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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.ew
\(\chi_{8007}(14,\cdot)\) \(\chi_{8007}(173,\cdot)\) \(\chi_{8007}(224,\cdot)\) \(\chi_{8007}(413,\cdot)\) \(\chi_{8007}(422,\cdot)\) \(\chi_{8007}(572,\cdot)\) \(\chi_{8007}(674,\cdot)\) \(\chi_{8007}(758,\cdot)\) \(\chi_{8007}(860,\cdot)\) \(\chi_{8007}(878,\cdot)\) \(\chi_{8007}(938,\cdot)\) \(\chi_{8007}(1043,\cdot)\) \(\chi_{8007}(1115,\cdot)\) \(\chi_{8007}(1145,\cdot)\) \(\chi_{8007}(1166,\cdot)\) \(\chi_{8007}(1229,\cdot)\) \(\chi_{8007}(1295,\cdot)\) \(\chi_{8007}(1331,\cdot)\) \(\chi_{8007}(1349,\cdot)\) \(\chi_{8007}(1355,\cdot)\) \(\chi_{8007}(1586,\cdot)\) \(\chi_{8007}(1637,\cdot)\) \(\chi_{8007}(1826,\cdot)\) \(\chi_{8007}(1880,\cdot)\) \(\chi_{8007}(1898,\cdot)\) \(\chi_{8007}(2171,\cdot)\) \(\chi_{8007}(2237,\cdot)\) \(\chi_{8007}(2273,\cdot)\) \(\chi_{8007}(2306,\cdot)\) \(\chi_{8007}(2351,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{208})$ |
| Fixed field: | Number field defined by a degree 208 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((-1,e\left(\frac{9}{16}\right),e\left(\frac{11}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(14, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{104}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{33}{208}\right)\) | \(e\left(\frac{119}{208}\right)\) | \(e\left(\frac{5}{104}\right)\) | \(e\left(\frac{175}{208}\right)\) | \(e\left(\frac{27}{208}\right)\) | \(i\) | \(e\left(\frac{53}{208}\right)\) | \(e\left(\frac{19}{26}\right)\) |