from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3483, base_ring=CyclotomicField(378))
M = H._module
chi = DirichletCharacter(H, M([175,333]))
chi.galois_orbit()
[g,chi] = znchar(Mod(20,3483))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(3483\) | |
| Conductor: | \(3483\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(378\) | 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: | $\Q(\zeta_{189})$ |
| Fixed field: | Number field defined by a degree 378 polynomial (not computed) |
First 31 of 108 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{3483}(20,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{189}\right)\) | \(e\left(\frac{94}{189}\right)\) | \(e\left(\frac{127}{189}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{169}{378}\right)\) | \(e\left(\frac{169}{189}\right)\) | \(e\left(\frac{185}{378}\right)\) | \(e\left(\frac{188}{189}\right)\) |
| \(\chi_{3483}(77,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{189}\right)\) | \(e\left(\frac{122}{189}\right)\) | \(e\left(\frac{8}{189}\right)\) | \(e\left(\frac{41}{54}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{155}{378}\right)\) | \(e\left(\frac{155}{189}\right)\) | \(e\left(\frac{31}{378}\right)\) | \(e\left(\frac{55}{189}\right)\) |
| \(\chi_{3483}(104,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{160}{189}\right)\) | \(e\left(\frac{131}{189}\right)\) | \(e\left(\frac{179}{189}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{137}{378}\right)\) | \(e\left(\frac{137}{189}\right)\) | \(e\left(\frac{103}{378}\right)\) | \(e\left(\frac{73}{189}\right)\) |
| \(\chi_{3483}(119,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{158}{189}\right)\) | \(e\left(\frac{127}{189}\right)\) | \(e\left(\frac{61}{189}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{355}{378}\right)\) | \(e\left(\frac{166}{189}\right)\) | \(e\left(\frac{71}{378}\right)\) | \(e\left(\frac{65}{189}\right)\) |
| \(\chi_{3483}(158,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{169}{189}\right)\) | \(e\left(\frac{149}{189}\right)\) | \(e\left(\frac{143}{189}\right)\) | \(e\left(\frac{41}{54}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{101}{378}\right)\) | \(e\left(\frac{101}{189}\right)\) | \(e\left(\frac{247}{378}\right)\) | \(e\left(\frac{109}{189}\right)\) |
| \(\chi_{3483}(191,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{170}{189}\right)\) | \(e\left(\frac{151}{189}\right)\) | \(e\left(\frac{13}{189}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{181}{378}\right)\) | \(e\left(\frac{181}{189}\right)\) | \(e\left(\frac{263}{378}\right)\) | \(e\left(\frac{113}{189}\right)\) |
| \(\chi_{3483}(218,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{188}{189}\right)\) | \(e\left(\frac{187}{189}\right)\) | \(e\left(\frac{130}{189}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{109}{378}\right)\) | \(e\left(\frac{109}{189}\right)\) | \(e\left(\frac{173}{378}\right)\) | \(e\left(\frac{185}{189}\right)\) |
| \(\chi_{3483}(227,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{176}{189}\right)\) | \(e\left(\frac{163}{189}\right)\) | \(e\left(\frac{178}{189}\right)\) | \(e\left(\frac{1}{54}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{283}{378}\right)\) | \(e\left(\frac{94}{189}\right)\) | \(e\left(\frac{359}{378}\right)\) | \(e\left(\frac{137}{189}\right)\) |
| \(\chi_{3483}(263,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{189}\right)\) | \(e\left(\frac{13}{189}\right)\) | \(e\left(\frac{100}{189}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{331}{378}\right)\) | \(e\left(\frac{142}{189}\right)\) | \(e\left(\frac{293}{378}\right)\) | \(e\left(\frac{26}{189}\right)\) |
