Properties

Label 4410.103
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([28,63,58]))
 
pari: [g,chi] = znchar(Mod(103,4410))
 

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 \(\chi_{2205}(103,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4410.ej

\(\chi_{4410}(103,\cdot)\) \(\chi_{4410}(367,\cdot)\) \(\chi_{4410}(493,\cdot)\) \(\chi_{4410}(733,\cdot)\) \(\chi_{4410}(997,\cdot)\) \(\chi_{4410}(1123,\cdot)\) \(\chi_{4410}(1237,\cdot)\) \(\chi_{4410}(1363,\cdot)\) \(\chi_{4410}(1627,\cdot)\) \(\chi_{4410}(1753,\cdot)\) \(\chi_{4410}(1867,\cdot)\) \(\chi_{4410}(1993,\cdot)\) \(\chi_{4410}(2257,\cdot)\) \(\chi_{4410}(2497,\cdot)\) \(\chi_{4410}(2623,\cdot)\) \(\chi_{4410}(2887,\cdot)\) \(\chi_{4410}(3013,\cdot)\) \(\chi_{4410}(3127,\cdot)\) \(\chi_{4410}(3517,\cdot)\) \(\chi_{4410}(3643,\cdot)\) \(\chi_{4410}(3757,\cdot)\) \(\chi_{4410}(3883,\cdot)\) \(\chi_{4410}(4273,\cdot)\) \(\chi_{4410}(4387,\cdot)\)

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

\((3431,2647,1081)\) → \((e\left(\frac{1}{3}\right),-i,e\left(\frac{29}{42}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{20}{21}\right)\)\(e\left(\frac{59}{84}\right)\)\(e\left(\frac{1}{84}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{13}{84}\right)\)\(e\left(\frac{11}{42}\right)\)\(-1\)\(e\left(\frac{71}{84}\right)\)\(e\left(\frac{1}{42}\right)\)\(e\left(\frac{61}{84}\right)\)
value at e.g. 2

Related number fields

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