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.cs
\(\chi_{1037}(7,\cdot)\) \(\chi_{1037}(31,\cdot)\) \(\chi_{1037}(44,\cdot)\) \(\chi_{1037}(54,\cdot)\) \(\chi_{1037}(71,\cdot)\) \(\chi_{1037}(79,\cdot)\) \(\chi_{1037}(91,\cdot)\) \(\chi_{1037}(112,\cdot)\) \(\chi_{1037}(129,\cdot)\) \(\chi_{1037}(139,\cdot)\) \(\chi_{1037}(165,\cdot)\) \(\chi_{1037}(177,\cdot)\) \(\chi_{1037}(218,\cdot)\) \(\chi_{1037}(226,\cdot)\) \(\chi_{1037}(227,\cdot)\) \(\chi_{1037}(250,\cdot)\) \(\chi_{1037}(262,\cdot)\) \(\chi_{1037}(275,\cdot)\) \(\chi_{1037}(295,\cdot)\) \(\chi_{1037}(299,\cdot)\) \(\chi_{1037}(303,\cdot)\) \(\chi_{1037}(311,\cdot)\) \(\chi_{1037}(312,\cdot)\) \(\chi_{1037}(368,\cdot)\) \(\chi_{1037}(384,\cdot)\) \(\chi_{1037}(420,\cdot)\) \(\chi_{1037}(437,\cdot)\) \(\chi_{1037}(453,\cdot)\) \(\chi_{1037}(462,\cdot)\) \(\chi_{1037}(481,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((428,307)\) → \((e\left(\frac{11}{16}\right),e\left(\frac{53}{60}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1037 }(1027, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{209}{240}\right)\) | \(e\left(\frac{119}{240}\right)\) | \(e\left(\frac{203}{240}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{91}{240}\right)\) | \(e\left(\frac{1}{16}\right)\) |