Properties

Label 7605.4598
Modulus 76057605
Conductor 25352535
Order 156156
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7605, base_ring=CyclotomicField(156)) M = H._module chi = DirichletCharacter(H, M([78,117,116]))
 
Copy content pari:[g,chi] = znchar(Mod(4598,7605))
 

Basic properties

Modulus: 76057605
Conductor: 25352535
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 156156
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ2535(2063,)\chi_{2535}(2063,\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 7605.ge

χ7605(107,)\chi_{7605}(107,\cdot) χ7605(152,)\chi_{7605}(152,\cdot) χ7605(458,)\chi_{7605}(458,\cdot) χ7605(503,)\chi_{7605}(503,\cdot) χ7605(692,)\chi_{7605}(692,\cdot) χ7605(737,)\chi_{7605}(737,\cdot) χ7605(1043,)\chi_{7605}(1043,\cdot) χ7605(1088,)\chi_{7605}(1088,\cdot) χ7605(1277,)\chi_{7605}(1277,\cdot) χ7605(1322,)\chi_{7605}(1322,\cdot) χ7605(1628,)\chi_{7605}(1628,\cdot) χ7605(1673,)\chi_{7605}(1673,\cdot) χ7605(1862,)\chi_{7605}(1862,\cdot) χ7605(1907,)\chi_{7605}(1907,\cdot) χ7605(2213,)\chi_{7605}(2213,\cdot) χ7605(2258,)\chi_{7605}(2258,\cdot) χ7605(2447,)\chi_{7605}(2447,\cdot) χ7605(2492,)\chi_{7605}(2492,\cdot) χ7605(2798,)\chi_{7605}(2798,\cdot) χ7605(2843,)\chi_{7605}(2843,\cdot) χ7605(3032,)\chi_{7605}(3032,\cdot) χ7605(3077,)\chi_{7605}(3077,\cdot) χ7605(3383,)\chi_{7605}(3383,\cdot) χ7605(3428,)\chi_{7605}(3428,\cdot) χ7605(3617,)\chi_{7605}(3617,\cdot) χ7605(3662,)\chi_{7605}(3662,\cdot) χ7605(3968,)\chi_{7605}(3968,\cdot) χ7605(4013,)\chi_{7605}(4013,\cdot) χ7605(4553,)\chi_{7605}(4553,\cdot) χ7605(4598,)\chi_{7605}(4598,\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(ζ156)\Q(\zeta_{156})
Fixed field: Number field defined by a degree 156 polynomial (not computed)

Values on generators

(6761,1522,6931)(6761,1522,6931)(1,i,e(2939))(-1,-i,e\left(\frac{29}{39}\right))

First values

aa 1-11122447788111114141616171719192222
χ7605(4598,a) \chi_{ 7605 }(4598, a) 1111e(155156)e\left(\frac{155}{156}\right)e(7778)e\left(\frac{77}{78}\right)e(49156)e\left(\frac{49}{156}\right)e(5152)e\left(\frac{51}{52}\right)e(778)e\left(\frac{7}{78}\right)e(413)e\left(\frac{4}{13}\right)e(3839)e\left(\frac{38}{39}\right)e(127156)e\left(\frac{127}{156}\right)e(56)e\left(\frac{5}{6}\right)e(112)e\left(\frac{1}{12}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ7605(4598,a)   \chi_{ 7605 }(4598,a) \; at   a=\;a = e.g. 2