Properties

Label 1470.41
Modulus $1470$
Conductor $147$
Order $14$
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(1470)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([7,0,5]))
 
pari: [g,chi] = znchar(Mod(41,1470))
 

Basic properties

Modulus: \(1470\)
Conductor: \(147\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(14\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{147}(41,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1470.be

\(\chi_{1470}(41,\cdot)\) \(\chi_{1470}(251,\cdot)\) \(\chi_{1470}(461,\cdot)\) \(\chi_{1470}(671,\cdot)\) \(\chi_{1470}(1091,\cdot)\) \(\chi_{1470}(1301,\cdot)\)

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

\((491,1177,1081)\) → \((-1,1,e\left(\frac{5}{14}\right))\)

Values

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

Related number fields

Field of values: \(\Q(\zeta_{7})\)
Fixed field: 14.14.2932917071205091238064909.1