Properties

Conductor 4008
Order 166
Real No
Primitive Yes
Parity Even
Orbit Label 4008.y

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[5]
pari: [g,chi] = znchar(Mod(5,4008))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4008
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 166
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 = 4008.y
Orbit index = 25

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 ]

\(\chi_{4008}(5,\cdot)\) \(\chi_{4008}(53,\cdot)\) \(\chi_{4008}(101,\cdot)\) \(\chi_{4008}(125,\cdot)\) \(\chi_{4008}(149,\cdot)\) \(\chi_{4008}(197,\cdot)\) \(\chi_{4008}(245,\cdot)\) \(\chi_{4008}(269,\cdot)\) \(\chi_{4008}(389,\cdot)\) \(\chi_{4008}(413,\cdot)\) \(\chi_{4008}(437,\cdot)\) \(\chi_{4008}(485,\cdot)\) \(\chi_{4008}(581,\cdot)\) \(\chi_{4008}(605,\cdot)\) \(\chi_{4008}(773,\cdot)\) \(\chi_{4008}(797,\cdot)\) \(\chi_{4008}(821,\cdot)\) \(\chi_{4008}(845,\cdot)\) \(\chi_{4008}(869,\cdot)\) \(\chi_{4008}(917,\cdot)\) \(\chi_{4008}(941,\cdot)\) \(\chi_{4008}(1037,\cdot)\) \(\chi_{4008}(1061,\cdot)\) \(\chi_{4008}(1085,\cdot)\) \(\chi_{4008}(1133,\cdot)\) \(\chi_{4008}(1157,\cdot)\) \(\chi_{4008}(1229,\cdot)\) \(\chi_{4008}(1325,\cdot)\) \(\chi_{4008}(1349,\cdot)\) \(\chi_{4008}(1373,\cdot)\) ...

Values on generators

\((3007,2005,1337,673)\) → \((1,-1,-1,e\left(\frac{1}{166}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{1}{166}\right)\)\(e\left(\frac{59}{83}\right)\)\(e\left(\frac{14}{83}\right)\)\(e\left(\frac{10}{83}\right)\)\(e\left(\frac{68}{83}\right)\)\(e\left(\frac{141}{166}\right)\)\(e\left(\frac{8}{83}\right)\)\(e\left(\frac{1}{83}\right)\)\(e\left(\frac{75}{83}\right)\)\(e\left(\frac{45}{83}\right)\)
value at  e.g. 2

Related number fields

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