Properties

Conductor 2009
Order 70
Real No
Primitive No
Parity Even
Orbit Label 6027.dn

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[64]
 
pari: [g,chi] = znchar(Mod(64,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2009
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 70
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.dn
Orbit index = 92

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 ]
 

\(\chi_{6027}(64,\cdot)\) \(\chi_{6027}(127,\cdot)\) \(\chi_{6027}(400,\cdot)\) \(\chi_{6027}(925,\cdot)\) \(\chi_{6027}(988,\cdot)\) \(\chi_{6027}(1009,\cdot)\) \(\chi_{6027}(1261,\cdot)\) \(\chi_{6027}(1786,\cdot)\) \(\chi_{6027}(1849,\cdot)\) \(\chi_{6027}(1870,\cdot)\) \(\chi_{6027}(2122,\cdot)\) \(\chi_{6027}(2710,\cdot)\) \(\chi_{6027}(2731,\cdot)\) \(\chi_{6027}(2983,\cdot)\) \(\chi_{6027}(3508,\cdot)\) \(\chi_{6027}(3571,\cdot)\) \(\chi_{6027}(3592,\cdot)\) \(\chi_{6027}(3844,\cdot)\) \(\chi_{6027}(4369,\cdot)\) \(\chi_{6027}(4432,\cdot)\) \(\chi_{6027}(4453,\cdot)\) \(\chi_{6027}(5230,\cdot)\) \(\chi_{6027}(5314,\cdot)\) \(\chi_{6027}(5566,\cdot)\)

Inducing primitive character

\(\chi_{2009}(64,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((1,e\left(\frac{5}{7}\right),e\left(\frac{9}{10}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{34}{35}\right)\)\(e\left(\frac{33}{35}\right)\)\(e\left(\frac{18}{35}\right)\)\(e\left(\frac{32}{35}\right)\)\(e\left(\frac{17}{35}\right)\)\(e\left(\frac{19}{70}\right)\)\(e\left(\frac{33}{70}\right)\)\(e\left(\frac{31}{35}\right)\)\(e\left(\frac{39}{70}\right)\)\(e\left(\frac{1}{10}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{35})\)