from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8024, base_ring=CyclotomicField(232))
M = H._module
chi = DirichletCharacter(H, M([0,116,203,88]))
chi.galois_orbit()
[g,chi] = znchar(Mod(53,8024))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(8024\) | |
| Conductor: | \(8024\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(232\) | 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: | $\Q(\zeta_{232})$ |
| Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
First 31 of 112 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{8024}(53,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{232}\right)\) | \(e\left(\frac{35}{232}\right)\) | \(e\left(\frac{105}{232}\right)\) | \(e\left(\frac{79}{116}\right)\) | \(e\left(\frac{25}{232}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{57}{116}\right)\) | \(e\left(\frac{19}{116}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{189}{232}\right)\) |
| \(\chi_{8024}(189,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{232}\right)\) | \(e\left(\frac{59}{232}\right)\) | \(e\left(\frac{177}{232}\right)\) | \(e\left(\frac{47}{116}\right)\) | \(e\left(\frac{9}{232}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{53}{116}\right)\) | \(e\left(\frac{95}{116}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{133}{232}\right)\) |
| \(\chi_{8024}(213,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{129}{232}\right)\) | \(e\left(\frac{157}{232}\right)\) | \(e\left(\frac{7}{232}\right)\) | \(e\left(\frac{13}{116}\right)\) | \(e\left(\frac{79}{232}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{27}{116}\right)\) | \(e\left(\frac{9}{116}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{59}{232}\right)\) |
| \(\chi_{8024}(253,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{232}\right)\) | \(e\left(\frac{119}{232}\right)\) | \(e\left(\frac{125}{232}\right)\) | \(e\left(\frac{83}{116}\right)\) | \(e\left(\frac{85}{232}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{101}{116}\right)\) | \(e\left(\frac{111}{116}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{225}{232}\right)\) |
| \(\chi_{8024}(389,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{131}{232}\right)\) | \(e\left(\frac{199}{232}\right)\) | \(e\left(\frac{133}{232}\right)\) | \(e\left(\frac{15}{116}\right)\) | \(e\left(\frac{109}{232}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{49}{116}\right)\) | \(e\left(\frac{55}{116}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{193}{232}\right)\) |
| \(\chi_{8024}(461,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{215}{232}\right)\) | \(e\left(\frac{107}{232}\right)\) | \(e\left(\frac{89}{232}\right)\) | \(e\left(\frac{99}{116}\right)\) | \(e\left(\frac{209}{232}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{45}{116}\right)\) | \(e\left(\frac{15}{116}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{21}{232}\right)\) |
| \(\chi_{8024}(501,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{232}\right)\) | \(e\left(\frac{121}{232}\right)\) | \(e\left(\frac{131}{232}\right)\) | \(e\left(\frac{61}{116}\right)\) | \(e\left(\frac{219}{232}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{91}{116}\right)\) | \(e\left(\frac{69}{116}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{143}{232}\right)\) |
| \(\chi_{8024}(525,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{195}{232}\right)\) | \(e\left(\frac{151}{232}\right)\) | \(e\left(\frac{221}{232}\right)\) | \(e\left(\frac{79}{116}\right)\) | \(e\left(\frac{141}{232}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{57}{116}\right)\) | \(e\left(\frac{19}{116}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{73}{232}\right)\) |
| \(\chi_{8024}(597,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{207}{232}\right)\) | \(e\left(\frac{171}{232}\right)\) | \(e\left(\frac{49}{232}\right)\) | \(e\left(\frac{91}{116}\right)\) | \(e\left(\frac{89}{232}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{73}{116}\right)\) | \(e\left(\frac{63}{116}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{181}{232}\right)\) |
