Properties

Label 1225.34
Modulus $1225$
Conductor $1225$
Order $70$
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([49,15]))
 
pari: [g,chi] = znchar(Mod(34,1225))
 

Basic properties

Modulus: \(1225\)
Conductor: \(1225\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(70\)
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.bk

\(\chi_{1225}(34,\cdot)\) \(\chi_{1225}(69,\cdot)\) \(\chi_{1225}(104,\cdot)\) \(\chi_{1225}(139,\cdot)\) \(\chi_{1225}(209,\cdot)\) \(\chi_{1225}(279,\cdot)\) \(\chi_{1225}(314,\cdot)\) \(\chi_{1225}(384,\cdot)\) \(\chi_{1225}(419,\cdot)\) \(\chi_{1225}(454,\cdot)\) \(\chi_{1225}(559,\cdot)\) \(\chi_{1225}(594,\cdot)\) \(\chi_{1225}(629,\cdot)\) \(\chi_{1225}(664,\cdot)\) \(\chi_{1225}(769,\cdot)\) \(\chi_{1225}(804,\cdot)\) \(\chi_{1225}(839,\cdot)\) \(\chi_{1225}(909,\cdot)\) \(\chi_{1225}(944,\cdot)\) \(\chi_{1225}(1014,\cdot)\) \(\chi_{1225}(1084,\cdot)\) \(\chi_{1225}(1119,\cdot)\) \(\chi_{1225}(1154,\cdot)\) \(\chi_{1225}(1189,\cdot)\)

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

\((1177,101)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{3}{14}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(8\)\(9\)\(11\)\(12\)\(13\)\(16\)
\(-1\)\(1\)\(e\left(\frac{19}{70}\right)\)\(e\left(\frac{4}{35}\right)\)\(e\left(\frac{19}{35}\right)\)\(e\left(\frac{27}{70}\right)\)\(e\left(\frac{57}{70}\right)\)\(e\left(\frac{8}{35}\right)\)\(e\left(\frac{27}{35}\right)\)\(e\left(\frac{23}{35}\right)\)\(e\left(\frac{13}{35}\right)\)\(e\left(\frac{3}{35}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{35})$
Fixed field: Number field defined by a degree 70 polynomial