Basic properties
Modulus: | \(1156\) | |
Conductor: | \(1156\) | 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 1156.t
\(\chi_{1156}(3,\cdot)\) \(\chi_{1156}(7,\cdot)\) \(\chi_{1156}(11,\cdot)\) \(\chi_{1156}(23,\cdot)\) \(\chi_{1156}(27,\cdot)\) \(\chi_{1156}(31,\cdot)\) \(\chi_{1156}(39,\cdot)\) \(\chi_{1156}(63,\cdot)\) \(\chi_{1156}(71,\cdot)\) \(\chi_{1156}(79,\cdot)\) \(\chi_{1156}(91,\cdot)\) \(\chi_{1156}(95,\cdot)\) \(\chi_{1156}(99,\cdot)\) \(\chi_{1156}(107,\cdot)\) \(\chi_{1156}(139,\cdot)\) \(\chi_{1156}(143,\cdot)\) \(\chi_{1156}(147,\cdot)\) \(\chi_{1156}(159,\cdot)\) \(\chi_{1156}(163,\cdot)\) \(\chi_{1156}(167,\cdot)\) \(\chi_{1156}(175,\cdot)\) \(\chi_{1156}(199,\cdot)\) \(\chi_{1156}(207,\cdot)\) \(\chi_{1156}(211,\cdot)\) \(\chi_{1156}(215,\cdot)\) \(\chi_{1156}(227,\cdot)\) \(\chi_{1156}(231,\cdot)\) \(\chi_{1156}(235,\cdot)\) \(\chi_{1156}(243,\cdot)\) \(\chi_{1156}(267,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{272})$ |
Fixed field: | Number field defined by a degree 272 polynomial (not computed) |
Values on generators
\((579,581)\) → \((-1,e\left(\frac{3}{272}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 1156 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{139}{272}\right)\) | \(e\left(\frac{143}{272}\right)\) | \(e\left(\frac{57}{272}\right)\) | \(e\left(\frac{3}{136}\right)\) | \(e\left(\frac{205}{272}\right)\) | \(e\left(\frac{11}{68}\right)\) | \(e\left(\frac{5}{136}\right)\) | \(e\left(\frac{89}{136}\right)\) | \(e\left(\frac{49}{68}\right)\) | \(e\left(\frac{261}{272}\right)\) |