Properties

Label 4025.3201
Modulus $4025$
Conductor $161$
Order $33$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4025, base_ring=CyclotomicField(66))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,22,12]))
 
pari: [g,chi] = znchar(Mod(3201,4025))
 

Basic properties

Modulus: \(4025\)
Conductor: \(161\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(33\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{161}(142,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4025.ca

\(\chi_{4025}(151,\cdot)\) \(\chi_{4025}(326,\cdot)\) \(\chi_{4025}(501,\cdot)\) \(\chi_{4025}(676,\cdot)\) \(\chi_{4025}(926,\cdot)\) \(\chi_{4025}(1451,\cdot)\) \(\chi_{4025}(1626,\cdot)\) \(\chi_{4025}(2076,\cdot)\) \(\chi_{4025}(2151,\cdot)\) \(\chi_{4025}(2326,\cdot)\) \(\chi_{4025}(2601,\cdot)\) \(\chi_{4025}(2676,\cdot)\) \(\chi_{4025}(2776,\cdot)\) \(\chi_{4025}(3026,\cdot)\) \(\chi_{4025}(3201,\cdot)\) \(\chi_{4025}(3301,\cdot)\) \(\chi_{4025}(3376,\cdot)\) \(\chi_{4025}(3476,\cdot)\) \(\chi_{4025}(3551,\cdot)\) \(\chi_{4025}(3826,\cdot)\)

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: \(\Q(\zeta_{33})\)
Fixed field: 33.33.277966181338944111003326058293667039541136678070715028736001.1

Values on generators

\((2577,1151,3501)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{2}{11}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(8\)\(9\)\(11\)\(12\)\(13\)\(16\)
\( \chi_{ 4025 }(3201, a) \) \(1\)\(1\)\(e\left(\frac{1}{33}\right)\)\(e\left(\frac{8}{33}\right)\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{16}{33}\right)\)\(e\left(\frac{32}{33}\right)\)\(e\left(\frac{10}{33}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{4}{33}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4025 }(3201,a) \;\) at \(\;a = \) e.g. 2