Basic properties
| Modulus: | \(7840\) | |
| Conductor: | \(3920\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3920}(957,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7840.hf
\(\chi_{7840}(297,\cdot)\) \(\chi_{7840}(633,\cdot)\) \(\chi_{7840}(1417,\cdot)\) \(\chi_{7840}(1433,\cdot)\) \(\chi_{7840}(1753,\cdot)\) \(\chi_{7840}(2217,\cdot)\) \(\chi_{7840}(2537,\cdot)\) \(\chi_{7840}(2553,\cdot)\) \(\chi_{7840}(3337,\cdot)\) \(\chi_{7840}(3673,\cdot)\) \(\chi_{7840}(3993,\cdot)\) \(\chi_{7840}(4457,\cdot)\) \(\chi_{7840}(4777,\cdot)\) \(\chi_{7840}(4793,\cdot)\) \(\chi_{7840}(5113,\cdot)\) \(\chi_{7840}(5577,\cdot)\) \(\chi_{7840}(5897,\cdot)\) \(\chi_{7840}(5913,\cdot)\) \(\chi_{7840}(6233,\cdot)\) \(\chi_{7840}(6697,\cdot)\) \(\chi_{7840}(7017,\cdot)\) \(\chi_{7840}(7033,\cdot)\) \(\chi_{7840}(7353,\cdot)\) \(\chi_{7840}(7817,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,4901,3137,3041)\) → \((1,-i,i,e\left(\frac{17}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 7840 }(7817, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{5}{6}\right)\) |