Properties

Conductor 89
Order 88
Real No
Primitive No
Parity Odd
Orbit Label 1157.bq

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[27]
pari: [g,chi] = znchar(Mod(27,1157))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 89
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 88
Real = No
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
Primitive = No
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Odd
Orbit label = 1157.bq
Orbit index = 43

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 ]

\(\chi_{1157}(14,\cdot)\) \(\chi_{1157}(27,\cdot)\) \(\chi_{1157}(66,\cdot)\) \(\chi_{1157}(92,\cdot)\) \(\chi_{1157}(118,\cdot)\) \(\chi_{1157}(209,\cdot)\) \(\chi_{1157}(248,\cdot)\) \(\chi_{1157}(261,\cdot)\) \(\chi_{1157}(274,\cdot)\) \(\chi_{1157}(300,\cdot)\) \(\chi_{1157}(313,\cdot)\) \(\chi_{1157}(326,\cdot)\) \(\chi_{1157}(391,\cdot)\) \(\chi_{1157}(404,\cdot)\) \(\chi_{1157}(417,\cdot)\) \(\chi_{1157}(430,\cdot)\) \(\chi_{1157}(469,\cdot)\) \(\chi_{1157}(508,\cdot)\) \(\chi_{1157}(521,\cdot)\) \(\chi_{1157}(547,\cdot)\) \(\chi_{1157}(560,\cdot)\) \(\chi_{1157}(599,\cdot)\) \(\chi_{1157}(638,\cdot)\) \(\chi_{1157}(651,\cdot)\) \(\chi_{1157}(664,\cdot)\) \(\chi_{1157}(677,\cdot)\) \(\chi_{1157}(742,\cdot)\) \(\chi_{1157}(755,\cdot)\) \(\chi_{1157}(768,\cdot)\) \(\chi_{1157}(794,\cdot)\) ...

Inducing primitive character

\(\chi_{89}(27,\cdot)\)

Values on generators

\((535,92)\) → \((1,e\left(\frac{3}{88}\right))\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{3}{88}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{17}{44}\right)\)\(e\left(\frac{51}{88}\right)\)\(e\left(\frac{67}{88}\right)\)\(e\left(\frac{7}{11}\right)\)\(e\left(\frac{3}{44}\right)\)\(e\left(\frac{41}{44}\right)\)\(e\left(\frac{19}{22}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{88})\)