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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 667.w
\(\chi_{667}(2,\cdot)\) \(\chi_{667}(3,\cdot)\) \(\chi_{667}(8,\cdot)\) \(\chi_{667}(18,\cdot)\) \(\chi_{667}(26,\cdot)\) \(\chi_{667}(27,\cdot)\) \(\chi_{667}(31,\cdot)\) \(\chi_{667}(32,\cdot)\) \(\chi_{667}(39,\cdot)\) \(\chi_{667}(48,\cdot)\) \(\chi_{667}(50,\cdot)\) \(\chi_{667}(55,\cdot)\) \(\chi_{667}(72,\cdot)\) \(\chi_{667}(73,\cdot)\) \(\chi_{667}(77,\cdot)\) \(\chi_{667}(85,\cdot)\) \(\chi_{667}(95,\cdot)\) \(\chi_{667}(98,\cdot)\) \(\chi_{667}(101,\cdot)\) \(\chi_{667}(105,\cdot)\) \(\chi_{667}(108,\cdot)\) \(\chi_{667}(118,\cdot)\) \(\chi_{667}(119,\cdot)\) \(\chi_{667}(124,\cdot)\) \(\chi_{667}(127,\cdot)\) \(\chi_{667}(131,\cdot)\) \(\chi_{667}(142,\cdot)\) \(\chi_{667}(147,\cdot)\) \(\chi_{667}(156,\cdot)\) \(\chi_{667}(163,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{308})$ |
Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((465,553)\) → \((e\left(\frac{1}{11}\right),e\left(\frac{1}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 667 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{308}\right)\) | \(e\left(\frac{195}{308}\right)\) | \(e\left(\frac{67}{154}\right)\) | \(e\left(\frac{135}{154}\right)\) | \(e\left(\frac{131}{154}\right)\) | \(e\left(\frac{12}{77}\right)\) | \(e\left(\frac{201}{308}\right)\) | \(e\left(\frac{41}{154}\right)\) | \(e\left(\frac{29}{308}\right)\) | \(e\left(\frac{219}{308}\right)\) |