LMFDB - Dirichlet character orbit 834.m

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(834, base_ring=CyclotomicField(138)) M = H._module chi = DirichletCharacter(H, M([0,50])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(7,834)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$834$
Conductor:	$139$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$69$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 139.g	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:	$\Q(\zeta_{69})$
Fixed field:	Number field defined by a degree 69 polynomial

First 31 of 44 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{834}(7,\cdot)$	$1$	$1$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{22}{69}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{20}{69}\right)$
$\chi_{834}(13,\cdot)$	$1$	$1$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{67}{69}\right)$
$\chi_{834}(25,\cdot)$	$1$	$1$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{22}{69}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{55}{69}\right)$
$\chi_{834}(31,\cdot)$	$1$	$1$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{50}{69}\right)$
$\chi_{834}(37,\cdot)$	$1$	$1$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{49}{69}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{32}{69}\right)$
$\chi_{834}(49,\cdot)$	$1$	$1$	$e\left(\frac{22}{69}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{40}{69}\right)$
$\chi_{834}(67,\cdot)$	$1$	$1$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{34}{69}\right)$
$\chi_{834}(121,\cdot)$	$1$	$1$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{49}{69}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{47}{69}\right)$
$\chi_{834}(127,\cdot)$	$1$	$1$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{31}{69}\right)$
$\chi_{834}(163,\cdot)$	$1$	$1$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{59}{69}\right)$
$\chi_{834}(169,\cdot)$	$1$	$1$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{65}{69}\right)$
$\chi_{834}(193,\cdot)$	$1$	$1$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{22}{69}\right)$
$\chi_{834}(205,\cdot)$	$1$	$1$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{61}{69}\right)$
$\chi_{834}(217,\cdot)$	$1$	$1$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{1}{69}\right)$
$\chi_{834}(259,\cdot)$	$1$	$1$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{52}{69}\right)$
$\chi_{834}(283,\cdot)$	$1$	$1$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{62}{69}\right)$
$\chi_{834}(289,\cdot)$	$1$	$1$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{58}{69}\right)$
$\chi_{834}(307,\cdot)$	$1$	$1$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{10}{69}\right)$
$\chi_{834}(313,\cdot)$	$1$	$1$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{13}{69}\right)$
$\chi_{834}(319,\cdot)$	$1$	$1$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{68}{69}\right)$
$\chi_{834}(325,\cdot)$	$1$	$1$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{22}{69}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{53}{69}\right)$
$\chi_{834}(349,\cdot)$	$1$	$1$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{16}{69}\right)$
$\chi_{834}(361,\cdot)$	$1$	$1$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{35}{69}\right)$
$\chi_{834}(367,\cdot)$	$1$	$1$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{14}{69}\right)$
$\chi_{834}(385,\cdot)$	$1$	$1$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{22}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{49}{69}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{2}{69}\right)$
$\chi_{834}(391,\cdot)$	$1$	$1$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{26}{69}\right)$
$\chi_{834}(415,\cdot)$	$1$	$1$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{28}{69}\right)$
$\chi_{834}(421,\cdot)$	$1$	$1$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{56}{69}\right)$
$\chi_{834}(433,\cdot)$	$1$	$1$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{43}{69}\right)$
$\chi_{834}(445,\cdot)$	$1$	$1$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{22}{69}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{7}{69}\right)$
$\chi_{834}(463,\cdot)$	$1$	$1$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{49}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{25}{69}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{834}(7,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{22}{69}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)
\(\chi_{834}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{67}{69}\right)\)
\(\chi_{834}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{22}{69}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{55}{69}\right)\)
\(\chi_{834}(31,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{50}{69}\right)\)
\(\chi_{834}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{49}{69}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{32}{69}\right)\)
\(\chi_{834}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{69}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{40}{69}\right)\)
\(\chi_{834}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{34}{69}\right)\)
\(\chi_{834}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{49}{69}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{47}{69}\right)\)
\(\chi_{834}(127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{31}{69}\right)\)
\(\chi_{834}(163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{59}{69}\right)\)
\(\chi_{834}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{65}{69}\right)\)
\(\chi_{834}(193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{22}{69}\right)\)
\(\chi_{834}(205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{61}{69}\right)\)
\(\chi_{834}(217,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{1}{69}\right)\)
\(\chi_{834}(259,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{52}{69}\right)\)
\(\chi_{834}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{62}{69}\right)\)
\(\chi_{834}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{58}{69}\right)\)
\(\chi_{834}(307,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{10}{69}\right)\)
\(\chi_{834}(313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{13}{69}\right)\)
\(\chi_{834}(319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{68}{69}\right)\)
\(\chi_{834}(325,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{22}{69}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{53}{69}\right)\)
\(\chi_{834}(349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{16}{69}\right)\)
\(\chi_{834}(361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{35}{69}\right)\)
\(\chi_{834}(367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{14}{69}\right)\)
\(\chi_{834}(385,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{22}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{49}{69}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{2}{69}\right)\)
\(\chi_{834}(391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)
\(\chi_{834}(415,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{28}{69}\right)\)
\(\chi_{834}(421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{56}{69}\right)\)
\(\chi_{834}(433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{43}{69}\right)\)
\(\chi_{834}(445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{22}{69}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)
\(\chi_{834}(463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{49}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{25}{69}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

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.m
Modulus	$834$
Conductor	$139$
Order	$69$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(834\)
Conductor:	\(139\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(69\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 139.g	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)