Basic properties
| Modulus: | \(3200\) | |
| Conductor: | \(3200\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(160\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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 3200.df
\(\chi_{3200}(29,\cdot)\) \(\chi_{3200}(69,\cdot)\) \(\chi_{3200}(109,\cdot)\) \(\chi_{3200}(189,\cdot)\) \(\chi_{3200}(229,\cdot)\) \(\chi_{3200}(269,\cdot)\) \(\chi_{3200}(309,\cdot)\) \(\chi_{3200}(389,\cdot)\) \(\chi_{3200}(429,\cdot)\) \(\chi_{3200}(469,\cdot)\) \(\chi_{3200}(509,\cdot)\) \(\chi_{3200}(589,\cdot)\) \(\chi_{3200}(629,\cdot)\) \(\chi_{3200}(669,\cdot)\) \(\chi_{3200}(709,\cdot)\) \(\chi_{3200}(789,\cdot)\) \(\chi_{3200}(829,\cdot)\) \(\chi_{3200}(869,\cdot)\) \(\chi_{3200}(909,\cdot)\) \(\chi_{3200}(989,\cdot)\) \(\chi_{3200}(1029,\cdot)\) \(\chi_{3200}(1069,\cdot)\) \(\chi_{3200}(1109,\cdot)\) \(\chi_{3200}(1189,\cdot)\) \(\chi_{3200}(1229,\cdot)\) \(\chi_{3200}(1269,\cdot)\) \(\chi_{3200}(1309,\cdot)\) \(\chi_{3200}(1389,\cdot)\) \(\chi_{3200}(1429,\cdot)\) \(\chi_{3200}(1469,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{160})$ |
| Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((1151,901,2177)\) → \((1,e\left(\frac{27}{32}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 3200 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{160}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{51}{160}\right)\) | \(e\left(\frac{89}{160}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{33}{160}\right)\) | \(e\left(\frac{27}{160}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{111}{160}\right)\) |