Properties

Label 2205.64
Modulus $2205$
Conductor $245$
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(2205, base_ring=CyclotomicField(14))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,7,10]))
 
pari: [g,chi] = znchar(Mod(64,2205))
 

Basic properties

Modulus: \(2205\)
Conductor: \(245\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(14\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{245}(64,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2205.cn

\(\chi_{2205}(64,\cdot)\) \(\chi_{2205}(379,\cdot)\) \(\chi_{2205}(694,\cdot)\) \(\chi_{2205}(1009,\cdot)\) \(\chi_{2205}(1639,\cdot)\) \(\chi_{2205}(1954,\cdot)\)

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\zeta_{7})\)
Fixed field: 14.14.14967283701606751125078125.1

Values on generators

\((1226,442,1081)\) → \((1,-1,e\left(\frac{5}{7}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(8\)\(11\)\(13\)\(16\)\(17\)\(19\)\(22\)\(23\)
\(1\)\(1\)\(e\left(\frac{1}{14}\right)\)\(e\left(\frac{1}{7}\right)\)\(e\left(\frac{3}{14}\right)\)\(e\left(\frac{4}{7}\right)\)\(e\left(\frac{1}{14}\right)\)\(e\left(\frac{2}{7}\right)\)\(e\left(\frac{5}{14}\right)\)\(1\)\(e\left(\frac{9}{14}\right)\)\(e\left(\frac{9}{14}\right)\)
value at e.g. 2