Properties

Label 2960.129
Modulus $2960$
Conductor $185$
Order $36$
Real no
Primitive no
Minimal no
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2960, base_ring=CyclotomicField(36))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,0,18,17]))
 
pari: [g,chi] = znchar(Mod(129,2960))
 

Basic properties

Modulus: \(2960\)
Conductor: \(185\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(36\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{185}(129,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2960.hz

\(\chi_{2960}(129,\cdot)\) \(\chi_{2960}(209,\cdot)\) \(\chi_{2960}(449,\cdot)\) \(\chi_{2960}(609,\cdot)\) \(\chi_{2960}(849,\cdot)\) \(\chi_{2960}(1169,\cdot)\) \(\chi_{2960}(1569,\cdot)\) \(\chi_{2960}(1889,\cdot)\) \(\chi_{2960}(2129,\cdot)\) \(\chi_{2960}(2289,\cdot)\) \(\chi_{2960}(2529,\cdot)\) \(\chi_{2960}(2609,\cdot)\)

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: \(\Q(\zeta_{36})\)
Fixed field: 36.0.29411719834995153896864925426307140281034671856927417346954345703125.1

Values on generators

\((2591,741,1777,2481)\) → \((1,1,-1,e\left(\frac{17}{36}\right))\)

Values

\(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)
\(-1\)\(1\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{25}{36}\right)\)\(e\left(\frac{29}{36}\right)\)\(e\left(\frac{19}{36}\right)\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{1}{3}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2960 }(129,a) \;\) at \(\;a = \) e.g. 2