from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9450, base_ring=CyclotomicField(90))
M = H._module
chi = DirichletCharacter(H, M([35,9,15]))
chi.galois_orbit()
[g,chi] = znchar(Mod(479,9450))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(9450\) | |
| Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 4725.gw | 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: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Characters in Galois orbit
| Character | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{9450}(479,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{1}{18}\right)\) |
| \(\chi_{9450}(509,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{17}{18}\right)\) |
| \(\chi_{9450}(1109,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{13}{18}\right)\) |
| \(\chi_{9450}(1139,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{11}{18}\right)\) |
| \(\chi_{9450}(1739,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{7}{18}\right)\) |
| \(\chi_{9450}(1769,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{5}{18}\right)\) |
| \(\chi_{9450}(2369,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{1}{18}\right)\) |
| \(\chi_{9450}(3029,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{11}{18}\right)\) |
| \(\chi_{9450}(3629,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{7}{18}\right)\) |
| \(\chi_{9450}(3659,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{5}{18}\right)\) |
| \(\chi_{9450}(4259,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{1}{18}\right)\) |
| \(\chi_{9450}(4289,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{17}{18}\right)\) |
| \(\chi_{9450}(4889,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{13}{18}\right)\) |
| \(\chi_{9450}(4919,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{11}{18}\right)\) |
| \(\chi_{9450}(5519,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{7}{18}\right)\) |
| \(\chi_{9450}(6179,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{17}{18}\right)\) |
| \(\chi_{9450}(6779,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{13}{18}\right)\) |
| \(\chi_{9450}(6809,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{11}{18}\right)\) |
| \(\chi_{9450}(7409,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{7}{18}\right)\) |
| \(\chi_{9450}(7439,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{5}{18}\right)\) |
| \(\chi_{9450}(8039,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{1}{18}\right)\) |
| \(\chi_{9450}(8069,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{17}{18}\right)\) |
| \(\chi_{9450}(8669,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{13}{18}\right)\) |
| \(\chi_{9450}(9329,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{5}{18}\right)\) |