Properties

Conductor 2805
Order 80
Real No
Primitive No
Parity Even
Orbit Label 5610.fb

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[173]
 
pari: [g,chi] = znchar(Mod(173,5610))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2805
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.fb
Orbit index = 132

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 ]
 

\(\chi_{5610}(173,\cdot)\) \(\chi_{5610}(227,\cdot)\) \(\chi_{5610}(233,\cdot)\) \(\chi_{5610}(347,\cdot)\) \(\chi_{5610}(413,\cdot)\) \(\chi_{5610}(743,\cdot)\) \(\chi_{5610}(827,\cdot)\) \(\chi_{5610}(1217,\cdot)\) \(\chi_{5610}(1337,\cdot)\) \(\chi_{5610}(1493,\cdot)\) \(\chi_{5610}(1757,\cdot)\) \(\chi_{5610}(1877,\cdot)\) \(\chi_{5610}(1943,\cdot)\) \(\chi_{5610}(2213,\cdot)\) \(\chi_{5610}(2273,\cdot)\) \(\chi_{5610}(2723,\cdot)\) \(\chi_{5610}(2747,\cdot)\) \(\chi_{5610}(2867,\cdot)\) \(\chi_{5610}(3407,\cdot)\) \(\chi_{5610}(3473,\cdot)\) \(\chi_{5610}(3533,\cdot)\) \(\chi_{5610}(3797,\cdot)\) \(\chi_{5610}(3803,\cdot)\) \(\chi_{5610}(4043,\cdot)\) \(\chi_{5610}(4253,\cdot)\) \(\chi_{5610}(4307,\cdot)\) \(\chi_{5610}(4397,\cdot)\) \(\chi_{5610}(4787,\cdot)\) \(\chi_{5610}(5297,\cdot)\) \(\chi_{5610}(5447,\cdot)\) ...

Inducing primitive character

\(\chi_{2805}(173,\cdot)\)

Values on generators

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

Values

-117131923293137414347
\(1\)\(1\)\(e\left(\frac{43}{80}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{11}{40}\right)\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{73}{80}\right)\)\(e\left(\frac{29}{80}\right)\)\(e\left(\frac{33}{80}\right)\)\(e\left(\frac{7}{80}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{9}{10}\right)\)
value at  e.g. 2

Related number fields

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