from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1073, base_ring=CyclotomicField(126))
M = H._module
chi = DirichletCharacter(H, M([72,35]))
chi.galois_orbit()
[g,chi] = znchar(Mod(25,1073))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(1073\) | |
Conductor: | \(1073\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | 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: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
First 31 of 36 characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1073}(25,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{107}{126}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{121}{126}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) |
\(\chi_{1073}(65,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{126}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) |
\(\chi_{1073}(78,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{115}{126}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{17}{126}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) |
\(\chi_{1073}(132,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{95}{126}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{25}{126}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) |
\(\chi_{1073}(136,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{126}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) |
\(\chi_{1073}(139,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{126}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{55}{126}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) |
\(\chi_{1073}(141,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{121}{126}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{65}{126}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) |
\(\chi_{1073}(152,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{126}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{89}{126}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) |
\(\chi_{1073}(169,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{126}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{43}{126}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) |
\(\chi_{1073}(210,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{126}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{103}{126}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) |
\(\chi_{1073}(226,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{126}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{125}{126}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) |
\(\chi_{1073}(252,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{101}{126}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) |
\(\chi_{1073}(284,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{125}{126}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{13}{126}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) |
\(\chi_{1073}(326,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{126}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{47}{126}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) |
\(\chi_{1073}(373,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{126}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) |
\(\chi_{1073}(400,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{126}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{83}{126}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) |
\(\chi_{1073}(484,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{126}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{59}{126}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) |
\(\chi_{1073}(509,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{126}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{109}{126}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) |
\(\chi_{1073}(546,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) |
\(\chi_{1073}(558,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{5}{126}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) |
\(\chi_{1073}(576,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{79}{126}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) |
\(\chi_{1073}(596,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{126}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) |
\(\chi_{1073}(632,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{55}{126}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{41}{126}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) |
\(\chi_{1073}(633,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{126}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) |
\(\chi_{1073}(654,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{67}{126}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) |
\(\chi_{1073}(687,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{126}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{115}{126}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) |
\(\chi_{1073}(691,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) |
\(\chi_{1073}(761,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{126}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{61}{126}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) |
\(\chi_{1073}(770,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{126}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{11}{126}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) |
\(\chi_{1073}(807,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) |
\(\chi_{1073}(835,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{126}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{97}{126}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) |