Properties

Label 8020.183
Modulus $8020$
Conductor $8020$
Order $100$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8020, base_ring=CyclotomicField(100))
 
M = H._module
 
chi = DirichletCharacter(H, M([50,75,71]))
 
pari: [g,chi] = znchar(Mod(183,8020))
 

Basic properties

Modulus: \(8020\)
Conductor: \(8020\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(100\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8020.dm

\(\chi_{8020}(183,\cdot)\) \(\chi_{8020}(703,\cdot)\) \(\chi_{8020}(1087,\cdot)\) \(\chi_{8020}(1103,\cdot)\) \(\chi_{8020}(1207,\cdot)\) \(\chi_{8020}(1407,\cdot)\) \(\chi_{8020}(1483,\cdot)\) \(\chi_{8020}(1523,\cdot)\) \(\chi_{8020}(1987,\cdot)\) \(\chi_{8020}(2023,\cdot)\) \(\chi_{8020}(2487,\cdot)\) \(\chi_{8020}(2527,\cdot)\) \(\chi_{8020}(2603,\cdot)\) \(\chi_{8020}(2803,\cdot)\) \(\chi_{8020}(2907,\cdot)\) \(\chi_{8020}(2923,\cdot)\) \(\chi_{8020}(3307,\cdot)\) \(\chi_{8020}(3827,\cdot)\) \(\chi_{8020}(4067,\cdot)\) \(\chi_{8020}(4103,\cdot)\) \(\chi_{8020}(4123,\cdot)\) \(\chi_{8020}(4347,\cdot)\) \(\chi_{8020}(4567,\cdot)\) \(\chi_{8020}(4743,\cdot)\) \(\chi_{8020}(5303,\cdot)\) \(\chi_{8020}(5307,\cdot)\) \(\chi_{8020}(5323,\cdot)\) \(\chi_{8020}(5663,\cdot)\) \(\chi_{8020}(5763,\cdot)\) \(\chi_{8020}(6267,\cdot)\) ...

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: $\Q(\zeta_{100})$
Fixed field: Number field defined by a degree 100 polynomial

Values on generators

\((4011,6417,7221)\) → \((-1,-i,e\left(\frac{71}{100}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)
\( \chi_{ 8020 }(183, a) \) \(1\)\(1\)\(e\left(\frac{23}{50}\right)\)\(e\left(\frac{27}{100}\right)\)\(e\left(\frac{23}{25}\right)\)\(e\left(\frac{6}{25}\right)\)\(e\left(\frac{37}{50}\right)\)\(e\left(\frac{17}{25}\right)\)\(e\left(\frac{73}{100}\right)\)\(e\left(\frac{73}{100}\right)\)\(e\left(\frac{9}{25}\right)\)\(e\left(\frac{19}{50}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 8020 }(183,a) \;\) at \(\;a = \) e.g. 2