Basic properties
| Modulus: | \(2347\) | |
| Conductor: | \(2347\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(782\) | 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 2347.n
\(\chi_{2347}(2,\cdot)\) \(\chi_{2347}(7,\cdot)\) \(\chi_{2347}(8,\cdot)\) \(\chi_{2347}(23,\cdot)\) \(\chi_{2347}(27,\cdot)\) \(\chi_{2347}(32,\cdot)\) \(\chi_{2347}(38,\cdot)\) \(\chi_{2347}(45,\cdot)\) \(\chi_{2347}(51,\cdot)\) \(\chi_{2347}(52,\cdot)\) \(\chi_{2347}(66,\cdot)\) \(\chi_{2347}(71,\cdot)\) \(\chi_{2347}(75,\cdot)\) \(\chi_{2347}(82,\cdot)\) \(\chi_{2347}(83,\cdot)\) \(\chi_{2347}(85,\cdot)\) \(\chi_{2347}(89,\cdot)\) \(\chi_{2347}(92,\cdot)\) \(\chi_{2347}(93,\cdot)\) \(\chi_{2347}(98,\cdot)\) \(\chi_{2347}(106,\cdot)\) \(\chi_{2347}(108,\cdot)\) \(\chi_{2347}(110,\cdot)\) \(\chi_{2347}(112,\cdot)\) \(\chi_{2347}(125,\cdot)\) \(\chi_{2347}(127,\cdot)\) \(\chi_{2347}(128,\cdot)\) \(\chi_{2347}(133,\cdot)\) \(\chi_{2347}(141,\cdot)\) \(\chi_{2347}(152,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{391})$ |
| Fixed field: | Number field defined by a degree 782 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1}{782}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2347 }(27, a) \) | \(-1\) | \(1\) | \(e\left(\frac{659}{782}\right)\) | \(e\left(\frac{1}{782}\right)\) | \(e\left(\frac{268}{391}\right)\) | \(e\left(\frac{231}{782}\right)\) | \(e\left(\frac{330}{391}\right)\) | \(e\left(\frac{361}{782}\right)\) | \(e\left(\frac{413}{782}\right)\) | \(e\left(\frac{1}{391}\right)\) | \(e\left(\frac{54}{391}\right)\) | \(e\left(\frac{239}{782}\right)\) |