Properties

Conductor 1157
Order 264
Real no
Primitive yes
Minimal yes
Parity odd
Orbit label 1157.cd

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(1157)
 
sage: chi = H[29]
 
pari: [g,chi] = znchar(Mod(29,1157))
 

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
Minimal = 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

\((535,92)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{59}{88}\right))\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{1}{264}\right)\)\(e\left(\frac{4}{33}\right)\)\(e\left(\frac{41}{44}\right)\)\(e\left(\frac{17}{264}\right)\)\(e\left(\frac{257}{264}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{1}{132}\right)\)\(e\left(\frac{131}{132}\right)\)\(e\left(\frac{43}{66}\right)\)
value at  e.g. 2

Related number fields

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