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Properties

Label 351.bu
Modulus $351$
Conductor $351$
Order $36$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(36)) M = H._module chi = DirichletCharacter(H, M([4,27])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(31,351)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(351\)
Conductor: \(351\)
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: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{36})\)
Fixed field: Number field defined by a degree 36 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(14\) \(16\) \(17\)
\(\chi_{351}(31,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{351}(34,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{351}(70,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{351}(112,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{351}(148,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{351}(151,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{351}(187,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{351}(229,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{351}(265,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{351}(268,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{351}(304,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{351}(346,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{6}\right)\)