Basic properties
| Modulus: | \(1805\) | |
| Conductor: | \(1805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(76\) | 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 1805.x
\(\chi_{1805}(18,\cdot)\) \(\chi_{1805}(37,\cdot)\) \(\chi_{1805}(113,\cdot)\) \(\chi_{1805}(132,\cdot)\) \(\chi_{1805}(208,\cdot)\) \(\chi_{1805}(227,\cdot)\) \(\chi_{1805}(303,\cdot)\) \(\chi_{1805}(322,\cdot)\) \(\chi_{1805}(398,\cdot)\) \(\chi_{1805}(417,\cdot)\) \(\chi_{1805}(493,\cdot)\) \(\chi_{1805}(512,\cdot)\) \(\chi_{1805}(588,\cdot)\) \(\chi_{1805}(607,\cdot)\) \(\chi_{1805}(683,\cdot)\) \(\chi_{1805}(702,\cdot)\) \(\chi_{1805}(778,\cdot)\) \(\chi_{1805}(797,\cdot)\) \(\chi_{1805}(873,\cdot)\) \(\chi_{1805}(892,\cdot)\) \(\chi_{1805}(968,\cdot)\) \(\chi_{1805}(987,\cdot)\) \(\chi_{1805}(1063,\cdot)\) \(\chi_{1805}(1158,\cdot)\) \(\chi_{1805}(1177,\cdot)\) \(\chi_{1805}(1253,\cdot)\) \(\chi_{1805}(1272,\cdot)\) \(\chi_{1805}(1348,\cdot)\) \(\chi_{1805}(1367,\cdot)\) \(\chi_{1805}(1462,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{76})$ |
| Fixed field: | Number field defined by a degree 76 polynomial |
Values on generators
\((362,1446)\) → \((i,e\left(\frac{1}{38}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1805 }(512, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{76}\right)\) | \(e\left(\frac{31}{76}\right)\) | \(e\left(\frac{21}{38}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{15}{76}\right)\) | \(e\left(\frac{63}{76}\right)\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{73}{76}\right)\) | \(e\left(\frac{31}{76}\right)\) |