Basic properties
| Modulus: | \(5776\) | |
| Conductor: | \(1444\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1444}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5776.cd
\(\chi_{5776}(31,\cdot)\) \(\chi_{5776}(255,\cdot)\) \(\chi_{5776}(335,\cdot)\) \(\chi_{5776}(559,\cdot)\) \(\chi_{5776}(639,\cdot)\) \(\chi_{5776}(863,\cdot)\) \(\chi_{5776}(943,\cdot)\) \(\chi_{5776}(1167,\cdot)\) \(\chi_{5776}(1247,\cdot)\) \(\chi_{5776}(1471,\cdot)\) \(\chi_{5776}(1551,\cdot)\) \(\chi_{5776}(1775,\cdot)\) \(\chi_{5776}(1855,\cdot)\) \(\chi_{5776}(2079,\cdot)\) \(\chi_{5776}(2159,\cdot)\) \(\chi_{5776}(2383,\cdot)\) \(\chi_{5776}(2463,\cdot)\) \(\chi_{5776}(2687,\cdot)\) \(\chi_{5776}(2767,\cdot)\) \(\chi_{5776}(2991,\cdot)\) \(\chi_{5776}(3071,\cdot)\) \(\chi_{5776}(3295,\cdot)\) \(\chi_{5776}(3375,\cdot)\) \(\chi_{5776}(3599,\cdot)\) \(\chi_{5776}(3983,\cdot)\) \(\chi_{5776}(4207,\cdot)\) \(\chi_{5776}(4287,\cdot)\) \(\chi_{5776}(4511,\cdot)\) \(\chi_{5776}(4591,\cdot)\) \(\chi_{5776}(4815,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((5055,1445,2529)\) → \((-1,1,e\left(\frac{101}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 5776 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{97}{114}\right)\) |