Properties

Label 4410.23
Modulus $4410$
Conductor $2205$
Order $84$
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([70,63,76]))
 
pari: [g,chi] = znchar(Mod(23,4410))
 

Basic properties

Modulus: \(4410\)
Conductor: \(2205\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(84\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2205}(23,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4410.eg

\(\chi_{4410}(23,\cdot)\) \(\chi_{4410}(137,\cdot)\) \(\chi_{4410}(527,\cdot)\) \(\chi_{4410}(653,\cdot)\) \(\chi_{4410}(767,\cdot)\) \(\chi_{4410}(893,\cdot)\) \(\chi_{4410}(1283,\cdot)\) \(\chi_{4410}(1397,\cdot)\) \(\chi_{4410}(1523,\cdot)\) \(\chi_{4410}(1787,\cdot)\) \(\chi_{4410}(1913,\cdot)\) \(\chi_{4410}(2153,\cdot)\) \(\chi_{4410}(2417,\cdot)\) \(\chi_{4410}(2543,\cdot)\) \(\chi_{4410}(2657,\cdot)\) \(\chi_{4410}(2783,\cdot)\) \(\chi_{4410}(3047,\cdot)\) \(\chi_{4410}(3173,\cdot)\) \(\chi_{4410}(3287,\cdot)\) \(\chi_{4410}(3413,\cdot)\) \(\chi_{4410}(3677,\cdot)\) \(\chi_{4410}(3917,\cdot)\) \(\chi_{4410}(4043,\cdot)\) \(\chi_{4410}(4307,\cdot)\)

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

\((3431,2647,1081)\) → \((e\left(\frac{5}{6}\right),-i,e\left(\frac{19}{21}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{1}{42}\right)\)\(e\left(\frac{65}{84}\right)\)\(e\left(\frac{73}{84}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{67}{84}\right)\)\(e\left(\frac{13}{21}\right)\)\(1\)\(e\left(\frac{59}{84}\right)\)\(e\left(\frac{31}{42}\right)\)\(e\left(\frac{1}{84}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{84})$
Fixed field: Number field defined by a degree 84 polynomial