Basic properties
Modulus: | \(867\) | |
Conductor: | \(867\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(136\) | 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 867.r
\(\chi_{867}(2,\cdot)\) \(\chi_{867}(8,\cdot)\) \(\chi_{867}(26,\cdot)\) \(\chi_{867}(32,\cdot)\) \(\chi_{867}(53,\cdot)\) \(\chi_{867}(59,\cdot)\) \(\chi_{867}(77,\cdot)\) \(\chi_{867}(83,\cdot)\) \(\chi_{867}(104,\cdot)\) \(\chi_{867}(128,\cdot)\) \(\chi_{867}(161,\cdot)\) \(\chi_{867}(185,\cdot)\) \(\chi_{867}(206,\cdot)\) \(\chi_{867}(212,\cdot)\) \(\chi_{867}(230,\cdot)\) \(\chi_{867}(236,\cdot)\) \(\chi_{867}(257,\cdot)\) \(\chi_{867}(263,\cdot)\) \(\chi_{867}(281,\cdot)\) \(\chi_{867}(287,\cdot)\) \(\chi_{867}(308,\cdot)\) \(\chi_{867}(314,\cdot)\) \(\chi_{867}(332,\cdot)\) \(\chi_{867}(338,\cdot)\) \(\chi_{867}(359,\cdot)\) \(\chi_{867}(365,\cdot)\) \(\chi_{867}(383,\cdot)\) \(\chi_{867}(389,\cdot)\) \(\chi_{867}(410,\cdot)\) \(\chi_{867}(416,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{136})$ |
Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((290,292)\) → \((-1,e\left(\frac{93}{136}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 867 }(314, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{68}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{13}{136}\right)\) | \(e\left(\frac{135}{136}\right)\) | \(e\left(\frac{19}{68}\right)\) | \(e\left(\frac{71}{136}\right)\) | \(e\left(\frac{31}{136}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{57}{136}\right)\) | \(e\left(\frac{12}{17}\right)\) |