Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(2669\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(208\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2669}(316,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.eq
\(\chi_{8007}(316,\cdot)\) \(\chi_{8007}(337,\cdot)\) \(\chi_{8007}(346,\cdot)\) \(\chi_{8007}(379,\cdot)\) \(\chi_{8007}(430,\cdot)\) \(\chi_{8007}(439,\cdot)\) \(\chi_{8007}(448,\cdot)\) \(\chi_{8007}(583,\cdot)\) \(\chi_{8007}(673,\cdot)\) \(\chi_{8007}(826,\cdot)\) \(\chi_{8007}(844,\cdot)\) \(\chi_{8007}(877,\cdot)\) \(\chi_{8007}(913,\cdot)\) \(\chi_{8007}(940,\cdot)\) \(\chi_{8007}(949,\cdot)\) \(\chi_{8007}(1153,\cdot)\) \(\chi_{8007}(1285,\cdot)\) \(\chi_{8007}(1315,\cdot)\) \(\chi_{8007}(1321,\cdot)\) \(\chi_{8007}(1372,\cdot)\) \(\chi_{8007}(1405,\cdot)\) \(\chi_{8007}(1525,\cdot)\) \(\chi_{8007}(1876,\cdot)\) \(\chi_{8007}(1882,\cdot)\) \(\chi_{8007}(2119,\cdot)\) \(\chi_{8007}(2200,\cdot)\) \(\chi_{8007}(2326,\cdot)\) \(\chi_{8007}(2434,\cdot)\) \(\chi_{8007}(2458,\cdot)\) \(\chi_{8007}(2557,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{208})$ |
| Fixed field: | Number field defined by a degree 208 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((1,e\left(\frac{3}{16}\right),e\left(\frac{47}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(316, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{104}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{175}{208}\right)\) | \(e\left(\frac{193}{208}\right)\) | \(e\left(\frac{21}{104}\right)\) | \(e\left(\frac{189}{208}\right)\) | \(e\left(\frac{129}{208}\right)\) | \(i\) | \(e\left(\frac{207}{208}\right)\) | \(e\left(\frac{7}{26}\right)\) |