from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(916, base_ring=CyclotomicField(228))
M = H._module
chi = DirichletCharacter(H, M([0,145]))
chi.galois_orbit()
[g,chi] = znchar(Mod(29,916))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(916\) | |
| Conductor: | \(229\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(228\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 229.l | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
First 31 of 72 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{916}(29,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{37}{114}\right)\) | \(e\left(\frac{11}{228}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{31}{76}\right)\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{25}{76}\right)\) |
| \(\chi_{916}(41,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{41}{114}\right)\) | \(e\left(\frac{157}{228}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{21}{76}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{39}{76}\right)\) |
| \(\chi_{916}(65,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{8}{57}\right)\) | \(e\left(\frac{47}{114}\right)\) | \(e\left(\frac{205}{228}\right)\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{25}{76}\right)\) | \(e\left(\frac{21}{38}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{3}{76}\right)\) |
| \(\chi_{916}(69,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{29}{114}\right)\) | \(e\left(\frac{175}{228}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{51}{76}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{73}{76}\right)\) |
| \(\chi_{916}(73,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{167}{228}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{63}{76}\right)\) | \(e\left(\frac{21}{38}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{41}{76}\right)\) |
| \(\chi_{916}(77,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{71}{114}\right)\) | \(e\left(\frac{55}{228}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{3}{76}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{49}{76}\right)\) |
| \(\chi_{916}(105,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{59}{114}\right)\) | \(e\left(\frac{187}{228}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{71}{76}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{45}{76}\right)\) |
| \(\chi_{916}(113,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{43}{114}\right)\) | \(e\left(\frac{59}{228}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{35}{76}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{65}{76}\right)\) |
| \(\chi_{916}(117,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{11}{114}\right)\) | \(e\left(\frac{31}{228}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{39}{76}\right)\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{29}{76}\right)\) |
| \(\chi_{916}(133,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{61}{114}\right)\) | \(e\left(\frac{89}{228}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{9}{76}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{71}{76}\right)\) |
| \(\chi_{916}(137,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{83}{228}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{75}{76}\right)\) | \(e\left(\frac{25}{38}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{9}{76}\right)\) |
| \(\chi_{916}(157,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{56}{57}\right)\) | \(e\left(\frac{101}{114}\right)\) | \(e\left(\frac{67}{228}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{23}{76}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{21}{76}\right)\) |
| \(\chi_{916}(189,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{23}{114}\right)\) | \(e\left(\frac{13}{228}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{9}{76}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{71}{76}\right)\) |
| \(\chi_{916}(201,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{97}{228}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{73}{76}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{27}{76}\right)\) |
| \(\chi_{916}(205,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{155}{228}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{21}{38}\right)\) | \(e\left(\frac{43}{76}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{69}{76}\right)\) |
| \(\chi_{916}(253,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{41}{228}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{21}{38}\right)\) | \(e\left(\frac{5}{76}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{31}{76}\right)\) |
| \(\chi_{916}(257,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{211}{228}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{35}{76}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{65}{76}\right)\) |
| \(\chi_{916}(269,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{23}{114}\right)\) | \(e\left(\frac{127}{228}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{47}{76}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{33}{76}\right)\) |
| \(\chi_{916}(301,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{56}{57}\right)\) | \(e\left(\frac{101}{114}\right)\) | \(e\left(\frac{181}{228}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{61}{76}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{59}{76}\right)\) |
| \(\chi_{916}(321,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{197}{228}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{37}{76}\right)\) | \(e\left(\frac{25}{38}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{47}{76}\right)\) |
| \(\chi_{916}(325,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{61}{114}\right)\) | \(e\left(\frac{203}{228}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{47}{76}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{33}{76}\right)\) |
| \(\chi_{916}(341,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{11}{114}\right)\) | \(e\left(\frac{145}{228}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{1}{76}\right)\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{67}{76}\right)\) |
| \(\chi_{916}(345,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{43}{114}\right)\) | \(e\left(\frac{173}{228}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{73}{76}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{27}{76}\right)\) |
| \(\chi_{916}(353,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{59}{114}\right)\) | \(e\left(\frac{73}{228}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{33}{76}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{7}{76}\right)\) |
| \(\chi_{916}(381,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{71}{114}\right)\) | \(e\left(\frac{169}{228}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{41}{76}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{11}{76}\right)\) |
| \(\chi_{916}(385,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{53}{228}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{25}{76}\right)\) | \(e\left(\frac{21}{38}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{3}{76}\right)\) |
| \(\chi_{916}(389,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{29}{114}\right)\) | \(e\left(\frac{61}{228}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{13}{76}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{35}{76}\right)\) |
| \(\chi_{916}(393,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{8}{57}\right)\) | \(e\left(\frac{47}{114}\right)\) | \(e\left(\frac{91}{228}\right)\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{63}{76}\right)\) | \(e\left(\frac{21}{38}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{41}{76}\right)\) |
| \(\chi_{916}(417,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{41}{114}\right)\) | \(e\left(\frac{43}{228}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{59}{76}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{1}{76}\right)\) |
| \(\chi_{916}(429,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{37}{114}\right)\) | \(e\left(\frac{125}{228}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{69}{76}\right)\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{63}{76}\right)\) |
| \(\chi_{916}(465,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{113}{114}\right)\) | \(e\left(\frac{49}{228}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{69}{76}\right)\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{63}{76}\right)\) |