from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8352, base_ring=CyclotomicField(56))
M = H._module
chi = DirichletCharacter(H, M([0,35,0,24]))
chi.galois_orbit()
[g,chi] = znchar(Mod(181,8352))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(8352\) | |
Conductor: | \(928\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(56\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 928.cc | 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: | $\Q(\zeta_{56})$ |
Fixed field: | Number field defined by a degree 56 polynomial |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(31\) | \(35\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{8352}(181,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(-1\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{25}{56}\right)\) |
\(\chi_{8352}(397,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{56}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{45}{56}\right)\) | \(e\left(\frac{31}{56}\right)\) | \(-1\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{43}{56}\right)\) |
\(\chi_{8352}(973,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{39}{56}\right)\) | \(-1\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{27}{56}\right)\) |
\(\chi_{8352}(1765,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{9}{56}\right)\) | \(-1\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{45}{56}\right)\) |
\(\chi_{8352}(1909,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{15}{56}\right)\) | \(e\left(\frac{29}{56}\right)\) | \(-1\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{33}{56}\right)\) |
\(\chi_{8352}(2053,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{27}{56}\right)\) | \(e\left(\frac{41}{56}\right)\) | \(-1\) | \(e\left(\frac{17}{56}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{37}{56}\right)\) |
\(\chi_{8352}(2269,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{45}{56}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{19}{56}\right)\) | \(-1\) | \(e\left(\frac{27}{56}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{39}{56}\right)\) |
\(\chi_{8352}(2485,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{27}{56}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{31}{56}\right)\) | \(e\left(\frac{45}{56}\right)\) | \(-1\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{56}\right)\) |
\(\chi_{8352}(3061,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{53}{56}\right)\) | \(-1\) | \(e\left(\frac{37}{56}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{41}{56}\right)\) |
\(\chi_{8352}(3853,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{56}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{37}{56}\right)\) | \(e\left(\frac{23}{56}\right)\) | \(-1\) | \(e\left(\frac{15}{56}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{3}{56}\right)\) |
\(\chi_{8352}(3997,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{56}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(-1\) | \(e\left(\frac{11}{56}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{47}{56}\right)\) |
\(\chi_{8352}(4141,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{55}{56}\right)\) | \(-1\) | \(e\left(\frac{31}{56}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{51}{56}\right)\) |
\(\chi_{8352}(4357,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{56}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{19}{56}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(-1\) | \(e\left(\frac{41}{56}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{53}{56}\right)\) |
\(\chi_{8352}(4573,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{17}{56}\right)\) | \(e\left(\frac{3}{56}\right)\) | \(-1\) | \(e\left(\frac{19}{56}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{15}{56}\right)\) |
\(\chi_{8352}(5149,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{25}{56}\right)\) | \(e\left(\frac{11}{56}\right)\) | \(-1\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{55}{56}\right)\) |
\(\chi_{8352}(5941,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{56}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{37}{56}\right)\) | \(-1\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{17}{56}\right)\) |
\(\chi_{8352}(6085,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{1}{56}\right)\) | \(-1\) | \(e\left(\frac{25}{56}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{56}\right)\) |
\(\chi_{8352}(6229,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{56}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{55}{56}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(-1\) | \(e\left(\frac{45}{56}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{9}{56}\right)\) |
\(\chi_{8352}(6445,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{56}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{47}{56}\right)\) | \(-1\) | \(e\left(\frac{55}{56}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{56}\right)\) |
\(\chi_{8352}(6661,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{55}{56}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{17}{56}\right)\) | \(-1\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{29}{56}\right)\) |
\(\chi_{8352}(7237,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{15}{56}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{11}{56}\right)\) | \(e\left(\frac{25}{56}\right)\) | \(-1\) | \(e\left(\frac{9}{56}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{13}{56}\right)\) |
\(\chi_{8352}(8029,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{9}{56}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(-1\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{31}{56}\right)\) |
\(\chi_{8352}(8173,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{56}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{15}{56}\right)\) | \(-1\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{19}{56}\right)\) |
\(\chi_{8352}(8317,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{41}{56}\right)\) | \(e\left(\frac{27}{56}\right)\) | \(-1\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{23}{56}\right)\) |