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 \(\chi_{1600}(1373,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3200.cv
\(\chi_{3200}(73,\cdot)\) \(\chi_{3200}(217,\cdot)\) \(\chi_{3200}(233,\cdot)\) \(\chi_{3200}(377,\cdot)\) \(\chi_{3200}(537,\cdot)\) \(\chi_{3200}(553,\cdot)\) \(\chi_{3200}(697,\cdot)\) \(\chi_{3200}(713,\cdot)\) \(\chi_{3200}(873,\cdot)\) \(\chi_{3200}(1017,\cdot)\) \(\chi_{3200}(1033,\cdot)\) \(\chi_{3200}(1177,\cdot)\) \(\chi_{3200}(1337,\cdot)\) \(\chi_{3200}(1353,\cdot)\) \(\chi_{3200}(1497,\cdot)\) \(\chi_{3200}(1513,\cdot)\) \(\chi_{3200}(1673,\cdot)\) \(\chi_{3200}(1817,\cdot)\) \(\chi_{3200}(1833,\cdot)\) \(\chi_{3200}(1977,\cdot)\) \(\chi_{3200}(2137,\cdot)\) \(\chi_{3200}(2153,\cdot)\) \(\chi_{3200}(2297,\cdot)\) \(\chi_{3200}(2313,\cdot)\) \(\chi_{3200}(2473,\cdot)\) \(\chi_{3200}(2617,\cdot)\) \(\chi_{3200}(2633,\cdot)\) \(\chi_{3200}(2777,\cdot)\) \(\chi_{3200}(2937,\cdot)\) \(\chi_{3200}(2953,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1151,901,2177)\) → \((1,e\left(\frac{11}{16}\right),e\left(\frac{11}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 3200 }(73, a) \) | \(-1\) | \(1\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{59}{80}\right)\) |