Basic properties
Modulus: | \(2601\) | |
Conductor: | \(867\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(136\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{867}(59,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2601.bf
\(\chi_{2601}(8,\cdot)\) \(\chi_{2601}(26,\cdot)\) \(\chi_{2601}(53,\cdot)\) \(\chi_{2601}(161,\cdot)\) \(\chi_{2601}(206,\cdot)\) \(\chi_{2601}(287,\cdot)\) \(\chi_{2601}(314,\cdot)\) \(\chi_{2601}(332,\cdot)\) \(\chi_{2601}(359,\cdot)\) \(\chi_{2601}(440,\cdot)\) \(\chi_{2601}(467,\cdot)\) \(\chi_{2601}(485,\cdot)\) \(\chi_{2601}(512,\cdot)\) \(\chi_{2601}(593,\cdot)\) \(\chi_{2601}(620,\cdot)\) \(\chi_{2601}(638,\cdot)\) \(\chi_{2601}(665,\cdot)\) \(\chi_{2601}(746,\cdot)\) \(\chi_{2601}(773,\cdot)\) \(\chi_{2601}(791,\cdot)\) \(\chi_{2601}(818,\cdot)\) \(\chi_{2601}(899,\cdot)\) \(\chi_{2601}(926,\cdot)\) \(\chi_{2601}(944,\cdot)\) \(\chi_{2601}(971,\cdot)\) \(\chi_{2601}(1052,\cdot)\) \(\chi_{2601}(1079,\cdot)\) \(\chi_{2601}(1097,\cdot)\) \(\chi_{2601}(1124,\cdot)\) \(\chi_{2601}(1205,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{136})$ |
Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((290,2026)\) → \((-1,e\left(\frac{117}{136}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2601 }(926, a) \) | \(-1\) | \(1\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{69}{136}\right)\) | \(e\left(\frac{47}{136}\right)\) | \(e\left(\frac{59}{68}\right)\) | \(e\left(\frac{63}{136}\right)\) | \(e\left(\frac{39}{136}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{41}{136}\right)\) | \(e\left(\frac{14}{17}\right)\) |