Basic properties
| Modulus: | \(3311\) | |
| Conductor: | \(3311\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3311.fq
\(\chi_{3311}(158,\cdot)\) \(\chi_{3311}(191,\cdot)\) \(\chi_{3311}(284,\cdot)\) \(\chi_{3311}(478,\cdot)\) \(\chi_{3311}(620,\cdot)\) \(\chi_{3311}(718,\cdot)\) \(\chi_{3311}(751,\cdot)\) \(\chi_{3311}(779,\cdot)\) \(\chi_{3311}(786,\cdot)\) \(\chi_{3311}(807,\cdot)\) \(\chi_{3311}(851,\cdot)\) \(\chi_{3311}(863,\cdot)\) \(\chi_{3311}(1061,\cdot)\) \(\chi_{3311}(1087,\cdot)\) \(\chi_{3311}(1094,\cdot)\) \(\chi_{3311}(1103,\cdot)\) \(\chi_{3311}(1164,\cdot)\) \(\chi_{3311}(1362,\cdot)\) \(\chi_{3311}(1395,\cdot)\) \(\chi_{3311}(1488,\cdot)\) \(\chi_{3311}(1523,\cdot)\) \(\chi_{3311}(1621,\cdot)\) \(\chi_{3311}(1654,\cdot)\) \(\chi_{3311}(1710,\cdot)\) \(\chi_{3311}(1754,\cdot)\) \(\chi_{3311}(1824,\cdot)\) \(\chi_{3311}(1983,\cdot)\) \(\chi_{3311}(2006,\cdot)\) \(\chi_{3311}(2011,\cdot)\) \(\chi_{3311}(2055,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1893,904,2927)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{1}{5}\right),e\left(\frac{41}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 3311 }(158, a) \) | \(-1\) | \(1\) | \(e\left(\frac{187}{210}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{113}{210}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{46}{105}\right)\) |