Basic properties
| Modulus: | \(5390\) | |
| Conductor: | \(2695\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2695}(417,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5390.cy
\(\chi_{5390}(417,\cdot)\) \(\chi_{5390}(527,\cdot)\) \(\chi_{5390}(1033,\cdot)\) \(\chi_{5390}(1143,\cdot)\) \(\chi_{5390}(1187,\cdot)\) \(\chi_{5390}(1297,\cdot)\) \(\chi_{5390}(1803,\cdot)\) \(\chi_{5390}(1913,\cdot)\) \(\chi_{5390}(1957,\cdot)\) \(\chi_{5390}(2067,\cdot)\) \(\chi_{5390}(2573,\cdot)\) \(\chi_{5390}(2683,\cdot)\) \(\chi_{5390}(2727,\cdot)\) \(\chi_{5390}(2837,\cdot)\) \(\chi_{5390}(3343,\cdot)\) \(\chi_{5390}(3453,\cdot)\) \(\chi_{5390}(4113,\cdot)\) \(\chi_{5390}(4223,\cdot)\) \(\chi_{5390}(4267,\cdot)\) \(\chi_{5390}(4377,\cdot)\) \(\chi_{5390}(4883,\cdot)\) \(\chi_{5390}(4993,\cdot)\) \(\chi_{5390}(5037,\cdot)\) \(\chi_{5390}(5147,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2157,4511,981)\) → \((i,e\left(\frac{8}{21}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 5390 }(417, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{37}{84}\right)\) |