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Properties

Label 12138.bt
Modulus $12138$
Conductor $119$
Order $48$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(12138, base_ring=CyclotomicField(48)) M = H._module chi = DirichletCharacter(H, M([0,8,9])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(1081,12138)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(12138\)
Conductor: \(119\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(48\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 119.s
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: \(\Q(\zeta_{48})\)
Fixed field: Number field defined by a degree 48 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(11\) \(13\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{12138}(1081,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(i\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{12138}(1405,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(i\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{12138}(1669,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(-i\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{12138}(3139,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(i\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{12138}(3337,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(-i\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{12138}(4177,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(-i\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{12138}(5071,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(-i\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{12138}(5911,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(-i\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{12138}(6109,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(i\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{12138}(7579,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(-i\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{12138}(7843,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(i\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{12138}(8167,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(i\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{12138}(9313,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(-i\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{12138}(9901,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(i\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{12138}(11485,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(i\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{12138}(12073,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(-i\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{3}{16}\right)\)