Properties

Conductor 575
Order 20
Real No
Primitive No
Parity Even
Orbit Label 4025.bj

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(4025)
 
sage: chi = H[22]
 
pari: [g,chi] = znchar(Mod(22,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 575
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 20
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 = 4025.bj
Orbit index = 36

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 ]
 

\(\chi_{4025}(22,\cdot)\) \(\chi_{4025}(183,\cdot)\) \(\chi_{4025}(827,\cdot)\) \(\chi_{4025}(988,\cdot)\) \(\chi_{4025}(2437,\cdot)\) \(\chi_{4025}(2598,\cdot)\) \(\chi_{4025}(3242,\cdot)\) \(\chi_{4025}(3403,\cdot)\)

Inducing primitive character

\(\chi_{575}(22,\cdot)\)

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{17}{20}\right),1,-1)\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{2}{5}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{20})\)