Properties

Conductor 167
Order 83
Real No
Primitive No
Parity Even
Orbit Label 4008.q

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(4008)
sage: chi = H[25]
pari: [g,chi] = znchar(Mod(25,4008))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 167
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 83
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 = 4008.q
Orbit index = 17

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 ]

\(\chi_{4008}(25,\cdot)\) \(\chi_{4008}(49,\cdot)\) \(\chi_{4008}(97,\cdot)\) \(\chi_{4008}(121,\cdot)\) \(\chi_{4008}(169,\cdot)\) \(\chi_{4008}(217,\cdot)\) \(\chi_{4008}(265,\cdot)\) \(\chi_{4008}(289,\cdot)\) \(\chi_{4008}(337,\cdot)\) \(\chi_{4008}(361,\cdot)\) \(\chi_{4008}(409,\cdot)\) \(\chi_{4008}(433,\cdot)\) \(\chi_{4008}(481,\cdot)\) \(\chi_{4008}(505,\cdot)\) \(\chi_{4008}(529,\cdot)\) \(\chi_{4008}(577,\cdot)\) \(\chi_{4008}(601,\cdot)\) \(\chi_{4008}(625,\cdot)\) \(\chi_{4008}(697,\cdot)\) \(\chi_{4008}(745,\cdot)\) \(\chi_{4008}(841,\cdot)\) \(\chi_{4008}(889,\cdot)\) \(\chi_{4008}(961,\cdot)\) \(\chi_{4008}(985,\cdot)\) \(\chi_{4008}(1009,\cdot)\) \(\chi_{4008}(1033,\cdot)\) \(\chi_{4008}(1129,\cdot)\) \(\chi_{4008}(1177,\cdot)\) \(\chi_{4008}(1201,\cdot)\) \(\chi_{4008}(1225,\cdot)\) ...

Inducing primitive character

\(\chi_{167}(25,\cdot)\)

Values on generators

\((3007,2005,1337,673)\) → \((1,1,1,e\left(\frac{1}{83}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{1}{83}\right)\)\(e\left(\frac{35}{83}\right)\)\(e\left(\frac{28}{83}\right)\)\(e\left(\frac{20}{83}\right)\)\(e\left(\frac{53}{83}\right)\)\(e\left(\frac{58}{83}\right)\)\(e\left(\frac{16}{83}\right)\)\(e\left(\frac{2}{83}\right)\)\(e\left(\frac{67}{83}\right)\)\(e\left(\frac{7}{83}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{83})\)