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.mn
\(\chi_{5733}(176,\cdot)\) \(\chi_{5733}(470,\cdot)\) \(\chi_{5733}(596,\cdot)\) \(\chi_{5733}(617,\cdot)\) \(\chi_{5733}(995,\cdot)\) \(\chi_{5733}(1289,\cdot)\) \(\chi_{5733}(1415,\cdot)\) \(\chi_{5733}(1436,\cdot)\) \(\chi_{5733}(2234,\cdot)\) \(\chi_{5733}(2633,\cdot)\) \(\chi_{5733}(2927,\cdot)\) \(\chi_{5733}(3053,\cdot)\) \(\chi_{5733}(3074,\cdot)\) \(\chi_{5733}(3452,\cdot)\) \(\chi_{5733}(3746,\cdot)\) \(\chi_{5733}(3893,\cdot)\) \(\chi_{5733}(4271,\cdot)\) \(\chi_{5733}(4565,\cdot)\) \(\chi_{5733}(4691,\cdot)\) \(\chi_{5733}(4712,\cdot)\) \(\chi_{5733}(5090,\cdot)\) \(\chi_{5733}(5384,\cdot)\) \(\chi_{5733}(5510,\cdot)\) \(\chi_{5733}(5531,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,1522,5293)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{3}{7}\right),e\left(\frac{11}{12}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 5733 }(176, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{53}{84}\right)\) |