Properties

Label 1148.ck
Modulus $1148$
Conductor $1148$
Order $120$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1148, base_ring=CyclotomicField(120))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([60,100,27]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(19,1148))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1148\)
Conductor: \(1148\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(120\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: $\Q(\zeta_{120})$
Fixed field: Number field defined by a degree 120 polynomial (not computed)

First 31 of 32 characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(23\) \(25\)
\(\chi_{1148}(19,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{61}{120}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{31}{120}\right)\) \(e\left(\frac{83}{120}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{1148}(47,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{109}{120}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{79}{120}\right)\) \(e\left(\frac{107}{120}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{1148}(75,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{31}{120}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{61}{120}\right)\) \(e\left(\frac{113}{120}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{1148}(171,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{120}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{41}{120}\right)\) \(e\left(\frac{13}{120}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{1148}(199,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{89}{120}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{59}{120}\right)\) \(e\left(\frac{7}{120}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{1148}(227,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{41}{120}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{11}{120}\right)\) \(e\left(\frac{103}{120}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{1148}(299,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{103}{120}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{13}{120}\right)\) \(e\left(\frac{89}{120}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{1148}(311,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{17}{120}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{107}{120}\right)\) \(e\left(\frac{31}{120}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{1148}(339,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{47}{120}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{77}{120}\right)\) \(e\left(\frac{1}{120}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{1148}(395,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{53}{120}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{23}{120}\right)\) \(e\left(\frac{19}{120}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{1148}(423,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{59}{120}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{89}{120}\right)\) \(e\left(\frac{37}{120}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{1148}(439,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{43}{120}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{73}{120}\right)\) \(e\left(\frac{29}{120}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{1148}(479,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{119}{120}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{29}{120}\right)\) \(e\left(\frac{97}{120}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{1148}(507,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{113}{120}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{83}{120}\right)\) \(e\left(\frac{79}{120}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{1148}(563,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{107}{120}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{17}{120}\right)\) \(e\left(\frac{61}{120}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{1148}(591,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{77}{120}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{47}{120}\right)\) \(e\left(\frac{91}{120}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{1148}(663,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{91}{120}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{1}{120}\right)\) \(e\left(\frac{53}{120}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{1148}(675,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{101}{120}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{71}{120}\right)\) \(e\left(\frac{43}{120}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{1148}(691,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{49}{120}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{19}{120}\right)\) \(e\left(\frac{47}{120}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{1148}(703,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{29}{120}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{119}{120}\right)\) \(e\left(\frac{67}{120}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{1148}(719,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{120}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{91}{120}\right)\) \(e\left(\frac{23}{120}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{1148}(731,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{71}{120}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{101}{120}\right)\) \(e\left(\frac{73}{120}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{1148}(803,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{97}{120}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{67}{120}\right)\) \(e\left(\frac{71}{120}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{1148}(831,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{120}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{37}{120}\right)\) \(e\left(\frac{41}{120}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{1148}(887,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{13}{120}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{103}{120}\right)\) \(e\left(\frac{59}{120}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{1148}(915,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{19}{120}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{49}{120}\right)\) \(e\left(\frac{77}{120}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{1148}(955,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{23}{120}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{53}{120}\right)\) \(e\left(\frac{49}{120}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{1148}(971,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{79}{120}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{109}{120}\right)\) \(e\left(\frac{17}{120}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{1148}(999,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{73}{120}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{43}{120}\right)\) \(e\left(\frac{119}{120}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{1148}(1055,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{67}{120}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{97}{120}\right)\) \(e\left(\frac{101}{120}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{1148}(1083,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{37}{120}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{7}{120}\right)\) \(e\left(\frac{11}{120}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\)