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.fj
\(\chi_{3311}(61,\cdot)\) \(\chi_{3311}(227,\cdot)\) \(\chi_{3311}(248,\cdot)\) \(\chi_{3311}(292,\cdot)\) \(\chi_{3311}(304,\cdot)\) \(\chi_{3311}(327,\cdot)\) \(\chi_{3311}(502,\cdot)\) \(\chi_{3311}(535,\cdot)\) \(\chi_{3311}(761,\cdot)\) \(\chi_{3311}(794,\cdot)\) \(\chi_{3311}(822,\cdot)\) \(\chi_{3311}(964,\cdot)\) \(\chi_{3311}(1062,\cdot)\) \(\chi_{3311}(1095,\cdot)\) \(\chi_{3311}(1130,\cdot)\) \(\chi_{3311}(1146,\cdot)\) \(\chi_{3311}(1151,\cdot)\) \(\chi_{3311}(1195,\cdot)\) \(\chi_{3311}(1207,\cdot)\) \(\chi_{3311}(1405,\cdot)\) \(\chi_{3311}(1438,\cdot)\) \(\chi_{3311}(1447,\cdot)\) \(\chi_{3311}(1531,\cdot)\) \(\chi_{3311}(1832,\cdot)\) \(\chi_{3311}(1867,\cdot)\) \(\chi_{3311}(1965,\cdot)\) \(\chi_{3311}(1998,\cdot)\) \(\chi_{3311}(2026,\cdot)\) \(\chi_{3311}(2054,\cdot)\) \(\chi_{3311}(2098,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1893,904,2927)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{9}{10}\right),e\left(\frac{29}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 3311 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{52}{105}\right)\) |