from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5950, base_ring=CyclotomicField(240))
M = H._module
chi = DirichletCharacter(H, M([12,80,165]))
chi.galois_orbit()
[g,chi] = znchar(Mod(177,5950))
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: | \(240\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 2975.fn | 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 | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(33\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{5950}(177,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{240}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{227}{240}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{127}{240}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{221}{240}\right)\) | \(e\left(\frac{19}{60}\right)\) |
| \(\chi_{5950}(233,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{240}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{101}{240}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{121}{240}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{203}{240}\right)\) | \(e\left(\frac{37}{60}\right)\) |
| \(\chi_{5950}(303,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{240}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{209}{240}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{229}{240}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{47}{240}\right)\) | \(e\left(\frac{13}{60}\right)\) |
| \(\chi_{5950}(317,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{77}{240}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{191}{240}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{91}{240}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{113}{240}\right)\) | \(e\left(\frac{7}{60}\right)\) |
| \(\chi_{5950}(347,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{240}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{19}{240}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{239}{240}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{157}{240}\right)\) | \(e\left(\frac{23}{60}\right)\) |
| \(\chi_{5950}(403,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{223}{240}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{229}{240}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{89}{240}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{187}{240}\right)\) | \(e\left(\frac{53}{60}\right)\) |
| \(\chi_{5950}(473,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{240}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{97}{240}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{197}{240}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{31}{240}\right)\) | \(e\left(\frac{29}{60}\right)\) |
| \(\chi_{5950}(487,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{240}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{223}{240}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{203}{240}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{49}{240}\right)\) | \(e\left(\frac{11}{60}\right)\) |
| \(\chi_{5950}(513,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{240}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{233}{240}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{13}{240}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{119}{240}\right)\) | \(e\left(\frac{1}{60}\right)\) |
| \(\chi_{5950}(583,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{167}{240}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{221}{240}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{1}{240}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{83}{240}\right)\) | \(e\left(\frac{37}{60}\right)\) |
| \(\chi_{5950}(683,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{187}{240}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{121}{240}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{221}{240}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{103}{240}\right)\) | \(e\left(\frac{17}{60}\right)\) |
| \(\chi_{5950}(737,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{240}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{23}{240}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{163}{240}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{89}{240}\right)\) | \(e\left(\frac{31}{60}\right)\) |
| \(\chi_{5950}(753,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{240}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{109}{240}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{209}{240}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{67}{240}\right)\) | \(e\left(\frac{53}{60}\right)\) |
| \(\chi_{5950}(877,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{209}{240}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{107}{240}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{7}{240}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{101}{240}\right)\) | \(e\left(\frac{19}{60}\right)\) |
| \(\chi_{5950}(1047,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{240}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{139}{240}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{119}{240}\right)\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{37}{240}\right)\) | \(e\left(\frac{23}{60}\right)\) |
| \(\chi_{5950}(1367,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{137}{240}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{131}{240}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{31}{240}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{173}{240}\right)\) | \(e\left(\frac{7}{60}\right)\) |
| \(\chi_{5950}(1423,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{239}{240}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{197}{240}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{217}{240}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{11}{240}\right)\) | \(e\left(\frac{49}{60}\right)\) |
| \(\chi_{5950}(1537,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{121}{240}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{163}{240}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{143}{240}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{109}{240}\right)\) | \(e\left(\frac{11}{60}\right)\) |
| \(\chi_{5950}(1663,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{211}{240}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{193}{240}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{53}{240}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{79}{240}\right)\) | \(e\left(\frac{41}{60}\right)\) |
| \(\chi_{5950}(1677,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{240}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{127}{240}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{107}{240}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{1}{240}\right)\) | \(e\left(\frac{59}{60}\right)\) |
| \(\chi_{5950}(1703,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{203}{240}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{89}{240}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{109}{240}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{167}{240}\right)\) | \(e\left(\frac{13}{60}\right)\) |
| \(\chi_{5950}(1773,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{240}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{77}{240}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{97}{240}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{131}{240}\right)\) | \(e\left(\frac{49}{60}\right)\) |
| \(\chi_{5950}(1873,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{139}{240}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{217}{240}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{77}{240}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{151}{240}\right)\) | \(e\left(\frac{29}{60}\right)\) |
| \(\chi_{5950}(1927,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{149}{240}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{167}{240}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{67}{240}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{41}{240}\right)\) | \(e\left(\frac{19}{60}\right)\) |
| \(\chi_{5950}(2067,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{240}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{11}{240}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{151}{240}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{53}{240}\right)\) | \(e\left(\frac{7}{60}\right)\) |
| \(\chi_{5950}(2097,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{133}{240}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{199}{240}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{179}{240}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{217}{240}\right)\) | \(e\left(\frac{23}{60}\right)\) |
| \(\chi_{5950}(2237,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{240}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{43}{240}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{23}{240}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{229}{240}\right)\) | \(e\left(\frac{11}{60}\right)\) |
| \(\chi_{5950}(2613,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{191}{240}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{53}{240}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{73}{240}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{59}{240}\right)\) | \(e\left(\frac{1}{60}\right)\) |
| \(\chi_{5950}(2683,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{227}{240}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{161}{240}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{181}{240}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{143}{240}\right)\) | \(e\left(\frac{37}{60}\right)\) |
| \(\chi_{5950}(2697,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{173}{240}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{239}{240}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{139}{240}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{17}{240}\right)\) | \(e\left(\frac{43}{60}\right)\) |
| \(\chi_{5950}(2727,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{169}{240}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{67}{240}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{47}{240}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{61}{240}\right)\) | \(e\left(\frac{59}{60}\right)\) |