Basic properties
Modulus: | \(7056\) | |
Conductor: | \(784\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{784}(451,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7056.il
\(\chi_{7056}(451,\cdot)\) \(\chi_{7056}(523,\cdot)\) \(\chi_{7056}(955,\cdot)\) \(\chi_{7056}(1027,\cdot)\) \(\chi_{7056}(1459,\cdot)\) \(\chi_{7056}(1531,\cdot)\) \(\chi_{7056}(1963,\cdot)\) \(\chi_{7056}(2035,\cdot)\) \(\chi_{7056}(2467,\cdot)\) \(\chi_{7056}(2539,\cdot)\) \(\chi_{7056}(3043,\cdot)\) \(\chi_{7056}(3475,\cdot)\) \(\chi_{7056}(3979,\cdot)\) \(\chi_{7056}(4051,\cdot)\) \(\chi_{7056}(4483,\cdot)\) \(\chi_{7056}(4555,\cdot)\) \(\chi_{7056}(4987,\cdot)\) \(\chi_{7056}(5059,\cdot)\) \(\chi_{7056}(5491,\cdot)\) \(\chi_{7056}(5563,\cdot)\) \(\chi_{7056}(5995,\cdot)\) \(\chi_{7056}(6067,\cdot)\) \(\chi_{7056}(6571,\cdot)\) \(\chi_{7056}(7003,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6175,1765,785,4609)\) → \((-1,-i,1,e\left(\frac{13}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 7056 }(451, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{55}{84}\right)\) |