Properties

Conductor 2475
Order 60
Real No
Primitive No
Parity Even
Orbit Label 9900.ld

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(9900)
sage: chi = H[113]
pari: [g,chi] = znchar(Mod(113,9900))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 2475
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 = No
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Even
Orbit label = 9900.ld
Orbit index = 290

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 ]

\(\chi_{9900}(113,\cdot)\) \(\chi_{9900}(317,\cdot)\) \(\chi_{9900}(797,\cdot)\) \(\chi_{9900}(1037,\cdot)\) \(\chi_{9900}(1577,\cdot)\) \(\chi_{9900}(1973,\cdot)\) \(\chi_{9900}(3413,\cdot)\) \(\chi_{9900}(4097,\cdot)\) \(\chi_{9900}(5153,\cdot)\) \(\chi_{9900}(5333,\cdot)\) \(\chi_{9900}(6917,\cdot)\) \(\chi_{9900}(7637,\cdot)\) \(\chi_{9900}(8177,\cdot)\) \(\chi_{9900}(8453,\cdot)\) \(\chi_{9900}(8573,\cdot)\) \(\chi_{9900}(8633,\cdot)\)

Inducing primitive character

\(\chi_{2475}(113,\cdot)\)

Values on generators

\((4951,5501,2377,4501)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{19}{20}\right),e\left(\frac{4}{5}\right))\)

Values

-117131719232931374143
\(1\)\(1\)\(e\left(\frac{41}{60}\right)\)\(e\left(\frac{31}{60}\right)\)\(e\left(\frac{1}{20}\right)\)\(-1\)\(e\left(\frac{37}{60}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{7}{12}\right)\)
value at  e.g. 2

Related number fields

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