Properties

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

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[202]
pari: [g,chi] = znchar(Mod(202,1157))

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.cc
Orbit index = 55

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 ]

\(\chi_{1157}(7,\cdot)\) \(\chi_{1157}(15,\cdot)\) \(\chi_{1157}(19,\cdot)\) \(\chi_{1157}(24,\cdot)\) \(\chi_{1157}(33,\cdot)\) \(\chi_{1157}(46,\cdot)\) \(\chi_{1157}(54,\cdot)\) \(\chi_{1157}(58,\cdot)\) \(\chi_{1157}(119,\cdot)\) \(\chi_{1157}(137,\cdot)\) \(\chi_{1157}(149,\cdot)\) \(\chi_{1157}(150,\cdot)\) \(\chi_{1157}(154,\cdot)\) \(\chi_{1157}(197,\cdot)\) \(\chi_{1157}(202,\cdot)\) \(\chi_{1157}(206,\cdot)\) \(\chi_{1157}(219,\cdot)\) \(\chi_{1157}(236,\cdot)\) \(\chi_{1157}(240,\cdot)\) \(\chi_{1157}(305,\cdot)\) \(\chi_{1157}(310,\cdot)\) \(\chi_{1157}(318,\cdot)\) \(\chi_{1157}(323,\cdot)\) \(\chi_{1157}(327,\cdot)\) \(\chi_{1157}(332,\cdot)\) \(\chi_{1157}(349,\cdot)\) \(\chi_{1157}(362,\cdot)\) \(\chi_{1157}(383,\cdot)\) \(\chi_{1157}(384,\cdot)\) \(\chi_{1157}(397,\cdot)\) ...

Values on generators

\((535,92)\) → \((e\left(\frac{11}{12}\right),e\left(\frac{49}{88}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{109}{132}\right)\)\(e\left(\frac{59}{264}\right)\)\(e\left(\frac{43}{66}\right)\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{13}{264}\right)\)\(e\left(\frac{49}{264}\right)\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{59}{132}\right)\)\(e\left(\frac{7}{132}\right)\)\(e\left(\frac{25}{132}\right)\)
value at  e.g. 2

Related number fields

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