Basic properties
| Modulus: | \(5376\) | |
| Conductor: | \(2688\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2688}(677,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5376.du
\(\chi_{5376}(89,\cdot)\) \(\chi_{5376}(185,\cdot)\) \(\chi_{5376}(425,\cdot)\) \(\chi_{5376}(521,\cdot)\) \(\chi_{5376}(761,\cdot)\) \(\chi_{5376}(857,\cdot)\) \(\chi_{5376}(1097,\cdot)\) \(\chi_{5376}(1193,\cdot)\) \(\chi_{5376}(1433,\cdot)\) \(\chi_{5376}(1529,\cdot)\) \(\chi_{5376}(1769,\cdot)\) \(\chi_{5376}(1865,\cdot)\) \(\chi_{5376}(2105,\cdot)\) \(\chi_{5376}(2201,\cdot)\) \(\chi_{5376}(2441,\cdot)\) \(\chi_{5376}(2537,\cdot)\) \(\chi_{5376}(2777,\cdot)\) \(\chi_{5376}(2873,\cdot)\) \(\chi_{5376}(3113,\cdot)\) \(\chi_{5376}(3209,\cdot)\) \(\chi_{5376}(3449,\cdot)\) \(\chi_{5376}(3545,\cdot)\) \(\chi_{5376}(3785,\cdot)\) \(\chi_{5376}(3881,\cdot)\) \(\chi_{5376}(4121,\cdot)\) \(\chi_{5376}(4217,\cdot)\) \(\chi_{5376}(4457,\cdot)\) \(\chi_{5376}(4553,\cdot)\) \(\chi_{5376}(4793,\cdot)\) \(\chi_{5376}(4889,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((2815,5125,1793,4609)\) → \((1,e\left(\frac{25}{32}\right),-1,e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 5376 }(89, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{96}\right)\) | \(e\left(\frac{23}{96}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{13}{96}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{19}{96}\right)\) |