Basic properties
| Modulus: | \(4023\) | |
| Conductor: | \(4023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(666\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4023.bg
\(\chi_{4023}(5,\cdot)\) \(\chi_{4023}(29,\cdot)\) \(\chi_{4023}(95,\cdot)\) \(\chi_{4023}(104,\cdot)\) \(\chi_{4023}(140,\cdot)\) \(\chi_{4023}(155,\cdot)\) \(\chi_{4023}(182,\cdot)\) \(\chi_{4023}(185,\cdot)\) \(\chi_{4023}(212,\cdot)\) \(\chi_{4023}(230,\cdot)\) \(\chi_{4023}(245,\cdot)\) \(\chi_{4023}(263,\cdot)\) \(\chi_{4023}(272,\cdot)\) \(\chi_{4023}(317,\cdot)\) \(\chi_{4023}(326,\cdot)\) \(\chi_{4023}(329,\cdot)\) \(\chi_{4023}(335,\cdot)\) \(\chi_{4023}(344,\cdot)\) \(\chi_{4023}(347,\cdot)\) \(\chi_{4023}(365,\cdot)\) \(\chi_{4023}(371,\cdot)\) \(\chi_{4023}(383,\cdot)\) \(\chi_{4023}(425,\cdot)\) \(\chi_{4023}(443,\cdot)\) \(\chi_{4023}(452,\cdot)\) \(\chi_{4023}(464,\cdot)\) \(\chi_{4023}(527,\cdot)\) \(\chi_{4023}(542,\cdot)\) \(\chi_{4023}(551,\cdot)\) \(\chi_{4023}(554,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{333})$ |
| Fixed field: | Number field defined by a degree 666 polynomial (not computed) |
Values on generators
\((299,3727)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{30}{37}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 4023 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{577}{666}\right)\) | \(e\left(\frac{244}{333}\right)\) | \(e\left(\frac{401}{666}\right)\) | \(e\left(\frac{8}{333}\right)\) | \(e\left(\frac{133}{222}\right)\) | \(e\left(\frac{52}{111}\right)\) | \(e\left(\frac{67}{666}\right)\) | \(e\left(\frac{139}{333}\right)\) | \(e\left(\frac{593}{666}\right)\) | \(e\left(\frac{155}{333}\right)\) |