Basic properties
| Modulus: | \(5077\) | |
| Conductor: | \(5077\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(423\) | 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 5077.r
\(\chi_{5077}(9,\cdot)\) \(\chi_{5077}(40,\cdot)\) \(\chi_{5077}(65,\cdot)\) \(\chi_{5077}(66,\cdot)\) \(\chi_{5077}(74,\cdot)\) \(\chi_{5077}(75,\cdot)\) \(\chi_{5077}(81,\cdot)\) \(\chi_{5077}(84,\cdot)\) \(\chi_{5077}(115,\cdot)\) \(\chi_{5077}(159,\cdot)\) \(\chi_{5077}(179,\cdot)\) \(\chi_{5077}(181,\cdot)\) \(\chi_{5077}(190,\cdot)\) \(\chi_{5077}(192,\cdot)\) \(\chi_{5077}(211,\cdot)\) \(\chi_{5077}(241,\cdot)\) \(\chi_{5077}(244,\cdot)\) \(\chi_{5077}(269,\cdot)\) \(\chi_{5077}(277,\cdot)\) \(\chi_{5077}(283,\cdot)\) \(\chi_{5077}(312,\cdot)\) \(\chi_{5077}(316,\cdot)\) \(\chi_{5077}(327,\cdot)\) \(\chi_{5077}(339,\cdot)\) \(\chi_{5077}(343,\cdot)\) \(\chi_{5077}(383,\cdot)\) \(\chi_{5077}(399,\cdot)\) \(\chi_{5077}(434,\cdot)\) \(\chi_{5077}(435,\cdot)\) \(\chi_{5077}(507,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{423})$ |
| Fixed field: | Number field defined by a degree 423 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{304}{423}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 5077 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{304}{423}\right)\) | \(e\left(\frac{122}{141}\right)\) | \(e\left(\frac{185}{423}\right)\) | \(e\left(\frac{21}{47}\right)\) | \(e\left(\frac{247}{423}\right)\) | \(e\left(\frac{10}{423}\right)\) | \(e\left(\frac{22}{141}\right)\) | \(e\left(\frac{103}{141}\right)\) | \(e\left(\frac{70}{423}\right)\) | \(e\left(\frac{389}{423}\right)\) |