from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5239, base_ring=CyclotomicField(260))
M = H._module
chi = DirichletCharacter(H, M([225,78]))
chi.galois_orbit()
[g,chi] = znchar(Mod(60,5239))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(5239\) | |
| Conductor: | \(5239\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(260\) | 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: | $\Q(\zeta_{260})$ |
| Fixed field: | Number field defined by a degree 260 polynomial (not computed) |
First 31 of 96 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{5239}(60,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{260}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{17}{130}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{259}{260}\right)\) | \(e\left(\frac{51}{260}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{111}{130}\right)\) | \(e\left(\frac{9}{260}\right)\) |
| \(\chi_{5239}(122,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{27}{260}\right)\) | \(e\left(\frac{49}{130}\right)\) | \(e\left(\frac{27}{130}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{29}{260}\right)\) | \(e\left(\frac{81}{260}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{31}{130}\right)\) | \(e\left(\frac{259}{260}\right)\) |
| \(\chi_{5239}(151,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{129}{260}\right)\) | \(e\left(\frac{3}{130}\right)\) | \(e\left(\frac{129}{130}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{23}{260}\right)\) | \(e\left(\frac{127}{260}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{47}{130}\right)\) | \(e\left(\frac{53}{260}\right)\) |
| \(\chi_{5239}(213,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{260}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{19}{130}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{213}{260}\right)\) | \(e\left(\frac{57}{260}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{17}{130}\right)\) | \(e\left(\frac{163}{260}\right)\) |
| \(\chi_{5239}(294,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{253}{260}\right)\) | \(e\left(\frac{21}{130}\right)\) | \(e\left(\frac{123}{130}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{31}{260}\right)\) | \(e\left(\frac{239}{260}\right)\) | \(e\left(\frac{21}{65}\right)\) | \(e\left(\frac{69}{130}\right)\) | \(e\left(\frac{241}{260}\right)\) |
| \(\chi_{5239}(333,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{260}\right)\) | \(e\left(\frac{7}{130}\right)\) | \(e\left(\frac{41}{130}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{227}{260}\right)\) | \(e\left(\frac{123}{260}\right)\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{37}{260}\right)\) |
| \(\chi_{5239}(356,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{260}\right)\) | \(e\left(\frac{81}{130}\right)\) | \(e\left(\frac{103}{130}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{101}{260}\right)\) | \(e\left(\frac{49}{260}\right)\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{131}{260}\right)\) |
| \(\chi_{5239}(395,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{211}{260}\right)\) | \(e\left(\frac{17}{130}\right)\) | \(e\left(\frac{81}{130}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{217}{260}\right)\) | \(e\left(\frac{113}{260}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{93}{130}\right)\) | \(e\left(\frac{127}{260}\right)\) |
| \(\chi_{5239}(463,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{260}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{97}{130}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{239}{260}\right)\) | \(e\left(\frac{31}{260}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{121}{130}\right)\) | \(e\left(\frac{189}{260}\right)\) |
| \(\chi_{5239}(525,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{207}{260}\right)\) | \(e\left(\frac{29}{130}\right)\) | \(e\left(\frac{77}{130}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{49}{260}\right)\) | \(e\left(\frac{101}{260}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{21}{130}\right)\) | \(e\left(\frac{79}{260}\right)\) |
| \(\chi_{5239}(554,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{209}{260}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{3}{260}\right)\) | \(e\left(\frac{107}{260}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{57}{130}\right)\) | \(e\left(\frac{233}{260}\right)\) |
| \(\chi_{5239}(616,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{199}{260}\right)\) | \(e\left(\frac{53}{130}\right)\) | \(e\left(\frac{69}{130}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{233}{260}\right)\) | \(e\left(\frac{77}{260}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{7}{130}\right)\) | \(e\left(\frac{243}{260}\right)\) |
| \(\chi_{5239}(697,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{260}\right)\) | \(e\left(\frac{41}{130}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{11}{260}\right)\) | \(e\left(\frac{219}{260}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{161}{260}\right)\) |
| \(\chi_{5239}(736,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{121}{260}\right)\) | \(e\left(\frac{27}{130}\right)\) | \(e\left(\frac{121}{130}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{207}{260}\right)\) | \(e\left(\frac{103}{260}\right)\) | \(e\left(\frac{27}{65}\right)\) | \(e\left(\frac{33}{130}\right)\) | \(e\left(\frac{217}{260}\right)\) |
| \(\chi_{5239}(759,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{260}\right)\) | \(e\left(\frac{61}{130}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{121}{260}\right)\) | \(e\left(\frac{69}{260}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{89}{130}\right)\) | \(e\left(\frac{211}{260}\right)\) |
