from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(799, base_ring=CyclotomicField(368))
M = H._module
chi = DirichletCharacter(H, M([115,8]))
chi.galois_orbit()
[g,chi] = znchar(Mod(5,799))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(799\) | |
| Conductor: | \(799\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(368\) | 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: | $\Q(\zeta_{368})$ |
| Fixed field: | Number field defined by a degree 368 polynomial (not computed) |
First 31 of 176 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{799}(5,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{141}{184}\right)\) | \(e\left(\frac{275}{368}\right)\) | \(e\left(\frac{49}{92}\right)\) | \(e\left(\frac{215}{368}\right)\) | \(e\left(\frac{189}{368}\right)\) | \(e\left(\frac{49}{368}\right)\) | \(e\left(\frac{55}{184}\right)\) | \(e\left(\frac{91}{184}\right)\) | \(e\left(\frac{129}{368}\right)\) | \(e\left(\frac{125}{368}\right)\) |
| \(\chi_{799}(10,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{184}\right)\) | \(e\left(\frac{165}{368}\right)\) | \(e\left(\frac{11}{92}\right)\) | \(e\left(\frac{129}{368}\right)\) | \(e\left(\frac{187}{368}\right)\) | \(e\left(\frac{103}{368}\right)\) | \(e\left(\frac{33}{184}\right)\) | \(e\left(\frac{165}{184}\right)\) | \(e\left(\frac{151}{368}\right)\) | \(e\left(\frac{75}{368}\right)\) |
| \(\chi_{799}(11,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{159}{184}\right)\) | \(e\left(\frac{177}{368}\right)\) | \(e\left(\frac{67}{92}\right)\) | \(e\left(\frac{125}{368}\right)\) | \(e\left(\frac{127}{368}\right)\) | \(e\left(\frac{251}{368}\right)\) | \(e\left(\frac{109}{184}\right)\) | \(e\left(\frac{177}{184}\right)\) | \(e\left(\frac{75}{368}\right)\) | \(e\left(\frac{47}{368}\right)\) |
| \(\chi_{799}(20,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{65}{184}\right)\) | \(e\left(\frac{55}{368}\right)\) | \(e\left(\frac{65}{92}\right)\) | \(e\left(\frac{43}{368}\right)\) | \(e\left(\frac{185}{368}\right)\) | \(e\left(\frac{157}{368}\right)\) | \(e\left(\frac{11}{184}\right)\) | \(e\left(\frac{55}{184}\right)\) | \(e\left(\frac{173}{368}\right)\) | \(e\left(\frac{25}{368}\right)\) |
| \(\chi_{799}(22,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{184}\right)\) | \(e\left(\frac{67}{368}\right)\) | \(e\left(\frac{29}{92}\right)\) | \(e\left(\frac{39}{368}\right)\) | \(e\left(\frac{125}{368}\right)\) | \(e\left(\frac{305}{368}\right)\) | \(e\left(\frac{87}{184}\right)\) | \(e\left(\frac{67}{184}\right)\) | \(e\left(\frac{97}{368}\right)\) | \(e\left(\frac{365}{368}\right)\) |
| \(\chi_{799}(23,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{15}{184}\right)\) | \(e\left(\frac{41}{368}\right)\) | \(e\left(\frac{15}{92}\right)\) | \(e\left(\frac{293}{368}\right)\) | \(e\left(\frac{71}{368}\right)\) | \(e\left(\frac{291}{368}\right)\) | \(e\left(\frac{45}{184}\right)\) | \(e\left(\frac{41}{184}\right)\) | \(e\left(\frac{323}{368}\right)\) | \(e\left(\frac{119}{368}\right)\) |
| \(\chi_{799}(29,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{184}\right)\) | \(e\left(\frac{11}{368}\right)\) | \(e\left(\frac{13}{92}\right)\) | \(e\left(\frac{303}{368}\right)\) | \(e\left(\frac{37}{368}\right)\) | \(e\left(\frac{105}{368}\right)\) | \(e\left(\frac{39}{184}\right)\) | \(e\left(\frac{11}{184}\right)\) | \(e\left(\frac{329}{368}\right)\) | \(e\left(\frac{5}{368}\right)\) |
