Properties

Label 6025.132
Modulus $6025$
Conductor $1205$
Order $240$
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(6025)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([60,107]))
 
pari: [g,chi] = znchar(Mod(132,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(1205\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(240\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1205}(132,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6025.jo

\(\chi_{6025}(132,\cdot)\) \(\chi_{6025}(157,\cdot)\) \(\chi_{6025}(368,\cdot)\) \(\chi_{6025}(443,\cdot)\) \(\chi_{6025}(568,\cdot)\) \(\chi_{6025}(793,\cdot)\) \(\chi_{6025}(807,\cdot)\) \(\chi_{6025}(832,\cdot)\) \(\chi_{6025}(1032,\cdot)\) \(\chi_{6025}(1068,\cdot)\) \(\chi_{6025}(1093,\cdot)\) \(\chi_{6025}(1143,\cdot)\) \(\chi_{6025}(1168,\cdot)\) \(\chi_{6025}(1257,\cdot)\) \(\chi_{6025}(1432,\cdot)\) \(\chi_{6025}(1632,\cdot)\) \(\chi_{6025}(1782,\cdot)\) \(\chi_{6025}(1818,\cdot)\) \(\chi_{6025}(1857,\cdot)\) \(\chi_{6025}(1882,\cdot)\) \(\chi_{6025}(2118,\cdot)\) \(\chi_{6025}(2182,\cdot)\) \(\chi_{6025}(2268,\cdot)\) \(\chi_{6025}(2318,\cdot)\) \(\chi_{6025}(2332,\cdot)\) \(\chi_{6025}(2368,\cdot)\) \(\chi_{6025}(2582,\cdot)\) \(\chi_{6025}(2682,\cdot)\) \(\chi_{6025}(2693,\cdot)\) \(\chi_{6025}(2707,\cdot)\) ...

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

\((2652,2176)\) → \((i,e\left(\frac{107}{240}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{23}{24}\right)\)\(e\left(\frac{107}{120}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{167}{240}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{47}{60}\right)\)\(e\left(\frac{7}{48}\right)\)\(e\left(\frac{97}{120}\right)\)\(e\left(\frac{169}{240}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{240})$
Fixed field: Number field defined by a degree 240 polynomial