Basic properties
| Modulus: | \(2548\) | |
| 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 \(\chi_{637}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2548.en
\(\chi_{2548}(37,\cdot)\) \(\chi_{2548}(93,\cdot)\) \(\chi_{2548}(137,\cdot)\) \(\chi_{2548}(305,\cdot)\) \(\chi_{2548}(401,\cdot)\) \(\chi_{2548}(457,\cdot)\) \(\chi_{2548}(501,\cdot)\) \(\chi_{2548}(669,\cdot)\) \(\chi_{2548}(821,\cdot)\) \(\chi_{2548}(865,\cdot)\) \(\chi_{2548}(1033,\cdot)\) \(\chi_{2548}(1129,\cdot)\) \(\chi_{2548}(1185,\cdot)\) \(\chi_{2548}(1229,\cdot)\) \(\chi_{2548}(1397,\cdot)\) \(\chi_{2548}(1493,\cdot)\) \(\chi_{2548}(1593,\cdot)\) \(\chi_{2548}(1761,\cdot)\) \(\chi_{2548}(1857,\cdot)\) \(\chi_{2548}(1913,\cdot)\) \(\chi_{2548}(1957,\cdot)\) \(\chi_{2548}(2221,\cdot)\) \(\chi_{2548}(2277,\cdot)\) \(\chi_{2548}(2489,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1275,885,197)\) → \((1,e\left(\frac{16}{21}\right),e\left(\frac{7}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2548 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{2}{7}\right)\) |