Basic properties
| Modulus: | \(5733\) | |
| Conductor: | \(637\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{637}(136,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5733.mq
\(\chi_{5733}(136,\cdot)\) \(\chi_{5733}(145,\cdot)\) \(\chi_{5733}(271,\cdot)\) \(\chi_{5733}(514,\cdot)\) \(\chi_{5733}(955,\cdot)\) \(\chi_{5733}(964,\cdot)\) \(\chi_{5733}(1090,\cdot)\) \(\chi_{5733}(1333,\cdot)\) \(\chi_{5733}(1774,\cdot)\) \(\chi_{5733}(1909,\cdot)\) \(\chi_{5733}(2152,\cdot)\) \(\chi_{5733}(2593,\cdot)\) \(\chi_{5733}(2602,\cdot)\) \(\chi_{5733}(2728,\cdot)\) \(\chi_{5733}(3421,\cdot)\) \(\chi_{5733}(3790,\cdot)\) \(\chi_{5733}(4231,\cdot)\) \(\chi_{5733}(4240,\cdot)\) \(\chi_{5733}(4366,\cdot)\) \(\chi_{5733}(4609,\cdot)\) \(\chi_{5733}(5050,\cdot)\) \(\chi_{5733}(5059,\cdot)\) \(\chi_{5733}(5185,\cdot)\) \(\chi_{5733}(5428,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2549,1522,5293)\) → \((1,e\left(\frac{19}{42}\right),e\left(\frac{5}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 5733 }(136, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{19}{84}\right)\) |