Properties

Label 287.u
Modulus $287$
Conductor $41$
Order $20$
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(287, base_ring=CyclotomicField(20))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,19]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(8,287))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(287\)
Conductor: \(41\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(20\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 41.g
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: \(\Q(\zeta_{20})\)
Fixed field: \(\Q(\zeta_{41})^+\)

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(8\) \(9\) \(10\) \(11\) \(12\)
\(\chi_{287}(8,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(i\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{13}{20}\right)\)
\(\chi_{287}(36,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(-i\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{287}(43,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(-i\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{20}\right)\)
\(\chi_{287}(162,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(i\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{287}(169,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(i\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{20}\right)\)
\(\chi_{287}(197,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(-i\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{287}(225,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(-i\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{19}{20}\right)\)
\(\chi_{287}(267,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(i\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{20}\right)\)