| \(\chi_{799}(31,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{184}\right)\) | \(e\left(\frac{319}{368}\right)\) | \(e\left(\frac{9}{92}\right)\) | \(e\left(\frac{323}{368}\right)\) | \(e\left(\frac{337}{368}\right)\) | \(e\left(\frac{101}{368}\right)\) | \(e\left(\frac{27}{184}\right)\) | \(e\left(\frac{135}{184}\right)\) | \(e\left(\frac{341}{368}\right)\) | \(e\left(\frac{145}{368}\right)\) |
| \(\chi_{799}(39,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{93}{184}\right)\) | \(e\left(\frac{291}{368}\right)\) | \(e\left(\frac{1}{92}\right)\) | \(e\left(\frac{87}{368}\right)\) | \(e\left(\frac{109}{368}\right)\) | \(e\left(\frac{1}{368}\right)\) | \(e\left(\frac{95}{184}\right)\) | \(e\left(\frac{107}{184}\right)\) | \(e\left(\frac{273}{368}\right)\) | \(e\left(\frac{333}{368}\right)\) |
| \(\chi_{799}(40,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{184}\right)\) | \(e\left(\frac{313}{368}\right)\) | \(e\left(\frac{27}{92}\right)\) | \(e\left(\frac{325}{368}\right)\) | \(e\left(\frac{183}{368}\right)\) | \(e\left(\frac{211}{368}\right)\) | \(e\left(\frac{173}{184}\right)\) | \(e\left(\frac{129}{184}\right)\) | \(e\left(\frac{195}{368}\right)\) | \(e\left(\frac{343}{368}\right)\) |
| \(\chi_{799}(41,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{91}{184}\right)\) | \(e\left(\frac{77}{368}\right)\) | \(e\left(\frac{91}{92}\right)\) | \(e\left(\frac{281}{368}\right)\) | \(e\left(\frac{259}{368}\right)\) | \(e\left(\frac{367}{368}\right)\) | \(e\left(\frac{89}{184}\right)\) | \(e\left(\frac{77}{184}\right)\) | \(e\left(\frac{95}{368}\right)\) | \(e\left(\frac{35}{368}\right)\) |
| \(\chi_{799}(44,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{184}\right)\) | \(e\left(\frac{325}{368}\right)\) | \(e\left(\frac{83}{92}\right)\) | \(e\left(\frac{321}{368}\right)\) | \(e\left(\frac{123}{368}\right)\) | \(e\left(\frac{359}{368}\right)\) | \(e\left(\frac{65}{184}\right)\) | \(e\left(\frac{141}{184}\right)\) | \(e\left(\frac{119}{368}\right)\) | \(e\left(\frac{315}{368}\right)\) |
| \(\chi_{799}(45,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{184}\right)\) | \(e\left(\frac{97}{368}\right)\) | \(e\left(\frac{31}{92}\right)\) | \(e\left(\frac{29}{368}\right)\) | \(e\left(\frac{159}{368}\right)\) | \(e\left(\frac{123}{368}\right)\) | \(e\left(\frac{93}{184}\right)\) | \(e\left(\frac{97}{184}\right)\) | \(e\left(\frac{91}{368}\right)\) | \(e\left(\frac{111}{368}\right)\) |
| \(\chi_{799}(57,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{184}\right)\) | \(e\left(\frac{73}{368}\right)\) | \(e\left(\frac{11}{92}\right)\) | \(e\left(\frac{37}{368}\right)\) | \(e\left(\frac{279}{368}\right)\) | \(e\left(\frac{195}{368}\right)\) | \(e\left(\frac{125}{184}\right)\) | \(e\left(\frac{73}{184}\right)\) | \(e\left(\frac{243}{368}\right)\) | \(e\left(\frac{167}{368}\right)\) |
| \(\chi_{799}(58,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{184}\right)\) | \(e\left(\frac{269}{368}\right)\) | \(e\left(\frac{67}{92}\right)\) | \(e\left(\frac{217}{368}\right)\) | \(e\left(\frac{35}{368}\right)\) | \(e\left(\frac{159}{368}\right)\) | \(e\left(\frac{17}{184}\right)\) | \(e\left(\frac{85}{184}\right)\) | \(e\left(\frac{351}{368}\right)\) | \(e\left(\frac{323}{368}\right)\) |
