Basic properties
Modulus: | \(1870\) | |
Conductor: | \(935\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{935}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1870.cs
\(\chi_{1870}(3,\cdot)\) \(\chi_{1870}(27,\cdot)\) \(\chi_{1870}(147,\cdot)\) \(\chi_{1870}(317,\cdot)\) \(\chi_{1870}(367,\cdot)\) \(\chi_{1870}(487,\cdot)\) \(\chi_{1870}(537,\cdot)\) \(\chi_{1870}(643,\cdot)\) \(\chi_{1870}(687,\cdot)\) \(\chi_{1870}(707,\cdot)\) \(\chi_{1870}(753,\cdot)\) \(\chi_{1870}(907,\cdot)\) \(\chi_{1870}(983,\cdot)\) \(\chi_{1870}(1027,\cdot)\) \(\chi_{1870}(1083,\cdot)\) \(\chi_{1870}(1093,\cdot)\) \(\chi_{1870}(1153,\cdot)\) \(\chi_{1870}(1193,\cdot)\) \(\chi_{1870}(1197,\cdot)\) \(\chi_{1870}(1247,\cdot)\) \(\chi_{1870}(1263,\cdot)\) \(\chi_{1870}(1323,\cdot)\) \(\chi_{1870}(1367,\cdot)\) \(\chi_{1870}(1417,\cdot)\) \(\chi_{1870}(1423,\cdot)\) \(\chi_{1870}(1433,\cdot)\) \(\chi_{1870}(1533,\cdot)\) \(\chi_{1870}(1587,\cdot)\) \(\chi_{1870}(1593,\cdot)\) \(\chi_{1870}(1677,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1497,1531,1431)\) → \((-i,e\left(\frac{4}{5}\right),e\left(\frac{1}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 1870 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(-i\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{29}{80}\right)\) |