Properties

Label 2205.23
Modulus $2205$
Conductor $2205$
Order $84$
Real no
Primitive yes
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(84))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([70,63,76]))
 
pari: [g,chi] = znchar(Mod(23,2205))
 

Basic properties

Modulus: \(2205\)
Conductor: \(2205\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(84\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2205.en

\(\chi_{2205}(23,\cdot)\) \(\chi_{2205}(137,\cdot)\) \(\chi_{2205}(212,\cdot)\) \(\chi_{2205}(338,\cdot)\) \(\chi_{2205}(452,\cdot)\) \(\chi_{2205}(527,\cdot)\) \(\chi_{2205}(578,\cdot)\) \(\chi_{2205}(653,\cdot)\) \(\chi_{2205}(767,\cdot)\) \(\chi_{2205}(842,\cdot)\) \(\chi_{2205}(893,\cdot)\) \(\chi_{2205}(968,\cdot)\) \(\chi_{2205}(1082,\cdot)\) \(\chi_{2205}(1208,\cdot)\) \(\chi_{2205}(1283,\cdot)\) \(\chi_{2205}(1397,\cdot)\) \(\chi_{2205}(1472,\cdot)\) \(\chi_{2205}(1523,\cdot)\) \(\chi_{2205}(1712,\cdot)\) \(\chi_{2205}(1787,\cdot)\) \(\chi_{2205}(1838,\cdot)\) \(\chi_{2205}(1913,\cdot)\) \(\chi_{2205}(2102,\cdot)\) \(\chi_{2205}(2153,\cdot)\)

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

Values on generators

\((1226,442,1081)\) → \((e\left(\frac{5}{6}\right),-i,e\left(\frac{19}{21}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(8\)\(11\)\(13\)\(16\)\(17\)\(19\)\(22\)\(23\)
\(1\)\(1\)\(e\left(\frac{3}{28}\right)\)\(e\left(\frac{3}{14}\right)\)\(e\left(\frac{9}{28}\right)\)\(e\left(\frac{1}{42}\right)\)\(e\left(\frac{65}{84}\right)\)\(e\left(\frac{3}{7}\right)\)\(e\left(\frac{73}{84}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{11}{84}\right)\)\(e\left(\frac{67}{84}\right)\)
value at e.g. 2