Basic properties
| Modulus: | \(39675\) | |
| Conductor: | \(39675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(5060\) | 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 39675.do
\(\chi_{39675}(17,\cdot)\) \(\chi_{39675}(38,\cdot)\) \(\chi_{39675}(53,\cdot)\) \(\chi_{39675}(83,\cdot)\) \(\chi_{39675}(113,\cdot)\) \(\chi_{39675}(122,\cdot)\) \(\chi_{39675}(152,\cdot)\) \(\chi_{39675}(158,\cdot)\) \(\chi_{39675}(203,\cdot)\) \(\chi_{39675}(212,\cdot)\) \(\chi_{39675}(227,\cdot)\) \(\chi_{39675}(272,\cdot)\) \(\chi_{39675}(287,\cdot)\) \(\chi_{39675}(362,\cdot)\) \(\chi_{39675}(383,\cdot)\) \(\chi_{39675}(398,\cdot)\) \(\chi_{39675}(428,\cdot)\) \(\chi_{39675}(452,\cdot)\) \(\chi_{39675}(458,\cdot)\) \(\chi_{39675}(467,\cdot)\) \(\chi_{39675}(488,\cdot)\) \(\chi_{39675}(497,\cdot)\) \(\chi_{39675}(503,\cdot)\) \(\chi_{39675}(527,\cdot)\) \(\chi_{39675}(548,\cdot)\) \(\chi_{39675}(563,\cdot)\) \(\chi_{39675}(572,\cdot)\) \(\chi_{39675}(608,\cdot)\) \(\chi_{39675}(617,\cdot)\) \(\chi_{39675}(638,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{5060})$ |
| Fixed field: | Number field defined by a degree 5060 polynomial (not computed) |
Values on generators
\((13226,36502,39151)\) → \((-1,e\left(\frac{7}{20}\right),e\left(\frac{305}{506}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 39675 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2041}{5060}\right)\) | \(e\left(\frac{2041}{2530}\right)\) | \(e\left(\frac{513}{1012}\right)\) | \(e\left(\frac{1063}{5060}\right)\) | \(e\left(\frac{939}{1265}\right)\) | \(e\left(\frac{889}{5060}\right)\) | \(e\left(\frac{2303}{2530}\right)\) | \(e\left(\frac{776}{1265}\right)\) | \(e\left(\frac{2683}{5060}\right)\) | \(e\left(\frac{102}{1265}\right)\) |