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
\(5\) → \(e\left(\frac{139}{1162}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1163 }(1160, a) \) | \(-1\) | \(1\) | \(e\left(\frac{131}{166}\right)\) | \(e\left(\frac{74}{581}\right)\) | \(e\left(\frac{48}{83}\right)\) | \(e\left(\frac{139}{1162}\right)\) | \(e\left(\frac{1065}{1162}\right)\) | \(e\left(\frac{397}{1162}\right)\) | \(e\left(\frac{61}{166}\right)\) | \(e\left(\frac{148}{581}\right)\) | \(e\left(\frac{528}{581}\right)\) | \(e\left(\frac{162}{581}\right)\) |