from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2183, base_ring=CyclotomicField(348))
M = H._module
chi = DirichletCharacter(H, M([29,18]))
chi.galois_orbit()
[g,chi] = znchar(Mod(8,2183))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(2183\) | |
| Conductor: | \(2183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(348\) | 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: | $\Q(\zeta_{348})$ |
| Fixed field: | Number field defined by a degree 348 polynomial (not computed) |
First 31 of 112 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2183}(8,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{348}\right)\) | \(e\left(\frac{131}{174}\right)\) | \(e\left(\frac{47}{174}\right)\) | \(e\left(\frac{79}{348}\right)\) | \(e\left(\frac{103}{116}\right)\) | \(e\left(\frac{52}{87}\right)\) | \(e\left(\frac{47}{116}\right)\) | \(e\left(\frac{44}{87}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{23}{29}\right)\) |
| \(\chi_{2183}(14,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{85}{348}\right)\) | \(e\left(\frac{37}{174}\right)\) | \(e\left(\frac{85}{174}\right)\) | \(e\left(\frac{17}{348}\right)\) | \(e\left(\frac{53}{116}\right)\) | \(e\left(\frac{20}{87}\right)\) | \(e\left(\frac{85}{116}\right)\) | \(e\left(\frac{37}{87}\right)\) | \(e\left(\frac{17}{58}\right)\) | \(e\left(\frac{20}{29}\right)\) |
| \(\chi_{2183}(23,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{235}{348}\right)\) | \(e\left(\frac{133}{174}\right)\) | \(e\left(\frac{61}{174}\right)\) | \(e\left(\frac{47}{348}\right)\) | \(e\left(\frac{51}{116}\right)\) | \(e\left(\frac{86}{87}\right)\) | \(e\left(\frac{3}{116}\right)\) | \(e\left(\frac{46}{87}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{28}{29}\right)\) |
| \(\chi_{2183}(82,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{348}\right)\) | \(e\left(\frac{17}{174}\right)\) | \(e\left(\frac{119}{174}\right)\) | \(e\left(\frac{163}{348}\right)\) | \(e\left(\frac{51}{116}\right)\) | \(e\left(\frac{28}{87}\right)\) | \(e\left(\frac{3}{116}\right)\) | \(e\left(\frac{17}{87}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{28}{29}\right)\) |
| \(\chi_{2183}(97,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{348}\right)\) | \(e\left(\frac{79}{174}\right)\) | \(e\left(\frac{31}{174}\right)\) | \(e\left(\frac{215}{348}\right)\) | \(e\left(\frac{63}{116}\right)\) | \(e\left(\frac{38}{87}\right)\) | \(e\left(\frac{31}{116}\right)\) | \(e\left(\frac{79}{87}\right)\) | \(e\left(\frac{41}{58}\right)\) | \(e\left(\frac{9}{29}\right)\) |
| \(\chi_{2183}(103,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{348}\right)\) | \(e\left(\frac{77}{174}\right)\) | \(e\left(\frac{17}{174}\right)\) | \(e\left(\frac{73}{348}\right)\) | \(e\left(\frac{57}{116}\right)\) | \(e\left(\frac{4}{87}\right)\) | \(e\left(\frac{17}{116}\right)\) | \(e\left(\frac{77}{87}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{4}{29}\right)\) |
| \(\chi_{2183}(156,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{263}{348}\right)\) | \(e\left(\frac{137}{174}\right)\) | \(e\left(\frac{89}{174}\right)\) | \(e\left(\frac{331}{348}\right)\) | \(e\left(\frac{63}{116}\right)\) | \(e\left(\frac{67}{87}\right)\) | \(e\left(\frac{31}{116}\right)\) | \(e\left(\frac{50}{87}\right)\) | \(e\left(\frac{41}{58}\right)\) | \(e\left(\frac{9}{29}\right)\) |
