Properties

Label 1225.841
Modulus $1225$
Conductor $1225$
Order $35$
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(70))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([14,60]))
 
pari: [g,chi] = znchar(Mod(841,1225))
 

Basic properties

Modulus: \(1225\)
Conductor: \(1225\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(35\)
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.bd

\(\chi_{1225}(36,\cdot)\) \(\chi_{1225}(71,\cdot)\) \(\chi_{1225}(106,\cdot)\) \(\chi_{1225}(141,\cdot)\) \(\chi_{1225}(211,\cdot)\) \(\chi_{1225}(281,\cdot)\) \(\chi_{1225}(316,\cdot)\) \(\chi_{1225}(386,\cdot)\) \(\chi_{1225}(421,\cdot)\) \(\chi_{1225}(456,\cdot)\) \(\chi_{1225}(561,\cdot)\) \(\chi_{1225}(596,\cdot)\) \(\chi_{1225}(631,\cdot)\) \(\chi_{1225}(666,\cdot)\) \(\chi_{1225}(771,\cdot)\) \(\chi_{1225}(806,\cdot)\) \(\chi_{1225}(841,\cdot)\) \(\chi_{1225}(911,\cdot)\) \(\chi_{1225}(946,\cdot)\) \(\chi_{1225}(1016,\cdot)\) \(\chi_{1225}(1086,\cdot)\) \(\chi_{1225}(1121,\cdot)\) \(\chi_{1225}(1156,\cdot)\) \(\chi_{1225}(1191,\cdot)\)

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: $\Q(\zeta_{35})$
Fixed field: 35.35.705021958507555897735769309192822159832506785420715156309512394727789796888828277587890625.1

Values on generators

\((1177,101)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{6}{7}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(8\)\(9\)\(11\)\(12\)\(13\)\(16\)
\(1\)\(1\)\(e\left(\frac{17}{35}\right)\)\(e\left(\frac{9}{35}\right)\)\(e\left(\frac{34}{35}\right)\)\(e\left(\frac{26}{35}\right)\)\(e\left(\frac{16}{35}\right)\)\(e\left(\frac{18}{35}\right)\)\(e\left(\frac{17}{35}\right)\)\(e\left(\frac{8}{35}\right)\)\(e\left(\frac{3}{35}\right)\)\(e\left(\frac{33}{35}\right)\)
value at e.g. 2