LMFDB - Dirichlet character orbit 834.n

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(834, base_ring=CyclotomicField(138)) M = H._module chi = DirichletCharacter(H, M([69,86])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,834)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$834$
Conductor:	$417$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$138$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 417.n	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{69})$
Fixed field:	Number field defined by a degree 138 polynomial (not computed)

First 31 of 44 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{834}(5,\cdot)$	$-1$	$1$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{119}{138}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{62}{69}\right)$
$\chi_{834}(11,\cdot)$	$-1$	$1$	$e\left(\frac{119}{138}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{49}{138}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{37}{138}\right)$	$e\left(\frac{58}{69}\right)$
$\chi_{834}(29,\cdot)$	$-1$	$1$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{37}{138}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{53}{138}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{73}{138}\right)$	$e\left(\frac{10}{69}\right)$
$\chi_{834}(35,\cdot)$	$-1$	$1$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{55}{138}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{131}{138}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{19}{138}\right)$	$e\left(\frac{13}{69}\right)$
$\chi_{834}(41,\cdot)$	$-1$	$1$	$e\left(\frac{61}{138}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{68}{69}\right)$
$\chi_{834}(47,\cdot)$	$-1$	$1$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{65}{138}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{22}{69}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{53}{69}\right)$
$\chi_{834}(71,\cdot)$	$-1$	$1$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{73}{138}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{103}{138}\right)$	$e\left(\frac{16}{69}\right)$
$\chi_{834}(83,\cdot)$	$-1$	$1$	$e\left(\frac{73}{138}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{95}{138}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{35}{69}\right)$
$\chi_{834}(89,\cdot)$	$-1$	$1$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{19}{138}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{47}{138}\right)$	$e\left(\frac{14}{69}\right)$
$\chi_{834}(107,\cdot)$	$-1$	$1$	$e\left(\frac{85}{138}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{22}{69}\right)$	$e\left(\frac{121}{138}\right)$	$e\left(\frac{49}{69}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{125}{138}\right)$	$e\left(\frac{2}{69}\right)$
$\chi_{834}(113,\cdot)$	$-1$	$1$	$e\left(\frac{1}{138}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{55}{138}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{26}{69}\right)$
$\chi_{834}(137,\cdot)$	$-1$	$1$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{28}{69}\right)$
$\chi_{834}(143,\cdot)$	$-1$	$1$	$e\left(\frac{103}{138}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{119}{138}\right)$	$e\left(\frac{56}{69}\right)$
$\chi_{834}(155,\cdot)$	$-1$	$1$	$e\left(\frac{137}{138}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{97}{138}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{31}{138}\right)$	$e\left(\frac{43}{69}\right)$
$\chi_{834}(167,\cdot)$	$-1$	$1$	$e\left(\frac{125}{138}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{19}{138}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{113}{138}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{127}{138}\right)$	$e\left(\frac{7}{69}\right)$
$\chi_{834}(185,\cdot)$	$-1$	$1$	$e\left(\frac{131}{138}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{127}{138}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{29}{138}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{25}{69}\right)$
$\chi_{834}(257,\cdot)$	$-1$	$1$	$e\left(\frac{29}{138}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{85}{138}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{77}{138}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{64}{69}\right)$
$\chi_{834}(263,\cdot)$	$-1$	$1$	$e\left(\frac{89}{138}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{61}{138}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{65}{138}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{1}{138}\right)$	$e\left(\frac{37}{69}\right)$
$\chi_{834}(275,\cdot)$	$-1$	$1$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{109}{138}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{44}{69}\right)$
$\chi_{834}(287,\cdot)$	$-1$	$1$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{49}{69}\right)$	$e\left(\frac{91}{138}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{49}{138}\right)$	$e\left(\frac{19}{69}\right)$
$\chi_{834}(329,\cdot)$	$-1$	$1$	$e\left(\frac{101}{138}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{1}{138}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{4}{69}\right)$
$\chi_{834}(347,\cdot)$	$-1$	$1$	$e\left(\frac{121}{138}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{131}{138}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{31}{138}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{113}{138}\right)$	$e\left(\frac{41}{69}\right)$
$\chi_{834}(359,\cdot)$	$-1$	$1$	$e\left(\frac{97}{138}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{113}{138}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{91}{138}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{29}{138}\right)$	$e\left(\frac{38}{69}\right)$
$\chi_{834}(377,\cdot)$	$-1$	$1$	$e\left(\frac{133}{138}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{1}{138}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{8}{69}\right)$
$\chi_{834}(395,\cdot)$	$-1$	$1$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{125}{138}\right)$	$e\left(\frac{49}{69}\right)$	$e\left(\frac{97}{138}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{131}{138}\right)$	$e\left(\frac{17}{69}\right)$
$\chi_{834}(437,\cdot)$	$-1$	$1$	$e\left(\frac{47}{138}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{133}{138}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{101}{138}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{61}{138}\right)$	$e\left(\frac{49}{69}\right)$
$\chi_{834}(455,\cdot)$	$-1$	$1$	$e\left(\frac{19}{138}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{89}{138}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{101}{138}\right)$	$e\left(\frac{11}{69}\right)$
$\chi_{834}(503,\cdot)$	$-1$	$1$	$e\left(\frac{109}{138}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{53}{138}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{61}{138}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{5}{69}\right)$
$\chi_{834}(539,\cdot)$	$-1$	$1$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{133}{138}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{53}{138}\right)$	$e\left(\frac{29}{69}\right)$
$\chi_{834}(563,\cdot)$	$-1$	$1$	$e\left(\frac{91}{138}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{5}{138}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{37}{138}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{22}{69}\right)$	$e\left(\frac{77}{138}\right)$	$e\left(\frac{20}{69}\right)$
$\chi_{834}(569,\cdot)$	$-1$	$1$	$e\left(\frac{53}{138}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{103}{138}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{67}{69}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{834}(5,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{119}{138}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{62}{69}\right)\)
