LMFDB - Dirichlet character orbit 7742.co

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7742, base_ring=CyclotomicField(546)) M = H._module chi = DirichletCharacter(H, M([26,14])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(9,7742)) 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.cp	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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{7742}(9,\cdot)$	$1$	$1$	$e\left(\frac{20}{273}\right)$	$e\left(\frac{265}{273}\right)$	$e\left(\frac{40}{273}\right)$	$e\left(\frac{59}{91}\right)$	$e\left(\frac{121}{273}\right)$	$e\left(\frac{4}{91}\right)$	$e\left(\frac{199}{273}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{257}{273}\right)$
$\chi_{7742}(25,\cdot)$	$1$	$1$	$e\left(\frac{265}{273}\right)$	$e\left(\frac{167}{273}\right)$	$e\left(\frac{257}{273}\right)$	$e\left(\frac{31}{91}\right)$	$e\left(\frac{170}{273}\right)$	$e\left(\frac{53}{91}\right)$	$e\left(\frac{248}{273}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{61}{273}\right)$
$\chi_{7742}(81,\cdot)$	$1$	$1$	$e\left(\frac{40}{273}\right)$	$e\left(\frac{257}{273}\right)$	$e\left(\frac{80}{273}\right)$	$e\left(\frac{27}{91}\right)$	$e\left(\frac{242}{273}\right)$	$e\left(\frac{8}{91}\right)$	$e\left(\frac{125}{273}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{241}{273}\right)$
$\chi_{7742}(95,\cdot)$	$1$	$1$	$e\left(\frac{199}{273}\right)$	$e\left(\frac{248}{273}\right)$	$e\left(\frac{125}{273}\right)$	$e\left(\frac{82}{91}\right)$	$e\left(\frac{71}{273}\right)$	$e\left(\frac{58}{91}\right)$	$e\left(\frac{110}{273}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{223}{273}\right)$
$\chi_{7742}(123,\cdot)$	$1$	$1$	$e\left(\frac{97}{273}\right)$	$e\left(\frac{125}{273}\right)$	$e\left(\frac{194}{273}\right)$	$e\left(\frac{45}{91}\right)$	$e\left(\frac{191}{273}\right)$	$e\left(\frac{74}{91}\right)$	$e\left(\frac{269}{273}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{250}{273}\right)$
$\chi_{7742}(163,\cdot)$	$1$	$1$	$e\left(\frac{74}{273}\right)$	$e\left(\frac{25}{273}\right)$	$e\left(\frac{148}{273}\right)$	$e\left(\frac{9}{91}\right)$	$e\left(\frac{202}{273}\right)$	$e\left(\frac{33}{91}\right)$	$e\left(\frac{163}{273}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{50}{273}\right)$
$\chi_{7742}(207,\cdot)$	$1$	$1$	$e\left(\frac{85}{273}\right)$	$e\left(\frac{239}{273}\right)$	$e\left(\frac{170}{273}\right)$	$e\left(\frac{46}{91}\right)$	$e\left(\frac{173}{273}\right)$	$e\left(\frac{17}{91}\right)$	$e\left(\frac{95}{273}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{205}{273}\right)$
$\chi_{7742}(431,\cdot)$	$1$	$1$	$e\left(\frac{256}{273}\right)$	$e\left(\frac{116}{273}\right)$	$e\left(\frac{239}{273}\right)$	$e\left(\frac{9}{91}\right)$	$e\left(\frac{20}{273}\right)$	$e\left(\frac{33}{91}\right)$	$e\left(\frac{254}{273}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{232}{273}\right)$
$\chi_{7742}(485,\cdot)$	$1$	$1$	$e\left(\frac{17}{273}\right)$	$e\left(\frac{157}{273}\right)$	$e\left(\frac{34}{273}\right)$	$e\left(\frac{82}{91}\right)$	$e\left(\frac{253}{273}\right)$	$e\left(\frac{58}{91}\right)$	$e\left(\frac{19}{273}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{41}{273}\right)$
$\chi_{7742}(487,\cdot)$	$1$	$1$	$e\left(\frac{262}{273}\right)$	$e\left(\frac{59}{273}\right)$	$e\left(\frac{251}{273}\right)$	$e\left(\frac{54}{91}\right)$	$e\left(\frac{29}{273}\right)$	$e\left(\frac{16}{91}\right)$	$e\left(\frac{68}{273}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{118}{273}\right)$
