Basic properties
Modulus: | \(1156\) | |
Conductor: | \(1156\) | 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 1156.r
\(\chi_{1156}(15,\cdot)\) \(\chi_{1156}(19,\cdot)\) \(\chi_{1156}(43,\cdot)\) \(\chi_{1156}(59,\cdot)\) \(\chi_{1156}(83,\cdot)\) \(\chi_{1156}(87,\cdot)\) \(\chi_{1156}(111,\cdot)\) \(\chi_{1156}(127,\cdot)\) \(\chi_{1156}(151,\cdot)\) \(\chi_{1156}(195,\cdot)\) \(\chi_{1156}(219,\cdot)\) \(\chi_{1156}(223,\cdot)\) \(\chi_{1156}(247,\cdot)\) \(\chi_{1156}(263,\cdot)\) \(\chi_{1156}(287,\cdot)\) \(\chi_{1156}(291,\cdot)\) \(\chi_{1156}(315,\cdot)\) \(\chi_{1156}(331,\cdot)\) \(\chi_{1156}(355,\cdot)\) \(\chi_{1156}(359,\cdot)\) \(\chi_{1156}(383,\cdot)\) \(\chi_{1156}(427,\cdot)\) \(\chi_{1156}(451,\cdot)\) \(\chi_{1156}(467,\cdot)\) \(\chi_{1156}(491,\cdot)\) \(\chi_{1156}(495,\cdot)\) \(\chi_{1156}(519,\cdot)\) \(\chi_{1156}(535,\cdot)\) \(\chi_{1156}(559,\cdot)\) \(\chi_{1156}(563,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{136})$ |
Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((579,581)\) → \((-1,e\left(\frac{71}{136}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 1156 }(427, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{136}\right)\) | \(e\left(\frac{75}{136}\right)\) | \(e\left(\frac{57}{136}\right)\) | \(e\left(\frac{3}{68}\right)\) | \(e\left(\frac{69}{136}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{125}{136}\right)\) |