from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4928, base_ring=CyclotomicField(80))
M = H._module
chi = DirichletCharacter(H, M([0,75,40,8]))
chi.galois_orbit()
[g,chi] = znchar(Mod(13,4928))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(4928\) | |
| Conductor: | \(4928\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | 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: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
First 31 of 32 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{4928}(13,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{27}{80}\right)\) |
| \(\chi_{4928}(237,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{3}{80}\right)\) |
| \(\chi_{4928}(293,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{29}{80}\right)\) |
| \(\chi_{4928}(349,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{71}{80}\right)\) |
| \(\chi_{4928}(629,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{57}{80}\right)\) |
| \(\chi_{4928}(853,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{33}{80}\right)\) |
| \(\chi_{4928}(909,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{59}{80}\right)\) |
| \(\chi_{4928}(965,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{21}{80}\right)\) |
| \(\chi_{4928}(1245,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{7}{80}\right)\) |
| \(\chi_{4928}(1469,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{63}{80}\right)\) |
| \(\chi_{4928}(1525,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{9}{80}\right)\) |
| \(\chi_{4928}(1581,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{51}{80}\right)\) |
| \(\chi_{4928}(1861,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{37}{80}\right)\) |
| \(\chi_{4928}(2085,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{13}{80}\right)\) |
| \(\chi_{4928}(2141,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{39}{80}\right)\) |
| \(\chi_{4928}(2197,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{1}{80}\right)\) |
| \(\chi_{4928}(2477,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{67}{80}\right)\) |
| \(\chi_{4928}(2701,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{43}{80}\right)\) |
| \(\chi_{4928}(2757,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{69}{80}\right)\) |
| \(\chi_{4928}(2813,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{31}{80}\right)\) |
| \(\chi_{4928}(3093,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{17}{80}\right)\) |
| \(\chi_{4928}(3317,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{73}{80}\right)\) |
| \(\chi_{4928}(3373,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{19}{80}\right)\) |
| \(\chi_{4928}(3429,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{61}{80}\right)\) |
| \(\chi_{4928}(3709,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{47}{80}\right)\) |
| \(\chi_{4928}(3933,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{23}{80}\right)\) |
| \(\chi_{4928}(3989,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{49}{80}\right)\) |
| \(\chi_{4928}(4045,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{11}{80}\right)\) |
| \(\chi_{4928}(4325,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{77}{80}\right)\) |
| \(\chi_{4928}(4549,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{53}{80}\right)\) |
| \(\chi_{4928}(4605,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{79}{80}\right)\) |