Properties

Label 1148.cd
Modulus $1148$
Conductor $41$
Order $40$
Real no
Primitive no
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(40))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,0,7]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(29,1148))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1148\)
Conductor: \(41\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(40\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 41.h
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: \(\Q(\zeta_{40})\)
Fixed field: \(\Q(\zeta_{41})\)

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(23\) \(25\)
\(\chi_{1148}(29,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{17}{20}\right)\) \(i\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{1148}(253,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{9}{20}\right)\) \(i\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{1148}(281,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{11}{20}\right)\) \(-i\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{1148}(309,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{20}\right)\) \(-i\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{1148}(393,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{20}\right)\) \(-i\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{1148}(421,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{20}\right)\) \(i\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{1148}(477,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{20}\right)\) \(-i\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{1148}(505,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{20}\right)\) \(i\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{1148}(561,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{20}\right)\) \(i\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{1148}(589,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{20}\right)\) \(-i\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{1148}(645,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{20}\right)\) \(i\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{1148}(673,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{20}\right)\) \(-i\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{1148}(757,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{19}{20}\right)\) \(-i\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{1148}(785,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{20}\right)\) \(-i\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{1148}(813,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{20}\right)\) \(i\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{1148}(1037,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{17}{20}\right)\) \(i\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\)