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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 485.br
\(\chi_{485}(7,\cdot)\) \(\chi_{485}(13,\cdot)\) \(\chi_{485}(23,\cdot)\) \(\chi_{485}(37,\cdot)\) \(\chi_{485}(57,\cdot)\) \(\chi_{485}(68,\cdot)\) \(\chi_{485}(82,\cdot)\) \(\chi_{485}(83,\cdot)\) \(\chi_{485}(87,\cdot)\) \(\chi_{485}(107,\cdot)\) \(\chi_{485}(112,\cdot)\) \(\chi_{485}(118,\cdot)\) \(\chi_{485}(137,\cdot)\) \(\chi_{485}(138,\cdot)\) \(\chi_{485}(153,\cdot)\) \(\chi_{485}(157,\cdot)\) \(\chi_{485}(173,\cdot)\) \(\chi_{485}(187,\cdot)\) \(\chi_{485}(208,\cdot)\) \(\chi_{485}(223,\cdot)\) \(\chi_{485}(232,\cdot)\) \(\chi_{485}(252,\cdot)\) \(\chi_{485}(268,\cdot)\) \(\chi_{485}(278,\cdot)\) \(\chi_{485}(308,\cdot)\) \(\chi_{485}(317,\cdot)\) \(\chi_{485}(362,\cdot)\) \(\chi_{485}(383,\cdot)\) \(\chi_{485}(393,\cdot)\) \(\chi_{485}(427,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((292,296)\) → \((-i,e\left(\frac{77}{96}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 485 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{59}{96}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{29}{96}\right)\) |