Basic properties
| Modulus: | \(2601\) | |
| Conductor: | \(289\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(272\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{289}(10,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2601.bi
\(\chi_{2601}(10,\cdot)\) \(\chi_{2601}(28,\cdot)\) \(\chi_{2601}(37,\cdot)\) \(\chi_{2601}(46,\cdot)\) \(\chi_{2601}(73,\cdot)\) \(\chi_{2601}(82,\cdot)\) \(\chi_{2601}(91,\cdot)\) \(\chi_{2601}(109,\cdot)\) \(\chi_{2601}(163,\cdot)\) \(\chi_{2601}(181,\cdot)\) \(\chi_{2601}(190,\cdot)\) \(\chi_{2601}(199,\cdot)\) \(\chi_{2601}(226,\cdot)\) \(\chi_{2601}(235,\cdot)\) \(\chi_{2601}(244,\cdot)\) \(\chi_{2601}(262,\cdot)\) \(\chi_{2601}(316,\cdot)\) \(\chi_{2601}(334,\cdot)\) \(\chi_{2601}(343,\cdot)\) \(\chi_{2601}(352,\cdot)\) \(\chi_{2601}(379,\cdot)\) \(\chi_{2601}(388,\cdot)\) \(\chi_{2601}(397,\cdot)\) \(\chi_{2601}(415,\cdot)\) \(\chi_{2601}(469,\cdot)\) \(\chi_{2601}(487,\cdot)\) \(\chi_{2601}(496,\cdot)\) \(\chi_{2601}(505,\cdot)\) \(\chi_{2601}(532,\cdot)\) \(\chi_{2601}(541,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{272})$ |
| Fixed field: | Number field defined by a degree 272 polynomial (not computed) |
Values on generators
\((290,2026)\) → \((1,e\left(\frac{147}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2601 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{93}{136}\right)\) | \(e\left(\frac{25}{68}\right)\) | \(e\left(\frac{207}{272}\right)\) | \(e\left(\frac{209}{272}\right)\) | \(e\left(\frac{7}{136}\right)\) | \(e\left(\frac{121}{272}\right)\) | \(e\left(\frac{117}{272}\right)\) | \(e\left(\frac{63}{68}\right)\) | \(e\left(\frac{123}{272}\right)\) | \(e\left(\frac{25}{34}\right)\) |