Properties

Label 1840.57
Modulus $1840$
Conductor $920$
Order $44$
Real no
Primitive no
Minimal no
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1840, base_ring=CyclotomicField(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,22,11,18]))
 
pari: [g,chi] = znchar(Mod(57,1840))
 

Basic properties

Modulus: \(1840\)
Conductor: \(920\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{920}(517,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1840.cm

\(\chi_{1840}(57,\cdot)\) \(\chi_{1840}(153,\cdot)\) \(\chi_{1840}(217,\cdot)\) \(\chi_{1840}(297,\cdot)\) \(\chi_{1840}(313,\cdot)\) \(\chi_{1840}(457,\cdot)\) \(\chi_{1840}(617,\cdot)\) \(\chi_{1840}(697,\cdot)\) \(\chi_{1840}(793,\cdot)\) \(\chi_{1840}(937,\cdot)\) \(\chi_{1840}(953,\cdot)\) \(\chi_{1840}(1017,\cdot)\) \(\chi_{1840}(1033,\cdot)\) \(\chi_{1840}(1193,\cdot)\) \(\chi_{1840}(1257,\cdot)\) \(\chi_{1840}(1353,\cdot)\) \(\chi_{1840}(1417,\cdot)\) \(\chi_{1840}(1433,\cdot)\) \(\chi_{1840}(1673,\cdot)\) \(\chi_{1840}(1753,\cdot)\)

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\zeta_{44})\)
Fixed field: 44.44.13383169230192059253459701104387771124501004765020501667165784506368000000000000000000000000000000000.1

Values on generators

\((1151,1381,737,1201)\) → \((1,-1,i,e\left(\frac{9}{22}\right))\)

Values

\(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(27\)\(29\)
\(1\)\(1\)\(e\left(\frac{35}{44}\right)\)\(e\left(\frac{1}{44}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{43}{44}\right)\)\(e\left(\frac{5}{44}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{17}{44}\right)\)\(e\left(\frac{4}{11}\right)\)
value at e.g. 2