Basic properties
| Modulus: | \(3332\) | |
| Conductor: | \(3332\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(56\) | 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 3332.ck
\(\chi_{3332}(15,\cdot)\) \(\chi_{3332}(43,\cdot)\) \(\chi_{3332}(127,\cdot)\) \(\chi_{3332}(155,\cdot)\) \(\chi_{3332}(519,\cdot)\) \(\chi_{3332}(603,\cdot)\) \(\chi_{3332}(631,\cdot)\) \(\chi_{3332}(967,\cdot)\) \(\chi_{3332}(995,\cdot)\) \(\chi_{3332}(1107,\cdot)\) \(\chi_{3332}(1443,\cdot)\) \(\chi_{3332}(1555,\cdot)\) \(\chi_{3332}(1583,\cdot)\) \(\chi_{3332}(1919,\cdot)\) \(\chi_{3332}(1947,\cdot)\) \(\chi_{3332}(2031,\cdot)\) \(\chi_{3332}(2395,\cdot)\) \(\chi_{3332}(2423,\cdot)\) \(\chi_{3332}(2507,\cdot)\) \(\chi_{3332}(2535,\cdot)\) \(\chi_{3332}(2871,\cdot)\) \(\chi_{3332}(2899,\cdot)\) \(\chi_{3332}(2983,\cdot)\) \(\chi_{3332}(3011,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((1667,885,785)\) → \((-1,e\left(\frac{5}{7}\right),e\left(\frac{3}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3332 }(15, a) \) | \(-1\) | \(1\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(-i\) | \(e\left(\frac{15}{56}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{43}{56}\right)\) |