from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16900, base_ring=CyclotomicField(260))
M = H._module
chi = DirichletCharacter(H, M([0,143,85]))
chi.galois_orbit()
[g,chi] = znchar(Mod(73,16900))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(16900\) | |
| Conductor: | \(4225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(260\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 4225.cs | 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 | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{16900}(73,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{260}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{101}{130}\right)\) | \(e\left(\frac{123}{260}\right)\) | \(e\left(\frac{229}{260}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{31}{260}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{43}{260}\right)\) | \(e\left(\frac{23}{130}\right)\) |
| \(\chi_{16900}(317,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{260}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{43}{130}\right)\) | \(e\left(\frac{109}{260}\right)\) | \(e\left(\frac{167}{260}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{93}{260}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{129}{260}\right)\) | \(e\left(\frac{69}{130}\right)\) |
| \(\chi_{16900}(333,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{260}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{53}{130}\right)\) | \(e\left(\frac{219}{260}\right)\) | \(e\left(\frac{97}{260}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{163}{260}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{159}{260}\right)\) | \(e\left(\frac{79}{130}\right)\) |
| \(\chi_{16900}(837,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{139}{260}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{9}{130}\right)\) | \(e\left(\frac{177}{260}\right)\) | \(e\left(\frac{171}{260}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{89}{260}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{157}{260}\right)\) | \(e\left(\frac{87}{130}\right)\) |
| \(\chi_{16900}(853,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{217}{260}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{87}{130}\right)\) | \(e\left(\frac{151}{260}\right)\) | \(e\left(\frac{93}{260}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{167}{260}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{131}{260}\right)\) | \(e\left(\frac{61}{130}\right)\) |
| \(\chi_{16900}(1097,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{187}{260}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{57}{130}\right)\) | \(e\left(\frac{81}{260}\right)\) | \(e\left(\frac{43}{260}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{217}{260}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{41}{260}\right)\) | \(e\left(\frac{31}{130}\right)\) |
| \(\chi_{16900}(1373,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{121}{260}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{121}{130}\right)\) | \(e\left(\frac{83}{260}\right)\) | \(e\left(\frac{89}{260}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{171}{260}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{103}{260}\right)\) | \(e\left(\frac{43}{130}\right)\) |
| \(\chi_{16900}(1617,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{260}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{149}{260}\right)\) | \(e\left(\frac{47}{260}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{213}{260}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{69}{260}\right)\) | \(e\left(\frac{49}{130}\right)\) |
| \(\chi_{16900}(1633,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{260}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{179}{260}\right)\) | \(e\left(\frac{217}{260}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{43}{260}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{219}{260}\right)\) | \(e\left(\frac{99}{130}\right)\) |
| \(\chi_{16900}(1877,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{260}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{71}{130}\right)\) | \(e\left(\frac{53}{260}\right)\) | \(e\left(\frac{179}{260}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{81}{260}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{213}{260}\right)\) | \(e\left(\frac{123}{130}\right)\) |
| \(\chi_{16900}(2137,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{260}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{119}{130}\right)\) | \(e\left(\frac{217}{260}\right)\) | \(e\left(\frac{51}{260}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{209}{260}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{97}{260}\right)\) | \(e\left(\frac{67}{130}\right)\) |
| \(\chi_{16900}(2153,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{237}{260}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{107}{130}\right)\) | \(e\left(\frac{111}{260}\right)\) | \(e\left(\frac{213}{260}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{47}{260}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{191}{260}\right)\) | \(e\left(\frac{81}{130}\right)\) |
| \(\chi_{16900}(2397,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{167}{260}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{37}{130}\right)\) | \(e\left(\frac{121}{260}\right)\) | \(e\left(\frac{183}{260}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{77}{260}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{241}{260}\right)\) | \(e\left(\frac{11}{130}\right)\) |
| \(\chi_{16900}(2413,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{189}{260}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{59}{130}\right)\) | \(e\left(\frac{207}{260}\right)\) | \(e\left(\frac{81}{260}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{179}{260}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{47}{260}\right)\) | \(e\left(\frac{7}{130}\right)\) |
| \(\chi_{16900}(2673,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{141}{260}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{11}{130}\right)\) | \(e\left(\frac{43}{260}\right)\) | \(e\left(\frac{209}{260}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{51}{260}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{163}{260}\right)\) | \(e\left(\frac{63}{130}\right)\) |
