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.mu
\(\chi_{5733}(229,\cdot)\) \(\chi_{5733}(304,\cdot)\) \(\chi_{5733}(733,\cdot)\) \(\chi_{5733}(1123,\cdot)\) \(\chi_{5733}(1438,\cdot)\) \(\chi_{5733}(1552,\cdot)\) \(\chi_{5733}(1867,\cdot)\) \(\chi_{5733}(2257,\cdot)\) \(\chi_{5733}(2686,\cdot)\) \(\chi_{5733}(2761,\cdot)\) \(\chi_{5733}(3076,\cdot)\) \(\chi_{5733}(3190,\cdot)\) \(\chi_{5733}(3505,\cdot)\) \(\chi_{5733}(3580,\cdot)\) \(\chi_{5733}(3895,\cdot)\) \(\chi_{5733}(4009,\cdot)\) \(\chi_{5733}(4324,\cdot)\) \(\chi_{5733}(4399,\cdot)\) \(\chi_{5733}(4714,\cdot)\) \(\chi_{5733}(4828,\cdot)\) \(\chi_{5733}(5143,\cdot)\) \(\chi_{5733}(5218,\cdot)\) \(\chi_{5733}(5533,\cdot)\) \(\chi_{5733}(5647,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,1522,5293)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{41}{42}\right),i)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 5733 }(229, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{84}\right)\) |