Basic properties
| Modulus: | \(5577\) | |
| Conductor: | \(1859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1859}(76,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5577.da
\(\chi_{5577}(76,\cdot)\) \(\chi_{5577}(175,\cdot)\) \(\chi_{5577}(241,\cdot)\) \(\chi_{5577}(340,\cdot)\) \(\chi_{5577}(505,\cdot)\) \(\chi_{5577}(604,\cdot)\) \(\chi_{5577}(670,\cdot)\) \(\chi_{5577}(769,\cdot)\) \(\chi_{5577}(1099,\cdot)\) \(\chi_{5577}(1198,\cdot)\) \(\chi_{5577}(1363,\cdot)\) \(\chi_{5577}(1462,\cdot)\) \(\chi_{5577}(1528,\cdot)\) \(\chi_{5577}(1627,\cdot)\) \(\chi_{5577}(1792,\cdot)\) \(\chi_{5577}(1891,\cdot)\) \(\chi_{5577}(1957,\cdot)\) \(\chi_{5577}(2056,\cdot)\) \(\chi_{5577}(2221,\cdot)\) \(\chi_{5577}(2320,\cdot)\) \(\chi_{5577}(2386,\cdot)\) \(\chi_{5577}(2485,\cdot)\) \(\chi_{5577}(2650,\cdot)\) \(\chi_{5577}(2749,\cdot)\) \(\chi_{5577}(2815,\cdot)\) \(\chi_{5577}(2914,\cdot)\) \(\chi_{5577}(3079,\cdot)\) \(\chi_{5577}(3178,\cdot)\) \(\chi_{5577}(3244,\cdot)\) \(\chi_{5577}(3343,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((3719,508,1354)\) → \((1,-1,e\left(\frac{67}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 5577 }(76, a) \) | \(1\) | \(1\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{71}{156}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{5}{12}\right)\) |