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.jb
\(\chi_{7056}(205,\cdot)\) \(\chi_{7056}(445,\cdot)\) \(\chi_{7056}(709,\cdot)\) \(\chi_{7056}(1213,\cdot)\) \(\chi_{7056}(1453,\cdot)\) \(\chi_{7056}(1717,\cdot)\) \(\chi_{7056}(1957,\cdot)\) \(\chi_{7056}(2221,\cdot)\) \(\chi_{7056}(2461,\cdot)\) \(\chi_{7056}(2965,\cdot)\) \(\chi_{7056}(3229,\cdot)\) \(\chi_{7056}(3469,\cdot)\) \(\chi_{7056}(3733,\cdot)\) \(\chi_{7056}(3973,\cdot)\) \(\chi_{7056}(4237,\cdot)\) \(\chi_{7056}(4741,\cdot)\) \(\chi_{7056}(4981,\cdot)\) \(\chi_{7056}(5245,\cdot)\) \(\chi_{7056}(5485,\cdot)\) \(\chi_{7056}(5749,\cdot)\) \(\chi_{7056}(5989,\cdot)\) \(\chi_{7056}(6493,\cdot)\) \(\chi_{7056}(6757,\cdot)\) \(\chi_{7056}(6997,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6175,1765,785,4609)\) → \((1,-i,e\left(\frac{2}{3}\right),e\left(\frac{1}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 7056 }(205, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{23}{84}\right)\) |