Properties

Conductor 125
Order 100
Real No
Primitive No
Parity Odd
Orbit Label 4000.cq

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(4000)
sage: chi = H[33]
pari: [g,chi] = znchar(Mod(33,4000))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 125
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 100
Real = No
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
Primitive = No
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Odd
Orbit label = 4000.cq
Orbit index = 69

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 ]

\(\chi_{4000}(33,\cdot)\) \(\chi_{4000}(97,\cdot)\) \(\chi_{4000}(353,\cdot)\) \(\chi_{4000}(417,\cdot)\) \(\chi_{4000}(513,\cdot)\) \(\chi_{4000}(577,\cdot)\) \(\chi_{4000}(673,\cdot)\) \(\chi_{4000}(737,\cdot)\) \(\chi_{4000}(833,\cdot)\) \(\chi_{4000}(897,\cdot)\) \(\chi_{4000}(1153,\cdot)\) \(\chi_{4000}(1217,\cdot)\) \(\chi_{4000}(1313,\cdot)\) \(\chi_{4000}(1377,\cdot)\) \(\chi_{4000}(1473,\cdot)\) \(\chi_{4000}(1537,\cdot)\) \(\chi_{4000}(1633,\cdot)\) \(\chi_{4000}(1697,\cdot)\) \(\chi_{4000}(1953,\cdot)\) \(\chi_{4000}(2017,\cdot)\) \(\chi_{4000}(2113,\cdot)\) \(\chi_{4000}(2177,\cdot)\) \(\chi_{4000}(2273,\cdot)\) \(\chi_{4000}(2337,\cdot)\) \(\chi_{4000}(2433,\cdot)\) \(\chi_{4000}(2497,\cdot)\) \(\chi_{4000}(2753,\cdot)\) \(\chi_{4000}(2817,\cdot)\) \(\chi_{4000}(2913,\cdot)\) \(\chi_{4000}(2977,\cdot)\) ...

Inducing primitive character

\(\chi_{125}(33,\cdot)\)

Values on generators

\((2751,2501,1377)\) → \((1,1,e\left(\frac{83}{100}\right))\)

Values

-1137911131719212327
\(-1\)\(1\)\(e\left(\frac{81}{100}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{31}{50}\right)\)\(e\left(\frac{2}{25}\right)\)\(e\left(\frac{37}{100}\right)\)\(e\left(\frac{59}{100}\right)\)\(e\left(\frac{47}{50}\right)\)\(e\left(\frac{9}{25}\right)\)\(e\left(\frac{73}{100}\right)\)\(e\left(\frac{43}{100}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{100})\)