Basic properties
| Modulus: | \(583\) | |
| Conductor: | \(583\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(65\) | 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.s
\(\chi_{583}(15,\cdot)\) \(\chi_{583}(16,\cdot)\) \(\chi_{583}(36,\cdot)\) \(\chi_{583}(42,\cdot)\) \(\chi_{583}(47,\cdot)\) \(\chi_{583}(49,\cdot)\) \(\chi_{583}(69,\cdot)\) \(\chi_{583}(81,\cdot)\) \(\chi_{583}(97,\cdot)\) \(\chi_{583}(102,\cdot)\) \(\chi_{583}(119,\cdot)\) \(\chi_{583}(130,\cdot)\) \(\chi_{583}(148,\cdot)\) \(\chi_{583}(152,\cdot)\) \(\chi_{583}(169,\cdot)\) \(\chi_{583}(174,\cdot)\) \(\chi_{583}(201,\cdot)\) \(\chi_{583}(203,\cdot)\) \(\chi_{583}(225,\cdot)\) \(\chi_{583}(236,\cdot)\) \(\chi_{583}(240,\cdot)\) \(\chi_{583}(256,\cdot)\) \(\chi_{583}(258,\cdot)\) \(\chi_{583}(278,\cdot)\) \(\chi_{583}(280,\cdot)\) \(\chi_{583}(289,\cdot)\) \(\chi_{583}(301,\cdot)\) \(\chi_{583}(311,\cdot)\) \(\chi_{583}(312,\cdot)\) \(\chi_{583}(328,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 65 polynomial |
Values on generators
\((266,320)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{3}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 583 }(15, a) \) | \(1\) | \(1\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{19}{65}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) |