Properties

Conductor 1336
Order 166
Real No
Primitive No
Parity Even
Orbit Label 4008.bb

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[61]
pari: [g,chi] = znchar(Mod(61,4008))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1336
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 = No
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Even
Orbit label = 4008.bb
Orbit index = 28

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 ]

\(\chi_{4008}(61,\cdot)\) \(\chi_{4008}(85,\cdot)\) \(\chi_{4008}(133,\cdot)\) \(\chi_{4008}(157,\cdot)\) \(\chi_{4008}(181,\cdot)\) \(\chi_{4008}(205,\cdot)\) \(\chi_{4008}(229,\cdot)\) \(\chi_{4008}(397,\cdot)\) \(\chi_{4008}(421,\cdot)\) \(\chi_{4008}(517,\cdot)\) \(\chi_{4008}(565,\cdot)\) \(\chi_{4008}(589,\cdot)\) \(\chi_{4008}(613,\cdot)\) \(\chi_{4008}(733,\cdot)\) \(\chi_{4008}(757,\cdot)\) \(\chi_{4008}(805,\cdot)\) \(\chi_{4008}(853,\cdot)\) \(\chi_{4008}(877,\cdot)\) \(\chi_{4008}(901,\cdot)\) \(\chi_{4008}(949,\cdot)\) \(\chi_{4008}(997,\cdot)\) \(\chi_{4008}(1021,\cdot)\) \(\chi_{4008}(1117,\cdot)\) \(\chi_{4008}(1213,\cdot)\) \(\chi_{4008}(1285,\cdot)\) \(\chi_{4008}(1357,\cdot)\) \(\chi_{4008}(1429,\cdot)\) \(\chi_{4008}(1477,\cdot)\) \(\chi_{4008}(1525,\cdot)\) \(\chi_{4008}(1597,\cdot)\) ...

Inducing primitive character

\(\chi_{1336}(61,\cdot)\)

Values on generators

\((3007,2005,1337,673)\) → \((1,-1,1,e\left(\frac{33}{83}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{149}{166}\right)\)\(e\left(\frac{76}{83}\right)\)\(e\left(\frac{105}{166}\right)\)\(e\left(\frac{75}{166}\right)\)\(e\left(\frac{6}{83}\right)\)\(e\left(\frac{93}{166}\right)\)\(e\left(\frac{30}{83}\right)\)\(e\left(\frac{66}{83}\right)\)\(e\left(\frac{23}{166}\right)\)\(e\left(\frac{65}{83}\right)\)
value at  e.g. 2

Related number fields

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