Basic properties
| Modulus: | \(7942\) | |
| Conductor: | \(3971\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(855\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3971}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7942.bs
\(\chi_{7942}(5,\cdot)\) \(\chi_{7942}(9,\cdot)\) \(\chi_{7942}(25,\cdot)\) \(\chi_{7942}(47,\cdot)\) \(\chi_{7942}(81,\cdot)\) \(\chi_{7942}(93,\cdot)\) \(\chi_{7942}(119,\cdot)\) \(\chi_{7942}(137,\cdot)\) \(\chi_{7942}(157,\cdot)\) \(\chi_{7942}(169,\cdot)\) \(\chi_{7942}(207,\cdot)\) \(\chi_{7942}(213,\cdot)\) \(\chi_{7942}(225,\cdot)\) \(\chi_{7942}(251,\cdot)\) \(\chi_{7942}(289,\cdot)\) \(\chi_{7942}(291,\cdot)\) \(\chi_{7942}(301,\cdot)\) \(\chi_{7942}(313,\cdot)\) \(\chi_{7942}(339,\cdot)\) \(\chi_{7942}(367,\cdot)\) \(\chi_{7942}(377,\cdot)\) \(\chi_{7942}(405,\cdot)\) \(\chi_{7942}(427,\cdot)\) \(\chi_{7942}(443,\cdot)\) \(\chi_{7942}(465,\cdot)\) \(\chi_{7942}(499,\cdot)\) \(\chi_{7942}(511,\cdot)\) \(\chi_{7942}(537,\cdot)\) \(\chi_{7942}(555,\cdot)\) \(\chi_{7942}(575,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{855})$ |
| Fixed field: | Number field defined by a degree 855 polynomial (not computed) |
Values on generators
\((5777,6139)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{116}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 7942 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{421}{855}\right)\) | \(e\left(\frac{838}{855}\right)\) | \(e\left(\frac{158}{285}\right)\) | \(e\left(\frac{842}{855}\right)\) | \(e\left(\frac{497}{855}\right)\) | \(e\left(\frac{404}{855}\right)\) | \(e\left(\frac{778}{855}\right)\) | \(e\left(\frac{8}{171}\right)\) | \(e\left(\frac{7}{171}\right)\) | \(e\left(\frac{821}{855}\right)\) |