Basic properties
| Modulus: | \(2347\) | |
| Conductor: | \(2347\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(391\) | 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 2347.m
\(\chi_{2347}(4,\cdot)\) \(\chi_{2347}(16,\cdot)\) \(\chi_{2347}(26,\cdot)\) \(\chi_{2347}(33,\cdot)\) \(\chi_{2347}(41,\cdot)\) \(\chi_{2347}(46,\cdot)\) \(\chi_{2347}(49,\cdot)\) \(\chi_{2347}(53,\cdot)\) \(\chi_{2347}(54,\cdot)\) \(\chi_{2347}(55,\cdot)\) \(\chi_{2347}(56,\cdot)\) \(\chi_{2347}(64,\cdot)\) \(\chi_{2347}(76,\cdot)\) \(\chi_{2347}(87,\cdot)\) \(\chi_{2347}(90,\cdot)\) \(\chi_{2347}(91,\cdot)\) \(\chi_{2347}(102,\cdot)\) \(\chi_{2347}(104,\cdot)\) \(\chi_{2347}(129,\cdot)\) \(\chi_{2347}(131,\cdot)\) \(\chi_{2347}(132,\cdot)\) \(\chi_{2347}(137,\cdot)\) \(\chi_{2347}(142,\cdot)\) \(\chi_{2347}(145,\cdot)\) \(\chi_{2347}(161,\cdot)\) \(\chi_{2347}(164,\cdot)\) \(\chi_{2347}(166,\cdot)\) \(\chi_{2347}(170,\cdot)\) \(\chi_{2347}(177,\cdot)\) \(\chi_{2347}(178,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{391})$ |
| Fixed field: | Number field defined by a degree 391 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{350}{391}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2347 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{351}{391}\right)\) | \(e\left(\frac{350}{391}\right)\) | \(e\left(\frac{311}{391}\right)\) | \(e\left(\frac{304}{391}\right)\) | \(e\left(\frac{310}{391}\right)\) | \(e\left(\frac{57}{391}\right)\) | \(e\left(\frac{271}{391}\right)\) | \(e\left(\frac{309}{391}\right)\) | \(e\left(\frac{264}{391}\right)\) | \(e\left(\frac{367}{391}\right)\) |