Basic properties
| Modulus: | \(8011\) | |
| Conductor: | \(8011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1602\) | 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 8011.u
\(\chi_{8011}(21,\cdot)\) \(\chi_{8011}(34,\cdot)\) \(\chi_{8011}(37,\cdot)\) \(\chi_{8011}(39,\cdot)\) \(\chi_{8011}(69,\cdot)\) \(\chi_{8011}(77,\cdot)\) \(\chi_{8011}(79,\cdot)\) \(\chi_{8011}(97,\cdot)\) \(\chi_{8011}(101,\cdot)\) \(\chi_{8011}(126,\cdot)\) \(\chi_{8011}(131,\cdot)\) \(\chi_{8011}(143,\cdot)\) \(\chi_{8011}(146,\cdot)\) \(\chi_{8011}(163,\cdot)\) \(\chi_{8011}(166,\cdot)\) \(\chi_{8011}(172,\cdot)\) \(\chi_{8011}(204,\cdot)\) \(\chi_{8011}(211,\cdot)\) \(\chi_{8011}(222,\cdot)\) \(\chi_{8011}(234,\cdot)\) \(\chi_{8011}(253,\cdot)\) \(\chi_{8011}(280,\cdot)\) \(\chi_{8011}(285,\cdot)\) \(\chi_{8011}(295,\cdot)\) \(\chi_{8011}(298,\cdot)\) \(\chi_{8011}(314,\cdot)\) \(\chi_{8011}(321,\cdot)\) \(\chi_{8011}(329,\cdot)\) \(\chi_{8011}(347,\cdot)\) \(\chi_{8011}(392,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{801})$ |
| Fixed field: | Number field defined by a degree 1602 polynomial (not computed) |
Values on generators
\(14\) → \(e\left(\frac{71}{1602}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8011 }(21, a) \) | \(-1\) | \(1\) | \(e\left(\frac{467}{534}\right)\) | \(e\left(\frac{301}{534}\right)\) | \(e\left(\frac{200}{267}\right)\) | \(e\left(\frac{74}{89}\right)\) | \(e\left(\frac{39}{89}\right)\) | \(e\left(\frac{136}{801}\right)\) | \(e\left(\frac{111}{178}\right)\) | \(e\left(\frac{34}{267}\right)\) | \(e\left(\frac{377}{534}\right)\) | \(e\left(\frac{43}{178}\right)\) |