Basic properties
| Modulus: | \(5376\) | |
| Conductor: | \(1792\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(192\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1792}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5376.eb
\(\chi_{5376}(37,\cdot)\) \(\chi_{5376}(109,\cdot)\) \(\chi_{5376}(205,\cdot)\) \(\chi_{5376}(277,\cdot)\) \(\chi_{5376}(373,\cdot)\) \(\chi_{5376}(445,\cdot)\) \(\chi_{5376}(541,\cdot)\) \(\chi_{5376}(613,\cdot)\) \(\chi_{5376}(709,\cdot)\) \(\chi_{5376}(781,\cdot)\) \(\chi_{5376}(877,\cdot)\) \(\chi_{5376}(949,\cdot)\) \(\chi_{5376}(1045,\cdot)\) \(\chi_{5376}(1117,\cdot)\) \(\chi_{5376}(1213,\cdot)\) \(\chi_{5376}(1285,\cdot)\) \(\chi_{5376}(1381,\cdot)\) \(\chi_{5376}(1453,\cdot)\) \(\chi_{5376}(1549,\cdot)\) \(\chi_{5376}(1621,\cdot)\) \(\chi_{5376}(1717,\cdot)\) \(\chi_{5376}(1789,\cdot)\) \(\chi_{5376}(1885,\cdot)\) \(\chi_{5376}(1957,\cdot)\) \(\chi_{5376}(2053,\cdot)\) \(\chi_{5376}(2125,\cdot)\) \(\chi_{5376}(2221,\cdot)\) \(\chi_{5376}(2293,\cdot)\) \(\chi_{5376}(2389,\cdot)\) \(\chi_{5376}(2461,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((2815,5125,1793,4609)\) → \((1,e\left(\frac{25}{64}\right),1,e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 5376 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{192}\right)\) | \(e\left(\frac{103}{192}\right)\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{125}{192}\right)\) | \(e\left(\frac{13}{96}\right)\) | \(e\left(\frac{11}{96}\right)\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{83}{192}\right)\) |