Basic properties
Modulus: | \(7056\) | |
Conductor: | \(7056\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | 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 7056.if
\(\chi_{7056}(187,\cdot)\) \(\chi_{7056}(283,\cdot)\) \(\chi_{7056}(691,\cdot)\) \(\chi_{7056}(787,\cdot)\) \(\chi_{7056}(1291,\cdot)\) \(\chi_{7056}(1699,\cdot)\) \(\chi_{7056}(2203,\cdot)\) \(\chi_{7056}(2299,\cdot)\) \(\chi_{7056}(2707,\cdot)\) \(\chi_{7056}(2803,\cdot)\) \(\chi_{7056}(3211,\cdot)\) \(\chi_{7056}(3307,\cdot)\) \(\chi_{7056}(3715,\cdot)\) \(\chi_{7056}(3811,\cdot)\) \(\chi_{7056}(4219,\cdot)\) \(\chi_{7056}(4315,\cdot)\) \(\chi_{7056}(4819,\cdot)\) \(\chi_{7056}(5227,\cdot)\) \(\chi_{7056}(5731,\cdot)\) \(\chi_{7056}(5827,\cdot)\) \(\chi_{7056}(6235,\cdot)\) \(\chi_{7056}(6331,\cdot)\) \(\chi_{7056}(6739,\cdot)\) \(\chi_{7056}(6835,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6175,1765,785,4609)\) → \((-1,i,e\left(\frac{2}{3}\right),e\left(\frac{23}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 7056 }(187, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{65}{84}\right)\) |