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.lb
\(\chi_{5733}(115,\cdot)\) \(\chi_{5733}(292,\cdot)\) \(\chi_{5733}(670,\cdot)\) \(\chi_{5733}(808,\cdot)\) \(\chi_{5733}(934,\cdot)\) \(\chi_{5733}(1111,\cdot)\) \(\chi_{5733}(1627,\cdot)\) \(\chi_{5733}(1753,\cdot)\) \(\chi_{5733}(2308,\cdot)\) \(\chi_{5733}(2446,\cdot)\) \(\chi_{5733}(2572,\cdot)\) \(\chi_{5733}(2749,\cdot)\) \(\chi_{5733}(3127,\cdot)\) \(\chi_{5733}(3391,\cdot)\) \(\chi_{5733}(3568,\cdot)\) \(\chi_{5733}(3946,\cdot)\) \(\chi_{5733}(4084,\cdot)\) \(\chi_{5733}(4210,\cdot)\) \(\chi_{5733}(4387,\cdot)\) \(\chi_{5733}(4765,\cdot)\) \(\chi_{5733}(4903,\cdot)\) \(\chi_{5733}(5206,\cdot)\) \(\chi_{5733}(5584,\cdot)\) \(\chi_{5733}(5722,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,1522,5293)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{25}{42}\right),e\left(\frac{7}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 5733 }(115, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(-i\) | \(e\left(\frac{25}{84}\right)\) |