Basic properties
| Modulus: | \(583\) | |
| Conductor: | \(583\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(130\) | 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 583.t
\(\chi_{583}(4,\cdot)\) \(\chi_{583}(9,\cdot)\) \(\chi_{583}(25,\cdot)\) \(\chi_{583}(37,\cdot)\) \(\chi_{583}(38,\cdot)\) \(\chi_{583}(59,\cdot)\) \(\chi_{583}(60,\cdot)\) \(\chi_{583}(64,\cdot)\) \(\chi_{583}(70,\cdot)\) \(\chi_{583}(82,\cdot)\) \(\chi_{583}(91,\cdot)\) \(\chi_{583}(93,\cdot)\) \(\chi_{583}(113,\cdot)\) \(\chi_{583}(115,\cdot)\) \(\chi_{583}(135,\cdot)\) \(\chi_{583}(146,\cdot)\) \(\chi_{583}(163,\cdot)\) \(\chi_{583}(168,\cdot)\) \(\chi_{583}(170,\cdot)\) \(\chi_{583}(196,\cdot)\) \(\chi_{583}(202,\cdot)\) \(\chi_{583}(218,\cdot)\) \(\chi_{583}(223,\cdot)\) \(\chi_{583}(229,\cdot)\) \(\chi_{583}(269,\cdot)\) \(\chi_{583}(290,\cdot)\) \(\chi_{583}(302,\cdot)\) \(\chi_{583}(322,\cdot)\) \(\chi_{583}(324,\cdot)\) \(\chi_{583}(335,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((266,320)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{1}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 583 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{130}\right)\) | \(e\left(\frac{33}{130}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{93}{130}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{19}{26}\right)\) |