Properties

Conductor 575
Order 220
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4025.df

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(4025)
 
sage: chi = H[113]
 
pari: [g,chi] = znchar(Mod(113,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 575
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 220
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 = 4025.df
Orbit index = 84

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 ]
 

\(\chi_{4025}(113,\cdot)\) \(\chi_{4025}(148,\cdot)\) \(\chi_{4025}(267,\cdot)\) \(\chi_{4025}(337,\cdot)\) \(\chi_{4025}(428,\cdot)\) \(\chi_{4025}(442,\cdot)\) \(\chi_{4025}(477,\cdot)\) \(\chi_{4025}(498,\cdot)\) \(\chi_{4025}(603,\cdot)\) \(\chi_{4025}(617,\cdot)\) \(\chi_{4025}(638,\cdot)\) \(\chi_{4025}(687,\cdot)\) \(\chi_{4025}(778,\cdot)\) \(\chi_{4025}(792,\cdot)\) \(\chi_{4025}(848,\cdot)\) \(\chi_{4025}(862,\cdot)\) \(\chi_{4025}(953,\cdot)\) \(\chi_{4025}(1023,\cdot)\) \(\chi_{4025}(1072,\cdot)\) \(\chi_{4025}(1142,\cdot)\) \(\chi_{4025}(1233,\cdot)\) \(\chi_{4025}(1247,\cdot)\) \(\chi_{4025}(1303,\cdot)\) \(\chi_{4025}(1387,\cdot)\) \(\chi_{4025}(1408,\cdot)\) \(\chi_{4025}(1422,\cdot)\) \(\chi_{4025}(1492,\cdot)\) \(\chi_{4025}(1548,\cdot)\) \(\chi_{4025}(1562,\cdot)\) \(\chi_{4025}(1583,\cdot)\) ...

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{19}{20}\right),1,e\left(\frac{13}{22}\right))\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{29}{220}\right)\)\(e\left(\frac{23}{220}\right)\)\(e\left(\frac{29}{110}\right)\)\(e\left(\frac{13}{55}\right)\)\(e\left(\frac{87}{220}\right)\)\(e\left(\frac{23}{110}\right)\)\(e\left(\frac{57}{110}\right)\)\(e\left(\frac{81}{220}\right)\)\(e\left(\frac{71}{220}\right)\)\(e\left(\frac{29}{55}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{220})\)