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.mt
\(\chi_{5733}(202,\cdot)\) \(\chi_{5733}(223,\cdot)\) \(\chi_{5733}(349,\cdot)\) \(\chi_{5733}(643,\cdot)\) \(\chi_{5733}(1021,\cdot)\) \(\chi_{5733}(1042,\cdot)\) \(\chi_{5733}(1168,\cdot)\) \(\chi_{5733}(1462,\cdot)\) \(\chi_{5733}(1840,\cdot)\) \(\chi_{5733}(1987,\cdot)\) \(\chi_{5733}(2281,\cdot)\) \(\chi_{5733}(2659,\cdot)\) \(\chi_{5733}(2680,\cdot)\) \(\chi_{5733}(2806,\cdot)\) \(\chi_{5733}(3100,\cdot)\) \(\chi_{5733}(3499,\cdot)\) \(\chi_{5733}(4297,\cdot)\) \(\chi_{5733}(4318,\cdot)\) \(\chi_{5733}(4444,\cdot)\) \(\chi_{5733}(4738,\cdot)\) \(\chi_{5733}(5116,\cdot)\) \(\chi_{5733}(5137,\cdot)\) \(\chi_{5733}(5263,\cdot)\) \(\chi_{5733}(5557,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,1522,5293)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{9}{14}\right),e\left(\frac{11}{12}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 5733 }(202, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{41}{84}\right)\) |