| \(\chi_{16900}(2917,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{260}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{3}{130}\right)\) | \(e\left(\frac{189}{260}\right)\) | \(e\left(\frac{187}{260}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{73}{260}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{9}{260}\right)\) | \(e\left(\frac{29}{130}\right)\) |
| \(\chi_{16900}(2933,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{93}{260}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{93}{130}\right)\) | \(e\left(\frac{139}{260}\right)\) | \(e\left(\frac{77}{260}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{183}{260}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{19}{260}\right)\) | \(e\left(\frac{119}{130}\right)\) |
| \(\chi_{16900}(3177,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{51}{260}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{51}{130}\right)\) | \(e\left(\frac{93}{260}\right)\) | \(e\left(\frac{59}{260}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{201}{260}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{153}{260}\right)\) | \(e\left(\frac{103}{130}\right)\) |
| \(\chi_{16900}(3437,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{99}{260}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{257}{260}\right)\) | \(e\left(\frac{191}{260}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{69}{260}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{37}{260}\right)\) | \(e\left(\frac{47}{130}\right)\) |
| \(\chi_{16900}(3453,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{257}{260}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{71}{260}\right)\) | \(e\left(\frac{73}{260}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{187}{260}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{251}{260}\right)\) | \(e\left(\frac{101}{130}\right)\) |
| \(\chi_{16900}(3697,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{147}{260}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{17}{130}\right)\) | \(e\left(\frac{161}{260}\right)\) | \(e\left(\frac{63}{260}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{197}{260}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{181}{260}\right)\) | \(e\left(\frac{121}{130}\right)\) |
| \(\chi_{16900}(3713,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{209}{260}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{167}{260}\right)\) | \(e\left(\frac{201}{260}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{59}{260}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{107}{260}\right)\) | \(e\left(\frac{27}{130}\right)\) |
| \(\chi_{16900}(3973,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{161}{260}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{31}{130}\right)\) | \(e\left(\frac{3}{260}\right)\) | \(e\left(\frac{69}{260}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{191}{260}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{223}{260}\right)\) | \(e\left(\frac{83}{130}\right)\) |
| \(\chi_{16900}(4217,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{243}{260}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{113}{130}\right)\) | \(e\left(\frac{229}{260}\right)\) | \(e\left(\frac{67}{260}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{193}{260}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{209}{260}\right)\) | \(e\left(\frac{9}{130}\right)\) |
| \(\chi_{16900}(4233,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{260}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{113}{130}\right)\) | \(e\left(\frac{99}{260}\right)\) | \(e\left(\frac{197}{260}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{63}{260}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{79}{260}\right)\) | \(e\left(\frac{9}{130}\right)\) |
| \(\chi_{16900}(4477,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{260}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{31}{130}\right)\) | \(e\left(\frac{133}{260}\right)\) | \(e\left(\frac{199}{260}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{61}{260}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{93}{260}\right)\) | \(e\left(\frac{83}{130}\right)\) |
| \(\chi_{16900}(4737,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{260}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{37}{260}\right)\) | \(e\left(\frac{71}{260}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{189}{260}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{237}{260}\right)\) | \(e\left(\frac{27}{130}\right)\) |
| \(\chi_{16900}(4753,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{260}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{17}{130}\right)\) | \(e\left(\frac{31}{260}\right)\) | \(e\left(\frac{193}{260}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{67}{260}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{51}{260}\right)\) | \(e\left(\frac{121}{130}\right)\) |
| \(\chi_{16900}(4997,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{127}{260}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{201}{260}\right)\) | \(e\left(\frac{203}{260}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{57}{260}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{121}{260}\right)\) | \(e\left(\frac{101}{130}\right)\) |
| \(\chi_{16900}(5013,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{229}{260}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{127}{260}\right)\) | \(e\left(\frac{61}{260}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{199}{260}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{167}{260}\right)\) | \(e\left(\frac{47}{130}\right)\) |
| \(\chi_{16900}(5273,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{181}{260}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{51}{130}\right)\) | \(e\left(\frac{223}{260}\right)\) | \(e\left(\frac{189}{260}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{71}{260}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{23}{260}\right)\) | \(e\left(\frac{103}{130}\right)\) |