from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(240))
M = H._module
chi = DirichletCharacter(H, M([156,143]))
chi.galois_orbit()
[g,chi] = znchar(Mod(167,6025))
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: | \(240\) | 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: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
First 31 of 64 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6025}(167,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{203}{240}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{71}{240}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{17}{48}\right)\) |
| \(\chi_{6025}(227,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{131}{240}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{47}{240}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{41}{48}\right)\) |
| \(\chi_{6025}(248,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{181}{240}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{217}{240}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{31}{48}\right)\) |
| \(\chi_{6025}(283,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{73}{240}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{61}{240}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{43}{48}\right)\) |
| \(\chi_{6025}(312,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{139}{240}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{103}{240}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{1}{48}\right)\) |
| \(\chi_{6025}(378,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{197}{240}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{89}{240}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{47}{48}\right)\) |
| \(\chi_{6025}(448,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{121}{240}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{157}{240}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{43}{48}\right)\) |
| \(\chi_{6025}(533,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{233}{240}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{221}{240}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{11}{48}\right)\) |
| \(\chi_{6025}(833,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{53}{240}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{41}{240}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{47}{48}\right)\) |
| \(\chi_{6025}(998,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{240}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{37}{240}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{19}{48}\right)\) |
| \(\chi_{6025}(1063,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{89}{240}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{173}{240}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{11}{48}\right)\) |
| \(\chi_{6025}(1078,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{157}{240}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{49}{240}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{7}{48}\right)\) |
| \(\chi_{6025}(1198,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{61}{240}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{97}{240}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{7}{48}\right)\) |
| \(\chi_{6025}(1477,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{211}{240}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{127}{240}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{25}{48}\right)\) |
| \(\chi_{6025}(1483,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{13}{240}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{1}{240}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{7}{48}\right)\) |
| \(\chi_{6025}(1502,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{151}{240}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{67}{240}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{37}{48}\right)\) |
| \(\chi_{6025}(1588,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{209}{240}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{53}{240}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{35}{48}\right)\) |
| \(\chi_{6025}(1592,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{163}{240}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{31}{240}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{25}{48}\right)\) |
| \(\chi_{6025}(1742,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{223}{240}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{91}{240}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{13}{48}\right)\) |
| \(\chi_{6025}(1753,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{97}{240}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{229}{240}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{19}{48}\right)\) |
| \(\chi_{6025}(2103,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{217}{240}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{109}{240}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{43}{48}\right)\) |
| \(\chi_{6025}(2298,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{101}{240}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{137}{240}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{47}{48}\right)\) |
| \(\chi_{6025}(2348,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{161}{240}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{197}{240}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{35}{48}\right)\) |
| \(\chi_{6025}(2397,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{227}{240}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{239}{240}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{41}{48}\right)\) |
| \(\chi_{6025}(2567,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{23}{240}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{131}{240}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{5}{48}\right)\) |
| \(\chi_{6025}(2697,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{67}{240}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{79}{240}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{25}{48}\right)\) |
| \(\chi_{6025}(2778,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{37}{240}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{169}{240}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{31}{48}\right)\) |
| \(\chi_{6025}(3062,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{19}{240}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{223}{240}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{25}{48}\right)\) |
| \(\chi_{6025}(3063,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{149}{240}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{233}{240}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{47}{48}\right)\) |
| \(\chi_{6025}(3077,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{31}{240}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{187}{240}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{13}{48}\right)\) |
| \(\chi_{6025}(3102,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{91}{240}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{7}{240}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{1}{48}\right)\) |