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.fh
\(\chi_{3311}(124,\cdot)\) \(\chi_{3311}(152,\cdot)\) \(\chi_{3311}(185,\cdot)\) \(\chi_{3311}(411,\cdot)\) \(\chi_{3311}(444,\cdot)\) \(\chi_{3311}(619,\cdot)\) \(\chi_{3311}(642,\cdot)\) \(\chi_{3311}(654,\cdot)\) \(\chi_{3311}(698,\cdot)\) \(\chi_{3311}(719,\cdot)\) \(\chi_{3311}(885,\cdot)\) \(\chi_{3311}(955,\cdot)\) \(\chi_{3311}(999,\cdot)\) \(\chi_{3311}(1004,\cdot)\) \(\chi_{3311}(1027,\cdot)\) \(\chi_{3311}(1186,\cdot)\) \(\chi_{3311}(1314,\cdot)\) \(\chi_{3311}(1347,\cdot)\) \(\chi_{3311}(1356,\cdot)\) \(\chi_{3311}(1389,\cdot)\) \(\chi_{3311}(1522,\cdot)\) \(\chi_{3311}(1545,\cdot)\) \(\chi_{3311}(1615,\cdot)\) \(\chi_{3311}(1622,\cdot)\) \(\chi_{3311}(1648,\cdot)\) \(\chi_{3311}(1846,\cdot)\) \(\chi_{3311}(1907,\cdot)\) \(\chi_{3311}(1923,\cdot)\) \(\chi_{3311}(1930,\cdot)\) \(\chi_{3311}(2159,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1893,904,2927)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{2}{5}\right),e\left(\frac{11}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
\( \chi_{ 3311 }(1545, a) \) | \(-1\) | \(1\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{181}{210}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{139}{210}\right)\) |