Properties

Conductor 287
Order 40
Real No
Primitive No
Parity Even
Orbit Label 6027.cr

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[97]
 
pari: [g,chi] = znchar(Mod(97,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 287
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.cr
Orbit index = 70

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 ]
 

\(\chi_{6027}(97,\cdot)\) \(\chi_{6027}(391,\cdot)\) \(\chi_{6027}(685,\cdot)\) \(\chi_{6027}(832,\cdot)\) \(\chi_{6027}(1126,\cdot)\) \(\chi_{6027}(1420,\cdot)\) \(\chi_{6027}(2302,\cdot)\) \(\chi_{6027}(2449,\cdot)\) \(\chi_{6027}(2596,\cdot)\) \(\chi_{6027}(3478,\cdot)\) \(\chi_{6027}(3625,\cdot)\) \(\chi_{6027}(3919,\cdot)\) \(\chi_{6027}(4066,\cdot)\) \(\chi_{6027}(4948,\cdot)\) \(\chi_{6027}(5095,\cdot)\) \(\chi_{6027}(5242,\cdot)\)

Inducing primitive character

\(\chi_{287}(97,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((1,-1,e\left(\frac{37}{40}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{31}{40}\right)\)\(e\left(\frac{7}{40}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{1}{40}\right)\)\(e\left(\frac{33}{40}\right)\)
value at  e.g. 2

Related number fields

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