	$1$	$e\left(\frac{253}{273}\right)$	$e\left(\frac{8}{273}\right)$	$e\left(\frac{233}{273}\right)$	$e\left(\frac{187}{273}\right)$	$e\left(\frac{81}{91}\right)$	$e\left(\frac{87}{91}\right)$	$e\left(\frac{256}{273}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{16}{273}\right)$
$\chi_{7742}(1045,\cdot)$	$1$	$1$	$e\left(\frac{151}{273}\right)$	$e\left(\frac{158}{273}\right)$	$e\left(\frac{29}{273}\right)$	$e\left(\frac{76}{273}\right)$	$e\left(\frac{30}{91}\right)$	$e\left(\frac{12}{91}\right)$	$e\left(\frac{142}{273}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{43}{273}\right)$
$\chi_{7742}(1073,\cdot)$	$1$	$1$	$e\left(\frac{157}{273}\right)$	$e\left(\frac{101}{273}\right)$	$e\left(\frac{41}{273}\right)$	$e\left(\frac{211}{273}\right)$	$e\left(\frac{33}{91}\right)$	$e\left(\frac{86}{91}\right)$	$e\left(\frac{229}{273}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{202}{273}\right)$
$\chi_{7742}(1089,\cdot)$	$1$	$1$	$e\left(\frac{197}{273}\right)$	$e\left(\frac{85}{273}\right)$	$e\left(\frac{121}{273}\right)$	$e\left(\frac{110}{273}\right)$	$e\left(\frac{53}{91}\right)$	$e\left(\frac{3}{91}\right)$	$e\left(\frac{263}{273}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{170}{273}\right)$
$\chi_{7742}(1171,\cdot)$	$1$	$1$	$e\left(\frac{115}{273}\right)$	$e\left(\frac{227}{273}\right)$	$e\left(\frac{230}{273}\right)$	$e\left(\frac{85}{273}\right)$	$e\left(\frac{12}{91}\right)$	$e\left(\frac{23}{91}\right)$	$e\left(\frac{166}{273}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{181}{273}\right)$
$\chi_{7742}(1173,\cdot)$	$1$	$1$	$e\left(\frac{38}{273}\right)$	$e\left(\frac{94}{273}\right)$	$e\left(\frac{76}{273}\right)$	$e\left(\frac{218}{273}\right)$	$e\left(\frac{19}{91}\right)$	$e\left(\frac{44}{91}\right)$	$e\left(\frac{5}{273}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{188}{273}\right)$
$\chi_{7742}(1285,\cdot)$	$1$	$1$	$e\left(\frac{176}{273}\right)$	$e\left(\frac{148}{273}\right)$	$e\left(\frac{79}{273}\right)$	$e\left(\frac{47}{273}\right)$	$e\left(\frac{88}{91}\right)$	$e\left(\frac{17}{91}\right)$	$e\left(\frac{95}{273}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{23}{273}\right)$
$\chi_{7742}(1381,\cdot)$	$1$	$1$	$e\left(\frac{139}{273}\right)$	$e\left(\frac{272}{273}\right)$	$e\left(\frac{5}{273}\right)$	$e\left(\frac{79}{273}\right)$	$e\left(\frac{24}{91}\right)$	$e\left(\frac{46}{91}\right)$	$e\left(\frac{241}{273}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{271}{273}\right)$
$\chi_{7742}(1395,\cdot)$	$1$	$1$	$e\left(\frac{121}{273}\right)$	$e\left(\frac{170}{273}\right)$	$e\left(\frac{242}{273}\right)$	$e\left(\frac{220}{273}\right)$	$e\left(\frac{15}{91}\right)$	$e\left(\frac{6}{91}\right)$	$e\left(\frac{253}{273}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{67}{273}\right)$
$\chi_{7742}(1509,\cdot)$	$1$	$1$	$e\left(\frac{263}{273}\right)$	$e\left(\frac{4}{273}\right)$	$e\left(\frac{253}{273}\right)$	$e\left(\frac{230}{273}\right)$	$e\left(\frac{86}{91}\right)$	$e\left(\frac{89}{91}\right)$	$e\left(\frac{128}{273}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{8}{273}\right)$
$\chi_{7742}(1523,\cdot)$	$1$	$1$	$e\left(\frac{44}{273}\right)$	$e\left(\frac{37}{273}\right)$	$e\left(\frac{88}{273}\right)$	$e\left(\frac{80}{273}\right)$	$e\left(\frac{22}{91}\right)$	$e\left(\frac{27}{91}\right)$	$e\left(\frac{92}{273}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{74}{273}\right)$
$\chi_{7742}(1563,\cdot)$	$1$	$1$	$e\left(\frac{262}{273}\right)$	$e\left(\frac{59}{273}\right)$	$e\left(\frac{251}{273}\right)$	$e\left(\frac{253}{273}\right)$	$e\left(\frac{40}{91}\right)$	$e\left(\frac{16}{91}\right)$	$e\left(\frac{250}{273}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{118}{273}\right)$
$\chi_{7742}(1565,\cdot)$	$1$	$1$	$e\left(\frac{227}{273}\right)$	$e\left(\frac{73}{273}\right)$	$e\left(\frac{181}{273}\right)$	$e\left(\frac{239}{273}\right)$	$e\left(\frac{68}{91}\right)$	$e\left(\frac{9}{91}\right)$	$e\left(\frac{152}{273}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{146}{273}\right)$
