Basic properties
| Modulus: | \(5245\) | |
| Conductor: | \(5245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(524\) | 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 5245.v
\(\chi_{5245}(2,\cdot)\) \(\chi_{5245}(8,\cdot)\) \(\chi_{5245}(13,\cdot)\) \(\chi_{5245}(32,\cdot)\) \(\chi_{5245}(38,\cdot)\) \(\chi_{5245}(42,\cdot)\) \(\chi_{5245}(43,\cdot)\) \(\chi_{5245}(52,\cdot)\) \(\chi_{5245}(73,\cdot)\) \(\chi_{5245}(97,\cdot)\) \(\chi_{5245}(122,\cdot)\) \(\chi_{5245}(128,\cdot)\) \(\chi_{5245}(152,\cdot)\) \(\chi_{5245}(163,\cdot)\) \(\chi_{5245}(168,\cdot)\) \(\chi_{5245}(172,\cdot)\) \(\chi_{5245}(208,\cdot)\) \(\chi_{5245}(247,\cdot)\) \(\chi_{5245}(257,\cdot)\) \(\chi_{5245}(262,\cdot)\) \(\chi_{5245}(273,\cdot)\) \(\chi_{5245}(287,\cdot)\) \(\chi_{5245}(292,\cdot)\) \(\chi_{5245}(303,\cdot)\) \(\chi_{5245}(338,\cdot)\) \(\chi_{5245}(373,\cdot)\) \(\chi_{5245}(388,\cdot)\) \(\chi_{5245}(443,\cdot)\) \(\chi_{5245}(488,\cdot)\) \(\chi_{5245}(497,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{524})$ |
| Fixed field: | Number field defined by a degree 524 polynomial (not computed) |
Values on generators
\((4197,2101)\) → \((i,e\left(\frac{71}{262}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 5245 }(52, a) \) | \(-1\) | \(1\) | \(e\left(\frac{399}{524}\right)\) | \(e\left(\frac{11}{524}\right)\) | \(e\left(\frac{137}{262}\right)\) | \(e\left(\frac{205}{262}\right)\) | \(e\left(\frac{185}{524}\right)\) | \(e\left(\frac{149}{524}\right)\) | \(e\left(\frac{11}{262}\right)\) | \(e\left(\frac{36}{131}\right)\) | \(e\left(\frac{285}{524}\right)\) | \(e\left(\frac{361}{524}\right)\) |