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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4023.bf
\(\chi_{4023}(4,\cdot)\) \(\chi_{4023}(7,\cdot)\) \(\chi_{4023}(22,\cdot)\) \(\chi_{4023}(61,\cdot)\) \(\chi_{4023}(76,\cdot)\) \(\chi_{4023}(103,\cdot)\) \(\chi_{4023}(112,\cdot)\) \(\chi_{4023}(121,\cdot)\) \(\chi_{4023}(124,\cdot)\) \(\chi_{4023}(130,\cdot)\) \(\chi_{4023}(133,\cdot)\) \(\chi_{4023}(169,\cdot)\) \(\chi_{4023}(175,\cdot)\) \(\chi_{4023}(184,\cdot)\) \(\chi_{4023}(196,\cdot)\) \(\chi_{4023}(202,\cdot)\) \(\chi_{4023}(259,\cdot)\) \(\chi_{4023}(265,\cdot)\) \(\chi_{4023}(268,\cdot)\) \(\chi_{4023}(292,\cdot)\) \(\chi_{4023}(322,\cdot)\) \(\chi_{4023}(340,\cdot)\) \(\chi_{4023}(367,\cdot)\) \(\chi_{4023}(418,\cdot)\) \(\chi_{4023}(430,\cdot)\) \(\chi_{4023}(454,\cdot)\) \(\chi_{4023}(508,\cdot)\) \(\chi_{4023}(511,\cdot)\) \(\chi_{4023}(529,\cdot)\) \(\chi_{4023}(547,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{333})$ |
| Fixed field: | Number field defined by a degree 666 polynomial (not computed) |
Values on generators
\((299,3727)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{1}{74}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 4023 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{666}\right)\) | \(e\left(\frac{83}{333}\right)\) | \(e\left(\frac{320}{333}\right)\) | \(e\left(\frac{232}{333}\right)\) | \(e\left(\frac{83}{222}\right)\) | \(e\left(\frac{19}{222}\right)\) | \(e\left(\frac{611}{666}\right)\) | \(e\left(\frac{403}{666}\right)\) | \(e\left(\frac{547}{666}\right)\) | \(e\left(\frac{166}{333}\right)\) |