Basic properties
Modulus: | \(367\) | |
Conductor: | \(367\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(366\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 367.h
\(\chi_{367}(6,\cdot)\) \(\chi_{367}(10,\cdot)\) \(\chi_{367}(11,\cdot)\) \(\chi_{367}(12,\cdot)\) \(\chi_{367}(17,\cdot)\) \(\chi_{367}(19,\cdot)\) \(\chi_{367}(20,\cdot)\) \(\chi_{367}(22,\cdot)\) \(\chi_{367}(34,\cdot)\) \(\chi_{367}(39,\cdot)\) \(\chi_{367}(42,\cdot)\) \(\chi_{367}(43,\cdot)\) \(\chi_{367}(48,\cdot)\) \(\chi_{367}(54,\cdot)\) \(\chi_{367}(58,\cdot)\) \(\chi_{367}(65,\cdot)\) \(\chi_{367}(69,\cdot)\) \(\chi_{367}(70,\cdot)\) \(\chi_{367}(71,\cdot)\) \(\chi_{367}(76,\cdot)\) \(\chi_{367}(77,\cdot)\) \(\chi_{367}(78,\cdot)\) \(\chi_{367}(79,\cdot)\) \(\chi_{367}(80,\cdot)\) \(\chi_{367}(88,\cdot)\) \(\chi_{367}(90,\cdot)\) \(\chi_{367}(93,\cdot)\) \(\chi_{367}(96,\cdot)\) \(\chi_{367}(97,\cdot)\) \(\chi_{367}(99,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{183})$ |
Fixed field: | Number field defined by a degree 366 polynomial (not computed) |
Values on generators
\(6\) → \(e\left(\frac{163}{366}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 367 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{8}{183}\right)\) | \(e\left(\frac{49}{122}\right)\) | \(e\left(\frac{16}{183}\right)\) | \(e\left(\frac{111}{122}\right)\) | \(e\left(\frac{163}{366}\right)\) | \(e\left(\frac{21}{61}\right)\) | \(e\left(\frac{8}{61}\right)\) | \(e\left(\frac{49}{61}\right)\) | \(e\left(\frac{349}{366}\right)\) | \(e\left(\frac{217}{366}\right)\) |