| \(\chi_{3483}(284,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{172}{189}\right)\) | \(e\left(\frac{155}{189}\right)\) | \(e\left(\frac{131}{189}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{341}{378}\right)\) | \(e\left(\frac{152}{189}\right)\) | \(e\left(\frac{295}{378}\right)\) | \(e\left(\frac{121}{189}\right)\) |
| \(\chi_{3483}(329,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{121}{189}\right)\) | \(e\left(\frac{53}{189}\right)\) | \(e\left(\frac{146}{189}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{41}{378}\right)\) | \(e\left(\frac{41}{189}\right)\) | \(e\left(\frac{235}{378}\right)\) | \(e\left(\frac{106}{189}\right)\) |
| \(\chi_{3483}(374,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{178}{189}\right)\) | \(e\left(\frac{167}{189}\right)\) | \(e\left(\frac{107}{189}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{65}{378}\right)\) | \(e\left(\frac{65}{189}\right)\) | \(e\left(\frac{13}{378}\right)\) | \(e\left(\frac{145}{189}\right)\) |
| \(\chi_{3483}(407,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{152}{189}\right)\) | \(e\left(\frac{115}{189}\right)\) | \(e\left(\frac{85}{189}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{253}{378}\right)\) | \(e\left(\frac{64}{189}\right)\) | \(e\left(\frac{353}{378}\right)\) | \(e\left(\frac{41}{189}\right)\) |
| \(\chi_{3483}(464,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{189}\right)\) | \(e\left(\frac{17}{189}\right)\) | \(e\left(\frac{29}{189}\right)\) | \(e\left(\frac{17}{54}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{113}{378}\right)\) | \(e\left(\frac{113}{189}\right)\) | \(e\left(\frac{325}{378}\right)\) | \(e\left(\frac{34}{189}\right)\) |
| \(\chi_{3483}(491,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{189}\right)\) | \(e\left(\frac{26}{189}\right)\) | \(e\left(\frac{11}{189}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{95}{378}\right)\) | \(e\left(\frac{95}{189}\right)\) | \(e\left(\frac{19}{378}\right)\) | \(e\left(\frac{52}{189}\right)\) |
| \(\chi_{3483}(506,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{74}{189}\right)\) | \(e\left(\frac{148}{189}\right)\) | \(e\left(\frac{19}{189}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{61}{378}\right)\) | \(e\left(\frac{61}{189}\right)\) | \(e\left(\frac{239}{378}\right)\) | \(e\left(\frac{107}{189}\right)\) |
| \(\chi_{3483}(545,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{22}{189}\right)\) | \(e\left(\frac{44}{189}\right)\) | \(e\left(\frac{164}{189}\right)\) | \(e\left(\frac{17}{54}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{59}{378}\right)\) | \(e\left(\frac{59}{189}\right)\) | \(e\left(\frac{163}{378}\right)\) | \(e\left(\frac{88}{189}\right)\) |
| \(\chi_{3483}(578,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{86}{189}\right)\) | \(e\left(\frac{172}{189}\right)\) | \(e\left(\frac{160}{189}\right)\) | \(e\left(\frac{37}{54}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{265}{378}\right)\) | \(e\left(\frac{76}{189}\right)\) | \(e\left(\frac{53}{378}\right)\) | \(e\left(\frac{155}{189}\right)\) |
| \(\chi_{3483}(605,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{104}{189}\right)\) | \(e\left(\frac{19}{189}\right)\) | \(e\left(\frac{88}{189}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{193}{378}\right)\) | \(e\left(\frac{4}{189}\right)\) | \(e\left(\frac{341}{378}\right)\) | \(e\left(\frac{38}{189}\right)\) |
| \(\chi_{3483}(614,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{92}{189}\right)\) | \(e\left(\frac{184}{189}\right)\) | \(e\left(\frac{136}{189}\right)\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{367}{378}\right)\) | \(e\left(\frac{178}{189}\right)\) | \(e\left(\frac{149}{378}\right)\) | \(e\left(\frac{179}{189}\right)\) |
