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 \(\chi_{608}(51,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3040.gd
\(\chi_{3040}(51,\cdot)\) \(\chi_{3040}(91,\cdot)\) \(\chi_{3040}(211,\cdot)\) \(\chi_{3040}(371,\cdot)\) \(\chi_{3040}(451,\cdot)\) \(\chi_{3040}(611,\cdot)\) \(\chi_{3040}(811,\cdot)\) \(\chi_{3040}(851,\cdot)\) \(\chi_{3040}(971,\cdot)\) \(\chi_{3040}(1131,\cdot)\) \(\chi_{3040}(1211,\cdot)\) \(\chi_{3040}(1371,\cdot)\) \(\chi_{3040}(1571,\cdot)\) \(\chi_{3040}(1611,\cdot)\) \(\chi_{3040}(1731,\cdot)\) \(\chi_{3040}(1891,\cdot)\) \(\chi_{3040}(1971,\cdot)\) \(\chi_{3040}(2131,\cdot)\) \(\chi_{3040}(2331,\cdot)\) \(\chi_{3040}(2371,\cdot)\) \(\chi_{3040}(2491,\cdot)\) \(\chi_{3040}(2651,\cdot)\) \(\chi_{3040}(2731,\cdot)\) \(\chi_{3040}(2891,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,2661,1217,1921)\) → \((-1,e\left(\frac{7}{8}\right),1,e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3040 }(51, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{25}{72}\right)\) |