Basic properties
| Modulus: | \(1163\) | |
| Conductor: | \(1163\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1162\) | 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 1163.h
\(\chi_{1163}(5,\cdot)\) \(\chi_{1163}(6,\cdot)\) \(\chi_{1163}(7,\cdot)\) \(\chi_{1163}(13,\cdot)\) \(\chi_{1163}(17,\cdot)\) \(\chi_{1163}(18,\cdot)\) \(\chi_{1163}(19,\cdot)\) \(\chi_{1163}(20,\cdot)\) \(\chi_{1163}(21,\cdot)\) \(\chi_{1163}(22,\cdot)\) \(\chi_{1163}(23,\cdot)\) \(\chi_{1163}(24,\cdot)\) \(\chi_{1163}(28,\cdot)\) \(\chi_{1163}(29,\cdot)\) \(\chi_{1163}(31,\cdot)\) \(\chi_{1163}(39,\cdot)\) \(\chi_{1163}(41,\cdot)\) \(\chi_{1163}(45,\cdot)\) \(\chi_{1163}(50,\cdot)\) \(\chi_{1163}(52,\cdot)\) \(\chi_{1163}(53,\cdot)\) \(\chi_{1163}(54,\cdot)\) \(\chi_{1163}(55,\cdot)\) \(\chi_{1163}(66,\cdot)\) \(\chi_{1163}(67,\cdot)\) \(\chi_{1163}(68,\cdot)\) \(\chi_{1163}(70,\cdot)\) \(\chi_{1163}(71,\cdot)\) \(\chi_{1163}(72,\cdot)\) \(\chi_{1163}(73,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{581})$ |
| Fixed field: | Number field defined by a degree 1162 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{643}{1162}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1163 }(6, a) \) | \(-1\) | \(1\) | \(e\left(\frac{65}{166}\right)\) | \(e\left(\frac{242}{581}\right)\) | \(e\left(\frac{65}{83}\right)\) | \(e\left(\frac{643}{1162}\right)\) | \(e\left(\frac{939}{1162}\right)\) | \(e\left(\frac{733}{1162}\right)\) | \(e\left(\frac{29}{166}\right)\) | \(e\left(\frac{484}{581}\right)\) | \(e\left(\frac{549}{581}\right)\) | \(e\left(\frac{43}{581}\right)\) |