Properties

Conductor 2009
Order 56
Real No
Primitive No
Parity Even
Orbit Label 6027.dc

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(6027)
 
sage: chi = H[55]
 
pari: [g,chi] = znchar(Mod(55,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2009
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 56
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 6027.dc
Orbit index = 81

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{6027}(55,\cdot)\) \(\chi_{6027}(202,\cdot)\) \(\chi_{6027}(454,\cdot)\) \(\chi_{6027}(601,\cdot)\) \(\chi_{6027}(916,\cdot)\) \(\chi_{6027}(1063,\cdot)\) \(\chi_{6027}(1315,\cdot)\) \(\chi_{6027}(1462,\cdot)\) \(\chi_{6027}(1777,\cdot)\) \(\chi_{6027}(1924,\cdot)\) \(\chi_{6027}(2176,\cdot)\) \(\chi_{6027}(2323,\cdot)\) \(\chi_{6027}(2638,\cdot)\) \(\chi_{6027}(2785,\cdot)\) \(\chi_{6027}(3499,\cdot)\) \(\chi_{6027}(3646,\cdot)\) \(\chi_{6027}(3898,\cdot)\) \(\chi_{6027}(4045,\cdot)\) \(\chi_{6027}(4759,\cdot)\) \(\chi_{6027}(4906,\cdot)\) \(\chi_{6027}(5221,\cdot)\) \(\chi_{6027}(5368,\cdot)\) \(\chi_{6027}(5620,\cdot)\) \(\chi_{6027}(5767,\cdot)\)

Inducing primitive character

\(\chi_{2009}(55,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((1,e\left(\frac{9}{14}\right),e\left(\frac{5}{8}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{27}{28}\right)\)\(e\left(\frac{13}{14}\right)\)\(e\left(\frac{11}{28}\right)\)\(e\left(\frac{25}{28}\right)\)\(e\left(\frac{5}{14}\right)\)\(e\left(\frac{33}{56}\right)\)\(e\left(\frac{33}{56}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{39}{56}\right)\)\(e\left(\frac{1}{8}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{56})\)