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.cs
\(\chi_{8033}(2,\cdot)\) \(\chi_{8033}(8,\cdot)\) \(\chi_{8033}(15,\cdot)\) \(\chi_{8033}(26,\cdot)\) \(\chi_{8033}(32,\cdot)\) \(\chi_{8033}(61,\cdot)\) \(\chi_{8033}(159,\cdot)\) \(\chi_{8033}(195,\cdot)\) \(\chi_{8033}(235,\cdot)\) \(\chi_{8033}(240,\cdot)\) \(\chi_{8033}(251,\cdot)\) \(\chi_{8033}(309,\cdot)\) \(\chi_{8033}(338,\cdot)\) \(\chi_{8033}(350,\cdot)\) \(\chi_{8033}(395,\cdot)\) \(\chi_{8033}(416,\cdot)\) \(\chi_{8033}(450,\cdot)\) \(\chi_{8033}(503,\cdot)\) \(\chi_{8033}(512,\cdot)\) \(\chi_{8033}(569,\cdot)\) \(\chi_{8033}(591,\cdot)\) \(\chi_{8033}(636,\cdot)\) \(\chi_{8033}(682,\cdot)\) \(\chi_{8033}(693,\cdot)\) \(\chi_{8033}(699,\cdot)\) \(\chi_{8033}(706,\cdot)\) \(\chi_{8033}(780,\cdot)\) \(\chi_{8033}(793,\cdot)\) \(\chi_{8033}(798,\cdot)\) \(\chi_{8033}(823,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{644})$ |
Fixed field: | Number field defined by a degree 644 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((e\left(\frac{1}{28}\right),e\left(\frac{49}{92}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{161}\right)\) | \(e\left(\frac{199}{644}\right)\) | \(e\left(\frac{106}{161}\right)\) | \(e\left(\frac{205}{644}\right)\) | \(e\left(\frac{411}{644}\right)\) | \(e\left(\frac{47}{322}\right)\) | \(e\left(\frac{159}{161}\right)\) | \(e\left(\frac{199}{322}\right)\) | \(e\left(\frac{417}{644}\right)\) | \(e\left(\frac{100}{161}\right)\) |