Basic properties
| Modulus: | \(7840\) | |
| Conductor: | \(7840\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(56\) | 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 7840.ha
\(\chi_{7840}(139,\cdot)\) \(\chi_{7840}(419,\cdot)\) \(\chi_{7840}(699,\cdot)\) \(\chi_{7840}(1259,\cdot)\) \(\chi_{7840}(1539,\cdot)\) \(\chi_{7840}(1819,\cdot)\) \(\chi_{7840}(2099,\cdot)\) \(\chi_{7840}(2379,\cdot)\) \(\chi_{7840}(2659,\cdot)\) \(\chi_{7840}(3219,\cdot)\) \(\chi_{7840}(3499,\cdot)\) \(\chi_{7840}(3779,\cdot)\) \(\chi_{7840}(4059,\cdot)\) \(\chi_{7840}(4339,\cdot)\) \(\chi_{7840}(4619,\cdot)\) \(\chi_{7840}(5179,\cdot)\) \(\chi_{7840}(5459,\cdot)\) \(\chi_{7840}(5739,\cdot)\) \(\chi_{7840}(6019,\cdot)\) \(\chi_{7840}(6299,\cdot)\) \(\chi_{7840}(6579,\cdot)\) \(\chi_{7840}(7139,\cdot)\) \(\chi_{7840}(7419,\cdot)\) \(\chi_{7840}(7699,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((1471,4901,3137,3041)\) → \((-1,e\left(\frac{7}{8}\right),-1,e\left(\frac{11}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 7840 }(6579, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{17}{56}\right)\) | \(e\left(\frac{31}{56}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(1\) |