Basic properties
| Modulus: | \(20627\) | |
| Conductor: | \(20627\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(20626\) | 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 20627.d
\(\chi_{20627}(2,\cdot)\) \(\chi_{20627}(5,\cdot)\) \(\chi_{20627}(6,\cdot)\) \(\chi_{20627}(8,\cdot)\) \(\chi_{20627}(14,\cdot)\) \(\chi_{20627}(15,\cdot)\) \(\chi_{20627}(17,\cdot)\) \(\chi_{20627}(18,\cdot)\) \(\chi_{20627}(20,\cdot)\) \(\chi_{20627}(22,\cdot)\) \(\chi_{20627}(24,\cdot)\) \(\chi_{20627}(26,\cdot)\) \(\chi_{20627}(29,\cdot)\) \(\chi_{20627}(32,\cdot)\) \(\chi_{20627}(35,\cdot)\) \(\chi_{20627}(37,\cdot)\) \(\chi_{20627}(38,\cdot)\) \(\chi_{20627}(42,\cdot)\) \(\chi_{20627}(45,\cdot)\) \(\chi_{20627}(46,\cdot)\) \(\chi_{20627}(50,\cdot)\) \(\chi_{20627}(51,\cdot)\) \(\chi_{20627}(54,\cdot)\) \(\chi_{20627}(55,\cdot)\) \(\chi_{20627}(56,\cdot)\) \(\chi_{20627}(59,\cdot)\) \(\chi_{20627}(60,\cdot)\) \(\chi_{20627}(62,\cdot)\) \(\chi_{20627}(65,\cdot)\) \(\chi_{20627}(66,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{10313})$ |
| Fixed field: | Number field defined by a degree 20626 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{20626}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 20627 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{20626}\right)\) | \(e\left(\frac{6751}{10313}\right)\) | \(e\left(\frac{1}{10313}\right)\) | \(e\left(\frac{19543}{20626}\right)\) | \(e\left(\frac{13503}{20626}\right)\) | \(e\left(\frac{9248}{10313}\right)\) | \(e\left(\frac{3}{20626}\right)\) | \(e\left(\frac{3189}{10313}\right)\) | \(e\left(\frac{9772}{10313}\right)\) | \(e\left(\frac{572}{10313}\right)\) |