| \(\chi_{2183}(162,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{133}{348}\right)\) | \(e\left(\frac{19}{174}\right)\) | \(e\left(\frac{133}{174}\right)\) | \(e\left(\frac{305}{348}\right)\) | \(e\left(\frac{57}{116}\right)\) | \(e\left(\frac{62}{87}\right)\) | \(e\left(\frac{17}{116}\right)\) | \(e\left(\frac{19}{87}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{4}{29}\right)\) |
| \(\chi_{2183}(208,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{91}{348}\right)\) | \(e\left(\frac{13}{174}\right)\) | \(e\left(\frac{91}{174}\right)\) | \(e\left(\frac{227}{348}\right)\) | \(e\left(\frac{39}{116}\right)\) | \(e\left(\frac{47}{87}\right)\) | \(e\left(\frac{91}{116}\right)\) | \(e\left(\frac{13}{87}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{18}{29}\right)\) |
| \(\chi_{2183}(214,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{185}{348}\right)\) | \(e\left(\frac{101}{174}\right)\) | \(e\left(\frac{11}{174}\right)\) | \(e\left(\frac{37}{348}\right)\) | \(e\left(\frac{13}{116}\right)\) | \(e\left(\frac{64}{87}\right)\) | \(e\left(\frac{69}{116}\right)\) | \(e\left(\frac{14}{87}\right)\) | \(e\left(\frac{37}{58}\right)\) | \(e\left(\frac{6}{29}\right)\) |
| \(\chi_{2183}(267,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{323}{348}\right)\) | \(e\left(\frac{71}{174}\right)\) | \(e\left(\frac{149}{174}\right)\) | \(e\left(\frac{343}{348}\right)\) | \(e\left(\frac{39}{116}\right)\) | \(e\left(\frac{76}{87}\right)\) | \(e\left(\frac{91}{116}\right)\) | \(e\left(\frac{71}{87}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{18}{29}\right)\) |
| \(\chi_{2183}(273,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{301}{348}\right)\) | \(e\left(\frac{43}{174}\right)\) | \(e\left(\frac{127}{174}\right)\) | \(e\left(\frac{269}{348}\right)\) | \(e\left(\frac{13}{116}\right)\) | \(e\left(\frac{35}{87}\right)\) | \(e\left(\frac{69}{116}\right)\) | \(e\left(\frac{43}{87}\right)\) | \(e\left(\frac{37}{58}\right)\) | \(e\left(\frac{6}{29}\right)\) |
| \(\chi_{2183}(288,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{137}{348}\right)\) | \(e\left(\frac{119}{174}\right)\) | \(e\left(\frac{137}{174}\right)\) | \(e\left(\frac{97}{348}\right)\) | \(e\left(\frac{9}{116}\right)\) | \(e\left(\frac{22}{87}\right)\) | \(e\left(\frac{21}{116}\right)\) | \(e\left(\frac{32}{87}\right)\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{22}{29}\right)\) |
| \(\chi_{2183}(319,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{115}{348}\right)\) | \(e\left(\frac{91}{174}\right)\) | \(e\left(\frac{115}{174}\right)\) | \(e\left(\frac{23}{348}\right)\) | \(e\left(\frac{99}{116}\right)\) | \(e\left(\frac{68}{87}\right)\) | \(e\left(\frac{115}{116}\right)\) | \(e\left(\frac{4}{87}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{10}{29}\right)\) |
| \(\chi_{2183}(325,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{197}{348}\right)\) | \(e\left(\frac{53}{174}\right)\) | \(e\left(\frac{23}{174}\right)\) | \(e\left(\frac{109}{348}\right)\) | \(e\left(\frac{101}{116}\right)\) | \(e\left(\frac{31}{87}\right)\) | \(e\left(\frac{81}{116}\right)\) | \(e\left(\frac{53}{87}\right)\) | \(e\left(\frac{51}{58}\right)\) | \(e\left(\frac{2}{29}\right)\) |
