Properties

Label 287.bb
Modulus $287$
Conductor $287$
Order $40$
Real no
Primitive yes
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(40))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([20,1]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(6,287))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(287\)
Conductor: \(287\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(40\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
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: \(\Q(\zeta_{40})\)
Fixed field: 40.40.63172957949423116502957480067191906200305068755882825968063357506461803384975161.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(8\) \(9\) \(10\) \(11\) \(12\)
\(\chi_{287}(6,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(-i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{7}{40}\right)\)
\(\chi_{287}(13,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{17}{40}\right)\)
\(\chi_{287}(34,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{13}{40}\right)\)
\(\chi_{287}(48,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{33}{40}\right)\)
\(\chi_{287}(69,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{37}{40}\right)\)
\(\chi_{287}(76,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(-i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{27}{40}\right)\)
\(\chi_{287}(97,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(-i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{19}{40}\right)\)
\(\chi_{287}(104,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(-i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{3}{40}\right)\)
\(\chi_{287}(111,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{9}{40}\right)\)
\(\chi_{287}(153,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{1}{40}\right)\)
\(\chi_{287}(181,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(-i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{31}{40}\right)\)
\(\chi_{287}(188,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(-i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{11}{40}\right)\)
\(\chi_{287}(216,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{21}{40}\right)\)
\(\chi_{287}(258,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{29}{40}\right)\)
\(\chi_{287}(265,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(-i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{23}{40}\right)\)
\(\chi_{287}(272,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(-i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{39}{40}\right)\)