Basic properties
Modulus: | \(4023\) | |
Conductor: | \(1341\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(111\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1341}(466,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4023.w
\(\chi_{4023}(19,\cdot)\) \(\chi_{4023}(37,\cdot)\) \(\chi_{4023}(46,\cdot)\) \(\chi_{4023}(73,\cdot)\) \(\chi_{4023}(127,\cdot)\) \(\chi_{4023}(145,\cdot)\) \(\chi_{4023}(154,\cdot)\) \(\chi_{4023}(253,\cdot)\) \(\chi_{4023}(289,\cdot)\) \(\chi_{4023}(334,\cdot)\) \(\chi_{4023}(361,\cdot)\) \(\chi_{4023}(478,\cdot)\) \(\chi_{4023}(496,\cdot)\) \(\chi_{4023}(532,\cdot)\) \(\chi_{4023}(613,\cdot)\) \(\chi_{4023}(721,\cdot)\) \(\chi_{4023}(775,\cdot)\) \(\chi_{4023}(847,\cdot)\) \(\chi_{4023}(874,\cdot)\) \(\chi_{4023}(910,\cdot)\) \(\chi_{4023}(982,\cdot)\) \(\chi_{4023}(1036,\cdot)\) \(\chi_{4023}(1072,\cdot)\) \(\chi_{4023}(1198,\cdot)\) \(\chi_{4023}(1225,\cdot)\) \(\chi_{4023}(1288,\cdot)\) \(\chi_{4023}(1306,\cdot)\) \(\chi_{4023}(1315,\cdot)\) \(\chi_{4023}(1360,\cdot)\) \(\chi_{4023}(1369,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{111})$ |
Fixed field: | Number field defined by a degree 111 polynomial (not computed) |
Values on generators
\((299,3727)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{21}{37}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4023 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{111}\right)\) | \(e\left(\frac{52}{111}\right)\) | \(e\left(\frac{40}{111}\right)\) | \(e\left(\frac{29}{111}\right)\) | \(e\left(\frac{26}{37}\right)\) | \(e\left(\frac{22}{37}\right)\) | \(e\left(\frac{59}{111}\right)\) | \(e\left(\frac{46}{111}\right)\) | \(e\left(\frac{55}{111}\right)\) | \(e\left(\frac{104}{111}\right)\) |