| \(\chi_{2183}(347,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{253}{348}\right)\) | \(e\left(\frac{61}{174}\right)\) | \(e\left(\frac{79}{174}\right)\) | \(e\left(\frac{329}{348}\right)\) | \(e\left(\frac{9}{116}\right)\) | \(e\left(\frac{80}{87}\right)\) | \(e\left(\frac{21}{116}\right)\) | \(e\left(\frac{61}{87}\right)\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{22}{29}\right)\) |
| \(\chi_{2183}(356,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{151}{348}\right)\) | \(e\left(\frac{121}{174}\right)\) | \(e\left(\frac{151}{174}\right)\) | \(e\left(\frac{239}{348}\right)\) | \(e\left(\frac{15}{116}\right)\) | \(e\left(\frac{56}{87}\right)\) | \(e\left(\frac{35}{116}\right)\) | \(e\left(\frac{34}{87}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{27}{29}\right)\) |
| \(\chi_{2183}(362,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{221}{348}\right)\) | \(e\left(\frac{131}{174}\right)\) | \(e\left(\frac{47}{174}\right)\) | \(e\left(\frac{253}{348}\right)\) | \(e\left(\frac{45}{116}\right)\) | \(e\left(\frac{52}{87}\right)\) | \(e\left(\frac{105}{116}\right)\) | \(e\left(\frac{44}{87}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{23}{29}\right)\) |
| \(\chi_{2183}(378,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{347}{348}\right)\) | \(e\left(\frac{149}{174}\right)\) | \(e\left(\frac{173}{174}\right)\) | \(e\left(\frac{139}{348}\right)\) | \(e\left(\frac{99}{116}\right)\) | \(e\left(\frac{10}{87}\right)\) | \(e\left(\frac{115}{116}\right)\) | \(e\left(\frac{62}{87}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{10}{29}\right)\) |
| \(\chi_{2183}(384,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{313}{348}\right)\) | \(e\left(\frac{169}{174}\right)\) | \(e\left(\frac{139}{174}\right)\) | \(e\left(\frac{341}{348}\right)\) | \(e\left(\frac{101}{116}\right)\) | \(e\left(\frac{2}{87}\right)\) | \(e\left(\frac{81}{116}\right)\) | \(e\left(\frac{82}{87}\right)\) | \(e\left(\frac{51}{58}\right)\) | \(e\left(\frac{2}{29}\right)\) |
| \(\chi_{2183}(393,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{348}\right)\) | \(e\left(\frac{127}{174}\right)\) | \(e\left(\frac{19}{174}\right)\) | \(e\left(\frac{143}{348}\right)\) | \(e\left(\frac{91}{116}\right)\) | \(e\left(\frac{71}{87}\right)\) | \(e\left(\frac{19}{116}\right)\) | \(e\left(\frac{40}{87}\right)\) | \(e\left(\frac{27}{58}\right)\) | \(e\left(\frac{13}{29}\right)\) |
| \(\chi_{2183}(415,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{35}{348}\right)\) | \(e\left(\frac{5}{174}\right)\) | \(e\left(\frac{35}{174}\right)\) | \(e\left(\frac{7}{348}\right)\) | \(e\left(\frac{15}{116}\right)\) | \(e\left(\frac{85}{87}\right)\) | \(e\left(\frac{35}{116}\right)\) | \(e\left(\frac{5}{87}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{27}{29}\right)\) |
| \(\chi_{2183}(421,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{337}{348}\right)\) | \(e\left(\frac{73}{174}\right)\) | \(e\left(\frac{163}{174}\right)\) | \(e\left(\frac{137}{348}\right)\) | \(e\left(\frac{45}{116}\right)\) | \(e\left(\frac{23}{87}\right)\) | \(e\left(\frac{105}{116}\right)\) | \(e\left(\frac{73}{87}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{23}{29}\right)\) |
