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.cc
\(\chi_{931}(36,\cdot)\) \(\chi_{931}(43,\cdot)\) \(\chi_{931}(85,\cdot)\) \(\chi_{931}(92,\cdot)\) \(\chi_{931}(120,\cdot)\) \(\chi_{931}(169,\cdot)\) \(\chi_{931}(176,\cdot)\) \(\chi_{931}(218,\cdot)\) \(\chi_{931}(225,\cdot)\) \(\chi_{931}(232,\cdot)\) \(\chi_{931}(253,\cdot)\) \(\chi_{931}(302,\cdot)\) \(\chi_{931}(309,\cdot)\) \(\chi_{931}(351,\cdot)\) \(\chi_{931}(358,\cdot)\) \(\chi_{931}(365,\cdot)\) \(\chi_{931}(386,\cdot)\) \(\chi_{931}(435,\cdot)\) \(\chi_{931}(484,\cdot)\) \(\chi_{931}(498,\cdot)\) \(\chi_{931}(519,\cdot)\) \(\chi_{931}(568,\cdot)\) \(\chi_{931}(575,\cdot)\) \(\chi_{931}(617,\cdot)\) \(\chi_{931}(624,\cdot)\) \(\chi_{931}(631,\cdot)\) \(\chi_{931}(652,\cdot)\) \(\chi_{931}(701,\cdot)\) \(\chi_{931}(708,\cdot)\) \(\chi_{931}(750,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((248,344)\) → \((e\left(\frac{2}{7}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 931 }(36, a) \) | \(1\) | \(1\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) |