| \(\chi_{799}(62,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{63}{184}\right)\) | \(e\left(\frac{209}{368}\right)\) | \(e\left(\frac{63}{92}\right)\) | \(e\left(\frac{237}{368}\right)\) | \(e\left(\frac{335}{368}\right)\) | \(e\left(\frac{155}{368}\right)\) | \(e\left(\frac{5}{184}\right)\) | \(e\left(\frac{25}{184}\right)\) | \(e\left(\frac{363}{368}\right)\) | \(e\left(\frac{95}{368}\right)\) |
| \(\chi_{799}(73,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{133}{184}\right)\) | \(e\left(\frac{339}{368}\right)\) | \(e\left(\frac{41}{92}\right)\) | \(e\left(\frac{71}{368}\right)\) | \(e\left(\frac{237}{368}\right)\) | \(e\left(\frac{225}{368}\right)\) | \(e\left(\frac{31}{184}\right)\) | \(e\left(\frac{155}{184}\right)\) | \(e\left(\frac{337}{368}\right)\) | \(e\left(\frac{221}{368}\right)\) |
| \(\chi_{799}(78,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{147}{184}\right)\) | \(e\left(\frac{181}{368}\right)\) | \(e\left(\frac{55}{92}\right)\) | \(e\left(\frac{1}{368}\right)\) | \(e\left(\frac{107}{368}\right)\) | \(e\left(\frac{55}{368}\right)\) | \(e\left(\frac{73}{184}\right)\) | \(e\left(\frac{181}{184}\right)\) | \(e\left(\frac{295}{368}\right)\) | \(e\left(\frac{283}{368}\right)\) |
| \(\chi_{799}(80,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{173}{184}\right)\) | \(e\left(\frac{203}{368}\right)\) | \(e\left(\frac{81}{92}\right)\) | \(e\left(\frac{239}{368}\right)\) | \(e\left(\frac{181}{368}\right)\) | \(e\left(\frac{265}{368}\right)\) | \(e\left(\frac{151}{184}\right)\) | \(e\left(\frac{19}{184}\right)\) | \(e\left(\frac{217}{368}\right)\) | \(e\left(\frac{293}{368}\right)\) |
| \(\chi_{799}(82,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{145}{184}\right)\) | \(e\left(\frac{335}{368}\right)\) | \(e\left(\frac{53}{92}\right)\) | \(e\left(\frac{195}{368}\right)\) | \(e\left(\frac{257}{368}\right)\) | \(e\left(\frac{53}{368}\right)\) | \(e\left(\frac{67}{184}\right)\) | \(e\left(\frac{151}{184}\right)\) | \(e\left(\frac{117}{368}\right)\) | \(e\left(\frac{353}{368}\right)\) |
| \(\chi_{799}(88,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{137}{184}\right)\) | \(e\left(\frac{215}{368}\right)\) | \(e\left(\frac{45}{92}\right)\) | \(e\left(\frac{235}{368}\right)\) | \(e\left(\frac{121}{368}\right)\) | \(e\left(\frac{45}{368}\right)\) | \(e\left(\frac{43}{184}\right)\) | \(e\left(\frac{31}{184}\right)\) | \(e\left(\frac{141}{368}\right)\) | \(e\left(\frac{265}{368}\right)\) |
| \(\chi_{799}(90,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{85}{184}\right)\) | \(e\left(\frac{355}{368}\right)\) | \(e\left(\frac{85}{92}\right)\) | \(e\left(\frac{311}{368}\right)\) | \(e\left(\frac{157}{368}\right)\) | \(e\left(\frac{177}{368}\right)\) | \(e\left(\frac{71}{184}\right)\) | \(e\left(\frac{171}{184}\right)\) | \(e\left(\frac{113}{368}\right)\) | \(e\left(\frac{61}{368}\right)\) |
| \(\chi_{799}(91,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{175}{184}\right)\) | \(e\left(\frac{233}{368}\right)\) | \(e\left(\frac{83}{92}\right)\) | \(e\left(\frac{229}{368}\right)\) | \(e\left(\frac{215}{368}\right)\) | \(e\left(\frac{83}{368}\right)\) | \(e\left(\frac{157}{184}\right)\) | \(e\left(\frac{49}{184}\right)\) | \(e\left(\frac{211}{368}\right)\) | \(e\left(\frac{39}{368}\right)\) |
