Basic properties
| Modulus: | \(5082\) | |
| Conductor: | \(363\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{363}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5082.by
\(\chi_{5082}(29,\cdot)\) \(\chi_{5082}(281,\cdot)\) \(\chi_{5082}(365,\cdot)\) \(\chi_{5082}(491,\cdot)\) \(\chi_{5082}(701,\cdot)\) \(\chi_{5082}(743,\cdot)\) \(\chi_{5082}(827,\cdot)\) \(\chi_{5082}(953,\cdot)\) \(\chi_{5082}(1163,\cdot)\) \(\chi_{5082}(1205,\cdot)\) \(\chi_{5082}(1289,\cdot)\) \(\chi_{5082}(1415,\cdot)\) \(\chi_{5082}(1625,\cdot)\) \(\chi_{5082}(1751,\cdot)\) \(\chi_{5082}(1877,\cdot)\) \(\chi_{5082}(2087,\cdot)\) \(\chi_{5082}(2129,\cdot)\) \(\chi_{5082}(2213,\cdot)\) \(\chi_{5082}(2549,\cdot)\) \(\chi_{5082}(2591,\cdot)\) \(\chi_{5082}(2675,\cdot)\) \(\chi_{5082}(2801,\cdot)\) \(\chi_{5082}(3011,\cdot)\) \(\chi_{5082}(3053,\cdot)\) \(\chi_{5082}(3263,\cdot)\) \(\chi_{5082}(3473,\cdot)\) \(\chi_{5082}(3515,\cdot)\) \(\chi_{5082}(3599,\cdot)\) \(\chi_{5082}(3725,\cdot)\) \(\chi_{5082}(3935,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3389,4357,2059)\) → \((-1,1,e\left(\frac{17}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5082 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{91}{110}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{3}{55}\right)\) |