$\chi_{7742}(1677,\cdot)$	$1$	$1$	$e\left(\frac{8}{273}\right)$	$e\left(\frac{106}{273}\right)$	$e\left(\frac{16}{273}\right)$	$e\left(\frac{89}{273}\right)$	$e\left(\frac{4}{91}\right)$	$e\left(\frac{38}{91}\right)$	$e\left(\frac{116}{273}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{212}{273}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{7742}(65,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{273}\right)\)	\(e\left(\frac{32}{273}\right)\)	\(e\left(\frac{113}{273}\right)\)	\(e\left(\frac{202}{273}\right)\)	\(e\left(\frac{51}{91}\right)\)	\(e\left(\frac{75}{91}\right)\)	\(e\left(\frac{205}{273}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{64}{273}\right)\)
\(\chi_{7742}(179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{215}{273}\right)\)	\(e\left(\frac{187}{273}\right)\)	\(e\left(\frac{157}{273}\right)\)	\(e\left(\frac{242}{273}\right)\)	\(e\left(\frac{62}{91}\right)\)	\(e\left(\frac{43}{91}\right)\)	\(e\left(\frac{251}{273}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{101}{273}\right)\)
\(\chi_{7742}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{273}\right)\)	\(e\left(\frac{113}{273}\right)\)	\(e\left(\frac{254}{273}\right)\)	\(e\left(\frac{82}{273}\right)\)	\(e\left(\frac{18}{91}\right)\)	\(e\left(\frac{80}{91}\right)\)	\(e\left(\frac{67}{273}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{226}{273}\right)\)
\(\chi_{7742}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{273}\right)\)	\(e\left(\frac{248}{273}\right)\)	\(e\left(\frac{125}{273}\right)\)	\(e\left(\frac{64}{273}\right)\)	\(e\left(\frac{54}{91}\right)\)	\(e\left(\frac{58}{91}\right)\)	\(e\left(\frac{19}{273}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{223}{273}\right)\)
\(\chi_{7742}(403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{273}\right)\)	\(e\left(\frac{43}{273}\right)\)	\(e\left(\frac{58}{273}\right)\)	\(e\left(\frac{152}{273}\right)\)	\(e\left(\frac{60}{91}\right)\)	\(e\left(\frac{24}{91}\right)\)	\(e\left(\frac{11}{273}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{86}{273}\right)\)
\(\chi_{7742}(417,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{273}\right)\)	\(e\left(\frac{76}{273}\right)\)	\(e\left(\frac{166}{273}\right)\)	\(e\left(\frac{2}{273}\right)\)	\(e\left(\frac{87}{91}\right)\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{248}{273}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{152}{273}\right)\)
\(\chi_{7742}(457,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{273}\right)\)	\(e\left(\frac{137}{273}\right)\)	\(e\left(\frac{134}{273}\right)\)	\(e\left(\frac{97}{273}\right)\)	\(e\left(\frac{79}{91}\right)\)	\(e\left(\frac{68}{91}\right)\)	\(e\left(\frac{16}{273}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{273}\right)\)
\(\chi_{7742}(541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{64}{273}\right)\)	\(e\left(\frac{29}{273}\right)\)	\(e\left(\frac{128}{273}\right)\)	\(e\left(\frac{166}{273}\right)\)	\(e\left(\frac{32}{91}\right)\)	\(e\left(\frac{31}{91}\right)\)	\(e\left(\frac{109}{273}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{58}{273}\right)\)
\(\chi_{7742}(571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{273}\right)\)	\(e\left(\frac{145}{273}\right)\)	\(e\left(\frac{94}{273}\right)\)	\(e\left(\frac{11}{273}\right)\)	\(e\left(\frac{69}{91}\right)\)	\(e\left(\frac{64}{91}\right)\)	\(e\left(\frac{272}{273}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{17}{273}\right)\)
\(\chi_{7742}(599,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{92}{273}\right)\)	\(e\left(\frac{127}{273}\right)\)	\(e\left(\frac{184}{273}\right)\)	\(e\left(\frac{68}{273}\right)\)	\(e\left(\frac{46}{91}\right)\)	\(e\left(\frac{73}{91}\right)\)	\(e\left(\frac{242}{273}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{254}{273}\right)\)
