Properties

Conductor 187
Order 80
Real No
Primitive No
Parity Even
Orbit Label 8041.dz

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[173]
 
pari: [g,chi] = znchar(Mod(173,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 187
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 80
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.dz
Orbit index = 104

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 ]
 

\(\chi_{8041}(173,\cdot)\) \(\chi_{8041}(216,\cdot)\) \(\chi_{8041}(431,\cdot)\) \(\chi_{8041}(904,\cdot)\) \(\chi_{8041}(1119,\cdot)\) \(\chi_{8041}(1162,\cdot)\) \(\chi_{8041}(1592,\cdot)\) \(\chi_{8041}(1635,\cdot)\) \(\chi_{8041}(1678,\cdot)\) \(\chi_{8041}(1850,\cdot)\) \(\chi_{8041}(2323,\cdot)\) \(\chi_{8041}(2538,\cdot)\) \(\chi_{8041}(2581,\cdot)\) \(\chi_{8041}(2624,\cdot)\) \(\chi_{8041}(3054,\cdot)\) \(\chi_{8041}(3097,\cdot)\) \(\chi_{8041}(3269,\cdot)\) \(\chi_{8041}(4000,\cdot)\) \(\chi_{8041}(4043,\cdot)\) \(\chi_{8041}(4430,\cdot)\) \(\chi_{8041}(4516,\cdot)\) \(\chi_{8041}(4903,\cdot)\) \(\chi_{8041}(5161,\cdot)\) \(\chi_{8041}(5462,\cdot)\) \(\chi_{8041}(5634,\cdot)\) \(\chi_{8041}(5892,\cdot)\) \(\chi_{8041}(6365,\cdot)\) \(\chi_{8041}(6795,\cdot)\) \(\chi_{8041}(7354,\cdot)\) \(\chi_{8041}(7526,\cdot)\) ...

Inducing primitive character

\(\chi_{187}(173,\cdot)\)

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{1}{16}\right),1)\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{7}{40}\right)\)\(e\left(\frac{37}{80}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{41}{80}\right)\)\(e\left(\frac{51}{80}\right)\)\(e\left(\frac{63}{80}\right)\)\(e\left(\frac{21}{40}\right)\)\(e\left(\frac{37}{40}\right)\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{13}{16}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{80})\)