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 \(\chi_{1152}(1141,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4608.bz
\(\chi_{4608}(49,\cdot)\) \(\chi_{4608}(241,\cdot)\) \(\chi_{4608}(337,\cdot)\) \(\chi_{4608}(529,\cdot)\) \(\chi_{4608}(625,\cdot)\) \(\chi_{4608}(817,\cdot)\) \(\chi_{4608}(913,\cdot)\) \(\chi_{4608}(1105,\cdot)\) \(\chi_{4608}(1201,\cdot)\) \(\chi_{4608}(1393,\cdot)\) \(\chi_{4608}(1489,\cdot)\) \(\chi_{4608}(1681,\cdot)\) \(\chi_{4608}(1777,\cdot)\) \(\chi_{4608}(1969,\cdot)\) \(\chi_{4608}(2065,\cdot)\) \(\chi_{4608}(2257,\cdot)\) \(\chi_{4608}(2353,\cdot)\) \(\chi_{4608}(2545,\cdot)\) \(\chi_{4608}(2641,\cdot)\) \(\chi_{4608}(2833,\cdot)\) \(\chi_{4608}(2929,\cdot)\) \(\chi_{4608}(3121,\cdot)\) \(\chi_{4608}(3217,\cdot)\) \(\chi_{4608}(3409,\cdot)\) \(\chi_{4608}(3505,\cdot)\) \(\chi_{4608}(3697,\cdot)\) \(\chi_{4608}(3793,\cdot)\) \(\chi_{4608}(3985,\cdot)\) \(\chi_{4608}(4081,\cdot)\) \(\chi_{4608}(4273,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((3583,2053,4097)\) → \((1,e\left(\frac{21}{32}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4608 }(817, a) \) | \(1\) | \(1\) | \(e\left(\frac{95}{96}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{43}{96}\right)\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{37}{96}\right)\) | \(e\left(\frac{7}{12}\right)\) |