Basic properties
| Modulus: | \(1193\) | |
| Conductor: | \(1193\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1192\) | 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 1193.h
\(\chi_{1193}(3,\cdot)\) \(\chi_{1193}(5,\cdot)\) \(\chi_{1193}(6,\cdot)\) \(\chi_{1193}(7,\cdot)\) \(\chi_{1193}(10,\cdot)\) \(\chi_{1193}(12,\cdot)\) \(\chi_{1193}(14,\cdot)\) \(\chi_{1193}(17,\cdot)\) \(\chi_{1193}(19,\cdot)\) \(\chi_{1193}(20,\cdot)\) \(\chi_{1193}(23,\cdot)\) \(\chi_{1193}(24,\cdot)\) \(\chi_{1193}(27,\cdot)\) \(\chi_{1193}(28,\cdot)\) \(\chi_{1193}(31,\cdot)\) \(\chi_{1193}(33,\cdot)\) \(\chi_{1193}(34,\cdot)\) \(\chi_{1193}(38,\cdot)\) \(\chi_{1193}(39,\cdot)\) \(\chi_{1193}(40,\cdot)\) \(\chi_{1193}(43,\cdot)\) \(\chi_{1193}(45,\cdot)\) \(\chi_{1193}(46,\cdot)\) \(\chi_{1193}(48,\cdot)\) \(\chi_{1193}(53,\cdot)\) \(\chi_{1193}(54,\cdot)\) \(\chi_{1193}(55,\cdot)\) \(\chi_{1193}(56,\cdot)\) \(\chi_{1193}(59,\cdot)\) \(\chi_{1193}(62,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1192})$ |
| Fixed field: | Number field defined by a degree 1192 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{597}{1192}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1193 }(1190, a) \) | \(-1\) | \(1\) | \(e\left(\frac{147}{298}\right)\) | \(e\left(\frac{597}{1192}\right)\) | \(e\left(\frac{147}{149}\right)\) | \(e\left(\frac{103}{1192}\right)\) | \(e\left(\frac{1185}{1192}\right)\) | \(e\left(\frac{771}{1192}\right)\) | \(e\left(\frac{143}{298}\right)\) | \(e\left(\frac{1}{596}\right)\) | \(e\left(\frac{691}{1192}\right)\) | \(e\left(\frac{29}{298}\right)\) |