Basic properties
Modulus: | \(1037\) | |
Conductor: | \(1037\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | 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 1037.cm
\(\chi_{1037}(26,\cdot)\) \(\chi_{1037}(104,\cdot)\) \(\chi_{1037}(189,\cdot)\) \(\chi_{1037}(213,\cdot)\) \(\chi_{1037}(246,\cdot)\) \(\chi_{1037}(287,\cdot)\) \(\chi_{1037}(331,\cdot)\) \(\chi_{1037}(349,\cdot)\) \(\chi_{1037}(359,\cdot)\) \(\chi_{1037}(372,\cdot)\) \(\chi_{1037}(376,\cdot)\) \(\chi_{1037}(417,\cdot)\) \(\chi_{1037}(434,\cdot)\) \(\chi_{1037}(444,\cdot)\) \(\chi_{1037}(518,\cdot)\) \(\chi_{1037}(542,\cdot)\) \(\chi_{1037}(559,\cdot)\) \(\chi_{1037}(580,\cdot)\) \(\chi_{1037}(604,\cdot)\) \(\chi_{1037}(627,\cdot)\) \(\chi_{1037}(654,\cdot)\) \(\chi_{1037}(689,\cdot)\) \(\chi_{1037}(722,\cdot)\) \(\chi_{1037}(739,\cdot)\) \(\chi_{1037}(763,\cdot)\) \(\chi_{1037}(767,\cdot)\) \(\chi_{1037}(852,\cdot)\) \(\chi_{1037}(909,\cdot)\) \(\chi_{1037}(950,\cdot)\) \(\chi_{1037}(978,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((428,307)\) → \((e\left(\frac{7}{8}\right),e\left(\frac{31}{60}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1037 }(852, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{7}{8}\right)\) |