Basic properties
| Modulus: | \(3234\) | |
| Conductor: | \(1617\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1617}(1193,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3234.cf
\(\chi_{3234}(5,\cdot)\) \(\chi_{3234}(47,\cdot)\) \(\chi_{3234}(59,\cdot)\) \(\chi_{3234}(185,\cdot)\) \(\chi_{3234}(257,\cdot)\) \(\chi_{3234}(269,\cdot)\) \(\chi_{3234}(311,\cdot)\) \(\chi_{3234}(383,\cdot)\) \(\chi_{3234}(467,\cdot)\) \(\chi_{3234}(647,\cdot)\) \(\chi_{3234}(719,\cdot)\) \(\chi_{3234}(731,\cdot)\) \(\chi_{3234}(773,\cdot)\) \(\chi_{3234}(845,\cdot)\) \(\chi_{3234}(929,\cdot)\) \(\chi_{3234}(971,\cdot)\) \(\chi_{3234}(983,\cdot)\) \(\chi_{3234}(1181,\cdot)\) \(\chi_{3234}(1193,\cdot)\) \(\chi_{3234}(1235,\cdot)\) \(\chi_{3234}(1307,\cdot)\) \(\chi_{3234}(1433,\cdot)\) \(\chi_{3234}(1445,\cdot)\) \(\chi_{3234}(1571,\cdot)\) \(\chi_{3234}(1643,\cdot)\) \(\chi_{3234}(1655,\cdot)\) \(\chi_{3234}(1769,\cdot)\) \(\chi_{3234}(1853,\cdot)\) \(\chi_{3234}(1895,\cdot)\) \(\chi_{3234}(1907,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1079,199,2059)\) → \((-1,e\left(\frac{25}{42}\right),e\left(\frac{2}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3234 }(1193, a) \) | \(1\) | \(1\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{22}{35}\right)\) |