| \(\chi_{8024}(661,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{163}{232}\right)\) | \(e\left(\frac{175}{232}\right)\) | \(e\left(\frac{61}{232}\right)\) | \(e\left(\frac{47}{116}\right)\) | \(e\left(\frac{125}{232}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{53}{116}\right)\) | \(e\left(\frac{95}{116}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{17}{232}\right)\) |
| \(\chi_{8024}(733,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{167}{232}\right)\) | \(e\left(\frac{27}{232}\right)\) | \(e\left(\frac{81}{232}\right)\) | \(e\left(\frac{51}{116}\right)\) | \(e\left(\frac{185}{232}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{97}{116}\right)\) | \(e\left(\frac{71}{116}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{53}{232}\right)\) |
| \(\chi_{8024}(757,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{153}{232}\right)\) | \(e\left(\frac{197}{232}\right)\) | \(e\left(\frac{127}{232}\right)\) | \(e\left(\frac{37}{116}\right)\) | \(e\left(\frac{207}{232}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{59}{116}\right)\) | \(e\left(\frac{97}{116}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{43}{232}\right)\) |
| \(\chi_{8024}(933,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{99}{232}\right)\) | \(e\left(\frac{223}{232}\right)\) | \(e\left(\frac{205}{232}\right)\) | \(e\left(\frac{99}{116}\right)\) | \(e\left(\frac{93}{232}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{45}{116}\right)\) | \(e\left(\frac{15}{116}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{137}{232}\right)\) |
| \(\chi_{8024}(1029,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{65}{232}\right)\) | \(e\left(\frac{205}{232}\right)\) | \(e\left(\frac{151}{232}\right)\) | \(e\left(\frac{65}{116}\right)\) | \(e\left(\frac{47}{232}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{19}{116}\right)\) | \(e\left(\frac{45}{116}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{179}{232}\right)\) |
| \(\chi_{8024}(1069,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{91}{232}\right)\) | \(e\left(\frac{55}{232}\right)\) | \(e\left(\frac{165}{232}\right)\) | \(e\left(\frac{91}{116}\right)\) | \(e\left(\frac{205}{232}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{73}{116}\right)\) | \(e\left(\frac{63}{116}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{65}{232}\right)\) |
| \(\chi_{8024}(1141,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{63}{232}\right)\) | \(e\left(\frac{163}{232}\right)\) | \(e\left(\frac{25}{232}\right)\) | \(e\left(\frac{63}{116}\right)\) | \(e\left(\frac{17}{232}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{113}{116}\right)\) | \(e\left(\frac{115}{116}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{45}{232}\right)\) |
| \(\chi_{8024}(1205,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{51}{232}\right)\) | \(e\left(\frac{143}{232}\right)\) | \(e\left(\frac{197}{232}\right)\) | \(e\left(\frac{51}{116}\right)\) | \(e\left(\frac{69}{232}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{97}{116}\right)\) | \(e\left(\frac{71}{116}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{169}{232}\right)\) |
| \(\chi_{8024}(1301,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{169}{232}\right)\) | \(e\left(\frac{69}{232}\right)\) | \(e\left(\frac{207}{232}\right)\) | \(e\left(\frac{53}{116}\right)\) | \(e\left(\frac{215}{232}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{3}{116}\right)\) | \(e\left(\frac{1}{116}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{187}{232}\right)\) |
| \(\chi_{8024}(1317,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{205}{232}\right)\) | \(e\left(\frac{129}{232}\right)\) | \(e\left(\frac{155}{232}\right)\) | \(e\left(\frac{89}{116}\right)\) | \(e\left(\frac{59}{232}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{51}{116}\right)\) | \(e\left(\frac{17}{116}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{47}{232}\right)\) |
| \(\chi_{8024}(1437,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{57}{232}\right)\) | \(e\left(\frac{37}{232}\right)\) | \(e\left(\frac{111}{232}\right)\) | \(e\left(\frac{57}{116}\right)\) | \(e\left(\frac{159}{232}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{47}{116}\right)\) | \(e\left(\frac{93}{116}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{107}{232}\right)\) |
