Basic properties
| Modulus: | \(3234\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(103,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3234.cj
\(\chi_{3234}(103,\cdot)\) \(\chi_{3234}(115,\cdot)\) \(\chi_{3234}(157,\cdot)\) \(\chi_{3234}(229,\cdot)\) \(\chi_{3234}(355,\cdot)\) \(\chi_{3234}(367,\cdot)\) \(\chi_{3234}(493,\cdot)\) \(\chi_{3234}(565,\cdot)\) \(\chi_{3234}(577,\cdot)\) \(\chi_{3234}(691,\cdot)\) \(\chi_{3234}(775,\cdot)\) \(\chi_{3234}(817,\cdot)\) \(\chi_{3234}(829,\cdot)\) \(\chi_{3234}(955,\cdot)\) \(\chi_{3234}(1027,\cdot)\) \(\chi_{3234}(1039,\cdot)\) \(\chi_{3234}(1081,\cdot)\) \(\chi_{3234}(1153,\cdot)\) \(\chi_{3234}(1237,\cdot)\) \(\chi_{3234}(1279,\cdot)\) \(\chi_{3234}(1291,\cdot)\) \(\chi_{3234}(1417,\cdot)\) \(\chi_{3234}(1543,\cdot)\) \(\chi_{3234}(1615,\cdot)\) \(\chi_{3234}(1699,\cdot)\) \(\chi_{3234}(1741,\cdot)\) \(\chi_{3234}(1753,\cdot)\) \(\chi_{3234}(1879,\cdot)\) \(\chi_{3234}(1951,\cdot)\) \(\chi_{3234}(1963,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1079,199,2059)\) → \((1,e\left(\frac{29}{42}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3234 }(103, a) \) | \(-1\) | \(1\) | \(e\left(\frac{173}{210}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{13}{210}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{67}{70}\right)\) |