Basic properties
| Modulus: | \(2805\) | |
| Conductor: | \(2805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2805.fj
\(\chi_{2805}(14,\cdot)\) \(\chi_{2805}(224,\cdot)\) \(\chi_{2805}(269,\cdot)\) \(\chi_{2805}(284,\cdot)\) \(\chi_{2805}(449,\cdot)\) \(\chi_{2805}(554,\cdot)\) \(\chi_{2805}(674,\cdot)\) \(\chi_{2805}(719,\cdot)\) \(\chi_{2805}(779,\cdot)\) \(\chi_{2805}(839,\cdot)\) \(\chi_{2805}(929,\cdot)\) \(\chi_{2805}(1049,\cdot)\) \(\chi_{2805}(1094,\cdot)\) \(\chi_{2805}(1214,\cdot)\) \(\chi_{2805}(1439,\cdot)\) \(\chi_{2805}(1499,\cdot)\) \(\chi_{2805}(1544,\cdot)\) \(\chi_{2805}(1604,\cdot)\) \(\chi_{2805}(1754,\cdot)\) \(\chi_{2805}(1829,\cdot)\) \(\chi_{2805}(1994,\cdot)\) \(\chi_{2805}(2084,\cdot)\) \(\chi_{2805}(2204,\cdot)\) \(\chi_{2805}(2249,\cdot)\) \(\chi_{2805}(2264,\cdot)\) \(\chi_{2805}(2324,\cdot)\) \(\chi_{2805}(2369,\cdot)\) \(\chi_{2805}(2489,\cdot)\) \(\chi_{2805}(2579,\cdot)\) \(\chi_{2805}(2594,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,562,1531,496)\) → \((-1,-1,e\left(\frac{4}{5}\right),e\left(\frac{9}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(19\) | \(23\) | \(26\) |
| \( \chi_{ 2805 }(14, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{9}{40}\right)\) |