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.cf
\(\chi_{637}(15,\cdot)\) \(\chi_{637}(71,\cdot)\) \(\chi_{637}(85,\cdot)\) \(\chi_{637}(106,\cdot)\) \(\chi_{637}(141,\cdot)\) \(\chi_{637}(162,\cdot)\) \(\chi_{637}(176,\cdot)\) \(\chi_{637}(232,\cdot)\) \(\chi_{637}(253,\cdot)\) \(\chi_{637}(267,\cdot)\) \(\chi_{637}(288,\cdot)\) \(\chi_{637}(323,\cdot)\) \(\chi_{637}(358,\cdot)\) \(\chi_{637}(379,\cdot)\) \(\chi_{637}(414,\cdot)\) \(\chi_{637}(435,\cdot)\) \(\chi_{637}(449,\cdot)\) \(\chi_{637}(470,\cdot)\) \(\chi_{637}(505,\cdot)\) \(\chi_{637}(526,\cdot)\) \(\chi_{637}(561,\cdot)\) \(\chi_{637}(596,\cdot)\) \(\chi_{637}(617,\cdot)\) \(\chi_{637}(631,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((248,197)\) → \((e\left(\frac{5}{7}\right),e\left(\frac{1}{12}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 637 }(15, a) \) | \(-1\) | \(1\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{5}{14}\right)\) |