Properties

Label 3520.73
Modulus 35203520
Conductor 17601760
Order 4040
Real no
Primitive no
Minimal no
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3520, base_ring=CyclotomicField(40)) M = H._module chi = DirichletCharacter(H, M([0,15,30,28]))
 
Copy content pari:[g,chi] = znchar(Mod(73,3520))
 

Basic properties

Modulus: 35203520
Conductor: 17601760
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 4040
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ1760(733,)\chi_{1760}(733,\cdot)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 3520.ei

χ3520(57,)\chi_{3520}(57,\cdot) χ3520(73,)\chi_{3520}(73,\cdot) χ3520(217,)\chi_{3520}(217,\cdot) χ3520(233,)\chi_{3520}(233,\cdot) χ3520(393,)\chi_{3520}(393,\cdot) χ3520(1337,)\chi_{3520}(1337,\cdot) χ3520(1513,)\chi_{3520}(1513,\cdot) χ3520(1657,)\chi_{3520}(1657,\cdot) χ3520(1817,)\chi_{3520}(1817,\cdot) χ3520(1833,)\chi_{3520}(1833,\cdot) χ3520(1977,)\chi_{3520}(1977,\cdot) χ3520(1993,)\chi_{3520}(1993,\cdot) χ3520(2153,)\chi_{3520}(2153,\cdot) χ3520(3097,)\chi_{3520}(3097,\cdot) χ3520(3273,)\chi_{3520}(3273,\cdot) χ3520(3417,)\chi_{3520}(3417,\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(ζ40)\Q(\zeta_{40})
Fixed field: 40.40.1314880012449506220994309247746612403564809108378301093397843089030698237952000000000000000000000000000000.2

Values on generators

(2751,1541,2817,321)(2751,1541,2817,321)(1,e(38),i,e(710))(1,e\left(\frac{3}{8}\right),-i,e\left(\frac{7}{10}\right))

First values

aa 1-1113377991313171719192121232327272929
χ3520(73,a) \chi_{ 3520 }(73, a) 1111e(3940)e\left(\frac{39}{40}\right)e(25)e\left(\frac{2}{5}\right)e(1920)e\left(\frac{19}{20}\right)e(2340)e\left(\frac{23}{40}\right)e(1120)e\left(\frac{11}{20}\right)e(940)e\left(\frac{9}{40}\right)e(38)e\left(\frac{3}{8}\right)1-1e(3740)e\left(\frac{37}{40}\right)e(2140)e\left(\frac{21}{40}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ3520(73,a)   \chi_{ 3520 }(73,a) \; at   a=\;a = e.g. 2