Basic properties
| Modulus: | \(2601\) | |
| Conductor: | \(2601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(204\) | 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 2601.bh
\(\chi_{2601}(47,\cdot)\) \(\chi_{2601}(140,\cdot)\) \(\chi_{2601}(149,\cdot)\) \(\chi_{2601}(191,\cdot)\) \(\chi_{2601}(200,\cdot)\) \(\chi_{2601}(293,\cdot)\) \(\chi_{2601}(302,\cdot)\) \(\chi_{2601}(344,\cdot)\) \(\chi_{2601}(353,\cdot)\) \(\chi_{2601}(446,\cdot)\) \(\chi_{2601}(455,\cdot)\) \(\chi_{2601}(497,\cdot)\) \(\chi_{2601}(506,\cdot)\) \(\chi_{2601}(599,\cdot)\) \(\chi_{2601}(608,\cdot)\) \(\chi_{2601}(650,\cdot)\) \(\chi_{2601}(659,\cdot)\) \(\chi_{2601}(752,\cdot)\) \(\chi_{2601}(761,\cdot)\) \(\chi_{2601}(803,\cdot)\) \(\chi_{2601}(812,\cdot)\) \(\chi_{2601}(914,\cdot)\) \(\chi_{2601}(956,\cdot)\) \(\chi_{2601}(965,\cdot)\) \(\chi_{2601}(1058,\cdot)\) \(\chi_{2601}(1067,\cdot)\) \(\chi_{2601}(1109,\cdot)\) \(\chi_{2601}(1211,\cdot)\) \(\chi_{2601}(1220,\cdot)\) \(\chi_{2601}(1262,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((290,2026)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{35}{68}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2601 }(497, a) \) | \(-1\) | \(1\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{47}{51}\right)\) | \(e\left(\frac{143}{204}\right)\) | \(e\left(\frac{91}{204}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{45}{68}\right)\) | \(e\left(\frac{1}{204}\right)\) | \(e\left(\frac{11}{51}\right)\) | \(e\left(\frac{83}{204}\right)\) | \(e\left(\frac{43}{51}\right)\) |