Basic properties
Modulus: | \(283\) | |
Conductor: | \(283\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(94\) | 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.f
\(\chi_{283}(2,\cdot)\) \(\chi_{283}(8,\cdot)\) \(\chi_{283}(19,\cdot)\) \(\chi_{283}(21,\cdot)\) \(\chi_{283}(27,\cdot)\) \(\chi_{283}(30,\cdot)\) \(\chi_{283}(32,\cdot)\) \(\chi_{283}(33,\cdot)\) \(\chi_{283}(39,\cdot)\) \(\chi_{283}(43,\cdot)\) \(\chi_{283}(53,\cdot)\) \(\chi_{283}(58,\cdot)\) \(\chi_{283}(67,\cdot)\) \(\chi_{283}(76,\cdot)\) \(\chi_{283}(79,\cdot)\) \(\chi_{283}(84,\cdot)\) \(\chi_{283}(102,\cdot)\) \(\chi_{283}(108,\cdot)\) \(\chi_{283}(115,\cdot)\) \(\chi_{283}(120,\cdot)\) \(\chi_{283}(122,\cdot)\) \(\chi_{283}(125,\cdot)\) \(\chi_{283}(128,\cdot)\) \(\chi_{283}(131,\cdot)\) \(\chi_{283}(132,\cdot)\) \(\chi_{283}(142,\cdot)\) \(\chi_{283}(149,\cdot)\) \(\chi_{283}(156,\cdot)\) \(\chi_{283}(167,\cdot)\) \(\chi_{283}(172,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{47})$ |
Fixed field: | Number field defined by a degree 94 polynomial |
Values on generators
\(3\) → \(e\left(\frac{37}{94}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 283 }(30, a) \) | \(-1\) | \(1\) | \(e\left(\frac{55}{94}\right)\) | \(e\left(\frac{37}{94}\right)\) | \(e\left(\frac{8}{47}\right)\) | \(e\left(\frac{67}{94}\right)\) | \(e\left(\frac{46}{47}\right)\) | \(e\left(\frac{20}{47}\right)\) | \(e\left(\frac{71}{94}\right)\) | \(e\left(\frac{37}{47}\right)\) | \(e\left(\frac{14}{47}\right)\) | \(e\left(\frac{39}{47}\right)\) |