from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3483, base_ring=CyclotomicField(126))
M = H._module
chi = DirichletCharacter(H, M([28,102]))
chi.galois_orbit()
[g,chi] = znchar(Mod(289,3483))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(3483\) | |
| Conductor: | \(1161\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 1161.ca | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
First 31 of 36 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{3483}(289,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) |
| \(\chi_{3483}(361,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{52}{63}\right)\) |
| \(\chi_{3483}(397,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{59}{63}\right)\) |
| \(\chi_{3483}(640,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) |
| \(\chi_{3483}(658,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{4}{63}\right)\) |
| \(\chi_{3483}(874,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{55}{63}\right)\) |
| \(\chi_{3483}(883,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) |
| \(\chi_{3483}(928,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) |
| \(\chi_{3483}(955,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{37}{63}\right)\) |
| \(\chi_{3483}(1072,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{8}{63}\right)\) |
| \(\chi_{3483}(1090,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) |
| \(\chi_{3483}(1099,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{47}{63}\right)\) |
| \(\chi_{3483}(1450,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{41}{63}\right)\) |
| \(\chi_{3483}(1522,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{10}{63}\right)\) |
| \(\chi_{3483}(1558,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{17}{63}\right)\) |
| \(\chi_{3483}(1801,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{53}{63}\right)\) |
| \(\chi_{3483}(1819,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) |
| \(\chi_{3483}(2035,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{13}{63}\right)\) |
| \(\chi_{3483}(2044,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{44}{63}\right)\) |
| \(\chi_{3483}(2089,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) |
| \(\chi_{3483}(2116,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{58}{63}\right)\) |
| \(\chi_{3483}(2233,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) |
| \(\chi_{3483}(2251,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{19}{63}\right)\) |
| \(\chi_{3483}(2260,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{5}{63}\right)\) |
| \(\chi_{3483}(2611,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) |
| \(\chi_{3483}(2683,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) |
| \(\chi_{3483}(2719,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) |
| \(\chi_{3483}(2962,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{11}{63}\right)\) |
| \(\chi_{3483}(2980,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{46}{63}\right)\) |
| \(\chi_{3483}(3196,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{34}{63}\right)\) |
| \(\chi_{3483}(3205,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{2}{63}\right)\) |