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.cf
\(\chi_{931}(15,\cdot)\) \(\chi_{931}(22,\cdot)\) \(\chi_{931}(29,\cdot)\) \(\chi_{931}(71,\cdot)\) \(\chi_{931}(78,\cdot)\) \(\chi_{931}(127,\cdot)\) \(\chi_{931}(155,\cdot)\) \(\chi_{931}(162,\cdot)\) \(\chi_{931}(204,\cdot)\) \(\chi_{931}(211,\cdot)\) \(\chi_{931}(260,\cdot)\) \(\chi_{931}(281,\cdot)\) \(\chi_{931}(288,\cdot)\) \(\chi_{931}(337,\cdot)\) \(\chi_{931}(414,\cdot)\) \(\chi_{931}(421,\cdot)\) \(\chi_{931}(428,\cdot)\) \(\chi_{931}(470,\cdot)\) \(\chi_{931}(477,\cdot)\) \(\chi_{931}(526,\cdot)\) \(\chi_{931}(547,\cdot)\) \(\chi_{931}(554,\cdot)\) \(\chi_{931}(561,\cdot)\) \(\chi_{931}(603,\cdot)\) \(\chi_{931}(610,\cdot)\) \(\chi_{931}(659,\cdot)\) \(\chi_{931}(680,\cdot)\) \(\chi_{931}(694,\cdot)\) \(\chi_{931}(743,\cdot)\) \(\chi_{931}(792,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((248,344)\) → \((e\left(\frac{5}{7}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 931 }(15, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{83}{126}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{1}{42}\right)\) |