Basic properties
| Modulus: | \(2601\) | |
| Conductor: | \(2601\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2601.bc
\(\chi_{2601}(50,\cdot)\) \(\chi_{2601}(101,\cdot)\) \(\chi_{2601}(203,\cdot)\) \(\chi_{2601}(254,\cdot)\) \(\chi_{2601}(356,\cdot)\) \(\chi_{2601}(407,\cdot)\) \(\chi_{2601}(509,\cdot)\) \(\chi_{2601}(560,\cdot)\) \(\chi_{2601}(662,\cdot)\) \(\chi_{2601}(713,\cdot)\) \(\chi_{2601}(815,\cdot)\) \(\chi_{2601}(968,\cdot)\) \(\chi_{2601}(1019,\cdot)\) \(\chi_{2601}(1121,\cdot)\) \(\chi_{2601}(1172,\cdot)\) \(\chi_{2601}(1274,\cdot)\) \(\chi_{2601}(1325,\cdot)\) \(\chi_{2601}(1427,\cdot)\) \(\chi_{2601}(1478,\cdot)\) \(\chi_{2601}(1580,\cdot)\) \(\chi_{2601}(1631,\cdot)\) \(\chi_{2601}(1784,\cdot)\) \(\chi_{2601}(1886,\cdot)\) \(\chi_{2601}(1937,\cdot)\) \(\chi_{2601}(2039,\cdot)\) \(\chi_{2601}(2090,\cdot)\) \(\chi_{2601}(2192,\cdot)\) \(\chi_{2601}(2243,\cdot)\) \(\chi_{2601}(2345,\cdot)\) \(\chi_{2601}(2396,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((290,2026)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{13}{34}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2601 }(50, a) \) | \(-1\) | \(1\) | \(e\left(\frac{49}{102}\right)\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{61}{102}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{47}{51}\right)\) |