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.ck
\(\chi_{931}(17,\cdot)\) \(\chi_{931}(24,\cdot)\) \(\chi_{931}(47,\cdot)\) \(\chi_{931}(61,\cdot)\) \(\chi_{931}(73,\cdot)\) \(\chi_{931}(82,\cdot)\) \(\chi_{931}(150,\cdot)\) \(\chi_{931}(157,\cdot)\) \(\chi_{931}(180,\cdot)\) \(\chi_{931}(194,\cdot)\) \(\chi_{931}(206,\cdot)\) \(\chi_{931}(283,\cdot)\) \(\chi_{931}(290,\cdot)\) \(\chi_{931}(327,\cdot)\) \(\chi_{931}(339,\cdot)\) \(\chi_{931}(348,\cdot)\) \(\chi_{931}(416,\cdot)\) \(\chi_{931}(446,\cdot)\) \(\chi_{931}(481,\cdot)\) \(\chi_{931}(549,\cdot)\) \(\chi_{931}(556,\cdot)\) \(\chi_{931}(579,\cdot)\) \(\chi_{931}(593,\cdot)\) \(\chi_{931}(605,\cdot)\) \(\chi_{931}(614,\cdot)\) \(\chi_{931}(682,\cdot)\) \(\chi_{931}(689,\cdot)\) \(\chi_{931}(712,\cdot)\) \(\chi_{931}(726,\cdot)\) \(\chi_{931}(738,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((248,344)\) → \((e\left(\frac{25}{42}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 931 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{103}{126}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{107}{126}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{37}{42}\right)\) |