Properties

Label 4410.3881
Modulus $4410$
Conductor $441$
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([7,0,13]))
 
pari: [g,chi] = znchar(Mod(3881,4410))
 

Basic properties

Modulus: \(4410\)
Conductor: \(441\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(42\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{441}(353,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4410.dg

\(\chi_{4410}(101,\cdot)\) \(\chi_{4410}(131,\cdot)\) \(\chi_{4410}(731,\cdot)\) \(\chi_{4410}(761,\cdot)\) \(\chi_{4410}(1361,\cdot)\) \(\chi_{4410}(2021,\cdot)\) \(\chi_{4410}(2621,\cdot)\) \(\chi_{4410}(2651,\cdot)\) \(\chi_{4410}(3251,\cdot)\) \(\chi_{4410}(3281,\cdot)\) \(\chi_{4410}(3881,\cdot)\) \(\chi_{4410}(3911,\cdot)\)

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

\((3431,2647,1081)\) → \((e\left(\frac{1}{6}\right),1,e\left(\frac{13}{42}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{23}{42}\right)\)\(e\left(\frac{23}{42}\right)\)\(e\left(\frac{5}{21}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{25}{42}\right)\)\(e\left(\frac{31}{42}\right)\)\(-1\)\(e\left(\frac{19}{21}\right)\)\(e\left(\frac{10}{21}\right)\)\(e\left(\frac{11}{21}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{21})\)
Fixed field: 42.42.135265838320508910021411644358796004615334045909367351934724248079056959678737055640870296813389.1