\(\chi_{7742}(653,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{273}\right)\)	\(e\left(\frac{200}{273}\right)\)	\(e\left(\frac{92}{273}\right)\)	\(e\left(\frac{34}{273}\right)\)	\(e\left(\frac{23}{91}\right)\)	\(e\left(\frac{82}{91}\right)\)	\(e\left(\frac{121}{273}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{127}{273}\right)\)
\(\chi_{7742}(697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{273}\right)\)	\(e\left(\frac{253}{273}\right)\)	\(e\left(\frac{100}{273}\right)\)	\(e\left(\frac{215}{273}\right)\)	\(e\left(\frac{25}{91}\right)\)	\(e\left(\frac{10}{91}\right)\)	\(e\left(\frac{179}{273}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{233}{273}\right)\)
\(\chi_{7742}(877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{273}\right)\)	\(e\left(\frac{17}{273}\right)\)	\(e\left(\frac{188}{273}\right)\)	\(e\left(\frac{22}{273}\right)\)	\(e\left(\frac{47}{91}\right)\)	\(e\left(\frac{37}{91}\right)\)	\(e\left(\frac{271}{273}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{34}{273}\right)\)
\(\chi_{7742}(879,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{273}\right)\)	\(e\left(\frac{178}{273}\right)\)	\(e\left(\frac{202}{273}\right)\)	\(e\left(\frac{134}{273}\right)\)	\(e\left(\frac{5}{91}\right)\)	\(e\left(\frac{2}{91}\right)\)	\(e\left(\frac{236}{273}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{83}{273}\right)\)
\(\chi_{7742}(891,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{265}{273}\right)\)	\(e\left(\frac{167}{273}\right)\)	\(e\left(\frac{257}{273}\right)\)	\(e\left(\frac{184}{273}\right)\)	\(e\left(\frac{87}{91}\right)\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{157}{273}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{61}{273}\right)\)
\(\chi_{7742}(907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{230}{273}\right)\)	\(e\left(\frac{181}{273}\right)\)	\(e\left(\frac{187}{273}\right)\)	\(e\left(\frac{170}{273}\right)\)	\(e\left(\frac{24}{91}\right)\)	\(e\left(\frac{46}{91}\right)\)	\(e\left(\frac{59}{273}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{89}{273}\right)\)
\(\chi_{7742}(921,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{273}\right)\)	\(e\left(\frac{235}{273}\right)\)	\(e\left(\frac{190}{273}\right)\)	\(e\left(\frac{272}{273}\right)\)	\(e\left(\frac{2}{91}\right)\)	\(e\left(\frac{19}{91}\right)\)	\(e\left(\frac{149}{273}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{197}{273}\right)\)
\(\chi_{7742}(933,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{273}\right)\)	\(e\left(\frac{8}{273}\right)\)	\(e\left(\frac{233}{273}\right)\)	\(e\left(\frac{187}{273}\right)\)	\(e\left(\frac{81}{91}\right)\)	\(e\left(\frac{87}{91}\right)\)	\(e\left(\frac{256}{273}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{16}{273}\right)\)
\(\chi_{7742}(1045,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{273}\right)\)	\(e\left(\frac{158}{273}\right)\)	\(e\left(\frac{29}{273}\right)\)	\(e\left(\frac{76}{273}\right)\)	\(e\left(\frac{30}{91}\right)\)	\(e\left(\frac{12}{91}\right)\)	\(e\left(\frac{142}{273}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{43}{273}\right)\)
\(\chi_{7742}(1073,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{273}\right)\)	\(e\left(\frac{101}{273}\right)\)	\(e\left(\frac{41}{273}\right)\)	\(e\left(\frac{211}{273}\right)\)	\(e\left(\frac{33}{91}\right)\)	\(e\left(\frac{86}{91}\right)\)	\(e\left(\frac{229}{273}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{202}{273}\right)\)
\(\chi_{7742}(1089,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{273}\right)\)	\(e\left(\frac{85}{273}\right)\)	\(e\left(\frac{121}{273}\right)\)	\(e\left(\frac{110}{273}\right)\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{3}{91}\right)\)	\(e\left(\frac{263}{273}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{170}{273}\right)\)