| \(\chi_{5239}(798,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{131}{260}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{1}{130}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{237}{260}\right)\) | \(e\left(\frac{133}{260}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{83}{130}\right)\) | \(e\left(\frac{207}{260}\right)\) |
| \(\chi_{5239}(866,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{177}{260}\right)\) | \(e\left(\frac{119}{130}\right)\) | \(e\left(\frac{47}{130}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{219}{260}\right)\) | \(e\left(\frac{11}{260}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{1}{130}\right)\) | \(e\left(\frac{109}{260}\right)\) |
| \(\chi_{5239}(928,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{127}{260}\right)\) | \(e\left(\frac{9}{130}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{69}{260}\right)\) | \(e\left(\frac{121}{260}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{11}{130}\right)\) | \(e\left(\frac{159}{260}\right)\) |
| \(\chi_{5239}(957,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{260}\right)\) | \(e\left(\frac{43}{130}\right)\) | \(e\left(\frac{29}{130}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{243}{260}\right)\) | \(e\left(\frac{87}{260}\right)\) | \(e\left(\frac{43}{65}\right)\) | \(e\left(\frac{67}{130}\right)\) | \(e\left(\frac{153}{260}\right)\) |
| \(\chi_{5239}(1019,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{260}\right)\) | \(e\left(\frac{33}{130}\right)\) | \(e\left(\frac{119}{130}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{253}{260}\right)\) | \(e\left(\frac{97}{260}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{63}{260}\right)\) |
| \(\chi_{5239}(1100,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{153}{260}\right)\) | \(e\left(\frac{61}{130}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{251}{260}\right)\) | \(e\left(\frac{199}{260}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{89}{130}\right)\) | \(e\left(\frac{81}{260}\right)\) |
| \(\chi_{5239}(1139,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{201}{260}\right)\) | \(e\left(\frac{47}{130}\right)\) | \(e\left(\frac{71}{130}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{187}{260}\right)\) | \(e\left(\frac{83}{260}\right)\) | \(e\left(\frac{47}{65}\right)\) | \(e\left(\frac{43}{130}\right)\) | \(e\left(\frac{137}{260}\right)\) |
| \(\chi_{5239}(1162,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{203}{260}\right)\) | \(e\left(\frac{41}{130}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{141}{260}\right)\) | \(e\left(\frac{89}{260}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{31}{260}\right)\) |
| \(\chi_{5239}(1201,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{51}{260}\right)\) | \(e\left(\frac{107}{130}\right)\) | \(e\left(\frac{51}{130}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{257}{260}\right)\) | \(e\left(\frac{153}{260}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{27}{260}\right)\) |
| \(\chi_{5239}(1269,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{257}{260}\right)\) | \(e\left(\frac{9}{130}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{199}{260}\right)\) | \(e\left(\frac{251}{260}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{11}{130}\right)\) | \(e\left(\frac{29}{260}\right)\) |
| \(\chi_{5239}(1331,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{260}\right)\) | \(e\left(\frac{119}{130}\right)\) | \(e\left(\frac{47}{130}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{89}{260}\right)\) | \(e\left(\frac{141}{260}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{1}{130}\right)\) | \(e\left(\frac{239}{260}\right)\) |
| \(\chi_{5239}(1360,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{260}\right)\) | \(e\left(\frac{63}{130}\right)\) | \(e\left(\frac{109}{130}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{223}{260}\right)\) | \(e\left(\frac{67}{260}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{77}{130}\right)\) | \(e\left(\frac{73}{260}\right)\) |
| \(\chi_{5239}(1503,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{233}{260}\right)\) | \(e\left(\frac{81}{130}\right)\) | \(e\left(\frac{103}{130}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{231}{260}\right)\) | \(e\left(\frac{179}{260}\right)\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{1}{260}\right)\) |
| \(\chi_{5239}(1542,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{21}{260}\right)\) | \(e\left(\frac{67}{130}\right)\) | \(e\left(\frac{21}{130}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{167}{260}\right)\) | \(e\left(\frac{63}{260}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{53}{130}\right)\) | \(e\left(\frac{57}{260}\right)\) |
| \(\chi_{5239}(1565,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{123}{260}\right)\) | \(e\left(\frac{21}{130}\right)\) | \(e\left(\frac{123}{130}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{161}{260}\right)\) | \(e\left(\frac{109}{260}\right)\) | \(e\left(\frac{21}{65}\right)\) | \(e\left(\frac{69}{130}\right)\) | \(e\left(\frac{111}{260}\right)\) |
| \(\chi_{5239}(1604,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{231}{260}\right)\) | \(e\left(\frac{87}{130}\right)\) | \(e\left(\frac{101}{130}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{17}{260}\right)\) | \(e\left(\frac{173}{260}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{63}{130}\right)\) | \(e\left(\frac{107}{260}\right)\) |