Basic properties
Modulus: | \(8011\) | |
Conductor: | \(8011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(267\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 8011.o
\(\chi_{8011}(22,\cdot)\) \(\chi_{8011}(80,\cdot)\) \(\chi_{8011}(94,\cdot)\) \(\chi_{8011}(124,\cdot)\) \(\chi_{8011}(132,\cdot)\) \(\chi_{8011}(225,\cdot)\) \(\chi_{8011}(355,\cdot)\) \(\chi_{8011}(401,\cdot)\) \(\chi_{8011}(480,\cdot)\) \(\chi_{8011}(484,\cdot)\) \(\chi_{8011}(500,\cdot)\) \(\chi_{8011}(511,\cdot)\) \(\chi_{8011}(534,\cdot)\) \(\chi_{8011}(564,\cdot)\) \(\chi_{8011}(581,\cdot)\) \(\chi_{8011}(744,\cdot)\) \(\chi_{8011}(751,\cdot)\) \(\chi_{8011}(777,\cdot)\) \(\chi_{8011}(792,\cdot)\) \(\chi_{8011}(825,\cdot)\) \(\chi_{8011}(904,\cdot)\) \(\chi_{8011}(939,\cdot)\) \(\chi_{8011}(1024,\cdot)\) \(\chi_{8011}(1028,\cdot)\) \(\chi_{8011}(1072,\cdot)\) \(\chi_{8011}(1099,\cdot)\) \(\chi_{8011}(1191,\cdot)\) \(\chi_{8011}(1258,\cdot)\) \(\chi_{8011}(1350,\cdot)\) \(\chi_{8011}(1402,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{267})$ |
Fixed field: | Number field defined by a degree 267 polynomial (not computed) |
Values on generators
\(14\) → \(e\left(\frac{58}{267}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8011 }(22, a) \) | \(1\) | \(1\) | \(e\left(\frac{28}{89}\right)\) | \(e\left(\frac{19}{89}\right)\) | \(e\left(\frac{56}{89}\right)\) | \(e\left(\frac{23}{89}\right)\) | \(e\left(\frac{47}{89}\right)\) | \(e\left(\frac{241}{267}\right)\) | \(e\left(\frac{84}{89}\right)\) | \(e\left(\frac{38}{89}\right)\) | \(e\left(\frac{51}{89}\right)\) | \(e\left(\frac{59}{89}\right)\) |