Basic properties
| Modulus: | \(8033\) | |
| Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | 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.bn
\(\chi_{8033}(95,\cdot)\) \(\chi_{8033}(242,\cdot)\) \(\chi_{8033}(519,\cdot)\) \(\chi_{8033}(736,\cdot)\) \(\chi_{8033}(926,\cdot)\) \(\chi_{8033}(1290,\cdot)\) \(\chi_{8033}(1974,\cdot)\) \(\chi_{8033}(2805,\cdot)\) \(\chi_{8033}(3142,\cdot)\) \(\chi_{8033}(3419,\cdot)\) \(\chi_{8033}(3636,\cdot)\) \(\chi_{8033}(3843,\cdot)\) \(\chi_{8033}(4190,\cdot)\) \(\chi_{8033}(4397,\cdot)\) \(\chi_{8033}(4614,\cdot)\) \(\chi_{8033}(4891,\cdot)\) \(\chi_{8033}(5228,\cdot)\) \(\chi_{8033}(6059,\cdot)\) \(\chi_{8033}(6743,\cdot)\) \(\chi_{8033}(7107,\cdot)\) \(\chi_{8033}(7297,\cdot)\) \(\chi_{8033}(7514,\cdot)\) \(\chi_{8033}(7791,\cdot)\) \(\chi_{8033}(7938,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((5541,1944)\) → \((e\left(\frac{3}{28}\right),e\left(\frac{11}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8033 }(95, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{2}{21}\right)\) |