Basic properties
| Modulus: | \(6171\) | |
| Conductor: | \(2057\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(880\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2057}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6171.cy
\(\chi_{6171}(7,\cdot)\) \(\chi_{6171}(28,\cdot)\) \(\chi_{6171}(46,\cdot)\) \(\chi_{6171}(61,\cdot)\) \(\chi_{6171}(73,\cdot)\) \(\chi_{6171}(79,\cdot)\) \(\chi_{6171}(139,\cdot)\) \(\chi_{6171}(160,\cdot)\) \(\chi_{6171}(184,\cdot)\) \(\chi_{6171}(193,\cdot)\) \(\chi_{6171}(211,\cdot)\) \(\chi_{6171}(226,\cdot)\) \(\chi_{6171}(244,\cdot)\) \(\chi_{6171}(250,\cdot)\) \(\chi_{6171}(277,\cdot)\) \(\chi_{6171}(283,\cdot)\) \(\chi_{6171}(292,\cdot)\) \(\chi_{6171}(316,\cdot)\) \(\chi_{6171}(337,\cdot)\) \(\chi_{6171}(343,\cdot)\) \(\chi_{6171}(415,\cdot)\) \(\chi_{6171}(436,\cdot)\) \(\chi_{6171}(448,\cdot)\) \(\chi_{6171}(469,\cdot)\) \(\chi_{6171}(490,\cdot)\) \(\chi_{6171}(541,\cdot)\) \(\chi_{6171}(547,\cdot)\) \(\chi_{6171}(556,\cdot)\) \(\chi_{6171}(568,\cdot)\) \(\chi_{6171}(589,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{880})$ |
| Fixed field: | Number field defined by a degree 880 polynomial (not computed) |
Values on generators
\((4115,970,2179)\) → \((1,e\left(\frac{7}{110}\right),e\left(\frac{11}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 6171 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{303}{440}\right)\) | \(e\left(\frac{83}{220}\right)\) | \(e\left(\frac{129}{880}\right)\) | \(e\left(\frac{7}{880}\right)\) | \(e\left(\frac{29}{440}\right)\) | \(e\left(\frac{147}{176}\right)\) | \(e\left(\frac{39}{220}\right)\) | \(e\left(\frac{613}{880}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{399}{440}\right)\) |