Properties

Conductor 1157
Order 264
Real No
Primitive Yes
Parity Odd
Orbit Label 1157.cd

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[3]
pari: [g,chi] = znchar(Mod(3,1157))

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 = Odd
Orbit label = 1157.cd
Orbit index = 56

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 ]

\(\chi_{1157}(3,\cdot)\) \(\chi_{1157}(29,\cdot)\) \(\chi_{1157}(35,\cdot)\) \(\chi_{1157}(48,\cdot)\) \(\chi_{1157}(61,\cdot)\) \(\chi_{1157}(74,\cdot)\) \(\chi_{1157}(113,\cdot)\) \(\chi_{1157}(120,\cdot)\) \(\chi_{1157}(152,\cdot)\) \(\chi_{1157}(159,\cdot)\) \(\chi_{1157}(165,\cdot)\) \(\chi_{1157}(172,\cdot)\) \(\chi_{1157}(185,\cdot)\) \(\chi_{1157}(191,\cdot)\) \(\chi_{1157}(204,\cdot)\) \(\chi_{1157}(211,\cdot)\) \(\chi_{1157}(224,\cdot)\) \(\chi_{1157}(237,\cdot)\) \(\chi_{1157}(243,\cdot)\) \(\chi_{1157}(282,\cdot)\) \(\chi_{1157}(295,\cdot)\) \(\chi_{1157}(302,\cdot)\) \(\chi_{1157}(308,\cdot)\) \(\chi_{1157}(315,\cdot)\) \(\chi_{1157}(321,\cdot)\) \(\chi_{1157}(328,\cdot)\) \(\chi_{1157}(341,\cdot)\) \(\chi_{1157}(380,\cdot)\) \(\chi_{1157}(386,\cdot)\) \(\chi_{1157}(399,\cdot)\) ...

Values on generators

\((535,92)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{88}\right))\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{17}{33}\right)\)\(e\left(\frac{91}{264}\right)\)\(e\left(\frac{1}{33}\right)\)\(e\left(\frac{35}{44}\right)\)\(e\left(\frac{227}{264}\right)\)\(e\left(\frac{155}{264}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{91}{132}\right)\)\(e\left(\frac{41}{132}\right)\)\(e\left(\frac{19}{66}\right)\)
value at  e.g. 2

Related number fields

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