Properties

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

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[29]
 
pari: [g,chi] = znchar(Mod(29,4033))
 

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.jg
Orbit index = 241

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 ]
 

\(\chi_{4033}(29,\cdot)\) \(\chi_{4033}(60,\cdot)\) \(\chi_{4033}(88,\cdot)\) \(\chi_{4033}(230,\cdot)\) \(\chi_{4033}(421,\cdot)\) \(\chi_{4033}(467,\cdot)\) \(\chi_{4033}(674,\cdot)\) \(\chi_{4033}(754,\cdot)\) \(\chi_{4033}(837,\cdot)\) \(\chi_{4033}(933,\cdot)\) \(\chi_{4033}(1102,\cdot)\) \(\chi_{4033}(1118,\cdot)\) \(\chi_{4033}(1192,\cdot)\) \(\chi_{4033}(1235,\cdot)\) \(\chi_{4033}(1303,\cdot)\) \(\chi_{4033}(1392,\cdot)\) \(\chi_{4033}(1414,\cdot)\) \(\chi_{4033}(1546,\cdot)\) \(\chi_{4033}(1614,\cdot)\) \(\chi_{4033}(1805,\cdot)\) \(\chi_{4033}(1947,\cdot)\) \(\chi_{4033}(1990,\cdot)\) \(\chi_{4033}(2049,\cdot)\) \(\chi_{4033}(2064,\cdot)\) \(\chi_{4033}(2154,\cdot)\) \(\chi_{4033}(2175,\cdot)\) \(\chi_{4033}(2280,\cdot)\) \(\chi_{4033}(2286,\cdot)\) \(\chi_{4033}(2567,\cdot)\) \(\chi_{4033}(2761,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{7}{12}\right),e\left(\frac{17}{54}\right))\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{19}{36}\right)\)\(e\left(\frac{29}{54}\right)\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{37}{108}\right)\)\(e\left(\frac{7}{108}\right)\)\(e\left(\frac{7}{27}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{2}{27}\right)\)\(e\left(\frac{47}{54}\right)\)\(e\left(\frac{17}{27}\right)\)
value at  e.g. 2

Related number fields

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