Properties

Label 1110.cd
Modulus $1110$
Conductor $555$
Order $36$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1110, base_ring=CyclotomicField(36))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([18,27,4]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(53,1110))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1110\)
Conductor: \(555\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(36\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 555.cc
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: 36.36.439367442482615395873395986525679537423670688802881171357698738574981689453125.1

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(41\) \(43\)
\(\chi_{1110}(53,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{13}{18}\right)\) \(i\)
\(\chi_{1110}(83,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{7}{18}\right)\) \(i\)
\(\chi_{1110}(107,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{11}{18}\right)\) \(-i\)
\(\chi_{1110}(197,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{18}\right)\) \(-i\)
\(\chi_{1110}(293,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{17}{18}\right)\) \(i\)
\(\chi_{1110}(377,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{5}{18}\right)\) \(-i\)
\(\chi_{1110}(497,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{13}{18}\right)\) \(-i\)
\(\chi_{1110}(527,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{7}{18}\right)\) \(-i\)
\(\chi_{1110}(737,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{17}{18}\right)\) \(-i\)
\(\chi_{1110}(773,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{11}{18}\right)\) \(i\)
\(\chi_{1110}(863,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{18}\right)\) \(i\)
\(\chi_{1110}(1043,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{5}{18}\right)\) \(i\)