Basic properties
Modulus: | \(1805\) | |
Conductor: | \(1805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.ba
\(\chi_{1805}(49,\cdot)\) \(\chi_{1805}(64,\cdot)\) \(\chi_{1805}(144,\cdot)\) \(\chi_{1805}(159,\cdot)\) \(\chi_{1805}(239,\cdot)\) \(\chi_{1805}(254,\cdot)\) \(\chi_{1805}(334,\cdot)\) \(\chi_{1805}(349,\cdot)\) \(\chi_{1805}(444,\cdot)\) \(\chi_{1805}(524,\cdot)\) \(\chi_{1805}(539,\cdot)\) \(\chi_{1805}(619,\cdot)\) \(\chi_{1805}(634,\cdot)\) \(\chi_{1805}(714,\cdot)\) \(\chi_{1805}(729,\cdot)\) \(\chi_{1805}(809,\cdot)\) \(\chi_{1805}(824,\cdot)\) \(\chi_{1805}(904,\cdot)\) \(\chi_{1805}(919,\cdot)\) \(\chi_{1805}(999,\cdot)\) \(\chi_{1805}(1094,\cdot)\) \(\chi_{1805}(1109,\cdot)\) \(\chi_{1805}(1189,\cdot)\) \(\chi_{1805}(1204,\cdot)\) \(\chi_{1805}(1284,\cdot)\) \(\chi_{1805}(1299,\cdot)\) \(\chi_{1805}(1379,\cdot)\) \(\chi_{1805}(1394,\cdot)\) \(\chi_{1805}(1474,\cdot)\) \(\chi_{1805}(1489,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((362,1446)\) → \((-1,e\left(\frac{14}{57}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 1805 }(1189, a) \) | \(1\) | \(1\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{73}{114}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{35}{114}\right)\) |