Basic properties
Modulus: | \(485\) | |
Conductor: | \(97\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{97}(21,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 485.bq
\(\chi_{485}(21,\cdot)\) \(\chi_{485}(26,\cdot)\) \(\chi_{485}(41,\cdot)\) \(\chi_{485}(56,\cdot)\) \(\chi_{485}(71,\cdot)\) \(\chi_{485}(76,\cdot)\) \(\chi_{485}(111,\cdot)\) \(\chi_{485}(126,\cdot)\) \(\chi_{485}(136,\cdot)\) \(\chi_{485}(156,\cdot)\) \(\chi_{485}(171,\cdot)\) \(\chi_{485}(181,\cdot)\) \(\chi_{485}(201,\cdot)\) \(\chi_{485}(211,\cdot)\) \(\chi_{485}(231,\cdot)\) \(\chi_{485}(251,\cdot)\) \(\chi_{485}(276,\cdot)\) \(\chi_{485}(281,\cdot)\) \(\chi_{485}(286,\cdot)\) \(\chi_{485}(296,\cdot)\) \(\chi_{485}(301,\cdot)\) \(\chi_{485}(306,\cdot)\) \(\chi_{485}(331,\cdot)\) \(\chi_{485}(351,\cdot)\) \(\chi_{485}(371,\cdot)\) \(\chi_{485}(381,\cdot)\) \(\chi_{485}(401,\cdot)\) \(\chi_{485}(411,\cdot)\) \(\chi_{485}(426,\cdot)\) \(\chi_{485}(446,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((292,296)\) → \((1,e\left(\frac{5}{96}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 485 }(21, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{59}{96}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{29}{96}\right)\) |