from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1375, base_ring=CyclotomicField(100))
M = H._module
chi = DirichletCharacter(H, M([93,60]))
chi.galois_orbit()
[g,chi] = znchar(Mod(42,1375))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(1375\) | |
Conductor: | \(1375\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(100\) | 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: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
First 31 of 40 characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1375}(42,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{31}{100}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(i\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{37}{100}\right)\) | \(e\left(\frac{87}{100}\right)\) | \(e\left(\frac{39}{50}\right)\) |
\(\chi_{1375}(48,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{100}\right)\) | \(e\left(\frac{37}{100}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(-i\) | \(e\left(\frac{93}{100}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{99}{100}\right)\) | \(e\left(\frac{49}{100}\right)\) | \(e\left(\frac{3}{50}\right)\) |
\(\chi_{1375}(108,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{83}{100}\right)\) | \(e\left(\frac{41}{100}\right)\) | \(e\left(\frac{33}{50}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(-i\) | \(e\left(\frac{49}{100}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{57}{100}\right)\) | \(e\left(\frac{29}{50}\right)\) |
\(\chi_{1375}(113,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(-i\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{31}{100}\right)\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{7}{50}\right)\) |
\(\chi_{1375}(202,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{87}{100}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(i\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{49}{100}\right)\) | \(e\left(\frac{99}{100}\right)\) | \(e\left(\frac{3}{50}\right)\) |
\(\chi_{1375}(203,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{87}{100}\right)\) | \(e\left(\frac{49}{100}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(-i\) | \(e\left(\frac{61}{100}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{23}{100}\right)\) | \(e\left(\frac{73}{100}\right)\) | \(e\left(\frac{31}{50}\right)\) |
\(\chi_{1375}(212,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{49}{100}\right)\) | \(e\left(\frac{23}{100}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(i\) | \(e\left(\frac{47}{100}\right)\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{21}{100}\right)\) | \(e\left(\frac{71}{100}\right)\) | \(e\left(\frac{37}{50}\right)\) |
\(\chi_{1375}(247,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{19}{100}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(i\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{13}{100}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{11}{50}\right)\) |
\(\chi_{1375}(317,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{73}{100}\right)\) | \(e\left(\frac{71}{100}\right)\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(i\) | \(e\left(\frac{19}{100}\right)\) | \(e\left(\frac{21}{50}\right)\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{67}{100}\right)\) | \(e\left(\frac{49}{50}\right)\) |
\(\chi_{1375}(323,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{100}\right)\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(-i\) | \(e\left(\frac{33}{100}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{19}{100}\right)\) | \(e\left(\frac{69}{100}\right)\) | \(e\left(\frac{43}{50}\right)\) |
\(\chi_{1375}(383,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(-i\) | \(e\left(\frac{89}{100}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{27}{100}\right)\) | \(e\left(\frac{77}{100}\right)\) | \(e\left(\frac{19}{50}\right)\) |
\(\chi_{1375}(388,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{19}{100}\right)\) | \(e\left(\frac{13}{100}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(-i\) | \(e\left(\frac{57}{100}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{51}{100}\right)\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{47}{50}\right)\) |
\(\chi_{1375}(477,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{27}{100}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(i\) | \(e\left(\frac{3}{100}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{79}{100}\right)\) | \(e\left(\frac{13}{50}\right)\) |
\(\chi_{1375}(478,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{67}{100}\right)\) | \(e\left(\frac{9}{100}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(-i\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{93}{100}\right)\) | \(e\left(\frac{21}{50}\right)\) |
\(\chi_{1375}(487,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{69}{100}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(i\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{51}{100}\right)\) | \(e\left(\frac{47}{50}\right)\) |
\(\chi_{1375}(522,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(i\) | \(e\left(\frac{51}{100}\right)\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{93}{100}\right)\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{21}{50}\right)\) |
\(\chi_{1375}(592,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{93}{100}\right)\) | \(e\left(\frac{11}{100}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(i\) | \(e\left(\frac{79}{100}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{47}{100}\right)\) | \(e\left(\frac{9}{50}\right)\) |
\(\chi_{1375}(598,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{57}{100}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(-i\) | \(e\left(\frac{73}{100}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{89}{100}\right)\) | \(e\left(\frac{33}{50}\right)\) |
\(\chi_{1375}(658,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{61}{100}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(-i\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{47}{100}\right)\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{9}{50}\right)\) |
\(\chi_{1375}(663,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{99}{100}\right)\) | \(e\left(\frac{73}{100}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(-i\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{71}{100}\right)\) | \(e\left(\frac{21}{100}\right)\) | \(e\left(\frac{37}{50}\right)\) |
\(\chi_{1375}(752,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{21}{100}\right)\) | \(e\left(\frac{67}{100}\right)\) | \(e\left(\frac{21}{50}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(i\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{9}{100}\right)\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{23}{50}\right)\) |
\(\chi_{1375}(753,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{47}{100}\right)\) | \(e\left(\frac{69}{100}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(-i\) | \(e\left(\frac{41}{100}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{13}{100}\right)\) | \(e\left(\frac{11}{50}\right)\) |
\(\chi_{1375}(762,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{89}{100}\right)\) | \(e\left(\frac{3}{100}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(i\) | \(e\left(\frac{67}{100}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{31}{100}\right)\) | \(e\left(\frac{7}{50}\right)\) |
\(\chi_{1375}(797,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{37}{100}\right)\) | \(e\left(\frac{99}{100}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(i\) | \(e\left(\frac{11}{100}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{73}{100}\right)\) | \(e\left(\frac{23}{100}\right)\) | \(e\left(\frac{31}{50}\right)\) |
\(\chi_{1375}(867,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{100}\right)\) | \(e\left(\frac{51}{100}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(i\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{77}{100}\right)\) | \(e\left(\frac{27}{100}\right)\) | \(e\left(\frac{19}{50}\right)\) |
\(\chi_{1375}(873,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{71}{100}\right)\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{21}{50}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(-i\) | \(e\left(\frac{13}{100}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{9}{100}\right)\) | \(e\left(\frac{23}{50}\right)\) |
\(\chi_{1375}(933,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{23}{100}\right)\) | \(e\left(\frac{21}{100}\right)\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(-i\) | \(e\left(\frac{69}{100}\right)\) | \(e\left(\frac{21}{50}\right)\) | \(e\left(\frac{67}{100}\right)\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{49}{50}\right)\) |
\(\chi_{1375}(938,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{79}{100}\right)\) | \(e\left(\frac{33}{100}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(-i\) | \(e\left(\frac{37}{100}\right)\) | \(e\left(\frac{33}{50}\right)\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{41}{100}\right)\) | \(e\left(\frac{27}{50}\right)\) |
\(\chi_{1375}(1027,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{100}\right)\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(i\) | \(e\left(\frac{23}{100}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{89}{100}\right)\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{33}{50}\right)\) |
\(\chi_{1375}(1028,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{27}{100}\right)\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(-i\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{83}{100}\right)\) | \(e\left(\frac{33}{100}\right)\) | \(e\left(\frac{1}{50}\right)\) |
\(\chi_{1375}(1037,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{100}\right)\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(i\) | \(e\left(\frac{27}{100}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{61}{100}\right)\) | \(e\left(\frac{11}{100}\right)\) | \(e\left(\frac{17}{50}\right)\) |