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.ch
\(\chi_{637}(24,\cdot)\) \(\chi_{637}(33,\cdot)\) \(\chi_{637}(110,\cdot)\) \(\chi_{637}(115,\cdot)\) \(\chi_{637}(124,\cdot)\) \(\chi_{637}(171,\cdot)\) \(\chi_{637}(201,\cdot)\) \(\chi_{637}(206,\cdot)\) \(\chi_{637}(262,\cdot)\) \(\chi_{637}(292,\cdot)\) \(\chi_{637}(297,\cdot)\) \(\chi_{637}(306,\cdot)\) \(\chi_{637}(353,\cdot)\) \(\chi_{637}(383,\cdot)\) \(\chi_{637}(388,\cdot)\) \(\chi_{637}(397,\cdot)\) \(\chi_{637}(444,\cdot)\) \(\chi_{637}(474,\cdot)\) \(\chi_{637}(479,\cdot)\) \(\chi_{637}(488,\cdot)\) \(\chi_{637}(535,\cdot)\) \(\chi_{637}(565,\cdot)\) \(\chi_{637}(579,\cdot)\) \(\chi_{637}(626,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((248,197)\) → \((e\left(\frac{25}{42}\right),e\left(\frac{1}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 637 }(262, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{1}{21}\right)\) |