Basic properties
| Modulus: | \(2805\) | |
| Conductor: | \(187\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{187}(184,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2805.fg
\(\chi_{2805}(46,\cdot)\) \(\chi_{2805}(61,\cdot)\) \(\chi_{2805}(211,\cdot)\) \(\chi_{2805}(226,\cdot)\) \(\chi_{2805}(316,\cdot)\) \(\chi_{2805}(436,\cdot)\) \(\chi_{2805}(481,\cdot)\) \(\chi_{2805}(541,\cdot)\) \(\chi_{2805}(556,\cdot)\) \(\chi_{2805}(601,\cdot)\) \(\chi_{2805}(721,\cdot)\) \(\chi_{2805}(811,\cdot)\) \(\chi_{2805}(976,\cdot)\) \(\chi_{2805}(1051,\cdot)\) \(\chi_{2805}(1201,\cdot)\) \(\chi_{2805}(1261,\cdot)\) \(\chi_{2805}(1306,\cdot)\) \(\chi_{2805}(1366,\cdot)\) \(\chi_{2805}(1591,\cdot)\) \(\chi_{2805}(1711,\cdot)\) \(\chi_{2805}(1756,\cdot)\) \(\chi_{2805}(1876,\cdot)\) \(\chi_{2805}(1966,\cdot)\) \(\chi_{2805}(2026,\cdot)\) \(\chi_{2805}(2086,\cdot)\) \(\chi_{2805}(2131,\cdot)\) \(\chi_{2805}(2251,\cdot)\) \(\chi_{2805}(2356,\cdot)\) \(\chi_{2805}(2521,\cdot)\) \(\chi_{2805}(2536,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,562,1531,496)\) → \((1,1,e\left(\frac{3}{10}\right),e\left(\frac{9}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(19\) | \(23\) | \(26\) |
| \( \chi_{ 2805 }(1306, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{29}{40}\right)\) |