Basic properties
| Modulus: | \(8670\) | |
| Conductor: | \(4335\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(136\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4335}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8670.cg
\(\chi_{8670}(53,\cdot)\) \(\chi_{8670}(77,\cdot)\) \(\chi_{8670}(83,\cdot)\) \(\chi_{8670}(467,\cdot)\) \(\chi_{8670}(563,\cdot)\) \(\chi_{8670}(587,\cdot)\) \(\chi_{8670}(593,\cdot)\) \(\chi_{8670}(1073,\cdot)\) \(\chi_{8670}(1097,\cdot)\) \(\chi_{8670}(1103,\cdot)\) \(\chi_{8670}(1487,\cdot)\) \(\chi_{8670}(1583,\cdot)\) \(\chi_{8670}(1607,\cdot)\) \(\chi_{8670}(1613,\cdot)\) \(\chi_{8670}(1997,\cdot)\) \(\chi_{8670}(2093,\cdot)\) \(\chi_{8670}(2117,\cdot)\) \(\chi_{8670}(2123,\cdot)\) \(\chi_{8670}(2507,\cdot)\) \(\chi_{8670}(2603,\cdot)\) \(\chi_{8670}(2627,\cdot)\) \(\chi_{8670}(2633,\cdot)\) \(\chi_{8670}(3017,\cdot)\) \(\chi_{8670}(3113,\cdot)\) \(\chi_{8670}(3137,\cdot)\) \(\chi_{8670}(3143,\cdot)\) \(\chi_{8670}(3527,\cdot)\) \(\chi_{8670}(3653,\cdot)\) \(\chi_{8670}(4037,\cdot)\) \(\chi_{8670}(4133,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{136})$ |
| Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((2891,6937,6361)\) → \((-1,-i,e\left(\frac{103}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8670 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{136}\right)\) | \(e\left(\frac{125}{136}\right)\) | \(e\left(\frac{47}{68}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{87}{136}\right)\) | \(e\left(\frac{91}{136}\right)\) | \(e\left(\frac{111}{136}\right)\) | \(e\left(\frac{61}{136}\right)\) | \(e\left(\frac{1}{136}\right)\) | \(e\left(\frac{7}{17}\right)\) |