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.cb
\(\chi_{637}(6,\cdot)\) \(\chi_{637}(20,\cdot)\) \(\chi_{637}(41,\cdot)\) \(\chi_{637}(76,\cdot)\) \(\chi_{637}(111,\cdot)\) \(\chi_{637}(132,\cdot)\) \(\chi_{637}(167,\cdot)\) \(\chi_{637}(188,\cdot)\) \(\chi_{637}(202,\cdot)\) \(\chi_{637}(223,\cdot)\) \(\chi_{637}(258,\cdot)\) \(\chi_{637}(279,\cdot)\) \(\chi_{637}(314,\cdot)\) \(\chi_{637}(349,\cdot)\) \(\chi_{637}(370,\cdot)\) \(\chi_{637}(384,\cdot)\) \(\chi_{637}(405,\cdot)\) \(\chi_{637}(461,\cdot)\) \(\chi_{637}(475,\cdot)\) \(\chi_{637}(496,\cdot)\) \(\chi_{637}(531,\cdot)\) \(\chi_{637}(552,\cdot)\) \(\chi_{637}(566,\cdot)\) \(\chi_{637}(622,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((248,197)\) → \((e\left(\frac{13}{14}\right),e\left(\frac{11}{12}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 637 }(20, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{5}{7}\right)\) |