Properties

Label 3822.1895
Modulus 38223822
Conductor 19111911
Order 4242
Real no
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3822, base_ring=CyclotomicField(42)) M = H._module chi = DirichletCharacter(H, M([21,41,35]))
 
Copy content pari:[g,chi] = znchar(Mod(1895,3822))
 

Basic properties

Modulus: 38223822
Conductor: 19111911
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 4242
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ1911(1895,)\chi_{1911}(1895,\cdot)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 3822.dh

χ3822(17,)\chi_{3822}(17,\cdot) χ3822(257,)\chi_{3822}(257,\cdot) χ3822(563,)\chi_{3822}(563,\cdot) χ3822(1349,)\chi_{3822}(1349,\cdot) χ3822(1655,)\chi_{3822}(1655,\cdot) χ3822(1895,)\chi_{3822}(1895,\cdot) χ3822(2201,)\chi_{3822}(2201,\cdot) χ3822(2441,)\chi_{3822}(2441,\cdot) χ3822(2747,)\chi_{3822}(2747,\cdot) χ3822(2987,)\chi_{3822}(2987,\cdot) χ3822(3293,)\chi_{3822}(3293,\cdot) χ3822(3533,)\chi_{3822}(3533,\cdot)

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

Related number fields

Field of values: Q(ζ21)\Q(\zeta_{21})
Fixed field: 42.42.1202576633106121975984008800872230106954348943357258503089346642257329625784069269338733771636030016535855830219497.1

Values on generators

(2549,3433,1471)(2549,3433,1471)(1,e(4142),e(56))(-1,e\left(\frac{41}{42}\right),e\left(\frac{5}{6}\right))

First values

aa 1-11155111117171919232325252929313137374141
χ3822(1895,a) \chi_{ 3822 }(1895, a) 1111e(1342)e\left(\frac{13}{42}\right)e(821)e\left(\frac{8}{21}\right)e(47)e\left(\frac{4}{7}\right)e(13)e\left(\frac{1}{3}\right)e(1314)e\left(\frac{13}{14}\right)e(1321)e\left(\frac{13}{21}\right)e(1742)e\left(\frac{17}{42}\right)e(13)e\left(\frac{1}{3}\right)e(114)e\left(\frac{1}{14}\right)e(4142)e\left(\frac{41}{42}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ3822(1895,a)   \chi_{ 3822 }(1895,a) \; at   a=\;a = e.g. 2