Basic properties
Modulus: | \(283\) | |
Conductor: | \(283\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(47\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 283.e
\(\chi_{283}(4,\cdot)\) \(\chi_{283}(15,\cdot)\) \(\chi_{283}(16,\cdot)\) \(\chi_{283}(29,\cdot)\) \(\chi_{283}(38,\cdot)\) \(\chi_{283}(42,\cdot)\) \(\chi_{283}(51,\cdot)\) \(\chi_{283}(54,\cdot)\) \(\chi_{283}(60,\cdot)\) \(\chi_{283}(61,\cdot)\) \(\chi_{283}(64,\cdot)\) \(\chi_{283}(66,\cdot)\) \(\chi_{283}(71,\cdot)\) \(\chi_{283}(78,\cdot)\) \(\chi_{283}(86,\cdot)\) \(\chi_{283}(106,\cdot)\) \(\chi_{283}(111,\cdot)\) \(\chi_{283}(116,\cdot)\) \(\chi_{283}(127,\cdot)\) \(\chi_{283}(134,\cdot)\) \(\chi_{283}(141,\cdot)\) \(\chi_{283}(151,\cdot)\) \(\chi_{283}(152,\cdot)\) \(\chi_{283}(155,\cdot)\) \(\chi_{283}(158,\cdot)\) \(\chi_{283}(161,\cdot)\) \(\chi_{283}(163,\cdot)\) \(\chi_{283}(168,\cdot)\) \(\chi_{283}(175,\cdot)\) \(\chi_{283}(181,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{47})$ |
Fixed field: | Number field defined by a degree 47 polynomial |
Values on generators
\(3\) → \(e\left(\frac{35}{47}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 283 }(230, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{47}\right)\) | \(e\left(\frac{35}{47}\right)\) | \(e\left(\frac{38}{47}\right)\) | \(e\left(\frac{24}{47}\right)\) | \(e\left(\frac{7}{47}\right)\) | \(e\left(\frac{1}{47}\right)\) | \(e\left(\frac{10}{47}\right)\) | \(e\left(\frac{23}{47}\right)\) | \(e\left(\frac{43}{47}\right)\) | \(e\left(\frac{9}{47}\right)\) |