$\chi_{7742}(625,\cdot)$	$1$	$1$	$e\left(\frac{257}{273}\right)$	$e\left(\frac{61}{273}\right)$	$e\left(\frac{241}{273}\right)$	$e\left(\frac{62}{91}\right)$	$e\left(\frac{67}{273}\right)$	$e\left(\frac{15}{91}\right)$	$e\left(\frac{223}{273}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{122}{273}\right)$
$\chi_{7742}(683,\cdot)$	$1$	$1$	$e\left(\frac{220}{273}\right)$	$e\left(\frac{185}{273}\right)$	$e\left(\frac{167}{273}\right)$	$e\left(\frac{12}{91}\right)$	$e\left(\frac{239}{273}\right)$	$e\left(\frac{44}{91}\right)$	$e\left(\frac{5}{273}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{97}{273}\right)$
$\chi_{7742}(737,\cdot)$	$1$	$1$	$e\left(\frac{29}{273}\right)$	$e\left(\frac{43}{273}\right)$	$e\left(\frac{58}{273}\right)$	$e\left(\frac{81}{91}\right)$	$e\left(\frac{271}{273}\right)$	$e\left(\frac{24}{91}\right)$	$e\left(\frac{193}{273}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{86}{273}\right)$
$\chi_{7742}(751,\cdot)$	$1$	$1$	$e\left(\frac{116}{273}\right)$	$e\left(\frac{172}{273}\right)$	$e\left(\frac{232}{273}\right)$	$e\left(\frac{51}{91}\right)$	$e\left(\frac{265}{273}\right)$	$e\left(\frac{5}{91}\right)$	$e\left(\frac{226}{273}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{71}{273}\right)$
$\chi_{7742}(821,\cdot)$	$1$	$1$	$e\left(\frac{131}{273}\right)$	$e\left(\frac{166}{273}\right)$	$e\left(\frac{262}{273}\right)$	$e\left(\frac{27}{91}\right)$	$e\left(\frac{151}{273}\right)$	$e\left(\frac{8}{91}\right)$	$e\left(\frac{34}{273}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{59}{273}\right)$
$\chi_{7742}(919,\cdot)$	$1$	$1$	$e\left(\frac{110}{273}\right)$	$e\left(\frac{229}{273}\right)$	$e\left(\frac{220}{273}\right)$	$e\left(\frac{6}{91}\right)$	$e\left(\frac{256}{273}\right)$	$e\left(\frac{22}{91}\right)$	$e\left(\frac{139}{273}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{185}{273}\right)$
$\chi_{7742}(1031,\cdot)$	$1$	$1$	$e\left(\frac{197}{273}\right)$	$e\left(\frac{85}{273}\right)$	$e\left(\frac{121}{273}\right)$	$e\left(\frac{67}{91}\right)$	$e\left(\frac{250}{273}\right)$	$e\left(\frac{3}{91}\right)$	$e\left(\frac{172}{273}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{170}{273}\right)$
$\chi_{7742}(1103,\cdot)$	$1$	$1$	$e\left(\frac{244}{273}\right)$	$e\left(\frac{230}{273}\right)$	$e\left(\frac{215}{273}\right)$	$e\left(\frac{10}{91}\right)$	$e\left(\frac{2}{273}\right)$	$e\left(\frac{67}{91}\right)$	$e\left(\frac{80}{273}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{187}{273}\right)$
$\chi_{7742}(1115,\cdot)$	$1$	$1$	$e\left(\frac{215}{273}\right)$	$e\left(\frac{187}{273}\right)$	$e\left(\frac{157}{273}\right)$	$e\left(\frac{20}{91}\right)$	$e\left(\frac{4}{273}\right)$	$e\left(\frac{43}{91}\right)$	$e\left(\frac{160}{273}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{101}{273}\right)$
$\chi_{7742}(1131,\cdot)$	$1$	$1$	$e\left(\frac{226}{273}\right)$	$e\left(\frac{128}{273}\right)$	$e\left(\frac{179}{273}\right)$	$e\left(\frac{57}{91}\right)$	$e\left(\frac{248}{273}\right)$	$e\left(\frac{27}{91}\right)$	$e\left(\frac{92}{273}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{256}{273}\right)$
$\chi_{7742}(1187,\cdot)$	$1$	$1$	$e\left(\frac{1}{273}\right)$	$e\left(\frac{218}{273}\right)$	$e\left(\frac{2}{273}\right)$	$e\left(\frac{53}{91}\right)$	$e\left(\frac{47}{273}\right)$	$e\left(\frac{73}{91}\right)$	$e\left(\frac{242}{273}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{163}{273}\right)$
