from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25920, base_ring=CyclotomicField(432))
M = H._module
chi = DirichletCharacter(H, M([216,27,368,108]))
chi.galois_orbit()
[g,chi] = znchar(Mod(187,25920))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(25920\) | |
| Conductor: | \(25920\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(432\) | 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: | $\Q(\zeta_{432})$ |
| Fixed field: | Number field defined by a degree 432 polynomial (not computed) |
First 31 of 144 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{25920}(187,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{216}\right)\) | \(e\left(\frac{383}{432}\right)\) | \(e\left(\frac{217}{432}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{47}{144}\right)\) | \(e\left(\frac{107}{216}\right)\) | \(e\left(\frac{305}{432}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(e\left(\frac{85}{144}\right)\) | \(e\left(\frac{5}{216}\right)\) |
| \(\chi_{25920}(403,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{199}{216}\right)\) | \(e\left(\frac{185}{432}\right)\) | \(e\left(\frac{415}{432}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{137}{144}\right)\) | \(e\left(\frac{125}{216}\right)\) | \(e\left(\frac{215}{432}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{67}{144}\right)\) | \(e\left(\frac{131}{216}\right)\) |
| \(\chi_{25920}(427,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{216}\right)\) | \(e\left(\frac{403}{432}\right)\) | \(e\left(\frac{5}{432}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{19}{144}\right)\) | \(e\left(\frac{103}{216}\right)\) | \(e\left(\frac{13}{432}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{65}{144}\right)\) | \(e\left(\frac{25}{216}\right)\) |
| \(\chi_{25920}(643,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{203}{216}\right)\) | \(e\left(\frac{205}{432}\right)\) | \(e\left(\frac{203}{432}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{109}{144}\right)\) | \(e\left(\frac{121}{216}\right)\) | \(e\left(\frac{355}{432}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{47}{144}\right)\) | \(e\left(\frac{151}{216}\right)\) |
| \(\chi_{25920}(907,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{216}\right)\) | \(e\left(\frac{11}{432}\right)\) | \(e\left(\frac{13}{432}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{107}{144}\right)\) | \(e\left(\frac{95}{216}\right)\) | \(e\left(\frac{293}{432}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{25}{144}\right)\) | \(e\left(\frac{65}{216}\right)\) |
| \(\chi_{25920}(1123,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{211}{216}\right)\) | \(e\left(\frac{245}{432}\right)\) | \(e\left(\frac{211}{432}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{53}{144}\right)\) | \(e\left(\frac{113}{216}\right)\) | \(e\left(\frac{203}{432}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{7}{144}\right)\) | \(e\left(\frac{191}{216}\right)\) |
| \(\chi_{25920}(1147,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{161}{216}\right)\) | \(e\left(\frac{319}{432}\right)\) | \(e\left(\frac{377}{432}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{79}{144}\right)\) | \(e\left(\frac{163}{216}\right)\) | \(e\left(\frac{289}{432}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{5}{144}\right)\) | \(e\left(\frac{157}{216}\right)\) |
| \(\chi_{25920}(1363,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{143}{216}\right)\) | \(e\left(\frac{121}{432}\right)\) | \(e\left(\frac{143}{432}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{25}{144}\right)\) | \(e\left(\frac{181}{216}\right)\) | \(e\left(\frac{199}{432}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{131}{144}\right)\) | \(e\left(\frac{67}{216}\right)\) |
| \(\chi_{25920}(1627,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{216}\right)\) | \(e\left(\frac{71}{432}\right)\) | \(e\left(\frac{241}{432}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{23}{144}\right)\) | \(e\left(\frac{83}{216}\right)\) | \(e\left(\frac{281}{432}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{109}{144}\right)\) | \(e\left(\frac{125}{216}\right)\) |
