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.je
\(\chi_{7056}(29,\cdot)\) \(\chi_{7056}(365,\cdot)\) \(\chi_{7056}(533,\cdot)\) \(\chi_{7056}(869,\cdot)\) \(\chi_{7056}(1037,\cdot)\) \(\chi_{7056}(1541,\cdot)\) \(\chi_{7056}(1877,\cdot)\) \(\chi_{7056}(2045,\cdot)\) \(\chi_{7056}(2381,\cdot)\) \(\chi_{7056}(2885,\cdot)\) \(\chi_{7056}(3053,\cdot)\) \(\chi_{7056}(3389,\cdot)\) \(\chi_{7056}(3557,\cdot)\) \(\chi_{7056}(3893,\cdot)\) \(\chi_{7056}(4061,\cdot)\) \(\chi_{7056}(4397,\cdot)\) \(\chi_{7056}(4565,\cdot)\) \(\chi_{7056}(5069,\cdot)\) \(\chi_{7056}(5405,\cdot)\) \(\chi_{7056}(5573,\cdot)\) \(\chi_{7056}(5909,\cdot)\) \(\chi_{7056}(6413,\cdot)\) \(\chi_{7056}(6581,\cdot)\) \(\chi_{7056}(6917,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6175,1765,785,4609)\) → \((1,-i,e\left(\frac{1}{6}\right),e\left(\frac{3}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 7056 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(i\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{28}\right)\) |