Basic properties
| Modulus: | \(2601\) | |
| Conductor: | \(867\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(272\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{867}(80,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2601.bj
\(\chi_{2601}(44,\cdot)\) \(\chi_{2601}(62,\cdot)\) \(\chi_{2601}(71,\cdot)\) \(\chi_{2601}(80,\cdot)\) \(\chi_{2601}(107,\cdot)\) \(\chi_{2601}(116,\cdot)\) \(\chi_{2601}(125,\cdot)\) \(\chi_{2601}(143,\cdot)\) \(\chi_{2601}(197,\cdot)\) \(\chi_{2601}(215,\cdot)\) \(\chi_{2601}(233,\cdot)\) \(\chi_{2601}(260,\cdot)\) \(\chi_{2601}(269,\cdot)\) \(\chi_{2601}(278,\cdot)\) \(\chi_{2601}(296,\cdot)\) \(\chi_{2601}(350,\cdot)\) \(\chi_{2601}(368,\cdot)\) \(\chi_{2601}(377,\cdot)\) \(\chi_{2601}(386,\cdot)\) \(\chi_{2601}(413,\cdot)\) \(\chi_{2601}(422,\cdot)\) \(\chi_{2601}(431,\cdot)\) \(\chi_{2601}(449,\cdot)\) \(\chi_{2601}(521,\cdot)\) \(\chi_{2601}(530,\cdot)\) \(\chi_{2601}(539,\cdot)\) \(\chi_{2601}(566,\cdot)\) \(\chi_{2601}(575,\cdot)\) \(\chi_{2601}(584,\cdot)\) \(\chi_{2601}(602,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{272})$ |
| Fixed field: | Number field defined by a degree 272 polynomial (not computed) |
Values on generators
\((290,2026)\) → \((-1,e\left(\frac{173}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2601 }(80, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{136}\right)\) | \(e\left(\frac{47}{68}\right)\) | \(e\left(\frac{41}{272}\right)\) | \(e\left(\frac{159}{272}\right)\) | \(e\left(\frac{5}{136}\right)\) | \(e\left(\frac{135}{272}\right)\) | \(e\left(\frac{35}{272}\right)\) | \(e\left(\frac{45}{68}\right)\) | \(e\left(\frac{253}{272}\right)\) | \(e\left(\frac{13}{34}\right)\) |