\(\chi_{834}(11,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{138}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{49}{138}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{37}{138}\right)\)	\(e\left(\frac{58}{69}\right)\)
\(\chi_{834}(29,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{37}{138}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{53}{138}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{73}{138}\right)\)	\(e\left(\frac{10}{69}\right)\)
\(\chi_{834}(35,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{55}{138}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{131}{138}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{19}{138}\right)\)	\(e\left(\frac{13}{69}\right)\)
\(\chi_{834}(41,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{138}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{68}{69}\right)\)
\(\chi_{834}(47,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{65}{138}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{22}{69}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{53}{69}\right)\)
\(\chi_{834}(71,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{73}{138}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{103}{138}\right)\)	\(e\left(\frac{16}{69}\right)\)
\(\chi_{834}(83,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{138}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{95}{138}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{35}{69}\right)\)
\(\chi_{834}(89,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{19}{138}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{47}{138}\right)\)	\(e\left(\frac{14}{69}\right)\)
\(\chi_{834}(107,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{138}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{22}{69}\right)\)	\(e\left(\frac{121}{138}\right)\)	\(e\left(\frac{49}{69}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{125}{138}\right)\)	\(e\left(\frac{2}{69}\right)\)
\(\chi_{834}(113,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{138}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{55}{138}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{26}{69}\right)\)
\(\chi_{834}(137,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{28}{69}\right)\)
\(\chi_{834}(143,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{138}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{119}{138}\right)\)	\(e\left(\frac{56}{69}\right)\)
\(\chi_{834}(155,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{138}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{97}{138}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{31}{138}\right)\)	\(e\left(\frac{43}{69}\right)\)
\(\chi_{834}(167,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{125}{138}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{19}{138}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{113}{138}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{127}{138}\right)\)	\(e\left(\frac{7}{69}\right)\)
\(\chi_{834}(185,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{138}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{127}{138}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{29}{138}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{25}{69}\right)\)
\(\chi_{834}(257,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{138}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{85}{138}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{77}{138}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{64}{69}\right)\)
\(\chi_{834}(263,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{138}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{61}{138}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{65}{138}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{1}{138}\right)\)	\(e\left(\frac{37}{69}\right)\)
\(\chi_{834}(275,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{109}{138}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{44}{69}\right)\)
\(\chi_{834}(287,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{49}{69}\right)\)	\(e\left(\frac{91}{138}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{49}{138}\right)\)	\(e\left(\frac{19}{69}\right)\)
\(\chi_{834}(329,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{138}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{1}{138}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{4}{69}\right)\)
\(\chi_{834}(347,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{138}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{131}{138}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{31}{138}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{113}{138}\right)\)	\(e\left(\frac{41}{69}\right)\)
\(\chi_{834}(359,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{138}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{113}{138}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{91}{138}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{29}{138}\right)\)	\(e\left(\frac{38}{69}\right)\)
\(\chi_{834}(377,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{138}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{1}{138}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{8}{69}\right)\)
\(\chi_{834}(395,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{125}{138}\right)\)	\(e\left(\frac{49}{69}\right)\)	\(e\left(\frac{97}{138}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{131}{138}\right)\)	\(e\left(\frac{17}{69}\right)\)
\(\chi_{834}(437,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{138}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{133}{138}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{101}{138}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{61}{138}\right)\)	\(e\left(\frac{49}{69}\right)\)
\(\chi_{834}(455,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{138}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{89}{138}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{101}{138}\right)\)	\(e\left(\frac{11}{69}\right)\)
\(\chi_{834}(503,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{138}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{53}{138}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{61}{138}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{5}{69}\right)\)
\(\chi_{834}(539,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{133}{138}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{53}{138}\right)\)	\(e\left(\frac{29}{69}\right)\)
\(\chi_{834}(563,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{138}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{5}{138}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{37}{138}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{22}{69}\right)\)	\(e\left(\frac{77}{138}\right)\)	\(e\left(\frac{20}{69}\right)\)
\(\chi_{834}(569,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{138}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{103}{138}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{67}{69}\right)\)

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First 31 of 44 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	834.n
Modulus	$834$
Conductor	$417$
Order	$138$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(834\)
Conductor:	\(417\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(138\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 417.n	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)