Properties

Conductor 1157
Order 132
Real No
Primitive Yes
Parity Even
Orbit Label 1157.bz

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[9]
pari: [g,chi] = znchar(Mod(9,1157))

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 = Even
Orbit label = 1157.bz
Orbit index = 52

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 ]

\(\chi_{1157}(9,\cdot)\) \(\chi_{1157}(42,\cdot)\) \(\chi_{1157}(68,\cdot)\) \(\chi_{1157}(94,\cdot)\) \(\chi_{1157}(107,\cdot)\) \(\chi_{1157}(198,\cdot)\) \(\chi_{1157}(250,\cdot)\) \(\chi_{1157}(276,\cdot)\) \(\chi_{1157}(347,\cdot)\) \(\chi_{1157}(373,\cdot)\) \(\chi_{1157}(425,\cdot)\) \(\chi_{1157}(516,\cdot)\) \(\chi_{1157}(529,\cdot)\) \(\chi_{1157}(555,\cdot)\) \(\chi_{1157}(581,\cdot)\) \(\chi_{1157}(614,\cdot)\) \(\chi_{1157}(633,\cdot)\) \(\chi_{1157}(640,\cdot)\) \(\chi_{1157}(659,\cdot)\) \(\chi_{1157}(672,\cdot)\) \(\chi_{1157}(692,\cdot)\) \(\chi_{1157}(783,\cdot)\) \(\chi_{1157}(796,\cdot)\) \(\chi_{1157}(822,\cdot)\) \(\chi_{1157}(841,\cdot)\) \(\chi_{1157}(848,\cdot)\) \(\chi_{1157}(854,\cdot)\) \(\chi_{1157}(880,\cdot)\) \(\chi_{1157}(900,\cdot)\) \(\chi_{1157}(926,\cdot)\) ...

Values on generators

\((535,92)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{1}{44}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{1}{33}\right)\)\(e\left(\frac{91}{132}\right)\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{95}{132}\right)\)\(e\left(\frac{23}{132}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{25}{66}\right)\)\(e\left(\frac{41}{66}\right)\)\(e\left(\frac{19}{33}\right)\)
value at  e.g. 2

Related number fields

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