Basic properties
Modulus: | \(3332\) | |
Conductor: | \(833\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(336\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{833}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3332.db
\(\chi_{3332}(5,\cdot)\) \(\chi_{3332}(45,\cdot)\) \(\chi_{3332}(61,\cdot)\) \(\chi_{3332}(73,\cdot)\) \(\chi_{3332}(173,\cdot)\) \(\chi_{3332}(201,\cdot)\) \(\chi_{3332}(241,\cdot)\) \(\chi_{3332}(269,\cdot)\) \(\chi_{3332}(369,\cdot)\) \(\chi_{3332}(381,\cdot)\) \(\chi_{3332}(397,\cdot)\) \(\chi_{3332}(437,\cdot)\) \(\chi_{3332}(453,\cdot)\) \(\chi_{3332}(465,\cdot)\) \(\chi_{3332}(481,\cdot)\) \(\chi_{3332}(537,\cdot)\) \(\chi_{3332}(549,\cdot)\) \(\chi_{3332}(605,\cdot)\) \(\chi_{3332}(649,\cdot)\) \(\chi_{3332}(677,\cdot)\) \(\chi_{3332}(745,\cdot)\) \(\chi_{3332}(789,\cdot)\) \(\chi_{3332}(845,\cdot)\) \(\chi_{3332}(857,\cdot)\) \(\chi_{3332}(873,\cdot)\) \(\chi_{3332}(929,\cdot)\) \(\chi_{3332}(941,\cdot)\) \(\chi_{3332}(957,\cdot)\) \(\chi_{3332}(997,\cdot)\) \(\chi_{3332}(1013,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{336})$ |
Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((1667,885,785)\) → \((1,e\left(\frac{29}{42}\right),e\left(\frac{5}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 3332 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{336}\right)\) | \(e\left(\frac{197}{336}\right)\) | \(e\left(\frac{1}{168}\right)\) | \(e\left(\frac{271}{336}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{311}{336}\right)\) | \(e\left(\frac{29}{168}\right)\) | \(e\left(\frac{1}{112}\right)\) |