$\chi_{7742}(1201,\cdot)$	$1$	$1$	$e\left(\frac{160}{273}\right)$	$e\left(\frac{209}{273}\right)$	$e\left(\frac{47}{273}\right)$	$e\left(\frac{17}{91}\right)$	$e\left(\frac{149}{273}\right)$	$e\left(\frac{32}{91}\right)$	$e\left(\frac{227}{273}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{145}{273}\right)$
$\chi_{7742}(1229,\cdot)$	$1$	$1$	$e\left(\frac{58}{273}\right)$	$e\left(\frac{86}{273}\right)$	$e\left(\frac{116}{273}\right)$	$e\left(\frac{71}{91}\right)$	$e\left(\frac{269}{273}\right)$	$e\left(\frac{48}{91}\right)$	$e\left(\frac{113}{273}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{172}{273}\right)$
$\chi_{7742}(1269,\cdot)$	$1$	$1$	$e\left(\frac{269}{273}\right)$	$e\left(\frac{220}{273}\right)$	$e\left(\frac{265}{273}\right)$	$e\left(\frac{61}{91}\right)$	$e\left(\frac{85}{273}\right)$	$e\left(\frac{72}{91}\right)$	$e\left(\frac{124}{273}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{167}{273}\right)$
$\chi_{7742}(1283,\cdot)$	$1$	$1$	$e\left(\frac{125}{273}\right)$	$e\left(\frac{223}{273}\right)$	$e\left(\frac{250}{273}\right)$	$e\left(\frac{73}{91}\right)$	$e\left(\frac{142}{273}\right)$	$e\left(\frac{25}{91}\right)$	$e\left(\frac{220}{273}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{173}{273}\right)$
$\chi_{7742}(1313,\cdot)$	$1$	$1$	$e\left(\frac{46}{273}\right)$	$e\left(\frac{200}{273}\right)$	$e\left(\frac{92}{273}\right)$	$e\left(\frac{72}{91}\right)$	$e\left(\frac{251}{273}\right)$	$e\left(\frac{82}{91}\right)$	$e\left(\frac{212}{273}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{127}{273}\right)$
$\chi_{7742}(1467,\cdot)$	$1$	$1$	$e\left(\frac{94}{273}\right)$	$e\left(\frac{17}{273}\right)$	$e\left(\frac{188}{273}\right)$	$e\left(\frac{68}{91}\right)$	$e\left(\frac{50}{273}\right)$	$e\left(\frac{37}{91}\right)$	$e\left(\frac{89}{273}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{34}{273}\right)$
$\chi_{7742}(1591,\cdot)$	$1$	$1$	$e\left(\frac{212}{273}\right)$	$e\left(\frac{79}{273}\right)$	$e\left(\frac{151}{273}\right)$	$e\left(\frac{43}{91}\right)$	$e\left(\frac{136}{273}\right)$	$e\left(\frac{6}{91}\right)$	$e\left(\frac{253}{273}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{158}{273}\right)$
$\chi_{7742}(1593,\cdot)$	$1$	$1$	$e\left(\frac{223}{273}\right)$	$e\left(\frac{20}{273}\right)$	$e\left(\frac{173}{273}\right)$	$e\left(\frac{80}{91}\right)$	$e\left(\frac{107}{273}\right)$	$e\left(\frac{81}{91}\right)$	$e\left(\frac{185}{273}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{40}{273}\right)$
$\chi_{7742}(1731,\cdot)$	$1$	$1$	$e\left(\frac{179}{273}\right)$	$e\left(\frac{256}{273}\right)$	$e\left(\frac{85}{273}\right)$	$e\left(\frac{23}{91}\right)$	$e\left(\frac{223}{273}\right)$	$e\left(\frac{54}{91}\right)$	$e\left(\frac{184}{273}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{239}{273}\right)$
$\chi_{7742}(1789,\cdot)$	$1$	$1$	$e\left(\frac{181}{273}\right)$	$e\left(\frac{146}{273}\right)$	$e\left(\frac{89}{273}\right)$	$e\left(\frac{38}{91}\right)$	$e\left(\frac{44}{273}\right)$	$e\left(\frac{18}{91}\right)$	$e\left(\frac{122}{273}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{19}{273}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{7742}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{273}\right)\)	\(e\left(\frac{265}{273}\right)\)	\(e\left(\frac{40}{273}\right)\)	\(e\left(\frac{59}{91}\right)\)	\(e\left(\frac{121}{273}\right)\)	\(e\left(\frac{4}{91}\right)\)	\(e\left(\frac{199}{273}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{257}{273}\right)\)
