Properties

Label 8034.367
Modulus $8034$
Conductor $1339$
Order $51$
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([0,17,14]))
 
pari: [g,chi] = znchar(Mod(367,8034))
 

Basic properties

Modulus: \(8034\)
Conductor: \(1339\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(51\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1339}(367,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.cr

\(\chi_{8034}(367,\cdot)\) \(\chi_{8034}(445,\cdot)\) \(\chi_{8034}(757,\cdot)\) \(\chi_{8034}(1225,\cdot)\) \(\chi_{8034}(1459,\cdot)\) \(\chi_{8034}(1777,\cdot)\) \(\chi_{8034}(1849,\cdot)\) \(\chi_{8034}(2089,\cdot)\) \(\chi_{8034}(2635,\cdot)\) \(\chi_{8034}(2785,\cdot)\) \(\chi_{8034}(2863,\cdot)\) \(\chi_{8034}(3019,\cdot)\) \(\chi_{8034}(3097,\cdot)\) \(\chi_{8034}(3337,\cdot)\) \(\chi_{8034}(3415,\cdot)\) \(\chi_{8034}(3565,\cdot)\) \(\chi_{8034}(3643,\cdot)\) \(\chi_{8034}(3727,\cdot)\) \(\chi_{8034}(3799,\cdot)\) \(\chi_{8034}(3805,\cdot)\) \(\chi_{8034}(4351,\cdot)\) \(\chi_{8034}(4663,\cdot)\) \(\chi_{8034}(4891,\cdot)\) \(\chi_{8034}(5209,\cdot)\) \(\chi_{8034}(6145,\cdot)\) \(\chi_{8034}(6301,\cdot)\) \(\chi_{8034}(6607,\cdot)\) \(\chi_{8034}(6847,\cdot)\) \(\chi_{8034}(7315,\cdot)\) \(\chi_{8034}(7471,\cdot)\) ...

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

\((5357,1237,5773)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{14}{51}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{14}{51}\right)\)\(e\left(\frac{13}{17}\right)\)\(e\left(\frac{4}{51}\right)\)\(e\left(\frac{15}{17}\right)\)\(e\left(\frac{32}{51}\right)\)\(e\left(\frac{47}{51}\right)\)\(e\left(\frac{28}{51}\right)\)\(e\left(\frac{16}{17}\right)\)\(e\left(\frac{11}{17}\right)\)\(e\left(\frac{2}{51}\right)\)
value at e.g. 2

Related number fields

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