Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(8007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(208\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.ex
\(\chi_{8007}(41,\cdot)\) \(\chi_{8007}(65,\cdot)\) \(\chi_{8007}(92,\cdot)\) \(\chi_{8007}(116,\cdot)\) \(\chi_{8007}(269,\cdot)\) \(\chi_{8007}(479,\cdot)\) \(\chi_{8007}(500,\cdot)\) \(\chi_{8007}(503,\cdot)\) \(\chi_{8007}(605,\cdot)\) \(\chi_{8007}(626,\cdot)\) \(\chi_{8007}(1040,\cdot)\) \(\chi_{8007}(1178,\cdot)\) \(\chi_{8007}(1472,\cdot)\) \(\chi_{8007}(1673,\cdot)\) \(\chi_{8007}(1877,\cdot)\) \(\chi_{8007}(1892,\cdot)\) \(\chi_{8007}(1907,\cdot)\) \(\chi_{8007}(2009,\cdot)\) \(\chi_{8007}(2033,\cdot)\) \(\chi_{8007}(2120,\cdot)\) \(\chi_{8007}(2357,\cdot)\) \(\chi_{8007}(2387,\cdot)\) \(\chi_{8007}(2453,\cdot)\) \(\chi_{8007}(2489,\cdot)\) \(\chi_{8007}(2519,\cdot)\) \(\chi_{8007}(2714,\cdot)\) \(\chi_{8007}(2723,\cdot)\) \(\chi_{8007}(2747,\cdot)\) \(\chi_{8007}(2828,\cdot)\) \(\chi_{8007}(2834,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{208})$ |
| Fixed field: | Number field defined by a degree 208 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((-1,e\left(\frac{11}{16}\right),e\left(\frac{7}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(41, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{104}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{15}{208}\right)\) | \(e\left(\frac{73}{208}\right)\) | \(e\left(\frac{33}{104}\right)\) | \(e\left(\frac{37}{208}\right)\) | \(e\left(\frac{17}{208}\right)\) | \(i\) | \(e\left(\frac{95}{208}\right)\) | \(e\left(\frac{11}{26}\right)\) |