Properties

Conductor 935
Order 80
Real No
Primitive No
Parity Even
Orbit Label 5610.fl

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[367]
 
pari: [g,chi] = znchar(Mod(367,5610))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 935
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.fl
Orbit index = 142

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 ]
 

\(\chi_{5610}(367,\cdot)\) \(\chi_{5610}(487,\cdot)\) \(\chi_{5610}(643,\cdot)\) \(\chi_{5610}(907,\cdot)\) \(\chi_{5610}(1027,\cdot)\) \(\chi_{5610}(1093,\cdot)\) \(\chi_{5610}(1153,\cdot)\) \(\chi_{5610}(1417,\cdot)\) \(\chi_{5610}(1423,\cdot)\) \(\chi_{5610}(1873,\cdot)\) \(\chi_{5610}(1897,\cdot)\) \(\chi_{5610}(2017,\cdot)\) \(\chi_{5610}(2407,\cdot)\) \(\chi_{5610}(2557,\cdot)\) \(\chi_{5610}(2623,\cdot)\) \(\chi_{5610}(2953,\cdot)\) \(\chi_{5610}(3067,\cdot)\) \(\chi_{5610}(3133,\cdot)\) \(\chi_{5610}(3193,\cdot)\) \(\chi_{5610}(3403,\cdot)\) \(\chi_{5610}(3457,\cdot)\) \(\chi_{5610}(3463,\cdot)\) \(\chi_{5610}(3547,\cdot)\) \(\chi_{5610}(4057,\cdot)\) \(\chi_{5610}(4447,\cdot)\) \(\chi_{5610}(4723,\cdot)\) \(\chi_{5610}(4933,\cdot)\) \(\chi_{5610}(4987,\cdot)\) \(\chi_{5610}(5107,\cdot)\) \(\chi_{5610}(5173,\cdot)\) ...

Inducing primitive character

\(\chi_{935}(367,\cdot)\)

Values on generators

\((1871,3367,1531,3301)\) → \((1,i,e\left(\frac{1}{5}\right),e\left(\frac{3}{16}\right))\)

Values

-117131923293137414347
\(1\)\(1\)\(e\left(\frac{57}{80}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{29}{40}\right)\)\(e\left(\frac{9}{16}\right)\)\(e\left(\frac{27}{80}\right)\)\(e\left(\frac{71}{80}\right)\)\(e\left(\frac{67}{80}\right)\)\(e\left(\frac{53}{80}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{3}{5}\right)\)
value at  e.g. 2

Related number fields

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