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.gb
\(\chi_{3040}(59,\cdot)\) \(\chi_{3040}(219,\cdot)\) \(\chi_{3040}(299,\cdot)\) \(\chi_{3040}(459,\cdot)\) \(\chi_{3040}(659,\cdot)\) \(\chi_{3040}(699,\cdot)\) \(\chi_{3040}(819,\cdot)\) \(\chi_{3040}(979,\cdot)\) \(\chi_{3040}(1059,\cdot)\) \(\chi_{3040}(1219,\cdot)\) \(\chi_{3040}(1419,\cdot)\) \(\chi_{3040}(1459,\cdot)\) \(\chi_{3040}(1579,\cdot)\) \(\chi_{3040}(1739,\cdot)\) \(\chi_{3040}(1819,\cdot)\) \(\chi_{3040}(1979,\cdot)\) \(\chi_{3040}(2179,\cdot)\) \(\chi_{3040}(2219,\cdot)\) \(\chi_{3040}(2339,\cdot)\) \(\chi_{3040}(2499,\cdot)\) \(\chi_{3040}(2579,\cdot)\) \(\chi_{3040}(2739,\cdot)\) \(\chi_{3040}(2939,\cdot)\) \(\chi_{3040}(2979,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,2661,1217,1921)\) → \((-1,e\left(\frac{1}{8}\right),-1,e\left(\frac{1}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3040 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{49}{72}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{23}{72}\right)\) |