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.bj
\(\chi_{1603}(9,\cdot)\) \(\chi_{1603}(25,\cdot)\) \(\chi_{1603}(81,\cdot)\) \(\chi_{1603}(149,\cdot)\) \(\chi_{1603}(151,\cdot)\) \(\chi_{1603}(277,\cdot)\) \(\chi_{1603}(312,\cdot)\) \(\chi_{1603}(359,\cdot)\) \(\chi_{1603}(361,\cdot)\) \(\chi_{1603}(373,\cdot)\) \(\chi_{1603}(387,\cdot)\) \(\chi_{1603}(422,\cdot)\) \(\chi_{1603}(478,\cdot)\) \(\chi_{1603}(513,\cdot)\) \(\chi_{1603}(569,\cdot)\) \(\chi_{1603}(611,\cdot)\) \(\chi_{1603}(625,\cdot)\) \(\chi_{1603}(641,\cdot)\) \(\chi_{1603}(690,\cdot)\) \(\chi_{1603}(816,\cdot)\) \(\chi_{1603}(858,\cdot)\) \(\chi_{1603}(1075,\cdot)\) \(\chi_{1603}(1096,\cdot)\) \(\chi_{1603}(1164,\cdot)\) \(\chi_{1603}(1220,\cdot)\) \(\chi_{1603}(1227,\cdot)\) \(\chi_{1603}(1271,\cdot)\) \(\chi_{1603}(1318,\cdot)\) \(\chi_{1603}(1341,\cdot)\) \(\chi_{1603}(1362,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((1375,1380)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{29}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1603 }(422, a) \) | \(1\) | \(1\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{49}{57}\right)\) |