Basic properties
Modulus: | \(667\) | |
Conductor: | \(667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(308\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 667.x
\(\chi_{667}(10,\cdot)\) \(\chi_{667}(11,\cdot)\) \(\chi_{667}(14,\cdot)\) \(\chi_{667}(15,\cdot)\) \(\chi_{667}(19,\cdot)\) \(\chi_{667}(21,\cdot)\) \(\chi_{667}(37,\cdot)\) \(\chi_{667}(40,\cdot)\) \(\chi_{667}(43,\cdot)\) \(\chi_{667}(44,\cdot)\) \(\chi_{667}(56,\cdot)\) \(\chi_{667}(60,\cdot)\) \(\chi_{667}(61,\cdot)\) \(\chi_{667}(66,\cdot)\) \(\chi_{667}(76,\cdot)\) \(\chi_{667}(79,\cdot)\) \(\chi_{667}(84,\cdot)\) \(\chi_{667}(89,\cdot)\) \(\chi_{667}(90,\cdot)\) \(\chi_{667}(97,\cdot)\) \(\chi_{667}(102,\cdot)\) \(\chi_{667}(106,\cdot)\) \(\chi_{667}(113,\cdot)\) \(\chi_{667}(126,\cdot)\) \(\chi_{667}(130,\cdot)\) \(\chi_{667}(134,\cdot)\) \(\chi_{667}(135,\cdot)\) \(\chi_{667}(143,\cdot)\) \(\chi_{667}(148,\cdot)\) \(\chi_{667}(153,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{308})$ |
Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((465,553)\) → \((e\left(\frac{15}{22}\right),e\left(\frac{9}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 667 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{211}{308}\right)\) | \(e\left(\frac{159}{308}\right)\) | \(e\left(\frac{57}{154}\right)\) | \(e\left(\frac{58}{77}\right)\) | \(e\left(\frac{31}{154}\right)\) | \(e\left(\frac{125}{154}\right)\) | \(e\left(\frac{17}{308}\right)\) | \(e\left(\frac{5}{154}\right)\) | \(e\left(\frac{135}{308}\right)\) | \(e\left(\frac{53}{308}\right)\) |