Properties

Label 8033.74
Modulus $8033$
Conductor $8033$
Order $322$
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(8033)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([46,273]))
 
pari: [g,chi] = znchar(Mod(74,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(8033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(322\)
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 8033.ck

\(\chi_{8033}(74,\cdot)\) \(\chi_{8033}(281,\cdot)\) \(\chi_{8033}(343,\cdot)\) \(\chi_{8033}(397,\cdot)\) \(\chi_{8033}(538,\cdot)\) \(\chi_{8033}(558,\cdot)\) \(\chi_{8033}(567,\cdot)\) \(\chi_{8033}(575,\cdot)\) \(\chi_{8033}(662,\cdot)\) \(\chi_{8033}(674,\cdot)\) \(\chi_{8033}(779,\cdot)\) \(\chi_{8033}(835,\cdot)\) \(\chi_{8033}(890,\cdot)\) \(\chi_{8033}(895,\cdot)\) \(\chi_{8033}(944,\cdot)\) \(\chi_{8033}(951,\cdot)\) \(\chi_{8033}(953,\cdot)\) \(\chi_{8033}(977,\cdot)\) \(\chi_{8033}(1039,\cdot)\) \(\chi_{8033}(1089,\cdot)\) \(\chi_{8033}(1167,\cdot)\) \(\chi_{8033}(1184,\cdot)\) \(\chi_{8033}(1254,\cdot)\) \(\chi_{8033}(1301,\cdot)\) \(\chi_{8033}(1358,\cdot)\) \(\chi_{8033}(1444,\cdot)\) \(\chi_{8033}(1531,\cdot)\) \(\chi_{8033}(1736,\cdot)\) \(\chi_{8033}(1764,\cdot)\) \(\chi_{8033}(1909,\cdot)\) ...

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

\((5541,1944)\) → \((e\left(\frac{1}{7}\right),e\left(\frac{39}{46}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{249}{322}\right)\)\(e\left(\frac{17}{161}\right)\)\(e\left(\frac{88}{161}\right)\)\(e\left(\frac{319}{322}\right)\)\(e\left(\frac{283}{322}\right)\)\(e\left(\frac{59}{161}\right)\)\(e\left(\frac{103}{322}\right)\)\(e\left(\frac{34}{161}\right)\)\(e\left(\frac{123}{161}\right)\)\(e\left(\frac{163}{322}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{161})$
Fixed field: Number field defined by a degree %d polynomial (not computed)