| \(\chi_{25920}(1843,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{216}\right)\) | \(e\left(\frac{305}{432}\right)\) | \(e\left(\frac{7}{432}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{113}{144}\right)\) | \(e\left(\frac{101}{216}\right)\) | \(e\left(\frac{191}{432}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{91}{144}\right)\) | \(e\left(\frac{35}{216}\right)\) |
| \(\chi_{25920}(1867,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{216}\right)\) | \(e\left(\frac{235}{432}\right)\) | \(e\left(\frac{317}{432}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{139}{144}\right)\) | \(e\left(\frac{7}{216}\right)\) | \(e\left(\frac{133}{432}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{89}{144}\right)\) | \(e\left(\frac{73}{216}\right)\) |
| \(\chi_{25920}(2083,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{216}\right)\) | \(e\left(\frac{37}{432}\right)\) | \(e\left(\frac{83}{432}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{85}{144}\right)\) | \(e\left(\frac{25}{216}\right)\) | \(e\left(\frac{43}{432}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{71}{144}\right)\) | \(e\left(\frac{199}{216}\right)\) |
| \(\chi_{25920}(2347,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{216}\right)\) | \(e\left(\frac{131}{432}\right)\) | \(e\left(\frac{37}{432}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{83}{144}\right)\) | \(e\left(\frac{71}{216}\right)\) | \(e\left(\frac{269}{432}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{49}{144}\right)\) | \(e\left(\frac{185}{216}\right)\) |
| \(\chi_{25920}(2563,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{216}\right)\) | \(e\left(\frac{365}{432}\right)\) | \(e\left(\frac{235}{432}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{29}{144}\right)\) | \(e\left(\frac{89}{216}\right)\) | \(e\left(\frac{179}{432}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{31}{144}\right)\) | \(e\left(\frac{95}{216}\right)\) |
| \(\chi_{25920}(2587,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{216}\right)\) | \(e\left(\frac{151}{432}\right)\) | \(e\left(\frac{257}{432}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{55}{144}\right)\) | \(e\left(\frac{67}{216}\right)\) | \(e\left(\frac{409}{432}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{29}{144}\right)\) | \(e\left(\frac{205}{216}\right)\) |
| \(\chi_{25920}(2803,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{216}\right)\) | \(e\left(\frac{385}{432}\right)\) | \(e\left(\frac{23}{432}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{144}\right)\) | \(e\left(\frac{85}{216}\right)\) | \(e\left(\frac{319}{432}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{11}{144}\right)\) | \(e\left(\frac{115}{216}\right)\) |
| \(\chi_{25920}(3067,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{216}\right)\) | \(e\left(\frac{191}{432}\right)\) | \(e\left(\frac{265}{432}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{143}{144}\right)\) | \(e\left(\frac{59}{216}\right)\) | \(e\left(\frac{257}{432}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{133}{144}\right)\) | \(e\left(\frac{29}{216}\right)\) |
| \(\chi_{25920}(3283,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{216}\right)\) | \(e\left(\frac{425}{432}\right)\) | \(e\left(\frac{31}{432}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{89}{144}\right)\) | \(e\left(\frac{77}{216}\right)\) | \(e\left(\frac{167}{432}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{115}{144}\right)\) | \(e\left(\frac{155}{216}\right)\) |
| \(\chi_{25920}(3307,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{197}{216}\right)\) | \(e\left(\frac{67}{432}\right)\) | \(e\left(\frac{197}{432}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{115}{144}\right)\) | \(e\left(\frac{127}{216}\right)\) | \(e\left(\frac{253}{432}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{113}{144}\right)\) | \(e\left(\frac{121}{216}\right)\) |
| \(\chi_{25920}(3523,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{179}{216}\right)\) | \(e\left(\frac{301}{432}\right)\) | \(e\left(\frac{395}{432}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{61}{144}\right)\) | \(e\left(\frac{145}{216}\right)\) | \(e\left(\frac{163}{432}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{95}{144}\right)\) | \(e\left(\frac{31}{216}\right)\) |
