Properties

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

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[20]
pari: [g,chi] = znchar(Mod(20,1157))

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.bw
Orbit index = 49

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 ]

\(\chi_{1157}(20,\cdot)\) \(\chi_{1157}(84,\cdot)\) \(\chi_{1157}(110,\cdot)\) \(\chi_{1157}(158,\cdot)\) \(\chi_{1157}(214,\cdot)\) \(\chi_{1157}(227,\cdot)\) \(\chi_{1157}(258,\cdot)\) \(\chi_{1157}(262,\cdot)\) \(\chi_{1157}(284,\cdot)\) \(\chi_{1157}(288,\cdot)\) \(\chi_{1157}(392,\cdot)\) \(\chi_{1157}(405,\cdot)\) \(\chi_{1157}(427,\cdot)\) \(\chi_{1157}(435,\cdot)\) \(\chi_{1157}(436,\cdot)\) \(\chi_{1157}(462,\cdot)\) \(\chi_{1157}(487,\cdot)\) \(\chi_{1157}(492,\cdot)\) \(\chi_{1157}(544,\cdot)\) \(\chi_{1157}(552,\cdot)\) \(\chi_{1157}(605,\cdot)\) \(\chi_{1157}(613,\cdot)\) \(\chi_{1157}(665,\cdot)\) \(\chi_{1157}(670,\cdot)\) \(\chi_{1157}(695,\cdot)\) \(\chi_{1157}(721,\cdot)\) \(\chi_{1157}(722,\cdot)\) \(\chi_{1157}(730,\cdot)\) \(\chi_{1157}(752,\cdot)\) \(\chi_{1157}(765,\cdot)\) ...

Values on generators

\((535,92)\) → \((e\left(\frac{11}{12}\right),e\left(\frac{7}{44}\right))\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{61}{132}\right)\)\(e\left(\frac{109}{132}\right)\)\(e\left(\frac{61}{66}\right)\)\(e\left(\frac{17}{44}\right)\)\(e\left(\frac{19}{66}\right)\)\(e\left(\frac{32}{33}\right)\)\(e\left(\frac{17}{44}\right)\)\(e\left(\frac{43}{66}\right)\)\(e\left(\frac{28}{33}\right)\)\(e\left(\frac{103}{132}\right)\)
value at  e.g. 2

Related number fields

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