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.mo
\(\chi_{5733}(86,\cdot)\) \(\chi_{5733}(200,\cdot)\) \(\chi_{5733}(515,\cdot)\) \(\chi_{5733}(590,\cdot)\) \(\chi_{5733}(905,\cdot)\) \(\chi_{5733}(1019,\cdot)\) \(\chi_{5733}(1334,\cdot)\) \(\chi_{5733}(1409,\cdot)\) \(\chi_{5733}(1724,\cdot)\) \(\chi_{5733}(1838,\cdot)\) \(\chi_{5733}(2153,\cdot)\) \(\chi_{5733}(2228,\cdot)\) \(\chi_{5733}(2543,\cdot)\) \(\chi_{5733}(2657,\cdot)\) \(\chi_{5733}(2972,\cdot)\) \(\chi_{5733}(3047,\cdot)\) \(\chi_{5733}(3476,\cdot)\) \(\chi_{5733}(3866,\cdot)\) \(\chi_{5733}(4181,\cdot)\) \(\chi_{5733}(4295,\cdot)\) \(\chi_{5733}(4610,\cdot)\) \(\chi_{5733}(5000,\cdot)\) \(\chi_{5733}(5429,\cdot)\) \(\chi_{5733}(5504,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,1522,5293)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{16}{21}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 5733 }(86, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{25}{84}\right)\) |