Basic properties
Modulus: | \(2601\) | |
Conductor: | \(289\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(272\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{289}(46,\cdot)\) | 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
\((290,2026)\) → \((1,e\left(\frac{141}{272}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2601 }(46, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{136}\right)\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{193}{272}\right)\) | \(e\left(\frac{95}{272}\right)\) | \(e\left(\frac{65}{136}\right)\) | \(e\left(\frac{55}{272}\right)\) | \(e\left(\frac{251}{272}\right)\) | \(e\left(\frac{41}{68}\right)\) | \(e\left(\frac{229}{272}\right)\) | \(e\left(\frac{33}{34}\right)\) |