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 \(\chi_{637}(149,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2548.ea
\(\chi_{2548}(149,\cdot)\) \(\chi_{2548}(193,\cdot)\) \(\chi_{2548}(249,\cdot)\) \(\chi_{2548}(345,\cdot)\) \(\chi_{2548}(513,\cdot)\) \(\chi_{2548}(613,\cdot)\) \(\chi_{2548}(709,\cdot)\) \(\chi_{2548}(877,\cdot)\) \(\chi_{2548}(921,\cdot)\) \(\chi_{2548}(977,\cdot)\) \(\chi_{2548}(1073,\cdot)\) \(\chi_{2548}(1241,\cdot)\) \(\chi_{2548}(1285,\cdot)\) \(\chi_{2548}(1437,\cdot)\) \(\chi_{2548}(1605,\cdot)\) \(\chi_{2548}(1649,\cdot)\) \(\chi_{2548}(1705,\cdot)\) \(\chi_{2548}(1801,\cdot)\) \(\chi_{2548}(1969,\cdot)\) \(\chi_{2548}(2013,\cdot)\) \(\chi_{2548}(2069,\cdot)\) \(\chi_{2548}(2165,\cdot)\) \(\chi_{2548}(2377,\cdot)\) \(\chi_{2548}(2433,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1275,885,197)\) → \((1,e\left(\frac{13}{21}\right),e\left(\frac{5}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2548 }(149, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(-i\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{6}{7}\right)\) |