Basic properties
| Modulus: | \(4998\) | |
| Conductor: | \(833\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(336\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{833}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4998.da
\(\chi_{4998}(61,\cdot)\) \(\chi_{4998}(73,\cdot)\) \(\chi_{4998}(199,\cdot)\) \(\chi_{4998}(241,\cdot)\) \(\chi_{4998}(283,\cdot)\) \(\chi_{4998}(367,\cdot)\) \(\chi_{4998}(397,\cdot)\) \(\chi_{4998}(439,\cdot)\) \(\chi_{4998}(481,\cdot)\) \(\chi_{4998}(649,\cdot)\) \(\chi_{4998}(691,\cdot)\) \(\chi_{4998}(703,\cdot)\) \(\chi_{4998}(745,\cdot)\) \(\chi_{4998}(775,\cdot)\) \(\chi_{4998}(787,\cdot)\) \(\chi_{4998}(955,\cdot)\) \(\chi_{4998}(997,\cdot)\) \(\chi_{4998}(1027,\cdot)\) \(\chi_{4998}(1081,\cdot)\) \(\chi_{4998}(1111,\cdot)\) \(\chi_{4998}(1153,\cdot)\) \(\chi_{4998}(1321,\cdot)\) \(\chi_{4998}(1333,\cdot)\) \(\chi_{4998}(1363,\cdot)\) \(\chi_{4998}(1405,\cdot)\) \(\chi_{4998}(1417,\cdot)\) \(\chi_{4998}(1459,\cdot)\) \(\chi_{4998}(1627,\cdot)\) \(\chi_{4998}(1669,\cdot)\) \(\chi_{4998}(1711,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{336})$ |
| Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((1667,2551,4117)\) → \((1,e\left(\frac{11}{42}\right),e\left(\frac{3}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 4998 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{179}{336}\right)\) | \(e\left(\frac{265}{336}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{257}{336}\right)\) | \(e\left(\frac{11}{168}\right)\) | \(e\left(\frac{17}{112}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{191}{336}\right)\) | \(e\left(\frac{111}{112}\right)\) |