from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(967, base_ring=CyclotomicField(138))
M = H._module
chi = DirichletCharacter(H, M([34]))
chi.galois_orbit()
[g,chi] = znchar(Mod(15,967))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(967\) | |
Conductor: | \(967\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(69\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{967}(15,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{10}{69}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{20}{69}\right)\) | \(e\left(\frac{17}{69}\right)\) | \(e\left(\frac{37}{69}\right)\) | \(e\left(\frac{35}{69}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) |
\(\chi_{967}(39,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{69}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{17}{69}\right)\) | \(e\left(\frac{11}{69}\right)\) | \(e\left(\frac{28}{69}\right)\) | \(e\left(\frac{47}{69}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) |
\(\chi_{967}(53,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{38}{69}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{7}{69}\right)\) | \(e\left(\frac{37}{69}\right)\) | \(e\left(\frac{44}{69}\right)\) | \(e\left(\frac{64}{69}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) |
\(\chi_{967}(61,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{22}{69}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{44}{69}\right)\) | \(e\left(\frac{65}{69}\right)\) | \(e\left(\frac{40}{69}\right)\) | \(e\left(\frac{8}{69}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) |
\(\chi_{967}(68,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{28}{69}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{56}{69}\right)\) | \(e\left(\frac{20}{69}\right)\) | \(e\left(\frac{7}{69}\right)\) | \(e\left(\frac{29}{69}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) |
\(\chi_{967}(73,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{69}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{62}{69}\right)\) | \(e\left(\frac{32}{69}\right)\) | \(e\left(\frac{25}{69}\right)\) | \(e\left(\frac{5}{69}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) |
\(\chi_{967}(113,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{69}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{8}{69}\right)\) | \(e\left(\frac{62}{69}\right)\) | \(e\left(\frac{1}{69}\right)\) | \(e\left(\frac{14}{69}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) |
\(\chi_{967}(124,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{26}{69}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{52}{69}\right)\) | \(e\left(\frac{58}{69}\right)\) | \(e\left(\frac{41}{69}\right)\) | \(e\left(\frac{22}{69}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) |
\(\chi_{967}(128,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{69}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{13}{69}\right)\) | \(e\left(\frac{49}{69}\right)\) | \(e\left(\frac{62}{69}\right)\) | \(e\left(\frac{40}{69}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) |
\(\chi_{967}(129,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{69}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{49}{69}\right)\) | \(e\left(\frac{52}{69}\right)\) | \(e\left(\frac{32}{69}\right)\) | \(e\left(\frac{34}{69}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) |
\(\chi_{967}(145,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{69}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{2}{69}\right)\) | \(e\left(\frac{50}{69}\right)\) | \(e\left(\frac{52}{69}\right)\) | \(e\left(\frac{38}{69}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) |
\(\chi_{967}(190,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{69}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{58}{69}\right)\) | \(e\left(\frac{1}{69}\right)\) | \(e\left(\frac{59}{69}\right)\) | \(e\left(\frac{67}{69}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) |
\(\chi_{967}(198,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{69}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{16}{69}\right)\) | \(e\left(\frac{55}{69}\right)\) | \(e\left(\frac{2}{69}\right)\) | \(e\left(\frac{28}{69}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) |
\(\chi_{967}(202,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{69}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{29}{69}\right)\) | \(e\left(\frac{35}{69}\right)\) | \(e\left(\frac{64}{69}\right)\) | \(e\left(\frac{68}{69}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) |
\(\chi_{967}(225,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{20}{69}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{40}{69}\right)\) | \(e\left(\frac{34}{69}\right)\) | \(e\left(\frac{5}{69}\right)\) | \(e\left(\frac{1}{69}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) |
\(\chi_{967}(241,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{69}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{22}{69}\right)\) | \(e\left(\frac{67}{69}\right)\) | \(e\left(\frac{20}{69}\right)\) | \(e\left(\frac{4}{69}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) |
\(\chi_{967}(280,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{50}{69}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{31}{69}\right)\) | \(e\left(\frac{16}{69}\right)\) | \(e\left(\frac{47}{69}\right)\) | \(e\left(\frac{37}{69}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) |
\(\chi_{967}(321,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{58}{69}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{47}{69}\right)\) | \(e\left(\frac{2}{69}\right)\) | \(e\left(\frac{49}{69}\right)\) | \(e\left(\frac{65}{69}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) |
\(\chi_{967}(335,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{69}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{38}{69}\right)\) | \(e\left(\frac{53}{69}\right)\) | \(e\left(\frac{22}{69}\right)\) | \(e\left(\frac{32}{69}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) |
\(\chi_{967}(341,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{40}{69}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{11}{69}\right)\) | \(e\left(\frac{68}{69}\right)\) | \(e\left(\frac{10}{69}\right)\) | \(e\left(\frac{2}{69}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) |
\(\chi_{967}(352,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{55}{69}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{41}{69}\right)\) | \(e\left(\frac{59}{69}\right)\) | \(e\left(\frac{31}{69}\right)\) | \(e\left(\frac{20}{69}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) |
\(\chi_{967}(377,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{34}{69}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{68}{69}\right)\) | \(e\left(\frac{44}{69}\right)\) | \(e\left(\frac{43}{69}\right)\) | \(e\left(\frac{50}{69}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) |
\(\chi_{967}(400,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{69}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{65}{69}\right)\) | \(e\left(\frac{38}{69}\right)\) | \(e\left(\frac{34}{69}\right)\) | \(e\left(\frac{62}{69}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) |
\(\chi_{967}(421,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{69}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{50}{69}\right)\) | \(e\left(\frac{8}{69}\right)\) | \(e\left(\frac{58}{69}\right)\) | \(e\left(\frac{53}{69}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) |
\(\chi_{967}(445,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{65}{69}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{61}{69}\right)\) | \(e\left(\frac{7}{69}\right)\) | \(e\left(\frac{68}{69}\right)\) | \(e\left(\frac{55}{69}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) |
\(\chi_{967}(494,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{62}{69}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{55}{69}\right)\) | \(e\left(\frac{64}{69}\right)\) | \(e\left(\frac{50}{69}\right)\) | \(e\left(\frac{10}{69}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) |
\(\chi_{967}(513,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{35}{69}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{1}{69}\right)\) | \(e\left(\frac{25}{69}\right)\) | \(e\left(\frac{26}{69}\right)\) | \(e\left(\frac{19}{69}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) |
\(\chi_{967}(524,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{69}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{32}{69}\right)\) | \(e\left(\frac{41}{69}\right)\) | \(e\left(\frac{4}{69}\right)\) | \(e\left(\frac{56}{69}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) |
\(\chi_{967}(539,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{69}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{25}{69}\right)\) | \(e\left(\frac{4}{69}\right)\) | \(e\left(\frac{29}{69}\right)\) | \(e\left(\frac{61}{69}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) |
\(\chi_{967}(554,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{69}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{34}{69}\right)\) | \(e\left(\frac{22}{69}\right)\) | \(e\left(\frac{56}{69}\right)\) | \(e\left(\frac{25}{69}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) |
\(\chi_{967}(585,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{69}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{37}{69}\right)\) | \(e\left(\frac{28}{69}\right)\) | \(e\left(\frac{65}{69}\right)\) | \(e\left(\frac{13}{69}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) |