Properties

Conductor 4001
Order 400
Real No
Primitive No
Parity Even
Orbit Label 8002.s

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(8002)
sage: chi = H[59]
pari: [g,chi] = znchar(Mod(59,8002))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4001
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 400
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 = Even
Orbit label = 8002.s
Orbit index = 19

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 ]

\(\chi_{8002}(59,\cdot)\) \(\chi_{8002}(63,\cdot)\) \(\chi_{8002}(69,\cdot)\) \(\chi_{8002}(127,\cdot)\) \(\chi_{8002}(129,\cdot)\) \(\chi_{8002}(217,\cdot)\) \(\chi_{8002}(223,\cdot)\) \(\chi_{8002}(241,\cdot)\) \(\chi_{8002}(295,\cdot)\) \(\chi_{8002}(303,\cdot)\) \(\chi_{8002}(315,\cdot)\) \(\chi_{8002}(329,\cdot)\) \(\chi_{8002}(345,\cdot)\) \(\chi_{8002}(397,\cdot)\) \(\chi_{8002}(401,\cdot)\) \(\chi_{8002}(409,\cdot)\) \(\chi_{8002}(427,\cdot)\) \(\chi_{8002}(429,\cdot)\) \(\chi_{8002}(581,\cdot)\) \(\chi_{8002}(605,\cdot)\) \(\chi_{8002}(607,\cdot)\) \(\chi_{8002}(623,\cdot)\) \(\chi_{8002}(645,\cdot)\) \(\chi_{8002}(701,\cdot)\) \(\chi_{8002}(829,\cdot)\) \(\chi_{8002}(879,\cdot)\) \(\chi_{8002}(937,\cdot)\) \(\chi_{8002}(963,\cdot)\) \(\chi_{8002}(1085,\cdot)\) \(\chi_{8002}(1139,\cdot)\) ...

Inducing primitive character

\(\chi_{4001}(59,\cdot)\)

Values on generators

\(3\) → \(e\left(\frac{381}{400}\right)\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{381}{400}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{17}{100}\right)\)\(e\left(\frac{181}{200}\right)\)\(e\left(\frac{5}{16}\right)\)\(e\left(\frac{21}{100}\right)\)\(e\left(\frac{361}{400}\right)\)\(e\left(\frac{11}{400}\right)\)\(e\left(\frac{61}{100}\right)\)\(e\left(\frac{49}{400}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{400})\)