Basic properties
| Modulus: | \(485\) | |
| Conductor: | \(485\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(96\) | 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 485.bp
\(\chi_{485}(14,\cdot)\) \(\chi_{485}(29,\cdot)\) \(\chi_{485}(39,\cdot)\) \(\chi_{485}(59,\cdot)\) \(\chi_{485}(74,\cdot)\) \(\chi_{485}(84,\cdot)\) \(\chi_{485}(104,\cdot)\) \(\chi_{485}(114,\cdot)\) \(\chi_{485}(134,\cdot)\) \(\chi_{485}(154,\cdot)\) \(\chi_{485}(179,\cdot)\) \(\chi_{485}(184,\cdot)\) \(\chi_{485}(189,\cdot)\) \(\chi_{485}(199,\cdot)\) \(\chi_{485}(204,\cdot)\) \(\chi_{485}(209,\cdot)\) \(\chi_{485}(234,\cdot)\) \(\chi_{485}(254,\cdot)\) \(\chi_{485}(274,\cdot)\) \(\chi_{485}(284,\cdot)\) \(\chi_{485}(304,\cdot)\) \(\chi_{485}(314,\cdot)\) \(\chi_{485}(329,\cdot)\) \(\chi_{485}(349,\cdot)\) \(\chi_{485}(359,\cdot)\) \(\chi_{485}(374,\cdot)\) \(\chi_{485}(409,\cdot)\) \(\chi_{485}(414,\cdot)\) \(\chi_{485}(429,\cdot)\) \(\chi_{485}(444,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((292,296)\) → \((-1,e\left(\frac{13}{96}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 485 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{67}{96}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{85}{96}\right)\) |