Basic properties
Modulus: | \(8007\) | |
Conductor: | \(8007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.ee
\(\chi_{8007}(47,\cdot)\) \(\chi_{8007}(89,\cdot)\) \(\chi_{8007}(344,\cdot)\) \(\chi_{8007}(395,\cdot)\) \(\chi_{8007}(446,\cdot)\) \(\chi_{8007}(506,\cdot)\) \(\chi_{8007}(752,\cdot)\) \(\chi_{8007}(1118,\cdot)\) \(\chi_{8007}(1220,\cdot)\) \(\chi_{8007}(1424,\cdot)\) \(\chi_{8007}(1526,\cdot)\) \(\chi_{8007}(1670,\cdot)\) \(\chi_{8007}(1679,\cdot)\) \(\chi_{8007}(1874,\cdot)\) \(\chi_{8007}(2078,\cdot)\) \(\chi_{8007}(2444,\cdot)\) \(\chi_{8007}(2699,\cdot)\) \(\chi_{8007}(2750,\cdot)\) \(\chi_{8007}(2801,\cdot)\) \(\chi_{8007}(2843,\cdot)\) \(\chi_{8007}(3098,\cdot)\) \(\chi_{8007}(3107,\cdot)\) \(\chi_{8007}(3149,\cdot)\) \(\chi_{8007}(3506,\cdot)\) \(\chi_{8007}(3608,\cdot)\) \(\chi_{8007}(3965,\cdot)\) \(\chi_{8007}(4025,\cdot)\) \(\chi_{8007}(4229,\cdot)\) \(\chi_{8007}(4433,\cdot)\) \(\chi_{8007}(4679,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((-1,i,e\left(\frac{23}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 8007 }(47, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{77}{156}\right)\) | \(e\left(\frac{119}{156}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{8}{13}\right)\) |