Properties

Conductor 847
Order 110
Real no
Primitive no
Minimal yes
Parity even
Orbit label 2541.by

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[13]
 
pari: [g,chi] = znchar(Mod(13,2541))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 847
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 = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 2541.by
Orbit index = 51

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 ]
 

\(\chi_{2541}(13,\cdot)\) \(\chi_{2541}(139,\cdot)\) \(\chi_{2541}(160,\cdot)\) \(\chi_{2541}(244,\cdot)\) \(\chi_{2541}(349,\cdot)\) \(\chi_{2541}(370,\cdot)\) \(\chi_{2541}(391,\cdot)\) \(\chi_{2541}(580,\cdot)\) \(\chi_{2541}(601,\cdot)\) \(\chi_{2541}(622,\cdot)\) \(\chi_{2541}(706,\cdot)\) \(\chi_{2541}(811,\cdot)\) \(\chi_{2541}(832,\cdot)\) \(\chi_{2541}(853,\cdot)\) \(\chi_{2541}(937,\cdot)\) \(\chi_{2541}(1042,\cdot)\) \(\chi_{2541}(1063,\cdot)\) \(\chi_{2541}(1084,\cdot)\) \(\chi_{2541}(1168,\cdot)\) \(\chi_{2541}(1273,\cdot)\) \(\chi_{2541}(1294,\cdot)\) \(\chi_{2541}(1315,\cdot)\) \(\chi_{2541}(1399,\cdot)\) \(\chi_{2541}(1504,\cdot)\) \(\chi_{2541}(1525,\cdot)\) \(\chi_{2541}(1630,\cdot)\) \(\chi_{2541}(1735,\cdot)\) \(\chi_{2541}(1756,\cdot)\) \(\chi_{2541}(1777,\cdot)\) \(\chi_{2541}(1861,\cdot)\) ...

Values on generators

\((848,1816,2059)\) → \((1,-1,e\left(\frac{101}{110}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{101}{110}\right)\)\(e\left(\frac{46}{55}\right)\)\(e\left(\frac{49}{110}\right)\)\(e\left(\frac{83}{110}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{13}{55}\right)\)\(e\left(\frac{37}{55}\right)\)\(e\left(\frac{27}{55}\right)\)\(e\left(\frac{39}{55}\right)\)\(e\left(\frac{31}{110}\right)\)
value at  e.g. 2

Related number fields

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