from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(801, base_ring=CyclotomicField(88))
M = H._module
chi = DirichletCharacter(H, M([0,35]))
chi.galois_orbit()
[g,chi] = znchar(Mod(19,801))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(801\) | |
Conductor: | \(89\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 89.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: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
First 31 of 40 characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{801}(19,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{19}{88}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{13}{88}\right)\) | \(e\left(\frac{51}{88}\right)\) | \(e\left(\frac{5}{11}\right)\) |
\(\chi_{801}(28,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{1}{88}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{47}{88}\right)\) | \(e\left(\frac{49}{88}\right)\) | \(e\left(\frac{2}{11}\right)\) |
\(\chi_{801}(46,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{17}{88}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{7}{88}\right)\) | \(e\left(\frac{41}{88}\right)\) | \(e\left(\frac{1}{11}\right)\) |
\(\chi_{801}(82,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{5}{88}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{59}{88}\right)\) | \(e\left(\frac{69}{88}\right)\) | \(e\left(\frac{10}{11}\right)\) |
\(\chi_{801}(118,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{27}{88}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{37}{88}\right)\) | \(e\left(\frac{3}{88}\right)\) | \(e\left(\frac{10}{11}\right)\) |
\(\chi_{801}(127,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{83}{88}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{29}{88}\right)\) | \(e\left(\frac{19}{88}\right)\) | \(e\left(\frac{1}{11}\right)\) |
\(\chi_{801}(145,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{65}{88}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{63}{88}\right)\) | \(e\left(\frac{17}{88}\right)\) | \(e\left(\frac{9}{11}\right)\) |
\(\chi_{801}(154,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{53}{88}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{27}{88}\right)\) | \(e\left(\frac{45}{88}\right)\) | \(e\left(\frac{7}{11}\right)\) |
\(\chi_{801}(163,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{75}{88}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{5}{88}\right)\) | \(e\left(\frac{67}{88}\right)\) | \(e\left(\frac{7}{11}\right)\) |
\(\chi_{801}(172,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{13}{88}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{83}{88}\right)\) | \(e\left(\frac{21}{88}\right)\) | \(e\left(\frac{4}{11}\right)\) |
\(\chi_{801}(181,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{81}{88}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{23}{88}\right)\) | \(e\left(\frac{9}{88}\right)\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{801}(208,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{7}{88}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{65}{88}\right)\) | \(e\left(\frac{79}{88}\right)\) | \(e\left(\frac{3}{11}\right)\) |
\(\chi_{801}(226,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{73}{88}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{87}{88}\right)\) | \(e\left(\frac{57}{88}\right)\) | \(e\left(\frac{3}{11}\right)\) |
\(\chi_{801}(244,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{85}{88}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{35}{88}\right)\) | \(e\left(\frac{29}{88}\right)\) | \(e\left(\frac{5}{11}\right)\) |
\(\chi_{801}(253,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{69}{88}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{75}{88}\right)\) | \(e\left(\frac{37}{88}\right)\) | \(e\left(\frac{6}{11}\right)\) |
\(\chi_{801}(280,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{1}{88}\right)\) | \(e\left(\frac{31}{88}\right)\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{801}(298,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{47}{88}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{9}{88}\right)\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{6}{11}\right)\) |
\(\chi_{801}(325,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{3}{88}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{53}{88}\right)\) | \(e\left(\frac{59}{88}\right)\) | \(e\left(\frac{6}{11}\right)\) |
\(\chi_{801}(343,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{59}{88}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{45}{88}\right)\) | \(e\left(\frac{75}{88}\right)\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{801}(370,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{25}{88}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{31}{88}\right)\) | \(e\left(\frac{81}{88}\right)\) | \(e\left(\frac{6}{11}\right)\) |
\(\chi_{801}(379,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{41}{88}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{79}{88}\right)\) | \(e\left(\frac{73}{88}\right)\) | \(e\left(\frac{5}{11}\right)\) |
\(\chi_{801}(397,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{29}{88}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{43}{88}\right)\) | \(e\left(\frac{13}{88}\right)\) | \(e\left(\frac{3}{11}\right)\) |
\(\chi_{801}(415,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{51}{88}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{21}{88}\right)\) | \(e\left(\frac{35}{88}\right)\) | \(e\left(\frac{3}{11}\right)\) |
\(\chi_{801}(442,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{37}{88}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{67}{88}\right)\) | \(e\left(\frac{53}{88}\right)\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{801}(451,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{57}{88}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{39}{88}\right)\) | \(e\left(\frac{65}{88}\right)\) | \(e\left(\frac{4}{11}\right)\) |
\(\chi_{801}(460,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{31}{88}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{49}{88}\right)\) | \(e\left(\frac{23}{88}\right)\) | \(e\left(\frac{7}{11}\right)\) |
\(\chi_{801}(469,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{9}{88}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{71}{88}\right)\) | \(e\left(\frac{1}{88}\right)\) | \(e\left(\frac{7}{11}\right)\) |
\(\chi_{801}(478,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{21}{88}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{19}{88}\right)\) | \(e\left(\frac{61}{88}\right)\) | \(e\left(\frac{9}{11}\right)\) |
\(\chi_{801}(496,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{39}{88}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{73}{88}\right)\) | \(e\left(\frac{63}{88}\right)\) | \(e\left(\frac{1}{11}\right)\) |
\(\chi_{801}(505,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{71}{88}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{81}{88}\right)\) | \(e\left(\frac{47}{88}\right)\) | \(e\left(\frac{10}{11}\right)\) |
\(\chi_{801}(541,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{49}{88}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{25}{88}\right)\) | \(e\left(\frac{10}{11}\right)\) |