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.ce
\(\chi_{637}(44,\cdot)\) \(\chi_{637}(60,\cdot)\) \(\chi_{637}(86,\cdot)\) \(\chi_{637}(109,\cdot)\) \(\chi_{637}(135,\cdot)\) \(\chi_{637}(151,\cdot)\) \(\chi_{637}(200,\cdot)\) \(\chi_{637}(242,\cdot)\) \(\chi_{637}(268,\cdot)\) \(\chi_{637}(291,\cdot)\) \(\chi_{637}(317,\cdot)\) \(\chi_{637}(333,\cdot)\) \(\chi_{637}(359,\cdot)\) \(\chi_{637}(382,\cdot)\) \(\chi_{637}(408,\cdot)\) \(\chi_{637}(424,\cdot)\) \(\chi_{637}(450,\cdot)\) \(\chi_{637}(473,\cdot)\) \(\chi_{637}(499,\cdot)\) \(\chi_{637}(515,\cdot)\) \(\chi_{637}(541,\cdot)\) \(\chi_{637}(564,\cdot)\) \(\chi_{637}(590,\cdot)\) \(\chi_{637}(632,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((248,197)\) → \((e\left(\frac{20}{21}\right),-i)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 637 }(109, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{41}{42}\right)\) |