Basic properties
| Modulus: | \(1045\) | |
| Conductor: | \(1045\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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
\((837,761,496)\) → \((-i,e\left(\frac{3}{5}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 1045 }(1043, a) \) | \(-1\) | \(1\) | \(e\left(\frac{163}{180}\right)\) | \(e\left(\frac{49}{180}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{113}{180}\right)\) | \(e\left(\frac{17}{90}\right)\) |