Properties

Label 121.f
Modulus $121$
Conductor $121$
Order $22$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(121, base_ring=CyclotomicField(22))
 
M = H._module
 
chi = DirichletCharacter(H, M([15]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(10,121))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(121\)
Conductor: \(121\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(22\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
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: \(\Q(\zeta_{11})\)
Fixed field: Number field defined by a degree 22 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(12\)
\(\chi_{121}(10,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{22}\right)\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{121}(21,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{121}(32,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{121}(43,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{121}(54,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{22}\right)\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(1\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{121}(65,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{22}\right)\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{121}(76,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{22}\right)\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{121}(87,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(1\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{121}(98,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(1\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{121}(109,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(1\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{11}\right)\)