from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(120))
M = H._module
chi = DirichletCharacter(H, M([84,55]))
chi.galois_orbit()
[g,chi] = znchar(Mod(209,6025))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(6025\) | |
Conductor: | \(6025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | 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: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
First 31 of 32 characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{6025}(209,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{101}{120}\right)\) |
\(\chi_{6025}(239,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{49}{120}\right)\) |
\(\chi_{6025}(354,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{103}{120}\right)\) |
\(\chi_{6025}(369,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{67}{120}\right)\) |
\(\chi_{6025}(484,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{61}{120}\right)\) |
\(\chi_{6025}(514,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{89}{120}\right)\) |
\(\chi_{6025}(844,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{107}{120}\right)\) |
\(\chi_{6025}(1084,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{71}{120}\right)\) |
\(\chi_{6025}(1414,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{29}{120}\right)\) |
\(\chi_{6025}(1444,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{97}{120}\right)\) |
\(\chi_{6025}(1559,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{31}{120}\right)\) |
\(\chi_{6025}(1689,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{109}{120}\right)\) |
\(\chi_{6025}(1719,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{17}{120}\right)\) |
\(\chi_{6025}(2289,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{119}{120}\right)\) |
\(\chi_{6025}(2619,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{77}{120}\right)\) |
\(\chi_{6025}(2764,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{79}{120}\right)\) |
\(\chi_{6025}(2779,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{43}{120}\right)\) |
\(\chi_{6025}(2894,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{37}{120}\right)\) |
\(\chi_{6025}(3254,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{83}{120}\right)\) |
\(\chi_{6025}(3494,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{47}{120}\right)\) |
\(\chi_{6025}(3854,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{73}{120}\right)\) |
\(\chi_{6025}(3969,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{7}{120}\right)\) |
\(\chi_{6025}(3984,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{91}{120}\right)\) |
\(\chi_{6025}(4129,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{113}{120}\right)\) |
\(\chi_{6025}(4459,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{11}{120}\right)\) |
\(\chi_{6025}(5029,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{53}{120}\right)\) |
\(\chi_{6025}(5059,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{1}{120}\right)\) |
\(\chi_{6025}(5189,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{19}{120}\right)\) |
\(\chi_{6025}(5304,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{13}{120}\right)\) |
\(\chi_{6025}(5334,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{41}{120}\right)\) |
\(\chi_{6025}(5664,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{59}{120}\right)\) |