Properties

Conductor 25
Order 20
Real No
Primitive No
Parity Odd
Orbit Label 1800.cq

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[73]
pari: [g,chi] = znchar(Mod(73,1800))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 25
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 20
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 = 1800.cq
Orbit index = 69

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 ]

\(\chi_{1800}(73,\cdot)\) \(\chi_{1800}(217,\cdot)\) \(\chi_{1800}(433,\cdot)\) \(\chi_{1800}(577,\cdot)\) \(\chi_{1800}(937,\cdot)\) \(\chi_{1800}(1153,\cdot)\) \(\chi_{1800}(1297,\cdot)\) \(\chi_{1800}(1513,\cdot)\)

Inducing primitive character

\(\chi_{25}(23,\cdot)\)

Values on generators

\((1351,901,1001,577)\) → \((1,1,1,e\left(\frac{11}{20}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(-i\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{1}{5}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{20})\)