from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27040, base_ring=CyclotomicField(104))
M = H._module
chi = DirichletCharacter(H, M([0,91,78,58]))
chi.galois_orbit()
[g,chi] = znchar(Mod(333,27040))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(27040\) | |
| Conductor: | \(27040\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(104\) | 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: | $\Q(\zeta_{104})$ |
| Fixed field: | Number field defined by a degree 104 polynomial (not computed) |
First 31 of 48 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{27040}(333,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{104}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{85}{104}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{21}{104}\right)\) | \(1\) | \(e\left(\frac{9}{104}\right)\) | \(e\left(\frac{45}{104}\right)\) |
| \(\chi_{27040}(837,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{104}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{11}{104}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{59}{104}\right)\) | \(1\) | \(e\left(\frac{55}{104}\right)\) | \(e\left(\frac{67}{104}\right)\) |
| \(\chi_{27040}(1373,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{104}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{41}{104}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{97}{104}\right)\) | \(1\) | \(e\left(\frac{101}{104}\right)\) | \(e\left(\frac{89}{104}\right)\) |
| \(\chi_{27040}(1877,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{57}{104}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{55}{104}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{87}{104}\right)\) | \(1\) | \(e\left(\frac{67}{104}\right)\) | \(e\left(\frac{23}{104}\right)\) |
| \(\chi_{27040}(2413,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{99}{104}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{101}{104}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{69}{104}\right)\) | \(1\) | \(e\left(\frac{89}{104}\right)\) | \(e\left(\frac{29}{104}\right)\) |
| \(\chi_{27040}(2917,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{104}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{99}{104}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{11}{104}\right)\) | \(1\) | \(e\left(\frac{79}{104}\right)\) | \(e\left(\frac{83}{104}\right)\) |
| \(\chi_{27040}(3453,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{95}{104}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{57}{104}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{41}{104}\right)\) | \(1\) | \(e\left(\frac{77}{104}\right)\) | \(e\left(\frac{73}{104}\right)\) |
| \(\chi_{27040}(4997,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{69}{104}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{83}{104}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{67}{104}\right)\) | \(1\) | \(e\left(\frac{103}{104}\right)\) | \(e\left(\frac{99}{104}\right)\) |
| \(\chi_{27040}(5533,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{87}{104}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{73}{104}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{89}{104}\right)\) | \(1\) | \(e\left(\frac{53}{104}\right)\) | \(e\left(\frac{57}{104}\right)\) |
| \(\chi_{27040}(6037,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{104}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{23}{104}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{95}{104}\right)\) | \(1\) | \(e\left(\frac{11}{104}\right)\) | \(e\left(\frac{55}{104}\right)\) |
| \(\chi_{27040}(6573,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{104}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{29}{104}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{61}{104}\right)\) | \(1\) | \(e\left(\frac{41}{104}\right)\) | \(e\left(\frac{101}{104}\right)\) |
| \(\chi_{27040}(7077,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{77}{104}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{67}{104}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{19}{104}\right)\) | \(1\) | \(e\left(\frac{23}{104}\right)\) | \(e\left(\frac{11}{104}\right)\) |
| \(\chi_{27040}(7613,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{104}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{89}{104}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{33}{104}\right)\) | \(1\) | \(e\left(\frac{29}{104}\right)\) | \(e\left(\frac{41}{104}\right)\) |
| \(\chi_{27040}(8117,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{81}{104}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{7}{104}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{47}{104}\right)\) | \(1\) | \(e\left(\frac{35}{104}\right)\) | \(e\left(\frac{71}{104}\right)\) |
| \(\chi_{27040}(8653,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{75}{104}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{45}{104}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{104}\right)\) | \(1\) | \(e\left(\frac{17}{104}\right)\) | \(e\left(\frac{85}{104}\right)\) |
| \(\chi_{27040}(9157,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{85}{104}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{51}{104}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{75}{104}\right)\) | \(1\) | \(e\left(\frac{47}{104}\right)\) | \(e\left(\frac{27}{104}\right)\) |
| \(\chi_{27040}(9693,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{104}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{1}{104}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{81}{104}\right)\) | \(1\) | \(e\left(\frac{5}{104}\right)\) | \(e\left(\frac{25}{104}\right)\) |
| \(\chi_{27040}(10197,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{104}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{95}{104}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{103}{104}\right)\) | \(1\) | \(e\left(\frac{59}{104}\right)\) | \(e\left(\frac{87}{104}\right)\) |
| \(\chi_{27040}(10733,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{104}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{61}{104}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{53}{104}\right)\) | \(1\) | \(e\left(\frac{97}{104}\right)\) | \(e\left(\frac{69}{104}\right)\) |
| \(\chi_{27040}(11237,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{93}{104}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{35}{104}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{27}{104}\right)\) | \(1\) | \(e\left(\frac{71}{104}\right)\) | \(e\left(\frac{43}{104}\right)\) |
| \(\chi_{27040}(11773,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{63}{104}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{17}{104}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{25}{104}\right)\) | \(1\) | \(e\left(\frac{85}{104}\right)\) | \(e\left(\frac{9}{104}\right)\) |
| \(\chi_{27040}(12277,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{104}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{79}{104}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{55}{104}\right)\) | \(1\) | \(e\left(\frac{83}{104}\right)\) | \(e\left(\frac{103}{104}\right)\) |
| \(\chi_{27040}(12813,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{104}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{77}{104}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{101}{104}\right)\) | \(1\) | \(e\left(\frac{73}{104}\right)\) | \(e\left(\frac{53}{104}\right)\) |
| \(\chi_{27040}(13317,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{104}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{19}{104}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{83}{104}\right)\) | \(1\) | \(e\left(\frac{95}{104}\right)\) | \(e\left(\frac{59}{104}\right)\) |
| \(\chi_{27040}(13853,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{55}{104}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{33}{104}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{73}{104}\right)\) | \(1\) | \(e\left(\frac{61}{104}\right)\) | \(e\left(\frac{97}{104}\right)\) |
| \(\chi_{27040}(14357,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{104}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{63}{104}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{104}\right)\) | \(1\) | \(e\left(\frac{3}{104}\right)\) | \(e\left(\frac{15}{104}\right)\) |
| \(\chi_{27040}(14893,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{51}{104}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{93}{104}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{45}{104}\right)\) | \(1\) | \(e\left(\frac{49}{104}\right)\) | \(e\left(\frac{37}{104}\right)\) |
| \(\chi_{27040}(15397,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{104}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{3}{104}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{35}{104}\right)\) | \(1\) | \(e\left(\frac{15}{104}\right)\) | \(e\left(\frac{75}{104}\right)\) |
| \(\chi_{27040}(15933,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{104}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{49}{104}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{17}{104}\right)\) | \(1\) | \(e\left(\frac{37}{104}\right)\) | \(e\left(\frac{81}{104}\right)\) |
| \(\chi_{27040}(16437,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{104}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{47}{104}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{63}{104}\right)\) | \(1\) | \(e\left(\frac{27}{104}\right)\) | \(e\left(\frac{31}{104}\right)\) |
| \(\chi_{27040}(16973,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{104}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{5}{104}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{93}{104}\right)\) | \(1\) | \(e\left(\frac{25}{104}\right)\) | \(e\left(\frac{21}{104}\right)\) |