from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2493, base_ring=CyclotomicField(276))
M = H._module
chi = DirichletCharacter(H, M([138,103]))
chi.galois_orbit()
[g,chi] = znchar(Mod(17,2493))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(2493\) | |
| Conductor: | \(831\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(276\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 831.w | 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: | $\Q(\zeta_{276})$ |
| Fixed field: | Number field defined by a degree 276 polynomial (not computed) |
First 31 of 88 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2493}(17,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{33}{92}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{241}{276}\right)\) | \(e\left(\frac{29}{138}\right)\) | \(e\left(\frac{7}{92}\right)\) | \(e\left(\frac{16}{69}\right)\) | \(e\left(\frac{31}{276}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{157}{276}\right)\) | \(e\left(\frac{10}{23}\right)\) |
| \(\chi_{2493}(44,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{75}{92}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{163}{276}\right)\) | \(e\left(\frac{137}{138}\right)\) | \(e\left(\frac{41}{92}\right)\) | \(e\left(\frac{28}{69}\right)\) | \(e\left(\frac{37}{276}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{223}{276}\right)\) | \(e\left(\frac{6}{23}\right)\) |
| \(\chi_{2493}(53,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{92}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{205}{276}\right)\) | \(e\left(\frac{47}{138}\right)\) | \(e\left(\frac{51}{92}\right)\) | \(e\left(\frac{64}{69}\right)\) | \(e\left(\frac{55}{276}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{145}{276}\right)\) | \(e\left(\frac{17}{23}\right)\) |
| \(\chi_{2493}(80,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{92}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{175}{276}\right)\) | \(e\left(\frac{131}{138}\right)\) | \(e\left(\frac{57}{92}\right)\) | \(e\left(\frac{58}{69}\right)\) | \(e\left(\frac{121}{276}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{43}{276}\right)\) | \(e\left(\frac{19}{23}\right)\) |
| \(\chi_{2493}(98,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{21}{92}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{53}{276}\right)\) | \(e\left(\frac{31}{138}\right)\) | \(e\left(\frac{63}{92}\right)\) | \(e\left(\frac{29}{69}\right)\) | \(e\left(\frac{95}{276}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{125}{276}\right)\) | \(e\left(\frac{21}{23}\right)\) |
| \(\chi_{2493}(107,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{63}{92}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{251}{276}\right)\) | \(e\left(\frac{1}{138}\right)\) | \(e\left(\frac{5}{92}\right)\) | \(e\left(\frac{41}{69}\right)\) | \(e\left(\frac{101}{276}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{191}{276}\right)\) | \(e\left(\frac{17}{23}\right)\) |
| \(\chi_{2493}(134,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{92}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{229}{276}\right)\) | \(e\left(\frac{35}{138}\right)\) | \(e\left(\frac{83}{92}\right)\) | \(e\left(\frac{55}{69}\right)\) | \(e\left(\frac{223}{276}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{61}{276}\right)\) | \(e\left(\frac{20}{23}\right)\) |
| \(\chi_{2493}(143,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{92}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{91}{276}\right)\) | \(e\left(\frac{35}{138}\right)\) | \(e\left(\frac{37}{92}\right)\) | \(e\left(\frac{55}{69}\right)\) | \(e\left(\frac{85}{276}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{199}{276}\right)\) | \(e\left(\frac{20}{23}\right)\) |
| \(\chi_{2493}(170,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{92}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{113}{276}\right)\) | \(e\left(\frac{1}{138}\right)\) | \(e\left(\frac{51}{92}\right)\) | \(e\left(\frac{41}{69}\right)\) | \(e\left(\frac{239}{276}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{53}{276}\right)\) | \(e\left(\frac{17}{23}\right)\) |
