Basic properties
| Modulus: | \(283\) | |
| Conductor: | \(283\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(282\) | 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 283.h
\(\chi_{283}(3,\cdot)\) \(\chi_{283}(5,\cdot)\) \(\chi_{283}(12,\cdot)\) \(\chi_{283}(14,\cdot)\) \(\chi_{283}(17,\cdot)\) \(\chi_{283}(18,\cdot)\) \(\chi_{283}(20,\cdot)\) \(\chi_{283}(22,\cdot)\) \(\chi_{283}(26,\cdot)\) \(\chi_{283}(31,\cdot)\) \(\chi_{283}(35,\cdot)\) \(\chi_{283}(37,\cdot)\) \(\chi_{283}(46,\cdot)\) \(\chi_{283}(47,\cdot)\) \(\chi_{283}(48,\cdot)\) \(\chi_{283}(50,\cdot)\) \(\chi_{283}(55,\cdot)\) \(\chi_{283}(56,\cdot)\) \(\chi_{283}(65,\cdot)\) \(\chi_{283}(68,\cdot)\) \(\chi_{283}(69,\cdot)\) \(\chi_{283}(72,\cdot)\) \(\chi_{283}(75,\cdot)\) \(\chi_{283}(80,\cdot)\) \(\chi_{283}(82,\cdot)\) \(\chi_{283}(87,\cdot)\) \(\chi_{283}(88,\cdot)\) \(\chi_{283}(98,\cdot)\) \(\chi_{283}(104,\cdot)\) \(\chi_{283}(107,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{141})$ |
| Fixed field: | Number field defined by a degree 282 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{197}{282}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 283 }(72, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{94}\right)\) | \(e\left(\frac{197}{282}\right)\) | \(e\left(\frac{7}{47}\right)\) | \(e\left(\frac{217}{282}\right)\) | \(e\left(\frac{109}{141}\right)\) | \(e\left(\frac{29}{141}\right)\) | \(e\left(\frac{21}{94}\right)\) | \(e\left(\frac{56}{141}\right)\) | \(e\left(\frac{119}{141}\right)\) | \(e\left(\frac{26}{141}\right)\) |