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 \(\chi_{784}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7056.it
\(\chi_{7056}(37,\cdot)\) \(\chi_{7056}(109,\cdot)\) \(\chi_{7056}(541,\cdot)\) \(\chi_{7056}(613,\cdot)\) \(\chi_{7056}(1045,\cdot)\) \(\chi_{7056}(1117,\cdot)\) \(\chi_{7056}(1621,\cdot)\) \(\chi_{7056}(2053,\cdot)\) \(\chi_{7056}(2557,\cdot)\) \(\chi_{7056}(2629,\cdot)\) \(\chi_{7056}(3061,\cdot)\) \(\chi_{7056}(3133,\cdot)\) \(\chi_{7056}(3565,\cdot)\) \(\chi_{7056}(3637,\cdot)\) \(\chi_{7056}(4069,\cdot)\) \(\chi_{7056}(4141,\cdot)\) \(\chi_{7056}(4573,\cdot)\) \(\chi_{7056}(4645,\cdot)\) \(\chi_{7056}(5149,\cdot)\) \(\chi_{7056}(5581,\cdot)\) \(\chi_{7056}(6085,\cdot)\) \(\chi_{7056}(6157,\cdot)\) \(\chi_{7056}(6589,\cdot)\) \(\chi_{7056}(6661,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6175,1765,785,4609)\) → \((1,i,1,e\left(\frac{16}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 7056 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{53}{84}\right)\) |