| \(\chi_{799}(92,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{123}{184}\right)\) | \(e\left(\frac{189}{368}\right)\) | \(e\left(\frac{31}{92}\right)\) | \(e\left(\frac{121}{368}\right)\) | \(e\left(\frac{67}{368}\right)\) | \(e\left(\frac{31}{368}\right)\) | \(e\left(\frac{1}{184}\right)\) | \(e\left(\frac{5}{184}\right)\) | \(e\left(\frac{367}{368}\right)\) | \(e\left(\frac{19}{368}\right)\) |
| \(\chi_{799}(99,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{184}\right)\) | \(e\left(\frac{367}{368}\right)\) | \(e\left(\frac{49}{92}\right)\) | \(e\left(\frac{307}{368}\right)\) | \(e\left(\frac{97}{368}\right)\) | \(e\left(\frac{325}{368}\right)\) | \(e\left(\frac{147}{184}\right)\) | \(e\left(\frac{183}{184}\right)\) | \(e\left(\frac{37}{368}\right)\) | \(e\left(\frac{33}{368}\right)\) |
| \(\chi_{799}(105,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{184}\right)\) | \(e\left(\frac{39}{368}\right)\) | \(e\left(\frac{21}{92}\right)\) | \(e\left(\frac{171}{368}\right)\) | \(e\left(\frac{265}{368}\right)\) | \(e\left(\frac{205}{368}\right)\) | \(e\left(\frac{155}{184}\right)\) | \(e\left(\frac{39}{184}\right)\) | \(e\left(\frac{29}{368}\right)\) | \(e\left(\frac{185}{368}\right)\) |
| \(\chi_{799}(107,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{125}{184}\right)\) | \(e\left(\frac{35}{368}\right)\) | \(e\left(\frac{33}{92}\right)\) | \(e\left(\frac{295}{368}\right)\) | \(e\left(\frac{285}{368}\right)\) | \(e\left(\frac{33}{368}\right)\) | \(e\left(\frac{7}{184}\right)\) | \(e\left(\frac{35}{184}\right)\) | \(e\left(\frac{177}{368}\right)\) | \(e\left(\frac{317}{368}\right)\) |
| \(\chi_{799}(109,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{155}{184}\right)\) | \(e\left(\frac{301}{368}\right)\) | \(e\left(\frac{63}{92}\right)\) | \(e\left(\frac{329}{368}\right)\) | \(e\left(\frac{243}{368}\right)\) | \(e\left(\frac{63}{368}\right)\) | \(e\left(\frac{97}{184}\right)\) | \(e\left(\frac{117}{184}\right)\) | \(e\left(\frac{271}{368}\right)\) | \(e\left(\frac{3}{368}\right)\) |
| \(\chi_{799}(113,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{135}{184}\right)\) | \(e\left(\frac{1}{368}\right)\) | \(e\left(\frac{43}{92}\right)\) | \(e\left(\frac{61}{368}\right)\) | \(e\left(\frac{271}{368}\right)\) | \(e\left(\frac{43}{368}\right)\) | \(e\left(\frac{37}{184}\right)\) | \(e\left(\frac{1}{184}\right)\) | \(e\left(\frac{331}{368}\right)\) | \(e\left(\frac{335}{368}\right)\) |
| \(\chi_{799}(114,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{157}{184}\right)\) | \(e\left(\frac{331}{368}\right)\) | \(e\left(\frac{65}{92}\right)\) | \(e\left(\frac{319}{368}\right)\) | \(e\left(\frac{277}{368}\right)\) | \(e\left(\frac{249}{368}\right)\) | \(e\left(\frac{103}{184}\right)\) | \(e\left(\frac{147}{184}\right)\) | \(e\left(\frac{265}{368}\right)\) | \(e\left(\frac{117}{368}\right)\) |
| \(\chi_{799}(116,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{121}{184}\right)\) | \(e\left(\frac{159}{368}\right)\) | \(e\left(\frac{29}{92}\right)\) | \(e\left(\frac{131}{368}\right)\) | \(e\left(\frac{33}{368}\right)\) | \(e\left(\frac{213}{368}\right)\) | \(e\left(\frac{179}{184}\right)\) | \(e\left(\frac{159}{184}\right)\) | \(e\left(\frac{5}{368}\right)\) | \(e\left(\frac{273}{368}\right)\) |