Properties

Label 4410.157
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([28,21,26]))
 
pari: [g,chi] = znchar(Mod(157,4410))
 

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 \(\chi_{2205}(157,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4410.ea

\(\chi_{4410}(157,\cdot)\) \(\chi_{4410}(187,\cdot)\) \(\chi_{4410}(283,\cdot)\) \(\chi_{4410}(787,\cdot)\) \(\chi_{4410}(817,\cdot)\) \(\chi_{4410}(943,\cdot)\) \(\chi_{4410}(1417,\cdot)\) \(\chi_{4410}(1447,\cdot)\) \(\chi_{4410}(1543,\cdot)\) \(\chi_{4410}(1573,\cdot)\) \(\chi_{4410}(2047,\cdot)\) \(\chi_{4410}(2173,\cdot)\) \(\chi_{4410}(2203,\cdot)\) \(\chi_{4410}(2707,\cdot)\) \(\chi_{4410}(2803,\cdot)\) \(\chi_{4410}(2833,\cdot)\) \(\chi_{4410}(3307,\cdot)\) \(\chi_{4410}(3337,\cdot)\) \(\chi_{4410}(3433,\cdot)\) \(\chi_{4410}(3463,\cdot)\) \(\chi_{4410}(3937,\cdot)\) \(\chi_{4410}(3967,\cdot)\) \(\chi_{4410}(4063,\cdot)\) \(\chi_{4410}(4093,\cdot)\)

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

\((3431,2647,1081)\) → \((e\left(\frac{1}{3}\right),i,e\left(\frac{13}{42}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{5}{7}\right)\)\(e\left(\frac{53}{84}\right)\)\(e\left(\frac{83}{84}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{5}{28}\right)\)\(e\left(\frac{17}{42}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{13}{84}\right)\)\(e\left(\frac{13}{42}\right)\)\(e\left(\frac{79}{84}\right)\)
value at e.g. 2

Related number fields

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