Basic properties
| Modulus: | \(5733\) | |
| Conductor: | \(5733\) | 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 5733.lr
\(\chi_{5733}(241,\cdot)\) \(\chi_{5733}(418,\cdot)\) \(\chi_{5733}(544,\cdot)\) \(\chi_{5733}(682,\cdot)\) \(\chi_{5733}(1237,\cdot)\) \(\chi_{5733}(1363,\cdot)\) \(\chi_{5733}(1879,\cdot)\) \(\chi_{5733}(2056,\cdot)\) \(\chi_{5733}(2182,\cdot)\) \(\chi_{5733}(2320,\cdot)\) \(\chi_{5733}(2698,\cdot)\) \(\chi_{5733}(2875,\cdot)\) \(\chi_{5733}(3001,\cdot)\) \(\chi_{5733}(3139,\cdot)\) \(\chi_{5733}(3517,\cdot)\) \(\chi_{5733}(3820,\cdot)\) \(\chi_{5733}(3958,\cdot)\) \(\chi_{5733}(4336,\cdot)\) \(\chi_{5733}(4513,\cdot)\) \(\chi_{5733}(4639,\cdot)\) \(\chi_{5733}(4777,\cdot)\) \(\chi_{5733}(5155,\cdot)\) \(\chi_{5733}(5332,\cdot)\) \(\chi_{5733}(5596,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,1522,5293)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{29}{42}\right),e\left(\frac{7}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 5733 }(544, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{19}{28}\right)\) |