| \(\chi_{25920}(3787,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{216}\right)\) | \(e\left(\frac{251}{432}\right)\) | \(e\left(\frac{61}{432}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{59}{144}\right)\) | \(e\left(\frac{47}{216}\right)\) | \(e\left(\frac{245}{432}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{73}{144}\right)\) | \(e\left(\frac{89}{216}\right)\) |
| \(\chi_{25920}(4003,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{216}\right)\) | \(e\left(\frac{53}{432}\right)\) | \(e\left(\frac{259}{432}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{5}{144}\right)\) | \(e\left(\frac{65}{216}\right)\) | \(e\left(\frac{155}{432}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{55}{144}\right)\) | \(e\left(\frac{215}{216}\right)\) |
| \(\chi_{25920}(4027,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{137}{216}\right)\) | \(e\left(\frac{415}{432}\right)\) | \(e\left(\frac{137}{432}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{31}{144}\right)\) | \(e\left(\frac{187}{216}\right)\) | \(e\left(\frac{97}{432}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{53}{144}\right)\) | \(e\left(\frac{37}{216}\right)\) |
| \(\chi_{25920}(4243,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{216}\right)\) | \(e\left(\frac{217}{432}\right)\) | \(e\left(\frac{335}{432}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{121}{144}\right)\) | \(e\left(\frac{205}{216}\right)\) | \(e\left(\frac{7}{432}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{35}{144}\right)\) | \(e\left(\frac{163}{216}\right)\) |
| \(\chi_{25920}(4507,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{216}\right)\) | \(e\left(\frac{311}{432}\right)\) | \(e\left(\frac{289}{432}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{119}{144}\right)\) | \(e\left(\frac{35}{216}\right)\) | \(e\left(\frac{233}{432}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{13}{144}\right)\) | \(e\left(\frac{149}{216}\right)\) |
| \(\chi_{25920}(4723,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{55}{216}\right)\) | \(e\left(\frac{113}{432}\right)\) | \(e\left(\frac{55}{432}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{65}{144}\right)\) | \(e\left(\frac{53}{216}\right)\) | \(e\left(\frac{143}{432}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(e\left(\frac{139}{144}\right)\) | \(e\left(\frac{59}{216}\right)\) |
| \(\chi_{25920}(4747,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{77}{216}\right)\) | \(e\left(\frac{331}{432}\right)\) | \(e\left(\frac{77}{432}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{91}{144}\right)\) | \(e\left(\frac{31}{216}\right)\) | \(e\left(\frac{373}{432}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{137}{144}\right)\) | \(e\left(\frac{169}{216}\right)\) |
| \(\chi_{25920}(4963,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{216}\right)\) | \(e\left(\frac{133}{432}\right)\) | \(e\left(\frac{275}{432}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{37}{144}\right)\) | \(e\left(\frac{49}{216}\right)\) | \(e\left(\frac{283}{432}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{119}{144}\right)\) | \(e\left(\frac{79}{216}\right)\) |
| \(\chi_{25920}(5227,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{85}{216}\right)\) | \(e\left(\frac{371}{432}\right)\) | \(e\left(\frac{85}{432}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{35}{144}\right)\) | \(e\left(\frac{23}{216}\right)\) | \(e\left(\frac{221}{432}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{97}{144}\right)\) | \(e\left(\frac{209}{216}\right)\) |
| \(\chi_{25920}(5443,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{216}\right)\) | \(e\left(\frac{173}{432}\right)\) | \(e\left(\frac{283}{432}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{125}{144}\right)\) | \(e\left(\frac{41}{216}\right)\) | \(e\left(\frac{131}{432}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{79}{144}\right)\) | \(e\left(\frac{119}{216}\right)\) |
| \(\chi_{25920}(5467,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{216}\right)\) | \(e\left(\frac{247}{432}\right)\) | \(e\left(\frac{17}{432}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{7}{144}\right)\) | \(e\left(\frac{91}{216}\right)\) | \(e\left(\frac{217}{432}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{77}{144}\right)\) | \(e\left(\frac{85}{216}\right)\) |