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.iw
\(\chi_{7056}(5,\cdot)\) \(\chi_{7056}(101,\cdot)\) \(\chi_{7056}(605,\cdot)\) \(\chi_{7056}(1013,\cdot)\) \(\chi_{7056}(1517,\cdot)\) \(\chi_{7056}(1613,\cdot)\) \(\chi_{7056}(2021,\cdot)\) \(\chi_{7056}(2117,\cdot)\) \(\chi_{7056}(2525,\cdot)\) \(\chi_{7056}(2621,\cdot)\) \(\chi_{7056}(3029,\cdot)\) \(\chi_{7056}(3125,\cdot)\) \(\chi_{7056}(3533,\cdot)\) \(\chi_{7056}(3629,\cdot)\) \(\chi_{7056}(4133,\cdot)\) \(\chi_{7056}(4541,\cdot)\) \(\chi_{7056}(5045,\cdot)\) \(\chi_{7056}(5141,\cdot)\) \(\chi_{7056}(5549,\cdot)\) \(\chi_{7056}(5645,\cdot)\) \(\chi_{7056}(6053,\cdot)\) \(\chi_{7056}(6149,\cdot)\) \(\chi_{7056}(6557,\cdot)\) \(\chi_{7056}(6653,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6175,1765,785,4609)\) → \((1,i,e\left(\frac{1}{6}\right),e\left(\frac{1}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 7056 }(101, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(-1\) | \(e\left(\frac{1}{84}\right)\) |