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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7056.ic
\(\chi_{7056}(43,\cdot)\) \(\chi_{7056}(211,\cdot)\) \(\chi_{7056}(547,\cdot)\) \(\chi_{7056}(715,\cdot)\) \(\chi_{7056}(1051,\cdot)\) \(\chi_{7056}(1219,\cdot)\) \(\chi_{7056}(1555,\cdot)\) \(\chi_{7056}(1723,\cdot)\) \(\chi_{7056}(2227,\cdot)\) \(\chi_{7056}(2563,\cdot)\) \(\chi_{7056}(2731,\cdot)\) \(\chi_{7056}(3067,\cdot)\) \(\chi_{7056}(3571,\cdot)\) \(\chi_{7056}(3739,\cdot)\) \(\chi_{7056}(4075,\cdot)\) \(\chi_{7056}(4243,\cdot)\) \(\chi_{7056}(4579,\cdot)\) \(\chi_{7056}(4747,\cdot)\) \(\chi_{7056}(5083,\cdot)\) \(\chi_{7056}(5251,\cdot)\) \(\chi_{7056}(5755,\cdot)\) \(\chi_{7056}(6091,\cdot)\) \(\chi_{7056}(6259,\cdot)\) \(\chi_{7056}(6595,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6175,1765,785,4609)\) → \((-1,i,e\left(\frac{2}{3}\right),e\left(\frac{1}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 7056 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(i\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{23}{28}\right)\) |