\(\chi_{7742}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{265}{273}\right)\)	\(e\left(\frac{167}{273}\right)\)	\(e\left(\frac{257}{273}\right)\)	\(e\left(\frac{31}{91}\right)\)	\(e\left(\frac{170}{273}\right)\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{248}{273}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{61}{273}\right)\)
\(\chi_{7742}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{40}{273}\right)\)	\(e\left(\frac{257}{273}\right)\)	\(e\left(\frac{80}{273}\right)\)	\(e\left(\frac{27}{91}\right)\)	\(e\left(\frac{242}{273}\right)\)	\(e\left(\frac{8}{91}\right)\)	\(e\left(\frac{125}{273}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{241}{273}\right)\)
\(\chi_{7742}(95,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{273}\right)\)	\(e\left(\frac{248}{273}\right)\)	\(e\left(\frac{125}{273}\right)\)	\(e\left(\frac{82}{91}\right)\)	\(e\left(\frac{71}{273}\right)\)	\(e\left(\frac{58}{91}\right)\)	\(e\left(\frac{110}{273}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{223}{273}\right)\)
\(\chi_{7742}(123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{273}\right)\)	\(e\left(\frac{125}{273}\right)\)	\(e\left(\frac{194}{273}\right)\)	\(e\left(\frac{45}{91}\right)\)	\(e\left(\frac{191}{273}\right)\)	\(e\left(\frac{74}{91}\right)\)	\(e\left(\frac{269}{273}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{250}{273}\right)\)
\(\chi_{7742}(163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{273}\right)\)	\(e\left(\frac{25}{273}\right)\)	\(e\left(\frac{148}{273}\right)\)	\(e\left(\frac{9}{91}\right)\)	\(e\left(\frac{202}{273}\right)\)	\(e\left(\frac{33}{91}\right)\)	\(e\left(\frac{163}{273}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{50}{273}\right)\)
\(\chi_{7742}(207,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{273}\right)\)	\(e\left(\frac{239}{273}\right)\)	\(e\left(\frac{170}{273}\right)\)	\(e\left(\frac{46}{91}\right)\)	\(e\left(\frac{173}{273}\right)\)	\(e\left(\frac{17}{91}\right)\)	\(e\left(\frac{95}{273}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{205}{273}\right)\)
\(\chi_{7742}(431,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{256}{273}\right)\)	\(e\left(\frac{116}{273}\right)\)	\(e\left(\frac{239}{273}\right)\)	\(e\left(\frac{9}{91}\right)\)	\(e\left(\frac{20}{273}\right)\)	\(e\left(\frac{33}{91}\right)\)	\(e\left(\frac{254}{273}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{232}{273}\right)\)
\(\chi_{7742}(485,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{273}\right)\)	\(e\left(\frac{157}{273}\right)\)	\(e\left(\frac{34}{273}\right)\)	\(e\left(\frac{82}{91}\right)\)	\(e\left(\frac{253}{273}\right)\)	\(e\left(\frac{58}{91}\right)\)	\(e\left(\frac{19}{273}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{41}{273}\right)\)
\(\chi_{7742}(487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{262}{273}\right)\)	\(e\left(\frac{59}{273}\right)\)	\(e\left(\frac{251}{273}\right)\)	\(e\left(\frac{54}{91}\right)\)	\(e\left(\frac{29}{273}\right)\)	\(e\left(\frac{16}{91}\right)\)	\(e\left(\frac{68}{273}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{118}{273}\right)\)
\(\chi_{7742}(625,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{257}{273}\right)\)	\(e\left(\frac{61}{273}\right)\)	\(e\left(\frac{241}{273}\right)\)	\(e\left(\frac{62}{91}\right)\)	\(e\left(\frac{67}{273}\right)\)	\(e\left(\frac{15}{91}\right)\)	\(e\left(\frac{223}{273}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{122}{273}\right)\)
