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.bl
\(\chi_{1603}(37,\cdot)\) \(\chi_{1603}(51,\cdot)\) \(\chi_{1603}(130,\cdot)\) \(\chi_{1603}(144,\cdot)\) \(\chi_{1603}(158,\cdot)\) \(\chi_{1603}(184,\cdot)\) \(\chi_{1603}(193,\cdot)\) \(\chi_{1603}(249,\cdot)\) \(\chi_{1603}(254,\cdot)\) \(\chi_{1603}(284,\cdot)\) \(\chi_{1603}(310,\cdot)\) \(\chi_{1603}(340,\cdot)\) \(\chi_{1603}(380,\cdot)\) \(\chi_{1603}(382,\cdot)\) \(\chi_{1603}(396,\cdot)\) \(\chi_{1603}(506,\cdot)\) \(\chi_{1603}(541,\cdot)\) \(\chi_{1603}(590,\cdot)\) \(\chi_{1603}(870,\cdot)\) \(\chi_{1603}(919,\cdot)\) \(\chi_{1603}(935,\cdot)\) \(\chi_{1603}(991,\cdot)\) \(\chi_{1603}(998,\cdot)\) \(\chi_{1603}(1045,\cdot)\) \(\chi_{1603}(1087,\cdot)\) \(\chi_{1603}(1089,\cdot)\) \(\chi_{1603}(1159,\cdot)\) \(\chi_{1603}(1236,\cdot)\) \(\chi_{1603}(1304,\cdot)\) \(\chi_{1603}(1325,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((1375,1380)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{43}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1603 }(184, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{5}{19}\right)\) |