↑

Properties

Label 2442.cb
Modulus $2442$
Conductor $407$
Order $36$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2442, base_ring=CyclotomicField(36)) M = H._module chi = DirichletCharacter(H, M([0,18,19])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(109,2442)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2442\)
Conductor: \(407\)
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 407.bb
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: \(\Q(\zeta_{36})\)
Fixed field: 36.36.42867551195672722495351149174628212645190717310766431451792643783547492533.1

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(7\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(35\)
\(\chi_{2442}(109,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{19}{36}\right)\)
\(\chi_{2442}(241,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(e\left(\frac{35}{36}\right)\)
\(\chi_{2442}(439,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{5}{36}\right)\)
\(\chi_{2442}(505,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{29}{36}\right)\)
\(\chi_{2442}(901,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(e\left(\frac{11}{36}\right)\)
\(\chi_{2442}(967,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(e\left(\frac{23}{36}\right)\)
\(\chi_{2442}(1165,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{17}{36}\right)\)
\(\chi_{2442}(1297,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(e\left(\frac{1}{36}\right)\)
\(\chi_{2442}(1495,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(e\left(\frac{13}{36}\right)\)
\(\chi_{2442}(1759,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(e\left(\frac{25}{36}\right)\)
\(\chi_{2442}(2089,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{7}{36}\right)\)
\(\chi_{2442}(2353,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{31}{36}\right)\)