Basic properties
Modulus: | \(1045\) | |
Conductor: | \(1045\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(180\) | 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 1045.cq
\(\chi_{1045}(2,\cdot)\) \(\chi_{1045}(13,\cdot)\) \(\chi_{1045}(52,\cdot)\) \(\chi_{1045}(72,\cdot)\) \(\chi_{1045}(117,\cdot)\) \(\chi_{1045}(127,\cdot)\) \(\chi_{1045}(128,\cdot)\) \(\chi_{1045}(162,\cdot)\) \(\chi_{1045}(167,\cdot)\) \(\chi_{1045}(173,\cdot)\) \(\chi_{1045}(193,\cdot)\) \(\chi_{1045}(222,\cdot)\) \(\chi_{1045}(238,\cdot)\) \(\chi_{1045}(288,\cdot)\) \(\chi_{1045}(337,\cdot)\) \(\chi_{1045}(338,\cdot)\) \(\chi_{1045}(382,\cdot)\) \(\chi_{1045}(393,\cdot)\) \(\chi_{1045}(402,\cdot)\) \(\chi_{1045}(413,\cdot)\) \(\chi_{1045}(447,\cdot)\) \(\chi_{1045}(458,\cdot)\) \(\chi_{1045}(497,\cdot)\) \(\chi_{1045}(508,\cdot)\) \(\chi_{1045}(523,\cdot)\) \(\chi_{1045}(547,\cdot)\) \(\chi_{1045}(602,\cdot)\) \(\chi_{1045}(618,\cdot)\) \(\chi_{1045}(622,\cdot)\) \(\chi_{1045}(623,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((837,761,496)\) → \((-i,e\left(\frac{9}{10}\right),e\left(\frac{17}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 1045 }(523, a) \) | \(-1\) | \(1\) | \(e\left(\frac{107}{180}\right)\) | \(e\left(\frac{131}{180}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{157}{180}\right)\) | \(e\left(\frac{14}{45}\right)\) |