| \(\chi_{8024}(1549,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{151}{232}\right)\) | \(e\left(\frac{155}{232}\right)\) | \(e\left(\frac{1}{232}\right)\) | \(e\left(\frac{35}{116}\right)\) | \(e\left(\frac{177}{232}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{37}{116}\right)\) | \(e\left(\frac{51}{116}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{141}{232}\right)\) |
| \(\chi_{8024}(1613,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{179}{232}\right)\) | \(e\left(\frac{47}{232}\right)\) | \(e\left(\frac{141}{232}\right)\) | \(e\left(\frac{63}{116}\right)\) | \(e\left(\frac{133}{232}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{113}{116}\right)\) | \(e\left(\frac{115}{116}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{161}{232}\right)\) |
| \(\chi_{8024}(1709,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{232}\right)\) | \(e\left(\frac{53}{232}\right)\) | \(e\left(\frac{159}{232}\right)\) | \(e\left(\frac{113}{116}\right)\) | \(e\left(\frac{71}{232}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{83}{116}\right)\) | \(e\left(\frac{105}{116}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{147}{232}\right)\) |
| \(\chi_{8024}(1821,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{223}{232}\right)\) | \(e\left(\frac{43}{232}\right)\) | \(e\left(\frac{129}{232}\right)\) | \(e\left(\frac{107}{116}\right)\) | \(e\left(\frac{97}{232}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{17}{116}\right)\) | \(e\left(\frac{83}{116}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{93}{232}\right)\) |
| \(\chi_{8024}(1845,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{232}\right)\) | \(e\left(\frac{125}{232}\right)\) | \(e\left(\frac{143}{232}\right)\) | \(e\left(\frac{17}{116}\right)\) | \(e\left(\frac{23}{232}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{71}{116}\right)\) | \(e\left(\frac{101}{116}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{211}{232}\right)\) |
| \(\chi_{8024}(2021,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{35}{232}\right)\) | \(e\left(\frac{39}{232}\right)\) | \(e\left(\frac{117}{232}\right)\) | \(e\left(\frac{35}{116}\right)\) | \(e\left(\frac{61}{232}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{37}{116}\right)\) | \(e\left(\frac{51}{116}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{25}{232}\right)\) |
| \(\chi_{8024}(2093,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{143}{232}\right)\) | \(e\left(\frac{219}{232}\right)\) | \(e\left(\frac{193}{232}\right)\) | \(e\left(\frac{27}{116}\right)\) | \(e\left(\frac{57}{232}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{65}{116}\right)\) | \(e\left(\frac{99}{116}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{69}{232}\right)\) |
| \(\chi_{8024}(2133,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{77}{232}\right)\) | \(e\left(\frac{225}{232}\right)\) | \(e\left(\frac{211}{232}\right)\) | \(e\left(\frac{77}{116}\right)\) | \(e\left(\frac{227}{232}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{35}{116}\right)\) | \(e\left(\frac{89}{116}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{55}{232}\right)\) |
| \(\chi_{8024}(2229,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{39}{232}\right)\) | \(e\left(\frac{123}{232}\right)\) | \(e\left(\frac{137}{232}\right)\) | \(e\left(\frac{39}{116}\right)\) | \(e\left(\frac{121}{232}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{81}{116}\right)\) | \(e\left(\frac{27}{116}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{61}{232}\right)\) |
| \(\chi_{8024}(2269,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{232}\right)\) | \(e\left(\frac{33}{232}\right)\) | \(e\left(\frac{99}{232}\right)\) | \(e\left(\frac{101}{116}\right)\) | \(e\left(\frac{123}{232}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{67}{116}\right)\) | \(e\left(\frac{61}{116}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{39}{232}\right)\) |
| \(\chi_{8024}(2293,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{107}{232}\right)\) | \(e\left(\frac{159}{232}\right)\) | \(e\left(\frac{13}{232}\right)\) | \(e\left(\frac{107}{116}\right)\) | \(e\left(\frac{213}{232}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{17}{116}\right)\) | \(e\left(\frac{83}{116}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{209}{232}\right)\) |