Basic properties
| Modulus: | \(1603\) | |
| Conductor: | \(1603\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(57\) | 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 1603.bk
\(\chi_{1603}(16,\cdot)\) \(\chi_{1603}(44,\cdot)\) \(\chi_{1603}(53,\cdot)\) \(\chi_{1603}(60,\cdot)\) \(\chi_{1603}(121,\cdot)\) \(\chi_{1603}(165,\cdot)\) \(\chi_{1603}(214,\cdot)\) \(\chi_{1603}(256,\cdot)\) \(\chi_{1603}(282,\cdot)\) \(\chi_{1603}(289,\cdot)\) \(\chi_{1603}(333,\cdot)\) \(\chi_{1603}(394,\cdot)\) \(\chi_{1603}(443,\cdot)\) \(\chi_{1603}(485,\cdot)\) \(\chi_{1603}(501,\cdot)\) \(\chi_{1603}(515,\cdot)\) \(\chi_{1603}(562,\cdot)\) \(\chi_{1603}(676,\cdot)\) \(\chi_{1603}(683,\cdot)\) \(\chi_{1603}(704,\cdot)\) \(\chi_{1603}(730,\cdot)\) \(\chi_{1603}(744,\cdot)\) \(\chi_{1603}(905,\cdot)\) \(\chi_{1603}(912,\cdot)\) \(\chi_{1603}(933,\cdot)\) \(\chi_{1603}(977,\cdot)\) \(\chi_{1603}(1187,\cdot)\) \(\chi_{1603}(1206,\cdot)\) \(\chi_{1603}(1306,\cdot)\) \(\chi_{1603}(1348,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((1375,1380)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{7}{19}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1603 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{44}{57}\right)\) |