Properties

Label 4830.13
Modulus $4830$
Conductor $805$
Order $44$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4830, base_ring=CyclotomicField(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,33,22,28]))
 
pari: [g,chi] = znchar(Mod(13,4830))
 

Basic properties

Modulus: \(4830\)
Conductor: \(805\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{805}(13,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4830.co

\(\chi_{4830}(13,\cdot)\) \(\chi_{4830}(223,\cdot)\) \(\chi_{4830}(307,\cdot)\) \(\chi_{4830}(853,\cdot)\) \(\chi_{4830}(1273,\cdot)\) \(\chi_{4830}(1567,\cdot)\) \(\chi_{4830}(1777,\cdot)\) \(\chi_{4830}(1987,\cdot)\) \(\chi_{4830}(2197,\cdot)\) \(\chi_{4830}(2533,\cdot)\) \(\chi_{4830}(2617,\cdot)\) \(\chi_{4830}(2743,\cdot)\) \(\chi_{4830}(2953,\cdot)\) \(\chi_{4830}(3163,\cdot)\) \(\chi_{4830}(3247,\cdot)\) \(\chi_{4830}(3583,\cdot)\) \(\chi_{4830}(3877,\cdot)\) \(\chi_{4830}(4087,\cdot)\) \(\chi_{4830}(4213,\cdot)\) \(\chi_{4830}(4717,\cdot)\)

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: 44.44.1340542119957152709801283008679613456161693073520931071709778240989995846641249954700469970703125.1

Values on generators

\((3221,967,2761,1891)\) → \((1,-i,-1,e\left(\frac{7}{11}\right))\)

Values

\(-1\)\(1\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)\(47\)
\(1\)\(1\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{29}{44}\right)\)\(e\left(\frac{31}{44}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{5}{44}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{19}{44}\right)\)\(i\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4830 }(13,a) \;\) at \(\;a = \) e.g. 2