from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(120))
M = H._module
chi = DirichletCharacter(H, M([0,47]))
chi.galois_orbit()
[g,chi] = znchar(Mod(651,6025))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(6025\) | |
| Conductor: | \(241\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 241.s | 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: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
First 31 of 32 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6025}(651,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(i\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{49}{120}\right)\) |
| \(\chi_{6025}(726,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(i\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{77}{120}\right)\) |
| \(\chi_{6025}(776,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(i\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{29}{120}\right)\) |
| \(\chi_{6025}(976,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(-i\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{7}{120}\right)\) |
| \(\chi_{6025}(1176,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(-i\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{79}{120}\right)\) |
| \(\chi_{6025}(1401,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(i\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{97}{120}\right)\) |
| \(\chi_{6025}(1426,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(i\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{113}{120}\right)\) |
| \(\chi_{6025}(1526,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(-i\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{103}{120}\right)\) |
| \(\chi_{6025}(1851,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(-i\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{71}{120}\right)\) |
| \(\chi_{6025}(2151,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(-i\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{119}{120}\right)\) |
| \(\chi_{6025}(2351,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(i\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{73}{120}\right)\) |
| \(\chi_{6025}(2576,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(-i\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{23}{120}\right)\) |
| \(\chi_{6025}(2601,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(-i\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{91}{120}\right)\) |
| \(\chi_{6025}(2701,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(-i\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{31}{120}\right)\) |
| \(\chi_{6025}(2726,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(-i\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{83}{120}\right)\) |
| \(\chi_{6025}(2951,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(i\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{13}{120}\right)\) |
| \(\chi_{6025}(3151,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(-i\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{59}{120}\right)\) |
| \(\chi_{6025}(3451,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(-i\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{11}{120}\right)\) |
| \(\chi_{6025}(3776,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(-i\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{43}{120}\right)\) |
| \(\chi_{6025}(3876,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(i\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{53}{120}\right)\) |
| \(\chi_{6025}(3901,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(i\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{37}{120}\right)\) |
| \(\chi_{6025}(4126,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(-i\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{19}{120}\right)\) |
| \(\chi_{6025}(4326,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(-i\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{67}{120}\right)\) |
| \(\chi_{6025}(4526,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(i\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{89}{120}\right)\) |
| \(\chi_{6025}(4576,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(i\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{17}{120}\right)\) |
| \(\chi_{6025}(4651,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(i\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{109}{120}\right)\) |
| \(\chi_{6025}(5351,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(-i\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{47}{120}\right)\) |
| \(\chi_{6025}(5476,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(i\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{1}{120}\right)\) |
| \(\chi_{6025}(5651,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(i\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{41}{120}\right)\) |
| \(\chi_{6025}(5676,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(i\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{101}{120}\right)\) |
| \(\chi_{6025}(5851,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(i\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{61}{120}\right)\) |