Properties

Conductor 2009
Order 70
Real No
Primitive Yes
Parity Even
Orbit Label 2009.bt

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(2009)
 
sage: chi = H[64]
 
pari: [g,chi] = znchar(Mod(64,2009))
 

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 = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 2009.bt
Orbit index = 46

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 ]
 

\(\chi_{2009}(64,\cdot)\) \(\chi_{2009}(113,\cdot)\) \(\chi_{2009}(127,\cdot)\) \(\chi_{2009}(351,\cdot)\) \(\chi_{2009}(400,\cdot)\) \(\chi_{2009}(414,\cdot)\) \(\chi_{2009}(435,\cdot)\) \(\chi_{2009}(701,\cdot)\) \(\chi_{2009}(722,\cdot)\) \(\chi_{2009}(925,\cdot)\) \(\chi_{2009}(974,\cdot)\) \(\chi_{2009}(988,\cdot)\) \(\chi_{2009}(1009,\cdot)\) \(\chi_{2009}(1212,\cdot)\) \(\chi_{2009}(1261,\cdot)\) \(\chi_{2009}(1296,\cdot)\) \(\chi_{2009}(1499,\cdot)\) \(\chi_{2009}(1548,\cdot)\) \(\chi_{2009}(1562,\cdot)\) \(\chi_{2009}(1583,\cdot)\) \(\chi_{2009}(1786,\cdot)\) \(\chi_{2009}(1835,\cdot)\) \(\chi_{2009}(1849,\cdot)\) \(\chi_{2009}(1870,\cdot)\)

Values on generators

\((493,785)\) → \((e\left(\frac{5}{7}\right),e\left(\frac{9}{10}\right))\)

Values

-112345689101112
\(1\)\(1\)\(e\left(\frac{34}{35}\right)\)\(e\left(\frac{3}{14}\right)\)\(e\left(\frac{33}{35}\right)\)\(e\left(\frac{18}{35}\right)\)\(e\left(\frac{13}{70}\right)\)\(e\left(\frac{32}{35}\right)\)\(e\left(\frac{3}{7}\right)\)\(e\left(\frac{17}{35}\right)\)\(e\left(\frac{19}{70}\right)\)\(e\left(\frac{11}{70}\right)\)
value at  e.g. 2

Related number fields

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