Basic properties
| Modulus: | \(688\) | |
| Conductor: | \(688\) | 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 688.bu
\(\chi_{688}(3,\cdot)\) \(\chi_{688}(19,\cdot)\) \(\chi_{688}(91,\cdot)\) \(\chi_{688}(115,\cdot)\) \(\chi_{688}(147,\cdot)\) \(\chi_{688}(155,\cdot)\) \(\chi_{688}(163,\cdot)\) \(\chi_{688}(227,\cdot)\) \(\chi_{688}(235,\cdot)\) \(\chi_{688}(243,\cdot)\) \(\chi_{688}(291,\cdot)\) \(\chi_{688}(331,\cdot)\) \(\chi_{688}(347,\cdot)\) \(\chi_{688}(363,\cdot)\) \(\chi_{688}(435,\cdot)\) \(\chi_{688}(459,\cdot)\) \(\chi_{688}(491,\cdot)\) \(\chi_{688}(499,\cdot)\) \(\chi_{688}(507,\cdot)\) \(\chi_{688}(571,\cdot)\) \(\chi_{688}(579,\cdot)\) \(\chi_{688}(587,\cdot)\) \(\chi_{688}(635,\cdot)\) \(\chi_{688}(675,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((431,517,433)\) → \((-1,-i,e\left(\frac{1}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 688 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{17}{28}\right)\) |