from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5950, base_ring=CyclotomicField(120))
M = H._module
chi = DirichletCharacter(H, M([84,40,15]))
chi.galois_orbit()
[g,chi] = znchar(Mod(9,5950))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(5950\) | |
| Conductor: | \(2975\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 2975.fb | 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 | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(33\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{5950}(9,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{23}{30}\right)\) |
| \(\chi_{5950}(179,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{19}{30}\right)\) |
| \(\chi_{5950}(219,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{11}{30}\right)\) |
| \(\chi_{5950}(359,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{23}{30}\right)\) |
| \(\chi_{5950}(389,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{7}{30}\right)\) |
| \(\chi_{5950}(529,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{19}{30}\right)\) |
| \(\chi_{5950}(569,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{11}{30}\right)\) |
| \(\chi_{5950}(739,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{7}{30}\right)\) |
| \(\chi_{5950}(1369,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{1}{30}\right)\) |
| \(\chi_{5950}(1409,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{23}{30}\right)\) |
| \(\chi_{5950}(1579,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{19}{30}\right)\) |
| \(\chi_{5950}(1719,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{1}{30}\right)\) |
| \(\chi_{5950}(1759,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{23}{30}\right)\) |
| \(\chi_{5950}(1929,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{19}{30}\right)\) |
| \(\chi_{5950}(2389,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{17}{30}\right)\) |
| \(\chi_{5950}(2559,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{13}{30}\right)\) |
| \(\chi_{5950}(2739,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{17}{30}\right)\) |
| \(\chi_{5950}(2769,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{1}{30}\right)\) |
| \(\chi_{5950}(2909,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{13}{30}\right)\) |
| \(\chi_{5950}(3119,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{1}{30}\right)\) |
| \(\chi_{5950}(3579,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{29}{30}\right)\) |
| \(\chi_{5950}(3789,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{17}{30}\right)\) |
| \(\chi_{5950}(3929,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{29}{30}\right)\) |
| \(\chi_{5950}(3959,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{13}{30}\right)\) |
| \(\chi_{5950}(4139,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{17}{30}\right)\) |
| \(\chi_{5950}(4309,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{13}{30}\right)\) |
| \(\chi_{5950}(4769,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{11}{30}\right)\) |
| \(\chi_{5950}(4939,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{7}{30}\right)\) |
| \(\chi_{5950}(4979,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{29}{30}\right)\) |
| \(\chi_{5950}(5119,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{11}{30}\right)\) |
| \(\chi_{5950}(5289,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{7}{30}\right)\) |