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.n
\(\chi_{5269}(2,\cdot)\) \(\chi_{5269}(6,\cdot)\) \(\chi_{5269}(7,\cdot)\) \(\chi_{5269}(8,\cdot)\) \(\chi_{5269}(18,\cdot)\) \(\chi_{5269}(24,\cdot)\) \(\chi_{5269}(28,\cdot)\) \(\chi_{5269}(30,\cdot)\) \(\chi_{5269}(35,\cdot)\) \(\chi_{5269}(40,\cdot)\) \(\chi_{5269}(46,\cdot)\) \(\chi_{5269}(50,\cdot)\) \(\chi_{5269}(61,\cdot)\) \(\chi_{5269}(63,\cdot)\) \(\chi_{5269}(72,\cdot)\) \(\chi_{5269}(73,\cdot)\) \(\chi_{5269}(84,\cdot)\) \(\chi_{5269}(90,\cdot)\) \(\chi_{5269}(96,\cdot)\) \(\chi_{5269}(105,\cdot)\) \(\chi_{5269}(107,\cdot)\) \(\chi_{5269}(112,\cdot)\) \(\chi_{5269}(128,\cdot)\) \(\chi_{5269}(138,\cdot)\) \(\chi_{5269}(139,\cdot)\) \(\chi_{5269}(140,\cdot)\) \(\chi_{5269}(150,\cdot)\) \(\chi_{5269}(151,\cdot)\) \(\chi_{5269}(160,\cdot)\) \(\chi_{5269}(161,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1195})$ |
| Fixed field: | Number field defined by a degree 2390 polynomial (not computed) |
Values on generators
\((959,4324)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{168}{239}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 5269 }(35, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1339}{2390}\right)\) | \(e\left(\frac{366}{1195}\right)\) | \(e\left(\frac{144}{1195}\right)\) | \(e\left(\frac{708}{1195}\right)\) | \(e\left(\frac{2071}{2390}\right)\) | \(e\left(\frac{1653}{2390}\right)\) | \(e\left(\frac{1627}{2390}\right)\) | \(e\left(\frac{732}{1195}\right)\) | \(e\left(\frac{73}{478}\right)\) | \(e\left(\frac{102}{239}\right)\) |