Properties

Conductor 1337
Order 570
Real No
Primitive Yes
Parity Odd
Orbit Label 1337.bf

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(1337)
 
sage: chi = H[40]
 
pari: [g,chi] = znchar(Mod(40,1337))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1337
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 570
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 = Odd
Orbit label = 1337.bf
Orbit index = 32

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 ]
 

\(\chi_{1337}(3,\cdot)\) \(\chi_{1337}(10,\cdot)\) \(\chi_{1337}(12,\cdot)\) \(\chi_{1337}(17,\cdot)\) \(\chi_{1337}(24,\cdot)\) \(\chi_{1337}(26,\cdot)\) \(\chi_{1337}(40,\cdot)\) \(\chi_{1337}(45,\cdot)\) \(\chi_{1337}(54,\cdot)\) \(\chi_{1337}(59,\cdot)\) \(\chi_{1337}(68,\cdot)\) \(\chi_{1337}(75,\cdot)\) \(\chi_{1337}(80,\cdot)\) \(\chi_{1337}(96,\cdot)\) \(\chi_{1337}(103,\cdot)\) \(\chi_{1337}(108,\cdot)\) \(\chi_{1337}(115,\cdot)\) \(\chi_{1337}(117,\cdot)\) \(\chi_{1337}(129,\cdot)\) \(\chi_{1337}(138,\cdot)\) \(\chi_{1337}(194,\cdot)\) \(\chi_{1337}(199,\cdot)\) \(\chi_{1337}(201,\cdot)\) \(\chi_{1337}(206,\cdot)\) \(\chi_{1337}(208,\cdot)\) \(\chi_{1337}(215,\cdot)\) \(\chi_{1337}(234,\cdot)\) \(\chi_{1337}(236,\cdot)\) \(\chi_{1337}(241,\cdot)\) \(\chi_{1337}(250,\cdot)\) ...

Values on generators

\((192,974)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{91}{95}\right))\)

Values

-112345689101112
\(-1\)\(1\)\(e\left(\frac{232}{285}\right)\)\(e\left(\frac{541}{570}\right)\)\(e\left(\frac{179}{285}\right)\)\(e\left(\frac{7}{114}\right)\)\(e\left(\frac{29}{38}\right)\)\(e\left(\frac{42}{95}\right)\)\(e\left(\frac{256}{285}\right)\)\(e\left(\frac{499}{570}\right)\)\(e\left(\frac{43}{57}\right)\)\(e\left(\frac{329}{570}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{285})\)