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Properties

Label 161.m
Modulus $161$
Conductor $161$
Order $33$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(161, base_ring=CyclotomicField(66)) M = H._module chi = DirichletCharacter(H, M([22,6])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(2,161)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(161\)
Conductor: \(161\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(33\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
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: \(\Q(\zeta_{33})\)
Fixed field: 33.33.277966181338944111003326058293667039541136678070715028736001.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(8\) \(9\) \(10\) \(11\) \(12\)
\(\chi_{161}(2,\cdot)\) \(1\) \(1\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{16}{33}\right)\)
\(\chi_{161}(4,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{32}{33}\right)\)
\(\chi_{161}(9,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{25}{33}\right)\)
\(\chi_{161}(16,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{31}{33}\right)\)
\(\chi_{161}(18,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{8}{33}\right)\)
\(\chi_{161}(25,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{5}{33}\right)\)
\(\chi_{161}(32,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{14}{33}\right)\)
\(\chi_{161}(39,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{20}{33}\right)\)
\(\chi_{161}(58,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{28}{33}\right)\)
\(\chi_{161}(72,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{7}{33}\right)\)
\(\chi_{161}(81,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{17}{33}\right)\)
\(\chi_{161}(95,\cdot)\) \(1\) \(1\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{29}{33}\right)\)
\(\chi_{161}(100,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{4}{33}\right)\)
\(\chi_{161}(121,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{1}{33}\right)\)
\(\chi_{161}(123,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{26}{33}\right)\)
\(\chi_{161}(128,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{13}{33}\right)\)
\(\chi_{161}(142,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{10}{33}\right)\)
\(\chi_{161}(144,\cdot)\) \(1\) \(1\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{23}{33}\right)\)
\(\chi_{161}(151,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{2}{33}\right)\)
\(\chi_{161}(156,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{19}{33}\right)\)