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.cl
\(\chi_{931}(6,\cdot)\) \(\chi_{931}(55,\cdot)\) \(\chi_{931}(62,\cdot)\) \(\chi_{931}(104,\cdot)\) \(\chi_{931}(111,\cdot)\) \(\chi_{931}(118,\cdot)\) \(\chi_{931}(139,\cdot)\) \(\chi_{931}(188,\cdot)\) \(\chi_{931}(237,\cdot)\) \(\chi_{931}(251,\cdot)\) \(\chi_{931}(272,\cdot)\) \(\chi_{931}(321,\cdot)\) \(\chi_{931}(328,\cdot)\) \(\chi_{931}(370,\cdot)\) \(\chi_{931}(377,\cdot)\) \(\chi_{931}(384,\cdot)\) \(\chi_{931}(405,\cdot)\) \(\chi_{931}(454,\cdot)\) \(\chi_{931}(461,\cdot)\) \(\chi_{931}(503,\cdot)\) \(\chi_{931}(510,\cdot)\) \(\chi_{931}(517,\cdot)\) \(\chi_{931}(594,\cdot)\) \(\chi_{931}(643,\cdot)\) \(\chi_{931}(650,\cdot)\) \(\chi_{931}(671,\cdot)\) \(\chi_{931}(720,\cdot)\) \(\chi_{931}(727,\cdot)\) \(\chi_{931}(769,\cdot)\) \(\chi_{931}(776,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((248,344)\) → \((e\left(\frac{5}{14}\right),e\left(\frac{4}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 931 }(237, a) \) | \(-1\) | \(1\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{17}{126}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{59}{126}\right)\) | \(e\left(\frac{109}{126}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{25}{126}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{25}{42}\right)\) |