from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3895, base_ring=CyclotomicField(360))
M = H._module
chi = DirichletCharacter(H, M([270,100,279]))
chi.galois_orbit()
[g,chi] = znchar(Mod(13,3895))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(3895\) | |
| Conductor: | \(3895\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(360\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{360})$ |
| Fixed field: | Number field defined by a degree 360 polynomial (not computed) |
First 31 of 96 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{3895}(13,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{35}{72}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{239}{360}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{239}{360}\right)\) |
| \(\chi_{3895}(22,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{1}{72}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{301}{360}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{301}{360}\right)\) |
| \(\chi_{3895}(48,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{11}{72}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{71}{360}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{71}{360}\right)\) |
| \(\chi_{3895}(53,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{23}{72}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{83}{360}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{83}{360}\right)\) |
| \(\chi_{3895}(67,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{29}{72}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{233}{360}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{233}{360}\right)\) |
| \(\chi_{3895}(97,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{25}{72}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{253}{360}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{253}{360}\right)\) |
| \(\chi_{3895}(117,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{1}{72}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{229}{360}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{229}{360}\right)\) |
| \(\chi_{3895}(147,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{49}{72}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{277}{360}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{277}{360}\right)\) |
| \(\chi_{3895}(193,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{103}{360}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{103}{360}\right)\) |
| \(\chi_{3895}(222,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{257}{360}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{257}{360}\right)\) |
| \(\chi_{3895}(298,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{71}{72}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{347}{360}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{347}{360}\right)\) |
| \(\chi_{3895}(352,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{197}{360}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{197}{360}\right)\) |
| \(\chi_{3895}(432,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{49}{72}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{61}{360}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{61}{360}\right)\) |
| \(\chi_{3895}(458,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{271}{360}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{271}{360}\right)\) |
| \(\chi_{3895}(477,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{73}{360}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{73}{360}\right)\) |
| \(\chi_{3895}(507,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{293}{360}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{293}{360}\right)\) |
| \(\chi_{3895}(527,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{49}{72}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{349}{360}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{349}{360}\right)\) |
| \(\chi_{3895}(603,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{223}{360}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{223}{360}\right)\) |
| \(\chi_{3895}(637,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{341}{360}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{341}{360}\right)\) |
| \(\chi_{3895}(668,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{283}{360}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{283}{360}\right)\) |
| \(\chi_{3895}(732,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{269}{360}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{269}{360}\right)\) |
| \(\chi_{3895}(762,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{25}{72}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{37}{360}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{37}{360}\right)\) |
| \(\chi_{3895}(808,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{11}{72}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{143}{360}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{143}{360}\right)\) |
| \(\chi_{3895}(813,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{23}{72}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{11}{360}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{11}{360}\right)\) |
| \(\chi_{3895}(868,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{35}{72}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{311}{360}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{311}{360}\right)\) |
| \(\chi_{3895}(887,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{113}{360}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{113}{360}\right)\) |
| \(\chi_{3895}(1047,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{25}{72}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{181}{360}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{181}{360}\right)\) |
| \(\chi_{3895}(1078,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{43}{360}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{43}{360}\right)\) |
| \(\chi_{3895}(1142,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{25}{72}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{109}{360}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{109}{360}\right)\) |
| \(\chi_{3895}(1172,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{77}{360}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{77}{360}\right)\) |
| \(\chi_{3895}(1218,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{343}{360}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{343}{360}\right)\) |