Properties

Conductor 1800
Order 60
Real No
Primitive Yes
Parity Odd
Orbit Label 1800.dl

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(1800)
sage: chi = H[13]
pari: [g,chi] = znchar(Mod(13,1800))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1800
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 60
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 = 1800.dl
Orbit index = 90

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 ]

\(\chi_{1800}(13,\cdot)\) \(\chi_{1800}(133,\cdot)\) \(\chi_{1800}(277,\cdot)\) \(\chi_{1800}(373,\cdot)\) \(\chi_{1800}(517,\cdot)\) \(\chi_{1800}(637,\cdot)\) \(\chi_{1800}(733,\cdot)\) \(\chi_{1800}(853,\cdot)\) \(\chi_{1800}(877,\cdot)\) \(\chi_{1800}(997,\cdot)\) \(\chi_{1800}(1213,\cdot)\) \(\chi_{1800}(1237,\cdot)\) \(\chi_{1800}(1453,\cdot)\) \(\chi_{1800}(1573,\cdot)\) \(\chi_{1800}(1597,\cdot)\) \(\chi_{1800}(1717,\cdot)\)

Values on generators

\((1351,901,1001,577)\) → \((1,-1,e\left(\frac{1}{3}\right),e\left(\frac{19}{20}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{13}{60}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{7}{60}\right)\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{7}{15}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{60})\)