Properties

Conductor 4725
Order 90
Real No
Primitive Yes
Parity Even
Orbit Label 4725.gm

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(4725)
sage: chi = H[3296]
pari: [g,chi] = znchar(Mod(3296,4725))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4725
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 90
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 = 4725.gm
Orbit index = 169

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 ]

\(\chi_{4725}(41,\cdot)\) \(\chi_{4725}(146,\cdot)\) \(\chi_{4725}(356,\cdot)\) \(\chi_{4725}(461,\cdot)\) \(\chi_{4725}(671,\cdot)\) \(\chi_{4725}(986,\cdot)\) \(\chi_{4725}(1091,\cdot)\) \(\chi_{4725}(1406,\cdot)\) \(\chi_{4725}(1616,\cdot)\) \(\chi_{4725}(1721,\cdot)\) \(\chi_{4725}(1931,\cdot)\) \(\chi_{4725}(2036,\cdot)\) \(\chi_{4725}(2246,\cdot)\) \(\chi_{4725}(2561,\cdot)\) \(\chi_{4725}(2666,\cdot)\) \(\chi_{4725}(2981,\cdot)\) \(\chi_{4725}(3191,\cdot)\) \(\chi_{4725}(3296,\cdot)\) \(\chi_{4725}(3506,\cdot)\) \(\chi_{4725}(3611,\cdot)\) \(\chi_{4725}(3821,\cdot)\) \(\chi_{4725}(4136,\cdot)\) \(\chi_{4725}(4241,\cdot)\) \(\chi_{4725}(4556,\cdot)\)

Values on generators

\((4376,1702,2026)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{3}{5}\right),-1)\)

Values

-1124811131617192223
\(1\)\(1\)\(e\left(\frac{59}{90}\right)\)\(e\left(\frac{14}{45}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{29}{90}\right)\)\(e\left(\frac{31}{90}\right)\)\(e\left(\frac{28}{45}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{44}{45}\right)\)\(e\left(\frac{19}{90}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{45})\)