Basic properties
| Modulus: | \(4425\) | |
| Conductor: | \(1475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(580\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1475}(583,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4425.bs
\(\chi_{4425}(13,\cdot)\) \(\chi_{4425}(37,\cdot)\) \(\chi_{4425}(52,\cdot)\) \(\chi_{4425}(67,\cdot)\) \(\chi_{4425}(73,\cdot)\) \(\chi_{4425}(97,\cdot)\) \(\chi_{4425}(103,\cdot)\) \(\chi_{4425}(142,\cdot)\) \(\chi_{4425}(148,\cdot)\) \(\chi_{4425}(172,\cdot)\) \(\chi_{4425}(187,\cdot)\) \(\chi_{4425}(208,\cdot)\) \(\chi_{4425}(217,\cdot)\) \(\chi_{4425}(238,\cdot)\) \(\chi_{4425}(247,\cdot)\) \(\chi_{4425}(283,\cdot)\) \(\chi_{4425}(292,\cdot)\) \(\chi_{4425}(313,\cdot)\) \(\chi_{4425}(328,\cdot)\) \(\chi_{4425}(337,\cdot)\) \(\chi_{4425}(367,\cdot)\) \(\chi_{4425}(388,\cdot)\) \(\chi_{4425}(397,\cdot)\) \(\chi_{4425}(427,\cdot)\) \(\chi_{4425}(463,\cdot)\) \(\chi_{4425}(478,\cdot)\) \(\chi_{4425}(502,\cdot)\) \(\chi_{4425}(562,\cdot)\) \(\chi_{4425}(583,\cdot)\) \(\chi_{4425}(592,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{580})$ |
| Fixed field: | Number field defined by a degree 580 polynomial (not computed) |
Values on generators
\((2951,2302,3601)\) → \((1,e\left(\frac{3}{20}\right),e\left(\frac{47}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4425 }(583, a) \) | \(1\) | \(1\) | \(e\left(\frac{557}{580}\right)\) | \(e\left(\frac{267}{290}\right)\) | \(e\left(\frac{39}{116}\right)\) | \(e\left(\frac{511}{580}\right)\) | \(e\left(\frac{191}{290}\right)\) | \(e\left(\frac{183}{580}\right)\) | \(e\left(\frac{43}{145}\right)\) | \(e\left(\frac{122}{145}\right)\) | \(e\left(\frac{211}{580}\right)\) | \(e\left(\frac{143}{290}\right)\) |