Properties

Conductor 1157
Order 264
Real No
Primitive Yes
Parity Even
Orbit Label 1157.cb

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[6]
pari: [g,chi] = znchar(Mod(6,1157))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1157
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 264
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.cb
Orbit index = 54

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 ]

\(\chi_{1157}(6,\cdot)\) \(\chi_{1157}(28,\cdot)\) \(\chi_{1157}(41,\cdot)\) \(\chi_{1157}(59,\cdot)\) \(\chi_{1157}(63,\cdot)\) \(\chi_{1157}(76,\cdot)\) \(\chi_{1157}(102,\cdot)\) \(\chi_{1157}(115,\cdot)\) \(\chi_{1157}(124,\cdot)\) \(\chi_{1157}(132,\cdot)\) \(\chi_{1157}(145,\cdot)\) \(\chi_{1157}(163,\cdot)\) \(\chi_{1157}(171,\cdot)\) \(\chi_{1157}(175,\cdot)\) \(\chi_{1157}(184,\cdot)\) \(\chi_{1157}(193,\cdot)\) \(\chi_{1157}(201,\cdot)\) \(\chi_{1157}(232,\cdot)\) \(\chi_{1157}(241,\cdot)\) \(\chi_{1157}(253,\cdot)\) \(\chi_{1157}(254,\cdot)\) \(\chi_{1157}(280,\cdot)\) \(\chi_{1157}(293,\cdot)\) \(\chi_{1157}(297,\cdot)\) \(\chi_{1157}(353,\cdot)\) \(\chi_{1157}(370,\cdot)\) \(\chi_{1157}(371,\cdot)\) \(\chi_{1157}(375,\cdot)\) \(\chi_{1157}(379,\cdot)\) \(\chi_{1157}(410,\cdot)\) ...

Values on generators

\((535,92)\) → \((e\left(\frac{5}{12}\right),e\left(\frac{17}{88}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{67}{132}\right)\)\(e\left(\frac{227}{264}\right)\)\(e\left(\frac{1}{66}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{97}{264}\right)\)\(e\left(\frac{61}{264}\right)\)\(e\left(\frac{23}{44}\right)\)\(e\left(\frac{95}{132}\right)\)\(e\left(\frac{103}{132}\right)\)\(e\left(\frac{19}{132}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{264})\)