Basic properties
| Modulus: | \(931\) | |
| Conductor: | \(931\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | 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 931.cg
\(\chi_{931}(51,\cdot)\) \(\chi_{931}(60,\cdot)\) \(\chi_{931}(72,\cdot)\) \(\chi_{931}(86,\cdot)\) \(\chi_{931}(109,\cdot)\) \(\chi_{931}(184,\cdot)\) \(\chi_{931}(193,\cdot)\) \(\chi_{931}(205,\cdot)\) \(\chi_{931}(219,\cdot)\) \(\chi_{931}(242,\cdot)\) \(\chi_{931}(249,\cdot)\) \(\chi_{931}(317,\cdot)\) \(\chi_{931}(326,\cdot)\) \(\chi_{931}(338,\cdot)\) \(\chi_{931}(352,\cdot)\) \(\chi_{931}(375,\cdot)\) \(\chi_{931}(382,\cdot)\) \(\chi_{931}(450,\cdot)\) \(\chi_{931}(485,\cdot)\) \(\chi_{931}(515,\cdot)\) \(\chi_{931}(583,\cdot)\) \(\chi_{931}(592,\cdot)\) \(\chi_{931}(604,\cdot)\) \(\chi_{931}(641,\cdot)\) \(\chi_{931}(648,\cdot)\) \(\chi_{931}(725,\cdot)\) \(\chi_{931}(737,\cdot)\) \(\chi_{931}(751,\cdot)\) \(\chi_{931}(774,\cdot)\) \(\chi_{931}(781,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((248,344)\) → \((e\left(\frac{13}{21}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 931 }(51, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{126}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{97}{126}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{41}{42}\right)\) |