Basic properties
| Modulus: | \(2023\) | |
| Conductor: | \(289\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(68\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{289}(64,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2023.z
\(\chi_{2023}(64,\cdot)\) \(\chi_{2023}(106,\cdot)\) \(\chi_{2023}(183,\cdot)\) \(\chi_{2023}(225,\cdot)\) \(\chi_{2023}(302,\cdot)\) \(\chi_{2023}(344,\cdot)\) \(\chi_{2023}(421,\cdot)\) \(\chi_{2023}(463,\cdot)\) \(\chi_{2023}(582,\cdot)\) \(\chi_{2023}(659,\cdot)\) \(\chi_{2023}(701,\cdot)\) \(\chi_{2023}(778,\cdot)\) \(\chi_{2023}(820,\cdot)\) \(\chi_{2023}(897,\cdot)\) \(\chi_{2023}(939,\cdot)\) \(\chi_{2023}(1016,\cdot)\) \(\chi_{2023}(1058,\cdot)\) \(\chi_{2023}(1135,\cdot)\) \(\chi_{2023}(1177,\cdot)\) \(\chi_{2023}(1254,\cdot)\) \(\chi_{2023}(1296,\cdot)\) \(\chi_{2023}(1373,\cdot)\) \(\chi_{2023}(1415,\cdot)\) \(\chi_{2023}(1492,\cdot)\) \(\chi_{2023}(1534,\cdot)\) \(\chi_{2023}(1611,\cdot)\) \(\chi_{2023}(1653,\cdot)\) \(\chi_{2023}(1730,\cdot)\) \(\chi_{2023}(1849,\cdot)\) \(\chi_{2023}(1891,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((290,1737)\) → \((1,e\left(\frac{13}{68}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2023 }(64, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{13}{68}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{53}{68}\right)\) | \(e\left(\frac{35}{68}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{27}{68}\right)\) | \(e\left(\frac{57}{68}\right)\) |