Basic properties
| Modulus: | \(2601\) | |
| Conductor: | \(2601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(408\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2601.bk
\(\chi_{2601}(25,\cdot)\) \(\chi_{2601}(43,\cdot)\) \(\chi_{2601}(49,\cdot)\) \(\chi_{2601}(70,\cdot)\) \(\chi_{2601}(76,\cdot)\) \(\chi_{2601}(94,\cdot)\) \(\chi_{2601}(121,\cdot)\) \(\chi_{2601}(151,\cdot)\) \(\chi_{2601}(178,\cdot)\) \(\chi_{2601}(196,\cdot)\) \(\chi_{2601}(202,\cdot)\) \(\chi_{2601}(223,\cdot)\) \(\chi_{2601}(229,\cdot)\) \(\chi_{2601}(247,\cdot)\) \(\chi_{2601}(274,\cdot)\) \(\chi_{2601}(304,\cdot)\) \(\chi_{2601}(331,\cdot)\) \(\chi_{2601}(349,\cdot)\) \(\chi_{2601}(355,\cdot)\) \(\chi_{2601}(376,\cdot)\) \(\chi_{2601}(382,\cdot)\) \(\chi_{2601}(400,\cdot)\) \(\chi_{2601}(427,\cdot)\) \(\chi_{2601}(457,\cdot)\) \(\chi_{2601}(484,\cdot)\) \(\chi_{2601}(502,\cdot)\) \(\chi_{2601}(508,\cdot)\) \(\chi_{2601}(529,\cdot)\) \(\chi_{2601}(535,\cdot)\) \(\chi_{2601}(553,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{408})$ |
| Fixed field: | Number field defined by a degree 408 polynomial (not computed) |
Values on generators
\((290,2026)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{63}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2601 }(376, a) \) | \(1\) | \(1\) | \(e\left(\frac{139}{204}\right)\) | \(e\left(\frac{37}{102}\right)\) | \(e\left(\frac{169}{408}\right)\) | \(e\left(\frac{191}{408}\right)\) | \(e\left(\frac{3}{68}\right)\) | \(e\left(\frac{13}{136}\right)\) | \(e\left(\frac{131}{408}\right)\) | \(e\left(\frac{13}{102}\right)\) | \(e\left(\frac{61}{408}\right)\) | \(e\left(\frac{37}{51}\right)\) |