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.cj
\(\chi_{931}(5,\cdot)\) \(\chi_{931}(54,\cdot)\) \(\chi_{931}(66,\cdot)\) \(\chi_{931}(101,\cdot)\) \(\chi_{931}(131,\cdot)\) \(\chi_{931}(138,\cdot)\) \(\chi_{931}(187,\cdot)\) \(\chi_{931}(199,\cdot)\) \(\chi_{931}(213,\cdot)\) \(\chi_{931}(234,\cdot)\) \(\chi_{931}(271,\cdot)\) \(\chi_{931}(320,\cdot)\) \(\chi_{931}(332,\cdot)\) \(\chi_{931}(346,\cdot)\) \(\chi_{931}(367,\cdot)\) \(\chi_{931}(397,\cdot)\) \(\chi_{931}(404,\cdot)\) \(\chi_{931}(453,\cdot)\) \(\chi_{931}(465,\cdot)\) \(\chi_{931}(479,\cdot)\) \(\chi_{931}(500,\cdot)\) \(\chi_{931}(530,\cdot)\) \(\chi_{931}(537,\cdot)\) \(\chi_{931}(586,\cdot)\) \(\chi_{931}(598,\cdot)\) \(\chi_{931}(612,\cdot)\) \(\chi_{931}(633,\cdot)\) \(\chi_{931}(663,\cdot)\) \(\chi_{931}(670,\cdot)\) \(\chi_{931}(719,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((248,344)\) → \((e\left(\frac{29}{42}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 931 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{11}{126}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{11}{126}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) |