from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5166, base_ring=CyclotomicField(120))
M = H._module
chi = DirichletCharacter(H, M([60,80,81]))
chi.galois_orbit()
[g,chi] = znchar(Mod(53,5166))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(5166\) | |
Conductor: | \(861\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 861.cl | 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 | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{5166}(53,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) |
\(\chi_{5166}(179,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) |
\(\chi_{5166}(233,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) |
\(\chi_{5166}(485,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) |
\(\chi_{5166}(557,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) |
\(\chi_{5166}(809,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) |
\(\chi_{5166}(1241,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) |
\(\chi_{5166}(1493,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) |
\(\chi_{5166}(1565,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) |
\(\chi_{5166}(1817,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) |
\(\chi_{5166}(1871,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{5166}(1997,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{5166}(2069,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) |
\(\chi_{5166}(2195,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) |
\(\chi_{5166}(2249,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) |
\(\chi_{5166}(2447,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) |
\(\chi_{5166}(2699,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) |
\(\chi_{5166}(2753,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) |
\(\chi_{5166}(3005,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{5166}(3131,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{5166}(3455,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) |
\(\chi_{5166}(3509,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) |
\(\chi_{5166}(3707,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) |
\(\chi_{5166}(3761,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) |
\(\chi_{5166}(4085,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) |
\(\chi_{5166}(4211,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) |
\(\chi_{5166}(4463,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) |
\(\chi_{5166}(4517,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) |
\(\chi_{5166}(4769,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) |
\(\chi_{5166}(4967,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) |
\(\chi_{5166}(5021,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) |