Basic properties
| Modulus: | \(6044\) | |
| Conductor: | \(1511\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(755\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1511}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6044.m
\(\chi_{6044}(5,\cdot)\) \(\chi_{6044}(13,\cdot)\) \(\chi_{6044}(17,\cdot)\) \(\chi_{6044}(21,\cdot)\) \(\chi_{6044}(25,\cdot)\) \(\chi_{6044}(45,\cdot)\) \(\chi_{6044}(49,\cdot)\) \(\chi_{6044}(57,\cdot)\) \(\chi_{6044}(61,\cdot)\) \(\chi_{6044}(65,\cdot)\) \(\chi_{6044}(85,\cdot)\) \(\chi_{6044}(93,\cdot)\) \(\chi_{6044}(105,\cdot)\) \(\chi_{6044}(109,\cdot)\) \(\chi_{6044}(117,\cdot)\) \(\chi_{6044}(121,\cdot)\) \(\chi_{6044}(125,\cdot)\) \(\chi_{6044}(133,\cdot)\) \(\chi_{6044}(137,\cdot)\) \(\chi_{6044}(153,\cdot)\) \(\chi_{6044}(169,\cdot)\) \(\chi_{6044}(189,\cdot)\) \(\chi_{6044}(197,\cdot)\) \(\chi_{6044}(217,\cdot)\) \(\chi_{6044}(225,\cdot)\) \(\chi_{6044}(233,\cdot)\) \(\chi_{6044}(245,\cdot)\) \(\chi_{6044}(253,\cdot)\) \(\chi_{6044}(257,\cdot)\) \(\chi_{6044}(269,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{755})$ |
| Fixed field: | Number field defined by a degree 755 polynomial (not computed) |
Values on generators
\((3023,3033)\) → \((1,e\left(\frac{562}{755}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6044 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{126}{151}\right)\) | \(e\left(\frac{508}{755}\right)\) | \(e\left(\frac{498}{755}\right)\) | \(e\left(\frac{101}{151}\right)\) | \(e\left(\frac{562}{755}\right)\) | \(e\left(\frac{736}{755}\right)\) | \(e\left(\frac{383}{755}\right)\) | \(e\left(\frac{699}{755}\right)\) | \(e\left(\frac{161}{755}\right)\) | \(e\left(\frac{373}{755}\right)\) |