Basic properties
| Modulus: | \(2023\) | |
| Conductor: | \(2023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | 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 2023.bb
\(\chi_{2023}(16,\cdot)\) \(\chi_{2023}(67,\cdot)\) \(\chi_{2023}(135,\cdot)\) \(\chi_{2023}(186,\cdot)\) \(\chi_{2023}(254,\cdot)\) \(\chi_{2023}(305,\cdot)\) \(\chi_{2023}(373,\cdot)\) \(\chi_{2023}(424,\cdot)\) \(\chi_{2023}(492,\cdot)\) \(\chi_{2023}(543,\cdot)\) \(\chi_{2023}(611,\cdot)\) \(\chi_{2023}(662,\cdot)\) \(\chi_{2023}(730,\cdot)\) \(\chi_{2023}(781,\cdot)\) \(\chi_{2023}(849,\cdot)\) \(\chi_{2023}(900,\cdot)\) \(\chi_{2023}(968,\cdot)\) \(\chi_{2023}(1019,\cdot)\) \(\chi_{2023}(1087,\cdot)\) \(\chi_{2023}(1138,\cdot)\) \(\chi_{2023}(1206,\cdot)\) \(\chi_{2023}(1257,\cdot)\) \(\chi_{2023}(1325,\cdot)\) \(\chi_{2023}(1376,\cdot)\) \(\chi_{2023}(1495,\cdot)\) \(\chi_{2023}(1563,\cdot)\) \(\chi_{2023}(1614,\cdot)\) \(\chi_{2023}(1682,\cdot)\) \(\chi_{2023}(1801,\cdot)\) \(\chi_{2023}(1852,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((290,1737)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{27}{34}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2023 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{28}{51}\right)\) | \(e\left(\frac{13}{102}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{53}{102}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{7}{102}\right)\) | \(e\left(\frac{61}{102}\right)\) | \(e\left(\frac{23}{102}\right)\) |