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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 931.ci
\(\chi_{931}(3,\cdot)\) \(\chi_{931}(52,\cdot)\) \(\chi_{931}(59,\cdot)\) \(\chi_{931}(89,\cdot)\) \(\chi_{931}(110,\cdot)\) \(\chi_{931}(124,\cdot)\) \(\chi_{931}(136,\cdot)\) \(\chi_{931}(185,\cdot)\) \(\chi_{931}(192,\cdot)\) \(\chi_{931}(222,\cdot)\) \(\chi_{931}(243,\cdot)\) \(\chi_{931}(257,\cdot)\) \(\chi_{931}(269,\cdot)\) \(\chi_{931}(318,\cdot)\) \(\chi_{931}(355,\cdot)\) \(\chi_{931}(376,\cdot)\) \(\chi_{931}(390,\cdot)\) \(\chi_{931}(402,\cdot)\) \(\chi_{931}(451,\cdot)\) \(\chi_{931}(458,\cdot)\) \(\chi_{931}(488,\cdot)\) \(\chi_{931}(523,\cdot)\) \(\chi_{931}(535,\cdot)\) \(\chi_{931}(584,\cdot)\) \(\chi_{931}(591,\cdot)\) \(\chi_{931}(621,\cdot)\) \(\chi_{931}(642,\cdot)\) \(\chi_{931}(724,\cdot)\) \(\chi_{931}(775,\cdot)\) \(\chi_{931}(789,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((248,344)\) → \((e\left(\frac{1}{42}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 931 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{126}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{95}{126}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) |