\(\chi_{7742}(683,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{220}{273}\right)\)	\(e\left(\frac{185}{273}\right)\)	\(e\left(\frac{167}{273}\right)\)	\(e\left(\frac{12}{91}\right)\)	\(e\left(\frac{239}{273}\right)\)	\(e\left(\frac{44}{91}\right)\)	\(e\left(\frac{5}{273}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{97}{273}\right)\)
\(\chi_{7742}(737,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{273}\right)\)	\(e\left(\frac{43}{273}\right)\)	\(e\left(\frac{58}{273}\right)\)	\(e\left(\frac{81}{91}\right)\)	\(e\left(\frac{271}{273}\right)\)	\(e\left(\frac{24}{91}\right)\)	\(e\left(\frac{193}{273}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{86}{273}\right)\)
\(\chi_{7742}(751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{116}{273}\right)\)	\(e\left(\frac{172}{273}\right)\)	\(e\left(\frac{232}{273}\right)\)	\(e\left(\frac{51}{91}\right)\)	\(e\left(\frac{265}{273}\right)\)	\(e\left(\frac{5}{91}\right)\)	\(e\left(\frac{226}{273}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{71}{273}\right)\)
\(\chi_{7742}(821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{273}\right)\)	\(e\left(\frac{166}{273}\right)\)	\(e\left(\frac{262}{273}\right)\)	\(e\left(\frac{27}{91}\right)\)	\(e\left(\frac{151}{273}\right)\)	\(e\left(\frac{8}{91}\right)\)	\(e\left(\frac{34}{273}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{59}{273}\right)\)
\(\chi_{7742}(919,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{110}{273}\right)\)	\(e\left(\frac{229}{273}\right)\)	\(e\left(\frac{220}{273}\right)\)	\(e\left(\frac{6}{91}\right)\)	\(e\left(\frac{256}{273}\right)\)	\(e\left(\frac{22}{91}\right)\)	\(e\left(\frac{139}{273}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{185}{273}\right)\)
\(\chi_{7742}(1031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{273}\right)\)	\(e\left(\frac{85}{273}\right)\)	\(e\left(\frac{121}{273}\right)\)	\(e\left(\frac{67}{91}\right)\)	\(e\left(\frac{250}{273}\right)\)	\(e\left(\frac{3}{91}\right)\)	\(e\left(\frac{172}{273}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{170}{273}\right)\)
\(\chi_{7742}(1103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{244}{273}\right)\)	\(e\left(\frac{230}{273}\right)\)	\(e\left(\frac{215}{273}\right)\)	\(e\left(\frac{10}{91}\right)\)	\(e\left(\frac{2}{273}\right)\)	\(e\left(\frac{67}{91}\right)\)	\(e\left(\frac{80}{273}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{187}{273}\right)\)
\(\chi_{7742}(1115,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{215}{273}\right)\)	\(e\left(\frac{187}{273}\right)\)	\(e\left(\frac{157}{273}\right)\)	\(e\left(\frac{20}{91}\right)\)	\(e\left(\frac{4}{273}\right)\)	\(e\left(\frac{43}{91}\right)\)	\(e\left(\frac{160}{273}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{101}{273}\right)\)
\(\chi_{7742}(1131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{226}{273}\right)\)	\(e\left(\frac{128}{273}\right)\)	\(e\left(\frac{179}{273}\right)\)	\(e\left(\frac{57}{91}\right)\)	\(e\left(\frac{248}{273}\right)\)	\(e\left(\frac{27}{91}\right)\)	\(e\left(\frac{92}{273}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{256}{273}\right)\)
\(\chi_{7742}(1187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{273}\right)\)	\(e\left(\frac{218}{273}\right)\)	\(e\left(\frac{2}{273}\right)\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{47}{273}\right)\)	\(e\left(\frac{73}{91}\right)\)	\(e\left(\frac{242}{273}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{163}{273}\right)\)
\(\chi_{7742}(1201,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{160}{273}\right)\)	\(e\left(\frac{209}{273}\right)\)	\(e\left(\frac{47}{273}\right)\)	\(e\left(\frac{17}{91}\right)\)	\(e\left(\frac{149}{273}\right)\)	\(e\left(\frac{32}{91}\right)\)	\(e\left(\frac{227}{273}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{145}{273}\right)\)
