Properties

Conductor 4033
Order 108
Real No
Primitive Yes
Parity Odd
Orbit Label 4033.il

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(4033)
 
sage: chi = H[31]
 
pari: [g,chi] = znchar(Mod(31,4033))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4033
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 108
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 = Odd
Orbit label = 4033.il
Orbit index = 220

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 ]
 

\(\chi_{4033}(31,\cdot)\) \(\chi_{4033}(302,\cdot)\) \(\chi_{4033}(339,\cdot)\) \(\chi_{4033}(401,\cdot)\) \(\chi_{4033}(524,\cdot)\) \(\chi_{4033}(783,\cdot)\) \(\chi_{4033}(857,\cdot)\) \(\chi_{4033}(956,\cdot)\) \(\chi_{4033}(993,\cdot)\) \(\chi_{4033}(1042,\cdot)\) \(\chi_{4033}(1178,\cdot)\) \(\chi_{4033}(1190,\cdot)\) \(\chi_{4033}(1227,\cdot)\) \(\chi_{4033}(1301,\cdot)\) \(\chi_{4033}(1412,\cdot)\) \(\chi_{4033}(1437,\cdot)\) \(\chi_{4033}(1511,\cdot)\) \(\chi_{4033}(1523,\cdot)\) \(\chi_{4033}(1671,\cdot)\) \(\chi_{4033}(1696,\cdot)\) \(\chi_{4033}(1844,\cdot)\) \(\chi_{4033}(1881,\cdot)\) \(\chi_{4033}(1955,\cdot)\) \(\chi_{4033}(2066,\cdot)\) \(\chi_{4033}(2177,\cdot)\) \(\chi_{4033}(2263,\cdot)\) \(\chi_{4033}(2325,\cdot)\) \(\chi_{4033}(2485,\cdot)\) \(\chi_{4033}(2917,\cdot)\) \(\chi_{4033}(3003,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((i,e\left(\frac{7}{54}\right))\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{23}{36}\right)\)\(e\left(\frac{13}{54}\right)\)\(e\left(\frac{5}{18}\right)\)\(e\left(\frac{65}{108}\right)\)\(e\left(\frac{95}{108}\right)\)\(e\left(\frac{5}{27}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{13}{27}\right)\)\(e\left(\frac{13}{54}\right)\)\(e\left(\frac{7}{27}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{108})\)