\(\chi_{7742}(1171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{273}\right)\)	\(e\left(\frac{227}{273}\right)\)	\(e\left(\frac{230}{273}\right)\)	\(e\left(\frac{85}{273}\right)\)	\(e\left(\frac{12}{91}\right)\)	\(e\left(\frac{23}{91}\right)\)	\(e\left(\frac{166}{273}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{181}{273}\right)\)
\(\chi_{7742}(1173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{273}\right)\)	\(e\left(\frac{94}{273}\right)\)	\(e\left(\frac{76}{273}\right)\)	\(e\left(\frac{218}{273}\right)\)	\(e\left(\frac{19}{91}\right)\)	\(e\left(\frac{44}{91}\right)\)	\(e\left(\frac{5}{273}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{188}{273}\right)\)
\(\chi_{7742}(1285,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{176}{273}\right)\)	\(e\left(\frac{148}{273}\right)\)	\(e\left(\frac{79}{273}\right)\)	\(e\left(\frac{47}{273}\right)\)	\(e\left(\frac{88}{91}\right)\)	\(e\left(\frac{17}{91}\right)\)	\(e\left(\frac{95}{273}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{23}{273}\right)\)
\(\chi_{7742}(1381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{273}\right)\)	\(e\left(\frac{272}{273}\right)\)	\(e\left(\frac{5}{273}\right)\)	\(e\left(\frac{79}{273}\right)\)	\(e\left(\frac{24}{91}\right)\)	\(e\left(\frac{46}{91}\right)\)	\(e\left(\frac{241}{273}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{271}{273}\right)\)
\(\chi_{7742}(1395,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{273}\right)\)	\(e\left(\frac{170}{273}\right)\)	\(e\left(\frac{242}{273}\right)\)	\(e\left(\frac{220}{273}\right)\)	\(e\left(\frac{15}{91}\right)\)	\(e\left(\frac{6}{91}\right)\)	\(e\left(\frac{253}{273}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{67}{273}\right)\)
\(\chi_{7742}(1509,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{263}{273}\right)\)	\(e\left(\frac{4}{273}\right)\)	\(e\left(\frac{253}{273}\right)\)	\(e\left(\frac{230}{273}\right)\)	\(e\left(\frac{86}{91}\right)\)	\(e\left(\frac{89}{91}\right)\)	\(e\left(\frac{128}{273}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{8}{273}\right)\)
\(\chi_{7742}(1523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{273}\right)\)	\(e\left(\frac{37}{273}\right)\)	\(e\left(\frac{88}{273}\right)\)	\(e\left(\frac{80}{273}\right)\)	\(e\left(\frac{22}{91}\right)\)	\(e\left(\frac{27}{91}\right)\)	\(e\left(\frac{92}{273}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{74}{273}\right)\)
\(\chi_{7742}(1563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{262}{273}\right)\)	\(e\left(\frac{59}{273}\right)\)	\(e\left(\frac{251}{273}\right)\)	\(e\left(\frac{253}{273}\right)\)	\(e\left(\frac{40}{91}\right)\)	\(e\left(\frac{16}{91}\right)\)	\(e\left(\frac{250}{273}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{118}{273}\right)\)
\(\chi_{7742}(1565,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{273}\right)\)	\(e\left(\frac{73}{273}\right)\)	\(e\left(\frac{181}{273}\right)\)	\(e\left(\frac{239}{273}\right)\)	\(e\left(\frac{68}{91}\right)\)	\(e\left(\frac{9}{91}\right)\)	\(e\left(\frac{152}{273}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{146}{273}\right)\)
\(\chi_{7742}(1677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{273}\right)\)	\(e\left(\frac{106}{273}\right)\)	\(e\left(\frac{16}{273}\right)\)	\(e\left(\frac{89}{273}\right)\)	\(e\left(\frac{4}{91}\right)\)	\(e\left(\frac{38}{91}\right)\)	\(e\left(\frac{116}{273}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{212}{273}\right)\)

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First 31 of 144 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	7742.cn
Modulus	$7742$
Conductor	$3871$
Order	$273$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(7742\)
Conductor:	\(3871\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(273\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 3871.cn	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)