Properties

Conductor 187
Order 40
Real No
Primitive No
Parity Even
Orbit Label 8041.cu

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(8041)
 
sage: chi = H[603]
 
pari: [g,chi] = znchar(Mod(603,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 187
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 40
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 8041.cu
Orbit index = 73

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{8041}(603,\cdot)\) \(\chi_{8041}(818,\cdot)\) \(\chi_{8041}(1334,\cdot)\) \(\chi_{8041}(1549,\cdot)\) \(\chi_{8041}(2280,\cdot)\) \(\chi_{8041}(2667,\cdot)\) \(\chi_{8041}(3613,\cdot)\) \(\chi_{8041}(4129,\cdot)\) \(\chi_{8041}(4860,\cdot)\) \(\chi_{8041}(5075,\cdot)\) \(\chi_{8041}(5591,\cdot)\) \(\chi_{8041}(5806,\cdot)\) \(\chi_{8041}(6451,\cdot)\) \(\chi_{8041}(6537,\cdot)\) \(\chi_{8041}(7397,\cdot)\) \(\chi_{8041}(7913,\cdot)\)

Inducing primitive character

\(\chi_{187}(42,\cdot)\)

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{5}{8}\right),1)\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{17}{40}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{21}{40}\right)\)\(e\left(\frac{31}{40}\right)\)\(e\left(\frac{3}{40}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{1}{8}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{40})\)