Basic properties
| Modulus: | \(5269\) | |
| Conductor: | \(5269\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2390\) | 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 5269.p
\(\chi_{5269}(26,\cdot)\) \(\chi_{5269}(31,\cdot)\) \(\chi_{5269}(37,\cdot)\) \(\chi_{5269}(38,\cdot)\) \(\chi_{5269}(47,\cdot)\) \(\chi_{5269}(53,\cdot)\) \(\chi_{5269}(58,\cdot)\) \(\chi_{5269}(59,\cdot)\) \(\chi_{5269}(82,\cdot)\) \(\chi_{5269}(86,\cdot)\) \(\chi_{5269}(91,\cdot)\) \(\chi_{5269}(93,\cdot)\) \(\chi_{5269}(102,\cdot)\) \(\chi_{5269}(104,\cdot)\) \(\chi_{5269}(113,\cdot)\) \(\chi_{5269}(114,\cdot)\) \(\chi_{5269}(119,\cdot)\) \(\chi_{5269}(124,\cdot)\) \(\chi_{5269}(130,\cdot)\) \(\chi_{5269}(136,\cdot)\) \(\chi_{5269}(141,\cdot)\) \(\chi_{5269}(148,\cdot)\) \(\chi_{5269}(152,\cdot)\) \(\chi_{5269}(157,\cdot)\) \(\chi_{5269}(158,\cdot)\) \(\chi_{5269}(159,\cdot)\) \(\chi_{5269}(170,\cdot)\) \(\chi_{5269}(174,\cdot)\) \(\chi_{5269}(179,\cdot)\) \(\chi_{5269}(185,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1195})$ |
| Fixed field: | Number field defined by a degree 2390 polynomial (not computed) |
Values on generators
\((959,4324)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{363}{478}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 5269 }(26, a) \) | \(-1\) | \(1\) | \(e\left(\frac{129}{1195}\right)\) | \(e\left(\frac{357}{1195}\right)\) | \(e\left(\frac{258}{1195}\right)\) | \(e\left(\frac{671}{1195}\right)\) | \(e\left(\frac{486}{1195}\right)\) | \(e\left(\frac{958}{1195}\right)\) | \(e\left(\frac{387}{1195}\right)\) | \(e\left(\frac{714}{1195}\right)\) | \(e\left(\frac{160}{239}\right)\) | \(e\left(\frac{123}{239}\right)\) |