Basic properties
| Modulus: | \(8670\) | |
| Conductor: | \(1445\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(136\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1445}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8670.ce
\(\chi_{8670}(19,\cdot)\) \(\chi_{8670}(49,\cdot)\) \(\chi_{8670}(229,\cdot)\) \(\chi_{8670}(349,\cdot)\) \(\chi_{8670}(529,\cdot)\) \(\chi_{8670}(559,\cdot)\) \(\chi_{8670}(739,\cdot)\) \(\chi_{8670}(859,\cdot)\) \(\chi_{8670}(1039,\cdot)\) \(\chi_{8670}(1069,\cdot)\) \(\chi_{8670}(1249,\cdot)\) \(\chi_{8670}(1369,\cdot)\) \(\chi_{8670}(1549,\cdot)\) \(\chi_{8670}(1759,\cdot)\) \(\chi_{8670}(1879,\cdot)\) \(\chi_{8670}(2059,\cdot)\) \(\chi_{8670}(2089,\cdot)\) \(\chi_{8670}(2269,\cdot)\) \(\chi_{8670}(2389,\cdot)\) \(\chi_{8670}(2569,\cdot)\) \(\chi_{8670}(2599,\cdot)\) \(\chi_{8670}(2779,\cdot)\) \(\chi_{8670}(2899,\cdot)\) \(\chi_{8670}(3079,\cdot)\) \(\chi_{8670}(3109,\cdot)\) \(\chi_{8670}(3409,\cdot)\) \(\chi_{8670}(3589,\cdot)\) \(\chi_{8670}(3619,\cdot)\) \(\chi_{8670}(3799,\cdot)\) \(\chi_{8670}(3919,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{136})$ |
| Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((2891,6937,6361)\) → \((1,-1,e\left(\frac{7}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8670 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{136}\right)\) | \(e\left(\frac{25}{136}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{49}{68}\right)\) | \(e\left(\frac{133}{136}\right)\) | \(e\left(\frac{59}{136}\right)\) | \(e\left(\frac{63}{136}\right)\) | \(e\left(\frac{19}{136}\right)\) | \(e\left(\frac{109}{136}\right)\) | \(e\left(\frac{9}{68}\right)\) |