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Properties

Label 3240.de
Modulus $3240$
Conductor $3240$
Order $54$
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(3240, base_ring=CyclotomicField(54)) M = H._module chi = DirichletCharacter(H, M([27,27,41,27])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(59,3240)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(3240\)
Conductor: \(3240\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(54\)
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: \(\Q(\zeta_{27})\)
Fixed field: Number field defined by a degree 54 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{3240}(59,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{13}{54}\right)\)
\(\chi_{3240}(299,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{35}{54}\right)\)
\(\chi_{3240}(419,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{37}{54}\right)\)
\(\chi_{3240}(659,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{7}{54}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{41}{54}\right)\)
\(\chi_{3240}(779,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{54}\right)\)
\(\chi_{3240}(1019,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{47}{54}\right)\)
\(\chi_{3240}(1139,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{31}{54}\right)\)
\(\chi_{3240}(1379,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{53}{54}\right)\)
\(\chi_{3240}(1499,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{7}{54}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{54}\right)\)
\(\chi_{3240}(1739,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{54}\right)\)
\(\chi_{3240}(1859,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{25}{54}\right)\)
\(\chi_{3240}(2099,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{11}{54}\right)\)
\(\chi_{3240}(2219,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{49}{54}\right)\)
\(\chi_{3240}(2459,\cdot)\) \(1\) \(1\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{17}{54}\right)\)
\(\chi_{3240}(2579,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{54}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{19}{54}\right)\)
\(\chi_{3240}(2819,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{23}{54}\right)\)
\(\chi_{3240}(2939,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{43}{54}\right)\)
\(\chi_{3240}(3179,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{29}{54}\right)\)