Basic properties
| Modulus: | \(5776\) | |
| Conductor: | \(5776\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(684\) | 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 5776.ct
\(\chi_{5776}(3,\cdot)\) \(\chi_{5776}(51,\cdot)\) \(\chi_{5776}(59,\cdot)\) \(\chi_{5776}(67,\cdot)\) \(\chi_{5776}(91,\cdot)\) \(\chi_{5776}(147,\cdot)\) \(\chi_{5776}(155,\cdot)\) \(\chi_{5776}(203,\cdot)\) \(\chi_{5776}(211,\cdot)\) \(\chi_{5776}(219,\cdot)\) \(\chi_{5776}(243,\cdot)\) \(\chi_{5776}(355,\cdot)\) \(\chi_{5776}(363,\cdot)\) \(\chi_{5776}(371,\cdot)\) \(\chi_{5776}(395,\cdot)\) \(\chi_{5776}(451,\cdot)\) \(\chi_{5776}(459,\cdot)\) \(\chi_{5776}(507,\cdot)\) \(\chi_{5776}(515,\cdot)\) \(\chi_{5776}(523,\cdot)\) \(\chi_{5776}(547,\cdot)\) \(\chi_{5776}(603,\cdot)\) \(\chi_{5776}(611,\cdot)\) \(\chi_{5776}(659,\cdot)\) \(\chi_{5776}(667,\cdot)\) \(\chi_{5776}(675,\cdot)\) \(\chi_{5776}(699,\cdot)\) \(\chi_{5776}(755,\cdot)\) \(\chi_{5776}(763,\cdot)\) \(\chi_{5776}(811,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{684})$ |
| Fixed field: | Number field defined by a degree 684 polynomial (not computed) |
Values on generators
\((5055,1445,2529)\) → \((-1,-i,e\left(\frac{139}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 5776 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{167}{684}\right)\) | \(e\left(\frac{29}{684}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{167}{342}\right)\) | \(e\left(\frac{161}{228}\right)\) | \(e\left(\frac{661}{684}\right)\) | \(e\left(\frac{49}{171}\right)\) | \(e\left(\frac{146}{171}\right)\) | \(e\left(\frac{143}{684}\right)\) | \(e\left(\frac{58}{171}\right)\) |