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 \(\chi_{1600}(509,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3200.cy
\(\chi_{3200}(9,\cdot)\) \(\chi_{3200}(89,\cdot)\) \(\chi_{3200}(169,\cdot)\) \(\chi_{3200}(329,\cdot)\) \(\chi_{3200}(409,\cdot)\) \(\chi_{3200}(489,\cdot)\) \(\chi_{3200}(569,\cdot)\) \(\chi_{3200}(729,\cdot)\) \(\chi_{3200}(809,\cdot)\) \(\chi_{3200}(889,\cdot)\) \(\chi_{3200}(969,\cdot)\) \(\chi_{3200}(1129,\cdot)\) \(\chi_{3200}(1209,\cdot)\) \(\chi_{3200}(1289,\cdot)\) \(\chi_{3200}(1369,\cdot)\) \(\chi_{3200}(1529,\cdot)\) \(\chi_{3200}(1609,\cdot)\) \(\chi_{3200}(1689,\cdot)\) \(\chi_{3200}(1769,\cdot)\) \(\chi_{3200}(1929,\cdot)\) \(\chi_{3200}(2009,\cdot)\) \(\chi_{3200}(2089,\cdot)\) \(\chi_{3200}(2169,\cdot)\) \(\chi_{3200}(2329,\cdot)\) \(\chi_{3200}(2409,\cdot)\) \(\chi_{3200}(2489,\cdot)\) \(\chi_{3200}(2569,\cdot)\) \(\chi_{3200}(2729,\cdot)\) \(\chi_{3200}(2809,\cdot)\) \(\chi_{3200}(2889,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1151,901,2177)\) → \((1,e\left(\frac{3}{16}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 3200 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{31}{80}\right)\) |