Basic properties
| Modulus: | \(950\) | |
| Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{475}(63,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 950.bj
\(\chi_{950}(17,\cdot)\) \(\chi_{950}(23,\cdot)\) \(\chi_{950}(47,\cdot)\) \(\chi_{950}(63,\cdot)\) \(\chi_{950}(73,\cdot)\) \(\chi_{950}(123,\cdot)\) \(\chi_{950}(137,\cdot)\) \(\chi_{950}(177,\cdot)\) \(\chi_{950}(187,\cdot)\) \(\chi_{950}(213,\cdot)\) \(\chi_{950}(233,\cdot)\) \(\chi_{950}(237,\cdot)\) \(\chi_{950}(253,\cdot)\) \(\chi_{950}(263,\cdot)\) \(\chi_{950}(283,\cdot)\) \(\chi_{950}(313,\cdot)\) \(\chi_{950}(327,\cdot)\) \(\chi_{950}(347,\cdot)\) \(\chi_{950}(367,\cdot)\) \(\chi_{950}(377,\cdot)\) \(\chi_{950}(397,\cdot)\) \(\chi_{950}(403,\cdot)\) \(\chi_{950}(423,\cdot)\) \(\chi_{950}(427,\cdot)\) \(\chi_{950}(453,\cdot)\) \(\chi_{950}(473,\cdot)\) \(\chi_{950}(503,\cdot)\) \(\chi_{950}(517,\cdot)\) \(\chi_{950}(537,\cdot)\) \(\chi_{950}(567,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((77,401)\) → \((e\left(\frac{19}{20}\right),e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 950 }(63, a) \) | \(-1\) | \(1\) | \(e\left(\frac{137}{180}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{169}{180}\right)\) | \(e\left(\frac{23}{180}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{1}{180}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{11}{90}\right)\) |