Basic properties
| Modulus: | \(1037\) | |
| Conductor: | \(1037\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(240\) | 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 1037.cr
\(\chi_{1037}(6,\cdot)\) \(\chi_{1037}(10,\cdot)\) \(\chi_{1037}(63,\cdot)\) \(\chi_{1037}(78,\cdot)\) \(\chi_{1037}(92,\cdot)\) \(\chi_{1037}(96,\cdot)\) \(\chi_{1037}(105,\cdot)\) \(\chi_{1037}(116,\cdot)\) \(\chi_{1037}(124,\cdot)\) \(\chi_{1037}(148,\cdot)\) \(\chi_{1037}(173,\cdot)\) \(\chi_{1037}(176,\cdot)\) \(\chi_{1037}(181,\cdot)\) \(\chi_{1037}(190,\cdot)\) \(\chi_{1037}(193,\cdot)\) \(\chi_{1037}(201,\cdot)\) \(\chi_{1037}(209,\cdot)\) \(\chi_{1037}(214,\cdot)\) \(\chi_{1037}(261,\cdot)\) \(\chi_{1037}(279,\cdot)\) \(\chi_{1037}(335,\cdot)\) \(\chi_{1037}(360,\cdot)\) \(\chi_{1037}(364,\cdot)\) \(\chi_{1037}(396,\cdot)\) \(\chi_{1037}(397,\cdot)\) \(\chi_{1037}(401,\cdot)\) \(\chi_{1037}(445,\cdot)\) \(\chi_{1037}(470,\cdot)\) \(\chi_{1037}(471,\cdot)\) \(\chi_{1037}(486,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((428,307)\) → \((e\left(\frac{1}{16}\right),e\left(\frac{49}{60}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1037 }(190, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{67}{240}\right)\) | \(e\left(\frac{157}{240}\right)\) | \(e\left(\frac{169}{240}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{233}{240}\right)\) | \(e\left(\frac{11}{16}\right)\) |