Properties

Conductor 1157
Order 132
Real No
Primitive Yes
Parity Even
Orbit Label 1157.bu

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[17]
pari: [g,chi] = znchar(Mod(17,1157))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1157
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 132
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.bu
Orbit index = 47

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 ]

\(\chi_{1157}(10,\cdot)\) \(\chi_{1157}(17,\cdot)\) \(\chi_{1157}(36,\cdot)\) \(\chi_{1157}(49,\cdot)\) \(\chi_{1157}(69,\cdot)\) \(\chi_{1157}(160,\cdot)\) \(\chi_{1157}(173,\cdot)\) \(\chi_{1157}(199,\cdot)\) \(\chi_{1157}(218,\cdot)\) \(\chi_{1157}(225,\cdot)\) \(\chi_{1157}(231,\cdot)\) \(\chi_{1157}(257,\cdot)\) \(\chi_{1157}(277,\cdot)\) \(\chi_{1157}(303,\cdot)\) \(\chi_{1157}(309,\cdot)\) \(\chi_{1157}(316,\cdot)\) \(\chi_{1157}(335,\cdot)\) \(\chi_{1157}(361,\cdot)\) \(\chi_{1157}(374,\cdot)\) \(\chi_{1157}(465,\cdot)\) \(\chi_{1157}(485,\cdot)\) \(\chi_{1157}(498,\cdot)\) \(\chi_{1157}(517,\cdot)\) \(\chi_{1157}(524,\cdot)\) \(\chi_{1157}(543,\cdot)\) \(\chi_{1157}(576,\cdot)\) \(\chi_{1157}(602,\cdot)\) \(\chi_{1157}(628,\cdot)\) \(\chi_{1157}(641,\cdot)\) \(\chi_{1157}(732,\cdot)\) ...

Values on generators

\((535,92)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{3}{44}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{17}{66}\right)\)\(e\left(\frac{97}{132}\right)\)\(e\left(\frac{17}{33}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{131}{132}\right)\)\(e\left(\frac{47}{132}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{31}{66}\right)\)\(e\left(\frac{35}{66}\right)\)\(e\left(\frac{59}{66}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{132})\)