Basic properties
| Modulus: | \(3040\) | |
| Conductor: | \(608\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{608}(461,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3040.ga
\(\chi_{3040}(61,\cdot)\) \(\chi_{3040}(101,\cdot)\) \(\chi_{3040}(301,\cdot)\) \(\chi_{3040}(461,\cdot)\) \(\chi_{3040}(541,\cdot)\) \(\chi_{3040}(701,\cdot)\) \(\chi_{3040}(821,\cdot)\) \(\chi_{3040}(861,\cdot)\) \(\chi_{3040}(1061,\cdot)\) \(\chi_{3040}(1221,\cdot)\) \(\chi_{3040}(1301,\cdot)\) \(\chi_{3040}(1461,\cdot)\) \(\chi_{3040}(1581,\cdot)\) \(\chi_{3040}(1621,\cdot)\) \(\chi_{3040}(1821,\cdot)\) \(\chi_{3040}(1981,\cdot)\) \(\chi_{3040}(2061,\cdot)\) \(\chi_{3040}(2221,\cdot)\) \(\chi_{3040}(2341,\cdot)\) \(\chi_{3040}(2381,\cdot)\) \(\chi_{3040}(2581,\cdot)\) \(\chi_{3040}(2741,\cdot)\) \(\chi_{3040}(2821,\cdot)\) \(\chi_{3040}(2981,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,2661,1217,1921)\) → \((1,e\left(\frac{7}{8}\right),1,e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3040 }(461, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{41}{72}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{53}{72}\right)\) |