Basic properties
Modulus: | \(2601\) | |
Conductor: | \(289\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(136\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{289}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2601.be
\(\chi_{2601}(19,\cdot)\) \(\chi_{2601}(100,\cdot)\) \(\chi_{2601}(127,\cdot)\) \(\chi_{2601}(145,\cdot)\) \(\chi_{2601}(172,\cdot)\) \(\chi_{2601}(253,\cdot)\) \(\chi_{2601}(280,\cdot)\) \(\chi_{2601}(298,\cdot)\) \(\chi_{2601}(325,\cdot)\) \(\chi_{2601}(406,\cdot)\) \(\chi_{2601}(433,\cdot)\) \(\chi_{2601}(451,\cdot)\) \(\chi_{2601}(478,\cdot)\) \(\chi_{2601}(559,\cdot)\) \(\chi_{2601}(586,\cdot)\) \(\chi_{2601}(604,\cdot)\) \(\chi_{2601}(631,\cdot)\) \(\chi_{2601}(739,\cdot)\) \(\chi_{2601}(784,\cdot)\) \(\chi_{2601}(865,\cdot)\) \(\chi_{2601}(892,\cdot)\) \(\chi_{2601}(910,\cdot)\) \(\chi_{2601}(937,\cdot)\) \(\chi_{2601}(1018,\cdot)\) \(\chi_{2601}(1045,\cdot)\) \(\chi_{2601}(1063,\cdot)\) \(\chi_{2601}(1090,\cdot)\) \(\chi_{2601}(1171,\cdot)\) \(\chi_{2601}(1198,\cdot)\) \(\chi_{2601}(1216,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{136})$ |
Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((290,2026)\) → \((1,e\left(\frac{93}{136}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2601 }(892, a) \) | \(1\) | \(1\) | \(e\left(\frac{63}{68}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{81}{136}\right)\) | \(e\left(\frac{135}{136}\right)\) | \(e\left(\frac{53}{68}\right)\) | \(e\left(\frac{71}{136}\right)\) | \(e\left(\frac{99}{136}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{125}{136}\right)\) | \(e\left(\frac{12}{17}\right)\) |