Properties

Label 6025.37
Modulus $6025$
Conductor $6025$
Order $240$
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(6025)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([108,73]))
 
pari: [g,chi] = znchar(Mod(37,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(240\)
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 6025.ix

\(\chi_{6025}(37,\cdot)\) \(\chi_{6025}(78,\cdot)\) \(\chi_{6025}(127,\cdot)\) \(\chi_{6025}(373,\cdot)\) \(\chi_{6025}(553,\cdot)\) \(\chi_{6025}(822,\cdot)\) \(\chi_{6025}(827,\cdot)\) \(\chi_{6025}(908,\cdot)\) \(\chi_{6025}(933,\cdot)\) \(\chi_{6025}(1038,\cdot)\) \(\chi_{6025}(1073,\cdot)\) \(\chi_{6025}(1267,\cdot)\) \(\chi_{6025}(1317,\cdot)\) \(\chi_{6025}(1347,\cdot)\) \(\chi_{6025}(1498,\cdot)\) \(\chi_{6025}(1613,\cdot)\) \(\chi_{6025}(2077,\cdot)\) \(\chi_{6025}(2123,\cdot)\) \(\chi_{6025}(2183,\cdot)\) \(\chi_{6025}(2417,\cdot)\) \(\chi_{6025}(2423,\cdot)\) \(\chi_{6025}(2502,\cdot)\) \(\chi_{6025}(2583,\cdot)\) \(\chi_{6025}(2617,\cdot)\) \(\chi_{6025}(2822,\cdot)\) \(\chi_{6025}(3038,\cdot)\) \(\chi_{6025}(3047,\cdot)\) \(\chi_{6025}(3167,\cdot)\) \(\chi_{6025}(3172,\cdot)\) \(\chi_{6025}(3188,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{9}{20}\right),e\left(\frac{73}{240}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{29}{120}\right)\)\(e\left(\frac{61}{120}\right)\)\(e\left(\frac{29}{60}\right)\)\(-i\)\(e\left(\frac{133}{240}\right)\)\(e\left(\frac{29}{40}\right)\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{193}{240}\right)\)\(e\left(\frac{119}{120}\right)\)\(e\left(\frac{203}{240}\right)\)
value at e.g. 2

Related number fields

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