Basic properties
| Modulus: | \(931\) | |
| Conductor: | \(931\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 931.cb
\(\chi_{931}(9,\cdot)\) \(\chi_{931}(23,\cdot)\) \(\chi_{931}(44,\cdot)\) \(\chi_{931}(74,\cdot)\) \(\chi_{931}(81,\cdot)\) \(\chi_{931}(130,\cdot)\) \(\chi_{931}(142,\cdot)\) \(\chi_{931}(156,\cdot)\) \(\chi_{931}(207,\cdot)\) \(\chi_{931}(289,\cdot)\) \(\chi_{931}(310,\cdot)\) \(\chi_{931}(340,\cdot)\) \(\chi_{931}(347,\cdot)\) \(\chi_{931}(396,\cdot)\) \(\chi_{931}(408,\cdot)\) \(\chi_{931}(443,\cdot)\) \(\chi_{931}(473,\cdot)\) \(\chi_{931}(480,\cdot)\) \(\chi_{931}(529,\cdot)\) \(\chi_{931}(541,\cdot)\) \(\chi_{931}(555,\cdot)\) \(\chi_{931}(576,\cdot)\) \(\chi_{931}(613,\cdot)\) \(\chi_{931}(662,\cdot)\) \(\chi_{931}(674,\cdot)\) \(\chi_{931}(688,\cdot)\) \(\chi_{931}(709,\cdot)\) \(\chi_{931}(739,\cdot)\) \(\chi_{931}(746,\cdot)\) \(\chi_{931}(795,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((248,344)\) → \((e\left(\frac{1}{21}\right),e\left(\frac{4}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 931 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) |