Properties

Conductor 1157
Order 132
Real No
Primitive Yes
Parity Odd
Orbit Label 1157.by

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[306]
pari: [g,chi] = znchar(Mod(306,1157))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1157
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 132
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.by
Orbit index = 51

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 ]

\(\chi_{1157}(2,\cdot)\) \(\chi_{1157}(32,\cdot)\) \(\chi_{1157}(45,\cdot)\) \(\chi_{1157}(67,\cdot)\) \(\chi_{1157}(93,\cdot)\) \(\chi_{1157}(97,\cdot)\) \(\chi_{1157}(128,\cdot)\) \(\chi_{1157}(167,\cdot)\) \(\chi_{1157}(180,\cdot)\) \(\chi_{1157}(210,\cdot)\) \(\chi_{1157}(223,\cdot)\) \(\chi_{1157}(245,\cdot)\) \(\chi_{1157}(271,\cdot)\) \(\chi_{1157}(275,\cdot)\) \(\chi_{1157}(306,\cdot)\) \(\chi_{1157}(331,\cdot)\) \(\chi_{1157}(345,\cdot)\) \(\chi_{1157}(358,\cdot)\) \(\chi_{1157}(388,\cdot)\) \(\chi_{1157}(401,\cdot)\) \(\chi_{1157}(423,\cdot)\) \(\chi_{1157}(449,\cdot)\) \(\chi_{1157}(453,\cdot)\) \(\chi_{1157}(461,\cdot)\) \(\chi_{1157}(509,\cdot)\) \(\chi_{1157}(566,\cdot)\) \(\chi_{1157}(579,\cdot)\) \(\chi_{1157}(631,\cdot)\) \(\chi_{1157}(639,\cdot)\) \(\chi_{1157}(687,\cdot)\) ...

Values on generators

\((535,92)\) → \((e\left(\frac{11}{12}\right),e\left(\frac{3}{11}\right))\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{37}{132}\right)\)\(e\left(\frac{31}{33}\right)\)\(e\left(\frac{37}{66}\right)\)\(e\left(\frac{15}{44}\right)\)\(e\left(\frac{29}{132}\right)\)\(e\left(\frac{23}{132}\right)\)\(e\left(\frac{37}{44}\right)\)\(e\left(\frac{29}{33}\right)\)\(e\left(\frac{41}{66}\right)\)\(e\left(\frac{43}{132}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{132})\)