Properties

Conductor 2365
Order 70
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4730.ct

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(4730)
 
sage: chi = H[59]
 
pari: [g,chi] = znchar(Mod(59,4730))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2365
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
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4730.ct
Orbit index = 72

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 ]
 

\(\chi_{4730}(59,\cdot)\) \(\chi_{4730}(269,\cdot)\) \(\chi_{4730}(279,\cdot)\) \(\chi_{4730}(379,\cdot)\) \(\chi_{4730}(489,\cdot)\) \(\chi_{4730}(709,\cdot)\) \(\chi_{4730}(729,\cdot)\) \(\chi_{4730}(1159,\cdot)\) \(\chi_{4730}(1589,\cdot)\) \(\chi_{4730}(1939,\cdot)\) \(\chi_{4730}(1989,\cdot)\) \(\chi_{4730}(2099,\cdot)\) \(\chi_{4730}(2209,\cdot)\) \(\chi_{4730}(2369,\cdot)\) \(\chi_{4730}(2429,\cdot)\) \(\chi_{4730}(2799,\cdot)\) \(\chi_{4730}(3309,\cdot)\) \(\chi_{4730}(4139,\cdot)\) \(\chi_{4730}(4249,\cdot)\) \(\chi_{4730}(4359,\cdot)\) \(\chi_{4730}(4519,\cdot)\) \(\chi_{4730}(4569,\cdot)\) \(\chi_{4730}(4579,\cdot)\) \(\chi_{4730}(4679,\cdot)\)

Values on generators

\((947,431,1981)\) → \((-1,e\left(\frac{1}{5}\right),e\left(\frac{4}{7}\right))\)

Values

-1137913171921232729
\(1\)\(1\)\(e\left(\frac{47}{70}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{12}{35}\right)\)\(e\left(\frac{69}{70}\right)\)\(e\left(\frac{1}{70}\right)\)\(e\left(\frac{16}{35}\right)\)\(e\left(\frac{4}{7}\right)\)\(e\left(\frac{9}{14}\right)\)\(e\left(\frac{1}{70}\right)\)\(e\left(\frac{29}{35}\right)\)
value at  e.g. 2

Related number fields

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