Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(2669\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(624\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2669}(40,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.fm
\(\chi_{8007}(37,\cdot)\) \(\chi_{8007}(40,\cdot)\) \(\chi_{8007}(109,\cdot)\) \(\chi_{8007}(124,\cdot)\) \(\chi_{8007}(283,\cdot)\) \(\chi_{8007}(385,\cdot)\) \(\chi_{8007}(403,\cdot)\) \(\chi_{8007}(490,\cdot)\) \(\chi_{8007}(571,\cdot)\) \(\chi_{8007}(592,\cdot)\) \(\chi_{8007}(658,\cdot)\) \(\chi_{8007}(709,\cdot)\) \(\chi_{8007}(754,\cdot)\) \(\chi_{8007}(760,\cdot)\) \(\chi_{8007}(775,\cdot)\) \(\chi_{8007}(796,\cdot)\) \(\chi_{8007}(802,\cdot)\) \(\chi_{8007}(856,\cdot)\) \(\chi_{8007}(874,\cdot)\) \(\chi_{8007}(898,\cdot)\) \(\chi_{8007}(979,\cdot)\) \(\chi_{8007}(1042,\cdot)\) \(\chi_{8007}(1048,\cdot)\) \(\chi_{8007}(1051,\cdot)\) \(\chi_{8007}(1057,\cdot)\) \(\chi_{8007}(1066,\cdot)\) \(\chi_{8007}(1108,\cdot)\) \(\chi_{8007}(1129,\cdot)\) \(\chi_{8007}(1180,\cdot)\) \(\chi_{8007}(1231,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{624})$ |
| Fixed field: | Number field defined by a degree 624 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((1,e\left(\frac{15}{16}\right),e\left(\frac{28}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(40, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{104}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{253}{624}\right)\) | \(e\left(\frac{177}{208}\right)\) | \(e\left(\frac{7}{104}\right)\) | \(e\left(\frac{475}{624}\right)\) | \(e\left(\frac{415}{624}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{43}{208}\right)\) | \(e\left(\frac{11}{26}\right)\) |