Properties

Conductor 187
Order 80
Real No
Primitive No
Parity Even
Orbit Label 5610.fc

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(5610)
 
sage: chi = H[61]
 
pari: [g,chi] = znchar(Mod(61,5610))
 

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 = 5610.fc
Orbit index = 133

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 ]
 

\(\chi_{5610}(61,\cdot)\) \(\chi_{5610}(211,\cdot)\) \(\chi_{5610}(481,\cdot)\) \(\chi_{5610}(541,\cdot)\) \(\chi_{5610}(601,\cdot)\) \(\chi_{5610}(721,\cdot)\) \(\chi_{5610}(811,\cdot)\) \(\chi_{5610}(1051,\cdot)\) \(\chi_{5610}(1201,\cdot)\) \(\chi_{5610}(1261,\cdot)\) \(\chi_{5610}(1591,\cdot)\) \(\chi_{5610}(1711,\cdot)\) \(\chi_{5610}(2131,\cdot)\) \(\chi_{5610}(2251,\cdot)\) \(\chi_{5610}(2521,\cdot)\) \(\chi_{5610}(2581,\cdot)\) \(\chi_{5610}(2791,\cdot)\) \(\chi_{5610}(2851,\cdot)\) \(\chi_{5610}(3031,\cdot)\) \(\chi_{5610}(3121,\cdot)\) \(\chi_{5610}(3241,\cdot)\) \(\chi_{5610}(3361,\cdot)\) \(\chi_{5610}(3781,\cdot)\) \(\chi_{5610}(4111,\cdot)\) \(\chi_{5610}(4171,\cdot)\) \(\chi_{5610}(4561,\cdot)\) \(\chi_{5610}(4681,\cdot)\) \(\chi_{5610}(4771,\cdot)\) \(\chi_{5610}(4831,\cdot)\) \(\chi_{5610}(4891,\cdot)\) ...

Inducing primitive character

\(\chi_{187}(61,\cdot)\)

Values on generators

\((1871,3367,1531,3301)\) → \((1,1,e\left(\frac{9}{10}\right),e\left(\frac{3}{16}\right))\)

Values

-117131923293137414347
\(1\)\(1\)\(e\left(\frac{29}{80}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{13}{40}\right)\)\(e\left(\frac{13}{16}\right)\)\(e\left(\frac{59}{80}\right)\)\(e\left(\frac{7}{80}\right)\)\(e\left(\frac{79}{80}\right)\)\(e\left(\frac{61}{80}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{19}{20}\right)\)
value at  e.g. 2

Related number fields

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