Basic properties
| Modulus: | \(8470\) | |
| Conductor: | \(4235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4235}(67,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.cz
\(\chi_{8470}(23,\cdot)\) \(\chi_{8470}(67,\cdot)\) \(\chi_{8470}(177,\cdot)\) \(\chi_{8470}(683,\cdot)\) \(\chi_{8470}(793,\cdot)\) \(\chi_{8470}(837,\cdot)\) \(\chi_{8470}(947,\cdot)\) \(\chi_{8470}(1563,\cdot)\) \(\chi_{8470}(1607,\cdot)\) \(\chi_{8470}(1717,\cdot)\) \(\chi_{8470}(2223,\cdot)\) \(\chi_{8470}(2333,\cdot)\) \(\chi_{8470}(2377,\cdot)\) \(\chi_{8470}(2487,\cdot)\) \(\chi_{8470}(2993,\cdot)\) \(\chi_{8470}(3103,\cdot)\) \(\chi_{8470}(3257,\cdot)\) \(\chi_{8470}(3763,\cdot)\) \(\chi_{8470}(3917,\cdot)\) \(\chi_{8470}(4027,\cdot)\) \(\chi_{8470}(4533,\cdot)\) \(\chi_{8470}(4643,\cdot)\) \(\chi_{8470}(4687,\cdot)\) \(\chi_{8470}(4797,\cdot)\) \(\chi_{8470}(5303,\cdot)\) \(\chi_{8470}(5413,\cdot)\) \(\chi_{8470}(5457,\cdot)\) \(\chi_{8470}(6073,\cdot)\) \(\chi_{8470}(6183,\cdot)\) \(\chi_{8470}(6227,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((i,e\left(\frac{2}{3}\right),e\left(\frac{10}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 8470 }(67, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{61}{132}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{95}{132}\right)\) | \(i\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{101}{132}\right)\) |