Properties

Conductor 1157
Order 66
Real No
Primitive Yes
Parity Even
Orbit Label 1157.bo

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[4]
pari: [g,chi] = znchar(Mod(4,1157))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1157
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 66
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.bo
Orbit index = 41

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 ]

\(\chi_{1157}(4,\cdot)\) \(\chi_{1157}(121,\cdot)\) \(\chi_{1157}(134,\cdot)\) \(\chi_{1157}(153,\cdot)\) \(\chi_{1157}(186,\cdot)\) \(\chi_{1157}(283,\cdot)\) \(\chi_{1157}(420,\cdot)\) \(\chi_{1157}(550,\cdot)\) \(\chi_{1157}(751,\cdot)\) \(\chi_{1157}(790,\cdot)\) \(\chi_{1157}(803,\cdot)\) \(\chi_{1157}(868,\cdot)\) \(\chi_{1157}(894,\cdot)\) \(\chi_{1157}(1011,\cdot)\) \(\chi_{1157}(1018,\cdot)\) \(\chi_{1157}(1024,\cdot)\) \(\chi_{1157}(1057,\cdot)\) \(\chi_{1157}(1070,\cdot)\) \(\chi_{1157}(1076,\cdot)\) \(\chi_{1157}(1135,\cdot)\)

Values on generators

\((535,92)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{4}{11}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{65}{66}\right)\)\(e\left(\frac{1}{33}\right)\)\(e\left(\frac{32}{33}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{1}{66}\right)\)\(e\left(\frac{19}{66}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{31}{33}\right)\)\(e\left(\frac{47}{66}\right)\)
value at  e.g. 2

Related number fields

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