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.cr
\(\chi_{5776}(5,\cdot)\) \(\chi_{5776}(61,\cdot)\) \(\chi_{5776}(85,\cdot)\) \(\chi_{5776}(93,\cdot)\) \(\chi_{5776}(101,\cdot)\) \(\chi_{5776}(149,\cdot)\) \(\chi_{5776}(157,\cdot)\) \(\chi_{5776}(213,\cdot)\) \(\chi_{5776}(237,\cdot)\) \(\chi_{5776}(253,\cdot)\) \(\chi_{5776}(301,\cdot)\) \(\chi_{5776}(309,\cdot)\) \(\chi_{5776}(365,\cdot)\) \(\chi_{5776}(397,\cdot)\) \(\chi_{5776}(405,\cdot)\) \(\chi_{5776}(453,\cdot)\) \(\chi_{5776}(461,\cdot)\) \(\chi_{5776}(517,\cdot)\) \(\chi_{5776}(541,\cdot)\) \(\chi_{5776}(549,\cdot)\) \(\chi_{5776}(557,\cdot)\) \(\chi_{5776}(605,\cdot)\) \(\chi_{5776}(613,\cdot)\) \(\chi_{5776}(669,\cdot)\) \(\chi_{5776}(693,\cdot)\) \(\chi_{5776}(701,\cdot)\) \(\chi_{5776}(709,\cdot)\) \(\chi_{5776}(757,\cdot)\) \(\chi_{5776}(765,\cdot)\) \(\chi_{5776}(845,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{684})$ |
| Fixed field: | Number field defined by a degree 684 polynomial (not computed) |
Values on generators
\((5055,1445,2529)\) → \((1,i,e\left(\frac{116}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 5776 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{684}\right)\) | \(e\left(\frac{431}{684}\right)\) | \(e\left(\frac{29}{114}\right)\) | \(e\left(\frac{29}{342}\right)\) | \(e\left(\frac{101}{228}\right)\) | \(e\left(\frac{637}{684}\right)\) | \(e\left(\frac{115}{171}\right)\) | \(e\left(\frac{53}{171}\right)\) | \(e\left(\frac{203}{684}\right)\) | \(e\left(\frac{185}{342}\right)\) |