| \(\chi_{3483}(650,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{189}\right)\) | \(e\left(\frac{34}{189}\right)\) | \(e\left(\frac{58}{189}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{37}{378}\right)\) | \(e\left(\frac{37}{189}\right)\) | \(e\left(\frac{83}{378}\right)\) | \(e\left(\frac{68}{189}\right)\) |
| \(\chi_{3483}(671,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{189}\right)\) | \(e\left(\frac{50}{189}\right)\) | \(e\left(\frac{152}{189}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{299}{378}\right)\) | \(e\left(\frac{110}{189}\right)\) | \(e\left(\frac{211}{378}\right)\) | \(e\left(\frac{100}{189}\right)\) |
| \(\chi_{3483}(716,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{163}{189}\right)\) | \(e\left(\frac{137}{189}\right)\) | \(e\left(\frac{167}{189}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{377}{378}\right)\) | \(e\left(\frac{188}{189}\right)\) | \(e\left(\frac{151}{378}\right)\) | \(e\left(\frac{85}{189}\right)\) |
| \(\chi_{3483}(761,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{189}\right)\) | \(e\left(\frac{62}{189}\right)\) | \(e\left(\frac{128}{189}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{23}{378}\right)\) | \(e\left(\frac{23}{189}\right)\) | \(e\left(\frac{307}{378}\right)\) | \(e\left(\frac{124}{189}\right)\) |
| \(\chi_{3483}(794,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{68}{189}\right)\) | \(e\left(\frac{136}{189}\right)\) | \(e\left(\frac{43}{189}\right)\) | \(e\left(\frac{1}{54}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{337}{378}\right)\) | \(e\left(\frac{148}{189}\right)\) | \(e\left(\frac{143}{378}\right)\) | \(e\left(\frac{83}{189}\right)\) |
| \(\chi_{3483}(851,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{145}{189}\right)\) | \(e\left(\frac{101}{189}\right)\) | \(e\left(\frac{50}{189}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{71}{378}\right)\) | \(e\left(\frac{71}{189}\right)\) | \(e\left(\frac{241}{378}\right)\) | \(e\left(\frac{13}{189}\right)\) |
| \(\chi_{3483}(878,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{55}{189}\right)\) | \(e\left(\frac{110}{189}\right)\) | \(e\left(\frac{32}{189}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{53}{378}\right)\) | \(e\left(\frac{53}{189}\right)\) | \(e\left(\frac{313}{378}\right)\) | \(e\left(\frac{31}{189}\right)\) |
| \(\chi_{3483}(893,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{179}{189}\right)\) | \(e\left(\frac{169}{189}\right)\) | \(e\left(\frac{166}{189}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{145}{378}\right)\) | \(e\left(\frac{145}{189}\right)\) | \(e\left(\frac{29}{378}\right)\) | \(e\left(\frac{149}{189}\right)\) |
| \(\chi_{3483}(932,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{64}{189}\right)\) | \(e\left(\frac{128}{189}\right)\) | \(e\left(\frac{185}{189}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{17}{378}\right)\) | \(e\left(\frac{17}{189}\right)\) | \(e\left(\frac{79}{378}\right)\) | \(e\left(\frac{67}{189}\right)\) |
| \(\chi_{3483}(965,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{189}\right)\) | \(e\left(\frac{4}{189}\right)\) | \(e\left(\frac{118}{189}\right)\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{349}{378}\right)\) | \(e\left(\frac{160}{189}\right)\) | \(e\left(\frac{221}{378}\right)\) | \(e\left(\frac{8}{189}\right)\) |
| \(\chi_{3483}(992,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{20}{189}\right)\) | \(e\left(\frac{40}{189}\right)\) | \(e\left(\frac{46}{189}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{277}{378}\right)\) | \(e\left(\frac{88}{189}\right)\) | \(e\left(\frac{131}{378}\right)\) | \(e\left(\frac{80}{189}\right)\) |