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Properties

Label 648.bc
Modulus $648$
Conductor $81$
Order $54$
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(54)) M = H._module chi = DirichletCharacter(H, M([0,0,53])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(41,648)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(648\)
Conductor: \(81\)
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: no, induced from 81.h
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: \(\Q(\zeta_{27})\)
Fixed field: Number field defined by a degree 54 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{648}(41,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{17}{27}\right)\)
\(\chi_{648}(65,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{13}{27}\right)\)
\(\chi_{648}(113,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{54}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{23}{27}\right)\)
\(\chi_{648}(137,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{1}{27}\right)\)
\(\chi_{648}(185,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{2}{27}\right)\)
\(\chi_{648}(209,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{16}{27}\right)\)
\(\chi_{648}(257,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{8}{27}\right)\)
\(\chi_{648}(281,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{4}{27}\right)\)
\(\chi_{648}(329,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{14}{27}\right)\)
\(\chi_{648}(353,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{19}{27}\right)\)
\(\chi_{648}(401,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{20}{27}\right)\)
\(\chi_{648}(425,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{7}{54}\right)\) \(e\left(\frac{7}{27}\right)\)
\(\chi_{648}(473,\cdot)\) \(-1\) \(1\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{54}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{26}{27}\right)\)
\(\chi_{648}(497,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{7}{54}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{22}{27}\right)\)
\(\chi_{648}(545,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{5}{27}\right)\)
\(\chi_{648}(569,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{10}{27}\right)\)
\(\chi_{648}(617,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{11}{27}\right)\)
\(\chi_{648}(641,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{25}{27}\right)\)