Basic properties
| Modulus: | \(1037\) | |
| Conductor: | \(1037\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | 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.ck
\(\chi_{1037}(28,\cdot)\) \(\chi_{1037}(114,\cdot)\) \(\chi_{1037}(130,\cdot)\) \(\chi_{1037}(159,\cdot)\) \(\chi_{1037}(160,\cdot)\) \(\chi_{1037}(175,\cdot)\) \(\chi_{1037}(207,\cdot)\) \(\chi_{1037}(211,\cdot)\) \(\chi_{1037}(216,\cdot)\) \(\chi_{1037}(267,\cdot)\) \(\chi_{1037}(277,\cdot)\) \(\chi_{1037}(282,\cdot)\) \(\chi_{1037}(313,\cdot)\) \(\chi_{1037}(328,\cdot)\) \(\chi_{1037}(333,\cdot)\) \(\chi_{1037}(435,\cdot)\) \(\chi_{1037}(465,\cdot)\) \(\chi_{1037}(516,\cdot)\) \(\chi_{1037}(541,\cdot)\) \(\chi_{1037}(573,\cdot)\) \(\chi_{1037}(618,\cdot)\) \(\chi_{1037}(634,\cdot)\) \(\chi_{1037}(643,\cdot)\) \(\chi_{1037}(694,\cdot)\) \(\chi_{1037}(708,\cdot)\) \(\chi_{1037}(785,\cdot)\) \(\chi_{1037}(887,\cdot)\) \(\chi_{1037}(891,\cdot)\) \(\chi_{1037}(938,\cdot)\) \(\chi_{1037}(1000,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((428,307)\) → \((e\left(\frac{7}{16}\right),e\left(\frac{17}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1037 }(28, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{13}{16}\right)\) |