Properties

Label 1470.1129
Modulus 14701470
Conductor 245245
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(1470, base_ring=CyclotomicField(42)) M = H._module chi = DirichletCharacter(H, M([0,21,26]))
 
Copy content pari:[g,chi] = znchar(Mod(1129,1470))
 

Basic properties

Modulus: 14701470
Conductor: 245245
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 χ245(149,)\chi_{245}(149,\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 1470.bq

χ1470(109,)\chi_{1470}(109,\cdot) χ1470(289,)\chi_{1470}(289,\cdot) χ1470(319,)\chi_{1470}(319,\cdot) χ1470(499,)\chi_{1470}(499,\cdot) χ1470(529,)\chi_{1470}(529,\cdot) χ1470(709,)\chi_{1470}(709,\cdot) χ1470(739,)\chi_{1470}(739,\cdot) χ1470(919,)\chi_{1470}(919,\cdot) χ1470(1129,)\chi_{1470}(1129,\cdot) χ1470(1159,)\chi_{1470}(1159,\cdot) χ1470(1339,)\chi_{1470}(1339,\cdot) χ1470(1369,)\chi_{1470}(1369,\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: 42.42.8050468075656610214837511220114705524038488445061950919170859146595001220703125.1

Values on generators

(491,1177,1081)(491,1177,1081)(1,1,e(1321))(1,-1,e\left(\frac{13}{21}\right))

First values

aa 1-1111111131317171919232329293131373741414343
χ1470(1129,a) \chi_{ 1470 }(1129, a) 1111e(1621)e\left(\frac{16}{21}\right)e(1314)e\left(\frac{13}{14}\right)e(4142)e\left(\frac{41}{42}\right)e(23)e\left(\frac{2}{3}\right)e(142)e\left(\frac{1}{42}\right)e(17)e\left(\frac{1}{7}\right)e(13)e\left(\frac{1}{3}\right)e(1342)e\left(\frac{13}{42}\right)e(27)e\left(\frac{2}{7}\right)e(314)e\left(\frac{3}{14}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ1470(1129,a)   \chi_{ 1470 }(1129,a) \; at   a=\;a = e.g. 2