Properties

Label 8034.121
Modulus $8034$
Conductor $1339$
Order $102$
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(8034)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,17,20]))
 
pari: [g,chi] = znchar(Mod(121,8034))
 

Basic properties

Modulus: \(8034\)
Conductor: \(1339\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(102\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1339}(121,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.dl

\(\chi_{8034}(121,\cdot)\) \(\chi_{8034}(361,\cdot)\) \(\chi_{8034}(667,\cdot)\) \(\chi_{8034}(985,\cdot)\) \(\chi_{8034}(1063,\cdot)\) \(\chi_{8034}(1135,\cdot)\) \(\chi_{8034}(1291,\cdot)\) \(\chi_{8034}(1375,\cdot)\) \(\chi_{8034}(1525,\cdot)\) \(\chi_{8034}(1843,\cdot)\) \(\chi_{8034}(2077,\cdot)\) \(\chi_{8034}(2467,\cdot)\) \(\chi_{8034}(3403,\cdot)\) \(\chi_{8034}(3481,\cdot)\) \(\chi_{8034}(3631,\cdot)\) \(\chi_{8034}(3637,\cdot)\) \(\chi_{8034}(3715,\cdot)\) \(\chi_{8034}(3943,\cdot)\) \(\chi_{8034}(4183,\cdot)\) \(\chi_{8034}(4261,\cdot)\) \(\chi_{8034}(4417,\cdot)\) \(\chi_{8034}(4489,\cdot)\) \(\chi_{8034}(5191,\cdot)\) \(\chi_{8034}(5269,\cdot)\) \(\chi_{8034}(5509,\cdot)\) \(\chi_{8034}(5581,\cdot)\) \(\chi_{8034}(5659,\cdot)\) \(\chi_{8034}(6205,\cdot)\) \(\chi_{8034}(6517,\cdot)\) \(\chi_{8034}(7063,\cdot)\) ...

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

\((5357,1237,5773)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{10}{51}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{71}{102}\right)\)\(e\left(\frac{21}{34}\right)\)\(e\left(\frac{13}{102}\right)\)\(e\left(\frac{1}{17}\right)\)\(e\left(\frac{53}{102}\right)\)\(e\left(\frac{19}{51}\right)\)\(e\left(\frac{20}{51}\right)\)\(e\left(\frac{9}{17}\right)\)\(e\left(\frac{23}{34}\right)\)\(e\left(\frac{16}{51}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{51})$
Fixed field: Number field defined by a degree 102 polynomial