Basic properties
| Modulus: | \(2805\) | |
| Conductor: | \(935\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{935}(278,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2805.fa
\(\chi_{2805}(37,\cdot)\) \(\chi_{2805}(58,\cdot)\) \(\chi_{2805}(82,\cdot)\) \(\chi_{2805}(97,\cdot)\) \(\chi_{2805}(163,\cdot)\) \(\chi_{2805}(313,\cdot)\) \(\chi_{2805}(532,\cdot)\) \(\chi_{2805}(592,\cdot)\) \(\chi_{2805}(823,\cdot)\) \(\chi_{2805}(862,\cdot)\) \(\chi_{2805}(928,\cdot)\) \(\chi_{2805}(1048,\cdot)\) \(\chi_{2805}(1213,\cdot)\) \(\chi_{2805}(1303,\cdot)\) \(\chi_{2805}(1312,\cdot)\) \(\chi_{2805}(1357,\cdot)\) \(\chi_{2805}(1468,\cdot)\) \(\chi_{2805}(1567,\cdot)\) \(\chi_{2805}(1588,\cdot)\) \(\chi_{2805}(1807,\cdot)\) \(\chi_{2805}(1813,\cdot)\) \(\chi_{2805}(1978,\cdot)\) \(\chi_{2805}(2062,\cdot)\) \(\chi_{2805}(2077,\cdot)\) \(\chi_{2805}(2137,\cdot)\) \(\chi_{2805}(2203,\cdot)\) \(\chi_{2805}(2392,\cdot)\) \(\chi_{2805}(2458,\cdot)\) \(\chi_{2805}(2572,\cdot)\) \(\chi_{2805}(2578,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,562,1531,496)\) → \((1,-i,e\left(\frac{4}{5}\right),e\left(\frac{15}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(19\) | \(23\) | \(26\) |
| \( \chi_{ 2805 }(1213, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{19}{40}\right)\) |