from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3020, base_ring=CyclotomicField(50))
M = H._module
chi = DirichletCharacter(H, M([25,25,49]))
chi.galois_orbit()
[g,chi] = znchar(Mod(79,3020))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(3020\) | |
Conductor: | \(3020\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(50\) | 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: | \(\Q(\zeta_{25})\) |
Fixed field: | Number field defined by a degree 50 polynomial |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{3020}(79,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{33}{50}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{50}\right)\) |
\(\chi_{3020}(179,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{17}{50}\right)\) |
\(\chi_{3020}(359,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{33}{50}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{50}\right)\) |
\(\chi_{3020}(479,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{21}{50}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{41}{50}\right)\) |
\(\chi_{3020}(779,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{21}{50}\right)\) |
\(\chi_{3020}(959,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{33}{50}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{49}{50}\right)\) |
\(\chi_{3020}(979,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{27}{50}\right)\) |
\(\chi_{3020}(1179,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{21}{50}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{50}\right)\) |
\(\chi_{3020}(1199,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{47}{50}\right)\) |
\(\chi_{3020}(1339,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{21}{50}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{37}{50}\right)\) |
\(\chi_{3020}(1419,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{23}{50}\right)\) |
\(\chi_{3020}(1839,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{33}{50}\right)\) |
\(\chi_{3020}(1879,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{50}\right)\) |
\(\chi_{3020}(1919,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{29}{50}\right)\) |
\(\chi_{3020}(2179,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{33}{50}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{43}{50}\right)\) |
\(\chi_{3020}(2419,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{11}{50}\right)\) |
\(\chi_{3020}(2499,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{21}{50}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{13}{50}\right)\) |
\(\chi_{3020}(2759,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{31}{50}\right)\) |
\(\chi_{3020}(2819,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{39}{50}\right)\) |
\(\chi_{3020}(2939,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{19}{50}\right)\) |