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Properties

Label 242.e
Modulus $242$
Conductor $121$
Order $11$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(242, base_ring=CyclotomicField(22)) M = H._module chi = DirichletCharacter(H, M([14])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(23,242)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(242\)
Conductor: \(121\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(11\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 121.e
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{11})\)
Fixed field: 11.11.672749994932560009201.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(13\) \(15\) \(17\) \(19\) \(21\) \(23\)
\(\chi_{242}(23,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{242}(45,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{242}(67,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{242}(89,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{242}(111,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{242}(133,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{242}(155,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{242}(177,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{242}(199,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{242}(221,\cdot)\) \(1\) \(1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{11}\right)\)