Basic properties
Modulus: | \(2601\) | |
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 \(\chi_{289}(55,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2601.ba
\(\chi_{2601}(55,\cdot)\) \(\chi_{2601}(64,\cdot)\) \(\chi_{2601}(208,\cdot)\) \(\chi_{2601}(217,\cdot)\) \(\chi_{2601}(361,\cdot)\) \(\chi_{2601}(370,\cdot)\) \(\chi_{2601}(514,\cdot)\) \(\chi_{2601}(523,\cdot)\) \(\chi_{2601}(667,\cdot)\) \(\chi_{2601}(676,\cdot)\) \(\chi_{2601}(820,\cdot)\) \(\chi_{2601}(973,\cdot)\) \(\chi_{2601}(982,\cdot)\) \(\chi_{2601}(1126,\cdot)\) \(\chi_{2601}(1135,\cdot)\) \(\chi_{2601}(1279,\cdot)\) \(\chi_{2601}(1288,\cdot)\) \(\chi_{2601}(1432,\cdot)\) \(\chi_{2601}(1441,\cdot)\) \(\chi_{2601}(1585,\cdot)\) \(\chi_{2601}(1594,\cdot)\) \(\chi_{2601}(1738,\cdot)\) \(\chi_{2601}(1747,\cdot)\) \(\chi_{2601}(1891,\cdot)\) \(\chi_{2601}(1900,\cdot)\) \(\chi_{2601}(2044,\cdot)\) \(\chi_{2601}(2053,\cdot)\) \(\chi_{2601}(2197,\cdot)\) \(\chi_{2601}(2206,\cdot)\) \(\chi_{2601}(2359,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{68})$ |
Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((290,2026)\) → \((1,e\left(\frac{63}{68}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2601 }(55, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{11}{68}\right)\) | \(e\left(\frac{41}{68}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{13}{68}\right)\) | \(e\left(\frac{21}{68}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{43}{68}\right)\) | \(e\left(\frac{2}{17}\right)\) |