Properties

Conductor 123
Order 40
Real No
Primitive No
Parity Even
Orbit Label 6027.co

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(6027)
 
sage: chi = H[785]
 
pari: [g,chi] = znchar(Mod(785,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 123
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 = 6027.co
Orbit index = 67

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 ]
 

\(\chi_{6027}(785,\cdot)\) \(\chi_{6027}(932,\cdot)\) \(\chi_{6027}(1079,\cdot)\) \(\chi_{6027}(1961,\cdot)\) \(\chi_{6027}(2108,\cdot)\) \(\chi_{6027}(2402,\cdot)\) \(\chi_{6027}(2549,\cdot)\) \(\chi_{6027}(3431,\cdot)\) \(\chi_{6027}(3578,\cdot)\) \(\chi_{6027}(3725,\cdot)\) \(\chi_{6027}(4607,\cdot)\) \(\chi_{6027}(4901,\cdot)\) \(\chi_{6027}(5195,\cdot)\) \(\chi_{6027}(5342,\cdot)\) \(\chi_{6027}(5636,\cdot)\) \(\chi_{6027}(5930,\cdot)\)

Inducing primitive character

\(\chi_{123}(47,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((-1,1,e\left(\frac{1}{40}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{23}{40}\right)\)\(e\left(\frac{31}{40}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{13}{40}\right)\)\(e\left(\frac{9}{40}\right)\)
value at  e.g. 2

Related number fields

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