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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5269.o
\(\chi_{5269}(13,\cdot)\) \(\chi_{5269}(17,\cdot)\) \(\chi_{5269}(19,\cdot)\) \(\chi_{5269}(29,\cdot)\) \(\chi_{5269}(39,\cdot)\) \(\chi_{5269}(41,\cdot)\) \(\chi_{5269}(51,\cdot)\) \(\chi_{5269}(52,\cdot)\) \(\chi_{5269}(57,\cdot)\) \(\chi_{5269}(62,\cdot)\) \(\chi_{5269}(68,\cdot)\) \(\chi_{5269}(74,\cdot)\) \(\chi_{5269}(79,\cdot)\) \(\chi_{5269}(83,\cdot)\) \(\chi_{5269}(85,\cdot)\) \(\chi_{5269}(94,\cdot)\) \(\chi_{5269}(95,\cdot)\) \(\chi_{5269}(101,\cdot)\) \(\chi_{5269}(106,\cdot)\) \(\chi_{5269}(116,\cdot)\) \(\chi_{5269}(117,\cdot)\) \(\chi_{5269}(118,\cdot)\) \(\chi_{5269}(123,\cdot)\) \(\chi_{5269}(127,\cdot)\) \(\chi_{5269}(129,\cdot)\) \(\chi_{5269}(134,\cdot)\) \(\chi_{5269}(145,\cdot)\) \(\chi_{5269}(149,\cdot)\) \(\chi_{5269}(156,\cdot)\) \(\chi_{5269}(171,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1195})$ |
| Fixed field: | Number field defined by a degree 2390 polynomial (not computed) |
Values on generators
\((959,4324)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{1}{478}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 5269 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{2049}{2390}\right)\) | \(e\left(\frac{876}{1195}\right)\) | \(e\left(\frac{854}{1195}\right)\) | \(e\left(\frac{813}{1195}\right)\) | \(e\left(\frac{1411}{2390}\right)\) | \(e\left(\frac{293}{2390}\right)\) | \(e\left(\frac{1367}{2390}\right)\) | \(e\left(\frac{557}{1195}\right)\) | \(e\left(\frac{257}{478}\right)\) | \(e\left(\frac{107}{239}\right)\) |