Properties

Label 4560.jb
Modulus $4560$
Conductor $304$
Order $36$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4560, base_ring=CyclotomicField(36))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,27,0,0,4]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(61,4560))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4560\)
Conductor: \(304\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(36\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 304.bi
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{36})\)
Fixed field: 36.36.52733281945045886724167383478270850720626086921526306402773390818541568.1

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{4560}(61,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{19}{36}\right)\)
\(\chi_{4560}(301,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{36}\right)\)
\(\chi_{4560}(541,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{31}{36}\right)\)
\(\chi_{4560}(1621,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{25}{36}\right)\)
\(\chi_{4560}(1981,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{35}{36}\right)\)
\(\chi_{4560}(2221,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{23}{36}\right)\)
\(\chi_{4560}(2341,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{36}\right)\)
\(\chi_{4560}(2581,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{29}{36}\right)\)
\(\chi_{4560}(2821,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{13}{36}\right)\)
\(\chi_{4560}(3901,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{36}\right)\)
\(\chi_{4560}(4261,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{17}{36}\right)\)
\(\chi_{4560}(4501,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{36}\right)\)