Basic properties
| Modulus: | \(8044\) | |
| Conductor: | \(2011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(335\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2011}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8044.v
\(\chi_{8044}(13,\cdot)\) \(\chi_{8044}(33,\cdot)\) \(\chi_{8044}(41,\cdot)\) \(\chi_{8044}(45,\cdot)\) \(\chi_{8044}(57,\cdot)\) \(\chi_{8044}(77,\cdot)\) \(\chi_{8044}(101,\cdot)\) \(\chi_{8044}(105,\cdot)\) \(\chi_{8044}(125,\cdot)\) \(\chi_{8044}(169,\cdot)\) \(\chi_{8044}(181,\cdot)\) \(\chi_{8044}(197,\cdot)\) \(\chi_{8044}(201,\cdot)\) \(\chi_{8044}(245,\cdot)\) \(\chi_{8044}(293,\cdot)\) \(\chi_{8044}(409,\cdot)\) \(\chi_{8044}(429,\cdot)\) \(\chi_{8044}(469,\cdot)\) \(\chi_{8044}(493,\cdot)\) \(\chi_{8044}(501,\cdot)\) \(\chi_{8044}(533,\cdot)\) \(\chi_{8044}(537,\cdot)\) \(\chi_{8044}(585,\cdot)\) \(\chi_{8044}(593,\cdot)\) \(\chi_{8044}(613,\cdot)\) \(\chi_{8044}(629,\cdot)\) \(\chi_{8044}(653,\cdot)\) \(\chi_{8044}(669,\cdot)\) \(\chi_{8044}(681,\cdot)\) \(\chi_{8044}(729,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{335})$ |
| Fixed field: | Number field defined by a degree 335 polynomial (not computed) |
Values on generators
\((4023,4025)\) → \((1,e\left(\frac{323}{335}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8044 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{323}{335}\right)\) | \(e\left(\frac{107}{335}\right)\) | \(e\left(\frac{91}{335}\right)\) | \(e\left(\frac{311}{335}\right)\) | \(e\left(\frac{286}{335}\right)\) | \(e\left(\frac{194}{335}\right)\) | \(e\left(\frac{19}{67}\right)\) | \(e\left(\frac{191}{335}\right)\) | \(e\left(\frac{114}{335}\right)\) | \(e\left(\frac{79}{335}\right)\) |