Properties

Conductor 1157
Order 88
Real No
Primitive Yes
Parity Even
Orbit Label 1157.bs

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(1157)
sage: chi = H[31]
pari: [g,chi] = znchar(Mod(31,1157))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1157
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 88
Real = No
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
Primitive = Yes
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Even
Orbit label = 1157.bs
Orbit index = 45

Galois orbit

sage: chi.sage_character().galois_orbit()
pari: order = charorder(g,chi)
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

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

Values on generators

\((535,92)\) → \((-i,e\left(\frac{31}{88}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{17}{44}\right)\)\(e\left(\frac{31}{88}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{65}{88}\right)\)\(e\left(\frac{69}{88}\right)\)\(e\left(\frac{7}{44}\right)\)\(e\left(\frac{31}{44}\right)\)\(e\left(\frac{35}{44}\right)\)\(e\left(\frac{37}{44}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{88})\)