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.ev
\(\chi_{8007}(56,\cdot)\) \(\chi_{8007}(143,\cdot)\) \(\chi_{8007}(215,\cdot)\) \(\chi_{8007}(275,\cdot)\) \(\chi_{8007}(632,\cdot)\) \(\chi_{8007}(677,\cdot)\) \(\chi_{8007}(686,\cdot)\) \(\chi_{8007}(692,\cdot)\) \(\chi_{8007}(896,\cdot)\) \(\chi_{8007}(998,\cdot)\) \(\chi_{8007}(1085,\cdot)\) \(\chi_{8007}(1163,\cdot)\) \(\chi_{8007}(1217,\cdot)\) \(\chi_{8007}(1346,\cdot)\) \(\chi_{8007}(1367,\cdot)\) \(\chi_{8007}(1397,\cdot)\) \(\chi_{8007}(1469,\cdot)\) \(\chi_{8007}(1574,\cdot)\) \(\chi_{8007}(1652,\cdot)\) \(\chi_{8007}(1688,\cdot)\) \(\chi_{8007}(1754,\cdot)\) \(\chi_{8007}(2045,\cdot)\) \(\chi_{8007}(2105,\cdot)\) \(\chi_{8007}(2288,\cdot)\) \(\chi_{8007}(2309,\cdot)\) \(\chi_{8007}(2339,\cdot)\) \(\chi_{8007}(2411,\cdot)\) \(\chi_{8007}(2561,\cdot)\) \(\chi_{8007}(2570,\cdot)\) \(\chi_{8007}(2594,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{208})$ |
| Fixed field: | Number field defined by a degree 208 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((-1,e\left(\frac{5}{16}\right),e\left(\frac{17}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(56, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{104}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{149}{208}\right)\) | \(e\left(\frac{115}{208}\right)\) | \(e\left(\frac{21}{104}\right)\) | \(e\left(\frac{163}{208}\right)\) | \(e\left(\frac{207}{208}\right)\) | \(i\) | \(e\left(\frac{129}{208}\right)\) | \(e\left(\frac{7}{26}\right)\) |