Basic properties
| Modulus: | \(4023\) | |
| Conductor: | \(1341\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(222\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1341}(929,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4023.bb
\(\chi_{4023}(35,\cdot)\) \(\chi_{4023}(116,\cdot)\) \(\chi_{4023}(143,\cdot)\) \(\chi_{4023}(305,\cdot)\) \(\chi_{4023}(359,\cdot)\) \(\chi_{4023}(422,\cdot)\) \(\chi_{4023}(467,\cdot)\) \(\chi_{4023}(494,\cdot)\) \(\chi_{4023}(557,\cdot)\) \(\chi_{4023}(638,\cdot)\) \(\chi_{4023}(665,\cdot)\) \(\chi_{4023}(827,\cdot)\) \(\chi_{4023}(845,\cdot)\) \(\chi_{4023}(962,\cdot)\) \(\chi_{4023}(980,\cdot)\) \(\chi_{4023}(1007,\cdot)\) \(\chi_{4023}(1088,\cdot)\) \(\chi_{4023}(1097,\cdot)\) \(\chi_{4023}(1196,\cdot)\) \(\chi_{4023}(1304,\cdot)\) \(\chi_{4023}(1313,\cdot)\) \(\chi_{4023}(1367,\cdot)\) \(\chi_{4023}(1394,\cdot)\) \(\chi_{4023}(1610,\cdot)\) \(\chi_{4023}(1763,\cdot)\) \(\chi_{4023}(1772,\cdot)\) \(\chi_{4023}(1898,\cdot)\) \(\chi_{4023}(1907,\cdot)\) \(\chi_{4023}(1961,\cdot)\) \(\chi_{4023}(1979,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 222 polynomial (not computed) |
Values on generators
\((299,3727)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{49}{74}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 4023 }(35, a) \) | \(-1\) | \(1\) | \(e\left(\frac{92}{111}\right)\) | \(e\left(\frac{73}{111}\right)\) | \(e\left(\frac{155}{222}\right)\) | \(e\left(\frac{77}{111}\right)\) | \(e\left(\frac{18}{37}\right)\) | \(e\left(\frac{39}{74}\right)\) | \(e\left(\frac{38}{111}\right)\) | \(e\left(\frac{95}{222}\right)\) | \(e\left(\frac{58}{111}\right)\) | \(e\left(\frac{35}{111}\right)\) |