Properties

Conductor 4000
Order 200
Real No
Primitive Yes
Parity Odd
Orbit Label 4000.cz

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[53]
pari: [g,chi] = znchar(Mod(53,4000))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4000
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 200
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 = 4000.cz
Orbit index = 78

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 ]

\(\chi_{4000}(53,\cdot)\) \(\chi_{4000}(77,\cdot)\) \(\chi_{4000}(133,\cdot)\) \(\chi_{4000}(213,\cdot)\) \(\chi_{4000}(237,\cdot)\) \(\chi_{4000}(317,\cdot)\) \(\chi_{4000}(373,\cdot)\) \(\chi_{4000}(397,\cdot)\) \(\chi_{4000}(453,\cdot)\) \(\chi_{4000}(477,\cdot)\) \(\chi_{4000}(533,\cdot)\) \(\chi_{4000}(613,\cdot)\) \(\chi_{4000}(637,\cdot)\) \(\chi_{4000}(717,\cdot)\) \(\chi_{4000}(773,\cdot)\) \(\chi_{4000}(797,\cdot)\) \(\chi_{4000}(853,\cdot)\) \(\chi_{4000}(877,\cdot)\) \(\chi_{4000}(933,\cdot)\) \(\chi_{4000}(1013,\cdot)\) \(\chi_{4000}(1037,\cdot)\) \(\chi_{4000}(1117,\cdot)\) \(\chi_{4000}(1173,\cdot)\) \(\chi_{4000}(1197,\cdot)\) \(\chi_{4000}(1253,\cdot)\) \(\chi_{4000}(1277,\cdot)\) \(\chi_{4000}(1333,\cdot)\) \(\chi_{4000}(1413,\cdot)\) \(\chi_{4000}(1437,\cdot)\) \(\chi_{4000}(1517,\cdot)\) ...

Values on generators

\((2751,2501,1377)\) → \((1,e\left(\frac{5}{8}\right),e\left(\frac{67}{100}\right))\)

Values

-1137911131719212327
\(-1\)\(1\)\(e\left(\frac{113}{200}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{13}{100}\right)\)\(e\left(\frac{9}{200}\right)\)\(e\left(\frac{101}{200}\right)\)\(e\left(\frac{41}{100}\right)\)\(e\left(\frac{87}{200}\right)\)\(e\left(\frac{153}{200}\right)\)\(e\left(\frac{13}{25}\right)\)\(e\left(\frac{139}{200}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{200})\)