Properties

Label 1157.281
Modulus $1157$
Conductor $1157$
Order $88$
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(1157)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([22,9]))
 
pari: [g,chi] = znchar(Mod(281,1157))
 

Basic properties

Modulus: \(1157\)
Conductor: \(1157\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(88\)
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 1157.bs

\(\chi_{1157}(31,\cdot)\) \(\chi_{1157}(70,\cdot)\) \(\chi_{1157}(86,\cdot)\) \(\chi_{1157}(112,\cdot)\) \(\chi_{1157}(148,\cdot)\) \(\chi_{1157}(164,\cdot)\) \(\chi_{1157}(213,\cdot)\) \(\chi_{1157}(252,\cdot)\) \(\chi_{1157}(281,\cdot)\) \(\chi_{1157}(330,\cdot)\) \(\chi_{1157}(333,\cdot)\) \(\chi_{1157}(343,\cdot)\) \(\chi_{1157}(359,\cdot)\) \(\chi_{1157}(369,\cdot)\) \(\chi_{1157}(382,\cdot)\) \(\chi_{1157}(460,\cdot)\) \(\chi_{1157}(499,\cdot)\) \(\chi_{1157}(528,\cdot)\) \(\chi_{1157}(541,\cdot)\) \(\chi_{1157}(564,\cdot)\) \(\chi_{1157}(567,\cdot)\) \(\chi_{1157}(580,\cdot)\) \(\chi_{1157}(642,\cdot)\) \(\chi_{1157}(671,\cdot)\) \(\chi_{1157}(681,\cdot)\) \(\chi_{1157}(684,\cdot)\) \(\chi_{1157}(736,\cdot)\) \(\chi_{1157}(772,\cdot)\) \(\chi_{1157}(863,\cdot)\) \(\chi_{1157}(866,\cdot)\) ...

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

\((535,92)\) → \((i,e\left(\frac{9}{88}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{39}{44}\right)\)\(e\left(\frac{9}{88}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{87}{88}\right)\)\(e\left(\frac{3}{88}\right)\)\(e\left(\frac{29}{44}\right)\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{13}{44}\right)\)\(e\left(\frac{15}{44}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{88})$
Fixed field: Number field defined by a degree 88 polynomial