Basic properties
Modulus: | \(867\) | |
Conductor: | \(867\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(272\) | 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 867.t
\(\chi_{867}(5,\cdot)\) \(\chi_{867}(11,\cdot)\) \(\chi_{867}(14,\cdot)\) \(\chi_{867}(20,\cdot)\) \(\chi_{867}(23,\cdot)\) \(\chi_{867}(29,\cdot)\) \(\chi_{867}(41,\cdot)\) \(\chi_{867}(44,\cdot)\) \(\chi_{867}(56,\cdot)\) \(\chi_{867}(62,\cdot)\) \(\chi_{867}(71,\cdot)\) \(\chi_{867}(74,\cdot)\) \(\chi_{867}(80,\cdot)\) \(\chi_{867}(92,\cdot)\) \(\chi_{867}(95,\cdot)\) \(\chi_{867}(107,\cdot)\) \(\chi_{867}(113,\cdot)\) \(\chi_{867}(116,\cdot)\) \(\chi_{867}(122,\cdot)\) \(\chi_{867}(125,\cdot)\) \(\chi_{867}(143,\cdot)\) \(\chi_{867}(146,\cdot)\) \(\chi_{867}(164,\cdot)\) \(\chi_{867}(167,\cdot)\) \(\chi_{867}(173,\cdot)\) \(\chi_{867}(176,\cdot)\) \(\chi_{867}(182,\cdot)\) \(\chi_{867}(194,\cdot)\) \(\chi_{867}(197,\cdot)\) \(\chi_{867}(209,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{272})$ |
Fixed field: | Number field defined by a degree 272 polynomial (not computed) |
Values on generators
\((290,292)\) → \((-1,e\left(\frac{91}{272}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 867 }(449, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{136}\right)\) | \(e\left(\frac{9}{68}\right)\) | \(e\left(\frac{31}{272}\right)\) | \(e\left(\frac{233}{272}\right)\) | \(e\left(\frac{27}{136}\right)\) | \(e\left(\frac{49}{272}\right)\) | \(e\left(\frac{53}{272}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{251}{272}\right)\) | \(e\left(\frac{9}{34}\right)\) |