Properties

Label 3895.274
Modulus 38953895
Conductor 38953895
Order 120120
Real no
Primitive yes
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(3895, base_ring=CyclotomicField(120)) M = H._module chi = DirichletCharacter(H, M([60,20,33]))
 
Copy content pari:[g,chi] = znchar(Mod(274,3895))
 

Basic properties

Modulus: 38953895
Conductor: 38953895
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 120120
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
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 3895.fn

χ3895(69,)\chi_{3895}(69,\cdot) χ3895(179,)\chi_{3895}(179,\cdot) χ3895(259,)\chi_{3895}(259,\cdot) χ3895(274,)\chi_{3895}(274,\cdot) χ3895(354,)\chi_{3895}(354,\cdot) χ3895(464,)\chi_{3895}(464,\cdot) χ3895(544,)\chi_{3895}(544,\cdot) χ3895(559,)\chi_{3895}(559,\cdot) χ3895(639,)\chi_{3895}(639,\cdot) χ3895(749,)\chi_{3895}(749,\cdot) χ3895(844,)\chi_{3895}(844,\cdot) χ3895(924,)\chi_{3895}(924,\cdot) χ3895(1019,)\chi_{3895}(1019,\cdot) χ3895(1114,)\chi_{3895}(1114,\cdot) χ3895(1129,)\chi_{3895}(1129,\cdot) χ3895(1224,)\chi_{3895}(1224,\cdot) χ3895(1319,)\chi_{3895}(1319,\cdot) χ3895(1874,)\chi_{3895}(1874,\cdot) χ3895(2079,)\chi_{3895}(2079,\cdot) χ3895(2349,)\chi_{3895}(2349,\cdot) χ3895(2554,)\chi_{3895}(2554,\cdot) χ3895(3109,)\chi_{3895}(3109,\cdot) χ3895(3204,)\chi_{3895}(3204,\cdot) χ3895(3299,)\chi_{3895}(3299,\cdot) χ3895(3314,)\chi_{3895}(3314,\cdot) χ3895(3409,)\chi_{3895}(3409,\cdot) χ3895(3504,)\chi_{3895}(3504,\cdot) χ3895(3584,)\chi_{3895}(3584,\cdot) χ3895(3679,)\chi_{3895}(3679,\cdot) χ3895(3789,)\chi_{3895}(3789,\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(ζ120)\Q(\zeta_{120})
Fixed field: Number field defined by a degree 120 polynomial (not computed)

Values on generators

(3117,2871,1236)(3117,2871,1236)(1,e(16),e(1140))(-1,e\left(\frac{1}{6}\right),e\left(\frac{11}{40}\right))

First values

aa 1-11122334466778899111112121313
χ3895(274,a) \chi_{ 3895 }(274, a) 1111e(4960)e\left(\frac{49}{60}\right)e(1924)e\left(\frac{19}{24}\right)e(1930)e\left(\frac{19}{30}\right)e(73120)e\left(\frac{73}{120}\right)e(940)e\left(\frac{9}{40}\right)e(920)e\left(\frac{9}{20}\right)e(712)e\left(\frac{7}{12}\right)e(3340)e\left(\frac{33}{40}\right)e(1740)e\left(\frac{17}{40}\right)e(103120)e\left(\frac{103}{120}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ3895(274,a)   \chi_{ 3895 }(274,a) \; at   a=\;a = e.g. 2