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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1045.cs
\(\chi_{1045}(17,\cdot)\) \(\chi_{1045}(28,\cdot)\) \(\chi_{1045}(62,\cdot)\) \(\chi_{1045}(63,\cdot)\) \(\chi_{1045}(73,\cdot)\) \(\chi_{1045}(112,\cdot)\) \(\chi_{1045}(118,\cdot)\) \(\chi_{1045}(123,\cdot)\) \(\chi_{1045}(138,\cdot)\) \(\chi_{1045}(233,\cdot)\) \(\chi_{1045}(237,\cdot)\) \(\chi_{1045}(272,\cdot)\) \(\chi_{1045}(282,\cdot)\) \(\chi_{1045}(283,\cdot)\) \(\chi_{1045}(327,\cdot)\) \(\chi_{1045}(332,\cdot)\) \(\chi_{1045}(347,\cdot)\) \(\chi_{1045}(348,\cdot)\) \(\chi_{1045}(358,\cdot)\) \(\chi_{1045}(403,\cdot)\) \(\chi_{1045}(442,\cdot)\) \(\chi_{1045}(453,\cdot)\) \(\chi_{1045}(492,\cdot)\) \(\chi_{1045}(503,\cdot)\) \(\chi_{1045}(557,\cdot)\) \(\chi_{1045}(567,\cdot)\) \(\chi_{1045}(568,\cdot)\) \(\chi_{1045}(612,\cdot)\) \(\chi_{1045}(613,\cdot)\) \(\chi_{1045}(633,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((837,761,496)\) → \((i,e\left(\frac{1}{10}\right),e\left(\frac{2}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 1045 }(662, a) \) | \(1\) | \(1\) | \(e\left(\frac{103}{180}\right)\) | \(e\left(\frac{79}{180}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{173}{180}\right)\) | \(e\left(\frac{77}{90}\right)\) |