Properties

Conductor 2541
Order 110
Real no
Primitive no
Minimal yes
Parity even
Orbit label 7623.eu

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(7623)
 
sage: chi = H[1637]
 
pari: [g,chi] = znchar(Mod(1637,7623))
 

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 = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 7623.eu
Orbit index = 125

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 ]
 

\(\chi_{7623}(125,\cdot)\) \(\chi_{7623}(377,\cdot)\) \(\chi_{7623}(566,\cdot)\) \(\chi_{7623}(818,\cdot)\) \(\chi_{7623}(944,\cdot)\) \(\chi_{7623}(1070,\cdot)\) \(\chi_{7623}(1259,\cdot)\) \(\chi_{7623}(1511,\cdot)\) \(\chi_{7623}(1637,\cdot)\) \(\chi_{7623}(1763,\cdot)\) \(\chi_{7623}(1952,\cdot)\) \(\chi_{7623}(2204,\cdot)\) \(\chi_{7623}(2330,\cdot)\) \(\chi_{7623}(2456,\cdot)\) \(\chi_{7623}(2645,\cdot)\) \(\chi_{7623}(2897,\cdot)\) \(\chi_{7623}(3023,\cdot)\) \(\chi_{7623}(3338,\cdot)\) \(\chi_{7623}(3716,\cdot)\) \(\chi_{7623}(3842,\cdot)\) \(\chi_{7623}(4031,\cdot)\) \(\chi_{7623}(4283,\cdot)\) \(\chi_{7623}(4409,\cdot)\) \(\chi_{7623}(4535,\cdot)\) \(\chi_{7623}(4724,\cdot)\) \(\chi_{7623}(4976,\cdot)\) \(\chi_{7623}(5102,\cdot)\) \(\chi_{7623}(5228,\cdot)\) \(\chi_{7623}(5417,\cdot)\) \(\chi_{7623}(5669,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((-1,-1,e\left(\frac{3}{55}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{61}{110}\right)\)\(e\left(\frac{6}{55}\right)\)\(e\left(\frac{2}{55}\right)\)\(e\left(\frac{73}{110}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{1}{110}\right)\)\(e\left(\frac{12}{55}\right)\)\(e\left(\frac{37}{55}\right)\)\(e\left(\frac{3}{110}\right)\)\(e\left(\frac{8}{55}\right)\)
value at  e.g. 2

Related number fields

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