\(\chi_{7742}(1229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{273}\right)\)	\(e\left(\frac{86}{273}\right)\)	\(e\left(\frac{116}{273}\right)\)	\(e\left(\frac{71}{91}\right)\)	\(e\left(\frac{269}{273}\right)\)	\(e\left(\frac{48}{91}\right)\)	\(e\left(\frac{113}{273}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{172}{273}\right)\)
\(\chi_{7742}(1269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{269}{273}\right)\)	\(e\left(\frac{220}{273}\right)\)	\(e\left(\frac{265}{273}\right)\)	\(e\left(\frac{61}{91}\right)\)	\(e\left(\frac{85}{273}\right)\)	\(e\left(\frac{72}{91}\right)\)	\(e\left(\frac{124}{273}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{167}{273}\right)\)
\(\chi_{7742}(1283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{273}\right)\)	\(e\left(\frac{223}{273}\right)\)	\(e\left(\frac{250}{273}\right)\)	\(e\left(\frac{73}{91}\right)\)	\(e\left(\frac{142}{273}\right)\)	\(e\left(\frac{25}{91}\right)\)	\(e\left(\frac{220}{273}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{173}{273}\right)\)
\(\chi_{7742}(1313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{273}\right)\)	\(e\left(\frac{200}{273}\right)\)	\(e\left(\frac{92}{273}\right)\)	\(e\left(\frac{72}{91}\right)\)	\(e\left(\frac{251}{273}\right)\)	\(e\left(\frac{82}{91}\right)\)	\(e\left(\frac{212}{273}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{127}{273}\right)\)
\(\chi_{7742}(1467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{273}\right)\)	\(e\left(\frac{17}{273}\right)\)	\(e\left(\frac{188}{273}\right)\)	\(e\left(\frac{68}{91}\right)\)	\(e\left(\frac{50}{273}\right)\)	\(e\left(\frac{37}{91}\right)\)	\(e\left(\frac{89}{273}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{34}{273}\right)\)
\(\chi_{7742}(1591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{212}{273}\right)\)	\(e\left(\frac{79}{273}\right)\)	\(e\left(\frac{151}{273}\right)\)	\(e\left(\frac{43}{91}\right)\)	\(e\left(\frac{136}{273}\right)\)	\(e\left(\frac{6}{91}\right)\)	\(e\left(\frac{253}{273}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{158}{273}\right)\)
\(\chi_{7742}(1593,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{223}{273}\right)\)	\(e\left(\frac{20}{273}\right)\)	\(e\left(\frac{173}{273}\right)\)	\(e\left(\frac{80}{91}\right)\)	\(e\left(\frac{107}{273}\right)\)	\(e\left(\frac{81}{91}\right)\)	\(e\left(\frac{185}{273}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{40}{273}\right)\)
\(\chi_{7742}(1731,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{273}\right)\)	\(e\left(\frac{256}{273}\right)\)	\(e\left(\frac{85}{273}\right)\)	\(e\left(\frac{23}{91}\right)\)	\(e\left(\frac{223}{273}\right)\)	\(e\left(\frac{54}{91}\right)\)	\(e\left(\frac{184}{273}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{239}{273}\right)\)
\(\chi_{7742}(1789,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{273}\right)\)	\(e\left(\frac{146}{273}\right)\)	\(e\left(\frac{89}{273}\right)\)	\(e\left(\frac{38}{91}\right)\)	\(e\left(\frac{44}{273}\right)\)	\(e\left(\frac{18}{91}\right)\)	\(e\left(\frac{122}{273}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{19}{273}\right)\)

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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.co
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.cp	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)