Properties

Conductor 5025
Order 330
Real No
Primitive Yes
Parity Odd

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(5025)
sage: chi = H[4871]
pari: [g,chi] = znchar(Mod(4871,5025))

Values on generators

sage: chi(k) for k in H.gens()
pari: [ chareval(g,chi,x) | x <- g.gen ] \\ value in Q/Z

\((538,3751,1676)\) → \((e\left(\frac{26}{165}\right),1,-1)\)

First values

1247811131416171922232628293132343738414344464749525356
1\(e\left(\frac{283}{330}\right)\)\(e\left(\frac{118}{165}\right)\)\(e\left(\frac{14}{33}\right)\)\(e\left(\frac{63}{110}\right)\)\(e\left(\frac{263}{330}\right)\)\(e\left(\frac{131}{165}\right)\)\(e\left(\frac{31}{110}\right)\)\(e\left(\frac{71}{165}\right)\)\(e\left(\frac{259}{330}\right)\)\(e\left(\frac{62}{165}\right)\)\(e\left(\frac{36}{55}\right)\)\(e\left(\frac{103}{330}\right)\)\(e\left(\frac{43}{66}\right)\)\(e\left(\frac{23}{165}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{67}{165}\right)\)\(e\left(\frac{19}{66}\right)\)\(e\left(\frac{106}{165}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{7}{30}\right)\)\(e\left(\frac{17}{330}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{169}{330}\right)\)\(e\left(\frac{28}{165}\right)\)\(e\left(\frac{191}{330}\right)\)\(e\left(\frac{28}{33}\right)\)\(e\left(\frac{28}{55}\right)\)\(e\left(\frac{97}{110}\right)\)\(e\left(\frac{329}{330}\right)\)
value at  e.g. 2

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 5025
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 330
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Odd
Real = No
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
Primitive = Yes

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 ]

\(\chi_{5025}(4871,\cdot)\) \(\chi_{5025}(3041,\cdot)\) \(\chi_{5025}(3611,\cdot)\) \(\chi_{5025}(3791,\cdot)\) \(\chi_{5025}(56,\cdot)\) \(\chi_{5025}(2636,\cdot)\) \(\chi_{5025}(2831,\cdot)\) \(\chi_{5025}(971,\cdot)\) \(\chi_{5025}(4091,\cdot)\) \(\chi_{5025}(2696,\cdot)\) \(\chi_{5025}(236,\cdot)\) \(\chi_{5025}(341,\cdot)\) \(\chi_{5025}(1931,\cdot)\) \(\chi_{5025}(86,\cdot)\) \(\chi_{5025}(3131,\cdot)\) \(\chi_{5025}(371,\cdot)\) \(\chi_{5025}(3866,\cdot)\) \(\chi_{5025}(1796,\cdot)\) \(\chi_{5025}(2036,\cdot)\) \(\chi_{5025}(2606,\cdot)\) \(\chi_{5025}(2786,\cdot)\) \(\chi_{5025}(1631,\cdot)\) \(\chi_{5025}(3371,\cdot)\) \(\chi_{5025}(4991,\cdot)\) \(\chi_{5025}(1271,\cdot)\) \(\chi_{5025}(3086,\cdot)\) \(\chi_{5025}(1691,\cdot)\) \(\chi_{5025}(4256,\cdot)\) \(\chi_{5025}(4361,\cdot)\) \(\chi_{5025}(4106,\cdot)\) ...

Related number fields

Field of values \(\Q(\zeta_{165})\)