Properties

Conductor 2541
Order 110
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 2541.ca

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(2541)
 
sage: chi = H[20]
 
pari: [g,chi] = znchar(Mod(20,2541))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2541
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 110
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 2541.ca
Orbit index = 53

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 ]
 

\(\chi_{2541}(20,\cdot)\) \(\chi_{2541}(104,\cdot)\) \(\chi_{2541}(125,\cdot)\) \(\chi_{2541}(146,\cdot)\) \(\chi_{2541}(335,\cdot)\) \(\chi_{2541}(356,\cdot)\) \(\chi_{2541}(377,\cdot)\) \(\chi_{2541}(482,\cdot)\) \(\chi_{2541}(566,\cdot)\) \(\chi_{2541}(587,\cdot)\) \(\chi_{2541}(713,\cdot)\) \(\chi_{2541}(797,\cdot)\) \(\chi_{2541}(818,\cdot)\) \(\chi_{2541}(839,\cdot)\) \(\chi_{2541}(944,\cdot)\) \(\chi_{2541}(1028,\cdot)\) \(\chi_{2541}(1070,\cdot)\) \(\chi_{2541}(1175,\cdot)\) \(\chi_{2541}(1259,\cdot)\) \(\chi_{2541}(1280,\cdot)\) \(\chi_{2541}(1301,\cdot)\) \(\chi_{2541}(1406,\cdot)\) \(\chi_{2541}(1490,\cdot)\) \(\chi_{2541}(1511,\cdot)\) \(\chi_{2541}(1532,\cdot)\) \(\chi_{2541}(1637,\cdot)\) \(\chi_{2541}(1742,\cdot)\) \(\chi_{2541}(1763,\cdot)\) \(\chi_{2541}(1868,\cdot)\) \(\chi_{2541}(1952,\cdot)\) ...

Values on generators

\((848,1816,2059)\) → \((-1,-1,e\left(\frac{38}{55}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{21}{110}\right)\)\(e\left(\frac{21}{55}\right)\)\(e\left(\frac{7}{55}\right)\)\(e\left(\frac{63}{110}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{31}{110}\right)\)\(e\left(\frac{42}{55}\right)\)\(e\left(\frac{47}{55}\right)\)\(e\left(\frac{93}{110}\right)\)\(e\left(\frac{28}{55}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{55})\)