Properties

Conductor 3009
Order 464
Real No
Primitive Yes
Parity Even
Orbit Label 3009.bm

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(3009)
 
sage: chi = H[5]
 
pari: [g,chi] = znchar(Mod(5,3009))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 3009
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 464
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 = 3009.bm
Orbit index = 39

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 ]
 

\(\chi_{3009}(5,\cdot)\) \(\chi_{3009}(20,\cdot)\) \(\chi_{3009}(29,\cdot)\) \(\chi_{3009}(41,\cdot)\) \(\chi_{3009}(62,\cdot)\) \(\chi_{3009}(71,\cdot)\) \(\chi_{3009}(74,\cdot)\) \(\chi_{3009}(80,\cdot)\) \(\chi_{3009}(95,\cdot)\) \(\chi_{3009}(107,\cdot)\) \(\chi_{3009}(116,\cdot)\) \(\chi_{3009}(122,\cdot)\) \(\chi_{3009}(125,\cdot)\) \(\chi_{3009}(143,\cdot)\) \(\chi_{3009}(146,\cdot)\) \(\chi_{3009}(164,\cdot)\) \(\chi_{3009}(167,\cdot)\) \(\chi_{3009}(182,\cdot)\) \(\chi_{3009}(194,\cdot)\) \(\chi_{3009}(197,\cdot)\) \(\chi_{3009}(218,\cdot)\) \(\chi_{3009}(245,\cdot)\) \(\chi_{3009}(248,\cdot)\) \(\chi_{3009}(284,\cdot)\) \(\chi_{3009}(299,\cdot)\) \(\chi_{3009}(311,\cdot)\) \(\chi_{3009}(317,\cdot)\) \(\chi_{3009}(320,\cdot)\) \(\chi_{3009}(371,\cdot)\) \(\chi_{3009}(380,\cdot)\) ...

Values on generators

\((1004,1771,1123)\) → \((-1,e\left(\frac{5}{16}\right),e\left(\frac{3}{29}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{227}{232}\right)\)\(e\left(\frac{111}{116}\right)\)\(e\left(\frac{317}{464}\right)\)\(e\left(\frac{139}{464}\right)\)\(e\left(\frac{217}{232}\right)\)\(e\left(\frac{307}{464}\right)\)\(e\left(\frac{127}{464}\right)\)\(e\left(\frac{105}{116}\right)\)\(e\left(\frac{129}{464}\right)\)\(e\left(\frac{53}{58}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{464})\)