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.cg
\(\chi_{637}(2,\cdot)\) \(\chi_{637}(32,\cdot)\) \(\chi_{637}(37,\cdot)\) \(\chi_{637}(46,\cdot)\) \(\chi_{637}(93,\cdot)\) \(\chi_{637}(123,\cdot)\) \(\chi_{637}(137,\cdot)\) \(\chi_{637}(184,\cdot)\) \(\chi_{637}(219,\cdot)\) \(\chi_{637}(228,\cdot)\) \(\chi_{637}(305,\cdot)\) \(\chi_{637}(310,\cdot)\) \(\chi_{637}(319,\cdot)\) \(\chi_{637}(366,\cdot)\) \(\chi_{637}(396,\cdot)\) \(\chi_{637}(401,\cdot)\) \(\chi_{637}(457,\cdot)\) \(\chi_{637}(487,\cdot)\) \(\chi_{637}(492,\cdot)\) \(\chi_{637}(501,\cdot)\) \(\chi_{637}(548,\cdot)\) \(\chi_{637}(578,\cdot)\) \(\chi_{637}(583,\cdot)\) \(\chi_{637}(592,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((248,197)\) → \((e\left(\frac{16}{21}\right),e\left(\frac{7}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 637 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) |