from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4725, base_ring=CyclotomicField(90))
M = H._module
chi = DirichletCharacter(H, M([65,72,60]))
chi.galois_orbit()
[g,chi] = znchar(Mod(11,4725))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(4725\) | |
Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | 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: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{4725}(11,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{7}{90}\right)\) |
\(\chi_{4725}(86,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{47}{90}\right)\) |
\(\chi_{4725}(641,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{73}{90}\right)\) |
\(\chi_{4725}(716,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{23}{90}\right)\) |
\(\chi_{4725}(956,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{61}{90}\right)\) |
\(\chi_{4725}(1031,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{11}{90}\right)\) |
\(\chi_{4725}(1271,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{49}{90}\right)\) |
\(\chi_{4725}(1346,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{89}{90}\right)\) |
\(\chi_{4725}(1586,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{37}{90}\right)\) |
\(\chi_{4725}(1661,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{77}{90}\right)\) |
\(\chi_{4725}(2216,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{13}{90}\right)\) |
\(\chi_{4725}(2291,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{53}{90}\right)\) |
\(\chi_{4725}(2531,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{1}{90}\right)\) |
\(\chi_{4725}(2606,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{41}{90}\right)\) |
\(\chi_{4725}(2846,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{79}{90}\right)\) |
\(\chi_{4725}(2921,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{29}{90}\right)\) |
\(\chi_{4725}(3161,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{67}{90}\right)\) |
\(\chi_{4725}(3236,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{17}{90}\right)\) |
\(\chi_{4725}(3791,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{43}{90}\right)\) |
\(\chi_{4725}(3866,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{83}{90}\right)\) |
\(\chi_{4725}(4106,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{31}{90}\right)\) |
\(\chi_{4725}(4181,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{71}{90}\right)\) |
\(\chi_{4725}(4421,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{19}{90}\right)\) |
\(\chi_{4725}(4496,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{59}{90}\right)\) |