Properties

Label 1225.27
Modulus $1225$
Conductor $1225$
Order $140$
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(1225, base_ring=CyclotomicField(140))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([7,10]))
 
pari: [g,chi] = znchar(Mod(27,1225))
 

Basic properties

Modulus: \(1225\)
Conductor: \(1225\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(140\)
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 1225.bp

\(\chi_{1225}(13,\cdot)\) \(\chi_{1225}(27,\cdot)\) \(\chi_{1225}(62,\cdot)\) \(\chi_{1225}(83,\cdot)\) \(\chi_{1225}(153,\cdot)\) \(\chi_{1225}(167,\cdot)\) \(\chi_{1225}(188,\cdot)\) \(\chi_{1225}(202,\cdot)\) \(\chi_{1225}(223,\cdot)\) \(\chi_{1225}(237,\cdot)\) \(\chi_{1225}(258,\cdot)\) \(\chi_{1225}(272,\cdot)\) \(\chi_{1225}(328,\cdot)\) \(\chi_{1225}(363,\cdot)\) \(\chi_{1225}(377,\cdot)\) \(\chi_{1225}(398,\cdot)\) \(\chi_{1225}(412,\cdot)\) \(\chi_{1225}(433,\cdot)\) \(\chi_{1225}(447,\cdot)\) \(\chi_{1225}(503,\cdot)\) \(\chi_{1225}(517,\cdot)\) \(\chi_{1225}(552,\cdot)\) \(\chi_{1225}(573,\cdot)\) \(\chi_{1225}(608,\cdot)\) \(\chi_{1225}(622,\cdot)\) \(\chi_{1225}(678,\cdot)\) \(\chi_{1225}(692,\cdot)\) \(\chi_{1225}(713,\cdot)\) \(\chi_{1225}(727,\cdot)\) \(\chi_{1225}(748,\cdot)\) ...

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: $\Q(\zeta_{140})$
Fixed field: Number field defined by a degree 140 polynomial (not computed)

Values on generators

\((1177,101)\) → \((e\left(\frac{1}{20}\right),e\left(\frac{1}{14}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(8\)\(9\)\(11\)\(12\)\(13\)\(16\)
\(1\)\(1\)\(e\left(\frac{127}{140}\right)\)\(e\left(\frac{59}{140}\right)\)\(e\left(\frac{57}{70}\right)\)\(e\left(\frac{23}{70}\right)\)\(e\left(\frac{101}{140}\right)\)\(e\left(\frac{59}{70}\right)\)\(e\left(\frac{23}{35}\right)\)\(e\left(\frac{33}{140}\right)\)\(e\left(\frac{43}{140}\right)\)\(e\left(\frac{22}{35}\right)\)
value at e.g. 2