Properties

Label 4410.341
Modulus $4410$
Conductor $147$
Order $42$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4410)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([21,0,5]))
 
pari: [g,chi] = znchar(Mod(341,4410))
 

Basic properties

Modulus: \(4410\)
Conductor: \(147\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(42\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{147}(47,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4410.dm

\(\chi_{4410}(341,\cdot)\) \(\chi_{4410}(971,\cdot)\) \(\chi_{4410}(1151,\cdot)\) \(\chi_{4410}(1601,\cdot)\) \(\chi_{4410}(1781,\cdot)\) \(\chi_{4410}(2231,\cdot)\) \(\chi_{4410}(2411,\cdot)\) \(\chi_{4410}(3041,\cdot)\) \(\chi_{4410}(3491,\cdot)\) \(\chi_{4410}(3671,\cdot)\) \(\chi_{4410}(4121,\cdot)\) \(\chi_{4410}(4301,\cdot)\)

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Values on generators

\((3431,2647,1081)\) → \((-1,1,e\left(\frac{5}{42}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{11}{42}\right)\)\(e\left(\frac{13}{14}\right)\)\(e\left(\frac{10}{21}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{1}{42}\right)\)\(e\left(\frac{9}{14}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{17}{21}\right)\)\(e\left(\frac{2}{7}\right)\)\(e\left(\frac{5}{7}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{21})\)
Fixed field: \(\Q(\zeta_{147})^+\)