Basic properties
Modulus: | \(4608\) | |
Conductor: | \(1152\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1152}(619,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4608.by
\(\chi_{4608}(79,\cdot)\) \(\chi_{4608}(175,\cdot)\) \(\chi_{4608}(367,\cdot)\) \(\chi_{4608}(463,\cdot)\) \(\chi_{4608}(655,\cdot)\) \(\chi_{4608}(751,\cdot)\) \(\chi_{4608}(943,\cdot)\) \(\chi_{4608}(1039,\cdot)\) \(\chi_{4608}(1231,\cdot)\) \(\chi_{4608}(1327,\cdot)\) \(\chi_{4608}(1519,\cdot)\) \(\chi_{4608}(1615,\cdot)\) \(\chi_{4608}(1807,\cdot)\) \(\chi_{4608}(1903,\cdot)\) \(\chi_{4608}(2095,\cdot)\) \(\chi_{4608}(2191,\cdot)\) \(\chi_{4608}(2383,\cdot)\) \(\chi_{4608}(2479,\cdot)\) \(\chi_{4608}(2671,\cdot)\) \(\chi_{4608}(2767,\cdot)\) \(\chi_{4608}(2959,\cdot)\) \(\chi_{4608}(3055,\cdot)\) \(\chi_{4608}(3247,\cdot)\) \(\chi_{4608}(3343,\cdot)\) \(\chi_{4608}(3535,\cdot)\) \(\chi_{4608}(3631,\cdot)\) \(\chi_{4608}(3823,\cdot)\) \(\chi_{4608}(3919,\cdot)\) \(\chi_{4608}(4111,\cdot)\) \(\chi_{4608}(4207,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((3583,2053,4097)\) → \((-1,e\left(\frac{13}{32}\right),e\left(\frac{2}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4608 }(79, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{96}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{67}{96}\right)\) | \(e\left(\frac{41}{96}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{61}{96}\right)\) | \(e\left(\frac{1}{12}\right)\) |