Basic properties
| Modulus: | \(8044\) | |
| Conductor: | \(8044\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(670\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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 8044.bb
\(\chi_{8044}(27,\cdot)\) \(\chi_{8044}(47,\cdot)\) \(\chi_{8044}(55,\cdot)\) \(\chi_{8044}(59,\cdot)\) \(\chi_{8044}(75,\cdot)\) \(\chi_{8044}(95,\cdot)\) \(\chi_{8044}(267,\cdot)\) \(\chi_{8044}(335,\cdot)\) \(\chi_{8044}(343,\cdot)\) \(\chi_{8044}(351,\cdot)\) \(\chi_{8044}(391,\cdot)\) \(\chi_{8044}(439,\cdot)\) \(\chi_{8044}(463,\cdot)\) \(\chi_{8044}(535,\cdot)\) \(\chi_{8044}(623,\cdot)\) \(\chi_{8044}(711,\cdot)\) \(\chi_{8044}(715,\cdot)\) \(\chi_{8044}(819,\cdot)\) \(\chi_{8044}(891,\cdot)\) \(\chi_{8044}(919,\cdot)\) \(\chi_{8044}(971,\cdot)\) \(\chi_{8044}(975,\cdot)\) \(\chi_{8044}(1107,\cdot)\) \(\chi_{8044}(1115,\cdot)\) \(\chi_{8044}(1135,\cdot)\) \(\chi_{8044}(1179,\cdot)\) \(\chi_{8044}(1199,\cdot)\) \(\chi_{8044}(1215,\cdot)\) \(\chi_{8044}(1251,\cdot)\) \(\chi_{8044}(1331,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{335})$ |
| Fixed field: | Number field defined by a degree 670 polynomial (not computed) |
Values on generators
\((4023,4025)\) → \((-1,e\left(\frac{663}{670}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8044 }(715, a) \) | \(1\) | \(1\) | \(e\left(\frac{164}{335}\right)\) | \(e\left(\frac{101}{335}\right)\) | \(e\left(\frac{208}{335}\right)\) | \(e\left(\frac{328}{335}\right)\) | \(e\left(\frac{223}{335}\right)\) | \(e\left(\frac{252}{335}\right)\) | \(e\left(\frac{53}{67}\right)\) | \(e\left(\frac{251}{670}\right)\) | \(e\left(\frac{117}{335}\right)\) | \(e\left(\frac{37}{335}\right)\) |