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.ct
\(\chi_{1045}(42,\cdot)\) \(\chi_{1045}(47,\cdot)\) \(\chi_{1045}(82,\cdot)\) \(\chi_{1045}(92,\cdot)\) \(\chi_{1045}(93,\cdot)\) \(\chi_{1045}(137,\cdot)\) \(\chi_{1045}(157,\cdot)\) \(\chi_{1045}(158,\cdot)\) \(\chi_{1045}(168,\cdot)\) \(\chi_{1045}(207,\cdot)\) \(\chi_{1045}(213,\cdot)\) \(\chi_{1045}(218,\cdot)\) \(\chi_{1045}(302,\cdot)\) \(\chi_{1045}(313,\cdot)\) \(\chi_{1045}(328,\cdot)\) \(\chi_{1045}(367,\cdot)\) \(\chi_{1045}(377,\cdot)\) \(\chi_{1045}(378,\cdot)\) \(\chi_{1045}(422,\cdot)\) \(\chi_{1045}(423,\cdot)\) \(\chi_{1045}(427,\cdot)\) \(\chi_{1045}(443,\cdot)\) \(\chi_{1045}(498,\cdot)\) \(\chi_{1045}(522,\cdot)\) \(\chi_{1045}(537,\cdot)\) \(\chi_{1045}(548,\cdot)\) \(\chi_{1045}(587,\cdot)\) \(\chi_{1045}(598,\cdot)\) \(\chi_{1045}(632,\cdot)\) \(\chi_{1045}(643,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((837,761,496)\) → \((-i,e\left(\frac{1}{5}\right),e\left(\frac{1}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 1045 }(213, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{180}\right)\) | \(e\left(\frac{53}{180}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{180}\right)\) | \(e\left(\frac{79}{90}\right)\) |