Basic properties
Modulus: | \(6009\) | |
Conductor: | \(6009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(286\) | 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 6009.bb
\(\chi_{6009}(2,\cdot)\) \(\chi_{6009}(8,\cdot)\) \(\chi_{6009}(11,\cdot)\) \(\chi_{6009}(23,\cdot)\) \(\chi_{6009}(32,\cdot)\) \(\chi_{6009}(44,\cdot)\) \(\chi_{6009}(71,\cdot)\) \(\chi_{6009}(92,\cdot)\) \(\chi_{6009}(128,\cdot)\) \(\chi_{6009}(149,\cdot)\) \(\chi_{6009}(176,\cdot)\) \(\chi_{6009}(239,\cdot)\) \(\chi_{6009}(242,\cdot)\) \(\chi_{6009}(284,\cdot)\) \(\chi_{6009}(368,\cdot)\) \(\chi_{6009}(377,\cdot)\) \(\chi_{6009}(380,\cdot)\) \(\chi_{6009}(506,\cdot)\) \(\chi_{6009}(512,\cdot)\) \(\chi_{6009}(563,\cdot)\) \(\chi_{6009}(704,\cdot)\) \(\chi_{6009}(845,\cdot)\) \(\chi_{6009}(956,\cdot)\) \(\chi_{6009}(968,\cdot)\) \(\chi_{6009}(1046,\cdot)\) \(\chi_{6009}(1058,\cdot)\) \(\chi_{6009}(1079,\cdot)\) \(\chi_{6009}(1094,\cdot)\) \(\chi_{6009}(1136,\cdot)\) \(\chi_{6009}(1241,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{143})$ |
Fixed field: | Number field defined by a degree 286 polynomial (not computed) |
Values on generators
\((4007,2008)\) → \((-1,e\left(\frac{7}{286}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6009 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{143}\right)\) | \(e\left(\frac{64}{143}\right)\) | \(e\left(\frac{75}{143}\right)\) | \(e\left(\frac{3}{286}\right)\) | \(e\left(\frac{96}{143}\right)\) | \(e\left(\frac{107}{143}\right)\) | \(e\left(\frac{100}{143}\right)\) | \(e\left(\frac{81}{143}\right)\) | \(e\left(\frac{67}{286}\right)\) | \(e\left(\frac{128}{143}\right)\) |