Basic properties
| Modulus: | \(8033\) | |
| Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(644\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8033.cp
\(\chi_{8033}(19,\cdot)\) \(\chi_{8033}(27,\cdot)\) \(\chi_{8033}(69,\cdot)\) \(\chi_{8033}(84,\cdot)\) \(\chi_{8033}(131,\cdot)\) \(\chi_{8033}(155,\cdot)\) \(\chi_{8033}(164,\cdot)\) \(\chi_{8033}(201,\cdot)\) \(\chi_{8033}(211,\cdot)\) \(\chi_{8033}(213,\cdot)\) \(\chi_{8033}(218,\cdot)\) \(\chi_{8033}(264,\cdot)\) \(\chi_{8033}(293,\cdot)\) \(\chi_{8033}(304,\cdot)\) \(\chi_{8033}(329,\cdot)\) \(\chi_{8033}(346,\cdot)\) \(\chi_{8033}(408,\cdot)\) \(\chi_{8033}(432,\cdot)\) \(\chi_{8033}(446,\cdot)\) \(\chi_{8033}(478,\cdot)\) \(\chi_{8033}(490,\cdot)\) \(\chi_{8033}(495,\cdot)\) \(\chi_{8033}(533,\cdot)\) \(\chi_{8033}(541,\cdot)\) \(\chi_{8033}(570,\cdot)\) \(\chi_{8033}(606,\cdot)\) \(\chi_{8033}(623,\cdot)\) \(\chi_{8033}(685,\cdot)\) \(\chi_{8033}(711,\cdot)\) \(\chi_{8033}(723,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{644})$ |
| Fixed field: | Number field defined by a degree 644 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((e\left(\frac{9}{28}\right),e\left(\frac{21}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8033 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{347}{644}\right)\) | \(e\left(\frac{167}{644}\right)\) | \(e\left(\frac{25}{322}\right)\) | \(e\left(\frac{317}{322}\right)\) | \(e\left(\frac{257}{322}\right)\) | \(e\left(\frac{152}{161}\right)\) | \(e\left(\frac{397}{644}\right)\) | \(e\left(\frac{167}{322}\right)\) | \(e\left(\frac{337}{644}\right)\) | \(e\left(\frac{275}{644}\right)\) |