Properties

Conductor 473
Order 70
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4730.cr

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[51]
 
pari: [g,chi] = znchar(Mod(51,4730))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 473
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.cr
Orbit index = 70

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 ]
 

\(\chi_{4730}(51,\cdot)\) \(\chi_{4730}(151,\cdot)\) \(\chi_{4730}(161,\cdot)\) \(\chi_{4730}(211,\cdot)\) \(\chi_{4730}(371,\cdot)\) \(\chi_{4730}(481,\cdot)\) \(\chi_{4730}(591,\cdot)\) \(\chi_{4730}(1421,\cdot)\) \(\chi_{4730}(1931,\cdot)\) \(\chi_{4730}(2301,\cdot)\) \(\chi_{4730}(2361,\cdot)\) \(\chi_{4730}(2521,\cdot)\) \(\chi_{4730}(2631,\cdot)\) \(\chi_{4730}(2741,\cdot)\) \(\chi_{4730}(2791,\cdot)\) \(\chi_{4730}(3141,\cdot)\) \(\chi_{4730}(3571,\cdot)\) \(\chi_{4730}(4001,\cdot)\) \(\chi_{4730}(4021,\cdot)\) \(\chi_{4730}(4241,\cdot)\) \(\chi_{4730}(4351,\cdot)\) \(\chi_{4730}(4451,\cdot)\) \(\chi_{4730}(4461,\cdot)\) \(\chi_{4730}(4671,\cdot)\)

Values on generators

\((947,431,1981)\) → \((1,e\left(\frac{7}{10}\right),e\left(\frac{13}{14}\right))\)

Values

-1137913171921232729
\(1\)\(1\)\(e\left(\frac{37}{70}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{2}{35}\right)\)\(e\left(\frac{29}{70}\right)\)\(e\left(\frac{41}{70}\right)\)\(e\left(\frac{26}{35}\right)\)\(e\left(\frac{13}{14}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{41}{70}\right)\)\(e\left(\frac{34}{35}\right)\)
value at  e.g. 2

Related number fields

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