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 \(\chi_{1600}(723,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3200.cu
\(\chi_{3200}(23,\cdot)\) \(\chi_{3200}(167,\cdot)\) \(\chi_{3200}(183,\cdot)\) \(\chi_{3200}(327,\cdot)\) \(\chi_{3200}(487,\cdot)\) \(\chi_{3200}(503,\cdot)\) \(\chi_{3200}(647,\cdot)\) \(\chi_{3200}(663,\cdot)\) \(\chi_{3200}(823,\cdot)\) \(\chi_{3200}(967,\cdot)\) \(\chi_{3200}(983,\cdot)\) \(\chi_{3200}(1127,\cdot)\) \(\chi_{3200}(1287,\cdot)\) \(\chi_{3200}(1303,\cdot)\) \(\chi_{3200}(1447,\cdot)\) \(\chi_{3200}(1463,\cdot)\) \(\chi_{3200}(1623,\cdot)\) \(\chi_{3200}(1767,\cdot)\) \(\chi_{3200}(1783,\cdot)\) \(\chi_{3200}(1927,\cdot)\) \(\chi_{3200}(2087,\cdot)\) \(\chi_{3200}(2103,\cdot)\) \(\chi_{3200}(2247,\cdot)\) \(\chi_{3200}(2263,\cdot)\) \(\chi_{3200}(2423,\cdot)\) \(\chi_{3200}(2567,\cdot)\) \(\chi_{3200}(2583,\cdot)\) \(\chi_{3200}(2727,\cdot)\) \(\chi_{3200}(2887,\cdot)\) \(\chi_{3200}(2903,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1151,901,2177)\) → \((-1,e\left(\frac{7}{16}\right),e\left(\frac{11}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 3200 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{79}{80}\right)\) |