| \(\chi_{2183}(436,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{293}{348}\right)\) | \(e\left(\frac{17}{174}\right)\) | \(e\left(\frac{119}{174}\right)\) | \(e\left(\frac{337}{348}\right)\) | \(e\left(\frac{109}{116}\right)\) | \(e\left(\frac{28}{87}\right)\) | \(e\left(\frac{61}{116}\right)\) | \(e\left(\frac{17}{87}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{28}{29}\right)\) |
| \(\chi_{2183}(452,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{251}{348}\right)\) | \(e\left(\frac{11}{174}\right)\) | \(e\left(\frac{77}{174}\right)\) | \(e\left(\frac{259}{348}\right)\) | \(e\left(\frac{91}{116}\right)\) | \(e\left(\frac{13}{87}\right)\) | \(e\left(\frac{19}{116}\right)\) | \(e\left(\frac{11}{87}\right)\) | \(e\left(\frac{27}{58}\right)\) | \(e\left(\frac{13}{29}\right)\) |
| \(\chi_{2183}(467,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{348}\right)\) | \(e\left(\frac{1}{174}\right)\) | \(e\left(\frac{7}{174}\right)\) | \(e\left(\frac{71}{348}\right)\) | \(e\left(\frac{3}{116}\right)\) | \(e\left(\frac{17}{87}\right)\) | \(e\left(\frac{7}{116}\right)\) | \(e\left(\frac{1}{87}\right)\) | \(e\left(\frac{13}{58}\right)\) | \(e\left(\frac{17}{29}\right)\) |
| \(\chi_{2183}(495,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{348}\right)\) | \(e\left(\frac{133}{174}\right)\) | \(e\left(\frac{61}{174}\right)\) | \(e\left(\frac{221}{348}\right)\) | \(e\left(\frac{109}{116}\right)\) | \(e\left(\frac{86}{87}\right)\) | \(e\left(\frac{61}{116}\right)\) | \(e\left(\frac{46}{87}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{28}{29}\right)\) |
| \(\chi_{2183}(504,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{175}{348}\right)\) | \(e\left(\frac{25}{174}\right)\) | \(e\left(\frac{1}{174}\right)\) | \(e\left(\frac{35}{348}\right)\) | \(e\left(\frac{75}{116}\right)\) | \(e\left(\frac{77}{87}\right)\) | \(e\left(\frac{59}{116}\right)\) | \(e\left(\frac{25}{87}\right)\) | \(e\left(\frac{35}{58}\right)\) | \(e\left(\frac{19}{29}\right)\) |
| \(\chi_{2183}(510,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{348}\right)\) | \(e\left(\frac{137}{174}\right)\) | \(e\left(\frac{89}{174}\right)\) | \(e\left(\frac{157}{348}\right)\) | \(e\left(\frac{5}{116}\right)\) | \(e\left(\frac{67}{87}\right)\) | \(e\left(\frac{89}{116}\right)\) | \(e\left(\frac{50}{87}\right)\) | \(e\left(\frac{41}{58}\right)\) | \(e\left(\frac{9}{29}\right)\) |
| \(\chi_{2183}(526,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{239}{348}\right)\) | \(e\left(\frac{59}{174}\right)\) | \(e\left(\frac{65}{174}\right)\) | \(e\left(\frac{187}{348}\right)\) | \(e\left(\frac{3}{116}\right)\) | \(e\left(\frac{46}{87}\right)\) | \(e\left(\frac{7}{116}\right)\) | \(e\left(\frac{59}{87}\right)\) | \(e\left(\frac{13}{58}\right)\) | \(e\left(\frac{17}{29}\right)\) |
| \(\chi_{2183}(541,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{187}{348}\right)\) | \(e\left(\frac{151}{174}\right)\) | \(e\left(\frac{13}{174}\right)\) | \(e\left(\frac{107}{348}\right)\) | \(e\left(\frac{47}{116}\right)\) | \(e\left(\frac{44}{87}\right)\) | \(e\left(\frac{71}{116}\right)\) | \(e\left(\frac{64}{87}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{15}{29}\right)\) |