Properties

Label 2790.19
Modulus $2790$
Conductor $155$
Order $30$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2790, base_ring=CyclotomicField(30))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,15,4]))
 
pari: [g,chi] = znchar(Mod(19,2790))
 

Basic properties

Modulus: \(2790\)
Conductor: \(155\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(30\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{155}(19,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2790.dh

\(\chi_{2790}(19,\cdot)\) \(\chi_{2790}(289,\cdot)\) \(\chi_{2790}(379,\cdot)\) \(\chi_{2790}(919,\cdot)\) \(\chi_{2790}(1099,\cdot)\) \(\chi_{2790}(1909,\cdot)\) \(\chi_{2790}(2179,\cdot)\) \(\chi_{2790}(2539,\cdot)\)

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: \(\Q(\zeta_{15})\)
Fixed field: 30.30.17485477327500765872904889567178150559785186767578125.1

Values on generators

\((2171,1117,1801)\) → \((1,-1,e\left(\frac{2}{15}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(37\)\(41\)\(43\)
\( \chi_{ 2790 }(19, a) \) \(1\)\(1\)\(e\left(\frac{7}{30}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{1}{30}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2790 }(19,a) \;\) at \(\;a = \) e.g. 2