from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(110))
M = H._module
chi = DirichletCharacter(H, M([0,3]))
chi.galois_orbit()
[g,chi] = znchar(Mod(8,847))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(847\) | |
Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 121.h | 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: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
First 31 of 40 characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{847}(8,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{83}{110}\right)\) |
\(\chi_{847}(29,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{67}{110}\right)\) |
\(\chi_{847}(50,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{89}{110}\right)\) |
\(\chi_{847}(57,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{1}{110}\right)\) |
\(\chi_{847}(85,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{103}{110}\right)\) |
\(\chi_{847}(106,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{27}{110}\right)\) |
\(\chi_{847}(127,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{79}{110}\right)\) |
\(\chi_{847}(134,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{81}{110}\right)\) |
\(\chi_{847}(162,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{13}{110}\right)\) |
\(\chi_{847}(183,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{97}{110}\right)\) |
\(\chi_{847}(204,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{69}{110}\right)\) |
\(\chi_{847}(211,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{51}{110}\right)\) |
\(\chi_{847}(260,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{91}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{57}{110}\right)\) |
\(\chi_{847}(281,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{59}{110}\right)\) |
\(\chi_{847}(288,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{21}{110}\right)\) |
\(\chi_{847}(316,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{53}{110}\right)\) |
\(\chi_{847}(337,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{17}{110}\right)\) |
\(\chi_{847}(358,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{49}{110}\right)\) |
\(\chi_{847}(365,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{101}{110}\right)\) |
\(\chi_{847}(393,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{73}{110}\right)\) |
\(\chi_{847}(414,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{27}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{87}{110}\right)\) |
\(\chi_{847}(435,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{91}{110}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{39}{110}\right)\) |
\(\chi_{847}(442,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{71}{110}\right)\) |
\(\chi_{847}(470,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{93}{110}\right)\) |
\(\chi_{847}(491,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{47}{110}\right)\) |
\(\chi_{847}(512,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{27}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{29}{110}\right)\) |
\(\chi_{847}(519,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{41}{110}\right)\) |
\(\chi_{847}(547,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{110}\right)\) |
\(\chi_{847}(568,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{7}{110}\right)\) |
\(\chi_{847}(589,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{19}{110}\right)\) |
\(\chi_{847}(624,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{23}{110}\right)\) |