Basic properties
Modulus: | \(8993\) | |
Conductor: | \(529\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(253\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{529}(18,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8993.bc
\(\chi_{8993}(18,\cdot)\) \(\chi_{8993}(35,\cdot)\) \(\chi_{8993}(52,\cdot)\) \(\chi_{8993}(154,\cdot)\) \(\chi_{8993}(188,\cdot)\) \(\chi_{8993}(239,\cdot)\) \(\chi_{8993}(256,\cdot)\) \(\chi_{8993}(307,\cdot)\) \(\chi_{8993}(324,\cdot)\) \(\chi_{8993}(358,\cdot)\) \(\chi_{8993}(409,\cdot)\) \(\chi_{8993}(426,\cdot)\) \(\chi_{8993}(443,\cdot)\) \(\chi_{8993}(545,\cdot)\) \(\chi_{8993}(579,\cdot)\) \(\chi_{8993}(630,\cdot)\) \(\chi_{8993}(698,\cdot)\) \(\chi_{8993}(715,\cdot)\) \(\chi_{8993}(749,\cdot)\) \(\chi_{8993}(800,\cdot)\) \(\chi_{8993}(817,\cdot)\) \(\chi_{8993}(834,\cdot)\) \(\chi_{8993}(936,\cdot)\) \(\chi_{8993}(970,\cdot)\) \(\chi_{8993}(1021,\cdot)\) \(\chi_{8993}(1038,\cdot)\) \(\chi_{8993}(1089,\cdot)\) \(\chi_{8993}(1106,\cdot)\) \(\chi_{8993}(1140,\cdot)\) \(\chi_{8993}(1191,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{253})$ |
Fixed field: | Number field defined by a degree 253 polynomial (not computed) |
Values on generators
\((530,7940)\) → \((1,e\left(\frac{116}{253}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8993 }(18, a) \) | \(1\) | \(1\) | \(e\left(\frac{177}{253}\right)\) | \(e\left(\frac{85}{253}\right)\) | \(e\left(\frac{101}{253}\right)\) | \(e\left(\frac{116}{253}\right)\) | \(e\left(\frac{9}{253}\right)\) | \(e\left(\frac{37}{253}\right)\) | \(e\left(\frac{25}{253}\right)\) | \(e\left(\frac{170}{253}\right)\) | \(e\left(\frac{40}{253}\right)\) | \(e\left(\frac{219}{253}\right)\) |