Basic properties
| Modulus: | \(5376\) | |
| Conductor: | \(896\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{896}(389,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5376.dy
\(\chi_{5376}(25,\cdot)\) \(\chi_{5376}(121,\cdot)\) \(\chi_{5376}(361,\cdot)\) \(\chi_{5376}(457,\cdot)\) \(\chi_{5376}(697,\cdot)\) \(\chi_{5376}(793,\cdot)\) \(\chi_{5376}(1033,\cdot)\) \(\chi_{5376}(1129,\cdot)\) \(\chi_{5376}(1369,\cdot)\) \(\chi_{5376}(1465,\cdot)\) \(\chi_{5376}(1705,\cdot)\) \(\chi_{5376}(1801,\cdot)\) \(\chi_{5376}(2041,\cdot)\) \(\chi_{5376}(2137,\cdot)\) \(\chi_{5376}(2377,\cdot)\) \(\chi_{5376}(2473,\cdot)\) \(\chi_{5376}(2713,\cdot)\) \(\chi_{5376}(2809,\cdot)\) \(\chi_{5376}(3049,\cdot)\) \(\chi_{5376}(3145,\cdot)\) \(\chi_{5376}(3385,\cdot)\) \(\chi_{5376}(3481,\cdot)\) \(\chi_{5376}(3721,\cdot)\) \(\chi_{5376}(3817,\cdot)\) \(\chi_{5376}(4057,\cdot)\) \(\chi_{5376}(4153,\cdot)\) \(\chi_{5376}(4393,\cdot)\) \(\chi_{5376}(4489,\cdot)\) \(\chi_{5376}(4729,\cdot)\) \(\chi_{5376}(4825,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((2815,5125,1793,4609)\) → \((1,e\left(\frac{1}{32}\right),1,e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 5376 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{96}\right)\) | \(e\left(\frac{31}{96}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{5}{96}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{96}\right)\) |