| \(\chi_{2493}(179,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{92}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{191}{276}\right)\) | \(e\left(\frac{31}{138}\right)\) | \(e\left(\frac{17}{92}\right)\) | \(e\left(\frac{29}{69}\right)\) | \(e\left(\frac{233}{276}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{263}{276}\right)\) | \(e\left(\frac{21}{23}\right)\) |
| \(\chi_{2493}(197,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{65}{92}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{37}{276}\right)\) | \(e\left(\frac{131}{138}\right)\) | \(e\left(\frac{11}{92}\right)\) | \(e\left(\frac{58}{69}\right)\) | \(e\left(\frac{259}{276}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{181}{276}\right)\) | \(e\left(\frac{19}{23}\right)\) |
| \(\chi_{2493}(224,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{63}{92}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{67}{276}\right)\) | \(e\left(\frac{47}{138}\right)\) | \(e\left(\frac{5}{92}\right)\) | \(e\left(\frac{64}{69}\right)\) | \(e\left(\frac{193}{276}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{7}{276}\right)\) | \(e\left(\frac{17}{23}\right)\) |
| \(\chi_{2493}(233,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{92}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{25}{276}\right)\) | \(e\left(\frac{137}{138}\right)\) | \(e\left(\frac{87}{92}\right)\) | \(e\left(\frac{28}{69}\right)\) | \(e\left(\frac{175}{276}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{85}{276}\right)\) | \(e\left(\frac{6}{23}\right)\) |
| \(\chi_{2493}(260,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{92}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{103}{276}\right)\) | \(e\left(\frac{29}{138}\right)\) | \(e\left(\frac{53}{92}\right)\) | \(e\left(\frac{16}{69}\right)\) | \(e\left(\frac{169}{276}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{19}{276}\right)\) | \(e\left(\frac{10}{23}\right)\) |
| \(\chi_{2493}(323,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{92}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{217}{276}\right)\) | \(e\left(\frac{41}{138}\right)\) | \(e\left(\frac{67}{92}\right)\) | \(e\left(\frac{25}{69}\right)\) | \(e\left(\frac{139}{276}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{241}{276}\right)\) | \(e\left(\frac{7}{23}\right)\) |
| \(\chi_{2493}(404,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{45}{92}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{61}{276}\right)\) | \(e\left(\frac{119}{138}\right)\) | \(e\left(\frac{43}{92}\right)\) | \(e\left(\frac{49}{69}\right)\) | \(e\left(\frac{151}{276}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{97}{276}\right)\) | \(e\left(\frac{22}{23}\right)\) |
| \(\chi_{2493}(440,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{92}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{35}{276}\right)\) | \(e\left(\frac{109}{138}\right)\) | \(e\left(\frac{85}{92}\right)\) | \(e\left(\frac{53}{69}\right)\) | \(e\left(\frac{245}{276}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{119}{276}\right)\) | \(e\left(\frac{13}{23}\right)\) |
| \(\chi_{2493}(449,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{35}{92}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{211}{276}\right)\) | \(e\left(\frac{113}{138}\right)\) | \(e\left(\frac{13}{92}\right)\) | \(e\left(\frac{10}{69}\right)\) | \(e\left(\frac{97}{276}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{55}{276}\right)\) | \(e\left(\frac{12}{23}\right)\) |
| \(\chi_{2493}(458,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{55}{92}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{95}{276}\right)\) | \(e\left(\frac{79}{138}\right)\) | \(e\left(\frac{73}{92}\right)\) | \(e\left(\frac{65}{69}\right)\) | \(e\left(\frac{113}{276}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{47}{276}\right)\) | \(e\left(\frac{9}{23}\right)\) |
| \(\chi_{2493}(476,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{92}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{5}{276}\right)\) | \(e\left(\frac{55}{138}\right)\) | \(e\left(\frac{91}{92}\right)\) | \(e\left(\frac{47}{69}\right)\) | \(e\left(\frac{35}{276}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{17}{276}\right)\) | \(e\left(\frac{15}{23}\right)\) |
