Properties

Label 1225.54
Modulus $1225$
Conductor $1225$
Order $210$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1225)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([21,145]))
 
pari: [g,chi] = znchar(Mod(54,1225))
 

Basic properties

Modulus: \(1225\)
Conductor: \(1225\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(210\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1225.bs

\(\chi_{1225}(54,\cdot)\) \(\chi_{1225}(59,\cdot)\) \(\chi_{1225}(89,\cdot)\) \(\chi_{1225}(94,\cdot)\) \(\chi_{1225}(159,\cdot)\) \(\chi_{1225}(164,\cdot)\) \(\chi_{1225}(194,\cdot)\) \(\chi_{1225}(229,\cdot)\) \(\chi_{1225}(234,\cdot)\) \(\chi_{1225}(269,\cdot)\) \(\chi_{1225}(304,\cdot)\) \(\chi_{1225}(334,\cdot)\) \(\chi_{1225}(339,\cdot)\) \(\chi_{1225}(369,\cdot)\) \(\chi_{1225}(404,\cdot)\) \(\chi_{1225}(409,\cdot)\) \(\chi_{1225}(439,\cdot)\) \(\chi_{1225}(444,\cdot)\) \(\chi_{1225}(479,\cdot)\) \(\chi_{1225}(514,\cdot)\) \(\chi_{1225}(544,\cdot)\) \(\chi_{1225}(579,\cdot)\) \(\chi_{1225}(584,\cdot)\) \(\chi_{1225}(614,\cdot)\) \(\chi_{1225}(654,\cdot)\) \(\chi_{1225}(684,\cdot)\) \(\chi_{1225}(689,\cdot)\) \(\chi_{1225}(719,\cdot)\) \(\chi_{1225}(759,\cdot)\) \(\chi_{1225}(789,\cdot)\) ...

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

\((1177,101)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{29}{42}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(8\)\(9\)\(11\)\(12\)\(13\)\(16\)
\(-1\)\(1\)\(e\left(\frac{11}{210}\right)\)\(e\left(\frac{41}{105}\right)\)\(e\left(\frac{11}{105}\right)\)\(e\left(\frac{31}{70}\right)\)\(e\left(\frac{11}{70}\right)\)\(e\left(\frac{82}{105}\right)\)\(e\left(\frac{23}{105}\right)\)\(e\left(\frac{52}{105}\right)\)\(e\left(\frac{24}{35}\right)\)\(e\left(\frac{22}{105}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{105})$
Fixed field: Number field defined by a degree 210 polynomial