Properties

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

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[23]
pari: [g,chi] = znchar(Mod(23,1157))

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.ca
Orbit index = 53

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 ]

\(\chi_{1157}(23,\cdot)\) \(\chi_{1157}(30,\cdot)\) \(\chi_{1157}(43,\cdot)\) \(\chi_{1157}(56,\cdot)\) \(\chi_{1157}(62,\cdot)\) \(\chi_{1157}(75,\cdot)\) \(\chi_{1157}(82,\cdot)\) \(\chi_{1157}(95,\cdot)\) \(\chi_{1157}(108,\cdot)\) \(\chi_{1157}(127,\cdot)\) \(\chi_{1157}(140,\cdot)\) \(\chi_{1157}(147,\cdot)\) \(\chi_{1157}(192,\cdot)\) \(\chi_{1157}(205,\cdot)\) \(\chi_{1157}(238,\cdot)\) \(\chi_{1157}(244,\cdot)\) \(\chi_{1157}(264,\cdot)\) \(\chi_{1157}(270,\cdot)\) \(\chi_{1157}(290,\cdot)\) \(\chi_{1157}(296,\cdot)\) \(\chi_{1157}(329,\cdot)\) \(\chi_{1157}(342,\cdot)\) \(\chi_{1157}(387,\cdot)\) \(\chi_{1157}(394,\cdot)\) \(\chi_{1157}(407,\cdot)\) \(\chi_{1157}(426,\cdot)\) \(\chi_{1157}(439,\cdot)\) \(\chi_{1157}(452,\cdot)\) \(\chi_{1157}(459,\cdot)\) \(\chi_{1157}(472,\cdot)\) ...

Values on generators

\((535,92)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{57}{88}\right))\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{13}{66}\right)\)\(e\left(\frac{259}{264}\right)\)\(e\left(\frac{13}{33}\right)\)\(e\left(\frac{37}{44}\right)\)\(e\left(\frac{47}{264}\right)\)\(e\left(\frac{167}{264}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{127}{132}\right)\)\(e\left(\frac{5}{132}\right)\)\(e\left(\frac{8}{33}\right)\)
value at  e.g. 2

Related number fields

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