Properties

Label 3822.2803
Modulus 38223822
Conductor 637637
Order 8484
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3822, base_ring=CyclotomicField(84))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,26,21]))
 
pari: [g,chi] = znchar(Mod(2803,3822))
 

Basic properties

Modulus: 38223822
Conductor: 637637
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 8484
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from χ637(255,)\chi_{637}(255,\cdot)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3822.ei

χ3822(73,)\chi_{3822}(73,\cdot) χ3822(187,)\chi_{3822}(187,\cdot) χ3822(229,)\chi_{3822}(229,\cdot) χ3822(577,)\chi_{3822}(577,\cdot) χ3822(733,)\chi_{3822}(733,\cdot) χ3822(775,)\chi_{3822}(775,\cdot) χ3822(1123,)\chi_{3822}(1123,\cdot) χ3822(1165,)\chi_{3822}(1165,\cdot) χ3822(1279,)\chi_{3822}(1279,\cdot) χ3822(1321,)\chi_{3822}(1321,\cdot) χ3822(1669,)\chi_{3822}(1669,\cdot) χ3822(1711,)\chi_{3822}(1711,\cdot) χ3822(1825,)\chi_{3822}(1825,\cdot) χ3822(1867,)\chi_{3822}(1867,\cdot) χ3822(2215,)\chi_{3822}(2215,\cdot) χ3822(2257,)\chi_{3822}(2257,\cdot) χ3822(2413,)\chi_{3822}(2413,\cdot) χ3822(2761,)\chi_{3822}(2761,\cdot) χ3822(2803,)\chi_{3822}(2803,\cdot) χ3822(2917,)\chi_{3822}(2917,\cdot) χ3822(3307,)\chi_{3822}(3307,\cdot) χ3822(3349,)\chi_{3822}(3349,\cdot) χ3822(3463,)\chi_{3822}(3463,\cdot) χ3822(3505,)\chi_{3822}(3505,\cdot)

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

Related number fields

Field of values: Q(ζ84)\Q(\zeta_{84})
Fixed field: Number field defined by a degree 84 polynomial

Values on generators

(2549,3433,1471)(2549,3433,1471)(1,e(1342),i)(1,e\left(\frac{13}{42}\right),i)

First values

aa 1-11155111117171919232325252929313137374141
χ3822(2803,a) \chi_{ 3822 }(2803, a) 1111e(1984)e\left(\frac{19}{84}\right)e(1184)e\left(\frac{11}{84}\right)e(521)e\left(\frac{5}{21}\right)e(112)e\left(\frac{1}{12}\right)e(1142)e\left(\frac{11}{42}\right)e(1942)e\left(\frac{19}{42}\right)e(47)e\left(\frac{4}{7}\right)e(512)e\left(\frac{5}{12}\right)e(5584)e\left(\frac{55}{84}\right)e(2528)e\left(\frac{25}{28}\right)
sage: chi.jacobi_sum(n)
 
χ3822(2803,a)   \chi_{ 3822 }(2803,a) \; at   a=\;a = e.g. 2