Basic properties
Modulus: | \(367\) | |
Conductor: | \(367\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(183\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 367.g
\(\chi_{367}(2,\cdot)\) \(\chi_{367}(4,\cdot)\) \(\chi_{367}(13,\cdot)\) \(\chi_{367}(14,\cdot)\) \(\chi_{367}(16,\cdot)\) \(\chi_{367}(18,\cdot)\) \(\chi_{367}(23,\cdot)\) \(\chi_{367}(26,\cdot)\) \(\chi_{367}(28,\cdot)\) \(\chi_{367}(30,\cdot)\) \(\chi_{367}(31,\cdot)\) \(\chi_{367}(32,\cdot)\) \(\chi_{367}(33,\cdot)\) \(\chi_{367}(36,\cdot)\) \(\chi_{367}(37,\cdot)\) \(\chi_{367}(41,\cdot)\) \(\chi_{367}(50,\cdot)\) \(\chi_{367}(51,\cdot)\) \(\chi_{367}(53,\cdot)\) \(\chi_{367}(55,\cdot)\) \(\chi_{367}(57,\cdot)\) \(\chi_{367}(60,\cdot)\) \(\chi_{367}(61,\cdot)\) \(\chi_{367}(62,\cdot)\) \(\chi_{367}(66,\cdot)\) \(\chi_{367}(67,\cdot)\) \(\chi_{367}(73,\cdot)\) \(\chi_{367}(82,\cdot)\) \(\chi_{367}(85,\cdot)\) \(\chi_{367}(89,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{183})$ |
Fixed field: | Number field defined by a degree 183 polynomial (not computed) |
Values on generators
\(6\) → \(e\left(\frac{146}{183}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 367 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{176}{183}\right)\) | \(e\left(\frac{51}{61}\right)\) | \(e\left(\frac{169}{183}\right)\) | \(e\left(\frac{1}{61}\right)\) | \(e\left(\frac{146}{183}\right)\) | \(e\left(\frac{35}{61}\right)\) | \(e\left(\frac{54}{61}\right)\) | \(e\left(\frac{41}{61}\right)\) | \(e\left(\frac{179}{183}\right)\) | \(e\left(\frac{8}{183}\right)\) |