Basic properties
| Modulus: | \(79350\) | |
| Conductor: | \(39675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(5060\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{39675}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 79350.do
\(\chi_{79350}(17,\cdot)\) \(\chi_{79350}(53,\cdot)\) \(\chi_{79350}(83,\cdot)\) \(\chi_{79350}(113,\cdot)\) \(\chi_{79350}(203,\cdot)\) \(\chi_{79350}(227,\cdot)\) \(\chi_{79350}(287,\cdot)\) \(\chi_{79350}(383,\cdot)\) \(\chi_{79350}(467,\cdot)\) \(\chi_{79350}(497,\cdot)\) \(\chi_{79350}(503,\cdot)\) \(\chi_{79350}(527,\cdot)\) \(\chi_{79350}(563,\cdot)\) \(\chi_{79350}(617,\cdot)\) \(\chi_{79350}(677,\cdot)\) \(\chi_{79350}(773,\cdot)\) \(\chi_{79350}(797,\cdot)\) \(\chi_{79350}(833,\cdot)\) \(\chi_{79350}(917,\cdot)\) \(\chi_{79350}(953,\cdot)\) \(\chi_{79350}(977,\cdot)\) \(\chi_{79350}(983,\cdot)\) \(\chi_{79350}(1073,\cdot)\) \(\chi_{79350}(1187,\cdot)\) \(\chi_{79350}(1217,\cdot)\) \(\chi_{79350}(1247,\cdot)\) \(\chi_{79350}(1367,\cdot)\) \(\chi_{79350}(1397,\cdot)\) \(\chi_{79350}(1433,\cdot)\) \(\chi_{79350}(1463,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{5060})$ |
| Fixed field: | Number field defined by a degree 5060 polynomial (not computed) |
Values on generators
\((52901,76177,39151)\) → \((-1,e\left(\frac{7}{20}\right),e\left(\frac{305}{506}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 79350 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{513}{1012}\right)\) | \(e\left(\frac{939}{1265}\right)\) | \(e\left(\frac{889}{5060}\right)\) | \(e\left(\frac{2683}{5060}\right)\) | \(e\left(\frac{102}{1265}\right)\) | \(e\left(\frac{778}{1265}\right)\) | \(e\left(\frac{472}{1265}\right)\) | \(e\left(\frac{4969}{5060}\right)\) | \(e\left(\frac{1217}{2530}\right)\) | \(e\left(\frac{531}{1012}\right)\) |