Basic properties
Modulus: | \(8007\) | |
Conductor: | \(8007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(312\) | 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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.fe
\(\chi_{8007}(26,\cdot)\) \(\chi_{8007}(77,\cdot)\) \(\chi_{8007}(104,\cdot)\) \(\chi_{8007}(308,\cdot)\) \(\chi_{8007}(338,\cdot)\) \(\chi_{8007}(416,\cdot)\) \(\chi_{8007}(791,\cdot)\) \(\chi_{8007}(995,\cdot)\) \(\chi_{8007}(1022,\cdot)\) \(\chi_{8007}(1073,\cdot)\) \(\chi_{8007}(1154,\cdot)\) \(\chi_{8007}(1232,\cdot)\) \(\chi_{8007}(1277,\cdot)\) \(\chi_{8007}(1352,\cdot)\) \(\chi_{8007}(1613,\cdot)\) \(\chi_{8007}(1658,\cdot)\) \(\chi_{8007}(1664,\cdot)\) \(\chi_{8007}(1709,\cdot)\) \(\chi_{8007}(1742,\cdot)\) \(\chi_{8007}(1787,\cdot)\) \(\chi_{8007}(1793,\cdot)\) \(\chi_{8007}(1811,\cdot)\) \(\chi_{8007}(1889,\cdot)\) \(\chi_{8007}(1946,\cdot)\) \(\chi_{8007}(2021,\cdot)\) \(\chi_{8007}(2270,\cdot)\) \(\chi_{8007}(2321,\cdot)\) \(\chi_{8007}(2429,\cdot)\) \(\chi_{8007}(2450,\cdot)\) \(\chi_{8007}(2474,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{312})$ |
Fixed field: | Number field defined by a degree 312 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{11}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 8007 }(26, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{61}{312}\right)\) | \(e\left(\frac{77}{104}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{121}{312}\right)\) | \(e\left(\frac{109}{312}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{97}{104}\right)\) | \(e\left(\frac{10}{13}\right)\) |