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.fk
\(\chi_{3311}(31,\cdot)\) \(\chi_{3311}(38,\cdot)\) \(\chi_{3311}(103,\cdot)\) \(\chi_{3311}(229,\cdot)\) \(\chi_{3311}(311,\cdot)\) \(\chi_{3311}(339,\cdot)\) \(\chi_{3311}(367,\cdot)\) \(\chi_{3311}(488,\cdot)\) \(\chi_{3311}(740,\cdot)\) \(\chi_{3311}(873,\cdot)\) \(\chi_{3311}(927,\cdot)\) \(\chi_{3311}(971,\cdot)\) \(\chi_{3311}(1006,\cdot)\) \(\chi_{3311}(1158,\cdot)\) \(\chi_{3311}(1214,\cdot)\) \(\chi_{3311}(1235,\cdot)\) \(\chi_{3311}(1270,\cdot)\) \(\chi_{3311}(1307,\cdot)\) \(\chi_{3311}(1391,\cdot)\) \(\chi_{3311}(1433,\cdot)\) \(\chi_{3311}(1543,\cdot)\) \(\chi_{3311}(1571,\cdot)\) \(\chi_{3311}(1643,\cdot)\) \(\chi_{3311}(1692,\cdot)\) \(\chi_{3311}(1776,\cdot)\) \(\chi_{3311}(1830,\cdot)\) \(\chi_{3311}(1874,\cdot)\) \(\chi_{3311}(2061,\cdot)\) \(\chi_{3311}(2077,\cdot)\) \(\chi_{3311}(2117,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1893,904,2927)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{3}{5}\right),e\left(\frac{17}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
\( \chi_{ 3311 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{163}{210}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{1}{210}\right)\) |