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Properties

Label 4320.fi
Modulus $4320$
Conductor $2160$
Order $36$
Real no
Primitive no
Minimal no
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4320, base_ring=CyclotomicField(36)) M = H._module chi = DirichletCharacter(H, M([0,27,2,9])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(137,4320)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4320\)
Conductor: \(2160\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(36\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 2160.ec
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{36})\)
Fixed field: 36.36.41216642617644769738384985747906299013992369570201489573102485504000000000000000000000000000.1

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{4320}(137,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{4320}(473,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{4320}(617,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{4320}(1433,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{4320}(1577,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{4320}(1913,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{4320}(2057,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{4320}(2873,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{4320}(3017,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{4320}(3353,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{4320}(3497,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{4320}(4313,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{9}\right)\)