Properties

Label 4410.53
Modulus $4410$
Conductor $735$
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([42,63,20]))
 
pari: [g,chi] = znchar(Mod(53,4410))
 

Basic properties

Modulus: \(4410\)
Conductor: \(735\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(84\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{735}(53,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4410.ef

\(\chi_{4410}(53,\cdot)\) \(\chi_{4410}(107,\cdot)\) \(\chi_{4410}(233,\cdot)\) \(\chi_{4410}(683,\cdot)\) \(\chi_{4410}(737,\cdot)\) \(\chi_{4410}(1187,\cdot)\) \(\chi_{4410}(1313,\cdot)\) \(\chi_{4410}(1367,\cdot)\) \(\chi_{4410}(1493,\cdot)\) \(\chi_{4410}(1817,\cdot)\) \(\chi_{4410}(1943,\cdot)\) \(\chi_{4410}(1997,\cdot)\) \(\chi_{4410}(2123,\cdot)\) \(\chi_{4410}(2447,\cdot)\) \(\chi_{4410}(2573,\cdot)\) \(\chi_{4410}(2753,\cdot)\) \(\chi_{4410}(3077,\cdot)\) \(\chi_{4410}(3257,\cdot)\) \(\chi_{4410}(3383,\cdot)\) \(\chi_{4410}(3707,\cdot)\) \(\chi_{4410}(3833,\cdot)\) \(\chi_{4410}(3887,\cdot)\) \(\chi_{4410}(4013,\cdot)\) \(\chi_{4410}(4337,\cdot)\)

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

\((3431,2647,1081)\) → \((-1,-i,e\left(\frac{5}{21}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{1}{42}\right)\)\(e\left(\frac{3}{28}\right)\)\(e\left(\frac{17}{84}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{67}{84}\right)\)\(e\left(\frac{2}{7}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{31}{84}\right)\)\(e\left(\frac{1}{14}\right)\)\(e\left(\frac{19}{28}\right)\)
value at e.g. 2

Related number fields

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