Basic properties
Modulus: | \(8007\) | |
Conductor: | \(471\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{471}(392,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.dk
\(\chi_{8007}(392,\cdot)\) \(\chi_{8007}(494,\cdot)\) \(\chi_{8007}(596,\cdot)\) \(\chi_{8007}(1106,\cdot)\) \(\chi_{8007}(1310,\cdot)\) \(\chi_{8007}(2483,\cdot)\) \(\chi_{8007}(2891,\cdot)\) \(\chi_{8007}(2942,\cdot)\) \(\chi_{8007}(3095,\cdot)\) \(\chi_{8007}(3299,\cdot)\) \(\chi_{8007}(3452,\cdot)\) \(\chi_{8007}(3656,\cdot)\) \(\chi_{8007}(3809,\cdot)\) \(\chi_{8007}(3860,\cdot)\) \(\chi_{8007}(4268,\cdot)\) \(\chi_{8007}(5441,\cdot)\) \(\chi_{8007}(5645,\cdot)\) \(\chi_{8007}(6155,\cdot)\) \(\chi_{8007}(6257,\cdot)\) \(\chi_{8007}(6359,\cdot)\) \(\chi_{8007}(7073,\cdot)\) \(\chi_{8007}(7124,\cdot)\) \(\chi_{8007}(7634,\cdot)\) \(\chi_{8007}(7685,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5339,1414,7855)\) → \((-1,1,e\left(\frac{31}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 8007 }(392, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(-1\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{3}{13}\right)\) |