Basic properties
Modulus: | \(2601\) | |
Conductor: | \(2601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(51\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 2601.y
\(\chi_{2601}(52,\cdot)\) \(\chi_{2601}(103,\cdot)\) \(\chi_{2601}(205,\cdot)\) \(\chi_{2601}(256,\cdot)\) \(\chi_{2601}(358,\cdot)\) \(\chi_{2601}(409,\cdot)\) \(\chi_{2601}(511,\cdot)\) \(\chi_{2601}(562,\cdot)\) \(\chi_{2601}(664,\cdot)\) \(\chi_{2601}(715,\cdot)\) \(\chi_{2601}(817,\cdot)\) \(\chi_{2601}(970,\cdot)\) \(\chi_{2601}(1021,\cdot)\) \(\chi_{2601}(1123,\cdot)\) \(\chi_{2601}(1174,\cdot)\) \(\chi_{2601}(1276,\cdot)\) \(\chi_{2601}(1327,\cdot)\) \(\chi_{2601}(1429,\cdot)\) \(\chi_{2601}(1480,\cdot)\) \(\chi_{2601}(1582,\cdot)\) \(\chi_{2601}(1633,\cdot)\) \(\chi_{2601}(1786,\cdot)\) \(\chi_{2601}(1888,\cdot)\) \(\chi_{2601}(1939,\cdot)\) \(\chi_{2601}(2041,\cdot)\) \(\chi_{2601}(2092,\cdot)\) \(\chi_{2601}(2194,\cdot)\) \(\chi_{2601}(2245,\cdot)\) \(\chi_{2601}(2347,\cdot)\) \(\chi_{2601}(2398,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((290,2026)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{5}{17}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2601 }(562, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{51}\right)\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{47}{51}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{7}{51}\right)\) | \(e\left(\frac{44}{51}\right)\) |