Basic properties
| Modulus: | \(2347\) | |
| Conductor: | \(2347\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1173\) | 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.o
\(\chi_{2347}(6,\cdot)\) \(\chi_{2347}(9,\cdot)\) \(\chi_{2347}(10,\cdot)\) \(\chi_{2347}(15,\cdot)\) \(\chi_{2347}(17,\cdot)\) \(\chi_{2347}(21,\cdot)\) \(\chi_{2347}(22,\cdot)\) \(\chi_{2347}(25,\cdot)\) \(\chi_{2347}(31,\cdot)\) \(\chi_{2347}(35,\cdot)\) \(\chi_{2347}(36,\cdot)\) \(\chi_{2347}(37,\cdot)\) \(\chi_{2347}(39,\cdot)\) \(\chi_{2347}(47,\cdot)\) \(\chi_{2347}(58,\cdot)\) \(\chi_{2347}(60,\cdot)\) \(\chi_{2347}(65,\cdot)\) \(\chi_{2347}(67,\cdot)\) \(\chi_{2347}(68,\cdot)\) \(\chi_{2347}(69,\cdot)\) \(\chi_{2347}(77,\cdot)\) \(\chi_{2347}(81,\cdot)\) \(\chi_{2347}(84,\cdot)\) \(\chi_{2347}(88,\cdot)\) \(\chi_{2347}(96,\cdot)\) \(\chi_{2347}(100,\cdot)\) \(\chi_{2347}(101,\cdot)\) \(\chi_{2347}(113,\cdot)\) \(\chi_{2347}(114,\cdot)\) \(\chi_{2347}(118,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1173})$ |
| Fixed field: | Number field defined by a degree 1173 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{58}{1173}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2347 }(22, a) \) | \(1\) | \(1\) | \(e\left(\frac{359}{391}\right)\) | \(e\left(\frac{58}{1173}\right)\) | \(e\left(\frac{327}{391}\right)\) | \(e\left(\frac{886}{1173}\right)\) | \(e\left(\frac{1135}{1173}\right)\) | \(e\left(\frac{202}{391}\right)\) | \(e\left(\frac{295}{391}\right)\) | \(e\left(\frac{116}{1173}\right)\) | \(e\left(\frac{790}{1173}\right)\) | \(e\left(\frac{959}{1173}\right)\) |