Basic properties
| Modulus: | \(3200\) | |
| Conductor: | \(1600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1600}(141,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3200.cz
\(\chi_{3200}(41,\cdot)\) \(\chi_{3200}(121,\cdot)\) \(\chi_{3200}(281,\cdot)\) \(\chi_{3200}(361,\cdot)\) \(\chi_{3200}(441,\cdot)\) \(\chi_{3200}(521,\cdot)\) \(\chi_{3200}(681,\cdot)\) \(\chi_{3200}(761,\cdot)\) \(\chi_{3200}(841,\cdot)\) \(\chi_{3200}(921,\cdot)\) \(\chi_{3200}(1081,\cdot)\) \(\chi_{3200}(1161,\cdot)\) \(\chi_{3200}(1241,\cdot)\) \(\chi_{3200}(1321,\cdot)\) \(\chi_{3200}(1481,\cdot)\) \(\chi_{3200}(1561,\cdot)\) \(\chi_{3200}(1641,\cdot)\) \(\chi_{3200}(1721,\cdot)\) \(\chi_{3200}(1881,\cdot)\) \(\chi_{3200}(1961,\cdot)\) \(\chi_{3200}(2041,\cdot)\) \(\chi_{3200}(2121,\cdot)\) \(\chi_{3200}(2281,\cdot)\) \(\chi_{3200}(2361,\cdot)\) \(\chi_{3200}(2441,\cdot)\) \(\chi_{3200}(2521,\cdot)\) \(\chi_{3200}(2681,\cdot)\) \(\chi_{3200}(2761,\cdot)\) \(\chi_{3200}(2841,\cdot)\) \(\chi_{3200}(2921,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1151,901,2177)\) → \((1,e\left(\frac{15}{16}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 3200 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{51}{80}\right)\) |