Properties

Conductor 1157
Order 33
Real No
Primitive Yes
Parity Even
Orbit Label 1157.bg

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[16]
pari: [g,chi] = znchar(Mod(16,1157))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1157
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 33
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.bg
Orbit index = 33

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 ]

\(\chi_{1157}(16,\cdot)\) \(\chi_{1157}(217,\cdot)\) \(\chi_{1157}(256,\cdot)\) \(\chi_{1157}(269,\cdot)\) \(\chi_{1157}(334,\cdot)\) \(\chi_{1157}(360,\cdot)\) \(\chi_{1157}(477,\cdot)\) \(\chi_{1157}(484,\cdot)\) \(\chi_{1157}(490,\cdot)\) \(\chi_{1157}(523,\cdot)\) \(\chi_{1157}(536,\cdot)\) \(\chi_{1157}(542,\cdot)\) \(\chi_{1157}(601,\cdot)\) \(\chi_{1157}(627,\cdot)\) \(\chi_{1157}(744,\cdot)\) \(\chi_{1157}(757,\cdot)\) \(\chi_{1157}(776,\cdot)\) \(\chi_{1157}(809,\cdot)\) \(\chi_{1157}(906,\cdot)\) \(\chi_{1157}(1043,\cdot)\)

Values on generators

\((535,92)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{8}{11}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{32}{33}\right)\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{31}{33}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{1}{33}\right)\)\(e\left(\frac{19}{33}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{4}{33}\right)\)\(e\left(\frac{29}{33}\right)\)\(e\left(\frac{14}{33}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{33})\)