Basic properties
| Modulus: | \(3040\) | |
| Conductor: | \(3040\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | 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 3040.gk
\(\chi_{3040}(43,\cdot)\) \(\chi_{3040}(123,\cdot)\) \(\chi_{3040}(283,\cdot)\) \(\chi_{3040}(443,\cdot)\) \(\chi_{3040}(707,\cdot)\) \(\chi_{3040}(947,\cdot)\) \(\chi_{3040}(1107,\cdot)\) \(\chi_{3040}(1163,\cdot)\) \(\chi_{3040}(1187,\cdot)\) \(\chi_{3040}(1347,\cdot)\) \(\chi_{3040}(1403,\cdot)\) \(\chi_{3040}(1507,\cdot)\) \(\chi_{3040}(1563,\cdot)\) \(\chi_{3040}(1643,\cdot)\) \(\chi_{3040}(1803,\cdot)\) \(\chi_{3040}(1963,\cdot)\) \(\chi_{3040}(2227,\cdot)\) \(\chi_{3040}(2467,\cdot)\) \(\chi_{3040}(2627,\cdot)\) \(\chi_{3040}(2683,\cdot)\) \(\chi_{3040}(2707,\cdot)\) \(\chi_{3040}(2867,\cdot)\) \(\chi_{3040}(2923,\cdot)\) \(\chi_{3040}(3027,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,2661,1217,1921)\) → \((-1,e\left(\frac{5}{8}\right),-i,e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3040 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{1}{72}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{35}{72}\right)\) |