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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 637.cc
\(\chi_{637}(5,\cdot)\) \(\chi_{637}(47,\cdot)\) \(\chi_{637}(73,\cdot)\) \(\chi_{637}(96,\cdot)\) \(\chi_{637}(122,\cdot)\) \(\chi_{637}(138,\cdot)\) \(\chi_{637}(164,\cdot)\) \(\chi_{637}(187,\cdot)\) \(\chi_{637}(213,\cdot)\) \(\chi_{637}(229,\cdot)\) \(\chi_{637}(255,\cdot)\) \(\chi_{637}(278,\cdot)\) \(\chi_{637}(304,\cdot)\) \(\chi_{637}(320,\cdot)\) \(\chi_{637}(346,\cdot)\) \(\chi_{637}(369,\cdot)\) \(\chi_{637}(395,\cdot)\) \(\chi_{637}(437,\cdot)\) \(\chi_{637}(486,\cdot)\) \(\chi_{637}(502,\cdot)\) \(\chi_{637}(528,\cdot)\) \(\chi_{637}(551,\cdot)\) \(\chi_{637}(577,\cdot)\) \(\chi_{637}(593,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((248,197)\) → \((e\left(\frac{29}{42}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 637 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{2}{21}\right)\) |