| \(\chi_{2493}(530,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{92}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{77}{276}\right)\) | \(e\left(\frac{19}{138}\right)\) | \(e\left(\frac{3}{92}\right)\) | \(e\left(\frac{20}{69}\right)\) | \(e\left(\frac{263}{276}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{41}{276}\right)\) | \(e\left(\frac{1}{23}\right)\) |
| \(\chi_{2493}(548,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{39}{92}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{59}{276}\right)\) | \(e\left(\frac{97}{138}\right)\) | \(e\left(\frac{25}{92}\right)\) | \(e\left(\frac{44}{69}\right)\) | \(e\left(\frac{137}{276}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{35}{276}\right)\) | \(e\left(\frac{16}{23}\right)\) |
| \(\chi_{2493}(647,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{92}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{97}{276}\right)\) | \(e\left(\frac{101}{138}\right)\) | \(e\left(\frac{91}{92}\right)\) | \(e\left(\frac{1}{69}\right)\) | \(e\left(\frac{127}{276}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{109}{276}\right)\) | \(e\left(\frac{15}{23}\right)\) |
| \(\chi_{2493}(665,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{92}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{137}{276}\right)\) | \(e\left(\frac{127}{138}\right)\) | \(e\left(\frac{83}{92}\right)\) | \(e\left(\frac{32}{69}\right)\) | \(e\left(\frac{131}{276}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{245}{276}\right)\) | \(e\left(\frac{20}{23}\right)\) |
| \(\chi_{2493}(728,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{92}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{271}{276}\right)\) | \(e\left(\frac{83}{138}\right)\) | \(e\left(\frac{1}{92}\right)\) | \(e\left(\frac{22}{69}\right)\) | \(e\left(\frac{241}{276}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{259}{276}\right)\) | \(e\left(\frac{8}{23}\right)\) |
| \(\chi_{2493}(737,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{92}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{89}{276}\right)\) | \(e\left(\frac{13}{138}\right)\) | \(e\left(\frac{19}{92}\right)\) | \(e\left(\frac{50}{69}\right)\) | \(e\left(\frac{71}{276}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{137}{276}\right)\) | \(e\left(\frac{14}{23}\right)\) |
| \(\chi_{2493}(773,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{65}{92}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{221}{276}\right)\) | \(e\left(\frac{85}{138}\right)\) | \(e\left(\frac{11}{92}\right)\) | \(e\left(\frac{35}{69}\right)\) | \(e\left(\frac{167}{276}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{89}{276}\right)\) | \(e\left(\frac{19}{23}\right)\) |
| \(\chi_{2493}(800,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{92}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{47}{276}\right)\) | \(e\left(\frac{103}{138}\right)\) | \(e\left(\frac{9}{92}\right)\) | \(e\left(\frac{14}{69}\right)\) | \(e\left(\frac{53}{276}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{215}{276}\right)\) | \(e\left(\frac{3}{23}\right)\) |
| \(\chi_{2493}(836,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{92}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{139}{276}\right)\) | \(e\left(\frac{11}{138}\right)\) | \(e\left(\frac{9}{92}\right)\) | \(e\left(\frac{37}{69}\right)\) | \(e\left(\frac{145}{276}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{31}{276}\right)\) | \(e\left(\frac{3}{23}\right)\) |
| \(\chi_{2493}(845,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{92}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{31}{276}\right)\) | \(e\left(\frac{65}{138}\right)\) | \(e\left(\frac{49}{92}\right)\) | \(e\left(\frac{43}{69}\right)\) | \(e\left(\frac{217}{276}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{271}{276}\right)\) | \(e\left(\frac{1}{23}\right)\) |
| \(\chi_{2493}(881,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{92}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{11}{276}\right)\) | \(e\left(\frac{121}{138}\right)\) | \(e\left(\frac{53}{92}\right)\) | \(e\left(\frac{62}{69}\right)\) | \(e\left(\frac{77}{276}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{203}{276}\right)\) | \(e\left(\frac{10}{23}\right)\) |