Basic properties
| Modulus: | \(637\) | |
| Conductor: | \(637\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 637.ca
\(\chi_{637}(11,\cdot)\) \(\chi_{637}(58,\cdot)\) \(\chi_{637}(72,\cdot)\) \(\chi_{637}(102,\cdot)\) \(\chi_{637}(149,\cdot)\) \(\chi_{637}(158,\cdot)\) \(\chi_{637}(163,\cdot)\) \(\chi_{637}(193,\cdot)\) \(\chi_{637}(240,\cdot)\) \(\chi_{637}(249,\cdot)\) \(\chi_{637}(254,\cdot)\) \(\chi_{637}(284,\cdot)\) \(\chi_{637}(331,\cdot)\) \(\chi_{637}(340,\cdot)\) \(\chi_{637}(345,\cdot)\) \(\chi_{637}(375,\cdot)\) \(\chi_{637}(431,\cdot)\) \(\chi_{637}(436,\cdot)\) \(\chi_{637}(466,\cdot)\) \(\chi_{637}(513,\cdot)\) \(\chi_{637}(522,\cdot)\) \(\chi_{637}(527,\cdot)\) \(\chi_{637}(604,\cdot)\) \(\chi_{637}(613,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((248,197)\) → \((e\left(\frac{20}{21}\right),e\left(\frac{7}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 637 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{41}{42}\right)\) |