Basic properties
| Modulus: | \(501\) | |
| Conductor: | \(501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(166\) | 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 501.h
\(\chi_{501}(2,\cdot)\) \(\chi_{501}(8,\cdot)\) \(\chi_{501}(11,\cdot)\) \(\chi_{501}(14,\cdot)\) \(\chi_{501}(29,\cdot)\) \(\chi_{501}(32,\cdot)\) \(\chi_{501}(38,\cdot)\) \(\chi_{501}(44,\cdot)\) \(\chi_{501}(47,\cdot)\) \(\chi_{501}(50,\cdot)\) \(\chi_{501}(56,\cdot)\) \(\chi_{501}(62,\cdot)\) \(\chi_{501}(65,\cdot)\) \(\chi_{501}(77,\cdot)\) \(\chi_{501}(89,\cdot)\) \(\chi_{501}(98,\cdot)\) \(\chi_{501}(107,\cdot)\) \(\chi_{501}(116,\cdot)\) \(\chi_{501}(122,\cdot)\) \(\chi_{501}(128,\cdot)\) \(\chi_{501}(137,\cdot)\) \(\chi_{501}(152,\cdot)\) \(\chi_{501}(170,\cdot)\) \(\chi_{501}(173,\cdot)\) \(\chi_{501}(176,\cdot)\) \(\chi_{501}(179,\cdot)\) \(\chi_{501}(185,\cdot)\) \(\chi_{501}(188,\cdot)\) \(\chi_{501}(191,\cdot)\) \(\chi_{501}(194,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((335,172)\) → \((-1,e\left(\frac{34}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 501 }(356, a) \) | \(-1\) | \(1\) | \(e\left(\frac{147}{166}\right)\) | \(e\left(\frac{64}{83}\right)\) | \(e\left(\frac{151}{166}\right)\) | \(e\left(\frac{28}{83}\right)\) | \(e\left(\frac{109}{166}\right)\) | \(e\left(\frac{66}{83}\right)\) | \(e\left(\frac{161}{166}\right)\) | \(e\left(\frac{16}{83}\right)\) | \(e\left(\frac{37}{166}\right)\) | \(e\left(\frac{45}{83}\right)\) |