Basic properties
Modulus: | \(8033\) | |
Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(644\) | 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 8033.cn
\(\chi_{8033}(37,\cdot)\) \(\chi_{8033}(73,\cdot)\) \(\chi_{8033}(118,\cdot)\) \(\chi_{8033}(148,\cdot)\) \(\chi_{8033}(269,\cdot)\) \(\chi_{8033}(275,\cdot)\) \(\chi_{8033}(279,\cdot)\) \(\chi_{8033}(292,\cdot)\) \(\chi_{8033}(359,\cdot)\) \(\chi_{8033}(409,\cdot)\) \(\chi_{8033}(425,\cdot)\) \(\chi_{8033}(445,\cdot)\) \(\chi_{8033}(472,\cdot)\) \(\chi_{8033}(562,\cdot)\) \(\chi_{8033}(627,\cdot)\) \(\chi_{8033}(686,\cdot)\) \(\chi_{8033}(722,\cdot)\) \(\chi_{8033}(727,\cdot)\) \(\chi_{8033}(794,\cdot)\) \(\chi_{8033}(868,\cdot)\) \(\chi_{8033}(873,\cdot)\) \(\chi_{8033}(885,\cdot)\) \(\chi_{8033}(913,\cdot)\) \(\chi_{8033}(949,\cdot)\) \(\chi_{8033}(959,\cdot)\) \(\chi_{8033}(1047,\cdot)\) \(\chi_{8033}(1075,\cdot)\) \(\chi_{8033}(1076,\cdot)\) \(\chi_{8033}(1100,\cdot)\) \(\chi_{8033}(1110,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{644})$ |
Fixed field: | Number field defined by a degree 644 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((e\left(\frac{15}{28}\right),e\left(\frac{9}{92}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(1100, a) \) | \(1\) | \(1\) | \(e\left(\frac{295}{322}\right)\) | \(e\left(\frac{45}{644}\right)\) | \(e\left(\frac{134}{161}\right)\) | \(e\left(\frac{569}{644}\right)\) | \(e\left(\frac{635}{644}\right)\) | \(e\left(\frac{187}{322}\right)\) | \(e\left(\frac{241}{322}\right)\) | \(e\left(\frac{45}{322}\right)\) | \(e\left(\frac{515}{644}\right)\) | \(e\left(\frac{25}{322}\right)\) |