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 \(\chi_{2669}(46,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.er
\(\chi_{8007}(46,\cdot)\) \(\chi_{8007}(130,\cdot)\) \(\chi_{8007}(232,\cdot)\) \(\chi_{8007}(250,\cdot)\) \(\chi_{8007}(265,\cdot)\) \(\chi_{8007}(328,\cdot)\) \(\chi_{8007}(415,\cdot)\) \(\chi_{8007}(487,\cdot)\) \(\chi_{8007}(517,\cdot)\) \(\chi_{8007}(538,\cdot)\) \(\chi_{8007}(601,\cdot)\) \(\chi_{8007}(703,\cdot)\) \(\chi_{8007}(721,\cdot)\) \(\chi_{8007}(736,\cdot)\) \(\chi_{8007}(958,\cdot)\) \(\chi_{8007}(1009,\cdot)\) \(\chi_{8007}(1252,\cdot)\) \(\chi_{8007}(1270,\cdot)\) \(\chi_{8007}(1357,\cdot)\) \(\chi_{8007}(1459,\cdot)\) \(\chi_{8007}(1609,\cdot)\) \(\chi_{8007}(1663,\cdot)\) \(\chi_{8007}(1669,\cdot)\) \(\chi_{8007}(1678,\cdot)\) \(\chi_{8007}(1723,\cdot)\) \(\chi_{8007}(1741,\cdot)\) \(\chi_{8007}(2080,\cdot)\) \(\chi_{8007}(2149,\cdot)\) \(\chi_{8007}(2485,\cdot)\) \(\chi_{8007}(2587,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{208})$ |
| Fixed field: | Number field defined by a degree 208 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((1,e\left(\frac{13}{16}\right),e\left(\frac{10}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(46, a) \) | \(-1\) | \(1\) | \(e\left(\frac{87}{104}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{173}{208}\right)\) | \(e\left(\frac{3}{208}\right)\) | \(e\left(\frac{53}{104}\right)\) | \(e\left(\frac{139}{208}\right)\) | \(e\left(\frac{47}{208}\right)\) | \(i\) | \(e\left(\frac{177}{208}\right)\) | \(e\left(\frac{9}{26}\right)\) |