Properties

Conductor 1157
Order 44
Real No
Primitive Yes
Parity Odd
Orbit Label 1157.bj

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[5]
pari: [g,chi] = znchar(Mod(5,1157))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1157
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 44
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.bj
Orbit index = 36

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 ]

\(\chi_{1157}(5,\cdot)\) \(\chi_{1157}(21,\cdot)\) \(\chi_{1157}(109,\cdot)\) \(\chi_{1157}(125,\cdot)\) \(\chi_{1157}(138,\cdot)\) \(\chi_{1157}(346,\cdot)\) \(\chi_{1157}(398,\cdot)\) \(\chi_{1157}(463,\cdot)\) \(\chi_{1157}(525,\cdot)\) \(\chi_{1157}(551,\cdot)\) \(\chi_{1157}(606,\cdot)\) \(\chi_{1157}(632,\cdot)\) \(\chi_{1157}(694,\cdot)\) \(\chi_{1157}(759,\cdot)\) \(\chi_{1157}(811,\cdot)\) \(\chi_{1157}(1019,\cdot)\) \(\chi_{1157}(1032,\cdot)\) \(\chi_{1157}(1048,\cdot)\) \(\chi_{1157}(1136,\cdot)\) \(\chi_{1157}(1152,\cdot)\)

Values on generators

\((535,92)\) → \((-i,e\left(\frac{35}{44}\right))\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{35}{44}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{19}{44}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{19}{44}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{3}{44}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{44})\)