Basic properties
| Modulus: | \(5077\) | |
| Conductor: | \(5077\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(564\) | 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 5077.s
\(\chi_{5077}(24,\cdot)\) \(\chi_{5077}(39,\cdot)\) \(\chi_{5077}(98,\cdot)\) \(\chi_{5077}(110,\cdot)\) \(\chi_{5077}(135,\cdot)\) \(\chi_{5077}(149,\cdot)\) \(\chi_{5077}(207,\cdot)\) \(\chi_{5077}(229,\cdot)\) \(\chi_{5077}(231,\cdot)\) \(\chi_{5077}(251,\cdot)\) \(\chi_{5077}(261,\cdot)\) \(\chi_{5077}(326,\cdot)\) \(\chi_{5077}(372,\cdot)\) \(\chi_{5077}(397,\cdot)\) \(\chi_{5077}(424,\cdot)\) \(\chi_{5077}(445,\cdot)\) \(\chi_{5077}(446,\cdot)\) \(\chi_{5077}(466,\cdot)\) \(\chi_{5077}(485,\cdot)\) \(\chi_{5077}(492,\cdot)\) \(\chi_{5077}(512,\cdot)\) \(\chi_{5077}(545,\cdot)\) \(\chi_{5077}(600,\cdot)\) \(\chi_{5077}(648,\cdot)\) \(\chi_{5077}(661,\cdot)\) \(\chi_{5077}(665,\cdot)\) \(\chi_{5077}(670,\cdot)\) \(\chi_{5077}(689,\cdot)\) \(\chi_{5077}(698,\cdot)\) \(\chi_{5077}(718,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{564})$ |
| Fixed field: | Number field defined by a degree 564 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{485}{564}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 5077 }(24, a) \) | \(-1\) | \(1\) | \(e\left(\frac{485}{564}\right)\) | \(e\left(\frac{1}{94}\right)\) | \(e\left(\frac{203}{282}\right)\) | \(e\left(\frac{75}{188}\right)\) | \(e\left(\frac{491}{564}\right)\) | \(e\left(\frac{116}{141}\right)\) | \(e\left(\frac{109}{188}\right)\) | \(e\left(\frac{1}{47}\right)\) | \(e\left(\frac{73}{282}\right)\) | \(e\left(\frac{481}{564}\right)\) |